LMFDB - Embedded newform 1183.2.a.p.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1183,2,Mod(1,1183)]

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, 0]))

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

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

chi := DirichletCharacter("1183.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1183 = 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1183.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$9.44630255912$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.7674048.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 5x^{4} + 8x^{3} + 7x^{2} - 6x - 2 $ x^6 - 2x^5 - 5x^4 + 8x^3 + 7x^2 - 6*x - 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-1.70320$ of defining polynomial
Character	$\chi$	$=$	1183.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.70320 q^{2} -0.345949 q^{3} +5.30727 q^{4} +3.25812 q^{5} -0.935168 q^{6} -1.00000 q^{7} +8.94020 q^{8} -2.88032 q^{9} +O(q^{10})$	\(q+2.70320 q^{2} -0.345949 q^{3} +5.30727 q^{4} +3.25812 q^{5} -0.935168 q^{6} -1.00000 q^{7} +8.94020 q^{8} -2.88032 q^{9} +8.80735 q^{10} -1.84603 q^{11} -1.83605 q^{12} -2.70320 q^{14} -1.12715 q^{15} +13.5526 q^{16} +2.15314 q^{17} -7.78607 q^{18} -2.40096 q^{19} +17.2917 q^{20} +0.345949 q^{21} -4.99017 q^{22} +1.81263 q^{23} -3.09285 q^{24} +5.61537 q^{25} +2.03429 q^{27} -5.30727 q^{28} -2.73406 q^{29} -3.04689 q^{30} +1.74236 q^{31} +18.7549 q^{32} +0.638632 q^{33} +5.82036 q^{34} -3.25812 q^{35} -15.2866 q^{36} -5.93565 q^{37} -6.49025 q^{38} +29.1283 q^{40} -4.22131 q^{41} +0.935168 q^{42} -8.68223 q^{43} -9.79737 q^{44} -9.38444 q^{45} +4.89989 q^{46} +5.87774 q^{47} -4.68850 q^{48} +1.00000 q^{49} +15.1794 q^{50} -0.744877 q^{51} -9.30628 q^{53} +5.49909 q^{54} -6.01459 q^{55} -8.94020 q^{56} +0.830609 q^{57} -7.39071 q^{58} -10.7523 q^{59} -5.98206 q^{60} +10.1101 q^{61} +4.70994 q^{62} +2.88032 q^{63} +23.5929 q^{64} +1.72635 q^{66} -0.826916 q^{67} +11.4273 q^{68} -0.627077 q^{69} -8.80735 q^{70} -2.35425 q^{71} -25.7506 q^{72} +3.19482 q^{73} -16.0452 q^{74} -1.94263 q^{75} -12.7425 q^{76} +1.84603 q^{77} +0.801911 q^{79} +44.1559 q^{80} +7.93720 q^{81} -11.4110 q^{82} +9.97031 q^{83} +1.83605 q^{84} +7.01520 q^{85} -23.4698 q^{86} +0.945847 q^{87} -16.5039 q^{88} +15.1135 q^{89} -25.3680 q^{90} +9.62010 q^{92} -0.602768 q^{93} +15.8887 q^{94} -7.82261 q^{95} -6.48823 q^{96} +9.23171 q^{97} +2.70320 q^{98} +5.31715 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 4 q^{2} + 4 q^{4} + 6 q^{5} + 4 q^{6} - 6 q^{7} + 12 q^{8} + 4 q^{9}+O(q^{10}) $ 6 * q + 4 * q^2 + 4 * q^4 + 6 * q^5 + 4 * q^6 - 6 * q^7 + 12 * q^8 + 4 * q^9	$ 6 q + 4 q^{2} + 4 q^{4} + 6 q^{5} + 4 q^{6} - 6 q^{7} + 12 q^{8} + 4 q^{9} + 12 q^{10} + 4 q^{11} + 2 q^{12} - 4 q^{14} + 20 q^{15} + 8 q^{16} - 4 q^{17} - 16 q^{18} + 2 q^{19} + 26 q^{20} - 6 q^{22} - 12 q^{23} + 2 q^{24} + 10 q^{25} + 6 q^{27} - 4 q^{28} - 8 q^{29} + 8 q^{30} - 14 q^{31} + 8 q^{32} + 16 q^{33} - 2 q^{34} - 6 q^{35} - 10 q^{36} + 12 q^{37} - 2 q^{38} + 46 q^{40} + 28 q^{41} - 4 q^{42} + 2 q^{43} - 20 q^{44} + 16 q^{45} + 20 q^{46} + 14 q^{47} + 2 q^{48} + 6 q^{49} + 32 q^{50} - 26 q^{51} - 22 q^{53} + 14 q^{54} + 6 q^{55} - 12 q^{56} + 4 q^{58} - 2 q^{59} - 14 q^{61} - 4 q^{62} - 4 q^{63} + 26 q^{64} - 26 q^{66} + 24 q^{67} + 8 q^{68} + 4 q^{69} - 12 q^{70} + 4 q^{71} + 8 q^{72} + 36 q^{73} - 6 q^{74} + 46 q^{75} - 26 q^{76} - 4 q^{77} - 28 q^{79} + 36 q^{80} - 2 q^{81} + 14 q^{82} + 26 q^{83} - 2 q^{84} - 20 q^{85} - 24 q^{86} + 2 q^{87} - 14 q^{88} + 42 q^{89} - 12 q^{90} + 12 q^{92} - 4 q^{94} - 22 q^{95} - 42 q^{96} + 24 q^{97} + 4 q^{98} + 16 q^{99}+O(q^{100}) $ 6 * q + 4 * q^2 + 4 * q^4 + 6 * q^5 + 4 * q^6 - 6 * q^7 + 12 * q^8 + 4 * q^9 + 12 * q^10 + 4 * q^11 + 2 * q^12 - 4 * q^14 + 20 * q^15 + 8 * q^16 - 4 * q^17 - 16 * q^18 + 2 * q^19 + 26 * q^20 - 6 * q^22 - 12 * q^23 + 2 * q^24 + 10 * q^25 + 6 * q^27 - 4 * q^28 - 8 * q^29 + 8 * q^30 - 14 * q^31 + 8 * q^32 + 16 * q^33 - 2 * q^34 - 6 * q^35 - 10 * q^36 + 12 * q^37 - 2 * q^38 + 46 * q^40 + 28 * q^41 - 4 * q^42 + 2 * q^43 - 20 * q^44 + 16 * q^45 + 20 * q^46 + 14 * q^47 + 2 * q^48 + 6 * q^49 + 32 * q^50 - 26 * q^51 - 22 * q^53 + 14 * q^54 + 6 * q^55 - 12 * q^56 + 4 * q^58 - 2 * q^59 - 14 * q^61 - 4 * q^62 - 4 * q^63 + 26 * q^64 - 26 * q^66 + 24 * q^67 + 8 * q^68 + 4 * q^69 - 12 * q^70 + 4 * q^71 + 8 * q^72 + 36 * q^73 - 6 * q^74 + 46 * q^75 - 26 * q^76 - 4 * q^77 - 28 * q^79 + 36 * q^80 - 2 * q^81 + 14 * q^82 + 26 * q^83 - 2 * q^84 - 20 * q^85 - 24 * q^86 + 2 * q^87 - 14 * q^88 + 42 * q^89 - 12 * q^90 + 12 * q^92 - 4 * q^94 - 22 * q^95 - 42 * q^96 + 24 * q^97 + 4 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.70320	1.91145	0.955724	−	0.294264i	$-0.0950745\pi$
$2$	2.70320	1.91145	0.955724	+	0.294264i	$0.0950745\pi$
$3$	−0.345949	−0.199734	−0.0998669	−	0.995001i	$-0.531842\pi$
$3$	−0.345949	−0.199734	−0.0998669	+	0.995001i	$0.531842\pi$
$4$	5.30727	2.65363
$5$	3.25812	1.45708	0.728539	−	0.685005i	$-0.240200\pi$
$5$	3.25812	1.45708	0.728539	+	0.685005i	$0.240200\pi$
$6$	−0.935168	−0.381781
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	8.94020	3.16084
$9$	−2.88032	−0.960106
$10$	8.80735	2.78513
$11$	−1.84603	−0.556598	−0.278299	−	0.960494i	$-0.589771\pi$
$11$	−1.84603	−0.556598	−0.278299	+	0.960494i	$0.589771\pi$
$12$	−1.83605	−0.530021
$13$	0	0
$13$	0	0
$14$	−2.70320	−0.722460
$15$	−1.12715	−0.291028
$16$	13.5526	3.38814
$17$	2.15314	0.522213	0.261107	−	0.965310i	$-0.415913\pi$
$17$	2.15314	0.522213	0.261107	+	0.965310i	$0.415913\pi$
$18$	−7.78607	−1.83519
$19$	−2.40096	−0.550817	−0.275408	−	0.961327i	$-0.588813\pi$
$19$	−2.40096	−0.550817	−0.275408	+	0.961327i	$0.588813\pi$
$20$	17.2917	3.86655
$21$	0.345949	0.0754923
$22$	−4.99017	−1.06391
$23$	1.81263	0.377959	0.188979	−	0.981981i	$-0.439482\pi$
$23$	1.81263	0.377959	0.188979	+	0.981981i	$0.439482\pi$
$24$	−3.09285	−0.631326
$25$	5.61537	1.12307
$26$	0	0
$27$	2.03429	0.391500
$28$	−5.30727	−1.00298
$29$	−2.73406	−0.507703	−0.253851	−	0.967243i	$-0.581697\pi$
$29$	−2.73406	−0.507703	−0.253851	+	0.967243i	$0.581697\pi$
$30$	−3.04689	−0.556284
$31$	1.74236	0.312937	0.156468	−	0.987683i	$-0.449989\pi$
$31$	1.74236	0.312937	0.156468	+	0.987683i	$0.449989\pi$
$32$	18.7549	3.31542
$33$	0.638632	0.111172
$34$	5.82036	0.998183
$35$	−3.25812	−0.550723
$36$	−15.2866	−2.54777
$37$	−5.93565	−0.975815	−0.487908	−	0.872895i	$-0.662240\pi$
$37$	−5.93565	−0.975815	−0.487908	+	0.872895i	$0.662240\pi$
$38$	−6.49025	−1.05286
$39$	0	0
$40$	29.1283	4.60558
$41$	−4.22131	−0.659259	−0.329629	−	0.944110i	$-0.606924\pi$
$41$	−4.22131	−0.659259	−0.329629	+	0.944110i	$0.606924\pi$
$42$	0.935168	0.144300
$43$	−8.68223	−1.32403	−0.662014	−	0.749492i	$-0.730298\pi$
$43$	−8.68223	−1.32403	−0.662014	+	0.749492i	$0.730298\pi$
$44$	−9.79737	−1.47701
$45$	−9.38444	−1.39895
$46$	4.89989	0.722449
$47$	5.87774	0.857357	0.428678	−	0.903457i	$-0.358979\pi$
$47$	5.87774	0.857357	0.428678	+	0.903457i	$0.358979\pi$
$48$	−4.68850	−0.676727
$49$	1.00000	0.142857
$50$	15.1794	2.14670
$51$	−0.744877	−0.104304
$52$	0	0
$53$	−9.30628	−1.27832	−0.639158	−	0.769076i	$-0.720717\pi$
$53$	−9.30628	−1.27832	−0.639158	+	0.769076i	$0.720717\pi$
$54$	5.49909	0.748331
$55$	−6.01459	−0.811007
$56$	−8.94020	−1.19468
$57$	0.830609	0.110017
$58$	−7.39071	−0.970447
$59$	−10.7523	−1.39982	−0.699912	−	0.714229i	$-0.746778\pi$
$59$	−10.7523	−1.39982	−0.699912	+	0.714229i	$0.746778\pi$
$60$	−5.98206	−0.772281
$61$	10.1101	1.29446	0.647231	−	0.762294i	$-0.275927\pi$
$61$	10.1101	1.29446	0.647231	+	0.762294i	$0.275927\pi$
$62$	4.70994	0.598163
$63$	2.88032	0.362886
$64$	23.5929	2.94911
$65$	0	0
$66$	1.72635	0.212499
$67$	−0.826916	−0.101024	−0.0505119	−	0.998723i	$-0.516085\pi$
$67$	−0.826916	−0.101024	−0.0505119	+	0.998723i	$0.516085\pi$
$68$	11.4273	1.38576
$69$	−0.627077	−0.0754912
$70$	−8.80735	−1.05268
$71$	−2.35425	−0.279398	−0.139699	−	0.990194i	$-0.544613\pi$
$71$	−2.35425	−0.279398	−0.139699	+	0.990194i	$0.544613\pi$
$72$	−25.7506	−3.03474
$73$	3.19482	0.373925	0.186963	−	0.982367i	$-0.440136\pi$
$73$	3.19482	0.373925	0.186963	+	0.982367i	$0.440136\pi$
$74$	−16.0452	−1.86522
$75$	−1.94263	−0.224316
$76$	−12.7425	−1.46167
$77$	1.84603	0.210374
$78$	0	0
$79$	0.801911	0.0902220	0.0451110	−	0.998982i	$-0.485636\pi$
$79$	0.801911	0.0902220	0.0451110	+	0.998982i	$0.485636\pi$
$80$	44.1559	4.93678
$81$	7.93720	0.881911
$82$	−11.4110	−1.26014
$83$	9.97031	1.09438	0.547192	−	0.837007i	$-0.315697\pi$
$83$	9.97031	1.09438	0.547192	+	0.837007i	$0.315697\pi$
$84$	1.83605	0.200329
$85$	7.01520	0.760905
$86$	−23.4698	−2.53081
$87$	0.945847	0.101405
$88$	−16.5039	−1.75932
$89$	15.1135	1.60202	0.801012	−	0.598648i	$-0.204295\pi$
$89$	15.1135	1.60202	0.801012	+	0.598648i	$0.204295\pi$
$90$	−25.3680	−2.67402
$91$	0	0
$92$	9.62010	1.00296
$93$	−0.602768	−0.0625041
$94$	15.8887	1.63879
$95$	−7.82261	−0.802583
$96$	−6.48823	−0.662202
$97$	9.23171	0.937338	0.468669	−	0.883374i	$-0.344734\pi$
$97$	9.23171	0.937338	0.468669	+	0.883374i	$0.344734\pi$
$98$	2.70320	0.273064
$99$	5.31715	0.534394
$100$	29.8023	2.98023
$101$	14.8234	1.47498	0.737491	−	0.675357i	$-0.236011\pi$
$101$	14.8234	1.47498	0.737491	+	0.675357i	$0.236011\pi$
$102$	−2.01355	−0.199371
$103$	−4.28286	−0.422003	−0.211001	−	0.977486i	$-0.567672\pi$
$103$	−4.28286	−0.422003	−0.211001	+	0.977486i	$0.567672\pi$
$104$	0	0
$105$	1.12715	0.109998
$106$	−25.1567	−2.44343
$107$	−19.1258	−1.84896	−0.924479	−	0.381233i	$-0.875500\pi$
$107$	−19.1258	−1.84896	−0.924479	+	0.381233i	$0.875500\pi$
$108$	10.7965	1.03890
$109$	4.27153	0.409139	0.204569	−	0.978852i	$-0.434421\pi$
$109$	4.27153	0.409139	0.204569	+	0.978852i	$0.434421\pi$
$110$	−16.2586	−1.55020
$111$	2.05343	0.194903
$112$	−13.5526	−1.28060
$113$	2.74976	0.258676	0.129338	−	0.991601i	$-0.458715\pi$
$113$	2.74976	0.258676	0.129338	+	0.991601i	$0.458715\pi$
$114$	2.24530	0.210291
$115$	5.90576	0.550715
$116$	−14.5104	−1.34726
$117$	0	0
$118$	−29.0655	−2.67569
$119$	−2.15314	−0.197378
$120$	−10.0769	−0.919891
$121$	−7.59218	−0.690198
$122$	27.3295	2.47430
$123$	1.46036	0.131676
$124$	9.24717	0.830420
$125$	2.00495	0.179329
$126$	7.78607	0.693638
$127$	−9.73438	−0.863786	−0.431893	−	0.901925i	$-0.642154\pi$
$127$	−9.73438	−0.863786	−0.431893	+	0.901925i	$0.642154\pi$
$128$	26.2666	2.32166
$129$	3.00361	0.264453
$130$	0	0
$131$	−18.6615	−1.63046	−0.815230	−	0.579138i	$-0.803389\pi$
$131$	−18.6615	−1.63046	−0.815230	+	0.579138i	$0.803389\pi$
$132$	3.38939	0.295009
$133$	2.40096	0.208189
$134$	−2.23532	−0.193102
$135$	6.62797	0.570445
$136$	19.2495	1.65063
$137$	8.42156	0.719502	0.359751	−	0.933048i	$-0.382862\pi$
$137$	8.42156	0.719502	0.359751	+	0.933048i	$0.382862\pi$
$138$	−1.69511	−0.144298
$139$	−17.6362	−1.49588	−0.747941	−	0.663765i	$-0.768957\pi$
$139$	−17.6362	−1.49588	−0.747941	+	0.663765i	$0.768957\pi$
$140$	−17.2917	−1.46142
$141$	−2.03340	−0.171243
$142$	−6.36399	−0.534054
$143$	0	0
$144$	−39.0357	−3.25298
$145$	−8.90791	−0.739762
$146$	8.63623	0.714739
$147$	−0.345949	−0.0285334
$148$	−31.5021	−2.58946
$149$	−4.02104	−0.329416	−0.164708	−	0.986342i	$-0.552668\pi$
$149$	−4.02104	−0.329416	−0.164708	+	0.986342i	$0.552668\pi$
$150$	−5.25132	−0.428768
$151$	18.9010	1.53814	0.769069	−	0.639165i	$-0.220720\pi$
$151$	18.9010	1.53814	0.769069	+	0.639165i	$0.220720\pi$
$152$	−21.4650	−1.74104
$153$	−6.20173	−0.501380
$154$	4.99017	0.402120
$155$	5.67682	0.455973
$156$	0	0
$157$	−11.5735	−0.923670	−0.461835	−	0.886966i	$-0.652809\pi$
$157$	−11.5735	−0.923670	−0.461835	+	0.886966i	$0.652809\pi$
$158$	2.16772	0.172455
$159$	3.21950	0.255323
$160$	61.1056	4.83082
$161$	−1.81263	−0.142855
$162$	21.4558	1.68573
$163$	4.40542	0.345059	0.172529	−	0.985004i	$-0.444806\pi$
$163$	4.40542	0.345059	0.172529	+	0.985004i	$0.444806\pi$
$164$	−22.4037	−1.74943
$165$	2.08074	0.161985
$166$	26.9517	2.09186
$167$	−9.01909	−0.697918	−0.348959	−	0.937138i	$-0.613465\pi$
$167$	−9.01909	−0.697918	−0.348959	+	0.937138i	$0.613465\pi$
$168$	3.09285	0.238619
$169$	0	0
$170$	18.9635	1.45443
$171$	6.91552	0.528843
$172$	−46.0789	−3.51349
$173$	6.09200	0.463166	0.231583	−	0.972815i	$-0.425609\pi$
$173$	6.09200	0.463166	0.231583	+	0.972815i	$0.425609\pi$
$174$	2.55681	0.193831
$175$	−5.61537	−0.424482
$176$	−25.0184	−1.88583
$177$	3.71974	0.279592
$178$	40.8547	3.06219
$179$	3.87964	0.289978	0.144989	−	0.989433i	$-0.453685\pi$
$179$	3.87964	0.289978	0.144989	+	0.989433i	$0.453685\pi$
$180$	−49.8057	−3.71230
$181$	6.58392	0.489379	0.244690	−	0.969601i	$-0.421314\pi$
$181$	6.58392	0.489379	0.244690	+	0.969601i	$0.421314\pi$
$182$	0	0
$183$	−3.49757	−0.258548
$184$	16.2052	1.19467
$185$	−19.3391	−1.42184
$186$	−1.62940	−0.119473
$187$	−3.97476	−0.290663
$188$	31.1948	2.27511
$189$	−2.03429	−0.147973
$190$	−21.1460	−1.53410
$191$	−13.7434	−0.994435	−0.497218	−	0.867626i	$-0.665645\pi$
$191$	−13.7434	−0.994435	−0.497218	+	0.867626i	$0.665645\pi$
$192$	−8.16195	−0.589038
$193$	22.7530	1.63780	0.818899	−	0.573937i	$-0.194585\pi$
$193$	22.7530	1.63780	0.818899	+	0.573937i	$0.194585\pi$
$194$	24.9551	1.79167
$195$	0	0
$196$	5.30727	0.379091
$197$	14.5272	1.03502	0.517509	−	0.855678i	$-0.326859\pi$
$197$	14.5272	1.03502	0.517509	+	0.855678i	$0.326859\pi$
$198$	14.3733	1.02147
$199$	23.8404	1.69000	0.845001	−	0.534765i	$-0.179600\pi$
$199$	23.8404	1.69000	0.845001	+	0.534765i	$0.179600\pi$
$200$	50.2025	3.54985
$201$	0.286071	0.0201779
$202$	40.0705	2.81935
$203$	2.73406	0.191894
$204$	−3.95326	−0.276784
$205$	−13.7536	−0.960591
$206$	−11.5774	−0.806637
$207$	−5.22095	−0.362881
$208$	0	0
$209$	4.43223	0.306584
$210$	3.04689	0.210256
$211$	4.31527	0.297076	0.148538	−	0.988907i	$-0.452543\pi$
$211$	4.31527	0.297076	0.148538	+	0.988907i	$0.452543\pi$
$212$	−49.3909	−3.39218
$213$	0.814450	0.0558052
$214$	−51.7007	−3.53419
$215$	−28.2878	−1.92921
$216$	18.1870	1.23747
$217$	−1.74236	−0.118279
$218$	11.5468	0.782047
$219$	−1.10525	−0.0746856
$220$	−31.9210	−2.15212
$221$	0	0
$222$	5.55083	0.372548
$223$	23.3947	1.56662	0.783312	−	0.621629i	$-0.213529\pi$
$223$	23.3947	1.56662	0.783312	+	0.621629i	$0.213529\pi$
$224$	−18.7549	−1.25311
$225$	−16.1741	−1.07827
$226$	7.43315	0.494446
$227$	−26.7229	−1.77366	−0.886829	−	0.462097i	$-0.847097\pi$
$227$	−26.7229	−1.77366	−0.886829	+	0.462097i	$0.847097\pi$
$228$	4.40826	0.291944
$229$	−3.00670	−0.198688	−0.0993442	−	0.995053i	$-0.531674\pi$
$229$	−3.00670	−0.198688	−0.0993442	+	0.995053i	$0.531674\pi$
$230$	15.9644	1.05266
$231$	−0.638632	−0.0420189
$232$	−24.4431	−1.60477
$233$	−11.7148	−0.767462	−0.383731	−	0.923445i	$-0.625361\pi$
$233$	−11.7148	−0.767462	−0.383731	+	0.923445i	$0.625361\pi$
$234$	0	0
$235$	19.1504	1.24924
$236$	−57.0651	−3.71462
$237$	−0.277420	−0.0180204
$238$	−5.82036	−0.377278
$239$	−1.42797	−0.0923677	−0.0461838	−	0.998933i	$-0.514706\pi$
$239$	−1.42797	−0.0923677	−0.0461838	+	0.998933i	$0.514706\pi$
$240$	−15.2757	−0.986043
$241$	2.67969	0.172614	0.0863069	−	0.996269i	$-0.472493\pi$
$241$	2.67969	0.172614	0.0863069	+	0.996269i	$0.472493\pi$
$242$	−20.5232	−1.31928
$243$	−8.84874	−0.567647
$244$	53.6569	3.43503
$245$	3.25812	0.208154
$246$	3.94764	0.251692
$247$	0	0
$248$	15.5770	0.989143
$249$	−3.44922	−0.218586
$250$	5.41978	0.342777
$251$	10.9339	0.690143	0.345072	−	0.938576i	$-0.387855\pi$
$251$	10.9339	0.690143	0.345072	+	0.938576i	$0.387855\pi$
$252$	15.2866	0.962967
$253$	−3.34616	−0.210371
$254$	−26.3139	−1.65108
$255$	−2.42690	−0.151978
$256$	23.8178	1.48861
$257$	4.15138	0.258956	0.129478	−	0.991582i	$-0.458670\pi$
$257$	4.15138	0.258956	0.129478	+	0.991582i	$0.458670\pi$
$258$	8.11935	0.505488
$259$	5.93565	0.368823
$260$	0	0
$261$	7.87497	0.487448
$262$	−50.4456	−3.11654
$263$	4.05360	0.249955	0.124978	−	0.992160i	$-0.460114\pi$
$263$	4.05360	0.249955	0.124978	+	0.992160i	$0.460114\pi$
$264$	5.70949	0.351395
$265$	−30.3210	−1.86260
$266$	6.49025	0.397943
$267$	−5.22849	−0.319979
$268$	−4.38866	−0.268080
$269$	4.00022	0.243898	0.121949	−	0.992536i	$-0.461086\pi$
$269$	4.00022	0.243898	0.121949	+	0.992536i	$0.461086\pi$
$270$	17.9167	1.09038
$271$	−2.78502	−0.169178	−0.0845888	−	0.996416i	$-0.526958\pi$
$271$	−2.78502	−0.169178	−0.0845888	+	0.996416i	$0.526958\pi$
$272$	29.1806	1.76933
$273$	0	0
$274$	22.7651	1.37529
$275$	−10.3661	−0.625101
$276$	−3.32807	−0.200326
$277$	16.6924	1.00295	0.501474	−	0.865173i	$-0.332791\pi$
$277$	16.6924	1.00295	0.501474	+	0.865173i	$0.332791\pi$
$278$	−47.6741	−2.85930
$279$	−5.01855	−0.300453
$280$	−29.1283	−1.74075
$281$	13.3731	0.797774	0.398887	−	0.917000i	$-0.369397\pi$
$281$	13.3731	0.797774	0.398887	+	0.917000i	$0.369397\pi$
$282$	−5.49668	−0.327322
$283$	−18.8862	−1.12267	−0.561335	−	0.827589i	$-0.689712\pi$
$283$	−18.8862	−1.12267	−0.561335	+	0.827589i	$0.689712\pi$
$284$	−12.4946	−0.741419
$285$	2.70623	0.160303
$286$	0	0
$287$	4.22131	0.249176
$288$	−54.0200	−3.18316
$289$	−12.3640	−0.727293
$290$	−24.0798	−1.41402
$291$	−3.19370	−0.187218
$292$	16.9558	0.992262
$293$	3.41790	0.199676	0.0998380	−	0.995004i	$-0.468168\pi$
$293$	3.41790	0.199676	0.0998380	+	0.995004i	$0.468168\pi$
$294$	−0.935168	−0.0545401
$295$	−35.0322	−2.03965
$296$	−53.0659	−3.08439
$297$	−3.75536	−0.217908
$298$	−10.8697	−0.629663
$299$	0	0
$300$	−10.3101	−0.595252
$301$	8.68223	0.500435
$302$	51.0930	2.94007
$303$	−5.12814	−0.294604
$304$	−32.5391	−1.86625
$305$	32.9399	1.88613
$306$	−16.7645	−0.958362
$307$	−16.3679	−0.934165	−0.467083	−	0.884214i	$-0.654695\pi$
$307$	−16.3679	−0.934165	−0.467083	+	0.884214i	$0.654695\pi$
$308$	9.79737	0.558257
$309$	1.48165	0.0842883
$310$	15.3456	0.871569
$311$	23.6979	1.34378	0.671891	−	0.740650i	$-0.265482\pi$
$311$	23.6979	1.34378	0.671891	+	0.740650i	$0.265482\pi$
$312$	0	0
$313$	−5.18025	−0.292805	−0.146403	−	0.989225i	$-0.546769\pi$
$313$	−5.18025	−0.292805	−0.146403	+	0.989225i	$0.546769\pi$
$314$	−31.2856	−1.76555
$315$	9.38444	0.528753
$316$	4.25596	0.239416
$317$	6.06537	0.340665	0.170332	−	0.985387i	$-0.445516\pi$
$317$	6.06537	0.340665	0.170332	+	0.985387i	$0.445516\pi$
$318$	8.70294	0.488037
$319$	5.04715	0.282586
$320$	76.8686	4.29709
$321$	6.61655	0.369300
$322$	−4.89989	−0.273060
$323$	−5.16959	−0.287644
$324$	42.1248	2.34027
$325$	0	0
$326$	11.9087	0.659562
$327$	−1.47773	−0.0817188
$328$	−37.7394	−2.08381
$329$	−5.87774	−0.324050
$330$	5.62465	0.309627
$331$	17.2749	0.949512	0.474756	−	0.880118i	$-0.342536\pi$
$331$	17.2749	0.949512	0.474756	+	0.880118i	$0.342536\pi$
$332$	52.9151	2.90410
$333$	17.0966	0.936886
$334$	−24.3804	−1.33403
$335$	−2.69419	−0.147200
$336$	4.68850	0.255779
$337$	8.35464	0.455106	0.227553	−	0.973766i	$-0.426927\pi$
$337$	8.35464	0.455106	0.227553	+	0.973766i	$0.426927\pi$
$338$	0	0
$339$	−0.951279	−0.0516664
$340$	37.2315	2.01916
$341$	−3.21644	−0.174180
$342$	18.6940	1.01086
$343$	−1.00000	−0.0539949
$344$	−77.6208	−4.18504
$345$	−2.04309	−0.109997
$346$	16.4679	0.885318
$347$	28.8220	1.54725	0.773623	−	0.633646i	$-0.218443\pi$
$347$	28.8220	1.54725	0.773623	+	0.633646i	$0.218443\pi$
$348$	5.01986	0.269093
$349$	−11.7221	−0.627467	−0.313734	−	0.949511i	$-0.601580\pi$
$349$	−11.7221	−0.627467	−0.313734	+	0.949511i	$0.601580\pi$
$350$	−15.1794	−0.811376
$351$	0	0
$352$	−34.6220	−1.84536
$353$	−17.8362	−0.949326	−0.474663	−	0.880168i	$-0.657430\pi$
$353$	−17.8362	−0.949326	−0.474663	+	0.880168i	$0.657430\pi$
$354$	10.0552	0.534426
$355$	−7.67043	−0.407104
$356$	80.2113	4.25119
$357$	0.744877	0.0394231
$358$	10.4874	0.554278
$359$	−5.68162	−0.299864	−0.149932	−	0.988696i	$-0.547906\pi$
$359$	−5.68162	−0.299864	−0.149932	+	0.988696i	$0.547906\pi$
$360$	−83.8987	−4.42185
$361$	−13.2354	−0.696601
$362$	17.7976	0.935423
$363$	2.62651	0.137856
$364$	0	0
$365$	10.4091	0.544838
$366$	−9.45462	−0.494201
$367$	−19.6316	−1.02476	−0.512381	−	0.858758i	$-0.671236\pi$
$367$	−19.6316	−1.02476	−0.512381	+	0.858758i	$0.671236\pi$
$368$	24.5658	1.28058
$369$	12.1587	0.632958
$370$	−52.2773	−2.71777
$371$	9.30628	0.483158
$372$	−3.19905	−0.165863
$373$	32.0645	1.66024	0.830119	−	0.557586i	$-0.188272\pi$
$373$	32.0645	1.66024	0.830119	+	0.557586i	$0.188272\pi$
$374$	−10.7445	−0.555587
$375$	−0.693612	−0.0358180
$376$	52.5482	2.70997
$377$	0	0
$378$	−5.49909	−0.282843
$379$	19.0231	0.977150	0.488575	−	0.872522i	$-0.337517\pi$
$379$	19.0231	0.977150	0.488575	+	0.872522i	$0.337517\pi$
$380$	−41.5167	−2.12976
$381$	3.36760	0.172527
$382$	−37.1510	−1.90081
$383$	0.699829	0.0357596	0.0178798	−	0.999840i	$-0.494308\pi$
$383$	0.699829	0.0357596	0.0178798	+	0.999840i	$0.494308\pi$
$384$	−9.08689	−0.463714
$385$	6.01459	0.306532
$386$	61.5059	3.13057
$387$	25.0076	1.27121
$388$	48.9951	2.48735
$389$	−20.0547	−1.01681	−0.508407	−	0.861117i	$-0.669765\pi$
$389$	−20.0547	−1.01681	−0.508407	+	0.861117i	$0.669765\pi$
$390$	0	0
$391$	3.90284	0.197375
$392$	8.94020	0.451548
$393$	6.45592	0.325658
$394$	39.2698	1.97838
$395$	2.61272	0.131460
$396$	28.2195	1.41809
$397$	22.2803	1.11822	0.559108	−	0.829095i	$-0.311144\pi$
$397$	22.2803	1.11822	0.559108	+	0.829095i	$0.311144\pi$
$398$	64.4453	3.23035
$399$	−0.830609	−0.0415824
$400$	76.1027	3.80513
$401$	−4.80749	−0.240074	−0.120037	−	0.992769i	$-0.538301\pi$
$401$	−4.80749	−0.240074	−0.120037	+	0.992769i	$0.538301\pi$
$402$	0.773306	0.0385690
$403$	0	0
$404$	78.6717	3.91406
$405$	25.8604	1.28501
$406$	7.39071	0.366795
$407$	10.9574	0.543137
$408$	−6.65935	−0.329687
$409$	36.8035	1.81981	0.909907	−	0.414811i	$-0.136152\pi$
$409$	36.8035	1.81981	0.909907	+	0.414811i	$0.136152\pi$
$410$	−37.1786	−1.83612
$411$	−2.91343	−0.143709
$412$	−22.7303	−1.11984
$413$	10.7523	0.529084
$414$	−14.1132	−0.693628
$415$	32.4845	1.59460
$416$	0	0
$417$	6.10122	0.298778
$418$	11.9812	0.586019
$419$	29.2667	1.42977	0.714887	−	0.699240i	$-0.246478\pi$
$419$	29.2667	1.42977	0.714887	+	0.699240i	$0.246478\pi$
$420$	5.98206	0.291895
$421$	7.53862	0.367410	0.183705	−	0.982981i	$-0.441191\pi$
$421$	7.53862	0.367410	0.183705	+	0.982981i	$0.441191\pi$
$422$	11.6650	0.567845
$423$	−16.9298	−0.823154
$424$	−83.2000	−4.04055
$425$	12.0907	0.586484
$426$	2.20162	0.106669
$427$	−10.1101	−0.489261
$428$	−101.506	−4.90646
$429$	0	0
$430$	−76.4674	−3.68759
$431$	31.2261	1.50411	0.752055	−	0.659101i	$-0.229063\pi$
$431$	31.2261	1.50411	0.752055	+	0.659101i	$0.229063\pi$
$432$	27.5699	1.32646
$433$	5.88404	0.282769	0.141384	−	0.989955i	$-0.454845\pi$
$433$	5.88404	0.282769	0.141384	+	0.989955i	$0.454845\pi$
$434$	−4.70994	−0.226084
$435$	3.08169	0.147755
$436$	22.6702	1.08570
$437$	−4.35204	−0.208186
$438$	−2.98770	−0.142758
$439$	−9.95642	−0.475194	−0.237597	−	0.971364i	$-0.576360\pi$
$439$	−9.95642	−0.475194	−0.237597	+	0.971364i	$0.576360\pi$
$440$	−53.7716	−2.56346
$441$	−2.88032	−0.137158
$442$	0	0
$443$	−35.8813	−1.70477	−0.852385	−	0.522915i	$-0.824845\pi$
$443$	−35.8813	−1.70477	−0.852385	+	0.522915i	$0.824845\pi$
$444$	10.8981	0.517202
$445$	49.2416	2.33427
$446$	63.2404	2.99452
$447$	1.39108	0.0657956
$448$	−23.5929	−1.11466
$449$	−3.99528	−0.188549	−0.0942744	−	0.995546i	$-0.530053\pi$
$449$	−3.99528	−0.188549	−0.0942744	+	0.995546i	$0.530053\pi$
$450$	−43.7217	−2.06106
$451$	7.79266	0.366942
$452$	14.5937	0.686432
$453$	−6.53877	−0.307218
$454$	−72.2371	−3.39026
$455$	0	0
$456$	7.42580	0.347745
$457$	−41.2222	−1.92829	−0.964147	−	0.265369i	$-0.914506\pi$
$457$	−41.2222	−1.92829	−0.964147	+	0.265369i	$0.914506\pi$
$458$	−8.12770	−0.379783
$459$	4.38011	0.204446
$460$	31.3435	1.46140
$461$	24.7266	1.15163	0.575816	−	0.817579i	$-0.304684\pi$
$461$	24.7266	1.15163	0.575816	+	0.817579i	$0.304684\pi$
$462$	−1.72635	−0.0803169
$463$	−24.4057	−1.13423	−0.567115	−	0.823639i	$-0.691940\pi$
$463$	−24.4057	−1.13423	−0.567115	+	0.823639i	$0.691940\pi$
$464$	−37.0536	−1.72017
$465$	−1.96389	−0.0910733
$466$	−31.6674	−1.46696
$467$	−4.44860	−0.205857	−0.102928	−	0.994689i	$-0.532821\pi$
$467$	−4.44860	−0.205857	−0.102928	+	0.994689i	$0.532821\pi$
$468$	0	0
$469$	0.826916	0.0381834
$470$	51.7673	2.38785
$471$	4.00386	0.184488
$472$	−96.1273	−4.42462
$473$	16.0276	0.736951
$474$	−0.749922	−0.0344450
$475$	−13.4823	−0.618608
$476$	−11.4273	−0.523769
$477$	26.8051	1.22732
$478$	−3.86008	−0.176556
$479$	−31.6766	−1.44734	−0.723671	−	0.690145i	$-0.757547\pi$
$479$	−31.6766	−1.44734	−0.723671	+	0.690145i	$0.757547\pi$
$480$	−21.1394	−0.964879
$481$	0	0
$482$	7.24372	0.329942
$483$	0.627077	0.0285330
$484$	−40.2938	−1.83153
$485$	30.0780	1.36577
$486$	−23.9199	−1.08503
$487$	26.9156	1.21966	0.609832	−	0.792531i	$-0.291237\pi$
$487$	26.9156	1.21966	0.609832	+	0.792531i	$0.291237\pi$
$488$	90.3860	4.09158
$489$	−1.52405	−0.0689200
$490$	8.80735	0.397875
$491$	9.72716	0.438980	0.219490	−	0.975615i	$-0.429561\pi$
$491$	9.72716	0.438980	0.219490	+	0.975615i	$0.429561\pi$
$492$	7.75052	0.349421
$493$	−5.88682	−0.265129
$494$	0	0
$495$	17.3239	0.778653
$496$	23.6134	1.06027
$497$	2.35425	0.105602
$498$	−9.32392	−0.417815
$499$	−7.87525	−0.352545	−0.176272	−	0.984341i	$-0.556404\pi$
$499$	−7.87525	−0.352545	−0.176272	+	0.984341i	$0.556404\pi$
$500$	10.6408	0.475872
$501$	3.12015	0.139398
$502$	29.5565	1.31917
$503$	−9.75206	−0.434823	−0.217411	−	0.976080i	$-0.569761\pi$
$503$	−9.75206	−0.434823	−0.217411	+	0.976080i	$0.569761\pi$
$504$	25.7506	1.14702
$505$	48.2964	2.14916
$506$	−9.04533	−0.402114
$507$	0	0
$508$	−51.6630	−2.29217
$509$	23.0256	1.02059	0.510295	−	0.859999i	$-0.329536\pi$
$509$	23.0256	1.02059	0.510295	+	0.859999i	$0.329536\pi$
$510$	−6.56039	−0.290499
$511$	−3.19482	−0.141331
$512$	11.8512	0.523752
$513$	−4.88424	−0.215645
$514$	11.2220	0.494981
$515$	−13.9541	−0.614891
$516$	15.9410	0.701762
$517$	−10.8505	−0.477203
$518$	16.0452	0.704987
$519$	−2.10752	−0.0925100
$520$	0	0
$521$	0.486481	0.0213131	0.0106566	−	0.999943i	$-0.496608\pi$
$521$	0.486481	0.0213131	0.0106566	+	0.999943i	$0.496608\pi$
$522$	21.2876	0.931733
$523$	−34.6270	−1.51413	−0.757065	−	0.653339i	$-0.773368\pi$
$523$	−34.6270	−1.51413	−0.757065	+	0.653339i	$0.773368\pi$
$524$	−99.0414	−4.32664
$525$	1.94263	0.0847834
$526$	10.9577	0.477777
$527$	3.75154	0.163420
$528$	8.65510	0.376665
$529$	−19.7144	−0.857147
$530$	−81.9636	−3.56027
$531$	30.9699	1.34398
$532$	12.7425	0.552458
$533$	0	0
$534$	−14.1336	−0.611622
$535$	−62.3141	−2.69408
$536$	−7.39279	−0.319320
$537$	−1.34216	−0.0579185
$538$	10.8134	0.466198
$539$	−1.84603	−0.0795140
$540$	35.1764	1.51375
$541$	22.5384	0.969002	0.484501	−	0.874791i	$-0.339001\pi$
$541$	22.5384	0.969002	0.484501	+	0.874791i	$0.339001\pi$
$542$	−7.52844	−0.323374
$543$	−2.27770	−0.0977456
$544$	40.3818	1.73136
$545$	13.9172	0.596146
$546$	0	0
$547$	39.3716	1.68341	0.841704	−	0.539940i	$-0.181553\pi$
$547$	39.3716	1.68341	0.841704	+	0.539940i	$0.181553\pi$
$548$	44.6955	1.90930
$549$	−29.1202	−1.24282
$550$	−28.0217	−1.19485
$551$	6.56436	0.279651
$552$	−5.60619	−0.238615
$553$	−0.801911	−0.0341007
$554$	45.1227	1.91708
$555$	6.69034	0.283989
$556$	−93.6000	−3.96952
$557$	0.726975	0.0308029	0.0154015	−	0.999881i	$-0.495097\pi$
$557$	0.726975	0.0308029	0.0154015	+	0.999881i	$0.495097\pi$
$558$	−13.5661	−0.574300
$559$	0	0
$560$	−44.1559	−1.86593
$561$	1.37506	0.0580552
$562$	36.1502	1.52490
$563$	41.6077	1.75355	0.876777	−	0.480897i	$-0.159689\pi$
$563$	41.6077	1.75355	0.876777	+	0.480897i	$0.159689\pi$
$564$	−10.7918	−0.454417
$565$	8.95907	0.376911
$566$	−51.0532	−2.14593
$567$	−7.93720	−0.333331
$568$	−21.0474	−0.883130
$569$	−25.3888	−1.06435	−0.532177	−	0.846633i	$-0.678626\pi$
$569$	−25.3888	−1.06435	−0.532177	+	0.846633i	$0.678626\pi$
$570$	7.31546	0.306411
$571$	16.9992	0.711393	0.355697	−	0.934602i	$-0.384244\pi$
$571$	16.9992	0.711393	0.355697	+	0.934602i	$0.384244\pi$
$572$	0	0
$573$	4.75451	0.198622
$574$	11.4110	0.476288
$575$	10.1786	0.424476
$576$	−67.9551	−2.83146
$577$	15.9759	0.665084	0.332542	−	0.943088i	$-0.392094\pi$
$577$	15.9759	0.665084	0.332542	+	0.943088i	$0.392094\pi$
$578$	−33.4223	−1.39018
$579$	−7.87139	−0.327124
$580$	−47.2767	−1.96306
$581$	−9.97031	−0.413638
$582$	−8.63320	−0.357858
$583$	17.1796	0.711508
$584$	28.5623	1.18192
$585$	0	0
$586$	9.23926	0.381670
$587$	15.9815	0.659627	0.329814	−	0.944046i	$-0.393014\pi$
$587$	15.9815	0.659627	0.329814	+	0.944046i	$0.393014\pi$
$588$	−1.83605	−0.0757172
$589$	−4.18333	−0.172371
$590$	−94.6989	−3.89869
$591$	−5.02566	−0.206728
$592$	−80.4433	−3.30620
$593$	−29.0532	−1.19307	−0.596536	−	0.802586i	$-0.703457\pi$
$593$	−29.0532	−1.19307	−0.596536	+	0.802586i	$0.703457\pi$
$594$	−10.1515	−0.416520
$595$	−7.01520	−0.287595
$596$	−21.3407	−0.874151
$597$	−8.24757	−0.337551
$598$	0	0
$599$	3.45554	0.141190	0.0705948	−	0.997505i	$-0.477510\pi$
$599$	3.45554	0.141190	0.0705948	+	0.997505i	$0.477510\pi$
$600$	−17.3675	−0.709026
$601$	15.5304	0.633497	0.316748	−	0.948510i	$-0.397409\pi$
$601$	15.5304	0.633497	0.316748	+	0.948510i	$0.397409\pi$
$602$	23.4698	0.956556
$603$	2.38178	0.0969936
$604$	100.313	4.08166
$605$	−24.7363	−1.00567
$606$	−13.8624	−0.563120
$607$	15.4784	0.628250	0.314125	−	0.949382i	$-0.398289\pi$
$607$	15.4784	0.628250	0.314125	+	0.949382i	$0.398289\pi$
$608$	−45.0296	−1.82619
$609$	−0.945847	−0.0383276
$610$	89.0429	3.60524
$611$	0	0
$612$	−32.9142	−1.33048
$613$	7.13223	0.288068	0.144034	−	0.989573i	$-0.453993\pi$
$613$	7.13223	0.288068	0.144034	+	0.989573i	$0.453993\pi$
$614$	−44.2456	−1.78561
$615$	4.75803	0.191862
$616$	16.5039	0.664959
$617$	−4.96685	−0.199958	−0.0999789	−	0.994990i	$-0.531878\pi$
$617$	−4.96685	−0.199958	−0.0999789	+	0.994990i	$0.531878\pi$
$618$	4.00520	0.161113
$619$	−42.3570	−1.70247	−0.851235	−	0.524784i	$-0.824146\pi$
$619$	−42.3570	−1.70247	−0.851235	+	0.524784i	$0.824146\pi$
$620$	30.1284	1.20999
$621$	3.68741	0.147971
$622$	64.0600	2.56857
$623$	−15.1135	−0.605508
$624$	0	0
$625$	−21.5445	−0.861779
$626$	−14.0032	−0.559682
$627$	−1.53333	−0.0612352
$628$	−61.4239	−2.45108
$629$	−12.7803	−0.509583
$630$	25.3680	1.01068
$631$	6.26775	0.249515	0.124758	−	0.992187i	$-0.460185\pi$
$631$	6.26775	0.249515	0.124758	+	0.992187i	$0.460185\pi$
$632$	7.16924	0.285177
$633$	−1.49286	−0.0593361
$634$	16.3959	0.651163
$635$	−31.7158	−1.25860
$636$	17.0868	0.677534
$637$	0	0
$638$	13.6434	0.540149
$639$	6.78098	0.268251
$640$	85.5797	3.38283
$641$	−31.5637	−1.24669	−0.623345	−	0.781947i	$-0.714227\pi$
$641$	−31.5637	−1.24669	−0.623345	+	0.781947i	$0.714227\pi$
$642$	17.8858	0.705897
$643$	18.2504	0.719725	0.359863	−	0.933005i	$-0.382824\pi$
$643$	18.2504	0.719725	0.359863	+	0.933005i	$0.382824\pi$
$644$	−9.62010	−0.379085
$645$	9.78613	0.385329
$646$	−13.9744	−0.549816
$647$	23.0273	0.905298	0.452649	−	0.891689i	$-0.350479\pi$
$647$	23.0273	0.905298	0.452649	+	0.891689i	$0.350479\pi$
$648$	70.9601	2.78758
$649$	19.8490	0.779140
$650$	0	0
$651$	0.602768	0.0236243
$652$	23.3807	0.915660
$653$	28.8124	1.12752	0.563759	−	0.825939i	$-0.309355\pi$
$653$	28.8124	1.12752	0.563759	+	0.825939i	$0.309355\pi$
$654$	−3.99460	−0.156201
$655$	−60.8014	−2.37571
$656$	−57.2096	−2.23366
$657$	−9.20210	−0.359008
$658$	−15.8887	−0.619406
$659$	−31.2228	−1.21627	−0.608134	−	0.793835i	$-0.708082\pi$
$659$	−31.2228	−1.21627	−0.608134	+	0.793835i	$0.708082\pi$
$660$	11.0431	0.429850
$661$	−26.5582	−1.03299	−0.516496	−	0.856289i	$-0.672764\pi$
$661$	−26.5582	−1.03299	−0.516496	+	0.856289i	$0.672764\pi$
$662$	46.6973	1.81494
$663$	0	0
$664$	89.1366	3.45917
$665$	7.82261	0.303348
$666$	46.2154	1.79081
$667$	−4.95584	−0.191891
$668$	−47.8667	−1.85202
$669$	−8.09337	−0.312908
$670$	−7.28293	−0.281364
$671$	−18.6635	−0.720495
$672$	6.48823	0.250289
$673$	−19.7386	−0.760867	−0.380434	−	0.924808i	$-0.624225\pi$
$673$	−19.7386	−0.760867	−0.380434	+	0.924808i	$0.624225\pi$
$674$	22.5842	0.869912
$675$	11.4233	0.439683
$676$	0	0
$677$	−13.1440	−0.505163	−0.252582	−	0.967576i	$-0.581280\pi$
$677$	−13.1440	−0.505163	−0.252582	+	0.967576i	$0.581280\pi$
$678$	−2.57149	−0.0987576
$679$	−9.23171	−0.354280
$680$	62.7172	2.40510
$681$	9.24475	0.354260
$682$	−8.69468	−0.332936
$683$	6.76255	0.258762	0.129381	−	0.991595i	$-0.458701\pi$
$683$	6.76255	0.258762	0.129381	+	0.991595i	$0.458701\pi$
$684$	36.7025	1.40336
$685$	27.4385	1.04837
$686$	−2.70320	−0.103209
$687$	1.04017	0.0396848
$688$	−117.666	−4.48599
$689$	0	0
$690$	−5.52288	−0.210253
$691$	−9.17090	−0.348877	−0.174439	−	0.984668i	$-0.555811\pi$
$691$	−9.17090	−0.348877	−0.174439	+	0.984668i	$0.555811\pi$
$692$	32.3319	1.22907
$693$	−5.31715	−0.201982
$694$	77.9115	2.95748
$695$	−57.4609	−2.17962
$696$	8.45605	0.320526
$697$	−9.08908	−0.344273
$698$	−31.6870	−1.19937
$699$	4.05272	0.153288
$700$	−29.8023	−1.12642
$701$	−47.4700	−1.79292	−0.896459	−	0.443127i	$-0.853869\pi$
$701$	−47.4700	−1.79292	−0.896459	+	0.443127i	$0.853869\pi$
$702$	0	0
$703$	14.2512	0.537495
$704$	−43.5532	−1.64147
$705$	−6.62507	−0.249515
$706$	−48.2148	−1.81459
$707$	−14.8234	−0.557491
$708$	19.7416	0.741936
$709$	−34.9719	−1.31340	−0.656699	−	0.754153i	$-0.728048\pi$
$709$	−34.9719	−1.31340	−0.656699	+	0.754153i	$0.728048\pi$
$710$	−20.7347	−0.778158
$711$	−2.30976	−0.0866227
$712$	135.117	5.06374
$713$	3.15825	0.118277
$714$	2.01355	0.0753552
$715$	0	0
$716$	20.5903	0.769496
$717$	0.494005	0.0184490
$718$	−15.3585	−0.573175
$719$	−8.36101	−0.311813	−0.155907	−	0.987772i	$-0.549830\pi$
$719$	−8.36101	−0.311813	−0.155907	+	0.987772i	$0.549830\pi$
$720$	−127.183	−4.73984
$721$	4.28286	0.159502
$722$	−35.7779	−1.33152
$723$	−0.927035	−0.0344768
$724$	34.9427	1.29863
$725$	−15.3528	−0.570188
$726$	7.09997	0.263505
$727$	27.4014	1.01626	0.508131	−	0.861280i	$-0.330337\pi$
$727$	27.4014	1.01626	0.508131	+	0.861280i	$0.330337\pi$
$728$	0	0
$729$	−20.7504	−0.768532
$730$	28.1379	1.04143
$731$	−18.6941	−0.691425
$732$	−18.5625	−0.686092
$733$	12.1569	0.449026	0.224513	−	0.974471i	$-0.427921\pi$
$733$	12.1569	0.449026	0.224513	+	0.974471i	$0.427921\pi$
$734$	−53.0681	−1.95878
$735$	−1.12715	−0.0415754
$736$	33.9956	1.25309
$737$	1.52651	0.0562297
$738$	32.8674	1.20987
$739$	−48.4439	−1.78204	−0.891019	−	0.453966i	$-0.850009\pi$
$739$	−48.4439	−1.78204	−0.891019	+	0.453966i	$0.850009\pi$
$740$	−102.638	−3.77304
$741$	0	0
$742$	25.1567	0.923531
$743$	16.9906	0.623326	0.311663	−	0.950193i	$-0.399114\pi$
$743$	16.9906	0.623326	0.311663	+	0.950193i	$0.399114\pi$
$744$	−5.38886	−0.197565
$745$	−13.1010	−0.479985
$746$	86.6767	3.17346
$747$	−28.7177	−1.05073
$748$	−21.0951	−0.771313
$749$	19.1258	0.698841
$750$	−1.87497	−0.0684642
$751$	43.0323	1.57027	0.785136	−	0.619323i	$-0.212593\pi$
$751$	43.0323	1.57027	0.785136	+	0.619323i	$0.212593\pi$
$752$	79.6585	2.90485
$753$	−3.78258	−0.137845
$754$	0	0
$755$	61.5817	2.24119
$756$	−10.7965	−0.392666
$757$	29.1785	1.06051	0.530255	−	0.847838i	$-0.322096\pi$
$757$	29.1785	1.06051	0.530255	+	0.847838i	$0.322096\pi$
$758$	51.4231	1.86777
$759$	1.15760	0.0420183
$760$	−69.9357	−2.53683
$761$	29.4251	1.06666	0.533330	−	0.845907i	$-0.320941\pi$
$761$	29.4251	1.06666	0.533330	+	0.845907i	$0.320941\pi$
$762$	9.10328	0.329777
$763$	−4.27153	−0.154640
$764$	−72.9398	−2.63887
$765$	−20.2060	−0.730550
$766$	1.89178	0.0683526
$767$	0	0
$768$	−8.23976	−0.297327
$769$	−17.1864	−0.619759	−0.309879	−	0.950776i	$-0.600289\pi$
$769$	−17.1864	−0.619759	−0.309879	+	0.950776i	$0.600289\pi$
$770$	16.2586	0.585920
$771$	−1.43617	−0.0517223
$772$	120.756	4.34612
$773$	21.9601	0.789851	0.394926	−	0.918713i	$-0.370770\pi$
$773$	21.9601	0.789851	0.394926	+	0.918713i	$0.370770\pi$
$774$	67.6004	2.42985
$775$	9.78399	0.351451
$776$	82.5333	2.96277
$777$	−2.05343	−0.0736665
$778$	−54.2118	−1.94359
$779$	10.1352	0.363131
$780$	0	0
$781$	4.34600	0.155512
$782$	10.5501	0.377272
$783$	−5.56188	−0.198765
$784$	13.5526	0.484020
$785$	−37.7081	−1.34586
$786$	17.4516	0.622478
$787$	2.33567	0.0832578	0.0416289	−	0.999133i	$-0.486745\pi$
$787$	2.33567	0.0832578	0.0416289	+	0.999133i	$0.486745\pi$
$788$	77.0996	2.74656
$789$	−1.40234	−0.0499246
$790$	7.06271	0.251280
$791$	−2.74976	−0.0977704
$792$	47.5364	1.68913
$793$	0	0
$794$	60.2280	2.13741
$795$	10.4895	0.372025
$796$	126.527	4.48465
$797$	27.8040	0.984869	0.492434	−	0.870350i	$-0.336107\pi$
$797$	27.8040	0.984869	0.492434	+	0.870350i	$0.336107\pi$
$798$	−2.24530	−0.0794827
$799$	12.6556	0.447723
$800$	105.315	3.72346
$801$	−43.5316	−1.53811
$802$	−12.9956	−0.458890
$803$	−5.89773	−0.208126
$804$	1.51825	0.0535447
$805$	−5.90576	−0.208151
$806$	0	0
$807$	−1.38387	−0.0487147
$808$	132.524	4.66218
$809$	15.0203	0.528087	0.264043	−	0.964511i	$-0.414944\pi$
$809$	15.0203	0.528087	0.264043	+	0.964511i	$0.414944\pi$
$810$	69.9056	2.45623
$811$	−43.6933	−1.53428	−0.767139	−	0.641481i	$-0.778320\pi$
$811$	−43.6933	−1.53428	−0.767139	+	0.641481i	$0.778320\pi$
$812$	14.5104	0.509215
$813$	0.963474	0.0337905
$814$	29.6199	1.03818
$815$	14.3534	0.502778
$816$	−10.0950	−0.353395
$817$	20.8456	0.729297
$818$	99.4870	3.47848
$819$	0	0
$820$	−72.9939	−2.54906
$821$	−18.0701	−0.630651	−0.315326	−	0.948984i	$-0.602114\pi$
$821$	−18.0701	−0.630651	−0.315326	+	0.948984i	$0.602114\pi$
$822$	−7.87557	−0.274692
$823$	4.45550	0.155309	0.0776544	−	0.996980i	$-0.475257\pi$
$823$	4.45550	0.155309	0.0776544	+	0.996980i	$0.475257\pi$
$824$	−38.2896	−1.33388
$825$	3.58615	0.124854
$826$	29.0655	1.01132
$827$	11.8352	0.411549	0.205774	−	0.978599i	$-0.434029\pi$
$827$	11.8352	0.411549	0.205774	+	0.978599i	$0.434029\pi$
$828$	−27.7090	−0.962953
$829$	−3.53894	−0.122913	−0.0614563	−	0.998110i	$-0.519574\pi$
$829$	−3.53894	−0.122913	−0.0614563	+	0.998110i	$0.519574\pi$
$830$	87.8120	3.04800
$831$	−5.77471	−0.200323
$832$	0	0
$833$	2.15314	0.0746019
$834$	16.4928	0.571099
$835$	−29.3853	−1.01692
$836$	23.5230	0.813561
$837$	3.54447	0.122515
$838$	79.1137	2.73294
$839$	33.4853	1.15604	0.578020	−	0.816023i	$-0.303826\pi$
$839$	33.4853	1.15604	0.578020	+	0.816023i	$0.303826\pi$
$840$	10.0769	0.347686
$841$	−21.5249	−0.742238
$842$	20.3784	0.702285
$843$	−4.62642	−0.159343
$844$	22.9023	0.788330
$845$	0	0
$846$	−45.7645	−1.57342
$847$	7.59218	0.260870
$848$	−126.124	−4.33112
$849$	6.53368	0.224235
$850$	32.6835	1.12103
$851$	−10.7591	−0.368818
$852$	4.32250	0.148087
$853$	22.0871	0.756248	0.378124	−	0.925755i	$-0.376569\pi$
$853$	22.0871	0.756248	0.378124	+	0.925755i	$0.376569\pi$
$854$	−27.3295	−0.935196
$855$	22.5316	0.770565
$856$	−170.988	−5.84426
$857$	−6.89363	−0.235482	−0.117741	−	0.993044i	$-0.537565\pi$
$857$	−6.89363	−0.235482	−0.117741	+	0.993044i	$0.537565\pi$
$858$	0	0
$859$	−37.4834	−1.27892	−0.639459	−	0.768825i	$-0.720842\pi$
$859$	−37.4834	−1.27892	−0.639459	+	0.768825i	$0.720842\pi$
$860$	−150.131	−5.11942
$861$	−1.46036	−0.0497689
$862$	84.4103	2.87503
$863$	17.5248	0.596552	0.298276	−	0.954480i	$-0.403588\pi$
$863$	17.5248	0.596552	0.298276	+	0.954480i	$0.403588\pi$
$864$	38.1528	1.29799
$865$	19.8485	0.674869
$866$	15.9057	0.540498
$867$	4.27731	0.145265
$868$	−9.24717	−0.313869
$869$	−1.48035	−0.0502174
$870$	8.33040	0.282427
$871$	0	0
$872$	38.1883	1.29322
$873$	−26.5903	−0.899944
$874$	−11.7644	−0.397937
$875$	−2.00495	−0.0677798
$876$	−5.86584	−0.198188
$877$	−46.7491	−1.57860	−0.789302	−	0.614005i	$-0.789557\pi$
$877$	−46.7491	−1.57860	−0.789302	+	0.614005i	$0.789557\pi$
$878$	−26.9142	−0.908309
$879$	−1.18242	−0.0398821
$880$	−81.5131	−2.74781
$881$	−2.91875	−0.0983350	−0.0491675	−	0.998791i	$-0.515657\pi$
$881$	−2.91875	−0.0983350	−0.0491675	+	0.998791i	$0.515657\pi$
$882$	−7.78607	−0.262171
$883$	−28.5505	−0.960801	−0.480400	−	0.877049i	$-0.659509\pi$
$883$	−28.5505	−0.960801	−0.480400	+	0.877049i	$0.659509\pi$
$884$	0	0
$885$	12.1194	0.407388
$886$	−96.9941	−3.25858
$887$	0.422914	0.0142001	0.00710004	−	0.999975i	$-0.497740\pi$
$887$	0.422914	0.0142001	0.00710004	+	0.999975i	$0.497740\pi$
$888$	18.3581	0.616058
$889$	9.73438	0.326480
$890$	133.110	4.46184
$891$	−14.6523	−0.490870
$892$	124.162	4.15725
$893$	−14.1122	−0.472247
$894$	3.76035	0.125765
$895$	12.6404	0.422521
$896$	−26.2666	−0.877504
$897$	0	0
$898$	−10.8000	−0.360401
$899$	−4.76372	−0.158879
$900$	−85.8401	−2.86134
$901$	−20.0377	−0.667553
$902$	21.0651	0.701391
$903$	−3.00361	−0.0999539
$904$	24.5834	0.817633
$905$	21.4512	0.713063
$906$	−17.6756	−0.587232
$907$	−22.4284	−0.744723	−0.372361	−	0.928088i	$-0.621452\pi$
$907$	−22.4284	−0.744723	−0.372361	+	0.928088i	$0.621452\pi$
$908$	−141.825	−4.70664
$909$	−42.6961	−1.41614
$910$	0	0
$911$	−32.5788	−1.07938	−0.539692	−	0.841863i	$-0.681459\pi$
$911$	−32.5788	−1.07938	−0.539692	+	0.841863i	$0.681459\pi$
$912$	11.2569	0.372752
$913$	−18.4055	−0.609132
$914$	−111.432	−3.68583
$915$	−11.3955	−0.376724
$916$	−15.9574	−0.527247
$917$	18.6615	0.616256
$918$	11.8403	0.390788
$919$	−9.87913	−0.325883	−0.162941	−	0.986636i	$-0.552098\pi$
$919$	−9.87913	−0.325883	−0.162941	+	0.986636i	$0.552098\pi$
$920$	52.7987	1.74072
$921$	5.66246	0.186584
$922$	66.8408	2.20129
$923$	0	0
$924$	−3.38939	−0.111503
$925$	−33.3309	−1.09591
$926$	−65.9734	−2.16802
$927$	12.3360	0.405168
$928$	−51.2769	−1.68325
$929$	29.9136	0.981434	0.490717	−	0.871319i	$-0.336735\pi$
$929$	29.9136	0.981434	0.490717	+	0.871319i	$0.336735\pi$
$930$	−5.30878	−0.174082
$931$	−2.40096	−0.0786881
$932$	−62.1736	−2.03656
$933$	−8.19826	−0.268399
$934$	−12.0255	−0.393485
$935$	−12.9502	−0.423518
$936$	0	0
$937$	−31.8296	−1.03983	−0.519914	−	0.854219i	$-0.674036\pi$
$937$	−31.8296	−1.03983	−0.519914	+	0.854219i	$0.674036\pi$
$938$	2.23532	0.0729856
$939$	1.79210	0.0584831
$940$	101.636	3.31501
$941$	42.0885	1.37205	0.686023	−	0.727580i	$-0.259355\pi$
$941$	42.0885	1.37205	0.686023	+	0.727580i	$0.259355\pi$
$942$	10.8232	0.352640
$943$	−7.65167	−0.249173
$944$	−145.721	−4.74280
$945$	−6.62797	−0.215608
$946$	43.3258	1.40864
$947$	60.3377	1.96071	0.980357	−	0.197234i	$-0.0631958\pi$
$947$	60.3377	1.96071	0.980357	+	0.197234i	$0.0631958\pi$
$948$	−1.47234	−0.0478195
$949$	0	0
$950$	−36.4452	−1.18244
$951$	−2.09831	−0.0680423
$952$	−19.2495	−0.623880
$953$	−17.3754	−0.562844	−0.281422	−	0.959584i	$-0.590806\pi$
$953$	−17.3754	−0.562844	−0.281422	+	0.959584i	$0.590806\pi$
$954$	72.4593	2.34596
$955$	−44.7776	−1.44897
$956$	−7.57862	−0.245110
$957$	−1.74606	−0.0564421
$958$	−85.6281	−2.76652
$959$	−8.42156	−0.271946
$960$	−26.5926	−0.858274
$961$	−27.9642	−0.902070
$962$	0	0
$963$	55.0883	1.77520
$964$	14.2218	0.458054
$965$	74.1322	2.38640
$966$	1.69511	0.0545393
$967$	−18.8630	−0.606594	−0.303297	−	0.952896i	$-0.598087\pi$
$967$	−18.8630	−0.606594	−0.303297	+	0.952896i	$0.598087\pi$
$968$	−67.8756	−2.18160
$969$	1.78842	0.0574522
$970$	81.3068	2.61061
$971$	−1.56446	−0.0502060	−0.0251030	−	0.999685i	$-0.507991\pi$
$971$	−1.56446	−0.0502060	−0.0251030	+	0.999685i	$0.507991\pi$
$972$	−46.9626	−1.50633
$973$	17.6362	0.565390
$974$	72.7582	2.33132
$975$	0	0
$976$	137.017	4.38582
$977$	27.8755	0.891817	0.445909	−	0.895078i	$-0.352881\pi$
$977$	27.8755	0.891817	0.445909	+	0.895078i	$0.352881\pi$
$978$	−4.11981	−0.131737
$979$	−27.8999	−0.891684
$980$	17.2917	0.552364
$981$	−12.3034	−0.392817
$982$	26.2944	0.839088
$983$	33.4239	1.06606	0.533029	−	0.846097i	$-0.321054\pi$
$983$	33.4239	1.06606	0.533029	+	0.846097i	$0.321054\pi$
$984$	13.0559	0.416207
$985$	47.3313	1.50810
$986$	−15.9132	−0.506780
$987$	2.03340	0.0647238
$988$	0	0
$989$	−15.7376	−0.500428
$990$	46.8300	1.48835
$991$	−18.9110	−0.600726	−0.300363	−	0.953825i	$-0.597108\pi$
$991$	−18.9110	−0.600726	−0.300363	+	0.953825i	$0.597108\pi$
$992$	32.6777	1.03752
$993$	−5.97622	−0.189650
$994$	6.36399	0.201853
$995$	77.6750	2.46246
$996$	−18.3059	−0.580046
$997$	43.5775	1.38011	0.690057	−	0.723755i	$-0.257585\pi$
$997$	43.5775	1.38011	0.690057	+	0.723755i	$0.257585\pi$
$998$	−21.2884	−0.673871
$999$	−12.0748	−0.382031

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.a.p.1.6		6
7.6	odd	2		8281.2.a.ch.1.6		6
13.5	odd	4		1183.2.c.i.337.1		12
13.6	odd	12		91.2.q.a.36.1	✓	12
13.8	odd	4		1183.2.c.i.337.12		12
13.11	odd	12		91.2.q.a.43.1	yes	12
13.12	even	2		1183.2.a.m.1.1		6
39.11	even	12		819.2.ct.a.316.6		12
39.32	even	12		819.2.ct.a.127.6		12
52.11	even	12		1456.2.cc.c.225.4		12
52.19	even	12		1456.2.cc.c.673.4		12
91.6	even	12		637.2.q.h.491.1		12
91.11	odd	12		637.2.u.h.30.6		12
91.19	even	12		637.2.u.i.361.6		12
91.24	even	12		637.2.u.i.30.6		12
91.32	odd	12		637.2.k.h.569.1		12
91.37	odd	12		637.2.k.h.459.6		12
91.45	even	12		637.2.k.g.569.1		12
91.58	odd	12		637.2.u.h.361.6		12
91.76	even	12		637.2.q.h.589.1		12
91.89	even	12		637.2.k.g.459.6		12
91.90	odd	2		8281.2.a.by.1.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.q.a.36.1	✓	12	13.6	odd	12
91.2.q.a.43.1	yes	12	13.11	odd	12
637.2.k.g.459.6		12	91.89	even	12
637.2.k.g.569.1		12	91.45	even	12
637.2.k.h.459.6		12	91.37	odd	12
637.2.k.h.569.1		12	91.32	odd	12
637.2.q.h.491.1		12	91.6	even	12
637.2.q.h.589.1		12	91.76	even	12
637.2.u.h.30.6		12	91.11	odd	12
637.2.u.h.361.6		12	91.58	odd	12
637.2.u.i.30.6		12	91.24	even	12
637.2.u.i.361.6		12	91.19	even	12
819.2.ct.a.127.6		12	39.32	even	12
819.2.ct.a.316.6		12	39.11	even	12
1183.2.a.m.1.1		6	13.12	even	2
1183.2.a.p.1.6		6	1.1	even	1	trivial
1183.2.c.i.337.1		12	13.5	odd	4
1183.2.c.i.337.12		12	13.8	odd	4
1456.2.cc.c.225.4		12	52.11	even	12
1456.2.cc.c.673.4		12	52.19	even	12
8281.2.a.by.1.1		6	91.90	odd	2
8281.2.a.ch.1.6		6	7.6	odd	2

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.a (trivial)

\(f(q)\)	\(=\)	\(q+2.70320 q^{2} -0.345949 q^{3} +5.30727 q^{4} +3.25812 q^{5} -0.935168 q^{6} -1.00000 q^{7} +8.94020 q^{8} -2.88032 q^{9} +O(q^{10})\)	\(q+2.70320 q^{2} -0.345949 q^{3} +5.30727 q^{4} +3.25812 q^{5} -0.935168 q^{6} -1.00000 q^{7} +8.94020 q^{8} -2.88032 q^{9} +8.80735 q^{10} -1.84603 q^{11} -1.83605 q^{12} -2.70320 q^{14} -1.12715 q^{15} +13.5526 q^{16} +2.15314 q^{17} -7.78607 q^{18} -2.40096 q^{19} +17.2917 q^{20} +0.345949 q^{21} -4.99017 q^{22} +1.81263 q^{23} -3.09285 q^{24} +5.61537 q^{25} +2.03429 q^{27} -5.30727 q^{28} -2.73406 q^{29} -3.04689 q^{30} +1.74236 q^{31} +18.7549 q^{32} +0.638632 q^{33} +5.82036 q^{34} -3.25812 q^{35} -15.2866 q^{36} -5.93565 q^{37} -6.49025 q^{38} +29.1283 q^{40} -4.22131 q^{41} +0.935168 q^{42} -8.68223 q^{43} -9.79737 q^{44} -9.38444 q^{45} +4.89989 q^{46} +5.87774 q^{47} -4.68850 q^{48} +1.00000 q^{49} +15.1794 q^{50} -0.744877 q^{51} -9.30628 q^{53} +5.49909 q^{54} -6.01459 q^{55} -8.94020 q^{56} +0.830609 q^{57} -7.39071 q^{58} -10.7523 q^{59} -5.98206 q^{60} +10.1101 q^{61} +4.70994 q^{62} +2.88032 q^{63} +23.5929 q^{64} +1.72635 q^{66} -0.826916 q^{67} +11.4273 q^{68} -0.627077 q^{69} -8.80735 q^{70} -2.35425 q^{71} -25.7506 q^{72} +3.19482 q^{73} -16.0452 q^{74} -1.94263 q^{75} -12.7425 q^{76} +1.84603 q^{77} +0.801911 q^{79} +44.1559 q^{80} +7.93720 q^{81} -11.4110 q^{82} +9.97031 q^{83} +1.83605 q^{84} +7.01520 q^{85} -23.4698 q^{86} +0.945847 q^{87} -16.5039 q^{88} +15.1135 q^{89} -25.3680 q^{90} +9.62010 q^{92} -0.602768 q^{93} +15.8887 q^{94} -7.82261 q^{95} -6.48823 q^{96} +9.23171 q^{97} +2.70320 q^{98} +5.31715 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 4 q^{2} + 4 q^{4} + 6 q^{5} + 4 q^{6} - 6 q^{7} + 12 q^{8} + 4 q^{9}+O(q^{10}) \) 6 * q + 4 * q^2 + 4 * q^4 + 6 * q^5 + 4 * q^6 - 6 * q^7 + 12 * q^8 + 4 * q^9	\( 6 q + 4 q^{2} + 4 q^{4} + 6 q^{5} + 4 q^{6} - 6 q^{7} + 12 q^{8} + 4 q^{9} + 12 q^{10} + 4 q^{11} + 2 q^{12} - 4 q^{14} + 20 q^{15} + 8 q^{16} - 4 q^{17} - 16 q^{18} + 2 q^{19} + 26 q^{20} - 6 q^{22} - 12 q^{23} + 2 q^{24} + 10 q^{25} + 6 q^{27} - 4 q^{28} - 8 q^{29} + 8 q^{30} - 14 q^{31} + 8 q^{32} + 16 q^{33} - 2 q^{34} - 6 q^{35} - 10 q^{36} + 12 q^{37} - 2 q^{38} + 46 q^{40} + 28 q^{41} - 4 q^{42} + 2 q^{43} - 20 q^{44} + 16 q^{45} + 20 q^{46} + 14 q^{47} + 2 q^{48} + 6 q^{49} + 32 q^{50} - 26 q^{51} - 22 q^{53} + 14 q^{54} + 6 q^{55} - 12 q^{56} + 4 q^{58} - 2 q^{59} - 14 q^{61} - 4 q^{62} - 4 q^{63} + 26 q^{64} - 26 q^{66} + 24 q^{67} + 8 q^{68} + 4 q^{69} - 12 q^{70} + 4 q^{71} + 8 q^{72} + 36 q^{73} - 6 q^{74} + 46 q^{75} - 26 q^{76} - 4 q^{77} - 28 q^{79} + 36 q^{80} - 2 q^{81} + 14 q^{82} + 26 q^{83} - 2 q^{84} - 20 q^{85} - 24 q^{86} + 2 q^{87} - 14 q^{88} + 42 q^{89} - 12 q^{90} + 12 q^{92} - 4 q^{94} - 22 q^{95} - 42 q^{96} + 24 q^{97} + 4 q^{98} + 16 q^{99}+O(q^{100}) \) 6 * q + 4 * q^2 + 4 * q^4 + 6 * q^5 + 4 * q^6 - 6 * q^7 + 12 * q^8 + 4 * q^9 + 12 * q^10 + 4 * q^11 + 2 * q^12 - 4 * q^14 + 20 * q^15 + 8 * q^16 - 4 * q^17 - 16 * q^18 + 2 * q^19 + 26 * q^20 - 6 * q^22 - 12 * q^23 + 2 * q^24 + 10 * q^25 + 6 * q^27 - 4 * q^28 - 8 * q^29 + 8 * q^30 - 14 * q^31 + 8 * q^32 + 16 * q^33 - 2 * q^34 - 6 * q^35 - 10 * q^36 + 12 * q^37 - 2 * q^38 + 46 * q^40 + 28 * q^41 - 4 * q^42 + 2 * q^43 - 20 * q^44 + 16 * q^45 + 20 * q^46 + 14 * q^47 + 2 * q^48 + 6 * q^49 + 32 * q^50 - 26 * q^51 - 22 * q^53 + 14 * q^54 + 6 * q^55 - 12 * q^56 + 4 * q^58 - 2 * q^59 - 14 * q^61 - 4 * q^62 - 4 * q^63 + 26 * q^64 - 26 * q^66 + 24 * q^67 + 8 * q^68 + 4 * q^69 - 12 * q^70 + 4 * q^71 + 8 * q^72 + 36 * q^73 - 6 * q^74 + 46 * q^75 - 26 * q^76 - 4 * q^77 - 28 * q^79 + 36 * q^80 - 2 * q^81 + 14 * q^82 + 26 * q^83 - 2 * q^84 - 20 * q^85 - 24 * q^86 + 2 * q^87 - 14 * q^88 + 42 * q^89 - 12 * q^90 + 12 * q^92 - 4 * q^94 - 22 * q^95 - 42 * q^96 + 24 * q^97 + 4 * q^98 + 16 * q^99

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