LMFDB - Embedded newform 1183.2.a.h.1.2

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:	$1$
Dimension:	$3$
Coefficient field:	3.3.148.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 3x + 1 $ x^3 - x^2 - 3*x + 1
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			1.2
Root			$0.311108$ 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)

$f(q)$	$=$	$q-0.688892 q^{2} -2.21432 q^{3} -1.52543 q^{4} -3.21432 q^{5} +1.52543 q^{6} +1.00000 q^{7} +2.42864 q^{8} +1.90321 q^{9} +O(q^{10})$	\(q-0.688892 q^{2} -2.21432 q^{3} -1.52543 q^{4} -3.21432 q^{5} +1.52543 q^{6} +1.00000 q^{7} +2.42864 q^{8} +1.90321 q^{9} +2.21432 q^{10} -2.68889 q^{11} +3.37778 q^{12} -0.688892 q^{14} +7.11753 q^{15} +1.37778 q^{16} +3.59210 q^{17} -1.31111 q^{18} +8.54617 q^{19} +4.90321 q^{20} -2.21432 q^{21} +1.85236 q^{22} -3.28100 q^{23} -5.37778 q^{24} +5.33185 q^{25} +2.42864 q^{27} -1.52543 q^{28} +2.05086 q^{29} -4.90321 q^{30} -5.83654 q^{31} -5.80642 q^{32} +5.95407 q^{33} -2.47457 q^{34} -3.21432 q^{35} -2.90321 q^{36} -3.93332 q^{37} -5.88739 q^{38} -7.80642 q^{40} -0.755569 q^{41} +1.52543 q^{42} +8.80642 q^{43} +4.10171 q^{44} -6.11753 q^{45} +2.26025 q^{46} -1.88247 q^{47} -3.05086 q^{48} +1.00000 q^{49} -3.67307 q^{50} -7.95407 q^{51} +2.52543 q^{53} -1.67307 q^{54} +8.64296 q^{55} +2.42864 q^{56} -18.9240 q^{57} -1.41282 q^{58} -7.33185 q^{59} -10.8573 q^{60} +9.05086 q^{61} +4.02074 q^{62} +1.90321 q^{63} +1.24443 q^{64} -4.10171 q^{66} -0.428639 q^{67} -5.47949 q^{68} +7.26517 q^{69} +2.21432 q^{70} -8.98418 q^{71} +4.62222 q^{72} -5.79060 q^{73} +2.70964 q^{74} -11.8064 q^{75} -13.0366 q^{76} -2.68889 q^{77} -4.47949 q^{79} -4.42864 q^{80} -11.0874 q^{81} +0.520505 q^{82} +10.8272 q^{83} +3.37778 q^{84} -11.5462 q^{85} -6.06668 q^{86} -4.54125 q^{87} -6.53035 q^{88} -5.36196 q^{89} +4.21432 q^{90} +5.00492 q^{92} +12.9240 q^{93} +1.29682 q^{94} -27.4701 q^{95} +12.8573 q^{96} -9.62867 q^{97} -0.688892 q^{98} -5.11753 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 2 q^{2} + 2 q^{4} - 3 q^{5} - 2 q^{6} + 3 q^{7} - 6 q^{8} - q^{9}+O(q^{10}) $ 3 * q - 2 * q^2 + 2 * q^4 - 3 * q^5 - 2 * q^6 + 3 * q^7 - 6 * q^8 - q^9	$ 3 q - 2 q^{2} + 2 q^{4} - 3 q^{5} - 2 q^{6} + 3 q^{7} - 6 q^{8} - q^{9} - 8 q^{11} + 10 q^{12} - 2 q^{14} + 8 q^{15} + 4 q^{16} + 4 q^{17} - 4 q^{18} - q^{19} + 8 q^{20} + 12 q^{22} - 3 q^{23} - 16 q^{24} - 4 q^{25} - 6 q^{27} + 2 q^{28} - 7 q^{29} - 8 q^{30} - 11 q^{31} - 4 q^{32} - 2 q^{33} - 14 q^{34} - 3 q^{35} - 2 q^{36} - 12 q^{37} + 2 q^{38} - 10 q^{40} - 2 q^{41} - 2 q^{42} + 13 q^{43} - 14 q^{44} - 5 q^{45} + 20 q^{46} - 19 q^{47} + 4 q^{48} + 3 q^{49} + 2 q^{50} - 4 q^{51} + q^{53} + 8 q^{54} + 6 q^{55} - 6 q^{56} - 30 q^{57} + 22 q^{58} - 2 q^{59} - 6 q^{60} + 14 q^{61} - 8 q^{62} - q^{63} + 4 q^{64} + 14 q^{66} + 12 q^{67} + 10 q^{68} + 2 q^{69} - 14 q^{71} + 14 q^{72} + 9 q^{73} - 12 q^{74} - 22 q^{75} - 32 q^{76} - 8 q^{77} + 13 q^{79} - 13 q^{81} + 28 q^{82} - q^{83} + 10 q^{84} - 8 q^{85} - 18 q^{86} - 20 q^{87} + 20 q^{88} - 3 q^{89} + 6 q^{90} - 18 q^{92} + 12 q^{93} + 10 q^{94} - 29 q^{95} + 12 q^{96} - 15 q^{97} - 2 q^{98} - 2 q^{99}+O(q^{100}) $ 3 * q - 2 * q^2 + 2 * q^4 - 3 * q^5 - 2 * q^6 + 3 * q^7 - 6 * q^8 - q^9 - 8 * q^11 + 10 * q^12 - 2 * q^14 + 8 * q^15 + 4 * q^16 + 4 * q^17 - 4 * q^18 - q^19 + 8 * q^20 + 12 * q^22 - 3 * q^23 - 16 * q^24 - 4 * q^25 - 6 * q^27 + 2 * q^28 - 7 * q^29 - 8 * q^30 - 11 * q^31 - 4 * q^32 - 2 * q^33 - 14 * q^34 - 3 * q^35 - 2 * q^36 - 12 * q^37 + 2 * q^38 - 10 * q^40 - 2 * q^41 - 2 * q^42 + 13 * q^43 - 14 * q^44 - 5 * q^45 + 20 * q^46 - 19 * q^47 + 4 * q^48 + 3 * q^49 + 2 * q^50 - 4 * q^51 + q^53 + 8 * q^54 + 6 * q^55 - 6 * q^56 - 30 * q^57 + 22 * q^58 - 2 * q^59 - 6 * q^60 + 14 * q^61 - 8 * q^62 - q^63 + 4 * q^64 + 14 * q^66 + 12 * q^67 + 10 * q^68 + 2 * q^69 - 14 * q^71 + 14 * q^72 + 9 * q^73 - 12 * q^74 - 22 * q^75 - 32 * q^76 - 8 * q^77 + 13 * q^79 - 13 * q^81 + 28 * q^82 - q^83 + 10 * q^84 - 8 * q^85 - 18 * q^86 - 20 * q^87 + 20 * q^88 - 3 * q^89 + 6 * q^90 - 18 * q^92 + 12 * q^93 + 10 * q^94 - 29 * q^95 + 12 * q^96 - 15 * q^97 - 2 * q^98 - 2 * 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 $

$2$	−0.688892	−0.487120	−0.243560	−	0.969886i	$-0.578315\pi$
$2$	−0.688892	−0.487120	−0.243560	+	0.969886i	$0.578315\pi$
$3$	−2.21432	−1.27844	−0.639219	−	0.769025i	$-0.720742\pi$
$3$	−2.21432	−1.27844	−0.639219	+	0.769025i	$0.720742\pi$
$4$	−1.52543	−0.762714
$5$	−3.21432	−1.43749	−0.718744	−	0.695275i	$-0.755283\pi$
$5$	−3.21432	−1.43749	−0.718744	+	0.695275i	$0.755283\pi$
$6$	1.52543	0.622753
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	2.42864	0.858654
$9$	1.90321	0.634404
$10$	2.21432	0.700229
$11$	−2.68889	−0.810731	−0.405366	−	0.914155i	$-0.632856\pi$
$11$	−2.68889	−0.810731	−0.405366	+	0.914155i	$0.632856\pi$
$12$	3.37778	0.975082
$13$	0	0
$13$	0	0
$14$	−0.688892	−0.184114
$15$	7.11753	1.83774
$16$	1.37778	0.344446
$17$	3.59210	0.871213	0.435607	−	0.900137i	$-0.356534\pi$
$17$	3.59210	0.871213	0.435607	+	0.900137i	$0.356534\pi$
$18$	−1.31111	−0.309031
$19$	8.54617	1.96063	0.980313	−	0.197449i	$-0.0632658\pi$
$19$	8.54617	1.96063	0.980313	+	0.197449i	$0.0632658\pi$
$20$	4.90321	1.09639
$21$	−2.21432	−0.483204
$22$	1.85236	0.394924
$23$	−3.28100	−0.684135	−0.342068	−	0.939675i	$-0.611127\pi$
$23$	−3.28100	−0.684135	−0.342068	+	0.939675i	$0.611127\pi$
$24$	−5.37778	−1.09774
$25$	5.33185	1.06637
$26$	0	0
$27$	2.42864	0.467392
$28$	−1.52543	−0.288279
$29$	2.05086	0.380834	0.190417	−	0.981703i	$-0.439016\pi$
$29$	2.05086	0.380834	0.190417	+	0.981703i	$0.439016\pi$
$30$	−4.90321	−0.895200
$31$	−5.83654	−1.04827	−0.524136	−	0.851634i	$-0.675612\pi$
$31$	−5.83654	−1.04827	−0.524136	+	0.851634i	$0.675612\pi$
$32$	−5.80642	−1.02644
$33$	5.95407	1.03647
$34$	−2.47457	−0.424386
$35$	−3.21432	−0.543319
$36$	−2.90321	−0.483869
$37$	−3.93332	−0.646634	−0.323317	−	0.946291i	$-0.604798\pi$
$37$	−3.93332	−0.646634	−0.323317	+	0.946291i	$0.604798\pi$
$38$	−5.88739	−0.955061
$39$	0	0
$40$	−7.80642	−1.23430
$41$	−0.755569	−0.118000	−0.0590000	−	0.998258i	$-0.518791\pi$
$41$	−0.755569	−0.118000	−0.0590000	+	0.998258i	$0.518791\pi$
$42$	1.52543	0.235379
$43$	8.80642	1.34297	0.671484	−	0.741019i	$-0.265657\pi$
$43$	8.80642	1.34297	0.671484	+	0.741019i	$0.265657\pi$
$44$	4.10171	0.618356
$45$	−6.11753	−0.911948
$46$	2.26025	0.333256
$47$	−1.88247	−0.274586	−0.137293	−	0.990530i	$-0.543840\pi$
$47$	−1.88247	−0.274586	−0.137293	+	0.990530i	$0.543840\pi$
$48$	−3.05086	−0.440353
$49$	1.00000	0.142857
$50$	−3.67307	−0.519451
$51$	−7.95407	−1.11379
$52$	0	0
$53$	2.52543	0.346894	0.173447	−	0.984843i	$-0.444509\pi$
$53$	2.52543	0.346894	0.173447	+	0.984843i	$0.444509\pi$
$54$	−1.67307	−0.227676
$55$	8.64296	1.16542
$56$	2.42864	0.324541
$57$	−18.9240	−2.50654
$58$	−1.41282	−0.185512
$59$	−7.33185	−0.954526	−0.477263	−	0.878761i	$-0.658371\pi$
$59$	−7.33185	−0.954526	−0.477263	+	0.878761i	$0.658371\pi$
$60$	−10.8573	−1.40167
$61$	9.05086	1.15884	0.579422	−	0.815028i	$-0.303278\pi$
$61$	9.05086	1.15884	0.579422	+	0.815028i	$0.303278\pi$
$62$	4.02074	0.510635
$63$	1.90321	0.239782
$64$	1.24443	0.155554
$65$	0	0
$66$	−4.10171	−0.504886
$67$	−0.428639	−0.0523666	−0.0261833	−	0.999657i	$-0.508335\pi$
$67$	−0.428639	−0.0523666	−0.0261833	+	0.999657i	$0.508335\pi$
$68$	−5.47949	−0.664486
$69$	7.26517	0.874624
$70$	2.21432	0.264662
$71$	−8.98418	−1.06623	−0.533113	−	0.846044i	$-0.678978\pi$
$71$	−8.98418	−1.06623	−0.533113	+	0.846044i	$0.678978\pi$
$72$	4.62222	0.544733
$73$	−5.79060	−0.677739	−0.338869	−	0.940833i	$-0.610044\pi$
$73$	−5.79060	−0.677739	−0.338869	+	0.940833i	$0.610044\pi$
$74$	2.70964	0.314989
$75$	−11.8064	−1.36329
$76$	−13.0366	−1.49540
$77$	−2.68889	−0.306428
$78$	0	0
$79$	−4.47949	−0.503983	−0.251991	−	0.967730i	$-0.581085\pi$
$79$	−4.47949	−0.503983	−0.251991	+	0.967730i	$0.581085\pi$
$80$	−4.42864	−0.495137
$81$	−11.0874	−1.23194
$82$	0.520505	0.0574802
$83$	10.8272	1.18844	0.594218	−	0.804304i	$-0.297462\pi$
$83$	10.8272	1.18844	0.594218	+	0.804304i	$0.297462\pi$
$84$	3.37778	0.368546
$85$	−11.5462	−1.25236
$86$	−6.06668	−0.654187
$87$	−4.54125	−0.486873
$88$	−6.53035	−0.696138
$89$	−5.36196	−0.568367	−0.284183	−	0.958770i	$-0.591722\pi$
$89$	−5.36196	−0.568367	−0.284183	+	0.958770i	$0.591722\pi$
$90$	4.21432	0.444228
$91$	0	0
$92$	5.00492	0.521799
$93$	12.9240	1.34015
$94$	1.29682	0.133757
$95$	−27.4701	−2.81838
$96$	12.8573	1.31224
$97$	−9.62867	−0.977643	−0.488822	−	0.872384i	$-0.662573\pi$
$97$	−9.62867	−0.977643	−0.488822	+	0.872384i	$0.662573\pi$
$98$	−0.688892	−0.0695886
$99$	−5.11753	−0.514331
$100$	−8.13335	−0.813335
$101$	13.6938	1.36259	0.681293	−	0.732011i	$-0.261418\pi$
$101$	13.6938	1.36259	0.681293	+	0.732011i	$0.261418\pi$
$102$	5.47949	0.542551
$103$	12.2953	1.21149	0.605745	−	0.795659i	$-0.292875\pi$
$103$	12.2953	1.21149	0.605745	+	0.795659i	$0.292875\pi$
$104$	0	0
$105$	7.11753	0.694600
$106$	−1.73975	−0.168979
$107$	−18.1891	−1.75841	−0.879205	−	0.476444i	$-0.841925\pi$
$107$	−18.1891	−1.75841	−0.879205	+	0.476444i	$0.841925\pi$
$108$	−3.70471	−0.356486
$109$	−8.36196	−0.800931	−0.400465	−	0.916312i	$-0.631152\pi$
$109$	−8.36196	−0.800931	−0.400465	+	0.916312i	$0.631152\pi$
$110$	−5.95407	−0.567698
$111$	8.70964	0.826682
$112$	1.37778	0.130188
$113$	−8.46520	−0.796339	−0.398170	−	0.917312i	$-0.630354\pi$
$113$	−8.46520	−0.796339	−0.398170	+	0.917312i	$0.630354\pi$
$114$	13.0366	1.22099
$115$	10.5462	0.983436
$116$	−3.12843	−0.290468
$117$	0	0
$118$	5.05086	0.464969
$119$	3.59210	0.329288
$120$	17.2859	1.57798
$121$	−3.76986	−0.342714
$122$	−6.23506	−0.564496
$123$	1.67307	0.150856
$124$	8.90321	0.799532
$125$	−1.06668	−0.0954065
$126$	−1.31111	−0.116803
$127$	4.08742	0.362700	0.181350	−	0.983419i	$-0.441953\pi$
$127$	4.08742	0.362700	0.181350	+	0.983419i	$0.441953\pi$
$128$	10.7556	0.950667
$129$	−19.5002	−1.71690
$130$	0	0
$131$	5.93978	0.518961	0.259480	−	0.965748i	$-0.416449\pi$
$131$	5.93978	0.518961	0.259480	+	0.965748i	$0.416449\pi$
$132$	−9.08250	−0.790530
$133$	8.54617	0.741047
$134$	0.295286	0.0255089
$135$	−7.80642	−0.671870
$136$	8.72393	0.748070
$137$	−16.3620	−1.39790	−0.698948	−	0.715172i	$-0.746348\pi$
$137$	−16.3620	−1.39790	−0.698948	+	0.715172i	$0.746348\pi$
$138$	−5.00492	−0.426047
$139$	3.03011	0.257011	0.128505	−	0.991709i	$-0.458982\pi$
$139$	3.03011	0.257011	0.128505	+	0.991709i	$0.458982\pi$
$140$	4.90321	0.414397
$141$	4.16839	0.351041
$142$	6.18913	0.519380
$143$	0	0
$144$	2.62222	0.218518
$145$	−6.59210	−0.547444
$146$	3.98910	0.330140
$147$	−2.21432	−0.182634
$148$	6.00000	0.493197
$149$	14.5368	1.19090	0.595451	−	0.803392i	$-0.296974\pi$
$149$	14.5368	1.19090	0.595451	+	0.803392i	$0.296974\pi$
$150$	8.13335	0.664085
$151$	19.9748	1.62553	0.812764	−	0.582594i	$-0.197962\pi$
$151$	19.9748	1.62553	0.812764	+	0.582594i	$0.197962\pi$
$152$	20.7556	1.68350
$153$	6.83654	0.552701
$154$	1.85236	0.149267
$155$	18.7605	1.50688
$156$	0	0
$157$	7.39853	0.590467	0.295233	−	0.955425i	$-0.404603\pi$
$157$	7.39853	0.590467	0.295233	+	0.955425i	$0.404603\pi$
$158$	3.08589	0.245500
$159$	−5.59210	−0.443483
$160$	18.6637	1.47550
$161$	−3.28100	−0.258579
$162$	7.63804	0.600101
$163$	−2.32693	−0.182259	−0.0911296	−	0.995839i	$-0.529048\pi$
$163$	−2.32693	−0.182259	−0.0911296	+	0.995839i	$0.529048\pi$
$164$	1.15257	0.0900002
$165$	−19.1383	−1.48991
$166$	−7.45875	−0.578911
$167$	3.42219	0.264817	0.132408	−	0.991195i	$-0.457729\pi$
$167$	3.42219	0.264817	0.132408	+	0.991195i	$0.457729\pi$
$168$	−5.37778	−0.414905
$169$	0	0
$170$	7.95407	0.610049
$171$	16.2652	1.24383
$172$	−13.4336	−1.02430
$173$	8.27454	0.629102	0.314551	−	0.949241i	$-0.398146\pi$
$173$	8.27454	0.629102	0.314551	+	0.949241i	$0.398146\pi$
$174$	3.12843	0.237166
$175$	5.33185	0.403050
$176$	−3.70471	−0.279253
$177$	16.2351	1.22030
$178$	3.69381	0.276863
$179$	−16.2257	−1.21277	−0.606383	−	0.795173i	$-0.707380\pi$
$179$	−16.2257	−1.21277	−0.606383	+	0.795173i	$0.707380\pi$
$180$	9.33185	0.695555
$181$	−9.20495	−0.684199	−0.342099	−	0.939664i	$-0.611138\pi$
$181$	−9.20495	−0.684199	−0.342099	+	0.939664i	$0.611138\pi$
$182$	0	0
$183$	−20.0415	−1.48151
$184$	−7.96836	−0.587435
$185$	12.6430	0.929529
$186$	−8.90321	−0.652815
$187$	−9.65878	−0.706320
$188$	2.87157	0.209431
$189$	2.42864	0.176658
$190$	18.9240	1.37289
$191$	−6.66815	−0.482490	−0.241245	−	0.970464i	$-0.577556\pi$
$191$	−6.66815	−0.482490	−0.241245	+	0.970464i	$0.577556\pi$
$192$	−2.75557	−0.198866
$193$	−20.6035	−1.48307	−0.741535	−	0.670914i	$-0.765902\pi$
$193$	−20.6035	−1.48307	−0.741535	+	0.670914i	$0.765902\pi$
$194$	6.63311	0.476230
$195$	0	0
$196$	−1.52543	−0.108959
$197$	8.36842	0.596225	0.298112	−	0.954531i	$-0.403643\pi$
$197$	8.36842	0.596225	0.298112	+	0.954531i	$0.403643\pi$
$198$	3.52543	0.250541
$199$	−0.601472	−0.0426372	−0.0213186	−	0.999773i	$-0.506786\pi$
$199$	−0.601472	−0.0426372	−0.0213186	+	0.999773i	$0.506786\pi$
$200$	12.9491	0.915643
$201$	0.949145	0.0669475
$202$	−9.43356	−0.663743
$203$	2.05086	0.143942
$204$	12.1334	0.849505
$205$	2.42864	0.169624
$206$	−8.47013	−0.590142
$207$	−6.24443	−0.434018
$208$	0	0
$209$	−22.9797	−1.58954
$210$	−4.90321	−0.338354
$211$	−1.90321	−0.131023	−0.0655113	−	0.997852i	$-0.520868\pi$
$211$	−1.90321	−0.131023	−0.0655113	+	0.997852i	$0.520868\pi$
$212$	−3.85236	−0.264581
$213$	19.8938	1.36310
$214$	12.5303	0.856557
$215$	−28.3067	−1.93050
$216$	5.89829	0.401328
$217$	−5.83654	−0.396210
$218$	5.76049	0.390150
$219$	12.8222	0.866447
$220$	−13.1842	−0.888879
$221$	0	0
$222$	−6.00000	−0.402694
$223$	−10.6336	−0.712078	−0.356039	−	0.934471i	$-0.615873\pi$
$223$	−10.6336	−0.712078	−0.356039	+	0.934471i	$0.615873\pi$
$224$	−5.80642	−0.387958
$225$	10.1476	0.676510
$226$	5.83161	0.387913
$227$	−15.0509	−0.998960	−0.499480	−	0.866325i	$-0.666476\pi$
$227$	−15.0509	−0.998960	−0.499480	+	0.866325i	$0.666476\pi$
$228$	28.8671	1.91177
$229$	6.53480	0.431831	0.215916	−	0.976412i	$-0.430726\pi$
$229$	6.53480	0.431831	0.215916	+	0.976412i	$0.430726\pi$
$230$	−7.26517	−0.479051
$231$	5.95407	0.391749
$232$	4.98079	0.327005
$233$	−27.9590	−1.83165	−0.915827	−	0.401573i	$-0.868464\pi$
$233$	−27.9590	−1.83165	−0.915827	+	0.401573i	$0.868464\pi$
$234$	0	0
$235$	6.05086	0.394714
$236$	11.1842	0.728030
$237$	9.91903	0.644310
$238$	−2.47457	−0.160403
$239$	19.5812	1.26660	0.633301	−	0.773905i	$-0.281699\pi$
$239$	19.5812	1.26660	0.633301	+	0.773905i	$0.281699\pi$
$240$	9.80642	0.633002
$241$	13.3575	0.860433	0.430217	−	0.902726i	$-0.358437\pi$
$241$	13.3575	0.860433	0.430217	+	0.902726i	$0.358437\pi$
$242$	2.59703	0.166943
$243$	17.2652	1.10756
$244$	−13.8064	−0.883866
$245$	−3.21432	−0.205355
$246$	−1.15257	−0.0734849
$247$	0	0
$248$	−14.1748	−0.900103
$249$	−23.9748	−1.51934
$250$	0.734825	0.0464744
$251$	3.29682	0.208093	0.104047	−	0.994572i	$-0.466821\pi$
$251$	3.29682	0.208093	0.104047	+	0.994572i	$0.466821\pi$
$252$	−2.90321	−0.182885
$253$	8.82225	0.554650
$254$	−2.81579	−0.176678
$255$	25.5669	1.60106
$256$	−9.89829	−0.618643
$257$	−23.6938	−1.47798	−0.738990	−	0.673717i	$-0.764697\pi$
$257$	−23.6938	−1.47798	−0.738990	+	0.673717i	$0.764697\pi$
$258$	13.4336	0.836337
$259$	−3.93332	−0.244405
$260$	0	0
$261$	3.90321	0.241603
$262$	−4.09187	−0.252796
$263$	9.99063	0.616049	0.308024	−	0.951378i	$-0.400332\pi$
$263$	9.99063	0.616049	0.308024	+	0.951378i	$0.400332\pi$
$264$	14.4603	0.889969
$265$	−8.11753	−0.498656
$266$	−5.88739	−0.360979
$267$	11.8731	0.726622
$268$	0.653858	0.0399408
$269$	−18.2034	−1.10988	−0.554941	−	0.831890i	$-0.687259\pi$
$269$	−18.2034	−1.10988	−0.554941	+	0.831890i	$0.687259\pi$
$270$	5.37778	0.327282
$271$	24.1748	1.46852	0.734258	−	0.678870i	$-0.237530\pi$
$271$	24.1748	1.46852	0.734258	+	0.678870i	$0.237530\pi$
$272$	4.94914	0.300086
$273$	0	0
$274$	11.2716	0.680944
$275$	−14.3368	−0.864540
$276$	−11.0825	−0.667088
$277$	1.69535	0.101863	0.0509317	−	0.998702i	$-0.483781\pi$
$277$	1.69535	0.101863	0.0509317	+	0.998702i	$0.483781\pi$
$278$	−2.08742	−0.125195
$279$	−11.1082	−0.665028
$280$	−7.80642	−0.466523
$281$	−11.6479	−0.694854	−0.347427	−	0.937707i	$-0.612945\pi$
$281$	−11.6479	−0.694854	−0.347427	+	0.937707i	$0.612945\pi$
$282$	−2.87157	−0.170999
$283$	12.1334	0.721253	0.360626	−	0.932710i	$-0.382563\pi$
$283$	12.1334	0.721253	0.360626	+	0.932710i	$0.382563\pi$
$284$	13.7047	0.813225
$285$	60.8276	3.60312
$286$	0	0
$287$	−0.755569	−0.0445998
$288$	−11.0509	−0.651178
$289$	−4.09679	−0.240988
$290$	4.54125	0.266671
$291$	21.3210	1.24986
$292$	8.83314	0.516921
$293$	−11.4538	−0.669140	−0.334570	−	0.942371i	$-0.608591\pi$
$293$	−11.4538	−0.669140	−0.334570	+	0.942371i	$0.608591\pi$
$294$	1.52543	0.0889647
$295$	23.5669	1.37212
$296$	−9.55262	−0.555235
$297$	−6.53035	−0.378929
$298$	−10.0143	−0.580112
$299$	0	0
$300$	18.0098	1.03980
$301$	8.80642	0.507594
$302$	−13.7605	−0.791827
$303$	−30.3225	−1.74198
$304$	11.7748	0.675330
$305$	−29.0923	−1.66582
$306$	−4.70964	−0.269232
$307$	−3.96989	−0.226574	−0.113287	−	0.993562i	$-0.536138\pi$
$307$	−3.96989	−0.226574	−0.113287	+	0.993562i	$0.536138\pi$
$308$	4.10171	0.233717
$309$	−27.2257	−1.54882
$310$	−12.9240	−0.734031
$311$	27.3481	1.55077	0.775386	−	0.631488i	$-0.217556\pi$
$311$	27.3481	1.55077	0.775386	+	0.631488i	$0.217556\pi$
$312$	0	0
$313$	−19.1032	−1.07978	−0.539890	−	0.841736i	$-0.681534\pi$
$313$	−19.1032	−1.07978	−0.539890	+	0.841736i	$0.681534\pi$
$314$	−5.09679	−0.287628
$315$	−6.11753	−0.344684
$316$	6.83314	0.384394
$317$	−9.90813	−0.556496	−0.278248	−	0.960509i	$-0.589754\pi$
$317$	−9.90813	−0.556496	−0.278248	+	0.960509i	$0.589754\pi$
$318$	3.85236	0.216029
$319$	−5.51453	−0.308754
$320$	−4.00000	−0.223607
$321$	40.2766	2.24802
$322$	2.26025	0.125959
$323$	30.6987	1.70812
$324$	16.9131	0.939614
$325$	0	0
$326$	1.60300	0.0887821
$327$	18.5161	1.02394
$328$	−1.83500	−0.101321
$329$	−1.88247	−0.103784
$330$	13.1842	0.725767
$331$	−23.4193	−1.28724	−0.643620	−	0.765345i	$-0.722568\pi$
$331$	−23.4193	−1.28724	−0.643620	+	0.765345i	$0.722568\pi$
$332$	−16.5161	−0.906437
$333$	−7.48595	−0.410227
$334$	−2.35752	−0.128998
$335$	1.37778	0.0752764
$336$	−3.05086	−0.166438
$337$	−7.51606	−0.409426	−0.204713	−	0.978822i	$-0.565626\pi$
$337$	−7.51606	−0.409426	−0.204713	+	0.978822i	$0.565626\pi$
$338$	0	0
$339$	18.7447	1.01807
$340$	17.6128	0.955191
$341$	15.6938	0.849868
$342$	−11.2050	−0.605894
$343$	1.00000	0.0539949
$344$	21.3876	1.15314
$345$	−23.3526	−1.25726
$346$	−5.70027	−0.306448
$347$	5.64449	0.303012	0.151506	−	0.988456i	$-0.451588\pi$
$347$	5.64449	0.303012	0.151506	+	0.988456i	$0.451588\pi$
$348$	6.92735	0.371345
$349$	−24.1590	−1.29320	−0.646601	−	0.762828i	$-0.723810\pi$
$349$	−24.1590	−1.29320	−0.646601	+	0.762828i	$0.723810\pi$
$350$	−3.67307	−0.196334
$351$	0	0
$352$	15.6128	0.832168
$353$	−36.1289	−1.92295	−0.961474	−	0.274896i	$-0.911356\pi$
$353$	−36.1289	−1.92295	−0.961474	+	0.274896i	$0.911356\pi$
$354$	−11.1842	−0.594434
$355$	28.8780	1.53269
$356$	8.17929	0.433501
$357$	−7.95407	−0.420974
$358$	11.1778	0.590763
$359$	−17.4128	−0.919013	−0.459507	−	0.888174i	$-0.651974\pi$
$359$	−17.4128	−0.919013	−0.459507	+	0.888174i	$0.651974\pi$
$360$	−14.8573	−0.783047
$361$	54.0370	2.84405
$362$	6.34122	0.333287
$363$	8.34767	0.438139
$364$	0	0
$365$	18.6128	0.974241
$366$	13.8064	0.721673
$367$	2.93825	0.153375	0.0766876	−	0.997055i	$-0.475566\pi$
$367$	2.93825	0.153375	0.0766876	+	0.997055i	$0.475566\pi$
$368$	−4.52051	−0.235648
$369$	−1.43801	−0.0748597
$370$	−8.70964	−0.452792
$371$	2.52543	0.131114
$372$	−19.7146	−1.02215
$373$	−18.7699	−0.971866	−0.485933	−	0.873996i	$-0.661520\pi$
$373$	−18.7699	−0.971866	−0.485933	+	0.873996i	$0.661520\pi$
$374$	6.65386	0.344063
$375$	2.36196	0.121971
$376$	−4.57184	−0.235774
$377$	0	0
$378$	−1.67307	−0.0860535
$379$	−23.6894	−1.21684	−0.608421	−	0.793615i	$-0.708197\pi$
$379$	−23.6894	−1.21684	−0.608421	+	0.793615i	$0.708197\pi$
$380$	41.9037	2.14961
$381$	−9.05086	−0.463689
$382$	4.59364	0.235031
$383$	−31.6128	−1.61534	−0.807671	−	0.589634i	$-0.799272\pi$
$383$	−31.6128	−1.61534	−0.807671	+	0.589634i	$0.799272\pi$
$384$	−23.8163	−1.21537
$385$	8.64296	0.440486
$386$	14.1936	0.722434
$387$	16.7605	0.851984
$388$	14.6878	0.745662
$389$	−20.0558	−1.01687	−0.508434	−	0.861101i	$-0.669775\pi$
$389$	−20.0558	−1.01687	−0.508434	+	0.861101i	$0.669775\pi$
$390$	0	0
$391$	−11.7857	−0.596027
$392$	2.42864	0.122665
$393$	−13.1526	−0.663459
$394$	−5.76494	−0.290433
$395$	14.3985	0.724469
$396$	7.80642	0.392288
$397$	−22.8731	−1.14797	−0.573984	−	0.818867i	$-0.694603\pi$
$397$	−22.8731	−1.14797	−0.573984	+	0.818867i	$0.694603\pi$
$398$	0.414349	0.0207695
$399$	−18.9240	−0.947383
$400$	7.34614	0.367307
$401$	5.61285	0.280292	0.140146	−	0.990131i	$-0.455243\pi$
$401$	5.61285	0.280292	0.140146	+	0.990131i	$0.455243\pi$
$402$	−0.653858	−0.0326115
$403$	0	0
$404$	−20.8889	−1.03926
$405$	35.6385	1.77089
$406$	−1.41282	−0.0701170
$407$	10.5763	0.524247
$408$	−19.3176	−0.956362
$409$	26.1175	1.29143	0.645714	−	0.763579i	$-0.276560\pi$
$409$	26.1175	1.29143	0.645714	+	0.763579i	$0.276560\pi$
$410$	−1.67307	−0.0826271
$411$	36.2306	1.78712
$412$	−18.7556	−0.924021
$413$	−7.33185	−0.360777
$414$	4.30174	0.211419
$415$	−34.8020	−1.70836
$416$	0	0
$417$	−6.70964	−0.328572
$418$	15.8306	0.774298
$419$	−25.2464	−1.23337	−0.616685	−	0.787210i	$-0.711525\pi$
$419$	−25.2464	−1.23337	−0.616685	+	0.787210i	$0.711525\pi$
$420$	−10.8573	−0.529781
$421$	8.22861	0.401038	0.200519	−	0.979690i	$-0.435737\pi$
$421$	8.22861	0.401038	0.200519	+	0.979690i	$0.435737\pi$
$422$	1.31111	0.0638237
$423$	−3.58274	−0.174199
$424$	6.13335	0.297862
$425$	19.1526	0.929036
$426$	−13.7047	−0.663996
$427$	9.05086	0.438002
$428$	27.7462	1.34116
$429$	0	0
$430$	19.5002	0.940385
$431$	1.43801	0.0692664	0.0346332	−	0.999400i	$-0.488974\pi$
$431$	1.43801	0.0692664	0.0346332	+	0.999400i	$0.488974\pi$
$432$	3.34614	0.160991
$433$	−16.5018	−0.793024	−0.396512	−	0.918029i	$-0.629780\pi$
$433$	−16.5018	−0.793024	−0.396512	+	0.918029i	$0.629780\pi$
$434$	4.02074	0.193002
$435$	14.5970	0.699874
$436$	12.7556	0.610881
$437$	−28.0400	−1.34133
$438$	−8.83314	−0.422064
$439$	−10.1619	−0.485003	−0.242501	−	0.970151i	$-0.577968\pi$
$439$	−10.1619	−0.485003	−0.242501	+	0.970151i	$0.577968\pi$
$440$	20.9906	1.00069
$441$	1.90321	0.0906291
$442$	0	0
$443$	3.20787	0.152410	0.0762052	−	0.997092i	$-0.475720\pi$
$443$	3.20787	0.152410	0.0762052	+	0.997092i	$0.475720\pi$
$444$	−13.2859	−0.630522
$445$	17.2351	0.817020
$446$	7.32540	0.346868
$447$	−32.1891	−1.52249
$448$	1.24443	0.0587939
$449$	18.4099	0.868817	0.434409	−	0.900716i	$-0.356957\pi$
$449$	18.4099	0.868817	0.434409	+	0.900716i	$0.356957\pi$
$450$	−6.99063	−0.329542
$451$	2.03164	0.0956663
$452$	12.9131	0.607379
$453$	−44.2306	−2.07814
$454$	10.3684	0.486614
$455$	0	0
$456$	−45.9595	−2.15225
$457$	−3.40297	−0.159184	−0.0795922	−	0.996828i	$-0.525362\pi$
$457$	−3.40297	−0.159184	−0.0795922	+	0.996828i	$0.525362\pi$
$458$	−4.50177	−0.210354
$459$	8.72393	0.407198
$460$	−16.0874	−0.750080
$461$	−17.5714	−0.818380	−0.409190	−	0.912449i	$-0.634189\pi$
$461$	−17.5714	−0.818380	−0.409190	+	0.912449i	$0.634189\pi$
$462$	−4.10171	−0.190829
$463$	−15.7714	−0.732959	−0.366479	−	0.930426i	$-0.619437\pi$
$463$	−15.7714	−0.732959	−0.366479	+	0.930426i	$0.619437\pi$
$464$	2.82564	0.131177
$465$	−41.5417	−1.92645
$466$	19.2607	0.892236
$467$	−3.76694	−0.174313	−0.0871567	−	0.996195i	$-0.527778\pi$
$467$	−3.76694	−0.174313	−0.0871567	+	0.996195i	$0.527778\pi$
$468$	0	0
$469$	−0.428639	−0.0197927
$470$	−4.16839	−0.192273
$471$	−16.3827	−0.754875
$472$	−17.8064	−0.819607
$473$	−23.6795	−1.08879
$474$	−6.83314	−0.313857
$475$	45.5669	2.09075
$476$	−5.47949	−0.251152
$477$	4.80642	0.220071
$478$	−13.4893	−0.616988
$479$	12.1032	0.553011	0.276506	−	0.961012i	$-0.410824\pi$
$479$	12.1032	0.553011	0.276506	+	0.961012i	$0.410824\pi$
$480$	−41.3274	−1.88633
$481$	0	0
$482$	−9.20189	−0.419135
$483$	7.26517	0.330577
$484$	5.75065	0.261393
$485$	30.9496	1.40535
$486$	−11.8938	−0.539516
$487$	17.3778	0.787463	0.393731	−	0.919226i	$-0.371184\pi$
$487$	17.3778	0.787463	0.393731	+	0.919226i	$0.371184\pi$
$488$	21.9813	0.995045
$489$	5.15257	0.233007
$490$	2.21432	0.100033
$491$	−19.3921	−0.875152	−0.437576	−	0.899181i	$-0.644163\pi$
$491$	−19.3921	−0.875152	−0.437576	+	0.899181i	$0.644163\pi$
$492$	−2.55215	−0.115060
$493$	7.36689	0.331788
$494$	0	0
$495$	16.4494	0.739345
$496$	−8.04149	−0.361073
$497$	−8.98418	−0.402995
$498$	16.5161	0.740102
$499$	10.6702	0.477662	0.238831	−	0.971061i	$-0.423236\pi$
$499$	10.6702	0.477662	0.238831	+	0.971061i	$0.423236\pi$
$500$	1.62714	0.0727678
$501$	−7.57781	−0.338552
$502$	−2.27115	−0.101366
$503$	−4.27655	−0.190682	−0.0953410	−	0.995445i	$-0.530394\pi$
$503$	−4.27655	−0.190682	−0.0953410	+	0.995445i	$0.530394\pi$
$504$	4.62222	0.205890
$505$	−44.0163	−1.95870
$506$	−6.07758	−0.270181
$507$	0	0
$508$	−6.23506	−0.276636
$509$	−33.0765	−1.46609	−0.733046	−	0.680180i	$-0.761902\pi$
$509$	−33.0765	−1.46609	−0.733046	+	0.680180i	$0.761902\pi$
$510$	−17.6128	−0.779910
$511$	−5.79060	−0.256161
$512$	−14.6923	−0.649313
$513$	20.7556	0.916381
$514$	16.3225	0.719954
$515$	−39.5210	−1.74150
$516$	29.7462	1.30950
$517$	5.06175	0.222616
$518$	2.70964	0.119055
$519$	−18.3225	−0.804268
$520$	0	0
$521$	24.3783	1.06803	0.534015	−	0.845475i	$-0.320682\pi$
$521$	24.3783	1.06803	0.534015	+	0.845475i	$0.320682\pi$
$522$	−2.68889	−0.117690
$523$	34.9403	1.52783	0.763915	−	0.645317i	$-0.223275\pi$
$523$	34.9403	1.52783	0.763915	+	0.645317i	$0.223275\pi$
$524$	−9.06070	−0.395818
$525$	−11.8064	−0.515275
$526$	−6.88247	−0.300090
$527$	−20.9654	−0.913269
$528$	8.20342	0.357008
$529$	−12.2351	−0.531959
$530$	5.59210	0.242905
$531$	−13.9541	−0.605555
$532$	−13.0366	−0.565207
$533$	0	0
$534$	−8.17929	−0.353952
$535$	58.4657	2.52769
$536$	−1.04101	−0.0449648
$537$	35.9289	1.55045
$538$	12.5402	0.540646
$539$	−2.68889	−0.115819
$540$	11.9081	0.512445
$541$	30.4953	1.31110	0.655548	−	0.755153i	$-0.272438\pi$
$541$	30.4953	1.31110	0.655548	+	0.755153i	$0.272438\pi$
$542$	−16.6539	−0.715344
$543$	20.3827	0.874706
$544$	−20.8573	−0.894248
$545$	26.8780	1.15133
$546$	0	0
$547$	−10.0049	−0.427780	−0.213890	−	0.976858i	$-0.568613\pi$
$547$	−10.0049	−0.427780	−0.213890	+	0.976858i	$0.568613\pi$
$548$	24.9590	1.06620
$549$	17.2257	0.735175
$550$	9.87649	0.421135
$551$	17.5270	0.746674
$552$	17.6445	0.750999
$553$	−4.47949	−0.190487
$554$	−1.16791	−0.0496198
$555$	−27.9956	−1.18835
$556$	−4.62222	−0.196026
$557$	−14.1936	−0.601401	−0.300701	−	0.953719i	$-0.597220\pi$
$557$	−14.1936	−0.601401	−0.300701	+	0.953719i	$0.597220\pi$
$558$	7.65233	0.323949
$559$	0	0
$560$	−4.42864	−0.187144
$561$	21.3876	0.902986
$562$	8.02413	0.338478
$563$	−21.3590	−0.900177	−0.450088	−	0.892984i	$-0.648607\pi$
$563$	−21.3590	−0.900177	−0.450088	+	0.892984i	$0.648607\pi$
$564$	−6.35857	−0.267744
$565$	27.2099	1.14473
$566$	−8.35857	−0.351337
$567$	−11.0874	−0.465628
$568$	−21.8193	−0.915519
$569$	34.2672	1.43656	0.718278	−	0.695757i	$-0.244931\pi$
$569$	34.2672	1.43656	0.718278	+	0.695757i	$0.244931\pi$
$570$	−41.9037	−1.75515
$571$	−37.6494	−1.57558	−0.787789	−	0.615945i	$-0.788774\pi$
$571$	−37.6494	−1.57558	−0.787789	+	0.615945i	$0.788774\pi$
$572$	0	0
$573$	14.7654	0.616834
$574$	0.520505	0.0217255
$575$	−17.4938	−0.729541
$576$	2.36842	0.0986840
$577$	−28.3970	−1.18218	−0.591091	−	0.806605i	$-0.701303\pi$
$577$	−28.3970	−1.18218	−0.591091	+	0.806605i	$0.701303\pi$
$578$	2.82225	0.117390
$579$	45.6227	1.89601
$580$	10.0558	0.417543
$581$	10.8272	0.449187
$582$	−14.6878	−0.608830
$583$	−6.79060	−0.281238
$584$	−14.0633	−0.581943
$585$	0	0
$586$	7.89045	0.325952
$587$	6.23659	0.257412	0.128706	−	0.991683i	$-0.458918\pi$
$587$	6.23659	0.257412	0.128706	+	0.991683i	$0.458918\pi$
$588$	3.37778	0.139297
$589$	−49.8800	−2.05527
$590$	−16.2351	−0.668387
$591$	−18.5303	−0.762237
$592$	−5.41927	−0.222731
$593$	−17.5698	−0.721506	−0.360753	−	0.932661i	$-0.617480\pi$
$593$	−17.5698	−0.721506	−0.360753	+	0.932661i	$0.617480\pi$
$594$	4.49871	0.184584
$595$	−11.5462	−0.473347
$596$	−22.1748	−0.908317
$597$	1.33185	0.0545090
$598$	0	0
$599$	16.9813	0.693836	0.346918	−	0.937896i	$-0.387228\pi$
$599$	16.9813	0.693836	0.346918	+	0.937896i	$0.387228\pi$
$600$	−28.6735	−1.17059
$601$	−18.7052	−0.763001	−0.381500	−	0.924369i	$-0.624592\pi$
$601$	−18.7052	−0.763001	−0.381500	+	0.924369i	$0.624592\pi$
$602$	−6.06668	−0.247259
$603$	−0.815792	−0.0332216
$604$	−30.4701	−1.23981
$605$	12.1175	0.492648
$606$	20.8889	0.848554
$607$	−10.3575	−0.420399	−0.210199	−	0.977659i	$-0.567411\pi$
$607$	−10.3575	−0.420399	−0.210199	+	0.977659i	$0.567411\pi$
$608$	−49.6227	−2.01247
$609$	−4.54125	−0.184021
$610$	20.0415	0.811456
$611$	0	0
$612$	−10.4286	−0.421553
$613$	7.02227	0.283627	0.141814	−	0.989893i	$-0.454707\pi$
$613$	7.02227	0.283627	0.141814	+	0.989893i	$0.454707\pi$
$614$	2.73483	0.110369
$615$	−5.37778	−0.216853
$616$	−6.53035	−0.263115
$617$	−29.9813	−1.20700	−0.603500	−	0.797363i	$-0.706228\pi$
$617$	−29.9813	−1.20700	−0.603500	+	0.797363i	$0.706228\pi$
$618$	18.7556	0.754460
$619$	−0.0285802	−0.00114874	−0.000574368	−	1.00000i	$-0.500183\pi$
$619$	−0.0285802	−0.00114874	−0.000574368		1.00000i	$0.500183\pi$
$620$	−28.6178	−1.14932
$621$	−7.96836	−0.319759
$622$	−18.8399	−0.755412
$623$	−5.36196	−0.214823
$624$	0	0
$625$	−23.2306	−0.929225
$626$	13.1601	0.525982
$627$	50.8845	2.03213
$628$	−11.2859	−0.450357
$629$	−14.1289	−0.563356
$630$	4.21432	0.167903
$631$	12.1936	0.485419	0.242709	−	0.970099i	$-0.421964\pi$
$631$	12.1936	0.485419	0.242709	+	0.970099i	$0.421964\pi$
$632$	−10.8791	−0.432746
$633$	4.21432	0.167504
$634$	6.82564	0.271081
$635$	−13.1383	−0.521377
$636$	8.53035	0.338250
$637$	0	0
$638$	3.79892	0.150401
$639$	−17.0988	−0.676418
$640$	−34.5718	−1.36657
$641$	−2.82516	−0.111587	−0.0557935	−	0.998442i	$-0.517769\pi$
$641$	−2.82516	−0.111587	−0.0557935	+	0.998442i	$0.517769\pi$
$642$	−27.7462	−1.09506
$643$	37.7275	1.48783	0.743913	−	0.668276i	$-0.232968\pi$
$643$	37.7275	1.48783	0.743913	+	0.668276i	$0.232968\pi$
$644$	5.00492	0.197222
$645$	62.6800	2.46802
$646$	−21.1481	−0.832062
$647$	12.3664	0.486174	0.243087	−	0.970005i	$-0.421840\pi$
$647$	12.3664	0.486174	0.243087	+	0.970005i	$0.421840\pi$
$648$	−26.9273	−1.05781
$649$	19.7146	0.773864
$650$	0	0
$651$	12.9240	0.506530
$652$	3.54956	0.139012
$653$	−33.0005	−1.29141	−0.645704	−	0.763588i	$-0.723436\pi$
$653$	−33.0005	−1.29141	−0.645704	+	0.763588i	$0.723436\pi$
$654$	−12.7556	−0.498782
$655$	−19.0923	−0.746000
$656$	−1.04101	−0.0406446
$657$	−11.0207	−0.429960
$658$	1.29682	0.0505552
$659$	32.8118	1.27817	0.639084	−	0.769137i	$-0.279314\pi$
$659$	32.8118	1.27817	0.639084	+	0.769137i	$0.279314\pi$
$660$	29.1941	1.13638
$661$	14.7067	0.572025	0.286013	−	0.958226i	$-0.407670\pi$
$661$	14.7067	0.572025	0.286013	+	0.958226i	$0.407670\pi$
$662$	16.1334	0.627041
$663$	0	0
$664$	26.2953	1.02046
$665$	−27.4701	−1.06525
$666$	5.15701	0.199830
$667$	−6.72885	−0.260542
$668$	−5.22030	−0.201979
$669$	23.5462	0.910348
$670$	−0.949145	−0.0366687
$671$	−24.3368	−0.939511
$672$	12.8573	0.495980
$673$	21.2908	0.820702	0.410351	−	0.911928i	$-0.365406\pi$
$673$	21.2908	0.820702	0.410351	+	0.911928i	$0.365406\pi$
$674$	5.17775	0.199440
$675$	12.9491	0.498413
$676$	0	0
$677$	−3.07160	−0.118051	−0.0590256	−	0.998256i	$-0.518799\pi$
$677$	−3.07160	−0.118051	−0.0590256	+	0.998256i	$0.518799\pi$
$678$	−12.9131	−0.495923
$679$	−9.62867	−0.369514
$680$	−28.0415	−1.07534
$681$	33.3274	1.27711
$682$	−10.8113	−0.413988
$683$	24.7971	0.948833	0.474416	−	0.880301i	$-0.342659\pi$
$683$	24.7971	0.948833	0.474416	+	0.880301i	$0.342659\pi$
$684$	−24.8113	−0.948686
$685$	52.5926	2.00946
$686$	−0.688892	−0.0263020
$687$	−14.4701	−0.552070
$688$	12.1334	0.462580
$689$	0	0
$690$	16.0874	0.612438
$691$	27.0953	1.03075	0.515376	−	0.856964i	$-0.327652\pi$
$691$	27.0953	1.03075	0.515376	+	0.856964i	$0.327652\pi$
$692$	−12.6222	−0.479825
$693$	−5.11753	−0.194399
$694$	−3.88845	−0.147603
$695$	−9.73975	−0.369450
$696$	−11.0291	−0.418055
$697$	−2.71408	−0.102803
$698$	16.6430	0.629945
$699$	61.9101	2.34166
$700$	−8.13335	−0.307412
$701$	13.5205	0.510662	0.255331	−	0.966854i	$-0.417815\pi$
$701$	13.5205	0.510662	0.255331	+	0.966854i	$0.417815\pi$
$702$	0	0
$703$	−33.6149	−1.26781
$704$	−3.34614	−0.126112
$705$	−13.3985	−0.504618
$706$	24.8889	0.936707
$707$	13.6938	0.515009
$708$	−24.7654	−0.930741
$709$	50.9753	1.91442	0.957209	−	0.289399i	$-0.0934554\pi$
$709$	50.9753	1.91442	0.957209	+	0.289399i	$0.0934554\pi$
$710$	−19.8938	−0.746603
$711$	−8.52543	−0.319729
$712$	−13.0223	−0.488030
$713$	19.1497	0.717160
$714$	5.47949	0.205065
$715$	0	0
$716$	24.7511	0.924993
$717$	−43.3590	−1.61927
$718$	11.9956	0.447670
$719$	41.5417	1.54924	0.774622	−	0.632424i	$-0.217940\pi$
$719$	41.5417	1.54924	0.774622	+	0.632424i	$0.217940\pi$
$720$	−8.42864	−0.314117
$721$	12.2953	0.457900
$722$	−37.2257	−1.38540
$723$	−29.5778	−1.10001
$724$	14.0415	0.521848
$725$	10.9349	0.406110
$726$	−5.75065	−0.213427
$727$	−20.8988	−0.775092	−0.387546	−	0.921850i	$-0.626677\pi$
$727$	−20.8988	−0.775092	−0.387546	+	0.921850i	$0.626677\pi$
$728$	0	0
$729$	−4.96836	−0.184013
$730$	−12.8222	−0.474573
$731$	31.6336	1.17001
$732$	30.5718	1.12997
$733$	−19.3575	−0.714986	−0.357493	−	0.933916i	$-0.616368\pi$
$733$	−19.3575	−0.714986	−0.357493	+	0.933916i	$0.616368\pi$
$734$	−2.02413	−0.0747122
$735$	7.11753	0.262534
$736$	19.0509	0.702224
$737$	1.15257	0.0424553
$738$	0.990632	0.0364657
$739$	1.31111	0.0482299	0.0241149	−	0.999709i	$-0.492323\pi$
$739$	1.31111	0.0482299	0.0241149	+	0.999709i	$0.492323\pi$
$740$	−19.2859	−0.708964
$741$	0	0
$742$	−1.73975	−0.0638681
$743$	21.5210	0.789528	0.394764	−	0.918783i	$-0.370826\pi$
$743$	21.5210	0.789528	0.394764	+	0.918783i	$0.370826\pi$
$744$	31.3876	1.15073
$745$	−46.7259	−1.71191
$746$	12.9304	0.473416
$747$	20.6064	0.753949
$748$	14.7338	0.538720
$749$	−18.1891	−0.664616
$750$	−1.62714	−0.0594147
$751$	−16.3176	−0.595436	−0.297718	−	0.954654i	$-0.596226\pi$
$751$	−16.3176	−0.595436	−0.297718	+	0.954654i	$0.596226\pi$
$752$	−2.59364	−0.0945802
$753$	−7.30021	−0.266034
$754$	0	0
$755$	−64.2054	−2.33667
$756$	−3.70471	−0.134739
$757$	−18.7462	−0.681342	−0.340671	−	0.940183i	$-0.610654\pi$
$757$	−18.7462	−0.681342	−0.340671	+	0.940183i	$0.610654\pi$
$758$	16.3194	0.592748
$759$	−19.5353	−0.709085
$760$	−66.7150	−2.42001
$761$	10.2968	0.373259	0.186630	−	0.982430i	$-0.440244\pi$
$761$	10.2968	0.373259	0.186630	+	0.982430i	$0.440244\pi$
$762$	6.23506	0.225873
$763$	−8.36196	−0.302723
$764$	10.1718	0.368002
$765$	−21.9748	−0.794501
$766$	21.7778	0.786865
$767$	0	0
$768$	21.9180	0.790897
$769$	−9.36641	−0.337761	−0.168881	−	0.985637i	$-0.554015\pi$
$769$	−9.36641	−0.337761	−0.168881	+	0.985637i	$0.554015\pi$
$770$	−5.95407	−0.214570
$771$	52.4657	1.88951
$772$	31.4291	1.13116
$773$	3.71456	0.133603	0.0668017	−	0.997766i	$-0.478721\pi$
$773$	3.71456	0.133603	0.0668017	+	0.997766i	$0.478721\pi$
$774$	−11.5462	−0.415019
$775$	−31.1195	−1.11785
$776$	−23.3846	−0.839457
$777$	8.70964	0.312456
$778$	13.8163	0.495337
$779$	−6.45722	−0.231354
$780$	0	0
$781$	24.1575	0.864423
$782$	8.11906	0.290337
$783$	4.98079	0.177999
$784$	1.37778	0.0492066
$785$	−23.7812	−0.848789
$786$	9.06070	0.323184
$787$	−6.23659	−0.222311	−0.111155	−	0.993803i	$-0.535455\pi$
$787$	−6.23659	−0.222311	−0.111155	+	0.993803i	$0.535455\pi$
$788$	−12.7654	−0.454749
$789$	−22.1225	−0.787580
$790$	−9.91903	−0.352903
$791$	−8.46520	−0.300988
$792$	−12.4286	−0.441632
$793$	0	0
$794$	15.7571	0.559199
$795$	17.9748	0.637501
$796$	0.917502	0.0325200
$797$	−40.0701	−1.41935	−0.709677	−	0.704527i	$-0.751159\pi$
$797$	−40.0701	−1.41935	−0.709677	+	0.704527i	$0.751159\pi$
$798$	13.0366	0.461489
$799$	−6.76202	−0.239223
$800$	−30.9590	−1.09457
$801$	−10.2050	−0.360574
$802$	−3.86665	−0.136536
$803$	15.5703	0.549464
$804$	−1.44785	−0.0510618
$805$	10.5462	0.371704
$806$	0	0
$807$	40.3082	1.41892
$808$	33.2573	1.16999
$809$	−2.57136	−0.0904042	−0.0452021	−	0.998978i	$-0.514393\pi$
$809$	−2.57136	−0.0904042	−0.0452021	+	0.998978i	$0.514393\pi$
$810$	−24.5511	−0.862637
$811$	28.3654	0.996042	0.498021	−	0.867165i	$-0.334060\pi$
$811$	28.3654	0.996042	0.498021	+	0.867165i	$0.334060\pi$
$812$	−3.12843	−0.109786
$813$	−53.5308	−1.87741
$814$	−7.28592	−0.255371
$815$	7.47949	0.261995
$816$	−10.9590	−0.383641
$817$	75.2612	2.63306
$818$	−17.9922	−0.629081
$819$	0	0
$820$	−3.70471	−0.129374
$821$	31.7846	1.10929	0.554646	−	0.832087i	$-0.312854\pi$
$821$	31.7846	1.10929	0.554646	+	0.832087i	$0.312854\pi$
$822$	−24.9590	−0.870545
$823$	30.9131	1.07756	0.538781	−	0.842446i	$-0.318885\pi$
$823$	30.9131	1.07756	0.538781	+	0.842446i	$0.318885\pi$
$824$	29.8608	1.04025
$825$	31.7462	1.10526
$826$	5.05086	0.175742
$827$	−49.7560	−1.73019	−0.865094	−	0.501610i	$-0.832741\pi$
$827$	−49.7560	−1.73019	−0.865094	+	0.501610i	$0.832741\pi$
$828$	9.52543	0.331031
$829$	−19.9190	−0.691817	−0.345908	−	0.938268i	$-0.612429\pi$
$829$	−19.9190	−0.691817	−0.345908	+	0.938268i	$0.612429\pi$
$830$	23.9748	0.832178
$831$	−3.75404	−0.130226
$832$	0	0
$833$	3.59210	0.124459
$834$	4.62222	0.160054
$835$	−11.0000	−0.380671
$836$	35.0539	1.21237
$837$	−14.1748	−0.489954
$838$	17.3921	0.600799
$839$	−11.5625	−0.399181	−0.199590	−	0.979879i	$-0.563961\pi$
$839$	−11.5625	−0.399181	−0.199590	+	0.979879i	$0.563961\pi$
$840$	17.2859	0.596421
$841$	−24.7940	−0.854965
$842$	−5.66862	−0.195354
$843$	25.7921	0.888328
$844$	2.90321	0.0999327
$845$	0	0
$846$	2.46812	0.0848557
$847$	−3.76986	−0.129534
$848$	3.47949	0.119486
$849$	−26.8671	−0.922077
$850$	−13.1941	−0.452552
$851$	12.9052	0.442385
$852$	−30.3466	−1.03966
$853$	−1.74467	−0.0597363	−0.0298682	−	0.999554i	$-0.509509\pi$
$853$	−1.74467	−0.0597363	−0.0298682	+	0.999554i	$0.509509\pi$
$854$	−6.23506	−0.213359
$855$	−52.2815	−1.78799
$856$	−44.1748	−1.50986
$857$	−42.3368	−1.44620	−0.723098	−	0.690745i	$-0.757283\pi$
$857$	−42.3368	−1.44620	−0.723098	+	0.690745i	$0.757283\pi$
$858$	0	0
$859$	−5.37778	−0.183488	−0.0917438	−	0.995783i	$-0.529244\pi$
$859$	−5.37778	−0.183488	−0.0917438	+	0.995783i	$0.529244\pi$
$860$	43.1798	1.47242
$861$	1.67307	0.0570181
$862$	−0.990632	−0.0337411
$863$	−15.4291	−0.525213	−0.262607	−	0.964903i	$-0.584582\pi$
$863$	−15.4291	−0.525213	−0.262607	+	0.964903i	$0.584582\pi$
$864$	−14.1017	−0.479750
$865$	−26.5970	−0.904326
$866$	11.3679	0.386298
$867$	9.07160	0.308088
$868$	8.90321	0.302195
$869$	12.0449	0.408595
$870$	−10.0558	−0.340923
$871$	0	0
$872$	−20.3082	−0.687722
$873$	−18.3254	−0.620221
$874$	19.3165	0.653391
$875$	−1.06668	−0.0360602
$876$	−19.5594	−0.660851
$877$	−38.5181	−1.30066	−0.650331	−	0.759651i	$-0.725370\pi$
$877$	−38.5181	−1.30066	−0.650331	+	0.759651i	$0.725370\pi$
$878$	7.00048	0.236255
$879$	25.3624	0.855454
$880$	11.9081	0.401423
$881$	−41.7373	−1.40617	−0.703083	−	0.711108i	$-0.748194\pi$
$881$	−41.7373	−1.40617	−0.703083	+	0.711108i	$0.748194\pi$
$882$	−1.31111	−0.0441473
$883$	52.8439	1.77834	0.889170	−	0.457577i	$-0.151283\pi$
$883$	52.8439	1.77834	0.889170	+	0.457577i	$0.151283\pi$
$884$	0	0
$885$	−52.1847	−1.75417
$886$	−2.20987	−0.0742422
$887$	8.99063	0.301876	0.150938	−	0.988543i	$-0.451771\pi$
$887$	8.99063	0.301876	0.150938	+	0.988543i	$0.451771\pi$
$888$	21.1526	0.709834
$889$	4.08742	0.137088
$890$	−11.8731	−0.397987
$891$	29.8129	0.998769
$892$	16.2208	0.543112
$893$	−16.0879	−0.538361
$894$	22.1748	0.741638
$895$	52.1546	1.74334
$896$	10.7556	0.359318
$897$	0	0
$898$	−12.6824	−0.423218
$899$	−11.9699	−0.399218
$900$	−15.4795	−0.515983
$901$	9.07160	0.302219
$902$	−1.39958	−0.0466010
$903$	−19.5002	−0.648927
$904$	−20.5589	−0.683780
$905$	29.5877	0.983527
$906$	30.4701	1.01230
$907$	−20.7003	−0.687341	−0.343671	−	0.939090i	$-0.611670\pi$
$907$	−20.7003	−0.687341	−0.343671	+	0.939090i	$0.611670\pi$
$908$	22.9590	0.761921
$909$	26.0622	0.864430
$910$	0	0
$911$	29.8988	0.990590	0.495295	−	0.868725i	$-0.335060\pi$
$911$	29.8988	0.990590	0.495295	+	0.868725i	$0.335060\pi$
$912$	−26.0731	−0.863368
$913$	−29.1131	−0.963503
$914$	2.34428	0.0775420
$915$	64.4197	2.12965
$916$	−9.96836	−0.329364
$917$	5.93978	0.196149
$918$	−6.00984	−0.198354
$919$	38.5847	1.27279	0.636397	−	0.771362i	$-0.280424\pi$
$919$	38.5847	1.27279	0.636397	+	0.771362i	$0.280424\pi$
$920$	25.6128	0.844431
$921$	8.79060	0.289660
$922$	12.1048	0.398649
$923$	0	0
$924$	−9.08250	−0.298792
$925$	−20.9719	−0.689552
$926$	10.8648	0.357039
$927$	23.4005	0.768574
$928$	−11.9081	−0.390904
$929$	−3.25581	−0.106820	−0.0534098	−	0.998573i	$-0.517009\pi$
$929$	−3.25581	−0.106820	−0.0534098	+	0.998573i	$0.517009\pi$
$930$	28.6178	0.938414
$931$	8.54617	0.280089
$932$	42.6494	1.39703
$933$	−60.5575	−1.98257
$934$	2.59502	0.0849116
$935$	31.0464	1.01533
$936$	0	0
$937$	−11.6840	−0.381699	−0.190849	−	0.981619i	$-0.561124\pi$
$937$	−11.6840	−0.381699	−0.190849	+	0.981619i	$0.561124\pi$
$938$	0.295286	0.00964144
$939$	42.3007	1.38043
$940$	−9.23014	−0.301054
$941$	41.9699	1.36818	0.684090	−	0.729398i	$-0.260200\pi$
$941$	41.9699	1.36818	0.684090	+	0.729398i	$0.260200\pi$
$942$	11.2859	0.367715
$943$	2.47902	0.0807279
$944$	−10.1017	−0.328783
$945$	−7.80642	−0.253943
$946$	16.3126	0.530370
$947$	20.3555	0.661465	0.330733	−	0.943725i	$-0.392704\pi$
$947$	20.3555	0.661465	0.330733	+	0.943725i	$0.392704\pi$
$948$	−15.1308	−0.491424
$949$	0	0
$950$	−31.3907	−1.01845
$951$	21.9398	0.711446
$952$	8.72393	0.282744
$953$	−30.5496	−0.989597	−0.494799	−	0.869008i	$-0.664758\pi$
$953$	−30.5496	−0.989597	−0.494799	+	0.869008i	$0.664758\pi$
$954$	−3.31111	−0.107201
$955$	21.4336	0.693574
$956$	−29.8697	−0.966055
$957$	12.2109	0.394723
$958$	−8.33783	−0.269383
$959$	−16.3620	−0.528355
$960$	8.85728	0.285867
$961$	3.06515	0.0988757
$962$	0	0
$963$	−34.6178	−1.11554
$964$	−20.3759	−0.656264
$965$	66.2262	2.13190
$966$	−5.00492	−0.161031
$967$	−54.4548	−1.75115	−0.875574	−	0.483084i	$-0.839516\pi$
$967$	−54.4548	−1.75115	−0.875574	+	0.483084i	$0.839516\pi$
$968$	−9.15563	−0.294273
$969$	−67.9768	−2.18373
$970$	−21.3210	−0.684575
$971$	−54.6035	−1.75231	−0.876155	−	0.482030i	$-0.839899\pi$
$971$	−54.6035	−1.75231	−0.876155	+	0.482030i	$0.839899\pi$
$972$	−26.3368	−0.844752
$973$	3.03011	0.0971409
$974$	−11.9714	−0.383589
$975$	0	0
$976$	12.4701	0.399159
$977$	−32.6474	−1.04448	−0.522242	−	0.852798i	$-0.674904\pi$
$977$	−32.6474	−1.04448	−0.522242	+	0.852798i	$0.674904\pi$
$978$	−3.54956	−0.113502
$979$	14.4177	0.460793
$980$	4.90321	0.156627
$981$	−15.9146	−0.508114
$982$	13.3590	0.426304
$983$	27.5052	0.877278	0.438639	−	0.898663i	$-0.355461\pi$
$983$	27.5052	0.877278	0.438639	+	0.898663i	$0.355461\pi$
$984$	4.06329	0.129533
$985$	−26.8988	−0.857066
$986$	−5.07499	−0.161621
$987$	4.16839	0.132681
$988$	0	0
$989$	−28.8938	−0.918771
$990$	−11.3319	−0.360150
$991$	−6.29390	−0.199932	−0.0999662	−	0.994991i	$-0.531873\pi$
$991$	−6.29390	−0.199932	−0.0999662	+	0.994991i	$0.531873\pi$
$992$	33.8894	1.07599
$993$	51.8578	1.64566
$994$	6.18913	0.196307
$995$	1.93332	0.0612905
$996$	36.5718	1.15882
$997$	−20.8702	−0.660965	−0.330483	−	0.943812i	$-0.607212\pi$
$997$	−20.8702	−0.660965	−0.330483	+	0.943812i	$0.607212\pi$
$998$	−7.35059	−0.232679
$999$	−9.55262	−0.302232

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.a.h.1.2		3
7.6	odd	2		8281.2.a.be.1.2		3
13.5	odd	4		91.2.c.a.64.4	yes	6
13.8	odd	4		91.2.c.a.64.3	✓	6
13.12	even	2		1183.2.a.j.1.2		3
39.5	even	4		819.2.c.b.64.3		6
39.8	even	4		819.2.c.b.64.4		6
52.31	even	4		1456.2.k.c.337.6		6
52.47	even	4		1456.2.k.c.337.5		6
91.5	even	12		637.2.r.d.116.4		12
91.18	odd	12		637.2.r.e.324.3		12
91.31	even	12		637.2.r.d.324.3		12
91.34	even	4		637.2.c.d.246.3		6
91.44	odd	12		637.2.r.e.116.4		12
91.47	even	12		637.2.r.d.116.3		12
91.60	odd	12		637.2.r.e.324.4		12
91.73	even	12		637.2.r.d.324.4		12
91.83	even	4		637.2.c.d.246.4		6
91.86	odd	12		637.2.r.e.116.3		12
91.90	odd	2		8281.2.a.bi.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.c.a.64.3	✓	6	13.8	odd	4
91.2.c.a.64.4	yes	6	13.5	odd	4
637.2.c.d.246.3		6	91.34	even	4
637.2.c.d.246.4		6	91.83	even	4
637.2.r.d.116.3		12	91.47	even	12
637.2.r.d.116.4		12	91.5	even	12
637.2.r.d.324.3		12	91.31	even	12
637.2.r.d.324.4		12	91.73	even	12
637.2.r.e.116.3		12	91.86	odd	12
637.2.r.e.116.4		12	91.44	odd	12
637.2.r.e.324.3		12	91.18	odd	12
637.2.r.e.324.4		12	91.60	odd	12
819.2.c.b.64.3		6	39.5	even	4
819.2.c.b.64.4		6	39.8	even	4
1183.2.a.h.1.2		3	1.1	even	1	trivial
1183.2.a.j.1.2		3	13.12	even	2
1456.2.k.c.337.5		6	52.47	even	4
1456.2.k.c.337.6		6	52.31	even	4
8281.2.a.be.1.2		3	7.6	odd	2
8281.2.a.bi.1.2		3	91.90	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)

\(f(q)\)	\(=\)	\(q-0.688892 q^{2} -2.21432 q^{3} -1.52543 q^{4} -3.21432 q^{5} +1.52543 q^{6} +1.00000 q^{7} +2.42864 q^{8} +1.90321 q^{9} +O(q^{10})\)	\(q-0.688892 q^{2} -2.21432 q^{3} -1.52543 q^{4} -3.21432 q^{5} +1.52543 q^{6} +1.00000 q^{7} +2.42864 q^{8} +1.90321 q^{9} +2.21432 q^{10} -2.68889 q^{11} +3.37778 q^{12} -0.688892 q^{14} +7.11753 q^{15} +1.37778 q^{16} +3.59210 q^{17} -1.31111 q^{18} +8.54617 q^{19} +4.90321 q^{20} -2.21432 q^{21} +1.85236 q^{22} -3.28100 q^{23} -5.37778 q^{24} +5.33185 q^{25} +2.42864 q^{27} -1.52543 q^{28} +2.05086 q^{29} -4.90321 q^{30} -5.83654 q^{31} -5.80642 q^{32} +5.95407 q^{33} -2.47457 q^{34} -3.21432 q^{35} -2.90321 q^{36} -3.93332 q^{37} -5.88739 q^{38} -7.80642 q^{40} -0.755569 q^{41} +1.52543 q^{42} +8.80642 q^{43} +4.10171 q^{44} -6.11753 q^{45} +2.26025 q^{46} -1.88247 q^{47} -3.05086 q^{48} +1.00000 q^{49} -3.67307 q^{50} -7.95407 q^{51} +2.52543 q^{53} -1.67307 q^{54} +8.64296 q^{55} +2.42864 q^{56} -18.9240 q^{57} -1.41282 q^{58} -7.33185 q^{59} -10.8573 q^{60} +9.05086 q^{61} +4.02074 q^{62} +1.90321 q^{63} +1.24443 q^{64} -4.10171 q^{66} -0.428639 q^{67} -5.47949 q^{68} +7.26517 q^{69} +2.21432 q^{70} -8.98418 q^{71} +4.62222 q^{72} -5.79060 q^{73} +2.70964 q^{74} -11.8064 q^{75} -13.0366 q^{76} -2.68889 q^{77} -4.47949 q^{79} -4.42864 q^{80} -11.0874 q^{81} +0.520505 q^{82} +10.8272 q^{83} +3.37778 q^{84} -11.5462 q^{85} -6.06668 q^{86} -4.54125 q^{87} -6.53035 q^{88} -5.36196 q^{89} +4.21432 q^{90} +5.00492 q^{92} +12.9240 q^{93} +1.29682 q^{94} -27.4701 q^{95} +12.8573 q^{96} -9.62867 q^{97} -0.688892 q^{98} -5.11753 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 2 q^{2} + 2 q^{4} - 3 q^{5} - 2 q^{6} + 3 q^{7} - 6 q^{8} - q^{9}+O(q^{10}) \) 3 * q - 2 * q^2 + 2 * q^4 - 3 * q^5 - 2 * q^6 + 3 * q^7 - 6 * q^8 - q^9	\( 3 q - 2 q^{2} + 2 q^{4} - 3 q^{5} - 2 q^{6} + 3 q^{7} - 6 q^{8} - q^{9} - 8 q^{11} + 10 q^{12} - 2 q^{14} + 8 q^{15} + 4 q^{16} + 4 q^{17} - 4 q^{18} - q^{19} + 8 q^{20} + 12 q^{22} - 3 q^{23} - 16 q^{24} - 4 q^{25} - 6 q^{27} + 2 q^{28} - 7 q^{29} - 8 q^{30} - 11 q^{31} - 4 q^{32} - 2 q^{33} - 14 q^{34} - 3 q^{35} - 2 q^{36} - 12 q^{37} + 2 q^{38} - 10 q^{40} - 2 q^{41} - 2 q^{42} + 13 q^{43} - 14 q^{44} - 5 q^{45} + 20 q^{46} - 19 q^{47} + 4 q^{48} + 3 q^{49} + 2 q^{50} - 4 q^{51} + q^{53} + 8 q^{54} + 6 q^{55} - 6 q^{56} - 30 q^{57} + 22 q^{58} - 2 q^{59} - 6 q^{60} + 14 q^{61} - 8 q^{62} - q^{63} + 4 q^{64} + 14 q^{66} + 12 q^{67} + 10 q^{68} + 2 q^{69} - 14 q^{71} + 14 q^{72} + 9 q^{73} - 12 q^{74} - 22 q^{75} - 32 q^{76} - 8 q^{77} + 13 q^{79} - 13 q^{81} + 28 q^{82} - q^{83} + 10 q^{84} - 8 q^{85} - 18 q^{86} - 20 q^{87} + 20 q^{88} - 3 q^{89} + 6 q^{90} - 18 q^{92} + 12 q^{93} + 10 q^{94} - 29 q^{95} + 12 q^{96} - 15 q^{97} - 2 q^{98} - 2 q^{99}+O(q^{100}) \) 3 * q - 2 * q^2 + 2 * q^4 - 3 * q^5 - 2 * q^6 + 3 * q^7 - 6 * q^8 - q^9 - 8 * q^11 + 10 * q^12 - 2 * q^14 + 8 * q^15 + 4 * q^16 + 4 * q^17 - 4 * q^18 - q^19 + 8 * q^20 + 12 * q^22 - 3 * q^23 - 16 * q^24 - 4 * q^25 - 6 * q^27 + 2 * q^28 - 7 * q^29 - 8 * q^30 - 11 * q^31 - 4 * q^32 - 2 * q^33 - 14 * q^34 - 3 * q^35 - 2 * q^36 - 12 * q^37 + 2 * q^38 - 10 * q^40 - 2 * q^41 - 2 * q^42 + 13 * q^43 - 14 * q^44 - 5 * q^45 + 20 * q^46 - 19 * q^47 + 4 * q^48 + 3 * q^49 + 2 * q^50 - 4 * q^51 + q^53 + 8 * q^54 + 6 * q^55 - 6 * q^56 - 30 * q^57 + 22 * q^58 - 2 * q^59 - 6 * q^60 + 14 * q^61 - 8 * q^62 - q^63 + 4 * q^64 + 14 * q^66 + 12 * q^67 + 10 * q^68 + 2 * q^69 - 14 * q^71 + 14 * q^72 + 9 * q^73 - 12 * q^74 - 22 * q^75 - 32 * q^76 - 8 * q^77 + 13 * q^79 - 13 * q^81 + 28 * q^82 - q^83 + 10 * q^84 - 8 * q^85 - 18 * q^86 - 20 * q^87 + 20 * q^88 - 3 * q^89 + 6 * q^90 - 18 * q^92 + 12 * q^93 + 10 * q^94 - 29 * q^95 + 12 * q^96 - 15 * q^97 - 2 * q^98 - 2 * q^99

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