LMFDB - Embedded newform 2166.2.a.w.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2166,2,Mod(1,2166)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2166, 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("2166.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2166 = 2 \cdot 3 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2166.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:	$17.2955970778$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{20})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 5x^{2} + 5 $ x^4 - 5*x^2 + 5
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.17557$ of defining polynomial
Character	$\chi$	$=$	2166.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.824429 q^{5} -1.00000 q^{6} +0.381966 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.824429 q^{5} -1.00000 q^{6} +0.381966 q^{7} -1.00000 q^{8} +1.00000 q^{9} -0.824429 q^{10} -1.13818 q^{11} +1.00000 q^{12} -0.568158 q^{13} -0.381966 q^{14} +0.824429 q^{15} +1.00000 q^{16} +1.78298 q^{17} -1.00000 q^{18} +0.824429 q^{20} +0.381966 q^{21} +1.13818 q^{22} +9.04029 q^{23} -1.00000 q^{24} -4.32032 q^{25} +0.568158 q^{26} +1.00000 q^{27} +0.381966 q^{28} -3.50296 q^{29} -0.824429 q^{30} +3.68323 q^{31} -1.00000 q^{32} -1.13818 q^{33} -1.78298 q^{34} +0.314904 q^{35} +1.00000 q^{36} -6.70228 q^{37} -0.568158 q^{39} -0.824429 q^{40} +7.25731 q^{41} -0.381966 q^{42} +11.1957 q^{43} -1.13818 q^{44} +0.824429 q^{45} -9.04029 q^{46} +10.0593 q^{47} +1.00000 q^{48} -6.85410 q^{49} +4.32032 q^{50} +1.78298 q^{51} -0.568158 q^{52} +3.50296 q^{53} -1.00000 q^{54} -0.938350 q^{55} -0.381966 q^{56} +3.50296 q^{58} +8.10549 q^{59} +0.824429 q^{60} +11.7426 q^{61} -3.68323 q^{62} +0.381966 q^{63} +1.00000 q^{64} -0.468406 q^{65} +1.13818 q^{66} -4.79830 q^{67} +1.78298 q^{68} +9.04029 q^{69} -0.314904 q^{70} -2.78890 q^{71} -1.00000 q^{72} +5.55638 q^{73} +6.70228 q^{74} -4.32032 q^{75} -0.434746 q^{77} +0.568158 q^{78} -14.6044 q^{79} +0.824429 q^{80} +1.00000 q^{81} -7.25731 q^{82} -9.57293 q^{83} +0.381966 q^{84} +1.46994 q^{85} -11.1957 q^{86} -3.50296 q^{87} +1.13818 q^{88} +0.195774 q^{89} -0.824429 q^{90} -0.217017 q^{91} +9.04029 q^{92} +3.68323 q^{93} -10.0593 q^{94} -1.00000 q^{96} +17.6890 q^{97} +6.85410 q^{98} -1.13818 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} + 8 q^{5} - 4 q^{6} + 6 q^{7} - 4 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 + 4 * q^3 + 4 * q^4 + 8 * q^5 - 4 * q^6 + 6 * q^7 - 4 * q^8 + 4 * q^9	\( 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} + 8 q^{5} - 4 q^{6} + 6 q^{7} - 4 q^{8} + 4 q^{9} - 8 q^{10} + 12 q^{11} + 4 q^{12} + 4 q^{13} - 6 q^{14} + 8 q^{15} + 4 q^{16} + 4 q^{17} - 4 q^{18} + 8 q^{20} + 6 q^{21} - 12 q^{22} + 12 q^{23} - 4 q^{24} + 6 q^{25} - 4 q^{26} + 4 q^{27} + 6 q^{28} - 10 q^{29} - 8 q^{30} + 8 q^{31} - 4 q^{32} + 12 q^{33} - 4 q^{34} + 12 q^{35} + 4 q^{36} - 8 q^{37} + 4 q^{39} - 8 q^{40} + 8 q^{41} - 6 q^{42} - 4 q^{43} + 12 q^{44} + 8 q^{45} - 12 q^{46} + 4 q^{47} + 4 q^{48} - 14 q^{49} - 6 q^{50} + 4 q^{51} + 4 q^{52} + 10 q^{53} - 4 q^{54} + 24 q^{55} - 6 q^{56} + 10 q^{58} + 6 q^{59} + 8 q^{60} + 4 q^{61} - 8 q^{62} + 6 q^{63} + 4 q^{64} + 8 q^{65} - 12 q^{66} - 12 q^{67} + 4 q^{68} + 12 q^{69} - 12 q^{70} - 4 q^{72} - 10 q^{73} + 8 q^{74} + 6 q^{75} + 28 q^{77} - 4 q^{78} - 32 q^{79} + 8 q^{80} + 4 q^{81} - 8 q^{82} + 8 q^{83} + 6 q^{84} - 12 q^{85} + 4 q^{86} - 10 q^{87} - 12 q^{88} + 16 q^{89} - 8 q^{90} - 4 q^{91} + 12 q^{92} + 8 q^{93} - 4 q^{94} - 4 q^{96} - 8 q^{97} + 14 q^{98} + 12 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 + 4 * q^3 + 4 * q^4 + 8 * q^5 - 4 * q^6 + 6 * q^7 - 4 * q^8 + 4 * q^9 - 8 * q^10 + 12 * q^11 + 4 * q^12 + 4 * q^13 - 6 * q^14 + 8 * q^15 + 4 * q^16 + 4 * q^17 - 4 * q^18 + 8 * q^20 + 6 * q^21 - 12 * q^22 + 12 * q^23 - 4 * q^24 + 6 * q^25 - 4 * q^26 + 4 * q^27 + 6 * q^28 - 10 * q^29 - 8 * q^30 + 8 * q^31 - 4 * q^32 + 12 * q^33 - 4 * q^34 + 12 * q^35 + 4 * q^36 - 8 * q^37 + 4 * q^39 - 8 * q^40 + 8 * q^41 - 6 * q^42 - 4 * q^43 + 12 * q^44 + 8 * q^45 - 12 * q^46 + 4 * q^47 + 4 * q^48 - 14 * q^49 - 6 * q^50 + 4 * q^51 + 4 * q^52 + 10 * q^53 - 4 * q^54 + 24 * q^55 - 6 * q^56 + 10 * q^58 + 6 * q^59 + 8 * q^60 + 4 * q^61 - 8 * q^62 + 6 * q^63 + 4 * q^64 + 8 * q^65 - 12 * q^66 - 12 * q^67 + 4 * q^68 + 12 * q^69 - 12 * q^70 - 4 * q^72 - 10 * q^73 + 8 * q^74 + 6 * q^75 + 28 * q^77 - 4 * q^78 - 32 * q^79 + 8 * q^80 + 4 * q^81 - 8 * q^82 + 8 * q^83 + 6 * q^84 - 12 * q^85 + 4 * q^86 - 10 * q^87 - 12 * q^88 + 16 * q^89 - 8 * q^90 - 4 * q^91 + 12 * q^92 + 8 * q^93 - 4 * q^94 - 4 * q^96 - 8 * q^97 + 14 * q^98 + 12 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	0.824429	0.368696	0.184348	−	0.982861i	$-0.440983\pi$
$5$	0.824429	0.368696	0.184348	+	0.982861i	$0.440983\pi$
$6$	−1.00000	−0.408248
$7$	0.381966	0.144370	0.0721848	−	0.997391i	$-0.477003\pi$
$7$	0.381966	0.144370	0.0721848	+	0.997391i	$0.477003\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−0.824429	−0.260707
$11$	−1.13818	−0.343174	−0.171587	−	0.985169i	$-0.554890\pi$
$11$	−1.13818	−0.343174	−0.171587	+	0.985169i	$0.554890\pi$
$12$	1.00000	0.288675
$13$	−0.568158	−0.157579	−0.0787894	−	0.996891i	$-0.525105\pi$
$13$	−0.568158	−0.157579	−0.0787894	+	0.996891i	$0.525105\pi$
$14$	−0.381966	−0.102085
$15$	0.824429	0.212867
$16$	1.00000	0.250000
$17$	1.78298	0.432437	0.216218	−	0.976345i	$-0.430628\pi$
$17$	1.78298	0.432437	0.216218	+	0.976345i	$0.430628\pi$
$18$	−1.00000	−0.235702
$19$	0	0
$19$	0	0
$20$	0.824429	0.184348
$21$	0.381966	0.0833518
$22$	1.13818	0.242661
$23$	9.04029	1.88503	0.942516	−	0.334162i	$-0.108453\pi$
$23$	9.04029	1.88503	0.942516	+	0.334162i	$0.108453\pi$
$24$	−1.00000	−0.204124
$25$	−4.32032	−0.864063
$26$	0.568158	0.111425
$27$	1.00000	0.192450
$28$	0.381966	0.0721848
$29$	−3.50296	−0.650484	−0.325242	−	0.945631i	$-0.605446\pi$
$29$	−3.50296	−0.650484	−0.325242	+	0.945631i	$0.605446\pi$
$30$	−0.824429	−0.150520
$31$	3.68323	0.661528	0.330764	−	0.943714i	$-0.392694\pi$
$31$	3.68323	0.661528	0.330764	+	0.943714i	$0.392694\pi$
$32$	−1.00000	−0.176777
$33$	−1.13818	−0.198132
$34$	−1.78298	−0.305779
$35$	0.314904	0.0532285
$36$	1.00000	0.166667
$37$	−6.70228	−1.10185	−0.550924	−	0.834555i	$-0.685725\pi$
$37$	−6.70228	−1.10185	−0.550924	+	0.834555i	$0.685725\pi$
$38$	0	0
$39$	−0.568158	−0.0909781
$40$	−0.824429	−0.130354
$41$	7.25731	1.13340	0.566701	−	0.823924i	$-0.308220\pi$
$41$	7.25731	1.13340	0.566701	+	0.823924i	$0.308220\pi$
$42$	−0.381966	−0.0589386
$43$	11.1957	1.70732	0.853661	−	0.520829i	$-0.174377\pi$
$43$	11.1957	1.70732	0.853661	+	0.520829i	$0.174377\pi$
$44$	−1.13818	−0.171587
$45$	0.824429	0.122899
$46$	−9.04029	−1.33292
$47$	10.0593	1.46731	0.733653	−	0.679524i	$-0.237814\pi$
$47$	10.0593	1.46731	0.733653	+	0.679524i	$0.237814\pi$
$48$	1.00000	0.144338
$49$	−6.85410	−0.979157
$50$	4.32032	0.610985
$51$	1.78298	0.249668
$52$	−0.568158	−0.0787894
$53$	3.50296	0.481169	0.240584	−	0.970628i	$-0.422661\pi$
$53$	3.50296	0.481169	0.240584	+	0.970628i	$0.422661\pi$
$54$	−1.00000	−0.136083
$55$	−0.938350	−0.126527
$56$	−0.381966	−0.0510424
$57$	0	0
$58$	3.50296	0.459961
$59$	8.10549	1.05525	0.527623	−	0.849479i	$-0.323084\pi$
$59$	8.10549	1.05525	0.527623	+	0.849479i	$0.323084\pi$
$60$	0.824429	0.106433
$61$	11.7426	1.50348	0.751741	−	0.659458i	$-0.229214\pi$
$61$	11.7426	1.50348	0.751741	+	0.659458i	$0.229214\pi$
$62$	−3.68323	−0.467771
$63$	0.381966	0.0481232
$64$	1.00000	0.125000
$65$	−0.468406	−0.0580986
$66$	1.13818	0.140100
$67$	−4.79830	−0.586206	−0.293103	−	0.956081i	$-0.594688\pi$
$67$	−4.79830	−0.586206	−0.293103	+	0.956081i	$0.594688\pi$
$68$	1.78298	0.216218
$69$	9.04029	1.08832
$70$	−0.314904	−0.0376382
$71$	−2.78890	−0.330982	−0.165491	−	0.986211i	$-0.552921\pi$
$71$	−2.78890	−0.330982	−0.165491	+	0.986211i	$0.552921\pi$
$72$	−1.00000	−0.117851
$73$	5.55638	0.650326	0.325163	−	0.945658i	$-0.394581\pi$
$73$	5.55638	0.650326	0.325163	+	0.945658i	$0.394581\pi$
$74$	6.70228	0.779124
$75$	−4.32032	−0.498867
$76$	0	0
$77$	−0.434746	−0.0495440
$78$	0.568158	0.0643312
$79$	−14.6044	−1.64312	−0.821561	−	0.570120i	$-0.806897\pi$
$79$	−14.6044	−1.64312	−0.821561	+	0.570120i	$0.806897\pi$
$80$	0.824429	0.0921740
$81$	1.00000	0.111111
$82$	−7.25731	−0.801436
$83$	−9.57293	−1.05077	−0.525383	−	0.850866i	$-0.676078\pi$
$83$	−9.57293	−1.05077	−0.525383	+	0.850866i	$0.676078\pi$
$84$	0.381966	0.0416759
$85$	1.46994	0.159438
$86$	−11.1957	−1.20726
$87$	−3.50296	−0.375557
$88$	1.13818	0.121331
$89$	0.195774	0.0207520	0.0103760	−	0.999946i	$-0.496697\pi$
$89$	0.195774	0.0207520	0.0103760	+	0.999946i	$0.496697\pi$
$90$	−0.824429	−0.0869025
$91$	−0.217017	−0.0227496
$92$	9.04029	0.942516
$93$	3.68323	0.381933
$94$	−10.0593	−1.03754
$95$	0	0
$96$	−1.00000	−0.102062
$97$	17.6890	1.79605	0.898025	−	0.439945i	$-0.145002\pi$
$97$	17.6890	1.79605	0.898025	+	0.439945i	$0.145002\pi$
$98$	6.85410	0.692369
$99$	−1.13818	−0.114391
$100$	−4.32032	−0.432032
$101$	9.37831	0.933176	0.466588	−	0.884475i	$-0.345483\pi$
$101$	9.37831	0.933176	0.466588	+	0.884475i	$0.345483\pi$
$102$	−1.78298	−0.176542
$103$	−10.8464	−1.06873	−0.534363	−	0.845255i	$-0.679448\pi$
$103$	−10.8464	−1.06873	−0.534363	+	0.845255i	$0.679448\pi$
$104$	0.568158	0.0557125
$105$	0.314904	0.0307315
$106$	−3.50296	−0.340238
$107$	2.86723	0.277186	0.138593	−	0.990349i	$-0.455742\pi$
$107$	2.86723	0.277186	0.138593	+	0.990349i	$0.455742\pi$
$108$	1.00000	0.0962250
$109$	5.93835	0.568791	0.284395	−	0.958707i	$-0.408207\pi$
$109$	5.93835	0.568791	0.284395	+	0.958707i	$0.408207\pi$
$110$	0.938350	0.0894682
$111$	−6.70228	−0.636152
$112$	0.381966	0.0360924
$113$	2.66791	0.250976	0.125488	−	0.992095i	$-0.459950\pi$
$113$	2.66791	0.250976	0.125488	+	0.992095i	$0.459950\pi$
$114$	0	0
$115$	7.45309	0.695004
$116$	−3.50296	−0.325242
$117$	−0.568158	−0.0525262
$118$	−8.10549	−0.746171
$119$	0.681039	0.0624307
$120$	−0.824429	−0.0752598
$121$	−9.70454	−0.882231
$122$	−11.7426	−1.06312
$123$	7.25731	0.654370
$124$	3.68323	0.330764
$125$	−7.68394	−0.687273
$126$	−0.381966	−0.0340282
$127$	−15.6720	−1.39066	−0.695331	−	0.718690i	$-0.744742\pi$
$127$	−15.6720	−1.39066	−0.695331	+	0.718690i	$0.744742\pi$
$128$	−1.00000	−0.0883883
$129$	11.1957	0.985723
$130$	0.468406	0.0410819
$131$	14.0070	1.22379	0.611897	−	0.790937i	$-0.290407\pi$
$131$	14.0070	1.22379	0.611897	+	0.790937i	$0.290407\pi$
$132$	−1.13818	−0.0990659
$133$	0	0
$134$	4.79830	0.414510
$135$	0.824429	0.0709556
$136$	−1.78298	−0.152890
$137$	15.2206	1.30039	0.650193	−	0.759769i	$-0.274688\pi$
$137$	15.2206	1.30039	0.650193	+	0.759769i	$0.274688\pi$
$138$	−9.04029	−0.769561
$139$	−5.37831	−0.456182	−0.228091	−	0.973640i	$-0.573248\pi$
$139$	−5.37831	−0.456182	−0.228091	+	0.973640i	$0.573248\pi$
$140$	0.314904	0.0266142
$141$	10.0593	0.847150
$142$	2.78890	0.234040
$143$	0.646667	0.0540770
$144$	1.00000	0.0833333
$145$	−2.88794	−0.239831
$146$	−5.55638	−0.459850
$147$	−6.85410	−0.565317
$148$	−6.70228	−0.550924
$149$	−5.13516	−0.420689	−0.210344	−	0.977627i	$-0.567459\pi$
$149$	−5.13516	−0.420689	−0.210344	+	0.977627i	$0.567459\pi$
$150$	4.32032	0.352752
$151$	5.51429	0.448747	0.224373	−	0.974503i	$-0.427966\pi$
$151$	5.51429	0.448747	0.224373	+	0.974503i	$0.427966\pi$
$152$	0	0
$153$	1.78298	0.144146
$154$	0.434746	0.0350329
$155$	3.03656	0.243903
$156$	−0.568158	−0.0454891
$157$	14.5871	1.16418	0.582089	−	0.813125i	$-0.302236\pi$
$157$	14.5871	1.16418	0.582089	+	0.813125i	$0.302236\pi$
$158$	14.6044	1.16186
$159$	3.50296	0.277803
$160$	−0.824429	−0.0651769
$161$	3.45309	0.272141
$162$	−1.00000	−0.0785674
$163$	3.25731	0.255132	0.127566	−	0.991830i	$-0.459283\pi$
$163$	3.25731	0.255132	0.127566	+	0.991830i	$0.459283\pi$
$164$	7.25731	0.566701
$165$	−0.938350	−0.0730504
$166$	9.57293	0.743003
$167$	−12.7829	−0.989168	−0.494584	−	0.869130i	$-0.664680\pi$
$167$	−12.7829	−0.989168	−0.494584	+	0.869130i	$0.664680\pi$
$168$	−0.381966	−0.0294693
$169$	−12.6772	−0.975169
$170$	−1.46994	−0.112740
$171$	0	0
$172$	11.1957	0.853661
$173$	12.1649	0.924884	0.462442	−	0.886650i	$-0.346973\pi$
$173$	12.1649	0.924884	0.462442	+	0.886650i	$0.346973\pi$
$174$	3.50296	0.265559
$175$	−1.65021	−0.124744
$176$	−1.13818	−0.0857936
$177$	8.10549	0.609246
$178$	−0.195774	−0.0146739
$179$	1.17306	0.0876789	0.0438394	−	0.999039i	$-0.486041\pi$
$179$	1.17306	0.0876789	0.0438394	+	0.999039i	$0.486041\pi$
$180$	0.824429	0.0614493
$181$	2.68104	0.199280	0.0996400	−	0.995024i	$-0.468231\pi$
$181$	2.68104	0.199280	0.0996400	+	0.995024i	$0.468231\pi$
$182$	0.217017	0.0160864
$183$	11.7426	0.868036
$184$	−9.04029	−0.666459
$185$	−5.52556	−0.406247
$186$	−3.68323	−0.270068
$187$	−2.02936	−0.148401
$188$	10.0593	0.733653
$189$	0.381966	0.0277839
$190$	0	0
$191$	−11.7851	−0.852737	−0.426369	−	0.904550i	$-0.640207\pi$
$191$	−11.7851	−0.852737	−0.426369	+	0.904550i	$0.640207\pi$
$192$	1.00000	0.0721688
$193$	−18.9431	−1.36356	−0.681778	−	0.731559i	$-0.738793\pi$
$193$	−18.9431	−1.36356	−0.681778	+	0.731559i	$0.738793\pi$
$194$	−17.6890	−1.27000
$195$	−0.468406	−0.0335433
$196$	−6.85410	−0.489579
$197$	−19.4145	−1.38323	−0.691614	−	0.722267i	$-0.743100\pi$
$197$	−19.4145	−1.38323	−0.691614	+	0.722267i	$0.743100\pi$
$198$	1.13818	0.0808870
$199$	0.276292	0.0195858	0.00979292	−	0.999952i	$-0.496883\pi$
$199$	0.276292	0.0195858	0.00979292	+	0.999952i	$0.496883\pi$
$200$	4.32032	0.305492
$201$	−4.79830	−0.338446
$202$	−9.37831	−0.659855
$203$	−1.33801	−0.0939100
$204$	1.78298	0.124834
$205$	5.98314	0.417881
$206$	10.8464	0.755703
$207$	9.04029	0.628344
$208$	−0.568158	−0.0393947
$209$	0	0
$210$	−0.314904	−0.0217304
$211$	9.68696	0.666878	0.333439	−	0.942772i	$-0.391791\pi$
$211$	9.68696	0.666878	0.333439	+	0.942772i	$0.391791\pi$
$212$	3.50296	0.240584
$213$	−2.78890	−0.191093
$214$	−2.86723	−0.196000
$215$	9.23003	0.629483
$216$	−1.00000	−0.0680414
$217$	1.40687	0.0955045
$218$	−5.93835	−0.402196
$219$	5.55638	0.375466
$220$	−0.938350	−0.0632635
$221$	−1.01302	−0.0681428
$222$	6.70228	0.449828
$223$	2.58617	0.173183	0.0865914	−	0.996244i	$-0.472403\pi$
$223$	2.58617	0.173183	0.0865914	+	0.996244i	$0.472403\pi$
$224$	−0.381966	−0.0255212
$225$	−4.32032	−0.288021
$226$	−2.66791	−0.177467
$227$	20.1839	1.33965	0.669826	−	0.742518i	$-0.266369\pi$
$227$	20.1839	1.33965	0.669826	+	0.742518i	$0.266369\pi$
$228$	0	0
$229$	19.7103	1.30249	0.651246	−	0.758867i	$-0.274247\pi$
$229$	19.7103	1.30249	0.651246	+	0.758867i	$0.274247\pi$
$230$	−7.45309	−0.491442
$231$	−0.434746	−0.0286042
$232$	3.50296	0.229981
$233$	−0.450893	−0.0295390	−0.0147695	−	0.999891i	$-0.504701\pi$
$233$	−0.450893	−0.0295390	−0.0147695	+	0.999891i	$0.504701\pi$
$234$	0.568158	0.0371417
$235$	8.29322	0.540990
$236$	8.10549	0.527623
$237$	−14.6044	−0.948657
$238$	−0.681039	−0.0441452
$239$	14.8576	0.961061	0.480531	−	0.876978i	$-0.340444\pi$
$239$	14.8576	0.961061	0.480531	+	0.876978i	$0.340444\pi$
$240$	0.824429	0.0532167
$241$	−11.1109	−0.715716	−0.357858	−	0.933776i	$-0.616493\pi$
$241$	−11.1109	−0.715716	−0.357858	+	0.933776i	$0.616493\pi$
$242$	9.70454	0.623832
$243$	1.00000	0.0641500
$244$	11.7426	0.751741
$245$	−5.65072	−0.361012
$246$	−7.25731	−0.462709
$247$	0	0
$248$	−3.68323	−0.233885
$249$	−9.57293	−0.606660
$250$	7.68394	0.485975
$251$	0.899921	0.0568025	0.0284012	−	0.999597i	$-0.490958\pi$
$251$	0.899921	0.0568025	0.0284012	+	0.999597i	$0.490958\pi$
$252$	0.381966	0.0240616
$253$	−10.2895	−0.646895
$254$	15.6720	0.983347
$255$	1.46994	0.0920514
$256$	1.00000	0.0625000
$257$	27.3379	1.70529	0.852646	−	0.522490i	$-0.174997\pi$
$257$	27.3379	1.70529	0.852646	+	0.522490i	$0.174997\pi$
$258$	−11.1957	−0.697011
$259$	−2.56004	−0.159073
$260$	−0.468406	−0.0290493
$261$	−3.50296	−0.216828
$262$	−14.0070	−0.865353
$263$	−26.3913	−1.62736	−0.813679	−	0.581314i	$-0.802539\pi$
$263$	−26.3913	−1.62736	−0.813679	+	0.581314i	$0.802539\pi$
$264$	1.13818	0.0700502
$265$	2.88794	0.177405
$266$	0	0
$267$	0.195774	0.0119812
$268$	−4.79830	−0.293103
$269$	29.0476	1.77106	0.885531	−	0.464581i	$-0.153795\pi$
$269$	29.0476	1.77106	0.885531	+	0.464581i	$0.153795\pi$
$270$	−0.824429	−0.0501732
$271$	13.7865	0.837472	0.418736	−	0.908108i	$-0.362473\pi$
$271$	13.7865	0.837472	0.418736	+	0.908108i	$0.362473\pi$
$272$	1.78298	0.108109
$273$	−0.217017	−0.0131345
$274$	−15.2206	−0.919512
$275$	4.91730	0.296524
$276$	9.04029	0.544162
$277$	10.8314	0.650795	0.325398	−	0.945577i	$-0.394502\pi$
$277$	10.8314	0.650795	0.325398	+	0.945577i	$0.394502\pi$
$278$	5.37831	0.322569
$279$	3.68323	0.220509
$280$	−0.314904	−0.0188191
$281$	4.65478	0.277681	0.138840	−	0.990315i	$-0.455662\pi$
$281$	4.65478	0.277681	0.138840	+	0.990315i	$0.455662\pi$
$282$	−10.0593	−0.599025
$283$	−32.5042	−1.93217	−0.966087	−	0.258216i	$-0.916865\pi$
$283$	−32.5042	−1.93217	−0.966087	+	0.258216i	$0.916865\pi$
$284$	−2.78890	−0.165491
$285$	0	0
$286$	−0.646667	−0.0382382
$287$	2.77205	0.163629
$288$	−1.00000	−0.0589256
$289$	−13.8210	−0.812998
$290$	2.88794	0.169586
$291$	17.6890	1.03695
$292$	5.55638	0.325163
$293$	12.5373	0.732439	0.366219	−	0.930529i	$-0.380652\pi$
$293$	12.5373	0.732439	0.366219	+	0.930529i	$0.380652\pi$
$294$	6.85410	0.399739
$295$	6.68241	0.389065
$296$	6.70228	0.389562
$297$	−1.13818	−0.0660440
$298$	5.13516	0.297472
$299$	−5.13632	−0.297041
$300$	−4.32032	−0.249434
$301$	4.27636	0.246485
$302$	−5.51429	−0.317312
$303$	9.37831	0.538770
$304$	0	0
$305$	9.68093	0.554328
$306$	−1.78298	−0.101926
$307$	−15.9869	−0.912419	−0.456209	−	0.889872i	$-0.650793\pi$
$307$	−15.9869	−0.912419	−0.456209	+	0.889872i	$0.650793\pi$
$308$	−0.434746	−0.0247720
$309$	−10.8464	−0.617029
$310$	−3.03656	−0.172465
$311$	2.69727	0.152948	0.0764740	−	0.997072i	$-0.475634\pi$
$311$	2.69727	0.152948	0.0764740	+	0.997072i	$0.475634\pi$
$312$	0.568158	0.0321656
$313$	−24.7470	−1.39878	−0.699392	−	0.714738i	$-0.746546\pi$
$313$	−24.7470	−1.39878	−0.699392	+	0.714738i	$0.746546\pi$
$314$	−14.5871	−0.823197
$315$	0.314904	0.0177428
$316$	−14.6044	−0.821561
$317$	31.2799	1.75685	0.878427	−	0.477876i	$-0.158593\pi$
$317$	31.2799	1.75685	0.878427	+	0.477876i	$0.158593\pi$
$318$	−3.50296	−0.196436
$319$	3.98700	0.223229
$320$	0.824429	0.0460870
$321$	2.86723	0.160033
$322$	−3.45309	−0.192433
$323$	0	0
$324$	1.00000	0.0555556
$325$	2.45462	0.136158
$326$	−3.25731	−0.180406
$327$	5.93835	0.328392
$328$	−7.25731	−0.400718
$329$	3.84233	0.211834
$330$	0.938350	0.0516545
$331$	1.17442	0.0645518	0.0322759	−	0.999479i	$-0.489724\pi$
$331$	1.17442	0.0645518	0.0322759	+	0.999479i	$0.489724\pi$
$332$	−9.57293	−0.525383
$333$	−6.70228	−0.367283
$334$	12.7829	0.699448
$335$	−3.95586	−0.216132
$336$	0.381966	0.0208380
$337$	13.3783	0.728763	0.364381	−	0.931250i	$-0.381280\pi$
$337$	13.3783	0.728763	0.364381	+	0.931250i	$0.381280\pi$
$338$	12.6772	0.689549
$339$	2.66791	0.144901
$340$	1.46994	0.0797189
$341$	−4.19218	−0.227019
$342$	0	0
$343$	−5.29180	−0.285730
$344$	−11.1957	−0.603630
$345$	7.45309	0.401261
$346$	−12.1649	−0.653992
$347$	−18.9080	−1.01504	−0.507518	−	0.861641i	$-0.669437\pi$
$347$	−18.9080	−1.01504	−0.507518	+	0.861641i	$0.669437\pi$
$348$	−3.50296	−0.187778
$349$	16.9999	0.909983	0.454992	−	0.890496i	$-0.349642\pi$
$349$	16.9999	0.909983	0.454992	+	0.890496i	$0.349642\pi$
$350$	1.65021	0.0882076
$351$	−0.568158	−0.0303260
$352$	1.13818	0.0606653
$353$	−4.19204	−0.223120	−0.111560	−	0.993758i	$-0.535585\pi$
$353$	−4.19204	−0.223120	−0.111560	+	0.993758i	$0.535585\pi$
$354$	−8.10549	−0.430802
$355$	−2.29926	−0.122032
$356$	0.195774	0.0103760
$357$	0.681039	0.0360444
$358$	−1.17306	−0.0619983
$359$	5.60034	0.295575	0.147787	−	0.989019i	$-0.452785\pi$
$359$	5.60034	0.295575	0.147787	+	0.989019i	$0.452785\pi$
$360$	−0.824429	−0.0434512
$361$	0	0
$362$	−2.68104	−0.140912
$363$	−9.70454	−0.509356
$364$	−0.217017	−0.0113748
$365$	4.58085	0.239772
$366$	−11.7426	−0.613794
$367$	−21.3238	−1.11309	−0.556545	−	0.830817i	$-0.687873\pi$
$367$	−21.3238	−1.11309	−0.556545	+	0.830817i	$0.687873\pi$
$368$	9.04029	0.471258
$369$	7.25731	0.377801
$370$	5.52556	0.287260
$371$	1.33801	0.0694661
$372$	3.68323	0.190967
$373$	−15.3073	−0.792580	−0.396290	−	0.918125i	$-0.629702\pi$
$373$	−15.3073	−0.792580	−0.396290	+	0.918125i	$0.629702\pi$
$374$	2.02936	0.104936
$375$	−7.68394	−0.396797
$376$	−10.0593	−0.518771
$377$	1.99024	0.102502
$378$	−0.381966	−0.0196462
$379$	28.6060	1.46939	0.734697	−	0.678396i	$-0.237325\pi$
$379$	28.6060	1.46939	0.734697	+	0.678396i	$0.237325\pi$
$380$	0	0
$381$	−15.6720	−0.802899
$382$	11.7851	0.602976
$383$	−28.8254	−1.47291	−0.736453	−	0.676488i	$-0.763501\pi$
$383$	−28.8254	−1.47291	−0.736453	+	0.676488i	$0.763501\pi$
$384$	−1.00000	−0.0510310
$385$	−0.358418	−0.0182667
$386$	18.9431	0.964179
$387$	11.1957	0.569107
$388$	17.6890	0.898025
$389$	−19.4589	−0.986605	−0.493303	−	0.869858i	$-0.664210\pi$
$389$	−19.4589	−0.986605	−0.493303	+	0.869858i	$0.664210\pi$
$390$	0.468406	0.0237187
$391$	16.1187	0.815157
$392$	6.85410	0.346184
$393$	14.0070	0.706558
$394$	19.4145	0.978091
$395$	−12.0403	−0.605813
$396$	−1.13818	−0.0571957
$397$	−28.0321	−1.40689	−0.703445	−	0.710750i	$-0.748356\pi$
$397$	−28.0321	−1.40689	−0.703445	+	0.710750i	$0.748356\pi$
$398$	−0.276292	−0.0138493
$399$	0	0
$400$	−4.32032	−0.216016
$401$	−23.8481	−1.19092	−0.595460	−	0.803385i	$-0.703030\pi$
$401$	−23.8481	−1.19092	−0.595460	+	0.803385i	$0.703030\pi$
$402$	4.79830	0.239318
$403$	−2.09266	−0.104243
$404$	9.37831	0.466588
$405$	0.824429	0.0409662
$406$	1.33801	0.0664044
$407$	7.62841	0.378126
$408$	−1.78298	−0.0882708
$409$	−28.7032	−1.41928	−0.709641	−	0.704563i	$-0.751143\pi$
$409$	−28.7032	−1.41928	−0.709641	+	0.704563i	$0.751143\pi$
$410$	−5.98314	−0.295486
$411$	15.2206	0.750779
$412$	−10.8464	−0.534363
$413$	3.09602	0.152345
$414$	−9.04029	−0.444306
$415$	−7.89220	−0.387413
$416$	0.568158	0.0278562
$417$	−5.37831	−0.263377
$418$	0	0
$419$	−37.2076	−1.81771	−0.908856	−	0.417110i	$-0.863043\pi$
$419$	−37.2076	−1.81771	−0.908856	+	0.417110i	$0.863043\pi$
$420$	0.314904	0.0153657
$421$	14.0843	0.686428	0.343214	−	0.939257i	$-0.388484\pi$
$421$	14.0843	0.686428	0.343214	+	0.939257i	$0.388484\pi$
$422$	−9.68696	−0.471554
$423$	10.0593	0.489102
$424$	−3.50296	−0.170119
$425$	−7.70305	−0.373653
$426$	2.78890	0.135123
$427$	4.48526	0.217057
$428$	2.86723	0.138593
$429$	0.646667	0.0312214
$430$	−9.23003	−0.445112
$431$	33.7353	1.62497	0.812485	−	0.582982i	$-0.198114\pi$
$431$	33.7353	1.62497	0.812485	+	0.582982i	$0.198114\pi$
$432$	1.00000	0.0481125
$433$	25.5868	1.22962	0.614811	−	0.788675i	$-0.289232\pi$
$433$	25.5868	1.22962	0.614811	+	0.788675i	$0.289232\pi$
$434$	−1.40687	−0.0675319
$435$	−2.88794	−0.138466
$436$	5.93835	0.284395
$437$	0	0
$438$	−5.55638	−0.265494
$439$	−27.5874	−1.31668	−0.658338	−	0.752722i	$-0.728740\pi$
$439$	−27.5874	−1.31668	−0.658338	+	0.752722i	$0.728740\pi$
$440$	0.938350	0.0447341
$441$	−6.85410	−0.326386
$442$	1.01302	0.0481843
$443$	−14.2327	−0.676217	−0.338109	−	0.941107i	$-0.609787\pi$
$443$	−14.2327	−0.676217	−0.338109	+	0.941107i	$0.609787\pi$
$444$	−6.70228	−0.318076
$445$	0.161402	0.00765118
$446$	−2.58617	−0.122459
$447$	−5.13516	−0.242885
$448$	0.381966	0.0180462
$449$	−39.2146	−1.85065	−0.925326	−	0.379173i	$-0.876208\pi$
$449$	−39.2146	−1.85065	−0.925326	+	0.379173i	$0.876208\pi$
$450$	4.32032	0.203662
$451$	−8.26013	−0.388955
$452$	2.66791	0.125488
$453$	5.51429	0.259084
$454$	−20.1839	−0.947277
$455$	−0.178915	−0.00838768
$456$	0	0
$457$	0.664180	0.0310690	0.0155345	−	0.999879i	$-0.495055\pi$
$457$	0.664180	0.0310690	0.0155345	+	0.999879i	$0.495055\pi$
$458$	−19.7103	−0.921001
$459$	1.78298	0.0832225
$460$	7.45309	0.347502
$461$	−10.1602	−0.473210	−0.236605	−	0.971606i	$-0.576035\pi$
$461$	−10.1602	−0.473210	−0.236605	+	0.971606i	$0.576035\pi$
$462$	0.434746	0.0202262
$463$	12.7367	0.591926	0.295963	−	0.955199i	$-0.404360\pi$
$463$	12.7367	0.591926	0.295963	+	0.955199i	$0.404360\pi$
$464$	−3.50296	−0.162621
$465$	3.03656	0.140817
$466$	0.450893	0.0208872
$467$	−13.3309	−0.616882	−0.308441	−	0.951243i	$-0.599807\pi$
$467$	−13.3309	−0.616882	−0.308441	+	0.951243i	$0.599807\pi$
$468$	−0.568158	−0.0262631
$469$	−1.83279	−0.0846303
$470$	−8.29322	−0.382538
$471$	14.5871	0.672138
$472$	−8.10549	−0.373085
$473$	−12.7427	−0.585909
$474$	14.6044	0.670802
$475$	0	0
$476$	0.681039	0.0312154
$477$	3.50296	0.160390
$478$	−14.8576	−0.679573
$479$	−5.64447	−0.257903	−0.128951	−	0.991651i	$-0.541161\pi$
$479$	−5.64447	−0.257903	−0.128951	+	0.991651i	$0.541161\pi$
$480$	−0.824429	−0.0376299
$481$	3.80796	0.173628
$482$	11.1109	0.506088
$483$	3.45309	0.157121
$484$	−9.70454	−0.441116
$485$	14.5834	0.662197
$486$	−1.00000	−0.0453609
$487$	−33.6013	−1.52262	−0.761309	−	0.648389i	$-0.775443\pi$
$487$	−33.6013	−1.52262	−0.761309	+	0.648389i	$0.775443\pi$
$488$	−11.7426	−0.531561
$489$	3.25731	0.147301
$490$	5.65072	0.255274
$491$	−24.4268	−1.10237	−0.551184	−	0.834384i	$-0.685824\pi$
$491$	−24.4268	−1.10237	−0.551184	+	0.834384i	$0.685824\pi$
$492$	7.25731	0.327185
$493$	−6.24572	−0.281293
$494$	0	0
$495$	−0.938350	−0.0421757
$496$	3.68323	0.165382
$497$	−1.06527	−0.0477837
$498$	9.57293	0.428973
$499$	8.78890	0.393445	0.196723	−	0.980459i	$-0.436970\pi$
$499$	8.78890	0.393445	0.196723	+	0.980459i	$0.436970\pi$
$500$	−7.68394	−0.343636
$501$	−12.7829	−0.571097
$502$	−0.899921	−0.0401654
$503$	−10.8125	−0.482103	−0.241052	−	0.970512i	$-0.577492\pi$
$503$	−10.8125	−0.482103	−0.241052	+	0.970512i	$0.577492\pi$
$504$	−0.381966	−0.0170141
$505$	7.73175	0.344058
$506$	10.2895	0.457424
$507$	−12.6772	−0.563014
$508$	−15.6720	−0.695331
$509$	−4.26909	−0.189224	−0.0946119	−	0.995514i	$-0.530161\pi$
$509$	−4.26909	−0.189224	−0.0946119	+	0.995514i	$0.530161\pi$
$510$	−1.46994	−0.0650902
$511$	2.12235	0.0938872
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	−27.3379	−1.20582
$515$	−8.94208	−0.394035
$516$	11.1957	0.492861
$517$	−11.4494	−0.503542
$518$	2.56004	0.112482
$519$	12.1649	0.533982
$520$	0.468406	0.0205410
$521$	32.0556	1.40438	0.702191	−	0.711989i	$-0.252205\pi$
$521$	32.0556	1.40438	0.702191	+	0.711989i	$0.252205\pi$
$522$	3.50296	0.153320
$523$	2.04622	0.0894748	0.0447374	−	0.998999i	$-0.485755\pi$
$523$	2.04622	0.0894748	0.0447374	+	0.998999i	$0.485755\pi$
$524$	14.0070	0.611897
$525$	−1.65021	−0.0720212
$526$	26.3913	1.15072
$527$	6.56714	0.286069
$528$	−1.13818	−0.0495330
$529$	58.7269	2.55334
$530$	−2.88794	−0.125444
$531$	8.10549	0.351748
$532$	0	0
$533$	−4.12330	−0.178600
$534$	−0.195774	−0.00847197
$535$	2.36383	0.102197
$536$	4.79830	0.207255
$537$	1.17306	0.0506214
$538$	−29.0476	−1.25233
$539$	7.80121	0.336022
$540$	0.824429	0.0354778
$541$	−25.5930	−1.10033	−0.550165	−	0.835056i	$-0.685435\pi$
$541$	−25.5930	−1.10033	−0.550165	+	0.835056i	$0.685435\pi$
$542$	−13.7865	−0.592182
$543$	2.68104	0.115054
$544$	−1.78298	−0.0764448
$545$	4.89575	0.209711
$546$	0.217017	0.00928747
$547$	−34.4888	−1.47463	−0.737317	−	0.675547i	$-0.763907\pi$
$547$	−34.4888	−1.47463	−0.737317	+	0.675547i	$0.763907\pi$
$548$	15.2206	0.650193
$549$	11.7426	0.501161
$550$	−4.91730	−0.209674
$551$	0	0
$552$	−9.04029	−0.384780
$553$	−5.57838	−0.237217
$554$	−10.8314	−0.460182
$555$	−5.52556	−0.234547
$556$	−5.37831	−0.228091
$557$	−41.9129	−1.77591	−0.887954	−	0.459932i	$-0.847874\pi$
$557$	−41.9129	−1.77591	−0.887954	+	0.459932i	$0.847874\pi$
$558$	−3.68323	−0.155924
$559$	−6.36091	−0.269038
$560$	0.314904	0.0133071
$561$	−2.02936	−0.0856795
$562$	−4.65478	−0.196350
$563$	15.6877	0.661157	0.330579	−	0.943778i	$-0.392756\pi$
$563$	15.6877	0.661157	0.330579	+	0.943778i	$0.392756\pi$
$564$	10.0593	0.423575
$565$	2.19950	0.0925338
$566$	32.5042	1.36625
$567$	0.381966	0.0160411
$568$	2.78890	0.117020
$569$	−16.5065	−0.691989	−0.345994	−	0.938237i	$-0.612458\pi$
$569$	−16.5065	−0.691989	−0.345994	+	0.938237i	$0.612458\pi$
$570$	0	0
$571$	−42.4507	−1.77651	−0.888253	−	0.459355i	$-0.848080\pi$
$571$	−42.4507	−1.77651	−0.888253	+	0.459355i	$0.848080\pi$
$572$	0.646667	0.0270385
$573$	−11.7851	−0.492328
$574$	−2.77205	−0.115703
$575$	−39.0569	−1.62879
$576$	1.00000	0.0416667
$577$	−39.6345	−1.65001	−0.825003	−	0.565129i	$-0.808826\pi$
$577$	−39.6345	−1.65001	−0.825003	+	0.565129i	$0.808826\pi$
$578$	13.8210	0.574877
$579$	−18.9431	−0.787249
$580$	−2.88794	−0.119915
$581$	−3.65653	−0.151699
$582$	−17.6890	−0.733234
$583$	−3.98700	−0.165125
$584$	−5.55638	−0.229925
$585$	−0.468406	−0.0193662
$586$	−12.5373	−0.517912
$587$	1.46054	0.0602831	0.0301416	−	0.999546i	$-0.490404\pi$
$587$	1.46054	0.0602831	0.0301416	+	0.999546i	$0.490404\pi$
$588$	−6.85410	−0.282658
$589$	0	0
$590$	−6.68241	−0.275110
$591$	−19.4145	−0.798608
$592$	−6.70228	−0.275462
$593$	−45.1163	−1.85270	−0.926352	−	0.376660i	$-0.877073\pi$
$593$	−45.1163	−1.85270	−0.926352	+	0.376660i	$0.877073\pi$
$594$	1.13818	0.0467001
$595$	0.561469	0.0230180
$596$	−5.13516	−0.210344
$597$	0.276292	0.0113079
$598$	5.13632	0.210040
$599$	−17.6407	−0.720781	−0.360391	−	0.932801i	$-0.617357\pi$
$599$	−17.6407	−0.720781	−0.360391	+	0.932801i	$0.617357\pi$
$600$	4.32032	0.176376
$601$	−7.79496	−0.317963	−0.158982	−	0.987282i	$-0.550821\pi$
$601$	−7.79496	−0.317963	−0.158982	+	0.987282i	$0.550821\pi$
$602$	−4.27636	−0.174292
$603$	−4.79830	−0.195402
$604$	5.51429	0.224373
$605$	−8.00071	−0.325275
$606$	−9.37831	−0.380968
$607$	−7.33324	−0.297647	−0.148824	−	0.988864i	$-0.547549\pi$
$607$	−7.33324	−0.297647	−0.148824	+	0.988864i	$0.547549\pi$
$608$	0	0
$609$	−1.33801	−0.0542190
$610$	−9.68093	−0.391969
$611$	−5.71530	−0.231216
$612$	1.78298	0.0720728
$613$	23.6355	0.954629	0.477315	−	0.878733i	$-0.341610\pi$
$613$	23.6355	0.954629	0.477315	+	0.878733i	$0.341610\pi$
$614$	15.9869	0.645178
$615$	5.98314	0.241264
$616$	0.434746	0.0175164
$617$	38.3297	1.54309	0.771547	−	0.636172i	$-0.219483\pi$
$617$	38.3297	1.54309	0.771547	+	0.636172i	$0.219483\pi$
$618$	10.8464	0.436306
$619$	31.5020	1.26617	0.633086	−	0.774081i	$-0.281788\pi$
$619$	31.5020	1.26617	0.633086	+	0.774081i	$0.281788\pi$
$620$	3.03656	0.121951
$621$	9.04029	0.362775
$622$	−2.69727	−0.108151
$623$	0.0747790	0.00299596
$624$	−0.568158	−0.0227445
$625$	15.2667	0.610668
$626$	24.7470	0.989090
$627$	0	0
$628$	14.5871	0.582089
$629$	−11.9501	−0.476480
$630$	−0.314904	−0.0125461
$631$	9.44954	0.376180	0.188090	−	0.982152i	$-0.439770\pi$
$631$	9.44954	0.376180	0.188090	+	0.982152i	$0.439770\pi$
$632$	14.6044	0.580932
$633$	9.68696	0.385022
$634$	−31.2799	−1.24228
$635$	−12.9204	−0.512732
$636$	3.50296	0.138901
$637$	3.89421	0.154294
$638$	−3.98700	−0.157847
$639$	−2.78890	−0.110327
$640$	−0.824429	−0.0325884
$641$	−31.1671	−1.23103	−0.615513	−	0.788127i	$-0.711051\pi$
$641$	−31.1671	−1.23103	−0.615513	+	0.788127i	$0.711051\pi$
$642$	−2.86723	−0.113161
$643$	−17.9383	−0.707419	−0.353710	−	0.935355i	$-0.615080\pi$
$643$	−17.9383	−0.707419	−0.353710	+	0.935355i	$0.615080\pi$
$644$	3.45309	0.136071
$645$	9.23003	0.363432
$646$	0	0
$647$	−0.817468	−0.0321380	−0.0160690	−	0.999871i	$-0.505115\pi$
$647$	−0.817468	−0.0321380	−0.0160690	+	0.999871i	$0.505115\pi$
$648$	−1.00000	−0.0392837
$649$	−9.22552	−0.362133
$650$	−2.45462	−0.0962782
$651$	1.40687	0.0551395
$652$	3.25731	0.127566
$653$	27.2680	1.06708	0.533540	−	0.845775i	$-0.320861\pi$
$653$	27.2680	1.06708	0.533540	+	0.845775i	$0.320861\pi$
$654$	−5.93835	−0.232208
$655$	11.5478	0.451208
$656$	7.25731	0.283350
$657$	5.55638	0.216775
$658$	−3.84233	−0.149790
$659$	−35.8636	−1.39705	−0.698525	−	0.715586i	$-0.746160\pi$
$659$	−35.8636	−1.39705	−0.698525	+	0.715586i	$0.746160\pi$
$660$	−0.938350	−0.0365252
$661$	20.8341	0.810353	0.405176	−	0.914239i	$-0.367210\pi$
$661$	20.8341	0.810353	0.405176	+	0.914239i	$0.367210\pi$
$662$	−1.17442	−0.0456451
$663$	−1.01302	−0.0393423
$664$	9.57293	0.371502
$665$	0	0
$666$	6.70228	0.259708
$667$	−31.6678	−1.22618
$668$	−12.7829	−0.494584
$669$	2.58617	0.0999871
$670$	3.95586	0.152828
$671$	−13.3652	−0.515957
$672$	−0.381966	−0.0147347
$673$	10.6642	0.411074	0.205537	−	0.978649i	$-0.434106\pi$
$673$	10.6642	0.411074	0.205537	+	0.978649i	$0.434106\pi$
$674$	−13.3783	−0.515313
$675$	−4.32032	−0.166289
$676$	−12.6772	−0.487584
$677$	−29.1495	−1.12031	−0.560153	−	0.828389i	$-0.689258\pi$
$677$	−29.1495	−1.12031	−0.560153	+	0.828389i	$0.689258\pi$
$678$	−2.66791	−0.102460
$679$	6.75661	0.259295
$680$	−1.46994	−0.0563698
$681$	20.1839	0.773448
$682$	4.19218	0.160527
$683$	−32.5988	−1.24736	−0.623678	−	0.781681i	$-0.714363\pi$
$683$	−32.5988	−1.24736	−0.623678	+	0.781681i	$0.714363\pi$
$684$	0	0
$685$	12.5483	0.479447
$686$	5.29180	0.202042
$687$	19.7103	0.751994
$688$	11.1957	0.426831
$689$	−1.99024	−0.0758219
$690$	−7.45309	−0.283734
$691$	42.4850	1.61621	0.808104	−	0.589040i	$-0.200494\pi$
$691$	42.4850	1.61621	0.808104	+	0.589040i	$0.200494\pi$
$692$	12.1649	0.462442
$693$	−0.434746	−0.0165147
$694$	18.9080	0.717739
$695$	−4.43403	−0.168193
$696$	3.50296	0.132779
$697$	12.9397	0.490125
$698$	−16.9999	−0.643455
$699$	−0.450893	−0.0170543
$700$	−1.65021	−0.0623722
$701$	2.06249	0.0778994	0.0389497	−	0.999241i	$-0.487599\pi$
$701$	2.06249	0.0778994	0.0389497	+	0.999241i	$0.487599\pi$
$702$	0.568158	0.0214437
$703$	0	0
$704$	−1.13818	−0.0428968
$705$	8.29322	0.312341
$706$	4.19204	0.157770
$707$	3.58219	0.134722
$708$	8.10549	0.304623
$709$	11.3132	0.424874	0.212437	−	0.977175i	$-0.431860\pi$
$709$	11.3132	0.424874	0.212437	+	0.977175i	$0.431860\pi$
$710$	2.29926	0.0862895
$711$	−14.6044	−0.547708
$712$	−0.195774	−0.00733694
$713$	33.2975	1.24700
$714$	−0.681039	−0.0254872
$715$	0.533131	0.0199380
$716$	1.17306	0.0438394
$717$	14.8576	0.554869
$718$	−5.60034	−0.209003
$719$	25.0057	0.932555	0.466278	−	0.884638i	$-0.345595\pi$
$719$	25.0057	0.932555	0.466278	+	0.884638i	$0.345595\pi$
$720$	0.824429	0.0307247
$721$	−4.14295	−0.154292
$722$	0	0
$723$	−11.1109	−0.413219
$724$	2.68104	0.0996400
$725$	15.1339	0.562059
$726$	9.70454	0.360169
$727$	−18.2148	−0.675549	−0.337774	−	0.941227i	$-0.609674\pi$
$727$	−18.2148	−0.675549	−0.337774	+	0.941227i	$0.609674\pi$
$728$	0.217017	0.00804319
$729$	1.00000	0.0370370
$730$	−4.58085	−0.169545
$731$	19.9617	0.738309
$732$	11.7426	0.434018
$733$	−23.9919	−0.886161	−0.443080	−	0.896482i	$-0.646114\pi$
$733$	−23.9919	−0.886161	−0.443080	+	0.896482i	$0.646114\pi$
$734$	21.3238	0.787074
$735$	−5.65072	−0.208430
$736$	−9.04029	−0.333230
$737$	5.46134	0.201171
$738$	−7.25731	−0.267145
$739$	5.89421	0.216822	0.108411	−	0.994106i	$-0.465424\pi$
$739$	5.89421	0.216822	0.108411	+	0.994106i	$0.465424\pi$
$740$	−5.52556	−0.203124
$741$	0	0
$742$	−1.33801	−0.0491200
$743$	2.48965	0.0913364	0.0456682	−	0.998957i	$-0.485458\pi$
$743$	2.48965	0.0913364	0.0456682	+	0.998957i	$0.485458\pi$
$744$	−3.68323	−0.135034
$745$	−4.23358	−0.155106
$746$	15.3073	0.560438
$747$	−9.57293	−0.350255
$748$	−2.02936	−0.0742007
$749$	1.09518	0.0400172
$750$	7.68394	0.280578
$751$	1.88158	0.0686599	0.0343300	−	0.999411i	$-0.489070\pi$
$751$	1.88158	0.0686599	0.0343300	+	0.999411i	$0.489070\pi$
$752$	10.0593	0.366827
$753$	0.899921	0.0327949
$754$	−1.99024	−0.0724801
$755$	4.54615	0.165451
$756$	0.381966	0.0138920
$757$	14.4009	0.523411	0.261706	−	0.965148i	$-0.415715\pi$
$757$	14.4009	0.523411	0.261706	+	0.965148i	$0.415715\pi$
$758$	−28.6060	−1.03902
$759$	−10.2895	−0.373485
$760$	0	0
$761$	14.3892	0.521610	0.260805	−	0.965392i	$-0.416012\pi$
$761$	14.3892	0.521610	0.260805	+	0.965392i	$0.416012\pi$
$762$	15.6720	0.567735
$763$	2.26825	0.0821161
$764$	−11.7851	−0.426369
$765$	1.46994	0.0531459
$766$	28.8254	1.04150
$767$	−4.60520	−0.166284
$768$	1.00000	0.0360844
$769$	14.4493	0.521056	0.260528	−	0.965466i	$-0.416103\pi$
$769$	14.4493	0.521056	0.260528	+	0.965466i	$0.416103\pi$
$770$	0.358418	0.0129165
$771$	27.3379	0.984550
$772$	−18.9431	−0.681778
$773$	19.7734	0.711200	0.355600	−	0.934638i	$-0.384277\pi$
$773$	19.7734	0.711200	0.355600	+	0.934638i	$0.384277\pi$
$774$	−11.1957	−0.402420
$775$	−15.9127	−0.571602
$776$	−17.6890	−0.635000
$777$	−2.56004	−0.0918411
$778$	19.4589	0.697635
$779$	0	0
$780$	−0.468406	−0.0167716
$781$	3.17428	0.113585
$782$	−16.1187	−0.576403
$783$	−3.50296	−0.125186
$784$	−6.85410	−0.244789
$785$	12.0260	0.429227
$786$	−14.0070	−0.499612
$787$	−43.8788	−1.56411	−0.782055	−	0.623210i	$-0.785828\pi$
$787$	−43.8788	−1.56411	−0.782055	+	0.623210i	$0.785828\pi$
$788$	−19.4145	−0.691614
$789$	−26.3913	−0.939556
$790$	12.0403	0.428374
$791$	1.01905	0.0362333
$792$	1.13818	0.0404435
$793$	−6.67164	−0.236917
$794$	28.0321	0.994821
$795$	2.88794	0.102425
$796$	0.276292	0.00979292
$797$	−19.1788	−0.679348	−0.339674	−	0.940543i	$-0.610317\pi$
$797$	−19.1788	−0.679348	−0.339674	+	0.940543i	$0.610317\pi$
$798$	0	0
$799$	17.9356	0.634517
$800$	4.32032	0.152746
$801$	0.195774	0.00691733
$802$	23.8481	0.842107
$803$	−6.32417	−0.223175
$804$	−4.79830	−0.169223
$805$	2.84683	0.100337
$806$	2.09266	0.0737107
$807$	29.0476	1.02252
$808$	−9.37831	−0.329928
$809$	−39.1411	−1.37613	−0.688064	−	0.725650i	$-0.741539\pi$
$809$	−39.1411	−1.37613	−0.688064	+	0.725650i	$0.741539\pi$
$810$	−0.824429	−0.0289675
$811$	−18.4375	−0.647430	−0.323715	−	0.946155i	$-0.604932\pi$
$811$	−18.4375	−0.647430	−0.323715	+	0.946155i	$0.604932\pi$
$812$	−1.33801	−0.0469550
$813$	13.7865	0.483515
$814$	−7.62841	−0.267376
$815$	2.68542	0.0940663
$816$	1.78298	0.0624169
$817$	0	0
$818$	28.7032	1.00358
$819$	−0.217017	−0.00758319
$820$	5.98314	0.208940
$821$	11.8323	0.412952	0.206476	−	0.978452i	$-0.433800\pi$
$821$	11.8323	0.412952	0.206476	+	0.978452i	$0.433800\pi$
$822$	−15.2206	−0.530881
$823$	44.1516	1.53903	0.769514	−	0.638630i	$-0.220499\pi$
$823$	44.1516	1.53903	0.769514	+	0.638630i	$0.220499\pi$
$824$	10.8464	0.377852
$825$	4.91730	0.171198
$826$	−3.09602	−0.107724
$827$	−2.31684	−0.0805644	−0.0402822	−	0.999188i	$-0.512826\pi$
$827$	−2.31684	−0.0805644	−0.0402822	+	0.999188i	$0.512826\pi$
$828$	9.04029	0.314172
$829$	27.0663	0.940052	0.470026	−	0.882652i	$-0.344244\pi$
$829$	27.0663	0.940052	0.470026	+	0.882652i	$0.344244\pi$
$830$	7.89220	0.273942
$831$	10.8314	0.375737
$832$	−0.568158	−0.0196973
$833$	−12.2207	−0.423424
$834$	5.37831	0.186236
$835$	−10.5386	−0.364702
$836$	0	0
$837$	3.68323	0.127311
$838$	37.2076	1.28532
$839$	−32.3757	−1.11773	−0.558867	−	0.829257i	$-0.688764\pi$
$839$	−32.3757	−1.11773	−0.558867	+	0.829257i	$0.688764\pi$
$840$	−0.314904	−0.0108652
$841$	−16.7293	−0.576871
$842$	−14.0843	−0.485378
$843$	4.65478	0.160319
$844$	9.68696	0.333439
$845$	−10.4515	−0.359541
$846$	−10.0593	−0.345847
$847$	−3.70681	−0.127367
$848$	3.50296	0.120292
$849$	−32.5042	−1.11554
$850$	7.70305	0.264212
$851$	−60.5906	−2.07702
$852$	−2.78890	−0.0955463
$853$	35.9727	1.23168	0.615841	−	0.787870i	$-0.288816\pi$
$853$	35.9727	1.23168	0.615841	+	0.787870i	$0.288816\pi$
$854$	−4.48526	−0.153483
$855$	0	0
$856$	−2.86723	−0.0979999
$857$	30.3048	1.03519	0.517597	−	0.855625i	$-0.326827\pi$
$857$	30.3048	1.03519	0.517597	+	0.855625i	$0.326827\pi$
$858$	−0.646667	−0.0220768
$859$	−28.7141	−0.979713	−0.489857	−	0.871803i	$-0.662951\pi$
$859$	−28.7141	−0.979713	−0.489857	+	0.871803i	$0.662951\pi$
$860$	9.23003	0.314742
$861$	2.77205	0.0944711
$862$	−33.7353	−1.14903
$863$	−3.29980	−0.112326	−0.0561632	−	0.998422i	$-0.517887\pi$
$863$	−3.29980	−0.112326	−0.0561632	+	0.998422i	$0.517887\pi$
$864$	−1.00000	−0.0340207
$865$	10.0291	0.341001
$866$	−25.5868	−0.869474
$867$	−13.8210	−0.469385
$868$	1.40687	0.0477522
$869$	16.6224	0.563878
$870$	2.88794	0.0979105
$871$	2.72620	0.0923736
$872$	−5.93835	−0.201098
$873$	17.6890	0.598683
$874$	0	0
$875$	−2.93501	−0.0992213
$876$	5.55638	0.187733
$877$	26.1885	0.884321	0.442161	−	0.896936i	$-0.354212\pi$
$877$	26.1885	0.884321	0.442161	+	0.896936i	$0.354212\pi$
$878$	27.5874	0.931030
$879$	12.5373	0.422874
$880$	−0.938350	−0.0316318
$881$	−25.2371	−0.850260	−0.425130	−	0.905132i	$-0.639772\pi$
$881$	−25.2371	−0.850260	−0.425130	+	0.905132i	$0.639772\pi$
$882$	6.85410	0.230790
$883$	9.34393	0.314448	0.157224	−	0.987563i	$-0.449745\pi$
$883$	9.34393	0.314448	0.157224	+	0.987563i	$0.449745\pi$
$884$	−1.01302	−0.0340714
$885$	6.68241	0.224627
$886$	14.2327	0.478158
$887$	−34.8813	−1.17120	−0.585600	−	0.810600i	$-0.699141\pi$
$887$	−34.8813	−1.17120	−0.585600	+	0.810600i	$0.699141\pi$
$888$	6.70228	0.224914
$889$	−5.98616	−0.200769
$890$	−0.161402	−0.00541020
$891$	−1.13818	−0.0381305
$892$	2.58617	0.0865914
$893$	0	0
$894$	5.13516	0.171746
$895$	0.967108	0.0323268
$896$	−0.381966	−0.0127606
$897$	−5.13632	−0.171497
$898$	39.2146	1.30861
$899$	−12.9022	−0.430313
$900$	−4.32032	−0.144011
$901$	6.24572	0.208075
$902$	8.26013	0.275032
$903$	4.27636	0.142308
$904$	−2.66791	−0.0887334
$905$	2.21033	0.0734738
$906$	−5.51429	−0.183200
$907$	−10.6831	−0.354727	−0.177364	−	0.984145i	$-0.556757\pi$
$907$	−10.6831	−0.354727	−0.177364	+	0.984145i	$0.556757\pi$
$908$	20.1839	0.669826
$909$	9.37831	0.311059
$910$	0.178915	0.00593098
$911$	16.0725	0.532505	0.266252	−	0.963903i	$-0.414215\pi$
$911$	16.0725	0.532505	0.266252	+	0.963903i	$0.414215\pi$
$912$	0	0
$913$	10.8957	0.360596
$914$	−0.664180	−0.0219691
$915$	9.68093	0.320042
$916$	19.7103	0.651246
$917$	5.35018	0.176679
$918$	−1.78298	−0.0588472
$919$	26.6487	0.879059	0.439529	−	0.898228i	$-0.355145\pi$
$919$	26.6487	0.879059	0.439529	+	0.898228i	$0.355145\pi$
$920$	−7.45309	−0.245721
$921$	−15.9869	−0.526785
$922$	10.1602	0.334610
$923$	1.58454	0.0521557
$924$	−0.434746	−0.0143021
$925$	28.9560	0.952067
$926$	−12.7367	−0.418555
$927$	−10.8464	−0.356242
$928$	3.50296	0.114990
$929$	−3.73318	−0.122482	−0.0612408	−	0.998123i	$-0.519506\pi$
$929$	−3.73318	−0.122482	−0.0612408	+	0.998123i	$0.519506\pi$
$930$	−3.03656	−0.0995729
$931$	0	0
$932$	−0.450893	−0.0147695
$933$	2.69727	0.0883046
$934$	13.3309	0.436202
$935$	−1.67306	−0.0547150
$936$	0.568158	0.0185708
$937$	4.56348	0.149082	0.0745412	−	0.997218i	$-0.476251\pi$
$937$	4.56348	0.149082	0.0745412	+	0.997218i	$0.476251\pi$
$938$	1.83279	0.0598427
$939$	−24.7470	−0.807589
$940$	8.29322	0.270495
$941$	−8.75797	−0.285502	−0.142751	−	0.989759i	$-0.545595\pi$
$941$	−8.75797	−0.285502	−0.142751	+	0.989759i	$0.545595\pi$
$942$	−14.5871	−0.475273
$943$	65.6082	2.13650
$944$	8.10549	0.263811
$945$	0.314904	0.0102438
$946$	12.7427	0.414301
$947$	−25.0604	−0.814353	−0.407177	−	0.913349i	$-0.633487\pi$
$947$	−25.0604	−0.814353	−0.407177	+	0.913349i	$0.633487\pi$
$948$	−14.6044	−0.474329
$949$	−3.15690	−0.102477
$950$	0	0
$951$	31.2799	1.01432
$952$	−0.681039	−0.0220726
$953$	50.4469	1.63414	0.817068	−	0.576541i	$-0.195598\pi$
$953$	50.4469	1.63414	0.817068	+	0.576541i	$0.195598\pi$
$954$	−3.50296	−0.113413
$955$	−9.71595	−0.314401
$956$	14.8576	0.480531
$957$	3.98700	0.128882
$958$	5.64447	0.182365
$959$	5.81376	0.187736
$960$	0.824429	0.0266083
$961$	−17.4338	−0.562381
$962$	−3.80796	−0.122773
$963$	2.86723	0.0923952
$964$	−11.1109	−0.357858
$965$	−15.6173	−0.502738
$966$	−3.45309	−0.111101
$967$	0.817538	0.0262902	0.0131451	−	0.999914i	$-0.495816\pi$
$967$	0.817538	0.0262902	0.0131451	+	0.999914i	$0.495816\pi$
$968$	9.70454	0.311916
$969$	0	0
$970$	−14.5834	−0.468244
$971$	46.2453	1.48408	0.742041	−	0.670354i	$-0.233858\pi$
$971$	46.2453	1.48408	0.742041	+	0.670354i	$0.233858\pi$
$972$	1.00000	0.0320750
$973$	−2.05433	−0.0658588
$974$	33.6013	1.07665
$975$	2.45462	0.0786108
$976$	11.7426	0.375871
$977$	−57.6692	−1.84500	−0.922501	−	0.385995i	$-0.873858\pi$
$977$	−57.6692	−1.84500	−0.922501	+	0.385995i	$0.873858\pi$
$978$	−3.25731	−0.104157
$979$	−0.222826	−0.00712156
$980$	−5.65072	−0.180506
$981$	5.93835	0.189597
$982$	24.4268	0.779492
$983$	39.3972	1.25658	0.628288	−	0.777980i	$-0.283756\pi$
$983$	39.3972	1.25658	0.628288	+	0.777980i	$0.283756\pi$
$984$	−7.25731	−0.231355
$985$	−16.0059	−0.509991
$986$	6.24572	0.198904
$987$	3.84233	0.122303
$988$	0	0
$989$	101.212	3.21836
$990$	0.938350	0.0298227
$991$	32.3887	1.02886	0.514431	−	0.857532i	$-0.328003\pi$
$991$	32.3887	1.02886	0.514431	+	0.857532i	$0.328003\pi$
$992$	−3.68323	−0.116943
$993$	1.17442	0.0372690
$994$	1.06527	0.0337882
$995$	0.227784	0.00722122
$996$	−9.57293	−0.303330
$997$	−14.5467	−0.460698	−0.230349	−	0.973108i	$-0.573987\pi$
$997$	−14.5467	−0.460698	−0.230349	+	0.973108i	$0.573987\pi$
$998$	−8.78890	−0.278208
$999$	−6.70228	−0.212051

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2166.2.a.w.1.2	✓	4
3.2	odd	2		6498.2.a.by.1.3		4
19.18	odd	2		2166.2.a.x.1.2	yes	4
57.56	even	2		6498.2.a.bv.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2166.2.a.w.1.2	✓	4	1.1	even	1	trivial
2166.2.a.x.1.2	yes	4	19.18	odd	2
6498.2.a.bv.1.3		4	57.56	even	2
6498.2.a.by.1.3		4	3.2	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:	\( N \)	\(=\)	\( 2166 = 2 \cdot 3 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2166.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.824429 q^{5} -1.00000 q^{6} +0.381966 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.824429 q^{5} -1.00000 q^{6} +0.381966 q^{7} -1.00000 q^{8} +1.00000 q^{9} -0.824429 q^{10} -1.13818 q^{11} +1.00000 q^{12} -0.568158 q^{13} -0.381966 q^{14} +0.824429 q^{15} +1.00000 q^{16} +1.78298 q^{17} -1.00000 q^{18} +0.824429 q^{20} +0.381966 q^{21} +1.13818 q^{22} +9.04029 q^{23} -1.00000 q^{24} -4.32032 q^{25} +0.568158 q^{26} +1.00000 q^{27} +0.381966 q^{28} -3.50296 q^{29} -0.824429 q^{30} +3.68323 q^{31} -1.00000 q^{32} -1.13818 q^{33} -1.78298 q^{34} +0.314904 q^{35} +1.00000 q^{36} -6.70228 q^{37} -0.568158 q^{39} -0.824429 q^{40} +7.25731 q^{41} -0.381966 q^{42} +11.1957 q^{43} -1.13818 q^{44} +0.824429 q^{45} -9.04029 q^{46} +10.0593 q^{47} +1.00000 q^{48} -6.85410 q^{49} +4.32032 q^{50} +1.78298 q^{51} -0.568158 q^{52} +3.50296 q^{53} -1.00000 q^{54} -0.938350 q^{55} -0.381966 q^{56} +3.50296 q^{58} +8.10549 q^{59} +0.824429 q^{60} +11.7426 q^{61} -3.68323 q^{62} +0.381966 q^{63} +1.00000 q^{64} -0.468406 q^{65} +1.13818 q^{66} -4.79830 q^{67} +1.78298 q^{68} +9.04029 q^{69} -0.314904 q^{70} -2.78890 q^{71} -1.00000 q^{72} +5.55638 q^{73} +6.70228 q^{74} -4.32032 q^{75} -0.434746 q^{77} +0.568158 q^{78} -14.6044 q^{79} +0.824429 q^{80} +1.00000 q^{81} -7.25731 q^{82} -9.57293 q^{83} +0.381966 q^{84} +1.46994 q^{85} -11.1957 q^{86} -3.50296 q^{87} +1.13818 q^{88} +0.195774 q^{89} -0.824429 q^{90} -0.217017 q^{91} +9.04029 q^{92} +3.68323 q^{93} -10.0593 q^{94} -1.00000 q^{96} +17.6890 q^{97} +6.85410 q^{98} -1.13818 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} + 8 q^{5} - 4 q^{6} + 6 q^{7} - 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 + 4 * q^3 + 4 * q^4 + 8 * q^5 - 4 * q^6 + 6 * q^7 - 4 * q^8 + 4 * q^9	\( 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} + 8 q^{5} - 4 q^{6} + 6 q^{7} - 4 q^{8} + 4 q^{9} - 8 q^{10} + 12 q^{11} + 4 q^{12} + 4 q^{13} - 6 q^{14} + 8 q^{15} + 4 q^{16} + 4 q^{17} - 4 q^{18} + 8 q^{20} + 6 q^{21} - 12 q^{22} + 12 q^{23} - 4 q^{24} + 6 q^{25} - 4 q^{26} + 4 q^{27} + 6 q^{28} - 10 q^{29} - 8 q^{30} + 8 q^{31} - 4 q^{32} + 12 q^{33} - 4 q^{34} + 12 q^{35} + 4 q^{36} - 8 q^{37} + 4 q^{39} - 8 q^{40} + 8 q^{41} - 6 q^{42} - 4 q^{43} + 12 q^{44} + 8 q^{45} - 12 q^{46} + 4 q^{47} + 4 q^{48} - 14 q^{49} - 6 q^{50} + 4 q^{51} + 4 q^{52} + 10 q^{53} - 4 q^{54} + 24 q^{55} - 6 q^{56} + 10 q^{58} + 6 q^{59} + 8 q^{60} + 4 q^{61} - 8 q^{62} + 6 q^{63} + 4 q^{64} + 8 q^{65} - 12 q^{66} - 12 q^{67} + 4 q^{68} + 12 q^{69} - 12 q^{70} - 4 q^{72} - 10 q^{73} + 8 q^{74} + 6 q^{75} + 28 q^{77} - 4 q^{78} - 32 q^{79} + 8 q^{80} + 4 q^{81} - 8 q^{82} + 8 q^{83} + 6 q^{84} - 12 q^{85} + 4 q^{86} - 10 q^{87} - 12 q^{88} + 16 q^{89} - 8 q^{90} - 4 q^{91} + 12 q^{92} + 8 q^{93} - 4 q^{94} - 4 q^{96} - 8 q^{97} + 14 q^{98} + 12 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 + 4 * q^3 + 4 * q^4 + 8 * q^5 - 4 * q^6 + 6 * q^7 - 4 * q^8 + 4 * q^9 - 8 * q^10 + 12 * q^11 + 4 * q^12 + 4 * q^13 - 6 * q^14 + 8 * q^15 + 4 * q^16 + 4 * q^17 - 4 * q^18 + 8 * q^20 + 6 * q^21 - 12 * q^22 + 12 * q^23 - 4 * q^24 + 6 * q^25 - 4 * q^26 + 4 * q^27 + 6 * q^28 - 10 * q^29 - 8 * q^30 + 8 * q^31 - 4 * q^32 + 12 * q^33 - 4 * q^34 + 12 * q^35 + 4 * q^36 - 8 * q^37 + 4 * q^39 - 8 * q^40 + 8 * q^41 - 6 * q^42 - 4 * q^43 + 12 * q^44 + 8 * q^45 - 12 * q^46 + 4 * q^47 + 4 * q^48 - 14 * q^49 - 6 * q^50 + 4 * q^51 + 4 * q^52 + 10 * q^53 - 4 * q^54 + 24 * q^55 - 6 * q^56 + 10 * q^58 + 6 * q^59 + 8 * q^60 + 4 * q^61 - 8 * q^62 + 6 * q^63 + 4 * q^64 + 8 * q^65 - 12 * q^66 - 12 * q^67 + 4 * q^68 + 12 * q^69 - 12 * q^70 - 4 * q^72 - 10 * q^73 + 8 * q^74 + 6 * q^75 + 28 * q^77 - 4 * q^78 - 32 * q^79 + 8 * q^80 + 4 * q^81 - 8 * q^82 + 8 * q^83 + 6 * q^84 - 12 * q^85 + 4 * q^86 - 10 * q^87 - 12 * q^88 + 16 * q^89 - 8 * q^90 - 4 * q^91 + 12 * q^92 + 8 * q^93 - 4 * q^94 - 4 * q^96 - 8 * q^97 + 14 * q^98 + 12 * q^99

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