LMFDB - Embedded newform 2006.2.a.u.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2006,2,Mod(1,2006)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2006, 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("2006.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2006 = 2 \cdot 17 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2006.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:	$16.0179906455$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - x^{8} - 23x^{7} + 18x^{6} + 185x^{5} - 91x^{4} - 615x^{3} + 126x^{2} + 668x - 44 $ x^9 - x^8 - 23x^7 + 18x^6 + 185x^5 - 91x^4 - 615x^3 + 126x^2 + 668*x - 44
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$2.73114$ of defining polynomial
Character	$\chi$	$=$	2006.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.73114 q^{3} +1.00000 q^{4} -1.91728 q^{5} +2.73114 q^{6} -0.139698 q^{7} -1.00000 q^{8} +4.45914 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.73114 q^{3} +1.00000 q^{4} -1.91728 q^{5} +2.73114 q^{6} -0.139698 q^{7} -1.00000 q^{8} +4.45914 q^{9} +1.91728 q^{10} +1.66073 q^{11} -2.73114 q^{12} -2.83785 q^{13} +0.139698 q^{14} +5.23638 q^{15} +1.00000 q^{16} +1.00000 q^{17} -4.45914 q^{18} +1.07176 q^{19} -1.91728 q^{20} +0.381536 q^{21} -1.66073 q^{22} -7.76009 q^{23} +2.73114 q^{24} -1.32402 q^{25} +2.83785 q^{26} -3.98513 q^{27} -0.139698 q^{28} +1.98704 q^{29} -5.23638 q^{30} +0.397204 q^{31} -1.00000 q^{32} -4.53569 q^{33} -1.00000 q^{34} +0.267841 q^{35} +4.45914 q^{36} +8.25202 q^{37} -1.07176 q^{38} +7.75057 q^{39} +1.91728 q^{40} -8.57605 q^{41} -0.381536 q^{42} -5.49940 q^{43} +1.66073 q^{44} -8.54945 q^{45} +7.76009 q^{46} -6.84632 q^{47} -2.73114 q^{48} -6.98048 q^{49} +1.32402 q^{50} -2.73114 q^{51} -2.83785 q^{52} -11.4134 q^{53} +3.98513 q^{54} -3.18409 q^{55} +0.139698 q^{56} -2.92714 q^{57} -1.98704 q^{58} -1.00000 q^{59} +5.23638 q^{60} +3.13949 q^{61} -0.397204 q^{62} -0.622935 q^{63} +1.00000 q^{64} +5.44096 q^{65} +4.53569 q^{66} -7.86135 q^{67} +1.00000 q^{68} +21.1939 q^{69} -0.267841 q^{70} +0.988179 q^{71} -4.45914 q^{72} +6.24131 q^{73} -8.25202 q^{74} +3.61610 q^{75} +1.07176 q^{76} -0.232001 q^{77} -7.75057 q^{78} +5.29320 q^{79} -1.91728 q^{80} -2.49346 q^{81} +8.57605 q^{82} +11.7775 q^{83} +0.381536 q^{84} -1.91728 q^{85} +5.49940 q^{86} -5.42688 q^{87} -1.66073 q^{88} +18.4316 q^{89} +8.54945 q^{90} +0.396443 q^{91} -7.76009 q^{92} -1.08482 q^{93} +6.84632 q^{94} -2.05487 q^{95} +2.73114 q^{96} +12.1042 q^{97} +6.98048 q^{98} +7.40543 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 9 q^{2} - q^{3} + 9 q^{4} + 7 q^{5} + q^{6} - 9 q^{8} + 20 q^{9}+O(q^{10}) $ 9 * q - 9 * q^2 - q^3 + 9 * q^4 + 7 * q^5 + q^6 - 9 * q^8 + 20 * q^9	\( 9 q - 9 q^{2} - q^{3} + 9 q^{4} + 7 q^{5} + q^{6} - 9 q^{8} + 20 q^{9} - 7 q^{10} + 5 q^{11} - q^{12} + 25 q^{13} - 5 q^{15} + 9 q^{16} + 9 q^{17} - 20 q^{18} + 14 q^{19} + 7 q^{20} - 7 q^{21} - 5 q^{22} + 2 q^{23} + q^{24} + 20 q^{25} - 25 q^{26} - 10 q^{27} + 18 q^{29} + 5 q^{30} + 6 q^{31} - 9 q^{32} - 9 q^{33} - 9 q^{34} - 17 q^{35} + 20 q^{36} + 11 q^{37} - 14 q^{38} - 8 q^{39} - 7 q^{40} + 18 q^{41} + 7 q^{42} - 10 q^{43} + 5 q^{44} + 27 q^{45} - 2 q^{46} - 20 q^{47} - q^{48} + 13 q^{49} - 20 q^{50} - q^{51} + 25 q^{52} - 7 q^{53} + 10 q^{54} + 29 q^{55} + 17 q^{57} - 18 q^{58} - 9 q^{59} - 5 q^{60} + 30 q^{61} - 6 q^{62} - 47 q^{63} + 9 q^{64} + 8 q^{65} + 9 q^{66} + 6 q^{67} + 9 q^{68} + 20 q^{69} + 17 q^{70} + 30 q^{71} - 20 q^{72} - 11 q^{74} - 7 q^{75} + 14 q^{76} - 3 q^{77} + 8 q^{78} + 29 q^{79} + 7 q^{80} - 3 q^{81} - 18 q^{82} + 9 q^{83} - 7 q^{84} + 7 q^{85} + 10 q^{86} + 44 q^{87} - 5 q^{88} + 8 q^{89} - 27 q^{90} + 13 q^{91} + 2 q^{92} + 7 q^{93} + 20 q^{94} + 27 q^{95} + q^{96} - 13 q^{97} - 13 q^{98} - 19 q^{99}+O(q^{100}) \) 9 * q - 9 * q^2 - q^3 + 9 * q^4 + 7 * q^5 + q^6 - 9 * q^8 + 20 * q^9 - 7 * q^10 + 5 * q^11 - q^12 + 25 * q^13 - 5 * q^15 + 9 * q^16 + 9 * q^17 - 20 * q^18 + 14 * q^19 + 7 * q^20 - 7 * q^21 - 5 * q^22 + 2 * q^23 + q^24 + 20 * q^25 - 25 * q^26 - 10 * q^27 + 18 * q^29 + 5 * q^30 + 6 * q^31 - 9 * q^32 - 9 * q^33 - 9 * q^34 - 17 * q^35 + 20 * q^36 + 11 * q^37 - 14 * q^38 - 8 * q^39 - 7 * q^40 + 18 * q^41 + 7 * q^42 - 10 * q^43 + 5 * q^44 + 27 * q^45 - 2 * q^46 - 20 * q^47 - q^48 + 13 * q^49 - 20 * q^50 - q^51 + 25 * q^52 - 7 * q^53 + 10 * q^54 + 29 * q^55 + 17 * q^57 - 18 * q^58 - 9 * q^59 - 5 * q^60 + 30 * q^61 - 6 * q^62 - 47 * q^63 + 9 * q^64 + 8 * q^65 + 9 * q^66 + 6 * q^67 + 9 * q^68 + 20 * q^69 + 17 * q^70 + 30 * q^71 - 20 * q^72 - 11 * q^74 - 7 * q^75 + 14 * q^76 - 3 * q^77 + 8 * q^78 + 29 * q^79 + 7 * q^80 - 3 * q^81 - 18 * q^82 + 9 * q^83 - 7 * q^84 + 7 * q^85 + 10 * q^86 + 44 * q^87 - 5 * q^88 + 8 * q^89 - 27 * q^90 + 13 * q^91 + 2 * q^92 + 7 * q^93 + 20 * q^94 + 27 * q^95 + q^96 - 13 * q^97 - 13 * q^98 - 19 * 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
$3$	−2.73114	−1.57683	−0.788413	−	0.615146i	$-0.789097\pi$
$3$	−2.73114	−1.57683	−0.788413	+	0.615146i	$0.789097\pi$
$4$	1.00000	0.500000
$5$	−1.91728	−0.857435	−0.428718	−	0.903439i	$-0.641034\pi$
$5$	−1.91728	−0.857435	−0.428718	+	0.903439i	$0.641034\pi$
$6$	2.73114	1.11498
$7$	−0.139698	−0.0528010	−0.0264005	−	0.999651i	$-0.508405\pi$
$7$	−0.139698	−0.0528010	−0.0264005	+	0.999651i	$0.508405\pi$
$8$	−1.00000	−0.353553
$9$	4.45914	1.48638
$10$	1.91728	0.606298
$11$	1.66073	0.500728	0.250364	−	0.968152i	$-0.419450\pi$
$11$	1.66073	0.500728	0.250364	+	0.968152i	$0.419450\pi$
$12$	−2.73114	−0.788413
$13$	−2.83785	−0.787077	−0.393539	−	0.919308i	$-0.628749\pi$
$13$	−2.83785	−0.787077	−0.393539	+	0.919308i	$0.628749\pi$
$14$	0.139698	0.0373359
$15$	5.23638	1.35203
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−4.45914	−1.05103
$19$	1.07176	0.245879	0.122940	−	0.992414i	$-0.460768\pi$
$19$	1.07176	0.245879	0.122940	+	0.992414i	$0.460768\pi$
$20$	−1.91728	−0.428718
$21$	0.381536	0.0832580
$22$	−1.66073	−0.354068
$23$	−7.76009	−1.61809	−0.809045	−	0.587746i	$-0.800015\pi$
$23$	−7.76009	−1.61809	−0.809045	+	0.587746i	$0.800015\pi$
$24$	2.73114	0.557492
$25$	−1.32402	−0.264805
$26$	2.83785	0.556548
$27$	−3.98513	−0.766939
$28$	−0.139698	−0.0264005
$29$	1.98704	0.368983	0.184492	−	0.982834i	$-0.440936\pi$
$29$	1.98704	0.368983	0.184492	+	0.982834i	$0.440936\pi$
$30$	−5.23638	−0.956027
$31$	0.397204	0.0713399	0.0356700	−	0.999364i	$-0.488643\pi$
$31$	0.397204	0.0713399	0.0356700	+	0.999364i	$0.488643\pi$
$32$	−1.00000	−0.176777
$33$	−4.53569	−0.789562
$34$	−1.00000	−0.171499
$35$	0.267841	0.0452734
$36$	4.45914	0.743191
$37$	8.25202	1.35662	0.678312	−	0.734774i	$-0.262712\pi$
$37$	8.25202	1.35662	0.678312	+	0.734774i	$0.262712\pi$
$38$	−1.07176	−0.173863
$39$	7.75057	1.24108
$40$	1.91728	0.303149
$41$	−8.57605	−1.33935	−0.669677	−	0.742653i	$-0.733567\pi$
$41$	−8.57605	−1.33935	−0.669677	+	0.742653i	$0.733567\pi$
$42$	−0.381536	−0.0588723
$43$	−5.49940	−0.838650	−0.419325	−	0.907836i	$-0.637733\pi$
$43$	−5.49940	−0.838650	−0.419325	+	0.907836i	$0.637733\pi$
$44$	1.66073	0.250364
$45$	−8.54945	−1.27448
$46$	7.76009	1.14416
$47$	−6.84632	−0.998639	−0.499319	−	0.866418i	$-0.666417\pi$
$47$	−6.84632	−0.998639	−0.499319	+	0.866418i	$0.666417\pi$
$48$	−2.73114	−0.394207
$49$	−6.98048	−0.997212
$50$	1.32402	0.187245
$51$	−2.73114	−0.382437
$52$	−2.83785	−0.393539
$53$	−11.4134	−1.56775	−0.783874	−	0.620920i	$-0.786759\pi$
$53$	−11.4134	−1.56775	−0.783874	+	0.620920i	$0.786759\pi$
$54$	3.98513	0.542308
$55$	−3.18409	−0.429342
$56$	0.139698	0.0186680
$57$	−2.92714	−0.387709
$58$	−1.98704	−0.260911
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	5.23638	0.676013
$61$	3.13949	0.401971	0.200986	−	0.979594i	$-0.435586\pi$
$61$	3.13949	0.401971	0.200986	+	0.979594i	$0.435586\pi$
$62$	−0.397204	−0.0504450
$63$	−0.622935	−0.0784824
$64$	1.00000	0.125000
$65$	5.44096	0.674868
$66$	4.53569	0.558305
$67$	−7.86135	−0.960417	−0.480208	−	0.877154i	$-0.659439\pi$
$67$	−7.86135	−0.960417	−0.480208	+	0.877154i	$0.659439\pi$
$68$	1.00000	0.121268
$69$	21.1939	2.55145
$70$	−0.267841	−0.0320132
$71$	0.988179	0.117275	0.0586376	−	0.998279i	$-0.481324\pi$
$71$	0.988179	0.117275	0.0586376	+	0.998279i	$0.481324\pi$
$72$	−4.45914	−0.525515
$73$	6.24131	0.730490	0.365245	−	0.930911i	$-0.380985\pi$
$73$	6.24131	0.730490	0.365245	+	0.930911i	$0.380985\pi$
$74$	−8.25202	−0.959278
$75$	3.61610	0.417551
$76$	1.07176	0.122940
$77$	−0.232001	−0.0264390
$78$	−7.75057	−0.877579
$79$	5.29320	0.595531	0.297766	−	0.954639i	$-0.403759\pi$
$79$	5.29320	0.595531	0.297766	+	0.954639i	$0.403759\pi$
$80$	−1.91728	−0.214359
$81$	−2.49346	−0.277052
$82$	8.57605	0.947066
$83$	11.7775	1.29274	0.646372	−	0.763022i	$-0.276285\pi$
$83$	11.7775	1.29274	0.646372	+	0.763022i	$0.276285\pi$
$84$	0.381536	0.0416290
$85$	−1.91728	−0.207959
$86$	5.49940	0.593015
$87$	−5.42688	−0.581823
$88$	−1.66073	−0.177034
$89$	18.4316	1.95374	0.976870	−	0.213833i	$-0.0685947\pi$
$89$	18.4316	1.95374	0.976870	+	0.213833i	$0.0685947\pi$
$90$	8.54945	0.901191
$91$	0.396443	0.0415585
$92$	−7.76009	−0.809045
$93$	−1.08482	−0.112491
$94$	6.84632	0.706144
$95$	−2.05487	−0.210825
$96$	2.73114	0.278746
$97$	12.1042	1.22900	0.614500	−	0.788917i	$-0.289358\pi$
$97$	12.1042	1.22900	0.614500	+	0.788917i	$0.289358\pi$
$98$	6.98048	0.705135
$99$	7.40543	0.744273
$100$	−1.32402	−0.132402
$101$	7.73557	0.769718	0.384859	−	0.922975i	$-0.374250\pi$
$101$	7.73557	0.769718	0.384859	+	0.922975i	$0.374250\pi$
$102$	2.73114	0.270423
$103$	−5.40471	−0.532542	−0.266271	−	0.963898i	$-0.585792\pi$
$103$	−5.40471	−0.532542	−0.266271	+	0.963898i	$0.585792\pi$
$104$	2.83785	0.278274
$105$	−0.731513	−0.0713884
$106$	11.4134	1.10857
$107$	−12.3032	−1.18940	−0.594699	−	0.803949i	$-0.702729\pi$
$107$	−12.3032	−1.18940	−0.594699	+	0.803949i	$0.702729\pi$
$108$	−3.98513	−0.383470
$109$	11.0894	1.06217	0.531084	−	0.847319i	$-0.321785\pi$
$109$	11.0894	1.06217	0.531084	+	0.847319i	$0.321785\pi$
$110$	3.18409	0.303591
$111$	−22.5375	−2.13916
$112$	−0.139698	−0.0132003
$113$	−9.67333	−0.909991	−0.454995	−	0.890494i	$-0.650359\pi$
$113$	−9.67333	−0.909991	−0.454995	+	0.890494i	$0.650359\pi$
$114$	2.92714	0.274151
$115$	14.8783	1.38741
$116$	1.98704	0.184492
$117$	−12.6544	−1.16990
$118$	1.00000	0.0920575
$119$	−0.139698	−0.0128061
$120$	−5.23638	−0.478014
$121$	−8.24198	−0.749271
$122$	−3.13949	−0.284236
$123$	23.4224	2.11193
$124$	0.397204	0.0356700
$125$	12.1249	1.08449
$126$	0.622935	0.0554955
$127$	−15.8625	−1.40757	−0.703786	−	0.710412i	$-0.748509\pi$
$127$	−15.8625	−1.40757	−0.703786	+	0.710412i	$0.748509\pi$
$128$	−1.00000	−0.0883883
$129$	15.0196	1.32241
$130$	−5.44096	−0.477204
$131$	−14.4941	−1.26636	−0.633179	−	0.774005i	$-0.718250\pi$
$131$	−14.4941	−1.26636	−0.633179	+	0.774005i	$0.718250\pi$
$132$	−4.53569	−0.394781
$133$	−0.149723	−0.0129827
$134$	7.86135	0.679117
$135$	7.64063	0.657601
$136$	−1.00000	−0.0857493
$137$	18.6688	1.59498	0.797490	−	0.603333i	$-0.206161\pi$
$137$	18.6688	1.59498	0.797490	+	0.603333i	$0.206161\pi$
$138$	−21.1939	−1.80415
$139$	22.0772	1.87257	0.936283	−	0.351248i	$-0.114242\pi$
$139$	22.0772	1.87257	0.936283	+	0.351248i	$0.114242\pi$
$140$	0.267841	0.0226367
$141$	18.6983	1.57468
$142$	−0.988179	−0.0829261
$143$	−4.71289	−0.394112
$144$	4.45914	0.371595
$145$	−3.80971	−0.316379
$146$	−6.24131	−0.516534
$147$	19.0647	1.57243
$148$	8.25202	0.678312
$149$	−12.0823	−0.989822	−0.494911	−	0.868944i	$-0.664799\pi$
$149$	−12.0823	−0.989822	−0.494911	+	0.868944i	$0.664799\pi$
$150$	−3.61610	−0.295253
$151$	1.76318	0.143486	0.0717429	−	0.997423i	$-0.477144\pi$
$151$	1.76318	0.143486	0.0717429	+	0.997423i	$0.477144\pi$
$152$	−1.07176	−0.0869314
$153$	4.45914	0.360500
$154$	0.232001	0.0186952
$155$	−0.761553	−0.0611694
$156$	7.75057	0.620542
$157$	18.9379	1.51141	0.755703	−	0.654914i	$-0.227295\pi$
$157$	18.9379	1.51141	0.755703	+	0.654914i	$0.227295\pi$
$158$	−5.29320	−0.421104
$159$	31.1716	2.47207
$160$	1.91728	0.151575
$161$	1.08407	0.0854368
$162$	2.49346	0.195905
$163$	20.3376	1.59296	0.796481	−	0.604664i	$-0.206693\pi$
$163$	20.3376	1.59296	0.796481	+	0.604664i	$0.206693\pi$
$164$	−8.57605	−0.669677
$165$	8.69620	0.676998
$166$	−11.7775	−0.914108
$167$	16.0986	1.24574	0.622872	−	0.782324i	$-0.285966\pi$
$167$	16.0986	1.24574	0.622872	+	0.782324i	$0.285966\pi$
$168$	−0.381536	−0.0294362
$169$	−4.94662	−0.380509
$170$	1.91728	0.147049
$171$	4.77914	0.365470
$172$	−5.49940	−0.419325
$173$	4.33252	0.329395	0.164698	−	0.986344i	$-0.447335\pi$
$173$	4.33252	0.329395	0.164698	+	0.986344i	$0.447335\pi$
$174$	5.42688	0.411411
$175$	0.184964	0.0139819
$176$	1.66073	0.125182
$177$	2.73114	0.205285
$178$	−18.4316	−1.38150
$179$	−11.8314	−0.884320	−0.442160	−	0.896936i	$-0.645788\pi$
$179$	−11.8314	−0.884320	−0.442160	+	0.896936i	$0.645788\pi$
$180$	−8.54945	−0.637238
$181$	15.3503	1.14098	0.570490	−	0.821304i	$-0.306753\pi$
$181$	15.3503	1.14098	0.570490	+	0.821304i	$0.306753\pi$
$182$	−0.396443	−0.0293863
$183$	−8.57441	−0.633838
$184$	7.76009	0.572081
$185$	−15.8215	−1.16322
$186$	1.08482	0.0795429
$187$	1.66073	0.121444
$188$	−6.84632	−0.499319
$189$	0.556716	0.0404952
$190$	2.05487	0.149076
$191$	11.0391	0.798758	0.399379	−	0.916786i	$-0.369226\pi$
$191$	11.0391	0.798758	0.399379	+	0.916786i	$0.369226\pi$
$192$	−2.73114	−0.197103
$193$	0.689470	0.0496291	0.0248146	−	0.999692i	$-0.492100\pi$
$193$	0.689470	0.0496291	0.0248146	+	0.999692i	$0.492100\pi$
$194$	−12.1042	−0.869034
$195$	−14.8600	−1.06415
$196$	−6.98048	−0.498606
$197$	11.3698	0.810068	0.405034	−	0.914302i	$-0.367260\pi$
$197$	11.3698	0.810068	0.405034	+	0.914302i	$0.367260\pi$
$198$	−7.40543	−0.526281
$199$	−3.10050	−0.219789	−0.109894	−	0.993943i	$-0.535051\pi$
$199$	−3.10050	−0.219789	−0.109894	+	0.993943i	$0.535051\pi$
$200$	1.32402	0.0936225
$201$	21.4705	1.51441
$202$	−7.73557	−0.544273
$203$	−0.277586	−0.0194827
$204$	−2.73114	−0.191218
$205$	16.4427	1.14841
$206$	5.40471	0.376564
$207$	−34.6034	−2.40510
$208$	−2.83785	−0.196769
$209$	1.77991	0.123119
$210$	0.731513	0.0504792
$211$	6.97843	0.480415	0.240208	−	0.970722i	$-0.422785\pi$
$211$	6.97843	0.480415	0.240208	+	0.970722i	$0.422785\pi$
$212$	−11.4134	−0.783874
$213$	−2.69886	−0.184923
$214$	12.3032	0.841031
$215$	10.5439	0.719089
$216$	3.98513	0.271154
$217$	−0.0554887	−0.00376682
$218$	−11.0894	−0.751066
$219$	−17.0459	−1.15186
$220$	−3.18409	−0.214671
$221$	−2.83785	−0.190894
$222$	22.5375	1.51262
$223$	17.1540	1.14872	0.574360	−	0.818603i	$-0.305251\pi$
$223$	17.1540	1.14872	0.574360	+	0.818603i	$0.305251\pi$
$224$	0.139698	0.00933399
$225$	−5.90401	−0.393601
$226$	9.67333	0.643461
$227$	−11.8506	−0.786553	−0.393277	−	0.919420i	$-0.628659\pi$
$227$	−11.8506	−0.786553	−0.393277	+	0.919420i	$0.628659\pi$
$228$	−2.92714	−0.193854
$229$	21.5465	1.42384	0.711918	−	0.702263i	$-0.247827\pi$
$229$	21.5465	1.42384	0.711918	+	0.702263i	$0.247827\pi$
$230$	−14.8783	−0.981046
$231$	0.633628	0.0416897
$232$	−1.98704	−0.130455
$233$	−9.26474	−0.606954	−0.303477	−	0.952839i	$-0.598147\pi$
$233$	−9.26474	−0.606954	−0.303477	+	0.952839i	$0.598147\pi$
$234$	12.6544	0.827242
$235$	13.1263	0.856268
$236$	−1.00000	−0.0650945
$237$	−14.4565	−0.939049
$238$	0.139698	0.00905530
$239$	−17.0094	−1.10025	−0.550123	−	0.835084i	$-0.685419\pi$
$239$	−17.0094	−1.10025	−0.550123	+	0.835084i	$0.685419\pi$
$240$	5.23638	0.338007
$241$	8.51980	0.548809	0.274404	−	0.961614i	$-0.411519\pi$
$241$	8.51980	0.548809	0.274404	+	0.961614i	$0.411519\pi$
$242$	8.24198	0.529815
$243$	18.7654	1.20380
$244$	3.13949	0.200986
$245$	13.3836	0.855045
$246$	−23.4224	−1.49336
$247$	−3.04150	−0.193526
$248$	−0.397204	−0.0252225
$249$	−32.1659	−2.03843
$250$	−12.1249	−0.766849
$251$	−18.3118	−1.15583	−0.577915	−	0.816097i	$-0.696134\pi$
$251$	−18.3118	−1.15583	−0.577915	+	0.816097i	$0.696134\pi$
$252$	−0.622935	−0.0392412
$253$	−12.8874	−0.810224
$254$	15.8625	0.995304
$255$	5.23638	0.327915
$256$	1.00000	0.0625000
$257$	−3.20662	−0.200023	−0.100012	−	0.994986i	$-0.531888\pi$
$257$	−3.20662	−0.200023	−0.100012	+	0.994986i	$0.531888\pi$
$258$	−15.0196	−0.935082
$259$	−1.15279	−0.0716311
$260$	5.44096	0.337434
$261$	8.86048	0.548450
$262$	14.4941	0.895450
$263$	−5.69419	−0.351119	−0.175559	−	0.984469i	$-0.556173\pi$
$263$	−5.69419	−0.351119	−0.175559	+	0.984469i	$0.556173\pi$
$264$	4.53569	0.279152
$265$	21.8827	1.34424
$266$	0.149723	0.00918013
$267$	−50.3392	−3.08071
$268$	−7.86135	−0.480208
$269$	17.7223	1.08055	0.540273	−	0.841490i	$-0.318321\pi$
$269$	17.7223	1.08055	0.540273	+	0.841490i	$0.318321\pi$
$270$	−7.64063	−0.464994
$271$	22.7446	1.38163	0.690817	−	0.723029i	$-0.257251\pi$
$271$	22.7446	1.38163	0.690817	+	0.723029i	$0.257251\pi$
$272$	1.00000	0.0606339
$273$	−1.08274	−0.0655305
$274$	−18.6688	−1.12782
$275$	−2.19884	−0.132595
$276$	21.1939	1.27572
$277$	23.3855	1.40510	0.702550	−	0.711635i	$-0.252045\pi$
$277$	23.3855	1.40510	0.702550	+	0.711635i	$0.252045\pi$
$278$	−22.0772	−1.32410
$279$	1.77119	0.106038
$280$	−0.267841	−0.0160066
$281$	2.59351	0.154716	0.0773578	−	0.997003i	$-0.475352\pi$
$281$	2.59351	0.154716	0.0773578	+	0.997003i	$0.475352\pi$
$282$	−18.6983	−1.11347
$283$	−22.5186	−1.33859	−0.669297	−	0.742995i	$-0.733405\pi$
$283$	−22.5186	−1.33859	−0.669297	+	0.742995i	$0.733405\pi$
$284$	0.988179	0.0586376
$285$	5.61215	0.332435
$286$	4.71289	0.278679
$287$	1.19806	0.0707192
$288$	−4.45914	−0.262758
$289$	1.00000	0.0588235
$290$	3.80971	0.223714
$291$	−33.0584	−1.93792
$292$	6.24131	0.365245
$293$	12.2541	0.715894	0.357947	−	0.933742i	$-0.383477\pi$
$293$	12.2541	0.715894	0.357947	+	0.933742i	$0.383477\pi$
$294$	−19.0647	−1.11188
$295$	1.91728	0.111629
$296$	−8.25202	−0.479639
$297$	−6.61822	−0.384028
$298$	12.0823	0.699910
$299$	22.0220	1.27356
$300$	3.61610	0.208775
$301$	0.768257	0.0442816
$302$	−1.76318	−0.101460
$303$	−21.1270	−1.21371
$304$	1.07176	0.0614698
$305$	−6.01930	−0.344664
$306$	−4.45914	−0.254912
$307$	3.95454	0.225698	0.112849	−	0.993612i	$-0.464002\pi$
$307$	3.95454	0.225698	0.112849	+	0.993612i	$0.464002\pi$
$308$	−0.232001	−0.0132195
$309$	14.7610	0.839726
$310$	0.761553	0.0432533
$311$	−0.158635	−0.00899539	−0.00449769	−	0.999990i	$-0.501432\pi$
$311$	−0.158635	−0.00899539	−0.00449769	+	0.999990i	$0.501432\pi$
$312$	−7.75057	−0.438790
$313$	−19.1532	−1.08260	−0.541301	−	0.840829i	$-0.682068\pi$
$313$	−19.1532	−1.08260	−0.541301	+	0.840829i	$0.682068\pi$
$314$	−18.9379	−1.06873
$315$	1.19434	0.0672936
$316$	5.29320	0.297766
$317$	−18.0779	−1.01535	−0.507677	−	0.861547i	$-0.669496\pi$
$317$	−18.0779	−1.01535	−0.507677	+	0.861547i	$0.669496\pi$
$318$	−31.1716	−1.74802
$319$	3.29993	0.184760
$320$	−1.91728	−0.107179
$321$	33.6019	1.87547
$322$	−1.08407	−0.0604129
$323$	1.07176	0.0596344
$324$	−2.49346	−0.138526
$325$	3.75738	0.208422
$326$	−20.3376	−1.12639
$327$	−30.2866	−1.67485
$328$	8.57605	0.473533
$329$	0.956420	0.0527291
$330$	−8.69620	−0.478710
$331$	−6.02440	−0.331131	−0.165566	−	0.986199i	$-0.552945\pi$
$331$	−6.02440	−0.331131	−0.165566	+	0.986199i	$0.552945\pi$
$332$	11.7775	0.646372
$333$	36.7970	2.01646
$334$	−16.0986	−0.880874
$335$	15.0724	0.823496
$336$	0.381536	0.0208145
$337$	5.15756	0.280950	0.140475	−	0.990084i	$-0.455137\pi$
$337$	5.15756	0.280950	0.140475	+	0.990084i	$0.455137\pi$
$338$	4.94662	0.269061
$339$	26.4193	1.43490
$340$	−1.91728	−0.103979
$341$	0.659648	0.0357219
$342$	−4.77914	−0.258426
$343$	1.95305	0.105455
$344$	5.49940	0.296508
$345$	−40.6348	−2.18770
$346$	−4.33252	−0.232918
$347$	−11.1501	−0.598570	−0.299285	−	0.954164i	$-0.596748\pi$
$347$	−11.1501	−0.598570	−0.299285	+	0.954164i	$0.596748\pi$
$348$	−5.42688	−0.290911
$349$	7.12571	0.381430	0.190715	−	0.981645i	$-0.438919\pi$
$349$	7.12571	0.381430	0.190715	+	0.981645i	$0.438919\pi$
$350$	−0.184964	−0.00988673
$351$	11.3092	0.603641
$352$	−1.66073	−0.0885171
$353$	0.838103	0.0446077	0.0223039	−	0.999751i	$-0.492900\pi$
$353$	0.838103	0.0446077	0.0223039	+	0.999751i	$0.492900\pi$
$354$	−2.73114	−0.145159
$355$	−1.89462	−0.100556
$356$	18.4316	0.976870
$357$	0.381536	0.0201930
$358$	11.8314	0.625309
$359$	−23.2049	−1.22471	−0.612355	−	0.790583i	$-0.709777\pi$
$359$	−23.2049	−1.22471	−0.612355	+	0.790583i	$0.709777\pi$
$360$	8.54945	0.450595
$361$	−17.8513	−0.939543
$362$	−15.3503	−0.806795
$363$	22.5100	1.18147
$364$	0.396443	0.0207792
$365$	−11.9664	−0.626348
$366$	8.57441	0.448191
$367$	7.98775	0.416957	0.208479	−	0.978027i	$-0.433149\pi$
$367$	7.98775	0.416957	0.208479	+	0.978027i	$0.433149\pi$
$368$	−7.76009	−0.404523
$369$	−38.2418	−1.99079
$370$	15.8215	0.822519
$371$	1.59443	0.0827787
$372$	−1.08482	−0.0562454
$373$	8.65514	0.448146	0.224073	−	0.974572i	$-0.428065\pi$
$373$	8.65514	0.448146	0.224073	+	0.974572i	$0.428065\pi$
$374$	−1.66073	−0.0858742
$375$	−33.1150	−1.71005
$376$	6.84632	0.353072
$377$	−5.63891	−0.290418
$378$	−0.556716	−0.0286344
$379$	−8.78908	−0.451465	−0.225732	−	0.974189i	$-0.572477\pi$
$379$	−8.78908	−0.451465	−0.225732	+	0.974189i	$0.572477\pi$
$380$	−2.05487	−0.105413
$381$	43.3228	2.21950
$382$	−11.0391	−0.564807
$383$	−32.7606	−1.67399	−0.836994	−	0.547212i	$-0.815689\pi$
$383$	−32.7606	−1.67399	−0.836994	+	0.547212i	$0.815689\pi$
$384$	2.73114	0.139373
$385$	0.444812	0.0226697
$386$	−0.689470	−0.0350931
$387$	−24.5226	−1.24655
$388$	12.1042	0.614500
$389$	37.2255	1.88741	0.943704	−	0.330792i	$-0.107316\pi$
$389$	37.2255	1.88741	0.943704	+	0.330792i	$0.107316\pi$
$390$	14.8600	0.752468
$391$	−7.76009	−0.392445
$392$	6.98048	0.352568
$393$	39.5856	1.99683
$394$	−11.3698	−0.572804
$395$	−10.1486	−0.510630
$396$	7.40543	0.372137
$397$	3.89173	0.195320	0.0976602	−	0.995220i	$-0.468864\pi$
$397$	3.89173	0.195320	0.0976602	+	0.995220i	$0.468864\pi$
$398$	3.10050	0.155414
$399$	0.408916	0.0204714
$400$	−1.32402	−0.0662011
$401$	1.09002	0.0544330	0.0272165	−	0.999630i	$-0.491336\pi$
$401$	1.09002	0.0544330	0.0272165	+	0.999630i	$0.491336\pi$
$402$	−21.4705	−1.07085
$403$	−1.12720	−0.0561501
$404$	7.73557	0.384859
$405$	4.78068	0.237554
$406$	0.277586	0.0137763
$407$	13.7044	0.679300
$408$	2.73114	0.135212
$409$	9.47425	0.468471	0.234236	−	0.972180i	$-0.424741\pi$
$409$	9.47425	0.468471	0.234236	+	0.972180i	$0.424741\pi$
$410$	−16.4427	−0.812048
$411$	−50.9870	−2.51501
$412$	−5.40471	−0.266271
$413$	0.139698	0.00687410
$414$	34.6034	1.70066
$415$	−22.5807	−1.10844
$416$	2.83785	0.139137
$417$	−60.2960	−2.95271
$418$	−1.77991	−0.0870580
$419$	15.6928	0.766645	0.383322	−	0.923615i	$-0.374780\pi$
$419$	15.6928	0.766645	0.383322	+	0.923615i	$0.374780\pi$
$420$	−0.731513	−0.0356942
$421$	34.2483	1.66916	0.834580	−	0.550887i	$-0.185711\pi$
$421$	34.2483	1.66916	0.834580	+	0.550887i	$0.185711\pi$
$422$	−6.97843	−0.339705
$423$	−30.5287	−1.48436
$424$	11.4134	0.554283
$425$	−1.32402	−0.0642245
$426$	2.69886	0.130760
$427$	−0.438582	−0.0212245
$428$	−12.3032	−0.594699
$429$	12.8716	0.621446
$430$	−10.5439	−0.508472
$431$	−18.5713	−0.894549	−0.447274	−	0.894397i	$-0.647605\pi$
$431$	−18.5713	−0.894549	−0.447274	+	0.894397i	$0.647605\pi$
$432$	−3.98513	−0.191735
$433$	0.883927	0.0424788	0.0212394	−	0.999774i	$-0.493239\pi$
$433$	0.883927	0.0424788	0.0212394	+	0.999774i	$0.493239\pi$
$434$	0.0554887	0.00266354
$435$	10.4049	0.498875
$436$	11.0894	0.531084
$437$	−8.31697	−0.397855
$438$	17.0459	0.814485
$439$	−20.3518	−0.971341	−0.485670	−	0.874142i	$-0.661424\pi$
$439$	−20.3518	−0.971341	−0.485670	+	0.874142i	$0.661424\pi$
$440$	3.18409	0.151795
$441$	−31.1270	−1.48224
$442$	2.83785	0.134983
$443$	−10.0809	−0.478956	−0.239478	−	0.970902i	$-0.576976\pi$
$443$	−10.0809	−0.478956	−0.239478	+	0.970902i	$0.576976\pi$
$444$	−22.5375	−1.06958
$445$	−35.3385	−1.67521
$446$	−17.1540	−0.812267
$447$	32.9985	1.56078
$448$	−0.139698	−0.00660013
$449$	27.1211	1.27992	0.639961	−	0.768407i	$-0.278950\pi$
$449$	27.1211	1.27992	0.639961	+	0.768407i	$0.278950\pi$
$450$	5.90401	0.278318
$451$	−14.2425	−0.670652
$452$	−9.67333	−0.454995
$453$	−4.81551	−0.226252
$454$	11.8506	0.556177
$455$	−0.760093	−0.0356337
$456$	2.92714	0.137076
$457$	−26.9865	−1.26238	−0.631188	−	0.775630i	$-0.717432\pi$
$457$	−26.9865	−1.26238	−0.631188	+	0.775630i	$0.717432\pi$
$458$	−21.5465	−1.00680
$459$	−3.98513	−0.186010
$460$	14.8783	0.693704
$461$	−22.0141	−1.02530	−0.512650	−	0.858598i	$-0.671336\pi$
$461$	−22.0141	−1.02530	−0.512650	+	0.858598i	$0.671336\pi$
$462$	−0.633628	−0.0294790
$463$	−8.65377	−0.402175	−0.201087	−	0.979573i	$-0.564447\pi$
$463$	−8.65377	−0.402175	−0.201087	+	0.979573i	$0.564447\pi$
$464$	1.98704	0.0922458
$465$	2.07991	0.0964535
$466$	9.26474	0.429181
$467$	31.4658	1.45606	0.728031	−	0.685544i	$-0.240436\pi$
$467$	31.4658	1.45606	0.728031	+	0.685544i	$0.240436\pi$
$468$	−12.6544	−0.584949
$469$	1.09822	0.0507110
$470$	−13.1263	−0.605473
$471$	−51.7220	−2.38323
$472$	1.00000	0.0460287
$473$	−9.13301	−0.419936
$474$	14.4565	0.664008
$475$	−1.41904	−0.0651099
$476$	−0.139698	−0.00640306
$477$	−50.8939	−2.33027
$478$	17.0094	0.777991
$479$	2.09881	0.0958972	0.0479486	−	0.998850i	$-0.484732\pi$
$479$	2.09881	0.0958972	0.0479486	+	0.998850i	$0.484732\pi$
$480$	−5.23638	−0.239007
$481$	−23.4180	−1.06777
$482$	−8.51980	−0.388066
$483$	−2.96075	−0.134719
$484$	−8.24198	−0.374636
$485$	−23.2073	−1.05379
$486$	−18.7654	−0.851216
$487$	32.7833	1.48555	0.742777	−	0.669539i	$-0.233508\pi$
$487$	32.7833	1.48555	0.742777	+	0.669539i	$0.233508\pi$
$488$	−3.13949	−0.142118
$489$	−55.5448	−2.51182
$490$	−13.3836	−0.604608
$491$	35.4746	1.60094	0.800472	−	0.599370i	$-0.204582\pi$
$491$	35.4746	1.60094	0.800472	+	0.599370i	$0.204582\pi$
$492$	23.4224	1.05596
$493$	1.98704	0.0894916
$494$	3.04150	0.136843
$495$	−14.1983	−0.638166
$496$	0.397204	0.0178350
$497$	−0.138047	−0.00619225
$498$	32.1659	1.44139
$499$	−28.6809	−1.28393	−0.641966	−	0.766733i	$-0.721881\pi$
$499$	−28.6809	−1.28393	−0.641966	+	0.766733i	$0.721881\pi$
$500$	12.1249	0.542244
$501$	−43.9675	−1.96432
$502$	18.3118	0.817295
$503$	−9.73612	−0.434112	−0.217056	−	0.976159i	$-0.569645\pi$
$503$	−9.73612	−0.434112	−0.217056	+	0.976159i	$0.569645\pi$
$504$	0.622935	0.0277477
$505$	−14.8313	−0.659983
$506$	12.8874	0.572915
$507$	13.5099	0.599997
$508$	−15.8625	−0.703786
$509$	−3.39703	−0.150571	−0.0752853	−	0.997162i	$-0.523987\pi$
$509$	−3.39703	−0.150571	−0.0752853	+	0.997162i	$0.523987\pi$
$510$	−5.23638	−0.231871
$511$	−0.871900	−0.0385706
$512$	−1.00000	−0.0441942
$513$	−4.27111	−0.188574
$514$	3.20662	0.141438
$515$	10.3624	0.456620
$516$	15.0196	0.661203
$517$	−11.3699	−0.500047
$518$	1.15279	0.0506509
$519$	−11.8327	−0.519399
$520$	−5.44096	−0.238602
$521$	−12.8240	−0.561828	−0.280914	−	0.959733i	$-0.590638\pi$
$521$	−12.8240	−0.561828	−0.280914	+	0.959733i	$0.590638\pi$
$522$	−8.86048	−0.387813
$523$	−2.84583	−0.124440	−0.0622198	−	0.998062i	$-0.519818\pi$
$523$	−2.84583	−0.124440	−0.0622198	+	0.998062i	$0.519818\pi$
$524$	−14.4941	−0.633179
$525$	−0.505163	−0.0220471
$526$	5.69419	0.248278
$527$	0.397204	0.0173025
$528$	−4.53569	−0.197390
$529$	37.2190	1.61822
$530$	−21.8827	−0.950523
$531$	−4.45914	−0.193510
$532$	−0.149723	−0.00649133
$533$	24.3375	1.05417
$534$	50.3392	2.17839
$535$	23.5888	1.01983
$536$	7.86135	0.339559
$537$	32.3132	1.39442
$538$	−17.7223	−0.764061
$539$	−11.5927	−0.499332
$540$	7.64063	0.328800
$541$	36.6513	1.57576	0.787882	−	0.615827i	$-0.211178\pi$
$541$	36.6513	1.57576	0.787882	+	0.615827i	$0.211178\pi$
$542$	−22.7446	−0.976963
$543$	−41.9239	−1.79913
$544$	−1.00000	−0.0428746
$545$	−21.2614	−0.910740
$546$	1.08274	0.0463371
$547$	3.23704	0.138406	0.0692029	−	0.997603i	$-0.477954\pi$
$547$	3.23704	0.138406	0.0692029	+	0.997603i	$0.477954\pi$
$548$	18.6688	0.797490
$549$	13.9995	0.597482
$550$	2.19884	0.0937589
$551$	2.12963	0.0907253
$552$	−21.1939	−0.902073
$553$	−0.739451	−0.0314446
$554$	−23.3855	−0.993555
$555$	43.2107	1.83419
$556$	22.0772	0.936283
$557$	−9.81743	−0.415978	−0.207989	−	0.978131i	$-0.566692\pi$
$557$	−9.81743	−0.415978	−0.207989	+	0.978131i	$0.566692\pi$
$558$	−1.77119	−0.0749804
$559$	15.6065	0.660083
$560$	0.267841	0.0113184
$561$	−4.53569	−0.191497
$562$	−2.59351	−0.109401
$563$	34.0836	1.43645	0.718227	−	0.695809i	$-0.244954\pi$
$563$	34.0836	1.43645	0.718227	+	0.695809i	$0.244954\pi$
$564$	18.6983	0.787340
$565$	18.5465	0.780258
$566$	22.5186	0.946529
$567$	0.348333	0.0146286
$568$	−0.988179	−0.0414631
$569$	6.29936	0.264083	0.132041	−	0.991244i	$-0.457847\pi$
$569$	6.29936	0.264083	0.132041	+	0.991244i	$0.457847\pi$
$570$	−5.61215	−0.235067
$571$	26.0208	1.08894	0.544469	−	0.838781i	$-0.316731\pi$
$571$	26.0208	1.08894	0.544469	+	0.838781i	$0.316731\pi$
$572$	−4.71289	−0.197056
$573$	−30.1492	−1.25950
$574$	−1.19806	−0.0500060
$575$	10.2745	0.428478
$576$	4.45914	0.185798
$577$	22.5868	0.940300	0.470150	−	0.882586i	$-0.344200\pi$
$577$	22.5868	0.940300	0.470150	+	0.882586i	$0.344200\pi$
$578$	−1.00000	−0.0415945
$579$	−1.88304	−0.0782565
$580$	−3.80971	−0.158190
$581$	−1.64529	−0.0682582
$582$	33.0584	1.37032
$583$	−18.9545	−0.785016
$584$	−6.24131	−0.258267
$585$	24.2620	1.00311
$586$	−12.2541	−0.506214
$587$	−12.2351	−0.504995	−0.252498	−	0.967598i	$-0.581252\pi$
$587$	−12.2351	−0.504995	−0.252498	+	0.967598i	$0.581252\pi$
$588$	19.0647	0.786215
$589$	0.425708	0.0175410
$590$	−1.91728	−0.0789333
$591$	−31.0527	−1.27734
$592$	8.25202	0.339156
$593$	−20.7586	−0.852453	−0.426227	−	0.904616i	$-0.640157\pi$
$593$	−20.7586	−0.852453	−0.426227	+	0.904616i	$0.640157\pi$
$594$	6.61822	0.271549
$595$	0.267841	0.0109804
$596$	−12.0823	−0.494911
$597$	8.46792	0.346569
$598$	−22.0220	−0.900545
$599$	16.3583	0.668380	0.334190	−	0.942506i	$-0.391537\pi$
$599$	16.3583	0.668380	0.334190	+	0.942506i	$0.391537\pi$
$600$	−3.61610	−0.147627
$601$	−34.7904	−1.41913	−0.709564	−	0.704641i	$-0.751108\pi$
$601$	−34.7904	−1.41913	−0.709564	+	0.704641i	$0.751108\pi$
$602$	−0.768257	−0.0313118
$603$	−35.0549	−1.42755
$604$	1.76318	0.0717429
$605$	15.8022	0.642451
$606$	21.1270	0.858224
$607$	35.9823	1.46047	0.730237	−	0.683194i	$-0.239410\pi$
$607$	35.9823	1.46047	0.730237	+	0.683194i	$0.239410\pi$
$608$	−1.07176	−0.0434657
$609$	0.758126	0.0307208
$610$	6.01930	0.243714
$611$	19.4288	0.786006
$612$	4.45914	0.180250
$613$	31.0162	1.25273	0.626366	−	0.779529i	$-0.284541\pi$
$613$	31.0162	1.25273	0.626366	+	0.779529i	$0.284541\pi$
$614$	−3.95454	−0.159592
$615$	−44.9074	−1.81084
$616$	0.232001	0.00934758
$617$	−19.0444	−0.766698	−0.383349	−	0.923604i	$-0.625229\pi$
$617$	−19.0444	−0.766698	−0.383349	+	0.923604i	$0.625229\pi$
$618$	−14.7610	−0.593776
$619$	−19.9852	−0.803274	−0.401637	−	0.915799i	$-0.631559\pi$
$619$	−19.9852	−0.803274	−0.401637	+	0.915799i	$0.631559\pi$
$620$	−0.761553	−0.0305847
$621$	30.9250	1.24098
$622$	0.158635	0.00636070
$623$	−2.57486	−0.103159
$624$	7.75057	0.310271
$625$	−16.6269	−0.665074
$626$	19.1532	0.765515
$627$	−4.86118	−0.194137
$628$	18.9379	0.755703
$629$	8.25202	0.329030
$630$	−1.19434	−0.0475838
$631$	25.7760	1.02613	0.513063	−	0.858351i	$-0.328511\pi$
$631$	25.7760	1.02613	0.513063	+	0.858351i	$0.328511\pi$
$632$	−5.29320	−0.210552
$633$	−19.0591	−0.757531
$634$	18.0779	0.717964
$635$	30.4130	1.20690
$636$	31.1716	1.23603
$637$	19.8096	0.784883
$638$	−3.29993	−0.130645
$639$	4.40643	0.174316
$640$	1.91728	0.0757873
$641$	10.2083	0.403204	0.201602	−	0.979468i	$-0.435385\pi$
$641$	10.2083	0.403204	0.201602	+	0.979468i	$0.435385\pi$
$642$	−33.6019	−1.32616
$643$	22.5522	0.889372	0.444686	−	0.895686i	$-0.353315\pi$
$643$	22.5522	0.889372	0.444686	+	0.895686i	$0.353315\pi$
$644$	1.08407	0.0427184
$645$	−28.7969	−1.13388
$646$	−1.07176	−0.0421679
$647$	−28.5643	−1.12298	−0.561489	−	0.827484i	$-0.689771\pi$
$647$	−28.5643	−1.12298	−0.561489	+	0.827484i	$0.689771\pi$
$648$	2.49346	0.0979525
$649$	−1.66073	−0.0651893
$650$	−3.75738	−0.147376
$651$	0.151548	0.00593962
$652$	20.3376	0.796481
$653$	34.3833	1.34552	0.672762	−	0.739859i	$-0.265108\pi$
$653$	34.3833	1.34552	0.672762	+	0.739859i	$0.265108\pi$
$654$	30.2866	1.18430
$655$	27.7894	1.08582
$656$	−8.57605	−0.334838
$657$	27.8309	1.08579
$658$	−0.956420	−0.0372851
$659$	26.1737	1.01958	0.509791	−	0.860298i	$-0.329723\pi$
$659$	26.1737	1.01958	0.509791	+	0.860298i	$0.329723\pi$
$660$	8.69620	0.338499
$661$	−8.29896	−0.322792	−0.161396	−	0.986890i	$-0.551600\pi$
$661$	−8.29896	−0.322792	−0.161396	+	0.986890i	$0.551600\pi$
$662$	6.02440	0.234145
$663$	7.75057	0.301007
$664$	−11.7775	−0.457054
$665$	0.287062	0.0111318
$666$	−36.7970	−1.42585
$667$	−15.4196	−0.597049
$668$	16.0986	0.622872
$669$	−46.8501	−1.81133
$670$	−15.0724	−0.582299
$671$	5.21385	0.201278
$672$	−0.381536	−0.0147181
$673$	4.85861	0.187286	0.0936428	−	0.995606i	$-0.470149\pi$
$673$	4.85861	0.187286	0.0936428	+	0.995606i	$0.470149\pi$
$674$	−5.15756	−0.198662
$675$	5.27641	0.203089
$676$	−4.94662	−0.190255
$677$	−26.6075	−1.02261	−0.511305	−	0.859400i	$-0.670838\pi$
$677$	−26.6075	−1.02261	−0.511305	+	0.859400i	$0.670838\pi$
$678$	−26.4193	−1.01463
$679$	−1.69094	−0.0648924
$680$	1.91728	0.0735245
$681$	32.3658	1.24026
$682$	−0.659648	−0.0252592
$683$	37.8109	1.44679	0.723396	−	0.690433i	$-0.242580\pi$
$683$	37.8109	1.44679	0.723396	+	0.690433i	$0.242580\pi$
$684$	4.77914	0.182735
$685$	−35.7933	−1.36759
$686$	−1.95305	−0.0745678
$687$	−58.8467	−2.24514
$688$	−5.49940	−0.209663
$689$	32.3894	1.23394
$690$	40.6348	1.54694
$691$	−12.4241	−0.472635	−0.236318	−	0.971676i	$-0.575941\pi$
$691$	−12.4241	−0.472635	−0.236318	+	0.971676i	$0.575941\pi$
$692$	4.33252	0.164698
$693$	−1.03453	−0.0392984
$694$	11.1501	0.423253
$695$	−42.3283	−1.60560
$696$	5.42688	0.205705
$697$	−8.57605	−0.324841
$698$	−7.12571	−0.269712
$699$	25.3033	0.957060
$700$	0.184964	0.00699097
$701$	35.2652	1.33195	0.665973	−	0.745976i	$-0.268017\pi$
$701$	35.2652	1.33195	0.665973	+	0.745976i	$0.268017\pi$
$702$	−11.3092	−0.426838
$703$	8.84421	0.333566
$704$	1.66073	0.0625911
$705$	−35.8499	−1.35019
$706$	−0.838103	−0.0315424
$707$	−1.08065	−0.0406419
$708$	2.73114	0.102643
$709$	7.96353	0.299077	0.149538	−	0.988756i	$-0.452221\pi$
$709$	7.96353	0.299077	0.149538	+	0.988756i	$0.452221\pi$
$710$	1.89462	0.0711038
$711$	23.6031	0.885187
$712$	−18.4316	−0.690752
$713$	−3.08234	−0.115434
$714$	−0.381536	−0.0142786
$715$	9.03596	0.337926
$716$	−11.8314	−0.442160
$717$	46.4551	1.73490
$718$	23.2049	0.866000
$719$	15.3257	0.571551	0.285776	−	0.958297i	$-0.407749\pi$
$719$	15.3257	0.571551	0.285776	+	0.958297i	$0.407749\pi$
$720$	−8.54945	−0.318619
$721$	0.755028	0.0281187
$722$	17.8513	0.664358
$723$	−23.2688	−0.865376
$724$	15.3503	0.570490
$725$	−2.63088	−0.0977085
$726$	−22.5100	−0.835426
$727$	−38.5678	−1.43040	−0.715201	−	0.698919i	$-0.753665\pi$
$727$	−38.5678	−1.43040	−0.715201	+	0.698919i	$0.753665\pi$
$728$	−0.396443	−0.0146931
$729$	−43.7706	−1.62113
$730$	11.9664	0.442895
$731$	−5.49940	−0.203403
$732$	−8.57441	−0.316919
$733$	4.24702	0.156867	0.0784337	−	0.996919i	$-0.475008\pi$
$733$	4.24702	0.156867	0.0784337	+	0.996919i	$0.475008\pi$
$734$	−7.98775	−0.294833
$735$	−36.5524	−1.34826
$736$	7.76009	0.286041
$737$	−13.0556	−0.480908
$738$	38.2418	1.40770
$739$	−51.5727	−1.89713	−0.948567	−	0.316576i	$-0.897467\pi$
$739$	−51.5727	−1.89713	−0.948567	+	0.316576i	$0.897467\pi$
$740$	−15.8215	−0.581609
$741$	8.30677	0.305157
$742$	−1.59443	−0.0585334
$743$	47.3432	1.73685	0.868426	−	0.495818i	$-0.165132\pi$
$743$	47.3432	1.73685	0.868426	+	0.495818i	$0.165132\pi$
$744$	1.08482	0.0397715
$745$	23.1652	0.848708
$746$	−8.65514	−0.316887
$747$	52.5174	1.92151
$748$	1.66073	0.0607222
$749$	1.71874	0.0628014
$750$	33.1150	1.20919
$751$	−5.63153	−0.205497	−0.102749	−	0.994707i	$-0.532764\pi$
$751$	−5.63153	−0.205497	−0.102749	+	0.994707i	$0.532764\pi$
$752$	−6.84632	−0.249660
$753$	50.0121	1.82254
$754$	5.63891	0.205357
$755$	−3.38052	−0.123030
$756$	0.556716	0.0202476
$757$	27.9923	1.01740	0.508699	−	0.860945i	$-0.330127\pi$
$757$	27.9923	1.01740	0.508699	+	0.860945i	$0.330127\pi$
$758$	8.78908	0.319234
$759$	35.1973	1.27758
$760$	2.05487	0.0745380
$761$	7.72669	0.280092	0.140046	−	0.990145i	$-0.455275\pi$
$761$	7.72669	0.280092	0.140046	+	0.990145i	$0.455275\pi$
$762$	−43.3228	−1.56942
$763$	−1.54916	−0.0560835
$764$	11.0391	0.399379
$765$	−8.54945	−0.309106
$766$	32.7606	1.18369
$767$	2.83785	0.102469
$768$	−2.73114	−0.0985517
$769$	−0.318773	−0.0114953	−0.00574763	−	0.999983i	$-0.501830\pi$
$769$	−0.318773	−0.0114953	−0.00574763	+	0.999983i	$0.501830\pi$
$770$	−0.444812	−0.0160299
$771$	8.75773	0.315402
$772$	0.689470	0.0248146
$773$	−5.75159	−0.206870	−0.103435	−	0.994636i	$-0.532983\pi$
$773$	−5.75159	−0.206870	−0.103435	+	0.994636i	$0.532983\pi$
$774$	24.5226	0.881447
$775$	−0.525907	−0.0188911
$776$	−12.1042	−0.434517
$777$	3.14845	0.112950
$778$	−37.2255	−1.33460
$779$	−9.19148	−0.329319
$780$	−14.8600	−0.532075
$781$	1.64110	0.0587230
$782$	7.76009	0.277500
$783$	−7.91860	−0.282988
$784$	−6.98048	−0.249303
$785$	−36.3093	−1.29593
$786$	−39.5856	−1.41197
$787$	34.4467	1.22789	0.613945	−	0.789348i	$-0.289581\pi$
$787$	34.4467	1.22789	0.613945	+	0.789348i	$0.289581\pi$
$788$	11.3698	0.405034
$789$	15.5516	0.553653
$790$	10.1486	0.361070
$791$	1.35135	0.0480484
$792$	−7.40543	−0.263140
$793$	−8.90941	−0.316382
$794$	−3.89173	−0.138112
$795$	−59.7648	−2.11964
$796$	−3.10050	−0.109894
$797$	6.76517	0.239635	0.119817	−	0.992796i	$-0.461769\pi$
$797$	6.76517	0.239635	0.119817	+	0.992796i	$0.461769\pi$
$798$	−0.408916	−0.0144755
$799$	−6.84632	−0.242205
$800$	1.32402	0.0468113
$801$	82.1890	2.90400
$802$	−1.09002	−0.0384900
$803$	10.3651	0.365777
$804$	21.4705	0.757205
$805$	−2.07847	−0.0732565
$806$	1.12720	0.0397041
$807$	−48.4021	−1.70383
$808$	−7.73557	−0.272136
$809$	−1.23591	−0.0434523	−0.0217261	−	0.999764i	$-0.506916\pi$
$809$	−1.23591	−0.0434523	−0.0217261	+	0.999764i	$0.506916\pi$
$810$	−4.78068	−0.167976
$811$	−37.3756	−1.31244	−0.656218	−	0.754572i	$-0.727845\pi$
$811$	−37.3756	−1.31244	−0.656218	+	0.754572i	$0.727845\pi$
$812$	−0.277586	−0.00974135
$813$	−62.1187	−2.17860
$814$	−13.7044	−0.480338
$815$	−38.9929	−1.36586
$816$	−2.73114	−0.0956091
$817$	−5.89405	−0.206207
$818$	−9.47425	−0.331259
$819$	1.76779	0.0617718
$820$	16.4427	0.574205
$821$	−6.44703	−0.225003	−0.112501	−	0.993652i	$-0.535886\pi$
$821$	−6.44703	−0.225003	−0.112501	+	0.993652i	$0.535886\pi$
$822$	50.9870	1.77838
$823$	52.2910	1.82275	0.911374	−	0.411579i	$-0.135023\pi$
$823$	52.2910	1.82275	0.911374	+	0.411579i	$0.135023\pi$
$824$	5.40471	0.188282
$825$	6.00535	0.209080
$826$	−0.139698	−0.00486073
$827$	26.2020	0.911131	0.455566	−	0.890202i	$-0.349437\pi$
$827$	26.2020	0.911131	0.455566	+	0.890202i	$0.349437\pi$
$828$	−34.6034	−1.20255
$829$	34.1844	1.18727	0.593637	−	0.804733i	$-0.297692\pi$
$829$	34.1844	1.18727	0.593637	+	0.804733i	$0.297692\pi$
$830$	22.5807	0.783789
$831$	−63.8692	−2.21560
$832$	−2.83785	−0.0983847
$833$	−6.98048	−0.241859
$834$	60.2960	2.08788
$835$	−30.8655	−1.06814
$836$	1.77991	0.0615593
$837$	−1.58291	−0.0547134
$838$	−15.6928	−0.542100
$839$	−16.6767	−0.575744	−0.287872	−	0.957669i	$-0.592948\pi$
$839$	−16.6767	−0.575744	−0.287872	+	0.957669i	$0.592948\pi$
$840$	0.731513	0.0252396
$841$	−25.0517	−0.863851
$842$	−34.2483	−1.18027
$843$	−7.08324	−0.243960
$844$	6.97843	0.240208
$845$	9.48407	0.326262
$846$	30.5287	1.04960
$847$	1.15139	0.0395623
$848$	−11.4134	−0.391937
$849$	61.5017	2.11073
$850$	1.32402	0.0454136
$851$	−64.0365	−2.19514
$852$	−2.69886	−0.0924613
$853$	−47.9138	−1.64054	−0.820269	−	0.571978i	$-0.806176\pi$
$853$	−47.9138	−1.64054	−0.820269	+	0.571978i	$0.806176\pi$
$854$	0.438582	0.0150080
$855$	−9.16297	−0.313367
$856$	12.3032	0.420516
$857$	−5.84269	−0.199583	−0.0997913	−	0.995008i	$-0.531818\pi$
$857$	−5.84269	−0.199583	−0.0997913	+	0.995008i	$0.531818\pi$
$858$	−12.8716	−0.439429
$859$	−30.1638	−1.02918	−0.514588	−	0.857438i	$-0.672055\pi$
$859$	−30.1638	−1.02918	−0.514588	+	0.857438i	$0.672055\pi$
$860$	10.5439	0.359544
$861$	−3.27207	−0.111512
$862$	18.5713	0.632541
$863$	−12.4093	−0.422418	−0.211209	−	0.977441i	$-0.567740\pi$
$863$	−12.4093	−0.422418	−0.211209	+	0.977441i	$0.567740\pi$
$864$	3.98513	0.135577
$865$	−8.30667	−0.282435
$866$	−0.883927	−0.0300371
$867$	−2.73114	−0.0927545
$868$	−0.0554887	−0.00188341
$869$	8.79056	0.298199
$870$	−10.4049	−0.352758
$871$	22.3093	0.755923
$872$	−11.0894	−0.375533
$873$	53.9746	1.82676
$874$	8.31697	0.281326
$875$	−1.69383	−0.0572621
$876$	−17.0459	−0.575928
$877$	4.87188	0.164512	0.0822559	−	0.996611i	$-0.473788\pi$
$877$	4.87188	0.164512	0.0822559	+	0.996611i	$0.473788\pi$
$878$	20.3518	0.686842
$879$	−33.4678	−1.12884
$880$	−3.18409	−0.107336
$881$	11.1101	0.374310	0.187155	−	0.982330i	$-0.440073\pi$
$881$	11.1101	0.374310	0.187155	+	0.982330i	$0.440073\pi$
$882$	31.1270	1.04810
$883$	11.5898	0.390027	0.195014	−	0.980801i	$-0.437525\pi$
$883$	11.5898	0.390027	0.195014	+	0.980801i	$0.437525\pi$
$884$	−2.83785	−0.0954472
$885$	−5.23638	−0.176019
$886$	10.0809	0.338673
$887$	3.88009	0.130281	0.0651403	−	0.997876i	$-0.479251\pi$
$887$	3.88009	0.130281	0.0651403	+	0.997876i	$0.479251\pi$
$888$	22.5375	0.756308
$889$	2.21597	0.0743212
$890$	35.3385	1.18455
$891$	−4.14097	−0.138728
$892$	17.1540	0.574360
$893$	−7.33763	−0.245544
$894$	−32.9985	−1.10364
$895$	22.6841	0.758247
$896$	0.139698	0.00466699
$897$	−60.1451	−2.00819
$898$	−27.1211	−0.905042
$899$	0.789259	0.0263233
$900$	−5.90401	−0.196800
$901$	−11.4134	−0.380235
$902$	14.2425	0.474223
$903$	−2.09822	−0.0698244
$904$	9.67333	0.321730
$905$	−29.4309	−0.978317
$906$	4.81551	0.159984
$907$	−4.74978	−0.157714	−0.0788570	−	0.996886i	$-0.525127\pi$
$907$	−4.74978	−0.157714	−0.0788570	+	0.996886i	$0.525127\pi$
$908$	−11.8506	−0.393277
$909$	34.4940	1.14409
$910$	0.760093	0.0251968
$911$	0.925443	0.0306613	0.0153307	−	0.999882i	$-0.495120\pi$
$911$	0.925443	0.0306613	0.0153307	+	0.999882i	$0.495120\pi$
$912$	−2.92714	−0.0969271
$913$	19.5592	0.647314
$914$	26.9865	0.892634
$915$	16.4396	0.543476
$916$	21.5465	0.711918
$917$	2.02481	0.0668650
$918$	3.98513	0.131529
$919$	24.0679	0.793925	0.396963	−	0.917835i	$-0.370064\pi$
$919$	24.0679	0.793925	0.396963	+	0.917835i	$0.370064\pi$
$920$	−14.8783	−0.490523
$921$	−10.8004	−0.355886
$922$	22.0141	0.724997
$923$	−2.80430	−0.0923047
$924$	0.633628	0.0208448
$925$	−10.9259	−0.359240
$926$	8.65377	0.284380
$927$	−24.1004	−0.791560
$928$	−1.98704	−0.0652277
$929$	41.3564	1.35686	0.678429	−	0.734666i	$-0.262661\pi$
$929$	41.3564	1.35686	0.678429	+	0.734666i	$0.262661\pi$
$930$	−2.07991	−0.0682029
$931$	−7.48142	−0.245194
$932$	−9.26474	−0.303477
$933$	0.433256	0.0141842
$934$	−31.4658	−1.02959
$935$	−3.18409	−0.104131
$936$	12.6544	0.413621
$937$	−37.7820	−1.23429	−0.617143	−	0.786851i	$-0.711710\pi$
$937$	−37.7820	−1.23429	−0.617143	+	0.786851i	$0.711710\pi$
$938$	−1.09822	−0.0358581
$939$	52.3101	1.70707
$940$	13.1263	0.428134
$941$	48.4653	1.57992	0.789962	−	0.613156i	$-0.210100\pi$
$941$	48.4653	1.57992	0.789962	+	0.613156i	$0.210100\pi$
$942$	51.7220	1.68520
$943$	66.5509	2.16720
$944$	−1.00000	−0.0325472
$945$	−1.06738	−0.0347220
$946$	9.13301	0.296940
$947$	25.6813	0.834531	0.417266	−	0.908785i	$-0.362988\pi$
$947$	25.6813	0.834531	0.417266	+	0.908785i	$0.362988\pi$
$948$	−14.4565	−0.469525
$949$	−17.7119	−0.574952
$950$	1.41904	0.0460396
$951$	49.3732	1.60104
$952$	0.139698	0.00452765
$953$	35.0530	1.13548	0.567739	−	0.823209i	$-0.307818\pi$
$953$	35.0530	1.13548	0.567739	+	0.823209i	$0.307818\pi$
$954$	50.8939	1.64775
$955$	−21.1650	−0.684884
$956$	−17.0094	−0.550123
$957$	−9.01258	−0.291335
$958$	−2.09881	−0.0678095
$959$	−2.60799	−0.0842165
$960$	5.23638	0.169003
$961$	−30.8422	−0.994911
$962$	23.4180	0.755026
$963$	−54.8619	−1.76790
$964$	8.51980	0.274404
$965$	−1.32191	−0.0425538
$966$	2.96075	0.0952607
$967$	21.8867	0.703830	0.351915	−	0.936032i	$-0.385531\pi$
$967$	21.8867	0.703830	0.351915	+	0.936032i	$0.385531\pi$
$968$	8.24198	0.264907
$969$	−2.92714	−0.0940331
$970$	23.2073	0.745141
$971$	27.0148	0.866947	0.433473	−	0.901166i	$-0.357288\pi$
$971$	27.0148	0.866947	0.433473	+	0.901166i	$0.357288\pi$
$972$	18.7654	0.601901
$973$	−3.08415	−0.0988733
$974$	−32.7833	−1.05045
$975$	−10.2619	−0.328645
$976$	3.13949	0.100493
$977$	33.3752	1.06777	0.533884	−	0.845558i	$-0.320732\pi$
$977$	33.3752	1.06777	0.533884	+	0.845558i	$0.320732\pi$
$978$	55.5448	1.77613
$979$	30.6098	0.978294
$980$	13.3836	0.427522
$981$	49.4490	1.57879
$982$	−35.4746	−1.13204
$983$	58.1241	1.85387	0.926936	−	0.375220i	$-0.122433\pi$
$983$	58.1241	1.85387	0.926936	+	0.375220i	$0.122433\pi$
$984$	−23.4224	−0.746679
$985$	−21.7992	−0.694581
$986$	−1.98704	−0.0632801
$987$	−2.61212	−0.0831447
$988$	−3.04150	−0.0967629
$989$	42.6758	1.35701
$990$	14.1983	0.451252
$991$	−8.06021	−0.256041	−0.128020	−	0.991772i	$-0.540862\pi$
$991$	−8.06021	−0.256041	−0.128020	+	0.991772i	$0.540862\pi$
$992$	−0.397204	−0.0126112
$993$	16.4535	0.522136
$994$	0.138047	0.00437858
$995$	5.94455	0.188455
$996$	−32.1659	−1.01922
$997$	3.57213	0.113131	0.0565653	−	0.998399i	$-0.481985\pi$
$997$	3.57213	0.113131	0.0565653	+	0.998399i	$0.481985\pi$
$998$	28.6809	0.907877
$999$	−32.8854	−1.04045

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2006.2.a.u.1.3	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2006.2.a.u.1.3	✓	9	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 2006 = 2 \cdot 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2006.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.73114 q^{3} +1.00000 q^{4} -1.91728 q^{5} +2.73114 q^{6} -0.139698 q^{7} -1.00000 q^{8} +4.45914 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.73114 q^{3} +1.00000 q^{4} -1.91728 q^{5} +2.73114 q^{6} -0.139698 q^{7} -1.00000 q^{8} +4.45914 q^{9} +1.91728 q^{10} +1.66073 q^{11} -2.73114 q^{12} -2.83785 q^{13} +0.139698 q^{14} +5.23638 q^{15} +1.00000 q^{16} +1.00000 q^{17} -4.45914 q^{18} +1.07176 q^{19} -1.91728 q^{20} +0.381536 q^{21} -1.66073 q^{22} -7.76009 q^{23} +2.73114 q^{24} -1.32402 q^{25} +2.83785 q^{26} -3.98513 q^{27} -0.139698 q^{28} +1.98704 q^{29} -5.23638 q^{30} +0.397204 q^{31} -1.00000 q^{32} -4.53569 q^{33} -1.00000 q^{34} +0.267841 q^{35} +4.45914 q^{36} +8.25202 q^{37} -1.07176 q^{38} +7.75057 q^{39} +1.91728 q^{40} -8.57605 q^{41} -0.381536 q^{42} -5.49940 q^{43} +1.66073 q^{44} -8.54945 q^{45} +7.76009 q^{46} -6.84632 q^{47} -2.73114 q^{48} -6.98048 q^{49} +1.32402 q^{50} -2.73114 q^{51} -2.83785 q^{52} -11.4134 q^{53} +3.98513 q^{54} -3.18409 q^{55} +0.139698 q^{56} -2.92714 q^{57} -1.98704 q^{58} -1.00000 q^{59} +5.23638 q^{60} +3.13949 q^{61} -0.397204 q^{62} -0.622935 q^{63} +1.00000 q^{64} +5.44096 q^{65} +4.53569 q^{66} -7.86135 q^{67} +1.00000 q^{68} +21.1939 q^{69} -0.267841 q^{70} +0.988179 q^{71} -4.45914 q^{72} +6.24131 q^{73} -8.25202 q^{74} +3.61610 q^{75} +1.07176 q^{76} -0.232001 q^{77} -7.75057 q^{78} +5.29320 q^{79} -1.91728 q^{80} -2.49346 q^{81} +8.57605 q^{82} +11.7775 q^{83} +0.381536 q^{84} -1.91728 q^{85} +5.49940 q^{86} -5.42688 q^{87} -1.66073 q^{88} +18.4316 q^{89} +8.54945 q^{90} +0.396443 q^{91} -7.76009 q^{92} -1.08482 q^{93} +6.84632 q^{94} -2.05487 q^{95} +2.73114 q^{96} +12.1042 q^{97} +6.98048 q^{98} +7.40543 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 9 q^{2} - q^{3} + 9 q^{4} + 7 q^{5} + q^{6} - 9 q^{8} + 20 q^{9}+O(q^{10}) \) 9 * q - 9 * q^2 - q^3 + 9 * q^4 + 7 * q^5 + q^6 - 9 * q^8 + 20 * q^9	\( 9 q - 9 q^{2} - q^{3} + 9 q^{4} + 7 q^{5} + q^{6} - 9 q^{8} + 20 q^{9} - 7 q^{10} + 5 q^{11} - q^{12} + 25 q^{13} - 5 q^{15} + 9 q^{16} + 9 q^{17} - 20 q^{18} + 14 q^{19} + 7 q^{20} - 7 q^{21} - 5 q^{22} + 2 q^{23} + q^{24} + 20 q^{25} - 25 q^{26} - 10 q^{27} + 18 q^{29} + 5 q^{30} + 6 q^{31} - 9 q^{32} - 9 q^{33} - 9 q^{34} - 17 q^{35} + 20 q^{36} + 11 q^{37} - 14 q^{38} - 8 q^{39} - 7 q^{40} + 18 q^{41} + 7 q^{42} - 10 q^{43} + 5 q^{44} + 27 q^{45} - 2 q^{46} - 20 q^{47} - q^{48} + 13 q^{49} - 20 q^{50} - q^{51} + 25 q^{52} - 7 q^{53} + 10 q^{54} + 29 q^{55} + 17 q^{57} - 18 q^{58} - 9 q^{59} - 5 q^{60} + 30 q^{61} - 6 q^{62} - 47 q^{63} + 9 q^{64} + 8 q^{65} + 9 q^{66} + 6 q^{67} + 9 q^{68} + 20 q^{69} + 17 q^{70} + 30 q^{71} - 20 q^{72} - 11 q^{74} - 7 q^{75} + 14 q^{76} - 3 q^{77} + 8 q^{78} + 29 q^{79} + 7 q^{80} - 3 q^{81} - 18 q^{82} + 9 q^{83} - 7 q^{84} + 7 q^{85} + 10 q^{86} + 44 q^{87} - 5 q^{88} + 8 q^{89} - 27 q^{90} + 13 q^{91} + 2 q^{92} + 7 q^{93} + 20 q^{94} + 27 q^{95} + q^{96} - 13 q^{97} - 13 q^{98} - 19 q^{99}+O(q^{100}) \) 9 * q - 9 * q^2 - q^3 + 9 * q^4 + 7 * q^5 + q^6 - 9 * q^8 + 20 * q^9 - 7 * q^10 + 5 * q^11 - q^12 + 25 * q^13 - 5 * q^15 + 9 * q^16 + 9 * q^17 - 20 * q^18 + 14 * q^19 + 7 * q^20 - 7 * q^21 - 5 * q^22 + 2 * q^23 + q^24 + 20 * q^25 - 25 * q^26 - 10 * q^27 + 18 * q^29 + 5 * q^30 + 6 * q^31 - 9 * q^32 - 9 * q^33 - 9 * q^34 - 17 * q^35 + 20 * q^36 + 11 * q^37 - 14 * q^38 - 8 * q^39 - 7 * q^40 + 18 * q^41 + 7 * q^42 - 10 * q^43 + 5 * q^44 + 27 * q^45 - 2 * q^46 - 20 * q^47 - q^48 + 13 * q^49 - 20 * q^50 - q^51 + 25 * q^52 - 7 * q^53 + 10 * q^54 + 29 * q^55 + 17 * q^57 - 18 * q^58 - 9 * q^59 - 5 * q^60 + 30 * q^61 - 6 * q^62 - 47 * q^63 + 9 * q^64 + 8 * q^65 + 9 * q^66 + 6 * q^67 + 9 * q^68 + 20 * q^69 + 17 * q^70 + 30 * q^71 - 20 * q^72 - 11 * q^74 - 7 * q^75 + 14 * q^76 - 3 * q^77 + 8 * q^78 + 29 * q^79 + 7 * q^80 - 3 * q^81 - 18 * q^82 + 9 * q^83 - 7 * q^84 + 7 * q^85 + 10 * q^86 + 44 * q^87 - 5 * q^88 + 8 * q^89 - 27 * q^90 + 13 * q^91 + 2 * q^92 + 7 * q^93 + 20 * q^94 + 27 * q^95 + q^96 - 13 * q^97 - 13 * q^98 - 19 * q^99

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