LMFDB - Embedded newform 6046.2.a.d.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6046,2,Mod(1,6046)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6046, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

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

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

chi := DirichletCharacter("6046.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6046 = 2 \cdot 3023 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6046.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:	$48.2775530621$
Analytic rank:	$1$
Dimension:	$55$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	6046.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.68677 q^{3} +1.00000 q^{4} +2.41964 q^{5} +2.68677 q^{6} +0.726544 q^{7} -1.00000 q^{8} +4.21874 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.68677 q^{3} +1.00000 q^{4} +2.41964 q^{5} +2.68677 q^{6} +0.726544 q^{7} -1.00000 q^{8} +4.21874 q^{9} -2.41964 q^{10} +0.503280 q^{11} -2.68677 q^{12} -5.74772 q^{13} -0.726544 q^{14} -6.50103 q^{15} +1.00000 q^{16} -0.321443 q^{17} -4.21874 q^{18} -0.651470 q^{19} +2.41964 q^{20} -1.95206 q^{21} -0.503280 q^{22} +7.49028 q^{23} +2.68677 q^{24} +0.854676 q^{25} +5.74772 q^{26} -3.27448 q^{27} +0.726544 q^{28} +2.54901 q^{29} +6.50103 q^{30} -4.47202 q^{31} -1.00000 q^{32} -1.35220 q^{33} +0.321443 q^{34} +1.75798 q^{35} +4.21874 q^{36} +2.53517 q^{37} +0.651470 q^{38} +15.4428 q^{39} -2.41964 q^{40} -3.58246 q^{41} +1.95206 q^{42} -8.96749 q^{43} +0.503280 q^{44} +10.2078 q^{45} -7.49028 q^{46} +11.2039 q^{47} -2.68677 q^{48} -6.47213 q^{49} -0.854676 q^{50} +0.863644 q^{51} -5.74772 q^{52} +9.93089 q^{53} +3.27448 q^{54} +1.21776 q^{55} -0.726544 q^{56} +1.75035 q^{57} -2.54901 q^{58} -5.77896 q^{59} -6.50103 q^{60} +3.63044 q^{61} +4.47202 q^{62} +3.06510 q^{63} +1.00000 q^{64} -13.9074 q^{65} +1.35220 q^{66} -12.4264 q^{67} -0.321443 q^{68} -20.1247 q^{69} -1.75798 q^{70} +0.0596592 q^{71} -4.21874 q^{72} +3.44435 q^{73} -2.53517 q^{74} -2.29632 q^{75} -0.651470 q^{76} +0.365655 q^{77} -15.4428 q^{78} -5.99275 q^{79} +2.41964 q^{80} -3.85845 q^{81} +3.58246 q^{82} +4.05204 q^{83} -1.95206 q^{84} -0.777778 q^{85} +8.96749 q^{86} -6.84861 q^{87} -0.503280 q^{88} -8.24531 q^{89} -10.2078 q^{90} -4.17597 q^{91} +7.49028 q^{92} +12.0153 q^{93} -11.2039 q^{94} -1.57632 q^{95} +2.68677 q^{96} -12.1772 q^{97} +6.47213 q^{98} +2.12321 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 55 q - 55 q^{2} - 4 q^{3} + 55 q^{4} - 7 q^{5} + 4 q^{6} + 17 q^{7} - 55 q^{8} + 29 q^{9}+O(q^{10}) $ 55 * q - 55 * q^2 - 4 * q^3 + 55 * q^4 - 7 * q^5 + 4 * q^6 + 17 * q^7 - 55 * q^8 + 29 * q^9	\( 55 q - 55 q^{2} - 4 q^{3} + 55 q^{4} - 7 q^{5} + 4 q^{6} + 17 q^{7} - 55 q^{8} + 29 q^{9} + 7 q^{10} - 28 q^{11} - 4 q^{12} + q^{13} - 17 q^{14} - 8 q^{15} + 55 q^{16} - 32 q^{17} - 29 q^{18} - 3 q^{19} - 7 q^{20} - 25 q^{21} + 28 q^{22} - 27 q^{23} + 4 q^{24} + 30 q^{25} - q^{26} - q^{27} + 17 q^{28} - 69 q^{29} + 8 q^{30} - 13 q^{31} - 55 q^{32} - 18 q^{33} + 32 q^{34} - 23 q^{35} + 29 q^{36} + 3 q^{37} + 3 q^{38} - 28 q^{39} + 7 q^{40} - 51 q^{41} + 25 q^{42} + 23 q^{43} - 28 q^{44} - 28 q^{45} + 27 q^{46} - 27 q^{47} - 4 q^{48} + 8 q^{49} - 30 q^{50} - 42 q^{51} + q^{52} - 61 q^{53} + q^{54} + 5 q^{55} - 17 q^{56} - 52 q^{57} + 69 q^{58} - 71 q^{59} - 8 q^{60} - 16 q^{61} + 13 q^{62} + 14 q^{63} + 55 q^{64} - 82 q^{65} + 18 q^{66} + 32 q^{67} - 32 q^{68} - 44 q^{69} + 23 q^{70} - 84 q^{71} - 29 q^{72} - 43 q^{73} - 3 q^{74} - 37 q^{75} - 3 q^{76} - 47 q^{77} + 28 q^{78} - 20 q^{79} - 7 q^{80} - 33 q^{81} + 51 q^{82} + 17 q^{83} - 25 q^{84} + 10 q^{85} - 23 q^{86} - q^{87} + 28 q^{88} - 92 q^{89} + 28 q^{90} - 34 q^{91} - 27 q^{92} - 13 q^{93} + 27 q^{94} - 60 q^{95} + 4 q^{96} - 45 q^{97} - 8 q^{98} - 73 q^{99}+O(q^{100}) \) 55 * q - 55 * q^2 - 4 * q^3 + 55 * q^4 - 7 * q^5 + 4 * q^6 + 17 * q^7 - 55 * q^8 + 29 * q^9 + 7 * q^10 - 28 * q^11 - 4 * q^12 + q^13 - 17 * q^14 - 8 * q^15 + 55 * q^16 - 32 * q^17 - 29 * q^18 - 3 * q^19 - 7 * q^20 - 25 * q^21 + 28 * q^22 - 27 * q^23 + 4 * q^24 + 30 * q^25 - q^26 - q^27 + 17 * q^28 - 69 * q^29 + 8 * q^30 - 13 * q^31 - 55 * q^32 - 18 * q^33 + 32 * q^34 - 23 * q^35 + 29 * q^36 + 3 * q^37 + 3 * q^38 - 28 * q^39 + 7 * q^40 - 51 * q^41 + 25 * q^42 + 23 * q^43 - 28 * q^44 - 28 * q^45 + 27 * q^46 - 27 * q^47 - 4 * q^48 + 8 * q^49 - 30 * q^50 - 42 * q^51 + q^52 - 61 * q^53 + q^54 + 5 * q^55 - 17 * q^56 - 52 * q^57 + 69 * q^58 - 71 * q^59 - 8 * q^60 - 16 * q^61 + 13 * q^62 + 14 * q^63 + 55 * q^64 - 82 * q^65 + 18 * q^66 + 32 * q^67 - 32 * q^68 - 44 * q^69 + 23 * q^70 - 84 * q^71 - 29 * q^72 - 43 * q^73 - 3 * q^74 - 37 * q^75 - 3 * q^76 - 47 * q^77 + 28 * q^78 - 20 * q^79 - 7 * q^80 - 33 * q^81 + 51 * q^82 + 17 * q^83 - 25 * q^84 + 10 * q^85 - 23 * q^86 - q^87 + 28 * q^88 - 92 * q^89 + 28 * q^90 - 34 * q^91 - 27 * q^92 - 13 * q^93 + 27 * q^94 - 60 * q^95 + 4 * q^96 - 45 * q^97 - 8 * q^98 - 73 * 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
$3$	−2.68677	−1.55121	−0.775604	−	0.631220i	$-0.782555\pi$
$3$	−2.68677	−1.55121	−0.775604	+	0.631220i	$0.782555\pi$
$4$	1.00000	0.500000
$5$	2.41964	1.08210	0.541049	−	0.840991i	$-0.318027\pi$
$5$	2.41964	1.08210	0.541049	+	0.840991i	$0.318027\pi$
$6$	2.68677	1.09687
$7$	0.726544	0.274608	0.137304	−	0.990529i	$-0.456156\pi$
$7$	0.726544	0.274608	0.137304	+	0.990529i	$0.456156\pi$
$8$	−1.00000	−0.353553
$9$	4.21874	1.40625
$10$	−2.41964	−0.765159
$11$	0.503280	0.151745	0.0758723	−	0.997118i	$-0.475826\pi$
$11$	0.503280	0.151745	0.0758723	+	0.997118i	$0.475826\pi$
$12$	−2.68677	−0.775604
$13$	−5.74772	−1.59413	−0.797066	−	0.603893i	$-0.793616\pi$
$13$	−5.74772	−1.59413	−0.797066	+	0.603893i	$0.793616\pi$
$14$	−0.726544	−0.194177
$15$	−6.50103	−1.67856
$16$	1.00000	0.250000
$17$	−0.321443	−0.0779614	−0.0389807	−	0.999240i	$-0.512411\pi$
$17$	−0.321443	−0.0779614	−0.0389807	+	0.999240i	$0.512411\pi$
$18$	−4.21874	−0.994367
$19$	−0.651470	−0.149457	−0.0747287	−	0.997204i	$-0.523809\pi$
$19$	−0.651470	−0.149457	−0.0747287	+	0.997204i	$0.523809\pi$
$20$	2.41964	0.541049
$21$	−1.95206	−0.425974
$22$	−0.503280	−0.107300
$23$	7.49028	1.56183	0.780916	−	0.624636i	$-0.214753\pi$
$23$	7.49028	1.56183	0.780916	+	0.624636i	$0.214753\pi$
$24$	2.68677	0.548435
$25$	0.854676	0.170935
$26$	5.74772	1.12722
$27$	−3.27448	−0.630173
$28$	0.726544	0.137304
$29$	2.54901	0.473340	0.236670	−	0.971590i	$-0.423944\pi$
$29$	2.54901	0.473340	0.236670	+	0.971590i	$0.423944\pi$
$30$	6.50103	1.18692
$31$	−4.47202	−0.803199	−0.401600	−	0.915815i	$-0.631546\pi$
$31$	−4.47202	−0.803199	−0.401600	+	0.915815i	$0.631546\pi$
$32$	−1.00000	−0.176777
$33$	−1.35220	−0.235387
$34$	0.321443	0.0551270
$35$	1.75798	0.297153
$36$	4.21874	0.703123
$37$	2.53517	0.416779	0.208390	−	0.978046i	$-0.433178\pi$
$37$	2.53517	0.416779	0.208390	+	0.978046i	$0.433178\pi$
$38$	0.651470	0.105682
$39$	15.4428	2.47283
$40$	−2.41964	−0.382579
$41$	−3.58246	−0.559486	−0.279743	−	0.960075i	$-0.590249\pi$
$41$	−3.58246	−0.559486	−0.279743	+	0.960075i	$0.590249\pi$
$42$	1.95206	0.301209
$43$	−8.96749	−1.36753	−0.683764	−	0.729703i	$-0.739658\pi$
$43$	−8.96749	−1.36753	−0.683764	+	0.729703i	$0.739658\pi$
$44$	0.503280	0.0758723
$45$	10.2078	1.52170
$46$	−7.49028	−1.10438
$47$	11.2039	1.63426	0.817129	−	0.576455i	$-0.195564\pi$
$47$	11.2039	1.63426	0.817129	+	0.576455i	$0.195564\pi$
$48$	−2.68677	−0.387802
$49$	−6.47213	−0.924591
$50$	−0.854676	−0.120869
$51$	0.863644	0.120934
$52$	−5.74772	−0.797066
$53$	9.93089	1.36411	0.682056	−	0.731300i	$-0.261086\pi$
$53$	9.93089	1.36411	0.682056	+	0.731300i	$0.261086\pi$
$54$	3.27448	0.445600
$55$	1.21776	0.164202
$56$	−0.726544	−0.0970885
$57$	1.75035	0.231839
$58$	−2.54901	−0.334702
$59$	−5.77896	−0.752357	−0.376178	−	0.926547i	$-0.622762\pi$
$59$	−5.77896	−0.752357	−0.376178	+	0.926547i	$0.622762\pi$
$60$	−6.50103	−0.839279
$61$	3.63044	0.464830	0.232415	−	0.972617i	$-0.425337\pi$
$61$	3.63044	0.464830	0.232415	+	0.972617i	$0.425337\pi$
$62$	4.47202	0.567948
$63$	3.06510	0.386166
$64$	1.00000	0.125000
$65$	−13.9074	−1.72501
$66$	1.35220	0.166444
$67$	−12.4264	−1.51812	−0.759062	−	0.651018i	$-0.774342\pi$
$67$	−12.4264	−1.51812	−0.759062	+	0.651018i	$0.774342\pi$
$68$	−0.321443	−0.0389807
$69$	−20.1247	−2.42273
$70$	−1.75798	−0.210119
$71$	0.0596592	0.00708025	0.00354012	−	0.999994i	$-0.498873\pi$
$71$	0.0596592	0.00708025	0.00354012	+	0.999994i	$0.498873\pi$
$72$	−4.21874	−0.497183
$73$	3.44435	0.403131	0.201566	−	0.979475i	$-0.435397\pi$
$73$	3.44435	0.403131	0.201566	+	0.979475i	$0.435397\pi$
$74$	−2.53517	−0.294708
$75$	−2.29632	−0.265156
$76$	−0.651470	−0.0747287
$77$	0.365655	0.0416703
$78$	−15.4428	−1.74855
$79$	−5.99275	−0.674237	−0.337118	−	0.941462i	$-0.609452\pi$
$79$	−5.99275	−0.674237	−0.337118	+	0.941462i	$0.609452\pi$
$80$	2.41964	0.270524
$81$	−3.85845	−0.428717
$82$	3.58246	0.395616
$83$	4.05204	0.444769	0.222385	−	0.974959i	$-0.428616\pi$
$83$	4.05204	0.444769	0.222385	+	0.974959i	$0.428616\pi$
$84$	−1.95206	−0.212987
$85$	−0.777778	−0.0843619
$86$	8.96749	0.966989
$87$	−6.84861	−0.734248
$88$	−0.503280	−0.0536498
$89$	−8.24531	−0.874002	−0.437001	−	0.899461i	$-0.643959\pi$
$89$	−8.24531	−0.874002	−0.437001	+	0.899461i	$0.643959\pi$
$90$	−10.2078	−1.07600
$91$	−4.17597	−0.437761
$92$	7.49028	0.780916
$93$	12.0153	1.24593
$94$	−11.2039	−1.15559
$95$	−1.57632	−0.161727
$96$	2.68677	0.274217
$97$	−12.1772	−1.23641	−0.618206	−	0.786016i	$-0.712140\pi$
$97$	−12.1772	−1.23641	−0.618206	+	0.786016i	$0.712140\pi$
$98$	6.47213	0.653784
$99$	2.12321	0.213390
$100$	0.854676	0.0854676
$101$	2.68599	0.267266	0.133633	−	0.991031i	$-0.457336\pi$
$101$	2.68599	0.267266	0.133633	+	0.991031i	$0.457336\pi$
$102$	−0.863644	−0.0855135
$103$	5.15469	0.507907	0.253954	−	0.967216i	$-0.418269\pi$
$103$	5.15469	0.507907	0.253954	+	0.967216i	$0.418269\pi$
$104$	5.74772	0.563611
$105$	−4.72328	−0.460945
$106$	−9.93089	−0.964573
$107$	11.3120	1.09357	0.546787	−	0.837272i	$-0.315851\pi$
$107$	11.3120	1.09357	0.546787	+	0.837272i	$0.315851\pi$
$108$	−3.27448	−0.315087
$109$	−5.55186	−0.531771	−0.265886	−	0.964005i	$-0.585664\pi$
$109$	−5.55186	−0.531771	−0.265886	+	0.964005i	$0.585664\pi$
$110$	−1.21776	−0.116109
$111$	−6.81142	−0.646512
$112$	0.726544	0.0686520
$113$	−12.4416	−1.17041	−0.585205	−	0.810885i	$-0.698986\pi$
$113$	−12.4416	−1.17041	−0.585205	+	0.810885i	$0.698986\pi$
$114$	−1.75035	−0.163935
$115$	18.1238	1.69005
$116$	2.54901	0.236670
$117$	−24.2481	−2.24174
$118$	5.77896	0.531997
$119$	−0.233543	−0.0214088
$120$	6.50103	0.593460
$121$	−10.7467	−0.976974
$122$	−3.63044	−0.328684
$123$	9.62524	0.867878
$124$	−4.47202	−0.401600
$125$	−10.0302	−0.897129
$126$	−3.06510	−0.273061
$127$	1.48656	0.131911	0.0659554	−	0.997823i	$-0.478990\pi$
$127$	1.48656	0.131911	0.0659554	+	0.997823i	$0.478990\pi$
$128$	−1.00000	−0.0883883
$129$	24.0936	2.12132
$130$	13.9074	1.21976
$131$	3.55062	0.310219	0.155109	−	0.987897i	$-0.450427\pi$
$131$	3.55062	0.310219	0.155109	+	0.987897i	$0.450427\pi$
$132$	−1.35220	−0.117694
$133$	−0.473321	−0.0410422
$134$	12.4264	1.07348
$135$	−7.92307	−0.681909
$136$	0.321443	0.0275635
$137$	5.17922	0.442490	0.221245	−	0.975218i	$-0.428988\pi$
$137$	5.17922	0.442490	0.221245	+	0.975218i	$0.428988\pi$
$138$	20.1247	1.71313
$139$	17.3443	1.47113	0.735564	−	0.677455i	$-0.236917\pi$
$139$	17.3443	1.47113	0.735564	+	0.677455i	$0.236917\pi$
$140$	1.75798	0.148576
$141$	−30.1023	−2.53507
$142$	−0.0596592	−0.00500649
$143$	−2.89271	−0.241901
$144$	4.21874	0.351562
$145$	6.16770	0.512200
$146$	−3.44435	−0.285057
$147$	17.3891	1.43423
$148$	2.53517	0.208390
$149$	−22.6644	−1.85674	−0.928368	−	0.371662i	$-0.878788\pi$
$149$	−22.6644	−1.85674	−0.928368	+	0.371662i	$0.878788\pi$
$150$	2.29632	0.187494
$151$	6.35548	0.517201	0.258601	−	0.965984i	$-0.416739\pi$
$151$	6.35548	0.517201	0.258601	+	0.965984i	$0.416739\pi$
$152$	0.651470	0.0528412
$153$	−1.35609	−0.109633
$154$	−0.365655	−0.0294653
$155$	−10.8207	−0.869140
$156$	15.4428	1.23641
$157$	17.1461	1.36841	0.684203	−	0.729292i	$-0.260150\pi$
$157$	17.1461	1.36841	0.684203	+	0.729292i	$0.260150\pi$
$158$	5.99275	0.476757
$159$	−26.6820	−2.11602
$160$	−2.41964	−0.191290
$161$	5.44202	0.428891
$162$	3.85845	0.303149
$163$	12.0212	0.941573	0.470786	−	0.882247i	$-0.343970\pi$
$163$	12.0212	0.941573	0.470786	+	0.882247i	$0.343970\pi$
$164$	−3.58246	−0.279743
$165$	−3.27184	−0.254712
$166$	−4.05204	−0.314499
$167$	−8.90564	−0.689139	−0.344569	−	0.938761i	$-0.611975\pi$
$167$	−8.90564	−0.689139	−0.344569	+	0.938761i	$0.611975\pi$
$168$	1.95206	0.150605
$169$	20.0363	1.54126
$170$	0.777778	0.0596528
$171$	−2.74838	−0.210174
$172$	−8.96749	−0.683764
$173$	7.91445	0.601725	0.300862	−	0.953668i	$-0.402726\pi$
$173$	7.91445	0.601725	0.300862	+	0.953668i	$0.402726\pi$
$174$	6.84861	0.519192
$175$	0.620960	0.0469401
$176$	0.503280	0.0379362
$177$	15.5268	1.16706
$178$	8.24531	0.618012
$179$	17.5361	1.31071	0.655355	−	0.755321i	$-0.272519\pi$
$179$	17.5361	1.31071	0.655355	+	0.755321i	$0.272519\pi$
$180$	10.2078	0.760848
$181$	−7.76300	−0.577020	−0.288510	−	0.957477i	$-0.593160\pi$
$181$	−7.76300	−0.577020	−0.288510	+	0.957477i	$0.593160\pi$
$182$	4.17597	0.309544
$183$	−9.75415	−0.721048
$184$	−7.49028	−0.552191
$185$	6.13421	0.450996
$186$	−12.0153	−0.881005
$187$	−0.161776	−0.0118302
$188$	11.2039	0.817129
$189$	−2.37905	−0.173051
$190$	1.57632	0.114359
$191$	−18.1550	−1.31365	−0.656825	−	0.754043i	$-0.728101\pi$
$191$	−18.1550	−1.31365	−0.656825	+	0.754043i	$0.728101\pi$
$192$	−2.68677	−0.193901
$193$	−10.8256	−0.779241	−0.389621	−	0.920975i	$-0.627394\pi$
$193$	−10.8256	−0.779241	−0.389621	+	0.920975i	$0.627394\pi$
$194$	12.1772	0.874276
$195$	37.3661	2.67584
$196$	−6.47213	−0.462295
$197$	5.94844	0.423809	0.211904	−	0.977290i	$-0.432033\pi$
$197$	5.94844	0.423809	0.211904	+	0.977290i	$0.432033\pi$
$198$	−2.12321	−0.150890
$199$	−23.0699	−1.63538	−0.817689	−	0.575660i	$-0.804745\pi$
$199$	−23.0699	−1.63538	−0.817689	+	0.575660i	$0.804745\pi$
$200$	−0.854676	−0.0604347
$201$	33.3869	2.35493
$202$	−2.68599	−0.188985
$203$	1.85197	0.129983
$204$	0.863644	0.0604672
$205$	−8.66827	−0.605418
$206$	−5.15469	−0.359145
$207$	31.5996	2.19632
$208$	−5.74772	−0.398533
$209$	−0.327872	−0.0226793
$210$	4.72328	0.325938
$211$	−1.41196	−0.0972034	−0.0486017	−	0.998818i	$-0.515476\pi$
$211$	−1.41196	−0.0972034	−0.0486017	+	0.998818i	$0.515476\pi$
$212$	9.93089	0.682056
$213$	−0.160291	−0.0109829
$214$	−11.3120	−0.773273
$215$	−21.6981	−1.47980
$216$	3.27448	0.222800
$217$	−3.24912	−0.220565
$218$	5.55186	0.376019
$219$	−9.25419	−0.625340
$220$	1.21776	0.0821012
$221$	1.84757	0.124281
$222$	6.81142	0.457153
$223$	12.1737	0.815214	0.407607	−	0.913157i	$-0.366363\pi$
$223$	12.1737	0.815214	0.407607	+	0.913157i	$0.366363\pi$
$224$	−0.726544	−0.0485443
$225$	3.60566	0.240377
$226$	12.4416	0.827605
$227$	19.0191	1.26234	0.631170	−	0.775644i	$-0.282575\pi$
$227$	19.0191	1.26234	0.631170	+	0.775644i	$0.282575\pi$
$228$	1.75035	0.115920
$229$	−11.6184	−0.767765	−0.383882	−	0.923382i	$-0.625413\pi$
$229$	−11.6184	−0.767765	−0.383882	+	0.923382i	$0.625413\pi$
$230$	−18.1238	−1.19505
$231$	−0.982432	−0.0646393
$232$	−2.54901	−0.167351
$233$	15.1058	0.989616	0.494808	−	0.869002i	$-0.335238\pi$
$233$	15.1058	0.989616	0.494808	+	0.869002i	$0.335238\pi$
$234$	24.2481	1.58515
$235$	27.1095	1.76843
$236$	−5.77896	−0.376178
$237$	16.1011	1.04588
$238$	0.233543	0.0151383
$239$	−20.4129	−1.32040	−0.660201	−	0.751089i	$-0.729529\pi$
$239$	−20.4129	−1.32040	−0.660201	+	0.751089i	$0.729529\pi$
$240$	−6.50103	−0.419640
$241$	15.2445	0.981986	0.490993	−	0.871164i	$-0.336634\pi$
$241$	15.2445	0.981986	0.490993	+	0.871164i	$0.336634\pi$
$242$	10.7467	0.690825
$243$	20.1902	1.29520
$244$	3.63044	0.232415
$245$	−15.6603	−1.00050
$246$	−9.62524	−0.613683
$247$	3.74447	0.238255
$248$	4.47202	0.283974
$249$	−10.8869	−0.689930
$250$	10.0302	0.634366
$251$	−6.64435	−0.419388	−0.209694	−	0.977767i	$-0.567247\pi$
$251$	−6.64435	−0.419388	−0.209694	+	0.977767i	$0.567247\pi$
$252$	3.06510	0.193083
$253$	3.76971	0.237000
$254$	−1.48656	−0.0932750
$255$	2.08971	0.130863
$256$	1.00000	0.0625000
$257$	−12.6836	−0.791182	−0.395591	−	0.918427i	$-0.629460\pi$
$257$	−12.6836	−0.791182	−0.395591	+	0.918427i	$0.629460\pi$
$258$	−24.0936	−1.50000
$259$	1.84191	0.114451
$260$	−13.9074	−0.862503
$261$	10.7536	0.665632
$262$	−3.55062	−0.219358
$263$	8.29694	0.511611	0.255806	−	0.966728i	$-0.417659\pi$
$263$	8.29694	0.511611	0.255806	+	0.966728i	$0.417659\pi$
$264$	1.35220	0.0832220
$265$	24.0292	1.47610
$266$	0.473321	0.0290212
$267$	22.1533	1.35576
$268$	−12.4264	−0.759062
$269$	10.8962	0.664355	0.332178	−	0.943217i	$-0.392217\pi$
$269$	10.8962	0.664355	0.332178	+	0.943217i	$0.392217\pi$
$270$	7.92307	0.482182
$271$	31.6380	1.92187	0.960936	−	0.276770i	$-0.0892639\pi$
$271$	31.6380	1.92187	0.960936	+	0.276770i	$0.0892639\pi$
$272$	−0.321443	−0.0194904
$273$	11.2199	0.679058
$274$	−5.17922	−0.312888
$275$	0.430141	0.0259385
$276$	−20.1247	−1.21136
$277$	−16.9896	−1.02081	−0.510403	−	0.859935i	$-0.670504\pi$
$277$	−16.9896	−1.02081	−0.510403	+	0.859935i	$0.670504\pi$
$278$	−17.3443	−1.04024
$279$	−18.8663	−1.12950
$280$	−1.75798	−0.105059
$281$	2.04737	0.122136	0.0610679	−	0.998134i	$-0.480549\pi$
$281$	2.04737	0.122136	0.0610679	+	0.998134i	$0.480549\pi$
$282$	30.1023	1.79257
$283$	29.1384	1.73210	0.866048	−	0.499961i	$-0.166652\pi$
$283$	29.1384	1.73210	0.866048	+	0.499961i	$0.166652\pi$
$284$	0.0596592	0.00354012
$285$	4.23522	0.250873
$286$	2.89271	0.171050
$287$	−2.60281	−0.153639
$288$	−4.21874	−0.248592
$289$	−16.8967	−0.993922
$290$	−6.16770	−0.362180
$291$	32.7175	1.91793
$292$	3.44435	0.201566
$293$	5.71590	0.333927	0.166963	−	0.985963i	$-0.446604\pi$
$293$	5.71590	0.333927	0.166963	+	0.985963i	$0.446604\pi$
$294$	−17.3891	−1.01416
$295$	−13.9830	−0.814124
$296$	−2.53517	−0.147354
$297$	−1.64798	−0.0956254
$298$	22.6644	1.31291
$299$	−43.0521	−2.48977
$300$	−2.29632	−0.132578
$301$	−6.51527	−0.375534
$302$	−6.35548	−0.365717
$303$	−7.21663	−0.414585
$304$	−0.651470	−0.0373643
$305$	8.78436	0.502991
$306$	1.35609	0.0775222
$307$	−8.38106	−0.478332	−0.239166	−	0.970979i	$-0.576874\pi$
$307$	−8.38106	−0.478332	−0.239166	+	0.970979i	$0.576874\pi$
$308$	0.365655	0.0208351
$309$	−13.8495	−0.787870
$310$	10.8207	0.614575
$311$	−3.82896	−0.217120	−0.108560	−	0.994090i	$-0.534624\pi$
$311$	−3.82896	−0.217120	−0.108560	+	0.994090i	$0.534624\pi$
$312$	−15.4428	−0.874277
$313$	−22.7116	−1.28374	−0.641868	−	0.766815i	$-0.721840\pi$
$313$	−22.7116	−1.28374	−0.641868	+	0.766815i	$0.721840\pi$
$314$	−17.1461	−0.967609
$315$	7.41645	0.417870
$316$	−5.99275	−0.337118
$317$	−23.4346	−1.31622	−0.658110	−	0.752922i	$-0.728644\pi$
$317$	−23.4346	−1.31622	−0.658110	+	0.752922i	$0.728644\pi$
$318$	26.6820	1.49625
$319$	1.28287	0.0718267
$320$	2.41964	0.135262
$321$	−30.3928	−1.69636
$322$	−5.44202	−0.303272
$323$	0.209410	0.0116519
$324$	−3.85845	−0.214358
$325$	−4.91244	−0.272493
$326$	−12.0212	−0.665793
$327$	14.9166	0.824888
$328$	3.58246	0.197808
$329$	8.14013	0.448780
$330$	3.27184	0.180109
$331$	0.223764	0.0122992	0.00614960	−	0.999981i	$-0.498043\pi$
$331$	0.223764	0.0122992	0.00614960	+	0.999981i	$0.498043\pi$
$332$	4.05204	0.222385
$333$	10.6952	0.586095
$334$	8.90564	0.487295
$335$	−30.0674	−1.64276
$336$	−1.95206	−0.106493
$337$	−25.1147	−1.36809	−0.684044	−	0.729441i	$-0.739780\pi$
$337$	−25.1147	−1.36809	−0.684044	+	0.729441i	$0.739780\pi$
$338$	−20.0363	−1.08983
$339$	33.4278	1.81555
$340$	−0.777778	−0.0421809
$341$	−2.25068	−0.121881
$342$	2.74838	0.148615
$343$	−9.78810	−0.528508
$344$	8.96749	0.483494
$345$	−48.6945	−2.62163
$346$	−7.91445	−0.425483
$347$	−34.7202	−1.86388	−0.931940	−	0.362613i	$-0.881885\pi$
$347$	−34.7202	−1.86388	−0.931940	+	0.362613i	$0.881885\pi$
$348$	−6.84861	−0.367124
$349$	−33.3608	−1.78576	−0.892881	−	0.450294i	$-0.851319\pi$
$349$	−33.3608	−1.78576	−0.892881	+	0.450294i	$0.851319\pi$
$350$	−0.620960	−0.0331917
$351$	18.8208	1.00458
$352$	−0.503280	−0.0268249
$353$	15.9976	0.851467	0.425734	−	0.904849i	$-0.360016\pi$
$353$	15.9976	0.851467	0.425734	+	0.904849i	$0.360016\pi$
$354$	−15.5268	−0.825238
$355$	0.144354	0.00766152
$356$	−8.24531	−0.437001
$357$	0.627476	0.0332095
$358$	−17.5361	−0.926811
$359$	−3.25558	−0.171823	−0.0859114	−	0.996303i	$-0.527380\pi$
$359$	−3.25558	−0.171823	−0.0859114	+	0.996303i	$0.527380\pi$
$360$	−10.2078	−0.538001
$361$	−18.5756	−0.977662
$362$	7.76300	0.408014
$363$	28.8740	1.51549
$364$	−4.17597	−0.218881
$365$	8.33411	0.436227
$366$	9.75415	0.509858
$367$	−31.4101	−1.63960	−0.819798	−	0.572654i	$-0.805914\pi$
$367$	−31.4101	−1.63960	−0.819798	+	0.572654i	$0.805914\pi$
$368$	7.49028	0.390458
$369$	−15.1134	−0.786775
$370$	−6.13421	−0.318902
$371$	7.21523	0.374596
$372$	12.0153	0.622965
$373$	−21.2766	−1.10166	−0.550829	−	0.834618i	$-0.685689\pi$
$373$	−21.2766	−1.10166	−0.550829	+	0.834618i	$0.685689\pi$
$374$	0.161776	0.00836523
$375$	26.9489	1.39163
$376$	−11.2039	−0.577797
$377$	−14.6510	−0.754566
$378$	2.37905	0.122365
$379$	−1.09172	−0.0560781	−0.0280390	−	0.999607i	$-0.508926\pi$
$379$	−1.09172	−0.0560781	−0.0280390	+	0.999607i	$0.508926\pi$
$380$	−1.57632	−0.0808637
$381$	−3.99405	−0.204621
$382$	18.1550	0.928891
$383$	−11.7811	−0.601986	−0.300993	−	0.953626i	$-0.597318\pi$
$383$	−11.7811	−0.601986	−0.300993	+	0.953626i	$0.597318\pi$
$384$	2.68677	0.137109
$385$	0.884755	0.0450913
$386$	10.8256	0.551007
$387$	−37.8315	−1.92308
$388$	−12.1772	−0.618206
$389$	−20.7435	−1.05174	−0.525869	−	0.850566i	$-0.676260\pi$
$389$	−20.7435	−1.05174	−0.525869	+	0.850566i	$0.676260\pi$
$390$	−37.3661	−1.89211
$391$	−2.40770	−0.121763
$392$	6.47213	0.326892
$393$	−9.53969	−0.481214
$394$	−5.94844	−0.299678
$395$	−14.5003	−0.729590
$396$	2.12321	0.106695
$397$	35.0331	1.75826	0.879132	−	0.476579i	$-0.158123\pi$
$397$	35.0331	1.75826	0.879132	+	0.476579i	$0.158123\pi$
$398$	23.0699	1.15639
$399$	1.27171	0.0636649
$400$	0.854676	0.0427338
$401$	13.6105	0.679677	0.339839	−	0.940484i	$-0.389628\pi$
$401$	13.6105	0.679677	0.339839	+	0.940484i	$0.389628\pi$
$402$	−33.3869	−1.66519
$403$	25.7040	1.28041
$404$	2.68599	0.133633
$405$	−9.33608	−0.463913
$406$	−1.85197	−0.0919117
$407$	1.27590	0.0632440
$408$	−0.863644	−0.0427568
$409$	−2.02389	−0.100075	−0.0500376	−	0.998747i	$-0.515934\pi$
$409$	−2.02389	−0.100075	−0.0500376	+	0.998747i	$0.515934\pi$
$410$	8.66827	0.428095
$411$	−13.9154	−0.686395
$412$	5.15469	0.253954
$413$	−4.19867	−0.206603
$414$	−31.5996	−1.55303
$415$	9.80450	0.481284
$416$	5.74772	0.281805
$417$	−46.6003	−2.28203
$418$	0.327872	0.0160367
$419$	18.0655	0.882559	0.441280	−	0.897370i	$-0.354525\pi$
$419$	18.0655	0.882559	0.441280	+	0.897370i	$0.354525\pi$
$420$	−4.72328	−0.230473
$421$	−31.3770	−1.52922	−0.764610	−	0.644493i	$-0.777068\pi$
$421$	−31.3770	−1.52922	−0.764610	+	0.644493i	$0.777068\pi$
$422$	1.41196	0.0687332
$423$	47.2664	2.29817
$424$	−9.93089	−0.482286
$425$	−0.274730	−0.0133263
$426$	0.160291	0.00776611
$427$	2.63767	0.127646
$428$	11.3120	0.546787
$429$	7.77206	0.375239
$430$	21.6981	1.04638
$431$	−17.8785	−0.861178	−0.430589	−	0.902548i	$-0.641694\pi$
$431$	−17.8785	−0.861178	−0.430589	+	0.902548i	$0.641694\pi$
$432$	−3.27448	−0.157543
$433$	−30.8295	−1.48157	−0.740786	−	0.671741i	$-0.765547\pi$
$433$	−30.8295	−1.48157	−0.740786	+	0.671741i	$0.765547\pi$
$434$	3.24912	0.155963
$435$	−16.5712	−0.794528
$436$	−5.55186	−0.265886
$437$	−4.87969	−0.233427
$438$	9.25419	0.442182
$439$	16.9075	0.806952	0.403476	−	0.914990i	$-0.367802\pi$
$439$	16.9075	0.806952	0.403476	+	0.914990i	$0.367802\pi$
$440$	−1.21776	−0.0580543
$441$	−27.3043	−1.30020
$442$	−1.84757	−0.0878798
$443$	−2.16137	−0.102690	−0.0513448	−	0.998681i	$-0.516351\pi$
$443$	−2.16137	−0.102690	−0.0513448	+	0.998681i	$0.516351\pi$
$444$	−6.81142	−0.323256
$445$	−19.9507	−0.945755
$446$	−12.1737	−0.576443
$447$	60.8939	2.88018
$448$	0.726544	0.0343260
$449$	−20.8890	−0.985813	−0.492906	−	0.870082i	$-0.664066\pi$
$449$	−20.8890	−0.985813	−0.492906	+	0.870082i	$0.664066\pi$
$450$	−3.60566	−0.169972
$451$	−1.80298	−0.0848989
$452$	−12.4416	−0.585205
$453$	−17.0757	−0.802287
$454$	−19.0191	−0.892610
$455$	−10.1044	−0.473700
$456$	−1.75035	−0.0819676
$457$	−4.31549	−0.201870	−0.100935	−	0.994893i	$-0.532183\pi$
$457$	−4.31549	−0.201870	−0.100935	+	0.994893i	$0.532183\pi$
$458$	11.6184	0.542892
$459$	1.05256	0.0491292
$460$	18.1238	0.845027
$461$	−20.4171	−0.950918	−0.475459	−	0.879738i	$-0.657718\pi$
$461$	−20.4171	−0.950918	−0.475459	+	0.879738i	$0.657718\pi$
$462$	0.982432	0.0457069
$463$	−25.7943	−1.19876	−0.599381	−	0.800464i	$-0.704586\pi$
$463$	−25.7943	−1.19876	−0.599381	+	0.800464i	$0.704586\pi$
$464$	2.54901	0.118335
$465$	29.0728	1.34822
$466$	−15.1058	−0.699764
$467$	−0.205438	−0.00950655	−0.00475328	−	0.999989i	$-0.501513\pi$
$467$	−0.205438	−0.00950655	−0.00475328	+	0.999989i	$0.501513\pi$
$468$	−24.2481	−1.12087
$469$	−9.02832	−0.416889
$470$	−27.1095	−1.25047
$471$	−46.0676	−2.12268
$472$	5.77896	0.265998
$473$	−4.51316	−0.207515
$474$	−16.1011	−0.739550
$475$	−0.556795	−0.0255475
$476$	−0.233543	−0.0107044
$477$	41.8958	1.91828
$478$	20.4129	0.933665
$479$	−22.9713	−1.04959	−0.524794	−	0.851230i	$-0.675857\pi$
$479$	−22.9713	−1.04959	−0.524794	+	0.851230i	$0.675857\pi$
$480$	6.50103	0.296730
$481$	−14.5715	−0.664401
$482$	−15.2445	−0.694369
$483$	−14.6215	−0.665300
$484$	−10.7467	−0.488487
$485$	−29.4646	−1.33792
$486$	−20.1902	−0.915846
$487$	−5.08641	−0.230487	−0.115244	−	0.993337i	$-0.536765\pi$
$487$	−5.08641	−0.230487	−0.115244	+	0.993337i	$0.536765\pi$
$488$	−3.63044	−0.164342
$489$	−32.2982	−1.46058
$490$	15.6603	0.707458
$491$	19.2098	0.866925	0.433462	−	0.901172i	$-0.357292\pi$
$491$	19.2098	0.866925	0.433462	+	0.901172i	$0.357292\pi$
$492$	9.62524	0.433939
$493$	−0.819362	−0.0369022
$494$	−3.74447	−0.168472
$495$	5.13741	0.230909
$496$	−4.47202	−0.200800
$497$	0.0433451	0.00194429
$498$	10.8869	0.487854
$499$	−9.01485	−0.403560	−0.201780	−	0.979431i	$-0.564673\pi$
$499$	−9.01485	−0.403560	−0.201780	+	0.979431i	$0.564673\pi$
$500$	−10.0302	−0.448565
$501$	23.9274	1.06900
$502$	6.64435	0.296552
$503$	17.7995	0.793641	0.396821	−	0.917896i	$-0.370114\pi$
$503$	17.7995	0.793641	0.396821	+	0.917896i	$0.370114\pi$
$504$	−3.06510	−0.136530
$505$	6.49913	0.289208
$506$	−3.76971	−0.167584
$507$	−53.8330	−2.39081
$508$	1.48656	0.0659554
$509$	−7.32803	−0.324809	−0.162405	−	0.986724i	$-0.551925\pi$
$509$	−7.32803	−0.324809	−0.162405	+	0.986724i	$0.551925\pi$
$510$	−2.08971	−0.0925340
$511$	2.50247	0.110703
$512$	−1.00000	−0.0441942
$513$	2.13322	0.0941840
$514$	12.6836	0.559450
$515$	12.4725	0.549605
$516$	24.0936	1.06066
$517$	5.63870	0.247990
$518$	−1.84191	−0.0809290
$519$	−21.2643	−0.933400
$520$	13.9074	0.609882
$521$	0.761835	0.0333766	0.0166883	−	0.999861i	$-0.494688\pi$
$521$	0.761835	0.0333766	0.0166883	+	0.999861i	$0.494688\pi$
$522$	−10.7536	−0.470673
$523$	25.6723	1.12257	0.561287	−	0.827622i	$-0.310307\pi$
$523$	25.6723	1.12257	0.561287	+	0.827622i	$0.310307\pi$
$524$	3.55062	0.155109
$525$	−1.66838	−0.0728139
$526$	−8.29694	−0.361764
$527$	1.43750	0.0626185
$528$	−1.35220	−0.0588469
$529$	33.1043	1.43932
$530$	−24.0292	−1.04376
$531$	−24.3799	−1.05800
$532$	−0.473321	−0.0205211
$533$	20.5910	0.891893
$534$	−22.1533	−0.958666
$535$	27.3710	1.18335
$536$	12.4264	0.536738
$537$	−47.1155	−2.03318
$538$	−10.8962	−0.469770
$539$	−3.25730	−0.140302
$540$	−7.92307	−0.340954
$541$	41.0552	1.76510	0.882551	−	0.470217i	$-0.155824\pi$
$541$	41.0552	1.76510	0.882551	+	0.470217i	$0.155824\pi$
$542$	−31.6380	−1.35897
$543$	20.8574	0.895077
$544$	0.321443	0.0137818
$545$	−13.4335	−0.575429
$546$	−11.2199	−0.480167
$547$	−28.2070	−1.20604	−0.603022	−	0.797725i	$-0.706037\pi$
$547$	−28.2070	−1.20604	−0.603022	+	0.797725i	$0.706037\pi$
$548$	5.17922	0.221245
$549$	15.3159	0.653665
$550$	−0.430141	−0.0183413
$551$	−1.66060	−0.0707441
$552$	20.1247	0.856563
$553$	−4.35399	−0.185151
$554$	16.9896	0.721819
$555$	−16.4812	−0.699589
$556$	17.3443	0.735564
$557$	−22.8655	−0.968843	−0.484421	−	0.874835i	$-0.660970\pi$
$557$	−22.8655	−0.968843	−0.484421	+	0.874835i	$0.660970\pi$
$558$	18.8663	0.798674
$559$	51.5426	2.18002
$560$	1.75798	0.0742881
$561$	0.434655	0.0183511
$562$	−2.04737	−0.0863630
$563$	−11.8895	−0.501083	−0.250541	−	0.968106i	$-0.580609\pi$
$563$	−11.8895	−0.501083	−0.250541	+	0.968106i	$0.580609\pi$
$564$	−30.1023	−1.26754
$565$	−30.1043	−1.26650
$566$	−29.1384	−1.22478
$567$	−2.80334	−0.117729
$568$	−0.0596592	−0.00250324
$569$	−8.10008	−0.339573	−0.169786	−	0.985481i	$-0.554308\pi$
$569$	−8.10008	−0.339573	−0.169786	+	0.985481i	$0.554308\pi$
$570$	−4.23522	−0.177394
$571$	23.0272	0.963659	0.481829	−	0.876265i	$-0.339972\pi$
$571$	23.0272	0.963659	0.481829	+	0.876265i	$0.339972\pi$
$572$	−2.89271	−0.120950
$573$	48.7784	2.03775
$574$	2.60281	0.108639
$575$	6.40176	0.266972
$576$	4.21874	0.175781
$577$	2.65853	0.110676	0.0553381	−	0.998468i	$-0.482376\pi$
$577$	2.65853	0.110676	0.0553381	+	0.998468i	$0.482376\pi$
$578$	16.8967	0.702809
$579$	29.0858	1.20877
$580$	6.16770	0.256100
$581$	2.94399	0.122137
$582$	−32.7175	−1.35618
$583$	4.99802	0.206997
$584$	−3.44435	−0.142528
$585$	−58.6719	−2.42578
$586$	−5.71590	−0.236122
$587$	44.1168	1.82089	0.910447	−	0.413626i	$-0.135738\pi$
$587$	44.1168	1.82089	0.910447	+	0.413626i	$0.135738\pi$
$588$	17.3891	0.717116
$589$	2.91339	0.120044
$590$	13.9830	0.575672
$591$	−15.9821	−0.657415
$592$	2.53517	0.104195
$593$	−0.747260	−0.0306863	−0.0153431	−	0.999882i	$-0.504884\pi$
$593$	−0.747260	−0.0306863	−0.0153431	+	0.999882i	$0.504884\pi$
$594$	1.64798	0.0676174
$595$	−0.565090	−0.0231664
$596$	−22.6644	−0.928368
$597$	61.9834	2.53681
$598$	43.0521	1.76053
$599$	−39.9527	−1.63242	−0.816212	−	0.577753i	$-0.803930\pi$
$599$	−39.9527	−1.63242	−0.816212	+	0.577753i	$0.803930\pi$
$600$	2.29632	0.0937468
$601$	−13.3784	−0.545718	−0.272859	−	0.962054i	$-0.587969\pi$
$601$	−13.3784	−0.545718	−0.272859	+	0.962054i	$0.587969\pi$
$602$	6.51527	0.265543
$603$	−52.4237	−2.13486
$604$	6.35548	0.258601
$605$	−26.0032	−1.05718
$606$	7.21663	0.293156
$607$	0.0944379	0.00383312	0.00191656	−	0.999998i	$-0.499390\pi$
$607$	0.0944379	0.00383312	0.00191656	+	0.999998i	$0.499390\pi$
$608$	0.651470	0.0264206
$609$	−4.97582	−0.201630
$610$	−8.78436	−0.355668
$611$	−64.3969	−2.60522
$612$	−1.35609	−0.0548165
$613$	18.3840	0.742521	0.371261	−	0.928529i	$-0.378926\pi$
$613$	18.3840	0.742521	0.371261	+	0.928529i	$0.378926\pi$
$614$	8.38106	0.338232
$615$	23.2896	0.939129
$616$	−0.365655	−0.0147327
$617$	−44.0160	−1.77202	−0.886010	−	0.463667i	$-0.846533\pi$
$617$	−44.0160	−1.77202	−0.886010	+	0.463667i	$0.846533\pi$
$618$	13.8495	0.557108
$619$	−1.76036	−0.0707549	−0.0353775	−	0.999374i	$-0.511263\pi$
$619$	−1.76036	−0.0707549	−0.0353775	+	0.999374i	$0.511263\pi$
$620$	−10.8207	−0.434570
$621$	−24.5268	−0.984225
$622$	3.82896	0.153527
$623$	−5.99058	−0.240008
$624$	15.4428	0.618207
$625$	−28.5429	−1.14172
$626$	22.7116	0.907739
$627$	0.880916	0.0351804
$628$	17.1461	0.684203
$629$	−0.814913	−0.0324927
$630$	−7.41645	−0.295479
$631$	−42.0704	−1.67480	−0.837399	−	0.546592i	$-0.815925\pi$
$631$	−42.0704	−1.67480	−0.837399	+	0.546592i	$0.815925\pi$
$632$	5.99275	0.238379
$633$	3.79361	0.150783
$634$	23.4346	0.930708
$635$	3.59694	0.142740
$636$	−26.6820	−1.05801
$637$	37.2000	1.47392
$638$	−1.28287	−0.0507892
$639$	0.251687	0.00995657
$640$	−2.41964	−0.0956448
$641$	35.1629	1.38885	0.694425	−	0.719565i	$-0.255659\pi$
$641$	35.1629	1.38885	0.694425	+	0.719565i	$0.255659\pi$
$642$	30.3928	1.19951
$643$	−25.4011	−1.00172	−0.500860	−	0.865528i	$-0.666983\pi$
$643$	−25.4011	−1.00172	−0.500860	+	0.865528i	$0.666983\pi$
$644$	5.44202	0.214446
$645$	58.2979	2.29548
$646$	−0.209410	−0.00823914
$647$	37.6137	1.47875	0.739373	−	0.673296i	$-0.235122\pi$
$647$	37.6137	1.47875	0.739373	+	0.673296i	$0.235122\pi$
$648$	3.85845	0.151574
$649$	−2.90844	−0.114166
$650$	4.91244	0.192682
$651$	8.72965	0.342142
$652$	12.0212	0.470786
$653$	−15.0726	−0.589835	−0.294918	−	0.955523i	$-0.595292\pi$
$653$	−15.0726	−0.589835	−0.294918	+	0.955523i	$0.595292\pi$
$654$	−14.9166	−0.583284
$655$	8.59123	0.335687
$656$	−3.58246	−0.139871
$657$	14.5308	0.566902
$658$	−8.14013	−0.317335
$659$	−34.4527	−1.34209	−0.671043	−	0.741418i	$-0.734154\pi$
$659$	−34.4527	−1.34209	−0.671043	+	0.741418i	$0.734154\pi$
$660$	−3.27184	−0.127356
$661$	15.7173	0.611334	0.305667	−	0.952139i	$-0.401121\pi$
$661$	15.7173	0.611334	0.305667	+	0.952139i	$0.401121\pi$
$662$	−0.223764	−0.00869685
$663$	−4.96399	−0.192785
$664$	−4.05204	−0.157250
$665$	−1.14527	−0.0444116
$666$	−10.6952	−0.414432
$667$	19.0928	0.739277
$668$	−8.90564	−0.344569
$669$	−32.7081	−1.26457
$670$	30.0674	1.16161
$671$	1.82713	0.0705354
$672$	1.95206	0.0753023
$673$	18.1463	0.699490	0.349745	−	0.936845i	$-0.386268\pi$
$673$	18.1463	0.699490	0.349745	+	0.936845i	$0.386268\pi$
$674$	25.1147	0.967384
$675$	−2.79862	−0.107719
$676$	20.0363	0.770628
$677$	4.71557	0.181234	0.0906170	−	0.995886i	$-0.471116\pi$
$677$	4.71557	0.181234	0.0906170	+	0.995886i	$0.471116\pi$
$678$	−33.4278	−1.28379
$679$	−8.84731	−0.339529
$680$	0.777778	0.0298264
$681$	−51.0999	−1.95815
$682$	2.25068	0.0861830
$683$	26.0556	0.996989	0.498494	−	0.866893i	$-0.333886\pi$
$683$	26.0556	0.996989	0.498494	+	0.866893i	$0.333886\pi$
$684$	−2.74838	−0.105087
$685$	12.5319	0.478818
$686$	9.78810	0.373711
$687$	31.2160	1.19096
$688$	−8.96749	−0.341882
$689$	−57.0800	−2.17457
$690$	48.6945	1.85377
$691$	6.69158	0.254560	0.127280	−	0.991867i	$-0.459375\pi$
$691$	6.69158	0.254560	0.127280	+	0.991867i	$0.459375\pi$
$692$	7.91445	0.300862
$693$	1.54260	0.0585987
$694$	34.7202	1.31796
$695$	41.9671	1.59190
$696$	6.84861	0.259596
$697$	1.15156	0.0436183
$698$	33.3608	1.26272
$699$	−40.5859	−1.53510
$700$	0.620960	0.0234701
$701$	−14.8845	−0.562181	−0.281091	−	0.959681i	$-0.590696\pi$
$701$	−14.8845	−0.562181	−0.281091	+	0.959681i	$0.590696\pi$
$702$	−18.8208	−0.710345
$703$	−1.65159	−0.0622908
$704$	0.503280	0.0189681
$705$	−72.8369	−2.74320
$706$	−15.9976	−0.602078
$707$	1.95149	0.0733933
$708$	15.5268	0.583531
$709$	−3.81593	−0.143310	−0.0716551	−	0.997429i	$-0.522828\pi$
$709$	−3.81593	−0.143310	−0.0716551	+	0.997429i	$0.522828\pi$
$710$	−0.144354	−0.00541751
$711$	−25.2818	−0.948143
$712$	8.24531	0.309006
$713$	−33.4967	−1.25446
$714$	−0.627476	−0.0234827
$715$	−6.99934	−0.261760
$716$	17.5361	0.655355
$717$	54.8448	2.04822
$718$	3.25558	0.121497
$719$	7.19464	0.268315	0.134157	−	0.990960i	$-0.457167\pi$
$719$	7.19464	0.268315	0.134157	+	0.990960i	$0.457167\pi$
$720$	10.2078	0.380424
$721$	3.74511	0.139475
$722$	18.5756	0.691312
$723$	−40.9585	−1.52326
$724$	−7.76300	−0.288510
$725$	2.17858	0.0809104
$726$	−28.8740	−1.07161
$727$	−24.0915	−0.893504	−0.446752	−	0.894658i	$-0.647419\pi$
$727$	−24.0915	−0.893504	−0.446752	+	0.894658i	$0.647419\pi$
$728$	4.17597	0.154772
$729$	−42.6711	−1.58041
$730$	−8.33411	−0.308459
$731$	2.88254	0.106614
$732$	−9.75415	−0.360524
$733$	23.9730	0.885462	0.442731	−	0.896655i	$-0.354010\pi$
$733$	23.9730	0.885462	0.442731	+	0.896655i	$0.354010\pi$
$734$	31.4101	1.15937
$735$	42.0755	1.55198
$736$	−7.49028	−0.276095
$737$	−6.25395	−0.230367
$738$	15.1134	0.556334
$739$	31.2470	1.14944	0.574720	−	0.818350i	$-0.305111\pi$
$739$	31.2470	1.14944	0.574720	+	0.818350i	$0.305111\pi$
$740$	6.13421	0.225498
$741$	−10.0605	−0.369583
$742$	−7.21523	−0.264879
$743$	−10.4043	−0.381698	−0.190849	−	0.981619i	$-0.561124\pi$
$743$	−10.4043	−0.381698	−0.190849	+	0.981619i	$0.561124\pi$
$744$	−12.0153	−0.440502
$745$	−54.8397	−2.00917
$746$	21.2766	0.778991
$747$	17.0945	0.625456
$748$	−0.161776	−0.00591511
$749$	8.21868	0.300304
$750$	−26.9489	−0.984034
$751$	−42.0345	−1.53386	−0.766931	−	0.641729i	$-0.778217\pi$
$751$	−42.0345	−1.53386	−0.766931	+	0.641729i	$0.778217\pi$
$752$	11.2039	0.408564
$753$	17.8519	0.650558
$754$	14.6510	0.533558
$755$	15.3780	0.559662
$756$	−2.37905	−0.0865253
$757$	−29.9845	−1.08980	−0.544902	−	0.838500i	$-0.683433\pi$
$757$	−29.9845	−1.08980	−0.544902	+	0.838500i	$0.683433\pi$
$758$	1.09172	0.0396532
$759$	−10.1283	−0.367636
$760$	1.57632	0.0571793
$761$	32.8812	1.19194	0.595972	−	0.803005i	$-0.296767\pi$
$761$	32.8812	1.19194	0.595972	+	0.803005i	$0.296767\pi$
$762$	3.99405	0.144689
$763$	−4.03367	−0.146029
$764$	−18.1550	−0.656825
$765$	−3.28124	−0.118634
$766$	11.7811	0.425668
$767$	33.2159	1.19936
$768$	−2.68677	−0.0969505
$769$	−18.0594	−0.651240	−0.325620	−	0.945501i	$-0.605573\pi$
$769$	−18.0594	−0.651240	−0.325620	+	0.945501i	$0.605573\pi$
$770$	−0.884755	−0.0318844
$771$	34.0779	1.22729
$772$	−10.8256	−0.389621
$773$	−38.2282	−1.37497	−0.687487	−	0.726196i	$-0.741286\pi$
$773$	−38.2282	−1.37497	−0.687487	+	0.726196i	$0.741286\pi$
$774$	37.8315	1.35983
$775$	−3.82213	−0.137295
$776$	12.1772	0.437138
$777$	−4.94880	−0.177537
$778$	20.7435	0.743690
$779$	2.33386	0.0836192
$780$	37.3661	1.33792
$781$	0.0300253	0.00107439
$782$	2.40770	0.0860992
$783$	−8.34668	−0.298286
$784$	−6.47213	−0.231148
$785$	41.4874	1.48075
$786$	9.53969	0.340270
$787$	−23.4195	−0.834813	−0.417407	−	0.908720i	$-0.637061\pi$
$787$	−23.4195	−0.834813	−0.417407	+	0.908720i	$0.637061\pi$
$788$	5.94844	0.211904
$789$	−22.2920	−0.793616
$790$	14.5003	0.515898
$791$	−9.03939	−0.321404
$792$	−2.12321	−0.0754449
$793$	−20.8667	−0.741000
$794$	−35.0331	−1.24328
$795$	−64.5610	−2.28974
$796$	−23.0699	−0.817689
$797$	−25.3188	−0.896838	−0.448419	−	0.893823i	$-0.648013\pi$
$797$	−25.3188	−0.896838	−0.448419	+	0.893823i	$0.648013\pi$
$798$	−1.27171	−0.0450179
$799$	−3.60142	−0.127409
$800$	−0.854676	−0.0302174
$801$	−34.7848	−1.22906
$802$	−13.6105	−0.480604
$803$	1.73347	0.0611730
$804$	33.3869	1.17746
$805$	13.1678	0.464102
$806$	−25.7040	−0.905383
$807$	−29.2757	−1.03055
$808$	−2.68599	−0.0944927
$809$	22.9593	0.807207	0.403604	−	0.914934i	$-0.367757\pi$
$809$	22.9593	0.807207	0.403604	+	0.914934i	$0.367757\pi$
$810$	9.33608	0.328036
$811$	26.4898	0.930184	0.465092	−	0.885262i	$-0.346021\pi$
$811$	26.4898	0.930184	0.465092	+	0.885262i	$0.346021\pi$
$812$	1.85197	0.0649914
$813$	−85.0041	−2.98122
$814$	−1.27590	−0.0447203
$815$	29.0870	1.01887
$816$	0.863644	0.0302336
$817$	5.84204	0.204387
$818$	2.02389	0.0707638
$819$	−17.6174	−0.615600
$820$	−8.66827	−0.302709
$821$	−49.3496	−1.72231	−0.861157	−	0.508339i	$-0.830260\pi$
$821$	−49.3496	−1.72231	−0.861157	+	0.508339i	$0.830260\pi$
$822$	13.9154	0.485354
$823$	31.0013	1.08064	0.540319	−	0.841460i	$-0.318303\pi$
$823$	31.0013	1.08064	0.540319	+	0.841460i	$0.318303\pi$
$824$	−5.15469	−0.179572
$825$	−1.15569	−0.0402360
$826$	4.19867	0.146090
$827$	−14.6183	−0.508328	−0.254164	−	0.967161i	$-0.581800\pi$
$827$	−14.6183	−0.508328	−0.254164	+	0.967161i	$0.581800\pi$
$828$	31.5996	1.09816
$829$	−15.1618	−0.526591	−0.263296	−	0.964715i	$-0.584809\pi$
$829$	−15.1618	−0.526591	−0.263296	+	0.964715i	$0.584809\pi$
$830$	−9.80450	−0.340319
$831$	45.6472	1.58348
$832$	−5.74772	−0.199266
$833$	2.08042	0.0720824
$834$	46.6003	1.61364
$835$	−21.5485	−0.745715
$836$	−0.327872	−0.0113397
$837$	14.6435	0.506155
$838$	−18.0655	−0.624064
$839$	38.4570	1.32768	0.663842	−	0.747873i	$-0.268925\pi$
$839$	38.4570	1.32768	0.663842	+	0.747873i	$0.268925\pi$
$840$	4.72328	0.162969
$841$	−22.5025	−0.775950
$842$	31.3770	1.08132
$843$	−5.50081	−0.189458
$844$	−1.41196	−0.0486017
$845$	48.4808	1.66779
$846$	−47.2664	−1.62505
$847$	−7.80796	−0.268285
$848$	9.93089	0.341028
$849$	−78.2881	−2.68684
$850$	0.274730	0.00942315
$851$	18.9891	0.650939
$852$	−0.160291	−0.00549147
$853$	−11.0411	−0.378039	−0.189019	−	0.981973i	$-0.560531\pi$
$853$	−11.0411	−0.378039	−0.189019	+	0.981973i	$0.560531\pi$
$854$	−2.63767	−0.0902593
$855$	−6.65010	−0.227429
$856$	−11.3120	−0.386637
$857$	3.50598	0.119762	0.0598811	−	0.998206i	$-0.480928\pi$
$857$	3.50598	0.119762	0.0598811	+	0.998206i	$0.480928\pi$
$858$	−7.77206	−0.265334
$859$	−22.3646	−0.763069	−0.381535	−	0.924355i	$-0.624604\pi$
$859$	−22.3646	−0.763069	−0.381535	+	0.924355i	$0.624604\pi$
$860$	−21.6981	−0.739900
$861$	6.99316	0.238326
$862$	17.8785	0.608945
$863$	−43.0474	−1.46535	−0.732674	−	0.680579i	$-0.761728\pi$
$863$	−43.0474	−1.46535	−0.732674	+	0.680579i	$0.761728\pi$
$864$	3.27448	0.111400
$865$	19.1502	0.651125
$866$	30.8295	1.04763
$867$	45.3975	1.54178
$868$	−3.24912	−0.110282
$869$	−3.01603	−0.102312
$870$	16.5712	0.561816
$871$	71.4234	2.42009
$872$	5.55186	0.188010
$873$	−51.3726	−1.73870
$874$	4.87969	0.165058
$875$	−7.28739	−0.246359
$876$	−9.25419	−0.312670
$877$	35.3667	1.19425	0.597124	−	0.802149i	$-0.296310\pi$
$877$	35.3667	1.19425	0.597124	+	0.802149i	$0.296310\pi$
$878$	−16.9075	−0.570601
$879$	−15.3573	−0.517990
$880$	1.21776	0.0410506
$881$	17.8053	0.599877	0.299939	−	0.953958i	$-0.403034\pi$
$881$	17.8053	0.599877	0.299939	+	0.953958i	$0.403034\pi$
$882$	27.3043	0.919382
$883$	−2.57721	−0.0867299	−0.0433650	−	0.999059i	$-0.513808\pi$
$883$	−2.57721	−0.0867299	−0.0433650	+	0.999059i	$0.513808\pi$
$884$	1.84757	0.0621404
$885$	37.5692	1.26288
$886$	2.16137	0.0726126
$887$	−19.9264	−0.669063	−0.334532	−	0.942384i	$-0.608578\pi$
$887$	−19.9264	−0.669063	−0.334532	+	0.942384i	$0.608578\pi$
$888$	6.81142	0.228576
$889$	1.08005	0.0362238
$890$	19.9507	0.668750
$891$	−1.94188	−0.0650555
$892$	12.1737	0.407607
$893$	−7.29900	−0.244252
$894$	−60.8939	−2.03660
$895$	42.4311	1.41832
$896$	−0.726544	−0.0242721
$897$	115.671	3.86214
$898$	20.8890	0.697075
$899$	−11.3992	−0.380186
$900$	3.60566	0.120189
$901$	−3.19222	−0.106348
$902$	1.80298	0.0600326
$903$	17.5051	0.582532
$904$	12.4416	0.413803
$905$	−18.7837	−0.624391
$906$	17.0757	0.567303
$907$	−7.52886	−0.249992	−0.124996	−	0.992157i	$-0.539892\pi$
$907$	−7.52886	−0.249992	−0.124996	+	0.992157i	$0.539892\pi$
$908$	19.0191	0.631170
$909$	11.3315	0.375841
$910$	10.1044	0.334957
$911$	30.1290	0.998219	0.499110	−	0.866539i	$-0.333660\pi$
$911$	30.1290	0.998219	0.499110	+	0.866539i	$0.333660\pi$
$912$	1.75035	0.0579599
$913$	2.03931	0.0674914
$914$	4.31549	0.142744
$915$	−23.6016	−0.780244
$916$	−11.6184	−0.383882
$917$	2.57968	0.0851885
$918$	−1.05256	−0.0347396
$919$	11.6250	0.383472	0.191736	−	0.981447i	$-0.438588\pi$
$919$	11.6250	0.383472	0.191736	+	0.981447i	$0.438588\pi$
$920$	−18.1238	−0.597524
$921$	22.5180	0.741993
$922$	20.4171	0.672401
$923$	−0.342905	−0.0112868
$924$	−0.982432	−0.0323196
$925$	2.16675	0.0712423
$926$	25.7943	0.847652
$927$	21.7463	0.714243
$928$	−2.54901	−0.0836754
$929$	1.11084	0.0364454	0.0182227	−	0.999834i	$-0.494199\pi$
$929$	1.11084	0.0364454	0.0182227	+	0.999834i	$0.494199\pi$
$930$	−29.0728	−0.953333
$931$	4.21640	0.138187
$932$	15.1058	0.494808
$933$	10.2875	0.336799
$934$	0.205438	0.00672215
$935$	−0.391440	−0.0128015
$936$	24.2481	0.792576
$937$	−6.95078	−0.227072	−0.113536	−	0.993534i	$-0.536218\pi$
$937$	−6.95078	−0.227072	−0.113536	+	0.993534i	$0.536218\pi$
$938$	9.02832	0.294785
$939$	61.0209	1.99134
$940$	27.1095	0.884213
$941$	−44.0104	−1.43470	−0.717349	−	0.696714i	$-0.754645\pi$
$941$	−44.0104	−1.43470	−0.717349	+	0.696714i	$0.754645\pi$
$942$	46.0676	1.50096
$943$	−26.8336	−0.873822
$944$	−5.77896	−0.188089
$945$	−5.75646	−0.187258
$946$	4.51316	0.146735
$947$	48.2152	1.56678	0.783391	−	0.621529i	$-0.213488\pi$
$947$	48.2152	1.56678	0.783391	+	0.621529i	$0.213488\pi$
$948$	16.1011	0.522941
$949$	−19.7972	−0.642644
$950$	0.556795	0.0180648
$951$	62.9635	2.04173
$952$	0.233543	0.00756916
$953$	0.360315	0.0116717	0.00583587	−	0.999983i	$-0.498142\pi$
$953$	0.360315	0.0116717	0.00583587	+	0.999983i	$0.498142\pi$
$954$	−41.8958	−1.35643
$955$	−43.9287	−1.42150
$956$	−20.4129	−0.660201
$957$	−3.44677	−0.111418
$958$	22.9713	0.742170
$959$	3.76293	0.121511
$960$	−6.50103	−0.209820
$961$	−11.0010	−0.354871
$962$	14.5715	0.469803
$963$	47.7224	1.53783
$964$	15.2445	0.490993
$965$	−26.1940	−0.843215
$966$	14.6215	0.470438
$967$	38.7580	1.24637	0.623187	−	0.782073i	$-0.285838\pi$
$967$	38.7580	1.24637	0.623187	+	0.782073i	$0.285838\pi$
$968$	10.7467	0.345412
$969$	−0.562638	−0.0180745
$970$	29.4646	0.946051
$971$	−19.9663	−0.640750	−0.320375	−	0.947291i	$-0.603809\pi$
$971$	−19.9663	−0.640750	−0.320375	+	0.947291i	$0.603809\pi$
$972$	20.1902	0.647601
$973$	12.6014	0.403983
$974$	5.08641	0.162979
$975$	13.1986	0.422694
$976$	3.63044	0.116207
$977$	2.89447	0.0926023	0.0463011	−	0.998928i	$-0.485257\pi$
$977$	2.89447	0.0926023	0.0463011	+	0.998928i	$0.485257\pi$
$978$	32.2982	1.03278
$979$	−4.14970	−0.132625
$980$	−15.6603	−0.500249
$981$	−23.4218	−0.747802
$982$	−19.2098	−0.613009
$983$	−32.5469	−1.03808	−0.519042	−	0.854748i	$-0.673711\pi$
$983$	−32.5469	−1.03808	−0.519042	+	0.854748i	$0.673711\pi$
$984$	−9.62524	−0.306841
$985$	14.3931	0.458602
$986$	0.819362	0.0260938
$987$	−21.8707	−0.696151
$988$	3.74447	0.119127
$989$	−67.1690	−2.13585
$990$	−5.13741	−0.163277
$991$	−14.9854	−0.476026	−0.238013	−	0.971262i	$-0.576496\pi$
$991$	−14.9854	−0.476026	−0.238013	+	0.971262i	$0.576496\pi$
$992$	4.47202	0.141987
$993$	−0.601204	−0.0190786
$994$	−0.0433451	−0.00137482
$995$	−55.8208	−1.76964
$996$	−10.8869	−0.344965
$997$	−25.8007	−0.817116	−0.408558	−	0.912732i	$-0.633968\pi$
$997$	−25.8007	−0.817116	−0.408558	+	0.912732i	$0.633968\pi$
$998$	9.01485	0.285360
$999$	−8.30136	−0.262643

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6046.2.a.d.1.6	✓	55

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6046.2.a.d.1.6	✓	55	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:	\( N \)	\(=\)	\( 6046 = 2 \cdot 3023 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6046.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.68677 q^{3} +1.00000 q^{4} +2.41964 q^{5} +2.68677 q^{6} +0.726544 q^{7} -1.00000 q^{8} +4.21874 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.68677 q^{3} +1.00000 q^{4} +2.41964 q^{5} +2.68677 q^{6} +0.726544 q^{7} -1.00000 q^{8} +4.21874 q^{9} -2.41964 q^{10} +0.503280 q^{11} -2.68677 q^{12} -5.74772 q^{13} -0.726544 q^{14} -6.50103 q^{15} +1.00000 q^{16} -0.321443 q^{17} -4.21874 q^{18} -0.651470 q^{19} +2.41964 q^{20} -1.95206 q^{21} -0.503280 q^{22} +7.49028 q^{23} +2.68677 q^{24} +0.854676 q^{25} +5.74772 q^{26} -3.27448 q^{27} +0.726544 q^{28} +2.54901 q^{29} +6.50103 q^{30} -4.47202 q^{31} -1.00000 q^{32} -1.35220 q^{33} +0.321443 q^{34} +1.75798 q^{35} +4.21874 q^{36} +2.53517 q^{37} +0.651470 q^{38} +15.4428 q^{39} -2.41964 q^{40} -3.58246 q^{41} +1.95206 q^{42} -8.96749 q^{43} +0.503280 q^{44} +10.2078 q^{45} -7.49028 q^{46} +11.2039 q^{47} -2.68677 q^{48} -6.47213 q^{49} -0.854676 q^{50} +0.863644 q^{51} -5.74772 q^{52} +9.93089 q^{53} +3.27448 q^{54} +1.21776 q^{55} -0.726544 q^{56} +1.75035 q^{57} -2.54901 q^{58} -5.77896 q^{59} -6.50103 q^{60} +3.63044 q^{61} +4.47202 q^{62} +3.06510 q^{63} +1.00000 q^{64} -13.9074 q^{65} +1.35220 q^{66} -12.4264 q^{67} -0.321443 q^{68} -20.1247 q^{69} -1.75798 q^{70} +0.0596592 q^{71} -4.21874 q^{72} +3.44435 q^{73} -2.53517 q^{74} -2.29632 q^{75} -0.651470 q^{76} +0.365655 q^{77} -15.4428 q^{78} -5.99275 q^{79} +2.41964 q^{80} -3.85845 q^{81} +3.58246 q^{82} +4.05204 q^{83} -1.95206 q^{84} -0.777778 q^{85} +8.96749 q^{86} -6.84861 q^{87} -0.503280 q^{88} -8.24531 q^{89} -10.2078 q^{90} -4.17597 q^{91} +7.49028 q^{92} +12.0153 q^{93} -11.2039 q^{94} -1.57632 q^{95} +2.68677 q^{96} -12.1772 q^{97} +6.47213 q^{98} +2.12321 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 55 q - 55 q^{2} - 4 q^{3} + 55 q^{4} - 7 q^{5} + 4 q^{6} + 17 q^{7} - 55 q^{8} + 29 q^{9}+O(q^{10}) \) 55 * q - 55 * q^2 - 4 * q^3 + 55 * q^4 - 7 * q^5 + 4 * q^6 + 17 * q^7 - 55 * q^8 + 29 * q^9	\( 55 q - 55 q^{2} - 4 q^{3} + 55 q^{4} - 7 q^{5} + 4 q^{6} + 17 q^{7} - 55 q^{8} + 29 q^{9} + 7 q^{10} - 28 q^{11} - 4 q^{12} + q^{13} - 17 q^{14} - 8 q^{15} + 55 q^{16} - 32 q^{17} - 29 q^{18} - 3 q^{19} - 7 q^{20} - 25 q^{21} + 28 q^{22} - 27 q^{23} + 4 q^{24} + 30 q^{25} - q^{26} - q^{27} + 17 q^{28} - 69 q^{29} + 8 q^{30} - 13 q^{31} - 55 q^{32} - 18 q^{33} + 32 q^{34} - 23 q^{35} + 29 q^{36} + 3 q^{37} + 3 q^{38} - 28 q^{39} + 7 q^{40} - 51 q^{41} + 25 q^{42} + 23 q^{43} - 28 q^{44} - 28 q^{45} + 27 q^{46} - 27 q^{47} - 4 q^{48} + 8 q^{49} - 30 q^{50} - 42 q^{51} + q^{52} - 61 q^{53} + q^{54} + 5 q^{55} - 17 q^{56} - 52 q^{57} + 69 q^{58} - 71 q^{59} - 8 q^{60} - 16 q^{61} + 13 q^{62} + 14 q^{63} + 55 q^{64} - 82 q^{65} + 18 q^{66} + 32 q^{67} - 32 q^{68} - 44 q^{69} + 23 q^{70} - 84 q^{71} - 29 q^{72} - 43 q^{73} - 3 q^{74} - 37 q^{75} - 3 q^{76} - 47 q^{77} + 28 q^{78} - 20 q^{79} - 7 q^{80} - 33 q^{81} + 51 q^{82} + 17 q^{83} - 25 q^{84} + 10 q^{85} - 23 q^{86} - q^{87} + 28 q^{88} - 92 q^{89} + 28 q^{90} - 34 q^{91} - 27 q^{92} - 13 q^{93} + 27 q^{94} - 60 q^{95} + 4 q^{96} - 45 q^{97} - 8 q^{98} - 73 q^{99}+O(q^{100}) \) 55 * q - 55 * q^2 - 4 * q^3 + 55 * q^4 - 7 * q^5 + 4 * q^6 + 17 * q^7 - 55 * q^8 + 29 * q^9 + 7 * q^10 - 28 * q^11 - 4 * q^12 + q^13 - 17 * q^14 - 8 * q^15 + 55 * q^16 - 32 * q^17 - 29 * q^18 - 3 * q^19 - 7 * q^20 - 25 * q^21 + 28 * q^22 - 27 * q^23 + 4 * q^24 + 30 * q^25 - q^26 - q^27 + 17 * q^28 - 69 * q^29 + 8 * q^30 - 13 * q^31 - 55 * q^32 - 18 * q^33 + 32 * q^34 - 23 * q^35 + 29 * q^36 + 3 * q^37 + 3 * q^38 - 28 * q^39 + 7 * q^40 - 51 * q^41 + 25 * q^42 + 23 * q^43 - 28 * q^44 - 28 * q^45 + 27 * q^46 - 27 * q^47 - 4 * q^48 + 8 * q^49 - 30 * q^50 - 42 * q^51 + q^52 - 61 * q^53 + q^54 + 5 * q^55 - 17 * q^56 - 52 * q^57 + 69 * q^58 - 71 * q^59 - 8 * q^60 - 16 * q^61 + 13 * q^62 + 14 * q^63 + 55 * q^64 - 82 * q^65 + 18 * q^66 + 32 * q^67 - 32 * q^68 - 44 * q^69 + 23 * q^70 - 84 * q^71 - 29 * q^72 - 43 * q^73 - 3 * q^74 - 37 * q^75 - 3 * q^76 - 47 * q^77 + 28 * q^78 - 20 * q^79 - 7 * q^80 - 33 * q^81 + 51 * q^82 + 17 * q^83 - 25 * q^84 + 10 * q^85 - 23 * q^86 - q^87 + 28 * q^88 - 92 * q^89 + 28 * q^90 - 34 * q^91 - 27 * q^92 - 13 * q^93 + 27 * q^94 - 60 * q^95 + 4 * q^96 - 45 * q^97 - 8 * q^98 - 73 * q^99

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