LMFDB - Embedded newform 8018.2.a.j.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8018,2,Mod(1,8018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8018, 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("8018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8018 = 2 \cdot 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8018.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:	$64.0240523407$
Analytic rank:	$0$
Dimension:	$47$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	8018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.41559 q^{3} +1.00000 q^{4} +0.828405 q^{5} -2.41559 q^{6} +0.635145 q^{7} +1.00000 q^{8} +2.83509 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.41559 q^{3} +1.00000 q^{4} +0.828405 q^{5} -2.41559 q^{6} +0.635145 q^{7} +1.00000 q^{8} +2.83509 q^{9} +0.828405 q^{10} +4.76175 q^{11} -2.41559 q^{12} +1.33861 q^{13} +0.635145 q^{14} -2.00109 q^{15} +1.00000 q^{16} +4.13113 q^{17} +2.83509 q^{18} -1.00000 q^{19} +0.828405 q^{20} -1.53425 q^{21} +4.76175 q^{22} +8.13489 q^{23} -2.41559 q^{24} -4.31374 q^{25} +1.33861 q^{26} +0.398357 q^{27} +0.635145 q^{28} -3.53077 q^{29} -2.00109 q^{30} +6.81222 q^{31} +1.00000 q^{32} -11.5024 q^{33} +4.13113 q^{34} +0.526157 q^{35} +2.83509 q^{36} +0.803490 q^{37} -1.00000 q^{38} -3.23353 q^{39} +0.828405 q^{40} +9.53625 q^{41} -1.53425 q^{42} +0.674754 q^{43} +4.76175 q^{44} +2.34860 q^{45} +8.13489 q^{46} -3.36611 q^{47} -2.41559 q^{48} -6.59659 q^{49} -4.31374 q^{50} -9.97912 q^{51} +1.33861 q^{52} +6.15273 q^{53} +0.398357 q^{54} +3.94466 q^{55} +0.635145 q^{56} +2.41559 q^{57} -3.53077 q^{58} +6.64260 q^{59} -2.00109 q^{60} -1.12180 q^{61} +6.81222 q^{62} +1.80069 q^{63} +1.00000 q^{64} +1.10891 q^{65} -11.5024 q^{66} -1.28127 q^{67} +4.13113 q^{68} -19.6506 q^{69} +0.526157 q^{70} +2.12031 q^{71} +2.83509 q^{72} -11.7665 q^{73} +0.803490 q^{74} +10.4203 q^{75} -1.00000 q^{76} +3.02440 q^{77} -3.23353 q^{78} -0.475054 q^{79} +0.828405 q^{80} -9.46754 q^{81} +9.53625 q^{82} -4.38717 q^{83} -1.53425 q^{84} +3.42225 q^{85} +0.674754 q^{86} +8.52890 q^{87} +4.76175 q^{88} +6.45159 q^{89} +2.34860 q^{90} +0.850209 q^{91} +8.13489 q^{92} -16.4555 q^{93} -3.36611 q^{94} -0.828405 q^{95} -2.41559 q^{96} +1.33445 q^{97} -6.59659 q^{98} +13.5000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 47 q + 47 q^{2} + 10 q^{3} + 47 q^{4} + 15 q^{5} + 10 q^{6} + 47 q^{8} + 69 q^{9}+O(q^{10}) $ 47 * q + 47 * q^2 + 10 * q^3 + 47 * q^4 + 15 * q^5 + 10 * q^6 + 47 * q^8 + 69 * q^9	\( 47 q + 47 q^{2} + 10 q^{3} + 47 q^{4} + 15 q^{5} + 10 q^{6} + 47 q^{8} + 69 q^{9} + 15 q^{10} + 17 q^{11} + 10 q^{12} + 27 q^{13} + 10 q^{15} + 47 q^{16} + 16 q^{17} + 69 q^{18} - 47 q^{19} + 15 q^{20} + 26 q^{21} + 17 q^{22} + 24 q^{23} + 10 q^{24} + 86 q^{25} + 27 q^{26} + 43 q^{27} + 58 q^{29} + 10 q^{30} + 21 q^{31} + 47 q^{32} + 18 q^{33} + 16 q^{34} + 24 q^{35} + 69 q^{36} + 78 q^{37} - 47 q^{38} - 4 q^{39} + 15 q^{40} + 53 q^{41} + 26 q^{42} + 47 q^{43} + 17 q^{44} + 23 q^{45} + 24 q^{46} + 16 q^{47} + 10 q^{48} + 93 q^{49} + 86 q^{50} + 28 q^{51} + 27 q^{52} + 43 q^{53} + 43 q^{54} + 23 q^{55} - 10 q^{57} + 58 q^{58} + 3 q^{59} + 10 q^{60} + 12 q^{61} + 21 q^{62} - 5 q^{63} + 47 q^{64} + 62 q^{65} + 18 q^{66} + 68 q^{67} + 16 q^{68} + 12 q^{69} + 24 q^{70} - 13 q^{71} + 69 q^{72} + 35 q^{73} + 78 q^{74} + 22 q^{75} - 47 q^{76} + 26 q^{77} - 4 q^{78} + 21 q^{79} + 15 q^{80} + 123 q^{81} + 53 q^{82} + 23 q^{83} + 26 q^{84} + 38 q^{85} + 47 q^{86} + 39 q^{87} + 17 q^{88} + 24 q^{89} + 23 q^{90} + 49 q^{91} + 24 q^{92} + 91 q^{93} + 16 q^{94} - 15 q^{95} + 10 q^{96} + 88 q^{97} + 93 q^{98} + 26 q^{99}+O(q^{100}) \) 47 * q + 47 * q^2 + 10 * q^3 + 47 * q^4 + 15 * q^5 + 10 * q^6 + 47 * q^8 + 69 * q^9 + 15 * q^10 + 17 * q^11 + 10 * q^12 + 27 * q^13 + 10 * q^15 + 47 * q^16 + 16 * q^17 + 69 * q^18 - 47 * q^19 + 15 * q^20 + 26 * q^21 + 17 * q^22 + 24 * q^23 + 10 * q^24 + 86 * q^25 + 27 * q^26 + 43 * q^27 + 58 * q^29 + 10 * q^30 + 21 * q^31 + 47 * q^32 + 18 * q^33 + 16 * q^34 + 24 * q^35 + 69 * q^36 + 78 * q^37 - 47 * q^38 - 4 * q^39 + 15 * q^40 + 53 * q^41 + 26 * q^42 + 47 * q^43 + 17 * q^44 + 23 * q^45 + 24 * q^46 + 16 * q^47 + 10 * q^48 + 93 * q^49 + 86 * q^50 + 28 * q^51 + 27 * q^52 + 43 * q^53 + 43 * q^54 + 23 * q^55 - 10 * q^57 + 58 * q^58 + 3 * q^59 + 10 * q^60 + 12 * q^61 + 21 * q^62 - 5 * q^63 + 47 * q^64 + 62 * q^65 + 18 * q^66 + 68 * q^67 + 16 * q^68 + 12 * q^69 + 24 * q^70 - 13 * q^71 + 69 * q^72 + 35 * q^73 + 78 * q^74 + 22 * q^75 - 47 * q^76 + 26 * q^77 - 4 * q^78 + 21 * q^79 + 15 * q^80 + 123 * q^81 + 53 * q^82 + 23 * q^83 + 26 * q^84 + 38 * q^85 + 47 * q^86 + 39 * q^87 + 17 * q^88 + 24 * q^89 + 23 * q^90 + 49 * q^91 + 24 * q^92 + 91 * q^93 + 16 * q^94 - 15 * q^95 + 10 * q^96 + 88 * q^97 + 93 * q^98 + 26 * 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
$3$	−2.41559	−1.39464	−0.697322	−	0.716758i	$-0.745625\pi$
$3$	−2.41559	−1.39464	−0.697322	+	0.716758i	$0.745625\pi$
$4$	1.00000	0.500000
$5$	0.828405	0.370474	0.185237	−	0.982694i	$-0.440695\pi$
$5$	0.828405	0.370474	0.185237	+	0.982694i	$0.440695\pi$
$6$	−2.41559	−0.986162
$7$	0.635145	0.240062	0.120031	−	0.992770i	$-0.461701\pi$
$7$	0.635145	0.240062	0.120031	+	0.992770i	$0.461701\pi$
$8$	1.00000	0.353553
$9$	2.83509	0.945030
$10$	0.828405	0.261965
$11$	4.76175	1.43572	0.717860	−	0.696187i	$-0.245122\pi$
$11$	4.76175	1.43572	0.717860	+	0.696187i	$0.245122\pi$
$12$	−2.41559	−0.697322
$13$	1.33861	0.371263	0.185631	−	0.982619i	$-0.440567\pi$
$13$	1.33861	0.371263	0.185631	+	0.982619i	$0.440567\pi$
$14$	0.635145	0.169750
$15$	−2.00109	−0.516679
$16$	1.00000	0.250000
$17$	4.13113	1.00195	0.500973	−	0.865463i	$-0.332976\pi$
$17$	4.13113	1.00195	0.500973	+	0.865463i	$0.332976\pi$
$18$	2.83509	0.668237
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	0.828405	0.185237
$21$	−1.53425	−0.334801
$22$	4.76175	1.01521
$23$	8.13489	1.69624	0.848121	−	0.529803i	$-0.177734\pi$
$23$	8.13489	1.69624	0.848121	+	0.529803i	$0.177734\pi$
$24$	−2.41559	−0.493081
$25$	−4.31374	−0.862749
$26$	1.33861	0.262522
$27$	0.398357	0.0766639
$28$	0.635145	0.120031
$29$	−3.53077	−0.655647	−0.327824	−	0.944739i	$-0.606315\pi$
$29$	−3.53077	−0.655647	−0.327824	+	0.944739i	$0.606315\pi$
$30$	−2.00109	−0.365347
$31$	6.81222	1.22351	0.611755	−	0.791047i	$-0.290464\pi$
$31$	6.81222	1.22351	0.611755	+	0.791047i	$0.290464\pi$
$32$	1.00000	0.176777
$33$	−11.5024	−2.00232
$34$	4.13113	0.708482
$35$	0.526157	0.0889368
$36$	2.83509	0.472515
$37$	0.803490	0.132093	0.0660464	−	0.997817i	$-0.478961\pi$
$37$	0.803490	0.132093	0.0660464	+	0.997817i	$0.478961\pi$
$38$	−1.00000	−0.162221
$39$	−3.23353	−0.517779
$40$	0.828405	0.130982
$41$	9.53625	1.48931	0.744656	−	0.667448i	$-0.232613\pi$
$41$	9.53625	1.48931	0.744656	+	0.667448i	$0.232613\pi$
$42$	−1.53425	−0.236740
$43$	0.674754	0.102899	0.0514495	−	0.998676i	$-0.483616\pi$
$43$	0.674754	0.102899	0.0514495	+	0.998676i	$0.483616\pi$
$44$	4.76175	0.717860
$45$	2.34860	0.350109
$46$	8.13489	1.19942
$47$	−3.36611	−0.490997	−0.245499	−	0.969397i	$-0.578952\pi$
$47$	−3.36611	−0.490997	−0.245499	+	0.969397i	$0.578952\pi$
$48$	−2.41559	−0.348661
$49$	−6.59659	−0.942370
$50$	−4.31374	−0.610056
$51$	−9.97912	−1.39736
$52$	1.33861	0.185631
$53$	6.15273	0.845142	0.422571	−	0.906330i	$-0.361128\pi$
$53$	6.15273	0.845142	0.422571	+	0.906330i	$0.361128\pi$
$54$	0.398357	0.0542096
$55$	3.94466	0.531897
$56$	0.635145	0.0848748
$57$	2.41559	0.319953
$58$	−3.53077	−0.463613
$59$	6.64260	0.864793	0.432397	−	0.901684i	$-0.357668\pi$
$59$	6.64260	0.864793	0.432397	+	0.901684i	$0.357668\pi$
$60$	−2.00109	−0.258340
$61$	−1.12180	−0.143631	−0.0718157	−	0.997418i	$-0.522879\pi$
$61$	−1.12180	−0.143631	−0.0718157	+	0.997418i	$0.522879\pi$
$62$	6.81222	0.865152
$63$	1.80069	0.226866
$64$	1.00000	0.125000
$65$	1.10891	0.137543
$66$	−11.5024	−1.41585
$67$	−1.28127	−0.156532	−0.0782659	−	0.996933i	$-0.524938\pi$
$67$	−1.28127	−0.156532	−0.0782659	+	0.996933i	$0.524938\pi$
$68$	4.13113	0.500973
$69$	−19.6506	−2.36565
$70$	0.526157	0.0628878
$71$	2.12031	0.251634	0.125817	−	0.992053i	$-0.459845\pi$
$71$	2.12031	0.251634	0.125817	+	0.992053i	$0.459845\pi$
$72$	2.83509	0.334118
$73$	−11.7665	−1.37717	−0.688583	−	0.725158i	$-0.741767\pi$
$73$	−11.7665	−1.37717	−0.688583	+	0.725158i	$0.741767\pi$
$74$	0.803490	0.0934038
$75$	10.4203	1.20323
$76$	−1.00000	−0.114708
$77$	3.02440	0.344662
$78$	−3.23353	−0.366125
$79$	−0.475054	−0.0534478	−0.0267239	−	0.999643i	$-0.508507\pi$
$79$	−0.475054	−0.0534478	−0.0267239	+	0.999643i	$0.508507\pi$
$80$	0.828405	0.0926185
$81$	−9.46754	−1.05195
$82$	9.53625	1.05310
$83$	−4.38717	−0.481555	−0.240777	−	0.970580i	$-0.577402\pi$
$83$	−4.38717	−0.481555	−0.240777	+	0.970580i	$0.577402\pi$
$84$	−1.53425	−0.167401
$85$	3.42225	0.371195
$86$	0.674754	0.0727606
$87$	8.52890	0.914394
$88$	4.76175	0.507604
$89$	6.45159	0.683867	0.341933	−	0.939724i	$-0.388918\pi$
$89$	6.45159	0.683867	0.341933	+	0.939724i	$0.388918\pi$
$90$	2.34860	0.247565
$91$	0.850209	0.0891261
$92$	8.13489	0.848121
$93$	−16.4555	−1.70636
$94$	−3.36611	−0.347188
$95$	−0.828405	−0.0849926
$96$	−2.41559	−0.246540
$97$	1.33445	0.135493	0.0677463	−	0.997703i	$-0.478419\pi$
$97$	1.33445	0.135493	0.0677463	+	0.997703i	$0.478419\pi$
$98$	−6.59659	−0.666356
$99$	13.5000	1.35680
$100$	−4.31374	−0.431374
$101$	3.18561	0.316980	0.158490	−	0.987361i	$-0.449337\pi$
$101$	3.18561	0.316980	0.158490	+	0.987361i	$0.449337\pi$
$102$	−9.97912	−0.988080
$103$	−11.1322	−1.09689	−0.548446	−	0.836186i	$-0.684780\pi$
$103$	−11.1322	−1.09689	−0.548446	+	0.836186i	$0.684780\pi$
$104$	1.33861	0.131261
$105$	−1.27098	−0.124035
$106$	6.15273	0.597606
$107$	−9.35251	−0.904141	−0.452071	−	0.891982i	$-0.649314\pi$
$107$	−9.35251	−0.904141	−0.452071	+	0.891982i	$0.649314\pi$
$108$	0.398357	0.0383319
$109$	−2.99989	−0.287337	−0.143669	−	0.989626i	$-0.545890\pi$
$109$	−2.99989	−0.287337	−0.143669	+	0.989626i	$0.545890\pi$
$110$	3.94466	0.376108
$111$	−1.94090	−0.184222
$112$	0.635145	0.0600155
$113$	2.04492	0.192370	0.0961851	−	0.995363i	$-0.469336\pi$
$113$	2.04492	0.192370	0.0961851	+	0.995363i	$0.469336\pi$
$114$	2.41559	0.226241
$115$	6.73898	0.628414
$116$	−3.53077	−0.327824
$117$	3.79507	0.350854
$118$	6.64260	0.611501
$119$	2.62386	0.240529
$120$	−2.00109	−0.182674
$121$	11.6742	1.06129
$122$	−1.12180	−0.101563
$123$	−23.0357	−2.07706
$124$	6.81222	0.611755
$125$	−7.71556	−0.690100
$126$	1.80069	0.160418
$127$	−0.791022	−0.0701918	−0.0350959	−	0.999384i	$-0.511174\pi$
$127$	−0.791022	−0.0701918	−0.0350959	+	0.999384i	$0.511174\pi$
$128$	1.00000	0.0883883
$129$	−1.62993	−0.143507
$130$	1.10891	0.0972578
$131$	3.06716	0.267979	0.133989	−	0.990983i	$-0.457221\pi$
$131$	3.06716	0.267979	0.133989	+	0.990983i	$0.457221\pi$
$132$	−11.5024	−1.00116
$133$	−0.635145	−0.0550740
$134$	−1.28127	−0.110685
$135$	0.330001	0.0284020
$136$	4.13113	0.354241
$137$	8.27758	0.707201	0.353601	−	0.935397i	$-0.384957\pi$
$137$	8.27758	0.707201	0.353601	+	0.935397i	$0.384957\pi$
$138$	−19.6506	−1.67277
$139$	−15.4336	−1.30906	−0.654530	−	0.756036i	$-0.727134\pi$
$139$	−15.4336	−1.30906	−0.654530	+	0.756036i	$0.727134\pi$
$140$	0.526157	0.0444684
$141$	8.13115	0.684766
$142$	2.12031	0.177932
$143$	6.37411	0.533030
$144$	2.83509	0.236257
$145$	−2.92491	−0.242900
$146$	−11.7665	−0.973803
$147$	15.9347	1.31427
$148$	0.803490	0.0660464
$149$	6.93021	0.567745	0.283872	−	0.958862i	$-0.408381\pi$
$149$	6.93021	0.567745	0.283872	+	0.958862i	$0.408381\pi$
$150$	10.4203	0.850810
$151$	−0.709930	−0.0577733	−0.0288866	−	0.999583i	$-0.509196\pi$
$151$	−0.709930	−0.0577733	−0.0288866	+	0.999583i	$0.509196\pi$
$152$	−1.00000	−0.0811107
$153$	11.7121	0.946868
$154$	3.02440	0.243713
$155$	5.64328	0.453279
$156$	−3.23353	−0.258890
$157$	10.5903	0.845199	0.422599	−	0.906317i	$-0.361118\pi$
$157$	10.5903	0.845199	0.422599	+	0.906317i	$0.361118\pi$
$158$	−0.475054	−0.0377933
$159$	−14.8625	−1.17867
$160$	0.828405	0.0654912
$161$	5.16683	0.407203
$162$	−9.46754	−0.743840
$163$	−20.8815	−1.63556	−0.817781	−	0.575530i	$-0.804796\pi$
$163$	−20.8815	−1.63556	−0.817781	+	0.575530i	$0.804796\pi$
$164$	9.53625	0.744656
$165$	−9.52868	−0.741807
$166$	−4.38717	−0.340511
$167$	−5.79451	−0.448393	−0.224196	−	0.974544i	$-0.571976\pi$
$167$	−5.79451	−0.448393	−0.224196	+	0.974544i	$0.571976\pi$
$168$	−1.53425	−0.118370
$169$	−11.2081	−0.862164
$170$	3.42225	0.262474
$171$	−2.83509	−0.216805
$172$	0.674754	0.0514495
$173$	6.43491	0.489237	0.244618	−	0.969619i	$-0.421337\pi$
$173$	6.43491	0.489237	0.244618	+	0.969619i	$0.421337\pi$
$174$	8.52890	0.646574
$175$	−2.73985	−0.207113
$176$	4.76175	0.358930
$177$	−16.0458	−1.20608
$178$	6.45159	0.483567
$179$	6.94931	0.519416	0.259708	−	0.965687i	$-0.416374\pi$
$179$	6.94931	0.519416	0.259708	+	0.965687i	$0.416374\pi$
$180$	2.34860	0.175055
$181$	7.34646	0.546058	0.273029	−	0.962006i	$-0.411974\pi$
$181$	7.34646	0.546058	0.273029	+	0.962006i	$0.411974\pi$
$182$	0.850209	0.0630217
$183$	2.70981	0.200315
$184$	8.13489	0.599712
$185$	0.665615	0.0489370
$186$	−16.4555	−1.20658
$187$	19.6714	1.43851
$188$	−3.36611	−0.245499
$189$	0.253015	0.0184041
$190$	−0.828405	−0.0600988
$191$	−16.3578	−1.18361	−0.591806	−	0.806081i	$-0.701585\pi$
$191$	−16.3578	−1.18361	−0.591806	+	0.806081i	$0.701585\pi$
$192$	−2.41559	−0.174330
$193$	9.39884	0.676543	0.338272	−	0.941049i	$-0.390158\pi$
$193$	9.39884	0.676543	0.338272	+	0.941049i	$0.390158\pi$
$194$	1.33445	0.0958077
$195$	−2.67867	−0.191824
$196$	−6.59659	−0.471185
$197$	21.2194	1.51182	0.755908	−	0.654677i	$-0.227196\pi$
$197$	21.2194	1.51182	0.755908	+	0.654677i	$0.227196\pi$
$198$	13.5000	0.959401
$199$	−27.9566	−1.98179	−0.990896	−	0.134626i	$-0.957017\pi$
$199$	−27.9566	−1.98179	−0.990896	+	0.134626i	$0.957017\pi$
$200$	−4.31374	−0.305028
$201$	3.09502	0.218306
$202$	3.18561	0.224139
$203$	−2.24255	−0.157396
$204$	−9.97912	−0.698678
$205$	7.89988	0.551752
$206$	−11.1322	−0.775620
$207$	23.0631	1.60300
$208$	1.33861	0.0928157
$209$	−4.76175	−0.329377
$210$	−1.27098	−0.0877061
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	6.15273	0.422571
$213$	−5.12179	−0.350940
$214$	−9.35251	−0.639324
$215$	0.558970	0.0381214
$216$	0.398357	0.0271048
$217$	4.32674	0.293719
$218$	−2.99989	−0.203178
$219$	28.4231	1.92065
$220$	3.94466	0.265949
$221$	5.52995	0.371985
$222$	−1.94090	−0.130265
$223$	−6.03373	−0.404049	−0.202024	−	0.979381i	$-0.564752\pi$
$223$	−6.03373	−0.404049	−0.202024	+	0.979381i	$0.564752\pi$
$224$	0.635145	0.0424374
$225$	−12.2299	−0.815323
$226$	2.04492	0.136026
$227$	2.85447	0.189458	0.0947291	−	0.995503i	$-0.469802\pi$
$227$	2.85447	0.189458	0.0947291	+	0.995503i	$0.469802\pi$
$228$	2.41559	0.159977
$229$	7.52528	0.497284	0.248642	−	0.968595i	$-0.420016\pi$
$229$	7.52528	0.497284	0.248642	+	0.968595i	$0.420016\pi$
$230$	6.73898	0.444355
$231$	−7.30572	−0.480681
$232$	−3.53077	−0.231806
$233$	−9.44916	−0.619035	−0.309517	−	0.950894i	$-0.600168\pi$
$233$	−9.44916	−0.619035	−0.309517	+	0.950894i	$0.600168\pi$
$234$	3.79507	0.248091
$235$	−2.78850	−0.181902
$236$	6.64260	0.432397
$237$	1.14754	0.0745406
$238$	2.62386	0.170080
$239$	8.19763	0.530260	0.265130	−	0.964213i	$-0.414585\pi$
$239$	8.19763	0.530260	0.265130	+	0.964213i	$0.414585\pi$
$240$	−2.00109	−0.129170
$241$	10.5796	0.681494	0.340747	−	0.940155i	$-0.389320\pi$
$241$	10.5796	0.681494	0.340747	+	0.940155i	$0.389320\pi$
$242$	11.6742	0.750448
$243$	21.6746	1.39043
$244$	−1.12180	−0.0718157
$245$	−5.46465	−0.349124
$246$	−23.0357	−1.46870
$247$	−1.33861	−0.0851735
$248$	6.81222	0.432576
$249$	10.5976	0.671597
$250$	−7.71556	−0.487975
$251$	0.109849	0.00693359	0.00346680	−	0.999994i	$-0.498896\pi$
$251$	0.109849	0.00693359	0.00346680	+	0.999994i	$0.498896\pi$
$252$	1.80069	0.113433
$253$	38.7363	2.43533
$254$	−0.791022	−0.0496331
$255$	−8.26676	−0.517684
$256$	1.00000	0.0625000
$257$	7.86185	0.490409	0.245204	−	0.969471i	$-0.421145\pi$
$257$	7.86185	0.490409	0.245204	+	0.969471i	$0.421145\pi$
$258$	−1.62993	−0.101475
$259$	0.510332	0.0317105
$260$	1.10891	0.0687716
$261$	−10.0100	−0.619606
$262$	3.06716	0.189490
$263$	21.6422	1.33452	0.667259	−	0.744826i	$-0.267467\pi$
$263$	21.6422	1.33452	0.667259	+	0.744826i	$0.267467\pi$
$264$	−11.5024	−0.707926
$265$	5.09695	0.313103
$266$	−0.635145	−0.0389432
$267$	−15.5844	−0.953750
$268$	−1.28127	−0.0782659
$269$	−4.79940	−0.292624	−0.146312	−	0.989238i	$-0.546740\pi$
$269$	−4.79940	−0.292624	−0.146312	+	0.989238i	$0.546740\pi$
$270$	0.330001	0.0200832
$271$	−8.60356	−0.522629	−0.261314	−	0.965254i	$-0.584156\pi$
$271$	−8.60356	−0.522629	−0.261314	+	0.965254i	$0.584156\pi$
$272$	4.13113	0.250486
$273$	−2.05376	−0.124299
$274$	8.27758	0.500067
$275$	−20.5410	−1.23867
$276$	−19.6506	−1.18283
$277$	19.9564	1.19906	0.599531	−	0.800351i	$-0.295354\pi$
$277$	19.9564	1.19906	0.599531	+	0.800351i	$0.295354\pi$
$278$	−15.4336	−0.925645
$279$	19.3132	1.15625
$280$	0.526157	0.0314439
$281$	17.7987	1.06178	0.530889	−	0.847441i	$-0.321858\pi$
$281$	17.7987	1.06178	0.530889	+	0.847441i	$0.321858\pi$
$282$	8.13115	0.484203
$283$	30.0238	1.78473	0.892366	−	0.451312i	$-0.149044\pi$
$283$	30.0238	1.78473	0.892366	+	0.451312i	$0.149044\pi$
$284$	2.12031	0.125817
$285$	2.00109	0.118534
$286$	6.37411	0.376909
$287$	6.05690	0.357528
$288$	2.83509	0.167059
$289$	0.0661984	0.00389403
$290$	−2.92491	−0.171757
$291$	−3.22348	−0.188964
$292$	−11.7665	−0.688583
$293$	18.3876	1.07421	0.537107	−	0.843514i	$-0.319517\pi$
$293$	18.3876	1.07421	0.537107	+	0.843514i	$0.319517\pi$
$294$	15.9347	0.929329
$295$	5.50277	0.320384
$296$	0.803490	0.0467019
$297$	1.89688	0.110068
$298$	6.93021	0.401456
$299$	10.8894	0.629751
$300$	10.4203	0.601613
$301$	0.428566	0.0247022
$302$	−0.709930	−0.0408519
$303$	−7.69513	−0.442074
$304$	−1.00000	−0.0573539
$305$	−0.929303	−0.0532117
$306$	11.7121	0.669537
$307$	−20.7591	−1.18479	−0.592393	−	0.805649i	$-0.701817\pi$
$307$	−20.7591	−1.18479	−0.592393	+	0.805649i	$0.701817\pi$
$308$	3.02440	0.172331
$309$	26.8909	1.52977
$310$	5.64328	0.320517
$311$	−24.9991	−1.41757	−0.708786	−	0.705424i	$-0.750757\pi$
$311$	−24.9991	−1.41757	−0.708786	+	0.705424i	$0.750757\pi$
$312$	−3.23353	−0.183063
$313$	−16.4582	−0.930273	−0.465136	−	0.885239i	$-0.653995\pi$
$313$	−16.4582	−0.930273	−0.465136	+	0.885239i	$0.653995\pi$
$314$	10.5903	0.597646
$315$	1.49170	0.0840480
$316$	−0.475054	−0.0267239
$317$	11.8239	0.664097	0.332048	−	0.943262i	$-0.392260\pi$
$317$	11.8239	0.664097	0.332048	+	0.943262i	$0.392260\pi$
$318$	−14.8625	−0.833447
$319$	−16.8126	−0.941326
$320$	0.828405	0.0463093
$321$	22.5919	1.26095
$322$	5.16683	0.287936
$323$	−4.13113	−0.229862
$324$	−9.46754	−0.525974
$325$	−5.77441	−0.320307
$326$	−20.8815	−1.15652
$327$	7.24651	0.400733
$328$	9.53625	0.526551
$329$	−2.13797	−0.117870
$330$	−9.52868	−0.524537
$331$	3.97060	0.218244	0.109122	−	0.994028i	$-0.465196\pi$
$331$	3.97060	0.218244	0.109122	+	0.994028i	$0.465196\pi$
$332$	−4.38717	−0.240777
$333$	2.27796	0.124832
$334$	−5.79451	−0.317062
$335$	−1.06141	−0.0579910
$336$	−1.53425	−0.0837003
$337$	7.60288	0.414155	0.207078	−	0.978325i	$-0.433605\pi$
$337$	7.60288	0.414155	0.207078	+	0.978325i	$0.433605\pi$
$338$	−11.2081	−0.609642
$339$	−4.93970	−0.268288
$340$	3.42225	0.185597
$341$	32.4380	1.75662
$342$	−2.83509	−0.153304
$343$	−8.63580	−0.466290
$344$	0.674754	0.0363803
$345$	−16.2786	−0.876413
$346$	6.43491	0.345943
$347$	−3.74842	−0.201226	−0.100613	−	0.994926i	$-0.532080\pi$
$347$	−3.74842	−0.201226	−0.100613	+	0.994926i	$0.532080\pi$
$348$	8.52890	0.457197
$349$	1.47489	0.0789489	0.0394745	−	0.999221i	$-0.487432\pi$
$349$	1.47489	0.0789489	0.0394745	+	0.999221i	$0.487432\pi$
$350$	−2.73985	−0.146451
$351$	0.533244	0.0284624
$352$	4.76175	0.253802
$353$	1.60152	0.0852403	0.0426202	−	0.999091i	$-0.486429\pi$
$353$	1.60152	0.0852403	0.0426202	+	0.999091i	$0.486429\pi$
$354$	−16.0458	−0.852826
$355$	1.75647	0.0932239
$356$	6.45159	0.341933
$357$	−6.33818	−0.335452
$358$	6.94931	0.367283
$359$	28.5063	1.50450	0.752252	−	0.658876i	$-0.228968\pi$
$359$	28.5063	1.50450	0.752252	+	0.658876i	$0.228968\pi$
$360$	2.34860	0.123782
$361$	1.00000	0.0526316
$362$	7.34646	0.386122
$363$	−28.2002	−1.48013
$364$	0.850209	0.0445631
$365$	−9.74744	−0.510204
$366$	2.70981	0.141644
$367$	−33.4257	−1.74481	−0.872404	−	0.488786i	$-0.837440\pi$
$367$	−33.4257	−1.74481	−0.872404	+	0.488786i	$0.837440\pi$
$368$	8.13489	0.424060
$369$	27.0361	1.40744
$370$	0.665615	0.0346037
$371$	3.90787	0.202887
$372$	−16.4555	−0.853180
$373$	26.1707	1.35507	0.677534	−	0.735491i	$-0.263049\pi$
$373$	26.1707	1.35507	0.677534	+	0.735491i	$0.263049\pi$
$374$	19.6714	1.01718
$375$	18.6376	0.962444
$376$	−3.36611	−0.173594
$377$	−4.72631	−0.243417
$378$	0.253015	0.0130137
$379$	−0.979375	−0.0503071	−0.0251536	−	0.999684i	$-0.508007\pi$
$379$	−0.979375	−0.0503071	−0.0251536	+	0.999684i	$0.508007\pi$
$380$	−0.828405	−0.0424963
$381$	1.91079	0.0978926
$382$	−16.3578	−0.836940
$383$	19.6342	1.00326	0.501631	−	0.865082i	$-0.332733\pi$
$383$	19.6342	1.00326	0.501631	+	0.865082i	$0.332733\pi$
$384$	−2.41559	−0.123270
$385$	2.50543	0.127688
$386$	9.39884	0.478388
$387$	1.91299	0.0972426
$388$	1.33445	0.0677463
$389$	−13.1836	−0.668435	−0.334218	−	0.942496i	$-0.608472\pi$
$389$	−13.1836	−0.668435	−0.334218	+	0.942496i	$0.608472\pi$
$390$	−2.67867	−0.135640
$391$	33.6062	1.69954
$392$	−6.59659	−0.333178
$393$	−7.40900	−0.373735
$394$	21.2194	1.06902
$395$	−0.393538	−0.0198010
$396$	13.5000	0.678399
$397$	−13.2270	−0.663844	−0.331922	−	0.943307i	$-0.607697\pi$
$397$	−13.2270	−0.663844	−0.331922	+	0.943307i	$0.607697\pi$
$398$	−27.9566	−1.40134
$399$	1.53425	0.0768086
$400$	−4.31374	−0.215687
$401$	−10.2977	−0.514245	−0.257122	−	0.966379i	$-0.582774\pi$
$401$	−10.2977	−0.514245	−0.257122	+	0.966379i	$0.582774\pi$
$402$	3.09502	0.154366
$403$	9.11888	0.454244
$404$	3.18561	0.158490
$405$	−7.84296	−0.389720
$406$	−2.24255	−0.111296
$407$	3.82601	0.189648
$408$	−9.97912	−0.494040
$409$	−21.2666	−1.05157	−0.525783	−	0.850619i	$-0.676228\pi$
$409$	−21.2666	−1.05157	−0.525783	+	0.850619i	$0.676228\pi$
$410$	7.89988	0.390147
$411$	−19.9953	−0.986293
$412$	−11.1322	−0.548446
$413$	4.21901	0.207604
$414$	23.0631	1.13349
$415$	−3.63436	−0.178404
$416$	1.33861	0.0656306
$417$	37.2813	1.82567
$418$	−4.76175	−0.232905
$419$	20.5713	1.00497	0.502486	−	0.864585i	$-0.332419\pi$
$419$	20.5713	1.00497	0.502486	+	0.864585i	$0.332419\pi$
$420$	−1.27098	−0.0620176
$421$	26.4209	1.28767	0.643837	−	0.765163i	$-0.277342\pi$
$421$	26.4209	1.28767	0.643837	+	0.765163i	$0.277342\pi$
$422$	−1.00000	−0.0486792
$423$	−9.54322	−0.464007
$424$	6.15273	0.298803
$425$	−17.8206	−0.864427
$426$	−5.12179	−0.248152
$427$	−0.712504	−0.0344805
$428$	−9.35251	−0.452071
$429$	−15.3972	−0.743386
$430$	0.558970	0.0269559
$431$	28.1887	1.35780	0.678900	−	0.734231i	$-0.262457\pi$
$431$	28.1887	1.35780	0.678900	+	0.734231i	$0.262457\pi$
$432$	0.398357	0.0191660
$433$	−28.8739	−1.38759	−0.693796	−	0.720171i	$-0.744063\pi$
$433$	−28.8739	−1.38759	−0.693796	+	0.720171i	$0.744063\pi$
$434$	4.32674	0.207690
$435$	7.06539	0.338759
$436$	−2.99989	−0.143669
$437$	−8.13489	−0.389144
$438$	28.4231	1.35811
$439$	10.1732	0.485540	0.242770	−	0.970084i	$-0.421944\pi$
$439$	10.1732	0.485540	0.242770	+	0.970084i	$0.421944\pi$
$440$	3.94466	0.188054
$441$	−18.7019	−0.890568
$442$	5.52995	0.263033
$443$	14.1030	0.670053	0.335026	−	0.942209i	$-0.391255\pi$
$443$	14.1030	0.670053	0.335026	+	0.942209i	$0.391255\pi$
$444$	−1.94090	−0.0921112
$445$	5.34453	0.253355
$446$	−6.03373	−0.285705
$447$	−16.7406	−0.791801
$448$	0.635145	0.0300078
$449$	0.195234	0.00921368	0.00460684	−	0.999989i	$-0.498534\pi$
$449$	0.195234	0.00921368	0.00460684	+	0.999989i	$0.498534\pi$
$450$	−12.2299	−0.576521
$451$	45.4092	2.13824
$452$	2.04492	0.0961851
$453$	1.71490	0.0805731
$454$	2.85447	0.133967
$455$	0.704318	0.0330189
$456$	2.41559	0.113121
$457$	26.1327	1.22243	0.611217	−	0.791463i	$-0.290680\pi$
$457$	26.1327	1.22243	0.611217	+	0.791463i	$0.290680\pi$
$458$	7.52528	0.351633
$459$	1.64566	0.0768130
$460$	6.73898	0.314207
$461$	−5.41612	−0.252254	−0.126127	−	0.992014i	$-0.540255\pi$
$461$	−5.41612	−0.252254	−0.126127	+	0.992014i	$0.540255\pi$
$462$	−7.30572	−0.339893
$463$	25.7914	1.19863	0.599314	−	0.800514i	$-0.295440\pi$
$463$	25.7914	1.19863	0.599314	+	0.800514i	$0.295440\pi$
$464$	−3.53077	−0.163912
$465$	−13.6319	−0.632162
$466$	−9.44916	−0.437724
$467$	−15.5157	−0.717981	−0.358991	−	0.933341i	$-0.616879\pi$
$467$	−15.5157	−0.717981	−0.358991	+	0.933341i	$0.616879\pi$
$468$	3.79507	0.175427
$469$	−0.813791	−0.0375774
$470$	−2.78850	−0.128624
$471$	−25.5819	−1.17875
$472$	6.64260	0.305751
$473$	3.21301	0.147734
$474$	1.14754	0.0527082
$475$	4.31374	0.197928
$476$	2.62386	0.120265
$477$	17.4435	0.798684
$478$	8.19763	0.374951
$479$	−2.13221	−0.0974231	−0.0487116	−	0.998813i	$-0.515512\pi$
$479$	−2.13221	−0.0974231	−0.0487116	+	0.998813i	$0.515512\pi$
$480$	−2.00109	−0.0913369
$481$	1.07556	0.0490412
$482$	10.5796	0.481889
$483$	−12.4810	−0.567903
$484$	11.6742	0.530647
$485$	1.10546	0.0501965
$486$	21.6746	0.983182
$487$	−10.0437	−0.455124	−0.227562	−	0.973764i	$-0.573075\pi$
$487$	−10.0437	−0.455124	−0.227562	+	0.973764i	$0.573075\pi$
$488$	−1.12180	−0.0507814
$489$	50.4411	2.28102
$490$	−5.46465	−0.246868
$491$	−25.2523	−1.13962	−0.569811	−	0.821776i	$-0.692984\pi$
$491$	−25.2523	−1.13962	−0.569811	+	0.821776i	$0.692984\pi$
$492$	−23.0357	−1.03853
$493$	−14.5860	−0.656923
$494$	−1.33861	−0.0602268
$495$	11.1835	0.502659
$496$	6.81222	0.305878
$497$	1.34670	0.0604078
$498$	10.5976	0.474891
$499$	−12.2963	−0.550456	−0.275228	−	0.961379i	$-0.588753\pi$
$499$	−12.2963	−0.550456	−0.275228	+	0.961379i	$0.588753\pi$
$500$	−7.71556	−0.345050
$501$	13.9972	0.625348
$502$	0.109849	0.00490279
$503$	25.4968	1.13684	0.568422	−	0.822737i	$-0.307554\pi$
$503$	25.4968	1.13684	0.568422	+	0.822737i	$0.307554\pi$
$504$	1.80069	0.0802092
$505$	2.63898	0.117433
$506$	38.7363	1.72204
$507$	27.0743	1.20241
$508$	−0.791022	−0.0350959
$509$	−18.1913	−0.806314	−0.403157	−	0.915131i	$-0.632087\pi$
$509$	−18.1913	−0.806314	−0.403157	+	0.915131i	$0.632087\pi$
$510$	−8.26676	−0.366058
$511$	−7.47344	−0.330605
$512$	1.00000	0.0441942
$513$	−0.398357	−0.0175879
$514$	7.86185	0.346771
$515$	−9.22200	−0.406370
$516$	−1.62993	−0.0717537
$517$	−16.0286	−0.704935
$518$	0.510332	0.0224227
$519$	−15.5441	−0.682311
$520$	1.10891	0.0486289
$521$	30.4690	1.33487	0.667437	−	0.744667i	$-0.267392\pi$
$521$	30.4690	1.33487	0.667437	+	0.744667i	$0.267392\pi$
$522$	−10.0100	−0.438128
$523$	−13.2742	−0.580440	−0.290220	−	0.956960i	$-0.593728\pi$
$523$	−13.2742	−0.580440	−0.290220	+	0.956960i	$0.593728\pi$
$524$	3.06716	0.133989
$525$	6.61837	0.288849
$526$	21.6422	0.943647
$527$	28.1421	1.22589
$528$	−11.5024	−0.500579
$529$	43.1764	1.87723
$530$	5.09695	0.221397
$531$	18.8324	0.817255
$532$	−0.635145	−0.0275370
$533$	12.7653	0.552926
$534$	−15.5844	−0.674403
$535$	−7.74767	−0.334961
$536$	−1.28127	−0.0553424
$537$	−16.7867	−0.724400
$538$	−4.79940	−0.206917
$539$	−31.4113	−1.35298
$540$	0.330001	0.0142010
$541$	−3.45816	−0.148678	−0.0743391	−	0.997233i	$-0.523685\pi$
$541$	−3.45816	−0.148678	−0.0743391	+	0.997233i	$0.523685\pi$
$542$	−8.60356	−0.369554
$543$	−17.7461	−0.761557
$544$	4.13113	0.177121
$545$	−2.48512	−0.106451
$546$	−2.05376	−0.0878928
$547$	−43.6707	−1.86722	−0.933612	−	0.358285i	$-0.883362\pi$
$547$	−43.6707	−1.86722	−0.933612	+	0.358285i	$0.883362\pi$
$548$	8.27758	0.353601
$549$	−3.18040	−0.135736
$550$	−20.5410	−0.875869
$551$	3.53077	0.150416
$552$	−19.6506	−0.836384
$553$	−0.301728	−0.0128308
$554$	19.9564	0.847865
$555$	−1.60786	−0.0682497
$556$	−15.4336	−0.654530
$557$	40.7250	1.72557	0.862787	−	0.505568i	$-0.168717\pi$
$557$	40.7250	1.72557	0.862787	+	0.505568i	$0.168717\pi$
$558$	19.3132	0.817595
$559$	0.903230	0.0382026
$560$	0.526157	0.0222342
$561$	−47.5180	−2.00621
$562$	17.7987	0.750791
$563$	−1.28414	−0.0541199	−0.0270599	−	0.999634i	$-0.508615\pi$
$563$	−1.28414	−0.0541199	−0.0270599	+	0.999634i	$0.508615\pi$
$564$	8.13115	0.342383
$565$	1.69403	0.0712682
$566$	30.0238	1.26200
$567$	−6.01326	−0.252533
$568$	2.12031	0.0889660
$569$	38.4213	1.61071	0.805353	−	0.592796i	$-0.201976\pi$
$569$	38.4213	1.61071	0.805353	+	0.592796i	$0.201976\pi$
$570$	2.00109	0.0838164
$571$	−22.3930	−0.937119	−0.468559	−	0.883432i	$-0.655227\pi$
$571$	−22.3930	−0.937119	−0.468559	+	0.883432i	$0.655227\pi$
$572$	6.37411	0.266515
$573$	39.5139	1.65072
$574$	6.05690	0.252810
$575$	−35.0918	−1.46343
$576$	2.83509	0.118129
$577$	0.391406	0.0162945	0.00814723	−	0.999967i	$-0.497407\pi$
$577$	0.391406	0.0162945	0.00814723	+	0.999967i	$0.497407\pi$
$578$	0.0661984	0.00275349
$579$	−22.7038	−0.943536
$580$	−2.92491	−0.121450
$581$	−2.78649	−0.115603
$582$	−3.22348	−0.133618
$583$	29.2977	1.21339
$584$	−11.7665	−0.486902
$585$	3.14386	0.129982
$586$	18.3876	0.759584
$587$	33.0618	1.36461	0.682303	−	0.731069i	$-0.260978\pi$
$587$	33.0618	1.36461	0.682303	+	0.731069i	$0.260978\pi$
$588$	15.9347	0.657135
$589$	−6.81222	−0.280693
$590$	5.50277	0.226545
$591$	−51.2573	−2.10845
$592$	0.803490	0.0330232
$593$	−28.2077	−1.15835	−0.579175	−	0.815203i	$-0.696625\pi$
$593$	−28.2077	−1.15835	−0.579175	+	0.815203i	$0.696625\pi$
$594$	1.89688	0.0778298
$595$	2.17362	0.0891098
$596$	6.93021	0.283872
$597$	67.5318	2.76389
$598$	10.8894	0.445301
$599$	−1.46904	−0.0600235	−0.0300118	−	0.999550i	$-0.509554\pi$
$599$	−1.46904	−0.0600235	−0.0300118	+	0.999550i	$0.509554\pi$
$600$	10.4203	0.425405
$601$	20.2253	0.825007	0.412504	−	0.910956i	$-0.364654\pi$
$601$	20.2253	0.825007	0.412504	+	0.910956i	$0.364654\pi$
$602$	0.428566	0.0174671
$603$	−3.63251	−0.147927
$604$	−0.709930	−0.0288866
$605$	9.67099	0.393182
$606$	−7.69513	−0.312593
$607$	−17.6276	−0.715483	−0.357741	−	0.933821i	$-0.616453\pi$
$607$	−17.6276	−0.715483	−0.357741	+	0.933821i	$0.616453\pi$
$608$	−1.00000	−0.0405554
$609$	5.41709	0.219511
$610$	−0.929303	−0.0376264
$611$	−4.50590	−0.182289
$612$	11.7121	0.473434
$613$	−9.54693	−0.385597	−0.192798	−	0.981238i	$-0.561756\pi$
$613$	−9.54693	−0.385597	−0.192798	+	0.981238i	$0.561756\pi$
$614$	−20.7591	−0.837771
$615$	−19.0829	−0.769497
$616$	3.02440	0.121856
$617$	41.8651	1.68543	0.842713	−	0.538363i	$-0.180957\pi$
$617$	41.8651	1.68543	0.842713	+	0.538363i	$0.180957\pi$
$618$	26.8909	1.08171
$619$	−40.5618	−1.63032	−0.815158	−	0.579239i	$-0.803350\pi$
$619$	−40.5618	−1.63032	−0.815158	+	0.579239i	$0.803350\pi$
$620$	5.64328	0.226639
$621$	3.24059	0.130040
$622$	−24.9991	−1.00237
$623$	4.09769	0.164171
$624$	−3.23353	−0.129445
$625$	15.1771	0.607085
$626$	−16.4582	−0.657802
$627$	11.5024	0.459363
$628$	10.5903	0.422599
$629$	3.31932	0.132350
$630$	1.49170	0.0594309
$631$	7.83752	0.312007	0.156003	−	0.987757i	$-0.450139\pi$
$631$	7.83752	0.312007	0.156003	+	0.987757i	$0.450139\pi$
$632$	−0.475054	−0.0188967
$633$	2.41559	0.0960112
$634$	11.8239	0.469587
$635$	−0.655287	−0.0260043
$636$	−14.8625	−0.589336
$637$	−8.83024	−0.349867
$638$	−16.8126	−0.665618
$639$	6.01125	0.237802
$640$	0.828405	0.0327456
$641$	22.5387	0.890226	0.445113	−	0.895474i	$-0.353163\pi$
$641$	22.5387	0.890226	0.445113	+	0.895474i	$0.353163\pi$
$642$	22.5919	0.891629
$643$	−3.92059	−0.154613	−0.0773064	−	0.997007i	$-0.524632\pi$
$643$	−3.92059	−0.154613	−0.0773064	+	0.997007i	$0.524632\pi$
$644$	5.16683	0.203602
$645$	−1.35024	−0.0531658
$646$	−4.13113	−0.162537
$647$	−16.0435	−0.630734	−0.315367	−	0.948970i	$-0.602128\pi$
$647$	−16.0435	−0.630734	−0.315367	+	0.948970i	$0.602128\pi$
$648$	−9.46754	−0.371920
$649$	31.6304	1.24160
$650$	−5.77441	−0.226491
$651$	−10.4517	−0.409633
$652$	−20.8815	−0.817781
$653$	−45.0187	−1.76172	−0.880859	−	0.473378i	$-0.843035\pi$
$653$	−45.0187	−1.76172	−0.880859	+	0.473378i	$0.843035\pi$
$654$	7.24651	0.283361
$655$	2.54085	0.0992792
$656$	9.53625	0.372328
$657$	−33.3591	−1.30146
$658$	−2.13797	−0.0833466
$659$	30.5203	1.18890	0.594451	−	0.804132i	$-0.297370\pi$
$659$	30.5203	1.18890	0.594451	+	0.804132i	$0.297370\pi$
$660$	−9.52868	−0.370904
$661$	−0.115839	−0.00450563	−0.00225282	−	0.999997i	$-0.500717\pi$
$661$	−0.115839	−0.00450563	−0.00225282	+	0.999997i	$0.500717\pi$
$662$	3.97060	0.154322
$663$	−13.3581	−0.518786
$664$	−4.38717	−0.170255
$665$	−0.526157	−0.0204035
$666$	2.27796	0.0882693
$667$	−28.7224	−1.11214
$668$	−5.79451	−0.224196
$669$	14.5750	0.563504
$670$	−1.06141	−0.0410058
$671$	−5.34171	−0.206215
$672$	−1.53425	−0.0591850
$673$	−12.2830	−0.473477	−0.236738	−	0.971573i	$-0.576078\pi$
$673$	−12.2830	−0.473477	−0.236738	+	0.971573i	$0.576078\pi$
$674$	7.60288	0.292852
$675$	−1.71841	−0.0661417
$676$	−11.2081	−0.431082
$677$	14.6420	0.562738	0.281369	−	0.959600i	$-0.409212\pi$
$677$	14.6420	0.562738	0.281369	+	0.959600i	$0.409212\pi$
$678$	−4.93970	−0.189708
$679$	0.847567	0.0325266
$680$	3.42225	0.131237
$681$	−6.89525	−0.264226
$682$	32.4380	1.24212
$683$	−11.6178	−0.444542	−0.222271	−	0.974985i	$-0.571347\pi$
$683$	−11.6178	−0.444542	−0.222271	+	0.974985i	$0.571347\pi$
$684$	−2.83509	−0.108402
$685$	6.85719	0.262000
$686$	−8.63580	−0.329717
$687$	−18.1780	−0.693534
$688$	0.674754	0.0257248
$689$	8.23608	0.313770
$690$	−16.2786	−0.619717
$691$	2.51172	0.0955504	0.0477752	−	0.998858i	$-0.484787\pi$
$691$	2.51172	0.0955504	0.0477752	+	0.998858i	$0.484787\pi$
$692$	6.43491	0.244618
$693$	8.57444	0.325716
$694$	−3.74842	−0.142288
$695$	−12.7853	−0.484973
$696$	8.52890	0.323287
$697$	39.3955	1.49221
$698$	1.47489	0.0558253
$699$	22.8253	0.863333
$700$	−2.73985	−0.103557
$701$	−32.1166	−1.21303	−0.606513	−	0.795073i	$-0.707432\pi$
$701$	−32.1166	−1.21303	−0.606513	+	0.795073i	$0.707432\pi$
$702$	0.533244	0.0201260
$703$	−0.803490	−0.0303042
$704$	4.76175	0.179465
$705$	6.73589	0.253688
$706$	1.60152	0.0602740
$707$	2.02332	0.0760949
$708$	−16.0458	−0.603039
$709$	28.2421	1.06066	0.530328	−	0.847793i	$-0.322069\pi$
$709$	28.2421	1.06066	0.530328	+	0.847793i	$0.322069\pi$
$710$	1.75647	0.0659192
$711$	−1.34682	−0.0505098
$712$	6.45159	0.241783
$713$	55.4166	2.07537
$714$	−6.33818	−0.237201
$715$	5.28034	0.197474
$716$	6.94931	0.259708
$717$	−19.8021	−0.739524
$718$	28.5063	1.06384
$719$	28.3906	1.05879	0.529395	−	0.848376i	$-0.322419\pi$
$719$	28.3906	1.05879	0.529395	+	0.848376i	$0.322419\pi$
$720$	2.34860	0.0875273
$721$	−7.07058	−0.263322
$722$	1.00000	0.0372161
$723$	−25.5561	−0.950441
$724$	7.34646	0.273029
$725$	15.2308	0.565659
$726$	−28.2002	−1.04661
$727$	−26.8529	−0.995920	−0.497960	−	0.867200i	$-0.665917\pi$
$727$	−26.8529	−0.995920	−0.497960	+	0.867200i	$0.665917\pi$
$728$	0.850209	0.0315109
$729$	−23.9545	−0.887204
$730$	−9.74744	−0.360769
$731$	2.78749	0.103099
$732$	2.70981	0.100157
$733$	−35.5174	−1.31187	−0.655933	−	0.754819i	$-0.727725\pi$
$733$	−35.5174	−1.31187	−0.655933	+	0.754819i	$0.727725\pi$
$734$	−33.4257	−1.23377
$735$	13.2004	0.486903
$736$	8.13489	0.299856
$737$	−6.10107	−0.224736
$738$	27.0361	0.995214
$739$	21.5191	0.791594	0.395797	−	0.918338i	$-0.370468\pi$
$739$	21.5191	0.791594	0.395797	+	0.918338i	$0.370468\pi$
$740$	0.665615	0.0244685
$741$	3.23353	0.118787
$742$	3.90787	0.143463
$743$	35.4893	1.30198	0.650988	−	0.759088i	$-0.274355\pi$
$743$	35.4893	1.30198	0.650988	+	0.759088i	$0.274355\pi$
$744$	−16.4555	−0.603289
$745$	5.74102	0.210335
$746$	26.1707	0.958178
$747$	−12.4380	−0.455084
$748$	19.6714	0.719257
$749$	−5.94020	−0.217050
$750$	18.6376	0.680551
$751$	−9.75862	−0.356097	−0.178049	−	0.984022i	$-0.556978\pi$
$751$	−9.75862	−0.356097	−0.178049	+	0.984022i	$0.556978\pi$
$752$	−3.36611	−0.122749
$753$	−0.265350	−0.00966989
$754$	−4.72631	−0.172122
$755$	−0.588110	−0.0214035
$756$	0.253015	0.00920205
$757$	23.0881	0.839150	0.419575	−	0.907721i	$-0.362179\pi$
$757$	23.0881	0.839150	0.419575	+	0.907721i	$0.362179\pi$
$758$	−0.979375	−0.0355725
$759$	−93.5711	−3.39641
$760$	−0.828405	−0.0300494
$761$	−42.4664	−1.53941	−0.769703	−	0.638402i	$-0.779596\pi$
$761$	−42.4664	−1.53941	−0.769703	+	0.638402i	$0.779596\pi$
$762$	1.91079	0.0692205
$763$	−1.90536	−0.0689788
$764$	−16.3578	−0.591806
$765$	9.70237	0.350790
$766$	19.6342	0.709414
$767$	8.89183	0.321066
$768$	−2.41559	−0.0871652
$769$	12.4318	0.448303	0.224152	−	0.974554i	$-0.428039\pi$
$769$	12.4318	0.448303	0.224152	+	0.974554i	$0.428039\pi$
$770$	2.50543	0.0902894
$771$	−18.9910	−0.683945
$772$	9.39884	0.338272
$773$	−9.34414	−0.336085	−0.168043	−	0.985780i	$-0.553745\pi$
$773$	−9.34414	−0.336085	−0.168043	+	0.985780i	$0.553745\pi$
$774$	1.91299	0.0687609
$775$	−29.3862	−1.05558
$776$	1.33445	0.0479039
$777$	−1.23276	−0.0442248
$778$	−13.1836	−0.472655
$779$	−9.53625	−0.341672
$780$	−2.67867	−0.0959119
$781$	10.0964	0.361276
$782$	33.6062	1.20176
$783$	−1.40651	−0.0502645
$784$	−6.59659	−0.235593
$785$	8.77307	0.313124
$786$	−7.40900	−0.264270
$787$	8.52190	0.303773	0.151886	−	0.988398i	$-0.451465\pi$
$787$	8.52190	0.303773	0.151886	+	0.988398i	$0.451465\pi$
$788$	21.2194	0.755908
$789$	−52.2788	−1.86118
$790$	−0.393538	−0.0140014
$791$	1.29882	0.0461808
$792$	13.5000	0.479701
$793$	−1.50165	−0.0533250
$794$	−13.2270	−0.469409
$795$	−12.3122	−0.436667
$796$	−27.9566	−0.990896
$797$	−27.7463	−0.982825	−0.491412	−	0.870927i	$-0.663519\pi$
$797$	−27.7463	−0.982825	−0.491412	+	0.870927i	$0.663519\pi$
$798$	1.53425	0.0543119
$799$	−13.9058	−0.491953
$800$	−4.31374	−0.152514
$801$	18.2908	0.646275
$802$	−10.2977	−0.363626
$803$	−56.0291	−1.97722
$804$	3.09502	0.109153
$805$	4.28023	0.150858
$806$	9.11888	0.321199
$807$	11.5934	0.408107
$808$	3.18561	0.112069
$809$	−42.7861	−1.50428	−0.752139	−	0.659004i	$-0.770978\pi$
$809$	−42.7861	−1.50428	−0.752139	+	0.659004i	$0.770978\pi$
$810$	−7.84296	−0.275573
$811$	21.6511	0.760272	0.380136	−	0.924931i	$-0.375877\pi$
$811$	21.6511	0.760272	0.380136	+	0.924931i	$0.375877\pi$
$812$	−2.24255	−0.0786981
$813$	20.7827	0.728881
$814$	3.82601	0.134102
$815$	−17.2983	−0.605933
$816$	−9.97912	−0.349339
$817$	−0.674754	−0.0236067
$818$	−21.2666	−0.743570
$819$	2.41042	0.0842269
$820$	7.89988	0.275876
$821$	−51.1735	−1.78597	−0.892984	−	0.450088i	$-0.851392\pi$
$821$	−51.1735	−1.78597	−0.892984	+	0.450088i	$0.851392\pi$
$822$	−19.9953	−0.697415
$823$	−17.4560	−0.608478	−0.304239	−	0.952596i	$-0.598402\pi$
$823$	−17.4560	−0.608478	−0.304239	+	0.952596i	$0.598402\pi$
$824$	−11.1322	−0.387810
$825$	49.6186	1.72750
$826$	4.21901	0.146798
$827$	−50.9896	−1.77308	−0.886541	−	0.462650i	$-0.846899\pi$
$827$	−50.9896	−1.77308	−0.886541	+	0.462650i	$0.846899\pi$
$828$	23.0631	0.801499
$829$	−28.7988	−1.00022	−0.500111	−	0.865961i	$-0.666707\pi$
$829$	−28.7988	−1.00022	−0.500111	+	0.865961i	$0.666707\pi$
$830$	−3.63436	−0.126150
$831$	−48.2065	−1.67226
$832$	1.33861	0.0464078
$833$	−27.2513	−0.944203
$834$	37.2813	1.29095
$835$	−4.80021	−0.166118
$836$	−4.76175	−0.164688
$837$	2.71370	0.0937991
$838$	20.5713	0.710623
$839$	−10.4016	−0.359104	−0.179552	−	0.983748i	$-0.557465\pi$
$839$	−10.4016	−0.359104	−0.179552	+	0.983748i	$0.557465\pi$
$840$	−1.27098	−0.0438530
$841$	−16.5337	−0.570127
$842$	26.4209	0.910523
$843$	−42.9943	−1.48080
$844$	−1.00000	−0.0344214
$845$	−9.28488	−0.319409
$846$	−9.54322	−0.328103
$847$	7.41483	0.254776
$848$	6.15273	0.211286
$849$	−72.5254	−2.48906
$850$	−17.8206	−0.611242
$851$	6.53630	0.224061
$852$	−5.12179	−0.175470
$853$	47.3750	1.62209	0.811045	−	0.584984i	$-0.198899\pi$
$853$	47.3750	1.62209	0.811045	+	0.584984i	$0.198899\pi$
$854$	−0.712504	−0.0243814
$855$	−2.34860	−0.0803205
$856$	−9.35251	−0.319662
$857$	2.64304	0.0902845	0.0451422	−	0.998981i	$-0.485626\pi$
$857$	2.64304	0.0902845	0.0451422	+	0.998981i	$0.485626\pi$
$858$	−15.3972	−0.525653
$859$	−19.9397	−0.680335	−0.340167	−	0.940365i	$-0.610484\pi$
$859$	−19.9397	−0.680335	−0.340167	+	0.940365i	$0.610484\pi$
$860$	0.558970	0.0190607
$861$	−14.6310	−0.498623
$862$	28.1887	0.960109
$863$	−0.458199	−0.0155973	−0.00779864	−	0.999970i	$-0.502482\pi$
$863$	−0.458199	−0.0155973	−0.00779864	+	0.999970i	$0.502482\pi$
$864$	0.398357	0.0135524
$865$	5.33071	0.181250
$866$	−28.8739	−0.981176
$867$	−0.159908	−0.00543078
$868$	4.32674	0.146859
$869$	−2.26209	−0.0767361
$870$	7.06539	0.239539
$871$	−1.71511	−0.0581144
$872$	−2.99989	−0.101589
$873$	3.78328	0.128045
$874$	−8.13489	−0.275167
$875$	−4.90050	−0.165667
$876$	28.4231	0.960327
$877$	35.4313	1.19643	0.598216	−	0.801335i	$-0.295877\pi$
$877$	35.4313	1.19643	0.598216	+	0.801335i	$0.295877\pi$
$878$	10.1732	0.343328
$879$	−44.4169	−1.49814
$880$	3.94466	0.132974
$881$	−34.2584	−1.15419	−0.577097	−	0.816676i	$-0.695815\pi$
$881$	−34.2584	−1.15419	−0.577097	+	0.816676i	$0.695815\pi$
$882$	−18.7019	−0.629727
$883$	7.96151	0.267926	0.133963	−	0.990986i	$-0.457230\pi$
$883$	7.96151	0.267926	0.133963	+	0.990986i	$0.457230\pi$
$884$	5.52995	0.185992
$885$	−13.2924	−0.446821
$886$	14.1030	0.473799
$887$	7.28917	0.244746	0.122373	−	0.992484i	$-0.460950\pi$
$887$	7.28917	0.244746	0.122373	+	0.992484i	$0.460950\pi$
$888$	−1.94090	−0.0651325
$889$	−0.502413	−0.0168504
$890$	5.34453	0.179149
$891$	−45.0820	−1.51030
$892$	−6.03373	−0.202024
$893$	3.36611	0.112643
$894$	−16.7406	−0.559888
$895$	5.75685	0.192430
$896$	0.635145	0.0212187
$897$	−26.3044	−0.878278
$898$	0.195234	0.00651505
$899$	−24.0524	−0.802191
$900$	−12.2299	−0.407662
$901$	25.4177	0.846786
$902$	45.4092	1.51196
$903$	−1.03524	−0.0344507
$904$	2.04492	0.0680131
$905$	6.08585	0.202301
$906$	1.71490	0.0569738
$907$	29.7969	0.989391	0.494695	−	0.869066i	$-0.335280\pi$
$907$	29.7969	0.989391	0.494695	+	0.869066i	$0.335280\pi$
$908$	2.85447	0.0947291
$909$	9.03149	0.299555
$910$	0.704318	0.0233479
$911$	−24.2141	−0.802250	−0.401125	−	0.916023i	$-0.631381\pi$
$911$	−24.2141	−0.802250	−0.401125	+	0.916023i	$0.631381\pi$
$912$	2.41559	0.0799883
$913$	−20.8906	−0.691378
$914$	26.1327	0.864391
$915$	2.24482	0.0742114
$916$	7.52528	0.248642
$917$	1.94809	0.0643315
$918$	1.64566	0.0543150
$919$	7.77547	0.256489	0.128244	−	0.991743i	$-0.459066\pi$
$919$	7.77547	0.256489	0.128244	+	0.991743i	$0.459066\pi$
$920$	6.73898	0.222178
$921$	50.1456	1.65235
$922$	−5.41612	−0.178370
$923$	2.83826	0.0934223
$924$	−7.30572	−0.240340
$925$	−3.46605	−0.113963
$926$	25.7914	0.847557
$927$	−31.5609	−1.03660
$928$	−3.53077	−0.115903
$929$	−16.8094	−0.551500	−0.275750	−	0.961229i	$-0.588926\pi$
$929$	−16.8094	−0.551500	−0.275750	+	0.961229i	$0.588926\pi$
$930$	−13.6319	−0.447006
$931$	6.59659	0.216195
$932$	−9.44916	−0.309517
$933$	60.3878	1.97701
$934$	−15.5157	−0.507690
$935$	16.2959	0.532932
$936$	3.79507	0.124046
$937$	5.22852	0.170808	0.0854041	−	0.996346i	$-0.472782\pi$
$937$	5.22852	0.170808	0.0854041	+	0.996346i	$0.472782\pi$
$938$	−0.813791	−0.0265712
$939$	39.7563	1.29740
$940$	−2.78850	−0.0909509
$941$	−13.3094	−0.433873	−0.216936	−	0.976186i	$-0.569606\pi$
$941$	−13.3094	−0.433873	−0.216936	+	0.976186i	$0.569606\pi$
$942$	−25.5819	−0.833503
$943$	77.5763	2.52623
$944$	6.64260	0.216198
$945$	0.209599	0.00681824
$946$	3.21301	0.104464
$947$	27.6878	0.899733	0.449867	−	0.893096i	$-0.351472\pi$
$947$	27.6878	0.899733	0.449867	+	0.893096i	$0.351472\pi$
$948$	1.14754	0.0372703
$949$	−15.7507	−0.511290
$950$	4.31374	0.139956
$951$	−28.5617	−0.926178
$952$	2.62386	0.0850399
$953$	−34.5165	−1.11810	−0.559050	−	0.829134i	$-0.688834\pi$
$953$	−34.5165	−1.11810	−0.559050	+	0.829134i	$0.688834\pi$
$954$	17.4435	0.564755
$955$	−13.5509	−0.438497
$956$	8.19763	0.265130
$957$	40.6125	1.31281
$958$	−2.13221	−0.0688885
$959$	5.25746	0.169772
$960$	−2.00109	−0.0645849
$961$	15.4063	0.496977
$962$	1.07556	0.0346773
$963$	−26.5152	−0.854440
$964$	10.5796	0.340747
$965$	7.78605	0.250642
$966$	−12.4810	−0.401568
$967$	−10.3428	−0.332601	−0.166300	−	0.986075i	$-0.553182\pi$
$967$	−10.3428	−0.332601	−0.166300	+	0.986075i	$0.553182\pi$
$968$	11.6742	0.375224
$969$	9.97912	0.320575
$970$	1.10546	0.0354943
$971$	28.7367	0.922206	0.461103	−	0.887347i	$-0.347454\pi$
$971$	28.7367	0.922206	0.461103	+	0.887347i	$0.347454\pi$
$972$	21.6746	0.695214
$973$	−9.80257	−0.314256
$974$	−10.0437	−0.321821
$975$	13.9486	0.446713
$976$	−1.12180	−0.0359079
$977$	13.8581	0.443361	0.221680	−	0.975119i	$-0.428846\pi$
$977$	13.8581	0.443361	0.221680	+	0.975119i	$0.428846\pi$
$978$	50.4411	1.61293
$979$	30.7208	0.981842
$980$	−5.46465	−0.174562
$981$	−8.50495	−0.271542
$982$	−25.2523	−0.805834
$983$	0.254699	0.00812363	0.00406181	−	0.999992i	$-0.498707\pi$
$983$	0.254699	0.00812363	0.00406181	+	0.999992i	$0.498707\pi$
$984$	−23.0357	−0.734351
$985$	17.5782	0.560089
$986$	−14.5860	−0.464514
$987$	5.16446	0.164386
$988$	−1.33861	−0.0425868
$989$	5.48905	0.174542
$990$	11.1835	0.355433
$991$	10.6407	0.338012	0.169006	−	0.985615i	$-0.445944\pi$
$991$	10.6407	0.338012	0.169006	+	0.985615i	$0.445944\pi$
$992$	6.81222	0.216288
$993$	−9.59136	−0.304372
$994$	1.34670	0.0427148
$995$	−23.1594	−0.734203
$996$	10.5976	0.335799
$997$	−17.2498	−0.546305	−0.273153	−	0.961971i	$-0.588066\pi$
$997$	−17.2498	−0.546305	−0.273153	+	0.961971i	$0.588066\pi$
$998$	−12.2963	−0.389231
$999$	0.320076	0.0101268

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.j.1.7	✓	47

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.j.1.7	✓	47	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:	\( N \)	\(=\)	\( 8018 = 2 \cdot 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8018.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.41559 q^{3} +1.00000 q^{4} +0.828405 q^{5} -2.41559 q^{6} +0.635145 q^{7} +1.00000 q^{8} +2.83509 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.41559 q^{3} +1.00000 q^{4} +0.828405 q^{5} -2.41559 q^{6} +0.635145 q^{7} +1.00000 q^{8} +2.83509 q^{9} +0.828405 q^{10} +4.76175 q^{11} -2.41559 q^{12} +1.33861 q^{13} +0.635145 q^{14} -2.00109 q^{15} +1.00000 q^{16} +4.13113 q^{17} +2.83509 q^{18} -1.00000 q^{19} +0.828405 q^{20} -1.53425 q^{21} +4.76175 q^{22} +8.13489 q^{23} -2.41559 q^{24} -4.31374 q^{25} +1.33861 q^{26} +0.398357 q^{27} +0.635145 q^{28} -3.53077 q^{29} -2.00109 q^{30} +6.81222 q^{31} +1.00000 q^{32} -11.5024 q^{33} +4.13113 q^{34} +0.526157 q^{35} +2.83509 q^{36} +0.803490 q^{37} -1.00000 q^{38} -3.23353 q^{39} +0.828405 q^{40} +9.53625 q^{41} -1.53425 q^{42} +0.674754 q^{43} +4.76175 q^{44} +2.34860 q^{45} +8.13489 q^{46} -3.36611 q^{47} -2.41559 q^{48} -6.59659 q^{49} -4.31374 q^{50} -9.97912 q^{51} +1.33861 q^{52} +6.15273 q^{53} +0.398357 q^{54} +3.94466 q^{55} +0.635145 q^{56} +2.41559 q^{57} -3.53077 q^{58} +6.64260 q^{59} -2.00109 q^{60} -1.12180 q^{61} +6.81222 q^{62} +1.80069 q^{63} +1.00000 q^{64} +1.10891 q^{65} -11.5024 q^{66} -1.28127 q^{67} +4.13113 q^{68} -19.6506 q^{69} +0.526157 q^{70} +2.12031 q^{71} +2.83509 q^{72} -11.7665 q^{73} +0.803490 q^{74} +10.4203 q^{75} -1.00000 q^{76} +3.02440 q^{77} -3.23353 q^{78} -0.475054 q^{79} +0.828405 q^{80} -9.46754 q^{81} +9.53625 q^{82} -4.38717 q^{83} -1.53425 q^{84} +3.42225 q^{85} +0.674754 q^{86} +8.52890 q^{87} +4.76175 q^{88} +6.45159 q^{89} +2.34860 q^{90} +0.850209 q^{91} +8.13489 q^{92} -16.4555 q^{93} -3.36611 q^{94} -0.828405 q^{95} -2.41559 q^{96} +1.33445 q^{97} -6.59659 q^{98} +13.5000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 47 q + 47 q^{2} + 10 q^{3} + 47 q^{4} + 15 q^{5} + 10 q^{6} + 47 q^{8} + 69 q^{9}+O(q^{10}) \) 47 * q + 47 * q^2 + 10 * q^3 + 47 * q^4 + 15 * q^5 + 10 * q^6 + 47 * q^8 + 69 * q^9	\( 47 q + 47 q^{2} + 10 q^{3} + 47 q^{4} + 15 q^{5} + 10 q^{6} + 47 q^{8} + 69 q^{9} + 15 q^{10} + 17 q^{11} + 10 q^{12} + 27 q^{13} + 10 q^{15} + 47 q^{16} + 16 q^{17} + 69 q^{18} - 47 q^{19} + 15 q^{20} + 26 q^{21} + 17 q^{22} + 24 q^{23} + 10 q^{24} + 86 q^{25} + 27 q^{26} + 43 q^{27} + 58 q^{29} + 10 q^{30} + 21 q^{31} + 47 q^{32} + 18 q^{33} + 16 q^{34} + 24 q^{35} + 69 q^{36} + 78 q^{37} - 47 q^{38} - 4 q^{39} + 15 q^{40} + 53 q^{41} + 26 q^{42} + 47 q^{43} + 17 q^{44} + 23 q^{45} + 24 q^{46} + 16 q^{47} + 10 q^{48} + 93 q^{49} + 86 q^{50} + 28 q^{51} + 27 q^{52} + 43 q^{53} + 43 q^{54} + 23 q^{55} - 10 q^{57} + 58 q^{58} + 3 q^{59} + 10 q^{60} + 12 q^{61} + 21 q^{62} - 5 q^{63} + 47 q^{64} + 62 q^{65} + 18 q^{66} + 68 q^{67} + 16 q^{68} + 12 q^{69} + 24 q^{70} - 13 q^{71} + 69 q^{72} + 35 q^{73} + 78 q^{74} + 22 q^{75} - 47 q^{76} + 26 q^{77} - 4 q^{78} + 21 q^{79} + 15 q^{80} + 123 q^{81} + 53 q^{82} + 23 q^{83} + 26 q^{84} + 38 q^{85} + 47 q^{86} + 39 q^{87} + 17 q^{88} + 24 q^{89} + 23 q^{90} + 49 q^{91} + 24 q^{92} + 91 q^{93} + 16 q^{94} - 15 q^{95} + 10 q^{96} + 88 q^{97} + 93 q^{98} + 26 q^{99}+O(q^{100}) \) 47 * q + 47 * q^2 + 10 * q^3 + 47 * q^4 + 15 * q^5 + 10 * q^6 + 47 * q^8 + 69 * q^9 + 15 * q^10 + 17 * q^11 + 10 * q^12 + 27 * q^13 + 10 * q^15 + 47 * q^16 + 16 * q^17 + 69 * q^18 - 47 * q^19 + 15 * q^20 + 26 * q^21 + 17 * q^22 + 24 * q^23 + 10 * q^24 + 86 * q^25 + 27 * q^26 + 43 * q^27 + 58 * q^29 + 10 * q^30 + 21 * q^31 + 47 * q^32 + 18 * q^33 + 16 * q^34 + 24 * q^35 + 69 * q^36 + 78 * q^37 - 47 * q^38 - 4 * q^39 + 15 * q^40 + 53 * q^41 + 26 * q^42 + 47 * q^43 + 17 * q^44 + 23 * q^45 + 24 * q^46 + 16 * q^47 + 10 * q^48 + 93 * q^49 + 86 * q^50 + 28 * q^51 + 27 * q^52 + 43 * q^53 + 43 * q^54 + 23 * q^55 - 10 * q^57 + 58 * q^58 + 3 * q^59 + 10 * q^60 + 12 * q^61 + 21 * q^62 - 5 * q^63 + 47 * q^64 + 62 * q^65 + 18 * q^66 + 68 * q^67 + 16 * q^68 + 12 * q^69 + 24 * q^70 - 13 * q^71 + 69 * q^72 + 35 * q^73 + 78 * q^74 + 22 * q^75 - 47 * q^76 + 26 * q^77 - 4 * q^78 + 21 * q^79 + 15 * q^80 + 123 * q^81 + 53 * q^82 + 23 * q^83 + 26 * q^84 + 38 * q^85 + 47 * q^86 + 39 * q^87 + 17 * q^88 + 24 * q^89 + 23 * q^90 + 49 * q^91 + 24 * q^92 + 91 * q^93 + 16 * q^94 - 15 * q^95 + 10 * q^96 + 88 * q^97 + 93 * q^98 + 26 * q^99

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