LMFDB - Embedded newform 4034.2.a.b.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4034,2,Mod(1,4034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4034, 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("4034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4034 = 2 \cdot 2017 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4034.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:	$32.2116521754$
Analytic rank:	$1$
Dimension:	$35$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	4034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.01951 q^{3} +1.00000 q^{4} +3.52220 q^{5} +2.01951 q^{6} -0.0194784 q^{7} -1.00000 q^{8} +1.07840 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.01951 q^{3} +1.00000 q^{4} +3.52220 q^{5} +2.01951 q^{6} -0.0194784 q^{7} -1.00000 q^{8} +1.07840 q^{9} -3.52220 q^{10} +2.98419 q^{11} -2.01951 q^{12} +6.73728 q^{13} +0.0194784 q^{14} -7.11310 q^{15} +1.00000 q^{16} -5.56265 q^{17} -1.07840 q^{18} -2.82168 q^{19} +3.52220 q^{20} +0.0393368 q^{21} -2.98419 q^{22} -5.57700 q^{23} +2.01951 q^{24} +7.40588 q^{25} -6.73728 q^{26} +3.88068 q^{27} -0.0194784 q^{28} -0.961590 q^{29} +7.11310 q^{30} -7.32179 q^{31} -1.00000 q^{32} -6.02659 q^{33} +5.56265 q^{34} -0.0686068 q^{35} +1.07840 q^{36} -6.86803 q^{37} +2.82168 q^{38} -13.6060 q^{39} -3.52220 q^{40} +0.282543 q^{41} -0.0393368 q^{42} -6.89460 q^{43} +2.98419 q^{44} +3.79834 q^{45} +5.57700 q^{46} -12.2882 q^{47} -2.01951 q^{48} -6.99962 q^{49} -7.40588 q^{50} +11.2338 q^{51} +6.73728 q^{52} +13.1452 q^{53} -3.88068 q^{54} +10.5109 q^{55} +0.0194784 q^{56} +5.69839 q^{57} +0.961590 q^{58} -12.2169 q^{59} -7.11310 q^{60} -11.4780 q^{61} +7.32179 q^{62} -0.0210056 q^{63} +1.00000 q^{64} +23.7300 q^{65} +6.02659 q^{66} -12.3508 q^{67} -5.56265 q^{68} +11.2628 q^{69} +0.0686068 q^{70} +13.0466 q^{71} -1.07840 q^{72} +1.77412 q^{73} +6.86803 q^{74} -14.9562 q^{75} -2.82168 q^{76} -0.0581273 q^{77} +13.6060 q^{78} -12.0391 q^{79} +3.52220 q^{80} -11.0723 q^{81} -0.282543 q^{82} -2.43861 q^{83} +0.0393368 q^{84} -19.5927 q^{85} +6.89460 q^{86} +1.94194 q^{87} -2.98419 q^{88} -13.3160 q^{89} -3.79834 q^{90} -0.131232 q^{91} -5.57700 q^{92} +14.7864 q^{93} +12.2882 q^{94} -9.93850 q^{95} +2.01951 q^{96} +10.3338 q^{97} +6.99962 q^{98} +3.21816 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 35 q - 35 q^{2} - 6 q^{3} + 35 q^{4} + 6 q^{5} + 6 q^{6} - 14 q^{7} - 35 q^{8} + 23 q^{9}+O(q^{10}) $ 35 * q - 35 * q^2 - 6 * q^3 + 35 * q^4 + 6 * q^5 + 6 * q^6 - 14 * q^7 - 35 * q^8 + 23 * q^9	\( 35 q - 35 q^{2} - 6 q^{3} + 35 q^{4} + 6 q^{5} + 6 q^{6} - 14 q^{7} - 35 q^{8} + 23 q^{9} - 6 q^{10} - 9 q^{11} - 6 q^{12} - 7 q^{13} + 14 q^{14} - 19 q^{15} + 35 q^{16} + 17 q^{17} - 23 q^{18} - 25 q^{19} + 6 q^{20} - 15 q^{21} + 9 q^{22} - 12 q^{23} + 6 q^{24} + 7 q^{25} + 7 q^{26} - 27 q^{27} - 14 q^{28} - 13 q^{29} + 19 q^{30} - 69 q^{31} - 35 q^{32} + q^{33} - 17 q^{34} - 4 q^{35} + 23 q^{36} - 22 q^{37} + 25 q^{38} - 38 q^{39} - 6 q^{40} + 15 q^{42} - 32 q^{43} - 9 q^{44} + 9 q^{45} + 12 q^{46} - 18 q^{47} - 6 q^{48} - 19 q^{49} - 7 q^{50} - 21 q^{51} - 7 q^{52} + 20 q^{53} + 27 q^{54} - 54 q^{55} + 14 q^{56} + 28 q^{57} + 13 q^{58} - 21 q^{59} - 19 q^{60} - 67 q^{61} + 69 q^{62} - 28 q^{63} + 35 q^{64} + 22 q^{65} - q^{66} - 18 q^{67} + 17 q^{68} - 42 q^{69} + 4 q^{70} - 36 q^{71} - 23 q^{72} - 18 q^{73} + 22 q^{74} - 49 q^{75} - 25 q^{76} + 20 q^{77} + 38 q^{78} - 92 q^{79} + 6 q^{80} - 25 q^{81} + 42 q^{83} - 15 q^{84} - 29 q^{85} + 32 q^{86} - 40 q^{87} + 9 q^{88} - 8 q^{89} - 9 q^{90} - 89 q^{91} - 12 q^{92} - q^{93} + 18 q^{94} - 62 q^{95} + 6 q^{96} - 40 q^{97} + 19 q^{98} - 64 q^{99}+O(q^{100}) \) 35 * q - 35 * q^2 - 6 * q^3 + 35 * q^4 + 6 * q^5 + 6 * q^6 - 14 * q^7 - 35 * q^8 + 23 * q^9 - 6 * q^10 - 9 * q^11 - 6 * q^12 - 7 * q^13 + 14 * q^14 - 19 * q^15 + 35 * q^16 + 17 * q^17 - 23 * q^18 - 25 * q^19 + 6 * q^20 - 15 * q^21 + 9 * q^22 - 12 * q^23 + 6 * q^24 + 7 * q^25 + 7 * q^26 - 27 * q^27 - 14 * q^28 - 13 * q^29 + 19 * q^30 - 69 * q^31 - 35 * q^32 + q^33 - 17 * q^34 - 4 * q^35 + 23 * q^36 - 22 * q^37 + 25 * q^38 - 38 * q^39 - 6 * q^40 + 15 * q^42 - 32 * q^43 - 9 * q^44 + 9 * q^45 + 12 * q^46 - 18 * q^47 - 6 * q^48 - 19 * q^49 - 7 * q^50 - 21 * q^51 - 7 * q^52 + 20 * q^53 + 27 * q^54 - 54 * q^55 + 14 * q^56 + 28 * q^57 + 13 * q^58 - 21 * q^59 - 19 * q^60 - 67 * q^61 + 69 * q^62 - 28 * q^63 + 35 * q^64 + 22 * q^65 - q^66 - 18 * q^67 + 17 * q^68 - 42 * q^69 + 4 * q^70 - 36 * q^71 - 23 * q^72 - 18 * q^73 + 22 * q^74 - 49 * q^75 - 25 * q^76 + 20 * q^77 + 38 * q^78 - 92 * q^79 + 6 * q^80 - 25 * q^81 + 42 * q^83 - 15 * q^84 - 29 * q^85 + 32 * q^86 - 40 * q^87 + 9 * q^88 - 8 * q^89 - 9 * q^90 - 89 * q^91 - 12 * q^92 - q^93 + 18 * q^94 - 62 * q^95 + 6 * q^96 - 40 * q^97 + 19 * q^98 - 64 * 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
$3$	−2.01951	−1.16596	−0.582981	−	0.812486i	$-0.698114\pi$
$3$	−2.01951	−1.16596	−0.582981	+	0.812486i	$0.698114\pi$
$4$	1.00000	0.500000
$5$	3.52220	1.57517	0.787587	−	0.616203i	$-0.211330\pi$
$5$	3.52220	1.57517	0.787587	+	0.616203i	$0.211330\pi$
$6$	2.01951	0.824460
$7$	−0.0194784	−0.00736215	−0.00368107	−	0.999993i	$-0.501172\pi$
$7$	−0.0194784	−0.00736215	−0.00368107	+	0.999993i	$0.501172\pi$
$8$	−1.00000	−0.353553
$9$	1.07840	0.359467
$10$	−3.52220	−1.11382
$11$	2.98419	0.899767	0.449884	−	0.893087i	$-0.351465\pi$
$11$	2.98419	0.899767	0.449884	+	0.893087i	$0.351465\pi$
$12$	−2.01951	−0.582981
$13$	6.73728	1.86859	0.934293	−	0.356506i	$-0.116032\pi$
$13$	6.73728	1.86859	0.934293	+	0.356506i	$0.116032\pi$
$14$	0.0194784	0.00520583
$15$	−7.11310	−1.83659
$16$	1.00000	0.250000
$17$	−5.56265	−1.34914	−0.674570	−	0.738211i	$-0.735671\pi$
$17$	−5.56265	−1.34914	−0.674570	+	0.738211i	$0.735671\pi$
$18$	−1.07840	−0.254182
$19$	−2.82168	−0.647337	−0.323669	−	0.946171i	$-0.604916\pi$
$19$	−2.82168	−0.647337	−0.323669	+	0.946171i	$0.604916\pi$
$20$	3.52220	0.787587
$21$	0.0393368	0.00858399
$22$	−2.98419	−0.636232
$23$	−5.57700	−1.16289	−0.581443	−	0.813587i	$-0.697512\pi$
$23$	−5.57700	−1.16289	−0.581443	+	0.813587i	$0.697512\pi$
$24$	2.01951	0.412230
$25$	7.40588	1.48118
$26$	−6.73728	−1.32129
$27$	3.88068	0.746837
$28$	−0.0194784	−0.00368107
$29$	−0.961590	−0.178563	−0.0892814	−	0.996006i	$-0.528457\pi$
$29$	−0.961590	−0.178563	−0.0892814	+	0.996006i	$0.528457\pi$
$30$	7.11310	1.29867
$31$	−7.32179	−1.31503	−0.657516	−	0.753440i	$-0.728393\pi$
$31$	−7.32179	−1.31503	−0.657516	+	0.753440i	$0.728393\pi$
$32$	−1.00000	−0.176777
$33$	−6.02659	−1.04909
$34$	5.56265	0.953986
$35$	−0.0686068	−0.0115967
$36$	1.07840	0.179734
$37$	−6.86803	−1.12910	−0.564549	−	0.825400i	$-0.690950\pi$
$37$	−6.86803	−1.12910	−0.564549	+	0.825400i	$0.690950\pi$
$38$	2.82168	0.457736
$39$	−13.6060	−2.17870
$40$	−3.52220	−0.556908
$41$	0.282543	0.0441258	0.0220629	−	0.999757i	$-0.492977\pi$
$41$	0.282543	0.0441258	0.0220629	+	0.999757i	$0.492977\pi$
$42$	−0.0393368	−0.00606979
$43$	−6.89460	−1.05142	−0.525709	−	0.850665i	$-0.676200\pi$
$43$	−6.89460	−1.05142	−0.525709	+	0.850665i	$0.676200\pi$
$44$	2.98419	0.449884
$45$	3.79834	0.566224
$46$	5.57700	0.822284
$47$	−12.2882	−1.79242	−0.896210	−	0.443630i	$-0.853690\pi$
$47$	−12.2882	−1.79242	−0.896210	+	0.443630i	$0.853690\pi$
$48$	−2.01951	−0.291490
$49$	−6.99962	−0.999946
$50$	−7.40588	−1.04735
$51$	11.2338	1.57305
$52$	6.73728	0.934293
$53$	13.1452	1.80563	0.902815	−	0.430030i	$-0.141497\pi$
$53$	13.1452	1.80563	0.902815	+	0.430030i	$0.141497\pi$
$54$	−3.88068	−0.528093
$55$	10.5109	1.41729
$56$	0.0194784	0.00260291
$57$	5.69839	0.754770
$58$	0.961590	0.126263
$59$	−12.2169	−1.59050	−0.795252	−	0.606279i	$-0.792661\pi$
$59$	−12.2169	−1.59050	−0.795252	+	0.606279i	$0.792661\pi$
$60$	−7.11310	−0.918297
$61$	−11.4780	−1.46960	−0.734802	−	0.678282i	$-0.762725\pi$
$61$	−11.4780	−1.46960	−0.734802	+	0.678282i	$0.762725\pi$
$62$	7.32179	0.929869
$63$	−0.0210056	−0.00264645
$64$	1.00000	0.125000
$65$	23.7300	2.94335
$66$	6.02659	0.741822
$67$	−12.3508	−1.50888	−0.754442	−	0.656366i	$-0.772093\pi$
$67$	−12.3508	−1.50888	−0.754442	+	0.656366i	$0.772093\pi$
$68$	−5.56265	−0.674570
$69$	11.2628	1.35588
$70$	0.0686068	0.00820009
$71$	13.0466	1.54834	0.774172	−	0.632975i	$-0.218167\pi$
$71$	13.0466	1.54834	0.774172	+	0.632975i	$0.218167\pi$
$72$	−1.07840	−0.127091
$73$	1.77412	0.207645	0.103823	−	0.994596i	$-0.466893\pi$
$73$	1.77412	0.207645	0.103823	+	0.994596i	$0.466893\pi$
$74$	6.86803	0.798393
$75$	−14.9562	−1.72699
$76$	−2.82168	−0.323669
$77$	−0.0581273	−0.00662422
$78$	13.6060	1.54057
$79$	−12.0391	−1.35450	−0.677252	−	0.735751i	$-0.736829\pi$
$79$	−12.0391	−1.35450	−0.677252	+	0.735751i	$0.736829\pi$
$80$	3.52220	0.393794
$81$	−11.0723	−1.23025
$82$	−0.282543	−0.0312016
$83$	−2.43861	−0.267673	−0.133836	−	0.991003i	$-0.542730\pi$
$83$	−2.43861	−0.267673	−0.133836	+	0.991003i	$0.542730\pi$
$84$	0.0393368	0.00429199
$85$	−19.5927	−2.12513
$86$	6.89460	0.743464
$87$	1.94194	0.208197
$88$	−2.98419	−0.318116
$89$	−13.3160	−1.41150	−0.705749	−	0.708462i	$-0.749389\pi$
$89$	−13.3160	−1.41150	−0.705749	+	0.708462i	$0.749389\pi$
$90$	−3.79834	−0.400381
$91$	−0.131232	−0.0137568
$92$	−5.57700	−0.581443
$93$	14.7864	1.53328
$94$	12.2882	1.26743
$95$	−9.93850	−1.01967
$96$	2.01951	0.206115
$97$	10.3338	1.04924	0.524621	−	0.851336i	$-0.324207\pi$
$97$	10.3338	1.04924	0.524621	+	0.851336i	$0.324207\pi$
$98$	6.99962	0.707068
$99$	3.21816	0.323437
$100$	7.40588	0.740588
$101$	−13.3981	−1.33316	−0.666582	−	0.745432i	$-0.732243\pi$
$101$	−13.3981	−1.33316	−0.666582	+	0.745432i	$0.732243\pi$
$102$	−11.2338	−1.11231
$103$	16.0799	1.58440	0.792199	−	0.610263i	$-0.208936\pi$
$103$	16.0799	1.58440	0.792199	+	0.610263i	$0.208936\pi$
$104$	−6.73728	−0.660645
$105$	0.138552	0.0135213
$106$	−13.1452	−1.27677
$107$	−5.24311	−0.506870	−0.253435	−	0.967352i	$-0.581560\pi$
$107$	−5.24311	−0.506870	−0.253435	+	0.967352i	$0.581560\pi$
$108$	3.88068	0.373418
$109$	8.49826	0.813986	0.406993	−	0.913431i	$-0.366577\pi$
$109$	8.49826	0.813986	0.406993	+	0.913431i	$0.366577\pi$
$110$	−10.5109	−1.00218
$111$	13.8700	1.31648
$112$	−0.0194784	−0.00184054
$113$	1.37177	0.129046	0.0645228	−	0.997916i	$-0.479447\pi$
$113$	1.37177	0.129046	0.0645228	+	0.997916i	$0.479447\pi$
$114$	−5.69839	−0.533703
$115$	−19.6433	−1.83175
$116$	−0.961590	−0.0892814
$117$	7.26550	0.671696
$118$	12.2169	1.12466
$119$	0.108352	0.00993257
$120$	7.11310	0.649334
$121$	−2.09460	−0.190419
$122$	11.4780	1.03917
$123$	−0.570597	−0.0514490
$124$	−7.32179	−0.657516
$125$	8.47398	0.757936
$126$	0.0210056	0.00187132
$127$	14.1815	1.25841	0.629203	−	0.777241i	$-0.283382\pi$
$127$	14.1815	1.25841	0.629203	+	0.777241i	$0.283382\pi$
$128$	−1.00000	−0.0883883
$129$	13.9237	1.22591
$130$	−23.7300	−2.08126
$131$	11.8198	1.03270	0.516348	−	0.856379i	$-0.327291\pi$
$131$	11.8198	1.03270	0.516348	+	0.856379i	$0.327291\pi$
$132$	−6.02659	−0.524547
$133$	0.0549618	0.00476579
$134$	12.3508	1.06694
$135$	13.6685	1.17640
$136$	5.56265	0.476993
$137$	16.3557	1.39736	0.698680	−	0.715434i	$-0.253771\pi$
$137$	16.3557	1.39736	0.698680	+	0.715434i	$0.253771\pi$
$138$	−11.2628	−0.958752
$139$	1.98850	0.168662	0.0843312	−	0.996438i	$-0.473125\pi$
$139$	1.98850	0.168662	0.0843312	+	0.996438i	$0.473125\pi$
$140$	−0.0686068	−0.00579834
$141$	24.8161	2.08989
$142$	−13.0466	−1.09484
$143$	20.1053	1.68129
$144$	1.07840	0.0898668
$145$	−3.38691	−0.281268
$146$	−1.77412	−0.146827
$147$	14.1358	1.16590
$148$	−6.86803	−0.564549
$149$	4.90660	0.401965	0.200982	−	0.979595i	$-0.435587\pi$
$149$	4.90660	0.401965	0.200982	+	0.979595i	$0.435587\pi$
$150$	14.9562	1.22117
$151$	−10.1268	−0.824107	−0.412053	−	0.911160i	$-0.635188\pi$
$151$	−10.1268	−0.824107	−0.412053	+	0.911160i	$0.635188\pi$
$152$	2.82168	0.228868
$153$	−5.99877	−0.484972
$154$	0.0581273	0.00468403
$155$	−25.7888	−2.07141
$156$	−13.6060	−1.08935
$157$	−8.00318	−0.638723	−0.319362	−	0.947633i	$-0.603468\pi$
$157$	−8.00318	−0.638723	−0.319362	+	0.947633i	$0.603468\pi$
$158$	12.0391	0.957779
$159$	−26.5468	−2.10529
$160$	−3.52220	−0.278454
$161$	0.108631	0.00856134
$162$	11.0723	0.869919
$163$	9.59717	0.751709	0.375854	−	0.926679i	$-0.377349\pi$
$163$	9.59717	0.751709	0.375854	+	0.926679i	$0.377349\pi$
$164$	0.282543	0.0220629
$165$	−21.2268	−1.65251
$166$	2.43861	0.189273
$167$	−8.75601	−0.677560	−0.338780	−	0.940866i	$-0.610014\pi$
$167$	−8.75601	−0.677560	−0.338780	+	0.940866i	$0.610014\pi$
$168$	−0.0393368	−0.00303490
$169$	32.3910	2.49161
$170$	19.5927	1.50270
$171$	−3.04290	−0.232696
$172$	−6.89460	−0.525709
$173$	−4.92494	−0.374437	−0.187218	−	0.982318i	$-0.559947\pi$
$173$	−4.92494	−0.374437	−0.187218	+	0.982318i	$0.559947\pi$
$174$	−1.94194	−0.147218
$175$	−0.144255	−0.0109046
$176$	2.98419	0.224942
$177$	24.6721	1.85447
$178$	13.3160	0.998080
$179$	−3.82697	−0.286041	−0.143020	−	0.989720i	$-0.545681\pi$
$179$	−3.82697	−0.286041	−0.143020	+	0.989720i	$0.545681\pi$
$180$	3.79834	0.283112
$181$	−18.7705	−1.39520	−0.697601	−	0.716487i	$-0.745749\pi$
$181$	−18.7705	−1.39520	−0.697601	+	0.716487i	$0.745749\pi$
$182$	0.131232	0.00972753
$183$	23.1798	1.71350
$184$	5.57700	0.411142
$185$	−24.1906	−1.77853
$186$	−14.7864	−1.08419
$187$	−16.6000	−1.21391
$188$	−12.2882	−0.896210
$189$	−0.0755895	−0.00549832
$190$	9.93850	0.721015
$191$	19.6589	1.42247	0.711233	−	0.702956i	$-0.248137\pi$
$191$	19.6589	1.42247	0.711233	+	0.702956i	$0.248137\pi$
$192$	−2.01951	−0.145745
$193$	8.55043	0.615473	0.307737	−	0.951472i	$-0.400428\pi$
$193$	8.55043	0.615473	0.307737	+	0.951472i	$0.400428\pi$
$194$	−10.3338	−0.741926
$195$	−47.9230	−3.43183
$196$	−6.99962	−0.499973
$197$	−12.4696	−0.888420	−0.444210	−	0.895923i	$-0.646516\pi$
$197$	−12.4696	−0.888420	−0.444210	+	0.895923i	$0.646516\pi$
$198$	−3.21816	−0.228704
$199$	4.34535	0.308034	0.154017	−	0.988068i	$-0.450779\pi$
$199$	4.34535	0.308034	0.154017	+	0.988068i	$0.450779\pi$
$200$	−7.40588	−0.523675
$201$	24.9424	1.75930
$202$	13.3981	0.942689
$203$	0.0187303	0.00131461
$204$	11.2338	0.786523
$205$	0.995172	0.0695058
$206$	−16.0799	−1.12034
$207$	−6.01425	−0.418019
$208$	6.73728	0.467147
$209$	−8.42042	−0.582453
$210$	−0.138552	−0.00956099
$211$	−2.03483	−0.140083	−0.0700417	−	0.997544i	$-0.522313\pi$
$211$	−2.03483	−0.140083	−0.0700417	+	0.997544i	$0.522313\pi$
$212$	13.1452	0.902815
$213$	−26.3476	−1.80531
$214$	5.24311	0.358411
$215$	−24.2842	−1.65617
$216$	−3.88068	−0.264047
$217$	0.142617	0.00968147
$218$	−8.49826	−0.575575
$219$	−3.58285	−0.242106
$220$	10.5109	0.708645
$221$	−37.4771	−2.52099
$222$	−13.8700	−0.930895
$223$	−2.18613	−0.146394	−0.0731971	−	0.997317i	$-0.523320\pi$
$223$	−2.18613	−0.146394	−0.0731971	+	0.997317i	$0.523320\pi$
$224$	0.0194784	0.00130146
$225$	7.98651	0.532434
$226$	−1.37177	−0.0912490
$227$	19.6953	1.30722	0.653612	−	0.756830i	$-0.273253\pi$
$227$	19.6953	1.30722	0.653612	+	0.756830i	$0.273253\pi$
$228$	5.69839	0.377385
$229$	−8.50215	−0.561838	−0.280919	−	0.959731i	$-0.590639\pi$
$229$	−8.50215	−0.561838	−0.280919	+	0.959731i	$0.590639\pi$
$230$	19.6433	1.29524
$231$	0.117388	0.00772359
$232$	0.961590	0.0631315
$233$	16.9950	1.11338	0.556691	−	0.830720i	$-0.312071\pi$
$233$	16.9950	1.11338	0.556691	+	0.830720i	$0.312071\pi$
$234$	−7.26550	−0.474960
$235$	−43.2815	−2.82337
$236$	−12.2169	−0.795252
$237$	24.3130	1.57930
$238$	−0.108352	−0.00702339
$239$	−19.3092	−1.24901	−0.624503	−	0.781022i	$-0.714699\pi$
$239$	−19.3092	−1.24901	−0.624503	+	0.781022i	$0.714699\pi$
$240$	−7.11310	−0.459148
$241$	17.0087	1.09563	0.547814	−	0.836600i	$-0.315460\pi$
$241$	17.0087	1.09563	0.547814	+	0.836600i	$0.315460\pi$
$242$	2.09460	0.134646
$243$	10.7184	0.687588
$244$	−11.4780	−0.734802
$245$	−24.6540	−1.57509
$246$	0.570597	0.0363799
$247$	−19.0104	−1.20961
$248$	7.32179	0.464934
$249$	4.92479	0.312096
$250$	−8.47398	−0.535941
$251$	17.0055	1.07338	0.536689	−	0.843780i	$-0.319675\pi$
$251$	17.0055	1.07338	0.536689	+	0.843780i	$0.319675\pi$
$252$	−0.0210056	−0.00132323
$253$	−16.6428	−1.04633
$254$	−14.1815	−0.889827
$255$	39.5677	2.47782
$256$	1.00000	0.0625000
$257$	−6.38881	−0.398523	−0.199262	−	0.979946i	$-0.563854\pi$
$257$	−6.38881	−0.398523	−0.199262	+	0.979946i	$0.563854\pi$
$258$	−13.9237	−0.866851
$259$	0.133778	0.00831259
$260$	23.7300	1.47167
$261$	−1.03698	−0.0641875
$262$	−11.8198	−0.730227
$263$	−21.5900	−1.33130	−0.665650	−	0.746264i	$-0.731845\pi$
$263$	−21.5900	−1.33130	−0.665650	+	0.746264i	$0.731845\pi$
$264$	6.02659	0.370911
$265$	46.2999	2.84418
$266$	−0.0549618	−0.00336992
$267$	26.8918	1.64575
$268$	−12.3508	−0.754442
$269$	7.71192	0.470204	0.235102	−	0.971971i	$-0.424458\pi$
$269$	7.71192	0.470204	0.235102	+	0.971971i	$0.424458\pi$
$270$	−13.6685	−0.831839
$271$	−8.41087	−0.510924	−0.255462	−	0.966819i	$-0.582228\pi$
$271$	−8.41087	−0.510924	−0.255462	+	0.966819i	$0.582228\pi$
$272$	−5.56265	−0.337285
$273$	0.265023	0.0160399
$274$	−16.3557	−0.988083
$275$	22.1006	1.33271
$276$	11.2628	0.677940
$277$	−0.783203	−0.0470581	−0.0235290	−	0.999723i	$-0.507490\pi$
$277$	−0.783203	−0.0470581	−0.0235290	+	0.999723i	$0.507490\pi$
$278$	−1.98850	−0.119262
$279$	−7.89584	−0.472711
$280$	0.0686068	0.00410004
$281$	14.3973	0.858869	0.429435	−	0.903098i	$-0.358713\pi$
$281$	14.3973	0.858869	0.429435	+	0.903098i	$0.358713\pi$
$282$	−24.8161	−1.47778
$283$	3.82304	0.227256	0.113628	−	0.993523i	$-0.463753\pi$
$283$	3.82304	0.227256	0.113628	+	0.993523i	$0.463753\pi$
$284$	13.0466	0.774172
$285$	20.0709	1.18890
$286$	−20.1053	−1.18885
$287$	−0.00550349	−0.000324861 0
$288$	−1.07840	−0.0635454
$289$	13.9431	0.820180
$290$	3.38691	0.198886
$291$	−20.8692	−1.22338
$292$	1.77412	0.103823
$293$	15.3307	0.895631	0.447816	−	0.894126i	$-0.352202\pi$
$293$	15.3307	0.895631	0.447816	+	0.894126i	$0.352202\pi$
$294$	−14.1358	−0.824415
$295$	−43.0303	−2.50532
$296$	6.86803	0.399196
$297$	11.5807	0.671979
$298$	−4.90660	−0.284232
$299$	−37.5738	−2.17295
$300$	−14.9562	−0.863497
$301$	0.134296	0.00774069
$302$	10.1268	0.582731
$303$	27.0576	1.55442
$304$	−2.82168	−0.161834
$305$	−40.4277	−2.31488
$306$	5.99877	0.342927
$307$	−4.47270	−0.255271	−0.127635	−	0.991821i	$-0.540739\pi$
$307$	−4.47270	−0.255271	−0.127635	+	0.991821i	$0.540739\pi$
$308$	−0.0581273	−0.00331211
$309$	−32.4734	−1.84735
$310$	25.7888	1.46471
$311$	−17.8382	−1.01151	−0.505755	−	0.862677i	$-0.668786\pi$
$311$	−17.8382	−1.01151	−0.505755	+	0.862677i	$0.668786\pi$
$312$	13.6060	0.770287
$313$	5.62078	0.317705	0.158853	−	0.987302i	$-0.449221\pi$
$313$	5.62078	0.317705	0.158853	+	0.987302i	$0.449221\pi$
$314$	8.00318	0.451646
$315$	−0.0739857	−0.00416862
$316$	−12.0391	−0.677252
$317$	−16.5745	−0.930915	−0.465457	−	0.885070i	$-0.654110\pi$
$317$	−16.5745	−0.930915	−0.465457	+	0.885070i	$0.654110\pi$
$318$	26.5468	1.48867
$319$	−2.86957	−0.160665
$320$	3.52220	0.196897
$321$	10.5885	0.590991
$322$	−0.108631	−0.00605378
$323$	15.6960	0.873349
$324$	−11.0723	−0.615125
$325$	49.8955	2.76770
$326$	−9.59717	−0.531538
$327$	−17.1623	−0.949076
$328$	−0.282543	−0.0156008
$329$	0.239355	0.0131961
$330$	21.2268	1.16850
$331$	−27.5654	−1.51513	−0.757567	−	0.652758i	$-0.773612\pi$
$331$	−27.5654	−1.51513	−0.757567	+	0.652758i	$0.773612\pi$
$332$	−2.43861	−0.133836
$333$	−7.40650	−0.405874
$334$	8.75601	0.479107
$335$	−43.5018	−2.37676
$336$	0.0393368	0.00214600
$337$	−7.80483	−0.425156	−0.212578	−	0.977144i	$-0.568186\pi$
$337$	−7.80483	−0.425156	−0.212578	+	0.977144i	$0.568186\pi$
$338$	−32.3910	−1.76184
$339$	−2.77030	−0.150462
$340$	−19.5927	−1.06257
$341$	−21.8496	−1.18322
$342$	3.04290	0.164541
$343$	0.272690	0.0147239
$344$	6.89460	0.371732
$345$	39.6698	2.13575
$346$	4.92494	0.264767
$347$	16.8568	0.904922	0.452461	−	0.891784i	$-0.350546\pi$
$347$	16.8568	0.904922	0.452461	+	0.891784i	$0.350546\pi$
$348$	1.94194	0.104099
$349$	2.18262	0.116833	0.0584164	−	0.998292i	$-0.481395\pi$
$349$	2.18262	0.116833	0.0584164	+	0.998292i	$0.481395\pi$
$350$	0.144255	0.00771074
$351$	26.1452	1.39553
$352$	−2.98419	−0.159058
$353$	−6.04381	−0.321679	−0.160840	−	0.986981i	$-0.551420\pi$
$353$	−6.04381	−0.321679	−0.160840	+	0.986981i	$0.551420\pi$
$354$	−24.6721	−1.31131
$355$	45.9526	2.43891
$356$	−13.3160	−0.705749
$357$	−0.218817	−0.0115810
$358$	3.82697	0.202261
$359$	−18.9833	−1.00190	−0.500949	−	0.865477i	$-0.667016\pi$
$359$	−18.9833	−1.00190	−0.500949	+	0.865477i	$0.667016\pi$
$360$	−3.79834	−0.200190
$361$	−11.0381	−0.580955
$362$	18.7705	0.986556
$363$	4.23007	0.222021
$364$	−0.131232	−0.00687841
$365$	6.24880	0.327077
$366$	−23.1798	−1.21163
$367$	23.5636	1.23001	0.615005	−	0.788523i	$-0.289154\pi$
$367$	23.5636	1.23001	0.615005	+	0.788523i	$0.289154\pi$
$368$	−5.57700	−0.290721
$369$	0.304695	0.0158618
$370$	24.1906	1.25761
$371$	−0.256047	−0.0132933
$372$	14.7864	0.766639
$373$	0.929008	0.0481022	0.0240511	−	0.999711i	$-0.492344\pi$
$373$	0.929008	0.0481022	0.0240511	+	0.999711i	$0.492344\pi$
$374$	16.6000	0.858366
$375$	−17.1132	−0.883724
$376$	12.2882	0.633716
$377$	−6.47850	−0.333660
$378$	0.0755895	0.00388790
$379$	−18.8701	−0.969293	−0.484646	−	0.874710i	$-0.661052\pi$
$379$	−18.8701	−0.969293	−0.484646	+	0.874710i	$0.661052\pi$
$380$	−9.93850	−0.509834
$381$	−28.6396	−1.46725
$382$	−19.6589	−1.00584
$383$	−26.0028	−1.32868	−0.664341	−	0.747430i	$-0.731288\pi$
$383$	−26.0028	−1.32868	−0.664341	+	0.747430i	$0.731288\pi$
$384$	2.01951	0.103057
$385$	−0.204736	−0.0104343
$386$	−8.55043	−0.435205
$387$	−7.43515	−0.377950
$388$	10.3338	0.524621
$389$	38.4348	1.94872	0.974360	−	0.224994i	$-0.0722364\pi$
$389$	38.4348	1.94872	0.974360	+	0.224994i	$0.0722364\pi$
$390$	47.9230	2.42667
$391$	31.0229	1.56890
$392$	6.99962	0.353534
$393$	−23.8701	−1.20408
$394$	12.4696	0.628207
$395$	−42.4041	−2.13358
$396$	3.21816	0.161718
$397$	0.262441	0.0131715	0.00658576	−	0.999978i	$-0.497904\pi$
$397$	0.262441	0.0131715	0.00658576	+	0.999978i	$0.497904\pi$
$398$	−4.34535	−0.217813
$399$	−0.110996	−0.00555673
$400$	7.40588	0.370294
$401$	−23.0742	−1.15227	−0.576134	−	0.817355i	$-0.695439\pi$
$401$	−23.0742	−1.15227	−0.576134	+	0.817355i	$0.695439\pi$
$402$	−24.9424	−1.24401
$403$	−49.3290	−2.45725
$404$	−13.3981	−0.666582
$405$	−38.9987	−1.93786
$406$	−0.0187303	−0.000929567 0
$407$	−20.4955	−1.01593
$408$	−11.2338	−0.556156
$409$	−33.8720	−1.67486	−0.837431	−	0.546543i	$-0.815944\pi$
$409$	−33.8720	−1.67486	−0.837431	+	0.546543i	$0.815944\pi$
$410$	−0.995172	−0.0491481
$411$	−33.0304	−1.62927
$412$	16.0799	0.792199
$413$	0.237966	0.0117095
$414$	6.01425	0.295584
$415$	−8.58928	−0.421631
$416$	−6.73728	−0.330322
$417$	−4.01579	−0.196654
$418$	8.42042	0.411856
$419$	−25.8125	−1.26102	−0.630512	−	0.776180i	$-0.717155\pi$
$419$	−25.8125	−1.26102	−0.630512	+	0.776180i	$0.717155\pi$
$420$	0.138552	0.00676064
$421$	−21.4768	−1.04672	−0.523358	−	0.852113i	$-0.675321\pi$
$421$	−21.4768	−1.04672	−0.523358	+	0.852113i	$0.675321\pi$
$422$	2.03483	0.0990539
$423$	−13.2516	−0.644316
$424$	−13.1452	−0.638386
$425$	−41.1963	−1.99831
$426$	26.3476	1.27655
$427$	0.223573	0.0108194
$428$	−5.24311	−0.253435
$429$	−40.6028	−1.96032
$430$	24.2842	1.17109
$431$	36.3208	1.74951	0.874755	−	0.484565i	$-0.161022\pi$
$431$	36.3208	1.74951	0.874755	+	0.484565i	$0.161022\pi$
$432$	3.88068	0.186709
$433$	−6.00561	−0.288611	−0.144306	−	0.989533i	$-0.546095\pi$
$433$	−6.00561	−0.288611	−0.144306	+	0.989533i	$0.546095\pi$
$434$	−0.142617	−0.00684583
$435$	6.83988	0.327947
$436$	8.49826	0.406993
$437$	15.7365	0.752779
$438$	3.58285	0.171195
$439$	−9.39722	−0.448505	−0.224252	−	0.974531i	$-0.571994\pi$
$439$	−9.39722	−0.448505	−0.224252	+	0.974531i	$0.571994\pi$
$440$	−10.5109	−0.501088
$441$	−7.54840	−0.359448
$442$	37.4771	1.78261
$443$	−12.3906	−0.588697	−0.294349	−	0.955698i	$-0.595103\pi$
$443$	−12.3906	−0.588697	−0.294349	+	0.955698i	$0.595103\pi$
$444$	13.8700	0.658242
$445$	−46.9017	−2.22336
$446$	2.18613	0.103516
$447$	−9.90891	−0.468675
$448$	−0.0194784	−0.000920269 0
$449$	19.9551	0.941737	0.470869	−	0.882203i	$-0.343941\pi$
$449$	19.9551	0.941737	0.470869	+	0.882203i	$0.343941\pi$
$450$	−7.98651	−0.376488
$451$	0.843162	0.0397030
$452$	1.37177	0.0645228
$453$	20.4511	0.960877
$454$	−19.6953	−0.924346
$455$	−0.462224	−0.0216694
$456$	−5.69839	−0.266852
$457$	−5.06840	−0.237090	−0.118545	−	0.992949i	$-0.537823\pi$
$457$	−5.06840	−0.237090	−0.118545	+	0.992949i	$0.537823\pi$
$458$	8.50215	0.397280
$459$	−21.5868	−1.00759
$460$	−19.6433	−0.915874
$461$	2.96522	0.138104	0.0690520	−	0.997613i	$-0.478003\pi$
$461$	2.96522	0.138104	0.0690520	+	0.997613i	$0.478003\pi$
$462$	−0.117388	−0.00546140
$463$	28.1876	1.30999	0.654995	−	0.755633i	$-0.272671\pi$
$463$	28.1876	1.30999	0.654995	+	0.755633i	$0.272671\pi$
$464$	−0.961590	−0.0446407
$465$	52.0806	2.41518
$466$	−16.9950	−0.787279
$467$	−23.8900	−1.10550	−0.552748	−	0.833348i	$-0.686421\pi$
$467$	−23.8900	−1.10550	−0.552748	+	0.833348i	$0.686421\pi$
$468$	7.26550	0.335848
$469$	0.240573	0.0111086
$470$	43.2815	1.99643
$471$	16.1625	0.744727
$472$	12.2169	0.562328
$473$	−20.5748	−0.946031
$474$	−24.3130	−1.11673
$475$	−20.8970	−0.958820
$476$	0.108352	0.00496629
$477$	14.1758	0.649065
$478$	19.3092	0.883181
$479$	24.1621	1.10400	0.551998	−	0.833845i	$-0.313866\pi$
$479$	24.1621	1.10400	0.551998	+	0.833845i	$0.313866\pi$
$480$	7.11310	0.324667
$481$	−46.2719	−2.10982
$482$	−17.0087	−0.774726
$483$	−0.219381	−0.00998219
$484$	−2.09460	−0.0952093
$485$	36.3978	1.65274
$486$	−10.7184	−0.486198
$487$	−25.7109	−1.16507	−0.582536	−	0.812805i	$-0.697939\pi$
$487$	−25.7109	−1.16507	−0.582536	+	0.812805i	$0.697939\pi$
$488$	11.4780	0.519583
$489$	−19.3815	−0.876464
$490$	24.6540	1.11376
$491$	5.43682	0.245360	0.122680	−	0.992446i	$-0.460851\pi$
$491$	5.43682	0.245360	0.122680	+	0.992446i	$0.460851\pi$
$492$	−0.570597	−0.0257245
$493$	5.34899	0.240906
$494$	19.0104	0.855320
$495$	11.3350	0.509470
$496$	−7.32179	−0.328758
$497$	−0.254127	−0.0113991
$498$	−4.92479	−0.220685
$499$	19.0086	0.850940	0.425470	−	0.904973i	$-0.360109\pi$
$499$	19.0086	0.850940	0.425470	+	0.904973i	$0.360109\pi$
$500$	8.47398	0.378968
$501$	17.6828	0.790009
$502$	−17.0055	−0.758993
$503$	−9.84107	−0.438791	−0.219396	−	0.975636i	$-0.570409\pi$
$503$	−9.84107	−0.438791	−0.219396	+	0.975636i	$0.570409\pi$
$504$	0.0210056	0.000935662 0
$505$	−47.1909	−2.09997
$506$	16.6428	0.739865
$507$	−65.4138	−2.90513
$508$	14.1815	0.629203
$509$	20.9671	0.929350	0.464675	−	0.885481i	$-0.346171\pi$
$509$	20.9671	0.929350	0.464675	+	0.885481i	$0.346171\pi$
$510$	−39.5677	−1.75209
$511$	−0.0345571	−0.00152871
$512$	−1.00000	−0.0441942
$513$	−10.9500	−0.483455
$514$	6.38881	0.281798
$515$	56.6365	2.49570
$516$	13.9237	0.612956
$517$	−36.6704	−1.61276
$518$	−0.133778	−0.00587789
$519$	9.94595	0.436579
$520$	−23.7300	−1.04063
$521$	35.2140	1.54275	0.771376	−	0.636379i	$-0.219569\pi$
$521$	35.2140	1.54275	0.771376	+	0.636379i	$0.219569\pi$
$522$	1.03698	0.0453874
$523$	8.20856	0.358935	0.179468	−	0.983764i	$-0.442562\pi$
$523$	8.20856	0.358935	0.179468	+	0.983764i	$0.442562\pi$
$524$	11.8198	0.516348
$525$	0.291323	0.0127144
$526$	21.5900	0.941371
$527$	40.7286	1.77416
$528$	−6.02659	−0.262274
$529$	8.10296	0.352303
$530$	−46.2999	−2.01114
$531$	−13.1747	−0.571734
$532$	0.0549618	0.00238290
$533$	1.90357	0.0824529
$534$	−26.8918	−1.16372
$535$	−18.4673	−0.798409
$536$	12.3508	0.533471
$537$	7.72858	0.333513
$538$	−7.71192	−0.332485
$539$	−20.8882	−0.899719
$540$	13.6685	0.588199
$541$	20.5068	0.881657	0.440828	−	0.897591i	$-0.354685\pi$
$541$	20.5068	0.881657	0.440828	+	0.897591i	$0.354685\pi$
$542$	8.41087	0.361278
$543$	37.9072	1.62675
$544$	5.56265	0.238497
$545$	29.9326	1.28217
$546$	−0.265023	−0.0113419
$547$	−37.8284	−1.61743	−0.808714	−	0.588202i	$-0.799836\pi$
$547$	−37.8284	−1.61743	−0.808714	+	0.588202i	$0.799836\pi$
$548$	16.3557	0.698680
$549$	−12.3779	−0.528274
$550$	−22.1006	−0.942371
$551$	2.71330	0.115590
$552$	−11.2628	−0.479376
$553$	0.234502	0.00997206
$554$	0.783203	0.0332751
$555$	48.8530	2.07369
$556$	1.98850	0.0843312
$557$	18.7341	0.793788	0.396894	−	0.917864i	$-0.370088\pi$
$557$	18.7341	0.793788	0.396894	+	0.917864i	$0.370088\pi$
$558$	7.89584	0.334257
$559$	−46.4509	−1.96466
$560$	−0.0686068	−0.00289917
$561$	33.5238	1.41538
$562$	−14.3973	−0.607312
$563$	−12.6464	−0.532982	−0.266491	−	0.963837i	$-0.585864\pi$
$563$	−12.6464	−0.532982	−0.266491	+	0.963837i	$0.585864\pi$
$564$	24.8161	1.04495
$565$	4.83166	0.203269
$566$	−3.82304	−0.160694
$567$	0.215670	0.00905729
$568$	−13.0466	−0.547422
$569$	−41.5405	−1.74147	−0.870735	−	0.491753i	$-0.836356\pi$
$569$	−41.5405	−1.74147	−0.870735	+	0.491753i	$0.836356\pi$
$570$	−20.0709	−0.840676
$571$	−33.1499	−1.38728	−0.693640	−	0.720322i	$-0.743994\pi$
$571$	−33.1499	−1.38728	−0.693640	+	0.720322i	$0.743994\pi$
$572$	20.1053	0.840646
$573$	−39.7012	−1.65854
$574$	0.00550349	0.000229711 0
$575$	−41.3026	−1.72244
$576$	1.07840	0.0449334
$577$	−19.4073	−0.807936	−0.403968	−	0.914773i	$-0.632369\pi$
$577$	−19.4073	−0.807936	−0.403968	+	0.914773i	$0.632369\pi$
$578$	−13.9431	−0.579955
$579$	−17.2676	−0.717618
$580$	−3.38691	−0.140634
$581$	0.0475003	0.00197065
$582$	20.8692	0.865058
$583$	39.2277	1.62465
$584$	−1.77412	−0.0734136
$585$	25.5905	1.05804
$586$	−15.3307	−0.633307
$587$	36.9893	1.52671	0.763357	−	0.645977i	$-0.223550\pi$
$587$	36.9893	1.52671	0.763357	+	0.645977i	$0.223550\pi$
$588$	14.1358	0.582949
$589$	20.6597	0.851270
$590$	43.0303	1.77153
$591$	25.1823	1.03586
$592$	−6.86803	−0.282274
$593$	15.2499	0.626238	0.313119	−	0.949714i	$-0.398626\pi$
$593$	15.2499	0.626238	0.313119	+	0.949714i	$0.398626\pi$
$594$	−11.5807	−0.475161
$595$	0.381636	0.0156455
$596$	4.90660	0.200982
$597$	−8.77546	−0.359156
$598$	37.5738	1.53651
$599$	21.0614	0.860545	0.430273	−	0.902699i	$-0.358417\pi$
$599$	21.0614	0.860545	0.430273	+	0.902699i	$0.358417\pi$
$600$	14.9562	0.610585
$601$	21.7381	0.886715	0.443358	−	0.896345i	$-0.353787\pi$
$601$	21.7381	0.886715	0.443358	+	0.896345i	$0.353787\pi$
$602$	−0.134296	−0.00547349
$603$	−13.3191	−0.542395
$604$	−10.1268	−0.412053
$605$	−7.37761	−0.299943
$606$	−27.0576	−1.09914
$607$	−18.0250	−0.731613	−0.365806	−	0.930691i	$-0.619207\pi$
$607$	−18.0250	−0.731613	−0.365806	+	0.930691i	$0.619207\pi$
$608$	2.82168	0.114434
$609$	−0.0378258	−0.00153278
$610$	40.4277	1.63687
$611$	−82.7892	−3.34929
$612$	−5.99877	−0.242486
$613$	−9.11476	−0.368142	−0.184071	−	0.982913i	$-0.558928\pi$
$613$	−9.11476	−0.368142	−0.184071	+	0.982913i	$0.558928\pi$
$614$	4.47270	0.180504
$615$	−2.00976	−0.0810412
$616$	0.0581273	0.00234202
$617$	43.1574	1.73745	0.868727	−	0.495292i	$-0.164939\pi$
$617$	43.1574	1.73745	0.868727	+	0.495292i	$0.164939\pi$
$618$	32.4734	1.30627
$619$	−1.01634	−0.0408501	−0.0204250	−	0.999791i	$-0.506502\pi$
$619$	−1.01634	−0.0408501	−0.0204250	+	0.999791i	$0.506502\pi$
$620$	−25.7888	−1.03570
$621$	−21.6426	−0.868486
$622$	17.8382	0.715245
$623$	0.259375	0.0103917
$624$	−13.6060	−0.544675
$625$	−7.18236	−0.287294
$626$	−5.62078	−0.224652
$627$	17.0051	0.679118
$628$	−8.00318	−0.319362
$629$	38.2044	1.52331
$630$	0.0739857	0.00294766
$631$	16.4531	0.654989	0.327494	−	0.944853i	$-0.393796\pi$
$631$	16.4531	0.654989	0.327494	+	0.944853i	$0.393796\pi$
$632$	12.0391	0.478889
$633$	4.10935	0.163332
$634$	16.5745	0.658256
$635$	49.9501	1.98221
$636$	−26.5468	−1.05265
$637$	−47.1584	−1.86848
$638$	2.86957	0.113607
$639$	14.0695	0.556579
$640$	−3.52220	−0.139227
$641$	24.2044	0.956018	0.478009	−	0.878355i	$-0.341359\pi$
$641$	24.2044	0.956018	0.478009	+	0.878355i	$0.341359\pi$
$642$	−10.5885	−0.417894
$643$	15.2214	0.600275	0.300138	−	0.953896i	$-0.402967\pi$
$643$	15.2214	0.600275	0.300138	+	0.953896i	$0.402967\pi$
$644$	0.108631	0.00428067
$645$	49.0420	1.93103
$646$	−15.6960	−0.617551
$647$	−22.7608	−0.894819	−0.447409	−	0.894329i	$-0.647653\pi$
$647$	−22.7608	−0.894819	−0.447409	+	0.894329i	$0.647653\pi$
$648$	11.0723	0.434959
$649$	−36.4575	−1.43108
$650$	−49.8955	−1.95706
$651$	−0.288016	−0.0112882
$652$	9.59717	0.375854
$653$	35.5897	1.39273	0.696366	−	0.717687i	$-0.254799\pi$
$653$	35.5897	1.39273	0.696366	+	0.717687i	$0.254799\pi$
$654$	17.1623	0.671098
$655$	41.6315	1.62668
$656$	0.282543	0.0110314
$657$	1.91321	0.0746416
$658$	−0.239355	−0.00933103
$659$	−26.5198	−1.03306	−0.516532	−	0.856268i	$-0.672777\pi$
$659$	−26.5198	−1.03306	−0.516532	+	0.856268i	$0.672777\pi$
$660$	−21.2268	−0.826254
$661$	−6.03844	−0.234868	−0.117434	−	0.993081i	$-0.537467\pi$
$661$	−6.03844	−0.234868	−0.117434	+	0.993081i	$0.537467\pi$
$662$	27.5654	1.07136
$663$	75.6853	2.93937
$664$	2.43861	0.0946365
$665$	0.193586	0.00750696
$666$	7.40650	0.286996
$667$	5.36279	0.207648
$668$	−8.75601	−0.338780
$669$	4.41491	0.170690
$670$	43.5018	1.68062
$671$	−34.2525	−1.32230
$672$	−0.0393368	−0.00151745
$673$	5.54802	0.213860	0.106930	−	0.994267i	$-0.465898\pi$
$673$	5.54802	0.213860	0.106930	+	0.994267i	$0.465898\pi$
$674$	7.80483	0.300631
$675$	28.7398	1.10620
$676$	32.3910	1.24581
$677$	47.6217	1.83025	0.915126	−	0.403168i	$-0.132091\pi$
$677$	47.6217	1.83025	0.915126	+	0.403168i	$0.132091\pi$
$678$	2.77030	0.106393
$679$	−0.201287	−0.00772468
$680$	19.5927	0.751348
$681$	−39.7748	−1.52417
$682$	21.8496	0.836666
$683$	38.4988	1.47312	0.736558	−	0.676374i	$-0.236450\pi$
$683$	38.4988	1.47312	0.736558	+	0.676374i	$0.236450\pi$
$684$	−3.04290	−0.116348
$685$	57.6079	2.20109
$686$	−0.272690	−0.0104114
$687$	17.1701	0.655082
$688$	−6.89460	−0.262854
$689$	88.5628	3.37397
$690$	−39.6698	−1.51020
$691$	20.4625	0.778431	0.389216	−	0.921147i	$-0.372746\pi$
$691$	20.4625	0.778431	0.389216	+	0.921147i	$0.372746\pi$
$692$	−4.92494	−0.187218
$693$	−0.0626846	−0.00238119
$694$	−16.8568	−0.639877
$695$	7.00389	0.265673
$696$	−1.94194	−0.0736089
$697$	−1.57169	−0.0595319
$698$	−2.18262	−0.0826132
$699$	−34.3215	−1.29816
$700$	−0.144255	−0.00545232
$701$	7.63665	0.288432	0.144216	−	0.989546i	$-0.453934\pi$
$701$	7.63665	0.288432	0.144216	+	0.989546i	$0.453934\pi$
$702$	−26.1452	−0.986788
$703$	19.3794	0.730907
$704$	2.98419	0.112471
$705$	87.4072	3.29195
$706$	6.04381	0.227462
$707$	0.260974	0.00981495
$708$	24.6721	0.927233
$709$	24.2779	0.911777	0.455888	−	0.890037i	$-0.349322\pi$
$709$	24.2779	0.911777	0.455888	+	0.890037i	$0.349322\pi$
$710$	−45.9526	−1.72457
$711$	−12.9830	−0.486900
$712$	13.3160	0.499040
$713$	40.8337	1.52923
$714$	0.218817	0.00818901
$715$	70.8150	2.64833
$716$	−3.82697	−0.143020
$717$	38.9950	1.45629
$718$	18.9833	0.708449
$719$	−41.1926	−1.53622	−0.768112	−	0.640316i	$-0.778804\pi$
$719$	−41.1926	−1.53622	−0.768112	+	0.640316i	$0.778804\pi$
$720$	3.79834	0.141556
$721$	−0.313211	−0.0116646
$722$	11.0381	0.410797
$723$	−34.3492	−1.27746
$724$	−18.7705	−0.697601
$725$	−7.12142	−0.264483
$726$	−4.23007	−0.156992
$727$	18.1598	0.673511	0.336755	−	0.941592i	$-0.390670\pi$
$727$	18.1598	0.673511	0.336755	+	0.941592i	$0.390670\pi$
$728$	0.131232	0.00486377
$729$	11.5708	0.428549
$730$	−6.24880	−0.231279
$731$	38.3522	1.41851
$732$	23.1798	0.856751
$733$	18.2652	0.674641	0.337320	−	0.941390i	$-0.390479\pi$
$733$	18.2652	0.674641	0.337320	+	0.941390i	$0.390479\pi$
$734$	−23.5636	−0.869749
$735$	49.7890	1.83649
$736$	5.57700	0.205571
$737$	−36.8570	−1.35765
$738$	−0.304695	−0.0112160
$739$	10.0605	0.370080	0.185040	−	0.982731i	$-0.440758\pi$
$739$	10.0605	0.370080	0.185040	+	0.982731i	$0.440758\pi$
$740$	−24.1906	−0.889263
$741$	38.3917	1.41035
$742$	0.256047	0.00939979
$743$	23.6570	0.867893	0.433946	−	0.900939i	$-0.357121\pi$
$743$	23.6570	0.867893	0.433946	+	0.900939i	$0.357121\pi$
$744$	−14.7864	−0.542096
$745$	17.2820	0.633165
$746$	−0.929008	−0.0340134
$747$	−2.62980	−0.0962195
$748$	−16.6000	−0.606956
$749$	0.102127	0.00373165
$750$	17.1132	0.624887
$751$	−29.1956	−1.06536	−0.532681	−	0.846316i	$-0.678815\pi$
$751$	−29.1956	−1.06536	−0.532681	+	0.846316i	$0.678815\pi$
$752$	−12.2882	−0.448105
$753$	−34.3427	−1.25152
$754$	6.47850	0.235933
$755$	−35.6686	−1.29811
$756$	−0.0755895	−0.00274916
$757$	−32.8920	−1.19548	−0.597740	−	0.801690i	$-0.703934\pi$
$757$	−32.8920	−1.19548	−0.597740	+	0.801690i	$0.703934\pi$
$758$	18.8701	0.685393
$759$	33.6103	1.21998
$760$	9.93850	0.360507
$761$	12.2399	0.443697	0.221849	−	0.975081i	$-0.428791\pi$
$761$	12.2399	0.443697	0.221849	+	0.975081i	$0.428791\pi$
$762$	28.6396	1.03750
$763$	−0.165533	−0.00599268
$764$	19.6589	0.711233
$765$	−21.1289	−0.763915
$766$	26.0028	0.939520
$767$	−82.3086	−2.97199
$768$	−2.01951	−0.0728726
$769$	19.7408	0.711870	0.355935	−	0.934511i	$-0.384162\pi$
$769$	19.7408	0.711870	0.355935	+	0.934511i	$0.384162\pi$
$770$	0.204736	0.00737817
$771$	12.9022	0.464663
$772$	8.55043	0.307737
$773$	−55.5213	−1.99696	−0.998480	−	0.0551082i	$-0.982450\pi$
$773$	−55.5213	−1.99696	−0.998480	+	0.0551082i	$0.982450\pi$
$774$	7.43515	0.267251
$775$	−54.2243	−1.94779
$776$	−10.3338	−0.370963
$777$	−0.270166	−0.00969216
$778$	−38.4348	−1.37795
$779$	−0.797245	−0.0285643
$780$	−47.9230	−1.71592
$781$	38.9335	1.39315
$782$	−31.0229	−1.10938
$783$	−3.73162	−0.133357
$784$	−6.99962	−0.249986
$785$	−28.1888	−1.00610
$786$	23.8701	0.851417
$787$	48.8172	1.74014	0.870072	−	0.492925i	$-0.164072\pi$
$787$	48.8172	1.74014	0.870072	+	0.492925i	$0.164072\pi$
$788$	−12.4696	−0.444210
$789$	43.6012	1.55224
$790$	42.4041	1.50867
$791$	−0.0267200	−0.000950053 0
$792$	−3.21816	−0.114352
$793$	−77.3303	−2.74608
$794$	−0.262441	−0.00931367
$795$	−93.5029	−3.31621
$796$	4.34535	0.154017
$797$	41.8147	1.48115	0.740576	−	0.671973i	$-0.234553\pi$
$797$	41.8147	1.48115	0.740576	+	0.671973i	$0.234553\pi$
$798$	0.110996	0.00392920
$799$	68.3550	2.41823
$800$	−7.40588	−0.261837
$801$	−14.3600	−0.507387
$802$	23.0742	0.814777
$803$	5.29431	0.186832
$804$	24.9424	0.879651
$805$	0.382621	0.0134856
$806$	49.3290	1.73754
$807$	−15.5743	−0.548240
$808$	13.3981	0.471344
$809$	−32.0092	−1.12539	−0.562693	−	0.826666i	$-0.690235\pi$
$809$	−32.0092	−1.12539	−0.562693	+	0.826666i	$0.690235\pi$
$810$	38.9987	1.37027
$811$	−50.7858	−1.78333	−0.891665	−	0.452695i	$-0.850463\pi$
$811$	−50.7858	−1.78333	−0.891665	+	0.452695i	$0.850463\pi$
$812$	0.0187303	0.000657303 0
$813$	16.9858	0.595718
$814$	20.4955	0.718368
$815$	33.8031	1.18407
$816$	11.2338	0.393262
$817$	19.4543	0.680621
$818$	33.8720	1.18431
$819$	−0.141520	−0.00494512
$820$	0.995172	0.0347529
$821$	49.9948	1.74483	0.872414	−	0.488767i	$-0.162553\pi$
$821$	49.9948	1.74483	0.872414	+	0.488767i	$0.162553\pi$
$822$	33.0304	1.15207
$823$	5.61819	0.195838	0.0979188	−	0.995194i	$-0.468781\pi$
$823$	5.61819	0.195838	0.0979188	+	0.995194i	$0.468781\pi$
$824$	−16.0799	−0.560169
$825$	−44.6322	−1.55389
$826$	−0.237966	−0.00827988
$827$	−2.18065	−0.0758286	−0.0379143	−	0.999281i	$-0.512071\pi$
$827$	−2.18065	−0.0758286	−0.0379143	+	0.999281i	$0.512071\pi$
$828$	−6.01425	−0.209010
$829$	28.2741	0.982000	0.491000	−	0.871159i	$-0.336631\pi$
$829$	28.2741	0.982000	0.491000	+	0.871159i	$0.336631\pi$
$830$	8.58928	0.298138
$831$	1.58168	0.0548679
$832$	6.73728	0.233573
$833$	38.9364	1.34907
$834$	4.01579	0.139055
$835$	−30.8404	−1.06728
$836$	−8.42042	−0.291226
$837$	−28.4135	−0.982115
$838$	25.8125	0.891678
$839$	32.4150	1.11909	0.559544	−	0.828800i	$-0.310976\pi$
$839$	32.4150	1.11909	0.559544	+	0.828800i	$0.310976\pi$
$840$	−0.138552	−0.00478049
$841$	−28.0753	−0.968115
$842$	21.4768	0.740140
$843$	−29.0754	−1.00141
$844$	−2.03483	−0.0700417
$845$	114.087	3.92473
$846$	13.2516	0.455600
$847$	0.0407996	0.00140189
$848$	13.1452	0.451407
$849$	−7.72064	−0.264972
$850$	41.1963	1.41302
$851$	38.3030	1.31301
$852$	−26.3476	−0.902655
$853$	−1.83579	−0.0628564	−0.0314282	−	0.999506i	$-0.510006\pi$
$853$	−1.83579	−0.0628564	−0.0314282	+	0.999506i	$0.510006\pi$
$854$	−0.223573	−0.00765050
$855$	−10.7177	−0.366538
$856$	5.24311	0.179206
$857$	37.6605	1.28646	0.643229	−	0.765674i	$-0.277595\pi$
$857$	37.6605	1.28646	0.643229	+	0.765674i	$0.277595\pi$
$858$	40.6028	1.38616
$859$	21.0850	0.719412	0.359706	−	0.933066i	$-0.382877\pi$
$859$	21.0850	0.719412	0.359706	+	0.933066i	$0.382877\pi$
$860$	−24.2842	−0.828083
$861$	0.0111143	0.000378775 0
$862$	−36.3208	−1.23709
$863$	23.1440	0.787830	0.393915	−	0.919147i	$-0.371120\pi$
$863$	23.1440	0.787830	0.393915	+	0.919147i	$0.371120\pi$
$864$	−3.88068	−0.132023
$865$	−17.3466	−0.589803
$866$	6.00561	0.204079
$867$	−28.1581	−0.956298
$868$	0.142617	0.00484073
$869$	−35.9269	−1.21874
$870$	−6.83988	−0.231894
$871$	−83.2105	−2.81948
$872$	−8.49826	−0.287787
$873$	11.1440	0.377168
$874$	−15.7365	−0.532295
$875$	−0.165060	−0.00558004
$876$	−3.58285	−0.121053
$877$	−3.62805	−0.122511	−0.0612553	−	0.998122i	$-0.519510\pi$
$877$	−3.62805	−0.122511	−0.0612553	+	0.998122i	$0.519510\pi$
$878$	9.39722	0.317141
$879$	−30.9605	−1.04427
$880$	10.5109	0.354323
$881$	−22.8866	−0.771070	−0.385535	−	0.922693i	$-0.625983\pi$
$881$	−22.8866	−0.771070	−0.385535	+	0.922693i	$0.625983\pi$
$882$	7.54840	0.254168
$883$	−23.9448	−0.805807	−0.402903	−	0.915243i	$-0.631999\pi$
$883$	−23.9448	−0.805807	−0.402903	+	0.915243i	$0.631999\pi$
$884$	−37.4771	−1.26049
$885$	86.8999	2.92111
$886$	12.3906	0.416272
$887$	16.4380	0.551934	0.275967	−	0.961167i	$-0.411002\pi$
$887$	16.4380	0.551934	0.275967	+	0.961167i	$0.411002\pi$
$888$	−13.8700	−0.465448
$889$	−0.276233	−0.00926457
$890$	46.9017	1.57215
$891$	−33.0417	−1.10694
$892$	−2.18613	−0.0731971
$893$	34.6734	1.16030
$894$	9.90891	0.331404
$895$	−13.4793	−0.450564
$896$	0.0194784	0.000650728 0
$897$	75.8806	2.53358
$898$	−19.9551	−0.665909
$899$	7.04056	0.234816
$900$	7.98651	0.266217
$901$	−73.1220	−2.43605
$902$	−0.843162	−0.0280742
$903$	−0.271211	−0.00902535
$904$	−1.37177	−0.0456245
$905$	−66.1135	−2.19769
$906$	−20.4511	−0.679443
$907$	13.8763	0.460753	0.230377	−	0.973102i	$-0.426004\pi$
$907$	13.8763	0.460753	0.230377	+	0.973102i	$0.426004\pi$
$908$	19.6953	0.653612
$909$	−14.4486	−0.479229
$910$	0.462224	0.0153226
$911$	−5.90654	−0.195692	−0.0978462	−	0.995202i	$-0.531195\pi$
$911$	−5.90654	−0.195692	−0.0978462	+	0.995202i	$0.531195\pi$
$912$	5.69839	0.188693
$913$	−7.27729	−0.240843
$914$	5.06840	0.167648
$915$	81.6439	2.69906
$916$	−8.50215	−0.280919
$917$	−0.230230	−0.00760287
$918$	21.5868	0.712472
$919$	4.45914	0.147093	0.0735467	−	0.997292i	$-0.476568\pi$
$919$	4.45914	0.147093	0.0735467	+	0.997292i	$0.476568\pi$
$920$	19.6433	0.647621
$921$	9.03265	0.297636
$922$	−2.96522	−0.0976543
$923$	87.8985	2.89321
$924$	0.117388	0.00386180
$925$	−50.8638	−1.67239
$926$	−28.1876	−0.926304
$927$	17.3406	0.569539
$928$	0.961590	0.0315657
$929$	−56.5412	−1.85506	−0.927528	−	0.373753i	$-0.878071\pi$
$929$	−56.5412	−1.85506	−0.927528	+	0.373753i	$0.878071\pi$
$930$	−52.0806	−1.70779
$931$	19.7507	0.647302
$932$	16.9950	0.556691
$933$	36.0243	1.17938
$934$	23.8900	0.781704
$935$	−58.4685	−1.91212
$936$	−7.26550	−0.237480
$937$	−43.9099	−1.43447	−0.717236	−	0.696830i	$-0.754593\pi$
$937$	−43.9099	−1.43447	−0.717236	+	0.696830i	$0.754593\pi$
$938$	−0.240573	−0.00785499
$939$	−11.3512	−0.370432
$940$	−43.2815	−1.41169
$941$	−46.8322	−1.52669	−0.763343	−	0.645993i	$-0.776444\pi$
$941$	−46.8322	−1.52669	−0.763343	+	0.645993i	$0.776444\pi$
$942$	−16.1625	−0.526602
$943$	−1.57574	−0.0513132
$944$	−12.2169	−0.397626
$945$	−0.266241	−0.00866082
$946$	20.5748	0.668945
$947$	−35.1874	−1.14344	−0.571719	−	0.820449i	$-0.693723\pi$
$947$	−35.1874	−1.14344	−0.571719	+	0.820449i	$0.693723\pi$
$948$	24.3130	0.789650
$949$	11.9528	0.388003
$950$	20.8970	0.677988
$951$	33.4722	1.08541
$952$	−0.108352	−0.00351170
$953$	0.510213	0.0165274	0.00826371	−	0.999966i	$-0.497370\pi$
$953$	0.510213	0.0165274	0.00826371	+	0.999966i	$0.497370\pi$
$954$	−14.1758	−0.458958
$955$	69.2424	2.24063
$956$	−19.3092	−0.624503
$957$	5.79511	0.187329
$958$	−24.1621	−0.780643
$959$	−0.318583	−0.0102876
$960$	−7.11310	−0.229574
$961$	22.6087	0.729312
$962$	46.2719	1.49187
$963$	−5.65418	−0.182203
$964$	17.0087	0.547814
$965$	30.1163	0.969478
$966$	0.219381	0.00705848
$967$	34.7842	1.11859	0.559293	−	0.828970i	$-0.311073\pi$
$967$	34.7842	1.11859	0.559293	+	0.828970i	$0.311073\pi$
$968$	2.09460	0.0673232
$969$	−31.6981	−1.01829
$970$	−36.3978	−1.16866
$971$	−1.43963	−0.0461999	−0.0231000	−	0.999733i	$-0.507354\pi$
$971$	−1.43963	−0.0461999	−0.0231000	+	0.999733i	$0.507354\pi$
$972$	10.7184	0.343794
$973$	−0.0387328	−0.00124172
$974$	25.7109	0.823830
$975$	−100.764	−3.22704
$976$	−11.4780	−0.367401
$977$	9.55245	0.305610	0.152805	−	0.988256i	$-0.451169\pi$
$977$	9.55245	0.305610	0.152805	+	0.988256i	$0.451169\pi$
$978$	19.3815	0.619753
$979$	−39.7376	−1.27002
$980$	−24.6540	−0.787545
$981$	9.16454	0.292601
$982$	−5.43682	−0.173496
$983$	58.6466	1.87053	0.935267	−	0.353942i	$-0.115159\pi$
$983$	58.6466	1.87053	0.935267	+	0.353942i	$0.115159\pi$
$984$	0.570597	0.0181900
$985$	−43.9203	−1.39942
$986$	−5.34899	−0.170346
$987$	−0.483378	−0.0153861
$988$	−19.0104	−0.604803
$989$	38.4512	1.22268
$990$	−11.3350	−0.360249
$991$	−52.6048	−1.67105	−0.835524	−	0.549454i	$-0.814836\pi$
$991$	−52.6048	−1.67105	−0.835524	+	0.549454i	$0.814836\pi$
$992$	7.32179	0.232467
$993$	55.6686	1.76659
$994$	0.254127	0.00806041
$995$	15.3052	0.485207
$996$	4.92479	0.156048
$997$	−50.0378	−1.58471	−0.792356	−	0.610059i	$-0.791146\pi$
$997$	−50.0378	−1.58471	−0.792356	+	0.610059i	$0.791146\pi$
$998$	−19.0086	−0.601705
$999$	−26.6526	−0.843252

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4034.2.a.b.1.7	✓	35

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4034.2.a.b.1.7	✓	35	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:	\( N \)	\(=\)	\( 4034 = 2 \cdot 2017 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4034.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.01951 q^{3} +1.00000 q^{4} +3.52220 q^{5} +2.01951 q^{6} -0.0194784 q^{7} -1.00000 q^{8} +1.07840 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.01951 q^{3} +1.00000 q^{4} +3.52220 q^{5} +2.01951 q^{6} -0.0194784 q^{7} -1.00000 q^{8} +1.07840 q^{9} -3.52220 q^{10} +2.98419 q^{11} -2.01951 q^{12} +6.73728 q^{13} +0.0194784 q^{14} -7.11310 q^{15} +1.00000 q^{16} -5.56265 q^{17} -1.07840 q^{18} -2.82168 q^{19} +3.52220 q^{20} +0.0393368 q^{21} -2.98419 q^{22} -5.57700 q^{23} +2.01951 q^{24} +7.40588 q^{25} -6.73728 q^{26} +3.88068 q^{27} -0.0194784 q^{28} -0.961590 q^{29} +7.11310 q^{30} -7.32179 q^{31} -1.00000 q^{32} -6.02659 q^{33} +5.56265 q^{34} -0.0686068 q^{35} +1.07840 q^{36} -6.86803 q^{37} +2.82168 q^{38} -13.6060 q^{39} -3.52220 q^{40} +0.282543 q^{41} -0.0393368 q^{42} -6.89460 q^{43} +2.98419 q^{44} +3.79834 q^{45} +5.57700 q^{46} -12.2882 q^{47} -2.01951 q^{48} -6.99962 q^{49} -7.40588 q^{50} +11.2338 q^{51} +6.73728 q^{52} +13.1452 q^{53} -3.88068 q^{54} +10.5109 q^{55} +0.0194784 q^{56} +5.69839 q^{57} +0.961590 q^{58} -12.2169 q^{59} -7.11310 q^{60} -11.4780 q^{61} +7.32179 q^{62} -0.0210056 q^{63} +1.00000 q^{64} +23.7300 q^{65} +6.02659 q^{66} -12.3508 q^{67} -5.56265 q^{68} +11.2628 q^{69} +0.0686068 q^{70} +13.0466 q^{71} -1.07840 q^{72} +1.77412 q^{73} +6.86803 q^{74} -14.9562 q^{75} -2.82168 q^{76} -0.0581273 q^{77} +13.6060 q^{78} -12.0391 q^{79} +3.52220 q^{80} -11.0723 q^{81} -0.282543 q^{82} -2.43861 q^{83} +0.0393368 q^{84} -19.5927 q^{85} +6.89460 q^{86} +1.94194 q^{87} -2.98419 q^{88} -13.3160 q^{89} -3.79834 q^{90} -0.131232 q^{91} -5.57700 q^{92} +14.7864 q^{93} +12.2882 q^{94} -9.93850 q^{95} +2.01951 q^{96} +10.3338 q^{97} +6.99962 q^{98} +3.21816 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 35 q - 35 q^{2} - 6 q^{3} + 35 q^{4} + 6 q^{5} + 6 q^{6} - 14 q^{7} - 35 q^{8} + 23 q^{9}+O(q^{10}) \) 35 * q - 35 * q^2 - 6 * q^3 + 35 * q^4 + 6 * q^5 + 6 * q^6 - 14 * q^7 - 35 * q^8 + 23 * q^9	\( 35 q - 35 q^{2} - 6 q^{3} + 35 q^{4} + 6 q^{5} + 6 q^{6} - 14 q^{7} - 35 q^{8} + 23 q^{9} - 6 q^{10} - 9 q^{11} - 6 q^{12} - 7 q^{13} + 14 q^{14} - 19 q^{15} + 35 q^{16} + 17 q^{17} - 23 q^{18} - 25 q^{19} + 6 q^{20} - 15 q^{21} + 9 q^{22} - 12 q^{23} + 6 q^{24} + 7 q^{25} + 7 q^{26} - 27 q^{27} - 14 q^{28} - 13 q^{29} + 19 q^{30} - 69 q^{31} - 35 q^{32} + q^{33} - 17 q^{34} - 4 q^{35} + 23 q^{36} - 22 q^{37} + 25 q^{38} - 38 q^{39} - 6 q^{40} + 15 q^{42} - 32 q^{43} - 9 q^{44} + 9 q^{45} + 12 q^{46} - 18 q^{47} - 6 q^{48} - 19 q^{49} - 7 q^{50} - 21 q^{51} - 7 q^{52} + 20 q^{53} + 27 q^{54} - 54 q^{55} + 14 q^{56} + 28 q^{57} + 13 q^{58} - 21 q^{59} - 19 q^{60} - 67 q^{61} + 69 q^{62} - 28 q^{63} + 35 q^{64} + 22 q^{65} - q^{66} - 18 q^{67} + 17 q^{68} - 42 q^{69} + 4 q^{70} - 36 q^{71} - 23 q^{72} - 18 q^{73} + 22 q^{74} - 49 q^{75} - 25 q^{76} + 20 q^{77} + 38 q^{78} - 92 q^{79} + 6 q^{80} - 25 q^{81} + 42 q^{83} - 15 q^{84} - 29 q^{85} + 32 q^{86} - 40 q^{87} + 9 q^{88} - 8 q^{89} - 9 q^{90} - 89 q^{91} - 12 q^{92} - q^{93} + 18 q^{94} - 62 q^{95} + 6 q^{96} - 40 q^{97} + 19 q^{98} - 64 q^{99}+O(q^{100}) \) 35 * q - 35 * q^2 - 6 * q^3 + 35 * q^4 + 6 * q^5 + 6 * q^6 - 14 * q^7 - 35 * q^8 + 23 * q^9 - 6 * q^10 - 9 * q^11 - 6 * q^12 - 7 * q^13 + 14 * q^14 - 19 * q^15 + 35 * q^16 + 17 * q^17 - 23 * q^18 - 25 * q^19 + 6 * q^20 - 15 * q^21 + 9 * q^22 - 12 * q^23 + 6 * q^24 + 7 * q^25 + 7 * q^26 - 27 * q^27 - 14 * q^28 - 13 * q^29 + 19 * q^30 - 69 * q^31 - 35 * q^32 + q^33 - 17 * q^34 - 4 * q^35 + 23 * q^36 - 22 * q^37 + 25 * q^38 - 38 * q^39 - 6 * q^40 + 15 * q^42 - 32 * q^43 - 9 * q^44 + 9 * q^45 + 12 * q^46 - 18 * q^47 - 6 * q^48 - 19 * q^49 - 7 * q^50 - 21 * q^51 - 7 * q^52 + 20 * q^53 + 27 * q^54 - 54 * q^55 + 14 * q^56 + 28 * q^57 + 13 * q^58 - 21 * q^59 - 19 * q^60 - 67 * q^61 + 69 * q^62 - 28 * q^63 + 35 * q^64 + 22 * q^65 - q^66 - 18 * q^67 + 17 * q^68 - 42 * q^69 + 4 * q^70 - 36 * q^71 - 23 * q^72 - 18 * q^73 + 22 * q^74 - 49 * q^75 - 25 * q^76 + 20 * q^77 + 38 * q^78 - 92 * q^79 + 6 * q^80 - 25 * q^81 + 42 * q^83 - 15 * q^84 - 29 * q^85 + 32 * q^86 - 40 * q^87 + 9 * q^88 - 8 * q^89 - 9 * q^90 - 89 * q^91 - 12 * q^92 - q^93 + 18 * q^94 - 62 * q^95 + 6 * q^96 - 40 * q^97 + 19 * q^98 - 64 * q^99

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