LMFDB - Embedded newform 4017.2.a.d.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4017,2,Mod(1,4017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4017, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4017 = 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4017.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:	$32.0759064919$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{8})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 2 $ x^2 - 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.41421$ of defining polynomial
Character	$\chi$	$=$	4017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.414214 q^{2} -1.00000 q^{3} -1.82843 q^{4} -0.585786 q^{5} -0.414214 q^{6} -2.82843 q^{7} -1.58579 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.414214 q^{2} -1.00000 q^{3} -1.82843 q^{4} -0.585786 q^{5} -0.414214 q^{6} -2.82843 q^{7} -1.58579 q^{8} +1.00000 q^{9} -0.242641 q^{10} -1.41421 q^{11} +1.82843 q^{12} +1.00000 q^{13} -1.17157 q^{14} +0.585786 q^{15} +3.00000 q^{16} +6.82843 q^{17} +0.414214 q^{18} -5.65685 q^{19} +1.07107 q^{20} +2.82843 q^{21} -0.585786 q^{22} +7.65685 q^{23} +1.58579 q^{24} -4.65685 q^{25} +0.414214 q^{26} -1.00000 q^{27} +5.17157 q^{28} +3.65685 q^{29} +0.242641 q^{30} -4.58579 q^{31} +4.41421 q^{32} +1.41421 q^{33} +2.82843 q^{34} +1.65685 q^{35} -1.82843 q^{36} +11.0711 q^{37} -2.34315 q^{38} -1.00000 q^{39} +0.928932 q^{40} +1.17157 q^{41} +1.17157 q^{42} -2.82843 q^{43} +2.58579 q^{44} -0.585786 q^{45} +3.17157 q^{46} +7.07107 q^{47} -3.00000 q^{48} +1.00000 q^{49} -1.92893 q^{50} -6.82843 q^{51} -1.82843 q^{52} -3.65685 q^{53} -0.414214 q^{54} +0.828427 q^{55} +4.48528 q^{56} +5.65685 q^{57} +1.51472 q^{58} -6.00000 q^{59} -1.07107 q^{60} +4.00000 q^{61} -1.89949 q^{62} -2.82843 q^{63} -4.17157 q^{64} -0.585786 q^{65} +0.585786 q^{66} -4.58579 q^{67} -12.4853 q^{68} -7.65685 q^{69} +0.686292 q^{70} +4.24264 q^{71} -1.58579 q^{72} -7.75736 q^{73} +4.58579 q^{74} +4.65685 q^{75} +10.3431 q^{76} +4.00000 q^{77} -0.414214 q^{78} -6.48528 q^{79} -1.75736 q^{80} +1.00000 q^{81} +0.485281 q^{82} -0.828427 q^{83} -5.17157 q^{84} -4.00000 q^{85} -1.17157 q^{86} -3.65685 q^{87} +2.24264 q^{88} +5.75736 q^{89} -0.242641 q^{90} -2.82843 q^{91} -14.0000 q^{92} +4.58579 q^{93} +2.92893 q^{94} +3.31371 q^{95} -4.41421 q^{96} +0.343146 q^{97} +0.414214 q^{98} -1.41421 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} - 4 q^{5} + 2 q^{6} - 6 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 - 4 * q^5 + 2 * q^6 - 6 * q^8 + 2 * q^9	$ 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} - 4 q^{5} + 2 q^{6} - 6 q^{8} + 2 q^{9} + 8 q^{10} - 2 q^{12} + 2 q^{13} - 8 q^{14} + 4 q^{15} + 6 q^{16} + 8 q^{17} - 2 q^{18} - 12 q^{20} - 4 q^{22} + 4 q^{23} + 6 q^{24} + 2 q^{25} - 2 q^{26} - 2 q^{27} + 16 q^{28} - 4 q^{29} - 8 q^{30} - 12 q^{31} + 6 q^{32} - 8 q^{35} + 2 q^{36} + 8 q^{37} - 16 q^{38} - 2 q^{39} + 16 q^{40} + 8 q^{41} + 8 q^{42} + 8 q^{44} - 4 q^{45} + 12 q^{46} - 6 q^{48} + 2 q^{49} - 18 q^{50} - 8 q^{51} + 2 q^{52} + 4 q^{53} + 2 q^{54} - 4 q^{55} - 8 q^{56} + 20 q^{58} - 12 q^{59} + 12 q^{60} + 8 q^{61} + 16 q^{62} - 14 q^{64} - 4 q^{65} + 4 q^{66} - 12 q^{67} - 8 q^{68} - 4 q^{69} + 24 q^{70} - 6 q^{72} - 24 q^{73} + 12 q^{74} - 2 q^{75} + 32 q^{76} + 8 q^{77} + 2 q^{78} + 4 q^{79} - 12 q^{80} + 2 q^{81} - 16 q^{82} + 4 q^{83} - 16 q^{84} - 8 q^{85} - 8 q^{86} + 4 q^{87} - 4 q^{88} + 20 q^{89} + 8 q^{90} - 28 q^{92} + 12 q^{93} + 20 q^{94} - 16 q^{95} - 6 q^{96} + 12 q^{97} - 2 q^{98}+O(q^{100}) $ 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 - 4 * q^5 + 2 * q^6 - 6 * q^8 + 2 * q^9 + 8 * q^10 - 2 * q^12 + 2 * q^13 - 8 * q^14 + 4 * q^15 + 6 * q^16 + 8 * q^17 - 2 * q^18 - 12 * q^20 - 4 * q^22 + 4 * q^23 + 6 * q^24 + 2 * q^25 - 2 * q^26 - 2 * q^27 + 16 * q^28 - 4 * q^29 - 8 * q^30 - 12 * q^31 + 6 * q^32 - 8 * q^35 + 2 * q^36 + 8 * q^37 - 16 * q^38 - 2 * q^39 + 16 * q^40 + 8 * q^41 + 8 * q^42 + 8 * q^44 - 4 * q^45 + 12 * q^46 - 6 * q^48 + 2 * q^49 - 18 * q^50 - 8 * q^51 + 2 * q^52 + 4 * q^53 + 2 * q^54 - 4 * q^55 - 8 * q^56 + 20 * q^58 - 12 * q^59 + 12 * q^60 + 8 * q^61 + 16 * q^62 - 14 * q^64 - 4 * q^65 + 4 * q^66 - 12 * q^67 - 8 * q^68 - 4 * q^69 + 24 * q^70 - 6 * q^72 - 24 * q^73 + 12 * q^74 - 2 * q^75 + 32 * q^76 + 8 * q^77 + 2 * q^78 + 4 * q^79 - 12 * q^80 + 2 * q^81 - 16 * q^82 + 4 * q^83 - 16 * q^84 - 8 * q^85 - 8 * q^86 + 4 * q^87 - 4 * q^88 + 20 * q^89 + 8 * q^90 - 28 * q^92 + 12 * q^93 + 20 * q^94 - 16 * q^95 - 6 * q^96 + 12 * q^97 - 2 * q^98

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 $

$2$	0.414214	0.292893	0.146447	−	0.989219i	$-0.453216\pi$
$2$	0.414214	0.292893	0.146447	+	0.989219i	$0.453216\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.82843	−0.914214
$5$	−0.585786	−0.261972	−0.130986	−	0.991384i	$-0.541814\pi$
$5$	−0.585786	−0.261972	−0.130986	+	0.991384i	$0.541814\pi$
$6$	−0.414214	−0.169102
$7$	−2.82843	−1.06904	−0.534522	−	0.845154i	$-0.679509\pi$
$7$	−2.82843	−1.06904	−0.534522	+	0.845154i	$0.679509\pi$
$8$	−1.58579	−0.560660
$9$	1.00000	0.333333
$10$	−0.242641	−0.0767297
$11$	−1.41421	−0.426401	−0.213201	−	0.977008i	$-0.568389\pi$
$11$	−1.41421	−0.426401	−0.213201	+	0.977008i	$0.568389\pi$
$12$	1.82843	0.527821
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−1.17157	−0.313116
$15$	0.585786	0.151249
$16$	3.00000	0.750000
$17$	6.82843	1.65614	0.828068	−	0.560627i	$-0.189440\pi$
$17$	6.82843	1.65614	0.828068	+	0.560627i	$0.189440\pi$
$18$	0.414214	0.0976311
$19$	−5.65685	−1.29777	−0.648886	−	0.760886i	$-0.724765\pi$
$19$	−5.65685	−1.29777	−0.648886	+	0.760886i	$0.724765\pi$
$20$	1.07107	0.239498
$21$	2.82843	0.617213
$22$	−0.585786	−0.124890
$23$	7.65685	1.59656	0.798282	−	0.602284i	$-0.205742\pi$
$23$	7.65685	1.59656	0.798282	+	0.602284i	$0.205742\pi$
$24$	1.58579	0.323697
$25$	−4.65685	−0.931371
$26$	0.414214	0.0812340
$27$	−1.00000	−0.192450
$28$	5.17157	0.977335
$29$	3.65685	0.679061	0.339530	−	0.940595i	$-0.389732\pi$
$29$	3.65685	0.679061	0.339530	+	0.940595i	$0.389732\pi$
$30$	0.242641	0.0442999
$31$	−4.58579	−0.823632	−0.411816	−	0.911267i	$-0.635105\pi$
$31$	−4.58579	−0.823632	−0.411816	+	0.911267i	$0.635105\pi$
$32$	4.41421	0.780330
$33$	1.41421	0.246183
$34$	2.82843	0.485071
$35$	1.65685	0.280059
$36$	−1.82843	−0.304738
$37$	11.0711	1.82007	0.910036	−	0.414529i	$-0.136054\pi$
$37$	11.0711	1.82007	0.910036	+	0.414529i	$0.136054\pi$
$38$	−2.34315	−0.380108
$39$	−1.00000	−0.160128
$40$	0.928932	0.146877
$41$	1.17157	0.182969	0.0914845	−	0.995807i	$-0.470839\pi$
$41$	1.17157	0.182969	0.0914845	+	0.995807i	$0.470839\pi$
$42$	1.17157	0.180778
$43$	−2.82843	−0.431331	−0.215666	−	0.976467i	$-0.569192\pi$
$43$	−2.82843	−0.431331	−0.215666	+	0.976467i	$0.569192\pi$
$44$	2.58579	0.389822
$45$	−0.585786	−0.0873239
$46$	3.17157	0.467623
$47$	7.07107	1.03142	0.515711	−	0.856763i	$-0.327528\pi$
$47$	7.07107	1.03142	0.515711	+	0.856763i	$0.327528\pi$
$48$	−3.00000	−0.433013
$49$	1.00000	0.142857
$50$	−1.92893	−0.272792
$51$	−6.82843	−0.956171
$52$	−1.82843	−0.253557
$53$	−3.65685	−0.502308	−0.251154	−	0.967947i	$-0.580810\pi$
$53$	−3.65685	−0.502308	−0.251154	+	0.967947i	$0.580810\pi$
$54$	−0.414214	−0.0563673
$55$	0.828427	0.111705
$56$	4.48528	0.599371
$57$	5.65685	0.749269
$58$	1.51472	0.198892
$59$	−6.00000	−0.781133	−0.390567	−	0.920575i	$-0.627721\pi$
$59$	−6.00000	−0.781133	−0.390567	+	0.920575i	$0.627721\pi$
$60$	−1.07107	−0.138274
$61$	4.00000	0.512148	0.256074	−	0.966657i	$-0.417571\pi$
$61$	4.00000	0.512148	0.256074	+	0.966657i	$0.417571\pi$
$62$	−1.89949	−0.241236
$63$	−2.82843	−0.356348
$64$	−4.17157	−0.521447
$65$	−0.585786	−0.0726579
$66$	0.585786	0.0721053
$67$	−4.58579	−0.560243	−0.280121	−	0.959965i	$-0.590375\pi$
$67$	−4.58579	−0.560243	−0.280121	+	0.959965i	$0.590375\pi$
$68$	−12.4853	−1.51406
$69$	−7.65685	−0.921777
$70$	0.686292	0.0820275
$71$	4.24264	0.503509	0.251754	−	0.967791i	$-0.418992\pi$
$71$	4.24264	0.503509	0.251754	+	0.967791i	$0.418992\pi$
$72$	−1.58579	−0.186887
$73$	−7.75736	−0.907930	−0.453965	−	0.891019i	$-0.649991\pi$
$73$	−7.75736	−0.907930	−0.453965	+	0.891019i	$0.649991\pi$
$74$	4.58579	0.533087
$75$	4.65685	0.537727
$76$	10.3431	1.18644
$77$	4.00000	0.455842
$78$	−0.414214	−0.0469005
$79$	−6.48528	−0.729651	−0.364826	−	0.931076i	$-0.618871\pi$
$79$	−6.48528	−0.729651	−0.364826	+	0.931076i	$0.618871\pi$
$80$	−1.75736	−0.196479
$81$	1.00000	0.111111
$82$	0.485281	0.0535904
$83$	−0.828427	−0.0909317	−0.0454658	−	0.998966i	$-0.514477\pi$
$83$	−0.828427	−0.0909317	−0.0454658	+	0.998966i	$0.514477\pi$
$84$	−5.17157	−0.564265
$85$	−4.00000	−0.433861
$86$	−1.17157	−0.126334
$87$	−3.65685	−0.392056
$88$	2.24264	0.239066
$89$	5.75736	0.610279	0.305139	−	0.952308i	$-0.401297\pi$
$89$	5.75736	0.610279	0.305139	+	0.952308i	$0.401297\pi$
$90$	−0.242641	−0.0255766
$91$	−2.82843	−0.296500
$92$	−14.0000	−1.45960
$93$	4.58579	0.475524
$94$	2.92893	0.302096
$95$	3.31371	0.339979
$96$	−4.41421	−0.450524
$97$	0.343146	0.0348412	0.0174206	−	0.999848i	$-0.494455\pi$
$97$	0.343146	0.0348412	0.0174206	+	0.999848i	$0.494455\pi$
$98$	0.414214	0.0418419
$99$	−1.41421	−0.142134
$100$	8.51472	0.851472
$101$	−3.65685	−0.363871	−0.181935	−	0.983311i	$-0.558236\pi$
$101$	−3.65685	−0.363871	−0.181935	+	0.983311i	$0.558236\pi$
$102$	−2.82843	−0.280056
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	−1.58579	−0.155499
$105$	−1.65685	−0.161692
$106$	−1.51472	−0.147122
$107$	2.34315	0.226520	0.113260	−	0.993565i	$-0.463871\pi$
$107$	2.34315	0.226520	0.113260	+	0.993565i	$0.463871\pi$
$108$	1.82843	0.175940
$109$	8.72792	0.835983	0.417992	−	0.908451i	$-0.362734\pi$
$109$	8.72792	0.835983	0.417992	+	0.908451i	$0.362734\pi$
$110$	0.343146	0.0327177
$111$	−11.0711	−1.05082
$112$	−8.48528	−0.801784
$113$	−10.0000	−0.940721	−0.470360	−	0.882474i	$-0.655876\pi$
$113$	−10.0000	−0.940721	−0.470360	+	0.882474i	$0.655876\pi$
$114$	2.34315	0.219456
$115$	−4.48528	−0.418255
$116$	−6.68629	−0.620807
$117$	1.00000	0.0924500
$118$	−2.48528	−0.228789
$119$	−19.3137	−1.77048
$120$	−0.928932	−0.0847995
$121$	−9.00000	−0.818182
$122$	1.65685	0.150005
$123$	−1.17157	−0.105637
$124$	8.38478	0.752975
$125$	5.65685	0.505964
$126$	−1.17157	−0.104372
$127$	0	0		−	1.00000i	$-0.5\pi$
$127$	0	0			1.00000i	$0.5\pi$
$128$	−10.5563	−0.933058
$129$	2.82843	0.249029
$130$	−0.242641	−0.0212810
$131$	−6.00000	−0.524222	−0.262111	−	0.965038i	$-0.584419\pi$
$131$	−6.00000	−0.524222	−0.262111	+	0.965038i	$0.584419\pi$
$132$	−2.58579	−0.225064
$133$	16.0000	1.38738
$134$	−1.89949	−0.164091
$135$	0.585786	0.0504165
$136$	−10.8284	−0.928530
$137$	−8.00000	−0.683486	−0.341743	−	0.939793i	$-0.611017\pi$
$137$	−8.00000	−0.683486	−0.341743	+	0.939793i	$0.611017\pi$
$138$	−3.17157	−0.269982
$139$	−8.14214	−0.690607	−0.345303	−	0.938491i	$-0.612224\pi$
$139$	−8.14214	−0.690607	−0.345303	+	0.938491i	$0.612224\pi$
$140$	−3.02944	−0.256034
$141$	−7.07107	−0.595491
$142$	1.75736	0.147474
$143$	−1.41421	−0.118262
$144$	3.00000	0.250000
$145$	−2.14214	−0.177895
$146$	−3.21320	−0.265927
$147$	−1.00000	−0.0824786
$148$	−20.2426	−1.66393
$149$	−4.00000	−0.327693	−0.163846	−	0.986486i	$-0.552390\pi$
$149$	−4.00000	−0.327693	−0.163846	+	0.986486i	$0.552390\pi$
$150$	1.92893	0.157497
$151$	−22.7279	−1.84957	−0.924786	−	0.380488i	$-0.875756\pi$
$151$	−22.7279	−1.84957	−0.924786	+	0.380488i	$0.875756\pi$
$152$	8.97056	0.727609
$153$	6.82843	0.552046
$154$	1.65685	0.133513
$155$	2.68629	0.215768
$156$	1.82843	0.146391
$157$	12.1421	0.969048	0.484524	−	0.874778i	$-0.338993\pi$
$157$	12.1421	0.969048	0.484524	+	0.874778i	$0.338993\pi$
$158$	−2.68629	−0.213710
$159$	3.65685	0.290007
$160$	−2.58579	−0.204424
$161$	−21.6569	−1.70680
$162$	0.414214	0.0325437
$163$	−5.65685	−0.443079	−0.221540	−	0.975151i	$-0.571108\pi$
$163$	−5.65685	−0.443079	−0.221540	+	0.975151i	$0.571108\pi$
$164$	−2.14214	−0.167273
$165$	−0.828427	−0.0644930
$166$	−0.343146	−0.0266333
$167$	4.14214	0.320528	0.160264	−	0.987074i	$-0.448765\pi$
$167$	4.14214	0.320528	0.160264	+	0.987074i	$0.448765\pi$
$168$	−4.48528	−0.346047
$169$	1.00000	0.0769231
$170$	−1.65685	−0.127075
$171$	−5.65685	−0.432590
$172$	5.17157	0.394329
$173$	13.7990	1.04912	0.524559	−	0.851374i	$-0.324230\pi$
$173$	13.7990	1.04912	0.524559	+	0.851374i	$0.324230\pi$
$174$	−1.51472	−0.114831
$175$	13.1716	0.995677
$176$	−4.24264	−0.319801
$177$	6.00000	0.450988
$178$	2.38478	0.178747
$179$	−9.31371	−0.696139	−0.348070	−	0.937469i	$-0.613163\pi$
$179$	−9.31371	−0.696139	−0.348070	+	0.937469i	$0.613163\pi$
$180$	1.07107	0.0798327
$181$	4.34315	0.322823	0.161412	−	0.986887i	$-0.448395\pi$
$181$	4.34315	0.322823	0.161412	+	0.986887i	$0.448395\pi$
$182$	−1.17157	−0.0868428
$183$	−4.00000	−0.295689
$184$	−12.1421	−0.895130
$185$	−6.48528	−0.476807
$186$	1.89949	0.139278
$187$	−9.65685	−0.706179
$188$	−12.9289	−0.942939
$189$	2.82843	0.205738
$190$	1.37258	0.0995776
$191$	−8.97056	−0.649087	−0.324544	−	0.945871i	$-0.605211\pi$
$191$	−8.97056	−0.649087	−0.324544	+	0.945871i	$0.605211\pi$
$192$	4.17157	0.301057
$193$	−16.7279	−1.20410	−0.602051	−	0.798458i	$-0.705650\pi$
$193$	−16.7279	−1.20410	−0.602051	+	0.798458i	$0.705650\pi$
$194$	0.142136	0.0102047
$195$	0.585786	0.0419490
$196$	−1.82843	−0.130602
$197$	−11.8995	−0.847804	−0.423902	−	0.905708i	$-0.639340\pi$
$197$	−11.8995	−0.847804	−0.423902	+	0.905708i	$0.639340\pi$
$198$	−0.585786	−0.0416300
$199$	−4.00000	−0.283552	−0.141776	−	0.989899i	$-0.545281\pi$
$199$	−4.00000	−0.283552	−0.141776	+	0.989899i	$0.545281\pi$
$200$	7.38478	0.522183
$201$	4.58579	0.323456
$202$	−1.51472	−0.106575
$203$	−10.3431	−0.725947
$204$	12.4853	0.874145
$205$	−0.686292	−0.0479327
$206$	0.414214	0.0288596
$207$	7.65685	0.532188
$208$	3.00000	0.208013
$209$	8.00000	0.553372
$210$	−0.686292	−0.0473586
$211$	5.17157	0.356026	0.178013	−	0.984028i	$-0.443033\pi$
$211$	5.17157	0.356026	0.178013	+	0.984028i	$0.443033\pi$
$212$	6.68629	0.459216
$213$	−4.24264	−0.290701
$214$	0.970563	0.0663463
$215$	1.65685	0.112997
$216$	1.58579	0.107899
$217$	12.9706	0.880499
$218$	3.61522	0.244854
$219$	7.75736	0.524194
$220$	−1.51472	−0.102122
$221$	6.82843	0.459330
$222$	−4.58579	−0.307778
$223$	0	0		−	1.00000i	$-0.5\pi$
$223$	0	0			1.00000i	$0.5\pi$
$224$	−12.4853	−0.834208
$225$	−4.65685	−0.310457
$226$	−4.14214	−0.275531
$227$	−7.75736	−0.514874	−0.257437	−	0.966295i	$-0.582878\pi$
$227$	−7.75736	−0.514874	−0.257437	+	0.966295i	$0.582878\pi$
$228$	−10.3431	−0.684992
$229$	−29.3137	−1.93710	−0.968552	−	0.248810i	$-0.919960\pi$
$229$	−29.3137	−1.93710	−0.968552	+	0.248810i	$0.919960\pi$
$230$	−1.85786	−0.122504
$231$	−4.00000	−0.263181
$232$	−5.79899	−0.380722
$233$	16.6274	1.08930	0.544649	−	0.838664i	$-0.316663\pi$
$233$	16.6274	1.08930	0.544649	+	0.838664i	$0.316663\pi$
$234$	0.414214	0.0270780
$235$	−4.14214	−0.270203
$236$	10.9706	0.714123
$237$	6.48528	0.421264
$238$	−8.00000	−0.518563
$239$	23.6569	1.53023	0.765117	−	0.643891i	$-0.222681\pi$
$239$	23.6569	1.53023	0.765117	+	0.643891i	$0.222681\pi$
$240$	1.75736	0.113437
$241$	4.72792	0.304552	0.152276	−	0.988338i	$-0.451340\pi$
$241$	4.72792	0.304552	0.152276	+	0.988338i	$0.451340\pi$
$242$	−3.72792	−0.239640
$243$	−1.00000	−0.0641500
$244$	−7.31371	−0.468212
$245$	−0.585786	−0.0374245
$246$	−0.485281	−0.0309404
$247$	−5.65685	−0.359937
$248$	7.27208	0.461777
$249$	0.828427	0.0524994
$250$	2.34315	0.148194
$251$	7.51472	0.474325	0.237162	−	0.971470i	$-0.423783\pi$
$251$	7.51472	0.474325	0.237162	+	0.971470i	$0.423783\pi$
$252$	5.17157	0.325778
$253$	−10.8284	−0.680777
$254$	0	0
$255$	4.00000	0.250490
$256$	3.97056	0.248160
$257$	−2.97056	−0.185299	−0.0926493	−	0.995699i	$-0.529534\pi$
$257$	−2.97056	−0.185299	−0.0926493	+	0.995699i	$0.529534\pi$
$258$	1.17157	0.0729389
$259$	−31.3137	−1.94574
$260$	1.07107	0.0664248
$261$	3.65685	0.226354
$262$	−2.48528	−0.153541
$263$	−6.82843	−0.421059	−0.210529	−	0.977588i	$-0.567519\pi$
$263$	−6.82843	−0.421059	−0.210529	+	0.977588i	$0.567519\pi$
$264$	−2.24264	−0.138025
$265$	2.14214	0.131590
$266$	6.62742	0.406353
$267$	−5.75736	−0.352345
$268$	8.38478	0.512182
$269$	−2.82843	−0.172452	−0.0862261	−	0.996276i	$-0.527481\pi$
$269$	−2.82843	−0.172452	−0.0862261	+	0.996276i	$0.527481\pi$
$270$	0.242641	0.0147666
$271$	−23.4142	−1.42231	−0.711156	−	0.703034i	$-0.751828\pi$
$271$	−23.4142	−1.42231	−0.711156	+	0.703034i	$0.751828\pi$
$272$	20.4853	1.24210
$273$	2.82843	0.171184
$274$	−3.31371	−0.200188
$275$	6.58579	0.397138
$276$	14.0000	0.842701
$277$	8.82843	0.530449	0.265224	−	0.964187i	$-0.414554\pi$
$277$	8.82843	0.530449	0.265224	+	0.964187i	$0.414554\pi$
$278$	−3.37258	−0.202274
$279$	−4.58579	−0.274544
$280$	−2.62742	−0.157018
$281$	−19.8995	−1.18710	−0.593552	−	0.804796i	$-0.702275\pi$
$281$	−19.8995	−1.18710	−0.593552	+	0.804796i	$0.702275\pi$
$282$	−2.92893	−0.174415
$283$	18.1421	1.07844	0.539219	−	0.842166i	$-0.318720\pi$
$283$	18.1421	1.07844	0.539219	+	0.842166i	$0.318720\pi$
$284$	−7.75736	−0.460315
$285$	−3.31371	−0.196287
$286$	−0.585786	−0.0346383
$287$	−3.31371	−0.195602
$288$	4.41421	0.260110
$289$	29.6274	1.74279
$290$	−0.887302	−0.0521041
$291$	−0.343146	−0.0201156
$292$	14.1838	0.830042
$293$	21.5563	1.25934	0.629668	−	0.776865i	$-0.283191\pi$
$293$	21.5563	1.25934	0.629668	+	0.776865i	$0.283191\pi$
$294$	−0.414214	−0.0241574
$295$	3.51472	0.204635
$296$	−17.5563	−1.02044
$297$	1.41421	0.0820610
$298$	−1.65685	−0.0959790
$299$	7.65685	0.442807
$300$	−8.51472	−0.491598
$301$	8.00000	0.461112
$302$	−9.41421	−0.541727
$303$	3.65685	0.210081
$304$	−16.9706	−0.973329
$305$	−2.34315	−0.134168
$306$	2.82843	0.161690
$307$	−6.92893	−0.395455	−0.197728	−	0.980257i	$-0.563356\pi$
$307$	−6.92893	−0.395455	−0.197728	+	0.980257i	$0.563356\pi$
$308$	−7.31371	−0.416737
$309$	−1.00000	−0.0568880
$310$	1.11270	0.0631970
$311$	−33.6569	−1.90851	−0.954253	−	0.299002i	$-0.903346\pi$
$311$	−33.6569	−1.90851	−0.954253	+	0.299002i	$0.903346\pi$
$312$	1.58579	0.0897775
$313$	29.3137	1.65691	0.828454	−	0.560057i	$-0.189221\pi$
$313$	29.3137	1.65691	0.828454	+	0.560057i	$0.189221\pi$
$314$	5.02944	0.283828
$315$	1.65685	0.0933532
$316$	11.8579	0.667057
$317$	25.4558	1.42974	0.714871	−	0.699256i	$-0.246485\pi$
$317$	25.4558	1.42974	0.714871	+	0.699256i	$0.246485\pi$
$318$	1.51472	0.0849412
$319$	−5.17157	−0.289552
$320$	2.44365	0.136604
$321$	−2.34315	−0.130782
$322$	−8.97056	−0.499910
$323$	−38.6274	−2.14929
$324$	−1.82843	−0.101579
$325$	−4.65685	−0.258316
$326$	−2.34315	−0.129775
$327$	−8.72792	−0.482655
$328$	−1.85786	−0.102583
$329$	−20.0000	−1.10264
$330$	−0.343146	−0.0188896
$331$	−9.07107	−0.498591	−0.249295	−	0.968427i	$-0.580199\pi$
$331$	−9.07107	−0.498591	−0.249295	+	0.968427i	$0.580199\pi$
$332$	1.51472	0.0831310
$333$	11.0711	0.606691
$334$	1.71573	0.0938805
$335$	2.68629	0.146768
$336$	8.48528	0.462910
$337$	−32.6274	−1.77733	−0.888664	−	0.458558i	$-0.848366\pi$
$337$	−32.6274	−1.77733	−0.888664	+	0.458558i	$0.848366\pi$
$338$	0.414214	0.0225302
$339$	10.0000	0.543125
$340$	7.31371	0.396642
$341$	6.48528	0.351198
$342$	−2.34315	−0.126703
$343$	16.9706	0.916324
$344$	4.48528	0.241830
$345$	4.48528	0.241479
$346$	5.71573	0.307279
$347$	28.0000	1.50312	0.751559	−	0.659665i	$-0.229302\pi$
$347$	28.0000	1.50312	0.751559	+	0.659665i	$0.229302\pi$
$348$	6.68629	0.358423
$349$	−22.8701	−1.22421	−0.612103	−	0.790778i	$-0.709676\pi$
$349$	−22.8701	−1.22421	−0.612103	+	0.790778i	$0.709676\pi$
$350$	5.45584	0.291627
$351$	−1.00000	−0.0533761
$352$	−6.24264	−0.332734
$353$	−29.0711	−1.54730	−0.773648	−	0.633615i	$-0.781570\pi$
$353$	−29.0711	−1.54730	−0.773648	+	0.633615i	$0.781570\pi$
$354$	2.48528	0.132091
$355$	−2.48528	−0.131905
$356$	−10.5269	−0.557925
$357$	19.3137	1.02219
$358$	−3.85786	−0.203894
$359$	5.51472	0.291056	0.145528	−	0.989354i	$-0.453512\pi$
$359$	5.51472	0.291056	0.145528	+	0.989354i	$0.453512\pi$
$360$	0.928932	0.0489590
$361$	13.0000	0.684211
$362$	1.79899	0.0945528
$363$	9.00000	0.472377
$364$	5.17157	0.271064
$365$	4.54416	0.237852
$366$	−1.65685	−0.0866052
$367$	−20.8284	−1.08724	−0.543618	−	0.839333i	$-0.682946\pi$
$367$	−20.8284	−1.08724	−0.543618	+	0.839333i	$0.682946\pi$
$368$	22.9706	1.19742
$369$	1.17157	0.0609896
$370$	−2.68629	−0.139654
$371$	10.3431	0.536989
$372$	−8.38478	−0.434730
$373$	−9.65685	−0.500013	−0.250006	−	0.968244i	$-0.580433\pi$
$373$	−9.65685	−0.500013	−0.250006	+	0.968244i	$0.580433\pi$
$374$	−4.00000	−0.206835
$375$	−5.65685	−0.292119
$376$	−11.2132	−0.578277
$377$	3.65685	0.188338
$378$	1.17157	0.0602592
$379$	−7.41421	−0.380843	−0.190421	−	0.981702i	$-0.560985\pi$
$379$	−7.41421	−0.380843	−0.190421	+	0.981702i	$0.560985\pi$
$380$	−6.05887	−0.310814
$381$	0	0
$382$	−3.71573	−0.190113
$383$	−5.41421	−0.276653	−0.138327	−	0.990387i	$-0.544172\pi$
$383$	−5.41421	−0.276653	−0.138327	+	0.990387i	$0.544172\pi$
$384$	10.5563	0.538701
$385$	−2.34315	−0.119418
$386$	−6.92893	−0.352673
$387$	−2.82843	−0.143777
$388$	−0.627417	−0.0318523
$389$	−6.48528	−0.328817	−0.164408	−	0.986392i	$-0.552571\pi$
$389$	−6.48528	−0.328817	−0.164408	+	0.986392i	$0.552571\pi$
$390$	0.242641	0.0122866
$391$	52.2843	2.64413
$392$	−1.58579	−0.0800943
$393$	6.00000	0.302660
$394$	−4.92893	−0.248316
$395$	3.79899	0.191148
$396$	2.58579	0.129941
$397$	26.8701	1.34857	0.674285	−	0.738471i	$-0.264452\pi$
$397$	26.8701	1.34857	0.674285	+	0.738471i	$0.264452\pi$
$398$	−1.65685	−0.0830506
$399$	−16.0000	−0.801002
$400$	−13.9706	−0.698528
$401$	−30.8284	−1.53950	−0.769749	−	0.638347i	$-0.779619\pi$
$401$	−30.8284	−1.53950	−0.769749	+	0.638347i	$0.779619\pi$
$402$	1.89949	0.0947382
$403$	−4.58579	−0.228434
$404$	6.68629	0.332655
$405$	−0.585786	−0.0291080
$406$	−4.28427	−0.212625
$407$	−15.6569	−0.776081
$408$	10.8284	0.536087
$409$	20.8284	1.02990	0.514950	−	0.857220i	$-0.327811\pi$
$409$	20.8284	1.02990	0.514950	+	0.857220i	$0.327811\pi$
$410$	−0.284271	−0.0140392
$411$	8.00000	0.394611
$412$	−1.82843	−0.0900801
$413$	16.9706	0.835067
$414$	3.17157	0.155874
$415$	0.485281	0.0238215
$416$	4.41421	0.216425
$417$	8.14214	0.398722
$418$	3.31371	0.162079
$419$	−18.3431	−0.896121	−0.448061	−	0.894003i	$-0.647885\pi$
$419$	−18.3431	−0.896121	−0.448061	+	0.894003i	$0.647885\pi$
$420$	3.02944	0.147821
$421$	6.48528	0.316073	0.158037	−	0.987433i	$-0.449484\pi$
$421$	6.48528	0.316073	0.158037	+	0.987433i	$0.449484\pi$
$422$	2.14214	0.104278
$423$	7.07107	0.343807
$424$	5.79899	0.281624
$425$	−31.7990	−1.54248
$426$	−1.75736	−0.0851443
$427$	−11.3137	−0.547509
$428$	−4.28427	−0.207088
$429$	1.41421	0.0682789
$430$	0.686292	0.0330959
$431$	−13.5147	−0.650981	−0.325491	−	0.945545i	$-0.605529\pi$
$431$	−13.5147	−0.650981	−0.325491	+	0.945545i	$0.605529\pi$
$432$	−3.00000	−0.144338
$433$	7.65685	0.367965	0.183982	−	0.982930i	$-0.441101\pi$
$433$	7.65685	0.367965	0.183982	+	0.982930i	$0.441101\pi$
$434$	5.37258	0.257892
$435$	2.14214	0.102708
$436$	−15.9584	−0.764267
$437$	−43.3137	−2.07198
$438$	3.21320	0.153533
$439$	25.4558	1.21494	0.607471	−	0.794342i	$-0.292184\pi$
$439$	25.4558	1.21494	0.607471	+	0.794342i	$0.292184\pi$
$440$	−1.31371	−0.0626286
$441$	1.00000	0.0476190
$442$	2.82843	0.134535
$443$	2.82843	0.134383	0.0671913	−	0.997740i	$-0.478596\pi$
$443$	2.82843	0.134383	0.0671913	+	0.997740i	$0.478596\pi$
$444$	20.2426	0.960673
$445$	−3.37258	−0.159876
$446$	0	0
$447$	4.00000	0.189194
$448$	11.7990	0.557450
$449$	−31.8995	−1.50543	−0.752715	−	0.658346i	$-0.771256\pi$
$449$	−31.8995	−1.50543	−0.752715	+	0.658346i	$0.771256\pi$
$450$	−1.92893	−0.0909307
$451$	−1.65685	−0.0780182
$452$	18.2843	0.860020
$453$	22.7279	1.06785
$454$	−3.21320	−0.150803
$455$	1.65685	0.0776745
$456$	−8.97056	−0.420085
$457$	−26.5858	−1.24363	−0.621815	−	0.783164i	$-0.713605\pi$
$457$	−26.5858	−1.24363	−0.621815	+	0.783164i	$0.713605\pi$
$458$	−12.1421	−0.567365
$459$	−6.82843	−0.318724
$460$	8.20101	0.382374
$461$	29.9411	1.39450	0.697249	−	0.716829i	$-0.254407\pi$
$461$	29.9411	1.39450	0.697249	+	0.716829i	$0.254407\pi$
$462$	−1.65685	−0.0770838
$463$	−9.75736	−0.453463	−0.226731	−	0.973957i	$-0.572804\pi$
$463$	−9.75736	−0.453463	−0.226731	+	0.973957i	$0.572804\pi$
$464$	10.9706	0.509296
$465$	−2.68629	−0.124574
$466$	6.88730	0.319048
$467$	35.3137	1.63412	0.817062	−	0.576550i	$-0.195601\pi$
$467$	35.3137	1.63412	0.817062	+	0.576550i	$0.195601\pi$
$468$	−1.82843	−0.0845191
$469$	12.9706	0.598925
$470$	−1.71573	−0.0791407
$471$	−12.1421	−0.559480
$472$	9.51472	0.437950
$473$	4.00000	0.183920
$474$	2.68629	0.123385
$475$	26.3431	1.20871
$476$	35.3137	1.61860
$477$	−3.65685	−0.167436
$478$	9.79899	0.448195
$479$	−2.58579	−0.118148	−0.0590738	−	0.998254i	$-0.518815\pi$
$479$	−2.58579	−0.118148	−0.0590738	+	0.998254i	$0.518815\pi$
$480$	2.58579	0.118024
$481$	11.0711	0.504797
$482$	1.95837	0.0892013
$483$	21.6569	0.985421
$484$	16.4558	0.747993
$485$	−0.201010	−0.00912740
$486$	−0.414214	−0.0187891
$487$	29.5563	1.33933	0.669663	−	0.742665i	$-0.266439\pi$
$487$	29.5563	1.33933	0.669663	+	0.742665i	$0.266439\pi$
$488$	−6.34315	−0.287141
$489$	5.65685	0.255812
$490$	−0.242641	−0.0109614
$491$	−18.3431	−0.827815	−0.413907	−	0.910319i	$-0.635836\pi$
$491$	−18.3431	−0.827815	−0.413907	+	0.910319i	$0.635836\pi$
$492$	2.14214	0.0965749
$493$	24.9706	1.12462
$494$	−2.34315	−0.105423
$495$	0.828427	0.0372350
$496$	−13.7574	−0.617724
$497$	−12.0000	−0.538274
$498$	0.343146	0.0153767
$499$	−3.41421	−0.152841	−0.0764206	−	0.997076i	$-0.524349\pi$
$499$	−3.41421	−0.152841	−0.0764206	+	0.997076i	$0.524349\pi$
$500$	−10.3431	−0.462560
$501$	−4.14214	−0.185057
$502$	3.11270	0.138927
$503$	−38.2843	−1.70701	−0.853506	−	0.521084i	$-0.825528\pi$
$503$	−38.2843	−1.70701	−0.853506	+	0.521084i	$0.825528\pi$
$504$	4.48528	0.199790
$505$	2.14214	0.0953238
$506$	−4.48528	−0.199395
$507$	−1.00000	−0.0444116
$508$	0	0
$509$	−29.4558	−1.30561	−0.652804	−	0.757527i	$-0.726407\pi$
$509$	−29.4558	−1.30561	−0.652804	+	0.757527i	$0.726407\pi$
$510$	1.65685	0.0733667
$511$	21.9411	0.970618
$512$	22.7574	1.00574
$513$	5.65685	0.249756
$514$	−1.23045	−0.0542727
$515$	−0.585786	−0.0258128
$516$	−5.17157	−0.227666
$517$	−10.0000	−0.439799
$518$	−12.9706	−0.569894
$519$	−13.7990	−0.605708
$520$	0.928932	0.0407364
$521$	−25.7990	−1.13027	−0.565137	−	0.824997i	$-0.691177\pi$
$521$	−25.7990	−1.13027	−0.565137	+	0.824997i	$0.691177\pi$
$522$	1.51472	0.0662974
$523$	0.142136	0.00621516	0.00310758	−	0.999995i	$-0.499011\pi$
$523$	0.142136	0.00621516	0.00310758	+	0.999995i	$0.499011\pi$
$524$	10.9706	0.479251
$525$	−13.1716	−0.574855
$526$	−2.82843	−0.123325
$527$	−31.3137	−1.36405
$528$	4.24264	0.184637
$529$	35.6274	1.54902
$530$	0.887302	0.0385419
$531$	−6.00000	−0.260378
$532$	−29.2548	−1.26836
$533$	1.17157	0.0507465
$534$	−2.38478	−0.103199
$535$	−1.37258	−0.0593419
$536$	7.27208	0.314106
$537$	9.31371	0.401916
$538$	−1.17157	−0.0505101
$539$	−1.41421	−0.0609145
$540$	−1.07107	−0.0460914
$541$	−25.1127	−1.07968	−0.539840	−	0.841768i	$-0.681515\pi$
$541$	−25.1127	−1.07968	−0.539840	+	0.841768i	$0.681515\pi$
$542$	−9.69848	−0.416586
$543$	−4.34315	−0.186382
$544$	30.1421	1.29233
$545$	−5.11270	−0.219004
$546$	1.17157	0.0501387
$547$	−12.8284	−0.548504	−0.274252	−	0.961658i	$-0.588430\pi$
$547$	−12.8284	−0.548504	−0.274252	+	0.961658i	$0.588430\pi$
$548$	14.6274	0.624852
$549$	4.00000	0.170716
$550$	2.72792	0.116319
$551$	−20.6863	−0.881266
$552$	12.1421	0.516804
$553$	18.3431	0.780030
$554$	3.65685	0.155365
$555$	6.48528	0.275285
$556$	14.8873	0.631362
$557$	−33.0711	−1.40127	−0.700633	−	0.713522i	$-0.747099\pi$
$557$	−33.0711	−1.40127	−0.700633	+	0.713522i	$0.747099\pi$
$558$	−1.89949	−0.0804120
$559$	−2.82843	−0.119630
$560$	4.97056	0.210045
$561$	9.65685	0.407713
$562$	−8.24264	−0.347695
$563$	−19.3137	−0.813976	−0.406988	−	0.913434i	$-0.633421\pi$
$563$	−19.3137	−0.813976	−0.406988	+	0.913434i	$0.633421\pi$
$564$	12.9289	0.544406
$565$	5.85786	0.246442
$566$	7.51472	0.315867
$567$	−2.82843	−0.118783
$568$	−6.72792	−0.282297
$569$	8.14214	0.341336	0.170668	−	0.985329i	$-0.445407\pi$
$569$	8.14214	0.341336	0.170668	+	0.985329i	$0.445407\pi$
$570$	−1.37258	−0.0574912
$571$	34.6274	1.44911	0.724556	−	0.689216i	$-0.242045\pi$
$571$	34.6274	1.44911	0.724556	+	0.689216i	$0.242045\pi$
$572$	2.58579	0.108117
$573$	8.97056	0.374751
$574$	−1.37258	−0.0572905
$575$	−35.6569	−1.48699
$576$	−4.17157	−0.173816
$577$	−18.3848	−0.765368	−0.382684	−	0.923879i	$-0.625000\pi$
$577$	−18.3848	−0.765368	−0.382684	+	0.923879i	$0.625000\pi$
$578$	12.2721	0.510451
$579$	16.7279	0.695189
$580$	3.91674	0.162634
$581$	2.34315	0.0972101
$582$	−0.142136	−0.00589171
$583$	5.17157	0.214185
$584$	12.3015	0.509040
$585$	−0.585786	−0.0242193
$586$	8.92893	0.368851
$587$	11.1716	0.461100	0.230550	−	0.973060i	$-0.425947\pi$
$587$	11.1716	0.461100	0.230550	+	0.973060i	$0.425947\pi$
$588$	1.82843	0.0754031
$589$	25.9411	1.06889
$590$	1.45584	0.0599362
$591$	11.8995	0.489480
$592$	33.2132	1.36505
$593$	−33.0711	−1.35807	−0.679033	−	0.734108i	$-0.737601\pi$
$593$	−33.0711	−1.35807	−0.679033	+	0.734108i	$0.737601\pi$
$594$	0.585786	0.0240351
$595$	11.3137	0.463817
$596$	7.31371	0.299581
$597$	4.00000	0.163709
$598$	3.17157	0.129695
$599$	27.1127	1.10779	0.553897	−	0.832585i	$-0.313140\pi$
$599$	27.1127	1.10779	0.553897	+	0.832585i	$0.313140\pi$
$600$	−7.38478	−0.301482
$601$	−17.3137	−0.706241	−0.353120	−	0.935578i	$-0.614879\pi$
$601$	−17.3137	−0.706241	−0.353120	+	0.935578i	$0.614879\pi$
$602$	3.31371	0.135057
$603$	−4.58579	−0.186748
$604$	41.5563	1.69090
$605$	5.27208	0.214340
$606$	1.51472	0.0615312
$607$	3.31371	0.134499	0.0672496	−	0.997736i	$-0.478578\pi$
$607$	3.31371	0.134499	0.0672496	+	0.997736i	$0.478578\pi$
$608$	−24.9706	−1.01269
$609$	10.3431	0.419125
$610$	−0.970563	−0.0392969
$611$	7.07107	0.286065
$612$	−12.4853	−0.504688
$613$	29.7990	1.20357	0.601785	−	0.798658i	$-0.294456\pi$
$613$	29.7990	1.20357	0.601785	+	0.798658i	$0.294456\pi$
$614$	−2.87006	−0.115826
$615$	0.686292	0.0276739
$616$	−6.34315	−0.255573
$617$	38.0416	1.53150	0.765749	−	0.643139i	$-0.222368\pi$
$617$	38.0416	1.53150	0.765749	+	0.643139i	$0.222368\pi$
$618$	−0.414214	−0.0166621
$619$	−38.8284	−1.56065	−0.780323	−	0.625377i	$-0.784945\pi$
$619$	−38.8284	−1.56065	−0.780323	+	0.625377i	$0.784945\pi$
$620$	−4.91169	−0.197258
$621$	−7.65685	−0.307259
$622$	−13.9411	−0.558988
$623$	−16.2843	−0.652416
$624$	−3.00000	−0.120096
$625$	19.9706	0.798823
$626$	12.1421	0.485297
$627$	−8.00000	−0.319489
$628$	−22.2010	−0.885917
$629$	75.5980	3.01429
$630$	0.686292	0.0273425
$631$	−11.5147	−0.458394	−0.229197	−	0.973380i	$-0.573610\pi$
$631$	−11.5147	−0.458394	−0.229197	+	0.973380i	$0.573610\pi$
$632$	10.2843	0.409086
$633$	−5.17157	−0.205552
$634$	10.5442	0.418762
$635$	0	0
$636$	−6.68629	−0.265129
$637$	1.00000	0.0396214
$638$	−2.14214	−0.0848080
$639$	4.24264	0.167836
$640$	6.18377	0.244435
$641$	−41.3137	−1.63179	−0.815897	−	0.578198i	$-0.803756\pi$
$641$	−41.3137	−1.63179	−0.815897	+	0.578198i	$0.803756\pi$
$642$	−0.970563	−0.0383051
$643$	33.4558	1.31937	0.659685	−	0.751542i	$-0.270690\pi$
$643$	33.4558	1.31937	0.659685	+	0.751542i	$0.270690\pi$
$644$	39.5980	1.56038
$645$	−1.65685	−0.0652386
$646$	−16.0000	−0.629512
$647$	0	0		−	1.00000i	$-0.5\pi$
$647$	0	0			1.00000i	$0.5\pi$
$648$	−1.58579	−0.0622956
$649$	8.48528	0.333076
$650$	−1.92893	−0.0756589
$651$	−12.9706	−0.508356
$652$	10.3431	0.405069
$653$	−11.1716	−0.437177	−0.218589	−	0.975817i	$-0.570145\pi$
$653$	−11.1716	−0.437177	−0.218589	+	0.975817i	$0.570145\pi$
$654$	−3.61522	−0.141366
$655$	3.51472	0.137331
$656$	3.51472	0.137227
$657$	−7.75736	−0.302643
$658$	−8.28427	−0.322955
$659$	−8.62742	−0.336076	−0.168038	−	0.985780i	$-0.553743\pi$
$659$	−8.62742	−0.336076	−0.168038	+	0.985780i	$0.553743\pi$
$660$	1.51472	0.0589603
$661$	23.0711	0.897361	0.448680	−	0.893692i	$-0.351894\pi$
$661$	23.0711	0.897361	0.448680	+	0.893692i	$0.351894\pi$
$662$	−3.75736	−0.146034
$663$	−6.82843	−0.265194
$664$	1.31371	0.0509818
$665$	−9.37258	−0.363453
$666$	4.58579	0.177696
$667$	28.0000	1.08416
$668$	−7.57359	−0.293031
$669$	0	0
$670$	1.11270	0.0429873
$671$	−5.65685	−0.218380
$672$	12.4853	0.481630
$673$	41.3137	1.59253	0.796263	−	0.604950i	$-0.206807\pi$
$673$	41.3137	1.59253	0.796263	+	0.604950i	$0.206807\pi$
$674$	−13.5147	−0.520568
$675$	4.65685	0.179242
$676$	−1.82843	−0.0703241
$677$	2.68629	0.103243	0.0516213	−	0.998667i	$-0.483561\pi$
$677$	2.68629	0.103243	0.0516213	+	0.998667i	$0.483561\pi$
$678$	4.14214	0.159078
$679$	−0.970563	−0.0372468
$680$	6.34315	0.243249
$681$	7.75736	0.297263
$682$	2.68629	0.102863
$683$	−17.6985	−0.677214	−0.338607	−	0.940928i	$-0.609956\pi$
$683$	−17.6985	−0.677214	−0.338607	+	0.940928i	$0.609956\pi$
$684$	10.3431	0.395480
$685$	4.68629	0.179054
$686$	7.02944	0.268385
$687$	29.3137	1.11839
$688$	−8.48528	−0.323498
$689$	−3.65685	−0.139315
$690$	1.85786	0.0707277
$691$	−8.87006	−0.337433	−0.168716	−	0.985665i	$-0.553962\pi$
$691$	−8.87006	−0.337433	−0.168716	+	0.985665i	$0.553962\pi$
$692$	−25.2304	−0.959118
$693$	4.00000	0.151947
$694$	11.5980	0.440253
$695$	4.76955	0.180919
$696$	5.79899	0.219810
$697$	8.00000	0.303022
$698$	−9.47309	−0.358562
$699$	−16.6274	−0.628907
$700$	−24.0833	−0.910262
$701$	35.1127	1.32619	0.663094	−	0.748536i	$-0.269243\pi$
$701$	35.1127	1.32619	0.663094	+	0.748536i	$0.269243\pi$
$702$	−0.414214	−0.0156335
$703$	−62.6274	−2.36204
$704$	5.89949	0.222346
$705$	4.14214	0.156002
$706$	−12.0416	−0.453193
$707$	10.3431	0.388994
$708$	−10.9706	−0.412299
$709$	30.0000	1.12667	0.563337	−	0.826227i	$-0.309517\pi$
$709$	30.0000	1.12667	0.563337	+	0.826227i	$0.309517\pi$
$710$	−1.02944	−0.0386341
$711$	−6.48528	−0.243217
$712$	−9.12994	−0.342159
$713$	−35.1127	−1.31498
$714$	8.00000	0.299392
$715$	0.828427	0.0309814
$716$	17.0294	0.636420
$717$	−23.6569	−0.883481
$718$	2.28427	0.0852482
$719$	43.7990	1.63343	0.816713	−	0.577044i	$-0.195794\pi$
$719$	43.7990	1.63343	0.816713	+	0.577044i	$0.195794\pi$
$720$	−1.75736	−0.0654929
$721$	−2.82843	−0.105336
$722$	5.38478	0.200401
$723$	−4.72792	−0.175833
$724$	−7.94113	−0.295130
$725$	−17.0294	−0.632457
$726$	3.72792	0.138356
$727$	−52.9706	−1.96457	−0.982285	−	0.187395i	$-0.939996\pi$
$727$	−52.9706	−1.96457	−0.982285	+	0.187395i	$0.939996\pi$
$728$	4.48528	0.166236
$729$	1.00000	0.0370370
$730$	1.88225	0.0696652
$731$	−19.3137	−0.714343
$732$	7.31371	0.270322
$733$	−53.2132	−1.96547	−0.982737	−	0.185007i	$-0.940769\pi$
$733$	−53.2132	−1.96547	−0.982737	+	0.185007i	$0.940769\pi$
$734$	−8.62742	−0.318444
$735$	0.585786	0.0216071
$736$	33.7990	1.24585
$737$	6.48528	0.238888
$738$	0.485281	0.0178635
$739$	34.6274	1.27379	0.636895	−	0.770951i	$-0.280218\pi$
$739$	34.6274	1.27379	0.636895	+	0.770951i	$0.280218\pi$
$740$	11.8579	0.435904
$741$	5.65685	0.207810
$742$	4.28427	0.157281
$743$	−29.8995	−1.09691	−0.548453	−	0.836181i	$-0.684783\pi$
$743$	−29.8995	−1.09691	−0.548453	+	0.836181i	$0.684783\pi$
$744$	−7.27208	−0.266607
$745$	2.34315	0.0858462
$746$	−4.00000	−0.146450
$747$	−0.828427	−0.0303106
$748$	17.6569	0.645599
$749$	−6.62742	−0.242161
$750$	−2.34315	−0.0855596
$751$	3.17157	0.115732	0.0578662	−	0.998324i	$-0.481570\pi$
$751$	3.17157	0.115732	0.0578662	+	0.998324i	$0.481570\pi$
$752$	21.2132	0.773566
$753$	−7.51472	−0.273852
$754$	1.51472	0.0551628
$755$	13.3137	0.484535
$756$	−5.17157	−0.188088
$757$	−23.6569	−0.859823	−0.429911	−	0.902871i	$-0.641455\pi$
$757$	−23.6569	−0.859823	−0.429911	+	0.902871i	$0.641455\pi$
$758$	−3.07107	−0.111546
$759$	10.8284	0.393047
$760$	−5.25483	−0.190613
$761$	−8.58579	−0.311235	−0.155617	−	0.987817i	$-0.549737\pi$
$761$	−8.58579	−0.311235	−0.155617	+	0.987817i	$0.549737\pi$
$762$	0	0
$763$	−24.6863	−0.893704
$764$	16.4020	0.593404
$765$	−4.00000	−0.144620
$766$	−2.24264	−0.0810299
$767$	−6.00000	−0.216647
$768$	−3.97056	−0.143275
$769$	2.58579	0.0932458	0.0466229	−	0.998913i	$-0.485154\pi$
$769$	2.58579	0.0932458	0.0466229	+	0.998913i	$0.485154\pi$
$770$	−0.970563	−0.0349767
$771$	2.97056	0.106982
$772$	30.5858	1.10081
$773$	−12.0000	−0.431610	−0.215805	−	0.976436i	$-0.569238\pi$
$773$	−12.0000	−0.431610	−0.215805	+	0.976436i	$0.569238\pi$
$774$	−1.17157	−0.0421113
$775$	21.3553	0.767106
$776$	−0.544156	−0.0195341
$777$	31.3137	1.12337
$778$	−2.68629	−0.0963082
$779$	−6.62742	−0.237452
$780$	−1.07107	−0.0383504
$781$	−6.00000	−0.214697
$782$	21.6569	0.774448
$783$	−3.65685	−0.130685
$784$	3.00000	0.107143
$785$	−7.11270	−0.253863
$786$	2.48528	0.0886471
$787$	−21.6569	−0.771983	−0.385992	−	0.922502i	$-0.626141\pi$
$787$	−21.6569	−0.771983	−0.385992	+	0.922502i	$0.626141\pi$
$788$	21.7574	0.775074
$789$	6.82843	0.243098
$790$	1.57359	0.0559859
$791$	28.2843	1.00567
$792$	2.24264	0.0796888
$793$	4.00000	0.142044
$794$	11.1299	0.394987
$795$	−2.14214	−0.0759737
$796$	7.31371	0.259228
$797$	41.3137	1.46341	0.731703	−	0.681623i	$-0.238726\pi$
$797$	41.3137	1.46341	0.731703	+	0.681623i	$0.238726\pi$
$798$	−6.62742	−0.234608
$799$	48.2843	1.70817
$800$	−20.5563	−0.726777
$801$	5.75736	0.203426
$802$	−12.7696	−0.450909
$803$	10.9706	0.387143
$804$	−8.38478	−0.295708
$805$	12.6863	0.447133
$806$	−1.89949	−0.0669069
$807$	2.82843	0.0995654
$808$	5.79899	0.204008
$809$	36.1421	1.27069	0.635345	−	0.772228i	$-0.280858\pi$
$809$	36.1421	1.27069	0.635345	+	0.772228i	$0.280858\pi$
$810$	−0.242641	−0.00852552
$811$	18.9289	0.664685	0.332342	−	0.943159i	$-0.392161\pi$
$811$	18.9289	0.664685	0.332342	+	0.943159i	$0.392161\pi$
$812$	18.9117	0.663670
$813$	23.4142	0.821172
$814$	−6.48528	−0.227309
$815$	3.31371	0.116074
$816$	−20.4853	−0.717128
$817$	16.0000	0.559769
$818$	8.62742	0.301651
$819$	−2.82843	−0.0988332
$820$	1.25483	0.0438207
$821$	15.3137	0.534452	0.267226	−	0.963634i	$-0.413893\pi$
$821$	15.3137	0.534452	0.267226	+	0.963634i	$0.413893\pi$
$822$	3.31371	0.115579
$823$	−27.5147	−0.959103	−0.479551	−	0.877514i	$-0.659201\pi$
$823$	−27.5147	−0.959103	−0.479551	+	0.877514i	$0.659201\pi$
$824$	−1.58579	−0.0552435
$825$	−6.58579	−0.229288
$826$	7.02944	0.244585
$827$	−32.5269	−1.13107	−0.565536	−	0.824724i	$-0.691331\pi$
$827$	−32.5269	−1.13107	−0.565536	+	0.824724i	$0.691331\pi$
$828$	−14.0000	−0.486534
$829$	24.6274	0.855346	0.427673	−	0.903934i	$-0.359334\pi$
$829$	24.6274	0.855346	0.427673	+	0.903934i	$0.359334\pi$
$830$	0.201010	0.00697716
$831$	−8.82843	−0.306255
$832$	−4.17157	−0.144623
$833$	6.82843	0.236591
$834$	3.37258	0.116783
$835$	−2.42641	−0.0839693
$836$	−14.6274	−0.505900
$837$	4.58579	0.158508
$838$	−7.59798	−0.262468
$839$	0.343146	0.0118467	0.00592335	−	0.999982i	$-0.498115\pi$
$839$	0.343146	0.0118467	0.00592335	+	0.999982i	$0.498115\pi$
$840$	2.62742	0.0906545
$841$	−15.6274	−0.538876
$842$	2.68629	0.0925757
$843$	19.8995	0.685375
$844$	−9.45584	−0.325484
$845$	−0.585786	−0.0201517
$846$	2.92893	0.100699
$847$	25.4558	0.874673
$848$	−10.9706	−0.376731
$849$	−18.1421	−0.622636
$850$	−13.1716	−0.451781
$851$	84.7696	2.90586
$852$	7.75736	0.265763
$853$	9.02944	0.309162	0.154581	−	0.987980i	$-0.450597\pi$
$853$	9.02944	0.309162	0.154581	+	0.987980i	$0.450597\pi$
$854$	−4.68629	−0.160362
$855$	3.31371	0.113326
$856$	−3.71573	−0.127001
$857$	−16.4853	−0.563126	−0.281563	−	0.959543i	$-0.590853\pi$
$857$	−16.4853	−0.563126	−0.281563	+	0.959543i	$0.590853\pi$
$858$	0.585786	0.0199984
$859$	−12.4853	−0.425992	−0.212996	−	0.977053i	$-0.568322\pi$
$859$	−12.4853	−0.425992	−0.212996	+	0.977053i	$0.568322\pi$
$860$	−3.02944	−0.103303
$861$	3.31371	0.112931
$862$	−5.59798	−0.190668
$863$	−16.4437	−0.559748	−0.279874	−	0.960037i	$-0.590293\pi$
$863$	−16.4437	−0.559748	−0.279874	+	0.960037i	$0.590293\pi$
$864$	−4.41421	−0.150175
$865$	−8.08326	−0.274839
$866$	3.17157	0.107774
$867$	−29.6274	−1.00620
$868$	−23.7157	−0.804964
$869$	9.17157	0.311124
$870$	0.887302	0.0300823
$871$	−4.58579	−0.155383
$872$	−13.8406	−0.468703
$873$	0.343146	0.0116137
$874$	−17.9411	−0.606868
$875$	−16.0000	−0.540899
$876$	−14.1838	−0.479225
$877$	−17.2132	−0.581249	−0.290624	−	0.956837i	$-0.593863\pi$
$877$	−17.2132	−0.581249	−0.290624	+	0.956837i	$0.593863\pi$
$878$	10.5442	0.355848
$879$	−21.5563	−0.727078
$880$	2.48528	0.0837788
$881$	17.5147	0.590086	0.295043	−	0.955484i	$-0.404666\pi$
$881$	17.5147	0.590086	0.295043	+	0.955484i	$0.404666\pi$
$882$	0.414214	0.0139473
$883$	−53.1127	−1.78738	−0.893692	−	0.448680i	$-0.851894\pi$
$883$	−53.1127	−1.78738	−0.893692	+	0.448680i	$0.851894\pi$
$884$	−12.4853	−0.419925
$885$	−3.51472	−0.118146
$886$	1.17157	0.0393598
$887$	44.2843	1.48692	0.743460	−	0.668780i	$-0.233183\pi$
$887$	44.2843	1.48692	0.743460	+	0.668780i	$0.233183\pi$
$888$	17.5563	0.589153
$889$	0	0
$890$	−1.39697	−0.0468265
$891$	−1.41421	−0.0473779
$892$	0	0
$893$	−40.0000	−1.33855
$894$	1.65685	0.0554135
$895$	5.45584	0.182369
$896$	29.8579	0.997481
$897$	−7.65685	−0.255655
$898$	−13.2132	−0.440930
$899$	−16.7696	−0.559296
$900$	8.51472	0.283824
$901$	−24.9706	−0.831890
$902$	−0.686292	−0.0228510
$903$	−8.00000	−0.266223
$904$	15.8579	0.527425
$905$	−2.54416	−0.0845706
$906$	9.41421	0.312766
$907$	47.3137	1.57103	0.785513	−	0.618845i	$-0.212399\pi$
$907$	47.3137	1.57103	0.785513	+	0.618845i	$0.212399\pi$
$908$	14.1838	0.470705
$909$	−3.65685	−0.121290
$910$	0.686292	0.0227503
$911$	−2.62742	−0.0870502	−0.0435251	−	0.999052i	$-0.513859\pi$
$911$	−2.62742	−0.0870502	−0.0435251	+	0.999052i	$0.513859\pi$
$912$	16.9706	0.561951
$913$	1.17157	0.0387734
$914$	−11.0122	−0.364251
$915$	2.34315	0.0774620
$916$	53.5980	1.77093
$917$	16.9706	0.560417
$918$	−2.82843	−0.0933520
$919$	46.8284	1.54473	0.772364	−	0.635181i	$-0.219074\pi$
$919$	46.8284	1.54473	0.772364	+	0.635181i	$0.219074\pi$
$920$	7.11270	0.234499
$921$	6.92893	0.228316
$922$	12.4020	0.408439
$923$	4.24264	0.139648
$924$	7.31371	0.240603
$925$	−51.5563	−1.69516
$926$	−4.04163	−0.132816
$927$	1.00000	0.0328443
$928$	16.1421	0.529892
$929$	−16.2843	−0.534270	−0.267135	−	0.963659i	$-0.586077\pi$
$929$	−16.2843	−0.534270	−0.267135	+	0.963659i	$0.586077\pi$
$930$	−1.11270	−0.0364868
$931$	−5.65685	−0.185396
$932$	−30.4020	−0.995851
$933$	33.6569	1.10188
$934$	14.6274	0.478624
$935$	5.65685	0.184999
$936$	−1.58579	−0.0518331
$937$	36.1421	1.18071	0.590356	−	0.807143i	$-0.298987\pi$
$937$	36.1421	1.18071	0.590356	+	0.807143i	$0.298987\pi$
$938$	5.37258	0.175421
$939$	−29.3137	−0.956617
$940$	7.57359	0.247023
$941$	−23.3137	−0.760005	−0.380003	−	0.924985i	$-0.624077\pi$
$941$	−23.3137	−0.760005	−0.380003	+	0.924985i	$0.624077\pi$
$942$	−5.02944	−0.163868
$943$	8.97056	0.292122
$944$	−18.0000	−0.585850
$945$	−1.65685	−0.0538975
$946$	1.65685	0.0538690
$947$	−1.61522	−0.0524877	−0.0262439	−	0.999656i	$-0.508355\pi$
$947$	−1.61522	−0.0524877	−0.0262439	+	0.999656i	$0.508355\pi$
$948$	−11.8579	−0.385126
$949$	−7.75736	−0.251815
$950$	10.9117	0.354022
$951$	−25.4558	−0.825462
$952$	30.6274	0.992640
$953$	−30.1421	−0.976400	−0.488200	−	0.872732i	$-0.662346\pi$
$953$	−30.1421	−0.976400	−0.488200	+	0.872732i	$0.662346\pi$
$954$	−1.51472	−0.0490408
$955$	5.25483	0.170042
$956$	−43.2548	−1.39896
$957$	5.17157	0.167173
$958$	−1.07107	−0.0346046
$959$	22.6274	0.730677
$960$	−2.44365	−0.0788685
$961$	−9.97056	−0.321631
$962$	4.58579	0.147852
$963$	2.34315	0.0755068
$964$	−8.64466	−0.278426
$965$	9.79899	0.315441
$966$	8.97056	0.288623
$967$	−17.2721	−0.555433	−0.277716	−	0.960663i	$-0.589578\pi$
$967$	−17.2721	−0.555433	−0.277716	+	0.960663i	$0.589578\pi$
$968$	14.2721	0.458722
$969$	38.6274	1.24089
$970$	−0.0832611	−0.00267335
$971$	−32.2843	−1.03605	−0.518026	−	0.855365i	$-0.673333\pi$
$971$	−32.2843	−1.03605	−0.518026	+	0.855365i	$0.673333\pi$
$972$	1.82843	0.0586468
$973$	23.0294	0.738290
$974$	12.2426	0.392280
$975$	4.65685	0.149139
$976$	12.0000	0.384111
$977$	−13.8579	−0.443352	−0.221676	−	0.975120i	$-0.571153\pi$
$977$	−13.8579	−0.443352	−0.221676	+	0.975120i	$0.571153\pi$
$978$	2.34315	0.0749255
$979$	−8.14214	−0.260224
$980$	1.07107	0.0342140
$981$	8.72792	0.278661
$982$	−7.59798	−0.242461
$983$	−47.4558	−1.51361	−0.756803	−	0.653643i	$-0.773240\pi$
$983$	−47.4558	−1.51361	−0.756803	+	0.653643i	$0.773240\pi$
$984$	1.85786	0.0592266
$985$	6.97056	0.222101
$986$	10.3431	0.329393
$987$	20.0000	0.636607
$988$	10.3431	0.329059
$989$	−21.6569	−0.688648
$990$	0.343146	0.0109059
$991$	3.17157	0.100748	0.0503742	−	0.998730i	$-0.483959\pi$
$991$	3.17157	0.100748	0.0503742	+	0.998730i	$0.483959\pi$
$992$	−20.2426	−0.642704
$993$	9.07107	0.287862
$994$	−4.97056	−0.157657
$995$	2.34315	0.0742827
$996$	−1.51472	−0.0479957
$997$	−24.3431	−0.770955	−0.385478	−	0.922717i	$-0.625963\pi$
$997$	−24.3431	−0.770955	−0.385478	+	0.922717i	$0.625963\pi$
$998$	−1.41421	−0.0447661
$999$	−11.0711	−0.350273

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.d.1.2	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.d.1.2	✓	2	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:	\( N \)	\(=\)	\( 4017 = 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4017.a (trivial)

\(f(q)\)	\(=\)	\(q+0.414214 q^{2} -1.00000 q^{3} -1.82843 q^{4} -0.585786 q^{5} -0.414214 q^{6} -2.82843 q^{7} -1.58579 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.414214 q^{2} -1.00000 q^{3} -1.82843 q^{4} -0.585786 q^{5} -0.414214 q^{6} -2.82843 q^{7} -1.58579 q^{8} +1.00000 q^{9} -0.242641 q^{10} -1.41421 q^{11} +1.82843 q^{12} +1.00000 q^{13} -1.17157 q^{14} +0.585786 q^{15} +3.00000 q^{16} +6.82843 q^{17} +0.414214 q^{18} -5.65685 q^{19} +1.07107 q^{20} +2.82843 q^{21} -0.585786 q^{22} +7.65685 q^{23} +1.58579 q^{24} -4.65685 q^{25} +0.414214 q^{26} -1.00000 q^{27} +5.17157 q^{28} +3.65685 q^{29} +0.242641 q^{30} -4.58579 q^{31} +4.41421 q^{32} +1.41421 q^{33} +2.82843 q^{34} +1.65685 q^{35} -1.82843 q^{36} +11.0711 q^{37} -2.34315 q^{38} -1.00000 q^{39} +0.928932 q^{40} +1.17157 q^{41} +1.17157 q^{42} -2.82843 q^{43} +2.58579 q^{44} -0.585786 q^{45} +3.17157 q^{46} +7.07107 q^{47} -3.00000 q^{48} +1.00000 q^{49} -1.92893 q^{50} -6.82843 q^{51} -1.82843 q^{52} -3.65685 q^{53} -0.414214 q^{54} +0.828427 q^{55} +4.48528 q^{56} +5.65685 q^{57} +1.51472 q^{58} -6.00000 q^{59} -1.07107 q^{60} +4.00000 q^{61} -1.89949 q^{62} -2.82843 q^{63} -4.17157 q^{64} -0.585786 q^{65} +0.585786 q^{66} -4.58579 q^{67} -12.4853 q^{68} -7.65685 q^{69} +0.686292 q^{70} +4.24264 q^{71} -1.58579 q^{72} -7.75736 q^{73} +4.58579 q^{74} +4.65685 q^{75} +10.3431 q^{76} +4.00000 q^{77} -0.414214 q^{78} -6.48528 q^{79} -1.75736 q^{80} +1.00000 q^{81} +0.485281 q^{82} -0.828427 q^{83} -5.17157 q^{84} -4.00000 q^{85} -1.17157 q^{86} -3.65685 q^{87} +2.24264 q^{88} +5.75736 q^{89} -0.242641 q^{90} -2.82843 q^{91} -14.0000 q^{92} +4.58579 q^{93} +2.92893 q^{94} +3.31371 q^{95} -4.41421 q^{96} +0.343146 q^{97} +0.414214 q^{98} -1.41421 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} - 4 q^{5} + 2 q^{6} - 6 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 - 4 * q^5 + 2 * q^6 - 6 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} - 4 q^{5} + 2 q^{6} - 6 q^{8} + 2 q^{9} + 8 q^{10} - 2 q^{12} + 2 q^{13} - 8 q^{14} + 4 q^{15} + 6 q^{16} + 8 q^{17} - 2 q^{18} - 12 q^{20} - 4 q^{22} + 4 q^{23} + 6 q^{24} + 2 q^{25} - 2 q^{26} - 2 q^{27} + 16 q^{28} - 4 q^{29} - 8 q^{30} - 12 q^{31} + 6 q^{32} - 8 q^{35} + 2 q^{36} + 8 q^{37} - 16 q^{38} - 2 q^{39} + 16 q^{40} + 8 q^{41} + 8 q^{42} + 8 q^{44} - 4 q^{45} + 12 q^{46} - 6 q^{48} + 2 q^{49} - 18 q^{50} - 8 q^{51} + 2 q^{52} + 4 q^{53} + 2 q^{54} - 4 q^{55} - 8 q^{56} + 20 q^{58} - 12 q^{59} + 12 q^{60} + 8 q^{61} + 16 q^{62} - 14 q^{64} - 4 q^{65} + 4 q^{66} - 12 q^{67} - 8 q^{68} - 4 q^{69} + 24 q^{70} - 6 q^{72} - 24 q^{73} + 12 q^{74} - 2 q^{75} + 32 q^{76} + 8 q^{77} + 2 q^{78} + 4 q^{79} - 12 q^{80} + 2 q^{81} - 16 q^{82} + 4 q^{83} - 16 q^{84} - 8 q^{85} - 8 q^{86} + 4 q^{87} - 4 q^{88} + 20 q^{89} + 8 q^{90} - 28 q^{92} + 12 q^{93} + 20 q^{94} - 16 q^{95} - 6 q^{96} + 12 q^{97} - 2 q^{98}+O(q^{100}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 - 4 * q^5 + 2 * q^6 - 6 * q^8 + 2 * q^9 + 8 * q^10 - 2 * q^12 + 2 * q^13 - 8 * q^14 + 4 * q^15 + 6 * q^16 + 8 * q^17 - 2 * q^18 - 12 * q^20 - 4 * q^22 + 4 * q^23 + 6 * q^24 + 2 * q^25 - 2 * q^26 - 2 * q^27 + 16 * q^28 - 4 * q^29 - 8 * q^30 - 12 * q^31 + 6 * q^32 - 8 * q^35 + 2 * q^36 + 8 * q^37 - 16 * q^38 - 2 * q^39 + 16 * q^40 + 8 * q^41 + 8 * q^42 + 8 * q^44 - 4 * q^45 + 12 * q^46 - 6 * q^48 + 2 * q^49 - 18 * q^50 - 8 * q^51 + 2 * q^52 + 4 * q^53 + 2 * q^54 - 4 * q^55 - 8 * q^56 + 20 * q^58 - 12 * q^59 + 12 * q^60 + 8 * q^61 + 16 * q^62 - 14 * q^64 - 4 * q^65 + 4 * q^66 - 12 * q^67 - 8 * q^68 - 4 * q^69 + 24 * q^70 - 6 * q^72 - 24 * q^73 + 12 * q^74 - 2 * q^75 + 32 * q^76 + 8 * q^77 + 2 * q^78 + 4 * q^79 - 12 * q^80 + 2 * q^81 - 16 * q^82 + 4 * q^83 - 16 * q^84 - 8 * q^85 - 8 * q^86 + 4 * q^87 - 4 * q^88 + 20 * q^89 + 8 * q^90 - 28 * q^92 + 12 * q^93 + 20 * q^94 - 16 * q^95 - 6 * q^96 + 12 * q^97 - 2 * q^98

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