LMFDB - Embedded newform 6015.2.a.c.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6015,2,Mod(1,6015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6015, 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("6015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6015 = 3 \cdot 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6015.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.0300168158$
Analytic rank:	$1$
Dimension:	$28$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	6015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.711184 q^{2} +1.00000 q^{3} -1.49422 q^{4} -1.00000 q^{5} -0.711184 q^{6} -4.85706 q^{7} +2.48503 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.711184 q^{2} +1.00000 q^{3} -1.49422 q^{4} -1.00000 q^{5} -0.711184 q^{6} -4.85706 q^{7} +2.48503 q^{8} +1.00000 q^{9} +0.711184 q^{10} -3.28142 q^{11} -1.49422 q^{12} -1.86197 q^{13} +3.45426 q^{14} -1.00000 q^{15} +1.22112 q^{16} +1.26562 q^{17} -0.711184 q^{18} +4.69828 q^{19} +1.49422 q^{20} -4.85706 q^{21} +2.33369 q^{22} -2.57737 q^{23} +2.48503 q^{24} +1.00000 q^{25} +1.32420 q^{26} +1.00000 q^{27} +7.25751 q^{28} +9.18011 q^{29} +0.711184 q^{30} +7.41722 q^{31} -5.83850 q^{32} -3.28142 q^{33} -0.900089 q^{34} +4.85706 q^{35} -1.49422 q^{36} -2.72888 q^{37} -3.34134 q^{38} -1.86197 q^{39} -2.48503 q^{40} +10.0728 q^{41} +3.45426 q^{42} -12.0825 q^{43} +4.90315 q^{44} -1.00000 q^{45} +1.83298 q^{46} -0.989041 q^{47} +1.22112 q^{48} +16.5911 q^{49} -0.711184 q^{50} +1.26562 q^{51} +2.78219 q^{52} -4.37856 q^{53} -0.711184 q^{54} +3.28142 q^{55} -12.0699 q^{56} +4.69828 q^{57} -6.52874 q^{58} -2.62566 q^{59} +1.49422 q^{60} +9.39258 q^{61} -5.27501 q^{62} -4.85706 q^{63} +1.71000 q^{64} +1.86197 q^{65} +2.33369 q^{66} +15.3509 q^{67} -1.89111 q^{68} -2.57737 q^{69} -3.45426 q^{70} -3.43993 q^{71} +2.48503 q^{72} -11.6203 q^{73} +1.94073 q^{74} +1.00000 q^{75} -7.02025 q^{76} +15.9381 q^{77} +1.32420 q^{78} +2.32466 q^{79} -1.22112 q^{80} +1.00000 q^{81} -7.16359 q^{82} +11.2486 q^{83} +7.25751 q^{84} -1.26562 q^{85} +8.59286 q^{86} +9.18011 q^{87} -8.15442 q^{88} -5.68101 q^{89} +0.711184 q^{90} +9.04369 q^{91} +3.85115 q^{92} +7.41722 q^{93} +0.703390 q^{94} -4.69828 q^{95} -5.83850 q^{96} -4.91197 q^{97} -11.7993 q^{98} -3.28142 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - q^{2} + 28 q^{3} + 21 q^{4} - 28 q^{5} - q^{6} - 20 q^{7} + 28 q^{9}+O(q^{10}) $ 28 * q - q^2 + 28 * q^3 + 21 * q^4 - 28 * q^5 - q^6 - 20 * q^7 + 28 * q^9	\( 28 q - q^{2} + 28 q^{3} + 21 q^{4} - 28 q^{5} - q^{6} - 20 q^{7} + 28 q^{9} + q^{10} - q^{11} + 21 q^{12} - 18 q^{13} - 4 q^{14} - 28 q^{15} - q^{16} - 28 q^{17} - q^{18} - 19 q^{19} - 21 q^{20} - 20 q^{21} - 35 q^{22} + 2 q^{23} + 28 q^{25} - 20 q^{26} + 28 q^{27} - 54 q^{28} + 9 q^{29} + q^{30} - 19 q^{31} - 6 q^{32} - q^{33} - 16 q^{34} + 20 q^{35} + 21 q^{36} - 32 q^{37} - 2 q^{38} - 18 q^{39} - 27 q^{41} - 4 q^{42} - 77 q^{43} + q^{44} - 28 q^{45} - 19 q^{46} + 10 q^{47} - q^{48} - 4 q^{49} - q^{50} - 28 q^{51} - 34 q^{52} - 21 q^{53} - q^{54} + q^{55} - 9 q^{56} - 19 q^{57} - 46 q^{58} - 7 q^{59} - 21 q^{60} - 31 q^{61} - 7 q^{62} - 20 q^{63} - 46 q^{64} + 18 q^{65} - 35 q^{66} - 50 q^{67} - 68 q^{68} + 2 q^{69} + 4 q^{70} - 4 q^{71} - 87 q^{73} + 4 q^{74} + 28 q^{75} - 40 q^{76} - 8 q^{77} - 20 q^{78} - 65 q^{79} + q^{80} + 28 q^{81} - 41 q^{82} + 13 q^{83} - 54 q^{84} + 28 q^{85} - 17 q^{86} + 9 q^{87} - 117 q^{88} - 33 q^{89} + q^{90} - 33 q^{91} + 3 q^{92} - 19 q^{93} - 60 q^{94} + 19 q^{95} - 6 q^{96} - 75 q^{97} - 18 q^{98} - q^{99}+O(q^{100}) \) 28 * q - q^2 + 28 * q^3 + 21 * q^4 - 28 * q^5 - q^6 - 20 * q^7 + 28 * q^9 + q^10 - q^11 + 21 * q^12 - 18 * q^13 - 4 * q^14 - 28 * q^15 - q^16 - 28 * q^17 - q^18 - 19 * q^19 - 21 * q^20 - 20 * q^21 - 35 * q^22 + 2 * q^23 + 28 * q^25 - 20 * q^26 + 28 * q^27 - 54 * q^28 + 9 * q^29 + q^30 - 19 * q^31 - 6 * q^32 - q^33 - 16 * q^34 + 20 * q^35 + 21 * q^36 - 32 * q^37 - 2 * q^38 - 18 * q^39 - 27 * q^41 - 4 * q^42 - 77 * q^43 + q^44 - 28 * q^45 - 19 * q^46 + 10 * q^47 - q^48 - 4 * q^49 - q^50 - 28 * q^51 - 34 * q^52 - 21 * q^53 - q^54 + q^55 - 9 * q^56 - 19 * q^57 - 46 * q^58 - 7 * q^59 - 21 * q^60 - 31 * q^61 - 7 * q^62 - 20 * q^63 - 46 * q^64 + 18 * q^65 - 35 * q^66 - 50 * q^67 - 68 * q^68 + 2 * q^69 + 4 * q^70 - 4 * q^71 - 87 * q^73 + 4 * q^74 + 28 * q^75 - 40 * q^76 - 8 * q^77 - 20 * q^78 - 65 * q^79 + q^80 + 28 * q^81 - 41 * q^82 + 13 * q^83 - 54 * q^84 + 28 * q^85 - 17 * q^86 + 9 * q^87 - 117 * q^88 - 33 * q^89 + q^90 - 33 * q^91 + 3 * q^92 - 19 * q^93 - 60 * q^94 + 19 * q^95 - 6 * q^96 - 75 * q^97 - 18 * q^98 - 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 $

$2$	−0.711184	−0.502883	−0.251441	−	0.967873i	$-0.580905\pi$
$2$	−0.711184	−0.502883	−0.251441	+	0.967873i	$0.580905\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.49422	−0.747109
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.711184	−0.290339
$7$	−4.85706	−1.83580	−0.917899	−	0.396815i	$-0.870115\pi$
$7$	−4.85706	−1.83580	−0.917899	+	0.396815i	$0.870115\pi$
$8$	2.48503	0.878591
$9$	1.00000	0.333333
$10$	0.711184	0.224896
$11$	−3.28142	−0.989385	−0.494692	−	0.869068i	$-0.664719\pi$
$11$	−3.28142	−0.989385	−0.494692	+	0.869068i	$0.664719\pi$
$12$	−1.49422	−0.431344
$13$	−1.86197	−0.516417	−0.258208	−	0.966089i	$-0.583132\pi$
$13$	−1.86197	−0.516417	−0.258208	+	0.966089i	$0.583132\pi$
$14$	3.45426	0.923191
$15$	−1.00000	−0.258199
$16$	1.22112	0.305281
$17$	1.26562	0.306958	0.153479	−	0.988152i	$-0.450952\pi$
$17$	1.26562	0.306958	0.153479	+	0.988152i	$0.450952\pi$
$18$	−0.711184	−0.167628
$19$	4.69828	1.07786	0.538929	−	0.842351i	$-0.318829\pi$
$19$	4.69828	1.07786	0.538929	+	0.842351i	$0.318829\pi$
$20$	1.49422	0.334117
$21$	−4.85706	−1.05990
$22$	2.33369	0.497545
$23$	−2.57737	−0.537419	−0.268709	−	0.963221i	$-0.586597\pi$
$23$	−2.57737	−0.537419	−0.268709	+	0.963221i	$0.586597\pi$
$24$	2.48503	0.507255
$25$	1.00000	0.200000
$26$	1.32420	0.259697
$27$	1.00000	0.192450
$28$	7.25751	1.37154
$29$	9.18011	1.70470	0.852352	−	0.522969i	$-0.175176\pi$
$29$	9.18011	1.70470	0.852352	+	0.522969i	$0.175176\pi$
$30$	0.711184	0.129844
$31$	7.41722	1.33217	0.666086	−	0.745875i	$-0.267968\pi$
$31$	7.41722	1.33217	0.666086	+	0.745875i	$0.267968\pi$
$32$	−5.83850	−1.03211
$33$	−3.28142	−0.571222
$34$	−0.900089	−0.154364
$35$	4.85706	0.820993
$36$	−1.49422	−0.249036
$37$	−2.72888	−0.448625	−0.224313	−	0.974517i	$-0.572014\pi$
$37$	−2.72888	−0.448625	−0.224313	+	0.974517i	$0.572014\pi$
$38$	−3.34134	−0.542036
$39$	−1.86197	−0.298153
$40$	−2.48503	−0.392918
$41$	10.0728	1.57310	0.786552	−	0.617525i	$-0.211864\pi$
$41$	10.0728	1.57310	0.786552	+	0.617525i	$0.211864\pi$
$42$	3.45426	0.533004
$43$	−12.0825	−1.84256	−0.921280	−	0.388900i	$-0.872855\pi$
$43$	−12.0825	−1.84256	−0.921280	+	0.388900i	$0.872855\pi$
$44$	4.90315	0.739178
$45$	−1.00000	−0.149071
$46$	1.83298	0.270259
$47$	−0.989041	−0.144266	−0.0721332	−	0.997395i	$-0.522981\pi$
$47$	−0.989041	−0.144266	−0.0721332	+	0.997395i	$0.522981\pi$
$48$	1.22112	0.176254
$49$	16.5911	2.37015
$50$	−0.711184	−0.100577
$51$	1.26562	0.177222
$52$	2.78219	0.385820
$53$	−4.37856	−0.601442	−0.300721	−	0.953712i	$-0.597227\pi$
$53$	−4.37856	−0.601442	−0.300721	+	0.953712i	$0.597227\pi$
$54$	−0.711184	−0.0967798
$55$	3.28142	0.442466
$56$	−12.0699	−1.61291
$57$	4.69828	0.622302
$58$	−6.52874	−0.857266
$59$	−2.62566	−0.341831	−0.170916	−	0.985286i	$-0.554673\pi$
$59$	−2.62566	−0.341831	−0.170916	+	0.985286i	$0.554673\pi$
$60$	1.49422	0.192903
$61$	9.39258	1.20260	0.601298	−	0.799025i	$-0.294650\pi$
$61$	9.39258	1.20260	0.601298	+	0.799025i	$0.294650\pi$
$62$	−5.27501	−0.669926
$63$	−4.85706	−0.611932
$64$	1.71000	0.213750
$65$	1.86197	0.230949
$66$	2.33369	0.287257
$67$	15.3509	1.87541	0.937703	−	0.347437i	$-0.112948\pi$
$67$	15.3509	1.87541	0.937703	+	0.347437i	$0.112948\pi$
$68$	−1.89111	−0.229331
$69$	−2.57737	−0.310279
$70$	−3.45426	−0.412863
$71$	−3.43993	−0.408244	−0.204122	−	0.978945i	$-0.565434\pi$
$71$	−3.43993	−0.408244	−0.204122	+	0.978945i	$0.565434\pi$
$72$	2.48503	0.292864
$73$	−11.6203	−1.36006	−0.680029	−	0.733185i	$-0.738033\pi$
$73$	−11.6203	−1.36006	−0.680029	+	0.733185i	$0.738033\pi$
$74$	1.94073	0.225606
$75$	1.00000	0.115470
$76$	−7.02025	−0.805278
$77$	15.9381	1.81631
$78$	1.32420	0.149936
$79$	2.32466	0.261545	0.130773	−	0.991412i	$-0.458254\pi$
$79$	2.32466	0.261545	0.130773	+	0.991412i	$0.458254\pi$
$80$	−1.22112	−0.136526
$81$	1.00000	0.111111
$82$	−7.16359	−0.791086
$83$	11.2486	1.23469	0.617347	−	0.786691i	$-0.288207\pi$
$83$	11.2486	1.23469	0.617347	+	0.786691i	$0.288207\pi$
$84$	7.25751	0.791859
$85$	−1.26562	−0.137276
$86$	8.59286	0.926592
$87$	9.18011	0.984211
$88$	−8.15442	−0.869265
$89$	−5.68101	−0.602185	−0.301093	−	0.953595i	$-0.597351\pi$
$89$	−5.68101	−0.602185	−0.301093	+	0.953595i	$0.597351\pi$
$90$	0.711184	0.0749653
$91$	9.04369	0.948037
$92$	3.85115	0.401510
$93$	7.41722	0.769130
$94$	0.703390	0.0725491
$95$	−4.69828	−0.482033
$96$	−5.83850	−0.595890
$97$	−4.91197	−0.498735	−0.249367	−	0.968409i	$-0.580223\pi$
$97$	−4.91197	−0.498735	−0.249367	+	0.968409i	$0.580223\pi$
$98$	−11.7993	−1.19191
$99$	−3.28142	−0.329795
$100$	−1.49422	−0.149422
$101$	−3.89343	−0.387411	−0.193705	−	0.981060i	$-0.562051\pi$
$101$	−3.89343	−0.387411	−0.193705	+	0.981060i	$0.562051\pi$
$102$	−0.900089	−0.0891221
$103$	1.47294	0.145133	0.0725665	−	0.997364i	$-0.476881\pi$
$103$	1.47294	0.145133	0.0725665	+	0.997364i	$0.476881\pi$
$104$	−4.62705	−0.453719
$105$	4.85706	0.474001
$106$	3.11396	0.302455
$107$	−9.27927	−0.897061	−0.448531	−	0.893768i	$-0.648052\pi$
$107$	−9.27927	−0.897061	−0.448531	+	0.893768i	$0.648052\pi$
$108$	−1.49422	−0.143781
$109$	−18.8760	−1.80799	−0.903996	−	0.427541i	$-0.859380\pi$
$109$	−18.8760	−1.80799	−0.903996	+	0.427541i	$0.859380\pi$
$110$	−2.33369	−0.222509
$111$	−2.72888	−0.259014
$112$	−5.93107	−0.560434
$113$	−20.0716	−1.88818	−0.944090	−	0.329688i	$-0.893057\pi$
$113$	−20.0716	−1.88818	−0.944090	+	0.329688i	$0.893057\pi$
$114$	−3.34134	−0.312945
$115$	2.57737	0.240341
$116$	−13.7171	−1.27360
$117$	−1.86197	−0.172139
$118$	1.86732	0.171901
$119$	−6.14720	−0.563513
$120$	−2.48503	−0.226851
$121$	−0.232295	−0.0211177
$122$	−6.67985	−0.604765
$123$	10.0728	0.908232
$124$	−11.0829	−0.995278
$125$	−1.00000	−0.0894427
$126$	3.45426	0.307730
$127$	20.1993	1.79240	0.896201	−	0.443649i	$-0.146316\pi$
$127$	20.1993	1.79240	0.896201	+	0.443649i	$0.146316\pi$
$128$	10.4609	0.924620
$129$	−12.0825	−1.06380
$130$	−1.32420	−0.116140
$131$	−15.0479	−1.31474	−0.657371	−	0.753567i	$-0.728332\pi$
$131$	−15.0479	−1.31474	−0.657371	+	0.753567i	$0.728332\pi$
$132$	4.90315	0.426765
$133$	−22.8198	−1.97873
$134$	−10.9173	−0.943110
$135$	−1.00000	−0.0860663
$136$	3.14511	0.269691
$137$	−11.3145	−0.966665	−0.483333	−	0.875437i	$-0.660574\pi$
$137$	−11.3145	−0.966665	−0.483333	+	0.875437i	$0.660574\pi$
$138$	1.83298	0.156034
$139$	16.8024	1.42516	0.712580	−	0.701591i	$-0.247527\pi$
$139$	16.8024	1.42516	0.712580	+	0.701591i	$0.247527\pi$
$140$	−7.25751	−0.613372
$141$	−0.989041	−0.0832923
$142$	2.44642	0.205299
$143$	6.10989	0.510935
$144$	1.22112	0.101760
$145$	−9.18011	−0.762366
$146$	8.26420	0.683950
$147$	16.5911	1.36841
$148$	4.07754	0.335172
$149$	9.24945	0.757744	0.378872	−	0.925449i	$-0.376312\pi$
$149$	9.24945	0.757744	0.378872	+	0.925449i	$0.376312\pi$
$150$	−0.711184	−0.0580679
$151$	17.2486	1.40367	0.701836	−	0.712339i	$-0.252364\pi$
$151$	17.2486	1.40367	0.701836	+	0.712339i	$0.252364\pi$
$152$	11.6754	0.946997
$153$	1.26562	0.102319
$154$	−11.3349	−0.913391
$155$	−7.41722	−0.595766
$156$	2.78219	0.222753
$157$	2.70674	0.216021	0.108011	−	0.994150i	$-0.465552\pi$
$157$	2.70674	0.216021	0.108011	+	0.994150i	$0.465552\pi$
$158$	−1.65326	−0.131526
$159$	−4.37856	−0.347242
$160$	5.83850	0.461574
$161$	12.5184	0.986592
$162$	−0.711184	−0.0558759
$163$	−14.8126	−1.16022	−0.580108	−	0.814540i	$-0.696990\pi$
$163$	−14.8126	−1.16022	−0.580108	+	0.814540i	$0.696990\pi$
$164$	−15.0509	−1.17528
$165$	3.28142	0.255458
$166$	−7.99982	−0.620907
$167$	18.7063	1.44754	0.723768	−	0.690043i	$-0.242408\pi$
$167$	18.7063	1.44754	0.723768	+	0.690043i	$0.242408\pi$
$168$	−12.0699	−0.931217
$169$	−9.53308	−0.733314
$170$	0.900089	0.0690336
$171$	4.69828	0.359286
$172$	18.0538	1.37659
$173$	−14.0197	−1.06590	−0.532950	−	0.846147i	$-0.678917\pi$
$173$	−14.0197	−1.06590	−0.532950	+	0.846147i	$0.678917\pi$
$174$	−6.52874	−0.494943
$175$	−4.85706	−0.367159
$176$	−4.00702	−0.302040
$177$	−2.62566	−0.197356
$178$	4.04024	0.302829
$179$	12.5479	0.937875	0.468937	−	0.883231i	$-0.344637\pi$
$179$	12.5479	0.937875	0.468937	+	0.883231i	$0.344637\pi$
$180$	1.49422	0.111372
$181$	−10.5512	−0.784267	−0.392134	−	0.919908i	$-0.628263\pi$
$181$	−10.5512	−0.784267	−0.392134	+	0.919908i	$0.628263\pi$
$182$	−6.43173	−0.476751
$183$	9.39258	0.694319
$184$	−6.40484	−0.472171
$185$	2.72888	0.200631
$186$	−5.27501	−0.386782
$187$	−4.15303	−0.303700
$188$	1.47784	0.107783
$189$	−4.85706	−0.353299
$190$	3.34134	0.242406
$191$	−1.35546	−0.0980779	−0.0490390	−	0.998797i	$-0.515616\pi$
$191$	−1.35546	−0.0980779	−0.0490390	+	0.998797i	$0.515616\pi$
$192$	1.71000	0.123409
$193$	−2.00070	−0.144013	−0.0720066	−	0.997404i	$-0.522940\pi$
$193$	−2.00070	−0.144013	−0.0720066	+	0.997404i	$0.522940\pi$
$194$	3.49331	0.250805
$195$	1.86197	0.133338
$196$	−24.7907	−1.77076
$197$	−5.34551	−0.380852	−0.190426	−	0.981702i	$-0.560987\pi$
$197$	−5.34551	−0.380852	−0.190426	+	0.981702i	$0.560987\pi$
$198$	2.33369	0.165848
$199$	−13.0935	−0.928176	−0.464088	−	0.885789i	$-0.653618\pi$
$199$	−13.0935	−0.928176	−0.464088	+	0.885789i	$0.653618\pi$
$200$	2.48503	0.175718
$201$	15.3509	1.08277
$202$	2.76894	0.194822
$203$	−44.5884	−3.12949
$204$	−1.89111	−0.132404
$205$	−10.0728	−0.703513
$206$	−1.04753	−0.0729849
$207$	−2.57737	−0.179140
$208$	−2.27369	−0.157652
$209$	−15.4170	−1.06642
$210$	−3.45426	−0.238367
$211$	−13.6288	−0.938248	−0.469124	−	0.883132i	$-0.655430\pi$
$211$	−13.6288	−0.938248	−0.469124	+	0.883132i	$0.655430\pi$
$212$	6.54252	0.449342
$213$	−3.43993	−0.235700
$214$	6.59927	0.451116
$215$	12.0825	0.824018
$216$	2.48503	0.169085
$217$	−36.0259	−2.44560
$218$	13.4243	0.909208
$219$	−11.6203	−0.785230
$220$	−4.90315	−0.330571
$221$	−2.35654	−0.158518
$222$	1.94073	0.130254
$223$	6.43683	0.431042	0.215521	−	0.976499i	$-0.430855\pi$
$223$	6.43683	0.431042	0.215521	+	0.976499i	$0.430855\pi$
$224$	28.3580	1.89475
$225$	1.00000	0.0666667
$226$	14.2746	0.949533
$227$	−6.36013	−0.422137	−0.211068	−	0.977471i	$-0.567694\pi$
$227$	−6.36013	−0.422137	−0.211068	+	0.977471i	$0.567694\pi$
$228$	−7.02025	−0.464927
$229$	21.8440	1.44349	0.721745	−	0.692159i	$-0.243340\pi$
$229$	21.8440	1.44349	0.721745	+	0.692159i	$0.243340\pi$
$230$	−1.83298	−0.120863
$231$	15.9381	1.04865
$232$	22.8128	1.49774
$233$	11.0345	0.722896	0.361448	−	0.932392i	$-0.382282\pi$
$233$	11.0345	0.722896	0.361448	+	0.932392i	$0.382282\pi$
$234$	1.32420	0.0865657
$235$	0.989041	0.0645179
$236$	3.92330	0.255385
$237$	2.32466	0.151003
$238$	4.37179	0.283381
$239$	−22.8536	−1.47828	−0.739138	−	0.673554i	$-0.764767\pi$
$239$	−22.8536	−1.47828	−0.739138	+	0.673554i	$0.764767\pi$
$240$	−1.22112	−0.0788232
$241$	−23.8590	−1.53689	−0.768447	−	0.639913i	$-0.778970\pi$
$241$	−23.8590	−1.53689	−0.768447	+	0.639913i	$0.778970\pi$
$242$	0.165204	0.0106197
$243$	1.00000	0.0641500
$244$	−14.0346	−0.898470
$245$	−16.5911	−1.05996
$246$	−7.16359	−0.456734
$247$	−8.74804	−0.556624
$248$	18.4320	1.17043
$249$	11.2486	0.712851
$250$	0.711184	0.0449792
$251$	−2.75990	−0.174203	−0.0871015	−	0.996199i	$-0.527760\pi$
$251$	−2.75990	−0.174203	−0.0871015	+	0.996199i	$0.527760\pi$
$252$	7.25751	0.457180
$253$	8.45743	0.531714
$254$	−14.3654	−0.901368
$255$	−1.26562	−0.0792562
$256$	−10.8596	−0.678726
$257$	−7.14111	−0.445450	−0.222725	−	0.974881i	$-0.571495\pi$
$257$	−7.14111	−0.445450	−0.222725	+	0.974881i	$0.571495\pi$
$258$	8.59286	0.534968
$259$	13.2543	0.823585
$260$	−2.78219	−0.172544
$261$	9.18011	0.568234
$262$	10.7018	0.661161
$263$	28.0988	1.73265	0.866324	−	0.499482i	$-0.166476\pi$
$263$	28.0988	1.73265	0.866324	+	0.499482i	$0.166476\pi$
$264$	−8.15442	−0.501870
$265$	4.37856	0.268973
$266$	16.2291	0.995069
$267$	−5.68101	−0.347672
$268$	−22.9375	−1.40113
$269$	−9.21563	−0.561887	−0.280943	−	0.959724i	$-0.590647\pi$
$269$	−9.21563	−0.561887	−0.280943	+	0.959724i	$0.590647\pi$
$270$	0.711184	0.0432813
$271$	0.963172	0.0585085	0.0292543	−	0.999572i	$-0.490687\pi$
$271$	0.963172	0.0585085	0.0292543	+	0.999572i	$0.490687\pi$
$272$	1.54548	0.0937084
$273$	9.04369	0.547349
$274$	8.04671	0.486119
$275$	−3.28142	−0.197877
$276$	3.85115	0.231812
$277$	−21.4592	−1.28936	−0.644680	−	0.764452i	$-0.723010\pi$
$277$	−21.4592	−1.28936	−0.644680	+	0.764452i	$0.723010\pi$
$278$	−11.9496	−0.716688
$279$	7.41722	0.444057
$280$	12.0699	0.721317
$281$	−4.52742	−0.270083	−0.135042	−	0.990840i	$-0.543117\pi$
$281$	−4.52742	−0.270083	−0.135042	+	0.990840i	$0.543117\pi$
$282$	0.703390	0.0418863
$283$	−7.09604	−0.421816	−0.210908	−	0.977506i	$-0.567642\pi$
$283$	−7.09604	−0.421816	−0.210908	+	0.977506i	$0.567642\pi$
$284$	5.14000	0.305003
$285$	−4.69828	−0.278302
$286$	−4.34526	−0.256940
$287$	−48.9241	−2.88790
$288$	−5.83850	−0.344037
$289$	−15.3982	−0.905777
$290$	6.52874	0.383381
$291$	−4.91197	−0.287945
$292$	17.3633	1.01611
$293$	18.4139	1.07575	0.537876	−	0.843024i	$-0.319227\pi$
$293$	18.4139	1.07575	0.537876	+	0.843024i	$0.319227\pi$
$294$	−11.7993	−0.688149
$295$	2.62566	0.152872
$296$	−6.78135	−0.394158
$297$	−3.28142	−0.190407
$298$	−6.57806	−0.381057
$299$	4.79898	0.277532
$300$	−1.49422	−0.0862687
$301$	58.6853	3.38257
$302$	−12.2669	−0.705882
$303$	−3.89343	−0.223672
$304$	5.73717	0.329049
$305$	−9.39258	−0.537817
$306$	−0.900089	−0.0514546
$307$	5.83097	0.332791	0.166396	−	0.986059i	$-0.446787\pi$
$307$	5.83097	0.332791	0.166396	+	0.986059i	$0.446787\pi$
$308$	−23.8149	−1.35698
$309$	1.47294	0.0837926
$310$	5.27501	0.299600
$311$	33.7499	1.91378	0.956891	−	0.290446i	$-0.0938037\pi$
$311$	33.7499	1.91378	0.956891	+	0.290446i	$0.0938037\pi$
$312$	−4.62705	−0.261955
$313$	−23.0493	−1.30283	−0.651413	−	0.758724i	$-0.725823\pi$
$313$	−23.0493	−1.30283	−0.651413	+	0.758724i	$0.725823\pi$
$314$	−1.92499	−0.108633
$315$	4.85706	0.273664
$316$	−3.47355	−0.195403
$317$	15.2891	0.858722	0.429361	−	0.903133i	$-0.358739\pi$
$317$	15.2891	0.858722	0.429361	+	0.903133i	$0.358739\pi$
$318$	3.11396	0.174622
$319$	−30.1238	−1.68661
$320$	−1.71000	−0.0955920
$321$	−9.27927	−0.517918
$322$	−8.90291	−0.496140
$323$	5.94623	0.330857
$324$	−1.49422	−0.0830121
$325$	−1.86197	−0.103283
$326$	10.5345	0.583452
$327$	−18.8760	−1.04384
$328$	25.0312	1.38211
$329$	4.80384	0.264844
$330$	−2.33369	−0.128465
$331$	−8.29353	−0.455854	−0.227927	−	0.973678i	$-0.573195\pi$
$331$	−8.29353	−0.455854	−0.227927	+	0.973678i	$0.573195\pi$
$332$	−16.8079	−0.922451
$333$	−2.72888	−0.149542
$334$	−13.3036	−0.727941
$335$	−15.3509	−0.838707
$336$	−5.93107	−0.323566
$337$	21.3748	1.16436	0.582179	−	0.813061i	$-0.302200\pi$
$337$	21.3748	1.16436	0.582179	+	0.813061i	$0.302200\pi$
$338$	6.77977	0.368771
$339$	−20.0716	−1.09014
$340$	1.89111	0.102560
$341$	−24.3390	−1.31803
$342$	−3.34134	−0.180679
$343$	−46.5844	−2.51532
$344$	−30.0253	−1.61886
$345$	2.57737	0.138761
$346$	9.97060	0.536023
$347$	14.4333	0.774819	0.387410	−	0.921908i	$-0.373370\pi$
$347$	14.4333	0.774819	0.387410	+	0.921908i	$0.373370\pi$
$348$	−13.7171	−0.735313
$349$	1.51777	0.0812445	0.0406223	−	0.999175i	$-0.487066\pi$
$349$	1.51777	0.0812445	0.0406223	+	0.999175i	$0.487066\pi$
$350$	3.45426	0.184638
$351$	−1.86197	−0.0993845
$352$	19.1586	1.02116
$353$	−6.81320	−0.362630	−0.181315	−	0.983425i	$-0.558035\pi$
$353$	−6.81320	−0.362630	−0.181315	+	0.983425i	$0.558035\pi$
$354$	1.86732	0.0992471
$355$	3.43993	0.182572
$356$	8.48866	0.449898
$357$	−6.14720	−0.325344
$358$	−8.92387	−0.471641
$359$	−11.5285	−0.608450	−0.304225	−	0.952600i	$-0.598397\pi$
$359$	−11.5285	−0.608450	−0.304225	+	0.952600i	$0.598397\pi$
$360$	−2.48503	−0.130973
$361$	3.07379	0.161778
$362$	7.50387	0.394394
$363$	−0.232295	−0.0121923
$364$	−13.5132	−0.708287
$365$	11.6203	0.608237
$366$	−6.67985	−0.349161
$367$	24.6546	1.28696	0.643479	−	0.765464i	$-0.277491\pi$
$367$	24.6546	1.28696	0.643479	+	0.765464i	$0.277491\pi$
$368$	−3.14728	−0.164064
$369$	10.0728	0.524368
$370$	−1.94073	−0.100894
$371$	21.2669	1.10412
$372$	−11.0829	−0.574624
$373$	−37.6704	−1.95050	−0.975250	−	0.221103i	$-0.929034\pi$
$373$	−37.6704	−1.95050	−0.975250	+	0.221103i	$0.929034\pi$
$374$	2.95357	0.152725
$375$	−1.00000	−0.0516398
$376$	−2.45780	−0.126751
$377$	−17.0931	−0.880338
$378$	3.45426	0.177668
$379$	−24.6699	−1.26721	−0.633603	−	0.773658i	$-0.718425\pi$
$379$	−24.6699	−1.26721	−0.633603	+	0.773658i	$0.718425\pi$
$380$	7.02025	0.360131
$381$	20.1993	1.03484
$382$	0.963983	0.0493217
$383$	16.2636	0.831030	0.415515	−	0.909586i	$-0.363601\pi$
$383$	16.2636	0.831030	0.415515	+	0.909586i	$0.363601\pi$
$384$	10.4609	0.533830
$385$	−15.9381	−0.812278
$386$	1.42286	0.0724218
$387$	−12.0825	−0.614187
$388$	7.33955	0.372609
$389$	11.7769	0.597114	0.298557	−	0.954392i	$-0.403495\pi$
$389$	11.7769	0.597114	0.298557	+	0.954392i	$0.403495\pi$
$390$	−1.32420	−0.0670535
$391$	−3.26197	−0.164965
$392$	41.2293	2.08239
$393$	−15.0479	−0.759067
$394$	3.80164	0.191524
$395$	−2.32466	−0.116966
$396$	4.90315	0.246393
$397$	−13.5503	−0.680071	−0.340035	−	0.940413i	$-0.610439\pi$
$397$	−13.5503	−0.680071	−0.340035	+	0.940413i	$0.610439\pi$
$398$	9.31190	0.466763
$399$	−22.8198	−1.14242
$400$	1.22112	0.0610562
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	−10.9173	−0.544505
$403$	−13.8106	−0.687956
$404$	5.81763	0.289438
$405$	−1.00000	−0.0496904
$406$	31.7105	1.57377
$407$	8.95459	0.443863
$408$	3.14511	0.155706
$409$	−4.82296	−0.238480	−0.119240	−	0.992865i	$-0.538046\pi$
$409$	−4.82296	−0.238480	−0.119240	+	0.992865i	$0.538046\pi$
$410$	7.16359	0.353785
$411$	−11.3145	−0.558105
$412$	−2.20089	−0.108430
$413$	12.7530	0.627533
$414$	1.83298	0.0900862
$415$	−11.2486	−0.552172
$416$	10.8711	0.533000
$417$	16.8024	0.822816
$418$	10.9643	0.536282
$419$	6.92970	0.338538	0.169269	−	0.985570i	$-0.445859\pi$
$419$	6.92970	0.338538	0.169269	+	0.985570i	$0.445859\pi$
$420$	−7.25751	−0.354130
$421$	22.9741	1.11969	0.559843	−	0.828598i	$-0.310861\pi$
$421$	22.9741	1.11969	0.559843	+	0.828598i	$0.310861\pi$
$422$	9.69260	0.471828
$423$	−0.989041	−0.0480888
$424$	−10.8809	−0.528421
$425$	1.26562	0.0613916
$426$	2.44642	0.118529
$427$	−45.6203	−2.20772
$428$	13.8653	0.670202
$429$	6.10989	0.294988
$430$	−8.59286	−0.414384
$431$	17.7597	0.855454	0.427727	−	0.903908i	$-0.359314\pi$
$431$	17.7597	0.855454	0.427727	+	0.903908i	$0.359314\pi$
$432$	1.22112	0.0587513
$433$	−30.8808	−1.48404	−0.742018	−	0.670379i	$-0.766131\pi$
$433$	−30.8808	−1.48404	−0.742018	+	0.670379i	$0.766131\pi$
$434$	25.6210	1.22985
$435$	−9.18011	−0.440152
$436$	28.2048	1.35077
$437$	−12.1092	−0.579261
$438$	8.26420	0.394879
$439$	14.8839	0.710369	0.355184	−	0.934796i	$-0.384418\pi$
$439$	14.8839	0.710369	0.355184	+	0.934796i	$0.384418\pi$
$440$	8.15442	0.388747
$441$	16.5911	0.790050
$442$	1.67594	0.0797161
$443$	−4.31121	−0.204832	−0.102416	−	0.994742i	$-0.532657\pi$
$443$	−4.31121	−0.204832	−0.102416	+	0.994742i	$0.532657\pi$
$444$	4.07754	0.193512
$445$	5.68101	0.269305
$446$	−4.57776	−0.216763
$447$	9.24945	0.437484
$448$	−8.30559	−0.392402
$449$	−13.9066	−0.656291	−0.328145	−	0.944627i	$-0.606424\pi$
$449$	−13.9066	−0.656291	−0.328145	+	0.944627i	$0.606424\pi$
$450$	−0.711184	−0.0335255
$451$	−33.0530	−1.55640
$452$	29.9914	1.41068
$453$	17.2486	0.810410
$454$	4.52322	0.212285
$455$	−9.04369	−0.423975
$456$	11.6754	0.546749
$457$	−18.3853	−0.860026	−0.430013	−	0.902823i	$-0.641491\pi$
$457$	−18.3853	−0.860026	−0.430013	+	0.902823i	$0.641491\pi$
$458$	−15.5351	−0.725906
$459$	1.26562	0.0590741
$460$	−3.85115	−0.179561
$461$	22.4593	1.04603	0.523016	−	0.852323i	$-0.324807\pi$
$461$	22.4593	1.04603	0.523016	+	0.852323i	$0.324807\pi$
$462$	−11.3349	−0.527346
$463$	−25.5343	−1.18668	−0.593341	−	0.804951i	$-0.702191\pi$
$463$	−25.5343	−1.18668	−0.593341	+	0.804951i	$0.702191\pi$
$464$	11.2100	0.520413
$465$	−7.41722	−0.343965
$466$	−7.84758	−0.363532
$467$	34.8072	1.61069	0.805343	−	0.592809i	$-0.201981\pi$
$467$	34.8072	1.61069	0.805343	+	0.592809i	$0.201981\pi$
$468$	2.78219	0.128607
$469$	−74.5601	−3.44287
$470$	−0.703390	−0.0324450
$471$	2.70674	0.124720
$472$	−6.52484	−0.300330
$473$	39.6476	1.82300
$474$	−1.65326	−0.0759368
$475$	4.69828	0.215572
$476$	9.18525	0.421005
$477$	−4.37856	−0.200481
$478$	16.2531	0.743400
$479$	−17.1632	−0.784206	−0.392103	−	0.919921i	$-0.628252\pi$
$479$	−17.1632	−0.784206	−0.392103	+	0.919921i	$0.628252\pi$
$480$	5.83850	0.266490
$481$	5.08108	0.231678
$482$	16.9681	0.772877
$483$	12.5184	0.569609
$484$	0.347099	0.0157772
$485$	4.91197	0.223041
$486$	−0.711184	−0.0322599
$487$	−23.6256	−1.07058	−0.535289	−	0.844669i	$-0.679797\pi$
$487$	−23.6256	−1.07058	−0.535289	+	0.844669i	$0.679797\pi$
$488$	23.3408	1.05659
$489$	−14.8126	−0.669851
$490$	11.7993	0.533038
$491$	12.7017	0.573218	0.286609	−	0.958048i	$-0.407472\pi$
$491$	12.7017	0.573218	0.286609	+	0.958048i	$0.407472\pi$
$492$	−15.0509	−0.678548
$493$	11.6185	0.523272
$494$	6.22146	0.279917
$495$	3.28142	0.147489
$496$	9.05734	0.406687
$497$	16.7079	0.749453
$498$	−7.99982	−0.358481
$499$	4.47221	0.200203	0.100102	−	0.994977i	$-0.468083\pi$
$499$	4.47221	0.200203	0.100102	+	0.994977i	$0.468083\pi$
$500$	1.49422	0.0668235
$501$	18.7063	0.835736
$502$	1.96279	0.0876037
$503$	4.09973	0.182798	0.0913990	−	0.995814i	$-0.470866\pi$
$503$	4.09973	0.182798	0.0913990	+	0.995814i	$0.470866\pi$
$504$	−12.0699	−0.537638
$505$	3.89343	0.173255
$506$	−6.01478	−0.267390
$507$	−9.53308	−0.423379
$508$	−30.1822	−1.33912
$509$	24.2793	1.07616	0.538081	−	0.842893i	$-0.319150\pi$
$509$	24.2793	1.07616	0.538081	+	0.842893i	$0.319150\pi$
$510$	0.900089	0.0398566
$511$	56.4407	2.49679
$512$	−13.1986	−0.583301
$513$	4.69828	0.207434
$514$	5.07864	0.224009
$515$	−1.47294	−0.0649054
$516$	18.0538	0.794776
$517$	3.24546	0.142735
$518$	−9.42627	−0.414166
$519$	−14.0197	−0.615398
$520$	4.62705	0.202909
$521$	−35.1762	−1.54110	−0.770548	−	0.637382i	$-0.780017\pi$
$521$	−35.1762	−1.54110	−0.770548	+	0.637382i	$0.780017\pi$
$522$	−6.52874	−0.285755
$523$	−39.0773	−1.70873	−0.854366	−	0.519671i	$-0.826055\pi$
$523$	−39.0773	−1.70873	−0.854366	+	0.519671i	$0.826055\pi$
$524$	22.4849	0.982255
$525$	−4.85706	−0.211980
$526$	−19.9834	−0.871319
$527$	9.38739	0.408921
$528$	−4.00702	−0.174383
$529$	−16.3572	−0.711181
$530$	−3.11396	−0.135262
$531$	−2.62566	−0.113944
$532$	34.0978	1.47833
$533$	−18.7552	−0.812377
$534$	4.04024	0.174838
$535$	9.27927	0.401178
$536$	38.1474	1.64772
$537$	12.5479	0.541482
$538$	6.55400	0.282563
$539$	−54.4422	−2.34499
$540$	1.49422	0.0643009
$541$	−6.76540	−0.290867	−0.145434	−	0.989368i	$-0.546458\pi$
$541$	−6.76540	−0.290867	−0.145434	+	0.989368i	$0.546458\pi$
$542$	−0.684992	−0.0294229
$543$	−10.5512	−0.452797
$544$	−7.38933	−0.316815
$545$	18.8760	0.808559
$546$	−6.43173	−0.275252
$547$	−43.6436	−1.86606	−0.933032	−	0.359794i	$-0.882847\pi$
$547$	−43.6436	−1.86606	−0.933032	+	0.359794i	$0.882847\pi$
$548$	16.9064	0.722204
$549$	9.39258	0.400865
$550$	2.33369	0.0995089
$551$	43.1307	1.83743
$552$	−6.40484	−0.272608
$553$	−11.2910	−0.480144
$554$	15.2615	0.648397
$555$	2.72888	0.115834
$556$	−25.1064	−1.06475
$557$	−30.2314	−1.28095	−0.640473	−	0.767981i	$-0.721262\pi$
$557$	−30.2314	−1.28095	−0.640473	+	0.767981i	$0.721262\pi$
$558$	−5.27501	−0.223309
$559$	22.4972	0.951529
$560$	5.93107	0.250634
$561$	−4.15303	−0.175341
$562$	3.21983	0.135820
$563$	28.9747	1.22114	0.610569	−	0.791963i	$-0.290941\pi$
$563$	28.9747	1.22114	0.610569	+	0.791963i	$0.290941\pi$
$564$	1.47784	0.0622284
$565$	20.0716	0.844420
$566$	5.04659	0.212124
$567$	−4.85706	−0.203977
$568$	−8.54832	−0.358680
$569$	−29.3967	−1.23237	−0.616187	−	0.787600i	$-0.711324\pi$
$569$	−29.3967	−1.23237	−0.616187	+	0.787600i	$0.711324\pi$
$570$	3.34134	0.139953
$571$	−35.4815	−1.48485	−0.742427	−	0.669927i	$-0.766325\pi$
$571$	−35.4815	−1.48485	−0.742427	+	0.669927i	$0.766325\pi$
$572$	−9.12951	−0.381724
$573$	−1.35546	−0.0566253
$574$	34.7940	1.45227
$575$	−2.57737	−0.107484
$576$	1.71000	0.0712501
$577$	−9.46048	−0.393845	−0.196922	−	0.980419i	$-0.563095\pi$
$577$	−9.46048	−0.393845	−0.196922	+	0.980419i	$0.563095\pi$
$578$	10.9510	0.455499
$579$	−2.00070	−0.0831461
$580$	13.7171	0.569571
$581$	−54.6352	−2.26665
$582$	3.49331	0.144802
$583$	14.3679	0.595057
$584$	−28.8769	−1.19494
$585$	1.86197	0.0769829
$586$	−13.0957	−0.540977
$587$	36.2273	1.49526	0.747631	−	0.664114i	$-0.231191\pi$
$587$	36.2273	1.49526	0.747631	+	0.664114i	$0.231191\pi$
$588$	−24.7907	−1.02235
$589$	34.8482	1.43589
$590$	−1.86732	−0.0768765
$591$	−5.34551	−0.219885
$592$	−3.33230	−0.136957
$593$	40.3343	1.65633	0.828166	−	0.560483i	$-0.189384\pi$
$593$	40.3343	1.65633	0.828166	+	0.560483i	$0.189384\pi$
$594$	2.33369	0.0957525
$595$	6.14720	0.252011
$596$	−13.8207	−0.566118
$597$	−13.0935	−0.535882
$598$	−3.41295	−0.139566
$599$	−4.06511	−0.166096	−0.0830479	−	0.996546i	$-0.526465\pi$
$599$	−4.06511	−0.166096	−0.0830479	+	0.996546i	$0.526465\pi$
$600$	2.48503	0.101451
$601$	−11.2927	−0.460637	−0.230318	−	0.973115i	$-0.573977\pi$
$601$	−11.2927	−0.460637	−0.230318	+	0.973115i	$0.573977\pi$
$602$	−41.7360	−1.70103
$603$	15.3509	0.625136
$604$	−25.7732	−1.04870
$605$	0.232295	0.00944413
$606$	2.76894	0.112481
$607$	29.1127	1.18165	0.590824	−	0.806800i	$-0.298803\pi$
$607$	29.1127	1.18165	0.590824	+	0.806800i	$0.298803\pi$
$608$	−27.4309	−1.11247
$609$	−44.5884	−1.80681
$610$	6.67985	0.270459
$611$	1.84156	0.0745017
$612$	−1.89111	−0.0764437
$613$	20.5071	0.828274	0.414137	−	0.910214i	$-0.364083\pi$
$613$	20.5071	0.828274	0.414137	+	0.910214i	$0.364083\pi$
$614$	−4.14689	−0.167355
$615$	−10.0728	−0.406173
$616$	39.6065	1.59579
$617$	21.3311	0.858757	0.429379	−	0.903125i	$-0.358733\pi$
$617$	21.3311	0.858757	0.429379	+	0.903125i	$0.358733\pi$
$618$	−1.04753	−0.0421378
$619$	−10.2943	−0.413761	−0.206880	−	0.978366i	$-0.566331\pi$
$619$	−10.2943	−0.413761	−0.206880	+	0.978366i	$0.566331\pi$
$620$	11.0829	0.445102
$621$	−2.57737	−0.103426
$622$	−24.0024	−0.962408
$623$	27.5930	1.10549
$624$	−2.27369	−0.0910205
$625$	1.00000	0.0400000
$626$	16.3923	0.655168
$627$	−15.4170	−0.615696
$628$	−4.04446	−0.161392
$629$	−3.45373	−0.137709
$630$	−3.45426	−0.137621
$631$	24.7662	0.985925	0.492962	−	0.870051i	$-0.335914\pi$
$631$	24.7662	0.985925	0.492962	+	0.870051i	$0.335914\pi$
$632$	5.77686	0.229791
$633$	−13.6288	−0.541697
$634$	−10.8734	−0.431836
$635$	−20.1993	−0.801586
$636$	6.54252	0.259428
$637$	−30.8920	−1.22399
$638$	21.4235	0.848166
$639$	−3.43993	−0.136081
$640$	−10.4609	−0.413503
$641$	−39.3531	−1.55435	−0.777177	−	0.629281i	$-0.783349\pi$
$641$	−39.3531	−1.55435	−0.777177	+	0.629281i	$0.783349\pi$
$642$	6.59927	0.260452
$643$	47.8809	1.88824	0.944119	−	0.329605i	$-0.106916\pi$
$643$	47.8809	1.88824	0.944119	+	0.329605i	$0.106916\pi$
$644$	−18.7053	−0.737091
$645$	12.0825	0.475747
$646$	−4.22886	−0.166382
$647$	6.22012	0.244538	0.122269	−	0.992497i	$-0.460983\pi$
$647$	6.22012	0.244538	0.122269	+	0.992497i	$0.460983\pi$
$648$	2.48503	0.0976212
$649$	8.61588	0.338203
$650$	1.32420	0.0519394
$651$	−36.0259	−1.41197
$652$	22.1333	0.866807
$653$	1.44591	0.0565827	0.0282913	−	0.999600i	$-0.490993\pi$
$653$	1.44591	0.0565827	0.0282913	+	0.999600i	$0.490993\pi$
$654$	13.4243	0.524932
$655$	15.0479	0.587970
$656$	12.3001	0.480238
$657$	−11.6203	−0.453353
$658$	−3.41641	−0.133185
$659$	−30.9268	−1.20474	−0.602368	−	0.798219i	$-0.705776\pi$
$659$	−30.9268	−1.20474	−0.602368	+	0.798219i	$0.705776\pi$
$660$	−4.90315	−0.190855
$661$	−23.7912	−0.925372	−0.462686	−	0.886522i	$-0.653114\pi$
$661$	−23.7912	−0.925372	−0.462686	+	0.886522i	$0.653114\pi$
$662$	5.89822	0.229241
$663$	−2.35654	−0.0915206
$664$	27.9531	1.08479
$665$	22.8198	0.884915
$666$	1.94073	0.0752019
$667$	−23.6605	−0.916139
$668$	−27.9513	−1.08147
$669$	6.43683	0.248862
$670$	10.9173	0.421771
$671$	−30.8210	−1.18983
$672$	28.3580	1.09393
$673$	0.107724	0.00415244	0.00207622	−	0.999998i	$-0.499339\pi$
$673$	0.107724	0.00415244	0.00207622	+	0.999998i	$0.499339\pi$
$674$	−15.2014	−0.585536
$675$	1.00000	0.0384900
$676$	14.2445	0.547865
$677$	−36.3270	−1.39616	−0.698080	−	0.716020i	$-0.745962\pi$
$677$	−36.3270	−1.39616	−0.698080	+	0.716020i	$0.745962\pi$
$678$	14.2746	0.548213
$679$	23.8577	0.915576
$680$	−3.14511	−0.120609
$681$	−6.36013	−0.243721
$682$	17.3095	0.662815
$683$	15.3811	0.588540	0.294270	−	0.955722i	$-0.404924\pi$
$683$	15.3811	0.588540	0.294270	+	0.955722i	$0.404924\pi$
$684$	−7.02025	−0.268426
$685$	11.3145	0.432306
$686$	33.1300	1.26491
$687$	21.8440	0.833399
$688$	−14.7542	−0.562498
$689$	8.15274	0.310595
$690$	−1.83298	−0.0697805
$691$	−8.88001	−0.337811	−0.168906	−	0.985632i	$-0.554023\pi$
$691$	−8.88001	−0.337811	−0.168906	+	0.985632i	$0.554023\pi$
$692$	20.9485	0.796343
$693$	15.9381	0.605437
$694$	−10.2647	−0.389643
$695$	−16.8024	−0.637351
$696$	22.8128	0.864719
$697$	12.7483	0.482877
$698$	−1.07942	−0.0408565
$699$	11.0345	0.417364
$700$	7.25751	0.274308
$701$	−20.5032	−0.774395	−0.387197	−	0.921997i	$-0.626557\pi$
$701$	−20.5032	−0.774395	−0.387197	+	0.921997i	$0.626557\pi$
$702$	1.32420	0.0499787
$703$	−12.8210	−0.483554
$704$	−5.61123	−0.211481
$705$	0.989041	0.0372494
$706$	4.84543	0.182360
$707$	18.9106	0.711207
$708$	3.92330	0.147447
$709$	−24.0543	−0.903379	−0.451689	−	0.892175i	$-0.649178\pi$
$709$	−24.0543	−0.903379	−0.451689	+	0.892175i	$0.649178\pi$
$710$	−2.44642	−0.0918125
$711$	2.32466	0.0871817
$712$	−14.1175	−0.529075
$713$	−19.1169	−0.715934
$714$	4.37179	0.163610
$715$	−6.10989	−0.228497
$716$	−18.7493	−0.700695
$717$	−22.8536	−0.853483
$718$	8.19887	0.305979
$719$	22.4791	0.838327	0.419164	−	0.907911i	$-0.362323\pi$
$719$	22.4791	0.838327	0.419164	+	0.907911i	$0.362323\pi$
$720$	−1.22112	−0.0455086
$721$	−7.15416	−0.266435
$722$	−2.18603	−0.0813556
$723$	−23.8590	−0.887326
$724$	15.7658	0.585933
$725$	9.18011	0.340941
$726$	0.165204	0.00613131
$727$	−3.73926	−0.138681	−0.0693407	−	0.997593i	$-0.522090\pi$
$727$	−3.73926	−0.138681	−0.0693407	+	0.997593i	$0.522090\pi$
$728$	22.4739	0.832936
$729$	1.00000	0.0370370
$730$	−8.26420	−0.305872
$731$	−15.2918	−0.565589
$732$	−14.0346	−0.518732
$733$	−39.9084	−1.47405	−0.737026	−	0.675865i	$-0.763770\pi$
$733$	−39.9084	−1.47405	−0.737026	+	0.675865i	$0.763770\pi$
$734$	−17.5339	−0.647189
$735$	−16.5911	−0.611970
$736$	15.0480	0.554676
$737$	−50.3726	−1.85550
$738$	−7.16359	−0.263695
$739$	−27.3203	−1.00499	−0.502497	−	0.864579i	$-0.667585\pi$
$739$	−27.3203	−1.00499	−0.502497	+	0.864579i	$0.667585\pi$
$740$	−4.07754	−0.149893
$741$	−8.74804	−0.321367
$742$	−15.1247	−0.555245
$743$	−31.5148	−1.15617	−0.578083	−	0.815978i	$-0.696199\pi$
$743$	−31.5148	−1.15617	−0.578083	+	0.815978i	$0.696199\pi$
$744$	18.4320	0.675751
$745$	−9.24945	−0.338874
$746$	26.7906	0.980873
$747$	11.2486	0.411565
$748$	6.20553	0.226897
$749$	45.0700	1.64682
$750$	0.711184	0.0259688
$751$	20.3543	0.742740	0.371370	−	0.928485i	$-0.378888\pi$
$751$	20.3543	0.742740	0.371370	+	0.928485i	$0.378888\pi$
$752$	−1.20774	−0.0440418
$753$	−2.75990	−0.100576
$754$	12.1563	0.442707
$755$	−17.2486	−0.627741
$756$	7.25751	0.263953
$757$	36.1338	1.31330	0.656652	−	0.754194i	$-0.271972\pi$
$757$	36.1338	1.31330	0.656652	+	0.754194i	$0.271972\pi$
$758$	17.5448	0.637256
$759$	8.45743	0.306985
$760$	−11.6754	−0.423510
$761$	−37.8989	−1.37383	−0.686917	−	0.726736i	$-0.741037\pi$
$761$	−37.8989	−1.37383	−0.686917	+	0.726736i	$0.741037\pi$
$762$	−14.3654	−0.520405
$763$	91.6819	3.31911
$764$	2.02536	0.0732749
$765$	−1.26562	−0.0457586
$766$	−11.5664	−0.417911
$767$	4.88889	0.176528
$768$	−10.8596	−0.391862
$769$	19.1905	0.692027	0.346014	−	0.938229i	$-0.387535\pi$
$769$	19.1905	0.692027	0.346014	+	0.938229i	$0.387535\pi$
$770$	11.3349	0.408481
$771$	−7.14111	−0.257181
$772$	2.98948	0.107594
$773$	38.6817	1.39128	0.695642	−	0.718389i	$-0.255120\pi$
$773$	38.6817	1.39128	0.695642	+	0.718389i	$0.255120\pi$
$774$	8.59286	0.308864
$775$	7.41722	0.266434
$776$	−12.2064	−0.438184
$777$	13.2543	0.475497
$778$	−8.37556	−0.300278
$779$	47.3247	1.69558
$780$	−2.78219	−0.0996182
$781$	11.2878	0.403911
$782$	2.31986	0.0829580
$783$	9.18011	0.328070
$784$	20.2597	0.723562
$785$	−2.70674	−0.0966077
$786$	10.7018	0.381721
$787$	9.29064	0.331176	0.165588	−	0.986195i	$-0.447048\pi$
$787$	9.29064	0.331176	0.165588	+	0.986195i	$0.447048\pi$
$788$	7.98735	0.284538
$789$	28.0988	1.00034
$790$	1.65326	0.0588204
$791$	97.4892	3.46632
$792$	−8.15442	−0.289755
$793$	−17.4887	−0.621041
$794$	9.63676	0.341996
$795$	4.37856	0.155292
$796$	19.5646	0.693448
$797$	30.8205	1.09172	0.545859	−	0.837877i	$-0.316204\pi$
$797$	30.8205	1.09172	0.545859	+	0.837877i	$0.316204\pi$
$798$	16.2291	0.574503
$799$	−1.25175	−0.0442838
$800$	−5.83850	−0.206422
$801$	−5.68101	−0.200728
$802$	−0.711184	−0.0251128
$803$	38.1312	1.34562
$804$	−22.9375	−0.808945
$805$	−12.5184	−0.441217
$806$	9.82189	0.345961
$807$	−9.21563	−0.324405
$808$	−9.67529	−0.340375
$809$	18.9043	0.664639	0.332319	−	0.943167i	$-0.392169\pi$
$809$	18.9043	0.664639	0.332319	+	0.943167i	$0.392169\pi$
$810$	0.711184	0.0249884
$811$	19.9205	0.699503	0.349752	−	0.936842i	$-0.386266\pi$
$811$	19.9205	0.699503	0.349752	+	0.936842i	$0.386266\pi$
$812$	66.6247	2.33807
$813$	0.963172	0.0337799
$814$	−6.36836	−0.223211
$815$	14.8126	0.518864
$816$	1.54548	0.0541026
$817$	−56.7668	−1.98602
$818$	3.43001	0.119927
$819$	9.04369	0.316012
$820$	15.0509	0.525601
$821$	−29.9053	−1.04370	−0.521851	−	0.853037i	$-0.674758\pi$
$821$	−29.9053	−1.04370	−0.521851	+	0.853037i	$0.674758\pi$
$822$	8.04671	0.280661
$823$	−2.71759	−0.0947292	−0.0473646	−	0.998878i	$-0.515082\pi$
$823$	−2.71759	−0.0947292	−0.0473646	+	0.998878i	$0.515082\pi$
$824$	3.66030	0.127513
$825$	−3.28142	−0.114244
$826$	−9.06971	−0.315576
$827$	15.5362	0.540248	0.270124	−	0.962826i	$-0.412935\pi$
$827$	15.5362	0.540248	0.270124	+	0.962826i	$0.412935\pi$
$828$	3.85115	0.133837
$829$	−18.3145	−0.636090	−0.318045	−	0.948076i	$-0.603026\pi$
$829$	−18.3145	−0.636090	−0.318045	+	0.948076i	$0.603026\pi$
$830$	7.99982	0.277678
$831$	−21.4592	−0.744413
$832$	−3.18397	−0.110384
$833$	20.9980	0.727537
$834$	−11.9496	−0.413780
$835$	−18.7063	−0.647358
$836$	23.0364	0.796729
$837$	7.41722	0.256377
$838$	−4.92829	−0.170245
$839$	−31.9228	−1.10210	−0.551049	−	0.834473i	$-0.685772\pi$
$839$	−31.9228	−1.10210	−0.551049	+	0.834473i	$0.685772\pi$
$840$	12.0699	0.416453
$841$	55.2744	1.90601
$842$	−16.3388	−0.563071
$843$	−4.52742	−0.155933
$844$	20.3644	0.700973
$845$	9.53308	0.327948
$846$	0.703390	0.0241830
$847$	1.12827	0.0387678
$848$	−5.34676	−0.183609
$849$	−7.09604	−0.243535
$850$	−0.900089	−0.0308728
$851$	7.03333	0.241099
$852$	5.14000	0.176093
$853$	36.6053	1.25334	0.626670	−	0.779284i	$-0.284417\pi$
$853$	36.6053	1.25334	0.626670	+	0.779284i	$0.284417\pi$
$854$	32.4444	1.11023
$855$	−4.69828	−0.160678
$856$	−23.0593	−0.788150
$857$	9.90573	0.338373	0.169187	−	0.985584i	$-0.445886\pi$
$857$	9.90573	0.338373	0.169187	+	0.985584i	$0.445886\pi$
$858$	−4.34526	−0.148345
$859$	18.0756	0.616732	0.308366	−	0.951268i	$-0.400218\pi$
$859$	18.0756	0.616732	0.308366	+	0.951268i	$0.400218\pi$
$860$	−18.0538	−0.615631
$861$	−48.9241	−1.66733
$862$	−12.6304	−0.430193
$863$	−22.4709	−0.764920	−0.382460	−	0.923972i	$-0.624923\pi$
$863$	−22.4709	−0.764920	−0.382460	+	0.923972i	$0.624923\pi$
$864$	−5.83850	−0.198630
$865$	14.0197	0.476685
$866$	21.9619	0.746297
$867$	−15.3982	−0.522950
$868$	53.8306	1.82713
$869$	−7.62819	−0.258769
$870$	6.52874	0.221345
$871$	−28.5828	−0.968492
$872$	−46.9074	−1.58849
$873$	−4.91197	−0.166245
$874$	8.61186	0.291300
$875$	4.85706	0.164199
$876$	17.3633	0.586652
$877$	−31.3851	−1.05980	−0.529899	−	0.848060i	$-0.677770\pi$
$877$	−31.3851	−1.05980	−0.529899	+	0.848060i	$0.677770\pi$
$878$	−10.5852	−0.357232
$879$	18.4139	0.621085
$880$	4.00702	0.135076
$881$	−46.8714	−1.57914	−0.789569	−	0.613662i	$-0.789696\pi$
$881$	−46.8714	−1.57914	−0.789569	+	0.613662i	$0.789696\pi$
$882$	−11.7993	−0.397303
$883$	−37.3531	−1.25703	−0.628516	−	0.777797i	$-0.716337\pi$
$883$	−37.3531	−1.25703	−0.628516	+	0.777797i	$0.716337\pi$
$884$	3.52119	0.118430
$885$	2.62566	0.0882605
$886$	3.06606	0.103006
$887$	−34.4584	−1.15700	−0.578500	−	0.815682i	$-0.696362\pi$
$887$	−34.4584	−1.15700	−0.578500	+	0.815682i	$0.696362\pi$
$888$	−6.78135	−0.227567
$889$	−98.1095	−3.29049
$890$	−4.04024	−0.135429
$891$	−3.28142	−0.109932
$892$	−9.61802	−0.322035
$893$	−4.64679	−0.155499
$894$	−6.57806	−0.220003
$895$	−12.5479	−0.419430
$896$	−50.8092	−1.69741
$897$	4.79898	0.160233
$898$	9.89011	0.330037
$899$	68.0909	2.27096
$900$	−1.49422	−0.0498073
$901$	−5.54160	−0.184617
$902$	23.5067	0.782689
$903$	58.6853	1.95293
$904$	−49.8786	−1.65894
$905$	10.5512	0.350735
$906$	−12.2669	−0.407541
$907$	−34.9904	−1.16184	−0.580919	−	0.813961i	$-0.697307\pi$
$907$	−34.9904	−1.16184	−0.580919	+	0.813961i	$0.697307\pi$
$908$	9.50342	0.315382
$909$	−3.89343	−0.129137
$910$	6.43173	0.213210
$911$	−47.4397	−1.57175	−0.785874	−	0.618386i	$-0.787787\pi$
$911$	−47.4397	−1.57175	−0.785874	+	0.618386i	$0.787787\pi$
$912$	5.73717	0.189977
$913$	−36.9114	−1.22159
$914$	13.0753	0.432492
$915$	−9.39258	−0.310509
$916$	−32.6397	−1.07844
$917$	73.0886	2.41360
$918$	−0.900089	−0.0297074
$919$	−16.2613	−0.536411	−0.268206	−	0.963362i	$-0.586431\pi$
$919$	−16.2613	−0.536411	−0.268206	+	0.963362i	$0.586431\pi$
$920$	6.40484	0.211161
$921$	5.83097	0.192137
$922$	−15.9727	−0.526032
$923$	6.40503	0.210824
$924$	−23.8149	−0.783454
$925$	−2.72888	−0.0897250
$926$	18.1596	0.596762
$927$	1.47294	0.0483777
$928$	−53.5981	−1.75944
$929$	−14.0886	−0.462232	−0.231116	−	0.972926i	$-0.574238\pi$
$929$	−14.0886	−0.462232	−0.231116	+	0.972926i	$0.574238\pi$
$930$	5.27501	0.172974
$931$	77.9494	2.55469
$932$	−16.4880	−0.540082
$933$	33.7499	1.10492
$934$	−24.7543	−0.809986
$935$	4.15303	0.135819
$936$	−4.62705	−0.151240
$937$	22.6586	0.740223	0.370112	−	0.928987i	$-0.379319\pi$
$937$	22.6586	0.740223	0.370112	+	0.928987i	$0.379319\pi$
$938$	53.0259	1.73136
$939$	−23.0493	−0.752187
$940$	−1.47784	−0.0482019
$941$	17.6556	0.575557	0.287778	−	0.957697i	$-0.407083\pi$
$941$	17.6556	0.575557	0.287778	+	0.957697i	$0.407083\pi$
$942$	−1.92499	−0.0627196
$943$	−25.9613	−0.845415
$944$	−3.20625	−0.104355
$945$	4.85706	0.158000
$946$	−28.1968	−0.916756
$947$	−14.1294	−0.459143	−0.229571	−	0.973292i	$-0.573732\pi$
$947$	−14.1294	−0.459143	−0.229571	+	0.973292i	$0.573732\pi$
$948$	−3.47355	−0.112816
$949$	21.6367	0.702357
$950$	−3.34134	−0.108407
$951$	15.2891	0.495783
$952$	−15.2760	−0.495097
$953$	−24.1953	−0.783763	−0.391882	−	0.920016i	$-0.628176\pi$
$953$	−24.1953	−0.783763	−0.391882	+	0.920016i	$0.628176\pi$
$954$	3.11396	0.100818
$955$	1.35546	0.0438618
$956$	34.1483	1.10443
$957$	−30.1238	−0.973763
$958$	12.2062	0.394364
$959$	54.9554	1.77460
$960$	−1.71000	−0.0551901
$961$	24.0152	0.774683
$962$	−3.61358	−0.116507
$963$	−9.27927	−0.299020
$964$	35.6506	1.14823
$965$	2.00070	0.0644047
$966$	−8.90291	−0.286446
$967$	−20.7409	−0.666981	−0.333491	−	0.942753i	$-0.608227\pi$
$967$	−20.7409	−0.666981	−0.333491	+	0.942753i	$0.608227\pi$
$968$	−0.577260	−0.0185538
$969$	5.94623	0.191021
$970$	−3.49331	−0.112163
$971$	−5.26914	−0.169095	−0.0845475	−	0.996419i	$-0.526944\pi$
$971$	−5.26914	−0.169095	−0.0845475	+	0.996419i	$0.526944\pi$
$972$	−1.49422	−0.0479271
$973$	−81.6102	−2.61630
$974$	16.8021	0.538375
$975$	−1.86197	−0.0596307
$976$	11.4695	0.367129
$977$	−35.5091	−1.13604	−0.568018	−	0.823016i	$-0.692290\pi$
$977$	−35.5091	−1.13604	−0.568018	+	0.823016i	$0.692290\pi$
$978$	10.5345	0.336856
$979$	18.6418	0.595793
$980$	24.7907	0.791909
$981$	−18.8760	−0.602664
$982$	−9.03322	−0.288262
$983$	7.33528	0.233959	0.116980	−	0.993134i	$-0.462679\pi$
$983$	7.33528	0.233959	0.116980	+	0.993134i	$0.462679\pi$
$984$	25.0312	0.797964
$985$	5.34551	0.170322
$986$	−8.26291	−0.263145
$987$	4.80384	0.152908
$988$	13.0715	0.415859
$989$	31.1410	0.990226
$990$	−2.33369	−0.0741696
$991$	7.81101	0.248125	0.124062	−	0.992274i	$-0.460408\pi$
$991$	7.81101	0.248125	0.124062	+	0.992274i	$0.460408\pi$
$992$	−43.3055	−1.37495
$993$	−8.29353	−0.263187
$994$	−11.8824	−0.376887
$995$	13.0935	0.415093
$996$	−16.8079	−0.532578
$997$	−49.9463	−1.58181	−0.790907	−	0.611936i	$-0.790391\pi$
$997$	−49.9463	−1.58181	−0.790907	+	0.611936i	$0.790391\pi$
$998$	−3.18056	−0.100679
$999$	−2.72888	−0.0863379

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6015.2.a.c.1.11	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6015.2.a.c.1.11	✓	28	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:	\( N \)	\(=\)	\( 6015 = 3 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6015.a (trivial)

\(f(q)\)	\(=\)	\(q-0.711184 q^{2} +1.00000 q^{3} -1.49422 q^{4} -1.00000 q^{5} -0.711184 q^{6} -4.85706 q^{7} +2.48503 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.711184 q^{2} +1.00000 q^{3} -1.49422 q^{4} -1.00000 q^{5} -0.711184 q^{6} -4.85706 q^{7} +2.48503 q^{8} +1.00000 q^{9} +0.711184 q^{10} -3.28142 q^{11} -1.49422 q^{12} -1.86197 q^{13} +3.45426 q^{14} -1.00000 q^{15} +1.22112 q^{16} +1.26562 q^{17} -0.711184 q^{18} +4.69828 q^{19} +1.49422 q^{20} -4.85706 q^{21} +2.33369 q^{22} -2.57737 q^{23} +2.48503 q^{24} +1.00000 q^{25} +1.32420 q^{26} +1.00000 q^{27} +7.25751 q^{28} +9.18011 q^{29} +0.711184 q^{30} +7.41722 q^{31} -5.83850 q^{32} -3.28142 q^{33} -0.900089 q^{34} +4.85706 q^{35} -1.49422 q^{36} -2.72888 q^{37} -3.34134 q^{38} -1.86197 q^{39} -2.48503 q^{40} +10.0728 q^{41} +3.45426 q^{42} -12.0825 q^{43} +4.90315 q^{44} -1.00000 q^{45} +1.83298 q^{46} -0.989041 q^{47} +1.22112 q^{48} +16.5911 q^{49} -0.711184 q^{50} +1.26562 q^{51} +2.78219 q^{52} -4.37856 q^{53} -0.711184 q^{54} +3.28142 q^{55} -12.0699 q^{56} +4.69828 q^{57} -6.52874 q^{58} -2.62566 q^{59} +1.49422 q^{60} +9.39258 q^{61} -5.27501 q^{62} -4.85706 q^{63} +1.71000 q^{64} +1.86197 q^{65} +2.33369 q^{66} +15.3509 q^{67} -1.89111 q^{68} -2.57737 q^{69} -3.45426 q^{70} -3.43993 q^{71} +2.48503 q^{72} -11.6203 q^{73} +1.94073 q^{74} +1.00000 q^{75} -7.02025 q^{76} +15.9381 q^{77} +1.32420 q^{78} +2.32466 q^{79} -1.22112 q^{80} +1.00000 q^{81} -7.16359 q^{82} +11.2486 q^{83} +7.25751 q^{84} -1.26562 q^{85} +8.59286 q^{86} +9.18011 q^{87} -8.15442 q^{88} -5.68101 q^{89} +0.711184 q^{90} +9.04369 q^{91} +3.85115 q^{92} +7.41722 q^{93} +0.703390 q^{94} -4.69828 q^{95} -5.83850 q^{96} -4.91197 q^{97} -11.7993 q^{98} -3.28142 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - q^{2} + 28 q^{3} + 21 q^{4} - 28 q^{5} - q^{6} - 20 q^{7} + 28 q^{9}+O(q^{10}) \) 28 * q - q^2 + 28 * q^3 + 21 * q^4 - 28 * q^5 - q^6 - 20 * q^7 + 28 * q^9	\( 28 q - q^{2} + 28 q^{3} + 21 q^{4} - 28 q^{5} - q^{6} - 20 q^{7} + 28 q^{9} + q^{10} - q^{11} + 21 q^{12} - 18 q^{13} - 4 q^{14} - 28 q^{15} - q^{16} - 28 q^{17} - q^{18} - 19 q^{19} - 21 q^{20} - 20 q^{21} - 35 q^{22} + 2 q^{23} + 28 q^{25} - 20 q^{26} + 28 q^{27} - 54 q^{28} + 9 q^{29} + q^{30} - 19 q^{31} - 6 q^{32} - q^{33} - 16 q^{34} + 20 q^{35} + 21 q^{36} - 32 q^{37} - 2 q^{38} - 18 q^{39} - 27 q^{41} - 4 q^{42} - 77 q^{43} + q^{44} - 28 q^{45} - 19 q^{46} + 10 q^{47} - q^{48} - 4 q^{49} - q^{50} - 28 q^{51} - 34 q^{52} - 21 q^{53} - q^{54} + q^{55} - 9 q^{56} - 19 q^{57} - 46 q^{58} - 7 q^{59} - 21 q^{60} - 31 q^{61} - 7 q^{62} - 20 q^{63} - 46 q^{64} + 18 q^{65} - 35 q^{66} - 50 q^{67} - 68 q^{68} + 2 q^{69} + 4 q^{70} - 4 q^{71} - 87 q^{73} + 4 q^{74} + 28 q^{75} - 40 q^{76} - 8 q^{77} - 20 q^{78} - 65 q^{79} + q^{80} + 28 q^{81} - 41 q^{82} + 13 q^{83} - 54 q^{84} + 28 q^{85} - 17 q^{86} + 9 q^{87} - 117 q^{88} - 33 q^{89} + q^{90} - 33 q^{91} + 3 q^{92} - 19 q^{93} - 60 q^{94} + 19 q^{95} - 6 q^{96} - 75 q^{97} - 18 q^{98} - q^{99}+O(q^{100}) \) 28 * q - q^2 + 28 * q^3 + 21 * q^4 - 28 * q^5 - q^6 - 20 * q^7 + 28 * q^9 + q^10 - q^11 + 21 * q^12 - 18 * q^13 - 4 * q^14 - 28 * q^15 - q^16 - 28 * q^17 - q^18 - 19 * q^19 - 21 * q^20 - 20 * q^21 - 35 * q^22 + 2 * q^23 + 28 * q^25 - 20 * q^26 + 28 * q^27 - 54 * q^28 + 9 * q^29 + q^30 - 19 * q^31 - 6 * q^32 - q^33 - 16 * q^34 + 20 * q^35 + 21 * q^36 - 32 * q^37 - 2 * q^38 - 18 * q^39 - 27 * q^41 - 4 * q^42 - 77 * q^43 + q^44 - 28 * q^45 - 19 * q^46 + 10 * q^47 - q^48 - 4 * q^49 - q^50 - 28 * q^51 - 34 * q^52 - 21 * q^53 - q^54 + q^55 - 9 * q^56 - 19 * q^57 - 46 * q^58 - 7 * q^59 - 21 * q^60 - 31 * q^61 - 7 * q^62 - 20 * q^63 - 46 * q^64 + 18 * q^65 - 35 * q^66 - 50 * q^67 - 68 * q^68 + 2 * q^69 + 4 * q^70 - 4 * q^71 - 87 * q^73 + 4 * q^74 + 28 * q^75 - 40 * q^76 - 8 * q^77 - 20 * q^78 - 65 * q^79 + q^80 + 28 * q^81 - 41 * q^82 + 13 * q^83 - 54 * q^84 + 28 * q^85 - 17 * q^86 + 9 * q^87 - 117 * q^88 - 33 * q^89 + q^90 - 33 * q^91 + 3 * q^92 - 19 * q^93 - 60 * q^94 + 19 * q^95 - 6 * q^96 - 75 * q^97 - 18 * q^98 - q^99

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