LMFDB - Embedded newform 8027.2.a.c.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8027,2,Mod(1,8027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8027, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8027 = 23 \cdot 349 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8027.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$64.0959177025$
Analytic rank:	$1$
Dimension:	$143$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	8027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.40779 q^{2} +2.53147 q^{3} +3.79745 q^{4} +0.438044 q^{5} -6.09525 q^{6} +1.85360 q^{7} -4.32788 q^{8} +3.40834 q^{9} +O(q^{10})$	\(q-2.40779 q^{2} +2.53147 q^{3} +3.79745 q^{4} +0.438044 q^{5} -6.09525 q^{6} +1.85360 q^{7} -4.32788 q^{8} +3.40834 q^{9} -1.05472 q^{10} -2.41584 q^{11} +9.61313 q^{12} +2.44507 q^{13} -4.46307 q^{14} +1.10890 q^{15} +2.82573 q^{16} -2.28373 q^{17} -8.20657 q^{18} -5.88842 q^{19} +1.66345 q^{20} +4.69232 q^{21} +5.81684 q^{22} +1.00000 q^{23} -10.9559 q^{24} -4.80812 q^{25} -5.88722 q^{26} +1.03370 q^{27} +7.03894 q^{28} +0.633981 q^{29} -2.66999 q^{30} -7.77763 q^{31} +1.85200 q^{32} -6.11563 q^{33} +5.49874 q^{34} +0.811957 q^{35} +12.9430 q^{36} -0.368777 q^{37} +14.1781 q^{38} +6.18963 q^{39} -1.89580 q^{40} +1.21706 q^{41} -11.2981 q^{42} +1.62620 q^{43} -9.17404 q^{44} +1.49300 q^{45} -2.40779 q^{46} +2.10885 q^{47} +7.15326 q^{48} -3.56418 q^{49} +11.5769 q^{50} -5.78120 q^{51} +9.28505 q^{52} +3.87503 q^{53} -2.48894 q^{54} -1.05825 q^{55} -8.02215 q^{56} -14.9064 q^{57} -1.52649 q^{58} +4.35648 q^{59} +4.21098 q^{60} +1.13229 q^{61} +18.7269 q^{62} +6.31769 q^{63} -10.1107 q^{64} +1.07105 q^{65} +14.7252 q^{66} +6.84097 q^{67} -8.67236 q^{68} +2.53147 q^{69} -1.95502 q^{70} -6.55604 q^{71} -14.7509 q^{72} -2.45192 q^{73} +0.887938 q^{74} -12.1716 q^{75} -22.3610 q^{76} -4.47800 q^{77} -14.9033 q^{78} -8.96780 q^{79} +1.23780 q^{80} -7.60823 q^{81} -2.93043 q^{82} -17.6759 q^{83} +17.8189 q^{84} -1.00037 q^{85} -3.91555 q^{86} +1.60491 q^{87} +10.4555 q^{88} +1.83595 q^{89} -3.59484 q^{90} +4.53218 q^{91} +3.79745 q^{92} -19.6888 q^{93} -5.07766 q^{94} -2.57939 q^{95} +4.68827 q^{96} -8.24908 q^{97} +8.58180 q^{98} -8.23402 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 143 q - 17 q^{2} - 17 q^{3} + 121 q^{4} - 22 q^{5} - 11 q^{6} - 33 q^{7} - 45 q^{8} + 104 q^{9}+O(q^{10}) $ 143 * q - 17 * q^2 - 17 * q^3 + 121 * q^4 - 22 * q^5 - 11 * q^6 - 33 * q^7 - 45 * q^8 + 104 * q^9	\( 143 q - 17 q^{2} - 17 q^{3} + 121 q^{4} - 22 q^{5} - 11 q^{6} - 33 q^{7} - 45 q^{8} + 104 q^{9} - 22 q^{10} - 14 q^{11} - 36 q^{12} - 87 q^{13} - 18 q^{14} - 19 q^{15} + 81 q^{16} - 14 q^{17} - 60 q^{18} - 18 q^{19} - 25 q^{20} - 26 q^{21} - 62 q^{22} + 143 q^{23} - 21 q^{24} + 67 q^{25} - 5 q^{26} - 47 q^{27} - 76 q^{28} - 54 q^{29} - 22 q^{30} - 62 q^{31} - 117 q^{32} - 59 q^{33} - 35 q^{34} - 52 q^{35} + 52 q^{36} - 190 q^{37} - 19 q^{38} - 43 q^{39} - 41 q^{40} - 50 q^{41} + 8 q^{42} - 50 q^{43} - 18 q^{44} - 75 q^{45} - 17 q^{46} - 63 q^{47} - 35 q^{48} + 74 q^{49} - 53 q^{50} - 33 q^{51} - 124 q^{52} - 100 q^{53} - 46 q^{54} - 61 q^{55} - 3 q^{56} - 80 q^{57} - 112 q^{58} - 109 q^{59} - 55 q^{60} - 76 q^{61} - 6 q^{62} - 93 q^{63} + 57 q^{64} - 17 q^{65} + 50 q^{66} - 120 q^{67} + 26 q^{68} - 17 q^{69} - 109 q^{71} - 153 q^{72} - 94 q^{73} + 35 q^{74} - 105 q^{75} - 16 q^{76} - 52 q^{77} - 59 q^{78} - 29 q^{79} - 30 q^{80} + 39 q^{81} - 65 q^{82} + 8 q^{83} + 11 q^{84} - 155 q^{85} - 15 q^{86} - 25 q^{87} - 139 q^{88} + 6 q^{89} + 82 q^{90} - 34 q^{91} + 121 q^{92} - 151 q^{93} - 3 q^{94} - 70 q^{95} - 23 q^{96} - 203 q^{97} - 18 q^{98} - 49 q^{99}+O(q^{100}) \) 143 * q - 17 * q^2 - 17 * q^3 + 121 * q^4 - 22 * q^5 - 11 * q^6 - 33 * q^7 - 45 * q^8 + 104 * q^9 - 22 * q^10 - 14 * q^11 - 36 * q^12 - 87 * q^13 - 18 * q^14 - 19 * q^15 + 81 * q^16 - 14 * q^17 - 60 * q^18 - 18 * q^19 - 25 * q^20 - 26 * q^21 - 62 * q^22 + 143 * q^23 - 21 * q^24 + 67 * q^25 - 5 * q^26 - 47 * q^27 - 76 * q^28 - 54 * q^29 - 22 * q^30 - 62 * q^31 - 117 * q^32 - 59 * q^33 - 35 * q^34 - 52 * q^35 + 52 * q^36 - 190 * q^37 - 19 * q^38 - 43 * q^39 - 41 * q^40 - 50 * q^41 + 8 * q^42 - 50 * q^43 - 18 * q^44 - 75 * q^45 - 17 * q^46 - 63 * q^47 - 35 * q^48 + 74 * q^49 - 53 * q^50 - 33 * q^51 - 124 * q^52 - 100 * q^53 - 46 * q^54 - 61 * q^55 - 3 * q^56 - 80 * q^57 - 112 * q^58 - 109 * q^59 - 55 * q^60 - 76 * q^61 - 6 * q^62 - 93 * q^63 + 57 * q^64 - 17 * q^65 + 50 * q^66 - 120 * q^67 + 26 * q^68 - 17 * q^69 - 109 * q^71 - 153 * q^72 - 94 * q^73 + 35 * q^74 - 105 * q^75 - 16 * q^76 - 52 * q^77 - 59 * q^78 - 29 * q^79 - 30 * q^80 + 39 * q^81 - 65 * q^82 + 8 * q^83 + 11 * q^84 - 155 * q^85 - 15 * q^86 - 25 * q^87 - 139 * q^88 + 6 * q^89 + 82 * q^90 - 34 * q^91 + 121 * q^92 - 151 * q^93 - 3 * q^94 - 70 * q^95 - 23 * q^96 - 203 * q^97 - 18 * q^98 - 49 * 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 $

$2$	−2.40779	−1.70256	−0.851282	−	0.524708i	$-0.824174\pi$
$2$	−2.40779	−1.70256	−0.851282	+	0.524708i	$0.824174\pi$
$3$	2.53147	1.46154	0.730772	−	0.682621i	$-0.239160\pi$
$3$	2.53147	1.46154	0.730772	+	0.682621i	$0.239160\pi$
$4$	3.79745	1.89873
$5$	0.438044	0.195899	0.0979496	−	0.995191i	$-0.468772\pi$
$5$	0.438044	0.195899	0.0979496	+	0.995191i	$0.468772\pi$
$6$	−6.09525	−2.48837
$7$	1.85360	0.700593	0.350297	−	0.936639i	$-0.386081\pi$
$7$	1.85360	0.700593	0.350297	+	0.936639i	$0.386081\pi$
$8$	−4.32788	−1.53014
$9$	3.40834	1.13611
$10$	−1.05472	−0.333531
$11$	−2.41584	−0.728404	−0.364202	−	0.931320i	$-0.618658\pi$
$11$	−2.41584	−0.728404	−0.364202	+	0.931320i	$0.618658\pi$
$12$	9.61313	2.77507
$13$	2.44507	0.678142	0.339071	−	0.940761i	$-0.389887\pi$
$13$	2.44507	0.678142	0.339071	+	0.940761i	$0.389887\pi$
$14$	−4.46307	−1.19281
$15$	1.10890	0.286316
$16$	2.82573	0.706434
$17$	−2.28373	−0.553886	−0.276943	−	0.960886i	$-0.589321\pi$
$17$	−2.28373	−0.553886	−0.276943	+	0.960886i	$0.589321\pi$
$18$	−8.20657	−1.93431
$19$	−5.88842	−1.35090	−0.675448	−	0.737408i	$-0.736050\pi$
$19$	−5.88842	−1.35090	−0.675448	+	0.737408i	$0.736050\pi$
$20$	1.66345	0.371959
$21$	4.69232	1.02395
$22$	5.81684	1.24015
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−10.9559	−2.23637
$25$	−4.80812	−0.961623
$26$	−5.88722	−1.15458
$27$	1.03370	0.198936
$28$	7.03894	1.33023
$29$	0.633981	0.117727	0.0588637	−	0.998266i	$-0.481252\pi$
$29$	0.633981	0.117727	0.0588637	+	0.998266i	$0.481252\pi$
$30$	−2.66999	−0.487471
$31$	−7.77763	−1.39690	−0.698451	−	0.715657i	$-0.746127\pi$
$31$	−7.77763	−1.39690	−0.698451	+	0.715657i	$0.746127\pi$
$32$	1.85200	0.327390
$33$	−6.11563	−1.06460
$34$	5.49874	0.943027
$35$	0.811957	0.137246
$36$	12.9430	2.15717
$37$	−0.368777	−0.0606266	−0.0303133	−	0.999540i	$-0.509651\pi$
$37$	−0.368777	−0.0606266	−0.0303133	+	0.999540i	$0.509651\pi$
$38$	14.1781	2.29999
$39$	6.18963	0.991134
$40$	−1.89580	−0.299753
$41$	1.21706	0.190073	0.0950367	−	0.995474i	$-0.469703\pi$
$41$	1.21706	0.190073	0.0950367	+	0.995474i	$0.469703\pi$
$42$	−11.2981	−1.74334
$43$	1.62620	0.247993	0.123997	−	0.992283i	$-0.460429\pi$
$43$	1.62620	0.247993	0.123997	+	0.992283i	$0.460429\pi$
$44$	−9.17404	−1.38304
$45$	1.49300	0.222564
$46$	−2.40779	−0.355009
$47$	2.10885	0.307607	0.153804	−	0.988101i	$-0.450848\pi$
$47$	2.10885	0.307607	0.153804	+	0.988101i	$0.450848\pi$
$48$	7.15326	1.03248
$49$	−3.56418	−0.509169
$50$	11.5769	1.63723
$51$	−5.78120	−0.809529
$52$	9.28505	1.28760
$53$	3.87503	0.532276	0.266138	−	0.963935i	$-0.414252\pi$
$53$	3.87503	0.532276	0.266138	+	0.963935i	$0.414252\pi$
$54$	−2.48894	−0.338702
$55$	−1.05825	−0.142694
$56$	−8.02215	−1.07200
$57$	−14.9064	−1.97440
$58$	−1.52649	−0.200438
$59$	4.35648	0.567165	0.283583	−	0.958948i	$-0.408477\pi$
$59$	4.35648	0.567165	0.283583	+	0.958948i	$0.408477\pi$
$60$	4.21098	0.543635
$61$	1.13229	0.144975	0.0724874	−	0.997369i	$-0.476906\pi$
$61$	1.13229	0.144975	0.0724874	+	0.997369i	$0.476906\pi$
$62$	18.7269	2.37832
$63$	6.31769	0.795954
$64$	−10.1107	−1.26384
$65$	1.07105	0.132847
$66$	14.7252	1.81254
$67$	6.84097	0.835757	0.417879	−	0.908503i	$-0.362774\pi$
$67$	6.84097	0.835757	0.417879	+	0.908503i	$0.362774\pi$
$68$	−8.67236	−1.05168
$69$	2.53147	0.304753
$70$	−1.95502	−0.233670
$71$	−6.55604	−0.778059	−0.389030	−	0.921225i	$-0.627190\pi$
$71$	−6.55604	−0.778059	−0.389030	+	0.921225i	$0.627190\pi$
$72$	−14.7509	−1.73841
$73$	−2.45192	−0.286975	−0.143488	−	0.989652i	$-0.545832\pi$
$73$	−2.45192	−0.286975	−0.143488	+	0.989652i	$0.545832\pi$
$74$	0.887938	0.103221
$75$	−12.1716	−1.40546
$76$	−22.3610	−2.56498
$77$	−4.47800	−0.510315
$78$	−14.9033	−1.68747
$79$	−8.96780	−1.00896	−0.504478	−	0.863424i	$-0.668315\pi$
$79$	−8.96780	−1.00896	−0.504478	+	0.863424i	$0.668315\pi$
$80$	1.23780	0.138390
$81$	−7.60823	−0.845359
$82$	−2.93043	−0.323612
$83$	−17.6759	−1.94018	−0.970090	−	0.242745i	$-0.921952\pi$
$83$	−17.6759	−1.94018	−0.970090	+	0.242745i	$0.921952\pi$
$84$	17.8189	1.94420
$85$	−1.00037	−0.108506
$86$	−3.91555	−0.422225
$87$	1.60491	0.172064
$88$	10.4555	1.11456
$89$	1.83595	0.194610	0.0973052	−	0.995255i	$-0.468978\pi$
$89$	1.83595	0.194610	0.0973052	+	0.995255i	$0.468978\pi$
$90$	−3.59484	−0.378929
$91$	4.53218	0.475102
$92$	3.79745	0.395912
$93$	−19.6888	−2.04164
$94$	−5.07766	−0.523721
$95$	−2.57939	−0.264640
$96$	4.68827	0.478495
$97$	−8.24908	−0.837568	−0.418784	−	0.908086i	$-0.637543\pi$
$97$	−8.24908	−0.837568	−0.418784	+	0.908086i	$0.637543\pi$
$98$	8.58180	0.866893
$99$	−8.23402	−0.827550
$100$	−18.2586	−1.82586
$101$	11.8728	1.18139	0.590696	−	0.806894i	$-0.298853\pi$
$101$	11.8728	1.18139	0.590696	+	0.806894i	$0.298853\pi$
$102$	13.9199	1.37828
$103$	11.3261	1.11599	0.557995	−	0.829844i	$-0.311571\pi$
$103$	11.3261	1.11599	0.557995	+	0.829844i	$0.311571\pi$
$104$	−10.5820	−1.03765
$105$	2.05544	0.200591
$106$	−9.33025	−0.906234
$107$	14.7774	1.42859	0.714295	−	0.699845i	$-0.246748\pi$
$107$	14.7774	1.42859	0.714295	+	0.699845i	$0.246748\pi$
$108$	3.92544	0.377725
$109$	8.98101	0.860225	0.430112	−	0.902775i	$-0.358474\pi$
$109$	8.98101	0.860225	0.430112	+	0.902775i	$0.358474\pi$
$110$	2.54803	0.242945
$111$	−0.933549	−0.0886085
$112$	5.23777	0.494923
$113$	1.00932	0.0949485	0.0474743	−	0.998872i	$-0.484883\pi$
$113$	1.00932	0.0949485	0.0474743	+	0.998872i	$0.484883\pi$
$114$	35.8914	3.36154
$115$	0.438044	0.0408478
$116$	2.40751	0.223532
$117$	8.33365	0.770446
$118$	−10.4895	−0.965635
$119$	−4.23311	−0.388049
$120$	−4.79917	−0.438102
$121$	−5.16370	−0.469428
$122$	−2.72631	−0.246829
$123$	3.08096	0.277801
$124$	−29.5352	−2.65234
$125$	−4.29639	−0.384281
$126$	−15.2117	−1.35516
$127$	−17.5105	−1.55381	−0.776903	−	0.629621i	$-0.783210\pi$
$127$	−17.5105	−1.55381	−0.776903	+	0.629621i	$0.783210\pi$
$128$	20.6404	1.82437
$129$	4.11668	0.362453
$130$	−2.57886	−0.226181
$131$	−8.88986	−0.776711	−0.388355	−	0.921510i	$-0.626957\pi$
$131$	−8.88986	−0.776711	−0.388355	+	0.921510i	$0.626957\pi$
$132$	−23.2238	−2.02137
$133$	−10.9148	−0.946429
$134$	−16.4716	−1.42293
$135$	0.452807	0.0389715
$136$	9.88372	0.847522
$137$	−13.6536	−1.16651	−0.583254	−	0.812290i	$-0.698221\pi$
$137$	−13.6536	−1.16651	−0.583254	+	0.812290i	$0.698221\pi$
$138$	−6.09525	−0.518862
$139$	−10.9133	−0.925650	−0.462825	−	0.886450i	$-0.653164\pi$
$139$	−10.9133	−0.925650	−0.462825	+	0.886450i	$0.653164\pi$
$140$	3.08337	0.260592
$141$	5.33849	0.449582
$142$	15.7856	1.32470
$143$	−5.90691	−0.493961
$144$	9.63107	0.802589
$145$	0.277712	0.0230627
$146$	5.90371	0.488594
$147$	−9.02262	−0.744173
$148$	−1.40041	−0.115113
$149$	−14.8591	−1.21731	−0.608653	−	0.793437i	$-0.708290\pi$
$149$	−14.8591	−1.21731	−0.608653	+	0.793437i	$0.708290\pi$
$150$	29.3067	2.39288
$151$	−22.9236	−1.86549	−0.932746	−	0.360534i	$-0.882594\pi$
$151$	−22.9236	−1.86549	−0.932746	+	0.360534i	$0.882594\pi$
$152$	25.4844	2.06706
$153$	−7.78373	−0.629278
$154$	10.7821	0.868844
$155$	−3.40694	−0.273652
$156$	23.5048	1.88189
$157$	−5.67857	−0.453199	−0.226600	−	0.973988i	$-0.572761\pi$
$157$	−5.67857	−0.453199	−0.226600	+	0.973988i	$0.572761\pi$
$158$	21.5926	1.71781
$159$	9.80952	0.777946
$160$	0.811256	0.0641354
$161$	1.85360	0.146084
$162$	18.3190	1.43928
$163$	21.0884	1.65177	0.825887	−	0.563836i	$-0.190675\pi$
$163$	21.0884	1.65177	0.825887	+	0.563836i	$0.190675\pi$
$164$	4.62174	0.360897
$165$	−2.67892	−0.208553
$166$	42.5598	3.30328
$167$	16.6481	1.28827	0.644133	−	0.764914i	$-0.277218\pi$
$167$	16.6481	1.28827	0.644133	+	0.764914i	$0.277218\pi$
$168$	−20.3078	−1.56678
$169$	−7.02161	−0.540124
$170$	2.40869	0.184738
$171$	−20.0697	−1.53477
$172$	6.17542	0.470871
$173$	4.64597	0.353226	0.176613	−	0.984280i	$-0.443486\pi$
$173$	4.64597	0.353226	0.176613	+	0.984280i	$0.443486\pi$
$174$	−3.86427	−0.292950
$175$	−8.91231	−0.673707
$176$	−6.82653	−0.514569
$177$	11.0283	0.828937
$178$	−4.42059	−0.331337
$179$	−6.03801	−0.451302	−0.225651	−	0.974208i	$-0.572451\pi$
$179$	−6.03801	−0.451302	−0.225651	+	0.974208i	$0.572451\pi$
$180$	5.66961	0.422588
$181$	7.33023	0.544852	0.272426	−	0.962177i	$-0.412174\pi$
$181$	7.33023	0.544852	0.272426	+	0.962177i	$0.412174\pi$
$182$	−10.9125	−0.808891
$183$	2.86636	0.211887
$184$	−4.32788	−0.319056
$185$	−0.161541	−0.0118767
$186$	47.4066	3.47602
$187$	5.51713	0.403453
$188$	8.00825	0.584062
$189$	1.91607	0.139373
$190$	6.21062	0.450566
$191$	−1.58144	−0.114429	−0.0572143	−	0.998362i	$-0.518222\pi$
$191$	−1.58144	−0.114429	−0.0572143	+	0.998362i	$0.518222\pi$
$192$	−25.5949	−1.84715
$193$	−14.6802	−1.05670	−0.528352	−	0.849025i	$-0.677190\pi$
$193$	−14.6802	−1.05670	−0.528352	+	0.849025i	$0.677190\pi$
$194$	19.8621	1.42601
$195$	2.71133	0.194162
$196$	−13.5348	−0.966772
$197$	24.6721	1.75781	0.878906	−	0.476995i	$-0.158274\pi$
$197$	24.6721	1.75781	0.878906	+	0.476995i	$0.158274\pi$
$198$	19.8258	1.40896
$199$	−10.7855	−0.764564	−0.382282	−	0.924046i	$-0.624862\pi$
$199$	−10.7855	−0.764564	−0.382282	+	0.924046i	$0.624862\pi$
$200$	20.8090	1.47142
$201$	17.3177	1.22150
$202$	−28.5873	−2.01140
$203$	1.17515	0.0824790
$204$	−21.9538	−1.53707
$205$	0.533127	0.0372352
$206$	−27.2708	−1.90005
$207$	3.40834	0.236896
$208$	6.90913	0.479062
$209$	14.2255	0.983998
$210$	−4.94908	−0.341519
$211$	−1.54679	−0.106485	−0.0532427	−	0.998582i	$-0.516956\pi$
$211$	−1.54679	−0.106485	−0.0532427	+	0.998582i	$0.516956\pi$
$212$	14.7152	1.01065
$213$	−16.5964	−1.13717
$214$	−35.5810	−2.43227
$215$	0.712348	0.0485817
$216$	−4.47375	−0.304400
$217$	−14.4166	−0.978661
$218$	−21.6244	−1.46459
$219$	−6.20696	−0.419428
$220$	−4.01864	−0.270936
$221$	−5.58389	−0.375613
$222$	2.24779	0.150862
$223$	26.9149	1.80235	0.901177	−	0.433451i	$-0.142704\pi$
$223$	26.9149	1.80235	0.901177	+	0.433451i	$0.142704\pi$
$224$	3.43285	0.229367
$225$	−16.3877	−1.09251
$226$	−2.43022	−0.161656
$227$	4.15285	0.275634	0.137817	−	0.990458i	$-0.455991\pi$
$227$	4.15285	0.275634	0.137817	+	0.990458i	$0.455991\pi$
$228$	−56.6062	−3.74884
$229$	−17.9705	−1.18752	−0.593761	−	0.804641i	$-0.702358\pi$
$229$	−17.9705	−1.18752	−0.593761	+	0.804641i	$0.702358\pi$
$230$	−1.05472	−0.0695460
$231$	−11.3359	−0.745848
$232$	−2.74380	−0.180139
$233$	−20.1926	−1.32286	−0.661430	−	0.750007i	$-0.730050\pi$
$233$	−20.1926	−1.32286	−0.661430	+	0.750007i	$0.730050\pi$
$234$	−20.0657	−1.31173
$235$	0.923768	0.0602600
$236$	16.5435	1.07689
$237$	−22.7017	−1.47464
$238$	10.1924	0.660678
$239$	−5.47429	−0.354103	−0.177051	−	0.984202i	$-0.556656\pi$
$239$	−5.47429	−0.354103	−0.177051	+	0.984202i	$0.556656\pi$
$240$	3.13344	0.202263
$241$	−21.4066	−1.37892	−0.689459	−	0.724325i	$-0.742152\pi$
$241$	−21.4066	−1.37892	−0.689459	+	0.724325i	$0.742152\pi$
$242$	12.4331	0.799231
$243$	−22.3611	−1.43447
$244$	4.29981	0.275267
$245$	−1.56127	−0.0997458
$246$	−7.41830	−0.472974
$247$	−14.3976	−0.916099
$248$	33.6607	2.13745
$249$	−44.7460	−2.83566
$250$	10.3448	0.654262
$251$	−19.5625	−1.23478	−0.617388	−	0.786659i	$-0.711809\pi$
$251$	−19.5625	−1.23478	−0.617388	+	0.786659i	$0.711809\pi$
$252$	23.9911	1.51130
$253$	−2.41584	−0.151883
$254$	42.1616	2.64545
$255$	−2.53242	−0.158586
$256$	−29.4764	−1.84228
$257$	−1.94072	−0.121059	−0.0605295	−	0.998166i	$-0.519279\pi$
$257$	−1.94072	−0.121059	−0.0605295	+	0.998166i	$0.519279\pi$
$258$	−9.91210	−0.617100
$259$	−0.683564	−0.0424746
$260$	4.06726	0.252241
$261$	2.16082	0.133752
$262$	21.4049	1.32240
$263$	27.7702	1.71238	0.856191	−	0.516660i	$-0.172825\pi$
$263$	27.7702	1.71238	0.856191	+	0.516660i	$0.172825\pi$
$264$	26.4678	1.62898
$265$	1.69743	0.104272
$266$	26.2804	1.61136
$267$	4.64766	0.284432
$268$	25.9782	1.58687
$269$	18.9511	1.15547	0.577735	−	0.816224i	$-0.303937\pi$
$269$	18.9511	1.15547	0.577735	+	0.816224i	$0.303937\pi$
$270$	−1.09027	−0.0663514
$271$	−31.1792	−1.89400	−0.947001	−	0.321232i	$-0.895903\pi$
$271$	−31.1792	−1.89400	−0.947001	+	0.321232i	$0.895903\pi$
$272$	−6.45322	−0.391284
$273$	11.4731	0.694382
$274$	32.8751	1.98605
$275$	11.6157	0.700450
$276$	9.61313	0.578643
$277$	−3.54097	−0.212756	−0.106378	−	0.994326i	$-0.533925\pi$
$277$	−3.54097	−0.212756	−0.106378	+	0.994326i	$0.533925\pi$
$278$	26.2768	1.57598
$279$	−26.5088	−1.58704
$280$	−3.51405	−0.210005
$281$	−13.9019	−0.829320	−0.414660	−	0.909976i	$-0.636099\pi$
$281$	−13.9019	−0.829320	−0.414660	+	0.909976i	$0.636099\pi$
$282$	−12.8540	−0.765442
$283$	−5.95084	−0.353741	−0.176870	−	0.984234i	$-0.556597\pi$
$283$	−5.95084	−0.353741	−0.176870	+	0.984234i	$0.556597\pi$
$284$	−24.8963	−1.47732
$285$	−6.52964	−0.386783
$286$	14.2226	0.841000
$287$	2.25594	0.133164
$288$	6.31223	0.371952
$289$	−11.7846	−0.693210
$290$	−0.668672	−0.0392657
$291$	−20.8823	−1.22414
$292$	−9.31104	−0.544888
$293$	1.23015	0.0718664	0.0359332	−	0.999354i	$-0.488560\pi$
$293$	1.23015	0.0718664	0.0359332	+	0.999354i	$0.488560\pi$
$294$	21.7246	1.26700
$295$	1.90833	0.111107
$296$	1.59603	0.0927671
$297$	−2.49726	−0.144906
$298$	35.7776	2.07254
$299$	2.44507	0.141402
$300$	−46.2211	−2.66858
$301$	3.01432	0.173743
$302$	55.1951	3.17612
$303$	30.0557	1.72666
$304$	−16.6391	−0.954318
$305$	0.495993	0.0284004
$306$	18.7416	1.07139
$307$	−22.6661	−1.29362	−0.646811	−	0.762651i	$-0.723898\pi$
$307$	−22.6661	−1.29362	−0.646811	+	0.762651i	$0.723898\pi$
$308$	−17.0050	−0.968948
$309$	28.6716	1.63107
$310$	8.20320	0.465911
$311$	2.76483	0.156779	0.0783896	−	0.996923i	$-0.475022\pi$
$311$	2.76483	0.156779	0.0783896	+	0.996923i	$0.475022\pi$
$312$	−26.7880	−1.51657
$313$	−28.6947	−1.62192	−0.810961	−	0.585100i	$-0.801055\pi$
$313$	−28.6947	−1.62192	−0.810961	+	0.585100i	$0.801055\pi$
$314$	13.6728	0.771601
$315$	2.76743	0.155927
$316$	−34.0548	−1.91573
$317$	34.2672	1.92464	0.962320	−	0.271921i	$-0.0876588\pi$
$317$	34.2672	1.92464	0.962320	+	0.271921i	$0.0876588\pi$
$318$	−23.6193	−1.32450
$319$	−1.53160	−0.0857531
$320$	−4.42893	−0.247584
$321$	37.4087	2.08795
$322$	−4.46307	−0.248717
$323$	13.4476	0.748243
$324$	−28.8919	−1.60511
$325$	−11.7562	−0.652117
$326$	−50.7765	−2.81225
$327$	22.7352	1.25726
$328$	−5.26731	−0.290838
$329$	3.90895	0.215508
$330$	6.45027	0.355076
$331$	0.958877	0.0527046	0.0263523	−	0.999653i	$-0.491611\pi$
$331$	0.958877	0.0527046	0.0263523	+	0.999653i	$0.491611\pi$
$332$	−67.1233	−3.68387
$333$	−1.25692	−0.0688787
$334$	−40.0850	−2.19336
$335$	2.99664	0.163724
$336$	13.2593	0.723352
$337$	−6.61874	−0.360546	−0.180273	−	0.983617i	$-0.557698\pi$
$337$	−6.61874	−0.360546	−0.180273	+	0.983617i	$0.557698\pi$
$338$	16.9066	0.919596
$339$	2.55505	0.138772
$340$	−3.79887	−0.206023
$341$	18.7895	1.01751
$342$	48.3237	2.61305
$343$	−19.5817	−1.05731
$344$	−7.03801	−0.379464
$345$	1.10890	0.0597009
$346$	−11.1865	−0.601390
$347$	13.6213	0.731227	0.365614	−	0.930767i	$-0.380859\pi$
$347$	13.6213	0.731227	0.365614	+	0.930767i	$0.380859\pi$
$348$	6.09455	0.326702
$349$	1.00000	0.0535288
$349$	1.00000	0.0535288
$350$	21.4590	1.14703
$351$	2.52748	0.134907
$352$	−4.47413	−0.238472
$353$	−16.0912	−0.856448	−0.428224	−	0.903673i	$-0.640861\pi$
$353$	−16.0912	−0.856448	−0.428224	+	0.903673i	$0.640861\pi$
$354$	−26.5538	−1.41132
$355$	−2.87184	−0.152421
$356$	6.97194	0.369512
$357$	−10.7160	−0.567151
$358$	14.5383	0.768370
$359$	−20.5763	−1.08597	−0.542987	−	0.839741i	$-0.682707\pi$
$359$	−20.5763	−1.08597	−0.542987	+	0.839741i	$0.682707\pi$
$360$	−6.46155	−0.340553
$361$	15.6735	0.824920
$362$	−17.6497	−0.927645
$363$	−13.0718	−0.686090
$364$	17.2107	0.902087
$365$	−1.07405	−0.0562183
$366$	−6.90158	−0.360752
$367$	32.9286	1.71886	0.859430	−	0.511254i	$-0.170819\pi$
$367$	32.9286	1.71886	0.859430	+	0.511254i	$0.170819\pi$
$368$	2.82573	0.147302
$369$	4.14817	0.215945
$370$	0.388956	0.0202209
$371$	7.18274	0.372909
$372$	−74.7674	−3.87651
$373$	24.6817	1.27797	0.638984	−	0.769220i	$-0.279355\pi$
$373$	24.6817	1.27797	0.638984	+	0.769220i	$0.279355\pi$
$374$	−13.2841	−0.686904
$375$	−10.8762	−0.561643
$376$	−9.12685	−0.470681
$377$	1.55013	0.0798358
$378$	−4.61349	−0.237292
$379$	−6.12561	−0.314651	−0.157326	−	0.987547i	$-0.550287\pi$
$379$	−6.12561	−0.314651	−0.157326	+	0.987547i	$0.550287\pi$
$380$	−9.79510	−0.502478
$381$	−44.3273	−2.27096
$382$	3.80776	0.194822
$383$	−12.3390	−0.630493	−0.315247	−	0.949010i	$-0.602087\pi$
$383$	−12.3390	−0.630493	−0.315247	+	0.949010i	$0.602087\pi$
$384$	52.2506	2.66640
$385$	−1.96156	−0.0999703
$386$	35.3469	1.79911
$387$	5.54265	0.281749
$388$	−31.3255	−1.59031
$389$	−31.5099	−1.59762	−0.798809	−	0.601585i	$-0.794536\pi$
$389$	−31.5099	−1.59762	−0.798809	+	0.601585i	$0.794536\pi$
$390$	−6.52832	−0.330574
$391$	−2.28373	−0.115493
$392$	15.4254	0.779099
$393$	−22.5044	−1.13520
$394$	−59.4051	−2.99279
$395$	−3.92829	−0.197654
$396$	−31.2683	−1.57129
$397$	6.69243	0.335884	0.167942	−	0.985797i	$-0.446288\pi$
$397$	6.69243	0.335884	0.167942	+	0.985797i	$0.446288\pi$
$398$	25.9692	1.30172
$399$	−27.6304	−1.38325
$400$	−13.5865	−0.679323
$401$	−27.0207	−1.34935	−0.674674	−	0.738116i	$-0.735716\pi$
$401$	−27.0207	−1.34935	−0.674674	+	0.738116i	$0.735716\pi$
$402$	−41.6974	−2.07968
$403$	−19.0169	−0.947298
$404$	45.0865	2.24314
$405$	−3.33274	−0.165605
$406$	−2.82950	−0.140426
$407$	0.890908	0.0441607
$408$	25.0204	1.23869
$409$	34.6394	1.71281	0.856405	−	0.516305i	$-0.172693\pi$
$409$	34.6394	1.71281	0.856405	+	0.516305i	$0.172693\pi$
$410$	−1.28366	−0.0633954
$411$	−34.5637	−1.70490
$412$	43.0102	2.11896
$413$	8.07515	0.397352
$414$	−8.20657	−0.403331
$415$	−7.74281	−0.380080
$416$	4.52827	0.222017
$417$	−27.6266	−1.35288
$418$	−34.2520	−1.67532
$419$	4.84215	0.236555	0.118277	−	0.992981i	$-0.462263\pi$
$419$	4.84215	0.236555	0.118277	+	0.992981i	$0.462263\pi$
$420$	7.80545	0.380867
$421$	34.9610	1.70390	0.851948	−	0.523627i	$-0.175421\pi$
$421$	34.9610	1.70390	0.851948	+	0.523627i	$0.175421\pi$
$422$	3.72435	0.181298
$423$	7.18767	0.349477
$424$	−16.7707	−0.814456
$425$	10.9804	0.532630
$426$	39.9607	1.93610
$427$	2.09881	0.101568
$428$	56.1166	2.71250
$429$	−14.9532	−0.721946
$430$	−1.71518	−0.0827135
$431$	28.3699	1.36653	0.683264	−	0.730171i	$-0.260560\pi$
$431$	28.3699	1.36653	0.683264	+	0.730171i	$0.260560\pi$
$432$	2.92097	0.140535
$433$	−32.3495	−1.55462	−0.777308	−	0.629120i	$-0.783415\pi$
$433$	−32.3495	−1.55462	−0.777308	+	0.629120i	$0.783415\pi$
$434$	34.7121	1.66623
$435$	0.703019	0.0337072
$436$	34.1050	1.63333
$437$	−5.88842	−0.281681
$438$	14.9451	0.714102
$439$	34.0843	1.62675	0.813377	−	0.581737i	$-0.197627\pi$
$439$	34.0843	1.62675	0.813377	+	0.581737i	$0.197627\pi$
$440$	4.57996	0.218341
$441$	−12.1479	−0.578474
$442$	13.4448	0.639506
$443$	19.8092	0.941162	0.470581	−	0.882357i	$-0.344044\pi$
$443$	19.8092	0.941162	0.470581	+	0.882357i	$0.344044\pi$
$444$	−3.54511	−0.168243
$445$	0.804228	0.0381240
$446$	−64.8054	−3.06862
$447$	−37.6154	−1.77915
$448$	−18.7411	−0.885435
$449$	−22.8519	−1.07845	−0.539224	−	0.842162i	$-0.681282\pi$
$449$	−22.8519	−1.07845	−0.539224	+	0.842162i	$0.681282\pi$
$450$	39.4581	1.86007
$451$	−2.94023	−0.138450
$452$	3.83283	0.180281
$453$	−58.0303	−2.72650
$454$	−9.99918	−0.469285
$455$	1.98529	0.0930720
$456$	64.5130	3.02110
$457$	32.1709	1.50489	0.752445	−	0.658656i	$-0.228875\pi$
$457$	32.1709	1.50489	0.752445	+	0.658656i	$0.228875\pi$
$458$	43.2691	2.02183
$459$	−2.36070	−0.110188
$460$	1.66345	0.0775588
$461$	−14.5943	−0.679724	−0.339862	−	0.940475i	$-0.610380\pi$
$461$	−14.5943	−0.679724	−0.339862	+	0.940475i	$0.610380\pi$
$462$	27.2945	1.26985
$463$	−25.9547	−1.20622	−0.603109	−	0.797659i	$-0.706072\pi$
$463$	−25.9547	−1.20622	−0.603109	+	0.797659i	$0.706072\pi$
$464$	1.79146	0.0831666
$465$	−8.62457	−0.399955
$466$	48.6195	2.25226
$467$	32.1420	1.48735	0.743677	−	0.668539i	$-0.233080\pi$
$467$	32.1420	1.48735	0.743677	+	0.668539i	$0.233080\pi$
$468$	31.6466	1.46287
$469$	12.6804	0.585526
$470$	−2.22424	−0.102597
$471$	−14.3751	−0.662371
$472$	−18.8543	−0.867841
$473$	−3.92865	−0.180639
$474$	54.6610	2.51066
$475$	28.3122	1.29905
$476$	−16.0750	−0.736798
$477$	13.2074	0.604726
$478$	13.1810	0.602883
$479$	−16.6829	−0.762260	−0.381130	−	0.924522i	$-0.624465\pi$
$479$	−16.6829	−0.762260	−0.381130	+	0.924522i	$0.624465\pi$
$480$	2.05367	0.0937368
$481$	−0.901688	−0.0411134
$482$	51.5425	2.34770
$483$	4.69232	0.213508
$484$	−19.6089	−0.891314
$485$	−3.61346	−0.164079
$486$	53.8409	2.44227
$487$	13.4500	0.609478	0.304739	−	0.952436i	$-0.401431\pi$
$487$	13.4500	0.609478	0.304739	+	0.952436i	$0.401431\pi$
$488$	−4.90042	−0.221831
$489$	53.3848	2.41414
$490$	3.75921	0.169824
$491$	9.99141	0.450906	0.225453	−	0.974254i	$-0.427614\pi$
$491$	9.99141	0.450906	0.225453	+	0.974254i	$0.427614\pi$
$492$	11.6998	0.527467
$493$	−1.44784	−0.0652076
$494$	34.6665	1.55972
$495$	−3.60686	−0.162116
$496$	−21.9775	−0.986819
$497$	−12.1523	−0.545103
$498$	107.739	4.82789
$499$	−39.1767	−1.75379	−0.876894	−	0.480683i	$-0.840389\pi$
$499$	−39.1767	−1.75379	−0.876894	+	0.480683i	$0.840389\pi$
$500$	−16.3153	−0.729643
$501$	42.1441	1.88286
$502$	47.1025	2.10229
$503$	39.7475	1.77225	0.886127	−	0.463443i	$-0.153386\pi$
$503$	39.7475	1.77225	0.886127	+	0.463443i	$0.153386\pi$
$504$	−27.3422	−1.21792
$505$	5.20083	0.231434
$506$	5.81684	0.258590
$507$	−17.7750	−0.789415
$508$	−66.4953	−2.95025
$509$	−40.7940	−1.80816	−0.904082	−	0.427359i	$-0.859444\pi$
$509$	−40.7940	−1.80816	−0.904082	+	0.427359i	$0.859444\pi$
$510$	6.09753	0.270003
$511$	−4.54487	−0.201053
$512$	29.6922	1.31222
$513$	−6.08688	−0.268742
$514$	4.67285	0.206111
$515$	4.96132	0.218622
$516$	15.6329	0.688200
$517$	−5.09465	−0.224062
$518$	1.64588	0.0723157
$519$	11.7611	0.516256
$520$	−4.63538	−0.203275
$521$	−30.2184	−1.32389	−0.661946	−	0.749551i	$-0.730269\pi$
$521$	−30.2184	−1.32389	−0.661946	+	0.749551i	$0.730269\pi$
$522$	−5.20281	−0.227721
$523$	34.4918	1.50822	0.754111	−	0.656747i	$-0.228068\pi$
$523$	34.4918	1.50822	0.754111	+	0.656747i	$0.228068\pi$
$524$	−33.7588	−1.47476
$525$	−22.5612	−0.984653
$526$	−66.8647	−2.91544
$527$	17.7620	0.773725
$528$	−17.2812	−0.752066
$529$	1.00000	0.0434783
$530$	−4.08706	−0.177531
$531$	14.8484	0.644364
$532$	−41.4482	−1.79701
$533$	2.97581	0.128897
$534$	−11.1906	−0.484264
$535$	6.47317	0.279860
$536$	−29.6069	−1.27882
$537$	−15.2850	−0.659598
$538$	−45.6303	−1.96726
$539$	8.61050	0.370881
$540$	1.71951	0.0739961
$541$	0.115906	0.00498320	0.00249160	−	0.999997i	$-0.499207\pi$
$541$	0.115906	0.00498320	0.00249160	+	0.999997i	$0.499207\pi$
$542$	75.0729	3.22466
$543$	18.5563	0.796325
$544$	−4.22946	−0.181337
$545$	3.93408	0.168517
$546$	−27.6248	−1.18223
$547$	1.78968	0.0765211	0.0382606	−	0.999268i	$-0.487818\pi$
$547$	1.78968	0.0765211	0.0382606	+	0.999268i	$0.487818\pi$
$548$	−51.8490	−2.21488
$549$	3.85923	0.164708
$550$	−27.9681	−1.19256
$551$	−3.73315	−0.159037
$552$	−10.9559	−0.466315
$553$	−16.6227	−0.706868
$554$	8.52591	0.362231
$555$	−0.408935	−0.0173583
$556$	−41.4426	−1.75756
$557$	2.92727	0.124032	0.0620161	−	0.998075i	$-0.480247\pi$
$557$	2.92727	0.124032	0.0620161	+	0.998075i	$0.480247\pi$
$558$	63.8276	2.70204
$559$	3.97618	0.168175
$560$	2.29437	0.0969550
$561$	13.9665	0.589664
$562$	33.4729	1.41197
$563$	4.18157	0.176232	0.0881162	−	0.996110i	$-0.471915\pi$
$563$	4.18157	0.176232	0.0881162	+	0.996110i	$0.471915\pi$
$564$	20.2726	0.853632
$565$	0.442125	0.0186003
$566$	14.3284	0.602266
$567$	−14.1026	−0.592253
$568$	28.3738	1.19054
$569$	32.3686	1.35696	0.678480	−	0.734619i	$-0.262639\pi$
$569$	32.3686	1.35696	0.678480	+	0.734619i	$0.262639\pi$
$570$	15.7220	0.658522
$571$	43.4205	1.81709	0.908547	−	0.417784i	$-0.137193\pi$
$571$	43.4205	1.81709	0.908547	+	0.417784i	$0.137193\pi$
$572$	−22.4312	−0.937896
$573$	−4.00336	−0.167243
$574$	−5.43184	−0.226720
$575$	−4.80812	−0.200512
$576$	−34.4607	−1.43586
$577$	0.920750	0.0383313	0.0191657	−	0.999816i	$-0.493899\pi$
$577$	0.920750	0.0383313	0.0191657	+	0.999816i	$0.493899\pi$
$578$	28.3748	1.18024
$579$	−37.1625	−1.54442
$580$	1.05460	0.0437898
$581$	−32.7639	−1.35928
$582$	50.2802	2.08418
$583$	−9.36146	−0.387712
$584$	10.6116	0.439112
$585$	3.65050	0.150930
$586$	−2.96195	−0.122357
$587$	0.707844	0.0292158	0.0146079	−	0.999893i	$-0.495350\pi$
$587$	0.707844	0.0292158	0.0146079	+	0.999893i	$0.495350\pi$
$588$	−34.2630	−1.41298
$589$	45.7979	1.88707
$590$	−4.59485	−0.189167
$591$	62.4566	2.56912
$592$	−1.04207	−0.0428287
$593$	−27.2904	−1.12068	−0.560342	−	0.828261i	$-0.689330\pi$
$593$	−27.2904	−1.12068	−0.560342	+	0.828261i	$0.689330\pi$
$594$	6.01289	0.246712
$595$	−1.85429	−0.0760185
$596$	−56.4267	−2.31133
$597$	−27.3032	−1.11744
$598$	−5.88722	−0.240747
$599$	47.1768	1.92759	0.963796	−	0.266640i	$-0.0859133\pi$
$599$	47.1768	1.92759	0.963796	+	0.266640i	$0.0859133\pi$
$600$	52.6773	2.15054
$601$	35.1764	1.43488	0.717438	−	0.696623i	$-0.245315\pi$
$601$	35.1764	1.43488	0.717438	+	0.696623i	$0.245315\pi$
$602$	−7.25785	−0.295808
$603$	23.3163	0.949515
$604$	−87.0511	−3.54206
$605$	−2.26193	−0.0919605
$606$	−72.3679	−2.93974
$607$	31.2479	1.26831	0.634156	−	0.773205i	$-0.281348\pi$
$607$	31.2479	1.26831	0.634156	+	0.773205i	$0.281348\pi$
$608$	−10.9053	−0.442270
$609$	2.97485	0.120547
$610$	−1.19425	−0.0483536
$611$	5.15629	0.208601
$612$	−29.5583	−1.19483
$613$	9.58971	0.387325	0.193662	−	0.981068i	$-0.437963\pi$
$613$	9.58971	0.387325	0.193662	+	0.981068i	$0.437963\pi$
$614$	54.5751	2.20247
$615$	1.34960	0.0544210
$616$	19.3803	0.780853
$617$	15.0165	0.604541	0.302271	−	0.953222i	$-0.402255\pi$
$617$	15.0165	0.604541	0.302271	+	0.953222i	$0.402255\pi$
$618$	−69.0352	−2.77700
$619$	20.2685	0.814661	0.407330	−	0.913281i	$-0.366460\pi$
$619$	20.2685	0.814661	0.407330	+	0.913281i	$0.366460\pi$
$620$	−12.9377	−0.519590
$621$	1.03370	0.0414811
$622$	−6.65713	−0.266927
$623$	3.40311	0.136343
$624$	17.4903	0.700171
$625$	22.1586	0.886343
$626$	69.0909	2.76143
$627$	36.0114	1.43816
$628$	−21.5641	−0.860501
$629$	0.842188	0.0335802
$630$	−6.66338	−0.265475
$631$	25.8377	1.02858	0.514291	−	0.857616i	$-0.328055\pi$
$631$	25.8377	1.02858	0.514291	+	0.857616i	$0.328055\pi$
$632$	38.8116	1.54384
$633$	−3.91565	−0.155633
$634$	−82.5083	−3.27682
$635$	−7.67037	−0.304389
$636$	37.2512	1.47711
$637$	−8.71469	−0.345289
$638$	3.68777	0.146000
$639$	−22.3452	−0.883964
$640$	9.04141	0.357393
$641$	22.5289	0.889837	0.444919	−	0.895571i	$-0.353233\pi$
$641$	22.5289	0.889837	0.444919	+	0.895571i	$0.353233\pi$
$642$	−90.0722	−3.55486
$643$	4.24996	0.167602	0.0838010	−	0.996483i	$-0.473294\pi$
$643$	4.24996	0.167602	0.0838010	+	0.996483i	$0.473294\pi$
$644$	7.03894	0.277373
$645$	1.80329	0.0710044
$646$	−32.3789	−1.27393
$647$	−0.510483	−0.0200691	−0.0100346	−	0.999950i	$-0.503194\pi$
$647$	−0.510483	−0.0200691	−0.0100346	+	0.999950i	$0.503194\pi$
$648$	32.9276	1.29352
$649$	−10.5246	−0.413125
$650$	28.3065	1.11027
$651$	−36.4951	−1.43036
$652$	80.0823	3.13627
$653$	−7.02869	−0.275054	−0.137527	−	0.990498i	$-0.543915\pi$
$653$	−7.02869	−0.275054	−0.137527	+	0.990498i	$0.543915\pi$
$654$	−54.7415	−2.14056
$655$	−3.89415	−0.152157
$656$	3.43910	0.134274
$657$	−8.35698	−0.326037
$658$	−9.41194	−0.366915
$659$	12.6439	0.492535	0.246267	−	0.969202i	$-0.420796\pi$
$659$	12.6439	0.492535	0.246267	+	0.969202i	$0.420796\pi$
$660$	−10.1731	−0.395986
$661$	−8.84762	−0.344133	−0.172066	−	0.985085i	$-0.555044\pi$
$661$	−8.84762	−0.344133	−0.172066	+	0.985085i	$0.555044\pi$
$662$	−2.30877	−0.0897330
$663$	−14.1355	−0.548976
$664$	76.4992	2.96874
$665$	−4.78114	−0.185405
$666$	3.02640	0.117270
$667$	0.633981	0.0245479
$668$	63.2202	2.44606
$669$	68.1342	2.63422
$670$	−7.21529	−0.278751
$671$	−2.73543	−0.105600
$672$	8.69016	0.335230
$673$	−41.4877	−1.59923	−0.799617	−	0.600511i	$-0.794964\pi$
$673$	−41.4877	−1.59923	−0.799617	+	0.600511i	$0.794964\pi$
$674$	15.9365	0.613852
$675$	−4.97017	−0.191302
$676$	−26.6642	−1.02555
$677$	41.8395	1.60802	0.804011	−	0.594615i	$-0.202695\pi$
$677$	41.8395	1.60802	0.804011	+	0.594615i	$0.202695\pi$
$678$	−6.15203	−0.236267
$679$	−15.2905	−0.586794
$680$	4.32951	0.166029
$681$	10.5128	0.402852
$682$	−45.2412	−1.73238
$683$	−34.9489	−1.33728	−0.668641	−	0.743585i	$-0.733124\pi$
$683$	−34.9489	−1.33728	−0.668641	+	0.743585i	$0.733124\pi$
$684$	−76.2139	−2.91411
$685$	−5.98089	−0.228518
$686$	47.1487	1.80014
$687$	−45.4917	−1.73562
$688$	4.59521	0.175191
$689$	9.47473	0.360959
$690$	−2.66999	−0.101645
$691$	37.6062	1.43061	0.715304	−	0.698813i	$-0.246288\pi$
$691$	37.6062	1.43061	0.715304	+	0.698813i	$0.246288\pi$
$692$	17.6428	0.670680
$693$	−15.2625	−0.579776
$694$	−32.7971	−1.24496
$695$	−4.78049	−0.181334
$696$	−6.94584	−0.263282
$697$	−2.77944	−0.105279
$698$	−2.40779	−0.0911362
$699$	−51.1169	−1.93342
$700$	−33.8441	−1.27918
$701$	20.2510	0.764868	0.382434	−	0.923983i	$-0.375086\pi$
$701$	20.2510	0.764868	0.382434	+	0.923983i	$0.375086\pi$
$702$	−6.08564	−0.229688
$703$	2.17152	0.0819002
$704$	24.4258	0.920583
$705$	2.33849	0.0880727
$706$	38.7442	1.45816
$707$	22.0074	0.827675
$708$	41.8794	1.57392
$709$	−14.0881	−0.529088	−0.264544	−	0.964374i	$-0.585221\pi$
$709$	−14.0881	−0.529088	−0.264544	+	0.964374i	$0.585221\pi$
$710$	6.91478	0.259507
$711$	−30.5653	−1.14629
$712$	−7.94579	−0.297781
$713$	−7.77763	−0.291274
$714$	25.8019	0.965611
$715$	−2.58749	−0.0967666
$716$	−22.9290	−0.856898
$717$	−13.8580	−0.517537
$718$	49.5434	1.84894
$719$	−41.0132	−1.52953	−0.764767	−	0.644307i	$-0.777146\pi$
$719$	−41.0132	−1.52953	−0.764767	+	0.644307i	$0.777146\pi$
$720$	4.21883	0.157227
$721$	20.9940	0.781856
$722$	−37.7385	−1.40448
$723$	−54.1901	−2.01535
$724$	27.8362	1.03452
$725$	−3.04826	−0.113209
$726$	31.4741	1.16811
$727$	−20.6236	−0.764888	−0.382444	−	0.923979i	$-0.624917\pi$
$727$	−20.6236	−0.764888	−0.382444	+	0.923979i	$0.624917\pi$
$728$	−19.6148	−0.726971
$729$	−33.7818	−1.25118
$730$	2.58608	0.0957152
$731$	−3.71381	−0.137360
$732$	10.8848	0.402316
$733$	−23.0247	−0.850435	−0.425218	−	0.905091i	$-0.639802\pi$
$733$	−23.0247	−0.850435	−0.425218	+	0.905091i	$0.639802\pi$
$734$	−79.2852	−2.92647
$735$	−3.95231	−0.145783
$736$	1.85200	0.0682655
$737$	−16.5267	−0.608769
$738$	−9.98791	−0.367660
$739$	24.2539	0.892196	0.446098	−	0.894984i	$-0.352813\pi$
$739$	24.2539	0.892196	0.446098	+	0.894984i	$0.352813\pi$
$740$	−0.613443	−0.0225506
$741$	−36.4472	−1.33892
$742$	−17.2945	−0.634902
$743$	25.3465	0.929873	0.464936	−	0.885344i	$-0.346077\pi$
$743$	25.3465	0.929873	0.464936	+	0.885344i	$0.346077\pi$
$744$	85.2110	3.12399
$745$	−6.50894	−0.238469
$746$	−59.4283	−2.17582
$747$	−60.2454	−2.20427
$748$	20.9510	0.766046
$749$	27.3914	1.00086
$750$	26.1875	0.956234
$751$	−37.7681	−1.37818	−0.689089	−	0.724677i	$-0.741989\pi$
$751$	−37.7681	−1.37818	−0.689089	+	0.724677i	$0.741989\pi$
$752$	5.95904	0.217304
$753$	−49.5220	−1.80468
$754$	−3.73239	−0.135926
$755$	−10.0415	−0.365448
$756$	7.27617	0.264632
$757$	16.2179	0.589450	0.294725	−	0.955582i	$-0.404772\pi$
$757$	16.2179	0.589450	0.294725	+	0.955582i	$0.404772\pi$
$758$	14.7492	0.535714
$759$	−6.11563	−0.221983
$760$	11.1633	0.404935
$761$	−23.9718	−0.868977	−0.434488	−	0.900677i	$-0.643071\pi$
$761$	−23.9718	−0.868977	−0.434488	+	0.900677i	$0.643071\pi$
$762$	106.731	3.86645
$763$	16.6472	0.602668
$764$	−6.00543	−0.217269
$765$	−3.40962	−0.123275
$766$	29.7097	1.07346
$767$	10.6519	0.384618
$768$	−74.6186	−2.69257
$769$	−47.6108	−1.71689	−0.858445	−	0.512905i	$-0.828569\pi$
$769$	−47.6108	−1.71689	−0.858445	+	0.512905i	$0.828569\pi$
$770$	4.72302	0.170206
$771$	−4.91288	−0.176933
$772$	−55.7474	−2.00639
$773$	−8.32217	−0.299327	−0.149664	−	0.988737i	$-0.547819\pi$
$773$	−8.32217	−0.299327	−0.149664	+	0.988737i	$0.547819\pi$
$774$	−13.3455	−0.479695
$775$	37.3957	1.34329
$776$	35.7011	1.28159
$777$	−1.73042	−0.0620785
$778$	75.8693	2.72005
$779$	−7.16658	−0.256769
$780$	10.2961	0.368661
$781$	15.8384	0.566741
$782$	5.49874	0.196635
$783$	0.655349	0.0234202
$784$	−10.0714	−0.359694
$785$	−2.48746	−0.0887814
$786$	54.1859	1.93275
$787$	4.82663	0.172051	0.0860253	−	0.996293i	$-0.472583\pi$
$787$	4.82663	0.172051	0.0860253	+	0.996293i	$0.472583\pi$
$788$	93.6910	3.33760
$789$	70.2993	2.50272
$790$	9.45850	0.336518
$791$	1.87086	0.0665203
$792$	35.6359	1.26627
$793$	2.76853	0.0983134
$794$	−16.1140	−0.571864
$795$	4.29700	0.152399
$796$	−40.9574	−1.45170
$797$	−26.7767	−0.948480	−0.474240	−	0.880396i	$-0.657277\pi$
$797$	−26.7767	−0.948480	−0.474240	+	0.880396i	$0.657277\pi$
$798$	66.5281	2.35507
$799$	−4.81604	−0.170379
$800$	−8.90462	−0.314826
$801$	6.25755	0.221100
$802$	65.0601	2.29735
$803$	5.92345	0.209034
$804$	65.7631	2.31929
$805$	0.811957	0.0286177
$806$	45.7886	1.61284
$807$	47.9742	1.68877
$808$	−51.3843	−1.80769
$809$	−5.15997	−0.181415	−0.0907075	−	0.995878i	$-0.528913\pi$
$809$	−5.15997	−0.181415	−0.0907075	+	0.995878i	$0.528913\pi$
$810$	8.02454	0.281954
$811$	−34.3954	−1.20779	−0.603893	−	0.797066i	$-0.706384\pi$
$811$	−34.3954	−1.20779	−0.603893	+	0.797066i	$0.706384\pi$
$812$	4.46256	0.156605
$813$	−78.9292	−2.76817
$814$	−2.14512	−0.0751864
$815$	9.23767	0.323581
$816$	−16.3361	−0.571879
$817$	−9.57576	−0.335013
$818$	−83.4044	−2.91617
$819$	15.4472	0.539769
$820$	2.02452	0.0706995
$821$	50.4759	1.76162	0.880810	−	0.473470i	$-0.156999\pi$
$821$	50.4759	1.76162	0.880810	+	0.473470i	$0.156999\pi$
$822$	83.2222	2.90271
$823$	−15.8876	−0.553808	−0.276904	−	0.960898i	$-0.589308\pi$
$823$	−15.8876	−0.553808	−0.276904	+	0.960898i	$0.589308\pi$
$824$	−49.0179	−1.70762
$825$	29.4047	1.02374
$826$	−19.4433	−0.676518
$827$	20.5392	0.714220	0.357110	−	0.934062i	$-0.383762\pi$
$827$	20.5392	0.714220	0.357110	+	0.934062i	$0.383762\pi$
$828$	12.9430	0.449801
$829$	25.5699	0.888080	0.444040	−	0.896007i	$-0.353545\pi$
$829$	25.5699	0.888080	0.444040	+	0.896007i	$0.353545\pi$
$830$	18.6431	0.647110
$831$	−8.96386	−0.310953
$832$	−24.7214	−0.857060
$833$	8.13963	0.282022
$834$	66.5190	2.30336
$835$	7.29258	0.252370
$836$	54.0206	1.86834
$837$	−8.03976	−0.277895
$838$	−11.6589	−0.402749
$839$	17.6313	0.608700	0.304350	−	0.952560i	$-0.401561\pi$
$839$	17.6313	0.608700	0.304350	+	0.952560i	$0.401561\pi$
$840$	−8.89572	−0.306932
$841$	−28.5981	−0.986140
$842$	−84.1788	−2.90099
$843$	−35.1923	−1.21209
$844$	−5.87386	−0.202187
$845$	−3.07578	−0.105810
$846$	−17.3064	−0.595007
$847$	−9.57142	−0.328878
$848$	10.9498	0.376018
$849$	−15.0644	−0.517008
$850$	−26.4386	−0.906837
$851$	−0.368777	−0.0126415
$852$	−63.0241	−2.15917
$853$	41.2618	1.41278	0.706388	−	0.707825i	$-0.250323\pi$
$853$	41.2618	1.41278	0.706388	+	0.707825i	$0.250323\pi$
$854$	−5.05349	−0.172927
$855$	−8.79143	−0.300661
$856$	−63.9551	−2.18594
$857$	18.4188	0.629173	0.314586	−	0.949229i	$-0.398134\pi$
$857$	18.4188	0.629173	0.314586	+	0.949229i	$0.398134\pi$
$858$	36.0041	1.22916
$859$	−17.3461	−0.591840	−0.295920	−	0.955213i	$-0.595626\pi$
$859$	−17.3461	−0.591840	−0.295920	+	0.955213i	$0.595626\pi$
$860$	2.70511	0.0922433
$861$	5.71085	0.194625
$862$	−68.3086	−2.32660
$863$	−38.9392	−1.32551	−0.662753	−	0.748838i	$-0.730612\pi$
$863$	−38.9392	−1.32551	−0.662753	+	0.748838i	$0.730612\pi$
$864$	1.91441	0.0651297
$865$	2.03514	0.0691967
$866$	77.8907	2.64683
$867$	−29.8323	−1.01316
$868$	−54.7462	−1.85821
$869$	21.6648	0.734928
$870$	−1.69272	−0.0573887
$871$	16.7267	0.566762
$872$	−38.8688	−1.31626
$873$	−28.1157	−0.951572
$874$	14.1781	0.479581
$875$	−7.96377	−0.269224
$876$	−23.5706	−0.796378
$877$	4.08776	0.138034	0.0690169	−	0.997615i	$-0.478014\pi$
$877$	4.08776	0.138034	0.0690169	+	0.997615i	$0.478014\pi$
$878$	−82.0677	−2.76965
$879$	3.11410	0.105036
$880$	−2.99032	−0.100804
$881$	−17.1818	−0.578869	−0.289435	−	0.957198i	$-0.593467\pi$
$881$	−17.1818	−0.578869	−0.289435	+	0.957198i	$0.593467\pi$
$882$	29.2497	0.984889
$883$	−30.4364	−1.02427	−0.512134	−	0.858906i	$-0.671145\pi$
$883$	−30.4364	−1.02427	−0.512134	+	0.858906i	$0.671145\pi$
$884$	−21.2046	−0.713186
$885$	4.83088	0.162388
$886$	−47.6963	−1.60239
$887$	−27.2472	−0.914871	−0.457436	−	0.889243i	$-0.651232\pi$
$887$	−27.2472	−0.914871	−0.457436	+	0.889243i	$0.651232\pi$
$888$	4.04029	0.135583
$889$	−32.4574	−1.08859
$890$	−1.93641	−0.0649086
$891$	18.3803	0.615763
$892$	102.208	3.42218
$893$	−12.4178	−0.415545
$894$	90.5699	3.02911
$895$	−2.64491	−0.0884097
$896$	38.2590	1.27814
$897$	6.18963	0.206666
$898$	55.0226	1.83613
$899$	−4.93087	−0.164454
$900$	−62.2315	−2.07438
$901$	−8.84952	−0.294820
$902$	7.07946	0.235720
$903$	7.63066	0.253933
$904$	−4.36821	−0.145284
$905$	3.21096	0.106736
$906$	139.725	4.64204
$907$	−3.65480	−0.121356	−0.0606778	−	0.998157i	$-0.519326\pi$
$907$	−3.65480	−0.121356	−0.0606778	+	0.998157i	$0.519326\pi$
$908$	15.7702	0.523353
$909$	40.4667	1.34220
$910$	−4.78017	−0.158461
$911$	−20.3568	−0.674451	−0.337225	−	0.941424i	$-0.609488\pi$
$911$	−20.3568	−0.674451	−0.337225	+	0.941424i	$0.609488\pi$
$912$	−42.1214	−1.39478
$913$	42.7022	1.41323
$914$	−77.4607	−2.56217
$915$	1.25559	0.0415085
$916$	−68.2420	−2.25478
$917$	−16.4782	−0.544158
$918$	5.68407	0.187602
$919$	−24.9865	−0.824229	−0.412114	−	0.911132i	$-0.635210\pi$
$919$	−24.9865	−0.824229	−0.412114	+	0.911132i	$0.635210\pi$
$920$	−1.89580	−0.0625028
$921$	−57.3785	−1.89069
$922$	35.1400	1.15727
$923$	−16.0300	−0.527634
$924$	−43.0476	−1.41616
$925$	1.77312	0.0583000
$926$	62.4935	2.05366
$927$	38.6031	1.26789
$928$	1.17413	0.0385427
$929$	−31.5923	−1.03651	−0.518255	−	0.855226i	$-0.673418\pi$
$929$	−31.5923	−1.03651	−0.518255	+	0.855226i	$0.673418\pi$
$930$	20.7662	0.680949
$931$	20.9874	0.687834
$932$	−76.6804	−2.51175
$933$	6.99909	0.229140
$934$	−77.3912	−2.53232
$935$	2.41675	0.0790361
$936$	−36.0671	−1.17889
$937$	−21.8801	−0.714792	−0.357396	−	0.933953i	$-0.616335\pi$
$937$	−21.8801	−0.714792	−0.357396	+	0.933953i	$0.616335\pi$
$938$	−30.5317	−0.996896
$939$	−72.6399	−2.37051
$940$	3.50797	0.114417
$941$	0.190737	0.00621783	0.00310892	−	0.999995i	$-0.499010\pi$
$941$	0.190737	0.00621783	0.00310892	+	0.999995i	$0.499010\pi$
$942$	34.6123	1.12773
$943$	1.21706	0.0396330
$944$	12.3102	0.400664
$945$	0.839322	0.0273032
$946$	9.45935	0.307550
$947$	−42.7522	−1.38926	−0.694630	−	0.719368i	$-0.744432\pi$
$947$	−42.7522	−1.38926	−0.694630	+	0.719368i	$0.744432\pi$
$948$	−86.2087	−2.79993
$949$	−5.99513	−0.194610
$950$	−68.1699	−2.21172
$951$	86.7465	2.81295
$952$	18.3204	0.593769
$953$	−20.1372	−0.652307	−0.326154	−	0.945317i	$-0.605753\pi$
$953$	−20.1372	−0.652307	−0.326154	+	0.945317i	$0.605753\pi$
$954$	−31.8007	−1.02959
$955$	−0.692738	−0.0224165
$956$	−20.7884	−0.672344
$957$	−3.87720	−0.125332
$958$	40.1688	1.29780
$959$	−25.3083	−0.817248
$960$	−11.2117	−0.361856
$961$	29.4915	0.951338
$962$	2.17107	0.0699983
$963$	50.3666	1.62304
$964$	−81.2904	−2.61819
$965$	−6.43058	−0.207008
$966$	−11.2981	−0.363511
$967$	33.1417	1.06577	0.532883	−	0.846189i	$-0.321109\pi$
$967$	33.1417	1.06577	0.532883	+	0.846189i	$0.321109\pi$
$968$	22.3479	0.718289
$969$	34.0421	1.09359
$970$	8.70046	0.279355
$971$	17.9610	0.576397	0.288199	−	0.957571i	$-0.406944\pi$
$971$	17.9610	0.576397	0.288199	+	0.957571i	$0.406944\pi$
$972$	−84.9153	−2.72366
$973$	−20.2288	−0.648504
$974$	−32.3848	−1.03768
$975$	−29.7605	−0.953098
$976$	3.19955	0.102415
$977$	−31.1991	−0.998147	−0.499074	−	0.866560i	$-0.666326\pi$
$977$	−31.1991	−0.998147	−0.499074	+	0.866560i	$0.666326\pi$
$978$	−128.539	−4.11023
$979$	−4.43537	−0.141755
$980$	−5.92884	−0.189390
$981$	30.6103	0.977313
$982$	−24.0572	−0.767696
$983$	21.2389	0.677417	0.338709	−	0.940891i	$-0.390010\pi$
$983$	21.2389	0.677417	0.338709	+	0.940891i	$0.390010\pi$
$984$	−13.3340	−0.425074
$985$	10.8075	0.344354
$986$	3.48610	0.111020
$987$	9.89540	0.314974
$988$	−54.6743	−1.73942
$989$	1.62620	0.0517102
$990$	8.68456	0.276014
$991$	−45.2562	−1.43761	−0.718805	−	0.695212i	$-0.755310\pi$
$991$	−45.2562	−1.43761	−0.718805	+	0.695212i	$0.755310\pi$
$992$	−14.4041	−0.457332
$993$	2.42737	0.0770302
$994$	29.2601	0.928073
$995$	−4.72452	−0.149777
$996$	−169.921	−5.38414
$997$	−17.8355	−0.564856	−0.282428	−	0.959289i	$-0.591140\pi$
$997$	−17.8355	−0.564856	−0.282428	+	0.959289i	$0.591140\pi$
$998$	94.3292	2.98594
$999$	−0.381206	−0.0120608

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8027.2.a.c.1.15	✓	143

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8027.2.a.c.1.15	✓	143	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:	\( N \)	\(=\)	\( 8027 = 23 \cdot 349 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8027.a (trivial)

\(f(q)\)	\(=\)	\(q-2.40779 q^{2} +2.53147 q^{3} +3.79745 q^{4} +0.438044 q^{5} -6.09525 q^{6} +1.85360 q^{7} -4.32788 q^{8} +3.40834 q^{9} +O(q^{10})\)	\(q-2.40779 q^{2} +2.53147 q^{3} +3.79745 q^{4} +0.438044 q^{5} -6.09525 q^{6} +1.85360 q^{7} -4.32788 q^{8} +3.40834 q^{9} -1.05472 q^{10} -2.41584 q^{11} +9.61313 q^{12} +2.44507 q^{13} -4.46307 q^{14} +1.10890 q^{15} +2.82573 q^{16} -2.28373 q^{17} -8.20657 q^{18} -5.88842 q^{19} +1.66345 q^{20} +4.69232 q^{21} +5.81684 q^{22} +1.00000 q^{23} -10.9559 q^{24} -4.80812 q^{25} -5.88722 q^{26} +1.03370 q^{27} +7.03894 q^{28} +0.633981 q^{29} -2.66999 q^{30} -7.77763 q^{31} +1.85200 q^{32} -6.11563 q^{33} +5.49874 q^{34} +0.811957 q^{35} +12.9430 q^{36} -0.368777 q^{37} +14.1781 q^{38} +6.18963 q^{39} -1.89580 q^{40} +1.21706 q^{41} -11.2981 q^{42} +1.62620 q^{43} -9.17404 q^{44} +1.49300 q^{45} -2.40779 q^{46} +2.10885 q^{47} +7.15326 q^{48} -3.56418 q^{49} +11.5769 q^{50} -5.78120 q^{51} +9.28505 q^{52} +3.87503 q^{53} -2.48894 q^{54} -1.05825 q^{55} -8.02215 q^{56} -14.9064 q^{57} -1.52649 q^{58} +4.35648 q^{59} +4.21098 q^{60} +1.13229 q^{61} +18.7269 q^{62} +6.31769 q^{63} -10.1107 q^{64} +1.07105 q^{65} +14.7252 q^{66} +6.84097 q^{67} -8.67236 q^{68} +2.53147 q^{69} -1.95502 q^{70} -6.55604 q^{71} -14.7509 q^{72} -2.45192 q^{73} +0.887938 q^{74} -12.1716 q^{75} -22.3610 q^{76} -4.47800 q^{77} -14.9033 q^{78} -8.96780 q^{79} +1.23780 q^{80} -7.60823 q^{81} -2.93043 q^{82} -17.6759 q^{83} +17.8189 q^{84} -1.00037 q^{85} -3.91555 q^{86} +1.60491 q^{87} +10.4555 q^{88} +1.83595 q^{89} -3.59484 q^{90} +4.53218 q^{91} +3.79745 q^{92} -19.6888 q^{93} -5.07766 q^{94} -2.57939 q^{95} +4.68827 q^{96} -8.24908 q^{97} +8.58180 q^{98} -8.23402 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 143 q - 17 q^{2} - 17 q^{3} + 121 q^{4} - 22 q^{5} - 11 q^{6} - 33 q^{7} - 45 q^{8} + 104 q^{9}+O(q^{10}) \) 143 * q - 17 * q^2 - 17 * q^3 + 121 * q^4 - 22 * q^5 - 11 * q^6 - 33 * q^7 - 45 * q^8 + 104 * q^9	\( 143 q - 17 q^{2} - 17 q^{3} + 121 q^{4} - 22 q^{5} - 11 q^{6} - 33 q^{7} - 45 q^{8} + 104 q^{9} - 22 q^{10} - 14 q^{11} - 36 q^{12} - 87 q^{13} - 18 q^{14} - 19 q^{15} + 81 q^{16} - 14 q^{17} - 60 q^{18} - 18 q^{19} - 25 q^{20} - 26 q^{21} - 62 q^{22} + 143 q^{23} - 21 q^{24} + 67 q^{25} - 5 q^{26} - 47 q^{27} - 76 q^{28} - 54 q^{29} - 22 q^{30} - 62 q^{31} - 117 q^{32} - 59 q^{33} - 35 q^{34} - 52 q^{35} + 52 q^{36} - 190 q^{37} - 19 q^{38} - 43 q^{39} - 41 q^{40} - 50 q^{41} + 8 q^{42} - 50 q^{43} - 18 q^{44} - 75 q^{45} - 17 q^{46} - 63 q^{47} - 35 q^{48} + 74 q^{49} - 53 q^{50} - 33 q^{51} - 124 q^{52} - 100 q^{53} - 46 q^{54} - 61 q^{55} - 3 q^{56} - 80 q^{57} - 112 q^{58} - 109 q^{59} - 55 q^{60} - 76 q^{61} - 6 q^{62} - 93 q^{63} + 57 q^{64} - 17 q^{65} + 50 q^{66} - 120 q^{67} + 26 q^{68} - 17 q^{69} - 109 q^{71} - 153 q^{72} - 94 q^{73} + 35 q^{74} - 105 q^{75} - 16 q^{76} - 52 q^{77} - 59 q^{78} - 29 q^{79} - 30 q^{80} + 39 q^{81} - 65 q^{82} + 8 q^{83} + 11 q^{84} - 155 q^{85} - 15 q^{86} - 25 q^{87} - 139 q^{88} + 6 q^{89} + 82 q^{90} - 34 q^{91} + 121 q^{92} - 151 q^{93} - 3 q^{94} - 70 q^{95} - 23 q^{96} - 203 q^{97} - 18 q^{98} - 49 q^{99}+O(q^{100}) \) 143 * q - 17 * q^2 - 17 * q^3 + 121 * q^4 - 22 * q^5 - 11 * q^6 - 33 * q^7 - 45 * q^8 + 104 * q^9 - 22 * q^10 - 14 * q^11 - 36 * q^12 - 87 * q^13 - 18 * q^14 - 19 * q^15 + 81 * q^16 - 14 * q^17 - 60 * q^18 - 18 * q^19 - 25 * q^20 - 26 * q^21 - 62 * q^22 + 143 * q^23 - 21 * q^24 + 67 * q^25 - 5 * q^26 - 47 * q^27 - 76 * q^28 - 54 * q^29 - 22 * q^30 - 62 * q^31 - 117 * q^32 - 59 * q^33 - 35 * q^34 - 52 * q^35 + 52 * q^36 - 190 * q^37 - 19 * q^38 - 43 * q^39 - 41 * q^40 - 50 * q^41 + 8 * q^42 - 50 * q^43 - 18 * q^44 - 75 * q^45 - 17 * q^46 - 63 * q^47 - 35 * q^48 + 74 * q^49 - 53 * q^50 - 33 * q^51 - 124 * q^52 - 100 * q^53 - 46 * q^54 - 61 * q^55 - 3 * q^56 - 80 * q^57 - 112 * q^58 - 109 * q^59 - 55 * q^60 - 76 * q^61 - 6 * q^62 - 93 * q^63 + 57 * q^64 - 17 * q^65 + 50 * q^66 - 120 * q^67 + 26 * q^68 - 17 * q^69 - 109 * q^71 - 153 * q^72 - 94 * q^73 + 35 * q^74 - 105 * q^75 - 16 * q^76 - 52 * q^77 - 59 * q^78 - 29 * q^79 - 30 * q^80 + 39 * q^81 - 65 * q^82 + 8 * q^83 + 11 * q^84 - 155 * q^85 - 15 * q^86 - 25 * q^87 - 139 * q^88 + 6 * q^89 + 82 * q^90 - 34 * q^91 + 121 * q^92 - 151 * q^93 - 3 * q^94 - 70 * q^95 - 23 * q^96 - 203 * q^97 - 18 * q^98 - 49 * q^99

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