LMFDB - Embedded newform 8015.2.a.o.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8015,2,Mod(1,8015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8015, 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("8015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8015 = 5 \cdot 7 \cdot 229 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8015.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:	$64.0000972201$
Analytic rank:	$0$
Dimension:	$73$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	8015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.68177 q^{2} -0.319561 q^{3} +5.19187 q^{4} +1.00000 q^{5} +0.856987 q^{6} +1.00000 q^{7} -8.55985 q^{8} -2.89788 q^{9} +O(q^{10})$	\(q-2.68177 q^{2} -0.319561 q^{3} +5.19187 q^{4} +1.00000 q^{5} +0.856987 q^{6} +1.00000 q^{7} -8.55985 q^{8} -2.89788 q^{9} -2.68177 q^{10} -5.35472 q^{11} -1.65912 q^{12} -4.26816 q^{13} -2.68177 q^{14} -0.319561 q^{15} +12.5718 q^{16} -3.80736 q^{17} +7.77144 q^{18} -3.73070 q^{19} +5.19187 q^{20} -0.319561 q^{21} +14.3601 q^{22} -5.80798 q^{23} +2.73539 q^{24} +1.00000 q^{25} +11.4462 q^{26} +1.88473 q^{27} +5.19187 q^{28} -8.36047 q^{29} +0.856987 q^{30} -3.40099 q^{31} -16.5949 q^{32} +1.71116 q^{33} +10.2105 q^{34} +1.00000 q^{35} -15.0454 q^{36} +3.87085 q^{37} +10.0049 q^{38} +1.36394 q^{39} -8.55985 q^{40} +9.94528 q^{41} +0.856987 q^{42} -5.20388 q^{43} -27.8010 q^{44} -2.89788 q^{45} +15.5756 q^{46} +0.348224 q^{47} -4.01745 q^{48} +1.00000 q^{49} -2.68177 q^{50} +1.21668 q^{51} -22.1597 q^{52} -6.01244 q^{53} -5.05441 q^{54} -5.35472 q^{55} -8.55985 q^{56} +1.19219 q^{57} +22.4208 q^{58} +2.86369 q^{59} -1.65912 q^{60} +10.7892 q^{61} +9.12067 q^{62} -2.89788 q^{63} +19.3600 q^{64} -4.26816 q^{65} -4.58893 q^{66} -9.27460 q^{67} -19.7673 q^{68} +1.85600 q^{69} -2.68177 q^{70} -7.80475 q^{71} +24.8054 q^{72} -8.60444 q^{73} -10.3807 q^{74} -0.319561 q^{75} -19.3693 q^{76} -5.35472 q^{77} -3.65776 q^{78} -11.0783 q^{79} +12.5718 q^{80} +8.09136 q^{81} -26.6709 q^{82} -14.6599 q^{83} -1.65912 q^{84} -3.80736 q^{85} +13.9556 q^{86} +2.67168 q^{87} +45.8356 q^{88} -6.25699 q^{89} +7.77144 q^{90} -4.26816 q^{91} -30.1543 q^{92} +1.08682 q^{93} -0.933855 q^{94} -3.73070 q^{95} +5.30308 q^{96} -7.34933 q^{97} -2.68177 q^{98} +15.5173 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 73 q + 7 q^{2} + 14 q^{3} + 95 q^{4} + 73 q^{5} - q^{6} + 73 q^{7} + 18 q^{8} + 111 q^{9}+O(q^{10}) $ 73 * q + 7 * q^2 + 14 * q^3 + 95 * q^4 + 73 * q^5 - q^6 + 73 * q^7 + 18 * q^8 + 111 * q^9	\( 73 q + 7 q^{2} + 14 q^{3} + 95 q^{4} + 73 q^{5} - q^{6} + 73 q^{7} + 18 q^{8} + 111 q^{9} + 7 q^{10} + 27 q^{11} + 21 q^{12} + 21 q^{13} + 7 q^{14} + 14 q^{15} + 135 q^{16} + 23 q^{17} + 41 q^{18} + 26 q^{19} + 95 q^{20} + 14 q^{21} + 48 q^{22} + 16 q^{23} - q^{24} + 73 q^{25} + 7 q^{26} + 44 q^{27} + 95 q^{28} + 66 q^{29} - q^{30} + 23 q^{31} + 3 q^{32} + 77 q^{33} + 29 q^{34} + 73 q^{35} + 142 q^{36} + 66 q^{37} - 12 q^{38} + 53 q^{39} + 18 q^{40} + 50 q^{41} - q^{42} + 43 q^{43} + 37 q^{44} + 111 q^{45} + 65 q^{46} + 28 q^{47} - 20 q^{48} + 73 q^{49} + 7 q^{50} + 71 q^{51} + 29 q^{52} - 7 q^{53} - 16 q^{54} + 27 q^{55} + 18 q^{56} + 33 q^{57} + 48 q^{58} + 16 q^{59} + 21 q^{60} + 42 q^{61} - 3 q^{62} + 111 q^{63} + 216 q^{64} + 21 q^{65} - 53 q^{66} + 48 q^{67} + 13 q^{68} + 73 q^{69} + 7 q^{70} + 68 q^{71} + 18 q^{72} + 65 q^{73} + 4 q^{74} + 14 q^{75} + 37 q^{76} + 27 q^{77} + 60 q^{78} + 116 q^{79} + 135 q^{80} + 177 q^{81} + 20 q^{82} + 40 q^{83} + 21 q^{84} + 23 q^{85} + 35 q^{86} - 14 q^{87} + 47 q^{88} + 59 q^{89} + 41 q^{90} + 21 q^{91} + 3 q^{92} + 37 q^{93} - 11 q^{94} + 26 q^{95} - 23 q^{96} + 70 q^{97} + 7 q^{98} + 49 q^{99}+O(q^{100}) \) 73 * q + 7 * q^2 + 14 * q^3 + 95 * q^4 + 73 * q^5 - q^6 + 73 * q^7 + 18 * q^8 + 111 * q^9 + 7 * q^10 + 27 * q^11 + 21 * q^12 + 21 * q^13 + 7 * q^14 + 14 * q^15 + 135 * q^16 + 23 * q^17 + 41 * q^18 + 26 * q^19 + 95 * q^20 + 14 * q^21 + 48 * q^22 + 16 * q^23 - q^24 + 73 * q^25 + 7 * q^26 + 44 * q^27 + 95 * q^28 + 66 * q^29 - q^30 + 23 * q^31 + 3 * q^32 + 77 * q^33 + 29 * q^34 + 73 * q^35 + 142 * q^36 + 66 * q^37 - 12 * q^38 + 53 * q^39 + 18 * q^40 + 50 * q^41 - q^42 + 43 * q^43 + 37 * q^44 + 111 * q^45 + 65 * q^46 + 28 * q^47 - 20 * q^48 + 73 * q^49 + 7 * q^50 + 71 * q^51 + 29 * q^52 - 7 * q^53 - 16 * q^54 + 27 * q^55 + 18 * q^56 + 33 * q^57 + 48 * q^58 + 16 * q^59 + 21 * q^60 + 42 * q^61 - 3 * q^62 + 111 * q^63 + 216 * q^64 + 21 * q^65 - 53 * q^66 + 48 * q^67 + 13 * q^68 + 73 * q^69 + 7 * q^70 + 68 * q^71 + 18 * q^72 + 65 * q^73 + 4 * q^74 + 14 * q^75 + 37 * q^76 + 27 * q^77 + 60 * q^78 + 116 * q^79 + 135 * q^80 + 177 * q^81 + 20 * q^82 + 40 * q^83 + 21 * q^84 + 23 * q^85 + 35 * q^86 - 14 * q^87 + 47 * q^88 + 59 * q^89 + 41 * q^90 + 21 * q^91 + 3 * q^92 + 37 * q^93 - 11 * q^94 + 26 * q^95 - 23 * q^96 + 70 * q^97 + 7 * 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 $

$2$	−2.68177	−1.89630	−0.948148	−	0.317830i	$-0.897046\pi$
$2$	−2.68177	−1.89630	−0.948148	+	0.317830i	$0.897046\pi$
$3$	−0.319561	−0.184499	−0.0922493	−	0.995736i	$-0.529406\pi$
$3$	−0.319561	−0.184499	−0.0922493	+	0.995736i	$0.529406\pi$
$4$	5.19187	2.59594
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.856987	0.349864
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−8.55985	−3.02637
$9$	−2.89788	−0.965960
$10$	−2.68177	−0.848049
$11$	−5.35472	−1.61451	−0.807255	−	0.590203i	$-0.799048\pi$
$11$	−5.35472	−1.61451	−0.807255	+	0.590203i	$0.799048\pi$
$12$	−1.65912	−0.478946
$13$	−4.26816	−1.18378	−0.591888	−	0.806021i	$-0.701617\pi$
$13$	−4.26816	−1.18378	−0.591888	+	0.806021i	$0.701617\pi$
$14$	−2.68177	−0.716732
$15$	−0.319561	−0.0825102
$16$	12.5718	3.14295
$17$	−3.80736	−0.923420	−0.461710	−	0.887031i	$-0.652764\pi$
$17$	−3.80736	−0.923420	−0.461710	+	0.887031i	$0.652764\pi$
$18$	7.77144	1.83175
$19$	−3.73070	−0.855881	−0.427941	−	0.903807i	$-0.640761\pi$
$19$	−3.73070	−0.855881	−0.427941	+	0.903807i	$0.640761\pi$
$20$	5.19187	1.16094
$21$	−0.319561	−0.0697339
$22$	14.3601	3.06159
$23$	−5.80798	−1.21105	−0.605523	−	0.795828i	$-0.707036\pi$
$23$	−5.80798	−1.21105	−0.605523	+	0.795828i	$0.707036\pi$
$24$	2.73539	0.558360
$25$	1.00000	0.200000
$26$	11.4462	2.24479
$27$	1.88473	0.362717
$28$	5.19187	0.981171
$29$	−8.36047	−1.55250	−0.776250	−	0.630425i	$-0.782881\pi$
$29$	−8.36047	−1.55250	−0.776250	+	0.630425i	$0.782881\pi$
$30$	0.856987	0.156464
$31$	−3.40099	−0.610836	−0.305418	−	0.952218i	$-0.598796\pi$
$31$	−3.40099	−0.610836	−0.305418	+	0.952218i	$0.598796\pi$
$32$	−16.5949	−2.93359
$33$	1.71116	0.297875
$34$	10.2105	1.75108
$35$	1.00000	0.169031
$36$	−15.0454	−2.50757
$37$	3.87085	0.636364	0.318182	−	0.948030i	$-0.396928\pi$
$37$	3.87085	0.636364	0.318182	+	0.948030i	$0.396928\pi$
$38$	10.0049	1.62300
$39$	1.36394	0.218405
$40$	−8.55985	−1.35343
$41$	9.94528	1.55319	0.776596	−	0.629999i	$-0.216945\pi$
$41$	9.94528	1.55319	0.776596	+	0.629999i	$0.216945\pi$
$42$	0.856987	0.132236
$43$	−5.20388	−0.793584	−0.396792	−	0.917909i	$-0.629877\pi$
$43$	−5.20388	−0.793584	−0.396792	+	0.917909i	$0.629877\pi$
$44$	−27.8010	−4.19116
$45$	−2.89788	−0.431991
$46$	15.5756	2.29650
$47$	0.348224	0.0507937	0.0253968	−	0.999677i	$-0.491915\pi$
$47$	0.348224	0.0507937	0.0253968	+	0.999677i	$0.491915\pi$
$48$	−4.01745	−0.579869
$49$	1.00000	0.142857
$50$	−2.68177	−0.379259
$51$	1.21668	0.170370
$52$	−22.1597	−3.07300
$53$	−6.01244	−0.825872	−0.412936	−	0.910760i	$-0.635497\pi$
$53$	−6.01244	−0.825872	−0.412936	+	0.910760i	$0.635497\pi$
$54$	−5.05441	−0.687818
$55$	−5.35472	−0.722031
$56$	−8.55985	−1.14386
$57$	1.19219	0.157909
$58$	22.4208	2.94400
$59$	2.86369	0.372821	0.186410	−	0.982472i	$-0.440315\pi$
$59$	2.86369	0.372821	0.186410	+	0.982472i	$0.440315\pi$
$60$	−1.65912	−0.214191
$61$	10.7892	1.38142	0.690709	−	0.723133i	$-0.257299\pi$
$61$	10.7892	1.38142	0.690709	+	0.723133i	$0.257299\pi$
$62$	9.12067	1.15833
$63$	−2.89788	−0.365099
$64$	19.3600	2.42001
$65$	−4.26816	−0.529400
$66$	−4.58893	−0.564858
$67$	−9.27460	−1.13307	−0.566536	−	0.824037i	$-0.691717\pi$
$67$	−9.27460	−1.13307	−0.566536	+	0.824037i	$0.691717\pi$
$68$	−19.7673	−2.39714
$69$	1.85600	0.223436
$70$	−2.68177	−0.320532
$71$	−7.80475	−0.926254	−0.463127	−	0.886292i	$-0.653273\pi$
$71$	−7.80475	−0.926254	−0.463127	+	0.886292i	$0.653273\pi$
$72$	24.8054	2.92335
$73$	−8.60444	−1.00707	−0.503537	−	0.863974i	$-0.667968\pi$
$73$	−8.60444	−1.00707	−0.503537	+	0.863974i	$0.667968\pi$
$74$	−10.3807	−1.20673
$75$	−0.319561	−0.0368997
$76$	−19.3693	−2.22181
$77$	−5.35472	−0.610227
$78$	−3.65776	−0.414160
$79$	−11.0783	−1.24641	−0.623205	−	0.782059i	$-0.714170\pi$
$79$	−11.0783	−1.24641	−0.623205	+	0.782059i	$0.714170\pi$
$80$	12.5718	1.40557
$81$	8.09136	0.899040
$82$	−26.6709	−2.94531
$83$	−14.6599	−1.60913	−0.804567	−	0.593861i	$-0.797603\pi$
$83$	−14.6599	−1.60913	−0.804567	+	0.593861i	$0.797603\pi$
$84$	−1.65912	−0.181025
$85$	−3.80736	−0.412966
$86$	13.9556	1.50487
$87$	2.67168	0.286434
$88$	45.8356	4.88610
$89$	−6.25699	−0.663240	−0.331620	−	0.943413i	$-0.607595\pi$
$89$	−6.25699	−0.663240	−0.331620	+	0.943413i	$0.607595\pi$
$90$	7.77144	0.819182
$91$	−4.26816	−0.447425
$92$	−30.1543	−3.14380
$93$	1.08682	0.112698
$94$	−0.933855	−0.0963198
$95$	−3.73070	−0.382762
$96$	5.30308	0.541243
$97$	−7.34933	−0.746211	−0.373106	−	0.927789i	$-0.621707\pi$
$97$	−7.34933	−0.746211	−0.373106	+	0.927789i	$0.621707\pi$
$98$	−2.68177	−0.270899
$99$	15.5173	1.55955
$100$	5.19187	0.519187
$101$	−6.75514	−0.672162	−0.336081	−	0.941833i	$-0.609102\pi$
$101$	−6.75514	−0.672162	−0.336081	+	0.941833i	$0.609102\pi$
$102$	−3.26286	−0.323071
$103$	3.20122	0.315426	0.157713	−	0.987485i	$-0.449588\pi$
$103$	3.20122	0.315426	0.157713	+	0.987485i	$0.449588\pi$
$104$	36.5348	3.58254
$105$	−0.319561	−0.0311859
$106$	16.1240	1.56610
$107$	−10.5553	−1.02042	−0.510212	−	0.860049i	$-0.670433\pi$
$107$	−10.5553	−1.02042	−0.510212	+	0.860049i	$0.670433\pi$
$108$	9.78528	0.941589
$109$	−2.22337	−0.212960	−0.106480	−	0.994315i	$-0.533958\pi$
$109$	−2.22337	−0.212960	−0.106480	+	0.994315i	$0.533958\pi$
$110$	14.3601	1.36918
$111$	−1.23697	−0.117408
$112$	12.5718	1.18792
$113$	−7.08836	−0.666816	−0.333408	−	0.942783i	$-0.608199\pi$
$113$	−7.08836	−0.666816	−0.333408	+	0.942783i	$0.608199\pi$
$114$	−3.19716	−0.299442
$115$	−5.80798	−0.541597
$116$	−43.4065	−4.03019
$117$	12.3686	1.14348
$118$	−7.67975	−0.706978
$119$	−3.80736	−0.349020
$120$	2.73539	0.249706
$121$	17.6730	1.60664
$122$	−28.9342	−2.61958
$123$	−3.17812	−0.286562
$124$	−17.6575	−1.58569
$125$	1.00000	0.0894427
$126$	7.77144	0.692335
$127$	−14.4501	−1.28224	−0.641118	−	0.767442i	$-0.721529\pi$
$127$	−14.4501	−1.28224	−0.641118	+	0.767442i	$0.721529\pi$
$128$	−18.7293	−1.65545
$129$	1.66296	0.146415
$130$	11.4462	1.00390
$131$	−5.40525	−0.472259	−0.236129	−	0.971722i	$-0.575879\pi$
$131$	−5.40525	−0.472259	−0.236129	+	0.971722i	$0.575879\pi$
$132$	8.88412	0.773263
$133$	−3.73070	−0.323493
$134$	24.8723	2.14864
$135$	1.88473	0.162212
$136$	32.5904	2.79461
$137$	7.34827	0.627805	0.313903	−	0.949455i	$-0.398363\pi$
$137$	7.34827	0.627805	0.313903	+	0.949455i	$0.398363\pi$
$138$	−4.97736	−0.423701
$139$	17.0118	1.44292	0.721462	−	0.692455i	$-0.243471\pi$
$139$	17.0118	1.44292	0.721462	+	0.692455i	$0.243471\pi$
$140$	5.19187	0.438793
$141$	−0.111279	−0.00937136
$142$	20.9305	1.75645
$143$	22.8548	1.91122
$144$	−36.4315	−3.03596
$145$	−8.36047	−0.694299
$146$	23.0751	1.90971
$147$	−0.319561	−0.0263569
$148$	20.0970	1.65196
$149$	−22.1035	−1.81079	−0.905395	−	0.424570i	$-0.860425\pi$
$149$	−22.1035	−1.81079	−0.905395	+	0.424570i	$0.860425\pi$
$150$	0.856987	0.0699727
$151$	12.3821	1.00764	0.503819	−	0.863809i	$-0.331928\pi$
$151$	12.3821	1.00764	0.503819	+	0.863809i	$0.331928\pi$
$152$	31.9342	2.59021
$153$	11.0333	0.891987
$154$	14.3601	1.15717
$155$	−3.40099	−0.273174
$156$	7.08139	0.566965
$157$	11.0161	0.879182	0.439591	−	0.898198i	$-0.355123\pi$
$157$	11.0161	0.879182	0.439591	+	0.898198i	$0.355123\pi$
$158$	29.7095	2.36356
$159$	1.92134	0.152372
$160$	−16.5949	−1.31194
$161$	−5.80798	−0.457733
$162$	−21.6991	−1.70484
$163$	−8.96123	−0.701898	−0.350949	−	0.936395i	$-0.614141\pi$
$163$	−8.96123	−0.701898	−0.350949	+	0.936395i	$0.614141\pi$
$164$	51.6346	4.03199
$165$	1.71116	0.133214
$166$	39.3145	3.05139
$167$	−10.3929	−0.804227	−0.402114	−	0.915590i	$-0.631724\pi$
$167$	−10.3929	−0.804227	−0.402114	+	0.915590i	$0.631724\pi$
$168$	2.73539	0.211040
$169$	5.21720	0.401323
$170$	10.2105	0.783106
$171$	10.8111	0.826747
$172$	−27.0179	−2.06009
$173$	2.49172	0.189442	0.0947210	−	0.995504i	$-0.469804\pi$
$173$	2.49172	0.189442	0.0947210	+	0.995504i	$0.469804\pi$
$174$	−7.16482	−0.543163
$175$	1.00000	0.0755929
$176$	−67.3184	−5.07432
$177$	−0.915123	−0.0687849
$178$	16.7798	1.25770
$179$	10.6687	0.797416	0.398708	−	0.917078i	$-0.369459\pi$
$179$	10.6687	0.797416	0.398708	+	0.917078i	$0.369459\pi$
$180$	−15.0454	−1.12142
$181$	19.1842	1.42595	0.712974	−	0.701190i	$-0.247348\pi$
$181$	19.1842	1.42595	0.712974	+	0.701190i	$0.247348\pi$
$182$	11.4462	0.848450
$183$	−3.44781	−0.254869
$184$	49.7154	3.66507
$185$	3.87085	0.284591
$186$	−2.91461	−0.213709
$187$	20.3874	1.49087
$188$	1.80793	0.131857
$189$	1.88473	0.137094
$190$	10.0049	0.725829
$191$	3.83417	0.277431	0.138716	−	0.990332i	$-0.455703\pi$
$191$	3.83417	0.277431	0.138716	+	0.990332i	$0.455703\pi$
$192$	−6.18671	−0.446487
$193$	16.1920	1.16552	0.582762	−	0.812643i	$-0.301972\pi$
$193$	16.1920	1.16552	0.582762	+	0.812643i	$0.301972\pi$
$194$	19.7092	1.41504
$195$	1.36394	0.0976736
$196$	5.19187	0.370848
$197$	−11.8516	−0.844393	−0.422197	−	0.906504i	$-0.638741\pi$
$197$	−11.8516	−0.844393	−0.422197	+	0.906504i	$0.638741\pi$
$198$	−41.6139	−2.95737
$199$	−6.34244	−0.449603	−0.224802	−	0.974405i	$-0.572173\pi$
$199$	−6.34244	−0.449603	−0.224802	+	0.974405i	$0.572173\pi$
$200$	−8.55985	−0.605273
$201$	2.96380	0.209050
$202$	18.1157	1.27462
$203$	−8.36047	−0.586790
$204$	6.31686	0.442269
$205$	9.94528	0.694608
$206$	−8.58492	−0.598140
$207$	16.8308	1.16982
$208$	−53.6584	−3.72054
$209$	19.9769	1.38183
$210$	0.856987	0.0591378
$211$	−0.793883	−0.0546532	−0.0273266	−	0.999627i	$-0.508699\pi$
$211$	−0.793883	−0.0546532	−0.0273266	+	0.999627i	$0.508699\pi$
$212$	−31.2158	−2.14391
$213$	2.49409	0.170892
$214$	28.3070	1.93502
$215$	−5.20388	−0.354902
$216$	−16.1330	−1.09771
$217$	−3.40099	−0.230874
$218$	5.96255	0.403835
$219$	2.74964	0.185804
$220$	−27.8010	−1.87435
$221$	16.2504	1.09312
$222$	3.31727	0.222641
$223$	2.08417	0.139566	0.0697830	−	0.997562i	$-0.477769\pi$
$223$	2.08417	0.139566	0.0697830	+	0.997562i	$0.477769\pi$
$224$	−16.5949	−1.10879
$225$	−2.89788	−0.193192
$226$	19.0093	1.26448
$227$	17.6889	1.17406	0.587028	−	0.809567i	$-0.300298\pi$
$227$	17.6889	1.17406	0.587028	+	0.809567i	$0.300298\pi$
$228$	6.18967	0.409921
$229$	1.00000	0.0660819
$229$	1.00000	0.0660819
$230$	15.5756	1.02703
$231$	1.71116	0.112586
$232$	71.5644	4.69843
$233$	−7.22480	−0.473312	−0.236656	−	0.971593i	$-0.576051\pi$
$233$	−7.22480	−0.473312	−0.236656	+	0.971593i	$0.576051\pi$
$234$	−33.1698	−2.16838
$235$	0.348224	0.0227156
$236$	14.8679	0.967819
$237$	3.54020	0.229961
$238$	10.2105	0.661845
$239$	−0.0565943	−0.00366078	−0.00183039	−	0.999998i	$-0.500583\pi$
$239$	−0.0565943	−0.00366078	−0.00183039	+	0.999998i	$0.500583\pi$
$240$	−4.01745	−0.259325
$241$	6.69479	0.431250	0.215625	−	0.976476i	$-0.430821\pi$
$241$	6.69479	0.431250	0.215625	+	0.976476i	$0.430821\pi$
$242$	−47.3950	−3.04667
$243$	−8.23987	−0.528588
$244$	56.0162	3.58607
$245$	1.00000	0.0638877
$246$	8.52298	0.543405
$247$	15.9232	1.01317
$248$	29.1120	1.84861
$249$	4.68473	0.296883
$250$	−2.68177	−0.169610
$251$	19.4144	1.22543	0.612715	−	0.790304i	$-0.290078\pi$
$251$	19.4144	1.22543	0.612715	+	0.790304i	$0.290078\pi$
$252$	−15.0454	−0.947773
$253$	31.1001	1.95525
$254$	38.7517	2.43150
$255$	1.21668	0.0761916
$256$	11.5076	0.719226
$257$	−16.0277	−0.999778	−0.499889	−	0.866090i	$-0.666626\pi$
$257$	−16.0277	−0.999778	−0.499889	+	0.866090i	$0.666626\pi$
$258$	−4.45966	−0.277646
$259$	3.87085	0.240523
$260$	−22.1597	−1.37429
$261$	24.2276	1.49965
$262$	14.4956	0.895542
$263$	−20.9381	−1.29110	−0.645548	−	0.763719i	$-0.723371\pi$
$263$	−20.9381	−1.29110	−0.645548	+	0.763719i	$0.723371\pi$
$264$	−14.6473	−0.901477
$265$	−6.01244	−0.369341
$266$	10.0049	0.613438
$267$	1.99949	0.122367
$268$	−48.1525	−2.94138
$269$	22.4544	1.36907	0.684533	−	0.728982i	$-0.260006\pi$
$269$	22.4544	1.36907	0.684533	+	0.728982i	$0.260006\pi$
$270$	−5.05441	−0.307602
$271$	−3.84272	−0.233429	−0.116714	−	0.993166i	$-0.537236\pi$
$271$	−3.84272	−0.233429	−0.116714	+	0.993166i	$0.537236\pi$
$272$	−47.8653	−2.90226
$273$	1.36394	0.0825492
$274$	−19.7063	−1.19050
$275$	−5.35472	−0.322902
$276$	9.63612	0.580026
$277$	−17.2186	−1.03456	−0.517282	−	0.855815i	$-0.673056\pi$
$277$	−17.2186	−1.03456	−0.517282	+	0.855815i	$0.673056\pi$
$278$	−45.6217	−2.73621
$279$	9.85567	0.590043
$280$	−8.55985	−0.511549
$281$	−8.92813	−0.532607	−0.266304	−	0.963889i	$-0.585802\pi$
$281$	−8.92813	−0.532607	−0.266304	+	0.963889i	$0.585802\pi$
$282$	0.298423	0.0177709
$283$	−3.99625	−0.237552	−0.118776	−	0.992921i	$-0.537897\pi$
$283$	−3.99625	−0.237552	−0.118776	+	0.992921i	$0.537897\pi$
$284$	−40.5213	−2.40450
$285$	1.19219	0.0706190
$286$	−61.2913	−3.62423
$287$	9.94528	0.587051
$288$	48.0900	2.83373
$289$	−2.50401	−0.147295
$290$	22.4208	1.31660
$291$	2.34856	0.137675
$292$	−44.6732	−2.61430
$293$	−22.3383	−1.30502	−0.652509	−	0.757781i	$-0.726283\pi$
$293$	−22.3383	−1.30502	−0.652509	+	0.757781i	$0.726283\pi$
$294$	0.856987	0.0499805
$295$	2.86369	0.166731
$296$	−33.1339	−1.92587
$297$	−10.0922	−0.585610
$298$	59.2764	3.43379
$299$	24.7894	1.43361
$300$	−1.65912	−0.0957893
$301$	−5.20388	−0.299947
$302$	−33.2058	−1.91078
$303$	2.15868	0.124013
$304$	−46.9016	−2.68999
$305$	10.7892	0.617789
$306$	−29.5887	−1.69147
$307$	−10.1515	−0.579379	−0.289689	−	0.957121i	$-0.593552\pi$
$307$	−10.1515	−0.579379	−0.289689	+	0.957121i	$0.593552\pi$
$308$	−27.8010	−1.58411
$309$	−1.02298	−0.0581955
$310$	9.12067	0.518019
$311$	−11.6215	−0.658992	−0.329496	−	0.944157i	$-0.606879\pi$
$311$	−11.6215	−0.658992	−0.329496	+	0.944157i	$0.606879\pi$
$312$	−11.6751	−0.660973
$313$	−27.4824	−1.55340	−0.776699	−	0.629872i	$-0.783107\pi$
$313$	−27.4824	−1.55340	−0.776699	+	0.629872i	$0.783107\pi$
$314$	−29.5427	−1.66719
$315$	−2.89788	−0.163277
$316$	−57.5172	−3.23560
$317$	−24.1301	−1.35528	−0.677641	−	0.735393i	$-0.736998\pi$
$317$	−24.1301	−1.35528	−0.677641	+	0.735393i	$0.736998\pi$
$318$	−5.15259	−0.288943
$319$	44.7680	2.50653
$320$	19.3600	1.08226
$321$	3.37307	0.188267
$322$	15.5756	0.867996
$323$	14.2041	0.790338
$324$	42.0093	2.33385
$325$	−4.26816	−0.236755
$326$	24.0319	1.33101
$327$	0.710501	0.0392908
$328$	−85.1301	−4.70053
$329$	0.348224	0.0191982
$330$	−4.58893	−0.252612
$331$	−30.1077	−1.65487	−0.827435	−	0.561562i	$-0.810201\pi$
$331$	−30.1077	−1.65487	−0.827435	+	0.561562i	$0.810201\pi$
$332$	−76.1124	−4.17721
$333$	−11.2173	−0.614702
$334$	27.8713	1.52505
$335$	−9.27460	−0.506726
$336$	−4.01745	−0.219170
$337$	18.5124	1.00843	0.504217	−	0.863577i	$-0.331781\pi$
$337$	18.5124	1.00843	0.504217	+	0.863577i	$0.331781\pi$
$338$	−13.9913	−0.761028
$339$	2.26516	0.123027
$340$	−19.7673	−1.07203
$341$	18.2114	0.986201
$342$	−28.9929	−1.56776
$343$	1.00000	0.0539949
$344$	44.5444	2.40167
$345$	1.85600	0.0999238
$346$	−6.68221	−0.359238
$347$	33.8931	1.81948	0.909739	−	0.415180i	$-0.136282\pi$
$347$	33.8931	1.81948	0.909739	+	0.415180i	$0.136282\pi$
$348$	13.8710	0.743564
$349$	7.11196	0.380694	0.190347	−	0.981717i	$-0.439039\pi$
$349$	7.11196	0.380694	0.190347	+	0.981717i	$0.439039\pi$
$350$	−2.68177	−0.143346
$351$	−8.04434	−0.429375
$352$	88.8610	4.73631
$353$	32.1742	1.71246	0.856231	−	0.516593i	$-0.172800\pi$
$353$	32.1742	1.71246	0.856231	+	0.516593i	$0.172800\pi$
$354$	2.45415	0.130436
$355$	−7.80475	−0.414233
$356$	−32.4855	−1.72173
$357$	1.21668	0.0643937
$358$	−28.6110	−1.51214
$359$	16.4169	0.866452	0.433226	−	0.901285i	$-0.357375\pi$
$359$	16.4169	0.866452	0.433226	+	0.901285i	$0.357375\pi$
$360$	24.8054	1.30736
$361$	−5.08188	−0.267467
$362$	−51.4475	−2.70402
$363$	−5.64761	−0.296423
$364$	−22.1597	−1.16149
$365$	−8.60444	−0.450377
$366$	9.24622	0.483308
$367$	−13.2511	−0.691702	−0.345851	−	0.938290i	$-0.612410\pi$
$367$	−13.2511	−0.691702	−0.345851	+	0.938290i	$0.612410\pi$
$368$	−73.0166	−3.80626
$369$	−28.8202	−1.50032
$370$	−10.3807	−0.539668
$371$	−6.01244	−0.312150
$372$	5.64265	0.292558
$373$	5.84901	0.302850	0.151425	−	0.988469i	$-0.451614\pi$
$373$	5.84901	0.302850	0.151425	+	0.988469i	$0.451614\pi$
$374$	−54.6741	−2.82713
$375$	−0.319561	−0.0165020
$376$	−2.98075	−0.153720
$377$	35.6838	1.83781
$378$	−5.05441	−0.259971
$379$	−1.74284	−0.0895236	−0.0447618	−	0.998998i	$-0.514253\pi$
$379$	−1.74284	−0.0895236	−0.0447618	+	0.998998i	$0.514253\pi$
$380$	−19.3693	−0.993625
$381$	4.61767	0.236571
$382$	−10.2824	−0.526091
$383$	18.0198	0.920767	0.460383	−	0.887720i	$-0.347712\pi$
$383$	18.0198	0.920767	0.460383	+	0.887720i	$0.347712\pi$
$384$	5.98516	0.305429
$385$	−5.35472	−0.272902
$386$	−43.4231	−2.21018
$387$	15.0802	0.766571
$388$	−38.1568	−1.93712
$389$	−10.2376	−0.519065	−0.259532	−	0.965734i	$-0.583568\pi$
$389$	−10.2376	−0.519065	−0.259532	+	0.965734i	$0.583568\pi$
$390$	−3.65776	−0.185218
$391$	22.1131	1.11831
$392$	−8.55985	−0.432338
$393$	1.72731	0.0871310
$394$	31.7833	1.60122
$395$	−11.0783	−0.557411
$396$	80.5641	4.04850
$397$	−15.2307	−0.764405	−0.382202	−	0.924079i	$-0.624834\pi$
$397$	−15.2307	−0.764405	−0.382202	+	0.924079i	$0.624834\pi$
$398$	17.0089	0.852581
$399$	1.19219	0.0596839
$400$	12.5718	0.628589
$401$	−10.4499	−0.521843	−0.260922	−	0.965360i	$-0.584026\pi$
$401$	−10.4499	−0.521843	−0.260922	+	0.965360i	$0.584026\pi$
$402$	−7.94822	−0.396421
$403$	14.5160	0.723093
$404$	−35.0718	−1.74489
$405$	8.09136	0.402063
$406$	22.4208	1.11273
$407$	−20.7273	−1.02742
$408$	−10.4146	−0.515601
$409$	36.9507	1.82709	0.913547	−	0.406732i	$-0.133332\pi$
$409$	36.9507	1.82709	0.913547	+	0.406732i	$0.133332\pi$
$410$	−26.6709	−1.31718
$411$	−2.34822	−0.115829
$412$	16.6203	0.818824
$413$	2.86369	0.140913
$414$	−45.1363	−2.21833
$415$	−14.6599	−0.719627
$416$	70.8297	3.47271
$417$	−5.43631	−0.266217
$418$	−53.5733	−2.62035
$419$	6.89799	0.336989	0.168494	−	0.985703i	$-0.446109\pi$
$419$	6.89799	0.336989	0.168494	+	0.985703i	$0.446109\pi$
$420$	−1.65912	−0.0809567
$421$	−14.1256	−0.688440	−0.344220	−	0.938889i	$-0.611857\pi$
$421$	−14.1256	−0.688440	−0.344220	+	0.938889i	$0.611857\pi$
$422$	2.12901	0.103639
$423$	−1.00911	−0.0490647
$424$	51.4656	2.49939
$425$	−3.80736	−0.184684
$426$	−6.68858	−0.324063
$427$	10.7892	0.522127
$428$	−54.8020	−2.64895
$429$	−7.30350	−0.352617
$430$	13.9556	0.672998
$431$	34.8503	1.67868	0.839340	−	0.543607i	$-0.182942\pi$
$431$	34.8503	1.67868	0.839340	+	0.543607i	$0.182942\pi$
$432$	23.6944	1.14000
$433$	25.7794	1.23888	0.619439	−	0.785045i	$-0.287360\pi$
$433$	25.7794	1.23888	0.619439	+	0.785045i	$0.287360\pi$
$434$	9.12067	0.437806
$435$	2.67168	0.128097
$436$	−11.5434	−0.552830
$437$	21.6678	1.03651
$438$	−7.37390	−0.352339
$439$	−19.1253	−0.912803	−0.456401	−	0.889774i	$-0.650862\pi$
$439$	−19.1253	−0.912803	−0.456401	+	0.889774i	$0.650862\pi$
$440$	45.8356	2.18513
$441$	−2.89788	−0.137994
$442$	−43.5799	−2.07288
$443$	15.2455	0.724337	0.362169	−	0.932113i	$-0.382036\pi$
$443$	15.2455	0.724337	0.362169	+	0.932113i	$0.382036\pi$
$444$	−6.42220	−0.304784
$445$	−6.25699	−0.296610
$446$	−5.58924	−0.264658
$447$	7.06341	0.334088
$448$	19.3600	0.914676
$449$	10.0497	0.474277	0.237138	−	0.971476i	$-0.423791\pi$
$449$	10.0497	0.474277	0.237138	+	0.971476i	$0.423791\pi$
$450$	7.77144	0.366349
$451$	−53.2542	−2.50764
$452$	−36.8018	−1.73101
$453$	−3.95682	−0.185908
$454$	−47.4376	−2.22636
$455$	−4.26816	−0.200095
$456$	−10.2049	−0.477890
$457$	22.2011	1.03852	0.519261	−	0.854616i	$-0.326207\pi$
$457$	22.2011	1.03852	0.519261	+	0.854616i	$0.326207\pi$
$458$	−2.68177	−0.125311
$459$	−7.17585	−0.334940
$460$	−30.1543	−1.40595
$461$	−1.35632	−0.0631701	−0.0315850	−	0.999501i	$-0.510056\pi$
$461$	−1.35632	−0.0631701	−0.0315850	+	0.999501i	$0.510056\pi$
$462$	−4.58893	−0.213496
$463$	−16.6160	−0.772213	−0.386106	−	0.922454i	$-0.626180\pi$
$463$	−16.6160	−0.772213	−0.386106	+	0.922454i	$0.626180\pi$
$464$	−105.106	−4.87942
$465$	1.08682	0.0504002
$466$	19.3752	0.897540
$467$	−21.7516	−1.00654	−0.503271	−	0.864129i	$-0.667870\pi$
$467$	−21.7516	−1.00654	−0.503271	+	0.864129i	$0.667870\pi$
$468$	64.2163	2.96840
$469$	−9.27460	−0.428261
$470$	−0.933855	−0.0430755
$471$	−3.52032	−0.162208
$472$	−24.5128	−1.12829
$473$	27.8653	1.28125
$474$	−9.49399	−0.436073
$475$	−3.73070	−0.171176
$476$	−19.7673	−0.906034
$477$	17.4233	0.797760
$478$	0.151773	0.00694192
$479$	−15.2251	−0.695654	−0.347827	−	0.937559i	$-0.613080\pi$
$479$	−15.2251	−0.695654	−0.347827	+	0.937559i	$0.613080\pi$
$480$	5.30308	0.242051
$481$	−16.5214	−0.753312
$482$	−17.9539	−0.817777
$483$	1.85600	0.0844510
$484$	91.7562	4.17074
$485$	−7.34933	−0.333716
$486$	22.0974	1.00236
$487$	38.5446	1.74662	0.873312	−	0.487161i	$-0.161968\pi$
$487$	38.5446	1.74662	0.873312	+	0.487161i	$0.161968\pi$
$488$	−92.3541	−4.18067
$489$	2.86366	0.129499
$490$	−2.68177	−0.121150
$491$	24.8720	1.12246	0.561229	−	0.827660i	$-0.310329\pi$
$491$	24.8720	1.12246	0.561229	+	0.827660i	$0.310329\pi$
$492$	−16.5004	−0.743895
$493$	31.8313	1.43361
$494$	−42.7024	−1.92127
$495$	15.5173	0.697453
$496$	−42.7565	−1.91983
$497$	−7.80475	−0.350091
$498$	−12.5634	−0.562978
$499$	23.6667	1.05947	0.529734	−	0.848164i	$-0.322292\pi$
$499$	23.6667	1.05947	0.529734	+	0.848164i	$0.322292\pi$
$500$	5.19187	0.232188
$501$	3.32117	0.148379
$502$	−52.0650	−2.32378
$503$	−41.2350	−1.83858	−0.919289	−	0.393583i	$-0.871235\pi$
$503$	−41.2350	−1.83858	−0.919289	+	0.393583i	$0.871235\pi$
$504$	24.8054	1.10492
$505$	−6.75514	−0.300600
$506$	−83.4032	−3.70772
$507$	−1.66721	−0.0740436
$508$	−75.0229	−3.32860
$509$	−41.8779	−1.85621	−0.928103	−	0.372323i	$-0.878562\pi$
$509$	−41.8779	−1.85621	−0.928103	+	0.372323i	$0.878562\pi$
$510$	−3.26286	−0.144482
$511$	−8.60444	−0.380638
$512$	6.59793	0.291590
$513$	−7.03137	−0.310442
$514$	42.9824	1.89587
$515$	3.20122	0.141063
$516$	8.63385	0.380084
$517$	−1.86464	−0.0820069
$518$	−10.3807	−0.456103
$519$	−0.796256	−0.0349518
$520$	36.5348	1.60216
$521$	26.8881	1.17799	0.588994	−	0.808138i	$-0.299524\pi$
$521$	26.8881	1.17799	0.588994	+	0.808138i	$0.299524\pi$
$522$	−64.9729	−2.84379
$523$	−2.53032	−0.110643	−0.0553216	−	0.998469i	$-0.517618\pi$
$523$	−2.53032	−0.110643	−0.0553216	+	0.998469i	$0.517618\pi$
$524$	−28.0634	−1.22595
$525$	−0.319561	−0.0139468
$526$	56.1510	2.44830
$527$	12.9488	0.564059
$528$	21.5123	0.936204
$529$	10.7326	0.466634
$530$	16.1240	0.700380
$531$	−8.29863	−0.360130
$532$	−19.3693	−0.839766
$533$	−42.4481	−1.83863
$534$	−5.36216	−0.232044
$535$	−10.5553	−0.456347
$536$	79.3892	3.42909
$537$	−3.40930	−0.147122
$538$	−60.2174	−2.59615
$539$	−5.35472	−0.230644
$540$	9.78528	0.421092
$541$	16.0617	0.690549	0.345274	−	0.938502i	$-0.387786\pi$
$541$	16.0617	0.690549	0.345274	+	0.938502i	$0.387786\pi$
$542$	10.3053	0.442649
$543$	−6.13051	−0.263085
$544$	63.1827	2.70894
$545$	−2.22337	−0.0952386
$546$	−3.65776	−0.156538
$547$	−26.6289	−1.13857	−0.569285	−	0.822141i	$-0.692780\pi$
$547$	−26.6289	−1.13857	−0.569285	+	0.822141i	$0.692780\pi$
$548$	38.1513	1.62974
$549$	−31.2659	−1.33439
$550$	14.3601	0.612317
$551$	31.1904	1.32876
$552$	−15.8871	−0.676200
$553$	−11.0783	−0.471098
$554$	46.1762	1.96184
$555$	−1.23697	−0.0525066
$556$	88.3231	3.74574
$557$	−42.2399	−1.78976	−0.894882	−	0.446304i	$-0.852740\pi$
$557$	−42.2399	−1.78976	−0.894882	+	0.446304i	$0.852740\pi$
$558$	−26.4306	−1.11890
$559$	22.2110	0.939425
$560$	12.5718	0.531255
$561$	−6.51500	−0.275063
$562$	23.9432	1.00998
$563$	36.6911	1.54635	0.773173	−	0.634196i	$-0.218669\pi$
$563$	36.6911	1.54635	0.773173	+	0.634196i	$0.218669\pi$
$564$	−0.577745	−0.0243274
$565$	−7.08836	−0.298209
$566$	10.7170	0.450470
$567$	8.09136	0.339805
$568$	66.8076	2.80318
$569$	21.2076	0.889068	0.444534	−	0.895762i	$-0.353369\pi$
$569$	21.2076	0.889068	0.444534	+	0.895762i	$0.353369\pi$
$570$	−3.19716	−0.133914
$571$	−37.5205	−1.57018	−0.785092	−	0.619379i	$-0.787385\pi$
$571$	−37.5205	−1.57018	−0.785092	+	0.619379i	$0.787385\pi$
$572$	118.659	4.96139
$573$	−1.22525	−0.0511856
$574$	−26.6709	−1.11322
$575$	−5.80798	−0.242209
$576$	−56.1031	−2.33763
$577$	38.8333	1.61665	0.808326	−	0.588735i	$-0.200374\pi$
$577$	38.8333	1.61665	0.808326	+	0.588735i	$0.200374\pi$
$578$	6.71517	0.279314
$579$	−5.17432	−0.215037
$580$	−43.4065	−1.80236
$581$	−14.6599	−0.608196
$582$	−6.29828	−0.261072
$583$	32.1949	1.33338
$584$	73.6528	3.04777
$585$	12.3686	0.511380
$586$	59.9061	2.47470
$587$	45.6229	1.88306	0.941530	−	0.336928i	$-0.109388\pi$
$587$	45.6229	1.88306	0.941530	+	0.336928i	$0.109388\pi$
$588$	−1.65912	−0.0684209
$589$	12.6881	0.522803
$590$	−7.67975	−0.316170
$591$	3.78731	0.155789
$592$	48.6635	2.00006
$593$	−21.7430	−0.892877	−0.446439	−	0.894814i	$-0.647308\pi$
$593$	−21.7430	−0.892877	−0.446439	+	0.894814i	$0.647308\pi$
$594$	27.0650	1.11049
$595$	−3.80736	−0.156087
$596$	−114.759	−4.70069
$597$	2.02679	0.0829512
$598$	−66.4793	−2.71854
$599$	23.3991	0.956063	0.478031	−	0.878343i	$-0.341351\pi$
$599$	23.3991	0.956063	0.478031	+	0.878343i	$0.341351\pi$
$600$	2.73539	0.111672
$601$	−17.4355	−0.711211	−0.355605	−	0.934636i	$-0.615725\pi$
$601$	−17.4355	−0.711211	−0.355605	+	0.934636i	$0.615725\pi$
$602$	13.9556	0.568787
$603$	26.8767	1.09450
$604$	64.2861	2.61576
$605$	17.6730	0.718512
$606$	−5.78907	−0.235165
$607$	20.3054	0.824169	0.412085	−	0.911146i	$-0.364801\pi$
$607$	20.3054	0.824169	0.412085	+	0.911146i	$0.364801\pi$
$608$	61.9105	2.51080
$609$	2.67168	0.108262
$610$	−28.9342	−1.17151
$611$	−1.48628	−0.0601283
$612$	57.2834	2.31554
$613$	−34.0607	−1.37570	−0.687850	−	0.725853i	$-0.741445\pi$
$613$	−34.0607	−1.37570	−0.687850	+	0.725853i	$0.741445\pi$
$614$	27.2241	1.09867
$615$	−3.17812	−0.128154
$616$	45.8356	1.84677
$617$	−17.2414	−0.694112	−0.347056	−	0.937844i	$-0.612819\pi$
$617$	−17.2414	−0.694112	−0.347056	+	0.937844i	$0.612819\pi$
$618$	2.74340	0.110356
$619$	7.19545	0.289210	0.144605	−	0.989489i	$-0.453809\pi$
$619$	7.19545	0.289210	0.144605	+	0.989489i	$0.453809\pi$
$620$	−17.6575	−0.709143
$621$	−10.9465	−0.439267
$622$	31.1660	1.24964
$623$	−6.25699	−0.250681
$624$	17.1471	0.686434
$625$	1.00000	0.0400000
$626$	73.7014	2.94570
$627$	−6.38382	−0.254945
$628$	57.1943	2.28230
$629$	−14.7377	−0.587632
$630$	7.77144	0.309622
$631$	−18.5446	−0.738247	−0.369124	−	0.929380i	$-0.620342\pi$
$631$	−18.5446	−0.738247	−0.369124	+	0.929380i	$0.620342\pi$
$632$	94.8289	3.77209
$633$	0.253694	0.0100834
$634$	64.7113	2.57001
$635$	−14.4501	−0.573433
$636$	9.97535	0.395548
$637$	−4.26816	−0.169111
$638$	−120.057	−4.75311
$639$	22.6173	0.894725
$640$	−18.7293	−0.740342
$641$	13.8554	0.547254	0.273627	−	0.961836i	$-0.411777\pi$
$641$	13.8554	0.547254	0.273627	+	0.961836i	$0.411777\pi$
$642$	−9.04579	−0.357009
$643$	7.16992	0.282754	0.141377	−	0.989956i	$-0.454847\pi$
$643$	7.16992	0.282754	0.141377	+	0.989956i	$0.454847\pi$
$644$	−30.1543	−1.18824
$645$	1.66296	0.0654788
$646$	−38.0921	−1.49871
$647$	32.1524	1.26404	0.632021	−	0.774951i	$-0.282226\pi$
$647$	32.1524	1.26404	0.632021	+	0.774951i	$0.282226\pi$
$648$	−69.2608	−2.72082
$649$	−15.3343	−0.601923
$650$	11.4462	0.448957
$651$	1.08682	0.0425960
$652$	−46.5256	−1.82208
$653$	37.7672	1.47794	0.738971	−	0.673737i	$-0.235312\pi$
$653$	37.7672	1.47794	0.738971	+	0.673737i	$0.235312\pi$
$654$	−1.90540	−0.0745070
$655$	−5.40525	−0.211201
$656$	125.030	4.88160
$657$	24.9347	0.972793
$658$	−0.933855	−0.0364055
$659$	−38.2607	−1.49043	−0.745213	−	0.666827i	$-0.767652\pi$
$659$	−38.2607	−1.49043	−0.745213	+	0.666827i	$0.767652\pi$
$660$	8.88412	0.345814
$661$	2.17098	0.0844414	0.0422207	−	0.999108i	$-0.486557\pi$
$661$	2.17098	0.0844414	0.0422207	+	0.999108i	$0.486557\pi$
$662$	80.7418	3.13812
$663$	−5.19300	−0.201679
$664$	125.487	4.86983
$665$	−3.73070	−0.144670
$666$	30.0821	1.16566
$667$	48.5574	1.88015
$668$	−53.9586	−2.08772
$669$	−0.666017	−0.0257497
$670$	24.8723	0.960901
$671$	−57.7733	−2.23031
$672$	5.30308	0.204571
$673$	−28.7822	−1.10947	−0.554736	−	0.832027i	$-0.687181\pi$
$673$	−28.7822	−1.10947	−0.554736	+	0.832027i	$0.687181\pi$
$674$	−49.6459	−1.91229
$675$	1.88473	0.0725433
$676$	27.0871	1.04181
$677$	−37.1003	−1.42588	−0.712941	−	0.701224i	$-0.752637\pi$
$677$	−37.1003	−1.42588	−0.712941	+	0.701224i	$0.752637\pi$
$678$	−6.07463	−0.233295
$679$	−7.34933	−0.282041
$680$	32.5904	1.24979
$681$	−5.65269	−0.216611
$682$	−48.8386	−1.87013
$683$	−43.2484	−1.65486	−0.827428	−	0.561572i	$-0.810197\pi$
$683$	−43.2484	−1.65486	−0.827428	+	0.561572i	$0.810197\pi$
$684$	56.1300	2.14618
$685$	7.34827	0.280763
$686$	−2.68177	−0.102390
$687$	−0.319561	−0.0121920
$688$	−65.4220	−2.49419
$689$	25.6621	0.977647
$690$	−4.97736	−0.189485
$691$	−7.05331	−0.268321	−0.134160	−	0.990960i	$-0.542834\pi$
$691$	−7.05331	−0.268321	−0.134160	+	0.990960i	$0.542834\pi$
$692$	12.9367	0.491779
$693$	15.5173	0.589455
$694$	−90.8934	−3.45027
$695$	17.0118	0.645295
$696$	−22.8692	−0.866854
$697$	−37.8653	−1.43425
$698$	−19.0726	−0.721909
$699$	2.30876	0.0873254
$700$	5.19187	0.196234
$701$	−13.7127	−0.517923	−0.258961	−	0.965888i	$-0.583380\pi$
$701$	−13.7127	−0.517923	−0.258961	+	0.965888i	$0.583380\pi$
$702$	21.5730	0.814222
$703$	−14.4410	−0.544652
$704$	−103.668	−3.90712
$705$	−0.111279	−0.00419100
$706$	−86.2838	−3.24733
$707$	−6.75514	−0.254053
$708$	−4.75120	−0.178561
$709$	35.2395	1.32345	0.661724	−	0.749748i	$-0.269825\pi$
$709$	35.2395	1.32345	0.661724	+	0.749748i	$0.269825\pi$
$710$	20.9305	0.785509
$711$	32.1037	1.20398
$712$	53.5589	2.00721
$713$	19.7529	0.739751
$714$	−3.26286	−0.122109
$715$	22.8548	0.854722
$716$	55.3905	2.07004
$717$	0.0180853	0.000675409 0
$718$	−44.0263	−1.64305
$719$	−38.7261	−1.44424	−0.722120	−	0.691768i	$-0.756832\pi$
$719$	−38.7261	−1.44424	−0.722120	+	0.691768i	$0.756832\pi$
$720$	−36.4315	−1.35772
$721$	3.20122	0.119220
$722$	13.6284	0.507197
$723$	−2.13939	−0.0795649
$724$	99.6018	3.70167
$725$	−8.36047	−0.310500
$726$	15.1456	0.562105
$727$	25.1789	0.933832	0.466916	−	0.884302i	$-0.345365\pi$
$727$	25.1789	0.933832	0.466916	+	0.884302i	$0.345365\pi$
$728$	36.5348	1.35407
$729$	−21.6409	−0.801516
$730$	23.0751	0.854048
$731$	19.8130	0.732812
$732$	−17.9006	−0.661625
$733$	41.6179	1.53719	0.768596	−	0.639735i	$-0.220956\pi$
$733$	41.6179	1.53719	0.768596	+	0.639735i	$0.220956\pi$
$734$	35.5364	1.31167
$735$	−0.319561	−0.0117872
$736$	96.3827	3.55271
$737$	49.6629	1.82936
$738$	77.2891	2.84505
$739$	−14.9216	−0.548899	−0.274450	−	0.961602i	$-0.588496\pi$
$739$	−14.9216	−0.548899	−0.274450	+	0.961602i	$0.588496\pi$
$740$	20.0970	0.738779
$741$	−5.08844	−0.186929
$742$	16.1240	0.591929
$743$	−24.4762	−0.897946	−0.448973	−	0.893545i	$-0.648210\pi$
$743$	−24.4762	−0.897946	−0.448973	+	0.893545i	$0.648210\pi$
$744$	−9.30305	−0.341066
$745$	−22.1035	−0.809810
$746$	−15.6857	−0.574294
$747$	42.4827	1.55436
$748$	105.849	3.87021
$749$	−10.5553	−0.385684
$750$	0.856987	0.0312928
$751$	18.1717	0.663093	0.331546	−	0.943439i	$-0.392430\pi$
$751$	18.1717	0.663093	0.331546	+	0.943439i	$0.392430\pi$
$752$	4.37780	0.159642
$753$	−6.20410	−0.226090
$754$	−95.6957	−3.48503
$755$	12.3821	0.450629
$756$	9.78528	0.355887
$757$	16.8605	0.612804	0.306402	−	0.951902i	$-0.400875\pi$
$757$	16.8605	0.612804	0.306402	+	0.951902i	$0.400875\pi$
$758$	4.67388	0.169763
$759$	−9.93837	−0.360740
$760$	31.9342	1.15838
$761$	48.1110	1.74402	0.872010	−	0.489487i	$-0.162816\pi$
$761$	48.1110	1.74402	0.872010	+	0.489487i	$0.162816\pi$
$762$	−12.3835	−0.448608
$763$	−2.22337	−0.0804913
$764$	19.9065	0.720193
$765$	11.0333	0.398909
$766$	−48.3248	−1.74605
$767$	−12.2227	−0.441336
$768$	−3.67738	−0.132696
$769$	−39.7424	−1.43315	−0.716574	−	0.697511i	$-0.754291\pi$
$769$	−39.7424	−1.43315	−0.716574	+	0.697511i	$0.754291\pi$
$770$	14.3601	0.517503
$771$	5.12181	0.184457
$772$	84.0667	3.02563
$773$	−9.46657	−0.340489	−0.170245	−	0.985402i	$-0.554456\pi$
$773$	−9.46657	−0.340489	−0.170245	+	0.985402i	$0.554456\pi$
$774$	−40.4416	−1.45364
$775$	−3.40099	−0.122167
$776$	62.9092	2.25831
$777$	−1.23697	−0.0443761
$778$	27.4547	0.984300
$779$	−37.1029	−1.32935
$780$	7.08139	0.253554
$781$	41.7923	1.49545
$782$	−59.3021	−2.12064
$783$	−15.7572	−0.563118
$784$	12.5718	0.448992
$785$	11.0161	0.393182
$786$	−4.63223	−0.165226
$787$	−5.21530	−0.185905	−0.0929526	−	0.995671i	$-0.529631\pi$
$787$	−5.21530	−0.185905	−0.0929526	+	0.995671i	$0.529631\pi$
$788$	−61.5321	−2.19199
$789$	6.69099	0.238205
$790$	29.7095	1.05702
$791$	−7.08836	−0.252033
$792$	−132.826	−4.71977
$793$	−46.0501	−1.63529
$794$	40.8451	1.44954
$795$	1.92134	0.0681429
$796$	−32.9291	−1.16714
$797$	8.21661	0.291047	0.145524	−	0.989355i	$-0.453513\pi$
$797$	8.21661	0.291047	0.145524	+	0.989355i	$0.453513\pi$
$798$	−3.19716	−0.113178
$799$	−1.32581	−0.0469039
$800$	−16.5949	−0.586718
$801$	18.1320	0.640663
$802$	28.0242	0.989569
$803$	46.0744	1.62593
$804$	15.3877	0.542681
$805$	−5.80798	−0.204704
$806$	−38.9285	−1.37120
$807$	−7.17553	−0.252591
$808$	57.8230	2.03421
$809$	−2.73528	−0.0961672	−0.0480836	−	0.998843i	$-0.515311\pi$
$809$	−2.73528	−0.0961672	−0.0480836	+	0.998843i	$0.515311\pi$
$810$	−21.6991	−0.762430
$811$	−48.1946	−1.69234	−0.846170	−	0.532913i	$-0.821097\pi$
$811$	−48.1946	−1.69234	−0.846170	+	0.532913i	$0.821097\pi$
$812$	−43.4065	−1.52327
$813$	1.22798	0.0430672
$814$	55.5859	1.94828
$815$	−8.96123	−0.313898
$816$	15.2959	0.535463
$817$	19.4141	0.679214
$818$	−99.0932	−3.46471
$819$	12.3686	0.432195
$820$	51.6346	1.80316
$821$	−12.4927	−0.435999	−0.218000	−	0.975949i	$-0.569953\pi$
$821$	−12.4927	−0.435999	−0.218000	+	0.975949i	$0.569953\pi$
$822$	6.29737	0.219646
$823$	−10.2777	−0.358258	−0.179129	−	0.983826i	$-0.557328\pi$
$823$	−10.2777	−0.358258	−0.179129	+	0.983826i	$0.557328\pi$
$824$	−27.4020	−0.954593
$825$	1.71116	0.0595749
$826$	−7.67975	−0.267213
$827$	−36.1218	−1.25608	−0.628039	−	0.778182i	$-0.716142\pi$
$827$	−36.1218	−1.25608	−0.628039	+	0.778182i	$0.716142\pi$
$828$	87.3835	3.03679
$829$	−9.87020	−0.342806	−0.171403	−	0.985201i	$-0.554830\pi$
$829$	−9.87020	−0.342806	−0.171403	+	0.985201i	$0.554830\pi$
$830$	39.3145	1.36463
$831$	5.50238	0.190876
$832$	−82.6318	−2.86474
$833$	−3.80736	−0.131917
$834$	14.5789	0.504826
$835$	−10.3929	−0.359661
$836$	103.717	3.58714
$837$	−6.40996	−0.221561
$838$	−18.4988	−0.639031
$839$	27.8685	0.962127	0.481063	−	0.876686i	$-0.340251\pi$
$839$	27.8685	0.962127	0.481063	+	0.876686i	$0.340251\pi$
$840$	2.73539	0.0943800
$841$	40.8974	1.41026
$842$	37.8816	1.30549
$843$	2.85308	0.0982653
$844$	−4.12174	−0.141876
$845$	5.21720	0.179477
$846$	2.70620	0.0930411
$847$	17.6730	0.607253
$848$	−75.5871	−2.59567
$849$	1.27704	0.0438281
$850$	10.2105	0.350216
$851$	−22.4818	−0.770667
$852$	12.9490	0.443626
$853$	45.6832	1.56416	0.782081	−	0.623177i	$-0.214158\pi$
$853$	45.6832	1.56416	0.782081	+	0.623177i	$0.214158\pi$
$854$	−28.9342	−0.990107
$855$	10.8111	0.369733
$856$	90.3522	3.08817
$857$	−6.20696	−0.212026	−0.106013	−	0.994365i	$-0.533808\pi$
$857$	−6.20696	−0.212026	−0.106013	+	0.994365i	$0.533808\pi$
$858$	19.5863	0.668665
$859$	9.79702	0.334270	0.167135	−	0.985934i	$-0.446548\pi$
$859$	9.79702	0.334270	0.167135	+	0.985934i	$0.446548\pi$
$860$	−27.0179	−0.921302
$861$	−3.17812	−0.108310
$862$	−93.4603	−3.18327
$863$	5.50993	0.187560	0.0937801	−	0.995593i	$-0.470105\pi$
$863$	5.50993	0.187560	0.0937801	+	0.995593i	$0.470105\pi$
$864$	−31.2769	−1.06406
$865$	2.49172	0.0847211
$866$	−69.1343	−2.34928
$867$	0.800183	0.0271756
$868$	−17.6575	−0.599335
$869$	59.3214	2.01234
$870$	−7.16482	−0.242910
$871$	39.5855	1.34130
$872$	19.0317	0.644495
$873$	21.2975	0.720810
$874$	−58.1080	−1.96553
$875$	1.00000	0.0338062
$876$	14.2758	0.482334
$877$	−39.5977	−1.33712	−0.668559	−	0.743659i	$-0.733089\pi$
$877$	−39.5977	−1.33712	−0.668559	+	0.743659i	$0.733089\pi$
$878$	51.2897	1.73094
$879$	7.13845	0.240774
$880$	−67.3184	−2.26930
$881$	6.87027	0.231465	0.115733	−	0.993280i	$-0.463078\pi$
$881$	6.87027	0.231465	0.115733	+	0.993280i	$0.463078\pi$
$882$	7.77144	0.261678
$883$	−7.22928	−0.243285	−0.121642	−	0.992574i	$-0.538816\pi$
$883$	−7.22928	−0.243285	−0.121642	+	0.992574i	$0.538816\pi$
$884$	84.3701	2.83767
$885$	−0.915123	−0.0307615
$886$	−40.8850	−1.37356
$887$	−6.26340	−0.210304	−0.105152	−	0.994456i	$-0.533533\pi$
$887$	−6.26340	−0.210304	−0.105152	+	0.994456i	$0.533533\pi$
$888$	10.5883	0.355320
$889$	−14.4501	−0.484640
$890$	16.7798	0.562460
$891$	−43.3270	−1.45151
$892$	10.8207	0.362304
$893$	−1.29912	−0.0434733
$894$	−18.9424	−0.633530
$895$	10.6687	0.356615
$896$	−18.7293	−0.625703
$897$	−7.92171	−0.264498
$898$	−26.9511	−0.899369
$899$	28.4339	0.948323
$900$	−15.0454	−0.501514
$901$	22.8915	0.762627
$902$	142.815	4.75523
$903$	1.66296	0.0553397
$904$	60.6753	2.01803
$905$	19.1842	0.637704
$906$	10.6113	0.352536
$907$	16.2465	0.539456	0.269728	−	0.962936i	$-0.413066\pi$
$907$	16.2465	0.539456	0.269728	+	0.962936i	$0.413066\pi$
$908$	91.8386	3.04777
$909$	19.5756	0.649282
$910$	11.4462	0.379438
$911$	−28.5317	−0.945298	−0.472649	−	0.881251i	$-0.656702\pi$
$911$	−28.5317	−0.945298	−0.472649	+	0.881251i	$0.656702\pi$
$912$	14.9879	0.496299
$913$	78.4998	2.59796
$914$	−59.5381	−1.96934
$915$	−3.44781	−0.113981
$916$	5.19187	0.171544
$917$	−5.40525	−0.178497
$918$	19.2440	0.635145
$919$	10.8042	0.356398	0.178199	−	0.983995i	$-0.442973\pi$
$919$	10.8042	0.356398	0.178199	+	0.983995i	$0.442973\pi$
$920$	49.7154	1.63907
$921$	3.24403	0.106895
$922$	3.63733	0.119789
$923$	33.3120	1.09648
$924$	8.88412	0.292266
$925$	3.87085	0.127273
$926$	44.5603	1.46434
$927$	−9.27675	−0.304689
$928$	138.741	4.55440
$929$	−46.1413	−1.51385	−0.756924	−	0.653503i	$-0.773298\pi$
$929$	−46.1413	−1.51385	−0.756924	+	0.653503i	$0.773298\pi$
$930$	−2.91461	−0.0955737
$931$	−3.73070	−0.122269
$932$	−37.5102	−1.22869
$933$	3.71376	0.121583
$934$	58.3326	1.90870
$935$	20.3874	0.666738
$936$	−105.874	−3.46059
$937$	28.8325	0.941915	0.470958	−	0.882156i	$-0.343908\pi$
$937$	28.8325	0.941915	0.470958	+	0.882156i	$0.343908\pi$
$938$	24.8723	0.812110
$939$	8.78230	0.286600
$940$	1.80793	0.0589683
$941$	−27.3520	−0.891649	−0.445824	−	0.895120i	$-0.647089\pi$
$941$	−27.3520	−0.891649	−0.445824	+	0.895120i	$0.647089\pi$
$942$	9.44068	0.307594
$943$	−57.7619	−1.88099
$944$	36.0017	1.17176
$945$	1.88473	0.0613103
$946$	−74.7283	−2.42963
$947$	−46.4492	−1.50940	−0.754698	−	0.656073i	$-0.772216\pi$
$947$	−46.4492	−1.50940	−0.754698	+	0.656073i	$0.772216\pi$
$948$	18.3803	0.596963
$949$	36.7252	1.19215
$950$	10.0049	0.324601
$951$	7.71104	0.250048
$952$	32.5904	1.05626
$953$	−53.1692	−1.72232	−0.861160	−	0.508334i	$-0.830262\pi$
$953$	−53.1692	−1.72232	−0.861160	+	0.508334i	$0.830262\pi$
$954$	−46.7253	−1.51279
$955$	3.83417	0.124071
$956$	−0.293830	−0.00950315
$957$	−14.3061	−0.462450
$958$	40.8303	1.31917
$959$	7.34827	0.237288
$960$	−6.18671	−0.199675
$961$	−19.4333	−0.626879
$962$	44.3066	1.42850
$963$	30.5881	0.985688
$964$	34.7585	1.11950
$965$	16.1920	0.521238
$966$	−4.97736	−0.160144
$967$	−35.0792	−1.12807	−0.564036	−	0.825750i	$-0.690752\pi$
$967$	−35.0792	−1.12807	−0.564036	+	0.825750i	$0.690752\pi$
$968$	−151.279	−4.86228
$969$	−4.53908	−0.145816
$970$	19.7092	0.632824
$971$	−23.8413	−0.765103	−0.382551	−	0.923934i	$-0.624954\pi$
$971$	−23.8413	−0.765103	−0.382551	+	0.923934i	$0.624954\pi$
$972$	−42.7804	−1.37218
$973$	17.0118	0.545374
$974$	−103.368	−3.31211
$975$	1.36394	0.0436809
$976$	135.640	4.34172
$977$	49.4872	1.58324	0.791618	−	0.611016i	$-0.209239\pi$
$977$	49.4872	1.58324	0.791618	+	0.611016i	$0.209239\pi$
$978$	−7.67966	−0.245569
$979$	33.5045	1.07081
$980$	5.19187	0.165848
$981$	6.44305	0.205711
$982$	−66.7010	−2.12851
$983$	−46.2466	−1.47504	−0.737519	−	0.675326i	$-0.764003\pi$
$983$	−46.2466	−1.47504	−0.737519	+	0.675326i	$0.764003\pi$
$984$	27.2043	0.867240
$985$	−11.8516	−0.377624
$986$	−85.3641	−2.71855
$987$	−0.111279	−0.00354204
$988$	82.6714	2.63013
$989$	30.2240	0.961067
$990$	−41.6139	−1.32258
$991$	47.5291	1.50981	0.754905	−	0.655834i	$-0.227683\pi$
$991$	47.5291	1.50981	0.754905	+	0.655834i	$0.227683\pi$
$992$	56.4391	1.79194
$993$	9.62124	0.305321
$994$	20.9305	0.663876
$995$	−6.34244	−0.201069
$996$	24.3225	0.770689
$997$	52.1431	1.65139	0.825695	−	0.564117i	$-0.190783\pi$
$997$	52.1431	1.65139	0.825695	+	0.564117i	$0.190783\pi$
$998$	−63.4686	−2.00906
$999$	7.29552	0.230820

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.o.1.5	✓	73

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.o.1.5	✓	73	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:	\( N \)	\(=\)	\( 8015 = 5 \cdot 7 \cdot 229 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8015.a (trivial)

\(f(q)\)	\(=\)	\(q-2.68177 q^{2} -0.319561 q^{3} +5.19187 q^{4} +1.00000 q^{5} +0.856987 q^{6} +1.00000 q^{7} -8.55985 q^{8} -2.89788 q^{9} +O(q^{10})\)	\(q-2.68177 q^{2} -0.319561 q^{3} +5.19187 q^{4} +1.00000 q^{5} +0.856987 q^{6} +1.00000 q^{7} -8.55985 q^{8} -2.89788 q^{9} -2.68177 q^{10} -5.35472 q^{11} -1.65912 q^{12} -4.26816 q^{13} -2.68177 q^{14} -0.319561 q^{15} +12.5718 q^{16} -3.80736 q^{17} +7.77144 q^{18} -3.73070 q^{19} +5.19187 q^{20} -0.319561 q^{21} +14.3601 q^{22} -5.80798 q^{23} +2.73539 q^{24} +1.00000 q^{25} +11.4462 q^{26} +1.88473 q^{27} +5.19187 q^{28} -8.36047 q^{29} +0.856987 q^{30} -3.40099 q^{31} -16.5949 q^{32} +1.71116 q^{33} +10.2105 q^{34} +1.00000 q^{35} -15.0454 q^{36} +3.87085 q^{37} +10.0049 q^{38} +1.36394 q^{39} -8.55985 q^{40} +9.94528 q^{41} +0.856987 q^{42} -5.20388 q^{43} -27.8010 q^{44} -2.89788 q^{45} +15.5756 q^{46} +0.348224 q^{47} -4.01745 q^{48} +1.00000 q^{49} -2.68177 q^{50} +1.21668 q^{51} -22.1597 q^{52} -6.01244 q^{53} -5.05441 q^{54} -5.35472 q^{55} -8.55985 q^{56} +1.19219 q^{57} +22.4208 q^{58} +2.86369 q^{59} -1.65912 q^{60} +10.7892 q^{61} +9.12067 q^{62} -2.89788 q^{63} +19.3600 q^{64} -4.26816 q^{65} -4.58893 q^{66} -9.27460 q^{67} -19.7673 q^{68} +1.85600 q^{69} -2.68177 q^{70} -7.80475 q^{71} +24.8054 q^{72} -8.60444 q^{73} -10.3807 q^{74} -0.319561 q^{75} -19.3693 q^{76} -5.35472 q^{77} -3.65776 q^{78} -11.0783 q^{79} +12.5718 q^{80} +8.09136 q^{81} -26.6709 q^{82} -14.6599 q^{83} -1.65912 q^{84} -3.80736 q^{85} +13.9556 q^{86} +2.67168 q^{87} +45.8356 q^{88} -6.25699 q^{89} +7.77144 q^{90} -4.26816 q^{91} -30.1543 q^{92} +1.08682 q^{93} -0.933855 q^{94} -3.73070 q^{95} +5.30308 q^{96} -7.34933 q^{97} -2.68177 q^{98} +15.5173 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 73 q + 7 q^{2} + 14 q^{3} + 95 q^{4} + 73 q^{5} - q^{6} + 73 q^{7} + 18 q^{8} + 111 q^{9}+O(q^{10}) \) 73 * q + 7 * q^2 + 14 * q^3 + 95 * q^4 + 73 * q^5 - q^6 + 73 * q^7 + 18 * q^8 + 111 * q^9	\( 73 q + 7 q^{2} + 14 q^{3} + 95 q^{4} + 73 q^{5} - q^{6} + 73 q^{7} + 18 q^{8} + 111 q^{9} + 7 q^{10} + 27 q^{11} + 21 q^{12} + 21 q^{13} + 7 q^{14} + 14 q^{15} + 135 q^{16} + 23 q^{17} + 41 q^{18} + 26 q^{19} + 95 q^{20} + 14 q^{21} + 48 q^{22} + 16 q^{23} - q^{24} + 73 q^{25} + 7 q^{26} + 44 q^{27} + 95 q^{28} + 66 q^{29} - q^{30} + 23 q^{31} + 3 q^{32} + 77 q^{33} + 29 q^{34} + 73 q^{35} + 142 q^{36} + 66 q^{37} - 12 q^{38} + 53 q^{39} + 18 q^{40} + 50 q^{41} - q^{42} + 43 q^{43} + 37 q^{44} + 111 q^{45} + 65 q^{46} + 28 q^{47} - 20 q^{48} + 73 q^{49} + 7 q^{50} + 71 q^{51} + 29 q^{52} - 7 q^{53} - 16 q^{54} + 27 q^{55} + 18 q^{56} + 33 q^{57} + 48 q^{58} + 16 q^{59} + 21 q^{60} + 42 q^{61} - 3 q^{62} + 111 q^{63} + 216 q^{64} + 21 q^{65} - 53 q^{66} + 48 q^{67} + 13 q^{68} + 73 q^{69} + 7 q^{70} + 68 q^{71} + 18 q^{72} + 65 q^{73} + 4 q^{74} + 14 q^{75} + 37 q^{76} + 27 q^{77} + 60 q^{78} + 116 q^{79} + 135 q^{80} + 177 q^{81} + 20 q^{82} + 40 q^{83} + 21 q^{84} + 23 q^{85} + 35 q^{86} - 14 q^{87} + 47 q^{88} + 59 q^{89} + 41 q^{90} + 21 q^{91} + 3 q^{92} + 37 q^{93} - 11 q^{94} + 26 q^{95} - 23 q^{96} + 70 q^{97} + 7 q^{98} + 49 q^{99}+O(q^{100}) \) 73 * q + 7 * q^2 + 14 * q^3 + 95 * q^4 + 73 * q^5 - q^6 + 73 * q^7 + 18 * q^8 + 111 * q^9 + 7 * q^10 + 27 * q^11 + 21 * q^12 + 21 * q^13 + 7 * q^14 + 14 * q^15 + 135 * q^16 + 23 * q^17 + 41 * q^18 + 26 * q^19 + 95 * q^20 + 14 * q^21 + 48 * q^22 + 16 * q^23 - q^24 + 73 * q^25 + 7 * q^26 + 44 * q^27 + 95 * q^28 + 66 * q^29 - q^30 + 23 * q^31 + 3 * q^32 + 77 * q^33 + 29 * q^34 + 73 * q^35 + 142 * q^36 + 66 * q^37 - 12 * q^38 + 53 * q^39 + 18 * q^40 + 50 * q^41 - q^42 + 43 * q^43 + 37 * q^44 + 111 * q^45 + 65 * q^46 + 28 * q^47 - 20 * q^48 + 73 * q^49 + 7 * q^50 + 71 * q^51 + 29 * q^52 - 7 * q^53 - 16 * q^54 + 27 * q^55 + 18 * q^56 + 33 * q^57 + 48 * q^58 + 16 * q^59 + 21 * q^60 + 42 * q^61 - 3 * q^62 + 111 * q^63 + 216 * q^64 + 21 * q^65 - 53 * q^66 + 48 * q^67 + 13 * q^68 + 73 * q^69 + 7 * q^70 + 68 * q^71 + 18 * q^72 + 65 * q^73 + 4 * q^74 + 14 * q^75 + 37 * q^76 + 27 * q^77 + 60 * q^78 + 116 * q^79 + 135 * q^80 + 177 * q^81 + 20 * q^82 + 40 * q^83 + 21 * q^84 + 23 * q^85 + 35 * q^86 - 14 * q^87 + 47 * q^88 + 59 * q^89 + 41 * q^90 + 21 * q^91 + 3 * q^92 + 37 * q^93 - 11 * q^94 + 26 * q^95 - 23 * q^96 + 70 * q^97 + 7 * q^98 + 49 * q^99

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