LMFDB - Embedded newform 8041.2.a.c.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8041,2,Mod(1,8041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8041, 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("8041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8041 = 11 \cdot 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8041.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:	$64.2077082653$
Analytic rank:	$1$
Dimension:	$60$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	8041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.66007 q^{2} -2.34749 q^{3} +5.07599 q^{4} -2.77927 q^{5} +6.24449 q^{6} +0.942946 q^{7} -8.18236 q^{8} +2.51070 q^{9} +O(q^{10})$	\(q-2.66007 q^{2} -2.34749 q^{3} +5.07599 q^{4} -2.77927 q^{5} +6.24449 q^{6} +0.942946 q^{7} -8.18236 q^{8} +2.51070 q^{9} +7.39305 q^{10} +1.00000 q^{11} -11.9158 q^{12} +3.43533 q^{13} -2.50830 q^{14} +6.52429 q^{15} +11.6137 q^{16} +1.00000 q^{17} -6.67866 q^{18} -0.555244 q^{19} -14.1075 q^{20} -2.21355 q^{21} -2.66007 q^{22} +1.29159 q^{23} +19.2080 q^{24} +2.72432 q^{25} -9.13823 q^{26} +1.14862 q^{27} +4.78638 q^{28} +0.667344 q^{29} -17.3551 q^{30} +3.78414 q^{31} -14.5286 q^{32} -2.34749 q^{33} -2.66007 q^{34} -2.62070 q^{35} +12.7443 q^{36} +0.320021 q^{37} +1.47699 q^{38} -8.06440 q^{39} +22.7409 q^{40} -6.11477 q^{41} +5.88822 q^{42} -1.00000 q^{43} +5.07599 q^{44} -6.97791 q^{45} -3.43573 q^{46} +12.3022 q^{47} -27.2630 q^{48} -6.11085 q^{49} -7.24688 q^{50} -2.34749 q^{51} +17.4377 q^{52} -11.0483 q^{53} -3.05541 q^{54} -2.77927 q^{55} -7.71552 q^{56} +1.30343 q^{57} -1.77518 q^{58} -10.5387 q^{59} +33.1173 q^{60} +3.19854 q^{61} -10.0661 q^{62} +2.36746 q^{63} +15.4196 q^{64} -9.54769 q^{65} +6.24449 q^{66} +14.9515 q^{67} +5.07599 q^{68} -3.03200 q^{69} +6.97124 q^{70} -5.09521 q^{71} -20.5435 q^{72} -13.7799 q^{73} -0.851278 q^{74} -6.39530 q^{75} -2.81841 q^{76} +0.942946 q^{77} +21.4519 q^{78} +15.5527 q^{79} -32.2775 q^{80} -10.2285 q^{81} +16.2657 q^{82} +5.11495 q^{83} -11.2360 q^{84} -2.77927 q^{85} +2.66007 q^{86} -1.56658 q^{87} -8.18236 q^{88} -13.1305 q^{89} +18.5618 q^{90} +3.23933 q^{91} +6.55611 q^{92} -8.88322 q^{93} -32.7248 q^{94} +1.54317 q^{95} +34.1056 q^{96} +11.2471 q^{97} +16.2553 q^{98} +2.51070 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 9 q^{2} - 6 q^{3} + 43 q^{4} - 15 q^{5} - 4 q^{6} - 17 q^{7} - 21 q^{8} + 40 q^{9}+O(q^{10}) $ 60 * q - 9 * q^2 - 6 * q^3 + 43 * q^4 - 15 * q^5 - 4 * q^6 - 17 * q^7 - 21 * q^8 + 40 * q^9	\( 60 q - 9 q^{2} - 6 q^{3} + 43 q^{4} - 15 q^{5} - 4 q^{6} - 17 q^{7} - 21 q^{8} + 40 q^{9} + q^{10} + 60 q^{11} - 13 q^{12} - 2 q^{13} - 15 q^{14} - 32 q^{15} + 21 q^{16} + 60 q^{17} - 41 q^{18} - 24 q^{19} - 33 q^{20} - 12 q^{21} - 9 q^{22} - 20 q^{23} + 9 q^{24} + 25 q^{25} - 40 q^{26} - 18 q^{27} - 3 q^{28} - 54 q^{29} - 18 q^{30} - 50 q^{31} - 51 q^{32} - 6 q^{33} - 9 q^{34} - 30 q^{35} + 27 q^{36} - 63 q^{37} - 38 q^{38} - 55 q^{39} - 5 q^{40} - 53 q^{41} - 47 q^{42} - 60 q^{43} + 43 q^{44} - 36 q^{45} - 27 q^{46} - 47 q^{47} - 38 q^{48} + 5 q^{49} - 4 q^{50} - 6 q^{51} - 13 q^{52} - 24 q^{53} - 58 q^{54} - 15 q^{55} - 45 q^{56} + 23 q^{57} + 16 q^{58} - 57 q^{59} - 4 q^{60} - 8 q^{61} - 3 q^{62} - 57 q^{63} - 5 q^{64} - 27 q^{65} - 4 q^{66} - 49 q^{67} + 43 q^{68} - 57 q^{69} - 7 q^{70} - 151 q^{71} - 29 q^{72} - 12 q^{73} + 18 q^{74} - 23 q^{75} - 38 q^{76} - 17 q^{77} + 37 q^{78} - 11 q^{79} - 21 q^{80} + 28 q^{81} + 44 q^{82} - 42 q^{83} + 16 q^{84} - 15 q^{85} + 9 q^{86} - 56 q^{87} - 21 q^{88} - 88 q^{89} + 47 q^{90} - 60 q^{91} + 26 q^{92} - 16 q^{93} + 37 q^{94} - 57 q^{95} + 108 q^{96} - 22 q^{97} + 8 q^{98} + 40 q^{99}+O(q^{100}) \) 60 * q - 9 * q^2 - 6 * q^3 + 43 * q^4 - 15 * q^5 - 4 * q^6 - 17 * q^7 - 21 * q^8 + 40 * q^9 + q^10 + 60 * q^11 - 13 * q^12 - 2 * q^13 - 15 * q^14 - 32 * q^15 + 21 * q^16 + 60 * q^17 - 41 * q^18 - 24 * q^19 - 33 * q^20 - 12 * q^21 - 9 * q^22 - 20 * q^23 + 9 * q^24 + 25 * q^25 - 40 * q^26 - 18 * q^27 - 3 * q^28 - 54 * q^29 - 18 * q^30 - 50 * q^31 - 51 * q^32 - 6 * q^33 - 9 * q^34 - 30 * q^35 + 27 * q^36 - 63 * q^37 - 38 * q^38 - 55 * q^39 - 5 * q^40 - 53 * q^41 - 47 * q^42 - 60 * q^43 + 43 * q^44 - 36 * q^45 - 27 * q^46 - 47 * q^47 - 38 * q^48 + 5 * q^49 - 4 * q^50 - 6 * q^51 - 13 * q^52 - 24 * q^53 - 58 * q^54 - 15 * q^55 - 45 * q^56 + 23 * q^57 + 16 * q^58 - 57 * q^59 - 4 * q^60 - 8 * q^61 - 3 * q^62 - 57 * q^63 - 5 * q^64 - 27 * q^65 - 4 * q^66 - 49 * q^67 + 43 * q^68 - 57 * q^69 - 7 * q^70 - 151 * q^71 - 29 * q^72 - 12 * q^73 + 18 * q^74 - 23 * q^75 - 38 * q^76 - 17 * q^77 + 37 * q^78 - 11 * q^79 - 21 * q^80 + 28 * q^81 + 44 * q^82 - 42 * q^83 + 16 * q^84 - 15 * q^85 + 9 * q^86 - 56 * q^87 - 21 * q^88 - 88 * q^89 + 47 * q^90 - 60 * q^91 + 26 * q^92 - 16 * q^93 + 37 * q^94 - 57 * q^95 + 108 * q^96 - 22 * q^97 + 8 * q^98 + 40 * 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 $

$2$	−2.66007	−1.88096	−0.940478	−	0.339855i	$-0.889622\pi$
$2$	−2.66007	−1.88096	−0.940478	+	0.339855i	$0.889622\pi$
$3$	−2.34749	−1.35532	−0.677662	−	0.735374i	$-0.737007\pi$
$3$	−2.34749	−1.35532	−0.677662	+	0.735374i	$0.737007\pi$
$4$	5.07599	2.53800
$5$	−2.77927	−1.24293	−0.621463	−	0.783444i	$-0.713461\pi$
$5$	−2.77927	−1.24293	−0.621463	+	0.783444i	$0.713461\pi$
$6$	6.24449	2.54930
$7$	0.942946	0.356400	0.178200	−	0.983994i	$-0.442973\pi$
$7$	0.942946	0.356400	0.178200	+	0.983994i	$0.442973\pi$
$8$	−8.18236	−2.89290
$9$	2.51070	0.836901
$10$	7.39305	2.33789
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−11.9158	−3.43980
$13$	3.43533	0.952789	0.476395	−	0.879232i	$-0.341943\pi$
$13$	3.43533	0.952789	0.476395	+	0.879232i	$0.341943\pi$
$14$	−2.50830	−0.670372
$15$	6.52429	1.68457
$16$	11.6137	2.90342
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−6.67866	−1.57417
$19$	−0.555244	−0.127382	−0.0636908	−	0.997970i	$-0.520287\pi$
$19$	−0.555244	−0.127382	−0.0636908	+	0.997970i	$0.520287\pi$
$20$	−14.1075	−3.15454
$21$	−2.21355	−0.483037
$22$	−2.66007	−0.567130
$23$	1.29159	0.269316	0.134658	−	0.990892i	$-0.457006\pi$
$23$	1.29159	0.269316	0.134658	+	0.990892i	$0.457006\pi$
$24$	19.2080	3.92082
$25$	2.72432	0.544863
$26$	−9.13823	−1.79215
$27$	1.14862	0.221052
$28$	4.78638	0.904541
$29$	0.667344	0.123923	0.0619613	−	0.998079i	$-0.480264\pi$
$29$	0.667344	0.123923	0.0619613	+	0.998079i	$0.480264\pi$
$30$	−17.3551	−3.16859
$31$	3.78414	0.679651	0.339826	−	0.940488i	$-0.389632\pi$
$31$	3.78414	0.679651	0.339826	+	0.940488i	$0.389632\pi$
$32$	−14.5286	−2.56831
$33$	−2.34749	−0.408645
$34$	−2.66007	−0.456199
$35$	−2.62070	−0.442978
$36$	12.7443	2.12405
$37$	0.320021	0.0526110	0.0263055	−	0.999654i	$-0.491626\pi$
$37$	0.320021	0.0526110	0.0263055	+	0.999654i	$0.491626\pi$
$38$	1.47699	0.239599
$39$	−8.06440	−1.29134
$40$	22.7409	3.59566
$41$	−6.11477	−0.954967	−0.477483	−	0.878641i	$-0.658451\pi$
$41$	−6.11477	−0.954967	−0.477483	+	0.878641i	$0.658451\pi$
$42$	5.88822	0.908571
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	5.07599	0.765234
$45$	−6.97791	−1.04021
$46$	−3.43573	−0.506571
$47$	12.3022	1.79446	0.897231	−	0.441562i	$-0.145575\pi$
$47$	12.3022	1.79446	0.897231	+	0.441562i	$0.145575\pi$
$48$	−27.2630	−3.93508
$49$	−6.11085	−0.872979
$50$	−7.24688	−1.02486
$51$	−2.34749	−0.328714
$52$	17.4377	2.41817
$53$	−11.0483	−1.51760	−0.758802	−	0.651321i	$-0.774215\pi$
$53$	−11.0483	−1.51760	−0.758802	+	0.651321i	$0.774215\pi$
$54$	−3.05541	−0.415788
$55$	−2.77927	−0.374756
$56$	−7.71552	−1.03103
$57$	1.30343	0.172643
$58$	−1.77518	−0.233093
$59$	−10.5387	−1.37202	−0.686011	−	0.727591i	$-0.740640\pi$
$59$	−10.5387	−1.37202	−0.686011	+	0.727591i	$0.740640\pi$
$60$	33.1173	4.27542
$61$	3.19854	0.409531	0.204765	−	0.978811i	$-0.434357\pi$
$61$	3.19854	0.409531	0.204765	+	0.978811i	$0.434357\pi$
$62$	−10.0661	−1.27839
$63$	2.36746	0.298272
$64$	15.4196	1.92746
$65$	−9.54769	−1.18425
$66$	6.24449	0.768644
$67$	14.9515	1.82662	0.913310	−	0.407266i	$-0.133518\pi$
$67$	14.9515	1.82662	0.913310	+	0.407266i	$0.133518\pi$
$68$	5.07599	0.615554
$69$	−3.03200	−0.365010
$70$	6.97124	0.833223
$71$	−5.09521	−0.604690	−0.302345	−	0.953199i	$-0.597769\pi$
$71$	−5.09521	−0.604690	−0.302345	+	0.953199i	$0.597769\pi$
$72$	−20.5435	−2.42107
$73$	−13.7799	−1.61282	−0.806409	−	0.591359i	$-0.798592\pi$
$73$	−13.7799	−1.61282	−0.806409	+	0.591359i	$0.798592\pi$
$74$	−0.851278	−0.0989591
$75$	−6.39530	−0.738466
$76$	−2.81841	−0.323294
$77$	0.942946	0.107459
$78$	21.4519	2.42895
$79$	15.5527	1.74981	0.874905	−	0.484295i	$-0.160924\pi$
$79$	15.5527	1.74981	0.874905	+	0.484295i	$0.160924\pi$
$80$	−32.2775	−3.60874
$81$	−10.2285	−1.13650
$82$	16.2657	1.79625
$83$	5.11495	0.561439	0.280720	−	0.959790i	$-0.409427\pi$
$83$	5.11495	0.561439	0.280720	+	0.959790i	$0.409427\pi$
$84$	−11.2360	−1.22595
$85$	−2.77927	−0.301454
$86$	2.66007	0.286843
$87$	−1.56658	−0.167955
$88$	−8.18236	−0.872242
$89$	−13.1305	−1.39183	−0.695914	−	0.718125i	$-0.745001\pi$
$89$	−13.1305	−1.39183	−0.695914	+	0.718125i	$0.745001\pi$
$90$	18.5618	1.95658
$91$	3.23933	0.339574
$92$	6.55611	0.683522
$93$	−8.88322	−0.921147
$94$	−32.7248	−3.37530
$95$	1.54317	0.158326
$96$	34.1056	3.48089
$97$	11.2471	1.14197	0.570983	−	0.820962i	$-0.306562\pi$
$97$	11.2471	1.14197	0.570983	+	0.820962i	$0.306562\pi$
$98$	16.2553	1.64204
$99$	2.51070	0.252335
$100$	13.8286	1.38286
$101$	7.91341	0.787414	0.393707	−	0.919236i	$-0.371192\pi$
$101$	7.91341	0.787414	0.393707	+	0.919236i	$0.371192\pi$
$102$	6.24449	0.618297
$103$	−18.3903	−1.81205	−0.906026	−	0.423223i	$-0.860899\pi$
$103$	−18.3903	−1.81205	−0.906026	+	0.423223i	$0.860899\pi$
$104$	−28.1091	−2.75632
$105$	6.15205	0.600379
$106$	29.3894	2.85455
$107$	4.43801	0.429039	0.214519	−	0.976720i	$-0.431181\pi$
$107$	4.43801	0.429039	0.214519	+	0.976720i	$0.431181\pi$
$108$	5.83037	0.561028
$109$	−14.1902	−1.35918	−0.679589	−	0.733593i	$-0.737842\pi$
$109$	−14.1902	−1.35918	−0.679589	+	0.733593i	$0.737842\pi$
$110$	7.39305	0.704900
$111$	−0.751245	−0.0713050
$112$	10.9511	1.03478
$113$	−15.7595	−1.48253	−0.741264	−	0.671213i	$-0.765773\pi$
$113$	−15.7595	−1.48253	−0.741264	+	0.671213i	$0.765773\pi$
$114$	−3.46722	−0.324734
$115$	−3.58968	−0.334739
$116$	3.38743	0.314515
$117$	8.62510	0.797390
$118$	28.0337	2.58071
$119$	0.942946	0.0864397
$120$	−53.3841	−4.87328
$121$	1.00000	0.0909091
$122$	−8.50834	−0.770309
$123$	14.3544	1.29429
$124$	19.2082	1.72495
$125$	6.32473	0.565701
$126$	−6.29761	−0.561036
$127$	−2.13547	−0.189493	−0.0947463	−	0.995501i	$-0.530204\pi$
$127$	−2.13547	−0.189493	−0.0947463	+	0.995501i	$0.530204\pi$
$128$	−11.9603	−1.05715
$129$	2.34749	0.206685
$130$	25.3976	2.22751
$131$	−10.1135	−0.883618	−0.441809	−	0.897109i	$-0.645663\pi$
$131$	−10.1135	−0.883618	−0.441809	+	0.897109i	$0.645663\pi$
$132$	−11.9158	−1.03714
$133$	−0.523565	−0.0453988
$134$	−39.7721	−3.43579
$135$	−3.19231	−0.274751
$136$	−8.18236	−0.701631
$137$	13.5460	1.15731	0.578656	−	0.815572i	$-0.303577\pi$
$137$	13.5460	1.15731	0.578656	+	0.815572i	$0.303577\pi$
$138$	8.06534	0.686567
$139$	−15.9464	−1.35256	−0.676278	−	0.736646i	$-0.736408\pi$
$139$	−15.9464	−1.35256	−0.676278	+	0.736646i	$0.736408\pi$
$140$	−13.3026	−1.12428
$141$	−28.8793	−2.43208
$142$	13.5536	1.13739
$143$	3.43533	0.287277
$144$	29.1585	2.42988
$145$	−1.85473	−0.154027
$146$	36.6556	3.03364
$147$	14.3452	1.18317
$148$	1.62442	0.133527
$149$	−21.4558	−1.75773	−0.878865	−	0.477070i	$-0.841699\pi$
$149$	−21.4558	−1.75773	−0.878865	+	0.477070i	$0.841699\pi$
$150$	17.0120	1.38902
$151$	16.6338	1.35364	0.676821	−	0.736148i	$-0.263357\pi$
$151$	16.6338	1.35364	0.676821	+	0.736148i	$0.263357\pi$
$152$	4.54320	0.368502
$153$	2.51070	0.202978
$154$	−2.50830	−0.202125
$155$	−10.5171	−0.844756
$156$	−40.9348	−3.27741
$157$	20.7614	1.65694	0.828469	−	0.560035i	$-0.189212\pi$
$157$	20.7614	1.65694	0.828469	+	0.560035i	$0.189212\pi$
$158$	−41.3712	−3.29132
$159$	25.9358	2.05685
$160$	40.3787	3.19222
$161$	1.21790	0.0959841
$162$	27.2085	2.13770
$163$	−5.33847	−0.418141	−0.209070	−	0.977901i	$-0.567044\pi$
$163$	−5.33847	−0.418141	−0.209070	+	0.977901i	$0.567044\pi$
$164$	−31.0385	−2.42370
$165$	6.52429	0.507916
$166$	−13.6062	−1.05604
$167$	−6.07978	−0.470468	−0.235234	−	0.971939i	$-0.575586\pi$
$167$	−6.07978	−0.470468	−0.235234	+	0.971939i	$0.575586\pi$
$168$	18.1121	1.39738
$169$	−1.19850	−0.0921926
$170$	7.39305	0.567021
$171$	−1.39405	−0.106606
$172$	−5.07599	−0.387041
$173$	3.65813	0.278122	0.139061	−	0.990284i	$-0.455592\pi$
$173$	3.65813	0.278122	0.139061	+	0.990284i	$0.455592\pi$
$174$	4.16722	0.315916
$175$	2.56888	0.194189
$176$	11.6137	0.875415
$177$	24.7395	1.85953
$178$	34.9280	2.61797
$179$	−16.0650	−1.20076	−0.600378	−	0.799717i	$-0.704983\pi$
$179$	−16.0650	−1.20076	−0.600378	+	0.799717i	$0.704983\pi$
$180$	−35.4198	−2.64004
$181$	13.7975	1.02556	0.512782	−	0.858519i	$-0.328615\pi$
$181$	13.7975	1.02556	0.512782	+	0.858519i	$0.328615\pi$
$182$	−8.61685	−0.638724
$183$	−7.50853	−0.555046
$184$	−10.5683	−0.779103
$185$	−0.889422	−0.0653916
$186$	23.6300	1.73264
$187$	1.00000	0.0731272
$188$	62.4459	4.55433
$189$	1.08308	0.0787828
$190$	−4.10494	−0.297804
$191$	16.0692	1.16273	0.581365	−	0.813643i	$-0.302519\pi$
$191$	16.0692	1.16273	0.581365	+	0.813643i	$0.302519\pi$
$192$	−36.1975	−2.61233
$193$	8.28514	0.596378	0.298189	−	0.954507i	$-0.403617\pi$
$193$	8.28514	0.596378	0.298189	+	0.954507i	$0.403617\pi$
$194$	−29.9180	−2.14799
$195$	22.4131	1.60504
$196$	−31.0186	−2.21562
$197$	10.9727	0.781770	0.390885	−	0.920440i	$-0.372169\pi$
$197$	10.9727	0.781770	0.390885	+	0.920440i	$0.372169\pi$
$198$	−6.67866	−0.474631
$199$	25.7002	1.82184	0.910918	−	0.412588i	$-0.135375\pi$
$199$	25.7002	1.82184	0.910918	+	0.412588i	$0.135375\pi$
$200$	−22.2913	−1.57623
$201$	−35.0985	−2.47566
$202$	−21.0503	−1.48109
$203$	0.629269	0.0441660
$204$	−11.9158	−0.834275
$205$	16.9946	1.18695
$206$	48.9196	3.40839
$207$	3.24281	0.225391
$208$	39.8969	2.76635
$209$	−0.555244	−0.0384070
$210$	−16.3649	−1.12929
$211$	−6.91238	−0.475868	−0.237934	−	0.971281i	$-0.576470\pi$
$211$	−6.91238	−0.475868	−0.237934	+	0.971281i	$0.576470\pi$
$212$	−56.0812	−3.85167
$213$	11.9609	0.819550
$214$	−11.8054	−0.807003
$215$	2.77927	0.189544
$216$	−9.39840	−0.639480
$217$	3.56824	0.242228
$218$	37.7471	2.55655
$219$	32.3482	2.18589
$220$	−14.1075	−0.951129
$221$	3.43533	0.231085
$222$	1.99837	0.134122
$223$	−27.6697	−1.85290	−0.926450	−	0.376418i	$-0.877156\pi$
$223$	−27.6697	−1.85290	−0.926450	+	0.376418i	$0.877156\pi$
$224$	−13.6996	−0.915346
$225$	6.83995	0.455997
$226$	41.9214	2.78857
$227$	−10.0000	−0.663724	−0.331862	−	0.943328i	$-0.607677\pi$
$227$	−10.0000	−0.663724	−0.331862	+	0.943328i	$0.607677\pi$
$228$	6.61619	0.438168
$229$	5.13343	0.339226	0.169613	−	0.985511i	$-0.445748\pi$
$229$	5.13343	0.339226	0.169613	+	0.985511i	$0.445748\pi$
$230$	9.54881	0.629630
$231$	−2.21355	−0.145641
$232$	−5.46045	−0.358496
$233$	13.1967	0.864543	0.432272	−	0.901743i	$-0.357712\pi$
$233$	13.1967	0.864543	0.432272	+	0.901743i	$0.357712\pi$
$234$	−22.9434	−1.49986
$235$	−34.1911	−2.23038
$236$	−53.4943	−3.48218
$237$	−36.5097	−2.37156
$238$	−2.50830	−0.162589
$239$	−12.2088	−0.789722	−0.394861	−	0.918741i	$-0.629207\pi$
$239$	−12.2088	−0.789722	−0.394861	+	0.918741i	$0.629207\pi$
$240$	75.7712	4.89101
$241$	−23.3817	−1.50615	−0.753075	−	0.657935i	$-0.771430\pi$
$241$	−23.3817	−1.50615	−0.753075	+	0.657935i	$0.771430\pi$
$242$	−2.66007	−0.170996
$243$	20.5654	1.31927
$244$	16.2357	1.03939
$245$	16.9837	1.08505
$246$	−38.1836	−2.43450
$247$	−1.90745	−0.121368
$248$	−30.9632	−1.96616
$249$	−12.0073	−0.760932
$250$	−16.8242	−1.06406
$251$	7.92556	0.500257	0.250128	−	0.968213i	$-0.419527\pi$
$251$	7.92556	0.500257	0.250128	+	0.968213i	$0.419527\pi$
$252$	12.0172	0.757012
$253$	1.29159	0.0812017
$254$	5.68051	0.356427
$255$	6.52429	0.408567
$256$	0.975908	0.0609942
$257$	−1.24132	−0.0774316	−0.0387158	−	0.999250i	$-0.512327\pi$
$257$	−1.24132	−0.0774316	−0.0387158	+	0.999250i	$0.512327\pi$
$258$	−6.24449	−0.388765
$259$	0.301762	0.0187506
$260$	−48.4640	−3.00561
$261$	1.67550	0.103711
$262$	26.9026	1.66205
$263$	−15.8981	−0.980320	−0.490160	−	0.871632i	$-0.663062\pi$
$263$	−15.8981	−0.980320	−0.490160	+	0.871632i	$0.663062\pi$
$264$	19.2080	1.18217
$265$	30.7062	1.88627
$266$	1.39272	0.0853932
$267$	30.8237	1.88638
$268$	75.8938	4.63595
$269$	24.1557	1.47280	0.736400	−	0.676547i	$-0.236524\pi$
$269$	24.1557	1.47280	0.736400	+	0.676547i	$0.236524\pi$
$270$	8.49179	0.516794
$271$	−24.8255	−1.50804	−0.754022	−	0.656849i	$-0.771889\pi$
$271$	−24.8255	−1.50804	−0.754022	+	0.656849i	$0.771889\pi$
$272$	11.6137	0.704184
$273$	−7.60429	−0.460233
$274$	−36.0333	−2.17685
$275$	2.72432	0.164282
$276$	−15.3904	−0.926393
$277$	13.9811	0.840044	0.420022	−	0.907514i	$-0.362022\pi$
$277$	13.9811	0.840044	0.420022	+	0.907514i	$0.362022\pi$
$278$	42.4186	2.54410
$279$	9.50085	0.568801
$280$	21.4435	1.28149
$281$	2.93745	0.175233	0.0876167	−	0.996154i	$-0.472075\pi$
$281$	2.93745	0.175233	0.0876167	+	0.996154i	$0.472075\pi$
$282$	76.8211	4.57463
$283$	24.0532	1.42982	0.714908	−	0.699219i	$-0.246469\pi$
$283$	24.0532	1.42982	0.714908	+	0.699219i	$0.246469\pi$
$284$	−25.8632	−1.53470
$285$	−3.62257	−0.214583
$286$	−9.13823	−0.540355
$287$	−5.76590	−0.340350
$288$	−36.4769	−2.14942
$289$	1.00000	0.0588235
$290$	4.93371	0.289717
$291$	−26.4024	−1.54773
$292$	−69.9467	−4.09332
$293$	−13.6641	−0.798263	−0.399132	−	0.916894i	$-0.630688\pi$
$293$	−13.6641	−0.798263	−0.399132	+	0.916894i	$0.630688\pi$
$294$	−38.1592	−2.22549
$295$	29.2898	1.70532
$296$	−2.61852	−0.152199
$297$	1.14862	0.0666496
$298$	57.0741	3.30621
$299$	4.43705	0.256601
$300$	−32.4625	−1.87422
$301$	−0.942946	−0.0543505
$302$	−44.2472	−2.54614
$303$	−18.5766	−1.06720
$304$	−6.44843	−0.369843
$305$	−8.88958	−0.509016
$306$	−6.67866	−0.381793
$307$	−1.11661	−0.0637283	−0.0318641	−	0.999492i	$-0.510144\pi$
$307$	−1.11661	−0.0637283	−0.0318641	+	0.999492i	$0.510144\pi$
$308$	4.78638	0.272729
$309$	43.1711	2.45592
$310$	27.9763	1.58895
$311$	9.53586	0.540729	0.270364	−	0.962758i	$-0.412856\pi$
$311$	9.53586	0.540729	0.270364	+	0.962758i	$0.412856\pi$
$312$	65.9858	3.73571
$313$	−3.40855	−0.192663	−0.0963313	−	0.995349i	$-0.530711\pi$
$313$	−3.40855	−0.192663	−0.0963313	+	0.995349i	$0.530711\pi$
$314$	−55.2268	−3.11663
$315$	−6.57979	−0.370729
$316$	78.9451	4.44101
$317$	24.8880	1.39785	0.698925	−	0.715195i	$-0.253662\pi$
$317$	24.8880	1.39785	0.698925	+	0.715195i	$0.253662\pi$
$318$	−68.9912	−3.86883
$319$	0.667344	0.0373641
$320$	−42.8553	−2.39568
$321$	−10.4182	−0.581486
$322$	−3.23971	−0.180542
$323$	−0.555244	−0.0308946
$324$	−51.9197	−2.88443
$325$	9.35892	0.519140
$326$	14.2007	0.786505
$327$	33.3114	1.84213
$328$	50.0332	2.76262
$329$	11.6003	0.639546
$330$	−17.3551	−0.955367
$331$	31.2517	1.71775	0.858874	−	0.512186i	$-0.171164\pi$
$331$	31.2517	1.71775	0.858874	+	0.512186i	$0.171164\pi$
$332$	25.9635	1.42493
$333$	0.803477	0.0440302
$334$	16.1727	0.884929
$335$	−41.5542	−2.27035
$336$	−25.7075	−1.40246
$337$	−6.02800	−0.328366	−0.164183	−	0.986430i	$-0.552499\pi$
$337$	−6.02800	−0.328366	−0.164183	+	0.986430i	$0.552499\pi$
$338$	3.18811	0.173410
$339$	36.9952	2.00931
$340$	−14.1075	−0.765088
$341$	3.78414	0.204923
$342$	3.70828	0.200521
$343$	−12.3628	−0.667530
$344$	8.18236	0.441163
$345$	8.42673	0.453680
$346$	−9.73089	−0.523136
$347$	2.19389	0.117774	0.0588871	−	0.998265i	$-0.481245\pi$
$347$	2.19389	0.117774	0.0588871	+	0.998265i	$0.481245\pi$
$348$	−7.95196	−0.426270
$349$	17.7091	0.947946	0.473973	−	0.880539i	$-0.342819\pi$
$349$	17.7091	0.947946	0.473973	+	0.880539i	$0.342819\pi$
$350$	−6.83341	−0.365261
$351$	3.94588	0.210616
$352$	−14.5286	−0.774375
$353$	11.0054	0.585759	0.292880	−	0.956149i	$-0.405386\pi$
$353$	11.0054	0.585759	0.292880	+	0.956149i	$0.405386\pi$
$354$	−65.8088	−3.49770
$355$	14.1609	0.751584
$356$	−66.6502	−3.53245
$357$	−2.21355	−0.117154
$358$	42.7341	2.25857
$359$	−29.9308	−1.57969	−0.789844	−	0.613308i	$-0.789838\pi$
$359$	−29.9308	−1.57969	−0.789844	+	0.613308i	$0.789838\pi$
$360$	57.0958	3.00921
$361$	−18.6917	−0.983774
$362$	−36.7025	−1.92904
$363$	−2.34749	−0.123211
$364$	16.4428	0.861837
$365$	38.2980	2.00461
$366$	19.9732	1.04402
$367$	9.10100	0.475068	0.237534	−	0.971379i	$-0.423661\pi$
$367$	9.10100	0.475068	0.237534	+	0.971379i	$0.423661\pi$
$368$	15.0002	0.781937
$369$	−15.3524	−0.799213
$370$	2.36593	0.122999
$371$	−10.4180	−0.540874
$372$	−45.0912	−2.33787
$373$	31.4387	1.62783	0.813916	−	0.580982i	$-0.197331\pi$
$373$	31.4387	1.62783	0.813916	+	0.580982i	$0.197331\pi$
$374$	−2.66007	−0.137549
$375$	−14.8472	−0.766708
$376$	−100.661	−5.19120
$377$	2.29255	0.118072
$378$	−2.88108	−0.148187
$379$	6.43941	0.330770	0.165385	−	0.986229i	$-0.447113\pi$
$379$	6.43941	0.330770	0.165385	+	0.986229i	$0.447113\pi$
$380$	7.83311	0.401830
$381$	5.01300	0.256824
$382$	−42.7453	−2.18704
$383$	30.4841	1.55766	0.778831	−	0.627233i	$-0.215813\pi$
$383$	30.4841	1.55766	0.778831	+	0.627233i	$0.215813\pi$
$384$	28.0766	1.43278
$385$	−2.62070	−0.133563
$386$	−22.0391	−1.12176
$387$	−2.51070	−0.127626
$388$	57.0900	2.89830
$389$	−12.5464	−0.636128	−0.318064	−	0.948069i	$-0.603033\pi$
$389$	−12.5464	−0.636128	−0.318064	+	0.948069i	$0.603033\pi$
$390$	−59.6205	−3.01900
$391$	1.29159	0.0653186
$392$	50.0012	2.52544
$393$	23.7413	1.19759
$394$	−29.1881	−1.47048
$395$	−43.2249	−2.17488
$396$	12.7443	0.640425
$397$	−7.09256	−0.355965	−0.177983	−	0.984034i	$-0.556957\pi$
$397$	−7.09256	−0.355965	−0.177983	+	0.984034i	$0.556957\pi$
$398$	−68.3643	−3.42679
$399$	1.22906	0.0615301
$400$	31.6394	1.58197
$401$	2.80951	0.140300	0.0701501	−	0.997536i	$-0.477652\pi$
$401$	2.80951	0.140300	0.0701501	+	0.997536i	$0.477652\pi$
$402$	93.3647	4.65661
$403$	12.9998	0.647565
$404$	40.1684	1.99845
$405$	28.4277	1.41258
$406$	−1.67390	−0.0830743
$407$	0.320021	0.0158628
$408$	19.2080	0.950937
$409$	−8.32094	−0.411444	−0.205722	−	0.978610i	$-0.565954\pi$
$409$	−8.32094	−0.411444	−0.205722	+	0.978610i	$0.565954\pi$
$410$	−45.2068	−2.23260
$411$	−31.7991	−1.56853
$412$	−93.3490	−4.59898
$413$	−9.93742	−0.488988
$414$	−8.62610	−0.423950
$415$	−14.2158	−0.697827
$416$	−49.9104	−2.44706
$417$	37.4340	1.83315
$418$	1.47699	0.0722419
$419$	−15.2637	−0.745683	−0.372841	−	0.927895i	$-0.621616\pi$
$419$	−15.2637	−0.745683	−0.372841	+	0.927895i	$0.621616\pi$
$420$	31.2278	1.52376
$421$	−17.3258	−0.844410	−0.422205	−	0.906500i	$-0.638744\pi$
$421$	−17.3258	−0.844410	−0.422205	+	0.906500i	$0.638744\pi$
$422$	18.3874	0.895086
$423$	30.8872	1.50179
$424$	90.4014	4.39028
$425$	2.72432	0.132149
$426$	−31.8170	−1.54154
$427$	3.01604	0.145957
$428$	22.5273	1.08890
$429$	−8.06440	−0.389353
$430$	−7.39305	−0.356525
$431$	24.5482	1.18245	0.591223	−	0.806508i	$-0.298645\pi$
$431$	24.5482	1.18245	0.591223	+	0.806508i	$0.298645\pi$
$432$	13.3397	0.641806
$433$	6.38109	0.306655	0.153328	−	0.988175i	$-0.451001\pi$
$433$	6.38109	0.306655	0.153328	+	0.988175i	$0.451001\pi$
$434$	−9.49177	−0.455620
$435$	4.35395	0.208756
$436$	−72.0295	−3.44959
$437$	−0.717149	−0.0343059
$438$	−86.0486	−4.11156
$439$	24.1170	1.15104	0.575522	−	0.817787i	$-0.304799\pi$
$439$	24.1170	1.15104	0.575522	+	0.817787i	$0.304799\pi$
$440$	22.7409	1.08413
$441$	−15.3425	−0.730597
$442$	−9.13823	−0.434661
$443$	−16.6905	−0.792991	−0.396496	−	0.918037i	$-0.629774\pi$
$443$	−16.6905	−0.792991	−0.396496	+	0.918037i	$0.629774\pi$
$444$	−3.81331	−0.180972
$445$	36.4931	1.72994
$446$	73.6034	3.48522
$447$	50.3673	2.38229
$448$	14.5399	0.686945
$449$	19.4708	0.918884	0.459442	−	0.888208i	$-0.348049\pi$
$449$	19.4708	0.918884	0.459442	+	0.888208i	$0.348049\pi$
$450$	−18.1948	−0.857709
$451$	−6.11477	−0.287933
$452$	−79.9950	−3.76265
$453$	−39.0477	−1.83462
$454$	26.6008	1.24844
$455$	−9.00296	−0.422065
$456$	−10.6651	−0.499440
$457$	19.1020	0.893554	0.446777	−	0.894645i	$-0.352572\pi$
$457$	19.1020	0.893554	0.446777	+	0.894645i	$0.352572\pi$
$458$	−13.6553	−0.638070
$459$	1.14862	0.0536129
$460$	−18.2212	−0.849566
$461$	11.8715	0.552910	0.276455	−	0.961027i	$-0.410840\pi$
$461$	11.8715	0.552910	0.276455	+	0.961027i	$0.410840\pi$
$462$	5.88822	0.273945
$463$	15.0303	0.698519	0.349260	−	0.937026i	$-0.386433\pi$
$463$	15.0303	0.698519	0.349260	+	0.937026i	$0.386433\pi$
$464$	7.75033	0.359800
$465$	24.6888	1.14492
$466$	−35.1041	−1.62617
$467$	20.2222	0.935773	0.467886	−	0.883789i	$-0.345016\pi$
$467$	20.2222	0.935773	0.467886	+	0.883789i	$0.345016\pi$
$468$	43.7809	2.02377
$469$	14.0985	0.651007
$470$	90.9508	4.19525
$471$	−48.7371	−2.24569
$472$	86.2314	3.96912
$473$	−1.00000	−0.0459800
$474$	97.1184	4.46080
$475$	−1.51266	−0.0694056
$476$	4.78638	0.219383
$477$	−27.7391	−1.27009
$478$	32.4763	1.48543
$479$	21.6668	0.989983	0.494991	−	0.868898i	$-0.335171\pi$
$479$	21.6668	0.989983	0.494991	+	0.868898i	$0.335171\pi$
$480$	−94.7886	−4.32649
$481$	1.09938	0.0501272
$482$	62.1971	2.83300
$483$	−2.85901	−0.130089
$484$	5.07599	0.230727
$485$	−31.2586	−1.41938
$486$	−54.7054	−2.48149
$487$	−16.3389	−0.740385	−0.370193	−	0.928955i	$-0.620708\pi$
$487$	−16.3389	−0.740385	−0.370193	+	0.928955i	$0.620708\pi$
$488$	−26.1716	−1.18473
$489$	12.5320	0.566716
$490$	−45.1778	−2.04093
$491$	10.1726	0.459081	0.229540	−	0.973299i	$-0.426278\pi$
$491$	10.1726	0.459081	0.229540	+	0.973299i	$0.426278\pi$
$492$	72.8626	3.28490
$493$	0.667344	0.0300557
$494$	5.07395	0.228288
$495$	−6.97791	−0.313634
$496$	43.9478	1.97332
$497$	−4.80450	−0.215511
$498$	31.9403	1.43128
$499$	−32.4285	−1.45170	−0.725850	−	0.687853i	$-0.758553\pi$
$499$	−32.4285	−1.45170	−0.725850	+	0.687853i	$0.758553\pi$
$500$	32.1043	1.43575
$501$	14.2722	0.637636
$502$	−21.0826	−0.940961
$503$	−9.52084	−0.424513	−0.212257	−	0.977214i	$-0.568081\pi$
$503$	−9.52084	−0.424513	−0.212257	+	0.977214i	$0.568081\pi$
$504$	−19.3714	−0.862870
$505$	−21.9935	−0.978697
$506$	−3.43573	−0.152737
$507$	2.81347	0.124951
$508$	−10.8396	−0.480931
$509$	22.3469	0.990510	0.495255	−	0.868748i	$-0.335075\pi$
$509$	22.3469	0.990510	0.495255	+	0.868748i	$0.335075\pi$
$510$	−17.3551	−0.768497
$511$	−12.9937	−0.574808
$512$	21.3246	0.942421
$513$	−0.637763	−0.0281579
$514$	3.30201	0.145645
$515$	51.1116	2.25224
$516$	11.9158	0.524565
$517$	12.3022	0.541051
$518$	−0.802709	−0.0352690
$519$	−8.58741	−0.376946
$520$	78.1227	3.42591
$521$	−32.3090	−1.41548	−0.707740	−	0.706473i	$-0.750285\pi$
$521$	−32.3090	−1.41548	−0.707740	+	0.706473i	$0.750285\pi$
$522$	−4.45696	−0.195076
$523$	14.4533	0.631998	0.315999	−	0.948760i	$-0.397660\pi$
$523$	14.4533	0.631998	0.315999	+	0.948760i	$0.397660\pi$
$524$	−51.3359	−2.24262
$525$	−6.03042	−0.263189
$526$	42.2902	1.84394
$527$	3.78414	0.164840
$528$	−27.2630	−1.18647
$529$	−21.3318	−0.927469
$530$	−81.6808	−3.54799
$531$	−26.4595	−1.14825
$532$	−2.65761	−0.115222
$533$	−21.0063	−0.909882
$534$	−81.9932	−3.54819
$535$	−12.3344	−0.533263
$536$	−122.339	−5.28423
$537$	37.7124	1.62741
$538$	−64.2560	−2.77027
$539$	−6.11085	−0.263213
$540$	−16.2042	−0.697316
$541$	19.6788	0.846056	0.423028	−	0.906117i	$-0.360967\pi$
$541$	19.6788	0.846056	0.423028	+	0.906117i	$0.360967\pi$
$542$	66.0378	2.83656
$543$	−32.3896	−1.38997
$544$	−14.5286	−0.622907
$545$	39.4384	1.68936
$546$	20.2280	0.865677
$547$	3.20216	0.136915	0.0684573	−	0.997654i	$-0.478192\pi$
$547$	3.20216	0.136915	0.0684573	+	0.997654i	$0.478192\pi$
$548$	68.7593	2.93725
$549$	8.03057	0.342737
$550$	−7.24688	−0.309008
$551$	−0.370539	−0.0157855
$552$	24.8089	1.05594
$553$	14.6653	0.623632
$554$	−37.1908	−1.58009
$555$	2.08791	0.0886268
$556$	−80.9438	−3.43278
$557$	37.3239	1.58147	0.790733	−	0.612162i	$-0.209700\pi$
$557$	37.3239	1.58147	0.790733	+	0.612162i	$0.209700\pi$
$558$	−25.2730	−1.06989
$559$	−3.43533	−0.145299
$560$	−30.4360	−1.28615
$561$	−2.34749	−0.0991111
$562$	−7.81382	−0.329606
$563$	5.28208	0.222613	0.111306	−	0.993786i	$-0.464496\pi$
$563$	5.28208	0.222613	0.111306	+	0.993786i	$0.464496\pi$
$564$	−146.591	−6.17260
$565$	43.7998	1.84267
$566$	−63.9833	−2.68942
$567$	−9.64490	−0.405048
$568$	41.6908	1.74931
$569$	−11.0034	−0.461288	−0.230644	−	0.973038i	$-0.574083\pi$
$569$	−11.0034	−0.461288	−0.230644	+	0.973038i	$0.574083\pi$
$570$	9.63631	0.403621
$571$	9.50965	0.397967	0.198983	−	0.980003i	$-0.436236\pi$
$571$	9.50965	0.397967	0.198983	+	0.980003i	$0.436236\pi$
$572$	17.4377	0.729107
$573$	−37.7224	−1.57587
$574$	15.3377	0.640183
$575$	3.51870	0.146740
$576$	38.7142	1.61309
$577$	−27.6222	−1.14993	−0.574965	−	0.818178i	$-0.694984\pi$
$577$	−27.6222	−1.14993	−0.574965	+	0.818178i	$0.694984\pi$
$578$	−2.66007	−0.110644
$579$	−19.4493	−0.808285
$580$	−9.41457	−0.390919
$581$	4.82312	0.200097
$582$	70.2322	2.91122
$583$	−11.0483	−0.457575
$584$	112.752	4.66572
$585$	−23.9714	−0.991097
$586$	36.3474	1.50150
$587$	−33.6429	−1.38859	−0.694296	−	0.719689i	$-0.744284\pi$
$587$	−33.6429	−1.38859	−0.694296	+	0.719689i	$0.744284\pi$
$588$	72.8159	3.00288
$589$	−2.10112	−0.0865751
$590$	−77.9131	−3.20763
$591$	−25.7582	−1.05955
$592$	3.71662	0.152752
$593$	24.8572	1.02076	0.510382	−	0.859948i	$-0.329504\pi$
$593$	24.8572	1.02076	0.510382	+	0.859948i	$0.329504\pi$
$594$	−3.05541	−0.125365
$595$	−2.62070	−0.107438
$596$	−108.910	−4.46111
$597$	−60.3308	−2.46918
$598$	−11.8029	−0.482655
$599$	−31.0750	−1.26969	−0.634845	−	0.772639i	$-0.718936\pi$
$599$	−31.0750	−1.26969	−0.634845	+	0.772639i	$0.718936\pi$
$600$	52.3286	2.13631
$601$	11.0477	0.450644	0.225322	−	0.974284i	$-0.427657\pi$
$601$	11.0477	0.450644	0.225322	+	0.974284i	$0.427657\pi$
$602$	2.50830	0.102231
$603$	37.5388	1.52870
$604$	84.4331	3.43554
$605$	−2.77927	−0.112993
$606$	49.4152	2.00736
$607$	−12.9682	−0.526363	−0.263181	−	0.964746i	$-0.584772\pi$
$607$	−12.9682	−0.526363	−0.263181	+	0.964746i	$0.584772\pi$
$608$	8.06689	0.327156
$609$	−1.47720	−0.0598592
$610$	23.6469	0.957436
$611$	42.2622	1.70974
$612$	12.7443	0.515158
$613$	−38.7415	−1.56475	−0.782377	−	0.622805i	$-0.785993\pi$
$613$	−38.7415	−1.56475	−0.782377	+	0.622805i	$0.785993\pi$
$614$	2.97026	0.119870
$615$	−39.8946	−1.60870
$616$	−7.71552	−0.310867
$617$	−16.0179	−0.644855	−0.322428	−	0.946594i	$-0.604499\pi$
$617$	−16.0179	−0.644855	−0.322428	+	0.946594i	$0.604499\pi$
$618$	−114.838	−4.61947
$619$	−23.5979	−0.948479	−0.474240	−	0.880396i	$-0.657277\pi$
$619$	−23.5979	−0.948479	−0.474240	+	0.880396i	$0.657277\pi$
$620$	−53.3848	−2.14399
$621$	1.48355	0.0595326
$622$	−25.3661	−1.01709
$623$	−12.3813	−0.496048
$624$	−93.6575	−3.74930
$625$	−31.1997	−1.24799
$626$	9.06699	0.362390
$627$	1.30343	0.0520539
$628$	105.384	4.20530
$629$	0.320021	0.0127601
$630$	17.5027	0.697325
$631$	−20.4830	−0.815415	−0.407708	−	0.913113i	$-0.633672\pi$
$631$	−20.4830	−0.815415	−0.407708	+	0.913113i	$0.633672\pi$
$632$	−127.257	−5.06203
$633$	16.2267	0.644954
$634$	−66.2040	−2.62930
$635$	5.93504	0.235525
$636$	131.650	5.22026
$637$	−20.9928	−0.831765
$638$	−1.77518	−0.0702802
$639$	−12.7926	−0.506066
$640$	33.2408	1.31396
$641$	−45.9164	−1.81359	−0.906795	−	0.421572i	$-0.861478\pi$
$641$	−45.9164	−1.81359	−0.906795	+	0.421572i	$0.861478\pi$
$642$	27.7131	1.09375
$643$	37.5433	1.48056	0.740282	−	0.672297i	$-0.234692\pi$
$643$	37.5433	1.48056	0.740282	+	0.672297i	$0.234692\pi$
$644$	6.18205	0.243607
$645$	−6.52429	−0.256894
$646$	1.47699	0.0581114
$647$	−34.2767	−1.34756	−0.673778	−	0.738933i	$-0.735330\pi$
$647$	−34.2767	−1.34756	−0.673778	+	0.738933i	$0.735330\pi$
$648$	83.6931	3.28777
$649$	−10.5387	−0.413680
$650$	−24.8954	−0.976479
$651$	−8.37640	−0.328297
$652$	−27.0980	−1.06124
$653$	29.7185	1.16298	0.581488	−	0.813555i	$-0.302471\pi$
$653$	29.7185	1.16298	0.581488	+	0.813555i	$0.302471\pi$
$654$	−88.6108	−3.46496
$655$	28.1080	1.09827
$656$	−71.0151	−2.77267
$657$	−34.5973	−1.34977
$658$	−30.8577	−1.20296
$659$	−1.63499	−0.0636902	−0.0318451	−	0.999493i	$-0.510138\pi$
$659$	−1.63499	−0.0636902	−0.0318451	+	0.999493i	$0.510138\pi$
$660$	33.1173	1.28909
$661$	9.16123	0.356330	0.178165	−	0.984001i	$-0.442984\pi$
$661$	9.16123	0.356330	0.178165	+	0.984001i	$0.442984\pi$
$662$	−83.1318	−3.23101
$663$	−8.06440	−0.313195
$664$	−41.8524	−1.62419
$665$	1.45512	0.0564273
$666$	−2.13731	−0.0828190
$667$	0.861936	0.0333743
$668$	−30.8609	−1.19405
$669$	64.9543	2.51128
$670$	110.537	4.27043
$671$	3.19854	0.123478
$672$	32.1598	1.24059
$673$	−31.9616	−1.23203	−0.616014	−	0.787735i	$-0.711253\pi$
$673$	−31.9616	−1.23203	−0.616014	+	0.787735i	$0.711253\pi$
$674$	16.0349	0.617642
$675$	3.12920	0.120443
$676$	−6.08359	−0.233984
$677$	−11.9691	−0.460011	−0.230006	−	0.973189i	$-0.573874\pi$
$677$	−11.9691	−0.460011	−0.230006	+	0.973189i	$0.573874\pi$
$678$	−98.4100	−3.77942
$679$	10.6054	0.406997
$680$	22.7409	0.872075
$681$	23.4749	0.899561
$682$	−10.0661	−0.385450
$683$	−31.8365	−1.21819	−0.609094	−	0.793098i	$-0.708467\pi$
$683$	−31.8365	−1.21819	−0.609094	+	0.793098i	$0.708467\pi$
$684$	−7.07620	−0.270565
$685$	−37.6479	−1.43845
$686$	32.8860	1.25559
$687$	−12.0507	−0.459761
$688$	−11.6137	−0.442768
$689$	−37.9547	−1.44596
$690$	−22.4157	−0.853352
$691$	−38.6653	−1.47090	−0.735449	−	0.677580i	$-0.763029\pi$
$691$	−38.6653	−1.47090	−0.735449	+	0.677580i	$0.763029\pi$
$692$	18.5686	0.705873
$693$	2.36746	0.0899322
$694$	−5.83591	−0.221528
$695$	44.3193	1.68113
$696$	12.8183	0.485878
$697$	−6.11477	−0.231613
$698$	−47.1075	−1.78304
$699$	−30.9791	−1.17174
$700$	13.0396	0.492851
$701$	−19.3405	−0.730482	−0.365241	−	0.930913i	$-0.619013\pi$
$701$	−19.3405	−0.730482	−0.365241	+	0.930913i	$0.619013\pi$
$702$	−10.4963	−0.396159
$703$	−0.177689	−0.00670168
$704$	15.4196	0.581150
$705$	80.2632	3.02289
$706$	−29.2752	−1.10179
$707$	7.46192	0.280634
$708$	125.577	4.71948
$709$	−16.3552	−0.614233	−0.307116	−	0.951672i	$-0.599364\pi$
$709$	−16.3552	−0.614233	−0.307116	+	0.951672i	$0.599364\pi$
$710$	−37.6691	−1.41370
$711$	39.0481	1.46442
$712$	107.438	4.02642
$713$	4.88756	0.183041
$714$	5.88822	0.220361
$715$	−9.54769	−0.357064
$716$	−81.5458	−3.04751
$717$	28.6600	1.07033
$718$	79.6181	2.97132
$719$	31.9171	1.19031	0.595154	−	0.803612i	$-0.297091\pi$
$719$	31.9171	1.19031	0.595154	+	0.803612i	$0.297091\pi$
$720$	−81.0393	−3.02016
$721$	−17.3411	−0.645815
$722$	49.7213	1.85044
$723$	54.8883	2.04132
$724$	70.0362	2.60288
$725$	1.81806	0.0675209
$726$	6.24449	0.231755
$727$	−10.0463	−0.372598	−0.186299	−	0.982493i	$-0.559649\pi$
$727$	−10.0463	−0.372598	−0.186299	+	0.982493i	$0.559649\pi$
$728$	−26.5054	−0.982354
$729$	−17.5916	−0.651540
$730$	−101.876	−3.77059
$731$	−1.00000	−0.0369863
$732$	−38.1132	−1.40870
$733$	9.50924	0.351232	0.175616	−	0.984459i	$-0.443808\pi$
$733$	9.50924	0.351232	0.175616	+	0.984459i	$0.443808\pi$
$734$	−24.2093	−0.893583
$735$	−39.8690	−1.47059
$736$	−18.7650	−0.691686
$737$	14.9515	0.550746
$738$	40.8384	1.50328
$739$	2.43305	0.0895012	0.0447506	−	0.998998i	$-0.485751\pi$
$739$	2.43305	0.0895012	0.0447506	+	0.998998i	$0.485751\pi$
$740$	−4.51470	−0.165964
$741$	4.47771	0.164493
$742$	27.7126	1.01736
$743$	11.7015	0.429286	0.214643	−	0.976693i	$-0.431141\pi$
$743$	11.7015	0.429286	0.214643	+	0.976693i	$0.431141\pi$
$744$	72.6857	2.66479
$745$	59.6315	2.18473
$746$	−83.6292	−3.06188
$747$	12.8421	0.469869
$748$	5.07599	0.185597
$749$	4.18480	0.152909
$750$	39.4947	1.44214
$751$	26.4565	0.965411	0.482706	−	0.875783i	$-0.339654\pi$
$751$	26.4565	0.965411	0.482706	+	0.875783i	$0.339654\pi$
$752$	142.874	5.21008
$753$	−18.6052	−0.678010
$754$	−6.09834	−0.222089
$755$	−46.2298	−1.68248
$756$	5.49772	0.199950
$757$	−44.3622	−1.61237	−0.806187	−	0.591661i	$-0.798472\pi$
$757$	−44.3622	−1.61237	−0.806187	+	0.591661i	$0.798472\pi$
$758$	−17.1293	−0.622164
$759$	−3.03200	−0.110055
$760$	−12.6268	−0.458021
$761$	2.49614	0.0904852	0.0452426	−	0.998976i	$-0.485594\pi$
$761$	2.49614	0.0904852	0.0452426	+	0.998976i	$0.485594\pi$
$762$	−13.3349	−0.483074
$763$	−13.3806	−0.484411
$764$	81.5673	2.95100
$765$	−6.97791	−0.252287
$766$	−81.0898	−2.92990
$767$	−36.2039	−1.30725
$768$	−2.29093	−0.0826669
$769$	−29.8877	−1.07778	−0.538889	−	0.842377i	$-0.681156\pi$
$769$	−29.8877	−1.07778	−0.538889	+	0.842377i	$0.681156\pi$
$770$	6.97124	0.251226
$771$	2.91399	0.104945
$772$	42.0553	1.51360
$773$	−0.786712	−0.0282961	−0.0141480	−	0.999900i	$-0.504504\pi$
$773$	−0.786712	−0.0282961	−0.0141480	+	0.999900i	$0.504504\pi$
$774$	6.67866	0.240059
$775$	10.3092	0.370317
$776$	−92.0275	−3.30359
$777$	−0.708383	−0.0254131
$778$	33.3743	1.19653
$779$	3.39519	0.121645
$780$	113.769	4.07357
$781$	−5.09521	−0.182321
$782$	−3.43573	−0.122861
$783$	0.766523	0.0273933
$784$	−70.9696	−2.53463
$785$	−57.7013	−2.05945
$786$	−63.1535	−2.25261
$787$	24.3369	0.867516	0.433758	−	0.901029i	$-0.357187\pi$
$787$	24.3369	0.867516	0.433758	+	0.901029i	$0.357187\pi$
$788$	55.6971	1.98413
$789$	37.3207	1.32865
$790$	114.982	4.09086
$791$	−14.8603	−0.528373
$792$	−20.5435	−0.729981
$793$	10.9880	0.390196
$794$	18.8667	0.669555
$795$	−72.0825	−2.55650
$796$	130.454	4.62381
$797$	−27.6625	−0.979856	−0.489928	−	0.871763i	$-0.662977\pi$
$797$	−27.6625	−0.979856	−0.489928	+	0.871763i	$0.662977\pi$
$798$	−3.26940	−0.115735
$799$	12.3022	0.435221
$800$	−39.5804	−1.39938
$801$	−32.9668	−1.16482
$802$	−7.47350	−0.263898
$803$	−13.7799	−0.486283
$804$	−178.160	−6.28321
$805$	−3.38487	−0.119301
$806$	−34.5803	−1.21804
$807$	−56.7053	−1.99612
$808$	−64.7504	−2.27791
$809$	−53.7695	−1.89044	−0.945218	−	0.326439i	$-0.894151\pi$
$809$	−53.7695	−1.89044	−0.945218	+	0.326439i	$0.894151\pi$
$810$	−75.6196	−2.65700
$811$	−44.5405	−1.56403	−0.782014	−	0.623261i	$-0.785808\pi$
$811$	−44.5405	−1.56403	−0.782014	+	0.623261i	$0.785808\pi$
$812$	3.19416	0.112093
$813$	58.2777	2.04389
$814$	−0.851278	−0.0298373
$815$	14.8370	0.519718
$816$	−27.2630	−0.954397
$817$	0.555244	0.0194255
$818$	22.1343	0.773908
$819$	8.13300	0.284190
$820$	86.2643	3.01248
$821$	20.3578	0.710492	0.355246	−	0.934773i	$-0.384397\pi$
$821$	20.3578	0.710492	0.355246	+	0.934773i	$0.384397\pi$
$822$	84.5879	2.95034
$823$	−46.8012	−1.63139	−0.815693	−	0.578485i	$-0.803644\pi$
$823$	−46.8012	−1.63139	−0.815693	+	0.578485i	$0.803644\pi$
$824$	150.476	5.24208
$825$	−6.39530	−0.222656
$826$	26.4343	0.919765
$827$	−40.7320	−1.41639	−0.708194	−	0.706017i	$-0.750490\pi$
$827$	−40.7320	−1.41639	−0.708194	+	0.706017i	$0.750490\pi$
$828$	16.4604	0.572040
$829$	−47.8115	−1.66056	−0.830281	−	0.557345i	$-0.811820\pi$
$829$	−47.8115	−1.66056	−0.830281	+	0.557345i	$0.811820\pi$
$830$	37.8151	1.31258
$831$	−32.8205	−1.13853
$832$	52.9716	1.83646
$833$	−6.11085	−0.211729
$834$	−99.5772	−3.44808
$835$	16.8973	0.584756
$836$	−2.81841	−0.0974768
$837$	4.34653	0.150238
$838$	40.6027	1.40260
$839$	5.50450	0.190036	0.0950181	−	0.995476i	$-0.469709\pi$
$839$	5.50450	0.190036	0.0950181	+	0.995476i	$0.469709\pi$
$840$	−50.3383	−1.73684
$841$	−28.5547	−0.984643
$842$	46.0880	1.58830
$843$	−6.89562	−0.237498
$844$	−35.0871	−1.20775
$845$	3.33096	0.114589
$846$	−82.1622	−2.82480
$847$	0.942946	0.0324000
$848$	−128.312	−4.40625
$849$	−56.4647	−1.93786
$850$	−7.24688	−0.248566
$851$	0.413336	0.0141690
$852$	60.7136	2.08001
$853$	12.2049	0.417889	0.208945	−	0.977927i	$-0.432997\pi$
$853$	12.2049	0.417889	0.208945	+	0.977927i	$0.432997\pi$
$854$	−8.02290	−0.274538
$855$	3.87444	0.132503
$856$	−36.3134	−1.24117
$857$	−28.2643	−0.965491	−0.482746	−	0.875761i	$-0.660360\pi$
$857$	−28.2643	−0.965491	−0.482746	+	0.875761i	$0.660360\pi$
$858$	21.4519	0.732356
$859$	21.4510	0.731898	0.365949	−	0.930635i	$-0.380744\pi$
$859$	21.4510	0.731898	0.365949	+	0.930635i	$0.380744\pi$
$860$	14.1075	0.481063
$861$	13.5354	0.461284
$862$	−65.3001	−2.22413
$863$	4.86167	0.165493	0.0827466	−	0.996571i	$-0.473631\pi$
$863$	4.86167	0.165493	0.0827466	+	0.996571i	$0.473631\pi$
$864$	−16.6878	−0.567729
$865$	−10.1669	−0.345685
$866$	−16.9742	−0.576805
$867$	−2.34749	−0.0797249
$868$	18.1123	0.614773
$869$	15.5527	0.527588
$870$	−11.5818	−0.392660
$871$	51.3634	1.74038
$872$	116.110	3.93197
$873$	28.2380	0.955713
$874$	1.90767	0.0645278
$875$	5.96388	0.201616
$876$	164.199	5.54777
$877$	0.787630	0.0265964	0.0132982	−	0.999912i	$-0.495767\pi$
$877$	0.787630	0.0265964	0.0132982	+	0.999912i	$0.495767\pi$
$878$	−64.1531	−2.16506
$879$	32.0762	1.08190
$880$	−32.2775	−1.08808
$881$	19.2360	0.648079	0.324039	−	0.946044i	$-0.394959\pi$
$881$	19.2360	0.648079	0.324039	+	0.946044i	$0.394959\pi$
$882$	40.8123	1.37422
$883$	−44.2757	−1.49000	−0.744998	−	0.667067i	$-0.767550\pi$
$883$	−44.2757	−1.49000	−0.744998	+	0.667067i	$0.767550\pi$
$884$	17.4377	0.586493
$885$	−68.7576	−2.31126
$886$	44.3981	1.49158
$887$	3.28819	0.110407	0.0552033	−	0.998475i	$-0.482419\pi$
$887$	3.28819	0.110407	0.0552033	+	0.998475i	$0.482419\pi$
$888$	6.14695	0.206278
$889$	−2.01363	−0.0675351
$890$	−97.0743	−3.25394
$891$	−10.2285	−0.342667
$892$	−140.451	−4.70265
$893$	−6.83073	−0.228582
$894$	−133.981	−4.48099
$895$	44.6489	1.49245
$896$	−11.2779	−0.376768
$897$	−10.4159	−0.347777
$898$	−51.7938	−1.72838
$899$	2.52532	0.0842242
$900$	34.7195	1.15732
$901$	−11.0483	−0.368073
$902$	16.2657	0.541590
$903$	2.21355	0.0736625
$904$	128.950	4.28881
$905$	−38.3470	−1.27470
$906$	103.870	3.45084
$907$	−14.8986	−0.494699	−0.247349	−	0.968926i	$-0.579560\pi$
$907$	−14.8986	−0.494699	−0.247349	+	0.968926i	$0.579560\pi$
$908$	−50.7600	−1.68453
$909$	19.8682	0.658988
$910$	23.9485	0.793886
$911$	10.8461	0.359348	0.179674	−	0.983726i	$-0.442496\pi$
$911$	10.8461	0.359348	0.179674	+	0.983726i	$0.442496\pi$
$912$	15.1376	0.501257
$913$	5.11495	0.169280
$914$	−50.8127	−1.68073
$915$	20.8682	0.689881
$916$	26.0572	0.860955
$917$	−9.53646	−0.314922
$918$	−3.05541	−0.100843
$919$	39.5254	1.30382	0.651912	−	0.758295i	$-0.273967\pi$
$919$	39.5254	1.30382	0.651912	+	0.758295i	$0.273967\pi$
$920$	29.3720	0.968367
$921$	2.62123	0.0863724
$922$	−31.5790	−1.04000
$923$	−17.5037	−0.576142
$924$	−11.2360	−0.369637
$925$	0.871837	0.0286658
$926$	−39.9818	−1.31388
$927$	−46.1726	−1.51651
$928$	−9.69555	−0.318272
$929$	57.0414	1.87147	0.935734	−	0.352707i	$-0.114739\pi$
$929$	57.0414	1.87147	0.935734	+	0.352707i	$0.114739\pi$
$930$	−65.6741	−2.15354
$931$	3.39301	0.111202
$932$	66.9862	2.19421
$933$	−22.3853	−0.732862
$934$	−53.7926	−1.76015
$935$	−2.77927	−0.0908917
$936$	−70.5736	−2.30677
$937$	11.6229	0.379703	0.189852	−	0.981813i	$-0.439199\pi$
$937$	11.6229	0.379703	0.189852	+	0.981813i	$0.439199\pi$
$938$	−37.5030	−1.22452
$939$	8.00153	0.261120
$940$	−173.554	−5.66070
$941$	−39.8096	−1.29776	−0.648878	−	0.760892i	$-0.724762\pi$
$941$	−39.8096	−1.29776	−0.648878	+	0.760892i	$0.724762\pi$
$942$	129.644	4.22404
$943$	−7.89779	−0.257187
$944$	−122.393	−3.98356
$945$	−3.01018	−0.0979211
$946$	2.66007	0.0864864
$947$	−0.276518	−0.00898563	−0.00449281	−	0.999990i	$-0.501430\pi$
$947$	−0.276518	−0.00898563	−0.00449281	+	0.999990i	$0.501430\pi$
$948$	−185.323	−6.01900
$949$	−47.3386	−1.53667
$950$	4.02378	0.130549
$951$	−58.4244	−1.89454
$952$	−7.71552	−0.250061
$953$	20.7757	0.672991	0.336496	−	0.941685i	$-0.390758\pi$
$953$	20.7757	0.672991	0.336496	+	0.941685i	$0.390758\pi$
$954$	73.7880	2.38897
$955$	−44.6607	−1.44519
$956$	−61.9718	−2.00431
$957$	−1.56658	−0.0506404
$958$	−57.6353	−1.86211
$959$	12.7731	0.412466
$960$	100.602	3.24693
$961$	−16.6803	−0.538074
$962$	−2.92442	−0.0942871
$963$	11.1425	0.359063
$964$	−118.685	−3.82260
$965$	−23.0266	−0.741253
$966$	7.60517	0.244692
$967$	12.4121	0.399145	0.199573	−	0.979883i	$-0.436045\pi$
$967$	12.4121	0.399145	0.199573	+	0.979883i	$0.436045\pi$
$968$	−8.18236	−0.262991
$969$	1.30343	0.0418722
$970$	83.1501	2.66979
$971$	−33.5914	−1.07800	−0.539000	−	0.842306i	$-0.681198\pi$
$971$	−33.5914	−1.07800	−0.539000	+	0.842306i	$0.681198\pi$
$972$	104.390	3.34830
$973$	−15.0366	−0.482051
$974$	43.4626	1.39263
$975$	−21.9700	−0.703602
$976$	37.1468	1.18904
$977$	20.4873	0.655446	0.327723	−	0.944774i	$-0.393719\pi$
$977$	20.4873	0.655446	0.327723	+	0.944774i	$0.393719\pi$
$978$	−33.3360	−1.06597
$979$	−13.1305	−0.419652
$980$	86.2090	2.75385
$981$	−35.6275	−1.13750
$982$	−27.0597	−0.863511
$983$	−27.6026	−0.880387	−0.440193	−	0.897903i	$-0.645090\pi$
$983$	−27.6026	−0.880387	−0.440193	+	0.897903i	$0.645090\pi$
$984$	−117.452	−3.74425
$985$	−30.4959	−0.971682
$986$	−1.77518	−0.0565334
$987$	−27.2316	−0.866792
$988$	−9.68218	−0.308031
$989$	−1.29159	−0.0410702
$990$	18.5618	0.589931
$991$	36.9749	1.17455	0.587273	−	0.809389i	$-0.300201\pi$
$991$	36.9749	1.17455	0.587273	+	0.809389i	$0.300201\pi$
$992$	−54.9781	−1.74556
$993$	−73.3630	−2.32810
$994$	12.7803	0.405367
$995$	−71.4276	−2.26441
$996$	−60.9489	−1.93124
$997$	−40.2410	−1.27444	−0.637222	−	0.770680i	$-0.719917\pi$
$997$	−40.2410	−1.27444	−0.637222	+	0.770680i	$0.719917\pi$
$998$	86.2622	2.73058
$999$	0.367581	0.0116298

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.c.1.2	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.c.1.2	✓	60	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:	\( N \)	\(=\)	\( 8041 = 11 \cdot 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8041.a (trivial)

\(f(q)\)	\(=\)	\(q-2.66007 q^{2} -2.34749 q^{3} +5.07599 q^{4} -2.77927 q^{5} +6.24449 q^{6} +0.942946 q^{7} -8.18236 q^{8} +2.51070 q^{9} +O(q^{10})\)	\(q-2.66007 q^{2} -2.34749 q^{3} +5.07599 q^{4} -2.77927 q^{5} +6.24449 q^{6} +0.942946 q^{7} -8.18236 q^{8} +2.51070 q^{9} +7.39305 q^{10} +1.00000 q^{11} -11.9158 q^{12} +3.43533 q^{13} -2.50830 q^{14} +6.52429 q^{15} +11.6137 q^{16} +1.00000 q^{17} -6.67866 q^{18} -0.555244 q^{19} -14.1075 q^{20} -2.21355 q^{21} -2.66007 q^{22} +1.29159 q^{23} +19.2080 q^{24} +2.72432 q^{25} -9.13823 q^{26} +1.14862 q^{27} +4.78638 q^{28} +0.667344 q^{29} -17.3551 q^{30} +3.78414 q^{31} -14.5286 q^{32} -2.34749 q^{33} -2.66007 q^{34} -2.62070 q^{35} +12.7443 q^{36} +0.320021 q^{37} +1.47699 q^{38} -8.06440 q^{39} +22.7409 q^{40} -6.11477 q^{41} +5.88822 q^{42} -1.00000 q^{43} +5.07599 q^{44} -6.97791 q^{45} -3.43573 q^{46} +12.3022 q^{47} -27.2630 q^{48} -6.11085 q^{49} -7.24688 q^{50} -2.34749 q^{51} +17.4377 q^{52} -11.0483 q^{53} -3.05541 q^{54} -2.77927 q^{55} -7.71552 q^{56} +1.30343 q^{57} -1.77518 q^{58} -10.5387 q^{59} +33.1173 q^{60} +3.19854 q^{61} -10.0661 q^{62} +2.36746 q^{63} +15.4196 q^{64} -9.54769 q^{65} +6.24449 q^{66} +14.9515 q^{67} +5.07599 q^{68} -3.03200 q^{69} +6.97124 q^{70} -5.09521 q^{71} -20.5435 q^{72} -13.7799 q^{73} -0.851278 q^{74} -6.39530 q^{75} -2.81841 q^{76} +0.942946 q^{77} +21.4519 q^{78} +15.5527 q^{79} -32.2775 q^{80} -10.2285 q^{81} +16.2657 q^{82} +5.11495 q^{83} -11.2360 q^{84} -2.77927 q^{85} +2.66007 q^{86} -1.56658 q^{87} -8.18236 q^{88} -13.1305 q^{89} +18.5618 q^{90} +3.23933 q^{91} +6.55611 q^{92} -8.88322 q^{93} -32.7248 q^{94} +1.54317 q^{95} +34.1056 q^{96} +11.2471 q^{97} +16.2553 q^{98} +2.51070 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 9 q^{2} - 6 q^{3} + 43 q^{4} - 15 q^{5} - 4 q^{6} - 17 q^{7} - 21 q^{8} + 40 q^{9}+O(q^{10}) \) 60 * q - 9 * q^2 - 6 * q^3 + 43 * q^4 - 15 * q^5 - 4 * q^6 - 17 * q^7 - 21 * q^8 + 40 * q^9	\( 60 q - 9 q^{2} - 6 q^{3} + 43 q^{4} - 15 q^{5} - 4 q^{6} - 17 q^{7} - 21 q^{8} + 40 q^{9} + q^{10} + 60 q^{11} - 13 q^{12} - 2 q^{13} - 15 q^{14} - 32 q^{15} + 21 q^{16} + 60 q^{17} - 41 q^{18} - 24 q^{19} - 33 q^{20} - 12 q^{21} - 9 q^{22} - 20 q^{23} + 9 q^{24} + 25 q^{25} - 40 q^{26} - 18 q^{27} - 3 q^{28} - 54 q^{29} - 18 q^{30} - 50 q^{31} - 51 q^{32} - 6 q^{33} - 9 q^{34} - 30 q^{35} + 27 q^{36} - 63 q^{37} - 38 q^{38} - 55 q^{39} - 5 q^{40} - 53 q^{41} - 47 q^{42} - 60 q^{43} + 43 q^{44} - 36 q^{45} - 27 q^{46} - 47 q^{47} - 38 q^{48} + 5 q^{49} - 4 q^{50} - 6 q^{51} - 13 q^{52} - 24 q^{53} - 58 q^{54} - 15 q^{55} - 45 q^{56} + 23 q^{57} + 16 q^{58} - 57 q^{59} - 4 q^{60} - 8 q^{61} - 3 q^{62} - 57 q^{63} - 5 q^{64} - 27 q^{65} - 4 q^{66} - 49 q^{67} + 43 q^{68} - 57 q^{69} - 7 q^{70} - 151 q^{71} - 29 q^{72} - 12 q^{73} + 18 q^{74} - 23 q^{75} - 38 q^{76} - 17 q^{77} + 37 q^{78} - 11 q^{79} - 21 q^{80} + 28 q^{81} + 44 q^{82} - 42 q^{83} + 16 q^{84} - 15 q^{85} + 9 q^{86} - 56 q^{87} - 21 q^{88} - 88 q^{89} + 47 q^{90} - 60 q^{91} + 26 q^{92} - 16 q^{93} + 37 q^{94} - 57 q^{95} + 108 q^{96} - 22 q^{97} + 8 q^{98} + 40 q^{99}+O(q^{100}) \) 60 * q - 9 * q^2 - 6 * q^3 + 43 * q^4 - 15 * q^5 - 4 * q^6 - 17 * q^7 - 21 * q^8 + 40 * q^9 + q^10 + 60 * q^11 - 13 * q^12 - 2 * q^13 - 15 * q^14 - 32 * q^15 + 21 * q^16 + 60 * q^17 - 41 * q^18 - 24 * q^19 - 33 * q^20 - 12 * q^21 - 9 * q^22 - 20 * q^23 + 9 * q^24 + 25 * q^25 - 40 * q^26 - 18 * q^27 - 3 * q^28 - 54 * q^29 - 18 * q^30 - 50 * q^31 - 51 * q^32 - 6 * q^33 - 9 * q^34 - 30 * q^35 + 27 * q^36 - 63 * q^37 - 38 * q^38 - 55 * q^39 - 5 * q^40 - 53 * q^41 - 47 * q^42 - 60 * q^43 + 43 * q^44 - 36 * q^45 - 27 * q^46 - 47 * q^47 - 38 * q^48 + 5 * q^49 - 4 * q^50 - 6 * q^51 - 13 * q^52 - 24 * q^53 - 58 * q^54 - 15 * q^55 - 45 * q^56 + 23 * q^57 + 16 * q^58 - 57 * q^59 - 4 * q^60 - 8 * q^61 - 3 * q^62 - 57 * q^63 - 5 * q^64 - 27 * q^65 - 4 * q^66 - 49 * q^67 + 43 * q^68 - 57 * q^69 - 7 * q^70 - 151 * q^71 - 29 * q^72 - 12 * q^73 + 18 * q^74 - 23 * q^75 - 38 * q^76 - 17 * q^77 + 37 * q^78 - 11 * q^79 - 21 * q^80 + 28 * q^81 + 44 * q^82 - 42 * q^83 + 16 * q^84 - 15 * q^85 + 9 * q^86 - 56 * q^87 - 21 * q^88 - 88 * q^89 + 47 * q^90 - 60 * q^91 + 26 * q^92 - 16 * q^93 + 37 * q^94 - 57 * q^95 + 108 * q^96 - 22 * q^97 + 8 * q^98 + 40 * q^99

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