LMFDB - Embedded newform 8041.2.a.c.1.12

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			1.12
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)

$f(q)$	$=$	$q-1.94215 q^{2} +1.51854 q^{3} +1.77194 q^{4} +3.53502 q^{5} -2.94923 q^{6} -1.41025 q^{7} +0.442922 q^{8} -0.694041 q^{9} +O(q^{10})$	\(q-1.94215 q^{2} +1.51854 q^{3} +1.77194 q^{4} +3.53502 q^{5} -2.94923 q^{6} -1.41025 q^{7} +0.442922 q^{8} -0.694041 q^{9} -6.86554 q^{10} +1.00000 q^{11} +2.69076 q^{12} +3.70725 q^{13} +2.73892 q^{14} +5.36807 q^{15} -4.40411 q^{16} +1.00000 q^{17} +1.34793 q^{18} -3.04836 q^{19} +6.26386 q^{20} -2.14152 q^{21} -1.94215 q^{22} +0.0341528 q^{23} +0.672594 q^{24} +7.49639 q^{25} -7.20004 q^{26} -5.60954 q^{27} -2.49888 q^{28} -3.51282 q^{29} -10.4256 q^{30} -3.96797 q^{31} +7.66758 q^{32} +1.51854 q^{33} -1.94215 q^{34} -4.98527 q^{35} -1.22980 q^{36} -1.77886 q^{37} +5.92038 q^{38} +5.62961 q^{39} +1.56574 q^{40} -4.53345 q^{41} +4.15915 q^{42} -1.00000 q^{43} +1.77194 q^{44} -2.45345 q^{45} -0.0663298 q^{46} -8.14459 q^{47} -6.68780 q^{48} -5.01119 q^{49} -14.5591 q^{50} +1.51854 q^{51} +6.56904 q^{52} -10.3883 q^{53} +10.8946 q^{54} +3.53502 q^{55} -0.624631 q^{56} -4.62906 q^{57} +6.82241 q^{58} -11.9633 q^{59} +9.51191 q^{60} -7.10236 q^{61} +7.70639 q^{62} +0.978772 q^{63} -6.08338 q^{64} +13.1052 q^{65} -2.94923 q^{66} -16.2637 q^{67} +1.77194 q^{68} +0.0518623 q^{69} +9.68214 q^{70} +5.38337 q^{71} -0.307406 q^{72} +9.86353 q^{73} +3.45481 q^{74} +11.3836 q^{75} -5.40152 q^{76} -1.41025 q^{77} -10.9335 q^{78} -10.5158 q^{79} -15.5686 q^{80} -6.43618 q^{81} +8.80463 q^{82} -1.08436 q^{83} -3.79465 q^{84} +3.53502 q^{85} +1.94215 q^{86} -5.33435 q^{87} +0.442922 q^{88} +14.4689 q^{89} +4.76497 q^{90} -5.22816 q^{91} +0.0605167 q^{92} -6.02551 q^{93} +15.8180 q^{94} -10.7760 q^{95} +11.6435 q^{96} -9.38783 q^{97} +9.73248 q^{98} -0.694041 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.94215	−1.37331	−0.686653	−	0.726985i	$-0.740921\pi$
$2$	−1.94215	−1.37331	−0.686653	+	0.726985i	$0.740921\pi$
$3$	1.51854	0.876729	0.438364	−	0.898797i	$-0.355558\pi$
$3$	1.51854	0.876729	0.438364	+	0.898797i	$0.355558\pi$
$4$	1.77194	0.885971
$5$	3.53502	1.58091	0.790455	−	0.612520i	$-0.209844\pi$
$5$	3.53502	1.58091	0.790455	+	0.612520i	$0.209844\pi$
$6$	−2.94923	−1.20402
$7$	−1.41025	−0.533025	−0.266512	−	0.963831i	$-0.585871\pi$
$7$	−1.41025	−0.533025	−0.266512	+	0.963831i	$0.585871\pi$
$8$	0.442922	0.156597
$9$	−0.694041	−0.231347
$10$	−6.86554	−2.17107
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	2.69076	0.776756
$13$	3.70725	1.02821	0.514104	−	0.857728i	$-0.328125\pi$
$13$	3.70725	1.02821	0.514104	+	0.857728i	$0.328125\pi$
$14$	2.73892	0.732007
$15$	5.36807	1.38603
$16$	−4.40411	−1.10103
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	1.34793	0.317710
$19$	−3.04836	−0.699343	−0.349671	−	0.936872i	$-0.613707\pi$
$19$	−3.04836	−0.699343	−0.349671	+	0.936872i	$0.613707\pi$
$20$	6.26386	1.40064
$21$	−2.14152	−0.467318
$22$	−1.94215	−0.414068
$23$	0.0341528	0.00712135	0.00356067	−	0.999994i	$-0.498867\pi$
$23$	0.0341528	0.00712135	0.00356067	+	0.999994i	$0.498867\pi$
$24$	0.672594	0.137293
$25$	7.49639	1.49928
$26$	−7.20004	−1.41204
$27$	−5.60954	−1.07956
$28$	−2.49888	−0.472245
$29$	−3.51282	−0.652314	−0.326157	−	0.945316i	$-0.605754\pi$
$29$	−3.51282	−0.652314	−0.326157	+	0.945316i	$0.605754\pi$
$30$	−10.4256	−1.90344
$31$	−3.96797	−0.712668	−0.356334	−	0.934359i	$-0.615974\pi$
$31$	−3.96797	−0.712668	−0.356334	+	0.934359i	$0.615974\pi$
$32$	7.66758	1.35545
$33$	1.51854	0.264344
$34$	−1.94215	−0.333076
$35$	−4.98527	−0.842665
$36$	−1.22980	−0.204967
$37$	−1.77886	−0.292443	−0.146221	−	0.989252i	$-0.546711\pi$
$37$	−1.77886	−0.292443	−0.146221	+	0.989252i	$0.546711\pi$
$38$	5.92038	0.960412
$39$	5.62961	0.901459
$40$	1.56574	0.247565
$41$	−4.53345	−0.708005	−0.354003	−	0.935244i	$-0.615180\pi$
$41$	−4.53345	−0.708005	−0.354003	+	0.935244i	$0.615180\pi$
$42$	4.15915	0.641771
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	1.77194	0.267130
$45$	−2.45345	−0.365739
$46$	−0.0663298	−0.00977979
$47$	−8.14459	−1.18801	−0.594006	−	0.804461i	$-0.702454\pi$
$47$	−8.14459	−1.18801	−0.594006	+	0.804461i	$0.702454\pi$
$48$	−6.68780	−0.965301
$49$	−5.01119	−0.715884
$50$	−14.5591	−2.05897
$51$	1.51854	0.212638
$52$	6.56904	0.910962
$53$	−10.3883	−1.42695	−0.713474	−	0.700682i	$-0.752879\pi$
$53$	−10.3883	−1.42695	−0.713474	+	0.700682i	$0.752879\pi$
$54$	10.8946	1.48256
$55$	3.53502	0.476662
$56$	−0.624631	−0.0834699
$57$	−4.62906	−0.613134
$58$	6.82241	0.895827
$59$	−11.9633	−1.55750	−0.778748	−	0.627337i	$-0.784145\pi$
$59$	−11.9633	−1.55750	−0.778748	+	0.627337i	$0.784145\pi$
$60$	9.51191	1.22798
$61$	−7.10236	−0.909364	−0.454682	−	0.890654i	$-0.650247\pi$
$61$	−7.10236	−0.909364	−0.454682	+	0.890654i	$0.650247\pi$
$62$	7.70639	0.978712
$63$	0.978772	0.123314
$64$	−6.08338	−0.760422
$65$	13.1052	1.62550
$66$	−2.94923	−0.363025
$67$	−16.2637	−1.98692	−0.993462	−	0.114165i	$-0.963581\pi$
$67$	−16.2637	−1.98692	−0.993462	+	0.114165i	$0.963581\pi$
$68$	1.77194	0.214880
$69$	0.0518623	0.00624349
$70$	9.68214	1.15724
$71$	5.38337	0.638888	0.319444	−	0.947605i	$-0.396504\pi$
$71$	5.38337	0.638888	0.319444	+	0.947605i	$0.396504\pi$
$72$	−0.307406	−0.0362281
$73$	9.86353	1.15444	0.577219	−	0.816589i	$-0.304138\pi$
$73$	9.86353	1.15444	0.577219	+	0.816589i	$0.304138\pi$
$74$	3.45481	0.401613
$75$	11.3836	1.31446
$76$	−5.40152	−0.619597
$77$	−1.41025	−0.160713
$78$	−10.9335	−1.23798
$79$	−10.5158	−1.18312	−0.591558	−	0.806263i	$-0.701487\pi$
$79$	−10.5158	−1.18312	−0.591558	+	0.806263i	$0.701487\pi$
$80$	−15.5686	−1.74062
$81$	−6.43618	−0.715132
$82$	8.80463	0.972308
$83$	−1.08436	−0.119024	−0.0595121	−	0.998228i	$-0.518954\pi$
$83$	−1.08436	−0.119024	−0.0595121	+	0.998228i	$0.518954\pi$
$84$	−3.79465	−0.414030
$85$	3.53502	0.383427
$86$	1.94215	0.209427
$87$	−5.33435	−0.571902
$88$	0.442922	0.0472157
$89$	14.4689	1.53370	0.766848	−	0.641828i	$-0.221824\pi$
$89$	14.4689	1.53370	0.766848	+	0.641828i	$0.221824\pi$
$90$	4.76497	0.502272
$91$	−5.22816	−0.548060
$92$	0.0605167	0.00630931
$93$	−6.02551	−0.624817
$94$	15.8180	1.63150
$95$	−10.7760	−1.10560
$96$	11.6435	1.18836
$97$	−9.38783	−0.953190	−0.476595	−	0.879123i	$-0.658129\pi$
$97$	−9.38783	−0.953190	−0.476595	+	0.879123i	$0.658129\pi$
$98$	9.73248	0.983129
$99$	−0.694041	−0.0697537
$100$	13.2832	1.32832
$101$	7.41896	0.738214	0.369107	−	0.929387i	$-0.379664\pi$
$101$	7.41896	0.738214	0.369107	+	0.929387i	$0.379664\pi$
$102$	−2.94923	−0.292017
$103$	−3.48941	−0.343822	−0.171911	−	0.985113i	$-0.554994\pi$
$103$	−3.48941	−0.343822	−0.171911	+	0.985113i	$0.554994\pi$
$104$	1.64203	0.161014
$105$	−7.57033	−0.738788
$106$	20.1757	1.95964
$107$	−5.03686	−0.486932	−0.243466	−	0.969909i	$-0.578284\pi$
$107$	−5.03686	−0.486932	−0.243466	+	0.969909i	$0.578284\pi$
$108$	−9.93979	−0.956456
$109$	−16.0745	−1.53965	−0.769827	−	0.638252i	$-0.779658\pi$
$109$	−16.0745	−1.53965	−0.769827	+	0.638252i	$0.779658\pi$
$110$	−6.86554	−0.654604
$111$	−2.70127	−0.256393
$112$	6.21089	0.586874
$113$	2.13395	0.200745	0.100373	−	0.994950i	$-0.467997\pi$
$113$	2.13395	0.200745	0.100373	+	0.994950i	$0.467997\pi$
$114$	8.99032	0.842021
$115$	0.120731	0.0112582
$116$	−6.22451	−0.577931
$117$	−2.57299	−0.237873
$118$	23.2346	2.13892
$119$	−1.41025	−0.129278
$120$	2.37764	0.217048
$121$	1.00000	0.0909091
$122$	13.7938	1.24884
$123$	−6.88421	−0.620729
$124$	−7.03101	−0.631404
$125$	8.82480	0.789314
$126$	−1.90092	−0.169347
$127$	−15.7718	−1.39952	−0.699761	−	0.714377i	$-0.746710\pi$
$127$	−15.7718	−1.39952	−0.699761	+	0.714377i	$0.746710\pi$
$128$	−3.52034	−0.311157
$129$	−1.51854	−0.133700
$130$	−25.4523	−2.23232
$131$	−0.604916	−0.0528518	−0.0264259	−	0.999651i	$-0.508413\pi$
$131$	−0.604916	−0.0528518	−0.0264259	+	0.999651i	$0.508413\pi$
$132$	2.69076	0.234201
$133$	4.29896	0.372767
$134$	31.5865	2.72866
$135$	−19.8299	−1.70668
$136$	0.442922	0.0379803
$137$	20.2775	1.73242	0.866212	−	0.499677i	$-0.166548\pi$
$137$	20.2775	1.73242	0.866212	+	0.499677i	$0.166548\pi$
$138$	−0.100724	−0.00857422
$139$	14.1178	1.19745	0.598727	−	0.800953i	$-0.295673\pi$
$139$	14.1178	1.19745	0.598727	+	0.800953i	$0.295673\pi$
$140$	−8.83361	−0.746577
$141$	−12.3679	−1.04156
$142$	−10.4553	−0.877389
$143$	3.70725	0.310016
$144$	3.05663	0.254719
$145$	−12.4179	−1.03125
$146$	−19.1564	−1.58540
$147$	−7.60969	−0.627636
$148$	−3.15204	−0.259096
$149$	20.2613	1.65987	0.829936	−	0.557858i	$-0.188377\pi$
$149$	20.2613	1.65987	0.829936	+	0.557858i	$0.188377\pi$
$150$	−22.1086	−1.80516
$151$	9.56184	0.778132	0.389066	−	0.921210i	$-0.372798\pi$
$151$	9.56184	0.778132	0.389066	+	0.921210i	$0.372798\pi$
$152$	−1.35019	−0.109515
$153$	−0.694041	−0.0561099
$154$	2.73892	0.220708
$155$	−14.0269	−1.12666
$156$	9.97534	0.798667
$157$	−11.2346	−0.896620	−0.448310	−	0.893878i	$-0.647974\pi$
$157$	−11.2346	−0.896620	−0.448310	+	0.893878i	$0.647974\pi$
$158$	20.4232	1.62478
$159$	−15.7751	−1.25105
$160$	27.1051	2.14285
$161$	−0.0481640	−0.00379585
$162$	12.5000	0.982095
$163$	3.17514	0.248696	0.124348	−	0.992239i	$-0.460316\pi$
$163$	3.17514	0.248696	0.124348	+	0.992239i	$0.460316\pi$
$164$	−8.03301	−0.627272
$165$	5.36807	0.417904
$166$	2.10599	0.163457
$167$	8.36359	0.647194	0.323597	−	0.946195i	$-0.395108\pi$
$167$	8.36359	0.647194	0.323597	+	0.946195i	$0.395108\pi$
$168$	−0.948527	−0.0731804
$169$	0.743739	0.0572107
$170$	−6.86554	−0.526563
$171$	2.11569	0.161791
$172$	−1.77194	−0.135109
$173$	3.19060	0.242577	0.121288	−	0.992617i	$-0.461297\pi$
$173$	3.19060	0.242577	0.121288	+	0.992617i	$0.461297\pi$
$174$	10.3601	0.785397
$175$	−10.5718	−0.799153
$176$	−4.40411	−0.331972
$177$	−18.1668	−1.36550
$178$	−28.1007	−2.10624
$179$	10.2364	0.765105	0.382553	−	0.923934i	$-0.375045\pi$
$179$	10.2364	0.765105	0.382553	+	0.923934i	$0.375045\pi$
$180$	−4.34737	−0.324034
$181$	17.9109	1.33130	0.665652	−	0.746262i	$-0.268154\pi$
$181$	17.9109	1.33130	0.665652	+	0.746262i	$0.268154\pi$
$182$	10.1539	0.752655
$183$	−10.7852	−0.797266
$184$	0.0151270	0.00111518
$185$	−6.28831	−0.462326
$186$	11.7024	0.858065
$187$	1.00000	0.0731272
$188$	−14.4318	−1.05254
$189$	7.91087	0.575431
$190$	20.9287	1.51833
$191$	−2.74637	−0.198720	−0.0993602	−	0.995052i	$-0.531680\pi$
$191$	−2.74637	−0.198720	−0.0993602	+	0.995052i	$0.531680\pi$
$192$	−9.23785	−0.666684
$193$	−8.82018	−0.634890	−0.317445	−	0.948277i	$-0.602825\pi$
$193$	−8.82018	−0.634890	−0.317445	+	0.948277i	$0.602825\pi$
$194$	18.2326	1.30902
$195$	19.9008	1.42513
$196$	−8.87954	−0.634253
$197$	−13.9041	−0.990623	−0.495312	−	0.868715i	$-0.664946\pi$
$197$	−13.9041	−0.990623	−0.495312	+	0.868715i	$0.664946\pi$
$198$	1.34793	0.0957933
$199$	−19.6966	−1.39625	−0.698126	−	0.715974i	$-0.745983\pi$
$199$	−19.6966	−1.39625	−0.698126	+	0.715974i	$0.745983\pi$
$200$	3.32032	0.234782
$201$	−24.6970	−1.74199
$202$	−14.4087	−1.01379
$203$	4.95395	0.347699
$204$	2.69076	0.188391
$205$	−16.0258	−1.11929
$206$	6.77695	0.472172
$207$	−0.0237034	−0.00164750
$208$	−16.3271	−1.13208
$209$	−3.04836	−0.210860
$210$	14.7027	1.01458
$211$	−5.06593	−0.348753	−0.174376	−	0.984679i	$-0.555791\pi$
$211$	−5.06593	−0.348753	−0.174376	+	0.984679i	$0.555791\pi$
$212$	−18.4075	−1.26424
$213$	8.17485	0.560132
$214$	9.78234	0.668707
$215$	−3.53502	−0.241087
$216$	−2.48459	−0.169055
$217$	5.59583	0.379870
$218$	31.2190	2.11442
$219$	14.9781	1.01213
$220$	6.26386	0.422309
$221$	3.70725	0.249377
$222$	5.24626	0.352106
$223$	−7.29242	−0.488336	−0.244168	−	0.969733i	$-0.578515\pi$
$223$	−7.29242	−0.488336	−0.244168	+	0.969733i	$0.578515\pi$
$224$	−10.8132	−0.722489
$225$	−5.20280	−0.346853
$226$	−4.14445	−0.275684
$227$	−22.3432	−1.48297	−0.741484	−	0.670970i	$-0.765878\pi$
$227$	−22.3432	−1.48297	−0.741484	+	0.670970i	$0.765878\pi$
$228$	−8.20242	−0.543219
$229$	−22.4646	−1.48451	−0.742253	−	0.670120i	$-0.766243\pi$
$229$	−22.4646	−1.48451	−0.742253	+	0.670120i	$0.766243\pi$
$230$	−0.234477	−0.0154610
$231$	−2.14152	−0.140902
$232$	−1.55590	−0.102150
$233$	20.4483	1.33961	0.669806	−	0.742536i	$-0.266377\pi$
$233$	20.4483	1.33961	0.669806	+	0.742536i	$0.266377\pi$
$234$	4.99712	0.326672
$235$	−28.7913	−1.87814
$236$	−21.1984	−1.37990
$237$	−15.9686	−1.03727
$238$	2.73892	0.177538
$239$	−0.949628	−0.0614263	−0.0307132	−	0.999528i	$-0.509778\pi$
$239$	−0.949628	−0.0614263	−0.0307132	+	0.999528i	$0.509778\pi$
$240$	−23.6415	−1.52605
$241$	15.2165	0.980183	0.490091	−	0.871671i	$-0.336963\pi$
$241$	15.2165	0.980183	0.490091	+	0.871671i	$0.336963\pi$
$242$	−1.94215	−0.124846
$243$	7.05504	0.452581
$244$	−12.5850	−0.805670
$245$	−17.7147	−1.13175
$246$	13.3702	0.852451
$247$	−11.3011	−0.719069
$248$	−1.75750	−0.111601
$249$	−1.64665	−0.104352
$250$	−17.1391	−1.08397
$251$	3.42246	0.216024	0.108012	−	0.994150i	$-0.465552\pi$
$251$	3.42246	0.216024	0.108012	+	0.994150i	$0.465552\pi$
$252$	1.73433	0.109252
$253$	0.0341528	0.00214717
$254$	30.6312	1.92197
$255$	5.36807	0.336162
$256$	19.0038	1.18774
$257$	−6.70330	−0.418140	−0.209070	−	0.977901i	$-0.567044\pi$
$257$	−6.70330	−0.418140	−0.209070	+	0.977901i	$0.567044\pi$
$258$	2.94923	0.183611
$259$	2.50864	0.155879
$260$	23.2217	1.44015
$261$	2.43804	0.150911
$262$	1.17484	0.0725817
$263$	16.7371	1.03205	0.516026	−	0.856573i	$-0.327411\pi$
$263$	16.7371	1.03205	0.516026	+	0.856573i	$0.327411\pi$
$264$	0.672594	0.0413953
$265$	−36.7230	−2.25588
$266$	−8.34922	−0.511923
$267$	21.9715	1.34464
$268$	−28.8183	−1.76036
$269$	−27.2672	−1.66251	−0.831256	−	0.555890i	$-0.812378\pi$
$269$	−27.2672	−1.66251	−0.831256	+	0.555890i	$0.812378\pi$
$270$	38.5126	2.34380
$271$	23.1278	1.40491	0.702457	−	0.711726i	$-0.252086\pi$
$271$	23.1278	1.40491	0.702457	+	0.711726i	$0.252086\pi$
$272$	−4.40411	−0.267038
$273$	−7.93916	−0.480500
$274$	−39.3819	−2.37915
$275$	7.49639	0.452049
$276$	0.0918970	0.00553155
$277$	13.0492	0.784051	0.392026	−	0.919954i	$-0.371774\pi$
$277$	13.0492	0.784051	0.392026	+	0.919954i	$0.371774\pi$
$278$	−27.4188	−1.64447
$279$	2.75393	0.164874
$280$	−2.20809	−0.131958
$281$	10.0827	0.601485	0.300742	−	0.953705i	$-0.402766\pi$
$281$	10.0827	0.601485	0.300742	+	0.953705i	$0.402766\pi$
$282$	24.0203	1.43039
$283$	18.6335	1.10765	0.553823	−	0.832634i	$-0.313168\pi$
$283$	18.6335	1.10765	0.553823	+	0.832634i	$0.313168\pi$
$284$	9.53902	0.566037
$285$	−16.3638	−0.969309
$286$	−7.20004	−0.425747
$287$	6.39330	0.377384
$288$	−5.32162	−0.313579
$289$	1.00000	0.0588235
$290$	24.1174	1.41622
$291$	−14.2558	−0.835689
$292$	17.4776	1.02280
$293$	−4.25782	−0.248744	−0.124372	−	0.992236i	$-0.539692\pi$
$293$	−4.25782	−0.248744	−0.124372	+	0.992236i	$0.539692\pi$
$294$	14.7791	0.861937
$295$	−42.2907	−2.46226
$296$	−0.787896	−0.0457955
$297$	−5.60954	−0.325499
$298$	−39.3505	−2.27951
$299$	0.126613	0.00732222
$300$	20.1710	1.16457
$301$	1.41025	0.0812855
$302$	−18.5705	−1.06861
$303$	11.2660	0.647213
$304$	13.4253	0.769995
$305$	−25.1070	−1.43762
$306$	1.34793	0.0770561
$307$	−13.3703	−0.763084	−0.381542	−	0.924351i	$-0.624607\pi$
$307$	−13.3703	−0.763084	−0.381542	+	0.924351i	$0.624607\pi$
$308$	−2.49888	−0.142387
$309$	−5.29880	−0.301438
$310$	27.2423	1.54726
$311$	10.7984	0.612322	0.306161	−	0.951980i	$-0.400955\pi$
$311$	10.7984	0.612322	0.306161	+	0.951980i	$0.400955\pi$
$312$	2.49348	0.141165
$313$	13.7362	0.776416	0.388208	−	0.921572i	$-0.373094\pi$
$313$	13.7362	0.776416	0.388208	+	0.921572i	$0.373094\pi$
$314$	21.8193	1.23133
$315$	3.45998	0.194948
$316$	−18.6333	−1.04821
$317$	−30.0726	−1.68905	−0.844523	−	0.535520i	$-0.820116\pi$
$317$	−30.0726	−1.68905	−0.844523	+	0.535520i	$0.820116\pi$
$318$	30.6376	1.71807
$319$	−3.51282	−0.196680
$320$	−21.5049	−1.20216
$321$	−7.64867	−0.426907
$322$	0.0935416	0.00521287
$323$	−3.04836	−0.169615
$324$	−11.4045	−0.633586
$325$	27.7910	1.54157
$326$	−6.16659	−0.341536
$327$	−24.4097	−1.34986
$328$	−2.00796	−0.110871
$329$	11.4859	0.633239
$330$	−10.4256	−0.573910
$331$	5.98590	0.329015	0.164507	−	0.986376i	$-0.447397\pi$
$331$	5.98590	0.329015	0.164507	+	0.986376i	$0.447397\pi$
$332$	−1.92143	−0.105452
$333$	1.23460	0.0676557
$334$	−16.2433	−0.888796
$335$	−57.4925	−3.14115
$336$	9.43148	0.514530
$337$	−6.23128	−0.339440	−0.169720	−	0.985492i	$-0.554286\pi$
$337$	−6.23128	−0.339440	−0.169720	+	0.985492i	$0.554286\pi$
$338$	−1.44445	−0.0785678
$339$	3.24048	0.175999
$340$	6.26386	0.339705
$341$	−3.96797	−0.214878
$342$	−4.10898	−0.222188
$343$	16.9388	0.914609
$344$	−0.442922	−0.0238808
$345$	0.183334	0.00987040
$346$	−6.19661	−0.333132
$347$	13.0887	0.702640	0.351320	−	0.936255i	$-0.385733\pi$
$347$	13.0887	0.702640	0.351320	+	0.936255i	$0.385733\pi$
$348$	−9.45216	−0.506689
$349$	19.9964	1.07038	0.535191	−	0.844731i	$-0.320240\pi$
$349$	19.9964	1.07038	0.535191	+	0.844731i	$0.320240\pi$
$350$	20.5320	1.09748
$351$	−20.7960	−1.11001
$352$	7.66758	0.408684
$353$	5.25054	0.279458	0.139729	−	0.990190i	$-0.455377\pi$
$353$	5.25054	0.279458	0.139729	+	0.990190i	$0.455377\pi$
$354$	35.2826	1.87525
$355$	19.0303	1.01003
$356$	25.6380	1.35881
$357$	−2.14152	−0.113341
$358$	−19.8806	−1.05072
$359$	35.9655	1.89819	0.949093	−	0.314995i	$-0.102003\pi$
$359$	35.9655	1.89819	0.949093	+	0.314995i	$0.102003\pi$
$360$	−1.08669	−0.0572735
$361$	−9.70748	−0.510920
$362$	−34.7856	−1.82829
$363$	1.51854	0.0797026
$364$	−9.26400	−0.485565
$365$	34.8678	1.82506
$366$	20.9465	1.09489
$367$	−14.3284	−0.747934	−0.373967	−	0.927442i	$-0.622003\pi$
$367$	−14.3284	−0.747934	−0.373967	+	0.927442i	$0.622003\pi$
$368$	−0.150412	−0.00784079
$369$	3.14640	0.163795
$370$	12.2128	0.634915
$371$	14.6502	0.760599
$372$	−10.6769	−0.553570
$373$	14.7526	0.763860	0.381930	−	0.924191i	$-0.375260\pi$
$373$	14.7526	0.763860	0.381930	+	0.924191i	$0.375260\pi$
$374$	−1.94215	−0.100426
$375$	13.4008	0.692014
$376$	−3.60742	−0.186038
$377$	−13.0229	−0.670714
$378$	−15.3641	−0.790243
$379$	−6.35525	−0.326447	−0.163224	−	0.986589i	$-0.552189\pi$
$379$	−6.35525	−0.326447	−0.163224	+	0.986589i	$0.552189\pi$
$380$	−19.0945	−0.979528
$381$	−23.9501	−1.22700
$382$	5.33386	0.272904
$383$	−31.7743	−1.62359	−0.811795	−	0.583943i	$-0.801509\pi$
$383$	−31.7743	−1.62359	−0.811795	+	0.583943i	$0.801509\pi$
$384$	−5.34577	−0.272800
$385$	−4.98527	−0.254073
$386$	17.1301	0.871899
$387$	0.694041	0.0352801
$388$	−16.6347	−0.844499
$389$	10.1154	0.512874	0.256437	−	0.966561i	$-0.417451\pi$
$389$	10.1154	0.512874	0.256437	+	0.966561i	$0.417451\pi$
$390$	−38.6503	−1.95713
$391$	0.0341528	0.00172718
$392$	−2.21957	−0.112105
$393$	−0.918589	−0.0463367
$394$	27.0038	1.36043
$395$	−37.1735	−1.87040
$396$	−1.22980	−0.0617998
$397$	36.8450	1.84920	0.924600	−	0.380940i	$-0.124400\pi$
$397$	36.8450	1.84920	0.924600	+	0.380940i	$0.124400\pi$
$398$	38.2537	1.91748
$399$	6.52813	0.326815
$400$	−33.0149	−1.65074
$401$	8.15161	0.407072	0.203536	−	0.979067i	$-0.434757\pi$
$401$	8.15161	0.407072	0.203536	+	0.979067i	$0.434757\pi$
$402$	47.9653	2.39229
$403$	−14.7103	−0.732771
$404$	13.1460	0.654036
$405$	−22.7521	−1.13056
$406$	−9.62132	−0.477498
$407$	−1.77886	−0.0881748
$408$	0.672594	0.0332984
$409$	−21.2094	−1.04874	−0.524369	−	0.851491i	$-0.675699\pi$
$409$	−21.2094	−1.04874	−0.524369	+	0.851491i	$0.675699\pi$
$410$	31.1246	1.53713
$411$	30.7922	1.51887
$412$	−6.18303	−0.304616
$413$	16.8713	0.830184
$414$	0.0460356	0.00226252
$415$	−3.83325	−0.188167
$416$	28.4257	1.39368
$417$	21.4384	1.04984
$418$	5.92038	0.289575
$419$	−3.49124	−0.170558	−0.0852792	−	0.996357i	$-0.527178\pi$
$419$	−3.49124	−0.170558	−0.0852792	+	0.996357i	$0.527178\pi$
$420$	−13.4142	−0.654545
$421$	28.7125	1.39936	0.699680	−	0.714457i	$-0.253326\pi$
$421$	28.7125	1.39936	0.699680	+	0.714457i	$0.253326\pi$
$422$	9.83878	0.478944
$423$	5.65268	0.274843
$424$	−4.60123	−0.223455
$425$	7.49639	0.363628
$426$	−15.8768	−0.769232
$427$	10.0161	0.484714
$428$	−8.92503	−0.431408
$429$	5.62961	0.271800
$430$	6.86554	0.331086
$431$	−10.6236	−0.511720	−0.255860	−	0.966714i	$-0.582359\pi$
$431$	−10.6236	−0.511720	−0.255860	+	0.966714i	$0.582359\pi$
$432$	24.7050	1.18862
$433$	18.9718	0.911725	0.455863	−	0.890050i	$-0.349331\pi$
$433$	18.9718	0.911725	0.455863	+	0.890050i	$0.349331\pi$
$434$	−10.8679	−0.521678
$435$	−18.8570	−0.904126
$436$	−28.4830	−1.36409
$437$	−0.104110	−0.00498026
$438$	−29.0898	−1.38996
$439$	7.22947	0.345044	0.172522	−	0.985006i	$-0.444808\pi$
$439$	7.22947	0.345044	0.172522	+	0.985006i	$0.444808\pi$
$440$	1.56574	0.0746437
$441$	3.47797	0.165618
$442$	−7.20004	−0.342471
$443$	17.3510	0.824372	0.412186	−	0.911100i	$-0.364765\pi$
$443$	17.3510	0.824372	0.412186	+	0.911100i	$0.364765\pi$
$444$	−4.78649	−0.227157
$445$	51.1478	2.42464
$446$	14.1630	0.670636
$447$	30.7676	1.45526
$448$	8.57909	0.405324
$449$	−7.53287	−0.355498	−0.177749	−	0.984076i	$-0.556882\pi$
$449$	−7.53287	−0.355498	−0.177749	+	0.984076i	$0.556882\pi$
$450$	10.1046	0.476336
$451$	−4.53345	−0.213472
$452$	3.78123	0.177854
$453$	14.5200	0.682210
$454$	43.3938	2.03657
$455$	−18.4817	−0.866434
$456$	−2.05031	−0.0960146
$457$	27.2549	1.27493	0.637464	−	0.770480i	$-0.279983\pi$
$457$	27.2549	1.27493	0.637464	+	0.770480i	$0.279983\pi$
$458$	43.6297	2.03868
$459$	−5.60954	−0.261831
$460$	0.213928	0.00997445
$461$	22.2289	1.03530	0.517652	−	0.855591i	$-0.326806\pi$
$461$	22.2289	1.03530	0.517652	+	0.855591i	$0.326806\pi$
$462$	4.15915	0.193501
$463$	−23.1359	−1.07522	−0.537609	−	0.843194i	$-0.680672\pi$
$463$	−23.1359	−1.07522	−0.537609	+	0.843194i	$0.680672\pi$
$464$	15.4708	0.718215
$465$	−21.3003	−0.987779
$466$	−39.7136	−1.83970
$467$	−1.20657	−0.0558332	−0.0279166	−	0.999610i	$-0.508887\pi$
$467$	−1.20657	−0.0558332	−0.0279166	+	0.999610i	$0.508887\pi$
$468$	−4.55918	−0.210748
$469$	22.9359	1.05908
$470$	55.9170	2.57926
$471$	−17.0602	−0.786093
$472$	−5.29883	−0.243898
$473$	−1.00000	−0.0459800
$474$	31.0134	1.42449
$475$	−22.8517	−1.04851
$476$	−2.49888	−0.114536
$477$	7.20993	0.330120
$478$	1.84432	0.0843571
$479$	12.1966	0.557278	0.278639	−	0.960396i	$-0.410117\pi$
$479$	12.1966	0.557278	0.278639	+	0.960396i	$0.410117\pi$
$480$	41.1601	1.87869
$481$	−6.59468	−0.300692
$482$	−29.5528	−1.34609
$483$	−0.0731389	−0.00332793
$484$	1.77194	0.0805428
$485$	−33.1862	−1.50691
$486$	−13.7019	−0.621532
$487$	32.4019	1.46827	0.734135	−	0.679003i	$-0.237588\pi$
$487$	32.4019	1.46827	0.734135	+	0.679003i	$0.237588\pi$
$488$	−3.14579	−0.142403
$489$	4.82157	0.218039
$490$	34.4045	1.55424
$491$	−10.1508	−0.458098	−0.229049	−	0.973415i	$-0.573562\pi$
$491$	−10.1508	−0.458098	−0.229049	+	0.973415i	$0.573562\pi$
$492$	−12.1984	−0.549948
$493$	−3.51282	−0.158209
$494$	21.9483	0.987503
$495$	−2.45345	−0.110274
$496$	17.4754	0.784667
$497$	−7.59190	−0.340543
$498$	3.19803	0.143307
$499$	36.6277	1.63968	0.819840	−	0.572593i	$-0.194062\pi$
$499$	36.6277	1.63968	0.819840	+	0.572593i	$0.194062\pi$
$500$	15.6370	0.699309
$501$	12.7004	0.567413
$502$	−6.64693	−0.296667
$503$	28.7943	1.28388	0.641938	−	0.766756i	$-0.278131\pi$
$503$	28.7943	1.28388	0.641938	+	0.766756i	$0.278131\pi$
$504$	0.433520	0.0193105
$505$	26.2262	1.16705
$506$	−0.0663298	−0.00294872
$507$	1.12940	0.0501582
$508$	−27.9468	−1.23994
$509$	9.31884	0.413051	0.206525	−	0.978441i	$-0.433784\pi$
$509$	9.31884	0.413051	0.206525	+	0.978441i	$0.433784\pi$
$510$	−10.4256	−0.461653
$511$	−13.9101	−0.615344
$512$	−29.8675	−1.31997
$513$	17.0999	0.754980
$514$	13.0188	0.574235
$515$	−12.3351	−0.543551
$516$	−2.69076	−0.118454
$517$	−8.14459	−0.358199
$518$	−4.87215	−0.214070
$519$	4.84504	0.212674
$520$	5.80460	0.254548
$521$	3.53891	0.155043	0.0775213	−	0.996991i	$-0.475299\pi$
$521$	3.53891	0.155043	0.0775213	+	0.996991i	$0.475299\pi$
$522$	−4.73503	−0.207247
$523$	−12.6939	−0.555065	−0.277532	−	0.960716i	$-0.589517\pi$
$523$	−12.6939	−0.555065	−0.277532	+	0.960716i	$0.589517\pi$
$524$	−1.07188	−0.0468252
$525$	−16.0537	−0.700640
$526$	−32.5059	−1.41732
$527$	−3.96797	−0.172847
$528$	−6.68780	−0.291049
$529$	−22.9988	−0.999949
$530$	71.3216	3.09801
$531$	8.30305	0.360322
$532$	7.61751	0.330261
$533$	−16.8066	−0.727976
$534$	−42.6720	−1.84660
$535$	−17.8054	−0.769796
$536$	−7.20354	−0.311145
$537$	15.5444	0.670790
$538$	52.9570	2.28314
$539$	−5.01119	−0.215847
$540$	−35.1374	−1.51207
$541$	44.5525	1.91546	0.957730	−	0.287669i	$-0.0928804\pi$
$541$	44.5525	1.91546	0.957730	+	0.287669i	$0.0928804\pi$
$542$	−44.9177	−1.92938
$543$	27.1983	1.16719
$544$	7.66758	0.328745
$545$	−56.8236	−2.43406
$546$	15.4190	0.659874
$547$	−11.0961	−0.474437	−0.237218	−	0.971456i	$-0.576236\pi$
$547$	−11.0961	−0.474437	−0.237218	+	0.971456i	$0.576236\pi$
$548$	35.9306	1.53488
$549$	4.92933	0.210379
$550$	−14.5591	−0.620802
$551$	10.7083	0.456191
$552$	0.0229710	0.000977709 0
$553$	14.8299	0.630630
$554$	−25.3435	−1.07674
$555$	−9.54904	−0.405334
$556$	25.0159	1.06091
$557$	29.2516	1.23943	0.619714	−	0.784827i	$-0.287248\pi$
$557$	29.2516	1.23943	0.619714	+	0.784827i	$0.287248\pi$
$558$	−5.34855	−0.226422
$559$	−3.70725	−0.156800
$560$	21.9557	0.927796
$561$	1.51854	0.0641127
$562$	−19.5821	−0.826023
$563$	−33.0808	−1.39419	−0.697095	−	0.716979i	$-0.745524\pi$
$563$	−33.0808	−1.39419	−0.697095	+	0.716979i	$0.745524\pi$
$564$	−21.9152	−0.922795
$565$	7.54356	0.317360
$566$	−36.1890	−1.52114
$567$	9.07664	0.381183
$568$	2.38441	0.100048
$569$	17.9272	0.751548	0.375774	−	0.926711i	$-0.377377\pi$
$569$	17.9272	0.751548	0.375774	+	0.926711i	$0.377377\pi$
$570$	31.7810	1.33116
$571$	7.00280	0.293058	0.146529	−	0.989206i	$-0.453190\pi$
$571$	7.00280	0.293058	0.146529	+	0.989206i	$0.453190\pi$
$572$	6.56904	0.274665
$573$	−4.17047	−0.174224
$574$	−12.4167	−0.518265
$575$	0.256023	0.0106769
$576$	4.22211	0.175921
$577$	−18.9736	−0.789880	−0.394940	−	0.918707i	$-0.629235\pi$
$577$	−18.9736	−0.789880	−0.394940	+	0.918707i	$0.629235\pi$
$578$	−1.94215	−0.0807827
$579$	−13.3938	−0.556627
$580$	−22.0038	−0.913657
$581$	1.52922	0.0634429
$582$	27.6869	1.14766
$583$	−10.3883	−0.430241
$584$	4.36877	0.180781
$585$	−9.09557	−0.376055
$586$	8.26932	0.341602
$587$	9.15740	0.377966	0.188983	−	0.981980i	$-0.439481\pi$
$587$	9.15740	0.377966	0.188983	+	0.981980i	$0.439481\pi$
$588$	−13.4839	−0.556068
$589$	12.0958	0.498399
$590$	82.1349	3.38144
$591$	−21.1139	−0.868508
$592$	7.83428	0.321987
$593$	−8.08111	−0.331851	−0.165926	−	0.986138i	$-0.553061\pi$
$593$	−8.08111	−0.331851	−0.165926	+	0.986138i	$0.553061\pi$
$594$	10.8946	0.447010
$595$	−4.98527	−0.204376
$596$	35.9019	1.47060
$597$	−29.9100	−1.22413
$598$	−0.245901	−0.0100557
$599$	−30.0584	−1.22815	−0.614076	−	0.789247i	$-0.710471\pi$
$599$	−30.0584	−1.22815	−0.614076	+	0.789247i	$0.710471\pi$
$600$	5.04203	0.205840
$601$	−10.6696	−0.435222	−0.217611	−	0.976036i	$-0.569826\pi$
$601$	−10.6696	−0.435222	−0.217611	+	0.976036i	$0.569826\pi$
$602$	−2.73892	−0.111630
$603$	11.2877	0.459669
$604$	16.9430	0.689402
$605$	3.53502	0.143719
$606$	−21.8802	−0.888822
$607$	−5.30095	−0.215159	−0.107579	−	0.994196i	$-0.534310\pi$
$607$	−5.30095	−0.215159	−0.107579	+	0.994196i	$0.534310\pi$
$608$	−23.3736	−0.947924
$609$	7.52277	0.304838
$610$	48.7616	1.97430
$611$	−30.1941	−1.22152
$612$	−1.22980	−0.0497117
$613$	−11.6326	−0.469836	−0.234918	−	0.972015i	$-0.575482\pi$
$613$	−11.6326	−0.469836	−0.234918	+	0.972015i	$0.575482\pi$
$614$	25.9671	1.04795
$615$	−24.3359	−0.981316
$616$	−0.624631	−0.0251671
$617$	−40.9023	−1.64667	−0.823333	−	0.567558i	$-0.807888\pi$
$617$	−40.9023	−1.64667	−0.823333	+	0.567558i	$0.807888\pi$
$618$	10.2911	0.413967
$619$	−28.0663	−1.12808	−0.564040	−	0.825747i	$-0.690754\pi$
$619$	−28.0663	−1.12808	−0.564040	+	0.825747i	$0.690754\pi$
$620$	−24.8548	−0.998193
$621$	−0.191581	−0.00768790
$622$	−20.9721	−0.840906
$623$	−20.4047	−0.817499
$624$	−24.7934	−0.992530
$625$	−6.28608	−0.251443
$626$	−26.6777	−1.06626
$627$	−4.62906	−0.184867
$628$	−19.9071	−0.794380
$629$	−1.77886	−0.0709278
$630$	−6.71980	−0.267723
$631$	−2.55536	−0.101727	−0.0508636	−	0.998706i	$-0.516197\pi$
$631$	−2.55536	−0.101727	−0.0508636	+	0.998706i	$0.516197\pi$
$632$	−4.65766	−0.185272
$633$	−7.69280	−0.305761
$634$	58.4055	2.31958
$635$	−55.7538	−2.21252
$636$	−27.9526	−1.10839
$637$	−18.5778	−0.736078
$638$	6.82241	0.270102
$639$	−3.73628	−0.147805
$640$	−12.4445	−0.491911
$641$	−12.9593	−0.511862	−0.255931	−	0.966695i	$-0.582382\pi$
$641$	−12.9593	−0.511862	−0.255931	+	0.966695i	$0.582382\pi$
$642$	14.8549	0.586274
$643$	16.8441	0.664267	0.332134	−	0.943232i	$-0.392232\pi$
$643$	16.8441	0.664267	0.332134	+	0.943232i	$0.392232\pi$
$644$	−0.0853438	−0.00336302
$645$	−5.36807	−0.211368
$646$	5.92038	0.232934
$647$	−40.7932	−1.60375	−0.801873	−	0.597494i	$-0.796163\pi$
$647$	−40.7932	−1.60375	−0.801873	+	0.597494i	$0.796163\pi$
$648$	−2.85073	−0.111987
$649$	−11.9633	−0.469602
$650$	−53.9743	−2.11705
$651$	8.49749	0.333043
$652$	5.62616	0.220338
$653$	33.9001	1.32662	0.663308	−	0.748347i	$-0.269152\pi$
$653$	33.9001	1.32662	0.663308	+	0.748347i	$0.269152\pi$
$654$	47.4073	1.85377
$655$	−2.13839	−0.0835539
$656$	19.9658	0.779533
$657$	−6.84569	−0.267076
$658$	−22.3074	−0.869632
$659$	−29.7266	−1.15798	−0.578991	−	0.815334i	$-0.696554\pi$
$659$	−29.7266	−1.15798	−0.578991	+	0.815334i	$0.696554\pi$
$660$	9.51191	0.370251
$661$	−39.4342	−1.53381	−0.766906	−	0.641759i	$-0.778205\pi$
$661$	−39.4342	−1.53381	−0.766906	+	0.641759i	$0.778205\pi$
$662$	−11.6255	−0.451838
$663$	5.62961	0.218636
$664$	−0.480288	−0.0186388
$665$	15.1969	0.589311
$666$	−2.39778	−0.0929120
$667$	−0.119972	−0.00464535
$668$	14.8198	0.573395
$669$	−11.0738	−0.428139
$670$	111.659	4.31376
$671$	−7.10236	−0.274184
$672$	−16.4203	−0.633426
$673$	−31.9957	−1.23334	−0.616672	−	0.787220i	$-0.711520\pi$
$673$	−31.9957	−1.23334	−0.616672	+	0.787220i	$0.711520\pi$
$674$	12.1021	0.466155
$675$	−42.0513	−1.61856
$676$	1.31786	0.0506870
$677$	−2.84708	−0.109422	−0.0547111	−	0.998502i	$-0.517424\pi$
$677$	−2.84708	−0.109422	−0.0547111	+	0.998502i	$0.517424\pi$
$678$	−6.29350	−0.241700
$679$	13.2392	0.508074
$680$	1.56574	0.0600434
$681$	−33.9290	−1.30016
$682$	7.70639	0.295093
$683$	43.2634	1.65543	0.827715	−	0.561149i	$-0.189640\pi$
$683$	43.2634	1.65543	0.827715	+	0.561149i	$0.189640\pi$
$684$	3.74888	0.143342
$685$	71.6815	2.73881
$686$	−32.8977	−1.25604
$687$	−34.1134	−1.30151
$688$	4.40411	0.167905
$689$	−38.5122	−1.46720
$690$	−0.356063	−0.0135551
$691$	17.6642	0.671977	0.335988	−	0.941866i	$-0.390930\pi$
$691$	17.6642	0.671977	0.335988	+	0.941866i	$0.390930\pi$
$692$	5.65355	0.214916
$693$	0.978772	0.0371805
$694$	−25.4203	−0.964940
$695$	49.9067	1.89307
$696$	−2.36270	−0.0895579
$697$	−4.53345	−0.171717
$698$	−38.8360	−1.46996
$699$	31.0515	1.17448
$700$	−18.7326	−0.708026
$701$	−12.6331	−0.477145	−0.238572	−	0.971125i	$-0.576679\pi$
$701$	−12.6331	−0.477145	−0.238572	+	0.971125i	$0.576679\pi$
$702$	40.3889	1.52438
$703$	5.42261	0.204518
$704$	−6.08338	−0.229276
$705$	−43.7207	−1.64662
$706$	−10.1973	−0.383781
$707$	−10.4626	−0.393486
$708$	−32.1905	−1.20979
$709$	−26.9954	−1.01383	−0.506916	−	0.861995i	$-0.669215\pi$
$709$	−26.9954	−1.01383	−0.506916	+	0.861995i	$0.669215\pi$
$710$	−36.9597	−1.38707
$711$	7.29837	0.273710
$712$	6.40858	0.240172
$713$	−0.135517	−0.00507516
$714$	4.15915	0.155652
$715$	13.1052	0.490108
$716$	18.1383	0.677861
$717$	−1.44205	−0.0538542
$718$	−69.8504	−2.60679
$719$	14.3523	0.535250	0.267625	−	0.963523i	$-0.413761\pi$
$719$	14.3523	0.535250	0.267625	+	0.963523i	$0.413761\pi$
$720$	10.8053	0.402688
$721$	4.92094	0.183265
$722$	18.8534	0.701650
$723$	23.1069	0.859354
$724$	31.7370	1.17950
$725$	−26.3334	−0.978000
$726$	−2.94923	−0.109456
$727$	−2.51254	−0.0931849	−0.0465924	−	0.998914i	$-0.514836\pi$
$727$	−2.51254	−0.0931849	−0.0465924	+	0.998914i	$0.514836\pi$
$728$	−2.31567	−0.0858244
$729$	30.0219	1.11192
$730$	−67.7185	−2.50637
$731$	−1.00000	−0.0369863
$732$	−19.1108	−0.706354
$733$	15.4122	0.569263	0.284632	−	0.958637i	$-0.408129\pi$
$733$	15.4122	0.569263	0.284632	+	0.958637i	$0.408129\pi$
$734$	27.8278	1.02714
$735$	−26.9004	−0.992237
$736$	0.261869	0.00965263
$737$	−16.2637	−0.599080
$738$	−6.11077	−0.224941
$739$	−14.0325	−0.516195	−0.258098	−	0.966119i	$-0.583096\pi$
$739$	−14.0325	−0.516195	−0.258098	+	0.966119i	$0.583096\pi$
$740$	−11.1425	−0.409607
$741$	−17.1611	−0.630429
$742$	−28.4528	−1.04454
$743$	4.79063	0.175751	0.0878757	−	0.996131i	$-0.471992\pi$
$743$	4.79063	0.175751	0.0878757	+	0.996131i	$0.471992\pi$
$744$	−2.66883	−0.0978442
$745$	71.6243	2.62411
$746$	−28.6517	−1.04901
$747$	0.752592	0.0275359
$748$	1.77194	0.0647886
$749$	7.10324	0.259547
$750$	−26.0263	−0.950348
$751$	0.407336	0.0148639	0.00743195	−	0.999972i	$-0.497634\pi$
$751$	0.407336	0.0148639	0.00743195	+	0.999972i	$0.497634\pi$
$752$	35.8696	1.30803
$753$	5.19714	0.189394
$754$	25.2924	0.921096
$755$	33.8013	1.23016
$756$	14.0176	0.509815
$757$	31.7298	1.15324	0.576619	−	0.817013i	$-0.304372\pi$
$757$	31.7298	1.15324	0.576619	+	0.817013i	$0.304372\pi$
$758$	12.3428	0.448312
$759$	0.0518623	0.00188248
$760$	−4.77294	−0.173133
$761$	17.6238	0.638863	0.319432	−	0.947609i	$-0.396508\pi$
$761$	17.6238	0.638863	0.319432	+	0.947609i	$0.396508\pi$
$762$	46.5147	1.68505
$763$	22.6690	0.820674
$764$	−4.86641	−0.176061
$765$	−2.45345	−0.0887047
$766$	61.7104	2.22969
$767$	−44.3512	−1.60143
$768$	28.8580	1.04132
$769$	−8.93711	−0.322280	−0.161140	−	0.986932i	$-0.551517\pi$
$769$	−8.93711	−0.322280	−0.161140	+	0.986932i	$0.551517\pi$
$770$	9.68214	0.348920
$771$	−10.1792	−0.366596
$772$	−15.6288	−0.562495
$773$	1.31765	0.0473926	0.0236963	−	0.999719i	$-0.492457\pi$
$773$	1.31765	0.0473926	0.0236963	+	0.999719i	$0.492457\pi$
$774$	−1.34793	−0.0484504
$775$	−29.7455	−1.06849
$776$	−4.15808	−0.149266
$777$	3.80946	0.136664
$778$	−19.6457	−0.704333
$779$	13.8196	0.495138
$780$	35.2631	1.26262
$781$	5.38337	0.192632
$782$	−0.0663298	−0.00237195
$783$	19.7053	0.704210
$784$	22.0698	0.788208
$785$	−39.7146	−1.41748
$786$	1.78404	0.0636345
$787$	41.1721	1.46763	0.733814	−	0.679351i	$-0.237739\pi$
$787$	41.1721	1.46763	0.733814	+	0.679351i	$0.237739\pi$
$788$	−24.6372	−0.877664
$789$	25.4159	0.904830
$790$	72.1964	2.56863
$791$	−3.00940	−0.107002
$792$	−0.307406	−0.0109232
$793$	−26.3303	−0.935015
$794$	−71.5586	−2.53952
$795$	−55.7653	−1.97779
$796$	−34.9012	−1.23704
$797$	11.8895	0.421147	0.210574	−	0.977578i	$-0.432467\pi$
$797$	11.8895	0.421147	0.210574	+	0.977578i	$0.432467\pi$
$798$	−12.6786	−0.448818
$799$	−8.14459	−0.288135
$800$	57.4792	2.03220
$801$	−10.0420	−0.354816
$802$	−15.8316	−0.559035
$803$	9.86353	0.348076
$804$	−43.7617	−1.54336
$805$	−0.170261	−0.00600091
$806$	28.5695	1.00632
$807$	−41.4063	−1.45757
$808$	3.28602	0.115602
$809$	−38.7350	−1.36185	−0.680925	−	0.732353i	$-0.738422\pi$
$809$	−38.7350	−1.36185	−0.680925	+	0.732353i	$0.738422\pi$
$810$	44.1879	1.55260
$811$	−21.4937	−0.754745	−0.377373	−	0.926062i	$-0.623172\pi$
$811$	−21.4937	−0.754745	−0.377373	+	0.926062i	$0.623172\pi$
$812$	8.77812	0.308052
$813$	35.1205	1.23173
$814$	3.45481	0.121091
$815$	11.2242	0.393166
$816$	−6.68780	−0.234120
$817$	3.04836	0.106649
$818$	41.1918	1.44024
$819$	3.62856	0.126792
$820$	−28.3969	−0.991661
$821$	−46.8394	−1.63471	−0.817354	−	0.576136i	$-0.804560\pi$
$821$	−46.8394	−1.63471	−0.817354	+	0.576136i	$0.804560\pi$
$822$	−59.8030	−2.08587
$823$	14.0137	0.488485	0.244243	−	0.969714i	$-0.421461\pi$
$823$	14.0137	0.488485	0.244243	+	0.969714i	$0.421461\pi$
$824$	−1.54554	−0.0538413
$825$	11.3836	0.396325
$826$	−32.7666	−1.14010
$827$	−44.7479	−1.55604	−0.778019	−	0.628241i	$-0.783775\pi$
$827$	−44.7479	−1.55604	−0.778019	+	0.628241i	$0.783775\pi$
$828$	−0.0420011	−0.00145964
$829$	42.9173	1.49058	0.745290	−	0.666741i	$-0.232311\pi$
$829$	42.9173	1.49058	0.745290	+	0.666741i	$0.232311\pi$
$830$	7.44473	0.258410
$831$	19.8157	0.687400
$832$	−22.5526	−0.781872
$833$	−5.01119	−0.173627
$834$	−41.6365	−1.44176
$835$	29.5655	1.02316
$836$	−5.40152	−0.186816
$837$	22.2585	0.769366
$838$	6.78051	0.234229
$839$	8.28100	0.285892	0.142946	−	0.989731i	$-0.454343\pi$
$839$	8.28100	0.285892	0.142946	+	0.989731i	$0.454343\pi$
$840$	−3.35306	−0.115692
$841$	−16.6601	−0.574487
$842$	−55.7639	−1.92175
$843$	15.3110	0.527339
$844$	−8.97653	−0.308985
$845$	2.62913	0.0904450
$846$	−10.9783	−0.377443
$847$	−1.41025	−0.0484568
$848$	45.7513	1.57111
$849$	28.2957	0.971106
$850$	−14.5591	−0.499373
$851$	−0.0607530	−0.00208259
$852$	14.4854	0.496260
$853$	−57.3615	−1.96402	−0.982010	−	0.188831i	$-0.939530\pi$
$853$	−57.3615	−1.96402	−0.982010	+	0.188831i	$0.939530\pi$
$854$	−19.4528	−0.665661
$855$	7.47901	0.255777
$856$	−2.23094	−0.0762519
$857$	−10.1631	−0.347166	−0.173583	−	0.984819i	$-0.555535\pi$
$857$	−10.1631	−0.347166	−0.173583	+	0.984819i	$0.555535\pi$
$858$	−10.9335	−0.373265
$859$	21.5084	0.733857	0.366928	−	0.930249i	$-0.380409\pi$
$859$	21.5084	0.733857	0.366928	+	0.930249i	$0.380409\pi$
$860$	−6.26386	−0.213596
$861$	9.70847	0.330864
$862$	20.6326	0.702749
$863$	−7.40477	−0.252061	−0.126031	−	0.992026i	$-0.540224\pi$
$863$	−7.40477	−0.252061	−0.126031	+	0.992026i	$0.540224\pi$
$864$	−43.0116	−1.46329
$865$	11.2788	0.383492
$866$	−36.8460	−1.25208
$867$	1.51854	0.0515723
$868$	9.91550	0.336554
$869$	−10.5158	−0.356723
$870$	36.6232	1.24164
$871$	−60.2936	−2.04297
$872$	−7.11973	−0.241105
$873$	6.51554	0.220518
$874$	0.202197	0.00683942
$875$	−12.4452	−0.420724
$876$	26.5404	0.896717
$877$	−21.9421	−0.740932	−0.370466	−	0.928846i	$-0.620802\pi$
$877$	−21.9421	−0.740932	−0.370466	+	0.928846i	$0.620802\pi$
$878$	−14.0407	−0.473851
$879$	−6.46566	−0.218081
$880$	−15.5686	−0.524818
$881$	21.4224	0.721737	0.360869	−	0.932617i	$-0.382480\pi$
$881$	21.4224	0.721737	0.360869	+	0.932617i	$0.382480\pi$
$882$	−6.75474	−0.227444
$883$	−30.0712	−1.01198	−0.505989	−	0.862540i	$-0.668872\pi$
$883$	−30.0712	−1.01198	−0.505989	+	0.862540i	$0.668872\pi$
$884$	6.56904	0.220941
$885$	−64.2201	−2.15873
$886$	−33.6983	−1.13212
$887$	−34.0167	−1.14217	−0.571084	−	0.820892i	$-0.693477\pi$
$887$	−34.0167	−1.14217	−0.571084	+	0.820892i	$0.693477\pi$
$888$	−1.19645	−0.0401502
$889$	22.2422	0.745980
$890$	−99.3366	−3.32977
$891$	−6.43618	−0.215620
$892$	−12.9217	−0.432652
$893$	24.8277	0.830827
$894$	−59.7553	−1.99852
$895$	36.1860	1.20956
$896$	4.96456	0.165854
$897$	0.192267	0.00641960
$898$	14.6300	0.488208
$899$	13.9388	0.464883
$900$	−9.21906	−0.307302
$901$	−10.3883	−0.346086
$902$	8.80463	0.293162
$903$	2.14152	0.0712653
$904$	0.945173	0.0314360
$905$	63.3153	2.10467
$906$	−28.2001	−0.936884
$907$	45.5689	1.51309	0.756546	−	0.653941i	$-0.226885\pi$
$907$	45.5689	1.51309	0.756546	+	0.653941i	$0.226885\pi$
$908$	−39.5908	−1.31387
$909$	−5.14906	−0.170784
$910$	35.8942	1.18988
$911$	−32.8021	−1.08678	−0.543391	−	0.839480i	$-0.682860\pi$
$911$	−32.8021	−1.08678	−0.543391	+	0.839480i	$0.682860\pi$
$912$	20.3869	0.675076
$913$	−1.08436	−0.0358871
$914$	−52.9330	−1.75087
$915$	−38.1260	−1.26041
$916$	−39.8061	−1.31523
$917$	0.853084	0.0281713
$918$	10.8946	0.359574
$919$	−41.5541	−1.37074	−0.685371	−	0.728194i	$-0.740360\pi$
$919$	−41.5541	−1.37074	−0.685371	+	0.728194i	$0.740360\pi$
$920$	0.0534744	0.00176300
$921$	−20.3033	−0.669018
$922$	−43.1719	−1.42179
$923$	19.9575	0.656910
$924$	−3.79465	−0.124835
$925$	−13.3350	−0.438453
$926$	44.9334	1.47660
$927$	2.42179	0.0795421
$928$	−26.9348	−0.884179
$929$	0.852507	0.0279699	0.0139849	−	0.999902i	$-0.495548\pi$
$929$	0.852507	0.0279699	0.0139849	+	0.999902i	$0.495548\pi$
$930$	41.3684	1.35652
$931$	15.2759	0.500649
$932$	36.2332	1.18686
$933$	16.3978	0.536840
$934$	2.34333	0.0766761
$935$	3.53502	0.115608
$936$	−1.13963	−0.0372500
$937$	54.6807	1.78634	0.893170	−	0.449719i	$-0.148476\pi$
$937$	54.6807	1.78634	0.893170	+	0.449719i	$0.148476\pi$
$938$	−44.5449	−1.45444
$939$	20.8589	0.680706
$940$	−51.0166	−1.66398
$941$	−34.0460	−1.10987	−0.554934	−	0.831895i	$-0.687256\pi$
$941$	−34.0460	−1.10987	−0.554934	+	0.831895i	$0.687256\pi$
$942$	33.1335	1.07955
$943$	−0.154830	−0.00504195
$944$	52.6878	1.71484
$945$	27.9651	0.909705
$946$	1.94215	0.0631447
$947$	5.74187	0.186586	0.0932929	−	0.995639i	$-0.470261\pi$
$947$	5.74187	0.186586	0.0932929	+	0.995639i	$0.470261\pi$
$948$	−28.2954	−0.918992
$949$	36.5666	1.18700
$950$	44.3815	1.43992
$951$	−45.6664	−1.48083
$952$	−0.624631	−0.0202444
$953$	−6.45888	−0.209224	−0.104612	−	0.994513i	$-0.533360\pi$
$953$	−6.45888	−0.209224	−0.104612	+	0.994513i	$0.533360\pi$
$954$	−14.0028	−0.453356
$955$	−9.70849	−0.314159
$956$	−1.68269	−0.0544219
$957$	−5.33435	−0.172435
$958$	−23.6877	−0.765313
$959$	−28.5964	−0.923425
$960$	−32.6560	−1.05397
$961$	−15.2552	−0.492104
$962$	12.8079	0.412942
$963$	3.49579	0.112650
$964$	26.9628	0.868414
$965$	−31.1795	−1.00370
$966$	0.142047	0.00457027
$967$	12.9026	0.414921	0.207460	−	0.978243i	$-0.433480\pi$
$967$	12.9026	0.414921	0.207460	+	0.978243i	$0.433480\pi$
$968$	0.442922	0.0142361
$969$	−4.62906	−0.148707
$970$	64.4525	2.06945
$971$	16.8402	0.540428	0.270214	−	0.962800i	$-0.412906\pi$
$971$	16.8402	0.540428	0.270214	+	0.962800i	$0.412906\pi$
$972$	12.5011	0.400973
$973$	−19.9096	−0.638273
$974$	−62.9293	−2.01639
$975$	42.2017	1.35154
$976$	31.2795	1.00123
$977$	−43.5067	−1.39190	−0.695951	−	0.718089i	$-0.745017\pi$
$977$	−43.5067	−1.39190	−0.695951	+	0.718089i	$0.745017\pi$
$978$	−9.36421	−0.299434
$979$	14.4689	0.462427
$980$	−31.3894	−1.00270
$981$	11.1563	0.356194
$982$	19.7143	0.629110
$983$	11.0934	0.353824	0.176912	−	0.984227i	$-0.443389\pi$
$983$	11.0934	0.353824	0.176912	+	0.984227i	$0.443389\pi$
$984$	−3.04917	−0.0972040
$985$	−49.1512	−1.56609
$986$	6.82241	0.217270
$987$	17.4418	0.555179
$988$	−20.0248	−0.637075
$989$	−0.0341528	−0.00108600
$990$	4.76497	0.151441
$991$	34.4108	1.09310	0.546548	−	0.837428i	$-0.315942\pi$
$991$	34.4108	1.09310	0.546548	+	0.837428i	$0.315942\pi$
$992$	−30.4247	−0.965986
$993$	9.08982	0.288457
$994$	14.7446	0.467670
$995$	−69.6278	−2.20735
$996$	−2.91776	−0.0924528
$997$	−1.09842	−0.0347873	−0.0173936	−	0.999849i	$-0.505537\pi$
$997$	−1.09842	−0.0347873	−0.0173936	+	0.999849i	$0.505537\pi$
$998$	−71.1364	−2.25178
$999$	9.97859	0.315709

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.c.1.12	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.c.1.12	✓	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)

\(f(q)\)	\(=\)	\(q-1.94215 q^{2} +1.51854 q^{3} +1.77194 q^{4} +3.53502 q^{5} -2.94923 q^{6} -1.41025 q^{7} +0.442922 q^{8} -0.694041 q^{9} +O(q^{10})\)	\(q-1.94215 q^{2} +1.51854 q^{3} +1.77194 q^{4} +3.53502 q^{5} -2.94923 q^{6} -1.41025 q^{7} +0.442922 q^{8} -0.694041 q^{9} -6.86554 q^{10} +1.00000 q^{11} +2.69076 q^{12} +3.70725 q^{13} +2.73892 q^{14} +5.36807 q^{15} -4.40411 q^{16} +1.00000 q^{17} +1.34793 q^{18} -3.04836 q^{19} +6.26386 q^{20} -2.14152 q^{21} -1.94215 q^{22} +0.0341528 q^{23} +0.672594 q^{24} +7.49639 q^{25} -7.20004 q^{26} -5.60954 q^{27} -2.49888 q^{28} -3.51282 q^{29} -10.4256 q^{30} -3.96797 q^{31} +7.66758 q^{32} +1.51854 q^{33} -1.94215 q^{34} -4.98527 q^{35} -1.22980 q^{36} -1.77886 q^{37} +5.92038 q^{38} +5.62961 q^{39} +1.56574 q^{40} -4.53345 q^{41} +4.15915 q^{42} -1.00000 q^{43} +1.77194 q^{44} -2.45345 q^{45} -0.0663298 q^{46} -8.14459 q^{47} -6.68780 q^{48} -5.01119 q^{49} -14.5591 q^{50} +1.51854 q^{51} +6.56904 q^{52} -10.3883 q^{53} +10.8946 q^{54} +3.53502 q^{55} -0.624631 q^{56} -4.62906 q^{57} +6.82241 q^{58} -11.9633 q^{59} +9.51191 q^{60} -7.10236 q^{61} +7.70639 q^{62} +0.978772 q^{63} -6.08338 q^{64} +13.1052 q^{65} -2.94923 q^{66} -16.2637 q^{67} +1.77194 q^{68} +0.0518623 q^{69} +9.68214 q^{70} +5.38337 q^{71} -0.307406 q^{72} +9.86353 q^{73} +3.45481 q^{74} +11.3836 q^{75} -5.40152 q^{76} -1.41025 q^{77} -10.9335 q^{78} -10.5158 q^{79} -15.5686 q^{80} -6.43618 q^{81} +8.80463 q^{82} -1.08436 q^{83} -3.79465 q^{84} +3.53502 q^{85} +1.94215 q^{86} -5.33435 q^{87} +0.442922 q^{88} +14.4689 q^{89} +4.76497 q^{90} -5.22816 q^{91} +0.0605167 q^{92} -6.02551 q^{93} +15.8180 q^{94} -10.7760 q^{95} +11.6435 q^{96} -9.38783 q^{97} +9.73248 q^{98} -0.694041 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 9 q^{2} - 6 q^{3} + 43 q^{4} - 15 q^{5} - 4 q^{6} - 17 q^{7} - 21 q^{8} + 40 q^{9}+O(q^{10}) \) 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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