LMFDB - Embedded newform 6045.2.a.bi.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6045,2,Mod(1,6045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6045, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("6045.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6045 = 3 \cdot 5 \cdot 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6045.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$48.2695680219$
Analytic rank:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 4 x^{17} - 21 x^{16} + 97 x^{15} + 156 x^{14} - 935 x^{13} - 411 x^{12} + 4582 x^{11} + \cdots - 112 $ x^18 - 4x^17 - 21x^16 + 97x^15 + 156x^14 - 935x^13 - 411x^12 + 4582x^11 - 446x^10 - 12159x^9 + 4398x^8 + 17347x^7 - 7839x^6 - 12832x^5 + 4744x^4 + 5064x^3 - 746x^2 - 892*x - 112
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Root			$2.34662$ of defining polynomial
Character	$\chi$	$=$	6045.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.34662 q^{2} +1.00000 q^{3} +3.50662 q^{4} +1.00000 q^{5} +2.34662 q^{6} -4.52573 q^{7} +3.53546 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.34662 q^{2} +1.00000 q^{3} +3.50662 q^{4} +1.00000 q^{5} +2.34662 q^{6} -4.52573 q^{7} +3.53546 q^{8} +1.00000 q^{9} +2.34662 q^{10} +3.02332 q^{11} +3.50662 q^{12} -1.00000 q^{13} -10.6202 q^{14} +1.00000 q^{15} +1.28314 q^{16} +3.96244 q^{17} +2.34662 q^{18} +3.32345 q^{19} +3.50662 q^{20} -4.52573 q^{21} +7.09458 q^{22} +5.56675 q^{23} +3.53546 q^{24} +1.00000 q^{25} -2.34662 q^{26} +1.00000 q^{27} -15.8700 q^{28} -3.14842 q^{29} +2.34662 q^{30} +1.00000 q^{31} -4.05988 q^{32} +3.02332 q^{33} +9.29833 q^{34} -4.52573 q^{35} +3.50662 q^{36} +8.60884 q^{37} +7.79887 q^{38} -1.00000 q^{39} +3.53546 q^{40} +4.01690 q^{41} -10.6202 q^{42} -3.55720 q^{43} +10.6016 q^{44} +1.00000 q^{45} +13.0630 q^{46} +5.94515 q^{47} +1.28314 q^{48} +13.4822 q^{49} +2.34662 q^{50} +3.96244 q^{51} -3.50662 q^{52} +12.1006 q^{53} +2.34662 q^{54} +3.02332 q^{55} -16.0005 q^{56} +3.32345 q^{57} -7.38815 q^{58} -3.39438 q^{59} +3.50662 q^{60} -6.87409 q^{61} +2.34662 q^{62} -4.52573 q^{63} -12.0933 q^{64} -1.00000 q^{65} +7.09458 q^{66} +10.4792 q^{67} +13.8948 q^{68} +5.56675 q^{69} -10.6202 q^{70} -2.61033 q^{71} +3.53546 q^{72} +0.145482 q^{73} +20.2017 q^{74} +1.00000 q^{75} +11.6541 q^{76} -13.6827 q^{77} -2.34662 q^{78} +2.68796 q^{79} +1.28314 q^{80} +1.00000 q^{81} +9.42614 q^{82} +0.718562 q^{83} -15.8700 q^{84} +3.96244 q^{85} -8.34740 q^{86} -3.14842 q^{87} +10.6888 q^{88} +8.86209 q^{89} +2.34662 q^{90} +4.52573 q^{91} +19.5205 q^{92} +1.00000 q^{93} +13.9510 q^{94} +3.32345 q^{95} -4.05988 q^{96} -5.72869 q^{97} +31.6376 q^{98} +3.02332 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 4 q^{2} + 18 q^{3} + 22 q^{4} + 18 q^{5} + 4 q^{6} + 8 q^{7} + 9 q^{8} + 18 q^{9}+O(q^{10}) $ 18 * q + 4 * q^2 + 18 * q^3 + 22 * q^4 + 18 * q^5 + 4 * q^6 + 8 * q^7 + 9 * q^8 + 18 * q^9	\( 18 q + 4 q^{2} + 18 q^{3} + 22 q^{4} + 18 q^{5} + 4 q^{6} + 8 q^{7} + 9 q^{8} + 18 q^{9} + 4 q^{10} + 6 q^{11} + 22 q^{12} - 18 q^{13} + 5 q^{14} + 18 q^{15} + 30 q^{16} + 18 q^{17} + 4 q^{18} + 12 q^{19} + 22 q^{20} + 8 q^{21} + 7 q^{22} + 32 q^{23} + 9 q^{24} + 18 q^{25} - 4 q^{26} + 18 q^{27} + 10 q^{28} + 7 q^{29} + 4 q^{30} + 18 q^{31} + 22 q^{32} + 6 q^{33} + 15 q^{34} + 8 q^{35} + 22 q^{36} + 3 q^{37} + 32 q^{38} - 18 q^{39} + 9 q^{40} + 4 q^{41} + 5 q^{42} + 14 q^{43} - 5 q^{44} + 18 q^{45} + 10 q^{46} + 23 q^{47} + 30 q^{48} + 28 q^{49} + 4 q^{50} + 18 q^{51} - 22 q^{52} + 35 q^{53} + 4 q^{54} + 6 q^{55} - 7 q^{56} + 12 q^{57} - 6 q^{58} + 28 q^{59} + 22 q^{60} + 19 q^{61} + 4 q^{62} + 8 q^{63} + 43 q^{64} - 18 q^{65} + 7 q^{66} + 34 q^{67} + 55 q^{68} + 32 q^{69} + 5 q^{70} - 8 q^{71} + 9 q^{72} + 22 q^{74} + 18 q^{75} + 2 q^{76} + 21 q^{77} - 4 q^{78} + 4 q^{79} + 30 q^{80} + 18 q^{81} + 29 q^{82} + 11 q^{83} + 10 q^{84} + 18 q^{85} - 22 q^{86} + 7 q^{87} - 31 q^{88} + 17 q^{89} + 4 q^{90} - 8 q^{91} + 33 q^{92} + 18 q^{93} - 14 q^{94} + 12 q^{95} + 22 q^{96} + 32 q^{97} + 20 q^{98} + 6 q^{99}+O(q^{100}) \) 18 * q + 4 * q^2 + 18 * q^3 + 22 * q^4 + 18 * q^5 + 4 * q^6 + 8 * q^7 + 9 * q^8 + 18 * q^9 + 4 * q^10 + 6 * q^11 + 22 * q^12 - 18 * q^13 + 5 * q^14 + 18 * q^15 + 30 * q^16 + 18 * q^17 + 4 * q^18 + 12 * q^19 + 22 * q^20 + 8 * q^21 + 7 * q^22 + 32 * q^23 + 9 * q^24 + 18 * q^25 - 4 * q^26 + 18 * q^27 + 10 * q^28 + 7 * q^29 + 4 * q^30 + 18 * q^31 + 22 * q^32 + 6 * q^33 + 15 * q^34 + 8 * q^35 + 22 * q^36 + 3 * q^37 + 32 * q^38 - 18 * q^39 + 9 * q^40 + 4 * q^41 + 5 * q^42 + 14 * q^43 - 5 * q^44 + 18 * q^45 + 10 * q^46 + 23 * q^47 + 30 * q^48 + 28 * q^49 + 4 * q^50 + 18 * q^51 - 22 * q^52 + 35 * q^53 + 4 * q^54 + 6 * q^55 - 7 * q^56 + 12 * q^57 - 6 * q^58 + 28 * q^59 + 22 * q^60 + 19 * q^61 + 4 * q^62 + 8 * q^63 + 43 * q^64 - 18 * q^65 + 7 * q^66 + 34 * q^67 + 55 * q^68 + 32 * q^69 + 5 * q^70 - 8 * q^71 + 9 * q^72 + 22 * q^74 + 18 * q^75 + 2 * q^76 + 21 * q^77 - 4 * q^78 + 4 * q^79 + 30 * q^80 + 18 * q^81 + 29 * q^82 + 11 * q^83 + 10 * q^84 + 18 * q^85 - 22 * q^86 + 7 * q^87 - 31 * q^88 + 17 * q^89 + 4 * q^90 - 8 * q^91 + 33 * q^92 + 18 * q^93 - 14 * q^94 + 12 * q^95 + 22 * q^96 + 32 * q^97 + 20 * q^98 + 6 * 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 $

$2$	2.34662	1.65931	0.829655	−	0.558276i	$-0.188537\pi$
$2$	2.34662	1.65931	0.829655	+	0.558276i	$0.188537\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	3.50662	1.75331
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.34662	0.958003
$7$	−4.52573	−1.71056	−0.855282	−	0.518163i	$-0.826616\pi$
$7$	−4.52573	−1.71056	−0.855282	+	0.518163i	$0.826616\pi$
$8$	3.53546	1.24997
$9$	1.00000	0.333333
$10$	2.34662	0.742066
$11$	3.02332	0.911565	0.455782	−	0.890091i	$-0.349360\pi$
$11$	3.02332	0.911565	0.455782	+	0.890091i	$0.349360\pi$
$12$	3.50662	1.01227
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−10.6202	−2.83836
$15$	1.00000	0.258199
$16$	1.28314	0.320785
$17$	3.96244	0.961032	0.480516	−	0.876986i	$-0.340449\pi$
$17$	3.96244	0.961032	0.480516	+	0.876986i	$0.340449\pi$
$18$	2.34662	0.553103
$19$	3.32345	0.762452	0.381226	−	0.924482i	$-0.375502\pi$
$19$	3.32345	0.762452	0.381226	+	0.924482i	$0.375502\pi$
$20$	3.50662	0.784104
$21$	−4.52573	−0.987594
$22$	7.09458	1.51257
$23$	5.56675	1.16075	0.580374	−	0.814350i	$-0.302906\pi$
$23$	5.56675	1.16075	0.580374	+	0.814350i	$0.302906\pi$
$24$	3.53546	0.721673
$25$	1.00000	0.200000
$26$	−2.34662	−0.460210
$27$	1.00000	0.192450
$28$	−15.8700	−2.99915
$29$	−3.14842	−0.584648	−0.292324	−	0.956319i	$-0.594429\pi$
$29$	−3.14842	−0.584648	−0.292324	+	0.956319i	$0.594429\pi$
$30$	2.34662	0.428432
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	−4.05988	−0.717692
$33$	3.02332	0.526292
$34$	9.29833	1.59465
$35$	−4.52573	−0.764987
$36$	3.50662	0.584437
$37$	8.60884	1.41528	0.707642	−	0.706571i	$-0.249759\pi$
$37$	8.60884	1.41528	0.707642	+	0.706571i	$0.249759\pi$
$38$	7.79887	1.26514
$39$	−1.00000	−0.160128
$40$	3.53546	0.559005
$41$	4.01690	0.627335	0.313667	−	0.949533i	$-0.398442\pi$
$41$	4.01690	0.627335	0.313667	+	0.949533i	$0.398442\pi$
$42$	−10.6202	−1.63873
$43$	−3.55720	−0.542468	−0.271234	−	0.962513i	$-0.587432\pi$
$43$	−3.55720	−0.542468	−0.271234	+	0.962513i	$0.587432\pi$
$44$	10.6016	1.59826
$45$	1.00000	0.149071
$46$	13.0630	1.92604
$47$	5.94515	0.867189	0.433595	−	0.901108i	$-0.357245\pi$
$47$	5.94515	0.867189	0.433595	+	0.901108i	$0.357245\pi$
$48$	1.28314	0.185205
$49$	13.4822	1.92603
$50$	2.34662	0.331862
$51$	3.96244	0.554852
$52$	−3.50662	−0.486281
$53$	12.1006	1.66215	0.831073	−	0.556164i	$-0.187727\pi$
$53$	12.1006	1.66215	0.831073	+	0.556164i	$0.187727\pi$
$54$	2.34662	0.319334
$55$	3.02332	0.407664
$56$	−16.0005	−2.13816
$57$	3.32345	0.440202
$58$	−7.38815	−0.970112
$59$	−3.39438	−0.441910	−0.220955	−	0.975284i	$-0.570917\pi$
$59$	−3.39438	−0.441910	−0.220955	+	0.975284i	$0.570917\pi$
$60$	3.50662	0.452703
$61$	−6.87409	−0.880137	−0.440068	−	0.897964i	$-0.645046\pi$
$61$	−6.87409	−0.880137	−0.440068	+	0.897964i	$0.645046\pi$
$62$	2.34662	0.298021
$63$	−4.52573	−0.570188
$64$	−12.0933	−1.51166
$65$	−1.00000	−0.124035
$66$	7.09458	0.873282
$67$	10.4792	1.28023	0.640116	−	0.768278i	$-0.278886\pi$
$67$	10.4792	1.28023	0.640116	+	0.768278i	$0.278886\pi$
$68$	13.8948	1.68499
$69$	5.56675	0.670158
$70$	−10.6202	−1.26935
$71$	−2.61033	−0.309789	−0.154895	−	0.987931i	$-0.549504\pi$
$71$	−2.61033	−0.309789	−0.154895	+	0.987931i	$0.549504\pi$
$72$	3.53546	0.416658
$73$	0.145482	0.0170274	0.00851370	−	0.999964i	$-0.497290\pi$
$73$	0.145482	0.0170274	0.00851370	+	0.999964i	$0.497290\pi$
$74$	20.2017	2.34839
$75$	1.00000	0.115470
$76$	11.6541	1.33681
$77$	−13.6827	−1.55929
$78$	−2.34662	−0.265702
$79$	2.68796	0.302419	0.151209	−	0.988502i	$-0.451683\pi$
$79$	2.68796	0.302419	0.151209	+	0.988502i	$0.451683\pi$
$80$	1.28314	0.143459
$81$	1.00000	0.111111
$82$	9.42614	1.04094
$83$	0.718562	0.0788724	0.0394362	−	0.999222i	$-0.487444\pi$
$83$	0.718562	0.0788724	0.0394362	+	0.999222i	$0.487444\pi$
$84$	−15.8700	−1.73156
$85$	3.96244	0.429787
$86$	−8.34740	−0.900123
$87$	−3.14842	−0.337546
$88$	10.6888	1.13943
$89$	8.86209	0.939380	0.469690	−	0.882832i	$-0.344366\pi$
$89$	8.86209	0.939380	0.469690	+	0.882832i	$0.344366\pi$
$90$	2.34662	0.247355
$91$	4.52573	0.474425
$92$	19.5205	2.03515
$93$	1.00000	0.103695
$94$	13.9510	1.43894
$95$	3.32345	0.340979
$96$	−4.05988	−0.414360
$97$	−5.72869	−0.581661	−0.290830	−	0.956775i	$-0.593931\pi$
$97$	−5.72869	−0.581661	−0.290830	+	0.956775i	$0.593931\pi$
$98$	31.6376	3.19588
$99$	3.02332	0.303855
$100$	3.50662	0.350662
$101$	−13.8939	−1.38249	−0.691247	−	0.722619i	$-0.742938\pi$
$101$	−13.8939	−1.38249	−0.691247	+	0.722619i	$0.742938\pi$
$102$	9.29833	0.920672
$103$	−0.577818	−0.0569341	−0.0284671	−	0.999595i	$-0.509063\pi$
$103$	−0.577818	−0.0569341	−0.0284671	+	0.999595i	$0.509063\pi$
$104$	−3.53546	−0.346680
$105$	−4.52573	−0.441666
$106$	28.3955	2.75801
$107$	−10.8391	−1.04785	−0.523926	−	0.851764i	$-0.675533\pi$
$107$	−10.8391	−1.04785	−0.523926	+	0.851764i	$0.675533\pi$
$108$	3.50662	0.337425
$109$	−8.55448	−0.819370	−0.409685	−	0.912227i	$-0.634361\pi$
$109$	−8.55448	−0.819370	−0.409685	+	0.912227i	$0.634361\pi$
$110$	7.09458	0.676441
$111$	8.60884	0.817115
$112$	−5.80714	−0.548723
$113$	2.71232	0.255154	0.127577	−	0.991829i	$-0.459280\pi$
$113$	2.71232	0.255154	0.127577	+	0.991829i	$0.459280\pi$
$114$	7.79887	0.730431
$115$	5.56675	0.519102
$116$	−11.0403	−1.02507
$117$	−1.00000	−0.0924500
$118$	−7.96531	−0.733266
$119$	−17.9329	−1.64391
$120$	3.53546	0.322742
$121$	−1.85955	−0.169050
$122$	−16.1309	−1.46042
$123$	4.01690	0.362192
$124$	3.50662	0.314904
$125$	1.00000	0.0894427
$126$	−10.6202	−0.946119
$127$	−17.9931	−1.59663	−0.798313	−	0.602243i	$-0.794274\pi$
$127$	−17.9931	−1.59663	−0.798313	+	0.602243i	$0.794274\pi$
$128$	−20.2585	−1.79062
$129$	−3.55720	−0.313194
$130$	−2.34662	−0.205812
$131$	3.54931	0.310104	0.155052	−	0.987906i	$-0.450445\pi$
$131$	3.54931	0.310104	0.155052	+	0.987906i	$0.450445\pi$
$132$	10.6016	0.922753
$133$	−15.0410	−1.30422
$134$	24.5906	2.12430
$135$	1.00000	0.0860663
$136$	14.0090	1.20127
$137$	−14.8698	−1.27041	−0.635206	−	0.772343i	$-0.719085\pi$
$137$	−14.8698	−1.27041	−0.635206	+	0.772343i	$0.719085\pi$
$138$	13.0630	1.11200
$139$	13.7508	1.16632	0.583162	−	0.812356i	$-0.301815\pi$
$139$	13.7508	1.16632	0.583162	+	0.812356i	$0.301815\pi$
$140$	−15.8700	−1.34126
$141$	5.94515	0.500672
$142$	−6.12545	−0.514036
$143$	−3.02332	−0.252823
$144$	1.28314	0.106928
$145$	−3.14842	−0.261462
$146$	0.341391	0.0282537
$147$	13.4822	1.11199
$148$	30.1879	2.48143
$149$	−11.6124	−0.951321	−0.475661	−	0.879629i	$-0.657791\pi$
$149$	−11.6124	−0.951321	−0.475661	+	0.879629i	$0.657791\pi$
$150$	2.34662	0.191601
$151$	23.8205	1.93849	0.969244	−	0.246102i	$-0.0791498\pi$
$151$	23.8205	1.93849	0.969244	+	0.246102i	$0.0791498\pi$
$152$	11.7499	0.953045
$153$	3.96244	0.320344
$154$	−32.1081	−2.58734
$155$	1.00000	0.0803219
$156$	−3.50662	−0.280754
$157$	−4.47302	−0.356986	−0.178493	−	0.983941i	$-0.557122\pi$
$157$	−4.47302	−0.356986	−0.178493	+	0.983941i	$0.557122\pi$
$158$	6.30761	0.501807
$159$	12.1006	0.959640
$160$	−4.05988	−0.320962
$161$	−25.1936	−1.98553
$162$	2.34662	0.184368
$163$	−8.56757	−0.671063	−0.335532	−	0.942029i	$-0.608916\pi$
$163$	−8.56757	−0.671063	−0.335532	+	0.942029i	$0.608916\pi$
$164$	14.0857	1.09991
$165$	3.02332	0.235365
$166$	1.68619	0.130874
$167$	7.83962	0.606648	0.303324	−	0.952887i	$-0.401904\pi$
$167$	7.83962	0.606648	0.303324	+	0.952887i	$0.401904\pi$
$168$	−16.0005	−1.23447
$169$	1.00000	0.0769231
$170$	9.29833	0.713149
$171$	3.32345	0.254151
$172$	−12.4738	−0.951115
$173$	−7.55634	−0.574498	−0.287249	−	0.957856i	$-0.592741\pi$
$173$	−7.55634	−0.574498	−0.287249	+	0.957856i	$0.592741\pi$
$174$	−7.38815	−0.560094
$175$	−4.52573	−0.342113
$176$	3.87934	0.292416
$177$	−3.39438	−0.255137
$178$	20.7959	1.55872
$179$	10.0001	0.747444	0.373722	−	0.927541i	$-0.378081\pi$
$179$	10.0001	0.747444	0.373722	+	0.927541i	$0.378081\pi$
$180$	3.50662	0.261368
$181$	1.20523	0.0895842	0.0447921	−	0.998996i	$-0.485737\pi$
$181$	1.20523	0.0895842	0.0447921	+	0.998996i	$0.485737\pi$
$182$	10.6202	0.787218
$183$	−6.87409	−0.508147
$184$	19.6810	1.45091
$185$	8.60884	0.632934
$186$	2.34662	0.172062
$187$	11.9797	0.876043
$188$	20.8474	1.52045
$189$	−4.52573	−0.329198
$190$	7.79887	0.565789
$191$	−10.2139	−0.739050	−0.369525	−	0.929221i	$-0.620480\pi$
$191$	−10.2139	−0.739050	−0.369525	+	0.929221i	$0.620480\pi$
$192$	−12.0933	−0.872757
$193$	8.17957	0.588778	0.294389	−	0.955686i	$-0.404884\pi$
$193$	8.17957	0.588778	0.294389	+	0.955686i	$0.404884\pi$
$194$	−13.4431	−0.965155
$195$	−1.00000	−0.0716115
$196$	47.2769	3.37692
$197$	−16.3040	−1.16161	−0.580806	−	0.814042i	$-0.697262\pi$
$197$	−16.3040	−1.16161	−0.580806	+	0.814042i	$0.697262\pi$
$198$	7.09458	0.504189
$199$	14.3646	1.01828	0.509141	−	0.860683i	$-0.329963\pi$
$199$	14.3646	1.01828	0.509141	+	0.860683i	$0.329963\pi$
$200$	3.53546	0.249995
$201$	10.4792	0.739143
$202$	−32.6037	−2.29399
$203$	14.2489	1.00008
$204$	13.8948	0.972828
$205$	4.01690	0.280553
$206$	−1.35592	−0.0944714
$207$	5.56675	0.386916
$208$	−1.28314	−0.0889698
$209$	10.0478	0.695024
$210$	−10.6202	−0.732860
$211$	16.8502	1.16001	0.580007	−	0.814612i	$-0.303050\pi$
$211$	16.8502	1.16001	0.580007	+	0.814612i	$0.303050\pi$
$212$	42.4322	2.91426
$213$	−2.61033	−0.178857
$214$	−25.4351	−1.73871
$215$	−3.55720	−0.242599
$216$	3.53546	0.240558
$217$	−4.52573	−0.307226
$218$	−20.0741	−1.35959
$219$	0.145482	0.00983077
$220$	10.6016	0.714761
$221$	−3.96244	−0.266542
$222$	20.2017	1.35585
$223$	−1.30146	−0.0871524	−0.0435762	−	0.999050i	$-0.513875\pi$
$223$	−1.30146	−0.0871524	−0.0435762	+	0.999050i	$0.513875\pi$
$224$	18.3739	1.22766
$225$	1.00000	0.0666667
$226$	6.36479	0.423379
$227$	−12.0936	−0.802678	−0.401339	−	0.915930i	$-0.631455\pi$
$227$	−12.0936	−0.802678	−0.401339	+	0.915930i	$0.631455\pi$
$228$	11.6541	0.771810
$229$	26.7490	1.76762	0.883812	−	0.467841i	$-0.154968\pi$
$229$	26.7490	1.76762	0.883812	+	0.467841i	$0.154968\pi$
$230$	13.0630	0.861352
$231$	−13.6827	−0.900256
$232$	−11.1311	−0.730794
$233$	−8.48883	−0.556122	−0.278061	−	0.960563i	$-0.589692\pi$
$233$	−8.48883	−0.556122	−0.278061	+	0.960563i	$0.589692\pi$
$234$	−2.34662	−0.153403
$235$	5.94515	0.387819
$236$	−11.9028	−0.774806
$237$	2.68796	0.174602
$238$	−42.0817	−2.72775
$239$	−16.7104	−1.08091	−0.540453	−	0.841374i	$-0.681747\pi$
$239$	−16.7104	−1.08091	−0.540453	+	0.841374i	$0.681747\pi$
$240$	1.28314	0.0828263
$241$	−16.7165	−1.07681	−0.538403	−	0.842687i	$-0.680972\pi$
$241$	−16.7165	−1.07681	−0.538403	+	0.842687i	$0.680972\pi$
$242$	−4.36365	−0.280506
$243$	1.00000	0.0641500
$244$	−24.1048	−1.54315
$245$	13.4822	0.861346
$246$	9.42614	0.600989
$247$	−3.32345	−0.211466
$248$	3.53546	0.224502
$249$	0.718562	0.0455370
$250$	2.34662	0.148413
$251$	1.58940	0.100322	0.0501610	−	0.998741i	$-0.484027\pi$
$251$	1.58940	0.100322	0.0501610	+	0.998741i	$0.484027\pi$
$252$	−15.8700	−0.999716
$253$	16.8301	1.05810
$254$	−42.2228	−2.64930
$255$	3.96244	0.248137
$256$	−23.3525	−1.45953
$257$	4.92595	0.307272	0.153636	−	0.988128i	$-0.450902\pi$
$257$	4.92595	0.307272	0.153636	+	0.988128i	$0.450902\pi$
$258$	−8.34740	−0.519686
$259$	−38.9612	−2.42093
$260$	−3.50662	−0.217471
$261$	−3.14842	−0.194883
$262$	8.32887	0.514559
$263$	4.07270	0.251134	0.125567	−	0.992085i	$-0.459925\pi$
$263$	4.07270	0.251134	0.125567	+	0.992085i	$0.459925\pi$
$264$	10.6888	0.657852
$265$	12.1006	0.743334
$266$	−35.2955	−2.16411
$267$	8.86209	0.542351
$268$	36.7464	2.24464
$269$	−11.9178	−0.726639	−0.363319	−	0.931665i	$-0.618357\pi$
$269$	−11.9178	−0.726639	−0.363319	+	0.931665i	$0.618357\pi$
$270$	2.34662	0.142811
$271$	−21.9565	−1.33377	−0.666883	−	0.745163i	$-0.732372\pi$
$271$	−21.9565	−1.33377	−0.666883	+	0.745163i	$0.732372\pi$
$272$	5.08436	0.308285
$273$	4.52573	0.273909
$274$	−34.8937	−2.10801
$275$	3.02332	0.182313
$276$	19.5205	1.17499
$277$	−20.7127	−1.24451	−0.622254	−	0.782815i	$-0.713783\pi$
$277$	−20.7127	−1.24451	−0.622254	+	0.782815i	$0.713783\pi$
$278$	32.2678	1.93529
$279$	1.00000	0.0598684
$280$	−16.0005	−0.956214
$281$	−10.4723	−0.624723	−0.312362	−	0.949963i	$-0.601120\pi$
$281$	−10.4723	−0.624723	−0.312362	+	0.949963i	$0.601120\pi$
$282$	13.9510	0.830770
$283$	−13.6174	−0.809469	−0.404735	−	0.914434i	$-0.632636\pi$
$283$	−13.6174	−0.809469	−0.404735	+	0.914434i	$0.632636\pi$
$284$	−9.15344	−0.543157
$285$	3.32345	0.196864
$286$	−7.09458	−0.419511
$287$	−18.1794	−1.07310
$288$	−4.05988	−0.239231
$289$	−1.29909	−0.0764169
$290$	−7.38815	−0.433847
$291$	−5.72869	−0.335822
$292$	0.510151	0.0298543
$293$	−13.4304	−0.784613	−0.392307	−	0.919834i	$-0.628323\pi$
$293$	−13.4304	−0.784613	−0.392307	+	0.919834i	$0.628323\pi$
$294$	31.6376	1.84514
$295$	−3.39438	−0.197628
$296$	30.4362	1.76907
$297$	3.02332	0.175431
$298$	−27.2498	−1.57854
$299$	−5.56675	−0.321934
$300$	3.50662	0.202455
$301$	16.0989	0.927926
$302$	55.8977	3.21655
$303$	−13.8939	−0.798183
$304$	4.26445	0.244583
$305$	−6.87409	−0.393609
$306$	9.29833	0.531550
$307$	10.1019	0.576545	0.288272	−	0.957548i	$-0.406919\pi$
$307$	10.1019	0.576545	0.288272	+	0.957548i	$0.406919\pi$
$308$	−47.9801	−2.73392
$309$	−0.577818	−0.0328709
$310$	2.34662	0.133279
$311$	−21.7113	−1.23114	−0.615568	−	0.788084i	$-0.711073\pi$
$311$	−21.7113	−1.23114	−0.615568	+	0.788084i	$0.711073\pi$
$312$	−3.53546	−0.200156
$313$	33.9813	1.92074	0.960370	−	0.278730i	$-0.0899134\pi$
$313$	33.9813	1.92074	0.960370	+	0.278730i	$0.0899134\pi$
$314$	−10.4965	−0.592350
$315$	−4.52573	−0.254996
$316$	9.42564	0.530234
$317$	17.8588	1.00305	0.501526	−	0.865142i	$-0.332772\pi$
$317$	17.8588	1.00305	0.501526	+	0.865142i	$0.332772\pi$
$318$	28.3955	1.59234
$319$	−9.51869	−0.532944
$320$	−12.0933	−0.676035
$321$	−10.8391	−0.604977
$322$	−59.1198	−3.29462
$323$	13.1690	0.732741
$324$	3.50662	0.194812
$325$	−1.00000	−0.0554700
$326$	−20.1048	−1.11350
$327$	−8.55448	−0.473064
$328$	14.2016	0.784152
$329$	−26.9061	−1.48338
$330$	7.09458	0.390544
$331$	4.66744	0.256545	0.128273	−	0.991739i	$-0.459057\pi$
$331$	4.66744	0.256545	0.128273	+	0.991739i	$0.459057\pi$
$332$	2.51972	0.138288
$333$	8.60884	0.471761
$334$	18.3966	1.00662
$335$	10.4792	0.572538
$336$	−5.80714	−0.316806
$337$	6.73186	0.366708	0.183354	−	0.983047i	$-0.441305\pi$
$337$	6.73186	0.366708	0.183354	+	0.983047i	$0.441305\pi$
$338$	2.34662	0.127639
$339$	2.71232	0.147313
$340$	13.8948	0.753549
$341$	3.02332	0.163722
$342$	7.79887	0.421715
$343$	−29.3367	−1.58403
$344$	−12.5763	−0.678071
$345$	5.56675	0.299704
$346$	−17.7319	−0.953270
$347$	−7.38694	−0.396552	−0.198276	−	0.980146i	$-0.563534\pi$
$347$	−7.38694	−0.396552	−0.198276	+	0.980146i	$0.563534\pi$
$348$	−11.0403	−0.591824
$349$	−9.27601	−0.496533	−0.248267	−	0.968692i	$-0.579861\pi$
$349$	−9.27601	−0.496533	−0.248267	+	0.968692i	$0.579861\pi$
$350$	−10.6202	−0.567671
$351$	−1.00000	−0.0533761
$352$	−12.2743	−0.654223
$353$	0.685243	0.0364718	0.0182359	−	0.999834i	$-0.494195\pi$
$353$	0.685243	0.0364718	0.0182359	+	0.999834i	$0.494195\pi$
$354$	−7.96531	−0.423351
$355$	−2.61033	−0.138542
$356$	31.0760	1.64702
$357$	−17.9329	−0.949110
$358$	23.4665	1.24024
$359$	−34.2241	−1.80628	−0.903141	−	0.429345i	$-0.858744\pi$
$359$	−34.2241	−1.80628	−0.903141	+	0.429345i	$0.858744\pi$
$360$	3.53546	0.186335
$361$	−7.95468	−0.418668
$362$	2.82822	0.148648
$363$	−1.85955	−0.0976009
$364$	15.8700	0.831814
$365$	0.145482	0.00761489
$366$	−16.1309	−0.843174
$367$	18.3923	0.960073	0.480036	−	0.877249i	$-0.340623\pi$
$367$	18.3923	0.960073	0.480036	+	0.877249i	$0.340623\pi$
$368$	7.14292	0.372351
$369$	4.01690	0.209112
$370$	20.2017	1.05023
$371$	−54.7640	−2.84321
$372$	3.50662	0.181810
$373$	18.8567	0.976362	0.488181	−	0.872742i	$-0.337661\pi$
$373$	18.8567	0.976362	0.488181	+	0.872742i	$0.337661\pi$
$374$	28.1118	1.45363
$375$	1.00000	0.0516398
$376$	21.0188	1.08396
$377$	3.14842	0.162152
$378$	−10.6202	−0.546242
$379$	2.02800	0.104171	0.0520857	−	0.998643i	$-0.483413\pi$
$379$	2.02800	0.104171	0.0520857	+	0.998643i	$0.483413\pi$
$380$	11.6541	0.597841
$381$	−17.9931	−0.921812
$382$	−23.9681	−1.22631
$383$	−31.0465	−1.58640	−0.793201	−	0.608960i	$-0.791587\pi$
$383$	−31.0465	−1.58640	−0.793201	+	0.608960i	$0.791587\pi$
$384$	−20.2585	−1.03381
$385$	−13.6827	−0.697336
$386$	19.1943	0.976966
$387$	−3.55720	−0.180823
$388$	−20.0883	−1.01983
$389$	37.2293	1.88760	0.943801	−	0.330514i	$-0.107222\pi$
$389$	37.2293	1.88760	0.943801	+	0.330514i	$0.107222\pi$
$390$	−2.34662	−0.118826
$391$	22.0579	1.11552
$392$	47.6658	2.40749
$393$	3.54931	0.179039
$394$	−38.2592	−1.92747
$395$	2.68796	0.135246
$396$	10.6016	0.532752
$397$	−1.85132	−0.0929148	−0.0464574	−	0.998920i	$-0.514793\pi$
$397$	−1.85132	−0.0929148	−0.0464574	+	0.998920i	$0.514793\pi$
$398$	33.7083	1.68964
$399$	−15.0410	−0.752993
$400$	1.28314	0.0641570
$401$	5.93900	0.296579	0.148290	−	0.988944i	$-0.452623\pi$
$401$	5.93900	0.296579	0.148290	+	0.988944i	$0.452623\pi$
$402$	24.5906	1.22647
$403$	−1.00000	−0.0498135
$404$	−48.7206	−2.42394
$405$	1.00000	0.0496904
$406$	33.4367	1.65944
$407$	26.0273	1.29012
$408$	14.0090	0.693551
$409$	−38.0633	−1.88211	−0.941056	−	0.338252i	$-0.890165\pi$
$409$	−38.0633	−1.88211	−0.941056	+	0.338252i	$0.890165\pi$
$410$	9.42614	0.465524
$411$	−14.8698	−0.733472
$412$	−2.02619	−0.0998231
$413$	15.3620	0.755916
$414$	13.0630	0.642014
$415$	0.718562	0.0352728
$416$	4.05988	0.199052
$417$	13.7508	0.673378
$418$	23.5785	1.15326
$419$	−3.22345	−0.157476	−0.0787378	−	0.996895i	$-0.525089\pi$
$419$	−3.22345	−0.157476	−0.0787378	+	0.996895i	$0.525089\pi$
$420$	−15.8700	−0.774377
$421$	−12.0750	−0.588501	−0.294250	−	0.955728i	$-0.595070\pi$
$421$	−12.0750	−0.588501	−0.294250	+	0.955728i	$0.595070\pi$
$422$	39.5409	1.92482
$423$	5.94515	0.289063
$424$	42.7812	2.07764
$425$	3.96244	0.192206
$426$	−6.12545	−0.296779
$427$	31.1102	1.50553
$428$	−38.0085	−1.83721
$429$	−3.02332	−0.145967
$430$	−8.34740	−0.402547
$431$	−12.8668	−0.619773	−0.309887	−	0.950774i	$-0.600291\pi$
$431$	−12.8668	−0.619773	−0.309887	+	0.950774i	$0.600291\pi$
$432$	1.28314	0.0617351
$433$	−0.527784	−0.0253637	−0.0126818	−	0.999920i	$-0.504037\pi$
$433$	−0.527784	−0.0253637	−0.0126818	+	0.999920i	$0.504037\pi$
$434$	−10.6202	−0.509784
$435$	−3.14842	−0.150955
$436$	−29.9973	−1.43661
$437$	18.5008	0.885014
$438$	0.341391	0.0163123
$439$	14.6457	0.699003	0.349501	−	0.936936i	$-0.386351\pi$
$439$	14.6457	0.699003	0.349501	+	0.936936i	$0.386351\pi$
$440$	10.6888	0.509570
$441$	13.4822	0.642010
$442$	−9.29833	−0.442276
$443$	12.4065	0.589449	0.294725	−	0.955582i	$-0.404772\pi$
$443$	12.4065	0.589449	0.294725	+	0.955582i	$0.404772\pi$
$444$	30.1879	1.43265
$445$	8.86209	0.420103
$446$	−3.05404	−0.144613
$447$	−11.6124	−0.549246
$448$	54.7308	2.58579
$449$	−21.0967	−0.995614	−0.497807	−	0.867288i	$-0.665861\pi$
$449$	−21.0967	−0.995614	−0.497807	+	0.867288i	$0.665861\pi$
$450$	2.34662	0.110621
$451$	12.1444	0.571856
$452$	9.51109	0.447364
$453$	23.8205	1.11919
$454$	−28.3790	−1.33189
$455$	4.52573	0.212169
$456$	11.7499	0.550241
$457$	20.0817	0.939382	0.469691	−	0.882831i	$-0.344365\pi$
$457$	20.0817	0.939382	0.469691	+	0.882831i	$0.344365\pi$
$458$	62.7697	2.93304
$459$	3.96244	0.184951
$460$	19.5205	0.910147
$461$	−22.1954	−1.03374	−0.516872	−	0.856063i	$-0.672904\pi$
$461$	−22.1954	−1.03374	−0.516872	+	0.856063i	$0.672904\pi$
$462$	−32.1081	−1.49380
$463$	27.1937	1.26380	0.631898	−	0.775051i	$-0.282276\pi$
$463$	27.1937	1.26380	0.631898	+	0.775051i	$0.282276\pi$
$464$	−4.03987	−0.187546
$465$	1.00000	0.0463739
$466$	−19.9200	−0.922778
$467$	28.6536	1.32593	0.662964	−	0.748651i	$-0.269298\pi$
$467$	28.6536	1.32593	0.662964	+	0.748651i	$0.269298\pi$
$468$	−3.50662	−0.162094
$469$	−47.4258	−2.18992
$470$	13.9510	0.643512
$471$	−4.47302	−0.206106
$472$	−12.0007	−0.552376
$473$	−10.7546	−0.494495
$474$	6.30761	0.289718
$475$	3.32345	0.152490
$476$	−62.8839	−2.88228
$477$	12.1006	0.554048
$478$	−39.2130	−1.79356
$479$	25.5100	1.16558	0.582790	−	0.812623i	$-0.301961\pi$
$479$	25.5100	1.16558	0.582790	+	0.812623i	$0.301961\pi$
$480$	−4.05988	−0.185307
$481$	−8.60884	−0.392529
$482$	−39.2273	−1.78676
$483$	−25.1936	−1.14635
$484$	−6.52072	−0.296396
$485$	−5.72869	−0.260126
$486$	2.34662	0.106445
$487$	−21.6539	−0.981234	−0.490617	−	0.871375i	$-0.663229\pi$
$487$	−21.6539	−0.981234	−0.490617	+	0.871375i	$0.663229\pi$
$488$	−24.3031	−1.10015
$489$	−8.56757	−0.387439
$490$	31.6376	1.42924
$491$	23.6623	1.06787	0.533933	−	0.845527i	$-0.320714\pi$
$491$	23.6623	1.06787	0.533933	+	0.845527i	$0.320714\pi$
$492$	14.0857	0.635035
$493$	−12.4754	−0.561865
$494$	−7.79887	−0.350888
$495$	3.02332	0.135888
$496$	1.28314	0.0576147
$497$	11.8136	0.529914
$498$	1.68619	0.0755600
$499$	25.1209	1.12457	0.562284	−	0.826944i	$-0.309923\pi$
$499$	25.1209	1.12457	0.562284	+	0.826944i	$0.309923\pi$
$500$	3.50662	0.156821
$501$	7.83962	0.350249
$502$	3.72972	0.166465
$503$	−19.5614	−0.872202	−0.436101	−	0.899898i	$-0.643641\pi$
$503$	−19.5614	−0.872202	−0.436101	+	0.899898i	$0.643641\pi$
$504$	−16.0005	−0.712720
$505$	−13.8939	−0.618270
$506$	39.4937	1.75571
$507$	1.00000	0.0444116
$508$	−63.0948	−2.79938
$509$	−33.4752	−1.48376	−0.741881	−	0.670532i	$-0.766066\pi$
$509$	−33.4752	−1.48376	−0.741881	+	0.670532i	$0.766066\pi$
$510$	9.29833	0.411737
$511$	−0.658413	−0.0291265
$512$	−14.2824	−0.631198
$513$	3.32345	0.146734
$514$	11.5593	0.509860
$515$	−0.577818	−0.0254617
$516$	−12.4738	−0.549126
$517$	17.9741	0.790499
$518$	−91.4272	−4.01708
$519$	−7.55634	−0.331687
$520$	−3.53546	−0.155040
$521$	−14.7069	−0.644321	−0.322161	−	0.946685i	$-0.604409\pi$
$521$	−14.7069	−0.644321	−0.322161	+	0.946685i	$0.604409\pi$
$522$	−7.38815	−0.323371
$523$	−37.5191	−1.64060	−0.820298	−	0.571936i	$-0.806193\pi$
$523$	−37.5191	−1.64060	−0.820298	+	0.571936i	$0.806193\pi$
$524$	12.4461	0.543709
$525$	−4.52573	−0.197519
$526$	9.55708	0.416709
$527$	3.96244	0.172606
$528$	3.87934	0.168827
$529$	7.98873	0.347336
$530$	28.3955	1.23342
$531$	−3.39438	−0.147303
$532$	−52.7431	−2.28671
$533$	−4.01690	−0.173991
$534$	20.7959	0.899928
$535$	−10.8391	−0.468613
$536$	37.0487	1.60026
$537$	10.0001	0.431537
$538$	−27.9664	−1.20572
$539$	40.7610	1.75570
$540$	3.50662	0.150901
$541$	−39.7368	−1.70842	−0.854208	−	0.519931i	$-0.825958\pi$
$541$	−39.7368	−1.70842	−0.854208	+	0.519931i	$0.825958\pi$
$542$	−51.5236	−2.21313
$543$	1.20523	0.0517215
$544$	−16.0870	−0.689726
$545$	−8.55448	−0.366434
$546$	10.6202	0.454501
$547$	−23.2660	−0.994784	−0.497392	−	0.867526i	$-0.665709\pi$
$547$	−23.2660	−0.994784	−0.497392	+	0.867526i	$0.665709\pi$
$548$	−52.1427	−2.22742
$549$	−6.87409	−0.293379
$550$	7.09458	0.302514
$551$	−10.4636	−0.445766
$552$	19.6810	0.837680
$553$	−12.1650	−0.517307
$554$	−48.6049	−2.06503
$555$	8.60884	0.365425
$556$	48.2187	2.04493
$557$	19.8414	0.840708	0.420354	−	0.907360i	$-0.361906\pi$
$557$	19.8414	0.840708	0.420354	+	0.907360i	$0.361906\pi$
$558$	2.34662	0.0993403
$559$	3.55720	0.150454
$560$	−5.80714	−0.245396
$561$	11.9797	0.505784
$562$	−24.5744	−1.03661
$563$	39.2606	1.65464	0.827318	−	0.561733i	$-0.189865\pi$
$563$	39.2606	1.65464	0.827318	+	0.561733i	$0.189865\pi$
$564$	20.8474	0.877833
$565$	2.71232	0.114108
$566$	−31.9548	−1.34316
$567$	−4.52573	−0.190063
$568$	−9.22872	−0.387229
$569$	42.8840	1.79779	0.898895	−	0.438163i	$-0.144371\pi$
$569$	42.8840	1.79779	0.898895	+	0.438163i	$0.144371\pi$
$570$	7.79887	0.326659
$571$	−14.3168	−0.599139	−0.299570	−	0.954074i	$-0.596843\pi$
$571$	−14.3168	−0.599139	−0.299570	+	0.954074i	$0.596843\pi$
$572$	−10.6016	−0.443276
$573$	−10.2139	−0.426691
$574$	−42.6601	−1.78060
$575$	5.56675	0.232150
$576$	−12.0933	−0.503886
$577$	1.24449	0.0518086	0.0259043	−	0.999664i	$-0.491753\pi$
$577$	1.24449	0.0518086	0.0259043	+	0.999664i	$0.491753\pi$
$578$	−3.04846	−0.126799
$579$	8.17957	0.339931
$580$	−11.0403	−0.458425
$581$	−3.25201	−0.134916
$582$	−13.4431	−0.557233
$583$	36.5840	1.51515
$584$	0.514347	0.0212838
$585$	−1.00000	−0.0413449
$586$	−31.5161	−1.30192
$587$	12.4286	0.512982	0.256491	−	0.966547i	$-0.417434\pi$
$587$	12.4286	0.512982	0.256491	+	0.966547i	$0.417434\pi$
$588$	47.2769	1.94967
$589$	3.32345	0.136940
$590$	−7.96531	−0.327927
$591$	−16.3040	−0.670656
$592$	11.0463	0.454002
$593$	−1.90478	−0.0782201	−0.0391101	−	0.999235i	$-0.512452\pi$
$593$	−1.90478	−0.0782201	−0.0391101	+	0.999235i	$0.512452\pi$
$594$	7.09458	0.291094
$595$	−17.9329	−0.735178
$596$	−40.7201	−1.66796
$597$	14.3646	0.587905
$598$	−13.0630	−0.534188
$599$	−9.06943	−0.370567	−0.185283	−	0.982685i	$-0.559320\pi$
$599$	−9.06943	−0.370567	−0.185283	+	0.982685i	$0.559320\pi$
$600$	3.53546	0.144335
$601$	−20.5882	−0.839812	−0.419906	−	0.907568i	$-0.637937\pi$
$601$	−20.5882	−0.839812	−0.419906	+	0.907568i	$0.637937\pi$
$602$	37.7780	1.53972
$603$	10.4792	0.426744
$604$	83.5296	3.39877
$605$	−1.85955	−0.0756013
$606$	−32.6037	−1.32443
$607$	44.2397	1.79563	0.897817	−	0.440369i	$-0.145152\pi$
$607$	44.2397	1.79563	0.897817	+	0.440369i	$0.145152\pi$
$608$	−13.4928	−0.547206
$609$	14.2489	0.577395
$610$	−16.1309	−0.653120
$611$	−5.94515	−0.240515
$612$	13.8948	0.561662
$613$	−27.2126	−1.09911	−0.549554	−	0.835458i	$-0.685202\pi$
$613$	−27.2126	−1.09911	−0.549554	+	0.835458i	$0.685202\pi$
$614$	23.7053	0.956666
$615$	4.01690	0.161977
$616$	−48.3747	−1.94907
$617$	31.4617	1.26660	0.633300	−	0.773907i	$-0.281700\pi$
$617$	31.4617	1.26660	0.633300	+	0.773907i	$0.281700\pi$
$618$	−1.35592	−0.0545431
$619$	9.72133	0.390733	0.195367	−	0.980730i	$-0.437410\pi$
$619$	9.72133	0.390733	0.195367	+	0.980730i	$0.437410\pi$
$620$	3.50662	0.140829
$621$	5.56675	0.223386
$622$	−50.9482	−2.04284
$623$	−40.1074	−1.60687
$624$	−1.28314	−0.0513667
$625$	1.00000	0.0400000
$626$	79.7413	3.18710
$627$	10.0478	0.401272
$628$	−15.6852	−0.625907
$629$	34.1120	1.36013
$630$	−10.6202	−0.423117
$631$	−43.6537	−1.73782	−0.868912	−	0.494966i	$-0.835180\pi$
$631$	−43.6537	−1.73782	−0.868912	+	0.494966i	$0.835180\pi$
$632$	9.50317	0.378016
$633$	16.8502	0.669734
$634$	41.9079	1.66438
$635$	−17.9931	−0.714033
$636$	42.4322	1.68255
$637$	−13.4822	−0.534184
$638$	−22.3367	−0.884320
$639$	−2.61033	−0.103263
$640$	−20.2585	−0.800789
$641$	−24.9297	−0.984666	−0.492333	−	0.870407i	$-0.663856\pi$
$641$	−24.9297	−0.984666	−0.492333	+	0.870407i	$0.663856\pi$
$642$	−25.4351	−1.00384
$643$	−13.2035	−0.520696	−0.260348	−	0.965515i	$-0.583837\pi$
$643$	−13.2035	−0.520696	−0.260348	+	0.965515i	$0.583837\pi$
$644$	−88.3443	−3.48125
$645$	−3.55720	−0.140065
$646$	30.9025	1.21584
$647$	3.98132	0.156522	0.0782610	−	0.996933i	$-0.475063\pi$
$647$	3.98132	0.156522	0.0782610	+	0.996933i	$0.475063\pi$
$648$	3.53546	0.138886
$649$	−10.2623	−0.402830
$650$	−2.34662	−0.0920420
$651$	−4.52573	−0.177377
$652$	−30.0432	−1.17658
$653$	21.6472	0.847122	0.423561	−	0.905868i	$-0.360780\pi$
$653$	21.6472	0.847122	0.423561	+	0.905868i	$0.360780\pi$
$654$	−20.0741	−0.784959
$655$	3.54931	0.138683
$656$	5.15425	0.201240
$657$	0.145482	0.00567580
$658$	−63.1384	−2.46139
$659$	2.07322	0.0807612	0.0403806	−	0.999184i	$-0.487143\pi$
$659$	2.07322	0.0807612	0.0403806	+	0.999184i	$0.487143\pi$
$660$	10.6016	0.412668
$661$	−21.4942	−0.836029	−0.418015	−	0.908440i	$-0.637274\pi$
$661$	−21.4942	−0.836029	−0.418015	+	0.908440i	$0.637274\pi$
$662$	10.9527	0.425688
$663$	−3.96244	−0.153888
$664$	2.54045	0.0985885
$665$	−15.0410	−0.583266
$666$	20.2017	0.782798
$667$	−17.5265	−0.678629
$668$	27.4906	1.06364
$669$	−1.30146	−0.0503175
$670$	24.5906	0.950017
$671$	−20.7826	−0.802302
$672$	18.3739	0.708789
$673$	−48.0244	−1.85121	−0.925603	−	0.378497i	$-0.876441\pi$
$673$	−48.0244	−1.85121	−0.925603	+	0.378497i	$0.876441\pi$
$674$	15.7971	0.608482
$675$	1.00000	0.0384900
$676$	3.50662	0.134870
$677$	6.87505	0.264229	0.132115	−	0.991234i	$-0.457823\pi$
$677$	6.87505	0.264229	0.132115	+	0.991234i	$0.457823\pi$
$678$	6.36479	0.244438
$679$	25.9265	0.994967
$680$	14.0090	0.537222
$681$	−12.0936	−0.463427
$682$	7.09458	0.271665
$683$	−47.1511	−1.80418	−0.902092	−	0.431543i	$-0.857969\pi$
$683$	−47.1511	−1.80418	−0.902092	+	0.431543i	$0.857969\pi$
$684$	11.6541	0.445605
$685$	−14.8698	−0.568145
$686$	−68.8420	−2.62840
$687$	26.7490	1.02054
$688$	−4.56439	−0.174016
$689$	−12.1006	−0.460996
$690$	13.0630	0.497302
$691$	−13.3824	−0.509092	−0.254546	−	0.967061i	$-0.581926\pi$
$691$	−13.3824	−0.509092	−0.254546	+	0.967061i	$0.581926\pi$
$692$	−26.4972	−1.00727
$693$	−13.6827	−0.519763
$694$	−17.3343	−0.658002
$695$	13.7508	0.521596
$696$	−11.1311	−0.421924
$697$	15.9167	0.602889
$698$	−21.7673	−0.823903
$699$	−8.48883	−0.321077
$700$	−15.8700	−0.599830
$701$	26.4615	0.999438	0.499719	−	0.866188i	$-0.333437\pi$
$701$	26.4615	0.999438	0.499719	+	0.866188i	$0.333437\pi$
$702$	−2.34662	−0.0885674
$703$	28.6110	1.07909
$704$	−36.5618	−1.37798
$705$	5.94515	0.223907
$706$	1.60800	0.0605180
$707$	62.8799	2.36484
$708$	−11.9028	−0.447334
$709$	11.3659	0.426854	0.213427	−	0.976959i	$-0.431538\pi$
$709$	11.3659	0.426854	0.213427	+	0.976959i	$0.431538\pi$
$710$	−6.12545	−0.229884
$711$	2.68796	0.100806
$712$	31.3316	1.17420
$713$	5.56675	0.208476
$714$	−42.0817	−1.57487
$715$	−3.02332	−0.113066
$716$	35.0666	1.31050
$717$	−16.7104	−0.624062
$718$	−80.3110	−2.99718
$719$	23.9614	0.893608	0.446804	−	0.894632i	$-0.352562\pi$
$719$	23.9614	0.893608	0.446804	+	0.894632i	$0.352562\pi$
$720$	1.28314	0.0478198
$721$	2.61505	0.0973894
$722$	−18.6666	−0.694699
$723$	−16.7165	−0.621694
$724$	4.22629	0.157069
$725$	−3.14842	−0.116930
$726$	−4.36365	−0.161950
$727$	−6.97413	−0.258656	−0.129328	−	0.991602i	$-0.541282\pi$
$727$	−6.97413	−0.258656	−0.129328	+	0.991602i	$0.541282\pi$
$728$	16.0005	0.593019
$729$	1.00000	0.0370370
$730$	0.341391	0.0126355
$731$	−14.0952	−0.521329
$732$	−24.1048	−0.890940
$733$	−5.38394	−0.198860	−0.0994301	−	0.995045i	$-0.531702\pi$
$733$	−5.38394	−0.198860	−0.0994301	+	0.995045i	$0.531702\pi$
$734$	43.1598	1.59306
$735$	13.4822	0.497298
$736$	−22.6004	−0.833060
$737$	31.6818	1.16702
$738$	9.42614	0.346981
$739$	22.0174	0.809923	0.404962	−	0.914334i	$-0.367285\pi$
$739$	22.0174	0.809923	0.404962	+	0.914334i	$0.367285\pi$
$740$	30.1879	1.10973
$741$	−3.32345	−0.122090
$742$	−128.510	−4.71776
$743$	4.47655	0.164229	0.0821143	−	0.996623i	$-0.473833\pi$
$743$	4.47655	0.164229	0.0821143	+	0.996623i	$0.473833\pi$
$744$	3.53546	0.129616
$745$	−11.6124	−0.425444
$746$	44.2495	1.62009
$747$	0.718562	0.0262908
$748$	42.0083	1.53597
$749$	49.0546	1.79242
$750$	2.34662	0.0856864
$751$	6.23005	0.227338	0.113669	−	0.993519i	$-0.463740\pi$
$751$	6.23005	0.227338	0.113669	+	0.993519i	$0.463740\pi$
$752$	7.62846	0.278181
$753$	1.58940	0.0579210
$754$	7.38815	0.269061
$755$	23.8205	0.866918
$756$	−15.8700	−0.577186
$757$	−8.30839	−0.301974	−0.150987	−	0.988536i	$-0.548245\pi$
$757$	−8.30839	−0.301974	−0.150987	+	0.988536i	$0.548245\pi$
$758$	4.75894	0.172853
$759$	16.8301	0.610893
$760$	11.7499	0.426215
$761$	−35.4948	−1.28669	−0.643343	−	0.765578i	$-0.722453\pi$
$761$	−35.4948	−1.28669	−0.643343	+	0.765578i	$0.722453\pi$
$762$	−42.2228	−1.52957
$763$	38.7152	1.40159
$764$	−35.8162	−1.29578
$765$	3.96244	0.143262
$766$	−72.8543	−2.63233
$767$	3.39438	0.122564
$768$	−23.3525	−0.842661
$769$	12.0386	0.434123	0.217061	−	0.976158i	$-0.430353\pi$
$769$	12.0386	0.434123	0.217061	+	0.976158i	$0.430353\pi$
$770$	−32.1081	−1.15710
$771$	4.92595	0.177404
$772$	28.6826	1.03231
$773$	31.3784	1.12860	0.564302	−	0.825569i	$-0.309146\pi$
$773$	31.3784	1.12860	0.564302	+	0.825569i	$0.309146\pi$
$774$	−8.34740	−0.300041
$775$	1.00000	0.0359211
$776$	−20.2536	−0.727061
$777$	−38.9612	−1.39773
$778$	87.3630	3.13212
$779$	13.3500	0.478312
$780$	−3.50662	−0.125557
$781$	−7.89186	−0.282393
$782$	51.7615	1.85099
$783$	−3.14842	−0.112515
$784$	17.2996	0.617841
$785$	−4.47302	−0.159649
$786$	8.32887	0.297081
$787$	47.1757	1.68163	0.840815	−	0.541322i	$-0.182076\pi$
$787$	47.1757	1.68163	0.840815	+	0.541322i	$0.182076\pi$
$788$	−57.1719	−2.03666
$789$	4.07270	0.144992
$790$	6.30761	0.224415
$791$	−12.2752	−0.436457
$792$	10.6888	0.379811
$793$	6.87409	0.244106
$794$	−4.34433	−0.154175
$795$	12.1006	0.429164
$796$	50.3713	1.78536
$797$	−36.3703	−1.28830	−0.644152	−	0.764898i	$-0.722790\pi$
$797$	−36.3703	−1.28830	−0.644152	+	0.764898i	$0.722790\pi$
$798$	−35.2955	−1.24945
$799$	23.5573	0.833397
$800$	−4.05988	−0.143538
$801$	8.86209	0.313127
$802$	13.9366	0.492117
$803$	0.439839	0.0155216
$804$	36.7464	1.29595
$805$	−25.1936	−0.887958
$806$	−2.34662	−0.0826561
$807$	−11.9178	−0.419525
$808$	−49.1213	−1.72808
$809$	−7.61463	−0.267716	−0.133858	−	0.991001i	$-0.542737\pi$
$809$	−7.61463	−0.267716	−0.133858	+	0.991001i	$0.542737\pi$
$810$	2.34662	0.0824518
$811$	10.0182	0.351787	0.175894	−	0.984409i	$-0.443719\pi$
$811$	10.0182	0.351787	0.175894	+	0.984409i	$0.443719\pi$
$812$	49.9655	1.75344
$813$	−21.9565	−0.770050
$814$	61.0760	2.14071
$815$	−8.56757	−0.300109
$816$	5.08436	0.177988
$817$	−11.8222	−0.413606
$818$	−89.3202	−3.12301
$819$	4.52573	0.158142
$820$	14.0857	0.491896
$821$	−3.13804	−0.109518	−0.0547592	−	0.998500i	$-0.517439\pi$
$821$	−3.13804	−0.109518	−0.0547592	+	0.998500i	$0.517439\pi$
$822$	−34.8937	−1.21706
$823$	40.1428	1.39929	0.699645	−	0.714490i	$-0.253341\pi$
$823$	40.1428	1.39929	0.699645	+	0.714490i	$0.253341\pi$
$824$	−2.04285	−0.0711662
$825$	3.02332	0.105258
$826$	36.0488	1.25430
$827$	12.9623	0.450745	0.225372	−	0.974273i	$-0.427640\pi$
$827$	12.9623	0.450745	0.225372	+	0.974273i	$0.427640\pi$
$828$	19.5205	0.678384
$829$	−20.6748	−0.718066	−0.359033	−	0.933325i	$-0.616893\pi$
$829$	−20.6748	−0.718066	−0.359033	+	0.933325i	$0.616893\pi$
$830$	1.68619	0.0585285
$831$	−20.7127	−0.718517
$832$	12.0933	0.419259
$833$	53.4224	1.85098
$834$	32.2678	1.11734
$835$	7.83962	0.271301
$836$	35.2340	1.21859
$837$	1.00000	0.0345651
$838$	−7.56420	−0.261301
$839$	−1.09288	−0.0377304	−0.0188652	−	0.999822i	$-0.506005\pi$
$839$	−1.09288	−0.0377304	−0.0188652	+	0.999822i	$0.506005\pi$
$840$	−16.0005	−0.552071
$841$	−19.0874	−0.658187
$842$	−28.3355	−0.976505
$843$	−10.4723	−0.360684
$844$	59.0871	2.03386
$845$	1.00000	0.0344010
$846$	13.9510	0.479645
$847$	8.41580	0.289170
$848$	15.5268	0.533191
$849$	−13.6174	−0.467347
$850$	9.29833	0.318930
$851$	47.9233	1.64279
$852$	−9.15344	−0.313592
$853$	50.5334	1.73023	0.865115	−	0.501574i	$-0.167246\pi$
$853$	50.5334	1.73023	0.865115	+	0.501574i	$0.167246\pi$
$854$	73.0039	2.49814
$855$	3.32345	0.113660
$856$	−38.3211	−1.30979
$857$	29.1471	0.995646	0.497823	−	0.867279i	$-0.334133\pi$
$857$	29.1471	0.995646	0.497823	+	0.867279i	$0.334133\pi$
$858$	−7.09458	−0.242205
$859$	21.2781	0.726001	0.363000	−	0.931789i	$-0.381752\pi$
$859$	21.2781	0.726001	0.363000	+	0.931789i	$0.381752\pi$
$860$	−12.4738	−0.425351
$861$	−18.1794	−0.619552
$862$	−30.1935	−1.02840
$863$	−8.96766	−0.305263	−0.152631	−	0.988283i	$-0.548775\pi$
$863$	−8.96766	−0.305263	−0.152631	+	0.988283i	$0.548775\pi$
$864$	−4.05988	−0.138120
$865$	−7.55634	−0.256923
$866$	−1.23851	−0.0420862
$867$	−1.29909	−0.0441193
$868$	−15.8700	−0.538663
$869$	8.12655	0.275674
$870$	−7.38815	−0.250482
$871$	−10.4792	−0.355073
$872$	−30.2440	−1.02419
$873$	−5.72869	−0.193887
$874$	43.4144	1.46851
$875$	−4.52573	−0.152997
$876$	0.510151	0.0172364
$877$	44.8310	1.51383	0.756917	−	0.653511i	$-0.226705\pi$
$877$	44.8310	1.51383	0.756917	+	0.653511i	$0.226705\pi$
$878$	34.3679	1.15986
$879$	−13.4304	−0.452997
$880$	3.87934	0.130773
$881$	4.02556	0.135625	0.0678123	−	0.997698i	$-0.478398\pi$
$881$	4.02556	0.135625	0.0678123	+	0.997698i	$0.478398\pi$
$882$	31.6376	1.06529
$883$	19.5688	0.658543	0.329271	−	0.944235i	$-0.393197\pi$
$883$	19.5688	0.658543	0.329271	+	0.944235i	$0.393197\pi$
$884$	−13.8948	−0.467331
$885$	−3.39438	−0.114101
$886$	29.1133	0.978079
$887$	12.3937	0.416141	0.208070	−	0.978114i	$-0.433282\pi$
$887$	12.3937	0.416141	0.208070	+	0.978114i	$0.433282\pi$
$888$	30.4362	1.02137
$889$	81.4316	2.73113
$890$	20.7959	0.697082
$891$	3.02332	0.101285
$892$	−4.56373	−0.152805
$893$	19.7584	0.661190
$894$	−27.2498	−0.911369
$895$	10.0001	0.334267
$896$	91.6846	3.06297
$897$	−5.56675	−0.185868
$898$	−49.5059	−1.65203
$899$	−3.14842	−0.105006
$900$	3.50662	0.116887
$901$	47.9479	1.59738
$902$	28.4982	0.948887
$903$	16.0989	0.535739
$904$	9.58931	0.318936
$905$	1.20523	0.0400633
$906$	55.8977	1.85708
$907$	−46.1127	−1.53115	−0.765574	−	0.643348i	$-0.777545\pi$
$907$	−46.1127	−1.53115	−0.765574	+	0.643348i	$0.777545\pi$
$908$	−42.4075	−1.40734
$909$	−13.8939	−0.460831
$910$	10.6202	0.352055
$911$	17.3827	0.575914	0.287957	−	0.957643i	$-0.407024\pi$
$911$	17.3827	0.575914	0.287957	+	0.957643i	$0.407024\pi$
$912$	4.26445	0.141210
$913$	2.17244	0.0718973
$914$	47.1241	1.55873
$915$	−6.87409	−0.227250
$916$	93.7986	3.09919
$917$	−16.0632	−0.530453
$918$	9.29833	0.306891
$919$	−23.4056	−0.772081	−0.386040	−	0.922482i	$-0.626157\pi$
$919$	−23.4056	−0.772081	−0.386040	+	0.922482i	$0.626157\pi$
$920$	19.6810	0.648864
$921$	10.1019	0.332868
$922$	−52.0842	−1.71530
$923$	2.61033	0.0859201
$924$	−47.9801	−1.57843
$925$	8.60884	0.283057
$926$	63.8132	2.09703
$927$	−0.577818	−0.0189780
$928$	12.7822	0.419597
$929$	25.1244	0.824305	0.412153	−	0.911115i	$-0.364777\pi$
$929$	25.1244	0.824305	0.412153	+	0.911115i	$0.364777\pi$
$930$	2.34662	0.0769487
$931$	44.8074	1.46850
$932$	−29.7671	−0.975053
$933$	−21.7113	−0.710797
$934$	67.2390	2.20013
$935$	11.9797	0.391778
$936$	−3.53546	−0.115560
$937$	46.8048	1.52905	0.764524	−	0.644595i	$-0.222974\pi$
$937$	46.8048	1.52905	0.764524	+	0.644595i	$0.222974\pi$
$938$	−111.290	−3.63376
$939$	33.9813	1.10894
$940$	20.8474	0.679966
$941$	−16.0684	−0.523815	−0.261907	−	0.965093i	$-0.584351\pi$
$941$	−16.0684	−0.523815	−0.261907	+	0.965093i	$0.584351\pi$
$942$	−10.4965	−0.341994
$943$	22.3611	0.728178
$944$	−4.35546	−0.141758
$945$	−4.52573	−0.147222
$946$	−25.2368	−0.820520
$947$	4.12349	0.133995	0.0669977	−	0.997753i	$-0.478658\pi$
$947$	4.12349	0.133995	0.0669977	+	0.997753i	$0.478658\pi$
$948$	9.42564	0.306131
$949$	−0.145482	−0.00472255
$950$	7.79887	0.253029
$951$	17.8588	0.579113
$952$	−63.4011	−2.05484
$953$	22.9884	0.744667	0.372333	−	0.928099i	$-0.378558\pi$
$953$	22.9884	0.744667	0.372333	+	0.928099i	$0.378558\pi$
$954$	28.3955	0.919338
$955$	−10.2139	−0.330513
$956$	−58.5971	−1.89516
$957$	−9.51869	−0.307695
$958$	59.8621	1.93406
$959$	67.2966	2.17312
$960$	−12.0933	−0.390309
$961$	1.00000	0.0322581
$962$	−20.2017	−0.651328
$963$	−10.8391	−0.349284
$964$	−58.6185	−1.88797
$965$	8.17957	0.263310
$966$	−59.1198	−1.90215
$967$	−23.5444	−0.757137	−0.378569	−	0.925573i	$-0.623584\pi$
$967$	−23.5444	−0.757137	−0.378569	+	0.925573i	$0.623584\pi$
$968$	−6.57435	−0.211308
$969$	13.1690	0.423048
$970$	−13.4431	−0.431630
$971$	−8.61341	−0.276417	−0.138209	−	0.990403i	$-0.544134\pi$
$971$	−8.61341	−0.276417	−0.138209	+	0.990403i	$0.544134\pi$
$972$	3.50662	0.112475
$973$	−62.2322	−1.99507
$974$	−50.8135	−1.62817
$975$	−1.00000	−0.0320256
$976$	−8.82042	−0.282335
$977$	−35.3211	−1.13002	−0.565011	−	0.825083i	$-0.691128\pi$
$977$	−35.3211	−1.13002	−0.565011	+	0.825083i	$0.691128\pi$
$978$	−20.1048	−0.642881
$979$	26.7929	0.856305
$980$	47.2769	1.51021
$981$	−8.55448	−0.273123
$982$	55.5264	1.77192
$983$	−38.6859	−1.23389	−0.616944	−	0.787007i	$-0.711630\pi$
$983$	−38.6859	−1.23389	−0.616944	+	0.787007i	$0.711630\pi$
$984$	14.2016	0.452731
$985$	−16.3040	−0.519488
$986$	−29.2751	−0.932309
$987$	−26.9061	−0.856431
$988$	−11.6541	−0.370765
$989$	−19.8021	−0.629669
$990$	7.09458	0.225480
$991$	−34.0393	−1.08129	−0.540647	−	0.841250i	$-0.681820\pi$
$991$	−34.0393	−1.08129	−0.540647	+	0.841250i	$0.681820\pi$
$992$	−4.05988	−0.128901
$993$	4.66744	0.148117
$994$	27.7221	0.879292
$995$	14.3646	0.455389
$996$	2.51972	0.0798405
$997$	−9.60781	−0.304282	−0.152141	−	0.988359i	$-0.548617\pi$
$997$	−9.60781	−0.304282	−0.152141	+	0.988359i	$0.548617\pi$
$998$	58.9492	1.86601
$999$	8.60884	0.272372

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6045.2.a.bi.1.15	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6045.2.a.bi.1.15	✓	18	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:	\( N \)	\(=\)	\( 6045 = 3 \cdot 5 \cdot 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6045.a (trivial)

\(f(q)\)	\(=\)	\(q+2.34662 q^{2} +1.00000 q^{3} +3.50662 q^{4} +1.00000 q^{5} +2.34662 q^{6} -4.52573 q^{7} +3.53546 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.34662 q^{2} +1.00000 q^{3} +3.50662 q^{4} +1.00000 q^{5} +2.34662 q^{6} -4.52573 q^{7} +3.53546 q^{8} +1.00000 q^{9} +2.34662 q^{10} +3.02332 q^{11} +3.50662 q^{12} -1.00000 q^{13} -10.6202 q^{14} +1.00000 q^{15} +1.28314 q^{16} +3.96244 q^{17} +2.34662 q^{18} +3.32345 q^{19} +3.50662 q^{20} -4.52573 q^{21} +7.09458 q^{22} +5.56675 q^{23} +3.53546 q^{24} +1.00000 q^{25} -2.34662 q^{26} +1.00000 q^{27} -15.8700 q^{28} -3.14842 q^{29} +2.34662 q^{30} +1.00000 q^{31} -4.05988 q^{32} +3.02332 q^{33} +9.29833 q^{34} -4.52573 q^{35} +3.50662 q^{36} +8.60884 q^{37} +7.79887 q^{38} -1.00000 q^{39} +3.53546 q^{40} +4.01690 q^{41} -10.6202 q^{42} -3.55720 q^{43} +10.6016 q^{44} +1.00000 q^{45} +13.0630 q^{46} +5.94515 q^{47} +1.28314 q^{48} +13.4822 q^{49} +2.34662 q^{50} +3.96244 q^{51} -3.50662 q^{52} +12.1006 q^{53} +2.34662 q^{54} +3.02332 q^{55} -16.0005 q^{56} +3.32345 q^{57} -7.38815 q^{58} -3.39438 q^{59} +3.50662 q^{60} -6.87409 q^{61} +2.34662 q^{62} -4.52573 q^{63} -12.0933 q^{64} -1.00000 q^{65} +7.09458 q^{66} +10.4792 q^{67} +13.8948 q^{68} +5.56675 q^{69} -10.6202 q^{70} -2.61033 q^{71} +3.53546 q^{72} +0.145482 q^{73} +20.2017 q^{74} +1.00000 q^{75} +11.6541 q^{76} -13.6827 q^{77} -2.34662 q^{78} +2.68796 q^{79} +1.28314 q^{80} +1.00000 q^{81} +9.42614 q^{82} +0.718562 q^{83} -15.8700 q^{84} +3.96244 q^{85} -8.34740 q^{86} -3.14842 q^{87} +10.6888 q^{88} +8.86209 q^{89} +2.34662 q^{90} +4.52573 q^{91} +19.5205 q^{92} +1.00000 q^{93} +13.9510 q^{94} +3.32345 q^{95} -4.05988 q^{96} -5.72869 q^{97} +31.6376 q^{98} +3.02332 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 4 q^{2} + 18 q^{3} + 22 q^{4} + 18 q^{5} + 4 q^{6} + 8 q^{7} + 9 q^{8} + 18 q^{9}+O(q^{10}) \) 18 * q + 4 * q^2 + 18 * q^3 + 22 * q^4 + 18 * q^5 + 4 * q^6 + 8 * q^7 + 9 * q^8 + 18 * q^9	\( 18 q + 4 q^{2} + 18 q^{3} + 22 q^{4} + 18 q^{5} + 4 q^{6} + 8 q^{7} + 9 q^{8} + 18 q^{9} + 4 q^{10} + 6 q^{11} + 22 q^{12} - 18 q^{13} + 5 q^{14} + 18 q^{15} + 30 q^{16} + 18 q^{17} + 4 q^{18} + 12 q^{19} + 22 q^{20} + 8 q^{21} + 7 q^{22} + 32 q^{23} + 9 q^{24} + 18 q^{25} - 4 q^{26} + 18 q^{27} + 10 q^{28} + 7 q^{29} + 4 q^{30} + 18 q^{31} + 22 q^{32} + 6 q^{33} + 15 q^{34} + 8 q^{35} + 22 q^{36} + 3 q^{37} + 32 q^{38} - 18 q^{39} + 9 q^{40} + 4 q^{41} + 5 q^{42} + 14 q^{43} - 5 q^{44} + 18 q^{45} + 10 q^{46} + 23 q^{47} + 30 q^{48} + 28 q^{49} + 4 q^{50} + 18 q^{51} - 22 q^{52} + 35 q^{53} + 4 q^{54} + 6 q^{55} - 7 q^{56} + 12 q^{57} - 6 q^{58} + 28 q^{59} + 22 q^{60} + 19 q^{61} + 4 q^{62} + 8 q^{63} + 43 q^{64} - 18 q^{65} + 7 q^{66} + 34 q^{67} + 55 q^{68} + 32 q^{69} + 5 q^{70} - 8 q^{71} + 9 q^{72} + 22 q^{74} + 18 q^{75} + 2 q^{76} + 21 q^{77} - 4 q^{78} + 4 q^{79} + 30 q^{80} + 18 q^{81} + 29 q^{82} + 11 q^{83} + 10 q^{84} + 18 q^{85} - 22 q^{86} + 7 q^{87} - 31 q^{88} + 17 q^{89} + 4 q^{90} - 8 q^{91} + 33 q^{92} + 18 q^{93} - 14 q^{94} + 12 q^{95} + 22 q^{96} + 32 q^{97} + 20 q^{98} + 6 q^{99}+O(q^{100}) \) 18 * q + 4 * q^2 + 18 * q^3 + 22 * q^4 + 18 * q^5 + 4 * q^6 + 8 * q^7 + 9 * q^8 + 18 * q^9 + 4 * q^10 + 6 * q^11 + 22 * q^12 - 18 * q^13 + 5 * q^14 + 18 * q^15 + 30 * q^16 + 18 * q^17 + 4 * q^18 + 12 * q^19 + 22 * q^20 + 8 * q^21 + 7 * q^22 + 32 * q^23 + 9 * q^24 + 18 * q^25 - 4 * q^26 + 18 * q^27 + 10 * q^28 + 7 * q^29 + 4 * q^30 + 18 * q^31 + 22 * q^32 + 6 * q^33 + 15 * q^34 + 8 * q^35 + 22 * q^36 + 3 * q^37 + 32 * q^38 - 18 * q^39 + 9 * q^40 + 4 * q^41 + 5 * q^42 + 14 * q^43 - 5 * q^44 + 18 * q^45 + 10 * q^46 + 23 * q^47 + 30 * q^48 + 28 * q^49 + 4 * q^50 + 18 * q^51 - 22 * q^52 + 35 * q^53 + 4 * q^54 + 6 * q^55 - 7 * q^56 + 12 * q^57 - 6 * q^58 + 28 * q^59 + 22 * q^60 + 19 * q^61 + 4 * q^62 + 8 * q^63 + 43 * q^64 - 18 * q^65 + 7 * q^66 + 34 * q^67 + 55 * q^68 + 32 * q^69 + 5 * q^70 - 8 * q^71 + 9 * q^72 + 22 * q^74 + 18 * q^75 + 2 * q^76 + 21 * q^77 - 4 * q^78 + 4 * q^79 + 30 * q^80 + 18 * q^81 + 29 * q^82 + 11 * q^83 + 10 * q^84 + 18 * q^85 - 22 * q^86 + 7 * q^87 - 31 * q^88 + 17 * q^89 + 4 * q^90 - 8 * q^91 + 33 * q^92 + 18 * q^93 - 14 * q^94 + 12 * q^95 + 22 * q^96 + 32 * q^97 + 20 * q^98 + 6 * q^99

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