LMFDB - Embedded newform 8007.2.a.c.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8007,2,Mod(1,8007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8007, 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("8007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8007 = 3 \cdot 17 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8007.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:	$63.9362168984$
Analytic rank:	$1$
Dimension:	$39$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	8007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.60951 q^{2} -1.00000 q^{3} +0.590533 q^{4} +2.17104 q^{5} +1.60951 q^{6} +3.27452 q^{7} +2.26856 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.60951 q^{2} -1.00000 q^{3} +0.590533 q^{4} +2.17104 q^{5} +1.60951 q^{6} +3.27452 q^{7} +2.26856 q^{8} +1.00000 q^{9} -3.49431 q^{10} +0.0669844 q^{11} -0.590533 q^{12} +0.443428 q^{13} -5.27038 q^{14} -2.17104 q^{15} -4.83234 q^{16} +1.00000 q^{17} -1.60951 q^{18} -3.50112 q^{19} +1.28207 q^{20} -3.27452 q^{21} -0.107812 q^{22} -4.40532 q^{23} -2.26856 q^{24} -0.286599 q^{25} -0.713703 q^{26} -1.00000 q^{27} +1.93371 q^{28} +8.76824 q^{29} +3.49431 q^{30} +9.92020 q^{31} +3.24060 q^{32} -0.0669844 q^{33} -1.60951 q^{34} +7.10909 q^{35} +0.590533 q^{36} -3.50206 q^{37} +5.63510 q^{38} -0.443428 q^{39} +4.92512 q^{40} -8.85328 q^{41} +5.27038 q^{42} -0.643560 q^{43} +0.0395565 q^{44} +2.17104 q^{45} +7.09041 q^{46} -10.7581 q^{47} +4.83234 q^{48} +3.72245 q^{49} +0.461284 q^{50} -1.00000 q^{51} +0.261859 q^{52} -10.1229 q^{53} +1.60951 q^{54} +0.145426 q^{55} +7.42842 q^{56} +3.50112 q^{57} -14.1126 q^{58} +7.39311 q^{59} -1.28207 q^{60} -7.94758 q^{61} -15.9667 q^{62} +3.27452 q^{63} +4.44889 q^{64} +0.962699 q^{65} +0.107812 q^{66} -15.6509 q^{67} +0.590533 q^{68} +4.40532 q^{69} -11.4422 q^{70} -2.66761 q^{71} +2.26856 q^{72} +11.0205 q^{73} +5.63661 q^{74} +0.286599 q^{75} -2.06753 q^{76} +0.219342 q^{77} +0.713703 q^{78} -6.51709 q^{79} -10.4912 q^{80} +1.00000 q^{81} +14.2495 q^{82} -3.88084 q^{83} -1.93371 q^{84} +2.17104 q^{85} +1.03582 q^{86} -8.76824 q^{87} +0.151958 q^{88} -12.6880 q^{89} -3.49431 q^{90} +1.45201 q^{91} -2.60148 q^{92} -9.92020 q^{93} +17.3154 q^{94} -7.60106 q^{95} -3.24060 q^{96} -10.3181 q^{97} -5.99134 q^{98} +0.0669844 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 39 q - 4 q^{2} - 39 q^{3} + 30 q^{4} - 3 q^{5} + 4 q^{6} - 5 q^{7} - 3 q^{8} + 39 q^{9}+O(q^{10}) $ 39 * q - 4 * q^2 - 39 * q^3 + 30 * q^4 - 3 * q^5 + 4 * q^6 - 5 * q^7 - 3 * q^8 + 39 * q^9	\( 39 q - 4 q^{2} - 39 q^{3} + 30 q^{4} - 3 q^{5} + 4 q^{6} - 5 q^{7} - 3 q^{8} + 39 q^{9} + 4 q^{10} + q^{11} - 30 q^{12} - 26 q^{13} - 4 q^{14} + 3 q^{15} + 8 q^{16} + 39 q^{17} - 4 q^{18} - 14 q^{19} - 14 q^{20} + 5 q^{21} - 17 q^{22} + 2 q^{23} + 3 q^{24} - 6 q^{25} - 17 q^{26} - 39 q^{27} - 14 q^{28} - 7 q^{29} - 4 q^{30} - q^{31} - 30 q^{32} - q^{33} - 4 q^{34} + q^{35} + 30 q^{36} - 24 q^{37} - 20 q^{38} + 26 q^{39} + 12 q^{40} + q^{41} + 4 q^{42} - 41 q^{43} - 2 q^{44} - 3 q^{45} - 6 q^{46} - 9 q^{47} - 8 q^{48} - 10 q^{49} - 9 q^{50} - 39 q^{51} - 37 q^{52} - 47 q^{53} + 4 q^{54} - 39 q^{55} + 8 q^{56} + 14 q^{57} - 27 q^{58} + 41 q^{59} + 14 q^{60} - 41 q^{61} + 36 q^{62} - 5 q^{63} - 47 q^{64} - 39 q^{65} + 17 q^{66} - 36 q^{67} + 30 q^{68} - 2 q^{69} - 52 q^{70} - 2 q^{71} - 3 q^{72} - 63 q^{73} - 6 q^{74} + 6 q^{75} - 34 q^{76} - 64 q^{77} + 17 q^{78} + 20 q^{79} - 28 q^{80} + 39 q^{81} - 37 q^{82} + 45 q^{83} + 14 q^{84} - 3 q^{85} + 32 q^{86} + 7 q^{87} + 6 q^{88} - 32 q^{89} + 4 q^{90} - 11 q^{91} + 28 q^{92} + q^{93} - 44 q^{94} + 22 q^{95} + 30 q^{96} - 20 q^{97} + 63 q^{98} + q^{99}+O(q^{100}) \) 39 * q - 4 * q^2 - 39 * q^3 + 30 * q^4 - 3 * q^5 + 4 * q^6 - 5 * q^7 - 3 * q^8 + 39 * q^9 + 4 * q^10 + q^11 - 30 * q^12 - 26 * q^13 - 4 * q^14 + 3 * q^15 + 8 * q^16 + 39 * q^17 - 4 * q^18 - 14 * q^19 - 14 * q^20 + 5 * q^21 - 17 * q^22 + 2 * q^23 + 3 * q^24 - 6 * q^25 - 17 * q^26 - 39 * q^27 - 14 * q^28 - 7 * q^29 - 4 * q^30 - q^31 - 30 * q^32 - q^33 - 4 * q^34 + q^35 + 30 * q^36 - 24 * q^37 - 20 * q^38 + 26 * q^39 + 12 * q^40 + q^41 + 4 * q^42 - 41 * q^43 - 2 * q^44 - 3 * q^45 - 6 * q^46 - 9 * q^47 - 8 * q^48 - 10 * q^49 - 9 * q^50 - 39 * q^51 - 37 * q^52 - 47 * q^53 + 4 * q^54 - 39 * q^55 + 8 * q^56 + 14 * q^57 - 27 * q^58 + 41 * q^59 + 14 * q^60 - 41 * q^61 + 36 * q^62 - 5 * q^63 - 47 * q^64 - 39 * q^65 + 17 * q^66 - 36 * q^67 + 30 * q^68 - 2 * q^69 - 52 * q^70 - 2 * q^71 - 3 * q^72 - 63 * q^73 - 6 * q^74 + 6 * q^75 - 34 * q^76 - 64 * q^77 + 17 * q^78 + 20 * q^79 - 28 * q^80 + 39 * q^81 - 37 * q^82 + 45 * q^83 + 14 * q^84 - 3 * q^85 + 32 * q^86 + 7 * q^87 + 6 * q^88 - 32 * q^89 + 4 * q^90 - 11 * q^91 + 28 * q^92 + q^93 - 44 * q^94 + 22 * q^95 + 30 * q^96 - 20 * q^97 + 63 * q^98 + 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 $

$2$	−1.60951	−1.13810	−0.569049	−	0.822304i	$-0.692688\pi$
$2$	−1.60951	−1.13810	−0.569049	+	0.822304i	$0.692688\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.590533	0.295266
$5$	2.17104	0.970917	0.485459	−	0.874260i	$-0.338653\pi$
$5$	2.17104	0.970917	0.485459	+	0.874260i	$0.338653\pi$
$6$	1.60951	0.657081
$7$	3.27452	1.23765	0.618825	−	0.785529i	$-0.287609\pi$
$7$	3.27452	1.23765	0.618825	+	0.785529i	$0.287609\pi$
$8$	2.26856	0.802056
$9$	1.00000	0.333333
$10$	−3.49431	−1.10500
$11$	0.0669844	0.0201966	0.0100983	−	0.999949i	$-0.496786\pi$
$11$	0.0669844	0.0201966	0.0100983	+	0.999949i	$0.496786\pi$
$12$	−0.590533	−0.170472
$13$	0.443428	0.122985	0.0614924	−	0.998108i	$-0.480414\pi$
$13$	0.443428	0.122985	0.0614924	+	0.998108i	$0.480414\pi$
$14$	−5.27038	−1.40857
$15$	−2.17104	−0.560559
$16$	−4.83234	−1.20808
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.60951	−0.379366
$19$	−3.50112	−0.803212	−0.401606	−	0.915813i	$-0.631548\pi$
$19$	−3.50112	−0.803212	−0.401606	+	0.915813i	$0.631548\pi$
$20$	1.28207	0.286679
$21$	−3.27452	−0.714558
$22$	−0.107812	−0.0229857
$23$	−4.40532	−0.918572	−0.459286	−	0.888288i	$-0.651895\pi$
$23$	−4.40532	−0.918572	−0.459286	+	0.888288i	$0.651895\pi$
$24$	−2.26856	−0.463067
$25$	−0.286599	−0.0573197
$26$	−0.713703	−0.139969
$27$	−1.00000	−0.192450
$28$	1.93371	0.365437
$29$	8.76824	1.62822	0.814111	−	0.580709i	$-0.197225\pi$
$29$	8.76824	1.62822	0.814111	+	0.580709i	$0.197225\pi$
$30$	3.49431	0.637971
$31$	9.92020	1.78172	0.890860	−	0.454277i	$-0.150103\pi$
$31$	9.92020	1.78172	0.890860	+	0.454277i	$0.150103\pi$
$32$	3.24060	0.572862
$33$	−0.0669844	−0.0116605
$34$	−1.60951	−0.276029
$35$	7.10909	1.20166
$36$	0.590533	0.0984221
$37$	−3.50206	−0.575735	−0.287868	−	0.957670i	$-0.592946\pi$
$37$	−3.50206	−0.575735	−0.287868	+	0.957670i	$0.592946\pi$
$38$	5.63510	0.914134
$39$	−0.443428	−0.0710053
$40$	4.92512	0.778730
$41$	−8.85328	−1.38265	−0.691325	−	0.722544i	$-0.742973\pi$
$41$	−8.85328	−1.38265	−0.691325	+	0.722544i	$0.742973\pi$
$42$	5.27038	0.813237
$43$	−0.643560	−0.0981420	−0.0490710	−	0.998795i	$-0.515626\pi$
$43$	−0.643560	−0.0981420	−0.0490710	+	0.998795i	$0.515626\pi$
$44$	0.0395565	0.00596337
$45$	2.17104	0.323639
$46$	7.09041	1.04542
$47$	−10.7581	−1.56924	−0.784618	−	0.619980i	$-0.787141\pi$
$47$	−10.7581	−1.56924	−0.784618	+	0.619980i	$0.787141\pi$
$48$	4.83234	0.697488
$49$	3.72245	0.531779
$50$	0.461284	0.0652355
$51$	−1.00000	−0.140028
$52$	0.261859	0.0363133
$53$	−10.1229	−1.39048	−0.695242	−	0.718776i	$-0.744703\pi$
$53$	−10.1229	−1.39048	−0.695242	+	0.718776i	$0.744703\pi$
$54$	1.60951	0.219027
$55$	0.145426	0.0196092
$56$	7.42842	0.992665
$57$	3.50112	0.463735
$58$	−14.1126	−1.85308
$59$	7.39311	0.962502	0.481251	−	0.876583i	$-0.340183\pi$
$59$	7.39311	0.962502	0.481251	+	0.876583i	$0.340183\pi$
$60$	−1.28207	−0.165514
$61$	−7.94758	−1.01758	−0.508791	−	0.860890i	$-0.669908\pi$
$61$	−7.94758	−1.01758	−0.508791	+	0.860890i	$0.669908\pi$
$62$	−15.9667	−2.02777
$63$	3.27452	0.412550
$64$	4.44889	0.556111
$65$	0.962699	0.119408
$66$	0.107812	0.0132708
$67$	−15.6509	−1.91207	−0.956033	−	0.293261i	$-0.905260\pi$
$67$	−15.6509	−1.91207	−0.956033	+	0.293261i	$0.905260\pi$
$68$	0.590533	0.0716126
$69$	4.40532	0.530338
$70$	−11.4422	−1.36760
$71$	−2.66761	−0.316587	−0.158293	−	0.987392i	$-0.550599\pi$
$71$	−2.66761	−0.316587	−0.158293	+	0.987392i	$0.550599\pi$
$72$	2.26856	0.267352
$73$	11.0205	1.28985	0.644925	−	0.764246i	$-0.276889\pi$
$73$	11.0205	1.28985	0.644925	+	0.764246i	$0.276889\pi$
$74$	5.63661	0.655243
$75$	0.286599	0.0330936
$76$	−2.06753	−0.237162
$77$	0.219342	0.0249963
$78$	0.713703	0.0808110
$79$	−6.51709	−0.733230	−0.366615	−	0.930373i	$-0.619483\pi$
$79$	−6.51709	−0.733230	−0.366615	+	0.930373i	$0.619483\pi$
$80$	−10.4912	−1.17295
$81$	1.00000	0.111111
$82$	14.2495	1.57359
$83$	−3.88084	−0.425978	−0.212989	−	0.977055i	$-0.568320\pi$
$83$	−3.88084	−0.425978	−0.212989	+	0.977055i	$0.568320\pi$
$84$	−1.93371	−0.210985
$85$	2.17104	0.235482
$86$	1.03582	0.111695
$87$	−8.76824	−0.940054
$88$	0.151958	0.0161988
$89$	−12.6880	−1.34492	−0.672462	−	0.740132i	$-0.734763\pi$
$89$	−12.6880	−1.34492	−0.672462	+	0.740132i	$0.734763\pi$
$90$	−3.49431	−0.368333
$91$	1.45201	0.152212
$92$	−2.60148	−0.271223
$93$	−9.92020	−1.02868
$94$	17.3154	1.78594
$95$	−7.60106	−0.779852
$96$	−3.24060	−0.330742
$97$	−10.3181	−1.04765	−0.523823	−	0.851827i	$-0.675495\pi$
$97$	−10.3181	−1.04765	−0.523823	+	0.851827i	$0.675495\pi$
$98$	−5.99134	−0.605217
$99$	0.0669844	0.00673219
$100$	−0.169246	−0.0169246
$101$	−4.57205	−0.454936	−0.227468	−	0.973786i	$-0.573045\pi$
$101$	−4.57205	−0.454936	−0.227468	+	0.973786i	$0.573045\pi$
$102$	1.60951	0.159366
$103$	−9.90284	−0.975756	−0.487878	−	0.872912i	$-0.662229\pi$
$103$	−9.90284	−0.975756	−0.487878	+	0.872912i	$0.662229\pi$
$104$	1.00594	0.0986407
$105$	−7.10909	−0.693777
$106$	16.2929	1.58251
$107$	−0.405221	−0.0391742	−0.0195871	−	0.999808i	$-0.506235\pi$
$107$	−0.405221	−0.0391742	−0.0195871	+	0.999808i	$0.506235\pi$
$108$	−0.590533	−0.0568241
$109$	−13.8464	−1.32625	−0.663123	−	0.748510i	$-0.730770\pi$
$109$	−13.8464	−1.32625	−0.663123	+	0.748510i	$0.730770\pi$
$110$	−0.234065	−0.0223172
$111$	3.50206	0.332401
$112$	−15.8236	−1.49519
$113$	−6.23069	−0.586134	−0.293067	−	0.956092i	$-0.594676\pi$
$113$	−6.23069	−0.586134	−0.293067	+	0.956092i	$0.594676\pi$
$114$	−5.63510	−0.527775
$115$	−9.56410	−0.891857
$116$	5.17794	0.480759
$117$	0.443428	0.0409949
$118$	−11.8993	−1.09542
$119$	3.27452	0.300174
$120$	−4.92512	−0.449600
$121$	−10.9955	−0.999592
$122$	12.7917	1.15811
$123$	8.85328	0.798274
$124$	5.85820	0.526082
$125$	−11.4774	−1.02657
$126$	−5.27038	−0.469522
$127$	0.307558	0.0272913	0.0136457	−	0.999907i	$-0.495656\pi$
$127$	0.307558	0.0272913	0.0136457	+	0.999907i	$0.495656\pi$
$128$	−13.6417	−1.20577
$129$	0.643560	0.0566623
$130$	−1.54948	−0.135898
$131$	1.76409	0.154130	0.0770648	−	0.997026i	$-0.475445\pi$
$131$	1.76409	0.154130	0.0770648	+	0.997026i	$0.475445\pi$
$132$	−0.0395565	−0.00344295
$133$	−11.4645	−0.994096
$134$	25.1904	2.17612
$135$	−2.17104	−0.186853
$136$	2.26856	0.194527
$137$	13.5368	1.15653	0.578264	−	0.815850i	$-0.303730\pi$
$137$	13.5368	1.15653	0.578264	+	0.815850i	$0.303730\pi$
$138$	−7.09041	−0.603576
$139$	−13.9370	−1.18212	−0.591062	−	0.806626i	$-0.701291\pi$
$139$	−13.9370	−1.18212	−0.591062	+	0.806626i	$0.701291\pi$
$140$	4.19815	0.354809
$141$	10.7581	0.905999
$142$	4.29355	0.360306
$143$	0.0297028	0.00248387
$144$	−4.83234	−0.402695
$145$	19.0362	1.58087
$146$	−17.7376	−1.46797
$147$	−3.72245	−0.307023
$148$	−2.06808	−0.169995
$149$	−15.3787	−1.25987	−0.629936	−	0.776647i	$-0.716919\pi$
$149$	−15.3787	−1.25987	−0.629936	+	0.776647i	$0.716919\pi$
$150$	−0.461284	−0.0376637
$151$	1.02768	0.0836313	0.0418157	−	0.999125i	$-0.486686\pi$
$151$	1.02768	0.0836313	0.0418157	+	0.999125i	$0.486686\pi$
$152$	−7.94249	−0.644221
$153$	1.00000	0.0808452
$154$	−0.353033	−0.0284482
$155$	21.5371	1.72990
$156$	−0.261859	−0.0209655
$157$	1.00000	0.0798087
$157$	1.00000	0.0798087
$158$	10.4893	0.834488
$159$	10.1229	0.802796
$160$	7.03546	0.556202
$161$	−14.4253	−1.13687
$162$	−1.60951	−0.126455
$163$	−15.8596	−1.24222	−0.621110	−	0.783723i	$-0.713318\pi$
$163$	−15.8596	−1.24222	−0.621110	+	0.783723i	$0.713318\pi$
$164$	−5.22815	−0.408250
$165$	−0.145426	−0.0113214
$166$	6.24627	0.484805
$167$	2.41485	0.186867	0.0934333	−	0.995626i	$-0.470216\pi$
$167$	2.41485	0.186867	0.0934333	+	0.995626i	$0.470216\pi$
$168$	−7.42842	−0.573115
$169$	−12.8034	−0.984875
$170$	−3.49431	−0.268002
$171$	−3.50112	−0.267737
$172$	−0.380043	−0.0289780
$173$	4.41983	0.336034	0.168017	−	0.985784i	$-0.446264\pi$
$173$	4.41983	0.336034	0.168017	+	0.985784i	$0.446264\pi$
$174$	14.1126	1.06987
$175$	−0.938472	−0.0709418
$176$	−0.323691	−0.0243992
$177$	−7.39311	−0.555701
$178$	20.4215	1.53065
$179$	17.2209	1.28715	0.643574	−	0.765384i	$-0.277451\pi$
$179$	17.2209	1.28715	0.643574	+	0.765384i	$0.277451\pi$
$180$	1.28207	0.0955598
$181$	12.4907	0.928429	0.464215	−	0.885723i	$-0.346337\pi$
$181$	12.4907	0.928429	0.464215	+	0.885723i	$0.346337\pi$
$182$	−2.33703	−0.173232
$183$	7.94758	0.587502
$184$	−9.99371	−0.736746
$185$	−7.60310	−0.558991
$186$	15.9667	1.17073
$187$	0.0669844	0.00489839
$188$	−6.35303	−0.463343
$189$	−3.27452	−0.238186
$190$	12.2340	0.887548
$191$	16.5568	1.19801	0.599003	−	0.800747i	$-0.295564\pi$
$191$	16.5568	1.19801	0.599003	+	0.800747i	$0.295564\pi$
$192$	−4.44889	−0.321071
$193$	2.28013	0.164127	0.0820636	−	0.996627i	$-0.473849\pi$
$193$	2.28013	0.164127	0.0820636	+	0.996627i	$0.473849\pi$
$194$	16.6071	1.19232
$195$	−0.962699	−0.0689403
$196$	2.19823	0.157017
$197$	9.31037	0.663337	0.331668	−	0.943396i	$-0.392389\pi$
$197$	9.31037	0.663337	0.331668	+	0.943396i	$0.392389\pi$
$198$	−0.107812	−0.00766189
$199$	−25.4449	−1.80374	−0.901870	−	0.432008i	$-0.857805\pi$
$199$	−25.4449	−1.80374	−0.901870	+	0.432008i	$0.857805\pi$
$200$	−0.650165	−0.0459736
$201$	15.6509	1.10393
$202$	7.35878	0.517762
$203$	28.7118	2.01517
$204$	−0.590533	−0.0413456
$205$	−19.2208	−1.34244
$206$	15.9388	1.11051
$207$	−4.40532	−0.306191
$208$	−2.14279	−0.148576
$209$	−0.234521	−0.0162221
$210$	11.4422	0.789586
$211$	19.0396	1.31074	0.655369	−	0.755309i	$-0.272513\pi$
$211$	19.0396	1.31074	0.655369	+	0.755309i	$0.272513\pi$
$212$	−5.97789	−0.410563
$213$	2.66761	0.182781
$214$	0.652209	0.0445841
$215$	−1.39719	−0.0952877
$216$	−2.26856	−0.154356
$217$	32.4839	2.20515
$218$	22.2860	1.50940
$219$	−11.0205	−0.744695
$220$	0.0858787	0.00578994
$221$	0.443428	0.0298282
$222$	−5.63661	−0.378305
$223$	27.9824	1.87384	0.936920	−	0.349543i	$-0.113663\pi$
$223$	27.9824	1.87384	0.936920	+	0.349543i	$0.113663\pi$
$224$	10.6114	0.709003
$225$	−0.286599	−0.0191066
$226$	10.0284	0.667078
$227$	−16.0912	−1.06801	−0.534004	−	0.845482i	$-0.679313\pi$
$227$	−16.0912	−1.06801	−0.534004	+	0.845482i	$0.679313\pi$
$228$	2.06753	0.136925
$229$	20.3353	1.34380	0.671899	−	0.740643i	$-0.265479\pi$
$229$	20.3353	1.34380	0.671899	+	0.740643i	$0.265479\pi$
$230$	15.3936	1.01502
$231$	−0.219342	−0.0144316
$232$	19.8913	1.30592
$233$	−1.86976	−0.122492	−0.0612460	−	0.998123i	$-0.519507\pi$
$233$	−1.86976	−0.122492	−0.0612460	+	0.998123i	$0.519507\pi$
$234$	−0.713703	−0.0466562
$235$	−23.3563	−1.52360
$236$	4.36588	0.284194
$237$	6.51709	0.423331
$238$	−5.27038	−0.341628
$239$	10.3252	0.667883	0.333941	−	0.942594i	$-0.391621\pi$
$239$	10.3252	0.667883	0.333941	+	0.942594i	$0.391621\pi$
$240$	10.4912	0.677203
$241$	−13.4017	−0.863279	−0.431639	−	0.902046i	$-0.642065\pi$
$241$	−13.4017	−0.863279	−0.431639	+	0.902046i	$0.642065\pi$
$242$	17.6974	1.13763
$243$	−1.00000	−0.0641500
$244$	−4.69330	−0.300458
$245$	8.08159	0.516314
$246$	−14.2495	−0.908513
$247$	−1.55249	−0.0987829
$248$	22.5045	1.42904
$249$	3.88084	0.245938
$250$	18.4730	1.16834
$251$	2.90309	0.183241	0.0916206	−	0.995794i	$-0.470795\pi$
$251$	2.90309	0.183241	0.0916206	+	0.995794i	$0.470795\pi$
$252$	1.93371	0.121812
$253$	−0.295088	−0.0185520
$254$	−0.495018	−0.0310602
$255$	−2.17104	−0.135956
$256$	13.0588	0.816174
$257$	−0.639767	−0.0399076	−0.0199538	−	0.999801i	$-0.506352\pi$
$257$	−0.639767	−0.0399076	−0.0199538	+	0.999801i	$0.506352\pi$
$258$	−1.03582	−0.0644872
$259$	−11.4676	−0.712559
$260$	0.568505	0.0352572
$261$	8.76824	0.542741
$262$	−2.83933	−0.175414
$263$	13.8260	0.852549	0.426274	−	0.904594i	$-0.359826\pi$
$263$	13.8260	0.852549	0.426274	+	0.904594i	$0.359826\pi$
$264$	−0.151958	−0.00935237
$265$	−21.9771	−1.35004
$266$	18.4522	1.13138
$267$	12.6880	0.776492
$268$	−9.24239	−0.564569
$269$	13.1386	0.801073	0.400536	−	0.916281i	$-0.368824\pi$
$269$	13.1386	0.801073	0.400536	+	0.916281i	$0.368824\pi$
$270$	3.49431	0.212657
$271$	8.33061	0.506049	0.253024	−	0.967460i	$-0.418575\pi$
$271$	8.33061	0.506049	0.253024	+	0.967460i	$0.418575\pi$
$272$	−4.83234	−0.293003
$273$	−1.45201	−0.0878798
$274$	−21.7877	−1.31624
$275$	−0.0191977	−0.00115766
$276$	2.60148	0.156591
$277$	−13.9593	−0.838730	−0.419365	−	0.907818i	$-0.637747\pi$
$277$	−13.9593	−0.838730	−0.419365	+	0.907818i	$0.637747\pi$
$278$	22.4319	1.34537
$279$	9.92020	0.593907
$280$	16.1274	0.963795
$281$	−26.8581	−1.60222	−0.801109	−	0.598518i	$-0.795756\pi$
$281$	−26.8581	−1.60222	−0.801109	+	0.598518i	$0.795756\pi$
$282$	−17.3154	−1.03111
$283$	−4.53638	−0.269660	−0.134830	−	0.990869i	$-0.543049\pi$
$283$	−4.53638	−0.269660	−0.134830	+	0.990869i	$0.543049\pi$
$284$	−1.57531	−0.0934774
$285$	7.60106	0.450248
$286$	−0.0478070	−0.00282689
$287$	−28.9902	−1.71124
$288$	3.24060	0.190954
$289$	1.00000	0.0588235
$290$	−30.6390	−1.79918
$291$	10.3181	0.604858
$292$	6.50795	0.380849
$293$	−11.6603	−0.681203	−0.340601	−	0.940208i	$-0.610631\pi$
$293$	−11.6603	−0.681203	−0.340601	+	0.940208i	$0.610631\pi$
$294$	5.99134	0.349422
$295$	16.0507	0.934509
$296$	−7.94462	−0.461772
$297$	−0.0669844	−0.00388683
$298$	24.7522	1.43386
$299$	−1.95344	−0.112970
$300$	0.169246	0.00977142
$301$	−2.10735	−0.121465
$302$	−1.65406	−0.0951806
$303$	4.57205	0.262658
$304$	16.9186	0.970348
$305$	−17.2545	−0.987989
$306$	−1.60951	−0.0920097
$307$	15.3874	0.878208	0.439104	−	0.898436i	$-0.355296\pi$
$307$	15.3874	0.878208	0.439104	+	0.898436i	$0.355296\pi$
$308$	0.129528	0.00738057
$309$	9.90284	0.563353
$310$	−34.6643	−1.96880
$311$	8.52143	0.483206	0.241603	−	0.970375i	$-0.422327\pi$
$311$	8.52143	0.483206	0.241603	+	0.970375i	$0.422327\pi$
$312$	−1.00594	−0.0569502
$313$	−16.7701	−0.947900	−0.473950	−	0.880552i	$-0.657172\pi$
$313$	−16.7701	−0.947900	−0.473950	+	0.880552i	$0.657172\pi$
$314$	−1.60951	−0.0908301
$315$	7.10909	0.400552
$316$	−3.84856	−0.216498
$317$	33.4976	1.88141	0.940707	−	0.339220i	$-0.110163\pi$
$317$	33.4976	1.88141	0.940707	+	0.339220i	$0.110163\pi$
$318$	−16.2929	−0.913660
$319$	0.587336	0.0328845
$320$	9.65870	0.539938
$321$	0.405221	0.0226172
$322$	23.2177	1.29387
$323$	−3.50112	−0.194808
$324$	0.590533	0.0328074
$325$	−0.127086	−0.00704946
$326$	25.5262	1.41377
$327$	13.8464	0.765709
$328$	−20.0842	−1.10896
$329$	−35.2277	−1.94217
$330$	0.234065	0.0128848
$331$	−17.3634	−0.954379	−0.477190	−	0.878800i	$-0.658344\pi$
$331$	−17.3634	−0.954379	−0.477190	+	0.878800i	$0.658344\pi$
$332$	−2.29177	−0.125777
$333$	−3.50206	−0.191912
$334$	−3.88673	−0.212672
$335$	−33.9787	−1.85646
$336$	15.8236	0.863246
$337$	−20.3177	−1.10677	−0.553387	−	0.832924i	$-0.686665\pi$
$337$	−20.3177	−1.10677	−0.553387	+	0.832924i	$0.686665\pi$
$338$	20.6072	1.12088
$339$	6.23069	0.338405
$340$	1.28207	0.0695299
$341$	0.664499	0.0359846
$342$	5.63510	0.304711
$343$	−10.7324	−0.579494
$344$	−1.45995	−0.0787153
$345$	9.56410	0.514914
$346$	−7.11378	−0.382439
$347$	8.12404	0.436121	0.218061	−	0.975935i	$-0.430027\pi$
$347$	8.12404	0.436121	0.218061	+	0.975935i	$0.430027\pi$
$348$	−5.17794	−0.277567
$349$	−9.01081	−0.482338	−0.241169	−	0.970483i	$-0.577531\pi$
$349$	−9.01081	−0.482338	−0.241169	+	0.970483i	$0.577531\pi$
$350$	1.51048	0.0807387
$351$	−0.443428	−0.0236684
$352$	0.217070	0.0115699
$353$	21.5948	1.14937	0.574687	−	0.818373i	$-0.305124\pi$
$353$	21.5948	1.14937	0.574687	+	0.818373i	$0.305124\pi$
$354$	11.8993	0.632441
$355$	−5.79147	−0.307379
$356$	−7.49267	−0.397111
$357$	−3.27452	−0.173306
$358$	−27.7172	−1.46490
$359$	3.96063	0.209034	0.104517	−	0.994523i	$-0.466670\pi$
$359$	3.96063	0.209034	0.104517	+	0.994523i	$0.466670\pi$
$360$	4.92512	0.259577
$361$	−6.74216	−0.354850
$362$	−20.1040	−1.05664
$363$	10.9955	0.577115
$364$	0.857461	0.0449432
$365$	23.9259	1.25234
$366$	−12.7917	−0.668634
$367$	−0.346579	−0.0180913	−0.00904564	−	0.999959i	$-0.502879\pi$
$367$	−0.346579	−0.0180913	−0.00904564	+	0.999959i	$0.502879\pi$
$368$	21.2880	1.10971
$369$	−8.85328	−0.460883
$370$	12.2373	0.636187
$371$	−33.1475	−1.72093
$372$	−5.85820	−0.303734
$373$	3.29447	0.170581	0.0852905	−	0.996356i	$-0.472818\pi$
$373$	3.29447	0.170581	0.0852905	+	0.996356i	$0.472818\pi$
$374$	−0.107812	−0.00557484
$375$	11.4774	0.592690
$376$	−24.4054	−1.25861
$377$	3.88808	0.200247
$378$	5.27038	0.271079
$379$	13.9258	0.715319	0.357660	−	0.933852i	$-0.383575\pi$
$379$	13.9258	0.715319	0.357660	+	0.933852i	$0.383575\pi$
$380$	−4.48868	−0.230264
$381$	−0.307558	−0.0157567
$382$	−26.6483	−1.36345
$383$	−17.7613	−0.907562	−0.453781	−	0.891113i	$-0.649925\pi$
$383$	−17.7613	−0.907562	−0.453781	+	0.891113i	$0.649925\pi$
$384$	13.6417	0.696152
$385$	0.476199	0.0242693
$386$	−3.66990	−0.186793
$387$	−0.643560	−0.0327140
$388$	−6.09318	−0.309335
$389$	21.5899	1.09465	0.547326	−	0.836920i	$-0.315646\pi$
$389$	21.5899	1.09465	0.547326	+	0.836920i	$0.315646\pi$
$390$	1.54948	0.0784608
$391$	−4.40532	−0.222786
$392$	8.44460	0.426517
$393$	−1.76409	−0.0889867
$394$	−14.9852	−0.754942
$395$	−14.1488	−0.711906
$396$	0.0395565	0.00198779
$397$	−17.2324	−0.864871	−0.432436	−	0.901665i	$-0.642346\pi$
$397$	−17.2324	−0.864871	−0.432436	+	0.901665i	$0.642346\pi$
$398$	40.9539	2.05283
$399$	11.4645	0.573942
$400$	1.38494	0.0692471
$401$	19.0021	0.948919	0.474460	−	0.880277i	$-0.342644\pi$
$401$	19.0021	0.948919	0.474460	+	0.880277i	$0.342644\pi$
$402$	−25.1904	−1.25638
$403$	4.39889	0.219125
$404$	−2.69995	−0.134327
$405$	2.17104	0.107880
$406$	−46.2119	−2.29346
$407$	−0.234584	−0.0116279
$408$	−2.26856	−0.112310
$409$	20.7015	1.02362	0.511811	−	0.859098i	$-0.328975\pi$
$409$	20.7015	1.02362	0.511811	+	0.859098i	$0.328975\pi$
$410$	30.9361	1.52783
$411$	−13.5368	−0.667722
$412$	−5.84795	−0.288108
$413$	24.2089	1.19124
$414$	7.09041	0.348475
$415$	−8.42546	−0.413589
$416$	1.43697	0.0704533
$417$	13.9370	0.682500
$418$	0.377464	0.0184624
$419$	20.9715	1.02452	0.512262	−	0.858829i	$-0.328808\pi$
$419$	20.9715	1.02452	0.512262	+	0.858829i	$0.328808\pi$
$420$	−4.19815	−0.204849
$421$	−32.3863	−1.57841	−0.789207	−	0.614127i	$-0.789508\pi$
$421$	−32.3863	−1.57841	−0.789207	+	0.614127i	$0.789508\pi$
$422$	−30.6445	−1.49175
$423$	−10.7581	−0.523079
$424$	−22.9643	−1.11524
$425$	−0.286599	−0.0139021
$426$	−4.29355	−0.208023
$427$	−26.0245	−1.25941
$428$	−0.239296	−0.0115668
$429$	−0.0297028	−0.00143406
$430$	2.24880	0.108447
$431$	16.5496	0.797166	0.398583	−	0.917132i	$-0.369502\pi$
$431$	16.5496	0.797166	0.398583	+	0.917132i	$0.369502\pi$
$432$	4.83234	0.232496
$433$	−17.0293	−0.818378	−0.409189	−	0.912450i	$-0.634188\pi$
$433$	−17.0293	−0.818378	−0.409189	+	0.912450i	$0.634188\pi$
$434$	−52.2832	−2.50967
$435$	−19.0362	−0.912715
$436$	−8.17677	−0.391596
$437$	15.4235	0.737808
$438$	17.7376	0.847536
$439$	20.6196	0.984118	0.492059	−	0.870562i	$-0.336244\pi$
$439$	20.6196	0.984118	0.492059	+	0.870562i	$0.336244\pi$
$440$	0.329906	0.0157277
$441$	3.72245	0.177260
$442$	−0.713703	−0.0339474
$443$	−13.8670	−0.658841	−0.329420	−	0.944183i	$-0.606853\pi$
$443$	−13.8670	−0.658841	−0.329420	+	0.944183i	$0.606853\pi$
$444$	2.06808	0.0981468
$445$	−27.5461	−1.30581
$446$	−45.0381	−2.13261
$447$	15.3787	0.727387
$448$	14.5680	0.688271
$449$	−22.0658	−1.04135	−0.520675	−	0.853755i	$-0.674319\pi$
$449$	−22.0658	−1.04135	−0.520675	+	0.853755i	$0.674319\pi$
$450$	0.461284	0.0217452
$451$	−0.593032	−0.0279248
$452$	−3.67943	−0.173066
$453$	−1.02768	−0.0482846
$454$	25.8990	1.21550
$455$	3.15237	0.147785
$456$	7.94249	0.371941
$457$	37.4863	1.75353	0.876767	−	0.480915i	$-0.159695\pi$
$457$	37.4863	1.75353	0.876767	+	0.480915i	$0.159695\pi$
$458$	−32.7300	−1.52937
$459$	−1.00000	−0.0466760
$460$	−5.64792	−0.263335
$461$	16.2066	0.754818	0.377409	−	0.926047i	$-0.376815\pi$
$461$	16.2066	0.754818	0.377409	+	0.926047i	$0.376815\pi$
$462$	0.353033	0.0164246
$463$	−5.22576	−0.242861	−0.121431	−	0.992600i	$-0.538748\pi$
$463$	−5.22576	−0.242861	−0.121431	+	0.992600i	$0.538748\pi$
$464$	−42.3711	−1.96703
$465$	−21.5371	−0.998760
$466$	3.00940	0.139408
$467$	−0.858711	−0.0397364	−0.0198682	−	0.999803i	$-0.506325\pi$
$467$	−0.858711	−0.0397364	−0.0198682	+	0.999803i	$0.506325\pi$
$468$	0.261859	0.0121044
$469$	−51.2492	−2.36647
$470$	37.5923	1.73400
$471$	−1.00000	−0.0460776
$472$	16.7717	0.771980
$473$	−0.0431085	−0.00198213
$474$	−10.4893	−0.481792
$475$	1.00342	0.0460399
$476$	1.93371	0.0886314
$477$	−10.1229	−0.463494
$478$	−16.6186	−0.760116
$479$	−16.8868	−0.771579	−0.385789	−	0.922587i	$-0.626071\pi$
$479$	−16.8868	−0.771579	−0.385789	+	0.922587i	$0.626071\pi$
$480$	−7.03546	−0.321123
$481$	−1.55291	−0.0708067
$482$	21.5702	0.982496
$483$	14.4253	0.656373
$484$	−6.49321	−0.295146
$485$	−22.4010	−1.01718
$486$	1.60951	0.0730090
$487$	8.20424	0.371770	0.185885	−	0.982572i	$-0.440485\pi$
$487$	8.20424	0.371770	0.185885	+	0.982572i	$0.440485\pi$
$488$	−18.0295	−0.816158
$489$	15.8596	0.717196
$490$	−13.0074	−0.587615
$491$	−10.5890	−0.477875	−0.238937	−	0.971035i	$-0.576799\pi$
$491$	−10.5890	−0.477875	−0.238937	+	0.971035i	$0.576799\pi$
$492$	5.22815	0.235703
$493$	8.76824	0.394902
$494$	2.49876	0.112425
$495$	0.145426	0.00653640
$496$	−47.9377	−2.15247
$497$	−8.73512	−0.391824
$498$	−6.24627	−0.279902
$499$	42.4502	1.90033	0.950167	−	0.311742i	$-0.100912\pi$
$499$	42.4502	1.90033	0.950167	+	0.311742i	$0.100912\pi$
$500$	−6.77778	−0.303112
$501$	−2.41485	−0.107888
$502$	−4.67256	−0.208546
$503$	2.89522	0.129091	0.0645457	−	0.997915i	$-0.479440\pi$
$503$	2.89522	0.129091	0.0645457	+	0.997915i	$0.479440\pi$
$504$	7.42842	0.330888
$505$	−9.92609	−0.441705
$506$	0.474947	0.0211140
$507$	12.8034	0.568618
$508$	0.181623	0.00805821
$509$	20.6225	0.914074	0.457037	−	0.889448i	$-0.348911\pi$
$509$	20.6225	0.914074	0.457037	+	0.889448i	$0.348911\pi$
$510$	3.49431	0.154731
$511$	36.0867	1.59638
$512$	6.26519	0.276885
$513$	3.50112	0.154578
$514$	1.02971	0.0454187
$515$	−21.4994	−0.947378
$516$	0.380043	0.0167305
$517$	−0.720628	−0.0316932
$518$	18.4572	0.810962
$519$	−4.41983	−0.194009
$520$	2.18394	0.0957719
$521$	2.79472	0.122439	0.0612196	−	0.998124i	$-0.480501\pi$
$521$	2.79472	0.122439	0.0612196	+	0.998124i	$0.480501\pi$
$522$	−14.1126	−0.617692
$523$	−13.1975	−0.577086	−0.288543	−	0.957467i	$-0.593171\pi$
$523$	−13.1975	−0.577086	−0.288543	+	0.957467i	$0.593171\pi$
$524$	1.04175	0.0455093
$525$	0.938472	0.0409583
$526$	−22.2532	−0.970284
$527$	9.92020	0.432131
$528$	0.323691	0.0140869
$529$	−3.59319	−0.156226
$530$	35.3725	1.53648
$531$	7.39311	0.320834
$532$	−6.77015	−0.293523
$533$	−3.92579	−0.170045
$534$	−20.4215	−0.883724
$535$	−0.879750	−0.0380349
$536$	−35.5050	−1.53358
$537$	−17.2209	−0.743135
$538$	−21.1467	−0.911699
$539$	0.249347	0.0107401
$540$	−1.28207	−0.0551714
$541$	−11.7990	−0.507277	−0.253638	−	0.967299i	$-0.581627\pi$
$541$	−11.7990	−0.507277	−0.253638	+	0.967299i	$0.581627\pi$
$542$	−13.4082	−0.575933
$543$	−12.4907	−0.536029
$544$	3.24060	0.138939
$545$	−30.0611	−1.28768
$546$	2.33703	0.100016
$547$	25.4673	1.08890	0.544452	−	0.838792i	$-0.316738\pi$
$547$	25.4673	1.08890	0.544452	+	0.838792i	$0.316738\pi$
$548$	7.99393	0.341484
$549$	−7.94758	−0.339194
$550$	0.0308989	0.00131753
$551$	−30.6987	−1.30781
$552$	9.99371	0.425360
$553$	−21.3403	−0.907483
$554$	22.4676	0.954557
$555$	7.60310	0.322734
$556$	−8.23028	−0.349042
$557$	33.5873	1.42314	0.711571	−	0.702614i	$-0.247984\pi$
$557$	33.5873	1.42314	0.711571	+	0.702614i	$0.247984\pi$
$558$	−15.9667	−0.675924
$559$	−0.285373	−0.0120700
$560$	−34.3535	−1.45170
$561$	−0.0669844	−0.00282809
$562$	43.2284	1.82348
$563$	−15.6933	−0.661392	−0.330696	−	0.943737i	$-0.607284\pi$
$563$	−15.6933	−0.661392	−0.330696	+	0.943737i	$0.607284\pi$
$564$	6.35303	0.267511
$565$	−13.5271	−0.569087
$566$	7.30137	0.306899
$567$	3.27452	0.137517
$568$	−6.05161	−0.253920
$569$	14.0025	0.587016	0.293508	−	0.955957i	$-0.405177\pi$
$569$	14.0025	0.587016	0.293508	+	0.955957i	$0.405177\pi$
$570$	−12.2340	−0.512426
$571$	−37.9480	−1.58807	−0.794037	−	0.607870i	$-0.792024\pi$
$571$	−37.9480	−1.58807	−0.794037	+	0.607870i	$0.792024\pi$
$572$	0.0175405	0.000733404 0
$573$	−16.5568	−0.691669
$574$	46.6601	1.94756
$575$	1.26256	0.0526523
$576$	4.44889	0.185370
$577$	−5.35312	−0.222853	−0.111427	−	0.993773i	$-0.535542\pi$
$577$	−5.35312	−0.222853	−0.111427	+	0.993773i	$0.535542\pi$
$578$	−1.60951	−0.0669469
$579$	−2.28013	−0.0947589
$580$	11.2415	0.466777
$581$	−12.7079	−0.527212
$582$	−16.6071	−0.688388
$583$	−0.678075	−0.0280830
$584$	25.0006	1.03453
$585$	0.962699	0.0398027
$586$	18.7674	0.775275
$587$	26.0412	1.07484	0.537418	−	0.843316i	$-0.319400\pi$
$587$	26.0412	1.07484	0.537418	+	0.843316i	$0.319400\pi$
$588$	−2.19823	−0.0906535
$589$	−34.7318	−1.43110
$590$	−25.8339	−1.06356
$591$	−9.31037	−0.382978
$592$	16.9231	0.695537
$593$	9.03662	0.371089	0.185545	−	0.982636i	$-0.440595\pi$
$593$	9.03662	0.371089	0.185545	+	0.982636i	$0.440595\pi$
$594$	0.107812	0.00442359
$595$	7.10909	0.291444
$596$	−9.08162	−0.371998
$597$	25.4449	1.04139
$598$	3.14409	0.128571
$599$	−15.7529	−0.643645	−0.321823	−	0.946800i	$-0.604295\pi$
$599$	−15.7529	−0.643645	−0.321823	+	0.946800i	$0.604295\pi$
$600$	0.650165	0.0265429
$601$	4.91630	0.200540	0.100270	−	0.994960i	$-0.468029\pi$
$601$	4.91630	0.200540	0.100270	+	0.994960i	$0.468029\pi$
$602$	3.39180	0.138240
$603$	−15.6509	−0.637355
$604$	0.606878	0.0246935
$605$	−23.8717	−0.970521
$606$	−7.35878	−0.298930
$607$	−45.4549	−1.84496	−0.922480	−	0.386046i	$-0.873841\pi$
$607$	−45.4549	−1.84496	−0.922480	+	0.386046i	$0.873841\pi$
$608$	−11.3457	−0.460130
$609$	−28.7118	−1.16346
$610$	27.7713	1.12443
$611$	−4.77046	−0.192992
$612$	0.590533	0.0238709
$613$	37.9669	1.53347	0.766734	−	0.641965i	$-0.221880\pi$
$613$	37.9669	1.53347	0.766734	+	0.641965i	$0.221880\pi$
$614$	−24.7663	−0.999486
$615$	19.2208	0.775058
$616$	0.497589	0.0200484
$617$	22.4257	0.902824	0.451412	−	0.892316i	$-0.350920\pi$
$617$	22.4257	0.902824	0.451412	+	0.892316i	$0.350920\pi$
$618$	−15.9388	−0.641151
$619$	24.8136	0.997342	0.498671	−	0.866791i	$-0.333822\pi$
$619$	24.8136	0.997342	0.498671	+	0.866791i	$0.333822\pi$
$620$	12.7184	0.510782
$621$	4.40532	0.176779
$622$	−13.7154	−0.549935
$623$	−41.5470	−1.66455
$624$	2.14279	0.0857804
$625$	−23.4849	−0.939395
$626$	26.9916	1.07880
$627$	0.234521	0.00936585
$628$	0.590533	0.0235648
$629$	−3.50206	−0.139636
$630$	−11.4422	−0.455867
$631$	−2.38149	−0.0948057	−0.0474028	−	0.998876i	$-0.515094\pi$
$631$	−2.38149	−0.0948057	−0.0474028	+	0.998876i	$0.515094\pi$
$632$	−14.7844	−0.588091
$633$	−19.0396	−0.756755
$634$	−53.9149	−2.14123
$635$	0.667719	0.0264976
$636$	5.97789	0.237039
$637$	1.65064	0.0654008
$638$	−0.945325	−0.0374258
$639$	−2.66761	−0.105529
$640$	−29.6167	−1.17070
$641$	3.98300	0.157319	0.0786595	−	0.996902i	$-0.474936\pi$
$641$	3.98300	0.157319	0.0786595	+	0.996902i	$0.474936\pi$
$642$	−0.652209	−0.0257406
$643$	37.9999	1.49857	0.749285	−	0.662248i	$-0.230397\pi$
$643$	37.9999	1.49857	0.749285	+	0.662248i	$0.230397\pi$
$644$	−8.51860	−0.335680
$645$	1.39719	0.0550144
$646$	5.63510	0.221710
$647$	21.9666	0.863598	0.431799	−	0.901970i	$-0.357879\pi$
$647$	21.9666	0.863598	0.431799	+	0.901970i	$0.357879\pi$
$648$	2.26856	0.0891173
$649$	0.495224	0.0194392
$650$	0.204546	0.00802297
$651$	−32.4839	−1.27314
$652$	−9.36562	−0.366786
$653$	11.2081	0.438607	0.219303	−	0.975657i	$-0.429622\pi$
$653$	11.2081	0.438607	0.219303	+	0.975657i	$0.429622\pi$
$654$	−22.2860	−0.871451
$655$	3.82991	0.149647
$656$	42.7820	1.67036
$657$	11.0205	0.429950
$658$	56.6994	2.21037
$659$	−13.9551	−0.543612	−0.271806	−	0.962352i	$-0.587621\pi$
$659$	−13.9551	−0.543612	−0.271806	+	0.962352i	$0.587621\pi$
$660$	−0.0858787	−0.00334282
$661$	−17.8764	−0.695311	−0.347656	−	0.937622i	$-0.613022\pi$
$661$	−17.8764	−0.695311	−0.347656	+	0.937622i	$0.613022\pi$
$662$	27.9466	1.08618
$663$	−0.443428	−0.0172213
$664$	−8.80391	−0.341658
$665$	−24.8898	−0.965185
$666$	5.63661	0.218414
$667$	−38.6269	−1.49564
$668$	1.42605	0.0551754
$669$	−27.9824	−1.08186
$670$	54.6892	2.11283
$671$	−0.532364	−0.0205517
$672$	−10.6114	−0.409343
$673$	11.4088	0.439776	0.219888	−	0.975525i	$-0.429431\pi$
$673$	11.4088	0.439776	0.219888	+	0.975525i	$0.429431\pi$
$674$	32.7016	1.25962
$675$	0.286599	0.0110312
$676$	−7.56081	−0.290800
$677$	−37.2245	−1.43065	−0.715327	−	0.698790i	$-0.753722\pi$
$677$	−37.2245	−1.43065	−0.715327	+	0.698790i	$0.753722\pi$
$678$	−10.0284	−0.385137
$679$	−33.7868	−1.29662
$680$	4.92512	0.188870
$681$	16.0912	0.616615
$682$	−1.06952	−0.0409540
$683$	−16.0374	−0.613655	−0.306828	−	0.951765i	$-0.599267\pi$
$683$	−16.0374	−0.613655	−0.306828	+	0.951765i	$0.599267\pi$
$684$	−2.06753	−0.0790539
$685$	29.3889	1.12289
$686$	17.2739	0.659521
$687$	−20.3353	−0.775842
$688$	3.10990	0.118564
$689$	−4.48876	−0.171008
$690$	−15.3936	−0.586022
$691$	1.77741	0.0676160	0.0338080	−	0.999428i	$-0.489237\pi$
$691$	1.77741	0.0676160	0.0338080	+	0.999428i	$0.489237\pi$
$692$	2.61006	0.0992195
$693$	0.219342	0.00833210
$694$	−13.0758	−0.496349
$695$	−30.2578	−1.14775
$696$	−19.8913	−0.753976
$697$	−8.85328	−0.335342
$698$	14.5030	0.548947
$699$	1.86976	0.0707208
$700$	−0.554198	−0.0209467
$701$	35.0386	1.32339	0.661695	−	0.749773i	$-0.269837\pi$
$701$	35.0386	1.32339	0.661695	+	0.749773i	$0.269837\pi$
$702$	0.713703	0.0269370
$703$	12.2611	0.462437
$704$	0.298006	0.0112315
$705$	23.3563	0.879650
$706$	−34.7571	−1.30810
$707$	−14.9713	−0.563052
$708$	−4.36588	−0.164080
$709$	−47.9107	−1.79932	−0.899661	−	0.436589i	$-0.856187\pi$
$709$	−47.9107	−1.79932	−0.899661	+	0.436589i	$0.856187\pi$
$710$	9.32145	0.349828
$711$	−6.51709	−0.244410
$712$	−28.7834	−1.07870
$713$	−43.7016	−1.63664
$714$	5.27038	0.197239
$715$	0.0644858	0.00241163
$716$	10.1695	0.380052
$717$	−10.3252	−0.385602
$718$	−6.37469	−0.237901
$719$	36.8251	1.37334	0.686672	−	0.726967i	$-0.259071\pi$
$719$	36.8251	1.37334	0.686672	+	0.726967i	$0.259071\pi$
$720$	−10.4912	−0.390983
$721$	−32.4270	−1.20765
$722$	10.8516	0.403854
$723$	13.4017	0.498414
$724$	7.37619	0.274134
$725$	−2.51297	−0.0933292
$726$	−17.6974	−0.656813
$727$	−7.33881	−0.272181	−0.136091	−	0.990696i	$-0.543454\pi$
$727$	−7.33881	−0.272181	−0.136091	+	0.990696i	$0.543454\pi$
$728$	3.29397	0.122083
$729$	1.00000	0.0370370
$730$	−38.5090	−1.42528
$731$	−0.643560	−0.0238029
$732$	4.69330	0.173470
$733$	−47.0217	−1.73679	−0.868394	−	0.495876i	$-0.834847\pi$
$733$	−47.0217	−1.73679	−0.868394	+	0.495876i	$0.834847\pi$
$734$	0.557823	0.0205896
$735$	−8.08159	−0.298094
$736$	−14.2759	−0.526215
$737$	−1.04837	−0.0386172
$738$	14.2495	0.524530
$739$	−7.96828	−0.293118	−0.146559	−	0.989202i	$-0.546820\pi$
$739$	−7.96828	−0.293118	−0.146559	+	0.989202i	$0.546820\pi$
$740$	−4.48988	−0.165051
$741$	1.55249	0.0570323
$742$	53.3513	1.95859
$743$	32.1751	1.18039	0.590195	−	0.807261i	$-0.299051\pi$
$743$	32.1751	1.18039	0.590195	+	0.807261i	$0.299051\pi$
$744$	−22.5045	−0.825056
$745$	−33.3877	−1.22323
$746$	−5.30249	−0.194138
$747$	−3.88084	−0.141993
$748$	0.0395565	0.00144633
$749$	−1.32690	−0.0484840
$750$	−18.4730	−0.674540
$751$	18.9490	0.691457	0.345729	−	0.938335i	$-0.387632\pi$
$751$	18.9490	0.691457	0.345729	+	0.938335i	$0.387632\pi$
$752$	51.9869	1.89577
$753$	−2.90309	−0.105794
$754$	−6.25792	−0.227900
$755$	2.23113	0.0811991
$756$	−1.93371	−0.0703283
$757$	−16.7262	−0.607925	−0.303963	−	0.952684i	$-0.598310\pi$
$757$	−16.7262	−0.607925	−0.303963	+	0.952684i	$0.598310\pi$
$758$	−22.4137	−0.814103
$759$	0.295088	0.0107110
$760$	−17.2434	−0.625485
$761$	9.47778	0.343569	0.171785	−	0.985135i	$-0.445047\pi$
$761$	9.47778	0.343569	0.171785	+	0.985135i	$0.445047\pi$
$762$	0.495018	0.0179326
$763$	−45.3403	−1.64143
$764$	9.77732	0.353731
$765$	2.17104	0.0784940
$766$	28.5871	1.03289
$767$	3.27831	0.118373
$768$	−13.0588	−0.471218
$769$	−39.5360	−1.42570	−0.712851	−	0.701315i	$-0.752597\pi$
$769$	−39.5360	−1.42570	−0.712851	+	0.701315i	$0.752597\pi$
$770$	−0.766448	−0.0276209
$771$	0.639767	0.0230407
$772$	1.34649	0.0484613
$773$	24.1185	0.867481	0.433740	−	0.901038i	$-0.357194\pi$
$773$	24.1185	0.867481	0.433740	+	0.901038i	$0.357194\pi$
$774$	1.03582	0.0372317
$775$	−2.84312	−0.102128
$776$	−23.4072	−0.840270
$777$	11.4676	0.411396
$778$	−34.7492	−1.24582
$779$	30.9964	1.11056
$780$	−0.568505	−0.0203557
$781$	−0.178688	−0.00639396
$782$	7.09041	0.253553
$783$	−8.76824	−0.313351
$784$	−17.9882	−0.642434
$785$	2.17104	0.0774876
$786$	2.83933	0.101276
$787$	−22.3996	−0.798459	−0.399230	−	0.916851i	$-0.630722\pi$
$787$	−22.3996	−0.798459	−0.399230	+	0.916851i	$0.630722\pi$
$788$	5.49808	0.195861
$789$	−13.8260	−0.492219
$790$	22.7728	0.810218
$791$	−20.4025	−0.725429
$792$	0.151958	0.00539959
$793$	−3.52418	−0.125147
$794$	27.7358	0.984308
$795$	21.9771	0.779448
$796$	−15.0260	−0.532584
$797$	−7.86697	−0.278662	−0.139331	−	0.990246i	$-0.544495\pi$
$797$	−7.86697	−0.278662	−0.139331	+	0.990246i	$0.544495\pi$
$798$	−18.4522	−0.653202
$799$	−10.7581	−0.380596
$800$	−0.928751	−0.0328363
$801$	−12.6880	−0.448308
$802$	−30.5841	−1.07996
$803$	0.738201	0.0260505
$804$	9.24239	0.325954
$805$	−31.3178	−1.10381
$806$	−7.08008	−0.249385
$807$	−13.1386	−0.462500
$808$	−10.3720	−0.364884
$809$	−14.1202	−0.496441	−0.248220	−	0.968704i	$-0.579846\pi$
$809$	−14.1202	−0.496441	−0.248220	+	0.968704i	$0.579846\pi$
$810$	−3.49431	−0.122778
$811$	−44.7232	−1.57044	−0.785222	−	0.619214i	$-0.787451\pi$
$811$	−44.7232	−1.57044	−0.785222	+	0.619214i	$0.787451\pi$
$812$	16.9552	0.595012
$813$	−8.33061	−0.292167
$814$	0.377565	0.0132337
$815$	−34.4318	−1.20609
$816$	4.83234	0.169166
$817$	2.25318	0.0788288
$818$	−33.3193	−1.16498
$819$	1.45201	0.0507374
$820$	−11.3505	−0.396377
$821$	−24.8849	−0.868488	−0.434244	−	0.900795i	$-0.642985\pi$
$821$	−24.8849	−0.868488	−0.434244	+	0.900795i	$0.642985\pi$
$822$	21.7877	0.759933
$823$	−4.27302	−0.148948	−0.0744741	−	0.997223i	$-0.523728\pi$
$823$	−4.27302	−0.148948	−0.0744741	+	0.997223i	$0.523728\pi$
$824$	−22.4652	−0.782611
$825$	0.0191977	0.000668376 0
$826$	−38.9645	−1.35575
$827$	46.9913	1.63405	0.817024	−	0.576604i	$-0.195623\pi$
$827$	46.9913	1.63405	0.817024	+	0.576604i	$0.195623\pi$
$828$	−2.60148	−0.0904078
$829$	12.9630	0.450224	0.225112	−	0.974333i	$-0.427725\pi$
$829$	12.9630	0.450224	0.225112	+	0.974333i	$0.427725\pi$
$830$	13.5609	0.470705
$831$	13.9593	0.484241
$832$	1.97276	0.0683932
$833$	3.72245	0.128975
$834$	−22.4319	−0.776752
$835$	5.24273	0.181432
$836$	−0.138492	−0.00478985
$837$	−9.92020	−0.342892
$838$	−33.7539	−1.16601
$839$	−37.1402	−1.28222	−0.641111	−	0.767448i	$-0.721526\pi$
$839$	−37.1402	−1.28222	−0.641111	+	0.767448i	$0.721526\pi$
$840$	−16.1274	−0.556447
$841$	47.8821	1.65111
$842$	52.1263	1.79639
$843$	26.8581	0.925041
$844$	11.2435	0.387017
$845$	−27.7966	−0.956232
$846$	17.3154	0.595315
$847$	−36.0050	−1.23715
$848$	48.9171	1.67982
$849$	4.53638	0.155688
$850$	0.461284	0.0158219
$851$	15.4277	0.528854
$852$	1.57531	0.0539692
$853$	−52.0333	−1.78159	−0.890793	−	0.454409i	$-0.849850\pi$
$853$	−52.0333	−1.78159	−0.890793	+	0.454409i	$0.849850\pi$
$854$	41.8867	1.43333
$855$	−7.60106	−0.259951
$856$	−0.919267	−0.0314199
$857$	14.3706	0.490890	0.245445	−	0.969411i	$-0.421066\pi$
$857$	14.3706	0.490890	0.245445	+	0.969411i	$0.421066\pi$
$858$	0.0478070	0.00163210
$859$	31.8322	1.08610	0.543050	−	0.839700i	$-0.317269\pi$
$859$	31.8322	1.08610	0.543050	+	0.839700i	$0.317269\pi$
$860$	−0.825088	−0.0281353
$861$	28.9902	0.987984
$862$	−26.6368	−0.907253
$863$	8.00074	0.272348	0.136174	−	0.990685i	$-0.456519\pi$
$863$	8.00074	0.272348	0.136174	+	0.990685i	$0.456519\pi$
$864$	−3.24060	−0.110247
$865$	9.59562	0.326261
$866$	27.4089	0.931394
$867$	−1.00000	−0.0339618
$868$	19.1828	0.651106
$869$	−0.436544	−0.0148087
$870$	30.6390	1.03876
$871$	−6.94006	−0.235155
$872$	−31.4114	−1.06372
$873$	−10.3181	−0.349215
$874$	−24.8244	−0.839698
$875$	−37.5829	−1.27053
$876$	−6.50795	−0.219883
$877$	−31.0189	−1.04743	−0.523717	−	0.851892i	$-0.675455\pi$
$877$	−31.0189	−1.04743	−0.523717	+	0.851892i	$0.675455\pi$
$878$	−33.1875	−1.12002
$879$	11.6603	0.393293
$880$	−0.702746	−0.0236896
$881$	−6.54277	−0.220432	−0.110216	−	0.993908i	$-0.535154\pi$
$881$	−6.54277	−0.220432	−0.110216	+	0.993908i	$0.535154\pi$
$882$	−5.99134	−0.201739
$883$	0.496200	0.0166985	0.00834923	−	0.999965i	$-0.497342\pi$
$883$	0.496200	0.0166985	0.00834923	+	0.999965i	$0.497342\pi$
$884$	0.261859	0.00880726
$885$	−16.0507	−0.539539
$886$	22.3191	0.749825
$887$	16.5058	0.554211	0.277105	−	0.960840i	$-0.410625\pi$
$887$	16.5058	0.554211	0.277105	+	0.960840i	$0.410625\pi$
$888$	7.94462	0.266604
$889$	1.00710	0.0337771
$890$	44.3358	1.48614
$891$	0.0669844	0.00224406
$892$	16.5245	0.553282
$893$	37.6655	1.26043
$894$	−24.7522	−0.827838
$895$	37.3871	1.24971
$896$	−44.6701	−1.49232
$897$	1.95344	0.0652235
$898$	35.5152	1.18516
$899$	86.9827	2.90104
$900$	−0.169246	−0.00564153
$901$	−10.1229	−0.337242
$902$	0.954493	0.0317811
$903$	2.10735	0.0701281
$904$	−14.1347	−0.470112
$905$	27.1179	0.901428
$906$	1.65406	0.0549526
$907$	37.1504	1.23356	0.616779	−	0.787136i	$-0.288437\pi$
$907$	37.1504	1.23356	0.616779	+	0.787136i	$0.288437\pi$
$908$	−9.50237	−0.315347
$909$	−4.57205	−0.151645
$910$	−5.07378	−0.168194
$911$	−11.7297	−0.388622	−0.194311	−	0.980940i	$-0.562247\pi$
$911$	−11.7297	−0.388622	−0.194311	+	0.980940i	$0.562247\pi$
$912$	−16.9186	−0.560231
$913$	−0.259956	−0.00860329
$914$	−60.3347	−1.99569
$915$	17.2545	0.570416
$916$	12.0087	0.396778
$917$	5.77655	0.190759
$918$	1.60951	0.0531219
$919$	21.8157	0.719634	0.359817	−	0.933023i	$-0.382839\pi$
$919$	21.8157	0.719634	0.359817	+	0.933023i	$0.382839\pi$
$920$	−21.6967	−0.715319
$921$	−15.3874	−0.507033
$922$	−26.0848	−0.859057
$923$	−1.18289	−0.0389353
$924$	−0.129528	−0.00426117
$925$	1.00369	0.0330010
$926$	8.41092	0.276400
$927$	−9.90284	−0.325252
$928$	28.4144	0.932747
$929$	41.0704	1.34747	0.673737	−	0.738971i	$-0.264688\pi$
$929$	41.0704	1.34747	0.673737	+	0.738971i	$0.264688\pi$
$930$	34.6643	1.13669
$931$	−13.0328	−0.427131
$932$	−1.10415	−0.0361678
$933$	−8.52143	−0.278979
$934$	1.38211	0.0452239
$935$	0.145426	0.00475593
$936$	1.00594	0.0328802
$937$	−18.3496	−0.599456	−0.299728	−	0.954025i	$-0.596896\pi$
$937$	−18.3496	−0.599456	−0.299728	+	0.954025i	$0.596896\pi$
$938$	82.4863	2.69327
$939$	16.7701	0.547270
$940$	−13.7927	−0.449867
$941$	1.36282	0.0444267	0.0222133	−	0.999753i	$-0.492929\pi$
$941$	1.36282	0.0444267	0.0222133	+	0.999753i	$0.492929\pi$
$942$	1.60951	0.0524408
$943$	39.0015	1.27006
$944$	−35.7260	−1.16278
$945$	−7.10909	−0.231259
$946$	0.0693837	0.00225586
$947$	8.20840	0.266737	0.133369	−	0.991067i	$-0.457421\pi$
$947$	8.20840	0.266737	0.133369	+	0.991067i	$0.457421\pi$
$948$	3.84856	0.124995
$949$	4.88679	0.158632
$950$	−1.61501	−0.0523979
$951$	−33.4976	−1.08624
$952$	7.42842	0.240757
$953$	−58.9189	−1.90857	−0.954284	−	0.298900i	$-0.903380\pi$
$953$	−58.9189	−1.90857	−0.954284	+	0.298900i	$0.903380\pi$
$954$	16.2929	0.527502
$955$	35.9454	1.16316
$956$	6.09738	0.197203
$957$	−0.587336	−0.0189859
$958$	27.1796	0.878132
$959$	44.3265	1.43138
$960$	−9.65870	−0.311733
$961$	67.4104	2.17453
$962$	2.49943	0.0805849
$963$	−0.405221	−0.0130581
$964$	−7.91414	−0.254897
$965$	4.95024	0.159354
$966$	−23.2177	−0.747016
$967$	25.3510	0.815233	0.407616	−	0.913153i	$-0.366360\pi$
$967$	25.3510	0.815233	0.407616	+	0.913153i	$0.366360\pi$
$968$	−24.9439	−0.801729
$969$	3.50112	0.112472
$970$	36.0547	1.15765
$971$	4.92467	0.158040	0.0790201	−	0.996873i	$-0.474821\pi$
$971$	4.92467	0.158040	0.0790201	+	0.996873i	$0.474821\pi$
$972$	−0.590533	−0.0189414
$973$	−45.6371	−1.46306
$974$	−13.2048	−0.423110
$975$	0.127086	0.00407000
$976$	38.4054	1.22933
$977$	8.17517	0.261547	0.130773	−	0.991412i	$-0.458254\pi$
$977$	8.17517	0.261547	0.130773	+	0.991412i	$0.458254\pi$
$978$	−25.5262	−0.816239
$979$	−0.849897	−0.0271628
$980$	4.77244	0.152450
$981$	−13.8464	−0.442082
$982$	17.0431	0.543868
$983$	−14.0328	−0.447576	−0.223788	−	0.974638i	$-0.571842\pi$
$983$	−14.0328	−0.447576	−0.223788	+	0.974638i	$0.571842\pi$
$984$	20.0842	0.640260
$985$	20.2132	0.644045
$986$	−14.1126	−0.449437
$987$	35.2277	1.12131
$988$	−0.916799	−0.0291673
$989$	2.83509	0.0901505
$990$	−0.234065	−0.00743906
$991$	−16.2156	−0.515105	−0.257553	−	0.966264i	$-0.582916\pi$
$991$	−16.2156	−0.515105	−0.257553	+	0.966264i	$0.582916\pi$
$992$	32.1474	1.02068
$993$	17.3634	0.551011
$994$	14.0593	0.445933
$995$	−55.2418	−1.75128
$996$	2.29177	0.0726174
$997$	34.4790	1.09196	0.545980	−	0.837798i	$-0.316157\pi$
$997$	34.4790	1.09196	0.545980	+	0.837798i	$0.316157\pi$
$998$	−68.3242	−2.16277
$999$	3.50206	0.110800

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.c.1.11	✓	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.c.1.11	✓	39	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:	\( N \)	\(=\)	\( 8007 = 3 \cdot 17 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8007.a (trivial)

\(f(q)\)	\(=\)	\(q-1.60951 q^{2} -1.00000 q^{3} +0.590533 q^{4} +2.17104 q^{5} +1.60951 q^{6} +3.27452 q^{7} +2.26856 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.60951 q^{2} -1.00000 q^{3} +0.590533 q^{4} +2.17104 q^{5} +1.60951 q^{6} +3.27452 q^{7} +2.26856 q^{8} +1.00000 q^{9} -3.49431 q^{10} +0.0669844 q^{11} -0.590533 q^{12} +0.443428 q^{13} -5.27038 q^{14} -2.17104 q^{15} -4.83234 q^{16} +1.00000 q^{17} -1.60951 q^{18} -3.50112 q^{19} +1.28207 q^{20} -3.27452 q^{21} -0.107812 q^{22} -4.40532 q^{23} -2.26856 q^{24} -0.286599 q^{25} -0.713703 q^{26} -1.00000 q^{27} +1.93371 q^{28} +8.76824 q^{29} +3.49431 q^{30} +9.92020 q^{31} +3.24060 q^{32} -0.0669844 q^{33} -1.60951 q^{34} +7.10909 q^{35} +0.590533 q^{36} -3.50206 q^{37} +5.63510 q^{38} -0.443428 q^{39} +4.92512 q^{40} -8.85328 q^{41} +5.27038 q^{42} -0.643560 q^{43} +0.0395565 q^{44} +2.17104 q^{45} +7.09041 q^{46} -10.7581 q^{47} +4.83234 q^{48} +3.72245 q^{49} +0.461284 q^{50} -1.00000 q^{51} +0.261859 q^{52} -10.1229 q^{53} +1.60951 q^{54} +0.145426 q^{55} +7.42842 q^{56} +3.50112 q^{57} -14.1126 q^{58} +7.39311 q^{59} -1.28207 q^{60} -7.94758 q^{61} -15.9667 q^{62} +3.27452 q^{63} +4.44889 q^{64} +0.962699 q^{65} +0.107812 q^{66} -15.6509 q^{67} +0.590533 q^{68} +4.40532 q^{69} -11.4422 q^{70} -2.66761 q^{71} +2.26856 q^{72} +11.0205 q^{73} +5.63661 q^{74} +0.286599 q^{75} -2.06753 q^{76} +0.219342 q^{77} +0.713703 q^{78} -6.51709 q^{79} -10.4912 q^{80} +1.00000 q^{81} +14.2495 q^{82} -3.88084 q^{83} -1.93371 q^{84} +2.17104 q^{85} +1.03582 q^{86} -8.76824 q^{87} +0.151958 q^{88} -12.6880 q^{89} -3.49431 q^{90} +1.45201 q^{91} -2.60148 q^{92} -9.92020 q^{93} +17.3154 q^{94} -7.60106 q^{95} -3.24060 q^{96} -10.3181 q^{97} -5.99134 q^{98} +0.0669844 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q - 4 q^{2} - 39 q^{3} + 30 q^{4} - 3 q^{5} + 4 q^{6} - 5 q^{7} - 3 q^{8} + 39 q^{9}+O(q^{10}) \) 39 * q - 4 * q^2 - 39 * q^3 + 30 * q^4 - 3 * q^5 + 4 * q^6 - 5 * q^7 - 3 * q^8 + 39 * q^9	\( 39 q - 4 q^{2} - 39 q^{3} + 30 q^{4} - 3 q^{5} + 4 q^{6} - 5 q^{7} - 3 q^{8} + 39 q^{9} + 4 q^{10} + q^{11} - 30 q^{12} - 26 q^{13} - 4 q^{14} + 3 q^{15} + 8 q^{16} + 39 q^{17} - 4 q^{18} - 14 q^{19} - 14 q^{20} + 5 q^{21} - 17 q^{22} + 2 q^{23} + 3 q^{24} - 6 q^{25} - 17 q^{26} - 39 q^{27} - 14 q^{28} - 7 q^{29} - 4 q^{30} - q^{31} - 30 q^{32} - q^{33} - 4 q^{34} + q^{35} + 30 q^{36} - 24 q^{37} - 20 q^{38} + 26 q^{39} + 12 q^{40} + q^{41} + 4 q^{42} - 41 q^{43} - 2 q^{44} - 3 q^{45} - 6 q^{46} - 9 q^{47} - 8 q^{48} - 10 q^{49} - 9 q^{50} - 39 q^{51} - 37 q^{52} - 47 q^{53} + 4 q^{54} - 39 q^{55} + 8 q^{56} + 14 q^{57} - 27 q^{58} + 41 q^{59} + 14 q^{60} - 41 q^{61} + 36 q^{62} - 5 q^{63} - 47 q^{64} - 39 q^{65} + 17 q^{66} - 36 q^{67} + 30 q^{68} - 2 q^{69} - 52 q^{70} - 2 q^{71} - 3 q^{72} - 63 q^{73} - 6 q^{74} + 6 q^{75} - 34 q^{76} - 64 q^{77} + 17 q^{78} + 20 q^{79} - 28 q^{80} + 39 q^{81} - 37 q^{82} + 45 q^{83} + 14 q^{84} - 3 q^{85} + 32 q^{86} + 7 q^{87} + 6 q^{88} - 32 q^{89} + 4 q^{90} - 11 q^{91} + 28 q^{92} + q^{93} - 44 q^{94} + 22 q^{95} + 30 q^{96} - 20 q^{97} + 63 q^{98} + q^{99}+O(q^{100}) \) 39 * q - 4 * q^2 - 39 * q^3 + 30 * q^4 - 3 * q^5 + 4 * q^6 - 5 * q^7 - 3 * q^8 + 39 * q^9 + 4 * q^10 + q^11 - 30 * q^12 - 26 * q^13 - 4 * q^14 + 3 * q^15 + 8 * q^16 + 39 * q^17 - 4 * q^18 - 14 * q^19 - 14 * q^20 + 5 * q^21 - 17 * q^22 + 2 * q^23 + 3 * q^24 - 6 * q^25 - 17 * q^26 - 39 * q^27 - 14 * q^28 - 7 * q^29 - 4 * q^30 - q^31 - 30 * q^32 - q^33 - 4 * q^34 + q^35 + 30 * q^36 - 24 * q^37 - 20 * q^38 + 26 * q^39 + 12 * q^40 + q^41 + 4 * q^42 - 41 * q^43 - 2 * q^44 - 3 * q^45 - 6 * q^46 - 9 * q^47 - 8 * q^48 - 10 * q^49 - 9 * q^50 - 39 * q^51 - 37 * q^52 - 47 * q^53 + 4 * q^54 - 39 * q^55 + 8 * q^56 + 14 * q^57 - 27 * q^58 + 41 * q^59 + 14 * q^60 - 41 * q^61 + 36 * q^62 - 5 * q^63 - 47 * q^64 - 39 * q^65 + 17 * q^66 - 36 * q^67 + 30 * q^68 - 2 * q^69 - 52 * q^70 - 2 * q^71 - 3 * q^72 - 63 * q^73 - 6 * q^74 + 6 * q^75 - 34 * q^76 - 64 * q^77 + 17 * q^78 + 20 * q^79 - 28 * q^80 + 39 * q^81 - 37 * q^82 + 45 * q^83 + 14 * q^84 - 3 * q^85 + 32 * q^86 + 7 * q^87 + 6 * q^88 - 32 * q^89 + 4 * q^90 - 11 * q^91 + 28 * q^92 + q^93 - 44 * q^94 + 22 * q^95 + 30 * q^96 - 20 * q^97 + 63 * q^98 + q^99

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