LMFDB - Embedded newform 8015.2.a.j.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8015, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8015 = 5 \cdot 7 \cdot 229 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8015.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$64.0000972201$
Analytic rank:	$1$
Dimension:	$45$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	8015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.21589 q^{2} -3.14559 q^{3} +2.91017 q^{4} -1.00000 q^{5} +6.97028 q^{6} +1.00000 q^{7} -2.01683 q^{8} +6.89472 q^{9} +O(q^{10})$	\(q-2.21589 q^{2} -3.14559 q^{3} +2.91017 q^{4} -1.00000 q^{5} +6.97028 q^{6} +1.00000 q^{7} -2.01683 q^{8} +6.89472 q^{9} +2.21589 q^{10} -0.929529 q^{11} -9.15419 q^{12} -3.79454 q^{13} -2.21589 q^{14} +3.14559 q^{15} -1.35126 q^{16} +4.22852 q^{17} -15.2779 q^{18} +6.05452 q^{19} -2.91017 q^{20} -3.14559 q^{21} +2.05973 q^{22} -2.31970 q^{23} +6.34413 q^{24} +1.00000 q^{25} +8.40829 q^{26} -12.2512 q^{27} +2.91017 q^{28} +3.23151 q^{29} -6.97028 q^{30} +0.815870 q^{31} +7.02790 q^{32} +2.92391 q^{33} -9.36994 q^{34} -1.00000 q^{35} +20.0648 q^{36} -3.25427 q^{37} -13.4162 q^{38} +11.9361 q^{39} +2.01683 q^{40} -0.482236 q^{41} +6.97028 q^{42} +5.80603 q^{43} -2.70509 q^{44} -6.89472 q^{45} +5.14020 q^{46} -3.95558 q^{47} +4.25049 q^{48} +1.00000 q^{49} -2.21589 q^{50} -13.3012 q^{51} -11.0428 q^{52} -0.427556 q^{53} +27.1473 q^{54} +0.929529 q^{55} -2.01683 q^{56} -19.0450 q^{57} -7.16067 q^{58} +4.82564 q^{59} +9.15419 q^{60} +2.67010 q^{61} -1.80788 q^{62} +6.89472 q^{63} -12.8705 q^{64} +3.79454 q^{65} -6.47907 q^{66} -8.28363 q^{67} +12.3057 q^{68} +7.29681 q^{69} +2.21589 q^{70} -4.46641 q^{71} -13.9055 q^{72} -12.0495 q^{73} +7.21111 q^{74} -3.14559 q^{75} +17.6197 q^{76} -0.929529 q^{77} -26.4490 q^{78} +1.55256 q^{79} +1.35126 q^{80} +17.8530 q^{81} +1.06858 q^{82} +9.54023 q^{83} -9.15419 q^{84} -4.22852 q^{85} -12.8655 q^{86} -10.1650 q^{87} +1.87471 q^{88} -7.86353 q^{89} +15.2779 q^{90} -3.79454 q^{91} -6.75071 q^{92} -2.56639 q^{93} +8.76513 q^{94} -6.05452 q^{95} -22.1069 q^{96} -15.4724 q^{97} -2.21589 q^{98} -6.40884 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 45 q - 6 q^{2} + 34 q^{4} - 45 q^{5} + q^{6} + 45 q^{7} - 15 q^{8} + 29 q^{9}+O(q^{10}) $ 45 * q - 6 * q^2 + 34 * q^4 - 45 * q^5 + q^6 + 45 * q^7 - 15 * q^8 + 29 * q^9	\( 45 q - 6 q^{2} + 34 q^{4} - 45 q^{5} + q^{6} + 45 q^{7} - 15 q^{8} + 29 q^{9} + 6 q^{10} - q^{11} - 3 q^{12} - 21 q^{13} - 6 q^{14} + 8 q^{16} - 7 q^{17} - 36 q^{18} - 20 q^{19} - 34 q^{20} - 34 q^{22} - 22 q^{23} - 11 q^{24} + 45 q^{25} - q^{26} + 12 q^{27} + 34 q^{28} + 10 q^{29} - q^{30} - 27 q^{31} - 26 q^{32} - 39 q^{33} - 13 q^{34} - 45 q^{35} - 3 q^{36} - 72 q^{37} + 2 q^{38} - 37 q^{39} + 15 q^{40} - 4 q^{41} + q^{42} - 49 q^{43} + 5 q^{44} - 29 q^{45} - 67 q^{46} + 2 q^{47} + 8 q^{48} + 45 q^{49} - 6 q^{50} - 49 q^{51} - 47 q^{52} - 35 q^{53} - 12 q^{54} + q^{55} - 15 q^{56} - 77 q^{57} - 50 q^{58} + 4 q^{59} + 3 q^{60} - 36 q^{61} + 17 q^{62} + 29 q^{63} + 5 q^{64} + 21 q^{65} - 8 q^{66} - 80 q^{67} + 27 q^{68} + 9 q^{69} + 6 q^{70} - 12 q^{71} - 97 q^{72} - 55 q^{73} + 32 q^{74} - 37 q^{76} - q^{77} + 20 q^{78} - 94 q^{79} - 8 q^{80} - 19 q^{81} - 36 q^{82} + 24 q^{83} - 3 q^{84} + 7 q^{85} - 3 q^{86} - 4 q^{87} - 95 q^{88} + q^{89} + 36 q^{90} - 21 q^{91} - 65 q^{92} - 71 q^{93} - 53 q^{94} + 20 q^{95} - 13 q^{96} - 110 q^{97} - 6 q^{98} - 27 q^{99}+O(q^{100}) \) 45 * q - 6 * q^2 + 34 * q^4 - 45 * q^5 + q^6 + 45 * q^7 - 15 * q^8 + 29 * q^9 + 6 * q^10 - q^11 - 3 * q^12 - 21 * q^13 - 6 * q^14 + 8 * q^16 - 7 * q^17 - 36 * q^18 - 20 * q^19 - 34 * q^20 - 34 * q^22 - 22 * q^23 - 11 * q^24 + 45 * q^25 - q^26 + 12 * q^27 + 34 * q^28 + 10 * q^29 - q^30 - 27 * q^31 - 26 * q^32 - 39 * q^33 - 13 * q^34 - 45 * q^35 - 3 * q^36 - 72 * q^37 + 2 * q^38 - 37 * q^39 + 15 * q^40 - 4 * q^41 + q^42 - 49 * q^43 + 5 * q^44 - 29 * q^45 - 67 * q^46 + 2 * q^47 + 8 * q^48 + 45 * q^49 - 6 * q^50 - 49 * q^51 - 47 * q^52 - 35 * q^53 - 12 * q^54 + q^55 - 15 * q^56 - 77 * q^57 - 50 * q^58 + 4 * q^59 + 3 * q^60 - 36 * q^61 + 17 * q^62 + 29 * q^63 + 5 * q^64 + 21 * q^65 - 8 * q^66 - 80 * q^67 + 27 * q^68 + 9 * q^69 + 6 * q^70 - 12 * q^71 - 97 * q^72 - 55 * q^73 + 32 * q^74 - 37 * q^76 - q^77 + 20 * q^78 - 94 * q^79 - 8 * q^80 - 19 * q^81 - 36 * q^82 + 24 * q^83 - 3 * q^84 + 7 * q^85 - 3 * q^86 - 4 * q^87 - 95 * q^88 + q^89 + 36 * q^90 - 21 * q^91 - 65 * q^92 - 71 * q^93 - 53 * q^94 + 20 * q^95 - 13 * q^96 - 110 * q^97 - 6 * q^98 - 27 * 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 $

$2$	−2.21589	−1.56687	−0.783435	−	0.621473i	$-0.786534\pi$
$2$	−2.21589	−1.56687	−0.783435	+	0.621473i	$0.786534\pi$
$3$	−3.14559	−1.81611	−0.908053	−	0.418856i	$-0.862431\pi$
$3$	−3.14559	−1.81611	−0.908053	+	0.418856i	$0.862431\pi$
$4$	2.91017	1.45508
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	6.97028	2.84560
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−2.01683	−0.713059
$9$	6.89472	2.29824
$10$	2.21589	0.700726
$11$	−0.929529	−0.280263	−0.140132	−	0.990133i	$-0.544753\pi$
$11$	−0.929529	−0.280263	−0.140132	+	0.990133i	$0.544753\pi$
$12$	−9.15419	−2.64259
$13$	−3.79454	−1.05242	−0.526208	−	0.850356i	$-0.676387\pi$
$13$	−3.79454	−1.05242	−0.526208	+	0.850356i	$0.676387\pi$
$14$	−2.21589	−0.592222
$15$	3.14559	0.812187
$16$	−1.35126	−0.337814
$17$	4.22852	1.02557	0.512784	−	0.858518i	$-0.328614\pi$
$17$	4.22852	1.02557	0.512784	+	0.858518i	$0.328614\pi$
$18$	−15.2779	−3.60104
$19$	6.05452	1.38900	0.694501	−	0.719491i	$-0.255625\pi$
$19$	6.05452	1.38900	0.694501	+	0.719491i	$0.255625\pi$
$20$	−2.91017	−0.650734
$21$	−3.14559	−0.686423
$22$	2.05973	0.439137
$23$	−2.31970	−0.483691	−0.241845	−	0.970315i	$-0.577753\pi$
$23$	−2.31970	−0.483691	−0.241845	+	0.970315i	$0.577753\pi$
$24$	6.34413	1.29499
$25$	1.00000	0.200000
$26$	8.40829	1.64900
$27$	−12.2512	−2.35774
$28$	2.91017	0.549970
$29$	3.23151	0.600077	0.300038	−	0.953927i	$-0.403001\pi$
$29$	3.23151	0.600077	0.300038	+	0.953927i	$0.403001\pi$
$30$	−6.97028	−1.27259
$31$	0.815870	0.146535	0.0732673	−	0.997312i	$-0.476657\pi$
$31$	0.815870	0.146535	0.0732673	+	0.997312i	$0.476657\pi$
$32$	7.02790	1.24237
$33$	2.92391	0.508988
$34$	−9.36994	−1.60693
$35$	−1.00000	−0.169031
$36$	20.0648	3.34413
$37$	−3.25427	−0.534999	−0.267500	−	0.963558i	$-0.586197\pi$
$37$	−3.25427	−0.534999	−0.267500	+	0.963558i	$0.586197\pi$
$38$	−13.4162	−2.17639
$39$	11.9361	1.91130
$40$	2.01683	0.318889
$41$	−0.482236	−0.0753126	−0.0376563	−	0.999291i	$-0.511989\pi$
$41$	−0.482236	−0.0753126	−0.0376563	+	0.999291i	$0.511989\pi$
$42$	6.97028	1.07554
$43$	5.80603	0.885411	0.442706	−	0.896667i	$-0.354019\pi$
$43$	5.80603	0.885411	0.442706	+	0.896667i	$0.354019\pi$
$44$	−2.70509	−0.407807
$45$	−6.89472	−1.02780
$46$	5.14020	0.757881
$47$	−3.95558	−0.576980	−0.288490	−	0.957483i	$-0.593153\pi$
$47$	−3.95558	−0.576980	−0.288490	+	0.957483i	$0.593153\pi$
$48$	4.25049	0.613505
$49$	1.00000	0.142857
$50$	−2.21589	−0.313374
$51$	−13.3012	−1.86254
$52$	−11.0428	−1.53135
$53$	−0.427556	−0.0587293	−0.0293646	−	0.999569i	$-0.509348\pi$
$53$	−0.427556	−0.0587293	−0.0293646	+	0.999569i	$0.509348\pi$
$54$	27.1473	3.69427
$55$	0.929529	0.125338
$56$	−2.01683	−0.269511
$57$	−19.0450	−2.52258
$58$	−7.16067	−0.940243
$59$	4.82564	0.628244	0.314122	−	0.949383i	$-0.398290\pi$
$59$	4.82564	0.628244	0.314122	+	0.949383i	$0.398290\pi$
$60$	9.15419	1.18180
$61$	2.67010	0.341872	0.170936	−	0.985282i	$-0.445321\pi$
$61$	2.67010	0.341872	0.170936	+	0.985282i	$0.445321\pi$
$62$	−1.80788	−0.229601
$63$	6.89472	0.868653
$64$	−12.8705	−1.60882
$65$	3.79454	0.470655
$66$	−6.47907	−0.797518
$67$	−8.28363	−1.01201	−0.506003	−	0.862532i	$-0.668878\pi$
$67$	−8.28363	−1.01201	−0.506003	+	0.862532i	$0.668878\pi$
$68$	12.3057	1.49229
$69$	7.29681	0.878433
$70$	2.21589	0.264850
$71$	−4.46641	−0.530065	−0.265032	−	0.964239i	$-0.585383\pi$
$71$	−4.46641	−0.530065	−0.265032	+	0.964239i	$0.585383\pi$
$72$	−13.9055	−1.63878
$73$	−12.0495	−1.41028	−0.705141	−	0.709067i	$-0.749116\pi$
$73$	−12.0495	−1.41028	−0.705141	+	0.709067i	$0.749116\pi$
$74$	7.21111	0.838274
$75$	−3.14559	−0.363221
$76$	17.6197	2.02112
$77$	−0.929529	−0.105930
$78$	−26.4490	−2.99476
$79$	1.55256	0.174677	0.0873386	−	0.996179i	$-0.472164\pi$
$79$	1.55256	0.174677	0.0873386	+	0.996179i	$0.472164\pi$
$80$	1.35126	0.151075
$81$	17.8530	1.98367
$82$	1.06858	0.118005
$83$	9.54023	1.04718	0.523588	−	0.851971i	$-0.324593\pi$
$83$	9.54023	1.04718	0.523588	+	0.851971i	$0.324593\pi$
$84$	−9.15419	−0.998804
$85$	−4.22852	−0.458648
$86$	−12.8655	−1.38733
$87$	−10.1650	−1.08980
$88$	1.87471	0.199844
$89$	−7.86353	−0.833532	−0.416766	−	0.909014i	$-0.636837\pi$
$89$	−7.86353	−0.833532	−0.416766	+	0.909014i	$0.636837\pi$
$90$	15.2779	1.61044
$91$	−3.79454	−0.397776
$92$	−6.75071	−0.703811
$93$	−2.56639	−0.266122
$94$	8.76513	0.904054
$95$	−6.05452	−0.621181
$96$	−22.1069	−2.25627
$97$	−15.4724	−1.57098	−0.785490	−	0.618874i	$-0.787589\pi$
$97$	−15.4724	−1.57098	−0.785490	+	0.618874i	$0.787589\pi$
$98$	−2.21589	−0.223839
$99$	−6.40884	−0.644113
$100$	2.91017	0.291017
$101$	17.4901	1.74033	0.870166	−	0.492759i	$-0.164011\pi$
$101$	17.4901	1.74033	0.870166	+	0.492759i	$0.164011\pi$
$102$	29.4740	2.91836
$103$	1.48600	0.146420	0.0732098	−	0.997317i	$-0.476676\pi$
$103$	1.48600	0.146420	0.0732098	+	0.997317i	$0.476676\pi$
$104$	7.65296	0.750434
$105$	3.14559	0.306978
$106$	0.947416	0.0920212
$107$	−11.5332	−1.11496	−0.557480	−	0.830190i	$-0.688232\pi$
$107$	−11.5332	−1.11496	−0.557480	+	0.830190i	$0.688232\pi$
$108$	−35.6530	−3.43071
$109$	−10.0790	−0.965390	−0.482695	−	0.875788i	$-0.660342\pi$
$109$	−10.0790	−0.965390	−0.482695	+	0.875788i	$0.660342\pi$
$110$	−2.05973	−0.196388
$111$	10.2366	0.971615
$112$	−1.35126	−0.127682
$113$	11.2506	1.05837	0.529186	−	0.848506i	$-0.322497\pi$
$113$	11.2506	1.05837	0.529186	+	0.848506i	$0.322497\pi$
$114$	42.2017	3.95255
$115$	2.31970	0.216313
$116$	9.40424	0.873162
$117$	−26.1623	−2.41870
$118$	−10.6931	−0.984378
$119$	4.22852	0.387628
$120$	−6.34413	−0.579137
$121$	−10.1360	−0.921452
$122$	−5.91665	−0.535669
$123$	1.51692	0.136776
$124$	2.37432	0.213220
$125$	−1.00000	−0.0894427
$126$	−15.2779	−1.36107
$127$	−8.48752	−0.753146	−0.376573	−	0.926387i	$-0.622898\pi$
$127$	−8.48752	−0.753146	−0.376573	+	0.926387i	$0.622898\pi$
$128$	14.4639	1.27844
$129$	−18.2634	−1.60800
$130$	−8.40829	−0.737455
$131$	−5.94843	−0.519716	−0.259858	−	0.965647i	$-0.583676\pi$
$131$	−5.94843	−0.519716	−0.259858	+	0.965647i	$0.583676\pi$
$132$	8.50908	0.740620
$133$	6.05452	0.524994
$134$	18.3556	1.58568
$135$	12.2512	1.05441
$136$	−8.52823	−0.731290
$137$	−21.2802	−1.81809	−0.909045	−	0.416698i	$-0.863187\pi$
$137$	−21.2802	−1.81809	−0.909045	+	0.416698i	$0.863187\pi$
$138$	−16.1689	−1.37639
$139$	4.33078	0.367332	0.183666	−	0.982989i	$-0.441204\pi$
$139$	4.33078	0.367332	0.183666	+	0.982989i	$0.441204\pi$
$140$	−2.91017	−0.245954
$141$	12.4426	1.04786
$142$	9.89707	0.830543
$143$	3.52713	0.294954
$144$	−9.31652	−0.776377
$145$	−3.23151	−0.268362
$146$	26.7003	2.20973
$147$	−3.14559	−0.259444
$148$	−9.47048	−0.778469
$149$	4.77359	0.391068	0.195534	−	0.980697i	$-0.437356\pi$
$149$	4.77359	0.391068	0.195534	+	0.980697i	$0.437356\pi$
$150$	6.97028	0.569121
$151$	−21.1509	−1.72124	−0.860619	−	0.509249i	$-0.829923\pi$
$151$	−21.1509	−1.72124	−0.860619	+	0.509249i	$0.829923\pi$
$152$	−12.2110	−0.990440
$153$	29.1545	2.35700
$154$	2.05973	0.165978
$155$	−0.815870	−0.0655322
$156$	34.7359	2.78110
$157$	13.6279	1.08762	0.543812	−	0.839207i	$-0.316981\pi$
$157$	13.6279	1.08762	0.543812	+	0.839207i	$0.316981\pi$
$158$	−3.44031	−0.273697
$159$	1.34491	0.106659
$160$	−7.02790	−0.555604
$161$	−2.31970	−0.182818
$162$	−39.5603	−3.10815
$163$	−8.35006	−0.654027	−0.327013	−	0.945020i	$-0.606042\pi$
$163$	−8.35006	−0.654027	−0.327013	+	0.945020i	$0.606042\pi$
$164$	−1.40339	−0.109586
$165$	−2.92391	−0.227626
$166$	−21.1401	−1.64079
$167$	4.17388	0.322985	0.161492	−	0.986874i	$-0.448369\pi$
$167$	4.17388	0.322985	0.161492	+	0.986874i	$0.448369\pi$
$168$	6.34413	0.489460
$169$	1.39854	0.107580
$170$	9.36994	0.718642
$171$	41.7442	3.19226
$172$	16.8965	1.28835
$173$	−4.39450	−0.334108	−0.167054	−	0.985948i	$-0.553425\pi$
$173$	−4.39450	−0.334108	−0.167054	+	0.985948i	$0.553425\pi$
$174$	22.5245	1.70758
$175$	1.00000	0.0755929
$176$	1.25603	0.0946768
$177$	−15.1795	−1.14096
$178$	17.4247	1.30604
$179$	4.86902	0.363927	0.181964	−	0.983305i	$-0.441755\pi$
$179$	4.86902	0.363927	0.181964	+	0.983305i	$0.441755\pi$
$180$	−20.0648	−1.49554
$181$	4.54154	0.337570	0.168785	−	0.985653i	$-0.446016\pi$
$181$	4.54154	0.337570	0.168785	+	0.985653i	$0.446016\pi$
$182$	8.40829	0.623264
$183$	−8.39904	−0.620875
$184$	4.67845	0.344900
$185$	3.25427	0.239259
$186$	5.68684	0.416979
$187$	−3.93053	−0.287429
$188$	−11.5114	−0.839555
$189$	−12.2512	−0.891142
$190$	13.4162	0.973310
$191$	−0.120771	−0.00873866	−0.00436933	−	0.999990i	$-0.501391\pi$
$191$	−0.120771	−0.00873866	−0.00436933	+	0.999990i	$0.501391\pi$
$192$	40.4854	2.92178
$193$	14.6143	1.05196	0.525979	−	0.850497i	$-0.323699\pi$
$193$	14.6143	1.05196	0.525979	+	0.850497i	$0.323699\pi$
$194$	34.2851	2.46152
$195$	−11.9361	−0.854759
$196$	2.91017	0.207869
$197$	15.7288	1.12063	0.560317	−	0.828278i	$-0.310679\pi$
$197$	15.7288	1.12063	0.560317	+	0.828278i	$0.310679\pi$
$198$	14.2013	1.00924
$199$	15.3544	1.08844	0.544222	−	0.838941i	$-0.316825\pi$
$199$	15.3544	1.08844	0.544222	+	0.838941i	$0.316825\pi$
$200$	−2.01683	−0.142612
$201$	26.0569	1.83791
$202$	−38.7562	−2.72688
$203$	3.23151	0.226808
$204$	−38.7087	−2.71015
$205$	0.482236	0.0336808
$206$	−3.29280	−0.229421
$207$	−15.9937	−1.11164
$208$	5.12739	0.355521
$209$	−5.62785	−0.389287
$210$	−6.97028	−0.480995
$211$	−7.51372	−0.517266	−0.258633	−	0.965976i	$-0.583272\pi$
$211$	−7.51372	−0.517266	−0.258633	+	0.965976i	$0.583272\pi$
$212$	−1.24426	−0.0854561
$213$	14.0495	0.962654
$214$	25.5564	1.74700
$215$	−5.80603	−0.395968
$216$	24.7086	1.68121
$217$	0.815870	0.0553849
$218$	22.3339	1.51264
$219$	37.9026	2.56122
$220$	2.70509	0.182377
$221$	−16.0453	−1.07932
$222$	−22.6832	−1.52239
$223$	2.83110	0.189584	0.0947922	−	0.995497i	$-0.469781\pi$
$223$	2.83110	0.189584	0.0947922	+	0.995497i	$0.469781\pi$
$224$	7.02790	0.469571
$225$	6.89472	0.459648
$226$	−24.9302	−1.65833
$227$	10.8886	0.722704	0.361352	−	0.932430i	$-0.382315\pi$
$227$	10.8886	0.722704	0.361352	+	0.932430i	$0.382315\pi$
$228$	−55.4243	−3.67056
$229$	1.00000	0.0660819
$229$	1.00000	0.0660819
$230$	−5.14020	−0.338935
$231$	2.92391	0.192379
$232$	−6.51742	−0.427890
$233$	−3.29142	−0.215628	−0.107814	−	0.994171i	$-0.534385\pi$
$233$	−3.29142	−0.215628	−0.107814	+	0.994171i	$0.534385\pi$
$234$	57.9728	3.78980
$235$	3.95558	0.258033
$236$	14.0434	0.914148
$237$	−4.88373	−0.317232
$238$	−9.36994	−0.607363
$239$	16.1190	1.04265	0.521325	−	0.853358i	$-0.325438\pi$
$239$	16.1190	1.04265	0.521325	+	0.853358i	$0.325438\pi$
$240$	−4.25049	−0.274368
$241$	18.9501	1.22068	0.610342	−	0.792138i	$-0.291032\pi$
$241$	18.9501	1.22068	0.610342	+	0.792138i	$0.291032\pi$
$242$	22.4602	1.44380
$243$	−19.4046	−1.24481
$244$	7.77045	0.497452
$245$	−1.00000	−0.0638877
$246$	−3.36132	−0.214310
$247$	−22.9741	−1.46181
$248$	−1.64547	−0.104488
$249$	−30.0096	−1.90178
$250$	2.21589	0.140145
$251$	21.2965	1.34422	0.672110	−	0.740451i	$-0.265388\pi$
$251$	21.2965	1.34422	0.672110	+	0.740451i	$0.265388\pi$
$252$	20.0648	1.26396
$253$	2.15623	0.135561
$254$	18.8074	1.18008
$255$	13.3012	0.832953
$256$	−6.30935	−0.394334
$257$	10.7075	0.667914	0.333957	−	0.942588i	$-0.391616\pi$
$257$	10.7075	0.667914	0.333957	+	0.942588i	$0.391616\pi$
$258$	40.4696	2.51953
$259$	−3.25427	−0.202211
$260$	11.0428	0.684843
$261$	22.2804	1.37912
$262$	13.1811	0.814328
$263$	−8.67860	−0.535145	−0.267573	−	0.963538i	$-0.586222\pi$
$263$	−8.67860	−0.535145	−0.267573	+	0.963538i	$0.586222\pi$
$264$	−5.89705	−0.362938
$265$	0.427556	0.0262645
$266$	−13.4162	−0.822597
$267$	24.7354	1.51378
$268$	−24.1068	−1.47255
$269$	2.56271	0.156251	0.0781256	−	0.996944i	$-0.475106\pi$
$269$	2.56271	0.156251	0.0781256	+	0.996944i	$0.475106\pi$
$270$	−27.1473	−1.65213
$271$	10.0616	0.611198	0.305599	−	0.952160i	$-0.401143\pi$
$271$	10.0616	0.611198	0.305599	+	0.952160i	$0.401143\pi$
$272$	−5.71381	−0.346451
$273$	11.9361	0.722403
$274$	47.1546	2.84871
$275$	−0.929529	−0.0560527
$276$	21.2350	1.27819
$277$	−4.83864	−0.290726	−0.145363	−	0.989378i	$-0.546435\pi$
$277$	−4.83864	−0.290726	−0.145363	+	0.989378i	$0.546435\pi$
$278$	−9.59654	−0.575562
$279$	5.62519	0.336772
$280$	2.01683	0.120529
$281$	−9.51226	−0.567454	−0.283727	−	0.958905i	$-0.591571\pi$
$281$	−9.51226	−0.567454	−0.283727	+	0.958905i	$0.591571\pi$
$282$	−27.5715	−1.64186
$283$	8.22496	0.488923	0.244461	−	0.969659i	$-0.421389\pi$
$283$	8.22496	0.488923	0.244461	+	0.969659i	$0.421389\pi$
$284$	−12.9980	−0.771289
$285$	19.0450	1.12813
$286$	−7.81574	−0.462154
$287$	−0.482236	−0.0284655
$288$	48.4554	2.85526
$289$	0.880410	0.0517888
$290$	7.16067	0.420489
$291$	48.6697	2.85307
$292$	−35.0660	−2.05208
$293$	−2.56527	−0.149865	−0.0749323	−	0.997189i	$-0.523874\pi$
$293$	−2.56527	−0.149865	−0.0749323	+	0.997189i	$0.523874\pi$
$294$	6.97028	0.406515
$295$	−4.82564	−0.280959
$296$	6.56333	0.381486
$297$	11.3878	0.660788
$298$	−10.5777	−0.612752
$299$	8.80219	0.509044
$300$	−9.15419	−0.528517
$301$	5.80603	0.334654
$302$	46.8681	2.69696
$303$	−55.0167	−3.16063
$304$	−8.18120	−0.469224
$305$	−2.67010	−0.152890
$306$	−64.6031	−3.69311
$307$	23.3257	1.33127	0.665633	−	0.746280i	$-0.268162\pi$
$307$	23.3257	1.33127	0.665633	+	0.746280i	$0.268162\pi$
$308$	−2.70509	−0.154137
$309$	−4.67433	−0.265913
$310$	1.80788	0.102681
$311$	6.65984	0.377645	0.188822	−	0.982011i	$-0.439533\pi$
$311$	6.65984	0.377645	0.188822	+	0.982011i	$0.439533\pi$
$312$	−24.0730	−1.36287
$313$	−26.2596	−1.48428	−0.742139	−	0.670246i	$-0.766189\pi$
$313$	−26.2596	−1.48428	−0.742139	+	0.670246i	$0.766189\pi$
$314$	−30.1979	−1.70417
$315$	−6.89472	−0.388473
$316$	4.51822	0.254170
$317$	−1.93190	−0.108506	−0.0542532	−	0.998527i	$-0.517278\pi$
$317$	−1.93190	−0.108506	−0.0542532	+	0.998527i	$0.517278\pi$
$318$	−2.98018	−0.167120
$319$	−3.00378	−0.168180
$320$	12.8705	0.719485
$321$	36.2788	2.02489
$322$	5.14020	0.286452
$323$	25.6017	1.42452
$324$	51.9552	2.88640
$325$	−3.79454	−0.210483
$326$	18.5028	1.02478
$327$	31.7043	1.75325
$328$	0.972590	0.0537023
$329$	−3.95558	−0.218078
$330$	6.47907	0.356661
$331$	−5.96283	−0.327747	−0.163873	−	0.986481i	$-0.552399\pi$
$331$	−5.96283	−0.327747	−0.163873	+	0.986481i	$0.552399\pi$
$332$	27.7637	1.52373
$333$	−22.4373	−1.22956
$334$	−9.24886	−0.506075
$335$	8.28363	0.452583
$336$	4.25049	0.231883
$337$	17.9343	0.976945	0.488472	−	0.872579i	$-0.337554\pi$
$337$	17.9343	0.976945	0.488472	+	0.872579i	$0.337554\pi$
$338$	−3.09901	−0.168564
$339$	−35.3899	−1.92212
$340$	−12.3057	−0.667371
$341$	−0.758374	−0.0410683
$342$	−92.5006	−5.00186
$343$	1.00000	0.0539949
$344$	−11.7098	−0.631350
$345$	−7.29681	−0.392847
$346$	9.73773	0.523503
$347$	8.27624	0.444292	0.222146	−	0.975013i	$-0.428694\pi$
$347$	8.27624	0.444292	0.222146	+	0.975013i	$0.428694\pi$
$348$	−29.5819	−1.58575
$349$	−18.2690	−0.977919	−0.488959	−	0.872307i	$-0.662623\pi$
$349$	−18.2690	−0.977919	−0.488959	+	0.872307i	$0.662623\pi$
$350$	−2.21589	−0.118444
$351$	46.4876	2.48132
$352$	−6.53264	−0.348191
$353$	−9.85497	−0.524527	−0.262264	−	0.964996i	$-0.584469\pi$
$353$	−9.85497	−0.524527	−0.262264	+	0.964996i	$0.584469\pi$
$354$	33.6360	1.78773
$355$	4.46641	0.237052
$356$	−22.8842	−1.21286
$357$	−13.3012	−0.703974
$358$	−10.7892	−0.570227
$359$	−13.2052	−0.696942	−0.348471	−	0.937319i	$-0.613299\pi$
$359$	−13.2052	−0.696942	−0.348471	+	0.937319i	$0.613299\pi$
$360$	13.9055	0.732884
$361$	17.6572	0.929329
$362$	−10.0636	−0.528929
$363$	31.8836	1.67345
$364$	−11.0428	−0.578798
$365$	12.0495	0.630697
$366$	18.6114	0.972831
$367$	20.5806	1.07430	0.537148	−	0.843488i	$-0.319502\pi$
$367$	20.5806	1.07430	0.537148	+	0.843488i	$0.319502\pi$
$368$	3.13450	0.163397
$369$	−3.32488	−0.173086
$370$	−7.21111	−0.374888
$371$	−0.427556	−0.0221976
$372$	−7.46863	−0.387230
$373$	−0.744277	−0.0385372	−0.0192686	−	0.999814i	$-0.506134\pi$
$373$	−0.744277	−0.0385372	−0.0192686	+	0.999814i	$0.506134\pi$
$374$	8.70963	0.450364
$375$	3.14559	0.162437
$376$	7.97774	0.411421
$377$	−12.2621	−0.631530
$378$	27.1473	1.39630
$379$	13.9653	0.717347	0.358673	−	0.933463i	$-0.383229\pi$
$379$	13.9653	0.717347	0.358673	+	0.933463i	$0.383229\pi$
$380$	−17.6197	−0.903871
$381$	26.6982	1.36779
$382$	0.267615	0.0136924
$383$	−24.9660	−1.27570	−0.637852	−	0.770159i	$-0.720177\pi$
$383$	−24.9660	−1.27570	−0.637852	+	0.770159i	$0.720177\pi$
$384$	−45.4975	−2.32178
$385$	0.929529	0.0473732
$386$	−32.3836	−1.64828
$387$	40.0309	2.03489
$388$	−45.0272	−2.28591
$389$	29.9435	1.51819	0.759097	−	0.650978i	$-0.225641\pi$
$389$	29.9435	1.51819	0.759097	+	0.650978i	$0.225641\pi$
$390$	26.4490	1.33930
$391$	−9.80890	−0.496057
$392$	−2.01683	−0.101866
$393$	18.7113	0.943860
$394$	−34.8534	−1.75589
$395$	−1.55256	−0.0781180
$396$	−18.6508	−0.937238
$397$	−0.959035	−0.0481326	−0.0240663	−	0.999710i	$-0.507661\pi$
$397$	−0.959035	−0.0481326	−0.0240663	+	0.999710i	$0.507661\pi$
$398$	−34.0237	−1.70545
$399$	−19.0450	−0.953444
$400$	−1.35126	−0.0675628
$401$	−2.03904	−0.101825	−0.0509123	−	0.998703i	$-0.516213\pi$
$401$	−2.03904	−0.101825	−0.0509123	+	0.998703i	$0.516213\pi$
$402$	−57.7392	−2.87977
$403$	−3.09585	−0.154215
$404$	50.8992	2.53233
$405$	−17.8530	−0.887122
$406$	−7.16067	−0.355378
$407$	3.02494	0.149941
$408$	26.8263	1.32810
$409$	−37.7758	−1.86789	−0.933946	−	0.357415i	$-0.883658\pi$
$409$	−37.7758	−1.86789	−0.933946	+	0.357415i	$0.883658\pi$
$410$	−1.06858	−0.0527735
$411$	66.9387	3.30184
$412$	4.32450	0.213053
$413$	4.82564	0.237454
$414$	35.4402	1.74179
$415$	−9.54023	−0.468312
$416$	−26.6677	−1.30749
$417$	−13.6229	−0.667114
$418$	12.4707	0.609962
$419$	30.7129	1.50042	0.750212	−	0.661198i	$-0.229952\pi$
$419$	30.7129	1.50042	0.750212	+	0.661198i	$0.229952\pi$
$420$	9.15419	0.446679
$421$	30.9308	1.50747	0.753736	−	0.657177i	$-0.228250\pi$
$421$	30.9308	1.50747	0.753736	+	0.657177i	$0.228250\pi$
$422$	16.6496	0.810489
$423$	−27.2726	−1.32604
$424$	0.862309	0.0418774
$425$	4.22852	0.205114
$426$	−31.1321	−1.50835
$427$	2.67010	0.129215
$428$	−33.5637	−1.62236
$429$	−11.0949	−0.535667
$430$	12.8655	0.620431
$431$	−26.9977	−1.30043	−0.650217	−	0.759749i	$-0.725322\pi$
$431$	−26.9977	−1.30043	−0.650217	+	0.759749i	$0.725322\pi$
$432$	16.5545	0.796477
$433$	−33.4758	−1.60875	−0.804373	−	0.594125i	$-0.797499\pi$
$433$	−33.4758	−1.60875	−0.804373	+	0.594125i	$0.797499\pi$
$434$	−1.80788	−0.0867809
$435$	10.1650	0.487375
$436$	−29.3315	−1.40472
$437$	−14.0447	−0.671848
$438$	−83.9880	−4.01310
$439$	−34.5987	−1.65131	−0.825654	−	0.564177i	$-0.809194\pi$
$439$	−34.5987	−1.65131	−0.825654	+	0.564177i	$0.809194\pi$
$440$	−1.87471	−0.0893731
$441$	6.89472	0.328320
$442$	35.5546	1.69116
$443$	30.8149	1.46406	0.732030	−	0.681273i	$-0.238573\pi$
$443$	30.8149	1.46406	0.732030	+	0.681273i	$0.238573\pi$
$444$	29.7902	1.41378
$445$	7.86353	0.372767
$446$	−6.27340	−0.297054
$447$	−15.0157	−0.710220
$448$	−12.8705	−0.608076
$449$	5.13727	0.242443	0.121221	−	0.992625i	$-0.461319\pi$
$449$	5.13727	0.242443	0.121221	+	0.992625i	$0.461319\pi$
$450$	−15.2779	−0.720209
$451$	0.448252	0.0211074
$452$	32.7413	1.54002
$453$	66.5321	3.12595
$454$	−24.1280	−1.13238
$455$	3.79454	0.177891
$456$	38.4107	1.79874
$457$	−6.18426	−0.289287	−0.144644	−	0.989484i	$-0.546204\pi$
$457$	−6.18426	−0.289287	−0.144644	+	0.989484i	$0.546204\pi$
$458$	−2.21589	−0.103542
$459$	−51.8044	−2.41802
$460$	6.75071	0.314754
$461$	−13.2158	−0.615521	−0.307761	−	0.951464i	$-0.599580\pi$
$461$	−13.2158	−0.615521	−0.307761	+	0.951464i	$0.599580\pi$
$462$	−6.47907	−0.301434
$463$	28.8297	1.33983	0.669915	−	0.742438i	$-0.266330\pi$
$463$	28.8297	1.33983	0.669915	+	0.742438i	$0.266330\pi$
$464$	−4.36660	−0.202714
$465$	2.56639	0.119013
$466$	7.29342	0.337861
$467$	−11.1778	−0.517246	−0.258623	−	0.965978i	$-0.583269\pi$
$467$	−11.1778	−0.517246	−0.258623	+	0.965978i	$0.583269\pi$
$468$	−76.1367	−3.51942
$469$	−8.28363	−0.382502
$470$	−8.76513	−0.404305
$471$	−42.8677	−1.97524
$472$	−9.73251	−0.447975
$473$	−5.39687	−0.248148
$474$	10.8218	0.497062
$475$	6.05452	0.277801
$476$	12.3057	0.564032
$477$	−2.94788	−0.134974
$478$	−35.7179	−1.63370
$479$	6.39233	0.292073	0.146037	−	0.989279i	$-0.453348\pi$
$479$	6.39233	0.292073	0.146037	+	0.989279i	$0.453348\pi$
$480$	22.1069	1.00904
$481$	12.3485	0.563042
$482$	−41.9914	−1.91265
$483$	7.29681	0.332017
$484$	−29.4974	−1.34079
$485$	15.4724	0.702564
$486$	42.9985	1.95045
$487$	−9.13095	−0.413763	−0.206881	−	0.978366i	$-0.566331\pi$
$487$	−9.13095	−0.413763	−0.206881	+	0.978366i	$0.566331\pi$
$488$	−5.38515	−0.243774
$489$	26.2658	1.18778
$490$	2.21589	0.100104
$491$	26.5159	1.19665	0.598323	−	0.801255i	$-0.295834\pi$
$491$	26.5159	1.19665	0.598323	+	0.801255i	$0.295834\pi$
$492$	4.41448	0.199020
$493$	13.6645	0.615419
$494$	50.9082	2.29047
$495$	6.40884	0.288056
$496$	−1.10245	−0.0495014
$497$	−4.46641	−0.200346
$498$	66.4981	2.97985
$499$	2.81383	0.125965	0.0629823	−	0.998015i	$-0.479939\pi$
$499$	2.81383	0.125965	0.0629823	+	0.998015i	$0.479939\pi$
$500$	−2.91017	−0.130147
$501$	−13.1293	−0.586574
$502$	−47.1906	−2.10622
$503$	41.4273	1.84715	0.923577	−	0.383414i	$-0.125252\pi$
$503$	41.4273	1.84715	0.923577	+	0.383414i	$0.125252\pi$
$504$	−13.9055	−0.619400
$505$	−17.4901	−0.778300
$506$	−4.77796	−0.212406
$507$	−4.39923	−0.195377
$508$	−24.7001	−1.09589
$509$	−8.60778	−0.381533	−0.190767	−	0.981635i	$-0.561097\pi$
$509$	−8.60778	−0.381533	−0.190767	+	0.981635i	$0.561097\pi$
$510$	−29.4740	−1.30513
$511$	−12.0495	−0.533037
$512$	−14.9470	−0.660570
$513$	−74.1750	−3.27491
$514$	−23.7266	−1.04653
$515$	−1.48600	−0.0654808
$516$	−53.1495	−2.33978
$517$	3.67682	0.161706
$518$	7.21111	0.316838
$519$	13.8233	0.606775
$520$	−7.65296	−0.335604
$521$	−5.34517	−0.234176	−0.117088	−	0.993122i	$-0.537356\pi$
$521$	−5.34517	−0.234176	−0.117088	+	0.993122i	$0.537356\pi$
$522$	−49.3708	−2.16090
$523$	−21.5069	−0.940430	−0.470215	−	0.882552i	$-0.655824\pi$
$523$	−21.5069	−0.940430	−0.470215	+	0.882552i	$0.655824\pi$
$524$	−17.3109	−0.756231
$525$	−3.14559	−0.137285
$526$	19.2308	0.838504
$527$	3.44992	0.150281
$528$	−3.95095	−0.171943
$529$	−17.6190	−0.766043
$530$	−0.947416	−0.0411531
$531$	33.2714	1.44386
$532$	17.6197	0.763910
$533$	1.82986	0.0792602
$534$	−54.8110	−2.37190
$535$	11.5332	0.498625
$536$	16.7067	0.721620
$537$	−15.3159	−0.660931
$538$	−5.67868	−0.244825
$539$	−0.929529	−0.0400376
$540$	35.6530	1.53426
$541$	−45.2695	−1.94629	−0.973144	−	0.230196i	$-0.926063\pi$
$541$	−45.2695	−1.94629	−0.973144	+	0.230196i	$0.926063\pi$
$542$	−22.2954	−0.957668
$543$	−14.2858	−0.613063
$544$	29.7176	1.27413
$545$	10.0790	0.431736
$546$	−26.4490	−1.13191
$547$	−5.29848	−0.226547	−0.113273	−	0.993564i	$-0.536134\pi$
$547$	−5.29848	−0.226547	−0.113273	+	0.993564i	$0.536134\pi$
$548$	−61.9290	−2.64547
$549$	18.4096	0.785703
$550$	2.05973	0.0878273
$551$	19.5653	0.833508
$552$	−14.7165	−0.626374
$553$	1.55256	0.0660217
$554$	10.7219	0.455530
$555$	−10.2366	−0.434519
$556$	12.6033	0.534499
$557$	−30.0202	−1.27200	−0.635998	−	0.771691i	$-0.719411\pi$
$557$	−30.0202	−1.27200	−0.635998	+	0.771691i	$0.719411\pi$
$558$	−12.4648	−0.527678
$559$	−22.0312	−0.931821
$560$	1.35126	0.0571009
$561$	12.3638	0.522002
$562$	21.0781	0.889127
$563$	14.9160	0.628633	0.314317	−	0.949318i	$-0.398225\pi$
$563$	14.9160	0.628633	0.314317	+	0.949318i	$0.398225\pi$
$564$	36.2101	1.52472
$565$	−11.2506	−0.473318
$566$	−18.2256	−0.766079
$567$	17.8530	0.749755
$568$	9.00800	0.377967
$569$	−9.31804	−0.390632	−0.195316	−	0.980740i	$-0.562573\pi$
$569$	−9.31804	−0.390632	−0.195316	+	0.980740i	$0.562573\pi$
$570$	−42.2017	−1.76763
$571$	−32.9746	−1.37995	−0.689973	−	0.723836i	$-0.742377\pi$
$571$	−32.9746	−1.37995	−0.689973	+	0.723836i	$0.742377\pi$
$572$	10.2646	0.429183
$573$	0.379895	0.0158703
$574$	1.06858	0.0446018
$575$	−2.31970	−0.0967381
$576$	−88.7388	−3.69745
$577$	−2.96794	−0.123557	−0.0617784	−	0.998090i	$-0.519677\pi$
$577$	−2.96794	−0.123557	−0.0617784	+	0.998090i	$0.519677\pi$
$578$	−1.95089	−0.0811464
$579$	−45.9705	−1.91047
$580$	−9.40424	−0.390490
$581$	9.54023	0.395796
$582$	−107.847	−4.47039
$583$	0.397425	0.0164597
$584$	24.3018	1.00561
$585$	26.1623	1.08168
$586$	5.68435	0.234818
$587$	−14.8172	−0.611572	−0.305786	−	0.952100i	$-0.598919\pi$
$587$	−14.8172	−0.611572	−0.305786	+	0.952100i	$0.598919\pi$
$588$	−9.15419	−0.377512
$589$	4.93970	0.203537
$590$	10.6931	0.440227
$591$	−49.4765	−2.03519
$592$	4.39735	0.180730
$593$	−39.1684	−1.60845	−0.804227	−	0.594322i	$-0.797420\pi$
$593$	−39.1684	−1.60845	−0.804227	+	0.594322i	$0.797420\pi$
$594$	−25.2342	−1.03537
$595$	−4.22852	−0.173353
$596$	13.8919	0.569036
$597$	−48.2986	−1.97673
$598$	−19.5047	−0.797606
$599$	4.83662	0.197619	0.0988095	−	0.995106i	$-0.468497\pi$
$599$	4.83662	0.197619	0.0988095	+	0.995106i	$0.468497\pi$
$600$	6.34413	0.258998
$601$	5.32722	0.217302	0.108651	−	0.994080i	$-0.465347\pi$
$601$	5.32722	0.217302	0.108651	+	0.994080i	$0.465347\pi$
$602$	−12.8655	−0.524360
$603$	−57.1133	−2.32583
$604$	−61.5528	−2.50455
$605$	10.1360	0.412086
$606$	121.911	4.95229
$607$	11.6838	0.474229	0.237114	−	0.971482i	$-0.423798\pi$
$607$	11.6838	0.474229	0.237114	+	0.971482i	$0.423798\pi$
$608$	42.5506	1.72565
$609$	−10.1650	−0.411907
$610$	5.91665	0.239558
$611$	15.0096	0.607223
$612$	84.8445	3.42963
$613$	−34.8571	−1.40786	−0.703932	−	0.710267i	$-0.748574\pi$
$613$	−34.8571	−1.40786	−0.703932	+	0.710267i	$0.748574\pi$
$614$	−51.6871	−2.08592
$615$	−1.51692	−0.0611680
$616$	1.87471	0.0755340
$617$	−2.26206	−0.0910671	−0.0455335	−	0.998963i	$-0.514499\pi$
$617$	−2.26206	−0.0910671	−0.0455335	+	0.998963i	$0.514499\pi$
$618$	10.3578	0.416652
$619$	−2.40526	−0.0966756	−0.0483378	−	0.998831i	$-0.515392\pi$
$619$	−2.40526	−0.0966756	−0.0483378	+	0.998831i	$0.515392\pi$
$620$	−2.37432	−0.0953550
$621$	28.4190	1.14042
$622$	−14.7575	−0.591721
$623$	−7.86353	−0.315046
$624$	−16.1287	−0.645663
$625$	1.00000	0.0400000
$626$	58.1883	2.32567
$627$	17.7029	0.706986
$628$	39.6594	1.58258
$629$	−13.7608	−0.548678
$630$	15.2779	0.608688
$631$	−42.8926	−1.70753	−0.853764	−	0.520661i	$-0.825686\pi$
$631$	−42.8926	−1.70753	−0.853764	+	0.520661i	$0.825686\pi$
$632$	−3.13126	−0.124555
$633$	23.6351	0.939410
$634$	4.28088	0.170015
$635$	8.48752	0.336817
$636$	3.91393	0.155197
$637$	−3.79454	−0.150345
$638$	6.65605	0.263516
$639$	−30.7946	−1.21822
$640$	−14.4639	−0.571736
$641$	24.2894	0.959374	0.479687	−	0.877440i	$-0.340750\pi$
$641$	24.2894	0.959374	0.479687	+	0.877440i	$0.340750\pi$
$642$	−80.3898	−3.17273
$643$	14.6492	0.577709	0.288854	−	0.957373i	$-0.406726\pi$
$643$	14.6492	0.577709	0.288854	+	0.957373i	$0.406726\pi$
$644$	−6.75071	−0.266015
$645$	18.2634	0.719120
$646$	−56.7305	−2.23203
$647$	43.8943	1.72566	0.862832	−	0.505492i	$-0.168689\pi$
$647$	43.8943	1.72566	0.862832	+	0.505492i	$0.168689\pi$
$648$	−36.0065	−1.41447
$649$	−4.48557	−0.176074
$650$	8.40829	0.329800
$651$	−2.56639	−0.100585
$652$	−24.3001	−0.951664
$653$	−5.12400	−0.200518	−0.100259	−	0.994961i	$-0.531967\pi$
$653$	−5.12400	−0.200518	−0.100259	+	0.994961i	$0.531967\pi$
$654$	−70.2532	−2.74712
$655$	5.94843	0.232424
$656$	0.651624	0.0254416
$657$	−83.0776	−3.24117
$658$	8.76513	0.341700
$659$	−37.7506	−1.47056	−0.735278	−	0.677766i	$-0.762948\pi$
$659$	−37.7506	−1.47056	−0.735278	+	0.677766i	$0.762948\pi$
$660$	−8.50908	−0.331216
$661$	−15.6765	−0.609746	−0.304873	−	0.952393i	$-0.598614\pi$
$661$	−15.6765	−0.609746	−0.304873	+	0.952393i	$0.598614\pi$
$662$	13.2130	0.513537
$663$	50.4719	1.96017
$664$	−19.2411	−0.746698
$665$	−6.05452	−0.234784
$666$	49.7186	1.92656
$667$	−7.49613	−0.290251
$668$	12.1467	0.469970
$669$	−8.90547	−0.344305
$670$	−18.3556	−0.709139
$671$	−2.48194	−0.0958141
$672$	−22.1069	−0.852791
$673$	40.8529	1.57476	0.787382	−	0.616465i	$-0.211436\pi$
$673$	40.8529	1.57476	0.787382	+	0.616465i	$0.211436\pi$
$674$	−39.7405	−1.53075
$675$	−12.2512	−0.471548
$676$	4.06998	0.156538
$677$	9.97677	0.383438	0.191719	−	0.981450i	$-0.438594\pi$
$677$	9.97677	0.383438	0.191719	+	0.981450i	$0.438594\pi$
$678$	78.4201	3.01171
$679$	−15.4724	−0.593775
$680$	8.52823	0.327043
$681$	−34.2511	−1.31251
$682$	1.68047	0.0643487
$683$	−3.73208	−0.142804	−0.0714020	−	0.997448i	$-0.522747\pi$
$683$	−3.73208	−0.142804	−0.0714020	+	0.997448i	$0.522747\pi$
$684$	121.483	4.64501
$685$	21.2802	0.813075
$686$	−2.21589	−0.0846031
$687$	−3.14559	−0.120012
$688$	−7.84543	−0.299104
$689$	1.62238	0.0618076
$690$	16.1689	0.615541
$691$	−4.91328	−0.186910	−0.0934550	−	0.995624i	$-0.529791\pi$
$691$	−4.91328	−0.186910	−0.0934550	+	0.995624i	$0.529791\pi$
$692$	−12.7887	−0.486155
$693$	−6.40884	−0.243452
$694$	−18.3392	−0.696148
$695$	−4.33078	−0.164276
$696$	20.5011	0.777093
$697$	−2.03915	−0.0772382
$698$	40.4822	1.53227
$699$	10.3534	0.391603
$700$	2.91017	0.109994
$701$	−1.11319	−0.0420447	−0.0210224	−	0.999779i	$-0.506692\pi$
$701$	−1.11319	−0.0420447	−0.0210224	+	0.999779i	$0.506692\pi$
$702$	−103.011	−3.88791
$703$	−19.7031	−0.743115
$704$	11.9635	0.450893
$705$	−12.4426	−0.468616
$706$	21.8375	0.821866
$707$	17.4901	0.657784
$708$	−44.1748	−1.66019
$709$	−25.8455	−0.970646	−0.485323	−	0.874335i	$-0.661298\pi$
$709$	−25.8455	−0.970646	−0.485323	+	0.874335i	$0.661298\pi$
$710$	−9.89707	−0.371430
$711$	10.7045	0.401450
$712$	15.8594	0.594357
$713$	−1.89257	−0.0708774
$714$	29.4740	1.10304
$715$	−3.52713	−0.131907
$716$	14.1697	0.529545
$717$	−50.7036	−1.89356
$718$	29.2612	1.09202
$719$	−2.73571	−0.102025	−0.0510124	−	0.998698i	$-0.516245\pi$
$719$	−2.73571	−0.102025	−0.0510124	+	0.998698i	$0.516245\pi$
$720$	9.31652	0.347206
$721$	1.48600	0.0553414
$722$	−39.1265	−1.45614
$723$	−59.6092	−2.21689
$724$	13.2167	0.491193
$725$	3.23151	0.120015
$726$	−70.6505	−2.62209
$727$	9.60553	0.356249	0.178125	−	0.984008i	$-0.442997\pi$
$727$	9.60553	0.356249	0.178125	+	0.984008i	$0.442997\pi$
$728$	7.65296	0.283638
$729$	7.47991	0.277034
$730$	−26.7003	−0.988221
$731$	24.5509	0.908049
$732$	−24.4426	−0.903426
$733$	16.3901	0.605381	0.302690	−	0.953089i	$-0.402115\pi$
$733$	16.3901	0.605381	0.302690	+	0.953089i	$0.402115\pi$
$734$	−45.6043	−1.68328
$735$	3.14559	0.116027
$736$	−16.3026	−0.600922
$737$	7.69987	0.283628
$738$	7.36758	0.271204
$739$	−0.148837	−0.00547506	−0.00273753	−	0.999996i	$-0.500871\pi$
$739$	−0.148837	−0.00547506	−0.00273753	+	0.999996i	$0.500871\pi$
$740$	9.47048	0.348142
$741$	72.2671	2.65480
$742$	0.947416	0.0347807
$743$	52.4293	1.92345	0.961723	−	0.274024i	$-0.0883548\pi$
$743$	52.4293	1.92345	0.961723	+	0.274024i	$0.0883548\pi$
$744$	5.17598	0.189761
$745$	−4.77359	−0.174891
$746$	1.64924	0.0603828
$747$	65.7772	2.40666
$748$	−11.4385	−0.418234
$749$	−11.5332	−0.421415
$750$	−6.97028	−0.254518
$751$	−4.89760	−0.178716	−0.0893580	−	0.996000i	$-0.528482\pi$
$751$	−4.89760	−0.178716	−0.0893580	+	0.996000i	$0.528482\pi$
$752$	5.34499	0.194912
$753$	−66.9899	−2.44125
$754$	27.1715	0.989527
$755$	21.1509	0.769761
$756$	−35.6530	−1.29669
$757$	30.2340	1.09887	0.549437	−	0.835535i	$-0.314842\pi$
$757$	30.2340	1.09887	0.549437	+	0.835535i	$0.314842\pi$
$758$	−30.9455	−1.12399
$759$	−6.78260	−0.246193
$760$	12.2110	0.442938
$761$	−32.0652	−1.16236	−0.581182	−	0.813774i	$-0.697410\pi$
$761$	−32.0652	−1.16236	−0.581182	+	0.813774i	$0.697410\pi$
$762$	−59.1604	−2.14315
$763$	−10.0790	−0.364883
$764$	−0.351463	−0.0127155
$765$	−29.1545	−1.05408
$766$	55.3219	1.99886
$767$	−18.3111	−0.661174
$768$	19.8466	0.716153
$769$	−21.8262	−0.787074	−0.393537	−	0.919309i	$-0.628749\pi$
$769$	−21.8262	−0.787074	−0.393537	+	0.919309i	$0.628749\pi$
$770$	−2.05973	−0.0742276
$771$	−33.6813	−1.21300
$772$	42.5300	1.53069
$773$	−11.3953	−0.409862	−0.204931	−	0.978776i	$-0.565697\pi$
$773$	−11.3953	−0.409862	−0.204931	+	0.978776i	$0.565697\pi$
$774$	−88.7042	−3.18841
$775$	0.815870	0.0293069
$776$	31.2052	1.12020
$777$	10.2366	0.367236
$778$	−66.3514	−2.37881
$779$	−2.91971	−0.104609
$780$	−34.7359	−1.24375
$781$	4.15165	0.148558
$782$	21.7354	0.777258
$783$	−39.5898	−1.41482
$784$	−1.35126	−0.0482591
$785$	−13.6279	−0.486400
$786$	−41.4622	−1.47891
$787$	14.6547	0.522385	0.261192	−	0.965287i	$-0.415884\pi$
$787$	14.6547	0.522385	0.261192	+	0.965287i	$0.415884\pi$
$788$	45.7736	1.63062
$789$	27.2993	0.971880
$790$	3.44031	0.122401
$791$	11.2506	0.400027
$792$	12.9256	0.459290
$793$	−10.1318	−0.359791
$794$	2.12512	0.0754175
$795$	−1.34491	−0.0476992
$796$	44.6839	1.58378
$797$	−19.6554	−0.696229	−0.348114	−	0.937452i	$-0.613178\pi$
$797$	−19.6554	−0.696229	−0.348114	+	0.937452i	$0.613178\pi$
$798$	42.2017	1.49392
$799$	−16.7263	−0.591732
$800$	7.02790	0.248474
$801$	−54.2168	−1.91566
$802$	4.51828	0.159546
$803$	11.2003	0.395251
$804$	75.8299	2.67431
$805$	2.31970	0.0817586
$806$	6.86007	0.241636
$807$	−8.06123	−0.283769
$808$	−35.2747	−1.24096
$809$	16.4216	0.577353	0.288676	−	0.957427i	$-0.406785\pi$
$809$	16.4216	0.577353	0.288676	+	0.957427i	$0.406785\pi$
$810$	39.5603	1.39001
$811$	44.8130	1.57360	0.786798	−	0.617210i	$-0.211737\pi$
$811$	44.8130	1.57360	0.786798	+	0.617210i	$0.211737\pi$
$812$	9.40424	0.330024
$813$	−31.6496	−1.11000
$814$	−6.70293	−0.234938
$815$	8.35006	0.292490
$816$	17.9733	0.629191
$817$	35.1527	1.22984
$818$	83.7069	2.92674
$819$	−26.1623	−0.914184
$820$	1.40339	0.0490085
$821$	6.27699	0.219068	0.109534	−	0.993983i	$-0.465064\pi$
$821$	6.27699	0.219068	0.109534	+	0.993983i	$0.465064\pi$
$822$	−148.329	−5.17356
$823$	−10.8542	−0.378353	−0.189177	−	0.981943i	$-0.560582\pi$
$823$	−10.8542	−0.378353	−0.189177	+	0.981943i	$0.560582\pi$
$824$	−2.99701	−0.104406
$825$	2.92391	0.101798
$826$	−10.6931	−0.372060
$827$	−1.87654	−0.0652535	−0.0326268	−	0.999468i	$-0.510387\pi$
$827$	−1.87654	−0.0652535	−0.0326268	+	0.999468i	$0.510387\pi$
$828$	−46.5443	−1.61753
$829$	−6.90355	−0.239770	−0.119885	−	0.992788i	$-0.538253\pi$
$829$	−6.90355	−0.239770	−0.119885	+	0.992788i	$0.538253\pi$
$830$	21.1401	0.733784
$831$	15.2204	0.527989
$832$	48.8378	1.69315
$833$	4.22852	0.146510
$834$	30.1867	1.04528
$835$	−4.17388	−0.144443
$836$	−16.3780	−0.566445
$837$	−9.99537	−0.345490
$838$	−68.0564	−2.35097
$839$	46.7946	1.61553	0.807764	−	0.589506i	$-0.200677\pi$
$839$	46.7946	1.61553	0.807764	+	0.589506i	$0.200677\pi$
$840$	−6.34413	−0.218893
$841$	−18.5573	−0.639908
$842$	−68.5392	−2.36202
$843$	29.9217	1.03056
$844$	−21.8662	−0.752666
$845$	−1.39854	−0.0481112
$846$	60.4331	2.07773
$847$	−10.1360	−0.348276
$848$	0.577737	0.0198396
$849$	−25.8723	−0.887936
$850$	−9.36994	−0.321386
$851$	7.54893	0.258774
$852$	40.8863	1.40074
$853$	19.4160	0.664793	0.332396	−	0.943140i	$-0.392143\pi$
$853$	19.4160	0.664793	0.332396	+	0.943140i	$0.392143\pi$
$854$	−5.91665	−0.202464
$855$	−41.7442	−1.42762
$856$	23.2606	0.795032
$857$	19.7713	0.675376	0.337688	−	0.941258i	$-0.390355\pi$
$857$	19.7713	0.675376	0.337688	+	0.941258i	$0.390355\pi$
$858$	24.5851	0.839321
$859$	15.0760	0.514386	0.257193	−	0.966360i	$-0.417202\pi$
$859$	15.0760	0.514386	0.257193	+	0.966360i	$0.417202\pi$
$860$	−16.8965	−0.576167
$861$	1.51692	0.0516964
$862$	59.8239	2.03761
$863$	8.08689	0.275281	0.137641	−	0.990482i	$-0.456048\pi$
$863$	8.08689	0.275281	0.137641	+	0.990482i	$0.456048\pi$
$864$	−86.1001	−2.92918
$865$	4.39450	0.149417
$866$	74.1788	2.52070
$867$	−2.76941	−0.0940539
$868$	2.37432	0.0805896
$869$	−1.44315	−0.0489556
$870$	−22.5245	−0.763653
$871$	31.4326	1.06505
$872$	20.3276	0.688380
$873$	−106.678	−3.61049
$874$	31.1214	1.05270
$875$	−1.00000	−0.0338062
$876$	110.303	3.72679
$877$	49.9046	1.68516	0.842580	−	0.538571i	$-0.181036\pi$
$877$	49.9046	1.68516	0.842580	+	0.538571i	$0.181036\pi$
$878$	76.6670	2.58739
$879$	8.06927	0.272170
$880$	−1.25603	−0.0423408
$881$	33.9757	1.14467	0.572336	−	0.820019i	$-0.306037\pi$
$881$	33.9757	1.14467	0.572336	+	0.820019i	$0.306037\pi$
$882$	−15.2779	−0.514435
$883$	−44.1013	−1.48413	−0.742064	−	0.670329i	$-0.766153\pi$
$883$	−44.1013	−1.48413	−0.742064	+	0.670329i	$0.766153\pi$
$884$	−46.6945	−1.57051
$885$	15.1795	0.510252
$886$	−68.2824	−2.29399
$887$	−27.2345	−0.914446	−0.457223	−	0.889352i	$-0.651156\pi$
$887$	−27.2345	−0.914446	−0.457223	+	0.889352i	$0.651156\pi$
$888$	−20.6455	−0.692818
$889$	−8.48752	−0.284662
$890$	−17.4247	−0.584078
$891$	−16.5949	−0.555949
$892$	8.23898	0.275861
$893$	−23.9491	−0.801427
$894$	33.2732	1.11282
$895$	−4.86902	−0.162753
$896$	14.4639	0.483205
$897$	−27.6881	−0.924477
$898$	−11.3836	−0.379877
$899$	2.63649	0.0879320
$900$	20.0648	0.668827
$901$	−1.80793	−0.0602308
$902$	−0.993278	−0.0330725
$903$	−18.2634	−0.607767
$904$	−22.6907	−0.754681
$905$	−4.54154	−0.150966
$906$	−147.428	−4.89796
$907$	11.2666	0.374100	0.187050	−	0.982350i	$-0.440107\pi$
$907$	11.2666	0.374100	0.187050	+	0.982350i	$0.440107\pi$
$908$	31.6877	1.05159
$909$	120.589	3.99970
$910$	−8.40829	−0.278732
$911$	45.5160	1.50801	0.754006	−	0.656868i	$-0.228119\pi$
$911$	45.5160	1.50801	0.754006	+	0.656868i	$0.228119\pi$
$912$	25.7347	0.852161
$913$	−8.86792	−0.293485
$914$	13.7036	0.453276
$915$	8.39904	0.277664
$916$	2.91017	0.0961547
$917$	−5.94843	−0.196434
$918$	114.793	3.78873
$919$	−42.5203	−1.40261	−0.701307	−	0.712859i	$-0.747400\pi$
$919$	−42.5203	−1.40261	−0.701307	+	0.712859i	$0.747400\pi$
$920$	−4.67845	−0.154244
$921$	−73.3729	−2.41772
$922$	29.2848	0.964443
$923$	16.9480	0.557849
$924$	8.50908	0.279928
$925$	−3.25427	−0.107000
$926$	−63.8835	−2.09934
$927$	10.2455	0.336507
$928$	22.7107	0.745517
$929$	14.6009	0.479042	0.239521	−	0.970891i	$-0.423010\pi$
$929$	14.6009	0.479042	0.239521	+	0.970891i	$0.423010\pi$
$930$	−5.68684	−0.186479
$931$	6.05452	0.198429
$932$	−9.57858	−0.313757
$933$	−20.9491	−0.685843
$934$	24.7687	0.810458
$935$	3.93053	0.128542
$936$	52.7650	1.72468
$937$	−43.6929	−1.42738	−0.713692	−	0.700459i	$-0.752978\pi$
$937$	−43.6929	−1.42738	−0.713692	+	0.700459i	$0.752978\pi$
$938$	18.3556	0.599332
$939$	82.6017	2.69560
$940$	11.5114	0.375460
$941$	−4.76272	−0.155260	−0.0776300	−	0.996982i	$-0.524735\pi$
$941$	−4.76272	−0.155260	−0.0776300	+	0.996982i	$0.524735\pi$
$942$	94.9901	3.09494
$943$	1.11864	0.0364280
$944$	−6.52066	−0.212230
$945$	12.2512	0.398531
$946$	11.9589	0.388817
$947$	9.77182	0.317542	0.158771	−	0.987315i	$-0.449247\pi$
$947$	9.77182	0.317542	0.158771	+	0.987315i	$0.449247\pi$
$948$	−14.2125	−0.461599
$949$	45.7222	1.48420
$950$	−13.4162	−0.435278
$951$	6.07696	0.197059
$952$	−8.52823	−0.276402
$953$	4.12408	0.133592	0.0667961	−	0.997767i	$-0.478722\pi$
$953$	4.12408	0.133592	0.0667961	+	0.997767i	$0.478722\pi$
$954$	6.53217	0.211487
$955$	0.120771	0.00390805
$956$	46.9089	1.51714
$957$	9.44866	0.305432
$958$	−14.1647	−0.457641
$959$	−21.2802	−0.687174
$960$	−40.4854	−1.30666
$961$	−30.3344	−0.978528
$962$	−27.3628	−0.882214
$963$	−79.5184	−2.56245
$964$	55.1480	1.77620
$965$	−14.6143	−0.470450
$966$	−16.1689	−0.520227
$967$	−26.9082	−0.865308	−0.432654	−	0.901560i	$-0.642423\pi$
$967$	−26.9082	−0.865308	−0.432654	+	0.901560i	$0.642423\pi$
$968$	20.4426	0.657049
$969$	−80.5324	−2.58707
$970$	−34.2851	−1.10083
$971$	−38.6452	−1.24018	−0.620092	−	0.784529i	$-0.712905\pi$
$971$	−38.6452	−1.24018	−0.620092	+	0.784529i	$0.712905\pi$
$972$	−56.4707	−1.81130
$973$	4.33078	0.138838
$974$	20.2332	0.648313
$975$	11.9361	0.382260
$976$	−3.60799	−0.115489
$977$	6.37591	0.203983	0.101992	−	0.994785i	$-0.467478\pi$
$977$	6.37591	0.203983	0.101992	+	0.994785i	$0.467478\pi$
$978$	−58.2022	−1.86110
$979$	7.30938	0.233609
$980$	−2.91017	−0.0929619
$981$	−69.4917	−2.21870
$982$	−58.7563	−1.87499
$983$	−43.1391	−1.37592	−0.687962	−	0.725747i	$-0.741494\pi$
$983$	−43.1391	−1.37592	−0.687962	+	0.725747i	$0.741494\pi$
$984$	−3.05937	−0.0975291
$985$	−15.7288	−0.501163
$986$	−30.2791	−0.964282
$987$	12.4426	0.396053
$988$	−66.8586	−2.12706
$989$	−13.4682	−0.428265
$990$	−14.2013	−0.451346
$991$	20.9843	0.666587	0.333293	−	0.942823i	$-0.391840\pi$
$991$	20.9843	0.666587	0.333293	+	0.942823i	$0.391840\pi$
$992$	5.73385	0.182050
$993$	18.7566	0.595222
$994$	9.89707	0.313916
$995$	−15.3544	−0.486767
$996$	−87.3331	−2.76726
$997$	−17.7494	−0.562128	−0.281064	−	0.959689i	$-0.590687\pi$
$997$	−17.7494	−0.562128	−0.281064	+	0.959689i	$0.590687\pi$
$998$	−6.23515	−0.197370
$999$	39.8687	1.26139

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.j.1.8	✓	45

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.j.1.8	✓	45	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8015 = 5 \cdot 7 \cdot 229 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8015.a (trivial)

\(f(q)\)	\(=\)	\(q-2.21589 q^{2} -3.14559 q^{3} +2.91017 q^{4} -1.00000 q^{5} +6.97028 q^{6} +1.00000 q^{7} -2.01683 q^{8} +6.89472 q^{9} +O(q^{10})\)	\(q-2.21589 q^{2} -3.14559 q^{3} +2.91017 q^{4} -1.00000 q^{5} +6.97028 q^{6} +1.00000 q^{7} -2.01683 q^{8} +6.89472 q^{9} +2.21589 q^{10} -0.929529 q^{11} -9.15419 q^{12} -3.79454 q^{13} -2.21589 q^{14} +3.14559 q^{15} -1.35126 q^{16} +4.22852 q^{17} -15.2779 q^{18} +6.05452 q^{19} -2.91017 q^{20} -3.14559 q^{21} +2.05973 q^{22} -2.31970 q^{23} +6.34413 q^{24} +1.00000 q^{25} +8.40829 q^{26} -12.2512 q^{27} +2.91017 q^{28} +3.23151 q^{29} -6.97028 q^{30} +0.815870 q^{31} +7.02790 q^{32} +2.92391 q^{33} -9.36994 q^{34} -1.00000 q^{35} +20.0648 q^{36} -3.25427 q^{37} -13.4162 q^{38} +11.9361 q^{39} +2.01683 q^{40} -0.482236 q^{41} +6.97028 q^{42} +5.80603 q^{43} -2.70509 q^{44} -6.89472 q^{45} +5.14020 q^{46} -3.95558 q^{47} +4.25049 q^{48} +1.00000 q^{49} -2.21589 q^{50} -13.3012 q^{51} -11.0428 q^{52} -0.427556 q^{53} +27.1473 q^{54} +0.929529 q^{55} -2.01683 q^{56} -19.0450 q^{57} -7.16067 q^{58} +4.82564 q^{59} +9.15419 q^{60} +2.67010 q^{61} -1.80788 q^{62} +6.89472 q^{63} -12.8705 q^{64} +3.79454 q^{65} -6.47907 q^{66} -8.28363 q^{67} +12.3057 q^{68} +7.29681 q^{69} +2.21589 q^{70} -4.46641 q^{71} -13.9055 q^{72} -12.0495 q^{73} +7.21111 q^{74} -3.14559 q^{75} +17.6197 q^{76} -0.929529 q^{77} -26.4490 q^{78} +1.55256 q^{79} +1.35126 q^{80} +17.8530 q^{81} +1.06858 q^{82} +9.54023 q^{83} -9.15419 q^{84} -4.22852 q^{85} -12.8655 q^{86} -10.1650 q^{87} +1.87471 q^{88} -7.86353 q^{89} +15.2779 q^{90} -3.79454 q^{91} -6.75071 q^{92} -2.56639 q^{93} +8.76513 q^{94} -6.05452 q^{95} -22.1069 q^{96} -15.4724 q^{97} -2.21589 q^{98} -6.40884 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 45 q - 6 q^{2} + 34 q^{4} - 45 q^{5} + q^{6} + 45 q^{7} - 15 q^{8} + 29 q^{9}+O(q^{10}) \) 45 * q - 6 * q^2 + 34 * q^4 - 45 * q^5 + q^6 + 45 * q^7 - 15 * q^8 + 29 * q^9	\( 45 q - 6 q^{2} + 34 q^{4} - 45 q^{5} + q^{6} + 45 q^{7} - 15 q^{8} + 29 q^{9} + 6 q^{10} - q^{11} - 3 q^{12} - 21 q^{13} - 6 q^{14} + 8 q^{16} - 7 q^{17} - 36 q^{18} - 20 q^{19} - 34 q^{20} - 34 q^{22} - 22 q^{23} - 11 q^{24} + 45 q^{25} - q^{26} + 12 q^{27} + 34 q^{28} + 10 q^{29} - q^{30} - 27 q^{31} - 26 q^{32} - 39 q^{33} - 13 q^{34} - 45 q^{35} - 3 q^{36} - 72 q^{37} + 2 q^{38} - 37 q^{39} + 15 q^{40} - 4 q^{41} + q^{42} - 49 q^{43} + 5 q^{44} - 29 q^{45} - 67 q^{46} + 2 q^{47} + 8 q^{48} + 45 q^{49} - 6 q^{50} - 49 q^{51} - 47 q^{52} - 35 q^{53} - 12 q^{54} + q^{55} - 15 q^{56} - 77 q^{57} - 50 q^{58} + 4 q^{59} + 3 q^{60} - 36 q^{61} + 17 q^{62} + 29 q^{63} + 5 q^{64} + 21 q^{65} - 8 q^{66} - 80 q^{67} + 27 q^{68} + 9 q^{69} + 6 q^{70} - 12 q^{71} - 97 q^{72} - 55 q^{73} + 32 q^{74} - 37 q^{76} - q^{77} + 20 q^{78} - 94 q^{79} - 8 q^{80} - 19 q^{81} - 36 q^{82} + 24 q^{83} - 3 q^{84} + 7 q^{85} - 3 q^{86} - 4 q^{87} - 95 q^{88} + q^{89} + 36 q^{90} - 21 q^{91} - 65 q^{92} - 71 q^{93} - 53 q^{94} + 20 q^{95} - 13 q^{96} - 110 q^{97} - 6 q^{98} - 27 q^{99}+O(q^{100}) \) 45 * q - 6 * q^2 + 34 * q^4 - 45 * q^5 + q^6 + 45 * q^7 - 15 * q^8 + 29 * q^9 + 6 * q^10 - q^11 - 3 * q^12 - 21 * q^13 - 6 * q^14 + 8 * q^16 - 7 * q^17 - 36 * q^18 - 20 * q^19 - 34 * q^20 - 34 * q^22 - 22 * q^23 - 11 * q^24 + 45 * q^25 - q^26 + 12 * q^27 + 34 * q^28 + 10 * q^29 - q^30 - 27 * q^31 - 26 * q^32 - 39 * q^33 - 13 * q^34 - 45 * q^35 - 3 * q^36 - 72 * q^37 + 2 * q^38 - 37 * q^39 + 15 * q^40 - 4 * q^41 + q^42 - 49 * q^43 + 5 * q^44 - 29 * q^45 - 67 * q^46 + 2 * q^47 + 8 * q^48 + 45 * q^49 - 6 * q^50 - 49 * q^51 - 47 * q^52 - 35 * q^53 - 12 * q^54 + q^55 - 15 * q^56 - 77 * q^57 - 50 * q^58 + 4 * q^59 + 3 * q^60 - 36 * q^61 + 17 * q^62 + 29 * q^63 + 5 * q^64 + 21 * q^65 - 8 * q^66 - 80 * q^67 + 27 * q^68 + 9 * q^69 + 6 * q^70 - 12 * q^71 - 97 * q^72 - 55 * q^73 + 32 * q^74 - 37 * q^76 - q^77 + 20 * q^78 - 94 * q^79 - 8 * q^80 - 19 * q^81 - 36 * q^82 + 24 * q^83 - 3 * q^84 + 7 * q^85 - 3 * q^86 - 4 * q^87 - 95 * q^88 + q^89 + 36 * q^90 - 21 * q^91 - 65 * q^92 - 71 * q^93 - 53 * q^94 + 20 * q^95 - 13 * q^96 - 110 * q^97 - 6 * q^98 - 27 * q^99

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