LMFDB - Embedded newform 8014.2.a.e.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8014,2,Mod(1,8014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8014, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8014.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8014 = 2 \cdot 4007 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8014.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:	$63.9921121799$
Analytic rank:	$0$
Dimension:	$91$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	8014.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.03768 q^{3} +1.00000 q^{4} -1.30464 q^{5} +2.03768 q^{6} -1.43874 q^{7} -1.00000 q^{8} +1.15214 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.03768 q^{3} +1.00000 q^{4} -1.30464 q^{5} +2.03768 q^{6} -1.43874 q^{7} -1.00000 q^{8} +1.15214 q^{9} +1.30464 q^{10} -4.39201 q^{11} -2.03768 q^{12} -2.80466 q^{13} +1.43874 q^{14} +2.65845 q^{15} +1.00000 q^{16} +4.77974 q^{17} -1.15214 q^{18} -3.69827 q^{19} -1.30464 q^{20} +2.93169 q^{21} +4.39201 q^{22} +3.25405 q^{23} +2.03768 q^{24} -3.29791 q^{25} +2.80466 q^{26} +3.76535 q^{27} -1.43874 q^{28} -3.27364 q^{29} -2.65845 q^{30} +7.77866 q^{31} -1.00000 q^{32} +8.94951 q^{33} -4.77974 q^{34} +1.87704 q^{35} +1.15214 q^{36} +1.64981 q^{37} +3.69827 q^{38} +5.71501 q^{39} +1.30464 q^{40} -10.6503 q^{41} -2.93169 q^{42} -0.867570 q^{43} -4.39201 q^{44} -1.50313 q^{45} -3.25405 q^{46} -6.49428 q^{47} -2.03768 q^{48} -4.93003 q^{49} +3.29791 q^{50} -9.73958 q^{51} -2.80466 q^{52} -1.59657 q^{53} -3.76535 q^{54} +5.73001 q^{55} +1.43874 q^{56} +7.53590 q^{57} +3.27364 q^{58} -13.7002 q^{59} +2.65845 q^{60} -9.46488 q^{61} -7.77866 q^{62} -1.65763 q^{63} +1.00000 q^{64} +3.65909 q^{65} -8.94951 q^{66} -5.59100 q^{67} +4.77974 q^{68} -6.63072 q^{69} -1.87704 q^{70} +6.48718 q^{71} -1.15214 q^{72} -13.2070 q^{73} -1.64981 q^{74} +6.72008 q^{75} -3.69827 q^{76} +6.31895 q^{77} -5.71501 q^{78} -7.09152 q^{79} -1.30464 q^{80} -11.1290 q^{81} +10.6503 q^{82} -10.9303 q^{83} +2.93169 q^{84} -6.23586 q^{85} +0.867570 q^{86} +6.67063 q^{87} +4.39201 q^{88} +7.40593 q^{89} +1.50313 q^{90} +4.03518 q^{91} +3.25405 q^{92} -15.8504 q^{93} +6.49428 q^{94} +4.82493 q^{95} +2.03768 q^{96} +0.515134 q^{97} +4.93003 q^{98} -5.06022 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 91 q - 91 q^{2} - 2 q^{3} + 91 q^{4} + 22 q^{5} + 2 q^{6} - 14 q^{7} - 91 q^{8} + 123 q^{9}+O(q^{10}) $ 91 * q - 91 * q^2 - 2 * q^3 + 91 * q^4 + 22 * q^5 + 2 * q^6 - 14 * q^7 - 91 * q^8 + 123 * q^9	\( 91 q - 91 q^{2} - 2 q^{3} + 91 q^{4} + 22 q^{5} + 2 q^{6} - 14 q^{7} - 91 q^{8} + 123 q^{9} - 22 q^{10} + 59 q^{11} - 2 q^{12} - 15 q^{13} + 14 q^{14} + 23 q^{15} + 91 q^{16} + 25 q^{17} - 123 q^{18} + 2 q^{19} + 22 q^{20} + 20 q^{21} - 59 q^{22} + 36 q^{23} + 2 q^{24} + 121 q^{25} + 15 q^{26} - 8 q^{27} - 14 q^{28} + 71 q^{29} - 23 q^{30} + 13 q^{31} - 91 q^{32} + 24 q^{33} - 25 q^{34} + 27 q^{35} + 123 q^{36} + 5 q^{37} - 2 q^{38} + 48 q^{39} - 22 q^{40} + 77 q^{41} - 20 q^{42} - 36 q^{43} + 59 q^{44} + 62 q^{45} - 36 q^{46} + 41 q^{47} - 2 q^{48} + 137 q^{49} - 121 q^{50} + 13 q^{51} - 15 q^{52} + 33 q^{53} + 8 q^{54} + 12 q^{55} + 14 q^{56} + 52 q^{57} - 71 q^{58} + 76 q^{59} + 23 q^{60} + 18 q^{61} - 13 q^{62} - 18 q^{63} + 91 q^{64} + 84 q^{65} - 24 q^{66} - 59 q^{67} + 25 q^{68} + 64 q^{69} - 27 q^{70} + 124 q^{71} - 123 q^{72} + 43 q^{73} - 5 q^{74} + 9 q^{75} + 2 q^{76} + 50 q^{77} - 48 q^{78} - 20 q^{79} + 22 q^{80} + 227 q^{81} - 77 q^{82} + 29 q^{83} + 20 q^{84} + 3 q^{85} + 36 q^{86} - 25 q^{87} - 59 q^{88} + 148 q^{89} - 62 q^{90} + 27 q^{91} + 36 q^{92} + 65 q^{93} - 41 q^{94} + 54 q^{95} + 2 q^{96} + 38 q^{97} - 137 q^{98} + 157 q^{99}+O(q^{100}) \) 91 * q - 91 * q^2 - 2 * q^3 + 91 * q^4 + 22 * q^5 + 2 * q^6 - 14 * q^7 - 91 * q^8 + 123 * q^9 - 22 * q^10 + 59 * q^11 - 2 * q^12 - 15 * q^13 + 14 * q^14 + 23 * q^15 + 91 * q^16 + 25 * q^17 - 123 * q^18 + 2 * q^19 + 22 * q^20 + 20 * q^21 - 59 * q^22 + 36 * q^23 + 2 * q^24 + 121 * q^25 + 15 * q^26 - 8 * q^27 - 14 * q^28 + 71 * q^29 - 23 * q^30 + 13 * q^31 - 91 * q^32 + 24 * q^33 - 25 * q^34 + 27 * q^35 + 123 * q^36 + 5 * q^37 - 2 * q^38 + 48 * q^39 - 22 * q^40 + 77 * q^41 - 20 * q^42 - 36 * q^43 + 59 * q^44 + 62 * q^45 - 36 * q^46 + 41 * q^47 - 2 * q^48 + 137 * q^49 - 121 * q^50 + 13 * q^51 - 15 * q^52 + 33 * q^53 + 8 * q^54 + 12 * q^55 + 14 * q^56 + 52 * q^57 - 71 * q^58 + 76 * q^59 + 23 * q^60 + 18 * q^61 - 13 * q^62 - 18 * q^63 + 91 * q^64 + 84 * q^65 - 24 * q^66 - 59 * q^67 + 25 * q^68 + 64 * q^69 - 27 * q^70 + 124 * q^71 - 123 * q^72 + 43 * q^73 - 5 * q^74 + 9 * q^75 + 2 * q^76 + 50 * q^77 - 48 * q^78 - 20 * q^79 + 22 * q^80 + 227 * q^81 - 77 * q^82 + 29 * q^83 + 20 * q^84 + 3 * q^85 + 36 * q^86 - 25 * q^87 - 59 * q^88 + 148 * q^89 - 62 * q^90 + 27 * q^91 + 36 * q^92 + 65 * q^93 - 41 * q^94 + 54 * q^95 + 2 * q^96 + 38 * q^97 - 137 * q^98 + 157 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.03768	−1.17646	−0.588228	−	0.808695i	$-0.700174\pi$
$3$	−2.03768	−1.17646	−0.588228	+	0.808695i	$0.700174\pi$
$4$	1.00000	0.500000
$5$	−1.30464	−0.583454	−0.291727	−	0.956502i	$-0.594230\pi$
$5$	−1.30464	−0.583454	−0.291727	+	0.956502i	$0.594230\pi$
$6$	2.03768	0.831880
$7$	−1.43874	−0.543792	−0.271896	−	0.962327i	$-0.587651\pi$
$7$	−1.43874	−0.543792	−0.271896	+	0.962327i	$0.587651\pi$
$8$	−1.00000	−0.353553
$9$	1.15214	0.384047
$10$	1.30464	0.412565
$11$	−4.39201	−1.32424	−0.662120	−	0.749398i	$-0.730343\pi$
$11$	−4.39201	−1.32424	−0.662120	+	0.749398i	$0.730343\pi$
$12$	−2.03768	−0.588228
$13$	−2.80466	−0.777874	−0.388937	−	0.921264i	$-0.627158\pi$
$13$	−2.80466	−0.777874	−0.388937	+	0.921264i	$0.627158\pi$
$14$	1.43874	0.384519
$15$	2.65845	0.686408
$16$	1.00000	0.250000
$17$	4.77974	1.15926	0.579628	−	0.814881i	$-0.303198\pi$
$17$	4.77974	1.15926	0.579628	+	0.814881i	$0.303198\pi$
$18$	−1.15214	−0.271562
$19$	−3.69827	−0.848442	−0.424221	−	0.905559i	$-0.639452\pi$
$19$	−3.69827	−0.848442	−0.424221	+	0.905559i	$0.639452\pi$
$20$	−1.30464	−0.291727
$21$	2.93169	0.639747
$22$	4.39201	0.936380
$23$	3.25405	0.678517	0.339258	−	0.940693i	$-0.389824\pi$
$23$	3.25405	0.678517	0.339258	+	0.940693i	$0.389824\pi$
$24$	2.03768	0.415940
$25$	−3.29791	−0.659581
$26$	2.80466	0.550040
$27$	3.76535	0.724641
$28$	−1.43874	−0.271896
$29$	−3.27364	−0.607900	−0.303950	−	0.952688i	$-0.598306\pi$
$29$	−3.27364	−0.607900	−0.303950	+	0.952688i	$0.598306\pi$
$30$	−2.65845	−0.485364
$31$	7.77866	1.39709	0.698544	−	0.715567i	$-0.253831\pi$
$31$	7.77866	1.39709	0.698544	+	0.715567i	$0.253831\pi$
$32$	−1.00000	−0.176777
$33$	8.94951	1.55791
$34$	−4.77974	−0.819718
$35$	1.87704	0.317278
$36$	1.15214	0.192024
$37$	1.64981	0.271227	0.135614	−	0.990762i	$-0.456699\pi$
$37$	1.64981	0.271227	0.135614	+	0.990762i	$0.456699\pi$
$38$	3.69827	0.599939
$39$	5.71501	0.915134
$40$	1.30464	0.206282
$41$	−10.6503	−1.66329	−0.831646	−	0.555306i	$-0.812601\pi$
$41$	−10.6503	−1.66329	−0.831646	+	0.555306i	$0.812601\pi$
$42$	−2.93169	−0.452369
$43$	−0.867570	−0.132303	−0.0661516	−	0.997810i	$-0.521072\pi$
$43$	−0.867570	−0.132303	−0.0661516	+	0.997810i	$0.521072\pi$
$44$	−4.39201	−0.662120
$45$	−1.50313	−0.224074
$46$	−3.25405	−0.479784
$47$	−6.49428	−0.947289	−0.473644	−	0.880716i	$-0.657062\pi$
$47$	−6.49428	−0.947289	−0.473644	+	0.880716i	$0.657062\pi$
$48$	−2.03768	−0.294114
$49$	−4.93003	−0.704291
$50$	3.29791	0.466394
$51$	−9.73958	−1.36381
$52$	−2.80466	−0.388937
$53$	−1.59657	−0.219306	−0.109653	−	0.993970i	$-0.534974\pi$
$53$	−1.59657	−0.219306	−0.109653	+	0.993970i	$0.534974\pi$
$54$	−3.76535	−0.512399
$55$	5.73001	0.772634
$56$	1.43874	0.192259
$57$	7.53590	0.998154
$58$	3.27364	0.429850
$59$	−13.7002	−1.78361	−0.891807	−	0.452415i	$-0.850562\pi$
$59$	−13.7002	−1.78361	−0.891807	+	0.452415i	$0.850562\pi$
$60$	2.65845	0.343204
$61$	−9.46488	−1.21185	−0.605927	−	0.795521i	$-0.707197\pi$
$61$	−9.46488	−1.21185	−0.605927	+	0.795521i	$0.707197\pi$
$62$	−7.77866	−0.987891
$63$	−1.65763	−0.208842
$64$	1.00000	0.125000
$65$	3.65909	0.453854
$66$	−8.94951	−1.10161
$67$	−5.59100	−0.683049	−0.341525	−	0.939873i	$-0.610943\pi$
$67$	−5.59100	−0.683049	−0.341525	+	0.939873i	$0.610943\pi$
$68$	4.77974	0.579628
$69$	−6.63072	−0.798244
$70$	−1.87704	−0.224349
$71$	6.48718	0.769886	0.384943	−	0.922940i	$-0.374221\pi$
$71$	6.48718	0.769886	0.384943	+	0.922940i	$0.374221\pi$
$72$	−1.15214	−0.135781
$73$	−13.2070	−1.54577	−0.772884	−	0.634548i	$-0.781186\pi$
$73$	−13.2070	−1.54577	−0.772884	+	0.634548i	$0.781186\pi$
$74$	−1.64981	−0.191787
$75$	6.72008	0.775968
$76$	−3.69827	−0.424221
$77$	6.31895	0.720111
$78$	−5.71501	−0.647097
$79$	−7.09152	−0.797859	−0.398929	−	0.916982i	$-0.630618\pi$
$79$	−7.09152	−0.797859	−0.398929	+	0.916982i	$0.630618\pi$
$80$	−1.30464	−0.145864
$81$	−11.1290	−1.23655
$82$	10.6503	1.17613
$83$	−10.9303	−1.19976	−0.599880	−	0.800090i	$-0.704785\pi$
$83$	−10.9303	−1.19976	−0.599880	+	0.800090i	$0.704785\pi$
$84$	2.93169	0.319873
$85$	−6.23586	−0.676373
$86$	0.867570	0.0935525
$87$	6.67063	0.715167
$88$	4.39201	0.468190
$89$	7.40593	0.785027	0.392514	−	0.919746i	$-0.371606\pi$
$89$	7.40593	0.785027	0.392514	+	0.919746i	$0.371606\pi$
$90$	1.50313	0.158444
$91$	4.03518	0.423001
$92$	3.25405	0.339258
$93$	−15.8504	−1.64361
$94$	6.49428	0.669834
$95$	4.82493	0.495027
$96$	2.03768	0.207970
$97$	0.515134	0.0523039	0.0261520	−	0.999658i	$-0.491675\pi$
$97$	0.515134	0.0523039	0.0261520	+	0.999658i	$0.491675\pi$
$98$	4.93003	0.498009
$99$	−5.06022	−0.508571
$100$	−3.29791	−0.329791
$101$	14.2902	1.42192	0.710962	−	0.703230i	$-0.248260\pi$
$101$	14.2902	1.42192	0.710962	+	0.703230i	$0.248260\pi$
$102$	9.73958	0.964362
$103$	−10.1556	−1.00066	−0.500329	−	0.865835i	$-0.666788\pi$
$103$	−10.1556	−1.00066	−0.500329	+	0.865835i	$0.666788\pi$
$104$	2.80466	0.275020
$105$	−3.82481	−0.373263
$106$	1.59657	0.155073
$107$	−3.83029	−0.370288	−0.185144	−	0.982711i	$-0.559275\pi$
$107$	−3.83029	−0.370288	−0.185144	+	0.982711i	$0.559275\pi$
$108$	3.76535	0.362321
$109$	−5.50571	−0.527352	−0.263676	−	0.964611i	$-0.584935\pi$
$109$	−5.50571	−0.527352	−0.263676	+	0.964611i	$0.584935\pi$
$110$	−5.73001	−0.546335
$111$	−3.36179	−0.319087
$112$	−1.43874	−0.135948
$113$	−13.0240	−1.22520	−0.612599	−	0.790394i	$-0.709876\pi$
$113$	−13.0240	−1.22520	−0.612599	+	0.790394i	$0.709876\pi$
$114$	−7.53590	−0.705802
$115$	−4.24538	−0.395883
$116$	−3.27364	−0.303950
$117$	−3.23137	−0.298740
$118$	13.7002	1.26121
$119$	−6.87679	−0.630394
$120$	−2.65845	−0.242682
$121$	8.28975	0.753613
$122$	9.46488	0.856910
$123$	21.7018	1.95679
$124$	7.77866	0.698544
$125$	10.8258	0.968290
$126$	1.65763	0.147673
$127$	3.62588	0.321745	0.160872	−	0.986975i	$-0.448569\pi$
$127$	3.62588	0.321745	0.160872	+	0.986975i	$0.448569\pi$
$128$	−1.00000	−0.0883883
$129$	1.76783	0.155649
$130$	−3.65909	−0.320923
$131$	−20.5623	−1.79654	−0.898269	−	0.439446i	$-0.855175\pi$
$131$	−20.5623	−1.79654	−0.898269	+	0.439446i	$0.855175\pi$
$132$	8.94951	0.778955
$133$	5.32085	0.461376
$134$	5.59100	0.482989
$135$	−4.91243	−0.422795
$136$	−4.77974	−0.409859
$137$	−11.8589	−1.01317	−0.506586	−	0.862189i	$-0.669093\pi$
$137$	−11.8589	−1.01317	−0.506586	+	0.862189i	$0.669093\pi$
$138$	6.63072	0.564444
$139$	−7.75184	−0.657502	−0.328751	−	0.944417i	$-0.606628\pi$
$139$	−7.75184	−0.657502	−0.328751	+	0.944417i	$0.606628\pi$
$140$	1.87704	0.158639
$141$	13.2333	1.11444
$142$	−6.48718	−0.544392
$143$	12.3181	1.03009
$144$	1.15214	0.0960118
$145$	4.27093	0.354682
$146$	13.2070	1.09302
$147$	10.0458	0.828566
$148$	1.64981	0.135614
$149$	17.8855	1.46524	0.732620	−	0.680638i	$-0.238297\pi$
$149$	17.8855	1.46524	0.732620	+	0.680638i	$0.238297\pi$
$150$	−6.72008	−0.548692
$151$	12.6920	1.03286	0.516430	−	0.856330i	$-0.327261\pi$
$151$	12.6920	1.03286	0.516430	+	0.856330i	$0.327261\pi$
$152$	3.69827	0.299970
$153$	5.50693	0.445209
$154$	−6.31895	−0.509195
$155$	−10.1484	−0.815138
$156$	5.71501	0.457567
$157$	−9.52005	−0.759783	−0.379891	−	0.925031i	$-0.624039\pi$
$157$	−9.52005	−0.759783	−0.379891	+	0.925031i	$0.624039\pi$
$158$	7.09152	0.564171
$159$	3.25331	0.258004
$160$	1.30464	0.103141
$161$	−4.68173	−0.368972
$162$	11.1290	0.874376
$163$	−5.72413	−0.448349	−0.224174	−	0.974549i	$-0.571969\pi$
$163$	−5.72413	−0.448349	−0.224174	+	0.974549i	$0.571969\pi$
$164$	−10.6503	−0.831646
$165$	−11.6759	−0.908969
$166$	10.9303	0.848358
$167$	2.28862	0.177099	0.0885494	−	0.996072i	$-0.471777\pi$
$167$	2.28862	0.177099	0.0885494	+	0.996072i	$0.471777\pi$
$168$	−2.93169	−0.226185
$169$	−5.13386	−0.394912
$170$	6.23586	0.478268
$171$	−4.26093	−0.325842
$172$	−0.867570	−0.0661516
$173$	8.67000	0.659168	0.329584	−	0.944126i	$-0.393092\pi$
$173$	8.67000	0.659168	0.329584	+	0.944126i	$0.393092\pi$
$174$	−6.67063	−0.505699
$175$	4.74482	0.358675
$176$	−4.39201	−0.331060
$177$	27.9166	2.09834
$178$	−7.40593	−0.555098
$179$	−21.1263	−1.57905	−0.789525	−	0.613718i	$-0.789673\pi$
$179$	−21.1263	−1.57905	−0.789525	+	0.613718i	$0.789673\pi$
$180$	−1.50313	−0.112037
$181$	20.8043	1.54637	0.773185	−	0.634180i	$-0.218662\pi$
$181$	20.8043	1.54637	0.773185	+	0.634180i	$0.218662\pi$
$182$	−4.03518	−0.299107
$183$	19.2864	1.42569
$184$	−3.25405	−0.239892
$185$	−2.15241	−0.158249
$186$	15.8504	1.16221
$187$	−20.9927	−1.53514
$188$	−6.49428	−0.473644
$189$	−5.41734	−0.394054
$190$	−4.82493	−0.350037
$191$	12.7143	0.919978	0.459989	−	0.887925i	$-0.347853\pi$
$191$	12.7143	0.919978	0.459989	+	0.887925i	$0.347853\pi$
$192$	−2.03768	−0.147057
$193$	9.61052	0.691780	0.345890	−	0.938275i	$-0.387577\pi$
$193$	9.61052	0.691780	0.345890	+	0.938275i	$0.387577\pi$
$194$	−0.515134	−0.0369845
$195$	−7.45605	−0.533939
$196$	−4.93003	−0.352145
$197$	−9.36313	−0.667095	−0.333548	−	0.942733i	$-0.608246\pi$
$197$	−9.36313	−0.667095	−0.333548	+	0.942733i	$0.608246\pi$
$198$	5.06022	0.359614
$199$	−23.1785	−1.64308	−0.821541	−	0.570150i	$-0.806885\pi$
$199$	−23.1785	−1.64308	−0.821541	+	0.570150i	$0.806885\pi$
$200$	3.29791	0.233197
$201$	11.3927	0.803577
$202$	−14.2902	−1.00545
$203$	4.70991	0.330571
$204$	−9.73958	−0.681907
$205$	13.8948	0.970455
$206$	10.1556	0.707573
$207$	3.74913	0.260582
$208$	−2.80466	−0.194468
$209$	16.2429	1.12354
$210$	3.82481	0.263937
$211$	−27.5030	−1.89339	−0.946694	−	0.322135i	$-0.895600\pi$
$211$	−27.5030	−1.89339	−0.946694	+	0.322135i	$0.895600\pi$
$212$	−1.59657	−0.109653
$213$	−13.2188	−0.905737
$214$	3.83029	0.261833
$215$	1.13187	0.0771929
$216$	−3.76535	−0.256199
$217$	−11.1915	−0.759725
$218$	5.50571	0.372894
$219$	26.9117	1.81853
$220$	5.73001	0.386317
$221$	−13.4056	−0.901756
$222$	3.36179	0.225628
$223$	−11.7658	−0.787896	−0.393948	−	0.919133i	$-0.628891\pi$
$223$	−11.7658	−0.787896	−0.393948	+	0.919133i	$0.628891\pi$
$224$	1.43874	0.0961297
$225$	−3.79965	−0.253310
$226$	13.0240	0.866345
$227$	−12.6356	−0.838651	−0.419326	−	0.907836i	$-0.637733\pi$
$227$	−12.6356	−0.838651	−0.419326	+	0.907836i	$0.637733\pi$
$228$	7.53590	0.499077
$229$	−24.1306	−1.59460	−0.797298	−	0.603586i	$-0.793738\pi$
$229$	−24.1306	−1.59460	−0.797298	+	0.603586i	$0.793738\pi$
$230$	4.24538	0.279932
$231$	−12.8760	−0.847178
$232$	3.27364	0.214925
$233$	−5.70245	−0.373580	−0.186790	−	0.982400i	$-0.559808\pi$
$233$	−5.70245	−0.373580	−0.186790	+	0.982400i	$0.559808\pi$
$234$	3.23137	0.211241
$235$	8.47273	0.552700
$236$	−13.7002	−0.891807
$237$	14.4503	0.938645
$238$	6.87679	0.445756
$239$	−9.58694	−0.620128	−0.310064	−	0.950716i	$-0.600350\pi$
$239$	−9.58694	−0.620128	−0.310064	+	0.950716i	$0.600350\pi$
$240$	2.65845	0.171602
$241$	22.5479	1.45244	0.726219	−	0.687464i	$-0.241276\pi$
$241$	22.5479	1.45244	0.726219	+	0.687464i	$0.241276\pi$
$242$	−8.28975	−0.532885
$243$	11.3813	0.730111
$244$	−9.46488	−0.605927
$245$	6.43194	0.410921
$246$	−21.7018	−1.38366
$247$	10.3724	0.659981
$248$	−7.77866	−0.493945
$249$	22.2725	1.41146
$250$	−10.8258	−0.684684
$251$	5.30416	0.334796	0.167398	−	0.985889i	$-0.446464\pi$
$251$	5.30416	0.334796	0.167398	+	0.985889i	$0.446464\pi$
$252$	−1.65763	−0.104421
$253$	−14.2918	−0.898519
$254$	−3.62588	−0.227508
$255$	12.7067	0.795723
$256$	1.00000	0.0625000
$257$	8.21260	0.512288	0.256144	−	0.966639i	$-0.417548\pi$
$257$	8.21260	0.512288	0.256144	+	0.966639i	$0.417548\pi$
$258$	−1.76783	−0.110060
$259$	−2.37364	−0.147491
$260$	3.65909	0.226927
$261$	−3.77170	−0.233462
$262$	20.5623	1.27034
$263$	−15.6764	−0.966646	−0.483323	−	0.875442i	$-0.660570\pi$
$263$	−15.6764	−0.966646	−0.483323	+	0.875442i	$0.660570\pi$
$264$	−8.94951	−0.550804
$265$	2.08296	0.127955
$266$	−5.32085	−0.326242
$267$	−15.0909	−0.923549
$268$	−5.59100	−0.341525
$269$	19.5142	1.18980	0.594900	−	0.803800i	$-0.297192\pi$
$269$	19.5142	1.18980	0.594900	+	0.803800i	$0.297192\pi$
$270$	4.91243	0.298961
$271$	−2.24542	−0.136399	−0.0681997	−	0.997672i	$-0.521726\pi$
$271$	−2.24542	−0.136399	−0.0681997	+	0.997672i	$0.521726\pi$
$272$	4.77974	0.289814
$273$	−8.22240	−0.497642
$274$	11.8589	0.716421
$275$	14.4844	0.873444
$276$	−6.63072	−0.399122
$277$	20.9901	1.26118	0.630588	−	0.776118i	$-0.282814\pi$
$277$	20.9901	1.26118	0.630588	+	0.776118i	$0.282814\pi$
$278$	7.75184	0.464924
$279$	8.96212	0.536548
$280$	−1.87704	−0.112175
$281$	3.45150	0.205899	0.102950	−	0.994687i	$-0.467172\pi$
$281$	3.45150	0.205899	0.102950	+	0.994687i	$0.467172\pi$
$282$	−13.2333	−0.788030
$283$	−9.84051	−0.584957	−0.292479	−	0.956272i	$-0.594480\pi$
$283$	−9.84051	−0.584957	−0.292479	+	0.956272i	$0.594480\pi$
$284$	6.48718	0.384943
$285$	−9.83166	−0.582377
$286$	−12.3181	−0.728385
$287$	15.3229	0.904485
$288$	−1.15214	−0.0678906
$289$	5.84590	0.343877
$290$	−4.27093	−0.250798
$291$	−1.04968	−0.0615333
$292$	−13.2070	−0.772884
$293$	13.3361	0.779102	0.389551	−	0.921005i	$-0.372630\pi$
$293$	13.3361	0.779102	0.389551	+	0.921005i	$0.372630\pi$
$294$	−10.0458	−0.585885
$295$	17.8739	1.04066
$296$	−1.64981	−0.0958933
$297$	−16.5374	−0.959599
$298$	−17.8855	−1.03608
$299$	−9.12652	−0.527800
$300$	6.72008	0.387984
$301$	1.24821	0.0719454
$302$	−12.6920	−0.730342
$303$	−29.1188	−1.67283
$304$	−3.69827	−0.212111
$305$	12.3483	0.707061
$306$	−5.50693	−0.314811
$307$	18.3823	1.04913	0.524566	−	0.851370i	$-0.324228\pi$
$307$	18.3823	1.04913	0.524566	+	0.851370i	$0.324228\pi$
$308$	6.31895	0.360056
$309$	20.6938	1.17723
$310$	10.1484	0.576389
$311$	−5.62330	−0.318868	−0.159434	−	0.987209i	$-0.550967\pi$
$311$	−5.62330	−0.318868	−0.159434	+	0.987209i	$0.550967\pi$
$312$	−5.71501	−0.323549
$313$	−6.93370	−0.391916	−0.195958	−	0.980612i	$-0.562782\pi$
$313$	−6.93370	−0.391916	−0.195958	+	0.980612i	$0.562782\pi$
$314$	9.52005	0.537248
$315$	2.16262	0.121850
$316$	−7.09152	−0.398929
$317$	−14.5955	−0.819767	−0.409883	−	0.912138i	$-0.634431\pi$
$317$	−14.5955	−0.819767	−0.409883	+	0.912138i	$0.634431\pi$
$318$	−3.25331	−0.182436
$319$	14.3779	0.805005
$320$	−1.30464	−0.0729318
$321$	7.80490	0.435627
$322$	4.68173	0.260902
$323$	−17.6768	−0.983562
$324$	−11.1290	−0.618277
$325$	9.24952	0.513071
$326$	5.72413	0.317030
$327$	11.2189	0.620406
$328$	10.6503	0.588063
$329$	9.34357	0.515128
$330$	11.6759	0.642738
$331$	3.70231	0.203497	0.101749	−	0.994810i	$-0.467556\pi$
$331$	3.70231	0.203497	0.101749	+	0.994810i	$0.467556\pi$
$332$	−10.9303	−0.599880
$333$	1.90081	0.104164
$334$	−2.28862	−0.125228
$335$	7.29426	0.398528
$336$	2.93169	0.159937
$337$	−27.7003	−1.50893	−0.754466	−	0.656340i	$-0.772104\pi$
$337$	−27.7003	−1.50893	−0.754466	+	0.656340i	$0.772104\pi$
$338$	5.13386	0.279245
$339$	26.5388	1.44139
$340$	−6.23586	−0.338187
$341$	−34.1640	−1.85008
$342$	4.26093	0.230405
$343$	17.1642	0.926779
$344$	0.867570	0.0467762
$345$	8.65072	0.465739
$346$	−8.67000	−0.466102
$347$	−16.2722	−0.873536	−0.436768	−	0.899574i	$-0.643877\pi$
$347$	−16.2722	−0.873536	−0.436768	+	0.899574i	$0.643877\pi$
$348$	6.67063	0.357583
$349$	−14.0166	−0.750289	−0.375144	−	0.926966i	$-0.622407\pi$
$349$	−14.0166	−0.750289	−0.375144	+	0.926966i	$0.622407\pi$
$350$	−4.74482	−0.253621
$351$	−10.5605	−0.563679
$352$	4.39201	0.234095
$353$	29.5237	1.57139	0.785695	−	0.618614i	$-0.212306\pi$
$353$	29.5237	1.57139	0.785695	+	0.618614i	$0.212306\pi$
$354$	−27.9166	−1.48375
$355$	−8.46345	−0.449194
$356$	7.40593	0.392514
$357$	14.0127	0.741631
$358$	21.1263	1.11656
$359$	27.9623	1.47579	0.737896	−	0.674914i	$-0.235819\pi$
$359$	27.9623	1.47579	0.737896	+	0.674914i	$0.235819\pi$
$360$	1.50313	0.0792221
$361$	−5.32277	−0.280146
$362$	−20.8043	−1.09345
$363$	−16.8919	−0.886592
$364$	4.03518	0.211501
$365$	17.2305	0.901884
$366$	−19.2864	−1.00812
$367$	−8.36646	−0.436726	−0.218363	−	0.975868i	$-0.570072\pi$
$367$	−8.36646	−0.436726	−0.218363	+	0.975868i	$0.570072\pi$
$368$	3.25405	0.169629
$369$	−12.2706	−0.638783
$370$	2.15241	0.111899
$371$	2.29705	0.119257
$372$	−15.8504	−0.821806
$373$	12.6911	0.657121	0.328561	−	0.944483i	$-0.393437\pi$
$373$	12.6911	0.657121	0.328561	+	0.944483i	$0.393437\pi$
$374$	20.9927	1.08550
$375$	−22.0595	−1.13915
$376$	6.49428	0.334917
$377$	9.18146	0.472869
$378$	5.41734	0.278638
$379$	−27.8897	−1.43260	−0.716298	−	0.697794i	$-0.754165\pi$
$379$	−27.8897	−1.43260	−0.716298	+	0.697794i	$0.754165\pi$
$380$	4.82493	0.247514
$381$	−7.38839	−0.378519
$382$	−12.7143	−0.650523
$383$	−8.86743	−0.453104	−0.226552	−	0.973999i	$-0.572745\pi$
$383$	−8.86743	−0.453104	−0.226552	+	0.973999i	$0.572745\pi$
$384$	2.03768	0.103985
$385$	−8.24398	−0.420152
$386$	−9.61052	−0.489163
$387$	−0.999563	−0.0508107
$388$	0.515134	0.0261520
$389$	9.06816	0.459774	0.229887	−	0.973217i	$-0.426164\pi$
$389$	9.06816	0.459774	0.229887	+	0.973217i	$0.426164\pi$
$390$	7.45605	0.377552
$391$	15.5535	0.786575
$392$	4.93003	0.249004
$393$	41.8994	2.11355
$394$	9.36313	0.471708
$395$	9.25191	0.465514
$396$	−5.06022	−0.254285
$397$	−4.27657	−0.214635	−0.107317	−	0.994225i	$-0.534226\pi$
$397$	−4.27657	−0.214635	−0.107317	+	0.994225i	$0.534226\pi$
$398$	23.1785	1.16183
$399$	−10.8422	−0.542788
$400$	−3.29791	−0.164895
$401$	20.3194	1.01470	0.507351	−	0.861740i	$-0.330625\pi$
$401$	20.3194	1.01470	0.507351	+	0.861740i	$0.330625\pi$
$402$	−11.3927	−0.568215
$403$	−21.8165	−1.08676
$404$	14.2902	0.710962
$405$	14.5194	0.721473
$406$	−4.70991	−0.233749
$407$	−7.24598	−0.359170
$408$	9.73958	0.482181
$409$	2.31704	0.114570	0.0572852	−	0.998358i	$-0.481756\pi$
$409$	2.31704	0.114570	0.0572852	+	0.998358i	$0.481756\pi$
$410$	−13.8948	−0.686215
$411$	24.1646	1.19195
$412$	−10.1556	−0.500329
$413$	19.7110	0.969915
$414$	−3.74913	−0.184260
$415$	14.2602	0.700005
$416$	2.80466	0.137510
$417$	15.7958	0.773522
$418$	−16.2429	−0.794464
$419$	−7.42824	−0.362893	−0.181447	−	0.983401i	$-0.558078\pi$
$419$	−7.42824	−0.362893	−0.181447	+	0.983401i	$0.558078\pi$
$420$	−3.82481	−0.186631
$421$	5.31672	0.259121	0.129561	−	0.991572i	$-0.458643\pi$
$421$	5.31672	0.259121	0.129561	+	0.991572i	$0.458643\pi$
$422$	27.5030	1.33883
$423$	−7.48233	−0.363804
$424$	1.59657	0.0775365
$425$	−15.7631	−0.764624
$426$	13.2188	0.640453
$427$	13.6175	0.658996
$428$	−3.83029	−0.185144
$429$	−25.1004	−1.21186
$430$	−1.13187	−0.0545836
$431$	19.0671	0.918431	0.459215	−	0.888325i	$-0.348131\pi$
$431$	19.0671	0.918431	0.459215	+	0.888325i	$0.348131\pi$
$432$	3.76535	0.181160
$433$	32.6331	1.56825	0.784124	−	0.620604i	$-0.213113\pi$
$433$	32.6331	1.56825	0.784124	+	0.620604i	$0.213113\pi$
$434$	11.1915	0.537207
$435$	−8.70280	−0.417267
$436$	−5.50571	−0.263676
$437$	−12.0344	−0.575682
$438$	−26.9117	−1.28589
$439$	18.7843	0.896528	0.448264	−	0.893901i	$-0.352042\pi$
$439$	18.7843	0.896528	0.448264	+	0.893901i	$0.352042\pi$
$440$	−5.73001	−0.273167
$441$	−5.68010	−0.270481
$442$	13.4056	0.637637
$443$	−4.50093	−0.213845	−0.106923	−	0.994267i	$-0.534100\pi$
$443$	−4.50093	−0.213845	−0.106923	+	0.994267i	$0.534100\pi$
$444$	−3.36179	−0.159543
$445$	−9.66210	−0.458028
$446$	11.7658	0.557126
$447$	−36.4450	−1.72379
$448$	−1.43874	−0.0679740
$449$	31.5527	1.48907	0.744533	−	0.667586i	$-0.232672\pi$
$449$	31.5527	1.48907	0.744533	+	0.667586i	$0.232672\pi$
$450$	3.79965	0.179117
$451$	46.7761	2.20260
$452$	−13.0240	−0.612599
$453$	−25.8622	−1.21511
$454$	12.6356	0.593016
$455$	−5.26447	−0.246802
$456$	−7.53590	−0.352901
$457$	0.501675	0.0234674	0.0117337	−	0.999931i	$-0.496265\pi$
$457$	0.501675	0.0234674	0.0117337	+	0.999931i	$0.496265\pi$
$458$	24.1306	1.12755
$459$	17.9974	0.840045
$460$	−4.24538	−0.197942
$461$	−9.85868	−0.459164	−0.229582	−	0.973289i	$-0.573736\pi$
$461$	−9.85868	−0.459164	−0.229582	+	0.973289i	$0.573736\pi$
$462$	12.8760	0.599046
$463$	−5.42868	−0.252292	−0.126146	−	0.992012i	$-0.540261\pi$
$463$	−5.42868	−0.252292	−0.126146	+	0.992012i	$0.540261\pi$
$464$	−3.27364	−0.151975
$465$	20.6792	0.958973
$466$	5.70245	0.264161
$467$	−23.8882	−1.10542	−0.552708	−	0.833375i	$-0.686405\pi$
$467$	−23.8882	−1.10542	−0.552708	+	0.833375i	$0.686405\pi$
$468$	−3.23137	−0.149370
$469$	8.04398	0.371436
$470$	−8.47273	−0.390818
$471$	19.3988	0.893851
$472$	13.7002	0.630603
$473$	3.81038	0.175201
$474$	−14.4503	−0.663722
$475$	12.1966	0.559616
$476$	−6.87679	−0.315197
$477$	−1.83948	−0.0842240
$478$	9.58694	0.438497
$479$	−8.30093	−0.379279	−0.189640	−	0.981854i	$-0.560732\pi$
$479$	−8.30093	−0.379279	−0.189640	+	0.981854i	$0.560732\pi$
$480$	−2.65845	−0.121341
$481$	−4.62716	−0.210980
$482$	−22.5479	−1.02703
$483$	9.53986	0.434079
$484$	8.28975	0.376807
$485$	−0.672066	−0.0305170
$486$	−11.3813	−0.516266
$487$	−17.5119	−0.793541	−0.396770	−	0.917918i	$-0.629869\pi$
$487$	−17.5119	−0.793541	−0.396770	+	0.917918i	$0.629869\pi$
$488$	9.46488	0.428455
$489$	11.6640	0.527462
$490$	−6.43194	−0.290565
$491$	−10.8478	−0.489555	−0.244777	−	0.969579i	$-0.578715\pi$
$491$	−10.8478	−0.489555	−0.244777	+	0.969579i	$0.578715\pi$
$492$	21.7018	0.978395
$493$	−15.6471	−0.704712
$494$	−10.3724	−0.466677
$495$	6.60178	0.296728
$496$	7.77866	0.349272
$497$	−9.33335	−0.418658
$498$	−22.2725	−0.998056
$499$	−38.0992	−1.70555	−0.852776	−	0.522276i	$-0.825083\pi$
$499$	−38.0992	−1.70555	−0.852776	+	0.522276i	$0.825083\pi$
$500$	10.8258	0.484145
$501$	−4.66348	−0.208349
$502$	−5.30416	−0.236736
$503$	−23.4878	−1.04727	−0.523634	−	0.851944i	$-0.675424\pi$
$503$	−23.4878	−1.04727	−0.523634	+	0.851944i	$0.675424\pi$
$504$	1.65763	0.0738367
$505$	−18.6436	−0.829628
$506$	14.2918	0.635349
$507$	10.4612	0.464597
$508$	3.62588	0.160872
$509$	14.7166	0.652302	0.326151	−	0.945318i	$-0.394248\pi$
$509$	14.7166	0.652302	0.326151	+	0.945318i	$0.394248\pi$
$510$	−12.7067	−0.562661
$511$	19.0015	0.840575
$512$	−1.00000	−0.0441942
$513$	−13.9253	−0.614816
$514$	−8.21260	−0.362242
$515$	13.2494	0.583839
$516$	1.76783	0.0778244
$517$	28.5230	1.25444
$518$	2.37364	0.104292
$519$	−17.6667	−0.775481
$520$	−3.65909	−0.160462
$521$	−22.4012	−0.981415	−0.490707	−	0.871324i	$-0.663262\pi$
$521$	−22.4012	−0.981415	−0.490707	+	0.871324i	$0.663262\pi$
$522$	3.77170	0.165083
$523$	−27.9221	−1.22095	−0.610474	−	0.792036i	$-0.709021\pi$
$523$	−27.9221	−1.22095	−0.610474	+	0.792036i	$0.709021\pi$
$524$	−20.5623	−0.898269
$525$	−9.66843	−0.421965
$526$	15.6764	0.683522
$527$	37.1800	1.61958
$528$	8.94951	0.389477
$529$	−12.4112	−0.539615
$530$	−2.08296	−0.0904780
$531$	−15.7846	−0.684992
$532$	5.32085	0.230688
$533$	29.8704	1.29383
$534$	15.0909	0.653048
$535$	4.99716	0.216046
$536$	5.59100	0.241494
$537$	43.0486	1.85768
$538$	−19.5142	−0.841316
$539$	21.6528	0.932650
$540$	−4.91243	−0.211397
$541$	36.3418	1.56246	0.781228	−	0.624246i	$-0.214594\pi$
$541$	36.3418	1.56246	0.781228	+	0.624246i	$0.214594\pi$
$542$	2.24542	0.0964490
$543$	−42.3925	−1.81924
$544$	−4.77974	−0.204930
$545$	7.18299	0.307686
$546$	8.22240	0.351886
$547$	−20.2356	−0.865212	−0.432606	−	0.901583i	$-0.642406\pi$
$547$	−20.2356	−0.865212	−0.432606	+	0.901583i	$0.642406\pi$
$548$	−11.8589	−0.506586
$549$	−10.9049	−0.465409
$550$	−14.4844	−0.617618
$551$	12.1068	0.515768
$552$	6.63072	0.282222
$553$	10.2028	0.433869
$554$	−20.9901	−0.891786
$555$	4.38593	0.186172
$556$	−7.75184	−0.328751
$557$	24.2357	1.02690	0.513450	−	0.858120i	$-0.328367\pi$
$557$	24.2357	1.02690	0.513450	+	0.858120i	$0.328367\pi$
$558$	−8.96212	−0.379397
$559$	2.43324	0.102915
$560$	1.87704	0.0793194
$561$	42.7763	1.80602
$562$	−3.45150	−0.145593
$563$	−38.6865	−1.63044	−0.815222	−	0.579149i	$-0.803385\pi$
$563$	−38.6865	−1.63044	−0.815222	+	0.579149i	$0.803385\pi$
$564$	13.2333	0.557221
$565$	16.9917	0.714847
$566$	9.84051	0.413627
$567$	16.0117	0.672428
$568$	−6.48718	−0.272196
$569$	−18.4034	−0.771512	−0.385756	−	0.922601i	$-0.626059\pi$
$569$	−18.4034	−0.771512	−0.385756	+	0.922601i	$0.626059\pi$
$570$	9.83166	0.411803
$571$	−28.2700	−1.18306	−0.591531	−	0.806283i	$-0.701476\pi$
$571$	−28.2700	−1.18306	−0.591531	+	0.806283i	$0.701476\pi$
$572$	12.3181	0.515046
$573$	−25.9078	−1.08231
$574$	−15.3229	−0.639567
$575$	−10.7316	−0.447537
$576$	1.15214	0.0480059
$577$	23.5219	0.979229	0.489615	−	0.871939i	$-0.337137\pi$
$577$	23.5219	0.979229	0.489615	+	0.871939i	$0.337137\pi$
$578$	−5.84590	−0.243157
$579$	−19.5832	−0.813849
$580$	4.27093	0.177341
$581$	15.7259	0.652420
$582$	1.04968	0.0435106
$583$	7.01217	0.290414
$584$	13.2070	0.546511
$585$	4.21579	0.174301
$586$	−13.3361	−0.550908
$587$	9.88874	0.408152	0.204076	−	0.978955i	$-0.434581\pi$
$587$	9.88874	0.408152	0.204076	+	0.978955i	$0.434581\pi$
$588$	10.0458	0.414283
$589$	−28.7676	−1.18535
$590$	−17.8739	−0.735856
$591$	19.0791	0.784808
$592$	1.64981	0.0678068
$593$	36.3661	1.49338	0.746689	−	0.665174i	$-0.231642\pi$
$593$	36.3661	1.49338	0.746689	+	0.665174i	$0.231642\pi$
$594$	16.5374	0.678539
$595$	8.97176	0.367806
$596$	17.8855	0.732620
$597$	47.2304	1.93301
$598$	9.12652	0.373211
$599$	33.6172	1.37356	0.686782	−	0.726864i	$-0.259023\pi$
$599$	33.6172	1.37356	0.686782	+	0.726864i	$0.259023\pi$
$600$	−6.72008	−0.274346
$601$	−20.5287	−0.837384	−0.418692	−	0.908128i	$-0.637511\pi$
$601$	−20.5287	−0.837384	−0.418692	+	0.908128i	$0.637511\pi$
$602$	−1.24821	−0.0508731
$603$	−6.44162	−0.262323
$604$	12.6920	0.516430
$605$	−10.8152	−0.439699
$606$	29.1188	1.18287
$607$	23.8199	0.966819	0.483410	−	0.875394i	$-0.339398\pi$
$607$	23.8199	0.966819	0.483410	+	0.875394i	$0.339398\pi$
$608$	3.69827	0.149985
$609$	−9.59729	−0.388902
$610$	−12.3483	−0.499968
$611$	18.2143	0.736871
$612$	5.50693	0.222605
$613$	−41.0565	−1.65826	−0.829128	−	0.559059i	$-0.811163\pi$
$613$	−41.0565	−1.65826	−0.829128	+	0.559059i	$0.811163\pi$
$614$	−18.3823	−0.741848
$615$	−28.3132	−1.14170
$616$	−6.31895	−0.254598
$617$	21.0048	0.845623	0.422812	−	0.906218i	$-0.361043\pi$
$617$	21.0048	0.845623	0.422812	+	0.906218i	$0.361043\pi$
$618$	−20.6938	−0.832428
$619$	12.0281	0.483450	0.241725	−	0.970345i	$-0.422287\pi$
$619$	12.0281	0.483450	0.241725	+	0.970345i	$0.422287\pi$
$620$	−10.1484	−0.407569
$621$	12.2526	0.491681
$622$	5.62330	0.225474
$623$	−10.6552	−0.426891
$624$	5.71501	0.228783
$625$	2.36570	0.0946282
$626$	6.93370	0.277126
$627$	−33.0977	−1.32180
$628$	−9.52005	−0.379891
$629$	7.88566	0.314422
$630$	−2.16262	−0.0861607
$631$	28.8900	1.15009	0.575047	−	0.818120i	$-0.304984\pi$
$631$	28.8900	1.15009	0.575047	+	0.818120i	$0.304984\pi$
$632$	7.09152	0.282086
$633$	56.0424	2.22749
$634$	14.5955	0.579663
$635$	−4.73048	−0.187723
$636$	3.25331	0.129002
$637$	13.8271	0.547849
$638$	−14.3779	−0.569225
$639$	7.47415	0.295673
$640$	1.30464	0.0515706
$641$	23.9930	0.947666	0.473833	−	0.880615i	$-0.342870\pi$
$641$	23.9930	0.947666	0.473833	+	0.880615i	$0.342870\pi$
$642$	−7.80490	−0.308035
$643$	28.1669	1.11079	0.555397	−	0.831586i	$-0.312567\pi$
$643$	28.1669	1.11079	0.555397	+	0.831586i	$0.312567\pi$
$644$	−4.68173	−0.184486
$645$	−2.30639	−0.0908140
$646$	17.6768	0.695484
$647$	17.0887	0.671824	0.335912	−	0.941893i	$-0.390955\pi$
$647$	17.0887	0.671824	0.335912	+	0.941893i	$0.390955\pi$
$648$	11.1290	0.437188
$649$	60.1714	2.36194
$650$	−9.24952	−0.362796
$651$	22.8046	0.893783
$652$	−5.72413	−0.224174
$653$	0.0909349	0.00355856	0.00177928	−	0.999998i	$-0.499434\pi$
$653$	0.0909349	0.00355856	0.00177928	+	0.999998i	$0.499434\pi$
$654$	−11.2189	−0.438693
$655$	26.8265	1.04820
$656$	−10.6503	−0.415823
$657$	−15.2164	−0.593647
$658$	−9.34357	−0.364250
$659$	25.7830	1.00436	0.502181	−	0.864762i	$-0.332531\pi$
$659$	25.7830	1.00436	0.502181	+	0.864762i	$0.332531\pi$
$660$	−11.6759	−0.454485
$661$	−36.6612	−1.42596	−0.712978	−	0.701186i	$-0.752654\pi$
$661$	−36.6612	−1.42596	−0.712978	+	0.701186i	$0.752654\pi$
$662$	−3.70231	−0.143894
$663$	27.3162	1.06088
$664$	10.9303	0.424179
$665$	−6.94181	−0.269192
$666$	−1.90081	−0.0736551
$667$	−10.6526	−0.412470
$668$	2.28862	0.0885494
$669$	23.9749	0.926924
$670$	−7.29426	−0.281802
$671$	41.5698	1.60479
$672$	−2.93169	−0.113092
$673$	22.1296	0.853034	0.426517	−	0.904480i	$-0.359740\pi$
$673$	22.1296	0.853034	0.426517	+	0.904480i	$0.359740\pi$
$674$	27.7003	1.06698
$675$	−12.4178	−0.477959
$676$	−5.13386	−0.197456
$677$	−24.6039	−0.945607	−0.472803	−	0.881168i	$-0.656758\pi$
$677$	−24.6039	−0.945607	−0.472803	+	0.881168i	$0.656758\pi$
$678$	−26.5388	−1.01922
$679$	−0.741143	−0.0284425
$680$	6.23586	0.239134
$681$	25.7472	0.986636
$682$	34.1640	1.30821
$683$	−3.04932	−0.116679	−0.0583394	−	0.998297i	$-0.518581\pi$
$683$	−3.04932	−0.116679	−0.0583394	+	0.998297i	$0.518581\pi$
$684$	−4.26093	−0.162921
$685$	15.4716	0.591140
$686$	−17.1642	−0.655332
$687$	49.1705	1.87597
$688$	−0.867570	−0.0330758
$689$	4.47785	0.170593
$690$	−8.65072	−0.329327
$691$	35.1874	1.33859	0.669295	−	0.742997i	$-0.266596\pi$
$691$	35.1874	1.33859	0.669295	+	0.742997i	$0.266596\pi$
$692$	8.67000	0.329584
$693$	7.28032	0.276557
$694$	16.2722	0.617684
$695$	10.1134	0.383623
$696$	−6.67063	−0.252850
$697$	−50.9055	−1.92818
$698$	14.0166	0.530534
$699$	11.6198	0.439500
$700$	4.74482	0.179337
$701$	21.1905	0.800353	0.400176	−	0.916438i	$-0.368949\pi$
$701$	21.1905	0.800353	0.400176	+	0.916438i	$0.368949\pi$
$702$	10.5605	0.398581
$703$	−6.10145	−0.230121
$704$	−4.39201	−0.165530
$705$	−17.2647	−0.650227
$706$	−29.5237	−1.11114
$707$	−20.5598	−0.773231
$708$	27.9166	1.04917
$709$	−8.76400	−0.329139	−0.164569	−	0.986365i	$-0.552623\pi$
$709$	−8.76400	−0.329139	−0.164569	+	0.986365i	$0.552623\pi$
$710$	8.46345	0.317628
$711$	−8.17044	−0.306415
$712$	−7.40593	−0.277549
$713$	25.3122	0.947948
$714$	−14.0127	−0.524412
$715$	−16.0707	−0.601012
$716$	−21.1263	−0.789525
$717$	19.5351	0.729553
$718$	−27.9623	−1.04354
$719$	18.4177	0.686865	0.343432	−	0.939177i	$-0.388410\pi$
$719$	18.4177	0.686865	0.343432	+	0.939177i	$0.388410\pi$
$720$	−1.50313	−0.0560185
$721$	14.6112	0.544150
$722$	5.32277	0.198093
$723$	−45.9454	−1.70873
$724$	20.8043	0.773185
$725$	10.7962	0.400959
$726$	16.8919	0.626915
$727$	−8.45463	−0.313565	−0.156782	−	0.987633i	$-0.550112\pi$
$727$	−8.45463	−0.313565	−0.156782	+	0.987633i	$0.550112\pi$
$728$	−4.03518	−0.149554
$729$	10.1955	0.377612
$730$	−17.2305	−0.637729
$731$	−4.14676	−0.153373
$732$	19.2864	0.712846
$733$	−28.4577	−1.05111	−0.525554	−	0.850760i	$-0.676142\pi$
$733$	−28.4577	−1.05111	−0.525554	+	0.850760i	$0.676142\pi$
$734$	8.36646	0.308812
$735$	−13.1062	−0.483431
$736$	−3.25405	−0.119946
$737$	24.5557	0.904521
$738$	12.2706	0.451688
$739$	44.1937	1.62569	0.812846	−	0.582478i	$-0.197917\pi$
$739$	44.1937	1.62569	0.812846	+	0.582478i	$0.197917\pi$
$740$	−2.15241	−0.0791243
$741$	−21.1357	−0.776438
$742$	−2.29705	−0.0843274
$743$	−32.0715	−1.17659	−0.588294	−	0.808647i	$-0.700200\pi$
$743$	−32.0715	−1.17659	−0.588294	+	0.808647i	$0.700200\pi$
$744$	15.8504	0.581105
$745$	−23.3343	−0.854901
$746$	−12.6911	−0.464655
$747$	−12.5933	−0.460764
$748$	−20.9927	−0.767568
$749$	5.51078	0.201359
$750$	22.0595	0.805500
$751$	1.93104	0.0704646	0.0352323	−	0.999379i	$-0.488783\pi$
$751$	1.93104	0.0704646	0.0352323	+	0.999379i	$0.488783\pi$
$752$	−6.49428	−0.236822
$753$	−10.8082	−0.393872
$754$	−9.18146	−0.334369
$755$	−16.5585	−0.602626
$756$	−5.41734	−0.197027
$757$	−3.79836	−0.138054	−0.0690269	−	0.997615i	$-0.521989\pi$
$757$	−3.79836	−0.138054	−0.0690269	+	0.997615i	$0.521989\pi$
$758$	27.8897	1.01300
$759$	29.1222	1.05707
$760$	−4.82493	−0.175019
$761$	39.1024	1.41746	0.708731	−	0.705479i	$-0.249268\pi$
$761$	39.1024	1.41746	0.708731	+	0.705479i	$0.249268\pi$
$762$	7.38839	0.267653
$763$	7.92127	0.286769
$764$	12.7143	0.459989
$765$	−7.18459	−0.259759
$766$	8.86743	0.320393
$767$	38.4245	1.38743
$768$	−2.03768	−0.0735285
$769$	−21.0734	−0.759925	−0.379962	−	0.925002i	$-0.624063\pi$
$769$	−21.0734	−0.759925	−0.379962	+	0.925002i	$0.624063\pi$
$770$	8.24398	0.297092
$771$	−16.7346	−0.602684
$772$	9.61052	0.345890
$773$	22.5518	0.811133	0.405567	−	0.914066i	$-0.367074\pi$
$773$	22.5518	0.811133	0.405567	+	0.914066i	$0.367074\pi$
$774$	0.999563	0.0359286
$775$	−25.6533	−0.921493
$776$	−0.515134	−0.0184922
$777$	4.83673	0.173517
$778$	−9.06816	−0.325109
$779$	39.3876	1.41121
$780$	−7.45605	−0.266969
$781$	−28.4917	−1.01951
$782$	−15.5535	−0.556193
$783$	−12.3264	−0.440509
$784$	−4.93003	−0.176073
$785$	12.4203	0.443299
$786$	−41.8994	−1.49450
$787$	−49.8863	−1.77825	−0.889127	−	0.457661i	$-0.848687\pi$
$787$	−49.8863	−1.77825	−0.889127	+	0.457661i	$0.848687\pi$
$788$	−9.36313	−0.333548
$789$	31.9434	1.13722
$790$	−9.25191	−0.329168
$791$	18.7382	0.666252
$792$	5.06022	0.179807
$793$	26.5458	0.942669
$794$	4.27657	0.151770
$795$	−4.24441	−0.150534
$796$	−23.1785	−0.821541
$797$	23.1056	0.818444	0.409222	−	0.912435i	$-0.365800\pi$
$797$	23.1056	0.818444	0.409222	+	0.912435i	$0.365800\pi$
$798$	10.8422	0.383809
$799$	−31.0410	−1.09815
$800$	3.29791	0.116599
$801$	8.53268	0.301487
$802$	−20.3194	−0.717502
$803$	58.0054	2.04697
$804$	11.3927	0.401788
$805$	6.10798	0.215278
$806$	21.8165	0.768454
$807$	−39.7637	−1.39975
$808$	−14.2902	−0.502726
$809$	38.3943	1.34987	0.674936	−	0.737876i	$-0.264171\pi$
$809$	38.3943	1.34987	0.674936	+	0.737876i	$0.264171\pi$
$810$	−14.5194	−0.510159
$811$	17.9565	0.630538	0.315269	−	0.949002i	$-0.397905\pi$
$811$	17.9565	0.630538	0.315269	+	0.949002i	$0.397905\pi$
$812$	4.70991	0.165285
$813$	4.57544	0.160468
$814$	7.24598	0.253972
$815$	7.46795	0.261591
$816$	−9.73958	−0.340953
$817$	3.20851	0.112252
$818$	−2.31704	−0.0810134
$819$	4.64909	0.162452
$820$	13.8948	0.485228
$821$	14.8524	0.518352	0.259176	−	0.965830i	$-0.416549\pi$
$821$	14.8524	0.518352	0.259176	+	0.965830i	$0.416549\pi$
$822$	−24.1646	−0.842837
$823$	−1.97279	−0.0687670	−0.0343835	−	0.999409i	$-0.510947\pi$
$823$	−1.97279	−0.0687670	−0.0343835	+	0.999409i	$0.510947\pi$
$824$	10.1556	0.353786
$825$	−29.5146	−1.02757
$826$	−19.7110	−0.685833
$827$	20.0337	0.696638	0.348319	−	0.937376i	$-0.386753\pi$
$827$	20.0337	0.696638	0.348319	+	0.937376i	$0.386753\pi$
$828$	3.74913	0.130291
$829$	−44.2706	−1.53758	−0.768791	−	0.639500i	$-0.779141\pi$
$829$	−44.2706	−1.53758	−0.768791	+	0.639500i	$0.779141\pi$
$830$	−14.2602	−0.494978
$831$	−42.7712	−1.48372
$832$	−2.80466	−0.0972342
$833$	−23.5643	−0.816454
$834$	−15.7958	−0.546963
$835$	−2.98583	−0.103329
$836$	16.2429	0.561771
$837$	29.2893	1.01239
$838$	7.42824	0.256604
$839$	−21.5496	−0.743974	−0.371987	−	0.928238i	$-0.621323\pi$
$839$	−21.5496	−0.743974	−0.371987	+	0.928238i	$0.621323\pi$
$840$	3.82481	0.131968
$841$	−18.2833	−0.630458
$842$	−5.31672	−0.183226
$843$	−7.03306	−0.242231
$844$	−27.5030	−0.946694
$845$	6.69786	0.230413
$846$	7.48233	0.257248
$847$	−11.9268	−0.409809
$848$	−1.59657	−0.0548266
$849$	20.0518	0.688176
$850$	15.7631	0.540671
$851$	5.36857	0.184032
$852$	−13.2188	−0.452868
$853$	39.4014	1.34908	0.674539	−	0.738239i	$-0.264342\pi$
$853$	39.4014	1.34908	0.674539	+	0.738239i	$0.264342\pi$
$854$	−13.6175	−0.465980
$855$	5.55900	0.190114
$856$	3.83029	0.130916
$857$	−1.55667	−0.0531748	−0.0265874	−	0.999646i	$-0.508464\pi$
$857$	−1.55667	−0.0531748	−0.0265874	+	0.999646i	$0.508464\pi$
$858$	25.1004	0.856912
$859$	−34.6440	−1.18204	−0.591020	−	0.806657i	$-0.701274\pi$
$859$	−34.6440	−1.18204	−0.591020	+	0.806657i	$0.701274\pi$
$860$	1.13187	0.0385964
$861$	−31.2233	−1.06409
$862$	−19.0671	−0.649429
$863$	4.81729	0.163982	0.0819912	−	0.996633i	$-0.473872\pi$
$863$	4.81729	0.163982	0.0819912	+	0.996633i	$0.473872\pi$
$864$	−3.76535	−0.128100
$865$	−11.3113	−0.384594
$866$	−32.6331	−1.10892
$867$	−11.9121	−0.404555
$868$	−11.1915	−0.379863
$869$	31.1460	1.05656
$870$	8.70280	0.295052
$871$	15.6809	0.531326
$872$	5.50571	0.186447
$873$	0.593507	0.0200872
$874$	12.0344	0.407069
$875$	−15.5755	−0.526548
$876$	26.9117	0.909263
$877$	−51.4857	−1.73855	−0.869274	−	0.494331i	$-0.835413\pi$
$877$	−51.4857	−1.73855	−0.869274	+	0.494331i	$0.835413\pi$
$878$	−18.7843	−0.633941
$879$	−27.1747	−0.916578
$880$	5.73001	0.193158
$881$	31.5152	1.06177	0.530887	−	0.847443i	$-0.321859\pi$
$881$	31.5152	1.06177	0.530887	+	0.847443i	$0.321859\pi$
$882$	5.68010	0.191259
$883$	1.31358	0.0442054	0.0221027	−	0.999756i	$-0.492964\pi$
$883$	1.31358	0.0442054	0.0221027	+	0.999756i	$0.492964\pi$
$884$	−13.4056	−0.450878
$885$	−36.4213	−1.22429
$886$	4.50093	0.151212
$887$	8.50006	0.285404	0.142702	−	0.989766i	$-0.454421\pi$
$887$	8.50006	0.285404	0.142702	+	0.989766i	$0.454421\pi$
$888$	3.36179	0.112814
$889$	−5.21669	−0.174962
$890$	9.66210	0.323874
$891$	48.8786	1.63750
$892$	−11.7658	−0.393948
$893$	24.0176	0.803720
$894$	36.4450	1.21890
$895$	27.5622	0.921304
$896$	1.43874	0.0480648
$897$	18.5969	0.620933
$898$	−31.5527	−1.05293
$899$	−25.4645	−0.849290
$900$	−3.79965	−0.126655
$901$	−7.63121	−0.254232
$902$	−46.7761	−1.55747
$903$	−2.54344	−0.0846405
$904$	13.0240	0.433173
$905$	−27.1422	−0.902237
$906$	25.8622	0.859215
$907$	39.6044	1.31504	0.657521	−	0.753436i	$-0.271605\pi$
$907$	39.6044	1.31504	0.657521	+	0.753436i	$0.271605\pi$
$908$	−12.6356	−0.419326
$909$	16.4643	0.546086
$910$	5.26447	0.174515
$911$	27.8470	0.922613	0.461307	−	0.887241i	$-0.347381\pi$
$911$	27.8470	0.922613	0.461307	+	0.887241i	$0.347381\pi$
$912$	7.53590	0.249539
$913$	48.0061	1.58877
$914$	−0.501675	−0.0165939
$915$	−25.1619	−0.831826
$916$	−24.1306	−0.797298
$917$	29.5838	0.976943
$918$	−17.9974	−0.594002
$919$	33.6588	1.11030	0.555151	−	0.831750i	$-0.312660\pi$
$919$	33.6588	1.11030	0.555151	+	0.831750i	$0.312660\pi$
$920$	4.24538	0.139966
$921$	−37.4572	−1.23426
$922$	9.85868	0.324678
$923$	−18.1944	−0.598874
$924$	−12.8760	−0.423589
$925$	−5.44092	−0.178896
$926$	5.42868	0.178398
$927$	−11.7007	−0.384300
$928$	3.27364	0.107462
$929$	−33.1366	−1.08718	−0.543588	−	0.839352i	$-0.682935\pi$
$929$	−33.1366	−1.08718	−0.543588	+	0.839352i	$0.682935\pi$
$930$	−20.6792	−0.678096
$931$	18.2326	0.597550
$932$	−5.70245	−0.186790
$933$	11.4585	0.375134
$934$	23.8882	0.781647
$935$	27.3879	0.895681
$936$	3.23137	0.105621
$937$	−46.7125	−1.52603	−0.763015	−	0.646380i	$-0.776282\pi$
$937$	−46.7125	−1.52603	−0.763015	+	0.646380i	$0.776282\pi$
$938$	−8.04398	−0.262645
$939$	14.1287	0.461072
$940$	8.47273	0.276350
$941$	30.6640	0.999617	0.499809	−	0.866136i	$-0.333404\pi$
$941$	30.6640	0.999617	0.499809	+	0.866136i	$0.333404\pi$
$942$	−19.3988	−0.632048
$943$	−34.6565	−1.12857
$944$	−13.7002	−0.445904
$945$	7.06770	0.229912
$946$	−3.81038	−0.123886
$947$	−20.2599	−0.658359	−0.329180	−	0.944267i	$-0.606772\pi$
$947$	−20.2599	−0.658359	−0.329180	+	0.944267i	$0.606772\pi$
$948$	14.4503	0.469322
$949$	37.0413	1.20241
$950$	−12.1966	−0.395709
$951$	29.7410	0.964419
$952$	6.87679	0.222878
$953$	−46.0738	−1.49248	−0.746238	−	0.665679i	$-0.768142\pi$
$953$	−46.0738	−1.49248	−0.746238	+	0.665679i	$0.768142\pi$
$954$	1.83948	0.0595553
$955$	−16.5877	−0.536765
$956$	−9.58694	−0.310064
$957$	−29.2975	−0.947053
$958$	8.30093	0.268191
$959$	17.0618	0.550955
$960$	2.65845	0.0858010
$961$	29.5076	0.951857
$962$	4.62716	0.149186
$963$	−4.41303	−0.142208
$964$	22.5479	0.726219
$965$	−12.5383	−0.403622
$966$	−9.53986	−0.306940
$967$	−35.6175	−1.14538	−0.572692	−	0.819771i	$-0.694101\pi$
$967$	−35.6175	−1.14538	−0.572692	+	0.819771i	$0.694101\pi$
$968$	−8.28975	−0.266443
$969$	36.0196	1.15712
$970$	0.672066	0.0215788
$971$	−4.69462	−0.150658	−0.0753288	−	0.997159i	$-0.524001\pi$
$971$	−4.69462	−0.150658	−0.0753288	+	0.997159i	$0.524001\pi$
$972$	11.3813	0.365055
$973$	11.1529	0.357544
$974$	17.5119	0.561118
$975$	−18.8476	−0.603605
$976$	−9.46488	−0.302963
$977$	−48.3128	−1.54566	−0.772831	−	0.634611i	$-0.781160\pi$
$977$	−48.3128	−1.54566	−0.772831	+	0.634611i	$0.781160\pi$
$978$	−11.6640	−0.372972
$979$	−32.5269	−1.03956
$980$	6.43194	0.205461
$981$	−6.34336	−0.202528
$982$	10.8478	0.346167
$983$	18.1258	0.578125	0.289062	−	0.957310i	$-0.406657\pi$
$983$	18.1258	0.578125	0.289062	+	0.957310i	$0.406657\pi$
$984$	−21.7018	−0.691829
$985$	12.2155	0.389220
$986$	15.6471	0.498306
$987$	−19.0392	−0.606025
$988$	10.3724	0.329990
$989$	−2.82312	−0.0897699
$990$	−6.60178	−0.209818
$991$	−0.999750	−0.0317581	−0.0158791	−	0.999874i	$-0.505055\pi$
$991$	−0.999750	−0.0317581	−0.0158791	+	0.999874i	$0.505055\pi$
$992$	−7.77866	−0.246973
$993$	−7.54413	−0.239406
$994$	9.33335	0.296036
$995$	30.2397	0.958663
$996$	22.2725	0.705732
$997$	−37.7255	−1.19478	−0.597390	−	0.801951i	$-0.703795\pi$
$997$	−37.7255	−1.19478	−0.597390	+	0.801951i	$0.703795\pi$
$998$	38.0992	1.20601
$999$	6.21211	0.196542

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8014.2.a.e.1.19	✓	91

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8014.2.a.e.1.19	✓	91	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:	\( N \)	\(=\)	\( 8014 = 2 \cdot 4007 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8014.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.03768 q^{3} +1.00000 q^{4} -1.30464 q^{5} +2.03768 q^{6} -1.43874 q^{7} -1.00000 q^{8} +1.15214 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.03768 q^{3} +1.00000 q^{4} -1.30464 q^{5} +2.03768 q^{6} -1.43874 q^{7} -1.00000 q^{8} +1.15214 q^{9} +1.30464 q^{10} -4.39201 q^{11} -2.03768 q^{12} -2.80466 q^{13} +1.43874 q^{14} +2.65845 q^{15} +1.00000 q^{16} +4.77974 q^{17} -1.15214 q^{18} -3.69827 q^{19} -1.30464 q^{20} +2.93169 q^{21} +4.39201 q^{22} +3.25405 q^{23} +2.03768 q^{24} -3.29791 q^{25} +2.80466 q^{26} +3.76535 q^{27} -1.43874 q^{28} -3.27364 q^{29} -2.65845 q^{30} +7.77866 q^{31} -1.00000 q^{32} +8.94951 q^{33} -4.77974 q^{34} +1.87704 q^{35} +1.15214 q^{36} +1.64981 q^{37} +3.69827 q^{38} +5.71501 q^{39} +1.30464 q^{40} -10.6503 q^{41} -2.93169 q^{42} -0.867570 q^{43} -4.39201 q^{44} -1.50313 q^{45} -3.25405 q^{46} -6.49428 q^{47} -2.03768 q^{48} -4.93003 q^{49} +3.29791 q^{50} -9.73958 q^{51} -2.80466 q^{52} -1.59657 q^{53} -3.76535 q^{54} +5.73001 q^{55} +1.43874 q^{56} +7.53590 q^{57} +3.27364 q^{58} -13.7002 q^{59} +2.65845 q^{60} -9.46488 q^{61} -7.77866 q^{62} -1.65763 q^{63} +1.00000 q^{64} +3.65909 q^{65} -8.94951 q^{66} -5.59100 q^{67} +4.77974 q^{68} -6.63072 q^{69} -1.87704 q^{70} +6.48718 q^{71} -1.15214 q^{72} -13.2070 q^{73} -1.64981 q^{74} +6.72008 q^{75} -3.69827 q^{76} +6.31895 q^{77} -5.71501 q^{78} -7.09152 q^{79} -1.30464 q^{80} -11.1290 q^{81} +10.6503 q^{82} -10.9303 q^{83} +2.93169 q^{84} -6.23586 q^{85} +0.867570 q^{86} +6.67063 q^{87} +4.39201 q^{88} +7.40593 q^{89} +1.50313 q^{90} +4.03518 q^{91} +3.25405 q^{92} -15.8504 q^{93} +6.49428 q^{94} +4.82493 q^{95} +2.03768 q^{96} +0.515134 q^{97} +4.93003 q^{98} -5.06022 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 91 q - 91 q^{2} - 2 q^{3} + 91 q^{4} + 22 q^{5} + 2 q^{6} - 14 q^{7} - 91 q^{8} + 123 q^{9}+O(q^{10}) \) 91 * q - 91 * q^2 - 2 * q^3 + 91 * q^4 + 22 * q^5 + 2 * q^6 - 14 * q^7 - 91 * q^8 + 123 * q^9	\( 91 q - 91 q^{2} - 2 q^{3} + 91 q^{4} + 22 q^{5} + 2 q^{6} - 14 q^{7} - 91 q^{8} + 123 q^{9} - 22 q^{10} + 59 q^{11} - 2 q^{12} - 15 q^{13} + 14 q^{14} + 23 q^{15} + 91 q^{16} + 25 q^{17} - 123 q^{18} + 2 q^{19} + 22 q^{20} + 20 q^{21} - 59 q^{22} + 36 q^{23} + 2 q^{24} + 121 q^{25} + 15 q^{26} - 8 q^{27} - 14 q^{28} + 71 q^{29} - 23 q^{30} + 13 q^{31} - 91 q^{32} + 24 q^{33} - 25 q^{34} + 27 q^{35} + 123 q^{36} + 5 q^{37} - 2 q^{38} + 48 q^{39} - 22 q^{40} + 77 q^{41} - 20 q^{42} - 36 q^{43} + 59 q^{44} + 62 q^{45} - 36 q^{46} + 41 q^{47} - 2 q^{48} + 137 q^{49} - 121 q^{50} + 13 q^{51} - 15 q^{52} + 33 q^{53} + 8 q^{54} + 12 q^{55} + 14 q^{56} + 52 q^{57} - 71 q^{58} + 76 q^{59} + 23 q^{60} + 18 q^{61} - 13 q^{62} - 18 q^{63} + 91 q^{64} + 84 q^{65} - 24 q^{66} - 59 q^{67} + 25 q^{68} + 64 q^{69} - 27 q^{70} + 124 q^{71} - 123 q^{72} + 43 q^{73} - 5 q^{74} + 9 q^{75} + 2 q^{76} + 50 q^{77} - 48 q^{78} - 20 q^{79} + 22 q^{80} + 227 q^{81} - 77 q^{82} + 29 q^{83} + 20 q^{84} + 3 q^{85} + 36 q^{86} - 25 q^{87} - 59 q^{88} + 148 q^{89} - 62 q^{90} + 27 q^{91} + 36 q^{92} + 65 q^{93} - 41 q^{94} + 54 q^{95} + 2 q^{96} + 38 q^{97} - 137 q^{98} + 157 q^{99}+O(q^{100}) \) 91 * q - 91 * q^2 - 2 * q^3 + 91 * q^4 + 22 * q^5 + 2 * q^6 - 14 * q^7 - 91 * q^8 + 123 * q^9 - 22 * q^10 + 59 * q^11 - 2 * q^12 - 15 * q^13 + 14 * q^14 + 23 * q^15 + 91 * q^16 + 25 * q^17 - 123 * q^18 + 2 * q^19 + 22 * q^20 + 20 * q^21 - 59 * q^22 + 36 * q^23 + 2 * q^24 + 121 * q^25 + 15 * q^26 - 8 * q^27 - 14 * q^28 + 71 * q^29 - 23 * q^30 + 13 * q^31 - 91 * q^32 + 24 * q^33 - 25 * q^34 + 27 * q^35 + 123 * q^36 + 5 * q^37 - 2 * q^38 + 48 * q^39 - 22 * q^40 + 77 * q^41 - 20 * q^42 - 36 * q^43 + 59 * q^44 + 62 * q^45 - 36 * q^46 + 41 * q^47 - 2 * q^48 + 137 * q^49 - 121 * q^50 + 13 * q^51 - 15 * q^52 + 33 * q^53 + 8 * q^54 + 12 * q^55 + 14 * q^56 + 52 * q^57 - 71 * q^58 + 76 * q^59 + 23 * q^60 + 18 * q^61 - 13 * q^62 - 18 * q^63 + 91 * q^64 + 84 * q^65 - 24 * q^66 - 59 * q^67 + 25 * q^68 + 64 * q^69 - 27 * q^70 + 124 * q^71 - 123 * q^72 + 43 * q^73 - 5 * q^74 + 9 * q^75 + 2 * q^76 + 50 * q^77 - 48 * q^78 - 20 * q^79 + 22 * q^80 + 227 * q^81 - 77 * q^82 + 29 * q^83 + 20 * q^84 + 3 * q^85 + 36 * q^86 - 25 * q^87 - 59 * q^88 + 148 * q^89 - 62 * q^90 + 27 * q^91 + 36 * q^92 + 65 * q^93 - 41 * q^94 + 54 * q^95 + 2 * q^96 + 38 * q^97 - 137 * q^98 + 157 * q^99

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