LMFDB - Embedded newform 8014.2.a.d.1.14

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:	$88$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
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)

$f(q)$	$=$	$q+1.00000 q^{2} -2.26140 q^{3} +1.00000 q^{4} -1.73870 q^{5} -2.26140 q^{6} -2.77914 q^{7} +1.00000 q^{8} +2.11392 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.26140 q^{3} +1.00000 q^{4} -1.73870 q^{5} -2.26140 q^{6} -2.77914 q^{7} +1.00000 q^{8} +2.11392 q^{9} -1.73870 q^{10} +4.49936 q^{11} -2.26140 q^{12} +3.58840 q^{13} -2.77914 q^{14} +3.93189 q^{15} +1.00000 q^{16} +7.32917 q^{17} +2.11392 q^{18} +2.05930 q^{19} -1.73870 q^{20} +6.28473 q^{21} +4.49936 q^{22} -2.85306 q^{23} -2.26140 q^{24} -1.97692 q^{25} +3.58840 q^{26} +2.00378 q^{27} -2.77914 q^{28} +2.95927 q^{29} +3.93189 q^{30} +3.96277 q^{31} +1.00000 q^{32} -10.1748 q^{33} +7.32917 q^{34} +4.83208 q^{35} +2.11392 q^{36} -0.0376675 q^{37} +2.05930 q^{38} -8.11479 q^{39} -1.73870 q^{40} -4.78130 q^{41} +6.28473 q^{42} -6.66844 q^{43} +4.49936 q^{44} -3.67547 q^{45} -2.85306 q^{46} -1.44754 q^{47} -2.26140 q^{48} +0.723593 q^{49} -1.97692 q^{50} -16.5742 q^{51} +3.58840 q^{52} -3.89902 q^{53} +2.00378 q^{54} -7.82303 q^{55} -2.77914 q^{56} -4.65690 q^{57} +2.95927 q^{58} -3.98196 q^{59} +3.93189 q^{60} -2.70423 q^{61} +3.96277 q^{62} -5.87487 q^{63} +1.00000 q^{64} -6.23914 q^{65} -10.1748 q^{66} +2.02850 q^{67} +7.32917 q^{68} +6.45191 q^{69} +4.83208 q^{70} +2.08685 q^{71} +2.11392 q^{72} -5.00913 q^{73} -0.0376675 q^{74} +4.47061 q^{75} +2.05930 q^{76} -12.5043 q^{77} -8.11479 q^{78} +16.6662 q^{79} -1.73870 q^{80} -10.8731 q^{81} -4.78130 q^{82} +17.1785 q^{83} +6.28473 q^{84} -12.7432 q^{85} -6.66844 q^{86} -6.69209 q^{87} +4.49936 q^{88} +6.07970 q^{89} -3.67547 q^{90} -9.97264 q^{91} -2.85306 q^{92} -8.96140 q^{93} -1.44754 q^{94} -3.58051 q^{95} -2.26140 q^{96} -2.99026 q^{97} +0.723593 q^{98} +9.51128 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 88 q^{2} + 22 q^{3} + 88 q^{4} + 25 q^{5} + 22 q^{6} + 33 q^{7} + 88 q^{8} + 108 q^{9}+O(q^{10}) $ 88 * q + 88 * q^2 + 22 * q^3 + 88 * q^4 + 25 * q^5 + 22 * q^6 + 33 * q^7 + 88 * q^8 + 108 * q^9	\( 88 q + 88 q^{2} + 22 q^{3} + 88 q^{4} + 25 q^{5} + 22 q^{6} + 33 q^{7} + 88 q^{8} + 108 q^{9} + 25 q^{10} + 70 q^{11} + 22 q^{12} + 31 q^{13} + 33 q^{14} + 47 q^{15} + 88 q^{16} + 19 q^{17} + 108 q^{18} + 33 q^{19} + 25 q^{20} + 48 q^{21} + 70 q^{22} + 77 q^{23} + 22 q^{24} + 109 q^{25} + 31 q^{26} + 88 q^{27} + 33 q^{28} + 83 q^{29} + 47 q^{30} + 51 q^{31} + 88 q^{32} + 30 q^{33} + 19 q^{34} + 40 q^{35} + 108 q^{36} + 45 q^{37} + 33 q^{38} + 82 q^{39} + 25 q^{40} + 35 q^{41} + 48 q^{42} + 78 q^{43} + 70 q^{44} + 37 q^{45} + 77 q^{46} + 59 q^{47} + 22 q^{48} + 103 q^{49} + 109 q^{50} + 21 q^{51} + 31 q^{52} + 58 q^{53} + 88 q^{54} + 35 q^{55} + 33 q^{56} - 16 q^{57} + 83 q^{58} + 54 q^{59} + 47 q^{60} + 18 q^{61} + 51 q^{62} + 47 q^{63} + 88 q^{64} + 34 q^{65} + 30 q^{66} + 88 q^{67} + 19 q^{68} + 62 q^{69} + 40 q^{70} + 139 q^{71} + 108 q^{72} - 6 q^{73} + 45 q^{74} + 45 q^{75} + 33 q^{76} + 37 q^{77} + 82 q^{78} + 94 q^{79} + 25 q^{80} + 112 q^{81} + 35 q^{82} + 58 q^{83} + 48 q^{84} + 83 q^{85} + 78 q^{86} + 21 q^{87} + 70 q^{88} + 99 q^{89} + 37 q^{90} + 53 q^{91} + 77 q^{92} + 57 q^{93} + 59 q^{94} + 92 q^{95} + 22 q^{96} + 16 q^{97} + 103 q^{98} + 150 q^{99}+O(q^{100}) \) 88 * q + 88 * q^2 + 22 * q^3 + 88 * q^4 + 25 * q^5 + 22 * q^6 + 33 * q^7 + 88 * q^8 + 108 * q^9 + 25 * q^10 + 70 * q^11 + 22 * q^12 + 31 * q^13 + 33 * q^14 + 47 * q^15 + 88 * q^16 + 19 * q^17 + 108 * q^18 + 33 * q^19 + 25 * q^20 + 48 * q^21 + 70 * q^22 + 77 * q^23 + 22 * q^24 + 109 * q^25 + 31 * q^26 + 88 * q^27 + 33 * q^28 + 83 * q^29 + 47 * q^30 + 51 * q^31 + 88 * q^32 + 30 * q^33 + 19 * q^34 + 40 * q^35 + 108 * q^36 + 45 * q^37 + 33 * q^38 + 82 * q^39 + 25 * q^40 + 35 * q^41 + 48 * q^42 + 78 * q^43 + 70 * q^44 + 37 * q^45 + 77 * q^46 + 59 * q^47 + 22 * q^48 + 103 * q^49 + 109 * q^50 + 21 * q^51 + 31 * q^52 + 58 * q^53 + 88 * q^54 + 35 * q^55 + 33 * q^56 - 16 * q^57 + 83 * q^58 + 54 * q^59 + 47 * q^60 + 18 * q^61 + 51 * q^62 + 47 * q^63 + 88 * q^64 + 34 * q^65 + 30 * q^66 + 88 * q^67 + 19 * q^68 + 62 * q^69 + 40 * q^70 + 139 * q^71 + 108 * q^72 - 6 * q^73 + 45 * q^74 + 45 * q^75 + 33 * q^76 + 37 * q^77 + 82 * q^78 + 94 * q^79 + 25 * q^80 + 112 * q^81 + 35 * q^82 + 58 * q^83 + 48 * q^84 + 83 * q^85 + 78 * q^86 + 21 * q^87 + 70 * q^88 + 99 * q^89 + 37 * q^90 + 53 * q^91 + 77 * q^92 + 57 * q^93 + 59 * q^94 + 92 * q^95 + 22 * q^96 + 16 * q^97 + 103 * q^98 + 150 * 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
$3$	−2.26140	−1.30562	−0.652809	−	0.757522i	$-0.726410\pi$
$3$	−2.26140	−1.30562	−0.652809	+	0.757522i	$0.726410\pi$
$4$	1.00000	0.500000
$5$	−1.73870	−0.777570	−0.388785	−	0.921328i	$-0.627105\pi$
$5$	−1.73870	−0.777570	−0.388785	+	0.921328i	$0.627105\pi$
$6$	−2.26140	−0.923212
$7$	−2.77914	−1.05041	−0.525207	−	0.850974i	$-0.676012\pi$
$7$	−2.77914	−1.05041	−0.525207	+	0.850974i	$0.676012\pi$
$8$	1.00000	0.353553
$9$	2.11392	0.704640
$10$	−1.73870	−0.549825
$11$	4.49936	1.35661	0.678303	−	0.734782i	$-0.262716\pi$
$11$	4.49936	1.35661	0.678303	+	0.734782i	$0.262716\pi$
$12$	−2.26140	−0.652809
$13$	3.58840	0.995242	0.497621	−	0.867395i	$-0.334207\pi$
$13$	3.58840	0.995242	0.497621	+	0.867395i	$0.334207\pi$
$14$	−2.77914	−0.742755
$15$	3.93189	1.01521
$16$	1.00000	0.250000
$17$	7.32917	1.77758	0.888792	−	0.458311i	$-0.151545\pi$
$17$	7.32917	1.77758	0.888792	+	0.458311i	$0.151545\pi$
$18$	2.11392	0.498256
$19$	2.05930	0.472436	0.236218	−	0.971700i	$-0.424092\pi$
$19$	2.05930	0.472436	0.236218	+	0.971700i	$0.424092\pi$
$20$	−1.73870	−0.388785
$21$	6.28473	1.37144
$22$	4.49936	0.959266
$23$	−2.85306	−0.594905	−0.297453	−	0.954737i	$-0.596137\pi$
$23$	−2.85306	−0.594905	−0.297453	+	0.954737i	$0.596137\pi$
$24$	−2.26140	−0.461606
$25$	−1.97692	−0.395385
$26$	3.58840	0.703742
$27$	2.00378	0.385628
$28$	−2.77914	−0.525207
$29$	2.95927	0.549523	0.274761	−	0.961512i	$-0.411401\pi$
$29$	2.95927	0.549523	0.274761	+	0.961512i	$0.411401\pi$
$30$	3.93189	0.717862
$31$	3.96277	0.711735	0.355867	−	0.934536i	$-0.384185\pi$
$31$	3.96277	0.711735	0.355867	+	0.934536i	$0.384185\pi$
$32$	1.00000	0.176777
$33$	−10.1748	−1.77121
$34$	7.32917	1.25694
$35$	4.83208	0.816771
$36$	2.11392	0.352320
$37$	−0.0376675	−0.00619250	−0.00309625	−	0.999995i	$-0.500986\pi$
$37$	−0.0376675	−0.00619250	−0.00309625	+	0.999995i	$0.500986\pi$
$38$	2.05930	0.334063
$39$	−8.11479	−1.29941
$40$	−1.73870	−0.274913
$41$	−4.78130	−0.746713	−0.373357	−	0.927688i	$-0.621793\pi$
$41$	−4.78130	−0.746713	−0.373357	+	0.927688i	$0.621793\pi$
$42$	6.28473	0.969755
$43$	−6.66844	−1.01693	−0.508464	−	0.861083i	$-0.669786\pi$
$43$	−6.66844	−1.01693	−0.508464	+	0.861083i	$0.669786\pi$
$44$	4.49936	0.678303
$45$	−3.67547	−0.547907
$46$	−2.85306	−0.420661
$47$	−1.44754	−0.211145	−0.105573	−	0.994412i	$-0.533668\pi$
$47$	−1.44754	−0.211145	−0.105573	+	0.994412i	$0.533668\pi$
$48$	−2.26140	−0.326405
$49$	0.723593	0.103370
$50$	−1.97692	−0.279579
$51$	−16.5742	−2.32085
$52$	3.58840	0.497621
$53$	−3.89902	−0.535571	−0.267785	−	0.963479i	$-0.586292\pi$
$53$	−3.89902	−0.535571	−0.267785	+	0.963479i	$0.586292\pi$
$54$	2.00378	0.272680
$55$	−7.82303	−1.05486
$56$	−2.77914	−0.371378
$57$	−4.65690	−0.616821
$58$	2.95927	0.388571
$59$	−3.98196	−0.518406	−0.259203	−	0.965823i	$-0.583460\pi$
$59$	−3.98196	−0.518406	−0.259203	+	0.965823i	$0.583460\pi$
$60$	3.93189	0.507605
$61$	−2.70423	−0.346242	−0.173121	−	0.984901i	$-0.555385\pi$
$61$	−2.70423	−0.346242	−0.173121	+	0.984901i	$0.555385\pi$
$62$	3.96277	0.503272
$63$	−5.87487	−0.740164
$64$	1.00000	0.125000
$65$	−6.23914	−0.773871
$66$	−10.1748	−1.25244
$67$	2.02850	0.247820	0.123910	−	0.992293i	$-0.460457\pi$
$67$	2.02850	0.247820	0.123910	+	0.992293i	$0.460457\pi$
$68$	7.32917	0.888792
$69$	6.45191	0.776719
$70$	4.83208	0.577544
$71$	2.08685	0.247664	0.123832	−	0.992303i	$-0.460482\pi$
$71$	2.08685	0.247664	0.123832	+	0.992303i	$0.460482\pi$
$72$	2.11392	0.249128
$73$	−5.00913	−0.586274	−0.293137	−	0.956070i	$-0.594699\pi$
$73$	−5.00913	−0.586274	−0.293137	+	0.956070i	$0.594699\pi$
$74$	−0.0376675	−0.00437876
$75$	4.47061	0.516222
$76$	2.05930	0.236218
$77$	−12.5043	−1.42500
$78$	−8.11479	−0.918819
$79$	16.6662	1.87509	0.937544	−	0.347866i	$-0.113093\pi$
$79$	16.6662	1.87509	0.937544	+	0.347866i	$0.113093\pi$
$80$	−1.73870	−0.194393
$81$	−10.8731	−1.20812
$82$	−4.78130	−0.528006
$83$	17.1785	1.88559	0.942793	−	0.333378i	$-0.108189\pi$
$83$	17.1785	1.88559	0.942793	+	0.333378i	$0.108189\pi$
$84$	6.28473	0.685720
$85$	−12.7432	−1.38220
$86$	−6.66844	−0.719076
$87$	−6.69209	−0.717467
$88$	4.49936	0.479633
$89$	6.07970	0.644447	0.322223	−	0.946664i	$-0.395570\pi$
$89$	6.07970	0.644447	0.322223	+	0.946664i	$0.395570\pi$
$90$	−3.67547	−0.387429
$91$	−9.97264	−1.04542
$92$	−2.85306	−0.297453
$93$	−8.96140	−0.929254
$94$	−1.44754	−0.149302
$95$	−3.58051	−0.367352
$96$	−2.26140	−0.230803
$97$	−2.99026	−0.303615	−0.151807	−	0.988410i	$-0.548509\pi$
$97$	−2.99026	−0.303615	−0.151807	+	0.988410i	$0.548509\pi$
$98$	0.723593	0.0730939
$99$	9.51128	0.955919
$100$	−1.97692	−0.197692
$101$	−18.1195	−1.80296	−0.901481	−	0.432819i	$-0.857519\pi$
$101$	−18.1195	−1.80296	−0.901481	+	0.432819i	$0.857519\pi$
$102$	−16.5742	−1.64109
$103$	10.9118	1.07517	0.537584	−	0.843210i	$-0.319337\pi$
$103$	10.9118	1.07517	0.537584	+	0.843210i	$0.319337\pi$
$104$	3.58840	0.351871
$105$	−10.9273	−1.06639
$106$	−3.89902	−0.378706
$107$	−17.2320	−1.66588	−0.832940	−	0.553364i	$-0.813344\pi$
$107$	−17.2320	−1.66588	−0.832940	+	0.553364i	$0.813344\pi$
$108$	2.00378	0.192814
$109$	8.76609	0.839639	0.419820	−	0.907608i	$-0.362093\pi$
$109$	8.76609	0.839639	0.419820	+	0.907608i	$0.362093\pi$
$110$	−7.82303	−0.745896
$111$	0.0851812	0.00808504
$112$	−2.77914	−0.262604
$113$	−0.888535	−0.0835863	−0.0417932	−	0.999126i	$-0.513307\pi$
$113$	−0.888535	−0.0835863	−0.0417932	+	0.999126i	$0.513307\pi$
$114$	−4.65690	−0.436158
$115$	4.96062	0.462580
$116$	2.95927	0.274761
$117$	7.58558	0.701287
$118$	−3.98196	−0.366569
$119$	−20.3687	−1.86720
$120$	3.93189	0.358931
$121$	9.24420	0.840382
$122$	−2.70423	−0.244830
$123$	10.8124	0.974923
$124$	3.96277	0.355867
$125$	12.1308	1.08501
$126$	−5.87487	−0.523375
$127$	−3.41541	−0.303068	−0.151534	−	0.988452i	$-0.548421\pi$
$127$	−3.41541	−0.303068	−0.151534	+	0.988452i	$0.548421\pi$
$128$	1.00000	0.0883883
$129$	15.0800	1.32772
$130$	−6.23914	−0.547209
$131$	12.9930	1.13520	0.567600	−	0.823304i	$-0.307872\pi$
$131$	12.9930	1.13520	0.567600	+	0.823304i	$0.307872\pi$
$132$	−10.1748	−0.885606
$133$	−5.72307	−0.496254
$134$	2.02850	0.175235
$135$	−3.48397	−0.299853
$136$	7.32917	0.628471
$137$	4.67693	0.399577	0.199788	−	0.979839i	$-0.435975\pi$
$137$	4.67693	0.399577	0.199788	+	0.979839i	$0.435975\pi$
$138$	6.45191	0.549223
$139$	−14.0172	−1.18893	−0.594463	−	0.804123i	$-0.702635\pi$
$139$	−14.0172	−1.18893	−0.594463	+	0.804123i	$0.702635\pi$
$140$	4.83208	0.408385
$141$	3.27346	0.275675
$142$	2.08685	0.175125
$143$	16.1455	1.35015
$144$	2.11392	0.176160
$145$	−5.14528	−0.427292
$146$	−5.00913	−0.414558
$147$	−1.63633	−0.134962
$148$	−0.0376675	−0.00309625
$149$	−2.15936	−0.176901	−0.0884507	−	0.996081i	$-0.528192\pi$
$149$	−2.15936	−0.176901	−0.0884507	+	0.996081i	$0.528192\pi$
$150$	4.47061	0.365024
$151$	19.2933	1.57007	0.785034	−	0.619453i	$-0.212645\pi$
$151$	19.2933	1.57007	0.785034	+	0.619453i	$0.212645\pi$
$152$	2.05930	0.167031
$153$	15.4933	1.25256
$154$	−12.5043	−1.00763
$155$	−6.89007	−0.553424
$156$	−8.11479	−0.649703
$157$	−1.39878	−0.111635	−0.0558174	−	0.998441i	$-0.517776\pi$
$157$	−1.39878	−0.111635	−0.0558174	+	0.998441i	$0.517776\pi$
$158$	16.6662	1.32589
$159$	8.81722	0.699251
$160$	−1.73870	−0.137456
$161$	7.92905	0.624897
$162$	−10.8731	−0.854272
$163$	−5.65612	−0.443022	−0.221511	−	0.975158i	$-0.571099\pi$
$163$	−5.65612	−0.443022	−0.221511	+	0.975158i	$0.571099\pi$
$164$	−4.78130	−0.373357
$165$	17.6910	1.37724
$166$	17.1785	1.33331
$167$	11.9869	0.927571	0.463786	−	0.885947i	$-0.346491\pi$
$167$	11.9869	0.927571	0.463786	+	0.885947i	$0.346491\pi$
$168$	6.28473	0.484877
$169$	−0.123409	−0.00949302
$170$	−12.7432	−0.977360
$171$	4.35320	0.332897
$172$	−6.66844	−0.508464
$173$	1.25193	0.0951822	0.0475911	−	0.998867i	$-0.484846\pi$
$173$	1.25193	0.0951822	0.0475911	+	0.998867i	$0.484846\pi$
$174$	−6.69209	−0.507326
$175$	5.49414	0.415318
$176$	4.49936	0.339152
$177$	9.00478	0.676841
$178$	6.07970	0.455693
$179$	13.1246	0.980976	0.490488	−	0.871448i	$-0.336818\pi$
$179$	13.1246	0.980976	0.490488	+	0.871448i	$0.336818\pi$
$180$	−3.67547	−0.273953
$181$	19.3385	1.43742	0.718708	−	0.695312i	$-0.244734\pi$
$181$	19.3385	1.43742	0.718708	+	0.695312i	$0.244734\pi$
$182$	−9.97264	−0.739221
$183$	6.11535	0.452060
$184$	−2.85306	−0.210331
$185$	0.0654925	0.00481510
$186$	−8.96140	−0.657082
$187$	32.9765	2.41148
$188$	−1.44754	−0.105573
$189$	−5.56878	−0.405069
$190$	−3.58051	−0.259757
$191$	3.55394	0.257154	0.128577	−	0.991700i	$-0.458959\pi$
$191$	3.55394	0.257154	0.128577	+	0.991700i	$0.458959\pi$
$192$	−2.26140	−0.163202
$193$	26.8029	1.92931	0.964657	−	0.263511i	$-0.0848804\pi$
$193$	26.8029	1.92931	0.964657	+	0.263511i	$0.0848804\pi$
$194$	−2.99026	−0.214688
$195$	14.1092	1.01038
$196$	0.723593	0.0516852
$197$	−13.8477	−0.986610	−0.493305	−	0.869856i	$-0.664211\pi$
$197$	−13.8477	−0.986610	−0.493305	+	0.869856i	$0.664211\pi$
$198$	9.51128	0.675937
$199$	−0.612398	−0.0434117	−0.0217059	−	0.999764i	$-0.506910\pi$
$199$	−0.612398	−0.0434117	−0.0217059	+	0.999764i	$0.506910\pi$
$200$	−1.97692	−0.139790
$201$	−4.58724	−0.323559
$202$	−18.1195	−1.27489
$203$	−8.22421	−0.577226
$204$	−16.5742	−1.16042
$205$	8.31324	0.580622
$206$	10.9118	0.760259
$207$	−6.03115	−0.419194
$208$	3.58840	0.248811
$209$	9.26553	0.640910
$210$	−10.9273	−0.754052
$211$	12.2864	0.845833	0.422916	−	0.906169i	$-0.361006\pi$
$211$	12.2864	0.845833	0.422916	+	0.906169i	$0.361006\pi$
$212$	−3.89902	−0.267785
$213$	−4.71921	−0.323355
$214$	−17.2320	−1.17795
$215$	11.5944	0.790732
$216$	2.00378	0.136340
$217$	−11.0131	−0.747616
$218$	8.76609	0.593715
$219$	11.3276	0.765450
$220$	−7.82303	−0.527428
$221$	26.3000	1.76913
$222$	0.0851812	0.00571699
$223$	24.1752	1.61889	0.809446	−	0.587194i	$-0.199767\pi$
$223$	24.1752	1.61889	0.809446	+	0.587194i	$0.199767\pi$
$224$	−2.77914	−0.185689
$225$	−4.17906	−0.278604
$226$	−0.888535	−0.0591045
$227$	−15.8495	−1.05197	−0.525985	−	0.850494i	$-0.676303\pi$
$227$	−15.8495	−1.05197	−0.525985	+	0.850494i	$0.676303\pi$
$228$	−4.65690	−0.308411
$229$	−5.59622	−0.369809	−0.184904	−	0.982757i	$-0.559198\pi$
$229$	−5.59622	−0.369809	−0.184904	+	0.982757i	$0.559198\pi$
$230$	4.96062	0.327094
$231$	28.2772	1.86051
$232$	2.95927	0.194286
$233$	−4.92493	−0.322643	−0.161322	−	0.986902i	$-0.551576\pi$
$233$	−4.92493	−0.322643	−0.161322	+	0.986902i	$0.551576\pi$
$234$	7.58558	0.495885
$235$	2.51684	0.164180
$236$	−3.98196	−0.259203
$237$	−37.6888	−2.44815
$238$	−20.3687	−1.32031
$239$	15.1732	0.981475	0.490738	−	0.871307i	$-0.336727\pi$
$239$	15.1732	0.981475	0.490738	+	0.871307i	$0.336727\pi$
$240$	3.93189	0.253802
$241$	−14.9580	−0.963533	−0.481766	−	0.876300i	$-0.660005\pi$
$241$	−14.9580	−0.963533	−0.481766	+	0.876300i	$0.660005\pi$
$242$	9.24420	0.594240
$243$	18.5771	1.19172
$244$	−2.70423	−0.173121
$245$	−1.25811	−0.0803777
$246$	10.8124	0.689375
$247$	7.38959	0.470188
$248$	3.96277	0.251636
$249$	−38.8474	−2.46186
$250$	12.1308	0.767218
$251$	10.5242	0.664284	0.332142	−	0.943229i	$-0.392229\pi$
$251$	10.5242	0.664284	0.332142	+	0.943229i	$0.392229\pi$
$252$	−5.87487	−0.370082
$253$	−12.8370	−0.807052
$254$	−3.41541	−0.214302
$255$	28.8175	1.80462
$256$	1.00000	0.0625000
$257$	−14.1319	−0.881521	−0.440760	−	0.897625i	$-0.645291\pi$
$257$	−14.1319	−0.881521	−0.440760	+	0.897625i	$0.645291\pi$
$258$	15.0800	0.938839
$259$	0.104683	0.00650469
$260$	−6.23914	−0.386935
$261$	6.25566	0.387215
$262$	12.9930	0.802708
$263$	0.180507	0.0111305	0.00556527	−	0.999985i	$-0.498229\pi$
$263$	0.180507	0.0111305	0.00556527	+	0.999985i	$0.498229\pi$
$264$	−10.1748	−0.626218
$265$	6.77922	0.416444
$266$	−5.72307	−0.350904
$267$	−13.7486	−0.841402
$268$	2.02850	0.123910
$269$	−11.0185	−0.671810	−0.335905	−	0.941896i	$-0.609042\pi$
$269$	−11.0185	−0.671810	−0.335905	+	0.941896i	$0.609042\pi$
$270$	−3.48397	−0.212028
$271$	−15.0306	−0.913043	−0.456522	−	0.889712i	$-0.650905\pi$
$271$	−15.0306	−0.913043	−0.456522	+	0.889712i	$0.650905\pi$
$272$	7.32917	0.444396
$273$	22.5521	1.36492
$274$	4.67693	0.282544
$275$	−8.89488	−0.536382
$276$	6.45191	0.388360
$277$	9.49172	0.570302	0.285151	−	0.958483i	$-0.407956\pi$
$277$	9.49172	0.570302	0.285151	+	0.958483i	$0.407956\pi$
$278$	−14.0172	−0.840697
$279$	8.37698	0.501517
$280$	4.83208	0.288772
$281$	10.1837	0.607507	0.303753	−	0.952751i	$-0.401760\pi$
$281$	10.1837	0.607507	0.303753	+	0.952751i	$0.401760\pi$
$282$	3.27346	0.194932
$283$	16.7903	0.998080	0.499040	−	0.866579i	$-0.333686\pi$
$283$	16.7903	0.998080	0.499040	+	0.866579i	$0.333686\pi$
$284$	2.08685	0.123832
$285$	8.09695	0.479622
$286$	16.1455	0.954702
$287$	13.2879	0.784358
$288$	2.11392	0.124564
$289$	36.7167	2.15981
$290$	−5.14528	−0.302141
$291$	6.76216	0.396405
$292$	−5.00913	−0.293137
$293$	−15.1865	−0.887204	−0.443602	−	0.896224i	$-0.646300\pi$
$293$	−15.1865	−0.887204	−0.443602	+	0.896224i	$0.646300\pi$
$294$	−1.63633	−0.0954328
$295$	6.92342	0.403097
$296$	−0.0376675	−0.00218938
$297$	9.01572	0.523145
$298$	−2.15936	−0.125088
$299$	−10.2379	−0.592075
$300$	4.47061	0.258111
$301$	18.5325	1.06820
$302$	19.2933	1.11021
$303$	40.9755	2.35398
$304$	2.05930	0.118109
$305$	4.70185	0.269227
$306$	15.4933	0.885691
$307$	−19.7753	−1.12863	−0.564317	−	0.825558i	$-0.690860\pi$
$307$	−19.7753	−1.12863	−0.564317	+	0.825558i	$0.690860\pi$
$308$	−12.5043	−0.712500
$309$	−24.6758	−1.40376
$310$	−6.89007	−0.391330
$311$	−14.3479	−0.813593	−0.406796	−	0.913519i	$-0.633354\pi$
$311$	−14.3479	−0.813593	−0.406796	+	0.913519i	$0.633354\pi$
$312$	−8.11479	−0.459410
$313$	1.10803	0.0626296	0.0313148	−	0.999510i	$-0.490031\pi$
$313$	1.10803	0.0626296	0.0313148	+	0.999510i	$0.490031\pi$
$314$	−1.39878	−0.0789377
$315$	10.2146	0.575529
$316$	16.6662	0.937544
$317$	11.4880	0.645229	0.322615	−	0.946530i	$-0.395438\pi$
$317$	11.4880	0.645229	0.322615	+	0.946530i	$0.395438\pi$
$318$	8.81722	0.494445
$319$	13.3148	0.745486
$320$	−1.73870	−0.0971963
$321$	38.9684	2.17500
$322$	7.92905	0.441869
$323$	15.0930	0.839795
$324$	−10.8731	−0.604061
$325$	−7.09399	−0.393504
$326$	−5.65612	−0.313264
$327$	−19.8236	−1.09625
$328$	−4.78130	−0.264003
$329$	4.02291	0.221790
$330$	17.6910	0.973856
$331$	−7.49261	−0.411831	−0.205916	−	0.978570i	$-0.566017\pi$
$331$	−7.49261	−0.411831	−0.205916	+	0.978570i	$0.566017\pi$
$332$	17.1785	0.942793
$333$	−0.0796261	−0.00436348
$334$	11.9869	0.655892
$335$	−3.52694	−0.192698
$336$	6.28473	0.342860
$337$	27.6673	1.50713	0.753566	−	0.657372i	$-0.228332\pi$
$337$	27.6673	1.50713	0.753566	+	0.657372i	$0.228332\pi$
$338$	−0.123409	−0.00671258
$339$	2.00933	0.109132
$340$	−12.7432	−0.691098
$341$	17.8299	0.965544
$342$	4.35320	0.235394
$343$	17.4430	0.941833
$344$	−6.66844	−0.359538
$345$	−11.2179	−0.603954
$346$	1.25193	0.0673040
$347$	−10.5342	−0.565503	−0.282752	−	0.959193i	$-0.591247\pi$
$347$	−10.5342	−0.565503	−0.282752	+	0.959193i	$0.591247\pi$
$348$	−6.69209	−0.358733
$349$	−17.0146	−0.910770	−0.455385	−	0.890295i	$-0.650498\pi$
$349$	−17.0146	−0.910770	−0.455385	+	0.890295i	$0.650498\pi$
$350$	5.49414	0.293674
$351$	7.19036	0.383793
$352$	4.49936	0.239816
$353$	−9.07402	−0.482962	−0.241481	−	0.970406i	$-0.577633\pi$
$353$	−9.07402	−0.482962	−0.241481	+	0.970406i	$0.577633\pi$
$354$	9.00478	0.478599
$355$	−3.62841	−0.192576
$356$	6.07970	0.322223
$357$	46.0618	2.43785
$358$	13.1246	0.693655
$359$	31.2453	1.64906	0.824531	−	0.565817i	$-0.191439\pi$
$359$	31.2453	1.64906	0.824531	+	0.565817i	$0.191439\pi$
$360$	−3.67547	−0.193714
$361$	−14.7593	−0.776804
$362$	19.3385	1.01641
$363$	−20.9048	−1.09722
$364$	−9.97264	−0.522708
$365$	8.70937	0.455869
$366$	6.11535	0.319654
$367$	−30.0209	−1.56708	−0.783539	−	0.621343i	$-0.786587\pi$
$367$	−30.0209	−1.56708	−0.783539	+	0.621343i	$0.786587\pi$
$368$	−2.85306	−0.148726
$369$	−10.1073	−0.526164
$370$	0.0654925	0.00340479
$371$	10.8359	0.562571
$372$	−8.96140	−0.464627
$373$	−25.3325	−1.31166	−0.655832	−	0.754907i	$-0.727682\pi$
$373$	−25.3325	−1.31166	−0.655832	+	0.754907i	$0.727682\pi$
$374$	32.9765	1.70518
$375$	−27.4325	−1.41661
$376$	−1.44754	−0.0746511
$377$	10.6190	0.546908
$378$	−5.56878	−0.286427
$379$	20.5068	1.05336	0.526681	−	0.850063i	$-0.323436\pi$
$379$	20.5068	1.05336	0.526681	+	0.850063i	$0.323436\pi$
$380$	−3.58051	−0.183676
$381$	7.72360	0.395692
$382$	3.55394	0.181836
$383$	0.0521543	0.00266496	0.00133248	−	0.999999i	$-0.499576\pi$
$383$	0.0521543	0.00266496	0.00133248	+	0.999999i	$0.499576\pi$
$384$	−2.26140	−0.115401
$385$	21.7413	1.10804
$386$	26.8029	1.36423
$387$	−14.0965	−0.716567
$388$	−2.99026	−0.151807
$389$	21.7332	1.10192	0.550959	−	0.834532i	$-0.314262\pi$
$389$	21.7332	1.10192	0.550959	+	0.834532i	$0.314262\pi$
$390$	14.1092	0.714446
$391$	−20.9106	−1.05749
$392$	0.723593	0.0365470
$393$	−29.3823	−1.48214
$394$	−13.8477	−0.697639
$395$	−28.9774	−1.45801
$396$	9.51128	0.477960
$397$	−15.5538	−0.780621	−0.390310	−	0.920683i	$-0.627632\pi$
$397$	−15.5538	−0.780621	−0.390310	+	0.920683i	$0.627632\pi$
$398$	−0.612398	−0.0306967
$399$	12.9421	0.647918
$400$	−1.97692	−0.0988462
$401$	29.0264	1.44951	0.724755	−	0.689006i	$-0.241953\pi$
$401$	29.0264	1.44951	0.724755	+	0.689006i	$0.241953\pi$
$402$	−4.58724	−0.228791
$403$	14.2200	0.708348
$404$	−18.1195	−0.901481
$405$	18.9051	0.939400
$406$	−8.22421	−0.408161
$407$	−0.169479	−0.00840079
$408$	−16.5742	−0.820543
$409$	−32.6940	−1.61661	−0.808306	−	0.588763i	$-0.799615\pi$
$409$	−32.6940	−1.61661	−0.808306	+	0.588763i	$0.799615\pi$
$410$	8.31324	0.410562
$411$	−10.5764	−0.521695
$412$	10.9118	0.537584
$413$	11.0664	0.544542
$414$	−6.03115	−0.296415
$415$	−29.8683	−1.46618
$416$	3.58840	0.175936
$417$	31.6985	1.55228
$418$	9.26553	0.453192
$419$	−17.5328	−0.856533	−0.428267	−	0.903652i	$-0.640876\pi$
$419$	−17.5328	−0.856533	−0.428267	+	0.903652i	$0.640876\pi$
$420$	−10.9273	−0.533196
$421$	27.3964	1.33522	0.667610	−	0.744511i	$-0.267317\pi$
$421$	27.3964	1.33522	0.667610	+	0.744511i	$0.267317\pi$
$422$	12.2864	0.598094
$423$	−3.05998	−0.148781
$424$	−3.89902	−0.189353
$425$	−14.4892	−0.702830
$426$	−4.71921	−0.228646
$427$	7.51543	0.363697
$428$	−17.2320	−0.832940
$429$	−36.5113	−1.76278
$430$	11.5944	0.559132
$431$	−34.6056	−1.66689	−0.833446	−	0.552601i	$-0.813635\pi$
$431$	−34.6056	−1.66689	−0.833446	+	0.552601i	$0.813635\pi$
$432$	2.00378	0.0964069
$433$	−6.88973	−0.331099	−0.165550	−	0.986201i	$-0.552940\pi$
$433$	−6.88973	−0.331099	−0.165550	+	0.986201i	$0.552940\pi$
$434$	−11.0131	−0.528645
$435$	11.6355	0.557881
$436$	8.76609	0.419820
$437$	−5.87532	−0.281055
$438$	11.3276	0.541255
$439$	8.82946	0.421407	0.210704	−	0.977550i	$-0.432425\pi$
$439$	8.82946	0.421407	0.210704	+	0.977550i	$0.432425\pi$
$440$	−7.82303	−0.372948
$441$	1.52962	0.0728389
$442$	26.3000	1.25096
$443$	−2.88869	−0.137246	−0.0686228	−	0.997643i	$-0.521860\pi$
$443$	−2.88869	−0.137246	−0.0686228	+	0.997643i	$0.521860\pi$
$444$	0.0851812	0.00404252
$445$	−10.5708	−0.501103
$446$	24.1752	1.14473
$447$	4.88316	0.230966
$448$	−2.77914	−0.131302
$449$	13.4273	0.633672	0.316836	−	0.948480i	$-0.397379\pi$
$449$	13.4273	0.633672	0.316836	+	0.948480i	$0.397379\pi$
$450$	−4.17906	−0.197003
$451$	−21.5128	−1.01300
$452$	−0.888535	−0.0417932
$453$	−43.6299	−2.04991
$454$	−15.8495	−0.743855
$455$	17.3394	0.812885
$456$	−4.65690	−0.218079
$457$	16.4468	0.769347	0.384673	−	0.923053i	$-0.374314\pi$
$457$	16.4468	0.769347	0.384673	+	0.923053i	$0.374314\pi$
$458$	−5.59622	−0.261494
$459$	14.6860	0.685486
$460$	4.96062	0.231290
$461$	30.5107	1.42102	0.710512	−	0.703685i	$-0.248463\pi$
$461$	30.5107	1.42102	0.710512	+	0.703685i	$0.248463\pi$
$462$	28.2772	1.31558
$463$	−0.468253	−0.0217616	−0.0108808	−	0.999941i	$-0.503464\pi$
$463$	−0.468253	−0.0217616	−0.0108808	+	0.999941i	$0.503464\pi$
$464$	2.95927	0.137381
$465$	15.5812	0.722560
$466$	−4.92493	−0.228143
$467$	30.5265	1.41260	0.706300	−	0.707913i	$-0.250363\pi$
$467$	30.5265	1.41260	0.706300	+	0.707913i	$0.250363\pi$
$468$	7.58558	0.350644
$469$	−5.63746	−0.260314
$470$	2.51684	0.116093
$471$	3.16320	0.145752
$472$	−3.98196	−0.183284
$473$	−30.0037	−1.37957
$474$	−37.6888	−1.73110
$475$	−4.07108	−0.186794
$476$	−20.3687	−0.933600
$477$	−8.24220	−0.377385
$478$	15.1732	0.694008
$479$	−39.5068	−1.80511	−0.902555	−	0.430574i	$-0.858311\pi$
$479$	−39.5068	−1.80511	−0.902555	+	0.430574i	$0.858311\pi$
$480$	3.93189	0.179465
$481$	−0.135166	−0.00616304
$482$	−14.9580	−0.681320
$483$	−17.9307	−0.815877
$484$	9.24420	0.420191
$485$	5.19916	0.236082
$486$	18.5771	0.842673
$487$	−24.4269	−1.10689	−0.553444	−	0.832886i	$-0.686687\pi$
$487$	−24.4269	−1.10689	−0.553444	+	0.832886i	$0.686687\pi$
$488$	−2.70423	−0.122415
$489$	12.7907	0.578417
$490$	−1.25811	−0.0568356
$491$	37.4458	1.68991	0.844953	−	0.534841i	$-0.179628\pi$
$491$	37.4458	1.68991	0.844953	+	0.534841i	$0.179628\pi$
$492$	10.8124	0.487461
$493$	21.6890	0.976823
$494$	7.38959	0.332473
$495$	−16.5373	−0.743294
$496$	3.96277	0.177934
$497$	−5.79965	−0.260150
$498$	−38.8474	−1.74080
$499$	22.1877	0.993257	0.496628	−	0.867963i	$-0.334571\pi$
$499$	22.1877	0.993257	0.496628	+	0.867963i	$0.334571\pi$
$500$	12.1308	0.542505
$501$	−27.1071	−1.21105
$502$	10.5242	0.469720
$503$	6.20321	0.276587	0.138294	−	0.990391i	$-0.455838\pi$
$503$	6.20321	0.276587	0.138294	+	0.990391i	$0.455838\pi$
$504$	−5.87487	−0.261687
$505$	31.5044	1.40193
$506$	−12.8370	−0.570672
$507$	0.279077	0.0123943
$508$	−3.41541	−0.151534
$509$	36.4262	1.61456	0.807282	−	0.590166i	$-0.200938\pi$
$509$	36.4262	1.61456	0.807282	+	0.590166i	$0.200938\pi$
$510$	28.8175	1.27606
$511$	13.9210	0.615831
$512$	1.00000	0.0441942
$513$	4.12639	0.182184
$514$	−14.1319	−0.623329
$515$	−18.9723	−0.836019
$516$	15.0800	0.663860
$517$	−6.51299	−0.286441
$518$	0.104683	0.00459951
$519$	−2.83110	−0.124272
$520$	−6.23914	−0.273605
$521$	−26.6798	−1.16886	−0.584432	−	0.811443i	$-0.698683\pi$
$521$	−26.6798	−1.16886	−0.584432	+	0.811443i	$0.698683\pi$
$522$	6.25566	0.273803
$523$	25.9912	1.13651	0.568257	−	0.822851i	$-0.307618\pi$
$523$	25.9912	1.13651	0.568257	+	0.822851i	$0.307618\pi$
$524$	12.9930	0.567600
$525$	−12.4244	−0.542247
$526$	0.180507	0.00787048
$527$	29.0438	1.26517
$528$	−10.1748	−0.442803
$529$	−14.8600	−0.646088
$530$	6.77922	0.294470
$531$	−8.41753	−0.365290
$532$	−5.72307	−0.248127
$533$	−17.1572	−0.743161
$534$	−13.7486	−0.594961
$535$	29.9613	1.29534
$536$	2.02850	0.0876177
$537$	−29.6799	−1.28078
$538$	−11.0185	−0.475041
$539$	3.25570	0.140233
$540$	−3.48397	−0.149926
$541$	32.7466	1.40789	0.703943	−	0.710256i	$-0.251421\pi$
$541$	32.7466	1.40789	0.703943	+	0.710256i	$0.251421\pi$
$542$	−15.0306	−0.645619
$543$	−43.7320	−1.87672
$544$	7.32917	0.314235
$545$	−15.2416	−0.652878
$546$	22.5521	0.965141
$547$	15.7278	0.672472	0.336236	−	0.941778i	$-0.390846\pi$
$547$	15.7278	0.672472	0.336236	+	0.941778i	$0.390846\pi$
$548$	4.67693	0.199788
$549$	−5.71653	−0.243976
$550$	−8.89488	−0.379279
$551$	6.09403	0.259614
$552$	6.45191	0.274612
$553$	−46.3175	−1.96962
$554$	9.49172	0.403264
$555$	−0.148105	−0.00628669
$556$	−14.0172	−0.594463
$557$	−30.7606	−1.30337	−0.651684	−	0.758491i	$-0.725937\pi$
$557$	−30.7606	−1.30337	−0.651684	+	0.758491i	$0.725937\pi$
$558$	8.37698	0.354626
$559$	−23.9290	−1.01209
$560$	4.83208	0.204193
$561$	−74.5731	−3.14848
$562$	10.1837	0.429572
$563$	−0.939706	−0.0396039	−0.0198019	−	0.999804i	$-0.506304\pi$
$563$	−0.939706	−0.0396039	−0.0198019	+	0.999804i	$0.506304\pi$
$564$	3.27346	0.137838
$565$	1.54490	0.0649942
$566$	16.7903	0.705749
$567$	30.2178	1.26903
$568$	2.08685	0.0875624
$569$	15.0674	0.631658	0.315829	−	0.948816i	$-0.397717\pi$
$569$	15.0674	0.631658	0.315829	+	0.948816i	$0.397717\pi$
$570$	8.09695	0.339144
$571$	39.2815	1.64388	0.821940	−	0.569574i	$-0.192892\pi$
$571$	39.2815	1.64388	0.821940	+	0.569574i	$0.192892\pi$
$572$	16.1455	0.675076
$573$	−8.03688	−0.335746
$574$	13.2879	0.554625
$575$	5.64029	0.235216
$576$	2.11392	0.0880800
$577$	−3.81871	−0.158975	−0.0794876	−	0.996836i	$-0.525328\pi$
$577$	−3.81871	−0.158975	−0.0794876	+	0.996836i	$0.525328\pi$
$578$	36.7167	1.52721
$579$	−60.6120	−2.51895
$580$	−5.14528	−0.213646
$581$	−47.7414	−1.98065
$582$	6.76216	0.280301
$583$	−17.5431	−0.726559
$584$	−5.00913	−0.207279
$585$	−13.1890	−0.545300
$586$	−15.1865	−0.627348
$587$	−20.0306	−0.826751	−0.413375	−	0.910561i	$-0.635650\pi$
$587$	−20.0306	−0.826751	−0.413375	+	0.910561i	$0.635650\pi$
$588$	−1.63633	−0.0674812
$589$	8.16054	0.336249
$590$	6.92342	0.285033
$591$	31.3152	1.28814
$592$	−0.0376675	−0.00154812
$593$	−12.1810	−0.500215	−0.250107	−	0.968218i	$-0.580466\pi$
$593$	−12.1810	−0.500215	−0.250107	+	0.968218i	$0.580466\pi$
$594$	9.01572	0.369919
$595$	35.4151	1.45188
$596$	−2.15936	−0.0884507
$597$	1.38487	0.0566791
$598$	−10.2379	−0.418660
$599$	16.3156	0.666636	0.333318	−	0.942814i	$-0.391832\pi$
$599$	16.3156	0.666636	0.333318	+	0.942814i	$0.391832\pi$
$600$	4.47061	0.182512
$601$	18.3766	0.749599	0.374799	−	0.927106i	$-0.377712\pi$
$601$	18.3766	0.749599	0.374799	+	0.927106i	$0.377712\pi$
$602$	18.5325	0.755328
$603$	4.28808	0.174624
$604$	19.2933	0.785034
$605$	−16.0729	−0.653456
$606$	40.9755	1.66451
$607$	37.3123	1.51446	0.757230	−	0.653149i	$-0.226552\pi$
$607$	37.3123	1.51446	0.757230	+	0.653149i	$0.226552\pi$
$608$	2.05930	0.0835157
$609$	18.5982	0.753638
$610$	4.70185	0.190372
$611$	−5.19434	−0.210141
$612$	15.4933	0.626278
$613$	−8.66144	−0.349832	−0.174916	−	0.984583i	$-0.555965\pi$
$613$	−8.66144	−0.349832	−0.174916	+	0.984583i	$0.555965\pi$
$614$	−19.7753	−0.798065
$615$	−18.7995	−0.758071
$616$	−12.5043	−0.503813
$617$	19.9584	0.803496	0.401748	−	0.915750i	$-0.368403\pi$
$617$	19.9584	0.803496	0.401748	+	0.915750i	$0.368403\pi$
$618$	−24.6758	−0.992608
$619$	12.4136	0.498944	0.249472	−	0.968382i	$-0.419743\pi$
$619$	12.4136	0.498944	0.249472	+	0.968382i	$0.419743\pi$
$620$	−6.89007	−0.276712
$621$	−5.71691	−0.229412
$622$	−14.3479	−0.575297
$623$	−16.8963	−0.676936
$624$	−8.11479	−0.324852
$625$	−11.2072	−0.448286
$626$	1.10803	0.0442858
$627$	−20.9530	−0.836784
$628$	−1.39878	−0.0558174
$629$	−0.276071	−0.0110077
$630$	10.2146	0.406961
$631$	23.4899	0.935120	0.467560	−	0.883961i	$-0.345133\pi$
$631$	23.4899	0.935120	0.467560	+	0.883961i	$0.345133\pi$
$632$	16.6662	0.662944
$633$	−27.7845	−1.10433
$634$	11.4880	0.456246
$635$	5.93837	0.235657
$636$	8.81722	0.349626
$637$	2.59654	0.102879
$638$	13.3148	0.527138
$639$	4.41144	0.174514
$640$	−1.73870	−0.0687281
$641$	1.48697	0.0587318	0.0293659	−	0.999569i	$-0.490651\pi$
$641$	1.48697	0.0587318	0.0293659	+	0.999569i	$0.490651\pi$
$642$	38.9684	1.53796
$643$	−19.1588	−0.755550	−0.377775	−	0.925897i	$-0.623311\pi$
$643$	−19.1588	−0.755550	−0.377775	+	0.925897i	$0.623311\pi$
$644$	7.92905	0.312448
$645$	−26.2196	−1.03239
$646$	15.0930	0.593825
$647$	−4.26334	−0.167609	−0.0838047	−	0.996482i	$-0.526707\pi$
$647$	−4.26334	−0.167609	−0.0838047	+	0.996482i	$0.526707\pi$
$648$	−10.8731	−0.427136
$649$	−17.9162	−0.703274
$650$	−7.09399	−0.278249
$651$	24.9049	0.976102
$652$	−5.65612	−0.221511
$653$	31.5498	1.23464	0.617319	−	0.786713i	$-0.288219\pi$
$653$	31.5498	1.23464	0.617319	+	0.786713i	$0.288219\pi$
$654$	−19.8236	−0.775165
$655$	−22.5909	−0.882698
$656$	−4.78130	−0.186678
$657$	−10.5889	−0.413112
$658$	4.02291	0.156829
$659$	−2.01390	−0.0784504	−0.0392252	−	0.999230i	$-0.512489\pi$
$659$	−2.01390	−0.0784504	−0.0392252	+	0.999230i	$0.512489\pi$
$660$	17.6910	0.688620
$661$	32.6012	1.26804	0.634021	−	0.773316i	$-0.281403\pi$
$661$	32.6012	1.26804	0.634021	+	0.773316i	$0.281403\pi$
$662$	−7.49261	−0.291209
$663$	−59.4747	−2.30980
$664$	17.1785	0.666655
$665$	9.95071	0.385872
$666$	−0.0796261	−0.00308545
$667$	−8.44299	−0.326914
$668$	11.9869	0.463786
$669$	−54.6698	−2.11366
$670$	−3.52694	−0.136258
$671$	−12.1673	−0.469714
$672$	6.28473	0.242439
$673$	44.1920	1.70348	0.851739	−	0.523967i	$-0.175548\pi$
$673$	44.1920	1.70348	0.851739	+	0.523967i	$0.175548\pi$
$674$	27.6673	1.06570
$675$	−3.96132	−0.152471
$676$	−0.123409	−0.00474651
$677$	−12.0518	−0.463188	−0.231594	−	0.972813i	$-0.574394\pi$
$677$	−12.0518	−0.463188	−0.231594	+	0.972813i	$0.574394\pi$
$678$	2.00933	0.0771679
$679$	8.31033	0.318921
$680$	−12.7432	−0.488680
$681$	35.8421	1.37347
$682$	17.8299	0.682743
$683$	17.2166	0.658774	0.329387	−	0.944195i	$-0.393158\pi$
$683$	17.2166	0.658774	0.329387	+	0.944195i	$0.393158\pi$
$684$	4.35320	0.166449
$685$	−8.13177	−0.310699
$686$	17.4430	0.665976
$687$	12.6553	0.482829
$688$	−6.66844	−0.254232
$689$	−13.9912	−0.533023
$690$	−11.2179	−0.427060
$691$	−27.5148	−1.04671	−0.523356	−	0.852114i	$-0.675320\pi$
$691$	−27.5148	−1.04671	−0.523356	+	0.852114i	$0.675320\pi$
$692$	1.25193	0.0475911
$693$	−26.4331	−1.00411
$694$	−10.5342	−0.399871
$695$	24.3717	0.924473
$696$	−6.69209	−0.253663
$697$	−35.0429	−1.32735
$698$	−17.0146	−0.644012
$699$	11.1372	0.421249
$700$	5.49414	0.207659
$701$	−7.19361	−0.271699	−0.135849	−	0.990729i	$-0.543376\pi$
$701$	−7.19361	−0.271699	−0.135849	+	0.990729i	$0.543376\pi$
$702$	7.19036	0.271383
$703$	−0.0775687	−0.00292556
$704$	4.49936	0.169576
$705$	−5.69157	−0.214357
$706$	−9.07402	−0.341505
$707$	50.3566	1.89386
$708$	9.00478	0.338421
$709$	−39.2739	−1.47496	−0.737482	−	0.675367i	$-0.763985\pi$
$709$	−39.2739	−1.47496	−0.737482	+	0.675367i	$0.763985\pi$
$710$	−3.62841	−0.136172
$711$	35.2309	1.32126
$712$	6.07970	0.227846
$713$	−11.3060	−0.423415
$714$	46.0618	1.72382
$715$	−28.0721	−1.04984
$716$	13.1246	0.490488
$717$	−34.3127	−1.28143
$718$	31.2453	1.16606
$719$	−5.51830	−0.205798	−0.102899	−	0.994692i	$-0.532812\pi$
$719$	−5.51830	−0.205798	−0.102899	+	0.994692i	$0.532812\pi$
$720$	−3.67547	−0.136977
$721$	−30.3253	−1.12937
$722$	−14.7593	−0.549284
$723$	33.8261	1.25801
$724$	19.3385	0.718708
$725$	−5.85025	−0.217273
$726$	−20.9048	−0.775850
$727$	0.410142	0.0152113	0.00760566	−	0.999971i	$-0.497579\pi$
$727$	0.410142	0.0152113	0.00760566	+	0.999971i	$0.497579\pi$
$728$	−9.97264	−0.369611
$729$	−9.39083	−0.347809
$730$	8.70937	0.322348
$731$	−48.8741	−1.80767
$732$	6.11535	0.226030
$733$	−44.9554	−1.66046	−0.830232	−	0.557417i	$-0.811792\pi$
$733$	−44.9554	−1.66046	−0.830232	+	0.557417i	$0.811792\pi$
$734$	−30.0209	−1.10809
$735$	2.84509	0.104943
$736$	−2.85306	−0.105165
$737$	9.12692	0.336195
$738$	−10.1073	−0.372054
$739$	−7.02473	−0.258409	−0.129204	−	0.991618i	$-0.541242\pi$
$739$	−7.02473	−0.258409	−0.129204	+	0.991618i	$0.541242\pi$
$740$	0.0654925	0.00240755
$741$	−16.7108	−0.613886
$742$	10.8359	0.397798
$743$	38.9299	1.42820	0.714100	−	0.700043i	$-0.246836\pi$
$743$	38.9299	1.42820	0.714100	+	0.700043i	$0.246836\pi$
$744$	−8.96140	−0.328541
$745$	3.75447	0.137553
$746$	−25.3325	−0.927487
$747$	36.3140	1.32866
$748$	32.9765	1.20574
$749$	47.8900	1.74986
$750$	−27.4325	−1.00169
$751$	37.6796	1.37495	0.687474	−	0.726209i	$-0.258719\pi$
$751$	37.6796	1.37495	0.687474	+	0.726209i	$0.258719\pi$
$752$	−1.44754	−0.0527863
$753$	−23.7995	−0.867302
$754$	10.6190	0.386722
$755$	−33.5453	−1.22084
$756$	−5.56878	−0.202534
$757$	11.1045	0.403599	0.201800	−	0.979427i	$-0.435321\pi$
$757$	11.1045	0.403599	0.201800	+	0.979427i	$0.435321\pi$
$758$	20.5068	0.744839
$759$	29.0295	1.05370
$760$	−3.58051	−0.129879
$761$	16.0109	0.580393	0.290197	−	0.956967i	$-0.406279\pi$
$761$	16.0109	0.580393	0.290197	+	0.956967i	$0.406279\pi$
$762$	7.72360	0.279796
$763$	−24.3621	−0.881969
$764$	3.55394	0.128577
$765$	−26.9381	−0.973951
$766$	0.0521543	0.00188441
$767$	−14.2888	−0.515940
$768$	−2.26140	−0.0816012
$769$	−51.9200	−1.87228	−0.936142	−	0.351622i	$-0.885630\pi$
$769$	−51.9200	−1.87228	−0.936142	+	0.351622i	$0.885630\pi$
$770$	21.7413	0.783500
$771$	31.9577	1.15093
$772$	26.8029	0.964657
$773$	−5.96613	−0.214587	−0.107293	−	0.994227i	$-0.534218\pi$
$773$	−5.96613	−0.214587	−0.107293	+	0.994227i	$0.534218\pi$
$774$	−14.0965	−0.506690
$775$	−7.83410	−0.281409
$776$	−2.99026	−0.107344
$777$	−0.236730	−0.00849264
$778$	21.7332	0.779174
$779$	−9.84613	−0.352774
$780$	14.1092	0.505190
$781$	9.38950	0.335983
$782$	−20.9106	−0.747761
$783$	5.92973	0.211911
$784$	0.723593	0.0258426
$785$	2.43206	0.0868039
$786$	−29.3823	−1.04803
$787$	−29.5114	−1.05197	−0.525984	−	0.850494i	$-0.676303\pi$
$787$	−29.5114	−1.05197	−0.525984	+	0.850494i	$0.676303\pi$
$788$	−13.8477	−0.493305
$789$	−0.408198	−0.0145322
$790$	−28.9774	−1.03097
$791$	2.46936	0.0878003
$792$	9.51128	0.337968
$793$	−9.70386	−0.344594
$794$	−15.5538	−0.551982
$795$	−15.3305	−0.543717
$796$	−0.612398	−0.0217059
$797$	11.3843	0.403254	0.201627	−	0.979462i	$-0.435377\pi$
$797$	11.3843	0.403254	0.201627	+	0.979462i	$0.435377\pi$
$798$	12.9421	0.458147
$799$	−10.6093	−0.375328
$800$	−1.97692	−0.0698948
$801$	12.8520	0.454103
$802$	29.0264	1.02496
$803$	−22.5378	−0.795343
$804$	−4.58724	−0.161779
$805$	−13.7862	−0.485901
$806$	14.2200	0.500878
$807$	24.9172	0.877128
$808$	−18.1195	−0.637443
$809$	24.0901	0.846964	0.423482	−	0.905905i	$-0.360808\pi$
$809$	24.0901	0.846964	0.423482	+	0.905905i	$0.360808\pi$
$810$	18.9051	0.664256
$811$	40.5275	1.42311	0.711557	−	0.702628i	$-0.247990\pi$
$811$	40.5275	1.42311	0.711557	+	0.702628i	$0.247990\pi$
$812$	−8.22421	−0.288613
$813$	33.9901	1.19209
$814$	−0.169479	−0.00594025
$815$	9.83429	0.344480
$816$	−16.5742	−0.580212
$817$	−13.7323	−0.480433
$818$	−32.6940	−1.14312
$819$	−21.0814	−0.736642
$820$	8.31324	0.290311
$821$	2.13761	0.0746029	0.0373015	−	0.999304i	$-0.488124\pi$
$821$	2.13761	0.0746029	0.0373015	+	0.999304i	$0.488124\pi$
$822$	−10.5764	−0.368894
$823$	12.3492	0.430465	0.215232	−	0.976563i	$-0.430949\pi$
$823$	12.3492	0.430465	0.215232	+	0.976563i	$0.430949\pi$
$824$	10.9118	0.380129
$825$	20.1149	0.700310
$826$	11.0664	0.385049
$827$	41.7237	1.45087	0.725437	−	0.688288i	$-0.241638\pi$
$827$	41.7237	1.45087	0.725437	+	0.688288i	$0.241638\pi$
$828$	−6.03115	−0.209597
$829$	36.1865	1.25681	0.628405	−	0.777886i	$-0.283708\pi$
$829$	36.1865	1.25681	0.628405	+	0.777886i	$0.283708\pi$
$830$	−29.8683	−1.03674
$831$	−21.4646	−0.744597
$832$	3.58840	0.124405
$833$	5.30333	0.183750
$834$	31.6985	1.09763
$835$	−20.8416	−0.721252
$836$	9.26553	0.320455
$837$	7.94052	0.274465
$838$	−17.5328	−0.605661
$839$	−44.4290	−1.53386	−0.766929	−	0.641732i	$-0.778216\pi$
$839$	−44.4290	−1.53386	−0.766929	+	0.641732i	$0.778216\pi$
$840$	−10.9273	−0.377026
$841$	−20.2427	−0.698025
$842$	27.3964	0.944143
$843$	−23.0293	−0.793172
$844$	12.2864	0.422916
$845$	0.214572	0.00738149
$846$	−3.05998	−0.105204
$847$	−25.6909	−0.882749
$848$	−3.89902	−0.133893
$849$	−37.9696	−1.30311
$850$	−14.4892	−0.496976
$851$	0.107468	0.00368395
$852$	−4.71921	−0.161677
$853$	36.2796	1.24219	0.621095	−	0.783735i	$-0.286688\pi$
$853$	36.2796	1.24219	0.621095	+	0.783735i	$0.286688\pi$
$854$	7.51543	0.257173
$855$	−7.56890	−0.258851
$856$	−17.2320	−0.588977
$857$	−43.6760	−1.49194	−0.745972	−	0.665977i	$-0.768015\pi$
$857$	−43.6760	−1.49194	−0.745972	+	0.665977i	$0.768015\pi$
$858$	−36.5113	−1.24648
$859$	17.8015	0.607378	0.303689	−	0.952771i	$-0.401782\pi$
$859$	17.8015	0.607378	0.303689	+	0.952771i	$0.401782\pi$
$860$	11.5944	0.395366
$861$	−30.0492	−1.02407
$862$	−34.6056	−1.17867
$863$	−11.1360	−0.379075	−0.189538	−	0.981873i	$-0.560699\pi$
$863$	−11.1360	−0.379075	−0.189538	+	0.981873i	$0.560699\pi$
$864$	2.00378	0.0681700
$865$	−2.17672	−0.0740109
$866$	−6.88973	−0.234123
$867$	−83.0311	−2.81988
$868$	−11.0131	−0.373808
$869$	74.9870	2.54376
$870$	11.6355	0.394481
$871$	7.27905	0.246641
$872$	8.76609	0.296857
$873$	−6.32116	−0.213939
$874$	−5.87532	−0.198736
$875$	−33.7131	−1.13971
$876$	11.3276	0.382725
$877$	−6.81563	−0.230148	−0.115074	−	0.993357i	$-0.536710\pi$
$877$	−6.81563	−0.230148	−0.115074	+	0.993357i	$0.536710\pi$
$878$	8.82946	0.297980
$879$	34.3427	1.15835
$880$	−7.82303	−0.263714
$881$	−17.7678	−0.598613	−0.299307	−	0.954157i	$-0.596755\pi$
$881$	−17.7678	−0.598613	−0.299307	+	0.954157i	$0.596755\pi$
$882$	1.52962	0.0515049
$883$	−3.57818	−0.120415	−0.0602076	−	0.998186i	$-0.519176\pi$
$883$	−3.57818	−0.120415	−0.0602076	+	0.998186i	$0.519176\pi$
$884$	26.3000	0.884563
$885$	−15.6566	−0.526291
$886$	−2.88869	−0.0970473
$887$	15.8570	0.532425	0.266213	−	0.963914i	$-0.414228\pi$
$887$	15.8570	0.532425	0.266213	+	0.963914i	$0.414228\pi$
$888$	0.0851812	0.00285849
$889$	9.49188	0.318348
$890$	−10.5708	−0.354333
$891$	−48.9220	−1.63895
$892$	24.1752	0.809446
$893$	−2.98092	−0.0997526
$894$	4.88316	0.163317
$895$	−22.8197	−0.762778
$896$	−2.77914	−0.0928444
$897$	23.1520	0.773024
$898$	13.4273	0.448074
$899$	11.7269	0.391114
$900$	−4.17906	−0.139302
$901$	−28.5765	−0.952022
$902$	−21.5128	−0.716297
$903$	−41.9093	−1.39466
$904$	−0.888535	−0.0295522
$905$	−33.6238	−1.11769
$906$	−43.6299	−1.44951
$907$	49.1334	1.63145	0.815724	−	0.578442i	$-0.196339\pi$
$907$	49.1334	1.63145	0.815724	+	0.578442i	$0.196339\pi$
$908$	−15.8495	−0.525985
$909$	−38.3032	−1.27044
$910$	17.3394	0.574796
$911$	54.4387	1.80363	0.901817	−	0.432119i	$-0.142234\pi$
$911$	54.4387	1.80363	0.901817	+	0.432119i	$0.142234\pi$
$912$	−4.65690	−0.154205
$913$	77.2922	2.55800
$914$	16.4468	0.544010
$915$	−10.6328	−0.351508
$916$	−5.59622	−0.184904
$917$	−36.1092	−1.19243
$918$	14.6860	0.484712
$919$	39.0966	1.28968	0.644838	−	0.764319i	$-0.276925\pi$
$919$	39.0966	1.28968	0.644838	+	0.764319i	$0.276925\pi$
$920$	4.96062	0.163547
$921$	44.7197	1.47357
$922$	30.5107	1.00482
$923$	7.48846	0.246486
$924$	28.2772	0.930253
$925$	0.0744658	0.00244842
$926$	−0.468253	−0.0153877
$927$	23.0666	0.757606
$928$	2.95927	0.0971428
$929$	2.99030	0.0981086	0.0490543	−	0.998796i	$-0.484379\pi$
$929$	2.99030	0.0981086	0.0490543	+	0.998796i	$0.484379\pi$
$930$	15.5812	0.510927
$931$	1.49009	0.0488359
$932$	−4.92493	−0.161322
$933$	32.4462	1.06224
$934$	30.5265	0.998859
$935$	−57.3363	−1.87510
$936$	7.58558	0.247943
$937$	−14.6880	−0.479835	−0.239917	−	0.970793i	$-0.577120\pi$
$937$	−14.6880	−0.479835	−0.239917	+	0.970793i	$0.577120\pi$
$938$	−5.63746	−0.184070
$939$	−2.50570	−0.0817704
$940$	2.51684	0.0820901
$941$	43.2962	1.41142	0.705708	−	0.708503i	$-0.250629\pi$
$941$	43.2962	1.41142	0.705708	+	0.708503i	$0.250629\pi$
$942$	3.16320	0.103063
$943$	13.6414	0.444224
$944$	−3.98196	−0.129602
$945$	9.68243	0.314969
$946$	−30.0037	−0.975504
$947$	−23.3480	−0.758709	−0.379354	−	0.925251i	$-0.623854\pi$
$947$	−23.3480	−0.758709	−0.379354	+	0.925251i	$0.623854\pi$
$948$	−37.6888	−1.22408
$949$	−17.9747	−0.583485
$950$	−4.07108	−0.132083
$951$	−25.9789	−0.842423
$952$	−20.3687	−0.660155
$953$	−40.2390	−1.30347	−0.651734	−	0.758447i	$-0.725958\pi$
$953$	−40.2390	−1.30347	−0.651734	+	0.758447i	$0.725958\pi$
$954$	−8.24220	−0.266851
$955$	−6.17924	−0.199956
$956$	15.1732	0.490738
$957$	−30.1101	−0.973320
$958$	−39.5068	−1.27641
$959$	−12.9978	−0.419721
$960$	3.93189	0.126901
$961$	−15.2964	−0.493434
$962$	−0.135166	−0.00435792
$963$	−36.4270	−1.17385
$964$	−14.9580	−0.481766
$965$	−46.6021	−1.50018
$966$	−17.9307	−0.576912
$967$	−18.2170	−0.585820	−0.292910	−	0.956140i	$-0.594624\pi$
$967$	−18.2170	−0.585820	−0.292910	+	0.956140i	$0.594624\pi$
$968$	9.24420	0.297120
$969$	−34.1312	−1.09645
$970$	5.19916	0.166935
$971$	55.7931	1.79048	0.895242	−	0.445579i	$-0.147002\pi$
$971$	55.7931	1.79048	0.895242	+	0.445579i	$0.147002\pi$
$972$	18.5771	0.595860
$973$	38.9558	1.24886
$974$	−24.4269	−0.782688
$975$	16.0423	0.513766
$976$	−2.70423	−0.0865604
$977$	−33.3645	−1.06743	−0.533713	−	0.845666i	$-0.679204\pi$
$977$	−33.3645	−1.06743	−0.533713	+	0.845666i	$0.679204\pi$
$978$	12.7907	0.409003
$979$	27.3547	0.874261
$980$	−1.25811	−0.0401889
$981$	18.5308	0.591643
$982$	37.4458	1.19494
$983$	4.19153	0.133689	0.0668445	−	0.997763i	$-0.478707\pi$
$983$	4.19153	0.133689	0.0668445	+	0.997763i	$0.478707\pi$
$984$	10.8124	0.344687
$985$	24.0771	0.767159
$986$	21.6890	0.690718
$987$	−9.09739	−0.289573
$988$	7.38959	0.235094
$989$	19.0255	0.604975
$990$	−16.5373	−0.525588
$991$	−41.7185	−1.32523	−0.662617	−	0.748959i	$-0.730554\pi$
$991$	−41.7185	−1.32523	−0.662617	+	0.748959i	$0.730554\pi$
$992$	3.96277	0.125818
$993$	16.9438	0.537695
$994$	−5.79965	−0.183954
$995$	1.06478	0.0337557
$996$	−38.8474	−1.23093
$997$	1.68805	0.0534610	0.0267305	−	0.999643i	$-0.491490\pi$
$997$	1.68805	0.0534610	0.0267305	+	0.999643i	$0.491490\pi$
$998$	22.1877	0.702339
$999$	−0.0754774	−0.00238800

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8014.2.a.d.1.14	✓	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8014.2.a.d.1.14	✓	88	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.26140 q^{3} +1.00000 q^{4} -1.73870 q^{5} -2.26140 q^{6} -2.77914 q^{7} +1.00000 q^{8} +2.11392 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.26140 q^{3} +1.00000 q^{4} -1.73870 q^{5} -2.26140 q^{6} -2.77914 q^{7} +1.00000 q^{8} +2.11392 q^{9} -1.73870 q^{10} +4.49936 q^{11} -2.26140 q^{12} +3.58840 q^{13} -2.77914 q^{14} +3.93189 q^{15} +1.00000 q^{16} +7.32917 q^{17} +2.11392 q^{18} +2.05930 q^{19} -1.73870 q^{20} +6.28473 q^{21} +4.49936 q^{22} -2.85306 q^{23} -2.26140 q^{24} -1.97692 q^{25} +3.58840 q^{26} +2.00378 q^{27} -2.77914 q^{28} +2.95927 q^{29} +3.93189 q^{30} +3.96277 q^{31} +1.00000 q^{32} -10.1748 q^{33} +7.32917 q^{34} +4.83208 q^{35} +2.11392 q^{36} -0.0376675 q^{37} +2.05930 q^{38} -8.11479 q^{39} -1.73870 q^{40} -4.78130 q^{41} +6.28473 q^{42} -6.66844 q^{43} +4.49936 q^{44} -3.67547 q^{45} -2.85306 q^{46} -1.44754 q^{47} -2.26140 q^{48} +0.723593 q^{49} -1.97692 q^{50} -16.5742 q^{51} +3.58840 q^{52} -3.89902 q^{53} +2.00378 q^{54} -7.82303 q^{55} -2.77914 q^{56} -4.65690 q^{57} +2.95927 q^{58} -3.98196 q^{59} +3.93189 q^{60} -2.70423 q^{61} +3.96277 q^{62} -5.87487 q^{63} +1.00000 q^{64} -6.23914 q^{65} -10.1748 q^{66} +2.02850 q^{67} +7.32917 q^{68} +6.45191 q^{69} +4.83208 q^{70} +2.08685 q^{71} +2.11392 q^{72} -5.00913 q^{73} -0.0376675 q^{74} +4.47061 q^{75} +2.05930 q^{76} -12.5043 q^{77} -8.11479 q^{78} +16.6662 q^{79} -1.73870 q^{80} -10.8731 q^{81} -4.78130 q^{82} +17.1785 q^{83} +6.28473 q^{84} -12.7432 q^{85} -6.66844 q^{86} -6.69209 q^{87} +4.49936 q^{88} +6.07970 q^{89} -3.67547 q^{90} -9.97264 q^{91} -2.85306 q^{92} -8.96140 q^{93} -1.44754 q^{94} -3.58051 q^{95} -2.26140 q^{96} -2.99026 q^{97} +0.723593 q^{98} +9.51128 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 88 q^{2} + 22 q^{3} + 88 q^{4} + 25 q^{5} + 22 q^{6} + 33 q^{7} + 88 q^{8} + 108 q^{9}+O(q^{10}) \) 88 * q + 88 * q^2 + 22 * q^3 + 88 * q^4 + 25 * q^5 + 22 * q^6 + 33 * q^7 + 88 * q^8 + 108 * q^9	\( 88 q + 88 q^{2} + 22 q^{3} + 88 q^{4} + 25 q^{5} + 22 q^{6} + 33 q^{7} + 88 q^{8} + 108 q^{9} + 25 q^{10} + 70 q^{11} + 22 q^{12} + 31 q^{13} + 33 q^{14} + 47 q^{15} + 88 q^{16} + 19 q^{17} + 108 q^{18} + 33 q^{19} + 25 q^{20} + 48 q^{21} + 70 q^{22} + 77 q^{23} + 22 q^{24} + 109 q^{25} + 31 q^{26} + 88 q^{27} + 33 q^{28} + 83 q^{29} + 47 q^{30} + 51 q^{31} + 88 q^{32} + 30 q^{33} + 19 q^{34} + 40 q^{35} + 108 q^{36} + 45 q^{37} + 33 q^{38} + 82 q^{39} + 25 q^{40} + 35 q^{41} + 48 q^{42} + 78 q^{43} + 70 q^{44} + 37 q^{45} + 77 q^{46} + 59 q^{47} + 22 q^{48} + 103 q^{49} + 109 q^{50} + 21 q^{51} + 31 q^{52} + 58 q^{53} + 88 q^{54} + 35 q^{55} + 33 q^{56} - 16 q^{57} + 83 q^{58} + 54 q^{59} + 47 q^{60} + 18 q^{61} + 51 q^{62} + 47 q^{63} + 88 q^{64} + 34 q^{65} + 30 q^{66} + 88 q^{67} + 19 q^{68} + 62 q^{69} + 40 q^{70} + 139 q^{71} + 108 q^{72} - 6 q^{73} + 45 q^{74} + 45 q^{75} + 33 q^{76} + 37 q^{77} + 82 q^{78} + 94 q^{79} + 25 q^{80} + 112 q^{81} + 35 q^{82} + 58 q^{83} + 48 q^{84} + 83 q^{85} + 78 q^{86} + 21 q^{87} + 70 q^{88} + 99 q^{89} + 37 q^{90} + 53 q^{91} + 77 q^{92} + 57 q^{93} + 59 q^{94} + 92 q^{95} + 22 q^{96} + 16 q^{97} + 103 q^{98} + 150 q^{99}+O(q^{100}) \) 88 * q + 88 * q^2 + 22 * q^3 + 88 * q^4 + 25 * q^5 + 22 * q^6 + 33 * q^7 + 88 * q^8 + 108 * q^9 + 25 * q^10 + 70 * q^11 + 22 * q^12 + 31 * q^13 + 33 * q^14 + 47 * q^15 + 88 * q^16 + 19 * q^17 + 108 * q^18 + 33 * q^19 + 25 * q^20 + 48 * q^21 + 70 * q^22 + 77 * q^23 + 22 * q^24 + 109 * q^25 + 31 * q^26 + 88 * q^27 + 33 * q^28 + 83 * q^29 + 47 * q^30 + 51 * q^31 + 88 * q^32 + 30 * q^33 + 19 * q^34 + 40 * q^35 + 108 * q^36 + 45 * q^37 + 33 * q^38 + 82 * q^39 + 25 * q^40 + 35 * q^41 + 48 * q^42 + 78 * q^43 + 70 * q^44 + 37 * q^45 + 77 * q^46 + 59 * q^47 + 22 * q^48 + 103 * q^49 + 109 * q^50 + 21 * q^51 + 31 * q^52 + 58 * q^53 + 88 * q^54 + 35 * q^55 + 33 * q^56 - 16 * q^57 + 83 * q^58 + 54 * q^59 + 47 * q^60 + 18 * q^61 + 51 * q^62 + 47 * q^63 + 88 * q^64 + 34 * q^65 + 30 * q^66 + 88 * q^67 + 19 * q^68 + 62 * q^69 + 40 * q^70 + 139 * q^71 + 108 * q^72 - 6 * q^73 + 45 * q^74 + 45 * q^75 + 33 * q^76 + 37 * q^77 + 82 * q^78 + 94 * q^79 + 25 * q^80 + 112 * q^81 + 35 * q^82 + 58 * q^83 + 48 * q^84 + 83 * q^85 + 78 * q^86 + 21 * q^87 + 70 * q^88 + 99 * q^89 + 37 * q^90 + 53 * q^91 + 77 * q^92 + 57 * q^93 + 59 * q^94 + 92 * q^95 + 22 * q^96 + 16 * q^97 + 103 * q^98 + 150 * q^99

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