LMFDB - Embedded newform 4002.2.a.bg.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4002,2,Mod(1,4002)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4002, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4002.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4002 = 2 \cdot 3 \cdot 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4002.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:	$31.9561308889$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 13x^{5} + 16x^{4} + 19x^{3} - 8x^{2} - 10x - 2 $ x^7 - x^6 - 13x^5 + 16x^4 + 19x^3 - 8x^2 - 10*x - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-0.340585$ of defining polynomial
Character	$\chi$	$=$	4002.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.46450 q^{5} +1.00000 q^{6} +1.26047 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.46450 q^{5} +1.00000 q^{6} +1.26047 q^{7} -1.00000 q^{8} +1.00000 q^{9} -3.46450 q^{10} -2.95054 q^{11} -1.00000 q^{12} -2.89870 q^{13} -1.26047 q^{14} -3.46450 q^{15} +1.00000 q^{16} -0.513960 q^{17} -1.00000 q^{18} -3.00622 q^{19} +3.46450 q^{20} -1.26047 q^{21} +2.95054 q^{22} +1.00000 q^{23} +1.00000 q^{24} +7.00274 q^{25} +2.89870 q^{26} -1.00000 q^{27} +1.26047 q^{28} +1.00000 q^{29} +3.46450 q^{30} -5.40982 q^{31} -1.00000 q^{32} +2.95054 q^{33} +0.513960 q^{34} +4.36688 q^{35} +1.00000 q^{36} +10.8799 q^{37} +3.00622 q^{38} +2.89870 q^{39} -3.46450 q^{40} -7.03067 q^{41} +1.26047 q^{42} -7.06738 q^{43} -2.95054 q^{44} +3.46450 q^{45} -1.00000 q^{46} -4.98736 q^{47} -1.00000 q^{48} -5.41122 q^{49} -7.00274 q^{50} +0.513960 q^{51} -2.89870 q^{52} -7.84635 q^{53} +1.00000 q^{54} -10.2221 q^{55} -1.26047 q^{56} +3.00622 q^{57} -1.00000 q^{58} -4.54958 q^{59} -3.46450 q^{60} -7.47147 q^{61} +5.40982 q^{62} +1.26047 q^{63} +1.00000 q^{64} -10.0425 q^{65} -2.95054 q^{66} -8.80796 q^{67} -0.513960 q^{68} -1.00000 q^{69} -4.36688 q^{70} +6.80747 q^{71} -1.00000 q^{72} +2.87765 q^{73} -10.8799 q^{74} -7.00274 q^{75} -3.00622 q^{76} -3.71905 q^{77} -2.89870 q^{78} -9.61800 q^{79} +3.46450 q^{80} +1.00000 q^{81} +7.03067 q^{82} +0.492258 q^{83} -1.26047 q^{84} -1.78061 q^{85} +7.06738 q^{86} -1.00000 q^{87} +2.95054 q^{88} +0.689007 q^{89} -3.46450 q^{90} -3.65372 q^{91} +1.00000 q^{92} +5.40982 q^{93} +4.98736 q^{94} -10.4150 q^{95} +1.00000 q^{96} -2.39041 q^{97} +5.41122 q^{98} -2.95054 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 7 q^{2} - 7 q^{3} + 7 q^{4} + 2 q^{5} + 7 q^{6} - 5 q^{7} - 7 q^{8} + 7 q^{9}+O(q^{10}) $ 7 * q - 7 * q^2 - 7 * q^3 + 7 * q^4 + 2 * q^5 + 7 * q^6 - 5 * q^7 - 7 * q^8 + 7 * q^9	\( 7 q - 7 q^{2} - 7 q^{3} + 7 q^{4} + 2 q^{5} + 7 q^{6} - 5 q^{7} - 7 q^{8} + 7 q^{9} - 2 q^{10} - q^{11} - 7 q^{12} + q^{13} + 5 q^{14} - 2 q^{15} + 7 q^{16} - q^{17} - 7 q^{18} - 9 q^{19} + 2 q^{20} + 5 q^{21} + q^{22} + 7 q^{23} + 7 q^{24} + q^{25} - q^{26} - 7 q^{27} - 5 q^{28} + 7 q^{29} + 2 q^{30} - 19 q^{31} - 7 q^{32} + q^{33} + q^{34} + 11 q^{35} + 7 q^{36} - 18 q^{37} + 9 q^{38} - q^{39} - 2 q^{40} + 4 q^{41} - 5 q^{42} - 9 q^{43} - q^{44} + 2 q^{45} - 7 q^{46} - 11 q^{47} - 7 q^{48} + 12 q^{49} - q^{50} + q^{51} + q^{52} + 8 q^{53} + 7 q^{54} - 11 q^{55} + 5 q^{56} + 9 q^{57} - 7 q^{58} + 12 q^{59} - 2 q^{60} - 5 q^{61} + 19 q^{62} - 5 q^{63} + 7 q^{64} + 23 q^{65} - q^{66} - 13 q^{67} - q^{68} - 7 q^{69} - 11 q^{70} - q^{71} - 7 q^{72} - 26 q^{73} + 18 q^{74} - q^{75} - 9 q^{76} + 6 q^{77} + q^{78} - 38 q^{79} + 2 q^{80} + 7 q^{81} - 4 q^{82} - 6 q^{83} + 5 q^{84} - 25 q^{85} + 9 q^{86} - 7 q^{87} + q^{88} + 20 q^{89} - 2 q^{90} + 2 q^{91} + 7 q^{92} + 19 q^{93} + 11 q^{94} - 31 q^{95} + 7 q^{96} - 8 q^{97} - 12 q^{98} - q^{99}+O(q^{100}) \) 7 * q - 7 * q^2 - 7 * q^3 + 7 * q^4 + 2 * q^5 + 7 * q^6 - 5 * q^7 - 7 * q^8 + 7 * q^9 - 2 * q^10 - q^11 - 7 * q^12 + q^13 + 5 * q^14 - 2 * q^15 + 7 * q^16 - q^17 - 7 * q^18 - 9 * q^19 + 2 * q^20 + 5 * q^21 + q^22 + 7 * q^23 + 7 * q^24 + q^25 - q^26 - 7 * q^27 - 5 * q^28 + 7 * q^29 + 2 * q^30 - 19 * q^31 - 7 * q^32 + q^33 + q^34 + 11 * q^35 + 7 * q^36 - 18 * q^37 + 9 * q^38 - q^39 - 2 * q^40 + 4 * q^41 - 5 * q^42 - 9 * q^43 - q^44 + 2 * q^45 - 7 * q^46 - 11 * q^47 - 7 * q^48 + 12 * q^49 - q^50 + q^51 + q^52 + 8 * q^53 + 7 * q^54 - 11 * q^55 + 5 * q^56 + 9 * q^57 - 7 * q^58 + 12 * q^59 - 2 * q^60 - 5 * q^61 + 19 * q^62 - 5 * q^63 + 7 * q^64 + 23 * q^65 - q^66 - 13 * q^67 - q^68 - 7 * q^69 - 11 * q^70 - q^71 - 7 * q^72 - 26 * q^73 + 18 * q^74 - q^75 - 9 * q^76 + 6 * q^77 + q^78 - 38 * q^79 + 2 * q^80 + 7 * q^81 - 4 * q^82 - 6 * q^83 + 5 * q^84 - 25 * q^85 + 9 * q^86 - 7 * q^87 + q^88 + 20 * q^89 - 2 * q^90 + 2 * q^91 + 7 * q^92 + 19 * q^93 + 11 * q^94 - 31 * q^95 + 7 * q^96 - 8 * q^97 - 12 * q^98 - q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	3.46450	1.54937	0.774685	−	0.632347i	$-0.217908\pi$
$5$	3.46450	1.54937	0.774685	+	0.632347i	$0.217908\pi$
$6$	1.00000	0.408248
$7$	1.26047	0.476412	0.238206	−	0.971215i	$-0.423441\pi$
$7$	1.26047	0.476412	0.238206	+	0.971215i	$0.423441\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−3.46450	−1.09557
$11$	−2.95054	−0.889621	−0.444810	−	0.895625i	$-0.646729\pi$
$11$	−2.95054	−0.889621	−0.444810	+	0.895625i	$0.646729\pi$
$12$	−1.00000	−0.288675
$13$	−2.89870	−0.803955	−0.401978	−	0.915649i	$-0.631677\pi$
$13$	−2.89870	−0.803955	−0.401978	+	0.915649i	$0.631677\pi$
$14$	−1.26047	−0.336874
$15$	−3.46450	−0.894529
$16$	1.00000	0.250000
$17$	−0.513960	−0.124654	−0.0623268	−	0.998056i	$-0.519852\pi$
$17$	−0.513960	−0.124654	−0.0623268	+	0.998056i	$0.519852\pi$
$18$	−1.00000	−0.235702
$19$	−3.00622	−0.689674	−0.344837	−	0.938663i	$-0.612066\pi$
$19$	−3.00622	−0.689674	−0.344837	+	0.938663i	$0.612066\pi$
$20$	3.46450	0.774685
$21$	−1.26047	−0.275056
$22$	2.95054	0.629057
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	1.00000	0.204124
$25$	7.00274	1.40055
$26$	2.89870	0.568482
$27$	−1.00000	−0.192450
$28$	1.26047	0.238206
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	3.46450	0.632528
$31$	−5.40982	−0.971632	−0.485816	−	0.874061i	$-0.661478\pi$
$31$	−5.40982	−0.971632	−0.485816	+	0.874061i	$0.661478\pi$
$32$	−1.00000	−0.176777
$33$	2.95054	0.513623
$34$	0.513960	0.0881434
$35$	4.36688	0.738138
$36$	1.00000	0.166667
$37$	10.8799	1.78865	0.894323	−	0.447423i	$-0.147658\pi$
$37$	10.8799	1.78865	0.894323	+	0.447423i	$0.147658\pi$
$38$	3.00622	0.487673
$39$	2.89870	0.464164
$40$	−3.46450	−0.547785
$41$	−7.03067	−1.09801	−0.549003	−	0.835821i	$-0.684992\pi$
$41$	−7.03067	−1.09801	−0.549003	+	0.835821i	$0.684992\pi$
$42$	1.26047	0.194494
$43$	−7.06738	−1.07777	−0.538883	−	0.842381i	$-0.681153\pi$
$43$	−7.06738	−1.07777	−0.538883	+	0.842381i	$0.681153\pi$
$44$	−2.95054	−0.444810
$45$	3.46450	0.516457
$46$	−1.00000	−0.147442
$47$	−4.98736	−0.727481	−0.363741	−	0.931500i	$-0.618501\pi$
$47$	−4.98736	−0.727481	−0.363741	+	0.931500i	$0.618501\pi$
$48$	−1.00000	−0.144338
$49$	−5.41122	−0.773032
$50$	−7.00274	−0.990338
$51$	0.513960	0.0719688
$52$	−2.89870	−0.401978
$53$	−7.84635	−1.07778	−0.538890	−	0.842376i	$-0.681156\pi$
$53$	−7.84635	−1.07778	−0.538890	+	0.842376i	$0.681156\pi$
$54$	1.00000	0.136083
$55$	−10.2221	−1.37835
$56$	−1.26047	−0.168437
$57$	3.00622	0.398183
$58$	−1.00000	−0.131306
$59$	−4.54958	−0.592304	−0.296152	−	0.955141i	$-0.595704\pi$
$59$	−4.54958	−0.592304	−0.296152	+	0.955141i	$0.595704\pi$
$60$	−3.46450	−0.447265
$61$	−7.47147	−0.956624	−0.478312	−	0.878190i	$-0.658751\pi$
$61$	−7.47147	−0.956624	−0.478312	+	0.878190i	$0.658751\pi$
$62$	5.40982	0.687048
$63$	1.26047	0.158804
$64$	1.00000	0.125000
$65$	−10.0425	−1.24562
$66$	−2.95054	−0.363186
$67$	−8.80796	−1.07606	−0.538032	−	0.842925i	$-0.680832\pi$
$67$	−8.80796	−1.07606	−0.538032	+	0.842925i	$0.680832\pi$
$68$	−0.513960	−0.0623268
$69$	−1.00000	−0.120386
$70$	−4.36688	−0.521943
$71$	6.80747	0.807898	0.403949	−	0.914782i	$-0.367637\pi$
$71$	6.80747	0.807898	0.403949	+	0.914782i	$0.367637\pi$
$72$	−1.00000	−0.117851
$73$	2.87765	0.336803	0.168402	−	0.985718i	$-0.446139\pi$
$73$	2.87765	0.336803	0.168402	+	0.985718i	$0.446139\pi$
$74$	−10.8799	−1.26476
$75$	−7.00274	−0.808607
$76$	−3.00622	−0.344837
$77$	−3.71905	−0.423826
$78$	−2.89870	−0.328213
$79$	−9.61800	−1.08211	−0.541055	−	0.840987i	$-0.681975\pi$
$79$	−9.61800	−1.08211	−0.541055	+	0.840987i	$0.681975\pi$
$80$	3.46450	0.387343
$81$	1.00000	0.111111
$82$	7.03067	0.776407
$83$	0.492258	0.0540323	0.0270162	−	0.999635i	$-0.491399\pi$
$83$	0.492258	0.0540323	0.0270162	+	0.999635i	$0.491399\pi$
$84$	−1.26047	−0.137528
$85$	−1.78061	−0.193135
$86$	7.06738	0.762095
$87$	−1.00000	−0.107211
$88$	2.95054	0.314528
$89$	0.689007	0.0730346	0.0365173	−	0.999333i	$-0.488374\pi$
$89$	0.689007	0.0730346	0.0365173	+	0.999333i	$0.488374\pi$
$90$	−3.46450	−0.365190
$91$	−3.65372	−0.383014
$92$	1.00000	0.104257
$93$	5.40982	0.560972
$94$	4.98736	0.514407
$95$	−10.4150	−1.06856
$96$	1.00000	0.102062
$97$	−2.39041	−0.242709	−0.121355	−	0.992609i	$-0.538724\pi$
$97$	−2.39041	−0.242709	−0.121355	+	0.992609i	$0.538724\pi$
$98$	5.41122	0.546616
$99$	−2.95054	−0.296540
$100$	7.00274	0.700274
$101$	5.52770	0.550026	0.275013	−	0.961440i	$-0.411318\pi$
$101$	5.52770	0.550026	0.275013	+	0.961440i	$0.411318\pi$
$102$	−0.513960	−0.0508896
$103$	−1.89297	−0.186520	−0.0932601	−	0.995642i	$-0.529729\pi$
$103$	−1.89297	−0.186520	−0.0932601	+	0.995642i	$0.529729\pi$
$104$	2.89870	0.284241
$105$	−4.36688	−0.426164
$106$	7.84635	0.762105
$107$	2.57025	0.248476	0.124238	−	0.992252i	$-0.460351\pi$
$107$	2.57025	0.248476	0.124238	+	0.992252i	$0.460351\pi$
$108$	−1.00000	−0.0962250
$109$	18.5551	1.77726	0.888628	−	0.458629i	$-0.151659\pi$
$109$	18.5551	1.77726	0.888628	+	0.458629i	$0.151659\pi$
$110$	10.2221	0.974642
$111$	−10.8799	−1.03267
$112$	1.26047	0.119103
$113$	−3.26945	−0.307564	−0.153782	−	0.988105i	$-0.549145\pi$
$113$	−3.26945	−0.307564	−0.153782	+	0.988105i	$0.549145\pi$
$114$	−3.00622	−0.281558
$115$	3.46450	0.323066
$116$	1.00000	0.0928477
$117$	−2.89870	−0.267985
$118$	4.54958	0.418822
$119$	−0.647830	−0.0593865
$120$	3.46450	0.316264
$121$	−2.29433	−0.208575
$122$	7.47147	0.676435
$123$	7.03067	0.633934
$124$	−5.40982	−0.485816
$125$	6.93850	0.620599
$126$	−1.26047	−0.112291
$127$	−8.28653	−0.735311	−0.367655	−	0.929962i	$-0.619839\pi$
$127$	−8.28653	−0.735311	−0.367655	+	0.929962i	$0.619839\pi$
$128$	−1.00000	−0.0883883
$129$	7.06738	0.622248
$130$	10.0425	0.880790
$131$	11.3326	0.990131	0.495065	−	0.868856i	$-0.335144\pi$
$131$	11.3326	0.990131	0.495065	+	0.868856i	$0.335144\pi$
$132$	2.95054	0.256811
$133$	−3.78924	−0.328569
$134$	8.80796	0.760891
$135$	−3.46450	−0.298176
$136$	0.513960	0.0440717
$137$	9.35007	0.798830	0.399415	−	0.916770i	$-0.369213\pi$
$137$	9.35007	0.798830	0.399415	+	0.916770i	$0.369213\pi$
$138$	1.00000	0.0851257
$139$	−5.33044	−0.452122	−0.226061	−	0.974113i	$-0.572585\pi$
$139$	−5.33044	−0.452122	−0.226061	+	0.974113i	$0.572585\pi$
$140$	4.36688	0.369069
$141$	4.98736	0.420011
$142$	−6.80747	−0.571270
$143$	8.55273	0.715215
$144$	1.00000	0.0833333
$145$	3.46450	0.287711
$146$	−2.87765	−0.238156
$147$	5.41122	0.446310
$148$	10.8799	0.894323
$149$	−3.37859	−0.276785	−0.138392	−	0.990377i	$-0.544193\pi$
$149$	−3.37859	−0.276785	−0.138392	+	0.990377i	$0.544193\pi$
$150$	7.00274	0.571772
$151$	11.4581	0.932447	0.466223	−	0.884667i	$-0.345614\pi$
$151$	11.4581	0.932447	0.466223	+	0.884667i	$0.345614\pi$
$152$	3.00622	0.243836
$153$	−0.513960	−0.0415512
$154$	3.71905	0.299690
$155$	−18.7423	−1.50542
$156$	2.89870	0.232082
$157$	−10.5662	−0.843277	−0.421638	−	0.906764i	$-0.638545\pi$
$157$	−10.5662	−0.843277	−0.421638	+	0.906764i	$0.638545\pi$
$158$	9.61800	0.765167
$159$	7.84635	0.622256
$160$	−3.46450	−0.273893
$161$	1.26047	0.0993387
$162$	−1.00000	−0.0785674
$163$	−22.6547	−1.77445	−0.887225	−	0.461336i	$-0.847370\pi$
$163$	−22.6547	−1.77445	−0.887225	+	0.461336i	$0.847370\pi$
$164$	−7.03067	−0.549003
$165$	10.2221	0.795792
$166$	−0.492258	−0.0382066
$167$	9.94700	0.769722	0.384861	−	0.922975i	$-0.374249\pi$
$167$	9.94700	0.769722	0.384861	+	0.922975i	$0.374249\pi$
$168$	1.26047	0.0972471
$169$	−4.59753	−0.353656
$170$	1.78061	0.136567
$171$	−3.00622	−0.229891
$172$	−7.06738	−0.538883
$173$	−8.41406	−0.639709	−0.319854	−	0.947467i	$-0.603634\pi$
$173$	−8.41406	−0.639709	−0.319854	+	0.947467i	$0.603634\pi$
$174$	1.00000	0.0758098
$175$	8.82673	0.667238
$176$	−2.95054	−0.222405
$177$	4.54958	0.341967
$178$	−0.689007	−0.0516433
$179$	−18.7011	−1.39779	−0.698894	−	0.715226i	$-0.746324\pi$
$179$	−18.7011	−1.39779	−0.698894	+	0.715226i	$0.746324\pi$
$180$	3.46450	0.258228
$181$	14.4459	1.07375	0.536877	−	0.843661i	$-0.319604\pi$
$181$	14.4459	1.07375	0.536877	+	0.843661i	$0.319604\pi$
$182$	3.65372	0.270832
$183$	7.47147	0.552307
$184$	−1.00000	−0.0737210
$185$	37.6934	2.77127
$186$	−5.40982	−0.396667
$187$	1.51646	0.110894
$188$	−4.98736	−0.363741
$189$	−1.26047	−0.0916855
$190$	10.4150	0.755586
$191$	18.1975	1.31673	0.658364	−	0.752700i	$-0.271249\pi$
$191$	18.1975	1.31673	0.658364	+	0.752700i	$0.271249\pi$
$192$	−1.00000	−0.0721688
$193$	−3.83991	−0.276403	−0.138201	−	0.990404i	$-0.544132\pi$
$193$	−3.83991	−0.276403	−0.138201	+	0.990404i	$0.544132\pi$
$194$	2.39041	0.171621
$195$	10.0425	0.719162
$196$	−5.41122	−0.386516
$197$	2.46376	0.175536	0.0877679	−	0.996141i	$-0.472027\pi$
$197$	2.46376	0.175536	0.0877679	+	0.996141i	$0.472027\pi$
$198$	2.95054	0.209686
$199$	−27.5015	−1.94953	−0.974765	−	0.223233i	$-0.928339\pi$
$199$	−27.5015	−1.94953	−0.974765	+	0.223233i	$0.928339\pi$
$200$	−7.00274	−0.495169
$201$	8.80796	0.621265
$202$	−5.52770	−0.388927
$203$	1.26047	0.0884674
$204$	0.513960	0.0359844
$205$	−24.3577	−1.70122
$206$	1.89297	0.131890
$207$	1.00000	0.0695048
$208$	−2.89870	−0.200989
$209$	8.86996	0.613548
$210$	4.36688	0.301344
$211$	−2.76261	−0.190186	−0.0950929	−	0.995468i	$-0.530315\pi$
$211$	−2.76261	−0.190186	−0.0950929	+	0.995468i	$0.530315\pi$
$212$	−7.84635	−0.538890
$213$	−6.80747	−0.466440
$214$	−2.57025	−0.175699
$215$	−24.4849	−1.66986
$216$	1.00000	0.0680414
$217$	−6.81890	−0.462897
$218$	−18.5551	−1.25671
$219$	−2.87765	−0.194453
$220$	−10.2221	−0.689176
$221$	1.48982	0.100216
$222$	10.8799	0.730211
$223$	21.6933	1.45269	0.726345	−	0.687331i	$-0.241218\pi$
$223$	21.6933	1.45269	0.726345	+	0.687331i	$0.241218\pi$
$224$	−1.26047	−0.0842185
$225$	7.00274	0.466850
$226$	3.26945	0.217481
$227$	26.6966	1.77191	0.885956	−	0.463769i	$-0.153503\pi$
$227$	26.6966	1.77191	0.885956	+	0.463769i	$0.153503\pi$
$228$	3.00622	0.199092
$229$	−4.48624	−0.296459	−0.148230	−	0.988953i	$-0.547357\pi$
$229$	−4.48624	−0.296459	−0.148230	+	0.988953i	$0.547357\pi$
$230$	−3.46450	−0.228442
$231$	3.71905	0.244696
$232$	−1.00000	−0.0656532
$233$	−30.0147	−1.96633	−0.983164	−	0.182727i	$-0.941508\pi$
$233$	−30.0147	−1.96633	−0.983164	+	0.182727i	$0.941508\pi$
$234$	2.89870	0.189494
$235$	−17.2787	−1.12714
$236$	−4.54958	−0.296152
$237$	9.61800	0.624756
$238$	0.647830	0.0419926
$239$	5.58901	0.361523	0.180761	−	0.983527i	$-0.442144\pi$
$239$	5.58901	0.361523	0.180761	+	0.983527i	$0.442144\pi$
$240$	−3.46450	−0.223632
$241$	21.2451	1.36852	0.684259	−	0.729239i	$-0.260126\pi$
$241$	21.2451	1.36852	0.684259	+	0.729239i	$0.260126\pi$
$242$	2.29433	0.147485
$243$	−1.00000	−0.0641500
$244$	−7.47147	−0.478312
$245$	−18.7472	−1.19771
$246$	−7.03067	−0.448259
$247$	8.71413	0.554467
$248$	5.40982	0.343524
$249$	−0.492258	−0.0311956
$250$	−6.93850	−0.438830
$251$	−2.14014	−0.135084	−0.0675422	−	0.997716i	$-0.521516\pi$
$251$	−2.14014	−0.135084	−0.0675422	+	0.997716i	$0.521516\pi$
$252$	1.26047	0.0794019
$253$	−2.95054	−0.185499
$254$	8.28653	0.519943
$255$	1.78061	0.111506
$256$	1.00000	0.0625000
$257$	31.3621	1.95632	0.978158	−	0.207862i	$-0.0666505\pi$
$257$	31.3621	1.95632	0.978158	+	0.207862i	$0.0666505\pi$
$258$	−7.06738	−0.439996
$259$	13.7138	0.852131
$260$	−10.0425	−0.622812
$261$	1.00000	0.0618984
$262$	−11.3326	−0.700128
$263$	−14.8260	−0.914211	−0.457106	−	0.889412i	$-0.651114\pi$
$263$	−14.8260	−0.914211	−0.457106	+	0.889412i	$0.651114\pi$
$264$	−2.95054	−0.181593
$265$	−27.1837	−1.66988
$266$	3.78924	0.232333
$267$	−0.689007	−0.0421666
$268$	−8.80796	−0.538032
$269$	25.6253	1.56240	0.781200	−	0.624281i	$-0.214608\pi$
$269$	25.6253	1.56240	0.781200	+	0.624281i	$0.214608\pi$
$270$	3.46450	0.210843
$271$	−13.5115	−0.820764	−0.410382	−	0.911914i	$-0.634605\pi$
$271$	−13.5115	−0.820764	−0.410382	+	0.911914i	$0.634605\pi$
$272$	−0.513960	−0.0311634
$273$	3.65372	0.221133
$274$	−9.35007	−0.564858
$275$	−20.6619	−1.24596
$276$	−1.00000	−0.0601929
$277$	18.8475	1.13244	0.566219	−	0.824255i	$-0.308406\pi$
$277$	18.8475	1.13244	0.566219	+	0.824255i	$0.308406\pi$
$278$	5.33044	0.319698
$279$	−5.40982	−0.323877
$280$	−4.36688	−0.260971
$281$	−22.0826	−1.31734	−0.658669	−	0.752432i	$-0.728880\pi$
$281$	−22.0826	−1.31734	−0.658669	+	0.752432i	$0.728880\pi$
$282$	−4.98736	−0.296993
$283$	4.52701	0.269103	0.134551	−	0.990907i	$-0.457041\pi$
$283$	4.52701	0.269103	0.134551	+	0.990907i	$0.457041\pi$
$284$	6.80747	0.403949
$285$	10.4150	0.616933
$286$	−8.55273	−0.505733
$287$	−8.86192	−0.523103
$288$	−1.00000	−0.0589256
$289$	−16.7358	−0.984461
$290$	−3.46450	−0.203442
$291$	2.39041	0.140128
$292$	2.87765	0.168402
$293$	−14.9075	−0.870906	−0.435453	−	0.900211i	$-0.643412\pi$
$293$	−14.9075	−0.870906	−0.435453	+	0.900211i	$0.643412\pi$
$294$	−5.41122	−0.315589
$295$	−15.7620	−0.917699
$296$	−10.8799	−0.632382
$297$	2.95054	0.171208
$298$	3.37859	0.195716
$299$	−2.89870	−0.167636
$300$	−7.00274	−0.404304
$301$	−8.90820	−0.513460
$302$	−11.4581	−0.659339
$303$	−5.52770	−0.317558
$304$	−3.00622	−0.172418
$305$	−25.8849	−1.48216
$306$	0.513960	0.0293811
$307$	−11.7337	−0.669679	−0.334839	−	0.942275i	$-0.608682\pi$
$307$	−11.7337	−0.669679	−0.334839	+	0.942275i	$0.608682\pi$
$308$	−3.71905	−0.211913
$309$	1.89297	0.107687
$310$	18.7423	1.06449
$311$	−12.9143	−0.732305	−0.366152	−	0.930555i	$-0.619325\pi$
$311$	−12.9143	−0.732305	−0.366152	+	0.930555i	$0.619325\pi$
$312$	−2.89870	−0.164107
$313$	−31.6900	−1.79122	−0.895612	−	0.444836i	$-0.853262\pi$
$313$	−31.6900	−1.79122	−0.895612	+	0.444836i	$0.853262\pi$
$314$	10.5662	0.596287
$315$	4.36688	0.246046
$316$	−9.61800	−0.541055
$317$	7.67149	0.430874	0.215437	−	0.976518i	$-0.430882\pi$
$317$	7.67149	0.430874	0.215437	+	0.976518i	$0.430882\pi$
$318$	−7.84635	−0.440002
$319$	−2.95054	−0.165198
$320$	3.46450	0.193671
$321$	−2.57025	−0.143458
$322$	−1.26047	−0.0702431
$323$	1.54508	0.0859703
$324$	1.00000	0.0555556
$325$	−20.2989	−1.12598
$326$	22.6547	1.25473
$327$	−18.5551	−1.02610
$328$	7.03067	0.388204
$329$	−6.28640	−0.346580
$330$	−10.2221	−0.562710
$331$	8.13519	0.447151	0.223575	−	0.974687i	$-0.428227\pi$
$331$	8.13519	0.447151	0.223575	+	0.974687i	$0.428227\pi$
$332$	0.492258	0.0270162
$333$	10.8799	0.596215
$334$	−9.94700	−0.544276
$335$	−30.5151	−1.66722
$336$	−1.26047	−0.0687641
$337$	−29.0056	−1.58004	−0.790018	−	0.613084i	$-0.789929\pi$
$337$	−29.0056	−1.58004	−0.790018	+	0.613084i	$0.789929\pi$
$338$	4.59753	0.250072
$339$	3.26945	0.177572
$340$	−1.78061	−0.0965673
$341$	15.9619	0.864384
$342$	3.00622	0.162558
$343$	−15.6439	−0.844693
$344$	7.06738	0.381048
$345$	−3.46450	−0.186522
$346$	8.41406	0.452343
$347$	4.85006	0.260365	0.130182	−	0.991490i	$-0.458444\pi$
$347$	4.85006	0.260365	0.130182	+	0.991490i	$0.458444\pi$
$348$	−1.00000	−0.0536056
$349$	26.2742	1.40642	0.703212	−	0.710980i	$-0.251748\pi$
$349$	26.2742	1.40642	0.703212	+	0.710980i	$0.251748\pi$
$350$	−8.82673	−0.471808
$351$	2.89870	0.154721
$352$	2.95054	0.157264
$353$	12.6947	0.675670	0.337835	−	0.941205i	$-0.390305\pi$
$353$	12.6947	0.675670	0.337835	+	0.941205i	$0.390305\pi$
$354$	−4.54958	−0.241807
$355$	23.5845	1.25173
$356$	0.689007	0.0365173
$357$	0.647830	0.0342868
$358$	18.7011	0.988385
$359$	7.06962	0.373121	0.186560	−	0.982444i	$-0.440266\pi$
$359$	7.06962	0.373121	0.186560	+	0.982444i	$0.440266\pi$
$360$	−3.46450	−0.182595
$361$	−9.96265	−0.524350
$362$	−14.4459	−0.759258
$363$	2.29433	0.120421
$364$	−3.65372	−0.191507
$365$	9.96961	0.521833
$366$	−7.47147	−0.390540
$367$	−38.1414	−1.99096	−0.995481	−	0.0949576i	$-0.969728\pi$
$367$	−38.1414	−1.99096	−0.995481	+	0.0949576i	$0.969728\pi$
$368$	1.00000	0.0521286
$369$	−7.03067	−0.366002
$370$	−37.6934	−1.95959
$371$	−9.89007	−0.513467
$372$	5.40982	0.280486
$373$	−33.0377	−1.71063	−0.855315	−	0.518109i	$-0.826636\pi$
$373$	−33.0377	−1.71063	−0.855315	+	0.518109i	$0.826636\pi$
$374$	−1.51646	−0.0784142
$375$	−6.93850	−0.358303
$376$	4.98736	0.257203
$377$	−2.89870	−0.149291
$378$	1.26047	0.0648314
$379$	4.28909	0.220316	0.110158	−	0.993914i	$-0.464864\pi$
$379$	4.28909	0.220316	0.110158	+	0.993914i	$0.464864\pi$
$380$	−10.4150	−0.534280
$381$	8.28653	0.424532
$382$	−18.1975	−0.931067
$383$	22.5405	1.15177	0.575884	−	0.817531i	$-0.304658\pi$
$383$	22.5405	1.15177	0.575884	+	0.817531i	$0.304658\pi$
$384$	1.00000	0.0510310
$385$	−12.8847	−0.656663
$386$	3.83991	0.195446
$387$	−7.06738	−0.359255
$388$	−2.39041	−0.121355
$389$	36.1082	1.83076	0.915380	−	0.402590i	$-0.131890\pi$
$389$	36.1082	1.83076	0.915380	+	0.402590i	$0.131890\pi$
$390$	−10.0425	−0.508524
$391$	−0.513960	−0.0259921
$392$	5.41122	0.273308
$393$	−11.3326	−0.571652
$394$	−2.46376	−0.124123
$395$	−33.3215	−1.67659
$396$	−2.95054	−0.148270
$397$	−4.49868	−0.225782	−0.112891	−	0.993607i	$-0.536011\pi$
$397$	−4.49868	−0.225782	−0.112891	+	0.993607i	$0.536011\pi$
$398$	27.5015	1.37853
$399$	3.78924	0.189699
$400$	7.00274	0.350137
$401$	18.7098	0.934321	0.467160	−	0.884173i	$-0.345277\pi$
$401$	18.7098	0.934321	0.467160	+	0.884173i	$0.345277\pi$
$402$	−8.80796	−0.439301
$403$	15.6815	0.781149
$404$	5.52770	0.275013
$405$	3.46450	0.172152
$406$	−1.26047	−0.0625559
$407$	−32.1016	−1.59122
$408$	−0.513960	−0.0254448
$409$	−11.9465	−0.590718	−0.295359	−	0.955386i	$-0.595439\pi$
$409$	−11.9465	−0.590718	−0.295359	+	0.955386i	$0.595439\pi$
$410$	24.3577	1.20294
$411$	−9.35007	−0.461205
$412$	−1.89297	−0.0932601
$413$	−5.73459	−0.282181
$414$	−1.00000	−0.0491473
$415$	1.70543	0.0837161
$416$	2.89870	0.142121
$417$	5.33044	0.261033
$418$	−8.86996	−0.433844
$419$	30.4419	1.48718	0.743591	−	0.668634i	$-0.233121\pi$
$419$	30.4419	1.48718	0.743591	+	0.668634i	$0.233121\pi$
$420$	−4.36688	−0.213082
$421$	35.5601	1.73309	0.866546	−	0.499098i	$-0.166335\pi$
$421$	35.5601	1.73309	0.866546	+	0.499098i	$0.166335\pi$
$422$	2.76261	0.134482
$423$	−4.98736	−0.242494
$424$	7.84635	0.381053
$425$	−3.59913	−0.174584
$426$	6.80747	0.329823
$427$	−9.41754	−0.455747
$428$	2.57025	0.124238
$429$	−8.55273	−0.412930
$430$	24.4849	1.18077
$431$	−16.2501	−0.782742	−0.391371	−	0.920233i	$-0.627999\pi$
$431$	−16.2501	−0.782742	−0.391371	+	0.920233i	$0.627999\pi$
$432$	−1.00000	−0.0481125
$433$	21.5186	1.03412	0.517059	−	0.855950i	$-0.327027\pi$
$433$	21.5186	1.03412	0.517059	+	0.855950i	$0.327027\pi$
$434$	6.81890	0.327318
$435$	−3.46450	−0.166110
$436$	18.5551	0.888628
$437$	−3.00622	−0.143807
$438$	2.87765	0.137499
$439$	7.30169	0.348491	0.174245	−	0.984702i	$-0.444251\pi$
$439$	7.30169	0.348491	0.174245	+	0.984702i	$0.444251\pi$
$440$	10.2221	0.487321
$441$	−5.41122	−0.257677
$442$	−1.48982	−0.0708634
$443$	−16.1535	−0.767476	−0.383738	−	0.923442i	$-0.625363\pi$
$443$	−16.1535	−0.767476	−0.383738	+	0.923442i	$0.625363\pi$
$444$	−10.8799	−0.516337
$445$	2.38706	0.113158
$446$	−21.6933	−1.02721
$447$	3.37859	0.159802
$448$	1.26047	0.0595515
$449$	2.04485	0.0965025	0.0482512	−	0.998835i	$-0.484635\pi$
$449$	2.04485	0.0965025	0.0482512	+	0.998835i	$0.484635\pi$
$450$	−7.00274	−0.330113
$451$	20.7442	0.976808
$452$	−3.26945	−0.153782
$453$	−11.4581	−0.538348
$454$	−26.6966	−1.25293
$455$	−12.6583	−0.593430
$456$	−3.00622	−0.140779
$457$	−26.9698	−1.26160	−0.630798	−	0.775947i	$-0.717272\pi$
$457$	−26.9698	−1.26160	−0.630798	+	0.775947i	$0.717272\pi$
$458$	4.48624	0.209628
$459$	0.513960	0.0239896
$460$	3.46450	0.161533
$461$	1.44799	0.0674395	0.0337197	−	0.999431i	$-0.489265\pi$
$461$	1.44799	0.0674395	0.0337197	+	0.999431i	$0.489265\pi$
$462$	−3.71905	−0.173026
$463$	−27.3529	−1.27120	−0.635598	−	0.772020i	$-0.719246\pi$
$463$	−27.3529	−1.27120	−0.635598	+	0.772020i	$0.719246\pi$
$464$	1.00000	0.0464238
$465$	18.7423	0.869154
$466$	30.0147	1.39040
$467$	5.17174	0.239320	0.119660	−	0.992815i	$-0.461820\pi$
$467$	5.17174	0.239320	0.119660	+	0.992815i	$0.461820\pi$
$468$	−2.89870	−0.133993
$469$	−11.1021	−0.512649
$470$	17.2787	0.797007
$471$	10.5662	0.486866
$472$	4.54958	0.209411
$473$	20.8526	0.958802
$474$	−9.61800	−0.441769
$475$	−21.0518	−0.965922
$476$	−0.647830	−0.0296932
$477$	−7.84635	−0.359260
$478$	−5.58901	−0.255635
$479$	13.5202	0.617754	0.308877	−	0.951102i	$-0.400047\pi$
$479$	13.5202	0.617754	0.308877	+	0.951102i	$0.400047\pi$
$480$	3.46450	0.158132
$481$	−31.5376	−1.43799
$482$	−21.2451	−0.967688
$483$	−1.26047	−0.0573532
$484$	−2.29433	−0.104288
$485$	−8.28156	−0.376046
$486$	1.00000	0.0453609
$487$	−6.08871	−0.275906	−0.137953	−	0.990439i	$-0.544052\pi$
$487$	−6.08871	−0.275906	−0.137953	+	0.990439i	$0.544052\pi$
$488$	7.47147	0.338218
$489$	22.6547	1.02448
$490$	18.7472	0.846911
$491$	−43.4519	−1.96096	−0.980479	−	0.196622i	$-0.937003\pi$
$491$	−43.4519	−1.96096	−0.980479	+	0.196622i	$0.937003\pi$
$492$	7.03067	0.316967
$493$	−0.513960	−0.0231476
$494$	−8.71413	−0.392067
$495$	−10.2221	−0.459451
$496$	−5.40982	−0.242908
$497$	8.58059	0.384892
$498$	0.492258	0.0220586
$499$	−13.3105	−0.595859	−0.297929	−	0.954588i	$-0.596296\pi$
$499$	−13.3105	−0.595859	−0.297929	+	0.954588i	$0.596296\pi$
$500$	6.93850	0.310299
$501$	−9.94700	−0.444399
$502$	2.14014	0.0955191
$503$	−35.6652	−1.59023	−0.795117	−	0.606456i	$-0.792590\pi$
$503$	−35.6652	−1.59023	−0.795117	+	0.606456i	$0.792590\pi$
$504$	−1.26047	−0.0561457
$505$	19.1507	0.852194
$506$	2.95054	0.131167
$507$	4.59753	0.204183
$508$	−8.28653	−0.367655
$509$	−6.42583	−0.284820	−0.142410	−	0.989808i	$-0.545485\pi$
$509$	−6.42583	−0.284820	−0.142410	+	0.989808i	$0.545485\pi$
$510$	−1.78061	−0.0788469
$511$	3.62718	0.160457
$512$	−1.00000	−0.0441942
$513$	3.00622	0.132728
$514$	−31.3621	−1.38332
$515$	−6.55820	−0.288989
$516$	7.06738	0.311124
$517$	14.7154	0.647182
$518$	−13.7138	−0.602548
$519$	8.41406	0.369336
$520$	10.0425	0.440395
$521$	8.10399	0.355042	0.177521	−	0.984117i	$-0.443192\pi$
$521$	8.10399	0.355042	0.177521	+	0.984117i	$0.443192\pi$
$522$	−1.00000	−0.0437688
$523$	−30.8590	−1.34937	−0.674684	−	0.738106i	$-0.735720\pi$
$523$	−30.8590	−1.34937	−0.674684	+	0.738106i	$0.735720\pi$
$524$	11.3326	0.495065
$525$	−8.82673	−0.385230
$526$	14.8260	0.646445
$527$	2.78043	0.121117
$528$	2.95054	0.128406
$529$	1.00000	0.0434783
$530$	27.1837	1.18078
$531$	−4.54958	−0.197435
$532$	−3.78924	−0.164284
$533$	20.3798	0.882747
$534$	0.689007	0.0298163
$535$	8.90464	0.384981
$536$	8.80796	0.380446
$537$	18.7011	0.807013
$538$	−25.6253	−1.10478
$539$	15.9660	0.687705
$540$	−3.46450	−0.149088
$541$	−3.31760	−0.142635	−0.0713175	−	0.997454i	$-0.522720\pi$
$541$	−3.31760	−0.142635	−0.0713175	+	0.997454i	$0.522720\pi$
$542$	13.5115	0.580368
$543$	−14.4459	−0.619932
$544$	0.513960	0.0220359
$545$	64.2841	2.75363
$546$	−3.65372	−0.156365
$547$	−9.46622	−0.404746	−0.202373	−	0.979308i	$-0.564865\pi$
$547$	−9.46622	−0.404746	−0.202373	+	0.979308i	$0.564865\pi$
$548$	9.35007	0.399415
$549$	−7.47147	−0.318875
$550$	20.6619	0.881025
$551$	−3.00622	−0.128069
$552$	1.00000	0.0425628
$553$	−12.1232	−0.515530
$554$	−18.8475	−0.800754
$555$	−37.6934	−1.60000
$556$	−5.33044	−0.226061
$557$	19.6472	0.832477	0.416238	−	0.909256i	$-0.363348\pi$
$557$	19.6472	0.832477	0.416238	+	0.909256i	$0.363348\pi$
$558$	5.40982	0.229016
$559$	20.4862	0.866475
$560$	4.36688	0.184535
$561$	−1.51646	−0.0640249
$562$	22.0826	0.931499
$563$	22.8751	0.964069	0.482034	−	0.876152i	$-0.339898\pi$
$563$	22.8751	0.964069	0.482034	+	0.876152i	$0.339898\pi$
$564$	4.98736	0.210006
$565$	−11.3270	−0.476531
$566$	−4.52701	−0.190284
$567$	1.26047	0.0529346
$568$	−6.80747	−0.285635
$569$	−21.5814	−0.904741	−0.452371	−	0.891830i	$-0.649422\pi$
$569$	−21.5814	−0.904741	−0.452371	+	0.891830i	$0.649422\pi$
$570$	−10.4150	−0.436238
$571$	−28.2634	−1.18279	−0.591394	−	0.806383i	$-0.701422\pi$
$571$	−28.2634	−1.18279	−0.591394	+	0.806383i	$0.701422\pi$
$572$	8.55273	0.357608
$573$	−18.1975	−0.760213
$574$	8.86192	0.369889
$575$	7.00274	0.292035
$576$	1.00000	0.0416667
$577$	−31.5236	−1.31234	−0.656172	−	0.754611i	$-0.727825\pi$
$577$	−31.5236	−1.31234	−0.656172	+	0.754611i	$0.727825\pi$
$578$	16.7358	0.696119
$579$	3.83991	0.159581
$580$	3.46450	0.143855
$581$	0.620475	0.0257416
$582$	−2.39041	−0.0990856
$583$	23.1510	0.958815
$584$	−2.87765	−0.119078
$585$	−10.0425	−0.415208
$586$	14.9075	0.615824
$587$	−9.43352	−0.389363	−0.194681	−	0.980867i	$-0.562367\pi$
$587$	−9.43352	−0.389363	−0.194681	+	0.980867i	$0.562367\pi$
$588$	5.41122	0.223155
$589$	16.2631	0.670109
$590$	15.7620	0.648911
$591$	−2.46376	−0.101346
$592$	10.8799	0.447161
$593$	−6.36764	−0.261488	−0.130744	−	0.991416i	$-0.541737\pi$
$593$	−6.36764	−0.261488	−0.130744	+	0.991416i	$0.541737\pi$
$594$	−2.95054	−0.121062
$595$	−2.24440	−0.0920116
$596$	−3.37859	−0.138392
$597$	27.5015	1.12556
$598$	2.89870	0.118537
$599$	−12.4811	−0.509964	−0.254982	−	0.966946i	$-0.582070\pi$
$599$	−12.4811	−0.509964	−0.254982	+	0.966946i	$0.582070\pi$
$600$	7.00274	0.285886
$601$	19.9100	0.812147	0.406074	−	0.913840i	$-0.366898\pi$
$601$	19.9100	0.812147	0.406074	+	0.913840i	$0.366898\pi$
$602$	8.90820	0.363071
$603$	−8.80796	−0.358688
$604$	11.4581	0.466223
$605$	−7.94869	−0.323160
$606$	5.52770	0.224547
$607$	−5.64098	−0.228960	−0.114480	−	0.993426i	$-0.536520\pi$
$607$	−5.64098	−0.228960	−0.114480	+	0.993426i	$0.536520\pi$
$608$	3.00622	0.121918
$609$	−1.26047	−0.0510767
$610$	25.8849	1.04805
$611$	14.4569	0.584862
$612$	−0.513960	−0.0207756
$613$	6.27248	0.253343	0.126671	−	0.991945i	$-0.459571\pi$
$613$	6.27248	0.253343	0.126671	+	0.991945i	$0.459571\pi$
$614$	11.7337	0.473534
$615$	24.3577	0.982198
$616$	3.71905	0.149845
$617$	7.90980	0.318436	0.159218	−	0.987243i	$-0.449103\pi$
$617$	7.90980	0.318436	0.159218	+	0.987243i	$0.449103\pi$
$618$	−1.89297	−0.0761465
$619$	−11.2820	−0.453460	−0.226730	−	0.973958i	$-0.572804\pi$
$619$	−11.2820	−0.453460	−0.226730	+	0.973958i	$0.572804\pi$
$620$	−18.7423	−0.752709
$621$	−1.00000	−0.0401286
$622$	12.9143	0.517818
$623$	0.868471	0.0347945
$624$	2.89870	0.116041
$625$	−10.9753	−0.439012
$626$	31.6900	1.26659
$627$	−8.86996	−0.354232
$628$	−10.5662	−0.421638
$629$	−5.59184	−0.222961
$630$	−4.36688	−0.173981
$631$	28.2132	1.12315	0.561574	−	0.827426i	$-0.310196\pi$
$631$	28.2132	1.12315	0.561574	+	0.827426i	$0.310196\pi$
$632$	9.61800	0.382584
$633$	2.76261	0.109804
$634$	−7.67149	−0.304674
$635$	−28.7087	−1.13927
$636$	7.84635	0.311128
$637$	15.6855	0.621483
$638$	2.95054	0.116813
$639$	6.80747	0.269299
$640$	−3.46450	−0.136946
$641$	49.8933	1.97067	0.985333	−	0.170642i	$-0.0545843\pi$
$641$	49.8933	1.97067	0.985333	+	0.170642i	$0.0545843\pi$
$642$	2.57025	0.101440
$643$	−2.02052	−0.0796814	−0.0398407	−	0.999206i	$-0.512685\pi$
$643$	−2.02052	−0.0796814	−0.0398407	+	0.999206i	$0.512685\pi$
$644$	1.26047	0.0496694
$645$	24.4849	0.964093
$646$	−1.54508	−0.0607902
$647$	0.309658	0.0121739	0.00608696	−	0.999981i	$-0.498062\pi$
$647$	0.309658	0.0121739	0.00608696	+	0.999981i	$0.498062\pi$
$648$	−1.00000	−0.0392837
$649$	13.4237	0.526926
$650$	20.2989	0.796187
$651$	6.81890	0.267254
$652$	−22.6547	−0.887225
$653$	28.5490	1.11721	0.558604	−	0.829434i	$-0.311337\pi$
$653$	28.5490	1.11721	0.558604	+	0.829434i	$0.311337\pi$
$654$	18.5551	0.725562
$655$	39.2616	1.53408
$656$	−7.03067	−0.274501
$657$	2.87765	0.112268
$658$	6.28640	0.245069
$659$	−21.4565	−0.835828	−0.417914	−	0.908487i	$-0.637239\pi$
$659$	−21.4565	−0.835828	−0.417914	+	0.908487i	$0.637239\pi$
$660$	10.2221	0.397896
$661$	−13.7477	−0.534723	−0.267362	−	0.963596i	$-0.586152\pi$
$661$	−13.7477	−0.534723	−0.267362	+	0.963596i	$0.586152\pi$
$662$	−8.13519	−0.316183
$663$	−1.48982	−0.0578597
$664$	−0.492258	−0.0191033
$665$	−13.1278	−0.509074
$666$	−10.8799	−0.421588
$667$	1.00000	0.0387202
$668$	9.94700	0.384861
$669$	−21.6933	−0.838711
$670$	30.5151	1.17890
$671$	22.0449	0.851032
$672$	1.26047	0.0486236
$673$	−5.90609	−0.227663	−0.113831	−	0.993500i	$-0.536312\pi$
$673$	−5.90609	−0.227663	−0.113831	+	0.993500i	$0.536312\pi$
$674$	29.0056	1.11725
$675$	−7.00274	−0.269536
$676$	−4.59753	−0.176828
$677$	−7.44020	−0.285950	−0.142975	−	0.989726i	$-0.545667\pi$
$677$	−7.44020	−0.285950	−0.142975	+	0.989726i	$0.545667\pi$
$678$	−3.26945	−0.125563
$679$	−3.01303	−0.115629
$680$	1.78061	0.0682834
$681$	−26.6966	−1.02301
$682$	−15.9619	−0.611212
$683$	9.21980	0.352786	0.176393	−	0.984320i	$-0.443557\pi$
$683$	9.21980	0.352786	0.176393	+	0.984320i	$0.443557\pi$
$684$	−3.00622	−0.114946
$685$	32.3933	1.23768
$686$	15.6439	0.597288
$687$	4.48624	0.171161
$688$	−7.06738	−0.269441
$689$	22.7442	0.866487
$690$	3.46450	0.131891
$691$	28.3126	1.07706	0.538531	−	0.842606i	$-0.318979\pi$
$691$	28.3126	1.07706	0.538531	+	0.842606i	$0.318979\pi$
$692$	−8.41406	−0.319854
$693$	−3.71905	−0.141275
$694$	−4.85006	−0.184106
$695$	−18.4673	−0.700504
$696$	1.00000	0.0379049
$697$	3.61348	0.136870
$698$	−26.2742	−0.994492
$699$	30.0147	1.13526
$700$	8.82673	0.333619
$701$	−27.6327	−1.04367	−0.521836	−	0.853046i	$-0.674753\pi$
$701$	−27.6327	−1.04367	−0.521836	+	0.853046i	$0.674753\pi$
$702$	−2.89870	−0.109404
$703$	−32.7074	−1.23358
$704$	−2.95054	−0.111203
$705$	17.2787	0.650753
$706$	−12.6947	−0.477771
$707$	6.96748	0.262039
$708$	4.54958	0.170984
$709$	35.8916	1.34794	0.673968	−	0.738760i	$-0.264588\pi$
$709$	35.8916	1.34794	0.673968	+	0.738760i	$0.264588\pi$
$710$	−23.5845	−0.885109
$711$	−9.61800	−0.360703
$712$	−0.689007	−0.0258216
$713$	−5.40982	−0.202599
$714$	−0.647830	−0.0242444
$715$	29.6309	1.10813
$716$	−18.7011	−0.698894
$717$	−5.58901	−0.208725
$718$	−7.06962	−0.263836
$719$	45.7915	1.70774	0.853868	−	0.520490i	$-0.174251\pi$
$719$	45.7915	1.70774	0.853868	+	0.520490i	$0.174251\pi$
$720$	3.46450	0.129114
$721$	−2.38603	−0.0888604
$722$	9.96265	0.370772
$723$	−21.2451	−0.790114
$724$	14.4459	0.536877
$725$	7.00274	0.260075
$726$	−2.29433	−0.0851505
$727$	19.0240	0.705562	0.352781	−	0.935706i	$-0.385236\pi$
$727$	19.0240	0.705562	0.352781	+	0.935706i	$0.385236\pi$
$728$	3.65372	0.135416
$729$	1.00000	0.0370370
$730$	−9.96961	−0.368992
$731$	3.63235	0.134347
$732$	7.47147	0.276154
$733$	−18.9003	−0.698100	−0.349050	−	0.937104i	$-0.613496\pi$
$733$	−18.9003	−0.698100	−0.349050	+	0.937104i	$0.613496\pi$
$734$	38.1414	1.40782
$735$	18.7472	0.691500
$736$	−1.00000	−0.0368605
$737$	25.9882	0.957288
$738$	7.03067	0.258802
$739$	−4.30945	−0.158526	−0.0792628	−	0.996854i	$-0.525257\pi$
$739$	−4.30945	−0.158526	−0.0792628	+	0.996854i	$0.525257\pi$
$740$	37.6934	1.38564
$741$	−8.71413	−0.320122
$742$	9.89007	0.363076
$743$	−23.7569	−0.871555	−0.435777	−	0.900055i	$-0.643526\pi$
$743$	−23.7569	−0.871555	−0.435777	+	0.900055i	$0.643526\pi$
$744$	−5.40982	−0.198334
$745$	−11.7051	−0.428842
$746$	33.0377	1.20960
$747$	0.492258	0.0180108
$748$	1.51646	0.0554472
$749$	3.23972	0.118377
$750$	6.93850	0.253358
$751$	21.6384	0.789597	0.394799	−	0.918768i	$-0.370814\pi$
$751$	21.6384	0.789597	0.394799	+	0.918768i	$0.370814\pi$
$752$	−4.98736	−0.181870
$753$	2.14014	0.0779910
$754$	2.89870	0.105565
$755$	39.6965	1.44471
$756$	−1.26047	−0.0458427
$757$	−35.9444	−1.30642	−0.653210	−	0.757176i	$-0.726578\pi$
$757$	−35.9444	−1.30642	−0.653210	+	0.757176i	$0.726578\pi$
$758$	−4.28909	−0.155787
$759$	2.95054	0.107098
$760$	10.4150	0.377793
$761$	1.00077	0.0362778	0.0181389	−	0.999835i	$-0.494226\pi$
$761$	1.00077	0.0362778	0.0181389	+	0.999835i	$0.494226\pi$
$762$	−8.28653	−0.300189
$763$	23.3881	0.846706
$764$	18.1975	0.658364
$765$	−1.78061	−0.0643782
$766$	−22.5405	−0.814423
$767$	13.1879	0.476186
$768$	−1.00000	−0.0360844
$769$	−16.7679	−0.604664	−0.302332	−	0.953203i	$-0.597765\pi$
$769$	−16.7679	−0.604664	−0.302332	+	0.953203i	$0.597765\pi$
$770$	12.8847	0.464331
$771$	−31.3621	−1.12948
$772$	−3.83991	−0.138201
$773$	18.2576	0.656680	0.328340	−	0.944560i	$-0.393511\pi$
$773$	18.2576	0.656680	0.328340	+	0.944560i	$0.393511\pi$
$774$	7.06738	0.254032
$775$	−37.8836	−1.36082
$776$	2.39041	0.0858106
$777$	−13.7138	−0.491978
$778$	−36.1082	−1.29454
$779$	21.1357	0.757265
$780$	10.0425	0.359581
$781$	−20.0857	−0.718722
$782$	0.513960	0.0183792
$783$	−1.00000	−0.0357371
$784$	−5.41122	−0.193258
$785$	−36.6067	−1.30655
$786$	11.3326	0.404219
$787$	17.1358	0.610824	0.305412	−	0.952220i	$-0.401206\pi$
$787$	17.1358	0.610824	0.305412	+	0.952220i	$0.401206\pi$
$788$	2.46376	0.0877679
$789$	14.8260	0.527820
$790$	33.3215	1.18553
$791$	−4.12104	−0.146527
$792$	2.95054	0.104843
$793$	21.6576	0.769083
$794$	4.49868	0.159652
$795$	27.1837	0.964106
$796$	−27.5015	−0.974765
$797$	27.1842	0.962912	0.481456	−	0.876470i	$-0.340108\pi$
$797$	27.1842	0.962912	0.481456	+	0.876470i	$0.340108\pi$
$798$	−3.78924	−0.134138
$799$	2.56330	0.0906832
$800$	−7.00274	−0.247584
$801$	0.689007	0.0243449
$802$	−18.7098	−0.660665
$803$	−8.49061	−0.299627
$804$	8.80796	0.310633
$805$	4.36688	0.153912
$806$	−15.6815	−0.552356
$807$	−25.6253	−0.902052
$808$	−5.52770	−0.194464
$809$	8.38840	0.294920	0.147460	−	0.989068i	$-0.452890\pi$
$809$	8.38840	0.294920	0.147460	+	0.989068i	$0.452890\pi$
$810$	−3.46450	−0.121730
$811$	−2.72534	−0.0956995	−0.0478498	−	0.998855i	$-0.515237\pi$
$811$	−2.72534	−0.0956995	−0.0478498	+	0.998855i	$0.515237\pi$
$812$	1.26047	0.0442337
$813$	13.5115	0.473869
$814$	32.1016	1.12516
$815$	−78.4871	−2.74928
$816$	0.513960	0.0179922
$817$	21.2461	0.743307
$818$	11.9465	0.417700
$819$	−3.65372	−0.127671
$820$	−24.3577	−0.850609
$821$	−14.2582	−0.497613	−0.248806	−	0.968553i	$-0.580038\pi$
$821$	−14.2582	−0.497613	−0.248806	+	0.968553i	$0.580038\pi$
$822$	9.35007	0.326121
$823$	22.7111	0.791660	0.395830	−	0.918324i	$-0.370457\pi$
$823$	22.7111	0.791660	0.395830	+	0.918324i	$0.370457\pi$
$824$	1.89297	0.0659448
$825$	20.6619	0.719354
$826$	5.73459	0.199532
$827$	−49.9690	−1.73759	−0.868796	−	0.495171i	$-0.835105\pi$
$827$	−49.9690	−1.73759	−0.868796	+	0.495171i	$0.835105\pi$
$828$	1.00000	0.0347524
$829$	11.4162	0.396500	0.198250	−	0.980152i	$-0.436474\pi$
$829$	11.4162	0.396500	0.198250	+	0.980152i	$0.436474\pi$
$830$	−1.70543	−0.0591962
$831$	−18.8475	−0.653813
$832$	−2.89870	−0.100494
$833$	2.78115	0.0963613
$834$	−5.33044	−0.184578
$835$	34.4614	1.19258
$836$	8.86996	0.306774
$837$	5.40982	0.186991
$838$	−30.4419	−1.05160
$839$	24.5479	0.847487	0.423744	−	0.905782i	$-0.360716\pi$
$839$	24.5479	0.847487	0.423744	+	0.905782i	$0.360716\pi$
$840$	4.36688	0.150672
$841$	1.00000	0.0344828
$842$	−35.5601	−1.22548
$843$	22.0826	0.760566
$844$	−2.76261	−0.0950929
$845$	−15.9281	−0.547944
$846$	4.98736	0.171469
$847$	−2.89192	−0.0993677
$848$	−7.84635	−0.269445
$849$	−4.52701	−0.155367
$850$	3.59913	0.123449
$851$	10.8799	0.372958
$852$	−6.80747	−0.233220
$853$	24.9890	0.855607	0.427803	−	0.903872i	$-0.359288\pi$
$853$	24.9890	0.855607	0.427803	+	0.903872i	$0.359288\pi$
$854$	9.41754	0.322262
$855$	−10.4150	−0.356187
$856$	−2.57025	−0.0878495
$857$	13.4262	0.458629	0.229314	−	0.973352i	$-0.426352\pi$
$857$	13.4262	0.458629	0.229314	+	0.973352i	$0.426352\pi$
$858$	8.55273	0.291985
$859$	−46.2045	−1.57648	−0.788238	−	0.615370i	$-0.789006\pi$
$859$	−46.2045	−1.57648	−0.788238	+	0.615370i	$0.789006\pi$
$860$	−24.4849	−0.834929
$861$	8.86192	0.302013
$862$	16.2501	0.553482
$863$	−46.7517	−1.59144	−0.795722	−	0.605661i	$-0.792909\pi$
$863$	−46.7517	−1.59144	−0.795722	+	0.605661i	$0.792909\pi$
$864$	1.00000	0.0340207
$865$	−29.1505	−0.991146
$866$	−21.5186	−0.731232
$867$	16.7358	0.568379
$868$	−6.81890	−0.231448
$869$	28.3783	0.962667
$870$	3.46450	0.117457
$871$	25.5316	0.865107
$872$	−18.5551	−0.628355
$873$	−2.39041	−0.0809030
$874$	3.00622	0.101687
$875$	8.74575	0.295660
$876$	−2.87765	−0.0972267
$877$	−7.76520	−0.262212	−0.131106	−	0.991368i	$-0.541853\pi$
$877$	−7.76520	−0.262212	−0.131106	+	0.991368i	$0.541853\pi$
$878$	−7.30169	−0.246420
$879$	14.9075	0.502818
$880$	−10.2221	−0.344588
$881$	30.8212	1.03839	0.519195	−	0.854656i	$-0.326232\pi$
$881$	30.8212	1.03839	0.519195	+	0.854656i	$0.326232\pi$
$882$	5.41122	0.182205
$883$	5.27954	0.177671	0.0888353	−	0.996046i	$-0.471686\pi$
$883$	5.27954	0.177671	0.0888353	+	0.996046i	$0.471686\pi$
$884$	1.48982	0.0501080
$885$	15.7620	0.529834
$886$	16.1535	0.542688
$887$	21.5391	0.723213	0.361607	−	0.932331i	$-0.382228\pi$
$887$	21.5391	0.723213	0.361607	+	0.932331i	$0.382228\pi$
$888$	10.8799	0.365106
$889$	−10.4449	−0.350311
$890$	−2.38706	−0.0800146
$891$	−2.95054	−0.0988467
$892$	21.6933	0.726345
$893$	14.9931	0.501725
$894$	−3.37859	−0.112997
$895$	−64.7900	−2.16569
$896$	−1.26047	−0.0421092
$897$	2.89870	0.0967848
$898$	−2.04485	−0.0682376
$899$	−5.40982	−0.180428
$900$	7.00274	0.233425
$901$	4.03271	0.134349
$902$	−20.7442	−0.690708
$903$	8.90820	0.296446
$904$	3.26945	0.108740
$905$	50.0477	1.66364
$906$	11.4581	0.380670
$907$	17.7000	0.587718	0.293859	−	0.955849i	$-0.405060\pi$
$907$	17.7000	0.587718	0.293859	+	0.955849i	$0.405060\pi$
$908$	26.6966	0.885956
$909$	5.52770	0.183342
$910$	12.6583	0.419618
$911$	50.8581	1.68500	0.842502	−	0.538692i	$-0.181082\pi$
$911$	50.8581	1.68500	0.842502	+	0.538692i	$0.181082\pi$
$912$	3.00622	0.0995458
$913$	−1.45243	−0.0480683
$914$	26.9698	0.892083
$915$	25.8849	0.855728
$916$	−4.48624	−0.148230
$917$	14.2843	0.471710
$918$	−0.513960	−0.0169632
$919$	−36.8992	−1.21719	−0.608596	−	0.793480i	$-0.708267\pi$
$919$	−36.8992	−1.21719	−0.608596	+	0.793480i	$0.708267\pi$
$920$	−3.46450	−0.114221
$921$	11.7337	0.386639
$922$	−1.44799	−0.0476869
$923$	−19.7328	−0.649514
$924$	3.71905	0.122348
$925$	76.1892	2.50509
$926$	27.3529	0.898871
$927$	−1.89297	−0.0621734
$928$	−1.00000	−0.0328266
$929$	8.06811	0.264706	0.132353	−	0.991203i	$-0.457747\pi$
$929$	8.06811	0.264706	0.132353	+	0.991203i	$0.457747\pi$
$930$	−18.7423	−0.614584
$931$	16.2673	0.533140
$932$	−30.0147	−0.983164
$933$	12.9143	0.422796
$934$	−5.17174	−0.169225
$935$	5.25377	0.171817
$936$	2.89870	0.0947470
$937$	−7.86456	−0.256924	−0.128462	−	0.991714i	$-0.541004\pi$
$937$	−7.86456	−0.256924	−0.128462	+	0.991714i	$0.541004\pi$
$938$	11.1021	0.362498
$939$	31.6900	1.03416
$940$	−17.2787	−0.563569
$941$	−34.9867	−1.14053	−0.570266	−	0.821460i	$-0.693160\pi$
$941$	−34.9867	−1.14053	−0.570266	+	0.821460i	$0.693160\pi$
$942$	−10.5662	−0.344266
$943$	−7.03067	−0.228950
$944$	−4.54958	−0.148076
$945$	−4.36688	−0.142055
$946$	−20.8526	−0.677976
$947$	15.6316	0.507958	0.253979	−	0.967210i	$-0.418261\pi$
$947$	15.6316	0.507958	0.253979	+	0.967210i	$0.418261\pi$
$948$	9.61800	0.312378
$949$	−8.34145	−0.270775
$950$	21.0518	0.683010
$951$	−7.67149	−0.248765
$952$	0.647830	0.0209963
$953$	−33.1722	−1.07455	−0.537277	−	0.843406i	$-0.680547\pi$
$953$	−33.1722	−1.07455	−0.537277	+	0.843406i	$0.680547\pi$
$954$	7.84635	0.254035
$955$	63.0453	2.04010
$956$	5.58901	0.180761
$957$	2.95054	0.0953773
$958$	−13.5202	−0.436818
$959$	11.7855	0.380572
$960$	−3.46450	−0.111816
$961$	−1.73386	−0.0559310
$962$	31.5376	1.01681
$963$	2.57025	0.0828253
$964$	21.2451	0.684259
$965$	−13.3034	−0.428250
$966$	1.26047	0.0405549
$967$	0.534347	0.0171834	0.00859172	−	0.999963i	$-0.497265\pi$
$967$	0.534347	0.0171834	0.00859172	+	0.999963i	$0.497265\pi$
$968$	2.29433	0.0737425
$969$	−1.54508	−0.0496350
$970$	8.28156	0.265905
$971$	−48.6158	−1.56015	−0.780077	−	0.625683i	$-0.784820\pi$
$971$	−48.6158	−1.56015	−0.780077	+	0.625683i	$0.784820\pi$
$972$	−1.00000	−0.0320750
$973$	−6.71884	−0.215396
$974$	6.08871	0.195095
$975$	20.2989	0.650084
$976$	−7.47147	−0.239156
$977$	−40.1654	−1.28500	−0.642502	−	0.766284i	$-0.722104\pi$
$977$	−40.1654	−1.28500	−0.642502	+	0.766284i	$0.722104\pi$
$978$	−22.6547	−0.724417
$979$	−2.03294	−0.0649731
$980$	−18.7472	−0.598856
$981$	18.5551	0.592419
$982$	43.4519	1.38661
$983$	45.5704	1.45347	0.726735	−	0.686918i	$-0.241037\pi$
$983$	45.5704	1.45347	0.726735	+	0.686918i	$0.241037\pi$
$984$	−7.03067	−0.224129
$985$	8.53570	0.271970
$986$	0.513960	0.0163678
$987$	6.28640	0.200098
$988$	8.71413	0.277233
$989$	−7.06738	−0.224730
$990$	10.2221	0.324881
$991$	56.6411	1.79926	0.899632	−	0.436649i	$-0.143835\pi$
$991$	56.6411	1.79926	0.899632	+	0.436649i	$0.143835\pi$
$992$	5.40982	0.171762
$993$	−8.13519	−0.258163
$994$	−8.58059	−0.272160
$995$	−95.2789	−3.02054
$996$	−0.492258	−0.0155978
$997$	56.1383	1.77792	0.888959	−	0.457987i	$-0.151429\pi$
$997$	56.1383	1.77792	0.888959	+	0.457987i	$0.151429\pi$
$998$	13.3105	0.421336
$999$	−10.8799	−0.344225

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4002.2.a.bg.1.7	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4002.2.a.bg.1.7	✓	7	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:	\( N \)	\(=\)	\( 4002 = 2 \cdot 3 \cdot 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4002.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.46450 q^{5} +1.00000 q^{6} +1.26047 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.46450 q^{5} +1.00000 q^{6} +1.26047 q^{7} -1.00000 q^{8} +1.00000 q^{9} -3.46450 q^{10} -2.95054 q^{11} -1.00000 q^{12} -2.89870 q^{13} -1.26047 q^{14} -3.46450 q^{15} +1.00000 q^{16} -0.513960 q^{17} -1.00000 q^{18} -3.00622 q^{19} +3.46450 q^{20} -1.26047 q^{21} +2.95054 q^{22} +1.00000 q^{23} +1.00000 q^{24} +7.00274 q^{25} +2.89870 q^{26} -1.00000 q^{27} +1.26047 q^{28} +1.00000 q^{29} +3.46450 q^{30} -5.40982 q^{31} -1.00000 q^{32} +2.95054 q^{33} +0.513960 q^{34} +4.36688 q^{35} +1.00000 q^{36} +10.8799 q^{37} +3.00622 q^{38} +2.89870 q^{39} -3.46450 q^{40} -7.03067 q^{41} +1.26047 q^{42} -7.06738 q^{43} -2.95054 q^{44} +3.46450 q^{45} -1.00000 q^{46} -4.98736 q^{47} -1.00000 q^{48} -5.41122 q^{49} -7.00274 q^{50} +0.513960 q^{51} -2.89870 q^{52} -7.84635 q^{53} +1.00000 q^{54} -10.2221 q^{55} -1.26047 q^{56} +3.00622 q^{57} -1.00000 q^{58} -4.54958 q^{59} -3.46450 q^{60} -7.47147 q^{61} +5.40982 q^{62} +1.26047 q^{63} +1.00000 q^{64} -10.0425 q^{65} -2.95054 q^{66} -8.80796 q^{67} -0.513960 q^{68} -1.00000 q^{69} -4.36688 q^{70} +6.80747 q^{71} -1.00000 q^{72} +2.87765 q^{73} -10.8799 q^{74} -7.00274 q^{75} -3.00622 q^{76} -3.71905 q^{77} -2.89870 q^{78} -9.61800 q^{79} +3.46450 q^{80} +1.00000 q^{81} +7.03067 q^{82} +0.492258 q^{83} -1.26047 q^{84} -1.78061 q^{85} +7.06738 q^{86} -1.00000 q^{87} +2.95054 q^{88} +0.689007 q^{89} -3.46450 q^{90} -3.65372 q^{91} +1.00000 q^{92} +5.40982 q^{93} +4.98736 q^{94} -10.4150 q^{95} +1.00000 q^{96} -2.39041 q^{97} +5.41122 q^{98} -2.95054 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 7 q^{2} - 7 q^{3} + 7 q^{4} + 2 q^{5} + 7 q^{6} - 5 q^{7} - 7 q^{8} + 7 q^{9}+O(q^{10}) \) 7 * q - 7 * q^2 - 7 * q^3 + 7 * q^4 + 2 * q^5 + 7 * q^6 - 5 * q^7 - 7 * q^8 + 7 * q^9	\( 7 q - 7 q^{2} - 7 q^{3} + 7 q^{4} + 2 q^{5} + 7 q^{6} - 5 q^{7} - 7 q^{8} + 7 q^{9} - 2 q^{10} - q^{11} - 7 q^{12} + q^{13} + 5 q^{14} - 2 q^{15} + 7 q^{16} - q^{17} - 7 q^{18} - 9 q^{19} + 2 q^{20} + 5 q^{21} + q^{22} + 7 q^{23} + 7 q^{24} + q^{25} - q^{26} - 7 q^{27} - 5 q^{28} + 7 q^{29} + 2 q^{30} - 19 q^{31} - 7 q^{32} + q^{33} + q^{34} + 11 q^{35} + 7 q^{36} - 18 q^{37} + 9 q^{38} - q^{39} - 2 q^{40} + 4 q^{41} - 5 q^{42} - 9 q^{43} - q^{44} + 2 q^{45} - 7 q^{46} - 11 q^{47} - 7 q^{48} + 12 q^{49} - q^{50} + q^{51} + q^{52} + 8 q^{53} + 7 q^{54} - 11 q^{55} + 5 q^{56} + 9 q^{57} - 7 q^{58} + 12 q^{59} - 2 q^{60} - 5 q^{61} + 19 q^{62} - 5 q^{63} + 7 q^{64} + 23 q^{65} - q^{66} - 13 q^{67} - q^{68} - 7 q^{69} - 11 q^{70} - q^{71} - 7 q^{72} - 26 q^{73} + 18 q^{74} - q^{75} - 9 q^{76} + 6 q^{77} + q^{78} - 38 q^{79} + 2 q^{80} + 7 q^{81} - 4 q^{82} - 6 q^{83} + 5 q^{84} - 25 q^{85} + 9 q^{86} - 7 q^{87} + q^{88} + 20 q^{89} - 2 q^{90} + 2 q^{91} + 7 q^{92} + 19 q^{93} + 11 q^{94} - 31 q^{95} + 7 q^{96} - 8 q^{97} - 12 q^{98} - q^{99}+O(q^{100}) \) 7 * q - 7 * q^2 - 7 * q^3 + 7 * q^4 + 2 * q^5 + 7 * q^6 - 5 * q^7 - 7 * q^8 + 7 * q^9 - 2 * q^10 - q^11 - 7 * q^12 + q^13 + 5 * q^14 - 2 * q^15 + 7 * q^16 - q^17 - 7 * q^18 - 9 * q^19 + 2 * q^20 + 5 * q^21 + q^22 + 7 * q^23 + 7 * q^24 + q^25 - q^26 - 7 * q^27 - 5 * q^28 + 7 * q^29 + 2 * q^30 - 19 * q^31 - 7 * q^32 + q^33 + q^34 + 11 * q^35 + 7 * q^36 - 18 * q^37 + 9 * q^38 - q^39 - 2 * q^40 + 4 * q^41 - 5 * q^42 - 9 * q^43 - q^44 + 2 * q^45 - 7 * q^46 - 11 * q^47 - 7 * q^48 + 12 * q^49 - q^50 + q^51 + q^52 + 8 * q^53 + 7 * q^54 - 11 * q^55 + 5 * q^56 + 9 * q^57 - 7 * q^58 + 12 * q^59 - 2 * q^60 - 5 * q^61 + 19 * q^62 - 5 * q^63 + 7 * q^64 + 23 * q^65 - q^66 - 13 * q^67 - q^68 - 7 * q^69 - 11 * q^70 - q^71 - 7 * q^72 - 26 * q^73 + 18 * q^74 - q^75 - 9 * q^76 + 6 * q^77 + q^78 - 38 * q^79 + 2 * q^80 + 7 * q^81 - 4 * q^82 - 6 * q^83 + 5 * q^84 - 25 * q^85 + 9 * q^86 - 7 * q^87 + q^88 + 20 * q^89 - 2 * q^90 + 2 * q^91 + 7 * q^92 + 19 * q^93 + 11 * q^94 - 31 * q^95 + 7 * q^96 - 8 * q^97 - 12 * q^98 - q^99

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