LMFDB - Embedded newform 8007.2.a.e.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8007, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8007 = 3 \cdot 17 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8007.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$63.9362168984$
Analytic rank:	$1$
Dimension:	$46$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	8007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.60999 q^{2} +1.00000 q^{3} +4.81203 q^{4} -2.83562 q^{5} -2.60999 q^{6} +1.53827 q^{7} -7.33937 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.60999 q^{2} +1.00000 q^{3} +4.81203 q^{4} -2.83562 q^{5} -2.60999 q^{6} +1.53827 q^{7} -7.33937 q^{8} +1.00000 q^{9} +7.40094 q^{10} -5.14470 q^{11} +4.81203 q^{12} -5.76308 q^{13} -4.01487 q^{14} -2.83562 q^{15} +9.53161 q^{16} -1.00000 q^{17} -2.60999 q^{18} +7.46231 q^{19} -13.6451 q^{20} +1.53827 q^{21} +13.4276 q^{22} +3.10447 q^{23} -7.33937 q^{24} +3.04076 q^{25} +15.0416 q^{26} +1.00000 q^{27} +7.40221 q^{28} +3.18309 q^{29} +7.40094 q^{30} +2.43358 q^{31} -10.1986 q^{32} -5.14470 q^{33} +2.60999 q^{34} -4.36196 q^{35} +4.81203 q^{36} -8.32995 q^{37} -19.4765 q^{38} -5.76308 q^{39} +20.8117 q^{40} -1.09141 q^{41} -4.01487 q^{42} +3.70310 q^{43} -24.7565 q^{44} -2.83562 q^{45} -8.10264 q^{46} -1.15137 q^{47} +9.53161 q^{48} -4.63372 q^{49} -7.93635 q^{50} -1.00000 q^{51} -27.7322 q^{52} -3.51007 q^{53} -2.60999 q^{54} +14.5884 q^{55} -11.2899 q^{56} +7.46231 q^{57} -8.30782 q^{58} +11.8360 q^{59} -13.6451 q^{60} +0.108053 q^{61} -6.35161 q^{62} +1.53827 q^{63} +7.55507 q^{64} +16.3419 q^{65} +13.4276 q^{66} +12.6485 q^{67} -4.81203 q^{68} +3.10447 q^{69} +11.3847 q^{70} +0.363136 q^{71} -7.33937 q^{72} +8.47199 q^{73} +21.7411 q^{74} +3.04076 q^{75} +35.9089 q^{76} -7.91394 q^{77} +15.0416 q^{78} +2.26541 q^{79} -27.0280 q^{80} +1.00000 q^{81} +2.84858 q^{82} -2.62989 q^{83} +7.40221 q^{84} +2.83562 q^{85} -9.66505 q^{86} +3.18309 q^{87} +37.7589 q^{88} +3.19988 q^{89} +7.40094 q^{90} -8.86518 q^{91} +14.9388 q^{92} +2.43358 q^{93} +3.00506 q^{94} -21.1603 q^{95} -10.1986 q^{96} +9.70271 q^{97} +12.0940 q^{98} -5.14470 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q - 5 q^{2} + 46 q^{3} + 43 q^{4} - 19 q^{5} - 5 q^{6} + q^{7} - 18 q^{8} + 46 q^{9}+O(q^{10}) $ 46 * q - 5 * q^2 + 46 * q^3 + 43 * q^4 - 19 * q^5 - 5 * q^6 + q^7 - 18 * q^8 + 46 * q^9	\( 46 q - 5 q^{2} + 46 q^{3} + 43 q^{4} - 19 q^{5} - 5 q^{6} + q^{7} - 18 q^{8} + 46 q^{9} - 10 q^{10} - 25 q^{11} + 43 q^{12} - 8 q^{13} - 28 q^{14} - 19 q^{15} + 33 q^{16} - 46 q^{17} - 5 q^{18} - 2 q^{19} - 56 q^{20} + q^{21} - 19 q^{22} - 64 q^{23} - 18 q^{24} + 11 q^{25} - 13 q^{26} + 46 q^{27} - 38 q^{28} - 51 q^{29} - 10 q^{30} - 19 q^{31} - 61 q^{32} - 25 q^{33} + 5 q^{34} - 39 q^{35} + 43 q^{36} - 46 q^{37} - 48 q^{38} - 8 q^{39} - 10 q^{40} - 53 q^{41} - 28 q^{42} - 33 q^{43} - 62 q^{44} - 19 q^{45} + 2 q^{46} - 45 q^{47} + 33 q^{48} + 21 q^{49} - 60 q^{50} - 46 q^{51} - 63 q^{52} - 47 q^{53} - 5 q^{54} + 5 q^{55} - 82 q^{56} - 2 q^{57} - 21 q^{58} - 65 q^{59} - 56 q^{60} - 37 q^{61} - 46 q^{62} + q^{63} + 74 q^{64} - 85 q^{65} - 19 q^{66} - 52 q^{67} - 43 q^{68} - 64 q^{69} - 20 q^{70} - 48 q^{71} - 18 q^{72} - 39 q^{73} - 16 q^{74} + 11 q^{75} + 42 q^{76} - 78 q^{77} - 13 q^{78} - 26 q^{79} - 78 q^{80} + 46 q^{81} + 3 q^{82} - 47 q^{83} - 38 q^{84} + 19 q^{85} - 6 q^{86} - 51 q^{87} - 58 q^{88} - 58 q^{89} - 10 q^{90} - 43 q^{91} - 68 q^{92} - 19 q^{93} - 78 q^{95} - 61 q^{96} - 44 q^{97} - 4 q^{98} - 25 q^{99}+O(q^{100}) \) 46 * q - 5 * q^2 + 46 * q^3 + 43 * q^4 - 19 * q^5 - 5 * q^6 + q^7 - 18 * q^8 + 46 * q^9 - 10 * q^10 - 25 * q^11 + 43 * q^12 - 8 * q^13 - 28 * q^14 - 19 * q^15 + 33 * q^16 - 46 * q^17 - 5 * q^18 - 2 * q^19 - 56 * q^20 + q^21 - 19 * q^22 - 64 * q^23 - 18 * q^24 + 11 * q^25 - 13 * q^26 + 46 * q^27 - 38 * q^28 - 51 * q^29 - 10 * q^30 - 19 * q^31 - 61 * q^32 - 25 * q^33 + 5 * q^34 - 39 * q^35 + 43 * q^36 - 46 * q^37 - 48 * q^38 - 8 * q^39 - 10 * q^40 - 53 * q^41 - 28 * q^42 - 33 * q^43 - 62 * q^44 - 19 * q^45 + 2 * q^46 - 45 * q^47 + 33 * q^48 + 21 * q^49 - 60 * q^50 - 46 * q^51 - 63 * q^52 - 47 * q^53 - 5 * q^54 + 5 * q^55 - 82 * q^56 - 2 * q^57 - 21 * q^58 - 65 * q^59 - 56 * q^60 - 37 * q^61 - 46 * q^62 + q^63 + 74 * q^64 - 85 * q^65 - 19 * q^66 - 52 * q^67 - 43 * q^68 - 64 * q^69 - 20 * q^70 - 48 * q^71 - 18 * q^72 - 39 * q^73 - 16 * q^74 + 11 * q^75 + 42 * q^76 - 78 * q^77 - 13 * q^78 - 26 * q^79 - 78 * q^80 + 46 * q^81 + 3 * q^82 - 47 * q^83 - 38 * q^84 + 19 * q^85 - 6 * q^86 - 51 * q^87 - 58 * q^88 - 58 * q^89 - 10 * q^90 - 43 * q^91 - 68 * q^92 - 19 * q^93 - 78 * q^95 - 61 * q^96 - 44 * q^97 - 4 * q^98 - 25 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.60999	−1.84554	−0.922770	−	0.385351i	$-0.874080\pi$
$2$	−2.60999	−1.84554	−0.922770	+	0.385351i	$0.874080\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.81203	2.40602
$5$	−2.83562	−1.26813	−0.634065	−	0.773280i	$-0.718615\pi$
$5$	−2.83562	−1.26813	−0.634065	+	0.773280i	$0.718615\pi$
$6$	−2.60999	−1.06552
$7$	1.53827	0.581412	0.290706	−	0.956812i	$-0.406110\pi$
$7$	1.53827	0.581412	0.290706	+	0.956812i	$0.406110\pi$
$8$	−7.33937	−2.59486
$9$	1.00000	0.333333
$10$	7.40094	2.34038
$11$	−5.14470	−1.55118	−0.775592	−	0.631234i	$-0.782549\pi$
$11$	−5.14470	−1.55118	−0.775592	+	0.631234i	$0.782549\pi$
$12$	4.81203	1.38911
$13$	−5.76308	−1.59839	−0.799196	−	0.601070i	$-0.794741\pi$
$13$	−5.76308	−1.59839	−0.799196	+	0.601070i	$0.794741\pi$
$14$	−4.01487	−1.07302
$15$	−2.83562	−0.732155
$16$	9.53161	2.38290
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−2.60999	−0.615180
$19$	7.46231	1.71197	0.855986	−	0.516999i	$-0.172951\pi$
$19$	7.46231	1.71197	0.855986	+	0.516999i	$0.172951\pi$
$20$	−13.6451	−3.05114
$21$	1.53827	0.335678
$22$	13.4276	2.86277
$23$	3.10447	0.647327	0.323664	−	0.946172i	$-0.395085\pi$
$23$	3.10447	0.647327	0.323664	+	0.946172i	$0.395085\pi$
$24$	−7.33937	−1.49814
$25$	3.04076	0.608152
$26$	15.0416	2.94990
$27$	1.00000	0.192450
$28$	7.40221	1.39889
$29$	3.18309	0.591085	0.295542	−	0.955330i	$-0.404500\pi$
$29$	3.18309	0.591085	0.295542	+	0.955330i	$0.404500\pi$
$30$	7.40094	1.35122
$31$	2.43358	0.437084	0.218542	−	0.975828i	$-0.429870\pi$
$31$	2.43358	0.437084	0.218542	+	0.975828i	$0.429870\pi$
$32$	−10.1986	−1.80288
$33$	−5.14470	−0.895577
$34$	2.60999	0.447609
$35$	−4.36196	−0.737305
$36$	4.81203	0.802006
$37$	−8.32995	−1.36944	−0.684718	−	0.728809i	$-0.740074\pi$
$37$	−8.32995	−1.36944	−0.684718	+	0.728809i	$0.740074\pi$
$38$	−19.4765	−3.15951
$39$	−5.76308	−0.922832
$40$	20.8117	3.29062
$41$	−1.09141	−0.170450	−0.0852251	−	0.996362i	$-0.527161\pi$
$41$	−1.09141	−0.170450	−0.0852251	+	0.996362i	$0.527161\pi$
$42$	−4.01487	−0.619507
$43$	3.70310	0.564718	0.282359	−	0.959309i	$-0.408883\pi$
$43$	3.70310	0.564718	0.282359	+	0.959309i	$0.408883\pi$
$44$	−24.7565	−3.73218
$45$	−2.83562	−0.422710
$46$	−8.10264	−1.19467
$47$	−1.15137	−0.167944	−0.0839722	−	0.996468i	$-0.526761\pi$
$47$	−1.15137	−0.167944	−0.0839722	+	0.996468i	$0.526761\pi$
$48$	9.53161	1.37577
$49$	−4.63372	−0.661960
$50$	−7.93635	−1.12237
$51$	−1.00000	−0.140028
$52$	−27.7322	−3.84576
$53$	−3.51007	−0.482145	−0.241073	−	0.970507i	$-0.577499\pi$
$53$	−3.51007	−0.482145	−0.241073	+	0.970507i	$0.577499\pi$
$54$	−2.60999	−0.355174
$55$	14.5884	1.96710
$56$	−11.2899	−1.50868
$57$	7.46231	0.988407
$58$	−8.30782	−1.09087
$59$	11.8360	1.54092	0.770458	−	0.637491i	$-0.220028\pi$
$59$	11.8360	1.54092	0.770458	+	0.637491i	$0.220028\pi$
$60$	−13.6451	−1.76158
$61$	0.108053	0.0138348	0.00691741	−	0.999976i	$-0.497798\pi$
$61$	0.108053	0.0138348	0.00691741	+	0.999976i	$0.497798\pi$
$62$	−6.35161	−0.806656
$63$	1.53827	0.193804
$64$	7.55507	0.944384
$65$	16.3419	2.02697
$66$	13.4276	1.65282
$67$	12.6485	1.54526	0.772632	−	0.634854i	$-0.218940\pi$
$67$	12.6485	1.54526	0.772632	+	0.634854i	$0.218940\pi$
$68$	−4.81203	−0.583545
$69$	3.10447	0.373735
$70$	11.3847	1.36073
$71$	0.363136	0.0430963	0.0215482	−	0.999768i	$-0.493140\pi$
$71$	0.363136	0.0430963	0.0215482	+	0.999768i	$0.493140\pi$
$72$	−7.33937	−0.864954
$73$	8.47199	0.991571	0.495786	−	0.868445i	$-0.334880\pi$
$73$	8.47199	0.991571	0.495786	+	0.868445i	$0.334880\pi$
$74$	21.7411	2.52735
$75$	3.04076	0.351117
$76$	35.9089	4.11903
$77$	−7.91394	−0.901877
$78$	15.0416	1.70312
$79$	2.26541	0.254879	0.127439	−	0.991846i	$-0.459324\pi$
$79$	2.26541	0.254879	0.127439	+	0.991846i	$0.459324\pi$
$80$	−27.0280	−3.02183
$81$	1.00000	0.111111
$82$	2.84858	0.314573
$83$	−2.62989	−0.288668	−0.144334	−	0.989529i	$-0.546104\pi$
$83$	−2.62989	−0.288668	−0.144334	+	0.989529i	$0.546104\pi$
$84$	7.40221	0.807648
$85$	2.83562	0.307567
$86$	−9.66505	−1.04221
$87$	3.18309	0.341263
$88$	37.7589	4.02511
$89$	3.19988	0.339187	0.169593	−	0.985514i	$-0.445755\pi$
$89$	3.19988	0.339187	0.169593	+	0.985514i	$0.445755\pi$
$90$	7.40094	0.780128
$91$	−8.86518	−0.929324
$92$	14.9388	1.55748
$93$	2.43358	0.252351
$94$	3.00506	0.309948
$95$	−21.1603	−2.17100
$96$	−10.1986	−1.04089
$97$	9.70271	0.985160	0.492580	−	0.870267i	$-0.336054\pi$
$97$	9.70271	0.985160	0.492580	+	0.870267i	$0.336054\pi$
$98$	12.0940	1.22167
$99$	−5.14470	−0.517061
$100$	14.6322	1.46322
$101$	5.05721	0.503211	0.251605	−	0.967830i	$-0.419041\pi$
$101$	5.05721	0.503211	0.251605	+	0.967830i	$0.419041\pi$
$102$	2.60999	0.258427
$103$	9.12966	0.899572	0.449786	−	0.893136i	$-0.351500\pi$
$103$	9.12966	0.899572	0.449786	+	0.893136i	$0.351500\pi$
$104$	42.2974	4.14760
$105$	−4.36196	−0.425683
$106$	9.16124	0.889818
$107$	−5.83628	−0.564214	−0.282107	−	0.959383i	$-0.591033\pi$
$107$	−5.83628	−0.564214	−0.282107	+	0.959383i	$0.591033\pi$
$108$	4.81203	0.463038
$109$	14.9628	1.43318	0.716590	−	0.697494i	$-0.245702\pi$
$109$	14.9628	1.43318	0.716590	+	0.697494i	$0.245702\pi$
$110$	−38.0756	−3.63037
$111$	−8.32995	−0.790644
$112$	14.6622	1.38545
$113$	−18.2850	−1.72011	−0.860055	−	0.510201i	$-0.829571\pi$
$113$	−18.2850	−1.72011	−0.860055	+	0.510201i	$0.829571\pi$
$114$	−19.4765	−1.82414
$115$	−8.80312	−0.820895
$116$	15.3171	1.42216
$117$	−5.76308	−0.532797
$118$	−30.8918	−2.84382
$119$	−1.53827	−0.141013
$120$	20.8117	1.89984
$121$	15.4679	1.40617
$122$	−0.282018	−0.0255327
$123$	−1.09141	−0.0984095
$124$	11.7105	1.05163
$125$	5.55567	0.496914
$126$	−4.01487	−0.357673
$127$	−18.4156	−1.63412	−0.817059	−	0.576554i	$-0.804397\pi$
$127$	−18.4156	−1.63412	−0.817059	+	0.576554i	$0.804397\pi$
$128$	0.678611	0.0599813
$129$	3.70310	0.326040
$130$	−42.6523	−3.74085
$131$	−13.5949	−1.18779	−0.593897	−	0.804541i	$-0.702411\pi$
$131$	−13.5949	−1.18779	−0.593897	+	0.804541i	$0.702411\pi$
$132$	−24.7565	−2.15477
$133$	11.4791	0.995360
$134$	−33.0125	−2.85185
$135$	−2.83562	−0.244052
$136$	7.33937	0.629346
$137$	−5.01134	−0.428147	−0.214074	−	0.976818i	$-0.568673\pi$
$137$	−5.01134	−0.428147	−0.214074	+	0.976818i	$0.568673\pi$
$138$	−8.10264	−0.689742
$139$	−7.14731	−0.606227	−0.303113	−	0.952955i	$-0.598026\pi$
$139$	−7.14731	−0.606227	−0.303113	+	0.952955i	$0.598026\pi$
$140$	−20.9899	−1.77397
$141$	−1.15137	−0.0969627
$142$	−0.947780	−0.0795360
$143$	29.6493	2.47940
$144$	9.53161	0.794301
$145$	−9.02604	−0.749572
$146$	−22.1118	−1.82998
$147$	−4.63372	−0.382183
$148$	−40.0840	−3.29488
$149$	−6.22325	−0.509829	−0.254914	−	0.966964i	$-0.582047\pi$
$149$	−6.22325	−0.509829	−0.254914	+	0.966964i	$0.582047\pi$
$150$	−7.93635	−0.648000
$151$	−1.69421	−0.137873	−0.0689363	−	0.997621i	$-0.521961\pi$
$151$	−1.69421	−0.137873	−0.0689363	+	0.997621i	$0.521961\pi$
$152$	−54.7687	−4.44233
$153$	−1.00000	−0.0808452
$154$	20.6553	1.66445
$155$	−6.90072	−0.554279
$156$	−27.7322	−2.22035
$157$	1.00000	0.0798087
$157$	1.00000	0.0798087
$158$	−5.91270	−0.470389
$159$	−3.51007	−0.278367
$160$	28.9195	2.28628
$161$	4.77552	0.376364
$162$	−2.60999	−0.205060
$163$	−6.60248	−0.517146	−0.258573	−	0.965992i	$-0.583252\pi$
$163$	−6.60248	−0.517146	−0.258573	+	0.965992i	$0.583252\pi$
$164$	−5.25192	−0.410106
$165$	14.5884	1.13571
$166$	6.86397	0.532748
$167$	−0.195685	−0.0151425	−0.00757127	−	0.999971i	$-0.502410\pi$
$167$	−0.195685	−0.0151425	−0.00757127	+	0.999971i	$0.502410\pi$
$168$	−11.2899	−0.871038
$169$	20.2131	1.55486
$170$	−7.40094	−0.567626
$171$	7.46231	0.570657
$172$	17.8194	1.35872
$173$	16.0672	1.22156	0.610782	−	0.791798i	$-0.290855\pi$
$173$	16.0672	1.22156	0.610782	+	0.791798i	$0.290855\pi$
$174$	−8.30782	−0.629814
$175$	4.67751	0.353587
$176$	−49.0372	−3.69632
$177$	11.8360	0.889648
$178$	−8.35165	−0.625983
$179$	−1.44212	−0.107789	−0.0538947	−	0.998547i	$-0.517164\pi$
$179$	−1.44212	−0.107789	−0.0538947	+	0.998547i	$0.517164\pi$
$180$	−13.6451	−1.01705
$181$	−9.39990	−0.698689	−0.349344	−	0.936994i	$-0.613596\pi$
$181$	−9.39990	−0.698689	−0.349344	+	0.936994i	$0.613596\pi$
$182$	23.1380	1.71510
$183$	0.108053	0.00798753
$184$	−22.7849	−1.67972
$185$	23.6206	1.73662
$186$	−6.35161	−0.465723
$187$	5.14470	0.376217
$188$	−5.54042	−0.404077
$189$	1.53827	0.111893
$190$	55.2281	4.00667
$191$	10.1320	0.733129	0.366565	−	0.930393i	$-0.380534\pi$
$191$	10.1320	0.733129	0.366565	+	0.930393i	$0.380534\pi$
$192$	7.55507	0.545240
$193$	−22.4580	−1.61656	−0.808281	−	0.588796i	$-0.799602\pi$
$193$	−22.4580	−1.61656	−0.808281	+	0.588796i	$0.799602\pi$
$194$	−25.3239	−1.81815
$195$	16.3419	1.17027
$196$	−22.2976	−1.59269
$197$	24.3674	1.73611	0.868053	−	0.496471i	$-0.165371\pi$
$197$	24.3674	1.73611	0.868053	+	0.496471i	$0.165371\pi$
$198$	13.4276	0.954258
$199$	−5.49168	−0.389295	−0.194648	−	0.980873i	$-0.562356\pi$
$199$	−5.49168	−0.389295	−0.194648	+	0.980873i	$0.562356\pi$
$200$	−22.3173	−1.57807
$201$	12.6485	0.892159
$202$	−13.1992	−0.928696
$203$	4.89645	0.343664
$204$	−4.81203	−0.336910
$205$	3.09484	0.216153
$206$	−23.8283	−1.66020
$207$	3.10447	0.215776
$208$	−54.9315	−3.80881
$209$	−38.3913	−2.65558
$210$	11.3847	0.785616
$211$	−22.3895	−1.54136	−0.770678	−	0.637225i	$-0.780082\pi$
$211$	−22.3895	−1.54136	−0.770678	+	0.637225i	$0.780082\pi$
$212$	−16.8906	−1.16005
$213$	0.363136	0.0248817
$214$	15.2326	1.04128
$215$	−10.5006	−0.716135
$216$	−7.33937	−0.499381
$217$	3.74351	0.254126
$218$	−39.0528	−2.64499
$219$	8.47199	0.572484
$220$	70.2000	4.73288
$221$	5.76308	0.387667
$222$	21.7411	1.45916
$223$	−25.1735	−1.68574	−0.842871	−	0.538115i	$-0.819137\pi$
$223$	−25.1735	−1.68574	−0.842871	+	0.538115i	$0.819137\pi$
$224$	−15.6882	−1.04822
$225$	3.04076	0.202717
$226$	47.7237	3.17453
$227$	−1.56993	−0.104200	−0.0520999	−	0.998642i	$-0.516591\pi$
$227$	−1.56993	−0.104200	−0.0520999	+	0.998642i	$0.516591\pi$
$228$	35.9089	2.37812
$229$	11.5907	0.765937	0.382968	−	0.923761i	$-0.374902\pi$
$229$	11.5907	0.765937	0.382968	+	0.923761i	$0.374902\pi$
$230$	22.9760	1.51499
$231$	−7.91394	−0.520699
$232$	−23.3619	−1.53378
$233$	−24.9761	−1.63624	−0.818119	−	0.575049i	$-0.804983\pi$
$233$	−24.9761	−1.63624	−0.818119	+	0.575049i	$0.804983\pi$
$234$	15.0416	0.983299
$235$	3.26485	0.212975
$236$	56.9553	3.70747
$237$	2.26541	0.147154
$238$	4.01487	0.260245
$239$	23.9646	1.55014	0.775072	−	0.631873i	$-0.217714\pi$
$239$	23.9646	1.55014	0.775072	+	0.631873i	$0.217714\pi$
$240$	−27.0280	−1.74465
$241$	7.24733	0.466841	0.233421	−	0.972376i	$-0.425008\pi$
$241$	7.24733	0.466841	0.233421	+	0.972376i	$0.425008\pi$
$242$	−40.3710	−2.59515
$243$	1.00000	0.0641500
$244$	0.519957	0.0332868
$245$	13.1395	0.839451
$246$	2.84858	0.181619
$247$	−43.0059	−2.73640
$248$	−17.8610	−1.13417
$249$	−2.62989	−0.166662
$250$	−14.5002	−0.917074
$251$	−5.10578	−0.322274	−0.161137	−	0.986932i	$-0.551516\pi$
$251$	−5.10578	−0.322274	−0.161137	+	0.986932i	$0.551516\pi$
$252$	7.40221	0.466296
$253$	−15.9716	−1.00412
$254$	48.0644	3.01583
$255$	2.83562	0.177574
$256$	−16.8813	−1.05508
$257$	−23.2465	−1.45008	−0.725038	−	0.688709i	$-0.758178\pi$
$257$	−23.2465	−1.45008	−0.725038	+	0.688709i	$0.758178\pi$
$258$	−9.66505	−0.601720
$259$	−12.8137	−0.796206
$260$	78.6380	4.87692
$261$	3.18309	0.197028
$262$	35.4826	2.19212
$263$	10.3425	0.637744	0.318872	−	0.947798i	$-0.396696\pi$
$263$	10.3425	0.637744	0.318872	+	0.947798i	$0.396696\pi$
$264$	37.7589	2.32390
$265$	9.95323	0.611422
$266$	−29.9602	−1.83698
$267$	3.19988	0.195830
$268$	60.8652	3.71793
$269$	22.9266	1.39786	0.698929	−	0.715191i	$-0.253660\pi$
$269$	22.9266	1.39786	0.698929	+	0.715191i	$0.253660\pi$
$270$	7.40094	0.450407
$271$	−6.62942	−0.402709	−0.201354	−	0.979518i	$-0.564534\pi$
$271$	−6.62942	−0.402709	−0.201354	+	0.979518i	$0.564534\pi$
$272$	−9.53161	−0.577939
$273$	−8.86518	−0.536545
$274$	13.0795	0.790163
$275$	−15.6438	−0.943356
$276$	14.9388	0.899212
$277$	−5.35349	−0.321660	−0.160830	−	0.986982i	$-0.551417\pi$
$277$	−5.35349	−0.321660	−0.160830	+	0.986982i	$0.551417\pi$
$278$	18.6544	1.11882
$279$	2.43358	0.145695
$280$	32.0140	1.91320
$281$	−8.55418	−0.510300	−0.255150	−	0.966902i	$-0.582125\pi$
$281$	−8.55418	−0.510300	−0.255150	+	0.966902i	$0.582125\pi$
$282$	3.00506	0.178949
$283$	−19.2640	−1.14512	−0.572562	−	0.819862i	$-0.694050\pi$
$283$	−19.2640	−1.14512	−0.572562	+	0.819862i	$0.694050\pi$
$284$	1.74742	0.103690
$285$	−21.1603	−1.25343
$286$	−77.3844	−4.57583
$287$	−1.67889	−0.0991018
$288$	−10.1986	−0.600960
$289$	1.00000	0.0588235
$290$	23.5578	1.38336
$291$	9.70271	0.568783
$292$	40.7675	2.38574
$293$	−22.0816	−1.29002	−0.645010	−	0.764174i	$-0.723147\pi$
$293$	−22.0816	−1.29002	−0.645010	+	0.764174i	$0.723147\pi$
$294$	12.0940	0.705334
$295$	−33.5624	−1.95408
$296$	61.1366	3.55349
$297$	−5.14470	−0.298526
$298$	16.2426	0.940909
$299$	−17.8913	−1.03468
$300$	14.6322	0.844793
$301$	5.69637	0.328333
$302$	4.42186	0.254449
$303$	5.05721	0.290529
$304$	71.1278	4.07946
$305$	−0.306399	−0.0175443
$306$	2.60999	0.149203
$307$	−8.90379	−0.508166	−0.254083	−	0.967182i	$-0.581774\pi$
$307$	−8.90379	−0.508166	−0.254083	+	0.967182i	$0.581774\pi$
$308$	−38.0821	−2.16993
$309$	9.12966	0.519368
$310$	18.0108	1.02294
$311$	−6.89073	−0.390738	−0.195369	−	0.980730i	$-0.562590\pi$
$311$	−6.89073	−0.390738	−0.195369	+	0.980730i	$0.562590\pi$
$312$	42.2974	2.39462
$313$	−21.8193	−1.23330	−0.616649	−	0.787238i	$-0.711510\pi$
$313$	−21.8193	−1.23330	−0.616649	+	0.787238i	$0.711510\pi$
$314$	−2.60999	−0.147290
$315$	−4.36196	−0.245768
$316$	10.9012	0.613243
$317$	33.8159	1.89929	0.949646	−	0.313325i	$-0.101443\pi$
$317$	33.8159	1.89929	0.949646	+	0.313325i	$0.101443\pi$
$318$	9.16124	0.513737
$319$	−16.3760	−0.916881
$320$	−21.4233	−1.19760
$321$	−5.83628	−0.325749
$322$	−12.4640	−0.694594
$323$	−7.46231	−0.415214
$324$	4.81203	0.267335
$325$	−17.5242	−0.972065
$326$	17.2324	0.954414
$327$	14.9628	0.827447
$328$	8.01030	0.442295
$329$	−1.77112	−0.0976448
$330$	−38.0756	−2.09599
$331$	7.59780	0.417613	0.208806	−	0.977957i	$-0.433042\pi$
$331$	7.59780	0.417613	0.208806	+	0.977957i	$0.433042\pi$
$332$	−12.6551	−0.694539
$333$	−8.32995	−0.456478
$334$	0.510735	0.0279462
$335$	−35.8665	−1.95960
$336$	14.6622	0.799888
$337$	−15.9663	−0.869740	−0.434870	−	0.900493i	$-0.643206\pi$
$337$	−15.9663	−0.869740	−0.434870	+	0.900493i	$0.643206\pi$
$338$	−52.7560	−2.86955
$339$	−18.2850	−0.993106
$340$	13.6451	0.740010
$341$	−12.5200	−0.677998
$342$	−19.4765	−1.05317
$343$	−17.8958	−0.966283
$344$	−27.1784	−1.46536
$345$	−8.80312	−0.473944
$346$	−41.9351	−2.25445
$347$	25.9387	1.39246	0.696230	−	0.717819i	$-0.254859\pi$
$347$	25.9387	1.39246	0.696230	+	0.717819i	$0.254859\pi$
$348$	15.3171	0.821084
$349$	17.1167	0.916234	0.458117	−	0.888892i	$-0.348524\pi$
$349$	17.1167	0.916234	0.458117	+	0.888892i	$0.348524\pi$
$350$	−12.2082	−0.652558
$351$	−5.76308	−0.307611
$352$	52.4688	2.79660
$353$	−18.2325	−0.970417	−0.485208	−	0.874399i	$-0.661256\pi$
$353$	−18.2325	−0.970417	−0.485208	+	0.874399i	$0.661256\pi$
$354$	−30.8918	−1.64188
$355$	−1.02972	−0.0546517
$356$	15.3979	0.816089
$357$	−1.53827	−0.0814139
$358$	3.76393	0.198930
$359$	1.35313	0.0714156	0.0357078	−	0.999362i	$-0.488631\pi$
$359$	1.35313	0.0714156	0.0357078	+	0.999362i	$0.488631\pi$
$360$	20.8117	1.09687
$361$	36.6861	1.93085
$362$	24.5336	1.28946
$363$	15.4679	0.811854
$364$	−42.6596	−2.23597
$365$	−24.0234	−1.25744
$366$	−0.282018	−0.0147413
$367$	−17.0472	−0.889854	−0.444927	−	0.895567i	$-0.646770\pi$
$367$	−17.0472	−0.889854	−0.444927	+	0.895567i	$0.646770\pi$
$368$	29.5906	1.54252
$369$	−1.09141	−0.0568167
$370$	−61.6495	−3.20500
$371$	−5.39944	−0.280325
$372$	11.7105	0.607160
$373$	30.1820	1.56277	0.781383	−	0.624052i	$-0.214515\pi$
$373$	30.1820	1.56277	0.781383	+	0.624052i	$0.214515\pi$
$374$	−13.4276	−0.694324
$375$	5.55567	0.286893
$376$	8.45032	0.435792
$377$	−18.3444	−0.944785
$378$	−4.01487	−0.206502
$379$	27.2270	1.39856	0.699279	−	0.714849i	$-0.253504\pi$
$379$	27.2270	1.39856	0.699279	+	0.714849i	$0.253504\pi$
$380$	−101.824	−5.22347
$381$	−18.4156	−0.943459
$382$	−26.4445	−1.35302
$383$	−8.42505	−0.430500	−0.215250	−	0.976559i	$-0.569057\pi$
$383$	−8.42505	−0.430500	−0.215250	+	0.976559i	$0.569057\pi$
$384$	0.678611	0.0346302
$385$	22.4409	1.14370
$386$	58.6151	2.98343
$387$	3.70310	0.188239
$388$	46.6898	2.37031
$389$	−29.2099	−1.48100	−0.740500	−	0.672056i	$-0.765411\pi$
$389$	−29.2099	−1.48100	−0.740500	+	0.672056i	$0.765411\pi$
$390$	−42.6523	−2.15978
$391$	−3.10447	−0.157000
$392$	34.0086	1.71770
$393$	−13.5949	−0.685774
$394$	−63.5987	−3.20405
$395$	−6.42386	−0.323219
$396$	−24.7565	−1.24406
$397$	23.1857	1.16366	0.581828	−	0.813312i	$-0.302338\pi$
$397$	23.1857	1.16366	0.581828	+	0.813312i	$0.302338\pi$
$398$	14.3332	0.718460
$399$	11.4791	0.574672
$400$	28.9833	1.44917
$401$	−22.6713	−1.13215	−0.566076	−	0.824353i	$-0.691539\pi$
$401$	−22.6713	−1.13215	−0.566076	+	0.824353i	$0.691539\pi$
$402$	−33.0125	−1.64652
$403$	−14.0249	−0.698631
$404$	24.3355	1.21073
$405$	−2.83562	−0.140903
$406$	−12.7797	−0.634245
$407$	42.8551	2.12425
$408$	7.33937	0.363353
$409$	14.7707	0.730365	0.365183	−	0.930936i	$-0.381007\pi$
$409$	14.7707	0.730365	0.365183	+	0.930936i	$0.381007\pi$
$410$	−8.07749	−0.398919
$411$	−5.01134	−0.247191
$412$	43.9322	2.16439
$413$	18.2070	0.895907
$414$	−8.10264	−0.398223
$415$	7.45737	0.366068
$416$	58.7755	2.88171
$417$	−7.14731	−0.350005
$418$	100.201	4.90099
$419$	−27.0745	−1.32267	−0.661337	−	0.750089i	$-0.730011\pi$
$419$	−27.0745	−1.32267	−0.661337	+	0.750089i	$0.730011\pi$
$420$	−20.9899	−1.02420
$421$	−9.56721	−0.466277	−0.233139	−	0.972443i	$-0.574900\pi$
$421$	−9.56721	−0.466277	−0.233139	+	0.972443i	$0.574900\pi$
$422$	58.4363	2.84463
$423$	−1.15137	−0.0559814
$424$	25.7617	1.25110
$425$	−3.04076	−0.147499
$426$	−0.947780	−0.0459201
$427$	0.166215	0.00804372
$428$	−28.0844	−1.35751
$429$	29.6493	1.43148
$430$	27.4064	1.32166
$431$	−39.9714	−1.92536	−0.962678	−	0.270648i	$-0.912762\pi$
$431$	−39.9714	−1.92536	−0.962678	+	0.270648i	$0.912762\pi$
$432$	9.53161	0.458590
$433$	−34.4056	−1.65343	−0.826713	−	0.562623i	$-0.809792\pi$
$433$	−34.4056	−1.65343	−0.826713	+	0.562623i	$0.809792\pi$
$434$	−9.77050	−0.468999
$435$	−9.02604	−0.432765
$436$	72.0017	3.44826
$437$	23.1665	1.10821
$438$	−22.1118	−1.05654
$439$	−30.7055	−1.46549	−0.732746	−	0.680502i	$-0.761762\pi$
$439$	−30.7055	−1.46549	−0.732746	+	0.680502i	$0.761762\pi$
$440$	−107.070	−5.10436
$441$	−4.63372	−0.220653
$442$	−15.0416	−0.715455
$443$	16.4766	0.782825	0.391412	−	0.920215i	$-0.371987\pi$
$443$	16.4766	0.782825	0.391412	+	0.920215i	$0.371987\pi$
$444$	−40.0840	−1.90230
$445$	−9.07366	−0.430133
$446$	65.7025	3.11111
$447$	−6.22325	−0.294350
$448$	11.6217	0.549076
$449$	22.6297	1.06796	0.533982	−	0.845496i	$-0.320695\pi$
$449$	22.6297	1.06796	0.533982	+	0.845496i	$0.320695\pi$
$450$	−7.93635	−0.374123
$451$	5.61499	0.264400
$452$	−87.9882	−4.13861
$453$	−1.69421	−0.0796008
$454$	4.09749	0.192305
$455$	25.1383	1.17850
$456$	−54.7687	−2.56478
$457$	−15.3551	−0.718282	−0.359141	−	0.933283i	$-0.616930\pi$
$457$	−15.3551	−0.718282	−0.359141	+	0.933283i	$0.616930\pi$
$458$	−30.2516	−1.41357
$459$	−1.00000	−0.0466760
$460$	−42.3609	−1.97509
$461$	8.46443	0.394228	0.197114	−	0.980381i	$-0.436843\pi$
$461$	8.46443	0.394228	0.197114	+	0.980381i	$0.436843\pi$
$462$	20.6553	0.960970
$463$	3.61812	0.168148	0.0840740	−	0.996460i	$-0.473207\pi$
$463$	3.61812	0.168148	0.0840740	+	0.996460i	$0.473207\pi$
$464$	30.3399	1.40850
$465$	−6.90072	−0.320013
$466$	65.1873	3.01974
$467$	20.4696	0.947218	0.473609	−	0.880735i	$-0.342951\pi$
$467$	20.4696	0.947218	0.473609	+	0.880735i	$0.342951\pi$
$468$	−27.7322	−1.28192
$469$	19.4569	0.898435
$470$	−8.52121	−0.393054
$471$	1.00000	0.0460776
$472$	−86.8689	−3.99846
$473$	−19.0513	−0.875981
$474$	−5.91270	−0.271579
$475$	22.6911	1.04114
$476$	−7.40221	−0.339280
$477$	−3.51007	−0.160715
$478$	−62.5474	−2.86085
$479$	19.5025	0.891094	0.445547	−	0.895259i	$-0.353009\pi$
$479$	19.5025	0.891094	0.445547	+	0.895259i	$0.353009\pi$
$480$	28.9195	1.31999
$481$	48.0062	2.18889
$482$	−18.9154	−0.861574
$483$	4.77552	0.217294
$484$	74.4321	3.38328
$485$	−27.5132	−1.24931
$486$	−2.60999	−0.118391
$487$	33.8528	1.53402	0.767009	−	0.641636i	$-0.221744\pi$
$487$	33.8528	1.53402	0.767009	+	0.641636i	$0.221744\pi$
$488$	−0.793044	−0.0358994
$489$	−6.60248	−0.298574
$490$	−34.2939	−1.54924
$491$	−15.0058	−0.677201	−0.338601	−	0.940930i	$-0.609954\pi$
$491$	−15.0058	−0.677201	−0.338601	+	0.940930i	$0.609954\pi$
$492$	−5.25192	−0.236775
$493$	−3.18309	−0.143359
$494$	112.245	5.05014
$495$	14.5884	0.655701
$496$	23.1959	1.04153
$497$	0.558601	0.0250567
$498$	6.86397	0.307582
$499$	−19.1435	−0.856979	−0.428489	−	0.903547i	$-0.640954\pi$
$499$	−19.1435	−0.856979	−0.428489	+	0.903547i	$0.640954\pi$
$500$	26.7341	1.19558
$501$	−0.195685	−0.00874255
$502$	13.3260	0.594770
$503$	−12.2645	−0.546846	−0.273423	−	0.961894i	$-0.588156\pi$
$503$	−12.2645	−0.546846	−0.273423	+	0.961894i	$0.588156\pi$
$504$	−11.2899	−0.502894
$505$	−14.3403	−0.638136
$506$	41.6856	1.85315
$507$	20.2131	0.897697
$508$	−88.6164	−3.93172
$509$	−18.7065	−0.829153	−0.414576	−	0.910014i	$-0.636070\pi$
$509$	−18.7065	−0.829153	−0.414576	+	0.910014i	$0.636070\pi$
$510$	−7.40094	−0.327719
$511$	13.0322	0.576511
$512$	42.7028	1.88721
$513$	7.46231	0.329469
$514$	60.6731	2.67617
$515$	−25.8883	−1.14077
$516$	17.8194	0.784458
$517$	5.92344	0.260513
$518$	33.4436	1.46943
$519$	16.0672	0.705271
$520$	−119.940	−5.25970
$521$	9.61955	0.421440	0.210720	−	0.977546i	$-0.432419\pi$
$521$	9.61955	0.421440	0.210720	+	0.977546i	$0.432419\pi$
$522$	−8.30782	−0.363623
$523$	20.0133	0.875121	0.437560	−	0.899189i	$-0.355843\pi$
$523$	20.0133	0.875121	0.437560	+	0.899189i	$0.355843\pi$
$524$	−65.4193	−2.85785
$525$	4.67751	0.204143
$526$	−26.9937	−1.17698
$527$	−2.43358	−0.106008
$528$	−49.0372	−2.13407
$529$	−13.3622	−0.580967
$530$	−25.9778	−1.12840
$531$	11.8360	0.513639
$532$	55.2376	2.39485
$533$	6.28991	0.272446
$534$	−8.35165	−0.361411
$535$	16.5495	0.715497
$536$	−92.8324	−4.00975
$537$	−1.44212	−0.0622322
$538$	−59.8381	−2.57980
$539$	23.8391	1.02682
$540$	−13.6451	−0.587192
$541$	−6.96291	−0.299359	−0.149679	−	0.988735i	$-0.547824\pi$
$541$	−6.96291	−0.299359	−0.149679	+	0.988735i	$0.547824\pi$
$542$	17.3027	0.743215
$543$	−9.39990	−0.403388
$544$	10.1986	0.437262
$545$	−42.4290	−1.81746
$546$	23.1380	0.990216
$547$	25.4701	1.08902	0.544511	−	0.838754i	$-0.316715\pi$
$547$	25.4701	1.08902	0.544511	+	0.838754i	$0.316715\pi$
$548$	−24.1147	−1.03013
$549$	0.108053	0.00461161
$550$	40.8301	1.74100
$551$	23.7532	1.01192
$552$	−22.7849	−0.969790
$553$	3.48482	0.148190
$554$	13.9725	0.593636
$555$	23.6206	1.00264
$556$	−34.3931	−1.45859
$557$	23.4048	0.991692	0.495846	−	0.868411i	$-0.334858\pi$
$557$	23.4048	0.991692	0.495846	+	0.868411i	$0.334858\pi$
$558$	−6.35161	−0.268885
$559$	−21.3413	−0.902640
$560$	−41.5765	−1.75693
$561$	5.14470	0.217209
$562$	22.3263	0.941779
$563$	−7.34508	−0.309558	−0.154779	−	0.987949i	$-0.549467\pi$
$563$	−7.34508	−0.309558	−0.154779	+	0.987949i	$0.549467\pi$
$564$	−5.54042	−0.233294
$565$	51.8494	2.18132
$566$	50.2787	2.11337
$567$	1.53827	0.0646013
$568$	−2.66519	−0.111829
$569$	7.08977	0.297219	0.148609	−	0.988896i	$-0.452520\pi$
$569$	7.08977	0.297219	0.148609	+	0.988896i	$0.452520\pi$
$570$	55.2281	2.31325
$571$	−15.5033	−0.648791	−0.324396	−	0.945922i	$-0.605161\pi$
$571$	−15.5033	−0.648791	−0.324396	+	0.945922i	$0.605161\pi$
$572$	142.674	5.96548
$573$	10.1320	0.423272
$574$	4.38188	0.182896
$575$	9.43996	0.393674
$576$	7.55507	0.314795
$577$	19.7041	0.820293	0.410147	−	0.912020i	$-0.365478\pi$
$577$	19.7041	0.820293	0.410147	+	0.912020i	$0.365478\pi$
$578$	−2.60999	−0.108561
$579$	−22.4580	−0.933323
$580$	−43.4336	−1.80348
$581$	−4.04548	−0.167835
$582$	−25.3239	−1.04971
$583$	18.0582	0.747896
$584$	−62.1791	−2.57299
$585$	16.3419	0.675656
$586$	57.6327	2.38079
$587$	−30.1098	−1.24277	−0.621383	−	0.783507i	$-0.713429\pi$
$587$	−30.1098	−1.24277	−0.621383	+	0.783507i	$0.713429\pi$
$588$	−22.2976	−0.919539
$589$	18.1601	0.748275
$590$	87.5976	3.60633
$591$	24.3674	1.00234
$592$	−79.3978	−3.26323
$593$	−25.8882	−1.06310	−0.531551	−	0.847026i	$-0.678391\pi$
$593$	−25.8882	−1.06310	−0.531551	+	0.847026i	$0.678391\pi$
$594$	13.4276	0.550941
$595$	4.36196	0.178823
$596$	−29.9465	−1.22666
$597$	−5.49168	−0.224760
$598$	46.6962	1.90955
$599$	35.9348	1.46826	0.734128	−	0.679011i	$-0.237591\pi$
$599$	35.9348	1.46826	0.734128	+	0.679011i	$0.237591\pi$
$600$	−22.3173	−0.911099
$601$	−43.2076	−1.76248	−0.881238	−	0.472673i	$-0.843289\pi$
$601$	−43.2076	−1.76248	−0.881238	+	0.472673i	$0.843289\pi$
$602$	−14.8675	−0.605952
$603$	12.6485	0.515088
$604$	−8.15258	−0.331724
$605$	−43.8611	−1.78321
$606$	−13.1992	−0.536183
$607$	−41.0049	−1.66434	−0.832168	−	0.554524i	$-0.812900\pi$
$607$	−41.0049	−1.66434	−0.832168	+	0.554524i	$0.812900\pi$
$608$	−76.1053	−3.08648
$609$	4.89645	0.198414
$610$	0.799697	0.0323788
$611$	6.63543	0.268441
$612$	−4.81203	−0.194515
$613$	−10.0742	−0.406894	−0.203447	−	0.979086i	$-0.565214\pi$
$613$	−10.0742	−0.406894	−0.203447	+	0.979086i	$0.565214\pi$
$614$	23.2388	0.937840
$615$	3.09484	0.124796
$616$	58.0833	2.34024
$617$	37.0303	1.49078	0.745391	−	0.666628i	$-0.232263\pi$
$617$	37.0303	1.49078	0.745391	+	0.666628i	$0.232263\pi$
$618$	−23.8283	−0.958514
$619$	−23.3925	−0.940226	−0.470113	−	0.882606i	$-0.655787\pi$
$619$	−23.3925	−0.940226	−0.470113	+	0.882606i	$0.655787\pi$
$620$	−33.2065	−1.33360
$621$	3.10447	0.124578
$622$	17.9847	0.721122
$623$	4.92228	0.197207
$624$	−54.9315	−2.19902
$625$	−30.9576	−1.23830
$626$	56.9480	2.27610
$627$	−38.3913	−1.53320
$628$	4.81203	0.192021
$629$	8.32995	0.332137
$630$	11.3847	0.453575
$631$	−40.2195	−1.60111	−0.800556	−	0.599258i	$-0.795462\pi$
$631$	−40.2195	−1.60111	−0.800556	+	0.599258i	$0.795462\pi$
$632$	−16.6267	−0.661375
$633$	−22.3895	−0.889902
$634$	−88.2592	−3.50522
$635$	52.2197	2.07227
$636$	−16.8906	−0.669755
$637$	26.7045	1.05807
$638$	42.7412	1.69214
$639$	0.363136	0.0143654
$640$	−1.92428	−0.0760640
$641$	−3.83723	−0.151562	−0.0757808	−	0.997124i	$-0.524145\pi$
$641$	−3.83723	−0.151562	−0.0757808	+	0.997124i	$0.524145\pi$
$642$	15.2326	0.601183
$643$	−44.6730	−1.76173	−0.880865	−	0.473368i	$-0.843038\pi$
$643$	−44.6730	−1.76173	−0.880865	+	0.473368i	$0.843038\pi$
$644$	22.9800	0.905538
$645$	−10.5006	−0.413461
$646$	19.4765	0.766294
$647$	25.3616	0.997067	0.498534	−	0.866870i	$-0.333872\pi$
$647$	25.3616	0.997067	0.498534	+	0.866870i	$0.333872\pi$
$648$	−7.33937	−0.288318
$649$	−60.8926	−2.39025
$650$	45.7378	1.79399
$651$	3.74351	0.146720
$652$	−31.7714	−1.24426
$653$	−2.41837	−0.0946382	−0.0473191	−	0.998880i	$-0.515068\pi$
$653$	−2.41837	−0.0946382	−0.0473191	+	0.998880i	$0.515068\pi$
$654$	−39.0528	−1.52709
$655$	38.5501	1.50628
$656$	−10.4029	−0.406166
$657$	8.47199	0.330524
$658$	4.62259	0.180207
$659$	50.4800	1.96642	0.983210	−	0.182477i	$-0.0584116\pi$
$659$	50.4800	1.96642	0.983210	+	0.182477i	$0.0584116\pi$
$660$	70.2000	2.73253
$661$	−27.6724	−1.07633	−0.538166	−	0.842839i	$-0.680883\pi$
$661$	−27.6724	−1.07633	−0.538166	+	0.842839i	$0.680883\pi$
$662$	−19.8302	−0.770721
$663$	5.76308	0.223820
$664$	19.3017	0.749053
$665$	−32.5503	−1.26225
$666$	21.7411	0.842449
$667$	9.88181	0.382625
$668$	−0.941642	−0.0364332
$669$	−25.1735	−0.973264
$670$	93.6111	3.61651
$671$	−0.555902	−0.0214603
$672$	−15.6882	−0.605187
$673$	−9.62601	−0.371055	−0.185528	−	0.982639i	$-0.559399\pi$
$673$	−9.62601	−0.371055	−0.185528	+	0.982639i	$0.559399\pi$
$674$	41.6719	1.60514
$675$	3.04076	0.117039
$676$	97.2663	3.74101
$677$	14.5655	0.559798	0.279899	−	0.960029i	$-0.409699\pi$
$677$	14.5655	0.559798	0.279899	+	0.960029i	$0.409699\pi$
$678$	47.7237	1.83282
$679$	14.9254	0.572784
$680$	−20.8117	−0.798092
$681$	−1.56993	−0.0601598
$682$	32.6771	1.25127
$683$	−26.7340	−1.02295	−0.511474	−	0.859299i	$-0.670900\pi$
$683$	−26.7340	−1.02295	−0.511474	+	0.859299i	$0.670900\pi$
$684$	35.9089	1.37301
$685$	14.2103	0.542946
$686$	46.7079	1.78331
$687$	11.5907	0.442214
$688$	35.2965	1.34567
$689$	20.2288	0.770657
$690$	22.9760	0.874682
$691$	9.52737	0.362438	0.181219	−	0.983443i	$-0.441996\pi$
$691$	9.52737	0.362438	0.181219	+	0.983443i	$0.441996\pi$
$692$	77.3158	2.93911
$693$	−7.91394	−0.300626
$694$	−67.6996	−2.56984
$695$	20.2671	0.768774
$696$	−23.3619	−0.885530
$697$	1.09141	0.0413403
$698$	−44.6743	−1.69095
$699$	−24.9761	−0.944683
$700$	22.5084	0.850736
$701$	11.6998	0.441894	0.220947	−	0.975286i	$-0.429085\pi$
$701$	11.6998	0.441894	0.220947	+	0.975286i	$0.429085\pi$
$702$	15.0416	0.567708
$703$	−62.1607	−2.34443
$704$	−38.8685	−1.46491
$705$	3.26485	0.122961
$706$	47.5865	1.79094
$707$	7.77935	0.292573
$708$	56.9553	2.14051
$709$	20.2296	0.759740	0.379870	−	0.925040i	$-0.375969\pi$
$709$	20.2296	0.759740	0.379870	+	0.925040i	$0.375969\pi$
$710$	2.68755	0.100862
$711$	2.26541	0.0849597
$712$	−23.4851	−0.880143
$713$	7.55499	0.282936
$714$	4.01487	0.150253
$715$	−84.0743	−3.14420
$716$	−6.93955	−0.259343
$717$	23.9646	0.894976
$718$	−3.53166	−0.131800
$719$	−23.8743	−0.890360	−0.445180	−	0.895441i	$-0.646860\pi$
$719$	−23.8743	−0.890360	−0.445180	+	0.895441i	$0.646860\pi$
$720$	−27.0280	−1.00728
$721$	14.0439	0.523022
$722$	−95.7502	−3.56345
$723$	7.24733	0.269531
$724$	−45.2326	−1.68106
$725$	9.67901	0.359469
$726$	−40.3710	−1.49831
$727$	−8.06820	−0.299233	−0.149617	−	0.988744i	$-0.547804\pi$
$727$	−8.06820	−0.299233	−0.149617	+	0.988744i	$0.547804\pi$
$728$	65.0649	2.41147
$729$	1.00000	0.0370370
$730$	62.7007	2.32066
$731$	−3.70310	−0.136964
$732$	0.519957	0.0192181
$733$	−4.09338	−0.151192	−0.0755962	−	0.997139i	$-0.524086\pi$
$733$	−4.09338	−0.151192	−0.0755962	+	0.997139i	$0.524086\pi$
$734$	44.4929	1.64226
$735$	13.1395	0.484658
$736$	−31.6614	−1.16705
$737$	−65.0729	−2.39699
$738$	2.84858	0.104858
$739$	22.2495	0.818462	0.409231	−	0.912431i	$-0.365797\pi$
$739$	22.2495	0.818462	0.409231	+	0.912431i	$0.365797\pi$
$740$	113.663	4.17834
$741$	−43.0059	−1.57986
$742$	14.0925	0.517351
$743$	14.9272	0.547625	0.273812	−	0.961783i	$-0.411715\pi$
$743$	14.9272	0.547625	0.273812	+	0.961783i	$0.411715\pi$
$744$	−17.8610	−0.654814
$745$	17.6468	0.646529
$746$	−78.7747	−2.88415
$747$	−2.62989	−0.0962226
$748$	24.7565	0.905186
$749$	−8.97778	−0.328041
$750$	−14.5002	−0.529473
$751$	−27.1988	−0.992498	−0.496249	−	0.868180i	$-0.665290\pi$
$751$	−27.1988	−0.992498	−0.496249	+	0.868180i	$0.665290\pi$
$752$	−10.9744	−0.400195
$753$	−5.10578	−0.186065
$754$	47.8787	1.74364
$755$	4.80413	0.174840
$756$	7.40221	0.269216
$757$	38.8350	1.41148	0.705741	−	0.708469i	$-0.250614\pi$
$757$	38.8350	1.41148	0.705741	+	0.708469i	$0.250614\pi$
$758$	−71.0622	−2.58110
$759$	−15.9716	−0.579731
$760$	155.303	5.63345
$761$	−14.2772	−0.517549	−0.258774	−	0.965938i	$-0.583319\pi$
$761$	−14.2772	−0.517549	−0.258774	+	0.965938i	$0.583319\pi$
$762$	48.0644	1.74119
$763$	23.0169	0.833268
$764$	48.7558	1.76392
$765$	2.83562	0.102522
$766$	21.9893	0.794504
$767$	−68.2119	−2.46299
$768$	−16.8813	−0.609152
$769$	−12.8623	−0.463828	−0.231914	−	0.972736i	$-0.574499\pi$
$769$	−12.8623	−0.463828	−0.231914	+	0.972736i	$0.574499\pi$
$770$	−58.5706	−2.11074
$771$	−23.2465	−0.837202
$772$	−108.069	−3.88948
$773$	−42.6196	−1.53292	−0.766459	−	0.642293i	$-0.777983\pi$
$773$	−42.6196	−1.53292	−0.766459	+	0.642293i	$0.777983\pi$
$774$	−9.66505	−0.347403
$775$	7.39993	0.265813
$776$	−71.2118	−2.55635
$777$	−12.8137	−0.459689
$778$	76.2375	2.73325
$779$	−8.14447	−0.291806
$780$	78.6380	2.81569
$781$	−1.86822	−0.0668503
$782$	8.10264	0.289750
$783$	3.18309	0.113754
$784$	−44.1668	−1.57739
$785$	−2.83562	−0.101208
$786$	35.4826	1.26562
$787$	−27.7398	−0.988819	−0.494409	−	0.869229i	$-0.664616\pi$
$787$	−27.7398	−0.988819	−0.494409	+	0.869229i	$0.664616\pi$
$788$	117.257	4.17710
$789$	10.3425	0.368202
$790$	16.7662	0.596514
$791$	−28.1273	−1.00009
$792$	37.7589	1.34170
$793$	−0.622721	−0.0221135
$794$	−60.5144	−2.14757
$795$	9.95323	0.353005
$796$	−26.4262	−0.936651
$797$	15.8699	0.562142	0.281071	−	0.959687i	$-0.409310\pi$
$797$	15.8699	0.562142	0.281071	+	0.959687i	$0.409310\pi$
$798$	−29.9602	−1.06058
$799$	1.15137	0.0407325
$800$	−31.0116	−1.09642
$801$	3.19988	0.113062
$802$	59.1719	2.08943
$803$	−43.5858	−1.53811
$804$	60.8652	2.14655
$805$	−13.5416	−0.477278
$806$	36.6049	1.28935
$807$	22.9266	0.807054
$808$	−37.1167	−1.30576
$809$	−13.1493	−0.462303	−0.231152	−	0.972918i	$-0.574249\pi$
$809$	−13.1493	−0.462303	−0.231152	+	0.972918i	$0.574249\pi$
$810$	7.40094	0.260043
$811$	28.7883	1.01089	0.505446	−	0.862858i	$-0.331328\pi$
$811$	28.7883	1.01089	0.505446	+	0.862858i	$0.331328\pi$
$812$	23.5619	0.826860
$813$	−6.62942	−0.232504
$814$	−111.851	−3.92038
$815$	18.7221	0.655808
$816$	−9.53161	−0.333673
$817$	27.6337	0.966780
$818$	−38.5514	−1.34792
$819$	−8.86518	−0.309775
$820$	14.8925	0.520068
$821$	31.0064	1.08213	0.541066	−	0.840980i	$-0.318021\pi$
$821$	31.0064	1.08213	0.541066	+	0.840980i	$0.318021\pi$
$822$	13.0795	0.456201
$823$	13.5514	0.472372	0.236186	−	0.971708i	$-0.424102\pi$
$823$	13.5514	0.472372	0.236186	+	0.971708i	$0.424102\pi$
$824$	−67.0060	−2.33426
$825$	−15.6438	−0.544647
$826$	−47.5200	−1.65343
$827$	−37.2520	−1.29538	−0.647689	−	0.761905i	$-0.724264\pi$
$827$	−37.2520	−1.29538	−0.647689	+	0.761905i	$0.724264\pi$
$828$	14.9388	0.519160
$829$	0.955146	0.0331736	0.0165868	−	0.999862i	$-0.494720\pi$
$829$	0.955146	0.0331736	0.0165868	+	0.999862i	$0.494720\pi$
$830$	−19.4636	−0.675593
$831$	−5.35349	−0.185710
$832$	−43.5405	−1.50950
$833$	4.63372	0.160549
$834$	18.6544	0.645948
$835$	0.554888	0.0192027
$836$	−184.740	−6.38938
$837$	2.43358	0.0841168
$838$	70.6640	2.44105
$839$	−32.5469	−1.12364	−0.561822	−	0.827258i	$-0.689899\pi$
$839$	−32.5469	−1.12364	−0.561822	+	0.827258i	$0.689899\pi$
$840$	32.0140	1.10459
$841$	−18.8679	−0.650619
$842$	24.9703	0.860534
$843$	−8.55418	−0.294622
$844$	−107.739	−3.70853
$845$	−57.3169	−1.97176
$846$	3.00506	0.103316
$847$	23.7938	0.817565
$848$	−33.4566	−1.14890
$849$	−19.2640	−0.661137
$850$	7.93635	0.272214
$851$	−25.8601	−0.886473
$852$	1.74742	0.0598657
$853$	−56.0334	−1.91855	−0.959274	−	0.282479i	$-0.908843\pi$
$853$	−56.0334	−1.91855	−0.959274	+	0.282479i	$0.908843\pi$
$854$	−0.433820	−0.0148450
$855$	−21.1603	−0.723667
$856$	42.8346	1.46406
$857$	−12.4530	−0.425387	−0.212693	−	0.977119i	$-0.568224\pi$
$857$	−12.4530	−0.425387	−0.212693	+	0.977119i	$0.568224\pi$
$858$	−77.3844	−2.64186
$859$	−44.6702	−1.52413	−0.762065	−	0.647501i	$-0.775814\pi$
$859$	−44.6702	−1.52413	−0.762065	+	0.647501i	$0.775814\pi$
$860$	−50.5292	−1.72303
$861$	−1.67889	−0.0572164
$862$	104.325	3.55332
$863$	29.8007	1.01443	0.507214	−	0.861820i	$-0.330675\pi$
$863$	29.8007	1.01443	0.507214	+	0.861820i	$0.330675\pi$
$864$	−10.1986	−0.346964
$865$	−45.5605	−1.54910
$866$	89.7981	3.05146
$867$	1.00000	0.0339618
$868$	18.0139	0.611431
$869$	−11.6549	−0.395364
$870$	23.5578	0.798686
$871$	−72.8946	−2.46994
$872$	−109.818	−3.71890
$873$	9.70271	0.328387
$874$	−60.4644	−2.04524
$875$	8.54612	0.288912
$876$	40.7675	1.37741
$877$	−9.01730	−0.304493	−0.152246	−	0.988343i	$-0.548651\pi$
$877$	−9.01730	−0.304493	−0.152246	+	0.988343i	$0.548651\pi$
$878$	80.1409	2.70463
$879$	−22.0816	−0.744794
$880$	139.051	4.68741
$881$	−38.0780	−1.28288	−0.641440	−	0.767173i	$-0.721663\pi$
$881$	−38.0780	−1.28288	−0.641440	+	0.767173i	$0.721663\pi$
$882$	12.0940	0.407225
$883$	−12.3661	−0.416153	−0.208077	−	0.978113i	$-0.566720\pi$
$883$	−12.3661	−0.416153	−0.208077	+	0.978113i	$0.566720\pi$
$884$	27.7322	0.932734
$885$	−33.5624	−1.12819
$886$	−43.0036	−1.44473
$887$	−3.37861	−0.113443	−0.0567213	−	0.998390i	$-0.518065\pi$
$887$	−3.37861	−0.113443	−0.0567213	+	0.998390i	$0.518065\pi$
$888$	61.1366	2.05161
$889$	−28.3282	−0.950096
$890$	23.6821	0.793827
$891$	−5.14470	−0.172354
$892$	−121.136	−4.05593
$893$	−8.59187	−0.287516
$894$	16.2426	0.543234
$895$	4.08932	0.136691
$896$	1.04389	0.0348738
$897$	−17.8913	−0.597375
$898$	−59.0634	−1.97097
$899$	7.74630	0.258354
$900$	14.6322	0.487741
$901$	3.51007	0.116937
$902$	−14.6551	−0.487960
$903$	5.69637	0.189563
$904$	134.201	4.46345
$905$	26.6546	0.886028
$906$	4.42186	0.146906
$907$	30.7818	1.02209	0.511047	−	0.859553i	$-0.329258\pi$
$907$	30.7818	1.02209	0.511047	+	0.859553i	$0.329258\pi$
$908$	−7.55455	−0.250707
$909$	5.05721	0.167737
$910$	−65.6107	−2.17497
$911$	−46.8287	−1.55150	−0.775752	−	0.631038i	$-0.782629\pi$
$911$	−46.8287	−1.55150	−0.775752	+	0.631038i	$0.782629\pi$
$912$	71.1278	2.35528
$913$	13.5300	0.447777
$914$	40.0766	1.32562
$915$	−0.306399	−0.0101292
$916$	55.7750	1.84286
$917$	−20.9127	−0.690598
$918$	2.60999	0.0861424
$919$	34.8807	1.15061	0.575303	−	0.817940i	$-0.304884\pi$
$919$	34.8807	1.15061	0.575303	+	0.817940i	$0.304884\pi$
$920$	64.6094	2.13011
$921$	−8.90379	−0.293390
$922$	−22.0921	−0.727563
$923$	−2.09278	−0.0688848
$924$	−38.0821	−1.25281
$925$	−25.3294	−0.832825
$926$	−9.44324	−0.310324
$927$	9.12966	0.299857
$928$	−32.4631	−1.06565
$929$	16.5301	0.542336	0.271168	−	0.962532i	$-0.412590\pi$
$929$	16.5301	0.542336	0.271168	+	0.962532i	$0.412590\pi$
$930$	18.0108	0.590597
$931$	−34.5783	−1.13326
$932$	−120.186	−3.93682
$933$	−6.89073	−0.225592
$934$	−53.4253	−1.74813
$935$	−14.5884	−0.477092
$936$	42.2974	1.38253
$937$	34.2602	1.11923	0.559616	−	0.828752i	$-0.310949\pi$
$937$	34.2602	1.11923	0.559616	+	0.828752i	$0.310949\pi$
$938$	−50.7822	−1.65810
$939$	−21.8193	−0.712045
$940$	15.7106	0.512422
$941$	−39.3180	−1.28173	−0.640864	−	0.767654i	$-0.721424\pi$
$941$	−39.3180	−1.28173	−0.640864	+	0.767654i	$0.721424\pi$
$942$	−2.60999	−0.0850380
$943$	−3.38827	−0.110337
$944$	112.816	3.67185
$945$	−4.36196	−0.141894
$946$	49.7237	1.61666
$947$	−6.28453	−0.204220	−0.102110	−	0.994773i	$-0.532559\pi$
$947$	−6.28453	−0.204220	−0.102110	+	0.994773i	$0.532559\pi$
$948$	10.9012	0.354056
$949$	−48.8248	−1.58492
$950$	−59.2235	−1.92146
$951$	33.8159	1.09656
$952$	11.2899	0.365909
$953$	−17.1216	−0.554624	−0.277312	−	0.960780i	$-0.589444\pi$
$953$	−17.1216	−0.554624	−0.277312	+	0.960780i	$0.589444\pi$
$954$	9.16124	0.296606
$955$	−28.7307	−0.929702
$956$	115.319	3.72967
$957$	−16.3760	−0.529362
$958$	−50.9014	−1.64455
$959$	−7.70879	−0.248930
$960$	−21.4233	−0.691435
$961$	−25.0777	−0.808958
$962$	−125.296	−4.03969
$963$	−5.83628	−0.188071
$964$	34.8744	1.12323
$965$	63.6825	2.05001
$966$	−12.4640	−0.401024
$967$	43.3991	1.39562	0.697810	−	0.716283i	$-0.254158\pi$
$967$	43.3991	1.39562	0.697810	+	0.716283i	$0.254158\pi$
$968$	−113.525	−3.64882
$969$	−7.46231	−0.239724
$970$	71.8092	2.30565
$971$	−58.5134	−1.87778	−0.938892	−	0.344211i	$-0.888147\pi$
$971$	−58.5134	−1.87778	−0.938892	+	0.344211i	$0.888147\pi$
$972$	4.81203	0.154346
$973$	−10.9945	−0.352467
$974$	−88.3555	−2.83109
$975$	−17.5242	−0.561222
$976$	1.02992	0.0329670
$977$	0.264856	0.00847350	0.00423675	−	0.999991i	$-0.498651\pi$
$977$	0.264856	0.00847350	0.00423675	+	0.999991i	$0.498651\pi$
$978$	17.2324	0.551031
$979$	−16.4624	−0.526141
$980$	63.2277	2.01973
$981$	14.9628	0.477727
$982$	39.1649	1.24980
$983$	−29.3955	−0.937569	−0.468785	−	0.883312i	$-0.655308\pi$
$983$	−29.3955	−0.937569	−0.468785	+	0.883312i	$0.655308\pi$
$984$	8.01030	0.255359
$985$	−69.0968	−2.20161
$986$	8.30782	0.264575
$987$	−1.77112	−0.0563752
$988$	−206.946	−6.58383
$989$	11.4962	0.365557
$990$	−38.0756	−1.21012
$991$	51.4409	1.63407	0.817037	−	0.576586i	$-0.195615\pi$
$991$	51.4409	1.63407	0.817037	+	0.576586i	$0.195615\pi$
$992$	−24.8192	−0.788010
$993$	7.59780	0.241109
$994$	−1.45794	−0.0462431
$995$	15.5723	0.493677
$996$	−12.6551	−0.400993
$997$	17.1842	0.544228	0.272114	−	0.962265i	$-0.412277\pi$
$997$	17.1842	0.544228	0.272114	+	0.962265i	$0.412277\pi$
$998$	49.9642	1.58159
$999$	−8.32995	−0.263548

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.e.1.3	✓	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.e.1.3	✓	46	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 8007 = 3 \cdot 17 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8007.a (trivial)

\(f(q)\)	\(=\)	\(q-2.60999 q^{2} +1.00000 q^{3} +4.81203 q^{4} -2.83562 q^{5} -2.60999 q^{6} +1.53827 q^{7} -7.33937 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.60999 q^{2} +1.00000 q^{3} +4.81203 q^{4} -2.83562 q^{5} -2.60999 q^{6} +1.53827 q^{7} -7.33937 q^{8} +1.00000 q^{9} +7.40094 q^{10} -5.14470 q^{11} +4.81203 q^{12} -5.76308 q^{13} -4.01487 q^{14} -2.83562 q^{15} +9.53161 q^{16} -1.00000 q^{17} -2.60999 q^{18} +7.46231 q^{19} -13.6451 q^{20} +1.53827 q^{21} +13.4276 q^{22} +3.10447 q^{23} -7.33937 q^{24} +3.04076 q^{25} +15.0416 q^{26} +1.00000 q^{27} +7.40221 q^{28} +3.18309 q^{29} +7.40094 q^{30} +2.43358 q^{31} -10.1986 q^{32} -5.14470 q^{33} +2.60999 q^{34} -4.36196 q^{35} +4.81203 q^{36} -8.32995 q^{37} -19.4765 q^{38} -5.76308 q^{39} +20.8117 q^{40} -1.09141 q^{41} -4.01487 q^{42} +3.70310 q^{43} -24.7565 q^{44} -2.83562 q^{45} -8.10264 q^{46} -1.15137 q^{47} +9.53161 q^{48} -4.63372 q^{49} -7.93635 q^{50} -1.00000 q^{51} -27.7322 q^{52} -3.51007 q^{53} -2.60999 q^{54} +14.5884 q^{55} -11.2899 q^{56} +7.46231 q^{57} -8.30782 q^{58} +11.8360 q^{59} -13.6451 q^{60} +0.108053 q^{61} -6.35161 q^{62} +1.53827 q^{63} +7.55507 q^{64} +16.3419 q^{65} +13.4276 q^{66} +12.6485 q^{67} -4.81203 q^{68} +3.10447 q^{69} +11.3847 q^{70} +0.363136 q^{71} -7.33937 q^{72} +8.47199 q^{73} +21.7411 q^{74} +3.04076 q^{75} +35.9089 q^{76} -7.91394 q^{77} +15.0416 q^{78} +2.26541 q^{79} -27.0280 q^{80} +1.00000 q^{81} +2.84858 q^{82} -2.62989 q^{83} +7.40221 q^{84} +2.83562 q^{85} -9.66505 q^{86} +3.18309 q^{87} +37.7589 q^{88} +3.19988 q^{89} +7.40094 q^{90} -8.86518 q^{91} +14.9388 q^{92} +2.43358 q^{93} +3.00506 q^{94} -21.1603 q^{95} -10.1986 q^{96} +9.70271 q^{97} +12.0940 q^{98} -5.14470 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q - 5 q^{2} + 46 q^{3} + 43 q^{4} - 19 q^{5} - 5 q^{6} + q^{7} - 18 q^{8} + 46 q^{9}+O(q^{10}) \) 46 * q - 5 * q^2 + 46 * q^3 + 43 * q^4 - 19 * q^5 - 5 * q^6 + q^7 - 18 * q^8 + 46 * q^9	\( 46 q - 5 q^{2} + 46 q^{3} + 43 q^{4} - 19 q^{5} - 5 q^{6} + q^{7} - 18 q^{8} + 46 q^{9} - 10 q^{10} - 25 q^{11} + 43 q^{12} - 8 q^{13} - 28 q^{14} - 19 q^{15} + 33 q^{16} - 46 q^{17} - 5 q^{18} - 2 q^{19} - 56 q^{20} + q^{21} - 19 q^{22} - 64 q^{23} - 18 q^{24} + 11 q^{25} - 13 q^{26} + 46 q^{27} - 38 q^{28} - 51 q^{29} - 10 q^{30} - 19 q^{31} - 61 q^{32} - 25 q^{33} + 5 q^{34} - 39 q^{35} + 43 q^{36} - 46 q^{37} - 48 q^{38} - 8 q^{39} - 10 q^{40} - 53 q^{41} - 28 q^{42} - 33 q^{43} - 62 q^{44} - 19 q^{45} + 2 q^{46} - 45 q^{47} + 33 q^{48} + 21 q^{49} - 60 q^{50} - 46 q^{51} - 63 q^{52} - 47 q^{53} - 5 q^{54} + 5 q^{55} - 82 q^{56} - 2 q^{57} - 21 q^{58} - 65 q^{59} - 56 q^{60} - 37 q^{61} - 46 q^{62} + q^{63} + 74 q^{64} - 85 q^{65} - 19 q^{66} - 52 q^{67} - 43 q^{68} - 64 q^{69} - 20 q^{70} - 48 q^{71} - 18 q^{72} - 39 q^{73} - 16 q^{74} + 11 q^{75} + 42 q^{76} - 78 q^{77} - 13 q^{78} - 26 q^{79} - 78 q^{80} + 46 q^{81} + 3 q^{82} - 47 q^{83} - 38 q^{84} + 19 q^{85} - 6 q^{86} - 51 q^{87} - 58 q^{88} - 58 q^{89} - 10 q^{90} - 43 q^{91} - 68 q^{92} - 19 q^{93} - 78 q^{95} - 61 q^{96} - 44 q^{97} - 4 q^{98} - 25 q^{99}+O(q^{100}) \) 46 * q - 5 * q^2 + 46 * q^3 + 43 * q^4 - 19 * q^5 - 5 * q^6 + q^7 - 18 * q^8 + 46 * q^9 - 10 * q^10 - 25 * q^11 + 43 * q^12 - 8 * q^13 - 28 * q^14 - 19 * q^15 + 33 * q^16 - 46 * q^17 - 5 * q^18 - 2 * q^19 - 56 * q^20 + q^21 - 19 * q^22 - 64 * q^23 - 18 * q^24 + 11 * q^25 - 13 * q^26 + 46 * q^27 - 38 * q^28 - 51 * q^29 - 10 * q^30 - 19 * q^31 - 61 * q^32 - 25 * q^33 + 5 * q^34 - 39 * q^35 + 43 * q^36 - 46 * q^37 - 48 * q^38 - 8 * q^39 - 10 * q^40 - 53 * q^41 - 28 * q^42 - 33 * q^43 - 62 * q^44 - 19 * q^45 + 2 * q^46 - 45 * q^47 + 33 * q^48 + 21 * q^49 - 60 * q^50 - 46 * q^51 - 63 * q^52 - 47 * q^53 - 5 * q^54 + 5 * q^55 - 82 * q^56 - 2 * q^57 - 21 * q^58 - 65 * q^59 - 56 * q^60 - 37 * q^61 - 46 * q^62 + q^63 + 74 * q^64 - 85 * q^65 - 19 * q^66 - 52 * q^67 - 43 * q^68 - 64 * q^69 - 20 * q^70 - 48 * q^71 - 18 * q^72 - 39 * q^73 - 16 * q^74 + 11 * q^75 + 42 * q^76 - 78 * q^77 - 13 * q^78 - 26 * q^79 - 78 * q^80 + 46 * q^81 + 3 * q^82 - 47 * q^83 - 38 * q^84 + 19 * q^85 - 6 * q^86 - 51 * q^87 - 58 * q^88 - 58 * q^89 - 10 * q^90 - 43 * q^91 - 68 * q^92 - 19 * q^93 - 78 * q^95 - 61 * q^96 - 44 * q^97 - 4 * q^98 - 25 * q^99

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