LMFDB - Embedded newform 8007.2.a.f.1.4

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:	$48$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
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)

$f(q)$	$=$	$q-2.46582 q^{2} -1.00000 q^{3} +4.08028 q^{4} +3.93570 q^{5} +2.46582 q^{6} -1.94268 q^{7} -5.12960 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.46582 q^{2} -1.00000 q^{3} +4.08028 q^{4} +3.93570 q^{5} +2.46582 q^{6} -1.94268 q^{7} -5.12960 q^{8} +1.00000 q^{9} -9.70474 q^{10} +2.09500 q^{11} -4.08028 q^{12} +1.26904 q^{13} +4.79030 q^{14} -3.93570 q^{15} +4.48813 q^{16} -1.00000 q^{17} -2.46582 q^{18} +6.20060 q^{19} +16.0588 q^{20} +1.94268 q^{21} -5.16591 q^{22} -3.25118 q^{23} +5.12960 q^{24} +10.4897 q^{25} -3.12923 q^{26} -1.00000 q^{27} -7.92668 q^{28} -0.821135 q^{29} +9.70474 q^{30} -6.07544 q^{31} -0.807730 q^{32} -2.09500 q^{33} +2.46582 q^{34} -7.64580 q^{35} +4.08028 q^{36} -5.69979 q^{37} -15.2896 q^{38} -1.26904 q^{39} -20.1886 q^{40} -5.88604 q^{41} -4.79030 q^{42} -3.21323 q^{43} +8.54820 q^{44} +3.93570 q^{45} +8.01683 q^{46} +6.01116 q^{47} -4.48813 q^{48} -3.22599 q^{49} -25.8658 q^{50} +1.00000 q^{51} +5.17804 q^{52} -12.3838 q^{53} +2.46582 q^{54} +8.24530 q^{55} +9.96518 q^{56} -6.20060 q^{57} +2.02477 q^{58} +1.39896 q^{59} -16.0588 q^{60} -0.577604 q^{61} +14.9810 q^{62} -1.94268 q^{63} -6.98455 q^{64} +4.99456 q^{65} +5.16591 q^{66} +10.3105 q^{67} -4.08028 q^{68} +3.25118 q^{69} +18.8532 q^{70} -8.11871 q^{71} -5.12960 q^{72} -12.1451 q^{73} +14.0547 q^{74} -10.4897 q^{75} +25.3002 q^{76} -4.06992 q^{77} +3.12923 q^{78} +15.1150 q^{79} +17.6639 q^{80} +1.00000 q^{81} +14.5139 q^{82} -14.8563 q^{83} +7.92668 q^{84} -3.93570 q^{85} +7.92326 q^{86} +0.821135 q^{87} -10.7465 q^{88} +9.36477 q^{89} -9.70474 q^{90} -2.46534 q^{91} -13.2657 q^{92} +6.07544 q^{93} -14.8224 q^{94} +24.4037 q^{95} +0.807730 q^{96} -13.6990 q^{97} +7.95473 q^{98} +2.09500 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - q^{2} - 48 q^{3} + 45 q^{4} + q^{5} + q^{6} - 13 q^{7} - 6 q^{8} + 48 q^{9}+O(q^{10}) $ 48 * q - q^2 - 48 * q^3 + 45 * q^4 + q^5 + q^6 - 13 * q^7 - 6 * q^8 + 48 * q^9	\( 48 q - q^{2} - 48 q^{3} + 45 q^{4} + q^{5} + q^{6} - 13 q^{7} - 6 q^{8} + 48 q^{9} - 20 q^{10} + 5 q^{11} - 45 q^{12} - 8 q^{13} + 4 q^{14} - q^{15} + 39 q^{16} - 48 q^{17} - q^{18} - 6 q^{19} + 6 q^{20} + 13 q^{21} - 35 q^{22} - 8 q^{23} + 6 q^{24} + 13 q^{25} + 17 q^{26} - 48 q^{27} - 38 q^{28} + q^{29} + 20 q^{30} - 21 q^{31} - 3 q^{32} - 5 q^{33} + q^{34} + 19 q^{35} + 45 q^{36} - 58 q^{37} - 14 q^{38} + 8 q^{39} - 54 q^{40} - 3 q^{41} - 4 q^{42} - 33 q^{43} + 2 q^{44} + q^{45} - 26 q^{46} + 9 q^{47} - 39 q^{48} + 11 q^{49} + 4 q^{50} + 48 q^{51} - 31 q^{52} - 33 q^{53} + q^{54} - 21 q^{55} + 6 q^{57} - 55 q^{58} + 77 q^{59} - 6 q^{60} - 29 q^{61} - 46 q^{62} - 13 q^{63} + 24 q^{64} - 49 q^{65} + 35 q^{66} - 44 q^{67} - 45 q^{68} + 8 q^{69} + 4 q^{70} + 22 q^{71} - 6 q^{72} - 63 q^{73} - 16 q^{74} - 13 q^{75} - 46 q^{76} - 30 q^{77} - 17 q^{78} - 46 q^{79} - 14 q^{80} + 48 q^{81} - 75 q^{82} + 11 q^{83} + 38 q^{84} - q^{85} + 8 q^{86} - q^{87} - 116 q^{88} + 10 q^{89} - 20 q^{90} - 67 q^{91} - 64 q^{92} + 21 q^{93} - 16 q^{94} - 8 q^{95} + 3 q^{96} - 96 q^{97} - 46 q^{98} + 5 q^{99}+O(q^{100}) \) 48 * q - q^2 - 48 * q^3 + 45 * q^4 + q^5 + q^6 - 13 * q^7 - 6 * q^8 + 48 * q^9 - 20 * q^10 + 5 * q^11 - 45 * q^12 - 8 * q^13 + 4 * q^14 - q^15 + 39 * q^16 - 48 * q^17 - q^18 - 6 * q^19 + 6 * q^20 + 13 * q^21 - 35 * q^22 - 8 * q^23 + 6 * q^24 + 13 * q^25 + 17 * q^26 - 48 * q^27 - 38 * q^28 + q^29 + 20 * q^30 - 21 * q^31 - 3 * q^32 - 5 * q^33 + q^34 + 19 * q^35 + 45 * q^36 - 58 * q^37 - 14 * q^38 + 8 * q^39 - 54 * q^40 - 3 * q^41 - 4 * q^42 - 33 * q^43 + 2 * q^44 + q^45 - 26 * q^46 + 9 * q^47 - 39 * q^48 + 11 * q^49 + 4 * q^50 + 48 * q^51 - 31 * q^52 - 33 * q^53 + q^54 - 21 * q^55 + 6 * q^57 - 55 * q^58 + 77 * q^59 - 6 * q^60 - 29 * q^61 - 46 * q^62 - 13 * q^63 + 24 * q^64 - 49 * q^65 + 35 * q^66 - 44 * q^67 - 45 * q^68 + 8 * q^69 + 4 * q^70 + 22 * q^71 - 6 * q^72 - 63 * q^73 - 16 * q^74 - 13 * q^75 - 46 * q^76 - 30 * q^77 - 17 * q^78 - 46 * q^79 - 14 * q^80 + 48 * q^81 - 75 * q^82 + 11 * q^83 + 38 * q^84 - q^85 + 8 * q^86 - q^87 - 116 * q^88 + 10 * q^89 - 20 * q^90 - 67 * q^91 - 64 * q^92 + 21 * q^93 - 16 * q^94 - 8 * q^95 + 3 * q^96 - 96 * q^97 - 46 * q^98 + 5 * 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 $

$2$	−2.46582	−1.74360	−0.871800	−	0.489862i	$-0.837047\pi$
$2$	−2.46582	−1.74360	−0.871800	+	0.489862i	$0.837047\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.08028	2.04014
$5$	3.93570	1.76010	0.880049	−	0.474883i	$-0.157510\pi$
$5$	3.93570	1.76010	0.880049	+	0.474883i	$0.157510\pi$
$6$	2.46582	1.00667
$7$	−1.94268	−0.734264	−0.367132	−	0.930169i	$-0.619660\pi$
$7$	−1.94268	−0.734264	−0.367132	+	0.930169i	$0.619660\pi$
$8$	−5.12960	−1.81359
$9$	1.00000	0.333333
$10$	−9.70474	−3.06891
$11$	2.09500	0.631667	0.315834	−	0.948815i	$-0.397716\pi$
$11$	2.09500	0.631667	0.315834	+	0.948815i	$0.397716\pi$
$12$	−4.08028	−1.17788
$13$	1.26904	0.351968	0.175984	−	0.984393i	$-0.443689\pi$
$13$	1.26904	0.351968	0.175984	+	0.984393i	$0.443689\pi$
$14$	4.79030	1.28026
$15$	−3.93570	−1.01619
$16$	4.48813	1.12203
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−2.46582	−0.581200
$19$	6.20060	1.42252	0.711258	−	0.702931i	$-0.248126\pi$
$19$	6.20060	1.42252	0.711258	+	0.702931i	$0.248126\pi$
$20$	16.0588	3.59085
$21$	1.94268	0.423928
$22$	−5.16591	−1.10138
$23$	−3.25118	−0.677917	−0.338959	−	0.940801i	$-0.610075\pi$
$23$	−3.25118	−0.677917	−0.338959	+	0.940801i	$0.610075\pi$
$24$	5.12960	1.04708
$25$	10.4897	2.09795
$26$	−3.12923	−0.613692
$27$	−1.00000	−0.192450
$28$	−7.92668	−1.49800
$29$	−0.821135	−0.152481	−0.0762405	−	0.997089i	$-0.524292\pi$
$29$	−0.821135	−0.152481	−0.0762405	+	0.997089i	$0.524292\pi$
$30$	9.70474	1.77183
$31$	−6.07544	−1.09118	−0.545590	−	0.838052i	$-0.683695\pi$
$31$	−6.07544	−1.09118	−0.545590	+	0.838052i	$0.683695\pi$
$32$	−0.807730	−0.142788
$33$	−2.09500	−0.364693
$34$	2.46582	0.422885
$35$	−7.64580	−1.29238
$36$	4.08028	0.680047
$37$	−5.69979	−0.937039	−0.468520	−	0.883453i	$-0.655212\pi$
$37$	−5.69979	−0.937039	−0.468520	+	0.883453i	$0.655212\pi$
$38$	−15.2896	−2.48030
$39$	−1.26904	−0.203209
$40$	−20.1886	−3.19209
$41$	−5.88604	−0.919246	−0.459623	−	0.888114i	$-0.652015\pi$
$41$	−5.88604	−0.919246	−0.459623	+	0.888114i	$0.652015\pi$
$42$	−4.79030	−0.739160
$43$	−3.21323	−0.490013	−0.245007	−	0.969521i	$-0.578790\pi$
$43$	−3.21323	−0.490013	−0.245007	+	0.969521i	$0.578790\pi$
$44$	8.54820	1.28869
$45$	3.93570	0.586699
$46$	8.01683	1.18202
$47$	6.01116	0.876817	0.438409	−	0.898776i	$-0.355542\pi$
$47$	6.01116	0.876817	0.438409	+	0.898776i	$0.355542\pi$
$48$	−4.48813	−0.647806
$49$	−3.22599	−0.460856
$50$	−25.8658	−3.65798
$51$	1.00000	0.140028
$52$	5.17804	0.718065
$53$	−12.3838	−1.70105	−0.850523	−	0.525937i	$-0.823715\pi$
$53$	−12.3838	−1.70105	−0.850523	+	0.525937i	$0.823715\pi$
$54$	2.46582	0.335556
$55$	8.24530	1.11180
$56$	9.96518	1.33165
$57$	−6.20060	−0.821290
$58$	2.02477	0.265866
$59$	1.39896	0.182130	0.0910649	−	0.995845i	$-0.470973\pi$
$59$	1.39896	0.182130	0.0910649	+	0.995845i	$0.470973\pi$
$60$	−16.0588	−2.07318
$61$	−0.577604	−0.0739547	−0.0369773	−	0.999316i	$-0.511773\pi$
$61$	−0.577604	−0.0739547	−0.0369773	+	0.999316i	$0.511773\pi$
$62$	14.9810	1.90258
$63$	−1.94268	−0.244755
$64$	−6.98455	−0.873068
$65$	4.99456	0.619499
$66$	5.16591	0.635879
$67$	10.3105	1.25962	0.629812	−	0.776748i	$-0.283132\pi$
$67$	10.3105	1.25962	0.629812	+	0.776748i	$0.283132\pi$
$68$	−4.08028	−0.494807
$69$	3.25118	0.391396
$70$	18.8532	2.25339
$71$	−8.11871	−0.963514	−0.481757	−	0.876305i	$-0.660001\pi$
$71$	−8.11871	−0.963514	−0.481757	+	0.876305i	$0.660001\pi$
$72$	−5.12960	−0.604530
$73$	−12.1451	−1.42148	−0.710739	−	0.703455i	$-0.751640\pi$
$73$	−12.1451	−1.42148	−0.710739	+	0.703455i	$0.751640\pi$
$74$	14.0547	1.63382
$75$	−10.4897	−1.21125
$76$	25.3002	2.90213
$77$	−4.06992	−0.463811
$78$	3.12923	0.354315
$79$	15.1150	1.70057	0.850284	−	0.526324i	$-0.176430\pi$
$79$	15.1150	1.70057	0.850284	+	0.526324i	$0.176430\pi$
$80$	17.6639	1.97489
$81$	1.00000	0.111111
$82$	14.5139	1.60280
$83$	−14.8563	−1.63069	−0.815344	−	0.578977i	$-0.803452\pi$
$83$	−14.8563	−1.63069	−0.815344	+	0.578977i	$0.803452\pi$
$84$	7.92668	0.864872
$85$	−3.93570	−0.426887
$86$	7.92326	0.854387
$87$	0.821135	0.0880349
$88$	−10.7465	−1.14559
$89$	9.36477	0.992663	0.496332	−	0.868133i	$-0.334680\pi$
$89$	9.36477	0.992663	0.496332	+	0.868133i	$0.334680\pi$
$90$	−9.70474	−1.02297
$91$	−2.46534	−0.258438
$92$	−13.2657	−1.38305
$93$	6.07544	0.629994
$94$	−14.8224	−1.52882
$95$	24.4037	2.50377
$96$	0.807730	0.0824386
$97$	−13.6990	−1.39092	−0.695461	−	0.718564i	$-0.744800\pi$
$97$	−13.6990	−1.39092	−0.695461	+	0.718564i	$0.744800\pi$
$98$	7.95473	0.803549
$99$	2.09500	0.210556
$100$	42.8010	4.28010
$101$	−12.5294	−1.24672	−0.623358	−	0.781936i	$-0.714232\pi$
$101$	−12.5294	−1.24672	−0.623358	+	0.781936i	$0.714232\pi$
$102$	−2.46582	−0.244153
$103$	−4.34464	−0.428090	−0.214045	−	0.976824i	$-0.568664\pi$
$103$	−4.34464	−0.428090	−0.214045	+	0.976824i	$0.568664\pi$
$104$	−6.50967	−0.638326
$105$	7.64580	0.746154
$106$	30.5363	2.96595
$107$	6.34145	0.613051	0.306526	−	0.951862i	$-0.400834\pi$
$107$	6.34145	0.613051	0.306526	+	0.951862i	$0.400834\pi$
$108$	−4.08028	−0.392625
$109$	−0.667254	−0.0639113	−0.0319557	−	0.999489i	$-0.510174\pi$
$109$	−0.667254	−0.0639113	−0.0319557	+	0.999489i	$0.510174\pi$
$110$	−20.3315	−1.93853
$111$	5.69979	0.541000
$112$	−8.71901	−0.823869
$113$	−5.41124	−0.509046	−0.254523	−	0.967067i	$-0.581919\pi$
$113$	−5.41124	−0.509046	−0.254523	+	0.967067i	$0.581919\pi$
$114$	15.2896	1.43200
$115$	−12.7957	−1.19320
$116$	−3.35046	−0.311083
$117$	1.26904	0.117323
$118$	−3.44960	−0.317561
$119$	1.94268	0.178085
$120$	20.1886	1.84296
$121$	−6.61096	−0.600996
$122$	1.42427	0.128947
$123$	5.88604	0.530727
$124$	−24.7895	−2.22616
$125$	21.6059	1.93249
$126$	4.79030	0.426754
$127$	−16.3485	−1.45069	−0.725347	−	0.688383i	$-0.758321\pi$
$127$	−16.3485	−1.45069	−0.725347	+	0.688383i	$0.758321\pi$
$128$	18.8381	1.66507
$129$	3.21323	0.282909
$130$	−12.3157	−1.08016
$131$	3.15110	0.275313	0.137656	−	0.990480i	$-0.456043\pi$
$131$	3.15110	0.275313	0.137656	+	0.990480i	$0.456043\pi$
$132$	−8.54820	−0.744026
$133$	−12.0458	−1.04450
$134$	−25.4238	−2.19628
$135$	−3.93570	−0.338731
$136$	5.12960	0.439860
$137$	6.04604	0.516548	0.258274	−	0.966072i	$-0.416846\pi$
$137$	6.04604	0.516548	0.258274	+	0.966072i	$0.416846\pi$
$138$	−8.01683	−0.682438
$139$	−10.2273	−0.867472	−0.433736	−	0.901040i	$-0.642805\pi$
$139$	−10.2273	−0.867472	−0.433736	+	0.901040i	$0.642805\pi$
$140$	−31.1970	−2.63663
$141$	−6.01116	−0.506231
$142$	20.0193	1.67998
$143$	2.65864	0.222327
$144$	4.48813	0.374011
$145$	−3.23174	−0.268381
$146$	29.9477	2.47849
$147$	3.22599	0.266075
$148$	−23.2567	−1.91169
$149$	−12.8668	−1.05409	−0.527044	−	0.849838i	$-0.676700\pi$
$149$	−12.8668	−1.05409	−0.527044	+	0.849838i	$0.676700\pi$
$150$	25.8658	2.11193
$151$	−1.25253	−0.101929	−0.0509646	−	0.998700i	$-0.516230\pi$
$151$	−1.25253	−0.101929	−0.0509646	+	0.998700i	$0.516230\pi$
$152$	−31.8066	−2.57986
$153$	−1.00000	−0.0808452
$154$	10.0357	0.808700
$155$	−23.9111	−1.92059
$156$	−5.17804	−0.414575
$157$	−1.00000	−0.0798087
$157$	−1.00000	−0.0798087
$158$	−37.2709	−2.96511
$159$	12.3838	0.982100
$160$	−3.17898	−0.251321
$161$	6.31600	0.497770
$162$	−2.46582	−0.193733
$163$	−18.4392	−1.44427	−0.722135	−	0.691752i	$-0.756839\pi$
$163$	−18.4392	−1.44427	−0.722135	+	0.691752i	$0.756839\pi$
$164$	−24.0167	−1.87539
$165$	−8.24530	−0.641896
$166$	36.6329	2.84327
$167$	−15.0426	−1.16403	−0.582016	−	0.813177i	$-0.697736\pi$
$167$	−15.0426	−1.16403	−0.582016	+	0.813177i	$0.697736\pi$
$168$	−9.96518	−0.768830
$169$	−11.3895	−0.876118
$170$	9.70474	0.744319
$171$	6.20060	0.474172
$172$	−13.1109	−0.999696
$173$	8.63339	0.656385	0.328192	−	0.944611i	$-0.393561\pi$
$173$	8.63339	0.656385	0.328192	+	0.944611i	$0.393561\pi$
$174$	−2.02477	−0.153498
$175$	−20.3782	−1.54045
$176$	9.40266	0.708752
$177$	−1.39896	−0.105153
$178$	−23.0919	−1.73081
$179$	22.8232	1.70589	0.852943	−	0.522004i	$-0.174816\pi$
$179$	22.8232	1.70589	0.852943	+	0.522004i	$0.174816\pi$
$180$	16.0588	1.19695
$181$	−5.37203	−0.399300	−0.199650	−	0.979867i	$-0.563980\pi$
$181$	−5.37203	−0.399300	−0.199650	+	0.979867i	$0.563980\pi$
$182$	6.07909	0.450612
$183$	0.577604	0.0426977
$184$	16.6773	1.22946
$185$	−22.4327	−1.64928
$186$	−14.9810	−1.09846
$187$	−2.09500	−0.153202
$188$	24.5272	1.78883
$189$	1.94268	0.141309
$190$	−60.1752	−4.36557
$191$	1.40332	0.101541	0.0507705	−	0.998710i	$-0.483832\pi$
$191$	1.40332	0.101541	0.0507705	+	0.998710i	$0.483832\pi$
$192$	6.98455	0.504066
$193$	−21.2256	−1.52785	−0.763924	−	0.645306i	$-0.776730\pi$
$193$	−21.2256	−1.52785	−0.763924	+	0.645306i	$0.776730\pi$
$194$	33.7793	2.42521
$195$	−4.99456	−0.357668
$196$	−13.1630	−0.940211
$197$	19.9176	1.41907	0.709534	−	0.704672i	$-0.248906\pi$
$197$	19.9176	1.41907	0.709534	+	0.704672i	$0.248906\pi$
$198$	−5.16591	−0.367125
$199$	−24.5012	−1.73684	−0.868420	−	0.495829i	$-0.834864\pi$
$199$	−24.5012	−1.73684	−0.868420	+	0.495829i	$0.834864\pi$
$200$	−53.8082	−3.80481
$201$	−10.3105	−0.727244
$202$	30.8952	2.17378
$203$	1.59520	0.111961
$204$	4.08028	0.285677
$205$	−23.1657	−1.61796
$206$	10.7131	0.746418
$207$	−3.25118	−0.225972
$208$	5.69562	0.394920
$209$	12.9903	0.898557
$210$	−18.8532	−1.30099
$211$	3.88948	0.267763	0.133881	−	0.990997i	$-0.457256\pi$
$211$	3.88948	0.267763	0.133881	+	0.990997i	$0.457256\pi$
$212$	−50.5294	−3.47037
$213$	8.11871	0.556285
$214$	−15.6369	−1.06892
$215$	−12.6463	−0.862471
$216$	5.12960	0.349025
$217$	11.8026	0.801215
$218$	1.64533	0.111436
$219$	12.1451	0.820691
$220$	33.6432	2.26822
$221$	−1.26904	−0.0853649
$222$	−14.0547	−0.943287
$223$	−2.47405	−0.165675	−0.0828373	−	0.996563i	$-0.526398\pi$
$223$	−2.47405	−0.165675	−0.0828373	+	0.996563i	$0.526398\pi$
$224$	1.56916	0.104844
$225$	10.4897	0.699315
$226$	13.3431	0.887573
$227$	−3.58147	−0.237710	−0.118855	−	0.992912i	$-0.537922\pi$
$227$	−3.58147	−0.237710	−0.118855	+	0.992912i	$0.537922\pi$
$228$	−25.3002	−1.67555
$229$	−25.5136	−1.68598	−0.842992	−	0.537926i	$-0.819208\pi$
$229$	−25.5136	−1.68598	−0.842992	+	0.537926i	$0.819208\pi$
$230$	31.5518	2.08046
$231$	4.06992	0.267781
$232$	4.21210	0.276538
$233$	−17.3310	−1.13539	−0.567694	−	0.823239i	$-0.692164\pi$
$233$	−17.3310	−1.13539	−0.567694	+	0.823239i	$0.692164\pi$
$234$	−3.12923	−0.204564
$235$	23.6581	1.54328
$236$	5.70817	0.371570
$237$	−15.1150	−0.981823
$238$	−4.79030	−0.310509
$239$	−1.09864	−0.0710650	−0.0355325	−	0.999369i	$-0.511313\pi$
$239$	−1.09864	−0.0710650	−0.0355325	+	0.999369i	$0.511313\pi$
$240$	−17.6639	−1.14020
$241$	15.8369	1.02014	0.510072	−	0.860132i	$-0.329619\pi$
$241$	15.8369	1.02014	0.510072	+	0.860132i	$0.329619\pi$
$242$	16.3015	1.04790
$243$	−1.00000	−0.0641500
$244$	−2.35679	−0.150878
$245$	−12.6965	−0.811152
$246$	−14.5139	−0.925375
$247$	7.86881	0.500681
$248$	31.1646	1.97895
$249$	14.8563	0.941478
$250$	−53.2764	−3.36949
$251$	13.2834	0.838441	0.419220	−	0.907885i	$-0.362303\pi$
$251$	13.2834	0.838441	0.419220	+	0.907885i	$0.362303\pi$
$252$	−7.92668	−0.499334
$253$	−6.81123	−0.428218
$254$	40.3125	2.52943
$255$	3.93570	0.246463
$256$	−32.4824	−2.03015
$257$	25.5220	1.59202	0.796010	−	0.605284i	$-0.206940\pi$
$257$	25.5220	1.59202	0.796010	+	0.605284i	$0.206940\pi$
$258$	−7.92326	−0.493281
$259$	11.0729	0.688034
$260$	20.3792	1.26386
$261$	−0.821135	−0.0508270
$262$	−7.77005	−0.480035
$263$	−13.7209	−0.846067	−0.423033	−	0.906114i	$-0.639035\pi$
$263$	−13.7209	−0.846067	−0.423033	+	0.906114i	$0.639035\pi$
$264$	10.7465	0.661404
$265$	−48.7389	−2.99401
$266$	29.7028	1.82119
$267$	−9.36477	−0.573114
$268$	42.0696	2.56981
$269$	24.0416	1.46584	0.732922	−	0.680313i	$-0.238156\pi$
$269$	24.0416	1.46584	0.732922	+	0.680313i	$0.238156\pi$
$270$	9.70474	0.590611
$271$	14.7868	0.898237	0.449118	−	0.893472i	$-0.351738\pi$
$271$	14.7868	0.898237	0.449118	+	0.893472i	$0.351738\pi$
$272$	−4.48813	−0.272133
$273$	2.46534	0.149209
$274$	−14.9085	−0.900653
$275$	21.9760	1.32520
$276$	13.2657	0.798502
$277$	3.69899	0.222251	0.111125	−	0.993806i	$-0.464555\pi$
$277$	3.69899	0.222251	0.111125	+	0.993806i	$0.464555\pi$
$278$	25.2188	1.51252
$279$	−6.07544	−0.363727
$280$	39.2200	2.34384
$281$	−5.31177	−0.316873	−0.158437	−	0.987369i	$-0.550645\pi$
$281$	−5.31177	−0.316873	−0.158437	+	0.987369i	$0.550645\pi$
$282$	14.8224	0.882664
$283$	5.29973	0.315036	0.157518	−	0.987516i	$-0.449651\pi$
$283$	5.29973	0.315036	0.157518	+	0.987516i	$0.449651\pi$
$284$	−33.1266	−1.96570
$285$	−24.4037	−1.44555
$286$	−6.55574	−0.387649
$287$	11.4347	0.674969
$288$	−0.807730	−0.0475959
$289$	1.00000	0.0588235
$290$	7.96890	0.467950
$291$	13.6990	0.803049
$292$	−49.5555	−2.90002
$293$	7.19362	0.420256	0.210128	−	0.977674i	$-0.432612\pi$
$293$	7.19362	0.420256	0.210128	+	0.977674i	$0.432612\pi$
$294$	−7.95473	−0.463929
$295$	5.50591	0.320566
$296$	29.2377	1.69940
$297$	−2.09500	−0.121564
$298$	31.7272	1.83791
$299$	−4.12587	−0.238605
$300$	−42.8010	−2.47112
$301$	6.24228	0.359799
$302$	3.08851	0.177724
$303$	12.5294	0.719792
$304$	27.8291	1.59611
$305$	−2.27328	−0.130167
$306$	2.46582	0.140962
$307$	23.9532	1.36708	0.683540	−	0.729913i	$-0.260440\pi$
$307$	23.9532	1.36708	0.683540	+	0.729913i	$0.260440\pi$
$308$	−16.6064	−0.946239
$309$	4.34464	0.247158
$310$	58.9605	3.34873
$311$	−15.8399	−0.898198	−0.449099	−	0.893482i	$-0.648255\pi$
$311$	−15.8399	−0.898198	−0.449099	+	0.893482i	$0.648255\pi$
$312$	6.50967	0.368538
$313$	−17.1781	−0.970966	−0.485483	−	0.874246i	$-0.661356\pi$
$313$	−17.1781	−0.970966	−0.485483	+	0.874246i	$0.661356\pi$
$314$	2.46582	0.139154
$315$	−7.64580	−0.430792
$316$	61.6734	3.46940
$317$	9.30425	0.522579	0.261289	−	0.965261i	$-0.415852\pi$
$317$	9.30425	0.522579	0.261289	+	0.965261i	$0.415852\pi$
$318$	−30.5363	−1.71239
$319$	−1.72028	−0.0963173
$320$	−27.4891	−1.53669
$321$	−6.34145	−0.353945
$322$	−15.5741	−0.867912
$323$	−6.20060	−0.345011
$324$	4.08028	0.226682
$325$	13.3119	0.738410
$326$	45.4678	2.51823
$327$	0.667254	0.0368992
$328$	30.1931	1.66713
$329$	−11.6778	−0.643815
$330$	20.3315	1.11921
$331$	14.6559	0.805559	0.402779	−	0.915297i	$-0.368044\pi$
$331$	14.6559	0.805559	0.402779	+	0.915297i	$0.368044\pi$
$332$	−60.6178	−3.32683
$333$	−5.69979	−0.312346
$334$	37.0924	2.02961
$335$	40.5789	2.21706
$336$	8.71901	0.475661
$337$	−26.1001	−1.42176	−0.710882	−	0.703312i	$-0.751704\pi$
$337$	−26.1001	−1.42176	−0.710882	+	0.703312i	$0.751704\pi$
$338$	28.0846	1.52760
$339$	5.41124	0.293898
$340$	−16.0588	−0.870909
$341$	−12.7281	−0.689263
$342$	−15.2896	−0.826766
$343$	19.8658	1.07265
$344$	16.4826	0.888683
$345$	12.7957	0.688895
$346$	−21.2884	−1.14447
$347$	−17.4252	−0.935435	−0.467717	−	0.883878i	$-0.654923\pi$
$347$	−17.4252	−0.935435	−0.467717	+	0.883878i	$0.654923\pi$
$348$	3.35046	0.179604
$349$	6.91286	0.370037	0.185019	−	0.982735i	$-0.440765\pi$
$349$	6.91286	0.370037	0.185019	+	0.982735i	$0.440765\pi$
$350$	50.2490	2.68592
$351$	−1.26904	−0.0677363
$352$	−1.69220	−0.0901944
$353$	4.07980	0.217146	0.108573	−	0.994089i	$-0.465372\pi$
$353$	4.07980	0.217146	0.108573	+	0.994089i	$0.465372\pi$
$354$	3.44960	0.183344
$355$	−31.9528	−1.69588
$356$	38.2109	2.02517
$357$	−1.94268	−0.102818
$358$	−56.2779	−2.97438
$359$	37.4720	1.97770	0.988849	−	0.148920i	$-0.0475796\pi$
$359$	37.4720	1.97770	0.988849	+	0.148920i	$0.0475796\pi$
$360$	−20.1886	−1.06403
$361$	19.4475	1.02355
$362$	13.2465	0.696219
$363$	6.61096	0.346985
$364$	−10.0593	−0.527249
$365$	−47.7995	−2.50194
$366$	−1.42427	−0.0744478
$367$	−26.3985	−1.37799	−0.688995	−	0.724767i	$-0.741948\pi$
$367$	−26.3985	−1.37799	−0.688995	+	0.724767i	$0.741948\pi$
$368$	−14.5917	−0.760646
$369$	−5.88604	−0.306415
$370$	55.3149	2.87569
$371$	24.0578	1.24902
$372$	24.7895	1.28528
$373$	7.28160	0.377027	0.188513	−	0.982071i	$-0.439633\pi$
$373$	7.28160	0.377027	0.188513	+	0.982071i	$0.439633\pi$
$374$	5.16591	0.267123
$375$	−21.6059	−1.11572
$376$	−30.8349	−1.59019
$377$	−1.04205	−0.0536685
$378$	−4.79030	−0.246387
$379$	15.9189	0.817699	0.408849	−	0.912602i	$-0.365930\pi$
$379$	15.9189	0.817699	0.408849	+	0.912602i	$0.365930\pi$
$380$	99.5740	5.10804
$381$	16.3485	0.837559
$382$	−3.46035	−0.177047
$383$	8.72967	0.446065	0.223033	−	0.974811i	$-0.428404\pi$
$383$	8.72967	0.446065	0.223033	+	0.974811i	$0.428404\pi$
$384$	−18.8381	−0.961328
$385$	−16.0180	−0.816352
$386$	52.3385	2.66396
$387$	−3.21323	−0.163338
$388$	−55.8957	−2.83768
$389$	−10.1002	−0.512100	−0.256050	−	0.966664i	$-0.582421\pi$
$389$	−10.1002	−0.512100	−0.256050	+	0.966664i	$0.582421\pi$
$390$	12.3157	0.623630
$391$	3.25118	0.164419
$392$	16.5481	0.835804
$393$	−3.15110	−0.158952
$394$	−49.1132	−2.47429
$395$	59.4880	2.99317
$396$	8.54820	0.429563
$397$	26.5414	1.33208	0.666038	−	0.745918i	$-0.267989\pi$
$397$	26.5414	1.33208	0.666038	+	0.745918i	$0.267989\pi$
$398$	60.4155	3.02836
$399$	12.0458	0.603044
$400$	47.0793	2.35396
$401$	−23.6062	−1.17884	−0.589419	−	0.807827i	$-0.700643\pi$
$401$	−23.6062	−1.17884	−0.589419	+	0.807827i	$0.700643\pi$
$402$	25.4238	1.26802
$403$	−7.70997	−0.384061
$404$	−51.1233	−2.54348
$405$	3.93570	0.195566
$406$	−3.93349	−0.195216
$407$	−11.9411	−0.591897
$408$	−5.12960	−0.253953
$409$	30.0177	1.48428	0.742141	−	0.670244i	$-0.233811\pi$
$409$	30.0177	1.48428	0.742141	+	0.670244i	$0.233811\pi$
$410$	57.1225	2.82108
$411$	−6.04604	−0.298229
$412$	−17.7274	−0.873364
$413$	−2.71774	−0.133731
$414$	8.01683	0.394005
$415$	−58.4698	−2.87017
$416$	−1.02504	−0.0502568
$417$	10.2273	0.500835
$418$	−32.0318	−1.56672
$419$	27.6615	1.35135	0.675676	−	0.737199i	$-0.263852\pi$
$419$	27.6615	1.35135	0.675676	+	0.737199i	$0.263852\pi$
$420$	31.1970	1.52226
$421$	−23.2516	−1.13321	−0.566607	−	0.823988i	$-0.691744\pi$
$421$	−23.2516	−1.13321	−0.566607	+	0.823988i	$0.691744\pi$
$422$	−9.59076	−0.466871
$423$	6.01116	0.292272
$424$	63.5240	3.08500
$425$	−10.4897	−0.508827
$426$	−20.0193	−0.969939
$427$	1.12210	0.0543022
$428$	25.8749	1.25071
$429$	−2.65864	−0.128361
$430$	31.1836	1.50381
$431$	33.2075	1.59955	0.799775	−	0.600300i	$-0.204952\pi$
$431$	33.2075	1.59955	0.799775	+	0.600300i	$0.204952\pi$
$432$	−4.48813	−0.215935
$433$	−16.8929	−0.811821	−0.405911	−	0.913913i	$-0.633046\pi$
$433$	−16.8929	−0.811821	−0.405911	+	0.913913i	$0.633046\pi$
$434$	−29.1032	−1.39700
$435$	3.23174	0.154950
$436$	−2.72258	−0.130388
$437$	−20.1593	−0.964348
$438$	−29.9477	−1.43096
$439$	15.2542	0.728043	0.364022	−	0.931390i	$-0.381403\pi$
$439$	15.2542	0.728043	0.364022	+	0.931390i	$0.381403\pi$
$440$	−42.2952	−2.01634
$441$	−3.22599	−0.153619
$442$	3.12923	0.148842
$443$	−3.06259	−0.145508	−0.0727539	−	0.997350i	$-0.523179\pi$
$443$	−3.06259	−0.145508	−0.0727539	+	0.997350i	$0.523179\pi$
$444$	23.2567	1.10372
$445$	36.8569	1.74718
$446$	6.10057	0.288870
$447$	12.8668	0.608578
$448$	13.5687	0.641063
$449$	−33.1299	−1.56350	−0.781748	−	0.623594i	$-0.785672\pi$
$449$	−33.1299	−1.56350	−0.781748	+	0.623594i	$0.785672\pi$
$450$	−25.8658	−1.21933
$451$	−12.3313	−0.580658
$452$	−22.0794	−1.03853
$453$	1.25253	0.0588489
$454$	8.83126	0.414471
$455$	−9.70283	−0.454876
$456$	31.8066	1.48948
$457$	0.285102	0.0133365	0.00666826	−	0.999978i	$-0.497877\pi$
$457$	0.285102	0.0133365	0.00666826	+	0.999978i	$0.497877\pi$
$458$	62.9119	2.93968
$459$	1.00000	0.0466760
$460$	−52.2099	−2.43430
$461$	−5.25587	−0.244790	−0.122395	−	0.992481i	$-0.539058\pi$
$461$	−5.25587	−0.244790	−0.122395	+	0.992481i	$0.539058\pi$
$462$	−10.0357	−0.466903
$463$	33.8046	1.57103	0.785517	−	0.618840i	$-0.212397\pi$
$463$	33.8046	1.57103	0.785517	+	0.618840i	$0.212397\pi$
$464$	−3.68536	−0.171089
$465$	23.9111	1.10885
$466$	42.7351	1.97966
$467$	−27.4259	−1.26912	−0.634560	−	0.772874i	$-0.718818\pi$
$467$	−27.4259	−1.26912	−0.634560	+	0.772874i	$0.718818\pi$
$468$	5.17804	0.239355
$469$	−20.0299	−0.924897
$470$	−58.3367	−2.69087
$471$	1.00000	0.0460776
$472$	−7.17614	−0.330308
$473$	−6.73173	−0.309525
$474$	37.2709	1.71191
$475$	65.0426	2.98436
$476$	7.92668	0.363319
$477$	−12.3838	−0.567016
$478$	2.70905	0.123909
$479$	4.87246	0.222628	0.111314	−	0.993785i	$-0.464494\pi$
$479$	4.87246	0.222628	0.111314	+	0.993785i	$0.464494\pi$
$480$	3.17898	0.145100
$481$	−7.23326	−0.329808
$482$	−39.0510	−1.77872
$483$	−6.31600	−0.287388
$484$	−26.9746	−1.22612
$485$	−53.9151	−2.44816
$486$	2.46582	0.111852
$487$	−24.0036	−1.08771	−0.543853	−	0.839181i	$-0.683035\pi$
$487$	−24.0036	−1.08771	−0.543853	+	0.839181i	$0.683035\pi$
$488$	2.96288	0.134123
$489$	18.4392	0.833850
$490$	31.3074	1.41432
$491$	14.5635	0.657242	0.328621	−	0.944462i	$-0.393416\pi$
$491$	14.5635	0.657242	0.328621	+	0.944462i	$0.393416\pi$
$492$	24.0167	1.08276
$493$	0.821135	0.0369821
$494$	−19.4031	−0.872987
$495$	8.24530	0.370599
$496$	−27.2674	−1.22434
$497$	15.7721	0.707474
$498$	−36.6329	−1.64156
$499$	−20.4267	−0.914424	−0.457212	−	0.889358i	$-0.651152\pi$
$499$	−20.4267	−0.914424	−0.457212	+	0.889358i	$0.651152\pi$
$500$	88.1582	3.94256
$501$	15.0426	0.672055
$502$	−32.7545	−1.46191
$503$	12.4664	0.555849	0.277924	−	0.960603i	$-0.410354\pi$
$503$	12.4664	0.555849	0.277924	+	0.960603i	$0.410354\pi$
$504$	9.96518	0.443884
$505$	−49.3118	−2.19434
$506$	16.7953	0.746641
$507$	11.3895	0.505827
$508$	−66.7065	−2.95962
$509$	−5.06355	−0.224438	−0.112219	−	0.993684i	$-0.535796\pi$
$509$	−5.06355	−0.224438	−0.112219	+	0.993684i	$0.535796\pi$
$510$	−9.70474	−0.429733
$511$	23.5941	1.04374
$512$	42.4195	1.87469
$513$	−6.20060	−0.273763
$514$	−62.9328	−2.77584
$515$	−17.0992	−0.753481
$516$	13.1109	0.577175
$517$	12.5934	0.553857
$518$	−27.3037	−1.19966
$519$	−8.63339	−0.378964
$520$	−25.6201	−1.12352
$521$	29.1125	1.27544	0.637721	−	0.770268i	$-0.279877\pi$
$521$	29.1125	1.27544	0.637721	+	0.770268i	$0.279877\pi$
$522$	2.02477	0.0886219
$523$	6.22075	0.272014	0.136007	−	0.990708i	$-0.456573\pi$
$523$	6.22075	0.272014	0.136007	+	0.990708i	$0.456573\pi$
$524$	12.8574	0.561676
$525$	20.3782	0.889377
$526$	33.8333	1.47520
$527$	6.07544	0.264650
$528$	−9.40266	−0.409198
$529$	−12.4298	−0.540428
$530$	120.182	5.22035
$531$	1.39896	0.0607099
$532$	−49.1502	−2.13093
$533$	−7.46962	−0.323545
$534$	23.0919	0.999282
$535$	24.9580	1.07903
$536$	−52.8886	−2.28444
$537$	−22.8232	−0.984894
$538$	−59.2824	−2.55585
$539$	−6.75847	−0.291108
$540$	−16.0588	−0.691059
$541$	−7.22076	−0.310445	−0.155222	−	0.987880i	$-0.549609\pi$
$541$	−7.22076	−0.310445	−0.155222	+	0.987880i	$0.549609\pi$
$542$	−36.4617	−1.56617
$543$	5.37203	0.230536
$544$	0.807730	0.0346311
$545$	−2.62611	−0.112490
$546$	−6.07909	−0.260161
$547$	15.4167	0.659173	0.329586	−	0.944125i	$-0.393091\pi$
$547$	15.4167	0.659173	0.329586	+	0.944125i	$0.393091\pi$
$548$	24.6695	1.05383
$549$	−0.577604	−0.0246516
$550$	−54.1890	−2.31063
$551$	−5.09153	−0.216907
$552$	−16.6773	−0.709831
$553$	−29.3636	−1.24867
$554$	−9.12105	−0.387516
$555$	22.4327	0.952213
$556$	−41.7305	−1.76977
$557$	5.61421	0.237882	0.118941	−	0.992901i	$-0.462050\pi$
$557$	5.61421	0.237882	0.118941	+	0.992901i	$0.462050\pi$
$558$	14.9810	0.634194
$559$	−4.07772	−0.172469
$560$	−34.3154	−1.45009
$561$	2.09500	0.0884511
$562$	13.0979	0.552500
$563$	23.9854	1.01086	0.505431	−	0.862867i	$-0.331333\pi$
$563$	23.9854	1.01086	0.505431	+	0.862867i	$0.331333\pi$
$564$	−24.5272	−1.03278
$565$	−21.2970	−0.895971
$566$	−13.0682	−0.549297
$567$	−1.94268	−0.0815849
$568$	41.6458	1.74742
$569$	32.3260	1.35518	0.677589	−	0.735441i	$-0.263025\pi$
$569$	32.3260	1.35518	0.677589	+	0.735441i	$0.263025\pi$
$570$	60.1752	2.52046
$571$	−25.9609	−1.08643	−0.543215	−	0.839593i	$-0.682793\pi$
$571$	−25.9609	−1.08643	−0.543215	+	0.839593i	$0.682793\pi$
$572$	10.8480	0.453578
$573$	−1.40332	−0.0586247
$574$	−28.1959	−1.17688
$575$	−34.1040	−1.42223
$576$	−6.98455	−0.291023
$577$	11.9944	0.499334	0.249667	−	0.968332i	$-0.419679\pi$
$577$	11.9944	0.499334	0.249667	+	0.968332i	$0.419679\pi$
$578$	−2.46582	−0.102565
$579$	21.2256	0.882104
$580$	−13.1864	−0.547536
$581$	28.8610	1.19736
$582$	−33.7793	−1.40020
$583$	−25.9441	−1.07450
$584$	62.2997	2.57798
$585$	4.99456	0.206500
$586$	−17.7382	−0.732758
$587$	25.1159	1.03665	0.518323	−	0.855185i	$-0.326557\pi$
$587$	25.1159	1.03665	0.518323	+	0.855185i	$0.326557\pi$
$588$	13.1630	0.542831
$589$	−37.6714	−1.55222
$590$	−13.5766	−0.558939
$591$	−19.9176	−0.819299
$592$	−25.5814	−1.05139
$593$	21.3427	0.876438	0.438219	−	0.898868i	$-0.355609\pi$
$593$	21.3427	0.876438	0.438219	+	0.898868i	$0.355609\pi$
$594$	5.16591	0.211960
$595$	7.64580	0.313447
$596$	−52.5001	−2.15049
$597$	24.5012	1.00277
$598$	10.1737	0.416032
$599$	35.9593	1.46926	0.734629	−	0.678469i	$-0.237356\pi$
$599$	35.9593	1.46926	0.734629	+	0.678469i	$0.237356\pi$
$600$	53.8082	2.19671
$601$	−17.8433	−0.727842	−0.363921	−	0.931430i	$-0.618562\pi$
$601$	−17.8433	−0.727842	−0.363921	+	0.931430i	$0.618562\pi$
$602$	−15.3924	−0.627346
$603$	10.3105	0.419875
$604$	−5.11067	−0.207950
$605$	−26.0187	−1.05781
$606$	−30.8952	−1.25503
$607$	42.1682	1.71155	0.855777	−	0.517345i	$-0.173080\pi$
$607$	42.1682	1.71155	0.855777	+	0.517345i	$0.173080\pi$
$608$	−5.00841	−0.203118
$609$	−1.59520	−0.0646409
$610$	5.60550	0.226960
$611$	7.62840	0.308612
$612$	−4.08028	−0.164936
$613$	0.581216	0.0234751	0.0117375	−	0.999931i	$-0.496264\pi$
$613$	0.581216	0.0234751	0.0117375	+	0.999931i	$0.496264\pi$
$614$	−59.0643	−2.38364
$615$	23.1657	0.934131
$616$	20.8771	0.841162
$617$	−39.8146	−1.60288	−0.801438	−	0.598077i	$-0.795931\pi$
$617$	−39.8146	−1.60288	−0.801438	+	0.598077i	$0.795931\pi$
$618$	−10.7131	−0.430945
$619$	−42.6835	−1.71559	−0.857797	−	0.513989i	$-0.828167\pi$
$619$	−42.6835	−1.71559	−0.857797	+	0.513989i	$0.828167\pi$
$620$	−97.5640	−3.91826
$621$	3.25118	0.130465
$622$	39.0584	1.56610
$623$	−18.1927	−0.728877
$624$	−5.69562	−0.228007
$625$	32.5857	1.30343
$626$	42.3583	1.69298
$627$	−12.9903	−0.518782
$628$	−4.08028	−0.162821
$629$	5.69979	0.227265
$630$	18.8532	0.751129
$631$	3.55088	0.141358	0.0706791	−	0.997499i	$-0.477483\pi$
$631$	3.55088	0.141358	0.0706791	+	0.997499i	$0.477483\pi$
$632$	−77.5339	−3.08413
$633$	−3.88948	−0.154593
$634$	−22.9426	−0.911168
$635$	−64.3428	−2.55336
$636$	50.5294	2.00362
$637$	−4.09391	−0.162207
$638$	4.24191	0.167939
$639$	−8.11871	−0.321171
$640$	74.1411	2.93069
$641$	28.4712	1.12454	0.562272	−	0.826952i	$-0.309927\pi$
$641$	28.4712	1.12454	0.562272	+	0.826952i	$0.309927\pi$
$642$	15.6369	0.617139
$643$	−12.7686	−0.503544	−0.251772	−	0.967787i	$-0.581013\pi$
$643$	−12.7686	−0.503544	−0.251772	+	0.967787i	$0.581013\pi$
$644$	25.7710	1.01552
$645$	12.6463	0.497948
$646$	15.2896	0.601561
$647$	16.6629	0.655088	0.327544	−	0.944836i	$-0.393779\pi$
$647$	16.6629	0.655088	0.327544	+	0.944836i	$0.393779\pi$
$648$	−5.12960	−0.201510
$649$	2.93084	0.115045
$650$	−32.8247	−1.28749
$651$	−11.8026	−0.462582
$652$	−75.2372	−2.94652
$653$	20.8416	0.815596	0.407798	−	0.913072i	$-0.366297\pi$
$653$	20.8416	0.815596	0.407798	+	0.913072i	$0.366297\pi$
$654$	−1.64533	−0.0643375
$655$	12.4018	0.484577
$656$	−26.4173	−1.03142
$657$	−12.1451	−0.473826
$658$	28.7953	1.12256
$659$	21.8267	0.850247	0.425124	−	0.905135i	$-0.360231\pi$
$659$	21.8267	0.850247	0.425124	+	0.905135i	$0.360231\pi$
$660$	−33.6432	−1.30956
$661$	−16.0059	−0.622558	−0.311279	−	0.950319i	$-0.600757\pi$
$661$	−16.0059	−0.622558	−0.311279	+	0.950319i	$0.600757\pi$
$662$	−36.1388	−1.40457
$663$	1.26904	0.0492854
$664$	76.2068	2.95740
$665$	−47.4086	−1.83843
$666$	14.0547	0.544607
$667$	2.66966	0.103369
$668$	−61.3781	−2.37479
$669$	2.47405	0.0956523
$670$	−100.060	−3.86567
$671$	−1.21008	−0.0467147
$672$	−1.56916	−0.0605317
$673$	12.3941	0.477758	0.238879	−	0.971049i	$-0.423220\pi$
$673$	12.3941	0.477758	0.238879	+	0.971049i	$0.423220\pi$
$674$	64.3582	2.47899
$675$	−10.4897	−0.403750
$676$	−46.4725	−1.78740
$677$	−39.1474	−1.50456	−0.752278	−	0.658846i	$-0.771045\pi$
$677$	−39.1474	−1.50456	−0.752278	+	0.658846i	$0.771045\pi$
$678$	−13.3431	−0.512441
$679$	26.6127	1.02130
$680$	20.1886	0.774197
$681$	3.58147	0.137242
$682$	31.3852	1.20180
$683$	11.8618	0.453878	0.226939	−	0.973909i	$-0.427128\pi$
$683$	11.8618	0.453878	0.226939	+	0.973909i	$0.427128\pi$
$684$	25.3002	0.967378
$685$	23.7954	0.909175
$686$	−48.9856	−1.87028
$687$	25.5136	0.973404
$688$	−14.4214	−0.549811
$689$	−15.7155	−0.598715
$690$	−31.5518	−1.20116
$691$	−5.90943	−0.224805	−0.112403	−	0.993663i	$-0.535855\pi$
$691$	−5.90943	−0.224805	−0.112403	+	0.993663i	$0.535855\pi$
$692$	35.2267	1.33912
$693$	−4.06992	−0.154604
$694$	42.9675	1.63102
$695$	−40.2518	−1.52684
$696$	−4.21210	−0.159659
$697$	5.88604	0.222950
$698$	−17.0459	−0.645197
$699$	17.3310	0.655517
$700$	−83.1487	−3.14273
$701$	3.44614	0.130159	0.0650794	−	0.997880i	$-0.479270\pi$
$701$	3.44614	0.130159	0.0650794	+	0.997880i	$0.479270\pi$
$702$	3.12923	0.118105
$703$	−35.3421	−1.33295
$704$	−14.6327	−0.551489
$705$	−23.6581	−0.891016
$706$	−10.0601	−0.378615
$707$	24.3405	0.915419
$708$	−5.70817	−0.214526
$709$	−30.8882	−1.16003	−0.580015	−	0.814606i	$-0.696953\pi$
$709$	−30.8882	−1.16003	−0.580015	+	0.814606i	$0.696953\pi$
$710$	78.7900	2.95694
$711$	15.1150	0.566856
$712$	−48.0376	−1.80028
$713$	19.7523	0.739730
$714$	4.79030	0.179273
$715$	10.4636	0.391317
$716$	93.1251	3.48025
$717$	1.09864	0.0410294
$718$	−92.3994	−3.44832
$719$	10.9851	0.409677	0.204838	−	0.978796i	$-0.434333\pi$
$719$	10.9851	0.409677	0.204838	+	0.978796i	$0.434333\pi$
$720$	17.6639	0.658296
$721$	8.44025	0.314331
$722$	−47.9541	−1.78467
$723$	−15.8369	−0.588980
$724$	−21.9194	−0.814628
$725$	−8.61348	−0.319897
$726$	−16.3015	−0.605004
$727$	−39.5232	−1.46583	−0.732916	−	0.680319i	$-0.761841\pi$
$727$	−39.5232	−1.46583	−0.732916	+	0.680319i	$0.761841\pi$
$728$	12.6462	0.468700
$729$	1.00000	0.0370370
$730$	117.865	4.36239
$731$	3.21323	0.118846
$732$	2.35679	0.0871094
$733$	7.05150	0.260453	0.130227	−	0.991484i	$-0.458430\pi$
$733$	7.05150	0.260453	0.130227	+	0.991484i	$0.458430\pi$
$734$	65.0940	2.40266
$735$	12.6965	0.468319
$736$	2.62607	0.0967983
$737$	21.6005	0.795663
$738$	14.5139	0.534266
$739$	−26.3589	−0.969627	−0.484813	−	0.874618i	$-0.661113\pi$
$739$	−26.3589	−0.969627	−0.484813	+	0.874618i	$0.661113\pi$
$740$	−91.5315	−3.36477
$741$	−7.86881	−0.289068
$742$	−59.3222	−2.17779
$743$	−18.9592	−0.695545	−0.347773	−	0.937579i	$-0.613062\pi$
$743$	−18.9592	−0.695545	−0.347773	+	0.937579i	$0.613062\pi$
$744$	−31.1646	−1.14255
$745$	−50.6398	−1.85530
$746$	−17.9551	−0.657384
$747$	−14.8563	−0.543563
$748$	−8.54820	−0.312553
$749$	−12.3194	−0.450141
$750$	53.2764	1.94538
$751$	34.6987	1.26618	0.633088	−	0.774080i	$-0.281787\pi$
$751$	34.6987	1.26618	0.633088	+	0.774080i	$0.281787\pi$
$752$	26.9789	0.983818
$753$	−13.2834	−0.484074
$754$	2.56952	0.0935763
$755$	−4.92957	−0.179406
$756$	7.92668	0.288291
$757$	−6.45257	−0.234523	−0.117261	−	0.993101i	$-0.537412\pi$
$757$	−6.45257	−0.234523	−0.117261	+	0.993101i	$0.537412\pi$
$758$	−39.2532	−1.42574
$759$	6.81123	0.247232
$760$	−125.181	−4.54081
$761$	−7.67557	−0.278239	−0.139120	−	0.990276i	$-0.544427\pi$
$761$	−7.67557	−0.278239	−0.139120	+	0.990276i	$0.544427\pi$
$762$	−40.3125	−1.46037
$763$	1.29626	0.0469278
$764$	5.72596	0.207158
$765$	−3.93570	−0.142296
$766$	−21.5258	−0.777759
$767$	1.77534	0.0641039
$768$	32.4824	1.17211
$769$	54.5833	1.96833	0.984163	−	0.177268i	$-0.0567259\pi$
$769$	54.5833	1.96833	0.984163	+	0.177268i	$0.0567259\pi$
$770$	39.4975	1.42339
$771$	−25.5220	−0.919153
$772$	−86.6062	−3.11703
$773$	−38.0567	−1.36880	−0.684402	−	0.729105i	$-0.739937\pi$
$773$	−38.0567	−1.36880	−0.684402	+	0.729105i	$0.739937\pi$
$774$	7.92326	0.284796
$775$	−63.7297	−2.28924
$776$	70.2704	2.52256
$777$	−11.0729	−0.397237
$778$	24.9053	0.892897
$779$	−36.4970	−1.30764
$780$	−20.3792	−0.729693
$781$	−17.0087	−0.608621
$782$	−8.01683	−0.286681
$783$	0.821135	0.0293450
$784$	−14.4787	−0.517096
$785$	−3.93570	−0.140471
$786$	7.77005	0.277148
$787$	−44.8200	−1.59766	−0.798830	−	0.601557i	$-0.794547\pi$
$787$	−44.8200	−1.59766	−0.798830	+	0.601557i	$0.794547\pi$
$788$	81.2692	2.89510
$789$	13.7209	0.488477
$790$	−146.687	−5.21889
$791$	10.5123	0.373774
$792$	−10.7465	−0.381862
$793$	−0.733003	−0.0260297
$794$	−65.4465	−2.32261
$795$	48.7389	1.72859
$796$	−99.9716	−3.54340
$797$	−4.98944	−0.176735	−0.0883675	−	0.996088i	$-0.528165\pi$
$797$	−4.98944	−0.176735	−0.0883675	+	0.996088i	$0.528165\pi$
$798$	−29.7028	−1.05147
$799$	−6.01116	−0.212659
$800$	−8.47286	−0.299561
$801$	9.36477	0.330888
$802$	58.2087	2.05542
$803$	−25.4441	−0.897902
$804$	−42.0696	−1.48368
$805$	24.8579	0.876125
$806$	19.0114	0.669649
$807$	−24.0416	−0.846305
$808$	64.2706	2.26103
$809$	−18.0208	−0.633576	−0.316788	−	0.948496i	$-0.602604\pi$
$809$	−18.0208	−0.633576	−0.316788	+	0.948496i	$0.602604\pi$
$810$	−9.70474	−0.340990
$811$	−28.4350	−0.998486	−0.499243	−	0.866462i	$-0.666389\pi$
$811$	−28.4350	−0.998486	−0.499243	+	0.866462i	$0.666389\pi$
$812$	6.50888	0.228417
$813$	−14.7868	−0.518597
$814$	29.4446	1.03203
$815$	−72.5712	−2.54206
$816$	4.48813	0.157116
$817$	−19.9240	−0.697052
$818$	−74.0184	−2.58799
$819$	−2.46534	−0.0861459
$820$	−94.5226	−3.30087
$821$	−19.3232	−0.674384	−0.337192	−	0.941436i	$-0.609477\pi$
$821$	−19.3232	−0.674384	−0.337192	+	0.941436i	$0.609477\pi$
$822$	14.9085	0.519992
$823$	52.8260	1.84140	0.920699	−	0.390273i	$-0.127619\pi$
$823$	52.8260	1.84140	0.920699	+	0.390273i	$0.127619\pi$
$824$	22.2863	0.776380
$825$	−21.9760	−0.765107
$826$	6.70147	0.233174
$827$	−46.0677	−1.60193	−0.800966	−	0.598710i	$-0.795680\pi$
$827$	−46.0677	−1.60193	−0.800966	+	0.598710i	$0.795680\pi$
$828$	−13.2657	−0.461016
$829$	0.186629	0.00648190	0.00324095	−	0.999995i	$-0.498968\pi$
$829$	0.186629	0.00648190	0.00324095	+	0.999995i	$0.498968\pi$
$830$	144.176	5.00443
$831$	−3.69899	−0.128316
$832$	−8.86367	−0.307292
$833$	3.22599	0.111774
$834$	−25.2188	−0.873256
$835$	−59.2032	−2.04881
$836$	53.0040	1.83318
$837$	6.07544	0.209998
$838$	−68.2083	−2.35622
$839$	20.0225	0.691255	0.345627	−	0.938372i	$-0.387666\pi$
$839$	20.0225	0.691255	0.345627	+	0.938372i	$0.387666\pi$
$840$	−39.2200	−1.35322
$841$	−28.3257	−0.976750
$842$	57.3344	1.97587
$843$	5.31177	0.182947
$844$	15.8702	0.546273
$845$	−44.8258	−1.54205
$846$	−14.8224	−0.509606
$847$	12.8430	0.441290
$848$	−55.5802	−1.90863
$849$	−5.29973	−0.181886
$850$	25.8658	0.887190
$851$	18.5310	0.635235
$852$	33.1266	1.13490
$853$	−12.8222	−0.439025	−0.219513	−	0.975610i	$-0.570447\pi$
$853$	−12.8222	−0.439025	−0.219513	+	0.975610i	$0.570447\pi$
$854$	−2.76690	−0.0946814
$855$	24.4037	0.834589
$856$	−32.5291	−1.11182
$857$	−1.72140	−0.0588019	−0.0294010	−	0.999568i	$-0.509360\pi$
$857$	−1.72140	−0.0588019	−0.0294010	+	0.999568i	$0.509360\pi$
$858$	6.55574	0.223809
$859$	7.52678	0.256810	0.128405	−	0.991722i	$-0.459014\pi$
$859$	7.52678	0.256810	0.128405	+	0.991722i	$0.459014\pi$
$860$	−51.6005	−1.75956
$861$	−11.4347	−0.389694
$862$	−81.8838	−2.78897
$863$	−57.4116	−1.95431	−0.977157	−	0.212517i	$-0.931834\pi$
$863$	−57.4116	−1.95431	−0.977157	+	0.212517i	$0.931834\pi$
$864$	0.807730	0.0274795
$865$	33.9784	1.15530
$866$	41.6549	1.41549
$867$	−1.00000	−0.0339618
$868$	48.1581	1.63459
$869$	31.6659	1.07419
$870$	−7.96890	−0.270171
$871$	13.0844	0.443348
$872$	3.42275	0.115909
$873$	−13.6990	−0.463640
$874$	49.7092	1.68144
$875$	−41.9734	−1.41896
$876$	49.5555	1.67433
$877$	23.6136	0.797375	0.398687	−	0.917087i	$-0.369466\pi$
$877$	23.6136	0.797375	0.398687	+	0.917087i	$0.369466\pi$
$878$	−37.6142	−1.26942
$879$	−7.19362	−0.242635
$880$	37.0060	1.24747
$881$	−28.2491	−0.951736	−0.475868	−	0.879517i	$-0.657866\pi$
$881$	−28.2491	−0.951736	−0.475868	+	0.879517i	$0.657866\pi$
$882$	7.95473	0.267850
$883$	14.9807	0.504142	0.252071	−	0.967709i	$-0.418888\pi$
$883$	14.9807	0.504142	0.252071	+	0.967709i	$0.418888\pi$
$884$	−5.17804	−0.174156
$885$	−5.50591	−0.185079
$886$	7.55179	0.253707
$887$	52.4711	1.76181	0.880903	−	0.473297i	$-0.156936\pi$
$887$	52.4711	1.76181	0.880903	+	0.473297i	$0.156936\pi$
$888$	−29.2377	−0.981152
$889$	31.7599	1.06519
$890$	−90.8826	−3.04639
$891$	2.09500	0.0701853
$892$	−10.0948	−0.338000
$893$	37.2728	1.24729
$894$	−31.7272	−1.06112
$895$	89.8252	3.00253
$896$	−36.5964	−1.22260
$897$	4.12587	0.137759
$898$	81.6924	2.72611
$899$	4.98875	0.166384
$900$	42.8010	1.42670
$901$	12.3838	0.412564
$902$	30.4068	1.01243
$903$	−6.24228	−0.207730
$904$	27.7575	0.923201
$905$	−21.1427	−0.702807
$906$	−3.08851	−0.102609
$907$	−1.65676	−0.0550117	−0.0275059	−	0.999622i	$-0.508756\pi$
$907$	−1.65676	−0.0550117	−0.0275059	+	0.999622i	$0.508756\pi$
$908$	−14.6134	−0.484962
$909$	−12.5294	−0.415572
$910$	23.9255	0.793121
$911$	−3.39647	−0.112530	−0.0562651	−	0.998416i	$-0.517919\pi$
$911$	−3.39647	−0.112530	−0.0562651	+	0.998416i	$0.517919\pi$
$912$	−27.8291	−0.921515
$913$	−31.1240	−1.03005
$914$	−0.703011	−0.0232535
$915$	2.27328	0.0751522
$916$	−104.103	−3.43965
$917$	−6.12157	−0.202152
$918$	−2.46582	−0.0813843
$919$	4.41358	0.145591	0.0727954	−	0.997347i	$-0.476808\pi$
$919$	4.41358	0.145591	0.0727954	+	0.997347i	$0.476808\pi$
$920$	65.6366	2.16398
$921$	−23.9532	−0.789284
$922$	12.9601	0.426817
$923$	−10.3030	−0.339126
$924$	16.6064	0.546311
$925$	−59.7892	−1.96586
$926$	−83.3562	−2.73926
$927$	−4.34464	−0.142697
$928$	0.663255	0.0217724
$929$	−6.46101	−0.211979	−0.105990	−	0.994367i	$-0.533801\pi$
$929$	−6.46101	−0.211979	−0.105990	+	0.994367i	$0.533801\pi$
$930$	−58.9605	−1.93339
$931$	−20.0031	−0.655575
$932$	−70.7152	−2.31635
$933$	15.8399	0.518575
$934$	67.6274	2.21284
$935$	−8.24530	−0.269650
$936$	−6.50967	−0.212775
$937$	−58.0645	−1.89689	−0.948443	−	0.316948i	$-0.897342\pi$
$937$	−58.0645	−1.89689	−0.948443	+	0.316948i	$0.897342\pi$
$938$	49.3903	1.61265
$939$	17.1781	0.560588
$940$	96.5317	3.14852
$941$	9.28817	0.302786	0.151393	−	0.988474i	$-0.451624\pi$
$941$	9.28817	0.302786	0.151393	+	0.988474i	$0.451624\pi$
$942$	−2.46582	−0.0803408
$943$	19.1366	0.623172
$944$	6.27874	0.204356
$945$	7.64580	0.248718
$946$	16.5993	0.539688
$947$	−44.6439	−1.45073	−0.725365	−	0.688364i	$-0.758329\pi$
$947$	−44.6439	−1.45073	−0.725365	+	0.688364i	$0.758329\pi$
$948$	−61.6734	−2.00306
$949$	−15.4126	−0.500316
$950$	−160.384	−5.20353
$951$	−9.30425	−0.301711
$952$	−9.96518	−0.322973
$953$	40.4899	1.31160	0.655799	−	0.754936i	$-0.272332\pi$
$953$	40.4899	1.31160	0.655799	+	0.754936i	$0.272332\pi$
$954$	30.5363	0.988648
$955$	5.52306	0.178722
$956$	−4.48275	−0.144983
$957$	1.72028	0.0556088
$958$	−12.0146	−0.388175
$959$	−11.7455	−0.379283
$960$	27.4891	0.887206
$961$	5.91094	0.190676
$962$	17.8359	0.575053
$963$	6.34145	0.204350
$964$	64.6189	2.08124
$965$	−83.5374	−2.68916
$966$	15.5741	0.501089
$967$	−21.5682	−0.693586	−0.346793	−	0.937942i	$-0.612729\pi$
$967$	−21.5682	−0.693586	−0.346793	+	0.937942i	$0.612729\pi$
$968$	33.9116	1.08996
$969$	6.20060	0.199192
$970$	132.945	4.26861
$971$	−46.8893	−1.50475	−0.752374	−	0.658736i	$-0.771092\pi$
$971$	−46.8893	−1.50475	−0.752374	+	0.658736i	$0.771092\pi$
$972$	−4.08028	−0.130875
$973$	19.8685	0.636954
$974$	59.1886	1.89652
$975$	−13.3119	−0.426321
$976$	−2.59236	−0.0829796
$977$	−3.52393	−0.112741	−0.0563703	−	0.998410i	$-0.517953\pi$
$977$	−3.52393	−0.112741	−0.0563703	+	0.998410i	$0.517953\pi$
$978$	−45.4678	−1.45390
$979$	19.6192	0.627033
$980$	−51.8055	−1.65486
$981$	−0.667254	−0.0213038
$982$	−35.9110	−1.14597
$983$	18.8358	0.600770	0.300385	−	0.953818i	$-0.402885\pi$
$983$	18.8358	0.600770	0.300385	+	0.953818i	$0.402885\pi$
$984$	−30.1931	−0.962520
$985$	78.3895	2.49770
$986$	−2.02477	−0.0644819
$987$	11.6778	0.371707
$988$	32.1070	1.02146
$989$	10.4468	0.332188
$990$	−20.3315	−0.646176
$991$	1.08870	0.0345838	0.0172919	−	0.999850i	$-0.494496\pi$
$991$	1.08870	0.0345838	0.0172919	+	0.999850i	$0.494496\pi$
$992$	4.90731	0.155807
$993$	−14.6559	−0.465090
$994$	−38.8911	−1.23355
$995$	−96.4292	−3.05701
$996$	60.6178	1.92075
$997$	−20.2724	−0.642034	−0.321017	−	0.947073i	$-0.604025\pi$
$997$	−20.2724	−0.642034	−0.321017	+	0.947073i	$0.604025\pi$
$998$	50.3686	1.59439
$999$	5.69979	0.180333

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.f.1.4	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.f.1.4	✓	48	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)

\(f(q)\)	\(=\)	\(q-2.46582 q^{2} -1.00000 q^{3} +4.08028 q^{4} +3.93570 q^{5} +2.46582 q^{6} -1.94268 q^{7} -5.12960 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.46582 q^{2} -1.00000 q^{3} +4.08028 q^{4} +3.93570 q^{5} +2.46582 q^{6} -1.94268 q^{7} -5.12960 q^{8} +1.00000 q^{9} -9.70474 q^{10} +2.09500 q^{11} -4.08028 q^{12} +1.26904 q^{13} +4.79030 q^{14} -3.93570 q^{15} +4.48813 q^{16} -1.00000 q^{17} -2.46582 q^{18} +6.20060 q^{19} +16.0588 q^{20} +1.94268 q^{21} -5.16591 q^{22} -3.25118 q^{23} +5.12960 q^{24} +10.4897 q^{25} -3.12923 q^{26} -1.00000 q^{27} -7.92668 q^{28} -0.821135 q^{29} +9.70474 q^{30} -6.07544 q^{31} -0.807730 q^{32} -2.09500 q^{33} +2.46582 q^{34} -7.64580 q^{35} +4.08028 q^{36} -5.69979 q^{37} -15.2896 q^{38} -1.26904 q^{39} -20.1886 q^{40} -5.88604 q^{41} -4.79030 q^{42} -3.21323 q^{43} +8.54820 q^{44} +3.93570 q^{45} +8.01683 q^{46} +6.01116 q^{47} -4.48813 q^{48} -3.22599 q^{49} -25.8658 q^{50} +1.00000 q^{51} +5.17804 q^{52} -12.3838 q^{53} +2.46582 q^{54} +8.24530 q^{55} +9.96518 q^{56} -6.20060 q^{57} +2.02477 q^{58} +1.39896 q^{59} -16.0588 q^{60} -0.577604 q^{61} +14.9810 q^{62} -1.94268 q^{63} -6.98455 q^{64} +4.99456 q^{65} +5.16591 q^{66} +10.3105 q^{67} -4.08028 q^{68} +3.25118 q^{69} +18.8532 q^{70} -8.11871 q^{71} -5.12960 q^{72} -12.1451 q^{73} +14.0547 q^{74} -10.4897 q^{75} +25.3002 q^{76} -4.06992 q^{77} +3.12923 q^{78} +15.1150 q^{79} +17.6639 q^{80} +1.00000 q^{81} +14.5139 q^{82} -14.8563 q^{83} +7.92668 q^{84} -3.93570 q^{85} +7.92326 q^{86} +0.821135 q^{87} -10.7465 q^{88} +9.36477 q^{89} -9.70474 q^{90} -2.46534 q^{91} -13.2657 q^{92} +6.07544 q^{93} -14.8224 q^{94} +24.4037 q^{95} +0.807730 q^{96} -13.6990 q^{97} +7.95473 q^{98} +2.09500 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - q^{2} - 48 q^{3} + 45 q^{4} + q^{5} + q^{6} - 13 q^{7} - 6 q^{8} + 48 q^{9}+O(q^{10}) \) 48 * q - q^2 - 48 * q^3 + 45 * q^4 + q^5 + q^6 - 13 * q^7 - 6 * q^8 + 48 * q^9	\( 48 q - q^{2} - 48 q^{3} + 45 q^{4} + q^{5} + q^{6} - 13 q^{7} - 6 q^{8} + 48 q^{9} - 20 q^{10} + 5 q^{11} - 45 q^{12} - 8 q^{13} + 4 q^{14} - q^{15} + 39 q^{16} - 48 q^{17} - q^{18} - 6 q^{19} + 6 q^{20} + 13 q^{21} - 35 q^{22} - 8 q^{23} + 6 q^{24} + 13 q^{25} + 17 q^{26} - 48 q^{27} - 38 q^{28} + q^{29} + 20 q^{30} - 21 q^{31} - 3 q^{32} - 5 q^{33} + q^{34} + 19 q^{35} + 45 q^{36} - 58 q^{37} - 14 q^{38} + 8 q^{39} - 54 q^{40} - 3 q^{41} - 4 q^{42} - 33 q^{43} + 2 q^{44} + q^{45} - 26 q^{46} + 9 q^{47} - 39 q^{48} + 11 q^{49} + 4 q^{50} + 48 q^{51} - 31 q^{52} - 33 q^{53} + q^{54} - 21 q^{55} + 6 q^{57} - 55 q^{58} + 77 q^{59} - 6 q^{60} - 29 q^{61} - 46 q^{62} - 13 q^{63} + 24 q^{64} - 49 q^{65} + 35 q^{66} - 44 q^{67} - 45 q^{68} + 8 q^{69} + 4 q^{70} + 22 q^{71} - 6 q^{72} - 63 q^{73} - 16 q^{74} - 13 q^{75} - 46 q^{76} - 30 q^{77} - 17 q^{78} - 46 q^{79} - 14 q^{80} + 48 q^{81} - 75 q^{82} + 11 q^{83} + 38 q^{84} - q^{85} + 8 q^{86} - q^{87} - 116 q^{88} + 10 q^{89} - 20 q^{90} - 67 q^{91} - 64 q^{92} + 21 q^{93} - 16 q^{94} - 8 q^{95} + 3 q^{96} - 96 q^{97} - 46 q^{98} + 5 q^{99}+O(q^{100}) \) 48 * q - q^2 - 48 * q^3 + 45 * q^4 + q^5 + q^6 - 13 * q^7 - 6 * q^8 + 48 * q^9 - 20 * q^10 + 5 * q^11 - 45 * q^12 - 8 * q^13 + 4 * q^14 - q^15 + 39 * q^16 - 48 * q^17 - q^18 - 6 * q^19 + 6 * q^20 + 13 * q^21 - 35 * q^22 - 8 * q^23 + 6 * q^24 + 13 * q^25 + 17 * q^26 - 48 * q^27 - 38 * q^28 + q^29 + 20 * q^30 - 21 * q^31 - 3 * q^32 - 5 * q^33 + q^34 + 19 * q^35 + 45 * q^36 - 58 * q^37 - 14 * q^38 + 8 * q^39 - 54 * q^40 - 3 * q^41 - 4 * q^42 - 33 * q^43 + 2 * q^44 + q^45 - 26 * q^46 + 9 * q^47 - 39 * q^48 + 11 * q^49 + 4 * q^50 + 48 * q^51 - 31 * q^52 - 33 * q^53 + q^54 - 21 * q^55 + 6 * q^57 - 55 * q^58 + 77 * q^59 - 6 * q^60 - 29 * q^61 - 46 * q^62 - 13 * q^63 + 24 * q^64 - 49 * q^65 + 35 * q^66 - 44 * q^67 - 45 * q^68 + 8 * q^69 + 4 * q^70 + 22 * q^71 - 6 * q^72 - 63 * q^73 - 16 * q^74 - 13 * q^75 - 46 * q^76 - 30 * q^77 - 17 * q^78 - 46 * q^79 - 14 * q^80 + 48 * q^81 - 75 * q^82 + 11 * q^83 + 38 * q^84 - q^85 + 8 * q^86 - q^87 - 116 * q^88 + 10 * q^89 - 20 * q^90 - 67 * q^91 - 64 * q^92 + 21 * q^93 - 16 * q^94 - 8 * q^95 + 3 * q^96 - 96 * q^97 - 46 * q^98 + 5 * q^99

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