LMFDB - Embedded newform 8007.2.a.d.1.14

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:	$40$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
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)

$f(q)$	$=$	$q-1.21037 q^{2} +1.00000 q^{3} -0.535004 q^{4} +3.43189 q^{5} -1.21037 q^{6} -1.42621 q^{7} +3.06829 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.21037 q^{2} +1.00000 q^{3} -0.535004 q^{4} +3.43189 q^{5} -1.21037 q^{6} -1.42621 q^{7} +3.06829 q^{8} +1.00000 q^{9} -4.15386 q^{10} -1.95164 q^{11} -0.535004 q^{12} -3.29089 q^{13} +1.72624 q^{14} +3.43189 q^{15} -2.64376 q^{16} +1.00000 q^{17} -1.21037 q^{18} +3.41080 q^{19} -1.83608 q^{20} -1.42621 q^{21} +2.36220 q^{22} -1.65236 q^{23} +3.06829 q^{24} +6.77790 q^{25} +3.98320 q^{26} +1.00000 q^{27} +0.763028 q^{28} +2.34426 q^{29} -4.15386 q^{30} -4.87786 q^{31} -2.93666 q^{32} -1.95164 q^{33} -1.21037 q^{34} -4.89460 q^{35} -0.535004 q^{36} -6.59756 q^{37} -4.12833 q^{38} -3.29089 q^{39} +10.5301 q^{40} +1.81668 q^{41} +1.72624 q^{42} -9.49474 q^{43} +1.04413 q^{44} +3.43189 q^{45} +1.99997 q^{46} +6.95480 q^{47} -2.64376 q^{48} -4.96593 q^{49} -8.20376 q^{50} +1.00000 q^{51} +1.76064 q^{52} -10.2048 q^{53} -1.21037 q^{54} -6.69781 q^{55} -4.37603 q^{56} +3.41080 q^{57} -2.83743 q^{58} -1.88202 q^{59} -1.83608 q^{60} -10.7989 q^{61} +5.90401 q^{62} -1.42621 q^{63} +8.84196 q^{64} -11.2940 q^{65} +2.36220 q^{66} -3.62737 q^{67} -0.535004 q^{68} -1.65236 q^{69} +5.92428 q^{70} +14.7855 q^{71} +3.06829 q^{72} +14.0835 q^{73} +7.98549 q^{74} +6.77790 q^{75} -1.82479 q^{76} +2.78344 q^{77} +3.98320 q^{78} +1.07179 q^{79} -9.07311 q^{80} +1.00000 q^{81} -2.19885 q^{82} +3.40432 q^{83} +0.763028 q^{84} +3.43189 q^{85} +11.4921 q^{86} +2.34426 q^{87} -5.98819 q^{88} +13.1116 q^{89} -4.15386 q^{90} +4.69350 q^{91} +0.884021 q^{92} -4.87786 q^{93} -8.41789 q^{94} +11.7055 q^{95} -2.93666 q^{96} -12.7262 q^{97} +6.01061 q^{98} -1.95164 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 7 q^{2} + 40 q^{3} + 29 q^{4} - 15 q^{5} - 7 q^{6} - 13 q^{7} - 18 q^{8} + 40 q^{9}+O(q^{10}) $ 40 * q - 7 * q^2 + 40 * q^3 + 29 * q^4 - 15 * q^5 - 7 * q^6 - 13 * q^7 - 18 * q^8 + 40 * q^9	\( 40 q - 7 q^{2} + 40 q^{3} + 29 q^{4} - 15 q^{5} - 7 q^{6} - 13 q^{7} - 18 q^{8} + 40 q^{9} - 6 q^{10} - 25 q^{11} + 29 q^{12} - 24 q^{13} - 22 q^{14} - 15 q^{15} + 7 q^{16} + 40 q^{17} - 7 q^{18} - 18 q^{19} - 20 q^{20} - 13 q^{21} - 25 q^{22} - 28 q^{23} - 18 q^{24} - 11 q^{25} - 13 q^{26} + 40 q^{27} - 8 q^{28} - 23 q^{29} - 6 q^{30} - 11 q^{31} - 23 q^{32} - 25 q^{33} - 7 q^{34} - 45 q^{35} + 29 q^{36} - 38 q^{37} - 30 q^{38} - 24 q^{39} - 12 q^{40} - 33 q^{41} - 22 q^{42} - 25 q^{43} - 14 q^{44} - 15 q^{45} + 8 q^{46} - 55 q^{47} + 7 q^{48} - 21 q^{49} + 2 q^{50} + 40 q^{51} - 39 q^{52} - 39 q^{53} - 7 q^{54} - 9 q^{55} - 48 q^{56} - 18 q^{57} - 13 q^{58} - 81 q^{59} - 20 q^{60} - 9 q^{61} - 16 q^{62} - 13 q^{63} - 4 q^{64} - 43 q^{65} - 25 q^{66} - 24 q^{67} + 29 q^{68} - 28 q^{69} + 48 q^{70} - 32 q^{71} - 18 q^{72} - 43 q^{73} - 20 q^{74} - 11 q^{75} - 58 q^{76} - 32 q^{77} - 13 q^{78} - 22 q^{79} - 48 q^{80} + 40 q^{81} - 11 q^{82} - 45 q^{83} - 8 q^{84} - 15 q^{85} - 30 q^{86} - 23 q^{87} - 48 q^{88} - 94 q^{89} - 6 q^{90} - 7 q^{91} - 98 q^{92} - 11 q^{93} + 32 q^{94} - 23 q^{96} - 28 q^{97} - 46 q^{98} - 25 q^{99}+O(q^{100}) \) 40 * q - 7 * q^2 + 40 * q^3 + 29 * q^4 - 15 * q^5 - 7 * q^6 - 13 * q^7 - 18 * q^8 + 40 * q^9 - 6 * q^10 - 25 * q^11 + 29 * q^12 - 24 * q^13 - 22 * q^14 - 15 * q^15 + 7 * q^16 + 40 * q^17 - 7 * q^18 - 18 * q^19 - 20 * q^20 - 13 * q^21 - 25 * q^22 - 28 * q^23 - 18 * q^24 - 11 * q^25 - 13 * q^26 + 40 * q^27 - 8 * q^28 - 23 * q^29 - 6 * q^30 - 11 * q^31 - 23 * q^32 - 25 * q^33 - 7 * q^34 - 45 * q^35 + 29 * q^36 - 38 * q^37 - 30 * q^38 - 24 * q^39 - 12 * q^40 - 33 * q^41 - 22 * q^42 - 25 * q^43 - 14 * q^44 - 15 * q^45 + 8 * q^46 - 55 * q^47 + 7 * q^48 - 21 * q^49 + 2 * q^50 + 40 * q^51 - 39 * q^52 - 39 * q^53 - 7 * q^54 - 9 * q^55 - 48 * q^56 - 18 * q^57 - 13 * q^58 - 81 * q^59 - 20 * q^60 - 9 * q^61 - 16 * q^62 - 13 * q^63 - 4 * q^64 - 43 * q^65 - 25 * q^66 - 24 * q^67 + 29 * q^68 - 28 * q^69 + 48 * q^70 - 32 * q^71 - 18 * q^72 - 43 * q^73 - 20 * q^74 - 11 * q^75 - 58 * q^76 - 32 * q^77 - 13 * q^78 - 22 * q^79 - 48 * q^80 + 40 * q^81 - 11 * q^82 - 45 * q^83 - 8 * q^84 - 15 * q^85 - 30 * q^86 - 23 * q^87 - 48 * q^88 - 94 * q^89 - 6 * q^90 - 7 * q^91 - 98 * q^92 - 11 * q^93 + 32 * q^94 - 23 * q^96 - 28 * q^97 - 46 * 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 $

$2$	−1.21037	−0.855861	−0.427930	−	0.903812i	$-0.640757\pi$
$2$	−1.21037	−0.855861	−0.427930	+	0.903812i	$0.640757\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.535004	−0.267502
$5$	3.43189	1.53479	0.767395	−	0.641175i	$-0.221553\pi$
$5$	3.43189	1.53479	0.767395	+	0.641175i	$0.221553\pi$
$6$	−1.21037	−0.494132
$7$	−1.42621	−0.539056	−0.269528	−	0.962992i	$-0.586868\pi$
$7$	−1.42621	−0.539056	−0.269528	+	0.962992i	$0.586868\pi$
$8$	3.06829	1.08481
$9$	1.00000	0.333333
$10$	−4.15386	−1.31357
$11$	−1.95164	−0.588440	−0.294220	−	0.955738i	$-0.595060\pi$
$11$	−1.95164	−0.588440	−0.294220	+	0.955738i	$0.595060\pi$
$12$	−0.535004	−0.154442
$13$	−3.29089	−0.912729	−0.456365	−	0.889793i	$-0.650849\pi$
$13$	−3.29089	−0.912729	−0.456365	+	0.889793i	$0.650849\pi$
$14$	1.72624	0.461357
$15$	3.43189	0.886111
$16$	−2.64376	−0.660940
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.21037	−0.285287
$19$	3.41080	0.782492	0.391246	−	0.920286i	$-0.372044\pi$
$19$	3.41080	0.782492	0.391246	+	0.920286i	$0.372044\pi$
$20$	−1.83608	−0.410560
$21$	−1.42621	−0.311224
$22$	2.36220	0.503623
$23$	−1.65236	−0.344541	−0.172271	−	0.985050i	$-0.555110\pi$
$23$	−1.65236	−0.344541	−0.172271	+	0.985050i	$0.555110\pi$
$24$	3.06829	0.626313
$25$	6.77790	1.35558
$26$	3.98320	0.781169
$27$	1.00000	0.192450
$28$	0.763028	0.144199
$29$	2.34426	0.435319	0.217660	−	0.976025i	$-0.430158\pi$
$29$	2.34426	0.435319	0.217660	+	0.976025i	$0.430158\pi$
$30$	−4.15386	−0.758388
$31$	−4.87786	−0.876089	−0.438044	−	0.898953i	$-0.644329\pi$
$31$	−4.87786	−0.876089	−0.438044	+	0.898953i	$0.644329\pi$
$32$	−2.93666	−0.519132
$33$	−1.95164	−0.339736
$34$	−1.21037	−0.207577
$35$	−4.89460	−0.827338
$36$	−0.535004	−0.0891674
$37$	−6.59756	−1.08463	−0.542316	−	0.840174i	$-0.682453\pi$
$37$	−6.59756	−1.08463	−0.542316	+	0.840174i	$0.682453\pi$
$38$	−4.12833	−0.669704
$39$	−3.29089	−0.526964
$40$	10.5301	1.66495
$41$	1.81668	0.283717	0.141859	−	0.989887i	$-0.454692\pi$
$41$	1.81668	0.283717	0.141859	+	0.989887i	$0.454692\pi$
$42$	1.72624	0.266365
$43$	−9.49474	−1.44793	−0.723967	−	0.689835i	$-0.757683\pi$
$43$	−9.49474	−1.44793	−0.723967	+	0.689835i	$0.757683\pi$
$44$	1.04413	0.157409
$45$	3.43189	0.511597
$46$	1.99997	0.294879
$47$	6.95480	1.01446	0.507231	−	0.861810i	$-0.330669\pi$
$47$	6.95480	1.01446	0.507231	+	0.861810i	$0.330669\pi$
$48$	−2.64376	−0.381594
$49$	−4.96593	−0.709418
$50$	−8.20376	−1.16019
$51$	1.00000	0.140028
$52$	1.76064	0.244157
$53$	−10.2048	−1.40173	−0.700867	−	0.713292i	$-0.747203\pi$
$53$	−10.2048	−1.40173	−0.700867	+	0.713292i	$0.747203\pi$
$54$	−1.21037	−0.164711
$55$	−6.69781	−0.903132
$56$	−4.37603	−0.584771
$57$	3.41080	0.451772
$58$	−2.83743	−0.372573
$59$	−1.88202	−0.245018	−0.122509	−	0.992467i	$-0.539094\pi$
$59$	−1.88202	−0.245018	−0.122509	+	0.992467i	$0.539094\pi$
$60$	−1.83608	−0.237037
$61$	−10.7989	−1.38266	−0.691330	−	0.722540i	$-0.742975\pi$
$61$	−10.7989	−1.38266	−0.691330	+	0.722540i	$0.742975\pi$
$62$	5.90401	0.749810
$63$	−1.42621	−0.179685
$64$	8.84196	1.10525
$65$	−11.2940	−1.40085
$66$	2.36220	0.290767
$67$	−3.62737	−0.443154	−0.221577	−	0.975143i	$-0.571120\pi$
$67$	−3.62737	−0.443154	−0.221577	+	0.975143i	$0.571120\pi$
$68$	−0.535004	−0.0648788
$69$	−1.65236	−0.198921
$70$	5.92428	0.708086
$71$	14.7855	1.75472	0.877359	−	0.479835i	$-0.159303\pi$
$71$	14.7855	1.75472	0.877359	+	0.479835i	$0.159303\pi$
$72$	3.06829	0.361602
$73$	14.0835	1.64834	0.824172	−	0.566339i	$-0.191641\pi$
$73$	14.0835	1.64834	0.824172	+	0.566339i	$0.191641\pi$
$74$	7.98549	0.928295
$75$	6.77790	0.782644
$76$	−1.82479	−0.209318
$77$	2.78344	0.317203
$78$	3.98320	0.451008
$79$	1.07179	0.120586	0.0602928	−	0.998181i	$-0.480797\pi$
$79$	1.07179	0.120586	0.0602928	+	0.998181i	$0.480797\pi$
$80$	−9.07311	−1.01440
$81$	1.00000	0.111111
$82$	−2.19885	−0.242822
$83$	3.40432	0.373672	0.186836	−	0.982391i	$-0.440177\pi$
$83$	3.40432	0.373672	0.186836	+	0.982391i	$0.440177\pi$
$84$	0.763028	0.0832532
$85$	3.43189	0.372241
$86$	11.4921	1.23923
$87$	2.34426	0.251332
$88$	−5.98819	−0.638343
$89$	13.1116	1.38982	0.694912	−	0.719095i	$-0.255443\pi$
$89$	13.1116	1.38982	0.694912	+	0.719095i	$0.255443\pi$
$90$	−4.15386	−0.437855
$91$	4.69350	0.492013
$92$	0.884021	0.0921656
$93$	−4.87786	−0.505810
$94$	−8.41789	−0.868239
$95$	11.7055	1.20096
$96$	−2.93666	−0.299721
$97$	−12.7262	−1.29215	−0.646073	−	0.763275i	$-0.723590\pi$
$97$	−12.7262	−1.29215	−0.646073	+	0.763275i	$0.723590\pi$
$98$	6.01061	0.607163
$99$	−1.95164	−0.196147
$100$	−3.62620	−0.362620
$101$	0.218206	0.0217124	0.0108562	−	0.999941i	$-0.496544\pi$
$101$	0.218206	0.0217124	0.0108562	+	0.999941i	$0.496544\pi$
$102$	−1.21037	−0.119844
$103$	−10.1769	−1.00276	−0.501382	−	0.865226i	$-0.667175\pi$
$103$	−10.1769	−1.00276	−0.501382	+	0.865226i	$0.667175\pi$
$104$	−10.0974	−0.990134
$105$	−4.89460	−0.477664
$106$	12.3516	1.19969
$107$	−2.62532	−0.253799	−0.126899	−	0.991916i	$-0.540503\pi$
$107$	−2.62532	−0.253799	−0.126899	+	0.991916i	$0.540503\pi$
$108$	−0.535004	−0.0514808
$109$	−19.9894	−1.91464	−0.957321	−	0.289028i	$-0.906668\pi$
$109$	−19.9894	−1.91464	−0.957321	+	0.289028i	$0.906668\pi$
$110$	8.10683	0.772956
$111$	−6.59756	−0.626213
$112$	3.77056	0.356284
$113$	0.468968	0.0441168	0.0220584	−	0.999757i	$-0.492978\pi$
$113$	0.468968	0.0441168	0.0220584	+	0.999757i	$0.492978\pi$
$114$	−4.12833	−0.386654
$115$	−5.67073	−0.528799
$116$	−1.25419	−0.116449
$117$	−3.29089	−0.304243
$118$	2.27794	0.209701
$119$	−1.42621	−0.130740
$120$	10.5301	0.961258
$121$	−7.19112	−0.653738
$122$	13.0707	1.18336
$123$	1.81668	0.163804
$124$	2.60967	0.234356
$125$	6.10156	0.545740
$126$	1.72624	0.153786
$127$	−2.63765	−0.234054	−0.117027	−	0.993129i	$-0.537336\pi$
$127$	−2.63765	−0.234054	−0.117027	+	0.993129i	$0.537336\pi$
$128$	−4.82874	−0.426804
$129$	−9.49474	−0.835965
$130$	13.6699	1.19893
$131$	−4.45526	−0.389258	−0.194629	−	0.980877i	$-0.562350\pi$
$131$	−4.45526	−0.389258	−0.194629	+	0.980877i	$0.562350\pi$
$132$	1.04413	0.0908802
$133$	−4.86452	−0.421807
$134$	4.39046	0.379278
$135$	3.43189	0.295370
$136$	3.06829	0.263104
$137$	4.74311	0.405231	0.202616	−	0.979258i	$-0.435056\pi$
$137$	4.74311	0.405231	0.202616	+	0.979258i	$0.435056\pi$
$138$	1.99997	0.170249
$139$	−4.89570	−0.415248	−0.207624	−	0.978209i	$-0.566573\pi$
$139$	−4.89570	−0.415248	−0.207624	+	0.978209i	$0.566573\pi$
$140$	2.61863	0.221315
$141$	6.95480	0.585700
$142$	−17.8959	−1.50179
$143$	6.42262	0.537087
$144$	−2.64376	−0.220313
$145$	8.04527	0.668123
$146$	−17.0462	−1.41075
$147$	−4.96593	−0.409583
$148$	3.52973	0.290142
$149$	−4.41068	−0.361337	−0.180669	−	0.983544i	$-0.557826\pi$
$149$	−4.41068	−0.361337	−0.180669	+	0.983544i	$0.557826\pi$
$150$	−8.20376	−0.669835
$151$	−0.135411	−0.0110196	−0.00550981	−	0.999985i	$-0.501754\pi$
$151$	−0.135411	−0.0110196	−0.00550981	+	0.999985i	$0.501754\pi$
$152$	10.4653	0.848852
$153$	1.00000	0.0808452
$154$	−3.36899	−0.271481
$155$	−16.7403	−1.34461
$156$	1.76064	0.140964
$157$	−1.00000	−0.0798087
$157$	−1.00000	−0.0798087
$158$	−1.29726	−0.103205
$159$	−10.2048	−0.809291
$160$	−10.0783	−0.796759
$161$	2.35661	0.185727
$162$	−1.21037	−0.0950957
$163$	−21.8971	−1.71511	−0.857556	−	0.514391i	$-0.828018\pi$
$163$	−21.8971	−1.71511	−0.857556	+	0.514391i	$0.828018\pi$
$164$	−0.971929	−0.0758949
$165$	−6.69781	−0.521424
$166$	−4.12048	−0.319811
$167$	−17.5656	−1.35927	−0.679634	−	0.733551i	$-0.737861\pi$
$167$	−17.5656	−1.35927	−0.679634	+	0.733551i	$0.737861\pi$
$168$	−4.37603	−0.337618
$169$	−2.17003	−0.166925
$170$	−4.15386	−0.318587
$171$	3.41080	0.260831
$172$	5.07973	0.387325
$173$	10.9191	0.830162	0.415081	−	0.909784i	$-0.363753\pi$
$173$	10.9191	0.830162	0.415081	+	0.909784i	$0.363753\pi$
$174$	−2.83743	−0.215105
$175$	−9.66670	−0.730734
$176$	5.15966	0.388924
$177$	−1.88202	−0.141461
$178$	−15.8699	−1.18950
$179$	−10.2734	−0.767871	−0.383936	−	0.923360i	$-0.625432\pi$
$179$	−10.2734	−0.767871	−0.383936	+	0.923360i	$0.625432\pi$
$180$	−1.83608	−0.136853
$181$	−2.39955	−0.178357	−0.0891787	−	0.996016i	$-0.528424\pi$
$181$	−2.39955	−0.178357	−0.0891787	+	0.996016i	$0.528424\pi$
$182$	−5.68087	−0.421094
$183$	−10.7989	−0.798279
$184$	−5.06993	−0.373760
$185$	−22.6421	−1.66468
$186$	5.90401	0.432903
$187$	−1.95164	−0.142718
$188$	−3.72085	−0.271371
$189$	−1.42621	−0.103741
$190$	−14.1680	−1.02786
$191$	11.6347	0.841859	0.420929	−	0.907093i	$-0.361704\pi$
$191$	11.6347	0.841859	0.420929	+	0.907093i	$0.361704\pi$
$192$	8.84196	0.638114
$193$	−17.5262	−1.26156	−0.630780	−	0.775962i	$-0.717265\pi$
$193$	−17.5262	−1.26156	−0.630780	+	0.775962i	$0.717265\pi$
$194$	15.4034	1.10590
$195$	−11.2940	−0.808780
$196$	2.65679	0.189771
$197$	−11.5675	−0.824147	−0.412074	−	0.911151i	$-0.635195\pi$
$197$	−11.5675	−0.824147	−0.412074	+	0.911151i	$0.635195\pi$
$198$	2.36220	0.167874
$199$	10.7585	0.762647	0.381323	−	0.924442i	$-0.375468\pi$
$199$	10.7585	0.762647	0.381323	+	0.924442i	$0.375468\pi$
$200$	20.7966	1.47054
$201$	−3.62737	−0.255855
$202$	−0.264111	−0.0185828
$203$	−3.34341	−0.234662
$204$	−0.535004	−0.0374578
$205$	6.23464	0.435446
$206$	12.3179	0.858226
$207$	−1.65236	−0.114847
$208$	8.70033	0.603260
$209$	−6.65665	−0.460450
$210$	5.92428	0.408814
$211$	13.6639	0.940660	0.470330	−	0.882491i	$-0.344135\pi$
$211$	13.6639	0.940660	0.470330	+	0.882491i	$0.344135\pi$
$212$	5.45960	0.374967
$213$	14.7855	1.01309
$214$	3.17760	0.217217
$215$	−32.5849	−2.22227
$216$	3.06829	0.208771
$217$	6.95684	0.472261
$218$	24.1946	1.63867
$219$	14.0835	0.951672
$220$	3.58336	0.241590
$221$	−3.29089	−0.221369
$222$	7.98549	0.535951
$223$	2.54287	0.170283	0.0851414	−	0.996369i	$-0.472866\pi$
$223$	2.54287	0.170283	0.0851414	+	0.996369i	$0.472866\pi$
$224$	4.18829	0.279842
$225$	6.77790	0.451860
$226$	−0.567625	−0.0377578
$227$	7.17845	0.476451	0.238225	−	0.971210i	$-0.423434\pi$
$227$	7.17845	0.476451	0.238225	+	0.971210i	$0.423434\pi$
$228$	−1.82479	−0.120850
$229$	−0.577952	−0.0381922	−0.0190961	−	0.999818i	$-0.506079\pi$
$229$	−0.577952	−0.0381922	−0.0190961	+	0.999818i	$0.506079\pi$
$230$	6.86369	0.452578
$231$	2.78344	0.183137
$232$	7.19289	0.472237
$233$	−10.6849	−0.699993	−0.349997	−	0.936751i	$-0.613817\pi$
$233$	−10.6849	−0.699993	−0.349997	+	0.936751i	$0.613817\pi$
$234$	3.98320	0.260390
$235$	23.8681	1.55699
$236$	1.00689	0.0655429
$237$	1.07179	0.0696202
$238$	1.72624	0.111896
$239$	6.05363	0.391576	0.195788	−	0.980646i	$-0.437273\pi$
$239$	6.05363	0.391576	0.195788	+	0.980646i	$0.437273\pi$
$240$	−9.07311	−0.585667
$241$	1.78394	0.114914	0.0574569	−	0.998348i	$-0.481701\pi$
$241$	1.78394	0.114914	0.0574569	+	0.998348i	$0.481701\pi$
$242$	8.70391	0.559509
$243$	1.00000	0.0641500
$244$	5.77747	0.369864
$245$	−17.0425	−1.08881
$246$	−2.19885	−0.140194
$247$	−11.2246	−0.714203
$248$	−14.9667	−0.950386
$249$	3.40432	0.215740
$250$	−7.38514	−0.467077
$251$	10.1997	0.643802	0.321901	−	0.946773i	$-0.395678\pi$
$251$	10.1997	0.643802	0.321901	+	0.946773i	$0.395678\pi$
$252$	0.763028	0.0480663
$253$	3.22481	0.202742
$254$	3.19254	0.200318
$255$	3.43189	0.214914
$256$	−11.8394	−0.739961
$257$	−21.5809	−1.34618	−0.673090	−	0.739560i	$-0.735033\pi$
$257$	−21.5809	−1.34618	−0.673090	+	0.739560i	$0.735033\pi$
$258$	11.4921	0.715470
$259$	9.40951	0.584678
$260$	6.04234	0.374730
$261$	2.34426	0.145106
$262$	5.39251	0.333151
$263$	−11.0200	−0.679523	−0.339762	−	0.940512i	$-0.610346\pi$
$263$	−11.0200	−0.679523	−0.339762	+	0.940512i	$0.610346\pi$
$264$	−5.98819	−0.368548
$265$	−35.0217	−2.15137
$266$	5.88787	0.361008
$267$	13.1116	0.802416
$268$	1.94066	0.118545
$269$	24.6422	1.50246	0.751230	−	0.660040i	$-0.229461\pi$
$269$	24.6422	1.50246	0.751230	+	0.660040i	$0.229461\pi$
$270$	−4.15386	−0.252796
$271$	21.4112	1.30064	0.650318	−	0.759662i	$-0.274636\pi$
$271$	21.4112	1.30064	0.650318	+	0.759662i	$0.274636\pi$
$272$	−2.64376	−0.160302
$273$	4.69350	0.284064
$274$	−5.74092	−0.346822
$275$	−13.2280	−0.797678
$276$	0.884021	0.0532118
$277$	12.9512	0.778164	0.389082	−	0.921203i	$-0.372792\pi$
$277$	12.9512	0.778164	0.389082	+	0.921203i	$0.372792\pi$
$278$	5.92561	0.355395
$279$	−4.87786	−0.292030
$280$	−15.0181	−0.897501
$281$	−12.0793	−0.720590	−0.360295	−	0.932838i	$-0.617324\pi$
$281$	−12.0793	−0.720590	−0.360295	+	0.932838i	$0.617324\pi$
$282$	−8.41789	−0.501278
$283$	8.41392	0.500156	0.250078	−	0.968226i	$-0.419544\pi$
$283$	8.41392	0.500156	0.250078	+	0.968226i	$0.419544\pi$
$284$	−7.91031	−0.469391
$285$	11.7055	0.693375
$286$	−7.77375	−0.459672
$287$	−2.59096	−0.152940
$288$	−2.93666	−0.173044
$289$	1.00000	0.0588235
$290$	−9.73775	−0.571821
$291$	−12.7262	−0.746021
$292$	−7.53471	−0.440936
$293$	10.5988	0.619188	0.309594	−	0.950869i	$-0.399807\pi$
$293$	10.5988	0.619188	0.309594	+	0.950869i	$0.399807\pi$
$294$	6.01061	0.350546
$295$	−6.45889	−0.376051
$296$	−20.2433	−1.17662
$297$	−1.95164	−0.113245
$298$	5.33856	0.309254
$299$	5.43775	0.314473
$300$	−3.62620	−0.209359
$301$	13.5415	0.780518
$302$	0.163898	0.00943127
$303$	0.218206	0.0125356
$304$	−9.01735	−0.517181
$305$	−37.0607	−2.12209
$306$	−1.21037	−0.0691923
$307$	6.43562	0.367300	0.183650	−	0.982992i	$-0.441209\pi$
$307$	6.43562	0.367300	0.183650	+	0.982992i	$0.441209\pi$
$308$	−1.48915	−0.0848524
$309$	−10.1769	−0.578946
$310$	20.2619	1.15080
$311$	5.41539	0.307079	0.153539	−	0.988143i	$-0.450933\pi$
$311$	5.41539	0.307079	0.153539	+	0.988143i	$0.450933\pi$
$312$	−10.0974	−0.571654
$313$	−26.2659	−1.48463	−0.742317	−	0.670049i	$-0.766273\pi$
$313$	−26.2659	−1.48463	−0.742317	+	0.670049i	$0.766273\pi$
$314$	1.21037	0.0683051
$315$	−4.89460	−0.275779
$316$	−0.573412	−0.0322569
$317$	5.87324	0.329874	0.164937	−	0.986304i	$-0.447258\pi$
$317$	5.87324	0.329874	0.164937	+	0.986304i	$0.447258\pi$
$318$	12.3516	0.692641
$319$	−4.57515	−0.256159
$320$	30.3447	1.69632
$321$	−2.62532	−0.146531
$322$	−2.85238	−0.158957
$323$	3.41080	0.189782
$324$	−0.535004	−0.0297225
$325$	−22.3053	−1.23728
$326$	26.5036	1.46790
$327$	−19.9894	−1.10542
$328$	5.57409	0.307778
$329$	−9.91900	−0.546852
$330$	8.10683	0.446266
$331$	13.9331	0.765834	0.382917	−	0.923783i	$-0.374920\pi$
$331$	13.9331	0.765834	0.382917	+	0.923783i	$0.374920\pi$
$332$	−1.82132	−0.0999581
$333$	−6.59756	−0.361544
$334$	21.2609	1.16334
$335$	−12.4487	−0.680148
$336$	3.77056	0.205701
$337$	18.7245	1.01999	0.509994	−	0.860178i	$-0.329648\pi$
$337$	18.7245	1.01999	0.509994	+	0.860178i	$0.329648\pi$
$338$	2.62654	0.142865
$339$	0.468968	0.0254708
$340$	−1.83608	−0.0995753
$341$	9.51980	0.515526
$342$	−4.12833	−0.223235
$343$	17.0659	0.921473
$344$	−29.1326	−1.57073
$345$	−5.67073	−0.305302
$346$	−13.2161	−0.710504
$347$	28.4983	1.52987	0.764935	−	0.644107i	$-0.222771\pi$
$347$	28.4983	1.52987	0.764935	+	0.644107i	$0.222771\pi$
$348$	−1.25419	−0.0672317
$349$	0.291525	0.0156050	0.00780248	−	0.999970i	$-0.497516\pi$
$349$	0.291525	0.0156050	0.00780248	+	0.999970i	$0.497516\pi$
$350$	11.7003	0.625406
$351$	−3.29089	−0.175655
$352$	5.73128	0.305479
$353$	1.52051	0.0809285	0.0404642	−	0.999181i	$-0.487116\pi$
$353$	1.52051	0.0809285	0.0404642	+	0.999181i	$0.487116\pi$
$354$	2.27794	0.121071
$355$	50.7423	2.69312
$356$	−7.01475	−0.371781
$357$	−1.42621	−0.0754830
$358$	12.4346	0.657191
$359$	−4.21797	−0.222616	−0.111308	−	0.993786i	$-0.535504\pi$
$359$	−4.21797	−0.222616	−0.111308	+	0.993786i	$0.535504\pi$
$360$	10.5301	0.554983
$361$	−7.36642	−0.387706
$362$	2.90435	0.152649
$363$	−7.19112	−0.377436
$364$	−2.51104	−0.131614
$365$	48.3330	2.52986
$366$	13.0707	0.683215
$367$	10.9120	0.569601	0.284801	−	0.958587i	$-0.408073\pi$
$367$	10.9120	0.569601	0.284801	+	0.958587i	$0.408073\pi$
$368$	4.36845	0.227721
$369$	1.81668	0.0945724
$370$	27.4054	1.42474
$371$	14.5541	0.755613
$372$	2.60967	0.135305
$373$	−7.13563	−0.369469	−0.184735	−	0.982788i	$-0.559143\pi$
$373$	−7.13563	−0.369469	−0.184735	+	0.982788i	$0.559143\pi$
$374$	2.36220	0.122147
$375$	6.10156	0.315083
$376$	21.3394	1.10049
$377$	−7.71472	−0.397328
$378$	1.72624	0.0887882
$379$	−33.7542	−1.73384	−0.866919	−	0.498448i	$-0.833903\pi$
$379$	−33.7542	−1.73384	−0.866919	+	0.498448i	$0.833903\pi$
$380$	−6.26250	−0.321260
$381$	−2.63765	−0.135131
$382$	−14.0823	−0.720514
$383$	−17.5757	−0.898077	−0.449038	−	0.893512i	$-0.648233\pi$
$383$	−17.5757	−0.898077	−0.449038	+	0.893512i	$0.648233\pi$
$384$	−4.82874	−0.246415
$385$	9.55248	0.486839
$386$	21.2131	1.07972
$387$	−9.49474	−0.482645
$388$	6.80856	0.345652
$389$	4.98233	0.252614	0.126307	−	0.991991i	$-0.459688\pi$
$389$	4.98233	0.252614	0.126307	+	0.991991i	$0.459688\pi$
$390$	13.6699	0.692203
$391$	−1.65236	−0.0835636
$392$	−15.2369	−0.769581
$393$	−4.45526	−0.224738
$394$	14.0009	0.705355
$395$	3.67827	0.185074
$396$	1.04413	0.0524697
$397$	−16.9879	−0.852599	−0.426299	−	0.904582i	$-0.640183\pi$
$397$	−16.9879	−0.852599	−0.426299	+	0.904582i	$0.640183\pi$
$398$	−13.0217	−0.652720
$399$	−4.86452	−0.243531
$400$	−17.9191	−0.895957
$401$	12.0444	0.601470	0.300735	−	0.953708i	$-0.402768\pi$
$401$	12.0444	0.601470	0.300735	+	0.953708i	$0.402768\pi$
$402$	4.39046	0.218976
$403$	16.0525	0.799632
$404$	−0.116741	−0.00580810
$405$	3.43189	0.170532
$406$	4.04677	0.200838
$407$	12.8760	0.638242
$408$	3.06829	0.151903
$409$	−34.5163	−1.70672	−0.853361	−	0.521321i	$-0.825440\pi$
$409$	−34.5163	−1.70672	−0.853361	+	0.521321i	$0.825440\pi$
$410$	−7.54622	−0.372681
$411$	4.74311	0.233960
$412$	5.44471	0.268242
$413$	2.68415	0.132079
$414$	1.99997	0.0982932
$415$	11.6833	0.573508
$416$	9.66422	0.473827
$417$	−4.89570	−0.239744
$418$	8.05701	0.394081
$419$	−24.4101	−1.19251	−0.596257	−	0.802794i	$-0.703346\pi$
$419$	−24.4101	−1.19251	−0.596257	+	0.802794i	$0.703346\pi$
$420$	2.61863	0.127776
$421$	27.5707	1.34371	0.671856	−	0.740682i	$-0.265497\pi$
$421$	27.5707	1.34371	0.671856	+	0.740682i	$0.265497\pi$
$422$	−16.5383	−0.805074
$423$	6.95480	0.338154
$424$	−31.3112	−1.52061
$425$	6.77790	0.328776
$426$	−17.8959	−0.867061
$427$	15.4015	0.745331
$428$	1.40456	0.0678917
$429$	6.42262	0.310087
$430$	39.4398	1.90196
$431$	7.33535	0.353332	0.176666	−	0.984271i	$-0.443469\pi$
$431$	7.33535	0.353332	0.176666	+	0.984271i	$0.443469\pi$
$432$	−2.64376	−0.127198
$433$	5.95158	0.286015	0.143007	−	0.989722i	$-0.454323\pi$
$433$	5.95158	0.286015	0.143007	+	0.989722i	$0.454323\pi$
$434$	−8.42035	−0.404190
$435$	8.04527	0.385741
$436$	10.6944	0.512171
$437$	−5.63588	−0.269601
$438$	−17.0462	−0.814499
$439$	6.10046	0.291159	0.145580	−	0.989347i	$-0.453495\pi$
$439$	6.10046	0.291159	0.145580	+	0.989347i	$0.453495\pi$
$440$	−20.5508	−0.979723
$441$	−4.96593	−0.236473
$442$	3.98320	0.189461
$443$	38.1130	1.81080	0.905401	−	0.424558i	$-0.139571\pi$
$443$	38.1130	1.81080	0.905401	+	0.424558i	$0.139571\pi$
$444$	3.52973	0.167513
$445$	44.9976	2.13309
$446$	−3.07781	−0.145738
$447$	−4.41068	−0.208618
$448$	−12.6105	−0.595790
$449$	−18.6583	−0.880538	−0.440269	−	0.897866i	$-0.645117\pi$
$449$	−18.6583	−0.880538	−0.440269	+	0.897866i	$0.645117\pi$
$450$	−8.20376	−0.386729
$451$	−3.54549	−0.166951
$452$	−0.250900	−0.0118013
$453$	−0.135411	−0.00636218
$454$	−8.68858	−0.407775
$455$	16.1076	0.755136
$456$	10.4653	0.490085
$457$	−33.6773	−1.57536	−0.787678	−	0.616088i	$-0.788717\pi$
$457$	−33.6773	−1.57536	−0.787678	+	0.616088i	$0.788717\pi$
$458$	0.699536	0.0326872
$459$	1.00000	0.0466760
$460$	3.03387	0.141455
$461$	−21.0108	−0.978569	−0.489284	−	0.872124i	$-0.662742\pi$
$461$	−21.0108	−0.978569	−0.489284	+	0.872124i	$0.662742\pi$
$462$	−3.36899	−0.156740
$463$	−11.6903	−0.543293	−0.271646	−	0.962397i	$-0.587568\pi$
$463$	−11.6903	−0.543293	−0.271646	+	0.962397i	$0.587568\pi$
$464$	−6.19768	−0.287720
$465$	−16.7403	−0.776312
$466$	12.9327	0.599097
$467$	−1.78711	−0.0826976	−0.0413488	−	0.999145i	$-0.513165\pi$
$467$	−1.78711	−0.0826976	−0.0413488	+	0.999145i	$0.513165\pi$
$468$	1.76064	0.0813857
$469$	5.17339	0.238885
$470$	−28.8893	−1.33256
$471$	−1.00000	−0.0460776
$472$	−5.77459	−0.265797
$473$	18.5303	0.852023
$474$	−1.29726	−0.0595852
$475$	23.1181	1.06073
$476$	0.763028	0.0349733
$477$	−10.2048	−0.467244
$478$	−7.32713	−0.335135
$479$	−3.29177	−0.150405	−0.0752024	−	0.997168i	$-0.523960\pi$
$479$	−3.29177	−0.150405	−0.0752024	+	0.997168i	$0.523960\pi$
$480$	−10.0783	−0.460009
$481$	21.7119	0.989976
$482$	−2.15923	−0.0983503
$483$	2.35661	0.107230
$484$	3.84728	0.174876
$485$	−43.6749	−1.98317
$486$	−1.21037	−0.0549035
$487$	−18.9464	−0.858541	−0.429271	−	0.903176i	$-0.641229\pi$
$487$	−18.9464	−0.858541	−0.429271	+	0.903176i	$0.641229\pi$
$488$	−33.1342	−1.49992
$489$	−21.8971	−0.990220
$490$	20.6278	0.931868
$491$	−15.8075	−0.713381	−0.356690	−	0.934223i	$-0.616095\pi$
$491$	−15.8075	−0.713381	−0.356690	+	0.934223i	$0.616095\pi$
$492$	−0.971929	−0.0438180
$493$	2.34426	0.105580
$494$	13.5859	0.611259
$495$	−6.69781	−0.301044
$496$	12.8959	0.579042
$497$	−21.0872	−0.945892
$498$	−4.12048	−0.184643
$499$	19.5969	0.877278	0.438639	−	0.898663i	$-0.355461\pi$
$499$	19.5969	0.877278	0.438639	+	0.898663i	$0.355461\pi$
$500$	−3.26436	−0.145987
$501$	−17.5656	−0.784774
$502$	−12.3455	−0.551005
$503$	−35.3697	−1.57705	−0.788527	−	0.615000i	$-0.789156\pi$
$503$	−35.3697	−1.57705	−0.788527	+	0.615000i	$0.789156\pi$
$504$	−4.37603	−0.194924
$505$	0.748862	0.0333239
$506$	−3.90321	−0.173519
$507$	−2.17003	−0.0963743
$508$	1.41116	0.0626099
$509$	−13.2844	−0.588818	−0.294409	−	0.955679i	$-0.595123\pi$
$509$	−13.2844	−0.588818	−0.294409	+	0.955679i	$0.595123\pi$
$510$	−4.15386	−0.183936
$511$	−20.0860	−0.888551
$512$	23.9875	1.06011
$513$	3.41080	0.150591
$514$	26.1209	1.15214
$515$	−34.9262	−1.53903
$516$	5.07973	0.223622
$517$	−13.5732	−0.596951
$518$	−11.3890	−0.500403
$519$	10.9191	0.479295
$520$	−34.6533	−1.51965
$521$	−33.5294	−1.46895	−0.734475	−	0.678636i	$-0.762571\pi$
$521$	−33.5294	−1.46895	−0.734475	+	0.678636i	$0.762571\pi$
$522$	−2.83743	−0.124191
$523$	31.3874	1.37247	0.686237	−	0.727378i	$-0.259261\pi$
$523$	31.3874	1.37247	0.686237	+	0.727378i	$0.259261\pi$
$524$	2.38358	0.104127
$525$	−9.66670	−0.421889
$526$	13.3383	0.581577
$527$	−4.87786	−0.212483
$528$	5.15966	0.224545
$529$	−20.2697	−0.881291
$530$	42.3892	1.84127
$531$	−1.88202	−0.0816727
$532$	2.60254	0.112834
$533$	−5.97848	−0.258957
$534$	−15.8699	−0.686756
$535$	−9.00981	−0.389528
$536$	−11.1298	−0.480736
$537$	−10.2734	−0.443331
$538$	−29.8262	−1.28590
$539$	9.69168	0.417450
$540$	−1.83608	−0.0790122
$541$	38.1869	1.64178	0.820892	−	0.571083i	$-0.193477\pi$
$541$	38.1869	1.64178	0.820892	+	0.571083i	$0.193477\pi$
$542$	−25.9154	−1.11316
$543$	−2.39955	−0.102975
$544$	−2.93666	−0.125908
$545$	−68.6016	−2.93857
$546$	−5.68087	−0.243119
$547$	−19.7745	−0.845497	−0.422748	−	0.906247i	$-0.638935\pi$
$547$	−19.7745	−0.845497	−0.422748	+	0.906247i	$0.638935\pi$
$548$	−2.53758	−0.108400
$549$	−10.7989	−0.460886
$550$	16.0108	0.682701
$551$	7.99583	0.340634
$552$	−5.06993	−0.215791
$553$	−1.52860	−0.0650025
$554$	−15.6758	−0.666000
$555$	−22.6421	−0.961105
$556$	2.61922	0.111080
$557$	6.78209	0.287367	0.143683	−	0.989624i	$-0.454105\pi$
$557$	6.78209	0.287367	0.143683	+	0.989624i	$0.454105\pi$
$558$	5.90401	0.249937
$559$	31.2462	1.32157
$560$	12.9402	0.546821
$561$	−1.95164	−0.0823981
$562$	14.6204	0.616724
$563$	−17.6650	−0.744491	−0.372245	−	0.928134i	$-0.621412\pi$
$563$	−17.6650	−0.744491	−0.372245	+	0.928134i	$0.621412\pi$
$564$	−3.72085	−0.156676
$565$	1.60945	0.0677100
$566$	−10.1840	−0.428064
$567$	−1.42621	−0.0598952
$568$	45.3663	1.90353
$569$	21.2913	0.892577	0.446288	−	0.894889i	$-0.352746\pi$
$569$	21.2913	0.892577	0.446288	+	0.894889i	$0.352746\pi$
$570$	−14.1680	−0.593432
$571$	8.54100	0.357430	0.178715	−	0.983901i	$-0.442806\pi$
$571$	8.54100	0.357430	0.178715	+	0.983901i	$0.442806\pi$
$572$	−3.43613	−0.143672
$573$	11.6347	0.486047
$574$	3.13602	0.130895
$575$	−11.1995	−0.467053
$576$	8.84196	0.368415
$577$	24.2424	1.00922	0.504612	−	0.863346i	$-0.331636\pi$
$577$	24.2424	1.00922	0.504612	+	0.863346i	$0.331636\pi$
$578$	−1.21037	−0.0503448
$579$	−17.5262	−0.728362
$580$	−4.30425	−0.178724
$581$	−4.85527	−0.201430
$582$	15.4034	0.638490
$583$	19.9160	0.824837
$584$	43.2122	1.78813
$585$	−11.2940	−0.466949
$586$	−12.8285	−0.529939
$587$	−46.3013	−1.91106	−0.955530	−	0.294894i	$-0.904716\pi$
$587$	−46.3013	−1.91106	−0.955530	+	0.294894i	$0.904716\pi$
$588$	2.65679	0.109564
$589$	−16.6374	−0.685532
$590$	7.81765	0.321848
$591$	−11.5675	−0.475822
$592$	17.4424	0.716878
$593$	−36.3277	−1.49180	−0.745899	−	0.666059i	$-0.767980\pi$
$593$	−36.3277	−1.49180	−0.745899	+	0.666059i	$0.767980\pi$
$594$	2.36220	0.0969223
$595$	−4.89460	−0.200659
$596$	2.35973	0.0966584
$597$	10.7585	0.440314
$598$	−6.58169	−0.269145
$599$	22.4370	0.916752	0.458376	−	0.888758i	$-0.348431\pi$
$599$	22.4370	0.916752	0.458376	+	0.888758i	$0.348431\pi$
$600$	20.7966	0.849017
$601$	24.3864	0.994740	0.497370	−	0.867538i	$-0.334299\pi$
$601$	24.3864	0.994740	0.497370	+	0.867538i	$0.334299\pi$
$602$	−16.3902	−0.668015
$603$	−3.62737	−0.147718
$604$	0.0724457	0.00294777
$605$	−24.6792	−1.00335
$606$	−0.264111	−0.0107288
$607$	−24.5671	−0.997148	−0.498574	−	0.866847i	$-0.666143\pi$
$607$	−24.5671	−0.997148	−0.498574	+	0.866847i	$0.666143\pi$
$608$	−10.0164	−0.406217
$609$	−3.34341	−0.135482
$610$	44.8572	1.81621
$611$	−22.8875	−0.925929
$612$	−0.535004	−0.0216263
$613$	−19.6595	−0.794040	−0.397020	−	0.917810i	$-0.629956\pi$
$613$	−19.6595	−0.794040	−0.397020	+	0.917810i	$0.629956\pi$
$614$	−7.78948	−0.314358
$615$	6.23464	0.251405
$616$	8.54041	0.344103
$617$	−22.9351	−0.923330	−0.461665	−	0.887054i	$-0.652748\pi$
$617$	−22.9351	−0.923330	−0.461665	+	0.887054i	$0.652748\pi$
$618$	12.3179	0.495497
$619$	−24.5688	−0.987504	−0.493752	−	0.869603i	$-0.664375\pi$
$619$	−24.5688	−0.987504	−0.493752	+	0.869603i	$0.664375\pi$
$620$	8.95612	0.359687
$621$	−1.65236	−0.0663070
$622$	−6.55462	−0.262816
$623$	−18.6999	−0.749194
$624$	8.70033	0.348292
$625$	−12.9496	−0.517984
$626$	31.7914	1.27064
$627$	−6.65665	−0.265841
$628$	0.535004	0.0213490
$629$	−6.59756	−0.263062
$630$	5.92428	0.236029
$631$	−18.2616	−0.726981	−0.363491	−	0.931598i	$-0.618415\pi$
$631$	−18.2616	−0.726981	−0.363491	+	0.931598i	$0.618415\pi$
$632$	3.28856	0.130812
$633$	13.6639	0.543090
$634$	−7.10880	−0.282326
$635$	−9.05215	−0.359223
$636$	5.45960	0.216487
$637$	16.3423	0.647507
$638$	5.53763	0.219237
$639$	14.7855	0.584906
$640$	−16.5717	−0.655054
$641$	5.57548	0.220218	0.110109	−	0.993920i	$-0.464880\pi$
$641$	5.57548	0.220218	0.110109	+	0.993920i	$0.464880\pi$
$642$	3.17760	0.125410
$643$	−24.0023	−0.946559	−0.473280	−	0.880912i	$-0.656930\pi$
$643$	−24.0023	−0.946559	−0.473280	+	0.880912i	$0.656930\pi$
$644$	−1.26080	−0.0496824
$645$	−32.5849	−1.28303
$646$	−4.12833	−0.162427
$647$	1.17135	0.0460506	0.0230253	−	0.999735i	$-0.492670\pi$
$647$	1.17135	0.0460506	0.0230253	+	0.999735i	$0.492670\pi$
$648$	3.06829	0.120534
$649$	3.67302	0.144179
$650$	26.9977	1.05894
$651$	6.95684	0.272660
$652$	11.7150	0.458796
$653$	−6.94215	−0.271667	−0.135834	−	0.990732i	$-0.543371\pi$
$653$	−6.94215	−0.271667	−0.135834	+	0.990732i	$0.543371\pi$
$654$	24.1946	0.946085
$655$	−15.2900	−0.597429
$656$	−4.80286	−0.187520
$657$	14.0835	0.549448
$658$	12.0057	0.468030
$659$	−8.10025	−0.315541	−0.157770	−	0.987476i	$-0.550431\pi$
$659$	−8.10025	−0.315541	−0.157770	+	0.987476i	$0.550431\pi$
$660$	3.58336	0.139482
$661$	−13.1041	−0.509689	−0.254845	−	0.966982i	$-0.582024\pi$
$661$	−13.1041	−0.509689	−0.254845	+	0.966982i	$0.582024\pi$
$662$	−16.8642	−0.655447
$663$	−3.29089	−0.127808
$664$	10.4454	0.405362
$665$	−16.6945	−0.647385
$666$	7.98549	0.309432
$667$	−3.87358	−0.149985
$668$	9.39768	0.363607
$669$	2.54287	0.0983129
$670$	15.0676	0.582112
$671$	21.0755	0.813613
$672$	4.18829	0.161567
$673$	33.1050	1.27610	0.638051	−	0.769994i	$-0.279741\pi$
$673$	33.1050	1.27610	0.638051	+	0.769994i	$0.279741\pi$
$674$	−22.6636	−0.872968
$675$	6.77790	0.260881
$676$	1.16097	0.0446529
$677$	14.2364	0.547151	0.273576	−	0.961851i	$-0.411794\pi$
$677$	14.2364	0.547151	0.273576	+	0.961851i	$0.411794\pi$
$678$	−0.567625	−0.0217995
$679$	18.1502	0.696540
$680$	10.5301	0.403809
$681$	7.17845	0.275079
$682$	−11.5225	−0.441219
$683$	9.94741	0.380627	0.190313	−	0.981723i	$-0.439050\pi$
$683$	9.94741	0.380627	0.190313	+	0.981723i	$0.439050\pi$
$684$	−1.82479	−0.0697728
$685$	16.2779	0.621945
$686$	−20.6561	−0.788653
$687$	−0.577952	−0.0220503
$688$	25.1018	0.956998
$689$	33.5828	1.27940
$690$	6.86369	0.261296
$691$	−20.6790	−0.786665	−0.393332	−	0.919396i	$-0.628678\pi$
$691$	−20.6790	−0.786665	−0.393332	+	0.919396i	$0.628678\pi$
$692$	−5.84176	−0.222070
$693$	2.78344	0.105734
$694$	−34.4935	−1.30936
$695$	−16.8015	−0.637319
$696$	7.19289	0.272646
$697$	1.81668	0.0688115
$698$	−0.352853	−0.0133557
$699$	−10.6849	−0.404141
$700$	5.17173	0.195473
$701$	−39.4859	−1.49136	−0.745682	−	0.666303i	$-0.767876\pi$
$701$	−39.4859	−1.49136	−0.745682	+	0.666303i	$0.767876\pi$
$702$	3.98320	0.150336
$703$	−22.5030	−0.848716
$704$	−17.2563	−0.650371
$705$	23.8681	0.898926
$706$	−1.84038	−0.0692635
$707$	−0.311208	−0.0117042
$708$	1.00689	0.0378412
$709$	7.90273	0.296793	0.148397	−	0.988928i	$-0.452589\pi$
$709$	7.90273	0.296793	0.148397	+	0.988928i	$0.452589\pi$
$710$	−61.4170	−2.30494
$711$	1.07179	0.0401952
$712$	40.2302	1.50769
$713$	8.05998	0.301849
$714$	1.72624	0.0646029
$715$	22.0418	0.824315
$716$	5.49632	0.205407
$717$	6.05363	0.226077
$718$	5.10531	0.190528
$719$	21.2111	0.791041	0.395520	−	0.918457i	$-0.370564\pi$
$719$	21.2111	0.791041	0.395520	+	0.918457i	$0.370564\pi$
$720$	−9.07311	−0.338135
$721$	14.5144	0.540546
$722$	8.91610	0.331823
$723$	1.78394	0.0663455
$724$	1.28377	0.0477110
$725$	15.8892	0.590110
$726$	8.70391	0.323032
$727$	11.2538	0.417382	0.208691	−	0.977982i	$-0.433080\pi$
$727$	11.2538	0.417382	0.208691	+	0.977982i	$0.433080\pi$
$728$	14.4010	0.533738
$729$	1.00000	0.0370370
$730$	−58.5008	−2.16521
$731$	−9.49474	−0.351176
$732$	5.77747	0.213541
$733$	−11.7544	−0.434158	−0.217079	−	0.976154i	$-0.569653\pi$
$733$	−11.7544	−0.434158	−0.217079	+	0.976154i	$0.569653\pi$
$734$	−13.2075	−0.487500
$735$	−17.0425	−0.628623
$736$	4.85242	0.178863
$737$	7.07931	0.260770
$738$	−2.19885	−0.0809408
$739$	22.2996	0.820305	0.410153	−	0.912017i	$-0.365475\pi$
$739$	22.2996	0.820305	0.410153	+	0.912017i	$0.365475\pi$
$740$	12.1136	0.445306
$741$	−11.2246	−0.412345
$742$	−17.6159	−0.646700
$743$	24.9689	0.916021	0.458011	−	0.888947i	$-0.348562\pi$
$743$	24.9689	0.916021	0.458011	+	0.888947i	$0.348562\pi$
$744$	−14.9667	−0.548706
$745$	−15.1370	−0.554576
$746$	8.63676	0.316214
$747$	3.40432	0.124557
$748$	1.04413	0.0381773
$749$	3.74425	0.136812
$750$	−7.38514	−0.269667
$751$	−7.09575	−0.258927	−0.129464	−	0.991584i	$-0.541326\pi$
$751$	−7.09575	−0.258927	−0.129464	+	0.991584i	$0.541326\pi$
$752$	−18.3868	−0.670499
$753$	10.1997	0.371699
$754$	9.33767	0.340058
$755$	−0.464718	−0.0169128
$756$	0.763028	0.0277511
$757$	23.1130	0.840057	0.420029	−	0.907511i	$-0.362020\pi$
$757$	23.1130	0.840057	0.420029	+	0.907511i	$0.362020\pi$
$758$	40.8551	1.48392
$759$	3.22481	0.117053
$760$	35.9160	1.30281
$761$	−44.1596	−1.60079	−0.800393	−	0.599476i	$-0.795376\pi$
$761$	−44.1596	−1.60079	−0.800393	+	0.599476i	$0.795376\pi$
$762$	3.19254	0.115653
$763$	28.5091	1.03210
$764$	−6.22462	−0.225199
$765$	3.43189	0.124080
$766$	21.2731	0.768629
$767$	6.19352	0.223635
$768$	−11.8394	−0.427217
$769$	24.7750	0.893408	0.446704	−	0.894682i	$-0.352598\pi$
$769$	24.7750	0.893408	0.446704	+	0.894682i	$0.352598\pi$
$770$	−11.5620	−0.416667
$771$	−21.5809	−0.777218
$772$	9.37657	0.337470
$773$	38.6984	1.39189	0.695943	−	0.718097i	$-0.254987\pi$
$773$	38.6984	1.39189	0.695943	+	0.718097i	$0.254987\pi$
$774$	11.4921	0.413077
$775$	−33.0616	−1.18761
$776$	−39.0476	−1.40173
$777$	9.40951	0.337564
$778$	−6.03046	−0.216202
$779$	6.19632	0.222006
$780$	6.04234	0.216350
$781$	−28.8559	−1.03255
$782$	1.99997	0.0715188
$783$	2.34426	0.0837772
$784$	13.1287	0.468883
$785$	−3.43189	−0.122490
$786$	5.39251	0.192345
$787$	−8.32948	−0.296914	−0.148457	−	0.988919i	$-0.547431\pi$
$787$	−8.32948	−0.296914	−0.148457	+	0.988919i	$0.547431\pi$
$788$	6.18864	0.220461
$789$	−11.0200	−0.392323
$790$	−4.45206	−0.158397
$791$	−0.668847	−0.0237814
$792$	−5.98819	−0.212781
$793$	35.5381	1.26199
$794$	20.5617	0.729706
$795$	−35.0217	−1.24209
$796$	−5.75582	−0.204010
$797$	−19.5366	−0.692023	−0.346012	−	0.938230i	$-0.612464\pi$
$797$	−19.5366	−0.692023	−0.346012	+	0.938230i	$0.612464\pi$
$798$	5.88787	0.208428
$799$	6.95480	0.246043
$800$	−19.9044	−0.703725
$801$	13.1116	0.463275
$802$	−14.5782	−0.514774
$803$	−27.4858	−0.969953
$804$	1.94066	0.0684418
$805$	8.08765	0.285052
$806$	−19.4295	−0.684374
$807$	24.6422	0.867446
$808$	0.669521	0.0235537
$809$	−19.6317	−0.690215	−0.345107	−	0.938563i	$-0.612158\pi$
$809$	−19.6317	−0.690215	−0.345107	+	0.938563i	$0.612158\pi$
$810$	−4.15386	−0.145952
$811$	−5.88443	−0.206630	−0.103315	−	0.994649i	$-0.532945\pi$
$811$	−5.88443	−0.206630	−0.103315	+	0.994649i	$0.532945\pi$
$812$	1.78874	0.0627725
$813$	21.4112	0.750923
$814$	−15.5848	−0.546246
$815$	−75.1484	−2.63234
$816$	−2.64376	−0.0925502
$817$	−32.3847	−1.13300
$818$	41.7775	1.46072
$819$	4.69350	0.164004
$820$	−3.33556	−0.116483
$821$	4.47632	0.156225	0.0781123	−	0.996945i	$-0.475111\pi$
$821$	4.47632	0.156225	0.0781123	+	0.996945i	$0.475111\pi$
$822$	−5.74092	−0.200238
$823$	−17.7789	−0.619733	−0.309867	−	0.950780i	$-0.600284\pi$
$823$	−17.7789	−0.619733	−0.309867	+	0.950780i	$0.600284\pi$
$824$	−31.2258	−1.08780
$825$	−13.2280	−0.460539
$826$	−3.24882	−0.113041
$827$	−17.5127	−0.608977	−0.304488	−	0.952516i	$-0.598485\pi$
$827$	−17.5127	−0.608977	−0.304488	+	0.952516i	$0.598485\pi$
$828$	0.884021	0.0307219
$829$	17.5194	0.608474	0.304237	−	0.952596i	$-0.401599\pi$
$829$	17.5194	0.608474	0.304237	+	0.952596i	$0.401599\pi$
$830$	−14.1411	−0.490843
$831$	12.9512	0.449273
$832$	−29.0980	−1.00879
$833$	−4.96593	−0.172059
$834$	5.92561	0.205187
$835$	−60.2833	−2.08619
$836$	3.56133	0.123171
$837$	−4.87786	−0.168603
$838$	29.5453	1.02063
$839$	17.1214	0.591095	0.295547	−	0.955328i	$-0.404498\pi$
$839$	17.1214	0.591095	0.295547	+	0.955328i	$0.404498\pi$
$840$	−15.0181	−0.518172
$841$	−23.5044	−0.810497
$842$	−33.3707	−1.15003
$843$	−12.0793	−0.416033
$844$	−7.31023	−0.251629
$845$	−7.44731	−0.256195
$846$	−8.41789	−0.289413
$847$	10.2560	0.352402
$848$	26.9790	0.926462
$849$	8.41392	0.288765
$850$	−8.20376	−0.281387
$851$	10.9016	0.373701
$852$	−7.91031	−0.271003
$853$	−0.248212	−0.00849863	−0.00424932	−	0.999991i	$-0.501353\pi$
$853$	−0.248212	−0.00849863	−0.00424932	+	0.999991i	$0.501353\pi$
$854$	−18.6415	−0.637900
$855$	11.7055	0.400320
$856$	−8.05524	−0.275322
$857$	41.3170	1.41136	0.705681	−	0.708530i	$-0.250641\pi$
$857$	41.3170	1.41136	0.705681	+	0.708530i	$0.250641\pi$
$858$	−7.77375	−0.265391
$859$	−20.3783	−0.695300	−0.347650	−	0.937624i	$-0.613020\pi$
$859$	−20.3783	−0.695300	−0.347650	+	0.937624i	$0.613020\pi$
$860$	17.4331	0.594463
$861$	−2.59096	−0.0882997
$862$	−8.87849	−0.302403
$863$	−15.6191	−0.531679	−0.265839	−	0.964017i	$-0.585649\pi$
$863$	−15.6191	−0.531679	−0.265839	+	0.964017i	$0.585649\pi$
$864$	−2.93666	−0.0999071
$865$	37.4731	1.27412
$866$	−7.20362	−0.244789
$867$	1.00000	0.0339618
$868$	−3.72194	−0.126331
$869$	−2.09174	−0.0709575
$870$	−9.73775	−0.330141
$871$	11.9373	0.404479
$872$	−61.3335	−2.07701
$873$	−12.7262	−0.430716
$874$	6.82150	0.230741
$875$	−8.70210	−0.294185
$876$	−7.53471	−0.254574
$877$	−4.73646	−0.159939	−0.0799694	−	0.996797i	$-0.525482\pi$
$877$	−4.73646	−0.159939	−0.0799694	+	0.996797i	$0.525482\pi$
$878$	−7.38382	−0.249192
$879$	10.5988	0.357488
$880$	17.7074	0.596917
$881$	−51.3295	−1.72933	−0.864667	−	0.502346i	$-0.832470\pi$
$881$	−51.3295	−1.72933	−0.864667	+	0.502346i	$0.832470\pi$
$882$	6.01061	0.202388
$883$	25.0589	0.843301	0.421650	−	0.906758i	$-0.361451\pi$
$883$	25.0589	0.843301	0.421650	+	0.906758i	$0.361451\pi$
$884$	1.76064	0.0592168
$885$	−6.45889	−0.217113
$886$	−46.1308	−1.54979
$887$	46.7425	1.56946	0.784729	−	0.619839i	$-0.212802\pi$
$887$	46.7425	1.56946	0.784729	+	0.619839i	$0.212802\pi$
$888$	−20.2433	−0.679319
$889$	3.76185	0.126168
$890$	−54.4637	−1.82563
$891$	−1.95164	−0.0653823
$892$	−1.36044	−0.0455510
$893$	23.7215	0.793809
$894$	5.33856	0.178548
$895$	−35.2573	−1.17852
$896$	6.88679	0.230071
$897$	5.43775	0.181561
$898$	22.5834	0.753618
$899$	−11.4350	−0.381378
$900$	−3.62620	−0.120873
$901$	−10.2048	−0.339970
$902$	4.29135	0.142886
$903$	13.5415	0.450632
$904$	1.43893	0.0478582
$905$	−8.23501	−0.273741
$906$	0.163898	0.00544514
$907$	45.8469	1.52232	0.761161	−	0.648563i	$-0.224630\pi$
$907$	45.8469	1.52232	0.761161	+	0.648563i	$0.224630\pi$
$908$	−3.84050	−0.127452
$909$	0.218206	0.00723745
$910$	−19.4962	−0.646291
$911$	0.464825	0.0154003	0.00770017	−	0.999970i	$-0.497549\pi$
$911$	0.464825	0.0154003	0.00770017	+	0.999970i	$0.497549\pi$
$912$	−9.01735	−0.298594
$913$	−6.64399	−0.219884
$914$	40.7619	1.34829
$915$	−37.0607	−1.22519
$916$	0.309207	0.0102165
$917$	6.35413	0.209832
$918$	−1.21037	−0.0399482
$919$	41.6199	1.37291	0.686457	−	0.727170i	$-0.259165\pi$
$919$	41.6199	1.37291	0.686457	+	0.727170i	$0.259165\pi$
$920$	−17.3995	−0.573644
$921$	6.43562	0.212061
$922$	25.4308	0.837519
$923$	−48.6575	−1.60158
$924$	−1.48915	−0.0489895
$925$	−44.7176	−1.47031
$926$	14.1495	0.464983
$927$	−10.1769	−0.334255
$928$	−6.88430	−0.225988
$929$	−0.553855	−0.0181714	−0.00908570	−	0.999959i	$-0.502892\pi$
$929$	−0.553855	−0.0181714	−0.00908570	+	0.999959i	$0.502892\pi$
$930$	20.2619	0.664415
$931$	−16.9378	−0.555114
$932$	5.71648	0.187250
$933$	5.41539	0.177292
$934$	2.16307	0.0707777
$935$	−6.69781	−0.219042
$936$	−10.0974	−0.330045
$937$	23.0599	0.753334	0.376667	−	0.926349i	$-0.377070\pi$
$937$	23.0599	0.753334	0.376667	+	0.926349i	$0.377070\pi$
$938$	−6.26171	−0.204452
$939$	−26.2659	−0.857154
$940$	−12.7696	−0.416497
$941$	36.8475	1.20119	0.600597	−	0.799552i	$-0.294929\pi$
$941$	36.8475	1.20119	0.600597	+	0.799552i	$0.294929\pi$
$942$	1.21037	0.0394360
$943$	−3.00181	−0.0977523
$944$	4.97561	0.161942
$945$	−4.89460	−0.159221
$946$	−22.4285	−0.729213
$947$	10.4808	0.340581	0.170291	−	0.985394i	$-0.445529\pi$
$947$	10.4808	0.340581	0.170291	+	0.985394i	$0.445529\pi$
$948$	−0.573412	−0.0186236
$949$	−46.3472	−1.50449
$950$	−27.9814	−0.907837
$951$	5.87324	0.190453
$952$	−4.37603	−0.141828
$953$	0.0648890	0.00210196	0.00105098	−	0.999999i	$-0.499665\pi$
$953$	0.0648890	0.00210196	0.00105098	+	0.999999i	$0.499665\pi$
$954$	12.3516	0.399896
$955$	39.9291	1.29208
$956$	−3.23872	−0.104748
$957$	−4.57515	−0.147894
$958$	3.98426	0.128726
$959$	−6.76467	−0.218443
$960$	30.3447	0.979371
$961$	−7.20653	−0.232469
$962$	−26.2794	−0.847282
$963$	−2.62532	−0.0845996
$964$	−0.954417	−0.0307397
$965$	−60.1479	−1.93623
$966$	−2.85238	−0.0917737
$967$	−25.7046	−0.826604	−0.413302	−	0.910594i	$-0.635625\pi$
$967$	−25.7046	−0.826604	−0.413302	+	0.910594i	$0.635625\pi$
$968$	−22.0645	−0.709178
$969$	3.41080	0.109571
$970$	52.8628	1.69732
$971$	33.6653	1.08037	0.540185	−	0.841546i	$-0.318354\pi$
$971$	33.6653	1.08037	0.540185	+	0.841546i	$0.318354\pi$
$972$	−0.535004	−0.0171603
$973$	6.98230	0.223842
$974$	22.9321	0.734792
$975$	−22.3053	−0.714342
$976$	28.5498	0.913855
$977$	−49.6014	−1.58689	−0.793445	−	0.608642i	$-0.791715\pi$
$977$	−49.6014	−1.58689	−0.793445	+	0.608642i	$0.791715\pi$
$978$	26.5036	0.847491
$979$	−25.5890	−0.817829
$980$	9.11783	0.291258
$981$	−19.9894	−0.638214
$982$	19.1329	0.610555
$983$	15.1418	0.482947	0.241474	−	0.970407i	$-0.422369\pi$
$983$	15.1418	0.482947	0.241474	+	0.970407i	$0.422369\pi$
$984$	5.57409	0.177696
$985$	−39.6983	−1.26489
$986$	−2.83743	−0.0903621
$987$	−9.91900	−0.315725
$988$	6.00520	0.191051
$989$	15.6887	0.498873
$990$	8.10683	0.257652
$991$	0.384448	0.0122124	0.00610620	−	0.999981i	$-0.498056\pi$
$991$	0.384448	0.0122124	0.00610620	+	0.999981i	$0.498056\pi$
$992$	14.3246	0.454806
$993$	13.9331	0.442155
$994$	25.5234	0.809552
$995$	36.9219	1.17050
$996$	−1.82132	−0.0577109
$997$	−35.2959	−1.11783	−0.558917	−	0.829224i	$-0.688783\pi$
$997$	−35.2959	−1.11783	−0.558917	+	0.829224i	$0.688783\pi$
$998$	−23.7195	−0.750828
$999$	−6.59756	−0.208738

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.d.1.14	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.d.1.14	✓	40	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)

\(f(q)\)	\(=\)	\(q-1.21037 q^{2} +1.00000 q^{3} -0.535004 q^{4} +3.43189 q^{5} -1.21037 q^{6} -1.42621 q^{7} +3.06829 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.21037 q^{2} +1.00000 q^{3} -0.535004 q^{4} +3.43189 q^{5} -1.21037 q^{6} -1.42621 q^{7} +3.06829 q^{8} +1.00000 q^{9} -4.15386 q^{10} -1.95164 q^{11} -0.535004 q^{12} -3.29089 q^{13} +1.72624 q^{14} +3.43189 q^{15} -2.64376 q^{16} +1.00000 q^{17} -1.21037 q^{18} +3.41080 q^{19} -1.83608 q^{20} -1.42621 q^{21} +2.36220 q^{22} -1.65236 q^{23} +3.06829 q^{24} +6.77790 q^{25} +3.98320 q^{26} +1.00000 q^{27} +0.763028 q^{28} +2.34426 q^{29} -4.15386 q^{30} -4.87786 q^{31} -2.93666 q^{32} -1.95164 q^{33} -1.21037 q^{34} -4.89460 q^{35} -0.535004 q^{36} -6.59756 q^{37} -4.12833 q^{38} -3.29089 q^{39} +10.5301 q^{40} +1.81668 q^{41} +1.72624 q^{42} -9.49474 q^{43} +1.04413 q^{44} +3.43189 q^{45} +1.99997 q^{46} +6.95480 q^{47} -2.64376 q^{48} -4.96593 q^{49} -8.20376 q^{50} +1.00000 q^{51} +1.76064 q^{52} -10.2048 q^{53} -1.21037 q^{54} -6.69781 q^{55} -4.37603 q^{56} +3.41080 q^{57} -2.83743 q^{58} -1.88202 q^{59} -1.83608 q^{60} -10.7989 q^{61} +5.90401 q^{62} -1.42621 q^{63} +8.84196 q^{64} -11.2940 q^{65} +2.36220 q^{66} -3.62737 q^{67} -0.535004 q^{68} -1.65236 q^{69} +5.92428 q^{70} +14.7855 q^{71} +3.06829 q^{72} +14.0835 q^{73} +7.98549 q^{74} +6.77790 q^{75} -1.82479 q^{76} +2.78344 q^{77} +3.98320 q^{78} +1.07179 q^{79} -9.07311 q^{80} +1.00000 q^{81} -2.19885 q^{82} +3.40432 q^{83} +0.763028 q^{84} +3.43189 q^{85} +11.4921 q^{86} +2.34426 q^{87} -5.98819 q^{88} +13.1116 q^{89} -4.15386 q^{90} +4.69350 q^{91} +0.884021 q^{92} -4.87786 q^{93} -8.41789 q^{94} +11.7055 q^{95} -2.93666 q^{96} -12.7262 q^{97} +6.01061 q^{98} -1.95164 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 7 q^{2} + 40 q^{3} + 29 q^{4} - 15 q^{5} - 7 q^{6} - 13 q^{7} - 18 q^{8} + 40 q^{9}+O(q^{10}) \) 40 * q - 7 * q^2 + 40 * q^3 + 29 * q^4 - 15 * q^5 - 7 * q^6 - 13 * q^7 - 18 * q^8 + 40 * q^9	\( 40 q - 7 q^{2} + 40 q^{3} + 29 q^{4} - 15 q^{5} - 7 q^{6} - 13 q^{7} - 18 q^{8} + 40 q^{9} - 6 q^{10} - 25 q^{11} + 29 q^{12} - 24 q^{13} - 22 q^{14} - 15 q^{15} + 7 q^{16} + 40 q^{17} - 7 q^{18} - 18 q^{19} - 20 q^{20} - 13 q^{21} - 25 q^{22} - 28 q^{23} - 18 q^{24} - 11 q^{25} - 13 q^{26} + 40 q^{27} - 8 q^{28} - 23 q^{29} - 6 q^{30} - 11 q^{31} - 23 q^{32} - 25 q^{33} - 7 q^{34} - 45 q^{35} + 29 q^{36} - 38 q^{37} - 30 q^{38} - 24 q^{39} - 12 q^{40} - 33 q^{41} - 22 q^{42} - 25 q^{43} - 14 q^{44} - 15 q^{45} + 8 q^{46} - 55 q^{47} + 7 q^{48} - 21 q^{49} + 2 q^{50} + 40 q^{51} - 39 q^{52} - 39 q^{53} - 7 q^{54} - 9 q^{55} - 48 q^{56} - 18 q^{57} - 13 q^{58} - 81 q^{59} - 20 q^{60} - 9 q^{61} - 16 q^{62} - 13 q^{63} - 4 q^{64} - 43 q^{65} - 25 q^{66} - 24 q^{67} + 29 q^{68} - 28 q^{69} + 48 q^{70} - 32 q^{71} - 18 q^{72} - 43 q^{73} - 20 q^{74} - 11 q^{75} - 58 q^{76} - 32 q^{77} - 13 q^{78} - 22 q^{79} - 48 q^{80} + 40 q^{81} - 11 q^{82} - 45 q^{83} - 8 q^{84} - 15 q^{85} - 30 q^{86} - 23 q^{87} - 48 q^{88} - 94 q^{89} - 6 q^{90} - 7 q^{91} - 98 q^{92} - 11 q^{93} + 32 q^{94} - 23 q^{96} - 28 q^{97} - 46 q^{98} - 25 q^{99}+O(q^{100}) \) 40 * q - 7 * q^2 + 40 * q^3 + 29 * q^4 - 15 * q^5 - 7 * q^6 - 13 * q^7 - 18 * q^8 + 40 * q^9 - 6 * q^10 - 25 * q^11 + 29 * q^12 - 24 * q^13 - 22 * q^14 - 15 * q^15 + 7 * q^16 + 40 * q^17 - 7 * q^18 - 18 * q^19 - 20 * q^20 - 13 * q^21 - 25 * q^22 - 28 * q^23 - 18 * q^24 - 11 * q^25 - 13 * q^26 + 40 * q^27 - 8 * q^28 - 23 * q^29 - 6 * q^30 - 11 * q^31 - 23 * q^32 - 25 * q^33 - 7 * q^34 - 45 * q^35 + 29 * q^36 - 38 * q^37 - 30 * q^38 - 24 * q^39 - 12 * q^40 - 33 * q^41 - 22 * q^42 - 25 * q^43 - 14 * q^44 - 15 * q^45 + 8 * q^46 - 55 * q^47 + 7 * q^48 - 21 * q^49 + 2 * q^50 + 40 * q^51 - 39 * q^52 - 39 * q^53 - 7 * q^54 - 9 * q^55 - 48 * q^56 - 18 * q^57 - 13 * q^58 - 81 * q^59 - 20 * q^60 - 9 * q^61 - 16 * q^62 - 13 * q^63 - 4 * q^64 - 43 * q^65 - 25 * q^66 - 24 * q^67 + 29 * q^68 - 28 * q^69 + 48 * q^70 - 32 * q^71 - 18 * q^72 - 43 * q^73 - 20 * q^74 - 11 * q^75 - 58 * q^76 - 32 * q^77 - 13 * q^78 - 22 * q^79 - 48 * q^80 + 40 * q^81 - 11 * q^82 - 45 * q^83 - 8 * q^84 - 15 * q^85 - 30 * q^86 - 23 * q^87 - 48 * q^88 - 94 * q^89 - 6 * q^90 - 7 * q^91 - 98 * q^92 - 11 * q^93 + 32 * q^94 - 23 * q^96 - 28 * q^97 - 46 * q^98 - 25 * q^99

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