LMFDB - Embedded newform 8007.2.a.f.1.7

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			1.7
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)

$f(q)$	$=$	$q-2.27518 q^{2} -1.00000 q^{3} +3.17643 q^{4} +2.61308 q^{5} +2.27518 q^{6} +3.54577 q^{7} -2.67658 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.27518 q^{2} -1.00000 q^{3} +3.17643 q^{4} +2.61308 q^{5} +2.27518 q^{6} +3.54577 q^{7} -2.67658 q^{8} +1.00000 q^{9} -5.94522 q^{10} +2.60663 q^{11} -3.17643 q^{12} -6.26473 q^{13} -8.06724 q^{14} -2.61308 q^{15} -0.263166 q^{16} -1.00000 q^{17} -2.27518 q^{18} +2.01130 q^{19} +8.30026 q^{20} -3.54577 q^{21} -5.93053 q^{22} -8.87413 q^{23} +2.67658 q^{24} +1.82820 q^{25} +14.2534 q^{26} -1.00000 q^{27} +11.2629 q^{28} -5.96949 q^{29} +5.94522 q^{30} +1.87052 q^{31} +5.95191 q^{32} -2.60663 q^{33} +2.27518 q^{34} +9.26538 q^{35} +3.17643 q^{36} +1.22700 q^{37} -4.57606 q^{38} +6.26473 q^{39} -6.99412 q^{40} +6.75629 q^{41} +8.06724 q^{42} -8.80703 q^{43} +8.27976 q^{44} +2.61308 q^{45} +20.1902 q^{46} -7.43338 q^{47} +0.263166 q^{48} +5.57246 q^{49} -4.15947 q^{50} +1.00000 q^{51} -19.8994 q^{52} -3.46416 q^{53} +2.27518 q^{54} +6.81133 q^{55} -9.49052 q^{56} -2.01130 q^{57} +13.5816 q^{58} +8.10288 q^{59} -8.30026 q^{60} +9.35388 q^{61} -4.25577 q^{62} +3.54577 q^{63} -13.0153 q^{64} -16.3702 q^{65} +5.93053 q^{66} -0.624312 q^{67} -3.17643 q^{68} +8.87413 q^{69} -21.0804 q^{70} +12.4781 q^{71} -2.67658 q^{72} -6.92684 q^{73} -2.79164 q^{74} -1.82820 q^{75} +6.38875 q^{76} +9.24249 q^{77} -14.2534 q^{78} -1.93136 q^{79} -0.687676 q^{80} +1.00000 q^{81} -15.3718 q^{82} +17.5002 q^{83} -11.2629 q^{84} -2.61308 q^{85} +20.0375 q^{86} +5.96949 q^{87} -6.97684 q^{88} -0.0410964 q^{89} -5.94522 q^{90} -22.2133 q^{91} -28.1880 q^{92} -1.87052 q^{93} +16.9123 q^{94} +5.25569 q^{95} -5.95191 q^{96} +12.3898 q^{97} -12.6783 q^{98} +2.60663 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.27518	−1.60879	−0.804396	−	0.594093i	$-0.797511\pi$
$2$	−2.27518	−1.60879	−0.804396	+	0.594093i	$0.797511\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	3.17643	1.58821
$5$	2.61308	1.16861	0.584303	−	0.811536i	$-0.301368\pi$
$5$	2.61308	1.16861	0.584303	+	0.811536i	$0.301368\pi$
$6$	2.27518	0.928837
$7$	3.54577	1.34017	0.670087	−	0.742283i	$-0.266257\pi$
$7$	3.54577	1.34017	0.670087	+	0.742283i	$0.266257\pi$
$8$	−2.67658	−0.946313
$9$	1.00000	0.333333
$10$	−5.94522	−1.88004
$11$	2.60663	0.785927	0.392964	−	0.919554i	$-0.371450\pi$
$11$	2.60663	0.785927	0.392964	+	0.919554i	$0.371450\pi$
$12$	−3.17643	−0.916955
$13$	−6.26473	−1.73752	−0.868761	−	0.495231i	$-0.835083\pi$
$13$	−6.26473	−1.73752	−0.868761	+	0.495231i	$0.835083\pi$
$14$	−8.06724	−2.15606
$15$	−2.61308	−0.674695
$16$	−0.263166	−0.0657916
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−2.27518	−0.536264
$19$	2.01130	0.461424	0.230712	−	0.973022i	$-0.425895\pi$
$19$	2.01130	0.461424	0.230712	+	0.973022i	$0.425895\pi$
$20$	8.30026	1.85600
$21$	−3.54577	−0.773750
$22$	−5.93053	−1.26439
$23$	−8.87413	−1.85038	−0.925192	−	0.379499i	$-0.876096\pi$
$23$	−8.87413	−1.85038	−0.925192	+	0.379499i	$0.876096\pi$
$24$	2.67658	0.546354
$25$	1.82820	0.365640
$26$	14.2534	2.79531
$27$	−1.00000	−0.192450
$28$	11.2629	2.12848
$29$	−5.96949	−1.10851	−0.554253	−	0.832348i	$-0.686996\pi$
$29$	−5.96949	−1.10851	−0.554253	+	0.832348i	$0.686996\pi$
$30$	5.94522	1.08544
$31$	1.87052	0.335956	0.167978	−	0.985791i	$-0.446276\pi$
$31$	1.87052	0.335956	0.167978	+	0.985791i	$0.446276\pi$
$32$	5.95191	1.05216
$33$	−2.60663	−0.453755
$34$	2.27518	0.390190
$35$	9.26538	1.56613
$36$	3.17643	0.529404
$37$	1.22700	0.201717	0.100859	−	0.994901i	$-0.467841\pi$
$37$	1.22700	0.201717	0.100859	+	0.994901i	$0.467841\pi$
$38$	−4.57606	−0.742335
$39$	6.26473	1.00316
$40$	−6.99412	−1.10587
$41$	6.75629	1.05516	0.527578	−	0.849507i	$-0.323100\pi$
$41$	6.75629	1.05516	0.527578	+	0.849507i	$0.323100\pi$
$42$	8.06724	1.24480
$43$	−8.80703	−1.34306	−0.671530	−	0.740978i	$-0.734362\pi$
$43$	−8.80703	−1.34306	−0.671530	+	0.740978i	$0.734362\pi$
$44$	8.27976	1.24822
$45$	2.61308	0.389535
$46$	20.1902	2.97688
$47$	−7.43338	−1.08427	−0.542135	−	0.840291i	$-0.682384\pi$
$47$	−7.43338	−1.08427	−0.542135	+	0.840291i	$0.682384\pi$
$48$	0.263166	0.0379848
$49$	5.57246	0.796066
$50$	−4.15947	−0.588239
$51$	1.00000	0.140028
$52$	−19.8994	−2.75956
$53$	−3.46416	−0.475839	−0.237920	−	0.971285i	$-0.576466\pi$
$53$	−3.46416	−0.475839	−0.237920	+	0.971285i	$0.576466\pi$
$54$	2.27518	0.309612
$55$	6.81133	0.918439
$56$	−9.49052	−1.26822
$57$	−2.01130	−0.266403
$58$	13.5816	1.78336
$59$	8.10288	1.05491	0.527453	−	0.849585i	$-0.323147\pi$
$59$	8.10288	1.05491	0.527453	+	0.849585i	$0.323147\pi$
$60$	−8.30026	−1.07156
$61$	9.35388	1.19764	0.598821	−	0.800883i	$-0.295636\pi$
$61$	9.35388	1.19764	0.598821	+	0.800883i	$0.295636\pi$
$62$	−4.25577	−0.540483
$63$	3.54577	0.446725
$64$	−13.0153	−1.62691
$65$	−16.3702	−2.03048
$66$	5.93053	0.729998
$67$	−0.624312	−0.0762718	−0.0381359	−	0.999273i	$-0.512142\pi$
$67$	−0.624312	−0.0762718	−0.0381359	+	0.999273i	$0.512142\pi$
$68$	−3.17643	−0.385198
$69$	8.87413	1.06832
$70$	−21.0804	−2.51959
$71$	12.4781	1.48088	0.740438	−	0.672125i	$-0.234618\pi$
$71$	12.4781	1.48088	0.740438	+	0.672125i	$0.234618\pi$
$72$	−2.67658	−0.315438
$73$	−6.92684	−0.810726	−0.405363	−	0.914156i	$-0.632855\pi$
$73$	−6.92684	−0.810726	−0.405363	+	0.914156i	$0.632855\pi$
$74$	−2.79164	−0.324522
$75$	−1.82820	−0.211102
$76$	6.38875	0.732839
$77$	9.24249	1.05328
$78$	−14.2534	−1.61387
$79$	−1.93136	−0.217296	−0.108648	−	0.994080i	$-0.534652\pi$
$79$	−1.93136	−0.217296	−0.108648	+	0.994080i	$0.534652\pi$
$80$	−0.687676	−0.0768845
$81$	1.00000	0.111111
$82$	−15.3718	−1.69753
$83$	17.5002	1.92089	0.960447	−	0.278462i	$-0.0898247\pi$
$83$	17.5002	1.92089	0.960447	+	0.278462i	$0.0898247\pi$
$84$	−11.2629	−1.22888
$85$	−2.61308	−0.283429
$86$	20.0375	2.16070
$87$	5.96949	0.639996
$88$	−6.97684	−0.743734
$89$	−0.0410964	−0.00435621	−0.00217810	−	0.999998i	$-0.500693\pi$
$89$	−0.0410964	−0.00435621	−0.00217810	+	0.999998i	$0.500693\pi$
$90$	−5.94522	−0.626681
$91$	−22.2133	−2.32858
$92$	−28.1880	−2.93881
$93$	−1.87052	−0.193964
$94$	16.9123	1.74437
$95$	5.25569	0.539222
$96$	−5.95191	−0.607464
$97$	12.3898	1.25800	0.628999	−	0.777406i	$-0.283465\pi$
$97$	12.3898	1.25800	0.628999	+	0.777406i	$0.283465\pi$
$98$	−12.6783	−1.28070
$99$	2.60663	0.261976
$100$	5.80714	0.580714
$101$	−11.5200	−1.14628	−0.573139	−	0.819458i	$-0.694275\pi$
$101$	−11.5200	−1.14628	−0.573139	+	0.819458i	$0.694275\pi$
$102$	−2.27518	−0.225276
$103$	−17.3391	−1.70847	−0.854234	−	0.519888i	$-0.825974\pi$
$103$	−17.3391	−1.70847	−0.854234	+	0.519888i	$0.825974\pi$
$104$	16.7680	1.64424
$105$	−9.26538	−0.904208
$106$	7.88158	0.765527
$107$	−7.48347	−0.723455	−0.361727	−	0.932284i	$-0.617813\pi$
$107$	−7.48347	−0.723455	−0.361727	+	0.932284i	$0.617813\pi$
$108$	−3.17643	−0.305652
$109$	1.60493	0.153724	0.0768621	−	0.997042i	$-0.475510\pi$
$109$	1.60493	0.153724	0.0768621	+	0.997042i	$0.475510\pi$
$110$	−15.4970	−1.47758
$111$	−1.22700	−0.116462
$112$	−0.933127	−0.0881722
$113$	−1.86353	−0.175306	−0.0876529	−	0.996151i	$-0.527937\pi$
$113$	−1.86353	−0.175306	−0.0876529	+	0.996151i	$0.527937\pi$
$114$	4.57606	0.428587
$115$	−23.1888	−2.16237
$116$	−18.9616	−1.76054
$117$	−6.26473	−0.579174
$118$	−18.4355	−1.69712
$119$	−3.54577	−0.325040
$120$	6.99412	0.638473
$121$	−4.20550	−0.382318
$122$	−21.2817	−1.92676
$123$	−6.75629	−0.609194
$124$	5.94158	0.533569
$125$	−8.28818	−0.741317
$126$	−8.06724	−0.718687
$127$	−8.33178	−0.739326	−0.369663	−	0.929166i	$-0.620527\pi$
$127$	−8.33178	−0.739326	−0.369663	+	0.929166i	$0.620527\pi$
$128$	17.7083	1.56521
$129$	8.80703	0.775416
$130$	37.2452	3.26662
$131$	−15.5784	−1.36109	−0.680546	−	0.732705i	$-0.738257\pi$
$131$	−15.5784	−1.36109	−0.680546	+	0.732705i	$0.738257\pi$
$132$	−8.27976	−0.720660
$133$	7.13160	0.618388
$134$	1.42042	0.122706
$135$	−2.61308	−0.224898
$136$	2.67658	0.229515
$137$	−12.7444	−1.08882	−0.544412	−	0.838818i	$-0.683247\pi$
$137$	−12.7444	−1.08882	−0.544412	+	0.838818i	$0.683247\pi$
$138$	−20.1902	−1.71870
$139$	−5.36138	−0.454746	−0.227373	−	0.973808i	$-0.573014\pi$
$139$	−5.36138	−0.454746	−0.227373	+	0.973808i	$0.573014\pi$
$140$	29.4308	2.48736
$141$	7.43338	0.626004
$142$	−28.3898	−2.38242
$143$	−16.3298	−1.36557
$144$	−0.263166	−0.0219305
$145$	−15.5988	−1.29541
$146$	15.7598	1.30429
$147$	−5.57246	−0.459609
$148$	3.89747	0.320370
$149$	21.8993	1.79406	0.897030	−	0.441971i	$-0.145720\pi$
$149$	21.8993	1.79406	0.897030	+	0.441971i	$0.145720\pi$
$150$	4.15947	0.339620
$151$	−19.0277	−1.54845	−0.774227	−	0.632908i	$-0.781861\pi$
$151$	−19.0277	−1.54845	−0.774227	+	0.632908i	$0.781861\pi$
$152$	−5.38340	−0.436651
$153$	−1.00000	−0.0808452
$154$	−21.0283	−1.69451
$155$	4.88783	0.392600
$156$	19.8994	1.59323
$157$	−1.00000	−0.0798087
$157$	−1.00000	−0.0798087
$158$	4.39420	0.349583
$159$	3.46416	0.274726
$160$	15.5528	1.22956
$161$	−31.4656	−2.47984
$162$	−2.27518	−0.178755
$163$	−13.9254	−1.09072	−0.545361	−	0.838201i	$-0.683608\pi$
$163$	−13.9254	−1.09072	−0.545361	+	0.838201i	$0.683608\pi$
$164$	21.4609	1.67581
$165$	−6.81133	−0.530261
$166$	−39.8160	−3.09032
$167$	6.04651	0.467893	0.233947	−	0.972249i	$-0.424836\pi$
$167$	6.04651	0.467893	0.233947	+	0.972249i	$0.424836\pi$
$168$	9.49052	0.732210
$169$	26.2468	2.01898
$170$	5.94522	0.455978
$171$	2.01130	0.153808
$172$	−27.9749	−2.13307
$173$	4.42199	0.336198	0.168099	−	0.985770i	$-0.446237\pi$
$173$	4.42199	0.336198	0.168099	+	0.985770i	$0.446237\pi$
$174$	−13.5816	−1.02962
$175$	6.48237	0.490021
$176$	−0.685977	−0.0517074
$177$	−8.10288	−0.609050
$178$	0.0935015	0.00700823
$179$	12.7749	0.954837	0.477419	−	0.878676i	$-0.341573\pi$
$179$	12.7749	0.954837	0.477419	+	0.878676i	$0.341573\pi$
$180$	8.30026	0.618665
$181$	−9.03612	−0.671650	−0.335825	−	0.941924i	$-0.609015\pi$
$181$	−9.03612	−0.671650	−0.335825	+	0.941924i	$0.609015\pi$
$182$	50.5391	3.74620
$183$	−9.35388	−0.691459
$184$	23.7523	1.75104
$185$	3.20625	0.235728
$186$	4.25577	0.312048
$187$	−2.60663	−0.190615
$188$	−23.6116	−1.72205
$189$	−3.54577	−0.257917
$190$	−11.9576	−0.867497
$191$	16.9747	1.22825	0.614123	−	0.789211i	$-0.289510\pi$
$191$	16.9747	1.22825	0.614123	+	0.789211i	$0.289510\pi$
$192$	13.0153	0.939299
$193$	24.4329	1.75872	0.879358	−	0.476162i	$-0.157972\pi$
$193$	24.4329	1.75872	0.879358	+	0.476162i	$0.157972\pi$
$194$	−28.1891	−2.02386
$195$	16.3702	1.17230
$196$	17.7005	1.26432
$197$	−16.1379	−1.14978	−0.574888	−	0.818232i	$-0.694954\pi$
$197$	−16.1379	−1.14978	−0.574888	+	0.818232i	$0.694954\pi$
$198$	−5.93053	−0.421465
$199$	−21.3513	−1.51355	−0.756777	−	0.653673i	$-0.773227\pi$
$199$	−21.3513	−1.51355	−0.756777	+	0.653673i	$0.773227\pi$
$200$	−4.89332	−0.346010
$201$	0.624312	0.0440356
$202$	26.2099	1.84412
$203$	−21.1664	−1.48559
$204$	3.17643	0.222394
$205$	17.6547	1.23306
$206$	39.4494	2.74857
$207$	−8.87413	−0.616795
$208$	1.64867	0.114314
$209$	5.24271	0.362646
$210$	21.0804	1.45468
$211$	−21.0376	−1.44829	−0.724144	−	0.689649i	$-0.757765\pi$
$211$	−21.0376	−1.44829	−0.724144	+	0.689649i	$0.757765\pi$
$212$	−11.0037	−0.755735
$213$	−12.4781	−0.854984
$214$	17.0262	1.16389
$215$	−23.0135	−1.56951
$216$	2.67658	0.182118
$217$	6.63243	0.450239
$218$	−3.65149	−0.247310
$219$	6.92684	0.468073
$220$	21.6357	1.45868
$221$	6.26473	0.421411
$222$	2.79164	0.187363
$223$	−10.4258	−0.698162	−0.349081	−	0.937093i	$-0.613506\pi$
$223$	−10.4258	−0.698162	−0.349081	+	0.937093i	$0.613506\pi$
$224$	21.1041	1.41007
$225$	1.82820	0.121880
$226$	4.23985	0.282031
$227$	14.8548	0.985947	0.492973	−	0.870044i	$-0.335910\pi$
$227$	14.8548	0.985947	0.492973	+	0.870044i	$0.335910\pi$
$228$	−6.38875	−0.423105
$229$	4.09762	0.270778	0.135389	−	0.990792i	$-0.456772\pi$
$229$	4.09762	0.270778	0.135389	+	0.990792i	$0.456772\pi$
$230$	52.7587	3.47880
$231$	−9.24249	−0.608111
$232$	15.9778	1.04899
$233$	25.5973	1.67694	0.838469	−	0.544949i	$-0.183451\pi$
$233$	25.5973	1.67694	0.838469	+	0.544949i	$0.183451\pi$
$234$	14.2534	0.931771
$235$	−19.4240	−1.26709
$236$	25.7382	1.67541
$237$	1.93136	0.125456
$238$	8.06724	0.522922
$239$	−3.45532	−0.223506	−0.111753	−	0.993736i	$-0.535647\pi$
$239$	−3.45532	−0.223506	−0.111753	+	0.993736i	$0.535647\pi$
$240$	0.687676	0.0443893
$241$	2.48706	0.160206	0.0801029	−	0.996787i	$-0.474475\pi$
$241$	2.48706	0.160206	0.0801029	+	0.996787i	$0.474475\pi$
$242$	9.56825	0.615070
$243$	−1.00000	−0.0641500
$244$	29.7119	1.90211
$245$	14.5613	0.930287
$246$	15.3718	0.980067
$247$	−12.6002	−0.801734
$248$	−5.00660	−0.317919
$249$	−17.5002	−1.10903
$250$	18.8571	1.19263
$251$	−6.99590	−0.441577	−0.220789	−	0.975322i	$-0.570863\pi$
$251$	−6.99590	−0.441577	−0.220789	+	0.975322i	$0.570863\pi$
$252$	11.2629	0.709494
$253$	−23.1315	−1.45427
$254$	18.9563	1.18942
$255$	2.61308	0.163638
$256$	−14.2589	−0.891180
$257$	−4.95624	−0.309162	−0.154581	−	0.987980i	$-0.549403\pi$
$257$	−4.95624	−0.309162	−0.154581	+	0.987980i	$0.549403\pi$
$258$	−20.0375	−1.24748
$259$	4.35065	0.270336
$260$	−51.9989	−3.22483
$261$	−5.96949	−0.369502
$262$	35.4436	2.18971
$263$	−6.67551	−0.411630	−0.205815	−	0.978591i	$-0.565984\pi$
$263$	−6.67551	−0.411630	−0.205815	+	0.978591i	$0.565984\pi$
$264$	6.97684	0.429395
$265$	−9.05214	−0.556069
$266$	−16.2256	−0.994858
$267$	0.0410964	0.00251506
$268$	−1.98308	−0.121136
$269$	−14.2545	−0.869110	−0.434555	−	0.900645i	$-0.643094\pi$
$269$	−14.2545	−0.869110	−0.434555	+	0.900645i	$0.643094\pi$
$270$	5.94522	0.361815
$271$	−20.4057	−1.23956	−0.619780	−	0.784776i	$-0.712778\pi$
$271$	−20.4057	−1.23956	−0.619780	+	0.784776i	$0.712778\pi$
$272$	0.263166	0.0159568
$273$	22.2133	1.34441
$274$	28.9957	1.75169
$275$	4.76543	0.287366
$276$	28.1880	1.69672
$277$	−27.0901	−1.62769	−0.813845	−	0.581083i	$-0.802629\pi$
$277$	−27.0901	−1.62769	−0.813845	+	0.581083i	$0.802629\pi$
$278$	12.1981	0.731592
$279$	1.87052	0.111985
$280$	−24.7995	−1.48205
$281$	−29.4109	−1.75451	−0.877255	−	0.480026i	$-0.840627\pi$
$281$	−29.4109	−1.75451	−0.877255	+	0.480026i	$0.840627\pi$
$282$	−16.9123	−1.00711
$283$	−31.9225	−1.89759	−0.948797	−	0.315886i	$-0.897698\pi$
$283$	−31.9225	−1.89759	−0.948797	+	0.315886i	$0.897698\pi$
$284$	39.6357	2.35195
$285$	−5.25569	−0.311320
$286$	37.1532	2.19691
$287$	23.9562	1.41409
$288$	5.95191	0.350719
$289$	1.00000	0.0588235
$290$	35.4899	2.08404
$291$	−12.3898	−0.726306
$292$	−22.0026	−1.28761
$293$	23.7604	1.38810	0.694050	−	0.719927i	$-0.255825\pi$
$293$	23.7604	1.38810	0.694050	+	0.719927i	$0.255825\pi$
$294$	12.6783	0.739415
$295$	21.1735	1.23277
$296$	−3.28416	−0.190888
$297$	−2.60663	−0.151252
$298$	−49.8247	−2.88627
$299$	55.5940	3.21508
$300$	−5.80714	−0.335275
$301$	−31.2277	−1.79993
$302$	43.2914	2.49114
$303$	11.5200	0.661804
$304$	−0.529306	−0.0303578
$305$	24.4425	1.39957
$306$	2.27518	0.130063
$307$	−0.229041	−0.0130721	−0.00653604	−	0.999979i	$-0.502080\pi$
$307$	−0.229041	−0.0130721	−0.00653604	+	0.999979i	$0.502080\pi$
$308$	29.3581	1.67283
$309$	17.3391	0.986385
$310$	−11.1207	−0.631612
$311$	26.6277	1.50992	0.754958	−	0.655773i	$-0.227657\pi$
$311$	26.6277	1.50992	0.754958	+	0.655773i	$0.227657\pi$
$312$	−16.7680	−0.949303
$313$	−3.03505	−0.171551	−0.0857755	−	0.996314i	$-0.527337\pi$
$313$	−3.03505	−0.171551	−0.0857755	+	0.996314i	$0.527337\pi$
$314$	2.27518	0.128396
$315$	9.26538	0.522045
$316$	−6.13484	−0.345112
$317$	14.1657	0.795623	0.397811	−	0.917467i	$-0.369770\pi$
$317$	14.1657	0.795623	0.397811	+	0.917467i	$0.369770\pi$
$318$	−7.88158	−0.441977
$319$	−15.5602	−0.871205
$320$	−34.0101	−1.90122
$321$	7.48347	0.417687
$322$	71.5898	3.98954
$323$	−2.01130	−0.111912
$324$	3.17643	0.176468
$325$	−11.4532	−0.635307
$326$	31.6828	1.75475
$327$	−1.60493	−0.0887527
$328$	−18.0837	−0.998508
$329$	−26.3570	−1.45311
$330$	15.4970	0.853080
$331$	2.25886	0.124158	0.0620792	−	0.998071i	$-0.480227\pi$
$331$	2.25886	0.124158	0.0620792	+	0.998071i	$0.480227\pi$
$332$	55.5880	3.05079
$333$	1.22700	0.0672391
$334$	−13.7569	−0.752743
$335$	−1.63138	−0.0891317
$336$	0.933127	0.0509062
$337$	−3.65934	−0.199337	−0.0996684	−	0.995021i	$-0.531778\pi$
$337$	−3.65934	−0.199337	−0.0996684	+	0.995021i	$0.531778\pi$
$338$	−59.7161	−3.24813
$339$	1.86353	0.101213
$340$	−8.30026	−0.450145
$341$	4.87575	0.264037
$342$	−4.57606	−0.247445
$343$	−5.06173	−0.273308
$344$	23.5727	1.27096
$345$	23.1888	1.24844
$346$	−10.0608	−0.540873
$347$	3.15473	0.169355	0.0846774	−	0.996408i	$-0.473014\pi$
$347$	3.15473	0.169355	0.0846774	+	0.996408i	$0.473014\pi$
$348$	18.9616	1.01645
$349$	−32.3893	−1.73376	−0.866879	−	0.498518i	$-0.833878\pi$
$349$	−32.3893	−1.73376	−0.866879	+	0.498518i	$0.833878\pi$
$350$	−14.7485	−0.788342
$351$	6.26473	0.334386
$352$	15.5144	0.826920
$353$	−3.49864	−0.186214	−0.0931069	−	0.995656i	$-0.529680\pi$
$353$	−3.49864	−0.186214	−0.0931069	+	0.995656i	$0.529680\pi$
$354$	18.4355	0.979835
$355$	32.6063	1.73056
$356$	−0.130540	−0.00691859
$357$	3.54577	0.187662
$358$	−29.0650	−1.53614
$359$	−7.56706	−0.399374	−0.199687	−	0.979860i	$-0.563993\pi$
$359$	−7.56706	−0.399374	−0.199687	+	0.979860i	$0.563993\pi$
$360$	−6.99412	−0.368622
$361$	−14.9547	−0.787088
$362$	20.5588	1.08055
$363$	4.20550	0.220731
$364$	−70.5588	−3.69828
$365$	−18.1004	−0.947419
$366$	21.2817	1.11241
$367$	28.3209	1.47834	0.739169	−	0.673520i	$-0.235219\pi$
$367$	28.3209	1.47834	0.739169	+	0.673520i	$0.235219\pi$
$368$	2.33537	0.121740
$369$	6.75629	0.351718
$370$	−7.29478	−0.379238
$371$	−12.2831	−0.637708
$372$	−5.94158	−0.308056
$373$	17.1973	0.890442	0.445221	−	0.895421i	$-0.353125\pi$
$373$	17.1973	0.890442	0.445221	+	0.895421i	$0.353125\pi$
$374$	5.93053	0.306661
$375$	8.28818	0.428000
$376$	19.8960	1.02606
$377$	37.3972	1.92605
$378$	8.06724	0.414934
$379$	27.4516	1.41010	0.705048	−	0.709160i	$-0.250925\pi$
$379$	27.4516	1.41010	0.705048	+	0.709160i	$0.250925\pi$
$380$	16.6943	0.856400
$381$	8.33178	0.426850
$382$	−38.6204	−1.97599
$383$	6.60303	0.337399	0.168700	−	0.985668i	$-0.446043\pi$
$383$	6.60303	0.337399	0.168700	+	0.985668i	$0.446043\pi$
$384$	−17.7083	−0.903673
$385$	24.1514	1.23087
$386$	−55.5890	−2.82941
$387$	−8.80703	−0.447687
$388$	39.3554	1.99797
$389$	−28.2248	−1.43106	−0.715528	−	0.698584i	$-0.753814\pi$
$389$	−28.2248	−1.43106	−0.715528	+	0.698584i	$0.753814\pi$
$390$	−37.2452	−1.88598
$391$	8.87413	0.448784
$392$	−14.9151	−0.753327
$393$	15.5784	0.785827
$394$	36.7165	1.84975
$395$	−5.04682	−0.253933
$396$	8.27976	0.416074
$397$	−10.6310	−0.533554	−0.266777	−	0.963758i	$-0.585959\pi$
$397$	−10.6310	−0.533554	−0.266777	+	0.963758i	$0.585959\pi$
$398$	48.5780	2.43499
$399$	−7.13160	−0.357026
$400$	−0.481121	−0.0240560
$401$	−11.9271	−0.595613	−0.297806	−	0.954626i	$-0.596255\pi$
$401$	−11.9271	−0.595613	−0.297806	+	0.954626i	$0.596255\pi$
$402$	−1.42042	−0.0708441
$403$	−11.7183	−0.583730
$404$	−36.5923	−1.82053
$405$	2.61308	0.129845
$406$	48.1573	2.39001
$407$	3.19833	0.158535
$408$	−2.67658	−0.132510
$409$	−10.7613	−0.532110	−0.266055	−	0.963958i	$-0.585720\pi$
$409$	−10.7613	−0.532110	−0.266055	+	0.963958i	$0.585720\pi$
$410$	−40.1677	−1.98374
$411$	12.7444	0.628633
$412$	−55.0763	−2.71341
$413$	28.7309	1.41376
$414$	20.1902	0.992295
$415$	45.7294	2.24477
$416$	−37.2871	−1.82815
$417$	5.36138	0.262548
$418$	−11.9281	−0.583421
$419$	9.97199	0.487164	0.243582	−	0.969880i	$-0.421678\pi$
$419$	9.97199	0.487164	0.243582	+	0.969880i	$0.421678\pi$
$420$	−29.4308	−1.43608
$421$	−26.2315	−1.27844	−0.639221	−	0.769023i	$-0.720743\pi$
$421$	−26.2315	−1.27844	−0.639221	+	0.769023i	$0.720743\pi$
$422$	47.8642	2.32999
$423$	−7.43338	−0.361424
$424$	9.27211	0.450293
$425$	−1.82820	−0.0886807
$426$	28.3898	1.37549
$427$	33.1667	1.60505
$428$	−23.7707	−1.14900
$429$	16.3298	0.788410
$430$	52.3598	2.52501
$431$	−8.75436	−0.421683	−0.210841	−	0.977520i	$-0.567620\pi$
$431$	−8.75436	−0.421683	−0.210841	+	0.977520i	$0.567620\pi$
$432$	0.263166	0.0126616
$433$	−15.8567	−0.762024	−0.381012	−	0.924570i	$-0.624424\pi$
$433$	−15.8567	−0.762024	−0.381012	+	0.924570i	$0.624424\pi$
$434$	−15.0900	−0.724341
$435$	15.5988	0.747903
$436$	5.09793	0.244147
$437$	−17.8485	−0.853811
$438$	−15.7598	−0.753032
$439$	31.0956	1.48411	0.742056	−	0.670338i	$-0.233851\pi$
$439$	31.0956	1.48411	0.742056	+	0.670338i	$0.233851\pi$
$440$	−18.2311	−0.869131
$441$	5.57246	0.265355
$442$	−14.2534	−0.677963
$443$	−20.4594	−0.972057	−0.486028	−	0.873943i	$-0.661555\pi$
$443$	−20.4594	−0.972057	−0.486028	+	0.873943i	$0.661555\pi$
$444$	−3.89747	−0.184966
$445$	−0.107388	−0.00509069
$446$	23.7205	1.12320
$447$	−21.8993	−1.03580
$448$	−46.1492	−2.18035
$449$	27.5789	1.30153	0.650764	−	0.759280i	$-0.274449\pi$
$449$	27.5789	1.30153	0.650764	+	0.759280i	$0.274449\pi$
$450$	−4.15947	−0.196080
$451$	17.6111	0.829276
$452$	−5.91935	−0.278423
$453$	19.0277	0.894000
$454$	−33.7973	−1.58618
$455$	−58.0451	−2.72119
$456$	5.38340	0.252101
$457$	−4.17445	−0.195273	−0.0976363	−	0.995222i	$-0.531128\pi$
$457$	−4.17445	−0.195273	−0.0976363	+	0.995222i	$0.531128\pi$
$458$	−9.32281	−0.435626
$459$	1.00000	0.0466760
$460$	−73.6576	−3.43430
$461$	4.42469	0.206078	0.103039	−	0.994677i	$-0.467143\pi$
$461$	4.42469	0.206078	0.103039	+	0.994677i	$0.467143\pi$
$462$	21.0283	0.978325
$463$	5.35314	0.248781	0.124391	−	0.992233i	$-0.460302\pi$
$463$	5.35314	0.248781	0.124391	+	0.992233i	$0.460302\pi$
$464$	1.57097	0.0729304
$465$	−4.88783	−0.226668
$466$	−58.2385	−2.69785
$467$	−5.66484	−0.262138	−0.131069	−	0.991373i	$-0.541841\pi$
$467$	−5.66484	−0.262138	−0.131069	+	0.991373i	$0.541841\pi$
$468$	−19.8994	−0.919852
$469$	−2.21366	−0.102217
$470$	44.1931	2.03848
$471$	1.00000	0.0460776
$472$	−21.6880	−0.998271
$473$	−22.9566	−1.05555
$474$	−4.39420	−0.201832
$475$	3.67706	0.168715
$476$	−11.2629	−0.516233
$477$	−3.46416	−0.158613
$478$	7.86147	0.359575
$479$	−15.6358	−0.714417	−0.357209	−	0.934025i	$-0.616271\pi$
$479$	−15.6358	−0.714417	−0.357209	+	0.934025i	$0.616271\pi$
$480$	−15.5528	−0.709886
$481$	−7.68681	−0.350489
$482$	−5.65851	−0.257738
$483$	31.4656	1.43173
$484$	−13.3585	−0.607203
$485$	32.3757	1.47010
$486$	2.27518	0.103204
$487$	−4.13638	−0.187437	−0.0937187	−	0.995599i	$-0.529875\pi$
$487$	−4.13638	−0.187437	−0.0937187	+	0.995599i	$0.529875\pi$
$488$	−25.0364	−1.13334
$489$	13.9254	0.629729
$490$	−33.1295	−1.49664
$491$	10.3555	0.467338	0.233669	−	0.972316i	$-0.424927\pi$
$491$	10.3555	0.467338	0.233669	+	0.972316i	$0.424927\pi$
$492$	−21.4609	−0.967530
$493$	5.96949	0.268852
$494$	28.6678	1.28982
$495$	6.81133	0.306146
$496$	−0.492259	−0.0221031
$497$	44.2444	1.98463
$498$	39.8160	1.78420
$499$	4.63554	0.207515	0.103758	−	0.994603i	$-0.466913\pi$
$499$	4.63554	0.207515	0.103758	+	0.994603i	$0.466913\pi$
$500$	−26.3268	−1.17737
$501$	−6.04651	−0.270138
$502$	15.9169	0.710406
$503$	−9.62014	−0.428941	−0.214470	−	0.976730i	$-0.568803\pi$
$503$	−9.62014	−0.428941	−0.214470	+	0.976730i	$0.568803\pi$
$504$	−9.49052	−0.422741
$505$	−30.1026	−1.33955
$506$	52.6283	2.33962
$507$	−26.2468	−1.16566
$508$	−26.4653	−1.17421
$509$	14.8763	0.659381	0.329691	−	0.944089i	$-0.393056\pi$
$509$	14.8763	0.659381	0.329691	+	0.944089i	$0.393056\pi$
$510$	−5.94522	−0.263259
$511$	−24.5610	−1.08651
$512$	−2.97511	−0.131483
$513$	−2.01130	−0.0888010
$514$	11.2763	0.497377
$515$	−45.3084	−1.99653
$516$	27.9749	1.23153
$517$	−19.3761	−0.852158
$518$	−9.89850	−0.434915
$519$	−4.42199	−0.194104
$520$	43.8162	1.92147
$521$	−37.9700	−1.66350	−0.831748	−	0.555153i	$-0.812660\pi$
$521$	−37.9700	−1.66350	−0.831748	+	0.555153i	$0.812660\pi$
$522$	13.5816	0.594452
$523$	−17.8279	−0.779562	−0.389781	−	0.920908i	$-0.627449\pi$
$523$	−17.8279	−0.779562	−0.389781	+	0.920908i	$0.627449\pi$
$524$	−49.4837	−2.16170
$525$	−6.48237	−0.282914
$526$	15.1880	0.662227
$527$	−1.87052	−0.0814812
$528$	0.685977	0.0298533
$529$	55.7502	2.42392
$530$	20.5952	0.894599
$531$	8.10288	0.351635
$532$	22.6530	0.982132
$533$	−42.3263	−1.83336
$534$	−0.0935015	−0.00404621
$535$	−19.5549	−0.845434
$536$	1.67102	0.0721770
$537$	−12.7749	−0.551276
$538$	32.4314	1.39822
$539$	14.5253	0.625650
$540$	−8.30026	−0.357187
$541$	30.5975	1.31549	0.657744	−	0.753242i	$-0.271511\pi$
$541$	30.5975	1.31549	0.657744	+	0.753242i	$0.271511\pi$
$542$	46.4266	1.99419
$543$	9.03612	0.387777
$544$	−5.95191	−0.255186
$545$	4.19381	0.179643
$546$	−50.5391	−2.16287
$547$	5.72836	0.244927	0.122464	−	0.992473i	$-0.460921\pi$
$547$	5.72836	0.244927	0.122464	+	0.992473i	$0.460921\pi$
$548$	−40.4815	−1.72929
$549$	9.35388	0.399214
$550$	−10.8422	−0.462313
$551$	−12.0064	−0.511491
$552$	−23.7523	−1.01097
$553$	−6.84817	−0.291214
$554$	61.6349	2.61861
$555$	−3.20625	−0.136098
$556$	−17.0300	−0.722234
$557$	−30.6480	−1.29860	−0.649299	−	0.760533i	$-0.724938\pi$
$557$	−30.6480	−1.29860	−0.649299	+	0.760533i	$0.724938\pi$
$558$	−4.25577	−0.180161
$559$	55.1736	2.33360
$560$	−2.43834	−0.103039
$561$	2.60663	0.110052
$562$	66.9151	2.82264
$563$	−5.47566	−0.230771	−0.115386	−	0.993321i	$-0.536810\pi$
$563$	−5.47566	−0.230771	−0.115386	+	0.993321i	$0.536810\pi$
$564$	23.6116	0.994228
$565$	−4.86955	−0.204863
$566$	72.6293	3.05284
$567$	3.54577	0.148908
$568$	−33.3986	−1.40137
$569$	−39.1643	−1.64185	−0.820926	−	0.571035i	$-0.806542\pi$
$569$	−39.1643	−1.64185	−0.820926	+	0.571035i	$0.806542\pi$
$570$	11.9576	0.500850
$571$	−12.3200	−0.515576	−0.257788	−	0.966201i	$-0.582994\pi$
$571$	−12.3200	−0.515576	−0.257788	+	0.966201i	$0.582994\pi$
$572$	−51.8704	−2.16881
$573$	−16.9747	−0.709128
$574$	−54.5046	−2.27498
$575$	−16.2237	−0.676574
$576$	−13.0153	−0.542304
$577$	−35.0333	−1.45845	−0.729227	−	0.684272i	$-0.760120\pi$
$577$	−35.0333	−1.45845	−0.729227	+	0.684272i	$0.760120\pi$
$578$	−2.27518	−0.0946349
$579$	−24.4329	−1.01539
$580$	−49.5483	−2.05738
$581$	62.0516	2.57433
$582$	28.1891	1.16848
$583$	−9.02978	−0.373975
$584$	18.5402	0.767201
$585$	−16.3702	−0.676826
$586$	−54.0592	−2.23316
$587$	−26.5707	−1.09669	−0.548344	−	0.836253i	$-0.684742\pi$
$587$	−26.5707	−1.09669	−0.548344	+	0.836253i	$0.684742\pi$
$588$	−17.7005	−0.729957
$589$	3.76218	0.155018
$590$	−48.1734	−1.98327
$591$	16.1379	0.663823
$592$	−0.322905	−0.0132713
$593$	−37.2391	−1.52923	−0.764613	−	0.644489i	$-0.777070\pi$
$593$	−37.2391	−1.52923	−0.764613	+	0.644489i	$0.777070\pi$
$594$	5.93053	0.243333
$595$	−9.26538	−0.379844
$596$	69.5615	2.84935
$597$	21.3513	0.873850
$598$	−126.486	−5.17240
$599$	22.9797	0.938927	0.469464	−	0.882952i	$-0.344447\pi$
$599$	22.9797	0.938927	0.469464	+	0.882952i	$0.344447\pi$
$600$	4.89332	0.199769
$601$	−39.6585	−1.61771	−0.808853	−	0.588011i	$-0.799911\pi$
$601$	−39.6585	−1.61771	−0.808853	+	0.588011i	$0.799911\pi$
$602$	71.0485	2.89572
$603$	−0.624312	−0.0254239
$604$	−60.4401	−2.45927
$605$	−10.9893	−0.446779
$606$	−26.2099	−1.06471
$607$	−18.6044	−0.755130	−0.377565	−	0.925983i	$-0.623238\pi$
$607$	−18.6044	−0.755130	−0.377565	+	0.925983i	$0.623238\pi$
$608$	11.9711	0.485491
$609$	21.1664	0.857706
$610$	−55.6109	−2.25162
$611$	46.5681	1.88394
$612$	−3.17643	−0.128399
$613$	38.5118	1.55548	0.777738	−	0.628588i	$-0.216367\pi$
$613$	38.5118	1.55548	0.777738	+	0.628588i	$0.216367\pi$
$614$	0.521109	0.0210302
$615$	−17.6547	−0.711908
$616$	−24.7382	−0.996732
$617$	11.7116	0.471493	0.235746	−	0.971815i	$-0.424247\pi$
$617$	11.7116	0.471493	0.235746	+	0.971815i	$0.424247\pi$
$618$	−39.4494	−1.58689
$619$	−4.34468	−0.174627	−0.0873137	−	0.996181i	$-0.527828\pi$
$619$	−4.34468	−0.174627	−0.0873137	+	0.996181i	$0.527828\pi$
$620$	15.5258	0.623532
$621$	8.87413	0.356107
$622$	−60.5826	−2.42914
$623$	−0.145718	−0.00583807
$624$	−1.64867	−0.0659994
$625$	−30.7987	−1.23195
$626$	6.90526	0.275990
$627$	−5.24271	−0.209374
$628$	−3.17643	−0.126753
$629$	−1.22700	−0.0489237
$630$	−21.0804	−0.839862
$631$	41.8931	1.66774	0.833869	−	0.551963i	$-0.186121\pi$
$631$	41.8931	1.66774	0.833869	+	0.551963i	$0.186121\pi$
$632$	5.16945	0.205630
$633$	21.0376	0.836169
$634$	−32.2294	−1.27999
$635$	−21.7716	−0.863981
$636$	11.0037	0.436324
$637$	−34.9099	−1.38318
$638$	35.4023	1.40159
$639$	12.4781	0.493625
$640$	46.2732	1.82911
$641$	−26.6015	−1.05069	−0.525347	−	0.850888i	$-0.676065\pi$
$641$	−26.6015	−1.05069	−0.525347	+	0.850888i	$0.676065\pi$
$642$	−17.0262	−0.671971
$643$	−37.2983	−1.47090	−0.735452	−	0.677577i	$-0.763030\pi$
$643$	−37.2983	−1.47090	−0.735452	+	0.677577i	$0.763030\pi$
$644$	−99.9482	−3.93851
$645$	23.0135	0.906156
$646$	4.57606	0.180043
$647$	−13.9677	−0.549127	−0.274563	−	0.961569i	$-0.588533\pi$
$647$	−13.9677	−0.549127	−0.274563	+	0.961569i	$0.588533\pi$
$648$	−2.67658	−0.105146
$649$	21.1212	0.829079
$650$	26.0580	1.02208
$651$	−6.63243	−0.259946
$652$	−44.2331	−1.73230
$653$	9.15541	0.358279	0.179139	−	0.983824i	$-0.442669\pi$
$653$	9.15541	0.358279	0.179139	+	0.983824i	$0.442669\pi$
$654$	3.65149	0.142785
$655$	−40.7077	−1.59058
$656$	−1.77803	−0.0694204
$657$	−6.92684	−0.270242
$658$	59.9669	2.33775
$659$	−4.77018	−0.185820	−0.0929100	−	0.995675i	$-0.529617\pi$
$659$	−4.77018	−0.185820	−0.0929100	+	0.995675i	$0.529617\pi$
$660$	−21.6357	−0.842168
$661$	−19.7353	−0.767614	−0.383807	−	0.923413i	$-0.625387\pi$
$661$	−19.7353	−0.767614	−0.383807	+	0.923413i	$0.625387\pi$
$662$	−5.13931	−0.199745
$663$	−6.26473	−0.243302
$664$	−46.8406	−1.81777
$665$	18.6355	0.722652
$666$	−2.79164	−0.108174
$667$	52.9740	2.05116
$668$	19.2063	0.743114
$669$	10.4258	0.403084
$670$	3.71167	0.143394
$671$	24.3821	0.941259
$672$	−21.1041	−0.814107
$673$	21.8824	0.843503	0.421752	−	0.906711i	$-0.361415\pi$
$673$	21.8824	0.843503	0.421752	+	0.906711i	$0.361415\pi$
$674$	8.32564	0.320692
$675$	−1.82820	−0.0703674
$676$	83.3710	3.20658
$677$	31.3801	1.20604	0.603018	−	0.797727i	$-0.293965\pi$
$677$	31.3801	1.20604	0.603018	+	0.797727i	$0.293965\pi$
$678$	−4.23985	−0.162830
$679$	43.9315	1.68594
$680$	6.99412	0.268212
$681$	−14.8548	−0.569237
$682$	−11.0932	−0.424780
$683$	17.0362	0.651873	0.325937	−	0.945392i	$-0.394320\pi$
$683$	17.0362	0.651873	0.325937	+	0.945392i	$0.394320\pi$
$684$	6.38875	0.244280
$685$	−33.3021	−1.27241
$686$	11.5163	0.439695
$687$	−4.09762	−0.156334
$688$	2.31771	0.0883621
$689$	21.7020	0.826782
$690$	−52.7587	−2.00849
$691$	−27.4752	−1.04520	−0.522602	−	0.852577i	$-0.675039\pi$
$691$	−27.4752	−1.04520	−0.522602	+	0.852577i	$0.675039\pi$
$692$	14.0461	0.533954
$693$	9.24249	0.351093
$694$	−7.17757	−0.272457
$695$	−14.0097	−0.531419
$696$	−15.9778	−0.605637
$697$	−6.75629	−0.255913
$698$	73.6913	2.78926
$699$	−25.5973	−0.968181
$700$	20.5908	0.778258
$701$	8.64248	0.326422	0.163211	−	0.986591i	$-0.447815\pi$
$701$	8.64248	0.326422	0.163211	+	0.986591i	$0.447815\pi$
$702$	−14.2534	−0.537958
$703$	2.46786	0.0930772
$704$	−33.9260	−1.27864
$705$	19.4240	0.731552
$706$	7.96002	0.299579
$707$	−40.8471	−1.53621
$708$	−25.7382	−0.967301
$709$	14.5344	0.545851	0.272925	−	0.962035i	$-0.412009\pi$
$709$	14.5344	0.545851	0.272925	+	0.962035i	$0.412009\pi$
$710$	−74.1850	−2.78411
$711$	−1.93136	−0.0724318
$712$	0.109998	0.00412234
$713$	−16.5993	−0.621647
$714$	−8.06724	−0.301909
$715$	−42.6711	−1.59581
$716$	40.5784	1.51649
$717$	3.45532	0.129041
$718$	17.2164	0.642510
$719$	−22.8626	−0.852631	−0.426315	−	0.904575i	$-0.640189\pi$
$719$	−22.8626	−0.852631	−0.426315	+	0.904575i	$0.640189\pi$
$720$	−0.687676	−0.0256282
$721$	−61.4803	−2.28965
$722$	34.0245	1.26626
$723$	−2.48706	−0.0924948
$724$	−28.7026	−1.06672
$725$	−10.9134	−0.405314
$726$	−9.56825	−0.355111
$727$	17.2472	0.639665	0.319832	−	0.947474i	$-0.396373\pi$
$727$	17.2472	0.639665	0.319832	+	0.947474i	$0.396373\pi$
$728$	59.4555	2.20357
$729$	1.00000	0.0370370
$730$	41.1816	1.52420
$731$	8.80703	0.325740
$732$	−29.7119	−1.09818
$733$	−14.0019	−0.517172	−0.258586	−	0.965988i	$-0.583257\pi$
$733$	−14.0019	−0.517172	−0.258586	+	0.965988i	$0.583257\pi$
$734$	−64.4350	−2.37834
$735$	−14.5613	−0.537101
$736$	−52.8180	−1.94690
$737$	−1.62735	−0.0599441
$738$	−15.3718	−0.565842
$739$	42.3491	1.55784	0.778918	−	0.627126i	$-0.215769\pi$
$739$	42.3491	1.55784	0.778918	+	0.627126i	$0.215769\pi$
$740$	10.1844	0.374387
$741$	12.6002	0.462881
$742$	27.9463	1.02594
$743$	46.3646	1.70095	0.850475	−	0.526015i	$-0.176314\pi$
$743$	46.3646	1.70095	0.850475	+	0.526015i	$0.176314\pi$
$744$	5.00660	0.183551
$745$	57.2246	2.09655
$746$	−39.1269	−1.43254
$747$	17.5002	0.640298
$748$	−8.27976	−0.302738
$749$	−26.5347	−0.969555
$750$	−18.8571	−0.688563
$751$	0.00194241	7.08797e−5 0	3.54399e−5	−	1.00000i	$-0.499989\pi$
$751$	0.00194241	7.08797e−5 0	3.54399e−5		1.00000i	$0.499989\pi$
$752$	1.95622	0.0713359
$753$	6.99590	0.254945
$754$	−85.0852	−3.09862
$755$	−49.7210	−1.80953
$756$	−11.2629	−0.409627
$757$	−42.3578	−1.53952	−0.769760	−	0.638333i	$-0.779624\pi$
$757$	−42.3578	−1.53952	−0.769760	+	0.638333i	$0.779624\pi$
$758$	−62.4573	−2.26855
$759$	23.1315	0.839622
$760$	−14.0673	−0.510273
$761$	−38.6416	−1.40076	−0.700379	−	0.713772i	$-0.746985\pi$
$761$	−38.6416	−1.40076	−0.700379	+	0.713772i	$0.746985\pi$
$762$	−18.9563	−0.686713
$763$	5.69070	0.206017
$764$	53.9188	1.95072
$765$	−2.61308	−0.0944762
$766$	−15.0231	−0.542805
$767$	−50.7623	−1.83292
$768$	14.2589	0.514523
$769$	9.97414	0.359677	0.179838	−	0.983696i	$-0.442443\pi$
$769$	9.97414	0.359677	0.179838	+	0.983696i	$0.442443\pi$
$770$	−54.9487	−1.98021
$771$	4.95624	0.178495
$772$	77.6092	2.79322
$773$	30.8573	1.10986	0.554930	−	0.831897i	$-0.312745\pi$
$773$	30.8573	1.10986	0.554930	+	0.831897i	$0.312745\pi$
$774$	20.0375	0.720235
$775$	3.41969	0.122839
$776$	−33.1624	−1.19046
$777$	−4.35065	−0.156079
$778$	64.2164	2.30227
$779$	13.5889	0.486874
$780$	51.9989	1.86186
$781$	32.5257	1.16386
$782$	−20.1902	−0.722001
$783$	5.96949	0.213332
$784$	−1.46648	−0.0523744
$785$	−2.61308	−0.0932649
$786$	−35.4436	−1.26423
$787$	−25.5568	−0.911003	−0.455501	−	0.890235i	$-0.650540\pi$
$787$	−25.5568	−0.911003	−0.455501	+	0.890235i	$0.650540\pi$
$788$	−51.2607	−1.82609
$789$	6.67551	0.237655
$790$	11.4824	0.408525
$791$	−6.60763	−0.234940
$792$	−6.97684	−0.247911
$793$	−58.5995	−2.08093
$794$	24.1874	0.858378
$795$	9.05214	0.321046
$796$	−67.8208	−2.40385
$797$	−14.0522	−0.497753	−0.248876	−	0.968535i	$-0.580061\pi$
$797$	−14.0522	−0.497753	−0.248876	+	0.968535i	$0.580061\pi$
$798$	16.2256	0.574381
$799$	7.43338	0.262974
$800$	10.8813	0.384711
$801$	−0.0410964	−0.00145207
$802$	27.1363	0.958218
$803$	−18.0557	−0.637172
$804$	1.98308	0.0699379
$805$	−82.2222	−2.89795
$806$	26.6612	0.939101
$807$	14.2545	0.501781
$808$	30.8341	1.08474
$809$	3.20618	0.112723	0.0563616	−	0.998410i	$-0.482050\pi$
$809$	3.20618	0.112723	0.0563616	+	0.998410i	$0.482050\pi$
$810$	−5.94522	−0.208894
$811$	−22.9380	−0.805463	−0.402732	−	0.915318i	$-0.631939\pi$
$811$	−22.9380	−0.805463	−0.402732	+	0.915318i	$0.631939\pi$
$812$	−67.2335	−2.35943
$813$	20.4057	0.715660
$814$	−7.27676	−0.255050
$815$	−36.3882	−1.27462
$816$	−0.263166	−0.00921267
$817$	−17.7136	−0.619720
$818$	24.4838	0.856055
$819$	−22.2133	−0.776194
$820$	56.0790	1.95836
$821$	16.1588	0.563944	0.281972	−	0.959423i	$-0.409011\pi$
$821$	16.1588	0.563944	0.281972	+	0.959423i	$0.409011\pi$
$822$	−28.9957	−1.01134
$823$	29.9380	1.04357	0.521786	−	0.853076i	$-0.325266\pi$
$823$	29.9380	1.04357	0.521786	+	0.853076i	$0.325266\pi$
$824$	46.4094	1.61675
$825$	−4.76543	−0.165911
$826$	−65.3679	−2.27444
$827$	8.11019	0.282019	0.141010	−	0.990008i	$-0.454965\pi$
$827$	8.11019	0.282019	0.141010	+	0.990008i	$0.454965\pi$
$828$	−28.1880	−0.979602
$829$	−33.6952	−1.17028	−0.585141	−	0.810932i	$-0.698961\pi$
$829$	−33.6952	−1.17028	−0.585141	+	0.810932i	$0.698961\pi$
$830$	−104.042	−3.61137
$831$	27.0901	0.939747
$832$	81.5373	2.82680
$833$	−5.57246	−0.193074
$834$	−12.1981	−0.422385
$835$	15.8000	0.546783
$836$	16.6531	0.575959
$837$	−1.87052	−0.0646547
$838$	−22.6880	−0.783745
$839$	50.6960	1.75022	0.875110	−	0.483924i	$-0.160789\pi$
$839$	50.6960	1.75022	0.875110	+	0.483924i	$0.160789\pi$
$840$	24.7995	0.855664
$841$	6.63478	0.228786
$842$	59.6812	2.05675
$843$	29.4109	1.01297
$844$	−66.8243	−2.30019
$845$	68.5850	2.35940
$846$	16.9123	0.581455
$847$	−14.9117	−0.512373
$848$	0.911652	0.0313062
$849$	31.9225	1.09558
$850$	4.15947	0.142669
$851$	−10.8886	−0.373255
$852$	−39.6357	−1.35790
$853$	5.26761	0.180360	0.0901798	−	0.995926i	$-0.471256\pi$
$853$	5.26761	0.180360	0.0901798	+	0.995926i	$0.471256\pi$
$854$	−75.4600	−2.58219
$855$	5.25569	0.179741
$856$	20.0301	0.684615
$857$	−16.9689	−0.579647	−0.289824	−	0.957080i	$-0.593597\pi$
$857$	−16.9689	−0.579647	−0.289824	+	0.957080i	$0.593597\pi$
$858$	−37.1532	−1.26839
$859$	−46.2794	−1.57903	−0.789516	−	0.613730i	$-0.789668\pi$
$859$	−46.2794	−1.57903	−0.789516	+	0.613730i	$0.789668\pi$
$860$	−73.1007	−2.49271
$861$	−23.9562	−0.816426
$862$	19.9177	0.678400
$863$	13.7140	0.466829	0.233414	−	0.972377i	$-0.425010\pi$
$863$	13.7140	0.466829	0.233414	+	0.972377i	$0.425010\pi$
$864$	−5.95191	−0.202488
$865$	11.5550	0.392883
$866$	36.0768	1.22594
$867$	−1.00000	−0.0339618
$868$	21.0674	0.715076
$869$	−5.03435	−0.170779
$870$	−35.4899	−1.20322
$871$	3.91114	0.132524
$872$	−4.29571	−0.145471
$873$	12.3898	0.419333
$874$	40.6086	1.37361
$875$	−29.3879	−0.993494
$876$	22.0026	0.743399
$877$	30.9732	1.04589	0.522946	−	0.852366i	$-0.324833\pi$
$877$	30.9732	1.04589	0.522946	+	0.852366i	$0.324833\pi$
$878$	−70.7480	−2.38763
$879$	−23.7604	−0.801419
$880$	−1.79251	−0.0604256
$881$	−43.5601	−1.46758	−0.733789	−	0.679377i	$-0.762250\pi$
$881$	−43.5601	−1.46758	−0.733789	+	0.679377i	$0.762250\pi$
$882$	−12.6783	−0.426901
$883$	7.62998	0.256769	0.128385	−	0.991724i	$-0.459021\pi$
$883$	7.62998	0.256769	0.128385	+	0.991724i	$0.459021\pi$
$884$	19.8994	0.669291
$885$	−21.1735	−0.711739
$886$	46.5488	1.56384
$887$	39.0212	1.31020	0.655102	−	0.755540i	$-0.272625\pi$
$887$	39.0212	1.31020	0.655102	+	0.755540i	$0.272625\pi$
$888$	3.28416	0.110209
$889$	−29.5426	−0.990825
$890$	0.244327	0.00818986
$891$	2.60663	0.0873253
$892$	−33.1167	−1.10883
$893$	−14.9508	−0.500308
$894$	49.8247	1.66639
$895$	33.3817	1.11583
$896$	62.7895	2.09765
$897$	−55.5940	−1.85623
$898$	−62.7468	−2.09389
$899$	−11.1661	−0.372409
$900$	5.80714	0.193571
$901$	3.46416	0.115408
$902$	−40.0684	−1.33413
$903$	31.2277	1.03919
$904$	4.98787	0.165894
$905$	−23.6121	−0.784894
$906$	−43.2914	−1.43826
$907$	15.5332	0.515770	0.257885	−	0.966176i	$-0.416974\pi$
$907$	15.5332	0.515770	0.257885	+	0.966176i	$0.416974\pi$
$908$	47.1851	1.56589
$909$	−11.5200	−0.382093
$910$	132.063	4.37784
$911$	17.6789	0.585729	0.292864	−	0.956154i	$-0.405392\pi$
$911$	17.6789	0.585729	0.292864	+	0.956154i	$0.405392\pi$
$912$	0.529306	0.0175271
$913$	45.6164	1.50968
$914$	9.49761	0.314153
$915$	−24.4425	−0.808043
$916$	13.0158	0.430054
$917$	−55.2374	−1.82410
$918$	−2.27518	−0.0750920
$919$	14.4888	0.477943	0.238971	−	0.971027i	$-0.423190\pi$
$919$	14.4888	0.477943	0.238971	+	0.971027i	$0.423190\pi$
$920$	62.0667	2.04628
$921$	0.229041	0.00754716
$922$	−10.0669	−0.331537
$923$	−78.1718	−2.57306
$924$	−29.3581	−0.965810
$925$	2.24320	0.0737559
$926$	−12.1793	−0.400238
$927$	−17.3391	−0.569490
$928$	−35.5298	−1.16632
$929$	−49.8482	−1.63547	−0.817734	−	0.575597i	$-0.804770\pi$
$929$	−49.8482	−1.63547	−0.817734	+	0.575597i	$0.804770\pi$
$930$	11.1207	0.364661
$931$	11.2079	0.367324
$932$	81.3081	2.66334
$933$	−26.6277	−0.871751
$934$	12.8885	0.421725
$935$	−6.81133	−0.222754
$936$	16.7680	0.548080
$937$	31.3338	1.02363	0.511815	−	0.859095i	$-0.328973\pi$
$937$	31.3338	1.02363	0.511815	+	0.859095i	$0.328973\pi$
$938$	5.03647	0.164447
$939$	3.03505	0.0990450
$940$	−61.6991	−2.01240
$941$	18.4634	0.601888	0.300944	−	0.953642i	$-0.402698\pi$
$941$	18.4634	0.601888	0.300944	+	0.953642i	$0.402698\pi$
$942$	−2.27518	−0.0741292
$943$	−59.9562	−1.95244
$944$	−2.13241	−0.0694039
$945$	−9.26538	−0.301403
$946$	52.2304	1.69816
$947$	−15.0986	−0.490637	−0.245319	−	0.969442i	$-0.578893\pi$
$947$	−15.0986	−0.490637	−0.245319	+	0.969442i	$0.578893\pi$
$948$	6.13484	0.199250
$949$	43.3948	1.40865
$950$	−8.36595	−0.271427
$951$	−14.1657	−0.459353
$952$	9.49052	0.307590
$953$	11.6863	0.378558	0.189279	−	0.981923i	$-0.439385\pi$
$953$	11.6863	0.378558	0.189279	+	0.981923i	$0.439385\pi$
$954$	7.88158	0.255176
$955$	44.3563	1.43533
$956$	−10.9756	−0.354976
$957$	15.5602	0.502991
$958$	35.5742	1.14935
$959$	−45.1885	−1.45921
$960$	34.0101	1.09767
$961$	−27.5011	−0.887134
$962$	17.4889	0.563863
$963$	−7.48347	−0.241152
$964$	7.89997	0.254441
$965$	63.8451	2.05525
$966$	−71.5898	−2.30336
$967$	−28.3352	−0.911200	−0.455600	−	0.890185i	$-0.650575\pi$
$967$	−28.3352	−0.911200	−0.455600	+	0.890185i	$0.650575\pi$
$968$	11.2563	0.361793
$969$	2.01130	0.0646122
$970$	−73.6604	−2.36509
$971$	55.6378	1.78550	0.892750	−	0.450552i	$-0.148773\pi$
$971$	55.6378	1.78550	0.892750	+	0.450552i	$0.148773\pi$
$972$	−3.17643	−0.101884
$973$	−19.0102	−0.609439
$974$	9.41100	0.301548
$975$	11.4532	0.366795
$976$	−2.46163	−0.0787947
$977$	−5.94578	−0.190222	−0.0951111	−	0.995467i	$-0.530321\pi$
$977$	−5.94578	−0.190222	−0.0951111	+	0.995467i	$0.530321\pi$
$978$	−31.6828	−1.01310
$979$	−0.107123	−0.00342366
$980$	46.2529	1.47749
$981$	1.60493	0.0512414
$982$	−23.5606	−0.751850
$983$	10.1332	0.323199	0.161599	−	0.986856i	$-0.448335\pi$
$983$	10.1332	0.323199	0.161599	+	0.986856i	$0.448335\pi$
$984$	18.0837	0.576489
$985$	−42.1696	−1.34363
$986$	−13.5816	−0.432527
$987$	26.3570	0.838954
$988$	−40.0237	−1.27332
$989$	78.1548	2.48518
$990$	−15.4970	−0.492526
$991$	20.5491	0.652763	0.326382	−	0.945238i	$-0.394171\pi$
$991$	20.5491	0.652763	0.326382	+	0.945238i	$0.394171\pi$
$992$	11.1332	0.353479
$993$	−2.25886	−0.0716829
$994$	−100.664	−3.19286
$995$	−55.7927	−1.76875
$996$	−55.5880	−1.76137
$997$	23.4582	0.742929	0.371465	−	0.928447i	$-0.378856\pi$
$997$	23.4582	0.742929	0.371465	+	0.928447i	$0.378856\pi$
$998$	−10.5467	−0.333849
$999$	−1.22700	−0.0388205

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.f.1.7	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.f.1.7	✓	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)

\(f(q)\)	\(=\)	\(q-2.27518 q^{2} -1.00000 q^{3} +3.17643 q^{4} +2.61308 q^{5} +2.27518 q^{6} +3.54577 q^{7} -2.67658 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.27518 q^{2} -1.00000 q^{3} +3.17643 q^{4} +2.61308 q^{5} +2.27518 q^{6} +3.54577 q^{7} -2.67658 q^{8} +1.00000 q^{9} -5.94522 q^{10} +2.60663 q^{11} -3.17643 q^{12} -6.26473 q^{13} -8.06724 q^{14} -2.61308 q^{15} -0.263166 q^{16} -1.00000 q^{17} -2.27518 q^{18} +2.01130 q^{19} +8.30026 q^{20} -3.54577 q^{21} -5.93053 q^{22} -8.87413 q^{23} +2.67658 q^{24} +1.82820 q^{25} +14.2534 q^{26} -1.00000 q^{27} +11.2629 q^{28} -5.96949 q^{29} +5.94522 q^{30} +1.87052 q^{31} +5.95191 q^{32} -2.60663 q^{33} +2.27518 q^{34} +9.26538 q^{35} +3.17643 q^{36} +1.22700 q^{37} -4.57606 q^{38} +6.26473 q^{39} -6.99412 q^{40} +6.75629 q^{41} +8.06724 q^{42} -8.80703 q^{43} +8.27976 q^{44} +2.61308 q^{45} +20.1902 q^{46} -7.43338 q^{47} +0.263166 q^{48} +5.57246 q^{49} -4.15947 q^{50} +1.00000 q^{51} -19.8994 q^{52} -3.46416 q^{53} +2.27518 q^{54} +6.81133 q^{55} -9.49052 q^{56} -2.01130 q^{57} +13.5816 q^{58} +8.10288 q^{59} -8.30026 q^{60} +9.35388 q^{61} -4.25577 q^{62} +3.54577 q^{63} -13.0153 q^{64} -16.3702 q^{65} +5.93053 q^{66} -0.624312 q^{67} -3.17643 q^{68} +8.87413 q^{69} -21.0804 q^{70} +12.4781 q^{71} -2.67658 q^{72} -6.92684 q^{73} -2.79164 q^{74} -1.82820 q^{75} +6.38875 q^{76} +9.24249 q^{77} -14.2534 q^{78} -1.93136 q^{79} -0.687676 q^{80} +1.00000 q^{81} -15.3718 q^{82} +17.5002 q^{83} -11.2629 q^{84} -2.61308 q^{85} +20.0375 q^{86} +5.96949 q^{87} -6.97684 q^{88} -0.0410964 q^{89} -5.94522 q^{90} -22.2133 q^{91} -28.1880 q^{92} -1.87052 q^{93} +16.9123 q^{94} +5.25569 q^{95} -5.95191 q^{96} +12.3898 q^{97} -12.6783 q^{98} +2.60663 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - q^{2} - 48 q^{3} + 45 q^{4} + q^{5} + q^{6} - 13 q^{7} - 6 q^{8} + 48 q^{9}+O(q^{10}) \) 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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