LMFDB - Embedded newform 8007.2.a.i.1.13

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:	$0$
Dimension:	$63$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
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)

$f(q)$	$=$	$q-1.80525 q^{2} +1.00000 q^{3} +1.25895 q^{4} -4.24051 q^{5} -1.80525 q^{6} -2.73260 q^{7} +1.33779 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.80525 q^{2} +1.00000 q^{3} +1.25895 q^{4} -4.24051 q^{5} -1.80525 q^{6} -2.73260 q^{7} +1.33779 q^{8} +1.00000 q^{9} +7.65520 q^{10} +2.72785 q^{11} +1.25895 q^{12} +6.01902 q^{13} +4.93303 q^{14} -4.24051 q^{15} -4.93295 q^{16} +1.00000 q^{17} -1.80525 q^{18} -7.97579 q^{19} -5.33857 q^{20} -2.73260 q^{21} -4.92447 q^{22} +1.26655 q^{23} +1.33779 q^{24} +12.9819 q^{25} -10.8659 q^{26} +1.00000 q^{27} -3.44019 q^{28} +6.96828 q^{29} +7.65520 q^{30} -0.382289 q^{31} +6.22964 q^{32} +2.72785 q^{33} -1.80525 q^{34} +11.5876 q^{35} +1.25895 q^{36} +2.64088 q^{37} +14.3983 q^{38} +6.01902 q^{39} -5.67292 q^{40} -1.76766 q^{41} +4.93303 q^{42} +5.49683 q^{43} +3.43422 q^{44} -4.24051 q^{45} -2.28645 q^{46} -11.0077 q^{47} -4.93295 q^{48} +0.467080 q^{49} -23.4357 q^{50} +1.00000 q^{51} +7.57762 q^{52} +7.72681 q^{53} -1.80525 q^{54} -11.5675 q^{55} -3.65565 q^{56} -7.97579 q^{57} -12.5795 q^{58} +5.10503 q^{59} -5.33857 q^{60} +2.45369 q^{61} +0.690129 q^{62} -2.73260 q^{63} -1.38020 q^{64} -25.5237 q^{65} -4.92447 q^{66} -0.256078 q^{67} +1.25895 q^{68} +1.26655 q^{69} -20.9186 q^{70} -1.13597 q^{71} +1.33779 q^{72} +0.874197 q^{73} -4.76746 q^{74} +12.9819 q^{75} -10.0411 q^{76} -7.45412 q^{77} -10.8659 q^{78} +5.24806 q^{79} +20.9182 q^{80} +1.00000 q^{81} +3.19108 q^{82} -9.71408 q^{83} -3.44019 q^{84} -4.24051 q^{85} -9.92317 q^{86} +6.96828 q^{87} +3.64930 q^{88} +2.17835 q^{89} +7.65520 q^{90} -16.4476 q^{91} +1.59452 q^{92} -0.382289 q^{93} +19.8716 q^{94} +33.8214 q^{95} +6.22964 q^{96} -5.90221 q^{97} -0.843198 q^{98} +2.72785 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 63 q + 10 q^{2} + 63 q^{3} + 70 q^{4} + 19 q^{5} + 10 q^{6} + 11 q^{7} + 27 q^{8} + 63 q^{9}+O(q^{10}) $ 63 * q + 10 * q^2 + 63 * q^3 + 70 * q^4 + 19 * q^5 + 10 * q^6 + 11 * q^7 + 27 * q^8 + 63 * q^9	\( 63 q + 10 q^{2} + 63 q^{3} + 70 q^{4} + 19 q^{5} + 10 q^{6} + 11 q^{7} + 27 q^{8} + 63 q^{9} + 4 q^{10} + 23 q^{11} + 70 q^{12} + 10 q^{13} + 18 q^{14} + 19 q^{15} + 72 q^{16} + 63 q^{17} + 10 q^{18} + 6 q^{19} + 48 q^{20} + 11 q^{21} + 21 q^{22} + 44 q^{23} + 27 q^{24} + 110 q^{25} + 41 q^{26} + 63 q^{27} + 26 q^{28} + 35 q^{29} + 4 q^{30} + q^{31} + 54 q^{32} + 23 q^{33} + 10 q^{34} + 47 q^{35} + 70 q^{36} + 40 q^{37} + 38 q^{38} + 10 q^{39} - 10 q^{40} + 35 q^{41} + 18 q^{42} + 27 q^{43} + 46 q^{44} + 19 q^{45} + 8 q^{46} + 29 q^{47} + 72 q^{48} + 114 q^{49} + 27 q^{50} + 63 q^{51} - q^{52} + 75 q^{53} + 10 q^{54} + 5 q^{55} + 24 q^{56} + 6 q^{57} + 41 q^{58} + 105 q^{59} + 48 q^{60} + 5 q^{61} + 22 q^{62} + 11 q^{63} + 61 q^{64} + 49 q^{65} + 21 q^{66} + 4 q^{67} + 70 q^{68} + 44 q^{69} - 16 q^{70} + 16 q^{71} + 27 q^{72} + 39 q^{73} + 54 q^{74} + 110 q^{75} + 6 q^{76} + 88 q^{77} + 41 q^{78} + 16 q^{79} + 102 q^{80} + 63 q^{81} - 29 q^{82} + 73 q^{83} + 26 q^{84} + 19 q^{85} + 46 q^{86} + 35 q^{87} + 18 q^{88} + 88 q^{89} + 4 q^{90} - 15 q^{91} + 110 q^{92} + q^{93} - 8 q^{94} + 28 q^{95} + 54 q^{96} + 70 q^{97} + 33 q^{98} + 23 q^{99}+O(q^{100}) \) 63 * q + 10 * q^2 + 63 * q^3 + 70 * q^4 + 19 * q^5 + 10 * q^6 + 11 * q^7 + 27 * q^8 + 63 * q^9 + 4 * q^10 + 23 * q^11 + 70 * q^12 + 10 * q^13 + 18 * q^14 + 19 * q^15 + 72 * q^16 + 63 * q^17 + 10 * q^18 + 6 * q^19 + 48 * q^20 + 11 * q^21 + 21 * q^22 + 44 * q^23 + 27 * q^24 + 110 * q^25 + 41 * q^26 + 63 * q^27 + 26 * q^28 + 35 * q^29 + 4 * q^30 + q^31 + 54 * q^32 + 23 * q^33 + 10 * q^34 + 47 * q^35 + 70 * q^36 + 40 * q^37 + 38 * q^38 + 10 * q^39 - 10 * q^40 + 35 * q^41 + 18 * q^42 + 27 * q^43 + 46 * q^44 + 19 * q^45 + 8 * q^46 + 29 * q^47 + 72 * q^48 + 114 * q^49 + 27 * q^50 + 63 * q^51 - q^52 + 75 * q^53 + 10 * q^54 + 5 * q^55 + 24 * q^56 + 6 * q^57 + 41 * q^58 + 105 * q^59 + 48 * q^60 + 5 * q^61 + 22 * q^62 + 11 * q^63 + 61 * q^64 + 49 * q^65 + 21 * q^66 + 4 * q^67 + 70 * q^68 + 44 * q^69 - 16 * q^70 + 16 * q^71 + 27 * q^72 + 39 * q^73 + 54 * q^74 + 110 * q^75 + 6 * q^76 + 88 * q^77 + 41 * q^78 + 16 * q^79 + 102 * q^80 + 63 * q^81 - 29 * q^82 + 73 * q^83 + 26 * q^84 + 19 * q^85 + 46 * q^86 + 35 * q^87 + 18 * q^88 + 88 * q^89 + 4 * q^90 - 15 * q^91 + 110 * q^92 + q^93 - 8 * q^94 + 28 * q^95 + 54 * q^96 + 70 * q^97 + 33 * q^98 + 23 * 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 $

$2$	−1.80525	−1.27651	−0.638254	−	0.769826i	$-0.720343\pi$
$2$	−1.80525	−1.27651	−0.638254	+	0.769826i	$0.720343\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.25895	0.629473
$5$	−4.24051	−1.89641	−0.948206	−	0.317655i	$-0.897105\pi$
$5$	−4.24051	−1.89641	−0.948206	+	0.317655i	$0.897105\pi$
$6$	−1.80525	−0.736992
$7$	−2.73260	−1.03282	−0.516412	−	0.856340i	$-0.672733\pi$
$7$	−2.73260	−1.03282	−0.516412	+	0.856340i	$0.672733\pi$
$8$	1.33779	0.472981
$9$	1.00000	0.333333
$10$	7.65520	2.42079
$11$	2.72785	0.822479	0.411240	−	0.911527i	$-0.365096\pi$
$11$	2.72785	0.822479	0.411240	+	0.911527i	$0.365096\pi$
$12$	1.25895	0.363426
$13$	6.01902	1.66938	0.834688	−	0.550723i	$-0.185648\pi$
$13$	6.01902	1.66938	0.834688	+	0.550723i	$0.185648\pi$
$14$	4.93303	1.31841
$15$	−4.24051	−1.09489
$16$	−4.93295	−1.23324
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.80525	−0.425503
$19$	−7.97579	−1.82977	−0.914886	−	0.403712i	$-0.867720\pi$
$19$	−7.97579	−1.82977	−0.914886	+	0.403712i	$0.867720\pi$
$20$	−5.33857	−1.19374
$21$	−2.73260	−0.596301
$22$	−4.92447	−1.04990
$23$	1.26655	0.264095	0.132047	−	0.991243i	$-0.457845\pi$
$23$	1.26655	0.264095	0.132047	+	0.991243i	$0.457845\pi$
$24$	1.33779	0.273076
$25$	12.9819	2.59638
$26$	−10.8659	−2.13097
$27$	1.00000	0.192450
$28$	−3.44019	−0.650135
$29$	6.96828	1.29398	0.646988	−	0.762500i	$-0.276028\pi$
$29$	6.96828	1.29398	0.646988	+	0.762500i	$0.276028\pi$
$30$	7.65520	1.39764
$31$	−0.382289	−0.0686611	−0.0343306	−	0.999411i	$-0.510930\pi$
$31$	−0.382289	−0.0686611	−0.0343306	+	0.999411i	$0.510930\pi$
$32$	6.22964	1.10126
$33$	2.72785	0.474859
$34$	−1.80525	−0.309599
$35$	11.5876	1.95866
$36$	1.25895	0.209824
$37$	2.64088	0.434158	0.217079	−	0.976154i	$-0.430347\pi$
$37$	2.64088	0.434158	0.217079	+	0.976154i	$0.430347\pi$
$38$	14.3983	2.33572
$39$	6.01902	0.963815
$40$	−5.67292	−0.896967
$41$	−1.76766	−0.276062	−0.138031	−	0.990428i	$-0.544077\pi$
$41$	−1.76766	−0.276062	−0.138031	+	0.990428i	$0.544077\pi$
$42$	4.93303	0.761183
$43$	5.49683	0.838258	0.419129	−	0.907927i	$-0.362335\pi$
$43$	5.49683	0.838258	0.419129	+	0.907927i	$0.362335\pi$
$44$	3.43422	0.517728
$45$	−4.24051	−0.632138
$46$	−2.28645	−0.337119
$47$	−11.0077	−1.60563	−0.802816	−	0.596226i	$-0.796666\pi$
$47$	−11.0077	−1.60563	−0.802816	+	0.596226i	$0.796666\pi$
$48$	−4.93295	−0.712010
$49$	0.467080	0.0667257
$50$	−23.4357	−3.31430
$51$	1.00000	0.140028
$52$	7.57762	1.05083
$53$	7.72681	1.06136	0.530679	−	0.847573i	$-0.321937\pi$
$53$	7.72681	1.06136	0.530679	+	0.847573i	$0.321937\pi$
$54$	−1.80525	−0.245664
$55$	−11.5675	−1.55976
$56$	−3.65565	−0.488506
$57$	−7.97579	−1.05642
$58$	−12.5795	−1.65177
$59$	5.10503	0.664618	0.332309	−	0.943171i	$-0.392172\pi$
$59$	5.10503	0.664618	0.332309	+	0.943171i	$0.392172\pi$
$60$	−5.33857	−0.689206
$61$	2.45369	0.314163	0.157082	−	0.987586i	$-0.449791\pi$
$61$	2.45369	0.314163	0.157082	+	0.987586i	$0.449791\pi$
$62$	0.690129	0.0876465
$63$	−2.73260	−0.344275
$64$	−1.38020	−0.172525
$65$	−25.5237	−3.16583
$66$	−4.92447	−0.606161
$67$	−0.256078	−0.0312849	−0.0156425	−	0.999878i	$-0.504979\pi$
$67$	−0.256078	−0.0312849	−0.0156425	+	0.999878i	$0.504979\pi$
$68$	1.25895	0.152670
$69$	1.26655	0.152475
$70$	−20.9186	−2.50025
$71$	−1.13597	−0.134815	−0.0674075	−	0.997726i	$-0.521473\pi$
$71$	−1.13597	−0.134815	−0.0674075	+	0.997726i	$0.521473\pi$
$72$	1.33779	0.157660
$73$	0.874197	0.102317	0.0511585	−	0.998691i	$-0.483709\pi$
$73$	0.874197	0.102317	0.0511585	+	0.998691i	$0.483709\pi$
$74$	−4.76746	−0.554206
$75$	12.9819	1.49902
$76$	−10.0411	−1.15179
$77$	−7.45412	−0.849476
$78$	−10.8659	−1.23032
$79$	5.24806	0.590453	0.295226	−	0.955427i	$-0.404605\pi$
$79$	5.24806	0.590453	0.295226	+	0.955427i	$0.404605\pi$
$80$	20.9182	2.33873
$81$	1.00000	0.111111
$82$	3.19108	0.352396
$83$	−9.71408	−1.06626	−0.533129	−	0.846034i	$-0.678984\pi$
$83$	−9.71408	−1.06626	−0.533129	+	0.846034i	$0.678984\pi$
$84$	−3.44019	−0.375355
$85$	−4.24051	−0.459948
$86$	−9.92317	−1.07004
$87$	6.96828	0.747078
$88$	3.64930	0.389017
$89$	2.17835	0.230905	0.115452	−	0.993313i	$-0.463168\pi$
$89$	2.17835	0.230905	0.115452	+	0.993313i	$0.463168\pi$
$90$	7.65520	0.806929
$91$	−16.4476	−1.72417
$92$	1.59452	0.166240
$93$	−0.382289	−0.0396415
$94$	19.8716	2.04960
$95$	33.8214	3.47000
$96$	6.22964	0.635810
$97$	−5.90221	−0.599279	−0.299640	−	0.954052i	$-0.596866\pi$
$97$	−5.90221	−0.599279	−0.299640	+	0.954052i	$0.596866\pi$
$98$	−0.843198	−0.0851759
$99$	2.72785	0.274160
$100$	16.3435	1.63435
$101$	−1.15079	−0.114508	−0.0572539	−	0.998360i	$-0.518234\pi$
$101$	−1.15079	−0.114508	−0.0572539	+	0.998360i	$0.518234\pi$
$102$	−1.80525	−0.178747
$103$	−9.44459	−0.930603	−0.465301	−	0.885152i	$-0.654054\pi$
$103$	−9.44459	−0.930603	−0.465301	+	0.885152i	$0.654054\pi$
$104$	8.05220	0.789583
$105$	11.5876	1.13083
$106$	−13.9489	−1.35483
$107$	18.3367	1.77267	0.886336	−	0.463042i	$-0.153242\pi$
$107$	18.3367	1.77267	0.886336	+	0.463042i	$0.153242\pi$
$108$	1.25895	0.121142
$109$	2.68152	0.256843	0.128422	−	0.991720i	$-0.459009\pi$
$109$	2.68152	0.256843	0.128422	+	0.991720i	$0.459009\pi$
$110$	20.8823	1.99105
$111$	2.64088	0.250661
$112$	13.4798	1.27372
$113$	−4.90270	−0.461207	−0.230604	−	0.973048i	$-0.574070\pi$
$113$	−4.90270	−0.461207	−0.230604	+	0.973048i	$0.574070\pi$
$114$	14.3983	1.34853
$115$	−5.37083	−0.500833
$116$	8.77268	0.814523
$117$	6.01902	0.556459
$118$	−9.21588	−0.848390
$119$	−2.73260	−0.250497
$120$	−5.67292	−0.517864
$121$	−3.55881	−0.323528
$122$	−4.42954	−0.401032
$123$	−1.76766	−0.159385
$124$	−0.481281	−0.0432203
$125$	−33.8473	−3.02740
$126$	4.93303	0.439469
$127$	−20.2922	−1.80064	−0.900321	−	0.435226i	$-0.856669\pi$
$127$	−20.2922	−1.80064	−0.900321	+	0.435226i	$0.856669\pi$
$128$	−9.96768	−0.881026
$129$	5.49683	0.483969
$130$	46.0768	4.04120
$131$	16.3759	1.43076	0.715382	−	0.698733i	$-0.246253\pi$
$131$	16.3759	1.43076	0.715382	+	0.698733i	$0.246253\pi$
$132$	3.43422	0.298910
$133$	21.7946	1.88983
$134$	0.462286	0.0399354
$135$	−4.24051	−0.364965
$136$	1.33779	0.114715
$137$	5.08333	0.434299	0.217149	−	0.976138i	$-0.430324\pi$
$137$	5.08333	0.434299	0.217149	+	0.976138i	$0.430324\pi$
$138$	−2.28645	−0.194636
$139$	−19.0355	−1.61457	−0.807283	−	0.590164i	$-0.799063\pi$
$139$	−19.0355	−1.61457	−0.807283	+	0.590164i	$0.799063\pi$
$140$	14.5881	1.23292
$141$	−11.0077	−0.927013
$142$	2.05072	0.172093
$143$	16.4190	1.37303
$144$	−4.93295	−0.411079
$145$	−29.5490	−2.45391
$146$	−1.57815	−0.130608
$147$	0.467080	0.0385241
$148$	3.32472	0.273291
$149$	23.4185	1.91852	0.959258	−	0.282533i	$-0.0911745\pi$
$149$	23.4185	1.91852	0.959258	+	0.282533i	$0.0911745\pi$
$150$	−23.4357	−1.91351
$151$	−10.8150	−0.880115	−0.440058	−	0.897970i	$-0.645042\pi$
$151$	−10.8150	−0.880115	−0.440058	+	0.897970i	$0.645042\pi$
$152$	−10.6700	−0.865448
$153$	1.00000	0.0808452
$154$	13.4566	1.08436
$155$	1.62110	0.130210
$156$	7.57762	0.606695
$157$	1.00000	0.0798087
$157$	1.00000	0.0798087
$158$	−9.47409	−0.753718
$159$	7.72681	0.612776
$160$	−26.4168	−2.08844
$161$	−3.46098	−0.272763
$162$	−1.80525	−0.141834
$163$	−23.7540	−1.86056	−0.930280	−	0.366851i	$-0.880436\pi$
$163$	−23.7540	−1.86056	−0.930280	+	0.366851i	$0.880436\pi$
$164$	−2.22539	−0.173774
$165$	−11.5675	−0.900528
$166$	17.5364	1.36109
$167$	−11.1679	−0.864195	−0.432097	−	0.901827i	$-0.642226\pi$
$167$	−11.1679	−0.864195	−0.432097	+	0.901827i	$0.642226\pi$
$168$	−3.65565	−0.282039
$169$	23.2286	1.78682
$170$	7.65520	0.587127
$171$	−7.97579	−0.609924
$172$	6.92020	0.527661
$173$	−11.1722	−0.849406	−0.424703	−	0.905333i	$-0.639621\pi$
$173$	−11.1722	−0.849406	−0.424703	+	0.905333i	$0.639621\pi$
$174$	−12.5795	−0.953651
$175$	−35.4743	−2.68161
$176$	−13.4564	−1.01431
$177$	5.10503	0.383717
$178$	−3.93248	−0.294752
$179$	2.59580	0.194020	0.0970098	−	0.995283i	$-0.469072\pi$
$179$	2.59580	0.194020	0.0970098	+	0.995283i	$0.469072\pi$
$180$	−5.33857	−0.397913
$181$	−8.82508	−0.655963	−0.327981	−	0.944684i	$-0.606368\pi$
$181$	−8.82508	−0.655963	−0.327981	+	0.944684i	$0.606368\pi$
$182$	29.6920	2.20092
$183$	2.45369	0.181382
$184$	1.69439	0.124912
$185$	−11.1987	−0.823343
$186$	0.690129	0.0506027
$187$	2.72785	0.199481
$188$	−13.8580	−1.01070
$189$	−2.73260	−0.198767
$190$	−61.0563	−4.42949
$191$	−0.911217	−0.0659333	−0.0329667	−	0.999456i	$-0.510496\pi$
$191$	−0.911217	−0.0659333	−0.0329667	+	0.999456i	$0.510496\pi$
$192$	−1.38020	−0.0996072
$193$	−15.4962	−1.11544	−0.557719	−	0.830030i	$-0.688323\pi$
$193$	−15.4962	−1.11544	−0.557719	+	0.830030i	$0.688323\pi$
$194$	10.6550	0.764984
$195$	−25.5237	−1.82779
$196$	0.588028	0.0420020
$197$	14.8974	1.06139	0.530697	−	0.847561i	$-0.321930\pi$
$197$	14.8974	1.06139	0.530697	+	0.847561i	$0.321930\pi$
$198$	−4.92447	−0.349967
$199$	−17.0825	−1.21095	−0.605474	−	0.795865i	$-0.707016\pi$
$199$	−17.0825	−1.21095	−0.605474	+	0.795865i	$0.707016\pi$
$200$	17.3671	1.22804
$201$	−0.256078	−0.0180624
$202$	2.07747	0.146170
$203$	−19.0415	−1.33645
$204$	1.25895	0.0881438
$205$	7.49578	0.523528
$206$	17.0499	1.18792
$207$	1.26655	0.0880316
$208$	−29.6915	−2.05874
$209$	−21.7568	−1.50495
$210$	−20.9186	−1.44352
$211$	4.00666	0.275830	0.137915	−	0.990444i	$-0.455960\pi$
$211$	4.00666	0.275830	0.137915	+	0.990444i	$0.455960\pi$
$212$	9.72763	0.668096
$213$	−1.13597	−0.0778355
$214$	−33.1024	−2.26283
$215$	−23.3093	−1.58968
$216$	1.33779	0.0910253
$217$	1.04464	0.0709149
$218$	−4.84083	−0.327862
$219$	0.874197	0.0590727
$220$	−14.5628	−0.981826
$221$	6.01902	0.404883
$222$	−4.76746	−0.319971
$223$	−20.2777	−1.35790	−0.678949	−	0.734186i	$-0.737564\pi$
$223$	−20.2777	−1.35790	−0.678949	+	0.734186i	$0.737564\pi$
$224$	−17.0231	−1.13740
$225$	12.9819	0.865461
$226$	8.85062	0.588735
$227$	−2.28806	−0.151864	−0.0759319	−	0.997113i	$-0.524193\pi$
$227$	−2.28806	−0.151864	−0.0759319	+	0.997113i	$0.524193\pi$
$228$	−10.0411	−0.664987
$229$	10.7045	0.707375	0.353687	−	0.935364i	$-0.384928\pi$
$229$	10.7045	0.707375	0.353687	+	0.935364i	$0.384928\pi$
$230$	9.69572	0.639317
$231$	−7.45412	−0.490445
$232$	9.32211	0.612027
$233$	0.971518	0.0636462	0.0318231	−	0.999494i	$-0.489869\pi$
$233$	0.971518	0.0636462	0.0318231	+	0.999494i	$0.489869\pi$
$234$	−10.8659	−0.710324
$235$	46.6781	3.04494
$236$	6.42695	0.418359
$237$	5.24806	0.340898
$238$	4.93303	0.319761
$239$	10.3590	0.670069	0.335035	−	0.942206i	$-0.391252\pi$
$239$	10.3590	0.670069	0.335035	+	0.942206i	$0.391252\pi$
$240$	20.9182	1.35026
$241$	25.0437	1.61321	0.806604	−	0.591092i	$-0.201303\pi$
$241$	25.0437	1.61321	0.806604	+	0.591092i	$0.201303\pi$
$242$	6.42456	0.412986
$243$	1.00000	0.0641500
$244$	3.08906	0.197757
$245$	−1.98066	−0.126539
$246$	3.19108	0.203456
$247$	−48.0065	−3.05458
$248$	−0.511423	−0.0324754
$249$	−9.71408	−0.615605
$250$	61.1031	3.86450
$251$	11.6652	0.736298	0.368149	−	0.929767i	$-0.379992\pi$
$251$	11.6652	0.736298	0.368149	+	0.929767i	$0.379992\pi$
$252$	−3.44019	−0.216712
$253$	3.45498	0.217212
$254$	36.6326	2.29853
$255$	−4.24051	−0.265551
$256$	20.7546	1.29716
$257$	22.6470	1.41268	0.706340	−	0.707872i	$-0.250345\pi$
$257$	22.6470	1.41268	0.706340	+	0.707872i	$0.250345\pi$
$258$	−9.92317	−0.617790
$259$	−7.21646	−0.448409
$260$	−32.1330	−1.99280
$261$	6.96828	0.431326
$262$	−29.5626	−1.82638
$263$	23.2350	1.43273	0.716364	−	0.697726i	$-0.245805\pi$
$263$	23.2350	1.43273	0.716364	+	0.697726i	$0.245805\pi$
$264$	3.64930	0.224599
$265$	−32.7656	−2.01277
$266$	−39.3448	−2.41239
$267$	2.17835	0.133313
$268$	−0.322388	−0.0196930
$269$	17.4343	1.06299	0.531494	−	0.847062i	$-0.321631\pi$
$269$	17.4343	1.06299	0.531494	+	0.847062i	$0.321631\pi$
$270$	7.65520	0.465881
$271$	−23.9592	−1.45542	−0.727709	−	0.685886i	$-0.759415\pi$
$271$	−23.9592	−1.45542	−0.727709	+	0.685886i	$0.759415\pi$
$272$	−4.93295	−0.299104
$273$	−16.4476	−0.995451
$274$	−9.17671	−0.554386
$275$	35.4128	2.13547
$276$	1.59452	0.0959790
$277$	26.0904	1.56762	0.783809	−	0.621002i	$-0.213274\pi$
$277$	26.0904	1.56762	0.783809	+	0.621002i	$0.213274\pi$
$278$	34.3639	2.06101
$279$	−0.382289	−0.0228870
$280$	15.5018	0.926410
$281$	−2.79861	−0.166951	−0.0834755	−	0.996510i	$-0.526602\pi$
$281$	−2.79861	−0.166951	−0.0834755	+	0.996510i	$0.526602\pi$
$282$	19.8716	1.18334
$283$	−4.32206	−0.256920	−0.128460	−	0.991715i	$-0.541003\pi$
$283$	−4.32206	−0.256920	−0.128460	+	0.991715i	$0.541003\pi$
$284$	−1.43013	−0.0848624
$285$	33.8214	2.00341
$286$	−29.6405	−1.75268
$287$	4.83030	0.285124
$288$	6.22964	0.367085
$289$	1.00000	0.0588235
$290$	53.3435	3.13244
$291$	−5.90221	−0.345994
$292$	1.10057	0.0644057
$293$	−6.52023	−0.380916	−0.190458	−	0.981695i	$-0.560997\pi$
$293$	−6.52023	−0.380916	−0.190458	+	0.981695i	$0.560997\pi$
$294$	−0.843198	−0.0491763
$295$	−21.6479	−1.26039
$296$	3.53295	0.205349
$297$	2.72785	0.158286
$298$	−42.2763	−2.44900
$299$	7.62342	0.440874
$300$	16.3435	0.943593
$301$	−15.0206	−0.865773
$302$	19.5239	1.12347
$303$	−1.15079	−0.0661111
$304$	39.3442	2.25654
$305$	−10.4049	−0.595783
$306$	−1.80525	−0.103200
$307$	15.2632	0.871118	0.435559	−	0.900160i	$-0.356551\pi$
$307$	15.2632	0.871118	0.435559	+	0.900160i	$0.356551\pi$
$308$	−9.38434	−0.534722
$309$	−9.44459	−0.537284
$310$	−2.92650	−0.166214
$311$	−4.78892	−0.271555	−0.135777	−	0.990739i	$-0.543353\pi$
$311$	−4.78892	−0.271555	−0.135777	+	0.990739i	$0.543353\pi$
$312$	8.05220	0.455866
$313$	−10.6920	−0.604350	−0.302175	−	0.953253i	$-0.597713\pi$
$313$	−10.6920	−0.604350	−0.302175	+	0.953253i	$0.597713\pi$
$314$	−1.80525	−0.101876
$315$	11.5876	0.652887
$316$	6.60702	0.371674
$317$	2.85345	0.160265	0.0801327	−	0.996784i	$-0.474466\pi$
$317$	2.85345	0.160265	0.0801327	+	0.996784i	$0.474466\pi$
$318$	−13.9489	−0.782213
$319$	19.0085	1.06427
$320$	5.85274	0.327178
$321$	18.3367	1.02345
$322$	6.24795	0.348185
$323$	−7.97579	−0.443785
$324$	1.25895	0.0699414
$325$	78.1384	4.33434
$326$	42.8821	2.37502
$327$	2.68152	0.148288
$328$	−2.36476	−0.130572
$329$	30.0795	1.65834
$330$	20.8823	1.14953
$331$	0.232011	0.0127525	0.00637624	−	0.999980i	$-0.497970\pi$
$331$	0.232011	0.0127525	0.00637624	+	0.999980i	$0.497970\pi$
$332$	−12.2295	−0.671181
$333$	2.64088	0.144719
$334$	20.1608	1.10315
$335$	1.08590	0.0593291
$336$	13.4798	0.735381
$337$	−5.33940	−0.290855	−0.145428	−	0.989369i	$-0.546456\pi$
$337$	−5.33940	−0.290855	−0.145428	+	0.989369i	$0.546456\pi$
$338$	−41.9336	−2.28089
$339$	−4.90270	−0.266278
$340$	−5.33857	−0.289524
$341$	−1.04283	−0.0564723
$342$	14.3983	0.778573
$343$	17.8518	0.963908
$344$	7.35361	0.396480
$345$	−5.37083	−0.289156
$346$	20.1686	1.08427
$347$	−22.6188	−1.21424	−0.607120	−	0.794610i	$-0.707675\pi$
$347$	−22.6188	−1.21424	−0.607120	+	0.794610i	$0.707675\pi$
$348$	8.77268	0.470265
$349$	9.90377	0.530137	0.265068	−	0.964230i	$-0.414605\pi$
$349$	9.90377	0.530137	0.265068	+	0.964230i	$0.414605\pi$
$350$	64.0402	3.42309
$351$	6.01902	0.321272
$352$	16.9936	0.905760
$353$	32.1155	1.70934	0.854668	−	0.519174i	$-0.173760\pi$
$353$	32.1155	1.70934	0.854668	+	0.519174i	$0.173760\pi$
$354$	−9.21588	−0.489818
$355$	4.81710	0.255665
$356$	2.74242	0.145348
$357$	−2.73260	−0.144624
$358$	−4.68609	−0.247667
$359$	21.1879	1.11826	0.559129	−	0.829081i	$-0.311136\pi$
$359$	21.1879	1.11826	0.559129	+	0.829081i	$0.311136\pi$
$360$	−5.67292	−0.298989
$361$	44.6133	2.34807
$362$	15.9315	0.837342
$363$	−3.55881	−0.186789
$364$	−20.7066	−1.08532
$365$	−3.70704	−0.194035
$366$	−4.42954	−0.231536
$367$	29.4949	1.53962	0.769811	−	0.638272i	$-0.220350\pi$
$367$	29.4949	1.53962	0.769811	+	0.638272i	$0.220350\pi$
$368$	−6.24785	−0.325691
$369$	−1.76766	−0.0920207
$370$	20.2165	1.05100
$371$	−21.1142	−1.09620
$372$	−0.481281	−0.0249532
$373$	22.4016	1.15991	0.579956	−	0.814648i	$-0.303070\pi$
$373$	22.4016	1.15991	0.579956	+	0.814648i	$0.303070\pi$
$374$	−4.92447	−0.254638
$375$	−33.8473	−1.74787
$376$	−14.7260	−0.759434
$377$	41.9422	2.16013
$378$	4.93303	0.253728
$379$	−14.9675	−0.768829	−0.384414	−	0.923161i	$-0.625597\pi$
$379$	−14.9675	−0.768829	−0.384414	+	0.923161i	$0.625597\pi$
$380$	42.5793	2.18427
$381$	−20.2922	−1.03960
$382$	1.64498	0.0841644
$383$	−6.21830	−0.317740	−0.158870	−	0.987299i	$-0.550785\pi$
$383$	−6.21830	−0.317740	−0.158870	+	0.987299i	$0.550785\pi$
$384$	−9.96768	−0.508661
$385$	31.6093	1.61096
$386$	27.9745	1.42387
$387$	5.49683	0.279419
$388$	−7.43056	−0.377230
$389$	−13.1042	−0.664410	−0.332205	−	0.943207i	$-0.607793\pi$
$389$	−13.1042	−0.664410	−0.332205	+	0.943207i	$0.607793\pi$
$390$	46.0768	2.33319
$391$	1.26655	0.0640524
$392$	0.624856	0.0315600
$393$	16.3759	0.826052
$394$	−26.8936	−1.35488
$395$	−22.2544	−1.11974
$396$	3.43422	0.172576
$397$	−15.1956	−0.762645	−0.381323	−	0.924442i	$-0.624531\pi$
$397$	−15.1956	−0.762645	−0.381323	+	0.924442i	$0.624531\pi$
$398$	30.8383	1.54579
$399$	21.7946	1.09110
$400$	−64.0391	−3.20195
$401$	−9.03474	−0.451173	−0.225587	−	0.974223i	$-0.572430\pi$
$401$	−9.03474	−0.451173	−0.225587	+	0.974223i	$0.572430\pi$
$402$	0.462286	0.0230567
$403$	−2.30101	−0.114621
$404$	−1.44878	−0.0720795
$405$	−4.24051	−0.210713
$406$	34.3747	1.70599
$407$	7.20394	0.357086
$408$	1.33779	0.0662306
$409$	10.8181	0.534921	0.267460	−	0.963569i	$-0.413816\pi$
$409$	10.8181	0.534921	0.267460	+	0.963569i	$0.413816\pi$
$410$	−13.5318	−0.668288
$411$	5.08333	0.250742
$412$	−11.8902	−0.585789
$413$	−13.9500	−0.686433
$414$	−2.28645	−0.112373
$415$	41.1926	2.02207
$416$	37.4963	1.83841
$417$	−19.0355	−0.932170
$418$	39.2766	1.92108
$419$	8.46907	0.413741	0.206871	−	0.978368i	$-0.433672\pi$
$419$	8.46907	0.413741	0.206871	+	0.978368i	$0.433672\pi$
$420$	14.5881	0.711829
$421$	17.6785	0.861597	0.430799	−	0.902448i	$-0.358232\pi$
$421$	17.6785	0.861597	0.430799	+	0.902448i	$0.358232\pi$
$422$	−7.23305	−0.352099
$423$	−11.0077	−0.535211
$424$	10.3369	0.502003
$425$	12.9819	0.629715
$426$	2.05072	0.0993577
$427$	−6.70495	−0.324475
$428$	23.0849	1.11585
$429$	16.4190	0.792718
$430$	42.0793	2.02924
$431$	−41.1502	−1.98213	−0.991067	−	0.133368i	$-0.957421\pi$
$431$	−41.1502	−1.98213	−0.991067	+	0.133368i	$0.957421\pi$
$432$	−4.93295	−0.237337
$433$	13.8889	0.667458	0.333729	−	0.942669i	$-0.391693\pi$
$433$	13.8889	0.667458	0.333729	+	0.942669i	$0.391693\pi$
$434$	−1.88584	−0.0905234
$435$	−29.5490	−1.41677
$436$	3.37589	0.161676
$437$	−10.1018	−0.483233
$438$	−1.57815	−0.0754068
$439$	−11.2700	−0.537888	−0.268944	−	0.963156i	$-0.586675\pi$
$439$	−11.2700	−0.537888	−0.268944	+	0.963156i	$0.586675\pi$
$440$	−15.4749	−0.737737
$441$	0.467080	0.0222419
$442$	−10.8659	−0.516837
$443$	18.2179	0.865561	0.432780	−	0.901499i	$-0.357533\pi$
$443$	18.2179	0.865561	0.432780	+	0.901499i	$0.357533\pi$
$444$	3.32472	0.157784
$445$	−9.23731	−0.437891
$446$	36.6065	1.73337
$447$	23.4185	1.10766
$448$	3.77152	0.178188
$449$	26.8240	1.26590	0.632952	−	0.774191i	$-0.281843\pi$
$449$	26.8240	1.26590	0.632952	+	0.774191i	$0.281843\pi$
$450$	−23.4357	−1.10477
$451$	−4.82192	−0.227055
$452$	−6.17223	−0.290317
$453$	−10.8150	−0.508135
$454$	4.13053	0.193855
$455$	69.7460	3.26974
$456$	−10.6700	−0.499667
$457$	28.6405	1.33974	0.669872	−	0.742477i	$-0.266349\pi$
$457$	28.6405	1.33974	0.669872	+	0.742477i	$0.266349\pi$
$458$	−19.3244	−0.902969
$459$	1.00000	0.0466760
$460$	−6.76159	−0.315261
$461$	−18.7732	−0.874354	−0.437177	−	0.899376i	$-0.644022\pi$
$461$	−18.7732	−0.874354	−0.437177	+	0.899376i	$0.644022\pi$
$462$	13.4566	0.626057
$463$	39.2606	1.82459	0.912297	−	0.409529i	$-0.134307\pi$
$463$	39.2606	1.82459	0.912297	+	0.409529i	$0.134307\pi$
$464$	−34.3741	−1.59578
$465$	1.62110	0.0751767
$466$	−1.75384	−0.0812449
$467$	−5.03155	−0.232833	−0.116416	−	0.993201i	$-0.537141\pi$
$467$	−5.03155	−0.232833	−0.116416	+	0.993201i	$0.537141\pi$
$468$	7.57762	0.350276
$469$	0.699758	0.0323118
$470$	−84.2659	−3.88689
$471$	1.00000	0.0460776
$472$	6.82947	0.314352
$473$	14.9945	0.689450
$474$	−9.47409	−0.435159
$475$	−103.541	−4.75079
$476$	−3.44019	−0.157681
$477$	7.72681	0.353786
$478$	−18.7007	−0.855349
$479$	−6.58857	−0.301040	−0.150520	−	0.988607i	$-0.548095\pi$
$479$	−6.58857	−0.301040	−0.150520	+	0.988607i	$0.548095\pi$
$480$	−26.4168	−1.20576
$481$	15.8955	0.724773
$482$	−45.2103	−2.05927
$483$	−3.46098	−0.157480
$484$	−4.48034	−0.203652
$485$	25.0284	1.13648
$486$	−1.80525	−0.0818880
$487$	−28.8213	−1.30602	−0.653010	−	0.757349i	$-0.726494\pi$
$487$	−28.8213	−1.30602	−0.653010	+	0.757349i	$0.726494\pi$
$488$	3.28253	0.148593
$489$	−23.7540	−1.07419
$490$	3.57559	0.161529
$491$	34.6631	1.56433	0.782163	−	0.623074i	$-0.214116\pi$
$491$	34.6631	1.56433	0.782163	+	0.623074i	$0.214116\pi$
$492$	−2.22539	−0.100328
$493$	6.96828	0.313835
$494$	86.6639	3.89919
$495$	−11.5675	−0.519920
$496$	1.88581	0.0846754
$497$	3.10415	0.139240
$498$	17.5364	0.785824
$499$	41.5456	1.85983	0.929917	−	0.367769i	$-0.119878\pi$
$499$	41.5456	1.85983	0.929917	+	0.367769i	$0.119878\pi$
$500$	−42.6120	−1.90566
$501$	−11.1679	−0.498943
$502$	−21.0586	−0.939891
$503$	−19.5013	−0.869521	−0.434761	−	0.900546i	$-0.643167\pi$
$503$	−19.5013	−0.869521	−0.434761	+	0.900546i	$0.643167\pi$
$504$	−3.65565	−0.162835
$505$	4.87993	0.217154
$506$	−6.23711	−0.277273
$507$	23.2286	1.03162
$508$	−25.5468	−1.13346
$509$	23.6390	1.04778	0.523890	−	0.851786i	$-0.324480\pi$
$509$	23.6390	1.04778	0.523890	+	0.851786i	$0.324480\pi$
$510$	7.65520	0.338978
$511$	−2.38883	−0.105675
$512$	−17.5320	−0.774811
$513$	−7.97579	−0.352140
$514$	−40.8836	−1.80330
$515$	40.0499	1.76481
$516$	6.92020	0.304645
$517$	−30.0273	−1.32060
$518$	13.0275	0.572398
$519$	−11.1722	−0.490405
$520$	−34.1454	−1.49738
$521$	13.0585	0.572103	0.286051	−	0.958214i	$-0.407657\pi$
$521$	13.0585	0.572103	0.286051	+	0.958214i	$0.407657\pi$
$522$	−12.5795	−0.550591
$523$	6.39364	0.279574	0.139787	−	0.990182i	$-0.455358\pi$
$523$	6.39364	0.279574	0.139787	+	0.990182i	$0.455358\pi$
$524$	20.6163	0.900627
$525$	−35.4743	−1.54823
$526$	−41.9450	−1.82889
$527$	−0.382289	−0.0166528
$528$	−13.4564	−0.585613
$529$	−21.3958	−0.930254
$530$	59.1503	2.56932
$531$	5.10503	0.221539
$532$	27.4382	1.18960
$533$	−10.6396	−0.460852
$534$	−3.93248	−0.170175
$535$	−77.7568	−3.36172
$536$	−0.342579	−0.0147972
$537$	2.59580	0.112017
$538$	−31.4734	−1.35691
$539$	1.27413	0.0548805
$540$	−5.33857	−0.229735
$541$	4.72434	0.203115	0.101558	−	0.994830i	$-0.467617\pi$
$541$	4.72434	0.203115	0.101558	+	0.994830i	$0.467617\pi$
$542$	43.2525	1.85785
$543$	−8.82508	−0.378720
$544$	6.22964	0.267094
$545$	−11.3710	−0.487080
$546$	29.6920	1.27070
$547$	38.6663	1.65325	0.826627	−	0.562751i	$-0.190257\pi$
$547$	38.6663	1.65325	0.826627	+	0.562751i	$0.190257\pi$
$548$	6.39964	0.273379
$549$	2.45369	0.104721
$550$	−63.9291	−2.72594
$551$	−55.5775	−2.36768
$552$	1.69439	0.0721179
$553$	−14.3408	−0.609834
$554$	−47.0998	−2.00108
$555$	−11.1987	−0.475357
$556$	−23.9646	−1.01633
$557$	2.28573	0.0968494	0.0484247	−	0.998827i	$-0.484580\pi$
$557$	2.28573	0.0968494	0.0484247	+	0.998827i	$0.484580\pi$
$558$	0.690129	0.0292155
$559$	33.0855	1.39937
$560$	−57.1610	−2.41549
$561$	2.72785	0.115170
$562$	5.05220	0.213114
$563$	5.50825	0.232145	0.116073	−	0.993241i	$-0.462969\pi$
$563$	5.50825	0.232145	0.116073	+	0.993241i	$0.462969\pi$
$564$	−13.8580	−0.583529
$565$	20.7899	0.874639
$566$	7.80242	0.327960
$567$	−2.73260	−0.114758
$568$	−1.51970	−0.0637650
$569$	−21.1739	−0.887658	−0.443829	−	0.896112i	$-0.646380\pi$
$569$	−21.1739	−0.887658	−0.443829	+	0.896112i	$0.646380\pi$
$570$	−61.0563	−2.55737
$571$	28.0182	1.17253	0.586263	−	0.810121i	$-0.300598\pi$
$571$	28.0182	1.17253	0.586263	+	0.810121i	$0.300598\pi$
$572$	20.6706	0.864283
$573$	−0.911217	−0.0380666
$574$	−8.71993	−0.363963
$575$	16.4423	0.685691
$576$	−1.38020	−0.0575082
$577$	−27.0122	−1.12453	−0.562267	−	0.826956i	$-0.690071\pi$
$577$	−27.0122	−1.12453	−0.562267	+	0.826956i	$0.690071\pi$
$578$	−1.80525	−0.0750887
$579$	−15.4962	−0.643998
$580$	−37.2006	−1.54467
$581$	26.5447	1.10126
$582$	10.6550	0.441664
$583$	21.0776	0.872946
$584$	1.16949	0.0483940
$585$	−25.5237	−1.05528
$586$	11.7707	0.486242
$587$	35.8697	1.48050	0.740250	−	0.672331i	$-0.234707\pi$
$587$	35.8697	1.48050	0.740250	+	0.672331i	$0.234707\pi$
$588$	0.588028	0.0242499
$589$	3.04906	0.125634
$590$	39.0800	1.60890
$591$	14.8974	0.612797
$592$	−13.0273	−0.535420
$593$	41.2759	1.69500	0.847499	−	0.530796i	$-0.178107\pi$
$593$	41.2759	1.69500	0.847499	+	0.530796i	$0.178107\pi$
$594$	−4.92447	−0.202054
$595$	11.5876	0.475045
$596$	29.4826	1.20765
$597$	−17.0825	−0.699141
$598$	−13.7622	−0.562779
$599$	−36.6009	−1.49547	−0.747737	−	0.663995i	$-0.768860\pi$
$599$	−36.6009	−1.49547	−0.747737	+	0.663995i	$0.768860\pi$
$600$	17.3671	0.709009
$601$	10.4497	0.426254	0.213127	−	0.977025i	$-0.431635\pi$
$601$	10.4497	0.426254	0.213127	+	0.977025i	$0.431635\pi$
$602$	27.1160	1.10517
$603$	−0.256078	−0.0104283
$604$	−13.6155	−0.554008
$605$	15.0912	0.613543
$606$	2.07747	0.0843914
$607$	40.6844	1.65133	0.825664	−	0.564162i	$-0.190801\pi$
$607$	40.6844	1.65133	0.825664	+	0.564162i	$0.190801\pi$
$608$	−49.6863	−2.01505
$609$	−19.0415	−0.771600
$610$	18.7835	0.760522
$611$	−66.2554	−2.68041
$612$	1.25895	0.0508898
$613$	−5.71026	−0.230635	−0.115318	−	0.993329i	$-0.536789\pi$
$613$	−5.71026	−0.230635	−0.115318	+	0.993329i	$0.536789\pi$
$614$	−27.5540	−1.11199
$615$	7.49578	0.302259
$616$	−9.97207	−0.401786
$617$	22.6849	0.913260	0.456630	−	0.889657i	$-0.349056\pi$
$617$	22.6849	0.913260	0.456630	+	0.889657i	$0.349056\pi$
$618$	17.0499	0.685847
$619$	37.0946	1.49096	0.745479	−	0.666529i	$-0.232221\pi$
$619$	37.0946	1.49096	0.745479	+	0.666529i	$0.232221\pi$
$620$	2.04088	0.0819635
$621$	1.26655	0.0508251
$622$	8.64522	0.346642
$623$	−5.95255	−0.238484
$624$	−29.6915	−1.18861
$625$	78.6204	3.14482
$626$	19.3019	0.771457
$627$	−21.7568	−0.868883
$628$	1.25895	0.0502374
$629$	2.64088	0.105299
$630$	−20.9186	−0.833415
$631$	−19.4189	−0.773056	−0.386528	−	0.922278i	$-0.626326\pi$
$631$	−19.4189	−0.773056	−0.386528	+	0.922278i	$0.626326\pi$
$632$	7.02082	0.279273
$633$	4.00666	0.159251
$634$	−5.15120	−0.204580
$635$	86.0493	3.41476
$636$	9.72763	0.385726
$637$	2.81136	0.111390
$638$	−34.3151	−1.35855
$639$	−1.13597	−0.0449384
$640$	42.2680	1.67079
$641$	−21.2616	−0.839781	−0.419891	−	0.907575i	$-0.637932\pi$
$641$	−21.2616	−0.839781	−0.419891	+	0.907575i	$0.637932\pi$
$642$	−33.1024	−1.30645
$643$	−8.69458	−0.342881	−0.171440	−	0.985195i	$-0.554842\pi$
$643$	−8.69458	−0.342881	−0.171440	+	0.985195i	$0.554842\pi$
$644$	−4.35719	−0.171697
$645$	−23.3093	−0.917804
$646$	14.3983	0.566495
$647$	−36.9487	−1.45260	−0.726302	−	0.687376i	$-0.758762\pi$
$647$	−36.9487	−1.45260	−0.726302	+	0.687376i	$0.758762\pi$
$648$	1.33779	0.0525535
$649$	13.9258	0.546634
$650$	−141.060	−5.53282
$651$	1.04464	0.0409427
$652$	−29.9050	−1.17117
$653$	−11.7604	−0.460219	−0.230110	−	0.973165i	$-0.573908\pi$
$653$	−11.7604	−0.460219	−0.230110	+	0.973165i	$0.573908\pi$
$654$	−4.84083	−0.189291
$655$	−69.4419	−2.71332
$656$	8.71978	0.340450
$657$	0.874197	0.0341057
$658$	−54.3012	−2.11688
$659$	36.1744	1.40915	0.704577	−	0.709627i	$-0.251137\pi$
$659$	36.1744	1.40915	0.704577	+	0.709627i	$0.251137\pi$
$660$	−14.5628	−0.566858
$661$	−12.2514	−0.476526	−0.238263	−	0.971201i	$-0.576578\pi$
$661$	−12.2514	−0.476526	−0.238263	+	0.971201i	$0.576578\pi$
$662$	−0.418839	−0.0162786
$663$	6.01902	0.233759
$664$	−12.9954	−0.504320
$665$	−92.4203	−3.58390
$666$	−4.76746	−0.184735
$667$	8.82570	0.341733
$668$	−14.0597	−0.543987
$669$	−20.2777	−0.783982
$670$	−1.96033	−0.0757341
$671$	6.69331	0.258393
$672$	−17.0231	−0.656680
$673$	−23.5754	−0.908765	−0.454382	−	0.890807i	$-0.650140\pi$
$673$	−23.5754	−0.908765	−0.454382	+	0.890807i	$0.650140\pi$
$674$	9.63897	0.371279
$675$	12.9819	0.499674
$676$	29.2436	1.12475
$677$	39.4610	1.51661	0.758304	−	0.651901i	$-0.226028\pi$
$677$	39.4610	1.51661	0.758304	+	0.651901i	$0.226028\pi$
$678$	8.85062	0.339906
$679$	16.1284	0.618950
$680$	−5.67292	−0.217547
$681$	−2.28806	−0.0876786
$682$	1.88257	0.0720874
$683$	−14.5451	−0.556553	−0.278276	−	0.960501i	$-0.589763\pi$
$683$	−14.5451	−0.556553	−0.278276	+	0.960501i	$0.589763\pi$
$684$	−10.0411	−0.383931
$685$	−21.5559	−0.823609
$686$	−32.2271	−1.23044
$687$	10.7045	0.408403
$688$	−27.1156	−1.03377
$689$	46.5078	1.77181
$690$	9.69572	0.369110
$691$	36.2643	1.37956	0.689779	−	0.724020i	$-0.257708\pi$
$691$	36.2643	1.37956	0.689779	+	0.724020i	$0.257708\pi$
$692$	−14.0652	−0.534678
$693$	−7.45412	−0.283159
$694$	40.8327	1.54999
$695$	80.7200	3.06188
$696$	9.32211	0.353354
$697$	−1.76766	−0.0669549
$698$	−17.8788	−0.676724
$699$	0.971518	0.0367462
$700$	−44.6602	−1.68800
$701$	14.5884	0.550997	0.275499	−	0.961301i	$-0.411157\pi$
$701$	14.5884	0.550997	0.275499	+	0.961301i	$0.411157\pi$
$702$	−10.8659	−0.410106
$703$	−21.0631	−0.794411
$704$	−3.76498	−0.141898
$705$	46.6781	1.75800
$706$	−57.9767	−2.18198
$707$	3.14464	0.118266
$708$	6.42695	0.241540
$709$	−29.1441	−1.09453	−0.547265	−	0.836959i	$-0.684331\pi$
$709$	−29.1441	−1.09453	−0.547265	+	0.836959i	$0.684331\pi$
$710$	−8.69609	−0.326359
$711$	5.24806	0.196818
$712$	2.91418	0.109214
$713$	−0.484190	−0.0181330
$714$	4.93303	0.184614
$715$	−69.6250	−2.60383
$716$	3.26798	0.122130
$717$	10.3590	0.386865
$718$	−38.2496	−1.42746
$719$	8.37071	0.312175	0.156087	−	0.987743i	$-0.450112\pi$
$719$	8.37071	0.312175	0.156087	+	0.987743i	$0.450112\pi$
$720$	20.9182	0.779575
$721$	25.8082	0.961149
$722$	−80.5383	−2.99733
$723$	25.0437	0.931387
$724$	−11.1103	−0.412911
$725$	90.4615	3.35966
$726$	6.42456	0.238438
$727$	4.24513	0.157443	0.0787216	−	0.996897i	$-0.474916\pi$
$727$	4.24513	0.157443	0.0787216	+	0.996897i	$0.474916\pi$
$728$	−22.0034	−0.815501
$729$	1.00000	0.0370370
$730$	6.69215	0.247688
$731$	5.49683	0.203307
$732$	3.08906	0.114175
$733$	−2.41153	−0.0890719	−0.0445359	−	0.999008i	$-0.514181\pi$
$733$	−2.41153	−0.0890719	−0.0445359	+	0.999008i	$0.514181\pi$
$734$	−53.2459	−1.96534
$735$	−1.98066	−0.0730576
$736$	7.89018	0.290836
$737$	−0.698544	−0.0257312
$738$	3.19108	0.117465
$739$	−36.7581	−1.35217	−0.676084	−	0.736824i	$-0.736324\pi$
$739$	−36.7581	−1.35217	−0.676084	+	0.736824i	$0.736324\pi$
$740$	−14.0985	−0.518272
$741$	−48.0065	−1.76356
$742$	38.1166	1.39930
$743$	39.6495	1.45460	0.727299	−	0.686321i	$-0.240775\pi$
$743$	39.6495	1.45460	0.727299	+	0.686321i	$0.240775\pi$
$744$	−0.511423	−0.0187497
$745$	−99.3062	−3.63830
$746$	−40.4406	−1.48064
$747$	−9.71408	−0.355420
$748$	3.43422	0.125568
$749$	−50.1067	−1.83086
$750$	61.1031	2.23117
$751$	17.9965	0.656701	0.328351	−	0.944556i	$-0.393507\pi$
$751$	17.9965	0.656701	0.328351	+	0.944556i	$0.393507\pi$
$752$	54.3002	1.98013
$753$	11.6652	0.425102
$754$	−75.7164	−2.75743
$755$	45.8612	1.66906
$756$	−3.44019	−0.125118
$757$	−4.40015	−0.159926	−0.0799630	−	0.996798i	$-0.525480\pi$
$757$	−4.40015	−0.159926	−0.0799630	+	0.996798i	$0.525480\pi$
$758$	27.0201	0.981416
$759$	3.45498	0.125408
$760$	45.2460	1.64125
$761$	−25.4137	−0.921247	−0.460623	−	0.887596i	$-0.652374\pi$
$761$	−25.4137	−0.921247	−0.460623	+	0.887596i	$0.652374\pi$
$762$	36.6326	1.32706
$763$	−7.32751	−0.265274
$764$	−1.14717	−0.0415032
$765$	−4.24051	−0.153316
$766$	11.2256	0.405598
$767$	30.7273	1.10950
$768$	20.7546	0.748917
$769$	39.2091	1.41392	0.706959	−	0.707255i	$-0.250067\pi$
$769$	39.2091	1.41392	0.706959	+	0.707255i	$0.250067\pi$
$770$	−57.0628	−2.05640
$771$	22.6470	0.815612
$772$	−19.5088	−0.702137
$773$	−0.401131	−0.0144277	−0.00721385	−	0.999974i	$-0.502296\pi$
$773$	−0.401131	−0.0144277	−0.00721385	+	0.999974i	$0.502296\pi$
$774$	−9.92317	−0.356681
$775$	−4.96284	−0.178270
$776$	−7.89594	−0.283448
$777$	−7.21646	−0.258889
$778$	23.6564	0.848124
$779$	14.0985	0.505131
$780$	−32.1330	−1.15054
$781$	−3.09877	−0.110883
$782$	−2.28645	−0.0817634
$783$	6.96828	0.249026
$784$	−2.30408	−0.0822886
$785$	−4.24051	−0.151350
$786$	−29.5626	−1.05446
$787$	24.1384	0.860440	0.430220	−	0.902724i	$-0.358436\pi$
$787$	24.1384	0.860440	0.430220	+	0.902724i	$0.358436\pi$
$788$	18.7550	0.668119
$789$	23.2350	0.827186
$790$	40.1749	1.42936
$791$	13.3971	0.476346
$792$	3.64930	0.129672
$793$	14.7688	0.524456
$794$	27.4319	0.973523
$795$	−32.7656	−1.16208
$796$	−21.5060	−0.762259
$797$	−1.41223	−0.0500237	−0.0250119	−	0.999687i	$-0.507962\pi$
$797$	−1.41223	−0.0500237	−0.0250119	+	0.999687i	$0.507962\pi$
$798$	−39.3448	−1.39279
$799$	−11.0077	−0.389423
$800$	80.8726	2.85928
$801$	2.17835	0.0769682
$802$	16.3100	0.575926
$803$	2.38468	0.0841536
$804$	−0.322388	−0.0113698
$805$	14.6763	0.517272
$806$	4.15390	0.146315
$807$	17.4343	0.613716
$808$	−1.53952	−0.0541600
$809$	2.65063	0.0931914	0.0465957	−	0.998914i	$-0.485163\pi$
$809$	2.65063	0.0931914	0.0465957	+	0.998914i	$0.485163\pi$
$810$	7.65520	0.268976
$811$	−38.9939	−1.36926	−0.684631	−	0.728890i	$-0.740037\pi$
$811$	−38.9939	−1.36926	−0.684631	+	0.728890i	$0.740037\pi$
$812$	−23.9722	−0.841259
$813$	−23.9592	−0.840286
$814$	−13.0049	−0.455823
$815$	100.729	3.52839
$816$	−4.93295	−0.172688
$817$	−43.8415	−1.53382
$818$	−19.5294	−0.682830
$819$	−16.4476	−0.574724
$820$	9.43678	0.329546
$821$	−27.6961	−0.966600	−0.483300	−	0.875455i	$-0.660562\pi$
$821$	−27.6961	−0.966600	−0.483300	+	0.875455i	$0.660562\pi$
$822$	−9.17671	−0.320075
$823$	−38.4025	−1.33863	−0.669314	−	0.742980i	$-0.733412\pi$
$823$	−38.4025	−1.33863	−0.669314	+	0.742980i	$0.733412\pi$
$824$	−12.6349	−0.440158
$825$	35.4128	1.23291
$826$	25.1833	0.876238
$827$	−42.6553	−1.48327	−0.741635	−	0.670804i	$-0.765949\pi$
$827$	−42.6553	−1.48327	−0.741635	+	0.670804i	$0.765949\pi$
$828$	1.59452	0.0554135
$829$	−20.3422	−0.706513	−0.353257	−	0.935526i	$-0.614926\pi$
$829$	−20.3422	−0.706513	−0.353257	+	0.935526i	$0.614926\pi$
$830$	−74.3632	−2.58118
$831$	26.0904	0.905065
$832$	−8.30744	−0.288009
$833$	0.467080	0.0161834
$834$	34.3639	1.18992
$835$	47.3574	1.63887
$836$	−27.3906	−0.947325
$837$	−0.382289	−0.0132138
$838$	−15.2888	−0.528144
$839$	−17.2602	−0.595889	−0.297945	−	0.954583i	$-0.596301\pi$
$839$	−17.2602	−0.595889	−0.297945	+	0.954583i	$0.596301\pi$
$840$	15.5018	0.534863
$841$	19.5569	0.674376
$842$	−31.9142	−1.09984
$843$	−2.79861	−0.0963893
$844$	5.04417	0.173627
$845$	−98.5011	−3.38854
$846$	19.8716	0.683201
$847$	9.72478	0.334148
$848$	−38.1159	−1.30891
$849$	−4.32206	−0.148333
$850$	−23.4357	−0.803836
$851$	3.34482	0.114659
$852$	−1.43013	−0.0489953
$853$	−30.0057	−1.02738	−0.513688	−	0.857977i	$-0.671721\pi$
$853$	−30.0057	−1.02738	−0.513688	+	0.857977i	$0.671721\pi$
$854$	12.1041	0.414195
$855$	33.8214	1.15667
$856$	24.5307	0.838440
$857$	17.5182	0.598410	0.299205	−	0.954189i	$-0.403278\pi$
$857$	17.5182	0.598410	0.299205	+	0.954189i	$0.403278\pi$
$858$	−29.6405	−1.01191
$859$	−21.3472	−0.728356	−0.364178	−	0.931329i	$-0.618650\pi$
$859$	−21.3472	−0.728356	−0.364178	+	0.931329i	$0.618650\pi$
$860$	−29.3452	−1.00066
$861$	4.83030	0.164616
$862$	74.2865	2.53021
$863$	−21.3034	−0.725175	−0.362587	−	0.931950i	$-0.618107\pi$
$863$	−21.3034	−0.725175	−0.362587	+	0.931950i	$0.618107\pi$
$864$	6.22964	0.211937
$865$	47.3757	1.61082
$866$	−25.0730	−0.852016
$867$	1.00000	0.0339618
$868$	1.31515	0.0446390
$869$	14.3159	0.485635
$870$	53.3435	1.80852
$871$	−1.54134	−0.0522263
$872$	3.58732	0.121482
$873$	−5.90221	−0.199760
$874$	18.2363	0.616851
$875$	92.4911	3.12677
$876$	1.10057	0.0371847
$877$	38.9902	1.31661	0.658303	−	0.752753i	$-0.271275\pi$
$877$	38.9902	1.31661	0.658303	+	0.752753i	$0.271275\pi$
$878$	20.3452	0.686618
$879$	−6.52023	−0.219922
$880$	57.0618	1.92355
$881$	−52.8992	−1.78222	−0.891110	−	0.453788i	$-0.850072\pi$
$881$	−52.8992	−1.78222	−0.891110	+	0.453788i	$0.850072\pi$
$882$	−0.843198	−0.0283920
$883$	25.7884	0.867848	0.433924	−	0.900950i	$-0.357129\pi$
$883$	25.7884	0.867848	0.433924	+	0.900950i	$0.357129\pi$
$884$	7.57762	0.254863
$885$	−21.6479	−0.727687
$886$	−32.8880	−1.10490
$887$	−59.0372	−1.98227	−0.991137	−	0.132840i	$-0.957590\pi$
$887$	−59.0372	−1.98227	−0.991137	+	0.132840i	$0.957590\pi$
$888$	3.53295	0.118558
$889$	55.4504	1.85975
$890$	16.6757	0.558971
$891$	2.72785	0.0913866
$892$	−25.5286	−0.854759
$893$	87.7949	2.93794
$894$	−42.2763	−1.41393
$895$	−11.0075	−0.367941
$896$	27.2376	0.909945
$897$	7.62342	0.254538
$898$	−48.4242	−1.61594
$899$	−2.66390	−0.0888459
$900$	16.3435	0.544784
$901$	7.72681	0.257417
$902$	8.70480	0.289838
$903$	−15.0206	−0.499854
$904$	−6.55880	−0.218142
$905$	37.4228	1.24398
$906$	19.5239	0.648638
$907$	12.5111	0.415425	0.207712	−	0.978190i	$-0.433398\pi$
$907$	12.5111	0.415425	0.207712	+	0.978190i	$0.433398\pi$
$908$	−2.88054	−0.0955942
$909$	−1.15079	−0.0381693
$910$	−125.909	−4.17385
$911$	−5.05941	−0.167626	−0.0838128	−	0.996482i	$-0.526710\pi$
$911$	−5.05941	−0.167626	−0.0838128	+	0.996482i	$0.526710\pi$
$912$	39.3442	1.30282
$913$	−26.4986	−0.876976
$914$	−51.7033	−1.71019
$915$	−10.4049	−0.343975
$916$	13.4764	0.445273
$917$	−44.7486	−1.47773
$918$	−1.80525	−0.0595823
$919$	29.3611	0.968535	0.484267	−	0.874920i	$-0.339086\pi$
$919$	29.3611	0.968535	0.484267	+	0.874920i	$0.339086\pi$
$920$	−7.18506	−0.236884
$921$	15.2632	0.502940
$922$	33.8904	1.11612
$923$	−6.83744	−0.225057
$924$	−9.38434	−0.308722
$925$	34.2837	1.12724
$926$	−70.8754	−2.32911
$927$	−9.44459	−0.310201
$928$	43.4099	1.42500
$929$	−18.8029	−0.616903	−0.308452	−	0.951240i	$-0.599811\pi$
$929$	−18.8029	−0.616903	−0.308452	+	0.951240i	$0.599811\pi$
$930$	−2.92650	−0.0959636
$931$	−3.72533	−0.122093
$932$	1.22309	0.0400636
$933$	−4.78892	−0.156782
$934$	9.08324	0.297213
$935$	−11.5675	−0.378297
$936$	8.05220	0.263194
$937$	40.7909	1.33258	0.666290	−	0.745693i	$-0.267881\pi$
$937$	40.7909	1.33258	0.666290	+	0.745693i	$0.267881\pi$
$938$	−1.26324	−0.0412463
$939$	−10.6920	−0.348921
$940$	58.7652	1.91671
$941$	−23.3061	−0.759756	−0.379878	−	0.925037i	$-0.624034\pi$
$941$	−23.3061	−0.759756	−0.379878	+	0.925037i	$0.624034\pi$
$942$	−1.80525	−0.0588184
$943$	−2.23884	−0.0729066
$944$	−25.1828	−0.819631
$945$	11.5876	0.376944
$946$	−27.0690	−0.880088
$947$	25.5027	0.828727	0.414364	−	0.910111i	$-0.364004\pi$
$947$	25.5027	0.828727	0.414364	+	0.910111i	$0.364004\pi$
$948$	6.60702	0.214586
$949$	5.26181	0.170806
$950$	186.918	6.06442
$951$	2.85345	0.0925293
$952$	−3.65565	−0.118480
$953$	−15.2218	−0.493083	−0.246542	−	0.969132i	$-0.579294\pi$
$953$	−15.2218	−0.493083	−0.246542	+	0.969132i	$0.579294\pi$
$954$	−13.9489	−0.451611
$955$	3.86402	0.125037
$956$	13.0414	0.421790
$957$	19.0085	0.614456
$958$	11.8941	0.384280
$959$	−13.8907	−0.448554
$960$	5.85274	0.188896
$961$	−30.8539	−0.995286
$962$	−28.6955	−0.925179
$963$	18.3367	0.590891
$964$	31.5287	1.01547
$965$	65.7116	2.11533
$966$	6.24795	0.201025
$967$	41.0147	1.31894	0.659471	−	0.751730i	$-0.270780\pi$
$967$	41.0147	1.31894	0.659471	+	0.751730i	$0.270780\pi$
$968$	−4.76095	−0.153023
$969$	−7.97579	−0.256219
$970$	−45.1826	−1.45073
$971$	−28.9586	−0.929327	−0.464664	−	0.885487i	$-0.653825\pi$
$971$	−28.9586	−0.929327	−0.464664	+	0.885487i	$0.653825\pi$
$972$	1.25895	0.0403807
$973$	52.0162	1.66756
$974$	52.0299	1.66714
$975$	78.1384	2.50243
$976$	−12.1039	−0.387437
$977$	44.9039	1.43660	0.718302	−	0.695732i	$-0.244920\pi$
$977$	44.9039	1.43660	0.718302	+	0.695732i	$0.244920\pi$
$978$	42.8821	1.37122
$979$	5.94222	0.189914
$980$	−2.49354	−0.0796531
$981$	2.68152	0.0856143
$982$	−62.5758	−1.99687
$983$	21.9950	0.701532	0.350766	−	0.936463i	$-0.385921\pi$
$983$	21.9950	0.701532	0.350766	+	0.936463i	$0.385921\pi$
$984$	−2.36476	−0.0753859
$985$	−63.1725	−2.01284
$986$	−12.5795	−0.400613
$987$	30.0795	0.957441
$988$	−60.4375	−1.92277
$989$	6.96203	0.221380
$990$	20.8823	0.663682
$991$	−7.96816	−0.253117	−0.126559	−	0.991959i	$-0.540393\pi$
$991$	−7.96816	−0.253117	−0.126559	+	0.991959i	$0.540393\pi$
$992$	−2.38152	−0.0756134
$993$	0.232011	0.00736265
$994$	−5.60379	−0.177741
$995$	72.4386	2.29646
$996$	−12.2295	−0.387506
$997$	−28.3869	−0.899022	−0.449511	−	0.893275i	$-0.648402\pi$
$997$	−28.3869	−0.899022	−0.449511	+	0.893275i	$0.648402\pi$
$998$	−75.0003	−2.37409
$999$	2.64088	0.0835538

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.i.1.13	✓	63

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.i.1.13	✓	63	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)

\(f(q)\)	\(=\)	\(q-1.80525 q^{2} +1.00000 q^{3} +1.25895 q^{4} -4.24051 q^{5} -1.80525 q^{6} -2.73260 q^{7} +1.33779 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.80525 q^{2} +1.00000 q^{3} +1.25895 q^{4} -4.24051 q^{5} -1.80525 q^{6} -2.73260 q^{7} +1.33779 q^{8} +1.00000 q^{9} +7.65520 q^{10} +2.72785 q^{11} +1.25895 q^{12} +6.01902 q^{13} +4.93303 q^{14} -4.24051 q^{15} -4.93295 q^{16} +1.00000 q^{17} -1.80525 q^{18} -7.97579 q^{19} -5.33857 q^{20} -2.73260 q^{21} -4.92447 q^{22} +1.26655 q^{23} +1.33779 q^{24} +12.9819 q^{25} -10.8659 q^{26} +1.00000 q^{27} -3.44019 q^{28} +6.96828 q^{29} +7.65520 q^{30} -0.382289 q^{31} +6.22964 q^{32} +2.72785 q^{33} -1.80525 q^{34} +11.5876 q^{35} +1.25895 q^{36} +2.64088 q^{37} +14.3983 q^{38} +6.01902 q^{39} -5.67292 q^{40} -1.76766 q^{41} +4.93303 q^{42} +5.49683 q^{43} +3.43422 q^{44} -4.24051 q^{45} -2.28645 q^{46} -11.0077 q^{47} -4.93295 q^{48} +0.467080 q^{49} -23.4357 q^{50} +1.00000 q^{51} +7.57762 q^{52} +7.72681 q^{53} -1.80525 q^{54} -11.5675 q^{55} -3.65565 q^{56} -7.97579 q^{57} -12.5795 q^{58} +5.10503 q^{59} -5.33857 q^{60} +2.45369 q^{61} +0.690129 q^{62} -2.73260 q^{63} -1.38020 q^{64} -25.5237 q^{65} -4.92447 q^{66} -0.256078 q^{67} +1.25895 q^{68} +1.26655 q^{69} -20.9186 q^{70} -1.13597 q^{71} +1.33779 q^{72} +0.874197 q^{73} -4.76746 q^{74} +12.9819 q^{75} -10.0411 q^{76} -7.45412 q^{77} -10.8659 q^{78} +5.24806 q^{79} +20.9182 q^{80} +1.00000 q^{81} +3.19108 q^{82} -9.71408 q^{83} -3.44019 q^{84} -4.24051 q^{85} -9.92317 q^{86} +6.96828 q^{87} +3.64930 q^{88} +2.17835 q^{89} +7.65520 q^{90} -16.4476 q^{91} +1.59452 q^{92} -0.382289 q^{93} +19.8716 q^{94} +33.8214 q^{95} +6.22964 q^{96} -5.90221 q^{97} -0.843198 q^{98} +2.72785 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 63 q + 10 q^{2} + 63 q^{3} + 70 q^{4} + 19 q^{5} + 10 q^{6} + 11 q^{7} + 27 q^{8} + 63 q^{9}+O(q^{10}) \) 63 * q + 10 * q^2 + 63 * q^3 + 70 * q^4 + 19 * q^5 + 10 * q^6 + 11 * q^7 + 27 * q^8 + 63 * q^9	\( 63 q + 10 q^{2} + 63 q^{3} + 70 q^{4} + 19 q^{5} + 10 q^{6} + 11 q^{7} + 27 q^{8} + 63 q^{9} + 4 q^{10} + 23 q^{11} + 70 q^{12} + 10 q^{13} + 18 q^{14} + 19 q^{15} + 72 q^{16} + 63 q^{17} + 10 q^{18} + 6 q^{19} + 48 q^{20} + 11 q^{21} + 21 q^{22} + 44 q^{23} + 27 q^{24} + 110 q^{25} + 41 q^{26} + 63 q^{27} + 26 q^{28} + 35 q^{29} + 4 q^{30} + q^{31} + 54 q^{32} + 23 q^{33} + 10 q^{34} + 47 q^{35} + 70 q^{36} + 40 q^{37} + 38 q^{38} + 10 q^{39} - 10 q^{40} + 35 q^{41} + 18 q^{42} + 27 q^{43} + 46 q^{44} + 19 q^{45} + 8 q^{46} + 29 q^{47} + 72 q^{48} + 114 q^{49} + 27 q^{50} + 63 q^{51} - q^{52} + 75 q^{53} + 10 q^{54} + 5 q^{55} + 24 q^{56} + 6 q^{57} + 41 q^{58} + 105 q^{59} + 48 q^{60} + 5 q^{61} + 22 q^{62} + 11 q^{63} + 61 q^{64} + 49 q^{65} + 21 q^{66} + 4 q^{67} + 70 q^{68} + 44 q^{69} - 16 q^{70} + 16 q^{71} + 27 q^{72} + 39 q^{73} + 54 q^{74} + 110 q^{75} + 6 q^{76} + 88 q^{77} + 41 q^{78} + 16 q^{79} + 102 q^{80} + 63 q^{81} - 29 q^{82} + 73 q^{83} + 26 q^{84} + 19 q^{85} + 46 q^{86} + 35 q^{87} + 18 q^{88} + 88 q^{89} + 4 q^{90} - 15 q^{91} + 110 q^{92} + q^{93} - 8 q^{94} + 28 q^{95} + 54 q^{96} + 70 q^{97} + 33 q^{98} + 23 q^{99}+O(q^{100}) \) 63 * q + 10 * q^2 + 63 * q^3 + 70 * q^4 + 19 * q^5 + 10 * q^6 + 11 * q^7 + 27 * q^8 + 63 * q^9 + 4 * q^10 + 23 * q^11 + 70 * q^12 + 10 * q^13 + 18 * q^14 + 19 * q^15 + 72 * q^16 + 63 * q^17 + 10 * q^18 + 6 * q^19 + 48 * q^20 + 11 * q^21 + 21 * q^22 + 44 * q^23 + 27 * q^24 + 110 * q^25 + 41 * q^26 + 63 * q^27 + 26 * q^28 + 35 * q^29 + 4 * q^30 + q^31 + 54 * q^32 + 23 * q^33 + 10 * q^34 + 47 * q^35 + 70 * q^36 + 40 * q^37 + 38 * q^38 + 10 * q^39 - 10 * q^40 + 35 * q^41 + 18 * q^42 + 27 * q^43 + 46 * q^44 + 19 * q^45 + 8 * q^46 + 29 * q^47 + 72 * q^48 + 114 * q^49 + 27 * q^50 + 63 * q^51 - q^52 + 75 * q^53 + 10 * q^54 + 5 * q^55 + 24 * q^56 + 6 * q^57 + 41 * q^58 + 105 * q^59 + 48 * q^60 + 5 * q^61 + 22 * q^62 + 11 * q^63 + 61 * q^64 + 49 * q^65 + 21 * q^66 + 4 * q^67 + 70 * q^68 + 44 * q^69 - 16 * q^70 + 16 * q^71 + 27 * q^72 + 39 * q^73 + 54 * q^74 + 110 * q^75 + 6 * q^76 + 88 * q^77 + 41 * q^78 + 16 * q^79 + 102 * q^80 + 63 * q^81 - 29 * q^82 + 73 * q^83 + 26 * q^84 + 19 * q^85 + 46 * q^86 + 35 * q^87 + 18 * q^88 + 88 * q^89 + 4 * q^90 - 15 * q^91 + 110 * q^92 + q^93 - 8 * q^94 + 28 * q^95 + 54 * q^96 + 70 * q^97 + 33 * q^98 + 23 * q^99

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