LMFDB - Embedded newform 8007.2.a.d.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:	$1$
Dimension:	$40$
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)

$f(q)$	$=$	$q-1.32783 q^{2} +1.00000 q^{3} -0.236868 q^{4} +2.41386 q^{5} -1.32783 q^{6} +0.553664 q^{7} +2.97018 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.32783 q^{2} +1.00000 q^{3} -0.236868 q^{4} +2.41386 q^{5} -1.32783 q^{6} +0.553664 q^{7} +2.97018 q^{8} +1.00000 q^{9} -3.20519 q^{10} -0.0504547 q^{11} -0.236868 q^{12} -2.00996 q^{13} -0.735171 q^{14} +2.41386 q^{15} -3.47016 q^{16} +1.00000 q^{17} -1.32783 q^{18} -7.25787 q^{19} -0.571766 q^{20} +0.553664 q^{21} +0.0669952 q^{22} +3.59294 q^{23} +2.97018 q^{24} +0.826709 q^{25} +2.66888 q^{26} +1.00000 q^{27} -0.131145 q^{28} -1.61089 q^{29} -3.20519 q^{30} -1.39126 q^{31} -1.33258 q^{32} -0.0504547 q^{33} -1.32783 q^{34} +1.33647 q^{35} -0.236868 q^{36} -9.04760 q^{37} +9.63722 q^{38} -2.00996 q^{39} +7.16959 q^{40} +3.56543 q^{41} -0.735171 q^{42} +3.35313 q^{43} +0.0119511 q^{44} +2.41386 q^{45} -4.77081 q^{46} +2.01172 q^{47} -3.47016 q^{48} -6.69346 q^{49} -1.09773 q^{50} +1.00000 q^{51} +0.476095 q^{52} +13.0015 q^{53} -1.32783 q^{54} -0.121790 q^{55} +1.64448 q^{56} -7.25787 q^{57} +2.13898 q^{58} -6.27918 q^{59} -0.571766 q^{60} -4.50894 q^{61} +1.84736 q^{62} +0.553664 q^{63} +8.70976 q^{64} -4.85175 q^{65} +0.0669952 q^{66} -11.0415 q^{67} -0.236868 q^{68} +3.59294 q^{69} -1.77460 q^{70} -9.22355 q^{71} +2.97018 q^{72} -4.15599 q^{73} +12.0137 q^{74} +0.826709 q^{75} +1.71916 q^{76} -0.0279349 q^{77} +2.66888 q^{78} -4.22154 q^{79} -8.37647 q^{80} +1.00000 q^{81} -4.73429 q^{82} +7.35373 q^{83} -0.131145 q^{84} +2.41386 q^{85} -4.45239 q^{86} -1.61089 q^{87} -0.149860 q^{88} -17.7277 q^{89} -3.20519 q^{90} -1.11284 q^{91} -0.851054 q^{92} -1.39126 q^{93} -2.67122 q^{94} -17.5195 q^{95} -1.33258 q^{96} -6.12639 q^{97} +8.88777 q^{98} -0.0504547 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 7 q^{2} + 40 q^{3} + 29 q^{4} - 15 q^{5} - 7 q^{6} - 13 q^{7} - 18 q^{8} + 40 q^{9}+O(q^{10}) $ 40 * q - 7 * q^2 + 40 * q^3 + 29 * q^4 - 15 * q^5 - 7 * q^6 - 13 * q^7 - 18 * q^8 + 40 * q^9	\( 40 q - 7 q^{2} + 40 q^{3} + 29 q^{4} - 15 q^{5} - 7 q^{6} - 13 q^{7} - 18 q^{8} + 40 q^{9} - 6 q^{10} - 25 q^{11} + 29 q^{12} - 24 q^{13} - 22 q^{14} - 15 q^{15} + 7 q^{16} + 40 q^{17} - 7 q^{18} - 18 q^{19} - 20 q^{20} - 13 q^{21} - 25 q^{22} - 28 q^{23} - 18 q^{24} - 11 q^{25} - 13 q^{26} + 40 q^{27} - 8 q^{28} - 23 q^{29} - 6 q^{30} - 11 q^{31} - 23 q^{32} - 25 q^{33} - 7 q^{34} - 45 q^{35} + 29 q^{36} - 38 q^{37} - 30 q^{38} - 24 q^{39} - 12 q^{40} - 33 q^{41} - 22 q^{42} - 25 q^{43} - 14 q^{44} - 15 q^{45} + 8 q^{46} - 55 q^{47} + 7 q^{48} - 21 q^{49} + 2 q^{50} + 40 q^{51} - 39 q^{52} - 39 q^{53} - 7 q^{54} - 9 q^{55} - 48 q^{56} - 18 q^{57} - 13 q^{58} - 81 q^{59} - 20 q^{60} - 9 q^{61} - 16 q^{62} - 13 q^{63} - 4 q^{64} - 43 q^{65} - 25 q^{66} - 24 q^{67} + 29 q^{68} - 28 q^{69} + 48 q^{70} - 32 q^{71} - 18 q^{72} - 43 q^{73} - 20 q^{74} - 11 q^{75} - 58 q^{76} - 32 q^{77} - 13 q^{78} - 22 q^{79} - 48 q^{80} + 40 q^{81} - 11 q^{82} - 45 q^{83} - 8 q^{84} - 15 q^{85} - 30 q^{86} - 23 q^{87} - 48 q^{88} - 94 q^{89} - 6 q^{90} - 7 q^{91} - 98 q^{92} - 11 q^{93} + 32 q^{94} - 23 q^{96} - 28 q^{97} - 46 q^{98} - 25 q^{99}+O(q^{100}) \) 40 * q - 7 * q^2 + 40 * q^3 + 29 * q^4 - 15 * q^5 - 7 * q^6 - 13 * q^7 - 18 * q^8 + 40 * q^9 - 6 * q^10 - 25 * q^11 + 29 * q^12 - 24 * q^13 - 22 * q^14 - 15 * q^15 + 7 * q^16 + 40 * q^17 - 7 * q^18 - 18 * q^19 - 20 * q^20 - 13 * q^21 - 25 * q^22 - 28 * q^23 - 18 * q^24 - 11 * q^25 - 13 * q^26 + 40 * q^27 - 8 * q^28 - 23 * q^29 - 6 * q^30 - 11 * q^31 - 23 * q^32 - 25 * q^33 - 7 * q^34 - 45 * q^35 + 29 * q^36 - 38 * q^37 - 30 * q^38 - 24 * q^39 - 12 * q^40 - 33 * q^41 - 22 * q^42 - 25 * q^43 - 14 * q^44 - 15 * q^45 + 8 * q^46 - 55 * q^47 + 7 * q^48 - 21 * q^49 + 2 * q^50 + 40 * q^51 - 39 * q^52 - 39 * q^53 - 7 * q^54 - 9 * q^55 - 48 * q^56 - 18 * q^57 - 13 * q^58 - 81 * q^59 - 20 * q^60 - 9 * q^61 - 16 * q^62 - 13 * q^63 - 4 * q^64 - 43 * q^65 - 25 * q^66 - 24 * q^67 + 29 * q^68 - 28 * q^69 + 48 * q^70 - 32 * q^71 - 18 * q^72 - 43 * q^73 - 20 * q^74 - 11 * q^75 - 58 * q^76 - 32 * q^77 - 13 * q^78 - 22 * q^79 - 48 * q^80 + 40 * q^81 - 11 * q^82 - 45 * q^83 - 8 * q^84 - 15 * q^85 - 30 * q^86 - 23 * q^87 - 48 * q^88 - 94 * q^89 - 6 * q^90 - 7 * q^91 - 98 * q^92 - 11 * q^93 + 32 * q^94 - 23 * q^96 - 28 * q^97 - 46 * q^98 - 25 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.32783	−0.938917	−0.469459	−	0.882954i	$-0.655551\pi$
$2$	−1.32783	−0.938917	−0.469459	+	0.882954i	$0.655551\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.236868	−0.118434
$5$	2.41386	1.07951	0.539755	−	0.841822i	$-0.318517\pi$
$5$	2.41386	1.07951	0.539755	+	0.841822i	$0.318517\pi$
$6$	−1.32783	−0.542084
$7$	0.553664	0.209265	0.104633	−	0.994511i	$-0.466633\pi$
$7$	0.553664	0.209265	0.104633	+	0.994511i	$0.466633\pi$
$8$	2.97018	1.05012
$9$	1.00000	0.333333
$10$	−3.20519	−1.01357
$11$	−0.0504547	−0.0152127	−0.00760633	−	0.999971i	$-0.502421\pi$
$11$	−0.0504547	−0.0152127	−0.00760633	+	0.999971i	$0.502421\pi$
$12$	−0.236868	−0.0683780
$13$	−2.00996	−0.557462	−0.278731	−	0.960369i	$-0.589914\pi$
$13$	−2.00996	−0.557462	−0.278731	+	0.960369i	$0.589914\pi$
$14$	−0.735171	−0.196483
$15$	2.41386	0.623255
$16$	−3.47016	−0.867539
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.32783	−0.312972
$19$	−7.25787	−1.66507	−0.832535	−	0.553973i	$-0.813111\pi$
$19$	−7.25787	−1.66507	−0.832535	+	0.553973i	$0.813111\pi$
$20$	−0.571766	−0.127851
$21$	0.553664	0.120819
$22$	0.0669952	0.0142834
$23$	3.59294	0.749180	0.374590	−	0.927191i	$-0.377783\pi$
$23$	3.59294	0.749180	0.374590	+	0.927191i	$0.377783\pi$
$24$	2.97018	0.606285
$25$	0.826709	0.165342
$26$	2.66888	0.523410
$27$	1.00000	0.192450
$28$	−0.131145	−0.0247841
$29$	−1.61089	−0.299134	−0.149567	−	0.988752i	$-0.547788\pi$
$29$	−1.61089	−0.299134	−0.149567	+	0.988752i	$0.547788\pi$
$30$	−3.20519	−0.585185
$31$	−1.39126	−0.249878	−0.124939	−	0.992164i	$-0.539873\pi$
$31$	−1.39126	−0.249878	−0.124939	+	0.992164i	$0.539873\pi$
$32$	−1.33258	−0.235570
$33$	−0.0504547	−0.00878303
$34$	−1.32783	−0.227721
$35$	1.33647	0.225904
$36$	−0.236868	−0.0394780
$37$	−9.04760	−1.48742	−0.743708	−	0.668505i	$-0.766935\pi$
$37$	−9.04760	−1.48742	−0.743708	+	0.668505i	$0.766935\pi$
$38$	9.63722	1.56336
$39$	−2.00996	−0.321851
$40$	7.16959	1.13361
$41$	3.56543	0.556827	0.278413	−	0.960461i	$-0.410191\pi$
$41$	3.56543	0.556827	0.278413	+	0.960461i	$0.410191\pi$
$42$	−0.735171	−0.113439
$43$	3.35313	0.511348	0.255674	−	0.966763i	$-0.417703\pi$
$43$	3.35313	0.511348	0.255674	+	0.966763i	$0.417703\pi$
$44$	0.0119511	0.00180170
$45$	2.41386	0.359837
$46$	−4.77081	−0.703418
$47$	2.01172	0.293439	0.146720	−	0.989178i	$-0.453128\pi$
$47$	2.01172	0.293439	0.146720	+	0.989178i	$0.453128\pi$
$48$	−3.47016	−0.500874
$49$	−6.69346	−0.956208
$50$	−1.09773	−0.155242
$51$	1.00000	0.140028
$52$	0.476095	0.0660225
$53$	13.0015	1.78589	0.892945	−	0.450166i	$-0.148635\pi$
$53$	13.0015	1.78589	0.892945	+	0.450166i	$0.148635\pi$
$54$	−1.32783	−0.180695
$55$	−0.121790	−0.0164222
$56$	1.64448	0.219753
$57$	−7.25787	−0.961328
$58$	2.13898	0.280862
$59$	−6.27918	−0.817480	−0.408740	−	0.912651i	$-0.634032\pi$
$59$	−6.27918	−0.817480	−0.408740	+	0.912651i	$0.634032\pi$
$60$	−0.571766	−0.0738147
$61$	−4.50894	−0.577311	−0.288656	−	0.957433i	$-0.593208\pi$
$61$	−4.50894	−0.577311	−0.288656	+	0.957433i	$0.593208\pi$
$62$	1.84736	0.234615
$63$	0.553664	0.0697551
$64$	8.70976	1.08872
$65$	−4.85175	−0.601785
$66$	0.0669952	0.00824654
$67$	−11.0415	−1.34894	−0.674469	−	0.738303i	$-0.735627\pi$
$67$	−11.0415	−1.34894	−0.674469	+	0.738303i	$0.735627\pi$
$68$	−0.236868	−0.0287245
$69$	3.59294	0.432539
$70$	−1.77460	−0.212105
$71$	−9.22355	−1.09463	−0.547317	−	0.836925i	$-0.684351\pi$
$71$	−9.22355	−1.09463	−0.547317	+	0.836925i	$0.684351\pi$
$72$	2.97018	0.350039
$73$	−4.15599	−0.486422	−0.243211	−	0.969973i	$-0.578201\pi$
$73$	−4.15599	−0.486422	−0.243211	+	0.969973i	$0.578201\pi$
$74$	12.0137	1.39656
$75$	0.826709	0.0954602
$76$	1.71916	0.197201
$77$	−0.0279349	−0.00318348
$78$	2.66888	0.302191
$79$	−4.22154	−0.474961	−0.237480	−	0.971392i	$-0.576322\pi$
$79$	−4.22154	−0.474961	−0.237480	+	0.971392i	$0.576322\pi$
$80$	−8.37647	−0.936517
$81$	1.00000	0.111111
$82$	−4.73429	−0.522814
$83$	7.35373	0.807177	0.403588	−	0.914941i	$-0.367763\pi$
$83$	7.35373	0.807177	0.403588	+	0.914941i	$0.367763\pi$
$84$	−0.131145	−0.0143091
$85$	2.41386	0.261820
$86$	−4.45239	−0.480114
$87$	−1.61089	−0.172705
$88$	−0.149860	−0.0159751
$89$	−17.7277	−1.87913	−0.939566	−	0.342368i	$-0.888771\pi$
$89$	−17.7277	−1.87913	−0.939566	+	0.342368i	$0.888771\pi$
$90$	−3.20519	−0.337857
$91$	−1.11284	−0.116657
$92$	−0.851054	−0.0887285
$93$	−1.39126	−0.144267
$94$	−2.67122	−0.275515
$95$	−17.5195	−1.79746
$96$	−1.33258	−0.136006
$97$	−6.12639	−0.622041	−0.311021	−	0.950403i	$-0.600671\pi$
$97$	−6.12639	−0.622041	−0.311021	+	0.950403i	$0.600671\pi$
$98$	8.88777	0.897800
$99$	−0.0504547	−0.00507089
$100$	−0.195821	−0.0195821
$101$	−3.55682	−0.353917	−0.176958	−	0.984218i	$-0.556626\pi$
$101$	−3.55682	−0.353917	−0.176958	+	0.984218i	$0.556626\pi$
$102$	−1.32783	−0.131475
$103$	7.38321	0.727489	0.363745	−	0.931499i	$-0.381498\pi$
$103$	7.38321	0.727489	0.363745	+	0.931499i	$0.381498\pi$
$104$	−5.96993	−0.585400
$105$	1.33647	0.130426
$106$	−17.2637	−1.67680
$107$	−3.10591	−0.300260	−0.150130	−	0.988666i	$-0.547969\pi$
$107$	−3.10591	−0.300260	−0.150130	+	0.988666i	$0.547969\pi$
$108$	−0.236868	−0.0227927
$109$	0.250085	0.0239538	0.0119769	−	0.999928i	$-0.496188\pi$
$109$	0.250085	0.0239538	0.0119769	+	0.999928i	$0.496188\pi$
$110$	0.161717	0.0154191
$111$	−9.04760	−0.858760
$112$	−1.92130	−0.181546
$113$	18.2101	1.71307	0.856533	−	0.516092i	$-0.172614\pi$
$113$	18.2101	1.71307	0.856533	+	0.516092i	$0.172614\pi$
$114$	9.63722	0.902608
$115$	8.67285	0.808747
$116$	0.381568	0.0354277
$117$	−2.00996	−0.185821
$118$	8.33768	0.767546
$119$	0.553664	0.0507543
$120$	7.16959	0.654491
$121$	−10.9975	−0.999769
$122$	5.98711	0.542048
$123$	3.56543	0.321484
$124$	0.329545	0.0295941
$125$	−10.0737	−0.901022
$126$	−0.735171	−0.0654943
$127$	−13.3376	−1.18352	−0.591761	−	0.806113i	$-0.701567\pi$
$127$	−13.3376	−1.18352	−0.591761	+	0.806113i	$0.701567\pi$
$128$	−8.89991	−0.786648
$129$	3.35313	0.295227
$130$	6.44230	0.565027
$131$	1.77550	0.155126	0.0775631	−	0.996987i	$-0.475286\pi$
$131$	1.77550	0.155126	0.0775631	+	0.996987i	$0.475286\pi$
$132$	0.0119511	0.00104021
$133$	−4.01842	−0.348441
$134$	14.6613	1.26654
$135$	2.41386	0.207752
$136$	2.97018	0.254691
$137$	3.07784	0.262957	0.131479	−	0.991319i	$-0.458028\pi$
$137$	3.07784	0.262957	0.131479	+	0.991319i	$0.458028\pi$
$138$	−4.77081	−0.406119
$139$	−9.18804	−0.779319	−0.389660	−	0.920959i	$-0.627407\pi$
$139$	−9.18804	−0.779319	−0.389660	+	0.920959i	$0.627407\pi$
$140$	−0.316566	−0.0267547
$141$	2.01172	0.169417
$142$	12.2473	1.02777
$143$	0.101412	0.00848048
$144$	−3.47016	−0.289180
$145$	−3.88845	−0.322918
$146$	5.51845	0.456710
$147$	−6.69346	−0.552067
$148$	2.14309	0.176161
$149$	−8.11168	−0.664535	−0.332267	−	0.943185i	$-0.607814\pi$
$149$	−8.11168	−0.664535	−0.332267	+	0.943185i	$0.607814\pi$
$150$	−1.09773	−0.0896292
$151$	−3.85015	−0.313321	−0.156661	−	0.987653i	$-0.550073\pi$
$151$	−3.85015	−0.313321	−0.156661	+	0.987653i	$0.550073\pi$
$152$	−21.5572	−1.74852
$153$	1.00000	0.0808452
$154$	0.0370928	0.00298903
$155$	−3.35831	−0.269746
$156$	0.476095	0.0381181
$157$	−1.00000	−0.0798087
$157$	−1.00000	−0.0798087
$158$	5.60549	0.445949
$159$	13.0015	1.03108
$160$	−3.21667	−0.254300
$161$	1.98928	0.156777
$162$	−1.32783	−0.104324
$163$	5.57276	0.436492	0.218246	−	0.975894i	$-0.429966\pi$
$163$	5.57276	0.436492	0.218246	+	0.975894i	$0.429966\pi$
$164$	−0.844538	−0.0659473
$165$	−0.121790	−0.00948137
$166$	−9.76450	−0.757872
$167$	21.0118	1.62594	0.812972	−	0.582303i	$-0.197848\pi$
$167$	21.0118	1.62594	0.812972	+	0.582303i	$0.197848\pi$
$168$	1.64448	0.126874
$169$	−8.96007	−0.689236
$170$	−3.20519	−0.245827
$171$	−7.25787	−0.555023
$172$	−0.794251	−0.0605611
$173$	−10.1994	−0.775448	−0.387724	−	0.921776i	$-0.626739\pi$
$173$	−10.1994	−0.775448	−0.387724	+	0.921776i	$0.626739\pi$
$174$	2.13898	0.162156
$175$	0.457719	0.0346003
$176$	0.175086	0.0131976
$177$	−6.27918	−0.471972
$178$	23.5394	1.76435
$179$	−7.80693	−0.583517	−0.291759	−	0.956492i	$-0.594240\pi$
$179$	−7.80693	−0.583517	−0.291759	+	0.956492i	$0.594240\pi$
$180$	−0.571766	−0.0426169
$181$	14.5974	1.08501	0.542507	−	0.840051i	$-0.317475\pi$
$181$	14.5974	1.08501	0.542507	+	0.840051i	$0.317475\pi$
$182$	1.47766	0.109532
$183$	−4.50894	−0.333311
$184$	10.6717	0.786727
$185$	−21.8396	−1.60568
$186$	1.84736	0.135455
$187$	−0.0504547	−0.00368961
$188$	−0.476512	−0.0347532
$189$	0.553664	0.0402731
$190$	23.2629	1.68767
$191$	−14.0734	−1.01832	−0.509158	−	0.860673i	$-0.670043\pi$
$191$	−14.0734	−1.01832	−0.509158	+	0.860673i	$0.670043\pi$
$192$	8.70976	0.628573
$193$	4.68720	0.337392	0.168696	−	0.985668i	$-0.446044\pi$
$193$	4.68720	0.337392	0.168696	+	0.985668i	$0.446044\pi$
$194$	8.13481	0.584045
$195$	−4.85175	−0.347441
$196$	1.58547	0.113248
$197$	−10.2314	−0.728959	−0.364480	−	0.931211i	$-0.618753\pi$
$197$	−10.2314	−0.728959	−0.364480	+	0.931211i	$0.618753\pi$
$198$	0.0669952	0.00476114
$199$	−12.5828	−0.891970	−0.445985	−	0.895040i	$-0.647147\pi$
$199$	−12.5828	−0.891970	−0.445985	+	0.895040i	$0.647147\pi$
$200$	2.45548	0.173628
$201$	−11.0415	−0.778810
$202$	4.72285	0.332298
$203$	−0.891890	−0.0625984
$204$	−0.236868	−0.0165841
$205$	8.60645	0.601100
$206$	−9.80365	−0.683052
$207$	3.59294	0.249727
$208$	6.97487	0.483620
$209$	0.366194	0.0253301
$210$	−1.77460	−0.122459
$211$	−1.89126	−0.130200	−0.0651000	−	0.997879i	$-0.520737\pi$
$211$	−1.89126	−0.130200	−0.0651000	+	0.997879i	$0.520737\pi$
$212$	−3.07964	−0.211510
$213$	−9.22355	−0.631987
$214$	4.12412	0.281919
$215$	8.09399	0.552005
$216$	2.97018	0.202095
$217$	−0.770291	−0.0522907
$218$	−0.332071	−0.0224907
$219$	−4.15599	−0.280836
$220$	0.0288483	0.00194495
$221$	−2.00996	−0.135204
$222$	12.0137	0.806304
$223$	−18.6700	−1.25023	−0.625117	−	0.780531i	$-0.714949\pi$
$223$	−18.6700	−1.25023	−0.625117	+	0.780531i	$0.714949\pi$
$224$	−0.737803	−0.0492965
$225$	0.826709	0.0551139
$226$	−24.1800	−1.60843
$227$	22.5269	1.49517	0.747583	−	0.664169i	$-0.231214\pi$
$227$	22.5269	1.49517	0.747583	+	0.664169i	$0.231214\pi$
$228$	1.71916	0.113854
$229$	11.0212	0.728299	0.364150	−	0.931340i	$-0.381360\pi$
$229$	11.0212	0.728299	0.364150	+	0.931340i	$0.381360\pi$
$230$	−11.5161	−0.759347
$231$	−0.0279349	−0.00183798
$232$	−4.78462	−0.314126
$233$	3.14050	0.205741	0.102870	−	0.994695i	$-0.467197\pi$
$233$	3.14050	0.205741	0.102870	+	0.994695i	$0.467197\pi$
$234$	2.66888	0.174470
$235$	4.85600	0.316771
$236$	1.48734	0.0968175
$237$	−4.22154	−0.274219
$238$	−0.735171	−0.0476541
$239$	7.60926	0.492202	0.246101	−	0.969244i	$-0.420851\pi$
$239$	7.60926	0.492202	0.246101	+	0.969244i	$0.420851\pi$
$240$	−8.37647	−0.540699
$241$	−3.97950	−0.256342	−0.128171	−	0.991752i	$-0.540911\pi$
$241$	−3.97950	−0.256342	−0.128171	+	0.991752i	$0.540911\pi$
$242$	14.6027	0.938700
$243$	1.00000	0.0641500
$244$	1.06803	0.0683733
$245$	−16.1571	−1.03224
$246$	−4.73429	−0.301847
$247$	14.5880	0.928213
$248$	−4.13229	−0.262401
$249$	7.35373	0.466024
$250$	13.3762	0.845985
$251$	4.51023	0.284683	0.142342	−	0.989818i	$-0.454537\pi$
$251$	4.51023	0.284683	0.142342	+	0.989818i	$0.454537\pi$
$252$	−0.131145	−0.00826138
$253$	−0.181281	−0.0113970
$254$	17.7101	1.11123
$255$	2.41386	0.151162
$256$	−5.60195	−0.350122
$257$	1.07844	0.0672713	0.0336357	−	0.999434i	$-0.489291\pi$
$257$	1.07844	0.0672713	0.0336357	+	0.999434i	$0.489291\pi$
$258$	−4.45239	−0.277194
$259$	−5.00933	−0.311264
$260$	1.14923	0.0712719
$261$	−1.61089	−0.0997114
$262$	−2.35756	−0.145651
$263$	29.7028	1.83155	0.915776	−	0.401689i	$-0.131577\pi$
$263$	29.7028	1.83155	0.915776	+	0.401689i	$0.131577\pi$
$264$	−0.149860	−0.00922322
$265$	31.3837	1.92789
$266$	5.33578	0.327157
$267$	−17.7277	−1.08492
$268$	2.61539	0.159760
$269$	18.9128	1.15313	0.576567	−	0.817050i	$-0.304392\pi$
$269$	18.9128	1.15313	0.576567	+	0.817050i	$0.304392\pi$
$270$	−3.20519	−0.195062
$271$	14.2519	0.865740	0.432870	−	0.901456i	$-0.357501\pi$
$271$	14.2519	0.865740	0.432870	+	0.901456i	$0.357501\pi$
$272$	−3.47016	−0.210409
$273$	−1.11284	−0.0673522
$274$	−4.08684	−0.246895
$275$	−0.0417114	−0.00251529
$276$	−0.851054	−0.0512274
$277$	−7.32097	−0.439874	−0.219937	−	0.975514i	$-0.570585\pi$
$277$	−7.32097	−0.439874	−0.219937	+	0.975514i	$0.570585\pi$
$278$	12.2001	0.731716
$279$	−1.39126	−0.0832926
$280$	3.96954	0.237226
$281$	19.5759	1.16780	0.583901	−	0.811825i	$-0.301526\pi$
$281$	19.5759	1.16780	0.583901	+	0.811825i	$0.301526\pi$
$282$	−2.67122	−0.159069
$283$	0.112031	0.00665953	0.00332976	−	0.999994i	$-0.498940\pi$
$283$	0.112031	0.00665953	0.00332976	+	0.999994i	$0.498940\pi$
$284$	2.18477	0.129642
$285$	−17.5195	−1.03776
$286$	−0.134658	−0.00796247
$287$	1.97405	0.116525
$288$	−1.33258	−0.0785232
$289$	1.00000	0.0588235
$290$	5.16320	0.303194
$291$	−6.12639	−0.359136
$292$	0.984423	0.0576090
$293$	−8.15206	−0.476248	−0.238124	−	0.971235i	$-0.576533\pi$
$293$	−8.15206	−0.476248	−0.238124	+	0.971235i	$0.576533\pi$
$294$	8.88777	0.518345
$295$	−15.1571	−0.882478
$296$	−26.8730	−1.56196
$297$	−0.0504547	−0.00292768
$298$	10.7709	0.623943
$299$	−7.22166	−0.417639
$300$	−0.195821	−0.0113057
$301$	1.85651	0.107007
$302$	5.11235	0.294183
$303$	−3.55682	−0.204334
$304$	25.1859	1.44451
$305$	−10.8840	−0.623213
$306$	−1.32783	−0.0759070
$307$	−18.0295	−1.02900	−0.514498	−	0.857492i	$-0.672022\pi$
$307$	−18.0295	−1.02900	−0.514498	+	0.857492i	$0.672022\pi$
$308$	0.00661690	0.000377033 0
$309$	7.38321	0.420016
$310$	4.45926	0.253269
$311$	−13.7148	−0.777692	−0.388846	−	0.921303i	$-0.627126\pi$
$311$	−13.7148	−0.777692	−0.388846	+	0.921303i	$0.627126\pi$
$312$	−5.96993	−0.337981
$313$	−8.18923	−0.462883	−0.231441	−	0.972849i	$-0.574344\pi$
$313$	−8.18923	−0.462883	−0.231441	+	0.972849i	$0.574344\pi$
$314$	1.32783	0.0749338
$315$	1.33647	0.0753013
$316$	0.999949	0.0562516
$317$	−18.6053	−1.04498	−0.522489	−	0.852646i	$-0.674997\pi$
$317$	−18.6053	−1.04498	−0.522489	+	0.852646i	$0.674997\pi$
$318$	−17.2637	−0.968103
$319$	0.0812768	0.00455063
$320$	21.0241	1.17528
$321$	−3.10591	−0.173355
$322$	−2.64143	−0.147201
$323$	−7.25787	−0.403839
$324$	−0.236868	−0.0131593
$325$	−1.66165	−0.0921717
$326$	−7.39968	−0.409830
$327$	0.250085	0.0138298
$328$	10.5900	0.584734
$329$	1.11382	0.0614066
$330$	0.161717	0.00890223
$331$	20.9839	1.15338	0.576689	−	0.816964i	$-0.304344\pi$
$331$	20.9839	1.15338	0.576689	+	0.816964i	$0.304344\pi$
$332$	−1.74187	−0.0955973
$333$	−9.04760	−0.495805
$334$	−27.9001	−1.52663
$335$	−26.6527	−1.45619
$336$	−1.92130	−0.104816
$337$	25.5881	1.39387	0.696935	−	0.717134i	$-0.254546\pi$
$337$	25.5881	1.39387	0.696935	+	0.717134i	$0.254546\pi$
$338$	11.8975	0.647136
$339$	18.2101	0.989039
$340$	−0.571766	−0.0310084
$341$	0.0701956	0.00380131
$342$	9.63722	0.521121
$343$	−7.58157	−0.409366
$344$	9.95941	0.536976
$345$	8.67285	0.466931
$346$	13.5431	0.728081
$347$	−12.6841	−0.680919	−0.340459	−	0.940259i	$-0.610583\pi$
$347$	−12.6841	−0.680919	−0.340459	+	0.940259i	$0.610583\pi$
$348$	0.381568	0.0204542
$349$	−34.5027	−1.84689	−0.923444	−	0.383733i	$-0.874638\pi$
$349$	−34.5027	−1.84689	−0.923444	+	0.383733i	$0.874638\pi$
$350$	−0.607773	−0.0324868
$351$	−2.00996	−0.107284
$352$	0.0672351	0.00358364
$353$	24.0289	1.27893	0.639466	−	0.768820i	$-0.279156\pi$
$353$	24.0289	1.27893	0.639466	+	0.768820i	$0.279156\pi$
$354$	8.33768	0.443143
$355$	−22.2643	−1.18167
$356$	4.19913	0.222553
$357$	0.553664	0.0293030
$358$	10.3663	0.547874
$359$	−20.9975	−1.10820	−0.554102	−	0.832449i	$-0.686938\pi$
$359$	−20.9975	−1.10820	−0.554102	+	0.832449i	$0.686938\pi$
$360$	7.16959	0.377871
$361$	33.6767	1.77246
$362$	−19.3828	−1.01874
$363$	−10.9975	−0.577217
$364$	0.263596	0.0138162
$365$	−10.0320	−0.525098
$366$	5.98711	0.312951
$367$	−2.09038	−0.109117	−0.0545584	−	0.998511i	$-0.517375\pi$
$367$	−2.09038	−0.109117	−0.0545584	+	0.998511i	$0.517375\pi$
$368$	−12.4681	−0.649943
$369$	3.56543	0.185609
$370$	28.9993	1.50760
$371$	7.19845	0.373725
$372$	0.329545	0.0170861
$373$	−33.2812	−1.72324	−0.861619	−	0.507556i	$-0.830549\pi$
$373$	−33.2812	−1.72324	−0.861619	+	0.507556i	$0.830549\pi$
$374$	0.0669952	0.00346424
$375$	−10.0737	−0.520205
$376$	5.97517	0.308146
$377$	3.23781	0.166756
$378$	−0.735171	−0.0378131
$379$	34.7450	1.78473	0.892364	−	0.451315i	$-0.149045\pi$
$379$	34.7450	1.78473	0.892364	+	0.451315i	$0.149045\pi$
$380$	4.14981	0.212881
$381$	−13.3376	−0.683307
$382$	18.6871	0.956115
$383$	11.4728	0.586231	0.293115	−	0.956077i	$-0.405308\pi$
$383$	11.4728	0.586231	0.293115	+	0.956077i	$0.405308\pi$
$384$	−8.89991	−0.454172
$385$	−0.0674310	−0.00343660
$386$	−6.22380	−0.316783
$387$	3.35313	0.170449
$388$	1.45115	0.0736709
$389$	−0.557480	−0.0282654	−0.0141327	−	0.999900i	$-0.504499\pi$
$389$	−0.557480	−0.0282654	−0.0141327	+	0.999900i	$0.504499\pi$
$390$	6.44230	0.326218
$391$	3.59294	0.181703
$392$	−19.8808	−1.00413
$393$	1.77550	0.0895621
$394$	13.5856	0.684432
$395$	−10.1902	−0.512725
$396$	0.0119511	0.000600566 0
$397$	21.3771	1.07289	0.536443	−	0.843936i	$-0.319767\pi$
$397$	21.3771	1.07289	0.536443	+	0.843936i	$0.319767\pi$
$398$	16.7078	0.837487
$399$	−4.01842	−0.201173
$400$	−2.86881	−0.143441
$401$	−32.6546	−1.63070	−0.815348	−	0.578972i	$-0.803454\pi$
$401$	−32.6546	−1.63070	−0.815348	+	0.578972i	$0.803454\pi$
$402$	14.6613	0.731238
$403$	2.79637	0.139297
$404$	0.842497	0.0419158
$405$	2.41386	0.119946
$406$	1.18428	0.0587747
$407$	0.456494	0.0226276
$408$	2.97018	0.147046
$409$	25.8625	1.27882	0.639408	−	0.768867i	$-0.279179\pi$
$409$	25.8625	1.27882	0.639408	+	0.768867i	$0.279179\pi$
$410$	−11.4279	−0.564383
$411$	3.07784	0.151819
$412$	−1.74885	−0.0861596
$413$	−3.47656	−0.171070
$414$	−4.77081	−0.234473
$415$	17.7509	0.871355
$416$	2.67843	0.131321
$417$	−9.18804	−0.449940
$418$	−0.486243	−0.0237829
$419$	−33.9823	−1.66014	−0.830071	−	0.557658i	$-0.811700\pi$
$419$	−33.9823	−1.66014	−0.830071	+	0.557658i	$0.811700\pi$
$420$	−0.316566	−0.0154469
$421$	−4.14710	−0.202117	−0.101059	−	0.994880i	$-0.532223\pi$
$421$	−4.14710	−0.202117	−0.101059	+	0.994880i	$0.532223\pi$
$422$	2.51128	0.122247
$423$	2.01172	0.0978131
$424$	38.6167	1.87539
$425$	0.826709	0.0401013
$426$	12.2473	0.593384
$427$	−2.49644	−0.120811
$428$	0.735692	0.0355610
$429$	0.101412	0.00489621
$430$	−10.7474	−0.518288
$431$	−0.673825	−0.0324570	−0.0162285	−	0.999868i	$-0.505166\pi$
$431$	−0.673825	−0.0324570	−0.0162285	+	0.999868i	$0.505166\pi$
$432$	−3.47016	−0.166958
$433$	22.5517	1.08376	0.541882	−	0.840455i	$-0.317712\pi$
$433$	22.5517	1.08376	0.541882	+	0.840455i	$0.317712\pi$
$434$	1.02281	0.0490967
$435$	−3.88845	−0.186437
$436$	−0.0592373	−0.00283695
$437$	−26.0771	−1.24744
$438$	5.51845	0.263682
$439$	−31.0179	−1.48040	−0.740202	−	0.672384i	$-0.765270\pi$
$439$	−31.0179	−1.48040	−0.740202	+	0.672384i	$0.765270\pi$
$440$	−0.361740	−0.0172453
$441$	−6.69346	−0.318736
$442$	2.66888	0.126946
$443$	7.70043	0.365859	0.182929	−	0.983126i	$-0.441442\pi$
$443$	7.70043	0.365859	0.182929	+	0.983126i	$0.441442\pi$
$444$	2.14309	0.101706
$445$	−42.7921	−2.02854
$446$	24.7905	1.17387
$447$	−8.11168	−0.383669
$448$	4.82228	0.227831
$449$	−24.2973	−1.14666	−0.573330	−	0.819325i	$-0.694349\pi$
$449$	−24.2973	−1.14666	−0.573330	+	0.819325i	$0.694349\pi$
$450$	−1.09773	−0.0517474
$451$	−0.179893	−0.00847082
$452$	−4.31340	−0.202885
$453$	−3.85015	−0.180896
$454$	−29.9119	−1.40384
$455$	−2.68624	−0.125933
$456$	−21.5572	−1.00951
$457$	15.6393	0.731576	0.365788	−	0.930698i	$-0.380799\pi$
$457$	15.6393	0.731576	0.365788	+	0.930698i	$0.380799\pi$
$458$	−14.6342	−0.683813
$459$	1.00000	0.0466760
$460$	−2.05432	−0.0957833
$461$	4.58418	0.213506	0.106753	−	0.994286i	$-0.465955\pi$
$461$	4.58418	0.213506	0.106753	+	0.994286i	$0.465955\pi$
$462$	0.0370928	0.00172571
$463$	3.22679	0.149962	0.0749809	−	0.997185i	$-0.476110\pi$
$463$	3.22679	0.149962	0.0749809	+	0.997185i	$0.476110\pi$
$464$	5.59003	0.259511
$465$	−3.35831	−0.155738
$466$	−4.17005	−0.193174
$467$	23.6430	1.09407	0.547034	−	0.837110i	$-0.315757\pi$
$467$	23.6430	1.09407	0.547034	+	0.837110i	$0.315757\pi$
$468$	0.476095	0.0220075
$469$	−6.11330	−0.282286
$470$	−6.44794	−0.297422
$471$	−1.00000	−0.0460776
$472$	−18.6503	−0.858450
$473$	−0.169181	−0.00777897
$474$	5.60549	0.257469
$475$	−6.00015	−0.275306
$476$	−0.131145	−0.00601104
$477$	13.0015	0.595297
$478$	−10.1038	−0.462137
$479$	13.0903	0.598112	0.299056	−	0.954236i	$-0.403328\pi$
$479$	13.0903	0.598112	0.299056	+	0.954236i	$0.403328\pi$
$480$	−3.21667	−0.146820
$481$	18.1853	0.829177
$482$	5.28409	0.240684
$483$	1.98928	0.0905154
$484$	2.60495	0.118407
$485$	−14.7882	−0.671500
$486$	−1.32783	−0.0602316
$487$	20.3524	0.922256	0.461128	−	0.887334i	$-0.347445\pi$
$487$	20.3524	0.922256	0.461128	+	0.887334i	$0.347445\pi$
$488$	−13.3924	−0.606244
$489$	5.57276	0.252009
$490$	21.4538	0.969184
$491$	−19.5929	−0.884215	−0.442107	−	0.896962i	$-0.645769\pi$
$491$	−19.5929	−0.884215	−0.442107	+	0.896962i	$0.645769\pi$
$492$	−0.844538	−0.0380747
$493$	−1.61089	−0.0725507
$494$	−19.3704	−0.871515
$495$	−0.121790	−0.00547407
$496$	4.82789	0.216779
$497$	−5.10675	−0.229069
$498$	−9.76450	−0.437558
$499$	−5.37507	−0.240621	−0.120311	−	0.992736i	$-0.538389\pi$
$499$	−5.37507	−0.240621	−0.120311	+	0.992736i	$0.538389\pi$
$500$	2.38615	0.106712
$501$	21.0118	0.938739
$502$	−5.98882	−0.267294
$503$	−26.9146	−1.20006	−0.600031	−	0.799976i	$-0.704845\pi$
$503$	−26.9146	−1.20006	−0.600031	+	0.799976i	$0.704845\pi$
$504$	1.64448	0.0732510
$505$	−8.58565	−0.382056
$506$	0.240710	0.0107009
$507$	−8.96007	−0.397931
$508$	3.15926	0.140169
$509$	−27.1299	−1.20251	−0.601256	−	0.799057i	$-0.705333\pi$
$509$	−27.1299	−1.20251	−0.601256	+	0.799057i	$0.705333\pi$
$510$	−3.20519	−0.141928
$511$	−2.30102	−0.101791
$512$	25.2383	1.11538
$513$	−7.25787	−0.320443
$514$	−1.43199	−0.0631622
$515$	17.8220	0.785332
$516$	−0.794251	−0.0349649
$517$	−0.101501	−0.00446399
$518$	6.65153	0.292252
$519$	−10.1994	−0.447705
$520$	−14.4106	−0.631945
$521$	−31.1032	−1.36266	−0.681329	−	0.731977i	$-0.738598\pi$
$521$	−31.1032	−1.36266	−0.681329	+	0.731977i	$0.738598\pi$
$522$	2.13898	0.0936208
$523$	−27.5421	−1.20433	−0.602166	−	0.798371i	$-0.705696\pi$
$523$	−27.5421	−1.20433	−0.602166	+	0.798371i	$0.705696\pi$
$524$	−0.420559	−0.0183722
$525$	0.457719	0.0199765
$526$	−39.4402	−1.71968
$527$	−1.39126	−0.0606043
$528$	0.175086	0.00761963
$529$	−10.0908	−0.438729
$530$	−41.6722	−1.81013
$531$	−6.27918	−0.272493
$532$	0.951836	0.0412673
$533$	−7.16636	−0.310410
$534$	23.5394	1.01865
$535$	−7.49723	−0.324133
$536$	−32.7953	−1.41654
$537$	−7.80693	−0.336894
$538$	−25.1130	−1.08270
$539$	0.337716	0.0145465
$540$	−0.571766	−0.0246049
$541$	18.5985	0.799612	0.399806	−	0.916600i	$-0.369077\pi$
$541$	18.5985	0.799612	0.399806	+	0.916600i	$0.369077\pi$
$542$	−18.9241	−0.812859
$543$	14.5974	0.626433
$544$	−1.33258	−0.0571340
$545$	0.603671	0.0258584
$546$	1.47766	0.0632381
$547$	45.5835	1.94901	0.974505	−	0.224366i	$-0.0720313\pi$
$547$	45.5835	1.94901	0.974505	+	0.224366i	$0.0720313\pi$
$548$	−0.729042	−0.0311431
$549$	−4.50894	−0.192437
$550$	0.0553856	0.00236165
$551$	11.6916	0.498079
$552$	10.6717	0.454217
$553$	−2.33732	−0.0993928
$554$	9.72099	0.413005
$555$	−21.8396	−0.927040
$556$	2.17635	0.0922980
$557$	−2.43056	−0.102986	−0.0514931	−	0.998673i	$-0.516398\pi$
$557$	−2.43056	−0.102986	−0.0514931	+	0.998673i	$0.516398\pi$
$558$	1.84736	0.0782049
$559$	−6.73965	−0.285057
$560$	−4.63775	−0.195981
$561$	−0.0504547	−0.00213020
$562$	−25.9935	−1.09647
$563$	10.5339	0.443952	0.221976	−	0.975052i	$-0.428749\pi$
$563$	10.5339	0.443952	0.221976	+	0.975052i	$0.428749\pi$
$564$	−0.476512	−0.0200648
$565$	43.9567	1.84927
$566$	−0.148758	−0.00625275
$567$	0.553664	0.0232517
$568$	−27.3956	−1.14949
$569$	−18.4295	−0.772605	−0.386303	−	0.922372i	$-0.626248\pi$
$569$	−18.4295	−0.772605	−0.386303	+	0.922372i	$0.626248\pi$
$570$	23.2629	0.974374
$571$	−27.2558	−1.14062	−0.570311	−	0.821429i	$-0.693177\pi$
$571$	−27.2558	−1.14062	−0.570311	+	0.821429i	$0.693177\pi$
$572$	−0.0240212	−0.00100438
$573$	−14.0734	−0.587925
$574$	−2.62120	−0.109407
$575$	2.97032	0.123871
$576$	8.70976	0.362907
$577$	−16.6908	−0.694849	−0.347424	−	0.937708i	$-0.612944\pi$
$577$	−16.6908	−0.694849	−0.347424	+	0.937708i	$0.612944\pi$
$578$	−1.32783	−0.0552304
$579$	4.68720	0.194793
$580$	0.921051	0.0382445
$581$	4.07149	0.168914
$582$	8.13481	0.337199
$583$	−0.655985	−0.0271681
$584$	−12.3441	−0.510801
$585$	−4.85175	−0.200595
$586$	10.8245	0.447158
$587$	37.8588	1.56260	0.781299	−	0.624157i	$-0.214557\pi$
$587$	37.8588	1.56260	0.781299	+	0.624157i	$0.214557\pi$
$588$	1.58547	0.0653836
$589$	10.0976	0.416064
$590$	20.1260	0.828574
$591$	−10.2314	−0.420865
$592$	31.3966	1.29039
$593$	−22.5803	−0.927260	−0.463630	−	0.886029i	$-0.653453\pi$
$593$	−22.5803	−0.927260	−0.463630	+	0.886029i	$0.653453\pi$
$594$	0.0669952	0.00274885
$595$	1.33647	0.0547897
$596$	1.92140	0.0787036
$597$	−12.5828	−0.514979
$598$	9.58913	0.392129
$599$	−26.2397	−1.07213	−0.536063	−	0.844178i	$-0.680089\pi$
$599$	−26.2397	−1.07213	−0.536063	+	0.844178i	$0.680089\pi$
$600$	2.45548	0.100244
$601$	−35.6016	−1.45222	−0.726109	−	0.687580i	$-0.758673\pi$
$601$	−35.6016	−1.45222	−0.726109	+	0.687580i	$0.758673\pi$
$602$	−2.46513	−0.100471
$603$	−11.0415	−0.449646
$604$	0.911979	0.0371079
$605$	−26.5463	−1.07926
$606$	4.72285	0.191853
$607$	33.0431	1.34118	0.670588	−	0.741830i	$-0.266042\pi$
$607$	33.0431	1.34118	0.670588	+	0.741830i	$0.266042\pi$
$608$	9.67171	0.392240
$609$	−0.891890	−0.0361412
$610$	14.4520	0.585146
$611$	−4.04347	−0.163581
$612$	−0.236868	−0.00957483
$613$	10.1310	0.409188	0.204594	−	0.978847i	$-0.434413\pi$
$613$	10.1310	0.409188	0.204594	+	0.978847i	$0.434413\pi$
$614$	23.9400	0.966142
$615$	8.60645	0.347045
$616$	−0.0829718	−0.00334303
$617$	20.2283	0.814362	0.407181	−	0.913348i	$-0.366512\pi$
$617$	20.2283	0.814362	0.407181	+	0.913348i	$0.366512\pi$
$618$	−9.80365	−0.394361
$619$	−3.68516	−0.148119	−0.0740596	−	0.997254i	$-0.523595\pi$
$619$	−3.68516	−0.148119	−0.0740596	+	0.997254i	$0.523595\pi$
$620$	0.795476	0.0319471
$621$	3.59294	0.144180
$622$	18.2109	0.730189
$623$	−9.81518	−0.393237
$624$	6.97487	0.279218
$625$	−28.4501	−1.13800
$626$	10.8739	0.434609
$627$	0.366194	0.0146244
$628$	0.236868	0.00945207
$629$	−9.04760	−0.360751
$630$	−1.77460	−0.0707017
$631$	45.1375	1.79689	0.898447	−	0.439082i	$-0.144696\pi$
$631$	45.1375	1.79689	0.898447	+	0.439082i	$0.144696\pi$
$632$	−12.5387	−0.498764
$633$	−1.89126	−0.0751710
$634$	24.7047	0.981149
$635$	−32.1951	−1.27762
$636$	−3.07964	−0.122116
$637$	13.4536	0.533049
$638$	−0.107922	−0.00427266
$639$	−9.22355	−0.364878
$640$	−21.4831	−0.849195
$641$	−33.3272	−1.31634	−0.658172	−	0.752868i	$-0.728670\pi$
$641$	−33.3272	−1.31634	−0.658172	+	0.752868i	$0.728670\pi$
$642$	4.12412	0.162766
$643$	24.6751	0.973092	0.486546	−	0.873655i	$-0.338257\pi$
$643$	24.6751	0.973092	0.486546	+	0.873655i	$0.338257\pi$
$644$	−0.471198	−0.0185678
$645$	8.09399	0.318700
$646$	9.63722	0.379171
$647$	−42.1781	−1.65819	−0.829096	−	0.559107i	$-0.811144\pi$
$647$	−42.1781	−1.65819	−0.829096	+	0.559107i	$0.811144\pi$
$648$	2.97018	0.116680
$649$	0.316814	0.0124360
$650$	2.20639	0.0865417
$651$	−0.770291	−0.0301901
$652$	−1.32001	−0.0516956
$653$	17.0706	0.668023	0.334012	−	0.942569i	$-0.391598\pi$
$653$	17.0706	0.668023	0.334012	+	0.942569i	$0.391598\pi$
$654$	−0.332071	−0.0129850
$655$	4.28580	0.167460
$656$	−12.3726	−0.483069
$657$	−4.15599	−0.162141
$658$	−1.47896	−0.0576558
$659$	−0.174435	−0.00679504	−0.00339752	−	0.999994i	$-0.501081\pi$
$659$	−0.174435	−0.00679504	−0.00339752	+	0.999994i	$0.501081\pi$
$660$	0.0288483	0.00112292
$661$	−2.61970	−0.101894	−0.0509472	−	0.998701i	$-0.516224\pi$
$661$	−2.61970	−0.101894	−0.0509472	+	0.998701i	$0.516224\pi$
$662$	−27.8630	−1.08293
$663$	−2.00996	−0.0780602
$664$	21.8419	0.847630
$665$	−9.69989	−0.376146
$666$	12.0137	0.465520
$667$	−5.78782	−0.224105
$668$	−4.97704	−0.192567
$669$	−18.6700	−0.721823
$670$	35.3902	1.36724
$671$	0.227497	0.00878244
$672$	−0.737803	−0.0284614
$673$	−35.6965	−1.37600	−0.687999	−	0.725712i	$-0.741511\pi$
$673$	−35.6965	−1.37600	−0.687999	+	0.725712i	$0.741511\pi$
$674$	−33.9766	−1.30873
$675$	0.826709	0.0318201
$676$	2.12236	0.0816291
$677$	39.6539	1.52402	0.762011	−	0.647564i	$-0.224212\pi$
$677$	39.6539	1.52402	0.762011	+	0.647564i	$0.224212\pi$
$678$	−24.1800	−0.928626
$679$	−3.39196	−0.130172
$680$	7.16959	0.274941
$681$	22.5269	0.863234
$682$	−0.0932078	−0.00356911
$683$	29.0643	1.11212	0.556058	−	0.831144i	$-0.312313\pi$
$683$	29.0643	1.11212	0.556058	+	0.831144i	$0.312313\pi$
$684$	1.71916	0.0657337
$685$	7.42946	0.283865
$686$	10.0670	0.384361
$687$	11.0212	0.420484
$688$	−11.6359	−0.443615
$689$	−26.1324	−0.995565
$690$	−11.5161	−0.438409
$691$	−16.0607	−0.610979	−0.305490	−	0.952195i	$-0.598820\pi$
$691$	−16.0607	−0.610979	−0.305490	+	0.952195i	$0.598820\pi$
$692$	2.41592	0.0918395
$693$	−0.0279349	−0.00106116
$694$	16.8423	0.639327
$695$	−22.1786	−0.841283
$696$	−4.78462	−0.181361
$697$	3.56543	0.135050
$698$	45.8137	1.73408
$699$	3.14050	0.118785
$700$	−0.108419	−0.00409786
$701$	34.7415	1.31217	0.656084	−	0.754688i	$-0.272212\pi$
$701$	34.7415	1.31217	0.656084	+	0.754688i	$0.272212\pi$
$702$	2.66888	0.100730
$703$	65.6663	2.47665
$704$	−0.439448	−0.0165623
$705$	4.85600	0.182888
$706$	−31.9063	−1.20081
$707$	−1.96928	−0.0740624
$708$	1.48734	0.0558976
$709$	18.3622	0.689608	0.344804	−	0.938675i	$-0.387945\pi$
$709$	18.3622	0.689608	0.344804	+	0.938675i	$0.387945\pi$
$710$	29.5633	1.10949
$711$	−4.22154	−0.158320
$712$	−52.6545	−1.97331
$713$	−4.99872	−0.187203
$714$	−0.735171	−0.0275131
$715$	0.244794	0.00915476
$716$	1.84921	0.0691084
$717$	7.60926	0.284173
$718$	27.8810	1.04051
$719$	−18.2982	−0.682407	−0.341203	−	0.939989i	$-0.610835\pi$
$719$	−18.2982	−0.682407	−0.341203	+	0.939989i	$0.610835\pi$
$720$	−8.37647	−0.312172
$721$	4.08782	0.152238
$722$	−44.7169	−1.66419
$723$	−3.97950	−0.147999
$724$	−3.45765	−0.128503
$725$	−1.33173	−0.0494594
$726$	14.6027	0.541959
$727$	−29.6981	−1.10144	−0.550721	−	0.834690i	$-0.685647\pi$
$727$	−29.6981	−1.10144	−0.550721	+	0.834690i	$0.685647\pi$
$728$	−3.30534	−0.122504
$729$	1.00000	0.0370370
$730$	13.3208	0.493023
$731$	3.35313	0.124020
$732$	1.06803	0.0394754
$733$	−29.9277	−1.10541	−0.552703	−	0.833378i	$-0.686404\pi$
$733$	−29.9277	−1.10541	−0.552703	+	0.833378i	$0.686404\pi$
$734$	2.77566	0.102452
$735$	−16.1571	−0.595962
$736$	−4.78789	−0.176484
$737$	0.557097	0.0205209
$738$	−4.73429	−0.174271
$739$	23.4106	0.861173	0.430586	−	0.902549i	$-0.358307\pi$
$739$	23.4106	0.861173	0.430586	+	0.902549i	$0.358307\pi$
$740$	5.17311	0.190167
$741$	14.5880	0.535904
$742$	−9.55831	−0.350897
$743$	46.9788	1.72348	0.861742	−	0.507347i	$-0.169374\pi$
$743$	46.9788	1.72348	0.861742	+	0.507347i	$0.169374\pi$
$744$	−4.13229	−0.151497
$745$	−19.5804	−0.717372
$746$	44.1918	1.61798
$747$	7.35373	0.269059
$748$	0.0119511	0.000436976 0
$749$	−1.71963	−0.0628339
$750$	13.3762	0.488430
$751$	−30.6974	−1.12016	−0.560082	−	0.828437i	$-0.689230\pi$
$751$	−30.6974	−1.12016	−0.560082	+	0.828437i	$0.689230\pi$
$752$	−6.98098	−0.254570
$753$	4.51023	0.164362
$754$	−4.29926	−0.156570
$755$	−9.29372	−0.338233
$756$	−0.131145	−0.00476971
$757$	5.70179	0.207235	0.103617	−	0.994617i	$-0.466958\pi$
$757$	5.70179	0.207235	0.103617	+	0.994617i	$0.466958\pi$
$758$	−46.1354	−1.67571
$759$	−0.181281	−0.00658008
$760$	−52.0360	−1.88754
$761$	−13.4666	−0.488164	−0.244082	−	0.969755i	$-0.578487\pi$
$761$	−13.4666	−0.488164	−0.244082	+	0.969755i	$0.578487\pi$
$762$	17.7101	0.641569
$763$	0.138463	0.00501271
$764$	3.33354	0.120603
$765$	2.41386	0.0872732
$766$	−15.2339	−0.550422
$767$	12.6209	0.455714
$768$	−5.60195	−0.202143
$769$	6.11274	0.220431	0.110216	−	0.993908i	$-0.464846\pi$
$769$	6.11274	0.220431	0.110216	+	0.993908i	$0.464846\pi$
$770$	0.0895368	0.00322668
$771$	1.07844	0.0388391
$772$	−1.11025	−0.0399587
$773$	14.1557	0.509147	0.254573	−	0.967053i	$-0.418065\pi$
$773$	14.1557	0.509147	0.254573	+	0.967053i	$0.418065\pi$
$774$	−4.45239	−0.160038
$775$	−1.15017	−0.0413153
$776$	−18.1965	−0.653216
$777$	−5.00933	−0.179709
$778$	0.740239	0.0265389
$779$	−25.8774	−0.927156
$780$	1.14923	0.0411489
$781$	0.465372	0.0166523
$782$	−4.77081	−0.170604
$783$	−1.61089	−0.0575684
$784$	23.2273	0.829548
$785$	−2.41386	−0.0861543
$786$	−2.35756	−0.0840914
$787$	4.45516	0.158809	0.0794047	−	0.996842i	$-0.474698\pi$
$787$	4.45516	0.158809	0.0794047	+	0.996842i	$0.474698\pi$
$788$	2.42350	0.0863336
$789$	29.7028	1.05745
$790$	13.5309	0.481406
$791$	10.0823	0.358485
$792$	−0.149860	−0.00532503
$793$	9.06278	0.321829
$794$	−28.3852	−1.00735
$795$	31.3837	1.11307
$796$	2.98046	0.105640
$797$	−46.0812	−1.63228	−0.816140	−	0.577855i	$-0.803890\pi$
$797$	−46.0812	−1.63228	−0.816140	+	0.577855i	$0.803890\pi$
$798$	5.33578	0.188884
$799$	2.01172	0.0711695
$800$	−1.10166	−0.0389495
$801$	−17.7277	−0.626377
$802$	43.3598	1.53109
$803$	0.209689	0.00739978
$804$	2.61539	0.0922376
$805$	4.80184	0.169243
$806$	−3.71311	−0.130789
$807$	18.9128	0.665762
$808$	−10.5644	−0.371654
$809$	3.45973	0.121638	0.0608188	−	0.998149i	$-0.480629\pi$
$809$	3.45973	0.121638	0.0608188	+	0.998149i	$0.480629\pi$
$810$	−3.20519	−0.112619
$811$	−8.12824	−0.285421	−0.142710	−	0.989764i	$-0.545582\pi$
$811$	−8.12824	−0.285421	−0.142710	+	0.989764i	$0.545582\pi$
$812$	0.211260	0.00741378
$813$	14.2519	0.499835
$814$	−0.606146	−0.0212454
$815$	13.4519	0.471198
$816$	−3.47016	−0.121480
$817$	−24.3366	−0.851430
$818$	−34.3409	−1.20070
$819$	−1.11284	−0.0388858
$820$	−2.03859	−0.0711908
$821$	6.17843	0.215629	0.107814	−	0.994171i	$-0.465615\pi$
$821$	6.17843	0.215629	0.107814	+	0.994171i	$0.465615\pi$
$822$	−4.08684	−0.142545
$823$	−20.2690	−0.706532	−0.353266	−	0.935523i	$-0.614929\pi$
$823$	−20.2690	−0.706532	−0.353266	+	0.935523i	$0.614929\pi$
$824$	21.9295	0.763949
$825$	−0.0417114	−0.00145220
$826$	4.61627	0.160621
$827$	20.0180	0.696095	0.348047	−	0.937477i	$-0.386845\pi$
$827$	20.0180	0.696095	0.348047	+	0.937477i	$0.386845\pi$
$828$	−0.851054	−0.0295762
$829$	24.8638	0.863556	0.431778	−	0.901980i	$-0.357886\pi$
$829$	24.8638	0.863556	0.431778	+	0.901980i	$0.357886\pi$
$830$	−23.5701	−0.818131
$831$	−7.32097	−0.253961
$832$	−17.5062	−0.606919
$833$	−6.69346	−0.231915
$834$	12.2001	0.422457
$835$	50.7196	1.75522
$836$	−0.0867396	−0.00299995
$837$	−1.39126	−0.0480890
$838$	45.1226	1.55874
$839$	−16.8215	−0.580743	−0.290372	−	0.956914i	$-0.593779\pi$
$839$	−16.8215	−0.580743	−0.290372	+	0.956914i	$0.593779\pi$
$840$	3.96954	0.136962
$841$	−26.4050	−0.910519
$842$	5.50664	0.189771
$843$	19.5759	0.674231
$844$	0.447980	0.0154201
$845$	−21.6283	−0.744038
$846$	−2.67122	−0.0918384
$847$	−6.08889	−0.209217
$848$	−45.1172	−1.54933
$849$	0.112031	0.00384488
$850$	−1.09773	−0.0376518
$851$	−32.5075	−1.11434
$852$	2.18477	0.0748489
$853$	33.7858	1.15680	0.578402	−	0.815752i	$-0.303677\pi$
$853$	33.7858	1.15680	0.578402	+	0.815752i	$0.303677\pi$
$854$	3.31485	0.113432
$855$	−17.5195	−0.599153
$856$	−9.22512	−0.315308
$857$	37.0981	1.26725	0.633623	−	0.773642i	$-0.281567\pi$
$857$	37.0981	1.26725	0.633623	+	0.773642i	$0.281567\pi$
$858$	−0.134658	−0.00459713
$859$	7.33435	0.250245	0.125122	−	0.992141i	$-0.460068\pi$
$859$	7.33435	0.250245	0.125122	+	0.992141i	$0.460068\pi$
$860$	−1.91721	−0.0653763
$861$	1.97405	0.0672755
$862$	0.894725	0.0304744
$863$	−21.9356	−0.746698	−0.373349	−	0.927691i	$-0.621791\pi$
$863$	−21.9356	−0.746698	−0.373349	+	0.927691i	$0.621791\pi$
$864$	−1.33258	−0.0453354
$865$	−24.6200	−0.837104
$866$	−29.9448	−1.01757
$867$	1.00000	0.0339618
$868$	0.182457	0.00619301
$869$	0.212997	0.00722542
$870$	5.16320	0.175049
$871$	22.1930	0.751981
$872$	0.742799	0.0251543
$873$	−6.12639	−0.207347
$874$	34.6260	1.17124
$875$	−5.57746	−0.188553
$876$	0.984423	0.0332606
$877$	−50.6130	−1.70908	−0.854540	−	0.519385i	$-0.826161\pi$
$877$	−50.6130	−1.70908	−0.854540	+	0.519385i	$0.826161\pi$
$878$	41.1865	1.38998
$879$	−8.15206	−0.274962
$880$	0.422632	0.0142469
$881$	−18.0794	−0.609112	−0.304556	−	0.952494i	$-0.598508\pi$
$881$	−18.0794	−0.609112	−0.304556	+	0.952494i	$0.598508\pi$
$882$	8.88777	0.299267
$883$	−32.9391	−1.10849	−0.554244	−	0.832354i	$-0.686992\pi$
$883$	−32.9391	−1.10849	−0.554244	+	0.832354i	$0.686992\pi$
$884$	0.476095	0.0160128
$885$	−15.1571	−0.509499
$886$	−10.2249	−0.343511
$887$	−13.3264	−0.447456	−0.223728	−	0.974652i	$-0.571823\pi$
$887$	−13.3264	−0.447456	−0.223728	+	0.974652i	$0.571823\pi$
$888$	−26.8730	−0.901798
$889$	−7.38456	−0.247670
$890$	56.8207	1.90463
$891$	−0.0504547	−0.00169030
$892$	4.42232	0.148070
$893$	−14.6008	−0.488597
$894$	10.7709	0.360234
$895$	−18.8448	−0.629913
$896$	−4.92756	−0.164618
$897$	−7.22166	−0.241124
$898$	32.2626	1.07662
$899$	2.24116	0.0747470
$900$	−0.195821	−0.00652737
$901$	13.0015	0.433142
$902$	0.238867	0.00795340
$903$	1.85651	0.0617807
$904$	54.0874	1.79892
$905$	35.2360	1.17128
$906$	5.11235	0.169846
$907$	−14.4746	−0.480621	−0.240310	−	0.970696i	$-0.577249\pi$
$907$	−14.4746	−0.480621	−0.240310	+	0.970696i	$0.577249\pi$
$908$	−5.33592	−0.177079
$909$	−3.55682	−0.117972
$910$	3.56687	0.118240
$911$	9.49756	0.314668	0.157334	−	0.987545i	$-0.449710\pi$
$911$	9.49756	0.314668	0.157334	+	0.987545i	$0.449710\pi$
$912$	25.1859	0.833990
$913$	−0.371030	−0.0122793
$914$	−20.7663	−0.686890
$915$	−10.8840	−0.359812
$916$	−2.61056	−0.0862555
$917$	0.983030	0.0324625
$918$	−1.32783	−0.0438249
$919$	−37.0773	−1.22307	−0.611534	−	0.791218i	$-0.709447\pi$
$919$	−37.0773	−1.22307	−0.611534	+	0.791218i	$0.709447\pi$
$920$	25.7599	0.849280
$921$	−18.0295	−0.594091
$922$	−6.08701	−0.200465
$923$	18.5389	0.610217
$924$	0.00661690	0.000217680 0
$925$	−7.47973	−0.245932
$926$	−4.28463	−0.140802
$927$	7.38321	0.242496
$928$	2.14664	0.0704669
$929$	−35.1644	−1.15371	−0.576853	−	0.816848i	$-0.695720\pi$
$929$	−35.1644	−1.15371	−0.576853	+	0.816848i	$0.695720\pi$
$930$	4.45926	0.146225
$931$	48.5802	1.59215
$932$	−0.743884	−0.0243667
$933$	−13.7148	−0.449001
$934$	−31.3939	−1.02724
$935$	−0.121790	−0.00398297
$936$	−5.96993	−0.195133
$937$	−8.33411	−0.272263	−0.136132	−	0.990691i	$-0.543467\pi$
$937$	−8.33411	−0.272263	−0.136132	+	0.990691i	$0.543467\pi$
$938$	8.11742	0.265043
$939$	−8.18923	−0.267245
$940$	−1.15023	−0.0375165
$941$	1.75364	0.0571669	0.0285835	−	0.999591i	$-0.490900\pi$
$941$	1.75364	0.0571669	0.0285835	+	0.999591i	$0.490900\pi$
$942$	1.32783	0.0432630
$943$	12.8104	0.417164
$944$	21.7897	0.709196
$945$	1.33647	0.0434752
$946$	0.224644	0.00730381
$947$	−18.2836	−0.594139	−0.297069	−	0.954856i	$-0.596009\pi$
$947$	−18.2836	−0.594139	−0.297069	+	0.954856i	$0.596009\pi$
$948$	0.999949	0.0324768
$949$	8.35337	0.271162
$950$	7.96718	0.258489
$951$	−18.6053	−0.603319
$952$	1.64448	0.0532979
$953$	7.55361	0.244685	0.122343	−	0.992488i	$-0.460959\pi$
$953$	7.55361	0.244685	0.122343	+	0.992488i	$0.460959\pi$
$954$	−17.2637	−0.558934
$955$	−33.9712	−1.09928
$956$	−1.80239	−0.0582935
$957$	0.0812768	0.00262731
$958$	−17.3817	−0.561578
$959$	1.70409	0.0550278
$960$	21.0241	0.678550
$961$	−29.0644	−0.937561
$962$	−24.1469	−0.778529
$963$	−3.10591	−0.100087
$964$	0.942616	0.0303596
$965$	11.3142	0.364218
$966$	−2.64143	−0.0849865
$967$	7.72662	0.248471	0.124236	−	0.992253i	$-0.460352\pi$
$967$	7.72662	0.248471	0.124236	+	0.992253i	$0.460352\pi$
$968$	−32.6644	−1.04987
$969$	−7.25787	−0.233156
$970$	19.6363	0.630483
$971$	−7.39736	−0.237393	−0.118696	−	0.992931i	$-0.537872\pi$
$971$	−7.39736	−0.237393	−0.118696	+	0.992931i	$0.537872\pi$
$972$	−0.236868	−0.00759755
$973$	−5.08708	−0.163084
$974$	−27.0246	−0.865923
$975$	−1.66165	−0.0532154
$976$	15.6467	0.500840
$977$	−40.6715	−1.30120	−0.650599	−	0.759421i	$-0.725482\pi$
$977$	−40.6715	−1.30120	−0.650599	+	0.759421i	$0.725482\pi$
$978$	−7.39968	−0.236616
$979$	0.894446	0.0285866
$980$	3.82709	0.122252
$981$	0.250085	0.00798461
$982$	26.0160	0.830204
$983$	−11.4955	−0.366649	−0.183324	−	0.983052i	$-0.558686\pi$
$983$	−11.4955	−0.366649	−0.183324	+	0.983052i	$0.558686\pi$
$984$	10.5900	0.337596
$985$	−24.6972	−0.786919
$986$	2.13898	0.0681191
$987$	1.11382	0.0354531
$988$	−3.45544	−0.109932
$989$	12.0476	0.383092
$990$	0.161717	0.00513970
$991$	13.0319	0.413971	0.206986	−	0.978344i	$-0.433635\pi$
$991$	13.0319	0.413971	0.206986	+	0.978344i	$0.433635\pi$
$992$	1.85397	0.0588636
$993$	20.9839	0.665903
$994$	6.78089	0.215077
$995$	−30.3731	−0.962891
$996$	−1.74187	−0.0551931
$997$	−57.2694	−1.81374	−0.906870	−	0.421411i	$-0.861535\pi$
$997$	−57.2694	−1.81374	−0.906870	+	0.421411i	$0.861535\pi$
$998$	7.13718	0.225924
$999$	−9.04760	−0.286253

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.d.1.13	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.d.1.13	✓	40	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.32783 q^{2} +1.00000 q^{3} -0.236868 q^{4} +2.41386 q^{5} -1.32783 q^{6} +0.553664 q^{7} +2.97018 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.32783 q^{2} +1.00000 q^{3} -0.236868 q^{4} +2.41386 q^{5} -1.32783 q^{6} +0.553664 q^{7} +2.97018 q^{8} +1.00000 q^{9} -3.20519 q^{10} -0.0504547 q^{11} -0.236868 q^{12} -2.00996 q^{13} -0.735171 q^{14} +2.41386 q^{15} -3.47016 q^{16} +1.00000 q^{17} -1.32783 q^{18} -7.25787 q^{19} -0.571766 q^{20} +0.553664 q^{21} +0.0669952 q^{22} +3.59294 q^{23} +2.97018 q^{24} +0.826709 q^{25} +2.66888 q^{26} +1.00000 q^{27} -0.131145 q^{28} -1.61089 q^{29} -3.20519 q^{30} -1.39126 q^{31} -1.33258 q^{32} -0.0504547 q^{33} -1.32783 q^{34} +1.33647 q^{35} -0.236868 q^{36} -9.04760 q^{37} +9.63722 q^{38} -2.00996 q^{39} +7.16959 q^{40} +3.56543 q^{41} -0.735171 q^{42} +3.35313 q^{43} +0.0119511 q^{44} +2.41386 q^{45} -4.77081 q^{46} +2.01172 q^{47} -3.47016 q^{48} -6.69346 q^{49} -1.09773 q^{50} +1.00000 q^{51} +0.476095 q^{52} +13.0015 q^{53} -1.32783 q^{54} -0.121790 q^{55} +1.64448 q^{56} -7.25787 q^{57} +2.13898 q^{58} -6.27918 q^{59} -0.571766 q^{60} -4.50894 q^{61} +1.84736 q^{62} +0.553664 q^{63} +8.70976 q^{64} -4.85175 q^{65} +0.0669952 q^{66} -11.0415 q^{67} -0.236868 q^{68} +3.59294 q^{69} -1.77460 q^{70} -9.22355 q^{71} +2.97018 q^{72} -4.15599 q^{73} +12.0137 q^{74} +0.826709 q^{75} +1.71916 q^{76} -0.0279349 q^{77} +2.66888 q^{78} -4.22154 q^{79} -8.37647 q^{80} +1.00000 q^{81} -4.73429 q^{82} +7.35373 q^{83} -0.131145 q^{84} +2.41386 q^{85} -4.45239 q^{86} -1.61089 q^{87} -0.149860 q^{88} -17.7277 q^{89} -3.20519 q^{90} -1.11284 q^{91} -0.851054 q^{92} -1.39126 q^{93} -2.67122 q^{94} -17.5195 q^{95} -1.33258 q^{96} -6.12639 q^{97} +8.88777 q^{98} -0.0504547 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 7 q^{2} + 40 q^{3} + 29 q^{4} - 15 q^{5} - 7 q^{6} - 13 q^{7} - 18 q^{8} + 40 q^{9}+O(q^{10}) \) 40 * q - 7 * q^2 + 40 * q^3 + 29 * q^4 - 15 * q^5 - 7 * q^6 - 13 * q^7 - 18 * q^8 + 40 * q^9	\( 40 q - 7 q^{2} + 40 q^{3} + 29 q^{4} - 15 q^{5} - 7 q^{6} - 13 q^{7} - 18 q^{8} + 40 q^{9} - 6 q^{10} - 25 q^{11} + 29 q^{12} - 24 q^{13} - 22 q^{14} - 15 q^{15} + 7 q^{16} + 40 q^{17} - 7 q^{18} - 18 q^{19} - 20 q^{20} - 13 q^{21} - 25 q^{22} - 28 q^{23} - 18 q^{24} - 11 q^{25} - 13 q^{26} + 40 q^{27} - 8 q^{28} - 23 q^{29} - 6 q^{30} - 11 q^{31} - 23 q^{32} - 25 q^{33} - 7 q^{34} - 45 q^{35} + 29 q^{36} - 38 q^{37} - 30 q^{38} - 24 q^{39} - 12 q^{40} - 33 q^{41} - 22 q^{42} - 25 q^{43} - 14 q^{44} - 15 q^{45} + 8 q^{46} - 55 q^{47} + 7 q^{48} - 21 q^{49} + 2 q^{50} + 40 q^{51} - 39 q^{52} - 39 q^{53} - 7 q^{54} - 9 q^{55} - 48 q^{56} - 18 q^{57} - 13 q^{58} - 81 q^{59} - 20 q^{60} - 9 q^{61} - 16 q^{62} - 13 q^{63} - 4 q^{64} - 43 q^{65} - 25 q^{66} - 24 q^{67} + 29 q^{68} - 28 q^{69} + 48 q^{70} - 32 q^{71} - 18 q^{72} - 43 q^{73} - 20 q^{74} - 11 q^{75} - 58 q^{76} - 32 q^{77} - 13 q^{78} - 22 q^{79} - 48 q^{80} + 40 q^{81} - 11 q^{82} - 45 q^{83} - 8 q^{84} - 15 q^{85} - 30 q^{86} - 23 q^{87} - 48 q^{88} - 94 q^{89} - 6 q^{90} - 7 q^{91} - 98 q^{92} - 11 q^{93} + 32 q^{94} - 23 q^{96} - 28 q^{97} - 46 q^{98} - 25 q^{99}+O(q^{100}) \) 40 * q - 7 * q^2 + 40 * q^3 + 29 * q^4 - 15 * q^5 - 7 * q^6 - 13 * q^7 - 18 * q^8 + 40 * q^9 - 6 * q^10 - 25 * q^11 + 29 * q^12 - 24 * q^13 - 22 * q^14 - 15 * q^15 + 7 * q^16 + 40 * q^17 - 7 * q^18 - 18 * q^19 - 20 * q^20 - 13 * q^21 - 25 * q^22 - 28 * q^23 - 18 * q^24 - 11 * q^25 - 13 * q^26 + 40 * q^27 - 8 * q^28 - 23 * q^29 - 6 * q^30 - 11 * q^31 - 23 * q^32 - 25 * q^33 - 7 * q^34 - 45 * q^35 + 29 * q^36 - 38 * q^37 - 30 * q^38 - 24 * q^39 - 12 * q^40 - 33 * q^41 - 22 * q^42 - 25 * q^43 - 14 * q^44 - 15 * q^45 + 8 * q^46 - 55 * q^47 + 7 * q^48 - 21 * q^49 + 2 * q^50 + 40 * q^51 - 39 * q^52 - 39 * q^53 - 7 * q^54 - 9 * q^55 - 48 * q^56 - 18 * q^57 - 13 * q^58 - 81 * q^59 - 20 * q^60 - 9 * q^61 - 16 * q^62 - 13 * q^63 - 4 * q^64 - 43 * q^65 - 25 * q^66 - 24 * q^67 + 29 * q^68 - 28 * q^69 + 48 * q^70 - 32 * q^71 - 18 * q^72 - 43 * q^73 - 20 * q^74 - 11 * q^75 - 58 * q^76 - 32 * q^77 - 13 * q^78 - 22 * q^79 - 48 * q^80 + 40 * q^81 - 11 * q^82 - 45 * q^83 - 8 * q^84 - 15 * q^85 - 30 * q^86 - 23 * q^87 - 48 * q^88 - 94 * q^89 - 6 * q^90 - 7 * q^91 - 98 * q^92 - 11 * q^93 + 32 * q^94 - 23 * q^96 - 28 * q^97 - 46 * q^98 - 25 * q^99

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