LMFDB - Embedded newform 8007.2.a.j.1.10

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:	$64$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	8007.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.16822 q^{2} -1.00000 q^{3} +2.70116 q^{4} -4.31017 q^{5} +2.16822 q^{6} -1.36362 q^{7} -1.52027 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.16822 q^{2} -1.00000 q^{3} +2.70116 q^{4} -4.31017 q^{5} +2.16822 q^{6} -1.36362 q^{7} -1.52027 q^{8} +1.00000 q^{9} +9.34539 q^{10} +0.114623 q^{11} -2.70116 q^{12} +0.931925 q^{13} +2.95662 q^{14} +4.31017 q^{15} -2.10606 q^{16} +1.00000 q^{17} -2.16822 q^{18} +6.13855 q^{19} -11.6425 q^{20} +1.36362 q^{21} -0.248527 q^{22} -4.88123 q^{23} +1.52027 q^{24} +13.5776 q^{25} -2.02061 q^{26} -1.00000 q^{27} -3.68336 q^{28} -7.21659 q^{29} -9.34539 q^{30} -5.66271 q^{31} +7.60691 q^{32} -0.114623 q^{33} -2.16822 q^{34} +5.87744 q^{35} +2.70116 q^{36} +7.77973 q^{37} -13.3097 q^{38} -0.931925 q^{39} +6.55261 q^{40} +11.3656 q^{41} -2.95662 q^{42} +2.77017 q^{43} +0.309614 q^{44} -4.31017 q^{45} +10.5836 q^{46} -7.97282 q^{47} +2.10606 q^{48} -5.14054 q^{49} -29.4391 q^{50} -1.00000 q^{51} +2.51728 q^{52} +12.4294 q^{53} +2.16822 q^{54} -0.494044 q^{55} +2.07307 q^{56} -6.13855 q^{57} +15.6471 q^{58} +5.18445 q^{59} +11.6425 q^{60} +14.4443 q^{61} +12.2780 q^{62} -1.36362 q^{63} -12.2813 q^{64} -4.01676 q^{65} +0.248527 q^{66} +7.29253 q^{67} +2.70116 q^{68} +4.88123 q^{69} -12.7436 q^{70} -4.93808 q^{71} -1.52027 q^{72} +7.06100 q^{73} -16.8681 q^{74} -13.5776 q^{75} +16.5812 q^{76} -0.156302 q^{77} +2.02061 q^{78} -12.1982 q^{79} +9.07746 q^{80} +1.00000 q^{81} -24.6431 q^{82} -7.31701 q^{83} +3.68336 q^{84} -4.31017 q^{85} -6.00633 q^{86} +7.21659 q^{87} -0.174257 q^{88} +8.87217 q^{89} +9.34539 q^{90} -1.27079 q^{91} -13.1850 q^{92} +5.66271 q^{93} +17.2868 q^{94} -26.4582 q^{95} -7.60691 q^{96} +15.8368 q^{97} +11.1458 q^{98} +0.114623 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9}+O(q^{10}) $ 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9} + 12 q^{10} - 7 q^{11} - 77 q^{12} + 24 q^{13} - 14 q^{14} + 3 q^{15} + 103 q^{16} + 64 q^{17} + 5 q^{18} + 26 q^{19} - 24 q^{20} - 5 q^{21} + 25 q^{22} + 20 q^{23} - 18 q^{24} + 141 q^{25} + 9 q^{26} - 64 q^{27} + 14 q^{28} + 5 q^{29} - 12 q^{30} + 11 q^{31} + 31 q^{32} + 7 q^{33} + 5 q^{34} - 3 q^{35} + 77 q^{36} + 50 q^{37} + 8 q^{38} - 24 q^{39} + 28 q^{40} - 9 q^{41} + 14 q^{42} + 59 q^{43} - 6 q^{44} - 3 q^{45} + 11 q^{47} - 103 q^{48} + 163 q^{49} + 20 q^{50} - 64 q^{51} + 65 q^{52} + 39 q^{53} - 5 q^{54} + 35 q^{55} - 34 q^{56} - 26 q^{57} - 27 q^{58} - 65 q^{59} + 24 q^{60} + 15 q^{61} + 18 q^{62} + 5 q^{63} + 152 q^{64} + 49 q^{65} - 25 q^{66} + 56 q^{67} + 77 q^{68} - 20 q^{69} + 28 q^{70} - 18 q^{71} + 18 q^{72} + 37 q^{73} - 76 q^{74} - 141 q^{75} + 30 q^{76} + 80 q^{77} - 9 q^{78} + 20 q^{79} - 144 q^{80} + 64 q^{81} + 27 q^{82} + 3 q^{83} - 14 q^{84} - 3 q^{85} + 12 q^{86} - 5 q^{87} + 108 q^{88} + 42 q^{89} + 12 q^{90} + 25 q^{91} + 18 q^{92} - 11 q^{93} + 60 q^{94} + 42 q^{95} - 31 q^{96} + 72 q^{97} + 18 q^{98} - 7 q^{99}+O(q^{100}) \) 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9 + 12 * q^10 - 7 * q^11 - 77 * q^12 + 24 * q^13 - 14 * q^14 + 3 * q^15 + 103 * q^16 + 64 * q^17 + 5 * q^18 + 26 * q^19 - 24 * q^20 - 5 * q^21 + 25 * q^22 + 20 * q^23 - 18 * q^24 + 141 * q^25 + 9 * q^26 - 64 * q^27 + 14 * q^28 + 5 * q^29 - 12 * q^30 + 11 * q^31 + 31 * q^32 + 7 * q^33 + 5 * q^34 - 3 * q^35 + 77 * q^36 + 50 * q^37 + 8 * q^38 - 24 * q^39 + 28 * q^40 - 9 * q^41 + 14 * q^42 + 59 * q^43 - 6 * q^44 - 3 * q^45 + 11 * q^47 - 103 * q^48 + 163 * q^49 + 20 * q^50 - 64 * q^51 + 65 * q^52 + 39 * q^53 - 5 * q^54 + 35 * q^55 - 34 * q^56 - 26 * q^57 - 27 * q^58 - 65 * q^59 + 24 * q^60 + 15 * q^61 + 18 * q^62 + 5 * q^63 + 152 * q^64 + 49 * q^65 - 25 * q^66 + 56 * q^67 + 77 * q^68 - 20 * q^69 + 28 * q^70 - 18 * q^71 + 18 * q^72 + 37 * q^73 - 76 * q^74 - 141 * q^75 + 30 * q^76 + 80 * q^77 - 9 * q^78 + 20 * q^79 - 144 * q^80 + 64 * q^81 + 27 * q^82 + 3 * q^83 - 14 * q^84 - 3 * q^85 + 12 * q^86 - 5 * q^87 + 108 * q^88 + 42 * q^89 + 12 * q^90 + 25 * q^91 + 18 * q^92 - 11 * q^93 + 60 * q^94 + 42 * q^95 - 31 * q^96 + 72 * q^97 + 18 * q^98 - 7 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.16822	−1.53316	−0.766580	−	0.642149i	$-0.778043\pi$
$2$	−2.16822	−1.53316	−0.766580	+	0.642149i	$0.778043\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	2.70116	1.35058
$5$	−4.31017	−1.92757	−0.963784	−	0.266684i	$-0.914072\pi$
$5$	−4.31017	−1.92757	−0.963784	+	0.266684i	$0.914072\pi$
$6$	2.16822	0.885170
$7$	−1.36362	−0.515400	−0.257700	−	0.966225i	$-0.582965\pi$
$7$	−1.36362	−0.515400	−0.257700	+	0.966225i	$0.582965\pi$
$8$	−1.52027	−0.537495
$9$	1.00000	0.333333
$10$	9.34539	2.95527
$11$	0.114623	0.0345600	0.0172800	−	0.999851i	$-0.494499\pi$
$11$	0.114623	0.0345600	0.0172800	+	0.999851i	$0.494499\pi$
$12$	−2.70116	−0.779758
$13$	0.931925	0.258469	0.129235	−	0.991614i	$-0.458748\pi$
$13$	0.931925	0.258469	0.129235	+	0.991614i	$0.458748\pi$
$14$	2.95662	0.790191
$15$	4.31017	1.11288
$16$	−2.10606	−0.526514
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−2.16822	−0.511053
$19$	6.13855	1.40828	0.704140	−	0.710062i	$-0.251333\pi$
$19$	6.13855	1.40828	0.704140	+	0.710062i	$0.251333\pi$
$20$	−11.6425	−2.60333
$21$	1.36362	0.297566
$22$	−0.248527	−0.0529861
$23$	−4.88123	−1.01781	−0.508904	−	0.860823i	$-0.669949\pi$
$23$	−4.88123	−1.01781	−0.508904	+	0.860823i	$0.669949\pi$
$24$	1.52027	0.310323
$25$	13.5776	2.71552
$26$	−2.02061	−0.396275
$27$	−1.00000	−0.192450
$28$	−3.68336	−0.696089
$29$	−7.21659	−1.34009	−0.670044	−	0.742322i	$-0.733725\pi$
$29$	−7.21659	−1.34009	−0.670044	+	0.742322i	$0.733725\pi$
$30$	−9.34539	−1.70623
$31$	−5.66271	−1.01705	−0.508526	−	0.861046i	$-0.669810\pi$
$31$	−5.66271	−1.01705	−0.508526	+	0.861046i	$0.669810\pi$
$32$	7.60691	1.34473
$33$	−0.114623	−0.0199533
$34$	−2.16822	−0.371846
$35$	5.87744	0.993468
$36$	2.70116	0.450193
$37$	7.77973	1.27898	0.639490	−	0.768800i	$-0.279146\pi$
$37$	7.77973	1.27898	0.639490	+	0.768800i	$0.279146\pi$
$38$	−13.3097	−2.15912
$39$	−0.931925	−0.149227
$40$	6.55261	1.03606
$41$	11.3656	1.77501	0.887505	−	0.460798i	$-0.152437\pi$
$41$	11.3656	1.77501	0.887505	+	0.460798i	$0.152437\pi$
$42$	−2.95662	−0.456217
$43$	2.77017	0.422447	0.211224	−	0.977438i	$-0.432255\pi$
$43$	2.77017	0.422447	0.211224	+	0.977438i	$0.432255\pi$
$44$	0.309614	0.0466761
$45$	−4.31017	−0.642523
$46$	10.5836	1.56046
$47$	−7.97282	−1.16296	−0.581478	−	0.813562i	$-0.697525\pi$
$47$	−7.97282	−1.16296	−0.581478	+	0.813562i	$0.697525\pi$
$48$	2.10606	0.303983
$49$	−5.14054	−0.734363
$50$	−29.4391	−4.16332
$51$	−1.00000	−0.140028
$52$	2.51728	0.349084
$53$	12.4294	1.70731	0.853653	−	0.520841i	$-0.174382\pi$
$53$	12.4294	1.70731	0.853653	+	0.520841i	$0.174382\pi$
$54$	2.16822	0.295057
$55$	−0.494044	−0.0666168
$56$	2.07307	0.277025
$57$	−6.13855	−0.813070
$58$	15.6471	2.05457
$59$	5.18445	0.674958	0.337479	−	0.941333i	$-0.390426\pi$
$59$	5.18445	0.674958	0.337479	+	0.941333i	$0.390426\pi$
$60$	11.6425	1.50304
$61$	14.4443	1.84940	0.924701	−	0.380694i	$-0.124315\pi$
$61$	14.4443	1.84940	0.924701	+	0.380694i	$0.124315\pi$
$62$	12.2780	1.55930
$63$	−1.36362	−0.171800
$64$	−12.2813	−1.53517
$65$	−4.01676	−0.498217
$66$	0.248527	0.0305915
$67$	7.29253	0.890925	0.445462	−	0.895301i	$-0.353039\pi$
$67$	7.29253	0.890925	0.445462	+	0.895301i	$0.353039\pi$
$68$	2.70116	0.327564
$69$	4.88123	0.587632
$70$	−12.7436	−1.52315
$71$	−4.93808	−0.586042	−0.293021	−	0.956106i	$-0.594661\pi$
$71$	−4.93808	−0.586042	−0.293021	+	0.956106i	$0.594661\pi$
$72$	−1.52027	−0.179165
$73$	7.06100	0.826427	0.413214	−	0.910634i	$-0.364406\pi$
$73$	7.06100	0.826427	0.413214	+	0.910634i	$0.364406\pi$
$74$	−16.8681	−1.96088
$75$	−13.5776	−1.56781
$76$	16.5812	1.90199
$77$	−0.156302	−0.0178122
$78$	2.02061	0.228790
$79$	−12.1982	−1.37240	−0.686201	−	0.727412i	$-0.740723\pi$
$79$	−12.1982	−1.37240	−0.686201	+	0.727412i	$0.740723\pi$
$80$	9.07746	1.01489
$81$	1.00000	0.111111
$82$	−24.6431	−2.72137
$83$	−7.31701	−0.803147	−0.401573	−	0.915827i	$-0.631537\pi$
$83$	−7.31701	−0.803147	−0.401573	+	0.915827i	$0.631537\pi$
$84$	3.68336	0.401887
$85$	−4.31017	−0.467504
$86$	−6.00633	−0.647679
$87$	7.21659	0.773700
$88$	−0.174257	−0.0185759
$89$	8.87217	0.940448	0.470224	−	0.882547i	$-0.344173\pi$
$89$	8.87217	0.940448	0.470224	+	0.882547i	$0.344173\pi$
$90$	9.34539	0.985090
$91$	−1.27079	−0.133215
$92$	−13.1850	−1.37463
$93$	5.66271	0.587196
$94$	17.2868	1.78300
$95$	−26.4582	−2.71455
$96$	−7.60691	−0.776377
$97$	15.8368	1.60798	0.803992	−	0.594640i	$-0.202705\pi$
$97$	15.8368	1.60798	0.803992	+	0.594640i	$0.202705\pi$
$98$	11.1458	1.12590
$99$	0.114623	0.0115200
$100$	36.6752	3.66752
$101$	16.8733	1.67895	0.839476	−	0.543397i	$-0.182862\pi$
$101$	16.8733	1.67895	0.839476	+	0.543397i	$0.182862\pi$
$102$	2.16822	0.214685
$103$	−12.1412	−1.19631	−0.598155	−	0.801380i	$-0.704099\pi$
$103$	−12.1412	−1.19631	−0.598155	+	0.801380i	$0.704099\pi$
$104$	−1.41677	−0.138926
$105$	−5.87744	−0.573579
$106$	−26.9496	−2.61757
$107$	−9.69737	−0.937480	−0.468740	−	0.883336i	$-0.655292\pi$
$107$	−9.69737	−0.937480	−0.468740	+	0.883336i	$0.655292\pi$
$108$	−2.70116	−0.259919
$109$	−1.05377	−0.100933	−0.0504666	−	0.998726i	$-0.516071\pi$
$109$	−1.05377	−0.100933	−0.0504666	+	0.998726i	$0.516071\pi$
$110$	1.07119	0.102134
$111$	−7.77973	−0.738419
$112$	2.87186	0.271365
$113$	−4.35515	−0.409698	−0.204849	−	0.978794i	$-0.565670\pi$
$113$	−4.35515	−0.409698	−0.204849	+	0.978794i	$0.565670\pi$
$114$	13.3097	1.24657
$115$	21.0390	1.96189
$116$	−19.4932	−1.80990
$117$	0.931925	0.0861565
$118$	−11.2410	−1.03482
$119$	−1.36362	−0.125003
$120$	−6.55261	−0.598169
$121$	−10.9869	−0.998806
$122$	−31.3183	−2.83543
$123$	−11.3656	−1.02480
$124$	−15.2959	−1.37361
$125$	−36.9709	−3.30678
$126$	2.95662	0.263397
$127$	17.7905	1.57865	0.789325	−	0.613976i	$-0.210431\pi$
$127$	17.7905	1.57865	0.789325	+	0.613976i	$0.210431\pi$
$128$	11.4147	1.00893
$129$	−2.77017	−0.243900
$130$	8.70920	0.763847
$131$	−17.0617	−1.49069	−0.745344	−	0.666680i	$-0.767715\pi$
$131$	−17.0617	−1.49069	−0.745344	+	0.666680i	$0.767715\pi$
$132$	−0.309614	−0.0269485
$133$	−8.37065	−0.725827
$134$	−15.8118	−1.36593
$135$	4.31017	0.370961
$136$	−1.52027	−0.130362
$137$	−13.9010	−1.18764	−0.593820	−	0.804598i	$-0.702381\pi$
$137$	−13.9010	−1.18764	−0.593820	+	0.804598i	$0.702381\pi$
$138$	−10.5836	−0.900933
$139$	−13.7253	−1.16417	−0.582083	−	0.813130i	$-0.697762\pi$
$139$	−13.7253	−1.16417	−0.582083	+	0.813130i	$0.697762\pi$
$140$	15.8759	1.34176
$141$	7.97282	0.671433
$142$	10.7068	0.898496
$143$	0.106820	0.00893272
$144$	−2.10606	−0.175505
$145$	31.1048	2.58311
$146$	−15.3098	−1.26705
$147$	5.14054	0.423985
$148$	21.0143	1.72736
$149$	−11.4677	−0.939475	−0.469737	−	0.882806i	$-0.655651\pi$
$149$	−11.4677	−0.939475	−0.469737	+	0.882806i	$0.655651\pi$
$150$	29.4391	2.40370
$151$	−3.57720	−0.291108	−0.145554	−	0.989350i	$-0.546496\pi$
$151$	−3.57720	−0.291108	−0.145554	+	0.989350i	$0.546496\pi$
$152$	−9.33222	−0.756943
$153$	1.00000	0.0808452
$154$	0.338896	0.0273090
$155$	24.4073	1.96044
$156$	−2.51728	−0.201544
$157$	−1.00000	−0.0798087
$157$	−1.00000	−0.0798087
$158$	26.4483	2.10411
$159$	−12.4294	−0.985714
$160$	−32.7871	−2.59205
$161$	6.65615	0.524578
$162$	−2.16822	−0.170351
$163$	−3.71098	−0.290666	−0.145333	−	0.989383i	$-0.546425\pi$
$163$	−3.71098	−0.290666	−0.145333	+	0.989383i	$0.546425\pi$
$164$	30.7003	2.39729
$165$	0.494044	0.0384612
$166$	15.8649	1.23135
$167$	−14.1416	−1.09431	−0.547154	−	0.837032i	$-0.684289\pi$
$167$	−14.1416	−1.09431	−0.547154	+	0.837032i	$0.684289\pi$
$168$	−2.07307	−0.159940
$169$	−12.1315	−0.933194
$170$	9.34539	0.716758
$171$	6.13855	0.469426
$172$	7.48268	0.570549
$173$	19.7602	1.50234	0.751170	−	0.660109i	$-0.229490\pi$
$173$	19.7602	1.50234	0.751170	+	0.660109i	$0.229490\pi$
$174$	−15.6471	−1.18621
$175$	−18.5147	−1.39958
$176$	−0.241402	−0.0181963
$177$	−5.18445	−0.389687
$178$	−19.2368	−1.44186
$179$	−6.93544	−0.518379	−0.259189	−	0.965827i	$-0.583455\pi$
$179$	−6.93544	−0.518379	−0.259189	+	0.965827i	$0.583455\pi$
$180$	−11.6425	−0.867778
$181$	−10.8175	−0.804059	−0.402029	−	0.915627i	$-0.631695\pi$
$181$	−10.8175	−0.804059	−0.402029	+	0.915627i	$0.631695\pi$
$182$	2.75535	0.204240
$183$	−14.4443	−1.06775
$184$	7.42077	0.547067
$185$	−33.5320	−2.46532
$186$	−12.2780	−0.900265
$187$	0.114623	0.00838204
$188$	−21.5359	−1.57066
$189$	1.36362	0.0991888
$190$	57.3671	4.16185
$191$	13.3118	0.963205	0.481603	−	0.876390i	$-0.340055\pi$
$191$	13.3118	0.963205	0.481603	+	0.876390i	$0.340055\pi$
$192$	12.2813	0.886328
$193$	−3.51300	−0.252871	−0.126436	−	0.991975i	$-0.540354\pi$
$193$	−3.51300	−0.252871	−0.126436	+	0.991975i	$0.540354\pi$
$194$	−34.3376	−2.46530
$195$	4.01676	0.287646
$196$	−13.8854	−0.991816
$197$	−5.48140	−0.390533	−0.195267	−	0.980750i	$-0.562557\pi$
$197$	−5.48140	−0.390533	−0.195267	+	0.980750i	$0.562557\pi$
$198$	−0.248527	−0.0176620
$199$	−12.7640	−0.904814	−0.452407	−	0.891812i	$-0.649434\pi$
$199$	−12.7640	−0.904814	−0.452407	+	0.891812i	$0.649434\pi$
$200$	−20.6415	−1.45958
$201$	−7.29253	−0.514376
$202$	−36.5849	−2.57410
$203$	9.84069	0.690681
$204$	−2.70116	−0.189119
$205$	−48.9877	−3.42145
$206$	26.3248	1.83414
$207$	−4.88123	−0.339269
$208$	−1.96269	−0.136088
$209$	0.703617	0.0486702
$210$	12.7436	0.879389
$211$	−12.0394	−0.828824	−0.414412	−	0.910089i	$-0.636013\pi$
$211$	−12.0394	−0.828824	−0.414412	+	0.910089i	$0.636013\pi$
$212$	33.5737	2.30585
$213$	4.93808	0.338351
$214$	21.0260	1.43731
$215$	−11.9399	−0.814296
$216$	1.52027	0.103441
$217$	7.72179	0.524189
$218$	2.28481	0.154747
$219$	−7.06100	−0.477138
$220$	−1.33449	−0.0899714
$221$	0.931925	0.0626881
$222$	16.8681	1.13211
$223$	5.99300	0.401321	0.200660	−	0.979661i	$-0.435691\pi$
$223$	5.99300	0.401321	0.200660	+	0.979661i	$0.435691\pi$
$224$	−10.3729	−0.693071
$225$	13.5776	0.905173
$226$	9.44291	0.628133
$227$	1.09079	0.0723981	0.0361991	−	0.999345i	$-0.488475\pi$
$227$	1.09079	0.0723981	0.0361991	+	0.999345i	$0.488475\pi$
$228$	−16.5812	−1.09812
$229$	−3.35295	−0.221569	−0.110785	−	0.993844i	$-0.535336\pi$
$229$	−3.35295	−0.221569	−0.110785	+	0.993844i	$0.535336\pi$
$230$	−45.6170	−3.00790
$231$	0.156302	0.0102839
$232$	10.9711	0.720291
$233$	6.21743	0.407317	0.203659	−	0.979042i	$-0.434717\pi$
$233$	6.21743	0.407317	0.203659	+	0.979042i	$0.434717\pi$
$234$	−2.02061	−0.132092
$235$	34.3642	2.24168
$236$	14.0040	0.911585
$237$	12.1982	0.792357
$238$	2.95662	0.191649
$239$	20.5409	1.32868	0.664341	−	0.747430i	$-0.268712\pi$
$239$	20.5409	1.32868	0.664341	+	0.747430i	$0.268712\pi$
$240$	−9.07746	−0.585948
$241$	−15.7471	−1.01436	−0.507180	−	0.861840i	$-0.669312\pi$
$241$	−15.7471	−1.01436	−0.507180	+	0.861840i	$0.669312\pi$
$242$	23.8219	1.53133
$243$	−1.00000	−0.0641500
$244$	39.0164	2.49777
$245$	22.1566	1.41553
$246$	24.6431	1.57119
$247$	5.72066	0.363997
$248$	8.60883	0.546661
$249$	7.31701	0.463697
$250$	80.1609	5.06982
$251$	−29.1549	−1.84024	−0.920121	−	0.391633i	$-0.871910\pi$
$251$	−29.1549	−1.84024	−0.920121	+	0.391633i	$0.871910\pi$
$252$	−3.68336	−0.232030
$253$	−0.559500	−0.0351755
$254$	−38.5736	−2.42032
$255$	4.31017	0.269914
$256$	−0.186947	−0.0116842
$257$	23.1484	1.44396	0.721979	−	0.691915i	$-0.243233\pi$
$257$	23.1484	1.44396	0.721979	+	0.691915i	$0.243233\pi$
$258$	6.00633	0.373938
$259$	−10.6086	−0.659186
$260$	−10.8499	−0.672882
$261$	−7.21659	−0.446696
$262$	36.9934	2.28546
$263$	−7.46636	−0.460396	−0.230198	−	0.973144i	$-0.573937\pi$
$263$	−7.46636	−0.460396	−0.230198	+	0.973144i	$0.573937\pi$
$264$	0.174257	0.0107248
$265$	−53.5728	−3.29095
$266$	18.1494	1.11281
$267$	−8.87217	−0.542968
$268$	19.6983	1.20326
$269$	−11.5724	−0.705581	−0.352791	−	0.935702i	$-0.614767\pi$
$269$	−11.5724	−0.705581	−0.352791	+	0.935702i	$0.614767\pi$
$270$	−9.34539	−0.568742
$271$	4.86324	0.295421	0.147711	−	0.989031i	$-0.452810\pi$
$271$	4.86324	0.295421	0.147711	+	0.989031i	$0.452810\pi$
$272$	−2.10606	−0.127698
$273$	1.27079	0.0769118
$274$	30.1403	1.82084
$275$	1.55630	0.0938484
$276$	13.1850	0.793643
$277$	12.5877	0.756320	0.378160	−	0.925740i	$-0.376557\pi$
$277$	12.5877	0.756320	0.378160	+	0.925740i	$0.376557\pi$
$278$	29.7594	1.78485
$279$	−5.66271	−0.339018
$280$	−8.93527	−0.533984
$281$	3.85751	0.230120	0.115060	−	0.993359i	$-0.463294\pi$
$281$	3.85751	0.230120	0.115060	+	0.993359i	$0.463294\pi$
$282$	−17.2868	−1.02941
$283$	19.5546	1.16240	0.581202	−	0.813760i	$-0.302583\pi$
$283$	19.5546	1.16240	0.581202	+	0.813760i	$0.302583\pi$
$284$	−13.3385	−0.791496
$285$	26.4582	1.56725
$286$	−0.231608	−0.0136953
$287$	−15.4984	−0.914840
$288$	7.60691	0.448242
$289$	1.00000	0.0588235
$290$	−67.4418	−3.96032
$291$	−15.8368	−0.928370
$292$	19.0729	1.11616
$293$	−30.0136	−1.75341	−0.876706	−	0.481026i	$-0.840264\pi$
$293$	−30.0136	−1.75341	−0.876706	+	0.481026i	$0.840264\pi$
$294$	−11.1458	−0.650036
$295$	−22.3459	−1.30103
$296$	−11.8273	−0.687445
$297$	−0.114623	−0.00665108
$298$	24.8646	1.44037
$299$	−4.54894	−0.263072
$300$	−36.6752	−2.11745
$301$	−3.77746	−0.217729
$302$	7.75614	0.446315
$303$	−16.8733	−0.969343
$304$	−12.9281	−0.741478
$305$	−62.2574	−3.56485
$306$	−2.16822	−0.123949
$307$	28.1322	1.60559	0.802794	−	0.596257i	$-0.203346\pi$
$307$	28.1322	1.60559	0.802794	+	0.596257i	$0.203346\pi$
$308$	−0.422196	−0.0240569
$309$	12.1412	0.690690
$310$	−52.9202	−3.00567
$311$	9.81225	0.556402	0.278201	−	0.960523i	$-0.410262\pi$
$311$	9.81225	0.556402	0.278201	+	0.960523i	$0.410262\pi$
$312$	1.41677	0.0802090
$313$	27.1723	1.53587	0.767935	−	0.640528i	$-0.221285\pi$
$313$	27.1723	1.53587	0.767935	+	0.640528i	$0.221285\pi$
$314$	2.16822	0.122359
$315$	5.87744	0.331156
$316$	−32.9492	−1.85354
$317$	−1.67557	−0.0941093	−0.0470547	−	0.998892i	$-0.514983\pi$
$317$	−1.67557	−0.0941093	−0.0470547	+	0.998892i	$0.514983\pi$
$318$	26.9496	1.51126
$319$	−0.827185	−0.0463135
$320$	52.9346	2.95913
$321$	9.69737	0.541255
$322$	−14.4320	−0.804262
$323$	6.13855	0.341558
$324$	2.70116	0.150064
$325$	12.6533	0.701879
$326$	8.04620	0.445638
$327$	1.05377	0.0582738
$328$	−17.2787	−0.954059
$329$	10.8719	0.599387
$330$	−1.07119	−0.0589672
$331$	7.75589	0.426302	0.213151	−	0.977019i	$-0.431627\pi$
$331$	7.75589	0.426302	0.213151	+	0.977019i	$0.431627\pi$
$332$	−19.7644	−1.08471
$333$	7.77973	0.426327
$334$	30.6620	1.67775
$335$	−31.4321	−1.71732
$336$	−2.87186	−0.156673
$337$	26.1123	1.42243	0.711213	−	0.702977i	$-0.248146\pi$
$337$	26.1123	1.42243	0.711213	+	0.702977i	$0.248146\pi$
$338$	26.3037	1.43074
$339$	4.35515	0.236539
$340$	−11.6425	−0.631401
$341$	−0.649075	−0.0351494
$342$	−13.3097	−0.719706
$343$	16.5551	0.893891
$344$	−4.21140	−0.227063
$345$	−21.0390	−1.13270
$346$	−42.8444	−2.30333
$347$	10.3882	0.557665	0.278833	−	0.960340i	$-0.410053\pi$
$347$	10.3882	0.557665	0.278833	+	0.960340i	$0.410053\pi$
$348$	19.4932	1.04494
$349$	−12.6661	−0.677999	−0.339000	−	0.940787i	$-0.610089\pi$
$349$	−12.6661	−0.677999	−0.339000	+	0.940787i	$0.610089\pi$
$350$	40.1438	2.14578
$351$	−0.931925	−0.0497425
$352$	0.871925	0.0464738
$353$	−20.0624	−1.06781	−0.533906	−	0.845544i	$-0.679276\pi$
$353$	−20.0624	−1.06781	−0.533906	+	0.845544i	$0.679276\pi$
$354$	11.2410	0.597453
$355$	21.2840	1.12964
$356$	23.9651	1.27015
$357$	1.36362	0.0721704
$358$	15.0375	0.794758
$359$	12.7533	0.673091	0.336546	−	0.941667i	$-0.390741\pi$
$359$	12.7533	0.673091	0.336546	+	0.941667i	$0.390741\pi$
$360$	6.55261	0.345353
$361$	18.6817	0.983250
$362$	23.4547	1.23275
$363$	10.9869	0.576661
$364$	−3.43261	−0.179918
$365$	−30.4341	−1.59299
$366$	31.3183	1.63704
$367$	−23.1275	−1.20725	−0.603624	−	0.797269i	$-0.706277\pi$
$367$	−23.1275	−1.20725	−0.603624	+	0.797269i	$0.706277\pi$
$368$	10.2802	0.535890
$369$	11.3656	0.591670
$370$	72.7046	3.77973
$371$	−16.9490	−0.879946
$372$	15.2959	0.793055
$373$	−13.0302	−0.674680	−0.337340	−	0.941383i	$-0.609527\pi$
$373$	−13.0302	−0.674680	−0.337340	+	0.941383i	$0.609527\pi$
$374$	−0.248527	−0.0128510
$375$	36.9709	1.90917
$376$	12.1208	0.625083
$377$	−6.72532	−0.346372
$378$	−2.95662	−0.152072
$379$	26.5772	1.36518	0.682589	−	0.730802i	$-0.260854\pi$
$379$	26.5772	1.36518	0.682589	+	0.730802i	$0.260854\pi$
$380$	−71.4678	−3.66622
$381$	−17.7905	−0.911434
$382$	−28.8628	−1.47675
$383$	−12.0316	−0.614785	−0.307393	−	0.951583i	$-0.599456\pi$
$383$	−12.0316	−0.614785	−0.307393	+	0.951583i	$0.599456\pi$
$384$	−11.4147	−0.582505
$385$	0.673688	0.0343343
$386$	7.61695	0.387692
$387$	2.77017	0.140816
$388$	42.7777	2.17171
$389$	−3.72378	−0.188803	−0.0944016	−	0.995534i	$-0.530094\pi$
$389$	−3.72378	−0.188803	−0.0944016	+	0.995534i	$0.530094\pi$
$390$	−8.70920	−0.441007
$391$	−4.88123	−0.246855
$392$	7.81499	0.394716
$393$	17.0617	0.860649
$394$	11.8849	0.598750
$395$	52.5762	2.64540
$396$	0.309614	0.0155587
$397$	2.15881	0.108348	0.0541739	−	0.998532i	$-0.482747\pi$
$397$	2.15881	0.108348	0.0541739	+	0.998532i	$0.482747\pi$
$398$	27.6750	1.38722
$399$	8.37065	0.419056
$400$	−28.5952	−1.42976
$401$	−19.9592	−0.996714	−0.498357	−	0.866972i	$-0.666063\pi$
$401$	−19.9592	−0.996714	−0.498357	+	0.866972i	$0.666063\pi$
$402$	15.8118	0.788620
$403$	−5.27722	−0.262877
$404$	45.5774	2.26756
$405$	−4.31017	−0.214174
$406$	−21.3367	−1.05892
$407$	0.891734	0.0442016
$408$	1.52027	0.0752644
$409$	26.8393	1.32712	0.663559	−	0.748124i	$-0.269045\pi$
$409$	26.8393	1.32712	0.663559	+	0.748124i	$0.269045\pi$
$410$	106.216	5.24563
$411$	13.9010	0.685684
$412$	−32.7954	−1.61571
$413$	−7.06963	−0.347874
$414$	10.5836	0.520154
$415$	31.5376	1.54812
$416$	7.08907	0.347570
$417$	13.7253	0.672131
$418$	−1.52559	−0.0746192
$419$	−4.58517	−0.224000	−0.112000	−	0.993708i	$-0.535726\pi$
$419$	−4.58517	−0.224000	−0.112000	+	0.993708i	$0.535726\pi$
$420$	−15.8759	−0.774665
$421$	17.4572	0.850813	0.425407	−	0.905002i	$-0.360131\pi$
$421$	17.4572	0.850813	0.425407	+	0.905002i	$0.360131\pi$
$422$	26.1040	1.27072
$423$	−7.97282	−0.387652
$424$	−18.8960	−0.917669
$425$	13.5776	0.658610
$426$	−10.7068	−0.518747
$427$	−19.6965	−0.953182
$428$	−26.1942	−1.26614
$429$	−0.106820	−0.00515731
$430$	25.8883	1.24845
$431$	20.4666	0.985841	0.492921	−	0.870074i	$-0.335929\pi$
$431$	20.4666	0.985841	0.492921	+	0.870074i	$0.335929\pi$
$432$	2.10606	0.101328
$433$	21.4035	1.02859	0.514294	−	0.857614i	$-0.328054\pi$
$433$	21.4035	1.02859	0.514294	+	0.857614i	$0.328054\pi$
$434$	−16.7425	−0.803666
$435$	−31.1048	−1.49136
$436$	−2.84641	−0.136318
$437$	−29.9637	−1.43336
$438$	15.3098	0.731529
$439$	11.6463	0.555847	0.277924	−	0.960603i	$-0.410354\pi$
$439$	11.6463	0.555847	0.277924	+	0.960603i	$0.410354\pi$
$440$	0.751078	0.0358062
$441$	−5.14054	−0.244788
$442$	−2.02061	−0.0961108
$443$	−9.18461	−0.436374	−0.218187	−	0.975907i	$-0.570014\pi$
$443$	−9.18461	−0.436374	−0.218187	+	0.975907i	$0.570014\pi$
$444$	−21.0143	−0.997294
$445$	−38.2406	−1.81278
$446$	−12.9941	−0.615289
$447$	11.4677	0.542406
$448$	16.7471	0.791224
$449$	3.77833	0.178310	0.0891551	−	0.996018i	$-0.471583\pi$
$449$	3.77833	0.178310	0.0891551	+	0.996018i	$0.471583\pi$
$450$	−29.4391	−1.38777
$451$	1.30276	0.0613444
$452$	−11.7640	−0.553330
$453$	3.57720	0.168071
$454$	−2.36506	−0.110998
$455$	5.47733	0.256781
$456$	9.33222	0.437021
$457$	−20.2882	−0.949043	−0.474521	−	0.880244i	$-0.657379\pi$
$457$	−20.2882	−0.949043	−0.474521	+	0.880244i	$0.657379\pi$
$458$	7.26992	0.339701
$459$	−1.00000	−0.0466760
$460$	56.8296	2.64969
$461$	−7.78141	−0.362417	−0.181208	−	0.983445i	$-0.558001\pi$
$461$	−7.78141	−0.362417	−0.181208	+	0.983445i	$0.558001\pi$
$462$	−0.338896	−0.0157669
$463$	12.3304	0.573040	0.286520	−	0.958074i	$-0.407501\pi$
$463$	12.3304	0.573040	0.286520	+	0.958074i	$0.407501\pi$
$464$	15.1985	0.705575
$465$	−24.4073	−1.13186
$466$	−13.4807	−0.624483
$467$	−34.3145	−1.58789	−0.793943	−	0.607992i	$-0.791975\pi$
$467$	−34.3145	−1.58789	−0.793943	+	0.607992i	$0.791975\pi$
$468$	2.51728	0.116361
$469$	−9.94424	−0.459183
$470$	−74.5091	−3.43685
$471$	1.00000	0.0460776
$472$	−7.88175	−0.362787
$473$	0.317525	0.0145998
$474$	−26.4483	−1.21481
$475$	83.3467	3.82421
$476$	−3.68336	−0.168826
$477$	12.4294	0.569102
$478$	−44.5371	−2.03708
$479$	38.2688	1.74855	0.874274	−	0.485433i	$-0.161338\pi$
$479$	38.2688	1.74855	0.874274	+	0.485433i	$0.161338\pi$
$480$	32.7871	1.49652
$481$	7.25012	0.330577
$482$	34.1431	1.55518
$483$	−6.65615	−0.302865
$484$	−29.6773	−1.34897
$485$	−68.2594	−3.09950
$486$	2.16822	0.0983523
$487$	−36.9846	−1.67593	−0.837967	−	0.545721i	$-0.816256\pi$
$487$	−36.9846	−1.67593	−0.837967	+	0.545721i	$0.816256\pi$
$488$	−21.9592	−0.994045
$489$	3.71098	0.167816
$490$	−48.0403	−2.17024
$491$	−18.1402	−0.818655	−0.409328	−	0.912387i	$-0.634237\pi$
$491$	−18.1402	−0.818655	−0.409328	+	0.912387i	$0.634237\pi$
$492$	−30.7003	−1.38408
$493$	−7.21659	−0.325019
$494$	−12.4036	−0.558066
$495$	−0.494044	−0.0222056
$496$	11.9260	0.535492
$497$	6.73366	0.302046
$498$	−15.8649	−0.710922
$499$	−8.71037	−0.389930	−0.194965	−	0.980810i	$-0.562459\pi$
$499$	−8.71037	−0.389930	−0.194965	+	0.980810i	$0.562459\pi$
$500$	−99.8643	−4.46607
$501$	14.1416	0.631799
$502$	63.2142	2.82139
$503$	−3.40185	−0.151681	−0.0758404	−	0.997120i	$-0.524164\pi$
$503$	−3.40185	−0.151681	−0.0758404	+	0.997120i	$0.524164\pi$
$504$	2.07307	0.0923417
$505$	−72.7267	−3.23629
$506$	1.21312	0.0539296
$507$	12.1315	0.538780
$508$	48.0549	2.13209
$509$	31.4767	1.39518	0.697591	−	0.716496i	$-0.254255\pi$
$509$	31.4767	1.39518	0.697591	+	0.716496i	$0.254255\pi$
$510$	−9.34539	−0.413821
$511$	−9.62852	−0.425941
$512$	−22.4241	−0.991015
$513$	−6.13855	−0.271023
$514$	−50.1907	−2.21382
$515$	52.3308	2.30597
$516$	−7.48268	−0.329406
$517$	−0.913866	−0.0401918
$518$	23.0017	1.01064
$519$	−19.7602	−0.867376
$520$	6.10654	0.267789
$521$	21.5342	0.943432	0.471716	−	0.881750i	$-0.343635\pi$
$521$	21.5342	0.943432	0.471716	+	0.881750i	$0.343635\pi$
$522$	15.6471	0.684856
$523$	19.7500	0.863608	0.431804	−	0.901968i	$-0.357877\pi$
$523$	19.7500	0.863608	0.431804	+	0.901968i	$0.357877\pi$
$524$	−46.0864	−2.01329
$525$	18.5147	0.808047
$526$	16.1887	0.705860
$527$	−5.66271	−0.246672
$528$	0.241402	0.0105057
$529$	0.826450	0.0359326
$530$	116.157	5.04555
$531$	5.18445	0.224986
$532$	−22.6104	−0.980287
$533$	10.5919	0.458786
$534$	19.2368	0.832457
$535$	41.7974	1.80706
$536$	−11.0866	−0.478868
$537$	6.93544	0.299286
$538$	25.0914	1.08177
$539$	−0.589223	−0.0253796
$540$	11.6425	0.501012
$541$	−14.1009	−0.606244	−0.303122	−	0.952952i	$-0.598029\pi$
$541$	−14.1009	−0.606244	−0.303122	+	0.952952i	$0.598029\pi$
$542$	−10.5446	−0.452928
$543$	10.8175	0.464224
$544$	7.60691	0.326144
$545$	4.54194	0.194555
$546$	−2.75535	−0.117918
$547$	−25.1485	−1.07527	−0.537636	−	0.843177i	$-0.680682\pi$
$547$	−25.1485	−1.07527	−0.537636	+	0.843177i	$0.680682\pi$
$548$	−37.5487	−1.60400
$549$	14.4443	0.616468
$550$	−3.37439	−0.143885
$551$	−44.2994	−1.88722
$552$	−7.42077	−0.315849
$553$	16.6337	0.707336
$554$	−27.2928	−1.15956
$555$	33.5320	1.42335
$556$	−37.0743	−1.57230
$557$	37.9372	1.60745	0.803725	−	0.595000i	$-0.202848\pi$
$557$	37.9372	1.60745	0.803725	+	0.595000i	$0.202848\pi$
$558$	12.2780	0.519768
$559$	2.58159	0.109190
$560$	−12.3782	−0.523075
$561$	−0.114623	−0.00483937
$562$	−8.36391	−0.352810
$563$	−8.73288	−0.368047	−0.184024	−	0.982922i	$-0.558912\pi$
$563$	−8.73288	−0.368047	−0.184024	+	0.982922i	$0.558912\pi$
$564$	21.5359	0.906823
$565$	18.7715	0.789721
$566$	−42.3987	−1.78215
$567$	−1.36362	−0.0572667
$568$	7.50719	0.314995
$569$	35.0367	1.46882	0.734408	−	0.678709i	$-0.237460\pi$
$569$	35.0367	1.46882	0.734408	+	0.678709i	$0.237460\pi$
$570$	−57.3671	−2.40284
$571$	16.3557	0.684467	0.342233	−	0.939615i	$-0.388817\pi$
$571$	16.3557	0.684467	0.342233	+	0.939615i	$0.388817\pi$
$572$	0.288537	0.0120643
$573$	−13.3118	−0.556107
$574$	33.6038	1.40260
$575$	−66.2754	−2.76388
$576$	−12.2813	−0.511722
$577$	−20.7701	−0.864670	−0.432335	−	0.901713i	$-0.642310\pi$
$577$	−20.7701	−0.864670	−0.432335	+	0.901713i	$0.642310\pi$
$578$	−2.16822	−0.0901859
$579$	3.51300	0.145995
$580$	84.0189	3.48870
$581$	9.97763	0.413942
$582$	34.3376	1.42334
$583$	1.42469	0.0590046
$584$	−10.7346	−0.444201
$585$	−4.01676	−0.166072
$586$	65.0759	2.68826
$587$	−1.75785	−0.0725544	−0.0362772	−	0.999342i	$-0.511550\pi$
$587$	−1.75785	−0.0725544	−0.0362772	+	0.999342i	$0.511550\pi$
$588$	13.8854	0.572625
$589$	−34.7608	−1.43229
$590$	48.4507	1.99468
$591$	5.48140	0.225475
$592$	−16.3845	−0.673401
$593$	−6.73374	−0.276522	−0.138261	−	0.990396i	$-0.544151\pi$
$593$	−6.73374	−0.276522	−0.138261	+	0.990396i	$0.544151\pi$
$594$	0.248527	0.0101972
$595$	5.87744	0.240952
$596$	−30.9762	−1.26884
$597$	12.7640	0.522394
$598$	9.86309	0.403332
$599$	−3.29737	−0.134727	−0.0673635	−	0.997729i	$-0.521459\pi$
$599$	−3.29737	−0.134727	−0.0673635	+	0.997729i	$0.521459\pi$
$600$	20.6415	0.842688
$601$	−39.3597	−1.60552	−0.802759	−	0.596304i	$-0.796635\pi$
$601$	−39.3597	−1.60552	−0.802759	+	0.596304i	$0.796635\pi$
$602$	8.19035	0.333814
$603$	7.29253	0.296975
$604$	−9.66258	−0.393165
$605$	47.3553	1.92527
$606$	36.5849	1.48616
$607$	17.4571	0.708563	0.354281	−	0.935139i	$-0.384725\pi$
$607$	17.4571	0.708563	0.354281	+	0.935139i	$0.384725\pi$
$608$	46.6954	1.89375
$609$	−9.84069	−0.398765
$610$	134.988	5.46548
$611$	−7.43007	−0.300588
$612$	2.70116	0.109188
$613$	−30.7059	−1.24020	−0.620101	−	0.784522i	$-0.712908\pi$
$613$	−30.7059	−1.24020	−0.620101	+	0.784522i	$0.712908\pi$
$614$	−60.9966	−2.46162
$615$	48.9877	1.97538
$616$	0.237620	0.00957400
$617$	11.8349	0.476455	0.238228	−	0.971209i	$-0.423434\pi$
$617$	11.8349	0.476455	0.238228	+	0.971209i	$0.423434\pi$
$618$	−26.3248	−1.05894
$619$	−14.6966	−0.590706	−0.295353	−	0.955388i	$-0.595437\pi$
$619$	−14.6966	−0.590706	−0.295353	+	0.955388i	$0.595437\pi$
$620$	65.9279	2.64773
$621$	4.88123	0.195877
$622$	−21.2751	−0.853053
$623$	−12.0983	−0.484707
$624$	1.96269	0.0785703
$625$	91.4630	3.65852
$626$	−58.9154	−2.35473
$627$	−0.703617	−0.0280997
$628$	−2.70116	−0.107788
$629$	7.77973	0.310198
$630$	−12.7436	−0.507715
$631$	−43.4787	−1.73086	−0.865430	−	0.501030i	$-0.832955\pi$
$631$	−43.4787	−1.73086	−0.865430	+	0.501030i	$0.832955\pi$
$632$	18.5445	0.737659
$633$	12.0394	0.478522
$634$	3.63299	0.144285
$635$	−76.6800	−3.04295
$636$	−33.5737	−1.33129
$637$	−4.79060	−0.189810
$638$	1.79352	0.0710060
$639$	−4.93808	−0.195347
$640$	−49.1994	−1.94478
$641$	14.3617	0.567253	0.283627	−	0.958935i	$-0.408462\pi$
$641$	14.3617	0.567253	0.283627	+	0.958935i	$0.408462\pi$
$642$	−21.0260	−0.829830
$643$	−28.6351	−1.12926	−0.564630	−	0.825344i	$-0.690981\pi$
$643$	−28.6351	−1.12926	−0.564630	+	0.825344i	$0.690981\pi$
$644$	17.9793	0.708485
$645$	11.9399	0.470134
$646$	−13.3097	−0.523663
$647$	44.3215	1.74246	0.871230	−	0.490875i	$-0.163323\pi$
$647$	44.3215	1.74246	0.871230	+	0.490875i	$0.163323\pi$
$648$	−1.52027	−0.0597217
$649$	0.594256	0.0233266
$650$	−27.4351	−1.07609
$651$	−7.72179	−0.302641
$652$	−10.0239	−0.392568
$653$	17.6276	0.689820	0.344910	−	0.938636i	$-0.387909\pi$
$653$	17.6276	0.689820	0.344910	+	0.938636i	$0.387909\pi$
$654$	−2.28481	−0.0893430
$655$	73.5389	2.87340
$656$	−23.9366	−0.934567
$657$	7.06100	0.275476
$658$	−23.5726	−0.918956
$659$	47.6082	1.85455	0.927277	−	0.374377i	$-0.122143\pi$
$659$	47.6082	1.85455	0.927277	+	0.374377i	$0.122143\pi$
$660$	1.33449	0.0519450
$661$	−12.7871	−0.497361	−0.248680	−	0.968586i	$-0.579997\pi$
$661$	−12.7871	−0.497361	−0.248680	+	0.968586i	$0.579997\pi$
$662$	−16.8164	−0.653590
$663$	−0.931925	−0.0361930
$664$	11.1238	0.431687
$665$	36.0789	1.39908
$666$	−16.8681	−0.653627
$667$	35.2259	1.36395
$668$	−38.1987	−1.47795
$669$	−5.99300	−0.231703
$670$	68.1515	2.63292
$671$	1.65564	0.0639154
$672$	10.3729	0.400145
$673$	41.7639	1.60988	0.804939	−	0.593357i	$-0.202198\pi$
$673$	41.7639	1.60988	0.804939	+	0.593357i	$0.202198\pi$
$674$	−56.6170	−2.18081
$675$	−13.5776	−0.522602
$676$	−32.7692	−1.26035
$677$	21.6080	0.830462	0.415231	−	0.909716i	$-0.363701\pi$
$677$	21.6080	0.830462	0.415231	+	0.909716i	$0.363701\pi$
$678$	−9.44291	−0.362653
$679$	−21.5954	−0.828755
$680$	6.55261	0.251281
$681$	−1.09079	−0.0417991
$682$	1.40734	0.0538897
$683$	7.47905	0.286178	0.143089	−	0.989710i	$-0.454296\pi$
$683$	7.47905	0.286178	0.143089	+	0.989710i	$0.454296\pi$
$684$	16.5812	0.633998
$685$	59.9156	2.28926
$686$	−35.8950	−1.37048
$687$	3.35295	0.127923
$688$	−5.83413	−0.222424
$689$	11.5832	0.441287
$690$	45.6170	1.73661
$691$	−40.8112	−1.55253	−0.776265	−	0.630406i	$-0.782888\pi$
$691$	−40.8112	−1.55253	−0.776265	+	0.630406i	$0.782888\pi$
$692$	53.3754	2.02903
$693$	−0.156302	−0.00593742
$694$	−22.5238	−0.854990
$695$	59.1585	2.24401
$696$	−10.9711	−0.415860
$697$	11.3656	0.430503
$698$	27.4628	1.03948
$699$	−6.21743	−0.235165
$700$	−50.0111	−1.89024
$701$	16.3422	0.617237	0.308619	−	0.951186i	$-0.400133\pi$
$701$	16.3422	0.617237	0.308619	+	0.951186i	$0.400133\pi$
$702$	2.02061	0.0762632
$703$	47.7562	1.80116
$704$	−1.40772	−0.0530554
$705$	−34.3642	−1.29423
$706$	43.4995	1.63713
$707$	−23.0087	−0.865332
$708$	−14.0040	−0.526304
$709$	3.37434	0.126726	0.0633630	−	0.997991i	$-0.479817\pi$
$709$	3.37434	0.126726	0.0633630	+	0.997991i	$0.479817\pi$
$710$	−46.1482	−1.73191
$711$	−12.1982	−0.457467
$712$	−13.4881	−0.505486
$713$	27.6410	1.03516
$714$	−2.95662	−0.110649
$715$	−0.460412	−0.0172184
$716$	−18.7337	−0.700112
$717$	−20.5409	−0.767114
$718$	−27.6518	−1.03196
$719$	−40.6353	−1.51544	−0.757720	−	0.652580i	$-0.773687\pi$
$719$	−40.6353	−1.51544	−0.757720	+	0.652580i	$0.773687\pi$
$720$	9.07746	0.338297
$721$	16.5560	0.616579
$722$	−40.5061	−1.50748
$723$	15.7471	0.585641
$724$	−29.2198	−1.08595
$725$	−97.9839	−3.63903
$726$	−23.8219	−0.884113
$727$	30.3830	1.12684	0.563422	−	0.826169i	$-0.309485\pi$
$727$	30.3830	1.12684	0.563422	+	0.826169i	$0.309485\pi$
$728$	1.93194	0.0716025
$729$	1.00000	0.0370370
$730$	65.9877	2.44232
$731$	2.77017	0.102458
$732$	−39.0164	−1.44209
$733$	−30.4662	−1.12529	−0.562647	−	0.826697i	$-0.690217\pi$
$733$	−30.4662	−1.12529	−0.562647	+	0.826697i	$0.690217\pi$
$734$	50.1455	1.85090
$735$	−22.1566	−0.817259
$736$	−37.1311	−1.36867
$737$	0.835890	0.0307904
$738$	−24.6431	−0.907125
$739$	−9.36228	−0.344397	−0.172199	−	0.985062i	$-0.555087\pi$
$739$	−9.36228	−0.344397	−0.172199	+	0.985062i	$0.555087\pi$
$740$	−90.5752	−3.32961
$741$	−5.72066	−0.210154
$742$	36.7490	1.34910
$743$	−15.4249	−0.565883	−0.282942	−	0.959137i	$-0.591310\pi$
$743$	−15.4249	−0.565883	−0.282942	+	0.959137i	$0.591310\pi$
$744$	−8.60883	−0.315615
$745$	49.4280	1.81090
$746$	28.2523	1.03439
$747$	−7.31701	−0.267716
$748$	0.309614	0.0113206
$749$	13.2235	0.483177
$750$	−80.1609	−2.92706
$751$	−7.67308	−0.279995	−0.139997	−	0.990152i	$-0.544709\pi$
$751$	−7.67308	−0.279995	−0.139997	+	0.990152i	$0.544709\pi$
$752$	16.7912	0.612312
$753$	29.1549	1.06246
$754$	14.5820	0.531043
$755$	15.4183	0.561131
$756$	3.68336	0.133962
$757$	−22.8009	−0.828711	−0.414356	−	0.910115i	$-0.635993\pi$
$757$	−22.8009	−0.828711	−0.414356	+	0.910115i	$0.635993\pi$
$758$	−57.6251	−2.09304
$759$	0.559500	0.0203086
$760$	40.2235	1.45906
$761$	23.4702	0.850796	0.425398	−	0.905006i	$-0.360134\pi$
$761$	23.4702	0.850796	0.425398	+	0.905006i	$0.360134\pi$
$762$	38.5736	1.39737
$763$	1.43695	0.0520209
$764$	35.9572	1.30089
$765$	−4.31017	−0.155835
$766$	26.0871	0.942564
$767$	4.83152	0.174456
$768$	0.186947	0.00674585
$769$	−54.1620	−1.95313	−0.976567	−	0.215215i	$-0.930955\pi$
$769$	−54.1620	−1.95313	−0.976567	+	0.215215i	$0.930955\pi$
$770$	−1.46070	−0.0526400
$771$	−23.1484	−0.833669
$772$	−9.48918	−0.341523
$773$	14.4316	0.519067	0.259533	−	0.965734i	$-0.416431\pi$
$773$	14.4316	0.519067	0.259533	+	0.965734i	$0.416431\pi$
$774$	−6.00633	−0.215893
$775$	−76.8860	−2.76183
$776$	−24.0762	−0.864283
$777$	10.6086	0.380581
$778$	8.07396	0.289466
$779$	69.7683	2.49971
$780$	10.8499	0.388489
$781$	−0.566016	−0.0202536
$782$	10.5836	0.378468
$783$	7.21659	0.257900
$784$	10.8263	0.386652
$785$	4.31017	0.153837
$786$	−36.9934	−1.31951
$787$	22.9611	0.818476	0.409238	−	0.912428i	$-0.365795\pi$
$787$	22.9611	0.818476	0.409238	+	0.912428i	$0.365795\pi$
$788$	−14.8061	−0.527447
$789$	7.46636	0.265810
$790$	−113.997	−4.05582
$791$	5.93877	0.211159
$792$	−0.174257	−0.00619195
$793$	13.4610	0.478014
$794$	−4.68078	−0.166115
$795$	53.5728	1.90003
$796$	−34.4775	−1.22202
$797$	26.7933	0.949068	0.474534	−	0.880237i	$-0.342617\pi$
$797$	26.7933	0.949068	0.474534	+	0.880237i	$0.342617\pi$
$798$	−18.1494	−0.642481
$799$	−7.97282	−0.282058
$800$	103.284	3.65163
$801$	8.87217	0.313483
$802$	43.2758	1.52812
$803$	0.809351	0.0285614
$804$	−19.6983	−0.694705
$805$	−28.6892	−1.01116
$806$	11.4422	0.403033
$807$	11.5724	0.407367
$808$	−25.6518	−0.902429
$809$	14.8429	0.521849	0.260924	−	0.965359i	$-0.415973\pi$
$809$	14.8429	0.521849	0.260924	+	0.965359i	$0.415973\pi$
$810$	9.34539	0.328363
$811$	27.9323	0.980835	0.490418	−	0.871487i	$-0.336844\pi$
$811$	27.9323	0.980835	0.490418	+	0.871487i	$0.336844\pi$
$812$	26.5813	0.932820
$813$	−4.86324	−0.170561
$814$	−1.93347	−0.0677681
$815$	15.9949	0.560279
$816$	2.10606	0.0737267
$817$	17.0048	0.594923
$818$	−58.1934	−2.03469
$819$	−1.27079	−0.0444051
$820$	−132.324	−4.62094
$821$	−51.4090	−1.79419	−0.897093	−	0.441841i	$-0.854325\pi$
$821$	−51.4090	−1.79419	−0.897093	+	0.441841i	$0.854325\pi$
$822$	−30.1403	−1.05126
$823$	−7.13857	−0.248835	−0.124418	−	0.992230i	$-0.539706\pi$
$823$	−7.13857	−0.248835	−0.124418	+	0.992230i	$0.539706\pi$
$824$	18.4579	0.643011
$825$	−1.55630	−0.0541834
$826$	15.3285	0.533346
$827$	26.9416	0.936850	0.468425	−	0.883503i	$-0.344822\pi$
$827$	26.9416	0.936850	0.468425	+	0.883503i	$0.344822\pi$
$828$	−13.1850	−0.458210
$829$	−5.74092	−0.199390	−0.0996951	−	0.995018i	$-0.531787\pi$
$829$	−5.74092	−0.199390	−0.0996951	+	0.995018i	$0.531787\pi$
$830$	−68.3803	−2.37352
$831$	−12.5877	−0.436662
$832$	−11.4453	−0.396793
$833$	−5.14054	−0.178109
$834$	−29.7594	−1.03048
$835$	60.9526	2.10935
$836$	1.90058	0.0657330
$837$	5.66271	0.195732
$838$	9.94163	0.343428
$839$	−49.2262	−1.69948	−0.849739	−	0.527203i	$-0.823241\pi$
$839$	−49.2262	−1.69948	−0.849739	+	0.527203i	$0.823241\pi$
$840$	8.93527	0.308296
$841$	23.0792	0.795835
$842$	−37.8510	−1.30443
$843$	−3.85751	−0.132860
$844$	−32.5203	−1.11939
$845$	52.2889	1.79879
$846$	17.2868	0.594332
$847$	14.9819	0.514784
$848$	−26.1770	−0.898921
$849$	−19.5546	−0.671114
$850$	−29.4391	−1.00975
$851$	−37.9747	−1.30176
$852$	13.3385	0.456971
$853$	24.7578	0.847690	0.423845	−	0.905735i	$-0.360680\pi$
$853$	24.7578	0.847690	0.423845	+	0.905735i	$0.360680\pi$
$854$	42.7063	1.46138
$855$	−26.4582	−0.904851
$856$	14.7426	0.503891
$857$	−24.9219	−0.851316	−0.425658	−	0.904884i	$-0.639957\pi$
$857$	−24.9219	−0.851316	−0.425658	+	0.904884i	$0.639957\pi$
$858$	0.231608	0.00790698
$859$	−4.11256	−0.140319	−0.0701594	−	0.997536i	$-0.522351\pi$
$859$	−4.11256	−0.140319	−0.0701594	+	0.997536i	$0.522351\pi$
$860$	−32.2516	−1.09977
$861$	15.4984	0.528183
$862$	−44.3760	−1.51145
$863$	14.6865	0.499934	0.249967	−	0.968254i	$-0.419580\pi$
$863$	14.6865	0.499934	0.249967	+	0.968254i	$0.419580\pi$
$864$	−7.60691	−0.258792
$865$	−85.1699	−2.89586
$866$	−46.4075	−1.57699
$867$	−1.00000	−0.0339618
$868$	20.8578	0.707959
$869$	−1.39819	−0.0474303
$870$	67.4418	2.28649
$871$	6.79609	0.230277
$872$	1.60201	0.0542511
$873$	15.8368	0.535995
$874$	64.9677	2.19757
$875$	50.4143	1.70431
$876$	−19.0729	−0.644413
$877$	31.6026	1.06714	0.533571	−	0.845755i	$-0.320850\pi$
$877$	31.6026	1.06714	0.533571	+	0.845755i	$0.320850\pi$
$878$	−25.2517	−0.852203
$879$	30.0136	1.01233
$880$	1.04048	0.0350747
$881$	−51.6522	−1.74021	−0.870103	−	0.492870i	$-0.835948\pi$
$881$	−51.6522	−1.74021	−0.870103	+	0.492870i	$0.835948\pi$
$882$	11.1458	0.375299
$883$	33.7952	1.13730	0.568650	−	0.822580i	$-0.307466\pi$
$883$	33.7952	1.13730	0.568650	+	0.822580i	$0.307466\pi$
$884$	2.51728	0.0846652
$885$	22.3459	0.751149
$886$	19.9142	0.669031
$887$	1.25186	0.0420333	0.0210166	−	0.999779i	$-0.493310\pi$
$887$	1.25186	0.0420333	0.0210166	+	0.999779i	$0.493310\pi$
$888$	11.8273	0.396897
$889$	−24.2595	−0.813636
$890$	82.9138	2.77928
$891$	0.114623	0.00384000
$892$	16.1880	0.542016
$893$	−48.9415	−1.63777
$894$	−24.8646	−0.831595
$895$	29.8929	0.999210
$896$	−15.5653	−0.520002
$897$	4.54894	0.151885
$898$	−8.19223	−0.273378
$899$	40.8655	1.36294
$900$	36.6752	1.22251
$901$	12.4294	0.414083
$902$	−2.82466	−0.0940508
$903$	3.77746	0.125706
$904$	6.62099	0.220211
$905$	46.6253	1.54988
$906$	−7.75614	−0.257680
$907$	42.7089	1.41812	0.709062	−	0.705146i	$-0.249118\pi$
$907$	42.7089	1.41812	0.709062	+	0.705146i	$0.249118\pi$
$908$	2.94639	0.0977794
$909$	16.8733	0.559651
$910$	−11.8760	−0.393687
$911$	−53.6336	−1.77696	−0.888480	−	0.458916i	$-0.848238\pi$
$911$	−53.6336	−1.77696	−0.888480	+	0.458916i	$0.848238\pi$
$912$	12.9281	0.428093
$913$	−0.838696	−0.0277568
$914$	43.9892	1.45503
$915$	62.2574	2.05817
$916$	−9.05685	−0.299247
$917$	23.2657	0.768300
$918$	2.16822	0.0715618
$919$	−53.2090	−1.75520	−0.877602	−	0.479390i	$-0.840858\pi$
$919$	−53.2090	−1.75520	−0.877602	+	0.479390i	$0.840858\pi$
$920$	−31.9848	−1.05451
$921$	−28.1322	−0.926986
$922$	16.8718	0.555643
$923$	−4.60192	−0.151474
$924$	0.422196	0.0138892
$925$	105.630	3.47309
$926$	−26.7349	−0.878562
$927$	−12.1412	−0.398770
$928$	−54.8960	−1.80205
$929$	41.8503	1.37307	0.686533	−	0.727099i	$-0.259132\pi$
$929$	41.8503	1.37307	0.686533	+	0.727099i	$0.259132\pi$
$930$	52.9202	1.73532
$931$	−31.5554	−1.03419
$932$	16.7943	0.550115
$933$	−9.81225	−0.321239
$934$	74.4013	2.43448
$935$	−0.494044	−0.0161570
$936$	−1.41677	−0.0463087
$937$	12.7481	0.416464	0.208232	−	0.978080i	$-0.433229\pi$
$937$	12.7481	0.416464	0.208232	+	0.978080i	$0.433229\pi$
$938$	21.5613	0.704000
$939$	−27.1723	−0.886735
$940$	92.8233	3.02756
$941$	−9.99812	−0.325930	−0.162965	−	0.986632i	$-0.552106\pi$
$941$	−9.99812	−0.325930	−0.162965	+	0.986632i	$0.552106\pi$
$942$	−2.16822	−0.0706443
$943$	−55.4782	−1.80662
$944$	−10.9187	−0.355375
$945$	−5.87744	−0.191193
$946$	−0.688462	−0.0223838
$947$	34.4391	1.11912	0.559561	−	0.828789i	$-0.310970\pi$
$947$	34.4391	1.11912	0.559561	+	0.828789i	$0.310970\pi$
$948$	32.9492	1.07014
$949$	6.58032	0.213606
$950$	−180.714	−5.86312
$951$	1.67557	0.0543340
$952$	2.07307	0.0671884
$953$	26.0267	0.843088	0.421544	−	0.906808i	$-0.361488\pi$
$953$	26.0267	0.843088	0.421544	+	0.906808i	$0.361488\pi$
$954$	−26.9496	−0.872525
$955$	−57.3760	−1.85664
$956$	55.4843	1.79449
$957$	0.827185	0.0267391
$958$	−82.9751	−2.68080
$959$	18.9556	0.612110
$960$	−52.9346	−1.70846
$961$	1.06630	0.0343967
$962$	−15.7198	−0.506828
$963$	−9.69737	−0.312493
$964$	−42.5355	−1.36997
$965$	15.1416	0.487427
$966$	14.4320	0.464341
$967$	54.6788	1.75835	0.879175	−	0.476498i	$-0.158094\pi$
$967$	54.6788	1.75835	0.879175	+	0.476498i	$0.158094\pi$
$968$	16.7029	0.536853
$969$	−6.13855	−0.197199
$970$	148.001	4.75203
$971$	11.0593	0.354910	0.177455	−	0.984129i	$-0.443214\pi$
$971$	11.0593	0.354910	0.177455	+	0.984129i	$0.443214\pi$
$972$	−2.70116	−0.0866397
$973$	18.7161	0.600011
$974$	80.1907	2.56948
$975$	−12.6533	−0.405230
$976$	−30.4205	−0.973736
$977$	27.3457	0.874868	0.437434	−	0.899251i	$-0.355887\pi$
$977$	27.3457	0.874868	0.437434	+	0.899251i	$0.355887\pi$
$978$	−8.04620	−0.257289
$979$	1.01695	0.0325019
$980$	59.8486	1.91179
$981$	−1.05377	−0.0336444
$982$	39.3318	1.25513
$983$	−41.7507	−1.33164	−0.665820	−	0.746112i	$-0.731918\pi$
$983$	−41.7507	−1.33164	−0.665820	+	0.746112i	$0.731918\pi$
$984$	17.2787	0.550826
$985$	23.6258	0.752780
$986$	15.6471	0.498306
$987$	−10.8719	−0.346056
$988$	15.4524	0.491607
$989$	−13.5219	−0.429970
$990$	1.07119	0.0340448
$991$	−11.4470	−0.363627	−0.181814	−	0.983333i	$-0.558197\pi$
$991$	−11.4470	−0.363627	−0.181814	+	0.983333i	$0.558197\pi$
$992$	−43.0758	−1.36766
$993$	−7.75589	−0.246126
$994$	−14.6000	−0.463085
$995$	55.0149	1.74409
$996$	19.7644	0.626260
$997$	−28.7757	−0.911337	−0.455668	−	0.890150i	$-0.650600\pi$
$997$	−28.7757	−0.911337	−0.455668	+	0.890150i	$0.650600\pi$
$998$	18.8860	0.597825
$999$	−7.77973	−0.246140

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.j.1.10	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.j.1.10	✓	64	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-2.16822 q^{2} -1.00000 q^{3} +2.70116 q^{4} -4.31017 q^{5} +2.16822 q^{6} -1.36362 q^{7} -1.52027 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.16822 q^{2} -1.00000 q^{3} +2.70116 q^{4} -4.31017 q^{5} +2.16822 q^{6} -1.36362 q^{7} -1.52027 q^{8} +1.00000 q^{9} +9.34539 q^{10} +0.114623 q^{11} -2.70116 q^{12} +0.931925 q^{13} +2.95662 q^{14} +4.31017 q^{15} -2.10606 q^{16} +1.00000 q^{17} -2.16822 q^{18} +6.13855 q^{19} -11.6425 q^{20} +1.36362 q^{21} -0.248527 q^{22} -4.88123 q^{23} +1.52027 q^{24} +13.5776 q^{25} -2.02061 q^{26} -1.00000 q^{27} -3.68336 q^{28} -7.21659 q^{29} -9.34539 q^{30} -5.66271 q^{31} +7.60691 q^{32} -0.114623 q^{33} -2.16822 q^{34} +5.87744 q^{35} +2.70116 q^{36} +7.77973 q^{37} -13.3097 q^{38} -0.931925 q^{39} +6.55261 q^{40} +11.3656 q^{41} -2.95662 q^{42} +2.77017 q^{43} +0.309614 q^{44} -4.31017 q^{45} +10.5836 q^{46} -7.97282 q^{47} +2.10606 q^{48} -5.14054 q^{49} -29.4391 q^{50} -1.00000 q^{51} +2.51728 q^{52} +12.4294 q^{53} +2.16822 q^{54} -0.494044 q^{55} +2.07307 q^{56} -6.13855 q^{57} +15.6471 q^{58} +5.18445 q^{59} +11.6425 q^{60} +14.4443 q^{61} +12.2780 q^{62} -1.36362 q^{63} -12.2813 q^{64} -4.01676 q^{65} +0.248527 q^{66} +7.29253 q^{67} +2.70116 q^{68} +4.88123 q^{69} -12.7436 q^{70} -4.93808 q^{71} -1.52027 q^{72} +7.06100 q^{73} -16.8681 q^{74} -13.5776 q^{75} +16.5812 q^{76} -0.156302 q^{77} +2.02061 q^{78} -12.1982 q^{79} +9.07746 q^{80} +1.00000 q^{81} -24.6431 q^{82} -7.31701 q^{83} +3.68336 q^{84} -4.31017 q^{85} -6.00633 q^{86} +7.21659 q^{87} -0.174257 q^{88} +8.87217 q^{89} +9.34539 q^{90} -1.27079 q^{91} -13.1850 q^{92} +5.66271 q^{93} +17.2868 q^{94} -26.4582 q^{95} -7.60691 q^{96} +15.8368 q^{97} +11.1458 q^{98} +0.114623 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9}+O(q^{10}) \) 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9} + 12 q^{10} - 7 q^{11} - 77 q^{12} + 24 q^{13} - 14 q^{14} + 3 q^{15} + 103 q^{16} + 64 q^{17} + 5 q^{18} + 26 q^{19} - 24 q^{20} - 5 q^{21} + 25 q^{22} + 20 q^{23} - 18 q^{24} + 141 q^{25} + 9 q^{26} - 64 q^{27} + 14 q^{28} + 5 q^{29} - 12 q^{30} + 11 q^{31} + 31 q^{32} + 7 q^{33} + 5 q^{34} - 3 q^{35} + 77 q^{36} + 50 q^{37} + 8 q^{38} - 24 q^{39} + 28 q^{40} - 9 q^{41} + 14 q^{42} + 59 q^{43} - 6 q^{44} - 3 q^{45} + 11 q^{47} - 103 q^{48} + 163 q^{49} + 20 q^{50} - 64 q^{51} + 65 q^{52} + 39 q^{53} - 5 q^{54} + 35 q^{55} - 34 q^{56} - 26 q^{57} - 27 q^{58} - 65 q^{59} + 24 q^{60} + 15 q^{61} + 18 q^{62} + 5 q^{63} + 152 q^{64} + 49 q^{65} - 25 q^{66} + 56 q^{67} + 77 q^{68} - 20 q^{69} + 28 q^{70} - 18 q^{71} + 18 q^{72} + 37 q^{73} - 76 q^{74} - 141 q^{75} + 30 q^{76} + 80 q^{77} - 9 q^{78} + 20 q^{79} - 144 q^{80} + 64 q^{81} + 27 q^{82} + 3 q^{83} - 14 q^{84} - 3 q^{85} + 12 q^{86} - 5 q^{87} + 108 q^{88} + 42 q^{89} + 12 q^{90} + 25 q^{91} + 18 q^{92} - 11 q^{93} + 60 q^{94} + 42 q^{95} - 31 q^{96} + 72 q^{97} + 18 q^{98} - 7 q^{99}+O(q^{100}) \) 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9 + 12 * q^10 - 7 * q^11 - 77 * q^12 + 24 * q^13 - 14 * q^14 + 3 * q^15 + 103 * q^16 + 64 * q^17 + 5 * q^18 + 26 * q^19 - 24 * q^20 - 5 * q^21 + 25 * q^22 + 20 * q^23 - 18 * q^24 + 141 * q^25 + 9 * q^26 - 64 * q^27 + 14 * q^28 + 5 * q^29 - 12 * q^30 + 11 * q^31 + 31 * q^32 + 7 * q^33 + 5 * q^34 - 3 * q^35 + 77 * q^36 + 50 * q^37 + 8 * q^38 - 24 * q^39 + 28 * q^40 - 9 * q^41 + 14 * q^42 + 59 * q^43 - 6 * q^44 - 3 * q^45 + 11 * q^47 - 103 * q^48 + 163 * q^49 + 20 * q^50 - 64 * q^51 + 65 * q^52 + 39 * q^53 - 5 * q^54 + 35 * q^55 - 34 * q^56 - 26 * q^57 - 27 * q^58 - 65 * q^59 + 24 * q^60 + 15 * q^61 + 18 * q^62 + 5 * q^63 + 152 * q^64 + 49 * q^65 - 25 * q^66 + 56 * q^67 + 77 * q^68 - 20 * q^69 + 28 * q^70 - 18 * q^71 + 18 * q^72 + 37 * q^73 - 76 * q^74 - 141 * q^75 + 30 * q^76 + 80 * q^77 - 9 * q^78 + 20 * q^79 - 144 * q^80 + 64 * q^81 + 27 * q^82 + 3 * q^83 - 14 * q^84 - 3 * q^85 + 12 * q^86 - 5 * q^87 + 108 * q^88 + 42 * q^89 + 12 * q^90 + 25 * q^91 + 18 * q^92 - 11 * q^93 + 60 * q^94 + 42 * q^95 - 31 * q^96 + 72 * q^97 + 18 * q^98 - 7 * q^99

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