LMFDB - Embedded newform 8018.2.a.h.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8018,2,Mod(1,8018)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8018, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("8018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8018 = 2 \cdot 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8018.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:	$64.0240523407$
Analytic rank:	$0$
Dimension:	$41$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	8018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +0.237080 q^{3} +1.00000 q^{4} +0.796437 q^{5} -0.237080 q^{6} +2.80350 q^{7} -1.00000 q^{8} -2.94379 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.237080 q^{3} +1.00000 q^{4} +0.796437 q^{5} -0.237080 q^{6} +2.80350 q^{7} -1.00000 q^{8} -2.94379 q^{9} -0.796437 q^{10} +4.74002 q^{11} +0.237080 q^{12} -2.18494 q^{13} -2.80350 q^{14} +0.188819 q^{15} +1.00000 q^{16} +6.02982 q^{17} +2.94379 q^{18} -1.00000 q^{19} +0.796437 q^{20} +0.664653 q^{21} -4.74002 q^{22} -6.41578 q^{23} -0.237080 q^{24} -4.36569 q^{25} +2.18494 q^{26} -1.40915 q^{27} +2.80350 q^{28} +3.23999 q^{29} -0.188819 q^{30} +0.792931 q^{31} -1.00000 q^{32} +1.12376 q^{33} -6.02982 q^{34} +2.23281 q^{35} -2.94379 q^{36} +11.7320 q^{37} +1.00000 q^{38} -0.518006 q^{39} -0.796437 q^{40} -3.14607 q^{41} -0.664653 q^{42} +1.10829 q^{43} +4.74002 q^{44} -2.34454 q^{45} +6.41578 q^{46} +4.60234 q^{47} +0.237080 q^{48} +0.859599 q^{49} +4.36569 q^{50} +1.42955 q^{51} -2.18494 q^{52} -4.63474 q^{53} +1.40915 q^{54} +3.77512 q^{55} -2.80350 q^{56} -0.237080 q^{57} -3.23999 q^{58} +8.43747 q^{59} +0.188819 q^{60} -11.8128 q^{61} -0.792931 q^{62} -8.25292 q^{63} +1.00000 q^{64} -1.74017 q^{65} -1.12376 q^{66} +12.0282 q^{67} +6.02982 q^{68} -1.52105 q^{69} -2.23281 q^{70} -1.83288 q^{71} +2.94379 q^{72} +0.274289 q^{73} -11.7320 q^{74} -1.03502 q^{75} -1.00000 q^{76} +13.2886 q^{77} +0.518006 q^{78} +10.6669 q^{79} +0.796437 q^{80} +8.49730 q^{81} +3.14607 q^{82} -13.3575 q^{83} +0.664653 q^{84} +4.80237 q^{85} -1.10829 q^{86} +0.768135 q^{87} -4.74002 q^{88} +9.60551 q^{89} +2.34454 q^{90} -6.12549 q^{91} -6.41578 q^{92} +0.187988 q^{93} -4.60234 q^{94} -0.796437 q^{95} -0.237080 q^{96} -2.53730 q^{97} -0.859599 q^{98} -13.9536 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 41 q - 41 q^{2} + 8 q^{3} + 41 q^{4} - 9 q^{5} - 8 q^{6} + 7 q^{7} - 41 q^{8} + 43 q^{9}+O(q^{10}) $ 41 * q - 41 * q^2 + 8 * q^3 + 41 * q^4 - 9 * q^5 - 8 * q^6 + 7 * q^7 - 41 * q^8 + 43 * q^9	\( 41 q - 41 q^{2} + 8 q^{3} + 41 q^{4} - 9 q^{5} - 8 q^{6} + 7 q^{7} - 41 q^{8} + 43 q^{9} + 9 q^{10} - 9 q^{11} + 8 q^{12} + 13 q^{13} - 7 q^{14} + 26 q^{15} + 41 q^{16} - 16 q^{17} - 43 q^{18} - 41 q^{19} - 9 q^{20} + 2 q^{21} + 9 q^{22} + 10 q^{23} - 8 q^{24} + 60 q^{25} - 13 q^{26} + 47 q^{27} + 7 q^{28} - 14 q^{29} - 26 q^{30} + 49 q^{31} - 41 q^{32} + 12 q^{33} + 16 q^{34} - 8 q^{35} + 43 q^{36} + 54 q^{37} + 41 q^{38} + 16 q^{39} + 9 q^{40} - 18 q^{41} - 2 q^{42} + 29 q^{43} - 9 q^{44} - 13 q^{45} - 10 q^{46} - 8 q^{47} + 8 q^{48} + 44 q^{49} - 60 q^{50} - 16 q^{51} + 13 q^{52} + 7 q^{53} - 47 q^{54} + 19 q^{55} - 7 q^{56} - 8 q^{57} + 14 q^{58} - 5 q^{59} + 26 q^{60} - 6 q^{61} - 49 q^{62} + 24 q^{63} + 41 q^{64} - 26 q^{65} - 12 q^{66} + 66 q^{67} - 16 q^{68} + 12 q^{69} + 8 q^{70} + 27 q^{71} - 43 q^{72} - q^{73} - 54 q^{74} + 62 q^{75} - 41 q^{76} - 8 q^{77} - 16 q^{78} + 87 q^{79} - 9 q^{80} + 73 q^{81} + 18 q^{82} - 41 q^{83} + 2 q^{84} + 14 q^{85} - 29 q^{86} + 35 q^{87} + 9 q^{88} - 4 q^{89} + 13 q^{90} + 39 q^{91} + 10 q^{92} + 17 q^{93} + 8 q^{94} + 9 q^{95} - 8 q^{96} + 64 q^{97} - 44 q^{98} + 40 q^{99}+O(q^{100}) \) 41 * q - 41 * q^2 + 8 * q^3 + 41 * q^4 - 9 * q^5 - 8 * q^6 + 7 * q^7 - 41 * q^8 + 43 * q^9 + 9 * q^10 - 9 * q^11 + 8 * q^12 + 13 * q^13 - 7 * q^14 + 26 * q^15 + 41 * q^16 - 16 * q^17 - 43 * q^18 - 41 * q^19 - 9 * q^20 + 2 * q^21 + 9 * q^22 + 10 * q^23 - 8 * q^24 + 60 * q^25 - 13 * q^26 + 47 * q^27 + 7 * q^28 - 14 * q^29 - 26 * q^30 + 49 * q^31 - 41 * q^32 + 12 * q^33 + 16 * q^34 - 8 * q^35 + 43 * q^36 + 54 * q^37 + 41 * q^38 + 16 * q^39 + 9 * q^40 - 18 * q^41 - 2 * q^42 + 29 * q^43 - 9 * q^44 - 13 * q^45 - 10 * q^46 - 8 * q^47 + 8 * q^48 + 44 * q^49 - 60 * q^50 - 16 * q^51 + 13 * q^52 + 7 * q^53 - 47 * q^54 + 19 * q^55 - 7 * q^56 - 8 * q^57 + 14 * q^58 - 5 * q^59 + 26 * q^60 - 6 * q^61 - 49 * q^62 + 24 * q^63 + 41 * q^64 - 26 * q^65 - 12 * q^66 + 66 * q^67 - 16 * q^68 + 12 * q^69 + 8 * q^70 + 27 * q^71 - 43 * q^72 - q^73 - 54 * q^74 + 62 * q^75 - 41 * q^76 - 8 * q^77 - 16 * q^78 + 87 * q^79 - 9 * q^80 + 73 * q^81 + 18 * q^82 - 41 * q^83 + 2 * q^84 + 14 * q^85 - 29 * q^86 + 35 * q^87 + 9 * q^88 - 4 * q^89 + 13 * q^90 + 39 * q^91 + 10 * q^92 + 17 * q^93 + 8 * q^94 + 9 * q^95 - 8 * q^96 + 64 * q^97 - 44 * q^98 + 40 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	0.237080	0.136878	0.0684390	−	0.997655i	$-0.478198\pi$
$3$	0.237080	0.136878	0.0684390	+	0.997655i	$0.478198\pi$
$4$	1.00000	0.500000
$5$	0.796437	0.356177	0.178089	−	0.984014i	$-0.443009\pi$
$5$	0.796437	0.356177	0.178089	+	0.984014i	$0.443009\pi$
$6$	−0.237080	−0.0967874
$7$	2.80350	1.05962	0.529811	−	0.848116i	$-0.322263\pi$
$7$	2.80350	1.05962	0.529811	+	0.848116i	$0.322263\pi$
$8$	−1.00000	−0.353553
$9$	−2.94379	−0.981264
$10$	−0.796437	−0.251855
$11$	4.74002	1.42917	0.714584	−	0.699549i	$-0.246616\pi$
$11$	4.74002	1.42917	0.714584	+	0.699549i	$0.246616\pi$
$12$	0.237080	0.0684390
$13$	−2.18494	−0.605995	−0.302997	−	0.952991i	$-0.597987\pi$
$13$	−2.18494	−0.605995	−0.302997	+	0.952991i	$0.597987\pi$
$14$	−2.80350	−0.749266
$15$	0.188819	0.0487529
$16$	1.00000	0.250000
$17$	6.02982	1.46245	0.731223	−	0.682138i	$-0.238950\pi$
$17$	6.02982	1.46245	0.731223	+	0.682138i	$0.238950\pi$
$18$	2.94379	0.693859
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	0.796437	0.178089
$21$	0.664653	0.145039
$22$	−4.74002	−1.01057
$23$	−6.41578	−1.33778	−0.668891	−	0.743360i	$-0.733231\pi$
$23$	−6.41578	−1.33778	−0.668891	+	0.743360i	$0.733231\pi$
$24$	−0.237080	−0.0483937
$25$	−4.36569	−0.873138
$26$	2.18494	0.428503
$27$	−1.40915	−0.271192
$28$	2.80350	0.529811
$29$	3.23999	0.601650	0.300825	−	0.953679i	$-0.402738\pi$
$29$	3.23999	0.601650	0.300825	+	0.953679i	$0.402738\pi$
$30$	−0.188819	−0.0344735
$31$	0.792931	0.142415	0.0712073	−	0.997462i	$-0.477315\pi$
$31$	0.792931	0.142415	0.0712073	+	0.997462i	$0.477315\pi$
$32$	−1.00000	−0.176777
$33$	1.12376	0.195622
$34$	−6.02982	−1.03411
$35$	2.23281	0.377413
$36$	−2.94379	−0.490632
$37$	11.7320	1.92872	0.964361	−	0.264589i	$-0.0852362\pi$
$37$	11.7320	1.92872	0.964361	+	0.264589i	$0.0852362\pi$
$38$	1.00000	0.162221
$39$	−0.518006	−0.0829474
$40$	−0.796437	−0.125928
$41$	−3.14607	−0.491333	−0.245667	−	0.969354i	$-0.579007\pi$
$41$	−3.14607	−0.491333	−0.245667	+	0.969354i	$0.579007\pi$
$42$	−0.664653	−0.102558
$43$	1.10829	0.169012	0.0845061	−	0.996423i	$-0.473069\pi$
$43$	1.10829	0.169012	0.0845061	+	0.996423i	$0.473069\pi$
$44$	4.74002	0.714584
$45$	−2.34454	−0.349504
$46$	6.41578	0.945955
$47$	4.60234	0.671321	0.335660	−	0.941983i	$-0.391041\pi$
$47$	4.60234	0.671321	0.335660	+	0.941983i	$0.391041\pi$
$48$	0.237080	0.0342195
$49$	0.859599	0.122800
$50$	4.36569	0.617402
$51$	1.42955	0.200177
$52$	−2.18494	−0.302997
$53$	−4.63474	−0.636630	−0.318315	−	0.947985i	$-0.603117\pi$
$53$	−4.63474	−0.636630	−0.318315	+	0.947985i	$0.603117\pi$
$54$	1.40915	0.191761
$55$	3.77512	0.509037
$56$	−2.80350	−0.374633
$57$	−0.237080	−0.0314020
$58$	−3.23999	−0.425431
$59$	8.43747	1.09847	0.549233	−	0.835669i	$-0.314920\pi$
$59$	8.43747	1.09847	0.549233	+	0.835669i	$0.314920\pi$
$60$	0.188819	0.0243764
$61$	−11.8128	−1.51248	−0.756240	−	0.654294i	$-0.772966\pi$
$61$	−11.8128	−1.51248	−0.756240	+	0.654294i	$0.772966\pi$
$62$	−0.792931	−0.100702
$63$	−8.25292	−1.03977
$64$	1.00000	0.125000
$65$	−1.74017	−0.215841
$66$	−1.12376	−0.138326
$67$	12.0282	1.46947	0.734737	−	0.678352i	$-0.237305\pi$
$67$	12.0282	1.46947	0.734737	+	0.678352i	$0.237305\pi$
$68$	6.02982	0.731223
$69$	−1.52105	−0.183113
$70$	−2.23281	−0.266872
$71$	−1.83288	−0.217523	−0.108762	−	0.994068i	$-0.534688\pi$
$71$	−1.83288	−0.217523	−0.108762	+	0.994068i	$0.534688\pi$
$72$	2.94379	0.346929
$73$	0.274289	0.0321031	0.0160516	−	0.999871i	$-0.494890\pi$
$73$	0.274289	0.0321031	0.0160516	+	0.999871i	$0.494890\pi$
$74$	−11.7320	−1.36381
$75$	−1.03502	−0.119513
$76$	−1.00000	−0.114708
$77$	13.2886	1.51438
$78$	0.518006	0.0586527
$79$	10.6669	1.20012	0.600058	−	0.799957i	$-0.295144\pi$
$79$	10.6669	1.20012	0.600058	+	0.799957i	$0.295144\pi$
$80$	0.796437	0.0890443
$81$	8.49730	0.944144
$82$	3.14607	0.347425
$83$	−13.3575	−1.46618	−0.733090	−	0.680132i	$-0.761923\pi$
$83$	−13.3575	−1.46618	−0.733090	+	0.680132i	$0.761923\pi$
$84$	0.664653	0.0725195
$85$	4.80237	0.520890
$86$	−1.10829	−0.119510
$87$	0.768135	0.0823527
$88$	−4.74002	−0.505287
$89$	9.60551	1.01818	0.509091	−	0.860713i	$-0.329982\pi$
$89$	9.60551	1.01818	0.509091	+	0.860713i	$0.329982\pi$
$90$	2.34454	0.247137
$91$	−6.12549	−0.642126
$92$	−6.41578	−0.668891
$93$	0.187988	0.0194935
$94$	−4.60234	−0.474695
$95$	−0.796437	−0.0817127
$96$	−0.237080	−0.0241969
$97$	−2.53730	−0.257623	−0.128812	−	0.991669i	$-0.541116\pi$
$97$	−2.53730	−0.257623	−0.128812	+	0.991669i	$0.541116\pi$
$98$	−0.859599	−0.0868326
$99$	−13.9536	−1.40239
$100$	−4.36569	−0.436569
$101$	15.5527	1.54755	0.773777	−	0.633458i	$-0.218365\pi$
$101$	15.5527	1.54755	0.773777	+	0.633458i	$0.218365\pi$
$102$	−1.42955	−0.141546
$103$	16.7261	1.64807	0.824037	−	0.566535i	$-0.191717\pi$
$103$	16.7261	1.64807	0.824037	+	0.566535i	$0.191717\pi$
$104$	2.18494	0.214251
$105$	0.529354	0.0516596
$106$	4.63474	0.450165
$107$	6.68154	0.645929	0.322964	−	0.946411i	$-0.395321\pi$
$107$	6.68154	0.645929	0.322964	+	0.946411i	$0.395321\pi$
$108$	−1.40915	−0.135596
$109$	3.41840	0.327424	0.163712	−	0.986508i	$-0.447653\pi$
$109$	3.41840	0.327424	0.163712	+	0.986508i	$0.447653\pi$
$110$	−3.77512	−0.359944
$111$	2.78141	0.264000
$112$	2.80350	0.264906
$113$	2.58372	0.243056	0.121528	−	0.992588i	$-0.461221\pi$
$113$	2.58372	0.243056	0.121528	+	0.992588i	$0.461221\pi$
$114$	0.237080	0.0222046
$115$	−5.10976	−0.476488
$116$	3.23999	0.300825
$117$	6.43203	0.594641
$118$	−8.43747	−0.776732
$119$	16.9046	1.54964
$120$	−0.188819	−0.0172367
$121$	11.4678	1.04252
$122$	11.8128	1.06948
$123$	−0.745869	−0.0672527
$124$	0.792931	0.0712073
$125$	−7.45918	−0.667169
$126$	8.25292	0.735228
$127$	−17.6380	−1.56512	−0.782561	−	0.622574i	$-0.786087\pi$
$127$	−17.6380	−1.56512	−0.782561	+	0.622574i	$0.786087\pi$
$128$	−1.00000	−0.0883883
$129$	0.262753	0.0231341
$130$	1.74017	0.152623
$131$	4.98659	0.435681	0.217840	−	0.975984i	$-0.430099\pi$
$131$	4.98659	0.435681	0.217840	+	0.975984i	$0.430099\pi$
$132$	1.12376	0.0978109
$133$	−2.80350	−0.243094
$134$	−12.0282	−1.03908
$135$	−1.12230	−0.0965923
$136$	−6.02982	−0.517053
$137$	−1.37086	−0.117120	−0.0585602	−	0.998284i	$-0.518651\pi$
$137$	−1.37086	−0.117120	−0.0585602	+	0.998284i	$0.518651\pi$
$138$	1.52105	0.129481
$139$	11.0267	0.935275	0.467638	−	0.883920i	$-0.345105\pi$
$139$	11.0267	0.935275	0.467638	+	0.883920i	$0.345105\pi$
$140$	2.23281	0.188707
$141$	1.09112	0.0918891
$142$	1.83288	0.153812
$143$	−10.3567	−0.866069
$144$	−2.94379	−0.245316
$145$	2.58044	0.214294
$146$	−0.274289	−0.0227003
$147$	0.203794	0.0168086
$148$	11.7320	0.964361
$149$	13.7411	1.12571	0.562857	−	0.826554i	$-0.309702\pi$
$149$	13.7411	1.12571	0.562857	+	0.826554i	$0.309702\pi$
$150$	1.03502	0.0845088
$151$	−24.2927	−1.97691	−0.988456	−	0.151508i	$-0.951587\pi$
$151$	−24.2927	−1.97691	−0.988456	+	0.151508i	$0.951587\pi$
$152$	1.00000	0.0811107
$153$	−17.7505	−1.43505
$154$	−13.2886	−1.07083
$155$	0.631520	0.0507249
$156$	−0.518006	−0.0414737
$157$	12.5534	1.00187	0.500934	−	0.865486i	$-0.332990\pi$
$157$	12.5534	1.00187	0.500934	+	0.865486i	$0.332990\pi$
$158$	−10.6669	−0.848610
$159$	−1.09880	−0.0871407
$160$	−0.796437	−0.0629638
$161$	−17.9866	−1.41754
$162$	−8.49730	−0.667611
$163$	−4.58633	−0.359229	−0.179615	−	0.983737i	$-0.557485\pi$
$163$	−4.58633	−0.359229	−0.179615	+	0.983737i	$0.557485\pi$
$164$	−3.14607	−0.245667
$165$	0.895005	0.0696761
$166$	13.3575	1.03675
$167$	−12.2850	−0.950645	−0.475323	−	0.879812i	$-0.657669\pi$
$167$	−12.2850	−0.950645	−0.475323	+	0.879812i	$0.657669\pi$
$168$	−0.664653	−0.0512791
$169$	−8.22602	−0.632771
$170$	−4.80237	−0.368325
$171$	2.94379	0.225117
$172$	1.10829	0.0845061
$173$	−5.04705	−0.383720	−0.191860	−	0.981422i	$-0.561452\pi$
$173$	−5.04705	−0.383720	−0.191860	+	0.981422i	$0.561452\pi$
$174$	−0.768135	−0.0582322
$175$	−12.2392	−0.925196
$176$	4.74002	0.357292
$177$	2.00035	0.150356
$178$	−9.60551	−0.719964
$179$	−9.77614	−0.730703	−0.365352	−	0.930870i	$-0.619051\pi$
$179$	−9.77614	−0.730703	−0.365352	+	0.930870i	$0.619051\pi$
$180$	−2.34454	−0.174752
$181$	6.61384	0.491603	0.245802	−	0.969320i	$-0.420949\pi$
$181$	6.61384	0.491603	0.245802	+	0.969320i	$0.420949\pi$
$182$	6.12549	0.454051
$183$	−2.80059	−0.207025
$184$	6.41578	0.472978
$185$	9.34376	0.686967
$186$	−0.187988	−0.0137840
$187$	28.5814	2.09008
$188$	4.60234	0.335660
$189$	−3.95056	−0.287361
$190$	0.796437	0.0577796
$191$	20.0904	1.45369	0.726844	−	0.686802i	$-0.240986\pi$
$191$	20.0904	1.45369	0.726844	+	0.686802i	$0.240986\pi$
$192$	0.237080	0.0171098
$193$	17.4991	1.25961	0.629807	−	0.776752i	$-0.283134\pi$
$193$	17.4991	1.25961	0.629807	+	0.776752i	$0.283134\pi$
$194$	2.53730	0.182167
$195$	−0.412559	−0.0295440
$196$	0.859599	0.0613999
$197$	5.51988	0.393275	0.196638	−	0.980476i	$-0.436998\pi$
$197$	5.51988	0.393275	0.196638	+	0.980476i	$0.436998\pi$
$198$	13.9536	0.991641
$199$	−2.23267	−0.158270	−0.0791350	−	0.996864i	$-0.525216\pi$
$199$	−2.23267	−0.158270	−0.0791350	+	0.996864i	$0.525216\pi$
$200$	4.36569	0.308701
$201$	2.85164	0.201139
$202$	−15.5527	−1.09429
$203$	9.08329	0.637522
$204$	1.42955	0.100088
$205$	−2.50564	−0.175002
$206$	−16.7261	−1.16536
$207$	18.8867	1.31272
$208$	−2.18494	−0.151499
$209$	−4.74002	−0.327874
$210$	−0.529354	−0.0365289
$211$	1.00000	0.0688428
$211$	1.00000	0.0688428
$212$	−4.63474	−0.318315
$213$	−0.434539	−0.0297741
$214$	−6.68154	−0.456741
$215$	0.882681	0.0601983
$216$	1.40915	0.0958807
$217$	2.22298	0.150906
$218$	−3.41840	−0.231523
$219$	0.0650284	0.00439421
$220$	3.77512	0.254519
$221$	−13.1748	−0.886235
$222$	−2.78141	−0.186676
$223$	−1.65228	−0.110645	−0.0553223	−	0.998469i	$-0.517619\pi$
$223$	−1.65228	−0.110645	−0.0553223	+	0.998469i	$0.517619\pi$
$224$	−2.80350	−0.187317
$225$	12.8517	0.856779
$226$	−2.58372	−0.171867
$227$	−3.88178	−0.257643	−0.128822	−	0.991668i	$-0.541119\pi$
$227$	−3.88178	−0.257643	−0.128822	+	0.991668i	$0.541119\pi$
$228$	−0.237080	−0.0157010
$229$	−6.59438	−0.435769	−0.217884	−	0.975975i	$-0.569916\pi$
$229$	−6.59438	−0.435769	−0.217884	+	0.975975i	$0.569916\pi$
$230$	5.10976	0.336928
$231$	3.15046	0.207285
$232$	−3.23999	−0.212715
$233$	12.1671	0.797096	0.398548	−	0.917148i	$-0.369514\pi$
$233$	12.1671	0.797096	0.398548	+	0.917148i	$0.369514\pi$
$234$	−6.43203	−0.420475
$235$	3.66547	0.239109
$236$	8.43747	0.549233
$237$	2.52890	0.164270
$238$	−16.9046	−1.09576
$239$	−0.200567	−0.0129736	−0.00648681	−	0.999979i	$-0.502065\pi$
$239$	−0.200567	−0.0129736	−0.00648681	+	0.999979i	$0.502065\pi$
$240$	0.188819	0.0121882
$241$	−3.87182	−0.249406	−0.124703	−	0.992194i	$-0.539798\pi$
$241$	−3.87182	−0.249406	−0.124703	+	0.992194i	$0.539798\pi$
$242$	−11.4678	−0.737175
$243$	6.24200	0.400424
$244$	−11.8128	−0.756240
$245$	0.684616	0.0437385
$246$	0.745869	0.0475549
$247$	2.18494	0.139025
$248$	−0.792931	−0.0503512
$249$	−3.16680	−0.200688
$250$	7.45918	0.471760
$251$	−2.25610	−0.142404	−0.0712019	−	0.997462i	$-0.522683\pi$
$251$	−2.25610	−0.142404	−0.0712019	+	0.997462i	$0.522683\pi$
$252$	−8.25292	−0.519885
$253$	−30.4109	−1.91192
$254$	17.6380	1.10671
$255$	1.13854	0.0712984
$256$	1.00000	0.0625000
$257$	4.51684	0.281752	0.140876	−	0.990027i	$-0.455008\pi$
$257$	4.51684	0.281752	0.140876	+	0.990027i	$0.455008\pi$
$258$	−0.262753	−0.0163583
$259$	32.8905	2.04372
$260$	−1.74017	−0.107921
$261$	−9.53785	−0.590378
$262$	−4.98659	−0.308073
$263$	8.32235	0.513178	0.256589	−	0.966521i	$-0.417401\pi$
$263$	8.32235	0.513178	0.256589	+	0.966521i	$0.417401\pi$
$264$	−1.12376	−0.0691628
$265$	−3.69127	−0.226753
$266$	2.80350	0.171893
$267$	2.27727	0.139367
$268$	12.0282	0.734737
$269$	13.3153	0.811850	0.405925	−	0.913906i	$-0.366949\pi$
$269$	13.3153	0.811850	0.405925	+	0.913906i	$0.366949\pi$
$270$	1.12230	0.0683011
$271$	8.31037	0.504819	0.252410	−	0.967620i	$-0.418777\pi$
$271$	8.31037	0.504819	0.252410	+	0.967620i	$0.418777\pi$
$272$	6.02982	0.365612
$273$	−1.45223	−0.0878929
$274$	1.37086	0.0828166
$275$	−20.6934	−1.24786
$276$	−1.52105	−0.0915565
$277$	−7.78159	−0.467550	−0.233775	−	0.972291i	$-0.575108\pi$
$277$	−7.78159	−0.467550	−0.233775	+	0.972291i	$0.575108\pi$
$278$	−11.0267	−0.661339
$279$	−2.33423	−0.139746
$280$	−2.23281	−0.133436
$281$	8.97741	0.535547	0.267774	−	0.963482i	$-0.413712\pi$
$281$	8.97741	0.535547	0.267774	+	0.963482i	$0.413712\pi$
$282$	−1.09112	−0.0649754
$283$	−10.5496	−0.627110	−0.313555	−	0.949570i	$-0.601520\pi$
$283$	−10.5496	−0.627110	−0.313555	+	0.949570i	$0.601520\pi$
$284$	−1.83288	−0.108762
$285$	−0.188819	−0.0111847
$286$	10.3567	0.612403
$287$	−8.81999	−0.520628
$288$	2.94379	0.173465
$289$	19.3587	1.13875
$290$	−2.58044	−0.151529
$291$	−0.601542	−0.0352630
$292$	0.274289	0.0160516
$293$	31.7950	1.85748	0.928741	−	0.370730i	$-0.120893\pi$
$293$	31.7950	1.85748	0.928741	+	0.370730i	$0.120893\pi$
$294$	−0.203794	−0.0118855
$295$	6.71991	0.391248
$296$	−11.7320	−0.681906
$297$	−6.67941	−0.387579
$298$	−13.7411	−0.796000
$299$	14.0181	0.810689
$300$	−1.03502	−0.0597567
$301$	3.10708	0.179089
$302$	24.2927	1.39789
$303$	3.68724	0.211826
$304$	−1.00000	−0.0573539
$305$	−9.40818	−0.538711
$306$	17.7505	1.01473
$307$	16.2302	0.926309	0.463154	−	0.886278i	$-0.346718\pi$
$307$	16.2302	0.926309	0.463154	+	0.886278i	$0.346718\pi$
$308$	13.2886	0.757190
$309$	3.96543	0.225585
$310$	−0.631520	−0.0358679
$311$	−19.9063	−1.12878	−0.564390	−	0.825508i	$-0.690889\pi$
$311$	−19.9063	−1.12878	−0.564390	+	0.825508i	$0.690889\pi$
$312$	0.518006	0.0293263
$313$	−5.50408	−0.311109	−0.155555	−	0.987827i	$-0.549716\pi$
$313$	−5.50408	−0.311109	−0.155555	+	0.987827i	$0.549716\pi$
$314$	−12.5534	−0.708427
$315$	−6.57292	−0.370342
$316$	10.6669	0.600058
$317$	14.4269	0.810298	0.405149	−	0.914251i	$-0.367220\pi$
$317$	14.4269	0.810298	0.405149	+	0.914251i	$0.367220\pi$
$318$	1.09880	0.0616178
$319$	15.3576	0.859860
$320$	0.796437	0.0445222
$321$	1.58406	0.0884135
$322$	17.9866	1.00236
$323$	−6.02982	−0.335508
$324$	8.49730	0.472072
$325$	9.53879	0.529117
$326$	4.58633	0.254013
$327$	0.810434	0.0448171
$328$	3.14607	0.173713
$329$	12.9027	0.711347
$330$	−0.895005	−0.0492684
$331$	9.33740	0.513230	0.256615	−	0.966514i	$-0.417393\pi$
$331$	9.33740	0.513230	0.256615	+	0.966514i	$0.417393\pi$
$332$	−13.3575	−0.733090
$333$	−34.5365	−1.89259
$334$	12.2850	0.672208
$335$	9.57967	0.523393
$336$	0.664653	0.0362598
$337$	0.379590	0.0206776	0.0103388	−	0.999947i	$-0.496709\pi$
$337$	0.379590	0.0206776	0.0103388	+	0.999947i	$0.496709\pi$
$338$	8.22602	0.447436
$339$	0.612549	0.0332691
$340$	4.80237	0.260445
$341$	3.75851	0.203535
$342$	−2.94379	−0.159182
$343$	−17.2146	−0.929501
$344$	−1.10829	−0.0597549
$345$	−1.21142	−0.0652207
$346$	5.04705	0.271331
$347$	−7.90658	−0.424448	−0.212224	−	0.977221i	$-0.568071\pi$
$347$	−7.90658	−0.424448	−0.212224	+	0.977221i	$0.568071\pi$
$348$	0.768135	0.0411764
$349$	0.827802	0.0443112	0.0221556	−	0.999755i	$-0.492947\pi$
$349$	0.827802	0.0443112	0.0221556	+	0.999755i	$0.492947\pi$
$350$	12.2392	0.654213
$351$	3.07892	0.164341
$352$	−4.74002	−0.252644
$353$	−16.6005	−0.883556	−0.441778	−	0.897124i	$-0.645652\pi$
$353$	−16.6005	−0.883556	−0.441778	+	0.897124i	$0.645652\pi$
$354$	−2.00035	−0.106318
$355$	−1.45977	−0.0774768
$356$	9.60551	0.509091
$357$	4.00774	0.212112
$358$	9.77614	0.516685
$359$	−36.9679	−1.95109	−0.975546	−	0.219796i	$-0.929461\pi$
$359$	−36.9679	−1.95109	−0.975546	+	0.219796i	$0.929461\pi$
$360$	2.34454	0.123568
$361$	1.00000	0.0526316
$362$	−6.61384	−0.347616
$363$	2.71877	0.142699
$364$	−6.12549	−0.321063
$365$	0.218454	0.0114344
$366$	2.80059	0.146389
$367$	9.88440	0.515962	0.257981	−	0.966150i	$-0.416943\pi$
$367$	9.88440	0.515962	0.257981	+	0.966150i	$0.416943\pi$
$368$	−6.41578	−0.334446
$369$	9.26137	0.482128
$370$	−9.34376	−0.485759
$371$	−12.9935	−0.674587
$372$	0.187988	0.00974673
$373$	4.81776	0.249454	0.124727	−	0.992191i	$-0.460194\pi$
$373$	4.81776	0.249454	0.124727	+	0.992191i	$0.460194\pi$
$374$	−28.5814	−1.47791
$375$	−1.76842	−0.0913208
$376$	−4.60234	−0.237348
$377$	−7.07919	−0.364597
$378$	3.95056	0.203195
$379$	15.4554	0.793888	0.396944	−	0.917843i	$-0.370071\pi$
$379$	15.4554	0.793888	0.396944	+	0.917843i	$0.370071\pi$
$380$	−0.796437	−0.0408563
$381$	−4.18162	−0.214231
$382$	−20.0904	−1.02791
$383$	−1.03318	−0.0527933	−0.0263966	−	0.999652i	$-0.508403\pi$
$383$	−1.03318	−0.0527933	−0.0263966	+	0.999652i	$0.508403\pi$
$384$	−0.237080	−0.0120984
$385$	10.5835	0.539387
$386$	−17.4991	−0.890682
$387$	−3.26257	−0.165846
$388$	−2.53730	−0.128812
$389$	−23.7639	−1.20488	−0.602439	−	0.798165i	$-0.705804\pi$
$389$	−23.7639	−1.20488	−0.602439	+	0.798165i	$0.705804\pi$
$390$	0.412559	0.0208907
$391$	−38.6860	−1.95644
$392$	−0.859599	−0.0434163
$393$	1.18222	0.0596351
$394$	−5.51988	−0.278088
$395$	8.49548	0.427454
$396$	−13.9536	−0.701196
$397$	−12.1950	−0.612049	−0.306024	−	0.952024i	$-0.598999\pi$
$397$	−12.1950	−0.612049	−0.306024	+	0.952024i	$0.598999\pi$
$398$	2.23267	0.111914
$399$	−0.664653	−0.0332743
$400$	−4.36569	−0.218284
$401$	−6.63757	−0.331464	−0.165732	−	0.986171i	$-0.552999\pi$
$401$	−6.63757	−0.331464	−0.165732	+	0.986171i	$0.552999\pi$
$402$	−2.85164	−0.142227
$403$	−1.73251	−0.0863025
$404$	15.5527	0.773777
$405$	6.76756	0.336283
$406$	−9.08329	−0.450796
$407$	55.6097	2.75647
$408$	−1.42955	−0.0707732
$409$	20.5774	1.01749	0.508744	−	0.860918i	$-0.330110\pi$
$409$	20.5774	1.01749	0.508744	+	0.860918i	$0.330110\pi$
$410$	2.50564	0.123745
$411$	−0.325003	−0.0160312
$412$	16.7261	0.824037
$413$	23.6544	1.16396
$414$	−18.8867	−0.928232
$415$	−10.6384	−0.522220
$416$	2.18494	0.107126
$417$	2.61422	0.128019
$418$	4.74002	0.231842
$419$	9.00900	0.440118	0.220059	−	0.975487i	$-0.429375\pi$
$419$	9.00900	0.440118	0.220059	+	0.975487i	$0.429375\pi$
$420$	0.529354	0.0258298
$421$	−7.90629	−0.385329	−0.192665	−	0.981265i	$-0.561713\pi$
$421$	−7.90629	−0.385329	−0.192665	+	0.981265i	$0.561713\pi$
$422$	−1.00000	−0.0486792
$423$	−13.5483	−0.658743
$424$	4.63474	0.225083
$425$	−26.3243	−1.27692
$426$	0.434539	0.0210535
$427$	−33.1173	−1.60266
$428$	6.68154	0.322964
$429$	−2.45536	−0.118546
$430$	−0.882681	−0.0425666
$431$	22.1765	1.06820	0.534102	−	0.845420i	$-0.320650\pi$
$431$	22.1765	1.06820	0.534102	+	0.845420i	$0.320650\pi$
$432$	−1.40915	−0.0677979
$433$	−12.1969	−0.586144	−0.293072	−	0.956090i	$-0.594677\pi$
$433$	−12.1969	−0.586144	−0.293072	+	0.956090i	$0.594677\pi$
$434$	−2.22298	−0.106707
$435$	0.611771	0.0293322
$436$	3.41840	0.163712
$437$	6.41578	0.306908
$438$	−0.0650284	−0.00310718
$439$	−11.6481	−0.555932	−0.277966	−	0.960591i	$-0.589660\pi$
$439$	−11.6481	−0.555932	−0.277966	+	0.960591i	$0.589660\pi$
$440$	−3.77512	−0.179972
$441$	−2.53048	−0.120499
$442$	13.1748	0.626663
$443$	−27.2039	−1.29249	−0.646247	−	0.763128i	$-0.723662\pi$
$443$	−27.2039	−1.29249	−0.646247	+	0.763128i	$0.723662\pi$
$444$	2.78141	0.132000
$445$	7.65018	0.362653
$446$	1.65228	0.0782375
$447$	3.25773	0.154086
$448$	2.80350	0.132453
$449$	19.5281	0.921586	0.460793	−	0.887508i	$-0.347565\pi$
$449$	19.5281	0.921586	0.460793	+	0.887508i	$0.347565\pi$
$450$	−12.8517	−0.605834
$451$	−14.9124	−0.702198
$452$	2.58372	0.121528
$453$	−5.75931	−0.270596
$454$	3.88178	0.182181
$455$	−4.87856	−0.228711
$456$	0.237080	0.0111023
$457$	−2.20192	−0.103001	−0.0515007	−	0.998673i	$-0.516400\pi$
$457$	−2.20192	−0.103001	−0.0515007	+	0.998673i	$0.516400\pi$
$458$	6.59438	0.308135
$459$	−8.49694	−0.396603
$460$	−5.10976	−0.238244
$461$	36.5871	1.70403	0.852016	−	0.523516i	$-0.175380\pi$
$461$	36.5871	1.70403	0.852016	+	0.523516i	$0.175380\pi$
$462$	−3.15046	−0.146573
$463$	28.0188	1.30214	0.651072	−	0.759016i	$-0.274319\pi$
$463$	28.0188	1.30214	0.651072	+	0.759016i	$0.274319\pi$
$464$	3.23999	0.150413
$465$	0.149721	0.00694312
$466$	−12.1671	−0.563632
$467$	−41.5663	−1.92346	−0.961729	−	0.274004i	$-0.911652\pi$
$467$	−41.5663	−1.92346	−0.961729	+	0.274004i	$0.911652\pi$
$468$	6.43203	0.297320
$469$	33.7209	1.55709
$470$	−3.66547	−0.169076
$471$	2.97615	0.137134
$472$	−8.43747	−0.388366
$473$	5.25330	0.241547
$474$	−2.52890	−0.116156
$475$	4.36569	0.200312
$476$	16.9046	0.774821
$477$	13.6437	0.624702
$478$	0.200567	0.00917373
$479$	−15.9662	−0.729513	−0.364757	−	0.931103i	$-0.618848\pi$
$479$	−15.9662	−0.729513	−0.364757	+	0.931103i	$0.618848\pi$
$480$	−0.188819	−0.00861837
$481$	−25.6337	−1.16880
$482$	3.87182	0.176357
$483$	−4.26426	−0.194031
$484$	11.4678	0.521262
$485$	−2.02080	−0.0917596
$486$	−6.24200	−0.283143
$487$	27.7570	1.25779	0.628895	−	0.777490i	$-0.283508\pi$
$487$	27.7570	1.25779	0.628895	+	0.777490i	$0.283508\pi$
$488$	11.8128	0.534742
$489$	−1.08733	−0.0491706
$490$	−0.684616	−0.0309278
$491$	−32.0305	−1.44552	−0.722759	−	0.691100i	$-0.757126\pi$
$491$	−32.0305	−1.44552	−0.722759	+	0.691100i	$0.757126\pi$
$492$	−0.745869	−0.0336264
$493$	19.5365	0.879881
$494$	−2.18494	−0.0983053
$495$	−11.1132	−0.499500
$496$	0.792931	0.0356037
$497$	−5.13848	−0.230492
$498$	3.16680	0.141908
$499$	−15.2312	−0.681843	−0.340921	−	0.940092i	$-0.610739\pi$
$499$	−15.2312	−0.681843	−0.340921	+	0.940092i	$0.610739\pi$
$500$	−7.45918	−0.333585
$501$	−2.91253	−0.130122
$502$	2.25610	0.100695
$503$	−23.1514	−1.03227	−0.516136	−	0.856507i	$-0.672630\pi$
$503$	−23.1514	−1.03227	−0.516136	+	0.856507i	$0.672630\pi$
$504$	8.25292	0.367614
$505$	12.3868	0.551203
$506$	30.4109	1.35193
$507$	−1.95022	−0.0866124
$508$	−17.6380	−0.782561
$509$	−28.4776	−1.26225	−0.631123	−	0.775683i	$-0.717406\pi$
$509$	−28.4776	−1.26225	−0.631123	+	0.775683i	$0.717406\pi$
$510$	−1.13854	−0.0504156
$511$	0.768969	0.0340172
$512$	−1.00000	−0.0441942
$513$	1.40915	0.0622156
$514$	−4.51684	−0.199229
$515$	13.3213	0.587007
$516$	0.262753	0.0115670
$517$	21.8152	0.959430
$518$	−32.8905	−1.44513
$519$	−1.19655	−0.0525229
$520$	1.74017	0.0763115
$521$	−35.4119	−1.55142	−0.775711	−	0.631088i	$-0.782609\pi$
$521$	−35.4119	−1.55142	−0.775711	+	0.631088i	$0.782609\pi$
$522$	9.53785	0.417460
$523$	17.5085	0.765593	0.382797	−	0.923833i	$-0.374961\pi$
$523$	17.5085	0.765593	0.382797	+	0.923833i	$0.374961\pi$
$524$	4.98659	0.217840
$525$	−2.90167	−0.126639
$526$	−8.32235	−0.362872
$527$	4.78123	0.208274
$528$	1.12376	0.0489055
$529$	18.1622	0.789662
$530$	3.69127	0.160339
$531$	−24.8382	−1.07788
$532$	−2.80350	−0.121547
$533$	6.87398	0.297745
$534$	−2.27727	−0.0985472
$535$	5.32142	0.230065
$536$	−12.0282	−0.519538
$537$	−2.31773	−0.100017
$538$	−13.3153	−0.574064
$539$	4.07451	0.175502
$540$	−1.12230	−0.0482961
$541$	38.0795	1.63717	0.818583	−	0.574389i	$-0.194760\pi$
$541$	38.0795	1.63717	0.818583	+	0.574389i	$0.194760\pi$
$542$	−8.31037	−0.356961
$543$	1.56801	0.0672897
$544$	−6.02982	−0.258526
$545$	2.72254	0.116621
$546$	1.45223	0.0621497
$547$	10.9403	0.467775	0.233887	−	0.972264i	$-0.424855\pi$
$547$	10.9403	0.467775	0.233887	+	0.972264i	$0.424855\pi$
$548$	−1.37086	−0.0585602
$549$	34.7746	1.48414
$550$	20.6934	0.882371
$551$	−3.23999	−0.138028
$552$	1.52105	0.0647403
$553$	29.9045	1.27167
$554$	7.78159	0.330608
$555$	2.21522	0.0940307
$556$	11.0267	0.467638
$557$	6.87702	0.291389	0.145694	−	0.989330i	$-0.453458\pi$
$557$	6.87702	0.291389	0.145694	+	0.989330i	$0.453458\pi$
$558$	2.33423	0.0988157
$559$	−2.42155	−0.102421
$560$	2.23281	0.0943534
$561$	6.77608	0.286086
$562$	−8.97741	−0.378689
$563$	25.0697	1.05656	0.528280	−	0.849070i	$-0.322837\pi$
$563$	25.0697	1.05656	0.528280	+	0.849070i	$0.322837\pi$
$564$	1.09112	0.0459445
$565$	2.05777	0.0865711
$566$	10.5496	0.443434
$567$	23.8222	1.00044
$568$	1.83288	0.0769060
$569$	38.8551	1.62889	0.814445	−	0.580241i	$-0.197042\pi$
$569$	38.8551	1.62889	0.814445	+	0.580241i	$0.197042\pi$
$570$	0.188819	0.00790876
$571$	−8.71079	−0.364535	−0.182268	−	0.983249i	$-0.558344\pi$
$571$	−8.71079	−0.364535	−0.182268	+	0.983249i	$0.558344\pi$
$572$	−10.3567	−0.433034
$573$	4.76302	0.198978
$574$	8.81999	0.368139
$575$	28.0093	1.16807
$576$	−2.94379	−0.122658
$577$	18.1506	0.755620	0.377810	−	0.925883i	$-0.376677\pi$
$577$	18.1506	0.755620	0.377810	+	0.925883i	$0.376677\pi$
$578$	−19.3587	−0.805218
$579$	4.14869	0.172414
$580$	2.58044	0.107147
$581$	−37.4478	−1.55360
$582$	0.601542	0.0249347
$583$	−21.9687	−0.909852
$584$	−0.274289	−0.0113502
$585$	5.12270	0.211798
$586$	−31.7950	−1.31344
$587$	22.3523	0.922579	0.461289	−	0.887250i	$-0.347387\pi$
$587$	22.3523	0.922579	0.461289	+	0.887250i	$0.347387\pi$
$588$	0.203794	0.00840430
$589$	−0.792931	−0.0326722
$590$	−6.71991	−0.276654
$591$	1.30865	0.0538308
$592$	11.7320	0.482181
$593$	−28.6467	−1.17638	−0.588189	−	0.808724i	$-0.700159\pi$
$593$	−28.6467	−1.17638	−0.588189	+	0.808724i	$0.700159\pi$
$594$	6.67941	0.274059
$595$	13.4634	0.551947
$596$	13.7411	0.562857
$597$	−0.529322	−0.0216637
$598$	−14.0181	−0.573244
$599$	−6.15284	−0.251398	−0.125699	−	0.992068i	$-0.540117\pi$
$599$	−6.15284	−0.251398	−0.125699	+	0.992068i	$0.540117\pi$
$600$	1.03502	0.0422544
$601$	−29.5567	−1.20564	−0.602821	−	0.797876i	$-0.705957\pi$
$601$	−29.5567	−1.20564	−0.602821	+	0.797876i	$0.705957\pi$
$602$	−3.10708	−0.126635
$603$	−35.4084	−1.44194
$604$	−24.2927	−0.988456
$605$	9.13334	0.371323
$606$	−3.68724	−0.149784
$607$	−16.1759	−0.656559	−0.328279	−	0.944581i	$-0.606469\pi$
$607$	−16.1759	−0.656559	−0.328279	+	0.944581i	$0.606469\pi$
$608$	1.00000	0.0405554
$609$	2.15346	0.0872628
$610$	9.40818	0.380926
$611$	−10.0559	−0.406817
$612$	−17.7505	−0.717523
$613$	9.30887	0.375982	0.187991	−	0.982171i	$-0.439802\pi$
$613$	9.30887	0.375982	0.187991	+	0.982171i	$0.439802\pi$
$614$	−16.2302	−0.654999
$615$	−0.594037	−0.0239539
$616$	−13.2886	−0.535414
$617$	−44.6222	−1.79642	−0.898211	−	0.439565i	$-0.855133\pi$
$617$	−44.6222	−1.79642	−0.898211	+	0.439565i	$0.855133\pi$
$618$	−3.96543	−0.159513
$619$	39.9917	1.60740	0.803701	−	0.595034i	$-0.202861\pi$
$619$	39.9917	1.60740	0.803701	+	0.595034i	$0.202861\pi$
$620$	0.631520	0.0253624
$621$	9.04082	0.362795
$622$	19.9063	0.798169
$623$	26.9290	1.07889
$624$	−0.518006	−0.0207368
$625$	15.8877	0.635507
$626$	5.50408	0.219987
$627$	−1.12376	−0.0448787
$628$	12.5534	0.500934
$629$	70.7416	2.82065
$630$	6.57292	0.261872
$631$	43.2124	1.72026	0.860130	−	0.510075i	$-0.170382\pi$
$631$	43.2124	1.72026	0.860130	+	0.510075i	$0.170382\pi$
$632$	−10.6669	−0.424305
$633$	0.237080	0.00942308
$634$	−14.4269	−0.572967
$635$	−14.0476	−0.557461
$636$	−1.09880	−0.0435703
$637$	−1.87818	−0.0744160
$638$	−15.3576	−0.608013
$639$	5.39563	0.213448
$640$	−0.796437	−0.0314819
$641$	−29.0630	−1.14792	−0.573960	−	0.818884i	$-0.694593\pi$
$641$	−29.0630	−1.14792	−0.573960	+	0.818884i	$0.694593\pi$
$642$	−1.58406	−0.0625178
$643$	21.5250	0.848862	0.424431	−	0.905460i	$-0.360474\pi$
$643$	21.5250	0.848862	0.424431	+	0.905460i	$0.360474\pi$
$644$	−17.9866	−0.708772
$645$	0.209266	0.00823983
$646$	6.02982	0.237240
$647$	−38.2295	−1.50295	−0.751477	−	0.659759i	$-0.770658\pi$
$647$	−38.2295	−1.50295	−0.751477	+	0.659759i	$0.770658\pi$
$648$	−8.49730	−0.333805
$649$	39.9938	1.56989
$650$	−9.53879	−0.374142
$651$	0.527024	0.0206557
$652$	−4.58633	−0.179615
$653$	−8.77932	−0.343561	−0.171781	−	0.985135i	$-0.554952\pi$
$653$	−8.77932	−0.343561	−0.171781	+	0.985135i	$0.554952\pi$
$654$	−0.810434	−0.0316905
$655$	3.97151	0.155180
$656$	−3.14607	−0.122833
$657$	−0.807450	−0.0315016
$658$	−12.9027	−0.502998
$659$	−24.3506	−0.948565	−0.474283	−	0.880373i	$-0.657293\pi$
$659$	−24.3506	−0.948565	−0.474283	+	0.880373i	$0.657293\pi$
$660$	0.895005	0.0348380
$661$	35.8758	1.39541	0.697704	−	0.716386i	$-0.254205\pi$
$661$	35.8758	1.39541	0.697704	+	0.716386i	$0.254205\pi$
$662$	−9.33740	−0.362908
$663$	−3.12348	−0.121306
$664$	13.3575	0.518373
$665$	−2.23281	−0.0865846
$666$	34.5365	1.33826
$667$	−20.7870	−0.804877
$668$	−12.2850	−0.475323
$669$	−0.391721	−0.0151448
$670$	−9.57967	−0.370095
$671$	−55.9931	−2.16159
$672$	−0.664653	−0.0256395
$673$	2.38936	0.0921031	0.0460516	−	0.998939i	$-0.485336\pi$
$673$	2.38936	0.0921031	0.0460516	+	0.998939i	$0.485336\pi$
$674$	−0.379590	−0.0146212
$675$	6.15192	0.236788
$676$	−8.22602	−0.316385
$677$	44.2452	1.70048	0.850240	−	0.526396i	$-0.176457\pi$
$677$	44.2452	1.70048	0.850240	+	0.526396i	$0.176457\pi$
$678$	−0.612549	−0.0235248
$679$	−7.11330	−0.272984
$680$	−4.80237	−0.184162
$681$	−0.920293	−0.0352657
$682$	−3.75851	−0.143921
$683$	29.2560	1.11945	0.559726	−	0.828678i	$-0.310907\pi$
$683$	29.2560	1.11945	0.559726	+	0.828678i	$0.310907\pi$
$684$	2.94379	0.112559
$685$	−1.09180	−0.0417156
$686$	17.2146	0.657256
$687$	−1.56339	−0.0596472
$688$	1.10829	0.0422531
$689$	10.1266	0.385794
$690$	1.21142	0.0461180
$691$	33.7427	1.28363	0.641816	−	0.766859i	$-0.278181\pi$
$691$	33.7427	1.28363	0.641816	+	0.766859i	$0.278181\pi$
$692$	−5.04705	−0.191860
$693$	−39.1190	−1.48601
$694$	7.90658	0.300130
$695$	8.78209	0.333124
$696$	−0.768135	−0.0291161
$697$	−18.9702	−0.718548
$698$	−0.827802	−0.0313328
$699$	2.88458	0.109105
$700$	−12.2392	−0.462598
$701$	−19.4305	−0.733878	−0.366939	−	0.930245i	$-0.619594\pi$
$701$	−19.4305	−0.733878	−0.366939	+	0.930245i	$0.619594\pi$
$702$	−3.07892	−0.116206
$703$	−11.7320	−0.442479
$704$	4.74002	0.178646
$705$	0.869010	0.0327288
$706$	16.6005	0.624768
$707$	43.6020	1.63982
$708$	2.00035	0.0751779
$709$	43.2623	1.62475	0.812375	−	0.583136i	$-0.198174\pi$
$709$	43.2623	1.62475	0.812375	+	0.583136i	$0.198174\pi$
$710$	1.45977	0.0547843
$711$	−31.4010	−1.17763
$712$	−9.60551	−0.359982
$713$	−5.08727	−0.190520
$714$	−4.00774	−0.149986
$715$	−8.24843	−0.308474
$716$	−9.77614	−0.365352
$717$	−0.0475504	−0.00177580
$718$	36.9679	1.37963
$719$	3.30694	0.123328	0.0616641	−	0.998097i	$-0.480359\pi$
$719$	3.30694	0.123328	0.0616641	+	0.998097i	$0.480359\pi$
$720$	−2.34454	−0.0873760
$721$	46.8917	1.74634
$722$	−1.00000	−0.0372161
$723$	−0.917931	−0.0341382
$724$	6.61384	0.245802
$725$	−14.1448	−0.525323
$726$	−2.71877	−0.100903
$727$	26.6851	0.989695	0.494847	−	0.868980i	$-0.335224\pi$
$727$	26.6851	0.989695	0.494847	+	0.868980i	$0.335224\pi$
$728$	6.12549	0.227026
$729$	−24.0120	−0.889335
$730$	−0.218454	−0.00808534
$731$	6.68278	0.247171
$732$	−2.80059	−0.103513
$733$	0.985023	0.0363827	0.0181913	−	0.999835i	$-0.494209\pi$
$733$	0.985023	0.0363827	0.0181913	+	0.999835i	$0.494209\pi$
$734$	−9.88440	−0.364840
$735$	0.162309	0.00598684
$736$	6.41578	0.236489
$737$	57.0137	2.10013
$738$	−9.26137	−0.340916
$739$	18.7916	0.691259	0.345630	−	0.938371i	$-0.387665\pi$
$739$	18.7916	0.691259	0.345630	+	0.938371i	$0.387665\pi$
$740$	9.34376	0.343484
$741$	0.518006	0.0190294
$742$	12.9935	0.477005
$743$	7.95243	0.291746	0.145873	−	0.989303i	$-0.453401\pi$
$743$	7.95243	0.291746	0.145873	+	0.989303i	$0.453401\pi$
$744$	−0.187988	−0.00689198
$745$	10.9439	0.400954
$746$	−4.81776	−0.176391
$747$	39.3218	1.43871
$748$	28.5814	1.04504
$749$	18.7317	0.684441
$750$	1.76842	0.0645736
$751$	53.3930	1.94834	0.974170	−	0.225817i	$-0.0725051\pi$
$751$	53.3930	1.94834	0.974170	+	0.225817i	$0.0725051\pi$
$752$	4.60234	0.167830
$753$	−0.534875	−0.0194919
$754$	7.07919	0.257809
$755$	−19.3476	−0.704131
$756$	−3.95056	−0.143680
$757$	20.9481	0.761370	0.380685	−	0.924705i	$-0.375688\pi$
$757$	20.9481	0.761370	0.380685	+	0.924705i	$0.375688\pi$
$758$	−15.4554	−0.561364
$759$	−7.20981	−0.261699
$760$	0.796437	0.0288898
$761$	21.0222	0.762054	0.381027	−	0.924564i	$-0.375570\pi$
$761$	21.0222	0.762054	0.381027	+	0.924564i	$0.375570\pi$
$762$	4.18162	0.151484
$763$	9.58348	0.346945
$764$	20.0904	0.726844
$765$	−14.1372	−0.511131
$766$	1.03318	0.0373305
$767$	−18.4354	−0.665664
$768$	0.237080	0.00855488
$769$	−1.27262	−0.0458917	−0.0229459	−	0.999737i	$-0.507305\pi$
$769$	−1.27262	−0.0458917	−0.0229459	+	0.999737i	$0.507305\pi$
$770$	−10.5835	−0.381405
$771$	1.07085	0.0385657
$772$	17.4991	0.629807
$773$	24.8387	0.893385	0.446693	−	0.894687i	$-0.352602\pi$
$773$	24.8387	0.893385	0.446693	+	0.894687i	$0.352602\pi$
$774$	3.26257	0.117271
$775$	−3.46169	−0.124348
$776$	2.53730	0.0910836
$777$	7.79768	0.279740
$778$	23.7639	0.851977
$779$	3.14607	0.112720
$780$	−0.412559	−0.0147720
$781$	−8.68789	−0.310877
$782$	38.6860	1.38341
$783$	−4.56564	−0.163163
$784$	0.859599	0.0307000
$785$	9.99796	0.356842
$786$	−1.18222	−0.0421684
$787$	51.3821	1.83157	0.915787	−	0.401664i	$-0.131568\pi$
$787$	51.3821	1.83157	0.915787	+	0.401664i	$0.131568\pi$
$788$	5.51988	0.196638
$789$	1.97306	0.0702429
$790$	−8.49548	−0.302256
$791$	7.24346	0.257548
$792$	13.9536	0.495821
$793$	25.8104	0.916555
$794$	12.1950	0.432784
$795$	−0.875126	−0.0310375
$796$	−2.23267	−0.0791350
$797$	−46.1364	−1.63424	−0.817118	−	0.576470i	$-0.804430\pi$
$797$	−46.1364	−1.63424	−0.817118	+	0.576470i	$0.804430\pi$
$798$	0.664653	0.0235284
$799$	27.7513	0.981771
$800$	4.36569	0.154350
$801$	−28.2766	−0.999106
$802$	6.63757	0.234381
$803$	1.30013	0.0458808
$804$	2.85164	0.100569
$805$	−14.3252	−0.504897
$806$	1.73251	0.0610251
$807$	3.15679	0.111124
$808$	−15.5527	−0.547143
$809$	16.2206	0.570285	0.285142	−	0.958485i	$-0.407959\pi$
$809$	16.2206	0.570285	0.285142	+	0.958485i	$0.407959\pi$
$810$	−6.76756	−0.237788
$811$	−46.7936	−1.64314	−0.821572	−	0.570104i	$-0.806903\pi$
$811$	−46.7936	−1.64314	−0.821572	+	0.570104i	$0.806903\pi$
$812$	9.08329	0.318761
$813$	1.97022	0.0690987
$814$	−55.6097	−1.94912
$815$	−3.65272	−0.127949
$816$	1.42955	0.0500442
$817$	−1.10829	−0.0387741
$818$	−20.5774	−0.719473
$819$	18.0322	0.630095
$820$	−2.50564	−0.0875008
$821$	8.86584	0.309420	0.154710	−	0.987960i	$-0.450556\pi$
$821$	8.86584	0.309420	0.154710	+	0.987960i	$0.450556\pi$
$822$	0.325003	0.0113358
$823$	−33.3108	−1.16114	−0.580571	−	0.814209i	$-0.697171\pi$
$823$	−33.3108	−1.16114	−0.580571	+	0.814209i	$0.697171\pi$
$824$	−16.7261	−0.582682
$825$	−4.90600	−0.170805
$826$	−23.6544	−0.823043
$827$	−15.4961	−0.538853	−0.269426	−	0.963021i	$-0.586834\pi$
$827$	−15.4961	−0.538853	−0.269426	+	0.963021i	$0.586834\pi$
$828$	18.8867	0.656359
$829$	13.5489	0.470574	0.235287	−	0.971926i	$-0.424397\pi$
$829$	13.5489	0.470574	0.235287	+	0.971926i	$0.424397\pi$
$830$	10.6384	0.369265
$831$	−1.84486	−0.0639974
$832$	−2.18494	−0.0757493
$833$	5.18323	0.179588
$834$	−2.61422	−0.0905229
$835$	−9.78426	−0.338598
$836$	−4.74002	−0.163937
$837$	−1.11736	−0.0386217
$838$	−9.00900	−0.311211
$839$	21.4194	0.739481	0.369740	−	0.929135i	$-0.379447\pi$
$839$	21.4194	0.739481	0.369740	+	0.929135i	$0.379447\pi$
$840$	−0.529354	−0.0182644
$841$	−18.5025	−0.638017
$842$	7.90629	0.272469
$843$	2.12836	0.0733047
$844$	1.00000	0.0344214
$845$	−6.55150	−0.225378
$846$	13.5483	0.465802
$847$	32.1498	1.10468
$848$	−4.63474	−0.159157
$849$	−2.50110	−0.0858377
$850$	26.3243	0.902917
$851$	−75.2697	−2.58021
$852$	−0.434539	−0.0148871
$853$	27.6082	0.945287	0.472643	−	0.881254i	$-0.343300\pi$
$853$	27.6082	0.945287	0.472643	+	0.881254i	$0.343300\pi$
$854$	33.1173	1.13325
$855$	2.34454	0.0801817
$856$	−6.68154	−0.228370
$857$	26.0097	0.888473	0.444237	−	0.895909i	$-0.353475\pi$
$857$	26.0097	0.888473	0.444237	+	0.895909i	$0.353475\pi$
$858$	2.45536	0.0838245
$859$	−11.2328	−0.383258	−0.191629	−	0.981467i	$-0.561377\pi$
$859$	−11.2328	−0.383258	−0.191629	+	0.981467i	$0.561377\pi$
$860$	0.882681	0.0300992
$861$	−2.09104	−0.0712625
$862$	−22.1765	−0.755335
$863$	14.9063	0.507416	0.253708	−	0.967281i	$-0.418350\pi$
$863$	14.9063	0.507416	0.253708	+	0.967281i	$0.418350\pi$
$864$	1.40915	0.0479404
$865$	−4.01965	−0.136672
$866$	12.1969	0.414466
$867$	4.58957	0.155870
$868$	2.22298	0.0754529
$869$	50.5611	1.71517
$870$	−0.611771	−0.0207410
$871$	−26.2809	−0.890494
$872$	−3.41840	−0.115762
$873$	7.46927	0.252797
$874$	−6.41578	−0.217017
$875$	−20.9118	−0.706947
$876$	0.0650284	0.00219711
$877$	3.27326	0.110530	0.0552651	−	0.998472i	$-0.482400\pi$
$877$	3.27326	0.110530	0.0552651	+	0.998472i	$0.482400\pi$
$878$	11.6481	0.393103
$879$	7.53794	0.254248
$880$	3.77512	0.127259
$881$	−13.1729	−0.443806	−0.221903	−	0.975069i	$-0.571227\pi$
$881$	−13.1729	−0.443806	−0.221903	+	0.975069i	$0.571227\pi$
$882$	2.53048	0.0852057
$883$	−1.16511	−0.0392092	−0.0196046	−	0.999808i	$-0.506241\pi$
$883$	−1.16511	−0.0392092	−0.0196046	+	0.999808i	$0.506241\pi$
$884$	−13.1748	−0.443117
$885$	1.59316	0.0535533
$886$	27.2039	0.913931
$887$	−8.52239	−0.286154	−0.143077	−	0.989712i	$-0.545700\pi$
$887$	−8.52239	−0.286154	−0.143077	+	0.989712i	$0.545700\pi$
$888$	−2.78141	−0.0933380
$889$	−49.4482	−1.65844
$890$	−7.65018	−0.256435
$891$	40.2773	1.34934
$892$	−1.65228	−0.0553223
$893$	−4.60234	−0.154012
$894$	−3.25773	−0.108955
$895$	−7.78608	−0.260260
$896$	−2.80350	−0.0936583
$897$	3.32341	0.110966
$898$	−19.5281	−0.651660
$899$	2.56909	0.0856838
$900$	12.8517	0.428390
$901$	−27.9466	−0.931037
$902$	14.9124	0.496529
$903$	0.736626	0.0245134
$904$	−2.58372	−0.0859334
$905$	5.26751	0.175098
$906$	5.75931	0.191340
$907$	50.1763	1.66608	0.833038	−	0.553215i	$-0.186599\pi$
$907$	50.1763	1.66608	0.833038	+	0.553215i	$0.186599\pi$
$908$	−3.88178	−0.128822
$909$	−45.7840	−1.51856
$910$	4.87856	0.161723
$911$	−10.5112	−0.348252	−0.174126	−	0.984723i	$-0.555710\pi$
$911$	−10.5112	−0.348252	−0.174126	+	0.984723i	$0.555710\pi$
$912$	−0.237080	−0.00785050
$913$	−63.3149	−2.09542
$914$	2.20192	0.0728330
$915$	−2.23049	−0.0737377
$916$	−6.59438	−0.217884
$917$	13.9799	0.461657
$918$	8.49694	0.280441
$919$	−20.9716	−0.691789	−0.345895	−	0.938273i	$-0.612425\pi$
$919$	−20.9716	−0.691789	−0.345895	+	0.938273i	$0.612425\pi$
$920$	5.10976	0.168464
$921$	3.84786	0.126791
$922$	−36.5871	−1.20493
$923$	4.00475	0.131818
$924$	3.15046	0.103643
$925$	−51.2181	−1.68404
$926$	−28.0188	−0.920755
$927$	−49.2383	−1.61720
$928$	−3.23999	−0.106358
$929$	8.57591	0.281367	0.140683	−	0.990055i	$-0.455070\pi$
$929$	8.57591	0.281367	0.140683	+	0.990055i	$0.455070\pi$
$930$	−0.149721	−0.00490953
$931$	−0.859599	−0.0281722
$932$	12.1671	0.398548
$933$	−4.71937	−0.154505
$934$	41.5663	1.36009
$935$	22.7633	0.744440
$936$	−6.43203	−0.210237
$937$	31.3884	1.02542	0.512708	−	0.858563i	$-0.328643\pi$
$937$	31.3884	1.02542	0.512708	+	0.858563i	$0.328643\pi$
$938$	−33.7209	−1.10103
$939$	−1.30491	−0.0425840
$940$	3.66547	0.119555
$941$	−41.1008	−1.33985	−0.669924	−	0.742430i	$-0.733673\pi$
$941$	−41.1008	−1.33985	−0.669924	+	0.742430i	$0.733673\pi$
$942$	−2.97615	−0.0969682
$943$	20.1845	0.657297
$944$	8.43747	0.274616
$945$	−3.14637	−0.102351
$946$	−5.25330	−0.170800
$947$	56.8589	1.84767	0.923833	−	0.382795i	$-0.125039\pi$
$947$	56.8589	1.84767	0.923833	+	0.382795i	$0.125039\pi$
$948$	2.52890	0.0821348
$949$	−0.599307	−0.0194543
$950$	−4.36569	−0.141642
$951$	3.42034	0.110912
$952$	−16.9046	−0.547881
$953$	14.7202	0.476833	0.238417	−	0.971163i	$-0.423372\pi$
$953$	14.7202	0.476833	0.238417	+	0.971163i	$0.423372\pi$
$954$	−13.6437	−0.441731
$955$	16.0007	0.517771
$956$	−0.200567	−0.00648681
$957$	3.64097	0.117696
$958$	15.9662	0.515844
$959$	−3.84320	−0.124103
$960$	0.188819	0.00609411
$961$	−30.3713	−0.979718
$962$	25.6337	0.826463
$963$	−19.6691	−0.633827
$964$	−3.87182	−0.124703
$965$	13.9369	0.448646
$966$	4.26426	0.137200
$967$	40.6887	1.30846	0.654230	−	0.756295i	$-0.272993\pi$
$967$	40.6887	1.30846	0.654230	+	0.756295i	$0.272993\pi$
$968$	−11.4678	−0.368588
$969$	−1.42955	−0.0459237
$970$	2.02080	0.0648838
$971$	−25.3784	−0.814432	−0.407216	−	0.913332i	$-0.633500\pi$
$971$	−25.3784	−0.814432	−0.407216	+	0.913332i	$0.633500\pi$
$972$	6.24200	0.200212
$973$	30.9134	0.991039
$974$	−27.7570	−0.889392
$975$	2.26145	0.0724245
$976$	−11.8128	−0.378120
$977$	−39.0591	−1.24961	−0.624806	−	0.780780i	$-0.714822\pi$
$977$	−39.0591	−1.24961	−0.624806	+	0.780780i	$0.714822\pi$
$978$	1.08733	0.0347689
$979$	45.5303	1.45515
$980$	0.684616	0.0218693
$981$	−10.0631	−0.321289
$982$	32.0305	1.02214
$983$	14.4996	0.462464	0.231232	−	0.972899i	$-0.425724\pi$
$983$	14.4996	0.462464	0.231232	+	0.972899i	$0.425724\pi$
$984$	0.745869	0.0237774
$985$	4.39624	0.140076
$986$	−19.5365	−0.622170
$987$	3.05896	0.0973677
$988$	2.18494	0.0695124
$989$	−7.11053	−0.226102
$990$	11.1132	0.353200
$991$	57.5515	1.82818	0.914092	−	0.405507i	$-0.132905\pi$
$991$	57.5515	1.82818	0.914092	+	0.405507i	$0.132905\pi$
$992$	−0.792931	−0.0251756
$993$	2.21371	0.0702499
$994$	5.13848	0.162983
$995$	−1.77818	−0.0563722
$996$	−3.16680	−0.100344
$997$	−32.0248	−1.01424	−0.507118	−	0.861877i	$-0.669289\pi$
$997$	−32.0248	−1.01424	−0.507118	+	0.861877i	$0.669289\pi$
$998$	15.2312	0.482135
$999$	−16.5321	−0.523054

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.h.1.20	✓	41

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.h.1.20	✓	41	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:	\( N \)	\(=\)	\( 8018 = 2 \cdot 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8018.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.237080 q^{3} +1.00000 q^{4} +0.796437 q^{5} -0.237080 q^{6} +2.80350 q^{7} -1.00000 q^{8} -2.94379 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.237080 q^{3} +1.00000 q^{4} +0.796437 q^{5} -0.237080 q^{6} +2.80350 q^{7} -1.00000 q^{8} -2.94379 q^{9} -0.796437 q^{10} +4.74002 q^{11} +0.237080 q^{12} -2.18494 q^{13} -2.80350 q^{14} +0.188819 q^{15} +1.00000 q^{16} +6.02982 q^{17} +2.94379 q^{18} -1.00000 q^{19} +0.796437 q^{20} +0.664653 q^{21} -4.74002 q^{22} -6.41578 q^{23} -0.237080 q^{24} -4.36569 q^{25} +2.18494 q^{26} -1.40915 q^{27} +2.80350 q^{28} +3.23999 q^{29} -0.188819 q^{30} +0.792931 q^{31} -1.00000 q^{32} +1.12376 q^{33} -6.02982 q^{34} +2.23281 q^{35} -2.94379 q^{36} +11.7320 q^{37} +1.00000 q^{38} -0.518006 q^{39} -0.796437 q^{40} -3.14607 q^{41} -0.664653 q^{42} +1.10829 q^{43} +4.74002 q^{44} -2.34454 q^{45} +6.41578 q^{46} +4.60234 q^{47} +0.237080 q^{48} +0.859599 q^{49} +4.36569 q^{50} +1.42955 q^{51} -2.18494 q^{52} -4.63474 q^{53} +1.40915 q^{54} +3.77512 q^{55} -2.80350 q^{56} -0.237080 q^{57} -3.23999 q^{58} +8.43747 q^{59} +0.188819 q^{60} -11.8128 q^{61} -0.792931 q^{62} -8.25292 q^{63} +1.00000 q^{64} -1.74017 q^{65} -1.12376 q^{66} +12.0282 q^{67} +6.02982 q^{68} -1.52105 q^{69} -2.23281 q^{70} -1.83288 q^{71} +2.94379 q^{72} +0.274289 q^{73} -11.7320 q^{74} -1.03502 q^{75} -1.00000 q^{76} +13.2886 q^{77} +0.518006 q^{78} +10.6669 q^{79} +0.796437 q^{80} +8.49730 q^{81} +3.14607 q^{82} -13.3575 q^{83} +0.664653 q^{84} +4.80237 q^{85} -1.10829 q^{86} +0.768135 q^{87} -4.74002 q^{88} +9.60551 q^{89} +2.34454 q^{90} -6.12549 q^{91} -6.41578 q^{92} +0.187988 q^{93} -4.60234 q^{94} -0.796437 q^{95} -0.237080 q^{96} -2.53730 q^{97} -0.859599 q^{98} -13.9536 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 41 q - 41 q^{2} + 8 q^{3} + 41 q^{4} - 9 q^{5} - 8 q^{6} + 7 q^{7} - 41 q^{8} + 43 q^{9}+O(q^{10}) \) 41 * q - 41 * q^2 + 8 * q^3 + 41 * q^4 - 9 * q^5 - 8 * q^6 + 7 * q^7 - 41 * q^8 + 43 * q^9	\( 41 q - 41 q^{2} + 8 q^{3} + 41 q^{4} - 9 q^{5} - 8 q^{6} + 7 q^{7} - 41 q^{8} + 43 q^{9} + 9 q^{10} - 9 q^{11} + 8 q^{12} + 13 q^{13} - 7 q^{14} + 26 q^{15} + 41 q^{16} - 16 q^{17} - 43 q^{18} - 41 q^{19} - 9 q^{20} + 2 q^{21} + 9 q^{22} + 10 q^{23} - 8 q^{24} + 60 q^{25} - 13 q^{26} + 47 q^{27} + 7 q^{28} - 14 q^{29} - 26 q^{30} + 49 q^{31} - 41 q^{32} + 12 q^{33} + 16 q^{34} - 8 q^{35} + 43 q^{36} + 54 q^{37} + 41 q^{38} + 16 q^{39} + 9 q^{40} - 18 q^{41} - 2 q^{42} + 29 q^{43} - 9 q^{44} - 13 q^{45} - 10 q^{46} - 8 q^{47} + 8 q^{48} + 44 q^{49} - 60 q^{50} - 16 q^{51} + 13 q^{52} + 7 q^{53} - 47 q^{54} + 19 q^{55} - 7 q^{56} - 8 q^{57} + 14 q^{58} - 5 q^{59} + 26 q^{60} - 6 q^{61} - 49 q^{62} + 24 q^{63} + 41 q^{64} - 26 q^{65} - 12 q^{66} + 66 q^{67} - 16 q^{68} + 12 q^{69} + 8 q^{70} + 27 q^{71} - 43 q^{72} - q^{73} - 54 q^{74} + 62 q^{75} - 41 q^{76} - 8 q^{77} - 16 q^{78} + 87 q^{79} - 9 q^{80} + 73 q^{81} + 18 q^{82} - 41 q^{83} + 2 q^{84} + 14 q^{85} - 29 q^{86} + 35 q^{87} + 9 q^{88} - 4 q^{89} + 13 q^{90} + 39 q^{91} + 10 q^{92} + 17 q^{93} + 8 q^{94} + 9 q^{95} - 8 q^{96} + 64 q^{97} - 44 q^{98} + 40 q^{99}+O(q^{100}) \) 41 * q - 41 * q^2 + 8 * q^3 + 41 * q^4 - 9 * q^5 - 8 * q^6 + 7 * q^7 - 41 * q^8 + 43 * q^9 + 9 * q^10 - 9 * q^11 + 8 * q^12 + 13 * q^13 - 7 * q^14 + 26 * q^15 + 41 * q^16 - 16 * q^17 - 43 * q^18 - 41 * q^19 - 9 * q^20 + 2 * q^21 + 9 * q^22 + 10 * q^23 - 8 * q^24 + 60 * q^25 - 13 * q^26 + 47 * q^27 + 7 * q^28 - 14 * q^29 - 26 * q^30 + 49 * q^31 - 41 * q^32 + 12 * q^33 + 16 * q^34 - 8 * q^35 + 43 * q^36 + 54 * q^37 + 41 * q^38 + 16 * q^39 + 9 * q^40 - 18 * q^41 - 2 * q^42 + 29 * q^43 - 9 * q^44 - 13 * q^45 - 10 * q^46 - 8 * q^47 + 8 * q^48 + 44 * q^49 - 60 * q^50 - 16 * q^51 + 13 * q^52 + 7 * q^53 - 47 * q^54 + 19 * q^55 - 7 * q^56 - 8 * q^57 + 14 * q^58 - 5 * q^59 + 26 * q^60 - 6 * q^61 - 49 * q^62 + 24 * q^63 + 41 * q^64 - 26 * q^65 - 12 * q^66 + 66 * q^67 - 16 * q^68 + 12 * q^69 + 8 * q^70 + 27 * q^71 - 43 * q^72 - q^73 - 54 * q^74 + 62 * q^75 - 41 * q^76 - 8 * q^77 - 16 * q^78 + 87 * q^79 - 9 * q^80 + 73 * q^81 + 18 * q^82 - 41 * q^83 + 2 * q^84 + 14 * q^85 - 29 * q^86 + 35 * q^87 + 9 * q^88 - 4 * q^89 + 13 * q^90 + 39 * q^91 + 10 * q^92 + 17 * q^93 + 8 * q^94 + 9 * q^95 - 8 * q^96 + 64 * q^97 - 44 * q^98 + 40 * q^99

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