LMFDB - Embedded newform 6034.2.a.k.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6034,2,Mod(1,6034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6034, 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("6034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6034 = 2 \cdot 7 \cdot 431 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6034.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:	$48.1817325796$
Analytic rank:	$1$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 3 x^{19} - 32 x^{18} + 106 x^{17} + 382 x^{16} - 1495 x^{15} - 1963 x^{14} + 10784 x^{13} + \cdots - 44 $ x^20 - 3x^19 - 32x^18 + 106x^17 + 382x^16 - 1495x^15 - 1963x^14 + 10784x^13 + 2170x^12 - 42069x^11 + 19553x^10 + 84697x^9 - 82713x^8 - 68589x^7 + 118845x^6 - 10051x^5 - 53572x^4 + 25598x^3 - 557x^2 - 1040*x - 44
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$-0.0460830$ of defining polynomial
Character	$\chi$	$=$	6034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -0.0460830 q^{3} +1.00000 q^{4} -3.28191 q^{5} +0.0460830 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.99788 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.0460830 q^{3} +1.00000 q^{4} -3.28191 q^{5} +0.0460830 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.99788 q^{9} +3.28191 q^{10} -3.80685 q^{11} -0.0460830 q^{12} +3.87638 q^{13} -1.00000 q^{14} +0.151240 q^{15} +1.00000 q^{16} +0.113850 q^{17} +2.99788 q^{18} +1.50010 q^{19} -3.28191 q^{20} -0.0460830 q^{21} +3.80685 q^{22} +3.61335 q^{23} +0.0460830 q^{24} +5.77092 q^{25} -3.87638 q^{26} +0.276400 q^{27} +1.00000 q^{28} -3.72146 q^{29} -0.151240 q^{30} -1.40212 q^{31} -1.00000 q^{32} +0.175431 q^{33} -0.113850 q^{34} -3.28191 q^{35} -2.99788 q^{36} +10.3718 q^{37} -1.50010 q^{38} -0.178635 q^{39} +3.28191 q^{40} -2.05162 q^{41} +0.0460830 q^{42} -9.84489 q^{43} -3.80685 q^{44} +9.83875 q^{45} -3.61335 q^{46} -4.07388 q^{47} -0.0460830 q^{48} +1.00000 q^{49} -5.77092 q^{50} -0.00524656 q^{51} +3.87638 q^{52} +7.94429 q^{53} -0.276400 q^{54} +12.4937 q^{55} -1.00000 q^{56} -0.0691293 q^{57} +3.72146 q^{58} -4.96245 q^{59} +0.151240 q^{60} +13.8750 q^{61} +1.40212 q^{62} -2.99788 q^{63} +1.00000 q^{64} -12.7219 q^{65} -0.175431 q^{66} +7.36362 q^{67} +0.113850 q^{68} -0.166514 q^{69} +3.28191 q^{70} +3.23758 q^{71} +2.99788 q^{72} -7.93538 q^{73} -10.3718 q^{74} -0.265941 q^{75} +1.50010 q^{76} -3.80685 q^{77} +0.178635 q^{78} +16.6194 q^{79} -3.28191 q^{80} +8.98089 q^{81} +2.05162 q^{82} -6.41067 q^{83} -0.0460830 q^{84} -0.373646 q^{85} +9.84489 q^{86} +0.171496 q^{87} +3.80685 q^{88} +9.78102 q^{89} -9.83875 q^{90} +3.87638 q^{91} +3.61335 q^{92} +0.0646141 q^{93} +4.07388 q^{94} -4.92320 q^{95} +0.0460830 q^{96} -17.1572 q^{97} -1.00000 q^{98} +11.4125 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 20 q^{2} + 3 q^{3} + 20 q^{4} - 3 q^{5} - 3 q^{6} + 20 q^{7} - 20 q^{8} + 13 q^{9}+O(q^{10}) $ 20 * q - 20 * q^2 + 3 * q^3 + 20 * q^4 - 3 * q^5 - 3 * q^6 + 20 * q^7 - 20 * q^8 + 13 * q^9	\( 20 q - 20 q^{2} + 3 q^{3} + 20 q^{4} - 3 q^{5} - 3 q^{6} + 20 q^{7} - 20 q^{8} + 13 q^{9} + 3 q^{10} - 8 q^{11} + 3 q^{12} - 4 q^{13} - 20 q^{14} - 25 q^{15} + 20 q^{16} + 9 q^{17} - 13 q^{18} - 14 q^{19} - 3 q^{20} + 3 q^{21} + 8 q^{22} - 23 q^{23} - 3 q^{24} + 31 q^{25} + 4 q^{26} - 21 q^{27} + 20 q^{28} - 48 q^{29} + 25 q^{30} - q^{31} - 20 q^{32} - 29 q^{33} - 9 q^{34} - 3 q^{35} + 13 q^{36} - q^{37} + 14 q^{38} - q^{39} + 3 q^{40} - 27 q^{41} - 3 q^{42} - 3 q^{43} - 8 q^{44} - 12 q^{45} + 23 q^{46} - 26 q^{47} + 3 q^{48} + 20 q^{49} - 31 q^{50} - 17 q^{51} - 4 q^{52} - 43 q^{53} + 21 q^{54} - 16 q^{55} - 20 q^{56} - 25 q^{57} + 48 q^{58} - 19 q^{59} - 25 q^{60} + 9 q^{61} + q^{62} + 13 q^{63} + 20 q^{64} - 87 q^{65} + 29 q^{66} + 32 q^{67} + 9 q^{68} - 23 q^{69} + 3 q^{70} - 63 q^{71} - 13 q^{72} + 2 q^{73} + q^{74} - 8 q^{75} - 14 q^{76} - 8 q^{77} + q^{78} - 51 q^{79} - 3 q^{80} + 4 q^{81} + 27 q^{82} - 24 q^{83} + 3 q^{84} + 31 q^{85} + 3 q^{86} - 33 q^{87} + 8 q^{88} - 35 q^{89} + 12 q^{90} - 4 q^{91} - 23 q^{92} + 17 q^{93} + 26 q^{94} - 30 q^{95} - 3 q^{96} + 5 q^{97} - 20 q^{98} - 31 q^{99}+O(q^{100}) \) 20 * q - 20 * q^2 + 3 * q^3 + 20 * q^4 - 3 * q^5 - 3 * q^6 + 20 * q^7 - 20 * q^8 + 13 * q^9 + 3 * q^10 - 8 * q^11 + 3 * q^12 - 4 * q^13 - 20 * q^14 - 25 * q^15 + 20 * q^16 + 9 * q^17 - 13 * q^18 - 14 * q^19 - 3 * q^20 + 3 * q^21 + 8 * q^22 - 23 * q^23 - 3 * q^24 + 31 * q^25 + 4 * q^26 - 21 * q^27 + 20 * q^28 - 48 * q^29 + 25 * q^30 - q^31 - 20 * q^32 - 29 * q^33 - 9 * q^34 - 3 * q^35 + 13 * q^36 - q^37 + 14 * q^38 - q^39 + 3 * q^40 - 27 * q^41 - 3 * q^42 - 3 * q^43 - 8 * q^44 - 12 * q^45 + 23 * q^46 - 26 * q^47 + 3 * q^48 + 20 * q^49 - 31 * q^50 - 17 * q^51 - 4 * q^52 - 43 * q^53 + 21 * q^54 - 16 * q^55 - 20 * q^56 - 25 * q^57 + 48 * q^58 - 19 * q^59 - 25 * q^60 + 9 * q^61 + q^62 + 13 * q^63 + 20 * q^64 - 87 * q^65 + 29 * q^66 + 32 * q^67 + 9 * q^68 - 23 * q^69 + 3 * q^70 - 63 * q^71 - 13 * q^72 + 2 * q^73 + q^74 - 8 * q^75 - 14 * q^76 - 8 * q^77 + q^78 - 51 * q^79 - 3 * q^80 + 4 * q^81 + 27 * q^82 - 24 * q^83 + 3 * q^84 + 31 * q^85 + 3 * q^86 - 33 * q^87 + 8 * q^88 - 35 * q^89 + 12 * q^90 - 4 * q^91 - 23 * q^92 + 17 * q^93 + 26 * q^94 - 30 * q^95 - 3 * q^96 + 5 * q^97 - 20 * q^98 - 31 * 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
$3$	−0.0460830	−0.0266060	−0.0133030	−	0.999912i	$-0.504235\pi$
$3$	−0.0460830	−0.0266060	−0.0133030	+	0.999912i	$0.504235\pi$
$4$	1.00000	0.500000
$5$	−3.28191	−1.46771	−0.733857	−	0.679304i	$-0.762282\pi$
$5$	−3.28191	−1.46771	−0.733857	+	0.679304i	$0.762282\pi$
$6$	0.0460830	0.0188133
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	−2.99788	−0.999292
$10$	3.28191	1.03783
$11$	−3.80685	−1.14781	−0.573904	−	0.818923i	$-0.694572\pi$
$11$	−3.80685	−1.14781	−0.573904	+	0.818923i	$0.694572\pi$
$12$	−0.0460830	−0.0133030
$13$	3.87638	1.07511	0.537557	−	0.843228i	$-0.319347\pi$
$13$	3.87638	1.07511	0.537557	+	0.843228i	$0.319347\pi$
$14$	−1.00000	−0.267261
$15$	0.151240	0.0390501
$16$	1.00000	0.250000
$17$	0.113850	0.0276127	0.0138064	−	0.999905i	$-0.495605\pi$
$17$	0.113850	0.0276127	0.0138064	+	0.999905i	$0.495605\pi$
$18$	2.99788	0.706606
$19$	1.50010	0.344147	0.172074	−	0.985084i	$-0.444953\pi$
$19$	1.50010	0.344147	0.172074	+	0.985084i	$0.444953\pi$
$20$	−3.28191	−0.733857
$21$	−0.0460830	−0.0100561
$22$	3.80685	0.811622
$23$	3.61335	0.753435	0.376717	−	0.926328i	$-0.377053\pi$
$23$	3.61335	0.753435	0.376717	+	0.926328i	$0.377053\pi$
$24$	0.0460830	0.00940666
$25$	5.77092	1.15418
$26$	−3.87638	−0.760220
$27$	0.276400	0.0531933
$28$	1.00000	0.188982
$29$	−3.72146	−0.691058	−0.345529	−	0.938408i	$-0.612300\pi$
$29$	−3.72146	−0.691058	−0.345529	+	0.938408i	$0.612300\pi$
$30$	−0.151240	−0.0276126
$31$	−1.40212	−0.251829	−0.125914	−	0.992041i	$-0.540186\pi$
$31$	−1.40212	−0.251829	−0.125914	+	0.992041i	$0.540186\pi$
$32$	−1.00000	−0.176777
$33$	0.175431	0.0305386
$34$	−0.113850	−0.0195251
$35$	−3.28191	−0.554744
$36$	−2.99788	−0.499646
$37$	10.3718	1.70512	0.852561	−	0.522629i	$-0.175049\pi$
$37$	10.3718	1.70512	0.852561	+	0.522629i	$0.175049\pi$
$38$	−1.50010	−0.243349
$39$	−0.178635	−0.0286045
$40$	3.28191	0.518915
$41$	−2.05162	−0.320409	−0.160204	−	0.987084i	$-0.551215\pi$
$41$	−2.05162	−0.320409	−0.160204	+	0.987084i	$0.551215\pi$
$42$	0.0460830	0.00711076
$43$	−9.84489	−1.50133	−0.750666	−	0.660682i	$-0.770267\pi$
$43$	−9.84489	−1.50133	−0.750666	+	0.660682i	$0.770267\pi$
$44$	−3.80685	−0.573904
$45$	9.83875	1.46667
$46$	−3.61335	−0.532759
$47$	−4.07388	−0.594237	−0.297118	−	0.954841i	$-0.596026\pi$
$47$	−4.07388	−0.594237	−0.297118	+	0.954841i	$0.596026\pi$
$48$	−0.0460830	−0.00665151
$49$	1.00000	0.142857
$50$	−5.77092	−0.816131
$51$	−0.00524656	−0.000734665 0
$52$	3.87638	0.537557
$53$	7.94429	1.09123	0.545616	−	0.838035i	$-0.316296\pi$
$53$	7.94429	1.09123	0.545616	+	0.838035i	$0.316296\pi$
$54$	−0.276400	−0.0376133
$55$	12.4937	1.68465
$56$	−1.00000	−0.133631
$57$	−0.0691293	−0.00915640
$58$	3.72146	0.488652
$59$	−4.96245	−0.646055	−0.323028	−	0.946390i	$-0.604701\pi$
$59$	−4.96245	−0.646055	−0.323028	+	0.946390i	$0.604701\pi$
$60$	0.151240	0.0195250
$61$	13.8750	1.77652	0.888258	−	0.459345i	$-0.151916\pi$
$61$	13.8750	1.77652	0.888258	+	0.459345i	$0.151916\pi$
$62$	1.40212	0.178070
$63$	−2.99788	−0.377697
$64$	1.00000	0.125000
$65$	−12.7219	−1.57796
$66$	−0.175431	−0.0215941
$67$	7.36362	0.899610	0.449805	−	0.893127i	$-0.351493\pi$
$67$	7.36362	0.899610	0.449805	+	0.893127i	$0.351493\pi$
$68$	0.113850	0.0138064
$69$	−0.166514	−0.0200459
$70$	3.28191	0.392263
$71$	3.23758	0.384230	0.192115	−	0.981372i	$-0.438465\pi$
$71$	3.23758	0.384230	0.192115	+	0.981372i	$0.438465\pi$
$72$	2.99788	0.353303
$73$	−7.93538	−0.928766	−0.464383	−	0.885634i	$-0.653724\pi$
$73$	−7.93538	−0.928766	−0.464383	+	0.885634i	$0.653724\pi$
$74$	−10.3718	−1.20570
$75$	−0.265941	−0.0307083
$76$	1.50010	0.172074
$77$	−3.80685	−0.433830
$78$	0.178635	0.0202264
$79$	16.6194	1.86983	0.934913	−	0.354877i	$-0.115477\pi$
$79$	16.6194	1.86983	0.934913	+	0.354877i	$0.115477\pi$
$80$	−3.28191	−0.366928
$81$	8.98089	0.997877
$82$	2.05162	0.226563
$83$	−6.41067	−0.703662	−0.351831	−	0.936063i	$-0.614441\pi$
$83$	−6.41067	−0.703662	−0.351831	+	0.936063i	$0.614441\pi$
$84$	−0.0460830	−0.00502807
$85$	−0.373646	−0.0405276
$86$	9.84489	1.06160
$87$	0.171496	0.0183863
$88$	3.80685	0.405811
$89$	9.78102	1.03679	0.518393	−	0.855142i	$-0.326530\pi$
$89$	9.78102	1.03679	0.518393	+	0.855142i	$0.326530\pi$
$90$	−9.83875	−1.03710
$91$	3.87638	0.406355
$92$	3.61335	0.376717
$93$	0.0646141	0.00670017
$94$	4.07388	0.420189
$95$	−4.92320	−0.505110
$96$	0.0460830	0.00470333
$97$	−17.1572	−1.74205	−0.871023	−	0.491242i	$-0.836543\pi$
$97$	−17.1572	−1.74205	−0.871023	+	0.491242i	$0.836543\pi$
$98$	−1.00000	−0.101015
$99$	11.4125	1.14699
$100$	5.77092	0.577092
$101$	7.48362	0.744648	0.372324	−	0.928103i	$-0.378561\pi$
$101$	7.48362	0.744648	0.372324	+	0.928103i	$0.378561\pi$
$102$	0.00524656	0.000519487 0
$103$	8.23256	0.811178	0.405589	−	0.914055i	$-0.367066\pi$
$103$	8.23256	0.811178	0.405589	+	0.914055i	$0.367066\pi$
$104$	−3.87638	−0.380110
$105$	0.151240	0.0147595
$106$	−7.94429	−0.771617
$107$	−2.45620	−0.237450	−0.118725	−	0.992927i	$-0.537881\pi$
$107$	−2.45620	−0.237450	−0.118725	+	0.992927i	$0.537881\pi$
$108$	0.276400	0.0265966
$109$	−4.49054	−0.430116	−0.215058	−	0.976601i	$-0.568994\pi$
$109$	−4.49054	−0.430116	−0.215058	+	0.976601i	$0.568994\pi$
$110$	−12.4937	−1.19123
$111$	−0.477966	−0.0453665
$112$	1.00000	0.0944911
$113$	−0.490530	−0.0461452	−0.0230726	−	0.999734i	$-0.507345\pi$
$113$	−0.490530	−0.0461452	−0.0230726	+	0.999734i	$0.507345\pi$
$114$	0.0691293	0.00647455
$115$	−11.8587	−1.10583
$116$	−3.72146	−0.345529
$117$	−11.6209	−1.07435
$118$	4.96245	0.456830
$119$	0.113850	0.0104366
$120$	−0.151240	−0.0138063
$121$	3.49208	0.317462
$122$	−13.8750	−1.25619
$123$	0.0945446	0.00852480
$124$	−1.40212	−0.125914
$125$	−2.53008	−0.226298
$126$	2.99788	0.267072
$127$	−12.3150	−1.09278	−0.546392	−	0.837530i	$-0.683999\pi$
$127$	−12.3150	−1.09278	−0.546392	+	0.837530i	$0.683999\pi$
$128$	−1.00000	−0.0883883
$129$	0.453682	0.0399445
$130$	12.7219	1.11579
$131$	−15.7438	−1.37554	−0.687771	−	0.725928i	$-0.741411\pi$
$131$	−15.7438	−1.37554	−0.687771	+	0.725928i	$0.741411\pi$
$132$	0.175431	0.0152693
$133$	1.50010	0.130075
$134$	−7.36362	−0.636120
$135$	−0.907120	−0.0780725
$136$	−0.113850	−0.00976257
$137$	−3.69328	−0.315538	−0.157769	−	0.987476i	$-0.550430\pi$
$137$	−3.69328	−0.315538	−0.157769	+	0.987476i	$0.550430\pi$
$138$	0.166514	0.0141746
$139$	16.1494	1.36978	0.684888	−	0.728648i	$-0.259851\pi$
$139$	16.1494	1.36978	0.684888	+	0.728648i	$0.259851\pi$
$140$	−3.28191	−0.277372
$141$	0.187737	0.0158103
$142$	−3.23758	−0.271692
$143$	−14.7568	−1.23402
$144$	−2.99788	−0.249823
$145$	12.2135	1.01428
$146$	7.93538	0.656737
$147$	−0.0460830	−0.00380086
$148$	10.3718	0.852561
$149$	4.92696	0.403632	0.201816	−	0.979423i	$-0.435316\pi$
$149$	4.92696	0.403632	0.201816	+	0.979423i	$0.435316\pi$
$150$	0.265941	0.0217140
$151$	−14.0859	−1.14630	−0.573148	−	0.819452i	$-0.694278\pi$
$151$	−14.0859	−1.14630	−0.573148	+	0.819452i	$0.694278\pi$
$152$	−1.50010	−0.121674
$153$	−0.341309	−0.0275932
$154$	3.80685	0.306764
$155$	4.60164	0.369613
$156$	−0.178635	−0.0143023
$157$	4.41549	0.352394	0.176197	−	0.984355i	$-0.443620\pi$
$157$	4.41549	0.352394	0.176197	+	0.984355i	$0.443620\pi$
$158$	−16.6194	−1.32217
$159$	−0.366097	−0.0290334
$160$	3.28191	0.259458
$161$	3.61335	0.284772
$162$	−8.98089	−0.705605
$163$	−18.8347	−1.47525	−0.737625	−	0.675211i	$-0.764053\pi$
$163$	−18.8347	−1.47525	−0.737625	+	0.675211i	$0.764053\pi$
$164$	−2.05162	−0.160204
$165$	−0.575748	−0.0448219
$166$	6.41067	0.497564
$167$	17.9102	1.38593	0.692966	−	0.720971i	$-0.256304\pi$
$167$	17.9102	1.38593	0.692966	+	0.720971i	$0.256304\pi$
$168$	0.0460830	0.00355538
$169$	2.02630	0.155869
$170$	0.373646	0.0286573
$171$	−4.49712	−0.343904
$172$	−9.84489	−0.750666
$173$	12.2738	0.933161	0.466580	−	0.884479i	$-0.345486\pi$
$173$	12.2738	0.933161	0.466580	+	0.884479i	$0.345486\pi$
$174$	−0.171496	−0.0130011
$175$	5.77092	0.436240
$176$	−3.80685	−0.286952
$177$	0.228684	0.0171890
$178$	−9.78102	−0.733119
$179$	−11.8458	−0.885393	−0.442697	−	0.896671i	$-0.645978\pi$
$179$	−11.8458	−0.885393	−0.442697	+	0.896671i	$0.645978\pi$
$180$	9.83875	0.733337
$181$	−25.4299	−1.89019	−0.945096	−	0.326794i	$-0.894032\pi$
$181$	−25.4299	−1.89019	−0.945096	+	0.326794i	$0.894032\pi$
$182$	−3.87638	−0.287336
$183$	−0.639403	−0.0472661
$184$	−3.61335	−0.266379
$185$	−34.0394	−2.50263
$186$	−0.0646141	−0.00473773
$187$	−0.433410	−0.0316941
$188$	−4.07388	−0.297118
$189$	0.276400	0.0201052
$190$	4.92320	0.357167
$191$	2.65278	0.191948	0.0959742	−	0.995384i	$-0.469403\pi$
$191$	2.65278	0.191948	0.0959742	+	0.995384i	$0.469403\pi$
$192$	−0.0460830	−0.00332576
$193$	1.10394	0.0794631	0.0397315	−	0.999210i	$-0.487350\pi$
$193$	1.10394	0.0794631	0.0397315	+	0.999210i	$0.487350\pi$
$194$	17.1572	1.23181
$195$	0.586264	0.0419832
$196$	1.00000	0.0714286
$197$	−20.9735	−1.49430	−0.747151	−	0.664654i	$-0.768579\pi$
$197$	−20.9735	−1.49430	−0.747151	+	0.664654i	$0.768579\pi$
$198$	−11.4125	−0.811048
$199$	−7.91939	−0.561391	−0.280695	−	0.959797i	$-0.590565\pi$
$199$	−7.91939	−0.561391	−0.280695	+	0.959797i	$0.590565\pi$
$200$	−5.77092	−0.408066
$201$	−0.339338	−0.0239351
$202$	−7.48362	−0.526546
$203$	−3.72146	−0.261195
$204$	−0.00524656	−0.000367333 0
$205$	6.73321	0.470268
$206$	−8.23256	−0.573590
$207$	−10.8324	−0.752902
$208$	3.87638	0.268778
$209$	−5.71066	−0.395015
$210$	−0.151240	−0.0104366
$211$	2.44592	0.168384	0.0841922	−	0.996450i	$-0.473169\pi$
$211$	2.44592	0.168384	0.0841922	+	0.996450i	$0.473169\pi$
$212$	7.94429	0.545616
$213$	−0.149197	−0.0102228
$214$	2.45620	0.167902
$215$	32.3100	2.20353
$216$	−0.276400	−0.0188067
$217$	−1.40212	−0.0951823
$218$	4.49054	0.304138
$219$	0.365686	0.0247108
$220$	12.4937	0.842326
$221$	0.441326	0.0296868
$222$	0.477966	0.0320790
$223$	−22.4435	−1.50293	−0.751464	−	0.659774i	$-0.770652\pi$
$223$	−22.4435	−1.50293	−0.751464	+	0.659774i	$0.770652\pi$
$224$	−1.00000	−0.0668153
$225$	−17.3005	−1.15337
$226$	0.490530	0.0326296
$227$	−14.5830	−0.967910	−0.483955	−	0.875093i	$-0.660800\pi$
$227$	−14.5830	−0.967910	−0.483955	+	0.875093i	$0.660800\pi$
$228$	−0.0691293	−0.00457820
$229$	17.1702	1.13464	0.567319	−	0.823498i	$-0.307981\pi$
$229$	17.1702	1.13464	0.567319	+	0.823498i	$0.307981\pi$
$230$	11.8587	0.781938
$231$	0.175431	0.0115425
$232$	3.72146	0.244326
$233$	−14.8047	−0.969889	−0.484945	−	0.874545i	$-0.661160\pi$
$233$	−14.8047	−0.969889	−0.484945	+	0.874545i	$0.661160\pi$
$234$	11.6209	0.759682
$235$	13.3701	0.872169
$236$	−4.96245	−0.323028
$237$	−0.765871	−0.0497487
$238$	−0.113850	−0.00737981
$239$	1.45274	0.0939702	0.0469851	−	0.998896i	$-0.485039\pi$
$239$	1.45274	0.0939702	0.0469851	+	0.998896i	$0.485039\pi$
$240$	0.151240	0.00976251
$241$	17.0045	1.09536	0.547678	−	0.836689i	$-0.315512\pi$
$241$	17.0045	1.09536	0.547678	+	0.836689i	$0.315512\pi$
$242$	−3.49208	−0.224479
$243$	−1.24307	−0.0797428
$244$	13.8750	0.888258
$245$	−3.28191	−0.209673
$246$	−0.0945446	−0.00602795
$247$	5.81497	0.369997
$248$	1.40212	0.0890349
$249$	0.295423	0.0187217
$250$	2.53008	0.160017
$251$	2.97200	0.187591	0.0937954	−	0.995591i	$-0.470100\pi$
$251$	2.97200	0.187591	0.0937954	+	0.995591i	$0.470100\pi$
$252$	−2.99788	−0.188848
$253$	−13.7555	−0.864798
$254$	12.3150	0.772714
$255$	0.0172187	0.00107828
$256$	1.00000	0.0625000
$257$	−6.37019	−0.397362	−0.198681	−	0.980064i	$-0.563666\pi$
$257$	−6.37019	−0.397362	−0.198681	+	0.980064i	$0.563666\pi$
$258$	−0.453682	−0.0282450
$259$	10.3718	0.644475
$260$	−12.7219	−0.788979
$261$	11.1565	0.690569
$262$	15.7438	0.972655
$263$	29.7354	1.83356	0.916781	−	0.399390i	$-0.130778\pi$
$263$	29.7354	1.83356	0.916781	+	0.399390i	$0.130778\pi$
$264$	−0.175431	−0.0107970
$265$	−26.0724	−1.60162
$266$	−1.50010	−0.0919772
$267$	−0.450739	−0.0275848
$268$	7.36362	0.449805
$269$	−21.4865	−1.31006	−0.655028	−	0.755604i	$-0.727343\pi$
$269$	−21.4865	−1.31006	−0.655028	+	0.755604i	$0.727343\pi$
$270$	0.907120	0.0552056
$271$	10.4450	0.634489	0.317245	−	0.948344i	$-0.397242\pi$
$271$	10.4450	0.634489	0.317245	+	0.948344i	$0.397242\pi$
$272$	0.113850	0.00690318
$273$	−0.178635	−0.0108115
$274$	3.69328	0.223119
$275$	−21.9690	−1.32478
$276$	−0.166514	−0.0100230
$277$	−10.3062	−0.619240	−0.309620	−	0.950860i	$-0.600202\pi$
$277$	−10.3062	−0.619240	−0.309620	+	0.950860i	$0.600202\pi$
$278$	−16.1494	−0.968578
$279$	4.20339	0.251650
$280$	3.28191	0.196132
$281$	−1.74237	−0.103941	−0.0519705	−	0.998649i	$-0.516550\pi$
$281$	−1.74237	−0.103941	−0.0519705	+	0.998649i	$0.516550\pi$
$282$	−0.187737	−0.0111796
$283$	10.9550	0.651206	0.325603	−	0.945507i	$-0.394433\pi$
$283$	10.9550	0.651206	0.325603	+	0.945507i	$0.394433\pi$
$284$	3.23758	0.192115
$285$	0.226876	0.0134390
$286$	14.7568	0.872586
$287$	−2.05162	−0.121103
$288$	2.99788	0.176652
$289$	−16.9870	−0.999238
$290$	−12.2135	−0.717201
$291$	0.790654	0.0463490
$292$	−7.93538	−0.464383
$293$	−11.8687	−0.693379	−0.346690	−	0.937980i	$-0.612694\pi$
$293$	−11.8687	−0.693379	−0.346690	+	0.937980i	$0.612694\pi$
$294$	0.0460830	0.00268762
$295$	16.2863	0.948224
$296$	−10.3718	−0.602851
$297$	−1.05221	−0.0610556
$298$	−4.92696	−0.285411
$299$	14.0067	0.810028
$300$	−0.265941	−0.0153541
$301$	−9.84489	−0.567450
$302$	14.0859	0.810553
$303$	−0.344868	−0.0198121
$304$	1.50010	0.0860368
$305$	−45.5366	−2.60742
$306$	0.341309	0.0195113
$307$	−20.8919	−1.19236	−0.596181	−	0.802850i	$-0.703316\pi$
$307$	−20.8919	−1.19236	−0.596181	+	0.802850i	$0.703316\pi$
$308$	−3.80685	−0.216915
$309$	−0.379381	−0.0215822
$310$	−4.60164	−0.261356
$311$	−0.483915	−0.0274403	−0.0137202	−	0.999906i	$-0.504367\pi$
$311$	−0.483915	−0.0274403	−0.0137202	+	0.999906i	$0.504367\pi$
$312$	0.178635	0.0101132
$313$	−13.4971	−0.762900	−0.381450	−	0.924390i	$-0.624575\pi$
$313$	−13.4971	−0.762900	−0.381450	+	0.924390i	$0.624575\pi$
$314$	−4.41549	−0.249180
$315$	9.83875	0.554351
$316$	16.6194	0.934913
$317$	14.8881	0.836198	0.418099	−	0.908402i	$-0.362697\pi$
$317$	14.8881	0.836198	0.418099	+	0.908402i	$0.362697\pi$
$318$	0.366097	0.0205297
$319$	14.1670	0.793201
$320$	−3.28191	−0.183464
$321$	0.113189	0.00631760
$322$	−3.61335	−0.201364
$323$	0.170787	0.00950285
$324$	8.98089	0.498938
$325$	22.3703	1.24088
$326$	18.8347	1.04316
$327$	0.206938	0.0114437
$328$	2.05162	0.113282
$329$	−4.07388	−0.224600
$330$	0.575748	0.0316939
$331$	−9.15885	−0.503416	−0.251708	−	0.967803i	$-0.580992\pi$
$331$	−9.15885	−0.503416	−0.251708	+	0.967803i	$0.580992\pi$
$332$	−6.41067	−0.351831
$333$	−31.0935	−1.70391
$334$	−17.9102	−0.980001
$335$	−24.1667	−1.32037
$336$	−0.0460830	−0.00251403
$337$	15.5716	0.848237	0.424119	−	0.905607i	$-0.360584\pi$
$337$	15.5716	0.848237	0.424119	+	0.905607i	$0.360584\pi$
$338$	−2.02630	−0.110216
$339$	0.0226051	0.00122774
$340$	−0.373646	−0.0202638
$341$	5.33767	0.289051
$342$	4.49712	0.243177
$343$	1.00000	0.0539949
$344$	9.84489	0.530801
$345$	0.546483	0.0294217
$346$	−12.2738	−0.659844
$347$	−24.1538	−1.29664	−0.648322	−	0.761366i	$-0.724529\pi$
$347$	−24.1538	−1.29664	−0.648322	+	0.761366i	$0.724529\pi$
$348$	0.171496	0.00919316
$349$	−26.2847	−1.40699	−0.703494	−	0.710701i	$-0.748378\pi$
$349$	−26.2847	−1.40699	−0.703494	+	0.710701i	$0.748378\pi$
$350$	−5.77092	−0.308469
$351$	1.07143	0.0571888
$352$	3.80685	0.202906
$353$	−24.0772	−1.28150	−0.640750	−	0.767750i	$-0.721376\pi$
$353$	−24.0772	−1.28150	−0.640750	+	0.767750i	$0.721376\pi$
$354$	−0.228684	−0.0121544
$355$	−10.6254	−0.563939
$356$	9.78102	0.518393
$357$	−0.00524656	−0.000277677 0
$358$	11.8458	0.626068
$359$	−4.47015	−0.235925	−0.117963	−	0.993018i	$-0.537636\pi$
$359$	−4.47015	−0.235925	−0.117963	+	0.993018i	$0.537636\pi$
$360$	−9.83875	−0.518548
$361$	−16.7497	−0.881563
$362$	25.4299	1.33657
$363$	−0.160926	−0.00844640
$364$	3.87638	0.203177
$365$	26.0432	1.36316
$366$	0.639403	0.0334222
$367$	1.48228	0.0773743	0.0386872	−	0.999251i	$-0.487682\pi$
$367$	1.48228	0.0773743	0.0386872	+	0.999251i	$0.487682\pi$
$368$	3.61335	0.188359
$369$	6.15049	0.320182
$370$	34.0394	1.76963
$371$	7.94429	0.412447
$372$	0.0646141	0.00335008
$373$	9.39778	0.486599	0.243299	−	0.969951i	$-0.421770\pi$
$373$	9.39778	0.486599	0.243299	+	0.969951i	$0.421770\pi$
$374$	0.433410	0.0224111
$375$	0.116594	0.00602088
$376$	4.07388	0.210094
$377$	−14.4258	−0.742966
$378$	−0.276400	−0.0142165
$379$	−6.64876	−0.341524	−0.170762	−	0.985312i	$-0.554623\pi$
$379$	−6.64876	−0.341524	−0.170762	+	0.985312i	$0.554623\pi$
$380$	−4.92320	−0.252555
$381$	0.567514	0.0290746
$382$	−2.65278	−0.135728
$383$	−10.1689	−0.519608	−0.259804	−	0.965661i	$-0.583658\pi$
$383$	−10.1689	−0.519608	−0.259804	+	0.965661i	$0.583658\pi$
$384$	0.0460830	0.00235166
$385$	12.4937	0.636739
$386$	−1.10394	−0.0561889
$387$	29.5138	1.50027
$388$	−17.1572	−0.871023
$389$	13.0287	0.660580	0.330290	−	0.943880i	$-0.392854\pi$
$389$	13.0287	0.660580	0.330290	+	0.943880i	$0.392854\pi$
$390$	−0.586264	−0.0296866
$391$	0.411380	0.0208044
$392$	−1.00000	−0.0505076
$393$	0.725522	0.0365977
$394$	20.9735	1.05663
$395$	−54.5433	−2.74437
$396$	11.4125	0.573497
$397$	1.61895	0.0812525	0.0406263	−	0.999174i	$-0.487065\pi$
$397$	1.61895	0.0812525	0.0406263	+	0.999174i	$0.487065\pi$
$398$	7.91939	0.396963
$399$	−0.0691293	−0.00346079
$400$	5.77092	0.288546
$401$	5.50786	0.275049	0.137525	−	0.990498i	$-0.456085\pi$
$401$	5.50786	0.275049	0.137525	+	0.990498i	$0.456085\pi$
$402$	0.339338	0.0169246
$403$	−5.43516	−0.270745
$404$	7.48362	0.372324
$405$	−29.4745	−1.46460
$406$	3.72146	0.184693
$407$	−39.4840	−1.95715
$408$	0.00524656	0.000259743 0
$409$	−9.55410	−0.472420	−0.236210	−	0.971702i	$-0.575905\pi$
$409$	−9.55410	−0.472420	−0.236210	+	0.971702i	$0.575905\pi$
$410$	−6.73321	−0.332530
$411$	0.170197	0.00839522
$412$	8.23256	0.405589
$413$	−4.96245	−0.244186
$414$	10.8324	0.532382
$415$	21.0392	1.03278
$416$	−3.87638	−0.190055
$417$	−0.744214	−0.0364443
$418$	5.71066	0.279318
$419$	21.4467	1.04774	0.523870	−	0.851798i	$-0.324488\pi$
$419$	21.4467	1.04774	0.523870	+	0.851798i	$0.324488\pi$
$420$	0.151240	0.00737977
$421$	30.4174	1.48245	0.741227	−	0.671255i	$-0.234244\pi$
$421$	30.4174	1.48245	0.741227	+	0.671255i	$0.234244\pi$
$422$	−2.44592	−0.119066
$423$	12.2130	0.593816
$424$	−7.94429	−0.385809
$425$	0.657020	0.0318702
$426$	0.149197	0.00722864
$427$	13.8750	0.671460
$428$	−2.45620	−0.118725
$429$	0.680037	0.0328325
$430$	−32.3100	−1.55813
$431$	1.00000	0.0481683
$431$	1.00000	0.0481683
$432$	0.276400	0.0132983
$433$	−12.4822	−0.599856	−0.299928	−	0.953962i	$-0.596963\pi$
$433$	−12.4822	−0.599856	−0.299928	+	0.953962i	$0.596963\pi$
$434$	1.40212	0.0673041
$435$	−0.562834	−0.0269858
$436$	−4.49054	−0.215058
$437$	5.42039	0.259293
$438$	−0.365686	−0.0174732
$439$	−12.9526	−0.618196	−0.309098	−	0.951030i	$-0.600027\pi$
$439$	−12.9526	−0.618196	−0.309098	+	0.951030i	$0.600027\pi$
$440$	−12.4937	−0.595615
$441$	−2.99788	−0.142756
$442$	−0.441326	−0.0209917
$443$	38.4433	1.82650	0.913248	−	0.407405i	$-0.133566\pi$
$443$	38.4433	1.82650	0.913248	+	0.407405i	$0.133566\pi$
$444$	−0.477966	−0.0226833
$445$	−32.1004	−1.52171
$446$	22.4435	1.06273
$447$	−0.227049	−0.0107391
$448$	1.00000	0.0472456
$449$	−32.2096	−1.52007	−0.760033	−	0.649885i	$-0.774817\pi$
$449$	−32.2096	−1.52007	−0.760033	+	0.649885i	$0.774817\pi$
$450$	17.3005	0.815553
$451$	7.81019	0.367767
$452$	−0.490530	−0.0230726
$453$	0.649122	0.0304984
$454$	14.5830	0.684415
$455$	−12.7219	−0.596412
$456$	0.0691293	0.00323728
$457$	6.25121	0.292419	0.146210	−	0.989254i	$-0.453293\pi$
$457$	6.25121	0.292419	0.146210	+	0.989254i	$0.453293\pi$
$458$	−17.1702	−0.802310
$459$	0.0314682	0.00146881
$460$	−11.8587	−0.552913
$461$	−3.95160	−0.184044	−0.0920222	−	0.995757i	$-0.529333\pi$
$461$	−3.95160	−0.184044	−0.0920222	+	0.995757i	$0.529333\pi$
$462$	−0.175431	−0.00816179
$463$	−22.1613	−1.02992	−0.514961	−	0.857213i	$-0.672194\pi$
$463$	−22.1613	−1.02992	−0.514961	+	0.857213i	$0.672194\pi$
$464$	−3.72146	−0.172764
$465$	−0.212057	−0.00983393
$466$	14.8047	0.685815
$467$	−30.8457	−1.42737	−0.713684	−	0.700468i	$-0.752975\pi$
$467$	−30.8457	−1.42737	−0.713684	+	0.700468i	$0.752975\pi$
$468$	−11.6209	−0.537176
$469$	7.36362	0.340021
$470$	−13.3701	−0.616717
$471$	−0.203479	−0.00937582
$472$	4.96245	0.228415
$473$	37.4780	1.72324
$474$	0.765871	0.0351776
$475$	8.65697	0.397209
$476$	0.113850	0.00521832
$477$	−23.8160	−1.09046
$478$	−1.45274	−0.0664470
$479$	21.9363	1.00229	0.501147	−	0.865362i	$-0.332912\pi$
$479$	21.9363	1.00229	0.501147	+	0.865362i	$0.332912\pi$
$480$	−0.151240	−0.00690314
$481$	40.2052	1.83320
$482$	−17.0045	−0.774534
$483$	−0.166514	−0.00757665
$484$	3.49208	0.158731
$485$	56.3083	2.55683
$486$	1.24307	0.0563867
$487$	6.94685	0.314792	0.157396	−	0.987536i	$-0.449690\pi$
$487$	6.94685	0.314792	0.157396	+	0.987536i	$0.449690\pi$
$488$	−13.8750	−0.628093
$489$	0.867961	0.0392506
$490$	3.28191	0.148261
$491$	−21.7549	−0.981783	−0.490891	−	0.871221i	$-0.663329\pi$
$491$	−21.7549	−0.981783	−0.490891	+	0.871221i	$0.663329\pi$
$492$	0.0945446	0.00426240
$493$	−0.423689	−0.0190820
$494$	−5.81497	−0.261628
$495$	−37.4546	−1.68346
$496$	−1.40212	−0.0629572
$497$	3.23758	0.145225
$498$	−0.295423	−0.0132382
$499$	−29.0962	−1.30253	−0.651263	−	0.758852i	$-0.725760\pi$
$499$	−29.0962	−1.30253	−0.651263	+	0.758852i	$0.725760\pi$
$500$	−2.53008	−0.113149
$501$	−0.825355	−0.0368741
$502$	−2.97200	−0.132647
$503$	−31.1978	−1.39104	−0.695521	−	0.718505i	$-0.744827\pi$
$503$	−31.1978	−1.39104	−0.695521	+	0.718505i	$0.744827\pi$
$504$	2.99788	0.133536
$505$	−24.5605	−1.09293
$506$	13.7555	0.611505
$507$	−0.0933779	−0.00414706
$508$	−12.3150	−0.546392
$509$	3.32173	0.147233	0.0736166	−	0.997287i	$-0.476546\pi$
$509$	3.32173	0.147233	0.0736166	+	0.997287i	$0.476546\pi$
$510$	−0.0172187	−0.000762458 0
$511$	−7.93538	−0.351041
$512$	−1.00000	−0.0441942
$513$	0.414629	0.0183063
$514$	6.37019	0.280977
$515$	−27.0185	−1.19058
$516$	0.453682	0.0199722
$517$	15.5086	0.682069
$518$	−10.3718	−0.455713
$519$	−0.565614	−0.0248277
$520$	12.7219	0.557893
$521$	−16.9666	−0.743321	−0.371661	−	0.928369i	$-0.621212\pi$
$521$	−16.9666	−0.743321	−0.371661	+	0.928369i	$0.621212\pi$
$522$	−11.1565	−0.488306
$523$	20.4529	0.894341	0.447170	−	0.894449i	$-0.352432\pi$
$523$	20.4529	0.894341	0.447170	+	0.894449i	$0.352432\pi$
$524$	−15.7438	−0.687771
$525$	−0.265941	−0.0116066
$526$	−29.7354	−1.29652
$527$	−0.159632	−0.00695368
$528$	0.175431	0.00763465
$529$	−9.94372	−0.432336
$530$	26.0724	1.13251
$531$	14.8768	0.645598
$532$	1.50010	0.0650377
$533$	−7.95284	−0.344476
$534$	0.450739	0.0195054
$535$	8.06102	0.348508
$536$	−7.36362	−0.318060
$537$	0.545888	0.0235568
$538$	21.4865	0.926350
$539$	−3.80685	−0.163972
$540$	−0.907120	−0.0390362
$541$	20.5920	0.885318	0.442659	−	0.896690i	$-0.354035\pi$
$541$	20.5920	0.885318	0.442659	+	0.896690i	$0.354035\pi$
$542$	−10.4450	−0.448652
$543$	1.17189	0.0502905
$544$	−0.113850	−0.00488129
$545$	14.7375	0.631287
$546$	0.178635	0.00764488
$547$	0.119363	0.00510361	0.00255181	−	0.999997i	$-0.499188\pi$
$547$	0.119363	0.00510361	0.00255181	+	0.999997i	$0.499188\pi$
$548$	−3.69328	−0.157769
$549$	−41.5956	−1.77526
$550$	21.9690	0.936761
$551$	−5.58258	−0.237826
$552$	0.166514	0.00708730
$553$	16.6194	0.706728
$554$	10.3062	0.437869
$555$	1.56864	0.0665851
$556$	16.1494	0.684888
$557$	−24.0483	−1.01896	−0.509479	−	0.860483i	$-0.670162\pi$
$557$	−24.0483	−1.01896	−0.509479	+	0.860483i	$0.670162\pi$
$558$	−4.20339	−0.177944
$559$	−38.1625	−1.61410
$560$	−3.28191	−0.138686
$561$	0.0199728	0.000843254 0
$562$	1.74237	0.0734973
$563$	31.5566	1.32995	0.664976	−	0.746865i	$-0.268442\pi$
$563$	31.5566	1.32995	0.664976	+	0.746865i	$0.268442\pi$
$564$	0.187737	0.00790514
$565$	1.60987	0.0677279
$566$	−10.9550	−0.460472
$567$	8.98089	0.377162
$568$	−3.23758	−0.135846
$569$	−35.9717	−1.50801	−0.754007	−	0.656867i	$-0.771881\pi$
$569$	−35.9717	−1.50801	−0.754007	+	0.656867i	$0.771881\pi$
$570$	−0.226876	−0.00950279
$571$	8.40273	0.351643	0.175822	−	0.984422i	$-0.443742\pi$
$571$	8.40273	0.351643	0.175822	+	0.984422i	$0.443742\pi$
$572$	−14.7568	−0.617012
$573$	−0.122248	−0.00510699
$574$	2.05162	0.0856328
$575$	20.8523	0.869602
$576$	−2.99788	−0.124912
$577$	36.3259	1.51227	0.756133	−	0.654418i	$-0.227086\pi$
$577$	36.3259	1.51227	0.756133	+	0.654418i	$0.227086\pi$
$578$	16.9870	0.706568
$579$	−0.0508727	−0.00211420
$580$	12.2135	0.507138
$581$	−6.41067	−0.265959
$582$	−0.790654	−0.0327737
$583$	−30.2427	−1.25252
$584$	7.93538	0.328368
$585$	38.1387	1.57684
$586$	11.8687	0.490293
$587$	15.0833	0.622553	0.311277	−	0.950319i	$-0.399243\pi$
$587$	15.0833	0.622553	0.311277	+	0.950319i	$0.399243\pi$
$588$	−0.0460830	−0.00190043
$589$	−2.10333	−0.0866662
$590$	−16.2863	−0.670496
$591$	0.966524	0.0397575
$592$	10.3718	0.426280
$593$	8.06954	0.331376	0.165688	−	0.986178i	$-0.447015\pi$
$593$	8.06954	0.331376	0.165688	+	0.986178i	$0.447015\pi$
$594$	1.05221	0.0431728
$595$	−0.373646	−0.0153180
$596$	4.92696	0.201816
$597$	0.364949	0.0149364
$598$	−14.0067	−0.572776
$599$	−29.5343	−1.20674	−0.603369	−	0.797462i	$-0.706175\pi$
$599$	−29.5343	−1.20674	−0.603369	+	0.797462i	$0.706175\pi$
$600$	0.265941	0.0108570
$601$	36.5380	1.49041	0.745207	−	0.666833i	$-0.232350\pi$
$601$	36.5380	1.49041	0.745207	+	0.666833i	$0.232350\pi$
$602$	9.84489	0.401248
$603$	−22.0752	−0.898973
$604$	−14.0859	−0.573148
$605$	−11.4607	−0.465943
$606$	0.344868	0.0140093
$607$	−5.25173	−0.213161	−0.106581	−	0.994304i	$-0.533990\pi$
$607$	−5.25173	−0.213161	−0.106581	+	0.994304i	$0.533990\pi$
$608$	−1.50010	−0.0608372
$609$	0.171496	0.00694937
$610$	45.5366	1.84372
$611$	−15.7919	−0.638872
$612$	−0.341309	−0.0137966
$613$	−7.55069	−0.304970	−0.152485	−	0.988306i	$-0.548727\pi$
$613$	−7.55069	−0.304970	−0.152485	+	0.988306i	$0.548727\pi$
$614$	20.8919	0.843127
$615$	−0.310287	−0.0125120
$616$	3.80685	0.153382
$617$	−21.3638	−0.860073	−0.430036	−	0.902812i	$-0.641499\pi$
$617$	−21.3638	−0.860073	−0.430036	+	0.902812i	$0.641499\pi$
$618$	0.379381	0.0152610
$619$	9.98479	0.401322	0.200661	−	0.979661i	$-0.435691\pi$
$619$	9.98479	0.401322	0.200661	+	0.979661i	$0.435691\pi$
$620$	4.60164	0.184806
$621$	0.998730	0.0400777
$622$	0.483915	0.0194032
$623$	9.78102	0.391868
$624$	−0.178635	−0.00715113
$625$	−20.5511	−0.822044
$626$	13.4971	0.539452
$627$	0.263165	0.0105098
$628$	4.41549	0.176197
$629$	1.18084	0.0470830
$630$	−9.83875	−0.391985
$631$	−27.4678	−1.09348	−0.546738	−	0.837304i	$-0.684131\pi$
$631$	−27.4678	−1.09348	−0.546738	+	0.837304i	$0.684131\pi$
$632$	−16.6194	−0.661083
$633$	−0.112716	−0.00448004
$634$	−14.8881	−0.591281
$635$	40.4168	1.60389
$636$	−0.366097	−0.0145167
$637$	3.87638	0.153588
$638$	−14.1670	−0.560878
$639$	−9.70586	−0.383958
$640$	3.28191	0.129729
$641$	6.37473	0.251787	0.125893	−	0.992044i	$-0.459820\pi$
$641$	6.37473	0.251787	0.125893	+	0.992044i	$0.459820\pi$
$642$	−0.113189	−0.00446722
$643$	−19.0918	−0.752907	−0.376453	−	0.926436i	$-0.622857\pi$
$643$	−19.0918	−0.752907	−0.376453	+	0.926436i	$0.622857\pi$
$644$	3.61335	0.142386
$645$	−1.48894	−0.0586271
$646$	−0.170787	−0.00671953
$647$	6.20138	0.243801	0.121901	−	0.992542i	$-0.461101\pi$
$647$	6.20138	0.243801	0.121901	+	0.992542i	$0.461101\pi$
$648$	−8.98089	−0.352803
$649$	18.8913	0.741547
$650$	−22.3703	−0.877434
$651$	0.0646141	0.00253243
$652$	−18.8347	−0.737625
$653$	6.91885	0.270756	0.135378	−	0.990794i	$-0.456775\pi$
$653$	6.91885	0.270756	0.135378	+	0.990794i	$0.456775\pi$
$654$	−0.206938	−0.00809191
$655$	51.6697	2.01890
$656$	−2.05162	−0.0801021
$657$	23.7893	0.928109
$658$	4.07388	0.158816
$659$	−7.63595	−0.297454	−0.148727	−	0.988878i	$-0.547518\pi$
$659$	−7.63595	−0.297454	−0.148727	+	0.988878i	$0.547518\pi$
$660$	−0.575748	−0.0224110
$661$	24.9975	0.972290	0.486145	−	0.873878i	$-0.338403\pi$
$661$	24.9975	0.972290	0.486145	+	0.873878i	$0.338403\pi$
$662$	9.15885	0.355969
$663$	−0.0203376	−0.000789849 0
$664$	6.41067	0.248782
$665$	−4.92320	−0.190914
$666$	31.0935	1.20485
$667$	−13.4469	−0.520667
$668$	17.9102	0.692966
$669$	1.03426	0.0399870
$670$	24.1667	0.933643
$671$	−52.8201	−2.03910
$672$	0.0460830	0.00177769
$673$	−34.4255	−1.32700	−0.663502	−	0.748174i	$-0.730931\pi$
$673$	−34.4255	−1.32700	−0.663502	+	0.748174i	$0.730931\pi$
$674$	−15.5716	−0.599794
$675$	1.59508	0.0613948
$676$	2.02630	0.0779345
$677$	3.75320	0.144247	0.0721237	−	0.997396i	$-0.477022\pi$
$677$	3.75320	0.144247	0.0721237	+	0.997396i	$0.477022\pi$
$678$	−0.0226051	−0.000868144 0
$679$	−17.1572	−0.658432
$680$	0.373646	0.0143287
$681$	0.672030	0.0257522
$682$	−5.33767	−0.204390
$683$	20.5394	0.785916	0.392958	−	0.919556i	$-0.371452\pi$
$683$	20.5394	0.785916	0.392958	+	0.919556i	$0.371452\pi$
$684$	−4.49712	−0.171952
$685$	12.1210	0.463120
$686$	−1.00000	−0.0381802
$687$	−0.791254	−0.0301882
$688$	−9.84489	−0.375333
$689$	30.7951	1.17320
$690$	−0.546483	−0.0208043
$691$	19.0933	0.726344	0.363172	−	0.931722i	$-0.381694\pi$
$691$	19.0933	0.726344	0.363172	+	0.931722i	$0.381694\pi$
$692$	12.2738	0.466580
$693$	11.4125	0.433523
$694$	24.1538	0.916866
$695$	−53.0009	−2.01044
$696$	−0.171496	−0.00650054
$697$	−0.233577	−0.00884735
$698$	26.2847	0.994891
$699$	0.682246	0.0258049
$700$	5.77092	0.218120
$701$	5.70630	0.215524	0.107762	−	0.994177i	$-0.465632\pi$
$701$	5.70630	0.215524	0.107762	+	0.994177i	$0.465632\pi$
$702$	−1.07143	−0.0404386
$703$	15.5588	0.586813
$704$	−3.80685	−0.143476
$705$	−0.616135	−0.0232050
$706$	24.0772	0.906157
$707$	7.48362	0.281450
$708$	0.228684	0.00859449
$709$	14.2238	0.534187	0.267093	−	0.963671i	$-0.413937\pi$
$709$	14.2238	0.534187	0.267093	+	0.963671i	$0.413937\pi$
$710$	10.6254	0.398765
$711$	−49.8228	−1.86850
$712$	−9.78102	−0.366559
$713$	−5.06636	−0.189737
$714$	0.00524656	0.000196348 0
$715$	48.4304	1.81119
$716$	−11.8458	−0.442697
$717$	−0.0669469	−0.00250018
$718$	4.47015	0.166824
$719$	16.4766	0.614475	0.307237	−	0.951633i	$-0.400595\pi$
$719$	16.4766	0.614475	0.307237	+	0.951633i	$0.400595\pi$
$720$	9.83875	0.366669
$721$	8.23256	0.306597
$722$	16.7497	0.623359
$723$	−0.783619	−0.0291431
$724$	−25.4299	−0.945096
$725$	−21.4762	−0.797608
$726$	0.160926	0.00597251
$727$	−32.9942	−1.22369	−0.611844	−	0.790979i	$-0.709572\pi$
$727$	−32.9942	−1.22369	−0.611844	+	0.790979i	$0.709572\pi$
$728$	−3.87638	−0.143668
$729$	−26.8854	−0.995755
$730$	−26.0432	−0.963902
$731$	−1.12084	−0.0414559
$732$	−0.639403	−0.0236330
$733$	−16.9100	−0.624586	−0.312293	−	0.949986i	$-0.601097\pi$
$733$	−16.9100	−0.624586	−0.312293	+	0.949986i	$0.601097\pi$
$734$	−1.48228	−0.0547119
$735$	0.151240	0.00557858
$736$	−3.61335	−0.133190
$737$	−28.0322	−1.03258
$738$	−6.15049	−0.226403
$739$	−24.4440	−0.899187	−0.449594	−	0.893233i	$-0.648431\pi$
$739$	−24.4440	−0.899187	−0.449594	+	0.893233i	$0.648431\pi$
$740$	−34.0394	−1.25131
$741$	−0.267971	−0.00984417
$742$	−7.94429	−0.291644
$743$	24.9076	0.913770	0.456885	−	0.889526i	$-0.348965\pi$
$743$	24.9076	0.913770	0.456885	+	0.889526i	$0.348965\pi$
$744$	−0.0646141	−0.00236887
$745$	−16.1698	−0.592416
$746$	−9.39778	−0.344077
$747$	19.2184	0.703164
$748$	−0.433410	−0.0158470
$749$	−2.45620	−0.0897476
$750$	−0.116594	−0.00425741
$751$	−20.4908	−0.747722	−0.373861	−	0.927485i	$-0.621966\pi$
$751$	−20.4908	−0.747722	−0.373861	+	0.927485i	$0.621966\pi$
$752$	−4.07388	−0.148559
$753$	−0.136959	−0.00499105
$754$	14.4258	0.525356
$755$	46.2287	1.68243
$756$	0.276400	0.0100526
$757$	−21.3751	−0.776891	−0.388445	−	0.921472i	$-0.626988\pi$
$757$	−21.3751	−0.776891	−0.388445	+	0.921472i	$0.626988\pi$
$758$	6.64876	0.241494
$759$	0.633893	0.0230089
$760$	4.92320	0.178583
$761$	−5.61308	−0.203474	−0.101737	−	0.994811i	$-0.532440\pi$
$761$	−5.61308	−0.203474	−0.101737	+	0.994811i	$0.532440\pi$
$762$	−0.567514	−0.0205589
$763$	−4.49054	−0.162569
$764$	2.65278	0.0959742
$765$	1.12014	0.0404989
$766$	10.1689	0.367418
$767$	−19.2363	−0.694583
$768$	−0.0460830	−0.00166288
$769$	−33.8882	−1.22204	−0.611020	−	0.791615i	$-0.709240\pi$
$769$	−33.8882	−1.22204	−0.611020	+	0.791615i	$0.709240\pi$
$770$	−12.4937	−0.450242
$771$	0.293558	0.0105722
$772$	1.10394	0.0397315
$773$	34.1139	1.22699	0.613495	−	0.789698i	$-0.289763\pi$
$773$	34.1139	1.22699	0.613495	+	0.789698i	$0.289763\pi$
$774$	−29.5138	−1.06085
$775$	−8.09154	−0.290657
$776$	17.1572	0.615907
$777$	−0.477966	−0.0171469
$778$	−13.0287	−0.467100
$779$	−3.07764	−0.110268
$780$	0.586264	0.0209916
$781$	−12.3250	−0.441022
$782$	−0.411380	−0.0147109
$783$	−1.02861	−0.0367596
$784$	1.00000	0.0357143
$785$	−14.4912	−0.517214
$786$	−0.725522	−0.0258785
$787$	−27.8410	−0.992425	−0.496213	−	0.868201i	$-0.665276\pi$
$787$	−27.8410	−0.992425	−0.496213	+	0.868201i	$0.665276\pi$
$788$	−20.9735	−0.747151
$789$	−1.37030	−0.0487838
$790$	54.5433	1.94056
$791$	−0.490530	−0.0174412
$792$	−11.4125	−0.405524
$793$	53.7849	1.90996
$794$	−1.61895	−0.0574542
$795$	1.20150	0.0426127
$796$	−7.91939	−0.280695
$797$	33.7351	1.19496	0.597478	−	0.801885i	$-0.296169\pi$
$797$	33.7351	1.19496	0.597478	+	0.801885i	$0.296169\pi$
$798$	0.0691293	0.00244715
$799$	−0.463812	−0.0164085
$800$	−5.77092	−0.204033
$801$	−29.3223	−1.03605
$802$	−5.50786	−0.194489
$803$	30.2088	1.06604
$804$	−0.339338	−0.0119675
$805$	−11.8587	−0.417963
$806$	5.43516	0.191445
$807$	0.990164	0.0348554
$808$	−7.48362	−0.263273
$809$	−47.6248	−1.67440	−0.837200	−	0.546897i	$-0.815809\pi$
$809$	−47.6248	−1.67440	−0.837200	+	0.546897i	$0.815809\pi$
$810$	29.4745	1.03563
$811$	−43.5506	−1.52927	−0.764634	−	0.644464i	$-0.777080\pi$
$811$	−43.5506	−1.52927	−0.764634	+	0.644464i	$0.777080\pi$
$812$	−3.72146	−0.130598
$813$	−0.481338	−0.0168813
$814$	39.4840	1.38391
$815$	61.8139	2.16525
$816$	−0.00524656	−0.000183666 0
$817$	−14.7684	−0.516679
$818$	9.55410	0.334051
$819$	−11.6209	−0.406067
$820$	6.73321	0.235134
$821$	−35.3912	−1.23516	−0.617581	−	0.786507i	$-0.711887\pi$
$821$	−35.3912	−1.23516	−0.617581	+	0.786507i	$0.711887\pi$
$822$	−0.170197	−0.00593632
$823$	4.84575	0.168912	0.0844561	−	0.996427i	$-0.473085\pi$
$823$	4.84575	0.168912	0.0844561	+	0.996427i	$0.473085\pi$
$824$	−8.23256	−0.286795
$825$	1.01240	0.0352472
$826$	4.96245	0.172666
$827$	22.6698	0.788308	0.394154	−	0.919044i	$-0.371038\pi$
$827$	22.6698	0.788308	0.394154	+	0.919044i	$0.371038\pi$
$828$	−10.8324	−0.376451
$829$	−7.22027	−0.250770	−0.125385	−	0.992108i	$-0.540017\pi$
$829$	−7.22027	−0.250770	−0.125385	+	0.992108i	$0.540017\pi$
$830$	−21.0392	−0.730282
$831$	0.474941	0.0164755
$832$	3.87638	0.134389
$833$	0.113850	0.00394468
$834$	0.744214	0.0257700
$835$	−58.7796	−2.03415
$836$	−5.71066	−0.197507
$837$	−0.387547	−0.0133956
$838$	−21.4467	−0.740864
$839$	−0.715049	−0.0246862	−0.0123431	−	0.999924i	$-0.503929\pi$
$839$	−0.715049	−0.0246862	−0.0123431	+	0.999924i	$0.503929\pi$
$840$	−0.151240	−0.00521828
$841$	−15.1507	−0.522439
$842$	−30.4174	−1.04825
$843$	0.0802936	0.00276546
$844$	2.44592	0.0841922
$845$	−6.65012	−0.228771
$846$	−12.2130	−0.419891
$847$	3.49208	0.119989
$848$	7.94429	0.272808
$849$	−0.504839	−0.0173260
$850$	−0.657020	−0.0225356
$851$	37.4771	1.28470
$852$	−0.149197	−0.00511142
$853$	−36.2065	−1.23969	−0.619844	−	0.784725i	$-0.712804\pi$
$853$	−36.2065	−1.23969	−0.619844	+	0.784725i	$0.712804\pi$
$854$	−13.8750	−0.474794
$855$	14.7591	0.504752
$856$	2.45620	0.0839512
$857$	38.2587	1.30689	0.653446	−	0.756973i	$-0.273323\pi$
$857$	38.2587	1.30689	0.653446	+	0.756973i	$0.273323\pi$
$858$	−0.680037	−0.0232161
$859$	30.5012	1.04069	0.520344	−	0.853957i	$-0.325804\pi$
$859$	30.5012	1.04069	0.520344	+	0.853957i	$0.325804\pi$
$860$	32.3100	1.10176
$861$	0.0945446	0.00322207
$862$	−1.00000	−0.0340601
$863$	28.5356	0.971362	0.485681	−	0.874136i	$-0.338572\pi$
$863$	28.5356	0.971362	0.485681	+	0.874136i	$0.338572\pi$
$864$	−0.276400	−0.00940333
$865$	−40.2815	−1.36961
$866$	12.4822	0.424162
$867$	0.782814	0.0265858
$868$	−1.40212	−0.0475912
$869$	−63.2674	−2.14620
$870$	0.562834	0.0190819
$871$	28.5442	0.967183
$872$	4.49054	0.152069
$873$	51.4351	1.74081
$874$	−5.42039	−0.183348
$875$	−2.53008	−0.0855324
$876$	0.365686	0.0123554
$877$	−5.59619	−0.188970	−0.0944850	−	0.995526i	$-0.530120\pi$
$877$	−5.59619	−0.188970	−0.0944850	+	0.995526i	$0.530120\pi$
$878$	12.9526	0.437130
$879$	0.546947	0.0184481
$880$	12.4937	0.421163
$881$	18.4198	0.620580	0.310290	−	0.950642i	$-0.399574\pi$
$881$	18.4198	0.620580	0.310290	+	0.950642i	$0.399574\pi$
$882$	2.99788	0.100944
$883$	20.9137	0.703802	0.351901	−	0.936037i	$-0.385535\pi$
$883$	20.9137	0.703802	0.351901	+	0.936037i	$0.385535\pi$
$884$	0.441326	0.0148434
$885$	−0.750521	−0.0252285
$886$	−38.4433	−1.29153
$887$	−16.8719	−0.566503	−0.283252	−	0.959046i	$-0.591413\pi$
$887$	−16.8719	−0.566503	−0.283252	+	0.959046i	$0.591413\pi$
$888$	0.477966	0.0160395
$889$	−12.3150	−0.413033
$890$	32.1004	1.07601
$891$	−34.1889	−1.14537
$892$	−22.4435	−0.751464
$893$	−6.11124	−0.204505
$894$	0.227049	0.00759366
$895$	38.8767	1.29950
$896$	−1.00000	−0.0334077
$897$	−0.645471	−0.0215516
$898$	32.2096	1.07485
$899$	5.21795	0.174028
$900$	−17.3005	−0.576683
$901$	0.904459	0.0301319
$902$	−7.81019	−0.260051
$903$	0.453682	0.0150976
$904$	0.490530	0.0163148
$905$	83.4586	2.77426
$906$	−0.649122	−0.0215656
$907$	30.7377	1.02063	0.510314	−	0.859988i	$-0.329529\pi$
$907$	30.7377	1.02063	0.510314	+	0.859988i	$0.329529\pi$
$908$	−14.5830	−0.483955
$909$	−22.4350	−0.744121
$910$	12.7219	0.421727
$911$	38.7326	1.28327	0.641634	−	0.767011i	$-0.278257\pi$
$911$	38.7326	1.28327	0.641634	+	0.767011i	$0.278257\pi$
$912$	−0.0691293	−0.00228910
$913$	24.4044	0.807669
$914$	−6.25121	−0.206772
$915$	2.09846	0.0693731
$916$	17.1702	0.567319
$917$	−15.7438	−0.519906
$918$	−0.0314682	−0.00103861
$919$	−5.65410	−0.186512	−0.0932558	−	0.995642i	$-0.529727\pi$
$919$	−5.65410	−0.186512	−0.0932558	+	0.995642i	$0.529727\pi$
$920$	11.8587	0.390969
$921$	0.962761	0.0317240
$922$	3.95160	0.130139
$923$	12.5501	0.413091
$924$	0.175431	0.00577125
$925$	59.8551	1.96802
$926$	22.1613	0.728265
$927$	−24.6802	−0.810604
$928$	3.72146	0.122163
$929$	3.43709	0.112767	0.0563836	−	0.998409i	$-0.482043\pi$
$929$	3.43709	0.112767	0.0563836	+	0.998409i	$0.482043\pi$
$930$	0.212057	0.00695364
$931$	1.50010	0.0491639
$932$	−14.8047	−0.484945
$933$	0.0223003	0.000730078 0
$934$	30.8457	1.00930
$935$	1.42241	0.0465179
$936$	11.6209	0.379841
$937$	32.6306	1.06600	0.532998	−	0.846117i	$-0.321065\pi$
$937$	32.6306	1.06600	0.532998	+	0.846117i	$0.321065\pi$
$938$	−7.36362	−0.240431
$939$	0.621986	0.0202977
$940$	13.3701	0.436085
$941$	21.4083	0.697890	0.348945	−	0.937143i	$-0.386540\pi$
$941$	21.4083	0.697890	0.348945	+	0.937143i	$0.386540\pi$
$942$	0.203479	0.00662970
$943$	−7.41320	−0.241407
$944$	−4.96245	−0.161514
$945$	−0.907120	−0.0295086
$946$	−37.4780	−1.21851
$947$	18.8346	0.612042	0.306021	−	0.952025i	$-0.401002\pi$
$947$	18.8346	0.612042	0.306021	+	0.952025i	$0.401002\pi$
$948$	−0.765871	−0.0248743
$949$	−30.7605	−0.998529
$950$	−8.65697	−0.280869
$951$	−0.686088	−0.0222479
$952$	−0.113850	−0.00368991
$953$	−5.84047	−0.189191	−0.0945957	−	0.995516i	$-0.530156\pi$
$953$	−5.84047	−0.189191	−0.0945957	+	0.995516i	$0.530156\pi$
$954$	23.8160	0.771071
$955$	−8.70618	−0.281725
$956$	1.45274	0.0469851
$957$	−0.652859	−0.0211039
$958$	−21.9363	−0.708729
$959$	−3.69328	−0.119262
$960$	0.151240	0.00488126
$961$	−29.0341	−0.936582
$962$	−40.2052	−1.29627
$963$	7.36338	0.237282
$964$	17.0045	0.547678
$965$	−3.62302	−0.116629
$966$	0.166514	0.00535750
$967$	−60.3304	−1.94010	−0.970048	−	0.242913i	$-0.921897\pi$
$967$	−60.3304	−1.94010	−0.970048	+	0.242913i	$0.921897\pi$
$968$	−3.49208	−0.112240
$969$	−0.00787038	−0.000252833 0
$970$	−56.3083	−1.80795
$971$	−6.21091	−0.199318	−0.0996588	−	0.995022i	$-0.531775\pi$
$971$	−6.21091	−0.199318	−0.0996588	+	0.995022i	$0.531775\pi$
$972$	−1.24307	−0.0398714
$973$	16.1494	0.517727
$974$	−6.94685	−0.222592
$975$	−1.03089	−0.0330149
$976$	13.8750	0.444129
$977$	15.9557	0.510467	0.255234	−	0.966879i	$-0.417848\pi$
$977$	15.9557	0.510467	0.255234	+	0.966879i	$0.417848\pi$
$978$	−0.867961	−0.0277543
$979$	−37.2349	−1.19003
$980$	−3.28191	−0.104837
$981$	13.4621	0.429811
$982$	21.7549	0.694225
$983$	10.1001	0.322143	0.161072	−	0.986943i	$-0.448505\pi$
$983$	10.1001	0.322143	0.161072	+	0.986943i	$0.448505\pi$
$984$	−0.0945446	−0.00301397
$985$	68.8332	2.19321
$986$	0.423689	0.0134930
$987$	0.187737	0.00597572
$988$	5.81497	0.184999
$989$	−35.5730	−1.13116
$990$	37.4546	1.19039
$991$	−59.2675	−1.88269	−0.941347	−	0.337439i	$-0.890439\pi$
$991$	−59.2675	−1.88269	−0.941347	+	0.337439i	$0.890439\pi$
$992$	1.40212	0.0445175
$993$	0.422067	0.0133939
$994$	−3.23758	−0.102690
$995$	25.9907	0.823961
$996$	0.295423	0.00936084
$997$	37.9171	1.20085	0.600424	−	0.799682i	$-0.294999\pi$
$997$	37.9171	1.20085	0.600424	+	0.799682i	$0.294999\pi$
$998$	29.0962	0.921024
$999$	2.86678	0.0907009

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.k.1.9	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.k.1.9	✓	20	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:	\( N \)	\(=\)	\( 6034 = 2 \cdot 7 \cdot 431 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6034.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.0460830 q^{3} +1.00000 q^{4} -3.28191 q^{5} +0.0460830 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.99788 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.0460830 q^{3} +1.00000 q^{4} -3.28191 q^{5} +0.0460830 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.99788 q^{9} +3.28191 q^{10} -3.80685 q^{11} -0.0460830 q^{12} +3.87638 q^{13} -1.00000 q^{14} +0.151240 q^{15} +1.00000 q^{16} +0.113850 q^{17} +2.99788 q^{18} +1.50010 q^{19} -3.28191 q^{20} -0.0460830 q^{21} +3.80685 q^{22} +3.61335 q^{23} +0.0460830 q^{24} +5.77092 q^{25} -3.87638 q^{26} +0.276400 q^{27} +1.00000 q^{28} -3.72146 q^{29} -0.151240 q^{30} -1.40212 q^{31} -1.00000 q^{32} +0.175431 q^{33} -0.113850 q^{34} -3.28191 q^{35} -2.99788 q^{36} +10.3718 q^{37} -1.50010 q^{38} -0.178635 q^{39} +3.28191 q^{40} -2.05162 q^{41} +0.0460830 q^{42} -9.84489 q^{43} -3.80685 q^{44} +9.83875 q^{45} -3.61335 q^{46} -4.07388 q^{47} -0.0460830 q^{48} +1.00000 q^{49} -5.77092 q^{50} -0.00524656 q^{51} +3.87638 q^{52} +7.94429 q^{53} -0.276400 q^{54} +12.4937 q^{55} -1.00000 q^{56} -0.0691293 q^{57} +3.72146 q^{58} -4.96245 q^{59} +0.151240 q^{60} +13.8750 q^{61} +1.40212 q^{62} -2.99788 q^{63} +1.00000 q^{64} -12.7219 q^{65} -0.175431 q^{66} +7.36362 q^{67} +0.113850 q^{68} -0.166514 q^{69} +3.28191 q^{70} +3.23758 q^{71} +2.99788 q^{72} -7.93538 q^{73} -10.3718 q^{74} -0.265941 q^{75} +1.50010 q^{76} -3.80685 q^{77} +0.178635 q^{78} +16.6194 q^{79} -3.28191 q^{80} +8.98089 q^{81} +2.05162 q^{82} -6.41067 q^{83} -0.0460830 q^{84} -0.373646 q^{85} +9.84489 q^{86} +0.171496 q^{87} +3.80685 q^{88} +9.78102 q^{89} -9.83875 q^{90} +3.87638 q^{91} +3.61335 q^{92} +0.0646141 q^{93} +4.07388 q^{94} -4.92320 q^{95} +0.0460830 q^{96} -17.1572 q^{97} -1.00000 q^{98} +11.4125 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 20 q^{2} + 3 q^{3} + 20 q^{4} - 3 q^{5} - 3 q^{6} + 20 q^{7} - 20 q^{8} + 13 q^{9}+O(q^{10}) \) 20 * q - 20 * q^2 + 3 * q^3 + 20 * q^4 - 3 * q^5 - 3 * q^6 + 20 * q^7 - 20 * q^8 + 13 * q^9	\( 20 q - 20 q^{2} + 3 q^{3} + 20 q^{4} - 3 q^{5} - 3 q^{6} + 20 q^{7} - 20 q^{8} + 13 q^{9} + 3 q^{10} - 8 q^{11} + 3 q^{12} - 4 q^{13} - 20 q^{14} - 25 q^{15} + 20 q^{16} + 9 q^{17} - 13 q^{18} - 14 q^{19} - 3 q^{20} + 3 q^{21} + 8 q^{22} - 23 q^{23} - 3 q^{24} + 31 q^{25} + 4 q^{26} - 21 q^{27} + 20 q^{28} - 48 q^{29} + 25 q^{30} - q^{31} - 20 q^{32} - 29 q^{33} - 9 q^{34} - 3 q^{35} + 13 q^{36} - q^{37} + 14 q^{38} - q^{39} + 3 q^{40} - 27 q^{41} - 3 q^{42} - 3 q^{43} - 8 q^{44} - 12 q^{45} + 23 q^{46} - 26 q^{47} + 3 q^{48} + 20 q^{49} - 31 q^{50} - 17 q^{51} - 4 q^{52} - 43 q^{53} + 21 q^{54} - 16 q^{55} - 20 q^{56} - 25 q^{57} + 48 q^{58} - 19 q^{59} - 25 q^{60} + 9 q^{61} + q^{62} + 13 q^{63} + 20 q^{64} - 87 q^{65} + 29 q^{66} + 32 q^{67} + 9 q^{68} - 23 q^{69} + 3 q^{70} - 63 q^{71} - 13 q^{72} + 2 q^{73} + q^{74} - 8 q^{75} - 14 q^{76} - 8 q^{77} + q^{78} - 51 q^{79} - 3 q^{80} + 4 q^{81} + 27 q^{82} - 24 q^{83} + 3 q^{84} + 31 q^{85} + 3 q^{86} - 33 q^{87} + 8 q^{88} - 35 q^{89} + 12 q^{90} - 4 q^{91} - 23 q^{92} + 17 q^{93} + 26 q^{94} - 30 q^{95} - 3 q^{96} + 5 q^{97} - 20 q^{98} - 31 q^{99}+O(q^{100}) \) 20 * q - 20 * q^2 + 3 * q^3 + 20 * q^4 - 3 * q^5 - 3 * q^6 + 20 * q^7 - 20 * q^8 + 13 * q^9 + 3 * q^10 - 8 * q^11 + 3 * q^12 - 4 * q^13 - 20 * q^14 - 25 * q^15 + 20 * q^16 + 9 * q^17 - 13 * q^18 - 14 * q^19 - 3 * q^20 + 3 * q^21 + 8 * q^22 - 23 * q^23 - 3 * q^24 + 31 * q^25 + 4 * q^26 - 21 * q^27 + 20 * q^28 - 48 * q^29 + 25 * q^30 - q^31 - 20 * q^32 - 29 * q^33 - 9 * q^34 - 3 * q^35 + 13 * q^36 - q^37 + 14 * q^38 - q^39 + 3 * q^40 - 27 * q^41 - 3 * q^42 - 3 * q^43 - 8 * q^44 - 12 * q^45 + 23 * q^46 - 26 * q^47 + 3 * q^48 + 20 * q^49 - 31 * q^50 - 17 * q^51 - 4 * q^52 - 43 * q^53 + 21 * q^54 - 16 * q^55 - 20 * q^56 - 25 * q^57 + 48 * q^58 - 19 * q^59 - 25 * q^60 + 9 * q^61 + q^62 + 13 * q^63 + 20 * q^64 - 87 * q^65 + 29 * q^66 + 32 * q^67 + 9 * q^68 - 23 * q^69 + 3 * q^70 - 63 * q^71 - 13 * q^72 + 2 * q^73 + q^74 - 8 * q^75 - 14 * q^76 - 8 * q^77 + q^78 - 51 * q^79 - 3 * q^80 + 4 * q^81 + 27 * q^82 - 24 * q^83 + 3 * q^84 + 31 * q^85 + 3 * q^86 - 33 * q^87 + 8 * q^88 - 35 * q^89 + 12 * q^90 - 4 * q^91 - 23 * q^92 + 17 * q^93 + 26 * q^94 - 30 * q^95 - 3 * q^96 + 5 * q^97 - 20 * q^98 - 31 * q^99

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