LMFDB - Embedded newform 462.2.g.d.419.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(419,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("462.419");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.g (of order $2$, degree $1$, minimal)

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:	no
Analytic conductor:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 3x^{2} + 1 $ x^4 + 3*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			419.1
Root			$0.618034i$ of defining polynomial
Character	$\chi$	$=$	462.419
Dual form			462.2.g.d.419.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(-0.618034 + 1.61803i) q^{3} -1.00000 q^{4} -1.23607 q^{5} +(1.61803 + 0.618034i) q^{6} +(2.61803 - 0.381966i) q^{7} +1.00000i q^{8} +(-2.23607 - 2.00000i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(-0.618034 + 1.61803i) q^{3} -1.00000 q^{4} -1.23607 q^{5} +(1.61803 + 0.618034i) q^{6} +(2.61803 - 0.381966i) q^{7} +1.00000i q^{8} +(-2.23607 - 2.00000i) q^{9} +1.23607i q^{10} +1.00000i q^{11} +(0.618034 - 1.61803i) q^{12} +6.00000i q^{13} +(-0.381966 - 2.61803i) q^{14} +(0.763932 - 2.00000i) q^{15} +1.00000 q^{16} -2.76393 q^{17} +(-2.00000 + 2.23607i) q^{18} +2.00000i q^{19} +1.23607 q^{20} +(-1.00000 + 4.47214i) q^{21} +1.00000 q^{22} +3.23607i q^{23} +(-1.61803 - 0.618034i) q^{24} -3.47214 q^{25} +6.00000 q^{26} +(4.61803 - 2.38197i) q^{27} +(-2.61803 + 0.381966i) q^{28} +8.47214i q^{29} +(-2.00000 - 0.763932i) q^{30} +5.23607i q^{31} -1.00000i q^{32} +(-1.61803 - 0.618034i) q^{33} +2.76393i q^{34} +(-3.23607 + 0.472136i) q^{35} +(2.23607 + 2.00000i) q^{36} +4.47214 q^{37} +2.00000 q^{38} +(-9.70820 - 3.70820i) q^{39} -1.23607i q^{40} +10.1803 q^{41} +(4.47214 + 1.00000i) q^{42} -6.94427 q^{43} -1.00000i q^{44} +(2.76393 + 2.47214i) q^{45} +3.23607 q^{46} -10.4721 q^{47} +(-0.618034 + 1.61803i) q^{48} +(6.70820 - 2.00000i) q^{49} +3.47214i q^{50} +(1.70820 - 4.47214i) q^{51} -6.00000i q^{52} +5.70820i q^{53} +(-2.38197 - 4.61803i) q^{54} -1.23607i q^{55} +(0.381966 + 2.61803i) q^{56} +(-3.23607 - 1.23607i) q^{57} +8.47214 q^{58} +1.23607 q^{59} +(-0.763932 + 2.00000i) q^{60} -12.4721i q^{61} +5.23607 q^{62} +(-6.61803 - 4.38197i) q^{63} -1.00000 q^{64} -7.41641i q^{65} +(-0.618034 + 1.61803i) q^{66} +10.4721 q^{67} +2.76393 q^{68} +(-5.23607 - 2.00000i) q^{69} +(0.472136 + 3.23607i) q^{70} -16.1803i q^{71} +(2.00000 - 2.23607i) q^{72} -8.18034i q^{73} -4.47214i q^{74} +(2.14590 - 5.61803i) q^{75} -2.00000i q^{76} +(0.381966 + 2.61803i) q^{77} +(-3.70820 + 9.70820i) q^{78} +2.76393 q^{79} -1.23607 q^{80} +(1.00000 + 8.94427i) q^{81} -10.1803i q^{82} -6.00000 q^{83} +(1.00000 - 4.47214i) q^{84} +3.41641 q^{85} +6.94427i q^{86} +(-13.7082 - 5.23607i) q^{87} -1.00000 q^{88} -4.94427 q^{89} +(2.47214 - 2.76393i) q^{90} +(2.29180 + 15.7082i) q^{91} -3.23607i q^{92} +(-8.47214 - 3.23607i) q^{93} +10.4721i q^{94} -2.47214i q^{95} +(1.61803 + 0.618034i) q^{96} +6.47214i q^{97} +(-2.00000 - 6.70820i) q^{98} +(2.00000 - 2.23607i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} - 4 q^{4} + 4 q^{5} + 2 q^{6} + 6 q^{7}+O(q^{10}) $ 4 * q + 2 * q^3 - 4 * q^4 + 4 * q^5 + 2 * q^6 + 6 * q^7	$ 4 q + 2 q^{3} - 4 q^{4} + 4 q^{5} + 2 q^{6} + 6 q^{7} - 2 q^{12} - 6 q^{14} + 12 q^{15} + 4 q^{16} - 20 q^{17} - 8 q^{18} - 4 q^{20} - 4 q^{21} + 4 q^{22} - 2 q^{24} + 4 q^{25} + 24 q^{26} + 14 q^{27} - 6 q^{28} - 8 q^{30} - 2 q^{33} - 4 q^{35} + 8 q^{38} - 12 q^{39} - 4 q^{41} + 8 q^{43} + 20 q^{45} + 4 q^{46} - 24 q^{47} + 2 q^{48} - 20 q^{51} - 14 q^{54} + 6 q^{56} - 4 q^{57} + 16 q^{58} - 4 q^{59} - 12 q^{60} + 12 q^{62} - 22 q^{63} - 4 q^{64} + 2 q^{66} + 24 q^{67} + 20 q^{68} - 12 q^{69} - 16 q^{70} + 8 q^{72} + 22 q^{75} + 6 q^{77} + 12 q^{78} + 20 q^{79} + 4 q^{80} + 4 q^{81} - 24 q^{83} + 4 q^{84} - 40 q^{85} - 28 q^{87} - 4 q^{88} + 16 q^{89} - 8 q^{90} + 36 q^{91} - 16 q^{93} + 2 q^{96} - 8 q^{98} + 8 q^{99}+O(q^{100}) $ 4 * q + 2 * q^3 - 4 * q^4 + 4 * q^5 + 2 * q^6 + 6 * q^7 - 2 * q^12 - 6 * q^14 + 12 * q^15 + 4 * q^16 - 20 * q^17 - 8 * q^18 - 4 * q^20 - 4 * q^21 + 4 * q^22 - 2 * q^24 + 4 * q^25 + 24 * q^26 + 14 * q^27 - 6 * q^28 - 8 * q^30 - 2 * q^33 - 4 * q^35 + 8 * q^38 - 12 * q^39 - 4 * q^41 + 8 * q^43 + 20 * q^45 + 4 * q^46 - 24 * q^47 + 2 * q^48 - 20 * q^51 - 14 * q^54 + 6 * q^56 - 4 * q^57 + 16 * q^58 - 4 * q^59 - 12 * q^60 + 12 * q^62 - 22 * q^63 - 4 * q^64 + 2 * q^66 + 24 * q^67 + 20 * q^68 - 12 * q^69 - 16 * q^70 + 8 * q^72 + 22 * q^75 + 6 * q^77 + 12 * q^78 + 20 * q^79 + 4 * q^80 + 4 * q^81 - 24 * q^83 + 4 * q^84 - 40 * q^85 - 28 * q^87 - 4 * q^88 + 16 * q^89 - 8 * q^90 + 36 * q^91 - 16 * q^93 + 2 * q^96 - 8 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	−0.618034	+	1.61803i	−0.356822	+	0.934172i
$3$	−0.618034	+	1.61803i	−0.356822	+	0.934172i
$4$	−1.00000			−0.500000
$5$	−1.23607			−0.552786			−0.276393	−	0.961045i	$-0.589139\pi$
$5$	−1.23607			−0.552786			−0.276393	+	0.961045i	$0.589139\pi$
$6$	1.61803	+	0.618034i	0.660560	+	0.252311i
$7$	2.61803	−	0.381966i	0.989524	−	0.144370i
$7$	2.61803	−	0.381966i	0.989524	−	0.144370i
$8$			1.00000i			0.353553i
$9$	−2.23607	−	2.00000i	−0.745356	−	0.666667i
$10$			1.23607i			0.390879i
$11$			1.00000i			0.301511i
$11$			1.00000i			0.301511i
$12$	0.618034	−	1.61803i	0.178411	−	0.467086i
$13$			6.00000i			1.66410i	0.554700	+	0.832050i	$0.312833\pi$
$13$			6.00000i			1.66410i	−0.554700	+	0.832050i	$0.687167\pi$
$14$	−0.381966	−	2.61803i	−0.102085	−	0.699699i
$15$	0.763932	−	2.00000i	0.197246	−	0.516398i
$16$	1.00000			0.250000
$17$	−2.76393			−0.670352			−0.335176	−	0.942156i	$-0.608796\pi$
$17$	−2.76393			−0.670352			−0.335176	+	0.942156i	$0.608796\pi$
$18$	−2.00000	+	2.23607i	−0.471405	+	0.527046i
$19$			2.00000i			0.458831i	0.973329	+	0.229416i	$0.0736815\pi$
$19$			2.00000i			0.458831i	−0.973329	+	0.229416i	$0.926318\pi$
$20$	1.23607			0.276393
$21$	−1.00000	+	4.47214i	−0.218218	+	0.975900i
$22$	1.00000			0.213201
$23$			3.23607i			0.674767i	0.941367	+	0.337383i	$0.109542\pi$
$23$			3.23607i			0.674767i	−0.941367	+	0.337383i	$0.890458\pi$
$24$	−1.61803	−	0.618034i	−0.330280	−	0.126156i
$25$	−3.47214			−0.694427
$26$	6.00000			1.17670
$27$	4.61803	−	2.38197i	0.888741	−	0.458410i
$28$	−2.61803	+	0.381966i	−0.494762	+	0.0721848i
$29$			8.47214i			1.57324i	0.617440	+	0.786618i	$0.288170\pi$
$29$			8.47214i			1.57324i	−0.617440	+	0.786618i	$0.711830\pi$
$30$	−2.00000	−	0.763932i	−0.365148	−	0.139474i
$31$			5.23607i			0.940426i	0.882553	+	0.470213i	$0.155823\pi$
$31$			5.23607i			0.940426i	−0.882553	+	0.470213i	$0.844177\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−1.61803	−	0.618034i	−0.281664	−	0.107586i
$34$			2.76393i			0.474010i
$35$	−3.23607	+	0.472136i	−0.546995	+	0.0798055i
$36$	2.23607	+	2.00000i	0.372678	+	0.333333i
$37$	4.47214			0.735215			0.367607	−	0.929981i	$-0.380177\pi$
$37$	4.47214			0.735215			0.367607	+	0.929981i	$0.380177\pi$
$38$	2.00000			0.324443
$39$	−9.70820	−	3.70820i	−1.55456	−	0.593788i
$40$		−	1.23607i		−	0.195440i
$41$	10.1803			1.58990			0.794951	−	0.606674i	$-0.207497\pi$
$41$	10.1803			1.58990			0.794951	+	0.606674i	$0.207497\pi$
$42$	4.47214	+	1.00000i	0.690066	+	0.154303i
$43$	−6.94427			−1.05899			−0.529496	−	0.848313i	$-0.677619\pi$
$43$	−6.94427			−1.05899			−0.529496	+	0.848313i	$0.677619\pi$
$44$		−	1.00000i		−	0.150756i
$45$	2.76393	+	2.47214i	0.412023	+	0.368524i
$46$	3.23607			0.477132
$47$	−10.4721			−1.52752			−0.763759	−	0.645501i	$-0.776648\pi$
$47$	−10.4721			−1.52752			−0.763759	+	0.645501i	$0.776648\pi$
$48$	−0.618034	+	1.61803i	−0.0892055	+	0.233543i
$49$	6.70820	−	2.00000i	0.958315	−	0.285714i
$50$			3.47214i			0.491034i
$51$	1.70820	−	4.47214i	0.239196	−	0.626224i
$52$		−	6.00000i		−	0.832050i
$53$			5.70820i			0.784082i	0.919948	+	0.392041i	$0.128231\pi$
$53$			5.70820i			0.784082i	−0.919948	+	0.392041i	$0.871769\pi$
$54$	−2.38197	−	4.61803i	−0.324145	−	0.628435i
$55$		−	1.23607i		−	0.166671i
$56$	0.381966	+	2.61803i	0.0510424	+	0.349850i
$57$	−3.23607	−	1.23607i	−0.428628	−	0.163721i
$58$	8.47214			1.11245
$59$	1.23607			0.160922			0.0804612	−	0.996758i	$-0.474361\pi$
$59$	1.23607			0.160922			0.0804612	+	0.996758i	$0.474361\pi$
$60$	−0.763932	+	2.00000i	−0.0986232	+	0.258199i
$61$		−	12.4721i		−	1.59689i	−0.602066	−	0.798447i	$-0.705655\pi$
$61$		−	12.4721i		−	1.59689i	0.602066	−	0.798447i	$-0.294345\pi$
$62$	5.23607			0.664981
$63$	−6.61803	−	4.38197i	−0.833794	−	0.552076i
$64$	−1.00000			−0.125000
$65$		−	7.41641i		−	0.919892i
$66$	−0.618034	+	1.61803i	−0.0760747	+	0.199166i
$67$	10.4721			1.27938			0.639688	−	0.768635i	$-0.279064\pi$
$67$	10.4721			1.27938			0.639688	+	0.768635i	$0.279064\pi$
$68$	2.76393			0.335176
$69$	−5.23607	−	2.00000i	−0.630349	−	0.240772i
$70$	0.472136	+	3.23607i	0.0564310	+	0.386784i
$71$		−	16.1803i		−	1.92025i	−0.279566	−	0.960127i	$-0.590191\pi$
$71$		−	16.1803i		−	1.92025i	0.279566	−	0.960127i	$-0.409809\pi$
$72$	2.00000	−	2.23607i	0.235702	−	0.263523i
$73$		−	8.18034i		−	0.957436i	−0.877969	−	0.478718i	$-0.841102\pi$
$73$		−	8.18034i		−	0.957436i	0.877969	−	0.478718i	$-0.158898\pi$
$74$		−	4.47214i		−	0.519875i
$75$	2.14590	−	5.61803i	0.247787	−	0.648715i
$76$		−	2.00000i		−	0.229416i
$77$	0.381966	+	2.61803i	0.0435291	+	0.298353i
$78$	−3.70820	+	9.70820i	−0.419871	+	1.09924i
$79$	2.76393			0.310967			0.155483	−	0.987839i	$-0.450307\pi$
$79$	2.76393			0.310967			0.155483	+	0.987839i	$0.450307\pi$
$80$	−1.23607			−0.138197
$81$	1.00000	+	8.94427i	0.111111	+	0.993808i
$82$		−	10.1803i		−	1.12423i
$83$	−6.00000			−0.658586			−0.329293	−	0.944228i	$-0.606810\pi$
$83$	−6.00000			−0.658586			−0.329293	+	0.944228i	$0.606810\pi$
$84$	1.00000	−	4.47214i	0.109109	−	0.487950i
$85$	3.41641			0.370561
$86$			6.94427i			0.748820i
$87$	−13.7082	−	5.23607i	−1.46967	−	0.561365i
$88$	−1.00000			−0.106600
$89$	−4.94427			−0.524092			−0.262046	−	0.965055i	$-0.584397\pi$
$89$	−4.94427			−0.524092			−0.262046	+	0.965055i	$0.584397\pi$
$90$	2.47214	−	2.76393i	0.260586	−	0.291344i
$91$	2.29180	+	15.7082i	0.240246	+	1.64667i
$92$		−	3.23607i		−	0.337383i
$93$	−8.47214	−	3.23607i	−0.878520	−	0.335565i
$94$			10.4721i			1.08012i
$95$		−	2.47214i		−	0.253636i
$96$	1.61803	+	0.618034i	0.165140	+	0.0630778i
$97$			6.47214i			0.657146i	0.944479	+	0.328573i	$0.106568\pi$
$97$			6.47214i			0.657146i	−0.944479	+	0.328573i	$0.893432\pi$
$98$	−2.00000	−	6.70820i	−0.202031	−	0.677631i
$99$	2.00000	−	2.23607i	0.201008	−	0.224733i
$100$	3.47214			0.347214
$101$	11.2361			1.11803			0.559015	−	0.829157i	$-0.311179\pi$
$101$	11.2361			1.11803			0.559015	+	0.829157i	$0.311179\pi$
$102$	−4.47214	−	1.70820i	−0.442807	−	0.169137i
$103$		−	3.70820i		−	0.365380i	−0.983171	−	0.182690i	$-0.941520\pi$
$103$		−	3.70820i		−	0.365380i	0.983171	−	0.182690i	$-0.0584805\pi$
$104$	−6.00000			−0.588348
$105$	1.23607	−	5.52786i	0.120628	−	0.539464i
$106$	5.70820			0.554430
$107$			8.94427i			0.864675i	0.901712	+	0.432338i	$0.142311\pi$
$107$			8.94427i			0.864675i	−0.901712	+	0.432338i	$0.857689\pi$
$108$	−4.61803	+	2.38197i	−0.444371	+	0.229205i
$109$	13.2361			1.26779			0.633893	−	0.773421i	$-0.281456\pi$
$109$	13.2361			1.26779			0.633893	+	0.773421i	$0.281456\pi$
$110$	−1.23607			−0.117854
$111$	−2.76393	+	7.23607i	−0.262341	+	0.686817i
$112$	2.61803	−	0.381966i	0.247381	−	0.0360924i
$113$			8.00000i			0.752577i	0.926503	+	0.376288i	$0.122800\pi$
$113$			8.00000i			0.752577i	−0.926503	+	0.376288i	$0.877200\pi$
$114$	−1.23607	+	3.23607i	−0.115768	+	0.303086i
$115$		−	4.00000i		−	0.373002i
$116$		−	8.47214i		−	0.786618i
$117$	12.0000	−	13.4164i	1.10940	−	1.24035i
$118$		−	1.23607i		−	0.113789i
$119$	−7.23607	+	1.05573i	−0.663329	+	0.0967784i
$120$	2.00000	+	0.763932i	0.182574	+	0.0697371i
$121$	−1.00000			−0.0909091
$122$	−12.4721			−1.12917
$123$	−6.29180	+	16.4721i	−0.567312	+	1.48524i
$124$		−	5.23607i		−	0.470213i
$125$	10.4721			0.936656
$126$	−4.38197	+	6.61803i	−0.390377	+	0.589581i
$127$	−4.29180			−0.380835			−0.190418	−	0.981703i	$-0.560984\pi$
$127$	−4.29180			−0.380835			−0.190418	+	0.981703i	$0.560984\pi$
$128$			1.00000i			0.0883883i
$129$	4.29180	−	11.2361i	0.377872	−	0.989281i
$130$	−7.41641			−0.650462
$131$	−17.4164			−1.52168			−0.760839	−	0.648940i	$-0.775212\pi$
$131$	−17.4164			−1.52168			−0.760839	+	0.648940i	$0.775212\pi$
$132$	1.61803	+	0.618034i	0.140832	+	0.0537930i
$133$	0.763932	+	5.23607i	0.0662413	+	0.454025i
$134$		−	10.4721i		−	0.904655i
$135$	−5.70820	+	2.94427i	−0.491284	+	0.253403i
$136$		−	2.76393i		−	0.237005i
$137$			2.47214i			0.211209i	0.994408	+	0.105604i	$0.0336777\pi$
$137$			2.47214i			0.211209i	−0.994408	+	0.105604i	$0.966322\pi$
$138$	−2.00000	+	5.23607i	−0.170251	+	0.445724i
$139$		−	10.0000i		−	0.848189i	−0.905618	−	0.424094i	$-0.860592\pi$
$139$		−	10.0000i		−	0.848189i	0.905618	−	0.424094i	$-0.139408\pi$
$140$	3.23607	−	0.472136i	0.273498	−	0.0399028i
$141$	6.47214	−	16.9443i	0.545052	−	1.42697i
$142$	−16.1803			−1.35782
$143$	−6.00000			−0.501745
$144$	−2.23607	−	2.00000i	−0.186339	−	0.166667i
$145$		−	10.4721i		−	0.869664i
$146$	−8.18034			−0.677010
$147$	−0.909830	+	12.0902i	−0.0750415	+	0.997180i
$148$	−4.47214			−0.367607
$149$			2.00000i			0.163846i	0.996639	+	0.0819232i	$0.0261062\pi$
$149$			2.00000i			0.163846i	−0.996639	+	0.0819232i	$0.973894\pi$
$150$	−5.61803	−	2.14590i	−0.458711	−	0.175212i
$151$	−10.1803			−0.828464			−0.414232	−	0.910171i	$-0.635950\pi$
$151$	−10.1803			−0.828464			−0.414232	+	0.910171i	$0.635950\pi$
$152$	−2.00000			−0.162221
$153$	6.18034	+	5.52786i	0.499651	+	0.446901i
$154$	2.61803	−	0.381966i	0.210967	−	0.0307797i
$155$		−	6.47214i		−	0.519854i
$156$	9.70820	+	3.70820i	0.777278	+	0.296894i
$157$		−	13.4164i		−	1.07075i	−0.844616	−	0.535373i	$-0.820171\pi$
$157$		−	13.4164i		−	1.07075i	0.844616	−	0.535373i	$-0.179829\pi$
$158$		−	2.76393i		−	0.219887i
$159$	−9.23607	−	3.52786i	−0.732468	−	0.279778i
$160$			1.23607i			0.0977198i
$161$	1.23607	+	8.47214i	0.0974158	+	0.667698i
$162$	8.94427	−	1.00000i	0.702728	−	0.0785674i
$163$	9.52786			0.746280			0.373140	−	0.927775i	$-0.378281\pi$
$163$	9.52786			0.746280			0.373140	+	0.927775i	$0.378281\pi$
$164$	−10.1803			−0.794951
$165$	2.00000	+	0.763932i	0.155700	+	0.0594720i
$166$			6.00000i			0.465690i
$167$	21.8885			1.69379			0.846893	−	0.531763i	$-0.178470\pi$
$167$	21.8885			1.69379			0.846893	+	0.531763i	$0.178470\pi$
$168$	−4.47214	−	1.00000i	−0.345033	−	0.0771517i
$169$	−23.0000			−1.76923
$170$		−	3.41641i		−	0.262027i
$171$	4.00000	−	4.47214i	0.305888	−	0.341993i
$172$	6.94427			0.529496
$173$	5.70820			0.433987			0.216993	−	0.976173i	$-0.430375\pi$
$173$	5.70820			0.433987			0.216993	+	0.976173i	$0.430375\pi$
$174$	−5.23607	+	13.7082i	−0.396945	+	1.03922i
$175$	−9.09017	+	1.32624i	−0.687152	+	0.100254i
$176$			1.00000i			0.0753778i
$177$	−0.763932	+	2.00000i	−0.0574206	+	0.150329i
$178$			4.94427i			0.370589i
$179$		−	4.94427i		−	0.369552i	−0.982781	−	0.184776i	$-0.940844\pi$
$179$		−	4.94427i		−	0.369552i	0.982781	−	0.184776i	$-0.0591560\pi$
$180$	−2.76393	−	2.47214i	−0.206011	−	0.184262i
$181$			12.4721i			0.927047i	0.886085	+	0.463523i	$0.153415\pi$
$181$			12.4721i			0.927047i	−0.886085	+	0.463523i	$0.846585\pi$
$182$	15.7082	−	2.29180i	1.16437	−	0.169879i
$183$	20.1803	+	7.70820i	1.49177	+	0.569807i
$184$	−3.23607			−0.238566
$185$	−5.52786			−0.406417
$186$	−3.23607	+	8.47214i	−0.237280	+	0.621207i
$187$		−	2.76393i		−	0.202119i
$188$	10.4721			0.763759
$189$	11.1803	−	8.00000i	0.813250	−	0.581914i
$190$	−2.47214			−0.179348
$191$			1.70820i			0.123601i	0.998089	+	0.0618006i	$0.0196843\pi$
$191$			1.70820i			0.123601i	−0.998089	+	0.0618006i	$0.980316\pi$
$192$	0.618034	−	1.61803i	0.0446028	−	0.116772i
$193$	14.9443			1.07571			0.537856	−	0.843037i	$-0.319234\pi$
$193$	14.9443			1.07571			0.537856	+	0.843037i	$0.319234\pi$
$194$	6.47214			0.464672
$195$	12.0000	+	4.58359i	0.859338	+	0.328238i
$196$	−6.70820	+	2.00000i	−0.479157	+	0.142857i
$197$			2.94427i			0.209771i	0.994484	+	0.104885i	$0.0334476\pi$
$197$			2.94427i			0.209771i	−0.994484	+	0.104885i	$0.966552\pi$
$198$	−2.23607	−	2.00000i	−0.158910	−	0.142134i
$199$		−	2.18034i		−	0.154560i	−0.997009	−	0.0772801i	$-0.975376\pi$
$199$		−	2.18034i		−	0.154560i	0.997009	−	0.0772801i	$-0.0246236\pi$
$200$		−	3.47214i		−	0.245517i
$201$	−6.47214	+	16.9443i	−0.456509	+	1.19516i
$202$		−	11.2361i		−	0.790567i
$203$	3.23607	+	22.1803i	0.227127	+	1.55675i
$204$	−1.70820	+	4.47214i	−0.119598	+	0.313112i
$205$	−12.5836			−0.878876
$206$	−3.70820			−0.258363
$207$	6.47214	−	7.23607i	0.449845	−	0.502941i
$208$			6.00000i			0.416025i
$209$	−2.00000			−0.138343
$210$	−5.52786	−	1.23607i	−0.381459	−	0.0852968i
$211$	−17.4164			−1.19899			−0.599497	−	0.800377i	$-0.704633\pi$
$211$	−17.4164			−1.19899			−0.599497	+	0.800377i	$0.704633\pi$
$212$		−	5.70820i		−	0.392041i
$213$	26.1803	+	10.0000i	1.79385	+	0.685189i
$214$	8.94427			0.611418
$215$	8.58359			0.585396
$216$	2.38197	+	4.61803i	0.162072	+	0.314217i
$217$	2.00000	+	13.7082i	0.135769	+	0.930574i
$218$		−	13.2361i		−	0.896460i
$219$	13.2361	+	5.05573i	0.894411	+	0.341634i
$220$			1.23607i			0.0833357i
$221$		−	16.5836i		−	1.11553i
$222$	7.23607	+	2.76393i	0.485653	+	0.185503i
$223$			25.5967i			1.71409i	0.515246	+	0.857043i	$0.327701\pi$
$223$			25.5967i			1.71409i	−0.515246	+	0.857043i	$0.672299\pi$
$224$	−0.381966	−	2.61803i	−0.0255212	−	0.174925i
$225$	7.76393	+	6.94427i	0.517595	+	0.462951i
$226$	8.00000			0.532152
$227$	22.0000			1.46019			0.730096	−	0.683345i	$-0.239475\pi$
$227$	22.0000			1.46019			0.730096	+	0.683345i	$0.239475\pi$
$228$	3.23607	+	1.23607i	0.214314	+	0.0818606i
$229$		−	2.00000i		−	0.132164i	−0.997814	−	0.0660819i	$-0.978950\pi$
$229$		−	2.00000i		−	0.132164i	0.997814	−	0.0660819i	$-0.0210498\pi$
$230$	−4.00000			−0.263752
$231$	−4.47214	−	1.00000i	−0.294245	−	0.0657952i
$232$	−8.47214			−0.556223
$233$			1.41641i			0.0927920i	0.998923	+	0.0463960i	$0.0147736\pi$
$233$			1.41641i			0.0927920i	−0.998923	+	0.0463960i	$0.985226\pi$
$234$	−13.4164	−	12.0000i	−0.877058	−	0.784465i
$235$	12.9443			0.844391
$236$	−1.23607			−0.0804612
$237$	−1.70820	+	4.47214i	−0.110960	+	0.290496i
$238$	1.05573	+	7.23607i	0.0684327	+	0.469045i
$239$			13.8885i			0.898375i	0.893437	+	0.449188i	$0.148287\pi$
$239$			13.8885i			0.898375i	−0.893437	+	0.449188i	$0.851713\pi$
$240$	0.763932	−	2.00000i	0.0493116	−	0.129099i
$241$			4.18034i			0.269279i	0.990895	+	0.134640i	$0.0429877\pi$
$241$			4.18034i			0.269279i	−0.990895	+	0.134640i	$0.957012\pi$
$242$			1.00000i			0.0642824i
$243$	−15.0902	−	3.90983i	−0.968035	−	0.250816i
$244$			12.4721i			0.798447i
$245$	−8.29180	+	2.47214i	−0.529743	+	0.157939i
$246$	16.4721	+	6.29180i	1.05023	+	0.401150i
$247$	−12.0000			−0.763542
$248$	−5.23607			−0.332491
$249$	3.70820	−	9.70820i	0.234998	−	0.615232i
$250$		−	10.4721i		−	0.662316i
$251$	−11.7082			−0.739015			−0.369508	−	0.929228i	$-0.620474\pi$
$251$	−11.7082			−0.739015			−0.369508	+	0.929228i	$0.620474\pi$
$252$	6.61803	+	4.38197i	0.416897	+	0.276038i
$253$	−3.23607			−0.203450
$254$			4.29180i			0.269291i
$255$	−2.11146	+	5.52786i	−0.132225	+	0.346168i
$256$	1.00000			0.0625000
$257$	16.9443			1.05695			0.528477	−	0.848947i	$-0.322763\pi$
$257$	16.9443			1.05695			0.528477	+	0.848947i	$0.322763\pi$
$258$	−11.2361	−	4.29180i	−0.699527	−	0.267196i
$259$	11.7082	−	1.70820i	0.727512	−	0.106143i
$260$			7.41641i			0.459946i
$261$	16.9443	−	18.9443i	1.04882	−	1.17262i
$262$			17.4164i			1.07599i
$263$		−	30.4721i		−	1.87899i	−0.342559	−	0.939496i	$-0.611294\pi$
$263$		−	30.4721i		−	1.87899i	0.342559	−	0.939496i	$-0.388706\pi$
$264$	0.618034	−	1.61803i	0.0380374	−	0.0995831i
$265$		−	7.05573i		−	0.433430i
$266$	5.23607	−	0.763932i	0.321044	−	0.0468397i
$267$	3.05573	−	8.00000i	0.187008	−	0.489592i
$268$	−10.4721			−0.639688
$269$	25.5967			1.56066			0.780331	−	0.625367i	$-0.215051\pi$
$269$	25.5967			1.56066			0.780331	+	0.625367i	$0.215051\pi$
$270$	2.94427	+	5.70820i	0.179183	+	0.347390i
$271$		−	10.2918i		−	0.625182i	−0.949888	−	0.312591i	$-0.898803\pi$
$271$		−	10.2918i		−	0.625182i	0.949888	−	0.312591i	$-0.101197\pi$
$272$	−2.76393			−0.167588
$273$	−26.8328	−	6.00000i	−1.62400	−	0.363137i
$274$	2.47214			0.149347
$275$		−	3.47214i		−	0.209378i
$276$	5.23607	+	2.00000i	0.315174	+	0.120386i
$277$	−1.81966			−0.109333			−0.0546664	−	0.998505i	$-0.517410\pi$
$277$	−1.81966			−0.109333			−0.0546664	+	0.998505i	$0.517410\pi$
$278$	−10.0000			−0.599760
$279$	10.4721	−	11.7082i	0.626950	−	0.700952i
$280$	−0.472136	−	3.23607i	−0.0282155	−	0.193392i
$281$		−	1.41641i		−	0.0844958i	−0.999107	−	0.0422479i	$-0.986548\pi$
$281$		−	1.41641i		−	0.0844958i	0.999107	−	0.0422479i	$-0.0134519\pi$
$282$	−16.9443	−	6.47214i	−1.00902	−	0.385410i
$283$		−	2.94427i		−	0.175019i	−0.996164	−	0.0875094i	$-0.972109\pi$
$283$		−	2.94427i		−	0.175019i	0.996164	−	0.0875094i	$-0.0278908\pi$
$284$			16.1803i			0.960127i
$285$	4.00000	+	1.52786i	0.236940	+	0.0905029i
$286$			6.00000i			0.354787i
$287$	26.6525	−	3.88854i	1.57325	−	0.229533i
$288$	−2.00000	+	2.23607i	−0.117851	+	0.131762i
$289$	−9.36068			−0.550628
$290$	−10.4721			−0.614945
$291$	−10.4721	−	4.00000i	−0.613887	−	0.234484i
$292$			8.18034i			0.478718i
$293$	4.18034			0.244218			0.122109	−	0.992517i	$-0.461034\pi$
$293$	4.18034			0.244218			0.122109	+	0.992517i	$0.461034\pi$
$294$	12.0902	+	0.909830i	0.705113	+	0.0530624i
$295$	−1.52786			−0.0889557
$296$			4.47214i			0.259938i
$297$	2.38197	+	4.61803i	0.138216	+	0.267966i
$298$	2.00000			0.115857
$299$	−19.4164			−1.12288
$300$	−2.14590	+	5.61803i	−0.123893	+	0.324357i
$301$	−18.1803	+	2.65248i	−1.04790	+	0.152886i
$302$			10.1803i			0.585813i
$303$	−6.94427	+	18.1803i	−0.398938	+	1.04443i
$304$			2.00000i			0.114708i
$305$			15.4164i			0.882741i
$306$	5.52786	−	6.18034i	0.316007	−	0.353307i
$307$			12.4721i			0.711822i	0.934520	+	0.355911i	$0.115829\pi$
$307$			12.4721i			0.711822i	−0.934520	+	0.355911i	$0.884171\pi$
$308$	−0.381966	−	2.61803i	−0.0217645	−	0.149176i
$309$	6.00000	+	2.29180i	0.341328	+	0.130376i
$310$	−6.47214			−0.367593
$311$	1.52786			0.0866372			0.0433186	−	0.999061i	$-0.486207\pi$
$311$	1.52786			0.0866372			0.0433186	+	0.999061i	$0.486207\pi$
$312$	3.70820	−	9.70820i	0.209936	−	0.549619i
$313$			8.00000i			0.452187i	0.974106	+	0.226093i	$0.0725954\pi$
$313$			8.00000i			0.452187i	−0.974106	+	0.226093i	$0.927405\pi$
$314$	−13.4164			−0.757132
$315$	8.18034	+	5.41641i	0.460910	+	0.305180i
$316$	−2.76393			−0.155483
$317$			25.7082i			1.44392i	0.691937	+	0.721958i	$0.256758\pi$
$317$			25.7082i			1.44392i	−0.691937	+	0.721958i	$0.743242\pi$
$318$	−3.52786	+	9.23607i	−0.197833	+	0.517933i
$319$	−8.47214			−0.474349
$320$	1.23607			0.0690983
$321$	−14.4721	−	5.52786i	−0.807756	−	0.308535i
$322$	8.47214	−	1.23607i	0.472134	−	0.0688834i
$323$		−	5.52786i		−	0.307579i
$324$	−1.00000	−	8.94427i	−0.0555556	−	0.496904i
$325$		−	20.8328i		−	1.15560i
$326$		−	9.52786i		−	0.527700i
$327$	−8.18034	+	21.4164i	−0.452374	+	1.18433i
$328$			10.1803i			0.562115i
$329$	−27.4164	+	4.00000i	−1.51152	+	0.220527i
$330$	0.763932	−	2.00000i	0.0420531	−	0.110096i
$331$	−8.94427			−0.491622			−0.245811	−	0.969318i	$-0.579054\pi$
$331$	−8.94427			−0.491622			−0.245811	+	0.969318i	$0.579054\pi$
$332$	6.00000			0.329293
$333$	−10.0000	−	8.94427i	−0.547997	−	0.490143i
$334$		−	21.8885i		−	1.19769i
$335$	−12.9443			−0.707221
$336$	−1.00000	+	4.47214i	−0.0545545	+	0.243975i
$337$	−13.4164			−0.730838			−0.365419	−	0.930843i	$-0.619074\pi$
$337$	−13.4164			−0.730838			−0.365419	+	0.930843i	$0.619074\pi$
$338$			23.0000i			1.25104i
$339$	−12.9443	−	4.94427i	−0.703036	−	0.268536i
$340$	−3.41641			−0.185281
$341$	−5.23607			−0.283549
$342$	−4.47214	−	4.00000i	−0.241825	−	0.216295i
$343$	16.7984	−	7.79837i	0.907027	−	0.421073i
$344$		−	6.94427i		−	0.374410i
$345$	6.47214	+	2.47214i	0.348448	+	0.133095i
$346$		−	5.70820i		−	0.306875i
$347$		−	0.944272i		−	0.0506912i	−0.999679	−	0.0253456i	$-0.991931\pi$
$347$		−	0.944272i		−	0.0506912i	0.999679	−	0.0253456i	$-0.00806861\pi$
$348$	13.7082	+	5.23607i	0.734837	+	0.280683i
$349$		−	22.0000i		−	1.17763i	−0.808267	−	0.588817i	$-0.799594\pi$
$349$		−	22.0000i		−	1.17763i	0.808267	−	0.588817i	$-0.200406\pi$
$350$	1.32624	+	9.09017i	0.0708904	+	0.485890i
$351$	14.2918	+	27.7082i	0.762840	+	1.47895i
$352$	1.00000			0.0533002
$353$	16.9443			0.901853			0.450926	−	0.892561i	$-0.351094\pi$
$353$	16.9443			0.901853			0.450926	+	0.892561i	$0.351094\pi$
$354$	2.00000	+	0.763932i	0.106299	+	0.0406025i
$355$			20.0000i			1.06149i
$356$	4.94427			0.262046
$357$	2.76393	−	12.3607i	0.146283	−	0.654197i
$358$	−4.94427			−0.261313
$359$		−	34.8328i		−	1.83841i	−0.393784	−	0.919203i	$-0.628834\pi$
$359$		−	34.8328i		−	1.83841i	0.393784	−	0.919203i	$-0.371166\pi$
$360$	−2.47214	+	2.76393i	−0.130293	+	0.145672i
$361$	15.0000			0.789474
$362$	12.4721			0.655521
$363$	0.618034	−	1.61803i	0.0324384	−	0.0849248i
$364$	−2.29180	−	15.7082i	−0.120123	−	0.823334i
$365$			10.1115i			0.529258i
$366$	7.70820	−	20.1803i	0.402914	−	1.05484i
$367$			4.65248i			0.242857i	0.992600	+	0.121429i	$0.0387476\pi$
$367$			4.65248i			0.242857i	−0.992600	+	0.121429i	$0.961252\pi$
$368$			3.23607i			0.168692i
$369$	−22.7639	−	20.3607i	−1.18504	−	1.05993i
$370$			5.52786i			0.287380i
$371$	2.18034	+	14.9443i	0.113198	+	0.775868i
$372$	8.47214	+	3.23607i	0.439260	+	0.167782i
$373$	−30.1803			−1.56268			−0.781339	−	0.624106i	$-0.785463\pi$
$373$	−30.1803			−1.56268			−0.781339	+	0.624106i	$0.785463\pi$
$374$	−2.76393			−0.142920
$375$	−6.47214	+	16.9443i	−0.334220	+	0.874998i
$376$		−	10.4721i		−	0.540059i
$377$	−50.8328			−2.61802
$378$	−8.00000	−	11.1803i	−0.411476	−	0.575055i
$379$	32.3607			1.66226			0.831128	−	0.556081i	$-0.187696\pi$
$379$	32.3607			1.66226			0.831128	+	0.556081i	$0.187696\pi$
$380$			2.47214i			0.126818i
$381$	2.65248	−	6.94427i	0.135890	−	0.355766i
$382$	1.70820			0.0873993
$383$	−20.0000			−1.02195			−0.510976	−	0.859595i	$-0.670716\pi$
$383$	−20.0000			−1.02195			−0.510976	+	0.859595i	$0.670716\pi$
$384$	−1.61803	−	0.618034i	−0.0825700	−	0.0315389i
$385$	−0.472136	−	3.23607i	−0.0240623	−	0.164925i
$386$		−	14.9443i		−	0.760643i
$387$	15.5279	+	13.8885i	0.789326	+	0.705994i
$388$		−	6.47214i		−	0.328573i
$389$			12.7639i			0.647157i	0.946201	+	0.323579i	$0.104886\pi$
$389$			12.7639i			0.647157i	−0.946201	+	0.323579i	$0.895114\pi$
$390$	4.58359	−	12.0000i	0.232099	−	0.607644i
$391$		−	8.94427i		−	0.452331i
$392$	2.00000	+	6.70820i	0.101015	+	0.338815i
$393$	10.7639	−	28.1803i	0.542969	−	1.42151i
$394$	2.94427			0.148330
$395$	−3.41641			−0.171898
$396$	−2.00000	+	2.23607i	−0.100504	+	0.112367i
$397$			2.94427i			0.147769i	0.997267	+	0.0738844i	$0.0235396\pi$
$397$			2.94427i			0.147769i	−0.997267	+	0.0738844i	$0.976460\pi$
$398$	−2.18034			−0.109291
$399$	−8.94427	−	2.00000i	−0.447774	−	0.100125i
$400$	−3.47214			−0.173607
$401$		−	6.47214i		−	0.323203i	−0.986856	−	0.161602i	$-0.948334\pi$
$401$		−	6.47214i		−	0.323203i	0.986856	−	0.161602i	$-0.0516659\pi$
$402$	16.9443	+	6.47214i	0.845103	+	0.322801i
$403$	−31.4164			−1.56496
$404$	−11.2361			−0.559015
$405$	−1.23607	−	11.0557i	−0.0614207	−	0.549364i
$406$	22.1803	−	3.23607i	1.10079	−	0.160603i
$407$			4.47214i			0.221676i
$408$	4.47214	+	1.70820i	0.221404	+	0.0845687i
$409$		−	0.763932i		−	0.0377740i	−0.999822	−	0.0188870i	$-0.993988\pi$
$409$		−	0.763932i		−	0.0377740i	0.999822	−	0.0188870i	$-0.00601228\pi$
$410$			12.5836i			0.621459i
$411$	−4.00000	−	1.52786i	−0.197305	−	0.0753640i
$412$			3.70820i			0.182690i
$413$	3.23607	−	0.472136i	0.159236	−	0.0232323i
$414$	−7.23607	−	6.47214i	−0.355633	−	0.318088i
$415$	7.41641			0.364057
$416$	6.00000			0.294174
$417$	16.1803	+	6.18034i	0.792355	+	0.302653i
$418$			2.00000i			0.0978232i
$419$	−31.1246			−1.52054			−0.760268	−	0.649609i	$-0.774933\pi$
$419$	−31.1246			−1.52054			−0.760268	+	0.649609i	$0.774933\pi$
$420$	−1.23607	+	5.52786i	−0.0603139	+	0.269732i
$421$	−4.47214			−0.217959			−0.108979	−	0.994044i	$-0.534758\pi$
$421$	−4.47214			−0.217959			−0.108979	+	0.994044i	$0.534758\pi$
$422$			17.4164i			0.847817i
$423$	23.4164	+	20.9443i	1.13854	+	1.01835i
$424$	−5.70820			−0.277215
$425$	9.59675			0.465511
$426$	10.0000	−	26.1803i	0.484502	−	1.26844i
$427$	−4.76393	−	32.6525i	−0.230543	−	1.58016i
$428$		−	8.94427i		−	0.432338i
$429$	3.70820	−	9.70820i	0.179034	−	0.468717i
$430$		−	8.58359i		−	0.413938i
$431$		−	29.8885i		−	1.43968i	−0.694140	−	0.719840i	$-0.744215\pi$
$431$		−	29.8885i		−	1.43968i	0.694140	−	0.719840i	$-0.255785\pi$
$432$	4.61803	−	2.38197i	0.222185	−	0.114602i
$433$			17.5279i			0.842335i	0.906983	+	0.421168i	$0.138380\pi$
$433$			17.5279i			0.842335i	−0.906983	+	0.421168i	$0.861620\pi$
$434$	13.7082	−	2.00000i	0.658015	−	0.0960031i
$435$	16.9443	+	6.47214i	0.812416	+	0.310315i
$436$	−13.2361			−0.633893
$437$	−6.47214			−0.309604
$438$	5.05573	−	13.2361i	0.241572	−	0.632444i
$439$		−	12.7639i		−	0.609189i	−0.952482	−	0.304595i	$-0.901479\pi$
$439$		−	12.7639i		−	0.609189i	0.952482	−	0.304595i	$-0.0985210\pi$
$440$	1.23607			0.0589272
$441$	−19.0000	−	8.94427i	−0.904762	−	0.425918i
$442$	−16.5836			−0.788801
$443$			5.88854i			0.279773i	0.990168	+	0.139887i	$0.0446738\pi$
$443$			5.88854i			0.279773i	−0.990168	+	0.139887i	$0.955326\pi$
$444$	2.76393	−	7.23607i	0.131170	−	0.343409i
$445$	6.11146			0.289711
$446$	25.5967			1.21204
$447$	−3.23607	−	1.23607i	−0.153061	−	0.0584640i
$448$	−2.61803	+	0.381966i	−0.123690	+	0.0180462i
$449$			4.58359i			0.216313i	0.994134	+	0.108157i	$0.0344948\pi$
$449$			4.58359i			0.216313i	−0.994134	+	0.108157i	$0.965505\pi$
$450$	6.94427	−	7.76393i	0.327356	−	0.365995i
$451$			10.1803i			0.479373i
$452$		−	8.00000i		−	0.376288i
$453$	6.29180	−	16.4721i	0.295614	−	0.773928i
$454$		−	22.0000i		−	1.03251i
$455$	−2.83282	−	19.4164i	−0.132804	−	0.910255i
$456$	1.23607	−	3.23607i	0.0578842	−	0.151543i
$457$	−2.00000			−0.0935561			−0.0467780	−	0.998905i	$-0.514895\pi$
$457$	−2.00000			−0.0935561			−0.0467780	+	0.998905i	$0.514895\pi$
$458$	−2.00000			−0.0934539
$459$	−12.7639	+	6.58359i	−0.595769	+	0.307296i
$460$			4.00000i			0.186501i
$461$	36.7639			1.71227			0.856134	−	0.516755i	$-0.172860\pi$
$461$	36.7639			1.71227			0.856134	+	0.516755i	$0.172860\pi$
$462$	−1.00000	+	4.47214i	−0.0465242	+	0.208063i
$463$	−17.5279			−0.814589			−0.407294	−	0.913297i	$-0.633528\pi$
$463$	−17.5279			−0.814589			−0.407294	+	0.913297i	$0.633528\pi$
$464$			8.47214i			0.393309i
$465$	10.4721	+	4.00000i	0.485634	+	0.185496i
$466$	1.41641			0.0656138
$467$	−8.65248			−0.400389			−0.200194	−	0.979756i	$-0.564157\pi$
$467$	−8.65248			−0.400389			−0.200194	+	0.979756i	$0.564157\pi$
$468$	−12.0000	+	13.4164i	−0.554700	+	0.620174i
$469$	27.4164	−	4.00000i	1.26597	−	0.184703i
$470$		−	12.9443i		−	0.597075i
$471$	21.7082	+	8.29180i	1.00026	+	0.382066i
$472$			1.23607i			0.0568946i
$473$		−	6.94427i		−	0.319298i
$474$	4.47214	+	1.70820i	0.205412	+	0.0784604i
$475$		−	6.94427i		−	0.318625i
$476$	7.23607	−	1.05573i	0.331665	−	0.0483892i
$477$	11.4164	−	12.7639i	0.522721	−	0.584420i
$478$	13.8885			0.635247
$479$	−16.9443			−0.774204			−0.387102	−	0.922037i	$-0.626524\pi$
$479$	−16.9443			−0.774204			−0.387102	+	0.922037i	$0.626524\pi$
$480$	−2.00000	−	0.763932i	−0.0912871	−	0.0348686i
$481$			26.8328i			1.22347i
$482$	4.18034			0.190409
$483$	−14.4721	−	3.23607i	−0.658505	−	0.147246i
$484$	1.00000			0.0454545
$485$		−	8.00000i		−	0.363261i
$486$	−3.90983	+	15.0902i	−0.177353	+	0.684504i
$487$	10.4721			0.474538			0.237269	−	0.971444i	$-0.423748\pi$
$487$	10.4721			0.474538			0.237269	+	0.971444i	$0.423748\pi$
$488$	12.4721			0.564587
$489$	−5.88854	+	15.4164i	−0.266289	+	0.697154i
$490$	2.47214	+	8.29180i	0.111680	+	0.374585i
$491$		0			0		1.00000			$0$
$491$		0			0		−1.00000			$\pi$
$492$	6.29180	−	16.4721i	0.283656	−	0.742621i
$493$		−	23.4164i		−	1.05462i
$494$			12.0000i			0.539906i
$495$	−2.47214	+	2.76393i	−0.111114	+	0.124230i
$496$			5.23607i			0.235106i
$497$	−6.18034	−	42.3607i	−0.277226	−	1.90014i
$498$	−9.70820	−	3.70820i	−0.435035	−	0.166169i
$499$	36.9443			1.65385			0.826926	−	0.562310i	$-0.190087\pi$
$499$	36.9443			1.65385			0.826926	+	0.562310i	$0.190087\pi$
$500$	−10.4721			−0.468328
$501$	−13.5279	+	35.4164i	−0.604380	+	1.58229i
$502$			11.7082i			0.522563i
$503$	31.4164			1.40079			0.700394	−	0.713756i	$-0.253008\pi$
$503$	31.4164			1.40079			0.700394	+	0.713756i	$0.253008\pi$
$504$	4.38197	−	6.61803i	0.195188	−	0.294791i
$505$	−13.8885			−0.618032
$506$			3.23607i			0.143861i
$507$	14.2148	−	37.2148i	0.631301	−	1.65277i
$508$	4.29180			0.190418
$509$	23.1246			1.02498			0.512490	−	0.858693i	$-0.328723\pi$
$509$	23.1246			1.02498			0.512490	+	0.858693i	$0.328723\pi$
$510$	5.52786	+	2.11146i	0.244778	+	0.0934969i
$511$	−3.12461	−	21.4164i	−0.138225	−	0.947406i
$512$		−	1.00000i		−	0.0441942i
$513$	4.76393	+	9.23607i	0.210333	+	0.407782i
$514$		−	16.9443i		−	0.747380i
$515$			4.58359i			0.201977i
$516$	−4.29180	+	11.2361i	−0.188936	+	0.494640i
$517$		−	10.4721i		−	0.460564i
$518$	−1.70820	−	11.7082i	−0.0750542	−	0.514429i
$519$	−3.52786	+	9.23607i	−0.154856	+	0.405418i
$520$	7.41641			0.325231
$521$	−36.9443			−1.61856			−0.809279	−	0.587425i	$-0.800142\pi$
$521$	−36.9443			−1.61856			−0.809279	+	0.587425i	$0.800142\pi$
$522$	−18.9443	−	16.9443i	−0.829168	−	0.741631i
$523$			41.7771i			1.82678i	0.407081	+	0.913392i	$0.366547\pi$
$523$			41.7771i			1.82678i	−0.407081	+	0.913392i	$0.633453\pi$
$524$	17.4164			0.760839
$525$	3.47214	−	15.5279i	0.151536	−	0.677692i
$526$	−30.4721			−1.32865
$527$		−	14.4721i		−	0.630416i
$528$	−1.61803	−	0.618034i	−0.0704159	−	0.0268965i
$529$	12.5279			0.544690
$530$	−7.05573			−0.306481
$531$	−2.76393	−	2.47214i	−0.119944	−	0.107282i
$532$	−0.763932	−	5.23607i	−0.0331207	−	0.227012i
$533$			61.0820i			2.64576i
$534$	−8.00000	−	3.05573i	−0.346194	−	0.132234i
$535$		−	11.0557i		−	0.477981i
$536$			10.4721i			0.452327i
$537$	8.00000	+	3.05573i	0.345225	+	0.131864i
$538$		−	25.5967i		−	1.10355i
$539$	2.00000	+	6.70820i	0.0861461	+	0.288943i
$540$	5.70820	−	2.94427i	0.245642	−	0.126701i
$541$	25.5967			1.10049			0.550245	−	0.835003i	$-0.314534\pi$
$541$	25.5967			1.10049			0.550245	+	0.835003i	$0.314534\pi$
$542$	−10.2918			−0.442070
$543$	−20.1803	−	7.70820i	−0.866021	−	0.330791i
$544$			2.76393i			0.118503i
$545$	−16.3607			−0.700815
$546$	−6.00000	+	26.8328i	−0.256776	+	1.14834i
$547$	−28.8328			−1.23280			−0.616401	−	0.787432i	$-0.711410\pi$
$547$	−28.8328			−1.23280			−0.616401	+	0.787432i	$0.711410\pi$
$548$		−	2.47214i		−	0.105604i
$549$	−24.9443	+	27.8885i	−1.06460	+	1.19025i
$550$	−3.47214			−0.148052
$551$	−16.9443			−0.721850
$552$	2.00000	−	5.23607i	0.0851257	−	0.222862i
$553$	7.23607	−	1.05573i	0.307709	−	0.0448941i
$554$			1.81966i			0.0773100i
$555$	3.41641	−	8.94427i	0.145018	−	0.379663i
$556$			10.0000i			0.424094i
$557$			26.9443i			1.14167i	0.821066	+	0.570833i	$0.193380\pi$
$557$			26.9443i			1.14167i	−0.821066	+	0.570833i	$0.806620\pi$
$558$	−11.7082	−	10.4721i	−0.495648	−	0.443321i
$559$		−	41.6656i		−	1.76227i
$560$	−3.23607	+	0.472136i	−0.136749	+	0.0199514i
$561$	4.47214	+	1.70820i	0.188814	+	0.0721204i
$562$	−1.41641			−0.0597476
$563$	32.4721			1.36854			0.684269	−	0.729230i	$-0.260122\pi$
$563$	32.4721			1.36854			0.684269	+	0.729230i	$0.260122\pi$
$564$	−6.47214	+	16.9443i	−0.272526	+	0.713483i
$565$		−	9.88854i		−	0.416014i
$566$	−2.94427			−0.123757
$567$	6.03444	+	23.0344i	0.253423	+	0.967356i
$568$	16.1803			0.678912
$569$			6.00000i			0.251533i	0.992060	+	0.125767i	$0.0401390\pi$
$569$			6.00000i			0.251533i	−0.992060	+	0.125767i	$0.959861\pi$
$570$	1.52786	−	4.00000i	0.0639952	−	0.167542i
$571$	−9.05573			−0.378970			−0.189485	−	0.981884i	$-0.560682\pi$
$571$	−9.05573			−0.378970			−0.189485	+	0.981884i	$0.560682\pi$
$572$	6.00000			0.250873
$573$	−2.76393	−	1.05573i	−0.115465	−	0.0441037i
$574$	−3.88854	−	26.6525i	−0.162305	−	1.11245i
$575$		−	11.2361i		−	0.468576i
$576$	2.23607	+	2.00000i	0.0931695	+	0.0833333i
$577$			46.4721i			1.93466i	0.253520	+	0.967330i	$0.418412\pi$
$577$			46.4721i			1.93466i	−0.253520	+	0.967330i	$0.581588\pi$
$578$			9.36068i			0.389353i
$579$	−9.23607	+	24.1803i	−0.383838	+	1.00490i
$580$			10.4721i			0.434832i
$581$	−15.7082	+	2.29180i	−0.651686	+	0.0950797i
$582$	−4.00000	+	10.4721i	−0.165805	+	0.434084i
$583$	−5.70820			−0.236410
$584$	8.18034			0.338505
$585$	−14.8328	+	16.5836i	−0.613261	+	0.685647i
$586$		−	4.18034i		−	0.172688i
$587$	21.5967			0.891393			0.445697	−	0.895184i	$-0.352956\pi$
$587$	21.5967			0.891393			0.445697	+	0.895184i	$0.352956\pi$
$588$	0.909830	−	12.0902i	0.0375208	−	0.498590i
$589$	−10.4721			−0.431497
$590$			1.52786i			0.0629012i
$591$	−4.76393	−	1.81966i	−0.195962	−	0.0748508i
$592$	4.47214			0.183804
$593$	11.7082			0.480798			0.240399	−	0.970674i	$-0.422722\pi$
$593$	11.7082			0.480798			0.240399	+	0.970674i	$0.422722\pi$
$594$	4.61803	−	2.38197i	0.189480	−	0.0977332i
$595$	8.94427	−	1.30495i	0.366679	−	0.0534978i
$596$		−	2.00000i		−	0.0819232i
$597$	3.52786	+	1.34752i	0.144386	+	0.0551505i
$598$			19.4164i			0.793996i
$599$		−	2.29180i		−	0.0936402i	−0.998903	−	0.0468201i	$-0.985091\pi$
$599$		−	2.29180i		−	0.0936402i	0.998903	−	0.0468201i	$-0.0149088\pi$
$600$	5.61803	+	2.14590i	0.229355	+	0.0876059i
$601$			4.76393i			0.194325i	0.995269	+	0.0971624i	$0.0309766\pi$
$601$			4.76393i			0.194325i	−0.995269	+	0.0971624i	$0.969023\pi$
$602$	2.65248	+	18.1803i	0.108107	+	0.740975i
$603$	−23.4164	−	20.9443i	−0.953590	−	0.852917i
$604$	10.1803			0.414232
$605$	1.23607			0.0502533
$606$	18.1803	+	6.94427i	0.738526	+	0.282092i
$607$			3.23607i			0.131348i	0.997841	+	0.0656740i	$0.0209197\pi$
$607$			3.23607i			0.131348i	−0.997841	+	0.0656740i	$0.979080\pi$
$608$	2.00000			0.0811107
$609$	−37.8885	−	8.47214i	−1.53532	−	0.343308i
$610$	15.4164			0.624192
$611$		−	62.8328i		−	2.54194i
$612$	−6.18034	−	5.52786i	−0.249825	−	0.223451i
$613$	18.1803			0.734297			0.367149	−	0.930162i	$-0.380334\pi$
$613$	18.1803			0.734297			0.367149	+	0.930162i	$0.380334\pi$
$614$	12.4721			0.503334
$615$	7.77709	−	20.3607i	0.313602	−	0.821022i
$616$	−2.61803	+	0.381966i	−0.105484	+	0.0153898i
$617$		−	28.9443i		−	1.16525i	−0.812740	−	0.582626i	$-0.802025\pi$
$617$		−	28.9443i		−	1.16525i	0.812740	−	0.582626i	$-0.197975\pi$
$618$	2.29180	−	6.00000i	0.0921896	−	0.241355i
$619$			16.7639i			0.673799i	0.941541	+	0.336900i	$0.109378\pi$
$619$			16.7639i			0.673799i	−0.941541	+	0.336900i	$0.890622\pi$
$620$			6.47214i			0.259927i
$621$	7.70820	+	14.9443i	0.309320	+	0.599693i
$622$		−	1.52786i		−	0.0612618i
$623$	−12.9443	+	1.88854i	−0.518601	+	0.0756629i
$624$	−9.70820	−	3.70820i	−0.388639	−	0.148447i
$625$	4.41641			0.176656
$626$	8.00000			0.319744
$627$	1.23607	−	3.23607i	0.0493638	−	0.129236i
$628$			13.4164i			0.535373i
$629$	−12.3607			−0.492853
$630$	5.41641	−	8.18034i	0.215795	−	0.325913i
$631$	−15.0557			−0.599359			−0.299680	−	0.954040i	$-0.596880\pi$
$631$	−15.0557			−0.599359			−0.299680	+	0.954040i	$0.596880\pi$
$632$			2.76393i			0.109943i
$633$	10.7639	−	28.1803i	0.427828	−	1.12007i
$634$	25.7082			1.02100
$635$	5.30495			0.210521
$636$	9.23607	+	3.52786i	0.366234	+	0.139889i
$637$	12.0000	+	40.2492i	0.475457	+	1.59473i
$638$			8.47214i			0.335415i
$639$	−32.3607	+	36.1803i	−1.28017	+	1.43127i
$640$		−	1.23607i		−	0.0488599i
$641$			12.3607i			0.488217i	0.969748	+	0.244109i	$0.0784954\pi$
$641$			12.3607i			0.488217i	−0.969748	+	0.244109i	$0.921505\pi$
$642$	−5.52786	+	14.4721i	−0.218167	+	0.571170i
$643$			26.0689i			1.02806i	0.857773	+	0.514028i	$0.171847\pi$
$643$			26.0689i			1.02806i	−0.857773	+	0.514028i	$0.828153\pi$
$644$	−1.23607	−	8.47214i	−0.0487079	−	0.333849i
$645$	−5.30495	+	13.8885i	−0.208882	+	0.546861i
$646$	−5.52786			−0.217491
$647$	29.8885			1.17504			0.587520	−	0.809210i	$-0.300104\pi$
$647$	29.8885			1.17504			0.587520	+	0.809210i	$0.300104\pi$
$648$	−8.94427	+	1.00000i	−0.351364	+	0.0392837i
$649$			1.23607i			0.0485199i
$650$	−20.8328			−0.817130
$651$	−23.4164	−	5.23607i	−0.917761	−	0.205218i
$652$	−9.52786			−0.373140
$653$		−	16.7639i		−	0.656023i	−0.944674	−	0.328012i	$-0.893621\pi$
$653$		−	16.7639i		−	0.656023i	0.944674	−	0.328012i	$-0.106379\pi$
$654$	21.4164	+	8.18034i	0.837448	+	0.319877i
$655$	21.5279			0.841163
$656$	10.1803			0.397475
$657$	−16.3607	+	18.2918i	−0.638291	+	0.713631i
$658$	4.00000	+	27.4164i	0.155936	+	1.06880i
$659$		−	25.8885i		−	1.00847i	−0.863565	−	0.504237i	$-0.831774\pi$
$659$		−	25.8885i		−	1.00847i	0.863565	−	0.504237i	$-0.168226\pi$
$660$	−2.00000	−	0.763932i	−0.0778499	−	0.0297360i
$661$			35.5279i			1.38187i	0.722915	+	0.690937i	$0.242802\pi$
$661$			35.5279i			1.38187i	−0.722915	+	0.690937i	$0.757198\pi$
$662$			8.94427i			0.347629i
$663$	26.8328	+	10.2492i	1.04210	+	0.398047i
$664$		−	6.00000i		−	0.232845i
$665$	−0.944272	−	6.47214i	−0.0366173	−	0.250979i
$666$	−8.94427	+	10.0000i	−0.346583	+	0.387492i
$667$	−27.4164			−1.06157
$668$	−21.8885			−0.846893
$669$	−41.4164	−	15.8197i	−1.60125	−	0.611623i
$670$			12.9443i			0.500081i
$671$	12.4721			0.481481
$672$	4.47214	+	1.00000i	0.172516	+	0.0385758i
$673$	51.3050			1.97766			0.988830	−	0.149046i	$-0.0476202\pi$
$673$	51.3050			1.97766			0.988830	+	0.149046i	$0.0476202\pi$
$674$			13.4164i			0.516781i
$675$	−16.0344	+	8.27051i	−0.617166	+	0.318332i
$676$	23.0000			0.884615
$677$	−7.23607			−0.278105			−0.139052	−	0.990285i	$-0.544406\pi$
$677$	−7.23607			−0.278105			−0.139052	+	0.990285i	$0.544406\pi$
$678$	−4.94427	+	12.9443i	−0.189884	+	0.497122i
$679$	2.47214	+	16.9443i	0.0948719	+	0.650261i
$680$			3.41641i			0.131013i
$681$	−13.5967	+	35.5967i	−0.521029	+	1.36407i
$682$			5.23607i			0.200499i
$683$		−	1.88854i		−	0.0722631i	−0.999347	−	0.0361316i	$-0.988496\pi$
$683$		−	1.88854i		−	0.0722631i	0.999347	−	0.0361316i	$-0.0115035\pi$
$684$	−4.00000	+	4.47214i	−0.152944	+	0.170996i
$685$		−	3.05573i		−	0.116753i
$686$	−7.79837	−	16.7984i	−0.297743	−	0.641365i
$687$	3.23607	+	1.23607i	0.123464	+	0.0471589i
$688$	−6.94427			−0.264748
$689$	−34.2492			−1.30479
$690$	2.47214	−	6.47214i	0.0941126	−	0.246390i
$691$			19.5967i			0.745495i	0.927933	+	0.372748i	$0.121584\pi$
$691$			19.5967i			0.745495i	−0.927933	+	0.372748i	$0.878416\pi$
$692$	−5.70820			−0.216993
$693$	4.38197	−	6.61803i	0.166457	−	0.251398i
$694$	−0.944272			−0.0358441
$695$			12.3607i			0.468867i
$696$	5.23607	−	13.7082i	0.198473	−	0.519608i
$697$	−28.1378			−1.06579
$698$	−22.0000			−0.832712
$699$	−2.29180	−	0.875388i	−0.0866837	−	0.0331102i
$700$	9.09017	−	1.32624i	0.343576	−	0.0501271i
$701$		−	9.41641i		−	0.355653i	−0.984062	−	0.177826i	$-0.943093\pi$
$701$		−	9.41641i		−	0.355653i	0.984062	−	0.177826i	$-0.0569066\pi$
$702$	27.7082	−	14.2918i	1.04578	−	0.539409i
$703$			8.94427i			0.337340i
$704$		−	1.00000i		−	0.0376889i
$705$	−8.00000	+	20.9443i	−0.301297	+	0.788807i
$706$		−	16.9443i		−	0.637706i
$707$	29.4164	−	4.29180i	1.10632	−	0.161410i
$708$	0.763932	−	2.00000i	0.0287103	−	0.0751646i
$709$	−49.4164			−1.85587			−0.927936	−	0.372739i	$-0.878419\pi$
$709$	−49.4164			−1.85587			−0.927936	+	0.372739i	$0.878419\pi$
$710$	20.0000			0.750587
$711$	−6.18034	−	5.52786i	−0.231781	−	0.207311i
$712$		−	4.94427i		−	0.185294i
$713$	−16.9443			−0.634568
$714$	−12.3607	−	2.76393i	−0.462587	−	0.103438i
$715$	7.41641			0.277358
$716$			4.94427i			0.184776i
$717$	−22.4721	−	8.58359i	−0.839237	−	0.320560i
$718$	−34.8328			−1.29995
$719$	26.4721			0.987244			0.493622	−	0.869677i	$-0.335673\pi$
$719$	26.4721			0.987244			0.493622	+	0.869677i	$0.335673\pi$
$720$	2.76393	+	2.47214i	0.103006	+	0.0921311i
$721$	−1.41641	−	9.70820i	−0.0527498	−	0.361552i
$722$		−	15.0000i		−	0.558242i
$723$	−6.76393	−	2.58359i	−0.251553	−	0.0960848i
$724$		−	12.4721i		−	0.463523i
$725$		−	29.4164i		−	1.09250i
$726$	−1.61803	−	0.618034i	−0.0600509	−	0.0229374i
$727$		−	15.7082i		−	0.582585i	−0.956634	−	0.291293i	$-0.905915\pi$
$727$		−	15.7082i		−	0.582585i	0.956634	−	0.291293i	$-0.0940853\pi$
$728$	−15.7082	+	2.29180i	−0.582185	+	0.0849396i
$729$	15.6525	−	22.0000i	0.579721	−	0.814815i
$730$	10.1115			0.374242
$731$	19.1935			0.709897
$732$	−20.1803	−	7.70820i	−0.745887	−	0.284903i
$733$			53.4164i			1.97298i	0.163821	+	0.986490i	$0.447618\pi$
$733$			53.4164i			1.97298i	−0.163821	+	0.986490i	$0.552382\pi$
$734$	4.65248			0.171726
$735$	1.12461	−	14.9443i	0.0414819	−	0.551228i
$736$	3.23607			0.119283
$737$			10.4721i			0.385746i
$738$	−20.3607	+	22.7639i	−0.749487	+	0.837952i
$739$	−17.4164			−0.640673			−0.320336	−	0.947304i	$-0.603796\pi$
$739$	−17.4164			−0.640673			−0.320336	+	0.947304i	$0.603796\pi$
$740$	5.52786			0.203208
$741$	7.41641	−	19.4164i	0.272449	−	0.713280i
$742$	14.9443	−	2.18034i	0.548621	−	0.0800428i
$743$		−	10.4721i		−	0.384185i	−0.981377	−	0.192093i	$-0.938473\pi$
$743$		−	10.4721i		−	0.384185i	0.981377	−	0.192093i	$-0.0615274\pi$
$744$	3.23607	−	8.47214i	0.118640	−	0.310604i
$745$		−	2.47214i		−	0.0905721i
$746$			30.1803i			1.10498i
$747$	13.4164	+	12.0000i	0.490881	+	0.439057i
$748$			2.76393i			0.101059i
$749$	3.41641	+	23.4164i	0.124833	+	0.855617i
$750$	16.9443	+	6.47214i	0.618717	+	0.236329i
$751$	12.3607			0.451048			0.225524	−	0.974238i	$-0.427591\pi$
$751$	12.3607			0.451048			0.225524	+	0.974238i	$0.427591\pi$
$752$	−10.4721			−0.381880
$753$	7.23607	−	18.9443i	0.263697	−	0.690368i
$754$			50.8328i			1.85122i
$755$	12.5836			0.457964
$756$	−11.1803	+	8.00000i	−0.406625	+	0.290957i
$757$	25.4164			0.923775			0.461888	−	0.886939i	$-0.347172\pi$
$757$	25.4164			0.923775			0.461888	+	0.886939i	$0.347172\pi$
$758$		−	32.3607i		−	1.17539i
$759$	2.00000	−	5.23607i	0.0725954	−	0.190057i
$760$	2.47214			0.0896738
$761$	−7.12461			−0.258267			−0.129133	−	0.991627i	$-0.541220\pi$
$761$	−7.12461			−0.258267			−0.129133	+	0.991627i	$0.541220\pi$
$762$	−6.94427	−	2.65248i	−0.251564	−	0.0960891i
$763$	34.6525	−	5.05573i	1.25450	−	0.183030i
$764$		−	1.70820i		−	0.0618006i
$765$	−7.63932	−	6.83282i	−0.276200	−	0.247041i
$766$			20.0000i			0.722629i
$767$			7.41641i			0.267791i
$768$	−0.618034	+	1.61803i	−0.0223014	+	0.0583858i
$769$		−	33.4853i		−	1.20751i	−0.797170	−	0.603755i	$-0.793670\pi$
$769$		−	33.4853i		−	1.20751i	0.797170	−	0.603755i	$-0.206330\pi$
$770$	−3.23607	+	0.472136i	−0.116620	+	0.0170146i
$771$	−10.4721	+	27.4164i	−0.377145	+	0.987378i
$772$	−14.9443			−0.537856
$773$	39.1246			1.40721			0.703607	−	0.710589i	$-0.251571\pi$
$773$	39.1246			1.40721			0.703607	+	0.710589i	$0.251571\pi$
$774$	13.8885	−	15.5279i	0.499213	−	0.558138i
$775$		−	18.1803i		−	0.653057i
$776$	−6.47214			−0.232336
$777$	−4.47214	+	20.0000i	−0.160437	+	0.717496i
$778$	12.7639			0.457609
$779$			20.3607i			0.729497i
$780$	−12.0000	−	4.58359i	−0.429669	−	0.164119i
$781$	16.1803			0.578978
$782$	−8.94427			−0.319847
$783$	20.1803	+	39.1246i	0.721187	+	1.39820i
$784$	6.70820	−	2.00000i	0.239579	−	0.0714286i
$785$			16.5836i			0.591894i
$786$	−28.1803	−	10.7639i	−1.00516	−	0.383937i
$787$		−	52.4721i		−	1.87043i	−0.354081	−	0.935215i	$-0.615206\pi$
$787$		−	52.4721i		−	1.87043i	0.354081	−	0.935215i	$-0.384794\pi$
$788$		−	2.94427i		−	0.104885i
$789$	49.3050	+	18.8328i	1.75530	+	0.670466i
$790$			3.41641i			0.121550i
$791$	3.05573	+	20.9443i	0.108649	+	0.744693i
$792$	2.23607	+	2.00000i	0.0794552	+	0.0710669i
$793$	74.8328			2.65739
$794$	2.94427			0.104488
$795$	11.4164	+	4.36068i	0.404898	+	0.154657i
$796$			2.18034i			0.0772801i
$797$	−36.2918			−1.28552			−0.642761	−	0.766067i	$-0.722211\pi$
$797$	−36.2918			−1.28552			−0.642761	+	0.766067i	$0.722211\pi$
$798$	−2.00000	+	8.94427i	−0.0707992	+	0.316624i
$799$	28.9443			1.02397
$800$			3.47214i			0.122759i
$801$	11.0557	+	9.88854i	0.390635	+	0.349395i
$802$	−6.47214			−0.228539
$803$	8.18034			0.288678
$804$	6.47214	−	16.9443i	0.228255	−	0.597578i
$805$	−1.52786	−	10.4721i	−0.0538501	−	0.369094i
$806$			31.4164i			1.10660i
$807$	−15.8197	+	41.4164i	−0.556878	+	1.45793i
$808$			11.2361i			0.395283i
$809$		−	36.8328i		−	1.29497i	−0.762077	−	0.647486i	$-0.775820\pi$
$809$		−	36.8328i		−	1.29497i	0.762077	−	0.647486i	$-0.224180\pi$
$810$	−11.0557	+	1.23607i	−0.388459	+	0.0434310i
$811$		−	42.7214i		−	1.50015i	−0.661353	−	0.750075i	$-0.730017\pi$
$811$		−	42.7214i		−	1.50015i	0.661353	−	0.750075i	$-0.269983\pi$
$812$	−3.23607	−	22.1803i	−0.113564	−	0.778377i
$813$	16.6525	+	6.36068i	0.584028	+	0.223079i
$814$	4.47214			0.156748
$815$	−11.7771			−0.412533
$816$	1.70820	−	4.47214i	0.0597991	−	0.156556i
$817$		−	13.8885i		−	0.485899i
$818$	−0.763932			−0.0267103
$819$	26.2918	−	39.7082i	0.918710	−	1.38752i
$820$	12.5836			0.439438
$821$		−	46.3607i		−	1.61800i	−0.587809	−	0.808999i	$-0.700010\pi$
$821$		−	46.3607i		−	1.61800i	0.587809	−	0.808999i	$-0.299990\pi$
$822$	−1.52786	+	4.00000i	−0.0532904	+	0.139516i
$823$	42.2492			1.47272			0.736358	−	0.676592i	$-0.236544\pi$
$823$	42.2492			1.47272			0.736358	+	0.676592i	$0.236544\pi$
$824$	3.70820			0.129181
$825$	5.61803	+	2.14590i	0.195595	+	0.0747106i
$826$	−0.472136	−	3.23607i	−0.0164277	−	0.112597i
$827$			0.944272i			0.0328356i	0.999865	+	0.0164178i	$0.00522618\pi$
$827$			0.944272i			0.0328356i	−0.999865	+	0.0164178i	$0.994774\pi$
$828$	−6.47214	+	7.23607i	−0.224922	+	0.251471i
$829$			11.8885i			0.412906i	0.978456	+	0.206453i	$0.0661921\pi$
$829$			11.8885i			0.412906i	−0.978456	+	0.206453i	$0.933808\pi$
$830$		−	7.41641i		−	0.257427i
$831$	1.12461	−	2.94427i	0.0390124	−	0.102136i
$832$		−	6.00000i		−	0.208013i
$833$	−18.5410	+	5.52786i	−0.642408	+	0.191529i
$834$	6.18034	−	16.1803i	0.214008	−	0.560279i
$835$	−27.0557			−0.936302
$836$	2.00000			0.0691714
$837$	12.4721	+	24.1803i	0.431100	+	0.835795i
$838$			31.1246i			1.07518i
$839$	31.0557			1.07216			0.536081	−	0.844166i	$-0.319904\pi$
$839$	31.0557			1.07216			0.536081	+	0.844166i	$0.319904\pi$
$840$	5.52786	+	1.23607i	0.190729	+	0.0426484i
$841$	−42.7771			−1.47507
$842$			4.47214i			0.154120i
$843$	2.29180	+	0.875388i	0.0789336	+	0.0301500i
$844$	17.4164			0.599497
$845$	28.4296			0.978007
$846$	20.9443	−	23.4164i	0.720079	−	0.805073i
$847$	−2.61803	+	0.381966i	−0.0899567	+	0.0131245i
$848$			5.70820i			0.196021i
$849$	4.76393	+	1.81966i	0.163498	+	0.0624506i
$850$		−	9.59675i		−	0.329166i
$851$			14.4721i			0.496098i
$852$	−26.1803	−	10.0000i	−0.896924	−	0.342594i
$853$		−	10.9443i		−	0.374725i	−0.982291	−	0.187362i	$-0.940006\pi$
$853$		−	10.9443i		−	0.374725i	0.982291	−	0.187362i	$-0.0599939\pi$
$854$	−32.6525	+	4.76393i	−1.11734	+	0.163018i
$855$	−4.94427	+	5.52786i	−0.169091	+	0.189049i
$856$	−8.94427			−0.305709
$857$	−31.7082			−1.08313			−0.541566	−	0.840658i	$-0.682168\pi$
$857$	−31.7082			−1.08313			−0.541566	+	0.840658i	$0.682168\pi$
$858$	−9.70820	−	3.70820i	−0.331433	−	0.126596i
$859$		−	26.6525i		−	0.909371i	−0.890652	−	0.454685i	$-0.849752\pi$
$859$		−	26.6525i		−	0.909371i	0.890652	−	0.454685i	$-0.150248\pi$
$860$	−8.58359			−0.292698
$861$	−10.1803	+	45.5279i	−0.346945	+	1.55159i
$862$	−29.8885			−1.01801
$863$		−	23.5967i		−	0.803243i	−0.915806	−	0.401621i	$-0.868447\pi$
$863$		−	23.5967i		−	0.803243i	0.915806	−	0.401621i	$-0.131553\pi$
$864$	−2.38197	−	4.61803i	−0.0810361	−	0.157109i
$865$	−7.05573			−0.239902
$866$	17.5279			0.595621
$867$	5.78522	−	15.1459i	0.196476	−	0.514382i
$868$	−2.00000	−	13.7082i	−0.0678844	−	0.465287i
$869$			2.76393i			0.0937600i
$870$	6.47214	−	16.9443i	0.219426	−	0.574465i
$871$			62.8328i			2.12901i
$872$			13.2361i			0.448230i
$873$	12.9443	−	14.4721i	0.438097	−	0.489808i
$874$			6.47214i			0.218923i
$875$	27.4164	−	4.00000i	0.926844	−	0.135225i
$876$	−13.2361	−	5.05573i	−0.447205	−	0.170817i
$877$	−21.0132			−0.709564			−0.354782	−	0.934949i	$-0.615445\pi$
$877$	−21.0132			−0.709564			−0.354782	+	0.934949i	$0.615445\pi$
$878$	−12.7639			−0.430762
$879$	−2.58359	+	6.76393i	−0.0871424	+	0.228142i
$880$		−	1.23607i		−	0.0416678i
$881$	−3.41641			−0.115102			−0.0575509	−	0.998343i	$-0.518329\pi$
$881$	−3.41641			−0.115102			−0.0575509	+	0.998343i	$0.518329\pi$
$882$	−8.94427	+	19.0000i	−0.301169	+	0.639763i
$883$	4.94427			0.166388			0.0831940	−	0.996533i	$-0.473488\pi$
$883$	4.94427			0.166388			0.0831940	+	0.996533i	$0.473488\pi$
$884$			16.5836i			0.557767i
$885$	0.944272	−	2.47214i	0.0317414	−	0.0830999i
$886$	5.88854			0.197829
$887$	−16.9443			−0.568933			−0.284466	−	0.958686i	$-0.591816\pi$
$887$	−16.9443			−0.568933			−0.284466	+	0.958686i	$0.591816\pi$
$888$	−7.23607	−	2.76393i	−0.242827	−	0.0927515i
$889$	−11.2361	+	1.63932i	−0.376846	+	0.0549810i
$890$		−	6.11146i		−	0.204856i
$891$	−8.94427	+	1.00000i	−0.299644	+	0.0335013i
$892$		−	25.5967i		−	0.857043i
$893$		−	20.9443i		−	0.700873i
$894$	−1.23607	+	3.23607i	−0.0413403	+	0.108230i
$895$			6.11146i			0.204283i
$896$	0.381966	+	2.61803i	0.0127606	+	0.0874624i
$897$	12.0000	−	31.4164i	0.400668	−	1.04896i
$898$	4.58359			0.152956
$899$	−44.3607			−1.47951
$900$	−7.76393	−	6.94427i	−0.258798	−	0.231476i
$901$		−	15.7771i		−	0.525611i
$902$	10.1803			0.338968
$903$	6.94427	−	31.0557i	0.231091	−	1.03347i
$904$	−8.00000			−0.266076
$905$		−	15.4164i		−	0.512459i
$906$	−16.4721	−	6.29180i	−0.547250	−	0.209031i
$907$	−28.5836			−0.949103			−0.474551	−	0.880228i	$-0.657390\pi$
$907$	−28.5836			−0.949103			−0.474551	+	0.880228i	$0.657390\pi$
$908$	−22.0000			−0.730096
$909$	−25.1246	−	22.4721i	−0.833331	−	0.745354i
$910$	−19.4164	+	2.83282i	−0.643648	+	0.0939069i
$911$			29.7082i			0.984277i	0.870517	+	0.492138i	$0.163785\pi$
$911$			29.7082i			0.984277i	−0.870517	+	0.492138i	$0.836215\pi$
$912$	−3.23607	−	1.23607i	−0.107157	−	0.0409303i
$913$		−	6.00000i		−	0.198571i
$914$			2.00000i			0.0661541i
$915$	−24.9443	−	9.52786i	−0.824632	−	0.314981i
$916$			2.00000i			0.0660819i
$917$	−45.5967	+	6.65248i	−1.50574	+	0.219684i
$918$	6.58359	+	12.7639i	0.217291	+	0.421273i
$919$	19.1246			0.630863			0.315431	−	0.948948i	$-0.397851\pi$
$919$	19.1246			0.630863			0.315431	+	0.948948i	$0.397851\pi$
$920$	4.00000			0.131876
$921$	−20.1803	−	7.70820i	−0.664965	−	0.253994i
$922$		−	36.7639i		−	1.21076i
$923$	97.0820			3.19549
$924$	4.47214	+	1.00000i	0.147122	+	0.0328976i
$925$	−15.5279			−0.510553
$926$			17.5279i			0.576001i
$927$	−7.41641	+	8.29180i	−0.243587	+	0.272338i
$928$	8.47214			0.278111
$929$	16.9443			0.555924			0.277962	−	0.960592i	$-0.410341\pi$
$929$	16.9443			0.555924			0.277962	+	0.960592i	$0.410341\pi$
$930$	4.00000	−	10.4721i	0.131165	−	0.343395i
$931$	4.00000	+	13.4164i	0.131095	+	0.439705i
$932$		−	1.41641i		−	0.0463960i
$933$	−0.944272	+	2.47214i	−0.0309141	+	0.0809341i
$934$			8.65248i			0.283118i
$935$			3.41641i			0.111728i
$936$	13.4164	+	12.0000i	0.438529	+	0.392232i
$937$		−	23.8197i		−	0.778154i	−0.921205	−	0.389077i	$-0.872794\pi$
$937$		−	23.8197i		−	0.778154i	0.921205	−	0.389077i	$-0.127206\pi$
$938$	−4.00000	−	27.4164i	−0.130605	−	0.895177i
$939$	−12.9443	−	4.94427i	−0.422420	−	0.161350i
$940$	−12.9443			−0.422196
$941$	45.7082			1.49004			0.745022	−	0.667039i	$-0.232439\pi$
$941$	45.7082			1.49004			0.745022	+	0.667039i	$0.232439\pi$
$942$	8.29180	−	21.7082i	0.270161	−	0.707292i
$943$			32.9443i			1.07281i
$944$	1.23607			0.0402306
$945$	−13.8197	+	9.88854i	−0.449554	+	0.321674i
$946$	−6.94427			−0.225778
$947$			32.0000i			1.03986i	0.854209	+	0.519930i	$0.174042\pi$
$947$			32.0000i			1.03986i	−0.854209	+	0.519930i	$0.825958\pi$
$948$	1.70820	−	4.47214i	0.0554799	−	0.145248i
$949$	49.0820			1.59327
$950$	−6.94427			−0.225302
$951$	−41.5967	−	15.8885i	−1.34887	−	0.515221i
$952$	−1.05573	−	7.23607i	−0.0342163	−	0.234522i
$953$			42.3607i			1.37220i	0.727509	+	0.686099i	$0.240678\pi$
$953$			42.3607i			1.37220i	−0.727509	+	0.686099i	$0.759322\pi$
$954$	−12.7639	−	11.4164i	−0.413248	−	0.369620i
$955$		−	2.11146i		−	0.0683251i
$956$		−	13.8885i		−	0.449188i
$957$	5.23607	−	13.7082i	0.169258	−	0.443123i
$958$			16.9443i			0.547445i
$959$	0.944272	+	6.47214i	0.0304921	+	0.208996i
$960$	−0.763932	+	2.00000i	−0.0246558	+	0.0645497i
$961$	3.58359			0.115600
$962$	26.8328			0.865125
$963$	17.8885	−	20.0000i	0.576450	−	0.644491i
$964$		−	4.18034i		−	0.134640i
$965$	−18.4721			−0.594639
$966$	−3.23607	+	14.4721i	−0.104119	+	0.465633i
$967$	20.0689			0.645372			0.322686	−	0.946506i	$-0.395414\pi$
$967$	20.0689			0.645372			0.322686	+	0.946506i	$0.395414\pi$
$968$		−	1.00000i		−	0.0321412i
$969$	8.94427	+	3.41641i	0.287331	+	0.109751i
$970$	−8.00000			−0.256865
$971$	13.2361			0.424766			0.212383	−	0.977187i	$-0.431878\pi$
$971$	13.2361			0.424766			0.212383	+	0.977187i	$0.431878\pi$
$972$	15.0902	+	3.90983i	0.484017	+	0.125408i
$973$	−3.81966	−	26.1803i	−0.122453	−	0.839303i
$974$		−	10.4721i		−	0.335549i
$975$	33.7082	+	12.8754i	1.07953	+	0.412342i
$976$		−	12.4721i		−	0.399223i
$977$			41.3050i			1.32146i	0.750623	+	0.660731i	$0.229754\pi$
$977$			41.3050i			1.32146i	−0.750623	+	0.660731i	$0.770246\pi$
$978$	15.4164	+	5.88854i	0.492962	+	0.188295i
$979$		−	4.94427i		−	0.158020i
$980$	8.29180	−	2.47214i	0.264872	−	0.0789695i
$981$	−29.5967	−	26.4721i	−0.944951	−	0.845190i
$982$		0			0
$983$	−32.9443			−1.05076			−0.525380	−	0.850868i	$-0.676077\pi$
$983$	−32.9443			−1.05076			−0.525380	+	0.850868i	$0.676077\pi$
$984$	−16.4721	−	6.29180i	−0.525113	−	0.200575i
$985$		−	3.63932i		−	0.115958i
$986$	−23.4164			−0.745730
$987$	10.4721	−	46.8328i	0.333332	−	1.49070i
$988$	12.0000			0.381771
$989$		−	22.4721i		−	0.714572i
$990$	2.76393	+	2.47214i	0.0878435	+	0.0785696i
$991$	16.9443			0.538253			0.269126	−	0.963105i	$-0.413265\pi$
$991$	16.9443			0.538253			0.269126	+	0.963105i	$0.413265\pi$
$992$	5.23607			0.166245
$993$	5.52786	−	14.4721i	0.175421	−	0.459259i
$994$	−42.3607	+	6.18034i	−1.34360	+	0.196028i
$995$			2.69505i			0.0854388i
$996$	−3.70820	+	9.70820i	−0.117499	+	0.307616i
$997$		−	23.5279i		−	0.745135i	−0.928005	−	0.372567i	$-0.878478\pi$
$997$		−	23.5279i		−	0.745135i	0.928005	−	0.372567i	$-0.121522\pi$
$998$		−	36.9443i		−	1.16945i
$999$	20.6525	−	10.6525i	0.653415	−	0.337029i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.g.d.419.1	yes	4
3.2	odd	2		462.2.g.a.419.4	yes	4
7.6	odd	2		462.2.g.a.419.2	✓	4
21.20	even	2	inner	462.2.g.d.419.3	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.g.a.419.2	✓	4	7.6	odd	2
462.2.g.a.419.4	yes	4	3.2	odd	2
462.2.g.d.419.1	yes	4	1.1	even	1	trivial
462.2.g.d.419.3	yes	4	21.20	even	2	inner

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:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-0.618034 + 1.61803i) q^{3} -1.00000 q^{4} -1.23607 q^{5} +(1.61803 + 0.618034i) q^{6} +(2.61803 - 0.381966i) q^{7} +1.00000i q^{8} +(-2.23607 - 2.00000i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(-0.618034 + 1.61803i) q^{3} -1.00000 q^{4} -1.23607 q^{5} +(1.61803 + 0.618034i) q^{6} +(2.61803 - 0.381966i) q^{7} +1.00000i q^{8} +(-2.23607 - 2.00000i) q^{9} +1.23607i q^{10} +1.00000i q^{11} +(0.618034 - 1.61803i) q^{12} +6.00000i q^{13} +(-0.381966 - 2.61803i) q^{14} +(0.763932 - 2.00000i) q^{15} +1.00000 q^{16} -2.76393 q^{17} +(-2.00000 + 2.23607i) q^{18} +2.00000i q^{19} +1.23607 q^{20} +(-1.00000 + 4.47214i) q^{21} +1.00000 q^{22} +3.23607i q^{23} +(-1.61803 - 0.618034i) q^{24} -3.47214 q^{25} +6.00000 q^{26} +(4.61803 - 2.38197i) q^{27} +(-2.61803 + 0.381966i) q^{28} +8.47214i q^{29} +(-2.00000 - 0.763932i) q^{30} +5.23607i q^{31} -1.00000i q^{32} +(-1.61803 - 0.618034i) q^{33} +2.76393i q^{34} +(-3.23607 + 0.472136i) q^{35} +(2.23607 + 2.00000i) q^{36} +4.47214 q^{37} +2.00000 q^{38} +(-9.70820 - 3.70820i) q^{39} -1.23607i q^{40} +10.1803 q^{41} +(4.47214 + 1.00000i) q^{42} -6.94427 q^{43} -1.00000i q^{44} +(2.76393 + 2.47214i) q^{45} +3.23607 q^{46} -10.4721 q^{47} +(-0.618034 + 1.61803i) q^{48} +(6.70820 - 2.00000i) q^{49} +3.47214i q^{50} +(1.70820 - 4.47214i) q^{51} -6.00000i q^{52} +5.70820i q^{53} +(-2.38197 - 4.61803i) q^{54} -1.23607i q^{55} +(0.381966 + 2.61803i) q^{56} +(-3.23607 - 1.23607i) q^{57} +8.47214 q^{58} +1.23607 q^{59} +(-0.763932 + 2.00000i) q^{60} -12.4721i q^{61} +5.23607 q^{62} +(-6.61803 - 4.38197i) q^{63} -1.00000 q^{64} -7.41641i q^{65} +(-0.618034 + 1.61803i) q^{66} +10.4721 q^{67} +2.76393 q^{68} +(-5.23607 - 2.00000i) q^{69} +(0.472136 + 3.23607i) q^{70} -16.1803i q^{71} +(2.00000 - 2.23607i) q^{72} -8.18034i q^{73} -4.47214i q^{74} +(2.14590 - 5.61803i) q^{75} -2.00000i q^{76} +(0.381966 + 2.61803i) q^{77} +(-3.70820 + 9.70820i) q^{78} +2.76393 q^{79} -1.23607 q^{80} +(1.00000 + 8.94427i) q^{81} -10.1803i q^{82} -6.00000 q^{83} +(1.00000 - 4.47214i) q^{84} +3.41641 q^{85} +6.94427i q^{86} +(-13.7082 - 5.23607i) q^{87} -1.00000 q^{88} -4.94427 q^{89} +(2.47214 - 2.76393i) q^{90} +(2.29180 + 15.7082i) q^{91} -3.23607i q^{92} +(-8.47214 - 3.23607i) q^{93} +10.4721i q^{94} -2.47214i q^{95} +(1.61803 + 0.618034i) q^{96} +6.47214i q^{97} +(-2.00000 - 6.70820i) q^{98} +(2.00000 - 2.23607i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} - 4 q^{4} + 4 q^{5} + 2 q^{6} + 6 q^{7}+O(q^{10}) \) 4 * q + 2 * q^3 - 4 * q^4 + 4 * q^5 + 2 * q^6 + 6 * q^7	\( 4 q + 2 q^{3} - 4 q^{4} + 4 q^{5} + 2 q^{6} + 6 q^{7} - 2 q^{12} - 6 q^{14} + 12 q^{15} + 4 q^{16} - 20 q^{17} - 8 q^{18} - 4 q^{20} - 4 q^{21} + 4 q^{22} - 2 q^{24} + 4 q^{25} + 24 q^{26} + 14 q^{27} - 6 q^{28} - 8 q^{30} - 2 q^{33} - 4 q^{35} + 8 q^{38} - 12 q^{39} - 4 q^{41} + 8 q^{43} + 20 q^{45} + 4 q^{46} - 24 q^{47} + 2 q^{48} - 20 q^{51} - 14 q^{54} + 6 q^{56} - 4 q^{57} + 16 q^{58} - 4 q^{59} - 12 q^{60} + 12 q^{62} - 22 q^{63} - 4 q^{64} + 2 q^{66} + 24 q^{67} + 20 q^{68} - 12 q^{69} - 16 q^{70} + 8 q^{72} + 22 q^{75} + 6 q^{77} + 12 q^{78} + 20 q^{79} + 4 q^{80} + 4 q^{81} - 24 q^{83} + 4 q^{84} - 40 q^{85} - 28 q^{87} - 4 q^{88} + 16 q^{89} - 8 q^{90} + 36 q^{91} - 16 q^{93} + 2 q^{96} - 8 q^{98} + 8 q^{99}+O(q^{100}) \) 4 * q + 2 * q^3 - 4 * q^4 + 4 * q^5 + 2 * q^6 + 6 * q^7 - 2 * q^12 - 6 * q^14 + 12 * q^15 + 4 * q^16 - 20 * q^17 - 8 * q^18 - 4 * q^20 - 4 * q^21 + 4 * q^22 - 2 * q^24 + 4 * q^25 + 24 * q^26 + 14 * q^27 - 6 * q^28 - 8 * q^30 - 2 * q^33 - 4 * q^35 + 8 * q^38 - 12 * q^39 - 4 * q^41 + 8 * q^43 + 20 * q^45 + 4 * q^46 - 24 * q^47 + 2 * q^48 - 20 * q^51 - 14 * q^54 + 6 * q^56 - 4 * q^57 + 16 * q^58 - 4 * q^59 - 12 * q^60 + 12 * q^62 - 22 * q^63 - 4 * q^64 + 2 * q^66 + 24 * q^67 + 20 * q^68 - 12 * q^69 - 16 * q^70 + 8 * q^72 + 22 * q^75 + 6 * q^77 + 12 * q^78 + 20 * q^79 + 4 * q^80 + 4 * q^81 - 24 * q^83 + 4 * q^84 - 40 * q^85 - 28 * q^87 - 4 * q^88 + 16 * q^89 - 8 * q^90 + 36 * q^91 - 16 * q^93 + 2 * q^96 - 8 * q^98 + 8 * q^99

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