LMFDB - Embedded newform 546.2.k.b.373.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(373,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 4]))

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

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

chi := DirichletCharacter("546.373");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.k (of order $3$, degree $2$, 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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.447703281.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 2x^{6} + 2x^{5} + 3x^{4} + 4x^{3} - 8x^{2} - 8x + 16 $ x^8 - x^7 - 2x^6 + 2x^5 + 3x^4 + 4x^3 - 8x^2 - 8x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			373.2
Root			$-0.571299 - 1.29368i$ of defining polynomial
Character	$\chi$	$=$	546.373
Dual form			546.2.k.b.445.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} -1.00000 q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.228205 + 0.395262i) q^{5} +(0.500000 + 0.866025i) q^{6} +(2.45374 + 0.989520i) q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} -1.00000 q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.228205 + 0.395262i) q^{5} +(0.500000 + 0.866025i) q^{6} +(2.45374 + 0.989520i) q^{7} +1.00000 q^{8} +1.00000 q^{9} +0.456409 q^{10} -3.83707 q^{11} +(0.500000 - 0.866025i) q^{12} +(-3.13422 + 1.78233i) q^{13} +(-0.369922 - 2.61976i) q^{14} +(0.228205 - 0.395262i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.775934 + 1.34396i) q^{17} +(-0.500000 - 0.866025i) q^{18} -2.88244 q^{19} +(-0.228205 - 0.395262i) q^{20} +(-2.45374 - 0.989520i) q^{21} +(1.91853 + 3.32300i) q^{22} +(-1.62170 - 2.80886i) q^{23} -1.00000 q^{24} +(2.39585 + 4.14973i) q^{25} +(3.11065 + 1.82315i) q^{26} -1.00000 q^{27} +(-2.08382 + 1.63024i) q^{28} +(-2.20552 + 3.82007i) q^{29} -0.456409 q^{30} +(4.80098 + 8.31553i) q^{31} +(-0.500000 + 0.866025i) q^{32} +3.83707 q^{33} +1.55187 q^{34} +(-0.951075 + 0.744058i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-0.140245 - 0.242912i) q^{37} +(1.44122 + 2.49627i) q^{38} +(3.13422 - 1.78233i) q^{39} +(-0.228205 + 0.395262i) q^{40} +(-3.57277 + 6.18822i) q^{41} +(0.369922 + 2.61976i) q^{42} +(1.21716 + 2.10818i) q^{43} +(1.91853 - 3.32300i) q^{44} +(-0.228205 + 0.395262i) q^{45} +(-1.62170 + 2.80886i) q^{46} +(-3.93105 + 6.80879i) q^{47} +(0.500000 + 0.866025i) q^{48} +(5.04170 + 4.85605i) q^{49} +(2.39585 - 4.14973i) q^{50} +(0.775934 - 1.34396i) q^{51} +(0.0235697 - 3.60547i) q^{52} +(0.550397 + 0.953315i) q^{53} +(0.500000 + 0.866025i) q^{54} +(0.875637 - 1.51665i) q^{55} +(2.45374 + 0.989520i) q^{56} +2.88244 q^{57} +4.41103 q^{58} +(4.68283 - 8.11090i) q^{59} +(0.228205 + 0.395262i) q^{60} -11.1037 q^{61} +(4.80098 - 8.31553i) q^{62} +(2.45374 + 0.989520i) q^{63} +1.00000 q^{64} +(0.0107575 - 1.64557i) q^{65} +(-1.91853 - 3.32300i) q^{66} -1.78993 q^{67} +(-0.775934 - 1.34396i) q^{68} +(1.62170 + 2.80886i) q^{69} +(1.11991 + 0.451626i) q^{70} +(-5.06527 - 8.77331i) q^{71} +1.00000 q^{72} +(1.40601 + 2.43529i) q^{73} +(-0.140245 + 0.242912i) q^{74} +(-2.39585 - 4.14973i) q^{75} +(1.44122 - 2.49627i) q^{76} +(-9.41517 - 3.79685i) q^{77} +(-3.11065 - 1.82315i) q^{78} +(2.70966 - 4.69326i) q^{79} +0.456409 q^{80} +1.00000 q^{81} +7.14554 q^{82} +1.35738 q^{83} +(2.08382 - 1.63024i) q^{84} +(-0.354144 - 0.613395i) q^{85} +(1.21716 - 2.10818i) q^{86} +(2.20552 - 3.82007i) q^{87} -3.83707 q^{88} +(0.0898485 + 0.155622i) q^{89} +0.456409 q^{90} +(-9.45421 + 1.27200i) q^{91} +3.24339 q^{92} +(-4.80098 - 8.31553i) q^{93} +7.86211 q^{94} +(0.657787 - 1.13932i) q^{95} +(0.500000 - 0.866025i) q^{96} +(4.73894 + 8.20808i) q^{97} +(1.68461 - 6.79427i) q^{98} -3.83707 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} - 8 q^{3} - 4 q^{4} + 2 q^{5} + 4 q^{6} + 3 q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q - 4 * q^2 - 8 * q^3 - 4 * q^4 + 2 * q^5 + 4 * q^6 + 3 * q^7 + 8 * q^8 + 8 * q^9	\( 8 q - 4 q^{2} - 8 q^{3} - 4 q^{4} + 2 q^{5} + 4 q^{6} + 3 q^{7} + 8 q^{8} + 8 q^{9} - 4 q^{10} + 12 q^{11} + 4 q^{12} - 11 q^{13} - 3 q^{14} - 2 q^{15} - 4 q^{16} + 4 q^{17} - 4 q^{18} - 12 q^{19} + 2 q^{20} - 3 q^{21} - 6 q^{22} - 10 q^{23} - 8 q^{24} - 18 q^{25} + 10 q^{26} - 8 q^{27} + 2 q^{29} + 4 q^{30} + 6 q^{31} - 4 q^{32} - 12 q^{33} - 8 q^{34} + 18 q^{35} - 4 q^{36} - 28 q^{37} + 6 q^{38} + 11 q^{39} + 2 q^{40} + 3 q^{42} - 6 q^{43} - 6 q^{44} + 2 q^{45} - 10 q^{46} + q^{47} + 4 q^{48} - 7 q^{49} - 18 q^{50} - 4 q^{51} + q^{52} + 7 q^{53} + 4 q^{54} + q^{55} + 3 q^{56} + 12 q^{57} - 4 q^{58} + 2 q^{59} - 2 q^{60} - 48 q^{61} + 6 q^{62} + 3 q^{63} + 8 q^{64} + 19 q^{65} + 6 q^{66} + 30 q^{67} + 4 q^{68} + 10 q^{69} - 18 q^{70} + 6 q^{71} + 8 q^{72} + q^{73} - 28 q^{74} + 18 q^{75} + 6 q^{76} - 22 q^{77} - 10 q^{78} - 12 q^{79} - 4 q^{80} + 8 q^{81} - 32 q^{83} - 13 q^{85} - 6 q^{86} - 2 q^{87} + 12 q^{88} + 25 q^{89} - 4 q^{90} + 34 q^{91} + 20 q^{92} - 6 q^{93} - 2 q^{94} - 8 q^{95} + 4 q^{96} - q^{97} + 2 q^{98} + 12 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 - 8 * q^3 - 4 * q^4 + 2 * q^5 + 4 * q^6 + 3 * q^7 + 8 * q^8 + 8 * q^9 - 4 * q^10 + 12 * q^11 + 4 * q^12 - 11 * q^13 - 3 * q^14 - 2 * q^15 - 4 * q^16 + 4 * q^17 - 4 * q^18 - 12 * q^19 + 2 * q^20 - 3 * q^21 - 6 * q^22 - 10 * q^23 - 8 * q^24 - 18 * q^25 + 10 * q^26 - 8 * q^27 + 2 * q^29 + 4 * q^30 + 6 * q^31 - 4 * q^32 - 12 * q^33 - 8 * q^34 + 18 * q^35 - 4 * q^36 - 28 * q^37 + 6 * q^38 + 11 * q^39 + 2 * q^40 + 3 * q^42 - 6 * q^43 - 6 * q^44 + 2 * q^45 - 10 * q^46 + q^47 + 4 * q^48 - 7 * q^49 - 18 * q^50 - 4 * q^51 + q^52 + 7 * q^53 + 4 * q^54 + q^55 + 3 * q^56 + 12 * q^57 - 4 * q^58 + 2 * q^59 - 2 * q^60 - 48 * q^61 + 6 * q^62 + 3 * q^63 + 8 * q^64 + 19 * q^65 + 6 * q^66 + 30 * q^67 + 4 * q^68 + 10 * q^69 - 18 * q^70 + 6 * q^71 + 8 * q^72 + q^73 - 28 * q^74 + 18 * q^75 + 6 * q^76 - 22 * q^77 - 10 * q^78 - 12 * q^79 - 4 * q^80 + 8 * q^81 - 32 * q^83 - 13 * q^85 - 6 * q^86 - 2 * q^87 + 12 * q^88 + 25 * q^89 - 4 * q^90 + 34 * q^91 + 20 * q^92 - 6 * q^93 - 2 * q^94 - 8 * q^95 + 4 * q^96 - q^97 + 2 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.228205	+	0.395262i	−0.102056	+	0.176767i	−0.912532	−	0.409006i	$-0.865875\pi$
$5$	−0.228205	+	0.395262i	−0.102056	+	0.176767i	0.810475	+	0.585773i	$0.199209\pi$
$6$	0.500000	+	0.866025i	0.204124	+	0.353553i
$7$	2.45374	+	0.989520i	0.927427	+	0.374003i
$7$	2.45374	+	0.989520i	0.927427	+	0.374003i
$8$	1.00000			0.353553
$9$	1.00000			0.333333
$10$	0.456409			0.144329
$11$	−3.83707			−1.15692			−0.578460	−	0.815711i	$-0.696346\pi$
$11$	−3.83707			−1.15692			−0.578460	+	0.815711i	$0.696346\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	−3.13422	+	1.78233i	−0.869275	+	0.494328i
$13$	−3.13422	+	1.78233i	−0.869275	+	0.494328i
$14$	−0.369922	−	2.61976i	−0.0988658	−	0.700161i
$15$	0.228205	−	0.395262i	0.0589222	−	0.102056i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.775934	+	1.34396i	−0.188192	+	0.325958i	−0.944647	−	0.328087i	$-0.893596\pi$
$17$	−0.775934	+	1.34396i	−0.188192	+	0.325958i	0.756456	+	0.654045i	$0.226929\pi$
$18$	−0.500000	−	0.866025i	−0.117851	−	0.204124i
$19$	−2.88244			−0.661278			−0.330639	−	0.943757i	$-0.607264\pi$
$19$	−2.88244			−0.661278			−0.330639	+	0.943757i	$0.607264\pi$
$20$	−0.228205	−	0.395262i	−0.0510281	−	0.0883833i
$21$	−2.45374	−	0.989520i	−0.535450	−	0.215931i
$22$	1.91853	+	3.32300i	0.409033	+	0.708465i
$23$	−1.62170	−	2.80886i	−0.338147	−	0.585688i	0.645937	−	0.763391i	$-0.276467\pi$
$23$	−1.62170	−	2.80886i	−0.338147	−	0.585688i	−0.984084	+	0.177703i	$0.943133\pi$
$24$	−1.00000			−0.204124
$25$	2.39585	+	4.14973i	0.479169	+	0.829945i
$26$	3.11065	+	1.82315i	0.610048	+	0.357549i
$27$	−1.00000			−0.192450
$28$	−2.08382	+	1.63024i	−0.393805	+	0.308087i
$29$	−2.20552	+	3.82007i	−0.409554	+	0.709369i	−0.994840	−	0.101459i	$-0.967649\pi$
$29$	−2.20552	+	3.82007i	−0.409554	+	0.709369i	0.585286	+	0.810827i	$0.300982\pi$
$30$	−0.456409			−0.0833286
$31$	4.80098	+	8.31553i	0.862281	+	1.49351i	0.869722	+	0.493542i	$0.164298\pi$
$31$	4.80098	+	8.31553i	0.862281	+	1.49351i	−0.00744135	+	0.999972i	$0.502369\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	3.83707			0.667948
$34$	1.55187			0.266143
$35$	−0.951075	+	0.744058i	−0.160761	+	0.125769i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	−0.140245	−	0.242912i	−0.0230562	−	0.0399345i	0.854267	−	0.519834i	$-0.174006\pi$
$37$	−0.140245	−	0.242912i	−0.0230562	−	0.0399345i	−0.877323	+	0.479900i	$0.840673\pi$
$38$	1.44122	+	2.49627i	0.233797	+	0.404948i
$39$	3.13422	−	1.78233i	0.501876	−	0.285400i
$40$	−0.228205	+	0.395262i	−0.0360823	+	0.0624964i
$41$	−3.57277	+	6.18822i	−0.557973	+	0.966438i	0.439692	+	0.898148i	$0.355087\pi$
$41$	−3.57277	+	6.18822i	−0.557973	+	0.966438i	−0.997666	+	0.0682894i	$0.978246\pi$
$42$	0.369922	+	2.61976i	0.0570802	+	0.404238i
$43$	1.21716	+	2.10818i	0.185615	+	0.321494i	0.943783	−	0.330564i	$-0.107239\pi$
$43$	1.21716	+	2.10818i	0.185615	+	0.321494i	−0.758169	+	0.652058i	$0.773906\pi$
$44$	1.91853	−	3.32300i	0.289230	−	0.500961i
$45$	−0.228205	+	0.395262i	−0.0340187	+	0.0589222i
$46$	−1.62170	+	2.80886i	−0.239106	+	0.414144i
$47$	−3.93105	+	6.80879i	−0.573403	+	0.993163i	0.422810	+	0.906218i	$0.361044\pi$
$47$	−3.93105	+	6.80879i	−0.573403	+	0.993163i	−0.996213	+	0.0869451i	$0.972290\pi$
$48$	0.500000	+	0.866025i	0.0721688	+	0.125000i
$49$	5.04170	+	4.85605i	0.720243	+	0.693722i
$50$	2.39585	−	4.14973i	0.338824	−	0.586860i
$51$	0.775934	−	1.34396i	0.108653	−	0.188192i
$52$	0.0235697	−	3.60547i	0.00326854	−	0.499989i
$53$	0.550397	+	0.953315i	0.0756028	+	0.130948i	0.901348	−	0.433095i	$-0.142579\pi$
$53$	0.550397	+	0.953315i	0.0756028	+	0.130948i	−0.825745	+	0.564043i	$0.809245\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$	0.875637	−	1.51665i	0.118071	−	0.204505i
$56$	2.45374	+	0.989520i	0.327895	+	0.132230i
$57$	2.88244			0.381789
$58$	4.41103			0.579197
$59$	4.68283	−	8.11090i	0.609652	−	1.05595i	−0.381645	−	0.924309i	$-0.624642\pi$
$59$	4.68283	−	8.11090i	0.609652	−	1.05595i	0.991298	−	0.131640i	$-0.0420243\pi$
$60$	0.228205	+	0.395262i	0.0294611	+	0.0510281i
$61$	−11.1037			−1.42169			−0.710844	−	0.703350i	$-0.751687\pi$
$61$	−11.1037			−1.42169			−0.710844	+	0.703350i	$0.751687\pi$
$62$	4.80098	−	8.31553i	0.609725	−	1.05607i
$63$	2.45374	+	0.989520i	0.309142	+	0.124668i
$64$	1.00000			0.125000
$65$	0.0107575	−	1.64557i	0.00133430	−	0.204108i
$66$	−1.91853	−	3.32300i	−0.236155	−	0.409033i
$67$	−1.78993			−0.218674			−0.109337	−	0.994005i	$-0.534873\pi$
$67$	−1.78993			−0.218674			−0.109337	+	0.994005i	$0.534873\pi$
$68$	−0.775934	−	1.34396i	−0.0940959	−	0.162979i
$69$	1.62170	+	2.80886i	0.195229	+	0.338147i
$70$	1.11991	+	0.451626i	0.133855	+	0.0539796i
$71$	−5.06527	−	8.77331i	−0.601137	−	1.04120i	−0.992649	−	0.121027i	$-0.961381\pi$
$71$	−5.06527	−	8.77331i	−0.601137	−	1.04120i	0.391512	−	0.920173i	$-0.371952\pi$
$72$	1.00000			0.117851
$73$	1.40601	+	2.43529i	0.164561	+	0.285029i	0.936499	−	0.350669i	$-0.114046\pi$
$73$	1.40601	+	2.43529i	0.164561	+	0.285029i	−0.771938	+	0.635698i	$0.780712\pi$
$74$	−0.140245	+	0.242912i	−0.0163032	+	0.0282379i
$75$	−2.39585	−	4.14973i	−0.276648	−	0.479169i
$76$	1.44122	−	2.49627i	0.165319	−	0.286342i
$77$	−9.41517	−	3.79685i	−1.07296	−	0.432692i
$78$	−3.11065	−	1.82315i	−0.352211	−	0.206431i
$79$	2.70966	−	4.69326i	0.304860	−	0.528033i	−0.672370	−	0.740215i	$-0.734724\pi$
$79$	2.70966	−	4.69326i	0.304860	−	0.528033i	0.977230	+	0.212182i	$0.0680570\pi$
$80$	0.456409			0.0510281
$81$	1.00000			0.111111
$82$	7.14554			0.789093
$83$	1.35738			0.148992			0.0744959	−	0.997221i	$-0.476265\pi$
$83$	1.35738			0.148992			0.0744959	+	0.997221i	$0.476265\pi$
$84$	2.08382	−	1.63024i	0.227363	−	0.177874i
$85$	−0.354144	−	0.613395i	−0.0384123	−	0.0665320i
$86$	1.21716	−	2.10818i	0.131249	−	0.227330i
$87$	2.20552	−	3.82007i	0.236456	−	0.409554i
$88$	−3.83707			−0.409033
$89$	0.0898485	+	0.155622i	0.00952392	+	0.0164959i	0.870748	−	0.491729i	$-0.163635\pi$
$89$	0.0898485	+	0.155622i	0.00952392	+	0.0164959i	−0.861224	+	0.508225i	$0.830302\pi$
$90$	0.456409			0.0481098
$91$	−9.45421	+	1.27200i	−0.991070	+	0.133341i
$92$	3.24339			0.338147
$93$	−4.80098	−	8.31553i	−0.497838	−	0.862281i
$94$	7.86211			0.810915
$95$	0.657787	−	1.13932i	0.0674875	−	0.116892i
$96$	0.500000	−	0.866025i	0.0510310	−	0.0883883i
$97$	4.73894	+	8.20808i	0.481166	+	0.833405i	0.999766	−	0.0216122i	$-0.00687993\pi$
$97$	4.73894	+	8.20808i	0.481166	+	0.833405i	−0.518600	+	0.855017i	$0.673547\pi$
$98$	1.68461	−	6.79427i	0.170172	−	0.686325i
$99$	−3.83707			−0.385640
$100$	−4.79169			−0.479169
$101$	6.36213			0.633056			0.316528	−	0.948583i	$-0.397483\pi$
$101$	6.36213			0.633056			0.316528	+	0.948583i	$0.397483\pi$
$102$	−1.55187			−0.153658
$103$	−8.28934	+	14.3576i	−0.816773	+	1.41469i	0.0912754	+	0.995826i	$0.470906\pi$
$103$	−8.28934	+	14.3576i	−0.816773	+	1.41469i	−0.908048	+	0.418866i	$0.862428\pi$
$104$	−3.13422	+	1.78233i	−0.307335	+	0.174771i
$105$	0.951075	−	0.744058i	0.0928154	−	0.0726126i
$106$	0.550397	−	0.953315i	0.0534593	−	0.0925942i
$107$	−8.46023	−	14.6536i	−0.817882	−	1.41661i	−0.907240	−	0.420613i	$-0.861815\pi$
$107$	−8.46023	−	14.6536i	−0.817882	−	1.41661i	0.0893583	−	0.996000i	$-0.471518\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	3.95108	+	6.84346i	0.378444	+	0.655485i	0.990836	−	0.135070i	$-0.0431258\pi$
$109$	3.95108	+	6.84346i	0.378444	+	0.655485i	−0.612392	+	0.790554i	$0.709792\pi$
$110$	−1.75127			−0.166977
$111$	0.140245	+	0.242912i	0.0133115	+	0.0230562i
$112$	−0.369922	−	2.61976i	−0.0349543	−	0.247544i
$113$	3.40689	+	5.90091i	0.320494	+	0.555111i	0.980590	−	0.196070i	$-0.0628179\pi$
$113$	3.40689	+	5.90091i	0.320494	+	0.555111i	−0.660096	+	0.751181i	$0.729485\pi$
$114$	−1.44122	−	2.49627i	−0.134983	−	0.233797i
$115$	1.48031			0.138040
$116$	−2.20552	−	3.82007i	−0.204777	−	0.354684i
$117$	−3.13422	+	1.78233i	−0.289758	+	0.164776i
$118$	−9.36566			−0.862179
$119$	−3.23382	+	2.52992i	−0.296443	+	0.231918i
$120$	0.228205	−	0.395262i	0.0208321	−	0.0360823i
$121$	3.72308			0.338462
$122$	5.55187	+	9.61612i	0.502643	+	0.870602i
$123$	3.57277	−	6.18822i	0.322146	−	0.557973i
$124$	−9.60195			−0.862281
$125$	−4.46902			−0.399721
$126$	−0.369922	−	2.61976i	−0.0329553	−	0.233387i
$127$	10.9334	−	18.9372i	0.970183	−	1.68041i	0.275190	−	0.961390i	$-0.411259\pi$
$127$	10.9334	−	18.9372i	0.970183	−	1.68041i	0.694993	−	0.719016i	$-0.255407\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−1.21716	−	2.10818i	−0.107165	−	0.185615i
$130$	−1.43049	+	0.813470i	−0.125462	+	0.0713460i
$131$	4.72554	−	8.18487i	0.412872	−	0.715116i	−0.582330	−	0.812952i	$-0.697859\pi$
$131$	4.72554	−	8.18487i	0.412872	−	0.715116i	0.995202	+	0.0978367i	$0.0311923\pi$
$132$	−1.91853	+	3.32300i	−0.166987	+	0.289230i
$133$	−7.07277	−	2.85223i	−0.613287	−	0.247320i
$134$	0.894964	+	1.55012i	0.0773131	+	0.133910i
$135$	0.228205	−	0.395262i	0.0196407	−	0.0340187i
$136$	−0.775934	+	1.34396i	−0.0665358	+	0.115243i
$137$	−1.22396	+	2.11996i	−0.104570	+	0.181121i	−0.913562	−	0.406698i	$-0.866680\pi$
$137$	−1.22396	+	2.11996i	−0.104570	+	0.181121i	0.808992	+	0.587819i	$0.200013\pi$
$138$	1.62170	−	2.80886i	0.138048	−	0.239106i
$139$	−5.37228	−	9.30505i	−0.455670	−	0.789244i	0.543056	−	0.839696i	$-0.317267\pi$
$139$	−5.37228	−	9.30505i	−0.455670	−	0.789244i	−0.998726	+	0.0504521i	$0.983934\pi$
$140$	−0.168836	−	1.19568i	−0.0142692	−	0.101054i
$141$	3.93105	−	6.80879i	0.331054	−	0.573403i
$142$	−5.06527	+	8.77331i	−0.425068	+	0.736240i
$143$	12.0262	−	6.83890i	1.00568	−	0.571898i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−1.00662	−	1.74351i	−0.0835951	−	0.144791i
$146$	1.40601	−	2.43529i	0.116362	−	0.201546i
$147$	−5.04170	−	4.85605i	−0.415833	−	0.400520i
$148$	0.280491			0.0230562
$149$	9.30314			0.762143			0.381072	−	0.924546i	$-0.375555\pi$
$149$	9.30314			0.762143			0.381072	+	0.924546i	$0.375555\pi$
$150$	−2.39585	+	4.14973i	−0.195620	+	0.338824i
$151$	−10.3722	−	17.9651i	−0.844075	−	1.46198i	−0.886422	−	0.462878i	$-0.846817\pi$
$151$	−10.3722	−	17.9651i	−0.844075	−	1.46198i	0.0423464	−	0.999103i	$-0.486517\pi$
$152$	−2.88244			−0.233797
$153$	−0.775934	+	1.34396i	−0.0627306	+	0.108653i
$154$	1.41942	+	10.0522i	0.114380	+	0.810030i
$155$	−4.38242			−0.352004
$156$	−0.0235697	+	3.60547i	−0.00188709	+	0.288669i
$157$	3.22701	+	5.58934i	0.257543	+	0.446078i	0.965583	−	0.260094i	$-0.0837536\pi$
$157$	3.22701	+	5.58934i	0.257543	+	0.446078i	−0.708040	+	0.706172i	$0.750420\pi$
$158$	−5.41931			−0.431137
$159$	−0.550397	−	0.953315i	−0.0436493	−	0.0756028i
$160$	−0.228205	−	0.395262i	−0.0180412	−	0.0312482i
$161$	−1.19980	−	8.49692i	−0.0945576	−	0.669651i
$162$	−0.500000	−	0.866025i	−0.0392837	−	0.0680414i
$163$	8.71775			0.682827			0.341413	−	0.939913i	$-0.389094\pi$
$163$	8.71775			0.682827			0.341413	+	0.939913i	$0.389094\pi$
$164$	−3.57277	−	6.18822i	−0.278987	−	0.483219i
$165$	−0.875637	+	1.51665i	−0.0681682	+	0.118071i
$166$	−0.678689	−	1.17552i	−0.0526765	−	0.0912384i
$167$	−11.4560	+	19.8424i	−0.886491	+	1.53545i	−0.0424965	+	0.999097i	$0.513531\pi$
$167$	−11.4560	+	19.8424i	−0.886491	+	1.53545i	−0.843995	+	0.536351i	$0.819802\pi$
$168$	−2.45374	−	0.989520i	−0.189310	−	0.0763431i
$169$	6.64663	−	11.1724i	0.511280	−	0.859414i
$170$	−0.354144	+	0.613395i	−0.0271616	+	0.0470452i
$171$	−2.88244			−0.220426
$172$	−2.43431			−0.185615
$173$	7.58716			0.576841			0.288421	−	0.957504i	$-0.406870\pi$
$173$	7.58716			0.576841			0.288421	+	0.957504i	$0.406870\pi$
$174$	−4.41103			−0.334400
$175$	1.77255	+	12.5531i	0.133992	+	0.948925i
$176$	1.91853	+	3.32300i	0.144615	+	0.250480i
$177$	−4.68283	+	8.11090i	−0.351983	+	0.609652i
$178$	0.0898485	−	0.155622i	0.00673443	−	0.0116644i
$179$	12.5041			0.934600			0.467300	−	0.884099i	$-0.345227\pi$
$179$	12.5041			0.934600			0.467300	+	0.884099i	$0.345227\pi$
$180$	−0.228205	−	0.395262i	−0.0170094	−	0.0294611i
$181$	−2.26428			−0.168303			−0.0841513	−	0.996453i	$-0.526818\pi$
$181$	−2.26428			−0.168303			−0.0841513	+	0.996453i	$0.526818\pi$
$182$	5.82868	+	7.55158i	0.432051	+	0.559761i
$183$	11.1037			0.820812
$184$	−1.62170	−	2.80886i	−0.119553	−	0.207072i
$185$	0.128019			0.00941211
$186$	−4.80098	+	8.31553i	−0.352025	+	0.609725i
$187$	2.97731	−	5.15686i	0.217723	−	0.377107i
$188$	−3.93105	−	6.80879i	−0.286702	−	0.496582i
$189$	−2.45374	−	0.989520i	−0.178483	−	0.0719770i
$190$	−1.31557			−0.0954418
$191$	−9.17297			−0.663733			−0.331867	−	0.943326i	$-0.607678\pi$
$191$	−9.17297			−0.663733			−0.331867	+	0.943326i	$0.607678\pi$
$192$	−1.00000			−0.0721688
$193$	−2.43985			−0.175624			−0.0878122	−	0.996137i	$-0.527988\pi$
$193$	−2.43985			−0.175624			−0.0878122	+	0.996137i	$0.527988\pi$
$194$	4.73894	−	8.20808i	0.340236	−	0.589306i
$195$	−0.0107575	+	1.64557i	−0.000770357	+	0.117842i
$196$	−6.72632	+	1.93822i	−0.480451	+	0.138444i
$197$	−13.4334	+	23.2673i	−0.957091	+	1.65773i	−0.227581	+	0.973759i	$0.573082\pi$
$197$	−13.4334	+	23.2673i	−0.957091	+	1.65773i	−0.729510	+	0.683971i	$0.760252\pi$
$198$	1.91853	+	3.32300i	0.136344	+	0.236155i
$199$	13.9509	−	24.1638i	0.988957	−	1.71292i	0.366129	−	0.930564i	$-0.380683\pi$
$199$	13.9509	−	24.1638i	0.988957	−	1.71292i	0.622828	−	0.782359i	$-0.285984\pi$
$200$	2.39585	+	4.14973i	0.169412	+	0.293430i
$201$	1.78993			0.126252
$202$	−3.18107	−	5.50977i	−0.223819	−	0.387666i
$203$	−9.19180	+	7.19106i	−0.645138	+	0.504713i
$204$	0.775934	+	1.34396i	0.0543263	+	0.0940959i
$205$	−1.63065	−	2.82436i	−0.113889	−	0.197262i
$206$	16.5787			1.15509
$207$	−1.62170	−	2.80886i	−0.112716	−	0.195229i
$208$	3.11065	+	1.82315i	0.215685	+	0.126413i
$209$	11.0601			0.765045
$210$	−1.11991	−	0.451626i	−0.0772812	−	0.0311652i
$211$	10.9871	−	19.0301i	0.756381	−	1.31009i	−0.188305	−	0.982111i	$-0.560299\pi$
$211$	10.9871	−	19.0301i	0.756381	−	1.31009i	0.944685	−	0.327979i	$-0.106367\pi$
$212$	−1.10079			−0.0756028
$213$	5.06527	+	8.77331i	0.347067	+	0.601137i
$214$	−8.46023	+	14.6536i	−0.578330	+	1.00170i
$215$	−1.11104			−0.0757725
$216$	−1.00000			−0.0680414
$217$	3.55197	+	25.1548i	0.241124	+	1.70762i
$218$	3.95108	−	6.84346i	0.267601	−	0.463498i
$219$	−1.40601	−	2.43529i	−0.0950095	−	0.164561i
$220$	0.875637	+	1.51665i	0.0590354	+	0.102252i
$221$	0.0365772	−	5.59522i	0.00246045	−	0.376375i
$222$	0.140245	−	0.242912i	0.00941265	−	0.0163032i
$223$	−6.87919	+	11.9151i	−0.460664	+	0.797894i	−0.998994	−	0.0448402i	$-0.985722\pi$
$223$	−6.87919	+	11.9151i	−0.460664	+	0.797894i	0.538330	+	0.842734i	$0.319055\pi$
$224$	−2.08382	+	1.63024i	−0.139231	+	0.108925i
$225$	2.39585	+	4.14973i	0.159723	+	0.276648i
$226$	3.40689	−	5.90091i	0.226623	−	0.392523i
$227$	−9.41545	+	16.3080i	−0.624925	+	1.08240i	0.363630	+	0.931543i	$0.381537\pi$
$227$	−9.41545	+	16.3080i	−0.624925	+	1.08240i	−0.988555	+	0.150859i	$0.951796\pi$
$228$	−1.44122	+	2.49627i	−0.0954472	+	0.165319i
$229$	1.74812	−	3.02784i	0.115519	−	0.200085i	−0.802468	−	0.596695i	$-0.796480\pi$
$229$	1.74812	−	3.02784i	0.115519	−	0.200085i	0.917987	+	0.396610i	$0.129814\pi$
$230$	−0.740157	−	1.28199i	−0.0488045	−	0.0845319i
$231$	9.41517	+	3.79685i	0.619473	+	0.249815i
$232$	−2.20552	+	3.82007i	−0.144799	+	0.250800i
$233$	9.74031	−	16.8707i	0.638109	−	1.10524i	−0.347739	−	0.937592i	$-0.613050\pi$
$233$	9.74031	−	16.8707i	0.638109	−	1.10524i	0.985847	−	0.167645i	$-0.0536163\pi$
$234$	3.11065	+	1.82315i	0.203349	+	0.119183i
$235$	−1.79417	−	3.10759i	−0.117039	−	0.202717i
$236$	4.68283	+	8.11090i	0.304826	+	0.527974i
$237$	−2.70966	+	4.69326i	−0.176011	+	0.304860i
$238$	3.80789	+	1.53560i	0.246829	+	0.0995385i
$239$	12.5469			0.811592			0.405796	−	0.913964i	$-0.366994\pi$
$239$	12.5469			0.811592			0.405796	+	0.913964i	$0.366994\pi$
$240$	−0.456409			−0.0294611
$241$	0.233225	−	0.403958i	0.0150234	−	0.0260212i	−0.858416	−	0.512954i	$-0.828551\pi$
$241$	0.233225	−	0.403958i	0.0150234	−	0.0260212i	0.873439	+	0.486933i	$0.161884\pi$
$242$	−1.86154	−	3.22428i	−0.119664	−	0.207265i
$243$	−1.00000			−0.0641500
$244$	5.55187	−	9.61612i	0.355422	−	0.615609i
$245$	−3.06995	+	0.884620i	−0.196132	+	0.0565163i
$246$	−7.14554			−0.455583
$247$	9.03420	−	5.13745i	0.574832	−	0.326888i
$248$	4.80098	+	8.31553i	0.304862	+	0.528037i
$249$	−1.35738			−0.0860204
$250$	2.23451	+	3.87028i	0.141323	+	0.244778i
$251$	12.7935	+	22.1590i	0.807517	+	1.39866i	0.914579	+	0.404408i	$0.132522\pi$
$251$	12.7935	+	22.1590i	0.807517	+	1.39866i	−0.107062	+	0.994252i	$0.534144\pi$
$252$	−2.08382	+	1.63024i	−0.131268	+	0.102696i
$253$	6.22256	+	10.7778i	0.391209	+	0.677594i
$254$	−21.8668			−1.37205
$255$	0.354144	+	0.613395i	0.0221773	+	0.0384123i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	1.88805	+	3.27020i	0.117774	+	0.203990i	0.918885	−	0.394525i	$-0.129091\pi$
$257$	1.88805	+	3.27020i	0.117774	+	0.203990i	−0.801112	+	0.598515i	$0.795758\pi$
$258$	−1.21716	+	2.10818i	−0.0757768	+	0.131249i
$259$	−0.103760	−	0.734819i	−0.00644731	−	0.0456594i
$260$	1.41973	+	0.832102i	0.0880478	+	0.0516048i
$261$	−2.20552	+	3.82007i	−0.136518	+	0.236456i
$262$	−9.45108			−0.583889
$263$	19.6872			1.21396			0.606981	−	0.794716i	$-0.292380\pi$
$263$	19.6872			1.21396			0.606981	+	0.794716i	$0.292380\pi$
$264$	3.83707			0.236155
$265$	−0.502413			−0.0308630
$266$	1.06628	+	7.55132i	0.0653777	+	0.463001i
$267$	−0.0898485	−	0.155622i	−0.00549864	−	0.00952392i
$268$	0.894964	−	1.55012i	0.0546686	−	0.0946888i
$269$	4.39082	−	7.60513i	0.267713	−	0.463693i	−0.700558	−	0.713596i	$-0.747065\pi$
$269$	4.39082	−	7.60513i	0.267713	−	0.463693i	0.968271	+	0.249903i	$0.0803987\pi$
$270$	−0.456409			−0.0277762
$271$	−14.4014	−	24.9439i	−0.874820	−	1.51523i	−0.856955	−	0.515392i	$-0.827646\pi$
$271$	−14.4014	−	24.9439i	−0.874820	−	1.51523i	−0.0178654	−	0.999840i	$-0.505687\pi$
$272$	1.55187			0.0940959
$273$	9.45421	−	1.27200i	0.572195	−	0.0769847i
$274$	2.44792			0.147884
$275$	−9.19302	−	15.9228i	−0.554360	−	0.960179i
$276$	−3.24339			−0.195229
$277$	−3.47496	+	6.01880i	−0.208790	+	0.361635i	−0.951334	−	0.308163i	$-0.900286\pi$
$277$	−3.47496	+	6.01880i	−0.208790	+	0.361635i	0.742544	+	0.669798i	$0.233619\pi$
$278$	−5.37228	+	9.30505i	−0.322208	+	0.558080i
$279$	4.80098	+	8.31553i	0.287427	+	0.497838i
$280$	−0.951075	+	0.744058i	−0.0568376	+	0.0444660i
$281$	−12.5116			−0.746381			−0.373190	−	0.927755i	$-0.621736\pi$
$281$	−12.5116			−0.746381			−0.373190	+	0.927755i	$0.621736\pi$
$282$	−7.86211			−0.468182
$283$	11.2039			0.666003			0.333001	−	0.942926i	$-0.391939\pi$
$283$	11.2039			0.666003			0.333001	+	0.942926i	$0.391939\pi$
$284$	10.1305			0.601137
$285$	−0.657787	+	1.13932i	−0.0389639	+	0.0674875i
$286$	−11.9358	−	6.99554i	−0.705776	−	0.413655i
$287$	−14.8900	+	11.6490i	−0.878931	+	0.687617i
$288$	−0.500000	+	0.866025i	−0.0294628	+	0.0510310i
$289$	7.29585	+	12.6368i	0.429168	+	0.743340i
$290$	−1.00662	+	1.74351i	−0.0591107	+	0.102383i
$291$	−4.73894	−	8.20808i	−0.277802	−	0.481166i
$292$	−2.81202			−0.164561
$293$	14.2699	+	24.7162i	0.833657	+	1.44394i	0.895119	+	0.445827i	$0.147090\pi$
$293$	14.2699	+	24.7162i	0.833657	+	1.44394i	−0.0614625	+	0.998109i	$0.519576\pi$
$294$	−1.68461	+	6.79427i	−0.0982487	+	0.396250i
$295$	2.13729	+	3.70189i	0.124438	+	0.215532i
$296$	−0.140245	−	0.242912i	−0.00815159	−	0.0141190i
$297$	3.83707			0.222649
$298$	−4.65157	−	8.05676i	−0.269458	−	0.466715i
$299$	10.0891	+	5.91319i	0.583465	+	0.341969i
$300$	4.79169			0.276648
$301$	0.900505	+	6.37732i	0.0519043	+	0.367583i
$302$	−10.3722	+	17.9651i	−0.596851	+	1.03378i
$303$	−6.36213			−0.365495
$304$	1.44122	+	2.49627i	0.0826597	+	0.143171i
$305$	2.53392	−	4.38889i	0.145092	−	0.251307i
$306$	1.55187			0.0887144
$307$	−23.1907			−1.32356			−0.661781	−	0.749698i	$-0.730199\pi$
$307$	−23.1907			−1.32356			−0.661781	+	0.749698i	$0.730199\pi$
$308$	7.99576	−	6.25535i	0.455601	−	0.356432i
$309$	8.28934	−	14.3576i	0.471564	−	0.816773i
$310$	2.19121	+	3.79529i	0.124452	+	0.215558i
$311$	11.6740	+	20.2200i	0.661973	+	1.14657i	0.980096	+	0.198522i	$0.0636142\pi$
$311$	11.6740	+	20.2200i	0.661973	+	1.14657i	−0.318123	+	0.948049i	$0.603052\pi$
$312$	3.13422	−	1.78233i	0.177440	−	0.100904i
$313$	7.26499	−	12.5833i	0.410641	−	0.711252i	−0.584319	−	0.811524i	$-0.698638\pi$
$313$	7.26499	−	12.5833i	0.410641	−	0.711252i	0.994960	+	0.100273i	$0.0319715\pi$
$314$	3.22701	−	5.58934i	0.182111	−	0.315425i
$315$	−0.951075	+	0.744058i	−0.0535870	+	0.0419229i
$316$	2.70966	+	4.69326i	0.152430	+	0.264017i
$317$	1.64596	−	2.85089i	0.0924463	−	0.160122i	−0.816094	−	0.577920i	$-0.803865\pi$
$317$	1.64596	−	2.85089i	0.0924463	−	0.160122i	0.908540	+	0.417798i	$0.137198\pi$
$318$	−0.550397	+	0.953315i	−0.0308647	+	0.0534593i
$319$	8.46271	−	14.6579i	0.473821	−	0.820682i
$320$	−0.228205	+	0.395262i	−0.0127570	+	0.0220958i
$321$	8.46023	+	14.6536i	0.472204	+	0.817882i
$322$	−6.75865	+	5.28752i	−0.376645	+	0.294662i
$323$	2.23659	−	3.87388i	0.124447	−	0.215549i
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	−14.9053	−	8.73597i	−0.826795	−	0.484584i
$326$	−4.35887	−	7.54979i	−0.241416	−	0.418144i
$327$	−3.95108	−	6.84346i	−0.218495	−	0.378444i
$328$	−3.57277	+	6.18822i	−0.197273	+	0.341687i
$329$	−16.3832	+	12.8171i	−0.903236	+	0.706632i
$330$	1.75127			0.0964044
$331$	16.1057			0.885250			0.442625	−	0.896707i	$-0.354047\pi$
$331$	16.1057			0.885250			0.442625	+	0.896707i	$0.354047\pi$
$332$	−0.678689	+	1.17552i	−0.0372479	+	0.0645153i
$333$	−0.140245	−	0.242912i	−0.00768540	−	0.0133115i
$334$	22.9120			1.25369
$335$	0.408470	−	0.707490i	0.0223171	−	0.0386543i
$336$	0.369922	+	2.61976i	0.0201809	+	0.142920i
$337$	−14.9134			−0.812383			−0.406192	−	0.913788i	$-0.633143\pi$
$337$	−14.9134			−0.812383			−0.406192	+	0.913788i	$0.633143\pi$
$338$	−12.9989	−	0.169960i	−0.707046	−	0.00924462i
$339$	−3.40689	−	5.90091i	−0.185037	−	0.320494i
$340$	0.708287			0.0384123
$341$	−18.4217	−	31.9073i	−0.997589	−	1.72787i
$342$	1.44122	+	2.49627i	0.0779323	+	0.134983i
$343$	7.56588	+	16.9044i	0.408519	+	0.912750i
$344$	1.21716	+	2.10818i	0.0656246	+	0.113665i
$345$	−1.48031			−0.0796975
$346$	−3.79358	−	6.57067i	−0.203944	−	0.353242i
$347$	−14.4006	+	24.9425i	−0.773062	+	1.33898i	0.162815	+	0.986657i	$0.447943\pi$
$347$	−14.4006	+	24.9425i	−0.773062	+	1.33898i	−0.935877	+	0.352326i	$0.885391\pi$
$348$	2.20552	+	3.82007i	0.118228	+	0.204777i
$349$	2.50740	−	4.34294i	0.134218	−	0.232472i	−0.791081	−	0.611712i	$-0.790481\pi$
$349$	2.50740	−	4.34294i	0.134218	−	0.232472i	0.925298	+	0.379240i	$0.123814\pi$
$350$	9.98502	−	7.81162i	0.533722	−	0.417549i
$351$	3.13422	−	1.78233i	0.167292	−	0.0951335i
$352$	1.91853	−	3.32300i	0.102258	−	0.177116i
$353$	−11.5667			−0.615631			−0.307816	−	0.951446i	$-0.599598\pi$
$353$	−11.5667			−0.615631			−0.307816	+	0.951446i	$0.599598\pi$
$354$	9.36566			0.497779
$355$	4.62367			0.245399
$356$	−0.179697			−0.00952392
$357$	3.23382	−	2.52992i	0.171152	−	0.133898i
$358$	−6.25205	−	10.8289i	−0.330431	−	0.572324i
$359$	−14.9173	+	25.8375i	−0.787306	+	1.36365i	0.140306	+	0.990108i	$0.455191\pi$
$359$	−14.9173	+	25.8375i	−0.787306	+	1.36365i	−0.927612	+	0.373546i	$0.878142\pi$
$360$	−0.228205	+	0.395262i	−0.0120274	+	0.0208321i
$361$	−10.6915			−0.562712
$362$	1.13214	+	1.96092i	0.0595040	+	0.103064i
$363$	−3.72308			−0.195411
$364$	3.62552	−	8.82358i	0.190029	−	0.462481i
$365$	−1.28343			−0.0671780
$366$	−5.55187	−	9.61612i	−0.290201	−	0.502643i
$367$	7.27789			0.379903			0.189951	−	0.981793i	$-0.439167\pi$
$367$	7.27789			0.379903			0.189951	+	0.981793i	$0.439167\pi$
$368$	−1.62170	+	2.80886i	−0.0845368	+	0.146422i
$369$	−3.57277	+	6.18822i	−0.185991	+	0.322146i
$370$	−0.0640093	−	0.110867i	−0.00332768	−	0.00576372i
$371$	0.407208	+	2.88382i	0.0211412	+	0.149720i
$372$	9.60195			0.497838
$373$	31.0916			1.60986			0.804932	−	0.593367i	$-0.202202\pi$
$373$	31.0916			1.60986			0.804932	+	0.593367i	$0.202202\pi$
$374$	−5.95462			−0.307906
$375$	4.46902			0.230779
$376$	−3.93105	+	6.80879i	−0.202729	+	0.351136i
$377$	0.103967	−	15.9039i	0.00535457	−	0.819091i
$378$	0.369922	+	2.61976i	0.0190267	+	0.134746i
$379$	−9.33146	+	16.1626i	−0.479325	+	0.830215i	−0.999719	−	0.0237115i	$-0.992452\pi$
$379$	−9.33146	+	16.1626i	−0.479325	+	0.830215i	0.520394	+	0.853926i	$0.325785\pi$
$380$	0.657787	+	1.13932i	0.0337438	+	0.0584459i
$381$	−10.9334	+	18.9372i	−0.560135	+	0.970183i
$382$	4.58649	+	7.94403i	0.234665	+	0.406452i
$383$	8.96269			0.457972			0.228986	−	0.973430i	$-0.426459\pi$
$383$	8.96269			0.457972			0.228986	+	0.973430i	$0.426459\pi$
$384$	0.500000	+	0.866025i	0.0255155	+	0.0441942i
$385$	3.64934	−	2.85500i	0.185988	−	0.145504i
$386$	1.21993	+	2.11297i	0.0620926	+	0.107548i
$387$	1.21716	+	2.10818i	0.0618715	+	0.107165i
$388$	−9.47788			−0.481166
$389$	−14.5103	−	25.1326i	−0.735702	−	1.27427i	−0.954415	−	0.298484i	$-0.903519\pi$
$389$	−14.5103	−	25.1326i	−0.735702	−	1.27427i	0.218712	−	0.975789i	$-0.429814\pi$
$390$	1.43049	−	0.813470i	0.0724355	−	0.0411916i
$391$	5.03332			0.254546
$392$	5.04170	+	4.85605i	0.254644	+	0.245268i
$393$	−4.72554	+	8.18487i	−0.238372	+	0.412872i
$394$	26.8668			1.35353
$395$	1.23671	+	2.14205i	0.0622257	+	0.107778i
$396$	1.91853	−	3.32300i	0.0964099	−	0.166987i
$397$	−4.34889			−0.218265			−0.109132	−	0.994027i	$-0.534807\pi$
$397$	−4.34889			−0.218265			−0.109132	+	0.994027i	$0.534807\pi$
$398$	−27.9019			−1.39860
$399$	7.07277	+	2.85223i	0.354081	+	0.142790i
$400$	2.39585	−	4.14973i	0.119792	−	0.207486i
$401$	−4.77562	−	8.27162i	−0.238483	−	0.413065i	0.721796	−	0.692106i	$-0.243317\pi$
$401$	−4.77562	−	8.27162i	−0.238483	−	0.413065i	−0.960279	+	0.279041i	$0.909984\pi$
$402$	−0.894964	−	1.55012i	−0.0446367	−	0.0773131i
$403$	−29.8683	−	17.5058i	−1.48785	−	0.872026i
$404$	−3.18107	+	5.50977i	−0.158264	+	0.274121i
$405$	−0.228205	+	0.395262i	−0.0113396	+	0.0196407i
$406$	10.8235	+	4.36480i	0.537163	+	0.216622i
$407$	0.538131	+	0.932070i	0.0266741	+	0.0462010i
$408$	0.775934	−	1.34396i	0.0384145	−	0.0665358i
$409$	−0.635121	+	1.10006i	−0.0314047	+	0.0543946i	−0.881301	−	0.472556i	$-0.843331\pi$
$409$	−0.635121	+	1.10006i	−0.0314047	+	0.0543946i	0.849896	+	0.526951i	$0.176665\pi$
$410$	−1.63065	+	2.82436i	−0.0805319	+	0.139485i
$411$	1.22396	−	2.11996i	0.0603736	−	0.104570i
$412$	−8.28934	−	14.3576i	−0.408386	−	0.707346i
$413$	19.5163	−	15.2683i	0.960337	−	0.751304i
$414$	−1.62170	+	2.80886i	−0.0797020	+	0.138048i
$415$	−0.309760	+	0.536520i	−0.0152055	+	0.0263368i
$416$	0.0235697	−	3.60547i	0.00115560	−	0.176773i
$417$	5.37228	+	9.30505i	0.263081	+	0.455670i
$418$	−5.53006	−	9.57835i	−0.270484	−	0.468492i
$419$	5.25472	−	9.10144i	0.256710	−	0.444634i	−0.708649	−	0.705561i	$-0.750695\pi$
$419$	5.25472	−	9.10144i	0.256710	−	0.444634i	0.965359	+	0.260927i	$0.0840282\pi$
$420$	0.168836	+	1.19568i	0.00823834	+	0.0583434i
$421$	−1.14121			−0.0556192			−0.0278096	−	0.999613i	$-0.508853\pi$
$421$	−1.14121			−0.0556192			−0.0278096	+	0.999613i	$0.508853\pi$
$422$	−21.9741			−1.06968
$423$	−3.93105	+	6.80879i	−0.191134	+	0.331054i
$424$	0.550397	+	0.953315i	0.0267296	+	0.0462971i
$425$	−7.43607			−0.360703
$426$	5.06527	−	8.77331i	0.245413	−	0.425068i
$427$	−27.2457	−	10.9874i	−1.31851	−	0.531716i
$428$	16.9205			0.817882
$429$	−12.0262	+	6.83890i	−0.580630	+	0.330185i
$430$	0.555521	+	0.962191i	0.0267896	+	0.0464010i
$431$	31.3274			1.50899			0.754493	−	0.656308i	$-0.227883\pi$
$431$	31.3274			1.50899			0.754493	+	0.656308i	$0.227883\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	−7.06113	−	12.2302i	−0.339336	−	0.587748i	0.644972	−	0.764206i	$-0.276869\pi$
$433$	−7.06113	−	12.2302i	−0.339336	−	0.587748i	−0.984308	+	0.176459i	$0.943536\pi$
$434$	20.0087	−	15.6535i	0.960450	−	0.751393i
$435$	1.00662	+	1.74351i	0.0482637	+	0.0835951i
$436$	−7.90215			−0.378444
$437$	4.67445	+	8.09638i	0.223609	+	0.387302i
$438$	−1.40601	+	2.43529i	−0.0671819	+	0.116362i
$439$	3.23066	+	5.59567i	0.154191	+	0.267067i	0.932764	−	0.360487i	$-0.117390\pi$
$439$	3.23066	+	5.59567i	0.154191	+	0.267067i	−0.778573	+	0.627554i	$0.784056\pi$
$440$	0.875637	−	1.51665i	0.0417443	−	0.0723033i
$441$	5.04170	+	4.85605i	0.240081	+	0.231241i
$442$	−4.86389	+	2.76593i	−0.231352	+	0.131562i
$443$	−5.70730	+	9.88534i	−0.271162	+	0.469667i	−0.969160	−	0.246434i	$-0.920741\pi$
$443$	−5.70730	+	9.88534i	−0.271162	+	0.469667i	0.697998	+	0.716100i	$0.254075\pi$
$444$	−0.280491			−0.0133115
$445$	−0.0820154			−0.00388790
$446$	13.7584			0.651478
$447$	−9.30314			−0.440024
$448$	2.45374	+	0.989520i	0.115928	+	0.0467504i
$449$	−19.8942	−	34.4578i	−0.938867	−	1.62617i	−0.767589	−	0.640942i	$-0.778544\pi$
$449$	−19.8942	−	34.4578i	−0.938867	−	1.62617i	−0.171278	−	0.985223i	$-0.554790\pi$
$450$	2.39585	−	4.14973i	0.112941	−	0.195620i
$451$	13.7090	−	23.7446i	0.645530	−	1.11809i
$452$	−6.81379			−0.320494
$453$	10.3722	+	17.9651i	0.487327	+	0.844075i
$454$	18.8309			0.883778
$455$	1.65472	−	4.02717i	0.0775746	−	0.188796i
$456$	2.88244			0.134983
$457$	2.62643	+	4.54910i	0.122859	+	0.212798i	0.920894	−	0.389813i	$-0.127460\pi$
$457$	2.62643	+	4.54910i	0.122859	+	0.212798i	−0.798035	+	0.602611i	$0.794127\pi$
$458$	−3.49624			−0.163369
$459$	0.775934	−	1.34396i	0.0362175	−	0.0627306i
$460$	−0.740157	+	1.28199i	−0.0345100	+	0.0597731i
$461$	9.59122	+	16.6125i	0.446707	+	0.773720i	0.998169	−	0.0604800i	$-0.0192631\pi$
$461$	9.59122	+	16.6125i	0.446707	+	0.773720i	−0.551462	+	0.834200i	$0.685930\pi$
$462$	−1.41942	−	10.0522i	−0.0660372	−	0.467671i
$463$	−17.5580			−0.815988			−0.407994	−	0.912985i	$-0.633772\pi$
$463$	−17.5580			−0.815988			−0.407994	+	0.912985i	$0.633772\pi$
$464$	4.41103			0.204777
$465$	4.38242			0.203230
$466$	−19.4806			−0.902422
$467$	−1.54111	+	2.66928i	−0.0713141	+	0.123520i	−0.899477	−	0.436967i	$-0.856053\pi$
$467$	−1.54111	+	2.66928i	−0.0713141	+	0.123520i	0.828163	+	0.560487i	$0.189386\pi$
$468$	0.0235697	−	3.60547i	0.00108951	−	0.166663i
$469$	−4.39202	−	1.77117i	−0.202805	−	0.0817849i
$470$	−1.79417	+	3.10759i	−0.0827589	+	0.143343i
$471$	−3.22701	−	5.58934i	−0.148693	−	0.257543i
$472$	4.68283	−	8.11090i	0.215545	−	0.373334i
$473$	−4.67031	−	8.08921i	−0.214741	−	0.371942i
$474$	5.41931			0.248917
$475$	−6.90589	−	11.9613i	−0.316864	−	0.548824i
$476$	−0.574070	−	4.06553i	−0.0263125	−	0.186343i
$477$	0.550397	+	0.953315i	0.0252009	+	0.0436493i
$478$	−6.27346	−	10.8659i	−0.286941	−	0.496997i
$479$	18.3621			0.838985			0.419493	−	0.907759i	$-0.362208\pi$
$479$	18.3621			0.838985			0.419493	+	0.907759i	$0.362208\pi$
$480$	0.228205	+	0.395262i	0.0104161	+	0.0180412i
$481$	0.872507	+	0.511376i	0.0397829	+	0.0233168i
$482$	−0.466451			−0.0212463
$483$	1.19980	+	8.49692i	0.0545929	+	0.386623i
$484$	−1.86154	+	3.22428i	−0.0846155	+	0.146558i
$485$	−4.32579			−0.196424
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	−9.00530	+	15.5976i	−0.408069	+	0.706796i	−0.994673	−	0.103077i	$-0.967131\pi$
$487$	−9.00530	+	15.5976i	−0.408069	+	0.706796i	0.586604	+	0.809874i	$0.300464\pi$
$488$	−11.1037			−0.502643
$489$	−8.71775			−0.394230
$490$	2.30108	+	2.21635i	0.103952	+	0.100124i
$491$	−7.98794	+	13.8355i	−0.360491	+	0.624388i	−0.988042	−	0.154187i	$-0.950724\pi$
$491$	−7.98794	+	13.8355i	−0.360491	+	0.624388i	0.627551	+	0.778576i	$0.284057\pi$
$492$	3.57277	+	6.18822i	0.161073	+	0.278987i
$493$	−3.42267	−	5.92824i	−0.154149	−	0.266995i
$494$	−8.96626	−	5.25512i	−0.403411	−	0.236439i
$495$	0.875637	−	1.51665i	0.0393569	−	0.0681682i
$496$	4.80098	−	8.31553i	0.215570	−	0.373379i
$497$	−3.74751	−	26.5396i	−0.168099	−	1.19046i
$498$	0.678689	+	1.17552i	0.0304128	+	0.0526765i
$499$	−4.06656	+	7.04348i	−0.182044	+	0.315309i	−0.942576	−	0.333990i	$-0.891605\pi$
$499$	−4.06656	+	7.04348i	−0.182044	+	0.315309i	0.760532	+	0.649300i	$0.224938\pi$
$500$	2.23451	−	3.87028i	0.0999303	−	0.173084i
$501$	11.4560	−	19.8424i	0.511816	−	0.886491i
$502$	12.7935	−	22.1590i	0.571001	−	0.989002i
$503$	−18.8326	−	32.6190i	−0.839705	−	1.45441i	−0.890142	−	0.455684i	$-0.849395\pi$
$503$	−18.8326	−	32.6190i	−0.839705	−	1.45441i	0.0504368	−	0.998727i	$-0.483939\pi$
$504$	2.45374	+	0.989520i	0.109298	+	0.0440767i
$505$	−1.45187	+	2.51471i	−0.0646073	+	0.111903i
$506$	6.22256	−	10.7778i	0.276626	−	0.479131i
$507$	−6.64663	+	11.1724i	−0.295187	+	0.496183i
$508$	10.9334	+	18.9372i	0.485092	+	0.840203i
$509$	13.8779	+	24.0372i	0.615127	+	1.06543i	0.990362	+	0.138501i	$0.0442284\pi$
$509$	13.8779	+	24.0372i	0.615127	+	1.06543i	−0.375236	+	0.926929i	$0.622438\pi$
$510$	0.354144	−	0.613395i	0.0156817	−	0.0271616i
$511$	1.04023	+	7.36684i	0.0460170	+	0.325890i
$512$	1.00000			0.0441942
$513$	2.88244			0.127263
$514$	1.88805	−	3.27020i	0.0832785	−	0.144243i
$515$	−3.78333	−	6.55292i	−0.166713	−	0.288756i
$516$	2.43431			0.107165
$517$	15.0837	−	26.1258i	0.663381	−	1.14901i
$518$	−0.584492	+	0.457268i	−0.0256811	+	0.0200912i
$519$	−7.58716			−0.333039
$520$	0.0107575	−	1.64557i	0.000471745	−	0.0721631i
$521$	−7.66182	−	13.2707i	−0.335671	−	0.581398i	0.647943	−	0.761689i	$-0.275630\pi$
$521$	−7.66182	−	13.2707i	−0.335671	−	0.581398i	−0.983613	+	0.180291i	$0.942296\pi$
$522$	4.41103			0.193066
$523$	−12.5383	−	21.7170i	−0.548263	−	0.949620i	−0.998394	−	0.0566571i	$-0.981956\pi$
$523$	−12.5383	−	21.7170i	−0.548263	−	0.949620i	0.450130	−	0.892963i	$-0.351378\pi$
$524$	4.72554	+	8.18487i	0.206436	+	0.357558i
$525$	−1.77255	−	12.5531i	−0.0773605	−	0.547862i
$526$	−9.84358	−	17.0496i	−0.429201	−	0.743397i
$527$	−14.9010			−0.649096
$528$	−1.91853	−	3.32300i	−0.0834934	−	0.144615i
$529$	6.24020	−	10.8083i	0.271313	−	0.469928i
$530$	0.251206	+	0.435102i	0.0109117	+	0.0188996i
$531$	4.68283	−	8.11090i	0.203217	−	0.351983i
$532$	6.00649	−	4.69908i	0.260414	−	0.203731i
$533$	0.168419	−	25.7631i	0.00729502	−	1.11592i
$534$	−0.0898485	+	0.155622i	−0.00388812	+	0.00673443i
$535$	7.72266			0.333880
$536$	−1.78993			−0.0773131
$537$	−12.5041			−0.539592
$538$	−8.78165			−0.378604
$539$	−19.3453	−	18.6330i	−0.833263	−	0.802580i
$540$	0.228205	+	0.395262i	0.00982037	+	0.0170094i
$541$	−14.2260	+	24.6402i	−0.611624	+	1.05936i	0.379343	+	0.925256i	$0.376150\pi$
$541$	−14.2260	+	24.6402i	−0.611624	+	1.05936i	−0.990967	+	0.134107i	$0.957183\pi$
$542$	−14.4014	+	24.9439i	−0.618591	+	1.07143i
$543$	2.26428			0.0971696
$544$	−0.775934	−	1.34396i	−0.0332679	−	0.0576217i
$545$	−3.60662			−0.154490
$546$	−5.82868	−	7.55158i	−0.249445	−	0.323178i
$547$	4.99706			0.213659			0.106829	−	0.994277i	$-0.465930\pi$
$547$	4.99706			0.213659			0.106829	+	0.994277i	$0.465930\pi$
$548$	−1.22396	−	2.11996i	−0.0522851	−	0.0905604i
$549$	−11.1037			−0.473896
$550$	−9.19302	+	15.9228i	−0.391992	+	0.678949i
$551$	6.35728	−	11.0111i	0.270829	−	0.469090i
$552$	1.62170	+	2.80886i	0.0690240	+	0.119553i
$553$	11.2929	−	8.83480i	0.480222	−	0.375694i
$554$	6.94992			0.295274
$555$	−0.128019			−0.00543408
$556$	10.7446			0.455670
$557$	31.7130			1.34372			0.671861	−	0.740677i	$-0.265495\pi$
$557$	31.7130			1.34372			0.671861	+	0.740677i	$0.265495\pi$
$558$	4.80098	−	8.31553i	0.203242	−	0.352025i
$559$	−7.57228	−	4.43811i	−0.320274	−	0.187712i
$560$	1.11991	+	0.451626i	0.0473249	+	0.0190847i
$561$	−2.97731	+	5.15686i	−0.125702	+	0.217723i
$562$	6.25581	+	10.8354i	0.263885	+	0.457063i
$563$	−11.9474	+	20.6935i	−0.503523	+	0.872127i	0.496469	+	0.868055i	$0.334630\pi$
$563$	−11.9474	+	20.6935i	−0.503523	+	0.872127i	−0.999992	+	0.00407268i	$0.998704\pi$
$564$	3.93105	+	6.80879i	0.165527	+	0.286702i
$565$	−3.10988			−0.130833
$566$	−5.60195	−	9.70287i	−0.235468	−	0.407842i
$567$	2.45374	+	0.989520i	0.103047	+	0.0415559i
$568$	−5.06527	−	8.77331i	−0.212534	−	0.368120i
$569$	19.2320	+	33.3109i	0.806249	+	1.39646i	0.915445	+	0.402443i	$0.131839\pi$
$569$	19.2320	+	33.3109i	0.806249	+	1.39646i	−0.109196	+	0.994020i	$0.534828\pi$
$570$	1.31557			0.0551033
$571$	15.8854	+	27.5143i	0.664782	+	1.15144i	0.979344	+	0.202199i	$0.0648088\pi$
$571$	15.8854	+	27.5143i	0.664782	+	1.15144i	−0.314563	+	0.949237i	$0.601858\pi$
$572$	−0.0904387	+	13.8344i	−0.00378143	+	0.578447i
$573$	9.17297			0.383207
$574$	17.5333	+	7.07066i	0.731827	+	0.295123i
$575$	7.77067	−	13.4592i	0.324059	−	0.561287i
$576$	1.00000			0.0416667
$577$	10.1750	+	17.6236i	0.423591	+	0.733682i	0.996288	−	0.0860858i	$-0.0274359\pi$
$577$	10.1750	+	17.6236i	0.423591	+	0.733682i	−0.572696	+	0.819768i	$0.694103\pi$
$578$	7.29585	−	12.6368i	0.303467	−	0.525621i
$579$	2.43985			0.101397
$580$	2.01324			0.0835951
$581$	3.33066	+	1.34315i	0.138179	+	0.0557234i
$582$	−4.73894	+	8.20808i	−0.196435	+	0.340236i
$583$	−2.11191	−	3.65793i	−0.0874664	−	0.151496i
$584$	1.40601	+	2.43529i	0.0581812	+	0.100773i
$585$	0.0107575	−	1.64557i	0.000444766	−	0.0680360i
$586$	14.2699	−	24.7162i	0.589484	−	1.02102i
$587$	−11.7425	+	20.3386i	−0.484664	+	0.839462i	−0.999845	−	0.0176191i	$-0.994391\pi$
$587$	−11.7425	+	20.3386i	−0.484664	+	0.839462i	0.515181	+	0.857081i	$0.327725\pi$
$588$	6.72632	−	1.93822i	0.277389	−	0.0799307i
$589$	−13.8385	−	23.9691i	−0.570207	−	0.987628i
$590$	2.13729	−	3.70189i	0.0879907	−	0.152404i
$591$	13.4334	−	23.2673i	0.552577	−	0.957091i
$592$	−0.140245	+	0.242912i	−0.00576405	+	0.00998362i
$593$	−0.268350	+	0.464796i	−0.0110198	+	0.0190869i	−0.871483	−	0.490426i	$-0.836841\pi$
$593$	−0.268350	+	0.464796i	−0.0110198	+	0.0190869i	0.860463	+	0.509513i	$0.170174\pi$
$594$	−1.91853	−	3.32300i	−0.0787184	−	0.136344i
$595$	−0.262011	−	1.85555i	−0.0107414	−	0.0760699i
$596$	−4.65157	+	8.05676i	−0.190536	+	0.330018i
$597$	−13.9509	+	24.1638i	−0.570974	+	0.988957i
$598$	0.0764459	−	11.6940i	0.00312611	−	0.478202i
$599$	9.68962	+	16.7829i	0.395907	+	0.685731i	0.993217	−	0.116280i	$-0.0370969\pi$
$599$	9.68962	+	16.7829i	0.395907	+	0.685731i	−0.597309	+	0.802011i	$0.703764\pi$
$600$	−2.39585	−	4.14973i	−0.0978100	−	0.169412i
$601$	7.74999	−	13.4234i	0.316129	−	0.547551i	−0.663548	−	0.748134i	$-0.730950\pi$
$601$	7.74999	−	13.4234i	0.316129	−	0.547551i	0.979677	+	0.200583i	$0.0642835\pi$
$602$	5.07267	−	3.96852i	0.206747	−	0.161745i
$603$	−1.78993			−0.0728915
$604$	20.7443			0.844075
$605$	−0.849624	+	1.47159i	−0.0345421	+	0.0598287i
$606$	3.18107	+	5.50977i	0.129222	+	0.223819i
$607$	15.7526			0.639379			0.319690	−	0.947522i	$-0.396421\pi$
$607$	15.7526			0.639379			0.319690	+	0.947522i	$0.396421\pi$
$608$	1.44122	−	2.49627i	0.0584492	−	0.101237i
$609$	9.19180	−	7.19106i	0.372471	−	0.291396i
$610$	−5.06785			−0.205191
$611$	0.185308	−	28.3466i	0.00749675	−	1.14678i
$612$	−0.775934	−	1.34396i	−0.0313653	−	0.0543263i
$613$	31.0881			1.25564			0.627818	−	0.778360i	$-0.283948\pi$
$613$	31.0881			1.25564			0.627818	+	0.778360i	$0.283948\pi$
$614$	11.5953	+	20.0837i	0.467950	+	0.810512i
$615$	1.63065	+	2.82436i	0.0657540	+	0.113889i
$616$	−9.41517	−	3.79685i	−0.379348	−	0.152980i
$617$	9.39918	+	16.2799i	0.378397	+	0.655403i	0.990829	−	0.135120i	$-0.0431421\pi$
$617$	9.39918	+	16.2799i	0.378397	+	0.655403i	−0.612432	+	0.790523i	$0.709809\pi$
$618$	−16.5787			−0.666892
$619$	−10.6461	−	18.4396i	−0.427904	−	0.741152i	0.568783	−	0.822488i	$-0.307415\pi$
$619$	−10.6461	−	18.4396i	−0.427904	−	0.741152i	−0.996687	+	0.0813361i	$0.974081\pi$
$620$	2.19121	−	3.79529i	0.0880011	−	0.152422i
$621$	1.62170	+	2.80886i	0.0650764	+	0.112716i
$622$	11.6740	−	20.2200i	0.468086	−	0.810749i
$623$	0.0664738	+	0.470763i	0.00266322	+	0.0188607i
$624$	−3.11065	−	1.82315i	−0.124526	−	0.0729844i
$625$	−10.9594	+	18.9822i	−0.438375	+	0.759288i
$626$	−14.5300			−0.580735
$627$	−11.0601			−0.441699
$628$	−6.45402			−0.257543
$629$	0.435285			0.0173559
$630$	1.11991	+	0.451626i	0.0446183	+	0.0179932i
$631$	−4.63522	−	8.02844i	−0.184525	−	0.319607i	0.758891	−	0.651218i	$-0.225741\pi$
$631$	−4.63522	−	8.02844i	−0.184525	−	0.319607i	−0.943416	+	0.331610i	$0.892408\pi$
$632$	2.70966	−	4.69326i	0.107784	−	0.186688i
$633$	−10.9871	+	19.0301i	−0.436697	+	0.756381i
$634$	−3.29192			−0.130739
$635$	4.99011	+	8.64312i	0.198026	+	0.342992i
$636$	1.10079			0.0436493
$637$	−24.4569	−	6.23397i	−0.969016	−	0.246999i
$638$	−16.9254			−0.670084
$639$	−5.06527	−	8.77331i	−0.200379	−	0.347067i
$640$	0.456409			0.0180412
$641$	−21.8796	+	37.8967i	−0.864194	+	1.49683i	0.00365084	+	0.999993i	$0.498838\pi$
$641$	−21.8796	+	37.8967i	−0.864194	+	1.49683i	−0.867845	+	0.496835i	$0.834495\pi$
$642$	8.46023	−	14.6536i	0.333899	−	0.578330i
$643$	10.6905	+	18.5165i	0.421593	+	0.730220i	0.996095	−	0.0882825i	$-0.0281378\pi$
$643$	10.6905	+	18.5165i	0.421593	+	0.730220i	−0.574503	+	0.818503i	$0.694805\pi$
$644$	7.95845	+	3.20940i	0.313607	+	0.126468i
$645$	1.11104			0.0437473
$646$	−4.47317			−0.175995
$647$	−8.13845			−0.319955			−0.159978	−	0.987121i	$-0.551142\pi$
$647$	−8.13845			−0.319955			−0.159978	+	0.987121i	$0.551142\pi$
$648$	1.00000			0.0392837
$649$	−17.9683	+	31.1221i	−0.705318	+	1.22165i
$650$	−0.112939	+	17.2763i	−0.00442983	+	0.677633i
$651$	−3.55197	−	25.1548i	−0.139213	−	0.985896i
$652$	−4.35887	+	7.54979i	−0.170707	+	0.295673i
$653$	9.93944	+	17.2156i	0.388960	+	0.673699i	0.992310	−	0.123778i	$-0.0395010\pi$
$653$	9.93944	+	17.2156i	0.388960	+	0.673699i	−0.603350	+	0.797477i	$0.706168\pi$
$654$	−3.95108	+	6.84346i	−0.154499	+	0.267601i
$655$	2.15678	+	3.73565i	0.0842723	+	0.145964i
$656$	7.14554			0.278987
$657$	1.40601	+	2.43529i	0.0548538	+	0.0950095i
$658$	19.2916	+	7.77971i	0.752064	+	0.303285i
$659$	−4.78352	−	8.28530i	−0.186339	−	0.322749i	0.757688	−	0.652617i	$-0.226329\pi$
$659$	−4.78352	−	8.28530i	−0.186339	−	0.322749i	−0.944027	+	0.329868i	$0.892996\pi$
$660$	−0.875637	−	1.51665i	−0.0340841	−	0.0590354i
$661$	−11.4187			−0.444135			−0.222068	−	0.975031i	$-0.571281\pi$
$661$	−11.4187			−0.444135			−0.222068	+	0.975031i	$0.571281\pi$
$662$	−8.05285	−	13.9480i	−0.312983	−	0.542103i
$663$	−0.0365772	+	5.59522i	−0.00142054	+	0.217300i
$664$	1.35738			0.0526765
$665$	2.74142	−	2.14471i	0.106308	−	0.0831681i
$666$	−0.140245	+	0.242912i	−0.00543440	+	0.00941265i
$667$	14.3067			0.553958
$668$	−11.4560	−	19.8424i	−0.443246	−	0.767724i
$669$	6.87919	−	11.9151i	0.265965	−	0.460664i
$670$	−0.816939			−0.0315611
$671$	42.6058			1.64478
$672$	2.08382	−	1.63024i	0.0803851	−	0.0628880i
$673$	−7.10491	+	12.3061i	−0.273874	+	0.474364i	−0.969850	−	0.243701i	$-0.921639\pi$
$673$	−7.10491	+	12.3061i	−0.273874	+	0.474364i	0.695976	+	0.718065i	$0.254972\pi$
$674$	7.45669	+	12.9154i	0.287221	+	0.497481i
$675$	−2.39585	−	4.14973i	−0.0922161	−	0.159723i
$676$	6.35225	+	11.3423i	0.244317	+	0.436244i
$677$	7.31125	−	12.6635i	0.280994	−	0.486696i	−0.690636	−	0.723203i	$-0.742669\pi$
$677$	7.31125	−	12.6635i	0.280994	−	0.486696i	0.971630	+	0.236507i	$0.0760025\pi$
$678$	−3.40689	+	5.90091i	−0.130841	+	0.226623i
$679$	3.50608	+	24.8298i	0.134551	+	0.952880i
$680$	−0.354144	−	0.613395i	−0.0135808	−	0.0235226i
$681$	9.41545	−	16.3080i	0.360801	−	0.624925i
$682$	−18.4217	+	31.9073i	−0.705402	+	1.22179i
$683$	17.5855	−	30.4589i	0.672890	−	1.16548i	−0.304191	−	0.952611i	$-0.598386\pi$
$683$	17.5855	−	30.4589i	0.672890	−	1.16548i	0.977081	−	0.212868i	$-0.0682805\pi$
$684$	1.44122	−	2.49627i	0.0551065	−	0.0954472i
$685$	−0.558628	−	0.967572i	−0.0213441	−	0.0369690i
$686$	10.8567	−	15.0044i	0.414510	−	0.572872i
$687$	−1.74812	+	3.02784i	−0.0666950	+	0.115519i
$688$	1.21716	−	2.10818i	0.0464036	−	0.0803734i
$689$	−3.42418	−	2.00691i	−0.130451	−	0.0764572i
$690$	0.740157	+	1.28199i	0.0281773	+	0.0488045i
$691$	−6.90574	−	11.9611i	−0.262707	−	0.455021i	0.704254	−	0.709948i	$-0.251282\pi$
$691$	−6.90574	−	11.9611i	−0.262707	−	0.455021i	−0.966960	+	0.254927i	$0.917948\pi$
$692$	−3.79358	+	6.57067i	−0.144210	+	0.249779i
$693$	−9.41517	−	3.79685i	−0.357653	−	0.144231i
$694$	28.8011			1.09327
$695$	4.90391			0.186016
$696$	2.20552	−	3.82007i	0.0835999	−	0.144799i
$697$	−5.54447	−	9.60331i	−0.210012	−	0.363751i
$698$	−5.01479			−0.189813
$699$	−9.74031	+	16.8707i	−0.368412	+	0.638109i
$700$	−11.7576	−	4.74147i	−0.444394	−	0.179211i
$701$	−17.6965			−0.668387			−0.334193	−	0.942504i	$-0.608464\pi$
$701$	−17.6965			−0.668387			−0.334193	+	0.942504i	$0.608464\pi$
$702$	−3.11065	−	1.82315i	−0.117404	−	0.0688103i
$703$	0.404249	+	0.700180i	0.0152465	+	0.0264078i
$704$	−3.83707			−0.144615
$705$	1.79417	+	3.10759i	0.0675723	+	0.117039i
$706$	5.78333	+	10.0170i	0.217659	+	0.376996i
$707$	15.6110	+	6.29545i	0.587113	+	0.236765i
$708$	−4.68283	−	8.11090i	−0.175991	−	0.304826i
$709$	34.8684			1.30951			0.654755	−	0.755842i	$-0.272772\pi$
$709$	34.8684			1.30951			0.654755	+	0.755842i	$0.272772\pi$
$710$	−2.31184	−	4.00422i	−0.0867617	−	0.150276i
$711$	2.70966	−	4.69326i	0.101620	−	0.176011i
$712$	0.0898485	+	0.155622i	0.00336721	+	0.00583218i
$713$	15.5715	−	26.9705i	0.583155	−	1.01005i
$714$	−3.80789	−	1.53560i	−0.142507	−	0.0574686i
$715$	−0.0412771	+	6.31417i	−0.00154367	+	0.236137i
$716$	−6.25205	+	10.8289i	−0.233650	+	0.404694i
$717$	−12.5469			−0.468573
$718$	29.8346			1.11342
$719$	3.11104			0.116022			0.0580112	−	0.998316i	$-0.481524\pi$
$719$	3.11104			0.116022			0.0580112	+	0.998316i	$0.481524\pi$
$720$	0.456409			0.0170094
$721$	−34.5470	+	27.0273i	−1.28660	+	1.00655i
$722$	5.34576	+	9.25913i	0.198949	+	0.344589i
$723$	−0.233225	+	0.403958i	−0.00867375	+	0.0150234i
$724$	1.13214	−	1.96092i	0.0420757	−	0.0728772i
$725$	−21.1363			−0.784983
$726$	1.86154	+	3.22428i	0.0690882	+	0.119664i
$727$	22.0591			0.818128			0.409064	−	0.912506i	$-0.365855\pi$
$727$	22.0591			0.818128			0.409064	+	0.912506i	$0.365855\pi$
$728$	−9.45421	+	1.27200i	−0.350396	+	0.0471433i
$729$	1.00000			0.0370370
$730$	0.641717	+	1.11149i	0.0237510	+	0.0411380i
$731$	−3.77773			−0.139724
$732$	−5.55187	+	9.61612i	−0.205203	+	0.355422i
$733$	−24.6272	+	42.6555i	−0.909626	+	1.57552i	−0.0950410	+	0.995473i	$0.530298\pi$
$733$	−24.6272	+	42.6555i	−0.909626	+	1.57552i	−0.814585	+	0.580045i	$0.803035\pi$
$734$	−3.63895	−	6.30284i	−0.134316	−	0.232642i
$735$	3.06995	−	0.884620i	0.113237	−	0.0326297i
$736$	3.24339			0.119553
$737$	6.86807			0.252989
$738$	7.14554			0.263031
$739$	−34.1376			−1.25577			−0.627886	−	0.778305i	$-0.716080\pi$
$739$	−34.1376			−1.25577			−0.627886	+	0.778305i	$0.716080\pi$
$740$	−0.0640093	+	0.110867i	−0.00235303	+	0.00407556i
$741$	−9.03420	+	5.13745i	−0.331880	+	0.188729i
$742$	2.29386	−	1.79456i	0.0842101	−	0.0658804i
$743$	−20.1806	+	34.9539i	−0.740356	+	1.28233i	0.211977	+	0.977275i	$0.432010\pi$
$743$	−20.1806	+	34.9539i	−0.740356	+	1.28233i	−0.952333	+	0.305060i	$0.901324\pi$
$744$	−4.80098	−	8.31553i	−0.176012	−	0.304862i
$745$	−2.12302	+	3.67718i	−0.0777815	+	0.134721i
$746$	−15.5458	−	26.9261i	−0.569173	−	0.985836i
$747$	1.35738			0.0496639
$748$	2.97731	+	5.15686i	0.108861	+	0.188553i
$749$	−6.25925	−	44.3276i	−0.228708	−	1.61970i
$750$	−2.23451	−	3.87028i	−0.0815928	−	0.141323i
$751$	16.9285	+	29.3210i	0.617729	+	1.06994i	0.989899	+	0.141773i	$0.0452803\pi$
$751$	16.9285	+	29.3210i	0.617729	+	1.06994i	−0.372170	+	0.928164i	$0.621386\pi$
$752$	7.86211			0.286702
$753$	−12.7935	−	22.1590i	−0.466220	−	0.807517i
$754$	−13.8251	+	7.86190i	−0.503482	+	0.286313i
$755$	9.46791			0.344573
$756$	2.08382	−	1.63024i	0.0757878	−	0.0592914i
$757$	−10.3752	+	17.9704i	−0.377094	+	0.653146i	−0.990638	−	0.136515i	$-0.956410\pi$
$757$	−10.3752	+	17.9704i	−0.377094	+	0.653146i	0.613544	+	0.789660i	$0.289743\pi$
$758$	18.6629			0.677867
$759$	−6.22256	−	10.7778i	−0.225865	−	0.391209i
$760$	0.657787	−	1.13932i	0.0238604	−	0.0413275i
$761$	1.15718			0.0419477			0.0209739	−	0.999780i	$-0.493323\pi$
$761$	1.15718			0.0419477			0.0209739	+	0.999780i	$0.493323\pi$
$762$	21.8668			0.792151
$763$	2.92318	+	20.7018i	0.105826	+	0.749454i
$764$	4.58649	−	7.94403i	0.165933	−	0.287405i
$765$	−0.354144	−	0.613395i	−0.0128041	−	0.0221773i
$766$	−4.48135	−	7.76192i	−0.161918	−	0.280450i
$767$	−0.220746	+	33.7676i	−0.00797068	+	1.21928i
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	16.9810	−	29.4120i	0.612352	−	1.06063i	−0.378491	−	0.925605i	$-0.623557\pi$
$769$	16.9810	−	29.4120i	0.612352	−	1.06063i	0.990843	−	0.135020i	$-0.0431099\pi$
$770$	−4.29717	−	1.73292i	−0.154859	−	0.0624501i
$771$	−1.88805	−	3.27020i	−0.0679966	−	0.117774i
$772$	1.21993	−	2.11297i	0.0439061	−	0.0760476i
$773$	12.7584	−	22.0983i	0.458889	−	0.794819i	−0.540013	−	0.841656i	$-0.681581\pi$
$773$	12.7584	−	22.0983i	0.458889	−	0.794819i	0.998903	+	0.0468371i	$0.0149142\pi$
$774$	1.21716	−	2.10818i	0.0437498	−	0.0757768i
$775$	−23.0048	+	39.8455i	−0.826357	+	1.43129i
$776$	4.73894	+	8.20808i	0.170118	+	0.294653i
$777$	0.103760	+	0.734819i	0.00372236	+	0.0263615i
$778$	−14.5103	+	25.1326i	−0.520220	+	0.901048i
$779$	10.2983	−	17.8372i	0.368975	−	0.639084i
$780$	−1.41973	−	0.832102i	−0.0508344	−	0.0297940i
$781$	19.4358	+	33.6638i	0.695467	+	1.20458i
$782$	−2.51666	−	4.35898i	−0.0899956	−	0.155877i
$783$	2.20552	−	3.82007i	0.0788187	−	0.136518i
$784$	1.68461	−	6.79427i	0.0601648	−	0.242652i
$785$	−2.94567			−0.105136
$786$	9.45108			0.337109
$787$	−25.0068	+	43.3130i	−0.891395	+	1.54394i	−0.0531913	+	0.998584i	$0.516939\pi$
$787$	−25.0068	+	43.3130i	−0.891395	+	1.54394i	−0.838204	+	0.545357i	$0.816394\pi$
$788$	−13.4334	−	23.2673i	−0.478545	−	0.828865i
$789$	−19.6872			−0.700882
$790$	1.23671	−	2.14205i	0.0440002	−	0.0762107i
$791$	2.52057	+	17.8505i	0.0896211	+	0.634691i
$792$	−3.83707			−0.136344
$793$	34.8015	−	19.7905i	1.23584	−	0.702780i
$794$	2.17445	+	3.76625i	0.0771682	+	0.133659i
$795$	0.502413			0.0178187
$796$	13.9509	+	24.1638i	0.494478	+	0.856462i
$797$	3.59277	+	6.22286i	0.127262	+	0.220425i	0.922615	−	0.385722i	$-0.126048\pi$
$797$	3.59277	+	6.22286i	0.127262	+	0.220425i	−0.795353	+	0.606147i	$0.792714\pi$
$798$	−1.06628	−	7.55132i	−0.0377459	−	0.267314i
$799$	−6.10048	−	10.5663i	−0.215819	−	0.373810i
$800$	−4.79169			−0.169412
$801$	0.0898485	+	0.155622i	0.00317464	+	0.00549864i
$802$	−4.77562	+	8.27162i	−0.168633	+	0.292081i
$803$	−5.39496	−	9.34435i	−0.190384	−	0.329755i
$804$	−0.894964	+	1.55012i	−0.0315629	+	0.0546686i
$805$	3.63231	+	1.46480i	0.128022	+	0.0516274i
$806$	−0.226316	+	34.6196i	−0.00797163	+	1.21942i
$807$	−4.39082	+	7.60513i	−0.154564	+	0.267713i
$808$	6.36213			0.223819
$809$	19.8527			0.697984			0.348992	−	0.937126i	$-0.386524\pi$
$809$	19.8527			0.697984			0.348992	+	0.937126i	$0.386524\pi$
$810$	0.456409			0.0160366
$811$	−49.7806			−1.74803			−0.874016	−	0.485897i	$-0.838493\pi$
$811$	−49.7806			−1.74803			−0.874016	+	0.485897i	$0.838493\pi$
$812$	−1.63174	−	11.5559i	−0.0572628	−	0.405531i
$813$	14.4014	+	24.9439i	0.505077	+	0.874820i
$814$	0.538131	−	0.932070i	0.0188615	−	0.0326690i
$815$	−1.98943	+	3.44579i	−0.0696867	+	0.120701i
$816$	−1.55187			−0.0543263
$817$	−3.50838	−	6.07670i	−0.122743	−	0.212597i
$818$	1.27024			0.0444130
$819$	−9.45421	+	1.27200i	−0.330357	+	0.0444472i
$820$	3.26129			0.113889
$821$	6.57078	+	11.3809i	0.229322	+	0.397197i	0.957607	−	0.288077i	$-0.0930159\pi$
$821$	6.57078	+	11.3809i	0.229322	+	0.397197i	−0.728286	+	0.685274i	$0.759683\pi$
$822$	−2.44792			−0.0853812
$823$	−16.5241	+	28.6206i	−0.575995	+	0.997653i	0.419937	+	0.907553i	$0.362052\pi$
$823$	−16.5241	+	28.6206i	−0.575995	+	0.997653i	−0.995933	+	0.0901000i	$0.971281\pi$
$824$	−8.28934	+	14.3576i	−0.288773	+	0.500169i
$825$	9.19302	+	15.9228i	0.320060	+	0.554360i
$826$	−22.9809	−	9.26750i	−0.799608	−	0.322458i
$827$	14.9763			0.520779			0.260389	−	0.965504i	$-0.416149\pi$
$827$	14.9763			0.520779			0.260389	+	0.965504i	$0.416149\pi$
$828$	3.24339			0.112716
$829$	−55.7966			−1.93789			−0.968947	−	0.247267i	$-0.920468\pi$
$829$	−55.7966			−1.93789			−0.968947	+	0.247267i	$0.920468\pi$
$830$	0.619520			0.0215039
$831$	3.47496	−	6.01880i	0.120545	−	0.208790i
$832$	−3.13422	+	1.78233i	−0.108659	+	0.0617910i
$833$	−10.4384	+	3.00786i	−0.361668	+	0.104216i
$834$	5.37228	−	9.30505i	0.186027	−	0.322208i
$835$	−5.22862	−	9.05624i	−0.180944	−	0.313404i
$836$	−5.53006	+	9.57835i	−0.191261	+	0.331274i
$837$	−4.80098	−	8.31553i	−0.165946	−	0.287427i
$838$	−10.5094			−0.363042
$839$	26.0623	+	45.1412i	0.899770	+	1.55845i	0.827788	+	0.561041i	$0.189599\pi$
$839$	26.0623	+	45.1412i	0.899770	+	1.55845i	0.0719812	+	0.997406i	$0.477068\pi$
$840$	0.951075	−	0.744058i	0.0328152	−	0.0256724i
$841$	4.77139	+	8.26429i	0.164531	+	0.284976i
$842$	0.570606	+	0.988318i	0.0196644	+	0.0340597i
$843$	12.5116			0.430923
$844$	10.9871	+	19.0301i	0.378190	+	0.655045i
$845$	2.89923	+	5.17675i	0.0997365	+	0.178086i
$846$	7.86211			0.270305
$847$	9.13548	+	3.68406i	0.313899	+	0.126586i
$848$	0.550397	−	0.953315i	0.0189007	−	0.0327370i
$849$	−11.2039			−0.384517
$850$	3.71804	+	6.43983i	0.127528	+	0.220884i
$851$	−0.454871	+	0.787859i	−0.0155928	+	0.0270075i
$852$	−10.1305			−0.347067
$853$	23.6670			0.810344			0.405172	−	0.914241i	$-0.367212\pi$
$853$	23.6670			0.810344			0.405172	+	0.914241i	$0.367212\pi$
$854$	4.10752	+	29.0892i	0.140556	+	0.995411i
$855$	0.657787	−	1.13932i	0.0224958	−	0.0389639i
$856$	−8.46023	−	14.6536i	−0.289165	−	0.500848i
$857$	−24.0347	−	41.6292i	−0.821008	−	1.42203i	−0.904932	−	0.425556i	$-0.860079\pi$
$857$	−24.0347	−	41.6292i	−0.821008	−	1.42203i	0.0839243	−	0.996472i	$-0.473255\pi$
$858$	11.9358	+	6.99554i	0.407480	+	0.238824i
$859$	7.34891	−	12.7287i	0.250742	−	0.434297i	−0.712989	−	0.701176i	$-0.752659\pi$
$859$	7.34891	−	12.7287i	0.250742	−	0.434297i	0.963730	+	0.266878i	$0.0859922\pi$
$860$	0.555521	−	0.962191i	0.0189431	−	0.0328104i
$861$	14.8900	−	11.6490i	0.507451	−	0.396996i
$862$	−15.6637	−	27.1303i	−0.533507	−	0.924062i
$863$	−13.6332	+	23.6134i	−0.464080	+	0.803810i	−0.999159	−	0.0409917i	$-0.986948\pi$
$863$	−13.6332	+	23.6134i	−0.464080	+	0.803810i	0.535080	+	0.844802i	$0.320282\pi$
$864$	0.500000	−	0.866025i	0.0170103	−	0.0294628i
$865$	−1.73143	+	2.99892i	−0.0588702	+	0.101966i
$866$	−7.06113	+	12.2302i	−0.239947	+	0.415600i
$867$	−7.29585	−	12.6368i	−0.247780	−	0.429168i
$868$	−23.5607	−	9.50132i	−0.799703	−	0.322496i
$869$	−10.3971	+	18.0084i	−0.352698	+	0.610892i
$870$	1.00662	−	1.74351i	0.0341276	−	0.0591107i
$871$	5.61002	−	3.19023i	0.190088	−	0.108097i
$872$	3.95108	+	6.84346i	0.133800	+	0.231749i
$873$	4.73894	+	8.20808i	0.160389	+	0.277802i
$874$	4.67445	−	8.09638i	0.158116	−	0.273864i
$875$	−10.9658	−	4.42218i	−0.370712	−	0.149497i
$876$	2.81202			0.0950095
$877$	−27.2132			−0.918923			−0.459461	−	0.888198i	$-0.651958\pi$
$877$	−27.2132			−0.918923			−0.459461	+	0.888198i	$0.651958\pi$
$878$	3.23066	−	5.59567i	0.109030	−	0.188845i
$879$	−14.2699	−	24.7162i	−0.481312	−	0.833657i
$880$	−1.75127			−0.0590354
$881$	5.52376	−	9.56743i	0.186100	−	0.322335i	−0.757847	−	0.652433i	$-0.773748\pi$
$881$	5.52376	−	9.56743i	0.186100	−	0.322335i	0.943947	+	0.330098i	$0.107082\pi$
$882$	1.68461	−	6.79427i	0.0567239	−	0.228775i
$883$	42.1202			1.41746			0.708729	−	0.705481i	$-0.249269\pi$
$883$	42.1202			1.41746			0.708729	+	0.705481i	$0.249269\pi$
$884$	4.82732	+	2.82929i	0.162360	+	0.0951593i
$885$	−2.13729	−	3.70189i	−0.0718441	−	0.124438i
$886$	11.4146			0.383481
$887$	−22.7345	−	39.3773i	−0.763349	−	1.32216i	−0.941115	−	0.338087i	$-0.890220\pi$
$887$	−22.7345	−	39.3773i	−0.763349	−	1.32216i	0.177765	−	0.984073i	$-0.443113\pi$
$888$	0.140245	+	0.242912i	0.00470632	+	0.00815159i
$889$	45.5665	−	35.6482i	1.52825	−	1.19560i
$890$	0.0410077	+	0.0710274i	0.00137458	+	0.00238084i
$891$	−3.83707			−0.128547
$892$	−6.87919	−	11.9151i	−0.230332	−	0.398947i
$893$	11.3310	−	19.6259i	0.379179	−	0.656757i
$894$	4.65157	+	8.05676i	0.155572	+	0.269458i
$895$	−2.85349	+	4.94240i	−0.0953818	+	0.165206i
$896$	−0.369922	−	2.61976i	−0.0123582	−	0.0875201i
$897$	−10.0891	−	5.91319i	−0.336864	−	0.197436i
$898$	−19.8942	+	34.4578i	−0.663879	+	1.14987i
$899$	−42.3545			−1.41260
$900$	−4.79169			−0.159723
$901$	−1.70829			−0.0569113
$902$	−27.4179			−0.912917
$903$	−0.900505	−	6.37732i	−0.0299669	−	0.212224i
$904$	3.40689	+	5.90091i	0.113312	+	0.196261i
$905$	0.516719	−	0.894984i	0.0171763	−	0.0297503i
$906$	10.3722	−	17.9651i	0.344592	−	0.596851i
$907$	−41.6270			−1.38220			−0.691101	−	0.722758i	$-0.742874\pi$
$907$	−41.6270			−1.38220			−0.691101	+	0.722758i	$0.742874\pi$
$908$	−9.41545	−	16.3080i	−0.312463	−	0.541201i
$909$	6.36213			0.211019
$910$	−4.31499	+	0.580551i	−0.143040	+	0.0192451i
$911$	50.3137			1.66697			0.833484	−	0.552544i	$-0.186343\pi$
$911$	50.3137			1.66697			0.833484	+	0.552544i	$0.186343\pi$
$912$	−1.44122	−	2.49627i	−0.0477236	−	0.0826597i
$913$	−5.20835			−0.172371
$914$	2.62643	−	4.54910i	0.0868744	−	0.150471i
$915$	−2.53392	+	4.38889i	−0.0837690	+	0.145092i
$916$	1.74812	+	3.02784i	0.0577596	+	0.100043i
$917$	19.6943	−	15.4076i	0.650364	−	0.508802i
$918$	−1.55187			−0.0512193
$919$	27.6186			0.911052			0.455526	−	0.890222i	$-0.349451\pi$
$919$	27.6186			0.911052			0.455526	+	0.890222i	$0.349451\pi$
$920$	1.48031			0.0488045
$921$	23.1907			0.764158
$922$	9.59122	−	16.6125i	0.315870	−	0.547103i
$923$	31.5125	+	18.4695i	1.03725	+	0.607931i
$924$	−7.99576	+	6.25535i	−0.263041	+	0.205786i
$925$	0.672012	−	1.16396i	0.0220956	−	0.0382707i
$926$	8.77898	+	15.2056i	0.288495	+	0.499688i
$927$	−8.28934	+	14.3576i	−0.272258	+	0.471564i
$928$	−2.20552	−	3.82007i	−0.0723996	−	0.125400i
$929$	12.2941			0.403355			0.201677	−	0.979452i	$-0.435361\pi$
$929$	12.2941			0.403355			0.201677	+	0.979452i	$0.435361\pi$
$930$	−2.19121	−	3.79529i	−0.0718526	−	0.124452i
$931$	−14.5324	−	13.9973i	−0.476281	−	0.458743i
$932$	9.74031	+	16.8707i	0.319054	+	0.552618i
$933$	−11.6740	−	20.2200i	−0.382191	−	0.661973i
$934$	3.08222			0.100853
$935$	1.35887	+	2.35364i	0.0444399	+	0.0769722i
$936$	−3.13422	+	1.78233i	−0.102445	+	0.0582571i
$937$	10.2719			0.335569			0.167785	−	0.985824i	$-0.446339\pi$
$937$	10.2719			0.335569			0.167785	+	0.985824i	$0.446339\pi$
$938$	0.662133	+	4.68918i	0.0216194	+	0.153107i
$939$	−7.26499	+	12.5833i	−0.237084	+	0.410641i
$940$	3.58834			0.117039
$941$	−22.3097	−	38.6416i	−0.727276	−	1.25968i	−0.958030	−	0.286667i	$-0.907453\pi$
$941$	−22.3097	−	38.6416i	−0.727276	−	1.25968i	0.230754	−	0.973012i	$-0.425881\pi$
$942$	−3.22701	+	5.58934i	−0.105142	+	0.182111i
$943$	23.1758			0.754708
$944$	−9.36566			−0.304826
$945$	0.951075	−	0.744058i	0.0309385	−	0.0242042i
$946$	−4.67031	+	8.08921i	−0.151845	+	0.263003i
$947$	13.7054	+	23.7385i	0.445366	+	0.771397i	0.998078	−	0.0619759i	$-0.0197402\pi$
$947$	13.7054	+	23.7385i	0.445366	+	0.771397i	−0.552712	+	0.833373i	$0.686407\pi$
$948$	−2.70966	−	4.69326i	−0.0880055	−	0.152430i
$949$	−8.74722	−	5.12674i	−0.283947	−	0.166421i
$950$	−6.90589	+	11.9613i	−0.224057	+	0.388077i
$951$	−1.64596	+	2.85089i	−0.0533739	+	0.0924463i
$952$	−3.23382	+	2.52992i	−0.104809	+	0.0819953i
$953$	−21.0794	−	36.5107i	−0.682830	−	1.18270i	−0.974114	−	0.226059i	$-0.927416\pi$
$953$	−21.0794	−	36.5107i	−0.682830	−	1.18270i	0.291284	−	0.956637i	$-0.405918\pi$
$954$	0.550397	−	0.953315i	0.0178198	−	0.0308647i
$955$	2.09332	−	3.62573i	0.0677381	−	0.117326i
$956$	−6.27346	+	10.8659i	−0.202898	+	0.351430i
$957$	−8.46271	+	14.6579i	−0.273561	+	0.473821i
$958$	−9.18104	−	15.9020i	−0.296626	−	0.513771i
$959$	−5.10103	+	3.99071i	−0.164721	+	0.128867i
$960$	0.228205	−	0.395262i	0.00736527	−	0.0127570i
$961$	−30.5987	+	52.9986i	−0.987056	+	1.70963i
$962$	0.00661109	−	1.01130i	0.000213150	−	0.0326057i
$963$	−8.46023	−	14.6536i	−0.272627	−	0.472204i
$964$	0.233225	+	0.403958i	0.00751169	+	0.0130106i
$965$	0.556786	−	0.964381i	0.0179236	−	0.0310445i
$966$	6.75865	−	5.28752i	0.217456	−	0.170123i
$967$	49.9926			1.60765			0.803827	−	0.594863i	$-0.202794\pi$
$967$	49.9926			1.60765			0.803827	+	0.594863i	$0.202794\pi$
$968$	3.72308			0.119664
$969$	−2.23659	+	3.87388i	−0.0718495	+	0.124447i
$970$	2.16290	+	3.74625i	0.0694464	+	0.120285i
$971$	−11.0753			−0.355424			−0.177712	−	0.984083i	$-0.556870\pi$
$971$	−11.0753			−0.355424			−0.177712	+	0.984083i	$0.556870\pi$
$972$	0.500000	−	0.866025i	0.0160375	−	0.0277778i
$973$	−3.97464	−	28.1482i	−0.127421	−	0.902389i
$974$	18.0106			0.577097
$975$	14.9053	+	8.73597i	0.477350	+	0.279775i
$976$	5.55187	+	9.61612i	0.177711	+	0.307804i
$977$	52.2443			1.67144			0.835722	−	0.549153i	$-0.185050\pi$
$977$	52.2443			1.67144			0.835722	+	0.549153i	$0.185050\pi$
$978$	4.35887	+	7.54979i	0.139381	+	0.241416i
$979$	−0.344755	−	0.597132i	−0.0110184	−	0.0190844i
$980$	0.768874	−	3.10097i	0.0245608	−	0.0990568i
$981$	3.95108	+	6.84346i	0.126148	+	0.218495i
$982$	15.9759			0.509811
$983$	18.4322	+	31.9255i	0.587896	+	1.01827i	0.994508	+	0.104665i	$0.0333770\pi$
$983$	18.4322	+	31.9255i	0.587896	+	1.01827i	−0.406611	+	0.913601i	$0.633290\pi$
$984$	3.57277	−	6.18822i	0.113896	−	0.197273i
$985$	−6.13113	−	10.6194i	−0.195354	−	0.338363i
$986$	−3.42267	+	5.92824i	−0.109000	+	0.188794i
$987$	16.3832	−	12.8171i	0.521484	−	0.407974i
$988$	−0.0679384	+	10.3926i	−0.00216141	+	0.330632i
$989$	3.94771	−	6.83764i	0.125530	−	0.217424i
$990$	−1.75127			−0.0556591
$991$	52.3315			1.66236			0.831182	−	0.556000i	$-0.187664\pi$
$991$	52.3315			1.66236			0.831182	+	0.556000i	$0.187664\pi$
$992$	−9.60195			−0.304862
$993$	−16.1057			−0.511099
$994$	−21.1102	+	16.5152i	−0.669576	+	0.523832i
$995$	6.36734	+	11.0286i	0.201858	+	0.349629i
$996$	0.678689	−	1.17552i	0.0215051	−	0.0372479i
$997$	10.0429	−	17.3949i	0.318063	−	0.550902i	−0.662021	−	0.749486i	$-0.730301\pi$
$997$	10.0429	−	17.3949i	0.318063	−	0.550902i	0.980084	+	0.198584i	$0.0636342\pi$
$998$	8.13311			0.257449
$999$	0.140245	+	0.242912i	0.00443717	+	0.00768540i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.k.b.373.2	yes	8
3.2	odd	2		1638.2.p.i.919.3		8
7.4	even	3		546.2.j.d.529.2	yes	8
13.3	even	3		546.2.j.d.289.2	✓	8
21.11	odd	6		1638.2.m.g.1621.3		8
39.29	odd	6		1638.2.m.g.289.3		8
91.81	even	3	inner	546.2.k.b.445.2	yes	8
273.263	odd	6		1638.2.p.i.991.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.j.d.289.2	✓	8	13.3	even	3
546.2.j.d.529.2	yes	8	7.4	even	3
546.2.k.b.373.2	yes	8	1.1	even	1	trivial
546.2.k.b.445.2	yes	8	91.81	even	3	inner
1638.2.m.g.289.3		8	39.29	odd	6
1638.2.m.g.1621.3		8	21.11	odd	6
1638.2.p.i.919.3		8	3.2	odd	2
1638.2.p.i.991.3		8	273.263	odd	6

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} -1.00000 q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.228205 + 0.395262i) q^{5} +(0.500000 + 0.866025i) q^{6} +(2.45374 + 0.989520i) q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} -1.00000 q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.228205 + 0.395262i) q^{5} +(0.500000 + 0.866025i) q^{6} +(2.45374 + 0.989520i) q^{7} +1.00000 q^{8} +1.00000 q^{9} +0.456409 q^{10} -3.83707 q^{11} +(0.500000 - 0.866025i) q^{12} +(-3.13422 + 1.78233i) q^{13} +(-0.369922 - 2.61976i) q^{14} +(0.228205 - 0.395262i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.775934 + 1.34396i) q^{17} +(-0.500000 - 0.866025i) q^{18} -2.88244 q^{19} +(-0.228205 - 0.395262i) q^{20} +(-2.45374 - 0.989520i) q^{21} +(1.91853 + 3.32300i) q^{22} +(-1.62170 - 2.80886i) q^{23} -1.00000 q^{24} +(2.39585 + 4.14973i) q^{25} +(3.11065 + 1.82315i) q^{26} -1.00000 q^{27} +(-2.08382 + 1.63024i) q^{28} +(-2.20552 + 3.82007i) q^{29} -0.456409 q^{30} +(4.80098 + 8.31553i) q^{31} +(-0.500000 + 0.866025i) q^{32} +3.83707 q^{33} +1.55187 q^{34} +(-0.951075 + 0.744058i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-0.140245 - 0.242912i) q^{37} +(1.44122 + 2.49627i) q^{38} +(3.13422 - 1.78233i) q^{39} +(-0.228205 + 0.395262i) q^{40} +(-3.57277 + 6.18822i) q^{41} +(0.369922 + 2.61976i) q^{42} +(1.21716 + 2.10818i) q^{43} +(1.91853 - 3.32300i) q^{44} +(-0.228205 + 0.395262i) q^{45} +(-1.62170 + 2.80886i) q^{46} +(-3.93105 + 6.80879i) q^{47} +(0.500000 + 0.866025i) q^{48} +(5.04170 + 4.85605i) q^{49} +(2.39585 - 4.14973i) q^{50} +(0.775934 - 1.34396i) q^{51} +(0.0235697 - 3.60547i) q^{52} +(0.550397 + 0.953315i) q^{53} +(0.500000 + 0.866025i) q^{54} +(0.875637 - 1.51665i) q^{55} +(2.45374 + 0.989520i) q^{56} +2.88244 q^{57} +4.41103 q^{58} +(4.68283 - 8.11090i) q^{59} +(0.228205 + 0.395262i) q^{60} -11.1037 q^{61} +(4.80098 - 8.31553i) q^{62} +(2.45374 + 0.989520i) q^{63} +1.00000 q^{64} +(0.0107575 - 1.64557i) q^{65} +(-1.91853 - 3.32300i) q^{66} -1.78993 q^{67} +(-0.775934 - 1.34396i) q^{68} +(1.62170 + 2.80886i) q^{69} +(1.11991 + 0.451626i) q^{70} +(-5.06527 - 8.77331i) q^{71} +1.00000 q^{72} +(1.40601 + 2.43529i) q^{73} +(-0.140245 + 0.242912i) q^{74} +(-2.39585 - 4.14973i) q^{75} +(1.44122 - 2.49627i) q^{76} +(-9.41517 - 3.79685i) q^{77} +(-3.11065 - 1.82315i) q^{78} +(2.70966 - 4.69326i) q^{79} +0.456409 q^{80} +1.00000 q^{81} +7.14554 q^{82} +1.35738 q^{83} +(2.08382 - 1.63024i) q^{84} +(-0.354144 - 0.613395i) q^{85} +(1.21716 - 2.10818i) q^{86} +(2.20552 - 3.82007i) q^{87} -3.83707 q^{88} +(0.0898485 + 0.155622i) q^{89} +0.456409 q^{90} +(-9.45421 + 1.27200i) q^{91} +3.24339 q^{92} +(-4.80098 - 8.31553i) q^{93} +7.86211 q^{94} +(0.657787 - 1.13932i) q^{95} +(0.500000 - 0.866025i) q^{96} +(4.73894 + 8.20808i) q^{97} +(1.68461 - 6.79427i) q^{98} -3.83707 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} - 8 q^{3} - 4 q^{4} + 2 q^{5} + 4 q^{6} + 3 q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q - 4 * q^2 - 8 * q^3 - 4 * q^4 + 2 * q^5 + 4 * q^6 + 3 * q^7 + 8 * q^8 + 8 * q^9	\( 8 q - 4 q^{2} - 8 q^{3} - 4 q^{4} + 2 q^{5} + 4 q^{6} + 3 q^{7} + 8 q^{8} + 8 q^{9} - 4 q^{10} + 12 q^{11} + 4 q^{12} - 11 q^{13} - 3 q^{14} - 2 q^{15} - 4 q^{16} + 4 q^{17} - 4 q^{18} - 12 q^{19} + 2 q^{20} - 3 q^{21} - 6 q^{22} - 10 q^{23} - 8 q^{24} - 18 q^{25} + 10 q^{26} - 8 q^{27} + 2 q^{29} + 4 q^{30} + 6 q^{31} - 4 q^{32} - 12 q^{33} - 8 q^{34} + 18 q^{35} - 4 q^{36} - 28 q^{37} + 6 q^{38} + 11 q^{39} + 2 q^{40} + 3 q^{42} - 6 q^{43} - 6 q^{44} + 2 q^{45} - 10 q^{46} + q^{47} + 4 q^{48} - 7 q^{49} - 18 q^{50} - 4 q^{51} + q^{52} + 7 q^{53} + 4 q^{54} + q^{55} + 3 q^{56} + 12 q^{57} - 4 q^{58} + 2 q^{59} - 2 q^{60} - 48 q^{61} + 6 q^{62} + 3 q^{63} + 8 q^{64} + 19 q^{65} + 6 q^{66} + 30 q^{67} + 4 q^{68} + 10 q^{69} - 18 q^{70} + 6 q^{71} + 8 q^{72} + q^{73} - 28 q^{74} + 18 q^{75} + 6 q^{76} - 22 q^{77} - 10 q^{78} - 12 q^{79} - 4 q^{80} + 8 q^{81} - 32 q^{83} - 13 q^{85} - 6 q^{86} - 2 q^{87} + 12 q^{88} + 25 q^{89} - 4 q^{90} + 34 q^{91} + 20 q^{92} - 6 q^{93} - 2 q^{94} - 8 q^{95} + 4 q^{96} - q^{97} + 2 q^{98} + 12 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 - 8 * q^3 - 4 * q^4 + 2 * q^5 + 4 * q^6 + 3 * q^7 + 8 * q^8 + 8 * q^9 - 4 * q^10 + 12 * q^11 + 4 * q^12 - 11 * q^13 - 3 * q^14 - 2 * q^15 - 4 * q^16 + 4 * q^17 - 4 * q^18 - 12 * q^19 + 2 * q^20 - 3 * q^21 - 6 * q^22 - 10 * q^23 - 8 * q^24 - 18 * q^25 + 10 * q^26 - 8 * q^27 + 2 * q^29 + 4 * q^30 + 6 * q^31 - 4 * q^32 - 12 * q^33 - 8 * q^34 + 18 * q^35 - 4 * q^36 - 28 * q^37 + 6 * q^38 + 11 * q^39 + 2 * q^40 + 3 * q^42 - 6 * q^43 - 6 * q^44 + 2 * q^45 - 10 * q^46 + q^47 + 4 * q^48 - 7 * q^49 - 18 * q^50 - 4 * q^51 + q^52 + 7 * q^53 + 4 * q^54 + q^55 + 3 * q^56 + 12 * q^57 - 4 * q^58 + 2 * q^59 - 2 * q^60 - 48 * q^61 + 6 * q^62 + 3 * q^63 + 8 * q^64 + 19 * q^65 + 6 * q^66 + 30 * q^67 + 4 * q^68 + 10 * q^69 - 18 * q^70 + 6 * q^71 + 8 * q^72 + q^73 - 28 * q^74 + 18 * q^75 + 6 * q^76 - 22 * q^77 - 10 * q^78 - 12 * q^79 - 4 * q^80 + 8 * q^81 - 32 * q^83 - 13 * q^85 - 6 * q^86 - 2 * q^87 + 12 * q^88 + 25 * q^89 - 4 * q^90 + 34 * q^91 + 20 * q^92 - 6 * q^93 - 2 * q^94 - 8 * q^95 + 4 * q^96 - q^97 + 2 * q^98 + 12 * q^99

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