LMFDB - Embedded newform 120.2.m.b.59.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [120,2,Mod(59,120)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(120, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("120.59");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 120 = 2^{3} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	120.m (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:	$0.958204824255$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 24x^{14} + 192x^{12} + 672x^{10} + 1092x^{8} + 880x^{6} + 352x^{4} + 64x^{2} + 4 $ x^16 + 24x^14 + 192x^12 + 672x^10 + 1092x^8 + 880x^6 + 352x^4 + 64*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{13} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			59.1
Root			$-0.724535i$ of defining polynomial
Character	$\chi$	$=$	120.59
Dual form			120.2.m.b.59.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.30656 - 0.541196i) q^{2} +(0.541196 - 1.64533i) q^{3} +(1.41421 + 1.41421i) q^{4} +(1.25928 + 1.84776i) q^{5} +(-1.59755 + 1.85683i) q^{6} +3.29066 q^{7} +(-1.08239 - 2.61313i) q^{8} +(-2.41421 - 1.78089i) q^{9} +O(q^{10})$	\(q+(-1.30656 - 0.541196i) q^{2} +(0.541196 - 1.64533i) q^{3} +(1.41421 + 1.41421i) q^{4} +(1.25928 + 1.84776i) q^{5} +(-1.59755 + 1.85683i) q^{6} +3.29066 q^{7} +(-1.08239 - 2.61313i) q^{8} +(-2.41421 - 1.78089i) q^{9} +(-0.645329 - 3.09573i) q^{10} -2.51856i q^{11} +(3.09221 - 1.56148i) q^{12} -4.65369 q^{13} +(-4.29945 - 1.78089i) q^{14} +(3.72169 - 1.07193i) q^{15} +4.00000i q^{16} +3.69552 q^{17} +(2.19051 + 3.63341i) q^{18} +0.828427 q^{19} +(-0.832235 + 4.39402i) q^{20} +(1.78089 - 5.41421i) q^{21} +(-1.36303 + 3.29066i) q^{22} +2.61313i q^{23} +(-4.88524 + 0.366677i) q^{24} +(-1.82843 + 4.65369i) q^{25} +(6.08034 + 2.51856i) q^{26} +(-4.23671 + 3.00836i) q^{27} +(4.65369 + 4.65369i) q^{28} -6.08034 q^{29} +(-5.44274 - 0.613620i) q^{30} +1.17157i q^{31} +(2.16478 - 5.22625i) q^{32} +(-4.14386 - 1.36303i) q^{33} +(-4.82843 - 2.00000i) q^{34} +(4.14386 + 6.08034i) q^{35} +(-0.895653 - 5.93277i) q^{36} -1.92762 q^{37} +(-1.08239 - 0.448342i) q^{38} +(-2.51856 + 7.65685i) q^{39} +(3.46539 - 5.29066i) q^{40} +8.59890i q^{41} +(-5.25700 + 6.11020i) q^{42} -6.01673i q^{43} +(3.56178 - 3.56178i) q^{44} +(0.250486 - 6.70353i) q^{45} +(1.41421 - 3.41421i) q^{46} -2.61313i q^{47} +(6.58132 + 2.16478i) q^{48} +3.82843 q^{49} +(4.90752 - 5.09080i) q^{50} +(2.00000 - 6.08034i) q^{51} +(-6.58132 - 6.58132i) q^{52} +4.59220i q^{53} +(7.16365 - 1.63772i) q^{54} +(4.65369 - 3.17157i) q^{55} +(-3.56178 - 8.59890i) q^{56} +(0.448342 - 1.36303i) q^{57} +(7.94435 + 3.29066i) q^{58} +2.51856i q^{59} +(6.77920 + 3.74732i) q^{60} +8.48528i q^{61} +(0.634051 - 1.53073i) q^{62} +(-7.94435 - 5.86030i) q^{63} +(-5.65685 + 5.65685i) q^{64} +(-5.86030 - 8.59890i) q^{65} +(4.67654 + 4.02353i) q^{66} +3.29066i q^{67} +(5.22625 + 5.22625i) q^{68} +(4.29945 + 1.41421i) q^{69} +(-2.12356 - 10.1870i) q^{70} -7.12356 q^{71} +(-2.04057 + 8.23627i) q^{72} -6.58132i q^{73} +(2.51856 + 1.04322i) q^{74} +(6.66732 + 5.52692i) q^{75} +(1.17157 + 1.17157i) q^{76} -8.28772i q^{77} +(7.43452 - 8.64113i) q^{78} -16.4853i q^{79} +(-7.39104 + 5.03712i) q^{80} +(2.65685 + 8.59890i) q^{81} +(4.65369 - 11.2350i) q^{82} -9.37011 q^{83} +(10.1754 - 5.13829i) q^{84} +(4.65369 + 6.82843i) q^{85} +(-3.25623 + 7.86123i) q^{86} +(-3.29066 + 10.0042i) q^{87} +(-6.58132 + 2.72607i) q^{88} -5.03712i q^{89} +(-3.95520 + 8.62302i) q^{90} -15.3137 q^{91} +(-3.69552 + 3.69552i) q^{92} +(1.92762 + 0.634051i) q^{93} +(-1.41421 + 3.41421i) q^{94} +(1.04322 + 1.53073i) q^{95} +(-7.42733 - 6.39021i) q^{96} +2.72607i q^{97} +(-5.00208 - 2.07193i) q^{98} +(-4.48528 + 6.08034i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{9}+O(q^{10}) $ 16 * q - 16 * q^9	$ 16 q - 16 q^{9} + 16 q^{10} - 32 q^{19} - 32 q^{24} + 16 q^{25} + 16 q^{30} - 32 q^{34} - 32 q^{36} + 32 q^{40} + 16 q^{49} + 32 q^{51} + 32 q^{54} + 64 q^{66} - 64 q^{70} + 32 q^{75} + 64 q^{76} - 48 q^{81} + 32 q^{84} - 16 q^{90} - 64 q^{91} + 64 q^{96} + 64 q^{99}+O(q^{100}) $ 16 * q - 16 * q^9 + 16 * q^10 - 32 * q^19 - 32 * q^24 + 16 * q^25 + 16 * q^30 - 32 * q^34 - 32 * q^36 + 32 * q^40 + 16 * q^49 + 32 * q^51 + 32 * q^54 + 64 * q^66 - 64 * q^70 + 32 * q^75 + 64 * q^76 - 48 * q^81 + 32 * q^84 - 16 * q^90 - 64 * q^91 + 64 * q^96 + 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/120\mathbb{Z}\right)^\times$.

$n$	$31$	$41$	$61$	$97$
$\chi(n)$	$-1$	$-1$	$-1$	$-1$

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 $

$2$	−1.30656	−	0.541196i	−0.923880	−	0.382683i
$2$	−1.30656	−	0.541196i	−0.923880	−	0.382683i
$3$	0.541196	−	1.64533i	0.312460	−	0.949931i
$3$	0.541196	−	1.64533i	0.312460	−	0.949931i
$4$	1.41421	+	1.41421i	0.707107	+	0.707107i
$5$	1.25928	+	1.84776i	0.563167	+	0.826343i
$5$	1.25928	+	1.84776i	0.563167	+	0.826343i
$6$	−1.59755	+	1.85683i	−0.652198	+	0.758049i
$7$	3.29066			1.24375			0.621876	−	0.783116i	$-0.286371\pi$
$7$	3.29066			1.24375			0.621876	+	0.783116i	$0.286371\pi$
$8$	−1.08239	−	2.61313i	−0.382683	−	0.923880i
$9$	−2.41421	−	1.78089i	−0.804738	−	0.593630i
$10$	−0.645329	−	3.09573i	−0.204071	−	0.978956i
$11$		−	2.51856i		−	0.759374i	−0.925115	−	0.379687i	$-0.876032\pi$
$11$		−	2.51856i		−	0.759374i	0.925115	−	0.379687i	$-0.123968\pi$
$12$	3.09221	−	1.56148i	0.892645	−	0.450760i
$13$	−4.65369			−1.29070			−0.645351	−	0.763886i	$-0.723289\pi$
$13$	−4.65369			−1.29070			−0.645351	+	0.763886i	$0.723289\pi$
$14$	−4.29945	−	1.78089i	−1.14908	−	0.475963i
$15$	3.72169	−	1.07193i	0.960936	−	0.276771i
$16$			4.00000i			1.00000i
$17$	3.69552			0.896295			0.448147	−	0.893960i	$-0.352084\pi$
$17$	3.69552			0.896295			0.448147	+	0.893960i	$0.352084\pi$
$18$	2.19051	+	3.63341i	0.516308	+	0.856403i
$19$	0.828427			0.190054			0.0950271	−	0.995475i	$-0.469706\pi$
$19$	0.828427			0.190054			0.0950271	+	0.995475i	$0.469706\pi$
$20$	−0.832235	+	4.39402i	−0.186093	+	0.982532i
$21$	1.78089	−	5.41421i	0.388622	−	1.18148i
$22$	−1.36303	+	3.29066i	−0.290600	+	0.701571i
$23$			2.61313i			0.544874i	0.962174	+	0.272437i	$0.0878297\pi$
$23$			2.61313i			0.544874i	−0.962174	+	0.272437i	$0.912170\pi$
$24$	−4.88524	+	0.366677i	−0.997195	+	0.0748477i
$25$	−1.82843	+	4.65369i	−0.365685	+	0.930739i
$26$	6.08034	+	2.51856i	1.19245	+	0.493930i
$27$	−4.23671	+	3.00836i	−0.815356	+	0.578960i
$28$	4.65369	+	4.65369i	0.879465	+	0.879465i
$29$	−6.08034			−1.12909			−0.564546	−	0.825402i	$-0.690949\pi$
$29$	−6.08034			−1.12909			−0.564546	+	0.825402i	$0.690949\pi$
$30$	−5.44274	−	0.613620i	−0.993705	−	0.112031i
$31$			1.17157i			0.210421i	0.994450	+	0.105210i	$0.0335516\pi$
$31$			1.17157i			0.210421i	−0.994450	+	0.105210i	$0.966448\pi$
$32$	2.16478	−	5.22625i	0.382683	−	0.923880i
$33$	−4.14386	−	1.36303i	−0.721353	−	0.237274i
$34$	−4.82843	−	2.00000i	−0.828068	−	0.342997i
$35$	4.14386	+	6.08034i	0.700440	+	1.02777i
$36$	−0.895653	−	5.93277i	−0.149276	−	0.988796i
$37$	−1.92762			−0.316899			−0.158450	−	0.987367i	$-0.550650\pi$
$37$	−1.92762			−0.316899			−0.158450	+	0.987367i	$0.550650\pi$
$38$	−1.08239	−	0.448342i	−0.175587	−	0.0727306i
$39$	−2.51856	+	7.65685i	−0.403292	+	1.22608i
$40$	3.46539	−	5.29066i	0.547927	−	0.836526i
$41$			8.59890i			1.34292i	0.741039	+	0.671461i	$0.234333\pi$
$41$			8.59890i			1.34292i	−0.741039	+	0.671461i	$0.765667\pi$
$42$	−5.25700	+	6.11020i	−0.811172	+	0.942824i
$43$		−	6.01673i		−	0.917542i	−0.888554	−	0.458771i	$-0.848290\pi$
$43$		−	6.01673i		−	0.917542i	0.888554	−	0.458771i	$-0.151710\pi$
$44$	3.56178	−	3.56178i	0.536959	−	0.536959i
$45$	0.250486	−	6.70353i	0.0373403	−	0.999303i
$46$	1.41421	−	3.41421i	0.208514	−	0.503398i
$47$		−	2.61313i		−	0.381164i	−0.981671	−	0.190582i	$-0.938963\pi$
$47$		−	2.61313i		−	0.381164i	0.981671	−	0.190582i	$-0.0610374\pi$
$48$	6.58132	+	2.16478i	0.949931	+	0.312460i
$49$	3.82843			0.546918
$50$	4.90752	−	5.09080i	0.694027	−	0.719949i
$51$	2.00000	−	6.08034i	0.280056	−	0.851418i
$52$	−6.58132	−	6.58132i	−0.912664	−	0.912664i
$53$			4.59220i			0.630787i	0.948961	+	0.315394i	$0.102137\pi$
$53$			4.59220i			0.630787i	−0.948961	+	0.315394i	$0.897863\pi$
$54$	7.16365	−	1.63772i	0.974849	−	0.222866i
$55$	4.65369	−	3.17157i	0.627504	−	0.427655i
$56$	−3.56178	−	8.59890i	−0.475963	−	1.14908i
$57$	0.448342	−	1.36303i	0.0593843	−	0.180538i
$58$	7.94435	+	3.29066i	1.04314	+	0.432085i
$59$			2.51856i			0.327889i	0.986470	+	0.163944i	$0.0524217\pi$
$59$			2.51856i			0.327889i	−0.986470	+	0.163944i	$0.947578\pi$
$60$	6.77920	+	3.74732i	0.875191	+	0.483778i
$61$			8.48528i			1.08643i	0.839594	+	0.543214i	$0.182793\pi$
$61$			8.48528i			1.08643i	−0.839594	+	0.543214i	$0.817207\pi$
$62$	0.634051	−	1.53073i	0.0805245	−	0.194403i
$63$	−7.94435	−	5.86030i	−1.00089	−	0.738329i
$64$	−5.65685	+	5.65685i	−0.707107	+	0.707107i
$65$	−5.86030	−	8.59890i	−0.726881	−	1.06656i
$66$	4.67654	+	4.02353i	0.575643	+	0.495263i
$67$			3.29066i			0.402018i	0.979589	+	0.201009i	$0.0644220\pi$
$67$			3.29066i			0.402018i	−0.979589	+	0.201009i	$0.935578\pi$
$68$	5.22625	+	5.22625i	0.633776	+	0.633776i
$69$	4.29945	+	1.41421i	0.517593	+	0.170251i
$70$	−2.12356	−	10.1870i	−0.253813	−	1.21758i
$71$	−7.12356			−0.845412			−0.422706	−	0.906267i	$-0.638920\pi$
$71$	−7.12356			−0.845412			−0.422706	+	0.906267i	$0.638920\pi$
$72$	−2.04057	+	8.23627i	−0.240483	+	0.970653i
$73$		−	6.58132i		−	0.770285i	−0.922857	−	0.385142i	$-0.874152\pi$
$73$		−	6.58132i		−	0.770285i	0.922857	−	0.385142i	$-0.125848\pi$
$74$	2.51856	+	1.04322i	0.292777	+	0.121272i
$75$	6.66732	+	5.52692i	0.769875	+	0.638194i
$76$	1.17157	+	1.17157i	0.134389	+	0.134389i
$77$		−	8.28772i		−	0.944473i
$78$	7.43452	−	8.64113i	0.841793	−	0.978415i
$79$		−	16.4853i		−	1.85474i	−0.374147	−	0.927370i	$-0.622064\pi$
$79$		−	16.4853i		−	1.85474i	0.374147	−	0.927370i	$-0.377936\pi$
$80$	−7.39104	+	5.03712i	−0.826343	+	0.563167i
$81$	2.65685	+	8.59890i	0.295206	+	0.955434i
$82$	4.65369	−	11.2350i	0.513914	−	1.24070i
$83$	−9.37011			−1.02850			−0.514252	−	0.857639i	$-0.671930\pi$
$83$	−9.37011			−1.02850			−0.514252	+	0.857639i	$0.671930\pi$
$84$	10.1754	−	5.13829i	1.11023	−	0.560634i
$85$	4.65369	+	6.82843i	0.504764	+	0.740647i
$86$	−3.25623	+	7.86123i	−0.351128	+	0.847699i
$87$	−3.29066	+	10.0042i	−0.352796	+	1.07256i
$88$	−6.58132	+	2.72607i	−0.701571	+	0.290600i
$89$		−	5.03712i		−	0.533934i	−0.963706	−	0.266967i	$-0.913979\pi$
$89$		−	5.03712i		−	0.533934i	0.963706	−	0.266967i	$-0.0860214\pi$
$90$	−3.95520	+	8.62302i	−0.416914	+	0.908946i
$91$	−15.3137			−1.60531
$92$	−3.69552	+	3.69552i	−0.385284	+	0.385284i
$93$	1.92762	+	0.634051i	0.199885	+	0.0657480i
$94$	−1.41421	+	3.41421i	−0.145865	+	0.352149i
$95$	1.04322	+	1.53073i	0.107032	+	0.157050i
$96$	−7.42733	−	6.39021i	−0.758049	−	0.652198i
$97$			2.72607i			0.276790i	0.990377	+	0.138395i	$0.0441944\pi$
$97$			2.72607i			0.276790i	−0.990377	+	0.138395i	$0.955806\pi$
$98$	−5.00208	−	2.07193i	−0.505286	−	0.209297i
$99$	−4.48528	+	6.08034i	−0.450788	+	0.611097i
$100$	−9.16710	+	3.99553i	−0.916710	+	0.399553i
$101$	13.2039			1.31384			0.656919	−	0.753961i	$-0.271859\pi$
$101$	13.2039			1.31384			0.656919	+	0.753961i	$0.271859\pi$
$102$	−5.90378	+	6.86196i	−0.584562	+	0.679435i
$103$	−6.01673			−0.592846			−0.296423	−	0.955057i	$-0.595794\pi$
$103$	−6.01673			−0.592846			−0.296423	+	0.955057i	$0.595794\pi$
$104$	5.03712	+	12.1607i	0.493930	+	1.19245i
$105$	12.2468	−	3.52735i	1.19517	−	0.344235i
$106$	2.48528	−	6.00000i	0.241392	−	0.582772i
$107$	8.47343			0.819157			0.409579	−	0.912275i	$-0.365676\pi$
$107$	8.47343			0.819157			0.409579	+	0.912275i	$0.365676\pi$
$108$	−10.2461	−	1.73715i	−0.985930	−	0.167157i
$109$		−	0.485281i		−	0.0464815i	−0.999730	−	0.0232408i	$-0.992602\pi$
$109$		−	0.485281i		−	0.0464815i	0.999730	−	0.0232408i	$-0.00739843\pi$
$110$	−7.79679	+	1.62530i	−0.743394	+	0.154966i
$111$	−1.04322	+	3.17157i	−0.0990182	+	0.301032i
$112$			13.1626i			1.24375i
$113$	8.92177			0.839290			0.419645	−	0.907688i	$-0.362155\pi$
$113$	8.92177			0.839290			0.419645	+	0.907688i	$0.362155\pi$
$114$	−1.32346	+	1.53825i	−0.123953	+	0.144070i
$115$	−4.82843	+	3.29066i	−0.450253	+	0.306855i
$116$	−8.59890	−	8.59890i	−0.798388	−	0.798388i
$117$	11.2350	+	8.28772i	1.03868	+	0.766200i
$118$	1.36303	−	3.29066i	0.125478	−	0.302930i
$119$	12.1607			1.11477
$120$	−6.82941	−	8.56499i	−0.623437	−	0.781873i
$121$	4.65685			0.423350
$122$	4.59220	−	11.0866i	0.415758	−	1.00373i
$123$	14.1480	+	4.65369i	1.27568	+	0.419609i
$124$	−1.65685	+	1.65685i	−0.148790	+	0.148790i
$125$	−10.9014	+	2.48181i	−0.975051	+	0.221980i
$126$	7.20822	+	11.9563i	0.642159	+	1.06515i
$127$	−3.29066			−0.291999			−0.145999	−	0.989285i	$-0.546640\pi$
$127$	−3.29066			−0.291999			−0.145999	+	0.989285i	$0.546640\pi$
$128$	10.4525	−	4.32957i	0.923880	−	0.382683i
$129$	−9.89949	−	3.25623i	−0.871602	−	0.286695i
$130$	3.00316	+	14.4066i	0.263395	+	1.26354i
$131$		−	21.8028i		−	1.90492i	−0.304663	−	0.952460i	$-0.598544\pi$
$131$		−	21.8028i		−	1.90492i	0.304663	−	0.952460i	$-0.401456\pi$
$132$	−3.93268	−	7.78793i	−0.342296	−	0.677852i
$133$	2.72607			0.236380
$134$	1.78089	−	4.29945i	0.153846	−	0.371416i
$135$	−10.8939	−	4.04005i	−0.937601	−	0.347713i
$136$	−4.00000	−	9.65685i	−0.342997	−	0.828068i
$137$	−11.9832			−1.02380			−0.511899	−	0.859046i	$-0.671058\pi$
$137$	−11.9832			−1.02380			−0.511899	+	0.859046i	$0.671058\pi$
$138$	−4.85214	−	4.17461i	−0.413041	−	0.355366i
$139$	14.4853			1.22863			0.614313	−	0.789063i	$-0.289433\pi$
$139$	14.4853			1.22863			0.614313	+	0.789063i	$0.289433\pi$
$140$	−2.73860	+	14.4592i	−0.231454	+	1.22203i
$141$	−4.29945	−	1.41421i	−0.362079	−	0.119098i
$142$	9.30739	+	3.85525i	0.781058	+	0.323525i
$143$			11.7206i			0.980126i
$144$	7.12356	−	9.65685i	0.593630	−	0.804738i
$145$	−7.65685	−	11.2350i	−0.635867	−	0.933017i
$146$	−3.56178	+	8.59890i	−0.294775	+	0.711650i
$147$	2.07193	−	6.29902i	0.170890	−	0.519535i
$148$	−2.72607	−	2.72607i	−0.224082	−	0.224082i
$149$	14.6792			1.20257			0.601285	−	0.799034i	$-0.294656\pi$
$149$	14.6792			1.20257			0.601285	+	0.799034i	$0.294656\pi$
$150$	−5.72012	−	10.8296i	−0.467046	−	0.884233i
$151$		−	2.82843i		−	0.230174i	−0.993355	−	0.115087i	$-0.963285\pi$
$151$		−	2.82843i		−	0.230174i	0.993355	−	0.115087i	$-0.0367147\pi$
$152$	−0.896683	−	2.16478i	−0.0727306	−	0.175587i
$153$	−8.92177	−	6.58132i	−0.721282	−	0.532068i
$154$	−4.48528	+	10.8284i	−0.361434	+	0.872580i
$155$	−2.16478	+	1.47534i	−0.173880	+	0.118502i
$156$	−14.3902	+	7.26665i	−1.15214	+	0.581797i
$157$	5.78287			0.461523			0.230762	−	0.973010i	$-0.425878\pi$
$157$	5.78287			0.461523			0.230762	+	0.973010i	$0.425878\pi$
$158$	−8.92177	+	21.5391i	−0.709778	+	1.71356i
$159$	7.55568	+	2.48528i	0.599204	+	0.197096i
$160$	12.3829	−	2.58132i	0.978956	−	0.204071i
$161$			8.59890i			0.677688i
$162$	1.18235	−	12.6729i	0.0928938	−	0.995676i
$163$			6.01673i			0.471266i	0.971842	+	0.235633i	$0.0757164\pi$
$163$			6.01673i			0.471266i	−0.971842	+	0.235633i	$0.924284\pi$
$164$	−12.1607	+	12.1607i	−0.949590	+	0.949590i
$165$	−2.69972	−	9.37330i	−0.210173	−	0.729710i
$166$	12.2426	+	5.07107i	0.950213	+	0.393591i
$167$		−	17.3952i		−	1.34608i	−0.739606	−	0.673040i	$-0.764988\pi$
$167$		−	17.3952i		−	1.34608i	0.739606	−	0.673040i	$-0.235012\pi$
$168$	−16.0756	+	1.20661i	−1.24026	+	0.0930920i
$169$	8.65685			0.665912
$170$	−2.38482	−	11.4403i	−0.182908	−	0.877433i
$171$	−2.00000	−	1.47534i	−0.152944	−	0.112822i
$172$	8.50894	−	8.50894i	0.648800	−	0.648800i
$173$		−	21.5391i		−	1.63758i	−0.574090	−	0.818792i	$-0.694644\pi$
$173$		−	21.5391i		−	1.63758i	0.574090	−	0.818792i	$-0.305356\pi$
$174$	9.71366	−	11.2902i	0.736391	−	0.855906i
$175$	−6.01673	+	15.3137i	−0.454822	+	1.15761i
$176$	10.0742			0.759374
$177$	4.14386	+	1.36303i	0.311472	+	0.102452i
$178$	−2.72607	+	6.58132i	−0.204328	+	0.493290i
$179$			9.64212i			0.720686i	0.932820	+	0.360343i	$0.117340\pi$
$179$			9.64212i			0.720686i	−0.932820	+	0.360343i	$0.882660\pi$
$180$	9.83446	−	9.12598i	0.733017	−	0.680210i
$181$		−	10.3431i		−	0.768800i	−0.923167	−	0.384400i	$-0.874408\pi$
$181$		−	10.3431i		−	0.768800i	0.923167	−	0.384400i	$-0.125592\pi$
$182$	20.0083	+	8.28772i	1.48312	+	0.614327i
$183$	13.9611	+	4.59220i	1.03203	+	0.339465i
$184$	6.82843	−	2.82843i	0.503398	−	0.208514i
$185$	−2.42742	−	3.56178i	−0.178467	−	0.261867i
$186$	−2.17541	−	1.87165i	−0.159509	−	0.137236i
$187$		−	9.30739i		−	0.680623i
$188$	3.69552	−	3.69552i	0.269523	−	0.269523i
$189$	−13.9416	+	9.89949i	−1.01410	+	0.720082i
$190$	−0.534608	−	2.56459i	−0.0387845	−	0.186055i
$191$	−5.03712			−0.364473			−0.182237	−	0.983255i	$-0.558334\pi$
$191$	−5.03712			−0.364473			−0.182237	+	0.983255i	$0.558334\pi$
$192$	6.24592	+	12.3689i	0.450760	+	0.892645i
$193$			19.7439i			1.42120i	0.703596	+	0.710600i	$0.251576\pi$
$193$			19.7439i			1.42120i	−0.703596	+	0.710600i	$0.748424\pi$
$194$	1.47534	−	3.56178i	0.105923	−	0.255721i
$195$	−17.3196	+	4.98843i	−1.24028	+	0.357229i
$196$	5.41421	+	5.41421i	0.386730	+	0.386730i
$197$			11.9832i			0.853770i	0.904306	+	0.426885i	$0.140389\pi$
$197$			11.9832i			0.853770i	−0.904306	+	0.426885i	$0.859611\pi$
$198$	9.15096	−	5.51693i	0.650330	−	0.392071i
$199$			9.17157i			0.650156i	0.945687	+	0.325078i	$0.105390\pi$
$199$			9.17157i			0.650156i	−0.945687	+	0.325078i	$0.894610\pi$
$200$	14.1398	−	0.259210i	0.999832	−	0.0183289i
$201$	5.41421	+	1.78089i	0.381889	+	0.125614i
$202$	−17.2517	−	7.14590i	−1.21383	−	0.502784i
$203$	−20.0083			−1.40431
$204$	11.4273	−	5.77048i	0.800073	−	0.404014i
$205$	−15.8887	+	10.8284i	−1.10971	+	0.756290i
$206$	7.86123	+	3.25623i	0.547718	+	0.226872i
$207$	4.65369	−	6.30864i	0.323454	−	0.438481i
$208$		−	18.6148i		−	1.29070i
$209$		−	2.08644i		−	0.144322i
$210$	−17.9102	−	2.01921i	−1.23592	−	0.139339i
$211$	18.4853			1.27258			0.636290	−	0.771450i	$-0.280468\pi$
$211$	18.4853			1.27258			0.636290	+	0.771450i	$0.280468\pi$
$212$	−6.49435	+	6.49435i	−0.446034	+	0.446034i
$213$	−3.85525	+	11.7206i	−0.264157	+	0.803083i
$214$	−11.0711	−	4.58579i	−0.756803	−	0.313478i
$215$	11.1175	−	7.57675i	0.758205	−	0.516730i
$216$	12.4470	+	7.81484i	0.846912	+	0.531732i
$217$			3.85525i			0.261711i
$218$	−0.262632	+	0.634051i	−0.0177877	+	0.0429433i
$219$	−10.8284	−	3.56178i	−0.731717	−	0.240683i
$220$	11.0666	+	2.09603i	0.746110	+	0.141315i
$221$	−17.1978			−1.15685
$222$	3.07948	−	3.57927i	0.206681	−	0.240225i
$223$	21.9054			1.46690			0.733448	−	0.679746i	$-0.237910\pi$
$223$	21.9054			1.46690			0.733448	+	0.679746i	$0.237910\pi$
$224$	7.12356	−	17.1978i	0.475963	−	1.14908i
$225$	12.7019	−	7.97878i	0.846796	−	0.531919i
$226$	−11.6569	−	4.82843i	−0.775402	−	0.321182i
$227$	4.14386			0.275038			0.137519	−	0.990499i	$-0.456087\pi$
$227$	4.14386			0.275038			0.137519	+	0.990499i	$0.456087\pi$
$228$	2.56167	−	1.29357i	0.169651	−	0.0856689i
$229$		−	19.3137i		−	1.27629i	−0.769918	−	0.638143i	$-0.779703\pi$
$229$		−	19.3137i		−	1.27629i	0.769918	−	0.638143i	$-0.220297\pi$
$230$	8.08954	−	1.68633i	0.533408	−	0.111193i
$231$	−13.6360	−	4.48528i	−0.897184	−	0.295110i
$232$	6.58132	+	15.8887i	0.432085	+	1.04314i
$233$	15.9414			1.04436			0.522178	−	0.852837i	$-0.325120\pi$
$233$	15.9414			1.04436			0.522178	+	0.852837i	$0.325120\pi$
$234$	−10.1940	−	16.9088i	−0.666400	−	1.10536i
$235$	4.82843	−	3.29066i	0.314972	−	0.214659i
$236$	−3.56178	+	3.56178i	−0.231852	+	0.231852i
$237$	−27.1237	−	8.92177i	−1.76187	−	0.579531i
$238$	−15.8887	−	6.58132i	−1.02991	−	0.426603i
$239$	−22.2349			−1.43826			−0.719129	−	0.694877i	$-0.755459\pi$
$239$	−22.2349			−1.43826			−0.719129	+	0.694877i	$0.755459\pi$
$240$	4.28772	+	14.8868i	0.276771	+	0.960936i
$241$	−6.48528			−0.417754			−0.208877	−	0.977942i	$-0.566981\pi$
$241$	−6.48528			−0.417754			−0.208877	+	0.977942i	$0.566981\pi$
$242$	−6.08447	−	2.52027i	−0.391125	−	0.162009i
$243$	15.5859	+	0.282294i	0.999836	+	0.0181092i
$244$	−12.0000	+	12.0000i	−0.768221	+	0.768221i
$245$	4.82106	+	7.07401i	0.308006	+	0.451942i
$246$	−15.9667	−	13.7372i	−1.01800	−	0.875852i
$247$	−3.85525			−0.245303
$248$	3.06147	−	1.26810i	0.194403	−	0.0805245i
$249$	−5.07107	+	15.4169i	−0.321366	+	0.977007i
$250$	15.5865	+	2.65716i	0.985778	+	0.168053i
$251$			11.7286i			0.740301i	0.928972	+	0.370150i	$0.120694\pi$
$251$			11.7286i			0.740301i	−0.928972	+	0.370150i	$0.879306\pi$
$252$	−2.94729	−	19.5227i	−0.185662	−	1.22982i
$253$	6.58132			0.413764
$254$	4.29945	+	1.78089i	0.269772	+	0.111743i
$255$	13.7536	−	3.96134i	0.861282	−	0.248068i
$256$	−16.0000			−1.00000
$257$	−16.3128			−1.01756			−0.508782	−	0.860895i	$-0.669904\pi$
$257$	−16.3128			−1.01756			−0.508782	+	0.860895i	$0.669904\pi$
$258$	11.1721	+	9.61204i	0.695542	+	0.598419i
$259$	−6.34315			−0.394144
$260$	3.87297	−	20.4484i	0.240191	−	1.26816i
$261$	14.6792	+	10.8284i	0.908622	+	0.670263i
$262$	−11.7996	+	28.4867i	−0.728981	+	1.75992i
$263$		−	22.2500i		−	1.37200i	−0.727604	−	0.685998i	$-0.759366\pi$
$263$		−	22.2500i		−	1.37200i	0.727604	−	0.685998i	$-0.240634\pi$
$264$	0.923499	+	12.3038i	0.0568375	+	0.757244i
$265$	−8.48528	+	5.78287i	−0.521247	+	0.355239i
$266$	−3.56178	−	1.47534i	−0.218387	−	0.0904588i
$267$	−8.28772	−	2.72607i	−0.507200	−	0.166833i
$268$	−4.65369	+	4.65369i	−0.284270	+	0.284270i
$269$	−9.64212			−0.587891			−0.293945	−	0.955822i	$-0.594968\pi$
$269$	−9.64212			−0.587891			−0.293945	+	0.955822i	$0.594968\pi$
$270$	12.0472	+	11.1743i	0.733167	+	0.680049i
$271$			14.1421i			0.859074i	0.903049	+	0.429537i	$0.141323\pi$
$271$			14.1421i			0.859074i	−0.903049	+	0.429537i	$0.858677\pi$
$272$			14.7821i			0.896295i
$273$	−8.28772	+	25.1961i	−0.501596	+	1.52494i
$274$	15.6569	+	6.48528i	0.945865	+	0.391790i
$275$	11.7206	+	4.60500i	0.706779	+	0.277692i
$276$	4.08034	+	8.08034i	0.245608	+	0.486379i
$277$	−15.0903			−0.906685			−0.453343	−	0.891336i	$-0.649769\pi$
$277$	−15.0903			−0.906685			−0.453343	+	0.891336i	$0.649769\pi$
$278$	−18.9259	−	7.83938i	−1.13510	−	0.470175i
$279$	2.08644	−	2.82843i	0.124912	−	0.169334i
$280$	11.4034	−	17.4097i	0.681485	−	1.04043i
$281$		−	3.56178i		−	0.212478i	−0.994341	−	0.106239i	$-0.966119\pi$
$281$		−	3.56178i		−	0.212478i	0.994341	−	0.106239i	$-0.0338809\pi$
$282$	4.85214	+	4.17461i	0.288941	+	0.248594i
$283$			18.0502i			1.07297i	0.843909	+	0.536486i	$0.180249\pi$
$283$			18.0502i			1.07297i	−0.843909	+	0.536486i	$0.819751\pi$
$284$	−10.0742	−	10.0742i	−0.597796	−	0.597796i
$285$	3.08315	−	0.888016i	0.182630	−	0.0526015i
$286$	6.34315	−	15.3137i	0.375078	−	0.905519i
$287$			28.2960i			1.67026i
$288$	−14.5336	+	8.76204i	−0.856403	+	0.516308i
$289$	−3.34315			−0.196656
$290$	3.92382	+	18.8231i	0.230415	+	1.10533i
$291$	4.48528	+	1.47534i	0.262932	+	0.0864859i
$292$	9.30739	−	9.30739i	0.544674	−	0.544674i
$293$			2.42742i			0.141811i	0.997483	+	0.0709056i	$0.0225889\pi$
$293$			2.42742i			0.141811i	−0.997483	+	0.0709056i	$0.977411\pi$
$294$	−6.11611	+	7.10875i	−0.356699	+	0.414591i
$295$	−4.65369	+	3.17157i	−0.270948	+	0.184656i
$296$	2.08644	+	5.03712i	0.121272	+	0.292777i
$297$	7.57675	+	10.6704i	0.439647	+	0.619161i
$298$	−19.1794	−	7.94435i	−1.11103	−	0.460204i
$299$		−	12.1607i		−	0.703271i
$300$	1.61276	+	17.2453i	0.0931127	+	0.995656i
$301$		−	19.7990i		−	1.14119i
$302$	−1.53073	+	3.69552i	−0.0880838	+	0.212653i
$303$	7.14590	−	21.7248i	0.410521	−	1.24806i
$304$			3.31371i			0.190054i
$305$	−15.6788	+	10.6853i	−0.897763	+	0.611841i
$306$	8.09507	+	13.4273i	0.462764	+	0.767589i
$307$		−	7.14590i		−	0.407838i	−0.978988	−	0.203919i	$-0.934632\pi$
$307$		−	7.14590i		−	0.407838i	0.978988	−	0.203919i	$-0.0653680\pi$
$308$	11.7206	−	11.7206i	0.667843	−	0.667843i
$309$	−3.25623	+	9.89949i	−0.185240	+	0.563163i
$310$	3.62687	−	0.756050i	0.205993	−	0.0429407i
$311$	34.3956			1.95040			0.975198	−	0.221334i	$-0.0710411\pi$
$311$	34.3956			1.95040			0.975198	+	0.221334i	$0.0710411\pi$
$312$	22.7344	−	1.70640i	1.28708	−	0.0966061i
$313$		−	17.0179i		−	0.961907i	−0.876746	−	0.480954i	$-0.840291\pi$
$313$		−	17.0179i		−	0.961907i	0.876746	−	0.480954i	$-0.159709\pi$
$314$	−7.55568	−	3.12967i	−0.426392	−	0.176617i
$315$	0.824265	−	22.0590i	0.0464421	−	1.24288i
$316$	23.3137	−	23.3137i	1.31150	−	1.31150i
$317$			13.2513i			0.744269i	0.928179	+	0.372135i	$0.121374\pi$
$317$			13.2513i			0.744269i	−0.928179	+	0.372135i	$0.878626\pi$
$318$	−8.52695	−	7.33628i	−0.478168	−	0.411398i
$319$			15.3137i			0.857403i
$320$	−17.5761	−	3.32894i	−0.982532	−	0.186093i
$321$	4.58579	−	13.9416i	0.255954	−	0.778143i
$322$	4.65369	−	11.2350i	0.259340	−	0.626102i
$323$	3.06147			0.170345
$324$	−8.40333	+	15.9180i	−0.466851	+	0.884336i
$325$	8.50894	−	21.6569i	0.471991	−	1.20131i
$326$	3.25623	−	7.86123i	0.180346	−	0.435393i
$327$	−0.798447	−	0.262632i	−0.0441542	−	0.0145236i
$328$	22.4700	−	9.30739i	1.24070	−	0.513914i
$329$		−	8.59890i		−	0.474073i
$330$	−1.54544	+	13.7079i	−0.0850736	+	0.754594i
$331$	−18.4853			−1.01604			−0.508021	−	0.861344i	$-0.669623\pi$
$331$	−18.4853			−1.01604			−0.508021	+	0.861344i	$0.669623\pi$
$332$	−13.2513	−	13.2513i	−0.727262	−	0.727262i
$333$	4.65369	+	3.43289i	0.255021	+	0.188121i
$334$	−9.41421	+	22.7279i	−0.515123	+	1.24362i
$335$	−6.08034	+	4.14386i	−0.332205	+	0.226403i
$336$	21.6569	+	7.12356i	1.18148	+	0.388622i
$337$		−	27.9222i		−	1.52102i	−0.649328	−	0.760508i	$-0.724950\pi$
$337$		−	27.9222i		−	1.52102i	0.649328	−	0.760508i	$-0.275050\pi$
$338$	−11.3107	−	4.68506i	−0.615222	−	0.254833i
$339$	4.82843	−	14.6792i	0.262244	−	0.797267i
$340$	−3.07554	+	16.2382i	−0.166795	+	0.880638i
$341$	2.95068			0.159788
$342$	1.81468	+	3.01001i	0.0981266	+	0.162763i
$343$	−10.4366			−0.563521
$344$	−15.7225	+	6.51246i	−0.847699	+	0.351128i
$345$	2.80109	+	9.72524i	0.150805	+	0.523589i
$346$	−11.6569	+	28.1421i	−0.626676	+	1.51293i
$347$	−0.185709			−0.00996939			−0.00498469	−	0.999988i	$-0.501587\pi$
$347$	−0.185709			−0.00996939			−0.00498469	+	0.999988i	$0.501587\pi$
$348$	−18.8017	+	9.49433i	−1.00788	+	0.508949i
$349$		−	2.34315i		−	0.125426i	−0.998032	−	0.0627129i	$-0.980025\pi$
$349$		−	2.34315i		−	0.125426i	0.998032	−	0.0627129i	$-0.0199752\pi$
$350$	16.1490	−	16.7521i	0.863198	−	0.895437i
$351$	19.7164	−	14.0000i	1.05238	−	0.747265i
$352$	−13.1626	−	5.45214i	−0.701571	−	0.290600i
$353$	32.3630			1.72251			0.861254	−	0.508175i	$-0.169680\pi$
$353$	32.3630			1.72251			0.861254	+	0.508175i	$0.169680\pi$
$354$	−4.67654	−	4.02353i	−0.248556	−	0.213848i
$355$	−8.97056	−	13.1626i	−0.476108	−	0.698600i
$356$	7.12356	−	7.12356i	0.377548	−	0.377548i
$357$	6.58132	−	20.0083i	0.348320	−	1.05895i
$358$	5.21828	−	12.5980i	0.275795	−	0.665827i
$359$	−9.21001			−0.486086			−0.243043	−	0.970016i	$-0.578146\pi$
$359$	−9.21001			−0.486086			−0.243043	+	0.970016i	$0.578146\pi$
$360$	−17.7883	+	6.60129i	−0.937525	+	0.347919i
$361$	−18.3137			−0.963879
$362$	−5.59767	+	13.5140i	−0.294207	+	0.710279i
$363$	2.52027	−	7.66206i	0.132280	−	0.402154i
$364$	−21.6569	−	21.6569i	−1.13513	−	1.13513i
$365$	12.1607	−	8.28772i	0.636519	−	0.433799i
$366$	−15.7557	−	13.5557i	−0.823566	−	0.708567i
$367$	−2.16148			−0.112828			−0.0564142	−	0.998407i	$-0.517967\pi$
$367$	−2.16148			−0.112828			−0.0564142	+	0.998407i	$0.517967\pi$
$368$	−10.4525			−0.544874
$369$	15.3137	−	20.7596i	0.797200	−	1.08070i
$370$	1.24395	+	5.96740i	0.0646699	+	0.310230i
$371$			15.1114i			0.784543i
$372$	1.82939	+	3.62275i	0.0948493	+	0.187831i
$373$	24.3976			1.26326			0.631631	−	0.775269i	$-0.282386\pi$
$373$	24.3976			1.26326			0.631631	+	0.775269i	$0.282386\pi$
$374$	−5.03712	+	12.1607i	−0.260463	+	0.628814i
$375$	−1.81640	+	19.2795i	−0.0937987	+	0.995591i
$376$	−6.82843	+	2.82843i	−0.352149	+	0.145865i
$377$	28.2960			1.45732
$378$	23.5731	−	5.38919i	1.21247	−	0.277190i
$379$	20.8284			1.06988			0.534942	−	0.844889i	$-0.320333\pi$
$379$	20.8284			1.06988			0.534942	+	0.844889i	$0.320333\pi$
$380$	−0.689446	+	3.64012i	−0.0353678	+	0.186734i
$381$	−1.78089	+	5.41421i	−0.0912378	+	0.277379i
$382$	6.58132	+	2.72607i	0.336729	+	0.139478i
$383$			29.1158i			1.48775i	0.668320	+	0.743874i	$0.267014\pi$
$383$			29.1158i			1.48775i	−0.668320	+	0.743874i	$0.732986\pi$
$384$	−1.46671	−	19.5410i	−0.0748477	−	0.997195i
$385$	15.3137	−	10.4366i	0.780459	−	0.531896i
$386$	10.6853	−	25.7967i	0.543870	−	1.31302i
$387$	−10.7151	+	14.5257i	−0.544681	+	0.738381i
$388$	−3.85525	+	3.85525i	−0.195720	+	0.195720i
$389$	−7.55568			−0.383088			−0.191544	−	0.981484i	$-0.561350\pi$
$389$	−7.55568			−0.383088			−0.191544	+	0.981484i	$0.561350\pi$
$390$	25.3289	+	2.85560i	1.28258	+	0.144599i
$391$			9.65685i			0.488368i
$392$	−4.14386	−	10.0042i	−0.209297	−	0.505286i
$393$	−35.8728	−	11.7996i	−1.80954	−	0.595211i
$394$	6.48528	−	15.6569i	0.326724	−	0.788781i
$395$	30.4608	−	20.7596i	1.53265	−	1.04453i
$396$	−14.9420	+	2.25576i	−0.750866	+	0.113356i
$397$	27.1237			1.36130			0.680650	−	0.732609i	$-0.261697\pi$
$397$	27.1237			1.36130			0.680650	+	0.732609i	$0.261697\pi$
$398$	4.96362	−	11.9832i	0.248804	−	0.600665i
$399$	1.47534	−	4.48528i	0.0738593	−	0.224545i
$400$	−18.6148	−	7.31371i	−0.930739	−	0.365685i
$401$		−	15.1114i		−	0.754625i	−0.926086	−	0.377313i	$-0.876848\pi$
$401$		−	15.1114i		−	0.754625i	0.926086	−	0.377313i	$-0.123152\pi$
$402$	−6.11020	−	5.25700i	−0.304749	−	0.262195i
$403$		−	5.45214i		−	0.271590i
$404$	18.6731	+	18.6731i	0.929024	+	0.929024i
$405$	−12.5430	+	15.7377i	−0.623266	+	0.782010i
$406$	26.1421	+	10.8284i	1.29741	+	0.537406i
$407$			4.85483i			0.240645i
$408$	−18.0535	+	1.35506i	−0.893781	+	0.0670856i
$409$	−12.8284			−0.634325			−0.317162	−	0.948371i	$-0.602730\pi$
$409$	−12.8284			−0.634325			−0.317162	+	0.948371i	$0.602730\pi$
$410$	26.6199	−	5.54912i	1.31466	−	0.274051i
$411$	−6.48528	+	19.7164i	−0.319895	+	0.972537i
$412$	−8.50894	−	8.50894i	−0.419205	−	0.419205i
$413$			8.28772i			0.407812i
$414$	−9.49456	+	5.72408i	−0.466632	+	0.281323i
$415$	−11.7996	−	17.3137i	−0.579219	−	0.849897i
$416$	−10.0742	+	24.3214i	−0.493930	+	1.19245i
$417$	7.83938	−	23.8331i	0.383896	−	1.16711i
$418$	−1.12918	+	2.72607i	−0.0552298	+	0.133336i
$419$		−	2.51856i		−	0.123040i	−0.998106	−	0.0615199i	$-0.980405\pi$
$419$		−	2.51856i		−	0.123040i	0.998106	−	0.0615199i	$-0.0195948\pi$
$420$	22.3080	+	12.3312i	1.08852	+	0.601699i
$421$			34.8284i			1.69743i	0.528848	+	0.848717i	$0.322624\pi$
$421$			34.8284i			1.69743i	−0.528848	+	0.848717i	$0.677376\pi$
$422$	−24.1522	−	10.0042i	−1.17571	−	0.486995i
$423$	−4.65369	+	6.30864i	−0.226270	+	0.306737i
$424$	12.0000	−	4.97056i	0.582772	−	0.241392i
$425$	−6.75699	+	17.1978i	−0.327762	+	0.834216i
$426$	11.3803	−	13.2273i	0.551376	−	0.640863i
$427$			27.9222i			1.35125i
$428$	11.9832	+	11.9832i	0.579232	+	0.579232i
$429$	19.2842	+	6.34315i	0.931052	+	0.306250i
$430$	−18.6262	+	3.88277i	−0.898234	+	0.187244i
$431$	−27.2720			−1.31365			−0.656824	−	0.754044i	$-0.728101\pi$
$431$	−27.2720			−1.31365			−0.656824	+	0.754044i	$0.728101\pi$
$432$	−12.0335	−	16.9469i	−0.578960	−	0.815356i
$433$			23.5992i			1.13410i	0.823682	+	0.567052i	$0.191916\pi$
$433$			23.5992i			1.13410i	−0.823682	+	0.567052i	$0.808084\pi$
$434$	2.08644	−	5.03712i	0.100152	−	0.241790i
$435$	−22.6291	+	6.51770i	−1.08498	+	0.312500i
$436$	0.686292	−	0.686292i	0.0328674	−	0.0328674i
$437$			2.16478i			0.103556i
$438$	12.2204	+	10.5140i	0.583913	+	0.502378i
$439$		−	28.4853i		−	1.35953i	−0.733431	−	0.679764i	$-0.762082\pi$
$439$		−	28.4853i		−	1.35953i	0.733431	−	0.679764i	$-0.237918\pi$
$440$	−13.3248	−	8.72780i	−0.635237	−	0.416081i
$441$	−9.24264	−	6.81801i	−0.440126	−	0.324667i
$442$	22.4700	+	9.30739i	1.06879	+	0.442707i
$443$	−1.60766			−0.0763821			−0.0381910	−	0.999270i	$-0.512160\pi$
$443$	−1.60766			−0.0763821			−0.0381910	+	0.999270i	$0.512160\pi$
$444$	−5.96062	+	3.00994i	−0.282878	+	0.142846i
$445$	9.30739	−	6.34315i	0.441212	−	0.300694i
$446$	−28.6208	−	11.8551i	−1.35524	−	0.561357i
$447$	7.94435	−	24.1522i	0.375755	−	1.14236i
$448$	−18.6148	+	18.6148i	−0.879465	+	0.879465i
$449$			35.0067i			1.65207i	0.563620	+	0.826035i	$0.309408\pi$
$449$			35.0067i			1.65207i	−0.563620	+	0.826035i	$0.690592\pi$
$450$	−20.9140	+	3.55054i	−0.985893	+	0.167374i
$451$	21.6569			1.01978
$452$	12.6173	+	12.6173i	0.593467	+	0.593467i
$453$	−4.65369	−	1.53073i	−0.218650	−	0.0719201i
$454$	−5.41421	−	2.24264i	−0.254102	−	0.105252i
$455$	−19.2842	−	28.2960i	−0.904060	−	1.32654i
$456$	−4.04706	+	0.303766i	−0.189521	+	0.0142251i
$457$			18.6148i			0.870762i	0.900246	+	0.435381i	$0.143386\pi$
$457$			18.6148i			0.870762i	−0.900246	+	0.435381i	$0.856614\pi$
$458$	−10.4525	+	25.2346i	−0.488413	+	1.17913i
$459$	−15.6569	+	11.1175i	−0.730799	+	0.518919i
$460$	−11.4821	−	2.17473i	−0.535357	−	0.101398i
$461$	3.99390			0.186014			0.0930072	−	0.995665i	$-0.470352\pi$
$461$	3.99390			0.186014			0.0930072	+	0.995665i	$0.470352\pi$
$462$	15.3889	+	13.2401i	0.715957	+	0.615984i
$463$	−25.7607			−1.19720			−0.598600	−	0.801048i	$-0.704276\pi$
$463$	−25.7607			−1.19720			−0.598600	+	0.801048i	$0.704276\pi$
$464$		−	24.3214i		−	1.12909i
$465$	1.25584	+	4.36023i	0.0582384	+	0.202201i
$466$	−20.8284	−	8.62742i	−0.964858	−	0.399657i
$467$	−15.8645			−0.734120			−0.367060	−	0.930197i	$-0.619636\pi$
$467$	−15.8645			−0.734120			−0.367060	+	0.930197i	$0.619636\pi$
$468$	4.16810	+	27.6093i	0.192670	+	1.27624i
$469$			10.8284i			0.500010i
$470$	−8.08954	+	1.68633i	−0.373142	+	0.0777844i
$471$	3.12967	−	9.51472i	0.144207	−	0.438415i
$472$	6.58132	−	2.72607i	0.302930	−	0.125478i
$473$	−15.1535			−0.696758
$474$	30.6104	+	26.3361i	1.40598	+	1.20966i
$475$	−1.51472	+	3.85525i	−0.0695001	+	0.176891i
$476$	17.1978	+	17.1978i	0.788260	+	0.788260i
$477$	8.17821	−	11.0866i	0.374455	−	0.507618i
$478$	29.0513	+	12.0335i	1.32878	+	0.550397i
$479$	19.2842			0.881120			0.440560	−	0.897723i	$-0.354780\pi$
$479$	19.2842			0.881120			0.440560	+	0.897723i	$0.354780\pi$
$480$	2.45448	−	21.7710i	0.112031	−	0.993705i
$481$	8.97056			0.409022
$482$	8.47343	+	3.50981i	0.385954	+	0.159867i
$483$	14.1480	+	4.65369i	0.643757	+	0.211750i
$484$	6.58579	+	6.58579i	0.299354	+	0.299354i
$485$	−5.03712	+	3.43289i	−0.228724	+	0.155879i
$486$	−20.2112	−	8.80386i	−0.916798	−	0.399351i
$487$	−8.74280			−0.396174			−0.198087	−	0.980184i	$-0.563473\pi$
$487$	−8.74280			−0.396174			−0.198087	+	0.980184i	$0.563473\pi$
$488$	22.1731	−	9.18440i	1.00373	−	0.415758i
$489$	9.89949	+	3.25623i	0.447671	+	0.147252i
$490$	−2.47059	−	11.8518i	−0.111610	−	0.535409i
$491$			36.9142i			1.66591i	0.553338	+	0.832957i	$0.313354\pi$
$491$			36.9142i			1.66591i	−0.553338	+	0.832957i	$0.686646\pi$
$492$	13.4270	+	26.5896i	0.605336	+	1.19875i
$493$	−22.4700			−1.01200
$494$	5.03712	+	2.08644i	0.226631	+	0.0938735i
$495$	−16.8832	−	0.630865i	−0.758845	−	0.0283553i
$496$	−4.68629			−0.210421
$497$	−23.4412			−1.05148
$498$	14.9692	−	17.3987i	0.670788	−	0.779656i
$499$	−37.1127			−1.66139			−0.830696	−	0.556726i	$-0.812057\pi$
$499$	−37.1127			−1.66139			−0.830696	+	0.556726i	$0.812057\pi$
$500$	−18.9267	−	11.9071i	−0.846429	−	0.532502i
$501$	−28.6208	−	9.41421i	−1.27868	−	0.420596i
$502$	6.34746	−	15.3241i	0.283301	−	0.683949i
$503$			9.63274i			0.429503i	0.976669	+	0.214751i	$0.0688941\pi$
$503$			9.63274i			0.429503i	−0.976669	+	0.214751i	$0.931106\pi$
$504$	−6.71481	+	27.1027i	−0.299101	+	1.20725i
$505$	16.6274	+	24.3976i	0.739910	+	1.08568i
$506$	−8.59890	−	3.56178i	−0.382268	−	0.158341i
$507$	4.68506	−	14.2434i	0.208071	−	0.632570i
$508$	−4.65369	−	4.65369i	−0.206474	−	0.206474i
$509$	13.2039			0.585253			0.292626	−	0.956227i	$-0.405471\pi$
$509$	13.2039			0.585253			0.292626	+	0.956227i	$0.405471\pi$
$510$	−20.1138	−	2.26764i	−0.890652	−	0.100413i
$511$		−	21.6569i		−	0.958043i
$512$	20.9050	+	8.65914i	0.923880	+	0.382683i
$513$	−3.50981	+	2.49221i	−0.154962	+	0.110034i
$514$	21.3137	+	8.82843i	0.940107	+	0.389405i
$515$	−7.57675	−	11.1175i	−0.333871	−	0.489894i
$516$	−9.39500	−	18.6050i	−0.413592	−	0.819040i
$517$	−6.58132			−0.289446
$518$	8.28772	+	3.43289i	0.364141	+	0.150832i
$519$	−35.4388	−	11.6569i	−1.55559	−	0.511679i
$520$	−16.1269	+	24.6211i	−0.707210	+	1.07971i
$521$		−	34.3956i		−	1.50690i	−0.657506	−	0.753450i	$-0.728388\pi$
$521$		−	34.3956i		−	1.50690i	0.657506	−	0.753450i	$-0.271612\pi$
$522$	−13.3191	−	22.0924i	−0.582959	−	0.966957i
$523$		−	12.5980i		−	0.550874i	−0.961319	−	0.275437i	$-0.911177\pi$
$523$		−	12.5980i		−	0.550874i	0.961319	−	0.275437i	$-0.0888225\pi$
$524$	30.8338	−	30.8338i	1.34698	−	1.34698i
$525$	21.9399	+	18.1872i	0.957534	+	0.793755i
$526$	−12.0416	+	29.0711i	−0.525040	+	1.26756i
$527$			4.32957i			0.188599i
$528$	5.45214	−	16.5754i	0.237274	−	0.721353i
$529$	16.1716			0.703112
$530$	14.2162	−	2.96348i	0.617513	−	0.128725i
$531$	4.48528	−	6.08034i	0.194645	−	0.263864i
$532$	3.85525	+	3.85525i	0.167146	+	0.167146i
$533$		−	40.0166i		−	1.73331i
$534$	9.35309	+	8.04706i	0.404748	+	0.348230i
$535$	10.6704	+	15.6569i	0.461322	+	0.676905i
$536$	8.59890	−	3.56178i	0.371416	−	0.153846i
$537$	15.8645	+	5.21828i	0.684602	+	0.225185i
$538$	12.5980	+	5.21828i	0.543140	+	0.224976i
$539$		−	9.64212i		−	0.415316i
$540$	−9.69286	−	21.1199i	−0.417114	−	0.908854i
$541$			16.0000i			0.687894i	0.938989	+	0.343947i	$0.111764\pi$
$541$			16.0000i			0.687894i	−0.938989	+	0.343947i	$0.888236\pi$
$542$	7.65367	−	18.4776i	0.328753	−	0.793680i
$543$	−17.0179	−	5.59767i	−0.730307	−	0.240219i
$544$	8.00000	−	19.3137i	0.342997	−	0.828068i
$545$	0.896683	−	0.611105i	0.0384097	−	0.0261769i
$546$	24.4645	−	28.4350i	1.04698	−	1.21691i
$547$			11.0011i			0.470375i	0.971950	+	0.235188i	$0.0755704\pi$
$547$			11.0011i			0.470375i	−0.971950	+	0.235188i	$0.924430\pi$
$548$	−16.9469	−	16.9469i	−0.723934	−	0.723934i
$549$	15.1114	−	20.4853i	0.644937	−	0.874291i
$550$	−12.8215	−	12.3599i	−0.546711	−	0.527027i
$551$	−5.03712			−0.214589
$552$	−0.958174	−	12.7657i	−0.0407826	−	0.543346i
$553$		−	54.2474i		−	2.30683i
$554$	19.7164	+	8.16679i	0.837668	+	0.346973i
$555$	−7.17401	+	2.06628i	−0.304520	+	0.0877085i
$556$	20.4853	+	20.4853i	0.868769	+	0.868769i
$557$		−	4.96362i		−	0.210315i	−0.994456	−	0.105158i	$-0.966465\pi$
$557$		−	4.96362i		−	0.210315i	0.994456	−	0.105158i	$-0.0335347\pi$
$558$	−4.25680	+	2.56634i	−0.180205	+	0.108642i
$559$			28.0000i			1.18427i
$560$	−24.3214	+	16.5754i	−1.02777	+	0.700440i
$561$	−15.3137	−	5.03712i	−0.646545	−	0.212667i
$562$	−1.92762	+	4.65369i	−0.0813119	+	0.196304i
$563$	−21.9874			−0.926658			−0.463329	−	0.886186i	$-0.653345\pi$
$563$	−21.9874			−0.926658			−0.463329	+	0.886186i	$0.653345\pi$
$564$	−4.08034	−	8.08034i	−0.171813	−	0.340244i
$565$	11.2350	+	16.4853i	0.472660	+	0.693541i
$566$	9.76869	−	23.5837i	0.410609	−	0.991297i
$567$	8.74280	+	28.2960i	0.367163	+	1.18832i
$568$	7.71049	+	18.6148i	0.323525	+	0.781058i
$569$			15.7225i			0.659120i	0.944135	+	0.329560i	$0.106900\pi$
$569$			15.7225i			0.659120i	−0.944135	+	0.329560i	$0.893100\pi$
$570$	−4.50892	−	0.508339i	−0.188858	−	0.0212920i
$571$	21.1127			0.883539			0.441769	−	0.897129i	$-0.354351\pi$
$571$	21.1127			0.883539			0.441769	+	0.897129i	$0.354351\pi$
$572$	−16.5754	+	16.5754i	−0.693054	+	0.693054i
$573$	−2.72607	+	8.28772i	−0.113883	+	0.346224i
$574$	15.3137	−	36.9706i	0.639182	−	1.54312i
$575$	−12.1607	−	4.77791i	−0.507136	−	0.199253i
$576$	23.7311	−	3.58261i	0.988796	−	0.149276i
$577$		−	3.85525i		−	0.160496i	−0.996775	−	0.0802480i	$-0.974429\pi$
$577$		−	3.85525i		−	0.160496i	0.996775	−	0.0802480i	$-0.0255712\pi$
$578$	4.36803	+	1.80930i	0.181686	+	0.0752569i
$579$	32.4853	+	10.6853i	1.35004	+	0.444068i
$580$	5.06027	−	26.7171i	0.210116	−	1.10937i
$581$	−30.8338			−1.27920
$582$	−5.06186	−	4.35504i	−0.209821	−	0.180522i
$583$	11.5657			0.479004
$584$	−17.1978	+	7.12356i	−0.711650	+	0.294775i
$585$	−1.16569	+	31.1961i	−0.0481952	+	1.28980i
$586$	1.31371	−	3.17157i	0.0542688	−	0.131016i
$587$	7.20533			0.297396			0.148698	−	0.988883i	$-0.452492\pi$
$587$	7.20533			0.297396			0.148698	+	0.988883i	$0.452492\pi$
$588$	11.8383	−	5.97801i	0.488204	−	0.246529i
$589$			0.970563i			0.0399913i
$590$	7.79679	−	1.62530i	0.320989	−	0.0669125i
$591$	19.7164	+	6.48528i	0.811023	+	0.266769i
$592$		−	7.71049i		−	0.316899i
$593$	1.00547			0.0412897			0.0206448	−	0.999787i	$-0.493428\pi$
$593$	1.00547			0.0412897			0.0206448	+	0.999787i	$0.493428\pi$
$594$	−4.12471	−	18.0421i	−0.169239	−	0.740276i
$595$	15.3137	+	22.4700i	0.627801	+	0.921181i
$596$	20.7596	+	20.7596i	0.850346	+	0.850346i
$597$	15.0903	+	4.96362i	0.617603	+	0.203147i
$598$	−6.58132	+	15.8887i	−0.269130	+	0.649737i
$599$	32.3092			1.32012			0.660058	−	0.751214i	$-0.270532\pi$
$599$	32.3092			1.32012			0.660058	+	0.751214i	$0.270532\pi$
$600$	7.22590	−	23.4048i	0.294996	−	0.955498i
$601$	13.5147			0.551277			0.275638	−	0.961261i	$-0.411111\pi$
$601$	13.5147			0.551277			0.275638	+	0.961261i	$0.411111\pi$
$602$	−10.7151	+	25.8686i	−0.436716	+	1.05433i
$603$	5.86030	−	7.94435i	0.238650	−	0.323519i
$604$	4.00000	−	4.00000i	0.162758	−	0.162758i
$605$	5.86428	+	8.60474i	0.238417	+	0.349833i
$606$	−21.0939	+	24.5174i	−0.856882	+	0.995953i
$607$	4.88755			0.198380			0.0991898	−	0.995069i	$-0.468375\pi$
$607$	4.88755			0.198380			0.0991898	+	0.995069i	$0.468375\pi$
$608$	1.79337	−	4.32957i	0.0727306	−	0.175587i
$609$	−10.8284	+	32.9203i	−0.438790	+	1.33400i
$610$	26.2681	−	5.47580i	1.06357	−	0.221709i
$611$			12.1607i			0.491969i
$612$	−3.30990	−	21.9247i	−0.133795	−	0.886252i
$613$	−23.2685			−0.939804			−0.469902	−	0.882718i	$-0.655711\pi$
$613$	−23.2685			−0.939804			−0.469902	+	0.882718i	$0.655711\pi$
$614$	−3.86733	+	9.33657i	−0.156073	+	0.376793i
$615$	9.21742	+	32.0024i	0.371682	+	1.29046i
$616$	−21.6569	+	8.97056i	−0.872580	+	0.361434i
$617$	−8.55035			−0.344224			−0.172112	−	0.985077i	$-0.555059\pi$
$617$	−8.55035			−0.344224			−0.172112	+	0.985077i	$0.555059\pi$
$618$	9.61204	−	11.1721i	0.386653	−	0.449406i
$619$	−2.48528			−0.0998919			−0.0499459	−	0.998752i	$-0.515905\pi$
$619$	−2.48528			−0.0998919			−0.0499459	+	0.998752i	$0.515905\pi$
$620$	−5.14791	−	0.975024i	−0.206745	−	0.0391579i
$621$	−7.86123	−	11.0711i	−0.315460	−	0.444267i
$622$	−44.9400	−	18.6148i	−1.80193	−	0.746384i
$623$		−	16.5754i		−	0.664081i
$624$	−30.6274	−	10.0742i	−1.22608	−	0.403292i
$625$	−18.3137	−	17.0179i	−0.732548	−	0.680715i
$626$	−9.21001	+	22.2349i	−0.368106	+	0.888686i
$627$	−3.43289	−	1.12918i	−0.137096	−	0.0450949i
$628$	8.17821	+	8.17821i	0.326346	+	0.326346i
$629$	−7.12356			−0.284035
$630$	−13.0152	+	28.3754i	−0.518538	+	1.13050i
$631$			2.14214i			0.0852771i	0.999091	+	0.0426385i	$0.0135764\pi$
$631$			2.14214i			0.0852771i	−0.999091	+	0.0426385i	$0.986424\pi$
$632$	−43.0781	+	17.8435i	−1.71356	+	0.709778i
$633$	10.0042	−	30.4144i	0.397630	−	1.20886i
$634$	7.17157	−	17.3137i	0.284820	−	0.687615i
$635$	−4.14386	−	6.08034i	−0.164444	−	0.241291i
$636$	7.17063	+	14.2001i	0.284334	+	0.563069i
$637$	−17.8163			−0.705908
$638$	8.28772	−	20.0083i	0.328114	−	0.792137i
$639$	17.1978	+	12.6863i	0.680335	+	0.501862i
$640$	21.1626	+	13.8616i	0.836526	+	0.547927i
$641$		−	35.0067i		−	1.38268i	−0.722529	−	0.691341i	$-0.757020\pi$
$641$		−	35.0067i		−	1.38268i	0.722529	−	0.691341i	$-0.242980\pi$
$642$	−13.5367	+	15.7337i	−0.534253	+	0.620961i
$643$		−	35.0681i		−	1.38295i	−0.722401	−	0.691475i	$-0.756961\pi$
$643$		−	35.0681i		−	1.38295i	0.722401	−	0.691475i	$-0.243039\pi$
$644$	−12.1607	+	12.1607i	−0.479198	+	0.479198i
$645$	−6.44951	−	22.3924i	−0.253949	−	0.881699i
$646$	−4.00000	−	1.65685i	−0.157378	−	0.0651881i
$647$		−	28.3730i		−	1.11546i	−0.830024	−	0.557728i	$-0.811673\pi$
$647$		−	28.3730i		−	1.11546i	0.830024	−	0.557728i	$-0.188327\pi$
$648$	19.5943	−	16.2501i	0.769735	−	0.638363i
$649$	6.34315			0.248990
$650$	−22.8381	+	23.6910i	−0.895783	+	0.929239i
$651$	6.34315	+	2.08644i	0.248607	+	0.0817742i
$652$	−8.50894	+	8.50894i	−0.333236	+	0.333236i
$653$			24.2291i			0.948158i	0.880482	+	0.474079i	$0.157219\pi$
$653$			24.2291i			0.948158i	−0.880482	+	0.474079i	$0.842781\pi$
$654$	0.901086	+	0.775262i	0.0352353	+	0.0303152i
$655$	40.2863	−	27.4558i	1.57412	−	1.07279i
$656$	−34.3956			−1.34292
$657$	−11.7206	+	15.8887i	−0.457264	+	0.619877i
$658$	−4.65369	+	11.2350i	−0.181420	+	0.437986i
$659$		−	14.6792i		−	0.571822i	−0.958256	−	0.285911i	$-0.907704\pi$
$659$		−	14.6792i		−	0.571822i	0.958256	−	0.285911i	$-0.0922962\pi$
$660$	9.43786	−	17.0738i	0.367368	−	0.664598i
$661$		−	44.7696i		−	1.74133i	−0.491873	−	0.870667i	$-0.663688\pi$
$661$		−	44.7696i		−	1.74133i	0.491873	−	0.870667i	$-0.336312\pi$
$662$	24.1522	+	10.0042i	0.938701	+	0.388823i
$663$	−9.30739	+	28.2960i	−0.361469	+	1.09893i
$664$	10.1421	+	24.4853i	0.393591	+	0.950213i
$665$	3.43289	+	5.03712i	0.133122	+	0.195331i
$666$	−4.22248	−	7.00384i	−0.163618	−	0.271393i
$667$		−	15.8887i		−	0.615213i
$668$	24.6005	−	24.6005i	0.951823	−	0.951823i
$669$	11.8551	−	36.0416i	0.458346	−	1.39345i
$670$	10.1870	−	2.12356i	0.393558	−	0.0820401i
$671$	21.3707			0.825006
$672$	−24.4408	−	21.0280i	−0.942824	−	0.811172i
$673$			47.6661i			1.83739i	0.394964	+	0.918697i	$0.370757\pi$
$673$			47.6661i			1.83739i	−0.394964	+	0.918697i	$0.629243\pi$
$674$	−15.1114	+	36.4821i	−0.582068	+	1.40524i
$675$	−6.25348	−	25.2169i	−0.240696	−	0.970600i
$676$	12.2426	+	12.2426i	0.470871	+	0.470871i
$677$			1.00547i			0.0386433i	0.999813	+	0.0193217i	$0.00615066\pi$
$677$			1.00547i			0.0386433i	−0.999813	+	0.0193217i	$0.993849\pi$
$678$	−14.2530	+	16.5662i	−0.547383	+	0.636222i
$679$			8.97056i			0.344259i
$680$	12.8064	−	19.5517i	0.491104	−	0.749774i
$681$	2.24264	−	6.81801i	0.0859382	−	0.261267i
$682$	−3.85525	−	1.59689i	−0.147625	−	0.0611483i
$683$	−14.9678			−0.572726			−0.286363	−	0.958121i	$-0.592446\pi$
$683$	−14.9678			−0.572726			−0.286363	+	0.958121i	$0.592446\pi$
$684$	−0.741983	−	4.91487i	−0.0283704	−	0.187925i
$685$	−15.0903	−	22.1421i	−0.576569	−	0.846008i
$686$	13.6360	+	5.64823i	0.520626	+	0.215650i
$687$	−31.7774	−	10.4525i	−1.21238	−	0.398788i
$688$	24.0669			0.917542
$689$		−	21.3707i		−	0.814159i
$690$	1.60347	−	14.2226i	0.0610429	−	0.541444i
$691$	−7.17157			−0.272819			−0.136410	−	0.990653i	$-0.543556\pi$
$691$	−7.17157			−0.272819			−0.136410	+	0.990653i	$0.543556\pi$
$692$	30.4608	−	30.4608i	1.15795	−	1.15795i
$693$	−14.7595	+	20.0083i	−0.560668	+	0.760053i
$694$	0.242641	+	0.100505i	0.00921051	+	0.00381512i
$695$	18.2410	+	26.7653i	0.691922	+	1.01527i
$696$	29.7039	−	2.22952i	1.12592	−	0.0845099i
$697$			31.7774i			1.20365i
$698$	−1.26810	+	3.06147i	−0.0479983	+	0.115878i
$699$	8.62742	−	26.2288i	0.326319	−	0.992065i
$700$	−30.1658	+	13.1479i	−1.14016	+	0.496945i
$701$	26.8399			1.01373			0.506865	−	0.862025i	$-0.330804\pi$
$701$	26.8399			1.01373			0.506865	+	0.862025i	$0.330804\pi$
$702$	−33.3374	+	7.62146i	−1.25824	+	0.287654i
$703$	−1.59689			−0.0602280
$704$	14.2471	+	14.2471i	0.536959	+	0.536959i
$705$	−2.80109	−	9.72524i	−0.105495	−	0.366274i
$706$	−42.2843	−	17.5147i	−1.59139	−	0.659175i
$707$	43.4495			1.63409
$708$	3.93268	+	7.78793i	0.147799	+	0.292688i
$709$			36.2843i			1.36268i	0.731965	+	0.681342i	$0.238603\pi$
$709$			36.2843i			1.36268i	−0.731965	+	0.681342i	$0.761397\pi$
$710$	4.59704	+	22.0526i	0.172524	+	0.827621i
$711$	−29.3585	+	39.7990i	−1.10103	+	1.49258i
$712$	−13.1626	+	5.45214i	−0.493290	+	0.204328i
$713$	−3.06147			−0.114653
$714$	−19.4273	+	22.5804i	−0.727050	+	0.845048i
$715$	−21.6569	+	14.7595i	−0.809920	+	0.551975i
$716$	−13.6360	+	13.6360i	−0.509602	+	0.509602i
$717$	−12.0335	+	36.5838i	−0.449398	+	1.36625i
$718$	12.0335	+	4.98442i	0.449085	+	0.186017i
$719$	−2.95068			−0.110042			−0.0550208	−	0.998485i	$-0.517523\pi$
$719$	−2.95068			−0.110042			−0.0550208	+	0.998485i	$0.517523\pi$
$720$	26.8141	+	1.00195i	0.999303	+	0.0373403i
$721$	−19.7990			−0.737353
$722$	23.9280	+	9.91131i	0.890508	+	0.368861i
$723$	−3.50981	+	10.6704i	−0.130531	+	0.396837i
$724$	14.6274	−	14.6274i	0.543624	−	0.543624i
$725$	11.1175	−	28.2960i	0.412892	−	1.05089i
$726$	−7.43957	+	8.64700i	−0.276108	+	0.320920i
$727$	47.1015			1.74690			0.873449	−	0.486915i	$-0.161878\pi$
$727$	47.1015			1.74690			0.873449	+	0.486915i	$0.161878\pi$
$728$	16.5754	+	40.0166i	0.614327	+	1.48312i
$729$	8.89949	−	25.4912i	0.329611	−	0.944117i
$730$	−20.3740	+	4.24711i	−0.754075	+	0.157193i
$731$		−	22.2349i		−	0.822388i
$732$	13.2496	+	26.2383i	0.489719	+	0.969795i
$733$	−9.63811			−0.355992			−0.177996	−	0.984031i	$-0.556961\pi$
$733$	−9.63811			−0.355992			−0.177996	+	0.984031i	$0.556961\pi$
$734$	2.82411	+	1.16979i	0.104240	+	0.0431776i
$735$	14.2482	−	4.10381i	0.525553	−	0.151371i
$736$	13.6569	+	5.65685i	0.503398	+	0.208514i
$737$	8.28772			0.305282
$738$	−31.2433	+	18.8360i	−1.15008	+	0.693362i
$739$	−27.1716			−0.999522			−0.499761	−	0.866163i	$-0.666579\pi$
$739$	−27.1716			−0.999522			−0.499761	+	0.866163i	$0.666579\pi$
$740$	1.60423	−	8.47001i	0.0589728	−	0.311364i
$741$	−2.08644	+	6.34315i	−0.0766474	+	0.233021i
$742$	8.17821	−	19.7439i	0.300232	−	0.724823i
$743$		−	15.2304i		−	0.558750i	−0.960182	−	0.279375i	$-0.909873\pi$
$743$		−	15.2304i		−	0.558750i	0.960182	−	0.279375i	$-0.0901272\pi$
$744$	−0.429589	−	5.72341i	−0.0157495	−	0.209830i
$745$	18.4853	+	27.1237i	0.677248	+	0.993736i
$746$	−31.8771	−	13.2039i	−1.16710	−	0.483429i
$747$	22.6215	+	16.6871i	0.827676	+	0.610551i
$748$	13.1626	−	13.1626i	0.481273	−	0.481273i
$749$	27.8832			1.01883
$750$	12.8073	−	24.2069i	0.467655	−	0.883911i
$751$		−	35.1127i		−	1.28128i	−0.767841	−	0.640640i	$-0.778669\pi$
$751$		−	35.1127i		−	1.28128i	0.767841	−	0.640640i	$-0.221331\pi$
$752$	10.4525			0.381164
$753$	19.2974	+	6.34746i	0.703235	+	0.231314i
$754$	−36.9706	−	15.3137i	−1.34639	−	0.557692i
$755$	5.22625	−	3.56178i	0.190203	−	0.129627i
$756$	−33.7164	−	5.71637i	−1.22625	−	0.207902i
$757$	−12.8319			−0.466383			−0.233192	−	0.972431i	$-0.574917\pi$
$757$	−12.8319			−0.466383			−0.233192	+	0.972431i	$0.574917\pi$
$758$	−27.2137	−	11.2723i	−0.988444	−	0.409427i
$759$	3.56178	−	10.8284i	0.129284	−	0.393047i
$760$	2.87082	−	4.38292i	0.104136	−	0.158985i
$761$			17.1978i			0.623420i	0.950177	+	0.311710i	$0.100902\pi$
$761$			17.1978i			0.623420i	−0.950177	+	0.311710i	$0.899098\pi$
$762$	5.25700	−	6.11020i	0.190441	−	0.221349i
$763$		−	1.59689i		−	0.0578115i
$764$	−7.12356	−	7.12356i	−0.257722	−	0.257722i
$765$	0.925677	−	24.7730i	0.0334679	−	0.895670i
$766$	15.7574	−	38.0416i	0.569337	−	1.37450i
$767$		−	11.7206i		−	0.423207i
$768$	−8.65914	+	26.3253i	−0.312460	+	0.949931i
$769$	−49.5980			−1.78855			−0.894274	−	0.447519i	$-0.852308\pi$
$769$	−49.5980			−1.78855			−0.894274	+	0.447519i	$0.852308\pi$
$770$	−25.6566	+	5.34830i	−0.924598	+	0.192739i
$771$	−8.82843	+	26.8399i	−0.317948	+	0.966616i
$772$	−27.9222	+	27.9222i	−1.00494	+	1.00494i
$773$			18.8490i			0.677952i	0.940795	+	0.338976i	$0.110081\pi$
$773$			18.8490i			0.677952i	−0.940795	+	0.338976i	$0.889919\pi$
$774$	21.8612	−	13.1797i	0.785786	−	0.473735i
$775$	−5.45214	−	2.14214i	−0.195847	−	0.0769478i
$776$	7.12356	−	2.95068i	0.255721	−	0.105923i
$777$	−3.43289	+	10.4366i	−0.123154	+	0.374410i
$778$	9.87197	+	4.08910i	0.353927	+	0.146602i
$779$			7.12356i			0.255228i
$780$	−31.5483	−	17.4389i	−1.12961	−	0.624413i
$781$			17.9411i			0.641984i
$782$	5.22625	−	12.6173i	0.186890	−	0.451193i
$783$	25.7607	−	18.2919i	0.920611	−	0.653699i
$784$			15.3137i			0.546918i
$785$	7.28225	+	10.6853i	0.259915	+	0.381376i
$786$	40.4842	+	34.8311i	1.44402	+	1.24239i
$787$		−	48.2307i		−	1.71924i	−0.510935	−	0.859619i	$-0.670701\pi$
$787$		−	48.2307i		−	1.71924i	0.510935	−	0.859619i	$-0.329299\pi$
$788$	−16.9469	+	16.9469i	−0.603707	+	0.603707i
$789$	−36.6086	−	12.0416i	−1.30330	−	0.428693i
$790$	−51.0340	+	10.6384i	−1.81571	+	0.378498i
$791$	29.3585			1.04387
$792$	20.7435	+	5.13929i	0.737089	+	0.182617i
$793$		−	39.4879i		−	1.40226i
$794$	−35.4388	−	14.6792i	−1.25768	−	0.520947i
$795$	4.92252	+	17.0907i	0.174584	+	0.606146i
$796$	−12.9706	+	12.9706i	−0.459729	+	0.459729i
$797$			8.92177i			0.316025i	0.987437	+	0.158013i	$0.0505087\pi$
$797$			8.92177i			0.316025i	−0.987437	+	0.158013i	$0.949491\pi$
$798$	−4.35504	+	5.06186i	−0.154167	+	0.179188i
$799$		−	9.65685i		−	0.341635i
$800$	20.3632	+	19.6301i	0.719949	+	0.694027i
$801$	−8.97056	+	12.1607i	−0.316959	+	0.429677i
$802$	−8.17821	+	19.7439i	−0.288783	+	0.697183i
$803$	−16.5754			−0.584935
$804$	5.13829	+	10.1754i	0.181214	+	0.358859i
$805$	−15.8887	+	10.8284i	−0.560003	+	0.381652i
$806$	−2.95068	+	7.12356i	−0.103933	+	0.250917i
$807$	−5.21828	+	15.8645i	−0.183692	+	0.558456i
$808$	−14.2918	−	34.5035i	−0.502784	−	1.21383i
$809$		−	4.17289i		−	0.146711i	−0.997306	−	0.0733555i	$-0.976629\pi$
$809$		−	4.17289i		−	0.146711i	0.997306	−	0.0733555i	$-0.0233708\pi$
$810$	24.9053	−	13.7740i	0.875085	−	0.483970i
$811$	−14.4853			−0.508647			−0.254324	−	0.967119i	$-0.581853\pi$
$811$	−14.4853			−0.508647			−0.254324	+	0.967119i	$0.581853\pi$
$812$	−28.2960	−	28.2960i	−0.992996	−	0.992996i
$813$	23.2685	+	7.65367i	0.816061	+	0.268426i
$814$	2.62742	−	6.34315i	0.0920909	−	0.222327i
$815$	−11.1175	+	7.57675i	−0.389428	+	0.265402i
$816$	24.3214	+	8.00000i	0.851418	+	0.280056i
$817$		−	4.98442i		−	0.174383i
$818$	16.7611	+	6.94269i	0.586040	+	0.242746i
$819$	36.9706	+	27.2720i	1.29186	+	0.952962i
$820$	−37.7837	−	7.15631i	−1.31946	−	0.249909i
$821$	−23.8893			−0.833741			−0.416870	−	0.908966i	$-0.636873\pi$
$821$	−23.8893			−0.833741			−0.416870	+	0.908966i	$0.636873\pi$
$822$	19.1438	−	22.2509i	0.667718	−	0.776088i
$823$	23.5023			0.819239			0.409620	−	0.912256i	$-0.365661\pi$
$823$	23.5023			0.819239			0.409620	+	0.912256i	$0.365661\pi$
$824$	6.51246	+	15.7225i	0.226872	+	0.547718i
$825$	13.9199	−	16.7920i	0.484628	−	0.584624i
$826$	4.48528	−	10.8284i	0.156063	−	0.376769i
$827$	−35.5014			−1.23450			−0.617252	−	0.786766i	$-0.711754\pi$
$827$	−35.5014			−1.23450			−0.617252	+	0.786766i	$0.711754\pi$
$828$	15.5031	−	2.34045i	0.538769	−	0.0813364i
$829$			5.17157i			0.179616i	0.995959	+	0.0898081i	$0.0286254\pi$
$829$			5.17157i			0.179616i	−0.995959	+	0.0898081i	$0.971375\pi$
$830$	6.04680	+	29.0073i	0.209888	+	1.00686i
$831$	−8.16679	+	24.8284i	−0.283303	+	0.861289i
$832$	26.3253	−	26.3253i	0.912664	−	0.912664i
$833$	14.1480			0.490200
$834$	−23.1410	+	26.8967i	−0.801307	+	0.931358i
$835$	32.1421	−	21.9054i	1.11232	−	0.758069i
$836$	2.95068	−	2.95068i	0.102051	−	0.102051i
$837$	−3.52452	−	4.96362i	−0.121825	−	0.171568i
$838$	−1.36303	+	3.29066i	−0.0470853	+	0.113674i
$839$	−53.6799			−1.85323			−0.926617	−	0.376006i	$-0.877297\pi$
$839$	−53.6799			−1.85323			−0.926617	+	0.376006i	$0.877297\pi$
$840$	−22.4733	−	28.1845i	−0.775401	−	0.972456i
$841$	7.97056			0.274847
$842$	18.8490	−	45.5055i	0.649580	−	1.56822i
$843$	−5.86030	−	1.92762i	−0.201840	−	0.0663908i
$844$	26.1421	+	26.1421i	0.899849	+	0.899849i
$845$	10.9014	+	15.9958i	0.375020	+	0.550272i
$846$	9.49456	−	5.72408i	0.326430	−	0.196798i
$847$	15.3241			0.526543
$848$	−18.3688			−0.630787
$849$	29.6985	+	9.76869i	1.01925	+	0.335261i
$850$	18.1358	−	18.8132i	0.622053	−	0.645286i
$851$		−	5.03712i		−	0.172670i
$852$	−22.0276	+	11.1233i	−0.754652	+	0.381078i
$853$	−36.4311			−1.24738			−0.623688	−	0.781673i	$-0.714367\pi$
$853$	−36.4311			−1.24738			−0.623688	+	0.781673i	$0.714367\pi$
$854$	15.1114	−	36.4821i	0.517100	−	1.24839i
$855$	0.207510	−	5.55338i	0.00709668	−	0.189922i
$856$	−9.17157	−	22.1421i	−0.313478	−	0.756803i
$857$	−28.5587			−0.975546			−0.487773	−	0.872971i	$-0.662191\pi$
$857$	−28.5587			−0.975546			−0.487773	+	0.872971i	$0.662191\pi$
$858$	−21.7632	−	18.7243i	−0.742983	−	0.639236i
$859$	3.85786			0.131629			0.0658143	−	0.997832i	$-0.479035\pi$
$859$	3.85786			0.131629			0.0658143	+	0.997832i	$0.479035\pi$
$860$	26.4376	+	5.00733i	0.901515	+	0.170749i
$861$	46.5563	+	15.3137i	1.58663	+	0.521890i
$862$	35.6326	+	14.7595i	1.21365	+	0.502711i
$863$			20.0852i			0.683710i	0.939753	+	0.341855i	$0.111055\pi$
$863$			20.0852i			0.683710i	−0.939753	+	0.341855i	$0.888945\pi$
$864$	6.55089	+	28.6546i	0.222866	+	0.974849i
$865$	39.7990	−	27.1237i	1.35321	−	0.922234i
$866$	12.7718	−	30.8338i	0.434003	−	1.04778i
$867$	−1.80930	+	5.50057i	−0.0614470	+	0.186809i
$868$	−5.45214	+	5.45214i	−0.185058	+	0.185058i
$869$	−41.5192			−1.40844
$870$	33.0938	+	3.73102i	1.12198	+	0.126493i
$871$		−	15.3137i		−	0.518885i
$872$	−1.26810	+	0.525265i	−0.0429433	+	0.0177877i
$873$	4.85483	−	6.58132i	0.164311	−	0.222744i
$874$	1.17157	−	2.82843i	0.0396290	−	0.0956730i
$875$	−35.8728	+	8.16679i	−1.21272	+	0.276088i
$876$	−10.2766	−	20.3508i	−0.347214	−	0.687591i
$877$	35.3019			1.19206			0.596031	−	0.802962i	$-0.296744\pi$
$877$	35.3019			1.19206			0.596031	+	0.802962i	$0.296744\pi$
$878$	−15.4161	+	37.2178i	−0.520269	+	1.25604i
$879$	3.99390	+	1.31371i	0.134711	+	0.0443103i
$880$	12.6863	+	18.6148i	0.427655	+	0.627504i
$881$			42.9945i			1.44852i	0.689526	+	0.724261i	$0.257819\pi$
$881$			42.9945i			1.44852i	−0.689526	+	0.724261i	$0.742181\pi$
$882$	8.38621	+	13.9102i	0.282378	+	0.468382i
$883$			37.7941i			1.27187i	0.771741	+	0.635937i	$0.219386\pi$
$883$			37.7941i			1.27187i	−0.771741	+	0.635937i	$0.780614\pi$
$884$	−24.3214	−	24.3214i	−0.818016	−	0.818016i
$885$	2.69972	+	9.37330i	0.0907501	+	0.315080i
$886$	2.10051	+	0.870058i	0.0705678	+	0.0292302i
$887$		−	12.5404i		−	0.421064i	−0.977587	−	0.210532i	$-0.932480\pi$
$887$		−	12.5404i		−	0.421064i	0.977587	−	0.210532i	$-0.0675197\pi$
$888$	9.41689	−	0.706816i	0.316010	−	0.0237192i
$889$	−10.8284			−0.363174
$890$	−15.5936	+	3.25060i	−0.522698	+	0.108960i
$891$	21.6569	−	6.69145i	0.725532	−	0.224172i
$892$	30.9790	+	30.9790i	1.03725	+	1.03725i
$893$		−	2.16478i		−	0.0724417i
$894$	−23.4509	+	27.2569i	−0.784314	+	0.911607i
$895$	−17.8163	+	12.1421i	−0.595534	+	0.405867i
$896$	34.3956	−	14.2471i	1.14908	−	0.475963i
$897$	−20.0083	−	6.58132i	−0.668059	−	0.219744i
$898$	18.9455	−	45.7385i	0.632219	−	1.52631i
$899$		−	7.12356i		−	0.237584i
$900$	29.2469	+	6.67955i	0.974898	+	0.222652i
$901$			16.9706i			0.565371i
$902$	−28.2960	−	11.7206i	−0.942155	−	0.390253i
$903$	−32.5758	−	10.7151i	−1.08406	−	0.356577i
$904$	−9.65685	−	23.3137i	−0.321182	−	0.775402i
$905$	19.1116	−	13.0249i	0.635292	−	0.432963i
$906$	5.25192	+	4.51856i	0.174483	+	0.150119i
$907$		−	7.61362i		−	0.252806i	−0.991979	−	0.126403i	$-0.959657\pi$
$907$		−	7.61362i		−	0.252806i	0.991979	−	0.126403i	$-0.0403433\pi$
$908$	5.86030	+	5.86030i	0.194481	+	0.194481i
$909$	−31.8771	−	23.5147i	−1.05730	−	0.779934i
$910$	9.88238	+	47.4071i	0.327598	+	1.57153i
$911$	2.95068			0.0977603			0.0488801	−	0.998805i	$-0.484435\pi$
$911$	2.95068			0.0977603			0.0488801	+	0.998805i	$0.484435\pi$
$912$	5.45214	+	1.79337i	0.180538	+	0.0593843i
$913$			23.5992i			0.781019i
$914$	10.0742	−	24.3214i	0.333226	−	0.804479i
$915$	9.09563	+	31.5796i	0.300692	+	1.04399i
$916$	27.3137	−	27.3137i	0.902470	−	0.902470i
$917$		−	71.7456i		−	2.36925i
$918$	26.4734	−	6.05224i	0.873752	−	0.199754i
$919$			6.14214i			0.202610i	0.994855	+	0.101305i	$0.0323019\pi$
$919$			6.14214i			0.202610i	−0.994855	+	0.101305i	$0.967698\pi$
$920$	13.8252	+	9.05551i	0.455802	+	0.298551i
$921$	−11.7574	−	3.86733i	−0.387418	−	0.127433i
$922$	−5.21828	−	2.16148i	−0.171855	−	0.0711846i
$923$	33.1509			1.09117
$924$	−12.9411	−	25.6274i	−0.425731	−	0.843079i
$925$	3.52452	−	8.97056i	0.115885	−	0.294950i
$926$	33.6579	+	13.9416i	1.10607	+	0.458149i
$927$	14.5257	+	10.7151i	0.477085	+	0.351931i
$928$	−13.1626	+	31.7774i	−0.432085	+	1.04314i
$929$		−	26.6609i		−	0.874717i	−0.899287	−	0.437359i	$-0.855914\pi$
$929$		−	26.6609i		−	0.874717i	0.899287	−	0.437359i	$-0.144086\pi$
$930$	0.718900	−	6.37657i	0.0235737	−	0.209096i
$931$	3.17157			0.103944
$932$	22.5445	+	22.5445i	0.738471	+	0.738471i
$933$	18.6148	−	56.5921i	0.609420	−	1.85274i
$934$	20.7279	+	8.58579i	0.678238	+	0.280936i
$935$	17.1978	−	11.7206i	0.562428	−	0.383305i
$936$	9.49617	−	38.3291i	0.310392	−	1.25282i
$937$		−	8.17821i		−	0.267170i	−0.991037	−	0.133585i	$-0.957351\pi$
$937$		−	8.17821i		−	0.267170i	0.991037	−	0.133585i	$-0.0426490\pi$
$938$	5.86030	−	14.1480i	0.191346	−	0.461949i
$939$	−28.0000	−	9.21001i	−0.913745	−	0.300557i
$940$	11.4821	+	2.17473i	0.374505	+	0.0709320i
$941$	23.2781			0.758846			0.379423	−	0.925223i	$-0.376123\pi$
$941$	23.2781			0.758846			0.379423	+	0.925223i	$0.376123\pi$
$942$	−9.23843	+	10.7378i	−0.301004	+	0.349857i
$943$	−22.4700			−0.731724
$944$	−10.0742			−0.327889
$945$	−35.8482	−	13.2944i	−1.16614	−	0.432468i
$946$	19.7990	+	8.20101i	0.643721	+	0.266638i
$947$	21.6160			0.702425			0.351213	−	0.936296i	$-0.385769\pi$
$947$	21.6160			0.702425			0.351213	+	0.936296i	$0.385769\pi$
$948$	−25.7414	−	50.9760i	−0.836043	−	1.65562i
$949$			30.6274i			0.994208i
$950$	4.06552	−	4.21736i	0.131903	−	0.136829i
$951$	21.8028	+	7.17157i	0.707005	+	0.232554i
$952$	−13.1626	−	31.7774i	−0.426603	−	1.02991i
$953$	−44.0836			−1.42801			−0.714004	−	0.700142i	$-0.753120\pi$
$953$	−44.0836			−1.42801			−0.714004	+	0.700142i	$0.753120\pi$
$954$	−16.6853	+	10.0593i	−0.540208	+	0.325681i
$955$	−6.34315	−	9.30739i	−0.205259	−	0.301180i
$956$	−31.4449	−	31.4449i	−1.01700	−	1.01700i
$957$	25.1961	+	8.28772i	0.814474	+	0.267904i
$958$	−25.1961	−	10.4366i	−0.814049	−	0.337190i
$959$	−39.4327			−1.27335
$960$	−14.9893	+	27.1168i	−0.483778	+	0.875191i
$961$	29.6274			0.955723
$962$	−11.7206	−	4.85483i	−0.377887	−	0.156526i
$963$	−20.4567	−	15.0903i	−0.659207	−	0.486277i
$964$	−9.17157	−	9.17157i	−0.295396	−	0.295396i
$965$	−36.4821	+	24.8632i	−1.17440	+	0.800373i
$966$	−15.9667	−	13.7372i	−0.513721	−	0.441987i
$967$	−55.2797			−1.77768			−0.888838	−	0.458222i	$-0.848487\pi$
$967$	−55.2797			−1.77768			−0.888838	+	0.458222i	$0.848487\pi$
$968$	−5.04054	−	12.1689i	−0.162009	−	0.391125i
$969$	1.65685	−	5.03712i	0.0532258	−	0.161816i
$970$	8.43918	−	1.75921i	0.270966	−	0.0564849i
$971$		−	13.8150i		−	0.443345i	−0.975121	−	0.221672i	$-0.928848\pi$
$971$		−	13.8150i		−	0.443345i	0.975121	−	0.221672i	$-0.0711516\pi$
$972$	21.6426	+	22.4410i	0.694186	+	0.719796i
$973$	47.6661			1.52811
$974$	11.4230	+	4.73157i	0.366017	+	0.151609i
$975$	−31.0276	−	25.7206i	−0.993680	−	0.823719i
$976$	−33.9411			−1.08643
$977$	33.2597			1.06407			0.532035	−	0.846722i	$-0.321427\pi$
$977$	33.2597			1.06407			0.532035	+	0.846722i	$0.321427\pi$
$978$	−11.1721	−	9.61204i	−0.357243	−	0.307359i
$979$	−12.6863			−0.405456
$980$	−3.18615	+	16.8222i	−0.101778	+	0.537365i
$981$	−0.864233	+	1.17157i	−0.0275928	+	0.0374054i
$982$	19.9778	−	48.2307i	0.637517	−	1.53910i
$983$			10.0042i			0.319083i	0.987191	+	0.159542i	$0.0510016\pi$
$983$			10.0042i			0.319083i	−0.987191	+	0.159542i	$0.948998\pi$
$984$	−3.15302	−	42.0077i	−0.100515	−	1.33916i
$985$	−22.1421	+	15.0903i	−0.705507	+	0.480815i
$986$	29.3585	+	12.1607i	0.934965	+	0.387275i
$987$	−14.1480	−	4.65369i	−0.450336	−	0.148129i
$988$	−5.45214	−	5.45214i	−0.173456	−	0.173456i
$989$	15.7225			0.499945
$990$	21.7176	+	9.96140i	0.690230	+	0.316594i
$991$			19.7990i			0.628936i	0.949268	+	0.314468i	$0.101826\pi$
$991$			19.7990i			0.628936i	−0.949268	+	0.314468i	$0.898174\pi$
$992$	6.12293	+	2.53620i	0.194403	+	0.0805245i
$993$	−10.0042	+	30.4144i	−0.317472	+	0.965171i
$994$	30.6274	+	12.6863i	0.971443	+	0.402385i
$995$	−16.9469	+	11.5496i	−0.537251	+	0.366146i
$996$	−28.9744	+	14.6312i	−0.918088	+	0.463608i
$997$	8.50894			0.269481			0.134740	−	0.990881i	$-0.456980\pi$
$997$	8.50894			0.269481			0.134740	+	0.990881i	$0.456980\pi$
$998$	48.4901	+	20.0852i	1.53493	+	0.635787i
$999$	8.16679	−	5.79899i	0.258386	−	0.183472i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	120.2.m.b.59.1	✓	16
3.2	odd	2	inner	120.2.m.b.59.15	yes	16
4.3	odd	2		480.2.m.b.239.8		16
5.2	odd	4		600.2.b.i.251.9		16
5.3	odd	4		600.2.b.i.251.8		16
5.4	even	2	inner	120.2.m.b.59.16	yes	16
8.3	odd	2	inner	120.2.m.b.59.3	yes	16
8.5	even	2		480.2.m.b.239.7		16
12.11	even	2		480.2.m.b.239.11		16
15.2	even	4		600.2.b.i.251.7		16
15.8	even	4		600.2.b.i.251.10		16
15.14	odd	2	inner	120.2.m.b.59.2	yes	16
20.3	even	4		2400.2.b.i.2351.2		16
20.7	even	4		2400.2.b.i.2351.15		16
20.19	odd	2		480.2.m.b.239.10		16
24.5	odd	2		480.2.m.b.239.12		16
24.11	even	2	inner	120.2.m.b.59.13	yes	16
40.3	even	4		600.2.b.i.251.12		16
40.13	odd	4		2400.2.b.i.2351.1		16
40.19	odd	2	inner	120.2.m.b.59.14	yes	16
40.27	even	4		600.2.b.i.251.5		16
40.29	even	2		480.2.m.b.239.9		16
40.37	odd	4		2400.2.b.i.2351.16		16
60.23	odd	4		2400.2.b.i.2351.4		16
60.47	odd	4		2400.2.b.i.2351.13		16
60.59	even	2		480.2.m.b.239.5		16
120.29	odd	2		480.2.m.b.239.6		16
120.53	even	4		2400.2.b.i.2351.3		16
120.59	even	2	inner	120.2.m.b.59.4	yes	16
120.77	even	4		2400.2.b.i.2351.14		16
120.83	odd	4		600.2.b.i.251.6		16
120.107	odd	4		600.2.b.i.251.11		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.2.m.b.59.1	✓	16	1.1	even	1	trivial
120.2.m.b.59.2	yes	16	15.14	odd	2	inner
120.2.m.b.59.3	yes	16	8.3	odd	2	inner
120.2.m.b.59.4	yes	16	120.59	even	2	inner
120.2.m.b.59.13	yes	16	24.11	even	2	inner
120.2.m.b.59.14	yes	16	40.19	odd	2	inner
120.2.m.b.59.15	yes	16	3.2	odd	2	inner
120.2.m.b.59.16	yes	16	5.4	even	2	inner
480.2.m.b.239.5		16	60.59	even	2
480.2.m.b.239.6		16	120.29	odd	2
480.2.m.b.239.7		16	8.5	even	2
480.2.m.b.239.8		16	4.3	odd	2
480.2.m.b.239.9		16	40.29	even	2
480.2.m.b.239.10		16	20.19	odd	2
480.2.m.b.239.11		16	12.11	even	2
480.2.m.b.239.12		16	24.5	odd	2
600.2.b.i.251.5		16	40.27	even	4
600.2.b.i.251.6		16	120.83	odd	4
600.2.b.i.251.7		16	15.2	even	4
600.2.b.i.251.8		16	5.3	odd	4
600.2.b.i.251.9		16	5.2	odd	4
600.2.b.i.251.10		16	15.8	even	4
600.2.b.i.251.11		16	120.107	odd	4
600.2.b.i.251.12		16	40.3	even	4
2400.2.b.i.2351.1		16	40.13	odd	4
2400.2.b.i.2351.2		16	20.3	even	4
2400.2.b.i.2351.3		16	120.53	even	4
2400.2.b.i.2351.4		16	60.23	odd	4
2400.2.b.i.2351.13		16	60.47	odd	4
2400.2.b.i.2351.14		16	120.77	even	4
2400.2.b.i.2351.15		16	20.7	even	4
2400.2.b.i.2351.16		16	40.37	odd	4

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:	\( N \)	\(=\)	\( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	120.m (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.30656 - 0.541196i) q^{2} +(0.541196 - 1.64533i) q^{3} +(1.41421 + 1.41421i) q^{4} +(1.25928 + 1.84776i) q^{5} +(-1.59755 + 1.85683i) q^{6} +3.29066 q^{7} +(-1.08239 - 2.61313i) q^{8} +(-2.41421 - 1.78089i) q^{9} +O(q^{10})\)	\(q+(-1.30656 - 0.541196i) q^{2} +(0.541196 - 1.64533i) q^{3} +(1.41421 + 1.41421i) q^{4} +(1.25928 + 1.84776i) q^{5} +(-1.59755 + 1.85683i) q^{6} +3.29066 q^{7} +(-1.08239 - 2.61313i) q^{8} +(-2.41421 - 1.78089i) q^{9} +(-0.645329 - 3.09573i) q^{10} -2.51856i q^{11} +(3.09221 - 1.56148i) q^{12} -4.65369 q^{13} +(-4.29945 - 1.78089i) q^{14} +(3.72169 - 1.07193i) q^{15} +4.00000i q^{16} +3.69552 q^{17} +(2.19051 + 3.63341i) q^{18} +0.828427 q^{19} +(-0.832235 + 4.39402i) q^{20} +(1.78089 - 5.41421i) q^{21} +(-1.36303 + 3.29066i) q^{22} +2.61313i q^{23} +(-4.88524 + 0.366677i) q^{24} +(-1.82843 + 4.65369i) q^{25} +(6.08034 + 2.51856i) q^{26} +(-4.23671 + 3.00836i) q^{27} +(4.65369 + 4.65369i) q^{28} -6.08034 q^{29} +(-5.44274 - 0.613620i) q^{30} +1.17157i q^{31} +(2.16478 - 5.22625i) q^{32} +(-4.14386 - 1.36303i) q^{33} +(-4.82843 - 2.00000i) q^{34} +(4.14386 + 6.08034i) q^{35} +(-0.895653 - 5.93277i) q^{36} -1.92762 q^{37} +(-1.08239 - 0.448342i) q^{38} +(-2.51856 + 7.65685i) q^{39} +(3.46539 - 5.29066i) q^{40} +8.59890i q^{41} +(-5.25700 + 6.11020i) q^{42} -6.01673i q^{43} +(3.56178 - 3.56178i) q^{44} +(0.250486 - 6.70353i) q^{45} +(1.41421 - 3.41421i) q^{46} -2.61313i q^{47} +(6.58132 + 2.16478i) q^{48} +3.82843 q^{49} +(4.90752 - 5.09080i) q^{50} +(2.00000 - 6.08034i) q^{51} +(-6.58132 - 6.58132i) q^{52} +4.59220i q^{53} +(7.16365 - 1.63772i) q^{54} +(4.65369 - 3.17157i) q^{55} +(-3.56178 - 8.59890i) q^{56} +(0.448342 - 1.36303i) q^{57} +(7.94435 + 3.29066i) q^{58} +2.51856i q^{59} +(6.77920 + 3.74732i) q^{60} +8.48528i q^{61} +(0.634051 - 1.53073i) q^{62} +(-7.94435 - 5.86030i) q^{63} +(-5.65685 + 5.65685i) q^{64} +(-5.86030 - 8.59890i) q^{65} +(4.67654 + 4.02353i) q^{66} +3.29066i q^{67} +(5.22625 + 5.22625i) q^{68} +(4.29945 + 1.41421i) q^{69} +(-2.12356 - 10.1870i) q^{70} -7.12356 q^{71} +(-2.04057 + 8.23627i) q^{72} -6.58132i q^{73} +(2.51856 + 1.04322i) q^{74} +(6.66732 + 5.52692i) q^{75} +(1.17157 + 1.17157i) q^{76} -8.28772i q^{77} +(7.43452 - 8.64113i) q^{78} -16.4853i q^{79} +(-7.39104 + 5.03712i) q^{80} +(2.65685 + 8.59890i) q^{81} +(4.65369 - 11.2350i) q^{82} -9.37011 q^{83} +(10.1754 - 5.13829i) q^{84} +(4.65369 + 6.82843i) q^{85} +(-3.25623 + 7.86123i) q^{86} +(-3.29066 + 10.0042i) q^{87} +(-6.58132 + 2.72607i) q^{88} -5.03712i q^{89} +(-3.95520 + 8.62302i) q^{90} -15.3137 q^{91} +(-3.69552 + 3.69552i) q^{92} +(1.92762 + 0.634051i) q^{93} +(-1.41421 + 3.41421i) q^{94} +(1.04322 + 1.53073i) q^{95} +(-7.42733 - 6.39021i) q^{96} +2.72607i q^{97} +(-5.00208 - 2.07193i) q^{98} +(-4.48528 + 6.08034i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{9}+O(q^{10}) \) 16 * q - 16 * q^9	\( 16 q - 16 q^{9} + 16 q^{10} - 32 q^{19} - 32 q^{24} + 16 q^{25} + 16 q^{30} - 32 q^{34} - 32 q^{36} + 32 q^{40} + 16 q^{49} + 32 q^{51} + 32 q^{54} + 64 q^{66} - 64 q^{70} + 32 q^{75} + 64 q^{76} - 48 q^{81} + 32 q^{84} - 16 q^{90} - 64 q^{91} + 64 q^{96} + 64 q^{99}+O(q^{100}) \) 16 * q - 16 * q^9 + 16 * q^10 - 32 * q^19 - 32 * q^24 + 16 * q^25 + 16 * q^30 - 32 * q^34 - 32 * q^36 + 32 * q^40 + 16 * q^49 + 32 * q^51 + 32 * q^54 + 64 * q^66 - 64 * q^70 + 32 * q^75 + 64 * q^76 - 48 * q^81 + 32 * q^84 - 16 * q^90 - 64 * q^91 + 64 * q^96 + 64 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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