LMFDB - Embedded newform 120.2.m.b.59.13

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			59.13
Root			$-0.357857i$ of defining polynomial
Character	$\chi$	$=$	120.59
Dual form			120.2.m.b.59.16

$q$-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} +(2.64533 + 1.73270i) q^{10} +2.51856i q^{11} +(-3.09221 - 1.56148i) q^{12} +4.65369 q^{13} +(-4.29945 + 1.78089i) q^{14} +(2.35865 - 3.07193i) q^{15} -4.00000i q^{16} -3.69552 q^{17} +(-2.19051 + 3.63341i) q^{18} +0.828427 q^{19} +(4.39402 + 0.832235i) 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} +(1.41921 - 5.29016i) 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} +(6.19146 - 1.29066i) q^{40} -8.59890i q^{41} +(5.25700 + 6.11020i) q^{42} -6.01673i q^{43} +(3.56178 + 3.56178i) q^{44} +(-6.33083 - 2.21824i) q^{45} +(1.41421 + 3.41421i) q^{46} -2.61313i q^{47} +(-6.58132 + 2.16478i) q^{48} +3.82843 q^{49} +(0.129605 + 7.06988i) 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} +(-1.00872 - 7.68000i) 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} +(-8.70487 - 5.70171i) q^{70} -7.12356 q^{71} +(2.04057 + 8.23627i) q^{72} -6.58132i q^{73} +(2.51856 - 1.04322i) q^{74} +(8.64639 + 0.489804i) 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} +(-9.47213 + 0.527944i) 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	$-0.713629\pi$
$7$	−3.29066			−1.24375			−0.621876	+	0.783116i	$0.713629\pi$
$8$	1.08239	−	2.61313i	0.382683	−	0.923880i
$9$	−2.41421	+	1.78089i	−0.804738	+	0.593630i
$10$	2.64533	+	1.73270i	0.836526	+	0.547927i
$11$			2.51856i			0.759374i	0.925115	+	0.379687i	$0.123968\pi$
$11$			2.51856i			0.759374i	−0.925115	+	0.379687i	$0.876032\pi$
$12$	−3.09221	−	1.56148i	−0.892645	−	0.450760i
$13$	4.65369			1.29070			0.645351	−	0.763886i	$-0.276711\pi$
$13$	4.65369			1.29070			0.645351	+	0.763886i	$0.276711\pi$
$14$	−4.29945	+	1.78089i	−1.14908	+	0.475963i
$15$	2.35865	−	3.07193i	0.609002	−	0.793169i
$16$		−	4.00000i		−	1.00000i
$17$	−3.69552			−0.896295			−0.448147	−	0.893960i	$-0.647916\pi$
$17$	−3.69552			−0.896295			−0.448147	+	0.893960i	$0.647916\pi$
$18$	−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	$0.469706\pi$
$20$	4.39402	+	0.832235i	0.982532	+	0.186093i
$21$	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	$0.690949\pi$
$30$	1.41921	−	5.29016i	0.259112	−	0.965847i
$31$		−	1.17157i		−	0.210421i	−0.994450	−	0.105210i	$-0.966448\pi$
$31$		−	1.17157i		−	0.210421i	0.994450	−	0.105210i	$-0.0335516\pi$
$32$	−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	$-0.449350\pi$
$37$	1.92762			0.316899			0.158450	+	0.987367i	$0.449350\pi$
$38$	1.08239	−	0.448342i	0.175587	−	0.0727306i
$39$	−2.51856	−	7.65685i	−0.403292	−	1.22608i
$40$	6.19146	−	1.29066i	0.978956	−	0.204071i
$41$		−	8.59890i		−	1.34292i	−0.741039	−	0.671461i	$-0.765667\pi$
$41$		−	8.59890i		−	1.34292i	0.741039	−	0.671461i	$-0.234333\pi$
$42$	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
$45$	−6.33083	−	2.21824i	−0.943744	−	0.330676i
$46$	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
$50$	0.129605	+	7.06988i	0.0183289	+	0.999832i
$51$	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	$-0.947578\pi$
$59$		−	2.51856i		−	0.327889i	0.986470	−	0.163944i	$-0.0524217\pi$
$60$	−1.00872	−	7.68000i	−0.130226	−	0.991484i
$61$		−	8.48528i		−	1.08643i	−0.839594	−	0.543214i	$-0.817207\pi$
$61$		−	8.48528i		−	1.08643i	0.839594	−	0.543214i	$-0.182793\pi$
$62$	−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
$70$	−8.70487	−	5.70171i	−1.04043	−	0.681485i
$71$	−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
$75$	8.64639	+	0.489804i	0.998399	+	0.0565576i
$76$	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	$0.377936\pi$
$79$			16.4853i			1.85474i	−0.374147	+	0.927370i	$0.622064\pi$
$80$	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	$-0.328070\pi$
$83$	9.37011			1.02850			0.514252	+	0.857639i	$0.328070\pi$
$84$	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	$0.0860214\pi$
$89$			5.03712i			0.533934i	−0.963706	+	0.266967i	$0.913979\pi$
$90$	−9.47213	+	0.527944i	−0.998450	+	0.0556502i
$91$	−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
$100$	3.99553	+	9.16710i	0.399553	+	0.916710i
$101$	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	$-0.404206\pi$
$103$	6.01673			0.592846			0.296423	+	0.955057i	$0.404206\pi$
$104$	5.03712	−	12.1607i	0.493930	−	1.19245i
$105$	−7.76152	+	10.1087i	−0.757447	+	0.986505i
$106$	2.48528	+	6.00000i	0.241392	+	0.582772i
$107$	−8.47343			−0.819157			−0.409579	−	0.912275i	$-0.634324\pi$
$107$	−8.47343			−0.819157			−0.409579	+	0.912275i	$0.634324\pi$
$108$	10.2461	−	1.73715i	0.985930	−	0.167157i
$109$			0.485281i			0.0464815i	0.999730	+	0.0232408i	$0.00739843\pi$
$109$			0.485281i			0.0464815i	−0.999730	+	0.0232408i	$0.992602\pi$
$110$	−4.36390	+	6.66242i	−0.416081	+	0.635237i
$111$	−1.04322	−	3.17157i	−0.0990182	−	0.301032i
$112$			13.1626i			1.24375i
$113$	−8.92177			−0.839290			−0.419645	−	0.907688i	$-0.637845\pi$
$113$	−8.92177			−0.839290			−0.419645	+	0.907688i	$0.637845\pi$
$114$	−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
$120$	−5.47435	−	9.48849i	−0.499738	−	0.866177i
$121$	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	$-0.453360\pi$
$127$	3.29066			0.291999			0.145999	+	0.989285i	$0.453360\pi$
$128$	−10.4525	−	4.32957i	−0.923880	−	0.382683i
$129$	−9.89949	+	3.25623i	−0.871602	+	0.286695i
$130$	12.3105	+	8.06343i	1.07971	+	0.707210i
$131$			21.8028i			1.90492i	0.304663	+	0.952460i	$0.401456\pi$
$131$			21.8028i			1.90492i	−0.304663	+	0.952460i	$0.598544\pi$
$132$	3.93268	−	7.78793i	0.342296	−	0.677852i
$133$	−2.72607			−0.236380
$134$	1.78089	+	4.29945i	0.153846	+	0.371416i
$135$	−0.223521	+	11.6168i	−0.0192377	+	0.999815i
$136$	−4.00000	+	9.65685i	−0.342997	+	0.828068i
$137$	11.9832			1.02380			0.511899	−	0.859046i	$-0.328942\pi$
$137$	11.9832			1.02380			0.511899	+	0.859046i	$0.328942\pi$
$138$	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	$0.289433\pi$
$140$	−14.4592	−	2.73860i	−1.22203	−	0.231454i
$141$	−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	$0.294656\pi$
$150$	11.5621	−	4.03943i	0.944044	−	0.329818i
$151$			2.82843i			0.230174i	0.993355	+	0.115087i	$0.0367147\pi$
$151$			2.82843i			0.230174i	−0.993355	+	0.115087i	$0.963285\pi$
$152$	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	$-0.574122\pi$
$157$	−5.78287			−0.461523			−0.230762	+	0.973010i	$0.574122\pi$
$158$	8.92177	+	21.5391i	0.709778	+	1.71356i
$159$	7.55568	−	2.48528i	0.599204	−	0.197096i
$160$	6.93078	−	10.5813i	0.547927	−	0.836526i
$161$		−	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
$165$	7.73684	+	5.94041i	0.602312	+	0.462460i
$166$	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
$170$	−9.77586	−	6.40321i	−0.749774	−	0.491104i
$171$	−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	$-0.882660\pi$
$179$		−	9.64212i		−	0.720686i	0.932820	−	0.360343i	$-0.117340\pi$
$180$	−12.0902	+	5.81607i	−0.901151	+	0.433504i
$181$			10.3431i			0.768800i	0.923167	+	0.384400i	$0.125592\pi$
$181$			10.3431i			0.768800i	−0.923167	+	0.384400i	$0.874408\pi$
$182$	−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
$190$	2.19146	+	1.43541i	0.158985	+	0.104136i
$191$	−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
$195$	10.9764	−	14.2958i	0.786040	−	1.02374i
$196$	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	$-0.894610\pi$
$199$		−	9.17157i		−	0.650156i	0.945687	−	0.325078i	$-0.105390\pi$
$200$	10.1816	+	9.81503i	0.719949	+	0.694027i
$201$	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
$210$	−4.67014	+	17.4081i	−0.322271	+	1.20127i
$211$	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
$220$	−2.09603	+	11.0666i	−0.141315	+	0.746110i
$221$	−17.1978			−1.15685
$222$	−3.07948	−	3.57927i	−0.206681	−	0.240225i
$223$	−21.9054			−1.46690			−0.733448	−	0.679746i	$-0.762090\pi$
$223$	−21.9054			−1.46690			−0.733448	+	0.679746i	$0.762090\pi$
$224$	7.12356	+	17.1978i	0.475963	+	1.14908i
$225$	−3.87351	−	14.4912i	−0.258234	−	0.966082i
$226$	−11.6569	+	4.82843i	−0.775402	+	0.321182i
$227$	−4.14386			−0.275038			−0.137519	−	0.990499i	$-0.543913\pi$
$227$	−4.14386			−0.275038			−0.137519	+	0.990499i	$0.543913\pi$
$228$	−2.56167	−	1.29357i	−0.169651	−	0.0856689i
$229$			19.3137i			1.27629i	0.769918	+	0.638143i	$0.220297\pi$
$229$			19.3137i			1.27629i	−0.769918	+	0.638143i	$0.779703\pi$
$230$	−4.52775	+	6.91258i	−0.298551	+	0.455802i
$231$	−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	$-0.674880\pi$
$233$	−15.9414			−1.04436			−0.522178	+	0.852837i	$0.674880\pi$
$234$	−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	$0.755459\pi$
$240$	−12.2877	−	9.43461i	−0.793169	−	0.609002i
$241$	−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
$250$	−12.9002	+	9.14244i	−0.815882	+	0.578219i
$251$		−	11.7286i		−	0.740301i	−0.928972	−	0.370150i	$-0.879306\pi$
$251$		−	11.7286i		−	0.740301i	0.928972	−	0.370150i	$-0.120694\pi$
$252$	2.94729	−	19.5227i	0.185662	−	1.22982i
$253$	−6.58132			−0.413764
$254$	4.29945	−	1.78089i	0.269772	−	0.111743i
$255$	−8.71645	+	11.3524i	−0.545845	+	0.710913i
$256$	−16.0000			−1.00000
$257$	16.3128			1.01756			0.508782	−	0.860895i	$-0.330096\pi$
$257$	16.3128			1.01756			0.508782	+	0.860895i	$0.330096\pi$
$258$	−11.1721	+	9.61204i	−0.695542	+	0.598419i
$259$	−6.34315			−0.394144
$260$	20.4484	+	3.87297i	1.26816	+	0.240191i
$261$	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	$0.594968\pi$
$270$	5.99492	+	15.2990i	0.364839	+	0.931070i
$271$		−	14.1421i		−	0.859074i	−0.903049	−	0.429537i	$-0.858677\pi$
$271$		−	14.1421i		−	0.859074i	0.903049	−	0.429537i	$-0.141323\pi$
$272$			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	$-0.350231\pi$
$277$	15.0903			0.906685			0.453343	+	0.891336i	$0.350231\pi$
$278$	18.9259	−	7.83938i	1.13510	−	0.470175i
$279$	2.08644	+	2.82843i	0.124912	+	0.169334i
$280$	−20.3740	+	4.24711i	−1.21758	+	0.253813i
$281$			3.56178i			0.212478i	0.994341	+	0.106239i	$0.0338809\pi$
$281$			3.56178i			0.212478i	−0.994341	+	0.106239i	$0.966119\pi$
$282$	−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
$285$	1.95397	−	2.54487i	0.115743	−	0.150745i
$286$	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
$290$	−16.0845	−	10.5354i	−0.944515	−	0.618659i
$291$	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
$300$	12.9205	−	11.5352i	0.745967	−	0.665983i
$301$			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
$310$	2.02998	−	3.09920i	0.115295	−	0.176022i
$311$	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
$315$	20.8326	+	7.29948i	1.17378	+	0.411279i
$316$	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
$320$	3.32894	−	17.5761i	0.186093	−	0.982532i
$321$	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
$330$	13.3236	+	3.57437i	0.733440	+	0.196763i
$331$	−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
$340$	−16.2382	−	3.07554i	−0.880638	−	0.166795i
$341$	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
$345$	8.02734	+	6.16346i	0.432177	+	0.331829i
$346$	−11.6569	−	28.1421i	−0.626676	−	1.51293i
$347$	0.185709			0.00996939			0.00498469	−	0.999988i	$-0.498413\pi$
$347$	0.185709			0.00996939			0.00498469	+	0.999988i	$0.498413\pi$
$348$	18.8017	+	9.49433i	1.00788	+	0.508949i
$349$			2.34315i			0.125426i	0.998032	+	0.0627129i	$0.0199752\pi$
$349$			2.34315i			0.125426i	−0.998032	+	0.0627129i	$0.980025\pi$
$350$	−0.426486	−	23.2646i	−0.0227966	−	1.24354i
$351$	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	$-0.830320\pi$
$353$	−32.3630			−1.72251			−0.861254	+	0.508175i	$0.830320\pi$
$354$	−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	$0.578146\pi$
$360$	−12.6490	+	14.1422i	−0.666660	+	0.745362i
$361$	−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	$-0.482033\pi$
$367$	2.16148			0.112828			0.0564142	+	0.998407i	$0.482033\pi$
$368$	10.4525			0.544874
$369$	15.3137	+	20.7596i	0.797200	+	1.08070i
$370$	5.09920	+	3.33998i	0.265095	+	0.173638i
$371$		−	15.1114i		−	0.784543i
$372$	−1.82939	+	3.62275i	−0.0948493	+	0.187831i
$373$	−24.3976			−1.26326			−0.631631	−	0.775269i	$-0.717614\pi$
$373$	−24.3976			−1.26326			−0.631631	+	0.775269i	$0.717614\pi$
$374$	−5.03712	−	12.1607i	−0.260463	−	0.628814i
$375$	9.98319	+	16.5932i	0.515530	+	0.856872i
$376$	−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	$0.320333\pi$
$380$	3.64012	+	0.689446i	0.186734	+	0.0353678i
$381$	−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	$0.561350\pi$
$390$	6.60458	−	24.6188i	0.334436	−	1.24662i
$391$		−	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	$-0.738303\pi$
$397$	−27.1237			−1.36130			−0.680650	+	0.732609i	$0.738303\pi$
$398$	−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	$0.123152\pi$
$401$			15.1114i			0.754625i	−0.926086	+	0.377313i	$0.876848\pi$
$402$	6.11020	−	5.25700i	0.304749	−	0.262195i
$403$		−	5.45214i		−	0.271590i
$404$	18.6731	−	18.6731i	0.929024	−	0.929024i
$405$	19.2344	−	5.91920i	0.955766	−	0.294127i
$406$	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	$0.602730\pi$
$410$	14.8993	−	22.7469i	0.735823	−	1.12339i
$411$	−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	$0.0195948\pi$
$419$			2.51856i			0.123040i	−0.998106	+	0.0615199i	$0.980405\pi$
$420$	3.31937	+	25.2723i	0.161969	+	1.23316i
$421$		−	34.8284i		−	1.69743i	−0.528848	−	0.848717i	$-0.677376\pi$
$421$		−	34.8284i		−	1.69743i	0.528848	−	0.848717i	$-0.322624\pi$
$422$	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
$430$	10.4252	−	15.9162i	0.502746	−	0.767548i
$431$	−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
$435$	−14.3414	+	18.6784i	−0.687619	+	0.895560i
$436$	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	$0.237918\pi$
$439$			28.4853i			1.35953i	−0.733431	+	0.679764i	$0.762082\pi$
$440$	3.25060	+	15.5936i	0.154966	+	0.743394i
$441$	−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	$-0.487840\pi$
$443$	1.60766			0.0763821			0.0381910	+	0.999270i	$0.487840\pi$
$444$	−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	$-0.690592\pi$
$449$		−	35.0067i		−	1.65207i	0.563620	−	0.826035i	$-0.309408\pi$
$450$	−12.9036	−	16.8374i	−0.608281	−	0.793722i
$451$	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
$460$	−2.17473	+	11.4821i	−0.101398	+	0.535357i
$461$	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	$-0.295724\pi$
$463$	25.7607			1.19720			0.598600	+	0.801048i	$0.295724\pi$
$464$			24.3214i			1.12909i
$465$	−3.59899	−	2.76333i	−0.166899	−	0.128147i
$466$	−20.8284	+	8.62742i	−0.964858	+	0.399657i
$467$	15.8645			0.734120			0.367060	−	0.930197i	$-0.380364\pi$
$467$	15.8645			0.734120			0.367060	+	0.930197i	$0.380364\pi$
$468$	−4.16810	+	27.6093i	−0.192670	+	1.27624i
$469$		−	10.8284i		−	0.500010i
$470$	4.52775	−	6.91258i	0.208850	−	0.318853i
$471$	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	$0.354780\pi$
$480$	−21.1607	−	5.67685i	−0.965847	−	0.259112i
$481$	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	$-0.436527\pi$
$487$	8.74280			0.396174			0.198087	+	0.980184i	$0.436527\pi$
$488$	−22.1731	−	9.18440i	−1.00373	−	0.415758i
$489$	9.89949	−	3.25623i	0.447671	−	0.147252i
$490$	10.1274	+	6.63350i	0.457511	+	0.299671i
$491$		−	36.9142i		−	1.66591i	−0.553338	−	0.832957i	$-0.686646\pi$
$491$		−	36.9142i		−	1.66591i	0.553338	−	0.832957i	$-0.313354\pi$
$492$	−13.4270	+	26.5896i	−0.605336	+	1.19875i
$493$	22.4700			1.01200
$494$	5.03712	−	2.08644i	0.226631	−	0.0938735i
$495$	5.58678	−	15.9446i	0.251107	−	0.716655i
$496$	−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	$0.812057\pi$
$500$	−11.9071	+	18.9267i	−0.532502	+	0.846429i
$501$	−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	$0.405471\pi$
$510$	−5.24473	+	19.5499i	−0.232240	+	0.865684i
$511$			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
$520$	28.8132	−	6.00632i	1.26354	−	0.263395i
$521$			34.3956i			1.50690i	0.657506	+	0.753450i	$0.271612\pi$
$521$			34.3956i			1.50690i	−0.657506	+	0.753450i	$0.728388\pi$
$522$	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
$525$	−28.4523	−	1.61178i	−1.24176	−	0.0703437i
$526$	−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
$530$	−7.95689	+	12.1479i	−0.345625	+	0.527670i
$531$	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
$540$	16.1125	+	16.7447i	0.693373	+	0.720579i
$541$		−	16.0000i		−	0.687894i	−0.938989	−	0.343947i	$-0.888236\pi$
$541$		−	16.0000i		−	0.687894i	0.938989	−	0.343947i	$-0.111764\pi$
$542$	−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
$550$	−17.8059	+	0.326418i	−0.759247	+	0.0139185i
$551$	−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
$555$	4.54659	−	5.92152i	0.192992	−	0.251355i
$556$	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	$-0.346655\pi$
$563$	21.9874			0.926658			0.463329	+	0.886186i	$0.346655\pi$
$564$	−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	$-0.893100\pi$
$569$		−	15.7225i		−	0.659120i	0.944135	−	0.329560i	$-0.106900\pi$
$570$	1.17571	−	4.38252i	0.0492453	−	0.183563i
$571$	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
$580$	−26.7171	−	5.06027i	−1.10937	−	0.210116i
$581$	−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
$585$	−29.4617	−	10.3230i	−1.21809	−	0.426805i
$586$	1.31371	+	3.17157i	0.0542688	+	0.131016i
$587$	−7.20533			−0.297396			−0.148698	−	0.988883i	$-0.547508\pi$
$587$	−7.20533			−0.297396			−0.148698	+	0.988883i	$0.547508\pi$
$588$	−11.8383	−	5.97801i	−0.488204	−	0.246529i
$589$		−	0.970563i		−	0.0399913i
$590$	4.36390	−	6.66242i	0.179659	−	0.274287i
$591$	19.7164	−	6.48528i	0.811023	−	0.266769i
$592$		−	7.71049i		−	0.316899i
$593$	−1.00547			−0.0412897			−0.0206448	−	0.999787i	$-0.506572\pi$
$593$	−1.00547			−0.0412897			−0.0206448	+	0.999787i	$0.506572\pi$
$594$	−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	$0.270532\pi$
$600$	10.6387	−	22.0640i	0.434323	−	0.900757i
$601$	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	$-0.531625\pi$
$607$	−4.88755			−0.198380			−0.0991898	+	0.995069i	$0.531625\pi$
$608$	−1.79337	−	4.32957i	−0.0727306	−	0.175587i
$609$	−10.8284	−	32.9203i	−0.438790	−	1.33400i
$610$	14.7024	−	22.4464i	0.595283	−	0.908827i
$611$		−	12.1607i		−	0.491969i
$612$	3.30990	−	21.9247i	0.133795	−	0.886252i
$613$	23.2685			0.939804			0.469902	−	0.882718i	$-0.344289\pi$
$613$	23.2685			0.939804			0.469902	+	0.882718i	$0.344289\pi$
$614$	−3.86733	−	9.33657i	−0.156073	−	0.376793i
$615$	−26.4152	−	20.2818i	−1.06516	−	0.817842i
$616$	−21.6569	−	8.97056i	−0.872580	−	0.361434i
$617$	8.55035			0.344224			0.172112	−	0.985077i	$-0.444941\pi$
$617$	8.55035			0.344224			0.172112	+	0.985077i	$0.444941\pi$
$618$	−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	$0.515905\pi$
$620$	0.975024	−	5.14791i	0.0391579	−	0.206745i
$621$	−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
$630$	31.1695	−	1.73728i	1.24182	−	0.0692150i
$631$		−	2.14214i		−	0.0852771i	−0.999091	−	0.0426385i	$-0.986424\pi$
$631$		−	2.14214i		−	0.0852771i	0.999091	−	0.0426385i	$-0.0135764\pi$
$632$	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
$640$	−5.16263	−	24.7658i	−0.204071	−	0.978956i
$641$			35.0067i			1.38268i	0.722529	+	0.691341i	$0.242980\pi$
$641$			35.0067i			1.38268i	−0.722529	+	0.691341i	$0.757020\pi$
$642$	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
$645$	−18.4830	−	14.1914i	−0.727766	−	0.558785i
$646$	−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
$650$	0.603142	+	32.9010i	0.0236572	+	1.29049i
$651$	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	$0.0922962\pi$
$659$			14.6792i			0.571822i	−0.958256	+	0.285911i	$0.907704\pi$
$660$	19.3426	−	2.54053i	0.752908	−	0.0988902i
$661$			44.7696i			1.74133i	0.491873	+	0.870667i	$0.336312\pi$
$661$			44.7696i			1.74133i	−0.491873	+	0.870667i	$0.663688\pi$
$662$	−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
$670$	−5.70171	+	8.70487i	−0.220276	+	0.336299i
$671$	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
$675$	−21.7465	+	14.2158i	−0.837024	+	0.547166i
$676$	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
$680$	−22.8807	+	4.76965i	−0.877433	+	0.182908i
$681$	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	$-0.407554\pi$
$683$	14.9678			0.572726			0.286363	+	0.958121i	$0.407554\pi$
$684$	−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
$690$	13.8239	+	3.70858i	0.526266	+	0.141183i
$691$	−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
$700$	−13.1479	−	30.1658i	−0.496945	−	1.14016i
$701$	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
$705$	−8.02734	−	6.16346i	−0.302327	−	0.232129i
$706$	−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	$-0.761397\pi$
$709$		−	36.2843i		−	1.36268i	0.731965	−	0.681342i	$-0.238603\pi$
$710$	−18.8442	−	12.3430i	−0.707209	−	0.463223i
$711$	−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	$0.517523\pi$
$720$	−8.87298	+	25.3233i	−0.330676	+	0.943744i
$721$	−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	$-0.838122\pi$
$727$	−47.1015			−1.74690			−0.873449	+	0.486915i	$0.838122\pi$
$728$	−16.5754	+	40.0166i	−0.614327	+	1.48312i
$729$	8.89949	+	25.4912i	0.329611	+	0.944117i
$730$	11.4034	−	17.4097i	0.422059	−	0.644363i
$731$			22.2349i			0.822388i
$732$	−13.2496	+	26.2383i	−0.489719	+	0.969795i
$733$	9.63811			0.355992			0.177996	−	0.984031i	$-0.443039\pi$
$733$	9.63811			0.355992			0.177996	+	0.984031i	$0.443039\pi$
$734$	2.82411	−	1.16979i	0.104240	−	0.0431776i
$735$	9.02993	−	11.7607i	0.333074	−	0.433798i
$736$	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	$0.666579\pi$
$740$	8.47001	+	1.60423i	0.311364	+	0.0589728i
$741$	−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
$750$	22.0239	+	16.2773i	0.804198	+	0.594362i
$751$			35.1127i			1.28128i	0.767841	+	0.640640i	$0.221331\pi$
$751$			35.1127i			1.28128i	−0.767841	+	0.640640i	$0.778669\pi$
$752$	−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	$-0.425083\pi$
$757$	12.8319			0.466383			0.233192	+	0.972431i	$0.425083\pi$
$758$	27.2137	−	11.2723i	0.988444	−	0.409427i
$759$	3.56178	+	10.8284i	0.129284	+	0.393047i
$760$	5.12918	−	1.06922i	0.186055	−	0.0387845i
$761$		−	17.1978i		−	0.623420i	−0.950177	−	0.311710i	$-0.899098\pi$
$761$		−	17.1978i		−	0.623420i	0.950177	−	0.311710i	$-0.100902\pi$
$762$	−5.25700	−	6.11020i	−0.190441	−	0.221349i
$763$		−	1.59689i		−	0.0578115i
$764$	−7.12356	+	7.12356i	−0.257722	+	0.257722i
$765$	23.3957	+	8.19756i	0.845873	+	0.296383i
$766$	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	$0.852308\pi$
$770$	14.3601	−	21.9237i	0.517502	−	0.790077i
$771$	−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
$780$	−4.69430	−	35.7404i	−0.168083	−	1.27971i
$781$		−	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
$790$	−28.5640	+	43.6090i	−1.01626	+	1.55154i
$791$	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
$795$	14.1069	+	10.8314i	0.500321	+	0.384151i
$796$	−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
$800$	28.2795	−	0.518420i	0.999832	−	0.0183289i
$801$	−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	$0.0233708\pi$
$809$			4.17289i			0.146711i	−0.997306	+	0.0733555i	$0.976629\pi$
$810$	21.9275	−	18.1434i	0.770455	−	0.637494i
$811$	−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
$820$	7.15631	−	37.7837i	0.249909	−	1.31946i
$821$	−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	$-0.634339\pi$
$823$	−23.5023			−0.819239			−0.409620	+	0.912256i	$0.634339\pi$
$824$	6.51246	−	15.7225i	0.226872	−	0.547718i
$825$	−1.23360	+	21.7765i	−0.0429484	+	0.758159i
$826$	4.48528	+	10.8284i	0.156063	+	0.376769i
$827$	35.5014			1.23450			0.617252	−	0.786766i	$-0.288246\pi$
$827$	35.5014			1.23450			0.617252	+	0.786766i	$0.288246\pi$
$828$	−15.5031	−	2.34045i	−0.538769	−	0.0813364i
$829$		−	5.17157i		−	0.179616i	−0.995959	−	0.0898081i	$-0.971375\pi$
$829$		−	5.17157i		−	0.179616i	0.995959	−	0.0898081i	$-0.0286254\pi$
$830$	24.7870	+	16.2356i	0.860370	+	0.563544i
$831$	−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	$0.877297\pi$
$840$	18.0142	+	31.2234i	0.621549	+	1.07731i
$841$	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
$850$	−0.478958	−	26.1269i	−0.0164281	−	0.896144i
$851$			5.03712i			0.172670i
$852$	22.0276	+	11.1233i	0.754652	+	0.381078i
$853$	36.4311			1.24738			0.623688	−	0.781673i	$-0.285633\pi$
$853$	36.4311			1.24738			0.623688	+	0.781673i	$0.285633\pi$
$854$	15.1114	+	36.4821i	0.517100	+	1.24839i
$855$	−5.24463	−	1.83765i	−0.179363	−	0.0628464i
$856$	−9.17157	+	22.1421i	−0.313478	+	0.756803i
$857$	28.5587			0.975546			0.487773	−	0.872971i	$-0.337809\pi$
$857$	28.5587			0.975546			0.487773	+	0.872971i	$0.337809\pi$
$858$	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	$0.479035\pi$
$860$	5.00733	−	26.4376i	0.170749	−	0.901515i
$861$	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
$870$	−8.62930	+	32.1660i	−0.292561	+	1.09053i
$871$			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	$-0.703256\pi$
$877$	−35.3019			−1.19206			−0.596031	+	0.802962i	$0.703256\pi$
$878$	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	$-0.742181\pi$
$881$		−	42.9945i		−	1.44852i	0.689526	−	0.724261i	$-0.257819\pi$
$882$	−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
$885$	−7.73684	−	5.94041i	−0.260071	−	0.199685i
$886$	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
$890$	−8.72780	+	13.3248i	−0.292556	+	0.446650i
$891$	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
$900$	−25.9717	−	15.0157i	−0.865722	−	0.500525i
$901$		−	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
$910$	−40.5098	−	26.5340i	−1.34289	−	0.879594i
$911$	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
$915$	−26.0662	−	20.0138i	−0.861722	−	0.661637i
$916$	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	$-0.967698\pi$
$919$		−	6.14214i		−	0.202610i	0.994855	−	0.101305i	$-0.0323019\pi$
$920$	3.37265	+	16.1791i	0.111193	+	0.533408i
$921$	−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	$0.144086\pi$
$929$			26.6609i			0.874717i	−0.899287	+	0.437359i	$0.855914\pi$
$930$	−6.19781	−	1.66271i	−0.203234	−	0.0545225i
$931$	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
$940$	2.17473	−	11.4821i	0.0709320	−	0.374505i
$941$	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
$945$	0.735532	−	38.2269i	0.0239269	−	1.24352i
$946$	19.7990	−	8.20101i	0.643721	−	0.266638i
$947$	−21.6160			−0.702425			−0.351213	−	0.936296i	$-0.614231\pi$
$947$	−21.6160			−0.702425			−0.351213	+	0.936296i	$0.614231\pi$
$948$	25.7414	−	50.9760i	0.836043	−	1.65562i
$949$		−	30.6274i		−	0.994208i
$950$	0.107368	+	5.85688i	0.00348349	+	0.190022i
$951$	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	$-0.246880\pi$
$953$	44.0836			1.42801			0.714004	+	0.700142i	$0.246880\pi$
$954$	−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
$960$	−30.7200	+	4.03490i	−0.991484	+	0.130226i
$961$	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	$-0.151513\pi$
$967$	55.2797			1.77768			0.888838	+	0.458222i	$0.151513\pi$
$968$	5.04054	−	12.1689i	0.162009	−	0.391125i
$969$	1.65685	+	5.03712i	0.0532258	+	0.161816i
$970$	−4.72345	+	7.21135i	−0.151661	+	0.231543i
$971$			13.8150i			0.443345i	0.975121	+	0.221672i	$0.0711516\pi$
$971$			13.8150i			0.443345i	−0.975121	+	0.221672i	$0.928848\pi$
$972$	−21.6426	+	22.4410i	−0.694186	+	0.719796i
$973$	−47.6661			−1.52811
$974$	11.4230	−	4.73157i	0.366017	−	0.151609i
$975$	40.2376	+	2.27939i	1.28864	+	0.0729991i
$976$	−33.9411			−1.08643
$977$	−33.2597			−1.06407			−0.532035	−	0.846722i	$-0.678573\pi$
$977$	−33.2597			−1.06407			−0.532035	+	0.846722i	$0.678573\pi$
$978$	11.1721	−	9.61204i	0.357243	−	0.307359i
$979$	−12.6863			−0.405456
$980$	16.8222	+	3.18615i	0.537365	+	0.101778i
$981$	−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
$990$	−1.32966	−	23.8561i	−0.0422593	−	0.758198i
$991$		−	19.7990i		−	0.628936i	−0.949268	−	0.314468i	$-0.898174\pi$
$991$		−	19.7990i		−	0.628936i	0.949268	−	0.314468i	$-0.101826\pi$
$992$	−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	$-0.543020\pi$
$997$	−8.50894			−0.269481			−0.134740	+	0.990881i	$0.543020\pi$
$998$	−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.59.13	yes	16
3.2	odd	2	inner	120.2.m.b.59.3	yes	16
4.3	odd	2		480.2.m.b.239.12		16
5.2	odd	4		600.2.b.i.251.11		16
5.3	odd	4		600.2.b.i.251.6		16
5.4	even	2	inner	120.2.m.b.59.4	yes	16
8.3	odd	2	inner	120.2.m.b.59.15	yes	16
8.5	even	2		480.2.m.b.239.11		16
12.11	even	2		480.2.m.b.239.7		16
15.2	even	4		600.2.b.i.251.5		16
15.8	even	4		600.2.b.i.251.12		16
15.14	odd	2	inner	120.2.m.b.59.14	yes	16
20.3	even	4		2400.2.b.i.2351.3		16
20.7	even	4		2400.2.b.i.2351.14		16
20.19	odd	2		480.2.m.b.239.6		16
24.5	odd	2		480.2.m.b.239.8		16
24.11	even	2	inner	120.2.m.b.59.1	✓	16
40.3	even	4		600.2.b.i.251.10		16
40.13	odd	4		2400.2.b.i.2351.4		16
40.19	odd	2	inner	120.2.m.b.59.2	yes	16
40.27	even	4		600.2.b.i.251.7		16
40.29	even	2		480.2.m.b.239.5		16
40.37	odd	4		2400.2.b.i.2351.13		16
60.23	odd	4		2400.2.b.i.2351.1		16
60.47	odd	4		2400.2.b.i.2351.16		16
60.59	even	2		480.2.m.b.239.9		16
120.29	odd	2		480.2.m.b.239.10		16
120.53	even	4		2400.2.b.i.2351.2		16
120.59	even	2	inner	120.2.m.b.59.16	yes	16
120.77	even	4		2400.2.b.i.2351.15		16
120.83	odd	4		600.2.b.i.251.8		16
120.107	odd	4		600.2.b.i.251.9		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.2.m.b.59.1	✓	16	24.11	even	2	inner
120.2.m.b.59.2	yes	16	40.19	odd	2	inner
120.2.m.b.59.3	yes	16	3.2	odd	2	inner
120.2.m.b.59.4	yes	16	5.4	even	2	inner
120.2.m.b.59.13	yes	16	1.1	even	1	trivial
120.2.m.b.59.14	yes	16	15.14	odd	2	inner
120.2.m.b.59.15	yes	16	8.3	odd	2	inner
120.2.m.b.59.16	yes	16	120.59	even	2	inner
480.2.m.b.239.5		16	40.29	even	2
480.2.m.b.239.6		16	20.19	odd	2
480.2.m.b.239.7		16	12.11	even	2
480.2.m.b.239.8		16	24.5	odd	2
480.2.m.b.239.9		16	60.59	even	2
480.2.m.b.239.10		16	120.29	odd	2
480.2.m.b.239.11		16	8.5	even	2
480.2.m.b.239.12		16	4.3	odd	2
600.2.b.i.251.5		16	15.2	even	4
600.2.b.i.251.6		16	5.3	odd	4
600.2.b.i.251.7		16	40.27	even	4
600.2.b.i.251.8		16	120.83	odd	4
600.2.b.i.251.9		16	120.107	odd	4
600.2.b.i.251.10		16	40.3	even	4
600.2.b.i.251.11		16	5.2	odd	4
600.2.b.i.251.12		16	15.8	even	4
2400.2.b.i.2351.1		16	60.23	odd	4
2400.2.b.i.2351.2		16	120.53	even	4
2400.2.b.i.2351.3		16	20.3	even	4
2400.2.b.i.2351.4		16	40.13	odd	4
2400.2.b.i.2351.13		16	40.37	odd	4
2400.2.b.i.2351.14		16	20.7	even	4
2400.2.b.i.2351.15		16	120.77	even	4
2400.2.b.i.2351.16		16	60.47	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} +(2.64533 + 1.73270i) q^{10} +2.51856i q^{11} +(-3.09221 - 1.56148i) q^{12} +4.65369 q^{13} +(-4.29945 + 1.78089i) q^{14} +(2.35865 - 3.07193i) q^{15} -4.00000i q^{16} -3.69552 q^{17} +(-2.19051 + 3.63341i) q^{18} +0.828427 q^{19} +(4.39402 + 0.832235i) 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} +(1.41921 - 5.29016i) 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} +(6.19146 - 1.29066i) q^{40} -8.59890i q^{41} +(5.25700 + 6.11020i) q^{42} -6.01673i q^{43} +(3.56178 + 3.56178i) q^{44} +(-6.33083 - 2.21824i) q^{45} +(1.41421 + 3.41421i) q^{46} -2.61313i q^{47} +(-6.58132 + 2.16478i) q^{48} +3.82843 q^{49} +(0.129605 + 7.06988i) 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} +(-1.00872 - 7.68000i) 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} +(-8.70487 - 5.70171i) q^{70} -7.12356 q^{71} +(2.04057 + 8.23627i) q^{72} -6.58132i q^{73} +(2.51856 - 1.04322i) q^{74} +(8.64639 + 0.489804i) 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} +(-9.47213 + 0.527944i) 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

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Database

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