LMFDB - Embedded newform 336.2.u.a.139.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,2,Mod(139,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0, 2]))

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

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

chi := DirichletCharacter("336.139");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	336.u (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.68297350792$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			139.10
Character	$\chi$	$=$	336.139
Dual form			336.2.u.a.307.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.777418 - 1.18136i) q^{2} +(0.707107 - 0.707107i) q^{3} +(-0.791242 + 1.83683i) q^{4} +(3.13913 - 3.13913i) q^{5} +(-1.38507 - 0.285633i) q^{6} +(1.14645 + 2.38446i) q^{7} +(2.78509 - 0.493238i) q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+(-0.777418 - 1.18136i) q^{2} +(0.707107 - 0.707107i) q^{3} +(-0.791242 + 1.83683i) q^{4} +(3.13913 - 3.13913i) q^{5} +(-1.38507 - 0.285633i) q^{6} +(1.14645 + 2.38446i) q^{7} +(2.78509 - 0.493238i) q^{8} -1.00000i q^{9} +(-6.14886 - 1.26804i) q^{10} +(0.422784 - 0.422784i) q^{11} +(0.739341 + 1.85833i) q^{12} +(3.06112 + 3.06112i) q^{13} +(1.92564 - 3.20810i) q^{14} -4.43939i q^{15} +(-2.74787 - 2.90675i) q^{16} +2.56875i q^{17} +(-1.18136 + 0.777418i) q^{18} +(-0.955253 + 0.955253i) q^{19} +(3.28222 + 8.24984i) q^{20} +(2.49673 + 0.875401i) q^{21} +(-0.828141 - 0.170782i) q^{22} -5.93702 q^{23} +(1.62058 - 2.31813i) q^{24} -14.7082i q^{25} +(1.23653 - 5.99607i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(-5.28696 + 0.219156i) q^{28} +(1.07143 - 1.07143i) q^{29} +(-5.24454 + 3.45127i) q^{30} -5.77245 q^{31} +(-1.29768 + 5.50600i) q^{32} -0.597907i q^{33} +(3.03462 - 1.99699i) q^{34} +(11.0840 + 3.88625i) q^{35} +(1.83683 + 0.791242i) q^{36} +(-3.30963 - 3.30963i) q^{37} +(1.87113 + 0.385870i) q^{38} +4.32908 q^{39} +(7.19440 - 10.2911i) q^{40} -6.17767 q^{41} +(-0.906838 - 3.63010i) q^{42} +(-3.35840 + 3.35840i) q^{43} +(0.442057 + 1.11111i) q^{44} +(-3.13913 - 3.13913i) q^{45} +(4.61554 + 7.01378i) q^{46} +4.38522 q^{47} +(-3.99842 - 0.112344i) q^{48} +(-4.37128 + 5.46735i) q^{49} +(-17.3758 + 11.4344i) q^{50} +(1.81638 + 1.81638i) q^{51} +(-8.04484 + 3.20066i) q^{52} +(-7.85667 - 7.85667i) q^{53} +(-0.285633 + 1.38507i) q^{54} -2.65434i q^{55} +(4.36908 + 6.07545i) q^{56} +1.35093i q^{57} +(-2.09869 - 0.432799i) q^{58} +(5.63360 + 5.63360i) q^{59} +(8.15440 + 3.51263i) q^{60} +(0.351526 + 0.351526i) q^{61} +(4.48761 + 6.81936i) q^{62} +(2.38446 - 1.14645i) q^{63} +(7.51343 - 2.74742i) q^{64} +19.2185 q^{65} +(-0.706345 + 0.464823i) q^{66} +(7.37756 + 7.37756i) q^{67} +(-4.71835 - 2.03250i) q^{68} +(-4.19810 + 4.19810i) q^{69} +(-4.02581 - 16.1155i) q^{70} -4.30558 q^{71} +(-0.493238 - 2.78509i) q^{72} +6.71670 q^{73} +(-1.33691 + 6.48284i) q^{74} +(-10.4003 - 10.4003i) q^{75} +(-0.998799 - 2.51047i) q^{76} +(1.49281 + 0.523408i) q^{77} +(-3.36550 - 5.11422i) q^{78} +8.39558i q^{79} +(-17.7506 - 0.498739i) q^{80} -1.00000 q^{81} +(4.80263 + 7.29807i) q^{82} +(-6.54381 + 6.54381i) q^{83} +(-3.58348 + 3.89341i) q^{84} +(8.06362 + 8.06362i) q^{85} +(6.57837 + 1.35661i) q^{86} -1.51523i q^{87} +(0.968957 - 1.38602i) q^{88} +14.8890 q^{89} +(-1.26804 + 6.14886i) q^{90} +(-3.78968 + 10.8086i) q^{91} +(4.69762 - 10.9053i) q^{92} +(-4.08174 + 4.08174i) q^{93} +(-3.40915 - 5.18054i) q^{94} +5.99732i q^{95} +(2.97573 + 4.81093i) q^{96} +3.86266i q^{97} +(9.85724 + 0.913663i) q^{98} +(-0.422784 - 0.422784i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 4 q^{4} + 24 q^{8}+O(q^{10}) $ 64 * q - 4 * q^4 + 24 * q^8	$ 64 q - 4 q^{4} + 24 q^{8} + 8 q^{11} - 16 q^{14} + 4 q^{16} - 4 q^{18} - 28 q^{22} - 16 q^{23} + 32 q^{28} + 16 q^{29} + 24 q^{35} + 16 q^{37} + 20 q^{42} - 8 q^{43} - 36 q^{44} - 40 q^{46} - 52 q^{50} + 16 q^{53} - 28 q^{56} - 92 q^{58} + 24 q^{60} - 52 q^{64} + 56 q^{67} - 40 q^{70} - 128 q^{71} + 4 q^{72} - 60 q^{74} - 64 q^{81} - 24 q^{84} + 92 q^{86} - 84 q^{88} + 8 q^{91} + 136 q^{92} - 64 q^{98} - 8 q^{99}+O(q^{100}) $ 64 * q - 4 * q^4 + 24 * q^8 + 8 * q^11 - 16 * q^14 + 4 * q^16 - 4 * q^18 - 28 * q^22 - 16 * q^23 + 32 * q^28 + 16 * q^29 + 24 * q^35 + 16 * q^37 + 20 * q^42 - 8 * q^43 - 36 * q^44 - 40 * q^46 - 52 * q^50 + 16 * q^53 - 28 * q^56 - 92 * q^58 + 24 * q^60 - 52 * q^64 + 56 * q^67 - 40 * q^70 - 128 * q^71 + 4 * q^72 - 60 * q^74 - 64 * q^81 - 24 * q^84 + 92 * q^86 - 84 * q^88 + 8 * q^91 + 136 * q^92 - 64 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$	$-1$

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 $

$2$	−0.777418	−	1.18136i	−0.549718	−	0.835351i
$2$	−0.777418	−	1.18136i	−0.549718	−	0.835351i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$	−0.791242	+	1.83683i	−0.395621	+	0.918414i
$5$	3.13913	−	3.13913i	1.40386	−	1.40386i	0.616521	−	0.787339i	$-0.288542\pi$
$5$	3.13913	−	3.13913i	1.40386	−	1.40386i	0.787339	−	0.616521i	$-0.211458\pi$
$6$	−1.38507	−	0.285633i	−0.565452	−	0.116609i
$7$	1.14645	+	2.38446i	0.433319	+	0.901241i
$7$	1.14645	+	2.38446i	0.433319	+	0.901241i
$8$	2.78509	−	0.493238i	0.984677	−	0.174386i
$9$		−	1.00000i		−	0.333333i
$10$	−6.14886	−	1.26804i	−1.94444	−	0.400988i
$11$	0.422784	−	0.422784i	0.127474	−	0.127474i	−0.640491	−	0.767965i	$-0.721269\pi$
$11$	0.422784	−	0.422784i	0.127474	−	0.127474i	0.767965	+	0.640491i	$0.221269\pi$
$12$	0.739341	+	1.85833i	0.213429	+	0.536452i
$13$	3.06112	+	3.06112i	0.849002	+	0.849002i	0.990009	−	0.141007i	$-0.0450339\pi$
$13$	3.06112	+	3.06112i	0.849002	+	0.849002i	−0.141007	+	0.990009i	$0.545034\pi$
$14$	1.92564	−	3.20810i	0.514649	−	0.857401i
$15$		−	4.43939i		−	1.14625i
$16$	−2.74787	−	2.90675i	−0.686968	−	0.726688i
$17$			2.56875i			0.623013i	0.950244	+	0.311506i	$0.100834\pi$
$17$			2.56875i			0.623013i	−0.950244	+	0.311506i	$0.899166\pi$
$18$	−1.18136	+	0.777418i	−0.278450	+	0.183239i
$19$	−0.955253	+	0.955253i	−0.219150	+	0.219150i	−0.808140	−	0.588990i	$-0.799526\pi$
$19$	−0.955253	+	0.955253i	−0.219150	+	0.219150i	0.588990	+	0.808140i	$0.299526\pi$
$20$	3.28222	+	8.24984i	0.733928	+	1.84472i
$21$	2.49673	+	0.875401i	0.544832	+	0.191028i
$22$	−0.828141	−	0.170782i	−0.176560	−	0.0364108i
$23$	−5.93702			−1.23795			−0.618977	−	0.785409i	$-0.712452\pi$
$23$	−5.93702			−1.23795			−0.618977	+	0.785409i	$0.712452\pi$
$24$	1.62058	−	2.31813i	0.330800	−	0.473186i
$25$		−	14.7082i		−	2.94164i
$26$	1.23653	−	5.99607i	0.242503	−	1.17593i
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	−5.28696	+	0.219156i	−0.999142	+	0.0414166i
$29$	1.07143	−	1.07143i	0.198959	−	0.198959i	−0.600595	−	0.799554i	$-0.705069\pi$
$29$	1.07143	−	1.07143i	0.198959	−	0.198959i	0.799554	+	0.600595i	$0.205069\pi$
$30$	−5.24454	+	3.45127i	−0.957518	+	0.630112i
$31$	−5.77245			−1.03676			−0.518381	−	0.855150i	$-0.673465\pi$
$31$	−5.77245			−1.03676			−0.518381	+	0.855150i	$0.673465\pi$
$32$	−1.29768	+	5.50600i	−0.229400	+	0.973332i
$33$		−	0.597907i		−	0.104082i
$34$	3.03462	−	1.99699i	0.520434	−	0.342481i
$35$	11.0840	+	3.88625i	1.87353	+	0.656896i
$36$	1.83683	+	0.791242i	0.306138	+	0.131874i
$37$	−3.30963	−	3.30963i	−0.544099	−	0.544099i	0.380629	−	0.924728i	$-0.375708\pi$
$37$	−3.30963	−	3.30963i	−0.544099	−	0.544099i	−0.924728	+	0.380629i	$0.875708\pi$
$38$	1.87113	+	0.385870i	0.303538	+	0.0625964i
$39$	4.32908			0.693207
$40$	7.19440	−	10.2911i	1.13754	−	1.62716i
$41$	−6.17767			−0.964790			−0.482395	−	0.875954i	$-0.660233\pi$
$41$	−6.17767			−0.964790			−0.482395	+	0.875954i	$0.660233\pi$
$42$	−0.906838	−	3.63010i	−0.139928	−	0.560137i
$43$	−3.35840	+	3.35840i	−0.512151	+	0.512151i	−0.915185	−	0.403034i	$-0.867956\pi$
$43$	−3.35840	+	3.35840i	−0.512151	+	0.512151i	0.403034	+	0.915185i	$0.367956\pi$
$44$	0.442057	+	1.11111i	0.0666425	+	0.167505i
$45$	−3.13913	−	3.13913i	−0.467953	−	0.467953i
$46$	4.61554	+	7.01378i	0.680525	+	1.03412i
$47$	4.38522			0.639650			0.319825	−	0.947477i	$-0.396376\pi$
$47$	4.38522			0.639650			0.319825	+	0.947477i	$0.396376\pi$
$48$	−3.99842	−	0.112344i	−0.577123	−	0.0162155i
$49$	−4.37128	+	5.46735i	−0.624469	+	0.781050i
$50$	−17.3758	+	11.4344i	−2.45730	+	1.61707i
$51$	1.81638	+	1.81638i	0.254344	+	0.254344i
$52$	−8.04484	+	3.20066i	−1.11562	+	0.443852i
$53$	−7.85667	−	7.85667i	−1.07920	−	1.07920i	−0.996582	−	0.0826143i	$-0.973673\pi$
$53$	−7.85667	−	7.85667i	−1.07920	−	1.07920i	−0.0826143	−	0.996582i	$-0.526327\pi$
$54$	−0.285633	+	1.38507i	−0.0388697	+	0.188484i
$55$		−	2.65434i		−	0.357911i
$56$	4.36908	+	6.07545i	0.583843	+	0.811866i
$57$			1.35093i			0.178935i
$58$	−2.09869	−	0.432799i	−0.275572	−	0.0568293i
$59$	5.63360	+	5.63360i	0.733432	+	0.733432i	0.971298	−	0.237866i	$-0.0764479\pi$
$59$	5.63360	+	5.63360i	0.733432	+	0.733432i	−0.237866	+	0.971298i	$0.576448\pi$
$60$	8.15440	+	3.51263i	1.05273	+	0.453479i
$61$	0.351526	+	0.351526i	0.0450083	+	0.0450083i	0.729253	−	0.684244i	$-0.239868\pi$
$61$	0.351526	+	0.351526i	0.0450083	+	0.0450083i	−0.684244	+	0.729253i	$0.739868\pi$
$62$	4.48761	+	6.81936i	0.569927	+	0.866060i
$63$	2.38446	−	1.14645i	0.300414	−	0.144440i
$64$	7.51343	−	2.74742i	0.939179	−	0.343428i
$65$	19.2185			2.38376
$66$	−0.706345	+	0.464823i	−0.0869451	+	0.0572158i
$67$	7.37756	+	7.37756i	0.901313	+	0.901313i	0.995550	−	0.0942371i	$-0.0300412\pi$
$67$	7.37756	+	7.37756i	0.901313	+	0.901313i	−0.0942371	+	0.995550i	$0.530041\pi$
$68$	−4.71835	−	2.03250i	−0.572183	−	0.246477i
$69$	−4.19810	+	4.19810i	−0.505392	+	0.505392i
$70$	−4.02581	−	16.1155i	−0.481176	−	1.92617i
$71$	−4.30558			−0.510978			−0.255489	−	0.966812i	$-0.582237\pi$
$71$	−4.30558			−0.510978			−0.255489	+	0.966812i	$0.582237\pi$
$72$	−0.493238	−	2.78509i	−0.0581287	−	0.328226i
$73$	6.71670			0.786131			0.393065	−	0.919511i	$-0.371415\pi$
$73$	6.71670			0.786131			0.393065	+	0.919511i	$0.371415\pi$
$74$	−1.33691	+	6.48284i	−0.155413	+	0.753615i
$75$	−10.4003	−	10.4003i	−1.20092	−	1.20092i
$76$	−0.998799	−	2.51047i	−0.114570	−	0.287971i
$77$	1.49281	+	0.523408i	0.170122	+	0.0596479i
$78$	−3.36550	−	5.11422i	−0.381068	−	0.579071i
$79$			8.39558i			0.944577i	0.881444	+	0.472288i	$0.156572\pi$
$79$			8.39558i			0.944577i	−0.881444	+	0.472288i	$0.843428\pi$
$80$	−17.7506	−	0.498739i	−1.98457	−	0.0557607i
$81$	−1.00000			−0.111111
$82$	4.80263	+	7.29807i	0.530362	+	0.805938i
$83$	−6.54381	+	6.54381i	−0.718277	+	0.718277i	−0.968252	−	0.249975i	$-0.919577\pi$
$83$	−6.54381	+	6.54381i	−0.718277	+	0.718277i	0.249975	+	0.968252i	$0.419577\pi$
$84$	−3.58348	+	3.89341i	−0.390990	+	0.424806i
$85$	8.06362	+	8.06362i	0.874622	+	0.874622i
$86$	6.57837	+	1.35661i	0.709364	+	0.146287i
$87$		−	1.51523i		−	0.162449i
$88$	0.968957	−	1.38602i	0.103291	−	0.147751i
$89$	14.8890			1.57823			0.789115	−	0.614246i	$-0.210540\pi$
$89$	14.8890			1.57823			0.789115	+	0.614246i	$0.210540\pi$
$90$	−1.26804	+	6.14886i	−0.133663	+	0.648147i
$91$	−3.78968	+	10.8086i	−0.397266	+	1.13304i
$92$	4.69762	−	10.9053i	0.489760	−	1.13695i
$93$	−4.08174	+	4.08174i	−0.423256	+	0.423256i
$94$	−3.40915	−	5.18054i	−0.351627	−	0.534332i
$95$			5.99732i			0.615312i
$96$	2.97573	+	4.81093i	0.303709	+	0.491014i
$97$			3.86266i			0.392193i	0.980585	+	0.196097i	$0.0628266\pi$
$97$			3.86266i			0.392193i	−0.980585	+	0.196097i	$0.937173\pi$
$98$	9.85724	+	0.913663i	0.995732	+	0.0922939i
$99$	−0.422784	−	0.422784i	−0.0424914	−	0.0424914i
$100$	27.0165	+	11.6378i	2.70165	+	1.16378i
$101$	1.63152	−	1.63152i	0.162343	−	0.162343i	−0.621261	−	0.783604i	$-0.713379\pi$
$101$	1.63152	−	1.63152i	0.162343	−	0.162343i	0.783604	+	0.621261i	$0.213379\pi$
$102$	0.733718	−	3.55789i	0.0726490	−	0.352284i
$103$		−	9.59390i		−	0.945315i	−0.881246	−	0.472657i	$-0.843295\pi$
$103$		−	9.59390i		−	0.945315i	0.881246	−	0.472657i	$-0.156705\pi$
$104$	10.0354	+	7.01563i	0.984047	+	0.687939i
$105$	10.5855	−	5.08956i	1.03304	−	0.496690i
$106$	−3.17367	+	15.3895i	−0.308254	+	1.49476i
$107$	10.1696	−	10.1696i	0.983130	−	0.983130i	−0.0167296	−	0.999860i	$-0.505325\pi$
$107$	10.1696	−	10.1696i	0.983130	−	0.983130i	0.999860	+	0.0167296i	$0.00532546\pi$
$108$	1.85833	−	0.739341i	0.178817	−	0.0711431i
$109$	−10.3263	+	10.3263i	−0.989076	+	0.989076i	−0.999941	−	0.0108654i	$-0.996541\pi$
$109$	−10.3263	+	10.3263i	−0.989076	+	0.989076i	0.0108654	+	0.999941i	$0.496541\pi$
$110$	−3.13574	+	2.06353i	−0.298981	+	0.196750i
$111$	−4.68052			−0.444255
$112$	3.78071	−	9.88464i	0.357244	−	0.934011i
$113$	1.12613			0.105937			0.0529686	−	0.998596i	$-0.483132\pi$
$113$	1.12613			0.105937			0.0529686	+	0.998596i	$0.483132\pi$
$114$	1.59594	−	1.05024i	0.149474	−	0.0983638i
$115$	−18.6370	+	18.6370i	−1.73791	+	1.73791i
$116$	1.12027	+	2.81579i	0.104014	+	0.261439i
$117$	3.06112	−	3.06112i	0.283001	−	0.283001i
$118$	2.27567	−	11.0350i	0.209492	−	1.01585i
$119$	−6.12507	+	2.94495i	−0.561484	+	0.269963i
$120$	−2.18968	−	12.3641i	−0.199889	−	1.12868i
$121$			10.6425i			0.967501i
$122$	0.141998	−	0.688563i	0.0128559	−	0.0623396i
$123$	−4.36827	+	4.36827i	−0.393874	+	0.393874i
$124$	4.56740	−	10.6030i	0.410165	−	0.952177i
$125$	−30.4753	−	30.4753i	−2.72579	−	2.72579i
$126$	−3.20810	−	1.92564i	−0.285800	−	0.171550i
$127$		−	15.6332i		−	1.38722i	−0.720349	−	0.693612i	$-0.756018\pi$
$127$		−	15.6332i		−	1.38722i	0.720349	−	0.693612i	$-0.243982\pi$
$128$	−9.08679	−	6.74020i	−0.803166	−	0.595755i
$129$			4.74949i			0.418169i
$130$	−14.9408	−	22.7040i	−1.31039	−	1.99127i
$131$	−4.20910	+	4.20910i	−0.367751	+	0.367751i	−0.866656	−	0.498905i	$-0.833736\pi$
$131$	−4.20910	+	4.20910i	−0.367751	+	0.367751i	0.498905	+	0.866656i	$0.333736\pi$
$132$	1.09825	+	0.473089i	0.0955905	+	0.0411771i
$133$	−3.37291	−	1.18261i	−0.292469	−	0.102545i
$134$	2.98014	−	14.4510i	0.257445	−	1.24838i
$135$	−4.43939			−0.382082
$136$	1.26700	+	7.15419i	0.108645	+	0.613466i
$137$			0.494682i			0.0422635i	0.999777	+	0.0211318i	$0.00672695\pi$
$137$			0.494682i			0.0422635i	−0.999777	+	0.0211318i	$0.993273\pi$
$138$	8.22317	+	1.69581i	0.700003	+	0.144357i
$139$	−2.46499	−	2.46499i	−0.209078	−	0.209078i	0.594798	−	0.803875i	$-0.297232\pi$
$139$	−2.46499	−	2.46499i	−0.209078	−	0.209078i	−0.803875	+	0.594798i	$0.797232\pi$
$140$	−15.9085	+	17.2844i	−1.34451	+	1.46080i
$141$	3.10082	−	3.10082i	0.261136	−	0.261136i
$142$	3.34724	+	5.08646i	0.280894	+	0.426846i
$143$	2.58838			0.216452
$144$	−2.90675	+	2.74787i	−0.242229	+	0.228989i
$145$		−	6.72669i		−	0.558621i
$146$	−5.22169	−	7.93487i	−0.432150	−	0.656695i
$147$	0.775034	+	6.95696i	0.0639237	+	0.573801i
$148$	8.69793	−	3.46050i	0.714965	−	0.284451i
$149$	−11.5750	−	11.5750i	−0.948265	−	0.948265i	0.0504610	−	0.998726i	$-0.483931\pi$
$149$	−11.5750	−	11.5750i	−0.948265	−	0.948265i	−0.998726	+	0.0504610i	$0.983931\pi$
$150$	−4.20115	+	20.3719i	−0.343022	+	1.66336i
$151$	−2.32516			−0.189219			−0.0946095	−	0.995514i	$-0.530160\pi$
$151$	−2.32516			−0.189219			−0.0946095	+	0.995514i	$0.530160\pi$
$152$	−2.18930	+	3.13163i	−0.177575	+	0.254009i
$153$	2.56875			0.207671
$154$	−0.542204	−	2.17046i	−0.0436921	−	0.174901i
$155$	−18.1204	+	18.1204i	−1.45547	+	1.45547i
$156$	−3.42535	+	7.95177i	−0.274247	+	0.636651i
$157$	15.6617	+	15.6617i	1.24994	+	1.24994i	0.955746	+	0.294192i	$0.0950505\pi$
$157$	15.6617	+	15.6617i	1.24994	+	1.24994i	0.294192	+	0.955746i	$0.404949\pi$
$158$	9.91824	−	6.52688i	0.789053	−	0.519250i
$159$	−11.1110			−0.881160
$160$	13.2104	+	21.3576i	1.04438	+	1.68847i
$161$	−6.80652	−	14.1566i	−0.536429	−	1.11569i
$162$	0.777418	+	1.18136i	0.0610797	+	0.0928167i
$163$	−15.0401	−	15.0401i	−1.17804	−	1.17804i	−0.980244	−	0.197791i	$-0.936623\pi$
$163$	−15.0401	−	15.0401i	−1.17804	−	1.17804i	−0.197791	−	0.980244i	$-0.563377\pi$
$164$	4.88803	−	11.3473i	0.381691	−	0.886076i
$165$	−1.87690	−	1.87690i	−0.146117	−	0.146117i
$166$	12.8179	+	2.64335i	0.994862	+	0.205163i
$167$		−	9.75468i		−	0.754840i	−0.926042	−	0.377420i	$-0.876811\pi$
$167$		−	9.75468i		−	0.754840i	0.926042	−	0.377420i	$-0.123189\pi$
$168$	7.38540	+	1.20658i	0.569796	+	0.0930900i
$169$			5.74092i			0.441609i
$170$	3.25727	−	15.7949i	0.249821	−	1.21141i
$171$	0.955253	+	0.955253i	0.0730500	+	0.0730500i
$172$	−3.51149	−	8.82610i	−0.267749	−	0.672984i
$173$	3.08743	+	3.08743i	0.234733	+	0.234733i	0.814665	−	0.579932i	$-0.196921\pi$
$173$	3.08743	+	3.08743i	0.234733	+	0.234733i	−0.579932	+	0.814665i	$0.696921\pi$
$174$	−1.79004	+	1.17797i	−0.135702	+	0.0893013i
$175$	35.0711	−	16.8623i	2.65113	−	1.27467i
$176$	−2.39068	−	0.0671712i	−0.180204	−	0.00506322i
$177$	7.96711			0.598845
$178$	−11.5750	−	17.5893i	−0.867581	−	1.31838i
$179$	9.33519	+	9.33519i	0.697745	+	0.697745i	0.963924	−	0.266179i	$-0.0857611\pi$
$179$	9.33519	+	9.33519i	0.697745	+	0.697745i	−0.266179	+	0.963924i	$0.585761\pi$
$180$	8.24984	−	3.28222i	0.614907	−	0.244643i
$181$	5.23801	−	5.23801i	0.389339	−	0.389339i	−0.485113	−	0.874451i	$-0.661222\pi$
$181$	5.23801	−	5.23801i	0.389339	−	0.389339i	0.874451	+	0.485113i	$0.161222\pi$
$182$	15.7150	−	3.92577i	1.16487	−	0.290998i
$183$	0.497133			0.0367491
$184$	−16.5351	+	2.92836i	−1.21898	+	0.215882i
$185$	−20.7787			−1.52768
$186$	7.99523	+	1.64880i	0.586239	+	0.120896i
$187$	1.08602	+	1.08602i	0.0794180	+	0.0794180i
$188$	−3.46977	+	8.05489i	−0.253059	+	0.587463i
$189$	0.875401	−	2.49673i	0.0636760	−	0.181611i
$190$	7.08501	−	4.66242i	0.514001	−	0.338248i
$191$		−	1.31624i		−	0.0952400i	−0.998866	−	0.0476200i	$-0.984836\pi$
$191$		−	1.31624i		−	0.0952400i	0.998866	−	0.0476200i	$-0.0151636\pi$
$192$	3.37008	−	7.25552i	0.243214	−	0.523622i
$193$	12.1525			0.874756			0.437378	−	0.899278i	$-0.355907\pi$
$193$	12.1525			0.874756			0.437378	+	0.899278i	$0.355907\pi$
$194$	4.56320	−	3.00290i	0.327619	−	0.215596i
$195$	13.5895	−	13.5895i	0.973166	−	0.973166i
$196$	−6.58383	−	12.3553i	−0.470274	−	0.882521i
$197$	6.99289	+	6.99289i	0.498223	+	0.498223i	0.910884	−	0.412662i	$-0.135401\pi$
$197$	6.99289	+	6.99289i	0.498223	+	0.498223i	−0.412662	+	0.910884i	$0.635401\pi$
$198$	−0.170782	+	0.828141i	−0.0121369	+	0.0588534i
$199$		−	17.9378i		−	1.27158i	−0.771862	−	0.635790i	$-0.780675\pi$
$199$		−	17.9378i		−	1.27158i	0.771862	−	0.635790i	$-0.219325\pi$
$200$	−7.25466	−	40.9637i	−0.512982	−	2.89657i
$201$	10.4334			0.735919
$202$	−3.19580	−	0.659047i	−0.224856	−	0.0463704i
$203$	3.78312	+	1.32643i	0.265523	+	0.0930973i
$204$	−4.77357	+	1.89918i	−0.334217	+	0.132969i
$205$	−19.3925	+	19.3925i	−1.35443	+	1.35443i
$206$	−11.3339	+	7.45847i	−0.789669	+	0.519656i
$207$			5.93702i			0.412651i
$208$	0.486346	−	17.3095i	0.0337220	−	1.20020i
$209$			0.807731i			0.0558719i
$210$	−14.2420	−	8.54867i	−0.982793	−	0.589914i
$211$	10.1381	+	10.1381i	0.697936	+	0.697936i	0.963965	−	0.266029i	$-0.0857118\pi$
$211$	10.1381	+	10.1381i	0.697936	+	0.697936i	−0.266029	+	0.963965i	$0.585712\pi$
$212$	20.6479	−	8.21482i	1.41810	−	0.564196i
$213$	−3.04450	+	3.04450i	−0.208606	+	0.208606i
$214$	−19.9200	−	4.10796i	−1.36170	−	0.280814i
$215$			21.0849i			1.43798i
$216$	−2.31813	−	1.62058i	−0.157729	−	0.110267i
$217$	−6.61785	−	13.7642i	−0.449249	−	0.934372i
$218$	20.2269	+	4.17125i	1.36994	+	0.282512i
$219$	4.74943	−	4.74943i	0.320936	−	0.320936i
$220$	4.87557	+	2.10023i	0.328711	+	0.141597i
$221$	−7.86324	+	7.86324i	−0.528939	+	0.528939i
$222$	3.63872	+	5.52940i	0.244215	+	0.371109i
$223$	−8.91647			−0.597091			−0.298545	−	0.954395i	$-0.596501\pi$
$223$	−8.91647			−0.597091			−0.298545	+	0.954395i	$0.596501\pi$
$224$	−14.6166	+	3.21810i	−0.976610	+	0.215018i
$225$	−14.7082			−0.980548
$226$	−0.875472	−	1.33037i	−0.0582356	−	0.0884947i
$227$	15.4137	−	15.4137i	1.02304	−	1.02304i	0.0233148	−	0.999728i	$-0.492578\pi$
$227$	15.4137	−	15.4137i	1.02304	−	1.02304i	0.999728	−	0.0233148i	$-0.00742199\pi$
$228$	−2.48143	−	1.06891i	−0.164337	−	0.0707905i
$229$	−9.56042	+	9.56042i	−0.631770	+	0.631770i	−0.948512	−	0.316742i	$-0.897411\pi$
$229$	−9.56042	+	9.56042i	−0.631770	+	0.631770i	0.316742	+	0.948512i	$0.397411\pi$
$230$	36.5059	+	7.52835i	2.40713	+	0.496405i
$231$	1.42568	−	0.685473i	0.0938031	−	0.0451008i
$232$	2.45555	−	3.51249i	0.161215	−	0.230606i
$233$		−	15.3607i		−	1.00631i	−0.864195	−	0.503157i	$-0.832172\pi$
$233$		−	15.3607i		−	1.00631i	0.864195	−	0.503157i	$-0.167828\pi$
$234$	−5.99607	−	1.23653i	−0.391975	−	0.0808343i
$235$	13.7658	−	13.7658i	0.897979	−	0.897979i
$236$	−14.8055	+	5.89041i	−0.963755	+	0.383433i
$237$	5.93657	+	5.93657i	0.385622	+	0.385622i
$238$	8.24080	+	4.94648i	0.534172	+	0.320633i
$239$		−	2.60913i		−	0.168771i	−0.996433	−	0.0843853i	$-0.973107\pi$
$239$		−	2.60913i		−	0.168771i	0.996433	−	0.0843853i	$-0.0268927\pi$
$240$	−12.9042	+	12.1989i	−0.832963	+	0.787435i
$241$			20.8007i			1.33989i	0.742411	+	0.669944i	$0.233682\pi$
$241$			20.8007i			1.33989i	−0.742411	+	0.669944i	$0.766318\pi$
$242$	12.5727	−	8.27368i	0.808202	−	0.531852i
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$	−0.923836	+	0.367551i	−0.0591425	+	0.0235300i
$245$	3.44068	+	30.8847i	0.219817	+	1.97315i
$246$	8.55649	+	1.76455i	0.545542	+	0.112503i
$247$	−5.84829			−0.372118
$248$	−16.0768	+	2.84719i	−1.02088	+	0.180797i
$249$			9.25435i			0.586471i
$250$	−12.3104	+	59.6945i	−0.778576	+	3.77541i
$251$	−3.34903	−	3.34903i	−0.211389	−	0.211389i	0.593469	−	0.804857i	$-0.297758\pi$
$251$	−3.34903	−	3.34903i	−0.211389	−	0.211389i	−0.804857	+	0.593469i	$0.797758\pi$
$252$	0.219156	+	5.28696i	0.0138055	+	0.333047i
$253$	−2.51007	+	2.51007i	−0.157807	+	0.157807i
$254$	−18.4685	+	12.1536i	−1.15882	+	0.762582i
$255$	11.4037			0.714126
$256$	−0.898397	+	15.9748i	−0.0561498	+	0.998422i
$257$		−	4.35968i		−	0.271949i	−0.990712	−	0.135975i	$-0.956583\pi$
$257$		−	4.35968i		−	0.271949i	0.990712	−	0.135975i	$-0.0434166\pi$
$258$	5.61088	−	3.69234i	0.349318	−	0.229875i
$259$	4.09733	−	11.6860i	0.254596	−	0.726133i
$260$	−15.2065	+	35.3010i	−0.943065	+	2.18928i
$261$	−1.07143	−	1.07143i	−0.0663197	−	0.0663197i
$262$	8.24472	+	1.70025i	0.509360	+	0.105042i
$263$	−10.9327			−0.674140			−0.337070	−	0.941480i	$-0.609436\pi$
$263$	−10.9327			−0.674140			−0.337070	+	0.941480i	$0.609436\pi$
$264$	−0.294910	−	1.66522i	−0.0181505	−	0.102487i
$265$	−49.3261			−3.03008
$266$	1.22508	+	4.90402i	0.0751142	+	0.300685i
$267$	10.5281	−	10.5281i	0.644310	−	0.644310i
$268$	−19.3887	+	7.71387i	−1.18436	+	0.471200i
$269$	4.06387	+	4.06387i	0.247779	+	0.247779i	0.820058	−	0.572280i	$-0.193941\pi$
$269$	4.06387	+	4.06387i	0.247779	+	0.247779i	−0.572280	+	0.820058i	$0.693941\pi$
$270$	3.45127	+	5.24454i	0.210037	+	0.319173i
$271$	−4.34285			−0.263810			−0.131905	−	0.991262i	$-0.542109\pi$
$271$	−4.34285			−0.263810			−0.131905	+	0.991262i	$0.542109\pi$
$272$	7.46671	−	7.05859i	0.452736	−	0.427990i
$273$	4.96309	+	10.3225i	0.300380	+	0.624747i
$274$	0.584400	−	0.384575i	0.0353049	−	0.0232330i
$275$	−6.21839	−	6.21839i	−0.374983	−	0.374983i
$276$	−4.38948	−	11.0329i	−0.264215	−	0.664103i
$277$	4.81640	+	4.81640i	0.289389	+	0.289389i	0.836839	−	0.547449i	$-0.184401\pi$
$277$	4.81640	+	4.81640i	0.289389	+	0.289389i	−0.547449	+	0.836839i	$0.684401\pi$
$278$	−0.995722	+	4.82838i	−0.0597195	+	0.289587i
$279$			5.77245i			0.345587i
$280$	32.7867	+	5.35650i	1.95938	+	0.320112i
$281$		−	4.22817i		−	0.252232i	−0.992016	−	0.126116i	$-0.959749\pi$
$281$		−	4.22817i		−	0.252232i	0.992016	−	0.126116i	$-0.0402511\pi$
$282$	−6.07383	−	1.25256i	−0.361691	−	0.0745890i
$283$	4.59280	+	4.59280i	0.273014	+	0.273014i	0.830312	−	0.557298i	$-0.188162\pi$
$283$	4.59280	+	4.59280i	0.273014	+	0.273014i	−0.557298	+	0.830312i	$0.688162\pi$
$284$	3.40676	−	7.90861i	0.202154	−	0.469290i
$285$	4.24074	+	4.24074i	0.251200	+	0.251200i
$286$	−2.01226	−	3.05782i	−0.118987	−	0.180813i
$287$	−7.08242	−	14.7304i	−0.418062	−	0.869508i
$288$	5.50600	+	1.29768i	0.324444	+	0.0764668i
$289$	10.4015			0.611855
$290$	−7.94667	+	5.22945i	−0.466645	+	0.307084i
$291$	2.73131	+	2.73131i	0.160112	+	0.160112i
$292$	−5.31454	+	12.3374i	−0.311010	+	0.721993i
$293$	−11.0062	+	11.0062i	−0.642991	+	0.642991i	−0.951290	−	0.308299i	$-0.900240\pi$
$293$	−11.0062	+	11.0062i	−0.642991	+	0.642991i	0.308299	+	0.951290i	$0.400240\pi$
$294$	7.61618	−	6.32407i	0.444185	−	0.368827i
$295$	35.3691			2.05927
$296$	−10.8500	−	7.58517i	−0.630646	−	0.440879i
$297$	−0.597907			−0.0346941
$298$	−4.67569	+	22.6730i	−0.270856	+	1.31341i
$299$	−18.1739	−	18.1739i	−1.05102	−	1.05102i
$300$	27.3327	−	10.8744i	1.57805	−	0.627833i
$301$	−11.8582	−	4.15771i	−0.683496	−	0.239646i
$302$	1.80762	+	2.74686i	0.104017	+	0.158064i
$303$		−	2.30732i		−	0.132552i
$304$	5.40159	+	0.151769i	0.309803	+	0.00870455i
$305$	2.20697			0.126371
$306$	−1.99699	−	3.03462i	−0.114160	−	0.173478i
$307$	1.20915	−	1.20915i	0.0690101	−	0.0690101i	−0.671759	−	0.740769i	$-0.734461\pi$
$307$	1.20915	−	1.20915i	0.0690101	−	0.0690101i	0.740769	+	0.671759i	$0.234461\pi$
$308$	−2.14259	+	2.32790i	−0.122085	+	0.132644i
$309$	−6.78391	−	6.78391i	−0.385923	−	0.385923i
$310$	35.4940	+	7.31968i	2.01592	+	0.415730i
$311$			27.0431i			1.53347i	0.641961	+	0.766737i	$0.278121\pi$
$311$			27.0431i			1.53347i	−0.641961	+	0.766737i	$0.721879\pi$
$312$	12.0569	−	2.13527i	0.682586	−	0.120886i
$313$	4.07592			0.230385			0.115192	−	0.993343i	$-0.463252\pi$
$313$	4.07592			0.230385			0.115192	+	0.993343i	$0.463252\pi$
$314$	6.32647	−	30.6778i	0.357023	−	1.73125i
$315$	3.88625	−	11.0840i	0.218965	−	0.624511i
$316$	−15.4212	−	6.64294i	−0.867512	−	0.373694i
$317$	10.2893	−	10.2893i	0.577905	−	0.577905i	−0.356420	−	0.934326i	$-0.616003\pi$
$317$	10.2893	−	10.2893i	0.577905	−	0.577905i	0.934326	+	0.356420i	$0.116003\pi$
$318$	8.63789	+	13.1261i	0.484389	+	0.736077i
$319$		−	0.905965i		−	0.0507243i
$320$	14.9611	−	32.2101i	0.836351	−	1.80060i
$321$		−	14.3820i		−	0.802723i
$322$	−11.4325	+	19.0465i	−0.637111	+	1.06142i
$323$	−2.45380	−	2.45380i	−0.136533	−	0.136533i
$324$	0.791242	−	1.83683i	0.0439579	−	0.102046i
$325$	45.0236	−	45.0236i	2.49746	−	2.49746i
$326$	−6.07540	+	29.4604i	−0.336486	+	1.63166i
$327$			14.6035i			0.807577i
$328$	−17.2053	+	3.04706i	−0.950006	+	0.168246i
$329$	5.02745	+	10.4564i	0.277173	+	0.576479i
$330$	−0.758167	+	3.67644i	−0.0417357	+	0.202382i
$331$	4.51356	−	4.51356i	0.248088	−	0.248088i	−0.572098	−	0.820186i	$-0.693870\pi$
$331$	4.51356	−	4.51356i	0.248088	−	0.248088i	0.820186	+	0.572098i	$0.193870\pi$
$332$	−6.84212	−	17.1976i	−0.375510	−	0.943841i
$333$	−3.30963	+	3.30963i	−0.181366	+	0.181366i
$334$	−11.5238	+	7.58346i	−0.630556	+	0.414949i
$335$	46.3182			2.53063
$336$	−4.31613	−	9.66287i	−0.235464	−	0.527153i
$337$	−4.16157			−0.226695			−0.113348	−	0.993555i	$-0.536157\pi$
$337$	−4.16157			−0.226695			−0.113348	+	0.993555i	$0.536157\pi$
$338$	6.78212	−	4.46310i	0.368898	−	0.242760i
$339$	0.796293	−	0.796293i	0.0432487	−	0.0432487i
$340$	−21.1917	+	8.43120i	−1.14928	+	0.457246i
$341$	−2.44050	+	2.44050i	−0.132160	+	0.132160i
$342$	0.385870	−	1.87113i	0.0208655	−	0.101179i
$343$	−18.0481	−	4.15508i	−0.974508	−	0.224353i
$344$	−7.69694	+	11.0099i	−0.414991	+	0.593615i
$345$			26.3567i			1.41900i
$346$	1.24716	−	6.04761i	0.0670475	−	0.325122i
$347$	9.38128	−	9.38128i	0.503613	−	0.503613i	−0.408945	−	0.912559i	$-0.634103\pi$
$347$	9.38128	−	9.38128i	0.503613	−	0.503613i	0.912559	+	0.408945i	$0.134103\pi$
$348$	2.78321	+	1.19891i	0.149196	+	0.0642684i
$349$	9.89989	+	9.89989i	0.529929	+	0.529929i	0.920551	−	0.390622i	$-0.127740\pi$
$349$	9.89989	+	9.89989i	0.529929	+	0.529929i	−0.390622	+	0.920551i	$0.627740\pi$
$350$	−47.1854	−	28.3227i	−2.52217	−	1.51391i
$351$		−	4.32908i		−	0.231069i
$352$	1.77921	+	2.87649i	0.0948320	+	0.153317i
$353$		−	4.23294i		−	0.225297i	−0.993635	−	0.112648i	$-0.964067\pi$
$353$		−	4.23294i		−	0.225297i	0.993635	−	0.112648i	$-0.0359334\pi$
$354$	−6.19378	−	9.41206i	−0.329195	−	0.500245i
$355$	−13.5158	+	13.5158i	−0.717342	+	0.717342i
$356$	−11.7808	+	27.3485i	−0.624381	+	1.44947i
$357$	−2.24868	+	6.41347i	−0.119013	+	0.339437i
$358$	3.77091	−	18.2856i	0.199299	−	0.966425i
$359$	23.0033			1.21407			0.607033	−	0.794677i	$-0.292360\pi$
$359$	23.0033			1.21407			0.607033	+	0.794677i	$0.292360\pi$
$360$	−10.2911	−	7.19440i	−0.542387	−	0.379178i
$361$			17.1750i			0.903947i
$362$	−10.2601	−	2.11587i	−0.539260	−	0.111208i
$363$	7.52539	+	7.52539i	0.394981	+	0.394981i
$364$	−16.8549	−	15.5132i	−0.883436	−	0.813111i
$365$	21.0846	−	21.0846i	1.10362	−	1.10362i
$366$	−0.386480	−	0.587295i	−0.0202017	−	0.0306984i
$367$	−21.1825			−1.10572			−0.552859	−	0.833275i	$-0.686463\pi$
$367$	−21.1825			−1.10572			−0.552859	+	0.833275i	$0.686463\pi$
$368$	16.3142	+	17.2574i	0.850434	+	0.899605i
$369$			6.17767i			0.321597i
$370$	16.1537	+	24.5472i	0.839791	+	1.27615i
$371$	9.72658	−	27.7412i	0.504979	−	1.44025i
$372$	−4.26781	−	10.7271i	−0.221275	−	0.556174i
$373$	7.70573	+	7.70573i	0.398987	+	0.398987i	0.877876	−	0.478888i	$-0.158960\pi$
$373$	7.70573	+	7.70573i	0.398987	+	0.398987i	−0.478888	+	0.877876i	$0.658960\pi$
$374$	0.438695	−	2.12729i	0.0226844	−	0.109999i
$375$	−43.0986			−2.22560
$376$	12.2132	−	2.16296i	0.629849	−	0.111546i
$377$	6.55954			0.337833
$378$	−3.63010	+	0.906838i	−0.186712	+	0.0466427i
$379$	2.73370	−	2.73370i	0.140421	−	0.140421i	−0.633402	−	0.773823i	$-0.718342\pi$
$379$	2.73370	−	2.73370i	0.140421	−	0.140421i	0.773823	+	0.633402i	$0.218342\pi$
$380$	−11.0160	−	4.74533i	−0.565111	−	0.243430i
$381$	−11.0544	−	11.0544i	−0.566332	−	0.566332i
$382$	−1.55496	+	1.02327i	−0.0795588	+	0.0523551i
$383$	−18.5055			−0.945588			−0.472794	−	0.881173i	$-0.656754\pi$
$383$	−18.5055			−0.945588			−0.472794	+	0.881173i	$0.656754\pi$
$384$	−11.1914	+	1.65929i	−0.571107	+	0.0846752i
$385$	6.32917	−	3.04308i	0.322564	−	0.155090i
$386$	−9.44757	−	14.3565i	−0.480869	−	0.730727i
$387$	3.35840	+	3.35840i	0.170717	+	0.170717i
$388$	−7.09503	−	3.05630i	−0.360196	−	0.155160i
$389$	18.4302	+	18.4302i	0.934449	+	0.934449i	0.997980	−	0.0635309i	$-0.0202361\pi$
$389$	18.4302	+	18.4302i	0.934449	+	0.934449i	−0.0635309	+	0.997980i	$0.520236\pi$
$390$	−26.6189	−	5.48943i	−1.34790	−	0.277968i
$391$		−	15.2507i		−	0.771260i
$392$	−9.47770	+	17.3831i	−0.478696	+	0.877981i
$393$			5.95257i			0.300268i
$394$	2.82475	−	13.6975i	0.142309	−	0.690072i
$395$	26.3548	+	26.3548i	1.32605	+	1.32605i
$396$	1.11111	−	0.442057i	0.0558351	−	0.0222142i
$397$	9.65214	+	9.65214i	0.484427	+	0.484427i	0.906542	−	0.422115i	$-0.138712\pi$
$397$	9.65214	+	9.65214i	0.484427	+	0.484427i	−0.422115	+	0.906542i	$0.638712\pi$
$398$	−21.1911	+	13.9452i	−1.06221	+	0.699010i
$399$	−3.22124	+	1.54878i	−0.161264	+	0.0775360i
$400$	−42.7531	+	40.4163i	−2.13766	+	2.02081i
$401$	−4.76372			−0.237889			−0.118944	−	0.992901i	$-0.537951\pi$
$401$	−4.76372			−0.237889			−0.118944	+	0.992901i	$0.537951\pi$
$402$	−8.11115	−	12.3257i	−0.404547	−	0.614750i
$403$	−17.6702	−	17.6702i	−0.880213	−	0.880213i
$404$	1.70590	+	4.28776i	0.0848716	+	0.213324i
$405$	−3.13913	+	3.13913i	−0.155984	+	0.155984i
$406$	−1.37407	−	5.50043i	−0.0681938	−	0.272982i
$407$	−2.79851			−0.138717
$408$	5.95468	+	4.16287i	0.294801	+	0.206093i
$409$	11.1720			0.552422			0.276211	−	0.961097i	$-0.410921\pi$
$409$	11.1720			0.552422			0.276211	+	0.961097i	$0.410921\pi$
$410$	37.9856	+	7.83351i	1.87598	+	0.386869i
$411$	0.349793	+	0.349793i	0.0172540	+	0.0172540i
$412$	17.6223	+	7.59110i	0.868190	+	0.373986i
$413$	−6.97441	+	19.8917i	−0.343188	+	0.978809i
$414$	7.01378	−	4.61554i	0.344708	−	0.226842i
$415$			41.0837i			2.01672i
$416$	−20.8269	+	12.8822i	−1.02112	+	0.631600i
$417$	−3.48602			−0.170711
$418$	0.954224	−	0.627944i	0.0466726	−	0.0307138i
$419$	−4.99890	+	4.99890i	−0.244212	+	0.244212i	−0.818590	−	0.574378i	$-0.805244\pi$
$419$	−4.99890	+	4.99890i	−0.244212	+	0.244212i	0.574378	+	0.818590i	$0.305244\pi$
$420$	0.972920	+	23.4709i	0.0474736	+	1.14526i
$421$	−28.0333	−	28.0333i	−1.36626	−	1.36626i	−0.865705	−	0.500554i	$-0.833130\pi$
$421$	−28.0333	−	28.0333i	−1.36626	−	1.36626i	−0.500554	−	0.865705i	$-0.666870\pi$
$422$	4.09524	−	19.8583i	0.199353	−	0.966689i
$423$		−	4.38522i		−	0.213217i
$424$	−25.7567	−	18.0063i	−1.25086	−	0.874463i
$425$	37.7817			1.83268
$426$	5.96352	+	1.22982i	0.288934	+	0.0595847i
$427$	−0.435191	+	1.24121i	−0.0210604	+	0.0600663i
$428$	10.6332	+	26.7264i	0.513974	+	1.29187i
$429$	1.83026	−	1.83026i	0.0883660	−	0.0883660i
$430$	24.9089	−	16.3918i	1.20121	−	0.790481i
$431$		−	39.6062i		−	1.90776i	−0.300181	−	0.953882i	$-0.597047\pi$
$431$		−	39.6062i		−	1.90776i	0.300181	−	0.953882i	$-0.402953\pi$
$432$	−0.112344	+	3.99842i	−0.00540515	+	0.192374i
$433$		−	37.9857i		−	1.82548i	−0.408546	−	0.912738i	$-0.633964\pi$
$433$		−	37.9857i		−	1.82548i	0.408546	−	0.912738i	$-0.366036\pi$
$434$	−11.1157	+	18.5186i	−0.533568	+	0.888921i
$435$	−4.75649	−	4.75649i	−0.228056	−	0.228056i
$436$	−10.7970	−	27.1381i	−0.517082	−	1.29968i
$437$	5.67135	−	5.67135i	0.271297	−	0.271297i
$438$	−9.30309	−	1.91851i	−0.444519	−	0.0916700i
$439$		−	9.40058i		−	0.448665i	−0.974513	−	0.224333i	$-0.927980\pi$
$439$		−	9.40058i		−	0.448665i	0.974513	−	0.224333i	$-0.0720202\pi$
$440$	−1.30922	−	7.39258i	−0.0624148	−	0.352427i
$441$	5.46735	+	4.37128i	0.260350	+	0.208156i
$442$	15.4024	+	3.17632i	0.732617	+	0.151082i
$443$	−15.1211	+	15.1211i	−0.718426	+	0.718426i	−0.968283	−	0.249857i	$-0.919616\pi$
$443$	−15.1211	+	15.1211i	−0.718426	+	0.718426i	0.249857	+	0.968283i	$0.419616\pi$
$444$	3.70342	−	8.59731i	0.175757	−	0.408010i
$445$	46.7384	−	46.7384i	2.21561	−	2.21561i
$446$	6.93183	+	10.5336i	0.328231	+	0.498780i
$447$	−16.3696			−0.774255
$448$	15.1649	+	14.7657i	0.716476	+	0.697612i
$449$	−37.7663			−1.78230			−0.891151	−	0.453707i	$-0.850101\pi$
$449$	−37.7663			−1.78230			−0.891151	+	0.453707i	$0.850101\pi$
$450$	11.4344	+	17.3758i	0.539024	+	0.819101i
$451$	−2.61182	+	2.61182i	−0.122986	+	0.122986i
$452$	−0.891040	+	2.06850i	−0.0419110	+	0.0972942i
$453$	−1.64414	+	1.64414i	−0.0772484	+	0.0772484i
$454$	−30.1921	−	6.22630i	−1.41698	−	0.292215i
$455$	22.0331	+	45.8257i	1.03293	+	2.14834i
$456$	0.666331	+	3.76246i	0.0312038	+	0.176193i
$457$		−	20.6321i		−	0.965129i	−0.875860	−	0.482564i	$-0.839705\pi$
$457$		−	20.6321i		−	0.965129i	0.875860	−	0.482564i	$-0.160295\pi$
$458$	18.7268	+	3.86189i	0.875045	+	0.180454i
$459$	1.81638	−	1.81638i	0.0847813	−	0.0847813i
$460$	−19.4866	−	48.9794i	−0.908568	−	2.28368i
$461$	−7.60470	−	7.60470i	−0.354186	−	0.354186i	0.507478	−	0.861665i	$-0.330578\pi$
$461$	−7.60470	−	7.60470i	−0.354186	−	0.354186i	−0.861665	+	0.507478i	$0.830578\pi$
$462$	−1.91814	−	1.15135i	−0.0892402	−	0.0535657i
$463$		−	3.46558i		−	0.161059i	−0.996752	−	0.0805297i	$-0.974339\pi$
$463$		−	3.46558i		−	0.161059i	0.996752	−	0.0805297i	$-0.0256612\pi$
$464$	−6.05852	−	0.170227i	−0.281260	−	0.00790257i
$465$			25.6262i			1.18839i
$466$	−18.1466	+	11.9417i	−0.840625	+	0.553189i
$467$	−12.3445	+	12.3445i	−0.571236	+	0.571236i	−0.932474	−	0.361238i	$-0.882354\pi$
$467$	−12.3445	+	12.3445i	−0.571236	+	0.571236i	0.361238	+	0.932474i	$0.382354\pi$
$468$	3.20066	+	8.04484i	0.147951	+	0.371873i
$469$	−9.13345	+	26.0495i	−0.421744	+	1.20286i
$470$	−26.9641	−	5.56062i	−1.24376	−	0.256492i
$471$	22.1490			1.02057
$472$	18.4688	+	12.9114i	0.850094	+	0.594293i
$473$			2.83975i			0.130572i
$474$	2.39805	−	11.6285i	0.110146	−	0.534112i
$475$	14.0501	+	14.0501i	0.644661	+	0.644661i
$476$	−0.562956	−	13.5809i	−0.0258031	−	0.622478i
$477$	−7.85667	+	7.85667i	−0.359732	+	0.359732i
$478$	−3.08233	+	2.02839i	−0.140983	+	0.0927762i
$479$	−24.4302			−1.11625			−0.558123	−	0.829758i	$-0.688478\pi$
$479$	−24.4302			−1.11625			−0.558123	+	0.829758i	$0.688478\pi$
$480$	24.4433	+	5.76093i	1.11568	+	0.262949i
$481$		−	20.2623i		−	0.923883i
$482$	24.5732	−	16.1708i	1.11928	−	0.736560i
$483$	−14.8231	−	5.19727i	−0.674476	−	0.236484i
$484$	−19.5485	−	8.42080i	−0.888566	−	0.382764i
$485$	12.1254	+	12.1254i	0.550584	+	0.550584i
$486$	1.38507	+	0.285633i	0.0628280	+	0.0129566i
$487$	36.2898			1.64445			0.822224	−	0.569164i	$-0.192733\pi$
$487$	36.2898			1.64445			0.822224	+	0.569164i	$0.192733\pi$
$488$	1.15242	+	0.805645i	0.0521675	+	0.0364699i
$489$	−21.2700			−0.961862
$490$	33.8112	−	28.0750i	1.52744	−	1.26830i
$491$	−2.77669	+	2.77669i	−0.125310	+	0.125310i	−0.766981	−	0.641670i	$-0.778242\pi$
$491$	−2.77669	+	2.77669i	−0.125310	+	0.125310i	0.641670	+	0.766981i	$0.278242\pi$
$492$	−4.56740	−	11.4801i	−0.205914	−	0.517564i
$493$	2.75223	+	2.75223i	0.123954	+	0.123954i
$494$	4.54656	+	6.90896i	0.204560	+	0.310849i
$495$	−2.65434			−0.119304
$496$	15.8620	+	16.7791i	0.712223	+	0.753402i
$497$	−4.93615	−	10.2665i	−0.221417	−	0.460514i
$498$	10.9328	−	7.19450i	0.489908	−	0.322393i
$499$	11.8814	+	11.8814i	0.531886	+	0.531886i	0.921133	−	0.389247i	$-0.127265\pi$
$499$	11.8814	+	11.8814i	0.531886	+	0.531886i	−0.389247	+	0.921133i	$0.627265\pi$
$500$	80.0912	−	31.8645i	3.58179	−	1.42503i
$501$	−6.89760	−	6.89760i	−0.308162	−	0.308162i
$502$	−1.35283	+	6.56001i	−0.0603796	+	0.292788i
$503$		−	26.7447i		−	1.19249i	−0.802804	−	0.596243i	$-0.796660\pi$
$503$		−	26.7447i		−	1.19249i	0.802804	−	0.596243i	$-0.203340\pi$
$504$	6.07545	−	4.36908i	0.270622	−	0.194614i
$505$		−	10.2431i		−	0.455813i
$506$	4.91669	+	1.01393i	0.218573	+	0.0450749i
$507$	4.05944	+	4.05944i	0.180286	+	0.180286i
$508$	28.7155	+	12.3697i	1.27405	+	0.548815i
$509$	−20.3067	−	20.3067i	−0.900079	−	0.900079i	0.0953637	−	0.995442i	$-0.469599\pi$
$509$	−20.3067	−	20.3067i	−0.900079	−	0.900079i	−0.995442	+	0.0953637i	$0.969599\pi$
$510$	−8.86543	−	13.4719i	−0.392568	−	0.596545i
$511$	7.70039	+	16.0157i	0.340645	+	0.708493i
$512$	19.5704	−	11.3577i	0.864899	−	0.501946i
$513$	1.35093			0.0596451
$514$	−5.15037	+	3.38930i	−0.227173	+	0.149495i
$515$	−30.1164	−	30.1164i	−1.32709	−	1.32709i
$516$	−8.72400	−	3.75800i	−0.384053	−	0.165437i
$517$	1.85400	−	1.85400i	0.0815388	−	0.0815388i
$518$	−16.9908	+	4.24447i	−0.746531	+	0.186491i
$519$	4.36629			0.191659
$520$	53.5252	−	9.47929i	2.34723	−	0.415694i
$521$	−6.58341			−0.288424			−0.144212	−	0.989547i	$-0.546065\pi$
$521$	−6.58341			−0.288424			−0.144212	+	0.989547i	$0.546065\pi$
$522$	−0.432799	+	2.09869i	−0.0189431	+	0.0918573i
$523$	−17.5584	−	17.5584i	−0.767775	−	0.767775i	0.209940	−	0.977714i	$-0.432673\pi$
$523$	−17.5584	−	17.5584i	−0.767775	−	0.767775i	−0.977714	+	0.209940i	$0.932673\pi$
$524$	−4.40098	−	11.0618i	−0.192258	−	0.483238i
$525$	12.8756	−	36.7225i	0.561936	−	1.60270i
$526$	8.49928	+	12.9155i	0.370586	+	0.563143i
$527$		−	14.8280i		−	0.645916i
$528$	−1.73797	+	1.64297i	−0.0756352	+	0.0715011i
$529$	12.2481			0.532528
$530$	38.3470	+	58.2721i	1.66569	+	2.53118i
$531$	5.63360	−	5.63360i	0.244477	−	0.244477i
$532$	4.84104	−	5.25973i	0.209885	−	0.228038i
$533$	−18.9106	−	18.9106i	−0.819108	−	0.819108i
$534$	−20.6223	−	4.25279i	−0.892413	−	0.184036i
$535$		−	63.8472i		−	2.76035i
$536$	24.1861	+	16.9083i	1.04468	+	0.730326i
$537$	13.2020			0.569706
$538$	1.64158	−	7.96024i	0.0707737	−	0.343190i
$539$	0.463398	+	4.15961i	0.0199600	+	0.179167i
$540$	3.51263	−	8.15440i	0.151160	−	0.350910i
$541$	13.1000	−	13.1000i	0.563215	−	0.563215i	−0.367005	−	0.930219i	$-0.619617\pi$
$541$	13.1000	−	13.1000i	0.563215	−	0.563215i	0.930219	+	0.367005i	$0.119617\pi$
$542$	3.37621	+	5.13049i	0.145021	+	0.220373i
$543$		−	7.40767i		−	0.317894i
$544$	−14.1435	−	3.33342i	−0.606398	−	0.142919i
$545$			64.8308i			2.77705i
$546$	8.33624	−	13.8881i	0.356758	−	0.594357i
$547$	−24.6751	−	24.6751i	−1.05503	−	1.05503i	−0.998395	−	0.0566382i	$-0.981962\pi$
$547$	−24.6751	−	24.6751i	−1.05503	−	1.05503i	−0.0566382	−	0.998395i	$-0.518038\pi$
$548$	−0.908646	−	0.391413i	−0.0388154	−	0.0167203i
$549$	0.351526	−	0.351526i	0.0150028	−	0.0150028i
$550$	−2.51189	+	12.1805i	−0.107108	+	0.519377i
$551$			2.04697i			0.0872038i
$552$	−9.62142	+	13.7628i	−0.409515	+	0.585782i
$553$	−20.0189	+	9.62515i	−0.851291	+	0.409303i
$554$	1.94556	−	9.43428i	0.0826591	−	0.400824i
$555$	−14.6927	+	14.6927i	−0.623672	+	0.623672i
$556$	6.47816	−	2.57736i	0.274735	−	0.109304i
$557$	−19.0634	+	19.0634i	−0.807740	+	0.807740i	−0.984291	−	0.176551i	$-0.943506\pi$
$557$	−19.0634	+	19.0634i	−0.807740	+	0.807740i	0.176551	+	0.984291i	$0.443506\pi$
$558$	6.81936	−	4.48761i	0.288687	−	0.189976i
$559$	−20.5609			−0.869634
$560$	−19.1610	−	42.8973i	−0.809700	−	1.81274i
$561$	1.53587			0.0648445
$562$	−4.99501	+	3.28706i	−0.210702	+	0.138656i
$563$	15.4083	−	15.4083i	0.649380	−	0.649380i	−0.303463	−	0.952843i	$-0.598143\pi$
$563$	15.4083	−	15.4083i	0.649380	−	0.649380i	0.952843	+	0.303463i	$0.0981428\pi$
$564$	3.24217	+	8.14917i	0.136520	+	0.343142i
$565$	3.53506	−	3.53506i	0.148721	−	0.148721i
$566$	1.85524	−	8.99630i	0.0779817	−	0.378143i
$567$	−1.14645	−	2.38446i	−0.0481466	−	0.100138i
$568$	−11.9914	+	2.12368i	−0.503149	+	0.0891075i
$569$			25.8165i			1.08228i	0.840931	+	0.541142i	$0.182008\pi$
$569$			25.8165i			1.08228i	−0.840931	+	0.541142i	$0.817992\pi$
$570$	1.71303	−	8.30669i	0.0717509	−	0.347929i
$571$	−17.9757	+	17.9757i	−0.752258	+	0.752258i	−0.974900	−	0.222642i	$-0.928532\pi$
$571$	−17.9757	+	17.9757i	−0.752258	+	0.752258i	0.222642	+	0.974900i	$0.428532\pi$
$572$	−2.04804	+	4.75442i	−0.0856328	+	0.198792i
$573$	−0.930724	−	0.930724i	−0.0388816	−	0.0388816i
$574$	−11.8960	+	19.8186i	−0.496528	+	0.827212i
$575$			87.3229i			3.64162i
$576$	−2.74742	−	7.51343i	−0.114476	−	0.313060i
$577$			2.60870i			0.108602i	0.998525	+	0.0543008i	$0.0172930\pi$
$577$			2.60870i			0.108602i	−0.998525	+	0.0543008i	$0.982707\pi$
$578$	−8.08635	−	12.2880i	−0.336348	−	0.511114i
$579$	8.59311	−	8.59311i	0.357117	−	0.357117i
$580$	12.3558	+	5.32244i	0.513046	+	0.221002i
$581$	−23.1056	−	8.10126i	−0.958583	−	0.336097i
$582$	1.10330	−	5.35004i	0.0457333	−	0.221766i
$583$	−6.64334			−0.275139
$584$	18.7066	−	3.31294i	0.774085	−	0.137090i
$585$		−	19.2185i		−	0.794586i
$586$	21.5588	+	4.44592i	0.890586	+	0.183659i
$587$	20.0167	+	20.0167i	0.826176	+	0.826176i	0.986986	−	0.160809i	$-0.0514103\pi$
$587$	20.0167	+	20.0167i	0.826176	+	0.826176i	−0.160809	+	0.986986i	$0.551410\pi$
$588$	−13.3920	−	4.08104i	−0.552276	−	0.168299i
$589$	5.51415	−	5.51415i	0.227206	−	0.227206i
$590$	−27.4966	−	41.7838i	−1.13202	−	1.72021i
$591$	9.88943			0.406797
$592$	−0.525828	+	18.7147i	−0.0216114	+	0.769169i
$593$			11.8075i			0.484877i	0.970167	+	0.242438i	$0.0779472\pi$
$593$			11.8075i			0.484877i	−0.970167	+	0.242438i	$0.922053\pi$
$594$	0.464823	+	0.706345i	0.0190719	+	0.0289817i
$595$	−9.98279	+	28.4719i	−0.409254	+	1.16724i
$596$	30.4200	−	12.1027i	1.24605	−	0.495746i
$597$	−12.6840	−	12.6840i	−0.519120	−	0.519120i
$598$	−7.34128	+	35.5988i	−0.300207	+	1.45574i
$599$	7.64439			0.312341			0.156171	−	0.987730i	$-0.450085\pi$
$599$	7.64439			0.312341			0.156171	+	0.987730i	$0.450085\pi$
$600$	−34.0955	−	23.8359i	−1.39194	−	0.973095i
$601$	−5.46690			−0.222999			−0.111500	−	0.993764i	$-0.535565\pi$
$601$	−5.46690			−0.222999			−0.111500	+	0.993764i	$0.535565\pi$
$602$	4.30702	+	17.2411i	0.175541	+	0.702697i
$603$	7.37756	−	7.37756i	0.300438	−	0.300438i
$604$	1.83977	−	4.27092i	0.0748590	−	0.173781i
$605$	33.4082	+	33.4082i	1.35824	+	1.35824i
$606$	−2.72579	+	1.79375i	−0.110728	+	0.0728663i
$607$	−11.1394			−0.452133			−0.226066	−	0.974112i	$-0.572587\pi$
$607$	−11.1394			−0.452133			−0.226066	+	0.974112i	$0.572587\pi$
$608$	−4.02000	−	6.49924i	−0.163033	−	0.263579i
$609$	3.61300	−	1.73714i	0.146406	−	0.0703925i
$610$	−1.71574	−	2.60724i	−0.0694682	−	0.105564i
$611$	13.4237	+	13.4237i	0.543064	+	0.543064i
$612$	−2.03250	+	4.71835i	−0.0821590	+	0.190728i
$613$	21.4823	+	21.4823i	0.867664	+	0.867664i	0.992213	−	0.124549i	$-0.0397485\pi$
$613$	21.4823	+	21.4823i	0.867664	+	0.867664i	−0.124549	+	0.992213i	$0.539749\pi$
$614$	−2.36847	−	0.488433i	−0.0955837	−	0.0197116i
$615$			27.4251i			1.10589i
$616$	4.41578	+	0.721425i	0.177917	+	0.0290670i
$617$			16.3658i			0.658862i	0.944180	+	0.329431i	$0.106857\pi$
$617$			16.3658i			0.658862i	−0.944180	+	0.329431i	$0.893143\pi$
$618$	−2.74033	+	13.2882i	−0.110232	+	0.534530i
$619$	28.3481	+	28.3481i	1.13941	+	1.13941i	0.988557	+	0.150851i	$0.0482012\pi$
$619$	28.3481	+	28.3481i	1.13941	+	1.13941i	0.150851	+	0.988557i	$0.451799\pi$
$620$	−18.9465	−	47.6218i	−0.760909	−	1.91254i
$621$	4.19810	+	4.19810i	0.168464	+	0.168464i
$622$	31.9478	−	21.0238i	1.28099	−	0.842978i
$623$	17.0696	+	35.5022i	0.683877	+	1.42236i
$624$	−11.8958	−	12.5836i	−0.476211	−	0.503745i
$625$	−117.790			−4.71162
$626$	−3.16870	−	4.81515i	−0.126647	−	0.192452i
$627$	0.571152	+	0.571152i	0.0228096	+	0.0228096i
$628$	−41.1600	+	16.3756i	−1.64246	+	0.653459i
$629$	8.50159	−	8.50159i	0.338981	−	0.338981i
$630$	−16.1155	+	4.02581i	−0.642055	+	0.160392i
$631$	14.8066			0.589443			0.294722	−	0.955583i	$-0.404773\pi$
$631$	14.8066			0.589443			0.294722	+	0.955583i	$0.404773\pi$
$632$	4.14102	+	23.3824i	0.164721	+	0.930103i
$633$	14.3374			0.569862
$634$	−20.1545	−	4.15633i	−0.800438	−	0.165069i
$635$	−49.0746	−	49.0746i	−1.94747	−	1.94747i
$636$	8.79149	−	20.4090i	0.348605	−	0.809269i
$637$	−30.1172	+	3.35518i	−1.19329	+	0.132937i
$638$	−1.07027	+	0.704313i	−0.0423726	+	0.0278840i
$639$			4.30558i			0.170326i
$640$	−49.6829	+	7.36623i	−1.96389	+	0.291176i
$641$	−41.8951			−1.65476			−0.827379	−	0.561644i	$-0.810169\pi$
$641$	−41.8951			−1.65476			−0.827379	+	0.561644i	$0.810169\pi$
$642$	−16.9903	+	11.1808i	−0.670555	+	0.441271i
$643$	22.2070	−	22.2070i	0.875757	−	0.875757i	−0.117335	−	0.993092i	$-0.537435\pi$
$643$	22.2070	−	22.2070i	0.875757	−	0.875757i	0.993092	+	0.117335i	$0.0374352\pi$
$644$	31.3888	−	1.30113i	1.23689	−	0.0512718i
$645$	14.9092	+	14.9092i	0.587051	+	0.587051i
$646$	−0.991203	+	4.80646i	−0.0389984	+	0.189108i
$647$		−	42.6451i		−	1.67655i	−0.545246	−	0.838276i	$-0.683564\pi$
$647$		−	42.6451i		−	1.67655i	0.545246	−	0.838276i	$-0.316436\pi$
$648$	−2.78509	+	0.493238i	−0.109409	+	0.0193762i
$649$	4.76359			0.186987
$650$	−88.1915	−	18.1871i	−3.45915	−	0.713357i
$651$	−14.4123	−	5.05321i	−0.564861	−	0.198051i
$652$	39.5266	−	15.7258i	1.54798	−	0.615868i
$653$	22.0201	−	22.0201i	0.861714	−	0.861714i	−0.129823	−	0.991537i	$-0.541441\pi$
$653$	22.0201	−	22.0201i	0.861714	−	0.861714i	0.991537	+	0.129823i	$0.0414410\pi$
$654$	17.2521	−	11.3530i	0.674610	−	0.443939i
$655$			26.4258i			1.03254i
$656$	16.9754	+	17.9569i	0.662780	+	0.701101i
$657$		−	6.71670i		−	0.262044i
$658$	8.44435	−	14.0682i	0.329195	−	0.548437i
$659$	17.1418	+	17.1418i	0.667749	+	0.667749i	0.957194	−	0.289446i	$-0.0934710\pi$
$659$	17.1418	+	17.1418i	0.667749	+	0.667749i	−0.289446	+	0.957194i	$0.593471\pi$
$660$	4.93263	−	1.96246i	0.192002	−	0.0763888i
$661$	3.64387	−	3.64387i	0.141730	−	0.141730i	−0.632682	−	0.774412i	$-0.718046\pi$
$661$	3.64387	−	3.64387i	0.141730	−	0.141730i	0.774412	+	0.632682i	$0.218046\pi$
$662$	−8.84109	−	1.82323i	−0.343619	−	0.0708620i
$663$			11.1203i			0.431877i
$664$	−14.9974	+	21.4528i	−0.582013	+	0.832528i
$665$	−14.3003	+	6.87565i	−0.554544	+	0.266626i
$666$	6.48284	+	1.33691i	0.251205	+	0.0518042i
$667$	−6.36108	+	6.36108i	−0.246302	+	0.246302i
$668$	17.9177	+	7.71831i	0.693255	+	0.298630i
$669$	−6.30490	+	6.30490i	−0.243761	+	0.243761i
$670$	−36.0086	−	54.7186i	−1.39113	−	2.11397i
$671$	0.297239			0.0114748
$672$	−8.05993	+	12.6110i	−0.310918	+	0.486480i
$673$	24.8436			0.957650			0.478825	−	0.877910i	$-0.341063\pi$
$673$	24.8436			0.957650			0.478825	+	0.877910i	$0.341063\pi$
$674$	3.23528	+	4.91633i	0.124618	+	0.189370i
$675$	−10.4003	+	10.4003i	−0.400307	+	0.400307i
$676$	−10.5451	−	4.54246i	−0.405580	−	0.174710i
$677$	−7.14618	+	7.14618i	−0.274650	+	0.274650i	−0.830969	−	0.556319i	$-0.812213\pi$
$677$	−7.14618	+	7.14618i	−0.274650	+	0.274650i	0.556319	+	0.830969i	$0.312213\pi$
$678$	−1.55976	−	0.321659i	−0.0599024	−	0.0123532i
$679$	−9.21034	+	4.42836i	−0.353461	+	0.169945i
$680$	26.4352	+	18.4806i	1.01374	+	0.708699i
$681$		−	21.7983i		−	0.835311i
$682$	4.78040	+	0.985829i	0.183051	+	0.0377493i
$683$	−3.09491	+	3.09491i	−0.118424	+	0.118424i	−0.763835	−	0.645411i	$-0.776686\pi$
$683$	−3.09491	+	3.09491i	−0.118424	+	0.118424i	0.645411	+	0.763835i	$0.276686\pi$
$684$	−2.51047	+	0.998799i	−0.0959902	+	0.0381900i
$685$	1.55287	+	1.55287i	0.0593321	+	0.0593321i
$686$	9.12229	+	24.5517i	0.348291	+	0.937387i
$687$			13.5205i			0.515838i
$688$	18.9905	+	0.533577i	0.724005	+	0.0203424i
$689$		−	48.1004i		−	1.83248i
$690$	31.1369	−	20.4902i	1.18536	−	0.780049i
$691$	21.8919	−	21.8919i	0.832807	−	0.832807i	−0.155093	−	0.987900i	$-0.549568\pi$
$691$	21.8919	−	21.8919i	0.832807	−	0.832807i	0.987900	+	0.155093i	$0.0495676\pi$
$692$	−8.11399	+	3.22818i	−0.308448	+	0.122717i
$693$	0.523408	−	1.49281i	0.0198826	−	0.0567073i
$694$	−18.3759	−	3.78953i	−0.697539	−	0.143849i
$695$	−15.4758			−0.587031
$696$	−0.747368	−	4.22004i	−0.0283289	−	0.159960i
$697$		−	15.8689i		−	0.601076i
$698$	3.99902	−	19.3917i	0.151365	−	0.733988i
$699$	−10.8617	−	10.8617i	−0.410826	−	0.410826i
$700$	3.22339	+	77.7618i	0.121833	+	2.93912i
$701$	9.94444	−	9.94444i	0.375596	−	0.375596i	−0.493914	−	0.869511i	$-0.664434\pi$
$701$	9.94444	−	9.94444i	0.375596	−	0.375596i	0.869511	+	0.493914i	$0.164434\pi$
$702$	−5.11422	+	3.36550i	−0.193024	+	0.127023i
$703$	6.32306			0.238479
$704$	2.01499	−	4.33812i	0.0759428	−	0.163499i
$705$		−	19.4677i		−	0.733197i
$706$	−5.00065	+	3.29077i	−0.188202	+	0.123850i
$707$	5.76077	+	2.01983i	0.216656	+	0.0759636i
$708$	−6.30391	+	14.6342i	−0.236916	+	0.549987i
$709$	27.3155	+	27.3155i	1.02585	+	1.02585i	0.999657	+	0.0261973i	$0.00833980\pi$
$709$	27.3155	+	27.3155i	1.02585	+	1.02585i	0.0261973	+	0.999657i	$0.491660\pi$
$710$	26.4744	+	5.45963i	0.993567	+	0.204896i
$711$	8.39558			0.314859
$712$	41.4672	−	7.34382i	1.55405	−	0.275221i
$713$	34.2711			1.28346
$714$	9.32481	−	2.32944i	0.348972	−	0.0871770i
$715$	8.12526	−	8.12526i	0.303868	−	0.303868i
$716$	−24.5335	+	9.76074i	−0.916861	+	0.364776i
$717$	−1.84493	−	1.84493i	−0.0689003	−	0.0689003i
$718$	−17.8831	−	27.1752i	−0.667393	−	1.01417i
$719$	−25.6353			−0.956034			−0.478017	−	0.878351i	$-0.658644\pi$
$719$	−25.6353			−0.956034			−0.478017	+	0.878351i	$0.658644\pi$
$720$	−0.498739	+	17.7506i	−0.0185869	+	0.661525i
$721$	22.8763	−	10.9990i	0.851956	−	0.409623i
$722$	20.2899	−	13.3521i	0.755112	−	0.496915i
$723$	14.7083	+	14.7083i	0.547007	+	0.547007i
$724$	5.47679	+	13.7659i	0.203543	+	0.511604i
$725$	−15.7588	−	15.7588i	−0.585267	−	0.585267i
$726$	3.03985	−	14.7406i	0.112819	−	0.547075i
$727$			17.7539i			0.658454i	0.944251	+	0.329227i	$0.106788\pi$
$727$			17.7539i			0.658454i	−0.944251	+	0.329227i	$0.893212\pi$
$728$	−5.22340	+	31.9720i	−0.193592	+	1.18496i
$729$			1.00000i			0.0370370i
$730$	−41.3001	−	8.51703i	−1.52858	−	0.315229i
$731$	−8.62687	−	8.62687i	−0.319076	−	0.319076i
$732$	−0.393353	+	0.913148i	−0.0145387	+	0.0337509i
$733$	27.9290	+	27.9290i	1.03158	+	1.03158i	0.999485	+	0.0320947i	$0.0102178\pi$
$733$	27.9290	+	27.9290i	1.03158	+	1.03158i	0.0320947	+	0.999485i	$0.489782\pi$
$734$	16.4677	+	25.0243i	0.607833	+	0.923663i
$735$	24.2717	+	19.4058i	0.895275	+	0.715795i
$736$	7.70437	−	32.6892i	0.283987	−	1.20494i
$737$	6.23823			0.229788
$738$	7.29807	−	4.80263i	0.268646	−	0.176787i
$739$	4.89433	+	4.89433i	0.180041	+	0.180041i	0.791374	−	0.611333i	$-0.209366\pi$
$739$	4.89433	+	4.89433i	0.180041	+	0.180041i	−0.611333	+	0.791374i	$0.709366\pi$
$740$	16.4410	−	38.1668i	0.604381	−	1.40304i
$741$	−4.13536	+	4.13536i	−0.151916	+	0.151916i
$742$	−40.3341	+	10.0759i	−1.48071	+	0.369897i
$743$	−39.5863			−1.45228			−0.726141	−	0.687546i	$-0.758688\pi$
$743$	−39.5863			−1.45228			−0.726141	+	0.687546i	$0.758688\pi$
$744$	−9.35473	+	13.3813i	−0.342961	+	0.490581i
$745$	−72.6711			−2.66246
$746$	3.11270	−	15.0938i	0.113964	−	0.552625i
$747$	6.54381	+	6.54381i	0.239426	+	0.239426i
$748$	−2.85415	+	1.13553i	−0.104358	+	0.0415191i
$749$	35.9079	+	12.5900i	1.31205	+	0.460028i
$750$	33.5056	+	50.9151i	1.22345	+	1.85916i
$751$		−	35.6555i		−	1.30109i	−0.759468	−	0.650545i	$-0.774541\pi$
$751$		−	35.6555i		−	1.30109i	0.759468	−	0.650545i	$-0.225459\pi$
$752$	−12.0500	−	12.7467i	−0.439419	−	0.464826i
$753$	−4.73624			−0.172598
$754$	−5.09951	−	7.74920i	−0.185713	−	0.282209i
$755$	−7.29898	+	7.29898i	−0.265637	+	0.265637i
$756$	3.89341	+	3.58348i	0.141602	+	0.130330i
$757$	15.1414	+	15.1414i	0.550324	+	0.550324i	0.926534	−	0.376210i	$-0.122773\pi$
$757$	15.1414	+	15.1414i	0.550324	+	0.550324i	−0.376210	+	0.926534i	$0.622773\pi$
$758$	−5.35472	−	1.10427i	−0.194492	−	0.0401087i
$759$			3.54978i			0.128849i
$760$	2.95811	+	16.7031i	0.107302	+	0.605883i
$761$	−4.79478			−0.173811			−0.0869053	−	0.996217i	$-0.527698\pi$
$761$	−4.79478			−0.173811			−0.0869053	+	0.996217i	$0.527698\pi$
$762$	−4.46536	+	21.6531i	−0.161763	+	0.784408i
$763$	−36.4611	−	12.7839i	−1.31998	−	0.462810i
$764$	2.41771	+	1.04147i	0.0874697	+	0.0376789i
$765$	8.06362	−	8.06362i	0.291541	−	0.291541i
$766$	14.3865	+	21.8618i	0.519806	+	0.789897i
$767$			34.4902i			1.24537i
$768$	10.6606	+	11.9311i	0.384681	+	0.430527i
$769$		−	4.32933i		−	0.156120i	−0.996949	−	0.0780598i	$-0.975128\pi$
$769$		−	4.32933i		−	0.156120i	0.996949	−	0.0780598i	$-0.0248725\pi$
$770$	−8.51540	−	5.11130i	−0.306874	−	0.184199i
$771$	−3.08276	−	3.08276i	−0.111023	−	0.111023i
$772$	−9.61556	+	22.3220i	−0.346072	+	0.803388i
$773$	28.7662	−	28.7662i	1.03465	−	1.03465i	0.0352718	−	0.999378i	$-0.488770\pi$
$773$	28.7662	−	28.7662i	1.03465	−	1.03465i	0.999378	−	0.0352718i	$-0.0112297\pi$
$774$	1.35661	−	6.57837i	0.0487624	−	0.236455i
$775$			84.9024i			3.04978i
$776$	1.90521	+	10.7578i	0.0683931	+	0.386184i
$777$	−5.36600	−	11.1605i	−0.192504	−	0.400381i
$778$	7.44481	−	36.1008i	0.266909	−	1.29428i
$779$	5.90123	−	5.90123i	0.211434	−	0.211434i
$780$	14.2090	+	35.7142i	0.508764	+	1.27877i
$781$	−1.82033	+	1.82033i	−0.0651365	+	0.0651365i
$782$	−18.0166	+	11.8562i	−0.644273	+	0.423975i
$783$	−1.51523			−0.0541498
$784$	27.9039	−	2.31734i	0.996569	−	0.0827621i
$785$	98.3280			3.50948
$786$	7.03215	−	4.62764i	0.250829	−	0.165062i
$787$	−20.7135	+	20.7135i	−0.738356	+	0.738356i	−0.972260	−	0.233904i	$-0.924850\pi$
$787$	−20.7135	+	20.7135i	−0.738356	+	0.738356i	0.233904	+	0.972260i	$0.424850\pi$
$788$	−18.3778	+	7.31166i	−0.654682	+	0.260467i
$789$	−7.73059	+	7.73059i	−0.275216	+	0.275216i
$790$	10.6459	−	51.6233i	0.378764	−	1.83667i
$791$	1.29105	+	2.68521i	0.0459046	+	0.0954749i
$792$	−1.38602	−	0.968957i	−0.0492502	−	0.0344304i
$793$			2.15213i			0.0764243i
$794$	3.89894	−	18.9064i	0.138368	−	0.670964i
$795$	−34.8788	+	34.8788i	−1.23702	+	1.23702i
$796$	32.9487	+	14.1932i	1.16784	+	0.503063i
$797$	14.7360	+	14.7360i	0.521977	+	0.521977i	0.918168	−	0.396191i	$-0.129668\pi$
$797$	14.7360	+	14.7360i	0.521977	+	0.521977i	−0.396191	+	0.918168i	$0.629668\pi$
$798$	4.33392	+	2.60141i	0.153419	+	0.0920888i
$799$			11.2645i			0.398510i
$800$	80.9834	+	19.0866i	2.86320	+	0.674814i
$801$		−	14.8890i		−	0.526077i
$802$	3.70340	+	5.62769i	0.130772	+	0.198721i
$803$	2.83971	−	2.83971i	0.100211	−	0.100211i
$804$	−8.25538	+	19.1644i	−0.291145	+	0.675878i
$805$	−65.8057	−	23.0727i	−2.31935	−	0.813206i
$806$	−7.13779	+	34.6120i	−0.251418	+	1.21916i
$807$	5.74718			0.202310
$808$	3.73921	−	5.34867i	0.131545	−	0.188165i
$809$			16.1272i			0.567002i	0.958972	+	0.283501i	$0.0914959\pi$
$809$			16.1272i			0.567002i	−0.958972	+	0.283501i	$0.908504\pi$
$810$	6.14886	+	1.26804i	0.216049	+	0.0445543i
$811$	27.1830	+	27.1830i	0.954525	+	0.954525i	0.999010	−	0.0444849i	$-0.0141646\pi$
$811$	27.1830	+	27.1830i	0.954525	+	0.954525i	−0.0444849	+	0.999010i	$0.514165\pi$
$812$	−5.42979	+	5.89941i	−0.190548	+	0.207029i
$813$	−3.07086	+	3.07086i	−0.107700	+	0.107700i
$814$	2.17561	+	3.30606i	0.0762553	+	0.115877i
$815$	−94.4258			−3.30759
$816$	0.288583	−	10.2709i	0.0101024	−	0.359555i
$817$		−	6.41624i		−	0.224476i
$818$	−8.68535	−	13.1982i	−0.303676	−	0.461466i
$819$	10.8086	+	3.78968i	0.377681	+	0.132422i
$820$	−20.2765	−	50.9648i	−0.708086	−	1.77977i
$821$	−28.4565	−	28.4565i	−0.993140	−	0.993140i	0.00683656	−	0.999977i	$-0.497824\pi$
$821$	−28.4565	−	28.4565i	−0.993140	−	0.993140i	−0.999977	+	0.00683656i	$0.997824\pi$
$822$	0.141297	−	0.685168i	0.00492831	−	0.0238980i
$823$	6.62917			0.231078			0.115539	−	0.993303i	$-0.463140\pi$
$823$	6.62917			0.231078			0.115539	+	0.993303i	$0.463140\pi$
$824$	−4.73208	−	26.7199i	−0.164850	−	0.930830i
$825$	−8.79414			−0.306173
$826$	28.9214	−	7.22488i	1.00631	−	0.251386i
$827$	7.69624	−	7.69624i	0.267625	−	0.267625i	−0.560518	−	0.828142i	$-0.689398\pi$
$827$	7.69624	−	7.69624i	0.267625	−	0.267625i	0.828142	+	0.560518i	$0.189398\pi$
$828$	−10.9053	−	4.69762i	−0.378984	−	0.163253i
$829$	−12.2451	−	12.2451i	−0.425288	−	0.425288i	0.461731	−	0.887020i	$-0.347228\pi$
$829$	−12.2451	−	12.2451i	−0.425288	−	0.425288i	−0.887020	+	0.461731i	$0.847228\pi$
$830$	48.5348	−	31.9392i	1.68467	−	1.10863i
$831$	6.81142			0.236285
$832$	31.4097	+	14.5893i	1.08894	+	0.505794i
$833$	−14.0442	−	11.2287i	−0.486604	−	0.389052i
$834$	2.71010	+	4.11826i	0.0938430	+	0.142604i
$835$	−30.6212	−	30.6212i	−1.05969	−	1.05969i
$836$	−1.48366	−	0.639110i	−0.0513135	−	0.0221041i
$837$	4.08174	+	4.08174i	0.141085	+	0.141085i
$838$	9.79176	+	2.01929i	0.338251	+	0.0697551i
$839$			32.2896i			1.11476i	0.830258	+	0.557380i	$0.188193\pi$
$839$			32.2896i			1.11476i	−0.830258	+	0.557380i	$0.811807\pi$
$840$	26.9713	−	19.3961i	0.930599	−	0.669228i
$841$			26.7041i			0.920831i
$842$	−11.3239	+	54.9111i	−0.390249	+	1.89236i
$843$	−2.98977	−	2.98977i	−0.102973	−	0.102973i
$844$	−26.6436	+	10.6003i	−0.917112	+	0.364876i
$845$	18.0215	+	18.0215i	0.619957	+	0.619957i
$846$	−5.18054	+	3.40915i	−0.178111	+	0.117209i
$847$	−25.3766	+	12.2012i	−0.871951	+	0.419237i
$848$	−1.24825	+	44.4265i	−0.0428652	+	1.52561i
$849$	6.49520			0.222915
$850$	−29.3722	−	44.6339i	−1.00746	−	1.53093i
$851$	19.6493	+	19.6493i	0.673569	+	0.673569i
$852$	−3.18329	−	8.00117i	−0.109058	−	0.274116i
$853$	−14.5661	+	14.5661i	−0.498733	+	0.498733i	−0.911043	−	0.412310i	$-0.864722\pi$
$853$	−14.5661	+	14.5661i	−0.498733	+	0.498733i	0.412310	+	0.911043i	$0.364722\pi$
$854$	1.80464	−	0.450819i	0.0617537	−	0.0154267i
$855$	5.99732			0.205104
$856$	23.3071	−	33.3392i	0.796622	−	1.13951i
$857$	−14.4706			−0.494307			−0.247153	−	0.968976i	$-0.579495\pi$
$857$	−14.4706			−0.494307			−0.247153	+	0.968976i	$0.579495\pi$
$858$	−3.58509	−	0.739328i	−0.122393	−	0.0252402i
$859$	−11.7304	−	11.7304i	−0.400236	−	0.400236i	0.478080	−	0.878316i	$-0.341333\pi$
$859$	−11.7304	−	11.7304i	−0.400236	−	0.400236i	−0.878316	+	0.478080i	$0.841333\pi$
$860$	−38.7293	−	16.6832i	−1.32066	−	0.568893i
$861$	−15.4240	−	5.40794i	−0.525648	−	0.184302i
$862$	−46.7894	+	30.7906i	−1.59365	+	1.04873i
$863$		−	36.3253i		−	1.23653i	−0.785971	−	0.618264i	$-0.787836\pi$
$863$		−	36.3253i		−	1.23653i	0.785971	−	0.618264i	$-0.212164\pi$
$864$	4.81093	−	2.97573i	0.163671	−	0.101236i
$865$	19.3837			0.659065
$866$	−44.8749	+	29.5308i	−1.52491	+	1.00350i
$867$	7.35500	−	7.35500i	0.249789	−	0.249789i
$868$	30.5187	−	1.26507i	1.03587	−	0.0429392i
$869$	3.54951	+	3.54951i	0.120409	+	0.120409i
$870$	−1.92136	+	9.31693i	−0.0651404	+	0.315873i
$871$			45.1672i			1.53043i
$872$	−23.6662	+	33.8528i	−0.801439	+	1.14640i
$873$	3.86266			0.130731
$874$	−11.1089	−	2.29092i	−0.375765	−	0.0774915i
$875$	37.7285	−	107.606i	1.27546	−	3.63773i
$876$	4.96593	+	12.4818i	0.167783	+	0.421722i
$877$	14.8508	−	14.8508i	0.501477	−	0.501477i	−0.410420	−	0.911897i	$-0.634618\pi$
$877$	14.8508	−	14.8508i	0.501477	−	0.501477i	0.911897	+	0.410420i	$0.134618\pi$
$878$	−11.1055	+	7.30818i	−0.374793	+	0.246639i
$879$			15.5652i			0.525000i
$880$	−7.71551	+	7.29379i	−0.260090	+	0.245874i
$881$			24.9375i			0.840166i	0.907486	+	0.420083i	$0.137999\pi$
$881$			24.9375i			0.840166i	−0.907486	+	0.420083i	$0.862001\pi$
$882$	0.913663	−	9.85724i	0.0307646	−	0.331911i
$883$	−12.3198	−	12.3198i	−0.414595	−	0.414595i	0.468741	−	0.883336i	$-0.344708\pi$
$883$	−12.3198	−	12.3198i	−0.414595	−	0.414595i	−0.883336	+	0.468741i	$0.844708\pi$
$884$	−8.22170	−	20.6652i	−0.276526	−	0.695044i
$885$	25.0098	−	25.0098i	0.840694	−	0.840694i
$886$	29.6190	+	6.10811i	0.995068	+	0.205206i
$887$		−	31.2525i		−	1.04936i	−0.851301	−	0.524678i	$-0.824186\pi$
$887$		−	31.2525i		−	1.04936i	0.851301	−	0.524678i	$-0.175814\pi$
$888$	−13.0357	+	2.30861i	−0.437448	+	0.0774719i
$889$	37.2768	−	17.9228i	1.25022	−	0.601111i
$890$	−91.5504	−	18.8798i	−3.06877	−	0.632852i
$891$	−0.422784	+	0.422784i	−0.0141638	+	0.0141638i
$892$	7.05508	−	16.3780i	0.236222	−	0.548377i
$893$	−4.18899	+	4.18899i	−0.140179	+	0.140179i
$894$	12.7260	+	19.3384i	0.425622	+	0.646774i
$895$	58.6087			1.95907
$896$	5.65414	−	29.3944i	0.188891	−	0.981998i
$897$	−25.7018			−0.858158
$898$	29.3602	+	44.6157i	0.979763	+	1.48885i
$899$	−6.18476	+	6.18476i	−0.206273	+	0.206273i
$900$	11.6378	−	27.0165i	0.387925	−	0.900548i
$901$	20.1818	−	20.1818i	0.672353	−	0.672353i
$902$	5.11598	+	1.05503i	0.170344	+	0.0351288i
$903$	−11.3250	+	5.44508i	−0.376871	+	0.181201i
$904$	3.13637	−	0.555450i	0.104314	−	0.0184740i
$905$		−	32.8856i		−	1.09315i
$906$	3.22051	+	0.664143i	0.106994	+	0.0220647i
$907$	13.1808	−	13.1808i	0.437663	−	0.437663i	−0.453562	−	0.891225i	$-0.649847\pi$
$907$	13.1808	−	13.1808i	0.437663	−	0.437663i	0.891225	+	0.453562i	$0.149847\pi$
$908$	16.1163	+	40.5083i	0.534840	+	1.34431i
$909$	−1.63152	−	1.63152i	−0.0541142	−	0.0541142i
$910$	37.0079	−	61.6548i	1.22680	−	2.04384i
$911$		−	23.9885i		−	0.794773i	−0.917651	−	0.397387i	$-0.869917\pi$
$911$		−	23.9885i		−	0.794773i	0.917651	−	0.397387i	$-0.130083\pi$
$912$	3.92682	−	3.71219i	0.130030	−	0.122923i
$913$			5.53324i			0.183123i
$914$	−24.3740	+	16.0398i	−0.806221	+	0.530548i
$915$	1.56056	−	1.56056i	0.0515906	−	0.0515906i
$916$	−9.99624	−	25.1254i	−0.330285	−	0.830168i
$917$	−14.8620	−	5.21089i	−0.490786	−	0.172079i
$918$	−3.55789	−	0.733718i	−0.117428	−	0.0242163i
$919$	−10.4093			−0.343373			−0.171686	−	0.985152i	$-0.554922\pi$
$919$	−10.4093			−0.343373			−0.171686	+	0.985152i	$0.554922\pi$
$920$	−42.7133	+	61.0983i	−1.40822	+	2.01435i
$921$		−	1.71000i		−	0.0563465i
$922$	−3.07189	+	14.8960i	−0.101167	+	0.490572i
$923$	−13.1799	−	13.1799i	−0.433822	−	0.433822i
$924$	0.131035	+	3.16111i	0.00431073	+	0.103993i
$925$	−48.6787	+	48.6787i	−1.60055	+	1.60055i
$926$	−4.09412	+	2.69421i	−0.134541	+	0.0885372i
$927$	−9.59390			−0.315105
$928$	4.50890	+	7.28966i	0.148012	+	0.239295i
$929$		−	30.0238i		−	0.985050i	−0.870298	−	0.492525i	$-0.836074\pi$
$929$		−	30.0238i		−	0.985050i	0.870298	−	0.492525i	$-0.163926\pi$
$930$	30.2738	−	19.9222i	0.992718	−	0.653276i
$931$	−1.04702	−	9.39838i	−0.0343146	−	0.308019i
$932$	28.2150	+	12.1540i	0.924213	+	0.398119i
$933$	19.1224	+	19.1224i	0.626038	+	0.626038i
$934$	24.1802	+	4.98652i	0.791201	+	0.163164i
$935$	6.81833			0.222983
$936$	7.01563	−	10.0354i	0.229313	−	0.328016i
$937$	32.6745			1.06743			0.533714	−	0.845665i	$-0.320796\pi$
$937$	32.6745			1.06743			0.533714	+	0.845665i	$0.320796\pi$
$938$	37.8745	−	9.46145i	1.23665	−	0.308927i
$939$	2.88211	−	2.88211i	0.0940542	−	0.0940542i
$940$	14.3933	+	36.1774i	0.469457	+	1.17998i
$941$	6.54400	+	6.54400i	0.213328	+	0.213328i	0.805680	−	0.592351i	$-0.201800\pi$
$941$	6.54400	+	6.54400i	0.213328	+	0.213328i	−0.592351	+	0.805680i	$0.701800\pi$
$942$	−17.2190	−	26.1660i	−0.561026	−	0.852534i
$943$	36.6769			1.19436
$944$	0.895056	−	31.8559i	0.0291316	−	1.03682i
$945$	−5.08956	−	10.5855i	−0.165563	−	0.344348i
$946$	3.35478	−	2.20767i	0.109073	−	0.0717777i
$947$	28.9233	+	28.9233i	0.939879	+	0.939879i	0.998292	−	0.0584131i	$-0.0186041\pi$
$947$	28.9233	+	28.9233i	0.939879	+	0.939879i	−0.0584131	+	0.998292i	$0.518604\pi$
$948$	−15.6017	+	6.20719i	−0.506720	+	0.201600i
$949$	20.5606	+	20.5606i	0.667427	+	0.667427i
$950$	5.67546	−	27.5210i	0.184136	−	0.892899i
$951$		−	14.5513i		−	0.471858i
$952$	−15.6063	+	11.2231i	−0.505803	+	0.363742i
$953$		−	20.7126i		−	0.670948i	−0.942049	−	0.335474i	$-0.891104\pi$
$953$		−	20.7126i		−	0.670948i	0.942049	−	0.335474i	$-0.108896\pi$
$954$	15.3895	+	3.17367i	0.498253	+	0.102751i
$955$	−4.13185	−	4.13185i	−0.133704	−	0.133704i
$956$	4.79252	+	2.06445i	0.155001	+	0.0667692i
$957$	−0.640614	−	0.640614i	−0.0207081	−	0.0207081i
$958$	18.9925	+	28.8610i	0.613620	+	0.932456i
$959$	−1.17955	+	0.567130i	−0.0380896	+	0.0183136i
$960$	−12.1969	−	33.3551i	−0.393653	−	1.07653i
$961$	2.32116			0.0748761
$962$	−23.9372	+	15.7523i	−0.771766	+	0.507875i
$963$	−10.1696	−	10.1696i	−0.327710	−	0.327710i
$964$	−38.2072	−	16.4584i	−1.23057	−	0.530088i
$965$	38.1482	−	38.1482i	1.22803	−	1.22803i
$966$	5.38391	+	21.5520i	0.173225	+	0.693423i
$967$	−20.3296			−0.653757			−0.326879	−	0.945066i	$-0.605997\pi$
$967$	−20.3296			−0.653757			−0.326879	+	0.945066i	$0.605997\pi$
$968$	5.24929	+	29.6403i	0.168719	+	0.952676i
$969$	−3.47020			−0.111479
$970$	4.89799	−	23.7509i	0.157265	−	0.762597i
$971$	26.0614	+	26.0614i	0.836352	+	0.836352i	0.988377	−	0.152025i	$-0.0485794\pi$
$971$	26.0614	+	26.0614i	0.836352	+	0.836352i	−0.152025	+	0.988377i	$0.548579\pi$
$972$	−0.739341	−	1.85833i	−0.0237144	−	0.0596058i
$973$	3.05167	−	8.70366i	0.0978319	−	0.279027i
$974$	−28.2124	−	42.8715i	−0.903982	−	1.37369i
$975$		−	63.6730i		−	2.03917i
$976$	0.0558499	−	1.98775i	0.00178771	−	0.0636263i
$977$	−26.1606			−0.836951			−0.418475	−	0.908228i	$-0.637435\pi$
$977$	−26.1606			−0.836951			−0.418475	+	0.908228i	$0.637435\pi$
$978$	16.5357	+	25.1276i	0.528752	+	0.803492i
$979$	6.29482	−	6.29482i	0.201183	−	0.201183i
$980$	−59.4523	−	18.1173i	−1.89913	−	0.578737i
$981$	10.3263	+	10.3263i	0.329692	+	0.329692i
$982$	5.43894	+	1.12163i	0.173563	+	0.0357928i
$983$		−	45.5195i		−	1.45185i	−0.687776	−	0.725923i	$-0.741413\pi$
$983$		−	45.5195i		−	1.45185i	0.687776	−	0.725923i	$-0.258587\pi$
$984$	−10.0114	+	14.3206i	−0.319152	+	0.456525i
$985$	43.9031			1.39887
$986$	1.11175	−	5.39101i	0.0354054	−	0.171685i
$987$	10.9487	+	3.83882i	0.348502	+	0.122191i
$988$	4.62741	−	10.7423i	0.147218	−	0.341758i
$989$	19.9389	−	19.9389i	0.634019	−	0.634019i
$990$	2.06353	+	3.13574i	0.0655834	+	0.0996605i
$991$			1.70803i			0.0542572i	0.999632	+	0.0271286i	$0.00863637\pi$
$991$			1.70803i			0.0542572i	−0.999632	+	0.0271286i	$0.991364\pi$
$992$	7.49082	−	31.7831i	0.237834	−	1.00911i
$993$		−	6.38314i		−	0.202563i
$994$	−8.29099	+	13.8127i	−0.262974	+	0.438113i
$995$	−56.3091	−	56.3091i	−1.78512	−	1.78512i
$996$	−16.9986	−	7.32243i	−0.538623	−	0.232020i
$997$	−25.4084	+	25.4084i	−0.804691	+	0.804691i	−0.983825	−	0.179134i	$-0.942670\pi$
$997$	−25.4084	+	25.4084i	−0.804691	+	0.804691i	0.179134	+	0.983825i	$0.442670\pi$
$998$	4.79946	−	23.2731i	0.151924	−	0.736699i
$999$			4.68052i			0.148085i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.u.a.139.10	yes	64
4.3	odd	2		1344.2.u.a.1231.1		64
7.6	odd	2	inner	336.2.u.a.139.9	✓	64
16.3	odd	4	inner	336.2.u.a.307.9	yes	64
16.13	even	4		1344.2.u.a.559.32		64
28.27	even	2		1344.2.u.a.1231.32		64
112.13	odd	4		1344.2.u.a.559.1		64
112.83	even	4	inner	336.2.u.a.307.10	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.u.a.139.9	✓	64	7.6	odd	2	inner
336.2.u.a.139.10	yes	64	1.1	even	1	trivial
336.2.u.a.307.9	yes	64	16.3	odd	4	inner
336.2.u.a.307.10	yes	64	112.83	even	4	inner
1344.2.u.a.559.1		64	112.13	odd	4
1344.2.u.a.559.32		64	16.13	even	4
1344.2.u.a.1231.1		64	4.3	odd	2
1344.2.u.a.1231.32		64	28.27	even	2

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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	336.u (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.777418 - 1.18136i) q^{2} +(0.707107 - 0.707107i) q^{3} +(-0.791242 + 1.83683i) q^{4} +(3.13913 - 3.13913i) q^{5} +(-1.38507 - 0.285633i) q^{6} +(1.14645 + 2.38446i) q^{7} +(2.78509 - 0.493238i) q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+(-0.777418 - 1.18136i) q^{2} +(0.707107 - 0.707107i) q^{3} +(-0.791242 + 1.83683i) q^{4} +(3.13913 - 3.13913i) q^{5} +(-1.38507 - 0.285633i) q^{6} +(1.14645 + 2.38446i) q^{7} +(2.78509 - 0.493238i) q^{8} -1.00000i q^{9} +(-6.14886 - 1.26804i) q^{10} +(0.422784 - 0.422784i) q^{11} +(0.739341 + 1.85833i) q^{12} +(3.06112 + 3.06112i) q^{13} +(1.92564 - 3.20810i) q^{14} -4.43939i q^{15} +(-2.74787 - 2.90675i) q^{16} +2.56875i q^{17} +(-1.18136 + 0.777418i) q^{18} +(-0.955253 + 0.955253i) q^{19} +(3.28222 + 8.24984i) q^{20} +(2.49673 + 0.875401i) q^{21} +(-0.828141 - 0.170782i) q^{22} -5.93702 q^{23} +(1.62058 - 2.31813i) q^{24} -14.7082i q^{25} +(1.23653 - 5.99607i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(-5.28696 + 0.219156i) q^{28} +(1.07143 - 1.07143i) q^{29} +(-5.24454 + 3.45127i) q^{30} -5.77245 q^{31} +(-1.29768 + 5.50600i) q^{32} -0.597907i q^{33} +(3.03462 - 1.99699i) q^{34} +(11.0840 + 3.88625i) q^{35} +(1.83683 + 0.791242i) q^{36} +(-3.30963 - 3.30963i) q^{37} +(1.87113 + 0.385870i) q^{38} +4.32908 q^{39} +(7.19440 - 10.2911i) q^{40} -6.17767 q^{41} +(-0.906838 - 3.63010i) q^{42} +(-3.35840 + 3.35840i) q^{43} +(0.442057 + 1.11111i) q^{44} +(-3.13913 - 3.13913i) q^{45} +(4.61554 + 7.01378i) q^{46} +4.38522 q^{47} +(-3.99842 - 0.112344i) q^{48} +(-4.37128 + 5.46735i) q^{49} +(-17.3758 + 11.4344i) q^{50} +(1.81638 + 1.81638i) q^{51} +(-8.04484 + 3.20066i) q^{52} +(-7.85667 - 7.85667i) q^{53} +(-0.285633 + 1.38507i) q^{54} -2.65434i q^{55} +(4.36908 + 6.07545i) q^{56} +1.35093i q^{57} +(-2.09869 - 0.432799i) q^{58} +(5.63360 + 5.63360i) q^{59} +(8.15440 + 3.51263i) q^{60} +(0.351526 + 0.351526i) q^{61} +(4.48761 + 6.81936i) q^{62} +(2.38446 - 1.14645i) q^{63} +(7.51343 - 2.74742i) q^{64} +19.2185 q^{65} +(-0.706345 + 0.464823i) q^{66} +(7.37756 + 7.37756i) q^{67} +(-4.71835 - 2.03250i) q^{68} +(-4.19810 + 4.19810i) q^{69} +(-4.02581 - 16.1155i) q^{70} -4.30558 q^{71} +(-0.493238 - 2.78509i) q^{72} +6.71670 q^{73} +(-1.33691 + 6.48284i) q^{74} +(-10.4003 - 10.4003i) q^{75} +(-0.998799 - 2.51047i) q^{76} +(1.49281 + 0.523408i) q^{77} +(-3.36550 - 5.11422i) q^{78} +8.39558i q^{79} +(-17.7506 - 0.498739i) q^{80} -1.00000 q^{81} +(4.80263 + 7.29807i) q^{82} +(-6.54381 + 6.54381i) q^{83} +(-3.58348 + 3.89341i) q^{84} +(8.06362 + 8.06362i) q^{85} +(6.57837 + 1.35661i) q^{86} -1.51523i q^{87} +(0.968957 - 1.38602i) q^{88} +14.8890 q^{89} +(-1.26804 + 6.14886i) q^{90} +(-3.78968 + 10.8086i) q^{91} +(4.69762 - 10.9053i) q^{92} +(-4.08174 + 4.08174i) q^{93} +(-3.40915 - 5.18054i) q^{94} +5.99732i q^{95} +(2.97573 + 4.81093i) q^{96} +3.86266i q^{97} +(9.85724 + 0.913663i) q^{98} +(-0.422784 - 0.422784i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 4 q^{4} + 24 q^{8}+O(q^{10}) \) 64 * q - 4 * q^4 + 24 * q^8	\( 64 q - 4 q^{4} + 24 q^{8} + 8 q^{11} - 16 q^{14} + 4 q^{16} - 4 q^{18} - 28 q^{22} - 16 q^{23} + 32 q^{28} + 16 q^{29} + 24 q^{35} + 16 q^{37} + 20 q^{42} - 8 q^{43} - 36 q^{44} - 40 q^{46} - 52 q^{50} + 16 q^{53} - 28 q^{56} - 92 q^{58} + 24 q^{60} - 52 q^{64} + 56 q^{67} - 40 q^{70} - 128 q^{71} + 4 q^{72} - 60 q^{74} - 64 q^{81} - 24 q^{84} + 92 q^{86} - 84 q^{88} + 8 q^{91} + 136 q^{92} - 64 q^{98} - 8 q^{99}+O(q^{100}) \) 64 * q - 4 * q^4 + 24 * q^8 + 8 * q^11 - 16 * q^14 + 4 * q^16 - 4 * q^18 - 28 * q^22 - 16 * q^23 + 32 * q^28 + 16 * q^29 + 24 * q^35 + 16 * q^37 + 20 * q^42 - 8 * q^43 - 36 * q^44 - 40 * q^46 - 52 * q^50 + 16 * q^53 - 28 * q^56 - 92 * q^58 + 24 * q^60 - 52 * q^64 + 56 * q^67 - 40 * q^70 - 128 * q^71 + 4 * q^72 - 60 * q^74 - 64 * q^81 - 24 * q^84 + 92 * q^86 - 84 * q^88 + 8 * q^91 + 136 * q^92 - 64 * q^98 - 8 * q^99

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