LMFDB - Embedded newform 336.2.u.a.139.9

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			139.9
Character	$\chi$	$=$	336.139
Dual form			336.2.u.a.307.9

$q$-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} +(-3.70819 + 0.499341i) 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} +(0.875401 + 2.49673i) 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} +(3.47272 + 3.99252i) 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} +(3.88625 + 11.0840i) 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} +(2.26900 - 2.97517i) 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} +(2.01687 - 7.20640i) 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} +(10.0730 - 13.2080i) 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} +(-0.523408 - 1.49281i) 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} +(-5.27872 - 0.367559i) 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} +(-10.8086 + 3.78968i) 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} +(-3.06061 + 9.41449i) 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	$0.711458\pi$
$5$	−3.13913	+	3.13913i	−1.40386	+	1.40386i	−0.787339	+	0.616521i	$0.788542\pi$
$6$	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	0.141007	−	0.990009i	$-0.454966\pi$
$13$	−3.06112	−	3.06112i	−0.849002	−	0.849002i	−0.990009	+	0.141007i	$0.954966\pi$
$14$	−3.70819	+	0.499341i	−0.991055	+	0.133454i
$15$		−	4.43939i		−	1.14625i
$16$	−2.74787	−	2.90675i	−0.686968	−	0.726688i
$17$		−	2.56875i		−	0.623013i	−0.950244	−	0.311506i	$-0.899166\pi$
$17$		−	2.56875i		−	0.623013i	0.950244	−	0.311506i	$-0.100834\pi$
$18$	−1.18136	+	0.777418i	−0.278450	+	0.183239i
$19$	0.955253	−	0.955253i	0.219150	−	0.219150i	−0.588990	−	0.808140i	$-0.700474\pi$
$19$	0.955253	−	0.955253i	0.219150	−	0.219150i	0.808140	+	0.588990i	$0.200474\pi$
$20$	−3.28222	−	8.24984i	−0.733928	−	1.84472i
$21$	0.875401	+	2.49673i	0.191028	+	0.544832i
$22$	−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
$28$	3.47272	+	3.99252i	0.656282	+	0.754516i
$29$	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	$-0.326535\pi$
$31$	5.77245			1.03676			0.518381	+	0.855150i	$0.326535\pi$
$32$	−1.29768	+	5.50600i	−0.229400	+	0.973332i
$33$			0.597907i			0.104082i
$34$	−3.03462	+	1.99699i	−0.520434	+	0.342481i
$35$	3.88625	+	11.0840i	0.656896	+	1.87353i
$36$	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	$-0.339767\pi$
$41$	6.17767			0.964790			0.482395	+	0.875954i	$0.339767\pi$
$42$	2.26900	−	2.97517i	0.350114	−	0.459079i
$43$	−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	$-0.603624\pi$
$47$	−4.38522			−0.639650			−0.319825	+	0.947477i	$0.603624\pi$
$48$	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
$56$	2.01687	−	7.20640i	0.269516	−	0.962996i
$57$			1.35093i			0.178935i
$58$	−2.09869	−	0.432799i	−0.275572	−	0.0568293i
$59$	−5.63360	−	5.63360i	−0.733432	−	0.733432i	0.237866	−	0.971298i	$-0.423552\pi$
$59$	−5.63360	−	5.63360i	−0.733432	−	0.733432i	−0.971298	+	0.237866i	$0.923552\pi$
$60$	8.15440	+	3.51263i	1.05273	+	0.453479i
$61$	−0.351526	−	0.351526i	−0.0450083	−	0.0450083i	0.684244	−	0.729253i	$-0.260132\pi$
$61$	−0.351526	−	0.351526i	−0.0450083	−	0.0450083i	−0.729253	+	0.684244i	$0.760132\pi$
$62$	−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
$70$	10.0730	−	13.2080i	1.20395	−	1.57865i
$71$	−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	$-0.628585\pi$
$73$	−6.71670			−0.786131			−0.393065	+	0.919511i	$0.628585\pi$
$74$	−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
$77$	−0.523408	−	1.49281i	−0.0596479	−	0.170122i
$78$	−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	−0.249975	−	0.968252i	$-0.580423\pi$
$83$	6.54381	−	6.54381i	0.718277	−	0.718277i	0.968252	+	0.249975i	$0.0804225\pi$
$84$	−5.27872	−	0.367559i	−0.575956	−	0.0401040i
$85$	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	$-0.789460\pi$
$89$	−14.8890			−1.57823			−0.789115	+	0.614246i	$0.789460\pi$
$90$	1.26804	−	6.14886i	0.133663	−	0.648147i
$91$	−10.8086	+	3.78968i	−1.13304	+	0.397266i
$92$	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	$-0.937173\pi$
$97$		−	3.86266i		−	0.392193i	0.980585	−	0.196097i	$-0.0628266\pi$
$98$	−3.06061	+	9.41449i	−0.309168	+	0.951007i
$99$	−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	−0.783604	−	0.621261i	$-0.786621\pi$
$101$	−1.63152	+	1.63152i	−0.162343	+	0.162343i	0.621261	+	0.783604i	$0.286621\pi$
$102$	0.733718	−	3.55789i	0.0726490	−	0.352284i
$103$			9.59390i			0.945315i	0.881246	+	0.472657i	$0.156705\pi$
$103$			9.59390i			0.945315i	−0.881246	+	0.472657i	$0.843295\pi$
$104$	−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
$112$	−10.0813	+	3.21973i	−0.952597	+	0.304236i
$113$	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
$126$	0.499341	+	3.70819i	0.0444848	+	0.330352i
$127$		−	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	−0.498905	−	0.866656i	$-0.666264\pi$
$131$	4.20910	−	4.20910i	0.367751	−	0.367751i	0.866656	+	0.498905i	$0.166264\pi$
$132$	−1.09825	−	0.473089i	−0.0955905	−	0.0411771i
$133$	−1.18261	−	3.37291i	−0.102545	−	0.292469i
$134$	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	0.803875	−	0.594798i	$-0.202768\pi$
$139$	2.46499	+	2.46499i	0.209078	+	0.209078i	−0.594798	+	0.803875i	$0.702768\pi$
$140$	−23.4343	−	1.63174i	−1.98056	−	0.137907i
$141$	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
$147$	6.95696	+	0.775034i	0.573801	+	0.0639237i
$148$	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
$154$	−1.35665	+	1.77887i	−0.109322	+	0.143346i
$155$	−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	$-0.904949\pi$
$157$	−15.6617	−	15.6617i	−1.24994	−	1.24994i	−0.294192	−	0.955746i	$-0.595051\pi$
$158$	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	$0.123189\pi$
$167$			9.75468i			0.754840i	−0.926042	+	0.377420i	$0.876811\pi$
$168$	3.66955	+	6.52184i	0.283112	+	0.503171i
$169$			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	0.579932	−	0.814665i	$-0.303079\pi$
$173$	−3.08743	−	3.08743i	−0.234733	−	0.234733i	−0.814665	+	0.579932i	$0.803079\pi$
$174$	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	−0.874451	−	0.485113i	$-0.838778\pi$
$181$	−5.23801	+	5.23801i	−0.389339	+	0.389339i	0.485113	+	0.874451i	$0.338778\pi$
$182$	12.8798	+	9.82267i	0.954711	+	0.728105i
$183$	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
$189$	2.49673	−	0.875401i	0.181611	−	0.0636760i
$190$	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
$196$	13.5013	−	3.70330i	0.964380	−	0.264521i
$197$	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	$0.219325\pi$
$199$			17.9378i			1.27158i	−0.771862	+	0.635790i	$0.780675\pi$
$200$	−7.25466	−	40.9637i	−0.512982	−	2.89657i
$201$	−10.4334			−0.735919
$202$	3.19580	+	0.659047i	0.224856	+	0.0463704i
$203$	−1.32643	−	3.78312i	−0.0930973	−	0.265523i
$204$	−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
$210$	2.21677	+	16.4621i	0.152972	+	1.13599i
$211$	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	$-0.403499\pi$
$223$	8.91647			0.597091			0.298545	+	0.954395i	$0.403499\pi$
$224$	11.6411	+	9.40665i	0.777803	+	0.628508i
$225$	−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	$0.507422\pi$
$227$	−15.4137	+	15.4137i	−1.02304	+	1.02304i	−0.999728	+	0.0233148i	$0.992578\pi$
$228$	−2.48143	−	1.06891i	−0.164337	−	0.0707905i
$229$	9.56042	−	9.56042i	0.631770	−	0.631770i	−0.316742	−	0.948512i	$-0.602589\pi$
$229$	9.56042	−	9.56042i	0.631770	−	0.631770i	0.948512	+	0.316742i	$0.102589\pi$
$230$	−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
$238$	1.28268	+	9.52540i	0.0831438	+	0.617440i
$239$		−	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	$-0.766318\pi$
$241$		−	20.8007i		−	1.33989i	0.742411	−	0.669944i	$-0.233682\pi$
$242$	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
$245$	30.8847	+	3.44068i	1.97315	+	0.219817i
$246$	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	0.804857	−	0.593469i	$-0.202242\pi$
$251$	3.34903	+	3.34903i	0.211389	+	0.211389i	−0.593469	+	0.804857i	$0.702242\pi$
$252$	3.99252	−	3.47272i	0.251505	−	0.218761i
$253$	−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	$0.0434166\pi$
$257$			4.35968i			0.271949i	−0.990712	+	0.135975i	$0.956583\pi$
$258$	−5.61088	+	3.69234i	−0.349318	+	0.229875i
$259$	−11.6860	+	4.09733i	−0.726133	+	0.254596i
$260$	−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
$266$	−3.06526	+	4.01925i	−0.187943	+	0.246436i
$267$	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	0.572280	−	0.820058i	$-0.306059\pi$
$269$	−4.06387	−	4.06387i	−0.247779	−	0.247779i	−0.820058	+	0.572280i	$0.806059\pi$
$270$	3.45127	+	5.24454i	0.210037	+	0.319173i
$271$	4.34285			0.263810			0.131905	−	0.991262i	$-0.457891\pi$
$271$	4.34285			0.263810			0.131905	+	0.991262i	$0.457891\pi$
$272$	−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
$280$	16.2906	+	28.9530i	0.973549	+	1.73027i
$281$		−	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	0.557298	−	0.830312i	$-0.311838\pi$
$283$	−4.59280	−	4.59280i	−0.273014	−	0.273014i	−0.830312	+	0.557298i	$0.811838\pi$
$284$	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	−0.308299	−	0.951290i	$-0.599760\pi$
$293$	11.0062	−	11.0062i	0.642991	−	0.642991i	0.951290	+	0.308299i	$0.0997596\pi$
$294$	−4.49287	−	8.82123i	−0.262030	−	0.514465i
$295$	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
$301$	4.15771	+	11.8582i	0.239646	+	0.683496i
$302$	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	−0.740769	−	0.671759i	$-0.765539\pi$
$307$	−1.20915	+	1.20915i	−0.0690101	+	0.0690101i	0.671759	+	0.740769i	$0.265539\pi$
$308$	3.15618	+	0.219766i	0.179840	+	0.0125223i
$309$	−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	$-0.721879\pi$
$311$		−	27.0431i		−	1.53347i	0.641961	−	0.766737i	$-0.278121\pi$
$312$	12.0569	−	2.13527i	0.682586	−	0.120886i
$313$	−4.07592			−0.230385			−0.115192	−	0.993343i	$-0.536748\pi$
$313$	−4.07592			−0.230385			−0.115192	+	0.993343i	$0.536748\pi$
$314$	−6.32647	+	30.6778i	−0.357023	+	1.73125i
$315$	11.0840	−	3.88625i	0.624511	−	0.218965i
$316$	−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
$322$	22.0156	−	2.96459i	1.22688	−	0.165210i
$323$	−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
$336$	4.85189	−	9.40527i	0.264692	−	0.513100i
$337$	−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	0.390622	−	0.920551i	$-0.372260\pi$
$349$	−9.89989	−	9.89989i	−0.529929	−	0.529929i	−0.920551	+	0.390622i	$0.872260\pi$
$350$	7.34441	+	54.5408i	0.392575	+	2.91533i
$351$		−	4.32908i		−	0.231069i
$352$	1.77921	+	2.87649i	0.0948320	+	0.153317i
$353$			4.23294i			0.225297i	0.993635	+	0.112648i	$0.0359334\pi$
$353$			4.23294i			0.225297i	−0.993635	+	0.112648i	$0.964067\pi$
$354$	−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
$357$	6.41347	−	2.24868i	0.339437	−	0.119013i
$358$	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
$364$	1.59119	−	22.8520i	0.0834011	−	1.19777i
$365$	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	$-0.313537\pi$
$367$	21.1825			1.10572			0.552859	+	0.833275i	$0.313537\pi$
$368$	16.3142	+	17.2574i	0.850434	+	0.899605i
$369$		−	6.17767i		−	0.321597i
$370$	−16.1537	−	24.5472i	−0.839791	−	1.27615i
$371$	−27.7412	+	9.72658i	−1.44025	+	0.504979i
$372$	−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
$378$	−2.97517	−	2.26900i	−0.153026	−	0.116705i
$379$	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	$-0.343246\pi$
$383$	18.5055			0.945588			0.472794	+	0.881173i	$0.343246\pi$
$384$	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
$392$	−14.8711	−	13.0710i	−0.751105	−	0.660183i
$393$			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	0.422115	−	0.906542i	$-0.361288\pi$
$397$	−9.65214	−	9.65214i	−0.484427	−	0.484427i	−0.906542	+	0.422115i	$0.861288\pi$
$398$	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
$406$	−3.43805	+	4.50806i	−0.170627	+	0.223731i
$407$	−2.79851			−0.138717
$408$	5.95468	+	4.16287i	0.294801	+	0.206093i
$409$	−11.1720			−0.552422			−0.276211	−	0.961097i	$-0.589079\pi$
$409$	−11.1720			−0.552422			−0.276211	+	0.961097i	$0.589079\pi$
$410$	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
$413$	−19.8917	+	6.97441i	−0.978809	+	0.343188i
$414$	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	−0.574378	−	0.818590i	$-0.694756\pi$
$419$	4.99890	−	4.99890i	0.244212	−	0.244212i	0.818590	+	0.574378i	$0.194756\pi$
$420$	17.7244	−	15.4168i	0.864861	−	0.752261i
$421$	−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
$427$	−1.24121	+	0.435191i	−0.0600663	+	0.0210604i
$428$	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	$0.366036\pi$
$433$			37.9857i			1.82548i	−0.408546	+	0.912738i	$0.633964\pi$
$434$	−21.4053	+	2.88242i	−1.02749	+	0.138361i
$435$	−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	$0.0720202\pi$
$439$			9.40058i			0.448665i	−0.974513	+	0.224333i	$0.927980\pi$
$440$	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
$448$	2.06269	−	21.0653i	0.0974529	−	0.995240i
$449$	−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	0.861665	−	0.507478i	$-0.169422\pi$
$461$	7.60470	+	7.60470i	0.354186	+	0.354186i	−0.507478	+	0.861665i	$0.669422\pi$
$462$	−0.298559	−	2.21715i	−0.0138902	−	0.103151i
$463$		−	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	−0.361238	−	0.932474i	$-0.617646\pi$
$467$	12.3445	−	12.3445i	0.571236	−	0.571236i	0.932474	+	0.361238i	$0.117646\pi$
$468$	−3.20066	−	8.04484i	−0.147951	−	0.371873i
$469$	26.0495	−	9.13345i	1.20286	−	0.421744i
$470$	−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
$476$	10.2558	−	8.92053i	0.470073	−	0.408872i
$477$	−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	$-0.311522\pi$
$479$	24.4302			1.11625			0.558123	+	0.829758i	$0.311522\pi$
$480$	24.4433	+	5.76093i	1.11568	+	0.262949i
$481$			20.2623i			0.923883i
$482$	−24.5732	+	16.1708i	−1.11928	+	0.736560i
$483$	−5.19727	−	14.8231i	−0.236484	−	0.674476i
$484$	−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
$490$	−19.9456	−	39.1609i	−0.901052	−	1.76911i
$491$	−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	$0.203340\pi$
$503$			26.7447i			1.19249i	−0.802804	+	0.596243i	$0.796660\pi$
$504$	−7.20640	−	2.01687i	−0.320999	−	0.0898386i
$505$		−	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	0.995442	−	0.0953637i	$-0.0304014\pi$
$509$	20.3067	+	20.3067i	0.900079	+	0.900079i	−0.0953637	+	0.995442i	$0.530401\pi$
$510$	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
$518$	13.9254	+	10.6201i	0.611845	+	0.466620i
$519$	4.36629			0.191659
$520$	53.5252	−	9.47929i	2.34723	−	0.415694i
$521$	6.58341			0.288424			0.144212	−	0.989547i	$-0.453935\pi$
$521$	6.58341			0.288424			0.144212	+	0.989547i	$0.453935\pi$
$522$	−0.432799	+	2.09869i	−0.0189431	+	0.0918573i
$523$	17.5584	+	17.5584i	0.767775	+	0.767775i	0.977714	−	0.209940i	$-0.0673267\pi$
$523$	17.5584	+	17.5584i	0.767775	+	0.767775i	−0.209940	+	0.977714i	$0.567327\pi$
$524$	4.40098	+	11.0618i	0.192258	+	0.483238i
$525$	36.7225	−	12.8756i	1.60270	−	0.561936i
$526$	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
$532$	7.13119	+	0.496547i	0.309176	+	0.0215280i
$533$	−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
$539$	−4.15961	−	0.463398i	−0.179167	−	0.0199600i
$540$	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
$546$	−16.0530	+	2.16169i	−0.687007	+	0.0925116i
$547$	−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
$560$	21.5394	−	41.7537i	0.910208	−	1.76442i
$561$	1.53587			0.0648445
$562$	−4.99501	+	3.28706i	−0.210702	+	0.138656i
$563$	−15.4083	+	15.4083i	−0.649380	+	0.649380i	−0.952843	−	0.303463i	$-0.901857\pi$
$563$	−15.4083	+	15.4083i	−0.649380	+	0.649380i	0.303463	+	0.952843i	$0.401857\pi$
$564$	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
$574$	−22.9080	+	3.08476i	−0.956160	+	0.128756i
$575$			87.3229i			3.64162i
$576$	−2.74742	−	7.51343i	−0.114476	−	0.313060i
$577$		−	2.60870i		−	0.108602i	−0.998525	−	0.0543008i	$-0.982707\pi$
$577$		−	2.60870i		−	0.108602i	0.998525	−	0.0543008i	$-0.0172930\pi$
$578$	−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
$581$	−8.10126	−	23.1056i	−0.336097	−	0.958583i
$582$	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	0.160809	−	0.986986i	$-0.448590\pi$
$587$	−20.0167	−	20.0167i	−0.826176	−	0.826176i	−0.986986	+	0.160809i	$0.948590\pi$
$588$	−6.92824	+	12.1655i	−0.285716	+	0.501697i
$589$	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	$-0.922053\pi$
$593$		−	11.8075i		−	0.484877i	0.970167	−	0.242438i	$-0.0779472\pi$
$594$	−0.464823	−	0.706345i	−0.0190719	−	0.0289817i
$595$	28.4719	−	9.98279i	1.16724	−	0.409254i
$596$	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	$-0.464435\pi$
$601$	5.46690			0.222999			0.111500	+	0.993764i	$0.464435\pi$
$602$	10.7766	−	14.1306i	0.439221	−	0.575919i
$603$	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	$-0.427413\pi$
$607$	11.1394			0.452133			0.226066	+	0.974112i	$0.427413\pi$
$608$	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
$616$	−2.19405	−	3.89945i	−0.0884008	−	0.157113i
$617$			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	$-0.951799\pi$
$619$	−28.3481	−	28.3481i	−1.13941	−	1.13941i	−0.150851	−	0.988557i	$-0.548201\pi$
$620$	−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
$630$	−13.2080	−	10.0730i	−0.526218	−	0.401317i
$631$	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
$637$	−3.35518	+	30.1172i	−0.132937	+	1.19329i
$638$	−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	−0.993092	−	0.117335i	$-0.962565\pi$
$643$	−22.2070	+	22.2070i	−0.875757	+	0.875757i	0.117335	+	0.993092i	$0.462565\pi$
$644$	−20.6176	−	23.7037i	−0.812446	−	0.934055i
$645$	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	$0.316436\pi$
$647$			42.6451i			1.67655i	−0.545246	+	0.838276i	$0.683564\pi$
$648$	−2.78509	+	0.493238i	−0.109409	+	0.0193762i
$649$	−4.76359			−0.186987
$650$	88.1915	+	18.1871i	3.45915	+	0.713357i
$651$	5.05321	+	14.4123i	0.198051	+	0.564861i
$652$	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
$658$	16.2612	−	2.18972i	0.633928	−	0.0853642i
$659$	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	−0.774412	−	0.632682i	$-0.781954\pi$
$661$	−3.64387	+	3.64387i	−0.141730	+	0.141730i	0.632682	+	0.774412i	$0.281954\pi$
$662$	−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
$672$	−14.8830	+	1.57998i	−0.574124	+	0.0609492i
$673$	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	−0.556319	−	0.830969i	$-0.687787\pi$
$677$	7.14618	−	7.14618i	0.274650	−	0.274650i	0.830969	+	0.556319i	$0.187787\pi$
$678$	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
$686$	18.9396	+	18.0912i	0.723118	+	0.690725i
$687$			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	−0.987900	−	0.155093i	$-0.950432\pi$
$691$	−21.8919	+	21.8919i	−0.832807	+	0.832807i	0.155093	+	0.987900i	$0.450432\pi$
$692$	8.11399	−	3.22818i	0.308448	−	0.122717i
$693$	−1.49281	+	0.523408i	−0.0567073	+	0.0198826i
$694$	−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
$700$	58.7229	−	51.0775i	2.21952	−	1.93055i
$701$	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
$707$	2.01983	+	5.76077i	0.0759636	+	0.216656i
$708$	−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
$714$	−7.64246	−	5.82848i	−0.286012	−	0.218125i
$715$	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	$-0.341356\pi$
$719$	25.6353			0.956034			0.478017	+	0.878351i	$0.341356\pi$
$720$	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	$-0.893212\pi$
$727$		−	17.7539i		−	0.658454i	0.944251	−	0.329227i	$-0.106788\pi$
$728$	−28.2336	+	15.8858i	−1.04641	+	0.588766i
$729$			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	$-0.989782\pi$
$733$	−27.9290	−	27.9290i	−1.03158	−	1.03158i	−0.0320947	−	0.999485i	$-0.510218\pi$
$734$	−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
$742$	33.0571	+	25.2108i	1.21357	+	0.925519i
$743$	−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
$749$	−12.5900	−	35.9079i	−0.460028	−	1.31205i
$750$	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
$756$	−0.367559	+	5.27872i	−0.0133680	+	0.191985i
$757$	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	$-0.472302\pi$
$761$	4.79478			0.173811			0.0869053	+	0.996217i	$0.472302\pi$
$762$	4.46536	−	21.6531i	0.161763	−	0.784408i
$763$	12.7839	+	36.4611i	0.462810	+	1.31998i
$764$	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	$0.0248725\pi$
$769$			4.32933i			0.156120i	−0.996949	+	0.0780598i	$0.975128\pi$
$770$	−1.32542	−	9.84280i	−0.0477649	−	0.354710i
$771$	−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	$0.511230\pi$
$773$	−28.7662	+	28.7662i	−1.03465	+	1.03465i	−0.999378	+	0.0352718i	$0.988770\pi$
$774$	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
$784$	−3.88048	+	27.7298i	−0.138589	+	0.990350i
$785$	98.3280			3.50948
$786$	7.03215	−	4.62764i	0.250829	−	0.165062i
$787$	20.7135	−	20.7135i	0.738356	−	0.738356i	−0.233904	−	0.972260i	$-0.575150\pi$
$787$	20.7135	−	20.7135i	0.738356	−	0.738356i	0.972260	+	0.233904i	$0.0751500\pi$
$788$	−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	0.396191	−	0.918168i	$-0.370332\pi$
$797$	−14.7360	−	14.7360i	−0.521977	−	0.521977i	−0.918168	+	0.396191i	$0.870332\pi$
$798$	−0.674575	−	5.00951i	−0.0238797	−	0.177335i
$799$			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
$805$	−23.0727	−	65.8057i	−0.813206	−	2.31935i
$806$	−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	0.0444849	−	0.999010i	$-0.485835\pi$
$811$	−27.1830	−	27.1830i	−0.954525	−	0.954525i	−0.999010	+	0.0444849i	$0.985835\pi$
$812$	7.99847	+	0.556936i	0.280691	+	0.0195446i
$813$	−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
$819$	3.78968	+	10.8086i	0.132422	+	0.377681i
$820$	−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
$826$	23.7035	+	18.0774i	0.824751	+	0.628992i
$827$	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	0.887020	−	0.461731i	$-0.152772\pi$
$829$	12.2451	+	12.2451i	0.425288	+	0.425288i	−0.461731	+	0.887020i	$0.652772\pi$
$830$	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	$-0.811807\pi$
$839$		−	32.2896i		−	1.11476i	0.830258	−	0.557380i	$-0.188193\pi$
$840$	−31.9921	−	8.95368i	−1.10383	−	0.308931i
$841$			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	−0.412310	−	0.911043i	$-0.635278\pi$
$853$	14.5661	−	14.5661i	0.498733	−	0.498733i	0.911043	+	0.412310i	$0.135278\pi$
$854$	1.47906	+	1.12799i	0.0506123	+	0.0385992i
$855$	5.99732			0.205104
$856$	23.3071	−	33.3392i	0.796622	−	1.13951i
$857$	14.4706			0.494307			0.247153	−	0.968976i	$-0.420505\pi$
$857$	14.4706			0.494307			0.247153	+	0.968976i	$0.420505\pi$
$858$	−3.58509	−	0.739328i	−0.122393	−	0.0252402i
$859$	11.7304	+	11.7304i	0.400236	+	0.400236i	0.878316	−	0.478080i	$-0.158667\pi$
$859$	11.7304	+	11.7304i	0.400236	+	0.400236i	−0.478080	+	0.878316i	$0.658667\pi$
$860$	38.7293	+	16.6832i	1.32066	+	0.568893i
$861$	5.40794	+	15.4240i	0.184302	+	0.525648i
$862$	−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
$868$	20.0461	+	23.0466i	0.680408	+	0.782254i
$869$	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
$875$	107.606	−	37.7285i	3.63773	−	1.27546i
$876$	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	$-0.862001\pi$
$881$		−	24.9375i		−	0.840166i	0.907486	−	0.420083i	$-0.137999\pi$
$882$	9.41449	+	3.06061i	0.317002	+	0.103056i
$883$	−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	$0.175814\pi$
$887$			31.2525i			1.04936i	−0.851301	+	0.524678i	$0.824186\pi$
$888$	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
$896$	−26.4893	+	13.9397i	−0.884946	+	0.465694i
$897$	−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
$910$	−71.2657	+	9.59658i	−2.36244	+	0.318123i
$911$		−	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
$917$	−5.21089	−	14.8620i	−0.172079	−	0.490786i
$918$	−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
$924$	−2.38716	+	2.07636i	−0.0785317	+	0.0683072i
$925$	−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	$0.163926\pi$
$929$			30.0238i			0.985050i	−0.870298	+	0.492525i	$0.836074\pi$
$930$	−30.2738	+	19.9222i	−0.992718	+	0.653276i
$931$	−9.39838	−	1.04702i	−0.308019	−	0.0343146i
$932$	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	$-0.679204\pi$
$937$	−32.6745			−1.06743			−0.533714	+	0.845665i	$0.679204\pi$
$938$	−31.0413	−	23.6735i	−1.01353	−	0.772966i
$939$	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	0.592351	−	0.805680i	$-0.298200\pi$
$941$	−6.54400	−	6.54400i	−0.213328	−	0.213328i	−0.805680	+	0.592351i	$0.798200\pi$
$942$	−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
$952$	−18.5114	−	5.18083i	−0.599959	−	0.167912i
$953$		−	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
$966$	−13.4711	+	17.6636i	−0.433425	+	0.568318i
$967$	−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	0.152025	−	0.988377i	$-0.451421\pi$
$971$	−26.0614	−	26.0614i	−0.836352	−	0.836352i	−0.988377	+	0.152025i	$0.951421\pi$
$972$	0.739341	+	1.85833i	0.0237144	+	0.0596058i
$973$	8.70366	−	3.05167i	0.279027	−	0.0978319i
$974$	−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
$980$	−30.7572	+	54.0074i	−0.982503	+	1.72520i
$981$	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	$0.258587\pi$
$983$			45.5195i			1.45185i	−0.687776	+	0.725923i	$0.741413\pi$
$984$	−10.0114	+	14.3206i	−0.319152	+	0.456525i
$985$	−43.9031			−1.39887
$986$	−1.11175	+	5.39101i	−0.0354054	+	0.171685i
$987$	−3.83882	−	10.9487i	−0.122191	−	0.348502i
$988$	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
$994$	15.9659	−	2.14995i	0.506408	−	0.0681924i
$995$	−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	−0.179134	−	0.983825i	$-0.557330\pi$
$997$	25.4084	−	25.4084i	0.804691	−	0.804691i	0.983825	+	0.179134i	$0.0573296\pi$
$998$	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.139.9	✓	64
4.3	odd	2		1344.2.u.a.1231.32		64
7.6	odd	2	inner	336.2.u.a.139.10	yes	64
16.3	odd	4	inner	336.2.u.a.307.10	yes	64
16.13	even	4		1344.2.u.a.559.1		64
28.27	even	2		1344.2.u.a.1231.1		64
112.13	odd	4		1344.2.u.a.559.32		64
112.83	even	4	inner	336.2.u.a.307.9	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.u.a.139.9	✓	64	1.1	even	1	trivial
336.2.u.a.139.10	yes	64	7.6	odd	2	inner
336.2.u.a.307.9	yes	64	112.83	even	4	inner
336.2.u.a.307.10	yes	64	16.3	odd	4	inner
1344.2.u.a.559.1		64	16.13	even	4
1344.2.u.a.559.32		64	112.13	odd	4
1344.2.u.a.1231.1		64	28.27	even	2
1344.2.u.a.1231.32		64	4.3	odd	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} +(-3.70819 + 0.499341i) 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} +(0.875401 + 2.49673i) 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} +(3.47272 + 3.99252i) 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} +(3.88625 + 11.0840i) 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} +(2.26900 - 2.97517i) 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} +(2.01687 - 7.20640i) 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} +(10.0730 - 13.2080i) 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} +(-0.523408 - 1.49281i) 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} +(-5.27872 - 0.367559i) 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} +(-10.8086 + 3.78968i) 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} +(-3.06061 + 9.41449i) 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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