LMFDB - Embedded newform 342.2.n.f.293.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [342,2,Mod(293,342)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(342, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 1]))

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

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

chi := DirichletCharacter("342.293");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 342 = 2 \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	342.n (of order $6$, 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:	$2.73088374913$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 5 x^{17} + 13 x^{16} - 30 x^{15} + 54 x^{14} - 69 x^{13} + 66 x^{12} + 36 x^{11} - 243 x^{10} + \cdots + 19683 $ x^18 - 5x^17 + 13x^16 - 30x^15 + 54x^14 - 69x^13 + 66x^12 + 36x^11 - 243x^10 + 432x^9 - 729x^8 + 324x^7 + 1782x^6 - 5589x^5 + 13122x^4 - 21870x^3 + 28431x^2 - 32805*x + 19683
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			293.3
Root			$-0.290848 - 1.70746i$ of defining polynomial
Character	$\chi$	$=$	342.293
Dual form			342.2.n.f.335.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(-1.33328 - 1.10561i) q^{3} +1.00000 q^{4} +(2.55682 - 1.47618i) q^{5} +(1.33328 + 1.10561i) q^{6} +(1.79740 + 3.11318i) q^{7} -1.00000 q^{8} +(0.555252 + 2.94817i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(-1.33328 - 1.10561i) q^{3} +1.00000 q^{4} +(2.55682 - 1.47618i) q^{5} +(1.33328 + 1.10561i) q^{6} +(1.79740 + 3.11318i) q^{7} -1.00000 q^{8} +(0.555252 + 2.94817i) q^{9} +(-2.55682 + 1.47618i) q^{10} +(-0.347788 + 0.200795i) q^{11} +(-1.33328 - 1.10561i) q^{12} -0.873668i q^{13} +(-1.79740 - 3.11318i) q^{14} +(-5.04103 - 0.858689i) q^{15} +1.00000 q^{16} +(5.57034 + 3.21604i) q^{17} +(-0.555252 - 2.94817i) q^{18} +(-1.19056 + 4.19316i) q^{19} +(2.55682 - 1.47618i) q^{20} +(1.04554 - 6.13795i) q^{21} +(0.347788 - 0.200795i) q^{22} -7.53500i q^{23} +(1.33328 + 1.10561i) q^{24} +(1.85822 - 3.21853i) q^{25} +0.873668i q^{26} +(2.51922 - 4.54462i) q^{27} +(1.79740 + 3.11318i) q^{28} +(3.41497 - 5.91491i) q^{29} +(5.04103 + 0.858689i) q^{30} +(4.73695 + 2.73488i) q^{31} -1.00000 q^{32} +(0.685699 + 0.116802i) q^{33} +(-5.57034 - 3.21604i) q^{34} +(9.19123 + 5.30656i) q^{35} +(0.555252 + 2.94817i) q^{36} -2.83050i q^{37} +(1.19056 - 4.19316i) q^{38} +(-0.965936 + 1.16484i) q^{39} +(-2.55682 + 1.47618i) q^{40} +(3.44559 + 5.96794i) q^{41} +(-1.04554 + 6.13795i) q^{42} -5.63883 q^{43} +(-0.347788 + 0.200795i) q^{44} +(5.77171 + 6.71828i) q^{45} +7.53500i q^{46} +(-1.51465 - 0.874481i) q^{47} +(-1.33328 - 1.10561i) q^{48} +(-2.96126 + 5.12905i) q^{49} +(-1.85822 + 3.21853i) q^{50} +(-3.87112 - 10.4465i) q^{51} -0.873668i q^{52} +(-5.55209 - 9.61651i) q^{53} +(-2.51922 + 4.54462i) q^{54} +(-0.592821 + 1.02680i) q^{55} +(-1.79740 - 3.11318i) q^{56} +(6.22334 - 4.27434i) q^{57} +(-3.41497 + 5.91491i) q^{58} +(-4.45687 - 7.71953i) q^{59} +(-5.04103 - 0.858689i) q^{60} +(0.270635 - 0.468753i) q^{61} +(-4.73695 - 2.73488i) q^{62} +(-8.18017 + 7.02762i) q^{63} +1.00000 q^{64} +(-1.28969 - 2.23381i) q^{65} +(-0.685699 - 0.116802i) q^{66} +7.78609i q^{67} +(5.57034 + 3.21604i) q^{68} +(-8.33077 + 10.0462i) q^{69} +(-9.19123 - 5.30656i) q^{70} +(-7.15737 + 12.3969i) q^{71} +(-0.555252 - 2.94817i) q^{72} +(6.91698 - 11.9806i) q^{73} +2.83050i q^{74} +(-6.03596 + 2.23673i) q^{75} +(-1.19056 + 4.19316i) q^{76} +(-1.25022 - 0.721817i) q^{77} +(0.965936 - 1.16484i) q^{78} +7.53520i q^{79} +(2.55682 - 1.47618i) q^{80} +(-8.38339 + 3.27396i) q^{81} +(-3.44559 - 5.96794i) q^{82} +(-4.87561 + 2.81493i) q^{83} +(1.04554 - 6.13795i) q^{84} +18.9898 q^{85} +5.63883 q^{86} +(-11.0927 + 4.11058i) q^{87} +(0.347788 - 0.200795i) q^{88} +(3.51823 + 6.09375i) q^{89} +(-5.77171 - 6.71828i) q^{90} +(2.71989 - 1.57033i) q^{91} -7.53500i q^{92} +(-3.29195 - 8.88356i) q^{93} +(1.51465 + 0.874481i) q^{94} +(3.14581 + 12.4786i) q^{95} +(1.33328 + 1.10561i) q^{96} +0.223639i q^{97} +(2.96126 - 5.12905i) q^{98} +(-0.785089 - 0.913845i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 18 q^{2} - q^{3} + 18 q^{4} + 3 q^{5} + q^{6} - 18 q^{8} + 5 q^{9}+O(q^{10}) $ 18 * q - 18 * q^2 - q^3 + 18 * q^4 + 3 * q^5 + q^6 - 18 * q^8 + 5 * q^9	$ 18 q - 18 q^{2} - q^{3} + 18 q^{4} + 3 q^{5} + q^{6} - 18 q^{8} + 5 q^{9} - 3 q^{10} + 15 q^{11} - q^{12} - 17 q^{15} + 18 q^{16} - 15 q^{17} - 5 q^{18} + 6 q^{19} + 3 q^{20} + q^{21} - 15 q^{22} + q^{24} + 18 q^{25} + 20 q^{27} + 18 q^{29} + 17 q^{30} + 9 q^{31} - 18 q^{32} + q^{33} + 15 q^{34} - 3 q^{35} + 5 q^{36} - 6 q^{38} + 18 q^{39} - 3 q^{40} - q^{42} + 12 q^{43} + 15 q^{44} - 17 q^{45} - 18 q^{47} - q^{48} + 3 q^{49} - 18 q^{50} + 10 q^{51} - 15 q^{53} - 20 q^{54} - 9 q^{55} + 23 q^{57} - 18 q^{58} - 17 q^{60} - 9 q^{61} - 9 q^{62} - 38 q^{63} + 18 q^{64} - 9 q^{65} - q^{66} - 15 q^{68} - 8 q^{69} + 3 q^{70} - 6 q^{71} - 5 q^{72} + 24 q^{73} - 9 q^{75} + 6 q^{76} + 3 q^{77} - 18 q^{78} + 3 q^{80} + 5 q^{81} + 3 q^{83} + q^{84} + 6 q^{85} - 12 q^{86} - 60 q^{87} - 15 q^{88} + 24 q^{89} + 17 q^{90} - 81 q^{91} - 3 q^{93} + 18 q^{94} - 9 q^{95} + q^{96} - 3 q^{98} - 56 q^{99}+O(q^{100}) $ 18 * q - 18 * q^2 - q^3 + 18 * q^4 + 3 * q^5 + q^6 - 18 * q^8 + 5 * q^9 - 3 * q^10 + 15 * q^11 - q^12 - 17 * q^15 + 18 * q^16 - 15 * q^17 - 5 * q^18 + 6 * q^19 + 3 * q^20 + q^21 - 15 * q^22 + q^24 + 18 * q^25 + 20 * q^27 + 18 * q^29 + 17 * q^30 + 9 * q^31 - 18 * q^32 + q^33 + 15 * q^34 - 3 * q^35 + 5 * q^36 - 6 * q^38 + 18 * q^39 - 3 * q^40 - q^42 + 12 * q^43 + 15 * q^44 - 17 * q^45 - 18 * q^47 - q^48 + 3 * q^49 - 18 * q^50 + 10 * q^51 - 15 * q^53 - 20 * q^54 - 9 * q^55 + 23 * q^57 - 18 * q^58 - 17 * q^60 - 9 * q^61 - 9 * q^62 - 38 * q^63 + 18 * q^64 - 9 * q^65 - q^66 - 15 * q^68 - 8 * q^69 + 3 * q^70 - 6 * q^71 - 5 * q^72 + 24 * q^73 - 9 * q^75 + 6 * q^76 + 3 * q^77 - 18 * q^78 + 3 * q^80 + 5 * q^81 + 3 * q^83 + q^84 + 6 * q^85 - 12 * q^86 - 60 * q^87 - 15 * q^88 + 24 * q^89 + 17 * q^90 - 81 * q^91 - 3 * q^93 + 18 * q^94 - 9 * q^95 + q^96 - 3 * q^98 - 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/342\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	−1.33328	−	1.10561i	−0.769768	−	0.638324i
$3$	−1.33328	−	1.10561i	−0.769768	−	0.638324i
$4$	1.00000			0.500000
$5$	2.55682	−	1.47618i	1.14344	−	0.660168i	0.196163	−	0.980571i	$-0.437152\pi$
$5$	2.55682	−	1.47618i	1.14344	−	0.660168i	0.947281	+	0.320403i	$0.103818\pi$
$6$	1.33328	+	1.10561i	0.544308	+	0.451363i
$7$	1.79740	+	3.11318i	0.679352	+	1.17667i	0.975176	+	0.221429i	$0.0710722\pi$
$7$	1.79740	+	3.11318i	0.679352	+	1.17667i	−0.295825	+	0.955242i	$0.595594\pi$
$8$	−1.00000			−0.353553
$9$	0.555252	+	2.94817i	0.185084	+	0.982723i
$10$	−2.55682	+	1.47618i	−0.808538	+	0.466809i
$11$	−0.347788	+	0.200795i	−0.104862	+	0.0605421i	−0.551514	−	0.834166i	$-0.685950\pi$
$11$	−0.347788	+	0.200795i	−0.104862	+	0.0605421i	0.446652	+	0.894708i	$0.352616\pi$
$12$	−1.33328	−	1.10561i	−0.384884	−	0.319162i
$13$		−	0.873668i		−	0.242312i	−0.992633	−	0.121156i	$-0.961340\pi$
$13$		−	0.873668i		−	0.242312i	0.992633	−	0.121156i	$-0.0386601\pi$
$14$	−1.79740	−	3.11318i	−0.480374	−	0.832032i
$15$	−5.04103	−	0.858689i	−1.30159	−	0.221713i
$16$	1.00000			0.250000
$17$	5.57034	+	3.21604i	1.35101	+	0.780004i	0.988391	−	0.151934i	$-0.0485503\pi$
$17$	5.57034	+	3.21604i	1.35101	+	0.780004i	0.362616	+	0.931939i	$0.381884\pi$
$18$	−0.555252	−	2.94817i	−0.130874	−	0.694890i
$19$	−1.19056	+	4.19316i	−0.273133	+	0.961976i
$19$	−1.19056	+	4.19316i	−0.273133	+	0.961976i
$20$	2.55682	−	1.47618i	0.571722	−	0.330084i
$21$	1.04554	−	6.13795i	0.228155	−	1.33941i
$22$	0.347788	−	0.200795i	0.0741486	−	0.0428097i
$23$		−	7.53500i		−	1.57116i	−0.618763	−	0.785578i	$-0.712366\pi$
$23$		−	7.53500i		−	1.57116i	0.618763	−	0.785578i	$-0.287634\pi$
$24$	1.33328	+	1.10561i	0.272154	+	0.225682i
$25$	1.85822	−	3.21853i	0.371644	−	0.643706i
$26$			0.873668i			0.171340i
$27$	2.51922	−	4.54462i	0.484824	−	0.874612i
$28$	1.79740	+	3.11318i	0.339676	+	0.588336i
$29$	3.41497	−	5.91491i	0.634145	−	1.09837i	−0.352551	−	0.935793i	$-0.614686\pi$
$29$	3.41497	−	5.91491i	0.634145	−	1.09837i	0.986696	−	0.162578i	$-0.0519809\pi$
$30$	5.04103	+	0.858689i	0.920362	+	0.156774i
$31$	4.73695	+	2.73488i	0.850781	+	0.491199i	0.860914	−	0.508750i	$-0.169892\pi$
$31$	4.73695	+	2.73488i	0.850781	+	0.491199i	−0.0101334	+	0.999949i	$0.503226\pi$
$32$	−1.00000			−0.176777
$33$	0.685699	+	0.116802i	0.119365	+	0.0203326i
$34$	−5.57034	−	3.21604i	−0.955306	−	0.551546i
$35$	9.19123	+	5.30656i	1.55360	+	0.896973i
$36$	0.555252	+	2.94817i	0.0925421	+	0.491361i
$37$		−	2.83050i		−	0.465331i	−0.972557	−	0.232665i	$-0.925255\pi$
$37$		−	2.83050i		−	0.465331i	0.972557	−	0.232665i	$-0.0747447\pi$
$38$	1.19056	−	4.19316i	0.193134	−	0.680220i
$39$	−0.965936	+	1.16484i	−0.154674	+	0.186524i
$40$	−2.55682	+	1.47618i	−0.404269	+	0.233405i
$41$	3.44559	+	5.96794i	0.538111	+	0.932036i	0.999006	+	0.0445811i	$0.0141953\pi$
$41$	3.44559	+	5.96794i	0.538111	+	0.932036i	−0.460894	+	0.887455i	$0.652471\pi$
$42$	−1.04554	+	6.13795i	−0.161330	+	0.947106i
$43$	−5.63883			−0.859913			−0.429957	−	0.902850i	$-0.641471\pi$
$43$	−5.63883			−0.859913			−0.429957	+	0.902850i	$0.641471\pi$
$44$	−0.347788	+	0.200795i	−0.0524310	+	0.0302710i
$45$	5.77171	+	6.71828i	0.860396	+	1.00150i
$46$			7.53500i			1.11097i
$47$	−1.51465	−	0.874481i	−0.220934	−	0.127556i	0.385449	−	0.922729i	$-0.374047\pi$
$47$	−1.51465	−	0.874481i	−0.220934	−	0.127556i	−0.606383	+	0.795173i	$0.707380\pi$
$48$	−1.33328	−	1.10561i	−0.192442	−	0.159581i
$49$	−2.96126	+	5.12905i	−0.423037	+	0.732722i
$50$	−1.85822	+	3.21853i	−0.262792	+	0.455169i
$51$	−3.87112	−	10.4465i	−0.542066	−	1.46280i
$52$		−	0.873668i		−	0.121156i
$53$	−5.55209	−	9.61651i	−0.762638	−	1.32093i	−0.941486	−	0.337052i	$-0.890570\pi$
$53$	−5.55209	−	9.61651i	−0.762638	−	1.32093i	0.178848	−	0.983877i	$-0.442763\pi$
$54$	−2.51922	+	4.54462i	−0.342822	+	0.618444i
$55$	−0.592821	+	1.02680i	−0.0799359	+	0.138453i
$56$	−1.79740	−	3.11318i	−0.240187	−	0.416016i
$57$	6.22334	−	4.27434i	0.824302	−	0.566151i
$58$	−3.41497	+	5.91491i	−0.448408	+	0.776665i
$59$	−4.45687	−	7.71953i	−0.580235	−	1.00500i	−0.995451	−	0.0952739i	$-0.969627\pi$
$59$	−4.45687	−	7.71953i	−0.580235	−	1.00500i	0.415216	−	0.909723i	$-0.363706\pi$
$60$	−5.04103	−	0.858689i	−0.650794	−	0.110856i
$61$	0.270635	−	0.468753i	0.0346512	−	0.0600177i	−0.848180	−	0.529709i	$-0.822301\pi$
$61$	0.270635	−	0.468753i	0.0346512	−	0.0600177i	0.882831	+	0.469691i	$0.155635\pi$
$62$	−4.73695	−	2.73488i	−0.601593	−	0.347330i
$63$	−8.18017	+	7.02762i	−1.03060	+	0.885398i
$64$	1.00000			0.125000
$65$	−1.28969	−	2.23381i	−0.159967	−	0.277070i
$66$	−0.685699	−	0.116802i	−0.0844037	−	0.0143773i
$67$			7.78609i			0.951222i	0.879656	+	0.475611i	$0.157773\pi$
$67$			7.78609i			0.951222i	−0.879656	+	0.475611i	$0.842227\pi$
$68$	5.57034	+	3.21604i	0.675503	+	0.390002i
$69$	−8.33077	+	10.0462i	−1.00291	+	1.20942i
$70$	−9.19123	−	5.30656i	−1.09856	−	0.634255i
$71$	−7.15737	+	12.3969i	−0.849423	+	1.47124i	0.0323004	+	0.999478i	$0.489717\pi$
$71$	−7.15737	+	12.3969i	−0.849423	+	1.47124i	−0.881724	+	0.471766i	$0.843617\pi$
$72$	−0.555252	−	2.94817i	−0.0654371	−	0.347445i
$73$	6.91698	−	11.9806i	0.809571	−	1.40222i	−0.103590	−	0.994620i	$-0.533033\pi$
$73$	6.91698	−	11.9806i	0.809571	−	1.40222i	0.913161	−	0.407598i	$-0.133634\pi$
$74$			2.83050i			0.329039i
$75$	−6.03596	+	2.23673i	−0.696973	+	0.258275i
$76$	−1.19056	+	4.19316i	−0.136566	+	0.480988i
$77$	−1.25022	−	0.721817i	−0.142476	−	0.0822587i
$78$	0.965936	−	1.16484i	0.109371	−	0.131892i
$79$			7.53520i			0.847777i	0.905714	+	0.423888i	$0.139335\pi$
$79$			7.53520i			0.847777i	−0.905714	+	0.423888i	$0.860665\pi$
$80$	2.55682	−	1.47618i	0.285861	−	0.165042i
$81$	−8.38339	+	3.27396i	−0.931488	+	0.363773i
$82$	−3.44559	−	5.96794i	−0.380502	−	0.659049i
$83$	−4.87561	+	2.81493i	−0.535167	+	0.308979i	−0.743118	−	0.669160i	$-0.766654\pi$
$83$	−4.87561	+	2.81493i	−0.535167	+	0.308979i	0.207951	+	0.978139i	$0.433321\pi$
$84$	1.04554	−	6.13795i	0.114078	−	0.669705i
$85$	18.9898			2.05974
$86$	5.63883			0.608050
$87$	−11.0927	+	4.11058i	−1.18926	+	0.440700i
$88$	0.347788	−	0.200795i	0.0370743	−	0.0214049i
$89$	3.51823	+	6.09375i	0.372931	+	0.645936i	0.990015	−	0.140962i	$-0.0450194\pi$
$89$	3.51823	+	6.09375i	0.372931	+	0.645936i	−0.617084	+	0.786897i	$0.711686\pi$
$90$	−5.77171	−	6.71828i	−0.608392	−	0.708169i
$91$	2.71989	−	1.57033i	0.285122	−	0.164615i
$92$		−	7.53500i		−	0.785578i
$93$	−3.29195	−	8.88356i	−0.341359	−	0.921183i
$94$	1.51465	+	0.874481i	0.156224	+	0.0901958i
$95$	3.14581	+	12.4786i	0.322754	+	1.28028i
$96$	1.33328	+	1.10561i	0.136077	+	0.112841i
$97$			0.223639i			0.0227071i	0.999936	+	0.0113535i	$0.00361402\pi$
$97$			0.223639i			0.0227071i	−0.999936	+	0.0113535i	$0.996386\pi$
$98$	2.96126	−	5.12905i	0.299133	−	0.518113i
$99$	−0.785089	−	0.913845i	−0.0789044	−	0.0918449i
$100$	1.85822	−	3.21853i	0.185822	−	0.321853i
$101$	−8.44696	−	4.87686i	−0.840504	−	0.485265i	0.0169314	−	0.999857i	$-0.494610\pi$
$101$	−8.44696	−	4.87686i	−0.840504	−	0.485265i	−0.857436	+	0.514591i	$0.827944\pi$
$102$	3.87112	+	10.4465i	0.383298	+	1.03436i
$103$	−6.59018	−	3.80484i	−0.649350	−	0.374902i	0.138857	−	0.990312i	$-0.455657\pi$
$103$	−6.59018	−	3.80484i	−0.649350	−	0.374902i	−0.788207	+	0.615410i	$0.788990\pi$
$104$			0.873668i			0.0856702i
$105$	−6.38747	−	17.2370i	−0.623353	−	1.68216i
$106$	5.55209	+	9.61651i	0.539267	+	0.934038i
$107$	8.12018			0.785007			0.392504	−	0.919750i	$-0.371609\pi$
$107$	8.12018			0.785007			0.392504	+	0.919750i	$0.371609\pi$
$108$	2.51922	−	4.54462i	0.242412	−	0.437306i
$109$	7.01856	+	4.05217i	0.672257	+	0.388128i	0.796931	−	0.604070i	$-0.206455\pi$
$109$	7.01856	+	4.05217i	0.672257	+	0.388128i	−0.124675	+	0.992198i	$0.539789\pi$
$110$	0.592821	−	1.02680i	0.0565232	−	0.0979011i
$111$	−3.12943	+	3.77383i	−0.297032	+	0.358197i
$112$	1.79740	+	3.11318i	0.169838	+	0.294168i
$113$	−3.63528	+	6.29649i	−0.341979	+	0.592324i	−0.984800	−	0.173692i	$-0.944430\pi$
$113$	−3.63528	+	6.29649i	−0.341979	+	0.592324i	0.642821	+	0.766016i	$0.277764\pi$
$114$	−6.22334	+	4.27434i	−0.582869	+	0.400329i
$115$	−11.1230	−	19.2656i	−1.03723	−	1.79653i
$116$	3.41497	−	5.91491i	0.317072	−	0.549185i
$117$	2.57572	−	0.485106i	0.238125	−	0.0448481i
$118$	4.45687	+	7.71953i	0.410288	+	0.710640i
$119$			23.1220i			2.11959i
$120$	5.04103	+	0.858689i	0.460181	+	0.0783872i
$121$	−5.41936	+	9.38661i	−0.492669	+	0.853328i
$122$	−0.270635	+	0.468753i	−0.0245021	+	0.0424389i
$123$	2.00429	−	11.7664i	0.180721	−	1.06094i
$124$	4.73695	+	2.73488i	0.425390	+	0.245599i
$125$			3.78953i			0.338946i
$126$	8.18017	−	7.02762i	0.728747	−	0.626071i
$127$	11.9875	−	6.92096i	1.06371	−	0.614136i	0.137257	−	0.990535i	$-0.456171\pi$
$127$	11.9875	−	6.92096i	1.06371	−	0.614136i	0.926458	+	0.376399i	$0.122838\pi$
$128$	−1.00000			−0.0883883
$129$	7.51812	+	6.23434i	0.661933	+	0.548903i
$130$	1.28969	+	2.23381i	0.113113	+	0.195918i
$131$	−3.94837	+	2.27959i	−0.344971	+	0.199169i	−0.662468	−	0.749090i	$-0.730491\pi$
$131$	−3.94837	+	2.27959i	−0.344971	+	0.199169i	0.317497	+	0.948259i	$0.397158\pi$
$132$	0.685699	+	0.116802i	0.0596824	+	0.0101663i
$133$	−15.1940	+	3.83034i	−1.31748	+	0.332132i
$134$		−	7.78609i		−	0.672616i
$135$	−0.267484	−	15.3386i	−0.0230213	−	1.32014i
$136$	−5.57034	−	3.21604i	−0.477653	−	0.275773i
$137$	−3.73376	−	2.15569i	−0.318997	−	0.184173i	0.331948	−	0.943298i	$-0.392294\pi$
$137$	−3.73376	−	2.15569i	−0.318997	−	0.184173i	−0.650945	+	0.759125i	$0.725627\pi$
$138$	8.33077	−	10.0462i	0.709162	−	0.855192i
$139$	7.60048			0.644664			0.322332	−	0.946627i	$-0.395533\pi$
$139$	7.60048			0.644664			0.322332	+	0.946627i	$0.395533\pi$
$140$	9.19123	+	5.30656i	0.776801	+	0.448486i
$141$	1.05261	+	2.84053i	0.0886454	+	0.239216i
$142$	7.15737	−	12.3969i	0.600633	−	1.04033i
$143$	0.175429	+	0.303851i	0.0146701	+	0.0254093i
$144$	0.555252	+	2.94817i	0.0462710	+	0.245681i
$145$		−	20.1645i		−	1.67457i
$146$	−6.91698	+	11.9806i	−0.572453	+	0.991518i
$147$	9.61891	−	3.56445i	0.793355	−	0.293991i
$148$		−	2.83050i		−	0.232665i
$149$	−12.5051	+	7.21981i	−1.02446	+	0.591470i	−0.915391	−	0.402565i	$-0.868119\pi$
$149$	−12.5051	+	7.21981i	−1.02446	+	0.591470i	−0.109064	+	0.994035i	$0.534785\pi$
$150$	6.03596	−	2.23673i	0.492834	−	0.182628i
$151$	−5.59829	+	3.23217i	−0.455582	+	0.263031i	−0.710185	−	0.704015i	$-0.751389\pi$
$151$	−5.59829	+	3.23217i	−0.455582	+	0.263031i	0.254603	+	0.967046i	$0.418055\pi$
$152$	1.19056	−	4.19316i	0.0965671	−	0.340110i
$153$	−6.38848	+	18.2080i	−0.516478	+	1.47203i
$154$	1.25022	+	0.721817i	0.100746	+	0.0581657i
$155$	16.1487			1.29709
$156$	−0.965936	+	1.16484i	−0.0773368	+	0.0932619i
$157$	−11.1431	−	19.3005i	−0.889320	−	1.54035i	−0.840681	−	0.541531i	$-0.817845\pi$
$157$	−11.1431	−	19.3005i	−0.889320	−	1.54035i	−0.0486391	−	0.998816i	$-0.515488\pi$
$158$		−	7.53520i		−	0.599469i
$159$	−3.22963	+	18.9599i	−0.256126	+	1.50362i
$160$	−2.55682	+	1.47618i	−0.202134	+	0.116702i
$161$	23.4578	−	13.5434i	1.84873	−	1.06737i
$162$	8.38339	−	3.27396i	0.658661	−	0.257226i
$163$	12.8336			1.00520			0.502602	−	0.864518i	$-0.332376\pi$
$163$	12.8336			1.00520			0.502602	+	0.864518i	$0.332376\pi$
$164$	3.44559	+	5.96794i	0.269056	+	0.466018i
$165$	1.92563	−	0.713574i	0.149910	−	0.0555516i
$166$	4.87561	−	2.81493i	0.378420	−	0.218481i
$167$	−17.2918			−1.33808			−0.669041	−	0.743225i	$-0.733295\pi$
$167$	−17.2918			−1.33808			−0.669041	+	0.743225i	$0.733295\pi$
$168$	−1.04554	+	6.13795i	−0.0806650	+	0.473553i
$169$	12.2367			0.941285
$170$	−18.9898			−1.45645
$171$	−13.0232	−	1.18171i	−0.995909	−	0.0903674i
$172$	−5.63883			−0.429957
$173$	7.58102			0.576374			0.288187	−	0.957574i	$-0.406948\pi$
$173$	7.58102			0.576374			0.288187	+	0.957574i	$0.406948\pi$
$174$	11.0927	−	4.11058i	0.840934	−	0.311622i
$175$	13.3598			1.00991
$176$	−0.347788	+	0.200795i	−0.0262155	+	0.0151355i
$177$	−2.59255	+	15.2198i	−0.194868	+	1.14399i
$178$	−3.51823	−	6.09375i	−0.263702	−	0.456746i
$179$	−8.65371			−0.646809			−0.323404	−	0.946261i	$-0.604827\pi$
$179$	−8.65371			−0.646809			−0.323404	+	0.946261i	$0.604827\pi$
$180$	5.77171	+	6.71828i	0.430198	+	0.500751i
$181$	−10.7954	+	6.23275i	−0.802418	+	0.463276i	−0.844316	−	0.535845i	$-0.819993\pi$
$181$	−10.7954	+	6.23275i	−0.802418	+	0.463276i	0.0418977	+	0.999122i	$0.486660\pi$
$182$	−2.71989	+	1.57033i	−0.201611	+	0.116400i
$183$	−0.879089	+	0.325761i	−0.0649841	+	0.0240809i
$184$			7.53500i			0.555487i
$185$	−4.17832	−	7.23707i	−0.307197	−	0.532080i
$186$	3.29195	+	8.88356i	0.241378	+	0.651375i
$187$	−2.58306			−0.188892
$188$	−1.51465	−	0.874481i	−0.110467	−	0.0637781i
$189$	18.6762	−	0.325688i	1.35850	−	0.0236903i
$190$	−3.14581	−	12.4786i	−0.228221	−	0.905295i
$191$	21.9809	−	12.6907i	1.59048	−	0.918266i	0.597260	−	0.802048i	$-0.296256\pi$
$191$	21.9809	−	12.6907i	1.59048	−	0.918266i	0.993224	−	0.116218i	$-0.0370773\pi$
$192$	−1.33328	−	1.10561i	−0.0962209	−	0.0797905i
$193$	−15.4798	+	8.93726i	−1.11426	+	0.643318i	−0.939929	−	0.341369i	$-0.889109\pi$
$193$	−15.4798	+	8.93726i	−1.11426	+	0.643318i	−0.174330	+	0.984687i	$0.555776\pi$
$194$		−	0.223639i		−	0.0160563i
$195$	−0.750209	+	4.40419i	−0.0537236	+	0.315390i
$196$	−2.96126	+	5.12905i	−0.211519	+	0.366361i
$197$			11.9456i			0.851092i	0.904937	+	0.425546i	$0.139918\pi$
$197$			11.9456i			0.851092i	−0.904937	+	0.425546i	$0.860082\pi$
$198$	0.785089	+	0.913845i	0.0557938	+	0.0649441i
$199$	−10.7216	−	18.5703i	−0.760033	−	1.31642i	−0.942833	−	0.333265i	$-0.891850\pi$
$199$	−10.7216	−	18.5703i	−0.760033	−	1.31642i	0.182801	−	0.983150i	$-0.441484\pi$
$200$	−1.85822	+	3.21853i	−0.131396	+	0.227585i
$201$	8.60838	−	10.3810i	0.607188	−	0.732220i
$202$	8.44696	+	4.87686i	0.594326	+	0.343134i
$203$	24.5522			1.72323
$204$	−3.87112	−	10.4465i	−0.271033	−	0.731401i
$205$	17.6195	+	10.1726i	1.23060	+	0.710488i
$206$	6.59018	+	3.80484i	0.459159	+	0.265096i
$207$	22.2144	−	4.18383i	1.54401	−	0.290796i
$208$		−	0.873668i		−	0.0605780i
$209$	−0.427905	−	1.69739i	−0.0295988	−	0.117411i
$210$	6.38747	+	17.2370i	0.440777	+	1.18947i
$211$	3.69705	−	2.13450i	0.254516	−	0.146945i	−0.367314	−	0.930097i	$-0.619723\pi$
$211$	3.69705	−	2.13450i	0.254516	−	0.146945i	0.621830	+	0.783152i	$0.286389\pi$
$212$	−5.55209	−	9.61651i	−0.381319	−	0.660464i
$213$	23.2489	−	8.61527i	1.59299	−	0.590309i
$214$	−8.12018			−0.555084
$215$	−14.4175	+	8.32393i	−0.983263	+	0.567687i
$216$	−2.51922	+	4.54462i	−0.171411	+	0.309222i
$217$			19.6626i			1.33479i
$218$	−7.01856	−	4.05217i	−0.475357	−	0.274448i
$219$	−22.4681	+	8.32591i	−1.51825	+	0.562613i
$220$	−0.592821	+	1.02680i	−0.0399680	+	0.0692265i
$221$	2.80975	−	4.86663i	0.189004	−	0.327365i
$222$	3.12943	−	3.77383i	0.210033	−	0.253283i
$223$		−	10.0653i		−	0.674025i	−0.941500	−	0.337012i	$-0.890584\pi$
$223$		−	10.0653i		−	0.674025i	0.941500	−	0.337012i	$-0.109416\pi$
$224$	−1.79740	−	3.11318i	−0.120094	−	0.208008i
$225$	10.5206	+	3.69125i	0.701370	+	0.246083i
$226$	3.63528	−	6.29649i	0.241815	−	0.418837i
$227$	−10.0498	−	17.4068i	−0.667031	−	1.15533i	−0.978730	−	0.205150i	$-0.934232\pi$
$227$	−10.0498	−	17.4068i	−0.667031	−	1.15533i	0.311700	−	0.950181i	$-0.399102\pi$
$228$	6.22334	−	4.27434i	0.412151	−	0.283075i
$229$	−10.6629	+	18.4687i	−0.704624	+	1.22044i	0.262204	+	0.965013i	$0.415551\pi$
$229$	−10.6629	+	18.4687i	−0.704624	+	1.22044i	−0.966827	+	0.255431i	$0.917783\pi$
$230$	11.1230	+	19.2656i	0.733430	+	1.27034i
$231$	0.868846	+	2.34464i	0.0571659	+	0.154266i
$232$	−3.41497	+	5.91491i	−0.224204	+	0.388333i
$233$	−16.3284	−	9.42721i	−1.06971	−	0.617597i	−0.141608	−	0.989923i	$-0.545227\pi$
$233$	−16.3284	−	9.42721i	−1.06971	−	0.617597i	−0.928102	+	0.372326i	$0.878560\pi$
$234$	−2.57572	+	0.485106i	−0.168380	+	0.0317124i
$235$	−5.16357			−0.336834
$236$	−4.45687	−	7.71953i	−0.290118	−	0.502498i
$237$	8.33100	−	10.0465i	0.541156	−	0.652591i
$238$		−	23.1220i		−	1.49878i
$239$	−18.2504	−	10.5369i	−1.18052	−	0.681574i	−0.224385	−	0.974501i	$-0.572037\pi$
$239$	−18.2504	−	10.5369i	−1.18052	−	0.681574i	−0.956135	+	0.292927i	$0.905371\pi$
$240$	−5.04103	−	0.858689i	−0.325397	−	0.0554281i
$241$	−4.05347	−	2.34027i	−0.261107	−	0.150750i	0.363733	−	0.931503i	$-0.381502\pi$
$241$	−4.05347	−	2.34027i	−0.261107	−	0.150750i	−0.624839	+	0.780753i	$0.714836\pi$
$242$	5.41936	−	9.38661i	0.348370	−	0.603394i
$243$	14.7971	+	4.90367i	0.949234	+	0.314571i
$244$	0.270635	−	0.468753i	0.0173256	−	0.0300088i
$245$			17.4854i			1.11710i
$246$	−2.00429	+	11.7664i	−0.127789	+	0.750198i
$247$	3.66343	+	1.04015i	0.233098	+	0.0661834i
$248$	−4.73695	−	2.73488i	−0.300796	−	0.173665i
$249$	9.61275	+	1.63744i	0.609183	+	0.103768i
$250$		−	3.78953i		−	0.239671i
$251$	−9.56957	+	5.52499i	−0.604026	+	0.348734i	−0.770624	−	0.637290i	$-0.780055\pi$
$251$	−9.56957	+	5.52499i	−0.604026	+	0.348734i	0.166598	+	0.986025i	$0.446722\pi$
$252$	−8.18017	+	7.02762i	−0.515302	+	0.442699i
$253$	1.51299	+	2.62058i	0.0951210	+	0.164754i
$254$	−11.9875	+	6.92096i	−0.752160	+	0.434260i
$255$	−25.3187	−	20.9953i	−1.58552	−	1.31478i
$256$	1.00000			0.0625000
$257$	−18.1566			−1.13258			−0.566290	−	0.824206i	$-0.691622\pi$
$257$	−18.1566			−1.13258			−0.566290	+	0.824206i	$0.691622\pi$
$258$	−7.51812	−	6.23434i	−0.468057	−	0.388133i
$259$	8.81185	−	5.08752i	0.547541	−	0.316123i
$260$	−1.28969	−	2.23381i	−0.0799833	−	0.138535i
$261$	19.3343	+	6.78365i	1.19676	+	0.419897i
$262$	3.94837	−	2.27959i	0.243931	−	0.140834i
$263$			3.07662i			0.189712i	0.995491	+	0.0948562i	$0.0302391\pi$
$263$			3.07662i			0.189712i	−0.995491	+	0.0948562i	$0.969761\pi$
$264$	−0.685699	−	0.116802i	−0.0422018	−	0.00718866i
$265$	−28.3914	−	16.3918i	−1.74407	−	1.00694i
$266$	15.1940	−	3.83034i	0.931601	−	0.234853i
$267$	2.04654	−	12.0144i	0.125246	−	0.735271i
$268$			7.78609i			0.475611i
$269$	11.3515	−	19.6613i	0.692112	−	1.19877i	−0.279033	−	0.960281i	$-0.590014\pi$
$269$	11.3515	−	19.6613i	0.692112	−	1.19877i	0.971145	−	0.238491i	$-0.0766528\pi$
$270$	0.267484	+	15.3386i	0.0162785	+	0.933477i
$271$	13.7948	−	23.8934i	0.837977	−	1.45142i	−0.0536063	−	0.998562i	$-0.517072\pi$
$271$	13.7948	−	23.8934i	0.837977	−	1.45142i	0.891583	−	0.452857i	$-0.149595\pi$
$272$	5.57034	+	3.21604i	0.337752	+	0.195001i
$273$	−5.36253	−	0.913454i	−0.324555	−	0.0552847i
$274$	3.73376	+	2.15569i	0.225565	+	0.130230i
$275$			1.49249i			0.0900004i
$276$	−8.33077	+	10.0462i	−0.501453	+	0.604712i
$277$	0.540776	+	0.936651i	0.0324921	+	0.0562779i	0.881814	−	0.471597i	$-0.156322\pi$
$277$	0.540776	+	0.936651i	0.0324921	+	0.0562779i	−0.849322	+	0.527875i	$0.822989\pi$
$278$	−7.60048			−0.455846
$279$	−5.43268	+	15.4839i	−0.325246	+	0.926995i
$280$	−9.19123	−	5.30656i	−0.549281	−	0.317128i
$281$	−0.270564	+	0.468631i	−0.0161405	+	0.0279562i	−0.873983	−	0.485957i	$-0.838471\pi$
$281$	−0.270564	+	0.468631i	−0.0161405	+	0.0279562i	0.857842	+	0.513913i	$0.171805\pi$
$282$	−1.05261	−	2.84053i	−0.0626818	−	0.169151i
$283$	−5.28099	−	9.14694i	−0.313922	−	0.543729i	0.665286	−	0.746589i	$-0.268310\pi$
$283$	−5.28099	−	9.14694i	−0.313922	−	0.543729i	−0.979208	+	0.202860i	$0.934976\pi$
$284$	−7.15737	+	12.3969i	−0.424712	+	0.735622i
$285$	9.60226	−	20.1155i	0.568789	−	1.19154i
$286$	−0.175429	−	0.303851i	−0.0103733	−	0.0179671i
$287$	−12.3862	+	21.4535i	−0.731134	+	1.26636i
$288$	−0.555252	−	2.94817i	−0.0327186	−	0.173722i
$289$	12.1858	+	21.1065i	0.716813	+	1.24156i
$290$			20.1645i			1.18410i
$291$	0.247258	−	0.298173i	0.0144945	−	0.0174792i
$292$	6.91698	−	11.9806i	0.404786	−	0.701109i
$293$	−5.55708	+	9.62515i	−0.324648	+	0.562307i	−0.981441	−	0.191764i	$-0.938579\pi$
$293$	−5.55708	+	9.62515i	−0.324648	+	0.562307i	0.656793	+	0.754071i	$0.271913\pi$
$294$	−9.61891	+	3.56445i	−0.560986	+	0.207883i
$295$	−22.7908	−	13.1583i	−1.32693	−	0.766106i
$296$			2.83050i			0.164519i
$297$	0.0363841	+	2.08641i	0.00211122	+	0.121066i
$298$	12.5051	−	7.21981i	0.724400	−	0.418232i
$299$	−6.58309			−0.380710
$300$	−6.03596	+	2.23673i	−0.348486	+	0.129137i
$301$	−10.1352	−	17.5547i	−0.584183	−	1.01184i
$302$	5.59829	−	3.23217i	0.322145	−	0.185991i
$303$	5.87023	+	15.8412i	0.337236	+	0.910056i
$304$	−1.19056	+	4.19316i	−0.0682832	+	0.240494i
$305$		−	1.59802i		−	0.0915025i
$306$	6.38848	−	18.2080i	0.365205	−	1.04088i
$307$	9.25533	+	5.34357i	0.528229	+	0.304973i	0.740295	−	0.672282i	$-0.234686\pi$
$307$	9.25533	+	5.34357i	0.528229	+	0.304973i	−0.212066	+	0.977255i	$0.568019\pi$
$308$	−1.25022	−	0.721817i	−0.0712382	−	0.0411294i
$309$	4.57986	+	12.3591i	0.260539	+	0.703083i
$310$	−16.1487			−0.917184
$311$	11.5305	+	6.65714i	0.653835	+	0.377492i	0.789924	−	0.613205i	$-0.210120\pi$
$311$	11.5305	+	6.65714i	0.653835	+	0.377492i	−0.136089	+	0.990697i	$0.543453\pi$
$312$	0.965936	−	1.16484i	0.0546854	−	0.0659461i
$313$	−5.51662	+	9.55506i	−0.311818	+	0.540084i	−0.978756	−	0.205029i	$-0.934271\pi$
$313$	−5.51662	+	9.55506i	−0.311818	+	0.540084i	0.666938	+	0.745113i	$0.267605\pi$
$314$	11.1431	+	19.3005i	0.628844	+	1.08919i
$315$	−10.5412	+	30.0438i	−0.593928	+	1.69278i
$316$			7.53520i			0.423888i
$317$	1.36483	−	2.36395i	0.0766563	−	0.132773i	−0.825149	−	0.564915i	$-0.808909\pi$
$317$	1.36483	−	2.36395i	0.0766563	−	0.132773i	0.901805	+	0.432143i	$0.142242\pi$
$318$	3.22963	−	18.9599i	0.181109	−	1.06322i
$319$			2.74284i			0.153570i
$320$	2.55682	−	1.47618i	0.142931	−	0.0825210i
$321$	−10.8264	−	8.97775i	−0.604273	−	0.501089i
$322$	−23.4578	+	13.5434i	−1.30725	+	0.754742i
$323$	−20.1172	+	19.5284i	−1.11935	+	1.08659i
$324$	−8.38339	+	3.27396i	−0.465744	+	0.181886i
$325$	−2.81193	−	1.62347i	−0.155978	−	0.0900538i
$326$	−12.8336			−0.710787
$327$	−4.87757	−	13.1625i	−0.269730	−	0.727886i
$328$	−3.44559	−	5.96794i	−0.190251	−	0.329525i
$329$		−	6.28715i		−	0.346622i
$330$	−1.92563	+	0.713574i	−0.106002	+	0.0392809i
$331$	−25.0298	+	14.4510i	−1.37576	+	0.794298i	−0.991646	−	0.128986i	$-0.958828\pi$
$331$	−25.0298	+	14.4510i	−1.37576	+	0.794298i	−0.384118	+	0.923284i	$0.625494\pi$
$332$	−4.87561	+	2.81493i	−0.267584	+	0.154489i
$333$	8.34478	−	1.57164i	0.457291	−	0.0861253i
$334$	17.2918			0.946167
$335$	11.4937	+	19.9076i	0.627966	+	1.08767i
$336$	1.04554	−	6.13795i	0.0570388	−	0.334853i
$337$	−4.76967	+	2.75377i	−0.259820	+	0.150007i	−0.624253	−	0.781223i	$-0.714596\pi$
$337$	−4.76967	+	2.75377i	−0.259820	+	0.150007i	0.364432	+	0.931230i	$0.381263\pi$
$338$	−12.2367			−0.665589
$339$	11.8083	−	4.37576i	0.641339	−	0.237659i
$340$	18.9898			1.02987
$341$	−2.19660			−0.118953
$342$	13.0232	+	1.18171i	0.704214	+	0.0638994i
$343$	3.87331			0.209139
$344$	5.63883			0.304025
$345$	−6.47022	+	37.9841i	−0.348345	+	2.04500i
$346$	−7.58102			−0.407558
$347$	−4.82996	+	2.78858i	−0.259286	+	0.149699i	−0.624009	−	0.781417i	$-0.714497\pi$
$347$	−4.82996	+	2.78858i	−0.259286	+	0.149699i	0.364723	+	0.931116i	$0.381164\pi$
$348$	−11.0927	+	4.11058i	−0.594630	+	0.220350i
$349$	15.4336	+	26.7318i	0.826141	+	1.43092i	0.901044	+	0.433728i	$0.142802\pi$
$349$	15.4336	+	26.7318i	0.826141	+	1.43092i	−0.0749026	+	0.997191i	$0.523865\pi$
$350$	−13.3598			−0.714113
$351$	−3.97049	−	2.20096i	−0.211929	−	0.117479i
$352$	0.347788	−	0.200795i	0.0185372	−	0.0107024i
$353$	−6.39762	+	3.69367i	−0.340511	+	0.196594i	−0.660498	−	0.750828i	$-0.729655\pi$
$353$	−6.39762	+	3.69367i	−0.340511	+	0.196594i	0.319987	+	0.947422i	$0.396321\pi$
$354$	2.59255	−	15.2198i	0.137792	−	0.808925i
$355$			42.2623i			2.24305i
$356$	3.51823	+	6.09375i	0.186466	+	0.322968i
$357$	25.5639	−	30.8280i	1.35298	−	1.63159i
$358$	8.65371			0.457363
$359$	−5.05646	−	2.91935i	−0.266870	−	0.154077i	0.360595	−	0.932723i	$-0.382574\pi$
$359$	−5.05646	−	2.91935i	−0.266870	−	0.154077i	−0.627464	+	0.778645i	$0.715907\pi$
$360$	−5.77171	−	6.71828i	−0.304196	−	0.354085i
$361$	−16.1651	−	9.98440i	−0.850797	−	0.525495i
$362$	10.7954	−	6.23275i	0.567396	−	0.327586i
$363$	17.6034	−	6.52325i	0.923941	−	0.342382i
$364$	2.71989	−	1.57033i	0.142561	−	0.0823075i
$365$		−	40.8428i		−	2.13781i
$366$	0.879089	−	0.325761i	0.0459507	−	0.0170278i
$367$	13.3734	−	23.1634i	0.698084	−	1.20912i	−0.271045	−	0.962567i	$-0.587369\pi$
$367$	13.3734	−	23.1634i	0.698084	−	1.20912i	0.969130	−	0.246551i	$-0.0792974\pi$
$368$		−	7.53500i		−	0.392789i
$369$	−15.6813	+	13.4719i	−0.816337	+	0.701319i
$370$	4.17832	+	7.23707i	0.217221	+	0.376237i
$371$	19.9586	−	34.5693i	1.03620	−	1.79475i
$372$	−3.29195	−	8.88356i	−0.170680	−	0.460591i
$373$	28.7871	+	16.6203i	1.49054	+	0.860564i	0.999941	−	0.0108212i	$-0.00344455\pi$
$373$	28.7871	+	16.6203i	1.49054	+	0.860564i	0.490599	+	0.871385i	$0.336778\pi$
$374$	2.58306			0.133567
$375$	4.18975	−	5.05250i	0.216358	−	0.260910i
$376$	1.51465	+	0.874481i	0.0781119	+	0.0450979i
$377$	−5.16766	−	2.98355i	−0.266148	−	0.153661i
$378$	−18.6762	+	0.325688i	−0.960602	+	0.0167516i
$379$			3.08682i			0.158559i	0.996852	+	0.0792796i	$0.0252620\pi$
$379$			3.08682i			0.158559i	−0.996852	+	0.0792796i	$0.974738\pi$
$380$	3.14581	+	12.4786i	0.161377	+	0.640140i
$381$	−23.6345	−	4.02590i	−1.21083	−	0.206253i
$382$	−21.9809	+	12.6907i	−1.12464	+	0.649312i
$383$	−6.18874	−	10.7192i	−0.316230	−	0.547726i	0.663468	−	0.748204i	$-0.269084\pi$
$383$	−6.18874	−	10.7192i	−0.316230	−	0.547726i	−0.979698	+	0.200478i	$0.935750\pi$
$384$	1.33328	+	1.10561i	0.0680385	+	0.0564204i
$385$	−4.26213			−0.217218
$386$	15.4798	−	8.93726i	0.787900	−	0.454894i
$387$	−3.13097	−	16.6242i	−0.159156	−	0.845056i
$388$			0.223639i			0.0113535i
$389$	−0.472234	−	0.272644i	−0.0239432	−	0.0138236i	0.487981	−	0.872854i	$-0.337734\pi$
$389$	−0.472234	−	0.272644i	−0.0239432	−	0.0138236i	−0.511924	+	0.859031i	$0.671067\pi$
$390$	0.750209	−	4.40419i	0.0379883	−	0.223015i
$391$	24.2328	−	41.9725i	1.22551	−	2.12264i
$392$	2.96126	−	5.12905i	0.149566	−	0.259056i
$393$	7.78461	+	1.32603i	0.392682	+	0.0668894i
$394$		−	11.9456i		−	0.601813i
$395$	11.1233	+	19.2662i	0.559675	+	0.969386i
$396$	−0.785089	−	0.913845i	−0.0394522	−	0.0459224i
$397$	−16.6785	+	28.8880i	−0.837070	+	1.44985i	0.0552643	+	0.998472i	$0.482400\pi$
$397$	−16.6785	+	28.8880i	−0.837070	+	1.44985i	−0.892334	+	0.451376i	$0.850933\pi$
$398$	10.7216	+	18.5703i	0.537424	+	0.930846i
$399$	24.4926	+	11.6917i	1.22616	+	0.585317i
$400$	1.85822	−	3.21853i	0.0929110	−	0.160927i
$401$	−5.00932	−	8.67639i	−0.250153	−	0.433278i	0.713415	−	0.700742i	$-0.247148\pi$
$401$	−5.00932	−	8.67639i	−0.250153	−	0.433278i	−0.963568	+	0.267464i	$0.913814\pi$
$402$	−8.60838	+	10.3810i	−0.429347	+	0.517758i
$403$	2.38938	−	4.13852i	0.119023	−	0.206154i
$404$	−8.44696	−	4.87686i	−0.420252	−	0.242633i
$405$	−16.6019	+	20.7463i	−0.824954	+	1.03089i
$406$	−24.5522			−1.21851
$407$	0.568351	+	0.984412i	0.0281721	+	0.0487955i
$408$	3.87112	+	10.4465i	0.191649	+	0.517179i
$409$			3.00333i			0.148505i	0.997239	+	0.0742525i	$0.0236571\pi$
$409$			3.00333i			0.148505i	−0.997239	+	0.0742525i	$0.976343\pi$
$410$	−17.6195	−	10.1726i	−0.870166	−	0.502391i
$411$	2.59479	+	7.00222i	0.127991	+	0.345394i
$412$	−6.59018	−	3.80484i	−0.324675	−	0.187451i
$413$	16.0215	−	27.7501i	0.788367	−	1.36549i
$414$	−22.2144	+	4.18383i	−1.09178	+	0.205624i
$415$	−8.31070	+	14.3946i	−0.407956	+	0.706601i
$416$			0.873668i			0.0428351i
$417$	−10.1335	−	8.40317i	−0.496242	−	0.411505i
$418$	0.427905	+	1.69739i	0.0209295	+	0.0830220i
$419$	18.8388	+	10.8766i	0.920336	+	0.531356i	0.883742	−	0.467974i	$-0.155016\pi$
$419$	18.8388	+	10.8766i	0.920336	+	0.531356i	0.0365939	+	0.999330i	$0.488349\pi$
$420$	−6.38747	−	17.2370i	−0.311677	−	0.841081i
$421$		−	20.4131i		−	0.994872i	−0.867501	−	0.497436i	$-0.834275\pi$
$421$		−	20.4131i		−	0.994872i	0.867501	−	0.497436i	$-0.165725\pi$
$422$	−3.69705	+	2.13450i	−0.179970	+	0.103906i
$423$	1.73711	−	4.95099i	0.0844610	−	0.240725i
$424$	5.55209	+	9.61651i	0.269633	+	0.467019i
$425$	20.7018	−	11.9522i	1.00419	−	0.579768i
$426$	−23.2489	+	8.61527i	−1.12641	+	0.417411i
$427$	1.94575			0.0941615
$428$	8.12018			0.392504
$429$	0.102046	−	0.599073i	0.00492683	−	0.0289235i
$430$	14.4175	−	8.32393i	0.695272	−	0.401415i
$431$	−2.12382	−	3.67856i	−0.102301	−	0.177190i	0.810331	−	0.585972i	$-0.199287\pi$
$431$	−2.12382	−	3.67856i	−0.102301	−	0.177190i	−0.912632	+	0.408782i	$0.865954\pi$
$432$	2.51922	−	4.54462i	0.121206	−	0.218653i
$433$	15.1361	−	8.73884i	0.727396	−	0.419962i	−0.0900730	−	0.995935i	$-0.528710\pi$
$433$	15.1361	−	8.73884i	0.727396	−	0.419962i	0.817469	+	0.575973i	$0.195377\pi$
$434$		−	19.6626i		−	0.943836i
$435$	−22.2940	+	26.8848i	−1.06892	+	1.28903i
$436$	7.01856	+	4.05217i	0.336128	+	0.194064i
$437$	31.5954	+	8.97086i	1.51141	+	0.429134i
$438$	22.4681	−	8.32591i	1.07357	−	0.397828i
$439$		−	5.13807i		−	0.245227i	−0.992455	−	0.122613i	$-0.960872\pi$
$439$		−	5.13807i		−	0.245227i	0.992455	−	0.122613i	$-0.0391275\pi$
$440$	0.592821	−	1.02680i	0.0282616	−	0.0489506i
$441$	−16.7656	−	5.88237i	−0.798360	−	0.280113i
$442$	−2.80975	+	4.86663i	−0.133646	+	0.231482i
$443$	8.44956	+	4.87835i	0.401451	+	0.231778i	0.687110	−	0.726554i	$-0.258879\pi$
$443$	8.44956	+	4.87835i	0.401451	+	0.231778i	−0.285659	+	0.958331i	$0.592212\pi$
$444$	−3.12943	+	3.77383i	−0.148516	+	0.179098i
$445$	17.9909	+	10.3871i	0.852852	+	0.492395i
$446$			10.0653i			0.476607i
$447$	24.6550	+	4.19974i	1.16614	+	0.198641i
$448$	1.79740	+	3.11318i	0.0849190	+	0.147084i
$449$	10.5516			0.497962			0.248981	−	0.968508i	$-0.419904\pi$
$449$	10.5516			0.497962			0.248981	+	0.968508i	$0.419904\pi$
$450$	−10.5206	−	3.69125i	−0.495944	−	0.174007i
$451$	−2.39667	−	1.38372i	−0.112855	−	0.0651568i
$452$	−3.63528	+	6.29649i	−0.170989	+	0.296162i
$453$	11.0376	+	1.88014i	0.518591	+	0.0883369i
$454$	10.0498	+	17.4068i	0.471662	+	0.816942i
$455$	4.63617	−	8.03009i	0.217347	−	0.376456i
$456$	−6.22334	+	4.27434i	−0.291435	+	0.200165i
$457$	−9.68365	−	16.7726i	−0.452982	−	0.784588i	0.545587	−	0.838054i	$-0.316307\pi$
$457$	−9.68365	−	16.7726i	−0.452982	−	0.784588i	−0.998570	+	0.0534656i	$0.982973\pi$
$458$	10.6629	−	18.4687i	0.498244	−	0.862984i
$459$	28.6486	−	17.2132i	1.33720	−	0.803442i
$460$	−11.1230	−	19.2656i	−0.518613	−	0.898265i
$461$		−	25.3709i		−	1.18164i	−0.806803	−	0.590821i	$-0.798804\pi$
$461$		−	25.3709i		−	1.18164i	0.806803	−	0.590821i	$-0.201196\pi$
$462$	−0.868846	−	2.34464i	−0.0404224	−	0.109083i
$463$	−8.29190	+	14.3620i	−0.385357	+	0.667458i	−0.991819	−	0.127655i	$-0.959255\pi$
$463$	−8.29190	+	14.3620i	−0.385357	+	0.667458i	0.606461	+	0.795113i	$0.292588\pi$
$464$	3.41497	−	5.91491i	0.158536	−	0.274593i
$465$	−21.5307	−	17.8542i	−0.998461	−	0.827967i
$466$	16.3284	+	9.42721i	0.756399	+	0.436707i
$467$		−	11.1994i		−	0.518244i	−0.965845	−	0.259122i	$-0.916567\pi$
$467$		−	11.1994i		−	0.518244i	0.965845	−	0.259122i	$-0.0834332\pi$
$468$	2.57572	−	0.485106i	0.119063	−	0.0224240i
$469$	−24.2395	+	13.9947i	−1.11928	+	0.646214i
$470$	5.16357			0.238178
$471$	−6.48193	+	38.0529i	−0.298672	+	1.75338i
$472$	4.45687	+	7.71953i	0.205144	+	0.355320i
$473$	1.96112	−	1.13225i	0.0901722	−	0.0520609i
$474$	−8.33100	+	10.0465i	−0.382655	+	0.461451i
$475$	11.2835	+	11.6237i	0.517722	+	0.533330i
$476$			23.1220i			1.05979i
$477$	25.2683	−	21.7081i	1.15695	−	0.993945i
$478$	18.2504	+	10.5369i	0.834754	+	0.481945i
$479$	1.60732	+	0.927988i	0.0734404	+	0.0424008i	0.536271	−	0.844046i	$-0.319833\pi$
$479$	1.60732	+	0.927988i	0.0734404	+	0.0424008i	−0.462830	+	0.886447i	$0.653166\pi$
$480$	5.04103	+	0.858689i	0.230090	+	0.0391936i
$481$	−2.47291			−0.112755
$482$	4.05347	+	2.34027i	0.184630	+	0.106596i
$483$	−46.2494	−	7.87813i	−2.10442	−	0.358467i
$484$	−5.41936	+	9.38661i	−0.246335	+	0.426664i
$485$	0.330132	+	0.571805i	0.0149905	+	0.0259643i
$486$	−14.7971	−	4.90367i	−0.671210	−	0.222435i
$487$		−	12.1257i		−	0.549467i	−0.961520	−	0.274733i	$-0.911410\pi$
$487$		−	12.1257i		−	0.549467i	0.961520	−	0.274733i	$-0.0885896\pi$
$488$	−0.270635	+	0.468753i	−0.0122511	+	0.0212195i
$489$	−17.1107	−	14.1889i	−0.773773	−	0.641646i
$490$		−	17.4854i		−	0.789911i
$491$	13.0571	−	7.53852i	0.589258	−	0.340208i	−0.175546	−	0.984471i	$-0.556169\pi$
$491$	13.0571	−	7.53852i	0.589258	−	0.340208i	0.764804	+	0.644263i	$0.222836\pi$
$492$	2.00429	−	11.7664i	0.0903603	−	0.530470i
$493$	38.0451	−	21.9654i	1.71347	−	0.989271i
$494$	−3.66343	−	1.04015i	−0.164825	−	0.0467987i
$495$	−3.35633	−	1.17760i	−0.150856	−	0.0529294i
$496$	4.73695	+	2.73488i	0.212695	+	0.122800i
$497$	−51.4585			−2.30823
$498$	−9.61275	−	1.63744i	−0.430758	−	0.0733753i
$499$	2.01097	+	3.48310i	0.0900232	+	0.155925i	0.907521	−	0.420007i	$-0.137973\pi$
$499$	2.01097	+	3.48310i	0.0900232	+	0.155925i	−0.817497	+	0.575932i	$0.804639\pi$
$500$			3.78953i			0.169473i
$501$	23.0548	+	19.1180i	1.03001	+	0.854131i
$502$	9.56957	−	5.52499i	0.427111	−	0.246592i
$503$	11.8007	−	6.81311i	0.526165	−	0.303782i	−0.213288	−	0.976989i	$-0.568417\pi$
$503$	11.8007	−	6.81311i	0.526165	−	0.303782i	0.739453	+	0.673208i	$0.235084\pi$
$504$	8.18017	−	7.02762i	0.364374	−	0.313035i
$505$	−28.7965			−1.28143
$506$	−1.51299	−	2.62058i	−0.0672607	−	0.116499i
$507$	−16.3149	−	13.5290i	−0.724571	−	0.600845i
$508$	11.9875	−	6.92096i	0.531857	−	0.307068i
$509$	−12.6948			−0.562687			−0.281344	−	0.959607i	$-0.590780\pi$
$509$	−12.6948			−0.562687			−0.281344	+	0.959607i	$0.590780\pi$
$510$	25.3187	+	20.9953i	1.12113	+	0.929689i
$511$	49.7302			2.19993
$512$	−1.00000			−0.0441942
$513$	16.0570	+	15.9741i	0.708934	+	0.705274i
$514$	18.1566			0.800855
$515$	−22.4665			−0.989994
$516$	7.51812	+	6.23434i	0.330967	+	0.274452i
$517$	0.702367			0.0308901
$518$	−8.81185	+	5.08752i	−0.387170	+	0.223533i
$519$	−10.1076	−	8.38165i	−0.443674	−	0.367913i
$520$	1.28969	+	2.23381i	0.0565567	+	0.0979591i
$521$	12.8459			0.562789			0.281394	−	0.959592i	$-0.409203\pi$
$521$	12.8459			0.562789			0.281394	+	0.959592i	$0.409203\pi$
$522$	−19.3343	−	6.78365i	−0.846240	−	0.296912i
$523$	−33.1727	+	19.1522i	−1.45054	+	0.837469i	−0.998512	−	0.0545348i	$-0.982632\pi$
$523$	−33.1727	+	19.1522i	−1.45054	+	0.837469i	−0.452027	+	0.892004i	$0.649299\pi$
$524$	−3.94837	+	2.27959i	−0.172485	+	0.0995845i
$525$	−17.8123	−	14.7708i	−0.777394	−	0.644649i
$526$		−	3.07662i		−	0.134147i
$527$	17.5909	+	30.4684i	0.766274	+	1.32723i
$528$	0.685699	+	0.116802i	0.0298412	+	0.00508315i
$529$	−33.7762			−1.46853
$530$	28.3914	+	16.3918i	1.23324	+	0.712014i
$531$	20.2838	−	17.4259i	0.880241	−	0.756219i
$532$	−15.1940	+	3.83034i	−0.658742	+	0.166066i
$533$	5.21400	−	3.01030i	0.225843	−	0.130391i
$534$	−2.04654	+	12.0144i	−0.0885624	+	0.519915i
$535$	20.7618	−	11.9869i	0.897612	−	0.518237i
$536$		−	7.78609i		−	0.336308i
$537$	11.5378	+	9.56763i	0.497893	+	0.412874i
$538$	−11.3515	+	19.6613i	−0.489397	+	0.847660i
$539$		−	2.37843i		−	0.102446i
$540$	−0.267484	−	15.3386i	−0.0115107	−	0.660068i
$541$	−4.95503	−	8.58237i	−0.213034	−	0.368985i	0.739629	−	0.673015i	$-0.235001\pi$
$541$	−4.95503	−	8.58237i	−0.213034	−	0.368985i	−0.952662	+	0.304030i	$0.901668\pi$
$542$	−13.7948	+	23.8934i	−0.592539	+	1.02631i
$543$	21.2843	+	3.62557i	0.913396	+	0.155588i
$544$	−5.57034	−	3.21604i	−0.238827	−	0.137887i
$545$	23.9269			1.02492
$546$	5.36253	+	0.913454i	0.229495	+	0.0390922i
$547$	2.91878	+	1.68516i	0.124798	+	0.0720523i	0.561100	−	0.827748i	$-0.310378\pi$
$547$	2.91878	+	1.68516i	0.124798	+	0.0720523i	−0.436301	+	0.899801i	$0.643712\pi$
$548$	−3.73376	−	2.15569i	−0.159499	−	0.0920865i
$549$	1.53223	+	0.537600i	0.0653941	+	0.0229442i
$550$		−	1.49249i		−	0.0636399i
$551$	20.7364	+	21.3616i	0.883401	+	0.910033i
$552$	8.33077	−	10.0462i	0.354581	−	0.427596i
$553$	−23.4584	+	13.5437i	−0.997555	+	0.575938i
$554$	−0.540776	−	0.936651i	−0.0229754	−	0.0397945i
$555$	−2.43052	+	14.2686i	−0.103170	+	0.605669i
$556$	7.60048			0.322332
$557$	17.2088	−	9.93548i	0.729158	−	0.420980i	−0.0889559	−	0.996036i	$-0.528353\pi$
$557$	17.2088	−	9.93548i	0.729158	−	0.420980i	0.818114	+	0.575056i	$0.195020\pi$
$558$	5.43268	−	15.4839i	0.229984	−	0.655484i
$559$			4.92646i			0.208367i
$560$	9.19123	+	5.30656i	0.388401	+	0.224243i
$561$	3.44394	+	2.85586i	0.145403	+	0.120575i
$562$	0.270564	−	0.468631i	0.0114131	−	0.0197680i
$563$	−2.04377	+	3.53992i	−0.0861348	+	0.149190i	−0.905874	−	0.423547i	$-0.860785\pi$
$563$	−2.04377	+	3.53992i	−0.0861348	+	0.149190i	0.819739	+	0.572737i	$0.194118\pi$
$564$	1.05261	+	2.84053i	0.0443227	+	0.119608i
$565$			21.4653i			0.903054i
$566$	5.28099	+	9.14694i	0.221977	+	0.384475i
$567$	−25.2607	−	20.2144i	−1.06085	−	0.848925i
$568$	7.15737	−	12.3969i	0.300316	−	0.520163i
$569$	−3.45828	−	5.98992i	−0.144979	−	0.251111i	0.784386	−	0.620273i	$-0.212978\pi$
$569$	−3.45828	−	5.98992i	−0.144979	−	0.251111i	−0.929365	+	0.369162i	$0.879645\pi$
$570$	−9.60226	+	20.1155i	−0.402194	+	0.842546i
$571$	19.0304	−	32.9617i	0.796399	−	1.37940i	−0.125547	−	0.992088i	$-0.540069\pi$
$571$	19.0304	−	32.9617i	0.796399	−	1.37940i	0.921947	−	0.387317i	$-0.126598\pi$
$572$	0.175429	+	0.303851i	0.00733503	+	0.0127047i
$573$	−43.3376	−	7.38213i	−1.81045	−	0.308393i
$574$	12.3862	−	21.4535i	0.516989	−	0.895452i
$575$	−24.2516	−	14.0017i	−1.01136	−	0.583911i
$576$	0.555252	+	2.94817i	0.0231355	+	0.122840i
$577$	−11.4644			−0.477269			−0.238635	−	0.971109i	$-0.576700\pi$
$577$	−11.4644			−0.477269			−0.238635	+	0.971109i	$0.576700\pi$
$578$	−12.1858	−	21.1065i	−0.506863	−	0.877913i
$579$	30.5200	+	5.19877i	1.26837	+	0.216054i
$580$		−	20.1645i		−	0.837284i
$581$	−17.5268	−	10.1191i	−0.727133	−	0.419811i
$582$	−0.247258	+	0.298173i	−0.0102492	+	0.0123597i
$583$	3.86190	+	2.22967i	0.159944	+	0.0923435i
$584$	−6.91698	+	11.9806i	−0.286227	+	0.495759i
$585$	5.86955	−	5.04256i	0.242676	−	0.208484i
$586$	5.55708	−	9.62515i	0.229561	−	0.397611i
$587$		−	21.8698i		−	0.902663i	−0.892356	−	0.451332i	$-0.850949\pi$
$587$		−	21.8698i		−	0.902663i	0.892356	−	0.451332i	$-0.149051\pi$
$588$	9.61891	−	3.56445i	0.396677	−	0.146995i
$589$	−17.1074	+	16.6067i	−0.704898	+	0.684268i
$590$	22.7908	+	13.1583i	0.938284	+	0.541718i
$591$	13.2072	−	15.9268i	0.543272	−	0.655143i
$592$		−	2.83050i		−	0.116333i
$593$	−3.78515	+	2.18536i	−0.155437	+	0.0897419i	−0.575701	−	0.817660i	$-0.695271\pi$
$593$	−3.78515	+	2.18536i	−0.155437	+	0.0897419i	0.420264	+	0.907402i	$0.361938\pi$
$594$	−0.0363841	−	2.08641i	−0.00149286	−	0.0856064i
$595$	34.1322	+	59.1187i	1.39928	+	2.42363i
$596$	−12.5051	+	7.21981i	−0.512228	+	0.295735i
$597$	−6.23670	+	36.6133i	−0.255251	+	1.49848i
$598$	6.58309			0.269202
$599$	−33.6713			−1.37577			−0.687886	−	0.725819i	$-0.741461\pi$
$599$	−33.6713			−1.37577			−0.687886	+	0.725819i	$0.741461\pi$
$600$	6.03596	−	2.23673i	0.246417	−	0.0913139i
$601$	−42.2429	+	24.3890i	−1.72312	+	0.994846i	−0.810865	+	0.585233i	$0.801003\pi$
$601$	−42.2429	+	24.3890i	−1.72312	+	0.994846i	−0.912259	+	0.409614i	$0.865664\pi$
$602$	10.1352	+	17.5547i	0.413080	+	0.715476i
$603$	−22.9547	+	4.32324i	−0.934787	+	0.176056i
$604$	−5.59829	+	3.23217i	−0.227791	+	0.131515i
$605$			31.9998i			1.30098i
$606$	−5.87023	−	15.8412i	−0.238462	−	0.643507i
$607$	14.2403	+	8.22165i	0.577997	+	0.333707i	0.760337	−	0.649529i	$-0.225034\pi$
$607$	14.2403	+	8.22165i	0.577997	+	0.333707i	−0.182340	+	0.983236i	$0.558367\pi$
$608$	1.19056	−	4.19316i	0.0482835	−	0.170055i
$609$	−32.7349	−	27.1452i	−1.32649	−	1.09998i
$610$			1.59802i			0.0647021i
$611$	−0.764006	+	1.32330i	−0.0309084	+	0.0535349i
$612$	−6.38848	+	18.2080i	−0.258239	+	0.736016i
$613$	−6.49743	+	11.2539i	−0.262429	+	0.454540i	−0.966887	−	0.255206i	$-0.917857\pi$
$613$	−6.49743	+	11.2539i	−0.262429	+	0.454540i	0.704458	+	0.709746i	$0.251190\pi$
$614$	−9.25533	−	5.34357i	−0.373515	−	0.215649i
$615$	−12.2447	−	33.0433i	−0.493755	−	1.33243i
$616$	1.25022	+	0.721817i	0.0503730	+	0.0290829i
$617$			45.3951i			1.82754i	0.406234	+	0.913769i	$0.366842\pi$
$617$			45.3951i			1.82754i	−0.406234	+	0.913769i	$0.633158\pi$
$618$	−4.57986	−	12.3591i	−0.184229	−	0.497155i
$619$	12.0243	+	20.8267i	0.483297	+	0.837094i	0.999816	−	0.0191813i	$-0.00610598\pi$
$619$	12.0243	+	20.8267i	0.483297	+	0.837094i	−0.516520	+	0.856275i	$0.672773\pi$
$620$	16.1487			0.648547
$621$	−34.2437	−	18.9823i	−1.37415	−	0.761734i
$622$	−11.5305	−	6.65714i	−0.462331	−	0.266927i
$623$	−12.6473	+	21.9057i	−0.506703	+	0.877635i
$624$	−0.965936	+	1.16484i	−0.0386684	+	0.0466310i
$625$	14.8851	+	25.7818i	0.595405	+	1.03127i
$626$	5.51662	−	9.55506i	0.220488	−	0.381897i
$627$	−1.30613	+	2.73618i	−0.0521620	+	0.109273i
$628$	−11.1431	−	19.3005i	−0.444660	−	0.770174i
$629$	9.10299	−	15.7668i	0.362960	−	0.628665i
$630$	10.5412	−	30.0438i	0.419971	−	1.19697i
$631$	15.6523	+	27.1106i	0.623108	+	1.07925i	0.988903	+	0.148559i	$0.0474636\pi$
$631$	15.6523	+	27.1106i	0.623108	+	1.07925i	−0.365796	+	0.930695i	$0.619203\pi$
$632$		−	7.53520i		−	0.299734i
$633$	−7.28912	−	1.24163i	−0.289716	−	0.0493503i
$634$	−1.36483	+	2.36395i	−0.0542042	+	0.0938844i
$635$	20.4332	−	35.3913i	0.810866	−	1.40446i
$636$	−3.22963	+	18.9599i	−0.128063	+	0.751809i
$637$	4.48109	+	2.58716i	0.177547	+	0.102507i
$638$		−	2.74284i		−	0.108590i
$639$	−40.5224	−	14.2177i	−1.60304	−	0.562444i
$640$	−2.55682	+	1.47618i	−0.101067	+	0.0583512i
$641$	7.61480			0.300767			0.150383	−	0.988628i	$-0.451949\pi$
$641$	7.61480			0.300767			0.150383	+	0.988628i	$0.451949\pi$
$642$	10.8264	+	8.97775i	0.427286	+	0.354324i
$643$	−23.9232	−	41.4361i	−0.943437	−	1.63408i	−0.758850	−	0.651265i	$-0.774239\pi$
$643$	−23.9232	−	41.4361i	−0.943437	−	1.63408i	−0.184587	−	0.982816i	$-0.559095\pi$
$644$	23.4578	−	13.5434i	0.924367	−	0.533684i
$645$	28.4255	+	4.84200i	1.11925	+	0.190654i
$646$	20.1172	−	19.5284i	0.791500	−	0.768336i
$647$			9.80844i			0.385610i	0.981237	+	0.192805i	$0.0617584\pi$
$647$			9.80844i			0.385610i	−0.981237	+	0.192805i	$0.938242\pi$
$648$	8.38339	−	3.27396i	0.329331	−	0.128613i
$649$	3.10009	+	1.78984i	0.121689	+	0.0702573i
$650$	2.81193	+	1.62347i	0.110293	+	0.0636776i
$651$	21.7392	−	26.2157i	0.852026	−	1.02747i
$652$	12.8336			0.502602
$653$	15.6965	+	9.06241i	0.614253	+	0.354639i	0.774628	−	0.632417i	$-0.217937\pi$
$653$	15.6965	+	9.06241i	0.614253	+	0.354639i	−0.160375	+	0.987056i	$0.551270\pi$
$654$	4.87757	+	13.1625i	0.190728	+	0.514693i
$655$	−6.73018	+	11.6570i	−0.262970	+	0.455477i
$656$	3.44559	+	5.96794i	0.134528	+	0.233009i
$657$	39.1614	+	13.7402i	1.52783	+	0.536055i
$658$			6.28715i			0.245099i
$659$	20.8684	−	36.1450i	0.812916	−	1.40801i	−0.0978994	−	0.995196i	$-0.531212\pi$
$659$	20.8684	−	36.1450i	0.812916	−	1.40801i	0.910815	−	0.412815i	$-0.135454\pi$
$660$	1.92563	−	0.713574i	0.0749550	−	0.0277758i
$661$		−	43.4341i		−	1.68939i	−0.535246	−	0.844696i	$-0.679781\pi$
$661$		−	43.4341i		−	1.68939i	0.535246	−	0.844696i	$-0.320219\pi$
$662$	25.0298	−	14.4510i	0.972812	−	0.561653i
$663$	−9.12677	+	3.38208i	−0.354454	+	0.131349i
$664$	4.87561	−	2.81493i	0.189210	−	0.109241i
$665$	−33.1940	+	32.2225i	−1.28721	+	1.24954i
$666$	−8.34478	+	1.57164i	−0.323354	+	0.0608998i
$667$	−44.5688	−	25.7318i	−1.72571	−	0.996340i
$668$	−17.2918			−0.669041
$669$	−11.1283	+	13.4199i	−0.430246	+	0.518842i
$670$	−11.4937	−	19.9076i	−0.444039	−	0.769099i
$671$			0.217369i			0.00839143i
$672$	−1.04554	+	6.13795i	−0.0403325	+	0.236777i
$673$	42.6758	−	24.6389i	1.64503	−	0.949759i	0.666024	−	0.745930i	$-0.267995\pi$
$673$	42.6758	−	24.6389i	1.64503	−	0.949759i	0.979007	−	0.203829i	$-0.0653386\pi$
$674$	4.76967	−	2.75377i	0.183721	−	0.106071i
$675$	−9.94573	−	16.5531i	−0.382811	−	0.637128i
$676$	12.2367			0.470642
$677$	2.06955	+	3.58456i	0.0795392	+	0.137766i	0.903051	−	0.429533i	$-0.141322\pi$
$677$	2.06955	+	3.58456i	0.0795392	+	0.137766i	−0.823512	+	0.567299i	$0.807988\pi$
$678$	−11.8083	+	4.37576i	−0.453495	+	0.168050i
$679$	−0.696228	+	0.401968i	−0.0267188	+	0.0154261i
$680$	−18.9898			−0.728227
$681$	−5.84595	+	34.3193i	−0.224017	+	1.31512i
$682$	2.19660			0.0841123
$683$	42.6184			1.63075			0.815373	−	0.578936i	$-0.196532\pi$
$683$	42.6184			1.63075			0.815373	+	0.578936i	$0.196532\pi$
$684$	−13.0232	−	1.18171i	−0.497954	−	0.0451837i
$685$	−12.7288			−0.486341
$686$	−3.87331			−0.147884
$687$	34.6357	−	12.8348i	1.32144	−	0.489680i
$688$	−5.63883			−0.214978
$689$	−8.40163	+	4.85069i	−0.320077	+	0.184796i
$690$	6.47022	−	37.9841i	0.246317	−	1.44603i
$691$	13.1067	+	22.7015i	0.498603	+	0.863606i	0.999999	−	0.00161202i	$-0.000513121\pi$
$691$	13.1067	+	22.7015i	0.498603	+	0.863606i	−0.501395	+	0.865218i	$0.667180\pi$
$692$	7.58102			0.288187
$693$	1.43385	−	4.08666i	0.0544674	−	0.155239i
$694$	4.82996	−	2.78858i	0.183343	−	0.105853i
$695$	19.4331	−	11.2197i	0.737138	−	0.425587i
$696$	11.0927	−	4.11058i	0.420467	−	0.155811i
$697$			44.3247i			1.67892i
$698$	−15.4336	−	26.7318i	−0.584170	−	1.01181i
$699$	11.3475	+	30.6219i	0.429201	+	1.15823i
$700$	13.3598			0.504954
$701$	−7.01031	−	4.04740i	−0.264776	−	0.152868i	0.361735	−	0.932281i	$-0.382184\pi$
$701$	−7.01031	−	4.04740i	−0.264776	−	0.152868i	−0.626511	+	0.779412i	$0.715518\pi$
$702$	3.97049	+	2.20096i	0.149856	+	0.0830699i
$703$	11.8687	+	3.36987i	0.447637	+	0.127097i
$704$	−0.347788	+	0.200795i	−0.0131077	+	0.00756776i
$705$	6.88446	+	5.70889i	0.259284	+	0.215009i
$706$	6.39762	−	3.69367i	0.240778	−	0.139013i
$707$		−	35.0626i		−	1.31866i
$708$	−2.59255	+	15.2198i	−0.0974338	+	0.571996i
$709$	−1.65857	+	2.87272i	−0.0622888	+	0.107887i	−0.895488	−	0.445085i	$-0.853173\pi$
$709$	−1.65857	+	2.87272i	−0.0622888	+	0.107887i	0.833199	+	0.552973i	$0.186507\pi$
$710$		−	42.2623i		−	1.58608i
$711$	−22.2150	+	4.18394i	−0.833129	+	0.156910i
$712$	−3.51823	−	6.09375i	−0.131851	−	0.228373i
$713$	20.6073	−	35.6929i	0.771749	−	1.33671i
$714$	−25.5639	+	30.8280i	−0.956705	+	1.15371i
$715$	0.897078	+	0.517928i	0.0335488	+	0.0193694i
$716$	−8.65371			−0.323404
$717$	12.6832	+	34.2264i	0.473661	+	1.27821i
$718$	5.05646	+	2.91935i	0.188705	+	0.108949i
$719$	−34.4728	−	19.9029i	−1.28562	−	0.742252i	−0.307749	−	0.951468i	$-0.599576\pi$
$719$	−34.4728	−	19.9029i	−1.28562	−	0.742252i	−0.977869	+	0.209216i	$0.932909\pi$
$720$	5.77171	+	6.71828i	0.215099	+	0.250376i
$721$		−	27.3552i		−	1.01876i
$722$	16.1651	+	9.98440i	0.601604	+	0.371581i
$723$	2.81697	+	7.60178i	0.104764	+	0.282713i
$724$	−10.7954	+	6.23275i	−0.401209	+	0.231638i
$725$	−12.6915	−	21.9824i	−0.471352	−	0.816406i
$726$	−17.6034	+	6.52325i	−0.653325	+	0.242100i
$727$	−24.2337			−0.898779			−0.449390	−	0.893336i	$-0.648358\pi$
$727$	−24.2337			−0.898779			−0.449390	+	0.893336i	$0.648358\pi$
$728$	−2.71989	+	1.57033i	−0.100806	+	0.0582002i
$729$	−14.3071	−	22.8978i	−0.529891	−	0.848066i
$730$			40.8428i			1.51166i
$731$	−31.4102	−	18.1347i	−1.16175	−	0.670736i
$732$	−0.879089	+	0.325761i	−0.0324921	+	0.0120405i
$733$	−2.34875	+	4.06815i	−0.0867530	+	0.150261i	−0.906137	−	0.422985i	$-0.860982\pi$
$733$	−2.34875	+	4.06815i	−0.0867530	+	0.150261i	0.819384	+	0.573245i	$0.194316\pi$
$734$	−13.3734	+	23.1634i	−0.493620	+	0.854975i
$735$	19.3321	−	23.3129i	0.713074	−	0.859910i
$736$			7.53500i			0.277744i
$737$	−1.56341	−	2.70791i	−0.0575890	−	0.0997470i
$738$	15.6813	−	13.4719i	0.577238	−	0.495908i
$739$	−6.91384	+	11.9751i	−0.254330	+	0.440512i	−0.964713	−	0.263303i	$-0.915188\pi$
$739$	−6.91384	+	11.9751i	−0.254330	+	0.440512i	0.710384	+	0.703815i	$0.248521\pi$
$740$	−4.17832	−	7.23707i	−0.153598	−	0.266040i
$741$	−3.73436	−	5.43713i	−0.137185	−	0.199738i
$742$	−19.9586	+	34.5693i	−0.732704	+	1.26908i
$743$	24.8324	+	43.0109i	0.911011	+	1.57792i	0.812638	+	0.582768i	$0.198030\pi$
$743$	24.8324	+	43.0109i	0.911011	+	1.57792i	0.0983728	+	0.995150i	$0.468636\pi$
$744$	3.29195	+	8.88356i	0.120689	+	0.325687i
$745$	−21.3155	+	36.9195i	−0.780939	+	1.35263i
$746$	−28.7871	−	16.6203i	−1.05397	−	0.608511i
$747$	−11.0061	−	12.8111i	−0.402692	−	0.468734i
$748$	−2.58306			−0.0944462
$749$	14.5952	+	25.2796i	0.533296	+	0.923696i
$750$	−4.18975	+	5.05250i	−0.152988	+	0.184491i
$751$		−	22.4063i		−	0.817616i	−0.912620	−	0.408808i	$-0.865945\pi$
$751$		−	22.4063i		−	0.817616i	0.912620	−	0.408808i	$-0.134055\pi$
$752$	−1.51465	−	0.874481i	−0.0552334	−	0.0318890i
$753$	18.8674	+	3.21387i	0.687565	+	0.117120i
$754$	5.16766	+	2.98355i	0.188195	+	0.108655i
$755$	−9.54254	+	16.5282i	−0.347289	+	0.601522i
$756$	18.6762	−	0.325688i	0.679248	−	0.0118452i
$757$	−14.6516	+	25.3773i	−0.532521	+	0.922354i	0.466757	+	0.884385i	$0.345422\pi$
$757$	−14.6516	+	25.3773i	−0.532521	+	0.922354i	−0.999279	+	0.0379689i	$0.987911\pi$
$758$		−	3.08682i		−	0.112118i
$759$	0.880102	−	5.16674i	0.0319457	−	0.187541i
$760$	−3.14581	−	12.4786i	−0.114111	−	0.452647i
$761$	−34.5581	−	19.9521i	−1.25273	−	0.723263i	−0.281078	−	0.959685i	$-0.590692\pi$
$761$	−34.5581	−	19.9521i	−1.25273	−	0.723263i	−0.971651	+	0.236422i	$0.924025\pi$
$762$	23.6345	+	4.02590i	0.856187	+	0.145843i
$763$			29.1334i			1.05470i
$764$	21.9809	−	12.6907i	0.795242	−	0.459133i
$765$	10.5441	+	55.9852i	0.381224	+	2.02415i
$766$	6.18874	+	10.7192i	0.223608	+	0.387301i
$767$	−6.74430	+	3.89383i	−0.243523	+	0.140598i
$768$	−1.33328	−	1.10561i	−0.0481105	−	0.0398953i
$769$	−4.95293			−0.178607			−0.0893036	−	0.996004i	$-0.528464\pi$
$769$	−4.95293			−0.178607			−0.0893036	+	0.996004i	$0.528464\pi$
$770$	4.26213			0.153597
$771$	24.2078	+	20.0742i	0.871823	+	0.722953i
$772$	−15.4798	+	8.93726i	−0.557130	+	0.321659i
$773$	−1.73056	−	2.99742i	−0.0622439	−	0.107810i	0.833224	−	0.552935i	$-0.186492\pi$
$773$	−1.73056	−	2.99742i	−0.0622439	−	0.107810i	−0.895468	+	0.445126i	$0.853159\pi$
$774$	3.13097	+	16.6242i	0.112540	+	0.597545i
$775$	17.6046	−	10.1640i	0.632375	−	0.365102i
$776$		−	0.223639i		−	0.00802817i
$777$	−17.3734	−	2.95939i	−0.623269	−	0.106168i
$778$	0.472234	+	0.272644i	0.0169304	+	0.00977477i
$779$	−29.1267	+	7.34273i	−1.04357	+	0.263081i
$780$	−0.750209	+	4.40419i	−0.0268618	+	0.157695i
$781$		−	5.74867i		−	0.205703i
$782$	−24.2328	+	41.9725i	−0.866565	+	1.50093i
$783$	−18.2779	−	30.4207i	−0.653199	−	1.08715i
$784$	−2.96126	+	5.12905i	−0.105759	+	0.183181i
$785$	−56.9820	−	32.8986i	−2.03378	−	1.17420i
$786$	−7.78461	−	1.32603i	−0.277668	−	0.0472980i
$787$	−19.0274	−	10.9855i	−0.678253	−	0.391589i	0.120944	−	0.992659i	$-0.461408\pi$
$787$	−19.0274	−	10.9855i	−0.678253	−	0.391589i	−0.799196	+	0.601070i	$0.794741\pi$
$788$			11.9456i			0.425546i
$789$	3.40154	−	4.10198i	0.121098	−	0.146034i
$790$	−11.1233	−	19.2662i	−0.395750	−	0.685459i
$791$	−26.1362			−0.929295
$792$	0.785089	+	0.913845i	0.0278969	+	0.0324721i
$793$	−0.409535	−	0.236445i	−0.0145430	−	0.00839640i
$794$	16.6785	−	28.8880i	0.591898	−	1.02520i
$795$	19.7307	+	53.2446i	0.699775	+	1.88839i
$796$	−10.7216	−	18.5703i	−0.380016	−	0.658208i
$797$	−22.0548	+	38.2001i	−0.781222	+	1.35312i	0.150008	+	0.988685i	$0.452070\pi$
$797$	−22.0548	+	38.2001i	−0.781222	+	1.35312i	−0.931230	+	0.364432i	$0.881263\pi$
$798$	−24.4926	−	11.6917i	−0.867029	−	0.413882i
$799$	−5.62473	−	9.74232i	−0.198989	−	0.344658i
$800$	−1.85822	+	3.21853i	−0.0656980	+	0.113792i
$801$	−16.0119	+	13.7559i	−0.565752	+	0.486040i
$802$	5.00932	+	8.67639i	0.176885	+	0.306374i
$803$			5.55559i			0.196052i
$804$	8.60838	−	10.3810i	0.303594	−	0.366110i
$805$	39.9849	−	69.2559i	1.40928	−	2.44095i
$806$	−2.38938	+	4.13852i	−0.0841621	+	0.145773i
$807$	−36.8724	+	13.6637i	−1.29797	+	0.480985i
$808$	8.44696	+	4.87686i	0.297163	+	0.171567i
$809$		−	10.3310i		−	0.363218i	−0.983371	−	0.181609i	$-0.941870\pi$
$809$		−	10.3310i		−	0.363218i	0.983371	−	0.181609i	$-0.0581305\pi$
$810$	16.6019	−	20.7463i	0.583330	−	0.728951i
$811$	−25.4270	+	14.6803i	−0.892862	+	0.515494i	−0.874877	−	0.484344i	$-0.839058\pi$
$811$	−25.4270	+	14.6803i	−0.892862	+	0.515494i	−0.0179843	+	0.999838i	$0.505725\pi$
$812$	24.5522			0.861614
$813$	−44.8091	+	16.6047i	−1.57152	+	0.582354i
$814$	−0.568351	−	0.984412i	−0.0199207	−	0.0345036i
$815$	32.8132	−	18.9447i	1.14940	−	0.663604i
$816$	−3.87112	−	10.4465i	−0.135516	−	0.365701i
$817$	6.71336	−	23.6445i	0.234871	−	0.827216i
$818$		−	3.00333i		−	0.105009i
$819$	6.13981	+	7.14675i	0.214542	+	0.249728i
$820$	17.6195	+	10.1726i	0.615301	+	0.355244i
$821$	−12.8388	−	7.41246i	−0.448076	−	0.258697i	0.258941	−	0.965893i	$-0.416626\pi$
$821$	−12.8388	−	7.41246i	−0.448076	−	0.258697i	−0.707017	+	0.707196i	$0.749960\pi$
$822$	−2.59479	−	7.00222i	−0.0905036	−	0.244230i
$823$	−24.6236			−0.858326			−0.429163	−	0.903227i	$-0.641191\pi$
$823$	−24.6236			−0.858326			−0.429163	+	0.903227i	$0.641191\pi$
$824$	6.59018	+	3.80484i	0.229580	+	0.132548i
$825$	1.65011	−	1.98990i	0.0574495	−	0.0692794i
$826$	−16.0215	+	27.7501i	−0.557460	+	0.965549i
$827$	25.1874	+	43.6258i	0.875851	+	1.51702i	0.855853	+	0.517219i	$0.173033\pi$
$827$	25.1874	+	43.6258i	0.875851	+	1.51702i	0.0199985	+	0.999800i	$0.493634\pi$
$828$	22.2144	−	4.18383i	0.772005	−	0.145398i
$829$		−	54.0619i		−	1.87765i	−0.344398	−	0.938824i	$-0.611917\pi$
$829$		−	54.0619i		−	1.87765i	0.344398	−	0.938824i	$-0.388083\pi$
$830$	8.31070	−	14.3946i	0.288469	−	0.499642i
$831$	0.314567	−	1.84670i	0.0109122	−	0.0640614i
$832$		−	0.873668i		−	0.0302890i
$833$	−32.9905	+	19.0471i	−1.14305	+	0.659942i
$834$	10.1335	+	8.40317i	0.350896	+	0.290978i
$835$	−44.2121	+	25.5259i	−1.53002	+	0.883360i
$836$	−0.427905	−	1.69739i	−0.0147994	−	0.0587054i
$837$	24.3624	−	14.6378i	0.842087	−	0.505958i
$838$	−18.8388	−	10.8766i	−0.650776	−	0.375726i
$839$	−5.02503			−0.173483			−0.0867417	−	0.996231i	$-0.527645\pi$
$839$	−5.02503			−0.173483			−0.0867417	+	0.996231i	$0.527645\pi$
$840$	6.38747	+	17.2370i	0.220389	+	0.594734i
$841$	−8.82408	−	15.2838i	−0.304279	−	0.527026i
$842$			20.4131i			0.703481i
$843$	0.878860	−	0.325676i	0.0302695	−	0.0112169i
$844$	3.69705	−	2.13450i	0.127258	−	0.0734724i
$845$	31.2871	−	18.0636i	1.07631	−	0.621406i
$846$	−1.73711	+	4.95099i	−0.0597229	+	0.170218i
$847$	−38.9629			−1.33878
$848$	−5.55209	−	9.61651i	−0.190660	−	0.330232i
$849$	−3.07193	+	18.0341i	−0.105428	+	0.618929i
$850$	−20.7018	+	11.9522i	−0.710068	+	0.409958i
$851$	−21.3278			−0.731107
$852$	23.2489	−	8.61527i	0.796495	−	0.295154i
$853$	−29.7758			−1.01951			−0.509753	−	0.860321i	$-0.670263\pi$
$853$	−29.7758			−1.01951			−0.509753	+	0.860321i	$0.670263\pi$
$854$	−1.94575			−0.0665822
$855$	−35.0424	+	16.2032i	−1.19842	+	0.554137i
$856$	−8.12018			−0.277542
$857$	25.5131			0.871510			0.435755	−	0.900065i	$-0.356481\pi$
$857$	25.5131			0.871510			0.435755	+	0.900065i	$0.356481\pi$
$858$	−0.102046	+	0.599073i	−0.00348380	+	0.0204520i
$859$	11.0395			0.376664			0.188332	−	0.982105i	$-0.439692\pi$
$859$	11.0395			0.376664			0.188332	+	0.982105i	$0.439692\pi$
$860$	−14.4175	+	8.32393i	−0.491632	+	0.283844i
$861$	40.2334	−	14.9092i	1.37115	−	0.508103i
$862$	2.12382	+	3.67856i	0.0723375	+	0.125292i
$863$	42.3821			1.44270			0.721352	−	0.692568i	$-0.243521\pi$
$863$	42.3821			1.44270			0.721352	+	0.692568i	$0.243521\pi$
$864$	−2.51922	+	4.54462i	−0.0857056	+	0.154611i
$865$	19.3833	−	11.1910i	0.659052	−	0.380504i
$866$	−15.1361	+	8.73884i	−0.514346	+	0.296958i
$867$	7.08845	−	41.6135i	0.240736	−	1.41327i
$868$			19.6626i			0.667393i
$869$	−1.51303	−	2.62065i	−0.0513262	−	0.0888995i
$870$	22.2940	−	26.8848i	0.755839	−	0.911481i
$871$	6.80246			0.230492
$872$	−7.01856	−	4.05217i	−0.237679	−	0.137224i
$873$	−0.659325	+	0.124176i	−0.0223148	+	0.00420272i
$874$	−31.5954	−	8.97086i	−1.06873	−	0.303444i
$875$	−11.7975	+	6.81129i	−0.398828	+	0.230264i
$876$	−22.4681	+	8.32591i	−0.759126	+	0.281307i
$877$	7.16553	−	4.13702i	0.241963	−	0.139697i	−0.374116	−	0.927382i	$-0.622054\pi$
$877$	7.16553	−	4.13702i	0.241963	−	0.139697i	0.616079	+	0.787685i	$0.288720\pi$
$878$			5.13807i			0.173402i
$879$	18.0508	−	6.68902i	0.608838	−	0.225615i
$880$	−0.592821	+	1.02680i	−0.0199840	+	0.0346133i
$881$			32.8183i			1.10568i	0.833289	+	0.552838i	$0.186455\pi$
$881$			32.8183i			1.10568i	−0.833289	+	0.552838i	$0.813545\pi$
$882$	16.7656	+	5.88237i	0.564526	+	0.198070i
$883$	3.62647	+	6.28123i	0.122040	+	0.211380i	0.920572	−	0.390572i	$-0.127723\pi$
$883$	3.62647	+	6.28123i	0.122040	+	0.211380i	−0.798532	+	0.601953i	$0.794390\pi$
$884$	2.80975	−	4.86663i	0.0945021	−	0.163683i
$885$	15.8385	+	42.7414i	0.532407	+	1.43674i
$886$	−8.44956	−	4.87835i	−0.283868	−	0.163892i
$887$	15.0935			0.506789			0.253394	−	0.967363i	$-0.418453\pi$
$887$	15.0935			0.506789			0.253394	+	0.967363i	$0.418453\pi$
$888$	3.12943	−	3.77383i	0.105017	−	0.126642i
$889$	43.0924	+	24.8794i	1.44527	+	0.834429i
$890$	−17.9909	−	10.3871i	−0.603058	−	0.348176i
$891$	2.25825	−	2.82199i	0.0756541	−	0.0945401i
$892$		−	10.0653i		−	0.337012i
$893$	5.47011	−	5.31003i	0.183050	−	0.177693i
$894$	−24.6550	−	4.19974i	−0.824587	−	0.140460i
$895$	−22.1260	+	12.7744i	−0.739590	+	0.427003i
$896$	−1.79740	−	3.11318i	−0.0600468	−	0.104004i
$897$	8.77707	+	7.27833i	0.293058	+	0.243016i
$898$	−10.5516			−0.352112
$899$	32.3531	−	18.6791i	1.07904	−	0.622982i
$900$	10.5206	+	3.69125i	0.350685	+	0.123042i
$901$		−	71.4230i		−	2.37944i
$902$	2.39667	+	1.38372i	0.0798004	+	0.0460728i
$903$	−5.89561	+	34.6108i	−0.196194	+	1.15178i
$904$	3.63528	−	6.29649i	0.120908	−	0.209418i
$905$	−18.4013	+	31.8720i	−0.611681	+	1.05946i
$906$	−11.0376	−	1.88014i	−0.366699	−	0.0624636i
$907$		−	12.0229i		−	0.399213i	−0.979876	−	0.199607i	$-0.936034\pi$
$907$		−	12.0229i		−	0.399213i	0.979876	−	0.199607i	$-0.0639665\pi$
$908$	−10.0498	−	17.4068i	−0.333515	−	0.577665i
$909$	9.68759	−	27.6110i	0.321317	−	0.915797i
$910$	−4.63617	+	8.03009i	−0.153688	+	0.266195i
$911$	12.3765	+	21.4367i	0.410051	+	0.710230i	0.994895	−	0.100916i	$-0.0321775\pi$
$911$	12.3765	+	21.4367i	0.410051	+	0.710230i	−0.584844	+	0.811146i	$0.698844\pi$
$912$	6.22334	−	4.27434i	0.206075	−	0.141538i
$913$	1.13045	−	1.95800i	0.0374125	−	0.0648003i
$914$	9.68365	+	16.7726i	0.320307	+	0.554788i
$915$	−1.76679	+	2.13061i	−0.0584083	+	0.0704357i
$916$	−10.6629	+	18.4687i	−0.352312	+	0.610222i
$917$	−14.1936	−	8.19466i	−0.468713	−	0.270611i
$918$	−28.6486	+	17.2132i	−0.945544	+	0.568119i
$919$	48.4176			1.59715			0.798575	−	0.601895i	$-0.205587\pi$
$919$	48.4176			1.59715			0.798575	+	0.601895i	$0.205587\pi$
$920$	11.1230	+	19.2656i	0.366715	+	0.635169i
$921$	−6.43201	−	17.3572i	−0.211942	−	0.571940i
$922$			25.3709i			0.835547i
$923$	10.8308	+	6.25316i	0.356500	+	0.205825i
$924$	0.868846	+	2.34464i	0.0285829	+	0.0771331i
$925$	−9.11004	−	5.25969i	−0.299536	−	0.172937i
$926$	8.29190	−	14.3620i	0.272489	−	0.471964i
$927$	7.55810	−	21.5416i	0.248241	−	0.707519i
$928$	−3.41497	+	5.91491i	−0.112102	+	0.194166i
$929$			7.58386i			0.248818i	0.992231	+	0.124409i	$0.0397035\pi$
$929$			7.58386i			0.248818i	−0.992231	+	0.124409i	$0.960296\pi$
$930$	21.5307	+	17.8542i	0.706019	+	0.585461i
$931$	−17.9814	−	18.5235i	−0.589316	−	0.607082i
$932$	−16.3284	−	9.42721i	−0.534855	−	0.308799i
$933$	−8.01316	−	21.6241i	−0.262339	−	0.707940i
$934$			11.1994i			0.366454i
$935$	−6.60443	+	3.81307i	−0.215988	+	0.124701i
$936$	−2.57572	+	0.485106i	−0.0841900	+	0.0158562i
$937$	3.37057	+	5.83801i	0.110112	+	0.190719i	0.915815	−	0.401600i	$-0.131546\pi$
$937$	3.37057	+	5.83801i	0.110112	+	0.190719i	−0.805703	+	0.592319i	$0.798212\pi$
$938$	24.2395	−	13.9947i	0.791448	−	0.456942i
$939$	17.9194	−	6.64031i	0.584776	−	0.216698i
$940$	−5.16357			−0.168417
$941$	23.7481			0.774166			0.387083	−	0.922045i	$-0.373483\pi$
$941$	23.7481			0.774166			0.387083	+	0.922045i	$0.373483\pi$
$942$	6.48193	−	38.0529i	0.211193	−	1.23983i
$943$	44.9684	−	25.9625i	1.46437	−	0.845456i
$944$	−4.45687	−	7.71953i	−0.145059	−	0.251249i
$945$	47.2710	−	28.4022i	1.53773	−	0.923925i
$946$	−1.96112	+	1.13225i	−0.0637614	+	0.0368126i
$947$			52.3941i			1.70258i	0.524697	+	0.851289i	$0.324179\pi$
$947$			52.3941i			1.70258i	−0.524697	+	0.851289i	$0.675821\pi$
$948$	8.33100	−	10.0465i	0.270578	−	0.326295i
$949$	−10.4670	−	6.04314i	−0.339774	−	0.196169i
$950$	−11.2835	−	11.6237i	−0.366085	−	0.377121i
$951$	−4.43330	+	1.64283i	−0.143759	+	0.0532725i
$952$		−	23.1220i		−	0.749388i
$953$	−16.6765	+	28.8845i	−0.540204	+	0.935660i	0.458688	+	0.888597i	$0.348319\pi$
$953$	−16.6765	+	28.8845i	−0.540204	+	0.935660i	−0.998892	+	0.0470630i	$0.985014\pi$
$954$	−25.2683	+	21.7081i	−0.818090	+	0.702825i
$955$	37.4675	−	64.8956i	1.21242	−	2.09997i
$956$	−18.2504	−	10.5369i	−0.590260	−	0.340787i
$957$	3.03252	−	3.65697i	0.0980273	−	0.118213i
$958$	−1.60732	−	0.927988i	−0.0519302	−	0.0299819i
$959$		−	15.4985i		−	0.500473i
$960$	−5.04103	−	0.858689i	−0.162699	−	0.0277141i
$961$	−0.540889	−	0.936848i	−0.0174480	−	0.0302209i
$962$	2.47291			0.0797300
$963$	4.50875	+	23.9396i	0.145292	+	0.771444i
$964$	−4.05347	−	2.34027i	−0.130553	−	0.0753750i
$965$	−26.3860	+	45.7019i	−0.849396	+	1.47120i
$966$	46.2494	+	7.87813i	1.48805	+	0.253475i
$967$	3.60920	+	6.25132i	0.116064	+	0.201029i	0.918205	−	0.396106i	$-0.129639\pi$
$967$	3.60920	+	6.25132i	0.116064	+	0.201029i	−0.802141	+	0.597135i	$0.796306\pi$
$968$	5.41936	−	9.38661i	0.174185	−	0.301697i
$969$	48.4126	−	3.79506i	1.55524	−	0.121915i
$970$	−0.330132	−	0.571805i	−0.0105999	−	0.0183595i
$971$	−17.9377	+	31.0689i	−0.575647	+	0.997050i	0.420324	+	0.907374i	$0.361916\pi$
$971$	−17.9377	+	31.0689i	−0.575647	+	0.997050i	−0.995971	+	0.0896758i	$0.971417\pi$
$972$	14.7971	+	4.90367i	0.474617	+	0.157285i
$973$	13.6611	+	23.6617i	0.437954	+	0.758558i
$974$			12.1257i			0.388532i
$975$	1.95416	+	5.27343i	0.0625831	+	0.168885i
$976$	0.270635	−	0.468753i	0.00866281	−	0.0150044i
$977$	10.4401	−	18.0827i	0.334008	−	0.578518i	−0.649286	−	0.760544i	$-0.724932\pi$
$977$	10.4401	−	18.0827i	0.334008	−	0.578518i	0.983294	+	0.182026i	$0.0582655\pi$
$978$	17.1107	+	14.1889i	0.547140	+	0.453712i
$979$	−2.44719	−	1.41289i	−0.0782126	−	0.0451561i
$980$			17.4854i			0.558551i
$981$	−8.04940	+	22.9419i	−0.256998	+	0.732478i
$982$	−13.0571	+	7.53852i	−0.416669	+	0.240564i
$983$	30.8580			0.984218			0.492109	−	0.870534i	$-0.336226\pi$
$983$	30.8580			0.984218			0.492109	+	0.870534i	$0.336226\pi$
$984$	−2.00429	+	11.7664i	−0.0638944	+	0.375099i
$985$	17.6339	+	30.5429i	0.561864	+	0.973176i
$986$	−38.0451	+	21.9654i	−1.21160	+	0.699520i
$987$	−6.95114	+	8.38251i	−0.221257	+	0.266818i
$988$	3.66343	+	1.04015i	0.116549	+	0.0330917i
$989$			42.4885i			1.35106i
$990$	3.35633	+	1.17760i	0.106671	+	0.0374267i
$991$	24.5472	+	14.1723i	0.779767	+	0.450199i	0.836348	−	0.548199i	$-0.184686\pi$
$991$	24.5472	+	14.1723i	0.779767	+	0.450199i	−0.0565806	+	0.998398i	$0.518020\pi$
$992$	−4.73695	−	2.73488i	−0.150398	−	0.0868325i
$993$	49.3489	+	8.40609i	1.56604	+	0.266759i
$994$	51.4585			1.63216
$995$	−54.8263	−	31.6540i	−1.73811	−	1.00350i
$996$	9.61275	+	1.63744i	0.304592	+	0.0518841i
$997$	21.3874	−	37.0441i	0.677346	−	1.17320i	−0.298431	−	0.954431i	$-0.596463\pi$
$997$	21.3874	−	37.0441i	0.677346	−	1.17320i	0.975777	−	0.218767i	$-0.0702033\pi$
$998$	−2.01097	−	3.48310i	−0.0636560	−	0.110255i
$999$	−12.8635	−	7.13064i	−0.406984	−	0.225604i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	342.2.n.f.293.3	yes	18
3.2	odd	2		1026.2.n.f.179.2		18
9.2	odd	6		342.2.j.f.65.1	✓	18
9.7	even	3		1026.2.j.f.521.8		18
19.12	odd	6		342.2.j.f.221.1	yes	18
57.50	even	6		1026.2.j.f.449.2		18
171.88	odd	6		1026.2.n.f.791.2		18
171.164	even	6	inner	342.2.n.f.335.3	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
342.2.j.f.65.1	✓	18	9.2	odd	6
342.2.j.f.221.1	yes	18	19.12	odd	6
342.2.n.f.293.3	yes	18	1.1	even	1	trivial
342.2.n.f.335.3	yes	18	171.164	even	6	inner
1026.2.j.f.449.2		18	57.50	even	6
1026.2.j.f.521.8		18	9.7	even	3
1026.2.n.f.179.2		18	3.2	odd	2
1026.2.n.f.791.2		18	171.88	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	342.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(-1.33328 - 1.10561i) q^{3} +1.00000 q^{4} +(2.55682 - 1.47618i) q^{5} +(1.33328 + 1.10561i) q^{6} +(1.79740 + 3.11318i) q^{7} -1.00000 q^{8} +(0.555252 + 2.94817i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(-1.33328 - 1.10561i) q^{3} +1.00000 q^{4} +(2.55682 - 1.47618i) q^{5} +(1.33328 + 1.10561i) q^{6} +(1.79740 + 3.11318i) q^{7} -1.00000 q^{8} +(0.555252 + 2.94817i) q^{9} +(-2.55682 + 1.47618i) q^{10} +(-0.347788 + 0.200795i) q^{11} +(-1.33328 - 1.10561i) q^{12} -0.873668i q^{13} +(-1.79740 - 3.11318i) q^{14} +(-5.04103 - 0.858689i) q^{15} +1.00000 q^{16} +(5.57034 + 3.21604i) q^{17} +(-0.555252 - 2.94817i) q^{18} +(-1.19056 + 4.19316i) q^{19} +(2.55682 - 1.47618i) q^{20} +(1.04554 - 6.13795i) q^{21} +(0.347788 - 0.200795i) q^{22} -7.53500i q^{23} +(1.33328 + 1.10561i) q^{24} +(1.85822 - 3.21853i) q^{25} +0.873668i q^{26} +(2.51922 - 4.54462i) q^{27} +(1.79740 + 3.11318i) q^{28} +(3.41497 - 5.91491i) q^{29} +(5.04103 + 0.858689i) q^{30} +(4.73695 + 2.73488i) q^{31} -1.00000 q^{32} +(0.685699 + 0.116802i) q^{33} +(-5.57034 - 3.21604i) q^{34} +(9.19123 + 5.30656i) q^{35} +(0.555252 + 2.94817i) q^{36} -2.83050i q^{37} +(1.19056 - 4.19316i) q^{38} +(-0.965936 + 1.16484i) q^{39} +(-2.55682 + 1.47618i) q^{40} +(3.44559 + 5.96794i) q^{41} +(-1.04554 + 6.13795i) q^{42} -5.63883 q^{43} +(-0.347788 + 0.200795i) q^{44} +(5.77171 + 6.71828i) q^{45} +7.53500i q^{46} +(-1.51465 - 0.874481i) q^{47} +(-1.33328 - 1.10561i) q^{48} +(-2.96126 + 5.12905i) q^{49} +(-1.85822 + 3.21853i) q^{50} +(-3.87112 - 10.4465i) q^{51} -0.873668i q^{52} +(-5.55209 - 9.61651i) q^{53} +(-2.51922 + 4.54462i) q^{54} +(-0.592821 + 1.02680i) q^{55} +(-1.79740 - 3.11318i) q^{56} +(6.22334 - 4.27434i) q^{57} +(-3.41497 + 5.91491i) q^{58} +(-4.45687 - 7.71953i) q^{59} +(-5.04103 - 0.858689i) q^{60} +(0.270635 - 0.468753i) q^{61} +(-4.73695 - 2.73488i) q^{62} +(-8.18017 + 7.02762i) q^{63} +1.00000 q^{64} +(-1.28969 - 2.23381i) q^{65} +(-0.685699 - 0.116802i) q^{66} +7.78609i q^{67} +(5.57034 + 3.21604i) q^{68} +(-8.33077 + 10.0462i) q^{69} +(-9.19123 - 5.30656i) q^{70} +(-7.15737 + 12.3969i) q^{71} +(-0.555252 - 2.94817i) q^{72} +(6.91698 - 11.9806i) q^{73} +2.83050i q^{74} +(-6.03596 + 2.23673i) q^{75} +(-1.19056 + 4.19316i) q^{76} +(-1.25022 - 0.721817i) q^{77} +(0.965936 - 1.16484i) q^{78} +7.53520i q^{79} +(2.55682 - 1.47618i) q^{80} +(-8.38339 + 3.27396i) q^{81} +(-3.44559 - 5.96794i) q^{82} +(-4.87561 + 2.81493i) q^{83} +(1.04554 - 6.13795i) q^{84} +18.9898 q^{85} +5.63883 q^{86} +(-11.0927 + 4.11058i) q^{87} +(0.347788 - 0.200795i) q^{88} +(3.51823 + 6.09375i) q^{89} +(-5.77171 - 6.71828i) q^{90} +(2.71989 - 1.57033i) q^{91} -7.53500i q^{92} +(-3.29195 - 8.88356i) q^{93} +(1.51465 + 0.874481i) q^{94} +(3.14581 + 12.4786i) q^{95} +(1.33328 + 1.10561i) q^{96} +0.223639i q^{97} +(2.96126 - 5.12905i) q^{98} +(-0.785089 - 0.913845i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 18 q^{2} - q^{3} + 18 q^{4} + 3 q^{5} + q^{6} - 18 q^{8} + 5 q^{9}+O(q^{10}) \) 18 * q - 18 * q^2 - q^3 + 18 * q^4 + 3 * q^5 + q^6 - 18 * q^8 + 5 * q^9	\( 18 q - 18 q^{2} - q^{3} + 18 q^{4} + 3 q^{5} + q^{6} - 18 q^{8} + 5 q^{9} - 3 q^{10} + 15 q^{11} - q^{12} - 17 q^{15} + 18 q^{16} - 15 q^{17} - 5 q^{18} + 6 q^{19} + 3 q^{20} + q^{21} - 15 q^{22} + q^{24} + 18 q^{25} + 20 q^{27} + 18 q^{29} + 17 q^{30} + 9 q^{31} - 18 q^{32} + q^{33} + 15 q^{34} - 3 q^{35} + 5 q^{36} - 6 q^{38} + 18 q^{39} - 3 q^{40} - q^{42} + 12 q^{43} + 15 q^{44} - 17 q^{45} - 18 q^{47} - q^{48} + 3 q^{49} - 18 q^{50} + 10 q^{51} - 15 q^{53} - 20 q^{54} - 9 q^{55} + 23 q^{57} - 18 q^{58} - 17 q^{60} - 9 q^{61} - 9 q^{62} - 38 q^{63} + 18 q^{64} - 9 q^{65} - q^{66} - 15 q^{68} - 8 q^{69} + 3 q^{70} - 6 q^{71} - 5 q^{72} + 24 q^{73} - 9 q^{75} + 6 q^{76} + 3 q^{77} - 18 q^{78} + 3 q^{80} + 5 q^{81} + 3 q^{83} + q^{84} + 6 q^{85} - 12 q^{86} - 60 q^{87} - 15 q^{88} + 24 q^{89} + 17 q^{90} - 81 q^{91} - 3 q^{93} + 18 q^{94} - 9 q^{95} + q^{96} - 3 q^{98} - 56 q^{99}+O(q^{100}) \) 18 * q - 18 * q^2 - q^3 + 18 * q^4 + 3 * q^5 + q^6 - 18 * q^8 + 5 * q^9 - 3 * q^10 + 15 * q^11 - q^12 - 17 * q^15 + 18 * q^16 - 15 * q^17 - 5 * q^18 + 6 * q^19 + 3 * q^20 + q^21 - 15 * q^22 + q^24 + 18 * q^25 + 20 * q^27 + 18 * q^29 + 17 * q^30 + 9 * q^31 - 18 * q^32 + q^33 + 15 * q^34 - 3 * q^35 + 5 * q^36 - 6 * q^38 + 18 * q^39 - 3 * q^40 - q^42 + 12 * q^43 + 15 * q^44 - 17 * q^45 - 18 * q^47 - q^48 + 3 * q^49 - 18 * q^50 + 10 * q^51 - 15 * q^53 - 20 * q^54 - 9 * q^55 + 23 * q^57 - 18 * q^58 - 17 * q^60 - 9 * q^61 - 9 * q^62 - 38 * q^63 + 18 * q^64 - 9 * q^65 - q^66 - 15 * q^68 - 8 * q^69 + 3 * q^70 - 6 * q^71 - 5 * q^72 + 24 * q^73 - 9 * q^75 + 6 * q^76 + 3 * q^77 - 18 * q^78 + 3 * q^80 + 5 * q^81 + 3 * q^83 + q^84 + 6 * q^85 - 12 * q^86 - 60 * q^87 - 15 * q^88 + 24 * q^89 + 17 * q^90 - 81 * q^91 - 3 * q^93 + 18 * q^94 - 9 * q^95 + q^96 - 3 * q^98 - 56 * q^99

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