LMFDB - Embedded newform 462.2.k.g.353.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(89,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 0]))

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

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

chi := DirichletCharacter("462.89");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.k (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:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 6 x^{19} + 19 x^{18} - 42 x^{17} + 62 x^{16} - 42 x^{15} - 25 x^{14} + 6 x^{13} + 445 x^{12} + \cdots + 59049 $ x^20 - 6x^19 + 19x^18 - 42x^17 + 62x^16 - 42x^15 - 25x^14 + 6x^13 + 445x^12 - 1764x^11 + 3864x^10 - 5292x^9 + 4005x^8 + 162x^7 - 2025x^6 - 10206x^5 + 45198x^4 - 91854x^3 + 124659x^2 - 118098*x + 59049
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			353.2
Root			$1.68119 - 0.416664i$ of defining polynomial
Character	$\chi$	$=$	462.353
Dual form			462.2.k.g.89.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(-1.20144 - 1.24762i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.798258 - 1.38262i) q^{5} +(1.66428 + 0.479752i) q^{6} +(0.157053 + 2.64109i) q^{7} +1.00000i q^{8} +(-0.113106 + 2.99787i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(-1.20144 - 1.24762i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.798258 - 1.38262i) q^{5} +(1.66428 + 0.479752i) q^{6} +(0.157053 + 2.64109i) q^{7} +1.00000i q^{8} +(-0.113106 + 2.99787i) q^{9} +(1.38262 + 0.798258i) q^{10} +(0.866025 + 0.500000i) q^{11} +(-1.68119 + 0.416664i) q^{12} +4.50963i q^{13} +(-1.45655 - 2.20872i) q^{14} +(-0.765932 + 2.65705i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.12084 - 5.40545i) q^{17} +(-1.40098 - 2.65278i) q^{18} +(6.07449 - 3.50711i) q^{19} -1.59652 q^{20} +(3.10638 - 3.36904i) q^{21} -1.00000 q^{22} +(-4.03733 + 2.33096i) q^{23} +(1.24762 - 1.20144i) q^{24} +(1.22557 - 2.12275i) q^{25} +(-2.25481 - 3.90545i) q^{26} +(3.87609 - 3.46063i) q^{27} +(2.36577 + 1.18453i) q^{28} -5.53777i q^{29} +(-0.665210 - 2.68404i) q^{30} +(7.88004 + 4.54954i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-0.416664 - 1.68119i) q^{33} +6.24168i q^{34} +(3.52626 - 2.32541i) q^{35} +(2.53968 + 1.59689i) q^{36} +(-0.285736 - 0.494910i) q^{37} +(-3.50711 + 6.07449i) q^{38} +(5.62629 - 5.41802i) q^{39} +(1.38262 - 0.798258i) q^{40} +1.59652 q^{41} +(-1.00569 + 4.47086i) q^{42} -1.54158 q^{43} +(0.866025 - 0.500000i) q^{44} +(4.23521 - 2.23669i) q^{45} +(2.33096 - 4.03733i) q^{46} +(3.56927 + 6.18215i) q^{47} +(-0.479752 + 1.66428i) q^{48} +(-6.95067 + 0.829582i) q^{49} +2.45114i q^{50} +(-10.4934 + 2.60068i) q^{51} +(3.90545 + 2.25481i) q^{52} +(8.14614 + 4.70318i) q^{53} +(-1.62647 + 4.93504i) q^{54} -1.59652i q^{55} +(-2.64109 + 0.157053i) q^{56} +(-11.6737 - 3.36509i) q^{57} +(2.76889 + 4.79585i) q^{58} +(2.62379 - 4.54453i) q^{59} +(1.91811 + 1.99184i) q^{60} +(1.88976 - 1.09105i) q^{61} -9.09908 q^{62} +(-7.93539 + 0.172101i) q^{63} -1.00000 q^{64} +(6.23511 - 3.59984i) q^{65} +(1.20144 + 1.24762i) q^{66} +(0.613735 - 1.06302i) q^{67} +(-3.12084 - 5.40545i) q^{68} +(7.75874 + 2.23656i) q^{69} +(-1.89112 + 3.77699i) q^{70} +9.47281i q^{71} +(-2.99787 - 0.113106i) q^{72} +(3.56995 + 2.06111i) q^{73} +(0.494910 + 0.285736i) q^{74} +(-4.12082 + 1.02130i) q^{75} -7.01422i q^{76} +(-1.18453 + 2.36577i) q^{77} +(-2.16350 + 7.50529i) q^{78} +(3.87063 + 6.70413i) q^{79} +(-0.798258 + 1.38262i) q^{80} +(-8.97441 - 0.678156i) q^{81} +(-1.38262 + 0.798258i) q^{82} +17.4510 q^{83} +(-1.36448 - 4.37472i) q^{84} -9.96493 q^{85} +(1.33504 - 0.770788i) q^{86} +(-6.90903 + 6.65328i) q^{87} +(-0.500000 + 0.866025i) q^{88} +(-6.69358 - 11.5936i) q^{89} +(-2.54945 + 4.05463i) q^{90} +(-11.9103 + 0.708251i) q^{91} +4.66191i q^{92} +(-3.79126 - 15.2973i) q^{93} +(-6.18215 - 3.56927i) q^{94} +(-9.69802 - 5.59916i) q^{95} +(-0.416664 - 1.68119i) q^{96} -7.11516i q^{97} +(5.60466 - 4.19377i) q^{98} +(-1.59689 + 2.53968i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 6 q^{3} + 10 q^{4} - 6 q^{7} - 2 q^{9}+O(q^{10}) $ 20 * q - 6 * q^3 + 10 * q^4 - 6 * q^7 - 2 * q^9	$ 20 q - 6 q^{3} + 10 q^{4} - 6 q^{7} - 2 q^{9} - 18 q^{10} - 6 q^{12} - 8 q^{15} - 10 q^{16} + 4 q^{18} + 36 q^{19} + 24 q^{21} - 20 q^{22} - 12 q^{25} - 22 q^{30} + 36 q^{31} - 4 q^{36} + 16 q^{37} + 4 q^{39} - 18 q^{40} + 32 q^{42} + 32 q^{43} + 24 q^{45} + 30 q^{46} - 42 q^{49} - 24 q^{52} - 36 q^{54} - 24 q^{57} + 32 q^{58} - 4 q^{60} + 42 q^{61} - 10 q^{63} - 20 q^{64} + 6 q^{66} - 10 q^{67} - 36 q^{70} - 4 q^{72} + 12 q^{73} - 108 q^{75} + 6 q^{79} + 42 q^{81} + 18 q^{82} + 18 q^{84} - 28 q^{85} + 36 q^{87} - 10 q^{88} - 112 q^{91} - 36 q^{93} + 42 q^{94} - 8 q^{99}+O(q^{100}) $ 20 * q - 6 * q^3 + 10 * q^4 - 6 * q^7 - 2 * q^9 - 18 * q^10 - 6 * q^12 - 8 * q^15 - 10 * q^16 + 4 * q^18 + 36 * q^19 + 24 * q^21 - 20 * q^22 - 12 * q^25 - 22 * q^30 + 36 * q^31 - 4 * q^36 + 16 * q^37 + 4 * q^39 - 18 * q^40 + 32 * q^42 + 32 * q^43 + 24 * q^45 + 30 * q^46 - 42 * q^49 - 24 * q^52 - 36 * q^54 - 24 * q^57 + 32 * q^58 - 4 * q^60 + 42 * q^61 - 10 * q^63 - 20 * q^64 + 6 * q^66 - 10 * q^67 - 36 * q^70 - 4 * q^72 + 12 * q^73 - 108 * q^75 + 6 * q^79 + 42 * q^81 + 18 * q^82 + 18 * q^84 - 28 * q^85 + 36 * q^87 - 10 * q^88 - 112 * q^91 - 36 * q^93 + 42 * q^94 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$1$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	−1.20144	−	1.24762i	−0.693649	−	0.720313i
$3$	−1.20144	−	1.24762i	−0.693649	−	0.720313i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−0.798258	−	1.38262i	−0.356992	−	0.618328i	0.630465	−	0.776218i	$-0.282864\pi$
$5$	−0.798258	−	1.38262i	−0.356992	−	0.618328i	−0.987457	+	0.157890i	$0.949531\pi$
$6$	1.66428	+	0.479752i	0.679441	+	0.195858i
$7$	0.157053	+	2.64109i	0.0593605	+	0.998237i
$7$	0.157053	+	2.64109i	0.0593605	+	0.998237i
$8$			1.00000i			0.353553i
$9$	−0.113106	+	2.99787i	−0.0377021	+	0.999289i
$10$	1.38262	+	0.798258i	0.437224	+	0.252431i
$11$	0.866025	+	0.500000i	0.261116	+	0.150756i
$11$	0.866025	+	0.500000i	0.261116	+	0.150756i
$12$	−1.68119	+	0.416664i	−0.485317	+	0.120281i
$13$			4.50963i			1.25074i	0.780326	+	0.625372i	$0.215053\pi$
$13$			4.50963i			1.25074i	−0.780326	+	0.625372i	$0.784947\pi$
$14$	−1.45655	−	2.20872i	−0.389281	−	0.590305i
$15$	−0.765932	+	2.65705i	−0.197763	+	0.686048i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	3.12084	−	5.40545i	0.756914	−	1.31101i	−0.187503	−	0.982264i	$-0.560039\pi$
$17$	3.12084	−	5.40545i	0.756914	−	1.31101i	0.944417	−	0.328750i	$-0.106627\pi$
$18$	−1.40098	−	2.65278i	−0.330214	−	0.625267i
$19$	6.07449	−	3.50711i	1.39358	−	0.804586i	0.399875	−	0.916570i	$-0.369054\pi$
$19$	6.07449	−	3.50711i	1.39358	−	0.804586i	0.993710	+	0.111983i	$0.0357203\pi$
$20$	−1.59652			−0.356992
$21$	3.10638	−	3.36904i	0.677868	−	0.735184i
$22$	−1.00000			−0.213201
$23$	−4.03733	+	2.33096i	−0.841842	+	0.486038i	−0.857890	−	0.513834i	$-0.828225\pi$
$23$	−4.03733	+	2.33096i	−0.841842	+	0.486038i	0.0160479	+	0.999871i	$0.494892\pi$
$24$	1.24762	−	1.20144i	0.254669	−	0.245242i
$25$	1.22557	−	2.12275i	0.245114	−	0.424550i
$26$	−2.25481	−	3.90545i	−0.442205	−	0.765922i
$27$	3.87609	−	3.46063i	0.745953	−	0.665998i
$28$	2.36577	+	1.18453i	0.447089	+	0.223855i
$29$		−	5.53777i		−	1.02834i	−0.857689	−	0.514169i	$-0.828100\pi$
$29$		−	5.53777i		−	1.02834i	0.857689	−	0.514169i	$-0.171900\pi$
$30$	−0.665210	−	2.68404i	−0.121450	−	0.490037i
$31$	7.88004	+	4.54954i	1.41530	+	0.817122i	0.995881	−	0.0906728i	$-0.0289017\pi$
$31$	7.88004	+	4.54954i	1.41530	+	0.817122i	0.419415	+	0.907794i	$0.362235\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	−0.416664	−	1.68119i	−0.0725319	−	0.292657i
$34$			6.24168i			1.07044i
$35$	3.52626	−	2.32541i	0.596046	−	0.393066i
$36$	2.53968	+	1.59689i	0.423279	+	0.266148i
$37$	−0.285736	−	0.494910i	−0.0469747	−	0.0813626i	0.841582	−	0.540129i	$-0.181625\pi$
$37$	−0.285736	−	0.494910i	−0.0469747	−	0.0813626i	−0.888557	+	0.458767i	$0.848291\pi$
$38$	−3.50711	+	6.07449i	−0.568929	+	0.985413i
$39$	5.62629	−	5.41802i	0.900928	−	0.867578i
$40$	1.38262	−	0.798258i	0.218612	−	0.126216i
$41$	1.59652			0.249334			0.124667	−	0.992199i	$-0.460214\pi$
$41$	1.59652			0.249334			0.124667	+	0.992199i	$0.460214\pi$
$42$	−1.00569	+	4.47086i	−0.155181	+	0.689869i
$43$	−1.54158			−0.235088			−0.117544	−	0.993068i	$-0.537502\pi$
$43$	−1.54158			−0.235088			−0.117544	+	0.993068i	$0.537502\pi$
$44$	0.866025	−	0.500000i	0.130558	−	0.0753778i
$45$	4.23521	−	2.23669i	0.631347	−	0.333426i
$46$	2.33096	−	4.03733i	0.343681	−	0.595272i
$47$	3.56927	+	6.18215i	0.520631	+	0.901759i	0.999712	+	0.0239887i	$0.00763658\pi$
$47$	3.56927	+	6.18215i	0.520631	+	0.901759i	−0.479081	+	0.877771i	$0.659030\pi$
$48$	−0.479752	+	1.66428i	−0.0692463	+	0.240219i
$49$	−6.95067	+	0.829582i	−0.992953	+	0.118512i
$50$			2.45114i			0.346643i
$51$	−10.4934	+	2.60068i	−1.46937	+	0.364168i
$52$	3.90545	+	2.25481i	0.541588	+	0.312686i
$53$	8.14614	+	4.70318i	1.11896	+	0.646031i	0.941135	−	0.338031i	$-0.109761\pi$
$53$	8.14614	+	4.70318i	1.11896	+	0.646031i	0.177824	+	0.984062i	$0.443094\pi$
$54$	−1.62647	+	4.93504i	−0.221335	+	0.671573i
$55$		−	1.59652i		−	0.215274i
$56$	−2.64109	+	0.157053i	−0.352930	+	0.0209871i
$57$	−11.6737	−	3.36509i	−1.54621	−	0.445717i
$58$	2.76889	+	4.79585i	0.363573	+	0.629726i
$59$	2.62379	−	4.54453i	0.341588	−	0.591648i	−0.643140	−	0.765749i	$-0.722369\pi$
$59$	2.62379	−	4.54453i	0.341588	−	0.591648i	0.984728	+	0.174101i	$0.0557019\pi$
$60$	1.91811	+	1.99184i	0.247627	+	0.257146i
$61$	1.88976	−	1.09105i	0.241959	−	0.139695i	−0.374118	−	0.927381i	$-0.622054\pi$
$61$	1.88976	−	1.09105i	0.241959	−	0.139695i	0.616077	+	0.787686i	$0.288721\pi$
$62$	−9.09908			−1.15558
$63$	−7.93539	+	0.172101i	−0.999765	+	0.0216827i
$64$	−1.00000			−0.125000
$65$	6.23511	−	3.59984i	0.773370	−	0.446506i
$66$	1.20144	+	1.24762i	0.147886	+	0.153571i
$67$	0.613735	−	1.06302i	0.0749797	−	0.129869i	−0.826098	−	0.563527i	$-0.809444\pi$
$67$	0.613735	−	1.06302i	0.0749797	−	0.129869i	0.901077	+	0.433658i	$0.142777\pi$
$68$	−3.12084	−	5.40545i	−0.378457	−	0.655507i
$69$	7.75874	+	2.23656i	0.934042	+	0.269250i
$70$	−1.89112	+	3.77699i	−0.226032	+	0.451437i
$71$			9.47281i			1.12422i	0.827064	+	0.562108i	$0.190009\pi$
$71$			9.47281i			1.12422i	−0.827064	+	0.562108i	$0.809991\pi$
$72$	−2.99787	−	0.113106i	−0.353302	−	0.0133297i
$73$	3.56995	+	2.06111i	0.417831	+	0.241235i	0.694149	−	0.719832i	$-0.255781\pi$
$73$	3.56995	+	2.06111i	0.417831	+	0.241235i	−0.276318	+	0.961066i	$0.589114\pi$
$74$	0.494910	+	0.285736i	0.0575321	+	0.0332162i
$75$	−4.12082	+	1.02130i	−0.475832	+	0.117930i
$76$		−	7.01422i		−	0.804586i
$77$	−1.18453	+	2.36577i	−0.134990	+	0.269605i
$78$	−2.16350	+	7.50529i	−0.244968	+	0.849807i
$79$	3.87063	+	6.70413i	0.435480	+	0.754273i	0.997335	−	0.0729625i	$-0.0232453\pi$
$79$	3.87063	+	6.70413i	0.435480	+	0.754273i	−0.561855	+	0.827236i	$0.689912\pi$
$80$	−0.798258	+	1.38262i	−0.0892479	+	0.154582i
$81$	−8.97441	−	0.678156i	−0.997157	−	0.0753506i
$82$	−1.38262	+	0.798258i	−0.152685	+	0.0881528i
$83$	17.4510			1.91550			0.957748	−	0.287608i	$-0.0928599\pi$
$83$	17.4510			1.91550			0.957748	+	0.287608i	$0.0928599\pi$
$84$	−1.36448	−	4.37472i	−0.148877	−	0.477321i
$85$	−9.96493			−1.08085
$86$	1.33504	−	0.770788i	0.143962	−	0.0831163i
$87$	−6.90903	+	6.65328i	−0.740726	+	0.713306i
$88$	−0.500000	+	0.866025i	−0.0533002	+	0.0923186i
$89$	−6.69358	−	11.5936i	−0.709518	−	1.22892i	−0.965036	−	0.262116i	$-0.915580\pi$
$89$	−6.69358	−	11.5936i	−0.709518	−	1.22892i	0.255519	−	0.966804i	$-0.417754\pi$
$90$	−2.54945	+	4.05463i	−0.268736	+	0.427396i
$91$	−11.9103	+	0.708251i	−1.24854	+	0.0742448i
$92$			4.66191i			0.486038i
$93$	−3.79126	−	15.2973i	−0.393135	−	1.58625i
$94$	−6.18215	−	3.56927i	−0.637640	−	0.368142i
$95$	−9.69802	−	5.59916i	−0.994996	−	0.574461i
$96$	−0.416664	−	1.68119i	−0.0425256	−	0.171585i
$97$		−	7.11516i		−	0.722435i	−0.932482	−	0.361218i	$-0.882361\pi$
$97$		−	7.11516i		−	0.722435i	0.932482	−	0.361218i	$-0.117639\pi$
$98$	5.60466	−	4.19377i	0.566157	−	0.423635i
$99$	−1.59689	+	2.53968i	−0.160493	+	0.255247i
$100$	−1.22557	−	2.12275i	−0.122557	−	0.212275i
$101$	−0.150693	+	0.261008i	−0.0149945	+	0.0259713i	−0.873425	−	0.486958i	$-0.838106\pi$
$101$	−0.150693	+	0.261008i	−0.0149945	+	0.0259713i	0.858431	+	0.512929i	$0.171440\pi$
$102$	7.78723	−	7.49897i	0.771051	−	0.742509i
$103$	−7.95453	+	4.59255i	−0.783783	+	0.452517i	−0.837769	−	0.546024i	$-0.816141\pi$
$103$	−7.95453	+	4.59255i	−0.783783	+	0.452517i	0.0539862	+	0.998542i	$0.482807\pi$
$104$	−4.50963			−0.442205
$105$	−7.13780	−	1.60559i	−0.696578	−	0.156690i
$106$	−9.40636			−0.913626
$107$	−7.30325	+	4.21653i	−0.706032	+	0.407628i	−0.809590	−	0.586996i	$-0.800311\pi$
$107$	−7.30325	+	4.21653i	−0.706032	+	0.407628i	0.103558	+	0.994623i	$0.466977\pi$
$108$	−1.05895	−	5.08710i	−0.101898	−	0.489507i
$109$	7.34270	−	12.7179i	0.703303	−	1.21816i	−0.263998	−	0.964523i	$-0.585041\pi$
$109$	7.34270	−	12.7179i	0.703303	−	1.21816i	0.967301	−	0.253633i	$-0.0816255\pi$
$110$	0.798258	+	1.38262i	0.0761109	+	0.131828i
$111$	−0.274165	+	0.951092i	−0.0260226	+	0.0902736i
$112$	2.20872	−	1.45655i	0.208705	−	0.137632i
$113$			10.5424i			0.991750i	0.868394	+	0.495875i	$0.165153\pi$
$113$			10.5424i			0.991750i	−0.868394	+	0.495875i	$0.834847\pi$
$114$	11.7922	−	2.92257i	1.10444	−	0.273724i
$115$	6.44566	+	3.72141i	0.601061	+	0.347023i
$116$	−4.79585	−	2.76889i	−0.445284	−	0.257085i
$117$	−13.5193	−	0.510067i	−1.24986	−	0.0471557i
$118$			5.24757i			0.483078i
$119$	14.7664	+	7.39346i	1.35363	+	0.677757i
$120$	−2.65705	−	0.765932i	−0.242555	−	0.0699197i
$121$	0.500000	+	0.866025i	0.0454545	+	0.0787296i
$122$	−1.09105	+	1.88976i	−0.0987792	+	0.171091i
$123$	−1.91811	−	1.99184i	−0.172950	−	0.179598i
$124$	7.88004	−	4.54954i	0.707648	−	0.408561i
$125$	−11.8959			−1.06400
$126$	6.78620	−	4.11674i	0.604562	−	0.366748i
$127$	−3.58256			−0.317901			−0.158950	−	0.987287i	$-0.550811\pi$
$127$	−3.58256			−0.317901			−0.158950	+	0.987287i	$0.550811\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	1.85210	+	1.92330i	0.163069	+	0.169337i
$130$	−3.59984	+	6.23511i	−0.315727	+	0.546855i
$131$	10.9882	+	19.0321i	0.960045	+	1.66285i	0.722377	+	0.691499i	$0.243049\pi$
$131$	10.9882	+	19.0321i	0.960045	+	1.66285i	0.237667	+	0.971347i	$0.423617\pi$
$132$	−1.66428	−	0.479752i	−0.144857	−	0.0417571i
$133$	10.2166	+	15.4925i	0.885892	+	1.34337i
$134$			1.22747i			0.106037i
$135$	−7.87886	−	2.59669i	−0.678104	−	0.223488i
$136$	5.40545	+	3.12084i	0.463513	+	0.267610i
$137$	−10.0400	−	5.79657i	−0.857771	−	0.495235i	0.00549399	−	0.999985i	$-0.498251\pi$
$137$	−10.0400	−	5.79657i	−0.857771	−	0.495235i	−0.863265	+	0.504750i	$0.831585\pi$
$138$	−7.83754	+	1.94245i	−0.667176	+	0.165352i
$139$		−	12.3113i		−	1.04423i	−0.852874	−	0.522116i	$-0.825143\pi$
$139$		−	12.3113i		−	1.04423i	0.852874	−	0.522116i	$-0.174857\pi$
$140$	−0.250738	−	4.21653i	−0.0211912	−	0.356362i
$141$	3.42473	−	11.8805i	0.288414	−	1.00052i
$142$	−4.73640	−	8.20369i	−0.397470	−	0.688439i
$143$	−2.25481	+	3.90545i	−0.188557	+	0.326590i
$144$	2.65278	−	1.40098i	0.221065	−	0.116748i
$145$	−7.65665	+	4.42057i	−0.635850	+	0.367108i
$146$	−4.12222			−0.341157
$147$	9.38578	+	7.67510i	0.774126	+	0.633031i
$148$	−0.571472			−0.0469747
$149$	−11.1729	+	6.45067i	−0.915318	+	0.528459i	−0.882139	−	0.470990i	$-0.843897\pi$
$149$	−11.1729	+	6.45067i	−0.915318	+	0.528459i	−0.0331799	+	0.999449i	$0.510563\pi$
$150$	3.05809	−	2.94489i	0.249692	−	0.240449i
$151$	4.50486	−	7.80264i	0.366600	−	0.634970i	−0.622432	−	0.782674i	$-0.713855\pi$
$151$	4.50486	−	7.80264i	0.366600	−	0.634970i	0.989032	+	0.147704i	$0.0471884\pi$
$152$	3.50711	+	6.07449i	0.284464	+	0.492707i
$153$	15.8518	+	9.96725i	1.28154	+	0.805804i
$154$	−0.157053	−	2.64109i	−0.0126557	−	0.212825i
$155$		−	14.5268i		−	1.16682i
$156$	−1.87900	−	7.58152i	−0.150440	−	0.607008i
$157$	2.83438	+	1.63643i	0.226208	+	0.130601i	0.608822	−	0.793307i	$-0.291643\pi$
$157$	2.83438	+	1.63643i	0.226208	+	0.130601i	−0.382613	+	0.923909i	$0.624976\pi$
$158$	−6.70413	−	3.87063i	−0.533352	−	0.307931i
$159$	−3.91929	−	15.8138i	−0.310820	−	1.25412i
$160$		−	1.59652i		−	0.126216i
$161$	−6.79033	−	10.2969i	−0.535153	−	0.811506i
$162$	8.11115	−	3.89991i	0.637272	−	0.306406i
$163$	7.81342	+	13.5332i	0.611994	+	1.06001i	0.990904	+	0.134572i	$0.0429658\pi$
$163$	7.81342	+	13.5332i	0.611994	+	1.06001i	−0.378910	+	0.925434i	$0.623701\pi$
$164$	0.798258	−	1.38262i	0.0623334	−	0.107965i
$165$	−1.99184	+	1.91811i	−0.155065	+	0.149325i
$166$	−15.1130	+	8.72550i	−1.17300	+	0.677230i
$167$	−19.7228			−1.52620			−0.763099	−	0.646282i	$-0.776323\pi$
$167$	−19.7228			−1.52620			−0.763099	+	0.646282i	$0.776323\pi$
$168$	3.36904	+	3.10638i	0.259927	+	0.239662i
$169$	−7.33672			−0.564363
$170$	8.62988	−	4.98247i	0.661882	−	0.382138i
$171$	9.82679	+	18.6072i	0.751473	+	1.42293i
$172$	−0.770788	+	1.33504i	−0.0587721	+	0.101796i
$173$	−0.301207	−	0.521706i	−0.0229003	−	0.0396645i	0.854348	−	0.519701i	$-0.173957\pi$
$173$	−0.301207	−	0.521706i	−0.0229003	−	0.0396645i	−0.877248	+	0.480037i	$0.840623\pi$
$174$	2.65676	−	9.21642i	0.201408	−	0.698695i
$175$	5.79884	+	2.90345i	0.438351	+	0.219480i
$176$		−	1.00000i		−	0.0753778i
$177$	−8.82216	+	2.18648i	−0.663114	+	0.164346i
$178$	11.5936	+	6.69358i	0.868978	+	0.501705i
$179$	20.9583	+	12.1003i	1.56650	+	0.904417i	0.996573	+	0.0827196i	$0.0263606\pi$
$179$	20.9583	+	12.1003i	1.56650	+	0.904417i	0.569924	+	0.821698i	$0.306973\pi$
$180$	0.180576	−	4.78614i	0.0134593	−	0.356738i
$181$		−	25.2747i		−	1.87865i	−0.343026	−	0.939326i	$-0.611452\pi$
$181$		−	25.2747i		−	1.87865i	0.343026	−	0.939326i	$-0.388548\pi$
$182$	9.96050	−	6.56852i	0.738322	−	0.486891i
$183$	−3.63164	−	1.04687i	−0.268458	−	0.0773868i
$184$	−2.33096	−	4.03733i	−0.171840	−	0.297636i
$185$	−0.456182	+	0.790131i	−0.0335392	+	0.0580916i
$186$	10.9320	+	11.3522i	0.801570	+	0.832383i
$187$	5.40545	−	3.12084i	0.395286	−	0.228218i
$188$	7.13853			0.520631
$189$	9.74857	+	9.69357i	0.709104	+	0.705104i
$190$	11.1983			0.812411
$191$	−9.98570	+	5.76525i	−0.722540	+	0.417159i	−0.815687	−	0.578494i	$-0.803641\pi$
$191$	−9.98570	+	5.76525i	−0.722540	+	0.417159i	0.0931470	+	0.995652i	$0.470307\pi$
$192$	1.20144	+	1.24762i	0.0867061	+	0.0900391i
$193$	−6.21106	+	10.7579i	−0.447082	+	0.774368i	−0.998195	−	0.0600625i	$-0.980870\pi$
$193$	−6.21106	+	10.7579i	−0.447082	+	0.774368i	0.551113	+	0.834431i	$0.314203\pi$
$194$	3.55758	+	6.16191i	0.255419	+	0.442399i
$195$	−11.9823	−	3.45406i	−0.858071	−	0.247351i
$196$	−2.75690	+	6.43425i	−0.196921	+	0.459589i
$197$		−	6.78332i		−	0.483291i	−0.970365	−	0.241646i	$-0.922313\pi$
$197$		−	6.78332i		−	0.483291i	0.970365	−	0.241646i	$-0.0776872\pi$
$198$	0.113106	−	2.99787i	0.00803812	−	0.213049i
$199$	−7.19446	−	4.15372i	−0.510002	−	0.294450i	0.222833	−	0.974857i	$-0.428470\pi$
$199$	−7.19446	−	4.15372i	−0.510002	−	0.294450i	−0.732834	+	0.680407i	$0.761803\pi$
$200$	2.12275	+	1.22557i	0.150101	+	0.0866609i
$201$	−2.06361	+	0.511443i	−0.145556	+	0.0360744i
$202$		−	0.301386i		−	0.0212055i
$203$	14.6257	−	0.869725i	1.02653	−	0.0610427i
$204$	−2.99446	+	10.3879i	−0.209654	+	0.727300i
$205$	−1.27443	−	2.20738i	−0.0890101	−	0.154170i
$206$	4.59255	−	7.95453i	0.319978	−	0.554218i
$207$	−6.53125	−	12.3670i	−0.453953	−	0.859568i
$208$	3.90545	−	2.25481i	0.270794	−	0.156343i
$209$	7.01422			0.485184
$210$	6.98431	−	2.17841i	0.481963	−	0.150325i
$211$	−2.69698			−0.185668			−0.0928339	−	0.995682i	$-0.529593\pi$
$211$	−2.69698			−0.185668			−0.0928339	+	0.995682i	$0.529593\pi$
$212$	8.14614	−	4.70318i	0.559479	−	0.323016i
$213$	11.8185	−	11.3810i	0.809787	−	0.779811i
$214$	4.21653	−	7.30325i	0.288236	−	0.499240i
$215$	1.23058	+	2.13142i	0.0839245	+	0.145362i
$216$	3.46063	+	3.87609i	0.235466	+	0.263734i
$217$	−10.7781	+	21.5264i	−0.731668	+	1.46131i
$218$			14.6854i			0.994620i
$219$	−1.71758	−	6.93022i	−0.116063	−	0.468301i
$220$	−1.38262	−	0.798258i	−0.0932164	−	0.0538185i
$221$	24.3766	+	14.0738i	1.63974	+	0.946707i
$222$	−0.238112	−	0.960752i	−0.0159810	−	0.0644815i
$223$			14.2135i			0.951806i	0.879498	+	0.475903i	$0.157879\pi$
$223$			14.2135i			0.951806i	−0.879498	+	0.475903i	$0.842121\pi$
$224$	−1.18453	+	2.36577i	−0.0791448	+	0.158070i
$225$	6.22510	+	3.91419i	0.415007	+	0.260946i
$226$	−5.27122	−	9.13003i	−0.350637	−	0.607320i
$227$	−2.67241	+	4.62875i	−0.177374	+	0.307221i	−0.940980	−	0.338461i	$-0.890094\pi$
$227$	−2.67241	+	4.62875i	−0.177374	+	0.307221i	0.763606	+	0.645682i	$0.223427\pi$
$228$	−8.75108	+	8.42713i	−0.579554	+	0.558101i
$229$	11.6567	−	6.73002i	0.770299	−	0.444732i	−0.0626824	−	0.998034i	$-0.519966\pi$
$229$	11.6567	−	6.73002i	0.770299	−	0.444732i	0.832981	+	0.553301i	$0.186632\pi$
$230$	−7.44281			−0.490764
$231$	4.37472	−	1.36448i	0.287836	−	0.0897763i
$232$	5.53777			0.363573
$233$	0.0187672	−	0.0108352i	0.00122948	−	0.000709840i	−0.499385	−	0.866380i	$-0.666441\pi$
$233$	0.0187672	−	0.0108352i	0.00122948	−	0.000709840i	0.500615	+	0.865670i	$0.333107\pi$
$234$	11.9631	−	6.31790i	0.782049	−	0.413014i
$235$	5.69839	−	9.86990i	0.371722	−	0.643841i
$236$	−2.62379	−	4.54453i	−0.170794	−	0.295824i
$237$	3.71389	−	12.8837i	0.241243	−	0.836883i
$238$	−16.4848	+	0.980275i	−1.06855	+	0.0635418i
$239$		−	10.4498i		−	0.675939i	−0.941157	−	0.337970i	$-0.890260\pi$
$239$		−	10.4498i		−	0.675939i	0.941157	−	0.337970i	$-0.109740\pi$
$240$	2.68404	−	0.665210i	0.173254	−	0.0429391i
$241$	3.78807	+	2.18704i	0.244011	+	0.140880i	0.617019	−	0.786948i	$-0.288340\pi$
$241$	3.78807	+	2.18704i	0.244011	+	0.140880i	−0.373008	+	0.927828i	$0.621674\pi$
$242$	−0.866025	−	0.500000i	−0.0556702	−	0.0321412i
$243$	9.93610	+	12.0114i	0.637401	+	0.770532i
$244$		−	2.18210i		−	0.139695i
$245$	6.69542	+	8.94793i	0.427755	+	0.571662i
$246$	2.65705	+	0.765932i	0.169408	+	0.0488340i
$247$	15.8158	+	27.3937i	1.00633	+	1.74302i
$248$	−4.54954	+	7.88004i	−0.288896	+	0.500383i
$249$	−20.9663	−	21.7722i	−1.32868	−	1.37976i
$250$	10.3021	−	5.94793i	0.651563	−	0.376180i
$251$	−6.32543			−0.399258			−0.199629	−	0.979872i	$-0.563974\pi$
$251$	−6.32543			−0.399258			−0.199629	+	0.979872i	$0.563974\pi$
$252$	−3.81865	+	6.95830i	−0.240552	+	0.438332i
$253$	−4.66191			−0.293092
$254$	3.10259	−	1.79128i	0.194674	−	0.112395i
$255$	11.9722	+	12.4324i	0.749729	+	0.778549i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	4.91340	+	8.51025i	0.306489	+	0.530855i	0.977592	−	0.210510i	$-0.0675123\pi$
$257$	4.91340	+	8.51025i	0.306489	+	0.530855i	−0.671103	+	0.741364i	$0.734179\pi$
$258$	−2.56562	−	0.739575i	−0.159729	−	0.0460439i
$259$	1.26222	−	0.832381i	0.0784307	−	0.0517216i
$260$		−	7.19968i		−	0.446506i
$261$	16.6015	+	0.626358i	1.02761	+	0.0387706i
$262$	−19.0321	−	10.9882i	−1.17581	−	0.678854i
$263$	−16.8992	−	9.75675i	−1.04205	−	0.601627i	−0.121635	−	0.992575i	$-0.538814\pi$
$263$	−16.8992	−	9.75675i	−1.04205	−	0.601627i	−0.920413	+	0.390948i	$0.872147\pi$
$264$	1.68119	−	0.416664i	0.103470	−	0.0256439i
$265$		−	15.0174i		−	0.922511i
$266$	−16.5941	−	8.30856i	−1.01745	−	0.509431i
$267$	−6.42251	+	22.2800i	−0.393051	+	1.36351i
$268$	−0.613735	−	1.06302i	−0.0374898	−	0.0649343i
$269$	−3.36084	+	5.82115i	−0.204914	+	0.354922i	−0.950105	−	0.311929i	$-0.899025\pi$
$269$	−3.36084	+	5.82115i	−0.204914	+	0.354922i	0.745191	+	0.666851i	$0.232358\pi$
$270$	8.12164	−	1.69063i	0.494267	−	0.102888i
$271$	8.89324	−	5.13451i	0.540226	−	0.311899i	−0.204945	−	0.978774i	$-0.565701\pi$
$271$	8.89324	−	5.13451i	0.540226	−	0.311899i	0.745170	+	0.666874i	$0.232368\pi$
$272$	−6.24168			−0.378457
$273$	15.1931	+	14.0086i	0.919528	+	0.847840i
$274$	11.5931			0.700367
$275$	2.12275	−	1.22557i	0.128007	−	0.0739046i
$276$	5.81629	−	5.60098i	0.350099	−	0.337140i
$277$	−0.340360	+	0.589521i	−0.0204502	+	0.0354209i	−0.876069	−	0.482185i	$-0.839843\pi$
$277$	−0.340360	+	0.589521i	−0.0204502	+	0.0354209i	0.855619	+	0.517606i	$0.173177\pi$
$278$	6.15566	+	10.6619i	0.369192	+	0.639459i
$279$	−14.5302	+	23.1087i	−0.869900	+	1.38348i
$280$	2.32541	+	3.52626i	0.138970	+	0.210734i
$281$		−	22.1693i		−	1.32251i	−0.750162	−	0.661254i	$-0.770024\pi$
$281$		−	22.1693i		−	1.32251i	0.750162	−	0.661254i	$-0.229976\pi$
$282$	2.97437	+	12.0012i	0.177121	+	0.714662i
$283$	−22.0002	−	12.7018i	−1.30778	−	0.755044i	−0.326051	−	0.945352i	$-0.605718\pi$
$283$	−22.0002	−	12.7018i	−1.30778	−	0.755044i	−0.981724	+	0.190308i	$0.939051\pi$
$284$	8.20369	+	4.73640i	0.486800	+	0.281054i
$285$	4.66593	+	18.8265i	0.276386	+	1.11518i
$286$		−	4.50963i		−	0.266660i
$287$	0.250738	+	4.21653i	0.0148006	+	0.248894i
$288$	−1.59689	+	2.53968i	−0.0940974	+	0.149652i
$289$	−10.9793	−	19.0166i	−0.645839	−	1.11863i
$290$	4.42057	−	7.65665i	0.259585	−	0.449614i
$291$	−8.87701	+	8.54841i	−0.520380	+	0.501116i
$292$	3.56995	−	2.06111i	0.208915	−	0.120617i
$293$	4.91386			0.287070			0.143535	−	0.989645i	$-0.454153\pi$
$293$	4.91386			0.287070			0.143535	+	0.989645i	$0.454153\pi$
$294$	−11.9659	−	1.95394i	−0.697864	−	0.113956i
$295$	−8.37783			−0.487776
$296$	0.494910	−	0.285736i	0.0287660	−	0.0166081i
$297$	5.08710	−	1.05895i	0.295184	−	0.0614465i
$298$	6.45067	−	11.1729i	0.373677	−	0.647228i
$299$	−10.5117	−	18.2069i	−0.607909	−	1.05293i
$300$	−1.17594	+	4.07939i	−0.0678929	+	0.235524i
$301$	−0.242109	−	4.07144i	−0.0139550	−	0.234674i
$302$			9.00971i			0.518451i
$303$	0.506687	−	0.125577i	0.0291084	−	0.00721420i
$304$	−6.07449	−	3.50711i	−0.348396	−	0.201147i
$305$	−3.01703	−	1.74188i	−0.172754	−	0.0997398i
$306$	−18.7117	−	0.705973i	−1.06968	−	0.0403578i
$307$		−	17.5786i		−	1.00326i	−0.865082	−	0.501631i	$-0.832734\pi$
$307$		−	17.5786i		−	1.00326i	0.865082	−	0.501631i	$-0.167266\pi$
$308$	1.45655	+	2.20872i	0.0829949	+	0.125854i
$309$	15.2866	+	4.40657i	0.869625	+	0.250681i
$310$	7.26341	+	12.5806i	0.412534	+	0.714530i
$311$	7.05301	−	12.2162i	0.399939	−	0.692715i	−0.593779	−	0.804628i	$-0.702365\pi$
$311$	7.05301	−	12.2162i	0.399939	−	0.692715i	0.993718	+	0.111913i	$0.0356979\pi$
$312$	5.41802	+	5.62629i	0.306735	+	0.318526i
$313$	−22.2006	+	12.8175i	−1.25485	+	0.724490i	−0.972069	−	0.234694i	$-0.924591\pi$
$313$	−22.2006	+	12.8175i	−1.25485	+	0.724490i	−0.282784	+	0.959184i	$0.591258\pi$
$314$	−3.27286			−0.184698
$315$	6.57243	+	10.8343i	0.370315	+	0.610442i
$316$	7.74126			0.435480
$317$	2.94082	−	1.69789i	0.165173	−	0.0953628i	−0.415135	−	0.909760i	$-0.636266\pi$
$317$	2.94082	−	1.69789i	0.165173	−	0.0953628i	0.580308	+	0.814397i	$0.302932\pi$
$318$	11.3011	+	11.7355i	0.633736	+	0.658097i
$319$	2.76889	−	4.79585i	0.155028	−	0.268516i
$320$	0.798258	+	1.38262i	0.0446240	+	0.0772910i
$321$	14.0350	+	4.04578i	0.783358	+	0.225814i
$322$	11.0290	+	5.52218i	0.614624	+	0.307739i
$323$		−	43.7805i		−	2.43601i
$324$	−5.07451	+	7.43299i	−0.281917	+	0.412944i
$325$	9.57280	+	5.52686i	0.531003	+	0.306575i
$326$	−13.5332	−	7.81342i	−0.749537	−	0.432745i
$327$	−24.6889	+	6.11887i	−1.36530	+	0.338375i
$328$			1.59652i			0.0881528i
$329$	−15.7670	+	10.3977i	−0.869264	+	0.573242i
$330$	0.765932	−	2.65705i	0.0421631	−	0.146266i
$331$	−1.09383	−	1.89457i	−0.0601223	−	0.104135i	0.834398	−	0.551163i	$-0.185816\pi$
$331$	−1.09383	−	1.89457i	−0.0601223	−	0.104135i	−0.894520	+	0.447028i	$0.852482\pi$
$332$	8.72550	−	15.1130i	0.478874	−	0.829434i
$333$	1.51599	−	0.800622i	0.0830758	−	0.0438738i
$334$	17.0805	−	9.86141i	0.934601	−	0.539592i
$335$	−1.95968			−0.107069
$336$	−4.47086	−	1.00569i	−0.243905	−	0.0548646i
$337$	29.9526			1.63162			0.815811	−	0.578318i	$-0.196291\pi$
$337$	29.9526			1.63162			0.815811	+	0.578318i	$0.196291\pi$
$338$	6.35378	−	3.66836i	0.345600	−	0.199532i
$339$	13.1530	−	12.6661i	0.714371	−	0.687926i
$340$	−4.98247	+	8.62988i	−0.270212	+	0.468021i
$341$	4.54954	+	7.88004i	0.246371	+	0.426728i
$342$	−17.8139	−	11.2009i	−0.963263	−	0.605676i
$343$	−3.28262	−	18.2270i	−0.177245	−	0.984167i
$344$		−	1.54158i		−	0.0831163i
$345$	−3.10115	−	12.5128i	−0.166960	−	0.673664i
$346$	0.521706	+	0.301207i	0.0280471	+	0.0161930i
$347$	−29.0172	−	16.7531i	−1.55772	−	0.899352i	−0.997474	−	0.0710275i	$-0.977372\pi$
$347$	−29.0172	−	16.7531i	−1.55772	−	0.899352i	−0.560249	−	0.828324i	$-0.689294\pi$
$348$	2.30739	+	9.31004i	0.123689	+	0.499070i
$349$			20.9221i			1.11993i	0.828516	+	0.559966i	$0.189186\pi$
$349$			20.9221i			1.11993i	−0.828516	+	0.559966i	$0.810814\pi$
$350$	−6.47367	+	0.384959i	−0.346032	+	0.0205769i
$351$	15.6061	+	17.4797i	0.832994	+	0.932997i
$352$	0.500000	+	0.866025i	0.0266501	+	0.0461593i
$353$	−2.78452	+	4.82293i	−0.148205	+	0.256698i	−0.930564	−	0.366129i	$-0.880683\pi$
$353$	−2.78452	+	4.82293i	−0.148205	+	0.256698i	0.782359	+	0.622828i	$0.214016\pi$
$354$	6.54697	−	6.30462i	0.347968	−	0.335087i
$355$	13.0973	−	7.56174i	0.695134	−	0.401336i
$356$	−13.3872			−0.709518
$357$	−8.51665	−	27.3056i	−0.450749	−	1.44517i
$358$	−24.2006			−1.27904
$359$	7.29047	−	4.20916i	0.384776	−	0.222151i	−0.295118	−	0.955461i	$-0.595359\pi$
$359$	7.29047	−	4.20916i	0.384776	−	0.222151i	0.679894	+	0.733310i	$0.262026\pi$
$360$	2.23669	+	4.23521i	0.117884	+	0.223215i
$361$	15.0997	−	26.1534i	0.794719	−	1.37649i
$362$	12.6373	+	21.8885i	0.664204	+	1.15043i
$363$	0.479752	−	1.66428i	0.0251805	−	0.0873522i
$364$	−5.34179	+	10.6688i	−0.279986	+	0.559195i
$365$		−	6.58119i		−	0.344475i
$366$	3.66853	−	0.909204i	0.191757	−	0.0475249i
$367$	−31.8854	−	18.4090i	−1.66440	−	0.960944i	−0.970573	−	0.240806i	$-0.922588\pi$
$367$	−31.8854	−	18.4090i	−1.66440	−	0.960944i	−0.693831	−	0.720138i	$-0.744078\pi$
$368$	4.03733	+	2.33096i	0.210461	+	0.121509i
$369$	−0.180576	+	4.78614i	−0.00940041	+	0.249157i
$370$		−	0.912364i		−	0.0474316i
$371$	−11.1421	+	22.2533i	−0.578470	+	1.15533i
$372$	−15.1434	−	4.36530i	−0.785151	−	0.226330i
$373$	−4.54391	−	7.87029i	−0.235275	−	0.407508i	0.724078	−	0.689718i	$-0.242266\pi$
$373$	−4.54391	−	7.87029i	−0.235275	−	0.407508i	−0.959353	+	0.282210i	$0.908932\pi$
$374$	−3.12084	+	5.40545i	−0.161375	+	0.279509i
$375$	14.2921	+	14.8415i	0.738041	+	0.766412i
$376$	−6.18215	+	3.56927i	−0.318820	+	0.184071i
$377$	24.9733			1.28619
$378$	−13.2893	−	3.52059i	−0.683528	−	0.181080i
$379$	−25.4673			−1.30817			−0.654085	−	0.756421i	$-0.726946\pi$
$379$	−25.4673			−1.30817			−0.654085	+	0.756421i	$0.726946\pi$
$380$	−9.69802	+	5.59916i	−0.497498	+	0.287231i
$381$	4.30421	+	4.46967i	0.220511	+	0.228988i
$382$	5.76525	−	9.98570i	0.294976	−	0.510913i
$383$	4.27006	+	7.39596i	0.218190	+	0.377916i	0.954255	−	0.298995i	$-0.0966515\pi$
$383$	4.27006	+	7.39596i	0.218190	+	0.377916i	−0.736065	+	0.676911i	$0.763318\pi$
$384$	−1.66428	−	0.479752i	−0.0849301	−	0.0244822i
$385$	4.21653	−	0.250738i	0.214894	−	0.0127788i
$386$		−	12.4221i		−	0.632269i
$387$	0.174362	−	4.62144i	0.00886333	−	0.234921i
$388$	−6.16191	−	3.55758i	−0.312824	−	0.180609i
$389$	−1.09167	−	0.630275i	−0.0553498	−	0.0319562i	0.472070	−	0.881561i	$-0.343507\pi$
$389$	−1.09167	−	0.630275i	−0.0553498	−	0.0319562i	−0.527420	+	0.849605i	$0.676840\pi$
$390$	12.1040	−	2.99985i	0.612911	−	0.151903i
$391$			29.0981i			1.47156i
$392$	−0.829582	−	6.95067i	−0.0419002	−	0.351062i
$393$	10.5432	−	36.5750i	0.531836	−	1.84496i
$394$	3.39166	+	5.87453i	0.170869	+	0.295954i
$395$	6.17952	−	10.7032i	0.310925	−	0.538539i
$396$	1.40098	+	2.65278i	0.0704019	+	0.133307i
$397$	1.93996	−	1.12004i	0.0973638	−	0.0562130i	−0.450528	−	0.892763i	$-0.648764\pi$
$397$	1.93996	−	1.12004i	0.0973638	−	0.0562130i	0.547891	+	0.836550i	$0.315431\pi$
$398$	8.30745			0.416415
$399$	7.05410	−	31.3596i	0.353147	−	1.56994i
$400$	−2.45114			−0.122557
$401$	−21.8208	+	12.5982i	−1.08968	+	0.629125i	−0.933491	−	0.358602i	$-0.883254\pi$
$401$	−21.8208	+	12.5982i	−1.08968	+	0.629125i	−0.156187	+	0.987728i	$0.549920\pi$
$402$	1.53142	−	1.47473i	0.0763801	−	0.0735527i
$403$	−20.5167	+	35.5360i	−1.02201	+	1.77017i
$404$	0.150693	+	0.261008i	0.00749726	+	0.0129856i
$405$	6.22626	+	12.9496i	0.309385	+	0.643469i
$406$	−12.2314	+	8.06607i	−0.607034	+	0.400312i
$407$		−	0.571472i		−	0.0283268i
$408$	−2.60068	−	10.4934i	−0.128753	−	0.519502i
$409$	−15.7714	−	9.10565i	−0.779848	−	0.450245i	0.0565286	−	0.998401i	$-0.481997\pi$
$409$	−15.7714	−	9.10565i	−0.779848	−	0.450245i	−0.836376	+	0.548156i	$0.815330\pi$
$410$	2.20738	+	1.27443i	0.109015	+	0.0629396i
$411$	4.83045	+	19.4902i	0.238268	+	0.961383i
$412$			9.18510i			0.452517i
$413$	12.4146	+	6.21591i	0.610881	+	0.305865i
$414$	11.8397	+	7.44454i	0.581891	+	0.365879i
$415$	−13.9304	−	24.1282i	−0.683816	−	1.18440i
$416$	−2.25481	+	3.90545i	−0.110551	+	0.191480i
$417$	−15.3598	+	14.7912i	−0.752174	+	0.724330i
$418$	−6.07449	+	3.50711i	−0.297113	+	0.171538i
$419$	−4.09314			−0.199963			−0.0999814	−	0.994989i	$-0.531878\pi$
$419$	−4.09314			−0.199963			−0.0999814	+	0.994989i	$0.531878\pi$
$420$	−4.95938	+	5.37872i	−0.241993	+	0.262455i
$421$	−31.3561			−1.52820			−0.764101	−	0.645097i	$-0.776817\pi$
$421$	−31.3561			−1.52820			−0.764101	+	0.645097i	$0.776817\pi$
$422$	2.33565	−	1.34849i	0.113698	−	0.0656435i
$423$	−18.9370	+	10.0009i	−0.920747	+	0.486263i
$424$	−4.70318	+	8.14614i	−0.228407	+	0.395612i
$425$	−7.64961	−	13.2495i	−0.371060	−	0.642696i
$426$	−4.54460	+	15.7654i	−0.220187	+	0.763838i
$427$	3.17835	+	4.81966i	0.153811	+	0.233240i
$428$			8.43307i			0.407628i
$429$	7.58152	−	1.87900i	0.366039	−	0.0907189i
$430$	−2.13142	−	1.23058i	−0.102786	−	0.0593436i
$431$	5.56332	+	3.21199i	0.267976	+	0.154716i	0.627967	−	0.778240i	$-0.283887\pi$
$431$	5.56332	+	3.21199i	0.267976	+	0.154716i	−0.359992	+	0.932956i	$0.617220\pi$
$432$	−4.93504	−	1.62647i	−0.237437	−	0.0782538i
$433$		−	9.32492i		−	0.448127i	−0.974575	−	0.224063i	$-0.928068\pi$
$433$		−	9.32492i		−	0.448127i	0.974575	−	0.224063i	$-0.0719323\pi$
$434$	−1.42904	−	24.0315i	−0.0685961	−	1.15355i
$435$	14.7142	+	4.24156i	0.705490	+	0.203367i
$436$	−7.34270	−	12.7179i	−0.351651	−	0.609078i
$437$	−16.3498	+	28.3187i	−0.782119	+	1.35467i
$438$	4.95258	+	5.14296i	0.236643	+	0.245740i
$439$	6.17648	−	3.56599i	0.294787	−	0.170196i	−0.345311	−	0.938488i	$-0.612227\pi$
$439$	6.17648	−	3.56599i	0.294787	−	0.170196i	0.640099	+	0.768293i	$0.278893\pi$
$440$	1.59652			0.0761109
$441$	−1.70081	−	20.9310i	−0.0809910	−	0.996715i
$442$	−28.1476			−1.33885
$443$	−7.28448	+	4.20570i	−0.346096	+	0.199819i	−0.662965	−	0.748651i	$-0.730702\pi$
$443$	−7.28448	+	4.20570i	−0.346096	+	0.199819i	0.316868	+	0.948470i	$0.397369\pi$
$444$	0.686587	+	0.712980i	0.0325840	+	0.0338365i
$445$	−10.6864	+	18.5094i	−0.506584	+	0.877429i
$446$	−7.10675	−	12.3092i	−0.336514	−	0.582860i
$447$	21.4715	+	6.18944i	1.01557	+	0.292751i
$448$	−0.157053	−	2.64109i	−0.00742006	−	0.124780i
$449$			16.9926i			0.801933i	0.916093	+	0.400966i	$0.131326\pi$
$449$			16.9926i			0.801933i	−0.916093	+	0.400966i	$0.868674\pi$
$450$	−7.34819	−	0.277239i	−0.346397	−	0.0130692i
$451$	1.38262	+	0.798258i	0.0651052	+	0.0375885i
$452$	9.13003	+	5.27122i	0.429440	+	0.247938i
$453$	−15.1470	+	3.75402i	−0.711669	+	0.176379i
$454$		−	5.34482i		−	0.250845i
$455$	10.4867	+	15.9021i	0.491626	+	0.745502i
$456$	3.36509	−	11.6737i	0.157585	−	0.546669i
$457$	16.0161	+	27.7407i	0.749203	+	1.29766i	0.948205	+	0.317658i	$0.102897\pi$
$457$	16.0161	+	27.7407i	0.749203	+	1.29766i	−0.199002	+	0.979999i	$0.563770\pi$
$458$	−6.73002	+	11.6567i	−0.314473	+	0.544684i
$459$	−6.60962	−	31.7521i	−0.308511	−	1.48206i
$460$	6.44566	−	3.72141i	0.300531	−	0.173511i
$461$	6.80255			0.316826			0.158413	−	0.987373i	$-0.449362\pi$
$461$	6.80255			0.316826			0.158413	+	0.987373i	$0.449362\pi$
$462$	−3.10638	+	3.36904i	−0.144522	+	0.156742i
$463$	−7.62180			−0.354215			−0.177108	−	0.984192i	$-0.556674\pi$
$463$	−7.62180			−0.354215			−0.177108	+	0.984192i	$0.556674\pi$
$464$	−4.79585	+	2.76889i	−0.222642	+	0.128542i
$465$	−18.1239	+	17.4530i	−0.840478	+	0.809365i
$466$	−0.0108352	+	0.0187672i	−0.000501933	+	0.000869373i
$467$	9.28685	+	16.0853i	0.429744	+	0.744339i	0.996850	−	0.0793060i	$-0.0252704\pi$
$467$	9.28685	+	16.0853i	0.429744	+	0.744339i	−0.567106	+	0.823645i	$0.691937\pi$
$468$	−7.20136	+	11.4530i	−0.332883	+	0.529414i
$469$	2.90392	+	1.45398i	0.134090	+	0.0671384i
$470$			11.3968i			0.525694i
$471$	−1.36368	−	5.50229i	−0.0628352	−	0.253532i
$472$	4.54453	+	2.62379i	0.209179	+	0.120770i
$473$	−1.33504	−	0.770788i	−0.0613854	−	0.0354409i
$474$	3.22551	+	13.0145i	0.148152	+	0.597776i
$475$		−	17.1928i		−	0.788861i
$476$	13.7861	−	9.09134i	0.631886	−	0.416701i
$477$	−15.0209	+	23.8891i	−0.687759	+	1.09381i
$478$	5.22488	+	9.04976i	0.238981	+	0.413927i
$479$	6.60898	−	11.4471i	0.301972	−	0.523031i	−0.674610	−	0.738174i	$-0.735688\pi$
$479$	6.60898	−	11.4471i	0.301972	−	0.523031i	0.976583	+	0.215143i	$0.0690217\pi$
$480$	−1.99184	+	1.91811i	−0.0909148	+	0.0875493i
$481$	2.23186	−	1.28856i	0.101764	−	0.0587534i
$482$	−4.37409			−0.199234
$483$	−4.68842	+	20.8428i	−0.213330	+	0.948378i
$484$	1.00000			0.0454545
$485$	−9.83758	+	5.67973i	−0.446702	+	0.257903i
$486$	−14.6106	−	5.43414i	−0.662751	−	0.246497i
$487$	10.7246	−	18.5756i	0.485980	−	0.841741i	−0.513891	−	0.857856i	$-0.671796\pi$
$487$	10.7246	−	18.5756i	0.485980	−	0.841741i	0.999870	+	0.0161145i	$0.00512963\pi$
$488$	1.09105	+	1.88976i	0.0493896	+	0.0855453i
$489$	7.49701	−	26.0075i	0.339026	−	1.17610i
$490$	−10.2724	−	4.40143i	−0.464058	−	0.198836i
$491$			4.02472i			0.181633i	0.995868	+	0.0908166i	$0.0289477\pi$
$491$			4.02472i			0.181633i	−0.995868	+	0.0908166i	$0.971052\pi$
$492$	−2.68404	+	0.665210i	−0.121006	+	0.0299900i
$493$	−29.9342	−	17.2825i	−1.34817	−	0.778365i
$494$	−27.3937	−	15.8158i	−1.23250	−	0.711585i
$495$	4.78614	+	0.180576i	0.215121	+	0.00811629i
$496$		−	9.09908i		−	0.408561i
$497$	−25.0185	+	1.48773i	−1.12223	+	0.0667340i
$498$	29.0434	+	8.37216i	1.30147	+	0.375165i
$499$	0.903651	+	1.56517i	0.0404530	+	0.0700666i	0.885543	−	0.464557i	$-0.153787\pi$
$499$	0.903651	+	1.56517i	0.0404530	+	0.0700666i	−0.845090	+	0.534624i	$0.820453\pi$
$500$	−5.94793	+	10.3021i	−0.265999	+	0.460725i
$501$	23.6957	+	24.6066i	1.05865	+	1.09934i
$502$	5.47798	−	3.16272i	0.244494	−	0.141159i
$503$	5.18163			0.231037			0.115519	−	0.993305i	$-0.463147\pi$
$503$	5.18163			0.231037			0.115519	+	0.993305i	$0.463147\pi$
$504$	−0.172101	−	7.93539i	−0.00766598	−	0.353470i
$505$	0.481168			0.0214117
$506$	4.03733	−	2.33096i	0.179481	−	0.103624i
$507$	8.81459	+	9.15343i	0.391470	+	0.406518i
$508$	−1.79128	+	3.10259i	−0.0794752	+	0.137655i
$509$	−2.70116	−	4.67854i	−0.119727	−	0.207373i	0.799933	−	0.600090i	$-0.204868\pi$
$509$	−2.70116	−	4.67854i	−0.119727	−	0.207373i	−0.919659	+	0.392717i	$0.871535\pi$
$510$	−16.5845	−	4.78070i	−0.734372	−	0.211693i
$511$	−4.88290	+	9.75224i	−0.216007	+	0.431414i
$512$		−	1.00000i		−	0.0441942i
$513$	11.4085	−	34.6154i	0.503695	−	1.52831i
$514$	−8.51025	−	4.91340i	−0.375371	−	0.216721i
$515$	12.6995	+	7.33208i	0.559608	+	0.323090i
$516$	2.59168	−	0.642320i	0.114092	−	0.0282765i
$517$			7.13853i			0.313952i
$518$	−0.676927	+	1.35197i	−0.0297425	+	0.0594024i
$519$	−0.289009	+	1.00259i	−0.0126861	+	0.0440087i
$520$	3.59984	+	6.23511i	0.157864	+	0.273428i
$521$	−0.537919	+	0.931703i	−0.0235667	+	0.0408187i	−0.877568	−	0.479452i	$-0.840836\pi$
$521$	−0.537919	+	0.931703i	−0.0235667	+	0.0408187i	0.854002	+	0.520270i	$0.174169\pi$
$522$	−14.6905	+	7.75831i	−0.642986	+	0.339572i
$523$	22.3360	−	12.8957i	0.976686	−	0.563890i	0.0754184	−	0.997152i	$-0.475971\pi$
$523$	22.3360	−	12.8957i	0.976686	−	0.563890i	0.901268	+	0.433262i	$0.142637\pi$
$524$	21.9764			0.960045
$525$	−3.34453	−	10.7231i	−0.145967	−	0.467992i
$526$	19.5135			0.850829
$527$	49.1846	−	28.3968i	2.14252	−	1.23698i
$528$	−1.24762	+	1.20144i	−0.0542956	+	0.0522858i
$529$	−0.633298	+	1.09690i	−0.0275347	+	0.0476915i
$530$	7.50870	+	13.0054i	0.326157	+	0.564920i
$531$	13.3271	+	8.37978i	0.578349	+	0.363652i
$532$	18.5252	−	1.10161i	0.803168	−	0.0477607i
$533$			7.19968i			0.311853i
$534$	−5.57794	−	22.5063i	−0.241381	−	0.973943i
$535$	11.6598	+	6.73176i	0.504095	+	0.291039i
$536$	1.06302	+	0.613735i	0.0459155	+	0.0265093i
$537$	−10.0835	−	40.6857i	−0.435135	−	1.75572i
$538$		−	6.72169i		−	0.289792i
$539$	−6.43425	−	2.75690i	−0.277143	−	0.118748i
$540$	−6.18823	+	5.52495i	−0.266299	+	0.237756i
$541$	7.73940	+	13.4050i	0.332743	+	0.576327i	0.983049	−	0.183345i	$-0.0586926\pi$
$541$	7.73940	+	13.4050i	0.332743	+	0.576327i	−0.650306	+	0.759672i	$0.725359\pi$
$542$	−5.13451	+	8.89324i	−0.220546	+	0.381997i
$543$	−31.5332	+	30.3659i	−1.35322	+	1.30312i
$544$	5.40545	−	3.12084i	0.231757	−	0.133805i
$545$	−23.4455			−1.00429
$546$	−20.1619	−	4.53526i	−0.862850	−	0.194091i
$547$	6.19696			0.264963			0.132481	−	0.991185i	$-0.457706\pi$
$547$	6.19696			0.264963			0.132481	+	0.991185i	$0.457706\pi$
$548$	−10.0400	+	5.79657i	−0.428886	+	0.247617i
$549$	3.05709	+	5.78865i	0.130473	+	0.247053i
$550$	−1.22557	+	2.12275i	−0.0522585	+	0.0905143i
$551$	−19.4216	−	33.6392i	−0.827388	−	1.43308i
$552$	−2.23656	+	7.75874i	−0.0951944	+	0.330234i
$553$	−17.0983	+	11.2756i	−0.727093	+	0.479486i
$554$		−	0.680720i		−	0.0289210i
$555$	1.53386	−	0.380149i	0.0651085	−	0.0161364i
$556$	−10.6619	−	6.15566i	−0.452166	−	0.261058i
$557$	6.93926	+	4.00638i	0.294026	+	0.169756i	0.639756	−	0.768578i	$-0.279035\pi$
$557$	6.93926	+	4.00638i	0.294026	+	0.169756i	−0.345730	+	0.938334i	$0.612369\pi$
$558$	1.02916	−	27.2778i	0.0435680	−	1.15476i
$559$		−	6.95193i		−	0.294035i
$560$	−3.77699	−	1.89112i	−0.159607	−	0.0799145i
$561$	−10.3879	−	2.99446i	−0.438578	−	0.126426i
$562$	11.0846	+	19.1992i	0.467577	+	0.809868i
$563$	18.8825	−	32.7054i	0.795801	−	1.37837i	−0.126528	−	0.991963i	$-0.540383\pi$
$563$	18.8825	−	32.7054i	0.795801	−	1.37837i	0.922329	−	0.386405i	$-0.126283\pi$
$564$	−8.57648	−	8.90617i	−0.361135	−	0.375017i
$565$	14.5762	−	8.41559i	0.613227	−	0.354046i
$566$	25.4036			1.06779
$567$	0.381608	−	23.8087i	0.0160260	−	0.999872i
$568$	−9.47281			−0.397470
$569$	30.7607	−	17.7597i	1.28956	−	0.744525i	0.310981	−	0.950416i	$-0.399342\pi$
$569$	30.7607	−	17.7597i	1.28956	−	0.744525i	0.978575	+	0.205891i	$0.0660091\pi$
$570$	−13.4540	−	13.9712i	−0.563528	−	0.585190i
$571$	−21.7959	+	37.7517i	−0.912132	+	1.57986i	−0.101085	+	0.994878i	$0.532231\pi$
$571$	−21.7959	+	37.7517i	−0.912132	+	1.57986i	−0.811047	+	0.584981i	$0.801102\pi$
$572$	2.25481	+	3.90545i	0.0942784	+	0.163295i
$573$	19.1900	+	5.53178i	0.801674	+	0.231093i
$574$	−2.32541	−	3.52626i	−0.0970608	−	0.147183i
$575$			11.4270i			0.476538i
$576$	0.113106	−	2.99787i	0.00471277	−	0.124911i
$577$	24.5749	+	14.1883i	1.02307	+	0.590668i	0.914991	−	0.403475i	$-0.132198\pi$
$577$	24.5749	+	14.1883i	1.02307	+	0.590668i	0.108076	+	0.994143i	$0.465531\pi$
$578$	19.0166	+	10.9793i	0.790988	+	0.456677i
$579$	20.8839	−	5.17585i	0.867905	−	0.215101i
$580$			8.84114i			0.367108i
$581$	2.74073	+	46.0896i	0.113705	+	1.91212i
$582$	3.41351	−	11.8416i	0.141495	−	0.490852i
$583$	4.70318	+	8.14614i	0.194786	+	0.337379i
$584$	−2.06111	+	3.56995i	−0.0852893	+	0.147725i
$585$	10.0866	+	19.0992i	0.417030	+	0.789655i
$586$	−4.25552	+	2.45693i	−0.175794	+	0.101495i
$587$	4.02886			0.166289			0.0831444	−	0.996538i	$-0.473504\pi$
$587$	4.02886			0.166289			0.0831444	+	0.996538i	$0.473504\pi$
$588$	11.3397	−	4.29078i	0.467642	−	0.176949i
$589$	63.8230			2.62978
$590$	7.25542	−	4.18892i	0.298701	−	0.172455i
$591$	−8.46300	+	8.14972i	−0.348121	+	0.335235i
$592$	−0.285736	+	0.494910i	−0.0117437	+	0.0203407i
$593$	−16.6336	−	28.8102i	−0.683060	−	1.18309i	−0.974042	−	0.226366i	$-0.927315\pi$
$593$	−16.6336	−	28.8102i	−0.683060	−	1.18309i	0.290982	−	0.956729i	$-0.406018\pi$
$594$	−3.87609	+	3.46063i	−0.159038	+	0.141991i
$595$	−1.56502	−	26.3182i	−0.0641597	−	1.07894i
$596$			12.9013i			0.528459i
$597$	3.46141	+	13.9664i	0.141666	+	0.571606i
$598$	18.2069	+	10.5117i	0.744534	+	0.429857i
$599$	18.2896	+	10.5595i	0.747291	+	0.431449i	0.824714	−	0.565550i	$-0.191336\pi$
$599$	18.2896	+	10.5595i	0.747291	+	0.431449i	−0.0774232	+	0.996998i	$0.524669\pi$
$600$	−1.02130	−	4.12082i	−0.0416945	−	0.168232i
$601$			13.1521i			0.536484i	0.963352	+	0.268242i	$0.0864427\pi$
$601$			13.1521i			0.536484i	−0.963352	+	0.268242i	$0.913557\pi$
$602$	2.24539	+	3.40491i	0.0915153	+	0.138774i
$603$	3.11738	+	1.96013i	0.126949	+	0.0798227i
$604$	−4.50486	−	7.80264i	−0.183300	−	0.317485i
$605$	0.798258	−	1.38262i	0.0324538	−	0.0562116i
$606$	−0.376015	+	0.362096i	−0.0152746	+	0.0147091i
$607$	29.6701	−	17.1300i	1.20427	−	0.695286i	0.242769	−	0.970084i	$-0.421944\pi$
$607$	29.6701	−	17.1300i	1.20427	−	0.695286i	0.961502	+	0.274798i	$0.0886110\pi$
$608$	7.01422			0.284464
$609$	−18.6570	−	17.2024i	−0.756018	−	0.697078i
$610$	3.48376			0.141053
$611$	−27.8792	+	16.0961i	−1.12787	+	0.651177i
$612$	16.5578	−	8.74447i	0.669310	−	0.353474i
$613$	0.628750	−	1.08903i	0.0253950	−	0.0439854i	−0.853049	−	0.521831i	$-0.825249\pi$
$613$	0.628750	−	1.08903i	0.0253950	−	0.0439854i	0.878444	+	0.477846i	$0.158582\pi$
$614$	8.78928	+	15.2235i	0.354707	+	0.614370i
$615$	−1.22282	+	4.24203i	−0.0493089	+	0.171055i
$616$	−2.36577	−	1.18453i	−0.0953197	−	0.0477261i
$617$			8.09880i			0.326045i	0.986622	+	0.163023i	$0.0521244\pi$
$617$			8.09880i			0.326045i	−0.986622	+	0.163023i	$0.947876\pi$
$618$	−15.4419	+	3.82710i	−0.621163	+	0.153949i
$619$	11.2505	+	6.49551i	0.452198	+	0.261076i	0.708758	−	0.705452i	$-0.249256\pi$
$619$	11.2505	+	6.49551i	0.452198	+	0.261076i	−0.256560	+	0.966528i	$0.582589\pi$
$620$	−12.5806	−	7.26341i	−0.505249	−	0.291706i
$621$	−7.58248	+	23.0067i	−0.304274	+	0.923227i
$622$			14.1060i			0.565600i
$623$	29.5685	−	19.4991i	1.18464	−	0.781216i
$624$	−7.50529	−	2.16350i	−0.300452	−	0.0866094i
$625$	3.36811	+	5.83374i	0.134724	+	0.233350i
$626$	12.8175	−	22.2006i	0.512292	−	0.887315i
$627$	−8.42713	−	8.75108i	−0.336547	−	0.349484i
$628$	2.83438	−	1.63643i	0.113104	−	0.0653007i
$629$	−3.56695			−0.142223
$630$	−11.1090	−	6.09653i	−0.442594	−	0.242892i
$631$	−4.49319			−0.178871			−0.0894356	−	0.995993i	$-0.528506\pi$
$631$	−4.49319			−0.178871			−0.0894356	+	0.995993i	$0.528506\pi$
$632$	−6.70413	+	3.87063i	−0.266676	+	0.153965i
$633$	3.24025	+	3.36480i	0.128788	+	0.133739i
$634$	−1.69789	+	2.94082i	−0.0674317	+	0.116795i
$635$	2.85980	+	4.95333i	0.113488	+	0.196567i
$636$	−15.6548	−	4.51272i	−0.620755	−	0.178941i
$637$	−3.74110	−	31.3449i	−0.148228	−	1.24193i
$638$			5.53777i			0.219243i
$639$	−28.3982	−	1.07144i	−1.12342	−	0.0423853i
$640$	−1.38262	−	0.798258i	−0.0546530	−	0.0315539i
$641$	−23.9171	−	13.8085i	−0.944668	−	0.545404i	−0.0532472	−	0.998581i	$-0.516957\pi$
$641$	−23.9171	−	13.8085i	−0.944668	−	0.545404i	−0.891420	+	0.453177i	$0.850290\pi$
$642$	−14.1776	+	3.51376i	−0.559544	+	0.138677i
$643$		−	2.44235i		−	0.0963168i	−0.998840	−	0.0481584i	$-0.984665\pi$
$643$		−	2.44235i		−	0.0963168i	0.998840	−	0.0481584i	$-0.0153352\pi$
$644$	−12.3125	+	0.732168i	−0.485181	+	0.0288514i
$645$	1.18074	−	4.09605i	0.0464917	−	0.161282i
$646$	21.8903	+	37.9150i	0.861260	+	1.49175i
$647$	6.42484	−	11.1282i	0.252587	−	0.437493i	−0.711651	−	0.702534i	$-0.752052\pi$
$647$	6.42484	−	11.1282i	0.252587	−	0.437493i	0.964237	+	0.265041i	$0.0853854\pi$
$648$	0.678156	−	8.97441i	0.0266405	−	0.352548i
$649$	4.54453	−	2.62379i	0.178389	−	0.102993i
$650$	−11.0537			−0.433563
$651$	39.8060	−	12.4155i	1.56012	−	0.486603i
$652$	15.6268			0.611994
$653$	7.70766	−	4.45002i	0.301624	−	0.174143i	−0.341548	−	0.939864i	$-0.610951\pi$
$653$	7.70766	−	4.45002i	0.301624	−	0.174143i	0.643172	+	0.765722i	$0.277618\pi$
$654$	18.3218	−	17.6435i	0.716438	−	0.689917i
$655$	17.5428	−	30.3851i	0.685456	−	1.18724i
$656$	−0.798258	−	1.38262i	−0.0311667	−	0.0539823i
$657$	−6.58272	+	10.4691i	−0.256816	+	0.408439i
$658$	8.45581	−	16.8882i	0.329642	−	0.658369i
$659$		−	31.7573i		−	1.23709i	−0.785751	−	0.618544i	$-0.787723\pi$
$659$		−	31.7573i		−	1.23709i	0.785751	−	0.618544i	$-0.212277\pi$
$660$	0.665210	+	2.68404i	0.0258933	+	0.104476i
$661$	−15.9605	−	9.21478i	−0.620790	−	0.358413i	0.156387	−	0.987696i	$-0.450015\pi$
$661$	−15.9605	−	9.21478i	−0.620790	−	0.358413i	−0.777177	+	0.629283i	$0.783349\pi$
$662$	1.89457	+	1.09383i	0.0736345	+	0.0425129i
$663$	−11.7281	−	47.3214i	−0.455482	−	1.83781i
$664$			17.4510i			0.677230i
$665$	13.2647	−	26.4927i	0.514385	−	1.02734i
$666$	−0.912577	+	1.45135i	−0.0353616	+	0.0562389i
$667$	12.9083	+	22.3578i	0.499812	+	0.865699i
$668$	−9.86141	+	17.0805i	−0.381549	+	0.660863i
$669$	17.7330	−	17.0766i	0.685599	−	0.660219i
$670$	1.69713	−	0.979838i	0.0655658	−	0.0378544i
$671$	2.18210			0.0842392
$672$	4.37472	−	1.36448i	0.168759	−	0.0526360i
$673$	−5.66645			−0.218426			−0.109213	−	0.994018i	$-0.534833\pi$
$673$	−5.66645			−0.218426			−0.109213	+	0.994018i	$0.534833\pi$
$674$	−25.9397	+	14.9763i	−0.999161	+	0.576866i
$675$	−2.59563	−	12.4692i	−0.0999060	−	0.479940i
$676$	−3.66836	+	6.35378i	−0.141091	+	0.244376i
$677$	−21.6601	−	37.5163i	−0.832464	−	1.44187i	−0.896079	−	0.443895i	$-0.853596\pi$
$677$	−21.6601	−	37.5163i	−0.832464	−	1.44187i	0.0636151	−	0.997975i	$-0.479737\pi$
$678$	−5.05776	+	17.5456i	−0.194242	+	0.673835i
$679$	18.7918	−	1.11746i	0.721161	−	0.0428841i
$680$		−	9.96493i		−	0.382138i
$681$	8.98564	−	2.22699i	0.344331	−	0.0853386i
$682$	−7.88004	−	4.54954i	−0.301742	−	0.174211i
$683$	−10.9764	−	6.33724i	−0.420001	−	0.242488i	0.275077	−	0.961422i	$-0.411297\pi$
$683$	−10.9764	−	6.33724i	−0.420001	−	0.242488i	−0.695078	+	0.718934i	$0.744630\pi$
$684$	21.0277	+	0.793353i	0.804014	+	0.0303346i
$685$			18.5086i			0.707178i
$686$	11.9563	+	14.1438i	0.456495	+	0.540011i
$687$	−22.4013	−	6.45748i	−0.854663	−	0.246368i
$688$	0.770788	+	1.33504i	0.0293860	+	0.0508981i
$689$	−21.2096	+	36.7361i	−0.808020	+	1.39953i
$690$	8.94206	+	9.28579i	0.340418	+	0.353504i
$691$	−30.5975	+	17.6655i	−1.16398	+	0.672026i	−0.952256	−	0.305302i	$-0.901243\pi$
$691$	−30.5975	+	17.6655i	−1.16398	+	0.672026i	−0.211728	+	0.977329i	$0.567909\pi$
$692$	−0.602414			−0.0229003
$693$	−6.95830	−	3.81865i	−0.264324	−	0.145059i
$694$	33.5061			1.27188
$695$	−17.0219	+	9.82760i	−0.645678	+	0.372782i
$696$	−6.65328	−	6.90903i	−0.252192	−	0.261886i
$697$	4.98247	−	8.62988i	0.188724	−	0.326880i
$698$	−10.4610	−	18.1190i	−0.395956	−	0.685815i
$699$	−0.0360658	−	0.0103965i	−0.00136413	−	0.000393230i
$700$	5.41388	−	3.57022i	0.204626	−	0.134942i
$701$			33.9878i			1.28370i	0.766830	+	0.641851i	$0.221833\pi$
$701$			33.9878i			1.28370i	−0.766830	+	0.641851i	$0.778167\pi$
$702$	−22.2552	−	7.33479i	−0.839967	−	0.276834i
$703$	−3.47141	−	2.00422i	−0.130927	−	0.0755905i
$704$	−0.866025	−	0.500000i	−0.0326396	−	0.0188445i
$705$	−19.1601	+	4.74863i	−0.721612	+	0.178844i
$706$		−	5.56904i		−	0.209593i
$707$	−0.713012	−	0.357001i	−0.0268156	−	0.0134264i
$708$	−2.51753	+	8.73345i	−0.0946148	+	0.328223i
$709$	16.3651	+	28.3452i	0.614604	+	1.06452i	0.990454	+	0.137844i	$0.0440174\pi$
$709$	16.3651	+	28.3452i	0.614604	+	1.06452i	−0.375850	+	0.926680i	$0.622649\pi$
$710$	−7.56174	+	13.0973i	−0.283787	+	0.491534i
$711$	−20.5359	+	10.8454i	−0.770156	+	0.406733i
$712$	11.5936	−	6.69358i	0.434489	−	0.250852i
$713$	−42.4191			−1.58861
$714$	21.0284	+	19.3890i	0.786969	+	0.725616i
$715$	7.19968			0.269253
$716$	20.9583	−	12.1003i	0.783248	−	0.452209i
$717$	−13.0373	+	12.5547i	−0.486888	+	0.468865i
$718$	−4.20916	+	7.29047i	−0.157084	+	0.272078i
$719$	12.5536	+	21.7435i	0.468172	+	0.810897i	0.999338	−	0.0363702i	$-0.0115795\pi$
$719$	12.5536	+	21.7435i	0.468172	+	0.810897i	−0.531167	+	0.847267i	$0.678246\pi$
$720$	−4.05463	−	2.54945i	−0.151107	−	0.0950125i
$721$	−13.3786	−	20.2873i	−0.498245	−	0.755539i
$722$			30.1993i			1.12390i
$723$	−1.82253	−	7.35366i	−0.0677805	−	0.273486i
$724$	−21.8885	−	12.6373i	−0.813480	−	0.469663i
$725$	−11.7553	−	6.78693i	−0.436581	−	0.252060i
$726$	0.416664	+	1.68119i	0.0154639	+	0.0623947i
$727$			32.7918i			1.21618i	0.793868	+	0.608090i	$0.208064\pi$
$727$			32.7918i			1.21618i	−0.793868	+	0.608090i	$0.791936\pi$
$728$	−0.708251	−	11.9103i	−0.0262495	−	0.441425i
$729$	3.04808	−	26.8274i	0.112892	−	0.993607i
$730$	3.29059	+	5.69947i	0.121790	+	0.210947i
$731$	−4.81101	+	8.33292i	−0.177942	+	0.308204i
$732$	−2.72243	+	2.62166i	−0.100624	+	0.0968992i
$733$	8.36398	−	4.82895i	0.308931	−	0.178361i	−0.337517	−	0.941319i	$-0.609587\pi$
$733$	8.36398	−	4.82895i	0.308931	−	0.178361i	0.646448	+	0.762958i	$0.276254\pi$
$734$	36.8181			1.35898
$735$	3.11949	−	19.1037i	0.115064	−	0.704651i
$736$	−4.66191			−0.171840
$737$	1.06302	−	0.613735i	0.0391569	−	0.0226072i
$738$	−2.23669	−	4.23521i	−0.0823336	−	0.155900i
$739$	−5.82847	+	10.0952i	−0.214404	+	0.371358i	−0.953088	−	0.302693i	$-0.902114\pi$
$739$	−5.82847	+	10.0952i	−0.214404	+	0.371358i	0.738684	+	0.674052i	$0.235447\pi$
$740$	0.456182	+	0.790131i	0.0167696	+	0.0290458i
$741$	15.1753	−	52.6438i	0.557478	−	1.93392i
$742$	−1.47730	−	24.8430i	−0.0542333	−	0.912015i
$743$			5.87724i			0.215615i	0.994172	+	0.107807i	$0.0343830\pi$
$743$			5.87724i			0.215615i	−0.994172	+	0.107807i	$0.965617\pi$
$744$	15.2973	−	3.79126i	0.560825	−	0.138994i
$745$	17.8377	+	10.2986i	0.653522	+	0.377311i
$746$	7.87029	+	4.54391i	0.288152	+	0.166364i
$747$	−1.97382	+	52.3158i	−0.0722183	+	1.91413i
$748$		−	6.24168i		−	0.228218i
$749$	−12.2832	−	18.6263i	−0.448819	−	0.680590i
$750$	−19.7981	−	5.70706i	−0.722923	−	0.208392i
$751$	9.95620	+	17.2447i	0.363307	+	0.629266i	0.988503	−	0.151202i	$-0.0483143\pi$
$751$	9.95620	+	17.2447i	0.363307	+	0.629266i	−0.625196	+	0.780468i	$0.714981\pi$
$752$	3.56927	−	6.18215i	0.130158	−	0.225440i
$753$	7.59960	+	7.89173i	0.276945	+	0.287591i
$754$	−21.6275	+	12.4866i	−0.787627	+	0.454737i
$755$	−14.3841			−0.523493
$756$	13.2692	−	3.59572i	0.482595	−	0.130775i
$757$	9.77216			0.355175			0.177588	−	0.984105i	$-0.443171\pi$
$757$	9.77216			0.355175			0.177588	+	0.984105i	$0.443171\pi$
$758$	22.0554	−	12.7337i	0.801087	−	0.462508i
$759$	5.60098	+	5.81629i	0.203303	+	0.211118i
$760$	5.59916	−	9.69802i	0.203103	−	0.351784i
$761$	−5.18661	−	8.98347i	−0.188014	−	0.325650i	0.756574	−	0.653908i	$-0.226872\pi$
$761$	−5.18661	−	8.98347i	−0.188014	−	0.325650i	−0.944588	+	0.328258i	$0.893538\pi$
$762$	−5.96239	−	1.71874i	−0.215995	−	0.0622634i
$763$	34.7423	+	17.3953i	1.25776	+	0.629752i
$764$			11.5305i			0.417159i
$765$	1.12710	−	29.8735i	0.0407503	−	1.08008i
$766$	−7.39596	−	4.27006i	−0.267227	−	0.154283i
$767$	20.4941	+	11.8323i	0.740000	+	0.427239i
$768$	1.68119	−	0.416664i	0.0606646	−	0.0150351i
$769$			20.5641i			0.741560i	0.928721	+	0.370780i	$0.120910\pi$
$769$			20.5641i			0.741560i	−0.928721	+	0.370780i	$0.879090\pi$
$770$	−3.52626	+	2.32541i	−0.127077	+	0.0838020i
$771$	4.71442	−	16.3546i	0.169786	−	0.588995i
$772$	6.21106	+	10.7579i	0.223541	+	0.387184i
$773$	−13.0535	+	22.6093i	−0.469501	+	0.813200i	−0.999392	−	0.0348658i	$-0.988900\pi$
$773$	−13.0535	+	22.6093i	−0.469501	+	0.813200i	0.529891	+	0.848066i	$0.322233\pi$
$774$	2.15972	+	4.08947i	0.0776295	+	0.146993i
$775$	19.3151	−	11.1516i	0.693818	−	0.400576i
$776$	7.11516			0.255419
$777$	−2.55497	−	0.574722i	−0.0916592	−	0.0206180i
$778$	1.26055			0.0451929
$779$	9.69802	−	5.59916i	0.347468	−	0.200611i
$780$	−8.98246	+	8.64996i	−0.321624	+	0.309718i
$781$	−4.73640	+	8.20369i	−0.169482	+	0.293551i
$782$	−14.5491	−	25.1997i	−0.520274	−	0.901140i
$783$	−19.1642	−	21.4649i	−0.684872	−	0.767093i
$784$	4.19377	+	5.60466i	0.149778	+	0.200167i
$785$		−	5.22517i		−	0.186494i
$786$	9.15678	+	36.9465i	0.326612	+	1.31784i
$787$	−41.8059	−	24.1366i	−1.49022	−	0.860378i	−0.490281	−	0.871565i	$-0.663106\pi$
$787$	−41.8059	−	24.1366i	−1.49022	−	0.860378i	−0.999937	+	0.0111869i	$0.996439\pi$
$788$	−5.87453	−	3.39166i	−0.209271	−	0.120823i
$789$	8.13057	+	32.8058i	0.289456	+	1.16792i
$790$			12.3590i			0.439715i
$791$	−27.8435	+	1.65572i	−0.990001	+	0.0588708i
$792$	−2.53968	−	1.59689i	−0.0902435	−	0.0567429i
$793$	4.92024	+	8.52210i	0.174723	+	0.302629i
$794$	−1.12004	+	1.93996i	−0.0397486	+	0.0688466i
$795$	−18.7360	+	18.0424i	−0.664497	+	0.639899i
$796$	−7.19446	+	4.15372i	−0.255001	+	0.147225i
$797$	36.1754			1.28140			0.640699	−	0.767793i	$-0.278645\pi$
$797$	36.1754			1.28140			0.640699	+	0.767793i	$0.278645\pi$
$798$	9.57077	+	30.6853i	0.338802	+	1.08625i
$799$	44.5564			1.57629
$800$	2.12275	−	1.22557i	0.0750505	−	0.0433304i
$801$	35.5132	−	18.7551i	1.25480	−	0.662680i
$802$	12.5982	−	21.8208i	0.444859	−	0.770518i
$803$	2.06111	+	3.56995i	0.0727350	+	0.125981i
$804$	−0.588882	+	2.04286i	−0.0207683	+	0.0720461i
$805$	−8.81624	+	17.6080i	−0.310732	+	0.620601i
$806$		−	41.0334i		−	1.44534i
$807$	11.3004	−	2.80068i	0.397793	−	0.0985888i
$808$	−0.261008	−	0.150693i	−0.00918224	−	0.00530137i
$809$	46.6225	+	26.9175i	1.63916	+	0.946369i	0.981124	+	0.193382i	$0.0619457\pi$
$809$	46.6225	+	26.9175i	1.63916	+	0.946369i	0.658035	+	0.752987i	$0.271388\pi$
$810$	−11.8669	−	8.10153i	−0.416960	−	0.284659i
$811$		−	23.9638i		−	0.841481i	−0.907181	−	0.420741i	$-0.861770\pi$
$811$		−	23.9638i		−	0.841481i	0.907181	−	0.420741i	$-0.138230\pi$
$812$	6.55967	−	13.1011i	0.230199	−	0.459759i
$813$	−17.0906	−	4.92659i	−0.599392	−	0.172783i
$814$	0.285736	+	0.494910i	0.0100150	+	0.0173466i
$815$	12.4742	−	21.6060i	0.436954	−	0.756826i
$816$	7.49897	+	7.78723i	0.262516	+	0.272608i
$817$	−9.36430	+	5.40648i	−0.327615	+	0.189149i
$818$	18.2113			0.636743
$819$	−0.776110	−	35.7856i	−0.0271195	−	1.25045i
$820$	−2.54886			−0.0890101
$821$	−22.9984	+	13.2781i	−0.802648	+	0.463409i	−0.844396	−	0.535719i	$-0.820041\pi$
$821$	−22.9984	+	13.2781i	−0.802648	+	0.463409i	0.0417481	+	0.999128i	$0.486707\pi$
$822$	−13.9284	−	14.4638i	−0.485809	−	0.504484i
$823$	−20.3657	+	35.2745i	−0.709905	+	1.22959i	0.254987	+	0.966945i	$0.417929\pi$
$823$	−20.3657	+	35.2745i	−0.709905	+	1.22959i	−0.964892	+	0.262647i	$0.915404\pi$
$824$	−4.59255	−	7.95453i	−0.159989	−	0.277109i
$825$	−4.07939	−	1.17594i	−0.142026	−	0.0409409i
$826$	−13.8593	+	0.824148i	−0.482227	+	0.0286758i
$827$		−	16.2449i		−	0.564889i	−0.959284	−	0.282444i	$-0.908855\pi$
$827$		−	16.2449i		−	0.564889i	0.959284	−	0.282444i	$-0.0911453\pi$
$828$	−13.9758	−	0.527292i	−0.485692	−	0.0183247i
$829$	−38.4036	−	22.1723i	−1.33381	−	0.770077i	−0.347930	−	0.937520i	$-0.613115\pi$
$829$	−38.4036	−	22.1723i	−1.33381	−	0.770077i	−0.985882	+	0.167444i	$0.946449\pi$
$830$	24.1282	+	13.9304i	0.837501	+	0.483531i
$831$	1.14442	−	0.283631i	0.0396994	−	0.00983906i
$832$		−	4.50963i		−	0.156343i
$833$	−17.2076	+	40.1605i	−0.596210	+	1.39148i
$834$	5.90638	−	20.4895i	0.204521	−	0.709494i
$835$	15.7439	+	27.2692i	0.544840	+	0.943690i
$836$	3.50711	−	6.07449i	0.121296	−	0.210091i
$837$	46.2880	−	9.63548i	1.59995	−	0.333051i
$838$	3.54476	−	2.04657i	0.122452	−	0.0706975i
$839$	−29.9098			−1.03260			−0.516301	−	0.856407i	$-0.672691\pi$
$839$	−29.9098			−1.03260			−0.516301	+	0.856407i	$0.672691\pi$
$840$	1.60559	−	7.13780i	0.0553982	−	0.246277i
$841$	−1.66695			−0.0574811
$842$	27.1552	−	15.6780i	0.935829	−	0.540301i
$843$	−27.6588	+	26.6350i	−0.952621	+	0.917357i
$844$	−1.34849	+	2.33565i	−0.0464169	+	0.0803965i
$845$	5.85659	+	10.1439i	0.201473	+	0.348961i
$846$	11.3994	−	18.1296i	0.391920	−	0.623307i
$847$	−2.20872	+	1.45655i	−0.0758925	+	0.0500478i
$848$		−	9.40636i		−	0.323016i
$849$	10.5848	+	42.7083i	0.363269	+	1.46574i
$850$	13.2495	+	7.64961i	0.454454	+	0.262379i
$851$	2.30722	+	1.33208i	0.0790906	+	0.0456630i
$852$	−3.94698	−	15.9256i	−0.135221	−	0.545601i
$853$			23.4111i			0.801581i	0.916170	+	0.400790i	$0.131264\pi$
$853$			23.4111i			0.801581i	−0.916170	+	0.400790i	$0.868736\pi$
$854$	−5.16237	−	2.58477i	−0.176653	−	0.0884490i
$855$	17.8824	−	28.4401i	0.611566	−	0.972630i
$856$	−4.21653	−	7.30325i	−0.144118	−	0.249620i
$857$	−17.0375	+	29.5098i	−0.581990	+	1.00804i	0.413253	+	0.910616i	$0.364393\pi$
$857$	−17.0375	+	29.5098i	−0.581990	+	1.00804i	−0.995243	+	0.0974207i	$0.968941\pi$
$858$	−5.62629	+	5.41802i	−0.192079	+	0.184968i
$859$	−18.3460	+	10.5921i	−0.625958	+	0.361397i	−0.779185	−	0.626794i	$-0.784367\pi$
$859$	−18.3460	+	10.5921i	−0.625958	+	0.361397i	0.153227	+	0.988191i	$0.451033\pi$
$860$	2.46115			0.0839245
$861$	4.95938	−	5.37872i	0.169015	−	0.183306i
$862$	−6.42397			−0.218801
$863$	−29.6507	+	17.1188i	−1.00932	+	0.582731i	−0.910992	−	0.412423i	$-0.864683\pi$
$863$	−29.6507	+	17.1188i	−1.00932	+	0.582731i	−0.0983275	+	0.995154i	$0.531349\pi$
$864$	5.08710	−	1.05895i	0.173067	−	0.0360262i
$865$	−0.480881	+	0.832911i	−0.0163505	+	0.0283198i
$866$	4.66246	+	8.07562i	0.158437	+	0.274421i
$867$	−10.5346	+	36.5452i	−0.357775	+	1.24114i
$868$	13.2533	+	20.0973i	0.449847	+	0.682148i
$869$			7.74126i			0.262604i
$870$	−14.8636	+	3.68379i	−0.503924	+	0.124892i
$871$	4.79382	+	2.76772i	0.162433	+	0.0937805i
$872$	12.7179	+	7.34270i	0.430683	+	0.248655i
$873$	21.3303	+	0.804770i	0.721921	+	0.0272373i
$874$		−	32.6997i		−	1.10608i
$875$	−1.86828	−	31.4180i	−0.0631594	−	1.06212i
$876$	−6.86054	−	1.97764i	−0.231796	−	0.0668184i
$877$	−23.3704	−	40.4788i	−0.789164	−	1.36687i	−0.926480	−	0.376344i	$-0.877181\pi$
$877$	−23.3704	−	40.4788i	−0.789164	−	1.36687i	0.137316	−	0.990527i	$-0.456152\pi$
$878$	−3.56599	+	6.17648i	−0.120346	+	0.208446i
$879$	−5.90368	−	6.13062i	−0.199126	−	0.206781i
$880$	−1.38262	+	0.798258i	−0.0466082	+	0.0269093i
$881$	0.862730			0.0290661			0.0145331	−	0.999894i	$-0.495374\pi$
$881$	0.862730			0.0290661			0.0145331	+	0.999894i	$0.495374\pi$
$882$	11.9385	+	17.2764i	0.401989	+	0.581726i
$883$	11.0309			0.371221			0.185610	−	0.982623i	$-0.440574\pi$
$883$	11.0309			0.371221			0.185610	+	0.982623i	$0.440574\pi$
$884$	24.3766	−	14.0738i	0.819872	−	0.473353i
$885$	10.0654	+	10.4523i	0.338346	+	0.351352i
$886$	4.20570	−	7.28448i	0.141293	−	0.244727i
$887$	21.4444	+	37.1429i	0.720034	+	1.24713i	0.960986	+	0.276598i	$0.0892070\pi$
$887$	21.4444	+	37.1429i	0.720034	+	1.24713i	−0.240952	+	0.970537i	$0.577460\pi$
$888$	−0.951092	−	0.274165i	−0.0319166	−	0.00920038i
$889$	−0.562652	−	9.46184i	−0.0188707	−	0.317340i
$890$		−	21.3728i		−	0.716418i
$891$	−7.43299	−	5.07451i	−0.249015	−	0.170002i
$892$	12.3092	+	7.10675i	0.412144	+	0.237952i
$893$	43.3630	+	25.0356i	1.45109	+	0.837785i
$894$	−21.6896	+	5.37552i	−0.725408	+	0.179784i
$895$		−	38.6366i		−	1.29148i
$896$	1.45655	+	2.20872i	0.0486601	+	0.0737882i
$897$	−10.0861	+	34.9890i	−0.336763	+	1.16825i
$898$	−8.49632	−	14.7161i	−0.283526	−	0.491081i
$899$	25.1943	−	43.6379i	0.840278	−	1.45540i
$900$	6.50234	−	3.43400i	0.216745	−	0.114467i
$901$	50.8456	−	29.3557i	1.69391	−	0.977981i
$902$	−1.59652			−0.0531581
$903$	−4.78872	+	5.19363i	−0.159359	+	0.172833i
$904$	−10.5424			−0.350637
$905$	−34.9453	+	20.1757i	−1.16162	+	0.670663i
$906$	11.2407	−	10.8246i	0.373447	−	0.359623i
$907$	7.81046	−	13.5281i	0.259342	−	0.449194i	−0.706724	−	0.707490i	$-0.749828\pi$
$907$	7.81046	−	13.5281i	0.259342	−	0.449194i	0.966066	+	0.258296i	$0.0831609\pi$
$908$	2.67241	+	4.62875i	0.0886870	+	0.153610i
$909$	−0.765423	−	0.481280i	−0.0253875	−	0.0159630i
$910$	−17.0328	−	8.52825i	−0.564633	−	0.282709i
$911$			39.7371i			1.31655i	0.752778	+	0.658274i	$0.228713\pi$
$911$			39.7371i			1.31655i	−0.752778	+	0.658274i	$0.771287\pi$
$912$	2.92257	+	11.7922i	0.0967761	+	0.390480i
$913$	15.1130	+	8.72550i	0.500168	+	0.288772i
$914$	−27.7407	−	16.0161i	−0.917582	−	0.529766i
$915$	1.45156	+	5.85686i	0.0479870	+	0.193622i
$916$		−	13.4600i		−	0.444732i
$917$	−48.5398	+	32.0099i	−1.60292	+	1.05706i
$918$	21.6001	+	24.1933i	0.712910	+	0.798497i
$919$	−1.87670	−	3.25054i	−0.0619066	−	0.107225i	0.833411	−	0.552654i	$-0.186385\pi$
$919$	−1.87670	−	3.25054i	−0.0619066	−	0.107225i	−0.895318	+	0.445428i	$0.853051\pi$
$920$	−3.72141	+	6.44566i	−0.122691	+	0.212507i
$921$	−21.9314	+	21.1195i	−0.722663	+	0.695912i
$922$	−5.89118	+	3.40127i	−0.194016	+	0.112015i
$923$	−42.7188			−1.40611
$924$	1.00569	−	4.47086i	0.0330846	−	0.147081i
$925$	−1.40076			−0.0460567
$926$	6.60067	−	3.81090i	0.216912	−	0.125234i
$927$	−12.8681	−	24.3661i	−0.422645	−	0.800287i
$928$	2.76889	−	4.79585i	0.0908932	−	0.157432i
$929$	−23.1654	−	40.1236i	−0.760031	−	1.31641i	−0.942834	−	0.333262i	$-0.891851\pi$
$929$	−23.1654	−	40.1236i	−0.760031	−	1.31641i	0.182803	−	0.983149i	$-0.441483\pi$
$930$	6.96927	−	24.1767i	0.228531	−	0.792787i
$931$	−39.3124	+	29.4161i	−1.28841	+	0.964072i
$932$		−	0.0216705i		−	0.000709840i
$933$	−23.7148	+	5.87747i	−0.776389	+	0.192420i
$934$	−16.0853	−	9.28685i	−0.526327	−	0.303875i
$935$	−8.62988	−	4.98247i	−0.282227	−	0.162944i
$936$	0.510067	−	13.5193i	0.0166721	−	0.441891i
$937$		−	8.98564i		−	0.293548i	−0.989170	−	0.146774i	$-0.953111\pi$
$937$		−	8.98564i		−	0.293548i	0.989170	−	0.146774i	$-0.0468890\pi$
$938$	−3.24186	+	0.192778i	−0.105850	+	0.00629443i
$939$	42.6640	+	12.2985i	1.39229	+	0.401346i
$940$	−5.69839	−	9.86990i	−0.185861	−	0.321921i
$941$	2.58343	−	4.47464i	0.0842176	−	0.145869i	−0.820840	−	0.571158i	$-0.806494\pi$
$941$	2.58343	−	4.47464i	0.0842176	−	0.145869i	0.905058	+	0.425289i	$0.139828\pi$
$942$	3.93213	+	4.08328i	0.128116	+	0.133041i
$943$	−6.44566	+	3.72141i	−0.209900	+	0.121186i
$944$	−5.24757			−0.170794
$945$	5.62068	−	21.2166i	0.182841	−	0.690175i
$946$	1.54158			0.0501210
$947$	−10.8381	+	6.25737i	−0.352190	+	0.203337i	−0.665649	−	0.746265i	$-0.731845\pi$
$947$	−10.8381	+	6.25737i	−0.352190	+	0.203337i	0.313459	+	0.949602i	$0.398512\pi$
$948$	−9.30063	−	9.65815i	−0.302070	−	0.313682i
$949$	−9.29483	+	16.0991i	−0.301723	+	0.522600i
$950$	8.59642	+	14.8894i	0.278905	+	0.483077i
$951$	−5.65152	−	1.62913i	−0.183263	−	0.0528281i
$952$	−7.39346	+	14.7664i	−0.239623	+	0.478582i
$953$		−	11.7126i		−	0.379409i	−0.981841	−	0.189704i	$-0.939247\pi$
$953$		−	11.7126i		−	0.379409i	0.981841	−	0.189704i	$-0.0607529\pi$
$954$	1.06392	−	28.1990i	0.0344456	−	0.912976i
$955$	15.9423	+	9.20430i	0.515881	+	0.297844i
$956$	−9.04976	−	5.22488i	−0.292690	−	0.168985i
$957$	−9.31004	+	2.30739i	−0.300951	+	0.0745874i
$958$			13.2180i			0.427053i
$959$	13.7324	−	27.4268i	0.443443	−	0.885656i
$960$	0.765932	−	2.65705i	0.0247203	−	0.0857560i
$961$	25.8966	+	44.8543i	0.835376	+	1.44691i
$962$	−1.28856	+	2.23186i	−0.0415449	+	0.0719580i
$963$	−11.8146	−	22.3711i	−0.380719	−	0.720898i
$964$	3.78807	−	2.18704i	0.122006	−	0.0704400i
$965$	19.8321			0.638418
$966$	−6.36109	−	20.3946i	−0.204665	−	0.656184i
$967$	−31.1290			−1.00104			−0.500521	−	0.865724i	$-0.666858\pi$
$967$	−31.1290			−1.00104			−0.500521	+	0.865724i	$0.666858\pi$
$968$	−0.866025	+	0.500000i	−0.0278351	+	0.0160706i
$969$	−54.6214	+	52.5994i	−1.75469	+	1.68974i
$970$	5.67973	−	9.83758i	0.182365	−	0.315866i
$971$	−22.8332	−	39.5482i	−0.732751	−	1.26916i	−0.955703	−	0.294333i	$-0.904903\pi$
$971$	−22.8332	−	39.5482i	−0.732751	−	1.26916i	0.222952	−	0.974829i	$-0.428431\pi$
$972$	15.3702	−	2.59921i	0.493001	−	0.0833696i
$973$	32.5152	−	1.93353i	1.04239	−	0.0619861i
$974$			21.4493i			0.687279i
$975$	−4.60569	−	18.5834i	−0.147500	−	0.595144i
$976$	−1.88976	−	1.09105i	−0.0604897	−	0.0349237i
$977$	2.20831	+	1.27497i	0.0706500	+	0.0407898i	0.534909	−	0.844910i	$-0.320346\pi$
$977$	2.20831	+	1.27497i	0.0706500	+	0.0407898i	−0.464259	+	0.885700i	$0.653679\pi$
$978$	6.51114	+	26.2716i	0.208203	+	0.840075i
$979$		−	13.3872i		−	0.427855i
$980$	11.0968	−	1.32444i	0.354476	−	0.0423077i
$981$	37.2961	+	23.4509i	1.19077	+	0.748730i
$982$	−2.01236	−	3.48551i	−0.0642170	−	0.111227i
$983$	23.9192	−	41.4293i	0.762905	−	1.32139i	−0.178443	−	0.983950i	$-0.557106\pi$
$983$	23.9192	−	41.4293i	0.762905	−	1.32139i	0.941347	−	0.337439i	$-0.109561\pi$
$984$	1.99184	−	1.91811i	0.0634976	−	0.0611471i
$985$	−9.37877	+	5.41483i	−0.298832	+	0.172531i
$986$	34.5650			1.10077
$987$	31.9154	+	7.17912i	1.01588	+	0.228514i
$988$	31.6315			1.00633
$989$	6.22386	−	3.59335i	0.197907	−	0.114262i
$990$	−4.23521	+	2.23669i	−0.134604	+	0.0710866i
$991$	−22.8840	+	39.6363i	−0.726935	+	1.25909i	0.231238	+	0.972897i	$0.425722\pi$
$991$	−22.8840	+	39.6363i	−0.726935	+	1.25909i	−0.958173	+	0.286191i	$0.907611\pi$
$992$	4.54954	+	7.88004i	0.144448	+	0.250191i
$993$	−1.04953	+	3.64088i	−0.0333059	+	0.115540i
$994$	20.9228	−	13.7977i	0.663631	−	0.437635i
$995$			13.2630i			0.420464i
$996$	−29.3384	+	7.27121i	−0.929623	+	0.230397i
$997$	−13.7032	−	7.91153i	−0.433984	−	0.250561i	0.267058	−	0.963680i	$-0.413948\pi$
$997$	−13.7032	−	7.91153i	−0.433984	−	0.250561i	−0.701042	+	0.713120i	$0.747282\pi$
$998$	−1.56517	−	0.903651i	−0.0495445	−	0.0286046i
$999$	−2.82024	−	0.929485i	−0.0892284	−	0.0294076i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.k.g.353.2	yes	20
3.2	odd	2	inner	462.2.k.g.353.7	yes	20
7.5	odd	6	inner	462.2.k.g.89.7	yes	20
21.5	even	6	inner	462.2.k.g.89.2	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.k.g.89.2	✓	20	21.5	even	6	inner
462.2.k.g.89.7	yes	20	7.5	odd	6	inner
462.2.k.g.353.2	yes	20	1.1	even	1	trivial
462.2.k.g.353.7	yes	20	3.2	odd	2	inner

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:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-1.20144 - 1.24762i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.798258 - 1.38262i) q^{5} +(1.66428 + 0.479752i) q^{6} +(0.157053 + 2.64109i) q^{7} +1.00000i q^{8} +(-0.113106 + 2.99787i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-1.20144 - 1.24762i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.798258 - 1.38262i) q^{5} +(1.66428 + 0.479752i) q^{6} +(0.157053 + 2.64109i) q^{7} +1.00000i q^{8} +(-0.113106 + 2.99787i) q^{9} +(1.38262 + 0.798258i) q^{10} +(0.866025 + 0.500000i) q^{11} +(-1.68119 + 0.416664i) q^{12} +4.50963i q^{13} +(-1.45655 - 2.20872i) q^{14} +(-0.765932 + 2.65705i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.12084 - 5.40545i) q^{17} +(-1.40098 - 2.65278i) q^{18} +(6.07449 - 3.50711i) q^{19} -1.59652 q^{20} +(3.10638 - 3.36904i) q^{21} -1.00000 q^{22} +(-4.03733 + 2.33096i) q^{23} +(1.24762 - 1.20144i) q^{24} +(1.22557 - 2.12275i) q^{25} +(-2.25481 - 3.90545i) q^{26} +(3.87609 - 3.46063i) q^{27} +(2.36577 + 1.18453i) q^{28} -5.53777i q^{29} +(-0.665210 - 2.68404i) q^{30} +(7.88004 + 4.54954i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-0.416664 - 1.68119i) q^{33} +6.24168i q^{34} +(3.52626 - 2.32541i) q^{35} +(2.53968 + 1.59689i) q^{36} +(-0.285736 - 0.494910i) q^{37} +(-3.50711 + 6.07449i) q^{38} +(5.62629 - 5.41802i) q^{39} +(1.38262 - 0.798258i) q^{40} +1.59652 q^{41} +(-1.00569 + 4.47086i) q^{42} -1.54158 q^{43} +(0.866025 - 0.500000i) q^{44} +(4.23521 - 2.23669i) q^{45} +(2.33096 - 4.03733i) q^{46} +(3.56927 + 6.18215i) q^{47} +(-0.479752 + 1.66428i) q^{48} +(-6.95067 + 0.829582i) q^{49} +2.45114i q^{50} +(-10.4934 + 2.60068i) q^{51} +(3.90545 + 2.25481i) q^{52} +(8.14614 + 4.70318i) q^{53} +(-1.62647 + 4.93504i) q^{54} -1.59652i q^{55} +(-2.64109 + 0.157053i) q^{56} +(-11.6737 - 3.36509i) q^{57} +(2.76889 + 4.79585i) q^{58} +(2.62379 - 4.54453i) q^{59} +(1.91811 + 1.99184i) q^{60} +(1.88976 - 1.09105i) q^{61} -9.09908 q^{62} +(-7.93539 + 0.172101i) q^{63} -1.00000 q^{64} +(6.23511 - 3.59984i) q^{65} +(1.20144 + 1.24762i) q^{66} +(0.613735 - 1.06302i) q^{67} +(-3.12084 - 5.40545i) q^{68} +(7.75874 + 2.23656i) q^{69} +(-1.89112 + 3.77699i) q^{70} +9.47281i q^{71} +(-2.99787 - 0.113106i) q^{72} +(3.56995 + 2.06111i) q^{73} +(0.494910 + 0.285736i) q^{74} +(-4.12082 + 1.02130i) q^{75} -7.01422i q^{76} +(-1.18453 + 2.36577i) q^{77} +(-2.16350 + 7.50529i) q^{78} +(3.87063 + 6.70413i) q^{79} +(-0.798258 + 1.38262i) q^{80} +(-8.97441 - 0.678156i) q^{81} +(-1.38262 + 0.798258i) q^{82} +17.4510 q^{83} +(-1.36448 - 4.37472i) q^{84} -9.96493 q^{85} +(1.33504 - 0.770788i) q^{86} +(-6.90903 + 6.65328i) q^{87} +(-0.500000 + 0.866025i) q^{88} +(-6.69358 - 11.5936i) q^{89} +(-2.54945 + 4.05463i) q^{90} +(-11.9103 + 0.708251i) q^{91} +4.66191i q^{92} +(-3.79126 - 15.2973i) q^{93} +(-6.18215 - 3.56927i) q^{94} +(-9.69802 - 5.59916i) q^{95} +(-0.416664 - 1.68119i) q^{96} -7.11516i q^{97} +(5.60466 - 4.19377i) q^{98} +(-1.59689 + 2.53968i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 6 q^{3} + 10 q^{4} - 6 q^{7} - 2 q^{9}+O(q^{10}) \) 20 * q - 6 * q^3 + 10 * q^4 - 6 * q^7 - 2 * q^9	\( 20 q - 6 q^{3} + 10 q^{4} - 6 q^{7} - 2 q^{9} - 18 q^{10} - 6 q^{12} - 8 q^{15} - 10 q^{16} + 4 q^{18} + 36 q^{19} + 24 q^{21} - 20 q^{22} - 12 q^{25} - 22 q^{30} + 36 q^{31} - 4 q^{36} + 16 q^{37} + 4 q^{39} - 18 q^{40} + 32 q^{42} + 32 q^{43} + 24 q^{45} + 30 q^{46} - 42 q^{49} - 24 q^{52} - 36 q^{54} - 24 q^{57} + 32 q^{58} - 4 q^{60} + 42 q^{61} - 10 q^{63} - 20 q^{64} + 6 q^{66} - 10 q^{67} - 36 q^{70} - 4 q^{72} + 12 q^{73} - 108 q^{75} + 6 q^{79} + 42 q^{81} + 18 q^{82} + 18 q^{84} - 28 q^{85} + 36 q^{87} - 10 q^{88} - 112 q^{91} - 36 q^{93} + 42 q^{94} - 8 q^{99}+O(q^{100}) \) 20 * q - 6 * q^3 + 10 * q^4 - 6 * q^7 - 2 * q^9 - 18 * q^10 - 6 * q^12 - 8 * q^15 - 10 * q^16 + 4 * q^18 + 36 * q^19 + 24 * q^21 - 20 * q^22 - 12 * q^25 - 22 * q^30 + 36 * q^31 - 4 * q^36 + 16 * q^37 + 4 * q^39 - 18 * q^40 + 32 * q^42 + 32 * q^43 + 24 * q^45 + 30 * q^46 - 42 * q^49 - 24 * q^52 - 36 * q^54 - 24 * q^57 + 32 * q^58 - 4 * q^60 + 42 * q^61 - 10 * q^63 - 20 * q^64 + 6 * q^66 - 10 * q^67 - 36 * q^70 - 4 * q^72 + 12 * q^73 - 108 * q^75 + 6 * q^79 + 42 * q^81 + 18 * q^82 + 18 * q^84 - 28 * q^85 + 36 * q^87 - 10 * q^88 - 112 * q^91 - 36 * q^93 + 42 * q^94 - 8 * q^99

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