LMFDB - Embedded newform 462.2.u.b.139.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(13,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 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("462.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.u (of order $10$, degree $4$, 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:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			139.2
Character	$\chi$	$=$	462.139
Dual form			462.2.u.b.349.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.587785 + 0.809017i) q^{2} +(0.951057 + 0.309017i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-0.946241 - 1.30239i) q^{5} +(-0.809017 + 0.587785i) q^{6} +(-2.49603 - 0.877400i) q^{7} +(0.951057 + 0.309017i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.587785 + 0.809017i) q^{2} +(0.951057 + 0.309017i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-0.946241 - 1.30239i) q^{5} +(-0.809017 + 0.587785i) q^{6} +(-2.49603 - 0.877400i) q^{7} +(0.951057 + 0.309017i) q^{8} +(0.809017 + 0.587785i) q^{9} +1.60984 q^{10} +(-2.29928 - 2.39025i) q^{11} -1.00000i q^{12} +(-1.19165 - 0.865782i) q^{13} +(2.17696 - 1.50361i) q^{14} +(-0.497468 - 1.53105i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-0.309576 + 0.224920i) q^{17} +(-0.951057 + 0.309017i) q^{18} +(2.11012 - 6.49427i) q^{19} +(-0.946241 + 1.30239i) q^{20} +(-2.10273 - 1.60577i) q^{21} +(3.28524 - 0.455199i) q^{22} -4.63860 q^{23} +(0.809017 + 0.587785i) q^{24} +(0.744240 - 2.29053i) q^{25} +(1.40086 - 0.455168i) q^{26} +(0.587785 + 0.809017i) q^{27} +(-0.0631409 + 2.64500i) q^{28} +(-8.63554 + 2.80586i) q^{29} +(1.53105 + 0.497468i) q^{30} +(4.73252 - 6.51375i) q^{31} -1.00000i q^{32} +(-1.44811 - 2.98378i) q^{33} -0.382657i q^{34} +(1.21913 + 4.08104i) q^{35} +(0.309017 - 0.951057i) q^{36} +(0.778315 + 2.39541i) q^{37} +(4.01368 + 5.52436i) q^{38} +(-0.865782 - 1.19165i) q^{39} +(-0.497468 - 1.53105i) q^{40} +(0.174539 - 0.537176i) q^{41} +(2.53505 - 0.757299i) q^{42} +2.15711i q^{43} +(-1.56275 + 2.92537i) q^{44} -1.60984i q^{45} +(2.72650 - 3.75271i) q^{46} +(3.78173 + 1.22876i) q^{47} +(-0.951057 + 0.309017i) q^{48} +(5.46034 + 4.38003i) q^{49} +(1.41563 + 1.94844i) q^{50} +(-0.363929 + 0.118248i) q^{51} +(-0.455168 + 1.40086i) q^{52} +(-1.56888 - 1.13986i) q^{53} -1.00000 q^{54} +(-0.937370 + 5.25631i) q^{55} +(-2.10273 - 1.60577i) q^{56} +(4.01368 - 5.52436i) q^{57} +(2.80586 - 8.63554i) q^{58} +(4.74690 - 1.54236i) q^{59} +(-1.30239 + 0.946241i) q^{60} +(-2.93476 + 2.13223i) q^{61} +(2.48803 + 7.65737i) q^{62} +(-1.50361 - 2.17696i) q^{63} +(0.809017 + 0.587785i) q^{64} +2.37123i q^{65} +(3.26511 + 0.582274i) q^{66} +10.2247 q^{67} +(0.309576 + 0.224920i) q^{68} +(-4.41157 - 1.43341i) q^{69} +(-4.01821 - 1.41247i) q^{70} +(1.45028 - 1.05369i) q^{71} +(0.587785 + 0.809017i) q^{72} +(-4.29106 - 13.2065i) q^{73} +(-2.39541 - 0.778315i) q^{74} +(1.41563 - 1.94844i) q^{75} -6.82848 q^{76} +(3.64186 + 7.98354i) q^{77} +1.47296 q^{78} +(-0.135244 + 0.186147i) q^{79} +(1.53105 + 0.497468i) q^{80} +(0.309017 + 0.951057i) q^{81} +(0.331993 + 0.456949i) q^{82} +(-11.4999 + 8.35514i) q^{83} +(-0.877400 + 2.49603i) q^{84} +(0.585867 + 0.190360i) q^{85} +(-1.74514 - 1.26792i) q^{86} -9.07995 q^{87} +(-1.44811 - 2.98378i) q^{88} -7.19895i q^{89} +(1.30239 + 0.946241i) q^{90} +(2.21475 + 3.20657i) q^{91} +(1.43341 + 4.41157i) q^{92} +(6.51375 - 4.73252i) q^{93} +(-3.21693 + 2.33724i) q^{94} +(-10.4547 + 3.39695i) q^{95} +(0.309017 - 0.951057i) q^{96} +(-9.25926 + 12.7443i) q^{97} +(-6.75303 + 1.84299i) q^{98} +(-0.455199 - 3.28524i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 8 q^{4} + 10 q^{5} - 8 q^{6} - 10 q^{7} + 8 q^{9}+O(q^{10}) $ 32 * q + 8 * q^4 + 10 * q^5 - 8 * q^6 - 10 * q^7 + 8 * q^9	$ 32 q + 8 q^{4} + 10 q^{5} - 8 q^{6} - 10 q^{7} + 8 q^{9} + 4 q^{10} + 8 q^{11} - 2 q^{14} + 6 q^{15} - 8 q^{16} - 12 q^{17} - 16 q^{19} + 10 q^{20} - 8 q^{21} - 4 q^{22} + 8 q^{23} + 8 q^{24} + 6 q^{25} + 10 q^{28} + 20 q^{29} - 50 q^{31} - 16 q^{33} - 12 q^{35} - 8 q^{36} - 16 q^{37} + 6 q^{40} + 40 q^{41} + 12 q^{44} + 52 q^{49} + 40 q^{51} - 32 q^{54} - 40 q^{55} - 8 q^{56} + 10 q^{58} + 60 q^{59} + 4 q^{60} - 4 q^{61} + 20 q^{62} - 10 q^{63} + 8 q^{64} + 8 q^{66} - 16 q^{67} + 12 q^{68} + 30 q^{69} - 28 q^{70} - 48 q^{71} - 74 q^{73} - 40 q^{74} - 24 q^{76} + 6 q^{77} - 60 q^{79} - 8 q^{81} + 20 q^{82} + 4 q^{83} - 2 q^{84} - 10 q^{85} - 36 q^{86} + 20 q^{87} - 16 q^{88} - 4 q^{90} - 20 q^{91} - 8 q^{92} - 10 q^{93} - 20 q^{95} - 8 q^{96} + 60 q^{97} - 40 q^{98} - 8 q^{99}+O(q^{100}) $ 32 * q + 8 * q^4 + 10 * q^5 - 8 * q^6 - 10 * q^7 + 8 * q^9 + 4 * q^10 + 8 * q^11 - 2 * q^14 + 6 * q^15 - 8 * q^16 - 12 * q^17 - 16 * q^19 + 10 * q^20 - 8 * q^21 - 4 * q^22 + 8 * q^23 + 8 * q^24 + 6 * q^25 + 10 * q^28 + 20 * q^29 - 50 * q^31 - 16 * q^33 - 12 * q^35 - 8 * q^36 - 16 * q^37 + 6 * q^40 + 40 * q^41 + 12 * q^44 + 52 * q^49 + 40 * q^51 - 32 * q^54 - 40 * q^55 - 8 * q^56 + 10 * q^58 + 60 * q^59 + 4 * q^60 - 4 * q^61 + 20 * q^62 - 10 * q^63 + 8 * q^64 + 8 * q^66 - 16 * q^67 + 12 * q^68 + 30 * q^69 - 28 * q^70 - 48 * q^71 - 74 * q^73 - 40 * q^74 - 24 * q^76 + 6 * q^77 - 60 * q^79 - 8 * q^81 + 20 * q^82 + 4 * q^83 - 2 * q^84 - 10 * q^85 - 36 * q^86 + 20 * q^87 - 16 * q^88 - 4 * q^90 - 20 * q^91 - 8 * q^92 - 10 * q^93 - 20 * q^95 - 8 * q^96 + 60 * q^97 - 40 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$-1$	$e\left(\frac{7}{10}\right)$

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 $

$2$	−0.587785	+	0.809017i	−0.415627	+	0.572061i
$2$	−0.587785	+	0.809017i	−0.415627	+	0.572061i
$3$	0.951057	+	0.309017i	0.549093	+	0.178411i
$3$	0.951057	+	0.309017i	0.549093	+	0.178411i
$4$	−0.309017	−	0.951057i	−0.154508	−	0.475528i
$5$	−0.946241	−	1.30239i	−0.423172	−	0.582446i	0.543197	−	0.839605i	$-0.317214\pi$
$5$	−0.946241	−	1.30239i	−0.423172	−	0.582446i	−0.966369	+	0.257159i	$0.917214\pi$
$6$	−0.809017	+	0.587785i	−0.330280	+	0.239962i
$7$	−2.49603	−	0.877400i	−0.943411	−	0.331626i
$7$	−2.49603	−	0.877400i	−0.943411	−	0.331626i
$8$	0.951057	+	0.309017i	0.336249	+	0.109254i
$9$	0.809017	+	0.587785i	0.269672	+	0.195928i
$10$	1.60984			0.509077
$11$	−2.29928	−	2.39025i	−0.693259	−	0.720689i
$11$	−2.29928	−	2.39025i	−0.693259	−	0.720689i
$12$		−	1.00000i		−	0.288675i
$13$	−1.19165	−	0.865782i	−0.330503	−	0.240125i	0.410141	−	0.912022i	$-0.365480\pi$
$13$	−1.19165	−	0.865782i	−0.330503	−	0.240125i	−0.740644	+	0.671898i	$0.765480\pi$
$14$	2.17696	−	1.50361i	0.581817	−	0.401856i
$15$	−0.497468	−	1.53105i	−0.128446	−	0.395316i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−0.309576	+	0.224920i	−0.0750832	+	0.0545512i	−0.624694	−	0.780870i	$-0.714776\pi$
$17$	−0.309576	+	0.224920i	−0.0750832	+	0.0545512i	0.549610	+	0.835421i	$0.314776\pi$
$18$	−0.951057	+	0.309017i	−0.224166	+	0.0728360i
$19$	2.11012	−	6.49427i	0.484094	−	1.48989i	−0.349195	−	0.937050i	$-0.613545\pi$
$19$	2.11012	−	6.49427i	0.484094	−	1.48989i	0.833289	−	0.552838i	$-0.186455\pi$
$20$	−0.946241	+	1.30239i	−0.211586	+	0.291223i
$21$	−2.10273	−	1.60577i	−0.458854	−	0.350408i
$22$	3.28524	−	0.455199i	0.700415	−	0.0970488i
$23$	−4.63860			−0.967216			−0.483608	−	0.875285i	$-0.660674\pi$
$23$	−4.63860			−0.967216			−0.483608	+	0.875285i	$0.660674\pi$
$24$	0.809017	+	0.587785i	0.165140	+	0.119981i
$25$	0.744240	−	2.29053i	0.148848	−	0.458107i
$26$	1.40086	−	0.455168i	0.274732	−	0.0892659i
$27$	0.587785	+	0.809017i	0.113119	+	0.155695i
$28$	−0.0631409	+	2.64500i	−0.0119325	+	0.499858i
$29$	−8.63554	+	2.80586i	−1.60358	+	0.521035i	−0.967989	−	0.250992i	$-0.919243\pi$
$29$	−8.63554	+	2.80586i	−1.60358	+	0.521035i	−0.635590	+	0.772026i	$0.719243\pi$
$30$	1.53105	+	0.497468i	0.279530	+	0.0908249i
$31$	4.73252	−	6.51375i	0.849985	−	1.16990i	−0.133881	−	0.990997i	$-0.542744\pi$
$31$	4.73252	−	6.51375i	0.849985	−	1.16990i	0.983866	−	0.178907i	$-0.0572561\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−1.44811	−	2.98378i	−0.252084	−	0.519410i
$34$		−	0.382657i		−	0.0656252i
$35$	1.21913	+	4.08104i	0.206071	+	0.689821i
$36$	0.309017	−	0.951057i	0.0515028	−	0.158509i
$37$	0.778315	+	2.39541i	0.127954	+	0.393803i	0.994428	−	0.105420i	$-0.0336188\pi$
$37$	0.778315	+	2.39541i	0.127954	+	0.393803i	−0.866474	+	0.499223i	$0.833619\pi$
$38$	4.01368	+	5.52436i	0.651105	+	0.896169i
$39$	−0.865782	−	1.19165i	−0.138636	−	0.190816i
$40$	−0.497468	−	1.53105i	−0.0786567	−	0.242080i
$41$	0.174539	−	0.537176i	0.0272584	−	0.0838928i	−0.936502	−	0.350663i	$-0.885956\pi$
$41$	0.174539	−	0.537176i	0.0272584	−	0.0838928i	0.963760	+	0.266770i	$0.0859564\pi$
$42$	2.53505	−	0.757299i	0.391167	−	0.116854i
$43$			2.15711i			0.328957i	0.986381	+	0.164478i	$0.0525941\pi$
$43$			2.15711i			0.328957i	−0.986381	+	0.164478i	$0.947406\pi$
$44$	−1.56275	+	2.92537i	−0.235594	+	0.441017i
$45$		−	1.60984i		−	0.239981i
$46$	2.72650	−	3.75271i	0.402001	−	0.553307i
$47$	3.78173	+	1.22876i	0.551622	+	0.179233i	0.571548	−	0.820569i	$-0.306343\pi$
$47$	3.78173	+	1.22876i	0.551622	+	0.179233i	−0.0199259	+	0.999801i	$0.506343\pi$
$48$	−0.951057	+	0.309017i	−0.137273	+	0.0446028i
$49$	5.46034	+	4.38003i	0.780048	+	0.625719i
$50$	1.41563	+	1.94844i	0.200200	+	0.275552i
$51$	−0.363929	+	0.118248i	−0.0509602	+	0.0165580i
$52$	−0.455168	+	1.40086i	−0.0631205	+	0.194265i
$53$	−1.56888	−	1.13986i	−0.215503	−	0.156572i	0.474797	−	0.880095i	$-0.342521\pi$
$53$	−1.56888	−	1.13986i	−0.215503	−	0.156572i	−0.690300	+	0.723523i	$0.742521\pi$
$54$	−1.00000			−0.136083
$55$	−0.937370	+	5.25631i	−0.126395	+	0.708761i
$56$	−2.10273	−	1.60577i	−0.280990	−	0.214580i
$57$	4.01368	−	5.52436i	0.531625	−	0.731719i
$58$	2.80586	−	8.63554i	0.368427	−	1.13390i
$59$	4.74690	−	1.54236i	0.617994	−	0.200798i	0.0167444	−	0.999860i	$-0.494670\pi$
$59$	4.74690	−	1.54236i	0.617994	−	0.200798i	0.601249	+	0.799061i	$0.294670\pi$
$60$	−1.30239	+	0.946241i	−0.168138	+	0.122159i
$61$	−2.93476	+	2.13223i	−0.375758	+	0.273004i	−0.759594	−	0.650397i	$-0.774603\pi$
$61$	−2.93476	+	2.13223i	−0.375758	+	0.273004i	0.383837	+	0.923401i	$0.374603\pi$
$62$	2.48803	+	7.65737i	0.315980	+	0.972487i
$63$	−1.50361	−	2.17696i	−0.189437	−	0.274271i
$64$	0.809017	+	0.587785i	0.101127	+	0.0734732i
$65$			2.37123i			0.294114i
$66$	3.26511	+	0.582274i	0.401908	+	0.0716730i
$67$	10.2247			1.24915			0.624575	−	0.780965i	$-0.285272\pi$
$67$	10.2247			1.24915			0.624575	+	0.780965i	$0.285272\pi$
$68$	0.309576	+	0.224920i	0.0375416	+	0.0272756i
$69$	−4.41157	−	1.43341i	−0.531091	−	0.172562i
$70$	−4.01821	−	1.41247i	−0.480268	−	0.168823i
$71$	1.45028	−	1.05369i	0.172117	−	0.125050i	−0.498392	−	0.866952i	$-0.666076\pi$
$71$	1.45028	−	1.05369i	0.172117	−	0.125050i	0.670509	+	0.741902i	$0.266076\pi$
$72$	0.587785	+	0.809017i	0.0692712	+	0.0953436i
$73$	−4.29106	−	13.2065i	−0.502230	−	1.54571i	−0.805378	−	0.592762i	$-0.798038\pi$
$73$	−4.29106	−	13.2065i	−0.502230	−	1.54571i	0.303148	−	0.952944i	$-0.401962\pi$
$74$	−2.39541	−	0.778315i	−0.278460	−	0.0904773i
$75$	1.41563	−	1.94844i	0.163463	−	0.224987i
$76$	−6.82848			−0.783280
$77$	3.64186	+	7.98354i	0.415029	+	0.909808i
$78$	1.47296			0.166779
$79$	−0.135244	+	0.186147i	−0.0152161	+	0.0209432i	−0.816557	−	0.577264i	$-0.804120\pi$
$79$	−0.135244	+	0.186147i	−0.0152161	+	0.0209432i	0.801341	+	0.598208i	$0.204120\pi$
$80$	1.53105	+	0.497468i	0.171177	+	0.0556187i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	0.331993	+	0.456949i	0.0366625	+	0.0504616i
$83$	−11.4999	+	8.35514i	−1.26227	+	0.917096i	−0.998867	−	0.0475889i	$-0.984846\pi$
$83$	−11.4999	+	8.35514i	−1.26227	+	0.917096i	−0.263407	+	0.964685i	$0.584846\pi$
$84$	−0.877400	+	2.49603i	−0.0957322	+	0.272339i
$85$	0.585867	+	0.190360i	0.0635462	+	0.0206474i
$86$	−1.74514	−	1.26792i	−0.188184	−	0.136723i
$87$	−9.07995			−0.973472
$88$	−1.44811	−	2.98378i	−0.154370	−	0.318072i
$89$		−	7.19895i		−	0.763087i	−0.924351	−	0.381543i	$-0.875393\pi$
$89$		−	7.19895i		−	0.763087i	0.924351	−	0.381543i	$-0.124607\pi$
$90$	1.30239	+	0.946241i	0.137284	+	0.0997426i
$91$	2.21475	+	3.20657i	0.232169	+	0.336140i
$92$	1.43341	+	4.41157i	0.149443	+	0.459938i
$93$	6.51375	−	4.73252i	0.675445	−	0.490739i
$94$	−3.21693	+	2.33724i	−0.331801	+	0.241068i
$95$	−10.4547	+	3.39695i	−1.07263	+	0.348520i
$96$	0.309017	−	0.951057i	0.0315389	−	0.0970668i
$97$	−9.25926	+	12.7443i	−0.940135	+	1.29399i	0.0156369	+	0.999878i	$0.495022\pi$
$97$	−9.25926	+	12.7443i	−0.940135	+	1.29399i	−0.955772	+	0.294108i	$0.904978\pi$
$98$	−6.75303	+	1.84299i	−0.682159	+	0.186170i
$99$	−0.455199	−	3.28524i	−0.0457492	−	0.330179i
$100$	−2.40841			−0.240841
$101$	2.45123	+	1.78093i	0.243907	+	0.177209i	0.703022	−	0.711168i	$-0.251833\pi$
$101$	2.45123	+	1.78093i	0.243907	+	0.177209i	−0.459115	+	0.888377i	$0.651833\pi$
$102$	0.118248	−	0.363929i	0.0117083	−	0.0360343i
$103$	5.99309	−	1.94727i	0.590516	−	0.191870i	0.00151003	−	0.999999i	$-0.499519\pi$
$103$	5.99309	−	1.94727i	0.590516	−	0.191870i	0.589006	+	0.808129i	$0.299519\pi$
$104$	−0.865782	−	1.19165i	−0.0848969	−	0.116851i
$105$	−0.101647	+	4.25803i	−0.00991971	+	0.415541i
$106$	1.84433	−	0.599260i	0.179138	−	0.0582053i
$107$	11.2808	+	3.66536i	1.09056	+	0.354344i	0.798462	−	0.602045i	$-0.205647\pi$
$107$	11.2808	+	3.66536i	1.09056	+	0.354344i	0.292096	+	0.956389i	$0.405647\pi$
$108$	0.587785	−	0.809017i	0.0565597	−	0.0778477i
$109$			17.6110i			1.68683i	0.537266	+	0.843413i	$0.319457\pi$
$109$			17.6110i			1.68683i	−0.537266	+	0.843413i	$0.680543\pi$
$110$	−3.70147	−	3.84793i	−0.352922	−	0.366886i
$111$			2.51868i			0.239063i
$112$	2.53505	−	0.757299i	0.239540	−	0.0715580i
$113$	−1.70131	+	5.23611i	−0.160046	+	0.492571i	−0.998637	−	0.0521901i	$-0.983380\pi$
$113$	−1.70131	+	5.23611i	−0.160046	+	0.492571i	0.838591	+	0.544762i	$0.183380\pi$
$114$	2.11012	+	6.49427i	0.197630	+	0.608244i
$115$	4.38924	+	6.04127i	0.409299	+	0.563351i
$116$	5.33706	+	7.34583i	0.495533	+	0.682043i
$117$	−0.455168	−	1.40086i	−0.0420803	−	0.129510i
$118$	−1.54236	+	4.74690i	−0.141986	+	0.436988i
$119$	0.970056	−	0.289786i	0.0889249	−	0.0265646i
$120$		−	1.60984i		−	0.146958i
$121$	−0.426634	+	10.9917i	−0.0387849	+	0.999248i
$122$		−	3.62757i		−	0.328424i
$123$	0.331993	−	0.456949i	0.0299348	−	0.0412017i
$124$	−7.65737	−	2.48803i	−0.687652	−	0.223432i
$125$	−11.3426	+	3.68545i	−1.01452	+	0.329637i
$126$	2.64500	+	0.0631409i	0.235635	+	0.00562503i
$127$	−4.80069	−	6.60758i	−0.425992	−	0.586328i	0.541035	−	0.841000i	$-0.318033\pi$
$127$	−4.80069	−	6.60758i	−0.425992	−	0.586328i	−0.967028	+	0.254672i	$0.918033\pi$
$128$	−0.951057	+	0.309017i	−0.0840623	+	0.0273135i
$129$	−0.666585	+	2.05154i	−0.0586895	+	0.180628i
$130$	−1.91836	−	1.39377i	−0.168251	−	0.122242i
$131$	−1.77394			−0.154990			−0.0774949	−	0.996993i	$-0.524692\pi$
$131$	−1.77394			−0.154990			−0.0774949	+	0.996993i	$0.524692\pi$
$132$	−2.39025	+	2.29928i	−0.208045	+	0.200127i
$133$	−10.9650	+	14.3585i	−0.950785	+	1.24504i
$134$	−6.00995	+	8.27198i	−0.519180	+	0.714591i
$135$	0.497468	−	1.53105i	0.0428153	−	0.131772i
$136$	−0.363929	+	0.118248i	−0.0312066	+	0.0101396i
$137$	16.2720	−	11.8223i	1.39021	−	1.01005i	0.394373	−	0.918951i	$-0.370962\pi$
$137$	16.2720	−	11.8223i	1.39021	−	1.01005i	0.995842	−	0.0910995i	$-0.0290381\pi$
$138$	3.75271	−	2.72650i	0.319452	−	0.232095i
$139$	−6.51783	−	20.0598i	−0.552835	−	1.70145i	−0.701594	−	0.712577i	$-0.747528\pi$
$139$	−6.51783	−	20.0598i	−0.552835	−	1.70145i	0.148759	−	0.988874i	$-0.452472\pi$
$140$	3.50456	−	2.42057i	0.296190	−	0.204576i
$141$	3.21693	+	2.33724i	0.270915	+	0.196831i
$142$			1.79265i			0.150436i
$143$	0.670488	+	4.83901i	0.0560690	+	0.404658i
$144$	−1.00000			−0.0833333
$145$	11.8256	+	8.59182i	0.982065	+	0.713512i
$146$	13.2065	+	4.29106i	1.09298	+	0.355130i
$147$	3.83959	+	5.85300i	0.316684	+	0.482747i
$148$	2.03766	−	1.48044i	0.167494	−	0.121692i
$149$	−6.37489	−	8.77428i	−0.522251	−	0.718817i	0.463674	−	0.886006i	$-0.346531\pi$
$149$	−6.37489	−	8.77428i	−0.522251	−	0.718817i	−0.985925	+	0.167189i	$0.946531\pi$
$150$	0.744240	+	2.29053i	0.0607669	+	0.187021i
$151$	4.88770	+	1.58811i	0.397756	+	0.129239i	0.501063	−	0.865411i	$-0.332943\pi$
$151$	4.88770	+	1.58811i	0.397756	+	0.129239i	−0.103307	+	0.994649i	$0.532943\pi$
$152$	4.01368	−	5.52436i	0.325552	−	0.448084i
$153$	−0.382657			−0.0309360
$154$	−8.59945	−	1.74628i	−0.692963	−	0.140719i
$155$	−12.9615			−1.04110
$156$	−0.865782	+	1.19165i	−0.0693180	+	0.0954081i
$157$	−10.0449	−	3.26379i	−0.801672	−	0.260479i	−0.120605	−	0.992701i	$-0.538484\pi$
$157$	−10.0449	−	3.26379i	−0.801672	−	0.260479i	−0.681067	+	0.732221i	$0.738484\pi$
$158$	−0.0711020	−	0.218829i	−0.00565657	−	0.0174091i
$159$	−1.13986	−	1.56888i	−0.0903968	−	0.124421i
$160$	−1.30239	+	0.946241i	−0.102963	+	0.0748069i
$161$	11.5781	+	4.06991i	0.912482	+	0.320754i
$162$	−0.951057	−	0.309017i	−0.0747221	−	0.0242787i
$163$	−5.96686	−	4.33518i	−0.467361	−	0.339557i	0.329051	−	0.944312i	$-0.393271\pi$
$163$	−5.96686	−	4.33518i	−0.467361	−	0.339557i	−0.796412	+	0.604755i	$0.793271\pi$
$164$	−0.564820			−0.0441051
$165$	−2.51578	+	4.70939i	−0.195853	+	0.366625i
$166$		−	14.2146i		−	1.10327i
$167$	10.2670	+	7.45941i	0.794485	+	0.577227i	0.909291	−	0.416161i	$-0.136625\pi$
$167$	10.2670	+	7.45941i	0.794485	+	0.577227i	−0.114806	+	0.993388i	$0.536625\pi$
$168$	−1.50361	−	2.17696i	−0.116006	−	0.167956i
$169$	−3.34678	−	10.3003i	−0.257444	−	0.792333i
$170$	−0.498369	+	0.362086i	−0.0382231	+	0.0277707i
$171$	5.52436	−	4.01368i	0.422458	−	0.306934i
$172$	2.05154	−	0.666585i	0.156428	−	0.0508266i
$173$	1.76252	−	5.42448i	0.134002	−	0.412415i	−0.861432	−	0.507874i	$-0.830432\pi$
$173$	1.76252	−	5.42448i	0.134002	−	0.412415i	0.995433	+	0.0954583i	$0.0304316\pi$
$174$	5.33706	−	7.34583i	0.404601	−	0.556886i
$175$	−3.86736	+	5.06425i	−0.292345	+	0.382821i
$176$	3.26511	+	0.582274i	0.246117	+	0.0438906i
$177$	4.99119			0.375161
$178$	5.82407	+	4.23143i	0.436533	+	0.317159i
$179$	1.77285	−	5.45629i	0.132509	−	0.407822i	−0.862685	−	0.505742i	$-0.831219\pi$
$179$	1.77285	−	5.45629i	0.132509	−	0.407822i	0.995194	+	0.0979198i	$0.0312189\pi$
$180$	−1.53105	+	0.497468i	−0.114118	+	0.0370791i
$181$	9.27830	+	12.7705i	0.689651	+	0.949223i	0.999999	−	0.00140000i	$-0.000445635\pi$
$181$	9.27830	+	12.7705i	0.689651	+	0.949223i	−0.310348	+	0.950623i	$0.600446\pi$
$182$	−3.89596	−	0.0930037i	−0.288788	−	0.00689389i
$183$	−3.45002	+	1.12098i	−0.255033	+	0.0828652i
$184$	−4.41157	−	1.43341i	−0.325226	−	0.105672i
$185$	2.38328	−	3.28030i	0.175222	−	0.241173i
$186$			8.05144i			0.590360i
$187$	1.24942	+	0.222811i	0.0913665	+	0.0162936i
$188$		−	3.97635i		−	0.290005i
$189$	−0.757299	−	2.53505i	−0.0550854	−	0.184398i
$190$	3.39695	−	10.4547i	0.246441	−	0.758467i
$191$	−3.72462	−	11.4632i	−0.269504	−	0.829449i	−0.990621	−	0.136636i	$-0.956371\pi$
$191$	−3.72462	−	11.4632i	−0.269504	−	0.829449i	0.721117	−	0.692813i	$-0.243629\pi$
$192$	0.587785	+	0.809017i	0.0424197	+	0.0583858i
$193$	4.38514	+	6.03562i	0.315649	+	0.434454i	0.937133	−	0.348974i	$-0.113470\pi$
$193$	4.38514	+	6.03562i	0.315649	+	0.434454i	−0.621484	+	0.783427i	$0.713470\pi$
$194$	−4.86788	−	14.9818i	−0.349493	−	1.07563i
$195$	−0.732749	+	2.25517i	−0.0524732	+	0.161496i
$196$	2.47832	−	6.54660i	0.177023	−	0.467614i
$197$			20.6955i			1.47450i	0.675622	+	0.737248i	$0.263875\pi$
$197$			20.6955i			1.47450i	−0.675622	+	0.737248i	$0.736125\pi$
$198$	2.92537	+	1.56275i	0.207897	+	0.111060i
$199$		−	12.8429i		−	0.910412i	−0.890386	−	0.455206i	$-0.849566\pi$
$199$		−	12.8429i		−	0.910412i	0.890386	−	0.455206i	$-0.150434\pi$
$200$	1.41563	−	1.94844i	0.100100	−	0.137776i
$201$	9.72430	+	3.15962i	0.685899	+	0.222862i
$202$	−2.88160	+	0.936288i	−0.202749	+	0.0658770i
$203$	24.0164	+	0.573316i	1.68562	+	0.0402389i
$204$	0.224920	+	0.309576i	0.0157476	+	0.0216747i
$205$	−0.864768	+	0.280980i	−0.0603980	+	0.0196245i
$206$	−1.94727	+	5.99309i	−0.135673	+	0.417558i
$207$	−3.75271	−	2.72650i	−0.260831	−	0.189505i
$208$	1.47296			0.102131
$209$	−20.3747	+	9.88842i	−1.40935	+	0.683996i
$210$	−3.38507	−	2.58504i	−0.233592	−	0.178385i
$211$	16.9175	−	23.2849i	1.16465	−	1.60300i	0.472302	−	0.881437i	$-0.343423\pi$
$211$	16.9175	−	23.2849i	1.16465	−	1.60300i	0.692347	−	0.721565i	$-0.256577\pi$
$212$	−0.599260	+	1.84433i	−0.0411574	+	0.126669i
$213$	1.70491	−	0.553958i	0.116818	−	0.0379566i
$214$	−9.59604	+	6.97193i	−0.655972	+	0.476592i
$215$	2.80940	−	2.04115i	0.191600	−	0.139205i
$216$	0.309017	+	0.951057i	0.0210259	+	0.0647112i
$217$	−17.5277	+	12.1062i	−1.18986	+	0.821823i
$218$	−14.2476	−	10.3515i	−0.964968	−	0.701090i
$219$		−	13.8861i		−	0.938339i
$220$	5.28871	−	0.732799i	0.356565	−	0.0494053i
$221$	0.563637			0.0379143
$222$	−2.03766	−	1.48044i	−0.136758	−	0.0993608i
$223$	17.8499	+	5.79979i	1.19532	+	0.388383i	0.838037	−	0.545614i	$-0.183703\pi$
$223$	17.8499	+	5.79979i	1.19532	+	0.388383i	0.357282	+	0.933997i	$0.383703\pi$
$224$	−0.877400	+	2.49603i	−0.0586237	+	0.166773i
$225$	1.94844	−	1.41563i	0.129896	−	0.0943752i
$226$	−3.23609	−	4.45410i	−0.215262	−	0.296282i
$227$	−8.96777	−	27.6000i	−0.595212	−	1.83187i	−0.553668	−	0.832737i	$-0.686772\pi$
$227$	−8.96777	−	27.6000i	−0.595212	−	1.83187i	−0.0415437	−	0.999137i	$-0.513228\pi$
$228$	−6.49427	−	2.11012i	−0.430094	−	0.139746i
$229$	9.75663	−	13.4289i	0.644736	−	0.887403i	−0.354121	−	0.935200i	$-0.615220\pi$
$229$	9.75663	−	13.4289i	0.644736	−	0.887403i	0.998857	+	0.0477963i	$0.0152198\pi$
$230$	−7.46742			−0.492387
$231$	0.996568	+	8.71819i	0.0655694	+	0.573615i
$232$	−9.07995			−0.596128
$233$	7.20786	−	9.92077i	0.472203	−	0.649931i	−0.504781	−	0.863248i	$-0.668427\pi$
$233$	7.20786	−	9.92077i	0.472203	−	0.649931i	0.976983	+	0.213317i	$0.0684266\pi$
$234$	1.40086	+	0.455168i	0.0915774	+	0.0297553i
$235$	−1.97811	−	6.08799i	−0.129037	−	0.397137i
$236$	−2.93375	−	4.03795i	−0.190971	−	0.262848i
$237$	−0.186147	+	0.135244i	−0.0120916	+	0.00878504i
$238$	−0.335743	+	0.955124i	−0.0217630	+	0.0619115i
$239$	−1.70397	−	0.553655i	−0.110221	−	0.0358129i	0.253387	−	0.967365i	$-0.418455\pi$
$239$	−1.70397	−	0.553655i	−0.110221	−	0.0358129i	−0.363608	+	0.931552i	$0.618455\pi$
$240$	1.30239	+	0.946241i	0.0840689	+	0.0610796i
$241$	1.74148			0.112179			0.0560894	−	0.998426i	$-0.482137\pi$
$241$	1.74148			0.112179			0.0560894	+	0.998426i	$0.482137\pi$
$242$	−8.64172	−	6.80593i	−0.555511	−	0.437502i
$243$			1.00000i			0.0641500i
$244$	2.93476	+	2.13223i	0.187879	+	0.136502i
$245$	0.537711	−	11.2561i	0.0343531	−	0.719123i
$246$	0.174539	+	0.537176i	0.0111282	+	0.0342491i
$247$	−8.13713	+	5.91197i	−0.517753	+	0.376170i
$248$	6.51375	−	4.73252i	0.413624	−	0.300515i
$249$	−13.5189	+	4.39256i	−0.856726	+	0.278367i
$250$	3.68545	−	11.3426i	0.233088	−	0.717372i
$251$	14.7837	−	20.3480i	0.933140	−	1.28436i	−0.0254826	−	0.999675i	$-0.508112\pi$
$251$	14.7837	−	20.3480i	0.933140	−	1.28436i	0.958622	−	0.284681i	$-0.0918878\pi$
$252$	−1.60577	+	2.10273i	−0.101154	+	0.132460i
$253$	10.6654	+	11.0874i	0.670531	+	0.697062i
$254$	8.16742			0.512469
$255$	0.498369	+	0.362086i	0.0312090	+	0.0226747i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	29.8896	−	9.71170i	1.86446	−	0.605799i	0.871047	−	0.491199i	$-0.163441\pi$
$257$	29.8896	−	9.71170i	1.86446	−	0.605799i	0.993412	−	0.114601i	$-0.0365588\pi$
$258$	−1.26792	−	1.74514i	−0.0789373	−	0.108648i
$259$	0.159032	−	6.66190i	0.00988174	−	0.413951i
$260$	2.25517	−	0.732749i	0.139860	−	0.0454432i
$261$	−8.63554	−	2.80586i	−0.534527	−	0.173678i
$262$	1.04270	−	1.43515i	0.0644179	−	0.0886637i
$263$		−	23.5862i		−	1.45439i	−0.686433	−	0.727193i	$-0.740824\pi$
$263$		−	23.5862i		−	1.45439i	0.686433	−	0.727193i	$-0.259176\pi$
$264$	−0.455199	−	3.28524i	−0.0280156	−	0.202192i
$265$			3.12188i			0.191776i
$266$	−5.17120	−	17.3106i	−0.317067	−	1.06138i
$267$	2.22460	−	6.84661i	0.136143	−	0.419005i
$268$	−3.15962	−	9.72430i	−0.193004	−	0.594006i
$269$	−14.2059	−	19.5527i	−0.866148	−	1.19215i	−0.980068	−	0.198660i	$-0.936341\pi$
$269$	−14.2059	−	19.5527i	−0.866148	−	1.19215i	0.113921	−	0.993490i	$-0.463659\pi$
$270$	0.946241	+	1.30239i	0.0575864	+	0.0792609i
$271$	−0.903050	−	2.77930i	−0.0548564	−	0.168831i	0.919875	−	0.392213i	$-0.128290\pi$
$271$	−0.903050	−	2.77930i	−0.0548564	−	0.168831i	−0.974731	+	0.223382i	$0.928290\pi$
$272$	0.118248	−	0.363929i	0.00716981	−	0.0220664i
$273$	1.11547	+	3.73402i	0.0675112	+	0.225993i
$274$			20.1134i			1.21509i
$275$	−7.18617	+	3.48765i	−0.433343	+	0.210313i
$276$			4.63860i			0.279211i
$277$	−13.8069	+	19.0036i	−0.829578	+	1.14182i	0.158423	+	0.987371i	$0.449359\pi$
$277$	−13.8069	+	19.0036i	−0.829578	+	1.14182i	−0.988001	+	0.154445i	$0.950641\pi$
$278$	20.0598	+	6.51783i	1.20311	+	0.390913i
$279$	7.65737	−	2.48803i	0.458435	−	0.148955i
$280$	−0.101647	+	4.25803i	−0.00607456	+	0.254466i
$281$	12.5826	+	17.3185i	0.750615	+	1.03313i	0.997937	+	0.0641993i	$0.0204493\pi$
$281$	12.5826	+	17.3185i	0.750615	+	1.03313i	−0.247322	+	0.968933i	$0.579551\pi$
$282$	−3.78173	+	1.22876i	−0.225199	+	0.0731715i
$283$	−4.17463	+	12.8482i	−0.248156	+	0.763745i	0.746946	+	0.664885i	$0.231520\pi$
$283$	−4.17463	+	12.8482i	−0.248156	+	0.763745i	−0.995101	+	0.0988598i	$0.968480\pi$
$284$	−1.45028	−	1.05369i	−0.0860584	−	0.0625251i
$285$	−10.9928			−0.651156
$286$	−4.30895	−	2.30186i	−0.254793	−	0.136112i
$287$	−0.906973	+	1.18767i	−0.0535369	+	0.0701058i
$288$	0.587785	−	0.809017i	0.0346356	−	0.0476718i
$289$	−5.20804	+	16.0287i	−0.306355	+	0.942865i
$290$	−13.9019	+	4.51699i	−0.816345	+	0.265247i
$291$	−12.7443	+	9.25926i	−0.747083	+	0.542787i
$292$	−11.2341	+	8.16207i	−0.657428	+	0.477649i
$293$	−2.52269	−	7.76405i	−0.147377	−	0.453580i	0.849932	−	0.526893i	$-0.176643\pi$
$293$	−2.52269	−	7.76405i	−0.147377	−	0.453580i	−0.997309	+	0.0733123i	$0.976643\pi$
$294$	−6.99203	−	0.334015i	−0.407783	−	0.0194801i
$295$	−6.50047	−	4.72287i	−0.378472	−	0.274976i
$296$			2.51868i			0.146395i
$297$	0.582274	−	3.26511i	0.0337870	−	0.189461i
$298$	10.8456			0.628269
$299$	5.52757	+	4.01602i	0.319668	+	0.232252i
$300$	−2.29053	−	0.744240i	−0.132244	−	0.0429687i
$301$	1.89265	−	5.38422i	0.109091	−	0.310342i
$302$	−4.15773	+	3.02077i	−0.239250	+	0.173826i
$303$	1.78093	+	2.45123i	0.102312	+	0.140820i
$304$	2.11012	+	6.49427i	0.121023	+	0.372472i
$305$	5.55399	+	1.80460i	0.318020	+	0.103331i
$306$	0.224920	−	0.309576i	0.0128578	−	0.0176973i
$307$	18.2790			1.04324			0.521619	−	0.853179i	$-0.325328\pi$
$307$	18.2790			1.04324			0.521619	+	0.853179i	$0.325328\pi$
$308$	6.46740	−	5.93066i	0.368514	−	0.337931i
$309$	6.30150			0.358480
$310$	7.61860	−	10.4861i	0.432708	−	0.595571i
$311$	−11.3117	−	3.67539i	−0.641427	−	0.208412i	−0.0297968	−	0.999556i	$-0.509486\pi$
$311$	−11.3117	−	3.67539i	−0.641427	−	0.208412i	−0.611630	+	0.791144i	$0.709486\pi$
$312$	−0.455168	−	1.40086i	−0.0257688	−	0.0793083i
$313$	8.06188	+	11.0962i	0.455685	+	0.627196i	0.973607	−	0.228232i	$-0.0732943\pi$
$313$	8.06188	+	11.0962i	0.455685	+	0.627196i	−0.517922	+	0.855428i	$0.673294\pi$
$314$	8.54472	−	6.20810i	0.482207	−	0.350344i
$315$	−1.41247	+	4.01821i	−0.0795839	+	0.226401i
$316$	0.218829	+	0.0711020i	0.0123101	+	0.00399980i
$317$	0.748300	+	0.543672i	0.0420287	+	0.0305356i	0.608601	−	0.793476i	$-0.291731\pi$
$317$	0.748300	+	0.543672i	0.0420287	+	0.0305356i	−0.566573	+	0.824012i	$0.691731\pi$
$318$	1.93925			0.108748
$319$	26.5622	+	14.1897i	1.48720	+	0.794470i
$320$		−	1.60984i		−	0.0899929i
$321$	9.59604	+	6.97193i	0.535599	+	0.389135i
$322$	−10.0981	+	6.97464i	−0.562743	+	0.388682i
$323$	0.807451	+	2.48508i	0.0449278	+	0.138273i
$324$	0.809017	−	0.587785i	0.0449454	−	0.0326547i
$325$	−2.86997	+	2.08516i	−0.159197	+	0.115664i
$326$	7.01447	−	2.27914i	0.388495	−	0.126230i
$327$	−5.44209	+	16.7490i	−0.300948	+	0.926224i
$328$	0.331993	−	0.456949i	0.0183312	−	0.0252308i
$329$	−8.36120	−	6.38511i	−0.460968	−	0.352023i
$330$	−2.33124	−	4.80342i	−0.128330	−	0.264420i
$331$	2.01259			0.110622			0.0553111	−	0.998469i	$-0.482385\pi$
$331$	2.01259			0.110622			0.0553111	+	0.998469i	$0.482385\pi$
$332$	11.4999	+	8.35514i	0.631137	+	0.458548i
$333$	−0.778315	+	2.39541i	−0.0426514	+	0.131268i
$334$	−12.0696	+	3.92165i	−0.660418	+	0.214583i
$335$	−9.67507	−	13.3166i	−0.528605	−	0.727563i
$336$	2.64500	+	0.0631409i	0.144296	+	0.00344462i
$337$	14.7827	−	4.80319i	0.805266	−	0.261647i	0.122674	−	0.992447i	$-0.460853\pi$
$337$	14.7827	−	4.80319i	0.805266	−	0.261647i	0.682591	+	0.730800i	$0.260853\pi$
$338$	10.3003	+	3.34678i	0.560264	+	0.182041i
$339$	−3.23609	+	4.45410i	−0.175760	+	0.241913i
$340$		−	0.616017i		−	0.0334082i
$341$	−26.4509	+	3.66501i	−1.43240	+	0.198471i
$342$			6.82848i			0.369242i
$343$	−9.78613	−	15.7236i	−0.528402	−	0.848995i
$344$	−0.666585	+	2.05154i	−0.0359399	+	0.110611i
$345$	2.30756	+	7.10194i	0.124235	+	0.382355i
$346$	3.35251	+	4.61434i	0.180232	+	0.248068i
$347$	18.0448	+	24.8366i	0.968698	+	1.33330i	0.942702	+	0.333637i	$0.108276\pi$
$347$	18.0448	+	24.8366i	0.968698	+	1.33330i	0.0259965	+	0.999662i	$0.491724\pi$
$348$	2.80586	+	8.63554i	0.150410	+	0.462914i
$349$	4.35316	−	13.3977i	0.233019	−	0.717160i	−0.764359	−	0.644791i	$-0.776944\pi$
$349$	4.35316	−	13.3977i	0.233019	−	0.717160i	0.997378	−	0.0723685i	$-0.0230558\pi$
$350$	−1.82389	−	6.10545i	−0.0974908	−	0.326350i
$351$		−	1.47296i		−	0.0786206i
$352$	−2.39025	+	2.29928i	−0.127401	+	0.122552i
$353$			6.97277i			0.371123i	0.982633	+	0.185562i	$0.0594104\pi$
$353$			6.97277i			0.371123i	−0.982633	+	0.185562i	$0.940590\pi$
$354$	−2.93375	+	4.03795i	−0.155927	+	0.214615i
$355$	−2.74463	−	0.891785i	−0.145670	−	0.0473310i
$356$	−6.84661	+	2.22460i	−0.362869	+	0.117903i
$357$	1.01213	+	0.0241613i	0.0535675	+	0.00127875i
$358$	3.37217	+	4.64139i	0.178225	+	0.245305i
$359$	−11.4983	+	3.73603i	−0.606859	+	0.197180i	−0.596297	−	0.802764i	$-0.703362\pi$
$359$	−11.4983	+	3.73603i	−0.606859	+	0.197180i	−0.0105616	+	0.999944i	$0.503362\pi$
$360$	0.497468	−	1.53105i	0.0262189	−	0.0806934i
$361$	−22.3516	−	16.2394i	−1.17640	−	0.854706i
$362$	−15.7852			−0.829651
$363$	−3.80238	+	10.3219i	−0.199573	+	0.541760i
$364$	2.36523	−	3.09724i	0.123972	−	0.162339i
$365$	−13.1396	+	18.0852i	−0.687760	+	0.946621i
$366$	1.12098	−	3.45002i	0.0585945	−	0.180335i
$367$	−15.9420	+	5.17987i	−0.832166	+	0.270387i	−0.693957	−	0.720016i	$-0.744134\pi$
$367$	−15.9420	+	5.17987i	−0.832166	+	0.270387i	−0.138208	+	0.990403i	$0.544134\pi$
$368$	3.75271	−	2.72650i	0.195623	−	0.142129i
$369$	0.456949	−	0.331993i	0.0237878	−	0.0172829i
$370$	1.25296	+	3.85623i	0.0651385	+	0.200476i
$371$	2.91587	+	4.22167i	0.151384	+	0.219178i
$372$	−6.51375	−	4.73252i	−0.337722	−	0.245370i
$373$		−	0.512448i		−	0.0265336i	−0.999912	−	0.0132668i	$-0.995777\pi$
$373$		−	0.512448i		−	0.0265336i	0.999912	−	0.0132668i	$-0.00422307\pi$
$374$	−0.914648	+	0.879835i	−0.0472953	+	0.0454952i
$375$	−11.9264			−0.615875
$376$	3.21693	+	2.33724i	0.165901	+	0.120534i
$377$	12.7198	+	4.13290i	0.655101	+	0.212855i
$378$	2.49603	+	0.877400i	0.128382	+	0.0451286i
$379$	−11.4691	+	8.33280i	−0.589129	+	0.428027i	−0.842004	−	0.539472i	$-0.818624\pi$
$379$	−11.4691	+	8.33280i	−0.589129	+	0.428027i	0.252875	+	0.967499i	$0.418624\pi$
$380$	6.46139	+	8.89334i	0.331462	+	0.456219i
$381$	−2.52387	−	7.76768i	−0.129302	−	0.397950i
$382$	11.4632	+	3.72462i	0.586509	+	0.190568i
$383$	−10.9236	+	15.0350i	−0.558169	+	0.768253i	−0.991092	−	0.133177i	$-0.957482\pi$
$383$	−10.9236	+	15.0350i	−0.558169	+	0.768253i	0.432924	+	0.901431i	$0.357482\pi$
$384$	−1.00000			−0.0510310
$385$	6.95159	−	12.2975i	0.354286	−	0.626737i
$386$	−7.46044			−0.379726
$387$	−1.26792	+	1.74514i	−0.0644520	+	0.0887106i
$388$	14.9818	+	4.86788i	0.760586	+	0.247129i
$389$	−6.64949	−	20.4650i	−0.337143	−	1.03762i	−0.965657	−	0.259821i	$-0.916337\pi$
$389$	−6.64949	−	20.4650i	−0.337143	−	1.03762i	0.628514	−	0.777798i	$-0.283663\pi$
$390$	−1.39377	−	1.91836i	−0.0705764	−	0.0971400i
$391$	1.43600	−	1.04332i	0.0726217	−	0.0527627i
$392$	3.83959	+	5.85300i	0.193928	+	0.295621i
$393$	−1.68712	−	0.548177i	−0.0851038	−	0.0276519i
$394$	−16.7430	−	12.1645i	−0.843502	−	0.612840i
$395$	0.370410			0.0186373
$396$	−2.98378	+	1.44811i	−0.149941	+	0.0727705i
$397$			3.07406i			0.154282i	0.997020	+	0.0771412i	$0.0245792\pi$
$397$			3.07406i			0.154282i	−0.997020	+	0.0771412i	$0.975421\pi$
$398$	10.3902	+	7.54889i	0.520812	+	0.378392i
$399$	−14.8653	+	10.2674i	−0.744198	+	0.514011i
$400$	0.744240	+	2.29053i	0.0372120	+	0.114527i
$401$	11.0736	−	8.04544i	0.552989	−	0.401770i	−0.275897	−	0.961187i	$-0.588975\pi$
$401$	11.0736	−	8.04544i	0.552989	−	0.401770i	0.828886	+	0.559417i	$0.188975\pi$
$402$	−8.27198	+	6.00995i	−0.412569	+	0.299749i
$403$	−11.2790	+	3.66476i	−0.561846	+	0.182555i
$404$	0.936288	−	2.88160i	0.0465821	−	0.143365i
$405$	0.946241	−	1.30239i	0.0470191	−	0.0647162i
$406$	−14.5803	+	19.0927i	−0.723610	+	0.947556i
$407$	3.93607	−	7.36808i	0.195104	−	0.365222i
$408$	−0.382657			−0.0189443
$409$	0.651083	+	0.473040i	0.0321940	+	0.0233903i	0.603766	−	0.797162i	$-0.293666\pi$
$409$	0.651083	+	0.473040i	0.0321940	+	0.0233903i	−0.571572	+	0.820552i	$0.693666\pi$
$410$	0.280980	−	0.864768i	0.0138766	−	0.0427079i
$411$	19.1289	−	6.21537i	0.943561	−	0.306581i
$412$	−3.70393	−	5.09802i	−0.182480	−	0.251162i
$413$	−13.2017	−	0.315148i	−0.649612	−	0.0155074i
$414$	4.41157	−	1.43341i	0.216817	−	0.0704481i
$415$	21.7633	+	7.07132i	1.06832	+	0.347118i
$416$	−0.865782	+	1.19165i	−0.0424484	+	0.0584253i
$417$		−	21.0921i		−	1.03289i
$418$	3.97605	−	22.2958i	0.194475	−	1.09052i
$419$			12.7131i			0.621075i	0.950561	+	0.310537i	$0.100509\pi$
$419$			12.7131i			0.621075i	−0.950561	+	0.310537i	$0.899491\pi$
$420$	4.08104	−	1.21913i	0.199134	−	0.0594875i
$421$	−0.0737747	+	0.227055i	−0.00359556	+	0.0110660i	−0.952838	−	0.303479i	$-0.901852\pi$
$421$	−0.0737747	+	0.227055i	−0.00359556	+	0.0110660i	0.949243	+	0.314545i	$0.101852\pi$
$422$	8.89406	+	27.3731i	0.432956	+	1.33250i
$423$	2.33724	+	3.21693i	0.113640	+	0.156413i
$424$	−1.13986	−	1.56888i	−0.0553565	−	0.0761917i
$425$	0.284789	+	0.876489i	0.0138143	+	0.0425160i
$426$	−0.553958	+	1.70491i	−0.0268394	+	0.0826031i
$427$	9.19608	−	2.74715i	0.445029	−	0.132944i
$428$		−	11.8614i		−	0.573341i
$429$	−0.857664	+	4.80937i	−0.0414084	+	0.232198i
$430$			3.47261i			0.167464i
$431$	13.5633	−	18.6682i	0.653319	−	0.899216i	−0.345918	−	0.938265i	$-0.612433\pi$
$431$	13.5633	−	18.6682i	0.653319	−	0.899216i	0.999237	+	0.0390482i	$0.0124326\pi$
$432$	−0.951057	−	0.309017i	−0.0457577	−	0.0148676i
$433$	−24.5426	+	7.97439i	−1.17944	+	0.383225i	−0.832160	−	0.554535i	$-0.812896\pi$
$433$	−24.5426	+	7.97439i	−1.17944	+	0.383225i	−0.347284	+	0.937760i	$0.612896\pi$
$434$	0.508375	−	21.2960i	0.0244028	−	1.02224i
$435$	8.59182	+	11.8256i	0.411946	+	0.566995i
$436$	16.7490	−	5.44209i	0.802133	−	0.260629i
$437$	−9.78799	+	30.1243i	−0.468223	+	1.44104i
$438$	11.2341	+	8.16207i	0.536787	+	0.389999i
$439$	−8.11843			−0.387472			−0.193736	−	0.981054i	$-0.562060\pi$
$439$	−8.11843			−0.387472			−0.193736	+	0.981054i	$0.562060\pi$
$440$	−2.51578	+	4.70939i	−0.119935	+	0.224511i
$441$	1.84299	+	6.75303i	0.0877613	+	0.321573i
$442$	−0.331298	+	0.455992i	−0.0157582	+	0.0216893i
$443$	−9.51730	+	29.2912i	−0.452181	+	1.39167i	0.422233	+	0.906487i	$0.361247\pi$
$443$	−9.51730	+	29.2912i	−0.452181	+	1.39167i	−0.874413	+	0.485182i	$0.838753\pi$
$444$	2.39541	−	0.778315i	0.113681	−	0.0369372i
$445$	−9.37583	+	6.81194i	−0.444457	+	0.322917i
$446$	−15.1840	+	11.0319i	−0.718985	+	0.522373i
$447$	−3.35148	−	10.3148i	−0.158519	−	0.487873i
$448$	−1.50361	−	2.17696i	−0.0710388	−	0.102852i
$449$	4.81142	+	3.49570i	0.227065	+	0.164972i	0.695501	−	0.718525i	$-0.255182\pi$
$449$	4.81142	+	3.49570i	0.227065	+	0.164972i	−0.468436	+	0.883497i	$0.655182\pi$
$450$			2.40841i			0.113534i
$451$	−1.68530	+	0.817925i	−0.0793577	+	0.0385146i
$452$	5.50557			0.258960
$453$	4.15773	+	3.02077i	0.195347	+	0.141928i
$454$	27.6000	+	8.96777i	1.29533	+	0.420878i
$455$	2.08051	−	5.91865i	0.0975359	−	0.277471i
$456$	5.52436	−	4.01368i	0.258702	−	0.187958i
$457$	−14.5934	−	20.0860i	−0.682649	−	0.939585i	0.317313	−	0.948321i	$-0.397219\pi$
$457$	−14.5934	−	20.0860i	−0.682649	−	0.939585i	−0.999962	+	0.00873553i	$0.997219\pi$
$458$	5.12936	+	15.7866i	0.239679	+	0.737658i
$459$	−0.363929	−	0.118248i	−0.0169867	−	0.00551932i
$460$	4.38924	−	6.04127i	0.204649	−	0.281676i
$461$	17.5615			0.817923			0.408961	−	0.912552i	$-0.365891\pi$
$461$	17.5615			0.817923			0.408961	+	0.912552i	$0.365891\pi$
$462$	−7.63893	−	4.31818i	−0.355395	−	0.200900i
$463$	35.0968			1.63109			0.815544	−	0.578695i	$-0.196438\pi$
$463$	35.0968			1.63109			0.815544	+	0.578695i	$0.196438\pi$
$464$	5.33706	−	7.34583i	0.247767	−	0.341022i
$465$	−12.3272	−	4.00534i	−0.571658	−	0.185743i
$466$	3.78940	+	11.6626i	0.175540	+	0.540258i
$467$	−1.24389	−	1.71206i	−0.0575603	−	0.0792249i	0.779266	−	0.626693i	$-0.215592\pi$
$467$	−1.24389	−	1.71206i	−0.0575603	−	0.0792249i	−0.836827	+	0.547468i	$0.815592\pi$
$468$	−1.19165	+	0.865782i	−0.0550839	+	0.0400208i
$469$	−25.5213	−	8.97118i	−1.17846	−	0.414251i
$470$	6.08799	+	1.97811i	0.280818	+	0.0912433i
$471$	−8.54472	−	6.20810i	−0.393720	−	0.286054i
$472$	4.99119			0.229738
$473$	5.15605	−	4.95981i	0.237076	−	0.228052i
$474$		−	0.230091i		−	0.0105684i
$475$	−13.3049	−	9.66659i	−0.610471	−	0.443533i
$476$	−0.575367	−	0.833030i	−0.0263719	−	0.0381819i
$477$	−0.599260	−	1.84433i	−0.0274382	−	0.0844462i
$478$	1.44949	−	1.05311i	0.0662980	−	0.0481683i
$479$	6.18347	−	4.49255i	0.282530	−	0.205270i	−0.437490	−	0.899223i	$-0.644133\pi$
$479$	6.18347	−	4.49255i	0.282530	−	0.205270i	0.720020	+	0.693953i	$0.244133\pi$
$480$	−1.53105	+	0.497468i	−0.0698826	+	0.0227062i
$481$	1.14642	−	3.52833i	0.0522724	−	0.160878i
$482$	−1.02362	+	1.40889i	−0.0466245	+	0.0641731i
$483$	9.75375	+	7.44854i	0.443811	+	0.338920i
$484$	10.5856	−	2.99088i	0.481163	−	0.135949i
$485$	25.3595			1.15152
$486$	−0.809017	−	0.587785i	−0.0366978	−	0.0266625i
$487$	5.88110	−	18.1002i	0.266498	−	0.820197i	−0.724846	−	0.688910i	$-0.758089\pi$
$487$	5.88110	−	18.1002i	0.266498	−	0.820197i	0.991345	−	0.131286i	$-0.0419107\pi$
$488$	−3.45002	+	1.12098i	−0.156175	+	0.0507444i
$489$	−4.33518	−	5.96686i	−0.196044	−	0.269831i
$490$	8.79028	+	7.05116i	0.397104	+	0.318539i
$491$	−39.5340	+	12.8454i	−1.78414	+	0.579703i	−0.999205	−	0.0398713i	$-0.987305\pi$
$491$	−39.5340	+	12.8454i	−1.78414	+	0.579703i	−0.784938	+	0.619574i	$0.787305\pi$
$492$	−0.537176	−	0.174539i	−0.0242178	−	0.00786883i
$493$	2.04226	−	2.81093i	0.0919789	−	0.126598i
$494$		−	10.0580i		−	0.452533i
$495$	−3.84793	+	3.70147i	−0.172952	+	0.166369i
$496$			8.05144i			0.361520i
$497$	−4.54446	+	1.35757i	−0.203847	+	0.0608953i
$498$	4.39256	−	13.5189i	0.196835	−	0.605796i
$499$	2.87770	+	8.85665i	0.128824	+	0.396478i	0.994578	−	0.103990i	$-0.0331611\pi$
$499$	2.87770	+	8.85665i	0.128824	+	0.396478i	−0.865755	+	0.500469i	$0.833161\pi$
$500$	7.01014	+	9.64863i	0.313503	+	0.431500i
$501$	7.45941	+	10.2670i	0.333262	+	0.458696i
$502$	7.77226	+	23.9205i	0.346893	+	1.06763i
$503$	11.8800	−	36.5628i	0.529702	−	1.63026i	−0.225123	−	0.974330i	$-0.572278\pi$
$503$	11.8800	−	36.5628i	0.529702	−	1.63026i	0.754825	−	0.655926i	$-0.227722\pi$
$504$	−0.757299	−	2.53505i	−0.0337328	−	0.112920i
$505$		−	4.87765i		−	0.217052i
$506$	−15.2389	+	2.11149i	−0.677453	+	0.0938671i
$507$		−	10.8304i		−	0.480995i
$508$	−4.80069	+	6.60758i	−0.212996	+	0.293164i
$509$	−30.3791	−	9.87075i	−1.34653	−	0.437513i	−0.455005	−	0.890489i	$-0.650363\pi$
$509$	−30.3791	−	9.87075i	−1.34653	−	0.437513i	−0.891523	+	0.452975i	$0.850363\pi$
$510$	−0.585867	+	0.190360i	−0.0259426	+	0.00842928i
$511$	−0.876783	+	36.7288i	−0.0387866	+	1.62479i
$512$	0.587785	+	0.809017i	0.0259767	+	0.0357538i
$513$	6.49427	−	2.11012i	0.286729	−	0.0931639i
$514$	−9.71170	+	29.8896i	−0.428365	+	1.31837i
$515$	−8.20701	−	5.96274i	−0.361644	−	0.262750i
$516$	2.15711			0.0949617
$517$	−5.75821	−	11.8646i	−0.253246	−	0.521803i
$518$	5.29612	+	4.04443i	0.232698	+	0.177702i
$519$	3.35251	−	4.61434i	0.147159	−	0.202547i
$520$	−0.732749	+	2.25517i	−0.0321332	+	0.0988957i
$521$	4.62717	−	1.50346i	0.202720	−	0.0658677i	−0.205897	−	0.978574i	$-0.566011\pi$
$521$	4.62717	−	1.50346i	0.202720	−	0.0658677i	0.408617	+	0.912706i	$0.366011\pi$
$522$	7.34583	−	5.33706i	0.321518	−	0.233597i
$523$	−26.7273	+	19.4185i	−1.16870	+	0.849113i	−0.990853	−	0.134944i	$-0.956915\pi$
$523$	−26.7273	+	19.4185i	−1.16870	+	0.849113i	−0.177851	+	0.984057i	$0.556915\pi$
$524$	0.548177	+	1.68712i	0.0239472	+	0.0737020i
$525$	−5.24302	+	3.62131i	−0.228824	+	0.158047i
$526$	19.0816	+	13.8636i	0.831998	+	0.604482i
$527$			3.08094i			0.134208i
$528$	2.92537	+	1.56275i	0.127311	+	0.0680100i
$529$	−1.48336			−0.0644939
$530$	−2.52565	−	1.83500i	−0.109707	−	0.0797071i
$531$	4.74690	+	1.54236i	0.205998	+	0.0669328i
$532$	17.0441	+	5.99131i	0.738955	+	0.259756i
$533$	−0.673066	+	0.489011i	−0.0291537	+	0.0211814i
$534$	4.23143	+	5.82407i	0.183112	+	0.252032i
$535$	−5.90065	−	18.1603i	−0.255107	−	0.785140i
$536$	9.72430	+	3.15962i	0.420026	+	0.136475i
$537$	3.37217	−	4.64139i	0.145520	−	0.200291i
$538$	24.1685			1.04198
$539$	−2.08545	−	23.1225i	−0.0898265	−	0.995957i
$540$	−1.60984			−0.0692766
$541$	9.76518	−	13.4406i	0.419838	−	0.577857i	−0.545745	−	0.837951i	$-0.683753\pi$
$541$	9.76518	−	13.4406i	0.419838	−	0.577857i	0.965583	+	0.260094i	$0.0837534\pi$
$542$	2.77930	+	0.903050i	0.119381	+	0.0387893i
$543$	4.87789	+	15.0126i	0.209330	+	0.644253i
$544$	0.224920	+	0.309576i	0.00964337	+	0.0132730i
$545$	22.9364	−	16.6642i	0.982485	−	0.713817i
$546$	−3.67654	−	1.29237i	−0.157342	−	0.0553084i
$547$	−4.04501	−	1.31430i	−0.172952	−	0.0561955i	0.221261	−	0.975215i	$-0.428983\pi$
$547$	−4.04501	−	1.31430i	−0.172952	−	0.0561955i	−0.394213	+	0.919019i	$0.628983\pi$
$548$	−16.2720	−	11.8223i	−0.695107	−	0.505025i
$549$	−3.62757			−0.154821
$550$	1.40236	−	7.86373i	0.0597966	−	0.335310i
$551$			62.0022i			2.64138i
$552$	−3.75271	−	2.72650i	−0.159726	−	0.116048i
$553$	0.500899	−	0.345967i	0.0213004	−	0.0147120i
$554$	−7.25873	−	22.3401i	−0.308394	−	0.949139i
$555$	3.28030	−	2.38328i	0.139241	−	0.101165i
$556$	−17.0639	+	12.3976i	−0.723670	+	0.525777i
$557$	8.12009	−	2.63838i	0.344059	−	0.111792i	−0.131890	−	0.991264i	$-0.542105\pi$
$557$	8.12009	−	2.63838i	0.344059	−	0.111792i	0.475949	+	0.879473i	$0.342105\pi$
$558$	−2.48803	+	7.65737i	−0.105327	+	0.324162i
$559$	1.86759	−	2.57052i	0.0789906	−	0.108721i
$560$	−3.38507	−	2.58504i	−0.143045	−	0.109238i
$561$	1.11941	+	0.597998i	0.0472617	+	0.0252475i
$562$	−21.4068			−0.902991
$563$	−3.54700	−	2.57704i	−0.149488	−	0.108609i	0.510527	−	0.859862i	$-0.329450\pi$
$563$	−3.54700	−	2.57704i	−0.149488	−	0.108609i	−0.660015	+	0.751252i	$0.729450\pi$
$564$	1.22876	−	3.78173i	0.0517401	−	0.159240i
$565$	8.42930	−	2.73885i	0.354623	−	0.115224i
$566$	−7.94061	−	10.9293i	−0.333769	−	0.459393i
$567$	0.0631409	−	2.64500i	0.00265167	−	0.111079i
$568$	1.70491	−	0.553958i	0.0715364	−	0.0232436i
$569$	−21.0878	−	6.85184i	−0.884046	−	0.287244i	−0.168410	−	0.985717i	$-0.553863\pi$
$569$	−21.0878	−	6.85184i	−0.884046	−	0.287244i	−0.715636	+	0.698473i	$0.753863\pi$
$570$	6.46139	−	8.89334i	0.270638	−	0.372501i
$571$		−	24.0111i		−	1.00483i	−0.864625	−	0.502417i	$-0.832444\pi$
$571$		−	24.0111i		−	1.00483i	0.864625	−	0.502417i	$-0.167556\pi$
$572$	4.39498	−	2.13301i	0.183763	−	0.0891856i
$573$		−	12.0531i		−	0.503527i
$574$	−0.427738	−	1.43185i	−0.0178534	−	0.0597643i
$575$	−3.45223	+	10.6249i	−0.143968	+	0.443088i
$576$	0.309017	+	0.951057i	0.0128757	+	0.0396274i
$577$	22.9791	+	31.6280i	0.956633	+	1.31669i	0.948517	+	0.316726i	$0.102583\pi$
$577$	22.9791	+	31.6280i	0.956633	+	1.31669i	0.00811598	+	0.999967i	$0.497417\pi$
$578$	−9.90628	−	13.6348i	−0.412047	−	0.567134i
$579$	2.30540	+	7.09530i	0.0958093	+	0.294871i
$580$	4.51699	−	13.9019i	0.187558	−	0.577243i
$581$	36.0348	−	10.7647i	1.49498	−	0.446595i
$582$		−	15.7528i		−	0.652974i
$583$	0.882744	+	6.37089i	0.0365595	+	0.263855i
$584$		−	13.8861i		−	0.574613i
$585$	−1.39377	+	1.91836i	−0.0576254	+	0.0793145i
$586$	7.76405	+	2.52269i	0.320730	+	0.104211i
$587$	−13.7839	+	4.47866i	−0.568923	+	0.184854i	−0.579332	−	0.815092i	$-0.696687\pi$
$587$	−13.7839	+	4.47866i	−0.568923	+	0.184854i	0.0104093	+	0.999946i	$0.496687\pi$
$588$	4.38003	−	5.46034i	0.180630	−	0.225181i
$589$	−32.3159	−	44.4790i	−1.33155	−	1.83273i
$590$	7.64176	−	2.48296i	0.314606	−	0.102222i
$591$	−6.39527	+	19.6826i	−0.263066	+	0.809635i
$592$	−2.03766	−	1.48044i	−0.0837471	−	0.0608458i
$593$	32.9078			1.35136			0.675680	−	0.737195i	$-0.263850\pi$
$593$	32.9078			1.35136			0.675680	+	0.737195i	$0.263850\pi$
$594$	2.29928	+	2.39025i	0.0943406	+	0.0980733i
$595$	−1.29532	−	0.989184i	−0.0531030	−	0.0405526i
$596$	−6.37489	+	8.77428i	−0.261126	+	0.359409i
$597$	3.96869	−	12.2144i	0.162428	−	0.499901i
$598$	−6.49805	+	2.11135i	−0.265725	+	0.0863393i
$599$	−2.33084	+	1.69345i	−0.0952355	+	0.0691927i	−0.634384	−	0.773018i	$-0.718746\pi$
$599$	−2.33084	+	1.69345i	−0.0952355	+	0.0691927i	0.539148	+	0.842211i	$0.318746\pi$
$600$	1.94844	−	1.41563i	0.0795449	−	0.0577928i
$601$	5.68536	+	17.4977i	0.231911	+	0.713747i	0.997516	+	0.0704372i	$0.0224394\pi$
$601$	5.68536	+	17.4977i	0.231911	+	0.713747i	−0.765606	+	0.643310i	$0.777561\pi$
$602$	3.24346	+	4.69595i	0.132193	+	0.191393i
$603$	8.27198	+	6.00995i	0.336861	+	0.244744i
$604$		−	5.13923i		−	0.209112i
$605$	14.7192	−	9.84518i	0.598421	−	0.400263i
$606$	−3.02989			−0.123081
$607$	−7.63053	−	5.54390i	−0.309714	−	0.225020i	0.422060	−	0.906568i	$-0.361307\pi$
$607$	−7.63053	−	5.54390i	−0.309714	−	0.225020i	−0.731774	+	0.681548i	$0.761307\pi$
$608$	−6.49427	−	2.11012i	−0.263377	−	0.0855765i
$609$	22.6638	+	7.96674i	0.918384	+	0.322829i
$610$	−4.72450	+	3.43255i	−0.191290	+	0.138980i
$611$	−3.44265	−	4.73840i	−0.139275	−	0.191695i
$612$	0.118248	+	0.363929i	0.00477987	+	0.0147109i
$613$	1.58617	+	0.515377i	0.0640647	+	0.0208159i	0.340874	−	0.940109i	$-0.389277\pi$
$613$	1.58617	+	0.515377i	0.0640647	+	0.0208159i	−0.276809	+	0.960925i	$0.589277\pi$
$614$	−10.7441	+	14.7880i	−0.433598	+	0.596796i
$615$	−0.909271			−0.0366654
$616$	0.996568	+	8.71819i	0.0401529	+	0.351266i
$617$	−25.6357			−1.03205			−0.516027	−	0.856572i	$-0.672590\pi$
$617$	−25.6357			−1.03205			−0.516027	+	0.856572i	$0.672590\pi$
$618$	−3.70393	+	5.09802i	−0.148994	+	0.205073i
$619$	−16.8041	−	5.46000i	−0.675415	−	0.219456i	−0.0488284	−	0.998807i	$-0.515549\pi$
$619$	−16.8041	−	5.46000i	−0.675415	−	0.219456i	−0.626587	+	0.779351i	$0.715549\pi$
$620$	4.00534	+	12.3272i	0.160858	+	0.495071i
$621$	−2.72650	−	3.75271i	−0.109411	−	0.150591i
$622$	9.62230	−	6.99101i	0.385819	−	0.280314i
$623$	−6.31635	+	17.9688i	−0.253059	+	0.719904i
$624$	1.40086	+	0.455168i	0.0560794	+	0.0182213i
$625$	5.79055	+	4.20708i	0.231622	+	0.168283i
$626$	−13.7157			−0.548189
$627$	−22.4332	+	3.10832i	−0.895895	+	0.124134i
$628$			10.5619i			0.421464i
$629$	−0.779723	−	0.566502i	−0.0310896	−	0.0225879i
$630$	−2.42057	−	3.50456i	−0.0964379	−	0.139625i
$631$	−4.85968	−	14.9566i	−0.193461	−	0.595411i	−0.999991	−	0.00421852i	$-0.998657\pi$
$631$	−4.85968	−	14.9566i	−0.193461	−	0.595411i	0.806530	−	0.591193i	$-0.201343\pi$
$632$	−0.186147	+	0.135244i	−0.00740455	+	0.00537972i
$633$	23.2849	−	16.9175i	0.925493	−	0.672410i
$634$	−0.879679	+	0.285825i	−0.0349365	+	0.0113516i
$635$	−4.06303	+	12.5047i	−0.161237	+	0.496235i
$636$	−1.13986	+	1.56888i	−0.0451984	+	0.0622103i
$637$	−2.71464	−	9.94691i	−0.107558	−	0.394111i
$638$	−27.0926	+	13.1488i	−1.07261	+	0.520566i
$639$	1.79265			0.0709160
$640$	1.30239	+	0.946241i	0.0514815	+	0.0374035i
$641$	−5.11727	+	15.7494i	−0.202120	+	0.622062i	0.797699	+	0.603056i	$0.206050\pi$
$641$	−5.11727	+	15.7494i	−0.202120	+	0.622062i	−0.999819	+	0.0190064i	$0.993950\pi$
$642$	−11.2808	+	3.66536i	−0.445219	+	0.144660i
$643$	−21.0022	−	28.9070i	−0.828244	−	1.13998i	−0.988247	−	0.152864i	$-0.951150\pi$
$643$	−21.0022	−	28.9070i	−0.828244	−	1.13998i	0.160003	−	0.987116i	$-0.448850\pi$
$644$	0.292885	−	12.2691i	0.0115413	−	0.483470i
$645$	3.30265	−	1.07310i	0.130042	−	0.0422531i
$646$	−2.48508	−	0.807451i	−0.0977741	−	0.0317687i
$647$	6.79705	−	9.35533i	0.267219	−	0.367796i	−0.654229	−	0.756296i	$-0.727007\pi$
$647$	6.79705	−	9.35533i	0.267219	−	0.367796i	0.921449	+	0.388500i	$0.127007\pi$
$648$			1.00000i			0.0392837i
$649$	−14.6011	−	7.79998i	−0.573143	−	0.306176i
$650$		−	3.54748i		−	0.139144i
$651$	−20.4108	+	6.09734i	−0.799964	+	0.238974i
$652$	−2.27914	+	7.01447i	−0.0892579	+	0.274708i
$653$	11.7177	+	36.0634i	0.458550	+	1.41127i	0.866916	+	0.498454i	$0.166099\pi$
$653$	11.7177	+	36.0634i	0.458550	+	1.41127i	−0.408366	+	0.912818i	$0.633901\pi$
$654$	−10.3515	−	14.2476i	−0.404775	−	0.557125i
$655$	1.67857	+	2.31036i	0.0655873	+	0.0902732i
$656$	0.174539	+	0.537176i	0.00681461	+	0.0209732i
$657$	4.29106	−	13.2065i	0.167410	−	0.515235i
$658$	10.0803	−	3.01128i	0.392969	−	0.117392i
$659$			19.2693i			0.750627i	0.926898	+	0.375313i	$0.122465\pi$
$659$			19.2693i			0.750627i	−0.926898	+	0.375313i	$0.877535\pi$
$660$	5.25631	+	0.937370i	0.204602	+	0.0364871i
$661$		−	39.9169i		−	1.55259i	−0.630371	−	0.776294i	$-0.717097\pi$
$661$		−	39.9169i		−	1.55259i	0.630371	−	0.776294i	$-0.282903\pi$
$662$	−1.18297	+	1.62822i	−0.0459776	+	0.0632827i
$663$	0.536051	+	0.174173i	0.0208185	+	0.00676433i
$664$	−13.5189	+	4.39256i	−0.524635	+	0.170464i
$665$	29.0759	+	0.694093i	1.12751	+	0.0269158i
$666$	−1.48044	−	2.03766i	−0.0573660	−	0.0789575i
$667$	40.0568	−	13.0153i	1.55101	−	0.503953i
$668$	3.92165	−	12.0696i	0.151733	−	0.466986i
$669$	15.1840	+	11.0319i	0.587049	+	0.426516i
$670$	16.4602			0.635913
$671$	11.8444	+	2.11224i	0.457248	+	0.0815421i
$672$	−1.60577	+	2.10273i	−0.0619440	+	0.0811148i
$673$	3.81017	−	5.24425i	0.146871	−	0.202151i	−0.729243	−	0.684255i	$-0.760127\pi$
$673$	3.81017	−	5.24425i	0.146871	−	0.202151i	0.876114	+	0.482104i	$0.160127\pi$
$674$	−4.80319	+	14.7827i	−0.185012	+	0.569409i
$675$	2.29053	−	0.744240i	0.0881627	−	0.0286458i
$676$	−8.76198	+	6.36595i	−0.336999	+	0.244844i
$677$	34.6602	−	25.1821i	1.33210	−	0.967828i	0.332406	−	0.943136i	$-0.392140\pi$
$677$	34.6602	−	25.1821i	1.33210	−	0.967828i	0.999695	−	0.0246914i	$-0.00786032\pi$
$678$	−1.70131	−	5.23611i	−0.0653386	−	0.201091i
$679$	34.2932	−	23.6860i	1.31605	−	0.908987i
$680$	0.498369	+	0.362086i	0.0191116	+	0.0138854i
$681$		−	29.0203i		−	1.11206i
$682$	12.5824	−	23.5535i	0.481805	−	0.901909i
$683$	6.46857			0.247513			0.123757	−	0.992313i	$-0.460506\pi$
$683$	6.46857			0.247513			0.123757	+	0.992313i	$0.460506\pi$
$684$	−5.52436	−	4.01368i	−0.211229	−	0.153467i
$685$	−30.7946	−	10.0058i	−1.17660	−	0.382300i
$686$	18.4728	+	1.32495i	0.705295	+	0.0505869i
$687$	13.4289	−	9.75663i	0.512343	−	0.372239i
$688$	−1.26792	−	1.74514i	−0.0483390	−	0.0665329i
$689$	0.882684	+	2.71662i	0.0336276	+	0.103495i
$690$	−7.10194	−	2.30756i	−0.270366	−	0.0878473i
$691$	−29.1222	+	40.0833i	−1.10786	+	1.52484i	−0.283334	+	0.959021i	$0.591440\pi$
$691$	−29.1222	+	40.0833i	−1.10786	+	1.52484i	−0.824529	+	0.565820i	$0.808560\pi$
$692$	−5.70363			−0.216820
$693$	−1.74628	+	8.59945i	−0.0663356	+	0.326666i
$694$	−30.6997			−1.16535
$695$	−19.9582	+	27.4702i	−0.757059	+	1.04200i
$696$	−8.63554	−	2.80586i	−0.327329	−	0.106356i
$697$	0.0667886	+	0.205554i	0.00252980	+	0.00778592i
$698$	8.28021	+	11.3967i	0.313410	+	0.431372i
$699$	9.92077	−	7.20786i	0.375238	−	0.272626i
$700$	6.01146	+	2.11314i	0.227212	+	0.0798691i
$701$	−18.5770	−	6.03605i	−0.701645	−	0.227978i	−0.0635980	−	0.997976i	$-0.520258\pi$
$701$	−18.5770	−	6.03605i	−0.701645	−	0.227978i	−0.638047	+	0.769997i	$0.720258\pi$
$702$	1.19165	+	0.865782i	0.0449758	+	0.0326768i
$703$	17.1988			0.648663
$704$	−0.455199	−	3.28524i	−0.0171560	−	0.123817i
$705$		−	6.40129i		−	0.241087i
$706$	−5.64109	−	4.09849i	−0.212305	−	0.154249i
$707$	−4.55577	−	6.59596i	−0.171337	−	0.248067i
$708$	−1.54236	−	4.74690i	−0.0579655	−	0.178399i
$709$	−38.4067	+	27.9041i	−1.44239	+	1.04796i	−0.454858	+	0.890564i	$0.650310\pi$
$709$	−38.4067	+	27.9041i	−1.44239	+	1.04796i	−0.987536	+	0.157396i	$0.949690\pi$
$710$	2.33472	−	1.69628i	0.0876206	−	0.0636601i
$711$	−0.218829	+	0.0711020i	−0.00820674	+	0.00266653i
$712$	2.22460	−	6.84661i	0.0833703	−	0.256587i
$713$	−21.9523	+	30.2147i	−0.822119	+	1.13155i
$714$	−0.614460	+	0.804626i	−0.0229956	+	0.0301124i
$715$	5.66783	−	5.45211i	0.211965	−	0.203897i
$716$	−5.73708			−0.214405
$717$	−1.44949	−	1.05311i	−0.0541321	−	0.0393292i
$718$	3.73603	−	11.4983i	0.139428	−	0.429114i
$719$	−5.40970	+	1.75772i	−0.201748	+	0.0655519i	−0.408148	−	0.912916i	$-0.633825\pi$
$719$	−5.40970	+	1.75772i	−0.201748	+	0.0655519i	0.206400	+	0.978468i	$0.433825\pi$
$720$	0.946241	+	1.30239i	0.0352643	+	0.0485372i
$721$	−16.6675	−	0.397882i	−0.620729	−	0.0148179i
$722$	26.2759	−	8.53756i	0.977888	−	0.317735i
$723$	1.65625	+	0.538148i	0.0615965	+	0.0200139i
$724$	9.27830	−	12.7705i	0.344825	−	0.474611i
$725$			21.8682i			0.812166i
$726$	−6.11562	−	9.14326i	−0.226972	−	0.339338i
$727$			8.06564i			0.299138i	0.988751	+	0.149569i	$0.0477886\pi$
$727$			8.06564i			0.299138i	−0.988751	+	0.149569i	$0.952211\pi$
$728$	1.11547	+	3.73402i	0.0413420	+	0.138392i
$729$	−0.309017	+	0.951057i	−0.0114451	+	0.0352243i
$730$	−6.90792	−	21.2604i	−0.255674	−	0.786882i
$731$	−0.485179	−	0.667791i	−0.0179450	−	0.0246991i
$732$	2.13223	+	2.93476i	0.0788095	+	0.108472i
$733$	7.16746	+	22.0592i	0.264736	+	0.814774i	0.991754	+	0.128156i	$0.0409057\pi$
$733$	7.16746	+	22.0592i	0.264736	+	0.814774i	−0.727018	+	0.686619i	$0.759094\pi$
$734$	5.17987	−	15.9420i	0.191192	−	0.588430i
$735$	3.98971	−	10.5390i	0.147163	−	0.388736i
$736$			4.63860i			0.170981i
$737$	−23.5095	−	24.4397i	−0.865984	−	0.900249i
$738$			0.564820i			0.0207913i
$739$	3.75934	−	5.17428i	0.138289	−	0.190339i	−0.734255	−	0.678874i	$-0.762468\pi$
$739$	3.75934	−	5.17428i	0.138289	−	0.190339i	0.872545	+	0.488535i	$0.162468\pi$
$740$	−3.85623	−	1.25296i	−0.141758	−	0.0460599i
$741$	−9.56577	+	3.10811i	−0.351407	+	0.114179i
$742$	−5.12930	−	0.122446i	−0.188303	−	0.00449512i
$743$	4.39387	+	6.04764i	0.161195	+	0.221867i	0.881973	−	0.471300i	$-0.156215\pi$
$743$	4.39387	+	6.04764i	0.161195	+	0.221867i	−0.720778	+	0.693166i	$0.756215\pi$
$744$	7.65737	−	2.48803i	0.280733	−	0.0912157i
$745$	−5.39535	+	16.6052i	−0.197670	+	0.608366i
$746$	0.414579	+	0.301210i	0.0151788	+	0.0110281i
$747$	−14.2146			−0.520086
$748$	−0.174185	−	1.25712i	−0.00636884	−	0.0459649i
$749$	−24.9413	−	19.0467i	−0.911335	−	0.695950i
$750$	7.01014	−	9.64863i	0.255974	−	0.352318i
$751$	−7.76066	+	23.8848i	−0.283190	+	0.871570i	0.703745	+	0.710453i	$0.251510\pi$
$751$	−7.76066	+	23.8848i	−0.283190	+	0.871570i	−0.986935	+	0.161118i	$0.948490\pi$
$752$	−3.78173	+	1.22876i	−0.137906	+	0.0448082i
$753$	20.3480	−	14.7837i	0.741524	−	0.538748i
$754$	−10.8201	+	7.86125i	−0.394044	+	0.286290i
$755$	−2.55661	−	7.86843i	−0.0930444	−	0.286361i
$756$	−2.17696	+	1.50361i	−0.0791753	+	0.0546857i
$757$	−22.9908	−	16.7038i	−0.835614	−	0.607109i	0.0855282	−	0.996336i	$-0.472742\pi$
$757$	−22.9908	−	16.7038i	−0.835614	−	0.607109i	−0.921142	+	0.389227i	$0.872742\pi$
$758$		−	14.1766i		−	0.514918i
$759$	6.71723	+	13.8406i	0.243820	+	0.502382i
$760$	−10.9928			−0.398750
$761$	28.8381	+	20.9521i	1.04538	+	0.759513i	0.971329	−	0.237741i	$-0.0764070\pi$
$761$	28.8381	+	20.9521i	1.04538	+	0.759513i	0.0740516	+	0.997254i	$0.476407\pi$
$762$	7.76768	+	2.52387i	0.281393	+	0.0914302i
$763$	15.4519	−	43.9576i	0.559395	−	1.59137i
$764$	−9.75119	+	7.08466i	−0.352786	+	0.256314i
$765$	0.362086	+	0.498369i	0.0130912	+	0.0180186i
$766$	−5.74286	−	17.6747i	−0.207498	−	0.638614i
$767$	−6.99197	−	2.27183i	−0.252466	−	0.0820310i
$768$	0.587785	−	0.809017i	0.0212099	−	0.0291929i
$769$	40.5911			1.46375			0.731876	−	0.681438i	$-0.238645\pi$
$769$	40.5911			1.46375			0.731876	+	0.681438i	$0.238645\pi$
$770$	5.86282	+	12.8522i	0.211281	+	0.463162i
$771$	31.4277			1.13184
$772$	4.38514	−	6.03562i	0.157825	−	0.217227i
$773$	−27.2708	−	8.86083i	−0.980864	−	0.318702i	−0.225670	−	0.974204i	$-0.572457\pi$
$773$	−27.2708	−	8.86083i	−0.980864	−	0.318702i	−0.755193	+	0.655502i	$0.772457\pi$
$774$	−0.666585	−	2.05154i	−0.0239599	−	0.0737410i
$775$	−11.3978	−	15.6878i	−0.409423	−	0.563522i
$776$	−12.7443	+	9.25926i	−0.457493	+	0.332388i
$777$	2.20989	−	6.28670i	0.0792793	−	0.225534i
$778$	20.4650	+	6.64949i	0.733707	+	0.238396i
$779$	−3.12027	−	2.26701i	−0.111795	−	0.0812240i
$780$	2.37123			0.0849035
$781$	−5.85319	−	1.04381i	−0.209444	−	0.0373505i
$782$			1.77499i			0.0634737i
$783$	−7.34583	−	5.33706i	−0.262519	−	0.190731i
$784$	−6.99203	−	0.334015i	−0.249715	−	0.0119291i
$785$	5.25419	+	16.1707i	0.187530	+	0.577158i
$786$	1.43515	−	1.04270i	0.0511900	−	0.0371917i
$787$	−21.2227	+	15.4192i	−0.756509	+	0.549636i	−0.897838	−	0.440327i	$-0.854863\pi$
$787$	−21.2227	+	15.4192i	−0.756509	+	0.549636i	0.141329	+	0.989963i	$0.454863\pi$
$788$	19.6826	−	6.39527i	0.701165	−	0.227822i
$789$	7.28853	−	22.4318i	0.259479	−	0.798593i
$790$	−0.217721	+	0.299668i	−0.00774618	+	0.0106617i
$791$	8.84069	−	11.5767i	0.314339	−	0.411622i
$792$	0.582274	−	3.26511i	0.0206902	−	0.116021i
$793$	5.34324			0.189744
$794$	−2.48696	−	1.80689i	−0.0882590	−	0.0641240i
$795$	−0.964714	+	2.96908i	−0.0342149	+	0.105303i
$796$	−12.2144	+	3.96869i	−0.432927	+	0.140666i
$797$	−8.36127	−	11.5083i	−0.296171	−	0.407645i	0.634835	−	0.772648i	$-0.281068\pi$
$797$	−8.36127	−	11.5083i	−0.296171	−	0.407645i	−0.931006	+	0.365003i	$0.881068\pi$
$798$	0.431156	−	18.0613i	0.0152628	−	0.639364i
$799$	−1.44711	+	0.470193i	−0.0511949	+	0.0166342i
$800$	−2.29053	−	0.744240i	−0.0809826	−	0.0263128i
$801$	4.23143	−	5.82407i	0.149510	−	0.205783i
$802$			13.6877i			0.483330i
$803$	−21.7006	+	40.6222i	−0.765797	+	1.43353i
$804$		−	10.2247i		−	0.360599i
$805$	−5.65507	−	18.9303i	−0.199315	−	0.667206i
$806$	3.66476	−	11.2790i	0.129086	−	0.397285i
$807$	−7.46847	−	22.9856i	−0.262903	−	0.809131i
$808$	1.78093	+	2.45123i	0.0626527	+	0.0862341i
$809$	−14.0388	−	19.3227i	−0.493578	−	0.679351i	0.487465	−	0.873142i	$-0.337922\pi$
$809$	−14.0388	−	19.3227i	−0.493578	−	0.679351i	−0.981043	+	0.193791i	$0.937922\pi$
$810$	0.497468	+	1.53105i	0.0174793	+	0.0537956i
$811$	16.6431	−	51.2221i	0.584418	−	1.79865i	−0.0171794	−	0.999852i	$-0.505469\pi$
$811$	16.6431	−	51.2221i	0.584418	−	1.79865i	0.601597	−	0.798800i	$-0.294531\pi$
$812$	−6.87623	−	23.0182i	−0.241308	−	0.807779i
$813$		−	2.92233i		−	0.102491i
$814$	3.64734	+	7.51520i	0.127839	+	0.263408i
$815$			11.8733i			0.415904i
$816$	0.224920	−	0.309576i	0.00787378	−	0.0108373i
$817$	14.0089	+	4.55176i	0.490109	+	0.159246i
$818$	−0.765394	+	0.248692i	−0.0267614	+	0.00869530i
$819$	−0.0930037	+	3.89596i	−0.00324981	+	0.136136i
$820$	0.534456	+	0.735616i	0.0186640	+	0.0256888i
$821$	−9.21508	+	2.99416i	−0.321608	+	0.104497i	−0.465372	−	0.885115i	$-0.654079\pi$
$821$	−9.21508	+	2.99416i	−0.321608	+	0.104497i	0.143764	+	0.989612i	$0.454079\pi$
$822$	−6.21537	+	19.1289i	−0.216786	+	0.667198i
$823$	1.62660	+	1.18179i	0.0566997	+	0.0411947i	0.615774	−	0.787923i	$-0.288843\pi$
$823$	1.62660	+	1.18179i	0.0566997	+	0.0411947i	−0.559074	+	0.829117i	$0.688843\pi$
$824$	6.30150			0.219523
$825$	−7.91220	+	1.09631i	−0.275467	+	0.0381685i
$826$	8.01471	−	10.4951i	0.278867	−	0.365173i
$827$	−8.19593	+	11.2807i	−0.285001	+	0.392270i	−0.927382	−	0.374115i	$-0.877946\pi$
$827$	−8.19593	+	11.2807i	−0.285001	+	0.392270i	0.642382	+	0.766385i	$0.277946\pi$
$828$	−1.43341	+	4.41157i	−0.0498143	+	0.153313i
$829$	1.93357	−	0.628256i	0.0671558	−	0.0218202i	−0.275246	−	0.961374i	$-0.588759\pi$
$829$	1.93357	−	0.628256i	0.0671558	−	0.0218202i	0.342402	+	0.939553i	$0.388759\pi$
$830$	−18.5130	+	13.4505i	−0.642594	+	0.466872i
$831$	−19.0036	+	13.8069i	−0.659228	+	0.478957i
$832$	−0.455168	−	1.40086i	−0.0157801	−	0.0485662i
$833$	−2.67555	−	0.127813i	−0.0927023	−	0.00442846i
$834$	17.0639	+	12.3976i	0.590874	+	0.429295i
$835$		−	20.4300i		−	0.707011i
$836$	15.7006	+	16.3218i	0.543016	+	0.564501i
$837$	8.05144			0.278298
$838$	−10.2851	−	7.47257i	−0.355293	−	0.258135i
$839$	37.1248	+	12.0626i	1.28169	+	0.416446i	0.869175	−	0.494505i	$-0.164651\pi$
$839$	37.1248	+	12.0626i	1.28169	+	0.416446i	0.412515	+	0.910951i	$0.364651\pi$
$840$	−1.41247	+	4.01821i	−0.0487350	+	0.138642i
$841$	43.2382	−	31.4144i	1.49097	−	1.08326i
$842$	−0.140328	−	0.193145i	−0.00483601	−	0.00665620i
$843$	6.61506	+	20.3591i	0.227835	+	0.701204i
$844$	−27.3731	−	8.89406i	−0.942221	−	0.306146i
$845$	−10.2482	+	14.1054i	−0.352548	+	0.485240i
$846$	−3.97635			−0.136710
$847$	10.7090	−	27.0614i	0.367967	−	0.929839i
$848$	1.93925			0.0665940
$849$	−7.94061	+	10.9293i	−0.272521	+	0.375093i
$850$	−0.876489	−	0.284789i	−0.0300633	−	0.00976817i
$851$	−3.61029	−	11.1113i	−0.123759	−	0.380892i
$852$	−1.05369	−	1.45028i	−0.0360989	−	0.0496858i
$853$	−2.34963	+	1.70711i	−0.0804499	+	0.0584503i	−0.627283	−	0.778791i	$-0.715833\pi$
$853$	−2.34963	+	1.70711i	−0.0804499	+	0.0584503i	0.546833	+	0.837241i	$0.315833\pi$
$854$	−3.18283	+	9.05452i	−0.108914	+	0.309839i
$855$	−10.4547	−	3.39695i	−0.357545	−	0.116173i
$856$	9.59604	+	6.97193i	0.327986	+	0.238296i
$857$	34.9241			1.19298			0.596492	−	0.802619i	$-0.296561\pi$
$857$	34.9241			1.19298			0.596492	+	0.802619i	$0.296561\pi$
$858$	−3.38674	−	3.52074i	−0.115621	−	0.120196i
$859$			45.1388i			1.54011i	0.637975	+	0.770057i	$0.279772\pi$
$859$			45.1388i			1.54011i	−0.637975	+	0.770057i	$0.720228\pi$
$860$	−2.80940	−	2.04115i	−0.0957998	−	0.0696027i
$861$	−1.22959	+	0.849269i	−0.0419044	+	0.0289430i
$862$	7.13062	+	21.9458i	0.242870	+	0.747477i
$863$	15.6354	−	11.3598i	0.532235	−	0.386692i	−0.288958	−	0.957342i	$-0.593309\pi$
$863$	15.6354	−	11.3598i	0.532235	−	0.386692i	0.821193	+	0.570650i	$0.193309\pi$
$864$	0.809017	−	0.587785i	0.0275233	−	0.0199969i
$865$	−8.73255	+	2.83738i	−0.296916	+	0.0964738i
$866$	7.97439	−	24.5426i	0.270981	−	0.833993i
$867$	−9.90628	+	13.6348i	−0.336435	+	0.463063i
$868$	16.9300	+	12.9288i	0.574643	+	0.438831i
$869$	0.755903	−	0.104737i	0.0256423	−	0.00355297i
$870$	−14.6173			−0.495572
$871$	−12.1843	−	8.85239i	−0.412848	−	0.299952i
$872$	−5.44209	+	16.7490i	−0.184293	+	0.567194i
$873$	−14.9818	+	4.86788i	−0.507057	+	0.164753i
$874$	−18.6179	−	25.6253i	−0.629759	−	0.866789i
$875$	31.5452	+	0.753041i	1.06642	+	0.0254574i
$876$	−13.2065	+	4.29106i	−0.446207	+	0.144981i
$877$	42.7279	+	13.8831i	1.44282	+	0.468801i	0.922775	−	0.385338i	$-0.125915\pi$
$877$	42.7279	+	13.8831i	1.44282	+	0.468801i	0.520045	+	0.854139i	$0.325915\pi$
$878$	4.77189	−	6.56795i	0.161044	−	0.221658i
$879$		−	8.16360i		−	0.275351i
$880$	−2.33124	−	4.80342i	−0.0785859	−	0.161923i
$881$			15.4334i			0.519966i	0.965613	+	0.259983i	$0.0837170\pi$
$881$			15.4334i			0.519966i	−0.965613	+	0.259983i	$0.916283\pi$
$882$	−6.54660	−	2.47832i	−0.220435	−	0.0834494i
$883$	4.47946	−	13.7864i	0.150746	−	0.463948i	−0.846959	−	0.531658i	$-0.821569\pi$
$883$	4.47946	−	13.7864i	0.150746	−	0.463948i	0.997705	+	0.0677097i	$0.0215692\pi$
$884$	−0.174173	−	0.536051i	−0.00585809	−	0.0180293i
$885$	−4.72287	−	6.50047i	−0.158757	−	0.218511i
$886$	−18.1030	−	24.9166i	−0.608182	−	0.837090i
$887$	7.65159	+	23.5492i	0.256915	+	0.790704i	0.993446	+	0.114300i	$0.0364625\pi$
$887$	7.65159	+	23.5492i	0.256915	+	0.790704i	−0.736531	+	0.676404i	$0.763538\pi$
$888$	−0.778315	+	2.39541i	−0.0261185	+	0.0803846i
$889$	6.18518	+	20.7048i	0.207444	+	0.694418i
$890$		−	11.5892i		−	0.388470i
$891$	1.56275	−	2.92537i	0.0523541	−	0.0980037i
$892$		−	18.7685i		−	0.628416i
$893$	15.9598	−	21.9668i	0.534074	−	0.735090i
$894$	10.3148	+	3.35148i	0.344978	+	0.112090i
$895$	−8.78376	+	2.85402i	−0.293609	+	0.0953992i
$896$	2.64500	+	0.0631409i	0.0883632	+	0.00210939i
$897$	4.01602	+	5.52757i	0.134091	+	0.184560i
$898$	−5.65617	+	1.83780i	−0.188749	+	0.0613282i
$899$	−22.5912	+	69.5285i	−0.753458	+	2.31891i
$900$	−1.94844	−	1.41563i	−0.0649481	−	0.0471876i
$901$	0.742067			0.0247218
$902$	0.328880	−	1.84420i	0.0109505	−	0.0614052i
$903$	3.46384	−	4.53584i	0.115269	−	0.150943i
$904$	−3.23609	+	4.45410i	−0.107631	+	0.148141i
$905$	7.85263	−	24.1679i	0.261030	−	0.803369i
$906$	−4.88770	+	1.58811i	−0.162383	+	0.0527614i
$907$	−42.3642	+	30.7794i	−1.40668	+	1.02201i	−0.412887	+	0.910782i	$0.635480\pi$
$907$	−42.3642	+	30.7794i	−1.40668	+	1.02201i	−0.993794	+	0.111232i	$0.964520\pi$
$908$	−23.4779	+	17.0577i	−0.779143	+	0.566080i
$909$	0.936288	+	2.88160i	0.0310547	+	0.0955766i
$910$	3.56540	+	5.16207i	0.118192	+	0.171121i
$911$	41.9107	+	30.4499i	1.38856	+	1.00885i	0.996021	+	0.0891175i	$0.0284047\pi$
$911$	41.9107	+	30.4499i	1.38856	+	1.00885i	0.392543	+	0.919734i	$0.371595\pi$
$912$			6.82848i			0.226114i
$913$	46.4123	+	8.27681i	1.53602	+	0.273922i
$914$	24.8277			0.821228
$915$	4.72450	+	3.43255i	0.156187	+	0.113477i
$916$	−15.7866	−	5.12936i	−0.521603	−	0.169479i
$917$	4.42781	+	1.55645i	0.146219	+	0.0513986i
$918$	0.309576	−	0.224920i	0.0102175	−	0.00742347i
$919$	29.9453	+	41.2162i	0.987804	+	1.35960i	0.932517	+	0.361125i	$0.117607\pi$
$919$	29.9453	+	41.2162i	0.987804	+	1.35960i	0.0552866	+	0.998471i	$0.482393\pi$
$920$	2.30756	+	7.10194i	0.0760780	+	0.234144i
$921$	17.3844	+	5.64852i	0.572834	+	0.186125i
$922$	−10.3224	+	14.2076i	−0.339951	+	0.467902i
$923$	−2.64049			−0.0869128
$924$	7.98354	−	3.64186i	0.262639	−	0.119808i
$925$	6.06601			0.199449
$926$	−20.6294	+	28.3939i	−0.677924	+	0.933083i
$927$	5.99309	+	1.94727i	0.196839	+	0.0639568i
$928$	2.80586	+	8.63554i	0.0921068	+	0.283476i
$929$	−20.9338	−	28.8129i	−0.686816	−	0.945321i	0.313175	−	0.949696i	$-0.398607\pi$
$929$	−20.9338	−	28.8129i	−0.686816	−	0.945321i	−0.999990	+	0.00437483i	$0.998607\pi$
$930$	10.4861	−	7.61860i	0.343853	−	0.249824i
$931$	39.9671	−	26.2185i	1.30987	−	0.859278i
$932$	−11.6626	−	3.78940i	−0.382020	−	0.124126i
$933$	−9.62230	−	6.99101i	−0.315020	−	0.228875i
$934$	2.11623			0.0692451
$935$	−0.892064	−	1.83806i	−0.0291736	−	0.0601111i
$936$		−	1.47296i		−	0.0481451i
$937$	24.1699	+	17.5605i	0.789597	+	0.573676i	0.907844	−	0.419309i	$-0.137727\pi$
$937$	24.1699	+	17.5605i	0.789597	+	0.573676i	−0.118247	+	0.992984i	$0.537727\pi$
$938$	22.2589	−	15.3740i	0.726777	−	0.501979i
$939$	4.23838	+	13.0444i	0.138314	+	0.425688i
$940$	−5.17875	+	3.76258i	−0.168912	+	0.122722i
$941$	13.7733	−	10.0069i	0.448996	−	0.326215i	−0.340203	−	0.940352i	$-0.610496\pi$
$941$	13.7733	−	10.0069i	0.448996	−	0.326215i	0.789199	+	0.614137i	$0.210496\pi$
$942$	10.0449	−	3.26379i	0.327281	−	0.106340i
$943$	−0.809617	+	2.49175i	−0.0263648	+	0.0811424i
$944$	−2.93375	+	4.03795i	−0.0954853	+	0.131424i
$945$	−2.58504	+	3.38507i	−0.0840914	+	0.110116i
$946$	0.981917	+	7.08664i	0.0319249	+	0.230406i
$947$	41.7442			1.35650			0.678252	−	0.734830i	$-0.262738\pi$
$947$	41.7442			1.35650			0.678252	+	0.734830i	$0.262738\pi$
$948$	0.186147	+	0.135244i	0.00604579	+	0.00439252i
$949$	−6.32053	+	19.4526i	−0.205173	+	0.631458i
$950$	15.6409	−	5.08202i	0.507457	−	0.164883i
$951$	0.543672	+	0.748300i	0.0176298	+	0.0242653i
$952$	1.01213	+	0.0241613i	0.0328032	+	0.000783072i
$953$	−8.01483	+	2.60418i	−0.259626	+	0.0843576i	−0.435938	−	0.899977i	$-0.643583\pi$
$953$	−8.01483	+	2.60418i	−0.259626	+	0.0843576i	0.176312	+	0.984334i	$0.443583\pi$
$954$	1.84433	+	0.599260i	0.0597125	+	0.0194018i
$955$	−11.4052	+	15.6979i	−0.369063	+	0.507971i
$956$			1.79166i			0.0579465i
$957$	20.8773	+	21.7034i	0.674868	+	0.701571i
$958$			7.64319i			0.246940i
$959$	−50.9884	+	15.2318i	−1.64650	+	0.491861i
$960$	0.497468	−	1.53105i	0.0160557	−	0.0494144i
$961$	−10.4527	−	32.1701i	−0.337184	−	1.03775i
$962$	2.18063	+	3.00138i	0.0703062	+	0.0967682i
$963$	6.97193	+	9.59604i	0.224667	+	0.309228i
$964$	−0.538148	−	1.65625i	−0.0173326	−	0.0533442i
$965$	3.71133	−	11.4223i	0.119472	−	0.367697i
$966$	−11.7591	+	3.51281i	−0.378343	+	0.113023i
$967$			34.7753i			1.11830i	0.829067	+	0.559150i	$0.188872\pi$
$967$			34.7753i			1.11830i	−0.829067	+	0.559150i	$0.811128\pi$
$968$	−3.80238	+	10.3219i	−0.122213	+	0.331759i
$969$			2.61297i			0.0839406i
$970$	−14.9059	+	20.5163i	−0.478601	+	0.658738i
$971$	−27.4564	−	8.92112i	−0.881117	−	0.286292i	−0.166696	−	0.986008i	$-0.553310\pi$
$971$	−27.4564	−	8.92112i	−0.881117	−	0.286292i	−0.714421	+	0.699716i	$0.753310\pi$
$972$	0.951057	−	0.309017i	0.0305052	−	0.00991172i
$973$	−1.33178	+	55.7886i	−0.0426948	+	1.78850i
$974$	11.1865	+	15.3969i	0.358439	+	0.493349i
$975$	−3.37385	+	1.09623i	−0.108050	+	0.0351075i
$976$	1.12098	−	3.45002i	0.0358817	−	0.110432i
$977$	26.1654	+	19.0103i	0.837106	+	0.608193i	0.921561	−	0.388234i	$-0.126915\pi$
$977$	26.1654	+	19.0103i	0.837106	+	0.608193i	−0.0844545	+	0.996427i	$0.526915\pi$
$978$	7.37545			0.235841
$979$	−17.2073	+	16.5524i	−0.549948	+	0.529017i
$980$	−10.8713	+	2.96692i	−0.347271	+	0.0947747i
$981$	−10.3515	+	14.2476i	−0.330497	+	0.454890i
$982$	12.8454	−	39.5340i	0.409912	−	1.26158i
$983$	−13.5171	+	4.39197i	−0.431128	+	0.140082i	−0.516539	−	0.856264i	$-0.672780\pi$
$983$	−13.5171	+	4.39197i	−0.431128	+	0.140082i	0.0854108	+	0.996346i	$0.472780\pi$
$984$	0.456949	−	0.331993i	0.0145670	−	0.0105836i
$985$	26.9537	−	19.5830i	0.858815	−	0.623965i
$986$	1.07368	+	3.30445i	0.0341930	+	0.105235i
$987$	−5.97887	−	8.65635i	−0.190310	−	0.275535i
$988$	8.13713	+	5.91197i	0.258877	+	0.188085i
$989$		−	10.0060i		−	0.318172i
$990$	−0.732799	−	5.28871i	−0.0232899	−	0.168086i
$991$	44.4857			1.41314			0.706568	−	0.707645i	$-0.250243\pi$
$991$	44.4857			1.41314			0.706568	+	0.707645i	$0.250243\pi$
$992$	−6.51375	−	4.73252i	−0.206812	−	0.150258i
$993$	1.91409	+	0.621926i	0.0607418	+	0.0197362i
$994$	1.57287	−	4.47450i	0.0498883	−	0.141923i
$995$	−16.7265	+	12.1525i	−0.530266	+	0.385261i
$996$	8.35514	+	11.4999i	0.264743	+	0.364387i
$997$	5.43481	+	16.7266i	0.172122	+	0.529738i	0.999490	−	0.0319224i	$-0.0101629\pi$
$997$	5.43481	+	16.7266i	0.172122	+	0.529738i	−0.827368	+	0.561660i	$0.810163\pi$
$998$	−8.85665	−	2.87770i	−0.280352	−	0.0910920i
$999$	−1.48044	+	2.03766i	−0.0468391	+	0.0644686i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.u.b.139.2	yes	32
7.6	odd	2		462.2.u.a.139.3	✓	32
11.8	odd	10		462.2.u.a.349.3	yes	32
77.41	even	10	inner	462.2.u.b.349.2	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.u.a.139.3	✓	32	7.6	odd	2
462.2.u.a.349.3	yes	32	11.8	odd	10
462.2.u.b.139.2	yes	32	1.1	even	1	trivial
462.2.u.b.349.2	yes	32	77.41	even	10	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.u (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.587785 + 0.809017i) q^{2} +(0.951057 + 0.309017i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-0.946241 - 1.30239i) q^{5} +(-0.809017 + 0.587785i) q^{6} +(-2.49603 - 0.877400i) q^{7} +(0.951057 + 0.309017i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.587785 + 0.809017i) q^{2} +(0.951057 + 0.309017i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-0.946241 - 1.30239i) q^{5} +(-0.809017 + 0.587785i) q^{6} +(-2.49603 - 0.877400i) q^{7} +(0.951057 + 0.309017i) q^{8} +(0.809017 + 0.587785i) q^{9} +1.60984 q^{10} +(-2.29928 - 2.39025i) q^{11} -1.00000i q^{12} +(-1.19165 - 0.865782i) q^{13} +(2.17696 - 1.50361i) q^{14} +(-0.497468 - 1.53105i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-0.309576 + 0.224920i) q^{17} +(-0.951057 + 0.309017i) q^{18} +(2.11012 - 6.49427i) q^{19} +(-0.946241 + 1.30239i) q^{20} +(-2.10273 - 1.60577i) q^{21} +(3.28524 - 0.455199i) q^{22} -4.63860 q^{23} +(0.809017 + 0.587785i) q^{24} +(0.744240 - 2.29053i) q^{25} +(1.40086 - 0.455168i) q^{26} +(0.587785 + 0.809017i) q^{27} +(-0.0631409 + 2.64500i) q^{28} +(-8.63554 + 2.80586i) q^{29} +(1.53105 + 0.497468i) q^{30} +(4.73252 - 6.51375i) q^{31} -1.00000i q^{32} +(-1.44811 - 2.98378i) q^{33} -0.382657i q^{34} +(1.21913 + 4.08104i) q^{35} +(0.309017 - 0.951057i) q^{36} +(0.778315 + 2.39541i) q^{37} +(4.01368 + 5.52436i) q^{38} +(-0.865782 - 1.19165i) q^{39} +(-0.497468 - 1.53105i) q^{40} +(0.174539 - 0.537176i) q^{41} +(2.53505 - 0.757299i) q^{42} +2.15711i q^{43} +(-1.56275 + 2.92537i) q^{44} -1.60984i q^{45} +(2.72650 - 3.75271i) q^{46} +(3.78173 + 1.22876i) q^{47} +(-0.951057 + 0.309017i) q^{48} +(5.46034 + 4.38003i) q^{49} +(1.41563 + 1.94844i) q^{50} +(-0.363929 + 0.118248i) q^{51} +(-0.455168 + 1.40086i) q^{52} +(-1.56888 - 1.13986i) q^{53} -1.00000 q^{54} +(-0.937370 + 5.25631i) q^{55} +(-2.10273 - 1.60577i) q^{56} +(4.01368 - 5.52436i) q^{57} +(2.80586 - 8.63554i) q^{58} +(4.74690 - 1.54236i) q^{59} +(-1.30239 + 0.946241i) q^{60} +(-2.93476 + 2.13223i) q^{61} +(2.48803 + 7.65737i) q^{62} +(-1.50361 - 2.17696i) q^{63} +(0.809017 + 0.587785i) q^{64} +2.37123i q^{65} +(3.26511 + 0.582274i) q^{66} +10.2247 q^{67} +(0.309576 + 0.224920i) q^{68} +(-4.41157 - 1.43341i) q^{69} +(-4.01821 - 1.41247i) q^{70} +(1.45028 - 1.05369i) q^{71} +(0.587785 + 0.809017i) q^{72} +(-4.29106 - 13.2065i) q^{73} +(-2.39541 - 0.778315i) q^{74} +(1.41563 - 1.94844i) q^{75} -6.82848 q^{76} +(3.64186 + 7.98354i) q^{77} +1.47296 q^{78} +(-0.135244 + 0.186147i) q^{79} +(1.53105 + 0.497468i) q^{80} +(0.309017 + 0.951057i) q^{81} +(0.331993 + 0.456949i) q^{82} +(-11.4999 + 8.35514i) q^{83} +(-0.877400 + 2.49603i) q^{84} +(0.585867 + 0.190360i) q^{85} +(-1.74514 - 1.26792i) q^{86} -9.07995 q^{87} +(-1.44811 - 2.98378i) q^{88} -7.19895i q^{89} +(1.30239 + 0.946241i) q^{90} +(2.21475 + 3.20657i) q^{91} +(1.43341 + 4.41157i) q^{92} +(6.51375 - 4.73252i) q^{93} +(-3.21693 + 2.33724i) q^{94} +(-10.4547 + 3.39695i) q^{95} +(0.309017 - 0.951057i) q^{96} +(-9.25926 + 12.7443i) q^{97} +(-6.75303 + 1.84299i) q^{98} +(-0.455199 - 3.28524i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{4} + 10 q^{5} - 8 q^{6} - 10 q^{7} + 8 q^{9}+O(q^{10}) \) 32 * q + 8 * q^4 + 10 * q^5 - 8 * q^6 - 10 * q^7 + 8 * q^9	\( 32 q + 8 q^{4} + 10 q^{5} - 8 q^{6} - 10 q^{7} + 8 q^{9} + 4 q^{10} + 8 q^{11} - 2 q^{14} + 6 q^{15} - 8 q^{16} - 12 q^{17} - 16 q^{19} + 10 q^{20} - 8 q^{21} - 4 q^{22} + 8 q^{23} + 8 q^{24} + 6 q^{25} + 10 q^{28} + 20 q^{29} - 50 q^{31} - 16 q^{33} - 12 q^{35} - 8 q^{36} - 16 q^{37} + 6 q^{40} + 40 q^{41} + 12 q^{44} + 52 q^{49} + 40 q^{51} - 32 q^{54} - 40 q^{55} - 8 q^{56} + 10 q^{58} + 60 q^{59} + 4 q^{60} - 4 q^{61} + 20 q^{62} - 10 q^{63} + 8 q^{64} + 8 q^{66} - 16 q^{67} + 12 q^{68} + 30 q^{69} - 28 q^{70} - 48 q^{71} - 74 q^{73} - 40 q^{74} - 24 q^{76} + 6 q^{77} - 60 q^{79} - 8 q^{81} + 20 q^{82} + 4 q^{83} - 2 q^{84} - 10 q^{85} - 36 q^{86} + 20 q^{87} - 16 q^{88} - 4 q^{90} - 20 q^{91} - 8 q^{92} - 10 q^{93} - 20 q^{95} - 8 q^{96} + 60 q^{97} - 40 q^{98} - 8 q^{99}+O(q^{100}) \) 32 * q + 8 * q^4 + 10 * q^5 - 8 * q^6 - 10 * q^7 + 8 * q^9 + 4 * q^10 + 8 * q^11 - 2 * q^14 + 6 * q^15 - 8 * q^16 - 12 * q^17 - 16 * q^19 + 10 * q^20 - 8 * q^21 - 4 * q^22 + 8 * q^23 + 8 * q^24 + 6 * q^25 + 10 * q^28 + 20 * q^29 - 50 * q^31 - 16 * q^33 - 12 * q^35 - 8 * q^36 - 16 * q^37 + 6 * q^40 + 40 * q^41 + 12 * q^44 + 52 * q^49 + 40 * q^51 - 32 * q^54 - 40 * q^55 - 8 * q^56 + 10 * q^58 + 60 * q^59 + 4 * q^60 - 4 * q^61 + 20 * q^62 - 10 * q^63 + 8 * q^64 + 8 * q^66 - 16 * q^67 + 12 * q^68 + 30 * q^69 - 28 * q^70 - 48 * q^71 - 74 * q^73 - 40 * q^74 - 24 * q^76 + 6 * q^77 - 60 * q^79 - 8 * q^81 + 20 * q^82 + 4 * q^83 - 2 * q^84 - 10 * q^85 - 36 * q^86 + 20 * q^87 - 16 * q^88 - 4 * q^90 - 20 * q^91 - 8 * q^92 - 10 * q^93 - 20 * q^95 - 8 * q^96 + 60 * q^97 - 40 * q^98 - 8 * q^99

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