LMFDB - Embedded newform 429.2.x.a.248.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(248,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 9, 0]))

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

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

chi := DirichletCharacter("429.248");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.x (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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$48$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			248.12
Character	$\chi$	$=$	429.248
Dual form			429.2.x.a.365.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.471771 - 1.45196i) q^{2} +(0.741004 + 1.56554i) q^{3} +(-0.267592 + 0.194417i) q^{4} +(-0.890567 - 0.289363i) q^{5} +(1.92352 - 1.81449i) q^{6} +(-2.98183 - 4.10413i) q^{7} +(-2.06170 - 1.49791i) q^{8} +(-1.90183 + 2.32014i) q^{9} +O(q^{10})$	\(q+(-0.471771 - 1.45196i) q^{2} +(0.741004 + 1.56554i) q^{3} +(-0.267592 + 0.194417i) q^{4} +(-0.890567 - 0.289363i) q^{5} +(1.92352 - 1.81449i) q^{6} +(-2.98183 - 4.10413i) q^{7} +(-2.06170 - 1.49791i) q^{8} +(-1.90183 + 2.32014i) q^{9} +1.42958i q^{10} +(-2.92141 + 1.57015i) q^{11} +(-0.502654 - 0.274862i) q^{12} +(0.951057 - 0.309017i) q^{13} +(-4.55231 + 6.26571i) q^{14} +(-0.206905 - 1.60864i) q^{15} +(-1.40668 + 4.32932i) q^{16} +(2.10428 - 6.47632i) q^{17} +(4.26598 + 1.66680i) q^{18} +(-3.53354 + 4.86350i) q^{19} +(0.294566 - 0.0957101i) q^{20} +(4.21564 - 7.70935i) q^{21} +(3.65803 + 3.50103i) q^{22} +3.14491i q^{23} +(0.817312 - 4.33763i) q^{24} +(-3.33571 - 2.42353i) q^{25} +(-0.897362 - 1.23511i) q^{26} +(-5.04153 - 1.25815i) q^{27} +(1.59583 + 0.518516i) q^{28} +(4.28324 - 3.11196i) q^{29} +(-2.23807 + 1.05933i) q^{30} +(-2.62605 - 8.08214i) q^{31} +1.85285 q^{32} +(-4.62290 - 3.41010i) q^{33} -10.3961 q^{34} +(1.46793 + 4.51783i) q^{35} +(0.0578384 - 0.990599i) q^{36} +(2.78496 - 2.02339i) q^{37} +(8.72863 + 2.83610i) q^{38} +(1.18851 + 1.25993i) q^{39} +(1.40264 + 1.93057i) q^{40} +(2.18770 + 1.58945i) q^{41} +(-13.1825 - 2.48390i) q^{42} -2.92656i q^{43} +(0.476483 - 0.988130i) q^{44} +(2.36507 - 1.51592i) q^{45} +(4.56628 - 1.48368i) q^{46} +(3.24004 - 4.45954i) q^{47} +(-7.82008 + 1.00583i) q^{48} +(-5.78950 + 17.8182i) q^{49} +(-1.94519 + 5.98667i) q^{50} +(11.6982 - 1.50464i) q^{51} +(-0.194417 + 0.267592i) q^{52} +(3.81987 - 1.24115i) q^{53} +(0.551667 + 7.91367i) q^{54} +(3.05605 - 0.552973i) q^{55} +12.9280i q^{56} +(-10.2324 - 1.92802i) q^{57} +(-6.53916 - 4.75098i) q^{58} +(1.31293 + 1.80709i) q^{59} +(0.368112 + 0.390232i) q^{60} +(-3.35414 - 1.08983i) q^{61} +(-10.4961 + 7.62584i) q^{62} +(15.1931 + 0.887084i) q^{63} +(1.93924 + 5.96838i) q^{64} -0.936397 q^{65} +(-2.77038 + 8.32107i) q^{66} +10.0945 q^{67} +(0.696017 + 2.14212i) q^{68} +(-4.92347 + 2.33039i) q^{69} +(5.86720 - 4.26277i) q^{70} +(-1.48896 - 0.483791i) q^{71} +(7.39635 - 1.93466i) q^{72} +(-1.41175 - 1.94311i) q^{73} +(-4.25175 - 3.08908i) q^{74} +(1.32236 - 7.01803i) q^{75} -1.98841i q^{76} +(15.1552 + 7.30796i) q^{77} +(1.26867 - 2.32008i) q^{78} +(1.35749 - 0.441076i) q^{79} +(2.50549 - 3.44851i) q^{80} +(-1.76612 - 8.82501i) q^{81} +(1.27574 - 3.92631i) q^{82} +(-3.32831 + 10.2435i) q^{83} +(0.370758 + 2.88255i) q^{84} +(-3.74801 + 5.15869i) q^{85} +(-4.24926 + 1.38067i) q^{86} +(8.04580 + 4.39961i) q^{87} +(8.37500 + 1.13885i) q^{88} -7.21849i q^{89} +(-3.31683 - 2.71882i) q^{90} +(-4.10413 - 2.98183i) q^{91} +(-0.611423 - 0.841552i) q^{92} +(10.7070 - 10.1001i) q^{93} +(-8.00363 - 2.60054i) q^{94} +(4.55416 - 3.30879i) q^{95} +(1.37297 + 2.90071i) q^{96} +(0.913962 + 2.81288i) q^{97} +28.6027 q^{98} +(1.91305 - 9.76423i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 6 q^{3} - 48 q^{4} - 10 q^{6} - 14 q^{9}+O(q^{10}) $ 192 * q + 6 * q^3 - 48 * q^4 - 10 * q^6 - 14 * q^9	$ 192 q + 6 q^{3} - 48 q^{4} - 10 q^{6} - 14 q^{9} - 20 q^{12} + 6 q^{15} - 28 q^{16} - 10 q^{18} - 60 q^{19} + 4 q^{22} + 30 q^{24} - 12 q^{25} + 30 q^{27} - 20 q^{28} + 12 q^{31} - 32 q^{33} + 56 q^{34} + 44 q^{36} + 60 q^{40} - 108 q^{42} - 40 q^{45} - 28 q^{48} - 24 q^{49} + 10 q^{51} + 20 q^{52} - 20 q^{55} + 50 q^{57} - 60 q^{58} + 36 q^{60} + 20 q^{61} - 30 q^{63} + 64 q^{64} - 30 q^{66} - 120 q^{67} - 16 q^{69} + 20 q^{70} + 150 q^{72} - 20 q^{73} + 18 q^{75} + 40 q^{78} - 160 q^{79} - 46 q^{81} + 88 q^{82} - 40 q^{85} + 72 q^{88} - 80 q^{90} + 8 q^{91} - 72 q^{93} - 120 q^{94} - 140 q^{96} - 88 q^{97} + 62 q^{99}+O(q^{100}) $ 192 * q + 6 * q^3 - 48 * q^4 - 10 * q^6 - 14 * q^9 - 20 * q^12 + 6 * q^15 - 28 * q^16 - 10 * q^18 - 60 * q^19 + 4 * q^22 + 30 * q^24 - 12 * q^25 + 30 * q^27 - 20 * q^28 + 12 * q^31 - 32 * q^33 + 56 * q^34 + 44 * q^36 + 60 * q^40 - 108 * q^42 - 40 * q^45 - 28 * q^48 - 24 * q^49 + 10 * q^51 + 20 * q^52 - 20 * q^55 + 50 * q^57 - 60 * q^58 + 36 * q^60 + 20 * q^61 - 30 * q^63 + 64 * q^64 - 30 * q^66 - 120 * q^67 - 16 * q^69 + 20 * q^70 + 150 * q^72 - 20 * q^73 + 18 * q^75 + 40 * q^78 - 160 * q^79 - 46 * q^81 + 88 * q^82 - 40 * q^85 + 72 * q^88 - 80 * q^90 + 8 * q^91 - 72 * q^93 - 120 * q^94 - 140 * q^96 - 88 * q^97 + 62 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$1$	$e\left(\frac{9}{10}\right)$	$-1$

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 $

$2$	−0.471771	−	1.45196i	−0.333593	−	1.02669i	−0.967411	−	0.253211i	$-0.918513\pi$
$2$	−0.471771	−	1.45196i	−0.333593	−	1.02669i	0.633819	−	0.773482i	$-0.281487\pi$
$3$	0.741004	+	1.56554i	0.427819	+	0.903864i
$3$	0.741004	+	1.56554i	0.427819	+	0.903864i
$4$	−0.267592	+	0.194417i	−0.133796	+	0.0972085i
$5$	−0.890567	−	0.289363i	−0.398274	−	0.129407i	0.103030	−	0.994678i	$-0.467146\pi$
$5$	−0.890567	−	0.289363i	−0.398274	−	0.129407i	−0.501304	+	0.865271i	$0.667146\pi$
$6$	1.92352	−	1.81449i	0.785273	−	0.740761i
$7$	−2.98183	−	4.10413i	−1.12703	−	1.55122i	−0.793600	−	0.608440i	$-0.791795\pi$
$7$	−2.98183	−	4.10413i	−1.12703	−	1.55122i	−0.333425	−	0.942776i	$-0.608205\pi$
$8$	−2.06170	−	1.49791i	−0.728920	−	0.529591i
$9$	−1.90183	+	2.32014i	−0.633942	+	0.773381i
$10$			1.42958i			0.452074i
$11$	−2.92141	+	1.57015i	−0.880839	+	0.473417i
$11$	−2.92141	+	1.57015i	−0.880839	+	0.473417i
$12$	−0.502654	−	0.274862i	−0.145104	−	0.0793458i
$13$	0.951057	−	0.309017i	0.263776	−	0.0857059i
$13$	0.951057	−	0.309017i	0.263776	−	0.0857059i
$14$	−4.55231	+	6.26571i	−1.21666	+	1.67458i
$15$	−0.206905	−	1.60864i	−0.0534226	−	0.415348i
$16$	−1.40668	+	4.32932i	−0.351671	+	1.08233i
$17$	2.10428	−	6.47632i	0.510364	−	1.57074i	−0.281199	−	0.959649i	$-0.590732\pi$
$17$	2.10428	−	6.47632i	0.510364	−	1.57074i	0.791563	−	0.611088i	$-0.209268\pi$
$18$	4.26598	+	1.66680i	1.00550	+	0.392869i
$19$	−3.53354	+	4.86350i	−0.810649	+	1.11576i	0.180574	+	0.983561i	$0.442204\pi$
$19$	−3.53354	+	4.86350i	−0.810649	+	1.11576i	−0.991223	+	0.132201i	$0.957796\pi$
$20$	0.294566	−	0.0957101i	0.0658669	−	0.0214014i
$21$	4.21564	−	7.70935i	0.919927	−	1.68232i
$22$	3.65803	+	3.50103i	0.779895	+	0.746422i
$23$			3.14491i			0.655758i	0.944720	+	0.327879i	$0.106334\pi$
$23$			3.14491i			0.655758i	−0.944720	+	0.327879i	$0.893666\pi$
$24$	0.817312	−	4.33763i	0.166833	−	0.885414i
$25$	−3.33571	−	2.42353i	−0.667141	−	0.484707i
$26$	−0.897362	−	1.23511i	−0.175987	−	0.242226i
$27$	−5.04153	−	1.25815i	−0.970244	−	0.242131i
$28$	1.59583	+	0.518516i	0.301583	+	0.0979902i
$29$	4.28324	−	3.11196i	0.795379	−	0.577876i	−0.114176	−	0.993461i	$-0.536423\pi$
$29$	4.28324	−	3.11196i	0.795379	−	0.577876i	0.909555	+	0.415584i	$0.136423\pi$
$30$	−2.23807	+	1.05933i	−0.408613	+	0.193406i
$31$	−2.62605	−	8.08214i	−0.471652	−	1.45159i	−0.850420	−	0.526104i	$-0.823652\pi$
$31$	−2.62605	−	8.08214i	−0.471652	−	1.45159i	0.378769	−	0.925491i	$-0.376348\pi$
$32$	1.85285			0.327541
$33$	−4.62290	−	3.41010i	−0.804744	−	0.593622i
$34$	−10.3961			−1.78292
$35$	1.46793	+	4.51783i	0.248126	+	0.763653i
$36$	0.0578384	−	0.990599i	0.00963974	−	0.165100i
$37$	2.78496	−	2.02339i	0.457845	−	0.332644i	−0.334840	−	0.942275i	$-0.608682\pi$
$37$	2.78496	−	2.02339i	0.457845	−	0.332644i	0.792685	+	0.609631i	$0.208682\pi$
$38$	8.72863	+	2.83610i	1.41597	+	0.460077i
$39$	1.18851	+	1.25993i	0.190315	+	0.201751i
$40$	1.40264	+	1.93057i	0.221777	+	0.305250i
$41$	2.18770	+	1.58945i	0.341661	+	0.248231i	0.745362	−	0.666660i	$-0.232277\pi$
$41$	2.18770	+	1.58945i	0.341661	+	0.248231i	−0.403701	+	0.914891i	$0.632277\pi$
$42$	−13.1825	−	2.48390i	−2.03410	−	0.383273i
$43$		−	2.92656i		−	0.446297i	−0.974784	−	0.223148i	$-0.928367\pi$
$43$		−	2.92656i		−	0.446297i	0.974784	−	0.223148i	$-0.0716334\pi$
$44$	0.476483	−	0.988130i	0.0718325	−	0.148966i
$45$	2.36507	−	1.51592i	0.352563	−	0.225981i
$46$	4.56628	−	1.48368i	0.673262	−	0.218756i
$47$	3.24004	−	4.45954i	0.472609	−	0.650490i	−0.504455	−	0.863438i	$-0.668306\pi$
$47$	3.24004	−	4.45954i	0.472609	−	0.650490i	0.977064	+	0.212948i	$0.0683065\pi$
$48$	−7.82008	+	1.00583i	−1.12873	+	0.145179i
$49$	−5.78950	+	17.8182i	−0.827071	+	2.54546i
$50$	−1.94519	+	5.98667i	−0.275091	+	0.846643i
$51$	11.6982	−	1.50464i	1.63808	−	0.210692i
$52$	−0.194417	+	0.267592i	−0.0269608	+	0.0371083i
$53$	3.81987	−	1.24115i	0.524700	−	0.170485i	−0.0346773	−	0.999399i	$-0.511040\pi$
$53$	3.81987	−	1.24115i	0.524700	−	0.170485i	0.559377	+	0.828913i	$0.311040\pi$
$54$	0.551667	+	7.91367i	0.0750723	+	1.07691i
$55$	3.05605	−	0.552973i	0.412078	−	0.0745628i
$56$			12.9280i			1.72758i
$57$	−10.2324	−	1.92802i	−1.35531	−	0.255372i
$58$	−6.53916	−	4.75098i	−0.858633	−	0.623834i
$59$	1.31293	+	1.80709i	0.170928	+	0.235263i	0.885884	−	0.463908i	$-0.153553\pi$
$59$	1.31293	+	1.80709i	0.170928	+	0.235263i	−0.714955	+	0.699170i	$0.753553\pi$
$60$	0.368112	+	0.390232i	0.0475231	+	0.0503788i
$61$	−3.35414	−	1.08983i	−0.429454	−	0.139538i	0.0863109	−	0.996268i	$-0.472492\pi$
$61$	−3.35414	−	1.08983i	−0.429454	−	0.139538i	−0.515765	+	0.856730i	$0.672492\pi$
$62$	−10.4961	+	7.62584i	−1.33300	+	0.968483i
$63$	15.1931	+	0.887084i	1.91415	+	0.111762i
$64$	1.93924	+	5.96838i	0.242405	+	0.746047i
$65$	−0.936397			−0.116146
$66$	−2.77038	+	8.32107i	−0.341010	+	1.02425i
$67$	10.0945			1.23324			0.616621	−	0.787260i	$-0.288501\pi$
$67$	10.0945			1.23324			0.616621	+	0.787260i	$0.288501\pi$
$68$	0.696017	+	2.14212i	0.0844044	+	0.259770i
$69$	−4.92347	+	2.33039i	−0.592716	+	0.280546i
$70$	5.86720	−	4.26277i	0.701264	−	0.509498i
$71$	−1.48896	−	0.483791i	−0.176706	−	0.0574154i	0.219327	−	0.975651i	$-0.429614\pi$
$71$	−1.48896	−	0.483791i	−0.176706	−	0.0574154i	−0.396034	+	0.918236i	$0.629614\pi$
$72$	7.39635	−	1.93466i	0.871669	−	0.228002i
$73$	−1.41175	−	1.94311i	−0.165233	−	0.227424i	0.718369	−	0.695662i	$-0.244889\pi$
$73$	−1.41175	−	1.94311i	−0.165233	−	0.227424i	−0.883602	+	0.468238i	$0.844889\pi$
$74$	−4.25175	−	3.08908i	−0.494256	−	0.359098i
$75$	1.32236	−	7.01803i	0.152693	−	0.810372i
$76$		−	1.98841i		−	0.228087i
$77$	15.1552	+	7.30796i	1.72710	+	0.832819i
$78$	1.26867	−	2.32008i	0.143648	−	0.262697i
$79$	1.35749	−	0.441076i	0.152730	−	0.0496250i	−0.231654	−	0.972798i	$-0.574414\pi$
$79$	1.35749	−	0.441076i	0.152730	−	0.0496250i	0.384384	+	0.923173i	$0.374414\pi$
$80$	2.50549	−	3.44851i	0.280122	−	0.385555i
$81$	−1.76612	−	8.82501i	−0.196235	−	0.980557i
$82$	1.27574	−	3.92631i	0.140881	−	0.433588i
$83$	−3.32831	+	10.2435i	−0.365329	+	1.12437i	0.584446	+	0.811433i	$0.301312\pi$
$83$	−3.32831	+	10.2435i	−0.365329	+	1.12437i	−0.949775	+	0.312934i	$0.898688\pi$
$84$	0.370758	+	2.88255i	0.0404530	+	0.314512i
$85$	−3.74801	+	5.15869i	−0.406529	+	0.559539i
$86$	−4.24926	+	1.38067i	−0.458209	+	0.148881i
$87$	8.04580	+	4.39961i	0.862600	+	0.471688i
$88$	8.37500	+	1.13885i	0.892778	+	0.121401i
$89$		−	7.21849i		−	0.765158i	−0.923923	−	0.382579i	$-0.875036\pi$
$89$		−	7.21849i		−	0.765158i	0.923923	−	0.382579i	$-0.124964\pi$
$90$	−3.31683	−	2.71882i	−0.349625	−	0.286588i
$91$	−4.10413	−	2.98183i	−0.430230	−	0.312581i
$92$	−0.611423	−	0.841552i	−0.0637453	−	0.0877378i
$93$	10.7070	−	10.1001i	1.11026	−	1.04733i
$94$	−8.00363	−	2.60054i	−0.825512	−	0.268225i
$95$	4.55416	−	3.30879i	0.467247	−	0.339475i
$96$	1.37297	+	2.90071i	0.140128	+	0.296052i
$97$	0.913962	+	2.81288i	0.0927987	+	0.285605i	0.986674	−	0.162711i	$-0.0520238\pi$
$97$	0.913962	+	2.81288i	0.0927987	+	0.285605i	−0.893875	+	0.448316i	$0.852024\pi$
$98$	28.6027			2.88931
$99$	1.91305	−	9.76423i	0.192269	−	0.981342i
$100$	1.36378			0.136378
$101$	−3.12088	−	9.60508i	−0.310539	−	0.955741i	−0.977552	−	0.210695i	$-0.932427\pi$
$101$	−3.12088	−	9.60508i	−0.310539	−	0.955741i	0.667013	−	0.745046i	$-0.267573\pi$
$102$	−7.70356	−	16.2755i	−0.762766	−	1.61152i
$103$	−2.30824	+	1.67704i	−0.227438	+	0.165243i	−0.695668	−	0.718363i	$-0.744892\pi$
$103$	−2.30824	+	1.67704i	−0.227438	+	0.165243i	0.468231	+	0.883606i	$0.344892\pi$
$104$	−2.42367	−	0.787498i	−0.237660	−	0.0772206i
$105$	−5.98510	+	5.64584i	−0.584086	+	0.550978i
$106$	−3.60421	−	4.96077i	−0.350072	−	0.481833i
$107$	−10.4945	−	7.62473i	−1.01454	−	0.737110i	−0.0493874	−	0.998780i	$-0.515727\pi$
$107$	−10.4945	−	7.62473i	−1.01454	−	0.737110i	−0.965157	+	0.261670i	$0.915727\pi$
$108$	1.59368	−	0.643489i	0.153352	−	0.0619198i
$109$		−	10.1322i		−	0.970487i	−0.874379	−	0.485244i	$-0.838731\pi$
$109$		−	10.1322i		−	0.970487i	0.874379	−	0.485244i	$-0.161269\pi$
$110$	−2.24465	−	4.17640i	−0.214019	−	0.398204i
$111$	5.23137	+	2.86062i	0.496540	+	0.271518i
$112$	21.9626	−	7.13608i	2.07527	−	0.674297i
$113$	−5.63361	+	7.75400i	−0.529966	+	0.729435i	−0.987125	−	0.159949i	$-0.948867\pi$
$113$	−5.63361	+	7.75400i	−0.529966	+	0.729435i	0.457159	+	0.889385i	$0.348867\pi$
$114$	2.02792	+	15.7666i	0.189932	+	1.47668i
$115$	0.910018	−	2.80075i	0.0848596	−	0.261171i
$116$	−0.541144	+	1.66547i	−0.0502440	+	0.154635i
$117$	−1.09178	+	2.79428i	−0.100935	+	0.258332i
$118$	2.00442	−	2.75885i	0.184522	−	0.253973i
$119$	−32.8543	+	10.6750i	−3.01175	+	0.978576i
$120$	−1.98302	+	3.62645i	−0.181024	+	0.331048i
$121$	6.06928	−	9.17408i	0.551753	−	0.834008i
$122$			5.38424i			0.487466i
$123$	−0.867261	+	4.60272i	−0.0781983	+	0.415013i
$124$	2.27401	+	1.65217i	0.204212	+	0.148369i
$125$	5.02139	+	6.91135i	0.449127	+	0.618170i
$126$	−5.87965	−	22.4783i	−0.523801	−	2.00253i
$127$	−5.44591	−	1.76948i	−0.483247	−	0.157016i	0.0572546	−	0.998360i	$-0.481765\pi$
$127$	−5.44591	−	1.76948i	−0.483247	−	0.157016i	−0.540501	+	0.841343i	$0.681765\pi$
$128$	10.7490	−	7.80957i	0.950082	−	0.690275i
$129$	4.58165	−	2.16860i	0.403392	−	0.190934i
$130$	0.441765	+	1.35961i	0.0387454	+	0.119246i
$131$	16.2203			1.41717			0.708586	−	0.705625i	$-0.249334\pi$
$131$	16.2203			1.41717			0.708586	+	0.705625i	$0.249334\pi$
$132$	1.90003	+	0.0137444i	0.165377	+	0.00119629i
$133$	30.4968			2.64441
$134$	−4.76231	−	14.6569i	−0.411401	−	1.26616i
$135$	4.12576	+	2.57930i	0.355089	+	0.221990i
$136$	−14.0393	+	10.2002i	−1.20386	+	0.874658i
$137$	4.84648	+	1.57472i	0.414063	+	0.134537i	0.508638	−	0.860981i	$-0.330149\pi$
$137$	4.84648	+	1.57472i	0.414063	+	0.134537i	−0.0945751	+	0.995518i	$0.530149\pi$
$138$	5.70639	+	6.04929i	0.485760	+	0.514949i
$139$	3.52470	+	4.85133i	0.298961	+	0.411485i	0.931899	−	0.362718i	$-0.118151\pi$
$139$	3.52470	+	4.85133i	0.298961	+	0.411485i	−0.632938	+	0.774203i	$0.718151\pi$
$140$	−1.27115	−	0.923545i	−0.107432	−	0.0780538i
$141$	9.38246	+	1.76788i	0.790146	+	0.148882i
$142$			2.39015i			0.200577i
$143$	−2.29323	+	2.39606i	−0.191769	+	0.200369i
$144$	−7.36938	−	11.4973i	−0.614115	−	0.958110i
$145$	−4.71500	+	1.53200i	−0.391559	+	0.127225i
$146$	−2.15530	+	2.96651i	−0.178374	+	0.245510i
$147$	−32.1852	+	4.13971i	−2.65459	+	0.341437i
$148$	−0.351852	+	1.08289i	−0.0289220	+	0.0890128i
$149$	−4.99177	+	15.3631i	−0.408942	+	1.25859i	0.508617	+	0.860993i	$0.330157\pi$
$149$	−4.99177	+	15.3631i	−0.408942	+	1.25859i	−0.917559	+	0.397600i	$0.869843\pi$
$150$	−10.8138	+	1.39088i	−0.882940	+	0.113565i
$151$	−0.516759	+	0.711257i	−0.0420532	+	0.0578813i	−0.829526	−	0.558468i	$-0.811389\pi$
$151$	−0.516759	+	0.711257i	−0.0420532	+	0.0578813i	0.787473	+	0.616350i	$0.211389\pi$
$152$	14.5702	−	4.73413i	1.18180	−	0.383989i
$153$	11.0240	+	17.1991i	0.891237	+	1.39046i
$154$	3.46107	−	25.4525i	0.278901	−	2.05102i
$155$			7.95756i			0.639167i
$156$	−0.562990	−	0.106081i	−0.0450752	−	0.00849325i
$157$	5.38131	+	3.90975i	0.429475	+	0.312032i	0.781439	−	0.623981i	$-0.214486\pi$
$157$	5.38131	+	3.90975i	0.429475	+	0.312032i	−0.351964	+	0.936014i	$0.614486\pi$
$158$	−1.28085	−	1.76294i	−0.101899	−	0.140252i
$159$	4.77361	+	5.06046i	0.378572	+	0.401321i
$160$	−1.65009	−	0.536146i	−0.130451	−	0.0423860i
$161$	12.9071	−	9.37757i	1.01722	−	0.739056i
$162$	−11.9804	+	6.72772i	−0.941268	+	0.528580i
$163$	−2.12710	−	6.54654i	−0.166607	−	0.512764i	0.832544	−	0.553959i	$-0.186884\pi$
$163$	−2.12710	−	6.54654i	−0.166607	−	0.512764i	−0.999151	+	0.0411947i	$0.986884\pi$
$164$	−0.894427			−0.0698430
$165$	3.13025	+	4.37462i	0.243689	+	0.340563i
$166$	16.4433			1.27625
$167$	0.729251	+	2.24440i	0.0564312	+	0.173677i	0.975299	−	0.220888i	$-0.0708954\pi$
$167$	0.729251	+	2.24440i	0.0564312	+	0.173677i	−0.918868	+	0.394565i	$0.870895\pi$
$168$	−20.2393	+	9.57970i	−1.56149	+	0.739090i
$169$	0.809017	−	0.587785i	0.0622321	−	0.0452143i
$170$	9.25843	+	3.00824i	0.710089	+	0.230722i
$171$	−4.56383	−	17.4478i	−0.349005	−	1.33427i
$172$	0.568974	+	0.783125i	0.0433838	+	0.0597127i
$173$	−1.38032	−	1.00286i	−0.104944	−	0.0762463i	0.534076	−	0.845437i	$-0.320660\pi$
$173$	−1.38032	−	1.00286i	−0.104944	−	0.0762463i	−0.639020	+	0.769190i	$0.720660\pi$
$174$	2.59230	−	13.7578i	0.196521	−	1.04298i
$175$			20.9167i			1.58116i
$176$	−2.68817	−	14.8564i	−0.202629	−	1.11985i
$177$	−1.85618	+	3.39449i	−0.139519	+	0.255146i
$178$	−10.4810	+	3.40547i	−0.785582	+	0.255251i
$179$	10.4803	−	14.4249i	0.783335	−	1.07817i	−0.211571	−	0.977363i	$-0.567858\pi$
$179$	10.4803	−	14.4249i	0.783335	−	1.07817i	0.994906	−	0.100806i	$-0.0321421\pi$
$180$	−0.338151	+	0.865458i	−0.0252043	+	0.0645074i
$181$	4.69015	−	14.4348i	0.348616	−	1.07293i	−0.611003	−	0.791628i	$-0.709234\pi$
$181$	4.69015	−	14.4348i	0.348616	−	1.07293i	0.959619	−	0.281302i	$-0.0907664\pi$
$182$	−2.39329	+	7.36579i	−0.177402	+	0.545988i
$183$	−0.779267	−	6.05861i	−0.0576050	−	0.447865i
$184$	4.71079	−	6.48384i	0.347284	−	0.477995i
$185$	−3.06569	+	0.996103i	−0.225394	+	0.0732349i
$186$	−19.7162	−	10.7812i	−1.44566	−	0.790518i
$187$	4.02129	+	22.2240i	0.294066	+	1.62518i
$188$			1.82326i			0.132975i
$189$	9.86938	+	24.4427i	0.717892	+	1.77795i
$190$	−6.95277	−	5.05148i	−0.504407	−	0.366473i
$191$	−6.82148	−	9.38896i	−0.493585	−	0.679361i	0.487459	−	0.873146i	$-0.337924\pi$
$191$	−6.82148	−	9.38896i	−0.493585	−	0.679361i	−0.981044	+	0.193784i	$0.937924\pi$
$192$	−7.90674	+	7.45856i	−0.570620	+	0.538275i
$193$	−11.7074	−	3.80396i	−0.842715	−	0.273815i	−0.144324	−	0.989531i	$-0.546101\pi$
$193$	−11.7074	−	3.80396i	−0.842715	−	0.273815i	−0.698392	+	0.715716i	$0.746101\pi$
$194$	3.65302	−	2.65408i	0.262272	−	0.190552i
$195$	−0.693874	−	1.46597i	−0.0496894	−	0.104980i
$196$	−1.91495	−	5.89360i	−0.136782	−	0.420971i
$197$	−4.62474			−0.329499			−0.164749	−	0.986335i	$-0.552682\pi$
$197$	−4.62474			−0.329499			−0.164749	+	0.986335i	$0.552682\pi$
$198$	−15.0798	+	1.82880i	−1.07168	+	0.129967i
$199$	−21.4188			−1.51834			−0.759170	−	0.650893i	$-0.774395\pi$
$199$	−21.4188			−1.51834			−0.759170	+	0.650893i	$0.774395\pi$
$200$	3.24698	+	9.99318i	0.229596	+	0.706625i
$201$	7.48009	+	15.8034i	0.527605	+	1.11468i
$202$	−12.4739	+	9.06280i	−0.877659	+	0.637656i
$203$	−25.5438	−	8.29968i	−1.79282	−	0.582524i
$204$	−2.83782	+	2.67696i	−0.198687	+	0.187425i
$205$	−1.48836	−	2.04855i	−0.103952	−	0.143077i
$206$	3.52395	+	2.56030i	0.245525	+	0.178385i
$207$	−7.29663	−	5.98106i	−0.507151	−	0.415713i
$208$			4.55212i			0.315633i
$209$	2.68651	−	19.7564i	0.185830	−	1.36658i
$210$	11.0211	+	6.02660i	0.760531	+	0.415875i
$211$	−11.8066	+	3.83620i	−0.812800	+	0.264095i	−0.685783	−	0.727806i	$-0.740540\pi$
$211$	−11.8066	+	3.83620i	−0.812800	+	0.264095i	−0.127017	+	0.991901i	$0.540540\pi$
$212$	−0.780867	+	1.07477i	−0.0536301	+	0.0738156i
$213$	−0.345928	−	2.68951i	−0.0237026	−	0.184282i
$214$	−6.11979	+	18.8348i	−0.418341	+	1.28752i
$215$	−0.846838	+	2.60630i	−0.0577539	+	0.177748i
$216$	8.50952	+	10.1457i	0.579000	+	0.690327i
$217$	−25.3398	+	34.8772i	−1.72018	+	2.36762i
$218$	−14.7115	+	4.78007i	−0.996392	+	0.323747i
$219$	1.99590	−	3.65000i	0.134870	−	0.246644i
$220$	−0.710268	+	0.742120i	−0.0478863	+	0.0500337i
$221$		−	6.80960i		−	0.458063i
$222$	1.68551	−	8.94531i	0.113124	−	0.600370i
$223$	16.5434	+	12.0195i	1.10783	+	0.804885i	0.982320	−	0.187207i	$-0.0599435\pi$
$223$	16.5434	+	12.0195i	1.10783	+	0.804885i	0.125509	+	0.992092i	$0.459944\pi$
$224$	−5.52488	−	7.60435i	−0.369147	−	0.508087i
$225$	11.9669	−	3.13018i	0.797792	−	0.208678i
$226$	13.9163	+	4.52168i	0.925698	+	0.300778i
$227$	−10.4379	+	7.58360i	−0.692790	+	0.503341i	−0.877576	−	0.479437i	$-0.840841\pi$
$227$	−10.4379	+	7.58360i	−0.692790	+	0.503341i	0.184786	+	0.982779i	$0.440841\pi$
$228$	3.11294	−	1.47342i	0.206159	−	0.0975797i
$229$	1.06835	+	3.28804i	0.0705985	+	0.217280i	0.980130	−	0.198354i	$-0.0635597\pi$
$229$	1.06835	+	3.28804i	0.0705985	+	0.217280i	−0.909532	+	0.415634i	$0.863560\pi$
$230$	−4.49590			−0.296451
$231$	−0.210801	+	29.1413i	−0.0138697	+	1.91736i
$232$	−13.4922			−0.885806
$233$	−4.40754	−	13.5650i	−0.288747	−	0.888673i	−0.985250	−	0.171119i	$-0.945262\pi$
$233$	−4.40754	−	13.5650i	−0.288747	−	0.888673i	0.696503	−	0.717554i	$-0.254738\pi$
$234$	4.57226	+	0.266962i	0.298898	+	0.0174519i
$235$	−4.17590	+	3.03397i	−0.272405	+	0.197914i
$236$	−0.702657	−	0.228307i	−0.0457390	−	0.0148615i
$237$	1.69643	+	1.79837i	0.110195	+	0.116817i
$238$	30.9994	+	42.6670i	2.00939	+	2.76569i
$239$	0.0573310	+	0.0416534i	0.00370844	+	0.00269434i	0.589638	−	0.807668i	$-0.299270\pi$
$239$	0.0573310	+	0.0416534i	0.00370844	+	0.00269434i	−0.585929	+	0.810362i	$0.699270\pi$
$240$	7.25536	+	1.36708i	0.468331	+	0.0882447i
$241$		−	24.2447i		−	1.56174i	−0.624693	−	0.780871i	$-0.714776\pi$
$241$		−	24.2447i		−	1.56174i	0.624693	−	0.780871i	$-0.285224\pi$
$242$	−16.1837	−	4.48430i	−1.04033	−	0.288262i
$243$	12.5072	−	9.30430i	0.802337	−	0.596871i
$244$	1.10942	−	0.360473i	0.0710235	−	0.0230769i
$245$	10.3119	−	14.1931i	0.658801	−	0.906762i
$246$	7.09212	−	0.912198i	0.452177	−	0.0581596i
$247$	−1.85769	+	5.71738i	−0.118202	+	0.363788i
$248$	−6.69221	+	20.5965i	−0.424956	+	1.30788i
$249$	−18.5028	+	2.37986i	−1.17257	+	0.150818i
$250$	7.66607	−	10.5514i	0.484845	−	0.667332i
$251$	−29.0922	+	9.45264i	−1.83629	+	0.596645i	−0.837550	+	0.546360i	$0.816013\pi$
$251$	−29.0922	+	9.45264i	−1.83629	+	0.596645i	−0.998735	+	0.0502851i	$0.983987\pi$
$252$	−4.23801	+	2.71642i	−0.266970	+	0.171118i
$253$	−4.93796	−	9.18756i	−0.310447	−	0.577617i
$254$			8.74205i			0.548525i
$255$	−10.8534	−	2.04504i	−0.679668	−	0.128066i
$256$	−6.25624	−	4.54542i	−0.391015	−	0.284089i
$257$	−8.71111	−	11.9898i	−0.543384	−	0.747904i	0.445712	−	0.895176i	$-0.352951\pi$
$257$	−8.71111	−	11.9898i	−0.543384	−	0.747904i	−0.989096	+	0.147273i	$0.952951\pi$
$258$	−5.31021	−	5.62930i	−0.330599	−	0.350465i
$259$	−16.6086	−	5.39645i	−1.03201	−	0.335319i
$260$	0.250572	−	0.182052i	0.0155398	−	0.0112904i
$261$	−0.925798	+	15.8561i	−0.0573054	+	0.981470i
$262$	−7.65225	−	23.5512i	−0.472758	−	1.45500i
$263$	−23.8889			−1.47305			−0.736526	−	0.676409i	$-0.763535\pi$
$263$	−23.8889			−1.47305			−0.736526	+	0.676409i	$0.763535\pi$
$264$	4.42300	+	13.9553i	0.272217	+	0.858888i
$265$	−3.76099			−0.231036
$266$	−14.3875	−	44.2803i	−0.882156	−	2.71500i
$267$	11.3008	−	5.34893i	0.691599	−	0.327349i
$268$	−2.70122	+	1.96255i	−0.165003	+	0.119882i
$269$	5.46751	+	1.77650i	0.333360	+	0.108315i	0.470914	−	0.882179i	$-0.343924\pi$
$269$	5.46751	+	1.77650i	0.333360	+	0.108315i	−0.137554	+	0.990494i	$0.543924\pi$
$270$	1.79863	−	7.20729i	0.109461	−	0.438621i
$271$	12.5573	+	17.2836i	0.762801	+	1.04991i	0.996976	+	0.0777107i	$0.0247611\pi$
$271$	12.5573	+	17.2836i	0.762801	+	1.04991i	−0.234175	+	0.972194i	$0.575239\pi$
$272$	25.0780	+	18.2202i	1.52058	+	1.10476i
$273$	1.62699	−	8.63473i	0.0984698	−	0.522598i
$274$		−	7.77981i		−	0.469995i
$275$	13.5503	+	1.84259i	0.817112	+	0.111112i
$276$	0.864415	−	1.58080i	0.0520317	−	0.0951530i
$277$	26.1809	−	8.50668i	1.57306	−	0.511117i	0.612800	−	0.790238i	$-0.290043\pi$
$277$	26.1809	−	8.50668i	1.57306	−	0.511117i	0.960256	+	0.279121i	$0.0900430\pi$
$278$	5.38110	−	7.40645i	0.322737	−	0.444209i
$279$	23.7460	+	9.27802i	1.42164	+	0.555461i
$280$	3.74088	−	11.5132i	0.223560	−	0.688048i
$281$	6.41142	−	19.7323i	0.382473	−	1.17713i	−0.555824	−	0.831300i	$-0.687597\pi$
$281$	6.41142	−	19.7323i	0.382473	−	1.17713i	0.938297	−	0.345831i	$-0.112403\pi$
$282$	−1.85948	−	14.4570i	−0.110730	−	0.860903i
$283$	13.0384	−	17.9458i	0.775050	−	1.06676i	−0.220761	−	0.975328i	$-0.570854\pi$
$283$	13.0384	−	17.9458i	0.775050	−	1.06676i	0.995811	−	0.0914364i	$-0.0291458\pi$
$284$	0.492490	−	0.160020i	0.0292239	−	0.00949542i
$285$	8.55470	+	4.67789i	0.506737	+	0.277094i
$286$	4.56087	+	2.19928i	0.269690	+	0.130046i
$287$		−	13.7181i		−	0.809752i
$288$	−3.52380	+	4.29888i	−0.207642	+	0.253314i
$289$	−23.7614	−	17.2637i	−1.39773	−	1.01551i
$290$	4.44880	+	6.12325i	0.261243	+	0.359570i
$291$	−3.72643	+	3.51520i	−0.218447	+	0.206065i
$292$	0.755546	+	0.245492i	0.0442150	+	0.0143663i
$293$	6.00563	−	4.36334i	0.350852	−	0.254909i	−0.398374	−	0.917223i	$-0.630425\pi$
$293$	6.00563	−	4.36334i	0.350852	−	0.254909i	0.749227	+	0.662314i	$0.230425\pi$
$294$	21.1947	+	44.7787i	1.23610	+	2.61155i
$295$	−0.646344	−	1.98924i	−0.0376316	−	0.115818i
$296$	−8.77261			−0.509898
$297$	16.7039	−	4.24038i	0.969257	−	0.246052i
$298$	24.6616			1.42861
$299$	0.971829	+	2.99098i	0.0562023	+	0.172973i
$300$	1.01057	+	2.13506i	0.0583453	+	0.123268i
$301$	−12.0110	+	8.72651i	−0.692303	+	0.502988i
$302$	1.27651	+	0.414763i	0.0734549	+	0.0238669i
$303$	12.7245	−	12.0033i	0.731006	−	0.689570i
$304$	−16.0851	−	22.1392i	−0.922543	−	1.26977i
$305$	2.67173	+	1.94113i	0.152983	+	0.111149i
$306$	19.7716	−	24.1204i	1.13027	−	1.37887i
$307$		−	7.32157i		−	0.417864i	−0.977930	−	0.208932i	$-0.933001\pi$
$307$		−	7.32157i		−	0.417864i	0.977930	−	0.208932i	$-0.0669987\pi$
$308$	−5.47621	+	0.990884i	−0.312036	+	0.0564609i
$309$	−4.33588	−	2.37095i	−0.246660	−	0.134879i
$310$	11.5541	−	3.75415i	0.656228	−	0.213221i
$311$	3.17279	−	4.36697i	0.179912	−	0.247628i	−0.709530	−	0.704675i	$-0.751093\pi$
$311$	3.17279	−	4.36697i	0.179912	−	0.247628i	0.889443	+	0.457047i	$0.151093\pi$
$312$	−0.563090	−	4.37789i	−0.0318787	−	0.247849i
$313$	−5.71311	+	17.5831i	−0.322924	+	0.993858i	0.649445	+	0.760409i	$0.275001\pi$
$313$	−5.71311	+	17.5831i	−0.322924	+	0.993858i	−0.972369	+	0.233449i	$0.924999\pi$
$314$	3.13806	−	9.65797i	0.177091	−	0.545031i
$315$	−13.2738	−	5.18632i	−0.747892	−	0.292216i
$316$	−0.277502	+	0.381948i	−0.0156107	+	0.0214863i
$317$	−4.00498	+	1.30130i	−0.224942	+	0.0730881i	−0.419320	−	0.907839i	$-0.637731\pi$
$317$	−4.00498	+	1.30130i	−0.224942	+	0.0730881i	0.194377	+	0.980927i	$0.437731\pi$
$318$	5.09555	−	9.31849i	0.285744	−	0.522555i
$319$	−7.62689	+	15.8166i	−0.427024	+	0.885561i
$320$		−	5.87638i		−	0.328500i
$321$	4.16031	−	22.0796i	0.232206	−	1.23236i
$322$	−19.7051	−	14.3166i	−1.09812	−	0.797832i
$323$	24.0620	+	33.1185i	1.33884	+	1.84276i
$324$	2.18833	+	2.01814i	0.121574	+	0.112119i
$325$	−3.92136	−	1.27413i	−0.217518	−	0.0706758i
$326$	−8.50182	+	6.17693i	−0.470872	+	0.342109i
$327$	15.8623	−	7.50799i	0.877189	−	0.415193i
$328$	−2.12951	−	6.55395i	−0.117582	−	0.361881i
$329$	−27.9638			−1.54169
$330$	4.87502	−	6.60882i	0.268361	−	0.363803i
$331$	−12.4953			−0.686803			−0.343401	−	0.939189i	$-0.611579\pi$
$331$	−12.4953			−0.686803			−0.343401	+	0.939189i	$0.611579\pi$
$332$	−1.10088	−	3.38815i	−0.0604185	−	0.185949i
$333$	−0.601953	+	10.3096i	−0.0329868	+	0.564965i
$334$	2.91475	−	2.11769i	0.159488	−	0.115875i
$335$	−8.98985	−	2.92098i	−0.491168	−	0.159590i
$336$	27.4462	+	29.0955i	1.49731	+	1.58729i
$337$	2.18997	+	3.01423i	0.119295	+	0.164196i	0.864488	−	0.502653i	$-0.167643\pi$
$337$	2.18997	+	3.01423i	0.119295	+	0.164196i	−0.745193	+	0.666849i	$0.767643\pi$
$338$	−1.23511	−	0.897362i	−0.0671813	−	0.0488101i
$339$	−16.3137	−	3.07389i	−0.886040	−	0.166951i
$340$		−	2.10910i		−	0.114382i
$341$	20.3619	+	19.4880i	1.10266	+	1.05533i
$342$	−23.1805	+	14.8579i	−1.25346	+	0.803423i
$343$	56.6189	−	18.3966i	3.05713	−	0.993322i
$344$	−4.38373	+	6.03369i	−0.236355	+	0.325315i
$345$	5.05901	−	0.650697i	0.272368	−	0.0350323i
$346$	−0.804923	+	2.47730i	−0.0432729	+	0.133180i
$347$	−4.32723	+	13.3178i	−0.232298	+	0.714939i	0.765171	+	0.643828i	$0.222655\pi$
$347$	−4.32723	+	13.3178i	−0.232298	+	0.714939i	−0.997468	+	0.0711115i	$0.977345\pi$
$348$	−3.00835	+	0.386938i	−0.161264	+	0.0207421i
$349$	−14.9424	+	20.5665i	−0.799850	+	1.10090i	0.192962	+	0.981206i	$0.438191\pi$
$349$	−14.9424	+	20.5665i	−0.799850	+	1.10090i	−0.992811	+	0.119692i	$0.961809\pi$
$350$	30.3703	−	9.86792i	1.62336	−	0.527462i
$351$	−5.18357	+	0.361350i	−0.276679	+	0.0192874i
$352$	−5.41294	+	2.90925i	−0.288511	+	0.155063i
$353$		−	33.1956i		−	1.76682i	−0.468597	−	0.883412i	$-0.655240\pi$
$353$		−	33.1956i		−	1.76682i	0.468597	−	0.883412i	$-0.344760\pi$
$354$	5.80437	+	1.09368i	0.308499	+	0.0581285i
$355$	1.18602	+	0.861696i	0.0629476	+	0.0457341i
$356$	1.40340	+	1.93161i	0.0743799	+	0.102375i
$357$	−41.0573	−	43.5244i	−2.17298	−	2.30356i
$358$	−25.8887	−	8.41176i	−1.36826	−	0.444575i
$359$	8.20914	−	5.96429i	0.433262	−	0.314783i	−0.349690	−	0.936865i	$-0.613713\pi$
$359$	8.20914	−	5.96429i	0.433262	−	0.314783i	0.782952	+	0.622082i	$0.213713\pi$
$360$	−7.14677	−	0.417281i	−0.376668	−	0.0219926i
$361$	−5.29639	−	16.3006i	−0.278757	−	0.857927i
$362$	−23.1715			−1.21787
$363$	18.8598	+	2.70367i	0.989880	+	0.141906i
$364$	1.67795			0.0879486
$365$	0.694995	+	2.13897i	0.0363777	+	0.111959i
$366$	−8.42923	+	3.98974i	−0.440603	+	0.208547i
$367$	5.00725	−	3.63798i	0.261376	−	0.189901i	−0.449377	−	0.893342i	$-0.648354\pi$
$367$	5.00725	−	3.63798i	0.261376	−	0.189901i	0.710754	+	0.703441i	$0.248354\pi$
$368$	−13.6153	−	4.42388i	−0.709747	−	0.230611i
$369$	−7.84838	+	2.05290i	−0.408570	+	0.106870i
$370$	2.89261	+	3.98133i	0.150379	+	0.206980i
$371$	−16.4841	−	11.9764i	−0.855810	−	0.621782i
$372$	−0.901480	+	4.78432i	−0.0467396	+	0.248056i
$373$		−	7.85813i		−	0.406879i	−0.979088	−	0.203439i	$-0.934788\pi$
$373$		−	7.85813i		−	0.406879i	0.979088	−	0.203439i	$-0.0652120\pi$
$374$	30.3713	−	16.3234i	1.57046	−	0.844063i
$375$	−7.09912	+	12.9825i	−0.366597	+	0.670415i
$376$	−13.3600	+	4.34092i	−0.688988	+	0.223866i
$377$	3.11196	−	4.28324i	0.160274	−	0.220598i
$378$	30.8338	−	25.8613i	1.58592	−	1.33016i
$379$	−1.32290	+	4.07147i	−0.0679528	+	0.209137i	−0.979267	−	0.202575i	$-0.935069\pi$
$379$	−1.32290	+	4.07147i	−0.0679528	+	0.209137i	0.911314	+	0.411712i	$0.135069\pi$
$380$	−0.575372	+	1.77081i	−0.0295160	+	0.0908408i
$381$	−1.26525	−	9.83698i	−0.0648205	−	0.503964i
$382$	−10.4142	+	14.3340i	−0.532839	+	0.733390i
$383$	−13.2565	+	4.30729i	−0.677374	+	0.220092i	−0.627445	−	0.778661i	$-0.715899\pi$
$383$	−13.2565	+	4.30729i	−0.677374	+	0.220092i	−0.0499285	+	0.998753i	$0.515899\pi$
$384$	20.1912	+	11.0410i	1.03038	+	0.563433i
$385$	−11.3821	−	10.8936i	−0.580085	−	0.555188i
$386$			18.7933i			0.956552i
$387$	6.79004	+	5.56581i	0.345157	+	0.282926i
$388$	−0.791441	−	0.575016i	−0.0401793	−	0.0291920i
$389$	9.06348	+	12.4748i	0.459536	+	0.632498i	0.974413	−	0.224767i	$-0.0721621\pi$
$389$	9.06348	+	12.4748i	0.459536	+	0.632498i	−0.514876	+	0.857265i	$0.672162\pi$
$390$	−1.80118	+	1.69908i	−0.0912062	+	0.0860362i
$391$	20.3674	+	6.61777i	1.03002	+	0.334675i
$392$	38.6263	−	28.0637i	1.95092	−	1.41743i
$393$	12.0193	+	25.3935i	0.606293	+	1.28093i
$394$	2.18182	+	6.71494i	0.109918	+	0.338294i
$395$	−1.33657			−0.0672501
$396$	1.38641	+	2.98476i	0.0696700	+	0.149990i
$397$	30.3678			1.52411			0.762057	−	0.647509i	$-0.224189\pi$
$397$	30.3678			1.52411			0.762057	+	0.647509i	$0.224189\pi$
$398$	10.1048	+	31.0993i	0.506507	+	1.55887i
$399$	22.5983	+	47.7440i	1.13133	+	2.39019i
$400$	15.1845	−	11.0322i	0.759227	−	0.551611i
$401$	−0.0604489	−	0.0196410i	−0.00301867	−	0.000980826i	0.307507	−	0.951546i	$-0.400505\pi$
$401$	−0.0604489	−	0.0196410i	−0.00301867	−	0.000980826i	−0.310526	+	0.950565i	$0.600505\pi$
$402$	19.4170	−	18.3164i	0.968433	−	0.913538i
$403$	−4.99504	−	6.87508i	−0.248820	−	0.342472i
$404$	2.70251	+	1.96349i	0.134455	+	0.0976873i
$405$	−0.980784	+	8.37031i	−0.0487355	+	0.415924i
$406$			41.0042i			2.03500i
$407$	−4.95899	+	10.2840i	−0.245808	+	0.509757i
$408$	−26.3720	−	14.4208i	−1.30561	−	0.713934i
$409$	−2.23942	+	0.727632i	−0.110732	+	0.0359791i	−0.363859	−	0.931454i	$-0.618541\pi$
$409$	−2.23942	+	0.727632i	−0.110732	+	0.0359791i	0.253127	+	0.967433i	$0.418541\pi$
$410$	−2.27226	+	3.12749i	−0.112219	+	0.154456i
$411$	1.12598	+	8.75422i	0.0555405	+	0.431814i
$412$	0.291623	−	0.897522i	0.0143672	−	0.0442178i
$413$	3.50161	−	10.7768i	0.172303	−	0.530294i
$414$	−5.24194	+	13.4161i	−0.257627	+	0.659366i
$415$	5.92816	−	8.15941i	0.291002	−	0.400530i
$416$	1.76217	−	0.572562i	0.0863973	−	0.0280722i
$417$	−4.98314	+	9.11292i	−0.244025	+	0.446261i
$418$	−29.9530	+	5.41980i	−1.46505	+	0.265091i
$419$		−	19.8575i		−	0.970104i	−0.874485	−	0.485052i	$-0.838801\pi$
$419$		−	19.8575i		−	0.970104i	0.874485	−	0.485052i	$-0.161199\pi$
$420$	0.503918	−	2.67439i	0.0245887	−	0.130497i
$421$	6.79023	+	4.93339i	0.330936	+	0.240439i	0.740827	−	0.671695i	$-0.234434\pi$
$421$	6.79023	+	4.93339i	0.330936	+	0.240439i	−0.409892	+	0.912134i	$0.634434\pi$
$422$	11.1400	+	15.3329i	0.542288	+	0.746395i
$423$	4.18476	+	15.9986i	0.203470	+	0.777879i
$424$	−9.73456	−	3.16295i	−0.472752	−	0.153606i
$425$	−22.7148	+	16.5033i	−1.10183	+	0.800527i
$426$	−3.74187	+	1.77111i	−0.181294	+	0.0858104i
$427$	5.52868	+	17.0155i	0.267552	+	0.823439i
$428$	4.29063			0.207395
$429$	−5.45042	−	1.81464i	−0.263149	−	0.0876117i
$430$	4.18376			0.201759
$431$	10.0690	+	30.9892i	0.485007	+	1.49270i	0.831971	+	0.554819i	$0.187212\pi$
$431$	10.0690	+	30.9892i	0.485007	+	1.49270i	−0.346965	+	0.937878i	$0.612788\pi$
$432$	12.5388	−	20.0566i	0.603272	−	0.964974i
$433$	−6.70454	+	4.87113i	−0.322200	+	0.234092i	−0.737113	−	0.675769i	$-0.763812\pi$
$433$	−6.70454	+	4.87113i	−0.322200	+	0.234092i	0.414914	+	0.909861i	$0.363812\pi$
$434$	62.5949	+	20.3383i	3.00465	+	0.976271i
$435$	−5.89223	−	6.24630i	−0.282511	−	0.299487i
$436$	1.96987	+	2.71129i	0.0943396	+	0.129847i
$437$	−15.2952	−	11.1126i	−0.731670	−	0.531590i
$438$	−6.24127	−	1.17600i	−0.298219	−	0.0561916i
$439$		−	1.39623i		−	0.0666385i	−0.999445	−	0.0333193i	$-0.989392\pi$
$439$		−	1.39623i		−	0.0666385i	0.999445	−	0.0333193i	$-0.0106078\pi$
$440$	−7.12896	−	3.43763i	−0.339860	−	0.163883i
$441$	−30.3302	−	47.3197i	−1.44430	−	2.25332i
$442$	−9.88728	+	3.21257i	−0.470290	+	0.152807i
$443$	−1.08964	+	1.49976i	−0.0517702	+	0.0712555i	−0.834117	−	0.551587i	$-0.814022\pi$
$443$	−1.08964	+	1.49976i	−0.0517702	+	0.0712555i	0.782347	+	0.622843i	$0.214022\pi$
$444$	−1.95603	+	0.251587i	−0.0928289	+	0.0119398i
$445$	−2.08876	+	6.42855i	−0.0990168	+	0.304742i
$446$	9.64715	−	29.6909i	0.456806	−	1.40590i
$447$	−27.7504	+	3.56930i	−1.31255	+	0.168822i
$448$	18.7125	−	25.7556i	0.884084	−	1.21684i
$449$	18.3174	−	5.95167i	0.864450	−	0.280877i	0.156964	−	0.987604i	$-0.449829\pi$
$449$	18.3174	−	5.95167i	0.864450	−	0.280877i	0.707486	+	0.706727i	$0.249829\pi$
$450$	−10.1905	−	15.8987i	−0.480386	−	0.749473i
$451$	−8.88683	−	1.20845i	−0.418465	−	0.0569035i
$452$		−	3.17018i		−	0.149113i
$453$	−1.49642	−	0.281961i	−0.0703080	−	0.0132477i
$454$	15.9354	+	11.5778i	0.747886	+	0.543371i
$455$	2.79218	+	3.84310i	0.130899	+	0.180167i
$456$	18.2080	+	19.3022i	0.852669	+	0.903906i
$457$	−15.8244	−	5.14166i	−0.740235	−	0.240517i	−0.0854606	−	0.996342i	$-0.527236\pi$
$457$	−15.8244	−	5.14166i	−0.740235	−	0.240517i	−0.654774	+	0.755825i	$0.727236\pi$
$458$	4.27009	−	3.10240i	0.199528	−	0.144966i
$459$	−18.7570	+	30.0031i	−0.875501	+	1.40042i
$460$	0.300999	+	0.926381i	0.0140342	+	0.0431927i
$461$	7.75833			0.361342			0.180671	−	0.983544i	$-0.442173\pi$
$461$	7.75833			0.361342			0.180671	+	0.983544i	$0.442173\pi$
$462$	42.4116	−	13.4420i	1.97316	−	0.625377i
$463$	−7.56904			−0.351763			−0.175882	−	0.984411i	$-0.556278\pi$
$463$	−7.56904			−0.351763			−0.175882	+	0.984411i	$0.556278\pi$
$464$	7.44751	+	22.9211i	0.345742	+	1.06408i
$465$	−12.4579	+	5.89659i	−0.577720	+	0.273448i
$466$	−17.6165	+	12.7992i	−0.816069	+	0.592909i
$467$	21.8971	+	7.11479i	1.01328	+	0.329233i	0.768158	−	0.640260i	$-0.221174\pi$
$467$	21.8971	+	7.11479i	1.01328	+	0.329233i	0.245117	+	0.969493i	$0.421174\pi$
$468$	−0.251104	−	0.959988i	−0.0116073	−	0.0443755i
$469$	−30.1001	−	41.4293i	−1.38990	−	1.91303i
$470$	6.37527	+	4.63191i	0.294069	+	0.213654i
$471$	−2.13330	+	11.3218i	−0.0982971	+	0.521681i
$472$		−	5.69231i		−	0.262010i
$473$	4.59513	+	8.54969i	0.211284	+	0.393115i
$474$	1.81084	−	3.31157i	0.0831745	−	0.152105i
$475$	23.5737	−	7.65955i	1.08163	−	0.351444i
$476$	6.71614	−	9.24398i	0.307834	−	0.423697i
$477$	−4.38508	+	11.2231i	−0.200779	+	0.513871i
$478$	0.0334321	−	0.102893i	0.00152915	−	0.00470623i
$479$	1.69878	−	5.22832i	0.0776194	−	0.238888i	−0.904716	−	0.426014i	$-0.859917\pi$
$479$	1.69878	−	5.22832i	0.0776194	−	0.238888i	0.982336	+	0.187126i	$0.0599173\pi$
$480$	−0.383364	−	2.98056i	−0.0174981	−	0.136043i
$481$	2.02339	−	2.78496i	0.0922588	−	0.126983i
$482$	−35.2024	+	11.4380i	−1.60343	+	0.520985i
$483$	24.2452	+	13.2578i	1.10319	+	0.603250i
$484$	0.159506	+	3.63488i	0.00725027	+	0.165222i
$485$		−	2.76953i		−	0.125758i
$486$	−19.4100	−	13.7705i	−0.880456	−	0.624642i
$487$	−7.72559	−	5.61297i	−0.350080	−	0.254348i	0.398823	−	0.917028i	$-0.369419\pi$
$487$	−7.72559	−	5.61297i	−0.350080	−	0.254348i	−0.748903	+	0.662680i	$0.769419\pi$
$488$	5.28276	+	7.27110i	0.239139	+	0.329147i
$489$	8.67267	−	8.18107i	0.392192	−	0.369961i
$490$	−25.4726	−	8.27656i	−1.15074	−	0.373897i
$491$	−25.8293	+	18.7661i	−1.16566	+	0.846902i	−0.990483	−	0.137635i	$-0.956050\pi$
$491$	−25.8293	+	18.7661i	−1.16566	+	0.846902i	−0.175178	+	0.984537i	$0.556050\pi$
$492$	−0.662774	−	1.40026i	−0.0298802	−	0.0631286i
$493$	−11.1409	−	34.2881i	−0.501760	−	1.54426i
$494$	9.17783			0.412930
$495$	−4.52911	+	8.14213i	−0.203568	+	0.365962i
$496$	38.6842			1.73697
$497$	2.45427	+	7.55345i	0.110089	+	0.338819i
$498$	12.1846	+	25.7427i	0.546004	+	1.15356i
$499$	8.73869	−	6.34903i	0.391197	−	0.284222i	−0.374749	−	0.927126i	$-0.622271\pi$
$499$	8.73869	−	6.34903i	0.391197	−	0.284222i	0.765946	+	0.642905i	$0.222271\pi$
$500$	−2.68737	−	0.873179i	−0.120183	−	0.0390498i
$501$	−2.97333	+	2.80478i	−0.132838	+	0.125309i
$502$	27.4497	+	37.7813i	1.22514	+	1.68626i
$503$	−32.3153	−	23.4785i	−1.44087	−	1.04685i	−0.987860	−	0.155348i	$-0.950350\pi$
$503$	−32.3153	−	23.4785i	−1.44087	−	1.04685i	−0.453010	−	0.891505i	$-0.649650\pi$
$504$	−29.9948	−	24.5868i	−1.33607	−	1.09518i
$505$			9.45703i			0.420832i
$506$	−11.0104	+	11.5042i	−0.489472	+	0.511422i
$507$	1.51969	+	0.830997i	0.0674916	+	0.0369059i
$508$	1.80130	−	0.585278i	0.0799198	−	0.0259675i
$509$	−10.6295	+	14.6303i	−0.471146	+	0.648476i	−0.976773	−	0.214275i	$-0.931261\pi$
$509$	−10.6295	+	14.6303i	−0.471146	+	0.648476i	0.505628	+	0.862752i	$0.331261\pi$
$510$	2.15101	+	16.7235i	0.0952482	+	0.740531i
$511$	−3.76518	+	11.5880i	−0.166562	+	0.512624i
$512$	4.56320	−	14.0441i	0.201667	−	0.620667i
$513$	23.9334	−	20.0738i	1.05669	−	0.886279i
$514$	−13.2991	+	18.3046i	−0.586598	+	0.807383i
$515$	2.54091	−	0.825593i	0.111966	−	0.0363800i
$516$	−0.804401	+	1.47105i	−0.0354118	+	0.0647593i
$517$	−2.46337	+	18.1155i	−0.108339	+	0.796718i
$518$			26.6609i			1.17141i
$519$	0.547197	−	2.90408i	0.0240193	−	0.127475i
$520$	1.93057	+	1.40264i	0.0846610	+	0.0615098i
$521$	16.0972	+	22.1559i	0.705232	+	0.970668i	0.999887	+	0.0150642i	$0.00479527\pi$
$521$	16.0972	+	22.1559i	0.705232	+	0.970668i	−0.294655	+	0.955604i	$0.595205\pi$
$522$	23.4593	−	6.13624i	1.02678	−	0.268576i
$523$	1.42171	+	0.461941i	0.0621670	+	0.0201993i	0.339935	−	0.940449i	$-0.389595\pi$
$523$	1.42171	+	0.461941i	0.0621670	+	0.0201993i	−0.277768	+	0.960648i	$0.589595\pi$
$524$	−4.34041	+	3.15350i	−0.189612	+	0.137761i
$525$	−32.7460	+	15.4994i	−1.42915	+	0.676449i
$526$	11.2701	+	34.6858i	0.491399	+	1.51237i
$527$	−57.8684			−2.52079
$528$	21.2664	−	15.2171i	0.925500	−	0.662240i
$529$	13.1096			0.569981
$530$	1.77433	+	5.46082i	0.0770719	+	0.237203i
$531$	−6.68965	−	0.390591i	−0.290306	−	0.0169502i
$532$	−8.16071	+	5.92910i	−0.353812	+	0.257059i
$533$	2.57179	+	0.835626i	0.111397	+	0.0361950i
$534$	−13.0978	−	13.8849i	−0.566799	−	0.600858i
$535$	7.13977	+	9.82705i	0.308679	+	0.424860i
$536$	−20.8119	−	15.1207i	−0.898936	−	0.653115i
$537$	30.3487	+	5.71842i	1.30964	+	0.246768i
$538$		−	8.77672i		−	0.378391i
$539$	−11.0637	−	61.1448i	−0.476549	−	2.63369i
$540$	−1.60548	+	0.111919i	−0.0690888	+	0.00481622i
$541$	−9.47253	+	3.07781i	−0.407256	+	0.132325i	−0.505479	−	0.862839i	$-0.668684\pi$
$541$	−9.47253	+	3.07781i	−0.407256	+	0.132325i	0.0982230	+	0.995164i	$0.468684\pi$
$542$	19.1710	−	26.3866i	0.823465	−	1.13340i
$543$	26.0737	−	3.35363i	1.11893	−	0.143918i
$544$	3.89892	−	11.9996i	0.167165	−	0.514481i
$545$	−2.93188	+	9.02338i	−0.125588	+	0.386519i
$546$	−13.3049	+	1.71129i	−0.569396	+	0.0732365i
$547$	16.9815	−	23.3730i	0.726076	−	0.999358i	−0.273224	−	0.961951i	$-0.588090\pi$
$547$	16.9815	−	23.3730i	0.726076	−	0.999358i	0.999300	−	0.0374079i	$-0.0119101\pi$
$548$	−1.60303	+	0.520856i	−0.0684781	+	0.0222499i
$549$	8.90755	−	5.70943i	0.380165	−	0.243672i
$550$	−3.71726	−	20.5438i	−0.158504	−	0.875989i
$551$			31.8278i			1.35591i
$552$	13.6414	+	2.57037i	0.580618	+	0.109402i
$553$	−5.85805	−	4.25612i	−0.249109	−	0.180989i
$554$	−24.7028	−	34.0004i	−1.04952	−	1.44454i
$555$	−3.83113	−	4.06134i	−0.162622	−	0.172394i
$556$	−1.88636	−	0.612917i	−0.0799996	−	0.0259935i
$557$	19.4265	−	14.1141i	0.823125	−	0.598036i	−0.0944807	−	0.995527i	$-0.530119\pi$
$557$	19.4265	−	14.1141i	0.823125	−	0.598036i	0.917606	+	0.397491i	$0.130119\pi$
$558$	2.26866	−	38.8554i	0.0960401	−	1.64488i
$559$	−0.904358	−	2.78333i	−0.0382503	−	0.117722i
$560$	−21.6241			−0.913784
$561$	−31.8128	+	22.7636i	−1.34314	+	0.961079i
$562$	−31.6753			−1.33614
$563$	4.48780	+	13.8120i	0.189138	+	0.582108i	0.999995	−	0.00313672i	$-0.000998450\pi$
$563$	4.48780	+	13.8120i	0.189138	+	0.582108i	−0.810857	+	0.585245i	$0.800998\pi$
$564$	−2.85438	+	1.35104i	−0.120191	+	0.0568890i
$565$	7.26083	−	5.27530i	0.305465	−	0.221934i
$566$	−32.2077	−	10.4649i	−1.35379	−	0.439873i
$567$	−30.9528	+	33.5630i	−1.29989	+	1.40952i
$568$	2.34510	+	3.22775i	0.0983982	+	0.135433i
$569$	−3.80702	−	2.76596i	−0.159598	−	0.115955i	0.505120	−	0.863049i	$-0.331448\pi$
$569$	−3.80702	−	2.76596i	−0.159598	−	0.115955i	−0.664718	+	0.747094i	$0.731448\pi$
$570$	2.75626	−	14.6280i	0.115447	−	0.612699i
$571$		−	32.8429i		−	1.37443i	−0.726453	−	0.687217i	$-0.758832\pi$
$571$		−	32.8429i		−	1.37443i	0.726453	−	0.687217i	$-0.241168\pi$
$572$	0.147813	−	1.08701i	0.00618039	−	0.0454501i
$573$	9.64404	−	17.6366i	0.402886	−	0.736778i
$574$	−19.9181	+	6.47179i	−0.831367	+	0.270127i
$575$	7.62178	−	10.4905i	0.317850	−	0.437483i
$576$	−17.5356	−	6.85150i	−0.730650	−	0.285479i
$577$	4.55282	−	14.0121i	0.189536	−	0.583333i	−0.810461	−	0.585793i	$-0.800783\pi$
$577$	4.55282	−	14.0121i	0.189536	−	0.583333i	0.999997	+	0.00246009i	$0.000783073\pi$
$578$	−13.8562	+	42.6451i	−0.576344	+	1.77380i
$579$	−2.71997	−	21.1471i	−0.113038	−	0.878844i
$580$	0.963850	−	1.32663i	0.0400217	−	0.0550851i
$581$	51.9650	−	16.8845i	2.15587	−	0.700485i
$582$	6.86196	+	3.75227i	0.284438	+	0.155536i
$583$	−9.21063	+	9.62367i	−0.381465	+	0.398572i
$584$			6.12077i			0.253279i
$585$	1.78086	−	2.17257i	0.0736297	−	0.0898249i
$586$	−9.16869	−	6.66144i	−0.378755	−	0.275182i
$587$	10.6284	+	14.6288i	0.438682	+	0.603794i	0.969919	−	0.243429i	$-0.0782724\pi$
$587$	10.6284	+	14.6288i	0.438682	+	0.603794i	−0.531236	+	0.847224i	$0.678272\pi$
$588$	7.80768	−	7.36510i	0.321983	−	0.303732i
$589$	48.5867	+	15.7868i	2.00198	+	0.650483i
$590$	−2.58338	+	1.87693i	−0.106356	+	0.0772722i
$591$	−3.42695	−	7.24021i	−0.140966	−	0.297822i
$592$	4.84237	+	14.9033i	0.199020	+	0.612521i
$593$	−4.96804			−0.204013			−0.102006	−	0.994784i	$-0.532526\pi$
$593$	−4.96804			−0.204013			−0.102006	+	0.994784i	$0.532526\pi$
$594$	−14.0373	−	22.2529i	−0.575956	−	0.913047i
$595$	32.3479			1.32613
$596$	−1.65109	−	5.08152i	−0.0676311	−	0.208147i
$597$	−15.8714	−	33.5320i	−0.649574	−	1.37237i
$598$	3.88431	−	2.82212i	0.158841	−	0.115405i
$599$	3.35968	+	1.09163i	0.137273	+	0.0446026i	0.376848	−	0.926275i	$-0.377008\pi$
$599$	3.35968	+	1.09163i	0.137273	+	0.0446026i	−0.239575	+	0.970878i	$0.577008\pi$
$600$	−13.2387	+	12.4883i	−0.540467	+	0.509831i
$601$	23.9424	+	32.9539i	0.976630	+	1.34422i	0.938625	+	0.344939i	$0.112100\pi$
$601$	23.9424	+	32.9539i	0.976630	+	1.34422i	0.0380049	+	0.999278i	$0.487900\pi$
$602$	18.3370	+	13.3226i	0.747361	+	0.542989i
$603$	−19.1980	+	23.4207i	−0.781804	+	0.953766i
$604$		−	0.290793i		−	0.0118322i
$605$	−8.05974	+	6.41391i	−0.327675	+	0.260762i
$606$	−23.4314	−	12.8128i	−0.951834	−	0.520483i
$607$	20.4159	−	6.63354i	0.828657	−	0.269247i	0.136177	−	0.990684i	$-0.456518\pi$
$607$	20.4159	−	6.63354i	0.828657	−	0.269247i	0.692480	+	0.721437i	$0.256518\pi$
$608$	−6.54712	+	9.01133i	−0.265521	+	0.365458i
$609$	−5.93458	−	46.1399i	−0.240481	−	1.86968i
$610$	1.55800	−	4.79502i	0.0630814	−	0.194145i
$611$	1.70339	−	5.24250i	0.0689118	−	0.212089i
$612$	−6.29372	−	2.45908i	−0.254409	−	0.0994024i
$613$	−1.93846	+	2.66806i	−0.0782935	+	0.107762i	−0.846368	−	0.532599i	$-0.821215\pi$
$613$	−1.93846	+	2.66806i	−0.0782935	+	0.107762i	0.768074	+	0.640361i	$0.221215\pi$
$614$	−10.6306	+	3.45410i	−0.429018	+	0.139396i
$615$	2.10421	−	3.84807i	0.0848499	−	0.155169i
$616$	−20.2988	−	37.7680i	−0.817864	−	1.52172i
$617$		−	9.10521i		−	0.366562i	−0.983061	−	0.183281i	$-0.941328\pi$
$617$		−	9.10521i		−	0.366562i	0.983061	−	0.183281i	$-0.0586718\pi$
$618$	−1.39699	+	7.41408i	−0.0561951	+	0.298238i
$619$	26.2365	+	19.0619i	1.05453	+	0.766164i	0.973070	−	0.230512i	$-0.0740401\pi$
$619$	26.2365	+	19.0619i	1.05453	+	0.766164i	0.0814652	+	0.996676i	$0.474040\pi$
$620$	−1.54709	−	2.12938i	−0.0621324	−	0.0855180i
$621$	3.95676	−	15.8551i	0.158779	−	0.636245i
$622$	−7.83750	−	2.54656i	−0.314255	−	0.102108i
$623$	−29.6256	+	21.5243i	−1.18693	+	0.862352i
$624$	−7.12652	+	3.37314i	−0.285289	+	0.135034i
$625$	3.89864	+	11.9988i	0.155945	+	0.479951i
$626$	28.2253			1.12811
$627$	32.9202	−	10.4338i	1.31471	−	0.416684i
$628$	−2.20012			−0.0877943
$629$	−7.24379	−	22.2941i	−0.288829	−	0.888923i
$630$	−1.26816	+	21.7198i	−0.0505247	+	0.865336i
$631$	0.294530	−	0.213989i	0.0117251	−	0.00851876i	−0.581907	−	0.813255i	$-0.697693\pi$
$631$	0.294530	−	0.213989i	0.0117251	−	0.00851876i	0.593632	+	0.804736i	$0.297693\pi$
$632$	−3.45943	−	1.12404i	−0.137609	−	0.0447118i
$633$	−14.7545	−	15.6411i	−0.586437	−	0.621676i
$634$	3.77887	+	5.20117i	0.150078	+	0.206565i
$635$	4.33792	+	3.15169i	0.172145	+	0.125071i
$636$	−2.26122	−	0.426068i	−0.0896632	−	0.0168947i
$637$			18.7352i			0.742316i
$638$	26.5633	+	3.61212i	1.05165	+	0.143005i
$639$	3.95420	−	2.53450i	0.156426	−	0.100263i
$640$	−11.8325	+	3.84460i	−0.467719	+	0.151971i
$641$	−4.42245	+	6.08697i	−0.174676	+	0.240421i	−0.887374	−	0.461050i	$-0.847473\pi$
$641$	−4.42245	+	6.08697i	−0.174676	+	0.240421i	0.712698	+	0.701471i	$0.247473\pi$
$642$	−34.0214	+	4.37588i	−1.34272	+	0.172702i
$643$	3.05167	−	9.39206i	0.120346	−	0.370387i	−0.872679	−	0.488295i	$-0.837619\pi$
$643$	3.05167	−	9.39206i	0.120346	−	0.370387i	0.993024	+	0.117908i	$0.0376189\pi$
$644$	−1.63068	+	5.01872i	−0.0642579	+	0.197765i
$645$	−4.70778	+	0.605521i	−0.185368	+	0.0238424i
$646$	36.7350	−	50.5614i	1.44532	−	1.98931i
$647$	44.3509	−	14.4105i	1.74362	−	0.566535i	0.748313	−	0.663346i	$-0.230864\pi$
$647$	44.3509	−	14.4105i	1.74362	−	0.566535i	0.995303	+	0.0968109i	$0.0308642\pi$
$648$	−9.57788	+	20.8400i	−0.376255	+	0.818672i
$649$	−6.67298	−	3.21776i	−0.261938	−	0.126308i
$650$			6.29476i			0.246901i
$651$	−73.3785	−	13.8262i	−2.87593	−	0.541893i
$652$	1.84195	+	1.33826i	0.0721364	+	0.0524102i
$653$	14.7346	+	20.2804i	0.576610	+	0.793635i	0.993319	−	0.115405i	$-0.0368166\pi$
$653$	14.7346	+	20.2804i	0.576610	+	0.793635i	−0.416709	+	0.909040i	$0.636817\pi$
$654$	−18.3847	−	19.4894i	−0.718899	−	0.762098i
$655$	−14.4452	−	4.69354i	−0.564422	−	0.183392i
$656$	−9.95866	+	7.23539i	−0.388820	+	0.282494i
$657$	7.19319	+	0.419991i	0.280633	+	0.0163854i
$658$	13.1925	+	40.6023i	0.514297	+	1.58284i
$659$	1.89711			0.0739009			0.0369505	−	0.999317i	$-0.488236\pi$
$659$	1.89711			0.0739009			0.0369505	+	0.999317i	$0.488236\pi$
$660$	−1.68813	−	0.562039i	−0.0657103	−	0.0218773i
$661$	−50.9393			−1.98131			−0.990655	−	0.136395i	$-0.956448\pi$
$661$	−50.9393			−1.98131			−0.990655	+	0.136395i	$0.956448\pi$
$662$	5.89491	+	18.1427i	0.229112	+	0.705135i
$663$	10.6607	−	5.04594i	0.414027	−	0.195968i
$664$	22.2058	−	16.1334i	0.861751	−	0.626099i
$665$	−27.1595	−	8.82465i	−1.05320	−	0.342205i
$666$	15.2532	−	3.98978i	0.591050	−	0.154601i
$667$	9.78682	+	13.4704i	0.378947	+	0.521576i
$668$	−0.631492	−	0.458806i	−0.0244332	−	0.0177517i
$669$	−6.55826	+	34.8059i	−0.253557	+	1.34567i
$670$			14.4310i			0.557516i
$671$	11.5100	−	2.08266i	0.444339	−	0.0804002i
$672$	7.81094	−	14.2843i	0.301314	−	0.551028i
$673$	6.42377	−	2.08721i	0.247618	−	0.0804560i	−0.182578	−	0.983191i	$-0.558444\pi$
$673$	6.42377	−	2.08721i	0.247618	−	0.0804560i	0.430196	+	0.902735i	$0.358444\pi$
$674$	3.34339	−	4.60178i	0.128782	−	0.177254i
$675$	13.7679	+	16.4151i	0.529927	+	0.631819i
$676$	−0.102211	+	0.314573i	−0.00393119	+	0.0120990i
$677$	8.14230	−	25.0594i	0.312934	−	0.963112i	−0.663663	−	0.748032i	$-0.730999\pi$
$677$	8.14230	−	25.0594i	0.312934	−	0.963112i	0.976597	−	0.215080i	$-0.0690011\pi$
$678$	3.23317	+	25.1371i	0.124169	+	0.965384i
$679$	8.81918	−	12.1386i	0.338449	−	0.465835i
$680$	15.4545	−	5.02148i	0.592654	−	0.192565i
$681$	−19.6070	−	10.7215i	−0.751341	−	0.410849i
$682$	18.6896	−	38.7586i	0.715663	−	1.48414i
$683$		−	19.3517i		−	0.740472i	−0.928938	−	0.370236i	$-0.879277\pi$
$683$		−	19.3517i		−	0.740472i	0.928938	−	0.370236i	$-0.120723\pi$
$684$	4.61340	+	3.78161i	0.176398	+	0.144594i
$685$	−3.86045	−	2.80478i	−0.147500	−	0.107165i
$686$	−53.4223	−	73.5295i	−2.03967	−	2.80737i
$687$	−4.35590	+	4.10899i	−0.166188	+	0.156768i
$688$	12.6700	+	4.11675i	0.483041	+	0.156949i
$689$	3.24938	−	2.36081i	0.123791	−	0.0899398i
$690$	−3.33148	−	7.03851i	−0.126827	−	0.267951i
$691$	4.05752	+	12.4878i	0.154355	+	0.475057i	0.998095	−	0.0616957i	$-0.0196508\pi$
$691$	4.05752	+	12.4878i	0.154355	+	0.475057i	−0.843740	+	0.536753i	$0.819651\pi$
$692$	0.564337			0.0214529
$693$	−45.7781	+	21.2638i	−1.73897	+	0.807746i
$694$	21.3785			0.811515
$695$	−1.73519	−	5.34035i	−0.0658194	−	0.202571i
$696$	−9.99777	−	21.1226i	−0.378964	−	0.800648i
$697$	14.8973	−	10.8236i	0.564277	−	0.409971i
$698$	36.9112	+	11.9932i	1.39711	+	0.453948i
$699$	17.9705	−	16.9519i	0.679708	−	0.641179i
$700$	−4.06657	−	5.59715i	−0.153702	−	0.211553i
$701$	−27.0350	−	19.6421i	−1.02110	−	0.741871i	−0.0545904	−	0.998509i	$-0.517385\pi$
$701$	−27.0350	−	19.6421i	−1.02110	−	0.741871i	−0.966508	+	0.256638i	$0.917385\pi$
$702$	2.97013	+	7.35588i	0.112100	+	0.277630i
$703$			20.6944i			0.780504i
$704$	−15.0366	−	14.3912i	−0.566711	−	0.542388i
$705$	−7.84415	−	4.28935i	−0.295428	−	0.161546i
$706$	−48.1988	+	15.6607i	−1.81398	+	0.589399i
$707$	−30.1146	+	41.4492i	−1.13258	+	1.55886i
$708$	−0.163248	−	1.26921i	−0.00613523	−	0.0476999i
$709$	−4.83075	+	14.8675i	−0.181422	+	0.558361i	−0.999868	−	0.0162226i	$-0.994836\pi$
$709$	−4.83075	+	14.8675i	−0.181422	+	0.558361i	0.818446	+	0.574584i	$0.194836\pi$
$710$	0.691619	−	2.12858i	0.0259560	−	0.0798843i
$711$	−1.55836	+	3.98843i	−0.0584429	+	0.149578i
$712$	−10.8127	+	14.8823i	−0.405221	+	0.557739i
$713$	25.4176	−	8.25867i	0.951895	−	0.309290i
$714$	−43.8262	+	80.1472i	−1.64015	+	2.99943i
$715$	2.73560	−	1.47028i	0.102306	−	0.0549854i
$716$			5.89754i			0.220402i
$717$	−0.0227276	+	0.120619i	−0.000848776	+	0.00450461i
$718$	−12.5328	−	9.10558i	−0.467718	−	0.339817i
$719$	20.0092	+	27.5403i	0.746217	+	1.02708i	0.998237	+	0.0593576i	$0.0189052\pi$
$719$	20.0092	+	27.5403i	0.746217	+	1.02708i	−0.252020	+	0.967722i	$0.581095\pi$
$720$	3.23603	+	12.3716i	0.120600	+	0.461061i
$721$	13.7656	+	4.47270i	0.512656	+	0.166572i
$722$	−21.1692	+	15.3803i	−0.787836	+	0.572396i
$723$	37.9561	−	17.9655i	1.41160	−	0.668142i
$724$	1.55132	+	4.77448i	0.0576545	+	0.177442i
$725$	−21.8296			−0.810730
$726$	−4.97186	−	28.6592i	−0.184523	−	1.06364i
$727$	30.0832			1.11572			0.557862	−	0.829933i	$-0.311622\pi$
$727$	30.0832			1.11572			0.557862	+	0.829933i	$0.311622\pi$
$728$	3.99497	+	12.2953i	0.148063	+	0.455692i
$729$	23.8341	+	12.6860i	0.882745	+	0.469852i
$730$	2.77783	−	2.01821i	0.102812	−	0.0746974i
$731$	−18.9534	−	6.15832i	−0.701015	−	0.227774i
$732$	1.38642	+	1.46973i	0.0512436	+	0.0543229i
$733$	13.7105	+	18.8709i	0.506409	+	0.697013i	0.983309	−	0.181945i	$-0.0582393\pi$
$733$	13.7105	+	18.8709i	0.506409	+	0.697013i	−0.476899	+	0.878958i	$0.658239\pi$
$734$	−7.64448	−	5.55404i	−0.282163	−	0.205003i
$735$	29.8609	+	5.62651i	1.10144	+	0.207537i
$736$			5.82704i			0.214788i
$737$	−29.4903	+	15.8499i	−1.08629	+	0.583838i
$738$	6.68337	+	10.4270i	0.246018	+	0.383825i
$739$	21.0205	−	6.82999i	0.773253	−	0.251245i	0.104296	−	0.994546i	$-0.466741\pi$
$739$	21.0205	−	6.82999i	0.773253	−	0.251245i	0.668957	+	0.743301i	$0.266741\pi$
$740$	0.626694	−	0.862571i	0.0230377	−	0.0317087i
$741$	−10.3273	+	1.32832i	−0.379384	+	0.0487970i
$742$	−9.61253	+	29.5843i	−0.352887	+	1.08608i
$743$	−11.5721	+	35.6152i	−0.424538	+	1.30659i	0.478898	+	0.877871i	$0.341036\pi$
$743$	−11.5721	+	35.6152i	−0.424538	+	1.30659i	−0.903436	+	0.428723i	$0.858964\pi$
$744$	−37.2036	+	4.78518i	−1.36395	+	0.175433i
$745$	8.89100	−	12.2374i	0.325741	−	0.448344i
$746$	−11.4097	+	3.70724i	−0.417739	+	0.135732i
$747$	−17.4364	−	27.2034i	−0.637966	−	0.995322i
$748$	−5.39679	−	5.16516i	−0.197326	−	0.188857i
$749$			65.8066i			2.40452i
$750$	22.1993	+	4.18287i	0.810604	+	0.152737i
$751$	−7.98011	−	5.79789i	−0.291199	−	0.211568i	0.432589	−	0.901591i	$-0.357600\pi$
$751$	−7.98011	−	5.79789i	−0.291199	−	0.211568i	−0.723787	+	0.690023i	$0.757600\pi$
$752$	14.7491	+	20.3003i	0.537843	+	0.740277i
$753$	−36.3559	−	38.5406i	−1.32488	−	1.40450i
$754$	−7.68724	−	2.49774i	−0.279953	−	0.0909622i
$755$	0.666019	−	0.483891i	0.0242389	−	0.0176106i
$756$	−7.39305	−	4.62190i	−0.268882	−	0.168097i
$757$	−3.66103	−	11.2675i	−0.133062	−	0.409524i	0.862221	−	0.506532i	$-0.169073\pi$
$757$	−3.66103	−	11.2675i	−0.133062	−	0.409524i	−0.995284	+	0.0970082i	$0.969073\pi$
$758$	6.53572			0.237388
$759$	10.7244	−	14.5386i	0.389272	−	0.527717i
$760$	−14.3456			−0.520369
$761$	13.1465	+	40.4606i	0.476559	+	1.46670i	0.843844	+	0.536589i	$0.180287\pi$
$761$	13.1465	+	40.4606i	0.476559	+	1.46670i	−0.367285	+	0.930108i	$0.619713\pi$
$762$	−13.6860	+	6.47789i	−0.495792	+	0.234669i
$763$	−41.5838	+	30.2124i	−1.50544	+	1.09376i
$764$	3.65075	+	1.18620i	0.132079	+	0.0429152i
$765$	−4.84084	−	18.5068i	−0.175021	−	0.669116i
$766$	12.5080	+	17.2158i	0.451934	+	0.622033i
$767$	1.80709	+	1.31293i	0.0652501	+	0.0474070i
$768$	2.48014	−	13.1626i	0.0894943	−	0.474963i
$769$		−	1.60824i		−	0.0579946i	−0.999579	−	0.0289973i	$-0.990769\pi$
$769$		−	1.60824i		−	0.0579946i	0.999579	−	0.0289973i	$-0.00923142\pi$
$770$	−10.4473	+	21.6656i	−0.376495	+	0.780776i
$771$	12.3155	−	22.5221i	0.443534	−	0.811113i
$772$	3.87235	−	1.25820i	0.139369	−	0.0452838i
$773$	4.48185	−	6.16874i	0.161201	−	0.221874i	−0.720774	−	0.693170i	$-0.756214\pi$
$773$	4.48185	−	6.16874i	0.161201	−	0.221874i	0.881975	+	0.471296i	$0.156214\pi$
$774$	4.87801	−	12.4847i	0.175336	−	0.448752i
$775$	−10.8276	+	33.3240i	−0.388939	+	1.19703i
$776$	2.32914	−	7.16835i	0.0836112	−	0.257329i
$777$	−3.85866	−	30.0001i	−0.138429	−	1.07625i
$778$	13.8371	−	19.0451i	0.496083	−	0.682799i
$779$	−15.4606	+	5.02346i	−0.553934	+	0.179984i
$780$	0.470684	+	0.257380i	0.0168532	+	0.00921568i
$781$	5.10947	−	0.924525i	0.182831	−	0.0330821i
$782$		−	32.6948i		−	1.16916i
$783$	−25.5094	+	10.3001i	−0.911633	+	0.368095i
$784$	−68.9970	−	50.1292i	−2.46418	−	1.79033i
$785$	−3.66108	−	5.03905i	−0.130670	−	0.179851i
$786$	31.2000	−	29.4315i	1.11287	−	1.04979i
$787$	−44.3797	−	14.4198i	−1.58196	−	0.514012i	−0.619403	−	0.785073i	$-0.712625\pi$
$787$	−44.3797	−	14.4198i	−1.58196	−	0.514012i	−0.962562	+	0.271062i	$0.912625\pi$
$788$	1.23754	−	0.899127i	0.0440856	−	0.0320301i
$789$	−17.7018	−	37.3990i	−0.630200	−	1.33144i
$790$	0.630555	+	1.94065i	0.0224341	+	0.0690451i
$791$	48.6219			1.72880
$792$	−18.5701	+	17.2653i	−0.659859	+	0.613496i
$793$	−3.52675			−0.125239
$794$	−14.3266	−	44.0929i	−0.508433	−	1.56480i
$795$	−2.78691	−	5.88798i	−0.0988416	−	0.208825i
$796$	5.73150	−	4.16418i	0.203148	−	0.147596i
$797$	18.3275	+	5.95496i	0.649192	+	0.210935i	0.615058	−	0.788482i	$-0.289133\pi$
$797$	18.3275	+	5.95496i	0.649192	+	0.210935i	0.0341344	+	0.999417i	$0.489133\pi$
$798$	58.6613	−	55.3361i	2.07659	−	1.95888i
$799$	−22.0634	−	30.3677i	−0.780547	−	1.07433i
$800$	−6.18057	−	4.49044i	−0.218516	−	0.158761i
$801$	16.7479	+	13.7283i	0.591759	+	0.485066i
$802$			0.0970355i			0.00342644i
$803$	7.17526	+	3.45996i	0.253210	+	0.122099i
$804$	−5.07406	−	2.77460i	−0.178948	−	0.0978527i
$805$	−14.2082	+	4.61651i	−0.500772	+	0.162711i
$806$	−7.62584	+	10.4961i	−0.268609	+	0.369708i
$807$	1.27026	+	9.87600i	0.0447154	+	0.347652i
$808$	−7.95324	+	24.4776i	−0.279794	+	0.861118i
$809$	−12.9273	+	39.7861i	−0.454500	+	1.39881i	0.417222	+	0.908805i	$0.363004\pi$
$809$	−12.9273	+	39.7861i	−0.454500	+	1.39881i	−0.871722	+	0.490001i	$0.836996\pi$
$810$	12.6161	−	2.52481i	0.443284	−	0.0887128i
$811$	−28.1730	+	38.7768i	−0.989288	+	1.36164i	−0.0576160	+	0.998339i	$0.518350\pi$
$811$	−28.1730	+	38.7768i	−0.989288	+	1.36164i	−0.931672	+	0.363300i	$0.881650\pi$
$812$	8.44892	−	2.74522i	0.296499	−	0.0963383i
$813$	−17.7532	+	32.4662i	−0.622631	+	1.13864i
$814$	17.2714	+	2.34860i	0.605363	+	0.0823183i
$815$			6.44563i			0.225781i
$816$	−9.94159	+	52.7619i	−0.348025	+	1.84704i
$817$	14.2333	+	10.3411i	0.497961	+	0.361790i
$818$	2.11299	+	2.90828i	0.0738789	+	0.101686i
$819$	14.7236	−	3.85126i	0.514485	−	0.134574i
$820$	0.796547	+	0.258814i	0.0278166	+	0.00903817i
$821$	31.0885	−	22.5871i	1.08500	−	0.788296i	0.106448	−	0.994318i	$-0.466052\pi$
$821$	31.0885	−	22.5871i	1.08500	−	0.788296i	0.978547	+	0.206023i	$0.0660521\pi$
$822$	12.1796	−	5.76487i	0.424812	−	0.201073i
$823$	−15.9220	−	49.0027i	−0.555004	−	1.70813i	−0.695932	−	0.718108i	$-0.745008\pi$
$823$	−15.9220	−	49.0027i	−0.555004	−	1.70813i	0.140927	−	0.990020i	$-0.454992\pi$
$824$	7.27094			0.253295
$825$	7.15616	+	22.5788i	0.249146	+	0.786094i
$826$	−17.2995			−0.601927
$827$	−17.0995	−	52.6270i	−0.594609	−	1.83002i	−0.556662	−	0.830739i	$-0.687918\pi$
$827$	−17.0995	−	52.6270i	−0.594609	−	1.83002i	−0.0379474	−	0.999280i	$-0.512082\pi$
$828$	3.11534	+	0.181896i	0.108266	+	0.00632134i
$829$	27.0021	−	19.6182i	0.937822	−	0.681368i	−0.0100735	−	0.999949i	$-0.503207\pi$
$829$	27.0021	−	19.6182i	0.937822	−	0.681368i	0.947895	+	0.318582i	$0.103207\pi$
$830$	−14.6439	−	4.75809i	−0.508297	−	0.165156i
$831$	32.7177	+	34.6837i	1.13496	+	1.20316i
$832$	3.68866	+	5.07701i	0.127881	+	0.176014i
$833$	103.214	+	74.9893i	3.57615	+	2.59822i
$834$	15.5825	+	2.93611i	0.539578	+	0.101669i
$835$		−	2.20981i		−	0.0764736i
$836$	3.12210	+	5.80897i	0.107980	+	0.200907i
$837$	3.07077	+	44.0503i	0.106141	+	1.52260i
$838$	−28.8324	+	9.36821i	−0.995998	+	0.323619i
$839$	28.1403	−	38.7318i	0.971511	−	1.33717i	0.0302311	−	0.999543i	$-0.490376\pi$
$839$	28.1403	−	38.7318i	0.971511	−	1.33717i	0.941280	−	0.337627i	$-0.109624\pi$
$840$	20.7964	−	2.67487i	0.717545	−	0.0922917i
$841$	−0.299600	+	0.922075i	−0.0103310	+	0.0317957i
$842$	3.95966	−	12.1866i	0.136459	−	0.419978i
$843$	35.6426	−	4.58440i	1.22760	−	0.157895i
$844$	2.41353	−	3.32194i	0.0830771	−	0.114346i
$845$	−0.890567	+	0.289363i	−0.0306364	+	0.00995438i
$846$	21.2551	−	13.6238i	0.730767	−	0.468396i
$847$	−55.7492	+	2.44639i	−1.91557	+	0.0840589i
$848$			18.2834i			0.627854i
$849$	37.7563	+	7.11418i	1.29579	+	0.244158i
$850$	34.6784	+	25.1953i	1.18946	+	0.864192i
$851$	6.36338	+	8.75844i	0.218134	+	0.300236i
$852$	0.615454	+	0.652437i	0.0210851	+	0.0223521i
$853$	−12.3900	−	4.02575i	−0.424225	−	0.137839i	0.0891211	−	0.996021i	$-0.471594\pi$
$853$	−12.3900	−	4.02575i	−0.424225	−	0.137839i	−0.513346	+	0.858182i	$0.671594\pi$
$854$	22.0976	−	16.0549i	0.756165	−	0.549386i
$855$	−0.984355	+	16.8591i	−0.0336642	+	0.576568i
$856$	10.2154	+	31.4397i	0.349155	+	1.07459i
$857$	39.7721			1.35859			0.679294	−	0.733866i	$-0.262286\pi$
$857$	39.7721			1.35859			0.679294	+	0.733866i	$0.262286\pi$
$858$	−0.0634392	+	8.76990i	−0.00216578	+	0.299399i
$859$	−18.2157			−0.621511			−0.310755	−	0.950490i	$-0.600582\pi$
$859$	−18.2157			−0.621511			−0.310755	+	0.950490i	$0.600582\pi$
$860$	−0.280102	−	0.862065i	−0.00955139	−	0.0293962i
$861$	21.4762	−	10.1652i	0.731907	−	0.346427i
$862$	40.2449	−	29.2396i	1.37075	−	0.995905i
$863$	50.9598	+	16.5578i	1.73469	+	0.563635i	0.994114	−	0.108337i	$-0.0345525\pi$
$863$	50.9598	+	16.5578i	1.73469	+	0.563635i	0.740576	+	0.671972i	$0.234553\pi$
$864$	−9.34121	−	2.33116i	−0.317794	−	0.0793077i
$865$	0.939079	+	1.29253i	0.0319296	+	0.0439474i
$866$	10.2357	+	7.43668i	0.347824	+	0.252709i
$867$	9.41965	−	49.9918i	0.319908	−	1.69781i
$868$		−	14.2593i		−	0.483994i
$869$	−3.27324	+	3.42003i	−0.111037	+	0.116016i
$870$	−6.28961	+	11.5021i	−0.213238	+	0.389959i
$871$	9.60047	−	3.11938i	0.325299	−	0.105696i
$872$	−15.1771	+	20.8895i	−0.513962	+	0.707407i
$873$	−8.26449	−	3.22910i	−0.279711	−	0.109288i
$874$	−8.91928	+	27.4507i	−0.301699	+	0.928535i
$875$	13.3922	−	41.2169i	0.452739	−	1.39339i
$876$	0.175536	+	1.36475i	0.00593080	+	0.0461105i
$877$	16.1454	−	22.2222i	0.545191	−	0.750391i	−0.444159	−	0.895948i	$-0.646497\pi$
$877$	16.1454	−	22.2222i	0.545191	−	0.750391i	0.989350	+	0.145557i	$0.0464974\pi$
$878$	−2.02728	+	0.658702i	−0.0684173	+	0.0222301i
$879$	11.2812	+	6.16879i	0.380505	+	0.208068i
$880$	−1.90490	+	14.0085i	−0.0642141	+	0.472226i
$881$			18.4648i			0.622096i	0.950394	+	0.311048i	$0.100680\pi$
$881$			18.4648i			0.622096i	−0.950394	+	0.311048i	$0.899320\pi$
$882$	−54.3974	+	66.3624i	−1.83166	+	2.23454i
$883$	17.7278	+	12.8800i	0.596587	+	0.433446i	0.844666	−	0.535294i	$-0.179799\pi$
$883$	17.7278	+	12.8800i	0.596587	+	0.433446i	−0.248078	+	0.968740i	$0.579799\pi$
$884$	1.32390	+	1.82220i	0.0445277	+	0.0612871i
$885$	2.63529	−	2.48591i	0.0885844	−	0.0835631i
$886$	2.69165	+	0.874569i	0.0904276	+	0.0293817i
$887$	30.2483	−	21.9767i	1.01564	−	0.737904i	0.0502535	−	0.998736i	$-0.483997\pi$
$887$	30.2483	−	21.9767i	1.01564	−	0.737904i	0.965384	+	0.260833i	$0.0839971\pi$
$888$	−6.50054	−	13.7339i	−0.218144	−	0.460878i
$889$	8.97657	+	27.6270i	0.301065	+	0.926581i
$890$	10.3194			0.345908
$891$	19.0161	+	23.0084i	0.637064	+	0.770811i
$892$	−6.76368			−0.226465
$893$	10.2401	+	31.5159i	0.342673	+	1.05464i
$894$	18.2743	+	38.6087i	0.611185	+	1.29127i
$895$	−13.5074	+	9.81374i	−0.451504	+	0.328037i
$896$	−64.1031	−	20.8284i	−2.14153	−	0.695826i
$897$	−3.96237	+	3.73777i	−0.132300	+	0.124800i
$898$	−17.2832	−	23.7883i	−0.576748	−	0.793826i
$899$	−36.3993	−	26.4456i	−1.21398	−	0.882011i
$900$	−2.59368	+	3.16417i	−0.0864560	+	0.105472i
$901$		−	27.3504i		−	0.911175i
$902$	2.43793	+	13.4735i	0.0811743	+	0.448617i
$903$	−22.5619	−	12.3373i	−0.750813	−	0.410561i
$904$	23.2296	−	7.54776i	0.772605	−	0.251035i
$905$	−8.35379	+	11.4980i	−0.277689	+	0.382207i
$906$	0.296571	+	2.30577i	0.00985292	+	0.0766040i
$907$	−4.10033	+	12.6195i	−0.136149	+	0.419024i	−0.995767	−	0.0919134i	$-0.970702\pi$
$907$	−4.10033	+	12.6195i	−0.136149	+	0.419024i	0.859618	+	0.510938i	$0.170702\pi$
$908$	1.31873	−	4.05862i	0.0437635	−	0.134690i
$909$	28.2205	+	11.0263i	0.936016	+	0.365719i
$910$	4.26277	−	5.86720i	0.141309	−	0.194496i
$911$	−39.3190	+	12.7755i	−1.30270	+	0.423272i	−0.876518	−	0.481368i	$-0.840140\pi$
$911$	−39.3190	+	12.7755i	−1.30270	+	0.423272i	−0.426177	+	0.904640i	$0.640140\pi$
$912$	22.7407	−	41.5871i	0.753020	−	1.37709i
$913$	−6.36040	−	35.1513i	−0.210498	−	1.16334i
$914$			25.4021i			0.840228i
$915$	−1.05915	+	5.62108i	−0.0350143	+	0.185827i
$916$	−0.925132	−	0.672148i	−0.0305672	−	0.0222084i
$917$	−48.3661	−	66.5702i	−1.59719	−	2.19834i
$918$	52.4123	+	13.0798i	1.72986	+	0.431699i
$919$	−12.6241	−	4.10183i	−0.416432	−	0.135307i	0.0933045	−	0.995638i	$-0.470257\pi$
$919$	−12.6241	−	4.10183i	−0.416432	−	0.135307i	−0.509736	+	0.860331i	$0.670257\pi$
$920$	−6.07145	+	4.41117i	−0.200170	+	0.145432i
$921$	11.4622	−	5.42531i	0.377692	−	0.178770i
$922$	−3.66016	−	11.2648i	−0.120541	−	0.370987i
$923$	−1.56558			−0.0515317
$924$	−5.60916	−	7.83897i	−0.184528	−	0.257883i
$925$	−14.1936			−0.466682
$926$	3.57086	+	10.9900i	0.117346	+	0.361153i
$927$	0.498912	−	8.54487i	0.0163864	−	0.280650i
$928$	7.93621	−	5.76600i	0.260519	−	0.189278i
$929$	49.2249	+	15.9941i	1.61502	+	0.524751i	0.970759	−	0.240058i	$-0.0771663\pi$
$929$	49.2249	+	15.9941i	1.61502	+	0.524751i	0.644258	+	0.764808i	$0.277166\pi$
$930$	14.4389	+	15.3065i	0.473470	+	0.501921i
$931$	−66.2016	−	91.1186i	−2.16967	−	2.98629i
$932$	3.81669	+	2.77299i	0.125020	+	0.0908322i
$933$	9.18771	+	1.73118i	0.300792	+	0.0566764i
$934$		−	35.1503i		−	1.15015i
$935$	2.84957	−	20.9556i	0.0931910	−	0.685321i
$936$	6.43651	−	4.12557i	0.210384	−	0.134849i
$937$	39.9086	−	12.9671i	1.30376	−	0.423616i	0.426870	−	0.904313i	$-0.359616\pi$
$937$	39.9086	−	12.9671i	1.30376	−	0.423616i	0.876887	+	0.480697i	$0.159616\pi$
$938$	−45.9534	+	63.2494i	−1.50043	+	2.06517i
$939$	−31.7605	+	4.08508i	−1.03647	+	0.133312i
$940$	0.527582	−	1.62373i	0.0172078	−	0.0529602i
$941$	14.5431	−	44.7590i	0.474091	−	1.45910i	−0.373090	−	0.927795i	$-0.621702\pi$
$941$	14.5431	−	44.7590i	0.474091	−	1.45910i	0.847180	−	0.531306i	$-0.178298\pi$
$942$	17.4452	−	2.24383i	0.568397	−	0.0731080i
$943$	−4.99868	+	6.88010i	−0.162780	+	0.224047i
$944$	−9.67033	+	3.14208i	−0.314742	+	0.102266i
$945$	−1.71653	−	24.6237i	−0.0558388	−	0.801009i
$946$	10.2460	−	10.7055i	0.333126	−	0.348064i
$947$		−	39.4432i		−	1.28173i	−0.767653	−	0.640865i	$-0.778576\pi$
$947$		−	39.4432i		−	1.28173i	0.767653	−	0.640865i	$-0.221424\pi$
$948$	−0.803585	−	0.151414i	−0.0260992	−	0.00491771i
$949$	−1.94311	−	1.41175i	−0.0630759	−	0.0458274i
$950$	−22.2428	−	30.6145i	−0.721651	−	0.993267i
$951$	−5.00494	−	5.30569i	−0.162296	−	0.172049i
$952$	83.7258	+	27.2042i	2.71357	+	0.881692i
$953$	−0.774365	+	0.562609i	−0.0250841	+	0.0182247i	−0.600257	−	0.799807i	$-0.704935\pi$
$953$	−0.774365	+	0.562609i	−0.0250841	+	0.0182247i	0.575173	+	0.818032i	$0.304935\pi$
$954$	18.3643	+	1.07224i	0.594565	+	0.0347151i
$955$	3.35817	+	10.3354i	0.108668	+	0.334445i
$956$	−0.0234395			−0.000758086
$957$	−30.4131	−	0.220001i	−0.983116	−	0.00711161i
$958$	−8.39276			−0.271158
$959$	−7.98852	−	24.5861i	−0.257963	−	0.793928i
$960$	9.19971	−	4.35442i	0.296919	−	0.140538i
$961$	−33.3453	+	24.2268i	−1.07566	+	0.781510i
$962$	−4.99824	−	1.62403i	−0.161150	−	0.0523607i
$963$	37.6492	−	9.84791i	1.21323	−	0.317344i
$964$	4.71359	+	6.48770i	0.151815	+	0.208955i
$965$	9.32548	+	6.77536i	0.300198	+	0.218106i
$966$	7.81162	−	41.4577i	0.251335	−	1.33388i
$967$		−	15.8845i		−	0.510811i	−0.966834	−	0.255405i	$-0.917791\pi$
$967$		−	15.8845i		−	0.510811i	0.966834	−	0.255405i	$-0.0822089\pi$
$968$	−26.2550	+	9.82294i	−0.843867	+	0.315721i
$969$	−34.0182	+	62.2109i	−1.09282	+	1.99850i
$970$	−4.02125	+	1.30658i	−0.129115	+	0.0419519i
$971$	−0.202515	+	0.278737i	−0.00649900	+	0.00894511i	−0.812254	−	0.583304i	$-0.801760\pi$
$971$	−0.202515	+	0.278737i	−0.00649900	+	0.00894511i	0.805755	+	0.592249i	$0.201760\pi$
$972$	−1.53791	+	4.92137i	−0.0493286	+	0.157853i
$973$	9.40048	−	28.9317i	0.301365	−	0.927507i
$974$	−4.50511	+	13.8653i	−0.144353	+	0.444273i
$975$	−0.911048	−	7.08317i	−0.0291769	−	0.226843i
$976$	9.43643	−	12.9881i	0.302053	−	0.415740i
$977$	−34.9810	+	11.3660i	−1.11914	+	0.363632i	−0.809440	−	0.587202i	$-0.800229\pi$
$977$	−34.9810	+	11.3660i	−1.11914	+	0.363632i	−0.309702	+	0.950834i	$0.600229\pi$
$978$	−15.9701	−	8.73280i	−0.510668	−	0.279244i
$979$	11.3341	+	21.0882i	0.362239	+	0.673981i
$980$			5.80276i			0.185362i
$981$	23.5081	+	19.2696i	0.750556	+	0.615232i
$982$	39.4332	+	28.6499i	1.25836	+	0.914255i
$983$	4.92310	+	6.77607i	0.157023	+	0.216123i	0.880279	−	0.474457i	$-0.157355\pi$
$983$	4.92310	+	6.77607i	0.157023	+	0.216123i	−0.723256	+	0.690580i	$0.757355\pi$
$984$	8.68249	−	8.19033i	0.276788	−	0.261098i
$985$	4.11864	+	1.33823i	0.131231	+	0.0426394i
$986$	−44.5291	+	32.3523i	−1.41809	+	1.03031i
$987$	−20.7213	−	43.7784i	−0.659565	−	1.39348i
$988$	−0.614453	−	1.89109i	−0.0195484	−	0.0601637i
$989$	9.20377			0.292663
$990$	13.9588	+	2.73487i	0.443639	+	0.0869197i
$991$	−18.5100			−0.587990			−0.293995	−	0.955807i	$-0.594985\pi$
$991$	−18.5100			−0.587990			−0.293995	+	0.955807i	$0.594985\pi$
$992$	−4.86567	−	14.9750i	−0.154485	−	0.475457i
$993$	−9.25906	−	19.5619i	−0.293827	−	0.620777i
$994$	9.80948	−	7.12700i	0.311138	−	0.226055i
$995$	19.0749	+	6.19781i	0.604714	+	0.196484i
$996$	4.48853	−	4.23410i	0.142224	−	0.134163i
$997$	23.7444	+	32.6814i	0.751994	+	1.03503i	0.997838	+	0.0657213i	$0.0209348\pi$
$997$	23.7444	+	32.6814i	0.751994	+	1.03503i	−0.245844	+	0.969309i	$0.579065\pi$
$998$	−13.3412	−	9.69296i	−0.422309	−	0.306825i
$999$	−16.5862	+	6.69711i	−0.524764	+	0.211887i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.x.a.248.12	✓	192
3.2	odd	2	inner	429.2.x.a.248.37	yes	192
11.2	odd	10	inner	429.2.x.a.365.37	yes	192
33.2	even	10	inner	429.2.x.a.365.12	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.x.a.248.12	✓	192	1.1	even	1	trivial
429.2.x.a.248.37	yes	192	3.2	odd	2	inner
429.2.x.a.365.12	yes	192	33.2	even	10	inner
429.2.x.a.365.37	yes	192	11.2	odd	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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.x (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.471771 - 1.45196i) q^{2} +(0.741004 + 1.56554i) q^{3} +(-0.267592 + 0.194417i) q^{4} +(-0.890567 - 0.289363i) q^{5} +(1.92352 - 1.81449i) q^{6} +(-2.98183 - 4.10413i) q^{7} +(-2.06170 - 1.49791i) q^{8} +(-1.90183 + 2.32014i) q^{9} +O(q^{10})\)	\(q+(-0.471771 - 1.45196i) q^{2} +(0.741004 + 1.56554i) q^{3} +(-0.267592 + 0.194417i) q^{4} +(-0.890567 - 0.289363i) q^{5} +(1.92352 - 1.81449i) q^{6} +(-2.98183 - 4.10413i) q^{7} +(-2.06170 - 1.49791i) q^{8} +(-1.90183 + 2.32014i) q^{9} +1.42958i q^{10} +(-2.92141 + 1.57015i) q^{11} +(-0.502654 - 0.274862i) q^{12} +(0.951057 - 0.309017i) q^{13} +(-4.55231 + 6.26571i) q^{14} +(-0.206905 - 1.60864i) q^{15} +(-1.40668 + 4.32932i) q^{16} +(2.10428 - 6.47632i) q^{17} +(4.26598 + 1.66680i) q^{18} +(-3.53354 + 4.86350i) q^{19} +(0.294566 - 0.0957101i) q^{20} +(4.21564 - 7.70935i) q^{21} +(3.65803 + 3.50103i) q^{22} +3.14491i q^{23} +(0.817312 - 4.33763i) q^{24} +(-3.33571 - 2.42353i) q^{25} +(-0.897362 - 1.23511i) q^{26} +(-5.04153 - 1.25815i) q^{27} +(1.59583 + 0.518516i) q^{28} +(4.28324 - 3.11196i) q^{29} +(-2.23807 + 1.05933i) q^{30} +(-2.62605 - 8.08214i) q^{31} +1.85285 q^{32} +(-4.62290 - 3.41010i) q^{33} -10.3961 q^{34} +(1.46793 + 4.51783i) q^{35} +(0.0578384 - 0.990599i) q^{36} +(2.78496 - 2.02339i) q^{37} +(8.72863 + 2.83610i) q^{38} +(1.18851 + 1.25993i) q^{39} +(1.40264 + 1.93057i) q^{40} +(2.18770 + 1.58945i) q^{41} +(-13.1825 - 2.48390i) q^{42} -2.92656i q^{43} +(0.476483 - 0.988130i) q^{44} +(2.36507 - 1.51592i) q^{45} +(4.56628 - 1.48368i) q^{46} +(3.24004 - 4.45954i) q^{47} +(-7.82008 + 1.00583i) q^{48} +(-5.78950 + 17.8182i) q^{49} +(-1.94519 + 5.98667i) q^{50} +(11.6982 - 1.50464i) q^{51} +(-0.194417 + 0.267592i) q^{52} +(3.81987 - 1.24115i) q^{53} +(0.551667 + 7.91367i) q^{54} +(3.05605 - 0.552973i) q^{55} +12.9280i q^{56} +(-10.2324 - 1.92802i) q^{57} +(-6.53916 - 4.75098i) q^{58} +(1.31293 + 1.80709i) q^{59} +(0.368112 + 0.390232i) q^{60} +(-3.35414 - 1.08983i) q^{61} +(-10.4961 + 7.62584i) q^{62} +(15.1931 + 0.887084i) q^{63} +(1.93924 + 5.96838i) q^{64} -0.936397 q^{65} +(-2.77038 + 8.32107i) q^{66} +10.0945 q^{67} +(0.696017 + 2.14212i) q^{68} +(-4.92347 + 2.33039i) q^{69} +(5.86720 - 4.26277i) q^{70} +(-1.48896 - 0.483791i) q^{71} +(7.39635 - 1.93466i) q^{72} +(-1.41175 - 1.94311i) q^{73} +(-4.25175 - 3.08908i) q^{74} +(1.32236 - 7.01803i) q^{75} -1.98841i q^{76} +(15.1552 + 7.30796i) q^{77} +(1.26867 - 2.32008i) q^{78} +(1.35749 - 0.441076i) q^{79} +(2.50549 - 3.44851i) q^{80} +(-1.76612 - 8.82501i) q^{81} +(1.27574 - 3.92631i) q^{82} +(-3.32831 + 10.2435i) q^{83} +(0.370758 + 2.88255i) q^{84} +(-3.74801 + 5.15869i) q^{85} +(-4.24926 + 1.38067i) q^{86} +(8.04580 + 4.39961i) q^{87} +(8.37500 + 1.13885i) q^{88} -7.21849i q^{89} +(-3.31683 - 2.71882i) q^{90} +(-4.10413 - 2.98183i) q^{91} +(-0.611423 - 0.841552i) q^{92} +(10.7070 - 10.1001i) q^{93} +(-8.00363 - 2.60054i) q^{94} +(4.55416 - 3.30879i) q^{95} +(1.37297 + 2.90071i) q^{96} +(0.913962 + 2.81288i) q^{97} +28.6027 q^{98} +(1.91305 - 9.76423i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 6 q^{3} - 48 q^{4} - 10 q^{6} - 14 q^{9}+O(q^{10}) \) 192 * q + 6 * q^3 - 48 * q^4 - 10 * q^6 - 14 * q^9	\( 192 q + 6 q^{3} - 48 q^{4} - 10 q^{6} - 14 q^{9} - 20 q^{12} + 6 q^{15} - 28 q^{16} - 10 q^{18} - 60 q^{19} + 4 q^{22} + 30 q^{24} - 12 q^{25} + 30 q^{27} - 20 q^{28} + 12 q^{31} - 32 q^{33} + 56 q^{34} + 44 q^{36} + 60 q^{40} - 108 q^{42} - 40 q^{45} - 28 q^{48} - 24 q^{49} + 10 q^{51} + 20 q^{52} - 20 q^{55} + 50 q^{57} - 60 q^{58} + 36 q^{60} + 20 q^{61} - 30 q^{63} + 64 q^{64} - 30 q^{66} - 120 q^{67} - 16 q^{69} + 20 q^{70} + 150 q^{72} - 20 q^{73} + 18 q^{75} + 40 q^{78} - 160 q^{79} - 46 q^{81} + 88 q^{82} - 40 q^{85} + 72 q^{88} - 80 q^{90} + 8 q^{91} - 72 q^{93} - 120 q^{94} - 140 q^{96} - 88 q^{97} + 62 q^{99}+O(q^{100}) \) 192 * q + 6 * q^3 - 48 * q^4 - 10 * q^6 - 14 * q^9 - 20 * q^12 + 6 * q^15 - 28 * q^16 - 10 * q^18 - 60 * q^19 + 4 * q^22 + 30 * q^24 - 12 * q^25 + 30 * q^27 - 20 * q^28 + 12 * q^31 - 32 * q^33 + 56 * q^34 + 44 * q^36 + 60 * q^40 - 108 * q^42 - 40 * q^45 - 28 * q^48 - 24 * q^49 + 10 * q^51 + 20 * q^52 - 20 * q^55 + 50 * q^57 - 60 * q^58 + 36 * q^60 + 20 * q^61 - 30 * q^63 + 64 * q^64 - 30 * q^66 - 120 * q^67 - 16 * q^69 + 20 * q^70 + 150 * q^72 - 20 * q^73 + 18 * q^75 + 40 * q^78 - 160 * q^79 - 46 * q^81 + 88 * q^82 - 40 * q^85 + 72 * q^88 - 80 * q^90 + 8 * q^91 - 72 * q^93 - 120 * q^94 - 140 * q^96 - 88 * q^97 + 62 * q^99

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