LMFDB - Embedded newform 560.2.bb.c.29.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(29,560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 2, 0]))

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

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

chi := DirichletCharacter("560.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.bb (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$70$
Relative dimension:	$35$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			29.13
Character	$\chi$	$=$	560.29
Dual form			560.2.bb.c.309.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.543124 + 1.30576i) q^{2} +(-0.0768379 + 0.0768379i) q^{3} +(-1.41003 - 1.41838i) q^{4} +(-1.44155 + 1.70937i) q^{5} +(-0.0585996 - 0.142065i) q^{6} -1.00000 q^{7} +(2.61789 - 1.07081i) q^{8} +2.98819i q^{9} +O(q^{10})$	\(q+(-0.543124 + 1.30576i) q^{2} +(-0.0768379 + 0.0768379i) q^{3} +(-1.41003 - 1.41838i) q^{4} +(-1.44155 + 1.70937i) q^{5} +(-0.0585996 - 0.142065i) q^{6} -1.00000 q^{7} +(2.61789 - 1.07081i) q^{8} +2.98819i q^{9} +(-1.44908 - 2.81072i) q^{10} +(-2.53224 + 2.53224i) q^{11} +(0.217330 + 0.000641467i) q^{12} +(2.35094 - 2.35094i) q^{13} +(0.543124 - 1.30576i) q^{14} +(-0.0205783 - 0.242110i) q^{15} +(-0.0236125 + 3.99993i) q^{16} -2.80265i q^{17} +(-3.90187 - 1.62296i) q^{18} +(-2.82791 - 2.82791i) q^{19} +(4.45717 - 0.365592i) q^{20} +(0.0768379 - 0.0768379i) q^{21} +(-1.93118 - 4.68182i) q^{22} -3.43836 q^{23} +(-0.118874 + 0.283433i) q^{24} +(-0.843859 - 4.92828i) q^{25} +(1.79292 + 4.34662i) q^{26} +(-0.460120 - 0.460120i) q^{27} +(1.41003 + 1.41838i) q^{28} +(-5.12248 - 5.12248i) q^{29} +(0.327315 + 0.104625i) q^{30} -0.729818 q^{31} +(-5.21014 - 2.20329i) q^{32} -0.389144i q^{33} +(3.65960 + 1.52219i) q^{34} +(1.44155 - 1.70937i) q^{35} +(4.23840 - 4.21345i) q^{36} +(-5.50691 - 5.50691i) q^{37} +(5.22849 - 2.15668i) q^{38} +0.361283i q^{39} +(-1.94342 + 6.01857i) q^{40} +8.53688i q^{41} +(0.0585996 + 0.142065i) q^{42} +(-5.13916 - 5.13916i) q^{43} +(7.16222 + 0.0211399i) q^{44} +(-5.10791 - 4.30763i) q^{45} +(1.86746 - 4.48969i) q^{46} -2.78411i q^{47} +(-0.305532 - 0.309161i) q^{48} +1.00000 q^{49} +(6.89348 + 1.57478i) q^{50} +(0.215350 + 0.215350i) q^{51} +(-6.64943 - 0.0196264i) q^{52} +(9.51318 + 9.51318i) q^{53} +(0.850710 - 0.350906i) q^{54} +(-0.678168 - 7.97887i) q^{55} +(-2.61789 + 1.07081i) q^{56} +0.434582 q^{57} +(9.47088 - 3.90660i) q^{58} +(-8.22878 + 8.22878i) q^{59} +(-0.314388 + 0.370571i) q^{60} +(-0.798316 - 0.798316i) q^{61} +(0.396381 - 0.952969i) q^{62} -2.98819i q^{63} +(5.70672 - 5.60654i) q^{64} +(0.629614 + 7.40762i) q^{65} +(0.508130 + 0.211353i) q^{66} +(-6.79877 + 6.79877i) q^{67} +(-3.97523 + 3.95183i) q^{68} +(0.264197 - 0.264197i) q^{69} +(1.44908 + 2.81072i) q^{70} -5.87744i q^{71} +(3.19979 + 7.82276i) q^{72} +14.4648 q^{73} +(10.1817 - 4.19979i) q^{74} +(0.443519 + 0.313838i) q^{75} +(-0.0236083 + 7.99851i) q^{76} +(2.53224 - 2.53224i) q^{77} +(-0.471750 - 0.196221i) q^{78} +6.81139 q^{79} +(-6.80330 - 5.80647i) q^{80} -8.89387 q^{81} +(-11.1471 - 4.63658i) q^{82} +(1.47708 - 1.47708i) q^{83} +(-0.217330 - 0.000641467i) q^{84} +(4.79076 + 4.04017i) q^{85} +(9.50172 - 3.91932i) q^{86} +0.787201 q^{87} +(-3.91757 + 9.34068i) q^{88} +14.1136i q^{89} +(8.39897 - 4.33014i) q^{90} +(-2.35094 + 2.35094i) q^{91} +(4.84821 + 4.87691i) q^{92} +(0.0560777 - 0.0560777i) q^{93} +(3.63538 + 1.51211i) q^{94} +(8.91052 - 0.757354i) q^{95} +(0.569632 - 0.231040i) q^{96} +11.1654i q^{97} +(-0.543124 + 1.30576i) q^{98} +(-7.56681 - 7.56681i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 70 q - 2 q^{2} - 2 q^{3} - 4 q^{5} - 70 q^{7} - 8 q^{8}+O(q^{10}) $ 70 * q - 2 * q^2 - 2 * q^3 - 4 * q^5 - 70 * q^7 - 8 * q^8	$ 70 q - 2 q^{2} - 2 q^{3} - 4 q^{5} - 70 q^{7} - 8 q^{8} + 6 q^{10} - 2 q^{11} + 4 q^{12} - 6 q^{13} + 2 q^{14} - 6 q^{15} + 4 q^{16} + 18 q^{18} + 14 q^{19} + 20 q^{20} + 2 q^{21} + 12 q^{22} + 20 q^{24} - 6 q^{25} - 36 q^{26} - 8 q^{27} + 2 q^{29} + 28 q^{30} + 16 q^{31} + 8 q^{32} + 4 q^{34} + 4 q^{35} - 40 q^{36} - 10 q^{37} + 12 q^{38} + 44 q^{40} - 2 q^{43} - 24 q^{44} + 22 q^{45} - 16 q^{46} + 44 q^{48} + 70 q^{49} - 74 q^{50} + 8 q^{51} - 28 q^{52} + 30 q^{53} - 32 q^{54} - 6 q^{55} + 8 q^{56} + 76 q^{57} - 56 q^{58} + 2 q^{59} - 64 q^{60} + 30 q^{61} - 48 q^{62} + 12 q^{64} - 10 q^{65} + 80 q^{66} - 6 q^{67} + 36 q^{68} - 16 q^{69} - 6 q^{70} - 4 q^{72} + 36 q^{73} - 32 q^{74} - 98 q^{75} + 44 q^{76} + 2 q^{77} + 84 q^{78} - 40 q^{79} - 24 q^{80} - 82 q^{81} - 24 q^{82} - 10 q^{83} - 4 q^{84} - 32 q^{85} + 32 q^{86} + 4 q^{87} - 32 q^{88} + 158 q^{90} + 6 q^{91} + 92 q^{92} + 56 q^{93} - 20 q^{94} + 6 q^{95} + 16 q^{96} - 2 q^{98} - 34 q^{99}+O(q^{100}) $ 70 * q - 2 * q^2 - 2 * q^3 - 4 * q^5 - 70 * q^7 - 8 * q^8 + 6 * q^10 - 2 * q^11 + 4 * q^12 - 6 * q^13 + 2 * q^14 - 6 * q^15 + 4 * q^16 + 18 * q^18 + 14 * q^19 + 20 * q^20 + 2 * q^21 + 12 * q^22 + 20 * q^24 - 6 * q^25 - 36 * q^26 - 8 * q^27 + 2 * q^29 + 28 * q^30 + 16 * q^31 + 8 * q^32 + 4 * q^34 + 4 * q^35 - 40 * q^36 - 10 * q^37 + 12 * q^38 + 44 * q^40 - 2 * q^43 - 24 * q^44 + 22 * q^45 - 16 * q^46 + 44 * q^48 + 70 * q^49 - 74 * q^50 + 8 * q^51 - 28 * q^52 + 30 * q^53 - 32 * q^54 - 6 * q^55 + 8 * q^56 + 76 * q^57 - 56 * q^58 + 2 * q^59 - 64 * q^60 + 30 * q^61 - 48 * q^62 + 12 * q^64 - 10 * q^65 + 80 * q^66 - 6 * q^67 + 36 * q^68 - 16 * q^69 - 6 * q^70 - 4 * q^72 + 36 * q^73 - 32 * q^74 - 98 * q^75 + 44 * q^76 + 2 * q^77 + 84 * q^78 - 40 * q^79 - 24 * q^80 - 82 * q^81 - 24 * q^82 - 10 * q^83 - 4 * q^84 - 32 * q^85 + 32 * q^86 + 4 * q^87 - 32 * q^88 + 158 * q^90 + 6 * q^91 + 92 * q^92 + 56 * q^93 - 20 * q^94 + 6 * q^95 + 16 * q^96 - 2 * q^98 - 34 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$1$	$-1$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.543124	+	1.30576i	−0.384046	+	0.923314i
$2$	−0.543124	+	1.30576i	−0.384046	+	0.923314i
$3$	−0.0768379	+	0.0768379i	−0.0443624	+	0.0443624i	−0.728940	−	0.684578i	$-0.759987\pi$
$3$	−0.0768379	+	0.0768379i	−0.0443624	+	0.0443624i	0.684578	+	0.728940i	$0.259987\pi$
$4$	−1.41003	−	1.41838i	−0.705017	−	0.709191i
$5$	−1.44155	+	1.70937i	−0.644681	+	0.764451i
$5$	−1.44155	+	1.70937i	−0.644681	+	0.764451i
$6$	−0.0585996	−	0.142065i	−0.0239232	−	0.0579976i
$7$	−1.00000			−0.377964
$7$	−1.00000			−0.377964
$8$	2.61789	−	1.07081i	0.925565	−	0.378589i
$9$			2.98819i			0.996064i
$10$	−1.44908	−	2.81072i	−0.458241	−	0.888828i
$11$	−2.53224	+	2.53224i	−0.763498	+	0.763498i	−0.976953	−	0.213455i	$-0.931528\pi$
$11$	−2.53224	+	2.53224i	−0.763498	+	0.763498i	0.213455	+	0.976953i	$0.431528\pi$
$12$	0.217330		0.000641467i	0.0627376		0.000185175i
$13$	2.35094	−	2.35094i	0.652034	−	0.652034i	−0.301449	−	0.953482i	$-0.597470\pi$
$13$	2.35094	−	2.35094i	0.652034	−	0.652034i	0.953482	+	0.301449i	$0.0974702\pi$
$14$	0.543124	−	1.30576i	0.145156	−	0.348980i
$15$	−0.0205783	−	0.242110i	−0.00531328	−	0.0625125i
$16$	−0.0236125	+	3.99993i	−0.00590312	+	0.999983i
$17$		−	2.80265i		−	0.679743i	−0.940472	−	0.339872i	$-0.889616\pi$
$17$		−	2.80265i		−	0.679743i	0.940472	−	0.339872i	$-0.110384\pi$
$18$	−3.90187	−	1.62296i	−0.919680	−	0.382535i
$19$	−2.82791	−	2.82791i	−0.648768	−	0.648768i	0.303927	−	0.952695i	$-0.401702\pi$
$19$	−2.82791	−	2.82791i	−0.648768	−	0.648768i	−0.952695	+	0.303927i	$0.901702\pi$
$20$	4.45717	−	0.365592i	0.996653	−	0.0817488i
$21$	0.0768379	−	0.0768379i	0.0167674	−	0.0167674i
$22$	−1.93118	−	4.68182i	−0.411730	−	0.998167i
$23$	−3.43836			−0.716948			−0.358474	−	0.933540i	$-0.616703\pi$
$23$	−3.43836			−0.716948			−0.358474	+	0.933540i	$0.616703\pi$
$24$	−0.118874	+	0.283433i	−0.0242651	+	0.0578554i
$25$	−0.843859	−	4.92828i	−0.168772	−	0.985655i
$26$	1.79292	+	4.34662i	0.351620	+	0.852443i
$27$	−0.460120	−	0.460120i	−0.0885502	−	0.0885502i
$28$	1.41003	+	1.41838i	0.266471	+	0.268049i
$29$	−5.12248	−	5.12248i	−0.951220	−	0.951220i	0.0476440	−	0.998864i	$-0.484829\pi$
$29$	−5.12248	−	5.12248i	−0.951220	−	0.951220i	−0.998864	+	0.0476440i	$0.984829\pi$
$30$	0.327315	+	0.104625i	0.0597592	+	0.0191019i
$31$	−0.729818			−0.131079			−0.0655396	−	0.997850i	$-0.520877\pi$
$31$	−0.729818			−0.131079			−0.0655396	+	0.997850i	$0.520877\pi$
$32$	−5.21014	−	2.20329i	−0.921031	−	0.389490i
$33$		−	0.389144i		−	0.0677413i
$34$	3.65960	+	1.52219i	0.627616	+	0.261053i
$35$	1.44155	−	1.70937i	0.243667	−	0.288935i
$36$	4.23840	−	4.21345i	0.706399	−	0.702242i
$37$	−5.50691	−	5.50691i	−0.905330	−	0.905330i	0.0905605	−	0.995891i	$-0.471134\pi$
$37$	−5.50691	−	5.50691i	−0.905330	−	0.905330i	−0.995891	+	0.0905605i	$0.971134\pi$
$38$	5.22849	−	2.15668i	0.848173	−	0.349859i
$39$			0.361283i			0.0578516i
$40$	−1.94342	+	6.01857i	−0.307281	+	0.951619i
$41$			8.53688i			1.33324i	0.745399	+	0.666619i	$0.232259\pi$
$41$			8.53688i			1.33324i	−0.745399	+	0.666619i	$0.767741\pi$
$42$	0.0585996	+	0.142065i	0.00904212	+	0.0219211i
$43$	−5.13916	−	5.13916i	−0.783714	−	0.783714i	0.196742	−	0.980455i	$-0.436964\pi$
$43$	−5.13916	−	5.13916i	−0.783714	−	0.783714i	−0.980455	+	0.196742i	$0.936964\pi$
$44$	7.16222	+	0.0211399i	1.07975	+	0.00318696i
$45$	−5.10791	−	4.30763i	−0.761442	−	0.642144i
$46$	1.86746	−	4.48969i	0.275341	−	0.661968i
$47$		−	2.78411i		−	0.406104i	−0.979168	−	0.203052i	$-0.934914\pi$
$47$		−	2.78411i		−	0.406104i	0.979168	−	0.203052i	$-0.0650860\pi$
$48$	−0.305532	−	0.309161i	−0.0440998	−	0.0446235i
$49$	1.00000			0.142857
$50$	6.89348	+	1.57478i	0.974885	+	0.222708i
$51$	0.215350	+	0.215350i	0.0301550	+	0.0301550i
$52$	−6.64943	−	0.0196264i	−0.922111	−	0.00272169i
$53$	9.51318	+	9.51318i	1.30674	+	1.30674i	0.923757	+	0.382978i	$0.125102\pi$
$53$	9.51318	+	9.51318i	1.30674	+	1.30674i	0.382978	+	0.923757i	$0.374898\pi$
$54$	0.850710	−	0.350906i	0.115767	−	0.0477522i
$55$	−0.678168	−	7.97887i	−0.0914442	−	1.07587i
$56$	−2.61789	+	1.07081i	−0.349831	+	0.143093i
$57$	0.434582			0.0575618
$58$	9.47088	−	3.90660i	1.24359	−	0.512962i
$59$	−8.22878	+	8.22878i	−1.07130	+	1.07130i	−0.0740410	+	0.997255i	$0.523590\pi$
$59$	−8.22878	+	8.22878i	−1.07130	+	1.07130i	−0.997255	+	0.0740410i	$0.976410\pi$
$60$	−0.314388	+	0.370571i	−0.0405874	+	0.0478405i
$61$	−0.798316	−	0.798316i	−0.102214	−	0.102214i	0.654151	−	0.756364i	$-0.273026\pi$
$61$	−0.798316	−	0.798316i	−0.102214	−	0.102214i	−0.756364	+	0.654151i	$0.773026\pi$
$62$	0.396381	−	0.952969i	0.0503405	−	0.121027i
$63$		−	2.98819i		−	0.376477i
$64$	5.70672	−	5.60654i	0.713340	−	0.700818i
$65$	0.629614	+	7.40762i	0.0780940	+	0.918802i
$66$	0.508130	+	0.211353i	0.0625464	+	0.0260158i
$67$	−6.79877	+	6.79877i	−0.830602	+	0.830602i	−0.987599	−	0.156997i	$-0.949819\pi$
$67$	−6.79877	+	6.79877i	−0.830602	+	0.830602i	0.156997	+	0.987599i	$0.449819\pi$
$68$	−3.97523	+	3.95183i	−0.482068	+	0.479230i
$69$	0.264197	−	0.264197i	0.0318056	−	0.0318056i
$70$	1.44908	+	2.81072i	0.173199	+	0.335945i
$71$		−	5.87744i		−	0.697524i	−0.937211	−	0.348762i	$-0.886602\pi$
$71$		−	5.87744i		−	0.697524i	0.937211	−	0.348762i	$-0.113398\pi$
$72$	3.19979	+	7.82276i	0.377099	+	0.921922i
$73$	14.4648			1.69298			0.846491	−	0.532403i	$-0.178711\pi$
$73$	14.4648			1.69298			0.846491	+	0.532403i	$0.178711\pi$
$74$	10.1817	−	4.19979i	1.18359	−	0.488215i
$75$	0.443519	+	0.313838i	0.0512132	+	0.0362389i
$76$	−0.0236083	+	7.99851i	−0.00270806	+	0.917492i
$77$	2.53224	−	2.53224i	0.288575	−	0.288575i
$78$	−0.471750	−	0.196221i	−0.0534151	−	0.0222177i
$79$	6.81139			0.766341			0.383171	−	0.923678i	$-0.374832\pi$
$79$	6.81139			0.766341			0.383171	+	0.923678i	$0.374832\pi$
$80$	−6.80330	−	5.80647i	−0.760632	−	0.649183i
$81$	−8.89387			−0.988207
$82$	−11.1471	−	4.63658i	−1.23100	−	0.512025i
$83$	1.47708	−	1.47708i	0.162131	−	0.162131i	−0.621379	−	0.783510i	$-0.713427\pi$
$83$	1.47708	−	1.47708i	0.162131	−	0.162131i	0.783510	+	0.621379i	$0.213427\pi$
$84$	−0.217330		0.000641467i	−0.0237126		6.99897e-5i
$85$	4.79076	+	4.04017i	0.519631	+	0.438218i
$86$	9.50172	−	3.91932i	1.02460	−	0.422631i
$87$	0.787201			0.0843969
$88$	−3.91757	+	9.34068i	−0.417615	+	0.995720i
$89$			14.1136i			1.49604i	0.663675	+	0.748021i	$0.268996\pi$
$89$			14.1136i			1.49604i	−0.663675	+	0.748021i	$0.731004\pi$
$90$	8.39897	−	4.33014i	0.885330	−	0.456437i
$91$	−2.35094	+	2.35094i	−0.246446	+	0.246446i
$92$	4.84821	+	4.87691i	0.505460	+	0.508453i
$93$	0.0560777	−	0.0560777i	0.00581499	−	0.00581499i
$94$	3.63538	+	1.51211i	0.374961	+	0.155963i
$95$	8.91052	−	0.757354i	0.914200	−	0.0777029i
$96$	0.569632	−	0.231040i	0.0581379	−	0.0235804i
$97$			11.1654i			1.13367i	0.823831	+	0.566836i	$0.191833\pi$
$97$			11.1654i			1.13367i	−0.823831	+	0.566836i	$0.808167\pi$
$98$	−0.543124	+	1.30576i	−0.0548638	+	0.131902i
$99$	−7.56681	−	7.56681i	−0.760493	−	0.760493i
$100$	−5.80031	+	8.14595i	−0.580031	+	0.814595i
$101$	5.26289	−	5.26289i	0.523677	−	0.523677i	−0.395003	−	0.918680i	$-0.629256\pi$
$101$	5.26289	−	5.26289i	0.523677	−	0.523677i	0.918680	+	0.395003i	$0.129256\pi$
$102$	−0.398158	+	0.164234i	−0.0394235	+	0.0162616i
$103$	−9.45362			−0.931493			−0.465746	−	0.884918i	$-0.654214\pi$
$103$	−9.45362			−0.931493			−0.465746	+	0.884918i	$0.654214\pi$
$104$	3.63709	−	8.67192i	0.356646	−	0.850352i
$105$	0.0205783	+	0.242110i	0.00200823	+	0.0236275i
$106$	−17.5888	+	7.25512i	−1.70837	+	0.704680i
$107$	−12.0824	−	12.0824i	−1.16805	−	1.16805i	−0.982666	−	0.185386i	$-0.940646\pi$
$107$	−12.0824	−	12.0824i	−1.16805	−	1.16805i	−0.185386	−	0.982666i	$-0.559354\pi$
$108$	−0.00384123	+	1.30141i	−0.000369622	+	0.125228i
$109$	−9.36933	−	9.36933i	−0.897419	−	0.897419i	0.0977881	−	0.995207i	$-0.468823\pi$
$109$	−9.36933	−	9.36933i	−0.897419	−	0.897419i	−0.995207	+	0.0977881i	$0.968823\pi$
$110$	10.7868	+	3.44799i	1.02848	+	0.328753i
$111$	0.846279			0.0803253
$112$	0.0236125	−	3.99993i	0.00223117	−	0.377958i
$113$			1.04018i			0.0978520i	0.998802	+	0.0489260i	$0.0155798\pi$
$113$			1.04018i			0.0978520i	−0.998802	+	0.0489260i	$0.984420\pi$
$114$	−0.236032	+	0.567461i	−0.0221064	+	0.0531476i
$115$	4.95658	−	5.87742i	0.462203	−	0.548072i
$116$	−0.0427640	+	14.4885i	−0.00397054	+	1.34522i
$117$	7.02506	+	7.02506i	0.649467	+	0.649467i
$118$	−6.27559	−	15.2141i	−0.577715	−	1.40057i
$119$			2.80265i			0.256919i
$120$	−0.313126	−	0.611782i	−0.0285844	−	0.0558478i
$121$		−	1.82445i		−	0.165860i
$122$	1.47600	−	0.608827i	0.133630	−	0.0551206i
$123$	−0.655957	−	0.655957i	−0.0591456	−	0.0591456i
$124$	1.02907	+	1.03516i	0.0924130	+	0.0929601i
$125$	9.64069	+	5.66190i	0.862289	+	0.506416i
$126$	3.90187	+	1.62296i	0.347606	+	0.144585i
$127$		−	1.17018i		−	0.103837i	−0.998651	−	0.0519184i	$-0.983466\pi$
$127$		−	1.17018i		−	0.103837i	0.998651	−	0.0519184i	$-0.0165336\pi$
$128$	4.22136	+	10.4967i	0.373119	+	0.927783i
$129$	0.789764			0.0695349
$130$	−10.0145	−	3.20113i	−0.878334	−	0.280757i
$131$	5.75913	+	5.75913i	0.503177	+	0.503177i	0.912424	−	0.409246i	$-0.134208\pi$
$131$	5.75913	+	5.75913i	0.503177	+	0.503177i	−0.409246	+	0.912424i	$0.634208\pi$
$132$	−0.551954	+	0.548706i	−0.0480415	+	0.0477587i
$133$	2.82791	+	2.82791i	0.245211	+	0.245211i
$134$	−5.18501	−	12.5702i	−0.447916	−	1.08590i
$135$	1.44980	−	0.123227i	0.124779	−	0.0106057i
$136$	−3.00111	−	7.33704i	−0.257343	−	0.629146i
$137$	−5.08773			−0.434674			−0.217337	−	0.976097i	$-0.569737\pi$
$137$	−5.08773			−0.434674			−0.217337	+	0.976097i	$0.569737\pi$
$138$	0.201487	+	0.488470i	0.0171517	+	0.0415813i
$139$	−14.3461	+	14.3461i	−1.21682	+	1.21682i	−0.248077	+	0.968740i	$0.579799\pi$
$139$	−14.3461	+	14.3461i	−1.21682	+	1.21682i	−0.968740	+	0.248077i	$0.920201\pi$
$140$	−4.45717	+	0.365592i	−0.376699	+	0.0308981i
$141$	0.213925	+	0.213925i	0.0180157	+	0.0180157i
$142$	7.67455	+	3.19218i	0.644034	+	0.267882i
$143$			11.9063i			0.995653i
$144$	−11.9526	−	0.0705586i	−0.996047	−	0.00587988i
$145$	16.1405	−	1.37187i	1.34040	−	0.113928i
$146$	−7.85620	+	18.8877i	−0.650184	+	1.56315i
$147$	−0.0768379	+	0.0768379i	−0.00633749	+	0.00633749i
$148$	−0.0459734	+	15.5758i	−0.00377899	+	1.28033i
$149$	−9.89647	+	9.89647i	−0.810750	+	0.810750i	−0.984746	−	0.173996i	$-0.944332\pi$
$149$	−9.89647	+	9.89647i	−0.810750	+	0.810750i	0.173996	+	0.984746i	$0.444332\pi$
$150$	−0.650684	+	0.408678i	−0.0531281	+	0.0333684i
$151$		−	0.563139i		−	0.0458276i	−0.999737	−	0.0229138i	$-0.992706\pi$
$151$		−	0.563139i		−	0.0458276i	0.999737	−	0.0229138i	$-0.00729432\pi$
$152$	−10.4313	−	4.37501i	−0.846093	−	0.354860i
$153$	8.37486			0.677068
$154$	1.93118	+	4.68182i	0.155619	+	0.377272i
$155$	1.05207	−	1.24752i	0.0845043	−	0.100204i
$156$	0.512437	−	0.509421i	0.0410278	−	0.0407863i
$157$	−5.71680	+	5.71680i	−0.456250	+	0.456250i	−0.897422	−	0.441172i	$-0.854563\pi$
$157$	−5.71680	+	5.71680i	−0.456250	+	0.456250i	0.441172	+	0.897422i	$0.354563\pi$
$158$	−3.69943	+	8.89406i	−0.294311	+	0.707573i
$159$	−1.46195			−0.115940
$160$	11.2769	−	5.72987i	0.891518	−	0.452986i
$161$	3.43836			0.270981
$162$	4.83047	−	11.6133i	0.379518	−	0.912425i
$163$	−17.7640	+	17.7640i	−1.39139	+	1.39139i	−0.569162	+	0.822225i	$0.692732\pi$
$163$	−17.7640	+	17.7640i	−1.39139	+	1.39139i	−0.822225	+	0.569162i	$0.807268\pi$
$164$	12.1086	−	12.0373i	0.945520	−	0.939954i
$165$	0.665189	+	0.560971i	0.0517849	+	0.0436715i
$166$	1.12648	+	2.73095i	0.0874317	+	0.211963i
$167$	−8.74372			−0.676609			−0.338305	−	0.941037i	$-0.609853\pi$
$167$	−8.74372			−0.676609			−0.338305	+	0.941037i	$0.609853\pi$
$168$	0.118874	−	0.283433i	0.00917136	−	0.0218673i
$169$			1.94616i			0.149705i
$170$	−7.87747	+	4.06128i	−0.604175	+	0.311486i
$171$	8.45035	−	8.45035i	0.646214	−	0.646214i
$172$	−0.0429032	+	14.5357i	−0.00327134	+	1.10833i
$173$	1.13434	−	1.13434i	0.0862421	−	0.0862421i	−0.662670	−	0.748912i	$-0.730577\pi$
$173$	1.13434	−	1.13434i	0.0862421	−	0.0862421i	0.748912	+	0.662670i	$0.230577\pi$
$174$	−0.427548	+	1.02790i	−0.0324123	+	0.0779248i
$175$	0.843859	+	4.92828i	0.0637897	+	0.372543i
$176$	−10.0690	−	10.1886i	−0.758978	−	0.767992i
$177$		−	1.26457i		−	0.0950506i
$178$	−18.4290	−	7.66544i	−1.38132	−	0.574549i
$179$	15.1190	+	15.1190i	1.13005	+	1.13005i	0.990168	+	0.139882i	$0.0446723\pi$
$179$	15.1190	+	15.1190i	1.13005	+	1.13005i	0.139882	+	0.990168i	$0.455328\pi$
$180$	1.09246	+	13.3189i	0.0814270	+	0.992730i
$181$	−0.223394	+	0.223394i	−0.0166048	+	0.0166048i	−0.715360	−	0.698756i	$-0.753737\pi$
$181$	−0.223394	+	0.223394i	−0.0166048	+	0.0166048i	0.698756	+	0.715360i	$0.253737\pi$
$182$	−1.79292	−	4.34662i	−0.132900	−	0.322193i
$183$	0.122682			0.00906891
$184$	−9.00126	+	3.68184i	−0.663582	+	0.271429i
$185$	17.3518	−	1.47483i	1.27573	−	0.108431i
$186$	0.0427670	+	0.103681i	0.00313583	+	0.00760228i
$187$	7.09698	+	7.09698i	0.518983	+	0.518983i
$188$	−3.94892	+	3.92568i	−0.288005	+	0.286310i
$189$	0.460120	+	0.460120i	0.0334688	+	0.0334688i
$190$	−3.85059	+	12.0464i	−0.279351	+	0.873935i
$191$	2.74921			0.198926			0.0994630	−	0.995041i	$-0.468288\pi$
$191$	2.74921			0.198926			0.0994630	+	0.995041i	$0.468288\pi$
$192$	−0.00769751	+	0.869288i	−0.000555520	+	0.0627355i
$193$		−	12.7459i		−	0.917469i	−0.888573	−	0.458734i	$-0.848303\pi$
$193$		−	12.7459i		−	0.917469i	0.888573	−	0.458734i	$-0.151697\pi$
$194$	−14.5793	−	6.06418i	−1.04673	−	0.435382i
$195$	−0.617564	−	0.520808i	−0.0442247	−	0.0372958i
$196$	−1.41003	−	1.41838i	−0.100717	−	0.101313i
$197$	−8.40364	−	8.40364i	−0.598735	−	0.598735i	0.341241	−	0.939976i	$-0.389153\pi$
$197$	−8.40364	−	8.40364i	−0.598735	−	0.598735i	−0.939976	+	0.341241i	$0.889153\pi$
$198$	13.9902	−	5.77075i	0.994239	−	0.410109i
$199$		−	16.7061i		−	1.18426i	−0.805841	−	0.592132i	$-0.798286\pi$
$199$		−	16.7061i		−	1.18426i	0.805841	−	0.592132i	$-0.201714\pi$
$200$	−7.48639	−	11.9981i	−0.529368	−	0.848392i
$201$		−	1.04481i		−	0.0736950i
$202$	4.01369	+	9.73049i	0.282402	+	0.684635i
$203$	5.12248	+	5.12248i	0.359528	+	0.359528i
$204$	0.00179781	−	0.609099i	0.000125872	−	0.0426455i
$205$	−14.5927	−	12.3064i	−1.01920	−	0.859513i
$206$	5.13449	−	12.3442i	0.357737	−	0.860060i
$207$		−	10.2745i		−	0.714126i
$208$	9.34809	+	9.45911i	0.648173	+	0.655871i
$209$	14.3219			0.990666
$210$	−0.327315	−	0.104625i	−0.0225869	−	0.00721983i
$211$	−8.22738	−	8.22738i	−0.566396	−	0.566396i	0.364721	−	0.931117i	$-0.381164\pi$
$211$	−8.22738	−	8.22738i	−0.566396	−	0.566396i	−0.931117	+	0.364721i	$0.881164\pi$
$212$	0.0794189	−	26.9072i	0.00545451	−	1.84800i
$213$	0.451611	+	0.451611i	0.0309439	+	0.0309439i
$214$	22.3390	−	9.21453i	1.52706	−	0.629892i
$215$	16.1931	−	1.37634i	1.10436	−	0.0938654i
$216$	−1.69725	−	0.711843i	−0.115483	−	0.0484348i
$217$	0.729818			0.0495432
$218$	17.3228	−	7.14542i	1.17325	−	0.483949i
$219$	−1.11145	+	1.11145i	−0.0751048	+	0.0751048i
$220$	−10.3608	+	12.2124i	−0.698528	+	0.823358i
$221$	−6.58887	−	6.58887i	−0.443215	−	0.443215i
$222$	−0.459634	+	1.10504i	−0.0308486	+	0.0741654i
$223$		−	0.187006i		−	0.0125229i	−0.999980	−	0.00626143i	$-0.998007\pi$
$223$		−	0.187006i		−	0.0125229i	0.999980	−	0.00626143i	$-0.00199309\pi$
$224$	5.21014	+	2.20329i	0.348117	+	0.147213i
$225$	14.7266	−	2.52161i	0.981776	−	0.168107i
$226$	−1.35823	−	0.564947i	−0.0903481	−	0.0375797i
$227$	19.9067	−	19.9067i	1.32125	−	1.32125i	0.408493	−	0.912761i	$-0.366054\pi$
$227$	19.9067	−	19.9067i	1.32125	−	1.32125i	0.912761	−	0.408493i	$-0.133946\pi$
$228$	−0.612775	−	0.616403i	−0.0405820	−	0.0408223i
$229$	−5.47281	+	5.47281i	−0.361654	+	0.361654i	−0.864421	−	0.502768i	$-0.832315\pi$
$229$	−5.47281	+	5.47281i	−0.361654	+	0.361654i	0.502768	+	0.864421i	$0.332315\pi$
$230$	4.98248	+	9.66428i	0.328535	+	0.637244i
$231$			0.389144i			0.0256038i
$232$	−18.8953	−	7.92488i	−1.24054	−	0.520294i
$233$	−15.8681			−1.03956			−0.519778	−	0.854301i	$-0.673985\pi$
$233$	−15.8681			−1.03956			−0.519778	+	0.854301i	$0.673985\pi$
$234$	−12.9885	+	5.35759i	−0.849087	+	0.350236i
$235$	4.75905	+	4.01343i	0.310446	+	0.261807i
$236$	23.2744	+	0.0686964i	1.51504	+	0.00447175i
$237$	−0.523373	+	0.523373i	−0.0339967	+	0.0339967i
$238$	−3.65960	−	1.52219i	−0.237217	−	0.0986687i
$239$	−6.12590			−0.396252			−0.198126	−	0.980177i	$-0.563485\pi$
$239$	−6.12590			−0.396252			−0.198126	+	0.980177i	$0.563485\pi$
$240$	0.968909	−	0.0765948i	0.0625428	−	0.00494417i
$241$	15.7628			1.01537			0.507685	−	0.861543i	$-0.330501\pi$
$241$	15.7628			1.01537			0.507685	+	0.861543i	$0.330501\pi$
$242$	2.38230	+	0.990905i	0.153140	+	0.0636978i
$243$	2.06375	−	2.06375i	0.132389	−	0.132389i
$244$	−0.00666459	+	2.25797i	−0.000426656	+	0.144552i
$245$	−1.44155	+	1.70937i	−0.0920973	+	0.109207i
$246$	1.21279	−	0.500258i	0.0773246	−	0.0318953i
$247$	−13.2965			−0.846037
$248$	−1.91058	+	0.781498i	−0.121322	+	0.0496252i
$249$			0.226992i			0.0143850i
$250$	−12.6292	+	9.51334i	−0.798740	+	0.601677i
$251$	9.56552	−	9.56552i	0.603770	−	0.603770i	−0.337541	−	0.941311i	$-0.609595\pi$
$251$	9.56552	−	9.56552i	0.603770	−	0.603770i	0.941311	+	0.337541i	$0.109595\pi$
$252$	−4.23840	+	4.21345i	−0.266994	+	0.265422i
$253$	8.70675	−	8.70675i	0.547389	−	0.547389i
$254$	1.52798	+	0.635553i	0.0958739	+	0.0398781i
$255$	−0.678550	+	0.0576737i	−0.0424925	+	0.00361167i
$256$	−15.9989	−	0.188896i	−0.999930	−	0.0118060i
$257$			5.76404i			0.359551i	0.983708	+	0.179775i	$0.0575371\pi$
$257$			5.76404i			0.359551i	−0.983708	+	0.179775i	$0.942463\pi$
$258$	−0.428940	+	1.03124i	−0.0267046	+	0.0642025i
$259$	5.50691	+	5.50691i	0.342183	+	0.342183i
$260$	9.61905	−	11.3380i	0.596548	−	0.703154i
$261$	15.3069	−	15.3069i	0.947476	−	0.947476i
$262$	−10.6480	+	4.39214i	−0.657834	+	0.271347i
$263$	10.4260			0.642894			0.321447	−	0.946928i	$-0.395831\pi$
$263$	10.4260			0.642894			0.321447	+	0.946928i	$0.395831\pi$
$264$	−0.416700	−	1.01874i	−0.0256461	−	0.0626989i
$265$	−29.9752	+	2.54776i	−1.84136	+	0.156508i
$266$	−5.22849	+	2.15668i	−0.320579	+	0.132234i
$267$	−1.08446	−	1.08446i	−0.0663680	−	0.0663680i
$268$	19.2297	+	0.0567582i	1.17464	+	0.00346706i
$269$	5.38527	+	5.38527i	0.328346	+	0.328346i	0.851957	−	0.523612i	$-0.175416\pi$
$269$	5.38527	+	5.38527i	0.328346	+	0.328346i	−0.523612	+	0.851957i	$0.675416\pi$
$270$	−0.626517	+	1.96002i	−0.0381286	+	0.119283i
$271$	24.3959			1.48195			0.740974	−	0.671534i	$-0.234364\pi$
$271$	24.3959			1.48195			0.740974	+	0.671534i	$0.234364\pi$
$272$	11.2104	+	0.0661775i	0.679731	+	0.00401260i
$273$		−	0.361283i		−	0.0218658i
$274$	2.76327	−	6.64337i	0.166935	−	0.401341i
$275$	14.6164	+	10.3427i	0.881403	+	0.623689i
$276$	−0.747258	−	0.00220560i	−0.0449796	−	0.000132761i
$277$	1.27841	+	1.27841i	0.0768123	+	0.0768123i	0.744469	−	0.667657i	$-0.232703\pi$
$277$	1.27841	+	1.27841i	0.0768123	+	0.0768123i	−0.667657	+	0.744469i	$0.732703\pi$
$278$	−10.9409	−	26.5242i	−0.656190	−	1.59082i
$279$		−	2.18083i		−	0.130563i
$280$	1.94342	−	6.01857i	0.116141	−	0.359678i
$281$		−	3.12323i		−	0.186316i	−0.995651	−	0.0931582i	$-0.970304\pi$
$281$		−	3.12323i		−	0.186316i	0.995651	−	0.0931582i	$-0.0296962\pi$
$282$	−0.395523	+	0.163148i	−0.0235530	+	0.00971529i
$283$	−15.4608	−	15.4608i	−0.919052	−	0.919052i	0.0779085	−	0.996961i	$-0.475176\pi$
$283$	−15.4608	−	15.4608i	−0.919052	−	0.919052i	−0.996961	+	0.0779085i	$0.975176\pi$
$284$	−8.33646	+	8.28739i	−0.494678	+	0.491766i
$285$	−0.626472	+	0.742859i	−0.0371090	+	0.0440032i
$286$	−15.5468	−	6.46658i	−0.919300	−	0.382377i
$287$		−	8.53688i		−	0.503916i
$288$	6.58385	−	15.5689i	0.387957	−	0.917405i
$289$	9.14514			0.537949
$290$	−6.97495	+	21.8208i	−0.409583	+	1.28136i
$291$	−0.857924	−	0.857924i	−0.0502924	−	0.0502924i
$292$	−20.3959	−	20.5167i	−1.19358	−	1.20065i
$293$	−11.8750	−	11.8750i	−0.693744	−	0.693744i	0.269309	−	0.963054i	$-0.413205\pi$
$293$	−11.8750	−	11.8750i	−0.693744	−	0.693744i	−0.963054	+	0.269309i	$0.913205\pi$
$294$	−0.0585996	−	0.142065i	−0.00341760	−	0.00828538i
$295$	−2.20378	−	25.9282i	−0.128309	−	1.50960i
$296$	−20.3134	−	8.51963i	−1.18069	−	0.495193i
$297$	2.33027			0.135216
$298$	−7.54743	−	18.2974i	−0.437211	−	1.05994i
$299$	−8.08339	+	8.08339i	−0.467474	+	0.467474i
$300$	−0.180234	−	1.07160i	−0.0104058	−	0.0618689i
$301$	5.13916	+	5.13916i	0.296216	+	0.296216i
$302$	0.735326	+	0.305854i	0.0423132	+	0.0175999i
$303$			0.808780i			0.0464632i
$304$	11.3782	−	11.2447i	0.652586	−	0.644927i
$305$	2.51543	−	0.213800i	0.144033	−	0.0122422i
$306$	−4.54859	+	10.9356i	−0.260025	+	0.625146i
$307$	−15.7017	+	15.7017i	−0.896145	+	0.896145i	−0.995093	−	0.0989472i	$-0.968452\pi$
$307$	−15.7017	+	15.7017i	−0.896145	+	0.896145i	0.0989472	+	0.995093i	$0.468452\pi$
$308$	−7.16222	−	0.0211399i	−0.408105	−	0.00120456i
$309$	0.726397	−	0.726397i	0.0413233	−	0.0413233i
$310$	1.05757	+	2.05131i	0.0600658	+	0.116507i
$311$			5.30352i			0.300735i	0.988630	+	0.150368i	$0.0480457\pi$
$311$			5.30352i			0.300735i	−0.988630	+	0.150368i	$0.951954\pi$
$312$	0.386866	+	0.945800i	0.0219020	+	0.0535454i
$313$	15.1891			0.858537			0.429268	−	0.903177i	$-0.358771\pi$
$313$	15.1891			0.858537			0.429268	+	0.903177i	$0.358771\pi$
$314$	−4.35985	−	10.5697i	−0.246041	−	0.596483i
$315$	5.10791	+	4.30763i	0.287798	+	0.242708i
$316$	−9.60428	−	9.66115i	−0.540283	−	0.543482i
$317$	−7.84152	+	7.84152i	−0.440424	+	0.440424i	−0.892154	−	0.451731i	$-0.850807\pi$
$317$	−7.84152	+	7.84152i	−0.440424	+	0.440424i	0.451731	+	0.892154i	$0.350807\pi$
$318$	0.794018	−	1.90896i	0.0445263	−	0.107049i
$319$	25.9427			1.45251
$320$	1.35710	+	17.8370i	0.0758640	+	0.997118i
$321$	1.85678			0.103635
$322$	−1.86746	+	4.48969i	−0.104069	+	0.250200i
$323$	−7.92566	+	7.92566i	−0.440995	+	0.440995i
$324$	12.5406	+	12.6149i	0.696703	+	0.700828i
$325$	−13.5699	−	9.60222i	−0.752725	−	0.532635i
$326$	−13.5476	−	32.8437i	−0.750330	−	1.81904i
$327$	1.43984			0.0796234
$328$	9.14140	+	22.3486i	0.504749	+	1.23400i
$329$			2.78411i			0.153493i
$330$	−1.09377	+	0.563902i	−0.0602103	+	0.0310418i
$331$	−7.69618	+	7.69618i	−0.423020	+	0.423020i	−0.886242	−	0.463222i	$-0.846693\pi$
$331$	−7.69618	+	7.69618i	−0.423020	+	0.423020i	0.463222	+	0.886242i	$0.346693\pi$
$332$	−4.17780	−	0.0123311i	−0.229286	−	0.000676758i
$333$	16.4557	−	16.4557i	0.901767	−	0.901767i
$334$	4.74892	−	11.4172i	0.259849	−	0.624723i
$335$	−1.82080	−	21.4224i	−0.0994811	−	1.17043i
$336$	0.305532	+	0.309161i	0.0166681	+	0.0168661i
$337$		−	9.07800i		−	0.494510i	−0.968950	−	0.247255i	$-0.920471\pi$
$337$		−	9.07800i		−	0.494510i	0.968950	−	0.247255i	$-0.0795286\pi$
$338$	−2.54122	−	1.05701i	−0.138224	−	0.0574935i
$339$	−0.0799254	−	0.0799254i	−0.00434095	−	0.00434095i
$340$	−1.02463	−	12.4919i	−0.0555682	−	0.677468i
$341$	1.84807	−	1.84807i	0.100079	−	0.100079i
$342$	6.44457	+	15.6237i	0.348482	+	0.844835i
$343$	−1.00000			−0.0539949
$344$	−18.9568	−	7.95069i	−1.02208	−	0.428672i
$345$	0.0707555	+	0.832462i	0.00380935	+	0.0448182i
$346$	0.865090	+	2.09726i	0.0465076	+	0.112750i
$347$	7.95256	+	7.95256i	0.426916	+	0.426916i	0.887576	−	0.460661i	$-0.152387\pi$
$347$	7.95256	+	7.95256i	0.426916	+	0.426916i	−0.460661	+	0.887576i	$0.652387\pi$
$348$	−1.10998	−	1.11655i	−0.0595012	−	0.0598535i
$349$	−3.02346	−	3.02346i	−0.161842	−	0.161842i	0.621540	−	0.783382i	$-0.286507\pi$
$349$	−3.02346	−	3.02346i	−0.161842	−	0.161842i	−0.783382	+	0.621540i	$0.786507\pi$
$350$	−6.89348	−	1.57478i	−0.368472	−	0.0841758i
$351$	−2.16343			−0.115475
$352$	18.7726	−	7.61405i	1.00058	−	0.405830i
$353$			9.76050i			0.519499i	0.965676	+	0.259749i	$0.0836400\pi$
$353$			9.76050i			0.519499i	−0.965676	+	0.259749i	$0.916360\pi$
$354$	1.65122	+	0.686816i	0.0877615	+	0.0365038i
$355$	10.0467	+	8.47264i	0.533223	+	0.449681i
$356$	20.0185	−	19.9007i	1.06098	−	1.05473i
$357$	−0.215350	−	0.215350i	−0.0113975	−	0.0113975i
$358$	−27.9534	+	11.5304i	−1.47738	+	0.609399i
$359$			12.4676i			0.658015i	0.944327	+	0.329007i	$0.106714\pi$
$359$			12.4676i			0.658015i	−0.944327	+	0.329007i	$0.893286\pi$
$360$	−17.9846	−	5.80730i	−0.947873	−	0.306072i
$361$		−	3.00581i		−	0.158201i
$362$	−0.170369	−	0.413031i	−0.00895441	−	0.0217084i
$363$	0.140187	+	0.140187i	0.00735793	+	0.00735793i
$364$	6.64943	+	0.0196264i	0.348525	+	0.00102870i
$365$	−20.8518	+	24.7257i	−1.09143	+	1.29420i
$366$	−0.0666315	+	0.160194i	−0.00348288	+	0.00837345i
$367$			29.5439i			1.54218i	0.636728	+	0.771088i	$0.280287\pi$
$367$			29.5439i			1.54218i	−0.636728	+	0.771088i	$0.719713\pi$
$368$	0.0811882	−	13.7532i	0.00423223	−	0.716936i
$369$	−25.5098			−1.32799
$370$	−7.49841	+	23.4584i	−0.389824	+	1.21954i
$371$	−9.51318	−	9.51318i	−0.493900	−	0.493900i
$372$	−0.158611		0.000468154i	−0.00822359		2.42726e-5i
$373$	−1.54001	−	1.54001i	−0.0797388	−	0.0797388i	0.666112	−	0.745851i	$-0.267957\pi$
$373$	−1.54001	−	1.54001i	−0.0797388	−	0.0797388i	−0.745851	+	0.666112i	$0.767957\pi$
$374$	−13.1215	+	5.41244i	−0.678497	+	0.279870i
$375$	−1.17582	+	0.305722i	−0.0607191	+	0.0157874i
$376$	−2.98125	−	7.28849i	−0.153746	−	0.375875i
$377$	−24.0853			−1.24046
$378$	−0.850710	+	0.350906i	−0.0437558	+	0.0180486i
$379$	−10.8009	+	10.8009i	−0.554803	+	0.554803i	−0.927823	−	0.373020i	$-0.878322\pi$
$379$	−10.8009	+	10.8009i	−0.554803	+	0.554803i	0.373020	+	0.927823i	$0.378322\pi$
$380$	−13.6383	−	11.5706i	−0.699632	−	0.593560i
$381$	0.0899143	+	0.0899143i	0.00460645	+	0.00460645i
$382$	−1.49316	+	3.58982i	−0.0763968	+	0.183671i
$383$			0.251246i			0.0128381i	0.999979	+	0.00641904i	$0.00204326\pi$
$383$			0.251246i			0.0128381i	−0.999979	+	0.00641904i	$0.997957\pi$
$384$	−1.13090	−	0.482182i	−0.0577112	−	0.0246063i
$385$	0.678168	+	7.97887i	0.0345626	+	0.406641i
$386$	16.6431	+	6.92259i	0.847112	+	0.352351i
$387$	15.3568	−	15.3568i	0.780629	−	0.780629i
$388$	15.8367	−	15.7435i	0.803989	−	0.799257i
$389$	−14.1929	+	14.1929i	−0.719608	+	0.719608i	−0.968525	−	0.248916i	$-0.919926\pi$
$389$	−14.1929	+	14.1929i	−0.719608	+	0.719608i	0.248916	+	0.968525i	$0.419926\pi$
$390$	1.01547	−	0.523529i	0.0514201	−	0.0265099i
$391$			9.63654i			0.487341i
$392$	2.61789	−	1.07081i	0.132224	−	0.0540842i
$393$	−0.885039			−0.0446443
$394$	15.5374	−	6.40895i	0.782762	−	0.322878i
$395$	−9.81897	+	11.6431i	−0.494046	+	0.585830i
$396$	−0.0631701	+	21.4021i	−0.00317441	+	1.07550i
$397$	24.4783	−	24.4783i	1.22853	−	1.22853i	0.264011	−	0.964520i	$-0.414954\pi$
$397$	24.4783	−	24.4783i	1.22853	−	1.22853i	0.964520	−	0.264011i	$-0.0850457\pi$
$398$	21.8142	+	9.07348i	1.09345	+	0.454812i
$399$	−0.434582			−0.0217563
$400$	19.7327	−	3.25901i	0.986634	−	0.162950i
$401$	−7.45144			−0.372107			−0.186054	−	0.982540i	$-0.559570\pi$
$401$	−7.45144			−0.372107			−0.186054	+	0.982540i	$0.559570\pi$
$402$	1.36427	+	0.567459i	0.0680436	+	0.0283023i
$403$	−1.71576	+	1.71576i	−0.0854680	+	0.0854680i
$404$	−14.8856	−	0.0439362i	−0.740588	−	0.00218591i
$405$	12.8210	−	15.2029i	0.637079	−	0.755436i
$406$	−9.47088	+	3.90660i	−0.470032	+	0.193881i
$407$	27.8896			1.38244
$408$	0.794363	+	0.333164i	0.0393268	+	0.0164941i
$409$			35.0006i			1.73067i	0.501195	+	0.865334i	$0.332894\pi$
$409$			35.0006i			1.73067i	−0.501195	+	0.865334i	$0.667106\pi$
$410$	23.9948	−	12.3707i	1.18502	−	0.610944i
$411$	0.390931	−	0.390931i	0.0192832	−	0.0192832i
$412$	13.3299	+	13.4088i	0.656718	+	0.660606i
$413$	8.22878	−	8.22878i	0.404912	−	0.404912i
$414$	13.4160	+	5.58032i	0.659363	+	0.274258i
$415$	0.395582	+	4.65416i	0.0194184	+	0.228464i
$416$	−17.4285	+	7.06892i	−0.854503	+	0.346582i
$417$		−	2.20464i		−	0.107962i
$418$	−7.77856	+	18.7010i	−0.380462	+	0.914696i
$419$	−4.21494	−	4.21494i	−0.205914	−	0.205914i	0.596614	−	0.802528i	$-0.296512\pi$
$419$	−4.21494	−	4.21494i	−0.205914	−	0.205914i	−0.802528	+	0.596614i	$0.796512\pi$
$420$	0.314388	−	0.370571i	0.0153406	−	0.0180820i
$421$	8.23957	−	8.23957i	0.401572	−	0.401572i	−0.477215	−	0.878787i	$-0.658354\pi$
$421$	8.23957	−	8.23957i	0.401572	−	0.401572i	0.878787	+	0.477215i	$0.158354\pi$
$422$	15.2115	−	6.27452i	0.740484	−	0.305439i
$423$	8.31944			0.404505
$424$	35.0913	+	14.7176i	1.70418	+	0.714752i
$425$	−13.8122	+	2.36504i	−0.669992	+	0.114721i
$426$	−0.834977	+	0.344416i	−0.0404548	+	0.0166870i
$427$	0.798316	+	0.798316i	0.0386332	+	0.0386332i
$428$	−0.100868	+	34.1741i	−0.00487563	+	1.65187i
$429$	−0.914854	−	0.914854i	−0.0441696	−	0.0441696i
$430$	−6.99766	+	21.8918i	−0.337457	+	1.05572i
$431$	13.6328			0.656667			0.328334	−	0.944562i	$-0.393513\pi$
$431$	13.6328			0.656667			0.328334	+	0.944562i	$0.393513\pi$
$432$	1.85131	−	1.82958i	0.0890714	−	0.0880259i
$433$		−	15.1116i		−	0.726218i	−0.931747	−	0.363109i	$-0.881715\pi$
$433$		−	15.1116i		−	0.726218i	0.931747	−	0.363109i	$-0.118285\pi$
$434$	−0.396381	+	0.952969i	−0.0190269	+	0.0457440i
$435$	−1.13479	+	1.34561i	−0.0544091	+	0.0645173i
$436$	−0.0782180	+	26.5004i	−0.00374596	+	1.26914i
$437$	9.72339	+	9.72339i	0.465133	+	0.465133i
$438$	−0.847635	−	2.05494i	−0.0405016	−	0.0981890i
$439$		−	15.1899i		−	0.724973i	−0.931989	−	0.362487i	$-0.881928\pi$
$439$		−	15.1899i		−	0.724973i	0.931989	−	0.362487i	$-0.118072\pi$
$440$	−10.3192	−	20.1616i	−0.491951	−	0.961168i
$441$			2.98819i			0.142295i
$442$	12.1821	−	5.02493i	0.579442	−	0.239011i
$443$	4.98717	+	4.98717i	0.236948	+	0.236948i	0.815585	−	0.578637i	$-0.196415\pi$
$443$	4.98717	+	4.98717i	0.236948	+	0.236948i	−0.578637	+	0.815585i	$0.696415\pi$
$444$	−1.19328	−	1.20035i	−0.0566307	−	0.0569659i
$445$	−24.1253	−	20.3455i	−1.14365	−	0.964470i
$446$	0.244186	+	0.101567i	0.0115625	+	0.00480936i
$447$		−	1.52085i		−	0.0719336i
$448$	−5.70672	+	5.60654i	−0.269617	+	0.264884i
$449$	−3.01083			−0.142090			−0.0710448	−	0.997473i	$-0.522633\pi$
$449$	−3.01083			−0.142090			−0.0710448	+	0.997473i	$0.522633\pi$
$450$	−4.70576	+	20.5990i	−0.221832	+	0.971048i
$451$	−21.6174	−	21.6174i	−1.01792	−	1.01792i
$452$	1.47537	−	1.46669i	0.0693957	−	0.0689873i
$453$	0.0432704	+	0.0432704i	0.00203302	+	0.00203302i
$454$	15.1816	+	36.8052i	0.712509	+	1.72736i
$455$	−0.629614	−	7.40762i	−0.0295168	−	0.347274i
$456$	1.13769	−	0.465356i	0.0532772	−	0.0217923i
$457$	−20.4670			−0.957406			−0.478703	−	0.877977i	$-0.658893\pi$
$457$	−20.4670			−0.957406			−0.478703	+	0.877977i	$0.658893\pi$
$458$	−4.17378	−	10.1186i	−0.195028	−	0.472812i
$459$	−1.28956	+	1.28956i	−0.0601914	+	0.0601914i
$460$	−15.3254	+	1.25704i	−0.714549	+	0.0586097i
$461$	4.53977	+	4.53977i	0.211438	+	0.211438i	0.804878	−	0.593440i	$-0.202231\pi$
$461$	4.53977	+	4.53977i	0.211438	+	0.211438i	−0.593440	+	0.804878i	$0.702231\pi$
$462$	−0.508130	−	0.211353i	−0.0236403	−	0.00983304i
$463$			16.0743i			0.747037i	0.927623	+	0.373519i	$0.121849\pi$
$463$			16.0743i			0.747037i	−0.927623	+	0.373519i	$0.878151\pi$
$464$	20.6105	−	20.3686i	0.956819	−	0.945589i
$465$	0.0150184	+	0.176696i	0.000696460	+	0.00819409i
$466$	8.61836	−	20.7200i	0.399238	−	0.959836i
$467$	19.6621	−	19.6621i	0.909852	−	0.909852i	−0.0864078	−	0.996260i	$-0.527539\pi$
$467$	19.6621	−	19.6621i	0.909852	−	0.909852i	0.996260	+	0.0864078i	$0.0275388\pi$
$468$	0.0586473	−	19.8698i	0.00271097	−	0.918481i
$469$	6.79877	−	6.79877i	0.313938	−	0.313938i
$470$	−7.82534	+	4.03440i	−0.360956	+	0.186093i
$471$		−	0.878534i		−	0.0404807i
$472$	−12.7306	+	30.3535i	−0.585973	+	1.39714i
$473$	26.0271			1.19673
$474$	−0.399145	−	0.967657i	−0.0183333	−	0.0444460i
$475$	−11.5504	+	16.3231i	−0.529968	+	0.748955i
$476$	3.97523	−	3.95183i	0.182204	−	0.181132i
$477$	−28.4272	+	28.4272i	−1.30159	+	1.30159i
$478$	3.32712	−	7.99897i	0.152179	−	0.365865i
$479$	−37.5978			−1.71789			−0.858944	−	0.512069i	$-0.828879\pi$
$479$	−37.5978			−1.71789			−0.858944	+	0.512069i	$0.828879\pi$
$480$	−0.426223	+	1.30677i	−0.0194543	+	0.0596454i
$481$	−25.8928			−1.18061
$482$	−8.56114	+	20.5825i	−0.389949	+	0.937505i
$483$	−0.264197	+	0.264197i	−0.0120214	+	0.0120214i
$484$	−2.58777	+	2.57254i	−0.117626	+	0.116934i
$485$	−19.0857	−	16.0955i	−0.866636	−	0.730857i
$486$	1.57389	+	3.81564i	0.0713933	+	0.173081i
$487$	30.5722			1.38536			0.692679	−	0.721246i	$-0.256430\pi$
$487$	30.5722			1.38536			0.692679	+	0.721246i	$0.256430\pi$
$488$	−2.94475	−	1.23506i	−0.133303	−	0.0559085i
$489$		−	2.72991i		−	0.123451i
$490$	−1.44908	−	2.81072i	−0.0654630	−	0.126975i
$491$	−2.34291	+	2.34291i	−0.105734	+	0.105734i	−0.757995	−	0.652261i	$-0.773821\pi$
$491$	−2.34291	+	2.34291i	−0.105734	+	0.105734i	0.652261	+	0.757995i	$0.273821\pi$
$492$	−0.00547613	+	1.85532i	−0.000246883	+	0.0836442i
$493$	−14.3565	+	14.3565i	−0.646585	+	0.646585i
$494$	7.22165	−	17.3621i	0.324917	−	0.781157i
$495$	23.8424	−	2.02650i	1.07164	−	0.0910842i
$496$	0.0172328	−	2.91922i	0.000773775	−	0.131077i
$497$			5.87744i			0.263639i
$498$	−0.296397	−	0.123285i	−0.0132819	−	0.00552451i
$499$	−1.06505	−	1.06505i	−0.0476782	−	0.0476782i	0.682866	−	0.730544i	$-0.260733\pi$
$499$	−1.06505	−	1.06505i	−0.0476782	−	0.0476782i	−0.730544	+	0.682866i	$0.760733\pi$
$500$	−5.56296	−	21.6576i	−0.248783	−	0.968559i
$501$	0.671850	−	0.671850i	0.0300160	−	0.0300160i
$502$	7.29504	+	17.6856i	0.325593	+	0.789345i
$503$	−39.5989			−1.76563			−0.882814	−	0.469723i	$-0.844354\pi$
$503$	−39.5989			−1.76563			−0.882814	+	0.469723i	$0.844354\pi$
$504$	−3.19979	−	7.82276i	−0.142530	−	0.348454i
$505$	1.40947	+	16.5829i	0.0627208	+	0.737931i
$506$	6.64011	+	16.0978i	0.295189	+	0.715634i
$507$	−0.149539	−	0.149539i	−0.00664126	−	0.00664126i
$508$	−1.65976	+	1.64999i	−0.0736401	+	0.0732066i
$509$	−21.8298	−	21.8298i	−0.967588	−	0.967588i	0.0319031	−	0.999491i	$-0.489843\pi$
$509$	−21.8298	−	21.8298i	−0.967588	−	0.967588i	−0.999491	+	0.0319031i	$0.989843\pi$
$510$	0.293228	−	0.917349i	0.0129844	−	0.0406209i
$511$	−14.4648			−0.639887
$512$	8.93603	−	20.7882i	0.394920	−	0.918715i
$513$			2.60236i			0.114897i
$514$	−7.52647	−	3.13059i	−0.331978	−	0.138084i
$515$	13.6279	−	16.1597i	0.600516	−	0.712081i
$516$	−1.11359	−	1.12019i	−0.0490232	−	0.0493135i
$517$	7.05002	+	7.05002i	0.310059	+	0.310059i
$518$	−10.1817	+	4.19979i	−0.447356	+	0.184528i
$519$			0.174320i			0.00765182i
$520$	9.58043	+	18.7181i	0.420130	+	0.820845i
$521$		−	0.517150i		−	0.0226568i	−0.999936	−	0.0113284i	$-0.996394\pi$
$521$		−	0.517150i		−	0.0226568i	0.999936	−	0.0113284i	$-0.00360601\pi$
$522$	11.6737	+	28.3008i	0.510943	+	1.23869i
$523$	23.9593	+	23.9593i	1.04767	+	1.04767i	0.998806	+	0.0488597i	$0.0155587\pi$
$523$	23.9593	+	23.9593i	1.04767	+	1.04767i	0.0488597	+	0.998806i	$0.484441\pi$
$524$	0.0480790	−	16.2892i	0.00210034	−	0.711597i
$525$	−0.443519	−	0.313838i	−0.0193568	−	0.0136970i
$526$	−5.66260	+	13.6139i	−0.246901	+	0.593593i
$527$			2.04543i			0.0891001i
$528$	1.55655	+	0.00918865i	0.0677401	+	0.000399885i
$529$	−11.1777			−0.485985
$530$	12.9535	−	40.5243i	0.562664	−	1.76026i
$531$	−24.5892	−	24.5892i	−1.06708	−	1.06708i
$532$	0.0236083	−	7.99851i	0.00102355	−	0.346779i
$533$	20.0697	+	20.0697i	0.869315	+	0.869315i
$534$	2.00505	−	0.827053i	0.0867669	−	0.0357901i
$535$	38.0707	−	3.23584i	1.64594	−	0.139898i
$536$	−10.5182	+	25.0787i	−0.454319	+	1.08323i
$537$	−2.32343			−0.100263
$538$	−9.95675	+	4.10702i	−0.429266	+	0.177066i
$539$	−2.53224	+	2.53224i	−0.109071	+	0.109071i
$540$	−2.21905	−	1.88262i	−0.0954927	−	0.0810150i
$541$	8.98526	+	8.98526i	0.386307	+	0.386307i	0.873368	−	0.487061i	$-0.161931\pi$
$541$	8.98526	+	8.98526i	0.386307	+	0.386307i	−0.487061	+	0.873368i	$0.661931\pi$
$542$	−13.2500	+	31.8553i	−0.569137	+	1.36830i
$543$		−	0.0343303i		−	0.00147326i
$544$	−6.17505	+	14.6022i	−0.264753	+	0.626064i
$545$	29.5220	−	2.50924i	1.26458	−	0.107484i
$546$	0.471750	+	0.196221i	0.0201890	+	0.00839750i
$547$	−4.97572	+	4.97572i	−0.212746	+	0.212746i	−0.805433	−	0.592687i	$-0.798067\pi$
$547$	−4.97572	+	4.97572i	−0.212746	+	0.212746i	0.592687	+	0.805433i	$0.298067\pi$
$548$	7.17387	+	7.21634i	0.306452	+	0.308267i
$549$	2.38552	−	2.38552i	0.101812	−	0.101812i
$550$	−21.4437	+	13.4682i	−0.914361	+	0.574286i
$551$			28.9718i			1.23424i
$552$	0.408734	−	0.974544i	0.0173969	−	0.0414793i
$553$	−6.81139			−0.289650
$554$	−2.36364	+	0.974967i	−0.100421	+	0.0414224i
$555$	−1.21996	+	1.44660i	−0.0517842	+	0.0614048i
$556$	40.5766	+	0.119765i	1.72083	+	0.00507918i
$557$	−9.48353	+	9.48353i	−0.401830	+	0.401830i	−0.878878	−	0.477047i	$-0.841707\pi$
$557$	−9.48353	+	9.48353i	−0.401830	+	0.401830i	0.477047	+	0.878878i	$0.341707\pi$
$558$	2.84765	+	1.18446i	0.120551	+	0.0501423i
$559$	−24.1637			−1.02202
$560$	6.80330	+	5.80647i	0.287492	+	0.245368i
$561$	−1.09064			−0.0460466
$562$	4.07820	+	1.69630i	0.172028	+	0.0715541i
$563$	−16.8222	+	16.8222i	−0.708973	+	0.708973i	−0.966319	−	0.257346i	$-0.917152\pi$
$563$	−16.8222	+	16.8222i	−0.708973	+	0.708973i	0.257346	+	0.966319i	$0.417152\pi$
$564$	0.00178591	−	0.605068i	7.52004e−5	−	0.0254780i
$565$	−1.77805	−	1.49947i	−0.0748031	−	0.0630834i
$566$	28.5854	−	11.7910i	1.20153	−	0.495615i
$567$	8.89387			0.373507
$568$	−6.29364	−	15.3865i	−0.264075	−	0.645604i
$569$		−	11.6105i		−	0.486736i	−0.969934	−	0.243368i	$-0.921748\pi$
$569$		−	11.6105i		−	0.486736i	0.969934	−	0.243368i	$-0.0782523\pi$
$570$	−0.629746	−	1.22149i	−0.0263772	−	0.0511625i
$571$	26.6079	−	26.6079i	1.11350	−	1.11350i	0.120831	−	0.992673i	$-0.461444\pi$
$571$	26.6079	−	26.6079i	1.11350	−	1.11350i	0.992673	−	0.120831i	$-0.0385558\pi$
$572$	16.8876	−	16.7882i	0.706108	−	0.701952i
$573$	−0.211244	+	0.211244i	−0.00882484	+	0.00882484i
$574$	11.1471	+	4.63658i	0.465273	+	0.193527i
$575$	2.90149	+	16.9452i	0.121001	+	0.706664i
$576$	16.7534	+	17.0528i	0.698059	+	0.710532i
$577$		−	34.7889i		−	1.44828i	−0.689653	−	0.724140i	$-0.742237\pi$
$577$		−	34.7889i		−	1.44828i	0.689653	−	0.724140i	$-0.257763\pi$
$578$	−4.96694	+	11.9414i	−0.206598	+	0.496696i
$579$	0.979368	+	0.979368i	0.0407011	+	0.0407011i
$580$	−24.7045	−	20.9590i	−1.02580	−	0.870276i
$581$	−1.47708	+	1.47708i	−0.0612796	+	0.0612796i
$582$	1.58620	−	0.654286i	0.0657503	−	0.0271210i
$583$	−48.1793			−1.99538
$584$	37.8674	−	15.4891i	1.56696	−	0.640945i
$585$	−22.1354	+	1.88141i	−0.915185	+	0.0777866i
$586$	21.9555	−	9.05633i	0.906974	−	0.374114i
$587$	32.2867	+	32.2867i	1.33261	+	1.33261i	0.903025	+	0.429589i	$0.141341\pi$
$587$	32.2867	+	32.2867i	1.33261	+	1.33261i	0.429589	+	0.903025i	$0.358659\pi$
$588$	0.217330		0.000641467i	0.00896252		2.64536e-5i
$589$	2.06386	+	2.06386i	0.0850399	+	0.0850399i
$590$	35.0530	+	11.2046i	1.44311	+	0.461286i
$591$	1.29144			0.0531226
$592$	22.1573	−	21.8972i	0.910659	−	0.899970i
$593$			19.1826i			0.787737i	0.919167	+	0.393868i	$0.128863\pi$
$593$			19.1826i			0.787737i	−0.919167	+	0.393868i	$0.871137\pi$
$594$	−1.26562	+	3.04278i	−0.0519292	+	0.124847i
$595$	−4.79076	−	4.04017i	−0.196402	−	0.165631i
$596$	27.9913	+	0.0826187i	1.14657	+	0.00338419i
$597$	1.28366	+	1.28366i	0.0525368	+	0.0525368i
$598$	−6.16471	−	14.9453i	−0.252094	−	0.611157i
$599$			20.5702i			0.840477i	0.907414	+	0.420238i	$0.138054\pi$
$599$			20.5702i			0.840477i	−0.907414	+	0.420238i	$0.861946\pi$
$600$	1.49715	+	0.346669i	0.0611208	+	0.0141527i
$601$		−	2.50910i		−	0.102348i	−0.998690	−	0.0511742i	$-0.983704\pi$
$601$		−	2.50910i		−	0.102348i	0.998690	−	0.0511742i	$-0.0162964\pi$
$602$	−9.50172	+	3.91932i	−0.387261	+	0.159740i
$603$	−20.3160	−	20.3160i	−0.827333	−	0.827333i
$604$	−0.798746	+	0.794044i	−0.0325005	+	0.0323092i
$605$	3.11866	+	2.63005i	0.126792	+	0.106927i
$606$	−1.05607	−	0.439267i	−0.0429001	−	0.0178440i
$607$		−	8.44783i		−	0.342887i	−0.985194	−	0.171443i	$-0.945157\pi$
$607$		−	8.44783i		−	0.342887i	0.985194	−	0.171443i	$-0.0548431\pi$
$608$	8.50310	+	20.9645i	0.344846	+	0.850224i
$609$	−0.787201			−0.0318990
$610$	−1.08702	+	3.40067i	−0.0440120	+	0.137689i
$611$	−6.54527	−	6.54527i	−0.264793	−	0.264793i
$612$	−11.8088	−	11.8788i	−0.477344	−	0.480170i
$613$	−23.2957	−	23.2957i	−0.940906	−	0.940906i	0.0574433	−	0.998349i	$-0.481705\pi$
$613$	−23.2957	−	23.2957i	−0.940906	−	0.940906i	−0.998349	+	0.0574433i	$0.981705\pi$
$614$	−11.9748	−	29.0307i	−0.483262	−	1.17158i
$615$	2.06686	−	0.175674i	0.0833440	−	0.00708387i
$616$	3.91757	−	9.34068i	0.157844	−	0.376347i
$617$	8.85620			0.356537			0.178269	−	0.983982i	$-0.442950\pi$
$617$	8.85620			0.356537			0.178269	+	0.983982i	$0.442950\pi$
$618$	0.553979	+	1.34303i	0.0222843	+	0.0540244i
$619$	20.4322	−	20.4322i	0.821239	−	0.821239i	−0.165047	−	0.986286i	$-0.552777\pi$
$619$	20.4322	−	20.4322i	0.821239	−	0.821239i	0.986286	+	0.165047i	$0.0527774\pi$
$620$	−3.25292	+	0.266815i	−0.130640	+	0.0107156i
$621$	1.58206	+	1.58206i	0.0634859	+	0.0634859i
$622$	−6.92514	−	2.88047i	−0.277673	−	0.115496i
$623$		−	14.1136i		−	0.565450i
$624$	−1.44511	−	0.00853078i	−0.0578505	−	0.000341505i
$625$	−23.5758	+	8.31754i	−0.943032	+	0.332701i
$626$	−8.24954	+	19.8333i	−0.329718	+	0.792699i
$627$	−1.10047	+	1.10047i	−0.0439483	+	0.0439483i
$628$	16.1695	+	0.0477256i	0.645232	+	0.00190446i
$629$	−15.4340	+	15.4340i	−0.615392	+	0.615392i
$630$	−8.39897	+	4.33014i	−0.334623	+	0.172517i
$631$			45.9852i			1.83064i	0.402725	+	0.915321i	$0.368063\pi$
$631$			45.9852i			1.83064i	−0.402725	+	0.915321i	$0.631937\pi$
$632$	17.8315	−	7.29372i	0.709298	−	0.290129i
$633$	1.26435			0.0502534
$634$	−5.98025	−	14.4981i	−0.237506	−	0.575792i
$635$	2.00027	+	1.68688i	0.0793781	+	0.0669416i
$636$	2.06139	+	2.07360i	0.0817395	+	0.0822235i
$637$	2.35094	−	2.35094i	0.0931476	−	0.0931476i
$638$	−14.0901	+	33.8750i	−0.557832	+	1.34112i
$639$	17.5629			0.694779
$640$	−24.0280	−	7.91565i	−0.949788	−	0.312893i
$641$	−48.5298			−1.91681			−0.958405	−	0.285411i	$-0.907870\pi$
$641$	−48.5298			−1.91681			−0.958405	+	0.285411i	$0.907870\pi$
$642$	−1.00846	+	2.42451i	−0.0398007	+	0.0956878i
$643$	13.3346	−	13.3346i	0.525865	−	0.525865i	−0.393471	−	0.919337i	$-0.628726\pi$
$643$	13.3346	−	13.3346i	0.525865	−	0.525865i	0.919337	+	0.393471i	$0.128726\pi$
$644$	−4.84821	−	4.87691i	−0.191046	−	0.192177i
$645$	−1.13849	+	1.35000i	−0.0448278	+	0.0531560i
$646$	−6.04442	−	14.6536i	−0.237814	−	0.576540i
$647$	31.9466			1.25595			0.627976	−	0.778233i	$-0.283884\pi$
$647$	31.9466			1.25595			0.627976	+	0.778233i	$0.283884\pi$
$648$	−23.2832	+	9.52366i	−0.914650	+	0.374125i
$649$		−	41.6745i		−	1.63587i
$650$	19.9084	−	12.5039i	0.780871	−	0.490445i
$651$	−0.0560777	+	0.0560777i	−0.00219786	+	0.00219786i
$652$	50.2441	+	0.148300i	1.96771	+	0.00580786i
$653$	−2.33389	+	2.33389i	−0.0913323	+	0.0913323i	−0.751297	−	0.659964i	$-0.770571\pi$
$653$	−2.33389	+	2.33389i	−0.0913323	+	0.0913323i	0.659964	+	0.751297i	$0.270571\pi$
$654$	−0.782011	+	1.88009i	−0.0305791	+	0.0735173i
$655$	−18.1465	+	1.54237i	−0.709044	+	0.0602655i
$656$	−34.1469	−	0.201577i	−1.33321	−	0.00787026i
$657$			43.2237i			1.68632i
$658$	−3.63538	−	1.51211i	−0.141722	−	0.0589483i
$659$	15.2799	+	15.2799i	0.595221	+	0.595221i	0.939037	−	0.343816i	$-0.111720\pi$
$659$	15.2799	+	15.2799i	0.595221	+	0.595221i	−0.343816	+	0.939037i	$0.611720\pi$
$660$	−0.142268	−	1.73448i	−0.00553777	−	0.0675145i
$661$	−2.95254	+	2.95254i	−0.114841	+	0.114841i	−0.762192	−	0.647351i	$-0.775877\pi$
$661$	−2.95254	+	2.95254i	−0.114841	+	0.114841i	0.647351	+	0.762192i	$0.275877\pi$
$662$	−5.86941	−	14.2294i	−0.228121	−	0.553040i
$663$	1.01255			0.0393242
$664$	2.28516	−	5.44851i	0.0886815	−	0.211443i
$665$	−8.91052	+	0.757354i	−0.345535	+	0.0293689i
$666$	12.5498	+	30.4247i	0.486293	+	1.17893i
$667$	17.6129	+	17.6129i	0.681976	+	0.681976i
$668$	12.3289	+	12.4019i	0.477021	+	0.479845i
$669$	0.0143692	+	0.0143692i	0.000555544	+	0.000555544i
$670$	28.9614	+	9.25745i	1.11888	+	0.357647i
$671$	4.04305			0.156080
$672$	−0.569632	+	0.231040i	−0.0219740	+	0.00891256i
$673$		−	50.1860i		−	1.93453i	−0.253769	−	0.967265i	$-0.581670\pi$
$673$		−	50.1860i		−	1.93453i	0.253769	−	0.967265i	$-0.418330\pi$
$674$	11.8537	+	4.93048i	0.456588	+	0.189915i
$675$	−1.87932	+	2.65588i	−0.0723352	+	0.102225i
$676$	2.76040	−	2.74415i	0.106169	−	0.105544i
$677$	−23.7200	−	23.7200i	−0.911633	−	0.911633i	0.0847681	−	0.996401i	$-0.472985\pi$
$677$	−23.7200	−	23.7200i	−0.911633	−	0.911633i	−0.996401	+	0.0847681i	$0.972985\pi$
$678$	0.147773	−	0.0609542i	0.00567519	−	0.00234093i
$679$		−	11.1654i		−	0.428487i
$680$	16.8679	+	5.44672i	0.646856	+	0.208872i
$681$			3.05918i			0.117228i
$682$	1.40941	+	3.41687i	0.0539692	+	0.130839i
$683$	−15.6986	−	15.6986i	−0.600691	−	0.600691i	0.339805	−	0.940496i	$-0.389639\pi$
$683$	−15.6986	−	15.6986i	−0.600691	−	0.600691i	−0.940496	+	0.339805i	$0.889639\pi$
$684$	−23.9011	−	0.0705461i	−0.913881	−	0.00269740i
$685$	7.33422	−	8.69679i	0.280226	−	0.332287i
$686$	0.543124	−	1.30576i	0.0207366	−	0.0498543i
$687$		−	0.841039i		−	0.0320877i
$688$	20.6776	−	20.4349i	0.788327	−	0.779074i
$689$	44.7298			1.70407
$690$	−1.12543	−	0.359740i	−0.0428443	−	0.0136951i
$691$	11.6710	+	11.6710i	0.443986	+	0.443986i	0.893349	−	0.449363i	$-0.148349\pi$
$691$	11.6710	+	11.6710i	0.443986	+	0.443986i	−0.449363	+	0.893349i	$0.648349\pi$
$692$	−3.20838	−	0.00946980i	−0.121964	−	0.000359988i
$693$	7.56681	+	7.56681i	0.287439	+	0.287439i
$694$	−14.7034	+	6.06493i	−0.558133	+	0.230222i
$695$	−3.84207	−	45.2033i	−0.145738	−	1.71466i
$696$	2.06081	−	0.842945i	0.0781148	−	0.0319518i
$697$	23.9259			0.906259
$698$	5.59003	−	2.30581i	0.211586	−	0.0872761i
$699$	1.21927	−	1.21927i	0.0461172	−	0.0461172i
$700$	5.80031	−	8.14595i	0.219231	−	0.307888i
$701$	20.5028	+	20.5028i	0.774379	+	0.774379i	0.978869	−	0.204490i	$-0.0655536\pi$
$701$	20.5028	+	20.5028i	0.774379	+	0.774379i	−0.204490	+	0.978869i	$0.565554\pi$
$702$	1.17501	−	2.82493i	0.0443479	−	0.106620i
$703$			31.1461i			1.17470i
$704$	−0.253676	+	28.6479i	−0.00956076	+	1.07971i
$705$	−0.674060	+	0.0572920i	−0.0253866	+	0.00215774i
$706$	−12.7449	−	5.30116i	−0.479660	−	0.199512i
$707$	−5.26289	+	5.26289i	−0.197931	+	0.197931i
$708$	−1.79364	+	1.78308i	−0.0674090	+	0.0670122i
$709$	−4.71343	+	4.71343i	−0.177017	+	0.177017i	−0.790054	−	0.613037i	$-0.789948\pi$
$709$	−4.71343	+	4.71343i	−0.177017	+	0.177017i	0.613037	+	0.790054i	$0.289948\pi$
$710$	−16.5199	+	8.51691i	−0.619979	+	0.319634i
$711$			20.3537i			0.763325i
$712$	15.1130	+	36.9480i	0.566385	+	1.38468i
$713$	2.50938			0.0939769
$714$	0.398158	−	0.164234i	0.0149007	−	0.00614632i
$715$	−20.3522	−	17.1635i	−0.761128	−	0.641879i
$716$	0.126218	−	42.7629i	0.00471700	−	1.59813i
$717$	0.470702	−	0.470702i	0.0175787	−	0.0175787i
$718$	−16.2797	−	6.77145i	−0.607554	−	0.252708i
$719$	−41.6746			−1.55420			−0.777101	−	0.629376i	$-0.783310\pi$
$719$	−41.6746			−1.55420			−0.777101	+	0.629376i	$0.783310\pi$
$720$	17.3508	−	20.3296i	0.646628	−	0.757639i
$721$	9.45362			0.352071
$722$	3.92488	+	1.63253i	0.146069	+	0.0607564i
$723$	−1.21118	+	1.21118i	−0.0450443	+	0.0450443i
$724$	0.631852	+	0.00186496i	0.0234826	+	6.93108e-5i
$725$	−20.9223	+	29.5676i	−0.777036	+	1.09811i
$726$	−0.259190	+	0.106912i	−0.00961946	+	0.00396789i
$727$	11.1288			0.412744			0.206372	−	0.978474i	$-0.433834\pi$
$727$	11.1288			0.412744			0.206372	+	0.978474i	$0.433834\pi$
$728$	−3.63709	+	8.67192i	−0.134800	+	0.321403i
$729$		−	26.3645i		−	0.976461i
$730$	−20.9608	−	40.6567i	−0.775794	−	1.50477i
$731$	−14.4033	+	14.4033i	−0.532724	+	0.532724i
$732$	−0.172986	−	0.174010i	−0.00639373	−	0.00643159i
$733$	26.0566	−	26.0566i	0.962422	−	0.962422i	−0.0368972	−	0.999319i	$-0.511747\pi$
$733$	26.0566	−	26.0566i	0.962422	−	0.962422i	0.999319	+	0.0368972i	$0.0117474\pi$
$734$	−38.5773	−	16.0460i	−1.42391	−	0.592268i
$735$	−0.0205783	−	0.242110i	−0.000759040	−	0.00893036i
$736$	17.9143	+	7.57571i	0.660331	+	0.279244i
$737$		−	34.4322i		−	1.26833i
$738$	13.8550	−	33.3098i	0.510010	−	1.22615i
$739$	27.5810	+	27.5810i	1.01458	+	1.01458i	0.999892	+	0.0146896i	$0.00467600\pi$
$739$	27.5810	+	27.5810i	1.01458	+	1.01458i	0.0146896	+	0.999892i	$0.495324\pi$
$740$	−26.5585	−	22.5319i	−0.976310	−	0.828291i
$741$	1.02168	−	1.02168i	0.0375322	−	0.0375322i
$742$	17.5888	−	7.25512i	0.645705	−	0.266344i
$743$	30.6075			1.12288			0.561440	−	0.827518i	$-0.310248\pi$
$743$	30.6075			1.12288			0.561440	+	0.827518i	$0.310248\pi$
$744$	0.0867567	−	0.206854i	0.00318065	−	0.00758364i
$745$	−2.65041	−	31.1829i	−0.0971035	−	1.14245i
$746$	2.84731	−	1.17447i	0.104247	−	0.0430005i
$747$	4.41380	+	4.41380i	0.161492	+	0.161492i
$748$	0.0592478	−	20.0732i	0.00216631	−	0.733949i
$749$	12.0824	+	12.0824i	0.441482	+	0.441482i
$750$	0.239415	−	1.70139i	0.00874220	−	0.0621258i
$751$	−39.9363			−1.45730			−0.728648	−	0.684889i	$-0.759851\pi$
$751$	−39.9363			−1.45730			−0.728648	+	0.684889i	$0.759851\pi$
$752$	11.1362	+	0.0657396i	0.406096	+	0.00239728i
$753$			1.46999i			0.0535694i
$754$	13.0813	−	31.4497i	0.476392	−	1.14533i
$755$	0.962610	+	0.811793i	0.0350330	+	0.0295442i
$756$	0.00384123	−	1.30141i	0.000139704	−	0.0473319i
$757$	−18.6332	−	18.6332i	−0.677236	−	0.677236i	0.282137	−	0.959374i	$-0.408957\pi$
$757$	−18.6332	−	18.6332i	−0.677236	−	0.677236i	−0.959374	+	0.282137i	$0.908957\pi$
$758$	−8.23716	−	19.9696i	−0.299187	−	0.725327i
$759$			1.33802i			0.0485670i
$760$	22.5158	−	11.5242i	0.816734	−	0.418025i
$761$		−	23.2940i		−	0.844405i	−0.906502	−	0.422203i	$-0.861257\pi$
$761$		−	23.2940i		−	0.844405i	0.906502	−	0.422203i	$-0.138743\pi$
$762$	−0.166241	+	0.0685721i	−0.00602229	+	0.00248411i
$763$	9.36933	+	9.36933i	0.339193	+	0.339193i
$764$	−3.87648	−	3.89943i	−0.140246	−	0.141077i
$765$	−12.0728	+	14.3157i	−0.436493	+	0.517585i
$766$	−0.328068	−	0.136458i	−0.0118536	−	0.00493042i
$767$			38.6908i			1.39704i
$768$	1.24384	−	1.21481i	0.0448831	−	0.0438356i
$769$	17.6407			0.636141			0.318070	−	0.948067i	$-0.396965\pi$
$769$	17.6407			0.636141			0.318070	+	0.948067i	$0.396965\pi$
$770$	−10.7868	−	3.44799i	−0.388731	−	0.124257i
$771$	−0.442897	−	0.442897i	−0.0159505	−	0.0159505i
$772$	−18.0785	+	17.9721i	−0.650660	+	0.646831i
$773$	−14.0014	−	14.0014i	−0.503595	−	0.503595i	0.408958	−	0.912553i	$-0.365892\pi$
$773$	−14.0014	−	14.0014i	−0.503595	−	0.503595i	−0.912553	+	0.408958i	$0.865892\pi$
$774$	11.7117	+	28.3929i	0.420968	+	1.02056i
$775$	0.615863	+	3.59674i	0.0221225	+	0.129199i
$776$	11.9560	+	29.2297i	0.429196	+	1.04929i
$777$	−0.846279			−0.0303601
$778$	−10.8241	−	26.2411i	−0.388061	−	0.940788i
$779$	24.1416	−	24.1416i	0.864961	−	0.864961i
$780$	0.132082	+	1.61030i	0.00472930	+	0.0576579i
$781$	14.8831	+	14.8831i	0.532559	+	0.532559i
$782$	−12.5830	−	5.23383i	−0.449968	−	0.187161i
$783$			4.71391i			0.168462i
$784$	−0.0236125	+	3.99993i	−0.000843302	+	0.142855i
$785$	−1.53104	−	18.0132i	−0.0546451	−	0.642917i
$786$	0.480686	−	1.15565i	0.0171455	−	0.0412207i
$787$	−1.98055	+	1.98055i	−0.0705988	+	0.0705988i	−0.741525	−	0.670926i	$-0.765897\pi$
$787$	−1.98055	+	1.98055i	−0.0705988	+	0.0705988i	0.670926	+	0.741525i	$0.265897\pi$
$788$	−0.0701562	+	23.7690i	−0.00249921	+	0.846735i
$789$	−0.801111	+	0.801111i	−0.0285203	+	0.0285203i
$790$	−9.87028	−	19.1449i	−0.351169	−	0.681145i
$791$		−	1.04018i		−	0.0369846i
$792$	−27.9117	−	11.7065i	−0.991800	−	0.415971i
$793$	−3.75359			−0.133294
$794$	18.6681	+	45.2576i	0.662507	+	1.60613i
$795$	2.10747	−	2.49900i	0.0747443	−	0.0886304i
$796$	−23.6956	+	23.5562i	−0.839869	+	0.834926i
$797$	7.95147	−	7.95147i	0.281655	−	0.281655i	−0.552113	−	0.833769i	$-0.686178\pi$
$797$	7.95147	−	7.95147i	0.281655	−	0.281655i	0.833769	+	0.552113i	$0.186178\pi$
$798$	0.236032	−	0.567461i	0.00835544	−	0.0200879i
$799$	−7.80288			−0.276046
$800$	−6.46180	+	27.5363i	−0.228459	+	0.973554i
$801$	−42.1742			−1.49015
$802$	4.04706	−	9.72982i	0.142907	−	0.343572i
$803$	−36.6284	+	36.6284i	−1.29259	+	1.29259i
$804$	−1.48193	+	1.47321i	−0.0522638	+	0.0519562i
$805$	−4.95658	+	5.87742i	−0.174696	+	0.207152i
$806$	−1.30850	−	3.17224i	−0.0460901	−	0.111737i
$807$	−0.827586			−0.0291324
$808$	8.14211	−	19.4133i	0.286439	−	0.682956i
$809$		−	23.4116i		−	0.823108i	−0.911385	−	0.411554i	$-0.864986\pi$
$809$		−	23.4116i		−	0.823108i	0.911385	−	0.411554i	$-0.135014\pi$
$810$	12.8880	+	24.9982i	0.452837	+	0.878346i
$811$	19.6434	−	19.6434i	0.689772	−	0.689772i	−0.272410	−	0.962181i	$-0.587821\pi$
$811$	19.6434	−	19.6434i	0.689772	−	0.689772i	0.962181	+	0.272410i	$0.0878206\pi$
$812$	0.0427640	−	14.4885i	0.00150072	−	0.508446i
$813$	−1.87453	+	1.87453i	−0.0657427	+	0.0657427i
$814$	−15.1475	+	36.4172i	−0.530920	+	1.27642i
$815$	−4.75746	−	55.9730i	−0.166646	−	1.96065i
$816$	−0.866470	+	0.856300i	−0.0303325	+	0.0299765i
$817$			29.0662i			1.01690i
$818$	−45.7025	−	19.0097i	−1.59795	−	0.664657i
$819$	−7.02506	−	7.02506i	−0.245475	−	0.245475i
$820$	3.12101	+	38.0503i	0.108991	+	1.32877i
$821$	−1.98930	+	1.98930i	−0.0694272	+	0.0694272i	−0.740968	−	0.671541i	$-0.765633\pi$
$821$	−1.98930	+	1.98930i	−0.0694272	+	0.0694272i	0.671541	+	0.740968i	$0.265633\pi$
$822$	0.298139	+	0.722787i	0.0103988	+	0.0252101i
$823$	−24.1133			−0.840538			−0.420269	−	0.907399i	$-0.638064\pi$
$823$	−24.1133			−0.840538			−0.420269	+	0.907399i	$0.638064\pi$
$824$	−24.7486	+	10.1231i	−0.862157	+	0.352653i
$825$	−1.91781	+	0.328382i	−0.0667695	+	0.0114328i
$826$	6.27559	+	15.2141i	0.218356	+	0.529366i
$827$	−27.3969	−	27.3969i	−0.952683	−	0.952683i	0.0462468	−	0.998930i	$-0.485274\pi$
$827$	−27.3969	−	27.3969i	−0.952683	−	0.952683i	−0.998930	+	0.0462468i	$0.985274\pi$
$828$	−14.5731	+	14.4874i	−0.506452	+	0.503471i
$829$	24.5081	+	24.5081i	0.851203	+	0.851203i	0.990281	−	0.139078i	$-0.0444139\pi$
$829$	24.5081	+	24.5081i	0.851203	+	0.851203i	−0.139078	+	0.990281i	$0.544414\pi$
$830$	−6.29208	−	2.01125i	−0.218401	−	0.0698114i
$831$	−0.196461			−0.00681516
$832$	0.235514	−	26.5968i	0.00816497	−	0.922078i
$833$		−	2.80265i		−	0.0971062i
$834$	2.87874	+	1.19739i	0.0996827	+	0.0414624i
$835$	12.6045	−	14.9462i	0.436198	−	0.517235i
$836$	−20.1943	−	20.3139i	−0.698436	−	0.702571i
$837$	0.335804	+	0.335804i	0.0116071	+	0.0116071i
$838$	7.79296	−	3.21448i	0.269203	−	0.111042i
$839$		−	29.3488i		−	1.01323i	−0.862171	−	0.506617i	$-0.830896\pi$
$839$		−	29.3488i		−	1.01323i	0.862171	−	0.506617i	$-0.169104\pi$
$840$	0.313126	+	0.611782i	0.0108039	+	0.0211085i
$841$			23.4796i			0.809641i
$842$	6.28382	+	15.2340i	0.216555	+	0.524999i
$843$	0.239983	+	0.239983i	0.00826544	+	0.00826544i
$844$	−0.0686846	+	23.2704i	−0.00236422	+	0.801001i
$845$	−3.32670	−	2.80549i	−0.114442	−	0.0965118i
$846$	−4.51849	+	10.8632i	−0.155349	+	0.373485i
$847$			1.82445i			0.0626890i
$848$	−38.2767	+	37.8274i	−1.31443	+	1.29900i
$849$	2.37596			0.0815427
$850$	4.41357	−	19.3200i	0.151384	−	0.662671i
$851$	18.9348	+	18.9348i	0.649075	+	0.649075i
$852$	0.00377018	−	1.27734i	0.000129164	−	0.0437610i
$853$	14.2270	+	14.2270i	0.487124	+	0.487124i	0.907398	−	0.420273i	$-0.138066\pi$
$853$	14.2270	+	14.2270i	0.487124	+	0.487124i	−0.420273	+	0.907398i	$0.638066\pi$
$854$	−1.47600	+	0.608827i	−0.0505075	+	0.0208336i
$855$	2.26312	+	26.6263i	0.0773970	+	0.910602i
$856$	−44.5685	−	18.6925i	−1.52332	−	0.638896i
$857$	25.2460			0.862387			0.431193	−	0.902260i	$-0.358093\pi$
$857$	25.2460			0.862387			0.431193	+	0.902260i	$0.358093\pi$
$858$	1.69146	−	0.697703i	0.0577455	−	0.0238192i
$859$	9.73380	−	9.73380i	0.332113	−	0.332113i	−0.521275	−	0.853388i	$-0.674544\pi$
$859$	9.73380	−	9.73380i	0.332113	−	0.332113i	0.853388	+	0.521275i	$0.174544\pi$
$860$	−24.7849	−	21.0272i	−0.845158	−	0.717023i
$861$	0.655957	+	0.655957i	0.0223549	+	0.0223549i
$862$	−7.40428	+	17.8012i	−0.252191	+	0.606310i
$863$		−	28.3873i		−	0.966315i	−0.875533	−	0.483157i	$-0.839490\pi$
$863$		−	28.3873i		−	0.966315i	0.875533	−	0.483157i	$-0.160510\pi$
$864$	1.38351	+	3.41107i	0.0470680	+	0.116047i
$865$	0.303791	+	3.57420i	0.0103292	+	0.121527i
$866$	19.7322	+	8.20748i	0.670527	+	0.278902i
$867$	−0.702694	+	0.702694i	−0.0238647	+	0.0238647i
$868$	−1.02907	−	1.03516i	−0.0349288	−	0.0351356i
$869$	−17.2481	+	17.2481i	−0.585100	+	0.585100i
$870$	−1.14072	−	2.21260i	−0.0386741	−	0.0750143i
$871$			31.9670i			1.08316i
$872$	−34.5607	−	14.4951i	−1.17037	−	0.490866i
$873$	−33.3643			−1.12921
$874$	−17.9774	+	7.41544i	−0.608096	+	0.250831i
$875$	−9.64069	−	5.66190i	−0.325915	−	0.191407i
$876$	3.14364	+	0.00927872i	0.106214	+	0.000313499i
$877$	22.5269	−	22.5269i	0.760678	−	0.760678i	−0.215767	−	0.976445i	$-0.569225\pi$
$877$	22.5269	−	22.5269i	0.760678	−	0.760678i	0.976445	+	0.215767i	$0.0692252\pi$
$878$	19.8344	+	8.24998i	0.669378	+	0.278423i
$879$	1.82490			0.0615523
$880$	31.9309	−	2.52422i	1.07639	−	0.0850916i
$881$	−55.9848			−1.88618			−0.943088	−	0.332544i	$-0.892093\pi$
$881$	−55.9848			−1.88618			−0.943088	+	0.332544i	$0.892093\pi$
$882$	−3.90187	−	1.62296i	−0.131383	−	0.0546478i
$883$	14.4223	−	14.4223i	0.485350	−	0.485350i	−0.421485	−	0.906835i	$-0.638491\pi$
$883$	14.4223	−	14.4223i	0.485350	−	0.485350i	0.906835	+	0.421485i	$0.138491\pi$
$884$	−0.0550059	+	18.6361i	−0.00185005	+	0.626798i
$885$	2.16160	+	1.82294i	0.0726615	+	0.0612773i
$886$	−9.22071	+	3.80341i	−0.309776	+	0.127778i
$887$	−52.5812			−1.76551			−0.882753	−	0.469838i	$-0.844312\pi$
$887$	−52.5812			−1.76551			−0.882753	+	0.469838i	$0.844312\pi$
$888$	2.21547	−	0.906206i	0.0743462	−	0.0304103i
$889$			1.17018i			0.0392466i
$890$	39.6695	−	20.4518i	1.32972	−	0.685547i
$891$	22.5214	−	22.5214i	0.754495	−	0.754495i
$892$	−0.265246	+	0.263685i	−0.00888109	+	0.00882882i
$893$	−7.87321	+	7.87321i	−0.263467	+	0.263467i
$894$	1.98587	+	0.826009i	0.0664173	+	0.0276259i
$895$	−47.6388	+	4.04909i	−1.59239	+	0.135346i
$896$	−4.22136	−	10.4967i	−0.141026	−	0.350669i
$897$		−	1.24222i		−	0.0414766i
$898$	1.63525	−	3.93143i	0.0545690	−	0.131193i
$899$	3.73848	+	3.73848i	0.124685	+	0.124685i
$900$	−24.3417	−	17.3324i	−0.811388	−	0.577748i
$901$	26.6621	−	26.6621i	0.888244	−	0.888244i
$902$	39.9682	−	16.4863i	1.33079	−	0.548933i
$903$	−0.789764			−0.0262817
$904$	1.11384	+	2.72308i	0.0370457	+	0.0905684i
$905$	−0.0598281	−	0.703897i	−0.00198875	−	0.0233983i
$906$	−0.0800021	+	0.0329997i	−0.00265789	+	0.00109634i
$907$	−10.8148	−	10.8148i	−0.359099	−	0.359099i	0.504382	−	0.863481i	$-0.331720\pi$
$907$	−10.8148	−	10.8148i	−0.359099	−	0.359099i	−0.863481	+	0.504382i	$0.831720\pi$
$908$	−56.3044	−	0.166187i	−1.86853	−	0.00551512i
$909$	15.7265	+	15.7265i	0.521616	+	0.521616i
$910$	10.0145	+	3.20113i	0.331979	+	0.106116i
$911$	−24.4259			−0.809267			−0.404634	−	0.914479i	$-0.632601\pi$
$911$	−24.4259			−0.809267			−0.404634	+	0.914479i	$0.632601\pi$
$912$	−0.0102616	+	1.73830i	−0.000339794	+	0.0575608i
$913$			7.48064i			0.247573i
$914$	11.1161	−	26.7251i	0.367689	−	0.883987i
$915$	−0.176852	+	0.209708i	−0.00584656	+	0.00693274i
$916$	15.4794	+	0.0456887i	0.511453	+	0.00150960i
$917$	−5.75913	−	5.75913i	−0.190183	−	0.190183i
$918$	−0.983467	−	2.38425i	−0.0324592	−	0.0786918i
$919$		−	10.4113i		−	0.343436i	−0.985146	−	0.171718i	$-0.945068\pi$
$919$		−	10.4113i		−	0.343436i	0.985146	−	0.171718i	$-0.0549318\pi$
$920$	6.68217	−	20.6940i	0.220305	−	0.682261i
$921$		−	2.41298i		−	0.0795103i
$922$	−8.39353	+	3.46221i	−0.276426	+	0.114022i
$923$	−13.8175	−	13.8175i	−0.454809	−	0.454809i
$924$	0.551954	−	0.548706i	0.0181580	−	0.0180511i
$925$	−22.4925	+	31.7866i	−0.739549	+	1.04514i
$926$	−20.9893	−	8.73035i	−0.689750	−	0.286897i
$927$		−	28.2492i		−	0.927826i
$928$	15.4025	+	37.9751i	0.505612	+	1.24659i
$929$	−17.6224			−0.578173			−0.289087	−	0.957303i	$-0.593352\pi$
$929$	−17.6224			−0.578173			−0.289087	+	0.957303i	$0.593352\pi$
$930$	−0.238880	−	0.0763574i	−0.00783319	−	0.00250386i
$931$	−2.82791	−	2.82791i	−0.0926811	−	0.0926811i
$932$	22.3746	+	22.5071i	0.732904	+	0.737243i
$933$	−0.407512	−	0.407512i	−0.0133413	−	0.0133413i
$934$	14.9951	+	36.3529i	0.490653	+	1.18950i
$935$	−22.3620	+	1.90067i	−0.731316	+	0.0621585i
$936$	25.9134	+	10.8683i	0.847005	+	0.355243i
$937$	−11.7145			−0.382695			−0.191348	−	0.981522i	$-0.561286\pi$
$937$	−11.7145			−0.382695			−0.191348	+	0.981522i	$0.561286\pi$
$938$	5.18501	+	12.5702i	0.169296	+	0.410430i
$939$	−1.16710	+	1.16710i	−0.0380868	+	0.0380868i
$940$	−1.01785	−	12.4092i	−0.0331985	−	0.404744i
$941$	36.0452	+	36.0452i	1.17504	+	1.17504i	0.980992	+	0.194048i	$0.0621616\pi$
$941$	36.0452	+	36.0452i	1.17504	+	1.17504i	0.194048	+	0.980992i	$0.437838\pi$
$942$	1.14716	+	0.477153i	0.0373764	+	0.0155465i
$943$		−	29.3529i		−	0.955862i
$944$	−32.7203	−	33.1089i	−1.06495	−	1.07760i
$945$	−1.44980	+	0.123227i	−0.0471620	+	0.00400856i
$946$	−14.1359	+	33.9853i	−0.459599	+	1.10496i
$947$	−17.8151	+	17.8151i	−0.578913	+	0.578913i	−0.934604	−	0.355691i	$-0.884246\pi$
$947$	−17.8151	+	17.8151i	−0.578913	+	0.578913i	0.355691	+	0.934604i	$0.384246\pi$
$948$	1.48032	+	0.00436928i	0.0480784	+	0.000141908i
$949$	34.0060	−	34.0060i	1.10388	−	1.10388i
$950$	−15.0408	−	23.9475i	−0.487988	−	0.776960i
$951$		−	1.20505i		−	0.0390765i
$952$	3.00111	+	7.33704i	0.0972667	+	0.237795i
$953$	48.5972			1.57422			0.787108	−	0.616815i	$-0.211577\pi$
$953$	48.5972			1.57422			0.787108	+	0.616815i	$0.211577\pi$
$954$	−21.6797	−	52.5587i	−0.701906	−	1.70165i
$955$	−3.96313	+	4.69941i	−0.128244	+	0.152069i
$956$	8.63772	+	8.68887i	0.279364	+	0.281018i
$957$	−1.99338	+	1.99338i	−0.0644369	+	0.0644369i
$958$	20.4203	−	49.0938i	0.659749	−	1.58615i
$959$	5.08773			0.164291
$960$	−1.47483	−	1.26628i	−0.0476001	−	0.0408691i
$961$	−30.4674			−0.982818
$962$	14.0630	−	33.8099i	0.453410	−	1.09007i
$963$	36.1046	−	36.1046i	1.16345	−	1.16345i
$964$	−22.2260	−	22.3576i	−0.715853	−	0.720091i
$965$	21.7874	+	18.3738i	0.701360	+	0.591475i
$966$	−0.201487	−	0.488470i	−0.00648273	−	0.0157163i
$967$	−16.0491			−0.516103			−0.258052	−	0.966131i	$-0.583080\pi$
$967$	−16.0491			−0.516103			−0.258052	+	0.966131i	$0.583080\pi$
$968$	−1.95365	−	4.77623i	−0.0627926	−	0.153514i
$969$		−	1.21798i		−	0.0391272i
$970$	31.3827	−	16.1796i	1.00764	−	0.519494i
$971$	27.5537	−	27.5537i	0.884242	−	0.884242i	−0.109721	−	0.993962i	$-0.534996\pi$
$971$	27.5537	−	27.5537i	0.884242	−	0.884242i	0.993962	+	0.109721i	$0.0349956\pi$
$972$	−5.83713	−	0.0172288i	−0.187226	−	0.000552614i
$973$	14.3461	−	14.3461i	0.459914	−	0.459914i
$974$	−16.6045	+	39.9200i	−0.532042	+	1.27912i
$975$	1.78050	−	0.304872i	0.0570217	−	0.00976371i
$976$	3.21206	−	3.17436i	0.102816	−	0.101609i
$977$			34.8390i			1.11460i	0.830311	+	0.557300i	$0.188163\pi$
$977$			34.8390i			1.11460i	−0.830311	+	0.557300i	$0.811837\pi$
$978$	3.56461	+	1.48268i	0.113984	+	0.0474108i
$979$	−35.7391	−	35.7391i	−1.14223	−	1.14223i
$980$	4.45717	−	0.365592i	0.142379	−	0.0116784i
$981$	27.9974	−	27.9974i	0.893887	−	0.893887i
$982$	−1.78680	−	4.33178i	−0.0570190	−	0.138233i
$983$	−34.8718			−1.11224			−0.556119	−	0.831103i	$-0.687710\pi$
$983$	−34.8718			−1.11224			−0.556119	+	0.831103i	$0.687710\pi$
$984$	−2.41963	−	1.01482i	−0.0771350	−	0.0323512i
$985$	26.4792	−	2.25061i	0.843697	−	0.0717104i
$986$	−10.9488	−	26.5436i	−0.348682	−	0.845320i
$987$	−0.213925	−	0.213925i	−0.00680931	−	0.00680931i
$988$	18.7485	+	18.8595i	0.596470	+	0.600001i
$989$	17.6703	+	17.6703i	0.561882	+	0.561882i
$990$	−10.3032	+	32.2331i	−0.327459	+	1.02444i
$991$	41.7055			1.32482			0.662409	−	0.749142i	$-0.269534\pi$
$991$	41.7055			1.32482			0.662409	+	0.749142i	$0.269534\pi$
$992$	3.80245	+	1.60800i	0.120728	+	0.0510540i
$993$		−	1.18272i		−	0.0375324i
$994$	−7.67455	−	3.19218i	−0.243422	−	0.101250i
$995$	28.5568	+	24.0827i	0.905312	+	0.763473i
$996$	0.321961	−	0.320066i	0.0102017	−	0.0101417i
$997$	37.8249	+	37.8249i	1.19793	+	1.19793i	0.974786	+	0.223142i	$0.0716314\pi$
$997$	37.8249	+	37.8249i	1.19793	+	1.19793i	0.223142	+	0.974786i	$0.428369\pi$
$998$	1.96916	−	0.812250i	0.0623326	−	0.0257113i
$999$			5.06768i			0.160334i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.bb.c.29.13	✓	70
5.4	even	2		560.2.bb.d.29.23	yes	70
16.5	even	4		560.2.bb.d.309.23	yes	70
80.69	even	4	inner	560.2.bb.c.309.13	yes	70

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.bb.c.29.13	✓	70	1.1	even	1	trivial
560.2.bb.c.309.13	yes	70	80.69	even	4	inner
560.2.bb.d.29.23	yes	70	5.4	even	2
560.2.bb.d.309.23	yes	70	16.5	even	4

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:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.bb (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.543124 + 1.30576i) q^{2} +(-0.0768379 + 0.0768379i) q^{3} +(-1.41003 - 1.41838i) q^{4} +(-1.44155 + 1.70937i) q^{5} +(-0.0585996 - 0.142065i) q^{6} -1.00000 q^{7} +(2.61789 - 1.07081i) q^{8} +2.98819i q^{9} +O(q^{10})\)	\(q+(-0.543124 + 1.30576i) q^{2} +(-0.0768379 + 0.0768379i) q^{3} +(-1.41003 - 1.41838i) q^{4} +(-1.44155 + 1.70937i) q^{5} +(-0.0585996 - 0.142065i) q^{6} -1.00000 q^{7} +(2.61789 - 1.07081i) q^{8} +2.98819i q^{9} +(-1.44908 - 2.81072i) q^{10} +(-2.53224 + 2.53224i) q^{11} +(0.217330 + 0.000641467i) q^{12} +(2.35094 - 2.35094i) q^{13} +(0.543124 - 1.30576i) q^{14} +(-0.0205783 - 0.242110i) q^{15} +(-0.0236125 + 3.99993i) q^{16} -2.80265i q^{17} +(-3.90187 - 1.62296i) q^{18} +(-2.82791 - 2.82791i) q^{19} +(4.45717 - 0.365592i) q^{20} +(0.0768379 - 0.0768379i) q^{21} +(-1.93118 - 4.68182i) q^{22} -3.43836 q^{23} +(-0.118874 + 0.283433i) q^{24} +(-0.843859 - 4.92828i) q^{25} +(1.79292 + 4.34662i) q^{26} +(-0.460120 - 0.460120i) q^{27} +(1.41003 + 1.41838i) q^{28} +(-5.12248 - 5.12248i) q^{29} +(0.327315 + 0.104625i) q^{30} -0.729818 q^{31} +(-5.21014 - 2.20329i) q^{32} -0.389144i q^{33} +(3.65960 + 1.52219i) q^{34} +(1.44155 - 1.70937i) q^{35} +(4.23840 - 4.21345i) q^{36} +(-5.50691 - 5.50691i) q^{37} +(5.22849 - 2.15668i) q^{38} +0.361283i q^{39} +(-1.94342 + 6.01857i) q^{40} +8.53688i q^{41} +(0.0585996 + 0.142065i) q^{42} +(-5.13916 - 5.13916i) q^{43} +(7.16222 + 0.0211399i) q^{44} +(-5.10791 - 4.30763i) q^{45} +(1.86746 - 4.48969i) q^{46} -2.78411i q^{47} +(-0.305532 - 0.309161i) q^{48} +1.00000 q^{49} +(6.89348 + 1.57478i) q^{50} +(0.215350 + 0.215350i) q^{51} +(-6.64943 - 0.0196264i) q^{52} +(9.51318 + 9.51318i) q^{53} +(0.850710 - 0.350906i) q^{54} +(-0.678168 - 7.97887i) q^{55} +(-2.61789 + 1.07081i) q^{56} +0.434582 q^{57} +(9.47088 - 3.90660i) q^{58} +(-8.22878 + 8.22878i) q^{59} +(-0.314388 + 0.370571i) q^{60} +(-0.798316 - 0.798316i) q^{61} +(0.396381 - 0.952969i) q^{62} -2.98819i q^{63} +(5.70672 - 5.60654i) q^{64} +(0.629614 + 7.40762i) q^{65} +(0.508130 + 0.211353i) q^{66} +(-6.79877 + 6.79877i) q^{67} +(-3.97523 + 3.95183i) q^{68} +(0.264197 - 0.264197i) q^{69} +(1.44908 + 2.81072i) q^{70} -5.87744i q^{71} +(3.19979 + 7.82276i) q^{72} +14.4648 q^{73} +(10.1817 - 4.19979i) q^{74} +(0.443519 + 0.313838i) q^{75} +(-0.0236083 + 7.99851i) q^{76} +(2.53224 - 2.53224i) q^{77} +(-0.471750 - 0.196221i) q^{78} +6.81139 q^{79} +(-6.80330 - 5.80647i) q^{80} -8.89387 q^{81} +(-11.1471 - 4.63658i) q^{82} +(1.47708 - 1.47708i) q^{83} +(-0.217330 - 0.000641467i) q^{84} +(4.79076 + 4.04017i) q^{85} +(9.50172 - 3.91932i) q^{86} +0.787201 q^{87} +(-3.91757 + 9.34068i) q^{88} +14.1136i q^{89} +(8.39897 - 4.33014i) q^{90} +(-2.35094 + 2.35094i) q^{91} +(4.84821 + 4.87691i) q^{92} +(0.0560777 - 0.0560777i) q^{93} +(3.63538 + 1.51211i) q^{94} +(8.91052 - 0.757354i) q^{95} +(0.569632 - 0.231040i) q^{96} +11.1654i q^{97} +(-0.543124 + 1.30576i) q^{98} +(-7.56681 - 7.56681i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 70 q - 2 q^{2} - 2 q^{3} - 4 q^{5} - 70 q^{7} - 8 q^{8}+O(q^{10}) \) 70 * q - 2 * q^2 - 2 * q^3 - 4 * q^5 - 70 * q^7 - 8 * q^8	\( 70 q - 2 q^{2} - 2 q^{3} - 4 q^{5} - 70 q^{7} - 8 q^{8} + 6 q^{10} - 2 q^{11} + 4 q^{12} - 6 q^{13} + 2 q^{14} - 6 q^{15} + 4 q^{16} + 18 q^{18} + 14 q^{19} + 20 q^{20} + 2 q^{21} + 12 q^{22} + 20 q^{24} - 6 q^{25} - 36 q^{26} - 8 q^{27} + 2 q^{29} + 28 q^{30} + 16 q^{31} + 8 q^{32} + 4 q^{34} + 4 q^{35} - 40 q^{36} - 10 q^{37} + 12 q^{38} + 44 q^{40} - 2 q^{43} - 24 q^{44} + 22 q^{45} - 16 q^{46} + 44 q^{48} + 70 q^{49} - 74 q^{50} + 8 q^{51} - 28 q^{52} + 30 q^{53} - 32 q^{54} - 6 q^{55} + 8 q^{56} + 76 q^{57} - 56 q^{58} + 2 q^{59} - 64 q^{60} + 30 q^{61} - 48 q^{62} + 12 q^{64} - 10 q^{65} + 80 q^{66} - 6 q^{67} + 36 q^{68} - 16 q^{69} - 6 q^{70} - 4 q^{72} + 36 q^{73} - 32 q^{74} - 98 q^{75} + 44 q^{76} + 2 q^{77} + 84 q^{78} - 40 q^{79} - 24 q^{80} - 82 q^{81} - 24 q^{82} - 10 q^{83} - 4 q^{84} - 32 q^{85} + 32 q^{86} + 4 q^{87} - 32 q^{88} + 158 q^{90} + 6 q^{91} + 92 q^{92} + 56 q^{93} - 20 q^{94} + 6 q^{95} + 16 q^{96} - 2 q^{98} - 34 q^{99}+O(q^{100}) \) 70 * q - 2 * q^2 - 2 * q^3 - 4 * q^5 - 70 * q^7 - 8 * q^8 + 6 * q^10 - 2 * q^11 + 4 * q^12 - 6 * q^13 + 2 * q^14 - 6 * q^15 + 4 * q^16 + 18 * q^18 + 14 * q^19 + 20 * q^20 + 2 * q^21 + 12 * q^22 + 20 * q^24 - 6 * q^25 - 36 * q^26 - 8 * q^27 + 2 * q^29 + 28 * q^30 + 16 * q^31 + 8 * q^32 + 4 * q^34 + 4 * q^35 - 40 * q^36 - 10 * q^37 + 12 * q^38 + 44 * q^40 - 2 * q^43 - 24 * q^44 + 22 * q^45 - 16 * q^46 + 44 * q^48 + 70 * q^49 - 74 * q^50 + 8 * q^51 - 28 * q^52 + 30 * q^53 - 32 * q^54 - 6 * q^55 + 8 * q^56 + 76 * q^57 - 56 * q^58 + 2 * q^59 - 64 * q^60 + 30 * q^61 - 48 * q^62 + 12 * q^64 - 10 * q^65 + 80 * q^66 - 6 * q^67 + 36 * q^68 - 16 * q^69 - 6 * q^70 - 4 * q^72 + 36 * q^73 - 32 * q^74 - 98 * q^75 + 44 * q^76 + 2 * q^77 + 84 * q^78 - 40 * q^79 - 24 * q^80 - 82 * q^81 - 24 * q^82 - 10 * q^83 - 4 * q^84 - 32 * q^85 + 32 * q^86 + 4 * q^87 - 32 * q^88 + 158 * q^90 + 6 * q^91 + 92 * q^92 + 56 * q^93 - 20 * q^94 + 6 * q^95 + 16 * q^96 - 2 * q^98 - 34 * q^99

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