LMFDB - Embedded newform 224.2.u.c.85.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,2,Mod(29,224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(224, base_ring=CyclotomicField(8))

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

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

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

chi := DirichletCharacter("224.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	224.u (of order $8$, 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:	$1.78864900528$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$13$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			85.4
Character	$\chi$	$=$	224.85
Dual form			224.2.u.c.29.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.926451 + 1.06850i) q^{2} +(-1.34443 + 0.556881i) q^{3} +(-0.283377 - 1.97982i) q^{4} +(0.598728 - 1.44546i) q^{5} +(0.650522 - 1.95244i) q^{6} +(0.707107 + 0.707107i) q^{7} +(2.37797 + 1.53142i) q^{8} +(-0.623944 + 0.623944i) q^{9} +O(q^{10})$	\(q+(-0.926451 + 1.06850i) q^{2} +(-1.34443 + 0.556881i) q^{3} +(-0.283377 - 1.97982i) q^{4} +(0.598728 - 1.44546i) q^{5} +(0.650522 - 1.95244i) q^{6} +(0.707107 + 0.707107i) q^{7} +(2.37797 + 1.53142i) q^{8} +(-0.623944 + 0.623944i) q^{9} +(0.989776 + 1.97888i) q^{10} +(5.12731 + 2.12380i) q^{11} +(1.48351 + 2.50393i) q^{12} +(0.400276 + 0.966351i) q^{13} +(-1.41064 + 0.100443i) q^{14} +2.27674i q^{15} +(-3.83939 + 1.12207i) q^{16} -5.01268i q^{17} +(-0.0886297 - 1.24474i) q^{18} +(3.12247 + 7.53831i) q^{19} +(-3.03141 - 0.775765i) q^{20} +(-1.34443 - 0.556881i) q^{21} +(-7.01947 + 3.51092i) q^{22} +(-6.09500 + 6.09500i) q^{23} +(-4.04984 - 0.734639i) q^{24} +(1.80466 + 1.80466i) q^{25} +(-1.40338 - 0.467583i) q^{26} +(2.16203 - 5.21960i) q^{27} +(1.19957 - 1.60032i) q^{28} +(6.49956 - 2.69221i) q^{29} +(-2.43269 - 2.10928i) q^{30} +3.18964 q^{31} +(2.35808 - 5.14193i) q^{32} -8.07601 q^{33} +(5.35604 + 4.64400i) q^{34} +(1.44546 - 0.598728i) q^{35} +(1.41211 + 1.05849i) q^{36} +(-0.234866 + 0.567017i) q^{37} +(-10.9475 - 3.64752i) q^{38} +(-1.07629 - 1.07629i) q^{39} +(3.63736 - 2.52035i) q^{40} +(-0.294979 + 0.294979i) q^{41} +(1.84058 - 0.920598i) q^{42} +(3.87959 + 1.60698i) q^{43} +(2.75178 - 10.7530i) q^{44} +(0.528312 + 1.27546i) q^{45} +(-0.865779 - 12.1592i) q^{46} -12.2167i q^{47} +(4.53694 - 3.64664i) q^{48} +1.00000i q^{49} +(-3.60021 + 0.256348i) q^{50} +(2.79147 + 6.73920i) q^{51} +(1.79978 - 1.06632i) q^{52} +(0.364896 + 0.151145i) q^{53} +(3.57412 + 7.14583i) q^{54} +(6.13972 - 6.13972i) q^{55} +(0.598603 + 2.76436i) q^{56} +(-8.39589 - 8.39589i) q^{57} +(-3.14491 + 9.43897i) q^{58} +(-1.82366 + 4.40271i) q^{59} +(4.50753 - 0.645175i) q^{60} +(-0.707613 + 0.293103i) q^{61} +(-2.95505 + 3.40813i) q^{62} -0.882391 q^{63} +(3.30950 + 7.28335i) q^{64} +1.63648 q^{65} +(7.48203 - 8.62920i) q^{66} +(-8.48098 + 3.51294i) q^{67} +(-9.92422 + 1.42048i) q^{68} +(4.80011 - 11.5885i) q^{69} +(-0.699405 + 2.09916i) q^{70} +(-8.29584 - 8.29584i) q^{71} +(-2.43924 + 0.528201i) q^{72} +(-0.270226 + 0.270226i) q^{73} +(-0.388265 - 0.776267i) q^{74} +(-3.43123 - 1.42126i) q^{75} +(14.0397 - 8.31812i) q^{76} +(2.12380 + 5.12731i) q^{77} +(2.14714 - 0.152884i) q^{78} +2.25443i q^{79} +(-0.676843 + 6.22149i) q^{80} +5.57422i q^{81} +(-0.0419011 - 0.588469i) q^{82} +(-2.31800 - 5.59616i) q^{83} +(-0.721545 + 2.81954i) q^{84} +(-7.24561 - 3.00123i) q^{85} +(-5.31131 + 2.65655i) q^{86} +(-7.23897 + 7.23897i) q^{87} +(8.94016 + 12.9024i) q^{88} +(-3.79550 - 3.79550i) q^{89} +(-1.85228 - 0.617148i) q^{90} +(-0.400276 + 0.966351i) q^{91} +(13.7942 + 10.3398i) q^{92} +(-4.28825 + 1.77625i) q^{93} +(13.0536 + 11.3182i) q^{94} +12.7658 q^{95} +(-0.306823 + 8.22614i) q^{96} -11.9502 q^{97} +(-1.06850 - 0.926451i) q^{98} +(-4.52429 + 1.87402i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - 20 q^{6}+O(q^{10}) $ 52 * q - 20 * q^6	$ 52 q - 20 q^{6} - 8 q^{10} + 12 q^{12} - 12 q^{16} - 20 q^{18} + 20 q^{22} - 20 q^{23} - 8 q^{24} + 20 q^{26} - 24 q^{27} - 8 q^{28} + 20 q^{30} + 60 q^{32} - 48 q^{33} + 48 q^{34} + 8 q^{36} - 60 q^{38} - 24 q^{39} + 20 q^{40} - 44 q^{43} + 32 q^{44} + 40 q^{45} - 32 q^{46} - 84 q^{48} - 124 q^{50} + 16 q^{51} - 32 q^{52} - 36 q^{53} + 96 q^{54} + 32 q^{55} + 16 q^{56} + 4 q^{58} - 92 q^{60} - 32 q^{61} + 12 q^{62} + 68 q^{63} + 48 q^{64} + 80 q^{65} + 16 q^{66} + 28 q^{67} - 4 q^{68} - 32 q^{69} + 8 q^{70} - 88 q^{72} + 36 q^{74} + 32 q^{75} + 96 q^{76} - 12 q^{77} + 12 q^{78} - 108 q^{80} - 96 q^{82} + 64 q^{85} + 76 q^{86} - 56 q^{87} + 104 q^{88} - 132 q^{90} + 32 q^{92} - 4 q^{94} - 64 q^{95} + 8 q^{96} - 72 q^{97} - 64 q^{99}+O(q^{100}) $ 52 * q - 20 * q^6 - 8 * q^10 + 12 * q^12 - 12 * q^16 - 20 * q^18 + 20 * q^22 - 20 * q^23 - 8 * q^24 + 20 * q^26 - 24 * q^27 - 8 * q^28 + 20 * q^30 + 60 * q^32 - 48 * q^33 + 48 * q^34 + 8 * q^36 - 60 * q^38 - 24 * q^39 + 20 * q^40 - 44 * q^43 + 32 * q^44 + 40 * q^45 - 32 * q^46 - 84 * q^48 - 124 * q^50 + 16 * q^51 - 32 * q^52 - 36 * q^53 + 96 * q^54 + 32 * q^55 + 16 * q^56 + 4 * q^58 - 92 * q^60 - 32 * q^61 + 12 * q^62 + 68 * q^63 + 48 * q^64 + 80 * q^65 + 16 * q^66 + 28 * q^67 - 4 * q^68 - 32 * q^69 + 8 * q^70 - 88 * q^72 + 36 * q^74 + 32 * q^75 + 96 * q^76 - 12 * q^77 + 12 * q^78 - 108 * q^80 - 96 * q^82 + 64 * q^85 + 76 * q^86 - 56 * q^87 + 104 * q^88 - 132 * q^90 + 32 * q^92 - 4 * q^94 - 64 * q^95 + 8 * q^96 - 72 * q^97 - 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{8}\right)$

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 $

$2$	−0.926451	+	1.06850i	−0.655100	+	0.755542i
$2$	−0.926451	+	1.06850i	−0.655100	+	0.755542i
$3$	−1.34443	+	0.556881i	−0.776207	+	0.321516i	−0.735384	−	0.677651i	$-0.762998\pi$
$3$	−1.34443	+	0.556881i	−0.776207	+	0.321516i	−0.0408234	+	0.999166i	$0.512998\pi$
$4$	−0.283377	−	1.97982i	−0.141689	−	0.989911i
$5$	0.598728	−	1.44546i	0.267759	−	0.646428i	−0.731618	−	0.681715i	$-0.761235\pi$
$5$	0.598728	−	1.44546i	0.267759	−	0.646428i	0.999377	+	0.0352870i	$0.0112345\pi$
$6$	0.650522	−	1.95244i	0.265574	−	0.797082i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$8$	2.37797	+	1.53142i	0.840740	+	0.541439i
$9$	−0.623944	+	0.623944i	−0.207981	+	0.207981i
$10$	0.989776	+	1.97888i	0.312995	+	0.625778i
$11$	5.12731	+	2.12380i	1.54594	+	0.640350i	0.982576	−	0.185859i	$-0.0595066\pi$
$11$	5.12731	+	2.12380i	1.54594	+	0.640350i	0.563365	+	0.826208i	$0.309507\pi$
$12$	1.48351	+	2.50393i	0.428252	+	0.722821i
$13$	0.400276	+	0.966351i	0.111017	+	0.268018i	0.969617	−	0.244627i	$-0.0786657\pi$
$13$	0.400276	+	0.966351i	0.111017	+	0.268018i	−0.858601	+	0.512645i	$0.828666\pi$
$14$	−1.41064	+	0.100443i	−0.377010	+	0.0268444i
$15$			2.27674i			0.587851i
$16$	−3.83939	+	1.12207i	−0.959849	+	0.280518i
$17$		−	5.01268i		−	1.21575i	−0.794031	−	0.607877i	$-0.792021\pi$
$17$		−	5.01268i		−	1.21575i	0.794031	−	0.607877i	$-0.207979\pi$
$18$	−0.0886297	−	1.24474i	−0.0208902	−	0.293387i
$19$	3.12247	+	7.53831i	0.716344	+	1.72941i	0.683505	+	0.729946i	$0.260455\pi$
$19$	3.12247	+	7.53831i	0.716344	+	1.72941i	0.0328387	+	0.999461i	$0.489545\pi$
$20$	−3.03141	−	0.775765i	−0.677845	−	0.173466i
$21$	−1.34443	−	0.556881i	−0.293379	−	0.121521i
$22$	−7.01947	+	3.51092i	−1.49656	+	0.748531i
$23$	−6.09500	+	6.09500i	−1.27090	+	1.27090i	−0.325276	+	0.945619i	$0.605457\pi$
$23$	−6.09500	+	6.09500i	−1.27090	+	1.27090i	−0.945619	+	0.325276i	$0.894543\pi$
$24$	−4.04984	−	0.734639i	−0.826670	−	0.149958i
$25$	1.80466	+	1.80466i	0.360933	+	0.360933i
$26$	−1.40338	−	0.467583i	−0.275226	−	0.0917006i
$27$	2.16203	−	5.21960i	0.416083	−	1.00451i
$28$	1.19957	−	1.60032i	0.226697	−	0.302433i
$29$	6.49956	−	2.69221i	1.20694	−	0.499930i	0.313704	−	0.949521i	$-0.398430\pi$
$29$	6.49956	−	2.69221i	1.20694	−	0.499930i	0.893235	+	0.449591i	$0.148430\pi$
$30$	−2.43269	−	2.10928i	−0.444146	−	0.385101i
$31$	3.18964			0.572877			0.286438	−	0.958099i	$-0.407529\pi$
$31$	3.18964			0.572877			0.286438	+	0.958099i	$0.407529\pi$
$32$	2.35808	−	5.14193i	0.416853	−	0.908974i
$33$	−8.07601			−1.40585
$34$	5.35604	+	4.64400i	0.918553	+	0.796440i
$35$	1.44546	−	0.598728i	0.244327	−	0.101203i
$36$	1.41211	+	1.05849i	0.235352	+	0.176415i
$37$	−0.234866	+	0.567017i	−0.0386118	+	0.0932170i	−0.942009	−	0.335588i	$-0.891065\pi$
$37$	−0.234866	+	0.567017i	−0.0386118	+	0.0932170i	0.903397	+	0.428805i	$0.141065\pi$
$38$	−10.9475	−	3.64752i	−1.77592	−	0.591706i
$39$	−1.07629	−	1.07629i	−0.172344	−	0.172344i
$40$	3.63736	−	2.52035i	0.575117	−	0.398503i
$41$	−0.294979	+	0.294979i	−0.0460681	+	0.0460681i	−0.729766	−	0.683697i	$-0.760371\pi$
$41$	−0.294979	+	0.294979i	−0.0460681	+	0.0460681i	0.683697	+	0.729766i	$0.260371\pi$
$42$	1.84058	−	0.920598i	0.284007	−	0.142051i
$43$	3.87959	+	1.60698i	0.591632	+	0.245062i	0.658353	−	0.752710i	$-0.271254\pi$
$43$	3.87959	+	1.60698i	0.591632	+	0.245062i	−0.0667205	+	0.997772i	$0.521254\pi$
$44$	2.75178	−	10.7530i	0.414847	−	1.62107i
$45$	0.528312	+	1.27546i	0.0787560	+	0.190134i
$46$	−0.865779	−	12.1592i	−0.127652	−	1.79278i
$47$		−	12.2167i		−	1.78199i	−0.454010	−	0.890996i	$-0.650007\pi$
$47$		−	12.2167i		−	1.78199i	0.454010	−	0.890996i	$-0.349993\pi$
$48$	4.53694	−	3.64664i	0.654850	−	0.526347i
$49$			1.00000i			0.142857i
$50$	−3.60021	+	0.256348i	−0.509147	+	0.0362531i
$51$	2.79147	+	6.73920i	0.390884	+	0.943677i
$52$	1.79978	−	1.06632i	0.249584	−	0.147872i
$53$	0.364896	+	0.151145i	0.0501223	+	0.0207613i	0.407604	−	0.913159i	$-0.366364\pi$
$53$	0.364896	+	0.151145i	0.0501223	+	0.0207613i	−0.357481	+	0.933920i	$0.616364\pi$
$54$	3.57412	+	7.14583i	0.486376	+	0.972425i
$55$	6.13972	−	6.13972i	0.827880	−	0.827880i
$56$	0.598603	+	2.76436i	0.0799917	+	0.369403i
$57$	−8.39589	−	8.39589i	−1.11206	−	1.11206i
$58$	−3.14491	+	9.43897i	−0.412947	+	1.23940i
$59$	−1.82366	+	4.40271i	−0.237421	+	0.573184i	−0.997015	−	0.0772133i	$-0.975398\pi$
$59$	−1.82366	+	4.40271i	−0.237421	+	0.573184i	0.759594	+	0.650398i	$0.225398\pi$
$60$	4.50753	−	0.645175i	0.581920	−	0.0832918i
$61$	−0.707613	+	0.293103i	−0.0906006	+	0.0375280i	−0.427523	−	0.904004i	$-0.640614\pi$
$61$	−0.707613	+	0.293103i	−0.0906006	+	0.0375280i	0.336923	+	0.941532i	$0.390614\pi$
$62$	−2.95505	+	3.40813i	−0.375291	+	0.432833i
$63$	−0.882391			−0.111171
$64$	3.30950	+	7.28335i	0.413688	+	0.910419i
$65$	1.63648			0.202980
$66$	7.48203	−	8.62920i	0.920974	−	1.06218i
$67$	−8.48098	+	3.51294i	−1.03612	+	0.429174i	−0.834917	−	0.550376i	$-0.814484\pi$
$67$	−8.48098	+	3.51294i	−1.03612	+	0.429174i	−0.201200	+	0.979550i	$0.564484\pi$
$68$	−9.92422	+	1.42048i	−1.20349	+	0.172259i
$69$	4.80011	−	11.5885i	0.577865	−	1.39509i
$70$	−0.699405	+	2.09916i	−0.0835949	+	0.250898i
$71$	−8.29584	−	8.29584i	−0.984536	−	0.984536i	0.0153466	−	0.999882i	$-0.495115\pi$
$71$	−8.29584	−	8.29584i	−0.984536	−	0.984536i	−0.999882	+	0.0153466i	$0.995115\pi$
$72$	−2.43924	+	0.528201i	−0.287468	+	0.0622491i
$73$	−0.270226	+	0.270226i	−0.0316276	+	0.0316276i	−0.722744	−	0.691116i	$-0.757119\pi$
$73$	−0.270226	+	0.270226i	−0.0316276	+	0.0316276i	0.691116	+	0.722744i	$0.257119\pi$
$74$	−0.388265	−	0.776267i	−0.0451349	−	0.0902393i
$75$	−3.43123	−	1.42126i	−0.396204	−	0.164113i
$76$	14.0397	−	8.31812i	1.61046	−	0.954154i
$77$	2.12380	+	5.12731i	0.242029	+	0.584311i
$78$	2.14714	−	0.152884i	0.243115	−	0.0173107i
$79$			2.25443i			0.253643i	0.991926	+	0.126821i	$0.0404775\pi$
$79$			2.25443i			0.253643i	−0.991926	+	0.126821i	$0.959522\pi$
$80$	−0.676843	+	6.22149i	−0.0756733	+	0.695584i
$81$			5.57422i			0.619357i
$82$	−0.0419011	−	0.588469i	−0.00462720	−	0.0649855i
$83$	−2.31800	−	5.59616i	−0.254434	−	0.614258i	0.744118	−	0.668048i	$-0.232870\pi$
$83$	−2.31800	−	5.59616i	−0.254434	−	0.614258i	−0.998552	+	0.0537899i	$0.982870\pi$
$84$	−0.721545	+	2.81954i	−0.0787270	+	0.307637i
$85$	−7.24561	−	3.00123i	−0.785897	−	0.325529i
$86$	−5.31131	+	2.65655i	−0.572733	+	0.286463i
$87$	−7.23897	+	7.23897i	−0.776099	+	0.776099i
$88$	8.94016	+	12.9024i	0.953025	+	1.37540i
$89$	−3.79550	−	3.79550i	−0.402323	−	0.402323i	0.476728	−	0.879051i	$-0.341823\pi$
$89$	−3.79550	−	3.79550i	−0.402323	−	0.402323i	−0.879051	+	0.476728i	$0.841823\pi$
$90$	−1.85228	−	0.617148i	−0.195247	−	0.0650531i
$91$	−0.400276	+	0.966351i	−0.0419603	+	0.101301i
$92$	13.7942	+	10.3398i	1.43814	+	1.07800i
$93$	−4.28825	+	1.77625i	−0.444671	+	0.184189i
$94$	13.0536	+	11.3182i	1.34637	+	1.16738i
$95$	12.7658			1.30974
$96$	−0.306823	+	8.22614i	−0.0313150	+	0.839577i
$97$	−11.9502			−1.21336			−0.606681	−	0.794946i	$-0.707499\pi$
$97$	−11.9502			−1.21336			−0.606681	+	0.794946i	$0.707499\pi$
$98$	−1.06850	−	0.926451i	−0.107935	−	0.0935857i
$99$	−4.52429	+	1.87402i	−0.454708	+	0.188346i
$100$	3.06151	−	4.08432i	0.306151	−	0.408432i
$101$	6.55185	−	15.8176i	0.651933	−	1.57391i	−0.158036	−	0.987433i	$-0.550516\pi$
$101$	6.55185	−	15.8176i	0.651933	−	1.57391i	0.809969	−	0.586473i	$-0.199484\pi$
$102$	−9.78698	−	3.26086i	−0.969056	−	0.322873i
$103$	−4.58080	−	4.58080i	−0.451360	−	0.451360i	0.444446	−	0.895806i	$-0.353401\pi$
$103$	−4.58080	−	4.58080i	−0.451360	−	0.451360i	−0.895806	+	0.444446i	$0.853401\pi$
$104$	−0.528045	+	2.91095i	−0.0517791	+	0.285442i
$105$	−1.60990	+	1.60990i	−0.157110	+	0.157110i
$106$	−0.499556	+	0.249862i	−0.0485211	+	0.0242688i
$107$	2.31989	+	0.960931i	0.224272	+	0.0928967i	0.491990	−	0.870601i	$-0.336270\pi$
$107$	2.31989	+	0.960931i	0.224272	+	0.0928967i	−0.267718	+	0.963497i	$0.586270\pi$
$108$	−10.9466	−	2.80132i	−1.05333	−	0.269557i
$109$	0.373959	+	0.902816i	0.0358187	+	0.0864741i	0.940777	−	0.339027i	$-0.110098\pi$
$109$	0.373959	+	0.902816i	0.0358187	+	0.0864741i	−0.904958	+	0.425501i	$0.860098\pi$
$110$	0.872131	+	12.2484i	0.0831545	+	1.16784i
$111$		−	0.893107i		−	0.0847700i
$112$	−3.50829	−	1.92144i	−0.331502	−	0.181559i
$113$			16.3444i			1.53755i	0.639521	+	0.768774i	$0.279133\pi$
$113$			16.3444i			1.53755i	−0.639521	+	0.768774i	$0.720867\pi$
$114$	16.7494	−	1.19261i	1.56872	−	0.111699i
$115$	5.16081	+	12.4593i	0.481248	+	1.16184i
$116$	−7.17192	−	12.1051i	−0.665896	−	1.12393i
$117$	−0.852699	−	0.353200i	−0.0788321	−	0.0326533i
$118$	−3.01476	−	6.02748i	−0.277531	−	0.554874i
$119$	3.54450	−	3.54450i	0.324924	−	0.324924i
$120$	−3.48664	+	5.41401i	−0.318285	+	0.494230i
$121$	14.0006	+	14.0006i	1.27278	+	1.27278i
$122$	0.342389	−	1.02763i	0.0309984	−	0.0930371i
$123$	0.232311	−	0.560848i	0.0209468	−	0.0505700i
$124$	−0.903872	−	6.31492i	−0.0811701	−	0.567097i
$125$	10.9163	−	4.52170i	0.976388	−	0.404433i
$126$	0.817491	−	0.942833i	0.0728279	−	0.0839942i
$127$	−5.52579			−0.490335			−0.245167	−	0.969481i	$-0.578843\pi$
$127$	−5.52579			−0.490335			−0.245167	+	0.969481i	$0.578843\pi$
$128$	−10.8483	−	3.21147i	−0.958867	−	0.283856i
$129$	−6.11074			−0.538020
$130$	−1.51611	+	1.74857i	−0.132972	+	0.153360i
$131$	−6.86741	+	2.84458i	−0.600009	+	0.248532i	−0.661950	−	0.749548i	$-0.730271\pi$
$131$	−6.86741	+	2.84458i	−0.600009	+	0.248532i	0.0619412	+	0.998080i	$0.480271\pi$
$132$	2.28856	+	15.9891i	0.199193	+	1.39167i
$133$	−3.12247	+	7.53831i	−0.270752	+	0.653654i
$134$	4.10365	−	12.3165i	0.354501	−	1.06398i
$135$	−6.25024	−	6.25024i	−0.537935	−	0.537935i
$136$	7.67652	−	11.9200i	0.658256	−	1.02213i
$137$	−2.80073	+	2.80073i	−0.239282	+	0.239282i	−0.816553	−	0.577271i	$-0.804118\pi$
$137$	−2.80073	+	2.80073i	−0.239282	+	0.239282i	0.577271	+	0.816553i	$0.304118\pi$
$138$	7.93522	+	15.8651i	0.675491	+	1.35053i
$139$	−2.86152	−	1.18528i	−0.242711	−	0.100534i	0.258012	−	0.966142i	$-0.416933\pi$
$139$	−2.86152	−	1.18528i	−0.242711	−	0.100534i	−0.500723	+	0.865607i	$0.666933\pi$
$140$	−1.59498	−	2.69208i	−0.134801	−	0.227522i
$141$	6.80327	+	16.4245i	0.572938	+	1.38320i
$142$	16.5498	−	1.17840i	1.38883	−	0.0988894i
$143$			5.80489i			0.485429i
$144$	1.69546	−	3.09568i	0.141288	−	0.257973i
$145$		−	11.0067i		−	0.914060i
$146$	−0.0383849	−	0.539087i	−0.00317676	−	0.0446152i
$147$	−0.556881	−	1.34443i	−0.0459308	−	0.110887i
$148$	1.18915	+	0.304313i	0.0977474	+	0.0250144i
$149$	−5.01452	−	2.07708i	−0.410806	−	0.170161i	0.167703	−	0.985838i	$-0.446365\pi$
$149$	−5.01452	−	2.07708i	−0.410806	−	0.170161i	−0.578509	+	0.815676i	$0.696365\pi$
$150$	4.69748	−	2.34953i	0.383548	−	0.191839i
$151$	1.96176	−	1.96176i	0.159646	−	0.159646i	−0.622764	−	0.782410i	$-0.713990\pi$
$151$	1.96176	−	1.96176i	0.159646	−	0.159646i	0.782410	+	0.622764i	$0.213990\pi$
$152$	−4.11917	+	22.7077i	−0.334109	+	1.84184i
$153$	3.12763	+	3.12763i	0.252854	+	0.252854i
$154$	−7.44612	−	2.48092i	−0.600025	−	0.199918i
$155$	1.90973	−	4.61049i	0.153393	−	0.370323i
$156$	−1.82586	+	2.43585i	−0.146186	+	0.195024i
$157$	12.0871	−	5.00663i	0.964653	−	0.399572i	0.155934	−	0.987768i	$-0.450161\pi$
$157$	12.0871	−	5.00663i	0.964653	−	0.399572i	0.808719	+	0.588195i	$0.200161\pi$
$158$	−2.40885	−	2.08862i	−0.191638	−	0.166161i
$159$	−0.574746			−0.0455804
$160$	−6.02059	−	6.48711i	−0.475970	−	0.512851i
$161$	−8.61963			−0.679322
$162$	−5.95604	−	5.16424i	−0.467951	−	0.405741i
$163$	10.8935	−	4.51224i	0.853246	−	0.353426i	0.0871834	−	0.996192i	$-0.472213\pi$
$163$	10.8935	−	4.51224i	0.853246	−	0.353426i	0.766062	+	0.642766i	$0.222213\pi$
$164$	0.667598	+	0.500417i	0.0521306	+	0.0390760i
$165$	−4.83533	+	11.6735i	−0.376430	+	0.908782i
$166$	8.12700	+	2.70778i	0.630778	+	0.210165i
$167$	4.64492	+	4.64492i	0.359435	+	0.359435i	0.863605	−	0.504170i	$-0.168201\pi$
$167$	4.64492	+	4.64492i	0.359435	+	0.359435i	−0.504170	+	0.863605i	$0.668201\pi$
$168$	−2.34420	−	3.38314i	−0.180859	−	0.261015i
$169$	8.41877	−	8.41877i	0.647598	−	0.647598i
$170$	9.91951	−	4.96143i	0.760792	−	0.380524i
$171$	−6.65173	−	2.75524i	−0.508671	−	0.210698i
$172$	2.08215	−	8.13628i	0.158762	−	0.620386i
$173$	0.684920	+	1.65354i	0.0520735	+	0.125717i	0.947775	−	0.318938i	$-0.103326\pi$
$173$	0.684920	+	1.65354i	0.0520735	+	0.125717i	−0.895702	+	0.444655i	$0.853326\pi$
$174$	−1.02828	−	14.4414i	−0.0779535	−	1.09480i
$175$			2.55218i			0.192927i
$176$	−22.0688	−	2.40089i	−1.66350	−	0.180974i
$177$		−	6.93470i		−	0.521244i
$178$	7.57184	−	0.539142i	0.567533	−	0.0404104i
$179$	2.64218	+	6.37880i	0.197486	+	0.476774i	0.991338	−	0.131338i	$-0.0419273\pi$
$179$	2.64218	+	6.37880i	0.197486	+	0.476774i	−0.793852	+	0.608112i	$0.791927\pi$
$180$	2.37547	−	1.40740i	0.177057	−	0.104901i
$181$	−16.7231	−	6.92692i	−1.24302	−	0.514874i	−0.338359	−	0.941017i	$-0.609872\pi$
$181$	−16.7231	−	6.92692i	−1.24302	−	0.514874i	−0.904656	+	0.426143i	$0.859872\pi$
$182$	−0.661709	−	1.32297i	−0.0490491	−	0.0980652i
$183$	0.788113	−	0.788113i	0.0582590	−	0.0582590i
$184$	−23.8277	+	5.15974i	−1.75660	+	0.380381i
$185$	0.678978	+	0.678978i	0.0499194	+	0.0499194i
$186$	2.07493	−	6.22760i	0.152141	−	0.456630i
$187$	10.6459	−	25.7016i	0.778508	−	1.87948i
$188$	−24.1870	+	3.46194i	−1.76401	+	0.252488i
$189$	5.21960	−	2.16203i	0.379670	−	0.157265i
$190$	−11.8269	+	13.6402i	−0.858013	+	0.989567i
$191$	0.551067			0.0398738			0.0199369	−	0.999801i	$-0.493653\pi$
$191$	0.551067			0.0398738			0.0199369	+	0.999801i	$0.493653\pi$
$192$	−8.50536	−	7.94895i	−0.613821	−	0.573666i
$193$	−4.23566			−0.304889			−0.152445	−	0.988312i	$-0.548715\pi$
$193$	−4.23566			−0.304889			−0.152445	+	0.988312i	$0.548715\pi$
$194$	11.0713	−	12.7688i	0.794872	−	0.916746i
$195$	−2.20013	+	0.911322i	−0.157554	+	0.0652612i
$196$	1.97982	−	0.283377i	0.141416	−	0.0202412i
$197$	4.81135	−	11.6156i	0.342795	−	0.827580i	−0.654636	−	0.755944i	$-0.727178\pi$
$197$	4.81135	−	11.6156i	0.342795	−	0.827580i	0.997431	−	0.0716356i	$-0.0228219\pi$
$198$	2.18914	−	6.57038i	0.155576	−	0.466937i
$199$	2.13203	+	2.13203i	0.151136	+	0.151136i	0.778625	−	0.627490i	$-0.215917\pi$
$199$	2.13203	+	2.13203i	0.151136	+	0.151136i	−0.627490	+	0.778625i	$0.715917\pi$
$200$	1.52774	+	7.05514i	0.108028	+	0.498874i
$201$	9.44580	−	9.44580i	0.666256	−	0.666256i
$202$	10.8311	+	21.6548i	0.762071	+	1.52363i
$203$	6.49956	+	2.69221i	0.456180	+	0.188956i
$204$	12.5514	−	7.43635i	0.878772	−	0.520648i
$205$	0.249768	+	0.602992i	0.0174445	+	0.0421148i
$206$	9.13847	−	0.650691i	0.636707	−	0.0453358i
$207$		−	7.60588i		−	0.528645i
$208$	−2.62113	−	3.26107i	−0.181743	−	0.226114i
$209$			45.2827i			3.13227i
$210$	−0.228681	−	3.21166i	−0.0157805	−	0.221626i
$211$	−6.47609	−	15.6347i	−0.445832	−	1.07633i	−0.973868	−	0.227113i	$-0.927071\pi$
$211$	−6.47609	−	15.6347i	−0.445832	−	1.07633i	0.528036	−	0.849222i	$-0.322929\pi$
$212$	0.195837	−	0.765260i	0.0134501	−	0.0525582i
$213$	15.7730	+	6.53338i	1.08075	+	0.447660i
$214$	−3.17602	+	1.58855i	−0.217108	+	0.108591i
$215$	4.64564	−	4.64564i	0.316830	−	0.316830i
$216$	13.1347	−	9.10110i	0.893700	−	0.619251i
$217$	2.25542	+	2.25542i	0.153108	+	0.153108i
$218$	−1.31111	−	0.436840i	−0.0887997	−	0.0295866i
$219$	0.212816	−	0.513784i	0.0143808	−	0.0347183i
$220$	−13.8954	−	10.4157i	−0.936829	−	0.702226i
$221$	4.84401	−	2.00646i	0.325843	−	0.134969i
$222$	0.954284	+	0.827420i	0.0640473	+	0.0555328i
$223$	2.15231			0.144129			0.0720646	−	0.997400i	$-0.477041\pi$
$223$	2.15231			0.144129			0.0720646	+	0.997400i	$0.477041\pi$
$224$	5.30331	−	1.96848i	0.354342	−	0.131525i
$225$	−2.25202			−0.150135
$226$	−17.4639	−	15.1422i	−1.16168	−	1.00725i
$227$	−12.3525	+	5.11659i	−0.819866	+	0.339600i	−0.752883	−	0.658154i	$-0.771337\pi$
$227$	−12.3525	+	5.11659i	−0.819866	+	0.339600i	−0.0669834	+	0.997754i	$0.521337\pi$
$228$	−14.2432	+	19.0016i	−0.943276	+	1.25841i
$229$	2.71946	−	6.56535i	0.179707	−	0.433851i	−0.808198	−	0.588910i	$-0.799557\pi$
$229$	2.71946	−	6.56535i	0.179707	−	0.433851i	0.987905	+	0.155060i	$0.0495571\pi$
$230$	−18.0940	−	6.02861i	−1.19308	−	0.397515i
$231$	−5.71060	−	5.71060i	−0.375730	−	0.375730i
$232$	19.5787	+	3.55157i	1.28540	+	0.233172i
$233$	11.7789	−	11.7789i	0.771664	−	0.771664i	−0.206733	−	0.978397i	$-0.566283\pi$
$233$	11.7789	−	11.7789i	0.771664	−	0.771664i	0.978397	+	0.206733i	$0.0662832\pi$
$234$	1.16738	−	0.583886i	0.0763138	−	0.0381698i
$235$	−17.6587	−	7.31449i	−1.15193	−	0.477145i
$236$	9.23337	+	2.36290i	0.601041	+	0.153812i
$237$	−1.25545	−	3.03092i	−0.0815502	−	0.196879i
$238$	0.503487	+	7.07110i	0.0326362	+	0.458351i
$239$		−	11.1273i		−	0.719767i	−0.932997	−	0.359884i	$-0.882816\pi$
$239$		−	11.1273i		−	0.719767i	0.932997	−	0.359884i	$-0.117184\pi$
$240$	−2.55467	−	8.74129i	−0.164903	−	0.564248i
$241$			0.671516i			0.0432562i	0.999766	+	0.0216281i	$0.00688497\pi$
$241$			0.671516i			0.0432562i	−0.999766	+	0.0216281i	$0.993115\pi$
$242$	−27.9304	+	1.98875i	−1.79544	+	0.127841i
$243$	3.38192	+	8.16467i	0.216950	+	0.523764i
$244$	0.780813	+	1.31789i	0.0499864	+	0.0843692i
$245$	1.44546	+	0.598728i	0.0923468	+	0.0382513i
$246$	0.384040	+	0.767822i	0.0244855	+	0.0489545i
$247$	−6.03481	+	6.03481i	−0.383986	+	0.383986i
$248$	7.58488	+	4.88468i	0.481640	+	0.310178i
$249$	6.23279	+	6.23279i	0.394987	+	0.394987i
$250$	−5.28203	+	15.8532i	−0.334065	+	1.00265i
$251$	5.86535	−	14.1602i	0.370218	−	0.893785i	−0.623495	−	0.781827i	$-0.714288\pi$
$251$	5.86535	−	14.1602i	0.370218	−	0.893785i	0.993713	−	0.111958i	$-0.0357121\pi$
$252$	0.250050	+	1.74698i	0.0157516	+	0.110049i
$253$	−44.1955	+	18.3064i	−2.77855	+	1.15091i
$254$	5.11938	−	5.90430i	0.321218	−	0.370469i
$255$	11.4125			0.714682
$256$	13.4819	−	8.61617i	0.842619	−	0.538511i
$257$	24.7211			1.54206			0.771029	−	0.636800i	$-0.219742\pi$
$257$	24.7211			1.54206			0.771029	+	0.636800i	$0.219742\pi$
$258$	5.66130	−	6.52931i	0.352457	−	0.406497i
$259$	−0.567017	+	0.234866i	−0.0352327	+	0.0145939i
$260$	−0.463740	−	3.23993i	−0.0287599	−	0.200932i
$261$	−2.37558	+	5.73515i	−0.147045	+	0.354997i
$262$	3.32290	−	9.97318i	0.205289	−	0.616145i
$263$	−20.2096	−	20.2096i	−1.24618	−	1.24618i	−0.957396	−	0.288780i	$-0.906750\pi$
$263$	−20.2096	−	20.2096i	−1.24618	−	1.24618i	−0.288780	−	0.957396i	$-0.593250\pi$
$264$	−19.2045	−	12.3678i	−1.18196	−	0.761183i
$265$	0.436946	−	0.436946i	0.0268414	−	0.0268414i
$266$	−5.16186	−	10.3202i	−0.316494	−	0.632774i
$267$	7.21644	+	2.98915i	0.441639	+	0.182933i
$268$	9.35831	+	15.7954i	0.571650	+	0.964855i
$269$	4.91039	+	11.8547i	0.299391	+	0.722795i	0.999958	+	0.00920747i	$0.00293087\pi$
$269$	4.91039	+	11.8547i	0.299391	+	0.722795i	−0.700566	+	0.713587i	$0.747069\pi$
$270$	12.4689	−	0.887831i	0.758834	−	0.0540317i
$271$			15.3940i			0.935120i	0.883961	+	0.467560i	$0.154867\pi$
$271$			15.3940i			0.935120i	−0.883961	+	0.467560i	$0.845133\pi$
$272$	5.62460	+	19.2457i	0.341041	+	1.16694i
$273$		−	1.52210i		−	0.0921216i
$274$	−0.397836	−	5.58731i	−0.0240342	−	0.337542i
$275$	5.42032	+	13.0858i	0.326858	+	0.789104i
$276$	−24.3034	−	6.21945i	−1.46289	−	0.374367i
$277$	8.95035	+	3.70736i	0.537774	+	0.222753i	0.635004	−	0.772508i	$-0.280998\pi$
$277$	8.95035	+	3.70736i	0.537774	+	0.222753i	−0.0972300	+	0.995262i	$0.530998\pi$
$278$	3.91753	−	1.95943i	0.234958	−	0.117519i
$279$	−1.99016	+	1.99016i	−0.119148	+	0.119148i
$280$	4.35416	+	0.789843i	0.260211	+	0.0472022i
$281$	10.0077	+	10.0077i	0.597012	+	0.597012i	0.939516	−	0.342504i	$-0.111275\pi$
$281$	10.0077	+	10.0077i	0.597012	+	0.597012i	−0.342504	+	0.939516i	$0.611275\pi$
$282$	−23.8525	−	7.94725i	−1.42039	−	0.473252i
$283$	−12.2245	+	29.5126i	−0.726672	+	1.75434i	−0.0732919	+	0.997311i	$0.523350\pi$
$283$	−12.2245	+	29.5126i	−0.726672	+	1.75434i	−0.653380	+	0.757030i	$0.726650\pi$
$284$	−14.0734	+	18.7752i	−0.835105	+	1.11410i
$285$	−17.1627	+	7.10904i	−1.01663	+	0.421103i
$286$	−6.20251	−	5.37794i	−0.366762	−	0.318004i
$287$	−0.417164			−0.0246244
$288$	1.73697	+	4.67959i	0.102352	+	0.275747i
$289$	−8.12697			−0.478057
$290$	11.7607	+	10.1972i	0.690611	+	0.598800i
$291$	16.0662	−	6.65485i	0.941820	−	0.390114i
$292$	0.611575	+	0.458423i	0.0357897	+	0.0268272i
$293$	−8.89125	+	21.4654i	−0.519433	+	1.25402i	0.418820	+	0.908069i	$0.362444\pi$
$293$	−8.89125	+	21.4654i	−0.519433	+	1.25402i	−0.938252	+	0.345952i	$0.887556\pi$
$294$	1.95244	+	0.650522i	0.113869	+	0.0379392i
$295$	5.27205	+	5.27205i	0.306951	+	0.306951i
$296$	−1.42685	+	0.988672i	−0.0829338	+	0.0574654i
$297$	22.1708	−	22.1708i	1.28648	−	1.28648i
$298$	6.86507	−	3.43369i	0.397683	−	0.198908i
$299$	−8.32959	−	3.45023i	−0.481713	−	0.199532i
$300$	−1.84151	+	7.19598i	−0.106320	+	0.415460i
$301$	1.60698	+	3.87959i	0.0926248	+	0.223616i
$302$	0.278663	+	3.91362i	0.0160353	+	0.225203i
$303$			24.9142i			1.43128i
$304$	−20.4469	−	25.4389i	−1.17271	−	1.45902i
$305$			1.19831i			0.0686152i
$306$	−6.23947	+	0.444272i	−0.356687	+	0.0253974i
$307$	−4.90755	−	11.8479i	−0.280089	−	0.676194i	0.719749	−	0.694235i	$-0.244257\pi$
$307$	−4.90755	−	11.8479i	−0.280089	−	0.676194i	−0.999837	+	0.0180410i	$0.994257\pi$
$308$	9.54932	−	5.65771i	0.544123	−	0.322378i
$309$	8.70953	+	3.60761i	0.495468	+	0.205229i
$310$	3.15703	+	6.31193i	0.179307	+	0.358494i
$311$	−2.71302	+	2.71302i	−0.153841	+	0.153841i	−0.779831	−	0.625990i	$-0.784695\pi$
$311$	−2.71302	+	2.71302i	−0.153841	+	0.153841i	0.625990	+	0.779831i	$0.284695\pi$
$312$	−0.911132	−	4.20762i	−0.0515827	−	0.238210i
$313$	−14.2113	−	14.2113i	−0.803269	−	0.803269i	0.180336	−	0.983605i	$-0.442282\pi$
$313$	−14.2113	−	14.2113i	−0.803269	−	0.803269i	−0.983605	+	0.180336i	$0.942282\pi$
$314$	−5.84850	+	17.5534i	−0.330050	+	0.990596i
$315$	−0.528312	+	1.27546i	−0.0297670	+	0.0718639i
$316$	4.46337	−	0.638854i	0.251084	−	0.0359383i
$317$	12.9906	−	5.38087i	0.729623	−	0.302220i	0.0132258	−	0.999913i	$-0.495790\pi$
$317$	12.9906	−	5.38087i	0.729623	−	0.302220i	0.716397	+	0.697693i	$0.245790\pi$
$318$	0.532474	−	0.614116i	0.0298597	−	0.0344379i
$319$	39.0430			2.18599
$320$	12.5093	−	0.423002i	0.699289	−	0.0236465i
$321$	−3.65406			−0.203950
$322$	7.98566	−	9.21006i	0.445024	−	0.513257i
$323$	37.7871	−	15.6519i	2.10253	−	0.870897i
$324$	11.0360	−	1.57961i	0.613109	−	0.0877559i
$325$	−1.02158	+	2.46630i	−0.0566669	+	0.136806i
$326$	−5.27098	+	15.8201i	−0.291933	+	0.876193i
$327$	−1.00552	−	1.00552i	−0.0556055	−	0.0556055i
$328$	−1.15319	+	0.249716i	−0.0636743	+	0.0137882i
$329$	8.63853	−	8.63853i	0.476258	−	0.476258i
$330$	−7.99344	−	15.9815i	−0.440024	−	0.879752i
$331$	15.5689	+	6.44885i	0.855744	+	0.354461i	0.767042	−	0.641597i	$-0.221728\pi$
$331$	15.5689	+	6.44885i	0.855744	+	0.354461i	0.0887025	+	0.996058i	$0.471728\pi$
$332$	−10.4225	+	6.17506i	−0.572011	+	0.338901i
$333$	−0.207244	−	0.500330i	−0.0113569	−	0.0274179i
$334$	−9.26638	+	0.659799i	−0.507034	+	0.0361026i
$335$			14.3622i			0.784690i
$336$	5.78666	+	0.629537i	0.315688	+	0.0343440i
$337$		−	21.5047i		−	1.17144i	−0.810515	−	0.585718i	$-0.800813\pi$
$337$		−	21.5047i		−	1.17144i	0.810515	−	0.585718i	$-0.199187\pi$
$338$	1.19587	+	16.7950i	0.0650465	+	0.913529i
$339$	−9.10187	−	21.9738i	−0.494346	−	1.19346i
$340$	−3.88866	+	15.1955i	−0.210892	+	0.824092i
$341$	16.3543	+	6.77416i	0.885633	+	0.366841i
$342$	9.10647	−	4.55477i	0.492421	−	0.246294i
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$	6.76460	+	9.76264i	0.364723	+	0.526366i
$345$	−13.8767	−	13.8767i	−0.747097	−	0.747097i
$346$	−2.40135	−	0.800091i	−0.129098	−	0.0430131i
$347$	2.76377	−	6.67234i	0.148367	−	0.358190i	−0.832171	−	0.554519i	$-0.812902\pi$
$347$	2.76377	−	6.67234i	0.148367	−	0.358190i	0.980538	+	0.196329i	$0.0629021\pi$
$348$	16.3832	+	12.2805i	0.878234	+	0.658305i
$349$	−7.01413	+	2.90535i	−0.375458	+	0.155520i	−0.562429	−	0.826846i	$-0.690133\pi$
$349$	−7.01413	+	2.90535i	−0.375458	+	0.155520i	0.186971	+	0.982365i	$0.440133\pi$
$350$	−2.72700	−	2.36447i	−0.145764	−	0.126386i
$351$	5.90938			0.315419
$352$	23.0110	−	21.3562i	1.22649	−	1.13829i
$353$	−8.12441			−0.432419			−0.216209	−	0.976347i	$-0.569369\pi$
$353$	−8.12441			−0.432419			−0.216209	+	0.976347i	$0.569369\pi$
$354$	7.40972	+	6.42466i	0.393822	+	0.341467i
$355$	−16.9582	+	7.02433i	−0.900050	+	0.372813i
$356$	−6.43887	+	8.58999i	−0.341259	+	0.455268i
$357$	−2.79147	+	6.73920i	−0.147740	+	0.356676i
$358$	−9.26359	−	3.08647i	−0.489596	−	0.163125i
$359$	−11.9566	−	11.9566i	−0.631045	−	0.631045i	0.317285	−	0.948330i	$-0.397229\pi$
$359$	−11.9566	−	11.9566i	−0.631045	−	0.631045i	−0.948330	+	0.317285i	$0.897229\pi$
$360$	−0.696950	+	3.84207i	−0.0367325	+	0.202495i
$361$	−33.6412	+	33.6412i	−1.77059	+	1.77059i
$362$	22.8945	−	11.4511i	1.20331	−	0.601857i
$363$	−26.6194	−	11.0261i	−1.39716	−	0.578722i
$364$	2.02663	+	0.518633i	0.106224	+	0.0271838i
$365$	0.228808	+	0.552392i	0.0119764	+	0.0289135i
$366$	0.111949	+	1.57224i	0.00585169	+	0.0821826i
$367$			14.9308i			0.779383i	0.920945	+	0.389691i	$0.127418\pi$
$367$			14.9308i			0.779383i	−0.920945	+	0.389691i	$0.872582\pi$
$368$	16.5621	−	30.2401i	0.863357	−	1.57638i
$369$		−	0.368102i		−	0.0191626i
$370$	−1.35453	+	0.0964470i	−0.0704184	+	0.00501404i
$371$	0.151145	+	0.364896i	0.00784704	+	0.0189444i
$372$	4.73186	+	7.98663i	0.245335	+	0.414087i
$373$	−11.7690	−	4.87489i	−0.609377	−	0.252412i	0.0565848	−	0.998398i	$-0.481979\pi$
$373$	−11.7690	−	4.87489i	−0.609377	−	0.252412i	−0.665962	+	0.745985i	$0.731979\pi$
$374$	17.5991	+	35.1864i	0.910029	+	1.81944i
$375$	−12.1582	+	12.1582i	−0.627848	+	0.627848i
$376$	18.7089	−	29.0510i	0.964840	−	1.49819i
$377$	5.20324	+	5.20324i	0.267980	+	0.267980i
$378$	−2.52558	+	7.58015i	−0.129902	+	0.389881i
$379$	6.37594	−	15.3929i	0.327510	−	0.790680i	−0.671266	−	0.741217i	$-0.734249\pi$
$379$	6.37594	−	15.3929i	0.327510	−	0.790680i	0.998776	−	0.0494629i	$-0.0157510\pi$
$380$	−3.61754	−	25.2740i	−0.185576	−	1.29653i
$381$	7.42904	−	3.07721i	0.380601	−	0.157650i
$382$	−0.510537	+	0.588814i	−0.0261213	+	0.0301264i
$383$	−34.4745			−1.76157			−0.880783	−	0.473520i	$-0.842983\pi$
$383$	−34.4745			−1.76157			−0.880783	+	0.473520i	$0.842983\pi$
$384$	16.3732	−	1.72365i	0.835544	−	0.0879595i
$385$	8.68288			0.442520
$386$	3.92413	−	4.52579i	0.199733	−	0.230357i
$387$	−3.42331	+	1.41798i	−0.174017	+	0.0720801i
$388$	3.38642	+	23.6593i	0.171920	+	1.20112i
$389$	6.15276	−	14.8541i	0.311957	−	0.753131i	−0.687675	−	0.726019i	$-0.741369\pi$
$389$	6.15276	−	14.8541i	0.311957	−	0.753131i	0.999632	−	0.0271129i	$-0.00863136\pi$
$390$	1.06456	−	3.19513i	0.0539062	−	0.161792i
$391$	30.5523	+	30.5523i	1.54510	+	1.54510i
$392$	−1.53142	+	2.37797i	−0.0773484	+	0.120106i
$393$	7.64867	−	7.64867i	0.385824	−	0.385824i
$394$	7.95380	+	15.9022i	0.400707	+	0.801143i
$395$	3.25868	+	1.34979i	0.163962	+	0.0679152i
$396$	4.99231	+	8.42623i	0.250873	+	0.423434i
$397$	−7.24498	−	17.4909i	−0.363615	−	0.877845i	−0.994765	−	0.102184i	$-0.967417\pi$
$397$	−7.24498	−	17.4909i	−0.363615	−	0.877845i	0.631150	−	0.775661i	$-0.282583\pi$
$398$	−4.25329	+	0.302849i	−0.213198	+	0.0151805i
$399$		−	11.8736i		−	0.594422i
$400$	−8.95378	−	4.90385i	−0.447689	−	0.245193i
$401$		−	33.7813i		−	1.68696i	−0.537164	−	0.843478i	$-0.680504\pi$
$401$		−	33.7813i		−	1.68696i	0.537164	−	0.843478i	$-0.319496\pi$
$402$	1.34175	+	18.8439i	0.0669205	+	0.939848i
$403$	1.27674	+	3.08231i	0.0635988	+	0.153541i
$404$	−33.1726	−	8.48916i	−1.65040	−	0.422351i
$405$	8.05729	+	3.33744i	0.400370	+	0.165839i
$406$	−8.89814	+	4.45057i	−0.441608	+	0.220878i
$407$	−2.40846	+	2.40846i	−0.119383	+	0.119383i
$408$	−3.68251	+	20.3005i	−0.182312	+	1.00503i
$409$	−10.4922	−	10.4922i	−0.518807	−	0.518807i	0.398404	−	0.917210i	$-0.369564\pi$
$409$	−10.4922	−	10.4922i	−0.518807	−	0.518807i	−0.917210	+	0.398404i	$0.869564\pi$
$410$	−0.875694	−	0.291767i	−0.0432474	−	0.0144093i
$411$	2.20571	−	5.32505i	0.108800	−	0.262666i
$412$	−7.77108	+	10.3673i	−0.382853	+	0.510759i
$413$	−4.40271	+	1.82366i	−0.216643	+	0.0897366i
$414$	8.12687	+	7.04647i	0.399414	+	0.346315i
$415$	−9.47686			−0.465201
$416$	5.91280	+	0.220539i	0.289899	+	0.0108128i
$417$	4.50718			0.220717
$418$	−48.3845	−	41.9522i	−2.36656	−	2.05195i
$419$	−30.8577	+	12.7817i	−1.50750	+	0.624426i	−0.975040	−	0.222029i	$-0.928732\pi$
$419$	−30.8577	+	12.7817i	−1.50750	+	0.624426i	−0.532459	+	0.846456i	$0.678732\pi$
$420$	3.64351	+	2.73110i	0.177785	+	0.133264i
$421$	−9.19315	+	22.1942i	−0.448047	+	1.08168i	0.525006	+	0.851098i	$0.324063\pi$
$421$	−9.19315	+	22.1942i	−0.448047	+	1.08168i	−0.973053	+	0.230582i	$0.925937\pi$
$422$	22.7054	+	7.56506i	1.10528	+	0.368261i
$423$	7.62256	+	7.62256i	0.370621	+	0.370621i
$424$	0.636246	+	0.918226i	0.0308988	+	0.0445930i
$425$	9.04621	−	9.04621i	0.438805	−	0.438805i
$426$	−21.5938	+	10.8005i	−1.04622	+	0.523288i
$427$	−0.707613	−	0.293103i	−0.0342438	−	0.0141842i
$428$	1.24507	−	4.86528i	0.0601826	−	0.235172i
$429$	−3.23263	−	7.80426i	−0.156073	−	0.376793i
$430$	0.659901	+	9.26781i	0.0318232	+	0.446934i
$431$			13.3156i			0.641392i	0.947182	+	0.320696i	$0.103917\pi$
$431$			13.3156i			0.641392i	−0.947182	+	0.320696i	$0.896083\pi$
$432$	−2.44411	+	22.4661i	−0.117592	+	1.08090i
$433$		−	14.1237i		−	0.678743i	−0.940652	−	0.339371i	$-0.889786\pi$
$433$		−	14.1237i		−	0.678743i	0.940652	−	0.339371i	$-0.110214\pi$
$434$	−4.49944	+	0.320376i	−0.215980	+	0.0153785i
$435$	6.12944	+	14.7978i	0.293884	+	0.709500i
$436$	1.68144	−	0.996209i	0.0805266	−	0.0477098i
$437$	−64.9774	−	26.9145i	−3.10829	−	1.28750i
$438$	0.351813	+	0.703389i	0.0168103	+	0.0336092i
$439$	4.01344	−	4.01344i	0.191551	−	0.191551i	−0.604815	−	0.796366i	$-0.706753\pi$
$439$	4.01344	−	4.01344i	0.191551	−	0.191551i	0.796366	+	0.604815i	$0.206753\pi$
$440$	24.0026	−	5.19759i	1.14428	−	0.247786i
$441$	−0.623944	−	0.623944i	−0.0297116	−	0.0297116i
$442$	−2.34384	+	7.03470i	−0.111485	+	0.334607i
$443$	6.01337	−	14.5176i	0.285704	−	0.689750i	−0.714245	−	0.699896i	$-0.753230\pi$
$443$	6.01337	−	14.5176i	0.285704	−	0.689750i	0.999949	+	0.0101459i	$0.00322961\pi$
$444$	−1.76819	+	0.253086i	−0.0839148	+	0.0120110i
$445$	−7.75871	+	3.21376i	−0.367798	+	0.152347i
$446$	−1.99401	+	2.29974i	−0.0944190	+	0.108896i
$447$	7.89836			0.373580
$448$	−2.80993	+	7.49028i	−0.132757	+	0.353882i
$449$	5.44978			0.257191			0.128595	−	0.991697i	$-0.458953\pi$
$449$	5.44978			0.257191			0.128595	+	0.991697i	$0.458953\pi$
$450$	2.08639	−	2.40628i	0.0983532	−	0.113433i
$451$	−2.13893	+	0.885973i	−0.100718	+	0.0417188i
$452$	32.3589	−	4.63162i	1.52204	−	0.217853i
$453$	−1.54498	+	3.72992i	−0.0725897	+	0.175247i
$454$	5.97695	−	17.9389i	0.280512	−	0.841916i
$455$	1.15716	+	1.15716i	0.0542486	+	0.0542486i
$456$	−7.10756	−	32.8228i	−0.332842	−	1.53707i
$457$	1.00810	−	1.00810i	0.0471571	−	0.0471571i	−0.683135	−	0.730292i	$-0.739384\pi$
$457$	1.00810	−	1.00810i	0.0471571	−	0.0471571i	0.730292	+	0.683135i	$0.239384\pi$
$458$	4.49562	+	8.98821i	0.210067	+	0.419991i
$459$	−26.1642	−	10.8376i	−1.22124	−	0.505854i
$460$	23.2047	−	13.7482i	1.08193	−	0.641012i
$461$	−6.63884	−	16.0276i	−0.309202	−	0.746479i	−0.999731	−	0.0231747i	$-0.992623\pi$
$461$	−6.63884	−	16.0276i	−0.309202	−	0.746479i	0.690530	−	0.723304i	$-0.257377\pi$
$462$	11.3924	−	0.811176i	0.530021	−	0.0377393i
$463$		−	28.6860i		−	1.33315i	−0.745438	−	0.666575i	$-0.767760\pi$
$463$		−	28.6860i		−	1.33315i	0.745438	−	0.666575i	$-0.232240\pi$
$464$	−21.9335	+	17.6294i	−1.01824	+	0.818426i
$465$			7.26197i			0.336766i
$466$	1.67317	+	23.4984i	0.0775080	+	1.08854i
$467$	14.9012	+	35.9746i	0.689544	+	1.66471i	0.745699	+	0.666283i	$0.232116\pi$
$467$	14.9012	+	35.9746i	0.689544	+	1.66471i	−0.0561550	+	0.998422i	$0.517884\pi$
$468$	−0.457637	+	1.78828i	−0.0211543	+	0.0826634i
$469$	−8.48098	−	3.51294i	−0.391615	−	0.162212i
$470$	24.1755	−	12.0918i	1.11513	−	0.557754i
$471$	−13.4621	+	13.4621i	−0.620302	+	0.620302i
$472$	−11.0790	+	7.67673i	−0.509953	+	0.353350i
$473$	16.4790	+	16.4790i	0.757703	+	0.757703i
$474$	4.40165	+	1.46655i	0.202174	+	0.0673611i
$475$	−7.96911	+	19.2391i	−0.365648	+	0.882752i
$476$	−8.02191	−	6.01305i	−0.367684	−	0.275608i
$477$	−0.321980	+	0.133369i	−0.0147425	+	0.00610653i
$478$	11.8895	+	10.3089i	0.543815	+	0.471519i
$479$	−15.3565			−0.701657			−0.350829	−	0.936440i	$-0.614100\pi$
$479$	−15.3565			−0.701657			−0.350829	+	0.936440i	$0.614100\pi$
$480$	11.7068	+	5.36872i	0.534341	+	0.245047i
$481$	−0.641949			−0.0292704
$482$	−0.717514	−	0.622127i	−0.0326819	−	0.0283371i
$483$	11.5885	−	4.80011i	0.527295	−	0.218413i
$484$	23.7512	−	31.6861i	1.07960	−	1.44028i
$485$	−7.15493	+	17.2735i	−0.324889	+	0.784350i
$486$	−11.8571	−	3.95059i	−0.537849	−	0.179202i
$487$	18.9858	+	18.9858i	0.860330	+	0.860330i	0.991376	−	0.131047i	$-0.0418337\pi$
$487$	18.9858	+	18.9858i	0.860330	+	0.860330i	−0.131047	+	0.991376i	$0.541834\pi$
$488$	−2.13155	−	0.386662i	−0.0964906	−	0.0175034i
$489$	−12.1328	+	12.1328i	−0.548664	+	0.548664i
$490$	−1.97888	+	0.989776i	−0.0893969	+	0.0447135i
$491$	4.64052	+	1.92217i	0.209424	+	0.0867462i	0.484929	−	0.874553i	$-0.338845\pi$
$491$	4.64052	+	1.92217i	0.209424	+	0.0867462i	−0.275506	+	0.961299i	$0.588845\pi$
$492$	−1.17621	−	0.301003i	−0.0530277	−	0.0135702i
$493$	−13.4952	−	32.5802i	−0.607792	−	1.46734i
$494$	−0.857229	−	12.0391i	−0.0385685	−	0.541666i
$495$			7.66169i			0.344367i
$496$	−12.2463	+	3.57901i	−0.549875	+	0.160702i
$497$		−	11.7321i		−	0.526256i
$498$	−12.4341	+	0.885352i	−0.557185	+	0.0396736i
$499$	−11.3051	−	27.2930i	−0.506087	−	1.22180i	−0.946119	−	0.323820i	$-0.895033\pi$
$499$	−11.3051	−	27.2930i	−0.506087	−	1.22180i	0.440032	−	0.897982i	$-0.354967\pi$
$500$	−12.0456	−	20.3311i	−0.538696	−	0.909234i
$501$	−8.83144	−	3.65810i	−0.394560	−	0.163432i
$502$	9.69620	+	19.3859i	0.432763	+	0.865233i
$503$	22.2886	−	22.2886i	0.993799	−	0.993799i	−0.00618176	−	0.999981i	$-0.501968\pi$
$503$	22.2886	−	22.2886i	0.993799	−	0.993799i	0.999981	+	0.00618176i	$0.00196773\pi$
$504$	−2.09830	−	1.35131i	−0.0934657	−	0.0601922i
$505$	−18.9408	−	18.9408i	−0.842855	−	0.842855i
$506$	21.3846	−	64.1828i	0.950663	−	2.85327i
$507$	−6.63020	+	16.0067i	−0.294457	+	0.710883i
$508$	1.56588	+	10.9401i	0.0694749	+	0.485388i
$509$	−10.4007	+	4.30811i	−0.461003	+	0.190954i	−0.601083	−	0.799187i	$-0.705264\pi$
$509$	−10.4007	+	4.30811i	−0.461003	+	0.190954i	0.140080	+	0.990140i	$0.455264\pi$
$510$	−10.5732	+	12.1943i	−0.468188	+	0.539972i
$511$	−0.382157			−0.0169056
$512$	−3.28396	+	22.3878i	−0.145132	+	0.989412i
$513$	46.0979			2.03527
$514$	−22.9028	+	26.4144i	−1.01020	+	1.16509i
$515$	−9.36400	+	3.87870i	−0.412627	+	0.170916i
$516$	1.73164	+	12.0982i	0.0762314	+	0.532592i
$517$	25.9459	−	62.6389i	1.14110	−	2.75486i
$518$	0.274359	−	0.823449i	0.0120547	−	0.0361803i
$519$	−1.84165	−	1.84165i	−0.0808396	−	0.0808396i
$520$	3.89149	+	2.50613i	0.170653	+	0.109901i
$521$	−4.19778	+	4.19778i	−0.183908	+	0.183908i	−0.793056	−	0.609148i	$-0.791511\pi$
$521$	−4.19778	+	4.19778i	−0.183908	+	0.183908i	0.609148	+	0.793056i	$0.291511\pi$
$522$	−3.92714	−	7.85164i	−0.171886	−	0.343657i
$523$	19.4480	+	8.05562i	0.850401	+	0.352248i	0.764946	−	0.644094i	$-0.222766\pi$
$523$	19.4480	+	8.05562i	0.850401	+	0.352248i	0.0854549	+	0.996342i	$0.472766\pi$
$524$	7.57782	+	12.7902i	0.331039	+	0.558741i
$525$	−1.42126	−	3.43123i	−0.0620289	−	0.149751i
$526$	40.3171	−	2.87072i	1.75791	−	0.125169i
$527$		−	15.9887i		−	0.696477i
$528$	31.0070	−	9.06188i	1.34941	−	0.394368i
$529$		−	51.2980i		−	2.23035i
$530$	0.0620671	+	0.871685i	0.00269602	+	0.0378636i
$531$	−1.60918	−	3.88491i	−0.0698326	−	0.168591i
$532$	15.8094	+	4.04575i	0.685422	+	0.175405i
$533$	−0.403127	−	0.166981i	−0.0174614	−	0.00723274i
$534$	−9.87957	+	4.94145i	−0.427531	+	0.213838i
$535$	2.77797	−	2.77797i	0.120102	−	0.120102i
$536$	−25.5473	−	4.63428i	−1.10348	−	0.200170i
$537$	−7.10447	−	7.10447i	−0.306580	−	0.306580i
$538$	−17.2160	−	5.73608i	−0.742234	−	0.247300i
$539$	−2.12380	+	5.12731i	−0.0914785	+	0.220849i
$540$	−10.6032	+	14.1455i	−0.456289	+	0.608727i
$541$	10.7416	−	4.44931i	0.461817	−	0.191291i	−0.139630	−	0.990204i	$-0.544591\pi$
$541$	10.7416	−	4.44931i	0.461817	−	0.191291i	0.601447	+	0.798913i	$0.294591\pi$
$542$	−16.4485	−	14.2618i	−0.706523	−	0.612597i
$543$	26.3405			1.13038
$544$	−25.7749	−	11.8203i	−1.10509	−	0.506791i
$545$	1.52888			0.0654900
$546$	1.62636	+	1.41015i	0.0696018	+	0.0603488i
$547$	−14.2126	+	5.88706i	−0.607688	+	0.251713i	−0.665240	−	0.746630i	$-0.731671\pi$
$547$	−14.2126	+	5.88706i	−0.607688	+	0.251713i	0.0575517	+	0.998343i	$0.481671\pi$
$548$	6.33861	+	4.75128i	0.270772	+	0.202965i
$549$	0.258631	−	0.624391i	0.0110381	−	0.0266484i
$550$	−19.0038	−	6.33176i	−0.810326	−	0.269987i
$551$	40.5894	+	40.5894i	1.72917	+	1.72917i
$552$	29.1614	−	20.2061i	1.24119	−	0.860030i
$553$	−1.59412	+	1.59412i	−0.0677889	+	0.0677889i
$554$	−12.2534	+	6.12875i	−0.520596	+	0.260386i
$555$	−1.29095	−	0.534728i	−0.0547977	−	0.0226979i
$556$	−1.53576	+	6.00119i	−0.0651305	+	0.254507i
$557$	−6.72077	−	16.2254i	−0.284768	−	0.687491i	0.715166	−	0.698954i	$-0.246351\pi$
$557$	−6.72077	−	16.2254i	−0.284768	−	0.687491i	−0.999934	+	0.0114635i	$0.996351\pi$
$558$	−0.282697	−	3.97027i	−0.0119675	−	0.168075i
$559$			4.39228i			0.185774i
$560$	−4.87786	+	3.92066i	−0.206127	+	0.165678i
$561$			40.4825i			1.70917i
$562$	−19.9649	+	1.42157i	−0.842170	+	0.0599655i
$563$	−14.5548	−	35.1383i	−0.613411	−	1.48090i	−0.859230	−	0.511589i	$-0.829057\pi$
$563$	−14.5548	−	35.1383i	−0.613411	−	1.48090i	0.245820	−	0.969316i	$-0.420943\pi$
$564$	30.5898	−	18.1236i	1.28806	−	0.763141i
$565$	23.6251	+	9.78582i	0.993914	+	0.411693i
$566$	−20.2087	−	40.4038i	−0.849436	−	1.69830i
$567$	−3.94157	+	3.94157i	−0.165530	+	0.165530i
$568$	−7.02287	−	32.4317i	−0.294673	−	1.36080i
$569$	6.53671	+	6.53671i	0.274033	+	0.274033i	0.830721	−	0.556688i	$-0.187928\pi$
$569$	6.53671	+	6.53671i	0.274033	+	0.274033i	−0.556688	+	0.830721i	$0.687928\pi$
$570$	8.30444	−	24.9245i	0.347835	−	1.04397i
$571$	2.69633	−	6.50951i	0.112838	−	0.272415i	−0.857365	−	0.514709i	$-0.827900\pi$
$571$	2.69633	−	6.50951i	0.112838	−	0.272415i	0.970203	+	0.242294i	$0.0779000\pi$
$572$	11.4926	−	1.64497i	0.480532	−	0.0687798i
$573$	−0.740871	+	0.306879i	−0.0309503	+	0.0128200i
$574$	0.386482	−	0.445739i	0.0161314	−	0.0186048i
$575$	−21.9989			−0.917416
$576$	−6.60935	−	2.47946i	−0.275390	−	0.103311i
$577$	16.0836			0.669571			0.334786	−	0.942294i	$-0.391336\pi$
$577$	16.0836			0.669571			0.334786	+	0.942294i	$0.391336\pi$
$578$	7.52924	−	8.68365i	0.313175	−	0.361192i
$579$	5.69454	−	2.35876i	0.236657	−	0.0980266i
$580$	−21.7914	+	3.11906i	−0.904838	+	0.129512i
$581$	2.31800	−	5.59616i	0.0961670	−	0.232168i
$582$	−7.77388	+	23.3321i	−0.322238	+	0.967148i
$583$	1.54993	+	1.54993i	0.0641916	+	0.0641916i
$584$	−1.05642	+	0.228760i	−0.0437149	+	0.00946617i
$585$	−1.02107	+	1.02107i	−0.0422160	+	0.0422160i
$586$	−14.6984	−	29.3869i	−0.607186	−	1.21396i
$587$	10.7860	+	4.46770i	0.445185	+	0.184402i	0.594003	−	0.804463i	$-0.297547\pi$
$587$	10.7860	+	4.46770i	0.445185	+	0.184402i	−0.148818	+	0.988865i	$0.547547\pi$
$588$	−2.50393	+	1.48351i	−0.103260	+	0.0611788i
$589$	9.95956	+	24.0445i	0.410376	+	0.990736i
$590$	−10.5175	+	0.748881i	−0.432998	+	0.0308310i
$591$			18.2958i			0.752587i
$592$	0.265509	−	2.44054i	0.0109123	−	0.100306i
$593$			30.2167i			1.24085i	0.784265	+	0.620427i	$0.213040\pi$
$593$			30.2167i			1.24085i	−0.784265	+	0.620427i	$0.786960\pi$
$594$	3.14930	+	44.2296i	0.129217	+	1.81476i
$595$	−3.00123	−	7.24561i	−0.123038	−	0.297041i
$596$	−2.69125	+	10.5165i	−0.110238	+	0.430771i
$597$	−4.05365	−	1.67908i	−0.165905	−	0.0687200i
$598$	11.4035	−	5.70369i	0.466325	−	0.233241i
$599$	−15.1682	+	15.1682i	−0.619754	+	0.619754i	−0.945468	−	0.325714i	$-0.894395\pi$
$599$	−15.1682	+	15.1682i	−0.619754	+	0.619754i	0.325714	+	0.945468i	$0.394395\pi$
$600$	−5.98282	−	8.63437i	−0.244248	−	0.352497i
$601$	17.3350	+	17.3350i	0.707108	+	0.707108i	0.965926	−	0.258818i	$-0.0833329\pi$
$601$	17.3350	+	17.3350i	0.707108	+	0.707108i	−0.258818	+	0.965926i	$0.583333\pi$
$602$	−5.63412	−	1.87720i	−0.229630	−	0.0765088i
$603$	3.09978	−	7.48354i	0.126233	−	0.304753i
$604$	−4.43986	−	3.32802i	−0.180655	−	0.135415i
$605$	28.6197	−	11.8547i	1.16356	−	0.481962i
$606$	−26.6208	−	23.0818i	−1.08140	−	0.937634i
$607$	−19.3803			−0.786621			−0.393310	−	0.919406i	$-0.628670\pi$
$607$	−19.3803			−0.786621			−0.393310	+	0.919406i	$0.628670\pi$
$608$	46.1245	+	1.72038i	1.87060	+	0.0697705i
$609$	−10.2374			−0.414842
$610$	−1.28039	−	1.11018i	−0.0518417	−	0.0449498i
$611$	11.8057	−	4.89006i	0.477606	−	0.197831i
$612$	5.30586	−	7.07846i	0.214477	−	0.286130i
$613$	−12.2551	+	29.5863i	−0.494977	+	1.19498i	0.457181	+	0.889374i	$0.348859\pi$
$613$	−12.2551	+	29.5863i	−0.494977	+	1.19498i	−0.952158	+	0.305606i	$0.901141\pi$
$614$	17.2060	+	5.73276i	0.694379	+	0.231356i
$615$	−0.671590	−	0.671590i	−0.0270811	−	0.0270811i
$616$	−2.80172	+	15.4450i	−0.112885	+	0.622298i
$617$	−22.4092	+	22.4092i	−0.902161	+	0.902161i	−0.995623	−	0.0934622i	$-0.970207\pi$
$617$	−22.4092	+	22.4092i	−0.902161	+	0.902161i	0.0934622	+	0.995623i	$0.470207\pi$
$618$	−11.9237	+	5.96385i	−0.479640	+	0.239901i
$619$	37.6276	+	15.5859i	1.51238	+	0.626448i	0.976047	−	0.217558i	$-0.0698093\pi$
$619$	37.6276	+	15.5859i	1.51238	+	0.626448i	0.536333	+	0.844007i	$0.319809\pi$
$620$	−9.66912	−	2.47441i	−0.388321	−	0.0993748i
$621$	18.6359	+	44.9911i	0.747833	+	1.80543i
$622$	−0.385377	−	5.41233i	−0.0154522	−	0.217015i
$623$		−	5.36765i		−	0.215051i
$624$	5.33996	+	2.92461i	0.213769	+	0.117078i
$625$		−	5.72547i		−	0.229019i
$626$	28.3508	−	2.01868i	1.13313	−	0.0806825i
$627$	−25.2171	−	60.8795i	−1.00707	−	2.43129i
$628$	−13.3374	−	22.5115i	−0.532221	−	0.898306i
$629$	2.84228	+	1.17731i	0.113329	+	0.0469424i
$630$	−0.873369	−	1.74615i	−0.0347959	−	0.0695682i
$631$	21.0911	−	21.0911i	0.839624	−	0.839624i	−0.149185	−	0.988809i	$-0.547665\pi$
$631$	21.0911	−	21.0911i	0.839624	−	0.839624i	0.988809	+	0.149185i	$0.0476650\pi$
$632$	−3.45248	+	5.36097i	−0.137332	+	0.213248i
$633$	17.4133	+	17.4133i	0.692117	+	0.692117i
$634$	−6.28567	+	18.8655i	−0.249636	+	0.749245i
$635$	−3.30844	+	7.98729i	−0.131292	+	0.316966i
$636$	0.162870	+	1.13790i	0.00645822	+	0.0451205i
$637$	−0.966351	+	0.400276i	−0.0382882	+	0.0158595i
$638$	−36.1714	+	41.7173i	−1.43204	+	1.65161i
$639$	10.3523			0.409530
$640$	−11.1372	+	13.7580i	−0.440238	+	0.543833i
$641$	−16.9074			−0.667802			−0.333901	−	0.942608i	$-0.608365\pi$
$641$	−16.9074			−0.667802			−0.333901	+	0.942608i	$0.608365\pi$
$642$	3.38531	−	3.90436i	0.133607	−	0.154093i
$643$	7.26431	−	3.00898i	0.286476	−	0.118662i	−0.234818	−	0.972039i	$-0.575449\pi$
$643$	7.26431	−	3.00898i	0.286476	−	0.118662i	0.521294	+	0.853377i	$0.325449\pi$
$644$	2.44261	+	17.0653i	0.0962523	+	0.672469i
$645$	−3.65867	+	8.83280i	−0.144060	+	0.347791i
$646$	−18.2838	+	54.8762i	−0.719368	+	2.15908i
$647$	−9.17385	−	9.17385i	−0.360661	−	0.360661i	0.503395	−	0.864056i	$-0.332084\pi$
$647$	−9.17385	−	9.17385i	−0.360661	−	0.360661i	−0.864056	+	0.503395i	$0.832084\pi$
$648$	−8.53647	+	13.2553i	−0.335344	+	0.520719i
$649$	−18.7010	+	18.7010i	−0.734077	+	0.734077i
$650$	−1.68880	−	3.37646i	−0.0662402	−	0.132436i
$651$	−4.28825	−	1.77625i	−0.168070	−	0.0696168i
$652$	−12.0204	−	20.2886i	−0.470756	−	0.794561i
$653$	−1.51353	−	3.65399i	−0.0592291	−	0.142992i	0.891494	−	0.453032i	$-0.149658\pi$
$653$	−1.51353	−	3.65399i	−0.0592291	−	0.142992i	−0.950724	+	0.310040i	$0.899658\pi$
$654$	2.00597	−	0.142832i	0.0784395	−	0.00558517i
$655$			11.6297i			0.454409i
$656$	0.801554	−	1.46353i	0.0312954	−	0.0571413i
$657$		−	0.337212i		−	0.0131559i
$658$	1.22708	+	17.2334i	0.0478366	+	0.671829i
$659$	13.4527	+	32.4777i	0.524042	+	1.26515i	0.935373	+	0.353664i	$0.115064\pi$
$659$	13.4527	+	32.4777i	0.524042	+	1.26515i	−0.411330	+	0.911486i	$0.634936\pi$
$660$	24.4817	+	6.26509i	0.952950	+	0.243868i
$661$	19.9390	+	8.25902i	0.775539	+	0.321239i	0.735114	−	0.677944i	$-0.237129\pi$
$661$	19.9390	+	8.25902i	0.775539	+	0.321239i	0.0404251	+	0.999183i	$0.487129\pi$
$662$	−21.3144	+	10.6608i	−0.828408	+	0.414344i
$663$	−5.39508	+	5.39508i	−0.209527	+	0.209527i
$664$	3.05792	−	16.8573i	0.118670	−	0.654192i
$665$	9.02679	+	9.02679i	0.350044	+	0.350044i
$666$	0.726603	+	0.242092i	0.0281553	+	0.00938088i
$667$	−23.2058	+	56.0238i	−0.898533	+	2.16925i
$668$	7.87985	−	10.5124i	0.304881	−	0.406736i
$669$	−2.89363	+	1.19858i	−0.111874	+	0.0463398i
$670$	−15.3460	−	13.3059i	−0.592867	−	0.514050i
$671$	−4.25064			−0.164094
$672$	−6.03372	+	5.59980i	−0.232756	+	0.216017i
$673$	24.2219			0.933686			0.466843	−	0.884340i	$-0.345391\pi$
$673$	24.2219			0.933686			0.466843	+	0.884340i	$0.345391\pi$
$674$	22.9778	+	19.9231i	0.885070	+	0.767408i
$675$	13.3214	−	5.51789i	0.512740	−	0.212384i
$676$	−19.0534	−	14.2820i	−0.732822	−	0.549307i
$677$	7.60567	−	18.3617i	0.292309	−	0.705697i	−0.707690	−	0.706523i	$-0.750263\pi$
$677$	7.60567	−	18.3617i	0.292309	−	0.705697i	1.00000		0.000825424i	$0.000262741\pi$
$678$	31.9115	+	10.6324i	1.22555	+	0.408333i
$679$	−8.45008	−	8.45008i	−0.324284	−	0.324284i
$680$	−12.6337	−	18.2329i	−0.484481	−	0.699201i
$681$	13.7578	−	13.7578i	0.527200	−	0.527200i
$682$	−22.3896	+	11.1986i	−0.857342	+	0.428816i
$683$	9.92674	+	4.11179i	0.379836	+	0.157333i	0.564429	−	0.825482i	$-0.309097\pi$
$683$	9.92674	+	4.11179i	0.379836	+	0.157333i	−0.184593	+	0.982815i	$0.559097\pi$
$684$	−3.56993	+	13.9500i	−0.136500	+	0.533392i
$685$	2.37146	+	5.72520i	0.0906087	+	0.218749i
$686$	−0.100443	−	1.41064i	−0.00383492	−	0.0538586i
$687$			10.3411i			0.394536i
$688$	−16.6984	−	1.81664i	−0.636622	−	0.0692587i
$689$			0.413117i			0.0157385i
$690$	27.6833	−	1.97115i	1.05389	−	0.0750404i
$691$	5.61116	+	13.5465i	0.213458	+	0.515334i	0.993950	−	0.109832i	$-0.0350312\pi$
$691$	5.61116	+	13.5465i	0.213458	+	0.515334i	−0.780492	+	0.625166i	$0.785031\pi$
$692$	3.07963	−	1.82460i	0.117070	−	0.0693608i
$693$	−4.52429	−	1.87402i	−0.171863	−	0.0711882i
$694$	4.56889	+	9.13469i	0.173433	+	0.346748i
$695$	−3.42654	+	3.42654i	−0.129976	+	0.129976i
$696$	−28.3000	+	6.12817i	−1.07271	+	0.232288i
$697$	1.47864	+	1.47864i	0.0560074	+	0.0560074i
$698$	3.39389	−	10.1863i	0.128461	−	0.385555i
$699$	−9.27649	+	22.3954i	−0.350869	+	0.847073i
$700$	5.05286	−	0.723230i	0.190980	−	0.0273355i
$701$	−7.38786	+	3.06015i	−0.279036	+	0.115580i	−0.517813	−	0.855494i	$-0.673254\pi$
$701$	−7.38786	+	3.06015i	−0.279036	+	0.115580i	0.238777	+	0.971074i	$0.423254\pi$
$702$	−5.47475	+	6.31416i	−0.206631	+	0.238313i
$703$	−5.00771			−0.188869
$704$	1.50047	+	44.3727i	0.0565510	+	1.67236i
$705$	27.8143			1.04755
$706$	7.52687	−	8.68092i	0.283277	−	0.326711i
$707$	15.8176	−	6.55185i	0.594881	−	0.246408i
$708$	−13.7295	+	1.96514i	−0.515986	+	0.0738544i
$709$	−14.9436	+	36.0772i	−0.561220	+	1.35491i	0.347570	+	0.937654i	$0.387007\pi$
$709$	−14.9436	+	36.0772i	−0.561220	+	1.35491i	−0.908791	+	0.417252i	$0.862993\pi$
$710$	8.20549	−	24.6275i	0.307946	−	0.924255i
$711$	−1.40664	−	1.40664i	−0.0527530	−	0.0527530i
$712$	−3.21309	−	14.8381i	−0.120416	−	0.556082i
$713$	−19.4409	+	19.4409i	−0.728066	+	0.728066i
$714$	−4.61467	−	9.22622i	−0.172700	−	0.345282i
$715$	8.39071	+	3.47555i	0.313795	+	0.129978i
$716$	11.8802	−	7.03866i	0.443982	−	0.263047i
$717$	6.19660	+	14.9599i	0.231416	+	0.558689i
$718$	23.8528	−	1.69840i	0.890179	−	0.0633839i
$719$		−	40.8747i		−	1.52437i	−0.647359	−	0.762185i	$-0.724127\pi$
$719$		−	40.8747i		−	1.52437i	0.647359	−	0.762185i	$-0.275873\pi$
$720$	−3.45955	−	4.30418i	−0.128930	−	0.160407i
$721$		−	6.47823i		−	0.241262i
$722$	−4.77865	−	67.1126i	−0.177843	−	2.49767i
$723$	−0.373955	−	0.902807i	−0.0139075	−	0.0335757i
$724$	−8.97513	+	35.0716i	−0.333558	+	1.30343i
$725$	16.5881	+	6.87100i	0.616065	+	0.255182i
$726$	36.4430	−	18.2277i	1.35253	−	0.676492i
$727$	14.8149	−	14.8149i	0.549453	−	0.549453i	−0.376829	−	0.926283i	$-0.622986\pi$
$727$	14.8149	−	14.8149i	0.549453	−	0.549453i	0.926283	+	0.376829i	$0.122986\pi$
$728$	−2.43174	+	1.68497i	−0.0901261	+	0.0624490i
$729$	−20.9182	−	20.9182i	−0.774748	−	0.774748i
$730$	−0.802209	−	0.267283i	−0.0296911	−	0.00989257i
$731$	8.05527	−	19.4472i	0.297935	−	0.719279i
$732$	−1.78366	−	1.33699i	−0.0659258	−	0.0494166i
$733$	−22.9346	+	9.49981i	−0.847108	+	0.350884i	−0.763652	−	0.645628i	$-0.776596\pi$
$733$	−22.9346	+	9.49981i	−0.847108	+	0.350884i	−0.0834557	+	0.996511i	$0.526596\pi$
$734$	−15.9536	−	13.8327i	−0.588857	−	0.510574i
$735$	−2.27674			−0.0839787
$736$	16.9676	+	45.7126i	0.625434	+	1.68499i
$737$	−50.9454			−1.87660
$738$	0.393316	+	0.341028i	0.0144782	+	0.0125534i
$739$	19.6132	−	8.12407i	0.721485	−	0.298849i	0.00843720	−	0.999964i	$-0.497314\pi$
$739$	19.6132	−	8.12407i	0.721485	−	0.298849i	0.713048	+	0.701116i	$0.247314\pi$
$740$	1.15185	−	1.53666i	0.0423428	−	0.0564888i
$741$	4.75271	−	11.4740i	0.174595	−	0.421510i
$742$	−0.529918	−	0.176560i	−0.0194539	−	0.00648172i
$743$	22.1633	+	22.1633i	0.813091	+	0.813091i	0.985096	−	0.172005i	$-0.0550245\pi$
$743$	22.1633	+	22.1633i	0.813091	+	0.813091i	−0.172005	+	0.985096i	$0.555025\pi$
$744$	−12.9175	−	2.34324i	−0.473580	−	0.0859072i
$745$	−6.00467	+	6.00467i	−0.219994	+	0.219994i
$746$	16.1122	−	8.05884i	0.589911	−	0.295055i
$747$	4.93800	+	2.04538i	0.180672	+	0.0748367i
$748$	−53.9013	−	13.7938i	−1.97083	−	0.504352i
$749$	0.960931	+	2.31989i	0.0351117	+	0.0847670i
$750$	−1.72704	−	24.2550i	−0.0630627	−	0.885669i
$751$		−	36.7384i		−	1.34060i	−0.742089	−	0.670301i	$-0.766165\pi$
$751$		−	36.7384i		−	1.34060i	0.742089	−	0.670301i	$-0.233835\pi$
$752$	13.7081	+	46.9048i	0.499882	+	1.71044i
$753$			22.3037i			0.812793i
$754$	−10.3802	+	0.739106i	−0.378024	+	0.0269167i
$755$	−1.66108	−	4.01021i	−0.0604529	−	0.145946i
$756$	−5.75955	−	9.72122i	−0.209473	−	0.353557i
$757$	27.8007	+	11.5154i	1.01043	+	0.418536i	0.825613	−	0.564237i	$-0.190829\pi$
$757$	27.8007	+	11.5154i	1.01043	+	0.418536i	0.184821	+	0.982772i	$0.440829\pi$
$758$	10.5403	+	21.0734i	0.382840	+	0.765422i
$759$	49.2233	−	49.2233i	1.78669	−	1.78669i
$760$	30.3567	+	19.5498i	1.10115	+	0.709146i
$761$	−15.3006	−	15.3006i	−0.554645	−	0.554645i	0.373133	−	0.927778i	$-0.378284\pi$
$761$	−15.3006	−	15.3006i	−0.554645	−	0.554645i	−0.927778	+	0.373133i	$0.878284\pi$
$762$	−3.59465	+	10.7888i	−0.130220	+	0.390837i
$763$	−0.373959	+	0.902816i	−0.0135382	+	0.0326841i
$764$	−0.156160	−	1.09101i	−0.00564967	−	0.0394715i
$765$	6.39346	−	2.64826i	0.231156	−	0.0957480i
$766$	31.9390	−	36.8360i	1.15400	−	1.33094i
$767$	−4.98454			−0.179981
$768$	−13.3273	+	19.0917i	−0.480907	+	0.688911i
$769$	15.4924			0.558671			0.279336	−	0.960194i	$-0.409886\pi$
$769$	15.4924			0.558671			0.279336	+	0.960194i	$0.409886\pi$
$770$	−8.04426	+	9.27764i	−0.289895	+	0.334343i
$771$	−33.2357	+	13.7667i	−1.19696	+	0.495795i
$772$	1.20029	+	8.38585i	0.0431994	+	0.301813i
$773$	−7.51163	+	18.1347i	−0.270175	+	0.652259i	−0.999490	−	0.0319178i	$-0.989839\pi$
$773$	−7.51163	+	18.1347i	−0.270175	+	0.652259i	0.729316	+	0.684177i	$0.239839\pi$
$774$	1.65642	−	4.97150i	0.0595388	−	0.178697i
$775$	5.75623	+	5.75623i	0.206770	+	0.206770i
$776$	−28.4173	−	18.3008i	−1.02012	−	0.656961i
$777$	0.631522	−	0.631522i	0.0226557	−	0.0226557i
$778$	10.1713	+	20.3358i	0.364660	+	0.729073i
$779$	−3.14471	−	1.30258i	−0.112671	−	0.0466698i
$780$	2.42772	+	4.09761i	0.0869264	+	0.146718i
$781$	−24.9166	−	60.1541i	−0.891587	−	2.15248i
$782$	−60.9503	+	4.33987i	−2.17958	+	0.155194i
$783$		−	39.7458i		−	1.42040i
$784$	−1.12207	−	3.83939i	−0.0400741	−	0.137121i
$785$		−	20.4689i		−	0.730567i
$786$	1.08647	+	15.2587i	0.0387532	+	0.544260i
$787$	−2.68866	−	6.49099i	−0.0958402	−	0.231379i	0.868687	−	0.495361i	$-0.164964\pi$
$787$	−2.68866	−	6.49099i	−0.0958402	−	0.231379i	−0.964528	+	0.263982i	$0.914964\pi$
$788$	−24.3603	−	6.23402i	−0.867801	−	0.222078i
$789$	38.4247	+	15.9160i	1.36796	+	0.566626i
$790$	−4.46125	+	2.23138i	−0.158724	+	0.0793889i
$791$	−11.5572	+	11.5572i	−0.410927	+	0.410927i
$792$	−13.6285	−	2.47221i	−0.484269	−	0.0878463i
$793$	−0.566481	−	0.566481i	−0.0201163	−	0.0201163i
$794$	25.4012	+	8.46324i	0.901454	+	0.300349i
$795$	−0.344117	+	0.830771i	−0.0122046	+	0.0294644i
$796$	3.61687	−	4.82521i	0.128197	−	0.171025i
$797$	34.2345	−	14.1804i	1.21265	−	0.502296i	0.317583	−	0.948230i	$-0.397129\pi$
$797$	34.2345	−	14.1804i	1.21265	−	0.502296i	0.895065	+	0.445935i	$0.147129\pi$
$798$	12.6869	+	11.0003i	0.449111	+	0.389406i
$799$	−61.2386			−2.16646
$800$	13.5350	−	5.02393i	0.478534	−	0.177623i
$801$	4.73637			0.167351
$802$	36.0952	+	31.2967i	1.27457	+	1.10512i
$803$	−1.95944	+	0.811625i	−0.0691470	+	0.0286416i
$804$	−21.3777	−	16.0243i	−0.753935	−	0.565133i
$805$	−5.16081	+	12.4593i	−0.181895	+	0.439133i
$806$	−4.47628	−	1.49142i	−0.157670	−	0.0525331i
$807$	−13.2033	−	13.2033i	−0.464780	−	0.464780i
$808$	39.8034	−	27.5801i	1.40028	−	0.970264i
$809$	−20.9069	+	20.9069i	−0.735047	+	0.735047i	−0.971615	−	0.236568i	$-0.923977\pi$
$809$	−20.9069	+	20.9069i	−0.735047	+	0.735047i	0.236568	+	0.971615i	$0.423977\pi$
$810$	−11.0307	+	5.51722i	−0.387580	+	0.193856i
$811$	−34.0094	−	14.0871i	−1.19423	−	0.494667i	−0.305100	−	0.952320i	$-0.598690\pi$
$811$	−34.0094	−	14.0871i	−1.19423	−	0.494667i	−0.889131	+	0.457654i	$0.848690\pi$
$812$	3.48826	−	13.6309i	0.122414	−	0.478351i
$813$	−8.57264	−	20.6962i	−0.300656	−	0.725847i
$814$	−0.342116	−	4.80476i	−0.0119911	−	0.168407i
$815$		−	18.4477i		−	0.646195i
$816$	−18.2794	−	22.7422i	−0.639908	−	0.796137i
$817$			34.2633i			1.19872i
$818$	20.9314	−	1.49039i	0.731851	−	0.0521103i
$819$	−0.353200	−	0.852699i	−0.0123418	−	0.0297957i
$820$	1.12304	−	0.665370i	0.0392182	−	0.0232357i
$821$	15.9073	+	6.58901i	0.555168	+	0.229958i	0.642586	−	0.766214i	$-0.277862\pi$
$821$	15.9073	+	6.58901i	0.555168	+	0.229958i	−0.0874180	+	0.996172i	$0.527862\pi$
$822$	3.64633	+	7.29020i	0.127180	+	0.254275i
$823$	11.8085	−	11.8085i	0.411618	−	0.411618i	−0.470684	−	0.882302i	$-0.655993\pi$
$823$	11.8085	−	11.8085i	0.411618	−	0.411618i	0.882302	+	0.470684i	$0.155993\pi$
$824$	−3.87789	−	17.9081i	−0.135093	−	0.623860i
$825$	−14.5745	−	14.5745i	−0.507419	−	0.507419i
$826$	2.13032	−	6.39383i	0.0741232	−	0.222470i
$827$	−10.8613	+	26.2215i	−0.377685	+	0.911812i	0.614714	+	0.788750i	$0.289271\pi$
$827$	−10.8613	+	26.2215i	−0.377685	+	0.911812i	−0.992399	+	0.123062i	$0.960729\pi$
$828$	−15.0583	+	2.15533i	−0.523312	+	0.0749031i
$829$	−1.99769	+	0.827469i	−0.0693826	+	0.0287392i	−0.417105	−	0.908858i	$-0.636955\pi$
$829$	−1.99769	+	0.827469i	−0.0693826	+	0.0287392i	0.347722	+	0.937598i	$0.386955\pi$
$830$	8.77984	−	10.1260i	0.304753	−	0.351479i
$831$	−14.0977			−0.489043
$832$	−5.71356	+	6.11349i	−0.198082	+	0.211947i
$833$	5.01268			0.173679
$834$	−4.17568	+	4.81591i	−0.144592	+	0.166761i
$835$	9.49507	−	3.93299i	0.328591	−	0.136107i
$836$	89.6517	−	12.8321i	3.10067	−	0.443807i
$837$	6.89610	−	16.6487i	0.238364	−	0.575462i
$838$	14.9310	−	44.8130i	0.515781	−	1.54804i
$839$	−2.13968	−	2.13968i	−0.0738701	−	0.0738701i	0.669206	−	0.743077i	$-0.266634\pi$
$839$	−2.13968	−	2.13968i	−0.0738701	−	0.0738701i	−0.743077	+	0.669206i	$0.766634\pi$
$840$	−6.29371	+	1.36286i	−0.217154	+	0.0470231i
$841$	14.4902	−	14.4902i	0.499663	−	0.499663i
$842$	−15.1975	−	30.3847i	−0.523740	−	1.04713i
$843$	−19.0278	−	7.88159i	−0.655354	−	0.271456i
$844$	−29.1187	+	17.2520i	−1.00231	+	0.593839i
$845$	−7.12842	−	17.2095i	−0.245225	−	0.592026i
$846$	−15.2066	+	1.08276i	−0.522814	+	0.0372262i
$847$			19.7998i			0.680329i
$848$	−1.57057	−	0.170864i	−0.0539337	−	0.00586751i
$849$		−	46.4852i		−	1.59537i
$850$	1.28499	+	18.0467i	0.0440748	+	0.618997i
$851$	−2.02446	−	4.88748i	−0.0693976	−	0.167541i
$852$	8.46523	−	33.0791i	0.290014	−	1.13327i
$853$	8.37993	+	3.47108i	0.286923	+	0.118848i	0.521503	−	0.853249i	$-0.325371\pi$
$853$	8.37993	+	3.47108i	0.286923	+	0.118848i	−0.234580	+	0.972097i	$0.575371\pi$
$854$	0.968749	−	0.484538i	0.0331499	−	0.0165805i
$855$	−7.96515	+	7.96515i	−0.272402	+	0.272402i
$856$	4.04505	+	5.83780i	0.138257	+	0.199532i
$857$	−16.8955	−	16.8955i	−0.577139	−	0.577139i	0.356975	−	0.934114i	$-0.383808\pi$
$857$	−16.8955	−	16.8955i	−0.577139	−	0.577139i	−0.934114	+	0.356975i	$0.883808\pi$
$858$	11.3337	+	3.77621i	0.386927	+	0.128918i
$859$	9.07000	−	21.8969i	0.309465	−	0.747113i	−0.690258	−	0.723563i	$-0.742503\pi$
$859$	9.07000	−	21.8969i	0.309465	−	0.747113i	0.999723	−	0.0235502i	$-0.00749697\pi$
$860$	−10.5140	−	7.88107i	−0.358525	−	0.268742i
$861$	0.560848	−	0.232311i	0.0191136	−	0.00791713i
$862$	−14.2277	−	12.3363i	−0.484599	−	0.420175i
$863$	−21.4642			−0.730649			−0.365324	−	0.930880i	$-0.619042\pi$
$863$	−21.4642			−0.730649			−0.365324	+	0.930880i	$0.619042\pi$
$864$	−21.7406	−	23.4252i	−0.739631	−	0.796943i
$865$	2.80020			0.0952098
$866$	15.0912	+	13.0849i	0.512819	+	0.444644i
$867$	10.9261	−	4.52576i	0.371071	−	0.153703i
$868$	3.82619	−	5.10446i	0.129869	−	0.173257i
$869$	−4.78795	+	11.5591i	−0.162420	+	0.392117i
$870$	−21.4900	−	7.16012i	−0.728581	−	0.242751i
$871$	−6.78947	−	6.78947i	−0.230052	−	0.230052i
$872$	−0.493327	+	2.71956i	−0.0167062	+	0.0920959i
$873$	7.45627	−	7.45627i	0.252357	−	0.252357i
$874$	88.9565	−	44.4933i	3.00900	−	1.50501i
$875$	10.9163	+	4.52170i	0.369040	+	0.152861i
$876$	−1.07751	−	0.275744i	−0.0364056	−	0.00931651i
$877$	17.1011	+	41.2856i	0.577462	+	1.39412i	0.895083	+	0.445899i	$0.147116\pi$
$877$	17.1011	+	41.2856i	0.577462	+	1.39412i	−0.317621	+	0.948218i	$0.602884\pi$
$878$	0.570098	+	8.00660i	0.0192399	+	0.270210i
$879$		−	33.8101i		−	1.14039i
$880$	−16.6836	+	30.4620i	−0.562404	+	1.02687i
$881$			52.2398i			1.76000i	0.474971	+	0.880001i	$0.342458\pi$
$881$			52.2398i			1.76000i	−0.474971	+	0.880001i	$0.657542\pi$
$882$	1.24474	−	0.0886297i	0.0419125	−	0.00298432i
$883$	4.55525	+	10.9973i	0.153296	+	0.370090i	0.981807	−	0.189884i	$-0.0608112\pi$
$883$	4.55525	+	10.9973i	0.153296	+	0.370090i	−0.828510	+	0.559974i	$0.810811\pi$
$884$	−5.34511	−	9.02170i	−0.179775	−	0.303433i
$885$	−10.0238	−	4.15200i	−0.336947	−	0.139568i
$886$	9.94090	+	19.8751i	0.333971	+	0.667717i
$887$	−36.5879	+	36.5879i	−1.22850	+	1.22850i	−0.263970	+	0.964531i	$0.585032\pi$
$887$	−36.5879	+	36.5879i	−1.22850	+	1.22850i	−0.964531	+	0.263970i	$0.914968\pi$
$888$	1.36772	−	2.12378i	0.0458978	−	0.0712695i
$889$	−3.90732	−	3.90732i	−0.131047	−	0.131047i
$890$	3.75416	−	11.2676i	0.125840	−	0.377690i
$891$	−11.8385	+	28.5807i	−0.396605	+	0.957490i
$892$	−0.609915	−	4.26119i	−0.0204215	−	0.142675i
$893$	92.0935	−	38.1464i	3.08179	−	1.27652i
$894$	−7.31745	+	8.43939i	−0.244732	+	0.282255i
$895$	10.8022			0.361079
$896$	−5.40009	−	9.94178i	−0.180404	−	0.332132i
$897$	13.1199			0.438062
$898$	−5.04895	+	5.82308i	−0.168486	+	0.194319i
$899$	20.7313	−	8.58718i	0.691427	−	0.286398i
$900$	0.638172	+	4.45860i	0.0212724	+	0.148620i
$901$	0.757640	−	1.82911i	0.0252407	−	0.0609363i
$902$	1.03495	−	3.10625i	0.0344601	−	0.103427i
$903$	−4.32094	−	4.32094i	−0.143792	−	0.143792i
$904$	−25.0301	+	38.8664i	−0.832488	+	1.29268i
$905$	−20.0251	+	20.0251i	−0.665657	+	0.665657i
$906$	−2.55406	−	5.10640i	−0.0848531	−	0.169649i
$907$	18.1029	+	7.49848i	0.601098	+	0.248983i	0.662417	−	0.749135i	$-0.269531\pi$
$907$	18.1029	+	7.49848i	0.601098	+	0.248983i	−0.0613190	+	0.998118i	$0.519531\pi$
$908$	13.6304	+	23.0059i	0.452339	+	0.763478i
$909$	5.78129	+	13.9573i	0.191753	+	0.462933i
$910$	−2.30848	+	0.164372i	−0.0765254	+	0.00544888i
$911$			18.1269i			0.600573i	0.953849	+	0.300286i	$0.0970822\pi$
$911$			18.1269i			0.600573i	−0.953849	+	0.300286i	$0.902918\pi$
$912$	41.6559	+	22.8143i	1.37937	+	0.755457i
$913$		−	33.6162i		−	1.11253i
$914$	0.143199	+	2.01112i	0.00473659	+	0.0665218i
$915$	−0.667318	−	1.61105i	−0.0220608	−	0.0532596i
$916$	−13.7689	−	3.52357i	−0.454936	−	0.116422i
$917$	−6.86741	−	2.84458i	−0.226782	−	0.0939362i
$918$	35.8198	−	17.9159i	1.18223	−	0.591314i
$919$	30.0241	−	30.0241i	0.990403	−	0.990403i	−0.00955166	−	0.999954i	$-0.503040\pi$
$919$	30.0241	−	30.0241i	0.990403	−	0.990403i	0.999954	+	0.00955166i	$0.00304044\pi$
$920$	−6.80816	+	37.5312i	−0.224458	+	1.23737i
$921$	13.1957	+	13.1957i	0.434814	+	0.434814i
$922$	23.2760	+	7.75517i	0.766554	+	0.255403i
$923$	4.69608	−	11.3373i	0.154573	−	0.373173i
$924$	−9.68772	+	12.9242i	−0.318703	+	0.425176i
$925$	−1.44713	+	0.599421i	−0.0475813	+	0.0197088i
$926$	30.6509	+	26.5761i	1.00725	+	0.873346i
$927$	5.71633			0.187749
$928$	1.48332	−	39.7687i	0.0486923	−	1.30547i
$929$	14.5189			0.476351			0.238176	−	0.971222i	$-0.423451\pi$
$929$	14.5189			0.476351			0.238176	+	0.971222i	$0.423451\pi$
$930$	−7.75940	−	6.72786i	−0.254441	−	0.220615i
$931$	−7.53831	+	3.12247i	−0.247058	+	0.102335i
$932$	−26.6581	−	19.9823i	−0.873215	−	0.654543i
$933$	2.13663	−	5.15829i	0.0699503	−	0.168875i
$934$	−52.2440	−	17.4068i	−1.70948	−	0.569569i
$935$	−30.7765	−	30.7765i	−1.00650	−	1.00650i
$936$	−1.48680	−	2.14574i	−0.0485975	−	0.0701357i
$937$	−9.65050	+	9.65050i	−0.315268	+	0.315268i	−0.846946	−	0.531678i	$-0.821562\pi$
$937$	−9.65050	+	9.65050i	−0.315268	+	0.315268i	0.531678	+	0.846946i	$0.321562\pi$
$938$	11.6108	−	5.80735i	0.379106	−	0.189617i
$939$	27.0201	+	11.1921i	0.881767	+	0.365240i
$940$	−9.47731	+	37.0339i	−0.309116	+	1.20791i
$941$	−10.0355	−	24.2279i	−0.327149	−	0.789808i	−0.998802	−	0.0489415i	$-0.984415\pi$
$941$	−10.0355	−	24.2279i	−0.327149	−	0.789808i	0.671653	−	0.740866i	$-0.265585\pi$
$942$	−1.91226	−	26.8562i	−0.0623048	−	0.875024i
$943$		−	3.59580i		−	0.117095i
$944$	2.06159	−	18.9500i	0.0670992	−	0.616771i
$945$		−	8.83918i		−	0.287538i
$946$	−32.8747	+	2.34079i	−1.06885	+	0.0761057i
$947$	−1.76274	−	4.25564i	−0.0572815	−	0.138290i	0.892648	−	0.450755i	$-0.148845\pi$
$947$	−1.76274	−	4.25564i	−0.0572815	−	0.138290i	−0.949929	+	0.312465i	$0.898845\pi$
$948$	−5.64492	+	3.34446i	−0.183338	+	0.108623i
$949$	−0.369298	−	0.152968i	−0.0119879	−	0.00496556i
$950$	−13.1740	−	26.3391i	−0.427421	−	0.854553i
$951$	−14.4684	+	14.4684i	−0.469170	+	0.469170i
$952$	13.8568	−	3.00060i	0.449103	−	0.0972502i
$953$	15.0438	+	15.0438i	0.487318	+	0.487318i	0.907459	−	0.420141i	$-0.138019\pi$
$953$	15.0438	+	15.0438i	0.487318	+	0.487318i	−0.420141	+	0.907459i	$0.638019\pi$
$954$	0.155795	−	0.467595i	0.00504405	−	0.0151389i
$955$	0.329939	−	0.796543i	0.0106766	−	0.0257755i
$956$	−22.0301	+	3.15323i	−0.712506	+	0.101983i
$957$	−52.4905	+	21.7423i	−1.69678	+	0.702829i
$958$	14.2271	−	16.4084i	0.459656	−	0.530132i
$959$	−3.96083			−0.127902
$960$	−16.5823	+	7.53487i	−0.535190	+	0.243187i
$961$	−20.8262			−0.671813
$962$	0.594734	−	0.685921i	0.0191750	−	0.0221150i
$963$	−2.04705	+	0.847916i	−0.0659653	+	0.0273237i
$964$	1.32948	−	0.190292i	0.0428198	−	0.00612891i
$965$	−2.53600	+	6.12246i	−0.0816369	+	0.197089i
$966$	−5.60726	+	16.8294i	−0.180411	+	0.541476i
$967$	−11.1469	−	11.1469i	−0.358460	−	0.358460i	0.504785	−	0.863245i	$-0.331572\pi$
$967$	−11.1469	−	11.1469i	−0.358460	−	0.358460i	−0.863245	+	0.504785i	$0.831572\pi$
$968$	11.8522	+	54.7337i	0.380945	+	1.75921i
$969$	−42.0859	+	42.0859i	−1.35199	+	1.35199i
$970$	−11.8280	−	23.6481i	−0.379776	−	0.759295i
$971$	21.5034	+	8.90699i	0.690076	+	0.285839i	0.700032	−	0.714112i	$-0.253169\pi$
$971$	21.5034	+	8.90699i	0.690076	+	0.285839i	−0.00995589	+	0.999950i	$0.503169\pi$
$972$	15.2062	−	9.00927i	0.487740	−	0.288973i
$973$	−1.18528	−	2.86152i	−0.0379984	−	0.0917361i
$974$	−37.8757	+	2.69689i	−1.21362	+	0.0864138i
$975$		−	3.88467i		−	0.124409i
$976$	2.38792	−	1.91933i	0.0764355	−	0.0614363i
$977$		−	24.1273i		−	0.771901i	−0.922520	−	0.385950i	$-0.873874\pi$
$977$		−	24.1273i		−	0.771901i	0.922520	−	0.385950i	$-0.126126\pi$
$978$	−1.72343	−	24.2043i	−0.0551092	−	0.773968i
$979$	−11.3998	−	27.5216i	−0.364340	−	0.879594i
$980$	0.775765	−	3.03141i	0.0247809	−	0.0968349i
$981$	−0.796636	−	0.329977i	−0.0254346	−	0.0105354i
$982$	−6.35305	+	3.17760i	−0.202734	+	0.101401i
$983$	−37.8385	+	37.8385i	−1.20686	+	1.20686i	−0.234822	+	0.972038i	$0.575451\pi$
$983$	−37.8385	+	37.8385i	−1.20686	+	1.20686i	−0.972038	+	0.234822i	$0.924549\pi$
$984$	1.41132	−	0.977915i	0.0449913	−	0.0311748i
$985$	−13.9092	−	13.9092i	−0.443184	−	0.443184i
$986$	47.3145	+	15.7644i	1.50680	+	0.502041i
$987$	−6.80327	+	16.4245i	−0.216550	+	0.522799i
$988$	13.6580	+	10.2377i	0.434518	+	0.325705i
$989$	−33.4406	+	13.8516i	−1.06335	+	0.440454i
$990$	−8.18650	−	7.09818i	−0.260184	−	0.225595i
$991$	−34.6491			−1.10066			−0.550332	−	0.834946i	$-0.685499\pi$
$991$	−34.6491			−1.10066			−0.550332	+	0.834946i	$0.685499\pi$
$992$	7.52142	−	16.4009i	0.238805	−	0.520730i
$993$	−24.5225			−0.778199
$994$	12.5357	+	10.8692i	0.397609	+	0.344750i
$995$	4.35826	−	1.80525i	0.138166	−	0.0572303i
$996$	10.5736	−	14.1061i	0.335037	−	0.446967i
$997$	−5.37980	+	12.9880i	−0.170380	+	0.411334i	−0.985887	−	0.167414i	$-0.946458\pi$
$997$	−5.37980	+	12.9880i	−0.170380	+	0.411334i	0.815507	+	0.578748i	$0.196458\pi$
$998$	39.6362	+	13.2061i	1.25466	+	0.418032i
$999$	2.45182	+	2.45182i	0.0775720	+	0.0775720i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.2.u.c.85.4	yes	52
4.3	odd	2		896.2.u.c.561.10		52
32.3	odd	8		896.2.u.c.337.10		52
32.29	even	8	inner	224.2.u.c.29.4	✓	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.u.c.29.4	✓	52	32.29	even	8	inner
224.2.u.c.85.4	yes	52	1.1	even	1	trivial
896.2.u.c.337.10		52	32.3	odd	8
896.2.u.c.561.10		52	4.3	odd	2

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:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	224.u (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.926451 + 1.06850i) q^{2} +(-1.34443 + 0.556881i) q^{3} +(-0.283377 - 1.97982i) q^{4} +(0.598728 - 1.44546i) q^{5} +(0.650522 - 1.95244i) q^{6} +(0.707107 + 0.707107i) q^{7} +(2.37797 + 1.53142i) q^{8} +(-0.623944 + 0.623944i) q^{9} +O(q^{10})\)	\(q+(-0.926451 + 1.06850i) q^{2} +(-1.34443 + 0.556881i) q^{3} +(-0.283377 - 1.97982i) q^{4} +(0.598728 - 1.44546i) q^{5} +(0.650522 - 1.95244i) q^{6} +(0.707107 + 0.707107i) q^{7} +(2.37797 + 1.53142i) q^{8} +(-0.623944 + 0.623944i) q^{9} +(0.989776 + 1.97888i) q^{10} +(5.12731 + 2.12380i) q^{11} +(1.48351 + 2.50393i) q^{12} +(0.400276 + 0.966351i) q^{13} +(-1.41064 + 0.100443i) q^{14} +2.27674i q^{15} +(-3.83939 + 1.12207i) q^{16} -5.01268i q^{17} +(-0.0886297 - 1.24474i) q^{18} +(3.12247 + 7.53831i) q^{19} +(-3.03141 - 0.775765i) q^{20} +(-1.34443 - 0.556881i) q^{21} +(-7.01947 + 3.51092i) q^{22} +(-6.09500 + 6.09500i) q^{23} +(-4.04984 - 0.734639i) q^{24} +(1.80466 + 1.80466i) q^{25} +(-1.40338 - 0.467583i) q^{26} +(2.16203 - 5.21960i) q^{27} +(1.19957 - 1.60032i) q^{28} +(6.49956 - 2.69221i) q^{29} +(-2.43269 - 2.10928i) q^{30} +3.18964 q^{31} +(2.35808 - 5.14193i) q^{32} -8.07601 q^{33} +(5.35604 + 4.64400i) q^{34} +(1.44546 - 0.598728i) q^{35} +(1.41211 + 1.05849i) q^{36} +(-0.234866 + 0.567017i) q^{37} +(-10.9475 - 3.64752i) q^{38} +(-1.07629 - 1.07629i) q^{39} +(3.63736 - 2.52035i) q^{40} +(-0.294979 + 0.294979i) q^{41} +(1.84058 - 0.920598i) q^{42} +(3.87959 + 1.60698i) q^{43} +(2.75178 - 10.7530i) q^{44} +(0.528312 + 1.27546i) q^{45} +(-0.865779 - 12.1592i) q^{46} -12.2167i q^{47} +(4.53694 - 3.64664i) q^{48} +1.00000i q^{49} +(-3.60021 + 0.256348i) q^{50} +(2.79147 + 6.73920i) q^{51} +(1.79978 - 1.06632i) q^{52} +(0.364896 + 0.151145i) q^{53} +(3.57412 + 7.14583i) q^{54} +(6.13972 - 6.13972i) q^{55} +(0.598603 + 2.76436i) q^{56} +(-8.39589 - 8.39589i) q^{57} +(-3.14491 + 9.43897i) q^{58} +(-1.82366 + 4.40271i) q^{59} +(4.50753 - 0.645175i) q^{60} +(-0.707613 + 0.293103i) q^{61} +(-2.95505 + 3.40813i) q^{62} -0.882391 q^{63} +(3.30950 + 7.28335i) q^{64} +1.63648 q^{65} +(7.48203 - 8.62920i) q^{66} +(-8.48098 + 3.51294i) q^{67} +(-9.92422 + 1.42048i) q^{68} +(4.80011 - 11.5885i) q^{69} +(-0.699405 + 2.09916i) q^{70} +(-8.29584 - 8.29584i) q^{71} +(-2.43924 + 0.528201i) q^{72} +(-0.270226 + 0.270226i) q^{73} +(-0.388265 - 0.776267i) q^{74} +(-3.43123 - 1.42126i) q^{75} +(14.0397 - 8.31812i) q^{76} +(2.12380 + 5.12731i) q^{77} +(2.14714 - 0.152884i) q^{78} +2.25443i q^{79} +(-0.676843 + 6.22149i) q^{80} +5.57422i q^{81} +(-0.0419011 - 0.588469i) q^{82} +(-2.31800 - 5.59616i) q^{83} +(-0.721545 + 2.81954i) q^{84} +(-7.24561 - 3.00123i) q^{85} +(-5.31131 + 2.65655i) q^{86} +(-7.23897 + 7.23897i) q^{87} +(8.94016 + 12.9024i) q^{88} +(-3.79550 - 3.79550i) q^{89} +(-1.85228 - 0.617148i) q^{90} +(-0.400276 + 0.966351i) q^{91} +(13.7942 + 10.3398i) q^{92} +(-4.28825 + 1.77625i) q^{93} +(13.0536 + 11.3182i) q^{94} +12.7658 q^{95} +(-0.306823 + 8.22614i) q^{96} -11.9502 q^{97} +(-1.06850 - 0.926451i) q^{98} +(-4.52429 + 1.87402i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 20 q^{6}+O(q^{10}) \) 52 * q - 20 * q^6	\( 52 q - 20 q^{6} - 8 q^{10} + 12 q^{12} - 12 q^{16} - 20 q^{18} + 20 q^{22} - 20 q^{23} - 8 q^{24} + 20 q^{26} - 24 q^{27} - 8 q^{28} + 20 q^{30} + 60 q^{32} - 48 q^{33} + 48 q^{34} + 8 q^{36} - 60 q^{38} - 24 q^{39} + 20 q^{40} - 44 q^{43} + 32 q^{44} + 40 q^{45} - 32 q^{46} - 84 q^{48} - 124 q^{50} + 16 q^{51} - 32 q^{52} - 36 q^{53} + 96 q^{54} + 32 q^{55} + 16 q^{56} + 4 q^{58} - 92 q^{60} - 32 q^{61} + 12 q^{62} + 68 q^{63} + 48 q^{64} + 80 q^{65} + 16 q^{66} + 28 q^{67} - 4 q^{68} - 32 q^{69} + 8 q^{70} - 88 q^{72} + 36 q^{74} + 32 q^{75} + 96 q^{76} - 12 q^{77} + 12 q^{78} - 108 q^{80} - 96 q^{82} + 64 q^{85} + 76 q^{86} - 56 q^{87} + 104 q^{88} - 132 q^{90} + 32 q^{92} - 4 q^{94} - 64 q^{95} + 8 q^{96} - 72 q^{97} - 64 q^{99}+O(q^{100}) \) 52 * q - 20 * q^6 - 8 * q^10 + 12 * q^12 - 12 * q^16 - 20 * q^18 + 20 * q^22 - 20 * q^23 - 8 * q^24 + 20 * q^26 - 24 * q^27 - 8 * q^28 + 20 * q^30 + 60 * q^32 - 48 * q^33 + 48 * q^34 + 8 * q^36 - 60 * q^38 - 24 * q^39 + 20 * q^40 - 44 * q^43 + 32 * q^44 + 40 * q^45 - 32 * q^46 - 84 * q^48 - 124 * q^50 + 16 * q^51 - 32 * q^52 - 36 * q^53 + 96 * q^54 + 32 * q^55 + 16 * q^56 + 4 * q^58 - 92 * q^60 - 32 * q^61 + 12 * q^62 + 68 * q^63 + 48 * q^64 + 80 * q^65 + 16 * q^66 + 28 * q^67 - 4 * q^68 - 32 * q^69 + 8 * q^70 - 88 * q^72 + 36 * q^74 + 32 * q^75 + 96 * q^76 - 12 * q^77 + 12 * q^78 - 108 * q^80 - 96 * q^82 + 64 * q^85 + 76 * q^86 - 56 * q^87 + 104 * q^88 - 132 * q^90 + 32 * q^92 - 4 * q^94 - 64 * q^95 + 8 * q^96 - 72 * q^97 - 64 * q^99

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