LMFDB - Embedded newform 475.2.n.a.39.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(39,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([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("475.39");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.n (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			39.18
Character	$\chi$	$=$	475.39
Dual form			475.2.n.a.134.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.30771 + 1.79991i) q^{2} +(1.66715 + 0.541690i) q^{3} +(-0.911532 + 2.80541i) q^{4} +(0.941634 - 2.02813i) q^{5} +(1.20516 + 3.70909i) q^{6} +2.10218i q^{7} +(-2.00966 + 0.652977i) q^{8} +(0.0589103 + 0.0428008i) q^{9} +O(q^{10})$	\(q+(1.30771 + 1.79991i) q^{2} +(1.66715 + 0.541690i) q^{3} +(-0.911532 + 2.80541i) q^{4} +(0.941634 - 2.02813i) q^{5} +(1.20516 + 3.70909i) q^{6} +2.10218i q^{7} +(-2.00966 + 0.652977i) q^{8} +(0.0589103 + 0.0428008i) q^{9} +(4.88184 - 0.957357i) q^{10} +(-0.0717015 + 0.0520942i) q^{11} +(-3.03932 + 4.18327i) q^{12} +(-0.213960 + 0.294491i) q^{13} +(-3.78374 + 2.74904i) q^{14} +(2.66846 - 2.87113i) q^{15} +(0.969497 + 0.704381i) q^{16} +(-2.37019 + 0.770120i) q^{17} +0.162004i q^{18} +(-0.309017 - 0.951057i) q^{19} +(4.83141 + 4.49037i) q^{20} +(-1.13873 + 3.50465i) q^{21} +(-0.187530 - 0.0609321i) q^{22} +(-0.469874 - 0.646726i) q^{23} -3.70411 q^{24} +(-3.22665 - 3.81952i) q^{25} -0.809854 q^{26} +(-3.01604 - 4.15122i) q^{27} +(-5.89747 - 1.91621i) q^{28} +(-0.337920 + 1.04001i) q^{29} +(8.65735 + 1.04839i) q^{30} +(-1.12049 - 3.44851i) q^{31} +6.89228i q^{32} +(-0.147756 + 0.0480089i) q^{33} +(-4.48566 - 3.25903i) q^{34} +(4.26351 + 1.97948i) q^{35} +(-0.173772 + 0.126253i) q^{36} +(1.01952 - 1.40325i) q^{37} +(1.30771 - 1.79991i) q^{38} +(-0.516226 + 0.375060i) q^{39} +(-0.568035 + 4.69071i) q^{40} +(6.67174 + 4.84730i) q^{41} +(-7.79718 + 2.53346i) q^{42} -10.6031i q^{43} +(-0.0807872 - 0.248637i) q^{44} +(0.142278 - 0.0791752i) q^{45} +(0.549589 - 1.69146i) q^{46} +(-10.6917 - 3.47394i) q^{47} +(1.23474 + 1.69947i) q^{48} +2.58083 q^{49} +(2.65526 - 10.8025i) q^{50} -4.36862 q^{51} +(-0.631135 - 0.868682i) q^{52} +(-2.21559 - 0.719890i) q^{53} +(3.52771 - 10.8572i) q^{54} +(0.0381375 + 0.194474i) q^{55} +(-1.37268 - 4.22466i) q^{56} -1.75295i q^{57} +(-2.31383 + 0.751808i) q^{58} +(0.904332 + 0.657036i) q^{59} +(5.62230 + 10.1033i) q^{60} +(3.19589 - 2.32195i) q^{61} +(4.74174 - 6.52644i) q^{62} +(-0.0899751 + 0.123840i) q^{63} +(-10.4665 + 7.60435i) q^{64} +(0.395795 + 0.711242i) q^{65} +(-0.279634 - 0.203166i) q^{66} +(-6.29348 + 2.04488i) q^{67} -7.35133i q^{68} +(-0.433026 - 1.33272i) q^{69} +(2.01254 + 10.2625i) q^{70} +(0.117287 - 0.360973i) q^{71} +(-0.146337 - 0.0475479i) q^{72} +(3.75393 + 5.16684i) q^{73} +3.85897 q^{74} +(-3.31032 - 8.11555i) q^{75} +2.94978 q^{76} +(-0.109512 - 0.150730i) q^{77} +(-1.35015 - 0.438690i) q^{78} +(-0.267556 + 0.823453i) q^{79} +(2.34149 - 1.30300i) q^{80} +(-2.84702 - 8.76223i) q^{81} +18.3474i q^{82} +(-6.99896 + 2.27410i) q^{83} +(-8.79398 - 6.38920i) q^{84} +(-0.669940 + 5.53223i) q^{85} +(19.0846 - 13.8658i) q^{86} +(-1.12673 + 1.55081i) q^{87} +(0.110079 - 0.151511i) q^{88} +(-1.98297 + 1.44071i) q^{89} +(0.328566 + 0.152549i) q^{90} +(-0.619073 - 0.449783i) q^{91} +(2.24263 - 0.728676i) q^{92} -6.35615i q^{93} +(-7.72886 - 23.7870i) q^{94} +(-2.21985 - 0.268819i) q^{95} +(-3.73348 + 11.4905i) q^{96} +(1.79481 + 0.583169i) q^{97} +(3.37498 + 4.64526i) q^{98} -0.00645363 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 16 q^{4} - 3 q^{5} + 6 q^{6} + 8 q^{9}+O(q^{10}) $ 80 * q + 16 * q^4 - 3 * q^5 + 6 * q^6 + 8 * q^9	$ 80 q + 16 q^{4} - 3 q^{5} + 6 q^{6} + 8 q^{9} - 36 q^{10} + 20 q^{11} + 45 q^{12} - 10 q^{14} - 20 q^{16} - 15 q^{17} + 20 q^{19} + 12 q^{20} + 16 q^{21} + 15 q^{23} + 72 q^{24} + 41 q^{25} - 84 q^{26} + 15 q^{27} + 30 q^{28} - 24 q^{29} - 40 q^{30} + 8 q^{31} - 75 q^{33} - 24 q^{34} - 33 q^{35} - 32 q^{36} - 15 q^{37} - 30 q^{39} - 28 q^{40} + 13 q^{41} - 130 q^{42} - 24 q^{44} + 6 q^{45} + 30 q^{46} + 145 q^{48} - 28 q^{49} + 77 q^{50} - 36 q^{51} - 5 q^{52} - 10 q^{53} + 15 q^{54} - 8 q^{55} + 48 q^{56} - 60 q^{58} - 19 q^{59} - 110 q^{60} + 8 q^{61} + 110 q^{62} + 55 q^{63} + 16 q^{64} - 43 q^{65} - 17 q^{66} - 65 q^{67} - 42 q^{69} + 4 q^{70} + 18 q^{71} + 100 q^{73} + 22 q^{74} + 115 q^{75} + 64 q^{76} - 145 q^{78} - 16 q^{79} - 97 q^{80} + q^{81} - 70 q^{83} - 46 q^{84} - 16 q^{85} + 64 q^{86} + 10 q^{87} + 30 q^{88} + 4 q^{89} - 8 q^{90} + 16 q^{91} - 135 q^{92} + 38 q^{94} - 2 q^{95} + 50 q^{96} + 150 q^{97} + 130 q^{98} + 178 q^{99}+O(q^{100}) $ 80 * q + 16 * q^4 - 3 * q^5 + 6 * q^6 + 8 * q^9 - 36 * q^10 + 20 * q^11 + 45 * q^12 - 10 * q^14 - 20 * q^16 - 15 * q^17 + 20 * q^19 + 12 * q^20 + 16 * q^21 + 15 * q^23 + 72 * q^24 + 41 * q^25 - 84 * q^26 + 15 * q^27 + 30 * q^28 - 24 * q^29 - 40 * q^30 + 8 * q^31 - 75 * q^33 - 24 * q^34 - 33 * q^35 - 32 * q^36 - 15 * q^37 - 30 * q^39 - 28 * q^40 + 13 * q^41 - 130 * q^42 - 24 * q^44 + 6 * q^45 + 30 * q^46 + 145 * q^48 - 28 * q^49 + 77 * q^50 - 36 * q^51 - 5 * q^52 - 10 * q^53 + 15 * q^54 - 8 * q^55 + 48 * q^56 - 60 * q^58 - 19 * q^59 - 110 * q^60 + 8 * q^61 + 110 * q^62 + 55 * q^63 + 16 * q^64 - 43 * q^65 - 17 * q^66 - 65 * q^67 - 42 * q^69 + 4 * q^70 + 18 * q^71 + 100 * q^73 + 22 * q^74 + 115 * q^75 + 64 * q^76 - 145 * q^78 - 16 * q^79 - 97 * q^80 + q^81 - 70 * q^83 - 46 * q^84 - 16 * q^85 + 64 * q^86 + 10 * q^87 + 30 * q^88 + 4 * q^89 - 8 * q^90 + 16 * q^91 - 135 * q^92 + 38 * q^94 - 2 * q^95 + 50 * q^96 + 150 * q^97 + 130 * q^98 + 178 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.30771	+	1.79991i	0.924691	+	1.27273i	0.961895	+	0.273420i	$0.0881549\pi$
$2$	1.30771	+	1.79991i	0.924691	+	1.27273i	−0.0372038	+	0.999308i	$0.511845\pi$
$3$	1.66715	+	0.541690i	0.962530	+	0.312745i	0.747797	−	0.663928i	$-0.231112\pi$
$3$	1.66715	+	0.541690i	0.962530	+	0.312745i	0.214733	+	0.976673i	$0.431112\pi$
$4$	−0.911532	+	2.80541i	−0.455766	+	1.40270i
$5$	0.941634	−	2.02813i	0.421111	−	0.907009i
$5$	0.941634	−	2.02813i	0.421111	−	0.907009i
$6$	1.20516	+	3.70909i	0.492003	+	1.51423i
$7$			2.10218i			0.794550i	0.917700	+	0.397275i	$0.130044\pi$
$7$			2.10218i			0.794550i	−0.917700	+	0.397275i	$0.869956\pi$
$8$	−2.00966	+	0.652977i	−0.710520	+	0.230862i
$9$	0.0589103	+	0.0428008i	0.0196368	+	0.0142669i
$10$	4.88184	−	0.957357i	1.54377	−	0.302743i
$11$	−0.0717015	+	0.0520942i	−0.0216188	+	0.0157070i	−0.598542	−	0.801091i	$-0.704253\pi$
$11$	−0.0717015	+	0.0520942i	−0.0216188	+	0.0157070i	0.576923	+	0.816798i	$0.304253\pi$
$12$	−3.03932	+	4.18327i	−0.877376	+	1.20760i
$13$	−0.213960	+	0.294491i	−0.0593418	+	0.0816770i	−0.837657	−	0.546197i	$-0.816075\pi$
$13$	−0.213960	+	0.294491i	−0.0593418	+	0.0816770i	0.778315	+	0.627874i	$0.216075\pi$
$14$	−3.78374	+	2.74904i	−1.01125	+	0.734713i
$15$	2.66846	−	2.87113i	0.688994	−	0.741323i
$16$	0.969497	+	0.704381i	0.242374	+	0.176095i
$17$	−2.37019	+	0.770120i	−0.574855	+	0.186782i	−0.581994	−	0.813193i	$-0.697727\pi$
$17$	−2.37019	+	0.770120i	−0.574855	+	0.186782i	0.00713952	+	0.999975i	$0.497727\pi$
$18$			0.162004i			0.0381848i
$19$	−0.309017	−	0.951057i	−0.0708934	−	0.218187i
$19$	−0.309017	−	0.951057i	−0.0708934	−	0.218187i
$20$	4.83141	+	4.49037i	1.08034	+	1.00408i
$21$	−1.13873	+	3.50465i	−0.248491	+	0.764778i
$22$	−0.187530	−	0.0609321i	−0.0399815	−	0.0129908i
$23$	−0.469874	−	0.646726i	−0.0979755	−	0.134852i	0.757215	−	0.653166i	$-0.226560\pi$
$23$	−0.469874	−	0.646726i	−0.0979755	−	0.134852i	−0.855190	+	0.518314i	$0.826560\pi$
$24$	−3.70411			−0.756098
$25$	−3.22665	−	3.81952i	−0.645331	−	0.763903i
$26$	−0.809854			−0.158825
$27$	−3.01604	−	4.15122i	−0.580437	−	0.798903i
$28$	−5.89747	−	1.91621i	−1.11452	−	0.362129i
$29$	−0.337920	+	1.04001i	−0.0627502	+	0.193125i	−0.977517	−	0.210857i	$-0.932374\pi$
$29$	−0.337920	+	1.04001i	−0.0627502	+	0.193125i	0.914767	+	0.403983i	$0.132374\pi$
$30$	8.65735	+	1.04839i	1.58061	+	0.191408i
$31$	−1.12049	−	3.44851i	−0.201246	−	0.619371i	−0.999847	−	0.0175103i	$-0.994426\pi$
$31$	−1.12049	−	3.44851i	−0.201246	−	0.619371i	0.798601	−	0.601861i	$-0.205574\pi$
$32$			6.89228i			1.21840i
$33$	−0.147756	+	0.0480089i	−0.0257210	+	0.00835727i
$34$	−4.48566	−	3.25903i	−0.769285	−	0.558918i
$35$	4.26351	+	1.97948i	0.720664	+	0.334594i
$36$	−0.173772	+	0.126253i	−0.0289620	+	0.0210422i
$37$	1.01952	−	1.40325i	0.167608	−	0.230693i	−0.716948	−	0.697127i	$-0.754461\pi$
$37$	1.01952	−	1.40325i	0.167608	−	0.230693i	0.884556	+	0.466434i	$0.154461\pi$
$38$	1.30771	−	1.79991i	0.212139	−	0.291984i
$39$	−0.516226	+	0.375060i	−0.0826623	+	0.0600577i
$40$	−0.568035	+	4.69071i	−0.0898142	+	0.741667i
$41$	6.67174	+	4.84730i	1.04195	+	0.757021i	0.970665	−	0.240435i	$-0.0772901\pi$
$41$	6.67174	+	4.84730i	1.04195	+	0.757021i	0.0712849	+	0.997456i	$0.477290\pi$
$42$	−7.79718	+	2.53346i	−1.20313	+	0.390921i
$43$		−	10.6031i		−	1.61695i	−0.588527	−	0.808477i	$-0.700292\pi$
$43$		−	10.6031i		−	1.61695i	0.588527	−	0.808477i	$-0.299708\pi$
$44$	−0.0807872	−	0.248637i	−0.0121791	−	0.0374835i
$45$	0.142278	−	0.0791752i	0.0212095	−	0.0118027i
$46$	0.549589	−	1.69146i	0.0810325	−	0.249392i
$47$	−10.6917	−	3.47394i	−1.55954	−	0.506727i	−0.602858	−	0.797848i	$-0.705972\pi$
$47$	−10.6917	−	3.47394i	−1.55954	−	0.506727i	−0.956686	+	0.291122i	$0.905972\pi$
$48$	1.23474	+	1.69947i	0.178219	+	0.245298i
$49$	2.58083			0.368690
$50$	2.65526	−	10.8025i	0.375510	−	1.52770i
$51$	−4.36862			−0.611730
$52$	−0.631135	−	0.868682i	−0.0875226	−	0.120465i
$53$	−2.21559	−	0.719890i	−0.304335	−	0.0988845i	0.152868	−	0.988247i	$-0.451149\pi$
$53$	−2.21559	−	0.719890i	−0.304335	−	0.0988845i	−0.457204	+	0.889362i	$0.651149\pi$
$54$	3.52771	−	10.8572i	0.480061	−	1.47748i
$55$	0.0381375	+	0.194474i	0.00514246	+	0.0262229i
$56$	−1.37268	−	4.22466i	−0.183431	−	0.564544i
$57$		−	1.75295i		−	0.232183i
$58$	−2.31383	+	0.751808i	−0.303821	+	0.0987173i
$59$	0.904332	+	0.657036i	0.117734	+	0.0855388i	0.645094	−	0.764103i	$-0.276818\pi$
$59$	0.904332	+	0.657036i	0.117734	+	0.0855388i	−0.527360	+	0.849642i	$0.676818\pi$
$60$	5.62230	+	10.1033i	0.725835	+	1.30432i
$61$	3.19589	−	2.32195i	0.409191	−	0.297295i	−0.364083	−	0.931367i	$-0.618618\pi$
$61$	3.19589	−	2.32195i	0.409191	−	0.297295i	0.773274	+	0.634072i	$0.218618\pi$
$62$	4.74174	−	6.52644i	0.602201	−	0.828859i
$63$	−0.0899751	+	0.123840i	−0.0113358	+	0.0156024i
$64$	−10.4665	+	7.60435i	−1.30831	+	0.950544i
$65$	0.395795	+	0.711242i	0.0490923	+	0.0882187i
$66$	−0.279634	−	0.203166i	−0.0344205	−	0.0250080i
$67$	−6.29348	+	2.04488i	−0.768871	+	0.249821i	−0.667082	−	0.744985i	$-0.732457\pi$
$67$	−6.29348	+	2.04488i	−0.768871	+	0.249821i	−0.101789	+	0.994806i	$0.532457\pi$
$68$		−	7.35133i		−	0.891479i
$69$	−0.433026	−	1.33272i	−0.0521302	−	0.160440i
$70$	2.01254	+	10.2625i	0.240544	+	1.22661i
$71$	0.117287	−	0.360973i	0.0139194	−	0.0428396i	−0.943856	−	0.330358i	$-0.892830\pi$
$71$	0.117287	−	0.360973i	0.0139194	−	0.0428396i	0.957775	+	0.287519i	$0.0928304\pi$
$72$	−0.146337	−	0.0475479i	−0.0172460	−	0.00560357i
$73$	3.75393	+	5.16684i	0.439364	+	0.604732i	0.970071	−	0.242823i	$-0.0780735\pi$
$73$	3.75393	+	5.16684i	0.439364	+	0.604732i	−0.530707	+	0.847555i	$0.678073\pi$
$74$	3.85897			0.448596
$75$	−3.31032	−	8.11555i	−0.382243	−	0.937103i
$76$	2.94978			0.338363
$77$	−0.109512	−	0.150730i	−0.0124800	−	0.0171772i
$78$	−1.35015	−	0.438690i	−0.152874	−	0.0496718i
$79$	−0.267556	+	0.823453i	−0.0301024	+	0.0926457i	−0.964979	−	0.262327i	$-0.915510\pi$
$79$	−0.267556	+	0.823453i	−0.0301024	+	0.0926457i	0.934877	+	0.354973i	$0.115510\pi$
$80$	2.34149	−	1.30300i	0.261786	−	0.145680i
$81$	−2.84702	−	8.76223i	−0.316336	−	0.973581i
$82$			18.3474i			2.02613i
$83$	−6.99896	+	2.27410i	−0.768235	+	0.249615i	−0.666809	−	0.745228i	$-0.732340\pi$
$83$	−6.99896	+	2.27410i	−0.768235	+	0.249615i	−0.101426	+	0.994843i	$0.532340\pi$
$84$	−8.79398	−	6.38920i	−0.959502	−	0.697119i
$85$	−0.669940	+	5.53223i	−0.0726652	+	0.600054i
$86$	19.0846	−	13.8658i	2.05794	−	1.49518i
$87$	−1.12673	+	1.55081i	−0.120798	+	0.166264i
$88$	0.110079	−	0.151511i	0.0117345	−	0.0161511i
$89$	−1.98297	+	1.44071i	−0.210195	+	0.152715i	−0.687902	−	0.725804i	$-0.741468\pi$
$89$	−1.98297	+	1.44071i	−0.210195	+	0.152715i	0.477707	+	0.878519i	$0.341468\pi$
$90$	0.328566	+	0.152549i	0.0346339	+	0.0160800i
$91$	−0.619073	−	0.449783i	−0.0648965	−	0.0471501i
$92$	2.24263	−	0.728676i	0.233811	−	0.0759697i
$93$		−	6.35615i		−	0.659102i
$94$	−7.72886	−	23.7870i	−0.797171	−	2.45344i
$95$	−2.21985	−	0.268819i	−0.227752	−	0.0275802i
$96$	−3.73348	+	11.4905i	−0.381047	+	1.17274i
$97$	1.79481	+	0.583169i	0.182235	+	0.0592119i	0.398713	−	0.917076i	$-0.369457\pi$
$97$	1.79481	+	0.583169i	0.182235	+	0.0592119i	−0.216478	+	0.976288i	$0.569457\pi$
$98$	3.37498	+	4.64526i	0.340925	+	0.469242i
$99$	−0.00645363			−0.000648615
$100$	13.6565	−	5.57046i	1.36565	−	0.557046i
$101$	12.6062			1.25436			0.627182	−	0.778873i	$-0.284208\pi$
$101$	12.6062			1.25436			0.627182	+	0.778873i	$0.284208\pi$
$102$	−5.71289	−	7.86312i	−0.565661	−	0.778565i
$103$	1.47725	+	0.479989i	0.145558	+	0.0472947i	0.380890	−	0.924620i	$-0.375618\pi$
$103$	1.47725	+	0.479989i	0.145558	+	0.0472947i	−0.235332	+	0.971915i	$0.575618\pi$
$104$	0.237690	−	0.731536i	0.0233075	−	0.0717330i
$105$	6.03564	+	5.60960i	0.589018	+	0.547441i
$106$	−1.60162	−	4.92927i	−0.155563	−	0.478773i
$107$			12.7376i			1.23139i	0.787983	+	0.615697i	$0.211125\pi$
$107$			12.7376i			1.23139i	−0.787983	+	0.615697i	$0.788875\pi$
$108$	14.3951	−	4.67724i	1.38517	−	0.450068i
$109$	15.1061	+	10.9752i	1.44690	+	1.05124i	0.986543	+	0.163505i	$0.0522800\pi$
$109$	15.1061	+	10.9752i	1.44690	+	1.05124i	0.460361	+	0.887732i	$0.347720\pi$
$110$	−0.300163	+	0.322960i	−0.0286194	+	0.0307930i
$111$	2.45982	−	1.78717i	0.233476	−	0.169630i
$112$	−1.48074	+	2.03806i	−0.139916	+	0.192578i
$113$	0.842922	−	1.16018i	0.0792954	−	0.109141i	−0.767527	−	0.641017i	$-0.778513\pi$
$113$	0.842922	−	1.16018i	0.0792954	−	0.109141i	0.846822	+	0.531876i	$0.178513\pi$
$114$	3.15514	−	2.29234i	0.295506	−	0.214698i
$115$	−1.75410	+	0.343988i	−0.163570	+	0.0320771i
$116$	−2.60963	−	1.89601i	−0.242298	−	0.176040i
$117$	−0.0252089	+	0.00819086i	−0.00233056	+	0.000757246i
$118$			2.48693i			0.228940i
$119$	−1.61893	−	4.98256i	−0.148407	−	0.456751i
$120$	−3.48791	+	7.51243i	−0.318401	+	0.685787i
$121$	−3.39676	+	10.4542i	−0.308796	+	0.950377i
$122$	8.35859	+	2.71587i	0.756751	+	0.245883i
$123$	8.49705	+	11.6952i	0.766153	+	1.05452i
$124$	10.6958			0.960515
$125$	−10.7848	+	2.94750i	−0.964623	+	0.263632i
$126$	−0.340562			−0.0303397
$127$	11.6320	+	16.0101i	1.03217	+	1.42066i	0.903303	+	0.429004i	$0.141135\pi$
$127$	11.6320	+	16.0101i	1.03217	+	1.42066i	0.128871	+	0.991661i	$0.458865\pi$
$128$	−14.2644	−	4.63478i	−1.26080	−	0.409660i
$129$	5.74358	−	17.6769i	0.505694	−	1.55637i
$130$	−0.762586	+	1.64249i	−0.0668832	+	0.144056i
$131$	−4.84162	−	14.9010i	−0.423014	−	1.30190i	−0.904883	−	0.425660i	$-0.860042\pi$
$131$	−4.84162	−	14.9010i	−0.423014	−	1.30190i	0.481869	−	0.876243i	$-0.339958\pi$
$132$		−	0.458278i		−	0.0398879i
$133$	1.99929	−	0.649610i	0.173361	−	0.0563283i
$134$	−11.9106	−	8.65358i	−1.02892	−	0.747556i
$135$	−11.2592	+	2.20800i	−0.969041	+	0.190034i
$136$	4.26039	−	3.09535i	0.365325	−	0.265424i
$137$	−9.12492	+	12.5594i	−0.779595	+	1.07302i	0.215732	+	0.976453i	$0.430786\pi$
$137$	−9.12492	+	12.5594i	−0.779595	+	1.07302i	−0.995326	+	0.0965672i	$0.969214\pi$
$138$	1.83249	−	2.52221i	0.155992	−	0.214705i
$139$	0.327406	−	0.237874i	0.0277702	−	0.0201762i	−0.573814	−	0.818986i	$-0.694537\pi$
$139$	0.327406	−	0.237874i	0.0277702	−	0.0201762i	0.601584	+	0.798810i	$0.294537\pi$
$140$	−9.43958	+	10.1565i	−0.797790	+	0.858381i
$141$	−15.9429	−	11.5832i	−1.34263	−	0.975479i
$142$	0.803096	−	0.260942i	0.0673943	−	0.0218977i
$143$		−	0.0322615i		−	0.00269784i
$144$	0.0269652	+	0.0829905i	0.00224710	+	0.00691588i
$145$	1.79109	+	1.66466i	0.148742	+	0.138242i
$146$	−4.39079	+	13.5134i	−0.363384	+	1.11838i
$147$	4.30263	+	1.39801i	0.354875	+	0.115306i
$148$	3.00737	+	4.13928i	0.247204	+	0.340247i
$149$	2.39332			0.196069			0.0980344	−	0.995183i	$-0.468744\pi$
$149$	2.39332			0.196069			0.0980344	+	0.995183i	$0.468744\pi$
$150$	10.2783	−	16.5711i	0.839221	−	1.35302i
$151$	−19.6779			−1.60136			−0.800682	−	0.599089i	$-0.795530\pi$
$151$	−19.6779			−1.60136			−0.800682	+	0.599089i	$0.795530\pi$
$152$	1.24204	+	1.70951i	0.100742	+	0.138660i
$153$	−0.172590	−	0.0560779i	−0.0139531	−	0.00453363i
$154$	0.128090	−	0.394222i	0.0103218	−	0.0317673i
$155$	−8.04914	−	0.974733i	−0.646522	−	0.0782924i
$156$	−0.581640	−	1.79010i	−0.0465685	−	0.143323i
$157$			0.106278i			0.00848187i	0.999991	+	0.00424094i	$0.00134994\pi$
$157$			0.106278i			0.00848187i	−0.999991	+	0.00424094i	$0.998650\pi$
$158$	−1.83203	+	0.595262i	−0.145748	+	0.0473565i
$159$	−3.30377	−	2.40033i	−0.262006	−	0.190358i
$160$	13.9785	+	6.49001i	1.10510	+	0.513080i
$161$	1.35954	−	0.987761i	0.107146	−	0.0778465i
$162$	12.0481	−	16.5828i	0.946591	−	1.30287i
$163$	7.56609	−	10.4138i	0.592622	−	0.815674i	−0.402386	−	0.915470i	$-0.631819\pi$
$163$	7.56609	−	10.4138i	0.592622	−	0.815674i	0.995008	+	0.0997958i	$0.0318190\pi$
$164$	−19.6801	+	14.2985i	−1.53676	+	1.11652i
$165$	−0.0417637	+	0.344876i	−0.00325130	+	0.0268486i
$166$	−13.2458	−	9.62362i	−1.02807	−	0.746938i
$167$	11.3661	−	3.69308i	0.879538	−	0.285779i	0.165773	−	0.986164i	$-0.446988\pi$
$167$	11.3661	−	3.69308i	0.879538	−	0.285779i	0.713765	+	0.700385i	$0.246988\pi$
$168$		−	7.78671i		−	0.600757i
$169$	3.97628	+	12.2377i	0.305867	+	0.941363i
$170$	−10.8336	+	6.02872i	−0.830899	+	0.462382i
$171$	0.0225017	−	0.0692532i	0.00172075	−	0.00529592i
$172$	29.7459	+	9.66504i	2.26811	+	0.736953i
$173$	0.384637	+	0.529408i	0.0292434	+	0.0402501i	0.823388	−	0.567478i	$-0.192081\pi$
$173$	0.384637	+	0.529408i	0.0292434	+	0.0402501i	−0.794145	+	0.607728i	$0.792081\pi$
$174$	−4.26475			−0.323310
$175$	8.02932	−	6.78301i	0.606960	−	0.512747i
$176$	−0.106209			−0.00800577
$177$	1.15175	+	1.58525i	0.0865707	+	0.119154i
$178$	−5.18631	−	1.68513i	−0.388730	−	0.126306i
$179$	0.287485	−	0.884788i	0.0214876	−	0.0661322i	−0.939738	−	0.341896i	$-0.888931\pi$
$179$	0.287485	−	0.884788i	0.0214876	−	0.0661322i	0.961225	+	0.275764i	$0.0889309\pi$
$180$	0.0924280	+	0.471317i	0.00688918	+	0.0351299i
$181$	−2.50353	−	7.70508i	−0.186086	−	0.572714i	0.813879	−	0.581034i	$-0.197352\pi$
$181$	−2.50353	−	7.70508i	−0.186086	−	0.572714i	−0.999965	+	0.00831975i	$0.997352\pi$
$182$		−	1.70246i		−	0.126195i
$183$	6.58580	−	2.13986i	0.486836	−	0.158183i
$184$	1.36658	+	0.992880i	0.100746	+	0.0731961i
$185$	−1.88597	−	3.38908i	−0.138659	−	0.249170i
$186$	11.4405	−	8.31200i	0.838857	−	0.609466i
$187$	0.129827	−	0.178692i	0.00949391	−	0.0130672i
$188$	19.4916	−	26.8279i	1.42157	−	1.95663i
$189$	8.72662	−	6.34026i	0.634768	−	0.461186i
$190$	−2.41907	−	4.34707i	−0.175498	−	0.315369i
$191$	−13.0797	−	9.50297i	−0.946415	−	0.687611i	0.00354130	−	0.999994i	$-0.498873\pi$
$191$	−13.0797	−	9.50297i	−0.946415	−	0.687611i	−0.949956	+	0.312383i	$0.898873\pi$
$192$	−21.5684	+	7.00800i	−1.55657	+	0.505759i
$193$		−	19.6327i		−	1.41320i	−0.707615	−	0.706598i	$-0.750229\pi$
$193$		−	19.6327i		−	1.41320i	0.707615	−	0.706598i	$-0.249771\pi$
$194$	1.29744	+	3.99311i	0.0931508	+	0.286689i
$195$	0.274576	+	1.40014i	0.0196628	+	0.100266i
$196$	−2.35251	+	7.24028i	−0.168036	+	0.517163i
$197$	−18.3425	−	5.95985i	−1.30685	−	0.424622i	−0.428891	−	0.903356i	$-0.641096\pi$
$197$	−18.3425	−	5.95985i	−1.30685	−	0.424622i	−0.877960	+	0.478734i	$0.841096\pi$
$198$	−0.00843948	−	0.0116160i	−0.000599768	−	0.000825510i
$199$	24.6200			1.74526			0.872632	−	0.488378i	$-0.162411\pi$
$199$	24.6200			1.74526			0.872632	+	0.488378i	$0.162411\pi$
$200$	8.97851	+	5.56898i	0.634877	+	0.393787i
$201$	−11.5999			−0.818191
$202$	16.4853	+	22.6900i	1.15990	+	1.59646i
$203$	−2.18629	−	0.710370i	−0.153448	−	0.0498582i
$204$	3.98214	−	12.2558i	0.278805	−	0.858075i
$205$	16.1133	−	8.96679i	1.12540	−	0.626268i
$206$	1.06788	+	3.28661i	0.0744029	+	0.228989i
$207$		−	0.0582098i		−	0.00404586i
$208$	−0.414867	+	0.134798i	−0.0287659	+	0.00934659i
$209$	0.0717015	+	0.0520942i	0.00495970	+	0.00360343i
$210$	−2.20390	+	18.1993i	−0.152083	+	1.25587i
$211$	−8.60718	+	6.25348i	−0.592543	+	0.430508i	−0.843224	−	0.537562i	$-0.819345\pi$
$211$	−8.60718	+	6.25348i	−0.592543	+	0.430508i	0.250681	+	0.968070i	$0.419345\pi$
$212$	4.03917	−	5.55944i	0.277411	−	0.381824i
$213$	0.391071	−	0.538263i	0.0267957	−	0.0368811i
$214$	−22.9266	+	16.6571i	−1.56723	+	1.13866i
$215$	−21.5045	−	9.98422i	−1.46659	−	0.680918i
$216$	8.77185	+	6.37312i	0.596849	+	0.433636i
$217$	7.24940	−	2.35547i	0.492122	−	0.159900i
$218$			41.5421i			2.81358i
$219$	3.45953	+	10.6474i	0.233774	+	0.719481i
$220$	−0.580342	−	0.0702781i	−0.0391267	−	0.00473815i
$221$	0.280332	−	0.862773i	0.0188572	−	0.0580364i
$222$	6.43348	+	2.09036i	0.431787	+	0.140296i
$223$	14.7156	+	20.2542i	0.985427	+	1.35632i	0.933854	+	0.357654i	$0.116423\pi$
$223$	14.7156	+	20.2542i	0.985427	+	1.35632i	0.0515724	+	0.998669i	$0.483577\pi$
$224$	−14.4888			−0.968076
$225$	−0.0266045	−	0.363112i	−0.00177363	−	0.0242075i
$226$	3.19052			0.212230
$227$	−4.28735	−	5.90103i	−0.284561	−	0.391665i	0.642677	−	0.766137i	$-0.277824\pi$
$227$	−4.28735	−	5.90103i	−0.284561	−	0.391665i	−0.927238	+	0.374472i	$0.877824\pi$
$228$	4.91772	+	1.59787i	0.325684	+	0.105821i
$229$	−1.64777	+	5.07131i	−0.108888	+	0.335122i	−0.990623	−	0.136622i	$-0.956375\pi$
$229$	−1.64777	+	5.07131i	−0.108888	+	0.335122i	0.881736	+	0.471744i	$0.156375\pi$
$230$	−2.91300	−	2.70738i	−0.192077	−	0.178519i
$231$	−0.100923	−	0.310610i	−0.00664027	−	0.0204367i
$232$		−	2.31072i		−	0.151706i
$233$	−20.6255	+	6.70162i	−1.35122	+	0.439037i	−0.893102	−	0.449855i	$-0.851476\pi$
$233$	−20.6255	+	6.70162i	−1.35122	+	0.439037i	−0.458117	+	0.888892i	$0.651476\pi$
$234$	−0.0477087	−	0.0346624i	−0.00311882	−	0.00226595i
$235$	−17.1133	+	18.4130i	−1.11635	+	1.20113i
$236$	−2.66758	+	1.93811i	−0.173645	+	0.126160i
$237$	−0.892113	+	1.22789i	−0.0579489	+	0.0797599i
$238$	6.85107	−	9.42968i	0.444089	−	0.611236i
$239$	−10.4353	+	7.58171i	−0.675005	+	0.490420i	−0.871697	−	0.490045i	$-0.836980\pi$
$239$	−10.4353	+	7.58171i	−0.675005	+	0.490420i	0.196692	+	0.980465i	$0.436980\pi$
$240$	4.60943	−	0.903937i	0.297538	−	0.0583489i
$241$	−21.9675	−	15.9603i	−1.41505	−	1.02809i	−0.992564	−	0.121726i	$-0.961157\pi$
$241$	−21.9675	−	15.9603i	−1.41505	−	1.02809i	−0.422487	−	0.906369i	$-0.638843\pi$
$242$	−23.2585	+	7.55714i	−1.49511	+	0.485792i
$243$		−	0.756572i		−	0.0485341i
$244$	3.60085	+	11.0823i	0.230521	+	0.709471i
$245$	2.43020	−	5.23427i	0.155260	−	0.334405i
$246$	−9.93859	+	30.5878i	−0.633661	+	1.95021i
$247$	0.346195	+	0.112485i	0.0220278	+	0.00715728i
$248$	4.50360	+	6.19867i	0.285979	+	0.393616i
$249$	−12.9002			−0.817515
$250$	−19.4086	−	15.5572i	−1.22751	−	0.983925i
$251$	10.5188			0.663939			0.331970	−	0.943290i	$-0.392287\pi$
$251$	10.5188			0.663939			0.331970	+	0.943290i	$0.392287\pi$
$252$	−0.265407	−	0.365301i	−0.0167190	−	0.0230118i
$253$	0.0673814	+	0.0218935i	0.00423623	+	0.00137644i
$254$	−13.6054	+	41.8731i	−0.853678	+	2.62735i
$255$	−4.11364	+	8.86015i	−0.257606	+	0.554844i
$256$	−2.31581	−	7.12732i	−0.144738	−	0.445458i
$257$		−	5.32199i		−	0.331976i	−0.986128	−	0.165988i	$-0.946919\pi$
$257$		−	5.32199i		−	0.331976i	0.986128	−	0.165988i	$-0.0530814\pi$
$258$	39.3278	−	12.7784i	2.44844	−	0.795547i
$259$	2.94989	+	2.14322i	0.183297	+	0.133173i
$260$	−2.35610	+	0.462045i	−0.146119	+	0.0286548i
$261$	−0.0644203	+	0.0468041i	−0.00398752	+	0.00289710i
$262$	20.4889	−	28.2006i	1.26581	−	1.74224i
$263$	−15.1956	+	20.9149i	−0.936998	+	1.28967i	0.0200680	+	0.999799i	$0.493612\pi$
$263$	−15.1956	+	20.9149i	−0.936998	+	1.28967i	−0.957066	+	0.289869i	$0.906388\pi$
$264$	0.265590	−	0.192963i	0.0163459	−	0.0118760i
$265$	−3.54631	+	3.81565i	−0.217848	+	0.234393i
$266$	3.78374	+	2.74904i	0.231996	+	0.168555i
$267$	−4.08633	+	1.32773i	−0.250079	+	0.0812557i
$268$		−	19.5197i		−	1.19236i
$269$	3.83485	+	11.8024i	0.233815	+	0.719608i	0.997276	+	0.0737545i	$0.0234981\pi$
$269$	3.83485	+	11.8024i	0.233815	+	0.719608i	−0.763462	+	0.645853i	$0.776502\pi$
$270$	−18.6980	−	17.3782i	−1.13793	−	1.05760i
$271$	−2.26696	+	6.97698i	−0.137708	+	0.423822i	−0.996001	−	0.0893377i	$-0.971525\pi$
$271$	−2.26696	+	6.97698i	−0.137708	+	0.423822i	0.858293	+	0.513159i	$0.171525\pi$
$272$	−2.84035	−	0.922884i	−0.172221	−	0.0559581i
$273$	−0.788445	−	1.08520i	−0.0477188	−	0.0656794i
$274$	−34.5385			−2.08655
$275$	0.430331	+	0.105775i	0.0259499	+	0.00637849i
$276$	4.13353			0.248809
$277$	11.2782	+	15.5232i	0.677643	+	0.932696i	0.999903	−	0.0139553i	$-0.00444225\pi$
$277$	11.2782	+	15.5232i	0.677643	+	0.932696i	−0.322259	+	0.946651i	$0.604442\pi$
$278$	0.856303	+	0.278230i	0.0513577	+	0.0166871i
$279$	0.0815909	−	0.251111i	0.00488472	−	0.0150336i
$280$	−9.86073	−	1.19411i	−0.589292	−	0.0713619i
$281$	−4.97255	−	15.3039i	−0.296637	−	0.912956i	−0.982667	−	0.185382i	$-0.940648\pi$
$281$	−4.97255	−	15.3039i	−0.296637	−	0.912956i	0.686029	−	0.727574i	$-0.259352\pi$
$282$		−	43.8431i		−	2.61082i
$283$	17.1307	−	5.56609i	1.01831	−	0.330870i	0.248153	−	0.968721i	$-0.420176\pi$
$283$	17.1307	−	5.56609i	1.01831	−	0.330870i	0.770160	+	0.637851i	$0.220176\pi$
$284$	0.905765	+	0.658076i	0.0537472	+	0.0390497i
$285$	−3.55521	−	1.65063i	−0.210592	−	0.0977750i
$286$	0.0580678	−	0.0421887i	0.00343362	−	0.00249467i
$287$	−10.1899	+	14.0252i	−0.601491	+	0.827881i
$288$	−0.294995	+	0.406026i	−0.0173828	+	0.0239253i
$289$	−8.72859	+	6.34169i	−0.513446	+	0.373041i
$290$	−0.654010	+	5.40068i	−0.0384048	+	0.317139i
$291$	2.67632	+	1.94446i	0.156889	+	0.113986i
$292$	−17.9169	+	5.82155i	−1.04851	+	0.340681i
$293$		−	3.38691i		−	0.197865i	−0.995094	−	0.0989327i	$-0.968457\pi$
$293$		−	3.38691i		−	0.197865i	0.995094	−	0.0989327i	$-0.0315428\pi$
$294$	3.11031	+	9.57254i	0.181397	+	0.558282i
$295$	2.18411	−	1.21542i	0.127164	−	0.0707645i
$296$	−1.13260	+	3.48578i	−0.0658309	+	0.202607i
$297$	0.432509	+	0.140531i	0.0250967	+	0.00815442i
$298$	3.12977	+	4.30777i	0.181303	+	0.249542i
$299$	0.290989			0.0168283
$300$	25.7849	−	1.88921i	1.48869	−	0.109073i
$301$	22.2896			1.28475
$302$	−25.7330	−	35.4184i	−1.48077	−	2.03810i
$303$	21.0164	+	6.82865i	1.20736	+	0.392296i
$304$	0.370315	−	1.13971i	0.0212390	−	0.0653669i
$305$	−1.69987	−	8.66811i	−0.0973340	−	0.496334i
$306$	−0.124763	−	0.383980i	−0.00713221	−	0.0219507i
$307$		−	12.3467i		−	0.704666i	−0.935875	−	0.352333i	$-0.885388\pi$
$307$		−	12.3467i		−	0.704666i	0.935875	−	0.352333i	$-0.114612\pi$
$308$	0.522681	−	0.169829i	0.0297825	−	0.00967693i
$309$	2.20280	+	1.60043i	0.125313	+	0.0910450i
$310$	−8.77151	−	15.7624i	−0.498188	−	0.895243i
$311$	3.23420	−	2.34978i	0.183395	−	0.133244i	−0.492300	−	0.870426i	$-0.663844\pi$
$311$	3.23420	−	2.34978i	0.183395	−	0.133244i	0.675695	+	0.737182i	$0.263844\pi$
$312$	0.792531	−	1.09083i	0.0448682	−	0.0617558i
$313$	−15.9669	+	21.9765i	−0.902502	+	1.24219i	0.0671605	+	0.997742i	$0.478606\pi$
$313$	−15.9669	+	21.9765i	−0.902502	+	1.24219i	−0.969663	+	0.244446i	$0.921394\pi$
$314$	−0.191290	+	0.138980i	−0.0107951	+	0.00784311i
$315$	0.166441	+	0.299094i	0.00937787	+	0.0168520i
$316$	−2.06623	−	1.50121i	−0.116235	−	0.0844495i
$317$	4.85799	−	1.57846i	0.272852	−	0.0886550i	−0.169395	−	0.985548i	$-0.554181\pi$
$317$	4.85799	−	1.57846i	0.272852	−	0.0886550i	0.442247	+	0.896893i	$0.354181\pi$
$318$		−	9.08542i		−	0.509485i
$319$	−0.0299492	−	0.0921741i	−0.00167683	−	0.00516076i
$320$	5.56704	+	28.3880i	0.311207	+	1.58693i
$321$	−6.89985	+	21.2356i	−0.385112	+	1.18525i
$322$	3.55576	+	1.15534i	0.198155	+	0.0643844i
$323$	1.46486	+	2.01620i	0.0815068	+	0.112184i
$324$	27.1767			1.50982
$325$	1.81519	−	0.132995i	0.100688	−	0.00737724i
$326$	28.6382			1.58612
$327$	19.2390	+	26.4802i	1.06392	+	1.46436i
$328$	−16.5731	−	5.38491i	−0.915094	−	0.297332i
$329$	7.30286	−	22.4759i	0.402620	−	1.23914i
$330$	−0.675360	+	0.375827i	−0.0371774	+	0.0206886i
$331$	−5.10758	−	15.7195i	−0.280738	−	0.864023i	−0.987644	−	0.156715i	$-0.949909\pi$
$331$	−5.10758	−	15.7195i	−0.280738	−	0.864023i	0.706906	−	0.707308i	$-0.250091\pi$
$332$		−	21.7078i		−	1.19137i
$333$	0.120121	−	0.0390296i	0.00658257	−	0.00213881i
$334$	21.5108	+	15.6285i	1.17702	+	0.855155i
$335$	−1.77887	+	14.6895i	−0.0971901	+	0.802575i
$336$	−3.57260	+	2.59565i	−0.194902	+	0.141604i
$337$	14.6890	−	20.2177i	0.800160	−	1.10133i	−0.192608	−	0.981276i	$-0.561695\pi$
$337$	14.6890	−	20.2177i	0.800160	−	1.10133i	0.992768	−	0.120050i	$-0.0383055\pi$
$338$	−16.8270	+	23.1603i	−0.915266	+	1.25976i
$339$	2.03374	−	1.47760i	0.110457	−	0.0802520i
$340$	−14.9095	−	6.92226i	−0.808580	−	0.375412i
$341$	0.259989	+	0.188893i	0.0140792	+	0.0102291i
$342$	0.154075	−	0.0500621i	0.00833143	−	0.00270705i
$343$			20.1406i			1.08749i
$344$	6.92356	+	21.3085i	0.373293	+	1.14888i
$345$	−3.11068	−	0.376696i	−0.167473	−	0.0202806i
$346$	−0.449892	+	1.38462i	−0.0241863	+	0.0744379i
$347$	−15.1189	−	4.91242i	−0.811624	−	0.263713i	−0.126339	−	0.991987i	$-0.540323\pi$
$347$	−15.1189	−	4.91242i	−0.811624	−	0.263713i	−0.685285	+	0.728275i	$0.740323\pi$
$348$	−3.32360	−	4.57454i	−0.178164	−	0.245221i
$349$	9.23377			0.494272			0.247136	−	0.968981i	$-0.420511\pi$
$349$	9.23377			0.494272			0.247136	+	0.968981i	$0.420511\pi$
$350$	22.7088	+	5.58183i	1.21384	+	0.298361i
$351$	1.86781			0.0996962
$352$	−0.359048	−	0.494187i	−0.0191373	−	0.0263403i
$353$	6.41667	+	2.08490i	0.341525	+	0.110968i	0.474757	−	0.880117i	$-0.342536\pi$
$353$	6.41667	+	2.08490i	0.341525	+	0.110968i	−0.133233	+	0.991085i	$0.542536\pi$
$354$	−1.34714	+	4.14608i	−0.0715999	+	0.220362i
$355$	−0.621660	−	0.577778i	−0.0329943	−	0.0306653i
$356$	−2.23424	−	6.87630i	−0.118415	−	0.364443i
$357$		−	9.18364i		−	0.486050i
$358$	1.96849	−	0.639600i	0.104038	−	0.0338039i
$359$	24.9763	+	18.1464i	1.31820	+	0.957728i	0.999953	+	0.00971974i	$0.00309394\pi$
$359$	24.9763	+	18.1464i	1.31820	+	0.957728i	0.318246	+	0.948008i	$0.396906\pi$
$360$	−0.234230	+	0.252019i	−0.0123450	+	0.0132826i
$361$	−0.809017	+	0.587785i	−0.0425798	+	0.0309361i
$362$	10.5946	−	14.5821i	0.556837	−	0.766421i
$363$	−11.3258	+	15.5886i	−0.594451	+	0.818192i
$364$	1.82613	−	1.32676i	0.0957151	−	0.0695411i
$365$	14.0139	−	2.74820i	0.733519	−	0.143847i
$366$	12.4639	+	9.05553i	0.651496	+	0.473340i
$367$	−18.3431	+	5.96003i	−0.957501	+	0.311111i	−0.745760	−	0.666215i	$-0.767913\pi$
$367$	−18.3431	+	5.96003i	−0.957501	+	0.311111i	−0.211741	+	0.977326i	$0.567913\pi$
$368$		−	0.957969i		−	0.0499376i
$369$	0.185565	+	0.571112i	0.00966015	+	0.0297309i
$370$	3.63373	−	7.82650i	0.188909	−	0.406880i
$371$	1.51334	−	4.65758i	0.0785687	−	0.241809i
$372$	17.8316	+	5.79383i	0.924524	+	0.300396i
$373$	3.09546	+	4.26054i	0.160277	+	0.220602i	0.881601	−	0.471996i	$-0.156466\pi$
$373$	3.09546	+	4.26054i	0.160277	+	0.220602i	−0.721324	+	0.692598i	$0.756466\pi$
$374$	0.491406			0.0254100
$375$	−19.5765	−	0.928106i	−1.01093	−	0.0479272i
$376$	23.7550			1.22507
$377$	−0.233972	−	0.322035i	−0.0120502	−	0.0165857i
$378$	22.8238	+	7.41590i	1.17393	+	0.381433i
$379$	8.12336	−	25.0011i	0.417269	−	1.28422i	−0.492937	−	0.870065i	$-0.664077\pi$
$379$	8.12336	−	25.0011i	0.417269	−	1.28422i	0.910206	−	0.414156i	$-0.135923\pi$
$380$	2.77761	−	5.98255i	0.142488	−	0.306898i
$381$	10.7198	+	32.9921i	0.549192	+	1.69024i
$382$		−	35.9694i		−	1.84036i
$383$	7.62060	−	2.47608i	0.389395	−	0.126522i	−0.107775	−	0.994175i	$-0.534373\pi$
$383$	7.62060	−	2.47608i	0.389395	−	0.126522i	0.497170	+	0.867653i	$0.334373\pi$
$384$	−21.2702	−	15.4537i	−1.08544	−	0.788620i
$385$	−0.408820	+	0.0801719i	−0.0208354	+	0.00408594i
$386$	35.3372	−	25.6739i	1.79861	−	1.30677i
$387$	0.453821	−	0.624630i	0.0230690	−	0.0317517i
$388$	−3.27205	+	4.50360i	−0.166113	+	0.228635i
$389$	14.1591	−	10.2872i	0.717893	−	0.521580i	−0.167817	−	0.985818i	$-0.553672\pi$
$389$	14.1591	−	10.2872i	0.717893	−	0.521580i	0.885710	+	0.464238i	$0.153672\pi$
$390$	−2.16107	+	2.32520i	−0.109430	+	0.117741i
$391$	1.61175	+	1.17100i	0.0815095	+	0.0592201i
$392$	−5.18658	+	1.68522i	−0.261962	+	0.0851166i
$393$		−	27.4648i		−	1.38542i
$394$	−13.2595	−	40.8086i	−0.668006	−	2.05591i
$395$	1.41813	+	1.31803i	0.0713540	+	0.0663173i
$396$	0.00588269	−	0.0181051i	0.000295616	−	0.000909814i
$397$	26.2078	+	8.51543i	1.31533	+	0.427377i	0.880889	−	0.473322i	$-0.156945\pi$
$397$	26.2078	+	8.51543i	1.31533	+	0.427377i	0.434443	+	0.900699i	$0.356945\pi$
$398$	32.1958	+	44.3137i	1.61383	+	2.22125i
$399$	3.68501			0.184481
$400$	−0.437835	−	5.97580i	−0.0218917	−	0.298790i
$401$	11.7589			0.587212			0.293606	−	0.955927i	$-0.405145\pi$
$401$	11.7589			0.587212			0.293606	+	0.955927i	$0.405145\pi$
$402$	−15.1693	−	20.8787i	−0.756574	−	1.04133i
$403$	1.25530	+	0.407870i	0.0625307	+	0.0203175i
$404$	−11.4910	+	35.3655i	−0.571696	+	1.75950i
$405$	−20.4518	−	2.47667i	−1.01626	−	0.123067i
$406$	−1.58044	−	4.86409i	−0.0784358	−	0.241401i
$407$			0.153727i			0.00761994i
$408$	8.77943	−	2.85261i	0.434646	−	0.141225i
$409$	17.9591	+	13.0480i	0.888019	+	0.645184i	0.935361	−	0.353695i	$-0.115075\pi$
$409$	17.9591	+	13.0480i	0.888019	+	0.645184i	−0.0473418	+	0.998879i	$0.515075\pi$
$410$	37.2109	+	17.2765i	1.83772	+	0.853226i
$411$	−22.0159	+	15.9955i	−1.08596	+	0.788999i
$412$	−2.69313	+	3.70677i	−0.132681	+	0.182619i
$413$	−1.38121	+	1.90107i	−0.0679648	+	0.0935456i
$414$	0.104772	−	0.0761216i	0.00514928	−	0.00374117i
$415$	−1.97828	+	16.3362i	−0.0971097	+	0.801912i
$416$	−2.02971	−	1.47467i	−0.0995149	−	0.0723018i
$417$	0.674688	−	0.219219i	0.0330396	−	0.0107352i
$418$			0.197180i			0.00964441i
$419$	−8.01952	−	24.6815i	−0.391779	−	1.20577i	−0.931442	−	0.363890i	$-0.881448\pi$
$419$	−8.01952	−	24.6815i	−0.391779	−	1.20577i	0.539663	−	0.841881i	$-0.318552\pi$
$420$	−21.2389	+	11.8191i	−1.03635	+	0.576712i
$421$	6.88511	−	21.1902i	0.335560	−	1.03275i	−0.630886	−	0.775876i	$-0.717308\pi$
$421$	6.88511	−	21.1902i	0.335560	−	1.03275i	0.966446	−	0.256871i	$-0.0826916\pi$
$422$	−22.5114	−	7.31440i	−1.09584	−	0.356059i
$423$	−0.481163	−	0.662264i	−0.0233950	−	0.0322004i
$424$	4.92265			0.239065
$425$	10.5893	+	6.56806i	0.513654	+	0.318598i
$426$	1.48023			0.0717174
$427$	4.88116	+	6.71833i	0.236216	+	0.325123i
$428$	−35.7342	−	11.6108i	−1.72728	−	0.561227i
$429$	0.0174757	−	0.0537848i	0.000843737	−	0.00259675i
$430$	−10.1509	−	51.7625i	−0.489521	−	2.49621i
$431$	−12.0698	−	37.1471i	−0.581382	−	1.78931i	−0.613337	−	0.789821i	$-0.710173\pi$
$431$	−12.0698	−	37.1471i	−0.581382	−	1.78931i	0.0319548	−	0.999489i	$-0.489827\pi$
$432$		−	6.14903i		−	0.295846i
$433$	0.0578840	−	0.0188077i	0.00278173	−	0.000903838i	−0.307626	−	0.951507i	$-0.599534\pi$
$433$	0.0578840	−	0.0188077i	0.00278173	−	0.000903838i	0.310408	+	0.950604i	$0.399534\pi$
$434$	13.7198	+	9.96799i	0.658570	+	0.478479i
$435$	2.08428	+	3.74545i	0.0999336	+	0.179580i
$436$	−44.5597	+	32.3745i	−2.13402	+	1.55046i
$437$	−0.469874	+	0.646726i	−0.0224771	+	0.0309371i
$438$	−14.6402	+	20.1505i	−0.699536	+	0.962828i
$439$	26.2169	−	19.0477i	1.25127	−	0.909098i	0.252972	−	0.967474i	$-0.418592\pi$
$439$	26.2169	−	19.0477i	1.25127	−	0.909098i	0.998295	+	0.0583756i	$0.0185921\pi$
$440$	−0.203630	−	0.365923i	−0.00970768	−	0.0174447i
$441$	0.152038	+	0.110462i	0.00723988	+	0.00526008i
$442$	1.91951	−	0.623685i	0.0913016	−	0.0296657i
$443$		−	14.1731i		−	0.673382i	−0.941615	−	0.336691i	$-0.890692\pi$
$443$		−	14.1731i		−	0.673382i	0.941615	−	0.336691i	$-0.109308\pi$
$444$	2.77152	+	8.52987i	0.131531	+	0.404809i
$445$	1.05473	+	5.37836i	0.0499988	+	0.254959i
$446$	−17.2121	+	52.9733i	−0.815015	+	2.50836i
$447$	3.99003	+	1.29644i	0.188722	+	0.0613195i
$448$	−15.9857	−	22.0025i	−0.755255	−	1.03952i
$449$	−5.15561			−0.243308			−0.121654	−	0.992573i	$-0.538820\pi$
$449$	−5.15561			−0.243308			−0.121654	+	0.992573i	$0.538820\pi$
$450$	0.618778	−	0.522731i	0.0291695	−	0.0246418i
$451$	−0.730890			−0.0344163
$452$	2.48643	+	3.42228i	0.116952	+	0.160971i
$453$	−32.8060	−	10.6593i	−1.54136	−	0.500818i
$454$	5.01470	−	15.4337i	0.235352	−	0.724338i
$455$	−1.49516	+	0.832032i	−0.0700942	+	0.0390063i
$456$	1.14463	+	3.52282i	0.0536023	+	0.164971i
$457$		−	19.3472i		−	0.905025i	−0.891758	−	0.452512i	$-0.850528\pi$
$457$		−	19.3472i		−	0.905025i	0.891758	−	0.452512i	$-0.149472\pi$
$458$	−11.2827	+	3.66597i	−0.527206	+	0.171300i
$459$	10.3455	+	7.51646i	0.482887	+	0.350838i
$460$	0.633887	−	5.23451i	0.0295552	−	0.244060i
$461$	31.3873	−	22.8042i	1.46185	−	1.06210i	0.478979	−	0.877826i	$-0.341007\pi$
$461$	31.3873	−	22.8042i	1.46185	−	1.06210i	0.982875	−	0.184273i	$-0.0589930\pi$
$462$	0.427092	−	0.587841i	0.0198701	−	0.0273488i
$463$	0.832089	−	1.14527i	0.0386705	−	0.0532253i	−0.789244	−	0.614080i	$-0.789527\pi$
$463$	0.832089	−	1.14527i	0.0386705	−	0.0532253i	0.827914	+	0.560854i	$0.189527\pi$
$464$	−1.06018	+	0.770263i	−0.0492175	+	0.0357586i
$465$	−12.8911	−	5.98516i	−0.597811	−	0.277555i
$466$	−39.0344	−	28.3602i	−1.80823	−	1.31376i
$467$	−20.9376	+	6.80305i	−0.968878	+	0.314808i	−0.750363	−	0.661026i	$-0.770121\pi$
$467$	−20.9376	+	6.80305i	−0.968878	+	0.314808i	−0.218515	+	0.975834i	$0.570121\pi$
$468$		−	0.0781874i		−	0.00361421i
$469$	−4.29870	−	13.2300i	−0.198495	−	0.610906i
$470$	−55.5210	−	6.72346i	−2.56099	−	0.310130i
$471$	−0.0575695	+	0.177181i	−0.00265266	+	0.00816405i
$472$	−2.24643	−	0.729908i	−0.103400	−	0.0335967i
$473$	0.552359	+	0.760257i	0.0253975	+	0.0349567i
$474$	−3.37671			−0.155097
$475$	−2.63549	+	4.24902i	−0.120924	+	0.194959i
$476$	15.4538			0.708325
$477$	−0.0997093	−	0.137238i	−0.00456538	−	0.00628370i
$478$	−27.2928	−	8.86796i	−1.24834	−	0.405611i
$479$	−6.10191	+	18.7798i	−0.278803	+	0.858069i	0.709384	+	0.704822i	$0.248973\pi$
$479$	−6.10191	+	18.7798i	−0.278803	+	0.858069i	−0.988188	+	0.153247i	$0.951027\pi$
$480$	19.7886	+	18.3918i	0.903224	+	0.839468i
$481$	0.195108	+	0.600480i	0.00889615	+	0.0273795i
$482$		−	60.4110i		−	2.75164i
$483$	2.80161	−	0.910298i	0.127478	−	0.0414200i
$484$	−26.2319	−	19.0586i	−1.19236	−	0.866299i
$485$	2.87280	−	3.09098i	0.130447	−	0.140354i
$486$	1.36176	−	0.989377i	0.0617707	−	0.0448790i
$487$	−21.9478	+	30.2085i	−0.994549	+	1.36888i	−0.0659379	+	0.997824i	$0.521004\pi$
$487$	−21.9478	+	30.2085i	−0.994549	+	1.36888i	−0.928611	+	0.371055i	$0.878996\pi$
$488$	−4.90645	+	6.75315i	−0.222105	+	0.305701i
$489$	18.2549	−	13.2629i	0.825514	−	0.599771i
$490$	12.5992	−	2.47078i	0.569174	−	0.111618i
$491$	18.7038	+	13.5891i	0.844092	+	0.613269i	0.923511	−	0.383572i	$-0.125306\pi$
$491$	18.7038	+	13.5891i	0.844092	+	0.613269i	−0.0794186	+	0.996841i	$0.525306\pi$
$492$	−40.5551	+	13.1771i	−1.82836	+	0.594072i
$493$		−	2.72526i		−	0.122740i
$494$	0.250259	+	0.770217i	0.0112597	+	0.0346537i
$495$	−0.00607696	+	0.0130888i	−0.000273139	+	0.000588299i
$496$	1.34275	−	4.13257i	0.0602915	−	0.185558i
$497$	0.758831	+	0.246559i	0.0340382	+	0.0110597i
$498$	−16.8697	−	23.2191i	−0.755948	−	1.04047i
$499$	−32.8726			−1.47158			−0.735791	−	0.677209i	$-0.763189\pi$
$499$	−32.8726			−1.47158			−0.735791	+	0.677209i	$0.763189\pi$
$500$	1.56178	−	32.9425i	0.0698448	−	1.47323i
$501$	20.9496			0.935957
$502$	13.7555	+	18.9328i	0.613939	+	0.845014i
$503$	16.5163	+	5.36646i	0.736424	+	0.239279i	0.653129	−	0.757246i	$-0.273456\pi$
$503$	16.5163	+	5.36646i	0.736424	+	0.239279i	0.0832946	+	0.996525i	$0.473456\pi$
$504$	0.0999542	−	0.307628i	0.00445232	−	0.0137028i
$505$	11.8704	−	25.5671i	0.528227	−	1.13772i
$506$	0.0487090	+	0.149911i	0.00216538	+	0.00666435i
$507$			22.5560i			1.00175i
$508$	−55.5177	+	18.0388i	−2.46320	+	0.800342i
$509$	19.6592	+	14.2832i	0.871377	+	0.633093i	0.930956	−	0.365131i	$-0.118976\pi$
$509$	19.6592	+	14.2832i	0.871377	+	0.633093i	−0.0595789	+	0.998224i	$0.518976\pi$
$510$	−21.3269	+	4.18233i	−0.944372	+	0.185197i
$511$	−10.8616	+	7.89143i	−0.480490	+	0.349097i
$512$	−7.83161	+	10.7793i	−0.346112	+	0.476382i
$513$	−3.01604	+	4.15122i	−0.133161	+	0.183281i
$514$	9.57909	−	6.95962i	0.422515	−	0.306975i
$515$	2.36451	−	2.54409i	0.104193	−	0.112106i
$516$	44.3555	+	32.2262i	1.95264	+	1.41868i
$517$	0.947583	−	0.307889i	0.0416747	−	0.0135409i
$518$			8.11225i			0.356432i
$519$	0.354473	+	1.09096i	0.0155596	+	0.0478877i
$520$	−1.25983	−	1.17091i	−0.0552474	−	0.0513476i
$521$	−1.17168	+	3.60607i	−0.0513324	+	0.157985i	−0.973437	−	0.228957i	$-0.926469\pi$
$521$	−1.17168	+	3.60607i	−0.0513324	+	0.157985i	0.922104	+	0.386942i	$0.126469\pi$
$522$	−0.168486	−	0.0547445i	−0.00737444	−	0.00239610i
$523$	−15.2490	−	20.9885i	−0.666794	−	0.917763i	0.332889	−	0.942966i	$-0.391977\pi$
$523$	−15.2490	−	20.9885i	−0.666794	−	0.917763i	−0.999682	+	0.0252035i	$0.991977\pi$
$524$	46.2165			2.01898
$525$	17.0604	−	6.95889i	0.744576	−	0.303711i
$526$	−57.5163			−2.50783
$527$	5.31154	+	7.31071i	0.231374	+	0.318460i
$528$	−0.177066	−	0.0575321i	−0.00770579	−	0.00250376i
$529$	6.90992	−	21.2665i	0.300431	−	0.924632i
$530$	−11.5054	−	1.39327i	−0.499761	−	0.0605199i
$531$	0.0251528	+	0.0774123i	0.00109154	+	0.00335941i
$532$			6.20097i			0.268846i
$533$	−2.85497	+	0.927636i	−0.123662	+	0.0401804i
$534$	−7.73353	−	5.61874i	−0.334663	−	0.243147i
$535$	25.8336	+	11.9942i	1.11689	+	0.518554i
$536$	11.3125	−	8.21899i	0.488624	−	0.355006i
$537$	0.958562	−	1.31935i	0.0413650	−	0.0569340i
$538$	−16.2285	+	22.3365i	−0.699658	+	0.962997i
$539$	−0.185050	+	0.134446i	−0.00797065	+	0.00579102i
$540$	4.06881	−	33.5994i	0.175094	−	1.44589i
$541$	23.0011	+	16.7112i	0.988893	+	0.718472i	0.959678	−	0.281101i	$-0.0906995\pi$
$541$	23.0011	+	16.7112i	0.988893	+	0.718472i	0.0292143	+	0.999573i	$0.490699\pi$
$542$	−15.5225	+	5.04355i	−0.666747	+	0.216639i
$543$		−	14.2017i		−	0.609452i
$544$	−5.30789	−	16.3360i	−0.227574	−	0.700400i
$545$	36.4837	−	20.3026i	1.56279	−	0.869667i
$546$	0.922206	−	2.83826i	0.0394668	−	0.121466i
$547$	38.0965	+	12.3783i	1.62889	+	0.529258i	0.974016	−	0.226480i	$-0.0727218\pi$
$547$	38.0965	+	12.3783i	1.62889	+	0.529258i	0.654874	+	0.755738i	$0.272722\pi$
$548$	−26.9165	−	37.0474i	−1.14982	−	1.58259i
$549$	0.287652			0.0122767
$550$	0.372362	+	0.912880i	0.0158776	+	0.0389253i
$551$	1.09353			0.0465861
$552$	1.74046	+	2.39554i	0.0740791	+	0.101961i
$553$	−1.73105	−	0.562452i	−0.0736117	−	0.0239179i
$554$	−13.1916	+	40.5996i	−0.560458	+	1.72491i
$555$	−1.30836	−	6.67171i	−0.0555368	−	0.283198i
$556$	0.368893	+	1.13534i	0.0156445	+	0.0481489i
$557$		−	4.62202i		−	0.195841i	−0.995194	−	0.0979207i	$-0.968781\pi$
$557$		−	4.62202i		−	0.195841i	0.995194	−	0.0979207i	$-0.0312191\pi$
$558$	0.558674	−	0.181524i	0.0236506	−	0.00768453i
$559$	3.12251	+	2.26864i	0.132068	+	0.0959530i
$560$	2.73914	+	4.92223i	0.115750	+	0.208002i
$561$	0.313237	−	0.227580i	0.0132249	−	0.00960844i
$562$	21.0430	−	28.9632i	0.887647	−	1.22174i
$563$	−8.44970	+	11.6300i	−0.356112	+	0.490146i	−0.949060	−	0.315094i	$-0.897964\pi$
$563$	−8.44970	+	11.6300i	−0.356112	+	0.490146i	0.592948	+	0.805241i	$0.297964\pi$
$564$	47.0279	−	34.1678i	1.98023	−	1.43872i
$565$	−1.55928	−	2.80203i	−0.0655995	−	0.117882i
$566$	32.4204	+	23.5548i	1.36273	+	0.990083i
$567$	18.4198	−	5.98495i	0.773558	−	0.251344i
$568$			0.802017i			0.0336519i
$569$	−0.763261	−	2.34908i	−0.0319976	−	0.0984784i	0.933782	−	0.357842i	$-0.116487\pi$
$569$	−0.763261	−	2.34908i	−0.0319976	−	0.0984784i	−0.965780	+	0.259363i	$0.916487\pi$
$570$	−1.67819	−	8.55760i	−0.0702918	−	0.358438i
$571$	7.92528	−	24.3915i	0.331663	−	1.02075i	−0.636680	−	0.771128i	$-0.719693\pi$
$571$	7.92528	−	24.3915i	0.331663	−	1.02075i	0.968343	−	0.249625i	$-0.0803073\pi$
$572$	0.0905067	+	0.0294074i	0.00378427	+	0.00122959i
$573$	−16.6582	−	22.9280i	−0.695906	−	0.957832i
$574$	−38.5695			−1.60986
$575$	−0.954062	+	3.88145i	−0.0397871	+	0.161868i
$576$	−0.942056			−0.0392523
$577$	10.9588	+	15.0835i	0.456221	+	0.627934i	0.973720	−	0.227750i	$-0.0731369\pi$
$577$	10.9588	+	15.0835i	0.456221	+	0.627934i	−0.517499	+	0.855684i	$0.673137\pi$
$578$	−22.8289	−	7.41757i	−0.949558	−	0.308530i
$579$	10.6349	−	32.7307i	0.441970	−	1.36024i
$580$	−6.30267	+	3.50733i	−0.261704	+	0.145634i
$581$	−4.78057	−	14.7131i	−0.198331	−	0.610401i
$582$			7.35993i			0.305079i
$583$	0.196364	−	0.0638024i	0.00813255	−	0.00264242i
$584$	−10.9179	−	7.93233i	−0.451787	−	0.328242i
$585$	−0.00712537	+	0.0588398i	−0.000294598	+	0.00243273i
$586$	6.09613	−	4.42910i	0.251829	−	0.182964i
$587$	−8.92780	+	12.2881i	−0.368490	+	0.507183i	−0.952490	−	0.304571i	$-0.901487\pi$
$587$	−8.92780	+	12.2881i	−0.368490	+	0.507183i	0.584000	+	0.811754i	$0.301487\pi$
$588$	−7.84397	+	10.7963i	−0.323480	+	0.445232i
$589$	−2.93348	+	2.13130i	−0.120872	+	0.0878187i
$590$	5.04382	+	2.34178i	0.207651	+	0.0964094i
$591$	−27.3514	−	19.8719i	−1.12508	−	0.817422i
$592$	1.97685	−	0.642317i	0.0812479	−	0.0263990i
$593$		−	11.3350i		−	0.465472i	−0.972540	−	0.232736i	$-0.925232\pi$
$593$		−	11.3350i		−	0.465472i	0.972540	−	0.232736i	$-0.0747678\pi$
$594$	0.312654	+	0.962251i	0.0128284	+	0.0394816i
$595$	−11.6297	−	1.40834i	−0.476773	−	0.0577362i
$596$	−2.18159	+	6.71425i	−0.0893614	+	0.275026i
$597$	41.0452	+	13.3364i	1.67987	+	0.545822i
$598$	0.380530	+	0.523754i	0.0155610	+	0.0214179i
$599$	−0.838295			−0.0342518			−0.0171259	−	0.999853i	$-0.505452\pi$
$599$	−0.838295			−0.0342518			−0.0171259	+	0.999853i	$0.505452\pi$
$600$	11.9519	+	14.1479i	0.487933	+	0.577586i
$601$	26.0999			1.06464			0.532318	−	0.846545i	$-0.321321\pi$
$601$	26.0999			1.06464			0.532318	+	0.846545i	$0.321321\pi$
$602$	29.1483	+	40.1193i	1.18800	+	1.63514i
$603$	−0.458273	−	0.148902i	−0.0186623	−	0.00606375i
$604$	17.9370	−	55.2045i	0.729847	−	2.24624i
$605$	18.0039	+	16.7331i	0.731963	+	0.680296i
$606$	15.1925	+	46.7576i	0.617151	+	1.89940i
$607$			3.10745i			0.126127i	0.998010	+	0.0630637i	$0.0200871\pi$
$607$			3.10745i			0.126127i	−0.998010	+	0.0630637i	$0.979913\pi$
$608$	6.55495	−	2.12983i	0.265838	−	0.0863761i
$609$	−3.26008	−	2.36859i	−0.132105	−	0.0959800i
$610$	13.3789	−	14.3950i	0.541695	−	0.582836i
$611$	3.31064	−	2.40532i	0.133934	−	0.0973088i
$612$	0.314643	−	0.433069i	0.0127187	−	0.0175058i
$613$	−18.5398	+	25.5179i	−0.748816	+	1.03066i	0.249246	+	0.968440i	$0.419817\pi$
$613$	−18.5398	+	25.5179i	−0.748816	+	1.03066i	−0.998063	+	0.0622173i	$0.980183\pi$
$614$	22.2230	−	16.1460i	0.896848	−	0.651598i
$615$	31.7205	−	6.22057i	1.27909	−	0.250838i
$616$	0.318503	+	0.231406i	0.0128329	+	0.00932362i
$617$	40.7235	−	13.2319i	1.63947	−	0.532695i	0.663047	−	0.748577i	$-0.269263\pi$
$617$	40.7235	−	13.2319i	1.63947	−	0.532695i	0.976419	+	0.215882i	$0.0692628\pi$
$618$			6.05773i			0.243678i
$619$	−3.31355	−	10.1981i	−0.133183	−	0.409895i	0.862120	−	0.506704i	$-0.169136\pi$
$619$	−3.31355	−	10.1981i	−0.133183	−	0.409895i	−0.995303	+	0.0968092i	$0.969136\pi$
$620$	10.0716	−	21.6926i	0.404484	−	0.871196i
$621$	−1.26755	+	3.90110i	−0.0508648	+	0.156546i
$622$	8.45879	+	2.74843i	0.339167	+	0.110202i
$623$	−3.02864	−	4.16857i	−0.121340	−	0.167010i
$624$	−0.764665			−0.0306111
$625$	−4.17743	+	24.6485i	−0.167097	+	0.985940i
$626$	−60.4359			−2.41550
$627$	0.0913183	+	0.125689i	0.00364690	+	0.00501953i
$628$	−0.298152	−	0.0968754i	−0.0118976	−	0.00386575i
$629$	−1.33579	+	4.11112i	−0.0532613	+	0.163921i
$630$	−0.320685	+	0.690706i	−0.0127764	+	0.0275184i
$631$	5.64592	+	17.3764i	0.224761	+	0.691742i	0.998316	+	0.0580132i	$0.0184765\pi$
$631$	5.64592	+	17.3764i	0.224761	+	0.691742i	−0.773555	+	0.633729i	$0.781523\pi$
$632$		−	1.82957i		−	0.0727762i
$633$	−17.7369	+	5.76307i	−0.704979	+	0.229062i
$634$	9.19392	+	6.67978i	0.365137	+	0.265288i
$635$	43.4237	−	8.51563i	1.72322	−	0.337933i
$636$	9.74539	−	7.08044i	0.386430	−	0.280758i
$637$	−0.552195	+	0.760031i	−0.0218788	+	0.0301135i
$638$	0.126740	−	0.174443i	0.00501769	−	0.00690626i
$639$	0.0223594	−	0.0162450i	0.000884522	−	0.000642643i
$640$	−22.8318	+	24.5658i	−0.902504	+	0.971048i
$641$	7.19414	+	5.22685i	0.284152	+	0.206448i	0.720726	−	0.693220i	$-0.243809\pi$
$641$	7.19414	+	5.22685i	0.284152	+	0.206448i	−0.436575	+	0.899668i	$0.643809\pi$
$642$	−47.2451	+	15.3509i	−1.86461	+	0.605850i
$643$		−	7.19473i		−	0.283732i	−0.989886	−	0.141866i	$-0.954690\pi$
$643$		−	7.19473i		−	0.283732i	0.989886	−	0.141866i	$-0.0453103\pi$
$644$	1.53181	+	4.71443i	0.0603618	+	0.185774i
$645$	−30.4428	−	28.2939i	−1.19868	−	1.11407i
$646$	−1.71337	+	5.27321i	−0.0674117	+	0.207472i
$647$	−23.7231	−	7.70811i	−0.932653	−	0.303037i	−0.197006	−	0.980402i	$-0.563122\pi$
$647$	−23.7231	−	7.70811i	−0.932653	−	0.303037i	−0.735647	+	0.677365i	$0.763122\pi$
$648$	11.4431	+	15.7500i	0.449526	+	0.618719i
$649$	−0.0990698			−0.00388883
$650$	2.61312	+	3.09325i	0.102495	+	0.121327i
$651$	13.3618			0.523689
$652$	22.3183	+	30.7185i	0.874052	+	1.20303i
$653$	−36.8849	−	11.9846i	−1.44342	−	0.468995i	−0.520457	−	0.853888i	$-0.674238\pi$
$653$	−36.8849	−	11.9846i	−1.44342	−	0.468995i	−0.922961	+	0.384893i	$0.874238\pi$
$654$	−22.5029	+	69.2568i	−0.879934	+	2.70816i
$655$	−34.7802	−	4.21180i	−1.35897	−	0.164569i
$656$	3.05388	+	9.39888i	0.119234	+	0.366965i
$657$			0.465051i			0.0181434i
$658$	50.0046	−	16.2475i	1.94938	−	0.633392i
$659$	−23.9989	−	17.4362i	−0.934864	−	0.679218i	0.0123149	−	0.999924i	$-0.496080\pi$
$659$	−23.9989	−	17.4362i	−0.934864	−	0.679218i	−0.947179	+	0.320706i	$0.896080\pi$
$660$	−0.929448	−	0.431530i	−0.0361787	−	0.0167973i
$661$	−15.2865	+	11.1063i	−0.594578	+	0.431986i	−0.843950	−	0.536422i	$-0.819776\pi$
$661$	−15.2865	+	11.1063i	−0.594578	+	0.431986i	0.249372	+	0.968408i	$0.419776\pi$
$662$	21.6145	−	29.7498i	0.840070	−	1.15626i
$663$	0.934711	−	1.28652i	0.0363012	−	0.0499643i
$664$	12.5806	−	9.14031i	0.488220	−	0.354713i
$665$	0.565106	−	4.66653i	0.0219139	−	0.180960i
$666$	0.227333	+	0.165167i	0.00880897	+	0.00640009i
$667$	0.831383	−	0.270133i	0.0321913	−	0.0104596i
$668$			35.2530i			1.36398i
$669$	13.5615	+	41.7381i	0.524319	+	1.61369i
$670$	−28.7661	+	16.0079i	−1.11133	+	0.618438i
$671$	−0.108190	+	0.332974i	−0.00417663	+	0.0128543i
$672$	−24.1551	−	7.84845i	−0.931802	−	0.302761i
$673$	−11.1730	−	15.3783i	−0.430687	−	0.592790i	0.537423	−	0.843313i	$-0.319398\pi$
$673$	−11.1730	−	15.3783i	−0.430687	−	0.592790i	−0.968111	+	0.250522i	$0.919398\pi$
$674$	55.5989			2.14159
$675$	−6.12395	+	24.9144i	−0.235711	+	0.958954i
$676$	−37.9563			−1.45986
$677$	17.5510	+	24.1568i	0.674538	+	0.928422i	0.999852	−	0.0171840i	$-0.00547009\pi$
$677$	17.5510	+	24.1568i	0.674538	+	0.928422i	−0.325314	+	0.945606i	$0.605470\pi$
$678$	5.31908	+	1.72827i	0.204278	+	0.0663739i
$679$	−1.22593	+	3.77302i	−0.0470468	+	0.144795i
$680$	−2.26607	−	11.5553i	−0.0868996	−	0.443126i
$681$	−3.95112	−	12.1603i	−0.151407	−	0.465984i
$682$			0.714973i			0.0273777i
$683$	−31.8080	+	10.3351i	−1.21710	+	0.395460i	−0.846025	−	0.533143i	$-0.821011\pi$
$683$	−31.8080	+	10.3351i	−1.21710	+	0.395460i	−0.371075	+	0.928603i	$0.621011\pi$
$684$	0.173772	+	0.126253i	0.00664435	+	0.00482740i
$685$	16.8798	+	30.3329i	0.644942	+	1.15896i
$686$	−36.2513	+	26.3381i	−1.38408	+	1.00559i
$687$	−5.49416	+	7.56206i	−0.209615	+	0.288511i
$688$	7.46860	−	10.2797i	0.284738	−	0.391908i
$689$	0.686049	−	0.498444i	0.0261364	−	0.0189892i
$690$	−3.38985	−	6.09154i	−0.129049	−	0.231901i
$691$	35.1522	+	25.5395i	1.33725	+	0.971570i	0.999540	+	0.0303201i	$0.00965267\pi$
$691$	35.1522	+	25.5395i	1.33725	+	0.971570i	0.337711	+	0.941250i	$0.390347\pi$
$692$	−1.83581	+	0.596492i	−0.0697871	+	0.0226752i
$693$		−	0.0135667i		−	0.000515357i
$694$	−10.9292	−	33.6366i	−0.414867	−	1.27683i
$695$	−0.174144	−	0.888012i	−0.00660567	−	0.0336842i
$696$	1.25169	−	3.85232i	0.0474453	−	0.146022i
$697$	−19.5463	−	6.35097i	−0.740368	−	0.240560i
$698$	12.0751	+	16.6199i	0.457049	+	0.629074i
$699$	−38.0159			−1.43789
$700$	11.7101	+	28.7084i	0.442601	+	1.08508i
$701$	−3.75707			−0.141903			−0.0709514	−	0.997480i	$-0.522604\pi$
$701$	−3.75707			−0.141903			−0.0709514	+	0.997480i	$0.522604\pi$
$702$	2.44255	+	3.36188i	0.0921882	+	0.126886i
$703$	−1.64962	−	0.535995i	−0.0622167	−	0.0202154i
$704$	0.354321	−	1.09049i	0.0133540	−	0.0410993i
$705$	−38.5045	+	21.4272i	−1.45017	+	0.806993i
$706$	4.63851	+	14.2759i	0.174573	+	0.537279i
$707$			26.5005i			0.996655i
$708$	−5.49711	+	1.78612i	−0.206594	+	0.0671265i
$709$	19.5505	+	14.2043i	0.734234	+	0.533452i	0.890900	−	0.454200i	$-0.150075\pi$
$709$	19.5505	+	14.2043i	0.734234	+	0.533452i	−0.156666	+	0.987652i	$0.550075\pi$
$710$	0.226997	−	1.87450i	0.00851906	−	0.0703486i
$711$	−0.0510063	+	0.0370582i	−0.00191289	+	0.00138979i
$712$	3.04434	−	4.19017i	0.114091	−	0.157033i
$713$	−1.70376	+	2.34502i	−0.0638061	+	0.0878216i
$714$	16.5297	−	12.0095i	0.618609	−	0.449446i
$715$	−0.0654307	−	0.0303785i	−0.00244697	−	0.00113609i
$716$	2.22014	+	1.61303i	0.0829705	+	0.0602816i
$717$	−21.5042	+	6.98713i	−0.803089	+	0.260939i
$718$			68.6853i			2.56331i
$719$	3.56002	+	10.9566i	0.132766	+	0.408612i	0.995236	−	0.0974964i	$-0.0310834\pi$
$719$	3.56002	+	10.9566i	0.132766	+	0.408612i	−0.862470	+	0.506109i	$0.831083\pi$
$720$	0.193707	+	0.0234575i	0.00721904	+	0.000874210i
$721$	−1.00902	+	3.10545i	−0.0375780	+	0.115653i
$722$	−2.11592	−	0.687504i	−0.0787464	−	0.0255863i
$723$	−27.9776	−	38.5078i	−1.04050	−	1.43212i
$724$	23.8979			0.888160
$725$	5.06269	−	2.06506i	0.188024	−	0.0766946i
$726$	−42.8690			−1.59102
$727$	−29.3080	−	40.3390i	−1.08697	−	1.49609i	−0.851605	−	0.524184i	$-0.824370\pi$
$727$	−29.3080	−	40.3390i	−1.08697	−	1.49609i	−0.235368	−	0.971906i	$-0.575630\pi$
$728$	1.53782	+	0.499668i	0.0569954	+	0.0185189i
$729$	−8.13123	+	25.0254i	−0.301157	+	0.926865i
$730$	23.2726	+	21.6298i	0.861356	+	0.800555i
$731$	8.16565	+	25.1313i	0.302017	+	0.929514i
$732$			20.4264i			0.754981i
$733$	28.3178	−	9.20102i	1.04594	−	0.339847i	0.264868	−	0.964285i	$-0.414672\pi$
$733$	28.3178	−	9.20102i	1.04594	−	0.339847i	0.781075	+	0.624438i	$0.214672\pi$
$734$	−34.7149	−	25.2219i	−1.28135	−	0.930956i
$735$	6.88686	−	7.40990i	0.254026	−	0.273318i
$736$	4.45742	−	3.23851i	0.164303	−	0.119373i
$737$	0.344726	−	0.474475i	0.0126981	−	0.0174775i
$738$	−0.785283	+	1.08085i	−0.0289067	+	0.0397866i
$739$	−15.4581	+	11.2310i	−0.568636	+	0.413138i	−0.834609	−	0.550842i	$-0.814307\pi$
$739$	−15.4581	+	11.2310i	−0.568636	+	0.413138i	0.265974	+	0.963980i	$0.414307\pi$
$740$	11.2269	−	2.20165i	0.412707	−	0.0809343i
$741$	0.516226	+	0.375060i	0.0189640	+	0.0137782i
$742$	10.3622	−	3.36689i	0.380409	−	0.123602i
$743$		−	9.85846i		−	0.361672i	−0.983513	−	0.180836i	$-0.942120\pi$
$743$		−	9.85846i		−	0.361672i	0.983513	−	0.180836i	$-0.0578803\pi$
$744$	4.15042	+	12.7737i	0.152162	+	0.468305i
$745$	2.25363	−	4.85398i	0.0825668	−	0.177836i
$746$	−3.62061	+	11.1431i	−0.132560	+	0.407978i
$747$	−0.509644	−	0.165593i	−0.0186469	−	0.00605874i
$748$	0.382962	+	0.527101i	0.0140025	+	0.0192727i
$749$	−26.7768			−0.978404
$750$	−23.9299	−	36.4497i	−0.873798	−	1.33095i
$751$	23.2616			0.848827			0.424413	−	0.905469i	$-0.360480\pi$
$751$	23.2616			0.848827			0.424413	+	0.905469i	$0.360480\pi$
$752$	−7.91859	−	10.8990i	−0.288761	−	0.397446i
$753$	17.5364	+	5.69791i	0.639061	+	0.207644i
$754$	0.273666	−	0.842258i	0.00996633	−	0.0306732i
$755$	−18.5294	+	39.9094i	−0.674353	+	1.45245i
$756$	9.83242	+	30.2611i	0.357602	+	1.10058i
$757$		−	40.8210i		−	1.48366i	−0.670586	−	0.741832i	$-0.733957\pi$
$757$		−	40.8210i		−	1.48366i	0.670586	−	0.741832i	$-0.266043\pi$
$758$	55.6227	−	18.0729i	2.02031	−	0.656438i
$759$	0.100475	+	0.0729996i	0.00364703	+	0.00264972i
$760$	4.63667	−	0.909277i	0.168190	−	0.0329829i
$761$	28.8084	−	20.9305i	1.04430	−	0.758731i	0.0731822	−	0.997319i	$-0.476685\pi$
$761$	28.8084	−	20.9305i	1.04430	−	0.758731i	0.971121	+	0.238588i	$0.0766845\pi$
$762$	−45.3645	+	62.4388i	−1.64338	+	2.26192i
$763$	−23.0719	+	31.7558i	−0.835260	+	1.14964i
$764$	38.5823	−	28.0317i	1.39586	−	1.01415i
$765$	−0.276250	+	0.297231i	−0.00998785	+	0.0107464i
$766$	14.4223	+	10.4784i	0.521098	+	0.378600i
$767$	−0.386982	+	0.125738i	−0.0139731	+	0.00454014i
$768$		−	13.1368i		−	0.474032i
$769$	−13.9343	−	42.8853i	−0.502483	−	1.54648i	−0.804961	−	0.593328i	$-0.797814\pi$
$769$	−13.9343	−	42.8853i	−0.502483	−	1.54648i	0.302477	−	0.953157i	$-0.402186\pi$
$770$	−0.678920	−	0.630997i	−0.0244666	−	0.0227395i
$771$	2.88287	−	8.87255i	0.103824	−	0.319537i
$772$	55.0778	+	17.8959i	1.98229	+	0.644086i
$773$	−12.6650	−	17.4319i	−0.455529	−	0.626981i	0.518045	−	0.855353i	$-0.326660\pi$
$773$	−12.6650	−	17.4319i	−0.455529	−	0.626981i	−0.973574	+	0.228372i	$0.926660\pi$
$774$	1.71774			0.0617430
$775$	−9.55623	+	15.4069i	−0.343270	+	0.553432i
$776$	−3.98775			−0.143152
$777$	3.75695	+	5.17100i	0.134780	+	0.185509i
$778$	37.0319	+	12.0324i	1.32766	+	0.431383i
$779$	2.54838	−	7.84310i	0.0913051	−	0.281008i
$780$	−4.17826	−	0.505978i	−0.149606	−	0.0181169i
$781$	0.0103949	+	0.0319923i	0.000371960	+	0.00114477i
$782$			4.43233i			0.158500i
$783$	5.33650	−	1.73393i	0.190711	−	0.0619657i
$784$	2.50211	+	1.81789i	0.0893610	+	0.0649246i
$785$	0.215545	+	0.100075i	0.00769314	+	0.00357181i
$786$	49.4341	−	35.9160i	1.76326	−	1.28108i
$787$	−5.80831	+	7.99445i	−0.207044	+	0.284971i	−0.899893	−	0.436111i	$-0.856355\pi$
$787$	−5.80831	+	7.99445i	−0.207044	+	0.284971i	0.692849	+	0.721083i	$0.256355\pi$
$788$	33.4396	−	46.0257i	1.19124	−	1.63960i
$789$	−36.6627	+	26.6370i	−1.30523	+	0.948302i
$790$	−0.517828	+	4.27611i	−0.0184235	+	0.152137i
$791$	2.43891	+	1.77198i	0.0867178	+	0.0630042i
$792$	0.0129696	−	0.00421407i	0.000460854	−	0.000149741i
$793$			1.43796i			0.0510636i
$794$	18.9452	+	58.3074i	0.672341	+	2.06925i
$795$	−7.97913	+	4.44025i	−0.282990	+	0.157480i
$796$	−22.4419	+	69.0691i	−0.795432	+	2.44809i
$797$	−30.7601	−	9.99456i	−1.08958	−	0.354025i	−0.291495	−	0.956572i	$-0.594153\pi$
$797$	−30.7601	−	9.99456i	−1.08958	−	0.354025i	−0.798083	+	0.602547i	$0.794153\pi$
$798$	4.81893	+	6.63268i	0.170588	+	0.234794i
$799$	28.0167			0.991159
$800$	26.3252	−	22.2390i	0.930736	−	0.786268i
$801$	−0.178481			−0.00630632
$802$	15.3772	+	21.1650i	0.542989	+	0.747361i
$803$	−0.538325	−	0.174912i	−0.0189971	−	0.00617252i
$804$	10.5736	−	32.5423i	0.372904	−	1.14768i
$805$	−0.723126	−	3.68743i	−0.0254868	−	0.129965i
$806$	0.907434	+	2.79279i	0.0319630	+	0.0983720i
$807$			21.7537i			0.765768i
$808$	−25.3341	+	8.23155i	−0.891251	+	0.289585i
$809$	−6.95358	−	5.05207i	−0.244475	−	0.177621i	0.458800	−	0.888540i	$-0.348280\pi$
$809$	−6.95358	−	5.05207i	−0.244475	−	0.177621i	−0.703275	+	0.710918i	$0.748280\pi$
$810$	−22.2873	−	40.0502i	−0.783095	−	1.40722i
$811$	−26.7538	+	19.4378i	−0.939452	+	0.682552i	−0.948289	−	0.317409i	$-0.897187\pi$
$811$	−26.7538	+	19.4378i	−0.939452	+	0.682552i	0.00883655	+	0.999961i	$0.497187\pi$
$812$	3.98575	−	5.48592i	0.139872	−	0.192518i
$813$	−7.55872	+	10.4037i	−0.265096	+	0.364873i
$814$	−0.276694	+	0.201030i	−0.00969811	+	0.00704609i
$815$	−13.9962	−	25.1511i	−0.490264	−	0.881003i
$816$	−4.23537	−	3.07717i	−0.148267	−	0.107723i
$817$	−10.0841	+	3.27653i	−0.352799	+	0.114631i
$818$			49.3877i			1.72680i
$819$	−0.0172187	−	0.0529937i	−0.000601670	−	0.00185175i
$820$	10.4677	+	53.3779i	0.365548	+	1.86404i
$821$	−15.1988	+	46.7772i	−0.530443	+	1.63254i	0.222851	+	0.974852i	$0.428464\pi$
$821$	−15.1988	+	46.7772i	−0.530443	+	1.63254i	−0.753294	+	0.657683i	$0.771536\pi$
$822$	−57.5808	−	18.7091i	−2.00836	−	0.652556i
$823$	19.3324	+	26.6087i	0.673883	+	0.927521i	0.999840	−	0.0178636i	$-0.00568648\pi$
$823$	19.3324	+	26.6087i	0.673883	+	0.927521i	−0.325957	+	0.945385i	$0.605686\pi$
$824$	−3.28219			−0.114341
$825$	0.660129	+	0.409449i	0.0229827	+	0.0142552i
$826$	−5.22798			−0.181905
$827$	7.31478	+	10.0679i	0.254360	+	0.350096i	0.917032	−	0.398813i	$-0.130578\pi$
$827$	7.31478	+	10.0679i	0.254360	+	0.350096i	−0.662672	+	0.748909i	$0.730578\pi$
$828$	0.163302	+	0.0530601i	0.00567514	+	0.00184397i
$829$	2.16170	−	6.65304i	0.0750790	−	0.231070i	−0.906473	−	0.422263i	$-0.861236\pi$
$829$	2.16170	−	6.65304i	0.0750790	−	0.231070i	0.981552	+	0.191194i	$0.0612358\pi$
$830$	−31.9907	+	17.8023i	−1.11041	+	0.617926i
$831$	10.3938	+	31.9887i	0.360556	+	1.10968i
$832$		−	4.70931i		−	0.163266i
$833$	−6.11705	+	1.98755i	−0.211943	+	0.0688646i
$834$	1.27687	+	0.927702i	0.0442145	+	0.0321237i
$835$	3.21267	−	26.5296i	0.111179	−	0.918094i
$836$	−0.211504	+	0.153666i	−0.00731501	+	0.00531466i
$837$	−10.9361	+	15.0523i	−0.378007	+	0.520282i
$838$	33.9373	−	46.7107i	1.17234	−	1.61359i
$839$	−38.8201	+	28.2045i	−1.34022	+	0.973726i	−0.340783	+	0.940142i	$0.610692\pi$
$839$	−38.8201	+	28.2045i	−1.34022	+	0.973726i	−0.999436	+	0.0335839i	$0.989308\pi$
$840$	−15.7925	−	7.33222i	−0.544892	−	0.252986i
$841$	22.4941	+	16.3429i	0.775657	+	0.563548i
$842$	47.1441	−	15.3181i	1.62469	−	0.527895i
$843$		−	28.2075i		−	0.971519i
$844$	−9.69784	−	29.8469i	−0.333813	−	1.02737i
$845$	28.5639	+	3.45903i	0.982629	+	0.118994i
$846$	0.562793	−	1.73210i	0.0193492	−	0.0595508i
$847$	−21.9765	−	7.14061i	−0.755122	−	0.245354i
$848$	−1.64093	−	2.25855i	−0.0563499	−	0.0775590i
$849$	31.5745			1.08363
$850$	2.02577	+	27.6488i	0.0694835	+	0.948347i
$851$	−1.38657			−0.0475309
$852$	1.15357	+	1.58776i	0.0395207	+	0.0543956i
$853$	42.6101	+	13.8448i	1.45894	+	0.474039i	0.927746	−	0.373212i	$-0.121743\pi$
$853$	42.6101	+	13.8448i	1.45894	+	0.474039i	0.531194	+	0.847250i	$0.321743\pi$
$854$	−5.70925	+	17.5713i	−0.195367	+	0.601277i
$855$	−0.119266	−	0.110848i	−0.00407882	−	0.00379091i
$856$	−8.31738	−	25.5983i	−0.284282	−	0.874931i
$857$		−	44.8942i		−	1.53356i	−0.641911	−	0.766779i	$-0.721858\pi$
$857$		−	44.8942i		−	1.53356i	0.641911	−	0.766779i	$-0.278142\pi$
$858$	0.119661	−	0.0388802i	0.00408516	−	0.00132735i
$859$	−3.85912	−	2.80381i	−0.131671	−	0.0956649i	0.520000	−	0.854166i	$-0.325932\pi$
$859$	−3.85912	−	2.80381i	−0.131671	−	0.0956649i	−0.651671	+	0.758501i	$0.725932\pi$
$860$	47.6118	−	51.2278i	1.62355	−	1.74685i
$861$	−24.5854	+	17.8623i	−0.837869	+	0.608747i
$862$	51.0775	−	70.3021i	1.73971	−	2.39450i
$863$	23.5670	−	32.4372i	0.802229	−	1.10417i	−0.190247	−	0.981736i	$-0.560929\pi$
$863$	23.5670	−	32.4372i	0.802229	−	1.10417i	0.992476	−	0.122437i	$-0.0390711\pi$
$864$	28.6114	−	20.7874i	0.973379	−	0.707202i
$865$	1.43590	−	0.281588i	0.0488220	−	0.00957427i
$866$	0.109548	+	0.0795910i	0.00372258	+	0.00270461i
$867$	−17.9871	+	5.84436i	−0.610874	+	0.198485i
$868$			22.4846i			0.763177i
$869$	−0.0237130	−	0.0729810i	−0.000804407	−	0.00247571i
$870$	−4.01583	+	8.64947i	−0.136149	+	0.293245i
$871$	0.744356	−	2.29089i	0.0252215	−	0.0776239i
$872$	−37.5247	−	12.1925i	−1.27075	−	0.412890i
$873$	0.0807727	+	0.111174i	0.00273374	+	0.00376267i
$874$	−1.77851			−0.0601589
$875$	−6.19617	−	22.6716i	−0.209469	−	0.766441i
$876$	−33.0236			−1.11576
$877$	−31.8459	−	43.8322i	−1.07536	−	1.48011i	−0.864528	−	0.502585i	$-0.832382\pi$
$877$	−31.8459	−	43.8322i	−1.07536	−	1.48011i	−0.210833	−	0.977522i	$-0.567618\pi$
$878$	68.5683	+	22.2792i	2.31407	+	0.751887i
$879$	1.83465	−	5.64648i	0.0618813	−	0.190451i
$880$	−0.100010	+	0.215405i	−0.00337132	+	0.00726131i
$881$	−1.43238	−	4.40842i	−0.0482582	−	0.148523i	0.924024	−	0.382335i	$-0.124880\pi$
$881$	−1.43238	−	4.40842i	−0.0482582	−	0.148523i	−0.972282	+	0.233812i	$0.924880\pi$
$882$			0.418106i			0.0140783i
$883$	32.1214	−	10.4369i	1.08097	−	0.351229i	0.286220	−	0.958164i	$-0.407601\pi$
$883$	32.1214	−	10.4369i	1.08097	−	0.351229i	0.794752	+	0.606935i	$0.207601\pi$
$884$	2.16490	+	1.57289i	0.0728134	+	0.0529020i
$885$	4.29961	−	0.843179i	0.144530	−	0.0283431i
$886$	25.5102	−	18.5342i	0.857032	−	0.622670i
$887$	5.09933	−	7.01863i	0.171219	−	0.235662i	−0.714781	−	0.699349i	$-0.753473\pi$
$887$	5.09933	−	7.01863i	0.171219	−	0.235662i	0.885999	+	0.463686i	$0.153473\pi$
$888$	−3.77642	+	5.19780i	−0.126728	+	0.174427i
$889$	−33.6561	+	24.4526i	−1.12879	+	0.820113i
$890$	−8.30127	+	8.93174i	−0.278259	+	0.299393i
$891$	0.660597	+	0.479952i	0.0221308	+	0.0160790i
$892$	−70.2350	+	22.8207i	−2.35164	+	0.764095i
$893$			11.2419i			0.376196i
$894$	2.88433	+	8.87706i	0.0964665	+	0.296893i
$895$	−1.52376	−	1.41620i	−0.0509338	−	0.0473385i
$896$	9.74314	−	29.9863i	0.325496	−	1.00177i
$897$	0.485123	+	0.157626i	0.0161978	+	0.00526297i
$898$	−6.74204	−	9.27963i	−0.224985	−	0.309665i
$899$	3.96513			0.132245
$900$	1.04293	+	0.256352i	0.0347643	+	0.00854506i
$901$	5.80577			0.193418
$902$	−0.955793	−	1.31554i	−0.0318244	−	0.0438025i
$903$	37.1601	+	12.0741i	1.23661	+	0.401799i
$904$	−0.936411	+	2.88198i	−0.0311446	+	0.0958531i
$905$	−17.9844	−	2.17786i	−0.597820	−	0.0723947i
$906$	−23.7150	−	72.9871i	−0.787877	−	2.42484i
$907$			38.2492i			1.27004i	0.772494	+	0.635022i	$0.219009\pi$
$907$			38.2492i			1.27004i	−0.772494	+	0.635022i	$0.780991\pi$
$908$	20.4628	−	6.64878i	0.679083	−	0.220647i
$909$	0.742635	+	0.539556i	0.0246316	+	0.0178959i
$910$	−3.45282	−	1.60309i	−0.114460	−	0.0531421i
$911$	13.5066	−	9.81314i	0.447494	−	0.325124i	−0.341111	−	0.940023i	$-0.610803\pi$
$911$	13.5066	−	9.81314i	0.447494	−	0.325124i	0.788606	+	0.614899i	$0.210803\pi$
$912$	1.23474	−	1.69947i	0.0408863	−	0.0562752i
$913$	0.383369	−	0.527662i	0.0126876	−	0.0174630i
$914$	34.8232	−	25.3006i	1.15185	−	0.836868i
$915$	1.86150	−	15.3718i	0.0615391	−	0.508177i
$916$	−12.7251	−	9.24533i	−0.420449	−	0.305474i
$917$	31.3245	−	10.1780i	1.03443	−	0.336106i
$918$			28.4503i			0.939001i
$919$	−12.5220	−	38.5388i	−0.413063	−	1.27128i	−0.913972	−	0.405778i	$-0.867001\pi$
$919$	−12.5220	−	38.5388i	−0.413063	−	1.27128i	0.500908	−	0.865500i	$-0.332999\pi$
$920$	3.30051	−	1.83668i	0.108815	−	0.0605536i
$921$	6.68810	−	20.5839i	0.220381	−	0.678262i
$922$	82.0911	+	26.6730i	2.70353	+	0.878429i
$923$	0.0812084	+	0.111774i	0.00267301	+	0.00367908i
$924$	0.963383			0.0316930
$925$	−8.64939	+	0.633724i	−0.284390	+	0.0208367i
$926$	3.14952			0.103500
$927$	0.0664815	+	0.0915039i	0.00218354	+	0.00300538i
$928$	−7.16806	−	2.32904i	−0.235303	−	0.0764546i
$929$	−1.10698	+	3.40693i	−0.0363188	+	0.111778i	−0.967572	−	0.252594i	$-0.918716\pi$
$929$	−1.10698	+	3.40693i	−0.0363188	+	0.111778i	0.931254	+	0.364372i	$0.118716\pi$
$930$	−6.08510	−	31.0297i	−0.199538	−	1.01750i
$931$	−0.797521	−	2.45452i	−0.0261377	−	0.0804435i
$932$		−	63.9715i		−	2.09546i
$933$	6.66475	−	2.16551i	0.218194	−	0.0708956i
$934$	−39.6252	−	28.7894i	−1.29658	−	0.942019i
$935$	−0.240161	−	0.431569i	−0.00785411	−	0.0141138i
$936$	0.0453127	−	0.0329216i	0.00148109	−	0.00107608i
$937$	−16.0188	+	22.0480i	−0.523313	+	0.720278i	−0.986093	−	0.166195i	$-0.946852\pi$
$937$	−16.0188	+	22.0480i	−0.523313	+	0.720278i	0.462780	+	0.886473i	$0.346852\pi$
$938$	18.1914	−	25.0383i	0.593970	−	0.817530i
$939$	−38.5237	+	27.9891i	−1.25717	+	0.913390i
$940$	−36.0567	−	64.7937i	−1.17604	−	2.11334i
$941$	17.4579	+	12.6839i	0.569111	+	0.413483i	0.834782	−	0.550580i	$-0.185594\pi$
$941$	17.4579	+	12.6839i	0.569111	+	0.413483i	−0.265671	+	0.964064i	$0.585594\pi$
$942$	−0.394193	+	0.128081i	−0.0128435	+	0.00417311i
$943$		−	6.59241i		−	0.214678i
$944$	0.413944	+	1.27399i	0.0134727	+	0.0414648i
$945$	−4.64162	−	23.6690i	−0.150992	−	0.769951i
$946$	−0.646068	+	1.98839i	−0.0210055	+	0.0646482i
$947$	−57.2271	−	18.5942i	−1.85963	−	0.604230i	−0.994760	−	0.102233i	$-0.967401\pi$
$947$	−57.2271	−	18.5942i	−1.85963	−	0.604230i	−0.864869	−	0.501997i	$-0.832599\pi$
$948$	−2.63153	−	3.62200i	−0.0854683	−	0.117637i
$949$	−2.32478			−0.0754654
$950$	−11.0943	+	0.812858i	−0.359947	+	0.0263726i
$951$	8.95403			0.290354
$952$	6.50699	+	8.95611i	0.210893	+	0.290269i
$953$	−51.4381	−	16.7132i	−1.66624	−	0.541395i	−0.684077	−	0.729410i	$-0.739795\pi$
$953$	−51.4381	−	16.7132i	−1.66624	−	0.541395i	−0.982166	+	0.188015i	$0.939795\pi$
$954$	0.116625	−	0.358935i	0.00377588	−	0.0116210i
$955$	−31.5896	+	17.5791i	−1.02222	+	0.568846i
$956$	−11.7576	−	36.1863i	−0.380269	−	1.17035i
$957$		−	0.169891i		−	0.00549181i
$958$	−41.7814	+	13.5756i	−1.34989	+	0.438607i
$959$	−26.4021	−	19.1822i	−0.852568	−	0.619427i
$960$	−6.09638	+	50.3426i	−0.196760	+	1.62480i
$961$	14.4428	−	10.4933i	0.465896	−	0.338493i
$962$	−0.825664	+	1.13643i	−0.0266205	+	0.0366400i
$963$	−0.545181	+	0.750378i	−0.0175682	+	0.0241806i
$964$	64.7993	−	47.0794i	2.08704	−	1.51633i
$965$	−39.8178	−	18.4869i	−1.28178	−	0.595113i
$966$	5.30215	+	3.85224i	0.170594	+	0.123944i
$967$	14.6986	−	4.77586i	0.472675	−	0.153581i	−0.0629864	−	0.998014i	$-0.520062\pi$
$967$	14.6986	−	4.77586i	0.472675	−	0.153581i	0.535661	+	0.844433i	$0.320062\pi$
$968$		−	23.2272i		−	0.746552i
$969$	1.34998	+	4.15481i	0.0433676	+	0.133472i
$970$	9.32028	+	1.12867i	0.299256	+	0.0362393i
$971$	3.19405	−	9.83026i	0.102502	−	0.315468i	−0.886634	−	0.462471i	$-0.846963\pi$
$971$	3.19405	−	9.83026i	0.102502	−	0.315468i	0.989136	+	0.147003i	$0.0469628\pi$
$972$	2.12249	+	0.689639i	0.0680789	+	0.0221202i
$973$	0.500054	+	0.688266i	0.0160310	+	0.0220648i
$974$	−83.0739			−2.66186
$975$	3.09823	+	0.761546i	0.0992228	+	0.0243890i
$976$	4.73394			0.151530
$977$	−22.1885	−	30.5399i	−0.709873	−	0.977057i	−0.999800	−	0.0200078i	$-0.993631\pi$
$977$	−22.1885	−	30.5399i	−0.709873	−	0.977057i	0.289927	−	0.957049i	$-0.406369\pi$
$978$	47.7442	+	15.5130i	1.52669	+	0.496052i
$979$	0.0671293	−	0.206603i	0.00214546	−	0.00660305i
$980$	12.4691	+	11.5889i	0.398309	+	0.370194i
$981$	0.420156	+	1.29311i	0.0134146	+	0.0412858i
$982$			51.4358i			1.64138i
$983$	−55.5951	+	18.0639i	−1.77321	+	0.576150i	−0.998426	−	0.0560791i	$-0.982140\pi$
$983$	−55.5951	+	18.0639i	−1.77321	+	0.576150i	−0.774781	+	0.632229i	$0.782140\pi$
$984$	−24.7128	−	17.9549i	−0.787816	−	0.572382i
$985$	−29.3593	+	31.5891i	−0.935466	+	1.00651i
$986$	4.90522	−	3.56385i	0.156214	−	0.113496i
$987$	24.3499	−	33.5148i	0.775067	−	1.06679i
$988$	−0.631135	+	0.868682i	−0.0200791	+	0.0276365i
$989$	−6.85729	+	4.98211i	−0.218049	+	0.158422i
$990$	−0.0315056	+	0.00617843i	−0.00100131	+	0.000196363i
$991$	−28.9968	−	21.0674i	−0.921115	−	0.669229i	0.0226865	−	0.999743i	$-0.492778\pi$
$991$	−28.9968	−	21.0674i	−0.921115	−	0.669229i	−0.943801	+	0.330514i	$0.892778\pi$
$992$	23.7681	−	7.72274i	0.754639	−	0.245197i
$993$		−	28.9735i		−	0.919447i
$994$	0.548547	+	1.68825i	0.0173989	+	0.0535482i
$995$	23.1830	−	49.9326i	0.734951	−	1.58297i
$996$	11.7589	−	36.1902i	0.372595	−	1.14673i
$997$	−24.0663	−	7.81962i	−0.762188	−	0.247650i	−0.0979706	−	0.995189i	$-0.531235\pi$
$997$	−24.0663	−	7.81962i	−0.762188	−	0.247650i	−0.664218	+	0.747539i	$0.731235\pi$
$998$	−42.9879	−	59.1678i	−1.36076	−	1.87292i
$999$	−8.90013			−0.281588

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.n.a.39.18	✓	80
25.9	even	10	inner	475.2.n.a.134.18	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
475.2.n.a.39.18	✓	80	1.1	even	1	trivial
475.2.n.a.134.18	yes	80	25.9	even	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.n (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.30771 + 1.79991i) q^{2} +(1.66715 + 0.541690i) q^{3} +(-0.911532 + 2.80541i) q^{4} +(0.941634 - 2.02813i) q^{5} +(1.20516 + 3.70909i) q^{6} +2.10218i q^{7} +(-2.00966 + 0.652977i) q^{8} +(0.0589103 + 0.0428008i) q^{9} +O(q^{10})\)	\(q+(1.30771 + 1.79991i) q^{2} +(1.66715 + 0.541690i) q^{3} +(-0.911532 + 2.80541i) q^{4} +(0.941634 - 2.02813i) q^{5} +(1.20516 + 3.70909i) q^{6} +2.10218i q^{7} +(-2.00966 + 0.652977i) q^{8} +(0.0589103 + 0.0428008i) q^{9} +(4.88184 - 0.957357i) q^{10} +(-0.0717015 + 0.0520942i) q^{11} +(-3.03932 + 4.18327i) q^{12} +(-0.213960 + 0.294491i) q^{13} +(-3.78374 + 2.74904i) q^{14} +(2.66846 - 2.87113i) q^{15} +(0.969497 + 0.704381i) q^{16} +(-2.37019 + 0.770120i) q^{17} +0.162004i q^{18} +(-0.309017 - 0.951057i) q^{19} +(4.83141 + 4.49037i) q^{20} +(-1.13873 + 3.50465i) q^{21} +(-0.187530 - 0.0609321i) q^{22} +(-0.469874 - 0.646726i) q^{23} -3.70411 q^{24} +(-3.22665 - 3.81952i) q^{25} -0.809854 q^{26} +(-3.01604 - 4.15122i) q^{27} +(-5.89747 - 1.91621i) q^{28} +(-0.337920 + 1.04001i) q^{29} +(8.65735 + 1.04839i) q^{30} +(-1.12049 - 3.44851i) q^{31} +6.89228i q^{32} +(-0.147756 + 0.0480089i) q^{33} +(-4.48566 - 3.25903i) q^{34} +(4.26351 + 1.97948i) q^{35} +(-0.173772 + 0.126253i) q^{36} +(1.01952 - 1.40325i) q^{37} +(1.30771 - 1.79991i) q^{38} +(-0.516226 + 0.375060i) q^{39} +(-0.568035 + 4.69071i) q^{40} +(6.67174 + 4.84730i) q^{41} +(-7.79718 + 2.53346i) q^{42} -10.6031i q^{43} +(-0.0807872 - 0.248637i) q^{44} +(0.142278 - 0.0791752i) q^{45} +(0.549589 - 1.69146i) q^{46} +(-10.6917 - 3.47394i) q^{47} +(1.23474 + 1.69947i) q^{48} +2.58083 q^{49} +(2.65526 - 10.8025i) q^{50} -4.36862 q^{51} +(-0.631135 - 0.868682i) q^{52} +(-2.21559 - 0.719890i) q^{53} +(3.52771 - 10.8572i) q^{54} +(0.0381375 + 0.194474i) q^{55} +(-1.37268 - 4.22466i) q^{56} -1.75295i q^{57} +(-2.31383 + 0.751808i) q^{58} +(0.904332 + 0.657036i) q^{59} +(5.62230 + 10.1033i) q^{60} +(3.19589 - 2.32195i) q^{61} +(4.74174 - 6.52644i) q^{62} +(-0.0899751 + 0.123840i) q^{63} +(-10.4665 + 7.60435i) q^{64} +(0.395795 + 0.711242i) q^{65} +(-0.279634 - 0.203166i) q^{66} +(-6.29348 + 2.04488i) q^{67} -7.35133i q^{68} +(-0.433026 - 1.33272i) q^{69} +(2.01254 + 10.2625i) q^{70} +(0.117287 - 0.360973i) q^{71} +(-0.146337 - 0.0475479i) q^{72} +(3.75393 + 5.16684i) q^{73} +3.85897 q^{74} +(-3.31032 - 8.11555i) q^{75} +2.94978 q^{76} +(-0.109512 - 0.150730i) q^{77} +(-1.35015 - 0.438690i) q^{78} +(-0.267556 + 0.823453i) q^{79} +(2.34149 - 1.30300i) q^{80} +(-2.84702 - 8.76223i) q^{81} +18.3474i q^{82} +(-6.99896 + 2.27410i) q^{83} +(-8.79398 - 6.38920i) q^{84} +(-0.669940 + 5.53223i) q^{85} +(19.0846 - 13.8658i) q^{86} +(-1.12673 + 1.55081i) q^{87} +(0.110079 - 0.151511i) q^{88} +(-1.98297 + 1.44071i) q^{89} +(0.328566 + 0.152549i) q^{90} +(-0.619073 - 0.449783i) q^{91} +(2.24263 - 0.728676i) q^{92} -6.35615i q^{93} +(-7.72886 - 23.7870i) q^{94} +(-2.21985 - 0.268819i) q^{95} +(-3.73348 + 11.4905i) q^{96} +(1.79481 + 0.583169i) q^{97} +(3.37498 + 4.64526i) q^{98} -0.00645363 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 16 q^{4} - 3 q^{5} + 6 q^{6} + 8 q^{9}+O(q^{10}) \) 80 * q + 16 * q^4 - 3 * q^5 + 6 * q^6 + 8 * q^9	\( 80 q + 16 q^{4} - 3 q^{5} + 6 q^{6} + 8 q^{9} - 36 q^{10} + 20 q^{11} + 45 q^{12} - 10 q^{14} - 20 q^{16} - 15 q^{17} + 20 q^{19} + 12 q^{20} + 16 q^{21} + 15 q^{23} + 72 q^{24} + 41 q^{25} - 84 q^{26} + 15 q^{27} + 30 q^{28} - 24 q^{29} - 40 q^{30} + 8 q^{31} - 75 q^{33} - 24 q^{34} - 33 q^{35} - 32 q^{36} - 15 q^{37} - 30 q^{39} - 28 q^{40} + 13 q^{41} - 130 q^{42} - 24 q^{44} + 6 q^{45} + 30 q^{46} + 145 q^{48} - 28 q^{49} + 77 q^{50} - 36 q^{51} - 5 q^{52} - 10 q^{53} + 15 q^{54} - 8 q^{55} + 48 q^{56} - 60 q^{58} - 19 q^{59} - 110 q^{60} + 8 q^{61} + 110 q^{62} + 55 q^{63} + 16 q^{64} - 43 q^{65} - 17 q^{66} - 65 q^{67} - 42 q^{69} + 4 q^{70} + 18 q^{71} + 100 q^{73} + 22 q^{74} + 115 q^{75} + 64 q^{76} - 145 q^{78} - 16 q^{79} - 97 q^{80} + q^{81} - 70 q^{83} - 46 q^{84} - 16 q^{85} + 64 q^{86} + 10 q^{87} + 30 q^{88} + 4 q^{89} - 8 q^{90} + 16 q^{91} - 135 q^{92} + 38 q^{94} - 2 q^{95} + 50 q^{96} + 150 q^{97} + 130 q^{98} + 178 q^{99}+O(q^{100}) \) 80 * q + 16 * q^4 - 3 * q^5 + 6 * q^6 + 8 * q^9 - 36 * q^10 + 20 * q^11 + 45 * q^12 - 10 * q^14 - 20 * q^16 - 15 * q^17 + 20 * q^19 + 12 * q^20 + 16 * q^21 + 15 * q^23 + 72 * q^24 + 41 * q^25 - 84 * q^26 + 15 * q^27 + 30 * q^28 - 24 * q^29 - 40 * q^30 + 8 * q^31 - 75 * q^33 - 24 * q^34 - 33 * q^35 - 32 * q^36 - 15 * q^37 - 30 * q^39 - 28 * q^40 + 13 * q^41 - 130 * q^42 - 24 * q^44 + 6 * q^45 + 30 * q^46 + 145 * q^48 - 28 * q^49 + 77 * q^50 - 36 * q^51 - 5 * q^52 - 10 * q^53 + 15 * q^54 - 8 * q^55 + 48 * q^56 - 60 * q^58 - 19 * q^59 - 110 * q^60 + 8 * q^61 + 110 * q^62 + 55 * q^63 + 16 * q^64 - 43 * q^65 - 17 * q^66 - 65 * q^67 - 42 * q^69 + 4 * q^70 + 18 * q^71 + 100 * q^73 + 22 * q^74 + 115 * q^75 + 64 * q^76 - 145 * q^78 - 16 * q^79 - 97 * q^80 + q^81 - 70 * q^83 - 46 * q^84 - 16 * q^85 + 64 * q^86 + 10 * q^87 + 30 * q^88 + 4 * q^89 - 8 * q^90 + 16 * q^91 - 135 * q^92 + 38 * q^94 - 2 * q^95 + 50 * q^96 + 150 * q^97 + 130 * q^98 + 178 * q^99

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