LMFDB - Embedded newform 770.2.n.f.71.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(71,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("770.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.n (of order $5$, 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:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.484000000.9
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + x^{6} + 16x^{4} + 66x^{2} + 121 $ x^8 + x^6 + 16x^4 + 66x^2 + 121
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			71.2
Root			$1.73855 - 1.26313i$ of defining polynomial
Character	$\chi$	$=$	770.71
Dual form			770.2.n.f.141.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 - 0.951057i) q^{2} +(2.54756 + 1.85091i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.309017 - 0.951057i) q^{5} +(0.973083 - 2.99484i) q^{6} +(0.809017 - 0.587785i) q^{7} +(0.809017 + 0.587785i) q^{8} +(2.13715 + 6.57747i) q^{9} +O(q^{10})$	\(q+(-0.309017 - 0.951057i) q^{2} +(2.54756 + 1.85091i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.309017 - 0.951057i) q^{5} +(0.973083 - 2.99484i) q^{6} +(0.809017 - 0.587785i) q^{7} +(0.809017 + 0.587785i) q^{8} +(2.13715 + 6.57747i) q^{9} -1.00000 q^{10} +(-3.22344 + 0.780656i) q^{11} -3.14896 q^{12} +(1.68070 + 5.17267i) q^{13} +(-0.809017 - 0.587785i) q^{14} +(2.54756 - 1.85091i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-0.147430 + 0.453742i) q^{17} +(5.59513 - 4.06510i) q^{18} +(4.78611 + 3.47731i) q^{19} +(0.309017 + 0.951057i) q^{20} +3.14896 q^{21} +(1.73855 + 2.82444i) q^{22} -2.65626 q^{23} +(0.973083 + 2.99484i) q^{24} +(-0.809017 - 0.587785i) q^{25} +(4.40013 - 3.19688i) q^{26} +(-3.81055 + 11.7277i) q^{27} +(-0.309017 + 0.951057i) q^{28} +(5.31303 - 3.86014i) q^{29} +(-2.54756 - 1.85091i) q^{30} +(-2.99423 - 9.21529i) q^{31} -1.00000 q^{32} +(-9.65685 - 3.97754i) q^{33} +0.477092 q^{34} +(-0.309017 - 0.951057i) q^{35} +(-5.59513 - 4.06510i) q^{36} +(3.69499 - 2.68457i) q^{37} +(1.82813 - 5.62641i) q^{38} +(-5.29246 + 16.2885i) q^{39} +(0.809017 - 0.587785i) q^{40} +(-2.04108 - 1.48293i) q^{41} +(-0.973083 - 2.99484i) q^{42} +11.9003 q^{43} +(2.14896 - 2.52626i) q^{44} +6.91596 q^{45} +(0.820830 + 2.52626i) q^{46} +(-7.62605 - 5.54065i) q^{47} +(2.54756 - 1.85091i) q^{48} +(0.309017 - 0.951057i) q^{49} +(-0.309017 + 0.951057i) q^{50} +(-1.21542 + 0.883056i) q^{51} +(-4.40013 - 3.19688i) q^{52} +(1.90167 + 5.85272i) q^{53} +12.3312 q^{54} +(-0.253650 + 3.30691i) q^{55} +1.00000 q^{56} +(5.75671 + 17.7173i) q^{57} +(-5.31303 - 3.86014i) q^{58} +(0.457978 - 0.332741i) q^{59} +(-0.973083 + 2.99484i) q^{60} +(0.633138 - 1.94860i) q^{61} +(-7.83900 + 5.69537i) q^{62} +(5.59513 + 4.06510i) q^{63} +(0.309017 + 0.951057i) q^{64} +5.43886 q^{65} +(-0.798735 + 10.4133i) q^{66} -1.24102 q^{67} +(-0.147430 - 0.453742i) q^{68} +(-6.76700 - 4.91651i) q^{69} +(-0.809017 + 0.587785i) q^{70} +(-1.11957 + 3.44567i) q^{71} +(-2.13715 + 6.57747i) q^{72} +(-12.6528 + 9.19282i) q^{73} +(-3.69499 - 2.68457i) q^{74} +(-0.973083 - 2.99484i) q^{75} -5.91596 q^{76} +(-2.14896 + 2.52626i) q^{77} +17.1268 q^{78} +(-1.04450 - 3.21464i) q^{79} +(-0.809017 - 0.587785i) q^{80} +(-14.6291 + 10.6287i) q^{81} +(-0.779621 + 2.39943i) q^{82} +(0.537282 - 1.65358i) q^{83} +(-2.54756 + 1.85091i) q^{84} +(0.385976 + 0.280428i) q^{85} +(-3.67741 - 11.3179i) q^{86} +20.6801 q^{87} +(-3.06668 - 1.26313i) q^{88} -9.54364 q^{89} +(-2.13715 - 6.57747i) q^{90} +(4.40013 + 3.19688i) q^{91} +(2.14896 - 1.56131i) q^{92} +(9.42872 - 29.0186i) q^{93} +(-2.91289 + 8.96496i) q^{94} +(4.78611 - 3.47731i) q^{95} +(-2.54756 - 1.85091i) q^{96} +(-1.21492 - 3.73914i) q^{97} -1.00000 q^{98} +(-12.0237 - 19.5337i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} + 2 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) $ 8 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 + 2 * q^7 + 2 * q^8 + 2 * q^9	$ 8 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} + 2 q^{7} + 2 q^{8} + 2 q^{9} - 8 q^{10} - 8 q^{12} - 2 q^{13} - 2 q^{14} + 2 q^{15} - 2 q^{16} - 6 q^{17} + 8 q^{18} + 6 q^{19} - 2 q^{20} + 8 q^{21} - 2 q^{24} - 2 q^{25} + 12 q^{26} - 4 q^{27} + 2 q^{28} + 20 q^{29} - 2 q^{30} - 6 q^{31} - 8 q^{32} - 8 q^{33} - 24 q^{34} + 2 q^{35} - 8 q^{36} + 16 q^{37} + 4 q^{38} + 20 q^{39} + 2 q^{40} - 12 q^{41} + 2 q^{42} + 20 q^{43} + 12 q^{45} - 16 q^{47} + 2 q^{48} - 2 q^{49} + 2 q^{50} - 20 q^{51} - 12 q^{52} - 30 q^{53} + 44 q^{54} + 8 q^{56} - 20 q^{58} - 18 q^{59} + 2 q^{60} + 8 q^{61} - 24 q^{62} + 8 q^{63} - 2 q^{64} + 28 q^{65} + 18 q^{66} - 6 q^{68} - 28 q^{69} - 2 q^{70} + 22 q^{71} - 2 q^{72} - 50 q^{73} - 16 q^{74} + 2 q^{75} - 4 q^{76} + 60 q^{78} - 34 q^{79} - 2 q^{80} - 28 q^{81} + 12 q^{82} - 34 q^{83} - 2 q^{84} - 6 q^{85} + 4 q^{87} - 8 q^{89} - 2 q^{90} + 12 q^{91} + 56 q^{93} - 24 q^{94} + 6 q^{95} - 2 q^{96} - 8 q^{98} - 24 q^{99}+O(q^{100}) $ 8 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 + 2 * q^7 + 2 * q^8 + 2 * q^9 - 8 * q^10 - 8 * q^12 - 2 * q^13 - 2 * q^14 + 2 * q^15 - 2 * q^16 - 6 * q^17 + 8 * q^18 + 6 * q^19 - 2 * q^20 + 8 * q^21 - 2 * q^24 - 2 * q^25 + 12 * q^26 - 4 * q^27 + 2 * q^28 + 20 * q^29 - 2 * q^30 - 6 * q^31 - 8 * q^32 - 8 * q^33 - 24 * q^34 + 2 * q^35 - 8 * q^36 + 16 * q^37 + 4 * q^38 + 20 * q^39 + 2 * q^40 - 12 * q^41 + 2 * q^42 + 20 * q^43 + 12 * q^45 - 16 * q^47 + 2 * q^48 - 2 * q^49 + 2 * q^50 - 20 * q^51 - 12 * q^52 - 30 * q^53 + 44 * q^54 + 8 * q^56 - 20 * q^58 - 18 * q^59 + 2 * q^60 + 8 * q^61 - 24 * q^62 + 8 * q^63 - 2 * q^64 + 28 * q^65 + 18 * q^66 - 6 * q^68 - 28 * q^69 - 2 * q^70 + 22 * q^71 - 2 * q^72 - 50 * q^73 - 16 * q^74 + 2 * q^75 - 4 * q^76 + 60 * q^78 - 34 * q^79 - 2 * q^80 - 28 * q^81 + 12 * q^82 - 34 * q^83 - 2 * q^84 - 6 * q^85 + 4 * q^87 - 8 * q^89 - 2 * q^90 + 12 * q^91 + 56 * q^93 - 24 * q^94 + 6 * q^95 - 2 * q^96 - 8 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i
$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i
$3$	2.54756	+	1.85091i	1.47084	+	1.06863i	0.980370	+	0.197165i	$0.0631734\pi$
$3$	2.54756	+	1.85091i	1.47084	+	1.06863i	0.490466	+	0.871460i	$0.336827\pi$
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$	0.309017	−	0.951057i	0.138197	−	0.425325i
$5$	0.309017	−	0.951057i	0.138197	−	0.425325i
$6$	0.973083	−	2.99484i	0.397259	−	1.22264i
$7$	0.809017	−	0.587785i	0.305780	−	0.222162i
$7$	0.809017	−	0.587785i	0.305780	−	0.222162i
$8$	0.809017	+	0.587785i	0.286031	+	0.207813i
$9$	2.13715	+	6.57747i	0.712383	+	2.19249i
$10$	−1.00000			−0.316228
$11$	−3.22344	+	0.780656i	−0.971904	+	0.235377i
$11$	−3.22344	+	0.780656i	−0.971904	+	0.235377i
$12$	−3.14896			−0.909027
$13$	1.68070	+	5.17267i	0.466143	+	1.43464i	0.857540	+	0.514418i	$0.171992\pi$
$13$	1.68070	+	5.17267i	0.466143	+	1.43464i	−0.391397	+	0.920222i	$0.628008\pi$
$14$	−0.809017	−	0.587785i	−0.216219	−	0.157092i
$15$	2.54756	−	1.85091i	0.657778	−	0.477904i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−0.147430	+	0.453742i	−0.0357569	+	0.110049i	−0.967342	−	0.253475i	$-0.918426\pi$
$17$	−0.147430	+	0.453742i	−0.0357569	+	0.110049i	0.931585	+	0.363524i	$0.118426\pi$
$18$	5.59513	−	4.06510i	1.31878	−	0.958153i
$19$	4.78611	+	3.47731i	1.09801	+	0.797750i	0.980734	−	0.195349i	$-0.0625841\pi$
$19$	4.78611	+	3.47731i	1.09801	+	0.797750i	0.117275	+	0.993099i	$0.462584\pi$
$20$	0.309017	+	0.951057i	0.0690983	+	0.212663i
$21$	3.14896			0.687160
$22$	1.73855	+	2.82444i	0.370659	+	0.602172i
$23$	−2.65626			−0.553869			−0.276934	−	0.960889i	$-0.589318\pi$
$23$	−2.65626			−0.553869			−0.276934	+	0.960889i	$0.589318\pi$
$24$	0.973083	+	2.99484i	0.198630	+	0.611319i
$25$	−0.809017	−	0.587785i	−0.161803	−	0.117557i
$26$	4.40013	−	3.19688i	0.862937	−	0.626961i
$27$	−3.81055	+	11.7277i	−0.733340	+	2.25699i
$28$	−0.309017	+	0.951057i	−0.0583987	+	0.179733i
$29$	5.31303	−	3.86014i	0.986604	−	0.716810i	0.0274294	−	0.999624i	$-0.491268\pi$
$29$	5.31303	−	3.86014i	0.986604	−	0.716810i	0.959175	+	0.282814i	$0.0912678\pi$
$30$	−2.54756	−	1.85091i	−0.465119	−	0.337929i
$31$	−2.99423	−	9.21529i	−0.537780	−	1.65512i	−0.737565	−	0.675276i	$-0.764024\pi$
$31$	−2.99423	−	9.21529i	−0.537780	−	1.65512i	0.199785	−	0.979840i	$-0.435976\pi$
$32$	−1.00000			−0.176777
$33$	−9.65685	−	3.97754i	−1.68104	−	0.692401i
$34$	0.477092			0.0818206
$35$	−0.309017	−	0.951057i	−0.0522334	−	0.160758i
$36$	−5.59513	−	4.06510i	−0.932521	−	0.677516i
$37$	3.69499	−	2.68457i	0.607453	−	0.441340i	−0.241063	−	0.970509i	$-0.577496\pi$
$37$	3.69499	−	2.68457i	0.607453	−	0.441340i	0.848517	+	0.529169i	$0.177496\pi$
$38$	1.82813	−	5.62641i	0.296562	−	0.912724i
$39$	−5.29246	+	16.2885i	−0.847472	+	2.60825i
$40$	0.809017	−	0.587785i	0.127917	−	0.0929370i
$41$	−2.04108	−	1.48293i	−0.318762	−	0.231594i	0.416885	−	0.908959i	$-0.363122\pi$
$41$	−2.04108	−	1.48293i	−0.318762	−	0.231594i	−0.735647	+	0.677365i	$0.763122\pi$
$42$	−0.973083	−	2.99484i	−0.150150	−	0.462114i
$43$	11.9003			1.81479			0.907393	−	0.420283i	$-0.138069\pi$
$43$	11.9003			1.81479			0.907393	+	0.420283i	$0.138069\pi$
$44$	2.14896	−	2.52626i	0.323968	−	0.380847i
$45$	6.91596			1.03097
$46$	0.820830	+	2.52626i	0.121025	+	0.372476i
$47$	−7.62605	−	5.54065i	−1.11237	−	0.808187i	−0.129338	−	0.991601i	$-0.541285\pi$
$47$	−7.62605	−	5.54065i	−1.11237	−	0.808187i	−0.983036	+	0.183413i	$0.941285\pi$
$48$	2.54756	−	1.85091i	0.367709	−	0.267156i
$49$	0.309017	−	0.951057i	0.0441453	−	0.135865i
$50$	−0.309017	+	0.951057i	−0.0437016	+	0.134500i
$51$	−1.21542	+	0.883056i	−0.170193	+	0.123653i
$52$	−4.40013	−	3.19688i	−0.610189	−	0.443328i
$53$	1.90167	+	5.85272i	0.261214	+	0.803933i	0.992542	+	0.121907i	$0.0389010\pi$
$53$	1.90167	+	5.85272i	0.261214	+	0.803933i	−0.731328	+	0.682026i	$0.761099\pi$
$54$	12.3312			1.67806
$55$	−0.253650	+	3.30691i	−0.0342022	+	0.445904i
$56$	1.00000			0.133631
$57$	5.75671	+	17.7173i	0.762495	+	2.34672i
$58$	−5.31303	−	3.86014i	−0.697635	−	0.506861i
$59$	0.457978	−	0.332741i	0.0596237	−	0.0433191i	−0.557574	−	0.830127i	$-0.688268\pi$
$59$	0.457978	−	0.332741i	0.0596237	−	0.0433191i	0.617198	+	0.786808i	$0.288268\pi$
$60$	−0.973083	+	2.99484i	−0.125624	+	0.386632i
$61$	0.633138	−	1.94860i	0.0810651	−	0.249493i	−0.902307	−	0.431094i	$-0.858128\pi$
$61$	0.633138	−	1.94860i	0.0810651	−	0.249493i	0.983372	+	0.181601i	$0.0581279\pi$
$62$	−7.83900	+	5.69537i	−0.995554	+	0.723312i
$63$	5.59513	+	4.06510i	0.704920	+	0.512154i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	5.43886			0.674608
$66$	−0.798735	+	10.4133i	−0.0983175	+	1.28179i
$67$	−1.24102			−0.151615			−0.0758076	−	0.997122i	$-0.524153\pi$
$67$	−1.24102			−0.151615			−0.0758076	+	0.997122i	$0.524153\pi$
$68$	−0.147430	−	0.453742i	−0.0178785	−	0.0550243i
$69$	−6.76700	−	4.91651i	−0.814650	−	0.591878i
$70$	−0.809017	+	0.587785i	−0.0966960	+	0.0702538i
$71$	−1.11957	+	3.44567i	−0.132868	+	0.408926i	−0.995252	−	0.0973286i	$-0.968970\pi$
$71$	−1.11957	+	3.44567i	−0.132868	+	0.408926i	0.862384	+	0.506254i	$0.168970\pi$
$72$	−2.13715	+	6.57747i	−0.251865	+	0.775162i
$73$	−12.6528	+	9.19282i	−1.48090	+	1.07594i	−0.503638	+	0.863915i	$0.668006\pi$
$73$	−12.6528	+	9.19282i	−1.48090	+	1.07594i	−0.977264	+	0.212024i	$0.931994\pi$
$74$	−3.69499	−	2.68457i	−0.429534	−	0.312075i
$75$	−0.973083	−	2.99484i	−0.112362	−	0.345814i
$76$	−5.91596			−0.678607
$77$	−2.14896	+	2.52626i	−0.244897	+	0.287894i
$78$	17.1268			1.93923
$79$	−1.04450	−	3.21464i	−0.117515	−	0.361675i	0.874948	−	0.484217i	$-0.160895\pi$
$79$	−1.04450	−	3.21464i	−0.117515	−	0.361675i	−0.992463	+	0.122542i	$0.960895\pi$
$80$	−0.809017	−	0.587785i	−0.0904508	−	0.0657164i
$81$	−14.6291	+	10.6287i	−1.62546	+	1.18096i
$82$	−0.779621	+	2.39943i	−0.0860948	+	0.264972i
$83$	0.537282	−	1.65358i	0.0589743	−	0.181504i	−0.917230	−	0.398359i	$-0.869580\pi$
$83$	0.537282	−	1.65358i	0.0589743	−	0.181504i	0.976204	+	0.216855i	$0.0695798\pi$
$84$	−2.54756	+	1.85091i	−0.277962	+	0.201951i
$85$	0.385976	+	0.280428i	0.0418649	+	0.0304167i
$86$	−3.67741	−	11.3179i	−0.396545	−	1.22044i
$87$	20.6801			2.21713
$88$	−3.06668	−	1.26313i	−0.326909	−	0.134650i
$89$	−9.54364			−1.01162			−0.505812	−	0.862644i	$-0.668807\pi$
$89$	−9.54364			−1.01162			−0.505812	+	0.862644i	$0.668807\pi$
$90$	−2.13715	−	6.57747i	−0.225275	−	0.693326i
$91$	4.40013	+	3.19688i	0.461259	+	0.335125i
$92$	2.14896	−	1.56131i	0.224045	−	0.162778i
$93$	9.42872	−	29.0186i	0.977712	−	3.00909i
$94$	−2.91289	+	8.96496i	−0.300442	+	0.924665i
$95$	4.78611	−	3.47731i	0.491044	−	0.356765i
$96$	−2.54756	−	1.85091i	−0.260010	−	0.188908i
$97$	−1.21492	−	3.73914i	−0.123356	−	0.379652i	0.870242	−	0.492625i	$-0.163963\pi$
$97$	−1.21492	−	3.73914i	−0.123356	−	0.379652i	−0.993598	+	0.112973i	$0.963963\pi$
$98$	−1.00000			−0.101015
$99$	−12.0237	−	19.5337i	−1.20843	−	1.96321i
$100$	1.00000			0.100000
$101$	−0.898602	−	2.76561i	−0.0894142	−	0.275189i	0.896344	−	0.443360i	$-0.146214\pi$
$101$	−0.898602	−	2.76561i	−0.0894142	−	0.275189i	−0.985758	+	0.168172i	$0.946214\pi$
$102$	1.21542	+	0.883056i	0.120345	+	0.0874356i
$103$	12.8866	−	9.36263i	1.26975	−	0.922528i	0.270558	−	0.962704i	$-0.412792\pi$
$103$	12.8866	−	9.36263i	1.26975	−	0.922528i	0.999193	+	0.0401759i	$0.0127918\pi$
$104$	−1.68070	+	5.17267i	−0.164806	+	0.507222i
$105$	0.973083	−	2.99484i	0.0949631	−	0.292266i
$106$	4.97862	−	3.61718i	0.483567	−	0.351332i
$107$	4.99351	+	3.62800i	0.482741	+	0.350732i	0.802386	−	0.596806i	$-0.203564\pi$
$107$	4.99351	+	3.62800i	0.482741	+	0.350732i	−0.319645	+	0.947537i	$0.603564\pi$
$108$	−3.81055	−	11.7277i	−0.366670	−	1.12849i
$109$	−14.9240			−1.42946			−0.714729	−	0.699402i	$-0.753450\pi$
$109$	−14.9240			−1.42946			−0.714729	+	0.699402i	$0.753450\pi$
$110$	3.22344	−	0.780656i	0.307343	−	0.0744326i
$111$	14.3821			1.36509
$112$	−0.309017	−	0.951057i	−0.0291994	−	0.0898664i
$113$	−15.4446	−	11.2212i	−1.45291	−	1.05560i	−0.985141	−	0.171747i	$-0.945059\pi$
$113$	−15.4446	−	11.2212i	−1.45291	−	1.05560i	−0.467767	−	0.883852i	$-0.654941\pi$
$114$	15.0713	−	10.9499i	1.41155	−	1.02555i
$115$	−0.820830	+	2.52626i	−0.0765428	+	0.235575i
$116$	−2.02940	+	6.24584i	−0.188425	+	0.579911i
$117$	−30.4311	+	22.1095i	−2.81336	+	2.04402i
$118$	−0.457978	−	0.332741i	−0.0421603	−	0.0306313i
$119$	0.147430	+	0.453742i	0.0135148	+	0.0415944i
$120$	3.14896			0.287460
$121$	9.78115	−	5.03280i	0.889196	−	0.457527i
$122$	−2.04888			−0.185497
$123$	−2.45500	−	7.55571i	−0.221360	−	0.681275i
$124$	7.83900	+	5.69537i	0.703963	+	0.511459i
$125$	−0.809017	+	0.587785i	−0.0723607	+	0.0525731i
$126$	2.13715	−	6.57747i	0.190392	−	0.585967i
$127$	5.06216	−	15.5797i	0.449194	−	1.38248i	−0.428623	−	0.903483i	$-0.641001\pi$
$127$	5.06216	−	15.5797i	0.449194	−	1.38248i	0.877818	−	0.478995i	$-0.158999\pi$
$128$	0.809017	−	0.587785i	0.0715077	−	0.0519534i
$129$	30.3169	+	22.0265i	2.66925	+	1.93933i
$130$	−1.68070	−	5.17267i	−0.147407	−	0.453673i
$131$	5.60812			0.489984			0.244992	−	0.969525i	$-0.421215\pi$
$131$	5.60812			0.489984			0.244992	+	0.969525i	$0.421215\pi$
$132$	10.1505	−	2.45825i	0.883487	−	0.213964i
$133$	5.91596			0.512978
$134$	0.383498	+	1.18028i	0.0331291	+	0.101961i
$135$	9.97615	+	7.24809i	0.858610	+	0.623817i
$136$	−0.385976	+	0.280428i	−0.0330971	+	0.0240465i
$137$	−0.775243	+	2.38595i	−0.0662334	+	0.203846i	−0.978696	−	0.205315i	$-0.934178\pi$
$137$	−0.775243	+	2.38595i	−0.0662334	+	0.203846i	0.912463	+	0.409160i	$0.134178\pi$
$138$	−2.58476	+	7.95508i	−0.220030	+	0.677181i
$139$	−2.67187	+	1.94123i	−0.226625	+	0.164653i	−0.695304	−	0.718716i	$-0.744730\pi$
$139$	−2.67187	+	1.94123i	−0.226625	+	0.164653i	0.468679	+	0.883369i	$0.344730\pi$
$140$	0.809017	+	0.587785i	0.0683744	+	0.0496769i
$141$	−9.17259	−	28.2303i	−0.772471	−	2.37742i
$142$	3.62299			0.304035
$143$	−9.45572	−	15.3617i	−0.790727	−	1.28461i
$144$	6.91596			0.576330
$145$	−2.02940	−	6.24584i	−0.168532	−	0.518689i
$146$	12.6528	+	9.19282i	1.04716	+	0.760804i
$147$	2.54756	−	1.85091i	0.210119	−	0.152661i
$148$	−1.41136	+	4.34372i	−0.116013	+	0.357052i
$149$	2.11073	−	6.49617i	0.172918	−	0.532187i	−0.826614	−	0.562769i	$-0.809736\pi$
$149$	2.11073	−	6.49617i	0.172918	−	0.532187i	0.999532	+	0.0305821i	$0.00973609\pi$
$150$	−2.54756	+	1.85091i	−0.208008	+	0.151126i
$151$	8.75270	+	6.35921i	0.712285	+	0.517505i	0.883910	−	0.467657i	$-0.154902\pi$
$151$	8.75270	+	6.35921i	0.712285	+	0.517505i	−0.171625	+	0.985162i	$0.554902\pi$
$152$	1.82813	+	5.62641i	0.148281	+	0.456362i
$153$	−3.29955			−0.266753
$154$	3.06668	+	1.26313i	0.247120	+	0.101786i
$155$	−9.68953			−0.778282
$156$	−5.29246	−	16.2885i	−0.423736	−	1.30413i
$157$	−6.48643	−	4.71267i	−0.517673	−	0.376112i	0.298053	−	0.954549i	$-0.403663\pi$
$157$	−6.48643	−	4.71267i	−0.517673	−	0.376112i	−0.815727	+	0.578438i	$0.803663\pi$
$158$	−2.73454	+	1.98676i	−0.217548	+	0.158058i
$159$	−5.98827	+	18.4300i	−0.474901	+	1.46159i
$160$	−0.309017	+	0.951057i	−0.0244299	+	0.0751876i
$161$	−2.14896	+	1.56131i	−0.169362	+	0.123049i
$162$	14.6291	+	10.6287i	1.14937	+	0.835068i
$163$	−5.65473	−	17.4035i	−0.442913	−	1.36315i	−0.884757	−	0.466053i	$-0.845676\pi$
$163$	−5.65473	−	17.4035i	−0.442913	−	1.36315i	0.441844	−	0.897092i	$-0.354324\pi$
$164$	2.52291			0.197006
$165$	−6.76700	+	7.95508i	−0.526810	+	0.619302i
$166$	−1.73868			−0.134948
$167$	−5.53945	−	17.0487i	−0.428655	−	1.31927i	−0.899450	−	0.437023i	$-0.856033\pi$
$167$	−5.53945	−	17.0487i	−0.428655	−	1.31927i	0.470795	−	0.882243i	$-0.343967\pi$
$168$	2.54756	+	1.85091i	0.196549	+	0.142801i
$169$	−13.4145	+	9.74621i	−1.03189	+	0.749708i
$170$	0.147430	−	0.453742i	0.0113073	−	0.0348004i
$171$	−12.6433	+	38.9120i	−0.966855	+	2.97567i
$172$	−9.62758	+	6.99485i	−0.734096	+	0.533352i
$173$	6.21965	+	4.51884i	0.472871	+	0.343561i	0.798559	−	0.601916i	$-0.205596\pi$
$173$	6.21965	+	4.51884i	0.472871	+	0.343561i	−0.325688	+	0.945477i	$0.605596\pi$
$174$	−6.39049	−	19.6679i	−0.484462	−	1.49102i
$175$	−1.00000			−0.0755929
$176$	−0.253650	+	3.30691i	−0.0191196	+	0.249268i
$177$	1.78260			0.133989
$178$	2.94915	+	9.07654i	0.221048	+	0.680315i
$179$	−18.3806	−	13.3543i	−1.37383	−	0.998148i	−0.997427	−	0.0716939i	$-0.977160\pi$
$179$	−18.3806	−	13.3543i	−1.37383	−	0.998148i	−0.376407	−	0.926455i	$-0.622840\pi$
$180$	−5.59513	+	4.06510i	−0.417036	+	0.302994i
$181$	−4.22015	+	12.9883i	−0.313681	+	0.965412i	0.662613	+	0.748962i	$0.269448\pi$
$181$	−4.22015	+	12.9883i	−0.313681	+	0.965412i	−0.976294	+	0.216449i	$0.930552\pi$
$182$	1.68070	−	5.17267i	0.124582	−	0.383424i
$183$	5.21965	−	3.79230i	0.385847	−	0.280335i
$184$	−2.14896	−	1.56131i	−0.158424	−	0.115101i
$185$	−1.41136	−	4.34372i	−0.103765	−	0.319357i
$186$	−30.5120			−2.23725
$187$	0.121015	−	1.57770i	0.00884947	−	0.115373i
$188$	9.42632			0.687485
$189$	3.81055	+	11.7277i	0.277177	+	0.853062i
$190$	−4.78611	−	3.47731i	−0.347221	−	0.252271i
$191$	−7.62241	+	5.53801i	−0.551538	+	0.400716i	−0.828352	−	0.560207i	$-0.810721\pi$
$191$	−7.62241	+	5.53801i	−0.551538	+	0.400716i	0.276814	+	0.960924i	$0.410721\pi$
$192$	−0.973083	+	2.99484i	−0.0702262	+	0.216134i
$193$	−1.57574	+	4.84962i	−0.113424	+	0.349083i	−0.991615	−	0.129227i	$-0.958751\pi$
$193$	−1.57574	+	4.84962i	−0.113424	+	0.349083i	0.878191	+	0.478310i	$0.158751\pi$
$194$	−3.18070	+	2.31091i	−0.228361	+	0.165914i
$195$	13.8558	+	10.0669i	0.992238	+	0.720903i
$196$	0.309017	+	0.951057i	0.0220726	+	0.0679326i
$197$	17.1284			1.22035			0.610174	−	0.792268i	$-0.291100\pi$
$197$	17.1284			1.22035			0.610174	+	0.792268i	$0.291100\pi$
$198$	−14.8621	+	17.4715i	−1.05620	+	1.24164i
$199$	11.9225			0.845166			0.422583	−	0.906324i	$-0.361123\pi$
$199$	11.9225			0.845166			0.422583	+	0.906324i	$0.361123\pi$
$200$	−0.309017	−	0.951057i	−0.0218508	−	0.0672499i
$201$	−3.16159	−	2.29703i	−0.223001	−	0.162020i
$202$	−2.35257	+	1.70924i	−0.165526	+	0.120262i
$203$	2.02940	−	6.24584i	0.142436	−	0.438372i
$204$	0.464250	−	1.42881i	0.0325040	−	0.100037i
$205$	−2.04108	+	1.48293i	−0.142555	+	0.103572i
$206$	−12.8866	−	9.36263i	−0.897849	−	0.652326i
$207$	−5.67683	−	17.4715i	−0.394567	−	1.21435i
$208$	5.43886			0.377117
$209$	−18.1423	−	7.47261i	−1.25493	−	0.516891i
$210$	−3.14896			−0.217299
$211$	7.05581	+	21.7156i	0.485742	+	1.49496i	0.830903	+	0.556417i	$0.187824\pi$
$211$	7.05581	+	21.7156i	0.485742	+	1.49496i	−0.345161	+	0.938543i	$0.612176\pi$
$212$	−4.97862	−	3.61718i	−0.341933	−	0.248429i
$213$	−9.22980	+	6.70584i	−0.632415	+	0.459477i
$214$	1.90735	−	5.87023i	0.130384	−	0.401280i
$215$	3.67741	−	11.3179i	0.250797	−	0.771875i
$216$	−9.97615	+	7.24809i	−0.678791	+	0.493170i
$217$	−7.83900	−	5.69537i	−0.532146	−	0.386627i
$218$	4.61176	+	14.1935i	0.312348	+	0.961308i
$219$	−49.2490			−3.32794
$220$	−1.73855	−	2.82444i	−0.117213	−	0.190424i
$221$	−2.59484			−0.174548
$222$	−4.44432	−	13.6782i	−0.298283	−	0.918022i
$223$	12.8457	+	9.33295i	0.860212	+	0.624980i	0.927943	−	0.372723i	$-0.121576\pi$
$223$	12.8457	+	9.33295i	0.860212	+	0.624980i	−0.0677308	+	0.997704i	$0.521576\pi$
$224$	−0.809017	+	0.587785i	−0.0540547	+	0.0392731i
$225$	2.13715	−	6.57747i	0.142477	−	0.438498i
$226$	−5.89932	+	18.1562i	−0.392417	+	1.20774i
$227$	6.81055	−	4.94815i	0.452032	−	0.328420i	−0.338366	−	0.941015i	$-0.609874\pi$
$227$	6.81055	−	4.94815i	0.452032	−	0.328420i	0.790398	+	0.612594i	$0.209874\pi$
$228$	−15.0713	−	10.9499i	−0.998119	−	0.725176i
$229$	6.88625	+	21.1937i	0.455056	+	1.40052i	0.871069	+	0.491160i	$0.163427\pi$
$229$	6.88625	+	21.1937i	0.455056	+	1.40052i	−0.416013	+	0.909359i	$0.636573\pi$
$230$	2.65626			0.175149
$231$	−10.1505	+	2.45825i	−0.667853	+	0.161741i
$232$	6.56726			0.431162
$233$	−3.83214	−	11.7941i	−0.251052	−	0.772658i	−0.994582	−	0.103956i	$-0.966850\pi$
$233$	−3.83214	−	11.7941i	−0.251052	−	0.772658i	0.743530	−	0.668703i	$-0.233150\pi$
$234$	30.4311	+	22.1095i	1.98935	+	1.44534i
$235$	−7.62605	+	5.54065i	−0.497469	+	0.361432i
$236$	−0.174932	+	0.538386i	−0.0113871	+	0.0350459i
$237$	3.28909	−	10.1228i	0.213649	−	0.657545i
$238$	0.385976	−	0.280428i	0.0250191	−	0.0181774i
$239$	−15.6603	−	11.3778i	−1.01298	−	0.735972i	−0.0481464	−	0.998840i	$-0.515331\pi$
$239$	−15.6603	−	11.3778i	−1.01298	−	0.735972i	−0.964832	+	0.262869i	$0.915331\pi$
$240$	−0.973083	−	2.99484i	−0.0628122	−	0.193316i
$241$	−5.12445			−0.330095			−0.165047	−	0.986286i	$-0.552778\pi$
$241$	−5.12445			−0.330095			−0.165047	+	0.986286i	$0.552778\pi$
$242$	−7.80902	−	7.74721i	−0.501983	−	0.498009i
$243$	−19.9478			−1.27965
$244$	0.633138	+	1.94860i	0.0405325	+	0.124746i
$245$	−0.809017	−	0.587785i	−0.0516862	−	0.0375522i
$246$	−6.42727	+	4.66968i	−0.409788	+	0.297728i
$247$	−9.94296	+	30.6013i	−0.632655	+	1.94711i
$248$	2.99423	−	9.21529i	0.190134	−	0.585172i
$249$	4.42940	−	3.21814i	0.280702	−	0.203942i
$250$	0.809017	+	0.587785i	0.0511667	+	0.0371748i
$251$	−2.77853	−	8.55145i	−0.175380	−	0.539763i	0.824271	−	0.566195i	$-0.191585\pi$
$251$	−2.77853	−	8.55145i	−0.175380	−	0.539763i	−0.999651	+	0.0264327i	$0.991585\pi$
$252$	−6.91596			−0.435664
$253$	8.56231	−	2.07363i	0.538308	−	0.130368i
$254$	−16.3815			−1.02787
$255$	0.464250	+	1.42881i	0.0290725	+	0.0894758i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	14.5199	−	10.5493i	0.905727	−	0.658049i	−0.0342033	−	0.999415i	$-0.510889\pi$
$257$	14.5199	−	10.5493i	0.905727	−	0.658049i	0.939931	+	0.341365i	$0.110889\pi$
$258$	11.5800	−	35.6396i	0.720941	−	2.21883i
$259$	1.41136	−	4.34372i	0.0876977	−	0.269906i
$260$	−4.40013	+	3.19688i	−0.272885	+	0.198262i
$261$	36.7447	+	26.6966i	2.27444	+	1.65248i
$262$	−1.73300	−	5.33364i	−0.107065	−	0.329513i
$263$	27.3312			1.68531			0.842657	−	0.538451i	$-0.180990\pi$
$263$	27.3312			1.68531			0.842657	+	0.538451i	$0.180990\pi$
$264$	−5.47461	−	8.89405i	−0.336939	−	0.547391i
$265$	6.15392			0.378032
$266$	−1.82813	−	5.62641i	−0.112090	−	0.344977i
$267$	−24.3130	−	17.6644i	−1.48793	−	1.08105i
$268$	1.00401	−	0.729456i	0.0613297	−	0.0445586i
$269$	−3.73214	+	11.4863i	−0.227553	+	0.700335i	0.770470	+	0.637476i	$0.220022\pi$
$269$	−3.73214	+	11.4863i	−0.227553	+	0.700335i	−0.998022	+	0.0628585i	$0.979978\pi$
$270$	3.81055	−	11.7277i	0.231903	−	0.713723i
$271$	−20.8990	+	15.1840i	−1.26952	+	0.922361i	−0.999183	−	0.0404043i	$-0.987135\pi$
$271$	−20.8990	+	15.1840i	−1.26952	+	0.922361i	−0.270338	+	0.962766i	$0.587135\pi$
$272$	0.385976	+	0.280428i	0.0234032	+	0.0170034i
$273$	5.29246	+	16.2885i	0.320314	+	0.985827i
$274$	2.50874			0.151558
$275$	3.06668	+	1.26313i	0.184928	+	0.0761695i
$276$	8.36447			0.503482
$277$	−5.63151	−	17.3320i	−0.338365	−	1.04138i	−0.965041	−	0.262100i	$-0.915585\pi$
$277$	−5.63151	−	17.3320i	−0.338365	−	1.04138i	0.626676	−	0.779280i	$-0.284415\pi$
$278$	2.67187	+	1.94123i	0.160248	+	0.116427i
$279$	54.2142	−	39.3889i	3.24572	−	2.35815i
$280$	0.309017	−	0.951057i	0.0184673	−	0.0568365i
$281$	−1.25446	+	3.86084i	−0.0748350	+	0.230319i	−0.981476	−	0.191584i	$-0.938638\pi$
$281$	−1.25446	+	3.86084i	−0.0748350	+	0.230319i	0.906641	+	0.421903i	$0.138638\pi$
$282$	−24.0141	+	17.4473i	−1.43002	+	1.03897i
$283$	2.56114	+	1.86077i	0.152244	+	0.110612i	0.661299	−	0.750122i	$-0.270005\pi$
$283$	2.56114	+	1.86077i	0.152244	+	0.110612i	−0.509056	+	0.860734i	$0.670005\pi$
$284$	−1.11957	−	3.44567i	−0.0664340	−	0.204463i
$285$	18.6291			1.10349
$286$	−11.6879	+	13.7400i	−0.691120	+	0.812461i
$287$	−2.52291			−0.148923
$288$	−2.13715	−	6.57747i	−0.125933	−	0.387581i
$289$	13.5691	+	9.85856i	0.798185	+	0.579915i
$290$	−5.31303	+	3.86014i	−0.311992	+	0.226675i
$291$	3.82574	−	11.7744i	0.224269	−	0.690228i
$292$	4.83295	−	14.8743i	0.282827	−	0.870453i
$293$	−8.29378	+	6.02578i	−0.484528	+	0.352030i	−0.803076	−	0.595877i	$-0.796805\pi$
$293$	−8.29378	+	6.02578i	−0.484528	+	0.352030i	0.318548	+	0.947907i	$0.396805\pi$
$294$	−2.54756	−	1.85091i	−0.148577	−	0.107947i
$295$	−0.174932	−	0.538386i	−0.0101849	−	0.0313460i
$296$	4.56726			0.265467
$297$	3.12781	−	40.7782i	0.181494	−	2.36619i
$298$	−6.83048			−0.395679
$299$	−4.46438	−	13.7400i	−0.258182	−	0.794602i
$300$	2.54756	+	1.85091i	0.147084	+	0.106863i
$301$	9.62758	−	6.99485i	0.554925	−	0.403176i
$302$	3.34324	−	10.2894i	0.192382	−	0.592090i
$303$	2.82966	−	8.70881i	0.162560	−	0.500308i
$304$	4.78611	−	3.47731i	0.274502	−	0.199438i
$305$	−1.65758	−	1.20430i	−0.0949126	−	0.0689581i
$306$	1.01962	+	3.13806i	0.0582876	+	0.179391i
$307$	−3.38972			−0.193461			−0.0967307	−	0.995311i	$-0.530839\pi$
$307$	−3.38972			−0.193461			−0.0967307	+	0.995311i	$0.530839\pi$
$308$	0.253650	−	3.30691i	0.0144531	−	0.188429i
$309$	50.1587			2.85343
$310$	2.99423	+	9.21529i	0.170061	+	0.523394i
$311$	23.8274	+	17.3116i	1.35113	+	0.981651i	0.998954	+	0.0457164i	$0.0145570\pi$
$311$	23.8274	+	17.3116i	1.35113	+	0.981651i	0.352173	+	0.935935i	$0.385443\pi$
$312$	−13.8558	+	10.0669i	−0.784433	+	0.569924i
$313$	−6.81829	+	20.9845i	−0.385393	+	1.18612i	0.550802	+	0.834636i	$0.314322\pi$
$313$	−6.81829	+	20.9845i	−0.385393	+	1.18612i	−0.936195	+	0.351481i	$0.885678\pi$
$314$	−2.47759	+	7.62525i	−0.139819	+	0.430318i
$315$	5.59513	−	4.06510i	0.315250	−	0.229042i
$316$	2.73454	+	1.98676i	0.153830	+	0.111764i
$317$	6.52516	+	20.0824i	0.366489	+	1.12794i	0.949043	+	0.315146i	$0.102054\pi$
$317$	6.52516	+	20.0824i	0.366489	+	1.12794i	−0.582554	+	0.812792i	$0.697946\pi$
$318$	19.3784			1.08669
$319$	−14.1128	+	16.5906i	−0.790165	+	0.928894i
$320$	1.00000			0.0559017
$321$	6.00618	+	18.4851i	0.335232	+	1.03174i
$322$	2.14896	+	1.56131i	0.119757	+	0.0870085i
$323$	−2.28342	+	1.65900i	−0.127053	+	0.0923091i
$324$	5.58783	−	17.1976i	0.310435	−	0.955420i
$325$	1.68070	−	5.17267i	0.0932285	−	0.286928i
$326$	−14.8043	+	10.7559i	−0.819933	+	0.595716i
$327$	−38.0198	−	27.6230i	−2.10250	−	1.52755i
$328$	−0.779621	−	2.39943i	−0.0430474	−	0.132486i
$329$	−9.42632			−0.519690
$330$	9.65685	+	3.97754i	0.531592	+	0.218956i
$331$	−31.1409			−1.71166			−0.855830	−	0.517258i	$-0.826953\pi$
$331$	−31.1409			−1.71166			−0.855830	+	0.517258i	$0.826953\pi$
$332$	0.537282	+	1.65358i	0.0294872	+	0.0907521i
$333$	25.5544	+	18.5664i	1.40037	+	1.01743i
$334$	−14.5025	+	10.5367i	−0.793540	+	0.576540i
$335$	−0.383498	+	1.18028i	−0.0209527	+	0.0644858i
$336$	0.973083	−	2.99484i	0.0530860	−	0.163382i
$337$	1.29523	−	0.941038i	0.0705556	−	0.0512616i	−0.551948	−	0.833878i	$-0.686115\pi$
$337$	1.29523	−	0.941038i	0.0705556	−	0.0512616i	0.622504	+	0.782617i	$0.286115\pi$
$338$	13.4145	+	9.74621i	0.729653	+	0.530124i
$339$	−18.5767	−	57.1733i	−1.00895	−	3.10523i
$340$	−0.477092			−0.0258740
$341$	16.8457	+	27.3675i	0.912246	+	1.48203i
$342$	40.9145			2.21240
$343$	−0.309017	−	0.951057i	−0.0166853	−	0.0513522i
$344$	9.62758	+	6.99485i	0.519085	+	0.377137i
$345$	−6.76700	+	4.91651i	−0.364323	+	0.264696i
$346$	2.37569	−	7.31163i	0.127718	−	0.393076i
$347$	6.09359	−	18.7542i	0.327121	−	1.00678i	−0.643353	−	0.765570i	$-0.722457\pi$
$347$	6.09359	−	18.7542i	0.327121	−	1.00678i	0.970474	−	0.241206i	$-0.0775429\pi$
$348$	−16.7305	+	12.1554i	−0.896850	+	0.651599i
$349$	−12.4419	−	9.03959i	−0.666001	−	0.483878i	0.202683	−	0.979244i	$-0.435034\pi$
$349$	−12.4419	−	9.03959i	−0.666001	−	0.483878i	−0.868684	+	0.495366i	$0.835034\pi$
$350$	0.309017	+	0.951057i	0.0165177	+	0.0508361i
$351$	−67.0677			−3.57981
$352$	3.22344	−	0.780656i	0.171810	−	0.0416091i
$353$	−10.3793			−0.552436			−0.276218	−	0.961095i	$-0.589081\pi$
$353$	−10.3793			−0.552436			−0.276218	+	0.961095i	$0.589081\pi$
$354$	−0.550854	−	1.69536i	−0.0292776	−	0.0901071i
$355$	2.93106	+	2.12954i	0.155565	+	0.113024i
$356$	7.72096	−	5.60961i	0.409210	−	0.297309i
$357$	−0.464250	+	1.42881i	−0.0245707	+	0.0756209i
$358$	−7.02078	+	21.6077i	−0.371060	+	1.14200i
$359$	−19.2804	+	14.0080i	−1.01758	+	0.739316i	−0.965786	−	0.259341i	$-0.916495\pi$
$359$	−19.2804	+	14.0080i	−1.01758	+	0.739316i	−0.0517960	+	0.998658i	$0.516495\pi$
$360$	5.59513	+	4.06510i	0.294889	+	0.214249i
$361$	4.94382	+	15.2155i	0.260201	+	0.800817i
$362$	13.6567			0.717780
$363$	34.2334	+	5.28269i	1.79679	+	0.277270i
$364$	−5.43886			−0.285074
$365$	4.83295	+	14.8743i	0.252968	+	0.778557i
$366$	−5.21965	−	3.79230i	−0.272835	−	0.198226i
$367$	15.6905	−	11.3998i	0.819036	−	0.595064i	−0.0974004	−	0.995245i	$-0.531053\pi$
$367$	15.6905	−	11.3998i	0.819036	−	0.595064i	0.916436	+	0.400181i	$0.131053\pi$
$368$	−0.820830	+	2.52626i	−0.0427887	+	0.131690i
$369$	5.39183	−	16.5943i	0.280687	−	0.863867i
$370$	−3.69499	+	2.68457i	−0.192094	+	0.139564i
$371$	4.97862	+	3.61718i	0.258477	+	0.187795i
$372$	9.42872	+	29.0186i	0.488856	+	1.50454i
$373$	10.9015			0.564459			0.282230	−	0.959347i	$-0.408926\pi$
$373$	10.9015			0.564459			0.282230	+	0.959347i	$0.408926\pi$
$374$	−1.53788	+	0.372445i	−0.0795218	+	0.0192587i
$375$	−3.14896			−0.162612
$376$	−2.91289	−	8.96496i	−0.150221	−	0.462333i
$377$	28.8968	+	20.9948i	1.48826	+	1.08129i
$378$	9.97615	−	7.24809i	0.513118	−	0.372802i
$379$	2.10368	−	6.47447i	0.108059	−	0.332571i	−0.882377	−	0.470543i	$-0.844058\pi$
$379$	2.10368	−	6.47447i	0.108059	−	0.332571i	0.990436	+	0.137971i	$0.0440582\pi$
$380$	−1.82813	+	5.62641i	−0.0937811	+	0.288629i
$381$	41.7329	−	30.3207i	2.13804	−	1.55338i
$382$	7.62241	+	5.53801i	0.389997	+	0.283349i
$383$	−7.48782	−	23.0451i	−0.382610	−	1.17755i	−0.938200	−	0.346095i	$-0.887508\pi$
$383$	−7.48782	−	23.0451i	−0.382610	−	1.17755i	0.555590	−	0.831456i	$-0.312492\pi$
$384$	3.14896			0.160695
$385$	1.73855	+	2.82444i	0.0886045	+	0.143947i
$386$	5.09919			0.259542
$387$	25.4328	+	78.2741i	1.29282	+	3.97890i
$388$	3.18070	+	2.31091i	0.161476	+	0.117319i
$389$	14.7687	−	10.7301i	0.748805	−	0.544039i	−0.146651	−	0.989188i	$-0.546850\pi$
$389$	14.7687	−	10.7301i	0.748805	−	0.544039i	0.895456	+	0.445150i	$0.146850\pi$
$390$	5.29246	−	16.2885i	0.267994	−	0.824802i
$391$	0.391612	−	1.20526i	0.0198047	−	0.0609524i
$392$	0.809017	−	0.587785i	0.0408615	−	0.0296876i
$393$	14.2870	+	10.3801i	0.720686	+	0.523609i
$394$	−5.29297	−	16.2901i	−0.266656	−	0.820682i
$395$	−3.38007			−0.170070
$396$	21.2090	+	8.73574i	1.06579	+	0.438987i
$397$	17.6742			0.887043			0.443522	−	0.896264i	$-0.353729\pi$
$397$	17.6742			0.887043			0.443522	+	0.896264i	$0.353729\pi$
$398$	−3.68427	−	11.3390i	−0.184676	−	0.568373i
$399$	15.0713	+	10.9499i	0.754507	+	0.548182i
$400$	−0.809017	+	0.587785i	−0.0404508	+	0.0293893i
$401$	9.39991	−	28.9299i	0.469409	−	1.44469i	−0.383943	−	0.923357i	$-0.625434\pi$
$401$	9.39991	−	28.9299i	0.469409	−	1.44469i	0.853352	−	0.521335i	$-0.174566\pi$
$402$	−1.20762	+	3.71667i	−0.0602306	+	0.185371i
$403$	42.6352	−	30.9763i	2.12381	−	1.54304i
$404$	2.35257	+	1.70924i	0.117045	+	0.0850380i
$405$	5.58783	+	17.1976i	0.277661	+	0.854554i
$406$	−6.56726			−0.325928
$407$	−9.81487	+	11.5381i	−0.486505	+	0.571921i
$408$	−1.50234			−0.0743771
$409$	4.76087	+	14.6524i	0.235410	+	0.724517i	0.997067	+	0.0765365i	$0.0243862\pi$
$409$	4.76087	+	14.6524i	0.235410	+	0.724517i	−0.761657	+	0.647980i	$0.775614\pi$
$410$	2.04108	+	1.48293i	0.100802	+	0.0732366i
$411$	−6.39117	+	4.64346i	−0.315253	+	0.229045i
$412$	−4.92223	+	15.1491i	−0.242501	+	0.746341i
$413$	0.174932	−	0.538386i	0.00860785	−	0.0264922i
$414$	−14.8621	+	10.7980i	−0.730433	+	0.530691i
$415$	−1.40662	−	1.02197i	−0.0690483	−	0.0501665i
$416$	−1.68070	−	5.17267i	−0.0824032	−	0.253611i
$417$	−10.3998			−0.509280
$418$	−1.50059	+	19.5635i	−0.0733960	+	0.956884i
$419$	3.21914			0.157265			0.0786327	−	0.996904i	$-0.474945\pi$
$419$	3.21914			0.157265			0.0786327	+	0.996904i	$0.474945\pi$
$420$	0.973083	+	2.99484i	0.0474816	+	0.146133i
$421$	−10.6470	−	7.73553i	−0.518905	−	0.377007i	0.297286	−	0.954788i	$-0.403919\pi$
$421$	−10.6470	−	7.73553i	−0.518905	−	0.377007i	−0.816191	+	0.577782i	$0.803919\pi$
$422$	18.4724	−	13.4209i	0.899220	−	0.653322i
$423$	20.1454	−	62.0013i	0.979505	−	3.01461i
$424$	−1.90167	+	5.85272i	−0.0923530	+	0.284233i
$425$	0.385976	−	0.280428i	0.0187226	−	0.0136027i
$426$	9.22980	+	6.70584i	0.447185	+	0.324899i
$427$	−0.633138	−	1.94860i	−0.0306397	−	0.0942993i
$428$	−6.17232			−0.298350
$429$	4.34421	−	56.6367i	0.209741	−	2.73445i
$430$	−11.9003			−0.573886
$431$	0.736786	+	2.26760i	0.0354898	+	0.109226i	0.967232	−	0.253894i	$-0.0817114\pi$
$431$	0.736786	+	2.26760i	0.0354898	+	0.109226i	−0.931742	+	0.363120i	$0.881711\pi$
$432$	9.97615	+	7.24809i	0.479978	+	0.348724i
$433$	−7.30193	+	5.30516i	−0.350908	+	0.254950i	−0.749250	−	0.662287i	$-0.769586\pi$
$433$	−7.30193	+	5.30516i	−0.350908	+	0.254950i	0.398342	+	0.917237i	$0.369586\pi$
$434$	−2.99423	+	9.21529i	−0.143728	+	0.442348i
$435$	6.39049	−	19.6679i	0.306400	−	0.943004i
$436$	12.0737	−	8.77209i	0.578228	−	0.420107i
$437$	−12.7132	−	9.23665i	−0.608153	−	0.441849i
$438$	15.2188	+	46.8386i	0.727182	+	2.23803i
$439$	23.1241			1.10366			0.551828	−	0.833958i	$-0.313931\pi$
$439$	23.1241			1.10366			0.551828	+	0.833958i	$0.313931\pi$
$440$	−2.14896	+	2.52626i	−0.102448	+	0.120434i
$441$	6.91596			0.329331
$442$	0.801849	+	2.46784i	0.0381401	+	0.117383i
$443$	5.49160	+	3.98988i	0.260914	+	0.189565i	0.710550	−	0.703647i	$-0.248446\pi$
$443$	5.49160	+	3.98988i	0.260914	+	0.189565i	−0.449636	+	0.893212i	$0.648446\pi$
$444$	−11.6354	+	8.45360i	−0.552191	+	0.401190i
$445$	−2.94915	+	9.07654i	−0.139803	+	0.430269i
$446$	4.90662	−	15.1010i	0.232335	−	0.715054i
$447$	17.4011	−	12.6426i	0.823042	−	0.597975i
$448$	0.809017	+	0.587785i	0.0382225	+	0.0277702i
$449$	4.05166	+	12.4697i	0.191209	+	0.588482i	1.00000		0.000385241i	$0.000122626\pi$
$449$	4.05166	+	12.4697i	0.191209	+	0.588482i	−0.808790	+	0.588097i	$0.799877\pi$
$450$	−6.91596			−0.326021
$451$	7.73694	+	3.18675i	0.364318	+	0.150058i
$452$	19.0906			0.897946
$453$	10.5277	+	32.4010i	0.494635	+	1.52233i
$454$	−6.81055	−	4.94815i	−0.319635	−	0.232228i
$455$	4.40013	−	3.19688i	0.206281	−	0.149872i
$456$	−5.75671	+	17.7173i	−0.269583	+	0.829691i
$457$	−5.87750	+	18.0891i	−0.274938	+	0.846172i	0.714298	+	0.699842i	$0.246746\pi$
$457$	−5.87750	+	18.0891i	−0.274938	+	0.846172i	−0.989236	+	0.146330i	$0.953254\pi$
$458$	18.0284	−	13.0984i	0.842414	−	0.612049i
$459$	−4.75954	−	3.45801i	−0.222156	−	0.161406i
$460$	−0.820830	−	2.52626i	−0.0382714	−	0.117787i
$461$	18.8767			0.879177			0.439588	−	0.898199i	$-0.355124\pi$
$461$	18.8767			0.879177			0.439588	+	0.898199i	$0.355124\pi$
$462$	5.47461	+	8.89405i	0.254702	+	0.413789i
$463$	13.6194			0.632945			0.316473	−	0.948602i	$-0.397501\pi$
$463$	13.6194			0.632945			0.316473	+	0.948602i	$0.397501\pi$
$464$	−2.02940	−	6.24584i	−0.0942123	−	0.289956i
$465$	−24.6847	−	17.9345i	−1.14473	−	0.831692i
$466$	−10.0327	+	7.28916i	−0.464755	+	0.337664i
$467$	−5.86518	+	18.0512i	−0.271408	+	0.835309i	0.718739	+	0.695280i	$0.244720\pi$
$467$	−5.86518	+	18.0512i	−0.271408	+	0.835309i	−0.990147	+	0.140029i	$0.955280\pi$
$468$	11.6237	−	35.7739i	0.537304	−	1.65365i
$469$	−1.00401	+	0.729456i	−0.0463609	+	0.0336831i
$470$	7.62605	+	5.54065i	0.351764	+	0.255571i
$471$	−7.80185	−	24.0116i	−0.359490	−	1.10640i
$472$	0.566092			0.0260565
$473$	−38.3601	+	9.29008i	−1.76380	+	0.427158i
$474$	−10.6437			−0.488882
$475$	−1.82813	−	5.62641i	−0.0838804	−	0.258157i
$476$	−0.385976	−	0.280428i	−0.0176912	−	0.0128534i
$477$	−34.4319	+	25.0163i	−1.57653	+	1.14542i
$478$	−5.98169	+	18.4097i	−0.273596	+	0.842042i
$479$	−1.70433	+	5.24538i	−0.0778727	+	0.239668i	−0.982413	−	0.186720i	$-0.940214\pi$
$479$	−1.70433	+	5.24538i	−0.0778727	+	0.239668i	0.904540	+	0.426388i	$0.140214\pi$
$480$	−2.54756	+	1.85091i	−0.116280	+	0.0844822i
$481$	20.0966	+	14.6010i	0.916324	+	0.665749i
$482$	1.58354	+	4.87364i	0.0721283	+	0.221988i
$483$	−8.36447			−0.380596
$484$	−4.95492	+	9.82084i	−0.225223	+	0.446402i
$485$	−3.93156			−0.178523
$486$	6.16420	+	18.9715i	0.279614	+	0.860563i
$487$	−22.6594	−	16.4631i	−1.02680	−	0.746012i	−0.0591323	−	0.998250i	$-0.518833\pi$
$487$	−22.6594	−	16.4631i	−1.02680	−	0.746012i	−0.967665	+	0.252238i	$0.918833\pi$
$488$	1.65758	−	1.20430i	0.0750350	−	0.0545161i
$489$	17.8065	−	54.8029i	0.805239	−	2.47827i
$490$	−0.309017	+	0.951057i	−0.0139600	+	0.0429644i
$491$	10.4804	−	7.61444i	0.472973	−	0.343635i	−0.325626	−	0.945499i	$-0.605575\pi$
$491$	10.4804	−	7.61444i	0.472973	−	0.343635i	0.798599	+	0.601864i	$0.205575\pi$
$492$	6.42727	+	4.66968i	0.289764	+	0.210526i
$493$	0.968209	+	2.97984i	0.0436059	+	0.134205i
$494$	32.1761			1.44767
$495$	−22.2932	+	5.39898i	−1.00200	+	0.242666i
$496$	−9.68953			−0.435073
$497$	1.11957	+	3.44567i	0.0502194	+	0.154559i
$498$	−4.42940	−	3.21814i	−0.198486	−	0.144208i
$499$	−3.18741	+	2.31579i	−0.142688	+	0.103669i	−0.656839	−	0.754031i	$-0.728107\pi$
$499$	−3.18741	+	2.31579i	−0.142688	+	0.103669i	0.514151	+	0.857699i	$0.328107\pi$
$500$	0.309017	−	0.951057i	0.0138197	−	0.0425325i
$501$	17.4435	−	53.6856i	0.779319	−	2.39850i
$502$	−7.27430	+	5.28509i	−0.324668	+	0.235885i
$503$	−23.2315	−	16.8787i	−1.03584	−	0.752584i	−0.0663735	−	0.997795i	$-0.521143\pi$
$503$	−23.2315	−	16.8787i	−1.03584	−	0.752584i	−0.969470	+	0.245211i	$0.921143\pi$
$504$	2.13715	+	6.57747i	0.0951961	+	0.292984i
$505$	−2.90794			−0.129401
$506$	−4.61803	−	7.50245i	−0.205297	−	0.333525i
$507$	−52.2137			−2.31889
$508$	5.06216	+	15.5797i	0.224597	+	0.691239i
$509$	−5.45134	−	3.96063i	−0.241626	−	0.175552i	0.460381	−	0.887721i	$-0.347713\pi$
$509$	−5.45134	−	3.96063i	−0.241626	−	0.175552i	−0.702008	+	0.712170i	$0.747713\pi$
$510$	1.21542	−	0.883056i	0.0538198	−	0.0391024i
$511$	−4.83295	+	14.8743i	−0.213797	+	0.658000i
$512$	−0.309017	+	0.951057i	−0.0136568	+	0.0420312i
$513$	−59.0184	+	42.8794i	−2.60573	+	1.89317i
$514$	−14.5199	−	10.5493i	−0.640446	−	0.465311i
$515$	−4.92223	−	15.1491i	−0.216899	−	0.667547i
$516$	−37.4737			−1.64969
$517$	28.9075	+	11.9066i	1.27135	+	0.523654i
$518$	−4.56726			−0.200674
$519$	7.48097	+	23.0241i	0.328378	+	1.01064i
$520$	4.40013	+	3.19688i	0.192959	+	0.140193i
$521$	−26.0506	+	18.9269i	−1.14130	+	0.829202i	−0.987300	−	0.158869i	$-0.949215\pi$
$521$	−26.0506	+	18.9269i	−1.14130	+	0.829202i	−0.153999	+	0.988071i	$0.549215\pi$
$522$	14.0352	−	43.1959i	0.614305	−	1.89063i
$523$	−8.78363	+	27.0332i	−0.384081	+	1.18208i	0.553063	+	0.833139i	$0.313459\pi$
$523$	−8.78363	+	27.0332i	−0.384081	+	1.18208i	−0.937144	+	0.348942i	$0.886541\pi$
$524$	−4.53707	+	3.29637i	−0.198203	+	0.144003i
$525$	−2.54756	−	1.85091i	−0.111185	−	0.0807805i
$526$	−8.44580	−	25.9935i	−0.368255	−	1.13337i
$527$	4.62280			0.201372
$528$	−6.76700	+	7.95508i	−0.294496	+	0.346200i
$529$	−15.9443			−0.693229
$530$	−1.90167	−	5.85272i	−0.0826031	−	0.254226i
$531$	3.16736	+	2.30122i	0.137452	+	0.0998644i
$532$	−4.78611	+	3.47731i	−0.207504	+	0.150761i
$533$	4.24025	−	13.0502i	0.183666	−	0.565265i
$534$	−9.28675	+	28.5817i	−0.401877	+	1.23685i
$535$	4.99351	−	3.62800i	0.215888	−	0.156852i
$536$	−1.00401	−	0.729456i	−0.0433666	−	0.0315077i
$537$	−22.1082	−	68.0419i	−0.954038	−	2.93623i
$538$	12.0775			0.520696
$539$	−0.253650	+	3.30691i	−0.0109255	+	0.142439i
$540$	−12.3312			−0.530650
$541$	6.67718	+	20.5503i	0.287074	+	0.883524i	0.985769	+	0.168104i	$0.0537646\pi$
$541$	6.67718	+	20.5503i	0.287074	+	0.883524i	−0.698695	+	0.715420i	$0.746235\pi$
$542$	20.8990	+	15.1840i	0.897687	+	0.652208i
$543$	−34.7913	+	25.2774i	−1.49304	+	1.08475i
$544$	0.147430	−	0.453742i	0.00632099	−	0.0194540i
$545$	−4.61176	+	14.1935i	−0.197546	+	0.607985i
$546$	13.8558	−	10.0669i	0.592976	−	0.430822i
$547$	−25.8394	−	18.7734i	−1.10481	−	0.802694i	−0.122975	−	0.992410i	$-0.539243\pi$
$547$	−25.8394	−	18.7734i	−1.10481	−	0.802694i	−0.981839	+	0.189716i	$0.939243\pi$
$548$	−0.775243	−	2.38595i	−0.0331167	−	0.101923i
$549$	14.1700			0.604759
$550$	0.253650	−	3.30691i	0.0108157	−	0.141007i
$551$	38.8516			1.65514
$552$	−2.58476	−	7.95508i	−0.110015	−	0.338591i
$553$	−2.73454	−	1.98676i	−0.116284	−	0.0844855i
$554$	−14.7435	+	10.7118i	−0.626391	+	0.455100i
$555$	4.44432	−	13.6782i	0.188651	−	0.580608i
$556$	1.02056	−	3.14097i	0.0432815	−	0.133207i
$557$	−15.1253	+	10.9891i	−0.640878	+	0.465625i	−0.860152	−	0.510038i	$-0.829631\pi$
$557$	−15.1253	+	10.9891i	−0.640878	+	0.465625i	0.219274	+	0.975663i	$0.429631\pi$
$558$	−54.2142	−	39.3889i	−2.29507	−	1.66746i
$559$	20.0009	+	61.5565i	0.845949	+	2.60356i
$560$	−1.00000			−0.0422577
$561$	3.22848	−	3.79531i	0.136307	−	0.160238i
$562$	4.05953			0.171241
$563$	12.9379	+	39.8188i	0.545268	+	1.67816i	0.720351	+	0.693609i	$0.243981\pi$
$563$	12.9379	+	39.8188i	0.545268	+	1.67816i	−0.175083	+	0.984554i	$0.556019\pi$
$564$	24.0141	+	17.4473i	1.01118	+	0.734664i
$565$	−15.4446	+	11.2212i	−0.649760	+	0.472078i
$566$	0.978267	−	3.01080i	0.0411196	−	0.126553i
$567$	−5.58783	+	17.1976i	−0.234667	+	0.722230i
$568$	−2.93106	+	2.12954i	−0.122985	+	0.0893535i
$569$	−11.9381	−	8.67356i	−0.500473	−	0.363615i	0.308725	−	0.951151i	$-0.400098\pi$
$569$	−11.9381	−	8.67356i	−0.500473	−	0.363615i	−0.809197	+	0.587537i	$0.800098\pi$
$570$	−5.75671	−	17.7173i	−0.241122	−	0.742098i
$571$	−43.4272			−1.81737			−0.908686	−	0.417481i	$-0.862913\pi$
$571$	−43.4272			−1.81737			−0.908686	+	0.417481i	$0.862913\pi$
$572$	16.6792	+	6.86998i	0.697394	+	0.287248i
$573$	−29.6689			−1.23944
$574$	0.779621	+	2.39943i	0.0325408	+	0.100150i
$575$	2.14896	+	1.56131i	0.0896179	+	0.0651112i
$576$	−5.59513	+	4.06510i	−0.233130	+	0.169379i
$577$	−5.92903	+	18.2477i	−0.246829	+	0.759660i	0.748502	+	0.663133i	$0.230774\pi$
$577$	−5.92903	+	18.2477i	−0.246829	+	0.759660i	−0.995330	+	0.0965275i	$0.969226\pi$
$578$	5.18295	−	15.9515i	0.215582	−	0.663494i
$579$	−12.9905	+	9.43816i	−0.539868	+	0.392237i
$580$	5.31303	+	3.86014i	0.220611	+	0.160284i
$581$	−0.537282	−	1.65358i	−0.0222902	−	0.0686022i
$582$	−12.3803			−0.513182
$583$	−10.6989	−	17.3814i	−0.443102	−	0.719863i
$584$	−15.6398			−0.647178
$585$	11.6237	+	35.7739i	0.480579	+	1.47907i
$586$	8.29378	+	6.02578i	0.342613	+	0.248923i
$587$	−3.04662	+	2.21350i	−0.125747	+	0.0913608i	−0.648881	−	0.760890i	$-0.724763\pi$
$587$	−3.04662	+	2.21350i	−0.125747	+	0.0913608i	0.523134	+	0.852251i	$0.324763\pi$
$588$	−0.973083	+	2.99484i	−0.0401292	+	0.123505i
$589$	17.7137	−	54.5173i	0.729882	−	2.24635i
$590$	−0.457978	+	0.332741i	−0.0188547	+	0.0136987i
$591$	43.6357	+	31.7032i	1.79493	+	1.30409i
$592$	−1.41136	−	4.34372i	−0.0580066	−	0.178526i
$593$	37.8401			1.55391			0.776954	−	0.629558i	$-0.216764\pi$
$593$	37.8401			1.55391			0.776954	+	0.629558i	$0.216764\pi$
$594$	−39.7489	+	9.62642i	−1.63092	+	0.394977i
$595$	0.477092			0.0195589
$596$	2.11073	+	6.49617i	0.0864590	+	0.266093i
$597$	30.3734	+	22.0676i	1.24310	+	0.903166i
$598$	−11.6879	+	8.49176i	−0.477954	+	0.347254i
$599$	−9.95550	+	30.6399i	−0.406771	+	1.25191i	0.512637	+	0.858605i	$0.328669\pi$
$599$	−9.95550	+	30.6399i	−0.406771	+	1.25191i	−0.919408	+	0.393306i	$0.871331\pi$
$600$	0.973083	−	2.99484i	0.0397259	−	0.122264i
$601$	−2.64044	+	1.91839i	−0.107706	+	0.0782528i	−0.640334	−	0.768096i	$-0.721204\pi$
$601$	−2.64044	+	1.91839i	−0.107706	+	0.0782528i	0.532629	+	0.846349i	$0.321204\pi$
$602$	−9.62758	−	6.99485i	−0.392391	−	0.285089i
$603$	−2.65225	−	8.16279i	−0.108008	−	0.332415i
$604$	−10.8189			−0.440216
$605$	−1.76393	−	10.8576i	−0.0717140	−	0.441426i
$606$	−9.15698			−0.371977
$607$	5.99234	+	18.4425i	0.243221	+	0.748559i	0.995924	+	0.0901978i	$0.0287499\pi$
$607$	5.99234	+	18.4425i	0.243221	+	0.748559i	−0.752702	+	0.658361i	$0.771250\pi$
$608$	−4.78611	−	3.47731i	−0.194102	−	0.141024i
$609$	16.7305	−	12.1554i	0.677955	−	0.492563i
$610$	−0.633138	+	1.94860i	−0.0256350	+	0.0788965i
$611$	15.8428	−	48.7592i	0.640932	−	1.97259i
$612$	2.66939	−	1.93943i	0.107904	−	0.0783966i
$613$	−24.1177	−	17.5225i	−0.974104	−	0.707728i	−0.0177205	−	0.999843i	$-0.505641\pi$
$613$	−24.1177	−	17.5225i	−0.974104	−	0.707728i	−0.956383	+	0.292115i	$0.905641\pi$
$614$	1.04748	+	3.22381i	0.0422729	+	0.130103i
$615$	−7.94454			−0.320355
$616$	−3.22344	+	0.780656i	−0.129876	+	0.0314535i
$617$	−3.60999			−0.145333			−0.0726664	−	0.997356i	$-0.523151\pi$
$617$	−3.60999			−0.145333			−0.0726664	+	0.997356i	$0.523151\pi$
$618$	−15.4999	−	47.7038i	−0.623498	−	1.91893i
$619$	−21.6532	−	15.7320i	−0.870315	−	0.632321i	0.0603564	−	0.998177i	$-0.480776\pi$
$619$	−21.6532	−	15.7320i	−0.870315	−	0.632321i	−0.930671	+	0.365856i	$0.880776\pi$
$620$	7.83900	−	5.69537i	0.314822	−	0.228731i
$621$	10.1218	−	31.1517i	0.406174	−	1.25008i
$622$	9.10125	−	28.0108i	0.364927	−	1.12313i
$623$	−7.72096	+	5.60961i	−0.309334	+	0.224744i
$624$	13.8558	+	10.0669i	0.554678	+	0.402997i
$625$	0.309017	+	0.951057i	0.0123607	+	0.0380423i
$626$	22.0645			0.881873
$627$	−32.3876	−	52.6168i	−1.29344	−	2.10131i
$628$	8.01766			0.319940
$629$	0.673350	+	2.07236i	0.0268482	+	0.0826303i
$630$	−5.59513	−	4.06510i	−0.222915	−	0.161957i
$631$	34.3550	−	24.9604i	1.36765	−	0.993656i	0.369734	−	0.929138i	$-0.379449\pi$
$631$	34.3550	−	24.9604i	1.36765	−	0.993656i	0.997917	−	0.0645185i	$-0.0205511\pi$
$632$	1.04450	−	3.21464i	0.0415480	−	0.127872i
$633$	−22.2185	+	68.3814i	−0.883105	+	2.71792i
$634$	17.0831	−	12.4116i	0.678456	−	0.492927i
$635$	−13.2529	−	9.62881i	−0.525926	−	0.382108i
$636$	−5.98827	−	18.4300i	−0.237450	−	0.730797i
$637$	5.43886			0.215496
$638$	20.1397	+	8.29529i	0.797337	+	0.328414i
$639$	−25.0564			−0.991218
$640$	−0.309017	−	0.951057i	−0.0122150	−	0.0375938i
$641$	10.3262	+	7.50244i	0.407861	+	0.296328i	0.772735	−	0.634728i	$-0.218888\pi$
$641$	10.3262	+	7.50244i	0.407861	+	0.296328i	−0.364874	+	0.931057i	$0.618888\pi$
$642$	15.7244	−	11.4244i	0.620592	−	0.450886i
$643$	0.356675	−	1.09773i	0.0140659	−	0.0432903i	−0.943777	−	0.330582i	$-0.892755\pi$
$643$	0.356675	−	1.09773i	0.0140659	−	0.0432903i	0.957843	+	0.287292i	$0.0927549\pi$
$644$	0.820830	−	2.52626i	0.0323452	−	0.0995484i
$645$	30.3169	−	22.0265i	1.19373	−	0.867293i
$646$	2.28342	+	1.65900i	0.0898398	+	0.0652724i
$647$	−3.44530	−	10.6035i	−0.135449	−	0.416868i	0.860211	−	0.509939i	$-0.170332\pi$
$647$	−3.44530	−	10.6035i	−0.135449	−	0.416868i	−0.995660	+	0.0930702i	$0.970332\pi$
$648$	−18.0826			−0.710351
$649$	−1.21651	+	1.43009i	−0.0477522	+	0.0561361i
$650$	−5.43886			−0.213330
$651$	−9.42872	−	29.0186i	−0.369541	−	1.13733i
$652$	14.8043	+	10.7559i	0.579780	+	0.421235i
$653$	−12.9720	+	9.42469i	−0.507632	+	0.368817i	−0.811925	−	0.583762i	$-0.801580\pi$
$653$	−12.9720	+	9.42469i	−0.507632	+	0.368817i	0.304292	+	0.952579i	$0.401580\pi$
$654$	−14.5223	+	44.6949i	−0.567865	+	1.74771i
$655$	1.73300	−	5.33364i	0.0677141	−	0.208403i
$656$	−2.04108	+	1.48293i	−0.0796906	+	0.0578986i
$657$	−87.5065	−	63.5772i	−3.41395	−	2.48038i
$658$	2.91289	+	8.96496i	0.113556	+	0.349491i
$659$	29.5362			1.15057			0.575283	−	0.817955i	$-0.304892\pi$
$659$	29.5362			1.15057			0.575283	+	0.817955i	$0.304892\pi$
$660$	0.798735	−	10.4133i	0.0310907	−	0.405339i
$661$	9.49650			0.369371			0.184686	−	0.982798i	$-0.440873\pi$
$661$	9.49650			0.369371			0.184686	+	0.982798i	$0.440873\pi$
$662$	9.62307	+	29.6168i	0.374011	+	1.15109i
$663$	−6.61052	−	4.80282i	−0.256731	−	0.186526i
$664$	1.40662	−	1.02197i	0.0545875	−	0.0396601i
$665$	1.82813	−	5.62641i	0.0708919	−	0.218183i
$666$	9.76092	−	30.0410i	0.378228	−	1.16407i
$667$	−14.1128	+	10.2535i	−0.546449	+	0.397019i
$668$	14.5025	+	10.5367i	0.561117	+	0.407676i
$669$	15.4508	+	47.5525i	0.597361	+	1.83849i
$670$	1.24102			0.0479449
$671$	−0.519699	+	6.77546i	−0.0200628	+	0.261564i
$672$	−3.14896			−0.121474
$673$	3.56568	+	10.9740i	0.137447	+	0.423018i	0.995963	−	0.0897690i	$-0.0286129\pi$
$673$	3.56568	+	10.9740i	0.137447	+	0.423018i	−0.858516	+	0.512787i	$0.828613\pi$
$674$	−1.29523	−	0.941038i	−0.0498903	−	0.0362474i
$675$	9.97615	−	7.24809i	0.383982	−	0.278979i
$676$	5.12389	−	15.7697i	0.197073	−	0.606527i
$677$	−15.0962	+	46.4613i	−0.580194	+	1.78565i	0.0375733	+	0.999294i	$0.488037\pi$
$677$	−15.0962	+	46.4613i	−0.580194	+	1.78565i	−0.617768	+	0.786361i	$0.711963\pi$
$678$	−48.6345	+	35.3350i	−1.86780	+	1.35703i
$679$	−3.18070	−	2.31091i	−0.122064	−	0.0886848i
$680$	0.147430	+	0.453742i	0.00565367	+	0.0174002i
$681$	26.5089			1.01582
$682$	20.8224	−	24.4782i	0.797332	−	0.937320i
$683$	35.4736			1.35736			0.678679	−	0.734435i	$-0.262553\pi$
$683$	35.4736			1.35736			0.678679	+	0.734435i	$0.262553\pi$
$684$	−12.6433	−	38.9120i	−0.483428	−	1.48784i
$685$	2.02961	+	1.47460i	0.0775475	+	0.0563415i
$686$	−0.809017	+	0.587785i	−0.0308884	+	0.0224417i
$687$	−21.6845	+	66.7381i	−0.827317	+	2.54622i
$688$	3.67741	−	11.3179i	0.140200	−	0.431491i
$689$	−27.0781	+	19.6734i	−1.03159	+	0.749495i
$690$	6.76700	+	4.91651i	0.257615	+	0.187168i
$691$	−9.32784	−	28.7082i	−0.354848	−	1.09211i	−0.956098	−	0.293048i	$-0.905330\pi$
$691$	−9.32784	−	28.7082i	−0.354848	−	1.09211i	0.601250	−	0.799061i	$-0.294670\pi$
$692$	−7.68791			−0.292250
$693$	−21.2090	−	8.73574i	−0.805663	−	0.331843i
$694$	−19.7193			−0.748534
$695$	1.02056	+	3.14097i	0.0387122	+	0.119144i
$696$	16.7305	+	12.1554i	0.634169	+	0.460750i
$697$	0.973781	−	0.707493i	0.0368846	−	0.0267982i
$698$	−4.75239	+	14.6264i	−0.179881	+	0.553616i
$699$	12.0673	−	37.1392i	0.456426	−	1.40473i
$700$	0.809017	−	0.587785i	0.0305780	−	0.0222162i
$701$	9.11674	+	6.62370i	0.344334	+	0.250174i	0.746488	−	0.665398i	$-0.231738\pi$
$701$	9.11674	+	6.62370i	0.344334	+	0.250174i	−0.402154	+	0.915572i	$0.631738\pi$
$702$	20.7251	+	63.7852i	0.782217	+	2.40742i
$703$	27.0197			1.01907
$704$	−1.73855	−	2.82444i	−0.0655239	−	0.106450i
$705$	−29.6831			−1.11793
$706$	3.20739	+	9.87133i	0.120712	+	0.371513i
$707$	−2.35257	−	1.70924i	−0.0884775	−	0.0642827i
$708$	−1.44216	+	1.04779i	−0.0541995	+	0.0393783i
$709$	−13.3134	+	40.9744i	−0.499995	+	1.53883i	0.309031	+	0.951052i	$0.399995\pi$
$709$	−13.3134	+	40.9744i	−0.499995	+	1.53883i	−0.809026	+	0.587773i	$0.800005\pi$
$710$	1.11957	−	3.44567i	0.0420165	−	0.129314i
$711$	18.9119	−	13.7403i	0.709253	−	0.515302i
$712$	−7.72096	−	5.60961i	−0.289355	−	0.210229i
$713$	7.95346	+	24.4782i	0.297859	+	0.916717i
$714$	1.50234			0.0562238
$715$	−17.5319	+	4.24588i	−0.655654	+	0.158787i
$716$	22.7197			0.849076
$717$	−18.8361	−	57.9716i	−0.703447	−	2.16499i
$718$	19.2804	+	14.0080i	0.719539	+	0.522776i
$719$	−21.9307	+	15.9336i	−0.817876	+	0.594222i	−0.916103	−	0.400942i	$-0.868683\pi$
$719$	−21.9307	+	15.9336i	−0.817876	+	0.594222i	0.0982271	+	0.995164i	$0.468683\pi$
$720$	2.13715	−	6.57747i	0.0796468	−	0.245128i
$721$	4.92223	−	15.1491i	0.183313	−	0.564181i
$722$	12.9431	−	9.40371i	0.481692	−	0.349970i
$723$	−13.0549	−	9.48490i	−0.485515	−	0.352747i
$724$	−4.22015	−	12.9883i	−0.156841	−	0.482706i
$725$	−6.56726			−0.243902
$726$	−5.55455	−	34.1903i	−0.206149	−	1.26892i
$727$	45.5273			1.68851			0.844257	−	0.535939i	$-0.180042\pi$
$727$	45.5273			1.68851			0.844257	+	0.535939i	$0.180042\pi$
$728$	1.68070	+	5.17267i	0.0622909	+	0.191712i
$729$	−6.93084	−	5.03555i	−0.256698	−	0.186502i
$730$	12.6528	−	9.19282i	0.468303	−	0.340242i
$731$	−1.75446	+	5.39968i	−0.0648912	+	0.199715i
$732$	−1.99373	+	6.13606i	−0.0736903	+	0.226795i
$733$	18.9313	−	13.7544i	0.699243	−	0.508030i	−0.180442	−	0.983586i	$-0.557753\pi$
$733$	18.9313	−	13.7544i	0.699243	−	0.508030i	0.879686	+	0.475556i	$0.157753\pi$
$734$	−15.6905	−	11.3998i	−0.579146	−	0.420774i
$735$	−0.973083	−	2.99484i	−0.0358927	−	0.110466i
$736$	2.65626			0.0979111
$737$	4.00037	−	0.968813i	0.147355	−	0.0356867i
$738$	−17.4483			−0.642282
$739$	12.6969	+	39.0770i	0.467062	+	1.43747i	0.856370	+	0.516362i	$0.172714\pi$
$739$	12.6969	+	39.0770i	0.467062	+	1.43747i	−0.389308	+	0.921108i	$0.627286\pi$
$740$	3.69499	+	2.68457i	0.135831	+	0.0986867i
$741$	−81.9706	+	59.5551i	−3.01127	+	2.18781i
$742$	1.90167	−	5.85272i	0.0698123	−	0.214860i
$743$	4.95392	−	15.2466i	0.181742	−	0.559343i	−0.818135	−	0.575026i	$-0.804992\pi$
$743$	4.95392	−	15.2466i	0.181742	−	0.559343i	0.999877	+	0.0156824i	$0.00499208\pi$
$744$	24.6847	−	17.9345i	0.904985	−	0.657510i
$745$	−5.52597	−	4.01485i	−0.202456	−	0.147093i
$746$	−3.36875	−	10.3680i	−0.123339	−	0.379598i
$747$	12.0246			0.439958
$748$	0.829447	+	1.34752i	0.0303276	+	0.0492701i
$749$	6.17232			0.225532
$750$	0.973083	+	2.99484i	0.0355319	+	0.109356i
$751$	−4.47426	−	3.25074i	−0.163268	−	0.118621i	0.503151	−	0.864198i	$-0.332174\pi$
$751$	−4.47426	−	3.25074i	−0.163268	−	0.118621i	−0.666419	+	0.745577i	$0.732174\pi$
$752$	−7.62605	+	5.54065i	−0.278094	+	0.202047i
$753$	8.74950	−	26.9282i	0.318849	−	0.981317i
$754$	11.0376	−	33.9703i	0.401966	−	1.23712i
$755$	8.75270	−	6.35921i	0.318544	−	0.231435i
$756$	−9.97615	−	7.24809i	−0.362829	−	0.263611i
$757$	7.75464	+	23.8663i	0.281847	+	0.867437i	0.987326	+	0.158706i	$0.0507321\pi$
$757$	7.75464	+	23.8663i	0.281847	+	0.867437i	−0.705479	+	0.708731i	$0.749268\pi$
$758$	−6.80767			−0.247266
$759$	25.6511	+	10.5654i	0.931077	+	0.383499i
$760$	5.91596			0.214594
$761$	0.994372	+	3.06036i	0.0360459	+	0.110938i	0.967461	−	0.253022i	$-0.0814245\pi$
$761$	0.994372	+	3.06036i	0.0360459	+	0.110938i	−0.931415	+	0.363960i	$0.881424\pi$
$762$	−41.7329	−	30.3207i	−1.51182	−	1.09840i
$763$	−12.0737	+	8.77209i	−0.437099	+	0.317571i
$764$	2.91150	−	8.96068i	0.105334	−	0.324186i
$765$	−1.01962	+	3.13806i	−0.0368643	+	0.113457i
$766$	−19.6034	+	14.2427i	−0.708298	+	0.514609i
$767$	2.49088	+	1.80973i	0.0899405	+	0.0653456i
$768$	−0.973083	−	2.99484i	−0.0351131	−	0.108067i
$769$	9.89520			0.356830			0.178415	−	0.983955i	$-0.442903\pi$
$769$	9.89520			0.356830			0.178415	+	0.983955i	$0.442903\pi$
$770$	2.14896	−	2.52626i	0.0774432	−	0.0910399i
$771$	56.5163			2.03538
$772$	−1.57574	−	4.84962i	−0.0567120	−	0.174542i
$773$	−14.8461	−	10.7863i	−0.533978	−	0.387958i	0.287865	−	0.957671i	$-0.407054\pi$
$773$	−14.8461	−	10.7863i	−0.533978	−	0.387958i	−0.821844	+	0.569713i	$0.807054\pi$
$774$	66.5840	−	48.3761i	2.39331	−	1.73884i
$775$	−2.99423	+	9.21529i	−0.107556	+	0.331023i
$776$	1.21492	−	3.73914i	0.0436131	−	0.134227i
$777$	11.6354	−	8.45360i	0.417417	−	0.303271i
$778$	−14.7687	−	10.7301i	−0.529485	−	0.384693i
$779$	−4.61221	−	14.1949i	−0.165249	−	0.508585i
$780$	−17.1268			−0.613237
$781$	0.918973	−	11.9809i	0.0328834	−	0.428711i
$782$	−1.26728			−0.0453179
$783$	25.0249	+	77.0186i	0.894316	+	2.75242i
$784$	−0.809017	−	0.587785i	−0.0288935	−	0.0209923i
$785$	−6.48643	+	4.71267i	−0.231511	+	0.168202i
$786$	5.45716	−	16.7954i	0.194651	−	0.599073i
$787$	1.86794	−	5.74893i	0.0665849	−	0.204927i	−0.912228	−	0.409682i	$-0.865640\pi$
$787$	1.86794	−	5.74893i	0.0665849	−	0.204927i	0.978813	+	0.204755i	$0.0656397\pi$
$788$	−13.8572	+	10.0678i	−0.493641	+	0.358651i
$789$	69.6279	+	50.5877i	2.47882	+	1.80097i
$790$	1.04450	+	3.21464i	0.0371616	+	0.114372i
$791$	−19.0906			−0.678784
$792$	1.75424	−	22.8705i	0.0623340	−	0.812666i
$793$	11.1436			0.395720
$794$	−5.46163	−	16.8092i	−0.193826	−	0.596535i
$795$	15.6775	+	11.3904i	0.556023	+	0.403975i
$796$	−9.64554	+	7.00789i	−0.341877	+	0.248388i
$797$	−2.15794	+	6.64145i	−0.0764381	+	0.235252i	−0.981974	−	0.189018i	$-0.939469\pi$
$797$	−2.15794	+	6.64145i	−0.0764381	+	0.235252i	0.905535	+	0.424271i	$0.139469\pi$
$798$	5.75671	−	17.7173i	0.203785	−	0.627187i
$799$	3.63833	−	2.64340i	0.128715	−	0.0935168i
$800$	0.809017	+	0.587785i	0.0286031	+	0.0207813i
$801$	−20.3962	−	62.7729i	−0.720663	−	2.21797i
$802$	−30.4187			−1.07412
$803$	33.6093	−	39.5100i	1.18604	−	1.39428i
$804$	3.90794			0.137822
$805$	0.820830	+	2.52626i	0.0289305	+	0.0890388i
$806$	−42.6352	−	30.9763i	−1.50176	−	1.09109i
$807$	−30.7681	+	22.3543i	−1.08309	+	0.786910i
$808$	0.898602	−	2.76561i	0.0316127	−	0.0972939i
$809$	−3.76070	+	11.5742i	−0.132219	+	0.406929i	−0.995147	−	0.0983983i	$-0.968628\pi$
$809$	−3.76070	+	11.5742i	−0.132219	+	0.406929i	0.862928	+	0.505327i	$0.168628\pi$
$810$	14.6291	−	10.6287i	0.514015	−	0.373454i
$811$	36.4737	+	26.4997i	1.28077	+	0.930531i	0.999576	−	0.0291217i	$-0.00927102\pi$
$811$	36.4737	+	26.4997i	1.28077	+	0.930531i	0.281190	+	0.959652i	$0.409271\pi$
$812$	2.02940	+	6.24584i	0.0712178	+	0.219186i
$813$	−81.3456			−2.85292
$814$	14.0063	+	5.76904i	0.490921	+	0.202205i
$815$	−18.2991			−0.640989
$816$	0.464250	+	1.42881i	0.0162520	+	0.0500185i
$817$	56.9564	+	41.3812i	1.99265	+	1.44775i
$818$	12.4641	−	9.05571i	0.435798	−	0.316626i
$819$	−11.6237	+	35.7739i	−0.406163	+	1.25004i
$820$	0.779621	−	2.39943i	0.0272256	−	0.0837917i
$821$	−3.06999	+	2.23048i	−0.107143	+	0.0778442i	−0.640067	−	0.768319i	$-0.721093\pi$
$821$	−3.06999	+	2.23048i	−0.107143	+	0.0778442i	0.532923	+	0.846163i	$0.321093\pi$
$822$	6.39117	+	4.64346i	0.222918	+	0.161959i
$823$	−12.2207	−	37.6113i	−0.425985	−	1.31105i	−0.902048	−	0.431636i	$-0.857936\pi$
$823$	−12.2207	−	37.6113i	−0.425985	−	1.31105i	0.476063	−	0.879411i	$-0.342064\pi$
$824$	15.9287			0.554901
$825$	5.47461	+	8.89405i	0.190602	+	0.309651i
$826$	−0.566092			−0.0196969
$827$	6.55319	+	20.1686i	0.227877	+	0.701332i	0.997987	+	0.0634213i	$0.0202012\pi$
$827$	6.55319	+	20.1686i	0.227877	+	0.701332i	−0.770110	+	0.637911i	$0.779799\pi$
$828$	14.8621	+	10.7980i	0.516494	+	0.375255i
$829$	13.4570	−	9.77711i	0.467382	−	0.339573i	−0.329038	−	0.944317i	$-0.606724\pi$
$829$	13.4570	−	9.77711i	0.467382	−	0.339573i	0.796420	+	0.604744i	$0.206724\pi$
$830$	−0.537282	+	1.65358i	−0.0186493	+	0.0573967i
$831$	17.7334	−	54.5778i	0.615165	−	1.89328i
$832$	−4.40013	+	3.19688i	−0.152547	+	0.110832i
$833$	0.385976	+	0.280428i	0.0133733	+	0.00971625i
$834$	3.21371	+	9.89079i	0.111282	+	0.342490i
$835$	−17.9260			−0.620356
$836$	19.0697	−	4.61833i	0.659541	−	0.159728i
$837$	119.484			4.12995
$838$	−0.994769	−	3.06159i	−0.0343637	−	0.105761i
$839$	−35.6477	−	25.8996i	−1.23070	−	0.894153i	−0.233754	−	0.972296i	$-0.575101\pi$
$839$	−35.6477	−	25.8996i	−1.23070	−	0.894153i	−0.996942	+	0.0781430i	$0.975101\pi$
$840$	2.54756	−	1.85091i	0.0878993	−	0.0638626i
$841$	4.36608	−	13.4374i	0.150554	−	0.463359i
$842$	−4.06681	+	12.5164i	−0.140152	+	0.431342i
$843$	−10.3419	+	7.51384i	−0.356194	+	0.258790i
$844$	−18.4724	−	13.4209i	−0.635845	−	0.461968i
$845$	5.12389	+	15.7697i	0.176267	+	0.542494i
$846$	−65.1920			−2.24135
$847$	4.95492	−	9.82084i	0.170253	−	0.337448i
$848$	6.15392			0.211326
$849$	3.08052	+	9.48088i	0.105723	+	0.325383i
$850$	−0.385976	−	0.280428i	−0.0132389	−	0.00961859i
$851$	−9.81487	+	7.13092i	−0.336449	+	0.244445i
$852$	3.52547	−	10.8503i	0.120781	−	0.371724i
$853$	2.70418	−	8.32262i	0.0925894	−	0.284961i	−0.894029	−	0.448010i	$-0.852133\pi$
$853$	2.70418	−	8.32262i	0.0925894	−	0.284961i	0.986618	+	0.163049i	$0.0521329\pi$
$854$	−1.65758	+	1.20430i	−0.0567211	+	0.0412103i
$855$	33.1005	+	24.0489i	1.13201	+	0.822456i
$856$	1.90735	+	5.87023i	0.0651919	+	0.200640i
$857$	0.827106			0.0282534			0.0141267	−	0.999900i	$-0.495503\pi$
$857$	0.827106			0.0282534			0.0141267	+	0.999900i	$0.495503\pi$
$858$	−55.2072	+	13.3701i	−1.88474	+	0.456448i
$859$	11.5033			0.392488			0.196244	−	0.980555i	$-0.437125\pi$
$859$	11.5033			0.392488			0.196244	+	0.980555i	$0.437125\pi$
$860$	3.67741	+	11.3179i	0.125399	+	0.385937i
$861$	−6.42727	−	4.66968i	−0.219041	−	0.159142i
$862$	1.92893	−	1.40145i	0.0656997	−	0.0477336i
$863$	4.32399	−	13.3079i	0.147190	−	0.453005i	−0.850096	−	0.526628i	$-0.823456\pi$
$863$	4.32399	−	13.3079i	0.147190	−	0.453005i	0.997286	+	0.0736229i	$0.0234561\pi$
$864$	3.81055	−	11.7277i	0.129637	−	0.398983i
$865$	6.21965	−	4.51884i	0.211474	−	0.153645i
$866$	7.30193	+	5.30516i	0.248130	+	0.180277i
$867$	16.3209	+	50.2306i	0.554287	+	1.70592i
$868$	9.68953			0.328884
$869$	5.87641	+	9.54681i	0.199344	+	0.323853i
$870$	−20.6801			−0.701119
$871$	−2.08579	−	6.41941i	−0.0706743	−	0.217513i
$872$	−12.0737	−	8.77209i	−0.408869	−	0.297061i
$873$	21.9976	−	15.9822i	0.744506	−	0.540915i
$874$	−4.85600	+	14.9452i	−0.164256	+	0.505529i
$875$	−0.309017	+	0.951057i	−0.0104467	+	0.0321516i
$876$	39.8433	−	28.9478i	1.34618	−	0.978057i
$877$	5.56370	+	4.04226i	0.187873	+	0.136497i	0.677746	−	0.735296i	$-0.262957\pi$
$877$	5.56370	+	4.04226i	0.187873	+	0.136497i	−0.489873	+	0.871794i	$0.662957\pi$
$878$	−7.14575	−	21.9924i	−0.241157	−	0.742206i
$879$	−32.2821			−1.08885
$880$	3.06668	+	1.26313i	0.103378	+	0.0425800i
$881$	−40.9746			−1.38047			−0.690235	−	0.723585i	$-0.742493\pi$
$881$	−40.9746			−1.38047			−0.690235	+	0.723585i	$0.742493\pi$
$882$	−2.13715	−	6.57747i	−0.0719615	−	0.221475i
$883$	−18.2919	−	13.2898i	−0.615570	−	0.447238i	0.235801	−	0.971801i	$-0.424229\pi$
$883$	−18.2919	−	13.2898i	−0.615570	−	0.447238i	−0.851371	+	0.524563i	$0.824229\pi$
$884$	2.09927	−	1.52521i	0.0706061	−	0.0512983i
$885$	0.550854	−	1.69536i	0.0185168	−	0.0569887i
$886$	2.09760	−	6.45576i	0.0704704	−	0.216886i
$887$	−2.54522	+	1.84921i	−0.0854601	+	0.0620904i	−0.629695	−	0.776843i	$-0.716820\pi$
$887$	−2.54522	+	1.84921i	−0.0854601	+	0.0620904i	0.544235	+	0.838933i	$0.316820\pi$
$888$	11.6354	+	8.45360i	0.390458	+	0.283684i
$889$	−5.06216	−	15.5797i	−0.169780	−	0.522528i
$890$	9.54364			0.319903
$891$	38.8588	−	45.6812i	1.30182	−	1.53038i
$892$	−15.8782			−0.531640
$893$	−17.2325	−	53.0363i	−0.576665	−	1.77479i
$894$	−17.4011	−	12.6426i	−0.581979	−	0.422832i
$895$	−18.3806	+	13.3543i	−0.614397	+	0.446386i
$896$	0.309017	−	0.951057i	0.0103235	−	0.0317726i
$897$	14.0582	−	43.2666i	0.469389	−	1.44463i
$898$	10.6074	−	7.70671i	0.353973	−	0.257176i
$899$	−51.4808	−	37.4030i	−1.71698	−	1.24746i
$900$	2.13715	+	6.57747i	0.0712383	+	0.219249i
$901$	−2.93599			−0.0978119
$902$	0.639937	−	8.34303i	0.0213076	−	0.277793i
$903$	37.4737			1.24705
$904$	−5.89932	−	18.1562i	−0.196208	−	0.603868i
$905$	11.0485	+	8.02720i	0.367264	+	0.266833i
$906$	27.5619	−	20.0249i	0.915684	−	0.665283i
$907$	2.03318	−	6.25748i	0.0675105	−	0.207776i	−0.911610	−	0.411056i	$-0.865160\pi$
$907$	2.03318	−	6.25748i	0.0675105	−	0.207776i	0.979121	+	0.203280i	$0.0651601\pi$
$908$	−2.60140	+	8.00628i	−0.0863304	+	0.265698i
$909$	16.2703	−	11.8210i	0.539651	−	0.392079i
$910$	−4.40013	−	3.19688i	−0.145863	−	0.105976i
$911$	−3.09156	−	9.51484i	−0.102428	−	0.315241i	0.886690	−	0.462364i	$-0.152999\pi$
$911$	−3.09156	−	9.51484i	−0.102428	−	0.315241i	−0.989118	+	0.147123i	$0.952999\pi$
$912$	18.6291			0.616872
$913$	−0.441017	+	5.74966i	−0.0145955	+	0.190286i
$914$	19.0200			0.629125
$915$	−1.99373	−	6.13606i	−0.0659106	−	0.202852i
$916$	−18.0284	−	13.0984i	−0.595676	−	0.432784i
$917$	4.53707	−	3.29637i	0.149827	−	0.108856i
$918$	−1.81798	+	5.59518i	−0.0600024	+	0.184668i
$919$	1.63144	−	5.02105i	0.0538161	−	0.165629i	−0.920536	−	0.390658i	$-0.872248\pi$
$919$	1.63144	−	5.02105i	0.0538161	−	0.165629i	0.974352	+	0.225029i	$0.0722476\pi$
$920$	−2.14896	+	1.56131i	−0.0708492	+	0.0514749i
$921$	−8.63552	−	6.27407i	−0.284550	−	0.206738i
$922$	−5.83323	−	17.9528i	−0.192107	−	0.591245i
$923$	−19.7050			−0.648596
$924$	6.76700	−	7.95508i	0.222618	−	0.261703i
$925$	−4.56726			−0.150171
$926$	−4.20861	−	12.9528i	−0.138304	−	0.425655i
$927$	89.1229	+	64.7516i	2.92718	+	2.12672i
$928$	−5.31303	+	3.86014i	−0.174409	+	0.126715i
$929$	−6.11006	+	18.8048i	−0.200465	+	0.616967i	0.799405	+	0.600793i	$0.205148\pi$
$929$	−6.11006	+	18.8048i	−0.200465	+	0.616967i	−0.999869	+	0.0161735i	$0.994852\pi$
$930$	−9.42872	+	29.0186i	−0.309180	+	0.951558i
$931$	4.78611	−	3.47731i	0.156858	−	0.113964i
$932$	10.0327	+	7.28916i	0.328631	+	0.238765i
$933$	28.6595	+	88.2048i	0.938270	+	2.88770i
$934$	18.9801			0.621049
$935$	−1.46309	−	0.602628i	−0.0478481	−	0.0197081i
$936$	−37.6149			−1.22948
$937$	−14.2156	−	43.7510i	−0.464403	−	1.42928i	−0.859732	−	0.510745i	$-0.829370\pi$
$937$	−14.2156	−	43.7510i	−0.464403	−	1.42928i	0.395330	−	0.918539i	$-0.370630\pi$
$938$	1.00401	+	0.729456i	0.0327821	+	0.0238176i
$939$	−56.2106	+	40.8394i	−1.83436	+	1.33274i
$940$	2.91289	−	8.96496i	0.0950081	−	0.292405i
$941$	−11.5284	+	35.4807i	−0.375815	+	1.15664i	0.567113	+	0.823640i	$0.308060\pi$
$941$	−11.5284	+	35.4807i	−0.375815	+	1.15664i	−0.942927	+	0.332998i	$0.891940\pi$
$942$	−20.4255	+	14.8400i	−0.665499	+	0.483513i
$943$	5.42163	+	3.93905i	0.176553	+	0.128273i
$944$	−0.174932	−	0.538386i	−0.00569355	−	0.0175230i
$945$	12.3312			0.401134
$946$	20.6893	+	33.6118i	0.672667	+	1.09281i
$947$	49.7593			1.61696			0.808479	−	0.588524i	$-0.200291\pi$
$947$	49.7593			1.61696			0.808479	+	0.588524i	$0.200291\pi$
$948$	3.28909	+	10.1228i	0.106825	+	0.328773i
$949$	−68.8171	−	49.9985i	−2.23390	−	1.62302i
$950$	−4.78611	+	3.47731i	−0.155282	+	0.112819i
$951$	−20.5475	+	63.2386i	−0.666297	+	2.05065i
$952$	−0.147430	+	0.453742i	−0.00477822	+	0.0147059i
$953$	−16.6602	+	12.1043i	−0.539676	+	0.392097i	−0.823965	−	0.566641i	$-0.808243\pi$
$953$	−16.6602	+	12.1043i	−0.539676	+	0.392097i	0.284289	+	0.958739i	$0.408243\pi$
$954$	34.4319	+	25.0163i	1.11478	+	0.809932i
$955$	2.91150	+	8.96068i	0.0942140	+	0.289961i
$956$	19.3571			0.626055
$957$	−66.6609	+	16.1440i	−2.15484	+	0.521862i
$958$	5.51532			0.178192
$959$	0.775243	+	2.38595i	0.0250339	+	0.0770464i
$960$	2.54756	+	1.85091i	0.0822222	+	0.0597380i
$961$	−50.8767	+	36.9641i	−1.64118	+	1.19239i
$962$	7.67620	−	23.6249i	0.247491	−	0.761698i
$963$	−13.1912	+	40.5982i	−0.425079	+	1.30826i
$964$	4.14576	−	3.01207i	0.133526	−	0.0970124i
$965$	4.12533	+	2.99723i	0.132799	+	0.0964843i
$966$	2.58476	+	7.95508i	0.0831634	+	0.255950i
$967$	−36.0618			−1.15967			−0.579834	−	0.814735i	$-0.696883\pi$
$967$	−36.0618			−1.15967			−0.579834	+	0.814735i	$0.696883\pi$
$968$	10.8713	+	1.67760i	0.349418	+	0.0539201i
$969$	−8.88781			−0.285517
$970$	1.21492	+	3.73914i	0.0390087	+	0.120057i
$971$	−3.47214	−	2.52265i	−0.111426	−	0.0809558i	0.530677	−	0.847574i	$-0.321938\pi$
$971$	−3.47214	−	2.52265i	−0.111426	−	0.0809558i	−0.642103	+	0.766618i	$0.721938\pi$
$972$	16.1381	−	11.7250i	0.517629	−	0.376080i
$973$	−1.02056	+	3.14097i	−0.0327178	+	0.100695i
$974$	−8.65514	+	26.6378i	−0.277329	+	0.853529i
$975$	13.8558	−	10.0669i	0.443742	−	0.322398i
$976$	−1.65758	−	1.20430i	−0.0530578	−	0.0385487i
$977$	11.2098	+	34.5002i	0.358634	+	1.10376i	0.953873	+	0.300212i	$0.0970574\pi$
$977$	11.2098	+	34.5002i	0.358634	+	1.10376i	−0.595239	+	0.803549i	$0.702943\pi$
$978$	−57.6231			−1.84258
$979$	30.7634	−	7.45029i	0.983201	−	0.238112i
$980$	1.00000			0.0319438
$981$	−31.8947	−	98.1619i	−1.01832	−	3.13407i
$982$	−10.4804	−	7.61444i	−0.334442	−	0.242986i
$983$	−15.3348	+	11.1414i	−0.489105	+	0.355356i	−0.804840	−	0.593492i	$-0.797749\pi$
$983$	−15.3348	+	11.1414i	−0.489105	+	0.355356i	0.315735	+	0.948847i	$0.397749\pi$
$984$	2.45500	−	7.55571i	0.0782625	−	0.240867i
$985$	5.29297	−	16.2901i	0.168648	−	0.519045i
$986$	2.53480	−	1.84164i	0.0807246	−	0.0586498i
$987$	−24.0141	−	17.4473i	−0.764379	−	0.555354i
$988$	−9.94296	−	30.6013i	−0.316328	−	0.973556i
$989$	−31.6104			−1.00515
$990$	12.0237	+	19.5337i	0.382139	+	0.620822i
$991$	−7.43374			−0.236141			−0.118070	−	0.993005i	$-0.537671\pi$
$991$	−7.43374			−0.236141			−0.118070	+	0.993005i	$0.537671\pi$
$992$	2.99423	+	9.21529i	0.0950669	+	0.292586i
$993$	−79.3335	−	57.6391i	−2.51757	−	1.82912i
$994$	2.93106	−	2.12954i	0.0929676	−	0.0675449i
$995$	3.68427	−	11.3390i	0.116799	−	0.359471i
$996$	−1.69188	+	5.20707i	−0.0536092	+	0.164992i
$997$	−17.7225	+	12.8761i	−0.561277	+	0.407792i	−0.831926	−	0.554886i	$-0.812762\pi$
$997$	−17.7225	+	12.8761i	−0.561277	+	0.407792i	0.270649	+	0.962678i	$0.412762\pi$
$998$	3.18741	+	2.31579i	0.100896	+	0.0733049i
$999$	17.4038	+	53.5633i	0.550631	+	1.69467i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.n.f.71.2	✓	8
11.3	even	5		8470.2.a.co.1.1		4
11.8	odd	10		8470.2.a.cs.1.1		4
11.9	even	5	inner	770.2.n.f.141.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.n.f.71.2	✓	8	1.1	even	1	trivial
770.2.n.f.141.2	yes	8	11.9	even	5	inner
8470.2.a.co.1.1		4	11.3	even	5
8470.2.a.cs.1.1		4	11.8	odd	10

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:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 - 0.951057i) q^{2} +(2.54756 + 1.85091i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.309017 - 0.951057i) q^{5} +(0.973083 - 2.99484i) q^{6} +(0.809017 - 0.587785i) q^{7} +(0.809017 + 0.587785i) q^{8} +(2.13715 + 6.57747i) q^{9} +O(q^{10})\)	\(q+(-0.309017 - 0.951057i) q^{2} +(2.54756 + 1.85091i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.309017 - 0.951057i) q^{5} +(0.973083 - 2.99484i) q^{6} +(0.809017 - 0.587785i) q^{7} +(0.809017 + 0.587785i) q^{8} +(2.13715 + 6.57747i) q^{9} -1.00000 q^{10} +(-3.22344 + 0.780656i) q^{11} -3.14896 q^{12} +(1.68070 + 5.17267i) q^{13} +(-0.809017 - 0.587785i) q^{14} +(2.54756 - 1.85091i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-0.147430 + 0.453742i) q^{17} +(5.59513 - 4.06510i) q^{18} +(4.78611 + 3.47731i) q^{19} +(0.309017 + 0.951057i) q^{20} +3.14896 q^{21} +(1.73855 + 2.82444i) q^{22} -2.65626 q^{23} +(0.973083 + 2.99484i) q^{24} +(-0.809017 - 0.587785i) q^{25} +(4.40013 - 3.19688i) q^{26} +(-3.81055 + 11.7277i) q^{27} +(-0.309017 + 0.951057i) q^{28} +(5.31303 - 3.86014i) q^{29} +(-2.54756 - 1.85091i) q^{30} +(-2.99423 - 9.21529i) q^{31} -1.00000 q^{32} +(-9.65685 - 3.97754i) q^{33} +0.477092 q^{34} +(-0.309017 - 0.951057i) q^{35} +(-5.59513 - 4.06510i) q^{36} +(3.69499 - 2.68457i) q^{37} +(1.82813 - 5.62641i) q^{38} +(-5.29246 + 16.2885i) q^{39} +(0.809017 - 0.587785i) q^{40} +(-2.04108 - 1.48293i) q^{41} +(-0.973083 - 2.99484i) q^{42} +11.9003 q^{43} +(2.14896 - 2.52626i) q^{44} +6.91596 q^{45} +(0.820830 + 2.52626i) q^{46} +(-7.62605 - 5.54065i) q^{47} +(2.54756 - 1.85091i) q^{48} +(0.309017 - 0.951057i) q^{49} +(-0.309017 + 0.951057i) q^{50} +(-1.21542 + 0.883056i) q^{51} +(-4.40013 - 3.19688i) q^{52} +(1.90167 + 5.85272i) q^{53} +12.3312 q^{54} +(-0.253650 + 3.30691i) q^{55} +1.00000 q^{56} +(5.75671 + 17.7173i) q^{57} +(-5.31303 - 3.86014i) q^{58} +(0.457978 - 0.332741i) q^{59} +(-0.973083 + 2.99484i) q^{60} +(0.633138 - 1.94860i) q^{61} +(-7.83900 + 5.69537i) q^{62} +(5.59513 + 4.06510i) q^{63} +(0.309017 + 0.951057i) q^{64} +5.43886 q^{65} +(-0.798735 + 10.4133i) q^{66} -1.24102 q^{67} +(-0.147430 - 0.453742i) q^{68} +(-6.76700 - 4.91651i) q^{69} +(-0.809017 + 0.587785i) q^{70} +(-1.11957 + 3.44567i) q^{71} +(-2.13715 + 6.57747i) q^{72} +(-12.6528 + 9.19282i) q^{73} +(-3.69499 - 2.68457i) q^{74} +(-0.973083 - 2.99484i) q^{75} -5.91596 q^{76} +(-2.14896 + 2.52626i) q^{77} +17.1268 q^{78} +(-1.04450 - 3.21464i) q^{79} +(-0.809017 - 0.587785i) q^{80} +(-14.6291 + 10.6287i) q^{81} +(-0.779621 + 2.39943i) q^{82} +(0.537282 - 1.65358i) q^{83} +(-2.54756 + 1.85091i) q^{84} +(0.385976 + 0.280428i) q^{85} +(-3.67741 - 11.3179i) q^{86} +20.6801 q^{87} +(-3.06668 - 1.26313i) q^{88} -9.54364 q^{89} +(-2.13715 - 6.57747i) q^{90} +(4.40013 + 3.19688i) q^{91} +(2.14896 - 1.56131i) q^{92} +(9.42872 - 29.0186i) q^{93} +(-2.91289 + 8.96496i) q^{94} +(4.78611 - 3.47731i) q^{95} +(-2.54756 - 1.85091i) q^{96} +(-1.21492 - 3.73914i) q^{97} -1.00000 q^{98} +(-12.0237 - 19.5337i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} + 2 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 8 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 + 2 * q^7 + 2 * q^8 + 2 * q^9	\( 8 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} + 2 q^{7} + 2 q^{8} + 2 q^{9} - 8 q^{10} - 8 q^{12} - 2 q^{13} - 2 q^{14} + 2 q^{15} - 2 q^{16} - 6 q^{17} + 8 q^{18} + 6 q^{19} - 2 q^{20} + 8 q^{21} - 2 q^{24} - 2 q^{25} + 12 q^{26} - 4 q^{27} + 2 q^{28} + 20 q^{29} - 2 q^{30} - 6 q^{31} - 8 q^{32} - 8 q^{33} - 24 q^{34} + 2 q^{35} - 8 q^{36} + 16 q^{37} + 4 q^{38} + 20 q^{39} + 2 q^{40} - 12 q^{41} + 2 q^{42} + 20 q^{43} + 12 q^{45} - 16 q^{47} + 2 q^{48} - 2 q^{49} + 2 q^{50} - 20 q^{51} - 12 q^{52} - 30 q^{53} + 44 q^{54} + 8 q^{56} - 20 q^{58} - 18 q^{59} + 2 q^{60} + 8 q^{61} - 24 q^{62} + 8 q^{63} - 2 q^{64} + 28 q^{65} + 18 q^{66} - 6 q^{68} - 28 q^{69} - 2 q^{70} + 22 q^{71} - 2 q^{72} - 50 q^{73} - 16 q^{74} + 2 q^{75} - 4 q^{76} + 60 q^{78} - 34 q^{79} - 2 q^{80} - 28 q^{81} + 12 q^{82} - 34 q^{83} - 2 q^{84} - 6 q^{85} + 4 q^{87} - 8 q^{89} - 2 q^{90} + 12 q^{91} + 56 q^{93} - 24 q^{94} + 6 q^{95} - 2 q^{96} - 8 q^{98} - 24 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 + 2 * q^7 + 2 * q^8 + 2 * q^9 - 8 * q^10 - 8 * q^12 - 2 * q^13 - 2 * q^14 + 2 * q^15 - 2 * q^16 - 6 * q^17 + 8 * q^18 + 6 * q^19 - 2 * q^20 + 8 * q^21 - 2 * q^24 - 2 * q^25 + 12 * q^26 - 4 * q^27 + 2 * q^28 + 20 * q^29 - 2 * q^30 - 6 * q^31 - 8 * q^32 - 8 * q^33 - 24 * q^34 + 2 * q^35 - 8 * q^36 + 16 * q^37 + 4 * q^38 + 20 * q^39 + 2 * q^40 - 12 * q^41 + 2 * q^42 + 20 * q^43 + 12 * q^45 - 16 * q^47 + 2 * q^48 - 2 * q^49 + 2 * q^50 - 20 * q^51 - 12 * q^52 - 30 * q^53 + 44 * q^54 + 8 * q^56 - 20 * q^58 - 18 * q^59 + 2 * q^60 + 8 * q^61 - 24 * q^62 + 8 * q^63 - 2 * q^64 + 28 * q^65 + 18 * q^66 - 6 * q^68 - 28 * q^69 - 2 * q^70 + 22 * q^71 - 2 * q^72 - 50 * q^73 - 16 * q^74 + 2 * q^75 - 4 * q^76 + 60 * q^78 - 34 * q^79 - 2 * q^80 - 28 * q^81 + 12 * q^82 - 34 * q^83 - 2 * q^84 - 6 * q^85 + 4 * q^87 - 8 * q^89 - 2 * q^90 + 12 * q^91 + 56 * q^93 - 24 * q^94 + 6 * q^95 - 2 * q^96 - 8 * q^98 - 24 * q^99

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