LMFDB - Embedded newform 574.2.e.d.165.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [574,2,Mod(165,574)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(574, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("574.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 574 = 2 \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	574.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.58341307602$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-11})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 2x^{2} - 3x + 9 $ x^4 - x^3 - 2x^2 - 3x + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			165.2
Root			$-1.18614 + 1.26217i$ of defining polynomial
Character	$\chi$	$=$	574.165
Dual form			574.2.e.d.247.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(1.18614 - 2.05446i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.18614 - 2.05446i) q^{5} +2.37228 q^{6} +(-2.50000 - 0.866025i) q^{7} -1.00000 q^{8} +(-1.31386 - 2.27567i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(1.18614 - 2.05446i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.18614 - 2.05446i) q^{5} +2.37228 q^{6} +(-2.50000 - 0.866025i) q^{7} -1.00000 q^{8} +(-1.31386 - 2.27567i) q^{9} +(1.18614 - 2.05446i) q^{10} +(2.18614 - 3.78651i) q^{11} +(1.18614 + 2.05446i) q^{12} -5.37228 q^{13} +(-0.500000 - 2.59808i) q^{14} -5.62772 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.37228 + 5.84096i) q^{17} +(1.31386 - 2.27567i) q^{18} +(-0.186141 - 0.322405i) q^{19} +2.37228 q^{20} +(-4.74456 + 4.10891i) q^{21} +4.37228 q^{22} +(-1.37228 - 2.37686i) q^{23} +(-1.18614 + 2.05446i) q^{24} +(-0.313859 + 0.543620i) q^{25} +(-2.68614 - 4.65253i) q^{26} +0.883156 q^{27} +(2.00000 - 1.73205i) q^{28} +10.1168 q^{29} +(-2.81386 - 4.87375i) q^{30} +(4.37228 - 7.57301i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-5.18614 - 8.98266i) q^{33} -6.74456 q^{34} +(1.18614 + 6.16337i) q^{35} +2.62772 q^{36} +(1.00000 + 1.73205i) q^{37} +(0.186141 - 0.322405i) q^{38} +(-6.37228 + 11.0371i) q^{39} +(1.18614 + 2.05446i) q^{40} -1.00000 q^{41} +(-5.93070 - 2.05446i) q^{42} -0.627719 q^{43} +(2.18614 + 3.78651i) q^{44} +(-3.11684 + 5.39853i) q^{45} +(1.37228 - 2.37686i) q^{46} +(-4.00000 - 6.92820i) q^{47} -2.37228 q^{48} +(5.50000 + 4.33013i) q^{49} -0.627719 q^{50} +(8.00000 + 13.8564i) q^{51} +(2.68614 - 4.65253i) q^{52} +(5.00000 - 8.66025i) q^{53} +(0.441578 + 0.764836i) q^{54} -10.3723 q^{55} +(2.50000 + 0.866025i) q^{56} -0.883156 q^{57} +(5.05842 + 8.76144i) q^{58} +(-2.68614 + 4.65253i) q^{59} +(2.81386 - 4.87375i) q^{60} +(-4.18614 - 7.25061i) q^{61} +8.74456 q^{62} +(1.31386 + 6.82701i) q^{63} +1.00000 q^{64} +(6.37228 + 11.0371i) q^{65} +(5.18614 - 8.98266i) q^{66} +(4.00000 - 6.92820i) q^{67} +(-3.37228 - 5.84096i) q^{68} -6.51087 q^{69} +(-4.74456 + 4.10891i) q^{70} -0.255437 q^{71} +(1.31386 + 2.27567i) q^{72} +(2.05842 - 3.56529i) q^{73} +(-1.00000 + 1.73205i) q^{74} +(0.744563 + 1.28962i) q^{75} +0.372281 q^{76} +(-8.74456 + 7.57301i) q^{77} -12.7446 q^{78} +(5.18614 + 8.98266i) q^{79} +(-1.18614 + 2.05446i) q^{80} +(4.98913 - 8.64142i) q^{81} +(-0.500000 - 0.866025i) q^{82} +5.37228 q^{83} +(-1.18614 - 6.16337i) q^{84} +16.0000 q^{85} +(-0.313859 - 0.543620i) q^{86} +(12.0000 - 20.7846i) q^{87} +(-2.18614 + 3.78651i) q^{88} +(1.00000 + 1.73205i) q^{89} -6.23369 q^{90} +(13.4307 + 4.65253i) q^{91} +2.74456 q^{92} +(-10.3723 - 17.9653i) q^{93} +(4.00000 - 6.92820i) q^{94} +(-0.441578 + 0.764836i) q^{95} +(-1.18614 - 2.05446i) q^{96} +8.00000 q^{97} +(-1.00000 + 6.92820i) q^{98} -11.4891 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - q^{3} - 2 q^{4} + q^{5} - 2 q^{6} - 10 q^{7} - 4 q^{8} - 11 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 - q^3 - 2 * q^4 + q^5 - 2 * q^6 - 10 * q^7 - 4 * q^8 - 11 * q^9	\( 4 q + 2 q^{2} - q^{3} - 2 q^{4} + q^{5} - 2 q^{6} - 10 q^{7} - 4 q^{8} - 11 q^{9} - q^{10} + 3 q^{11} - q^{12} - 10 q^{13} - 2 q^{14} - 34 q^{15} - 2 q^{16} - 2 q^{17} + 11 q^{18} + 5 q^{19} - 2 q^{20} + 4 q^{21} + 6 q^{22} + 6 q^{23} + q^{24} - 7 q^{25} - 5 q^{26} + 38 q^{27} + 8 q^{28} + 6 q^{29} - 17 q^{30} + 6 q^{31} + 2 q^{32} - 15 q^{33} - 4 q^{34} - q^{35} + 22 q^{36} + 4 q^{37} - 5 q^{38} - 14 q^{39} - q^{40} - 4 q^{41} + 5 q^{42} - 14 q^{43} + 3 q^{44} + 22 q^{45} - 6 q^{46} - 16 q^{47} + 2 q^{48} + 22 q^{49} - 14 q^{50} + 32 q^{51} + 5 q^{52} + 20 q^{53} + 19 q^{54} - 30 q^{55} + 10 q^{56} - 38 q^{57} + 3 q^{58} - 5 q^{59} + 17 q^{60} - 11 q^{61} + 12 q^{62} + 11 q^{63} + 4 q^{64} + 14 q^{65} + 15 q^{66} + 16 q^{67} - 2 q^{68} - 72 q^{69} + 4 q^{70} - 24 q^{71} + 11 q^{72} - 9 q^{73} - 4 q^{74} - 20 q^{75} - 10 q^{76} - 12 q^{77} - 28 q^{78} + 15 q^{79} + q^{80} - 26 q^{81} - 2 q^{82} + 10 q^{83} + q^{84} + 64 q^{85} - 7 q^{86} + 48 q^{87} - 3 q^{88} + 4 q^{89} + 44 q^{90} + 25 q^{91} - 12 q^{92} - 30 q^{93} + 16 q^{94} - 19 q^{95} + q^{96} + 32 q^{97} - 4 q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 - q^3 - 2 * q^4 + q^5 - 2 * q^6 - 10 * q^7 - 4 * q^8 - 11 * q^9 - q^10 + 3 * q^11 - q^12 - 10 * q^13 - 2 * q^14 - 34 * q^15 - 2 * q^16 - 2 * q^17 + 11 * q^18 + 5 * q^19 - 2 * q^20 + 4 * q^21 + 6 * q^22 + 6 * q^23 + q^24 - 7 * q^25 - 5 * q^26 + 38 * q^27 + 8 * q^28 + 6 * q^29 - 17 * q^30 + 6 * q^31 + 2 * q^32 - 15 * q^33 - 4 * q^34 - q^35 + 22 * q^36 + 4 * q^37 - 5 * q^38 - 14 * q^39 - q^40 - 4 * q^41 + 5 * q^42 - 14 * q^43 + 3 * q^44 + 22 * q^45 - 6 * q^46 - 16 * q^47 + 2 * q^48 + 22 * q^49 - 14 * q^50 + 32 * q^51 + 5 * q^52 + 20 * q^53 + 19 * q^54 - 30 * q^55 + 10 * q^56 - 38 * q^57 + 3 * q^58 - 5 * q^59 + 17 * q^60 - 11 * q^61 + 12 * q^62 + 11 * q^63 + 4 * q^64 + 14 * q^65 + 15 * q^66 + 16 * q^67 - 2 * q^68 - 72 * q^69 + 4 * q^70 - 24 * q^71 + 11 * q^72 - 9 * q^73 - 4 * q^74 - 20 * q^75 - 10 * q^76 - 12 * q^77 - 28 * q^78 + 15 * q^79 + q^80 - 26 * q^81 - 2 * q^82 + 10 * q^83 + q^84 + 64 * q^85 - 7 * q^86 + 48 * q^87 - 3 * q^88 + 4 * q^89 + 44 * q^90 + 25 * q^91 - 12 * q^92 - 30 * q^93 + 16 * q^94 - 19 * q^95 + q^96 + 32 * q^97 - 4 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/574\mathbb{Z}\right)^\times$.

$n$	$211$	$493$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	1.18614	−	2.05446i	0.684819	−	1.18614i	−0.288675	−	0.957427i	$-0.593215\pi$
$3$	1.18614	−	2.05446i	0.684819	−	1.18614i	0.973494	−	0.228714i	$-0.0734519\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−1.18614	−	2.05446i	−0.530458	−	0.918781i	−0.999368	−	0.0355348i	$-0.988687\pi$
$5$	−1.18614	−	2.05446i	−0.530458	−	0.918781i	0.468910	−	0.883246i	$-0.344647\pi$
$6$	2.37228			0.968480
$7$	−2.50000	−	0.866025i	−0.944911	−	0.327327i
$7$	−2.50000	−	0.866025i	−0.944911	−	0.327327i
$8$	−1.00000			−0.353553
$9$	−1.31386	−	2.27567i	−0.437953	−	0.758557i
$10$	1.18614	−	2.05446i	0.375091	−	0.649676i
$11$	2.18614	−	3.78651i	0.659146	−	1.14167i	−0.321691	−	0.946845i	$-0.604251\pi$
$11$	2.18614	−	3.78651i	0.659146	−	1.14167i	0.980837	−	0.194830i	$-0.0624155\pi$
$12$	1.18614	+	2.05446i	0.342409	+	0.593070i
$13$	−5.37228			−1.49000			−0.745001	−	0.667063i	$-0.767551\pi$
$13$	−5.37228			−1.49000			−0.745001	+	0.667063i	$0.767551\pi$
$14$	−0.500000	−	2.59808i	−0.133631	−	0.694365i
$15$	−5.62772			−1.45307
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−3.37228	+	5.84096i	−0.817898	+	1.41664i	0.0893296	+	0.996002i	$0.471528\pi$
$17$	−3.37228	+	5.84096i	−0.817898	+	1.41664i	−0.907228	+	0.420639i	$0.861806\pi$
$18$	1.31386	−	2.27567i	0.309680	−	0.536381i
$19$	−0.186141	−	0.322405i	−0.0427036	−	0.0739648i	0.843884	−	0.536526i	$-0.180264\pi$
$19$	−0.186141	−	0.322405i	−0.0427036	−	0.0739648i	−0.886587	+	0.462561i	$0.846930\pi$
$20$	2.37228			0.530458
$21$	−4.74456	+	4.10891i	−1.03535	+	0.896638i
$22$	4.37228			0.932174
$23$	−1.37228	−	2.37686i	−0.286140	−	0.495610i	0.686745	−	0.726899i	$-0.259039\pi$
$23$	−1.37228	−	2.37686i	−0.286140	−	0.495610i	−0.972885	+	0.231289i	$0.925706\pi$
$24$	−1.18614	+	2.05446i	−0.242120	+	0.419364i
$25$	−0.313859	+	0.543620i	−0.0627719	+	0.108724i
$26$	−2.68614	−	4.65253i	−0.526796	−	0.912437i
$27$	0.883156			0.169963
$28$	2.00000	−	1.73205i	0.377964	−	0.327327i
$29$	10.1168			1.87865			0.939325	−	0.343027i	$-0.111452\pi$
$29$	10.1168			1.87865			0.939325	+	0.343027i	$0.111452\pi$
$30$	−2.81386	−	4.87375i	−0.513738	−	0.889820i
$31$	4.37228	−	7.57301i	0.785285	−	1.36015i	−0.143544	−	0.989644i	$-0.545850\pi$
$31$	4.37228	−	7.57301i	0.785285	−	1.36015i	0.928829	−	0.370509i	$-0.120817\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−5.18614	−	8.98266i	−0.902791	−	1.56368i
$34$	−6.74456			−1.15668
$35$	1.18614	+	6.16337i	0.200494	+	1.04180i
$36$	2.62772			0.437953
$37$	1.00000	+	1.73205i	0.164399	+	0.284747i	0.936442	−	0.350823i	$-0.114098\pi$
$37$	1.00000	+	1.73205i	0.164399	+	0.284747i	−0.772043	+	0.635571i	$0.780765\pi$
$38$	0.186141	−	0.322405i	0.0301960	−	0.0523010i
$39$	−6.37228	+	11.0371i	−1.02038	+	1.76735i
$40$	1.18614	+	2.05446i	0.187545	+	0.324838i
$41$	−1.00000			−0.156174
$41$	−1.00000			−0.156174
$42$	−5.93070	−	2.05446i	−0.915127	−	0.317009i
$43$	−0.627719			−0.0957262			−0.0478631	−	0.998854i	$-0.515241\pi$
$43$	−0.627719			−0.0957262			−0.0478631	+	0.998854i	$0.515241\pi$
$44$	2.18614	+	3.78651i	0.329573	+	0.570837i
$45$	−3.11684	+	5.39853i	−0.464632	+	0.804766i
$46$	1.37228	−	2.37686i	0.202332	−	0.350449i
$47$	−4.00000	−	6.92820i	−0.583460	−	1.01058i	−0.995066	−	0.0992202i	$-0.968365\pi$
$47$	−4.00000	−	6.92820i	−0.583460	−	1.01058i	0.411606	−	0.911362i	$-0.364968\pi$
$48$	−2.37228			−0.342409
$49$	5.50000	+	4.33013i	0.785714	+	0.618590i
$50$	−0.627719			−0.0887728
$51$	8.00000	+	13.8564i	1.12022	+	1.94029i
$52$	2.68614	−	4.65253i	0.372501	−	0.645190i
$53$	5.00000	−	8.66025i	0.686803	−	1.18958i	−0.286064	−	0.958211i	$-0.592347\pi$
$53$	5.00000	−	8.66025i	0.686803	−	1.18958i	0.972867	−	0.231367i	$-0.0743197\pi$
$54$	0.441578	+	0.764836i	0.0600912	+	0.104081i
$55$	−10.3723			−1.39860
$56$	2.50000	+	0.866025i	0.334077	+	0.115728i
$57$	−0.883156			−0.116977
$58$	5.05842	+	8.76144i	0.664203	+	1.15043i
$59$	−2.68614	+	4.65253i	−0.349706	+	0.605708i	−0.986197	−	0.165576i	$-0.947052\pi$
$59$	−2.68614	+	4.65253i	−0.349706	+	0.605708i	0.636491	+	0.771284i	$0.280385\pi$
$60$	2.81386	−	4.87375i	0.363268	−	0.629198i
$61$	−4.18614	−	7.25061i	−0.535980	−	0.928345i	−0.999115	−	0.0420574i	$-0.986609\pi$
$61$	−4.18614	−	7.25061i	−0.535980	−	0.928345i	0.463135	−	0.886288i	$-0.346725\pi$
$62$	8.74456			1.11056
$63$	1.31386	+	6.82701i	0.165531	+	0.860123i
$64$	1.00000			0.125000
$65$	6.37228	+	11.0371i	0.790384	+	1.36899i
$66$	5.18614	−	8.98266i	0.638370	−	1.10569i
$67$	4.00000	−	6.92820i	0.488678	−	0.846415i	−0.511237	−	0.859440i	$-0.670813\pi$
$67$	4.00000	−	6.92820i	0.488678	−	0.846415i	0.999915	+	0.0130248i	$0.00414604\pi$
$68$	−3.37228	−	5.84096i	−0.408949	−	0.708321i
$69$	−6.51087			−0.783817
$70$	−4.74456	+	4.10891i	−0.567084	+	0.491109i
$71$	−0.255437			−0.0303148			−0.0151574	−	0.999885i	$-0.504825\pi$
$71$	−0.255437			−0.0303148			−0.0151574	+	0.999885i	$0.504825\pi$
$72$	1.31386	+	2.27567i	0.154840	+	0.268190i
$73$	2.05842	−	3.56529i	0.240920	−	0.417286i	−0.720057	−	0.693915i	$-0.755884\pi$
$73$	2.05842	−	3.56529i	0.240920	−	0.417286i	0.960977	+	0.276630i	$0.0892175\pi$
$74$	−1.00000	+	1.73205i	−0.116248	+	0.201347i
$75$	0.744563	+	1.28962i	0.0859747	+	0.148913i
$76$	0.372281			0.0427036
$77$	−8.74456	+	7.57301i	−0.996535	+	0.863025i
$78$	−12.7446			−1.44304
$79$	5.18614	+	8.98266i	0.583486	+	1.01063i	0.995062	+	0.0992526i	$0.0316452\pi$
$79$	5.18614	+	8.98266i	0.583486	+	1.01063i	−0.411576	+	0.911376i	$0.635021\pi$
$80$	−1.18614	+	2.05446i	−0.132615	+	0.229695i
$81$	4.98913	−	8.64142i	0.554347	−	0.960158i
$82$	−0.500000	−	0.866025i	−0.0552158	−	0.0956365i
$83$	5.37228			0.589684			0.294842	−	0.955546i	$-0.404733\pi$
$83$	5.37228			0.589684			0.294842	+	0.955546i	$0.404733\pi$
$84$	−1.18614	−	6.16337i	−0.129419	−	0.672479i
$85$	16.0000			1.73544
$86$	−0.313859	−	0.543620i	−0.0338443	−	0.0586201i
$87$	12.0000	−	20.7846i	1.28654	−	2.22834i
$88$	−2.18614	+	3.78651i	−0.233043	+	0.403643i
$89$	1.00000	+	1.73205i	0.106000	+	0.183597i	0.914146	−	0.405385i	$-0.132862\pi$
$89$	1.00000	+	1.73205i	0.106000	+	0.183597i	−0.808146	+	0.588982i	$0.799529\pi$
$90$	−6.23369			−0.657088
$91$	13.4307	+	4.65253i	1.40792	+	0.487718i
$92$	2.74456			0.286140
$93$	−10.3723	−	17.9653i	−1.07556	−	1.86292i
$94$	4.00000	−	6.92820i	0.412568	−	0.714590i
$95$	−0.441578	+	0.764836i	−0.0453049	+	0.0784705i
$96$	−1.18614	−	2.05446i	−0.121060	−	0.209682i
$97$	8.00000			0.812277			0.406138	−	0.913812i	$-0.366875\pi$
$97$	8.00000			0.812277			0.406138	+	0.913812i	$0.366875\pi$
$98$	−1.00000	+	6.92820i	−0.101015	+	0.699854i
$99$	−11.4891			−1.15470
$100$	−0.313859	−	0.543620i	−0.0313859	−	0.0543620i
$101$	−7.37228	+	12.7692i	−0.733569	+	1.27058i	0.221779	+	0.975097i	$0.428814\pi$
$101$	−7.37228	+	12.7692i	−0.733569	+	1.27058i	−0.955348	+	0.295482i	$0.904520\pi$
$102$	−8.00000	+	13.8564i	−0.792118	+	1.37199i
$103$	−0.372281	−	0.644810i	−0.0366820	−	0.0635350i	0.847102	−	0.531431i	$-0.178346\pi$
$103$	−0.372281	−	0.644810i	−0.0366820	−	0.0635350i	−0.883784	+	0.467896i	$0.845012\pi$
$104$	5.37228			0.526796
$105$	14.0693	+	4.87375i	1.37302	+	0.475629i
$106$	10.0000			0.971286
$107$	8.05842	+	13.9576i	0.779037	+	1.34933i	0.932497	+	0.361177i	$0.117625\pi$
$107$	8.05842	+	13.9576i	0.779037	+	1.34933i	−0.153460	+	0.988155i	$0.549042\pi$
$108$	−0.441578	+	0.764836i	−0.0424909	+	0.0735963i
$109$	−5.68614	+	9.84868i	−0.544633	+	0.943333i	0.453996	+	0.891004i	$0.349998\pi$
$109$	−5.68614	+	9.84868i	−0.544633	+	0.943333i	−0.998630	+	0.0523294i	$0.983335\pi$
$110$	−5.18614	−	8.98266i	−0.494479	−	0.856463i
$111$	4.74456			0.450334
$112$	0.500000	+	2.59808i	0.0472456	+	0.245495i
$113$	−16.4891			−1.55117			−0.775583	−	0.631245i	$-0.782544\pi$
$113$	−16.4891			−1.55117			−0.775583	+	0.631245i	$0.782544\pi$
$114$	−0.441578	−	0.764836i	−0.0413576	−	0.0716334i
$115$	−3.25544	+	5.63858i	−0.303571	+	0.525801i
$116$	−5.05842	+	8.76144i	−0.469663	+	0.813480i
$117$	7.05842	+	12.2255i	0.652551	+	1.13025i
$118$	−5.37228			−0.494559
$119$	13.4891	−	11.6819i	1.23655	−	1.07088i
$120$	5.62772			0.513738
$121$	−4.05842	−	7.02939i	−0.368947	−	0.639036i
$122$	4.18614	−	7.25061i	0.378995	−	0.656439i
$123$	−1.18614	+	2.05446i	−0.106951	+	0.185244i
$124$	4.37228	+	7.57301i	0.392642	+	0.680077i
$125$	−10.3723			−0.927725
$126$	−5.25544	+	4.55134i	−0.468192	+	0.405466i
$127$	−6.00000			−0.532414			−0.266207	−	0.963916i	$-0.585770\pi$
$127$	−6.00000			−0.532414			−0.266207	+	0.963916i	$0.585770\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−0.744563	+	1.28962i	−0.0655551	+	0.113545i
$130$	−6.37228	+	11.0371i	−0.558886	+	0.968019i
$131$	6.00000	+	10.3923i	0.524222	+	0.907980i	0.999602	+	0.0281993i	$0.00897729\pi$
$131$	6.00000	+	10.3923i	0.524222	+	0.907980i	−0.475380	+	0.879781i	$0.657689\pi$
$132$	10.3723			0.902791
$133$	0.186141	+	0.967215i	0.0161404	+	0.0838682i
$134$	8.00000			0.691095
$135$	−1.04755	−	1.81441i	−0.0901585	−	0.156159i
$136$	3.37228	−	5.84096i	0.289171	−	0.500858i
$137$	4.37228	−	7.57301i	0.373549	−	0.647006i	−0.616560	−	0.787308i	$-0.711474\pi$
$137$	4.37228	−	7.57301i	0.373549	−	0.647006i	0.990109	+	0.140302i	$0.0448074\pi$
$138$	−3.25544	−	5.63858i	−0.277121	−	0.479988i
$139$	16.7446			1.42026			0.710128	−	0.704073i	$-0.248637\pi$
$139$	16.7446			1.42026			0.710128	+	0.704073i	$0.248637\pi$
$140$	−5.93070	−	2.05446i	−0.501236	−	0.173633i
$141$	−18.9783			−1.59826
$142$	−0.127719	−	0.221215i	−0.0107179	−	0.0185640i
$143$	−11.7446	+	20.3422i	−0.982130	+	1.70110i
$144$	−1.31386	+	2.27567i	−0.109488	+	0.189639i
$145$	−12.0000	−	20.7846i	−0.996546	−	1.72607i
$146$	4.11684			0.340712
$147$	15.4198	−	6.16337i	1.27181	−	0.508346i
$148$	−2.00000			−0.164399
$149$	−10.0584	−	17.4217i	−0.824018	−	1.42724i	−0.902667	−	0.430339i	$-0.858394\pi$
$149$	−10.0584	−	17.4217i	−0.824018	−	1.42724i	0.0786494	−	0.996902i	$-0.474939\pi$
$150$	−0.744563	+	1.28962i	−0.0607933	+	0.105297i
$151$	9.05842	−	15.6896i	0.737164	−	1.27681i	−0.216603	−	0.976260i	$-0.569498\pi$
$151$	9.05842	−	15.6896i	0.737164	−	1.27681i	0.953767	−	0.300546i	$-0.0971688\pi$
$152$	0.186141	+	0.322405i	0.0150980	+	0.0261505i
$153$	17.7228			1.43280
$154$	−10.9307	−	3.78651i	−0.880821	−	0.305125i
$155$	−20.7446			−1.66624
$156$	−6.37228	−	11.0371i	−0.510191	−	0.883676i
$157$	−6.43070	+	11.1383i	−0.513226	+	0.888934i	0.486656	+	0.873594i	$0.338216\pi$
$157$	−6.43070	+	11.1383i	−0.513226	+	0.888934i	−0.999882	+	0.0153400i	$0.995117\pi$
$158$	−5.18614	+	8.98266i	−0.412587	+	0.714622i
$159$	−11.8614	−	20.5446i	−0.940671	−	1.62929i
$160$	−2.37228			−0.187545
$161$	1.37228	+	7.13058i	0.108151	+	0.561969i
$162$	9.97825			0.783965
$163$	2.05842	+	3.56529i	0.161228	+	0.279255i	0.935309	−	0.353831i	$-0.115121\pi$
$163$	2.05842	+	3.56529i	0.161228	+	0.279255i	−0.774081	+	0.633086i	$0.781788\pi$
$164$	0.500000	−	0.866025i	0.0390434	−	0.0676252i
$165$	−12.3030	+	21.3094i	−0.957786	+	1.65893i
$166$	2.68614	+	4.65253i	0.208485	+	0.361107i
$167$	−19.3723			−1.49907			−0.749536	−	0.661964i	$-0.769723\pi$
$167$	−19.3723			−1.49907			−0.749536	+	0.661964i	$0.769723\pi$
$168$	4.74456	−	4.10891i	0.366051	−	0.317009i
$169$	15.8614			1.22011
$170$	8.00000	+	13.8564i	0.613572	+	1.06274i
$171$	−0.489125	+	0.847190i	−0.0374043	+	0.0647862i
$172$	0.313859	−	0.543620i	0.0239316	−	0.0414507i
$173$	−3.55842	−	6.16337i	−0.270542	−	0.468592i	0.698459	−	0.715650i	$-0.253870\pi$
$173$	−3.55842	−	6.16337i	−0.270542	−	0.468592i	−0.969001	+	0.247058i	$0.920536\pi$
$174$	24.0000			1.81944
$175$	1.25544	−	1.08724i	0.0949021	−	0.0821877i
$176$	−4.37228			−0.329573
$177$	6.37228	+	11.0371i	0.478970	+	0.829600i
$178$	−1.00000	+	1.73205i	−0.0749532	+	0.129823i
$179$	−3.81386	+	6.60580i	−0.285061	+	0.493741i	−0.972624	−	0.232384i	$-0.925347\pi$
$179$	−3.81386	+	6.60580i	−0.285061	+	0.493741i	0.687563	+	0.726125i	$0.258681\pi$
$180$	−3.11684	−	5.39853i	−0.232316	−	0.402383i
$181$	0.510875			0.0379730			0.0189865	−	0.999820i	$-0.493956\pi$
$181$	0.510875			0.0379730			0.0189865	+	0.999820i	$0.493956\pi$
$182$	2.68614	+	13.9576i	0.199110	+	1.03461i
$183$	−19.8614			−1.46820
$184$	1.37228	+	2.37686i	0.101166	+	0.175225i
$185$	2.37228	−	4.10891i	0.174414	−	0.302093i
$186$	10.3723	−	17.9653i	0.760533	−	1.31728i
$187$	14.7446	+	25.5383i	1.07823	+	1.86755i
$188$	8.00000			0.583460
$189$	−2.20789	−	0.764836i	−0.160600	−	0.0556336i
$190$	−0.883156			−0.0640709
$191$	9.68614	+	16.7769i	0.700865	+	1.21393i	0.968163	+	0.250319i	$0.0805356\pi$
$191$	9.68614	+	16.7769i	0.700865	+	1.21393i	−0.267299	+	0.963614i	$0.586131\pi$
$192$	1.18614	−	2.05446i	0.0856023	−	0.148268i
$193$	−6.37228	+	11.0371i	−0.458687	+	0.794469i	−0.998892	−	0.0470645i	$-0.985013\pi$
$193$	−6.37228	+	11.0371i	−0.458687	+	0.794469i	0.540205	+	0.841533i	$0.318347\pi$
$194$	4.00000	+	6.92820i	0.287183	+	0.497416i
$195$	30.2337			2.16508
$196$	−6.50000	+	2.59808i	−0.464286	+	0.185577i
$197$	1.62772			0.115970			0.0579851	−	0.998317i	$-0.481532\pi$
$197$	1.62772			0.115970			0.0579851	+	0.998317i	$0.481532\pi$
$198$	−5.74456	−	9.94987i	−0.408248	−	0.707107i
$199$	1.68614	−	2.92048i	0.119527	−	0.207027i	−0.800053	−	0.599929i	$-0.795195\pi$
$199$	1.68614	−	2.92048i	0.119527	−	0.207027i	0.919580	+	0.392902i	$0.128529\pi$
$200$	0.313859	−	0.543620i	0.0221932	−	0.0384398i
$201$	−9.48913	−	16.4356i	−0.669311	−	1.15928i
$202$	−14.7446			−1.03742
$203$	−25.2921	−	8.76144i	−1.77516	−	0.614933i
$204$	−16.0000			−1.12022
$205$	1.18614	+	2.05446i	0.0828437	+	0.143489i
$206$	0.372281	−	0.644810i	0.0259381	−	0.0449261i
$207$	−3.60597	+	6.24572i	−0.250632	+	0.434108i
$208$	2.68614	+	4.65253i	0.186250	+	0.322595i
$209$	−1.62772			−0.112592
$210$	2.81386	+	14.6212i	0.194175	+	1.00896i
$211$	9.11684			0.627629			0.313815	−	0.949484i	$-0.398393\pi$
$211$	9.11684			0.627629			0.313815	+	0.949484i	$0.398393\pi$
$212$	5.00000	+	8.66025i	0.343401	+	0.594789i
$213$	−0.302985	+	0.524785i	−0.0207602	+	0.0359577i
$214$	−8.05842	+	13.9576i	−0.550862	+	0.954122i
$215$	0.744563	+	1.28962i	0.0507788	+	0.0879514i
$216$	−0.883156			−0.0600912
$217$	−17.4891	+	15.1460i	−1.18724	+	1.02818i
$218$	−11.3723			−0.770228
$219$	−4.88316	−	8.45787i	−0.329973	−	0.571530i
$220$	5.18614	−	8.98266i	0.349650	−	0.605611i
$221$	18.1168	−	31.3793i	1.21867	−	2.11080i
$222$	2.37228	+	4.10891i	0.159217	+	0.275772i
$223$	14.7446			0.987369			0.493684	−	0.869641i	$-0.335650\pi$
$223$	14.7446			0.987369			0.493684	+	0.869641i	$0.335650\pi$
$224$	−2.00000	+	1.73205i	−0.133631	+	0.115728i
$225$	1.64947			0.109965
$226$	−8.24456	−	14.2800i	−0.548420	−	0.949892i
$227$	−2.81386	+	4.87375i	−0.186762	+	0.323482i	−0.944169	−	0.329462i	$-0.893133\pi$
$227$	−2.81386	+	4.87375i	−0.186762	+	0.323482i	0.757407	+	0.652944i	$0.226466\pi$
$228$	0.441578	−	0.764836i	0.0292442	−	0.0506525i
$229$	5.68614	+	9.84868i	0.375751	+	0.650819i	0.990439	−	0.137951i	$-0.0440515\pi$
$229$	5.68614	+	9.84868i	0.375751	+	0.650819i	−0.614688	+	0.788770i	$0.710718\pi$
$230$	−6.51087			−0.429314
$231$	5.18614	+	26.9480i	0.341223	+	1.77305i
$232$	−10.1168			−0.664203
$233$	0.255437	+	0.442430i	0.0167343	+	0.0289846i	0.874271	−	0.485438i	$-0.161340\pi$
$233$	0.255437	+	0.442430i	0.0167343	+	0.0289846i	−0.857537	+	0.514422i	$0.828006\pi$
$234$	−7.05842	+	12.2255i	−0.461423	+	0.799209i
$235$	−9.48913	+	16.4356i	−0.619002	+	1.07214i
$236$	−2.68614	−	4.65253i	−0.174853	−	0.302854i
$237$	24.6060			1.59833
$238$	16.8614	+	5.84096i	1.09296	+	0.378613i
$239$	−13.6277			−0.881504			−0.440752	−	0.897629i	$-0.645288\pi$
$239$	−13.6277			−0.881504			−0.440752	+	0.897629i	$0.645288\pi$
$240$	2.81386	+	4.87375i	0.181634	+	0.314599i
$241$	12.0584	−	20.8858i	0.776751	−	1.34537i	−0.157054	−	0.987590i	$-0.550200\pi$
$241$	12.0584	−	20.8858i	0.776751	−	1.34537i	0.933805	−	0.357783i	$-0.116467\pi$
$242$	4.05842	−	7.02939i	0.260885	−	0.451867i
$243$	−10.5109	−	18.2054i	−0.674273	−	1.16787i
$244$	8.37228			0.535980
$245$	2.37228	−	16.4356i	0.151559	−	1.05003i
$246$	−2.37228			−0.151251
$247$	1.00000	+	1.73205i	0.0636285	+	0.110208i
$248$	−4.37228	+	7.57301i	−0.277640	+	0.480887i
$249$	6.37228	−	11.0371i	0.403827	−	0.699449i
$250$	−5.18614	−	8.98266i	−0.328000	−	0.568113i
$251$	−14.8614			−0.938044			−0.469022	−	0.883187i	$-0.655393\pi$
$251$	−14.8614			−0.938044			−0.469022	+	0.883187i	$0.655393\pi$
$252$	−6.56930	−	2.27567i	−0.413827	−	0.143354i
$253$	−12.0000			−0.754434
$254$	−3.00000	−	5.19615i	−0.188237	−	0.326036i
$255$	18.9783	−	32.8713i	1.18846	−	2.05848i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$257$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$258$	−1.48913			−0.0927089
$259$	−1.00000	−	5.19615i	−0.0621370	−	0.322873i
$260$	−12.7446			−0.790384
$261$	−13.2921	−	23.0226i	−0.822761	−	1.42506i
$262$	−6.00000	+	10.3923i	−0.370681	+	0.642039i
$263$	9.68614	−	16.7769i	0.597273	−	1.03451i	−0.395949	−	0.918273i	$-0.629584\pi$
$263$	9.68614	−	16.7769i	0.597273	−	1.03451i	0.993222	−	0.116235i	$-0.0370824\pi$
$264$	5.18614	+	8.98266i	0.319185	+	0.552844i
$265$	−23.7228			−1.45728
$266$	−0.744563	+	0.644810i	−0.0456521	+	0.0395358i
$267$	4.74456			0.290363
$268$	4.00000	+	6.92820i	0.244339	+	0.423207i
$269$	11.6753	−	20.2222i	0.711854	−	1.23297i	−0.252307	−	0.967647i	$-0.581189\pi$
$269$	11.6753	−	20.2222i	0.711854	−	1.23297i	0.964161	−	0.265319i	$-0.0854774\pi$
$270$	1.04755	−	1.81441i	0.0637517	−	0.110421i
$271$	8.62772	+	14.9436i	0.524097	+	0.907762i	0.999606	+	0.0280515i	$0.00893025\pi$
$271$	8.62772	+	14.9436i	0.524097	+	0.907762i	−0.475510	+	0.879710i	$0.657736\pi$
$272$	6.74456			0.408949
$273$	25.4891	−	22.0742i	1.54267	−	1.33599i
$274$	8.74456			0.528278
$275$	1.37228	+	2.37686i	0.0827517	+	0.143330i
$276$	3.25544	−	5.63858i	0.195954	−	0.339403i
$277$	11.3030	−	19.5773i	0.679131	−	1.17629i	−0.296113	−	0.955153i	$-0.595690\pi$
$277$	11.3030	−	19.5773i	0.679131	−	1.17629i	0.975243	−	0.221136i	$-0.0709763\pi$
$278$	8.37228	+	14.5012i	0.502136	+	0.869725i
$279$	−22.9783			−1.37567
$280$	−1.18614	−	6.16337i	−0.0708855	−	0.368332i
$281$	−18.7446			−1.11821			−0.559103	−	0.829098i	$-0.688855\pi$
$281$	−18.7446			−1.11821			−0.559103	+	0.829098i	$0.688855\pi$
$282$	−9.48913	−	16.4356i	−0.565069	−	0.978729i
$283$	12.6861	−	21.9730i	0.754113	−	1.30616i	−0.191701	−	0.981453i	$-0.561401\pi$
$283$	12.6861	−	21.9730i	0.754113	−	1.30616i	0.945814	−	0.324708i	$-0.105266\pi$
$284$	0.127719	−	0.221215i	0.00757871	−	0.0131267i
$285$	1.04755	+	1.81441i	0.0620513	+	0.107476i
$286$	−23.4891			−1.38894
$287$	2.50000	+	0.866025i	0.147570	+	0.0511199i
$288$	−2.62772			−0.154840
$289$	−14.2446	−	24.6723i	−0.837915	−	1.45131i
$290$	12.0000	−	20.7846i	0.704664	−	1.22051i
$291$	9.48913	−	16.4356i	0.556262	−	0.963475i
$292$	2.05842	+	3.56529i	0.120460	+	0.208643i
$293$	−7.37228			−0.430693			−0.215347	−	0.976538i	$-0.569088\pi$
$293$	−7.37228			−0.430693			−0.215347	+	0.976538i	$0.569088\pi$
$294$	13.0475	+	10.2723i	0.760948	+	0.599092i
$295$	12.7446			0.742017
$296$	−1.00000	−	1.73205i	−0.0581238	−	0.100673i
$297$	1.93070	−	3.34408i	0.112031	−	0.194043i
$298$	10.0584	−	17.4217i	0.582669	−	1.00921i
$299$	7.37228	+	12.7692i	0.426350	+	0.738460i
$300$	−1.48913			−0.0859747
$301$	1.56930	+	0.543620i	0.0904528	+	0.0313338i
$302$	18.1168			1.04251
$303$	17.4891	+	30.2921i	1.00472	+	1.74023i
$304$	−0.186141	+	0.322405i	−0.0106759	+	0.0184912i
$305$	−9.93070	+	17.2005i	−0.568630	+	0.984897i
$306$	8.86141	+	15.3484i	0.506573	+	0.877410i
$307$	−4.86141			−0.277455			−0.138728	−	0.990331i	$-0.544301\pi$
$307$	−4.86141			−0.277455			−0.138728	+	0.990331i	$0.544301\pi$
$308$	−2.18614	−	11.3595i	−0.124567	−	0.647269i
$309$	−1.76631			−0.100482
$310$	−10.3723	−	17.9653i	−0.589106	−	1.02036i
$311$	−2.31386	+	4.00772i	−0.131207	+	0.227257i	−0.924142	−	0.382049i	$-0.875219\pi$
$311$	−2.31386	+	4.00772i	−0.131207	+	0.227257i	0.792935	+	0.609306i	$0.208552\pi$
$312$	6.37228	−	11.0371i	0.360759	−	0.624854i
$313$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$313$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$314$	−12.8614			−0.725811
$315$	12.4674	−	10.7971i	0.702457	−	0.608346i
$316$	−10.3723			−0.583486
$317$	6.62772	+	11.4795i	0.372250	+	0.644756i	0.989911	−	0.141689i	$-0.0452531\pi$
$317$	6.62772	+	11.4795i	0.372250	+	0.644756i	−0.617662	+	0.786444i	$0.711920\pi$
$318$	11.8614	−	20.5446i	0.665155	−	1.15208i
$319$	22.1168	−	38.3075i	1.23831	−	2.14481i
$320$	−1.18614	−	2.05446i	−0.0663073	−	0.114848i
$321$	38.2337			2.13400
$322$	−5.48913	+	4.75372i	−0.305897	+	0.264915i
$323$	2.51087			0.139709
$324$	4.98913	+	8.64142i	0.277174	+	0.480079i
$325$	1.68614	−	2.92048i	0.0935303	−	0.161999i
$326$	−2.05842	+	3.56529i	−0.114005	+	0.197463i
$327$	13.4891	+	23.3639i	0.745950	+	1.29202i
$328$	1.00000			0.0552158
$329$	4.00000	+	20.7846i	0.220527	+	1.14589i
$330$	−24.6060			−1.35451
$331$	−5.37228	−	9.30506i	−0.295287	−	0.511453i	0.679764	−	0.733431i	$-0.262082\pi$
$331$	−5.37228	−	9.30506i	−0.295287	−	0.511453i	−0.975052	+	0.221978i	$0.928749\pi$
$332$	−2.68614	+	4.65253i	−0.147421	+	0.255341i
$333$	2.62772	−	4.55134i	0.143998	−	0.249412i
$334$	−9.68614	−	16.7769i	−0.530002	−	0.917990i
$335$	−18.9783			−1.03689
$336$	5.93070	+	2.05446i	0.323546	+	0.112080i
$337$	−5.00000			−0.272367			−0.136184	−	0.990684i	$-0.543484\pi$
$337$	−5.00000			−0.272367			−0.136184	+	0.990684i	$0.543484\pi$
$338$	7.93070	+	13.7364i	0.431373	+	0.747161i
$339$	−19.5584	+	33.8762i	−1.06227	+	1.83990i
$340$	−8.00000	+	13.8564i	−0.433861	+	0.751469i
$341$	−19.1168	−	33.1113i	−1.03524	−	1.79308i
$342$	−0.978251			−0.0528977
$343$	−10.0000	−	15.5885i	−0.539949	−	0.841698i
$344$	0.627719			0.0338443
$345$	7.72281	+	13.3763i	0.415782	+	0.720156i
$346$	3.55842	−	6.16337i	0.191302	−	0.331345i
$347$	−12.3030	+	21.3094i	−0.660459	+	1.14395i	0.320036	+	0.947405i	$0.396305\pi$
$347$	−12.3030	+	21.3094i	−0.660459	+	1.14395i	−0.980495	+	0.196543i	$0.937028\pi$
$348$	12.0000	+	20.7846i	0.643268	+	1.11417i
$349$	11.2554			0.602490			0.301245	−	0.953547i	$-0.402598\pi$
$349$	11.2554			0.602490			0.301245	+	0.953547i	$0.402598\pi$
$350$	1.56930	+	0.543620i	0.0838824	+	0.0290577i
$351$	−4.74456			−0.253246
$352$	−2.18614	−	3.78651i	−0.116522	−	0.201821i
$353$	17.5000	−	30.3109i	0.931431	−	1.61329i	0.150553	−	0.988602i	$-0.451894\pi$
$353$	17.5000	−	30.3109i	0.931431	−	1.61329i	0.780878	−	0.624684i	$-0.214772\pi$
$354$	−6.37228	+	11.0371i	−0.338683	+	0.586616i
$355$	0.302985	+	0.524785i	0.0160808	+	0.0278527i
$356$	−2.00000			−0.106000
$357$	−8.00000	−	41.5692i	−0.423405	−	2.20008i
$358$	−7.62772			−0.403137
$359$	−6.25544	−	10.8347i	−0.330149	−	0.571835i	0.652392	−	0.757882i	$-0.273766\pi$
$359$	−6.25544	−	10.8347i	−0.330149	−	0.571835i	−0.982541	+	0.186047i	$0.940432\pi$
$360$	3.11684	−	5.39853i	0.164272	−	0.284528i
$361$	9.43070	−	16.3345i	0.496353	−	0.859708i
$362$	0.255437	+	0.442430i	0.0134255	+	0.0232536i
$363$	−19.2554			−1.01065
$364$	−10.7446	+	9.30506i	−0.563168	+	0.487718i
$365$	−9.76631			−0.511192
$366$	−9.93070	−	17.2005i	−0.519086	−	0.899084i
$367$	5.00000	−	8.66025i	0.260998	−	0.452062i	−0.705509	−	0.708700i	$-0.749282\pi$
$367$	5.00000	−	8.66025i	0.260998	−	0.452062i	0.966507	+	0.256639i	$0.0826151\pi$
$368$	−1.37228	+	2.37686i	−0.0715351	+	0.123902i
$369$	1.31386	+	2.27567i	0.0683968	+	0.118467i
$370$	4.74456			0.246658
$371$	−20.0000	+	17.3205i	−1.03835	+	0.899236i
$372$	20.7446			1.07556
$373$	10.1861	+	17.6429i	0.527418	+	0.913515i	0.999489	+	0.0319549i	$0.0101733\pi$
$373$	10.1861	+	17.6429i	0.527418	+	0.913515i	−0.472071	+	0.881561i	$0.656493\pi$
$374$	−14.7446	+	25.5383i	−0.762423	+	1.32056i
$375$	−12.3030	+	21.3094i	−0.635323	+	1.10041i
$376$	4.00000	+	6.92820i	0.206284	+	0.357295i
$377$	−54.3505			−2.79919
$378$	−0.441578	−	2.29451i	−0.0227123	−	0.118017i
$379$	5.13859			0.263952			0.131976	−	0.991253i	$-0.457868\pi$
$379$	5.13859			0.263952			0.131976	+	0.991253i	$0.457868\pi$
$380$	−0.441578	−	0.764836i	−0.0226525	−	0.0392352i
$381$	−7.11684	+	12.3267i	−0.364607	+	0.631518i
$382$	−9.68614	+	16.7769i	−0.495586	+	0.858380i
$383$	16.7337	+	28.9836i	0.855052	+	1.48099i	0.876597	+	0.481225i	$0.159808\pi$
$383$	16.7337	+	28.9836i	0.855052	+	1.48099i	−0.0215457	+	0.999768i	$0.506859\pi$
$384$	2.37228			0.121060
$385$	25.9307	+	8.98266i	1.32155	+	0.457799i
$386$	−12.7446			−0.648681
$387$	0.824734	+	1.42848i	0.0419236	+	0.0726138i
$388$	−4.00000	+	6.92820i	−0.203069	+	0.351726i
$389$	−7.55842	+	13.0916i	−0.383227	+	0.663769i	−0.991522	−	0.129943i	$-0.958521\pi$
$389$	−7.55842	+	13.0916i	−0.383227	+	0.663769i	0.608294	+	0.793712i	$0.291854\pi$
$390$	15.1168	+	26.1831i	0.765471	+	1.32583i
$391$	18.5109			0.936135
$392$	−5.50000	−	4.33013i	−0.277792	−	0.218704i
$393$	28.4674			1.43599
$394$	0.813859	+	1.40965i	0.0410016	+	0.0710169i
$395$	12.3030	−	21.3094i	0.619030	−	1.07219i
$396$	5.74456	−	9.94987i	0.288675	−	0.500000i
$397$	7.00000	+	12.1244i	0.351320	+	0.608504i	0.986481	−	0.163876i	$-0.0523996\pi$
$397$	7.00000	+	12.1244i	0.351320	+	0.608504i	−0.635161	+	0.772380i	$0.719066\pi$
$398$	3.37228			0.169037
$399$	2.20789	+	0.764836i	0.110533	+	0.0382897i
$400$	0.627719			0.0313859
$401$	1.12772	+	1.95327i	0.0563156	+	0.0975415i	0.892809	−	0.450436i	$-0.148731\pi$
$401$	1.12772	+	1.95327i	0.0563156	+	0.0975415i	−0.836493	+	0.547977i	$0.815398\pi$
$402$	9.48913	−	16.4356i	0.473275	−	0.819736i
$403$	−23.4891	+	40.6844i	−1.17008	+	2.02663i
$404$	−7.37228	−	12.7692i	−0.366785	−	0.635290i
$405$	−23.6712			−1.17623
$406$	−5.05842	−	26.2843i	−0.251045	−	1.30447i
$407$	8.74456			0.433452
$408$	−8.00000	−	13.8564i	−0.396059	−	0.685994i
$409$	2.12772	−	3.68532i	0.105209	−	0.182227i	−0.808615	−	0.588339i	$-0.799782\pi$
$409$	2.12772	−	3.68532i	0.105209	−	0.182227i	0.913824	+	0.406111i	$0.133116\pi$
$410$	−1.18614	+	2.05446i	−0.0585793	+	0.101462i
$411$	−10.3723	−	17.9653i	−0.511627	−	0.886164i
$412$	0.744563			0.0366820
$413$	10.7446	−	9.30506i	0.528705	−	0.457872i
$414$	−7.21194			−0.354447
$415$	−6.37228	−	11.0371i	−0.312803	−	0.541791i
$416$	−2.68614	+	4.65253i	−0.131699	+	0.228109i
$417$	19.8614	−	34.4010i	0.972617	−	1.68462i
$418$	−0.813859	−	1.40965i	−0.0398072	−	0.0689480i
$419$	28.8614			1.40997			0.704986	−	0.709221i	$-0.250953\pi$
$419$	28.8614			1.40997			0.704986	+	0.709221i	$0.250953\pi$
$420$	−11.2554	+	9.74749i	−0.549209	+	0.475629i
$421$	2.00000			0.0974740			0.0487370	−	0.998812i	$-0.484480\pi$
$421$	2.00000			0.0974740			0.0487370	+	0.998812i	$0.484480\pi$
$422$	4.55842	+	7.89542i	0.221901	+	0.384343i
$423$	−10.5109	+	18.2054i	−0.511056	+	0.885175i
$424$	−5.00000	+	8.66025i	−0.242821	+	0.420579i
$425$	−2.11684	−	3.66648i	−0.102682	−	0.177850i
$426$	−0.605969			−0.0293593
$427$	4.18614	+	21.7518i	0.202582	+	1.05264i
$428$	−16.1168			−0.779037
$429$	27.8614	+	48.2574i	1.34516	+	2.32989i
$430$	−0.744563	+	1.28962i	−0.0359060	+	0.0621910i
$431$	−6.74456	+	11.6819i	−0.324874	+	0.562699i	−0.981487	−	0.191529i	$-0.938655\pi$
$431$	−6.74456	+	11.6819i	−0.324874	+	0.562699i	0.656613	+	0.754228i	$0.271989\pi$
$432$	−0.441578	−	0.764836i	−0.0212454	−	0.0367982i
$433$	−16.3723			−0.786802			−0.393401	−	0.919367i	$-0.628702\pi$
$433$	−16.3723			−0.786802			−0.393401	+	0.919367i	$0.628702\pi$
$434$	−21.8614	−	7.57301i	−1.04938	−	0.363516i
$435$	−56.9348			−2.72981
$436$	−5.68614	−	9.84868i	−0.272317	−	0.471666i
$437$	−0.510875	+	0.884861i	−0.0244385	+	0.0423286i
$438$	4.88316	−	8.45787i	0.233326	−	0.404133i
$439$	−3.87228	−	6.70699i	−0.184814	−	0.320107i	0.758700	−	0.651440i	$-0.225835\pi$
$439$	−3.87228	−	6.70699i	−0.184814	−	0.320107i	−0.943514	+	0.331333i	$0.892502\pi$
$440$	10.3723			0.494479
$441$	2.62772	−	18.2054i	0.125129	−	0.866922i
$442$	36.2337			1.72346
$443$	9.17527	+	15.8920i	0.435930	+	0.755053i	0.997371	−	0.0724638i	$-0.0230862\pi$
$443$	9.17527	+	15.8920i	0.435930	+	0.755053i	−0.561441	+	0.827517i	$0.689753\pi$
$444$	−2.37228	+	4.10891i	−0.112583	+	0.195000i
$445$	2.37228	−	4.10891i	0.112457	−	0.194781i
$446$	7.37228	+	12.7692i	0.349088	+	0.604638i
$447$	−47.7228			−2.25721
$448$	−2.50000	−	0.866025i	−0.118114	−	0.0409159i
$449$	−11.2337			−0.530151			−0.265075	−	0.964228i	$-0.585397\pi$
$449$	−11.2337			−0.530151			−0.265075	+	0.964228i	$0.585397\pi$
$450$	0.824734	+	1.42848i	0.0388783	+	0.0673393i
$451$	−2.18614	+	3.78651i	−0.102941	+	0.178300i
$452$	8.24456	−	14.2800i	0.387792	−	0.671675i
$453$	−21.4891	−	37.2203i	−1.00965	−	1.74876i
$454$	−5.62772			−0.264122
$455$	−6.37228	−	33.1113i	−0.298737	−	1.55228i
$456$	0.883156			0.0413576
$457$	4.11684	+	7.13058i	0.192578	+	0.333555i	0.946104	−	0.323864i	$-0.104982\pi$
$457$	4.11684	+	7.13058i	0.192578	+	0.333555i	−0.753526	+	0.657418i	$0.771649\pi$
$458$	−5.68614	+	9.84868i	−0.265696	+	0.460199i
$459$	−2.97825	+	5.15848i	−0.139013	+	0.240777i
$460$	−3.25544	−	5.63858i	−0.151786	−	0.262900i
$461$	36.6060			1.70491			0.852455	−	0.522801i	$-0.175113\pi$
$461$	36.6060			1.70491			0.852455	+	0.522801i	$0.175113\pi$
$462$	−20.7446	+	17.9653i	−0.965124	+	0.835822i
$463$	6.25544			0.290715			0.145357	−	0.989379i	$-0.453567\pi$
$463$	6.25544			0.290715			0.145357	+	0.989379i	$0.453567\pi$
$464$	−5.05842	−	8.76144i	−0.234831	−	0.406740i
$465$	−24.6060	+	42.6188i	−1.14107	+	1.97640i
$466$	−0.255437	+	0.442430i	−0.0118329	+	0.0204952i
$467$	16.7446	+	29.0024i	0.774846	+	1.34207i	0.934881	+	0.354961i	$0.115506\pi$
$467$	16.7446	+	29.0024i	0.774846	+	1.34207i	−0.160035	+	0.987111i	$0.551161\pi$
$468$	−14.1168			−0.652551
$469$	−16.0000	+	13.8564i	−0.738811	+	0.639829i
$470$	−18.9783			−0.875401
$471$	15.2554	+	26.4232i	0.702933	+	1.21752i
$472$	2.68614	−	4.65253i	0.123640	−	0.214150i
$473$	−1.37228	+	2.37686i	−0.0630976	+	0.109288i
$474$	12.3030	+	21.3094i	0.565095	+	0.978773i
$475$	0.233688			0.0107223
$476$	3.37228	+	17.5229i	0.154568	+	0.803160i
$477$	−26.2772			−1.20315
$478$	−6.81386	−	11.8020i	−0.311659	−	0.539809i
$479$	−0.755437	+	1.30846i	−0.0345168	+	0.0597849i	−0.882768	−	0.469810i	$-0.844323\pi$
$479$	−0.755437	+	1.30846i	−0.0345168	+	0.0597849i	0.848251	+	0.529594i	$0.177656\pi$
$480$	−2.81386	+	4.87375i	−0.128435	+	0.222455i
$481$	−5.37228	−	9.30506i	−0.244955	−	0.424274i
$482$	24.1168			1.09849
$483$	16.2772	+	5.63858i	0.740638	+	0.256564i
$484$	8.11684			0.368947
$485$	−9.48913	−	16.4356i	−0.430879	−	0.746304i
$486$	10.5109	−	18.2054i	0.476783	−	0.825812i
$487$	12.3723	−	21.4294i	0.560642	−	0.971060i	−0.436799	−	0.899559i	$-0.643888\pi$
$487$	12.3723	−	21.4294i	0.560642	−	0.971060i	0.997441	−	0.0715006i	$-0.0227788\pi$
$488$	4.18614	+	7.25061i	0.189498	+	0.328220i
$489$	9.76631			0.441648
$490$	15.4198	−	6.16337i	0.696597	−	0.278433i
$491$	0.116844			0.00527309			0.00263655	−	0.999997i	$-0.499161\pi$
$491$	0.116844			0.00527309			0.00263655	+	0.999997i	$0.499161\pi$
$492$	−1.18614	−	2.05446i	−0.0534754	−	0.0926220i
$493$	−34.1168	+	59.0921i	−1.53655	+	2.66137i
$494$	−1.00000	+	1.73205i	−0.0449921	+	0.0779287i
$495$	13.6277	+	23.6039i	0.612520	+	1.06092i
$496$	−8.74456			−0.392642
$497$	0.638593	+	0.221215i	0.0286448	+	0.00992286i
$498$	12.7446			0.571098
$499$	−3.37228	−	5.84096i	−0.150964	−	0.261477i	0.780618	−	0.625008i	$-0.214904\pi$
$499$	−3.37228	−	5.84096i	−0.150964	−	0.261477i	−0.931582	+	0.363531i	$0.881571\pi$
$500$	5.18614	−	8.98266i	0.231931	−	0.401717i
$501$	−22.9783	+	39.7995i	−1.02659	+	1.77811i
$502$	−7.43070	−	12.8704i	−0.331649	−	0.574432i
$503$	−29.6277			−1.32103			−0.660517	−	0.750811i	$-0.729663\pi$
$503$	−29.6277			−1.32103			−0.660517	+	0.750811i	$0.729663\pi$
$504$	−1.31386	−	6.82701i	−0.0585239	−	0.304099i
$505$	34.9783			1.55651
$506$	−6.00000	−	10.3923i	−0.266733	−	0.461994i
$507$	18.8139	−	32.5866i	0.835553	−	1.44722i
$508$	3.00000	−	5.19615i	0.133103	−	0.230542i
$509$	−16.5475	−	28.6612i	−0.733457	−	1.27039i	−0.955397	−	0.295325i	$-0.904572\pi$
$509$	−16.5475	−	28.6612i	−0.733457	−	1.27039i	0.221940	−	0.975060i	$-0.428761\pi$
$510$	37.9565			1.68074
$511$	−8.23369	+	7.13058i	−0.364237	+	0.315438i
$512$	−1.00000			−0.0441942
$513$	−0.164391	−	0.284734i	−0.00725805	−	0.0125713i
$514$		0			0
$515$	−0.883156	+	1.52967i	−0.0389165	+	0.0674054i
$516$	−0.744563	−	1.28962i	−0.0327775	−	0.0567724i
$517$	−34.9783			−1.53834
$518$	4.00000	−	3.46410i	0.175750	−	0.152204i
$519$	−16.8832			−0.741088
$520$	−6.37228	−	11.0371i	−0.279443	−	0.484010i
$521$	6.37228	−	11.0371i	0.279175	−	0.483545i	−0.692005	−	0.721893i	$-0.743272\pi$
$521$	6.37228	−	11.0371i	0.279175	−	0.483545i	0.971180	+	0.238348i	$0.0766058\pi$
$522$	13.2921	−	23.0226i	0.581780	−	1.00767i
$523$	−20.2337	−	35.0458i	−0.884757	−	1.53244i	−0.845991	−	0.533196i	$-0.820991\pi$
$523$	−20.2337	−	35.0458i	−0.884757	−	1.53244i	−0.0387659	−	0.999248i	$-0.512343\pi$
$524$	−12.0000			−0.524222
$525$	−0.744563	−	3.86886i	−0.0324954	−	0.168851i
$526$	19.3723			0.844672
$527$	29.4891	+	51.0767i	1.28457	+	2.22493i
$528$	−5.18614	+	8.98266i	−0.225698	+	0.390920i
$529$	7.73369	−	13.3951i	0.336247	−	0.582397i
$530$	−11.8614	−	20.5446i	−0.515227	−	0.892399i
$531$	14.1168			0.612619
$532$	−0.930703	−	0.322405i	−0.0403511	−	0.0139780i
$533$	5.37228			0.232699
$534$	2.37228	+	4.10891i	0.102659	+	0.177810i
$535$	19.1168	−	33.1113i	0.826493	−	1.43153i
$536$	−4.00000	+	6.92820i	−0.172774	+	0.299253i
$537$	9.04755	+	15.6708i	0.390430	+	0.676245i
$538$	23.3505			1.00671
$539$	28.4198	−	11.3595i	1.22413	−	0.489289i
$540$	2.09509			0.0901585
$541$	8.48913	+	14.7036i	0.364976	+	0.632157i	0.988772	−	0.149430i	$-0.0477439\pi$
$541$	8.48913	+	14.7036i	0.364976	+	0.632157i	−0.623796	+	0.781587i	$0.714411\pi$
$542$	−8.62772	+	14.9436i	−0.370592	+	0.641885i
$543$	0.605969	−	1.04957i	0.0260046	−	0.0450413i
$544$	3.37228	+	5.84096i	0.144585	+	0.250429i
$545$	26.9783			1.15562
$546$	31.8614	+	11.0371i	1.36354	+	0.472345i
$547$	−17.4891			−0.747781			−0.373890	−	0.927473i	$-0.621976\pi$
$547$	−17.4891			−0.747781			−0.373890	+	0.927473i	$0.621976\pi$
$548$	4.37228	+	7.57301i	0.186775	+	0.323503i
$549$	−11.0000	+	19.0526i	−0.469469	+	0.813143i
$550$	−1.37228	+	2.37686i	−0.0585143	+	0.101350i
$551$	−1.88316	−	3.26172i	−0.0802251	−	0.138954i
$552$	6.51087			0.277121
$553$	−5.18614	−	26.9480i	−0.220537	−	1.14594i
$554$	22.6060			0.960436
$555$	−5.62772	−	9.74749i	−0.238883	−	0.413758i
$556$	−8.37228	+	14.5012i	−0.355064	+	0.614989i
$557$	−8.17527	+	14.1600i	−0.346397	+	0.599977i	−0.985607	−	0.169055i	$-0.945928\pi$
$557$	−8.17527	+	14.1600i	−0.346397	+	0.599977i	0.639209	+	0.769033i	$0.279262\pi$
$558$	−11.4891	−	19.8997i	−0.486373	−	0.842424i
$559$	3.37228			0.142632
$560$	4.74456	−	4.10891i	0.200494	−	0.173633i
$561$	69.9565			2.95357
$562$	−9.37228	−	16.2333i	−0.395346	−	0.684759i
$563$	5.81386	−	10.0699i	0.245025	−	0.424396i	−0.717114	−	0.696956i	$-0.754537\pi$
$563$	5.81386	−	10.0699i	0.245025	−	0.424396i	0.962139	+	0.272561i	$0.0878705\pi$
$564$	9.48913	−	16.4356i	0.399564	−	0.692066i
$565$	19.5584	+	33.8762i	0.822829	+	1.42518i
$566$	25.3723			1.06648
$567$	−19.9565	+	17.2828i	−0.838094	+	0.725811i
$568$	0.255437			0.0107179
$569$	14.9198	+	25.8419i	0.625472	+	1.08335i	0.988449	+	0.151551i	$0.0484268\pi$
$569$	14.9198	+	25.8419i	0.625472	+	1.08335i	−0.362978	+	0.931798i	$0.618240\pi$
$570$	−1.04755	+	1.81441i	−0.0438769	+	0.0759971i
$571$	7.30298	−	12.6491i	0.305620	−	0.529350i	−0.671779	−	0.740752i	$-0.734469\pi$
$571$	7.30298	−	12.6491i	0.305620	−	0.529350i	0.977399	+	0.211402i	$0.0678028\pi$
$572$	−11.7446	−	20.3422i	−0.491065	−	0.850549i
$573$	45.9565			1.91986
$574$	0.500000	+	2.59808i	0.0208696	+	0.108442i
$575$	1.72281			0.0718463
$576$	−1.31386	−	2.27567i	−0.0547441	−	0.0948196i
$577$	−16.3723	+	28.3576i	−0.681587	+	1.18054i	0.292909	+	0.956140i	$0.405377\pi$
$577$	−16.3723	+	28.3576i	−0.681587	+	1.18054i	−0.974496	+	0.224403i	$0.927957\pi$
$578$	14.2446	−	24.6723i	0.592496	−	1.02623i
$579$	15.1168	+	26.1831i	0.628235	+	1.08813i
$580$	24.0000			0.996546
$581$	−13.4307	−	4.65253i	−0.557199	−	0.193020i
$582$	18.9783			0.786674
$583$	−21.8614	−	37.8651i	−0.905407	−	1.56821i
$584$	−2.05842	+	3.56529i	−0.0851781	+	0.147533i
$585$	16.7446	−	29.0024i	0.692302	−	1.19910i
$586$	−3.68614	−	6.38458i	−0.152273	−	0.263745i
$587$	31.6277			1.30542			0.652708	−	0.757610i	$-0.273633\pi$
$587$	31.6277			1.30542			0.652708	+	0.757610i	$0.273633\pi$
$588$	−2.37228	+	16.4356i	−0.0978312	+	0.677795i
$589$	−3.25544			−0.134138
$590$	6.37228	+	11.0371i	0.262343	+	0.454391i
$591$	1.93070	−	3.34408i	0.0794185	−	0.137557i
$592$	1.00000	−	1.73205i	0.0410997	−	0.0711868i
$593$	4.11684	+	7.13058i	0.169059	+	0.292818i	0.938089	−	0.346394i	$-0.112594\pi$
$593$	4.11684	+	7.13058i	0.169059	+	0.292818i	−0.769031	+	0.639212i	$0.779261\pi$
$594$	3.86141			0.158435
$595$	−40.0000	−	13.8564i	−1.63984	−	0.568057i
$596$	20.1168			0.824018
$597$	−4.00000	−	6.92820i	−0.163709	−	0.283552i
$598$	−7.37228	+	12.7692i	−0.301475	+	0.522170i
$599$	−14.7446	+	25.5383i	−0.602446	+	1.04347i	0.390003	+	0.920814i	$0.372474\pi$
$599$	−14.7446	+	25.5383i	−0.602446	+	1.04347i	−0.992449	+	0.122654i	$0.960859\pi$
$600$	−0.744563	−	1.28962i	−0.0303966	−	0.0526485i
$601$	26.0000			1.06056			0.530281	−	0.847822i	$-0.322086\pi$
$601$	26.0000			1.06056			0.530281	+	0.847822i	$0.322086\pi$
$602$	0.313859	+	1.63086i	0.0127920	+	0.0664689i
$603$	−21.0217			−0.856072
$604$	9.05842	+	15.6896i	0.368582	+	0.638403i
$605$	−9.62772	+	16.6757i	−0.391422	+	0.677964i
$606$	−17.4891	+	30.2921i	−0.710447	+	1.23053i
$607$	−5.74456	−	9.94987i	−0.233165	−	0.403853i	0.725573	−	0.688145i	$-0.241575\pi$
$607$	−5.74456	−	9.94987i	−0.233165	−	0.403853i	−0.958738	+	0.284292i	$0.908241\pi$
$608$	−0.372281			−0.0150980
$609$	−48.0000	+	41.5692i	−1.94506	+	1.68447i
$610$	−19.8614			−0.804165
$611$	21.4891	+	37.2203i	0.869357	+	1.50577i
$612$	−8.86141	+	15.3484i	−0.358201	+	0.620423i
$613$	10.8139	−	18.7302i	0.436768	−	0.756504i	−0.560670	−	0.828039i	$-0.689457\pi$
$613$	10.8139	−	18.7302i	0.436768	−	0.756504i	0.997438	+	0.0715353i	$0.0227899\pi$
$614$	−2.43070	−	4.21010i	−0.0980952	−	0.169906i
$615$	5.62772			0.226932
$616$	8.74456	−	7.57301i	0.352328	−	0.305125i
$617$	42.4891			1.71055			0.855274	−	0.518176i	$-0.173389\pi$
$617$	42.4891			1.71055			0.855274	+	0.518176i	$0.173389\pi$
$618$	−0.883156	−	1.52967i	−0.0355257	−	0.0615324i
$619$	3.19702	−	5.53739i	0.128499	−	0.222567i	−0.794596	−	0.607138i	$-0.792317\pi$
$619$	3.19702	−	5.53739i	0.128499	−	0.222567i	0.923095	+	0.384572i	$0.125651\pi$
$620$	10.3723	−	17.9653i	0.416561	−	0.721505i
$621$	−1.21194	−	2.09914i	−0.0486334	−	0.0842356i
$622$	−4.62772			−0.185555
$623$	−1.00000	−	5.19615i	−0.0400642	−	0.208179i
$624$	12.7446			0.510191
$625$	13.8723	+	24.0275i	0.554891	+	0.961100i
$626$		0			0
$627$	−1.93070	+	3.34408i	−0.0771049	+	0.133550i
$628$	−6.43070	−	11.1383i	−0.256613	−	0.444467i
$629$	−13.4891			−0.537847
$630$	15.5842	+	5.39853i	0.620890	+	0.215083i
$631$	14.0000			0.557331			0.278666	−	0.960388i	$-0.410108\pi$
$631$	14.0000			0.557331			0.278666	+	0.960388i	$0.410108\pi$
$632$	−5.18614	−	8.98266i	−0.206294	−	0.357311i
$633$	10.8139	−	18.7302i	0.429812	−	0.744457i
$634$	−6.62772	+	11.4795i	−0.263220	+	0.455911i
$635$	7.11684	+	12.3267i	0.282423	+	0.489172i
$636$	23.7228			0.940671
$637$	−29.5475	−	23.2627i	−1.17072	−	0.921700i
$638$	44.2337			1.75123
$639$	0.335609	+	0.581291i	0.0132765	+	0.0229955i
$640$	1.18614	−	2.05446i	0.0468863	−	0.0812095i
$641$	−15.2337	+	26.3855i	−0.601694	+	1.04217i	0.390870	+	0.920446i	$0.372174\pi$
$641$	−15.2337	+	26.3855i	−0.601694	+	1.04217i	−0.992565	+	0.121720i	$0.961159\pi$
$642$	19.1168	+	33.1113i	0.754482	+	1.30680i
$643$	−32.0951			−1.26571			−0.632853	−	0.774272i	$-0.718116\pi$
$643$	−32.0951			−1.26571			−0.632853	+	0.774272i	$0.718116\pi$
$644$	−6.86141	−	2.37686i	−0.270377	−	0.0936614i
$645$	3.53262			0.139097
$646$	1.25544	+	2.17448i	0.0493945	+	0.0855538i
$647$	13.1168	−	22.7190i	0.515676	−	0.893178i	−0.484158	−	0.874981i	$-0.660874\pi$
$647$	13.1168	−	22.7190i	0.515676	−	0.893178i	0.999834	−	0.0181971i	$-0.00579263\pi$
$648$	−4.98913	+	8.64142i	−0.195991	+	0.339467i
$649$	11.7446	+	20.3422i	0.461014	+	0.798500i
$650$	3.37228			0.132272
$651$	10.3723	+	53.8960i	0.406522	+	2.11235i
$652$	−4.11684			−0.161228
$653$	12.4307	+	21.5306i	0.486451	+	0.842558i	0.999879	−	0.0155750i	$-0.00495787\pi$
$653$	12.4307	+	21.5306i	0.486451	+	0.842558i	−0.513428	+	0.858133i	$0.671625\pi$
$654$	−13.4891	+	23.3639i	−0.527467	+	0.913599i
$655$	14.2337	−	24.6535i	0.556156	−	0.963291i
$656$	0.500000	+	0.866025i	0.0195217	+	0.0338126i
$657$	−10.8179			−0.422047
$658$	−16.0000	+	13.8564i	−0.623745	+	0.540179i
$659$	−17.4891			−0.681280			−0.340640	−	0.940194i	$-0.610644\pi$
$659$	−17.4891			−0.681280			−0.340640	+	0.940194i	$0.610644\pi$
$660$	−12.3030	−	21.3094i	−0.478893	−	0.829467i
$661$	−11.8139	+	20.4622i	−0.459506	+	0.795888i	−0.998935	−	0.0461436i	$-0.985307\pi$
$661$	−11.8139	+	20.4622i	−0.459506	+	0.795888i	0.539429	+	0.842031i	$0.318640\pi$
$662$	5.37228	−	9.30506i	0.208800	−	0.361652i
$663$	−42.9783	−	74.4405i	−1.66914	−	2.89103i
$664$	−5.37228			−0.208485
$665$	1.76631	−	1.52967i	0.0684946	−	0.0593181i
$666$	5.25544			0.203644
$667$	−13.8832	−	24.0463i	−0.537558	−	0.931078i
$668$	9.68614	−	16.7769i	0.374768	−	0.649117i
$669$	17.4891	−	30.2921i	0.676169	−	1.17116i
$670$	−9.48913	−	16.4356i	−0.366597	−	0.634964i
$671$	−36.6060			−1.41316
$672$	1.18614	+	6.16337i	0.0457564	+	0.237757i
$673$	−31.4891			−1.21382			−0.606908	−	0.794772i	$-0.707590\pi$
$673$	−31.4891			−1.21382			−0.606908	+	0.794772i	$0.707590\pi$
$674$	−2.50000	−	4.33013i	−0.0962964	−	0.166790i
$675$	−0.277187	+	0.480102i	−0.0106689	+	0.0184791i
$676$	−7.93070	+	13.7364i	−0.305027	+	0.528322i
$677$	15.5584	+	26.9480i	0.597959	+	1.03569i	0.993122	+	0.117084i	$0.0373547\pi$
$677$	15.5584	+	26.9480i	0.597959	+	1.03569i	−0.395163	+	0.918611i	$0.629312\pi$
$678$	−39.1168			−1.50227
$679$	−20.0000	−	6.92820i	−0.767530	−	0.265880i
$680$	−16.0000			−0.613572
$681$	6.67527	+	11.5619i	0.255797	+	0.443053i
$682$	19.1168	−	33.1113i	0.732022	−	1.26790i
$683$	4.62772	−	8.01544i	0.177075	−	0.306702i	−0.763803	−	0.645450i	$-0.776670\pi$
$683$	4.62772	−	8.01544i	0.177075	−	0.306702i	0.940877	+	0.338747i	$0.110003\pi$
$684$	−0.489125	−	0.847190i	−0.0187022	−	0.0323931i
$685$	−20.7446			−0.792609
$686$	8.50000	−	16.4545i	0.324532	−	0.628235i
$687$	26.9783			1.02928
$688$	0.313859	+	0.543620i	0.0119658	+	0.0207253i
$689$	−26.8614	+	46.5253i	−1.02334	+	1.77247i
$690$	−7.72281	+	13.3763i	−0.294002	+	0.509227i
$691$	−3.18614	−	5.51856i	−0.121207	−	0.209936i	0.799037	−	0.601282i	$-0.205343\pi$
$691$	−3.18614	−	5.51856i	−0.121207	−	0.209936i	−0.920244	+	0.391346i	$0.872010\pi$
$692$	7.11684			0.270542
$693$	28.7228	+	9.94987i	1.09109	+	0.377964i
$694$	−24.6060			−0.934030
$695$	−19.8614	−	34.4010i	−0.753386	−	1.30490i
$696$	−12.0000	+	20.7846i	−0.454859	+	0.787839i
$697$	3.37228	−	5.84096i	0.127734	−	0.221242i
$698$	5.62772	+	9.74749i	0.213012	+	0.368948i
$699$	1.21194			0.0458397
$700$	0.313859	+	1.63086i	0.0118628	+	0.0616408i
$701$	−13.1168			−0.495416			−0.247708	−	0.968835i	$-0.579677\pi$
$701$	−13.1168			−0.495416			−0.247708	+	0.968835i	$0.579677\pi$
$702$	−2.37228	−	4.10891i	−0.0895360	−	0.155081i
$703$	0.372281	−	0.644810i	0.0140409	−	0.0243195i
$704$	2.18614	−	3.78651i	0.0823933	−	0.142709i
$705$	22.5109	+	38.9900i	0.847809	+	1.46845i
$706$	35.0000			1.31724
$707$	29.4891	−	25.5383i	1.10905	−	0.960468i
$708$	−12.7446			−0.478970
$709$	−18.3139	−	31.7205i	−0.687791	−	1.19129i	−0.972551	−	0.232691i	$-0.925247\pi$
$709$	−18.3139	−	31.7205i	−0.687791	−	1.19129i	0.284759	−	0.958599i	$-0.408086\pi$
$710$	−0.302985	+	0.524785i	−0.0113708	+	0.0196948i
$711$	13.6277	−	23.6039i	0.511079	−	0.885215i
$712$	−1.00000	−	1.73205i	−0.0374766	−	0.0649113i
$713$	−24.0000			−0.898807
$714$	32.0000	−	27.7128i	1.19757	−	1.03713i
$715$	55.7228			2.08392
$716$	−3.81386	−	6.60580i	−0.142531	−	0.246870i
$717$	−16.1644	+	27.9975i	−0.603670	+	1.04559i
$718$	6.25544	−	10.8347i	0.233451	−	0.404349i
$719$	11.6168	+	20.1210i	0.433235	+	0.750385i	0.997150	−	0.0754478i	$-0.0240386\pi$
$719$	11.6168	+	20.1210i	0.433235	+	0.750385i	−0.563915	+	0.825833i	$0.690705\pi$
$720$	6.23369			0.232316
$721$	0.372281	+	1.93443i	0.0138645	+	0.0720420i
$722$	18.8614			0.701949
$723$	−28.6060	−	49.5470i	−1.06387	−	1.84267i
$724$	−0.255437	+	0.442430i	−0.00949325	+	0.0164428i
$725$	−3.17527	+	5.49972i	−0.117926	+	0.204255i
$726$	−9.62772	−	16.6757i	−0.357318	−	0.618893i
$727$	−14.3505			−0.532232			−0.266116	−	0.963941i	$-0.585740\pi$
$727$	−14.3505			−0.532232			−0.266116	+	0.963941i	$0.585740\pi$
$728$	−13.4307	−	4.65253i	−0.497775	−	0.172434i
$729$	−19.9348			−0.738324
$730$	−4.88316	−	8.45787i	−0.180734	−	0.313040i
$731$	2.11684	−	3.66648i	0.0782943	−	0.135610i
$732$	9.93070	−	17.2005i	0.367049	−	0.635748i
$733$	20.3723	+	35.2858i	0.752467	+	1.30331i	0.946624	+	0.322341i	$0.104470\pi$
$733$	20.3723	+	35.2858i	0.752467	+	1.30331i	−0.194156	+	0.980971i	$0.562197\pi$
$734$	10.0000			0.369107
$735$	−30.9525	−	24.3687i	−1.14170	−	0.898854i
$736$	−2.74456			−0.101166
$737$	−17.4891	−	30.2921i	−0.644220	−	1.11582i
$738$	−1.31386	+	2.27567i	−0.0483638	+	0.0837686i
$739$	−8.68614	+	15.0448i	−0.319525	+	0.553433i	−0.980389	−	0.197072i	$-0.936857\pi$
$739$	−8.68614	+	15.0448i	−0.319525	+	0.553433i	0.660864	+	0.750506i	$0.270190\pi$
$740$	2.37228	+	4.10891i	0.0872068	+	0.151047i
$741$	4.74456			0.174296
$742$	−25.0000	−	8.66025i	−0.917779	−	0.317928i
$743$	33.7228			1.23717			0.618585	−	0.785718i	$-0.287706\pi$
$743$	33.7228			1.23717			0.618585	+	0.785718i	$0.287706\pi$
$744$	10.3723	+	17.9653i	0.380266	+	0.658641i
$745$	−23.8614	+	41.3292i	−0.874214	+	1.51418i
$746$	−10.1861	+	17.6429i	−0.372941	+	0.645953i
$747$	−7.05842	−	12.2255i	−0.258254	−	0.447309i
$748$	−29.4891			−1.07823
$749$	−8.05842	−	41.8728i	−0.294448	−	1.53000i
$750$	−24.6060			−0.898483
$751$	25.4783	+	44.1296i	0.929715	+	1.61031i	0.783798	+	0.621016i	$0.213280\pi$
$751$	25.4783	+	44.1296i	0.929715	+	1.61031i	0.145917	+	0.989297i	$0.453387\pi$
$752$	−4.00000	+	6.92820i	−0.145865	+	0.252646i
$753$	−17.6277	+	30.5321i	−0.642390	+	1.11265i
$754$	−27.1753	−	47.0689i	−0.989665	−	1.71415i
$755$	−42.9783			−1.56414
$756$	1.76631	−	1.52967i	0.0642401	−	0.0556336i
$757$	−42.3505			−1.53926			−0.769628	−	0.638492i	$-0.779558\pi$
$757$	−42.3505			−1.53926			−0.769628	+	0.638492i	$0.779558\pi$
$758$	2.56930	+	4.45015i	0.0933211	+	0.161637i
$759$	−14.2337	+	24.6535i	−0.516650	+	0.894864i
$760$	0.441578	−	0.764836i	0.0160177	−	0.0277435i
$761$	1.51087	+	2.61691i	0.0547692	+	0.0948630i	0.892110	−	0.451818i	$-0.149224\pi$
$761$	1.51087	+	2.61691i	0.0547692	+	0.0948630i	−0.837341	+	0.546681i	$0.815891\pi$
$762$	−14.2337			−0.515632
$763$	22.7446	−	19.6974i	0.823408	−	0.713093i
$764$	−19.3723			−0.700865
$765$	−21.0217	−	36.4107i	−0.760043	−	1.31643i
$766$	−16.7337	+	28.9836i	−0.604613	+	1.04722i
$767$	14.4307	−	24.9947i	0.521062	−	0.902507i
$768$	1.18614	+	2.05446i	0.0428012	+	0.0741338i
$769$	−16.3723			−0.590400			−0.295200	−	0.955436i	$-0.595386\pi$
$769$	−16.3723			−0.590400			−0.295200	+	0.955436i	$0.595386\pi$
$770$	5.18614	+	26.9480i	0.186896	+	0.971138i
$771$		0			0
$772$	−6.37228	−	11.0371i	−0.229343	−	0.397234i
$773$	−13.7446	+	23.8063i	−0.494358	+	0.856252i	−0.999979	−	0.00650312i	$-0.997930\pi$
$773$	−13.7446	+	23.8063i	−0.494358	+	0.856252i	0.505621	+	0.862756i	$0.331263\pi$
$774$	−0.824734	+	1.42848i	−0.0296445	+	0.0513457i
$775$	2.74456	+	4.75372i	0.0985876	+	0.170759i
$776$	−8.00000			−0.287183
$777$	−11.8614	−	4.10891i	−0.425526	−	0.147406i
$778$	−15.1168			−0.541965
$779$	0.186141	+	0.322405i	0.00666918	+	0.0115514i
$780$	−15.1168	+	26.1831i	−0.541270	+	0.937507i
$781$	−0.558422	+	0.967215i	−0.0199819	+	0.0346097i
$782$	9.25544	+	16.0309i	0.330974	+	0.573263i
$783$	8.93475			0.319302
$784$	1.00000	−	6.92820i	0.0357143	−	0.247436i
$785$	30.5109			1.08898
$786$	14.2337	+	24.6535i	0.507699	+	0.879360i
$787$	−10.0000	+	17.3205i	−0.356462	+	0.617409i	−0.987367	−	0.158450i	$-0.949350\pi$
$787$	−10.0000	+	17.3205i	−0.356462	+	0.617409i	0.630905	+	0.775860i	$0.282684\pi$
$788$	−0.813859	+	1.40965i	−0.0289925	+	0.0502165i
$789$	−22.9783	−	39.7995i	−0.818047	−	1.41690i
$790$	24.6060			0.875441
$791$	41.2228	+	14.2800i	1.46571	+	0.507738i
$792$	11.4891			0.408248
$793$	22.4891	+	38.9523i	0.798612	+	1.38324i
$794$	−7.00000	+	12.1244i	−0.248421	+	0.430277i
$795$	−28.1386	+	48.7375i	−0.997973	+	1.72854i
$796$	1.68614	+	2.92048i	0.0597637	+	0.103514i
$797$	−52.7446			−1.86831			−0.934154	−	0.356870i	$-0.883844\pi$
$797$	−52.7446			−1.86831			−0.934154	+	0.356870i	$0.883844\pi$
$798$	0.441578	+	2.29451i	0.0156317	+	0.0812247i
$799$	53.9565			1.90884
$800$	0.313859	+	0.543620i	0.0110966	+	0.0192199i
$801$	2.62772	−	4.55134i	0.0928459	−	0.160814i
$802$	−1.12772	+	1.95327i	−0.0398211	+	0.0689722i
$803$	−9.00000	−	15.5885i	−0.317603	−	0.550105i
$804$	18.9783			0.669311
$805$	13.0217	−	11.2772i	0.458956	−	0.397468i
$806$	−46.9783			−1.65474
$807$	−27.6970	−	47.9726i	−0.974981	−	1.68872i
$808$	7.37228	−	12.7692i	0.259356	−	0.449218i
$809$	10.7446	−	18.6101i	0.377759	−	0.654297i	−0.612977	−	0.790101i	$-0.710028\pi$
$809$	10.7446	−	18.6101i	0.377759	−	0.654297i	0.990736	+	0.135803i	$0.0433616\pi$
$810$	−11.8356	−	20.4999i	−0.415861	−	0.720292i
$811$	41.8397			1.46919			0.734595	−	0.678506i	$-0.237372\pi$
$811$	41.8397			1.46919			0.734595	+	0.678506i	$0.237372\pi$
$812$	20.2337	−	17.5229i	0.710063	−	0.614933i
$813$	40.9348			1.43564
$814$	4.37228	+	7.57301i	0.153248	+	0.265434i
$815$	4.88316	−	8.45787i	0.171049	−	0.296266i
$816$	8.00000	−	13.8564i	0.280056	−	0.485071i
$817$	0.116844	+	0.202380i	0.00408785	+	0.00708037i
$818$	4.25544			0.148788
$819$	−7.05842	−	36.6766i	−0.246641	−	1.28159i
$820$	−2.37228			−0.0828437
$821$	1.30298	+	2.25684i	0.0454745	+	0.0787641i	0.887867	−	0.460101i	$-0.152187\pi$
$821$	1.30298	+	2.25684i	0.0454745	+	0.0787641i	−0.842392	+	0.538865i	$0.818853\pi$
$822$	10.3723	−	17.9653i	0.361775	−	0.626612i
$823$	−0.441578	+	0.764836i	−0.0153924	+	0.0266605i	−0.873619	−	0.486611i	$-0.838233\pi$
$823$	−0.441578	+	0.764836i	−0.0153924	+	0.0266605i	0.858227	+	0.513271i	$0.171566\pi$
$824$	0.372281	+	0.644810i	0.0129690	+	0.0224630i
$825$	6.51087			0.226680
$826$	13.4307	+	4.65253i	0.467314	+	0.161882i
$827$	−10.9783			−0.381751			−0.190876	−	0.981614i	$-0.561133\pi$
$827$	−10.9783			−0.381751			−0.190876	+	0.981614i	$0.561133\pi$
$828$	−3.60597	−	6.24572i	−0.125316	−	0.217054i
$829$	19.8614	−	34.4010i	0.689815	−	1.19479i	−0.282082	−	0.959390i	$-0.591025\pi$
$829$	19.8614	−	34.4010i	0.689815	−	1.19479i	0.971897	−	0.235405i	$-0.0756416\pi$
$830$	6.37228	−	11.0371i	0.221185	−	0.383104i
$831$	−26.8139	−	46.4430i	−0.930162	−	1.61109i
$832$	−5.37228			−0.186250
$833$	−43.8397	+	17.5229i	−1.51895	+	0.607132i
$834$	39.7228			1.37549
$835$	22.9783	+	39.7995i	0.795195	+	1.37732i
$836$	0.813859	−	1.40965i	0.0281479	−	0.0487536i
$837$	3.86141	−	6.68815i	0.133470	−	0.231176i
$838$	14.4307	+	24.9947i	0.498500	+	0.863428i
$839$	55.2337			1.90688			0.953439	−	0.301585i	$-0.0975157\pi$
$839$	55.2337			1.90688			0.953439	+	0.301585i	$0.0975157\pi$
$840$	−14.0693	−	4.87375i	−0.485437	−	0.168160i
$841$	73.3505			2.52933
$842$	1.00000	+	1.73205i	0.0344623	+	0.0596904i
$843$	−22.2337	+	38.5099i	−0.765769	+	1.32635i
$844$	−4.55842	+	7.89542i	−0.156907	+	0.271772i
$845$	−18.8139	−	32.5866i	−0.647216	−	1.12101i
$846$	−21.0217			−0.722743
$847$	4.05842	+	21.0882i	0.139449	+	0.724598i
$848$	−10.0000			−0.343401
$849$	−30.0951	−	52.1262i	−1.03286	−	1.78897i
$850$	2.11684	−	3.66648i	0.0726071	−	0.125759i
$851$	2.74456	−	4.75372i	0.0940824	−	0.162955i
$852$	−0.302985	−	0.524785i	−0.0103801	−	0.0179788i
$853$	−22.6060			−0.774014			−0.387007	−	0.922077i	$-0.626491\pi$
$853$	−22.6060			−0.774014			−0.387007	+	0.922077i	$0.626491\pi$
$854$	−16.7446	+	14.5012i	−0.572987	+	0.496221i
$855$	2.32069			0.0793658
$856$	−8.05842	−	13.9576i	−0.275431	−	0.477061i
$857$	−0.383156	+	0.663646i	−0.0130884	+	0.0226697i	−0.872495	−	0.488622i	$-0.837500\pi$
$857$	−0.383156	+	0.663646i	−0.0130884	+	0.0226697i	0.859407	+	0.511292i	$0.170833\pi$
$858$	−27.8614	+	48.2574i	−0.951173	+	1.64748i
$859$	16.1753	+	28.0164i	0.551893	+	0.955907i	0.998138	+	0.0609958i	$0.0194276\pi$
$859$	16.1753	+	28.0164i	0.551893	+	0.955907i	−0.446245	+	0.894911i	$0.647239\pi$
$860$	−1.48913			−0.0507788
$861$	4.74456	−	4.10891i	0.161694	−	0.140031i
$862$	−13.4891			−0.459441
$863$	14.2554	+	24.6911i	0.485261	+	0.840496i	0.999857	−	0.0169366i	$-0.00539135\pi$
$863$	14.2554	+	24.6911i	0.485261	+	0.840496i	−0.514596	+	0.857433i	$0.672058\pi$
$864$	0.441578	−	0.764836i	0.0150228	−	0.0260202i
$865$	−8.44158	+	14.6212i	−0.287022	+	0.497137i
$866$	−8.18614	−	14.1788i	−0.278176	−	0.481816i
$867$	−67.5842			−2.29528
$868$	−4.37228	−	22.7190i	−0.148405	−	0.771134i
$869$	45.3505			1.53841
$870$	−28.4674	−	49.3069i	−0.965134	−	1.67166i
$871$	−21.4891	+	37.2203i	−0.728131	+	1.26116i
$872$	5.68614	−	9.84868i	0.192557	−	0.333519i
$873$	−10.5109	−	18.2054i	−0.355739	−	0.616158i
$874$	−1.02175			−0.0345612
$875$	25.9307	+	8.98266i	0.876618	+	0.303669i
$876$	9.76631			0.329973
$877$	3.55842	+	6.16337i	0.120159	+	0.208122i	0.919830	−	0.392316i	$-0.128326\pi$
$877$	3.55842	+	6.16337i	0.120159	+	0.208122i	−0.799671	+	0.600438i	$0.794993\pi$
$878$	3.87228	−	6.70699i	0.130683	−	0.226350i
$879$	−8.74456	+	15.1460i	−0.294947	+	0.510863i
$880$	5.18614	+	8.98266i	0.174825	+	0.302805i
$881$	−9.97825			−0.336176			−0.168088	−	0.985772i	$-0.553759\pi$
$881$	−9.97825			−0.336176			−0.168088	+	0.985772i	$0.553759\pi$
$882$	17.0802	−	6.82701i	0.575119	−	0.229877i
$883$	−8.23369			−0.277086			−0.138543	−	0.990356i	$-0.544242\pi$
$883$	−8.23369			−0.277086			−0.138543	+	0.990356i	$0.544242\pi$
$884$	18.1168	+	31.3793i	0.609335	+	1.05540i
$885$	15.1168	−	26.1831i	0.508147	−	0.880137i
$886$	−9.17527	+	15.8920i	−0.308249	+	0.533903i
$887$	1.61684	+	2.80046i	0.0542883	+	0.0940301i	0.891892	−	0.452248i	$-0.149378\pi$
$887$	1.61684	+	2.80046i	0.0542883	+	0.0940301i	−0.837604	+	0.546278i	$0.816044\pi$
$888$	−4.74456			−0.159217
$889$	15.0000	+	5.19615i	0.503084	+	0.174273i
$890$	4.74456			0.159038
$891$	−21.8139	−	37.7827i	−0.730792	−	1.26577i
$892$	−7.37228	+	12.7692i	−0.246842	+	0.427543i
$893$	−1.48913	+	2.57924i	−0.0498317	+	0.0863110i
$894$	−23.8614	−	41.3292i	−0.798045	−	1.38225i
$895$	18.0951			0.604852
$896$	−0.500000	−	2.59808i	−0.0167038	−	0.0867956i
$897$	34.9783			1.16789
$898$	−5.61684	−	9.72866i	−0.187437	−	0.324650i
$899$	44.2337	−	76.6150i	1.47528	−	2.55525i
$900$	−0.824734	+	1.42848i	−0.0274911	+	0.0476160i
$901$	33.7228	+	58.4096i	1.12347	+	1.94591i
$902$	−4.37228			−0.145581
$903$	2.97825	−	2.57924i	0.0991100	−	0.0858318i
$904$	16.4891			0.548420
$905$	−0.605969	−	1.04957i	−0.0201431	−	0.0348889i
$906$	21.4891	−	37.2203i	0.713928	−	1.23656i
$907$	11.4307	−	19.7986i	0.379550	−	0.657400i	−0.611447	−	0.791286i	$-0.709412\pi$
$907$	11.4307	−	19.7986i	0.379550	−	0.657400i	0.990997	+	0.133885i	$0.0427454\pi$
$908$	−2.81386	−	4.87375i	−0.0933812	−	0.161741i
$909$	38.7446			1.28508
$910$	25.4891	−	22.0742i	0.844956	−	0.731754i
$911$	−45.2554			−1.49938			−0.749690	−	0.661789i	$-0.769797\pi$
$911$	−45.2554			−1.49938			−0.749690	+	0.661789i	$0.769797\pi$
$912$	0.441578	+	0.764836i	0.0146221	+	0.0253262i
$913$	11.7446	−	20.3422i	0.388688	−	0.673228i
$914$	−4.11684	+	7.13058i	−0.136173	+	0.235859i
$915$	23.5584	+	40.8044i	0.778817	+	1.34895i
$916$	−11.3723			−0.375751
$917$	−6.00000	−	31.1769i	−0.198137	−	1.02955i
$918$	−5.95650			−0.196594
$919$	−16.5000	−	28.5788i	−0.544285	−	0.942729i	−0.998652	−	0.0519142i	$-0.983468\pi$
$919$	−16.5000	−	28.5788i	−0.544285	−	0.942729i	0.454367	−	0.890815i	$-0.349866\pi$
$920$	3.25544	−	5.63858i	0.107329	−	0.185899i
$921$	−5.76631	+	9.98755i	−0.190006	+	0.329101i
$922$	18.3030	+	31.7017i	0.602777	+	1.04404i
$923$	1.37228			0.0451692
$924$	−25.9307	−	8.98266i	−0.853058	−	0.295508i
$925$	−1.25544			−0.0412785
$926$	3.12772	+	5.41737i	0.102783	+	0.178026i
$927$	−0.978251	+	1.69438i	−0.0321300	+	0.0556507i
$928$	5.05842	−	8.76144i	0.166051	−	0.287608i
$929$	−17.0000	−	29.4449i	−0.557752	−	0.966055i	−0.997684	−	0.0680235i	$-0.978331\pi$
$929$	−17.0000	−	29.4449i	−0.557752	−	0.966055i	0.439932	−	0.898031i	$-0.355003\pi$
$930$	−49.2119			−1.61372
$931$	0.372281	−	2.57924i	0.0122010	−	0.0845312i
$932$	−0.510875			−0.0167343
$933$	5.48913	+	9.50744i	0.179706	+	0.311260i
$934$	−16.7446	+	29.0024i	−0.547899	+	0.948989i
$935$	34.9783	−	60.5841i	1.14391	−	1.98131i
$936$	−7.05842	−	12.2255i	−0.230712	−	0.399604i
$937$	28.4674			0.929989			0.464994	−	0.885314i	$-0.346056\pi$
$937$	28.4674			0.929989			0.464994	+	0.885314i	$0.346056\pi$
$938$	−20.0000	−	6.92820i	−0.653023	−	0.226214i
$939$		0			0
$940$	−9.48913	−	16.4356i	−0.309501	−	0.536072i
$941$	−20.3030	+	35.1658i	−0.661858	+	1.14637i	0.318268	+	0.948001i	$0.396899\pi$
$941$	−20.3030	+	35.1658i	−0.661858	+	1.14637i	−0.980127	+	0.198372i	$0.936435\pi$
$942$	−15.2554	+	26.4232i	−0.497049	+	0.860914i
$943$	1.37228	+	2.37686i	0.0446876	+	0.0774012i
$944$	5.37228			0.174853
$945$	1.04755	+	5.44322i	0.0340767	+	0.177068i
$946$	−2.74456			−0.0892334
$947$	−22.5475	−	39.0535i	−0.732697	−	1.26907i	−0.955726	−	0.294256i	$-0.904928\pi$
$947$	−22.5475	−	39.0535i	−0.732697	−	1.26907i	0.223030	−	0.974812i	$-0.428405\pi$
$948$	−12.3030	+	21.3094i	−0.399582	+	0.692097i
$949$	−11.0584	+	19.1537i	−0.358972	+	0.621757i
$950$	0.116844	+	0.202380i	0.00379092	+	0.00656606i
$951$	31.4456			1.01969
$952$	−13.4891	+	11.6819i	−0.437185	+	0.378613i
$953$	−13.1386			−0.425601			−0.212800	−	0.977096i	$-0.568258\pi$
$953$	−13.1386			−0.425601			−0.212800	+	0.977096i	$0.568258\pi$
$954$	−13.1386	−	22.7567i	−0.425378	−	0.736776i
$955$	22.9783	−	39.7995i	0.743559	−	1.28788i
$956$	6.81386	−	11.8020i	0.220376	−	0.381702i
$957$	−52.4674	−	90.8762i	−1.69603	−	2.93761i
$958$	−1.51087			−0.0488141
$959$	−17.4891	+	15.1460i	−0.564753	+	0.489091i
$960$	−5.62772			−0.181634
$961$	−22.7337	−	39.3759i	−0.733345	−	1.27019i
$962$	5.37228	−	9.30506i	0.173209	−	0.300007i
$963$	21.1753	−	36.6766i	0.682363	−	1.18189i
$964$	12.0584	+	20.8858i	0.388376	+	0.672686i
$965$	30.2337			0.973257
$966$	3.25544	+	16.9157i	0.104742	+	0.544255i
$967$	38.4891			1.23773			0.618863	−	0.785499i	$-0.287593\pi$
$967$	38.4891			1.23773			0.618863	+	0.785499i	$0.287593\pi$
$968$	4.05842	+	7.02939i	0.130443	+	0.225933i
$969$	2.97825	−	5.15848i	0.0956752	−	0.165714i
$970$	9.48913	−	16.4356i	0.304677	−	0.527717i
$971$	−6.00000	−	10.3923i	−0.192549	−	0.333505i	0.753545	−	0.657396i	$-0.228342\pi$
$971$	−6.00000	−	10.3923i	−0.192549	−	0.333505i	−0.946094	+	0.323891i	$0.895009\pi$
$972$	21.0217			0.674273
$973$	−41.8614	−	14.5012i	−1.34202	−	0.464888i
$974$	24.7446			0.792867
$975$	−4.00000	−	6.92820i	−0.128103	−	0.221880i
$976$	−4.18614	+	7.25061i	−0.133995	+	0.232086i
$977$	−1.62772	+	2.81929i	−0.0520753	+	0.0901971i	−0.890888	−	0.454223i	$-0.849917\pi$
$977$	−1.62772	+	2.81929i	−0.0520753	+	0.0901971i	0.838813	+	0.544420i	$0.183250\pi$
$978$	4.88316	+	8.45787i	0.156146	+	0.270453i
$979$	8.74456			0.279477
$980$	13.0475	+	10.2723i	0.416789	+	0.328136i
$981$	29.8832			0.954096
$982$	0.0584220	+	0.101190i	0.00186432	+	0.00322910i
$983$	−6.00000	+	10.3923i	−0.191370	+	0.331463i	−0.945705	−	0.325027i	$-0.894626\pi$
$983$	−6.00000	+	10.3923i	−0.191370	+	0.331463i	0.754334	+	0.656490i	$0.227960\pi$
$984$	1.18614	−	2.05446i	0.0378128	−	0.0654937i
$985$	−1.93070	−	3.34408i	−0.0615173	−	0.106551i
$986$	−68.2337			−2.17300
$987$	47.4456	+	16.4356i	1.51021	+	0.523152i
$988$	−2.00000			−0.0636285
$989$	0.861407	+	1.49200i	0.0273911	+	0.0474428i
$990$	−13.6277	+	23.6039i	−0.433117	+	0.750181i
$991$	−10.9891	+	19.0337i	−0.349081	+	0.604626i	−0.986086	−	0.166233i	$-0.946840\pi$
$991$	−10.9891	+	19.0337i	−0.349081	+	0.604626i	0.637005	+	0.770859i	$0.280173\pi$
$992$	−4.37228	−	7.57301i	−0.138820	−	0.240443i
$993$	−25.4891			−0.808873
$994$	0.127719	+	0.663646i	0.00405099	+	0.0210496i
$995$	−8.00000			−0.253617
$996$	6.37228	+	11.0371i	0.201913	+	0.349724i
$997$	10.1753	−	17.6241i	0.322254	−	0.558160i	−0.658699	−	0.752407i	$-0.728893\pi$
$997$	10.1753	−	17.6241i	0.322254	−	0.558160i	0.980953	+	0.194247i	$0.0622262\pi$
$998$	3.37228	−	5.84096i	0.106748	−	0.184892i
$999$	0.883156	+	1.52967i	0.0279418	+	0.0483967i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	574.2.e.d.165.2	✓	4
7.2	even	3	inner	574.2.e.d.247.2	yes	4
7.3	odd	6		4018.2.a.u.1.2		2
7.4	even	3		4018.2.a.v.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
574.2.e.d.165.2	✓	4	1.1	even	1	trivial
574.2.e.d.247.2	yes	4	7.2	even	3	inner
4018.2.a.u.1.2		2	7.3	odd	6
4018.2.a.v.1.1		2	7.4	even	3

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:	\( N \)	\(=\)	\( 574 = 2 \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	574.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(1.18614 - 2.05446i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.18614 - 2.05446i) q^{5} +2.37228 q^{6} +(-2.50000 - 0.866025i) q^{7} -1.00000 q^{8} +(-1.31386 - 2.27567i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(1.18614 - 2.05446i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.18614 - 2.05446i) q^{5} +2.37228 q^{6} +(-2.50000 - 0.866025i) q^{7} -1.00000 q^{8} +(-1.31386 - 2.27567i) q^{9} +(1.18614 - 2.05446i) q^{10} +(2.18614 - 3.78651i) q^{11} +(1.18614 + 2.05446i) q^{12} -5.37228 q^{13} +(-0.500000 - 2.59808i) q^{14} -5.62772 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.37228 + 5.84096i) q^{17} +(1.31386 - 2.27567i) q^{18} +(-0.186141 - 0.322405i) q^{19} +2.37228 q^{20} +(-4.74456 + 4.10891i) q^{21} +4.37228 q^{22} +(-1.37228 - 2.37686i) q^{23} +(-1.18614 + 2.05446i) q^{24} +(-0.313859 + 0.543620i) q^{25} +(-2.68614 - 4.65253i) q^{26} +0.883156 q^{27} +(2.00000 - 1.73205i) q^{28} +10.1168 q^{29} +(-2.81386 - 4.87375i) q^{30} +(4.37228 - 7.57301i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-5.18614 - 8.98266i) q^{33} -6.74456 q^{34} +(1.18614 + 6.16337i) q^{35} +2.62772 q^{36} +(1.00000 + 1.73205i) q^{37} +(0.186141 - 0.322405i) q^{38} +(-6.37228 + 11.0371i) q^{39} +(1.18614 + 2.05446i) q^{40} -1.00000 q^{41} +(-5.93070 - 2.05446i) q^{42} -0.627719 q^{43} +(2.18614 + 3.78651i) q^{44} +(-3.11684 + 5.39853i) q^{45} +(1.37228 - 2.37686i) q^{46} +(-4.00000 - 6.92820i) q^{47} -2.37228 q^{48} +(5.50000 + 4.33013i) q^{49} -0.627719 q^{50} +(8.00000 + 13.8564i) q^{51} +(2.68614 - 4.65253i) q^{52} +(5.00000 - 8.66025i) q^{53} +(0.441578 + 0.764836i) q^{54} -10.3723 q^{55} +(2.50000 + 0.866025i) q^{56} -0.883156 q^{57} +(5.05842 + 8.76144i) q^{58} +(-2.68614 + 4.65253i) q^{59} +(2.81386 - 4.87375i) q^{60} +(-4.18614 - 7.25061i) q^{61} +8.74456 q^{62} +(1.31386 + 6.82701i) q^{63} +1.00000 q^{64} +(6.37228 + 11.0371i) q^{65} +(5.18614 - 8.98266i) q^{66} +(4.00000 - 6.92820i) q^{67} +(-3.37228 - 5.84096i) q^{68} -6.51087 q^{69} +(-4.74456 + 4.10891i) q^{70} -0.255437 q^{71} +(1.31386 + 2.27567i) q^{72} +(2.05842 - 3.56529i) q^{73} +(-1.00000 + 1.73205i) q^{74} +(0.744563 + 1.28962i) q^{75} +0.372281 q^{76} +(-8.74456 + 7.57301i) q^{77} -12.7446 q^{78} +(5.18614 + 8.98266i) q^{79} +(-1.18614 + 2.05446i) q^{80} +(4.98913 - 8.64142i) q^{81} +(-0.500000 - 0.866025i) q^{82} +5.37228 q^{83} +(-1.18614 - 6.16337i) q^{84} +16.0000 q^{85} +(-0.313859 - 0.543620i) q^{86} +(12.0000 - 20.7846i) q^{87} +(-2.18614 + 3.78651i) q^{88} +(1.00000 + 1.73205i) q^{89} -6.23369 q^{90} +(13.4307 + 4.65253i) q^{91} +2.74456 q^{92} +(-10.3723 - 17.9653i) q^{93} +(4.00000 - 6.92820i) q^{94} +(-0.441578 + 0.764836i) q^{95} +(-1.18614 - 2.05446i) q^{96} +8.00000 q^{97} +(-1.00000 + 6.92820i) q^{98} -11.4891 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - q^{3} - 2 q^{4} + q^{5} - 2 q^{6} - 10 q^{7} - 4 q^{8} - 11 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 - q^3 - 2 * q^4 + q^5 - 2 * q^6 - 10 * q^7 - 4 * q^8 - 11 * q^9	\( 4 q + 2 q^{2} - q^{3} - 2 q^{4} + q^{5} - 2 q^{6} - 10 q^{7} - 4 q^{8} - 11 q^{9} - q^{10} + 3 q^{11} - q^{12} - 10 q^{13} - 2 q^{14} - 34 q^{15} - 2 q^{16} - 2 q^{17} + 11 q^{18} + 5 q^{19} - 2 q^{20} + 4 q^{21} + 6 q^{22} + 6 q^{23} + q^{24} - 7 q^{25} - 5 q^{26} + 38 q^{27} + 8 q^{28} + 6 q^{29} - 17 q^{30} + 6 q^{31} + 2 q^{32} - 15 q^{33} - 4 q^{34} - q^{35} + 22 q^{36} + 4 q^{37} - 5 q^{38} - 14 q^{39} - q^{40} - 4 q^{41} + 5 q^{42} - 14 q^{43} + 3 q^{44} + 22 q^{45} - 6 q^{46} - 16 q^{47} + 2 q^{48} + 22 q^{49} - 14 q^{50} + 32 q^{51} + 5 q^{52} + 20 q^{53} + 19 q^{54} - 30 q^{55} + 10 q^{56} - 38 q^{57} + 3 q^{58} - 5 q^{59} + 17 q^{60} - 11 q^{61} + 12 q^{62} + 11 q^{63} + 4 q^{64} + 14 q^{65} + 15 q^{66} + 16 q^{67} - 2 q^{68} - 72 q^{69} + 4 q^{70} - 24 q^{71} + 11 q^{72} - 9 q^{73} - 4 q^{74} - 20 q^{75} - 10 q^{76} - 12 q^{77} - 28 q^{78} + 15 q^{79} + q^{80} - 26 q^{81} - 2 q^{82} + 10 q^{83} + q^{84} + 64 q^{85} - 7 q^{86} + 48 q^{87} - 3 q^{88} + 4 q^{89} + 44 q^{90} + 25 q^{91} - 12 q^{92} - 30 q^{93} + 16 q^{94} - 19 q^{95} + q^{96} + 32 q^{97} - 4 q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 - q^3 - 2 * q^4 + q^5 - 2 * q^6 - 10 * q^7 - 4 * q^8 - 11 * q^9 - q^10 + 3 * q^11 - q^12 - 10 * q^13 - 2 * q^14 - 34 * q^15 - 2 * q^16 - 2 * q^17 + 11 * q^18 + 5 * q^19 - 2 * q^20 + 4 * q^21 + 6 * q^22 + 6 * q^23 + q^24 - 7 * q^25 - 5 * q^26 + 38 * q^27 + 8 * q^28 + 6 * q^29 - 17 * q^30 + 6 * q^31 + 2 * q^32 - 15 * q^33 - 4 * q^34 - q^35 + 22 * q^36 + 4 * q^37 - 5 * q^38 - 14 * q^39 - q^40 - 4 * q^41 + 5 * q^42 - 14 * q^43 + 3 * q^44 + 22 * q^45 - 6 * q^46 - 16 * q^47 + 2 * q^48 + 22 * q^49 - 14 * q^50 + 32 * q^51 + 5 * q^52 + 20 * q^53 + 19 * q^54 - 30 * q^55 + 10 * q^56 - 38 * q^57 + 3 * q^58 - 5 * q^59 + 17 * q^60 - 11 * q^61 + 12 * q^62 + 11 * q^63 + 4 * q^64 + 14 * q^65 + 15 * q^66 + 16 * q^67 - 2 * q^68 - 72 * q^69 + 4 * q^70 - 24 * q^71 + 11 * q^72 - 9 * q^73 - 4 * q^74 - 20 * q^75 - 10 * q^76 - 12 * q^77 - 28 * q^78 + 15 * q^79 + q^80 - 26 * q^81 - 2 * q^82 + 10 * q^83 + q^84 + 64 * q^85 - 7 * q^86 + 48 * q^87 - 3 * q^88 + 4 * q^89 + 44 * q^90 + 25 * q^91 - 12 * q^92 - 30 * q^93 + 16 * q^94 - 19 * q^95 + q^96 + 32 * q^97 - 4 * q^98

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