LMFDB - Embedded newform 574.2.e.g.247.3

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:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 11 x^{10} - 8 x^{9} + 85 x^{8} - 60 x^{7} + 305 x^{6} - 145 x^{5} + 748 x^{4} + \cdots + 1 $ x^12 - x^11 + 11x^10 - 8x^9 + 85x^8 - 60x^7 + 305x^6 - 145x^5 + 748x^4 - 450x^3 + 300x^2 - 18x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			247.3
Root			$0.0302735 + 0.0524352i$ of defining polynomial
Character	$\chi$	$=$	574.247
Dual form			574.2.e.g.165.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.151256 - 0.261984i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.33775 - 2.31706i) q^{5} -0.302513 q^{6} +(-1.36803 - 2.26462i) q^{7} -1.00000 q^{8} +(1.45424 - 2.51882i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.151256 - 0.261984i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.33775 - 2.31706i) q^{5} -0.302513 q^{6} +(-1.36803 - 2.26462i) q^{7} -1.00000 q^{8} +(1.45424 - 2.51882i) q^{9} +(-1.33775 - 2.31706i) q^{10} +(2.26591 + 3.92468i) q^{11} +(-0.151256 + 0.261984i) q^{12} -5.61129 q^{13} +(-2.64523 + 0.0524352i) q^{14} -0.809374 q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.616490 + 1.06779i) q^{17} +(-1.45424 - 2.51882i) q^{18} +(2.72199 - 4.71462i) q^{19} -2.67551 q^{20} +(-0.386371 + 0.700939i) q^{21} +4.53183 q^{22} +(-2.16041 + 3.74195i) q^{23} +(0.151256 + 0.261984i) q^{24} +(-1.07916 - 1.86917i) q^{25} +(-2.80565 + 4.85952i) q^{26} -1.78739 q^{27} +(-1.27721 + 2.31706i) q^{28} -2.63327 q^{29} +(-0.404687 + 0.700939i) q^{30} +(0.418749 + 0.725295i) q^{31} +(0.500000 + 0.866025i) q^{32} +(0.685468 - 1.18726i) q^{33} +1.23298 q^{34} +(-7.07733 + 0.140291i) q^{35} -2.90849 q^{36} +(5.34324 - 9.25477i) q^{37} +(-2.72199 - 4.71462i) q^{38} +(0.848744 + 1.47007i) q^{39} +(-1.33775 + 2.31706i) q^{40} +1.00000 q^{41} +(0.413845 + 0.685076i) q^{42} -0.192081 q^{43} +(2.26591 - 3.92468i) q^{44} +(-3.89083 - 6.73912i) q^{45} +(2.16041 + 3.74195i) q^{46} +(4.62412 - 8.00920i) q^{47} +0.302513 q^{48} +(-3.25701 + 6.19612i) q^{49} -2.15833 q^{50} +(0.186496 - 0.323021i) q^{51} +(2.80565 + 4.85952i) q^{52} +(-3.55386 - 6.15546i) q^{53} +(-0.893696 + 1.54793i) q^{54} +12.1249 q^{55} +(1.36803 + 2.26462i) q^{56} -1.64687 q^{57} +(-1.31664 + 2.28048i) q^{58} +(2.67081 + 4.62598i) q^{59} +(0.404687 + 0.700939i) q^{60} +(0.929740 - 1.61036i) q^{61} +0.837499 q^{62} +(-7.69362 + 0.152507i) q^{63} +1.00000 q^{64} +(-7.50652 + 13.0017i) q^{65} +(-0.685468 - 1.18726i) q^{66} +(7.93703 + 13.7473i) q^{67} +(0.616490 - 1.06779i) q^{68} +1.30711 q^{69} +(-3.41717 + 6.19929i) q^{70} +11.9802 q^{71} +(-1.45424 + 2.51882i) q^{72} +(-4.35479 - 7.54272i) q^{73} +(-5.34324 - 9.25477i) q^{74} +(-0.326461 + 0.565447i) q^{75} -5.44398 q^{76} +(5.78808 - 10.5005i) q^{77} +1.69749 q^{78} +(-5.37086 + 9.30260i) q^{79} +(1.33775 + 2.31706i) q^{80} +(-4.09237 - 7.08820i) q^{81} +(0.500000 - 0.866025i) q^{82} +8.34120 q^{83} +(0.800216 - 0.0158623i) q^{84} +3.29885 q^{85} +(-0.0960406 + 0.166347i) q^{86} +(0.398300 + 0.689875i) q^{87} +(-2.26591 - 3.92468i) q^{88} +(-1.02164 + 1.76953i) q^{89} -7.78167 q^{90} +(7.67639 + 12.7074i) q^{91} +4.32083 q^{92} +(0.126677 - 0.219411i) q^{93} +(-4.62412 - 8.00920i) q^{94} +(-7.28270 - 12.6140i) q^{95} +(0.151256 - 0.261984i) q^{96} -2.40675 q^{97} +(3.73749 + 5.91871i) q^{98} +13.1808 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{2} - q^{3} - 6 q^{4} - 2 q^{6} - q^{7} - 12 q^{8} - 5 q^{9}+O(q^{10}) $ 12 * q + 6 * q^2 - q^3 - 6 * q^4 - 2 * q^6 - q^7 - 12 * q^8 - 5 * q^9	$ 12 q + 6 q^{2} - q^{3} - 6 q^{4} - 2 q^{6} - q^{7} - 12 q^{8} - 5 q^{9} - q^{11} - q^{12} + 8 q^{13} + q^{14} + 4 q^{15} - 6 q^{16} + q^{17} + 5 q^{18} + 3 q^{19} - 6 q^{21} - 2 q^{22} - 21 q^{23} + q^{24} + 4 q^{26} + 26 q^{27} + 2 q^{28} + 10 q^{29} + 2 q^{30} - 3 q^{31} + 6 q^{32} + 19 q^{33} + 2 q^{34} - 51 q^{35} + 10 q^{36} + 2 q^{37} - 3 q^{38} + 11 q^{39} + 12 q^{41} - 6 q^{42} + 24 q^{43} - q^{44} - 28 q^{45} + 21 q^{46} + 18 q^{47} + 2 q^{48} - 15 q^{49} - 13 q^{51} - 4 q^{52} - 14 q^{53} + 13 q^{54} - 14 q^{55} + q^{56} + 10 q^{57} + 5 q^{58} - 16 q^{59} - 2 q^{60} + 20 q^{61} - 6 q^{62} - 41 q^{63} + 12 q^{64} - 18 q^{65} - 19 q^{66} + 13 q^{67} + q^{68} + 30 q^{69} - 12 q^{70} + 22 q^{71} + 5 q^{72} - q^{73} - 2 q^{74} + 23 q^{75} - 6 q^{76} - 11 q^{77} + 22 q^{78} - 19 q^{79} + 6 q^{81} + 6 q^{82} + 30 q^{83} - 4 q^{85} + 12 q^{86} - 10 q^{87} + q^{88} + 14 q^{89} - 56 q^{90} + 5 q^{91} + 42 q^{92} - 35 q^{93} - 18 q^{94} - 24 q^{95} + q^{96} + 2 q^{97} + 6 q^{98} + 20 q^{99}+O(q^{100}) $ 12 * q + 6 * q^2 - q^3 - 6 * q^4 - 2 * q^6 - q^7 - 12 * q^8 - 5 * q^9 - q^11 - q^12 + 8 * q^13 + q^14 + 4 * q^15 - 6 * q^16 + q^17 + 5 * q^18 + 3 * q^19 - 6 * q^21 - 2 * q^22 - 21 * q^23 + q^24 + 4 * q^26 + 26 * q^27 + 2 * q^28 + 10 * q^29 + 2 * q^30 - 3 * q^31 + 6 * q^32 + 19 * q^33 + 2 * q^34 - 51 * q^35 + 10 * q^36 + 2 * q^37 - 3 * q^38 + 11 * q^39 + 12 * q^41 - 6 * q^42 + 24 * q^43 - q^44 - 28 * q^45 + 21 * q^46 + 18 * q^47 + 2 * q^48 - 15 * q^49 - 13 * q^51 - 4 * q^52 - 14 * q^53 + 13 * q^54 - 14 * q^55 + q^56 + 10 * q^57 + 5 * q^58 - 16 * q^59 - 2 * q^60 + 20 * q^61 - 6 * q^62 - 41 * q^63 + 12 * q^64 - 18 * q^65 - 19 * q^66 + 13 * q^67 + q^68 + 30 * q^69 - 12 * q^70 + 22 * q^71 + 5 * q^72 - q^73 - 2 * q^74 + 23 * q^75 - 6 * q^76 - 11 * q^77 + 22 * q^78 - 19 * q^79 + 6 * q^81 + 6 * q^82 + 30 * q^83 - 4 * q^85 + 12 * q^86 - 10 * q^87 + q^88 + 14 * q^89 - 56 * q^90 + 5 * q^91 + 42 * q^92 - 35 * q^93 - 18 * q^94 - 24 * q^95 + q^96 + 2 * q^97 + 6 * q^98 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	−0.151256	−	0.261984i	−0.0873279	−	0.151256i	0.819053	−	0.573718i	$-0.194499\pi$
$3$	−0.151256	−	0.261984i	−0.0873279	−	0.151256i	−0.906381	+	0.422462i	$0.861166\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	1.33775	−	2.31706i	0.598261	−	1.03622i	−0.394817	−	0.918760i	$-0.629192\pi$
$5$	1.33775	−	2.31706i	0.598261	−	1.03622i	0.993078	−	0.117459i	$-0.0374748\pi$
$6$	−0.302513			−0.123500
$7$	−1.36803	−	2.26462i	−0.517065	−	0.855946i
$7$	−1.36803	−	2.26462i	−0.517065	−	0.855946i
$8$	−1.00000			−0.353553
$9$	1.45424	−	2.51882i	0.484748	−	0.839608i
$10$	−1.33775	−	2.31706i	−0.423035	−	0.732717i
$11$	2.26591	+	3.92468i	0.683199	+	1.18333i	0.973999	+	0.226551i	$0.0727451\pi$
$11$	2.26591	+	3.92468i	0.683199	+	1.18333i	−0.290801	+	0.956784i	$0.593922\pi$
$12$	−0.151256	+	0.261984i	−0.0436639	+	0.0756282i
$13$	−5.61129			−1.55629			−0.778146	−	0.628083i	$-0.783840\pi$
$13$	−5.61129			−1.55629			−0.778146	+	0.628083i	$0.783840\pi$
$14$	−2.64523	+	0.0524352i	−0.706968	+	0.0140139i
$15$	−0.809374			−0.208980
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	0.616490	+	1.06779i	0.149521	+	0.258978i	0.931050	−	0.364890i	$-0.118894\pi$
$17$	0.616490	+	1.06779i	0.149521	+	0.258978i	−0.781530	+	0.623868i	$0.785560\pi$
$18$	−1.45424	−	2.51882i	−0.342768	−	0.593692i
$19$	2.72199	−	4.71462i	0.624467	−	1.08161i	−0.364176	−	0.931330i	$-0.618649\pi$
$19$	2.72199	−	4.71462i	0.624467	−	1.08161i	0.988644	−	0.150279i	$-0.0480172\pi$
$20$	−2.67551			−0.598261
$21$	−0.386371	+	0.700939i	−0.0843131	+	0.152957i
$22$	4.53183			0.966189
$23$	−2.16041	+	3.74195i	−0.450478	+	0.780250i	−0.998416	−	0.0562689i	$-0.982080\pi$
$23$	−2.16041	+	3.74195i	−0.450478	+	0.780250i	0.547938	+	0.836519i	$0.315413\pi$
$24$	0.151256	+	0.261984i	0.0308751	+	0.0534772i
$25$	−1.07916	−	1.86917i	−0.215833	−	0.373833i
$26$	−2.80565	+	4.85952i	−0.550232	+	0.953031i
$27$	−1.78739			−0.343984
$28$	−1.27721	+	2.31706i	−0.241369	+	0.437882i
$29$	−2.63327			−0.488987			−0.244493	−	0.969651i	$-0.578622\pi$
$29$	−2.63327			−0.488987			−0.244493	+	0.969651i	$0.578622\pi$
$30$	−0.404687	+	0.700939i	−0.0738854	+	0.127973i
$31$	0.418749	+	0.725295i	0.0752096	+	0.130267i	0.901177	−	0.433450i	$-0.142704\pi$
$31$	0.418749	+	0.725295i	0.0752096	+	0.130267i	−0.825968	+	0.563717i	$0.809371\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	0.685468	−	1.18726i	0.119325	−	0.206676i
$34$	1.23298			0.211454
$35$	−7.07733	+	0.140291i	−1.19629	+	0.0237134i
$36$	−2.90849			−0.484748
$37$	5.34324	−	9.25477i	0.878424	−	1.52148i	0.0253540	−	0.999679i	$-0.491929\pi$
$37$	5.34324	−	9.25477i	0.878424	−	1.52148i	0.853070	−	0.521797i	$-0.174738\pi$
$38$	−2.72199	−	4.71462i	−0.441565	−	0.764813i
$39$	0.848744	+	1.47007i	0.135908	+	0.235399i
$40$	−1.33775	+	2.31706i	−0.211517	+	0.366359i
$41$	1.00000			0.156174
$41$	1.00000			0.156174
$42$	0.413845	+	0.685076i	0.0638577	+	0.105710i
$43$	−0.192081			−0.0292921			−0.0146461	−	0.999893i	$-0.504662\pi$
$43$	−0.192081			−0.0292921			−0.0146461	+	0.999893i	$0.504662\pi$
$44$	2.26591	−	3.92468i	0.341599	−	0.591667i
$45$	−3.89083	−	6.73912i	−0.580011	−	1.00461i
$46$	2.16041	+	3.74195i	0.318536	+	0.551720i
$47$	4.62412	−	8.00920i	0.674497	−	1.16826i	−0.302119	−	0.953270i	$-0.597694\pi$
$47$	4.62412	−	8.00920i	0.674497	−	1.16826i	0.976616	−	0.214992i	$-0.0689727\pi$
$48$	0.302513			0.0436639
$49$	−3.25701	+	6.19612i	−0.465287	+	0.885160i
$50$	−2.15833			−0.305234
$51$	0.186496	−	0.323021i	0.0261147	−	0.0452320i
$52$	2.80565	+	4.85952i	0.389073	+	0.673894i
$53$	−3.55386	−	6.15546i	−0.488160	−	0.845518i	0.511747	−	0.859136i	$-0.328998\pi$
$53$	−3.55386	−	6.15546i	−0.488160	−	0.845518i	−0.999907	+	0.0136184i	$0.995665\pi$
$54$	−0.893696	+	1.54793i	−0.121617	+	0.210646i
$55$	12.1249			1.63492
$56$	1.36803	+	2.26462i	0.182810	+	0.302623i
$57$	−1.64687			−0.218134
$58$	−1.31664	+	2.28048i	−0.172883	+	0.299442i
$59$	2.67081	+	4.62598i	0.347710	+	0.602251i	0.985842	−	0.167675i	$-0.0536261\pi$
$59$	2.67081	+	4.62598i	0.347710	+	0.602251i	−0.638132	+	0.769927i	$0.720293\pi$
$60$	0.404687	+	0.700939i	0.0522449	+	0.0904908i
$61$	0.929740	−	1.61036i	0.119041	−	0.206185i	−0.800347	−	0.599537i	$-0.795351\pi$
$61$	0.929740	−	1.61036i	0.119041	−	0.206185i	0.919388	+	0.393352i	$0.128685\pi$
$62$	0.837499			0.106362
$63$	−7.69362	+	0.152507i	−0.969305	+	0.0192141i
$64$	1.00000			0.125000
$65$	−7.50652	+	13.0017i	−0.931069	+	1.61266i
$66$	−0.685468	−	1.18726i	−0.0843752	−	0.146142i
$67$	7.93703	+	13.7473i	0.969662	+	1.67950i	0.696531	+	0.717527i	$0.254726\pi$
$67$	7.93703	+	13.7473i	0.969662	+	1.67950i	0.273131	+	0.961977i	$0.411941\pi$
$68$	0.616490	−	1.06779i	0.0747604	−	0.129489i
$69$	1.30711			0.157357
$70$	−3.41717	+	6.19929i	−0.408430	+	0.740957i
$71$	11.9802			1.42179			0.710894	−	0.703299i	$-0.248291\pi$
$71$	11.9802			1.42179			0.710894	+	0.703299i	$0.248291\pi$
$72$	−1.45424	+	2.51882i	−0.171384	+	0.296846i
$73$	−4.35479	−	7.54272i	−0.509690	−	0.882808i	−0.999937	−	0.0112250i	$-0.996427\pi$
$73$	−4.35479	−	7.54272i	−0.509690	−	0.882808i	0.490247	−	0.871583i	$-0.336906\pi$
$74$	−5.34324	−	9.25477i	−0.621140	−	1.07585i
$75$	−0.326461	+	0.565447i	−0.0376964	+	0.0652922i
$76$	−5.44398			−0.624467
$77$	5.78808	−	10.5005i	0.659612	−	1.19664i
$78$	1.69749			0.192203
$79$	−5.37086	+	9.30260i	−0.604269	+	1.04662i	0.387898	+	0.921702i	$0.373201\pi$
$79$	−5.37086	+	9.30260i	−0.604269	+	1.04662i	−0.992167	+	0.124922i	$0.960132\pi$
$80$	1.33775	+	2.31706i	0.149565	+	0.259055i
$81$	−4.09237	−	7.08820i	−0.454708	−	0.787578i
$82$	0.500000	−	0.866025i	0.0552158	−	0.0956365i
$83$	8.34120			0.915566			0.457783	−	0.889064i	$-0.348644\pi$
$83$	8.34120			0.915566			0.457783	+	0.889064i	$0.348644\pi$
$84$	0.800216	−	0.0158623i	0.0873107	−	0.00173072i
$85$	3.29885			0.357810
$86$	−0.0960406	+	0.166347i	−0.0103563	+	0.0179377i
$87$	0.398300	+	0.689875i	0.0427022	+	0.0739624i
$88$	−2.26591	−	3.92468i	−0.241547	−	0.418372i
$89$	−1.02164	+	1.76953i	−0.108294	+	0.187570i	−0.915079	−	0.403274i	$-0.867872\pi$
$89$	−1.02164	+	1.76953i	−0.108294	+	0.187570i	0.806785	+	0.590845i	$0.201205\pi$
$90$	−7.78167			−0.820260
$91$	7.67639	+	12.7074i	0.804705	+	1.33210i
$92$	4.32083			0.450478
$93$	0.126677	−	0.219411i	0.0131358	−	0.0227519i
$94$	−4.62412	−	8.00920i	−0.476941	−	0.826086i
$95$	−7.28270	−	12.6140i	−0.747189	−	1.29417i
$96$	0.151256	−	0.261984i	0.0154375	−	0.0267386i
$97$	−2.40675			−0.244368			−0.122184	−	0.992507i	$-0.538990\pi$
$97$	−2.40675			−0.244368			−0.122184	+	0.992507i	$0.538990\pi$
$98$	3.73749	+	5.91871i	0.377544	+	0.597880i
$99$	13.1808			1.32472
$100$	−1.07916	+	1.86917i	−0.107916	+	0.186917i
$101$	7.11602	+	12.3253i	0.708070	+	1.22641i	0.965572	+	0.260136i	$0.0837674\pi$
$101$	7.11602	+	12.3253i	0.708070	+	1.22641i	−0.257501	+	0.966278i	$0.582899\pi$
$102$	−0.186496	−	0.323021i	−0.0184659	−	0.0319838i
$103$	6.22016	−	10.7736i	0.612890	−	1.06156i	−0.377860	−	0.925863i	$-0.623340\pi$
$103$	6.22016	−	10.7736i	0.612890	−	1.06156i	0.990751	−	0.135695i	$-0.0433266\pi$
$104$	5.61129			0.550232
$105$	1.10725	+	1.83293i	0.108056	+	0.178875i
$106$	−7.10771			−0.690362
$107$	−3.37968	+	5.85378i	−0.326726	+	0.565906i	−0.981860	−	0.189606i	$-0.939279\pi$
$107$	−3.37968	+	5.85378i	−0.326726	+	0.565906i	0.655134	+	0.755513i	$0.272612\pi$
$108$	0.893696	+	1.54793i	0.0859959	+	0.148949i
$109$	4.09558	+	7.09376i	0.392286	+	0.679459i	0.992751	−	0.120192i	$-0.0383511\pi$
$109$	4.09558	+	7.09376i	0.392286	+	0.679459i	−0.600465	+	0.799651i	$0.705018\pi$
$110$	6.06246	−	10.5005i	0.578033	−	1.00118i
$111$	−3.23280			−0.306844
$112$	2.64523	−	0.0524352i	0.249951	−	0.00495466i
$113$	12.2861			1.15578			0.577888	−	0.816116i	$-0.303877\pi$
$113$	12.2861			1.15578			0.577888	+	0.816116i	$0.303877\pi$
$114$	−0.823437	+	1.42623i	−0.0771219	+	0.133579i
$115$	5.78020	+	10.0116i	0.539006	+	0.933587i
$116$	1.31664	+	2.28048i	0.122247	+	0.211737i
$117$	−8.16018	+	14.1339i	−0.754409	+	1.30667i
$118$	5.34162			0.491736
$119$	1.57477	−	2.85689i	0.144359	−	0.261890i
$120$	0.809374			0.0738854
$121$	−4.76873	+	8.25968i	−0.433521	+	0.750880i
$122$	−0.929740	−	1.61036i	−0.0841747	−	0.145795i
$123$	−0.151256	−	0.261984i	−0.0136383	−	0.0236223i
$124$	0.418749	−	0.725295i	0.0376048	−	0.0651334i
$125$	7.60291			0.680025
$126$	−3.71473	+	6.73912i	−0.330935	+	0.600369i
$127$	2.23213			0.198069			0.0990346	−	0.995084i	$-0.468425\pi$
$127$	2.23213			0.198069			0.0990346	+	0.995084i	$0.468425\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	0.0290535	+	0.0503221i	0.00255802	+	0.00443062i
$130$	7.50652	+	13.0017i	0.658365	+	1.14032i
$131$	10.5170	−	18.2160i	0.918875	−	1.59154i	0.117749	−	0.993043i	$-0.462432\pi$
$131$	10.5170	−	18.2160i	0.918875	−	1.59154i	0.801126	−	0.598495i	$-0.204234\pi$
$132$	−1.37094			−0.119325
$133$	−14.4006	+	0.285456i	−1.24869	+	0.0247522i
$134$	15.8741			1.37131
$135$	−2.39109	+	4.14149i	−0.205792	+	0.356442i
$136$	−0.616490	−	1.06779i	−0.0528636	−	0.0915625i
$137$	1.77409	+	3.07281i	0.151571	+	0.262528i	0.931805	−	0.362959i	$-0.118234\pi$
$137$	1.77409	+	3.07281i	0.151571	+	0.262528i	−0.780234	+	0.625487i	$0.784900\pi$
$138$	0.653553	−	1.13199i	0.0556341	−	0.0963611i
$139$	−2.80375			−0.237811			−0.118905	−	0.992906i	$-0.537938\pi$
$139$	−2.80375			−0.237811			−0.118905	+	0.992906i	$0.537938\pi$
$140$	3.66016	+	6.05900i	0.309340	+	0.512079i
$141$	−2.79771			−0.235610
$142$	5.99010	−	10.3752i	0.502678	−	0.870664i
$143$	−12.7147	−	22.0225i	−1.06326	−	1.84162i
$144$	1.45424	+	2.51882i	0.121187	+	0.209902i
$145$	−3.52267	+	6.10144i	−0.292542	+	0.506697i
$146$	−8.70958			−0.720810
$147$	2.11593	−	0.0839190i	0.174519	−	0.00692152i
$148$	−10.6865			−0.878424
$149$	0.0151425	−	0.0262276i	0.00124052	−	0.00214865i	−0.865404	−	0.501074i	$-0.832938\pi$
$149$	0.0151425	−	0.0262276i	0.00124052	−	0.00214865i	0.866645	+	0.498925i	$0.166272\pi$
$150$	0.326461	+	0.565447i	0.0266554	+	0.0461685i
$151$	8.60996	+	14.9129i	0.700669	+	1.21359i	0.968232	+	0.250054i	$0.0804482\pi$
$151$	8.60996	+	14.9129i	0.700669	+	1.21359i	−0.267563	+	0.963540i	$0.586218\pi$
$152$	−2.72199	+	4.71462i	−0.220783	+	0.382407i
$153$	3.58611			0.289920
$154$	−6.19966	−	10.2629i	−0.499583	−	0.827006i
$155$	2.24073			0.179980
$156$	0.848744	−	1.47007i	0.0679539	−	0.117700i
$157$	−9.18826	−	15.9145i	−0.733303	−	1.27012i	−0.955464	−	0.295108i	$-0.904644\pi$
$157$	−9.18826	−	15.9145i	−0.733303	−	1.27012i	0.222161	−	0.975010i	$-0.428689\pi$
$158$	5.37086	+	9.30260i	0.427283	+	0.740075i
$159$	−1.07509	+	1.86211i	−0.0852599	+	0.147675i
$160$	2.67551			0.211517
$161$	11.4296	−	0.226563i	0.900778	−	0.0178557i
$162$	−8.18475			−0.643055
$163$	1.52952	−	2.64920i	0.119801	−	0.207501i	−0.799888	−	0.600150i	$-0.795108\pi$
$163$	1.52952	−	2.64920i	0.119801	−	0.207501i	0.919689	+	0.392648i	$0.128441\pi$
$164$	−0.500000	−	0.866025i	−0.0390434	−	0.0676252i
$165$	−1.83397	−	3.17653i	−0.142775	−	0.247293i
$166$	4.17060	−	7.22369i	0.323701	−	0.560667i
$167$	−9.88049			−0.764575			−0.382287	−	0.924043i	$-0.624864\pi$
$167$	−9.88049			−0.764575			−0.382287	+	0.924043i	$0.624864\pi$
$168$	0.386371	−	0.700939i	0.0298092	−	0.0540786i
$169$	18.4866			1.42205
$170$	1.64942	−	2.85689i	0.126505	−	0.219113i
$171$	−7.91687	−	13.7124i	−0.605418	−	1.04861i
$172$	0.0960406	+	0.166347i	0.00732303	+	0.0126839i
$173$	5.83869	−	10.1129i	0.443907	−	0.768870i	−0.554068	−	0.832471i	$-0.686925\pi$
$173$	5.83869	−	10.1129i	0.443907	−	0.768870i	0.997975	+	0.0636013i	$0.0202586\pi$
$174$	0.796599			0.0603900
$175$	−2.75663	+	5.00096i	−0.208382	+	0.378037i
$176$	−4.53183			−0.341599
$177$	0.807954	−	1.39942i	0.0607296	−	0.105187i
$178$	1.02164	+	1.76953i	0.0765752	+	0.132632i
$179$	−3.60442	−	6.24304i	−0.269407	−	0.466627i	0.699302	−	0.714827i	$-0.253494\pi$
$179$	−3.60442	−	6.24304i	−0.269407	−	0.466627i	−0.968709	+	0.248200i	$0.920161\pi$
$180$	−3.89083	+	6.73912i	−0.290006	+	0.502305i
$181$	−17.2003			−1.27849			−0.639246	−	0.769002i	$-0.720753\pi$
$181$	−17.2003			−1.27849			−0.639246	+	0.769002i	$0.720753\pi$
$182$	14.8432	−	0.294229i	1.10025	−	0.0218097i
$183$	−0.562517			−0.0415824
$184$	2.16041	−	3.74195i	0.159268	−	0.275860i
$185$	−14.2959	−	24.7612i	−1.05105	−	1.82048i
$186$	−0.126677	−	0.219411i	−0.00928841	−	0.0160880i
$187$	−2.79383	+	4.83905i	−0.204305	+	0.353867i
$188$	−9.24823			−0.674497
$189$	2.44520	+	4.04776i	0.177862	+	0.294432i
$190$	−14.5654			−1.05668
$191$	−4.57262	+	7.92001i	−0.330863	+	0.573072i	−0.982681	−	0.185304i	$-0.940673\pi$
$191$	−4.57262	+	7.92001i	−0.330863	+	0.573072i	0.651818	+	0.758375i	$0.274006\pi$
$192$	−0.151256	−	0.261984i	−0.0109160	−	0.0189070i
$193$	6.70892	+	11.6202i	0.482918	+	0.836439i	0.999808	−	0.0196132i	$-0.00624346\pi$
$193$	6.70892	+	11.6202i	0.482918	+	0.836439i	−0.516889	+	0.856052i	$0.672910\pi$
$194$	−1.20337	+	2.08430i	−0.0863971	+	0.149644i
$195$	4.54164			0.325233
$196$	6.99450	−	0.277406i	0.499607	−	0.0198147i
$197$	−16.3793			−1.16698			−0.583489	−	0.812121i	$-0.698313\pi$
$197$	−16.3793			−1.16698			−0.583489	+	0.812121i	$0.698313\pi$
$198$	6.59038	−	11.4149i	0.468358	−	0.811220i
$199$	5.88706	+	10.1967i	0.417322	+	0.722824i	0.995669	−	0.0929674i	$-0.0296352\pi$
$199$	5.88706	+	10.1967i	0.417322	+	0.722824i	−0.578347	+	0.815791i	$0.696302\pi$
$200$	1.07916	+	1.86917i	0.0763084	+	0.132170i
$201$	2.40105	−	4.15874i	0.169357	−	0.293335i
$202$	14.2320			1.00136
$203$	3.60239	+	5.96337i	0.252838	+	0.418546i
$204$	−0.372992			−0.0261147
$205$	1.33775	−	2.31706i	0.0934327	−	0.161830i
$206$	−6.22016	−	10.7736i	−0.433379	−	0.750634i
$207$	6.28354	+	10.8834i	0.436736	+	0.756449i
$208$	2.80565	−	4.85952i	0.194537	−	0.336947i
$209$	24.6712			1.70654
$210$	2.14098	−	0.0424397i	0.147742	−	0.00292862i
$211$	18.3313			1.26198			0.630990	−	0.775791i	$-0.282649\pi$
$211$	18.3313			1.26198			0.630990	+	0.775791i	$0.282649\pi$
$212$	−3.55386	+	6.15546i	−0.244080	+	0.422759i
$213$	−1.81208	−	3.13862i	−0.124162	−	0.215054i
$214$	3.37968	+	5.85378i	0.231030	+	0.400156i
$215$	−0.256957	+	0.445063i	−0.0175243	+	0.0303530i
$216$	1.78739			0.121617
$217$	1.06966	−	1.94053i	0.0726131	−	0.131732i
$218$	8.19117			0.554776
$219$	−1.31738	+	2.28177i	−0.0890203	+	0.154188i
$220$	−6.06246	−	10.5005i	−0.408731	−	0.707943i
$221$	−3.45931	−	5.99170i	−0.232698	−	0.403045i
$222$	−1.61640	+	2.79969i	−0.108486	+	0.187903i
$223$	−19.6446			−1.31550			−0.657749	−	0.753237i	$-0.728491\pi$
$223$	−19.6446			−1.31550			−0.657749	+	0.753237i	$0.728491\pi$
$224$	1.27721	−	2.31706i	0.0853369	−	0.154815i
$225$	−6.27747			−0.418498
$226$	6.14304	−	10.6400i	0.408629	−	0.707766i
$227$	4.39247	+	7.60797i	0.291538	+	0.504959i	0.974174	−	0.225800i	$-0.0724996\pi$
$227$	4.39247	+	7.60797i	0.291538	+	0.504959i	−0.682635	+	0.730759i	$0.739166\pi$
$228$	0.823437	+	1.42623i	0.0545334	+	0.0944547i
$229$	−3.44825	+	5.97254i	−0.227867	+	0.394676i	−0.957176	−	0.289508i	$-0.906508\pi$
$229$	−3.44825	+	5.97254i	−0.227867	+	0.394676i	0.729309	+	0.684184i	$0.239842\pi$
$230$	11.5604			0.762270
$231$	−3.62644	+	0.0718853i	−0.238602	+	0.00472970i
$232$	2.63327			0.172883
$233$	−15.2116	+	26.3473i	−0.996547	+	1.72607i	−0.426370	+	0.904549i	$0.640208\pi$
$233$	−15.2116	+	26.3473i	−0.996547	+	1.72607i	−0.570178	+	0.821522i	$0.693126\pi$
$234$	8.16018	+	14.1339i	0.533448	+	0.923959i
$235$	−12.3718	−	21.4287i	−0.807050	−	1.39785i
$236$	2.67081	−	4.62598i	0.173855	−	0.301126i
$237$	3.24951			0.211078
$238$	−1.68675	−	2.79223i	−0.109336	−	0.180994i
$239$	6.29887			0.407440			0.203720	−	0.979029i	$-0.434697\pi$
$239$	6.29887			0.407440			0.203720	+	0.979029i	$0.434697\pi$
$240$	0.404687	−	0.700939i	0.0261224	−	0.0452454i
$241$	−4.74977	−	8.22684i	−0.305959	−	0.529937i	0.671515	−	0.740991i	$-0.265644\pi$
$241$	−4.74977	−	8.22684i	−0.305959	−	0.529937i	−0.977474	+	0.211054i	$0.932311\pi$
$242$	4.76873	+	8.25968i	0.306546	+	0.530953i
$243$	−3.91908	+	6.78805i	−0.251409	+	0.435454i
$244$	−1.85948			−0.119041
$245$	9.99968	+	15.8355i	0.638856	+	1.01170i
$246$	−0.302513			−0.0192875
$247$	−15.2739	+	26.4551i	−0.971854	+	1.68330i
$248$	−0.418749	−	0.725295i	−0.0265906	−	0.0460563i
$249$	−1.26166	−	2.18526i	−0.0799544	−	0.138485i
$250$	3.80145	−	6.58431i	0.240425	−	0.416428i
$251$	−11.1562			−0.704173			−0.352087	−	0.935967i	$-0.614528\pi$
$251$	−11.1562			−0.704173			−0.352087	+	0.935967i	$0.614528\pi$
$252$	3.97888	+	6.58662i	0.250646	+	0.414918i
$253$	−19.5813			−1.23106
$254$	1.11606	−	1.93308i	0.0700280	−	0.121292i
$255$	−0.498972	−	0.864244i	−0.0312468	−	0.0541211i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−6.82745	+	11.8255i	−0.425884	+	0.737653i	−0.996503	−	0.0835622i	$-0.973370\pi$
$257$	−6.82745	+	11.8255i	−0.425884	+	0.737653i	0.570618	+	0.821215i	$0.306704\pi$
$258$	0.0581070			0.00361758
$259$	−28.2682	+	0.560348i	−1.75650	+	0.0348183i
$260$	15.0130			0.931069
$261$	−3.82942	+	6.63275i	−0.237035	+	0.410557i
$262$	−10.5170	−	18.2160i	−0.649743	−	1.12539i
$263$	−2.71566	−	4.70366i	−0.167455	−	0.290040i	0.770070	−	0.637960i	$-0.220221\pi$
$263$	−2.71566	−	4.70366i	−0.167455	−	0.290040i	−0.937524	+	0.347920i	$0.886888\pi$
$264$	−0.685468	+	1.18726i	−0.0421876	+	0.0730711i
$265$	−19.0167			−1.16819
$266$	−6.95308	+	12.6140i	−0.426321	+	0.773414i
$267$	0.618119			0.0378283
$268$	7.93703	−	13.7473i	0.484831	−	0.839752i
$269$	−9.68182	−	16.7694i	−0.590311	−	1.02245i	−0.994190	−	0.107636i	$-0.965672\pi$
$269$	−9.68182	−	16.7694i	−0.590311	−	1.02245i	0.403879	−	0.914812i	$-0.367662\pi$
$270$	2.39109	+	4.14149i	0.145517	+	0.252043i
$271$	−7.82888	+	13.5600i	−0.475571	+	0.823713i	−0.999608	−	0.0279822i	$-0.991092\pi$
$271$	−7.82888	+	13.5600i	−0.475571	+	0.823713i	0.524038	+	0.851695i	$0.324425\pi$
$272$	−1.23298			−0.0747604
$273$	2.16804	−	3.93317i	0.131216	−	0.238046i
$274$	3.54818			0.214353
$275$	4.89058	−	8.47074i	0.294913	−	0.510805i
$276$	−0.653553	−	1.13199i	−0.0393393	−	0.0681376i
$277$	−0.722191	−	1.25087i	−0.0433923	−	0.0751576i	0.843514	−	0.537108i	$-0.180483\pi$
$277$	−0.722191	−	1.25087i	−0.0433923	−	0.0751576i	−0.886906	+	0.461950i	$0.847150\pi$
$278$	−1.40187	+	2.42811i	−0.0840787	+	0.145629i
$279$	2.43585			0.145831
$280$	7.07733	−	0.140291i	0.422951	−	0.00838397i
$281$	−9.76875			−0.582755			−0.291377	−	0.956608i	$-0.594113\pi$
$281$	−9.76875			−0.582755			−0.291377	+	0.956608i	$0.594113\pi$
$282$	−1.39885	+	2.42289i	−0.0833005	+	0.144281i
$283$	9.43527	+	16.3424i	0.560869	+	0.971453i	0.997421	+	0.0717742i	$0.0228661\pi$
$283$	9.43527	+	16.3424i	0.560869	+	0.971453i	−0.436552	+	0.899679i	$0.643801\pi$
$284$	−5.99010	−	10.3752i	−0.355447	−	0.615652i
$285$	−2.20311	+	3.81590i	−0.130501	+	0.226034i
$286$	−25.4294			−1.50367
$287$	−1.36803	−	2.26462i	−0.0807520	−	0.133676i
$288$	2.90849			0.171384
$289$	7.73988	−	13.4059i	0.455287	−	0.788580i
$290$	3.52267	+	6.10144i	0.206858	+	0.358289i
$291$	0.364036	+	0.630528i	0.0213401	+	0.0369622i
$292$	−4.35479	+	7.54272i	−0.254845	+	0.441404i
$293$	7.66092			0.447556			0.223778	−	0.974640i	$-0.428161\pi$
$293$	7.66092			0.447556			0.223778	+	0.974640i	$0.428161\pi$
$294$	0.985287	−	1.87440i	0.0574631	−	0.109318i
$295$	14.2915			0.832085
$296$	−5.34324	+	9.25477i	−0.310570	+	0.537923i
$297$	−4.05008	−	7.01494i	−0.235009	−	0.407048i
$298$	−0.0151425	−	0.0262276i	−0.000877182	−	0.00151932i
$299$	12.1227	−	20.9972i	0.701075	−	1.21430i
$300$	0.652922			0.0376964
$301$	0.262772	+	0.434991i	0.0151459	+	0.0250725i
$302$	17.2199			0.990895
$303$	2.15269	−	3.72856i	0.123669	−	0.214200i
$304$	2.72199	+	4.71462i	0.156117	+	0.270402i
$305$	−2.48753	−	4.30852i	−0.142435	−	0.246705i
$306$	1.79305	−	3.10566i	0.102502	−	0.177539i
$307$	−3.85361			−0.219937			−0.109969	−	0.993935i	$-0.535075\pi$
$307$	−3.85361			−0.219937			−0.109969	+	0.993935i	$0.535075\pi$
$308$	−11.9877	+	0.237627i	−0.683065	+	0.0135401i
$309$	−3.76335			−0.214090
$310$	1.12037	−	1.94053i	0.0636325	−	0.110215i
$311$	0.475953	+	0.824375i	0.0269888	+	0.0467460i	0.879204	−	0.476445i	$-0.158075\pi$
$311$	0.475953	+	0.824375i	0.0269888	+	0.0467460i	−0.852216	+	0.523191i	$0.824741\pi$
$312$	−0.848744	−	1.47007i	−0.0480506	−	0.0832262i
$313$	11.8927	−	20.5987i	0.672213	−	1.16431i	−0.305062	−	0.952332i	$-0.598677\pi$
$313$	11.8927	−	20.5987i	0.672213	−	1.16431i	0.977275	−	0.211975i	$-0.0679894\pi$
$314$	−18.3765			−1.03705
$315$	−9.93879	+	18.0306i	−0.559987	+	1.01591i
$316$	10.7417			0.604269
$317$	3.72119	−	6.44528i	0.209003	−	0.362003i	−0.742398	−	0.669959i	$-0.766312\pi$
$317$	3.72119	−	6.44528i	0.209003	−	0.362003i	0.951401	+	0.307956i	$0.0996450\pi$
$318$	1.07509	+	1.86211i	0.0602879	+	0.104422i
$319$	−5.96677	−	10.3348i	−0.334075	−	0.578635i
$320$	1.33775	−	2.31706i	0.0747826	−	0.129527i
$321$	2.04479			0.114129
$322$	5.51859	−	10.0116i	0.307539	−	0.557925i
$323$	6.71232			0.373484
$324$	−4.09237	+	7.08820i	−0.227354	+	0.393789i
$325$	6.05550	+	10.4884i	0.335899	+	0.581794i
$326$	−1.52952	−	2.64920i	−0.0847121	−	0.146726i
$327$	1.23897	−	2.14595i	0.0685150	−	0.118671i
$328$	−1.00000			−0.0552158
$329$	−24.4637	+	0.484933i	−1.34873	+	0.0267352i
$330$	−3.66795			−0.201914
$331$	−10.1635	+	17.6036i	−0.558634	+	0.967583i	0.438977	+	0.898499i	$0.355341\pi$
$331$	−10.1635	+	17.6036i	−0.558634	+	0.967583i	−0.997611	+	0.0690844i	$0.977992\pi$
$332$	−4.17060	−	7.22369i	−0.228891	−	0.396452i
$333$	−15.5408	−	26.9174i	−0.851628	−	1.47506i
$334$	−4.94024	+	8.55675i	−0.270318	+	0.468205i
$335$	42.4711			2.32044
$336$	−0.413845	−	0.685076i	−0.0225771	−	0.0373740i
$337$	−32.6366			−1.77783			−0.888914	−	0.458075i	$-0.848539\pi$
$337$	−32.6366			−1.77783			−0.888914	+	0.458075i	$0.848539\pi$
$338$	9.24330	−	16.0099i	0.502769	−	0.870822i
$339$	−1.85835	−	3.21875i	−0.100932	−	0.174819i
$340$	−1.64942	−	2.85689i	−0.0894525	−	0.154936i
$341$	−1.89770	+	3.28691i	−0.102766	+	0.177996i
$342$	−15.8337			−0.856191
$343$	18.4875	−	1.10056i	0.998233	−	0.0594248i
$344$	0.192081			0.0103563
$345$	1.74858	−	3.02864i	0.0941406	−	0.163056i
$346$	−5.83869	−	10.1129i	−0.313890	−	0.543673i
$347$	−17.4883	−	30.2907i	−0.938824	−	1.62609i	−0.767669	−	0.640846i	$-0.778584\pi$
$347$	−17.4883	−	30.2907i	−0.938824	−	1.62609i	−0.171154	−	0.985244i	$-0.554750\pi$
$348$	0.398300	−	0.689875i	0.0213511	−	0.0369812i
$349$	−2.25155			−0.120523			−0.0602614	−	0.998183i	$-0.519193\pi$
$349$	−2.25155			−0.120523			−0.0602614	+	0.998183i	$0.519193\pi$
$350$	2.95265	+	4.88779i	0.157826	+	0.261264i
$351$	10.0296			0.535339
$352$	−2.26591	+	3.92468i	−0.120774	+	0.209186i
$353$	15.3110	+	26.5194i	0.814921	+	1.41149i	0.909384	+	0.415957i	$0.136553\pi$
$353$	15.3110	+	26.5194i	0.814921	+	1.41149i	−0.0944629	+	0.995528i	$0.530113\pi$
$354$	−0.807954	−	1.39942i	−0.0429423	−	0.0743782i
$355$	16.0265	−	27.7588i	0.850601	−	1.47328i
$356$	2.04328			0.108294
$357$	−0.986651	+	0.0195579i	−0.0522191	+	0.00103512i
$358$	−7.20884			−0.380999
$359$	9.58504	−	16.6018i	0.505879	−	0.876208i	−0.494098	−	0.869406i	$-0.664502\pi$
$359$	9.58504	−	16.6018i	0.505879	−	0.876208i	0.999977	−	0.00680197i	$-0.00216515\pi$
$360$	3.89083	+	6.73912i	0.205065	+	0.355183i
$361$	−5.31846	−	9.21184i	−0.279919	−	0.484834i
$362$	−8.60017	+	14.8959i	−0.452015	+	0.782913i
$363$	2.88520			0.151434
$364$	7.16677	−	13.0017i	0.375641	−	0.681473i
$365$	−23.3025			−1.21971
$366$	−0.281258	+	0.487154i	−0.0147016	+	0.0254639i
$367$	15.1512	+	26.2427i	0.790887	+	1.36986i	0.925419	+	0.378947i	$0.123714\pi$
$367$	15.1512	+	26.2427i	0.790887	+	1.36986i	−0.134532	+	0.990909i	$0.542953\pi$
$368$	−2.16041	−	3.74195i	−0.112619	−	0.195063i
$369$	1.45424	−	2.51882i	0.0757049	−	0.131125i
$370$	−28.5918			−1.48641
$371$	−9.07801	+	16.4690i	−0.471307	+	0.855026i
$372$	−0.253354			−0.0131358
$373$	−14.2836	+	24.7399i	−0.739575	+	1.28098i	0.213112	+	0.977028i	$0.431640\pi$
$373$	−14.2836	+	24.7399i	−0.739575	+	1.28098i	−0.952687	+	0.303954i	$0.901693\pi$
$374$	2.79383	+	4.83905i	0.144465	+	0.250221i
$375$	−1.14999	−	1.99184i	−0.0593851	−	0.102858i
$376$	−4.62412	+	8.00920i	−0.238471	+	0.413043i
$377$	14.7761			0.761006
$378$	4.72807	−	0.0937222i	0.243185	−	0.00482055i
$379$	−33.0736			−1.69888			−0.849439	−	0.527687i	$-0.823060\pi$
$379$	−33.0736			−1.69888			−0.849439	+	0.527687i	$0.823060\pi$
$380$	−7.28270	+	12.6140i	−0.373595	+	0.647085i
$381$	−0.337623	−	0.584781i	−0.0172970	−	0.0299592i
$382$	4.57262	+	7.92001i	0.233956	+	0.405223i
$383$	−8.50365	+	14.7287i	−0.434516	+	0.752604i	−0.997256	−	0.0740301i	$-0.976414\pi$
$383$	−8.50365	+	14.7287i	−0.434516	+	0.752604i	0.562740	+	0.826634i	$0.309747\pi$
$384$	−0.302513			−0.0154375
$385$	−16.5872	−	27.4584i	−0.845363	−	1.39941i
$386$	13.4178			0.682950
$387$	−0.279333	+	0.483818i	−0.0141993	+	0.0245939i
$388$	1.20337	+	2.08430i	0.0610920	+	0.105814i
$389$	−10.1342	−	17.5529i	−0.513824	−	0.889969i	−0.999871	−	0.0160368i	$-0.994895\pi$
$389$	−10.1342	−	17.5529i	−0.513824	−	0.889969i	0.486047	−	0.873932i	$-0.338438\pi$
$390$	2.27082	−	3.93317i	0.114987	−	0.199164i
$391$	−5.32750			−0.269423
$392$	3.25701	−	6.19612i	0.164504	−	0.312951i
$393$	−6.36306			−0.320974
$394$	−8.18965	+	14.1849i	−0.412589	+	0.714625i
$395$	14.3698	+	24.8892i	0.723021	+	1.25231i
$396$	−6.59038	−	11.4149i	−0.331179	−	0.573619i
$397$	5.46001	−	9.45701i	0.274030	−	0.474634i	−0.695860	−	0.718177i	$-0.744977\pi$
$397$	5.46001	−	9.45701i	0.274030	−	0.474634i	0.969890	+	0.243544i	$0.0783099\pi$
$398$	11.7741			0.590183
$399$	2.25297	+	3.72954i	0.112789	+	0.186711i
$400$	2.15833			0.107916
$401$	6.66417	−	11.5427i	0.332793	−	0.576414i	−0.650265	−	0.759707i	$-0.725342\pi$
$401$	6.66417	−	11.5427i	0.332793	−	0.576414i	0.983058	+	0.183293i	$0.0586757\pi$
$402$	−2.40105	−	4.15874i	−0.119754	−	0.207419i
$403$	−2.34973	−	4.06984i	−0.117048	−	0.202733i
$404$	7.11602	−	12.3253i	0.354035	−	0.613207i
$405$	−21.8983			−1.08814
$406$	6.96562	−	0.138076i	0.345698	−	0.00685261i
$407$	48.4293			2.40055
$408$	−0.186496	+	0.323021i	−0.00923294	+	0.0159919i
$409$	9.40545	+	16.2907i	0.465070	+	0.805524i	0.999205	−	0.0398749i	$-0.0126959\pi$
$409$	9.40545	+	16.2907i	0.465070	+	0.805524i	−0.534135	+	0.845399i	$0.679363\pi$
$410$	−1.33775	−	2.31706i	−0.0660669	−	0.114431i
$411$	0.536685	−	0.929566i	0.0264727	−	0.0458521i
$412$	−12.4403			−0.612890
$413$	6.82235	−	12.3768i	0.335706	−	0.609024i
$414$	12.5671			0.617638
$415$	11.1585	−	19.3270i	0.547747	−	0.948726i
$416$	−2.80565	−	4.85952i	−0.137558	−	0.238258i
$417$	0.424084	+	0.734536i	0.0207675	+	0.0359704i
$418$	12.3356	−	21.3659i	0.603353	−	1.04504i
$419$	8.19107			0.400160			0.200080	−	0.979780i	$-0.435880\pi$
$419$	8.19107			0.400160			0.200080	+	0.979780i	$0.435880\pi$
$420$	1.03374	−	1.87537i	0.0504412	−	0.0915085i
$421$	40.6667			1.98198			0.990988	−	0.133951i	$-0.0427665\pi$
$421$	40.6667			1.98198			0.990988	+	0.133951i	$0.0427665\pi$
$422$	9.16566	−	15.8754i	0.446177	−	0.772802i
$423$	−13.4492	−	23.2947i	−0.653921	−	1.13263i
$424$	3.55386	+	6.15546i	0.172591	+	0.298936i
$425$	1.33059	−	2.30465i	0.0645430	−	0.111792i
$426$	−3.62416			−0.175591
$427$	−4.91876	+	0.0975022i	−0.238035	+	0.00471846i
$428$	6.75937			0.326726
$429$	−3.84636	+	6.66209i	−0.185704	+	0.321649i
$430$	0.256957	+	0.445063i	0.0123916	+	0.0214628i
$431$	5.42268	+	9.39235i	0.261201	+	0.452414i	0.966561	−	0.256435i	$-0.0825481\pi$
$431$	5.42268	+	9.39235i	0.261201	+	0.452414i	−0.705360	+	0.708849i	$0.749215\pi$
$432$	0.893696	−	1.54793i	0.0429980	−	0.0744747i
$433$	−12.5834			−0.604719			−0.302360	−	0.953194i	$-0.597774\pi$
$433$	−12.5834			−0.604719			−0.302360	+	0.953194i	$0.597774\pi$
$434$	−1.14572	−	1.89662i	−0.0549963	−	0.0910405i
$435$	2.13130			0.102188
$436$	4.09558	−	7.09376i	0.196143	−	0.339730i
$437$	11.7613	+	20.3711i	0.562617	+	0.974481i
$438$	1.31738	+	2.28177i	0.0629468	+	0.109027i
$439$	−15.1512	+	26.2426i	−0.723126	+	1.25249i	0.236615	+	0.971604i	$0.423962\pi$
$439$	−15.1512	+	26.2426i	−0.723126	+	1.25249i	−0.959741	+	0.280887i	$0.909371\pi$
$440$	−12.1249			−0.578033
$441$	10.8704	+	17.2145i	0.517640	+	0.819738i
$442$	−6.91862			−0.329085
$443$	10.0280	−	17.3691i	0.476447	−	0.825230i	−0.523189	−	0.852217i	$-0.675258\pi$
$443$	10.0280	−	17.3691i	0.476447	−	0.825230i	0.999636	+	0.0269868i	$0.00859122\pi$
$444$	1.61640	+	2.79969i	0.0767109	+	0.132867i
$445$	2.73341	+	4.73440i	0.129576	+	0.224432i
$446$	−9.82229	+	17.0127i	−0.465099	+	0.805575i
$447$	−0.00916161			−0.000433329
$448$	−1.36803	−	2.26462i	−0.0646332	−	0.106993i
$449$	35.2349			1.66284			0.831420	−	0.555645i	$-0.187529\pi$
$449$	35.2349			1.66284			0.831420	+	0.555645i	$0.187529\pi$
$450$	−3.13873	+	5.43645i	−0.147961	+	0.256276i
$451$	2.26591	+	3.92468i	0.106698	+	0.184806i
$452$	−6.14304	−	10.6400i	−0.288944	−	0.500466i
$453$	2.60462	−	4.51134i	0.122376	−	0.211961i
$454$	8.78493			0.412297
$455$	39.7130	−	0.787212i	1.86177	−	0.0369050i
$456$	1.64687			0.0771219
$457$	−16.9532	+	29.3638i	−0.793036	+	1.37358i	0.131042	+	0.991377i	$0.458168\pi$
$457$	−16.9532	+	29.3638i	−0.793036	+	1.37358i	−0.924079	+	0.382202i	$0.875166\pi$
$458$	3.44825	+	5.97254i	0.161126	+	0.279078i
$459$	−1.10191	−	1.90856i	−0.0514328	−	0.0890842i
$460$	5.78020	−	10.0116i	0.269503	−	0.466793i
$461$	12.2136			0.568845			0.284423	−	0.958699i	$-0.408198\pi$
$461$	12.2136			0.568845			0.284423	+	0.958699i	$0.408198\pi$
$462$	−1.75097	+	3.17653i	−0.0814623	+	0.147786i
$463$	−9.17302			−0.426306			−0.213153	−	0.977019i	$-0.568373\pi$
$463$	−9.17302			−0.426306			−0.213153	+	0.977019i	$0.568373\pi$
$464$	1.31664	−	2.28048i	0.0611233	−	0.105869i
$465$	−0.338925	−	0.587035i	−0.0157173	−	0.0272231i
$466$	15.2116	+	26.3473i	0.704665	+	1.22052i
$467$	−8.65156	+	14.9849i	−0.400346	+	0.693420i	−0.993768	−	0.111472i	$-0.964444\pi$
$467$	−8.65156	+	14.9849i	−0.400346	+	0.693420i	0.593421	+	0.804892i	$0.297777\pi$
$468$	16.3204			0.754409
$469$	20.2744	−	36.7811i	0.936186	−	1.69839i
$470$	−24.7437			−1.14134
$471$	−2.77957	+	4.81435i	−0.128076	+	0.221833i
$472$	−2.67081	−	4.62598i	−0.122934	−	0.212928i
$473$	−0.435239	−	0.753857i	−0.0200123	−	0.0346624i
$474$	1.62475	−	2.81415i	0.0746274	−	0.129258i
$475$	−11.7499			−0.539122
$476$	−3.26152	+	0.0646516i	−0.149492	+	0.00296330i
$477$	−20.6727			−0.946537
$478$	3.14943	−	5.45498i	0.144052	−	0.249505i
$479$	−19.3213	−	33.4655i	−0.882813	−	1.52908i	−0.848200	−	0.529677i	$-0.822313\pi$
$479$	−19.3213	−	33.4655i	−0.882813	−	1.52908i	−0.0346139	−	0.999401i	$-0.511020\pi$
$480$	−0.404687	−	0.700939i	−0.0184714	−	0.0319933i
$481$	−29.9825	+	51.9312i	−1.36708	+	2.36786i
$482$	−9.49953			−0.432692
$483$	−1.78815	−	2.96010i	−0.0813639	−	0.134689i
$484$	9.53746			0.433521
$485$	−3.21963	+	5.57656i	−0.146196	+	0.253219i
$486$	3.91908	+	6.78805i	0.177773	+	0.307912i
$487$	7.53797	+	13.0561i	0.341578	+	0.591630i	0.984726	−	0.174112i	$-0.0557054\pi$
$487$	7.53797	+	13.0561i	0.341578	+	0.591630i	−0.643148	+	0.765742i	$0.722372\pi$
$488$	−0.929740	+	1.61036i	−0.0420874	+	0.0728975i
$489$	−0.925397			−0.0418479
$490$	18.7138	−	0.742202i	0.845404	−	0.0335293i
$491$	−2.05333			−0.0926653			−0.0463327	−	0.998926i	$-0.514753\pi$
$491$	−2.05333			−0.0926653			−0.0463327	+	0.998926i	$0.514753\pi$
$492$	−0.151256	+	0.261984i	−0.00681916	+	0.0118111i
$493$	−1.62339	−	2.81179i	−0.0731137	−	0.126637i
$494$	15.2739	+	26.4551i	0.687204	+	1.19027i
$495$	17.6326	−	30.5405i	0.792526	−	1.37270i
$496$	−0.837499			−0.0376048
$497$	−16.3892	−	27.1306i	−0.735157	−	1.21697i
$498$	−2.52332			−0.113073
$499$	3.44733	−	5.97095i	0.154324	−	0.267297i	−0.778489	−	0.627658i	$-0.784013\pi$
$499$	3.44733	−	5.97095i	0.154324	−	0.267297i	0.932813	+	0.360362i	$0.117347\pi$
$500$	−3.80145	−	6.58431i	−0.170006	−	0.294459i
$501$	1.49449	+	2.58853i	0.0667687	+	0.115647i
$502$	−5.57810	+	9.66156i	−0.248963	+	0.431216i
$503$	−29.2548			−1.30441			−0.652204	−	0.758043i	$-0.726156\pi$
$503$	−29.2548			−1.30441			−0.652204	+	0.758043i	$0.726156\pi$
$504$	7.69362	−	0.152507i	0.342701	−	0.00679320i
$505$	38.0779			1.69444
$506$	−9.79063	+	16.9579i	−0.435246	+	0.753869i
$507$	−2.79622	−	4.84319i	−0.124184	−	0.215094i
$508$	−1.11606	−	1.93308i	−0.0495173	−	0.0857665i
$509$	8.08608	−	14.0055i	0.358409	−	0.620783i	−0.629286	−	0.777174i	$-0.716653\pi$
$509$	8.08608	−	14.0055i	0.358409	−	0.620783i	0.987695	+	0.156391i	$0.0499859\pi$
$510$	−0.997943			−0.0441897
$511$	−11.1239	+	20.1806i	−0.492093	+	0.892736i
$512$	−1.00000			−0.0441942
$513$	−4.86526	+	8.42688i	−0.214807	+	0.372056i
$514$	6.82745	+	11.8255i	0.301146	+	0.521600i
$515$	−16.6421	−	28.8249i	−0.733337	−	1.27018i
$516$	0.0290535	−	0.0503221i	0.00127901	−	0.00221531i
$517$	41.9114			1.84326
$518$	−13.6488	+	24.7612i	−0.599696	+	1.08794i
$519$	−3.53256			−0.155062
$520$	7.50652	−	13.0017i	0.329183	−	0.570161i
$521$	6.06447	+	10.5040i	0.265689	+	0.460188i	0.967744	−	0.251936i	$-0.0810671\pi$
$521$	6.06447	+	10.5040i	0.265689	+	0.460188i	−0.702055	+	0.712123i	$0.747734\pi$
$522$	3.82942	+	6.63275i	0.167609	+	0.290308i
$523$	−1.07584	+	1.86342i	−0.0470434	+	0.0814816i	−0.888588	−	0.458706i	$-0.848313\pi$
$523$	−1.07584	+	1.86342i	−0.0470434	+	0.0814816i	0.841545	+	0.540187i	$0.181647\pi$
$524$	−21.0340			−0.918875
$525$	1.72713	−	0.0342361i	0.0753781	−	0.00149418i
$526$	−5.43132			−0.236817
$527$	−0.516310	+	0.894275i	−0.0224908	+	0.0389552i
$528$	0.685468	+	1.18726i	0.0298312	+	0.0516691i
$529$	2.16522	+	3.75027i	0.0941399	+	0.163055i
$530$	−9.50836	+	16.4690i	−0.413017	+	0.715366i
$531$	15.5360			0.674206
$532$	7.44751	+	12.3285i	0.322890	+	0.534510i
$533$	−5.61129			−0.243052
$534$	0.309059	−	0.535307i	0.0133743	−	0.0231650i
$535$	9.04236	+	15.6618i	0.390935	+	0.677120i
$536$	−7.93703	−	13.7473i	−0.342827	−	0.593794i
$537$	−1.09038	+	1.88860i	−0.0470535	+	0.0814991i
$538$	−19.3636			−0.834826
$539$	−31.6979	+	1.25716i	−1.36532	+	0.0541496i
$540$	4.78218			0.205792
$541$	7.43179	−	12.8722i	0.319517	−	0.553421i	−0.660870	−	0.750500i	$-0.729813\pi$
$541$	7.43179	−	12.8722i	0.319517	−	0.553421i	0.980387	+	0.197080i	$0.0631459\pi$
$542$	7.82888	+	13.5600i	0.336279	+	0.582453i
$543$	2.60166	+	4.50621i	0.111648	+	0.193380i
$544$	−0.616490	+	1.06779i	−0.0264318	+	0.0457812i
$545$	21.9155			0.938758
$546$	−2.32221	−	3.84416i	−0.0993813	−	0.164515i
$547$	−6.71360			−0.287053			−0.143526	−	0.989646i	$-0.545844\pi$
$547$	−6.71360			−0.287053			−0.143526	+	0.989646i	$0.545844\pi$
$548$	1.77409	−	3.07281i	0.0757854	−	0.131264i
$549$	−2.70414	−	4.68370i	−0.115410	−	0.199896i
$550$	−4.89058	−	8.47074i	−0.208535	−	0.361194i
$551$	−7.16775	+	12.4149i	−0.305356	+	0.528893i
$552$	−1.30711			−0.0556341
$553$	28.4143	−	0.563244i	1.20830	−	0.0239516i
$554$	−1.44438			−0.0613659
$555$	−4.32469	+	7.49057i	−0.183573	+	0.317957i
$556$	1.40187	+	2.42811i	0.0594526	+	0.102975i
$557$	−12.9333	−	22.4011i	−0.548002	−	0.949167i	−0.998411	−	0.0563446i	$-0.982055\pi$
$557$	−12.9333	−	22.4011i	−0.548002	−	0.949167i	0.450410	−	0.892822i	$-0.351278\pi$
$558$	1.21793	−	2.10951i	0.0515590	−	0.0893027i
$559$	1.07782			0.0455871
$560$	3.41717	−	6.19929i	0.144402	−	0.261968i
$561$	1.69034			0.0713661
$562$	−4.88437	+	8.45998i	−0.206035	+	0.356863i
$563$	4.59020	+	7.95045i	0.193454	+	0.335072i	0.946393	−	0.323019i	$-0.104698\pi$
$563$	4.59020	+	7.95045i	0.193454	+	0.335072i	−0.752939	+	0.658091i	$0.771364\pi$
$564$	1.39885	+	2.42289i	0.0589024	+	0.102022i
$565$	16.4357	−	28.4675i	0.691456	−	1.19764i
$566$	18.8705			0.793188
$567$	−10.4536	+	18.9645i	−0.439010	+	0.796435i
$568$	−11.9802			−0.502678
$569$	−2.34087	+	4.05451i	−0.0981346	+	0.169974i	−0.910913	−	0.412600i	$-0.864621\pi$
$569$	−2.34087	+	4.05451i	−0.0981346	+	0.169974i	0.812778	+	0.582574i	$0.197954\pi$
$570$	2.20311	+	3.81590i	0.0922781	+	0.159830i
$571$	17.8545	+	30.9249i	0.747188	+	1.29417i	0.949165	+	0.314778i	$0.101930\pi$
$571$	17.8545	+	30.9249i	0.747188	+	1.29417i	−0.201977	+	0.979390i	$0.564737\pi$
$572$	−12.7147	+	22.0225i	−0.531629	+	0.920808i
$573$	2.76655			0.115574
$574$	−2.64523	+	0.0524352i	−0.110410	+	0.00218860i
$575$	9.32576			0.388911
$576$	1.45424	−	2.51882i	0.0605935	−	0.104951i
$577$	−10.3837	−	17.9852i	−0.432281	−	0.748733i	0.564788	−	0.825236i	$-0.308958\pi$
$577$	−10.3837	−	17.9852i	−0.432281	−	0.748733i	−0.997069	+	0.0765032i	$0.975624\pi$
$578$	−7.73988	−	13.4059i	−0.321937	−	0.557610i
$579$	2.02953	−	3.51525i	0.0843445	−	0.146089i
$580$	7.04534			0.292542
$581$	−11.4110	−	18.8897i	−0.473407	−	0.783675i
$582$	0.728071			0.0301795
$583$	16.1055	−	27.8955i	0.667020	−	1.15531i
$584$	4.35479	+	7.54272i	0.180203	+	0.312120i
$585$	21.8326	+	37.8152i	0.902667	+	1.56347i
$586$	3.83046	−	6.63455i	0.158235	−	0.274071i
$587$	−3.24039			−0.133745			−0.0668727	−	0.997762i	$-0.521302\pi$
$587$	−3.24039			−0.133745			−0.0668727	+	0.997762i	$0.521302\pi$
$588$	−1.13064	−	1.79049i	−0.0466268	−	0.0738384i
$589$	4.55933			0.187864
$590$	7.14577	−	12.3768i	0.294187	−	0.509546i
$591$	2.47747	+	4.29111i	0.101910	+	0.176513i
$592$	5.34324	+	9.25477i	0.219606	+	0.380369i
$593$	3.20981	−	5.55955i	0.131811	−	0.228304i	−0.792564	−	0.609789i	$-0.791254\pi$
$593$	3.20981	−	5.55955i	0.131811	−	0.228304i	0.924375	+	0.381486i	$0.124587\pi$
$594$	−8.10015			−0.332353
$595$	−4.51291	−	7.47064i	−0.185011	−	0.306266i
$596$	−0.0302850			−0.00124052
$597$	1.78091	−	3.08463i	0.0728878	−	0.126245i
$598$	−12.1227	−	20.9972i	−0.495735	−	0.858638i
$599$	9.40542	+	16.2907i	0.384295	+	0.665619i	0.991671	−	0.128796i	$-0.0411112\pi$
$599$	9.40542	+	16.2907i	0.384295	+	0.665619i	−0.607376	+	0.794414i	$0.707778\pi$
$600$	0.326461	−	0.565447i	0.0133277	−	0.0230843i
$601$	25.4939			1.03992			0.519959	−	0.854191i	$-0.325947\pi$
$601$	25.4939			1.03992			0.519959	+	0.854191i	$0.325947\pi$
$602$	0.508099	−	0.0100718i	0.0207086	−	0.000410496i
$603$	46.1695			1.88017
$604$	8.60996	−	14.9129i	0.350334	−	0.606797i
$605$	12.7588	+	22.0988i	0.518718	+	0.898445i
$606$	−2.15269	−	3.72856i	−0.0874469	−	0.151463i
$607$	−17.6654	+	30.5975i	−0.717018	+	1.24191i	0.245157	+	0.969483i	$0.421160\pi$
$607$	−17.6654	+	30.5975i	−0.717018	+	1.24191i	−0.962176	+	0.272429i	$0.912173\pi$
$608$	5.44398			0.220783
$609$	1.01742	−	1.84576i	0.0412280	−	0.0747941i
$610$	−4.97505			−0.201434
$611$	−25.9473	+	44.9420i	−1.04971	+	1.81816i
$612$	−1.79305	−	3.10566i	−0.0724799	−	0.125539i
$613$	4.17051	+	7.22353i	0.168445	+	0.291756i	0.937873	−	0.346978i	$-0.112792\pi$
$613$	4.17051	+	7.22353i	0.168445	+	0.291756i	−0.769428	+	0.638733i	$0.779459\pi$
$614$	−1.92681	+	3.33732i	−0.0777595	+	0.134683i
$615$	−0.809374			−0.0326371
$616$	−5.78808	+	10.5005i	−0.233208	+	0.423077i
$617$	18.8143			0.757435			0.378717	−	0.925512i	$-0.376365\pi$
$617$	18.8143			0.757435			0.378717	+	0.925512i	$0.376365\pi$
$618$	−1.88168	+	3.25916i	−0.0756921	+	0.131103i
$619$	15.4713	+	26.7971i	0.621844	+	1.07706i	0.989142	+	0.146962i	$0.0469494\pi$
$619$	15.4713	+	26.7971i	0.621844	+	1.07706i	−0.367299	+	0.930103i	$0.619717\pi$
$620$	−1.12037	−	1.94053i	−0.0449950	−	0.0779336i
$621$	3.86151	−	6.68833i	0.154957	−	0.268393i
$622$	0.951906			0.0381680
$623$	5.40496	−	0.107140i	0.216545	−	0.00429247i
$624$	−1.69749			−0.0679539
$625$	15.5666	−	26.9622i	0.622665	−	1.07849i
$626$	−11.8927	−	20.5987i	−0.475326	−	0.823289i
$627$	−3.73167	−	6.46345i	−0.149029	−	0.258125i
$628$	−9.18826	+	15.9145i	−0.366651	+	0.635059i
$629$	13.1762			0.525371
$630$	10.6455	+	17.6225i	0.424128	+	0.702098i
$631$	−14.4094			−0.573629			−0.286815	−	0.957986i	$-0.592596\pi$
$631$	−14.4094			−0.573629			−0.286815	+	0.957986i	$0.592596\pi$
$632$	5.37086	−	9.30260i	0.213641	−	0.370038i
$633$	−2.77273	−	4.80251i	−0.110206	−	0.190882i
$634$	−3.72119	−	6.44528i	−0.147787	−	0.255975i
$635$	2.98603	−	5.17196i	0.118497	−	0.205243i
$636$	2.15017			0.0852599
$637$	18.2760	−	34.7682i	0.724123	−	1.37757i
$638$	−11.9335			−0.472454
$639$	17.4221	−	30.1760i	0.689208	−	1.19374i
$640$	−1.33775	−	2.31706i	−0.0528793	−	0.0915897i
$641$	24.7015	+	42.7842i	0.975650	+	1.68987i	0.677774	+	0.735270i	$0.262945\pi$
$641$	24.7015	+	42.7842i	0.975650	+	1.68987i	0.297875	+	0.954605i	$0.403722\pi$
$642$	1.02240	−	1.77084i	0.0403508	−	0.0698896i
$643$	−0.960171			−0.0378655			−0.0189327	−	0.999821i	$-0.506027\pi$
$643$	−0.960171			−0.0378655			−0.0189327	+	0.999821i	$0.506027\pi$
$644$	−5.91101	−	9.78504i	−0.232926	−	0.385584i
$645$	0.155466			0.00612145
$646$	3.35616	−	5.81304i	0.132046	−	0.228711i
$647$	14.2146	+	24.6204i	0.558833	+	0.967926i	0.997594	+	0.0693230i	$0.0220839\pi$
$647$	14.2146	+	24.6204i	0.558833	+	0.967926i	−0.438762	+	0.898603i	$0.644583\pi$
$648$	4.09237	+	7.08820i	0.160764	+	0.278451i
$649$	−12.1037	+	20.9641i	−0.475110	+	0.822915i
$650$	12.1110			0.475033
$651$	−0.670180	+	0.0132847i	−0.0262664	+	0.000520667i
$652$	−3.05903			−0.119801
$653$	22.7865	−	39.4673i	0.891703	−	1.54447i	0.0538702	−	0.998548i	$-0.482844\pi$
$653$	22.7865	−	39.4673i	0.891703	−	1.54447i	0.837833	−	0.545927i	$-0.183822\pi$
$654$	−1.23897	−	2.14595i	−0.0484474	−	0.0839134i
$655$	−28.1383	−	48.7370i	−1.09945	−	1.90431i
$656$	−0.500000	+	0.866025i	−0.0195217	+	0.0338126i
$657$	−25.3317			−0.988284
$658$	−11.8119	+	21.4287i	−0.460476	+	0.835376i
$659$	−27.5301			−1.07242			−0.536211	−	0.844084i	$-0.680145\pi$
$659$	−27.5301			−1.07242			−0.536211	+	0.844084i	$0.680145\pi$
$660$	−1.83397	+	3.17653i	−0.0713873	+	0.123646i
$661$	18.2820	+	31.6653i	0.711087	+	1.23164i	0.964450	+	0.264267i	$0.0851301\pi$
$661$	18.2820	+	31.6653i	0.711087	+	1.23164i	−0.253363	+	0.967371i	$0.581537\pi$
$662$	10.1635	+	17.6036i	0.395014	+	0.684184i
$663$	−1.04648	+	1.81256i	−0.0406421	+	0.0703942i
$664$	−8.34120			−0.323701
$665$	−18.6030	+	33.7488i	−0.721394	+	1.30872i
$666$	−31.0815			−1.20438
$667$	5.68896	−	9.85357i	0.220278	−	0.381532i
$668$	4.94024	+	8.55675i	0.191144	+	0.331071i
$669$	2.97137	+	5.14656i	0.114880	+	0.198978i
$670$	21.2356	−	36.7811i	0.820401	−	1.42098i
$671$	8.42685			0.325315
$672$	−0.800216	+	0.0158623i	−0.0308690	+	0.000611902i
$673$	18.2388			0.703053			0.351526	−	0.936178i	$-0.385663\pi$
$673$	18.2388			0.703053			0.351526	+	0.936178i	$0.385663\pi$
$674$	−16.3183	+	28.2641i	−0.628557	+	1.08869i
$675$	1.92889	+	3.34093i	0.0742430	+	0.128593i
$676$	−9.24330	−	16.0099i	−0.355512	−	0.615764i
$677$	−3.20342	+	5.54848i	−0.123117	+	0.213245i	−0.920995	−	0.389573i	$-0.872622\pi$
$677$	−3.20342	+	5.54848i	−0.123117	+	0.213245i	0.797878	+	0.602819i	$0.205956\pi$
$678$	−3.71669			−0.142739
$679$	3.29249	+	5.45037i	0.126354	+	0.209166i
$680$	−3.29885			−0.126505
$681$	1.32878	−	2.30151i	0.0509188	−	0.0881940i
$682$	1.89770	+	3.28691i	0.0726667	+	0.125862i
$683$	−10.7307	−	18.5861i	−0.410598	−	0.711176i	0.584358	−	0.811496i	$-0.301347\pi$
$683$	−10.7307	−	18.5861i	−0.410598	−	0.711176i	−0.994955	+	0.100320i	$0.968013\pi$
$684$	−7.91687	+	13.7124i	−0.302709	+	0.524307i
$685$	9.49318			0.362716
$686$	8.29065	−	16.5610i	0.316538	−	0.632300i
$687$	2.08628			0.0795964
$688$	0.0960406	−	0.166347i	0.00366151	−	0.00634193i
$689$	19.9417	+	34.5401i	0.759719	+	1.31587i
$690$	−1.74858	−	3.02864i	−0.0665675	−	0.115298i
$691$	−11.7270	+	20.3117i	−0.446115	+	0.772695i	−0.998129	−	0.0611404i	$-0.980526\pi$
$691$	−11.7270	+	20.3117i	−0.446115	+	0.772695i	0.552014	+	0.833835i	$0.313860\pi$
$692$	−11.6774			−0.443907
$693$	−18.0316	−	29.8494i	−0.684965	−	1.13389i
$694$	−34.9767			−1.32770
$695$	−3.75072	+	6.49643i	−0.142273	+	0.246424i
$696$	−0.398300	−	0.689875i	−0.0150975	−	0.0261496i
$697$	0.616490	+	1.06779i	0.0233512	+	0.0404455i
$698$	−1.12578	+	1.94990i	−0.0426113	+	0.0738049i
$699$	9.20343			0.348106
$700$	5.70928	−	0.113172i	0.215790	−	0.00427751i
$701$	−28.1862			−1.06458			−0.532290	−	0.846562i	$-0.678668\pi$
$701$	−28.1862			−1.06458			−0.532290	+	0.846562i	$0.678668\pi$
$702$	5.01479	−	8.68587i	0.189271	−	0.327827i
$703$	−29.0885	−	50.3828i	−1.09709	−	1.90022i
$704$	2.26591	+	3.92468i	0.0853998	+	0.147917i
$705$	−3.74264	+	6.48244i	−0.140956	+	0.244143i
$706$	30.6220			1.15247
$707$	18.1772	−	32.9764i	0.683626	−	1.24021i
$708$	−1.61591			−0.0607296
$709$	2.95255	−	5.11397i	0.110885	−	0.192059i	−0.805242	−	0.592946i	$-0.797965\pi$
$709$	2.95255	−	5.11397i	0.110885	−	0.192059i	0.916127	+	0.400887i	$0.131298\pi$
$710$	−16.0265	−	27.7588i	−0.601465	−	1.04177i
$711$	15.6211	+	27.0565i	0.585836	+	1.01470i
$712$	1.02164	−	1.76953i	0.0382876	−	0.0663161i
$713$	−3.61869			−0.135521
$714$	−0.476388	+	0.864244i	−0.0178284	+	0.0323435i
$715$	−68.0365			−2.54442
$716$	−3.60442	+	6.24304i	−0.134704	+	0.233313i
$717$	−0.952744	−	1.65020i	−0.0355809	−	0.0616279i
$718$	−9.58504	−	16.6018i	−0.357711	−	0.619573i
$719$	−17.0073	+	29.4575i	−0.634265	+	1.09858i	0.352405	+	0.935848i	$0.385364\pi$
$719$	−17.0073	+	29.4575i	−0.634265	+	1.09858i	−0.986670	+	0.162732i	$0.947969\pi$
$720$	7.78167			0.290006
$721$	−32.9075	+	0.652310i	−1.22554	+	0.0242933i
$722$	−10.6369			−0.395865
$723$	−1.43686	+	2.48872i	−0.0534376	+	0.0925566i
$724$	8.60017	+	14.8959i	0.319623	+	0.553603i
$725$	2.84173	+	4.92203i	0.105539	+	0.182800i
$726$	1.44260	−	2.49866i	0.0535400	−	0.0927340i
$727$	24.5472			0.910405			0.455202	−	0.890388i	$-0.349567\pi$
$727$	24.5472			0.910405			0.455202	+	0.890388i	$0.349567\pi$
$728$	−7.67639	−	12.7074i	−0.284506	−	0.470969i
$729$	−22.1831			−0.821596
$730$	−11.6513	+	20.1806i	−0.431233	+	0.746917i
$731$	−0.118416	−	0.205103i	−0.00437978	−	0.00758600i
$732$	0.281258	+	0.487154i	0.0103956	+	0.0180057i
$733$	−19.1727	+	33.2082i	−0.708162	+	1.22657i	0.257377	+	0.966311i	$0.417142\pi$
$733$	−19.1727	+	33.2082i	−0.708162	+	1.22657i	−0.965538	+	0.260261i	$0.916191\pi$
$734$	30.3024			1.11848
$735$	2.63614	−	5.01498i	0.0972355	−	0.184980i
$736$	−4.32083			−0.159268
$737$	−35.9692	+	62.3005i	−1.32494	+	2.29487i
$738$	−1.45424	−	2.51882i	−0.0535314	−	0.0927191i
$739$	−11.1455	−	19.3045i	−0.409993	−	0.710129i	0.584895	−	0.811109i	$-0.301136\pi$
$739$	−11.1455	−	19.3045i	−0.409993	−	0.710129i	−0.994888	+	0.100980i	$0.967802\pi$
$740$	−14.2959	+	24.7612i	−0.525527	+	0.910239i
$741$	9.24109			0.339480
$742$	9.72354	+	16.0963i	0.356962	+	0.590913i
$743$	23.7524			0.871392			0.435696	−	0.900094i	$-0.356502\pi$
$743$	23.7524			0.871392			0.435696	+	0.900094i	$0.356502\pi$
$744$	−0.126677	+	0.219411i	−0.00464420	+	0.00804400i
$745$	−0.0405139	−	0.0701721i	−0.00148431	−	0.00257091i
$746$	14.2836	+	24.7399i	0.522959	+	0.905791i
$747$	12.1301	−	21.0100i	0.443818	−	0.768716i
$748$	5.58766			0.204305
$749$	17.8801	−	0.354429i	0.653324	−	0.0129505i
$750$	−2.29998			−0.0839833
$751$	−16.2939	+	28.2219i	−0.594574	+	1.02983i	0.399033	+	0.916937i	$0.369346\pi$
$751$	−16.2939	+	28.2219i	−0.594574	+	1.02983i	−0.993607	+	0.112896i	$0.963987\pi$
$752$	4.62412	+	8.00920i	0.168624	+	0.292066i
$753$	1.68745	+	2.92274i	0.0614940	+	0.106511i
$754$	7.38804	−	12.7965i	0.269056	−	0.466019i
$755$	46.0720			1.67673
$756$	2.28287	−	4.14149i	0.0830271	−	0.150624i
$757$	−22.8281			−0.829702			−0.414851	−	0.909889i	$-0.636166\pi$
$757$	−22.8281			−0.829702			−0.414851	+	0.909889i	$0.636166\pi$
$758$	−16.5368	+	28.6426i	−0.600644	+	1.04035i
$759$	2.96179	+	5.12997i	0.107506	+	0.186206i
$760$	7.28270	+	12.6140i	0.264171	+	0.457558i
$761$	24.3640	−	42.1997i	0.883195	−	1.52974i	0.0354256	−	0.999372i	$-0.488721\pi$
$761$	24.3640	−	42.1997i	0.883195	−	1.52974i	0.847769	−	0.530366i	$-0.177945\pi$
$762$	−0.675247			−0.0244616
$763$	10.4618	−	18.9794i	0.378743	−	0.687100i
$764$	9.14524			0.330863
$765$	4.79732	−	8.30921i	0.173448	−	0.300420i
$766$	8.50365	+	14.7287i	0.307249	+	0.532171i
$767$	−14.9867	−	25.9577i	−0.541138	−	0.937279i
$768$	−0.151256	+	0.261984i	−0.00545799	+	0.00945352i
$769$	21.9943			0.793135			0.396568	−	0.918006i	$-0.370201\pi$
$769$	21.9943			0.793135			0.396568	+	0.918006i	$0.370201\pi$
$770$	−32.0732	+	0.635773i	−1.15584	+	0.0229117i
$771$	4.13078			0.148766
$772$	6.70892	−	11.6202i	0.241459	−	0.418220i
$773$	−25.9012	−	44.8622i	−0.931602	−	1.61358i	−0.780585	−	0.625050i	$-0.785079\pi$
$773$	−25.9012	−	44.8622i	−0.931602	−	1.61358i	−0.151017	−	0.988531i	$-0.548255\pi$
$774$	0.279333	+	0.483818i	0.0100404	+	0.0173905i
$775$	0.903798	−	1.56542i	0.0324654	−	0.0562317i
$776$	2.40675			0.0863971
$777$	4.42255	+	7.32106i	0.158658	+	0.262642i
$778$	−20.2684			−0.726657
$779$	2.72199	−	4.71462i	0.0975254	−	0.168919i
$780$	−2.27082	−	3.93317i	−0.0813083	−	0.140830i
$781$	27.1461	+	47.0184i	0.971364	+	1.68245i
$782$	−2.66375	+	4.61375i	−0.0952555	+	0.164987i
$783$	4.70669			0.168204
$784$	−3.73749	−	5.91871i	−0.133482	−	0.211383i
$785$	−49.1665			−1.75483
$786$	−3.18153	+	5.51057i	−0.113481	+	0.196555i
$787$	−18.5814	−	32.1840i	−0.662357	−	1.14724i	−0.979995	−	0.199024i	$-0.936223\pi$
$787$	−18.5814	−	32.1840i	−0.662357	−	1.14724i	0.317638	−	0.948212i	$-0.397110\pi$
$788$	8.18965	+	14.1849i	0.291744	+	0.505316i
$789$	−0.821522	+	1.42292i	−0.0292470	+	0.0506572i
$790$	28.7395			1.02251
$791$	−16.8077	−	27.8233i	−0.597612	−	0.989282i
$792$	−13.1808			−0.468358
$793$	−5.21705	+	9.03619i	−0.185263	+	0.320884i
$794$	−5.46001	−	9.45701i	−0.193768	−	0.335617i
$795$	2.87640	+	4.98207i	0.102015	+	0.176696i
$796$	5.88706	−	10.1967i	0.208661	−	0.361412i
$797$	18.7534			0.664279			0.332139	−	0.943230i	$-0.392230\pi$
$797$	18.7534			0.664279			0.332139	+	0.943230i	$0.392230\pi$
$798$	4.35636	−	0.0863541i	0.154214	−	0.00305690i
$799$	11.4029			0.403405
$800$	1.07916	−	1.86917i	0.0381542	−	0.0660850i
$801$	2.97143	+	5.14667i	0.104990	+	0.181849i
$802$	−6.66417	−	11.5427i	−0.235320	−	0.407586i
$803$	19.7352	−	34.1823i	0.696439	−	1.20627i
$804$	−4.80210			−0.169357
$805$	14.7650	−	26.7861i	0.520398	−	0.944086i
$806$	−4.69945			−0.165531
$807$	−2.92887	+	5.07296i	−0.103101	+	0.178577i
$808$	−7.11602	−	12.3253i	−0.250341	−	0.433603i
$809$	−6.51382	−	11.2823i	−0.229014	−	0.396664i	0.728502	−	0.685043i	$-0.240217\pi$
$809$	−6.51382	−	11.2823i	−0.229014	−	0.396664i	−0.957516	+	0.288380i	$0.906883\pi$
$810$	−10.9492	+	18.9645i	−0.384715	+	0.666345i
$811$	−35.4164			−1.24364			−0.621819	−	0.783161i	$-0.713606\pi$
$811$	−35.4164			−1.24364			−0.621819	+	0.783161i	$0.713606\pi$
$812$	3.36323	−	6.10144i	0.118026	−	0.214119i
$813$	4.73667			0.166122
$814$	24.2147	−	41.9410i	0.848724	−	1.47003i
$815$	−4.09223	−	7.08795i	−0.143345	−	0.248280i
$816$	0.186496	+	0.323021i	0.00652867	+	0.0113080i
$817$	−0.522843	+	0.905591i	−0.0182920	+	0.0316826i
$818$	18.8109			0.657708
$819$	43.1711	−	0.855761i	1.50852	−	0.0299027i
$820$	−2.67551			−0.0934327
$821$	21.8902	−	37.9149i	0.763972	−	1.32324i	−0.176817	−	0.984244i	$-0.556580\pi$
$821$	21.8902	−	37.9149i	0.763972	−	1.32324i	0.940788	−	0.338994i	$-0.110087\pi$
$822$	−0.536685	−	0.929566i	−0.0187190	−	0.0324223i
$823$	−16.1159	−	27.9135i	−0.561764	−	0.973003i	−0.997343	−	0.0728528i	$-0.976790\pi$
$823$	−16.1159	−	27.9135i	−0.561764	−	0.973003i	0.435579	−	0.900151i	$-0.356544\pi$
$824$	−6.22016	+	10.7736i	−0.216689	+	0.375317i
$825$	−2.95893			−0.103017
$826$	−7.30748	−	12.0967i	−0.254260	−	0.420900i
$827$	12.4846			0.434132			0.217066	−	0.976157i	$-0.430351\pi$
$827$	12.4846			0.434132			0.217066	+	0.976157i	$0.430351\pi$
$828$	6.28354	−	10.8834i	0.218368	−	0.378224i
$829$	10.6931	+	18.5210i	0.371387	+	0.643262i	0.989779	−	0.142608i	$-0.0455489\pi$
$829$	10.6931	+	18.5210i	0.371387	+	0.643262i	−0.618392	+	0.785870i	$0.712216\pi$
$830$	−11.1585	−	19.3270i	−0.387316	−	0.670851i
$831$	−0.218472	+	0.378405i	−0.00757871	+	0.0131267i
$832$	−5.61129			−0.194537
$833$	−8.62409	+	0.342037i	−0.298807	+	0.0118509i
$834$	0.848169			0.0293697
$835$	−13.2176	+	22.8936i	−0.457415	+	0.792267i
$836$	−12.3356	−	21.3659i	−0.426635	−	0.738954i
$837$	−0.748469	−	1.29639i	−0.0258709	−	0.0448097i
$838$	4.09553	−	7.09367i	0.141478	−	0.245047i
$839$	−48.9609			−1.69032			−0.845159	−	0.534515i	$-0.820494\pi$
$839$	−48.9609			−1.69032			−0.845159	+	0.534515i	$0.820494\pi$
$840$	−1.10725	−	1.83293i	−0.0382036	−	0.0632419i
$841$	−22.0659			−0.760892
$842$	20.3334	−	35.2184i	0.700734	−	1.21371i
$843$	1.47758	+	2.55925i	0.0508907	+	0.0881453i
$844$	−9.16566	−	15.8754i	−0.315495	−	0.546453i
$845$	24.7305	−	42.8345i	0.850755	−	1.47355i
$846$	−26.8984			−0.924785
$847$	25.2288	−	0.500099i	0.866872	−	0.0171836i
$848$	7.10771			0.244080
$849$	2.85429	−	4.94378i	0.0979590	−	0.169670i
$850$	−1.33059	−	2.30465i	−0.0456388	−	0.0790487i
$851$	23.0872	+	39.9883i	0.791421	+	1.37078i
$852$	−1.81208	+	3.13862i	−0.0620809	+	0.107527i
$853$	−24.1910			−0.828284			−0.414142	−	0.910212i	$-0.635918\pi$
$853$	−24.1910			−0.828284			−0.414142	+	0.910212i	$0.635918\pi$
$854$	−2.37494	+	4.30852i	−0.0812688	+	0.147435i
$855$	−42.3633			−1.44879
$856$	3.37968	−	5.85378i	0.115515	−	0.200078i
$857$	23.7773	+	41.1836i	0.812218	+	1.40680i	0.911308	+	0.411725i	$0.135074\pi$
$857$	23.7773	+	41.1836i	0.812218	+	1.40680i	−0.0990896	+	0.995079i	$0.531593\pi$
$858$	3.84636	+	6.66209i	0.131313	+	0.227440i
$859$	13.8527	−	23.9937i	0.472649	−	0.818653i	−0.526861	−	0.849952i	$-0.676631\pi$
$859$	13.8527	−	23.9937i	0.472649	−	0.818653i	0.999510	+	0.0312989i	$0.00996437\pi$
$860$	0.513914			0.0175243
$861$	−0.386371	+	0.700939i	−0.0131675	+	0.0238879i
$862$	10.8454			0.369394
$863$	2.02805	−	3.51268i	0.0690355	−	0.119573i	−0.829441	−	0.558594i	$-0.811341\pi$
$863$	2.02805	−	3.51268i	0.0690355	−	0.119573i	0.898477	+	0.439021i	$0.144674\pi$
$864$	−0.893696	−	1.54793i	−0.0304042	−	0.0526615i
$865$	−15.6214	−	27.0571i	−0.531145	−	0.919970i
$866$	−6.29170	+	10.8975i	−0.213801	+	0.370313i
$867$	−4.68282			−0.159037
$868$	−2.21538	+	0.0439144i	−0.0751948	+	0.00149055i
$869$	−48.6796			−1.65134
$870$	1.06565	−	1.84576i	0.0361290	−	0.0625773i
$871$	−44.5370	−	77.1403i	−1.50908	−	2.61380i
$872$	−4.09558	−	7.09376i	−0.138694	−	0.240225i
$873$	−3.49999	+	6.06217i	−0.118457	+	0.205173i
$874$	23.5225			0.795661
$875$	−10.4010	−	17.2177i	−0.351617	−	0.582065i
$876$	2.63476			0.0890203
$877$	17.8434	−	30.9056i	0.602527	−	1.04361i	−0.389910	−	0.920853i	$-0.627494\pi$
$877$	17.8434	−	30.9056i	0.602527	−	1.04361i	0.992437	−	0.122755i	$-0.0391729\pi$
$878$	15.1512	+	26.2426i	0.511327	+	0.885645i
$879$	−1.15876	−	2.00704i	−0.0390841	−	0.0676957i
$880$	−6.06246	+	10.5005i	−0.204366	+	0.353972i
$881$	−53.2845			−1.79520			−0.897601	−	0.440809i	$-0.854692\pi$
$881$	−53.2845			−1.79520			−0.897601	+	0.440809i	$0.854692\pi$
$882$	20.3434	−	0.806833i	0.684998	−	0.0271675i
$883$	29.6827			0.998902			0.499451	−	0.866342i	$-0.333535\pi$
$883$	29.6827			0.998902			0.499451	+	0.866342i	$0.333535\pi$
$884$	−3.45931	+	5.99170i	−0.116349	+	0.201523i
$885$	−2.16169	−	3.74415i	−0.0726643	−	0.125858i
$886$	−10.0280	−	17.3691i	−0.336899	−	0.583526i
$887$	−7.49033	+	12.9736i	−0.251501	+	0.435612i	−0.963939	−	0.266123i	$-0.914257\pi$
$887$	−7.49033	+	12.9736i	−0.251501	+	0.435612i	0.712439	+	0.701734i	$0.247591\pi$
$888$	3.23280			0.108486
$889$	−3.05361	−	5.05492i	−0.102415	−	0.169537i
$890$	5.46681			0.183248
$891$	18.5459	−	32.1225i	0.621312	−	1.07614i
$892$	9.82229	+	17.0127i	0.328875	+	0.569628i
$893$	−25.1736	−	43.6019i	−0.842402	−	1.45908i
$894$	−0.00458080	+	0.00793418i	−0.000153205	+	0.000265359i
$895$	−19.2873			−0.644703
$896$	−2.64523	+	0.0524352i	−0.0883710	+	0.00175174i
$897$	−7.33455			−0.244894
$898$	17.6175	−	30.5144i	0.587903	−	1.01828i
$899$	−1.10268	−	1.90990i	−0.0367765	−	0.0636988i
$900$	3.13873	+	5.43645i	0.104624	+	0.181215i
$901$	4.38184	−	7.58957i	0.145980	−	0.252845i
$902$	4.53183			0.150893
$903$	0.0742146	−	0.134637i	0.00246971	−	0.00448044i
$904$	−12.2861			−0.408629
$905$	−23.0098	+	39.8542i	−0.764872	+	1.32480i
$906$	−2.60462	−	4.51134i	−0.0865328	−	0.149879i
$907$	−13.1130	−	22.7123i	−0.435409	−	0.754151i	0.561920	−	0.827192i	$-0.310063\pi$
$907$	−13.1130	−	22.7123i	−0.435409	−	0.754151i	−0.997329	+	0.0730410i	$0.976730\pi$
$908$	4.39247	−	7.60797i	0.145769	−	0.252480i
$909$	41.3937			1.37294
$910$	19.1747	−	34.7860i	0.635636	−	1.15315i
$911$	−10.6221			−0.351926			−0.175963	−	0.984397i	$-0.556304\pi$
$911$	−10.6221			−0.351926			−0.175963	+	0.984397i	$0.556304\pi$
$912$	0.823437	−	1.42623i	0.0272667	−	0.0472273i
$913$	18.9004	+	32.7365i	0.625513	+	1.08342i
$914$	16.9532	+	29.3638i	0.560761	+	0.971267i
$915$	−0.752508	+	1.30338i	−0.0248771	+	0.0430885i
$916$	6.89649			0.227867
$917$	−55.6398	+	1.10292i	−1.83739	+	0.0364217i
$918$	−2.20382			−0.0727369
$919$	−9.44462	+	16.3586i	−0.311549	+	0.539619i	−0.978698	−	0.205305i	$-0.934181\pi$
$919$	−9.44462	+	16.3586i	−0.311549	+	0.539619i	0.667149	+	0.744925i	$0.267515\pi$
$920$	−5.78020	−	10.0116i	−0.190568	−	0.330073i
$921$	0.582883	+	1.00958i	0.0192067	+	0.0332669i
$922$	6.10681	−	10.5773i	0.201117	−	0.348345i
$923$	−67.2244			−2.21272
$924$	1.87548	+	3.10465i	0.0616986	+	0.102135i
$925$	−23.0649			−0.758371
$926$	−4.58651	+	7.94407i	−0.150722	+	0.261058i
$927$	−18.0912	−	31.3349i	−0.594194	−	1.02917i
$928$	−1.31664	−	2.28048i	−0.0432207	−	0.0748605i
$929$	−4.68854	+	8.12078i	−0.153826	+	0.266434i	−0.932631	−	0.360832i	$-0.882493\pi$
$929$	−4.68854	+	8.12078i	−0.153826	+	0.266434i	0.778805	+	0.627266i	$0.215826\pi$
$930$	−0.677850			−0.0222276
$931$	20.3468	+	32.2214i	0.666840	+	1.05601i
$932$	30.4233			0.996547
$933$	0.143982	−	0.249384i	0.00471376	−	0.00816446i
$934$	8.65156	+	14.9849i	0.283088	+	0.490322i
$935$	7.47490	+	12.9469i	0.244455	+	0.423409i
$936$	8.16018	−	14.1339i	0.266724	−	0.461979i
$937$	−48.0417			−1.56945			−0.784727	−	0.619841i	$-0.787197\pi$
$937$	−48.0417			−1.56945			−0.784727	+	0.619841i	$0.787197\pi$
$938$	−21.7161	−	35.9487i	−0.709056	−	1.17377i
$939$	−7.19536			−0.234812
$940$	−12.3718	+	21.4287i	−0.403525	+	0.698926i
$941$	−3.31228	−	5.73703i	−0.107977	−	0.187022i	0.806974	−	0.590588i	$-0.201104\pi$
$941$	−3.31228	−	5.73703i	−0.107977	−	0.187022i	−0.914951	+	0.403566i	$0.867771\pi$
$942$	2.77957	+	4.81435i	0.0905631	+	0.156860i
$943$	−2.16041	+	3.74195i	−0.0703528	+	0.121855i
$944$	−5.34162			−0.173855
$945$	12.6500	−	0.250754i	0.411503	−	0.00815704i
$946$	−0.870479			−0.0283017
$947$	−19.0805	+	33.0483i	−0.620032	+	1.07393i	0.369447	+	0.929252i	$0.379547\pi$
$947$	−19.0805	+	33.0483i	−0.620032	+	1.07393i	−0.989479	+	0.144675i	$0.953786\pi$
$948$	−1.62475	−	2.81415i	−0.0527695	−	0.0913995i
$949$	24.4360	+	42.3244i	0.793226	+	1.37391i
$950$	−5.87495	+	10.1757i	−0.190608	+	0.330143i
$951$	−2.25141			−0.0730070
$952$	−1.57477	+	2.85689i	−0.0510386	+	0.0925922i
$953$	−5.36423			−0.173765			−0.0868823	−	0.996219i	$-0.527690\pi$
$953$	−5.36423			−0.173765			−0.0868823	+	0.996219i	$0.527690\pi$
$954$	−10.3363	+	17.9031i	−0.334651	+	0.579633i
$955$	12.2341	+	21.1900i	0.395885	+	0.685693i
$956$	−3.14943	−	5.45498i	−0.101860	−	0.176427i
$957$	−1.80502	+	3.12639i	−0.0583482	+	0.101062i
$958$	−38.6426			−1.24849
$959$	4.53176	−	8.22133i	0.146338	−	0.265481i
$960$	−0.809374			−0.0261224
$961$	15.1493	−	26.2394i	0.488687	−	0.846431i
$962$	29.9825	+	51.9312i	0.966675	+	1.67433i
$963$	9.82976	+	17.0256i	0.316760	+	0.548644i
$964$	−4.74977	+	8.22684i	−0.152980	+	0.264969i
$965$	35.8995			1.15565
$966$	−3.45760	+	0.0685383i	−0.111246	+	0.00220518i
$967$	−17.2209			−0.553786			−0.276893	−	0.960901i	$-0.589305\pi$
$967$	−17.2209			−0.553786			−0.276893	+	0.960901i	$0.589305\pi$
$968$	4.76873	−	8.25968i	0.153273	−	0.265476i
$969$	−1.01528	−	1.75852i	−0.0326155	−	0.0564918i
$970$	3.21963	+	5.57656i	0.103376	+	0.179053i
$971$	22.6551	−	39.2398i	0.727037	−	1.25926i	−0.231093	−	0.972932i	$-0.574230\pi$
$971$	22.6551	−	39.2398i	0.727037	−	1.25926i	0.958130	−	0.286333i	$-0.0924365\pi$
$972$	7.83817			0.251409
$973$	3.83560	+	6.34942i	0.122964	+	0.203553i
$974$	15.0759			0.483064
$975$	1.83187	−	3.17289i	0.0586667	−	0.101614i
$976$	0.929740	+	1.61036i	0.0297603	+	0.0515463i
$977$	19.1407	+	33.1526i	0.612364	+	1.06065i	0.990841	+	0.135035i	$0.0431147\pi$
$977$	19.1407	+	33.1526i	0.612364	+	1.06065i	−0.378477	+	0.925611i	$0.623552\pi$
$978$	−0.462698	+	0.801417i	−0.0147955	+	0.0256265i
$979$	−9.25980			−0.295945
$980$	8.71415	−	16.5777i	0.278363	−	0.529557i
$981$	23.8239			0.760639
$982$	−1.02666	+	1.77823i	−0.0327621	+	0.0567457i
$983$	−6.20783	−	10.7523i	−0.197999	−	0.342944i	0.749880	−	0.661573i	$-0.230111\pi$
$983$	−6.20783	−	10.7523i	−0.197999	−	0.342944i	−0.947880	+	0.318629i	$0.896778\pi$
$984$	0.151256	+	0.261984i	0.00482188	+	0.00835174i
$985$	−21.9115	+	37.9518i	−0.698157	+	1.20924i
$986$	−3.24678			−0.103398
$987$	3.82734	+	6.33575i	0.121825	+	0.201669i
$988$	30.5478			0.971854
$989$	0.414975	−	0.718758i	0.0131954	−	0.0228552i
$990$	−17.6326	−	30.5405i	−0.560401	−	0.970642i
$991$	11.6518	+	20.1814i	0.370130	+	0.641084i	0.989585	−	0.143948i	$-0.0459798\pi$
$991$	11.6518	+	20.1814i	0.370130	+	0.641084i	−0.619455	+	0.785032i	$0.712646\pi$
$992$	−0.418749	+	0.725295i	−0.0132953	+	0.0230281i
$993$	6.14915			0.195137
$994$	−31.6904	+	0.628184i	−1.00516	+	0.0199248i
$995$	31.5017			0.998671
$996$	−1.26166	+	2.18526i	−0.0399772	+	0.0692426i
$997$	16.2842	+	28.2051i	0.515727	+	0.893266i	0.999833	+	0.0182566i	$0.00581157\pi$
$997$	16.2842	+	28.2051i	0.515727	+	0.893266i	−0.484106	+	0.875009i	$0.660855\pi$
$998$	−3.44733	−	5.97095i	−0.109123	−	0.189007i
$999$	−9.55047	+	16.5419i	−0.302164	+	0.523363i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	574.2.e.g.247.3	yes	12
7.2	even	3		4018.2.a.bo.1.4		6
7.4	even	3	inner	574.2.e.g.165.3	✓	12
7.5	odd	6		4018.2.a.bn.1.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
574.2.e.g.165.3	✓	12	7.4	even	3	inner
574.2.e.g.247.3	yes	12	1.1	even	1	trivial
4018.2.a.bn.1.3		6	7.5	odd	6
4018.2.a.bo.1.4		6	7.2	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)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.151256 - 0.261984i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.33775 - 2.31706i) q^{5} -0.302513 q^{6} +(-1.36803 - 2.26462i) q^{7} -1.00000 q^{8} +(1.45424 - 2.51882i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.151256 - 0.261984i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.33775 - 2.31706i) q^{5} -0.302513 q^{6} +(-1.36803 - 2.26462i) q^{7} -1.00000 q^{8} +(1.45424 - 2.51882i) q^{9} +(-1.33775 - 2.31706i) q^{10} +(2.26591 + 3.92468i) q^{11} +(-0.151256 + 0.261984i) q^{12} -5.61129 q^{13} +(-2.64523 + 0.0524352i) q^{14} -0.809374 q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.616490 + 1.06779i) q^{17} +(-1.45424 - 2.51882i) q^{18} +(2.72199 - 4.71462i) q^{19} -2.67551 q^{20} +(-0.386371 + 0.700939i) q^{21} +4.53183 q^{22} +(-2.16041 + 3.74195i) q^{23} +(0.151256 + 0.261984i) q^{24} +(-1.07916 - 1.86917i) q^{25} +(-2.80565 + 4.85952i) q^{26} -1.78739 q^{27} +(-1.27721 + 2.31706i) q^{28} -2.63327 q^{29} +(-0.404687 + 0.700939i) q^{30} +(0.418749 + 0.725295i) q^{31} +(0.500000 + 0.866025i) q^{32} +(0.685468 - 1.18726i) q^{33} +1.23298 q^{34} +(-7.07733 + 0.140291i) q^{35} -2.90849 q^{36} +(5.34324 - 9.25477i) q^{37} +(-2.72199 - 4.71462i) q^{38} +(0.848744 + 1.47007i) q^{39} +(-1.33775 + 2.31706i) q^{40} +1.00000 q^{41} +(0.413845 + 0.685076i) q^{42} -0.192081 q^{43} +(2.26591 - 3.92468i) q^{44} +(-3.89083 - 6.73912i) q^{45} +(2.16041 + 3.74195i) q^{46} +(4.62412 - 8.00920i) q^{47} +0.302513 q^{48} +(-3.25701 + 6.19612i) q^{49} -2.15833 q^{50} +(0.186496 - 0.323021i) q^{51} +(2.80565 + 4.85952i) q^{52} +(-3.55386 - 6.15546i) q^{53} +(-0.893696 + 1.54793i) q^{54} +12.1249 q^{55} +(1.36803 + 2.26462i) q^{56} -1.64687 q^{57} +(-1.31664 + 2.28048i) q^{58} +(2.67081 + 4.62598i) q^{59} +(0.404687 + 0.700939i) q^{60} +(0.929740 - 1.61036i) q^{61} +0.837499 q^{62} +(-7.69362 + 0.152507i) q^{63} +1.00000 q^{64} +(-7.50652 + 13.0017i) q^{65} +(-0.685468 - 1.18726i) q^{66} +(7.93703 + 13.7473i) q^{67} +(0.616490 - 1.06779i) q^{68} +1.30711 q^{69} +(-3.41717 + 6.19929i) q^{70} +11.9802 q^{71} +(-1.45424 + 2.51882i) q^{72} +(-4.35479 - 7.54272i) q^{73} +(-5.34324 - 9.25477i) q^{74} +(-0.326461 + 0.565447i) q^{75} -5.44398 q^{76} +(5.78808 - 10.5005i) q^{77} +1.69749 q^{78} +(-5.37086 + 9.30260i) q^{79} +(1.33775 + 2.31706i) q^{80} +(-4.09237 - 7.08820i) q^{81} +(0.500000 - 0.866025i) q^{82} +8.34120 q^{83} +(0.800216 - 0.0158623i) q^{84} +3.29885 q^{85} +(-0.0960406 + 0.166347i) q^{86} +(0.398300 + 0.689875i) q^{87} +(-2.26591 - 3.92468i) q^{88} +(-1.02164 + 1.76953i) q^{89} -7.78167 q^{90} +(7.67639 + 12.7074i) q^{91} +4.32083 q^{92} +(0.126677 - 0.219411i) q^{93} +(-4.62412 - 8.00920i) q^{94} +(-7.28270 - 12.6140i) q^{95} +(0.151256 - 0.261984i) q^{96} -2.40675 q^{97} +(3.73749 + 5.91871i) q^{98} +13.1808 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{2} - q^{3} - 6 q^{4} - 2 q^{6} - q^{7} - 12 q^{8} - 5 q^{9}+O(q^{10}) \) 12 * q + 6 * q^2 - q^3 - 6 * q^4 - 2 * q^6 - q^7 - 12 * q^8 - 5 * q^9	\( 12 q + 6 q^{2} - q^{3} - 6 q^{4} - 2 q^{6} - q^{7} - 12 q^{8} - 5 q^{9} - q^{11} - q^{12} + 8 q^{13} + q^{14} + 4 q^{15} - 6 q^{16} + q^{17} + 5 q^{18} + 3 q^{19} - 6 q^{21} - 2 q^{22} - 21 q^{23} + q^{24} + 4 q^{26} + 26 q^{27} + 2 q^{28} + 10 q^{29} + 2 q^{30} - 3 q^{31} + 6 q^{32} + 19 q^{33} + 2 q^{34} - 51 q^{35} + 10 q^{36} + 2 q^{37} - 3 q^{38} + 11 q^{39} + 12 q^{41} - 6 q^{42} + 24 q^{43} - q^{44} - 28 q^{45} + 21 q^{46} + 18 q^{47} + 2 q^{48} - 15 q^{49} - 13 q^{51} - 4 q^{52} - 14 q^{53} + 13 q^{54} - 14 q^{55} + q^{56} + 10 q^{57} + 5 q^{58} - 16 q^{59} - 2 q^{60} + 20 q^{61} - 6 q^{62} - 41 q^{63} + 12 q^{64} - 18 q^{65} - 19 q^{66} + 13 q^{67} + q^{68} + 30 q^{69} - 12 q^{70} + 22 q^{71} + 5 q^{72} - q^{73} - 2 q^{74} + 23 q^{75} - 6 q^{76} - 11 q^{77} + 22 q^{78} - 19 q^{79} + 6 q^{81} + 6 q^{82} + 30 q^{83} - 4 q^{85} + 12 q^{86} - 10 q^{87} + q^{88} + 14 q^{89} - 56 q^{90} + 5 q^{91} + 42 q^{92} - 35 q^{93} - 18 q^{94} - 24 q^{95} + q^{96} + 2 q^{97} + 6 q^{98} + 20 q^{99}+O(q^{100}) \) 12 * q + 6 * q^2 - q^3 - 6 * q^4 - 2 * q^6 - q^7 - 12 * q^8 - 5 * q^9 - q^11 - q^12 + 8 * q^13 + q^14 + 4 * q^15 - 6 * q^16 + q^17 + 5 * q^18 + 3 * q^19 - 6 * q^21 - 2 * q^22 - 21 * q^23 + q^24 + 4 * q^26 + 26 * q^27 + 2 * q^28 + 10 * q^29 + 2 * q^30 - 3 * q^31 + 6 * q^32 + 19 * q^33 + 2 * q^34 - 51 * q^35 + 10 * q^36 + 2 * q^37 - 3 * q^38 + 11 * q^39 + 12 * q^41 - 6 * q^42 + 24 * q^43 - q^44 - 28 * q^45 + 21 * q^46 + 18 * q^47 + 2 * q^48 - 15 * q^49 - 13 * q^51 - 4 * q^52 - 14 * q^53 + 13 * q^54 - 14 * q^55 + q^56 + 10 * q^57 + 5 * q^58 - 16 * q^59 - 2 * q^60 + 20 * q^61 - 6 * q^62 - 41 * q^63 + 12 * q^64 - 18 * q^65 - 19 * q^66 + 13 * q^67 + q^68 + 30 * q^69 - 12 * q^70 + 22 * q^71 + 5 * q^72 - q^73 - 2 * q^74 + 23 * q^75 - 6 * q^76 - 11 * q^77 + 22 * q^78 - 19 * q^79 + 6 * q^81 + 6 * q^82 + 30 * q^83 - 4 * q^85 + 12 * q^86 - 10 * q^87 + q^88 + 14 * q^89 - 56 * q^90 + 5 * q^91 + 42 * q^92 - 35 * q^93 - 18 * q^94 - 24 * q^95 + q^96 + 2 * q^97 + 6 * q^98 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more