LMFDB - Embedded newform 539.2.f.e.148.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [539,2,Mod(148,539)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(539, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("539.148");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 539 = 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	539.f (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.30393666895$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 14 x^{14} - 32 x^{13} + 86 x^{12} - 145 x^{11} + 245 x^{10} - 245 x^{9} + 640 x^{8} + \cdots + 25 $ x^16 - 3x^15 + 14x^14 - 32x^13 + 86x^12 - 145x^11 + 245x^10 - 245x^9 + 640x^8 - 1175x^7 + 2135x^6 - 2300x^5 + 1850x^4 - 925x^3 + 700x^2 - 200*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 5 $
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			148.2
Root			$0.435488 + 1.34029i$ of defining polynomial
Character	$\chi$	$=$	539.148
Dual form			539.2.f.e.295.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.435488 - 1.34029i) q^{2} +(-1.75021 - 1.27160i) q^{3} +(0.0112975 - 0.00820814i) q^{4} +(0.565930 - 1.74175i) q^{5} +(-0.942126 + 2.89957i) q^{6} +(-2.29616 - 1.66826i) q^{8} +(0.519216 + 1.59798i) q^{9} +O(q^{10})$	\(q+(-0.435488 - 1.34029i) q^{2} +(-1.75021 - 1.27160i) q^{3} +(0.0112975 - 0.00820814i) q^{4} +(0.565930 - 1.74175i) q^{5} +(-0.942126 + 2.89957i) q^{6} +(-2.29616 - 1.66826i) q^{8} +(0.519216 + 1.59798i) q^{9} -2.58091 q^{10} +(-2.26009 - 2.42734i) q^{11} -0.0302106 q^{12} +(1.43602 + 4.41961i) q^{13} +(-3.20531 + 2.32880i) q^{15} +(-1.22738 + 3.77748i) q^{16} +(1.69039 - 5.20248i) q^{17} +(1.91565 - 1.39180i) q^{18} +(-4.69325 - 3.40985i) q^{19} +(-0.00790293 - 0.0243227i) q^{20} +(-2.26911 + 4.08626i) q^{22} -0.719682 q^{23} +(1.89741 + 5.83962i) q^{24} +(1.33166 + 0.967509i) q^{25} +(5.29821 - 3.84937i) q^{26} +(-0.882303 + 2.71545i) q^{27} +(0.948551 - 0.689163i) q^{29} +(4.51715 + 3.28190i) q^{30} +(0.404153 + 1.24385i) q^{31} -0.0789938 q^{32} +(0.869026 + 7.12230i) q^{33} -7.70900 q^{34} +(0.0189823 + 0.0137915i) q^{36} +(-1.69468 + 1.23126i) q^{37} +(-2.52634 + 7.77528i) q^{38} +(3.10666 - 9.56131i) q^{39} +(-4.20516 + 3.05523i) q^{40} +(-0.741582 - 0.538791i) q^{41} +8.02379 q^{43} +(-0.0454574 - 0.00887181i) q^{44} +3.07713 q^{45} +(0.313413 + 0.964586i) q^{46} +(4.83455 + 3.51251i) q^{47} +(6.95163 - 5.05065i) q^{48} +(0.716823 - 2.20615i) q^{50} +(-9.57403 + 6.95594i) q^{51} +(0.0525003 + 0.0381437i) q^{52} +(3.13496 + 9.64840i) q^{53} +4.02373 q^{54} +(-5.50688 + 2.56282i) q^{55} +(3.87821 + 11.9359i) q^{57} +(-1.33676 - 0.971215i) q^{58} +(-6.21390 + 4.51466i) q^{59} +(-0.0170971 + 0.0526193i) q^{60} +(1.93943 - 5.96895i) q^{61} +(1.49113 - 1.08337i) q^{62} +(2.48916 + 7.66083i) q^{64} +8.51056 q^{65} +(9.16752 - 4.26643i) q^{66} -15.4673 q^{67} +(-0.0236055 - 0.0726501i) q^{68} +(1.25960 + 0.915151i) q^{69} +(4.29593 - 13.2215i) q^{71} +(1.47365 - 4.53542i) q^{72} +(4.86593 - 3.53531i) q^{73} +(2.38826 + 1.73517i) q^{74} +(-1.10040 - 3.38669i) q^{75} -0.0810106 q^{76} -14.1679 q^{78} +(-4.83332 - 14.8754i) q^{79} +(5.88482 + 4.27557i) q^{80} +(9.07517 - 6.59349i) q^{81} +(-0.399188 + 1.22857i) q^{82} +(1.35217 - 4.16157i) q^{83} +(-8.10479 - 5.88848i) q^{85} +(-3.49426 - 10.7542i) q^{86} -2.53651 q^{87} +(1.14011 + 9.34400i) q^{88} -15.3437 q^{89} +(-1.34005 - 4.12425i) q^{90} +(-0.00813063 + 0.00590725i) q^{92} +(0.874336 - 2.69093i) q^{93} +(2.60240 - 8.00937i) q^{94} +(-8.59515 + 6.24474i) q^{95} +(0.138256 + 0.100449i) q^{96} +(-0.745114 - 2.29323i) q^{97} +(2.70537 - 4.87190i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 3 q^{2} + 2 q^{3} - 11 q^{4} + 5 q^{5} - 3 q^{6} - 5 q^{8} - 12 q^{9}+O(q^{10}) $ 16 * q - 3 * q^2 + 2 * q^3 - 11 * q^4 + 5 * q^5 - 3 * q^6 - 5 * q^8 - 12 * q^9	$ 16 q - 3 q^{2} + 2 q^{3} - 11 q^{4} + 5 q^{5} - 3 q^{6} - 5 q^{8} - 12 q^{9} - 12 q^{10} - 3 q^{11} - 18 q^{12} + 7 q^{13} - 18 q^{15} + 17 q^{16} + 5 q^{17} + 11 q^{18} - 19 q^{19} - q^{20} - 33 q^{22} + 32 q^{23} + 35 q^{24} + 7 q^{25} + 27 q^{26} - 10 q^{27} + 3 q^{29} - 2 q^{30} + 7 q^{31} + 32 q^{32} + 26 q^{33} + 24 q^{34} + 52 q^{36} + 4 q^{37} + 5 q^{38} + 11 q^{39} + 10 q^{40} + 10 q^{41} - 8 q^{43} - 38 q^{44} - 70 q^{45} - 42 q^{46} + 23 q^{47} + 36 q^{48} + 52 q^{50} - 29 q^{51} - 33 q^{52} + 4 q^{53} - 60 q^{54} + 12 q^{55} - 11 q^{57} + 20 q^{58} - 17 q^{59} - 30 q^{60} + 7 q^{61} - 79 q^{62} + 7 q^{64} - 8 q^{65} - 8 q^{66} - 38 q^{67} + 2 q^{68} - 10 q^{69} - 14 q^{71} + 35 q^{73} - 29 q^{74} - 9 q^{75} - 52 q^{76} - 58 q^{78} + 15 q^{79} + 87 q^{80} - 14 q^{81} - 19 q^{82} - 5 q^{83} + 6 q^{85} - 52 q^{86} + 72 q^{87} + 55 q^{88} - 74 q^{89} + 14 q^{90} - 55 q^{92} + 32 q^{93} + 24 q^{94} + 32 q^{95} + 42 q^{96} - 20 q^{97} + 16 q^{99}+O(q^{100}) $ 16 * q - 3 * q^2 + 2 * q^3 - 11 * q^4 + 5 * q^5 - 3 * q^6 - 5 * q^8 - 12 * q^9 - 12 * q^10 - 3 * q^11 - 18 * q^12 + 7 * q^13 - 18 * q^15 + 17 * q^16 + 5 * q^17 + 11 * q^18 - 19 * q^19 - q^20 - 33 * q^22 + 32 * q^23 + 35 * q^24 + 7 * q^25 + 27 * q^26 - 10 * q^27 + 3 * q^29 - 2 * q^30 + 7 * q^31 + 32 * q^32 + 26 * q^33 + 24 * q^34 + 52 * q^36 + 4 * q^37 + 5 * q^38 + 11 * q^39 + 10 * q^40 + 10 * q^41 - 8 * q^43 - 38 * q^44 - 70 * q^45 - 42 * q^46 + 23 * q^47 + 36 * q^48 + 52 * q^50 - 29 * q^51 - 33 * q^52 + 4 * q^53 - 60 * q^54 + 12 * q^55 - 11 * q^57 + 20 * q^58 - 17 * q^59 - 30 * q^60 + 7 * q^61 - 79 * q^62 + 7 * q^64 - 8 * q^65 - 8 * q^66 - 38 * q^67 + 2 * q^68 - 10 * q^69 - 14 * q^71 + 35 * q^73 - 29 * q^74 - 9 * q^75 - 52 * q^76 - 58 * q^78 + 15 * q^79 + 87 * q^80 - 14 * q^81 - 19 * q^82 - 5 * q^83 + 6 * q^85 - 52 * q^86 + 72 * q^87 + 55 * q^88 - 74 * q^89 + 14 * q^90 - 55 * q^92 + 32 * q^93 + 24 * q^94 + 32 * q^95 + 42 * q^96 - 20 * q^97 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/539\mathbb{Z}\right)^\times$.

$n$	$199$	$442$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−0.435488	−	1.34029i	−0.307936	−	0.947730i	−0.978565	−	0.205937i	$-0.933976\pi$
$2$	−0.435488	−	1.34029i	−0.307936	−	0.947730i	0.670629	−	0.741793i	$-0.266024\pi$
$3$	−1.75021	−	1.27160i	−1.01049	−	0.734161i	−0.0461746	−	0.998933i	$-0.514703\pi$
$3$	−1.75021	−	1.27160i	−1.01049	−	0.734161i	−0.964311	+	0.264773i	$0.914703\pi$
$4$	0.0112975	−	0.00820814i	0.00564876	−	0.00410407i
$5$	0.565930	−	1.74175i	0.253091	−	0.778935i	−0.741108	−	0.671385i	$-0.765700\pi$
$5$	0.565930	−	1.74175i	0.253091	−	0.778935i	0.994200	−	0.107550i	$-0.0343005\pi$
$6$	−0.942126	+	2.89957i	−0.384621	+	1.18374i
$7$		0			0
$7$		0			0
$8$	−2.29616	−	1.66826i	−0.811817	−	0.589819i
$9$	0.519216	+	1.59798i	0.173072	+	0.532661i
$10$	−2.58091			−0.816157
$11$	−2.26009	−	2.42734i	−0.681444	−	0.731871i
$11$	−2.26009	−	2.42734i	−0.681444	−	0.731871i
$12$	−0.0302106			−0.00872104
$13$	1.43602	+	4.41961i	0.398280	+	1.22578i	0.926377	+	0.376596i	$0.122906\pi$
$13$	1.43602	+	4.41961i	0.398280	+	1.22578i	−0.528097	+	0.849184i	$0.677094\pi$
$14$		0			0
$15$	−3.20531	+	2.32880i	−0.827609	+	0.601293i
$16$	−1.22738	+	3.77748i	−0.306844	+	0.944370i
$17$	1.69039	−	5.20248i	0.409980	−	1.26179i	−0.506685	−	0.862131i	$-0.669129\pi$
$17$	1.69039	−	5.20248i	0.409980	−	1.26179i	0.916665	−	0.399656i	$-0.130871\pi$
$18$	1.91565	−	1.39180i	0.451524	−	0.328051i
$19$	−4.69325	−	3.40985i	−1.07671	−	0.782272i	−0.0995999	−	0.995028i	$-0.531756\pi$
$19$	−4.69325	−	3.40985i	−1.07671	−	0.782272i	−0.977106	+	0.212755i	$0.931756\pi$
$20$	−0.00790293	−	0.0243227i	−0.00176715	−	0.00543873i
$21$		0			0
$22$	−2.26911	+	4.08626i	−0.483775	+	0.871194i
$23$	−0.719682			−0.150064			−0.0750321	−	0.997181i	$-0.523906\pi$
$23$	−0.719682			−0.150064			−0.0750321	+	0.997181i	$0.523906\pi$
$24$	1.89741	+	5.83962i	0.387307	+	1.19201i
$25$	1.33166	+	0.967509i	0.266332	+	0.193502i
$26$	5.29821	−	3.84937i	1.03906	−	0.754924i
$27$	−0.882303	+	2.71545i	−0.169799	+	0.522588i
$28$		0			0
$29$	0.948551	−	0.689163i	0.176142	−	0.127974i	−0.496221	−	0.868196i	$-0.665280\pi$
$29$	0.948551	−	0.689163i	0.176142	−	0.127974i	0.672363	+	0.740222i	$0.265280\pi$
$30$	4.51715	+	3.28190i	0.824714	+	0.599190i
$31$	0.404153	+	1.24385i	0.0725879	+	0.223403i	0.980768	−	0.195177i	$-0.0625281\pi$
$31$	0.404153	+	1.24385i	0.0725879	+	0.223403i	−0.908180	+	0.418580i	$0.862528\pi$
$32$	−0.0789938			−0.0139643
$33$	0.869026	+	7.12230i	0.151278	+	1.23983i
$34$	−7.70900			−1.32208
$35$		0			0
$36$	0.0189823	+	0.0137915i	0.00316372	+	0.00229858i
$37$	−1.69468	+	1.23126i	−0.278604	+	0.202417i	−0.718308	−	0.695725i	$-0.755083\pi$
$37$	−1.69468	+	1.23126i	−0.278604	+	0.202417i	0.439705	+	0.898142i	$0.355083\pi$
$38$	−2.52634	+	7.77528i	−0.409827	+	1.26132i
$39$	3.10666	−	9.56131i	0.497463	−	1.53103i
$40$	−4.20516	+	3.05523i	−0.664895	+	0.483074i
$41$	−0.741582	−	0.538791i	−0.115816	−	0.0841449i	0.528370	−	0.849014i	$-0.322803\pi$
$41$	−0.741582	−	0.538791i	−0.115816	−	0.0841449i	−0.644185	+	0.764869i	$0.722803\pi$
$42$		0			0
$43$	8.02379			1.22362			0.611808	−	0.791006i	$-0.290442\pi$
$43$	8.02379			1.22362			0.611808	+	0.791006i	$0.290442\pi$
$44$	−0.0454574	−	0.00887181i	−0.00685296	−	0.00133748i
$45$	3.07713			0.458711
$46$	0.313413	+	0.964586i	0.0462102	+	0.142220i
$47$	4.83455	+	3.51251i	0.705192	+	0.512352i	0.881619	−	0.471962i	$-0.156454\pi$
$47$	4.83455	+	3.51251i	0.705192	+	0.512352i	−0.176427	+	0.984314i	$0.556454\pi$
$48$	6.95163	−	5.05065i	1.00338	−	0.728999i
$49$		0			0
$50$	0.716823	−	2.20615i	0.101374	−	0.311997i
$51$	−9.57403	+	6.95594i	−1.34063	+	0.974027i
$52$	0.0525003	+	0.0381437i	0.00728048	+	0.00528958i
$53$	3.13496	+	9.64840i	0.430619	+	1.32531i	0.897510	+	0.440995i	$0.145374\pi$
$53$	3.13496	+	9.64840i	0.430619	+	1.32531i	−0.466890	+	0.884315i	$0.654626\pi$
$54$	4.02373			0.547560
$55$	−5.50688	+	2.56282i	−0.742547	+	0.345570i
$56$		0			0
$57$	3.87821	+	11.9359i	0.513682	+	1.58095i
$58$	−1.33676	−	0.971215i	−0.175526	−	0.127527i
$59$	−6.21390	+	4.51466i	−0.808981	+	0.587759i	−0.913535	−	0.406760i	$-0.866659\pi$
$59$	−6.21390	+	4.51466i	−0.808981	+	0.587759i	0.104554	+	0.994519i	$0.466659\pi$
$60$	−0.0170971	+	0.0526193i	−0.00220722	+	0.00679312i
$61$	1.93943	−	5.96895i	0.248318	−	0.764246i	−0.746754	−	0.665100i	$-0.768389\pi$
$61$	1.93943	−	5.96895i	0.248318	−	0.764246i	0.995073	−	0.0991458i	$-0.0316110\pi$
$62$	1.49113	−	1.08337i	0.189373	−	0.137588i
$63$		0			0
$64$	2.48916	+	7.66083i	0.311144	+	0.957604i
$65$	8.51056			1.05560
$66$	9.16752	−	4.26643i	1.12844	−	0.525161i
$67$	−15.4673			−1.88963			−0.944814	−	0.327608i	$-0.893758\pi$
$67$	−15.4673			−1.88963			−0.944814	+	0.327608i	$0.893758\pi$
$68$	−0.0236055	−	0.0726501i	−0.00286258	−	0.00881012i
$69$	1.25960	+	0.915151i	0.151638	+	0.110171i
$70$		0			0
$71$	4.29593	−	13.2215i	0.509833	−	1.56910i	−0.282659	−	0.959221i	$-0.591216\pi$
$71$	4.29593	−	13.2215i	0.509833	−	1.56910i	0.792491	−	0.609883i	$-0.208784\pi$
$72$	1.47365	−	4.53542i	0.173671	−	0.534504i
$73$	4.86593	−	3.53531i	0.569514	−	0.413776i	−0.265414	−	0.964134i	$-0.585509\pi$
$73$	4.86593	−	3.53531i	0.569514	−	0.413776i	0.834929	+	0.550358i	$0.185509\pi$
$74$	2.38826	+	1.73517i	0.277629	+	0.201709i
$75$	−1.10040	−	3.38669i	−0.127064	−	0.391061i
$76$	−0.0810106			−0.00929255
$77$		0			0
$78$	−14.1679			−1.60420
$79$	−4.83332	−	14.8754i	−0.543791	−	1.67362i	−0.723848	−	0.689959i	$-0.757628\pi$
$79$	−4.83332	−	14.8754i	−0.543791	−	1.67362i	0.180058	−	0.983656i	$-0.442372\pi$
$80$	5.88482	+	4.27557i	0.657943	+	0.478024i
$81$	9.07517	−	6.59349i	1.00835	−	0.732610i
$82$	−0.399188	+	1.22857i	−0.0440829	+	0.135673i
$83$	1.35217	−	4.16157i	0.148420	−	0.456791i	−0.849015	−	0.528370i	$-0.822804\pi$
$83$	1.35217	−	4.16157i	0.148420	−	0.456791i	0.997435	+	0.0715783i	$0.0228036\pi$
$84$		0			0
$85$	−8.10479	−	5.88848i	−0.879088	−	0.638695i
$86$	−3.49426	−	10.7542i	−0.376796	−	1.15966i
$87$	−2.53651			−0.271942
$88$	1.14011	+	9.34400i	0.121536	+	0.996073i
$89$	−15.3437			−1.62643			−0.813215	−	0.581963i	$-0.802285\pi$
$89$	−15.3437			−1.62643			−0.813215	+	0.581963i	$0.802285\pi$
$90$	−1.34005	−	4.12425i	−0.141254	−	0.434735i
$91$		0			0
$92$	−0.00813063	+	0.00590725i	−0.000847677	+	0.000615873i
$93$	0.874336	−	2.69093i	0.0906644	−	0.279036i
$94$	2.60240	−	8.00937i	0.268417	−	0.826104i
$95$	−8.59515	+	6.24474i	−0.881844	+	0.640697i
$96$	0.138256	+	0.100449i	0.0141107	+	0.0102520i
$97$	−0.745114	−	2.29323i	−0.0756549	−	0.232842i	0.906077	−	0.423114i	$-0.139063\pi$
$97$	−0.745114	−	2.29323i	−0.0756549	−	0.232842i	−0.981731	+	0.190272i	$0.939063\pi$
$98$		0			0
$99$	2.70537	−	4.87190i	0.271900	−	0.489645i
$100$	0.0229859			0.00229859
$101$	−3.67603	−	11.3136i	−0.365778	−	1.12575i	−0.949492	−	0.313790i	$-0.898401\pi$
$101$	−3.67603	−	11.3136i	−0.365778	−	1.12575i	0.583714	−	0.811959i	$-0.301599\pi$
$102$	13.4924	+	9.80279i	1.33594	+	0.970620i
$103$	0.320625	−	0.232947i	0.0315921	−	0.0229530i	−0.571877	−	0.820339i	$-0.693785\pi$
$103$	0.320625	−	0.232947i	0.0315921	−	0.0229530i	0.603469	+	0.797386i	$0.293785\pi$
$104$	4.07573	−	12.5438i	0.399658	−	1.23002i
$105$		0			0
$106$	11.5665	−	8.40352i	1.12343	−	0.816222i
$107$	2.64496	+	1.92168i	0.255698	+	0.185776i	0.708248	−	0.705963i	$-0.249486\pi$
$107$	2.64496	+	1.92168i	0.255698	+	0.185776i	−0.452550	+	0.891739i	$0.649486\pi$
$108$	0.0123209	+	0.0379199i	0.00118558	+	0.00364885i
$109$	−2.84638			−0.272634			−0.136317	−	0.990665i	$-0.543527\pi$
$109$	−2.84638			−0.272634			−0.136317	+	0.990665i	$0.543527\pi$
$110$	5.83310	+	6.26476i	0.556165	+	0.597321i
$111$	4.53172			0.430132
$112$		0			0
$113$	−11.7668	−	8.54906i	−1.10692	−	0.804228i	−0.124748	−	0.992188i	$-0.539812\pi$
$113$	−11.7668	−	8.54906i	−1.10692	−	0.804228i	−0.982177	+	0.187961i	$0.939812\pi$
$114$	14.3087	−	10.3959i	1.34013	−	0.973663i
$115$	−0.407290	+	1.25351i	−0.0379799	+	0.116890i
$116$	0.00505954	−	0.0155717i	0.000469767	−	0.00144579i
$117$	−6.31686	+	4.58947i	−0.583994	+	0.424296i
$118$	8.75705	+	6.36237i	0.806152	+	0.585704i
$119$		0			0
$120$	11.2450			1.02652
$121$	−0.783964	+	10.9720i	−0.0712695	+	0.997457i
$122$	−8.84474			−0.800765
$123$	0.612797	+	1.88600i	0.0552541	+	0.170054i
$124$	0.0147756	+	0.0107351i	0.00132689	+	0.000964044i
$125$	9.84690	−	7.15419i	0.880734	−	0.639890i
$126$		0			0
$127$	1.55524	−	4.78655i	0.138006	−	0.424737i	−0.858040	−	0.513583i	$-0.828318\pi$
$127$	1.55524	−	4.78655i	0.138006	−	0.424737i	0.996045	+	0.0888458i	$0.0283178\pi$
$128$	9.05595	−	6.57953i	0.800440	−	0.581554i
$129$	−14.0433	−	10.2031i	−1.23645	−	0.898331i
$130$	−3.70624	−	11.4066i	−0.325059	−	1.00043i
$131$	0.180053			0.0157313			0.00786565	−	0.999969i	$-0.497496\pi$
$131$	0.180053			0.0157313			0.00786565	+	0.999969i	$0.497496\pi$
$132$	0.0682787	+	0.0733313i	0.00594290	+	0.00638267i
$133$		0			0
$134$	6.73581	+	20.7307i	0.581885	+	1.79086i
$135$	4.23032	+	3.07350i	0.364088	+	0.264525i
$136$	−12.5605	+	9.12574i	−1.07705	+	0.782526i
$137$	2.57224	−	7.91655i	0.219762	−	0.676357i	−0.779020	−	0.627000i	$-0.784283\pi$
$137$	2.57224	−	7.91655i	0.219762	−	0.676357i	0.998781	−	0.0493570i	$-0.0157172\pi$
$138$	0.678031	−	2.08677i	0.0577179	−	0.177637i
$139$	−5.63172	+	4.09169i	−0.477677	+	0.347052i	−0.800425	−	0.599432i	$-0.795393\pi$
$139$	−5.63172	+	4.09169i	−0.477677	+	0.347052i	0.322749	+	0.946485i	$0.395393\pi$
$140$		0			0
$141$	−3.99497	−	12.2953i	−0.336438	−	1.03545i
$142$	−19.5915			−1.64408
$143$	7.48237	−	13.4744i	0.625707	−	1.12679i
$144$	−6.67362			−0.556135
$145$	−0.663538	−	2.04216i	−0.0551038	−	0.169592i
$146$	−6.85740	−	4.98219i	−0.567523	−	0.412329i
$147$		0			0
$148$	−0.00903937	+	0.0278203i	−0.000743031	+	0.00228682i
$149$	−0.993277	+	3.05699i	−0.0813724	+	0.250439i	−0.983463	−	0.181108i	$-0.942032\pi$
$149$	−0.993277	+	3.05699i	−0.0813724	+	0.250439i	0.902091	+	0.431546i	$0.142032\pi$
$150$	−4.05995	+	2.94972i	−0.331493	+	0.240844i
$151$	−18.0144	−	13.0882i	−1.46599	−	1.06510i	−0.981752	−	0.190168i	$-0.939097\pi$
$151$	−18.0144	−	13.0882i	−1.46599	−	1.06510i	−0.484239	−	0.874936i	$-0.660903\pi$
$152$	5.08796	+	15.6591i	0.412688	+	1.27012i
$153$	9.19115			0.743061
$154$		0			0
$155$	2.39521			0.192388
$156$	−0.0433830	−	0.133519i	−0.00347342	−	0.0106901i
$157$	10.7233	+	7.79096i	0.855816	+	0.621786i	0.926743	−	0.375695i	$-0.122596\pi$
$157$	10.7233	+	7.79096i	0.855816	+	0.621786i	−0.0709277	+	0.997481i	$0.522596\pi$
$158$	−17.8326	+	12.9561i	−1.41868	+	1.03073i
$159$	6.78211	−	20.8732i	0.537856	−	1.65535i
$160$	−0.0447049	+	0.137588i	−0.00353423	+	0.0108773i
$161$		0			0
$162$	−12.7893	−	9.29200i	−1.00483	−	0.730048i
$163$	4.23920	+	13.0469i	0.332040	+	1.02191i	0.968162	+	0.250325i	$0.0805375\pi$
$163$	4.23920	+	13.0469i	0.332040	+	1.02191i	−0.636122	+	0.771589i	$0.719462\pi$
$164$	−0.0128005			−0.000999552
$165$	12.8971	+	2.51709i	1.00404	+	0.195955i
$166$	−6.16657			−0.478619
$167$	−2.87651	−	8.85300i	−0.222591	−	0.685066i	−0.998527	−	0.0542539i	$-0.982722\pi$
$167$	−2.87651	−	8.85300i	−0.222591	−	0.685066i	0.775936	−	0.630812i	$-0.217278\pi$
$168$		0			0
$169$	−6.95361	+	5.05209i	−0.534893	+	0.388623i
$170$	−4.36275	+	13.4272i	−0.334608	+	1.02982i
$171$	3.01206	−	9.27018i	0.230338	−	0.708908i
$172$	0.0906490	−	0.0658604i	0.00691192	−	0.00502181i
$173$	8.49927	+	6.17508i	0.646188	+	0.469483i	0.861970	−	0.506959i	$-0.169230\pi$
$173$	8.49927	+	6.17508i	0.646188	+	0.469483i	−0.215783	+	0.976441i	$0.569230\pi$
$174$	1.10462	+	3.39966i	0.0837409	+	0.257728i
$175$		0			0
$176$	11.9432	−	5.55819i	0.900254	−	0.418964i
$177$	16.6165			1.24897
$178$	6.68200	+	20.5651i	0.500837	+	1.54142i
$179$	6.73370	+	4.89232i	0.503300	+	0.365669i	0.810276	−	0.586048i	$-0.199317\pi$
$179$	6.73370	+	4.89232i	0.503300	+	0.365669i	−0.306976	+	0.951717i	$0.599317\pi$
$180$	0.0347639	−	0.0252575i	0.00259115	−	0.00188258i
$181$	4.57437	−	14.0785i	0.340010	−	1.04644i	−0.624191	−	0.781272i	$-0.714571\pi$
$181$	4.57437	−	14.0785i	0.340010	−	1.04644i	0.964201	−	0.265172i	$-0.0854286\pi$
$182$		0			0
$183$	−10.9845	+	7.98074i	−0.812001	+	0.589953i
$184$	1.65251	+	1.20062i	0.121825	+	0.0885107i
$185$	1.18547	+	3.64852i	0.0871578	+	0.268244i
$186$	−3.98740			−0.292370
$187$	−16.4486	+	7.65494i	−1.20284	+	0.559785i
$188$	0.0834496			0.00608619
$189$		0			0
$190$	12.1129	+	8.80052i	0.878760	+	0.638457i
$191$	7.77203	−	5.64671i	0.562364	−	0.408582i	−0.269959	−	0.962872i	$-0.587010\pi$
$191$	7.77203	−	5.64671i	0.562364	−	0.408582i	0.832324	+	0.554290i	$0.187010\pi$
$192$	5.38499	−	16.5733i	0.388628	−	1.19607i
$193$	−0.459758	+	1.41499i	−0.0330941	+	0.101853i	−0.966239	−	0.257647i	$-0.917053\pi$
$193$	−0.459758	+	1.41499i	−0.0330941	+	0.101853i	0.933145	+	0.359500i	$0.117053\pi$
$194$	−2.74911	+	1.99734i	−0.197374	+	0.143401i
$195$	−14.8953	−	10.8221i	−1.06667	−	0.774983i
$196$		0			0
$197$	−14.0434			−1.00055			−0.500274	−	0.865867i	$-0.666767\pi$
$197$	−14.0434			−1.00055			−0.500274	+	0.865867i	$0.666767\pi$
$198$	−7.70793	−	1.50434i	−0.547779	−	0.106909i
$199$	4.28729			0.303918			0.151959	−	0.988387i	$-0.451442\pi$
$199$	4.28729			0.303918			0.151959	+	0.988387i	$0.451442\pi$
$200$	−1.44366	−	4.44312i	−0.102082	−	0.314176i
$201$	27.0710	+	19.6682i	1.90944	+	1.38729i
$202$	−13.5627	+	9.85391i	−0.954271	+	0.693318i
$203$		0			0
$204$	−0.0510676	+	0.157170i	−0.00357545	+	0.0110041i
$205$	−1.35812	+	0.986734i	−0.0948554	+	0.0689165i
$206$	−0.451846	−	0.328285i	−0.0314816	−	0.0228727i
$207$	−0.373671	−	1.15004i	−0.0259719	−	0.0799333i
$208$	−18.4575			−1.27980
$209$	2.33032	+	19.0987i	0.161192	+	1.32108i
$210$		0			0
$211$	−0.449704	−	1.38405i	−0.0309589	−	0.0952816i	0.934383	−	0.356270i	$-0.115952\pi$
$211$	−0.449704	−	1.38405i	−0.0309589	−	0.0952816i	−0.965342	+	0.260988i	$0.915952\pi$
$212$	0.114613	+	0.0832710i	0.00787163	+	0.00571907i
$213$	−24.3313	+	17.6777i	−1.66715	+	1.21126i
$214$	1.42376	−	4.38189i	0.0973264	−	0.299540i
$215$	4.54090	−	13.9755i	0.309687	−	0.953118i
$216$	6.55599	−	4.76320i	0.446079	−	0.324095i
$217$		0			0
$218$	1.23957	+	3.81499i	0.0839540	+	0.258384i
$219$	−13.0119			−0.879264
$220$	−0.0411782	+	0.0741547i	−0.00277623	+	0.00499951i
$221$	25.4204			1.70996
$222$	−1.97351	−	6.07383i	−0.132453	−	0.407649i
$223$	−3.92893	−	2.85453i	−0.263101	−	0.191154i	0.448412	−	0.893827i	$-0.351990\pi$
$223$	−3.92893	−	2.85453i	−0.263101	−	0.191154i	−0.711513	+	0.702673i	$0.751990\pi$
$224$		0			0
$225$	−0.854642	+	2.63032i	−0.0569761	+	0.175354i
$226$	−6.33396	+	19.4939i	−0.421329	+	1.29672i
$227$	0.321296	−	0.233435i	0.0213252	−	0.0154936i	−0.577072	−	0.816694i	$-0.695805\pi$
$227$	0.321296	−	0.233435i	0.0213252	−	0.0154936i	0.598397	+	0.801200i	$0.295805\pi$
$228$	0.141786	+	0.103013i	0.00938999	+	0.00682223i
$229$	−0.676634	−	2.08246i	−0.0447132	−	0.137613i	0.926208	−	0.377014i	$-0.123049\pi$
$229$	−0.676634	−	2.08246i	−0.0447132	−	0.137613i	−0.970921	+	0.239401i	$0.923049\pi$
$230$	1.85744			0.122476
$231$		0			0
$232$	−3.32773			−0.218476
$233$	−0.389410	−	1.19848i	−0.0255111	−	0.0785150i	0.937490	−	0.348011i	$-0.113143\pi$
$233$	−0.389410	−	1.19848i	−0.0255111	−	0.0785150i	−0.963001	+	0.269496i	$0.913143\pi$
$234$	8.90215	+	6.46779i	0.581952	+	0.422813i
$235$	8.85393	−	6.43276i	0.577567	−	0.419627i
$236$	−0.0331448	+	0.102009i	−0.00215754	+	0.00664023i
$237$	−10.4563	+	32.1812i	−0.679210	+	2.09039i
$238$		0			0
$239$	9.02997	+	6.56066i	0.584100	+	0.424374i	0.840200	−	0.542277i	$-0.182438\pi$
$239$	9.02997	+	6.56066i	0.584100	+	0.424374i	−0.256100	+	0.966650i	$0.582438\pi$
$240$	−4.86285	−	14.9663i	−0.313896	−	0.966072i
$241$	21.4843			1.38392			0.691962	−	0.721934i	$-0.256746\pi$
$241$	21.4843			1.38392			0.691962	+	0.721934i	$0.256746\pi$
$242$	15.0471	−	3.72744i	0.967267	−	0.239609i
$243$	−15.7022			−1.00730
$244$	−0.0270832	−	0.0833535i	−0.00173382	−	0.00533616i
$245$		0			0
$246$	2.26092	−	1.64266i	0.144151	−	0.104732i
$247$	8.33060	−	25.6390i	0.530063	−	1.63137i
$248$	1.14707	−	3.53032i	0.0728391	−	0.224176i
$249$	−7.65846	+	5.56419i	−0.485335	+	0.352616i
$250$	−13.8769	−	10.0822i	−0.877653	−	0.637652i
$251$	0.130968	+	0.403077i	0.00826660	+	0.0254420i	0.955105	−	0.296268i	$-0.0957423\pi$
$251$	0.130968	+	0.403077i	0.00826660	+	0.0254420i	−0.946838	+	0.321710i	$0.895742\pi$
$252$		0			0
$253$	1.62655	+	1.74691i	0.102260	+	0.109828i
$254$	−7.09267			−0.445033
$255$	6.69730	+	20.6122i	0.419401	+	1.29078i
$256$	0.271127	+	0.196986i	0.0169455	+	0.0123116i
$257$	14.1093	−	10.2510i	0.880115	−	0.639441i	−0.0531672	−	0.998586i	$-0.516932\pi$
$257$	14.1093	−	10.2510i	0.880115	−	0.639441i	0.933282	+	0.359145i	$0.116932\pi$
$258$	−7.55942	+	23.2655i	−0.470629	+	1.44845i
$259$		0			0
$260$	0.0961483	−	0.0698558i	0.00596286	−	0.00433227i
$261$	1.59377	+	1.15794i	0.0986521	+	0.0716749i
$262$	−0.0784109	−	0.241324i	−0.00484424	−	0.0149090i
$263$	1.51519			0.0934307			0.0467153	−	0.998908i	$-0.485125\pi$
$263$	1.51519			0.0934307			0.0467153	+	0.998908i	$0.485125\pi$
$264$	9.88643	−	17.8037i	0.608468	−	1.09574i
$265$	18.5793			1.14132
$266$		0			0
$267$	26.8548	+	19.5111i	1.64348	+	1.19406i
$268$	−0.174742	+	0.126957i	−0.0106741	+	0.00775516i
$269$	0.627622	−	1.93162i	0.0382668	−	0.117773i	−0.930098	−	0.367311i	$-0.880279\pi$
$269$	0.627622	−	1.93162i	0.0382668	−	0.117773i	0.968365	+	0.249538i	$0.0802786\pi$
$270$	2.27715	−	7.00834i	0.138583	−	0.426514i
$271$	6.15212	−	4.46978i	0.373715	−	0.271520i	−0.385035	−	0.922902i	$-0.625811\pi$
$271$	6.15212	−	4.46978i	0.373715	−	0.271520i	0.758750	+	0.651382i	$0.225811\pi$
$272$	17.5775	+	12.7708i	1.06579	+	0.774344i
$273$		0			0
$274$	−11.7307			−0.708676
$275$	−0.661205	−	5.41905i	−0.0398722	−	0.326781i
$276$	0.0217420			0.00130872
$277$	4.45813	+	13.7207i	0.267863	+	0.824398i	0.991020	+	0.133714i	$0.0426903\pi$
$277$	4.45813	+	13.7207i	0.267863	+	0.824398i	−0.723157	+	0.690684i	$0.757310\pi$
$278$	7.93661	+	5.76628i	0.476006	+	0.345839i
$279$	−1.77781	+	1.29166i	−0.106435	+	0.0773295i
$280$		0			0
$281$	5.48494	−	16.8809i	0.327204	−	1.00703i	−0.643232	−	0.765672i	$-0.722407\pi$
$281$	5.48494	−	16.8809i	0.327204	−	1.00703i	0.970436	−	0.241359i	$-0.0775933\pi$
$282$	−14.7395	+	10.7089i	−0.877725	+	0.637704i
$283$	−25.1897	−	18.3014i	−1.49737	−	1.08790i	−0.971414	−	0.237392i	$-0.923708\pi$
$283$	−25.1897	−	18.3014i	−1.49737	−	1.08790i	−0.525956	−	0.850512i	$-0.676292\pi$
$284$	−0.0599905	−	0.184632i	−0.00355978	−	0.0109559i
$285$	22.9842			1.36147
$286$	−21.3182	−	4.16062i	−1.26057	−	0.246022i
$287$		0			0
$288$	−0.0410148	−	0.126231i	−0.00241682	−	0.00743821i
$289$	−10.4551	−	7.59609i	−0.615007	−	0.446829i
$290$	−2.44813	+	1.77867i	−0.143759	+	0.104447i
$291$	−1.61197	+	4.96112i	−0.0944951	+	0.290826i
$292$	0.0259547	−	0.0798805i	0.00151889	−	0.00467465i
$293$	−19.4409	+	14.1247i	−1.13575	+	0.825171i	−0.986522	−	0.163632i	$-0.947679\pi$
$293$	−19.4409	+	14.1247i	−1.13575	+	0.825171i	−0.149229	+	0.988803i	$0.547679\pi$
$294$		0			0
$295$	4.34679	+	13.3781i	0.253080	+	0.778901i
$296$	5.94532			0.345565
$297$	8.58540	−	3.99552i	0.498176	−	0.231843i
$298$	4.52983			0.262406
$299$	−1.03348	−	3.18072i	−0.0597676	−	0.183946i
$300$	−0.0402302	−	0.0292290i	−0.00232269	−	0.00168754i
$301$		0			0
$302$	−9.69701	+	29.8443i	−0.558000	+	1.71735i
$303$	−7.95265	+	24.4757i	−0.456868	+	1.40609i
$304$	18.6410	−	13.5435i	1.06914	−	0.776772i
$305$	−9.29885	−	6.75601i	−0.532450	−	0.386848i
$306$	−4.00263	−	12.3188i	−0.228815	−	0.704221i
$307$	5.46298			0.311789			0.155894	−	0.987774i	$-0.450174\pi$
$307$	5.46298			0.311789			0.155894	+	0.987774i	$0.450174\pi$
$308$		0			0
$309$	−0.857378			−0.0487745
$310$	−1.04308	−	3.21028i	−0.0592431	−	0.182332i
$311$	11.2360	+	8.16342i	0.637134	+	0.462905i	0.858864	−	0.512203i	$-0.171170\pi$
$311$	11.2360	+	8.16342i	0.637134	+	0.462905i	−0.221730	+	0.975108i	$0.571170\pi$
$312$	−23.0842	+	16.7716i	−1.30688	+	0.949506i
$313$	−8.48207	+	26.1051i	−0.479435	+	1.47555i	0.360447	+	0.932780i	$0.382624\pi$
$313$	−8.48207	+	26.1051i	−0.479435	+	1.47555i	−0.839882	+	0.542770i	$0.817376\pi$
$314$	5.77229	−	17.7653i	0.325749	−	1.00255i
$315$		0			0
$316$	−0.176704	−	0.128383i	−0.00994038	−	0.00722211i
$317$	2.41828	+	7.44269i	0.135824	+	0.418023i	0.995717	−	0.0924507i	$-0.0294701\pi$
$317$	2.41828	+	7.44269i	0.135824	+	0.418023i	−0.859893	+	0.510474i	$0.829470\pi$
$318$	−30.9297			−1.73445
$319$	−3.81665	−	0.744885i	−0.213691	−	0.0417056i
$320$	14.7520			0.824659
$321$	−2.18563	−	6.72669i	−0.121990	−	0.375447i
$322$		0			0
$323$	−25.6731	+	18.6526i	−1.42849	+	1.03786i
$324$	0.0484067	−	0.148980i	0.00268926	−	0.00827669i
$325$	−2.36372	+	7.27479i	−0.131116	+	0.403533i
$326$	15.6406	−	11.3635i	0.866252	−	0.629369i
$327$	4.98178	+	3.61947i	0.275493	+	0.200157i
$328$	0.803950	+	2.47430i	0.0443907	+	0.136621i
$329$		0			0
$330$	−2.24288	−	18.3820i	−0.123467	−	1.01190i
$331$	−28.1462			−1.54705			−0.773527	−	0.633764i	$-0.781509\pi$
$331$	−28.1462			−1.54705			−0.773527	+	0.633764i	$0.781509\pi$
$332$	−0.0188825	−	0.0581143i	−0.00103631	−	0.00318943i
$333$	−2.84743	−	2.06878i	−0.156038	−	0.113368i
$334$	−10.6129	+	7.71075i	−0.580714	+	0.421913i
$335$	−8.75338	+	26.9401i	−0.478248	+	1.47190i
$336$		0			0
$337$	20.2084	−	14.6823i	1.10082	−	0.799793i	0.119628	−	0.992819i	$-0.461830\pi$
$337$	20.2084	−	14.6823i	1.10082	−	0.799793i	0.981194	+	0.193025i	$0.0618300\pi$
$338$	9.79950	+	7.11975i	0.533022	+	0.387263i
$339$	9.72333	+	29.9253i	0.528099	+	1.62532i
$340$	−0.139898			−0.00758701
$341$	2.10583	−	3.79224i	0.114037	−	0.205361i
$342$	−13.7365			−0.742783
$343$		0			0
$344$	−18.4239	−	13.3858i	−0.993352	−	0.721713i
$345$	2.30681	−	1.67599i	0.124194	−	0.0902325i
$346$	4.57509	−	14.0807i	0.245959	−	0.756983i
$347$	6.38096	−	19.6386i	0.342548	−	1.05425i	−0.620335	−	0.784337i	$-0.713003\pi$
$347$	6.38096	−	19.6386i	0.342548	−	1.05425i	0.962883	−	0.269918i	$-0.0869965\pi$
$348$	−0.0286563	+	0.0208200i	−0.00153614	+	0.00111607i
$349$	−4.85185	−	3.52507i	−0.259713	−	0.188693i	0.450307	−	0.892874i	$-0.351314\pi$
$349$	−4.85185	−	3.52507i	−0.259713	−	0.188693i	−0.710021	+	0.704181i	$0.751314\pi$
$350$		0			0
$351$	−13.2682			−0.708206
$352$	0.178533	+	0.191745i	0.00951585	+	0.0102200i
$353$	−24.0382			−1.27942			−0.639712	−	0.768615i	$-0.720946\pi$
$353$	−24.0382			−1.27942			−0.639712	+	0.768615i	$0.720946\pi$
$354$	−7.23629	−	22.2710i	−0.384604	−	1.18369i
$355$	−20.5974	−	14.9649i	−1.09320	−	0.794253i
$356$	−0.173346	+	0.125943i	−0.00918732	+	0.00667498i
$357$		0			0
$358$	3.62470	−	11.1557i	0.191571	−	0.589596i
$359$	8.85883	−	6.43632i	0.467551	−	0.339696i	−0.328935	−	0.944353i	$-0.606690\pi$
$359$	8.85883	−	6.43632i	0.467551	−	0.339696i	0.796486	+	0.604657i	$0.206690\pi$
$360$	−7.06559	−	5.13345i	−0.372389	−	0.270557i
$361$	4.52822	+	13.9364i	0.238328	+	0.733497i
$362$	−20.8613			−1.09645
$363$	15.3242	−	18.2065i	0.804311	−	0.955593i
$364$		0			0
$365$	−3.40385	−	10.4760i	−0.178166	−	0.548338i
$366$	15.4802	+	11.2470i	0.809161	+	0.587890i
$367$	8.58995	−	6.24096i	0.448392	−	0.325776i	−0.340569	−	0.940220i	$-0.610620\pi$
$367$	8.58995	−	6.24096i	0.448392	−	0.325776i	0.788960	+	0.614444i	$0.210620\pi$
$368$	0.883322	−	2.71859i	0.0460463	−	0.141716i
$369$	0.475937	−	1.46478i	0.0247763	−	0.0762535i
$370$	4.37382	−	3.17777i	0.227384	−	0.165204i
$371$		0			0
$372$	−0.0122097	−	0.0375775i	−0.000633042	−	0.00194830i
$373$	36.6036			1.89526			0.947631	−	0.319367i	$-0.103470\pi$
$373$	36.6036			1.89526			0.947631	+	0.319367i	$0.103470\pi$
$374$	17.4230	+	18.7124i	0.900924	+	0.967593i
$375$	−26.3315			−1.35975
$376$	−5.24115	−	16.1306i	−0.270292	−	0.831872i
$377$	4.40797	+	3.20258i	0.227022	+	0.164941i
$378$		0			0
$379$	−3.91147	+	12.0383i	−0.200919	+	0.618364i	0.798938	+	0.601414i	$0.205396\pi$
$379$	−3.91147	+	12.0383i	−0.200919	+	0.618364i	−0.999856	+	0.0169501i	$0.994604\pi$
$380$	−0.0458463	+	0.141100i	−0.00235187	+	0.00723830i
$381$	−8.80860	+	6.39982i	−0.451278	+	0.327873i
$382$	−10.9529	−	7.95773i	−0.560398	−	0.407153i
$383$	4.77984	+	14.7108i	0.244238	+	0.751688i	0.995761	+	0.0919809i	$0.0293199\pi$
$383$	4.77984	+	14.7108i	0.244238	+	0.751688i	−0.751522	+	0.659708i	$0.770680\pi$
$384$	−24.2164			−1.23579
$385$		0			0
$386$	2.09672			0.106720
$387$	4.16608	+	12.8219i	0.211774	+	0.651773i
$388$	−0.0272411	−	0.0197918i	−0.00138296	−	0.00100478i
$389$	10.2850	−	7.47249i	0.521470	−	0.378870i	−0.295687	−	0.955285i	$-0.595549\pi$
$389$	10.2850	−	7.47249i	0.521470	−	0.378870i	0.817157	+	0.576415i	$0.195549\pi$
$390$	−8.01801	+	24.6769i	−0.406008	+	1.24956i
$391$	−1.21654	+	3.74414i	−0.0615232	+	0.189349i
$392$		0			0
$393$	−0.315131	−	0.228956i	−0.0158963	−	0.0115493i
$394$	6.11571	+	18.8222i	0.308105	+	0.948250i
$395$	−28.6446			−1.44127
$396$	−0.00942522	−	0.0772465i	−0.000473635	−	0.00388178i
$397$	18.9574			0.951445			0.475722	−	0.879596i	$-0.342187\pi$
$397$	18.9574			0.951445			0.475722	+	0.879596i	$0.342187\pi$
$398$	−1.86706	−	5.74622i	−0.0935873	−	0.288032i
$399$		0			0
$400$	−5.28919	+	3.84282i	−0.264460	+	0.192141i
$401$	−2.68291	+	8.25715i	−0.133978	+	0.412343i	−0.995430	−	0.0954974i	$-0.969556\pi$
$401$	−2.68291	+	8.25715i	−0.133978	+	0.412343i	0.861451	+	0.507840i	$0.169556\pi$
$402$	14.5721	−	44.8484i	0.726791	−	2.23683i
$403$	−4.91698	+	3.57240i	−0.244932	+	0.177954i
$404$	−0.134394	−	0.0976429i	−0.00668635	−	0.00485792i
$405$	−6.34833	−	19.5381i	−0.315451	−	0.970858i
$406$		0			0
$407$	6.81881	+	1.33081i	0.337996	+	0.0659658i
$408$	33.5879			1.66285
$409$	−1.76574	−	5.43440i	−0.0873104	−	0.268714i	0.897863	−	0.440275i	$-0.145119\pi$
$409$	−1.76574	−	5.43440i	−0.0873104	−	0.268714i	−0.985173	+	0.171561i	$0.945119\pi$
$410$	1.91396	+	1.39057i	0.0945237	+	0.0686755i
$411$	−14.5687	+	10.5848i	−0.718620	+	0.522108i
$412$	0.00171020	−	0.00526346i	8.42556e−5	−	0.000259312i
$413$		0			0
$414$	−1.37866	+	1.00166i	−0.0677575	+	0.0492287i
$415$	−6.48318	−	4.71031i	−0.318247	−	0.231220i
$416$	−0.113437	−	0.349122i	−0.00556169	−	0.0171171i
$417$	15.0597			0.737477
$418$	24.5830	−	11.4406i	1.20239	−	0.559576i
$419$	27.1909			1.32836			0.664181	−	0.747571i	$-0.268780\pi$
$419$	27.1909			1.32836			0.664181	+	0.747571i	$0.268780\pi$
$420$		0			0
$421$	19.3881	+	14.0863i	0.944921	+	0.686525i	0.949600	−	0.313464i	$-0.101490\pi$
$421$	19.3881	+	14.0863i	0.944921	+	0.686525i	−0.00467947	+	0.999989i	$0.501490\pi$
$422$	−1.65919	+	1.20547i	−0.0807679	+	0.0586813i
$423$	−3.10275	+	9.54928i	−0.150861	+	0.464302i
$424$	8.89768	−	27.3842i	0.432110	−	1.32990i
$425$	7.28447	−	5.29248i	0.353349	−	0.256723i
$426$	34.2893	+	24.9126i	1.66132	+	1.20702i
$427$		0			0
$428$	0.0456549			0.00220681
$429$	−30.2299	+	14.0685i	−1.45951	+	0.679235i
$430$	−20.7087			−0.998663
$431$	5.09049	+	15.6669i	0.245200	+	0.754649i	0.995603	+	0.0936683i	$0.0298593\pi$
$431$	5.09049	+	15.6669i	0.245200	+	0.754649i	−0.750403	+	0.660980i	$0.770141\pi$
$432$	−9.17463	−	6.66576i	−0.441415	−	0.320706i
$433$	16.2539	−	11.8092i	0.781113	−	0.567512i	−0.124200	−	0.992257i	$-0.539636\pi$
$433$	16.2539	−	11.8092i	0.781113	−	0.567512i	0.905313	+	0.424745i	$0.139636\pi$
$434$		0			0
$435$	−1.43548	+	4.41797i	−0.0688262	+	0.211825i
$436$	−0.0321571	+	0.0233635i	−0.00154005	+	0.00111891i
$437$	3.37765	+	2.45401i	0.161575	+	0.117391i
$438$	5.66653	+	17.4398i	0.270757	+	0.833306i
$439$	−26.7682			−1.27758			−0.638788	−	0.769383i	$-0.720564\pi$
$439$	−26.7682			−1.27758			−0.638788	+	0.769383i	$0.720564\pi$
$440$	16.9201	+	3.30226i	0.806636	+	0.157429i
$441$		0			0
$442$	−11.0703	−	34.0708i	−0.526559	−	1.62058i
$443$	−21.2086	−	15.4090i	−1.00765	−	0.732103i	−0.0439378	−	0.999034i	$-0.513990\pi$
$443$	−21.2086	−	15.4090i	−1.00765	−	0.732103i	−0.963716	+	0.266931i	$0.913990\pi$
$444$	0.0511972	−	0.0371970i	0.00242971	−	0.00176529i
$445$	−8.68346	+	26.7249i	−0.411635	+	1.26688i
$446$	−2.11491	+	6.50903i	−0.100144	+	0.308212i
$447$	5.62573	−	4.08733i	0.266088	−	0.193324i
$448$		0			0
$449$	3.01211	+	9.27033i	0.142150	+	0.437494i	0.996634	−	0.0819851i	$-0.0261260\pi$
$449$	3.01211	+	9.27033i	0.142150	+	0.437494i	−0.854483	+	0.519479i	$0.826126\pi$
$450$	3.89758			0.183734
$451$	0.368215	+	3.01779i	0.0173386	+	0.142102i
$452$	−0.203107			−0.00955336
$453$	14.8860	+	45.8143i	0.699404	+	2.15254i
$454$	−0.452792	−	0.328973i	−0.0212506	−	0.0154395i
$455$		0			0
$456$	11.0072	−	33.8767i	0.515459	−	1.58642i
$457$	3.67276	−	11.3036i	0.171805	−	0.528760i	−0.827669	−	0.561217i	$-0.810333\pi$
$457$	3.67276	−	11.3036i	0.171805	−	0.528760i	0.999473	+	0.0324572i	$0.0103333\pi$
$458$	−2.49645	+	1.81378i	−0.116651	+	0.0847522i
$459$	12.6356	+	9.18033i	0.589781	+	0.428501i
$460$	0.00568760	+	0.0175046i	0.000265186	+	0.000816158i
$461$	−9.14737			−0.426035			−0.213018	−	0.977048i	$-0.568329\pi$
$461$	−9.14737			−0.426035			−0.213018	+	0.977048i	$0.568329\pi$
$462$		0			0
$463$	38.9342			1.80943			0.904713	−	0.426021i	$-0.140085\pi$
$463$	38.9342			1.80943			0.904713	+	0.426021i	$0.140085\pi$
$464$	1.43907	+	4.42899i	0.0668070	+	0.205611i
$465$	−4.19212	−	3.04575i	−0.194405	−	0.141243i
$466$	−1.43673	+	1.04385i	−0.0665553	+	0.0483552i
$467$	6.42243	−	19.7662i	0.297195	−	0.914671i	−0.685281	−	0.728279i	$-0.740320\pi$
$467$	6.42243	−	19.7662i	0.297195	−	0.914671i	0.982475	−	0.186392i	$-0.0596795\pi$
$468$	−0.0336939	+	0.103699i	−0.00155750	+	0.00479350i
$469$		0			0
$470$	−12.4776	−	9.06548i	−0.575547	−	0.418159i
$471$	−8.86110	−	27.2717i	−0.408298	−	1.25661i
$472$	21.7998			1.00342
$473$	−18.1345	−	19.4765i	−0.833826	−	0.895529i
$474$	47.6858			2.19028
$475$	−2.95076	−	9.08152i	−0.135390	−	0.416689i
$476$		0			0
$477$	−13.7903	+	10.0192i	−0.631413	+	0.458748i
$478$	4.86076	−	14.9599i	0.222326	−	0.684249i
$479$	7.58214	−	23.3354i	0.346437	−	1.06622i	−0.614374	−	0.789015i	$-0.710591\pi$
$479$	7.58214	−	23.3354i	0.346437	−	1.06622i	0.960810	−	0.277207i	$-0.0894088\pi$
$480$	0.253200	−	0.183960i	0.0115569	−	0.00839661i
$481$	−7.87527	−	5.72172i	−0.359081	−	0.260888i
$482$	−9.35614	−	28.7952i	−0.426161	−	1.31159i
$483$		0			0
$484$	0.0812030	+	0.130392i	0.00369105	+	0.00592690i
$485$	−4.41591			−0.200516
$486$	6.83811	+	21.0456i	0.310183	+	0.954646i
$487$	10.0086	+	7.27168i	0.453533	+	0.329511i	0.790989	−	0.611830i	$-0.209566\pi$
$487$	10.0086	+	7.27168i	0.453533	+	0.329511i	−0.337456	+	0.941341i	$0.609566\pi$
$488$	−14.4110	+	10.4702i	−0.652356	+	0.473964i
$489$	9.17101	−	28.2255i	0.414727	−	1.27640i
$490$		0			0
$491$	−13.3691	+	9.71320i	−0.603338	+	0.438350i	−0.847062	−	0.531494i	$-0.821631\pi$
$491$	−13.3691	+	9.71320i	−0.603338	+	0.438350i	0.243724	+	0.969845i	$0.421631\pi$
$492$	0.0224036	+	0.0162772i	0.00101003	+	0.000733831i
$493$	−1.98194	−	6.09977i	−0.0892620	−	0.274720i
$494$	−37.9916			−1.70932
$495$	−6.95459	−	7.46924i	−0.312586	−	0.335717i
$496$	−5.19468			−0.233248
$497$		0			0
$498$	10.7928	+	7.84144i	0.483638	+	0.351383i
$499$	11.1167	−	8.07673i	0.497650	−	0.361564i	−0.310469	−	0.950584i	$-0.600486\pi$
$499$	11.1167	−	8.07673i	0.497650	−	0.361564i	0.808119	+	0.589020i	$0.200486\pi$
$500$	0.0525231	−	0.161649i	0.00234890	−	0.00722918i
$501$	−6.22300	+	19.1524i	−0.278023	+	0.855667i
$502$	0.483206	−	0.351070i	0.0215665	−	0.0156690i
$503$	−18.2812	−	13.2820i	−0.815117	−	0.592217i	0.100193	−	0.994968i	$-0.468054\pi$
$503$	−18.2812	−	13.2820i	−0.815117	−	0.592217i	−0.915310	+	0.402751i	$0.868054\pi$
$504$		0			0
$505$	−21.7859			−0.969461
$506$	1.63304	−	2.94081i	0.0725973	−	0.130735i
$507$	18.5946			0.825813
$508$	−0.0217182	−	0.0668418i	−0.000963590	−	0.00296563i
$509$	−17.3644	−	12.6160i	−0.769664	−	0.559194i	0.132195	−	0.991224i	$-0.457798\pi$
$509$	−17.3644	−	12.6160i	−0.769664	−	0.559194i	−0.901859	+	0.432030i	$0.857798\pi$
$510$	24.7098	−	17.9527i	1.09417	−	0.794958i
$511$		0			0
$512$	7.06408	−	21.7410i	0.312191	−	0.960825i
$513$	13.4001	−	9.73576i	0.591630	−	0.429844i
$514$	−19.8838	−	14.4464i	−0.877037	−	0.637204i
$515$	−0.224286	−	0.690280i	−0.00988321	−	0.0304174i
$516$	−0.242403			−0.0106712
$517$	−2.40048	−	19.6737i	−0.105573	−	0.865248i
$518$		0			0
$519$	−7.02327	−	21.6154i	−0.308287	−	0.948811i
$520$	−19.5416	−	14.1978i	−0.856957	−	0.622616i
$521$	28.0822	−	20.4029i	1.23031	−	0.893869i	0.233393	−	0.972383i	$-0.425017\pi$
$521$	28.0822	−	20.4029i	1.23031	−	0.893869i	0.996913	+	0.0785132i	$0.0250173\pi$
$522$	0.857916	−	2.64039i	0.0375500	−	0.115567i
$523$	−6.09633	+	18.7626i	−0.266574	+	0.820430i	0.724753	+	0.689009i	$0.241954\pi$
$523$	−6.09633	+	18.7626i	−0.266574	+	0.820430i	−0.991327	+	0.131421i	$0.958046\pi$
$524$	0.00203415	−	0.00147790i	8.88624e−5	−	6.45623e-5i
$525$		0			0
$526$	−0.659847	−	2.03080i	−0.0287707	−	0.0885471i
$527$	7.15430			0.311646
$528$	−27.9710	−	5.45902i	−1.21728	−	0.237573i
$529$	−22.4821			−0.977481
$530$	−8.09105	−	24.9017i	−0.351453	−	1.08166i
$531$	−10.4407	−	7.58562i	−0.453088	−	0.329188i
$532$		0			0
$533$	1.31632	−	4.05122i	0.0570162	−	0.175478i
$534$	14.4557	−	44.4901i	0.625560	−	1.92527i
$535$	4.84395	−	3.51933i	0.209422	−	0.152154i
$536$	35.5154	+	25.8034i	1.53403	+	1.11454i
$537$	−5.56431	−	17.1252i	−0.240118	−	0.739006i
$538$	−2.86226			−0.123401
$539$		0			0
$540$	0.0730199			0.00314227
$541$	−1.71487	−	5.27782i	−0.0737279	−	0.226911i	0.907401	−	0.420266i	$-0.138063\pi$
$541$	−1.71487	−	5.27782i	−0.0737279	−	0.226911i	−0.981129	+	0.193355i	$0.938063\pi$
$542$	−8.66998	−	6.29911i	−0.372408	−	0.270570i
$543$	−25.9083	+	18.8235i	−1.11183	+	0.807794i
$544$	−0.133530	+	0.410964i	−0.00572506	+	0.0176199i
$545$	−1.61085	+	4.95770i	−0.0690014	+	0.212364i
$546$		0			0
$547$	6.83353	+	4.96485i	0.292181	+	0.212282i	0.724213	−	0.689576i	$-0.242203\pi$
$547$	6.83353	+	4.96485i	0.292181	+	0.212282i	−0.432032	+	0.901858i	$0.642203\pi$
$548$	−0.0359201	−	0.110551i	−0.00153443	−	0.00472250i
$549$	10.5453			0.450061
$550$	−6.97518	+	3.24614i	−0.297422	+	0.138416i
$551$	−6.80173			−0.289763
$552$	−1.36553	−	4.20267i	−0.0581209	−	0.178878i
$553$		0			0
$554$	16.4483	−	11.9504i	0.698822	−	0.507724i
$555$	2.56463	−	7.89313i	0.108863	−	0.335045i
$556$	−0.0300394	+	0.0924519i	−0.00127396	+	0.00392083i
$557$	9.85665	−	7.16128i	0.417640	−	0.303433i	−0.359048	−	0.933319i	$-0.616898\pi$
$557$	9.85665	−	7.16128i	0.417640	−	0.303433i	0.776687	+	0.629886i	$0.216898\pi$
$558$	2.50542	+	1.82029i	0.106063	+	0.0770591i
$559$	11.5223	+	35.4620i	0.487342	+	1.49988i
$560$		0			0
$561$	38.5226	+	7.51837i	1.62643	+	0.317426i
$562$	−25.0140			−1.05515
$563$	8.45270	+	26.0147i	0.356239	+	1.09639i	0.955288	+	0.295678i	$0.0955456\pi$
$563$	8.45270	+	26.0147i	0.356239	+	1.09639i	−0.599049	+	0.800713i	$0.704454\pi$
$564$	−0.146055	−	0.106115i	−0.00615001	−	0.00446824i
$565$	−21.5495	+	15.6566i	−0.906594	+	0.658679i
$566$	−13.5594	+	41.7316i	−0.569944	+	1.75411i
$567$		0			0
$568$	−31.9211	+	23.1920i	−1.33938	+	0.973115i
$569$	−5.77253	−	4.19399i	−0.241997	−	0.175821i	0.460176	−	0.887828i	$-0.347786\pi$
$569$	−5.77253	−	4.19399i	−0.241997	−	0.175821i	−0.702173	+	0.712007i	$0.747786\pi$
$570$	−10.0093	−	30.8055i	−0.419245	−	1.29030i
$571$	32.4839			1.35941			0.679705	−	0.733486i	$-0.262108\pi$
$571$	32.4839			1.35941			0.679705	+	0.733486i	$0.262108\pi$
$572$	−0.0260678	−	0.213644i	−0.00108995	−	0.00893291i
$573$	−20.7831			−0.868226
$574$		0			0
$575$	−0.958373	−	0.696299i	−0.0399669	−	0.0290377i
$576$	−10.9495	+	7.95525i	−0.456228	+	0.331469i
$577$	−10.7482	+	33.0795i	−0.447453	+	1.37712i	0.432317	+	0.901721i	$0.357696\pi$
$577$	−10.7482	+	33.0795i	−0.447453	+	1.37712i	−0.879771	+	0.475398i	$0.842304\pi$
$578$	−5.62791	+	17.3209i	−0.234090	+	0.720456i
$579$	2.60398	−	1.89190i	0.108218	−	0.0786248i
$580$	−0.0242587	−	0.0176249i	−0.00100729	−	0.000731836i
$581$		0			0
$582$	7.35135			0.304723
$583$	16.3347	−	29.4159i	0.676513	−	1.21828i
$584$	−17.0708			−0.706395
$585$	4.41882	+	13.5997i	0.182696	+	0.562279i
$586$	27.3975	+	19.9054i	1.13178	+	0.822285i
$587$	−11.7105	+	8.50816i	−0.483343	+	0.351169i	−0.802618	−	0.596493i	$-0.796560\pi$
$587$	−11.7105	+	8.50816i	−0.483343	+	0.351169i	0.319276	+	0.947662i	$0.396560\pi$
$588$		0			0
$589$	2.34456	−	7.21581i	0.0966059	−	0.297322i
$590$	16.0375	−	11.6520i	0.660255	−	0.479704i
$591$	24.5789	+	17.8576i	1.01104	+	0.734563i
$592$	−2.57103	−	7.91283i	−0.105669	−	0.325215i
$593$	15.0291			0.617169			0.308585	−	0.951197i	$-0.400145\pi$
$593$	15.0291			0.617169			0.308585	+	0.951197i	$0.400145\pi$
$594$	−9.09400	−	9.76696i	−0.373131	−	0.400743i
$595$		0			0
$596$	0.0138706	+	0.0426894i	0.000568163	+	0.00174863i
$597$	−7.50366	−	5.45173i	−0.307104	−	0.223124i
$598$	−3.81303	+	2.77033i	−0.155926	+	0.113287i
$599$	0.544010	−	1.67429i	0.0222276	−	0.0684097i	−0.939327	−	0.343022i	$-0.888549\pi$
$599$	0.544010	−	1.67429i	0.0222276	−	0.0684097i	0.961555	+	0.274612i	$0.0885495\pi$
$600$	−3.12318	+	9.61216i	−0.127503	+	0.392415i
$601$	18.9605	−	13.7756i	0.773415	−	0.561919i	−0.129581	−	0.991569i	$-0.541363\pi$
$601$	18.9605	−	13.7756i	0.773415	−	0.561919i	0.902995	+	0.429650i	$0.141363\pi$
$602$		0			0
$603$	−8.03085	−	24.7164i	−0.327042	−	1.00653i
$604$	−0.310948			−0.0126523
$605$	18.6669	+	7.57487i	0.758917	+	0.307962i
$606$	36.2679			1.47328
$607$	7.81149	+	24.0413i	0.317059	+	0.975806i	0.974899	+	0.222649i	$0.0714703\pi$
$607$	7.81149	+	24.0413i	0.317059	+	0.975806i	−0.657840	+	0.753158i	$0.728530\pi$
$608$	0.370738	+	0.269357i	0.0150354	+	0.0109239i
$609$		0			0
$610$	−5.00550	+	15.4053i	−0.202667	+	0.623744i
$611$	−8.58142	+	26.4109i	−0.347167	+	1.06847i
$612$	0.103837	−	0.0754422i	0.00419737	−	0.00304957i
$613$	−0.939222	−	0.682385i	−0.0379348	−	0.0275613i	0.568656	−	0.822575i	$-0.307463\pi$
$613$	−0.939222	−	0.682385i	−0.0379348	−	0.0275613i	−0.606591	+	0.795014i	$0.707463\pi$
$614$	−2.37906	−	7.32199i	−0.0960110	−	0.295492i
$615$	3.63174			0.146446
$616$		0			0
$617$	12.9711			0.522197			0.261098	−	0.965312i	$-0.415915\pi$
$617$	12.9711			0.522197			0.261098	+	0.965312i	$0.415915\pi$
$618$	0.373377	+	1.14914i	0.0150194	+	0.0462251i
$619$	37.0465	+	26.9158i	1.48902	+	1.08184i	0.974507	+	0.224358i	$0.0720286\pi$
$619$	37.0465	+	26.9158i	1.48902	+	1.08184i	0.514517	+	0.857480i	$0.327971\pi$
$620$	0.0270599	−	0.0196602i	0.00108675	−	0.000789572i
$621$	0.634978	−	1.95426i	0.0254808	−	0.0784218i
$622$	6.04824	−	18.6146i	0.242512	−	0.746377i
$623$		0			0
$624$	32.3046	+	23.4707i	1.29322	+	0.939578i
$625$	−4.34493	−	13.3723i	−0.173797	−	0.534893i
$626$	38.6824			1.54606
$627$	20.2074	−	36.3900i	0.807006	−	1.45328i
$628$	0.185097			0.00738615
$629$	3.54092	+	10.8978i	0.141186	+	0.434525i
$630$		0			0
$631$	10.2103	−	7.41824i	0.406467	−	0.295316i	−0.365703	−	0.930732i	$-0.619171\pi$
$631$	10.2103	−	7.41824i	0.406467	−	0.295316i	0.772170	+	0.635416i	$0.219171\pi$
$632$	−13.7180	+	42.2196i	−0.545672	+	1.67941i
$633$	−0.972881	+	2.99422i	−0.0386685	+	0.119009i
$634$	8.92225	−	6.48240i	0.354348	−	0.257449i
$635$	−7.45682	−	5.41770i	−0.295915	−	0.214995i
$636$	−0.0947088	−	0.291484i	−0.00375545	−	0.0115581i
$637$		0			0
$638$	0.663738	+	5.43981i	0.0262776	+	0.215364i
$639$	23.3582			0.924038
$640$	−6.33488	−	19.4968i	−0.250408	−	0.770678i
$641$	−22.6175	−	16.4326i	−0.893336	−	0.649047i	0.0434095	−	0.999057i	$-0.486178\pi$
$641$	−22.6175	−	16.4326i	−0.893336	−	0.649047i	−0.936746	+	0.350011i	$0.886178\pi$
$642$	−8.06392	+	5.85878i	−0.318257	+	0.231228i
$643$	15.3575	−	47.2657i	0.605642	−	1.86398i	0.113330	−	0.993557i	$-0.463848\pi$
$643$	15.3575	−	47.2657i	0.605642	−	1.86398i	0.492313	−	0.870418i	$-0.336152\pi$
$644$		0			0
$645$	−25.7188	+	18.6858i	−1.01268	+	0.735752i
$646$	36.1802	+	26.2865i	1.42349	+	1.03423i
$647$	3.40125	+	10.4680i	0.133717	+	0.411539i	0.995388	−	0.0959281i	$-0.0305819\pi$
$647$	3.40125	+	10.4680i	0.133717	+	0.411539i	−0.861671	+	0.507467i	$0.830582\pi$
$648$	−31.8377			−1.25070
$649$	25.0026	+	4.87970i	0.981439	+	0.191545i
$650$	10.7797			0.422816
$651$		0			0
$652$	0.154983	+	0.112602i	0.00606962	+	0.00440984i
$653$	−23.4100	+	17.0084i	−0.916106	+	0.665590i	−0.942552	−	0.334060i	$-0.891581\pi$
$653$	−23.4100	+	17.0084i	−0.916106	+	0.665590i	0.0264458	+	0.999650i	$0.491581\pi$
$654$	2.68165	−	8.25328i	0.104861	−	0.322729i
$655$	0.101897	−	0.313608i	0.00398146	−	0.0122537i
$656$	2.94547	−	2.14001i	0.115001	−	0.0835533i
$657$	8.17583	+	5.94009i	0.318969	+	0.231745i
$658$		0			0
$659$	10.8405			0.422288			0.211144	−	0.977455i	$-0.432281\pi$
$659$	10.8405			0.422288			0.211144	+	0.977455i	$0.432281\pi$
$660$	0.166366	−	0.0774241i	0.00647578	−	0.00301373i
$661$	−20.3444			−0.791305			−0.395652	−	0.918400i	$-0.629481\pi$
$661$	−20.3444			−0.791305			−0.395652	+	0.918400i	$0.629481\pi$
$662$	12.2573	+	37.7241i	0.476394	+	1.46619i
$663$	−44.4911	−	32.3247i	−1.72789	−	1.25539i
$664$	−10.0474	+	7.29986i	−0.389915	+	0.283289i
$665$		0			0
$666$	−1.53275	+	4.71732i	−0.0593929	+	0.182792i
$667$	−0.682656	+	0.495978i	−0.0264325	+	0.0192044i
$668$	−0.105164	−	0.0764062i	−0.00406892	−	0.00295625i
$669$	3.24662	+	9.99208i	0.125522	+	0.386316i
$670$	39.9197			1.54223
$671$	−18.8720	+	8.78272i	−0.728544	+	0.339053i
$672$		0			0
$673$	−3.73255	−	11.4876i	−0.143879	−	0.442815i	0.852986	−	0.521934i	$-0.174789\pi$
$673$	−3.73255	−	11.4876i	−0.143879	−	0.442815i	−0.996865	+	0.0791188i	$0.974789\pi$
$674$	−28.4790	−	20.6912i	−1.09697	−	0.796996i
$675$	−3.80215	+	2.76242i	−0.146345	+	0.106326i
$676$	−0.0370903	+	0.114152i	−0.00142655	+	0.00439047i
$677$	−1.04951	+	3.23007i	−0.0403361	+	0.124142i	−0.969197	−	0.246287i	$-0.920789\pi$
$677$	−1.04951	+	3.23007i	−0.0403361	+	0.124142i	0.928861	+	0.370429i	$0.120789\pi$
$678$	35.8743	−	26.0642i	1.37775	−	1.00099i
$679$		0			0
$680$	8.78642	+	27.0418i	0.336944	+	1.03701i
$681$	−0.859173			−0.0329236
$682$	−5.99978	−	1.17096i	−0.229743	−	0.0448384i
$683$	−4.75643			−0.182000			−0.0909999	−	0.995851i	$-0.529006\pi$
$683$	−4.75643			−0.182000			−0.0909999	+	0.995851i	$0.529006\pi$
$684$	−0.0420620	−	0.129454i	−0.00160828	−	0.00494978i
$685$	−12.3330	−	8.96042i	−0.471218	−	0.342360i
$686$		0			0
$687$	−1.46382	+	4.50516i	−0.0558481	+	0.171883i
$688$	−9.84822	+	30.3097i	−0.375460	+	1.15555i
$689$	−38.1404	+	27.7106i	−1.45303	+	1.05569i
$690$	−3.25091	−	2.36193i	−0.123760	−	0.0899170i
$691$	−2.04998	−	6.30920i	−0.0779850	−	0.240013i	0.904462	−	0.426554i	$-0.140272\pi$
$691$	−2.04998	−	6.30920i	−0.0779850	−	0.240013i	−0.982447	+	0.186540i	$0.940272\pi$
$692$	0.146707			0.00557695
$693$		0			0
$694$	−29.1003			−1.10463
$695$	3.93955	+	12.1247i	0.149435	+	0.459915i
$696$	5.82424	+	4.23156i	0.220767	+	0.160397i
$697$	−4.05661	+	2.94730i	−0.153655	+	0.111637i
$698$	−2.61171	+	8.03802i	−0.0988547	+	0.304244i
$699$	−0.842441	+	2.59277i	−0.0318641	+	0.0980675i
$700$		0			0
$701$	−2.45134	−	1.78101i	−0.0925860	−	0.0672677i	0.540529	−	0.841325i	$-0.318224\pi$
$701$	−2.45134	−	1.78101i	−0.0925860	−	0.0672677i	−0.633115	+	0.774058i	$0.718224\pi$
$702$	5.77815	+	17.7833i	0.218082	+	0.671188i
$703$	12.1519			0.458319
$704$	12.9697	−	23.3562i	0.488815	−	0.880270i
$705$	−23.6762			−0.891697
$706$	10.4683	+	32.2182i	0.393981	+	1.21255i
$707$		0			0
$708$	0.187726	−	0.136391i	0.00705516	−	0.00512587i
$709$	−4.22026	+	12.9886i	−0.158495	+	0.487798i	−0.998498	−	0.0547836i	$-0.982553\pi$
$709$	−4.22026	+	12.9886i	−0.158495	+	0.487798i	0.840003	+	0.542582i	$0.182553\pi$
$710$	−11.0874	+	34.1236i	−0.416103	+	1.28063i
$711$	21.2611	−	15.4471i	0.797354	−	0.579312i
$712$	35.2317	+	25.5973i	1.32036	+	0.959300i
$713$	−0.290862	−	0.895180i	−0.0108928	−	0.0335247i
$714$		0			0
$715$	−19.2346	−	20.6580i	−0.719335	−	0.772566i
$716$	0.116231			0.00434376
$717$	−7.46181	−	22.9651i	−0.278666	−	0.857647i
$718$	−12.4845	−	9.07050i	−0.465916	−	0.338508i
$719$	−1.53737	+	1.11696i	−0.0573341	+	0.0416557i	−0.616083	−	0.787681i	$-0.711281\pi$
$719$	−1.53737	+	1.11696i	−0.0573341	+	0.0416557i	0.558749	+	0.829337i	$0.311281\pi$
$720$	−3.77680	+	11.6238i	−0.140753	+	0.433193i
$721$		0			0
$722$	16.7069	−	12.1383i	0.621768	−	0.451741i
$723$	−37.6021	−	27.3195i	−1.39844	−	1.01602i
$724$	−0.0638788	−	0.196599i	−0.00237404	−	0.00730654i
$725$	1.92992			0.0716754
$726$	−31.0755	−	12.6102i	−1.15332	−	0.468008i
$727$	13.8211			0.512595			0.256298	−	0.966598i	$-0.417497\pi$
$727$	13.8211			0.512595			0.256298	+	0.966598i	$0.417497\pi$
$728$		0			0
$729$	0.256684	+	0.186492i	0.00950682	+	0.00690711i
$730$	−12.5586	+	9.12432i	−0.464813	+	0.337706i
$731$	13.5633	−	41.7436i	0.501658	−	1.54394i
$732$	−0.0585912	+	0.180325i	−0.00216559	+	0.00666502i
$733$	39.1357	−	28.4337i	1.44551	−	1.05022i	0.458655	−	0.888615i	$-0.348331\pi$
$733$	39.1357	−	28.4337i	1.44551	−	1.05022i	0.986855	−	0.161610i	$-0.0516685\pi$
$734$	−12.1055	−	8.79519i	−0.446824	−	0.324636i
$735$		0			0
$736$	0.0568504			0.00209553
$737$	34.9575	+	37.5443i	1.28767	+	1.38296i
$738$	−2.17050			−0.0798973
$739$	7.17170	+	22.0722i	0.263815	+	0.811939i	0.991964	+	0.126520i	$0.0403809\pi$
$739$	7.17170	+	22.0722i	0.263815	+	0.811939i	−0.728149	+	0.685419i	$0.759619\pi$
$740$	0.0433404	+	0.0314887i	0.00159323	+	0.00115755i
$741$	−47.1829	+	34.2804i	−1.73331	+	1.25932i
$742$		0			0
$743$	−13.8536	+	42.6369i	−0.508238	+	1.56420i	0.287019	+	0.957925i	$0.407336\pi$
$743$	−13.8536	+	42.6369i	−0.508238	+	1.56420i	−0.795257	+	0.606272i	$0.792664\pi$
$744$	−6.49679	+	4.72020i	−0.238184	+	0.173051i
$745$	4.76240	+	3.46009i	0.174481	+	0.126768i
$746$	−15.9404	−	49.0596i	−0.583620	−	1.79620i
$747$	7.35218			0.269002
$748$	−0.122996	+	0.221495i	−0.00449718	+	0.00809864i
$749$		0			0
$750$	11.4670	+	35.2919i	0.418717	+	1.28868i
$751$	33.3199	+	24.2083i	1.21586	+	0.883373i	0.995750	−	0.0921022i	$-0.0293587\pi$
$751$	33.3199	+	24.2083i	1.21586	+	0.883373i	0.220109	+	0.975475i	$0.429359\pi$
$752$	−19.2022	+	13.9512i	−0.700234	+	0.508750i
$753$	0.283333	−	0.872008i	0.0103252	−	0.0317777i
$754$	2.37278	−	7.30266i	0.0864115	−	0.265947i
$755$	−32.9913	+	23.9696i	−1.20068	+	0.872343i
$756$		0			0
$757$	−6.76401	−	20.8175i	−0.245842	−	0.756624i	−0.995497	−	0.0947948i	$-0.969781\pi$
$757$	−6.76401	−	20.8175i	−0.245842	−	0.756624i	0.749655	−	0.661829i	$-0.230219\pi$
$758$	17.8382			0.647912
$759$	−0.625423	−	5.12580i	−0.0227014	−	0.186055i
$760$	30.1537			1.09379
$761$	11.0367	+	33.9673i	0.400078	+	1.23131i	0.924935	+	0.380124i	$0.124119\pi$
$761$	11.0367	+	33.9673i	0.400078	+	1.23131i	−0.524857	+	0.851190i	$0.675881\pi$
$762$	12.4137	+	9.01906i	0.449700	+	0.326726i
$763$		0			0
$764$	0.0414558	−	0.127588i	0.00149982	−	0.00461596i
$765$	5.20154	−	16.0087i	0.188062	−	0.578796i
$766$	17.6353	−	12.8128i	0.637188	−	0.462944i
$767$	−28.8764	−	20.9799i	−1.04266	−	0.757540i
$768$	−0.224043	−	0.689533i	−0.00808445	−	0.0248814i
$769$	−5.30246			−0.191212			−0.0956058	−	0.995419i	$-0.530479\pi$
$769$	−5.30246			−0.191212			−0.0956058	+	0.995419i	$0.530479\pi$
$770$		0			0
$771$	−37.7295			−1.35880
$772$	0.00642030	+	0.0197596i	0.000231072	+	0.000711165i
$773$	−40.3628	−	29.3253i	−1.45175	−	1.05476i	−0.985418	−	0.170149i	$-0.945575\pi$
$773$	−40.3628	−	29.3253i	−1.45175	−	1.05476i	−0.466332	−	0.884610i	$-0.654425\pi$
$774$	15.3708	−	11.1675i	0.552492	−	0.401409i
$775$	−0.665245	+	2.04741i	−0.0238963	+	0.0735452i
$776$	−2.11479	+	6.50867i	−0.0759167	+	0.233648i
$777$		0			0
$778$	−14.4943	−	10.5307i	−0.519646	−	0.377545i
$779$	1.64324	+	5.05736i	0.0588750	+	0.181199i
$780$	−0.257109			−0.00920597
$781$	−41.8023	+	19.4541i	−1.49580	+	0.696124i
$782$	5.54803			0.198397
$783$	1.03448	+	3.18379i	0.0369692	+	0.113779i
$784$		0			0
$785$	19.6386	−	14.2683i	0.700931	−	0.509256i
$786$	−0.169633	+	0.522075i	−0.00605059	+	0.0186218i
$787$	−11.0804	+	34.1020i	−0.394974	+	1.21560i	0.534008	+	0.845479i	$0.320685\pi$
$787$	−11.0804	+	34.1020i	−0.394974	+	1.21560i	−0.928982	+	0.370125i	$0.879315\pi$
$788$	−0.158655	+	0.115270i	−0.00565186	+	0.00410632i
$789$	−2.65191	−	1.92672i	−0.0944103	−	0.0685931i
$790$	12.4744	+	38.3922i	0.443818	+	1.36593i
$791$		0			0
$792$	−14.3396	+	6.67342i	−0.509535	+	0.237130i
$793$	29.1655			1.03570
$794$	−8.25571	−	25.4085i	−0.292984	−	0.901713i
$795$	−32.5177	−	23.6255i	−1.15328	−	0.837910i
$796$	0.0484357	−	0.0351906i	0.00171676	−	0.00124730i
$797$	−4.55530	+	14.0198i	−0.161357	+	0.496606i	−0.998749	−	0.0499962i	$-0.984079\pi$
$797$	−4.55530	+	14.0198i	−0.161357	+	0.496606i	0.837392	+	0.546602i	$0.184079\pi$
$798$		0			0
$799$	26.4460	−	19.2142i	0.935593	−	0.679748i
$800$	−0.105193	−	0.0764272i	−0.00371913	−	0.00270211i
$801$	−7.96670	−	24.5190i	−0.281489	−	0.866336i
$802$	12.2354			0.432046
$803$	−19.5789	−	3.82116i	−0.690923	−	0.134846i
$804$	0.467275			0.0164795
$805$		0			0
$806$	6.92934	+	5.03446i	0.244076	+	0.177331i
$807$	−3.55473	+	2.58266i	−0.125132	+	0.0909140i
$808$	−10.4334	+	32.1106i	−0.367044	+	1.12965i
$809$	−8.33599	+	25.6556i	−0.293078	+	0.902001i	0.690782	+	0.723063i	$0.257266\pi$
$809$	−8.33599	+	25.6556i	−0.293078	+	0.902001i	−0.983860	+	0.178938i	$0.942734\pi$
$810$	−23.4222	+	17.0172i	−0.822973	+	0.597925i
$811$	1.18472	+	0.860750i	0.0416012	+	0.0302250i	0.608392	−	0.793637i	$-0.291815\pi$
$811$	1.18472	+	0.860750i	0.0416012	+	0.0302250i	−0.566790	+	0.823862i	$0.691815\pi$
$812$		0			0
$813$	−16.4513			−0.576972
$814$	−1.18583	−	9.71876i	−0.0415634	−	0.340642i
$815$	25.1236			0.880041
$816$	−14.5250	−	44.7033i	−0.508476	−	1.56493i
$817$	−37.6577	−	27.3599i	−1.31747	−	0.957201i
$818$	−6.51473	+	4.73323i	−0.227782	+	0.165493i
$819$		0			0
$820$	−0.00724418	+	0.0222953i	−0.000252978	+	0.000778586i
$821$	−24.7791	+	18.0031i	−0.864797	+	0.628312i	−0.929186	−	0.369613i	$-0.879490\pi$
$821$	−24.7791	+	18.0031i	−0.864797	+	0.628312i	0.0643886	+	0.997925i	$0.479490\pi$
$822$	20.5312	+	14.9168i	0.716107	+	0.520282i
$823$	−7.58137	−	23.3330i	−0.264270	−	0.813339i	−0.991861	−	0.127328i	$-0.959360\pi$
$823$	−7.58137	−	23.3330i	−0.264270	−	0.813339i	0.727591	−	0.686011i	$-0.240640\pi$
$824$	−1.12482			−0.0391851
$825$	−5.73364	+	10.3253i	−0.199620	+	0.359480i
$826$		0			0
$827$	−2.02927	−	6.24545i	−0.0705646	−	0.217176i	0.909555	−	0.415584i	$-0.136423\pi$
$827$	−2.02927	−	6.24545i	−0.0705646	−	0.217176i	−0.980119	+	0.198408i	$0.936423\pi$
$828$	−0.0136612	−	0.00992547i	−0.000474761	−	0.000344934i
$829$	−16.0543	+	11.6642i	−0.557590	+	0.405113i	−0.830576	−	0.556905i	$-0.811989\pi$
$829$	−16.0543	+	11.6642i	−0.557590	+	0.405113i	0.272986	+	0.962018i	$0.411989\pi$
$830$	−3.48985	+	10.7406i	−0.121134	+	0.372813i
$831$	9.64463	−	29.6831i	0.334569	−	1.02970i
$832$	−30.2834	+	22.0022i	−1.04989	+	0.762789i
$833$		0			0
$834$	−6.55832	−	20.1844i	−0.227096	−	0.698930i
$835$	−17.0476			−0.589958
$836$	0.183091	+	0.196640i	0.00633235	+	0.00680095i
$837$	−3.73421			−0.129073
$838$	−11.8413	−	36.4438i	−0.409051	−	1.25893i
$839$	−6.44019	−	4.67907i	−0.222340	−	0.161539i	0.471039	−	0.882112i	$-0.343879\pi$
$839$	−6.44019	−	4.67907i	−0.222340	−	0.161539i	−0.693379	+	0.720573i	$0.743879\pi$
$840$		0			0
$841$	−8.53669	+	26.2732i	−0.294369	+	0.905973i
$842$	10.4365	−	32.1202i	0.359665	−	1.10694i
$843$	−31.0656	+	22.5705i	−1.06996	+	0.777370i
$844$	−0.0164410	−	0.0119451i	−0.000565922	−	0.000411166i
$845$	4.86424	+	14.9706i	0.167335	+	0.515004i
$846$	14.1500			0.486489
$847$		0			0
$848$	−40.2944			−1.38372
$849$	20.8152	+	64.0625i	0.714375	+	2.19862i
$850$	−10.2658	−	7.45852i	−0.352113	−	0.255825i
$851$	1.21963	−	0.886114i	0.0418084	−	0.0303756i
$852$	−0.129782	+	0.399429i	−0.00444627	+	0.0136842i
$853$	−10.5292	+	32.4055i	−0.360513	+	1.10954i	0.592231	+	0.805768i	$0.298247\pi$
$853$	−10.5292	+	32.4055i	−0.360513	+	1.10954i	−0.952744	+	0.303776i	$0.901753\pi$
$854$		0			0
$855$	−14.4417	−	10.4925i	−0.493897	−	0.358837i
$856$	−2.86741	−	8.82497i	−0.0980060	−	0.301631i
$857$	−24.8539			−0.848992			−0.424496	−	0.905430i	$-0.639549\pi$
$857$	−24.8539			−0.848992			−0.424496	+	0.905430i	$0.639549\pi$
$858$	32.0207	+	34.3902i	1.09317	+	1.17406i
$859$	−2.05654			−0.0701683			−0.0350841	−	0.999384i	$-0.511170\pi$
$859$	−2.05654			−0.0701683			−0.0350841	+	0.999384i	$0.511170\pi$
$860$	−0.0634115	−	0.195160i	−0.00216231	−	0.00665491i
$861$		0			0
$862$	18.7814	−	13.6455i	0.639697	−	0.464767i
$863$	−0.0801824	+	0.246776i	−0.00272944	+	0.00840035i	−0.952412	−	0.304814i	$-0.901406\pi$
$863$	−0.0801824	+	0.246776i	−0.00272944	+	0.00840035i	0.949683	+	0.313214i	$0.101406\pi$
$864$	0.0696964	−	0.214504i	0.00237112	−	0.00729756i
$865$	15.5655	−	11.3090i	0.529241	−	0.384516i
$866$	−22.9061	−	16.6423i	−0.778381	−	0.565527i
$867$	8.63946	+	26.5895i	0.293412	+	0.903028i
$868$		0			0
$869$	−25.1840	+	45.3519i	−0.854307	+	1.53846i
$870$	6.54651			0.221947
$871$	−22.2113	−	68.3593i	−0.752601	−	2.31627i
$872$	6.53577	+	4.74851i	0.221329	+	0.160805i
$873$	3.27766	−	2.38136i	0.110932	−	0.0805968i
$874$	1.81816	−	5.59573i	0.0615003	−	0.189278i
$875$		0			0
$876$	−0.147003	+	0.106804i	−0.00496676	+	0.00360856i
$877$	−15.0420	−	10.9287i	−0.507934	−	0.369035i	0.304106	−	0.952638i	$-0.401642\pi$
$877$	−15.0420	−	10.9287i	−0.507934	−	0.369035i	−0.812039	+	0.583603i	$0.801642\pi$
$878$	11.6572	+	35.8772i	0.393412	+	1.21080i
$879$	51.9867			1.75347
$880$	−2.92197	−	23.9477i	−0.0984996	−	0.807275i
$881$	−6.45292			−0.217404			−0.108702	−	0.994074i	$-0.534670\pi$
$881$	−6.45292			−0.217404			−0.108702	+	0.994074i	$0.534670\pi$
$882$		0			0
$883$	0.225301	+	0.163691i	0.00758198	+	0.00550863i	0.591570	−	0.806254i	$-0.298508\pi$
$883$	0.225301	+	0.163691i	0.00758198	+	0.00550863i	−0.583988	+	0.811762i	$0.698508\pi$
$884$	0.287188	−	0.208654i	0.00965917	−	0.00701779i
$885$	9.40377	−	28.9418i	0.316104	−	0.972869i
$886$	−11.4165	+	35.1362i	−0.383543	+	1.18042i
$887$	24.7211	−	17.9609i	0.830054	−	0.603069i	−0.0895209	−	0.995985i	$-0.528534\pi$
$887$	24.7211	−	17.9609i	0.830054	−	0.603069i	0.919575	+	0.392916i	$0.128534\pi$
$888$	−10.4056	−	7.56009i	−0.349188	−	0.253700i
$889$		0			0
$890$	39.6008			1.32742
$891$	−36.5154	−	7.12661i	−1.22331	−	0.238750i
$892$	−0.0678176			−0.00227070
$893$	−10.7127	−	32.9702i	−0.358485	−	1.10330i
$894$	−7.92816	−	5.76014i	−0.265157	−	0.192648i
$895$	12.3320	−	8.95972i	0.412213	−	0.299491i
$896$		0			0
$897$	−2.23581	+	6.88111i	−0.0746514	+	0.229753i
$898$	11.1132	−	8.07423i	0.370853	−	0.269441i
$899$	1.24058	+	0.901332i	0.0413756	+	0.0300611i
$900$	0.0119347	+	0.0367311i	0.000397822	+	0.00122437i
$901$	55.4949			1.84880
$902$	3.88437	−	1.80773i	0.129335	−	0.0601907i
$903$		0			0
$904$	12.7564	+	39.2601i	0.424271	+	1.30577i
$905$	−21.9324	−	15.9348i	−0.729058	−	0.529692i
$906$	54.9220	−	39.9031i	1.82466	−	1.32569i
$907$	9.86836	−	30.3717i	0.327674	−	1.00848i	−0.642546	−	0.766247i	$-0.722122\pi$
$907$	9.86836	−	30.3717i	0.327674	−	1.00848i	0.970219	−	0.242228i	$-0.0778782\pi$
$908$	0.00171378	−	0.00527448i	5.68739e−5	−	0.000175040i
$909$	16.1704	−	11.7484i	0.536337	−	0.389671i
$910$		0			0
$911$	0.865378	+	2.66336i	0.0286713	+	0.0882411i	0.964368	−	0.264564i	$-0.0852280\pi$
$911$	0.865378	+	2.66336i	0.0286713	+	0.0882411i	−0.935697	+	0.352805i	$0.885228\pi$
$912$	−49.8477			−1.65062
$913$	−13.1576	+	6.12334i	−0.435452	+	0.202653i
$914$	−16.7496			−0.554027
$915$	7.68399	+	23.6489i	0.254025	+	0.781808i
$916$	−0.0247374	−	0.0179728i	−0.000817348	−	0.000593838i
$917$		0			0
$918$	6.80167	−	20.9334i	0.224488	−	0.690904i
$919$	−4.89293	+	15.0589i	−0.161403	+	0.496747i	−0.998753	−	0.0499194i	$-0.984104\pi$
$919$	−4.89293	+	15.0589i	−0.161403	+	0.496747i	0.837350	+	0.546667i	$0.184104\pi$
$920$	3.02638	−	2.19880i	0.0997769	−	0.0724922i
$921$	−9.56137	−	6.94674i	−0.315058	−	0.228903i
$922$	3.98356	+	12.2602i	0.131192	+	0.403767i
$923$	64.6030			2.12643
$924$		0			0
$925$	−3.44799			−0.113369
$926$	−16.9554	−	52.1833i	−0.557188	−	1.71485i
$927$	0.538719	+	0.391402i	0.0176939	+	0.0128553i
$928$	−0.0749296	+	0.0544396i	−0.00245969	+	0.00178707i
$929$	8.49282	−	26.1382i	0.278640	−	0.857567i	−0.709593	−	0.704612i	$-0.751121\pi$
$929$	8.49282	−	26.1382i	0.278640	−	0.857567i	0.988233	−	0.152955i	$-0.0488790\pi$
$930$	−2.25659	+	6.94506i	−0.0739964	+	0.227737i
$931$		0			0
$932$	−0.0142366	−	0.0103435i	−0.000466337	−	0.000338814i
$933$	−9.28472	−	28.5754i	−0.303968	−	0.935517i
$934$	−29.2894			−0.958379
$935$	4.02424	+	32.9816i	0.131607	+	1.07861i
$936$	22.1610			0.724354
$937$	3.80357	+	11.7062i	0.124257	+	0.382425i	0.993765	−	0.111495i	$-0.0355638\pi$
$937$	3.80357	+	11.7062i	0.124257	+	0.382425i	−0.869508	+	0.493919i	$0.835564\pi$
$938$		0			0
$939$	48.0408	−	34.9037i	1.56775	−	1.13904i
$940$	0.0472266	−	0.145349i	0.00154036	−	0.00474075i
$941$	−0.451208	+	1.38867i	−0.0147089	+	0.0452695i	−0.958142	−	0.286295i	$-0.907576\pi$
$941$	−0.451208	+	1.38867i	−0.0147089	+	0.0452695i	0.943433	+	0.331564i	$0.107576\pi$
$942$	−32.6931	+	23.7530i	−1.06520	+	0.773913i
$943$	0.533703	+	0.387758i	0.0173798	+	0.0126271i
$944$	−9.42725	−	29.0141i	−0.306831	−	0.944328i
$945$		0			0
$946$	−18.2068	+	32.7873i	−0.591955	+	1.06601i
$947$	11.0714			0.359771			0.179885	−	0.983688i	$-0.442427\pi$
$947$	11.0714			0.359771			0.179885	+	0.983688i	$0.442427\pi$
$948$	0.146017	+	0.449395i	0.00474242	+	0.0145957i
$949$	22.6123	+	16.4288i	0.734025	+	0.533301i
$950$	−10.8869	+	7.90978i	−0.353217	+	0.256627i
$951$	5.23165	−	16.1014i	0.169648	−	0.522123i
$952$		0			0
$953$	11.9924	−	8.71296i	0.388471	−	0.282240i	−0.376358	−	0.926474i	$-0.622824\pi$
$953$	11.9924	−	8.71296i	0.388471	−	0.282240i	0.764828	+	0.644234i	$0.222824\pi$
$954$	19.4342	+	14.1197i	0.629204	+	0.457144i
$955$	−5.43675	−	16.7326i	−0.175929	−	0.541454i
$956$	0.155867			0.00504110
$957$	5.73274	+	6.15697i	0.185313	+	0.199027i
$958$	−34.5782			−1.11717
$959$		0			0
$960$	−25.8191	−	18.7586i	−0.833306	−	0.605432i
$961$	23.6957	−	17.2159i	0.764377	−	0.555353i
$962$	−4.23920	+	13.0469i	−0.136677	+	0.420649i
$963$	−1.69750	+	5.22437i	−0.0547012	+	0.168353i
$964$	0.242719	−	0.176346i	0.00781746	−	0.00567972i
$965$	2.20437	+	1.60157i	0.0709612	+	0.0515563i
$966$		0			0
$967$	16.5193			0.531224			0.265612	−	0.964080i	$-0.414426\pi$
$967$	16.5193			0.531224			0.265612	+	0.964080i	$0.414426\pi$
$968$	20.1043	−	23.8857i	0.646177	−	0.767716i
$969$	68.6520			2.20542
$970$	1.92308	+	5.91862i	0.0617462	+	0.190035i
$971$	33.0073	+	23.9812i	1.05926	+	0.769595i	0.973951	−	0.226760i	$-0.0728134\pi$
$971$	33.0073	+	23.9812i	1.05926	+	0.769595i	0.0853055	+	0.996355i	$0.472813\pi$
$972$	−0.177396	+	0.128886i	−0.00568998	+	0.00413401i
$973$		0			0
$974$	5.38755	−	16.5812i	0.172628	−	0.531296i
$975$	13.3877	−	9.72671i	0.428748	−	0.311504i
$976$	20.1672	+	14.6523i	0.645535	+	0.469009i
$977$	15.1772	+	46.7107i	0.485562	+	1.49441i	0.831165	+	0.556025i	$0.187674\pi$
$977$	15.1772	+	46.7107i	0.485562	+	1.49441i	−0.345603	+	0.938381i	$0.612326\pi$
$978$	−41.8243			−1.33739
$979$	34.6782	+	37.2444i	1.10832	+	1.19034i
$980$		0			0
$981$	−1.47789	−	4.54847i	−0.0471853	−	0.145222i
$982$	18.8406	+	13.6885i	0.601228	+	0.436817i
$983$	0.895411	−	0.650554i	0.0285592	−	0.0207495i	−0.573414	−	0.819266i	$-0.694381\pi$
$983$	0.895411	−	0.650554i	0.0285592	−	0.0207495i	0.601973	+	0.798516i	$0.294381\pi$
$984$	1.73925	−	5.35286i	0.0554453	−	0.170643i
$985$	−7.94756	+	24.4601i	−0.253230	+	0.779362i
$986$	−7.31238	+	5.31275i	−0.232874	+	0.169193i
$987$		0			0
$988$	−0.116333	−	0.358036i	−0.00370104	−	0.0113906i
$989$	−5.77458			−0.183621
$990$	−6.98233	+	12.5740i	−0.221913	+	0.399627i
$991$	41.7851			1.32735			0.663674	−	0.748022i	$-0.268996\pi$
$991$	41.7851			1.32735			0.663674	+	0.748022i	$0.268996\pi$
$992$	−0.0319255	−	0.0982567i	−0.00101364	−	0.00311965i
$993$	49.2618	+	35.7908i	1.56328	+	1.13579i
$994$		0			0
$995$	2.42630	−	7.46739i	0.0769189	−	0.236732i
$996$	−0.0408500	+	0.125723i	−0.00129438	+	0.00398369i
$997$	35.7541	−	25.9769i	1.13234	−	0.822695i	0.146309	−	0.989239i	$-0.453261\pi$
$997$	35.7541	−	25.9769i	1.13234	−	0.822695i	0.986034	+	0.166543i	$0.0532606\pi$
$998$	−15.6664	−	11.3823i	−0.495910	−	0.360300i
$999$	−1.84819	−	5.68816i	−0.0584743	−	0.179965i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	539.2.f.e.148.2		16
7.2	even	3		539.2.q.f.214.2		32
7.3	odd	6		539.2.q.g.324.3		32
7.4	even	3		539.2.q.f.324.3		32
7.5	odd	6		539.2.q.g.214.2		32
7.6	odd	2		77.2.f.b.71.2	yes	16
11.3	even	5		5929.2.a.bt.1.3		8
11.8	odd	10		5929.2.a.bs.1.6		8
11.9	even	5	inner	539.2.f.e.295.2		16
21.20	even	2		693.2.m.i.379.3		16
77.6	even	10		847.2.f.v.323.2		16
77.9	even	15		539.2.q.f.361.3		32
77.13	even	10		847.2.f.x.372.3		16
77.20	odd	10		77.2.f.b.64.2	✓	16
77.27	odd	10		847.2.f.w.323.3		16
77.31	odd	30		539.2.q.g.471.2		32
77.41	even	10		847.2.a.o.1.6		8
77.48	odd	10		847.2.f.w.729.3		16
77.53	even	15		539.2.q.f.471.2		32
77.62	even	10		847.2.f.v.729.2		16
77.69	odd	10		847.2.a.p.1.3		8
77.75	odd	30		539.2.q.g.361.3		32
77.76	even	2		847.2.f.x.148.3		16
231.20	even	10		693.2.m.i.64.3		16
231.41	odd	10		7623.2.a.cw.1.3		8
231.146	even	10		7623.2.a.ct.1.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.f.b.64.2	✓	16	77.20	odd	10
77.2.f.b.71.2	yes	16	7.6	odd	2
539.2.f.e.148.2		16	1.1	even	1	trivial
539.2.f.e.295.2		16	11.9	even	5	inner
539.2.q.f.214.2		32	7.2	even	3
539.2.q.f.324.3		32	7.4	even	3
539.2.q.f.361.3		32	77.9	even	15
539.2.q.f.471.2		32	77.53	even	15
539.2.q.g.214.2		32	7.5	odd	6
539.2.q.g.324.3		32	7.3	odd	6
539.2.q.g.361.3		32	77.75	odd	30
539.2.q.g.471.2		32	77.31	odd	30
693.2.m.i.64.3		16	231.20	even	10
693.2.m.i.379.3		16	21.20	even	2
847.2.a.o.1.6		8	77.41	even	10
847.2.a.p.1.3		8	77.69	odd	10
847.2.f.v.323.2		16	77.6	even	10
847.2.f.v.729.2		16	77.62	even	10
847.2.f.w.323.3		16	77.27	odd	10
847.2.f.w.729.3		16	77.48	odd	10
847.2.f.x.148.3		16	77.76	even	2
847.2.f.x.372.3		16	77.13	even	10
5929.2.a.bs.1.6		8	11.8	odd	10
5929.2.a.bt.1.3		8	11.3	even	5
7623.2.a.ct.1.6		8	231.146	even	10
7623.2.a.cw.1.3		8	231.41	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 539 = 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	539.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.435488 - 1.34029i) q^{2} +(-1.75021 - 1.27160i) q^{3} +(0.0112975 - 0.00820814i) q^{4} +(0.565930 - 1.74175i) q^{5} +(-0.942126 + 2.89957i) q^{6} +(-2.29616 - 1.66826i) q^{8} +(0.519216 + 1.59798i) q^{9} +O(q^{10})\)	\(q+(-0.435488 - 1.34029i) q^{2} +(-1.75021 - 1.27160i) q^{3} +(0.0112975 - 0.00820814i) q^{4} +(0.565930 - 1.74175i) q^{5} +(-0.942126 + 2.89957i) q^{6} +(-2.29616 - 1.66826i) q^{8} +(0.519216 + 1.59798i) q^{9} -2.58091 q^{10} +(-2.26009 - 2.42734i) q^{11} -0.0302106 q^{12} +(1.43602 + 4.41961i) q^{13} +(-3.20531 + 2.32880i) q^{15} +(-1.22738 + 3.77748i) q^{16} +(1.69039 - 5.20248i) q^{17} +(1.91565 - 1.39180i) q^{18} +(-4.69325 - 3.40985i) q^{19} +(-0.00790293 - 0.0243227i) q^{20} +(-2.26911 + 4.08626i) q^{22} -0.719682 q^{23} +(1.89741 + 5.83962i) q^{24} +(1.33166 + 0.967509i) q^{25} +(5.29821 - 3.84937i) q^{26} +(-0.882303 + 2.71545i) q^{27} +(0.948551 - 0.689163i) q^{29} +(4.51715 + 3.28190i) q^{30} +(0.404153 + 1.24385i) q^{31} -0.0789938 q^{32} +(0.869026 + 7.12230i) q^{33} -7.70900 q^{34} +(0.0189823 + 0.0137915i) q^{36} +(-1.69468 + 1.23126i) q^{37} +(-2.52634 + 7.77528i) q^{38} +(3.10666 - 9.56131i) q^{39} +(-4.20516 + 3.05523i) q^{40} +(-0.741582 - 0.538791i) q^{41} +8.02379 q^{43} +(-0.0454574 - 0.00887181i) q^{44} +3.07713 q^{45} +(0.313413 + 0.964586i) q^{46} +(4.83455 + 3.51251i) q^{47} +(6.95163 - 5.05065i) q^{48} +(0.716823 - 2.20615i) q^{50} +(-9.57403 + 6.95594i) q^{51} +(0.0525003 + 0.0381437i) q^{52} +(3.13496 + 9.64840i) q^{53} +4.02373 q^{54} +(-5.50688 + 2.56282i) q^{55} +(3.87821 + 11.9359i) q^{57} +(-1.33676 - 0.971215i) q^{58} +(-6.21390 + 4.51466i) q^{59} +(-0.0170971 + 0.0526193i) q^{60} +(1.93943 - 5.96895i) q^{61} +(1.49113 - 1.08337i) q^{62} +(2.48916 + 7.66083i) q^{64} +8.51056 q^{65} +(9.16752 - 4.26643i) q^{66} -15.4673 q^{67} +(-0.0236055 - 0.0726501i) q^{68} +(1.25960 + 0.915151i) q^{69} +(4.29593 - 13.2215i) q^{71} +(1.47365 - 4.53542i) q^{72} +(4.86593 - 3.53531i) q^{73} +(2.38826 + 1.73517i) q^{74} +(-1.10040 - 3.38669i) q^{75} -0.0810106 q^{76} -14.1679 q^{78} +(-4.83332 - 14.8754i) q^{79} +(5.88482 + 4.27557i) q^{80} +(9.07517 - 6.59349i) q^{81} +(-0.399188 + 1.22857i) q^{82} +(1.35217 - 4.16157i) q^{83} +(-8.10479 - 5.88848i) q^{85} +(-3.49426 - 10.7542i) q^{86} -2.53651 q^{87} +(1.14011 + 9.34400i) q^{88} -15.3437 q^{89} +(-1.34005 - 4.12425i) q^{90} +(-0.00813063 + 0.00590725i) q^{92} +(0.874336 - 2.69093i) q^{93} +(2.60240 - 8.00937i) q^{94} +(-8.59515 + 6.24474i) q^{95} +(0.138256 + 0.100449i) q^{96} +(-0.745114 - 2.29323i) q^{97} +(2.70537 - 4.87190i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 3 q^{2} + 2 q^{3} - 11 q^{4} + 5 q^{5} - 3 q^{6} - 5 q^{8} - 12 q^{9}+O(q^{10}) \) 16 * q - 3 * q^2 + 2 * q^3 - 11 * q^4 + 5 * q^5 - 3 * q^6 - 5 * q^8 - 12 * q^9	\( 16 q - 3 q^{2} + 2 q^{3} - 11 q^{4} + 5 q^{5} - 3 q^{6} - 5 q^{8} - 12 q^{9} - 12 q^{10} - 3 q^{11} - 18 q^{12} + 7 q^{13} - 18 q^{15} + 17 q^{16} + 5 q^{17} + 11 q^{18} - 19 q^{19} - q^{20} - 33 q^{22} + 32 q^{23} + 35 q^{24} + 7 q^{25} + 27 q^{26} - 10 q^{27} + 3 q^{29} - 2 q^{30} + 7 q^{31} + 32 q^{32} + 26 q^{33} + 24 q^{34} + 52 q^{36} + 4 q^{37} + 5 q^{38} + 11 q^{39} + 10 q^{40} + 10 q^{41} - 8 q^{43} - 38 q^{44} - 70 q^{45} - 42 q^{46} + 23 q^{47} + 36 q^{48} + 52 q^{50} - 29 q^{51} - 33 q^{52} + 4 q^{53} - 60 q^{54} + 12 q^{55} - 11 q^{57} + 20 q^{58} - 17 q^{59} - 30 q^{60} + 7 q^{61} - 79 q^{62} + 7 q^{64} - 8 q^{65} - 8 q^{66} - 38 q^{67} + 2 q^{68} - 10 q^{69} - 14 q^{71} + 35 q^{73} - 29 q^{74} - 9 q^{75} - 52 q^{76} - 58 q^{78} + 15 q^{79} + 87 q^{80} - 14 q^{81} - 19 q^{82} - 5 q^{83} + 6 q^{85} - 52 q^{86} + 72 q^{87} + 55 q^{88} - 74 q^{89} + 14 q^{90} - 55 q^{92} + 32 q^{93} + 24 q^{94} + 32 q^{95} + 42 q^{96} - 20 q^{97} + 16 q^{99}+O(q^{100}) \) 16 * q - 3 * q^2 + 2 * q^3 - 11 * q^4 + 5 * q^5 - 3 * q^6 - 5 * q^8 - 12 * q^9 - 12 * q^10 - 3 * q^11 - 18 * q^12 + 7 * q^13 - 18 * q^15 + 17 * q^16 + 5 * q^17 + 11 * q^18 - 19 * q^19 - q^20 - 33 * q^22 + 32 * q^23 + 35 * q^24 + 7 * q^25 + 27 * q^26 - 10 * q^27 + 3 * q^29 - 2 * q^30 + 7 * q^31 + 32 * q^32 + 26 * q^33 + 24 * q^34 + 52 * q^36 + 4 * q^37 + 5 * q^38 + 11 * q^39 + 10 * q^40 + 10 * q^41 - 8 * q^43 - 38 * q^44 - 70 * q^45 - 42 * q^46 + 23 * q^47 + 36 * q^48 + 52 * q^50 - 29 * q^51 - 33 * q^52 + 4 * q^53 - 60 * q^54 + 12 * q^55 - 11 * q^57 + 20 * q^58 - 17 * q^59 - 30 * q^60 + 7 * q^61 - 79 * q^62 + 7 * q^64 - 8 * q^65 - 8 * q^66 - 38 * q^67 + 2 * q^68 - 10 * q^69 - 14 * q^71 + 35 * q^73 - 29 * q^74 - 9 * q^75 - 52 * q^76 - 58 * q^78 + 15 * q^79 + 87 * q^80 - 14 * q^81 - 19 * q^82 - 5 * q^83 + 6 * q^85 - 52 * q^86 + 72 * q^87 + 55 * q^88 - 74 * q^89 + 14 * q^90 - 55 * q^92 + 32 * q^93 + 24 * q^94 + 32 * q^95 + 42 * q^96 - 20 * q^97 + 16 * q^99

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