LMFDB - Embedded newform 125.2.e.b.74.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [125,2,Mod(24,125)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(125, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("125.24");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 125 = 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	125.e (of order $10$, degree $4$, not 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:	$0.998130025266$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	8.0.58140625.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 4x^{6} - 7x^{5} + 11x^{4} + 5x^{3} - 10x^{2} - 25x + 25 $ x^8 - 3x^7 + 4x^6 - 7x^5 + 11x^4 + 5x^3 - 10x^2 - 25*x + 25
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 25)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			74.2
Root			$-0.357358 - 1.86824i$ of defining polynomial
Character	$\chi$	$=$	125.74
Dual form			125.2.e.b.49.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.35736 + 1.86824i) q^{2} +(0.451659 + 0.146753i) q^{3} +(-1.02988 + 3.16963i) q^{4} +(0.338893 + 1.04301i) q^{6} -3.03582i q^{7} +(-2.92705 + 0.951057i) q^{8} +(-2.24459 - 1.63079i) q^{9} +O(q^{10})$	\(q+(1.35736 + 1.86824i) q^{2} +(0.451659 + 0.146753i) q^{3} +(-1.02988 + 3.16963i) q^{4} +(0.338893 + 1.04301i) q^{6} -3.03582i q^{7} +(-2.92705 + 0.951057i) q^{8} +(-2.24459 - 1.63079i) q^{9} +(-1.61803 + 1.17557i) q^{11} +(-0.930307 + 1.28046i) q^{12} +(-0.838893 + 1.15464i) q^{13} +(5.67164 - 4.12069i) q^{14} +(-0.357358 - 0.259635i) q^{16} +(1.76920 - 0.574848i) q^{17} -6.40701i q^{18} +(-0.279141 - 0.859107i) q^{19} +(0.445515 - 1.37116i) q^{21} +(-4.39250 - 1.42721i) q^{22} +(1.95693 + 2.69348i) q^{23} -1.46160 q^{24} -3.29582 q^{26} +(-1.61189 - 2.21858i) q^{27} +(9.62243 + 3.12652i) q^{28} +(-1.22466 + 3.76910i) q^{29} +(-1.99006 - 6.12477i) q^{31} +5.13532i q^{32} +(-0.903319 + 0.293506i) q^{33} +(3.47539 + 2.52502i) q^{34} +(7.48066 - 5.43502i) q^{36} +(-2.24547 + 3.09062i) q^{37} +(1.22613 - 1.68762i) q^{38} +(-0.548341 + 0.398393i) q^{39} +(1.48391 + 1.07813i) q^{41} +(3.16637 - 1.02882i) q^{42} -3.59445i q^{43} +(-2.05975 - 6.33927i) q^{44} +(-2.37582 + 7.31203i) q^{46} +(4.56502 + 1.48326i) q^{47} +(-0.123302 - 0.169710i) q^{48} -2.21619 q^{49} +0.883436 q^{51} +(-2.79582 - 3.84812i) q^{52} +(-9.03953 - 2.93712i) q^{53} +(1.95693 - 6.02280i) q^{54} +(2.88723 + 8.88599i) q^{56} -0.428989i q^{57} +(-8.70390 + 2.82807i) q^{58} +(8.61248 + 6.25734i) q^{59} +(-11.5481 + 8.39016i) q^{61} +(8.74134 - 12.0314i) q^{62} +(-4.95078 + 6.81417i) q^{63} +(-10.3087 + 7.48973i) q^{64} +(-1.77447 - 1.28923i) q^{66} +(-10.1670 + 3.30345i) q^{67} +6.19974i q^{68} +(0.488588 + 1.50372i) q^{69} +(3.85030 - 11.8500i) q^{71} +(8.12101 + 2.63868i) q^{72} +(-0.157310 - 0.216518i) q^{73} -8.82193 q^{74} +3.01054 q^{76} +(3.56882 + 4.91206i) q^{77} +(-1.48859 - 0.483672i) q^{78} +(2.64882 - 8.15223i) q^{79} +(2.16963 + 6.67743i) q^{81} +4.23572i q^{82} +(12.0006 - 3.89923i) q^{83} +(3.88723 + 2.82424i) q^{84} +(6.71531 - 4.87896i) q^{86} +(-1.10626 + 1.52263i) q^{87} +(3.61803 - 4.97980i) q^{88} +(-3.85736 + 2.80253i) q^{89} +(3.50527 + 2.54673i) q^{91} +(-10.5527 + 3.42879i) q^{92} -3.05836i q^{93} +(3.42527 + 10.5419i) q^{94} +(-0.753624 + 2.31942i) q^{96} +(9.47067 + 3.07721i) q^{97} +(-3.00816 - 4.14037i) q^{98} +5.54893 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 5 q^{2} + 5 q^{3} - q^{4} - 9 q^{6} - 10 q^{8} + q^{9}+O(q^{10}) $ 8 * q + 5 * q^2 + 5 * q^3 - q^4 - 9 * q^6 - 10 * q^8 + q^9	$ 8 q + 5 q^{2} + 5 q^{3} - q^{4} - 9 q^{6} - 10 q^{8} + q^{9} - 4 q^{11} - 15 q^{12} + 5 q^{13} + 13 q^{14} + 3 q^{16} + 10 q^{17} - 5 q^{19} - 4 q^{21} - 5 q^{23} - 20 q^{24} + 6 q^{26} + 5 q^{27} + 15 q^{28} - 5 q^{29} - 9 q^{31} - 10 q^{33} + 13 q^{34} + 23 q^{36} - 30 q^{37} - 15 q^{38} - 3 q^{39} - 4 q^{41} + 15 q^{42} - 2 q^{44} - 19 q^{46} + 30 q^{48} + 14 q^{49} - 4 q^{51} + 10 q^{52} + 10 q^{53} - 5 q^{54} + 10 q^{56} - 20 q^{58} - 9 q^{61} + 30 q^{62} - 10 q^{63} + 4 q^{64} + 12 q^{66} - 20 q^{67} + 17 q^{69} + 6 q^{71} - 5 q^{72} - 15 q^{73} - 12 q^{74} - 20 q^{76} - 10 q^{77} - 25 q^{78} + 15 q^{79} + 28 q^{81} + 45 q^{83} + 18 q^{84} - 9 q^{86} + 20 q^{87} + 20 q^{88} - 25 q^{89} + 6 q^{91} - 30 q^{92} - 27 q^{94} + 16 q^{96} + 60 q^{97} + 10 q^{98} - 8 q^{99}+O(q^{100}) $ 8 * q + 5 * q^2 + 5 * q^3 - q^4 - 9 * q^6 - 10 * q^8 + q^9 - 4 * q^11 - 15 * q^12 + 5 * q^13 + 13 * q^14 + 3 * q^16 + 10 * q^17 - 5 * q^19 - 4 * q^21 - 5 * q^23 - 20 * q^24 + 6 * q^26 + 5 * q^27 + 15 * q^28 - 5 * q^29 - 9 * q^31 - 10 * q^33 + 13 * q^34 + 23 * q^36 - 30 * q^37 - 15 * q^38 - 3 * q^39 - 4 * q^41 + 15 * q^42 - 2 * q^44 - 19 * q^46 + 30 * q^48 + 14 * q^49 - 4 * q^51 + 10 * q^52 + 10 * q^53 - 5 * q^54 + 10 * q^56 - 20 * q^58 - 9 * q^61 + 30 * q^62 - 10 * q^63 + 4 * q^64 + 12 * q^66 - 20 * q^67 + 17 * q^69 + 6 * q^71 - 5 * q^72 - 15 * q^73 - 12 * q^74 - 20 * q^76 - 10 * q^77 - 25 * q^78 + 15 * q^79 + 28 * q^81 + 45 * q^83 + 18 * q^84 - 9 * q^86 + 20 * q^87 + 20 * q^88 - 25 * q^89 + 6 * q^91 - 30 * q^92 - 27 * q^94 + 16 * q^96 + 60 * q^97 + 10 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/125\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{10}\right)$

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 $

$2$	1.35736	+	1.86824i	0.959797	+	1.32105i	0.947036	+	0.321128i	$0.104062\pi$
$2$	1.35736	+	1.86824i	0.959797	+	1.32105i	0.0127610	+	0.999919i	$0.495938\pi$
$3$	0.451659	+	0.146753i	0.260766	+	0.0847279i	0.436482	−	0.899713i	$-0.356224\pi$
$3$	0.451659	+	0.146753i	0.260766	+	0.0847279i	−0.175716	+	0.984441i	$0.556224\pi$
$4$	−1.02988	+	3.16963i	−0.514938	+	1.58482i
$5$		0			0
$5$		0			0
$6$	0.338893	+	1.04301i	0.138353	+	0.425805i
$7$		−	3.03582i		−	1.14743i	−0.819055	−	0.573716i	$-0.805502\pi$
$7$		−	3.03582i		−	1.14743i	0.819055	−	0.573716i	$-0.194498\pi$
$8$	−2.92705	+	0.951057i	−1.03487	+	0.336249i
$9$	−2.24459	−	1.63079i	−0.748197	−	0.543597i
$10$		0			0
$11$	−1.61803	+	1.17557i	−0.487856	+	0.354448i	−0.804359	−	0.594144i	$-0.797491\pi$
$11$	−1.61803	+	1.17557i	−0.487856	+	0.354448i	0.316503	+	0.948591i	$0.397491\pi$
$12$	−0.930307	+	1.28046i	−0.268556	+	0.369636i
$13$	−0.838893	+	1.15464i	−0.232667	+	0.320239i	−0.909347	−	0.416039i	$-0.863418\pi$
$13$	−0.838893	+	1.15464i	−0.232667	+	0.320239i	0.676680	+	0.736277i	$0.263418\pi$
$14$	5.67164	−	4.12069i	1.51581	−	1.10130i
$15$		0			0
$16$	−0.357358	−	0.259635i	−0.0893394	−	0.0649089i
$17$	1.76920	−	0.574848i	0.429094	−	0.139421i	−0.0865044	−	0.996251i	$-0.527570\pi$
$17$	1.76920	−	0.574848i	0.429094	−	0.139421i	0.515598	+	0.856830i	$0.327570\pi$
$18$		−	6.40701i		−	1.51015i
$19$	−0.279141	−	0.859107i	−0.0640393	−	0.197093i	0.913918	−	0.405900i	$-0.133042\pi$
$19$	−0.279141	−	0.859107i	−0.0640393	−	0.197093i	−0.977957	+	0.208807i	$0.933042\pi$
$20$		0			0
$21$	0.445515	−	1.37116i	0.0972194	−	0.299211i
$22$	−4.39250	−	1.42721i	−0.936484	−	0.304282i
$23$	1.95693	+	2.69348i	0.408048	+	0.561629i	0.962741	−	0.270426i	$-0.0871644\pi$
$23$	1.95693	+	2.69348i	0.408048	+	0.561629i	−0.554693	+	0.832055i	$0.687164\pi$
$24$	−1.46160			−0.298348
$25$		0			0
$26$	−3.29582			−0.646364
$27$	−1.61189	−	2.21858i	−0.310208	−	0.426965i
$28$	9.62243	+	3.12652i	1.81847	+	0.590856i
$29$	−1.22466	+	3.76910i	−0.227413	+	0.699905i	0.770625	+	0.637289i	$0.219944\pi$
$29$	−1.22466	+	3.76910i	−0.227413	+	0.699905i	−0.998038	+	0.0626159i	$0.980056\pi$
$30$		0			0
$31$	−1.99006	−	6.12477i	−0.357425	−	1.10004i	−0.954590	−	0.297923i	$-0.903706\pi$
$31$	−1.99006	−	6.12477i	−0.357425	−	1.10004i	0.597165	−	0.802119i	$-0.296294\pi$
$32$			5.13532i			0.907805i
$33$	−0.903319	+	0.293506i	−0.157248	+	0.0510929i
$34$	3.47539	+	2.52502i	0.596025	+	0.433037i
$35$		0			0
$36$	7.48066	−	5.43502i	1.24678	−	0.905836i
$37$	−2.24547	+	3.09062i	−0.369153	+	0.508095i	−0.952670	−	0.304005i	$-0.901676\pi$
$37$	−2.24547	+	3.09062i	−0.369153	+	0.508095i	0.583518	+	0.812100i	$0.301676\pi$
$38$	1.22613	−	1.68762i	0.198904	−	0.273768i
$39$	−0.548341	+	0.398393i	−0.0878048	+	0.0637939i
$40$		0			0
$41$	1.48391	+	1.07813i	0.231749	+	0.168375i	0.697599	−	0.716488i	$-0.254252\pi$
$41$	1.48391	+	1.07813i	0.231749	+	0.168375i	−0.465851	+	0.884863i	$0.654252\pi$
$42$	3.16637	−	1.02882i	0.488582	−	0.158750i
$43$		−	3.59445i		−	0.548149i	−0.961708	−	0.274074i	$-0.911629\pi$
$43$		−	3.59445i		−	0.548149i	0.961708	−	0.274074i	$-0.0883715\pi$
$44$	−2.05975	−	6.33927i	−0.310519	−	0.955680i
$45$		0			0
$46$	−2.37582	+	7.31203i	−0.350296	+	1.07810i
$47$	4.56502	+	1.48326i	0.665877	+	0.216356i	0.622402	−	0.782698i	$-0.286157\pi$
$47$	4.56502	+	1.48326i	0.665877	+	0.216356i	0.0434750	+	0.999055i	$0.486157\pi$
$48$	−0.123302	−	0.169710i	−0.0177971	−	0.0244955i
$49$	−2.21619			−0.316598
$50$		0			0
$51$	0.883436			0.123706
$52$	−2.79582	−	3.84812i	−0.387711	−	0.533638i
$53$	−9.03953	−	2.93712i	−1.24168	−	0.403445i	−0.386745	−	0.922187i	$-0.626401\pi$
$53$	−9.03953	−	2.93712i	−1.24168	−	0.403445i	−0.854931	+	0.518742i	$0.826401\pi$
$54$	1.95693	−	6.02280i	0.266304	−	0.819600i
$55$		0			0
$56$	2.88723	+	8.88599i	0.385823	+	1.18744i
$57$		−	0.428989i		−	0.0568209i
$58$	−8.70390	+	2.82807i	−1.14288	+	0.371343i
$59$	8.61248	+	6.25734i	1.12125	+	0.814636i	0.984398	−	0.175956i	$-0.0563016\pi$
$59$	8.61248	+	6.25734i	1.12125	+	0.814636i	0.136852	+	0.990592i	$0.456302\pi$
$60$		0			0
$61$	−11.5481	+	8.39016i	−1.47858	+	1.07425i	−0.500566	+	0.865698i	$0.666875\pi$
$61$	−11.5481	+	8.39016i	−1.47858	+	1.07425i	−0.978012	+	0.208551i	$0.933125\pi$
$62$	8.74134	−	12.0314i	1.11015	−	1.52799i
$63$	−4.95078	+	6.81417i	−0.623740	+	0.858505i
$64$	−10.3087	+	7.48973i	−1.28859	+	0.936217i
$65$		0			0
$66$	−1.77447	−	1.28923i	−0.218422	−	0.158693i
$67$	−10.1670	+	3.30345i	−1.24209	+	0.403580i	−0.855081	−	0.518494i	$-0.826493\pi$
$67$	−10.1670	+	3.30345i	−1.24209	+	0.403580i	−0.387012	+	0.922075i	$0.626493\pi$
$68$			6.19974i			0.751828i
$69$	0.488588	+	1.50372i	0.0588191	+	0.181027i
$70$		0			0
$71$	3.85030	−	11.8500i	0.456947	−	1.40634i	−0.411887	−	0.911235i	$-0.635130\pi$
$71$	3.85030	−	11.8500i	0.456947	−	1.40634i	0.868834	−	0.495104i	$-0.164870\pi$
$72$	8.12101	+	2.63868i	0.957070	+	0.310971i
$73$	−0.157310	−	0.216518i	−0.0184117	−	0.0253415i	0.799712	−	0.600384i	$-0.204986\pi$
$73$	−0.157310	−	0.216518i	−0.0184117	−	0.0253415i	−0.818124	+	0.575042i	$0.804986\pi$
$74$	−8.82193			−1.02553
$75$		0			0
$76$	3.01054			0.345332
$77$	3.56882	+	4.91206i	0.406704	+	0.559781i
$78$	−1.48859	−	0.483672i	−0.168549	−	0.0547650i
$79$	2.64882	−	8.15223i	0.298015	−	0.917197i	−0.684176	−	0.729316i	$-0.739838\pi$
$79$	2.64882	−	8.15223i	0.298015	−	0.917197i	0.982192	−	0.187881i	$-0.0601618\pi$
$80$		0			0
$81$	2.16963	+	6.67743i	0.241070	+	0.741937i
$82$			4.23572i			0.467757i
$83$	12.0006	−	3.89923i	1.31724	−	0.427996i	0.435691	−	0.900096i	$-0.356504\pi$
$83$	12.0006	−	3.89923i	1.31724	−	0.427996i	0.881545	+	0.472100i	$0.156504\pi$
$84$	3.88723	+	2.82424i	0.424132	+	0.308150i
$85$		0			0
$86$	6.71531	−	4.87896i	0.724130	−	0.526112i
$87$	−1.10626	+	1.52263i	−0.118603	+	0.163243i
$88$	3.61803	−	4.97980i	0.385684	−	0.530848i
$89$	−3.85736	+	2.80253i	−0.408879	+	0.297068i	−0.773148	−	0.634226i	$-0.781319\pi$
$89$	−3.85736	+	2.80253i	−0.408879	+	0.297068i	0.364269	+	0.931294i	$0.381319\pi$
$90$		0			0
$91$	3.50527	+	2.54673i	0.367452	+	0.266969i
$92$	−10.5527	+	3.42879i	−1.10020	+	0.357476i
$93$		−	3.05836i		−	0.317137i
$94$	3.42527	+	10.5419i	0.353289	+	1.08731i
$95$		0			0
$96$	−0.753624	+	2.31942i	−0.0769164	+	0.236724i
$97$	9.47067	+	3.07721i	0.961600	+	0.312443i	0.747420	−	0.664351i	$-0.231292\pi$
$97$	9.47067	+	3.07721i	0.961600	+	0.312443i	0.214180	+	0.976794i	$0.431292\pi$
$98$	−3.00816	−	4.14037i	−0.303870	−	0.418241i
$99$	5.54893			0.557689
$100$		0			0
$101$	9.34612			0.929974			0.464987	−	0.885318i	$-0.346059\pi$
$101$	9.34612			0.929974			0.464987	+	0.885318i	$0.346059\pi$
$102$	1.19914	+	1.65047i	0.118732	+	0.163421i
$103$	8.63947	+	2.80713i	0.851272	+	0.276595i	0.701979	−	0.712198i	$-0.252300\pi$
$103$	8.63947	+	2.80713i	0.851272	+	0.276595i	0.149294	+	0.988793i	$0.452300\pi$
$104$	1.35736	−	4.17752i	0.133100	−	0.409639i
$105$		0			0
$106$	−6.78262	−	20.8748i	−0.658787	−	2.02754i
$107$		−	5.62871i		−	0.544148i	−0.962276	−	0.272074i	$-0.912290\pi$
$107$		−	5.62871i		−	0.544148i	0.962276	−	0.272074i	$-0.0877096\pi$
$108$	8.69212	−	2.82424i	0.836400	−	0.271763i
$109$	−8.18158	−	5.94427i	−0.783654	−	0.569358i	0.122420	−	0.992478i	$-0.460935\pi$
$109$	−8.18158	−	5.94427i	−0.783654	−	0.569358i	−0.906073	+	0.423121i	$0.860935\pi$
$110$		0			0
$111$	−1.46774	+	1.06638i	−0.139312	+	0.101216i
$112$	−0.788206	+	1.08487i	−0.0744784	+	0.102511i
$113$	6.29636	−	8.66620i	0.592312	−	0.815247i	−0.402666	−	0.915347i	$-0.631916\pi$
$113$	6.29636	−	8.66620i	0.592312	−	0.815247i	0.994977	+	0.100100i	$0.0319162\pi$
$114$	0.801455	−	0.582291i	0.0750631	−	0.0545366i
$115$		0			0
$116$	−10.6854	−	7.76342i	−0.992118	−	0.720816i
$117$	3.76594	−	1.22363i	0.348162	−	0.113125i
$118$			24.5836i			2.26311i
$119$	−1.74513	−	5.37097i	−0.159976	−	0.492356i
$120$		0			0
$121$	−2.16312	+	6.65740i	−0.196647	+	0.605218i
$122$	−31.3497	−	10.1861i	−2.83827	−	0.922209i
$123$	0.512006	+	0.704715i	0.0461660	+	0.0635420i
$124$	21.4628			1.92742
$125$		0			0
$126$	−19.4505			−1.73279
$127$	−6.67779	−	9.19118i	−0.592558	−	0.815586i	0.402444	−	0.915445i	$-0.368161\pi$
$127$	−6.67779	−	9.19118i	−0.592558	−	0.815586i	−0.995002	+	0.0998589i	$0.968161\pi$
$128$	−18.2173	−	5.91917i	−1.61020	−	0.523185i
$129$	0.527497	−	1.62347i	0.0464435	−	0.142938i
$130$		0			0
$131$	2.46834	+	7.59677i	0.215660	+	0.663732i	0.999106	+	0.0422730i	$0.0134599\pi$
$131$	2.46834	+	7.59677i	0.215660	+	0.663732i	−0.783446	+	0.621459i	$0.786540\pi$
$132$		−	3.16546i		−	0.275518i
$133$	−2.60809	+	0.847421i	−0.226150	+	0.0734807i
$134$	−19.9719	−	14.5104i	−1.72531	−	1.25351i
$135$		0			0
$136$	−4.63182	+	3.36522i	−0.397176	+	0.288565i
$137$	−5.48831	+	7.55401i	−0.468898	+	0.645382i	−0.976324	−	0.216313i	$-0.930597\pi$
$137$	−5.48831	+	7.55401i	−0.468898	+	0.645382i	0.507426	+	0.861695i	$0.330597\pi$
$138$	−2.14612	+	2.95389i	−0.182690	+	0.251452i
$139$	14.4936	−	10.5302i	1.22933	−	0.893160i	0.232489	−	0.972599i	$-0.425313\pi$
$139$	14.4936	−	10.5302i	1.22933	−	0.893160i	0.996840	+	0.0794393i	$0.0253130\pi$
$140$		0			0
$141$	1.84416	+	1.33986i	0.155306	+	0.112837i
$142$	27.3649	−	8.89141i	2.29642	−	0.746151i
$143$		−	2.85442i		−	0.238699i
$144$	0.378710	+	1.16555i	0.0315592	+	0.0971292i
$145$		0			0
$146$	0.190983	−	0.587785i	0.0158059	−	0.0486455i
$147$	−1.00096	−	0.325232i	−0.0825579	−	0.0268247i
$148$	−7.48358	−	10.3003i	−0.615146	−	0.846676i
$149$	6.31395			0.517259			0.258629	−	0.965977i	$-0.416729\pi$
$149$	6.31395			0.517259			0.258629	+	0.965977i	$0.416729\pi$
$150$		0			0
$151$	4.71947			0.384065			0.192033	−	0.981389i	$-0.438492\pi$
$151$	4.71947			0.384065			0.192033	+	0.981389i	$0.438492\pi$
$152$	1.63412	+	2.24917i	0.132545	+	0.182432i
$153$	−4.90859	−	1.59490i	−0.396836	−	0.128940i
$154$	−4.33275	+	13.3348i	−0.349143	+	1.07455i
$155$		0			0
$156$	−0.698036	−	2.14833i	−0.0558876	−	0.172004i
$157$		−	1.46908i		−	0.117245i	−0.998280	−	0.0586225i	$-0.981329\pi$
$157$		−	1.46908i		−	0.117245i	0.998280	−	0.0586225i	$-0.0186708\pi$
$158$	18.8257	−	6.11685i	1.49769	−	0.486630i
$159$	−3.65176	−	2.65316i	−0.289603	−	0.210409i
$160$		0			0
$161$	8.17691	−	5.94087i	0.644431	−	0.468206i
$162$	−9.53010	+	13.1171i	−0.748756	+	1.03057i
$163$	2.62134	−	3.60797i	0.205319	−	0.282598i	−0.693922	−	0.720050i	$-0.744119\pi$
$163$	2.62134	−	3.60797i	0.205319	−	0.282598i	0.899242	+	0.437452i	$0.144119\pi$
$164$	−4.94552	+	3.59313i	−0.386180	+	0.280576i
$165$		0			0
$166$	23.5738	+	17.1274i	1.82968	+	1.32934i
$167$	9.92300	−	3.22418i	0.767865	−	0.249494i	0.101214	−	0.994865i	$-0.467727\pi$
$167$	9.92300	−	3.22418i	0.767865	−	0.249494i	0.666651	+	0.745370i	$0.267727\pi$
$168$			4.43715i			0.342334i
$169$	3.38778	+	10.4265i	0.260598	+	0.802038i
$170$		0			0
$171$	−0.774467	+	2.38357i	−0.0592250	+	0.182276i
$172$	11.3931	+	3.70184i	0.868715	+	0.282263i
$173$	4.51195	+	6.21017i	0.343037	+	0.472151i	0.945326	−	0.326128i	$-0.105744\pi$
$173$	4.51195	+	6.21017i	0.343037	+	0.472151i	−0.602288	+	0.798279i	$0.705744\pi$
$174$	−4.34623			−0.329486
$175$		0			0
$176$	0.883436			0.0665915
$177$	2.97163	+	4.09009i	0.223361	+	0.307430i
$178$	−10.4716	−	3.40244i	−0.784882	−	0.255023i
$179$	−4.79494	+	14.7573i	−0.358391	+	1.10301i	0.595626	+	0.803262i	$0.296904\pi$
$179$	−4.79494	+	14.7573i	−0.358391	+	1.10301i	−0.954017	+	0.299752i	$0.903096\pi$
$180$		0			0
$181$	−0.491509	−	1.51271i	−0.0365336	−	0.112439i	0.931127	−	0.364696i	$-0.118827\pi$
$181$	−0.491509	−	1.51271i	−0.0365336	−	0.112439i	−0.967660	+	0.252257i	$0.918827\pi$
$182$			10.0055i			0.741658i
$183$	−6.44707	+	2.09478i	−0.476581	+	0.154851i
$184$	−8.28968	−	6.02280i	−0.611123	−	0.444007i
$185$		0			0
$186$	5.71375	−	4.15129i	0.418953	−	0.304387i
$187$	−2.18685	+	3.00994i	−0.159918	+	0.220109i
$188$	−9.40281	+	12.9419i	−0.685770	+	0.943882i
$189$	−6.73519	+	4.89340i	−0.489913	+	0.355943i
$190$		0			0
$191$	−15.9121	−	11.5608i	−1.15136	−	0.836511i	−0.162698	−	0.986676i	$-0.552020\pi$
$191$	−15.9121	−	11.5608i	−1.15136	−	0.836511i	−0.988661	+	0.150164i	$0.952020\pi$
$192$	−5.75518	+	1.86997i	−0.415344	+	0.134954i
$193$			13.1100i			0.943680i	0.881684	+	0.471840i	$0.156410\pi$
$193$			13.1100i			0.943680i	−0.881684	+	0.471840i	$0.843590\pi$
$194$	7.10611	+	21.8704i	0.510189	+	1.57020i
$195$		0			0
$196$	2.28240	−	7.02449i	0.163028	−	0.501750i
$197$	3.26164	+	1.05977i	0.232382	+	0.0755055i	0.422893	−	0.906180i	$-0.361015\pi$
$197$	3.26164	+	1.05977i	0.232382	+	0.0755055i	−0.190511	+	0.981685i	$0.561015\pi$
$198$	7.53189	+	10.3668i	0.535268	+	0.736733i
$199$	−17.6959			−1.25443			−0.627215	−	0.778846i	$-0.715805\pi$
$199$	−17.6959			−1.25443			−0.627215	+	0.778846i	$0.715805\pi$
$200$		0			0
$201$	−5.07680			−0.358090
$202$	12.6860	+	17.4608i	0.892586	+	1.22854i
$203$	11.4423	+	3.71783i	0.803093	+	0.260941i
$204$	−0.909830	+	2.80017i	−0.0637008	+	0.196051i
$205$		0			0
$206$	6.48244	+	19.9509i	0.451653	+	1.39005i
$207$		−	9.23710i		−	0.642023i
$208$	0.599570	−	0.194812i	0.0415727	−	0.0135078i
$209$	1.46160	+	1.06192i	0.101101	+	0.0734542i
$210$		0			0
$211$	2.62418	−	1.90658i	0.180656	−	0.131254i	−0.493782	−	0.869586i	$-0.664386\pi$
$211$	2.62418	−	1.90658i	0.180656	−	0.131254i	0.674438	+	0.738331i	$0.264386\pi$
$212$	18.6192	−	25.6271i	1.27877	−	1.76008i
$213$	3.47805	−	4.78713i	0.238312	−	0.328009i
$214$	10.5158	−	7.64018i	0.718845	−	0.522272i
$215$		0			0
$216$	6.82808	+	4.96089i	0.464592	+	0.337546i
$217$	−18.5937	+	6.04145i	−1.26222	+	0.410121i
$218$		−	23.3537i		−	1.58171i
$219$	−0.0392757	−	0.120878i	−0.00265401	−	0.00816819i
$220$		0			0
$221$	−0.820429	+	2.52502i	−0.0551880	+	0.169851i
$222$	−3.98451	−	1.29465i	−0.267423	−	0.0868909i
$223$	−16.8781	−	23.2307i	−1.13024	−	1.55564i	−0.787609	−	0.616175i	$-0.788681\pi$
$223$	−16.8781	−	23.2307i	−1.13024	−	1.55564i	−0.342633	−	0.939469i	$-0.611319\pi$
$224$	15.5899			1.04164
$225$		0			0
$226$	24.7370			1.64548
$227$	6.88921	+	9.48219i	0.457253	+	0.629355i	0.973936	−	0.226822i	$-0.0728335\pi$
$227$	6.88921	+	9.48219i	0.457253	+	0.629355i	−0.516683	+	0.856177i	$0.672833\pi$
$228$	1.35974	+	0.441805i	0.0900508	+	0.0292593i
$229$	5.06828	−	15.5985i	0.334921	−	1.03078i	−0.631840	−	0.775099i	$-0.717700\pi$
$229$	5.06828	−	15.5985i	0.334921	−	1.03078i	0.966761	−	0.255682i	$-0.0823000\pi$
$230$		0			0
$231$	0.891031	+	2.74231i	0.0586255	+	0.180431i
$232$		−	12.1971i		−	0.800777i
$233$	−21.4126	+	6.95739i	−1.40279	+	0.455794i	−0.910092	−	0.414407i	$-0.863989\pi$
$233$	−21.4126	+	6.95739i	−1.40279	+	0.455794i	−0.492697	+	0.870201i	$0.663989\pi$
$234$	7.39777	+	5.37479i	0.483607	+	0.351361i
$235$		0			0
$236$	−28.7032	+	20.8541i	−1.86842	+	1.35749i
$237$	2.39273	−	3.29331i	0.155424	−	0.213923i
$238$	7.66550	−	10.5507i	0.496880	−	0.683897i
$239$	−5.36647	+	3.89897i	−0.347128	+	0.252204i	−0.747663	−	0.664078i	$-0.768824\pi$
$239$	−5.36647	+	3.89897i	−0.347128	+	0.252204i	0.400535	+	0.916281i	$0.368824\pi$
$240$		0			0
$241$	−21.2173	−	15.4153i	−1.36673	−	0.992986i	−0.997985	−	0.0634545i	$-0.979788\pi$
$241$	−21.2173	−	15.4153i	−1.36673	−	0.992986i	−0.368743	−	0.929531i	$-0.620212\pi$
$242$	−15.3738	+	4.99524i	−0.988262	+	0.321106i
$243$			11.5613i			0.741655i
$244$	−14.7006	−	45.2439i	−0.941112	−	2.89645i
$245$		0			0
$246$	−0.621604	+	1.91310i	−0.0396320	+	0.121975i
$247$	1.22613	+	0.398393i	0.0780166	+	0.0253491i
$248$	11.6500	+	16.0349i	0.739776	+	1.01821i
$249$	5.99241			0.379753
$250$		0			0
$251$	−10.9121			−0.688766			−0.344383	−	0.938829i	$-0.611912\pi$
$251$	−10.9121			−0.688766			−0.344383	+	0.938829i	$0.611912\pi$
$252$	−16.4997	−	22.7099i	−1.03938	−	1.43059i
$253$	−6.33275	−	2.05763i	−0.398137	−	0.129362i
$254$	8.10722	−	24.9514i	0.508692	−	1.56559i
$255$		0			0
$256$	−5.79381	−	17.8315i	−0.362113	−	1.11447i
$257$		−	6.58051i		−	0.410481i	−0.978712	−	0.205240i	$-0.934202\pi$
$257$		−	6.58051i		−	0.410481i	0.978712	−	0.205240i	$-0.0657976\pi$
$258$	3.74903	−	1.21814i	0.233405	−	0.0758378i
$259$	9.38256	+	6.81683i	0.583004	+	0.423577i
$260$		0			0
$261$	8.89547	−	6.46294i	0.550616	−	0.400046i
$262$	−10.8422	+	14.9230i	−0.669832	+	0.921945i
$263$	−15.9332	+	21.9302i	−0.982486	+	1.35228i	−0.0470069	+	0.998895i	$0.514968\pi$
$263$	−15.9332	+	21.9302i	−0.982486	+	1.35228i	−0.935479	+	0.353382i	$0.885032\pi$
$264$	2.36492	−	1.71821i	0.145551	−	0.105749i
$265$		0			0
$266$	−5.12330	−	3.72230i	−0.314130	−	0.228229i
$267$	−2.15349	+	0.699712i	−0.131792	+	0.0428217i
$268$		−	35.6277i		−	2.17631i
$269$	−0.311938	−	0.960046i	−0.0190192	−	0.0585350i	0.941096	−	0.338138i	$-0.109797\pi$
$269$	−0.311938	−	0.960046i	−0.0190192	−	0.0585350i	−0.960116	+	0.279603i	$0.909797\pi$
$270$		0			0
$271$	1.93198	−	5.94603i	0.117360	−	0.361196i	−0.875072	−	0.483992i	$-0.839186\pi$
$271$	1.93198	−	5.94603i	0.117360	−	0.361196i	0.992432	+	0.122796i	$0.0391862\pi$
$272$	−0.781488	−	0.253921i	−0.0473847	−	0.0153962i
$273$	1.20945	+	1.66466i	0.0731991	+	0.100750i
$274$	−21.5623			−1.30263
$275$		0			0
$276$	−5.26943			−0.317182
$277$	−14.5009	−	19.9587i	−0.871272	−	1.19920i	−0.978763	−	0.204997i	$-0.934282\pi$
$277$	−14.5009	−	19.9587i	−0.871272	−	1.19920i	0.107491	−	0.994206i	$-0.465718\pi$
$278$	39.3459	+	12.7843i	2.35981	+	0.766749i
$279$	−5.52135	+	16.9930i	−0.330555	+	1.01734i
$280$		0			0
$281$	0.568255	+	1.74891i	0.0338993	+	0.104331i	0.966574	−	0.256386i	$-0.0825319\pi$
$281$	0.568255	+	1.74891i	0.0338993	+	0.104331i	−0.932675	+	0.360717i	$0.882532\pi$
$282$			5.26401i			0.313467i
$283$	8.21823	−	2.67026i	0.488523	−	0.158731i	−0.0543898	−	0.998520i	$-0.517321\pi$
$283$	8.21823	−	2.67026i	0.488523	−	0.158731i	0.542913	+	0.839789i	$0.317321\pi$
$284$	33.5949	+	24.4081i	1.99349	+	1.44835i
$285$		0			0
$286$	5.33275	−	3.87447i	0.315332	−	0.229102i
$287$	3.27300	−	4.50489i	0.193199	−	0.265915i
$288$	8.37463	−	11.5267i	0.493480	−	0.679217i
$289$	−10.9537	+	7.95831i	−0.644334	+	0.468136i
$290$		0			0
$291$	3.82593	+	2.77970i	0.224280	+	0.162949i
$292$	0.848293	−	0.275627i	0.0496426	−	0.0161299i
$293$			6.29156i			0.367557i	0.982968	+	0.183779i	$0.0588329\pi$
$293$			6.29156i			0.367557i	−0.982968	+	0.183779i	$0.941167\pi$
$294$	−0.751050	−	2.31149i	−0.0438021	−	0.134809i
$295$		0			0
$296$	3.63324	−	11.1820i	0.211178	−	0.649939i
$297$	5.21619	+	1.69484i	0.302674	+	0.0983447i
$298$	8.57029	+	11.7960i	0.496463	+	0.683323i
$299$	−4.75164			−0.274795
$300$		0			0
$301$	−10.9121			−0.628963
$302$	6.40601	+	8.81712i	0.368625	+	0.507368i
$303$	4.22126	+	1.37157i	0.242505	+	0.0787947i
$304$	−0.123302	+	0.379483i	−0.00707183	+	0.0217649i
$305$		0			0
$306$	−3.68305	−	11.3353i	−0.210546	−	0.647994i
$307$			28.6661i			1.63606i	0.575175	+	0.818030i	$0.304934\pi$
$307$			28.6661i			1.63606i	−0.575175	+	0.818030i	$0.695066\pi$
$308$	−19.2449	+	6.25303i	−1.09658	+	0.356300i
$309$	3.49014	+	2.53574i	0.198547	+	0.144253i
$310$		0			0
$311$	6.33985	−	4.60617i	0.359500	−	0.261192i	−0.393343	−	0.919392i	$-0.628682\pi$
$311$	6.33985	−	4.60617i	0.359500	−	0.261192i	0.752844	+	0.658199i	$0.228682\pi$
$312$	1.22613	−	1.68762i	0.0694158	−	0.0955426i
$313$	12.5840	−	17.3205i	0.711292	−	0.979010i	−0.288476	−	0.957487i	$-0.593149\pi$
$313$	12.5840	−	17.3205i	0.711292	−	0.979010i	0.999768	−	0.0215228i	$-0.00685144\pi$
$314$	2.74459	−	1.99406i	0.154886	−	0.112531i
$315$		0			0
$316$	23.1116	+	16.7916i	1.30013	+	0.944599i
$317$	3.82309	−	1.24220i	0.214726	−	0.0697688i	−0.199679	−	0.979861i	$-0.563990\pi$
$317$	3.82309	−	1.24220i	0.214726	−	0.0697688i	0.414405	+	0.910093i	$0.363990\pi$
$318$		−	10.4237i		−	0.584530i
$319$	−2.44931	−	7.53821i	−0.137135	−	0.422059i
$320$		0			0
$321$	0.826031	−	2.54226i	0.0461046	−	0.141895i
$322$	22.1980	+	7.21256i	1.23705	+	0.401940i
$323$	−0.987712	−	1.35947i	−0.0549578	−	0.0756429i
$324$	−23.3995			−1.29997
$325$		0			0
$326$	10.2987			0.570390
$327$	−2.82295	−	3.88546i	−0.156109	−	0.214866i
$328$	−5.36885	−	1.74445i	−0.296445	−	0.0963209i
$329$	4.50292	−	13.8586i	0.248254	−	0.764047i
$330$		0			0
$331$	3.59815	+	11.0740i	0.197772	+	0.608681i	0.999933	+	0.0115724i	$0.00368369\pi$
$331$	3.59815	+	11.0740i	0.197772	+	0.608681i	−0.802161	+	0.597108i	$0.796316\pi$
$332$			42.0532i			2.30797i
$333$	10.0803	−	3.27529i	0.552398	−	0.179485i
$334$	19.4926	+	14.1622i	1.06659	+	0.774922i
$335$		0			0
$336$	−0.515209	+	0.374321i	−0.0281069	+	0.0204209i
$337$	12.6578	−	17.4220i	0.689516	−	0.949037i	−0.310483	−	0.950579i	$-0.600491\pi$
$337$	12.6578	−	17.4220i	0.689516	−	0.949037i	0.999999	+	0.00154181i	$0.000490773\pi$
$338$	−14.8808	+	20.4817i	−0.809409	+	1.11406i
$339$	4.11560	−	2.99016i	0.223529	−	0.162403i
$340$		0			0
$341$	10.4201	+	7.57063i	0.564279	+	0.409973i
$342$	−5.50431	+	1.78846i	−0.297639	+	0.0967087i
$343$		−	14.5228i		−	0.784157i
$344$	3.41853	+	10.5211i	0.184315	+	0.567262i
$345$		0			0
$346$	−5.47777	+	16.8588i	−0.294487	+	0.906337i
$347$	−14.8339	−	4.81981i	−0.796323	−	0.258741i	−0.117529	−	0.993069i	$-0.537497\pi$
$347$	−14.8339	−	4.81981i	−0.796323	−	0.258741i	−0.678794	+	0.734328i	$0.737497\pi$
$348$	−3.68687	−	5.07454i	−0.197637	−	0.272024i
$349$	−5.56598			−0.297940			−0.148970	−	0.988842i	$-0.547596\pi$
$349$	−5.56598			−0.297940			−0.148970	+	0.988842i	$0.547596\pi$
$350$		0			0
$351$	3.91385			0.208906
$352$	−6.03693	−	8.30912i	−0.321769	−	0.442878i
$353$	7.62953	+	2.47898i	0.406079	+	0.131943i	0.504932	−	0.863159i	$-0.331517\pi$
$353$	7.62953	+	2.47898i	0.406079	+	0.131943i	−0.0988533	+	0.995102i	$0.531517\pi$
$354$	−3.60773	+	11.1034i	−0.191748	+	0.590141i
$355$		0			0
$356$	−4.91040	−	15.1127i	−0.260251	−	0.800970i
$357$		−	2.68195i		−	0.141944i
$358$	−34.0787	+	11.0728i	−1.80112	+	0.585218i
$359$	−9.98547	−	7.25487i	−0.527013	−	0.382897i	0.292226	−	0.956349i	$-0.405604\pi$
$359$	−9.98547	−	7.25487i	−0.527013	−	0.382897i	−0.819239	+	0.573452i	$0.805604\pi$
$360$		0			0
$361$	14.7112	−	10.6883i	0.774272	−	0.562542i
$362$	2.15895	−	2.97155i	0.113472	−	0.156181i
$363$	−1.95399	+	2.68943i	−0.102558	+	0.141159i
$364$	−11.6822	+	8.48760i	−0.612312	+	0.444871i
$365$		0			0
$366$	−12.6645	−	9.20132i	−0.661986	−	0.480961i
$367$	25.5596	−	8.30481i	1.33420	−	0.433508i	0.446852	−	0.894608i	$-0.352545\pi$
$367$	25.5596	−	8.30481i	1.33420	−	0.433508i	0.887348	+	0.461100i	$0.152545\pi$
$368$		−	1.47062i		−	0.0766615i
$369$	−1.57258	−	4.83991i	−0.0818653	−	0.251956i
$370$		0			0
$371$	−8.91657	+	27.4424i	−0.462925	+	1.42474i
$372$	9.69387	+	3.14973i	0.502604	+	0.163306i
$373$	16.2457	+	22.3604i	0.841173	+	1.15778i	0.985739	+	0.168280i	$0.0538213\pi$
$373$	16.2457	+	22.3604i	0.841173	+	1.15778i	−0.144566	+	0.989495i	$0.546179\pi$
$374$	−8.59164			−0.444263
$375$		0			0
$376$	−14.7727			−0.761845
$377$	−3.32459	−	4.57591i	−0.171225	−	0.235671i
$378$	−18.2841	−	5.94087i	−0.940434	−	0.305566i
$379$	1.07372	−	3.30456i	0.0551532	−	0.169744i	−0.919685	−	0.392656i	$-0.871556\pi$
$379$	1.07372	−	3.30456i	0.0551532	−	0.169744i	0.974839	+	0.222912i	$0.0715563\pi$
$380$		0			0
$381$	−1.66725	−	5.13127i	−0.0854159	−	0.262883i
$382$		−	45.4198i		−	2.32388i
$383$	−26.0322	+	8.45837i	−1.33018	+	0.432203i	−0.885980	−	0.463723i	$-0.846513\pi$
$383$	−26.0322	+	8.45837i	−1.33018	+	0.432203i	−0.444203	+	0.895926i	$0.646513\pi$
$384$	−7.35937	−	5.34689i	−0.375556	−	0.272858i
$385$		0			0
$386$	−24.4927	+	17.7950i	−1.24665	+	0.905741i
$387$	−5.86180	+	8.06808i	−0.297972	+	0.410123i
$388$	−19.5072	+	26.8494i	−0.990329	+	1.36307i
$389$	8.80576	−	6.39776i	0.446470	−	0.324379i	−0.341731	−	0.939798i	$-0.611013\pi$
$389$	8.80576	−	6.39776i	0.446470	−	0.324379i	0.788200	+	0.615419i	$0.211013\pi$
$390$		0			0
$391$	5.01054	+	3.64037i	0.253394	+	0.184101i
$392$	6.48689	−	2.10772i	0.327637	−	0.106456i
$393$			3.79339i			0.191351i
$394$	2.44730	+	7.53202i	0.123293	+	0.379458i
$395$		0			0
$396$	−5.71472	+	17.5881i	−0.287175	+	0.883835i
$397$	−15.4273	−	5.01264i	−0.774275	−	0.251577i	−0.104881	−	0.994485i	$-0.533446\pi$
$397$	−15.4273	−	5.01264i	−0.774275	−	0.251577i	−0.669394	+	0.742908i	$0.733446\pi$
$398$	−24.0197	−	33.0603i	−1.20400	−	1.65716i
$399$	−1.30233			−0.0651981
$400$		0			0
$401$	3.78686			0.189107			0.0945534	−	0.995520i	$-0.469858\pi$
$401$	3.78686			0.189107			0.0945534	+	0.995520i	$0.469858\pi$
$402$	−6.89103	−	9.48469i	−0.343693	−	0.473053i
$403$	8.74134	+	2.84023i	0.435437	+	0.141482i
$404$	−9.62535	+	29.6238i	−0.478879	+	1.47384i
$405$		0			0
$406$	8.58550	+	26.4234i	0.426091	+	1.31137i
$407$		−	7.64044i		−	0.378722i
$408$	−2.58586	+	0.840198i	−0.128019	+	0.0415960i
$409$	1.50142	+	1.09084i	0.0742403	+	0.0539388i	0.624286	−	0.781196i	$-0.285390\pi$
$409$	1.50142	+	1.09084i	0.0742403	+	0.0539388i	−0.550046	+	0.835134i	$0.685390\pi$
$410$		0			0
$411$	−3.58742	+	2.60641i	−0.176954	+	0.128565i
$412$	−17.7952	+	24.4930i	−0.876705	+	1.20668i
$413$	18.9961	−	26.1459i	0.934738	−	1.28656i
$414$	17.2571	−	12.5380i	0.848142	−	0.616211i
$415$		0			0
$416$	−5.92943	−	4.30798i	−0.290714	−	0.211216i
$417$	8.09150	−	2.62909i	0.396242	−	0.128747i
$418$			4.17202i			0.204060i
$419$	−4.43353	−	13.6450i	−0.216592	−	0.666602i	−0.999037	−	0.0438818i	$-0.986028\pi$
$419$	−4.43353	−	13.6450i	−0.216592	−	0.666602i	0.782445	−	0.622720i	$-0.213972\pi$
$420$		0			0
$421$	4.77571	−	14.6981i	0.232754	−	0.716343i	−0.764658	−	0.644437i	$-0.777092\pi$
$421$	4.77571	−	14.6981i	0.232754	−	0.716343i	0.997411	−	0.0719060i	$-0.0229082\pi$
$422$	7.12390	+	2.31469i	0.346786	+	0.112678i
$423$	−7.82771	−	10.7739i	−0.380596	−	0.523846i
$424$	29.2525			1.42063
$425$		0			0
$426$	13.6645			0.662046
$427$	25.4710	+	35.0578i	1.23263	+	1.69657i
$428$	17.8410	+	5.79688i	0.862375	+	0.280203i
$429$	0.418895	−	1.28923i	0.0202244	−	0.0622444i
$430$		0			0
$431$	3.86404	+	11.8923i	0.186124	+	0.572832i	0.999966	−	0.00825486i	$-0.00262763\pi$
$431$	3.86404	+	11.8923i	0.186124	+	0.572832i	−0.813842	+	0.581087i	$0.802628\pi$
$432$			1.21133i			0.0582801i
$433$	21.3941	−	6.95138i	1.02814	−	0.334062i	0.254084	−	0.967182i	$-0.418226\pi$
$433$	21.3941	−	6.95138i	1.02814	−	0.334062i	0.774053	+	0.633120i	$0.218226\pi$
$434$	−36.5252	−	26.5371i	−1.75326	−	1.27382i
$435$		0			0
$436$	27.2672	−	19.8108i	1.30586	−	0.948763i
$437$	1.76773	−	2.43307i	0.0845620	−	0.116390i
$438$	0.172519	−	0.237451i	0.00824326	−	0.0113459i
$439$	9.85186	−	7.15780i	0.470204	−	0.341623i	−0.327317	−	0.944915i	$-0.606145\pi$
$439$	9.85186	−	7.15780i	0.470204	−	0.341623i	0.797521	+	0.603292i	$0.206145\pi$
$440$		0			0
$441$	4.97443	+	3.61414i	0.236878	+	0.172102i
$442$	−5.83096	+	1.89460i	−0.277351	+	0.0901167i
$443$		−	20.7101i		−	0.983968i	−0.870604	−	0.491984i	$-0.836272\pi$
$443$		−	20.7101i		−	0.983968i	0.870604	−	0.491984i	$-0.163728\pi$
$444$	−1.86843	−	5.75045i	−0.0886720	−	0.272904i
$445$		0			0
$446$	20.4910	−	63.0648i	0.970277	−	2.98621i
$447$	2.85176	+	0.926591i	0.134883	+	0.0438263i
$448$	22.7375	+	31.2954i	1.07424	+	1.47857i
$449$	25.9539			1.22484			0.612420	−	0.790533i	$-0.290196\pi$
$449$	25.9539			1.22484			0.612420	+	0.790533i	$0.290196\pi$
$450$		0			0
$451$	−3.66844			−0.172740
$452$	20.9842	+	28.8823i	0.987013	+	1.35851i
$453$	2.13159	+	0.692597i	0.100151	+	0.0325411i
$454$	−8.36390	+	25.7414i	−0.392537	+	1.20811i
$455$		0			0
$456$	0.407993	+	1.25567i	0.0191060	+	0.0588022i
$457$			8.50150i			0.397684i	0.980032	+	0.198842i	$0.0637180\pi$
$457$			8.50150i			0.397684i	−0.980032	+	0.198842i	$0.936282\pi$
$458$	36.0213	−	11.7040i	1.68317	−	0.546894i
$459$	−4.12710	−	2.99851i	−0.192636	−	0.139959i
$460$		0			0
$461$	−11.9614	+	8.69044i	−0.557097	+	0.404754i	−0.830395	−	0.557175i	$-0.811885\pi$
$461$	−11.9614	+	8.69044i	−0.557097	+	0.404754i	0.273299	+	0.961929i	$0.411885\pi$
$462$	−3.91385	+	5.38696i	−0.182089	+	0.250624i
$463$	−13.0442	+	17.9538i	−0.606215	+	0.834384i	−0.996259	−	0.0864125i	$-0.972460\pi$
$463$	−13.0442	+	17.9538i	−0.606215	+	0.834384i	0.390044	+	0.920796i	$0.372460\pi$
$464$	1.41623	−	1.02895i	0.0657470	−	0.0477680i
$465$		0			0
$466$	−42.0627	−	30.5603i	−1.94852	−	1.41568i
$467$	−27.1064	+	8.80741i	−1.25434	+	0.407558i	−0.859473	−	0.511182i	$-0.829208\pi$
$467$	−27.1064	+	8.80741i	−1.25434	+	0.407558i	−0.394863	+	0.918740i	$0.629208\pi$
$468$			13.1968i			0.610024i
$469$	10.0287	+	30.8651i	0.463081	+	1.42522i
$470$		0			0
$471$	0.215591	−	0.663522i	0.00993393	−	0.0305735i
$472$	−31.1603	−	10.1246i	−1.43427	−	0.466022i
$473$	4.22553	+	5.81595i	0.194290	+	0.267418i
$474$	9.40048			0.431779
$475$		0			0
$476$	18.8213			0.862671
$477$	15.5002	+	21.3342i	0.709707	+	0.976827i
$478$	−14.5684	−	4.73358i	−0.666345	−	0.216509i
$479$	−7.74301	+	23.8305i	−0.353787	+	1.08885i	0.602922	+	0.797800i	$0.294003\pi$
$479$	−7.74301	+	23.8305i	−0.353787	+	1.08885i	−0.956709	+	0.291045i	$0.905997\pi$
$480$		0			0
$481$	−1.68484	−	5.18540i	−0.0768220	−	0.236434i
$482$		−	60.5632i		−	2.75858i
$483$	4.56502	−	1.48326i	0.207716	−	0.0674909i
$484$	−18.8738	−	13.7126i	−0.857898	−	0.623299i
$485$		0			0
$486$	−21.5992	+	15.6928i	−0.979761	+	0.711838i
$487$	0.860980	−	1.18504i	0.0390147	−	0.0536992i	−0.789064	−	0.614311i	$-0.789434\pi$
$487$	0.860980	−	1.18504i	0.0390147	−	0.0536992i	0.828079	+	0.560612i	$0.189434\pi$
$488$	25.8222	−	35.5413i	1.16892	−	1.60888i
$489$	1.71343	−	1.24488i	0.0774842	−	0.0562955i
$490$		0			0
$491$	16.2359	+	11.7961i	0.732715	+	0.532348i	0.890421	−	0.455138i	$-0.150410\pi$
$491$	16.2359	+	11.7961i	0.732715	+	0.532348i	−0.157706	+	0.987486i	$0.550410\pi$
$492$	−2.76099	+	0.897100i	−0.124475	+	0.0404444i
$493$			7.37229i			0.332031i
$494$	0.919998	+	2.83146i	0.0413927	+	0.127394i
$495$		0			0
$496$	−0.879045	+	2.70542i	−0.0394703	+	0.121477i
$497$	−35.9745	−	11.6888i	−1.61368	−	0.524315i
$498$	8.13384	+	11.1953i	0.364486	+	0.501672i
$499$	−0.624999			−0.0279788			−0.0139894	−	0.999902i	$-0.504453\pi$
$499$	−0.624999			−0.0279788			−0.0139894	+	0.999902i	$0.504453\pi$
$500$		0			0
$501$	4.95498			0.221372
$502$	−14.8116	−	20.3865i	−0.661075	−	0.909892i
$503$	−18.3603	−	5.96563i	−0.818647	−	0.265994i	−0.130391	−	0.991463i	$-0.541623\pi$
$503$	−18.3603	−	5.96563i	−0.818647	−	0.265994i	−0.688256	+	0.725468i	$0.741623\pi$
$504$	8.01054	−	24.6539i	0.356818	−	1.09817i
$505$		0			0
$506$	−4.75164	−	14.6241i	−0.211236	−	0.650119i
$507$			5.20639i			0.231224i
$508$	36.0100	−	11.7003i	1.59768	−	0.519119i
$509$	−8.51099	−	6.18360i	−0.377243	−	0.274083i	0.382965	−	0.923763i	$-0.374903\pi$
$509$	−8.51099	−	6.18360i	−0.377243	−	0.274083i	−0.760208	+	0.649680i	$0.774903\pi$
$510$		0			0
$511$	−0.657310	+	0.477563i	−0.0290777	+	0.0211262i
$512$	2.93146	−	4.03481i	0.129554	−	0.178315i
$513$	−1.45605	+	2.00408i	−0.0642862	+	0.0884824i
$514$	12.2940	−	8.93210i	0.542264	−	0.393978i
$515$		0			0
$516$	4.60254	+	3.34394i	0.202616	+	0.147209i
$517$	−9.13004	+	2.96653i	−0.401539	+	0.130468i
$518$			26.7818i			1.17672i
$519$	1.12650	+	3.46703i	0.0494481	+	0.152186i
$520$		0			0
$521$	−3.09232	+	9.51719i	−0.135477	+	0.416956i	−0.995664	−	0.0930234i	$-0.970347\pi$
$521$	−3.09232	+	9.51719i	−0.135477	+	0.416956i	0.860187	+	0.509979i	$0.170347\pi$
$522$	24.1487	+	7.84638i	1.05696	+	0.343427i
$523$	−13.3915	−	18.4319i	−0.585571	−	0.805970i	0.408721	−	0.912659i	$-0.365975\pi$
$523$	−13.3915	−	18.4319i	−0.585571	−	0.805970i	−0.994292	+	0.106690i	$0.965975\pi$
$524$	−26.6210			−1.16295
$525$		0			0
$526$	−62.5981			−2.72941
$527$	−7.04162	−	9.69196i	−0.306738	−	0.422188i
$528$	0.399012	+	0.129647i	0.0173648	+	0.00564216i
$529$	3.68213	−	11.3324i	0.160092	−	0.492714i
$530$		0			0
$531$	−9.12710	−	28.0903i	−0.396082	−	1.21902i
$532$		−	9.13943i		−	0.396245i
$533$	−2.48969	+	0.808950i	−0.107841	+	0.0350395i
$534$	−4.23029	−	3.07349i	−0.183063	−	0.133003i
$535$		0			0
$536$	26.6175	−	19.3387i	1.14970	−	0.835306i
$537$	−4.33136	+	5.96161i	−0.186912	+	0.257262i
$538$	1.37019	−	1.88590i	0.0590730	−	0.0813070i
$539$	3.58586	−	2.60528i	0.154454	−	0.112217i
$540$		0			0
$541$	−2.63658	−	1.91559i	−0.113356	−	0.0823576i	0.529663	−	0.848208i	$-0.322318\pi$
$541$	−2.63658	−	1.91559i	−0.113356	−	0.0823576i	−0.643019	+	0.765850i	$0.722318\pi$
$542$	13.7310	−	4.46148i	0.589798	−	0.191637i
$543$		−	0.755360i		−	0.0324156i
$544$	2.95203	+	9.08540i	0.126567	+	0.389533i
$545$		0			0
$546$	−1.46834	+	4.51908i	−0.0628391	+	0.193399i
$547$	12.9232	+	4.19901i	0.552557	+	0.179537i	0.571970	−	0.820275i	$-0.306179\pi$
$547$	12.9232	+	4.19901i	0.552557	+	0.179537i	−0.0194122	+	0.999812i	$0.506179\pi$
$548$	−18.2911	−	25.1756i	−0.781359	−	1.07545i
$549$	39.6033			1.69023
$550$		0			0
$551$	3.57992			0.152510
$552$	−2.86025	−	3.93679i	−0.121740	−	0.167561i
$553$	−24.7487	−	8.04133i	−1.05242	−	0.341952i
$554$	17.6049	−	54.1822i	0.747959	−	2.30198i
$555$		0			0
$556$	18.4503	+	56.7841i	0.782466	+	2.40818i
$557$			27.6399i			1.17114i	0.810621	+	0.585571i	$0.199130\pi$
$557$			27.6399i			1.17114i	−0.810621	+	0.585571i	$0.800870\pi$
$558$	−39.2414	+	12.7503i	−1.66122	+	0.539764i
$559$	4.15029	+	3.01536i	0.175539	+	0.127536i
$560$		0			0
$561$	−1.42943	+	1.03854i	−0.0603506	+	0.0438473i
$562$	−2.49606	+	3.43554i	−0.105290	+	0.144919i
$563$	−0.975284	+	1.34236i	−0.0411033	+	0.0565738i	−0.829074	−	0.559139i	$-0.811132\pi$
$563$	−0.975284	+	1.34236i	−0.0411033	+	0.0565738i	0.787971	+	0.615713i	$0.211132\pi$
$564$	−6.14612	+	4.46542i	−0.258799	+	0.188028i
$565$		0			0
$566$	16.1438	+	11.7291i	0.678574	+	0.493013i
$567$	20.2715	−	6.58660i	0.851322	−	0.276611i
$568$			38.3475i			1.60902i
$569$	−5.52609	−	17.0076i	−0.231666	−	0.712994i	−0.997546	−	0.0700110i	$-0.977697\pi$
$569$	−5.52609	−	17.0076i	−0.231666	−	0.712994i	0.765880	−	0.642983i	$-0.222303\pi$
$570$		0			0
$571$	−11.3942	+	35.0677i	−0.476832	+	1.46754i	0.366640	+	0.930363i	$0.380508\pi$
$571$	−11.3942	+	35.0677i	−0.476832	+	1.46754i	−0.843472	+	0.537174i	$0.819492\pi$
$572$	9.04746	+	2.93970i	0.378293	+	0.122915i
$573$	−5.49027	−	7.55670i	−0.229359	−	0.315686i
$574$	12.8589			0.536718
$575$		0			0
$576$	35.3531			1.47305
$577$	−13.4095	−	18.4567i	−0.558247	−	0.768361i	0.432855	−	0.901463i	$-0.357506\pi$
$577$	−13.4095	−	18.4567i	−0.558247	−	0.768361i	−0.991102	+	0.133103i	$0.957506\pi$
$578$	−29.7361	−	9.66184i	−1.23686	−	0.401880i
$579$	−1.92394	+	5.92127i	−0.0799560	+	0.246079i
$580$		0			0
$581$	−11.8373	−	36.4316i	−0.491096	−	1.51144i
$582$			10.9208i			0.452682i
$583$	18.0791	−	5.87425i	0.748759	−	0.243286i
$584$	0.666375	+	0.484149i	0.0275748	+	0.0200342i
$585$		0			0
$586$	−11.7542	+	8.53990i	−0.485560	+	0.352780i
$587$	6.51588	−	8.96834i	0.268939	−	0.370163i	−0.653092	−	0.757278i	$-0.726529\pi$
$587$	6.51588	−	8.96834i	0.268939	−	0.370163i	0.922031	+	0.387116i	$0.126529\pi$
$588$	2.06173	−	2.83773i	0.0850244	−	0.117026i
$589$	−4.70633	+	3.41935i	−0.193921	+	0.140892i
$590$		0			0
$591$	1.31762	+	0.957311i	0.0541998	+	0.0393785i
$592$	1.60487	−	0.521454i	0.0659597	−	0.0214316i
$593$			11.1321i			0.457139i	0.973528	+	0.228570i	$0.0734049\pi$
$593$			11.1321i			0.457139i	−0.973528	+	0.228570i	$0.926595\pi$
$594$	3.91385	+	12.0456i	0.160587	+	0.494237i
$595$		0			0
$596$	−6.50259	+	20.0129i	−0.266356	+	0.819760i
$597$	−7.99253	−	2.59693i	−0.327112	−	0.106285i
$598$	−6.44968	−	8.87722i	−0.263747	−	0.363017i
$599$	−36.2736			−1.48210			−0.741049	−	0.671451i	$-0.765671\pi$
$599$	−36.2736			−1.48210			−0.741049	+	0.671451i	$0.765671\pi$
$600$		0			0
$601$	−15.1051			−0.616150			−0.308075	−	0.951362i	$-0.599685\pi$
$601$	−15.1051			−0.616150			−0.308075	+	0.951362i	$0.599685\pi$
$602$	−14.8116	−	20.3865i	−0.603677	−	0.830890i
$603$	28.2079	+	9.16531i	1.14872	+	0.373240i
$604$	−4.86047	+	14.9590i	−0.197770	+	0.608673i
$605$		0			0
$606$	3.16734	+	9.74806i	0.128664	+	0.395988i
$607$			33.5066i			1.35999i	0.733216	+	0.679996i	$0.238018\pi$
$607$			33.5066i			1.35999i	−0.733216	+	0.679996i	$0.761982\pi$
$608$	4.41179	−	1.43348i	0.178922	−	0.0581352i
$609$	4.62243	+	3.35839i	0.187310	+	0.136089i
$610$		0			0
$611$	−5.54220	+	4.02664i	−0.224213	+	0.162900i
$612$	10.1105	−	13.9159i	0.408692	−	0.562516i
$613$	−16.4750	+	22.6758i	−0.665418	+	0.915869i	−0.999646	−	0.0266235i	$-0.991524\pi$
$613$	−16.4750	+	22.6758i	−0.665418	+	0.915869i	0.334228	+	0.942492i	$0.391524\pi$
$614$	−53.5552	+	38.9102i	−2.16131	+	1.57029i
$615$		0			0
$616$	−15.1178	−	10.9837i	−0.609112	−	0.442545i
$617$	29.0284	−	9.43191i	1.16864	−	0.379714i	0.340505	−	0.940243i	$-0.389402\pi$
$617$	29.0284	−	9.43191i	1.16864	−	0.379714i	0.828135	+	0.560528i	$0.189402\pi$
$618$			9.96234i			0.400744i
$619$	6.70477	+	20.6352i	0.269488	+	0.829398i	0.990625	+	0.136606i	$0.0436194\pi$
$619$	6.70477	+	20.6352i	0.269488	+	0.829398i	−0.721138	+	0.692792i	$0.756381\pi$
$620$		0			0
$621$	2.82134	−	8.68318i	0.113216	−	0.348444i
$622$	17.2109	+	5.59216i	0.690094	+	0.224225i
$623$	8.50798	+	11.7102i	0.340865	+	0.469161i
$624$	0.299391			0.0119852
$625$		0			0
$626$	49.4399			1.97601
$627$	0.504306	+	0.694118i	0.0201401	+	0.0277204i
$628$	4.65643	+	1.51297i	0.185812	+	0.0603740i
$629$	−2.19604	+	6.75873i	−0.0875620	+	0.269488i
$630$		0			0
$631$	−5.01463	−	15.4335i	−0.199629	−	0.614396i	−0.999891	−	0.0147456i	$-0.995306\pi$
$631$	−5.01463	−	15.4335i	−0.199629	−	0.614396i	0.800262	−	0.599651i	$-0.204694\pi$
$632$			26.3812i			1.04939i
$633$	1.46503	−	0.476017i	0.0582297	−	0.0189200i
$634$	7.51003	+	5.45635i	0.298261	+	0.216699i
$635$		0			0
$636$	12.1704	−	8.84231i	0.482588	−	0.350620i
$637$	1.85914	−	2.55889i	0.0736619	−	0.101387i
$638$	10.7586	−	14.8080i	0.425937	−	0.586253i
$639$	−27.9673	+	20.3194i	−1.10637	+	0.803823i
$640$		0			0
$641$	17.9419	+	13.0356i	0.708663	+	0.514874i	0.882742	−	0.469858i	$-0.155695\pi$
$641$	17.9419	+	13.0356i	0.708663	+	0.514874i	−0.174079	+	0.984732i	$0.555695\pi$
$642$	5.87078	−	1.90753i	0.231701	−	0.0752843i
$643$		−	13.2767i		−	0.523583i	−0.965124	−	0.261792i	$-0.915687\pi$
$643$		−	13.2767i		−	0.523583i	0.965124	−	0.261792i	$-0.0843133\pi$
$644$	10.4092	+	32.0362i	0.410179	+	1.26240i
$645$		0			0
$646$	1.19914	−	3.69057i	0.0471795	−	0.145204i
$647$	10.7329	+	3.48735i	0.421956	+	0.137102i	0.512295	−	0.858809i	$-0.328795\pi$
$647$	10.7329	+	3.48735i	0.421956	+	0.137102i	−0.0903397	+	0.995911i	$0.528795\pi$
$648$	−12.7012	−	17.4818i	−0.498952	−	0.686748i
$649$	−21.2912			−0.835754
$650$		0			0
$651$	−9.28462			−0.363893
$652$	8.73627	+	12.0245i	0.342139	+	0.470914i
$653$	−34.0606	−	11.0669i	−1.33289	−	0.433083i	−0.445989	−	0.895038i	$-0.647148\pi$
$653$	−34.0606	−	11.0669i	−1.33289	−	0.433083i	−0.886903	+	0.461955i	$0.847148\pi$
$654$	3.42722	−	10.5479i	0.134015	−	0.412456i
$655$		0			0
$656$	−0.250368	−	0.770554i	−0.00977523	−	0.0300851i
$657$			0.742534i			0.0289690i
$658$	32.0032	−	10.3985i	1.24762	−	0.405375i
$659$	32.1710	+	23.3736i	1.25320	+	0.910506i	0.998403	−	0.0564876i	$-0.0179902\pi$
$659$	32.1710	+	23.3736i	1.25320	+	0.910506i	0.254801	+	0.966994i	$0.417990\pi$
$660$		0			0
$661$	5.05420	−	3.67209i	0.196586	−	0.142828i	−0.485138	−	0.874438i	$-0.661231\pi$
$661$	5.05420	−	3.67209i	0.196586	−	0.142828i	0.681724	+	0.731610i	$0.261231\pi$
$662$	−15.8049	+	21.7536i	−0.614274	+	0.845476i
$663$	−0.741109	+	1.02005i	−0.0287823	+	0.0396154i
$664$	−31.4180	+	22.8265i	−1.21925	+	0.885839i
$665$		0			0
$666$	19.8016	+	14.3867i	0.767298	+	0.557474i
$667$	−12.5486	+	4.07728i	−0.485882	+	0.157873i
$668$			34.7728i			1.34540i
$669$	−4.21398	−	12.9693i	−0.162922	−	0.501422i
$670$		0			0
$671$	8.82193	−	27.1511i	0.340567	−	1.04816i
$672$	7.04132	+	2.28786i	0.271625	+	0.0882563i
$673$	24.3712	+	33.5441i	0.939440	+	1.29303i	0.956061	+	0.293166i	$0.0947090\pi$
$673$	24.3712	+	33.5441i	0.939440	+	1.29303i	−0.0166215	+	0.999862i	$0.505291\pi$
$674$	49.7297			1.91552
$675$		0			0
$676$	−36.5372			−1.40528
$677$	−0.845914	−	1.16430i	−0.0325111	−	0.0447477i	0.792452	−	0.609934i	$-0.208804\pi$
$677$	−0.845914	−	1.16430i	−0.0325111	−	0.0447477i	−0.824963	+	0.565187i	$0.808804\pi$
$678$	11.1727	+	3.63023i	0.429084	+	0.139418i
$679$	9.34183	−	28.7512i	0.358507	−	1.10337i
$680$		0			0
$681$	1.72004	+	5.29373i	0.0659120	+	0.202856i
$682$			29.7433i			1.13893i
$683$	8.07088	−	2.62239i	0.308824	−	0.100343i	−0.150505	−	0.988609i	$-0.548090\pi$
$683$	8.07088	−	2.62239i	0.308824	−	0.100343i	0.459329	+	0.888266i	$0.348090\pi$
$684$	−6.75742	−	4.90955i	−0.258376	−	0.187721i
$685$		0			0
$686$	27.1321	−	19.7126i	1.03591	−	0.752631i
$687$	4.57827	−	6.30145i	0.174672	−	0.240415i
$688$	−0.933247	+	1.28450i	−0.0355797	+	0.0489713i
$689$	10.9745	−	7.97345i	0.418096	−	0.303764i
$690$		0			0
$691$	35.4186	+	25.7331i	1.34739	+	0.978933i	0.999137	+	0.0415304i	$0.0132233\pi$
$691$	35.4186	+	25.7331i	1.34739	+	0.978933i	0.348248	+	0.937402i	$0.386777\pi$
$692$	−24.3307	+	7.90553i	−0.924915	+	0.300523i
$693$		−	16.8456i		−	0.639910i
$694$	−11.1303	−	34.2554i	−0.422499	−	1.30032i
$695$		0			0
$696$	1.78996	−	5.50893i	0.0678482	−	0.208815i
$697$	3.24510	+	1.05440i	0.122917	+	0.0399381i
$698$	−7.55503	−	10.3986i	−0.285962	−	0.393593i
$699$	−10.6922			−0.404418
$700$		0			0
$701$	0.840795			0.0317564			0.0158782	−	0.999874i	$-0.494946\pi$
$701$	0.840795			0.0317564			0.0158782	+	0.999874i	$0.494946\pi$
$702$	5.31250	+	7.31203i	0.200507	+	0.275975i
$703$	3.28198	+	1.06638i	0.123782	+	0.0402192i
$704$	7.87517	−	24.2373i	0.296807	−	0.913477i
$705$		0			0
$706$	5.72466	+	17.6187i	0.215450	+	0.663088i
$707$		−	28.3731i		−	1.06708i
$708$	−16.0245	+	5.20668i	−0.602238	+	0.195679i
$709$	−10.8256	−	7.86529i	−0.406566	−	0.295387i	0.365644	−	0.930755i	$-0.380849\pi$
$709$	−10.8256	−	7.86529i	−0.406566	−	0.295387i	−0.772210	+	0.635367i	$0.780849\pi$
$710$		0			0
$711$	−19.2401	+	13.9787i	−0.721560	+	0.524244i
$712$	8.62531	−	11.8717i	0.323247	−	0.444912i
$713$	12.6025	−	17.3459i	0.471969	−	0.649610i
$714$	5.01054	−	3.64037i	0.187515	−	0.136237i
$715$		0			0
$716$	−41.8371	−	30.3964i	−1.56353	−	1.13597i
$717$	−2.99601	+	0.973461i	−0.111888	+	0.0363546i
$718$		−	28.5027i		−	1.06371i
$719$	−13.4159	−	41.2900i	−0.500329	−	1.53986i	−0.808483	−	0.588519i	$-0.799711\pi$
$719$	−13.4159	−	41.2900i	−0.500329	−	1.53986i	0.308154	−	0.951336i	$-0.400289\pi$
$720$		0			0
$721$	8.52195	−	26.2279i	0.317374	−	0.976776i
$722$	39.9367	+	12.9762i	1.48629	+	0.482924i
$723$	−7.32076	−	10.0762i	−0.272262	−	0.374737i
$724$	5.30093			0.197007
$725$		0			0
$726$	−7.67677			−0.284912
$727$	−18.8373	−	25.9274i	−0.698639	−	0.961593i	−0.999967	−	0.00807318i	$-0.997430\pi$
$727$	−18.8373	−	25.9274i	−0.698639	−	0.961593i	0.301329	−	0.953520i	$-0.402570\pi$
$728$	−12.6822	−	4.12069i	−0.470033	−	0.152723i
$729$	4.81224	−	14.8106i	0.178231	−	0.548539i
$730$		0			0
$731$	−2.06626	−	6.35930i	−0.0764235	−	0.235207i
$732$		−	22.5922i		−	0.835032i
$733$	−7.74091	+	2.51517i	−0.285917	+	0.0929001i	−0.448465	−	0.893801i	$-0.648029\pi$
$733$	−7.74091	+	2.51517i	−0.285917	+	0.0929001i	0.162547	+	0.986701i	$0.448029\pi$
$734$	50.2089	+	36.4789i	1.85324	+	1.34646i
$735$		0			0
$736$	−13.8319	+	10.0494i	−0.509850	+	0.370427i
$737$	12.5671	−	17.2971i	0.462914	−	0.637146i
$738$	6.90757	−	9.50745i	0.254271	−	0.349974i
$739$	−5.76598	+	4.18923i	−0.212105	+	0.154103i	−0.688766	−	0.724984i	$-0.741847\pi$
$739$	−5.76598	+	4.18923i	−0.212105	+	0.154103i	0.476661	+	0.879087i	$0.341847\pi$
$740$		0			0
$741$	0.495326	+	0.359876i	0.0181963	+	0.0132204i
$742$	−63.3720	+	20.5908i	−2.32646	+	0.755912i
$743$			21.9040i			0.803578i	0.915732	+	0.401789i	$0.131612\pi$
$743$			21.9040i			0.803578i	−0.915732	+	0.401789i	$0.868388\pi$
$744$	2.90867	+	8.95197i	0.106637	+	0.328195i
$745$		0			0
$746$	−19.7233	+	60.7020i	−0.722120	+	2.22246i
$747$	−33.2953	−	10.8183i	−1.21821	−	0.395820i
$748$	−7.28823	−	10.0314i	−0.266484	−	0.366784i
$749$	−17.0877			−0.624373
$750$		0			0
$751$	9.21909			0.336409			0.168205	−	0.985752i	$-0.446203\pi$
$751$	9.21909			0.336409			0.168205	+	0.985752i	$0.446203\pi$
$752$	−1.24624	−	1.71530i	−0.0454456	−	0.0625504i
$753$	−4.92855	−	1.60138i	−0.179606	−	0.0583577i
$754$	4.03625	−	12.4223i	0.146991	−	0.452393i
$755$		0			0
$756$	−8.57388	−	26.3877i	−0.311829	−	0.959711i
$757$		−	45.6524i		−	1.65926i	−0.558311	−	0.829632i	$-0.688550\pi$
$757$		−	45.6524i		−	1.65926i	0.558311	−	0.829632i	$-0.311450\pi$
$758$	7.63114	−	2.47951i	0.277176	−	0.0900598i
$759$	−2.55828	−	1.85870i	−0.0928597	−	0.0674666i
$760$		0			0
$761$	−32.2844	+	23.4560i	−1.17031	+	0.850280i	−0.991046	−	0.133521i	$-0.957372\pi$
$761$	−32.2844	+	23.4560i	−1.17031	+	0.850280i	−0.179264	+	0.983801i	$0.557372\pi$
$762$	7.32340	−	10.0798i	0.265299	−	0.365153i
$763$	−18.0457	+	24.8378i	−0.653299	+	0.899188i
$764$	53.0310	−	38.5293i	1.91860	−	1.39394i
$765$		0			0
$766$	−51.1373	−	37.1534i	−1.84767	−	1.34241i
$767$	−14.4499	+	4.69506i	−0.521756	+	0.169529i
$768$		−	8.90403i		−	0.321296i
$769$	13.7024	+	42.1717i	0.494122	+	1.52075i	0.818320	+	0.574762i	$0.194906\pi$
$769$	13.7024	+	42.1717i	0.494122	+	1.52075i	−0.324198	+	0.945989i	$0.605094\pi$
$770$		0			0
$771$	0.965710	−	2.97215i	0.0347792	−	0.107039i
$772$	−41.5540	−	13.5017i	−1.49556	−	0.485937i
$773$	22.6264	+	31.1426i	0.813816	+	1.12012i	0.990723	+	0.135894i	$0.0433907\pi$
$773$	22.6264	+	31.1426i	0.813816	+	1.12012i	−0.176907	+	0.984228i	$0.556609\pi$
$774$	−23.0297			−0.827785
$775$		0			0
$776$	−30.6477			−1.10019
$777$	3.23733	+	4.45580i	0.116139	+	0.159851i
$778$	23.9051	+	7.76725i	0.857041	+	0.278469i
$779$	0.512006	−	1.57579i	0.0183445	−	0.0564586i
$780$		0			0
$781$	7.70061	+	23.7000i	0.275549	+	0.848054i
$782$			14.3022i			0.511445i
$783$	10.3361	−	3.35839i	0.369381	−	0.120019i
$784$	0.791971	+	0.575400i	0.0282847	+	0.0205500i
$785$		0			0
$786$	−7.08697	+	5.14898i	−0.252784	+	0.183658i
$787$	31.1645	−	42.8942i	1.11089	−	1.52901i	0.290801	−	0.956784i	$-0.406078\pi$
$787$	31.1645	−	42.8942i	1.11089	−	1.52901i	0.820093	−	0.572231i	$-0.193922\pi$
$788$	−6.71817	+	9.24676i	−0.239325	+	0.329402i
$789$	−10.4147	+	7.56674i	−0.370774	+	0.269383i
$790$		0			0
$791$	−26.3090	−	19.1146i	−0.935440	−	0.679637i
$792$	−16.2420	+	5.27735i	−0.577135	+	0.187522i
$793$		−	20.3723i		−	0.723440i
$794$	−11.5756	−	35.6259i	−0.410801	−	1.26432i
$795$		0			0
$796$	18.2246	−	56.0896i	0.645954	−	1.98804i
$797$	12.0564	+	3.91737i	0.427060	+	0.138760i	0.514658	−	0.857396i	$-0.327919\pi$
$797$	12.0564	+	3.91737i	0.427060	+	0.138760i	−0.0875977	+	0.996156i	$0.527919\pi$
$798$	−1.76773	−	2.43307i	−0.0625769	−	0.0861298i
$799$	8.92908			0.315888
$800$		0			0
$801$	13.2285			0.467407
$802$	5.14012	+	7.07477i	0.181504	+	0.249819i
$803$	0.509065	+	0.165405i	0.0179645	+	0.00583702i
$804$	5.22847	−	16.0916i	0.184394	−	0.567507i
$805$		0			0
$806$	6.55888	+	20.1861i	0.231027	+	0.711027i
$807$		−	0.479392i		−	0.0168754i
$808$	−27.3566	+	8.88869i	−0.962401	+	0.312703i
$809$	−33.8926	−	24.6244i	−1.19160	−	0.865747i	−0.198167	−	0.980168i	$-0.563499\pi$
$809$	−33.8926	−	24.6244i	−1.19160	−	0.865747i	−0.993432	+	0.114421i	$0.963499\pi$
$810$		0			0
$811$	27.9504	−	20.3072i	0.981472	−	0.713081i	0.0234348	−	0.999725i	$-0.492540\pi$
$811$	27.9504	−	20.3072i	0.981472	−	0.713081i	0.958037	+	0.286644i	$0.0925398\pi$
$812$	−23.5683	+	32.4390i	−0.827086	+	1.13839i
$813$	1.74520	−	2.40206i	0.0612068	−	0.0842439i
$814$	14.2742	−	10.3708i	0.500310	−	0.363496i
$815$		0			0
$816$	−0.315703	−	0.229371i	−0.0110518	−	0.00802961i
$817$	−3.08802	+	1.00336i	−0.108036	+	0.0351031i
$818$			4.28568i			0.149845i
$819$	−3.71472	−	11.4327i	−0.129803	−	0.399491i
$820$		0			0
$821$	−6.53103	+	20.1004i	−0.227935	+	0.701511i	0.770046	+	0.637989i	$0.220233\pi$
$821$	−6.53103	+	20.1004i	−0.227935	+	0.701511i	−0.997980	+	0.0635220i	$0.979767\pi$
$822$	−9.73882	−	3.16433i	−0.339680	−	0.110369i
$823$	−1.86747	−	2.57036i	−0.0650960	−	0.0895970i	0.775228	−	0.631682i	$-0.217635\pi$
$823$	−1.86747	−	2.57036i	−0.0650960	−	0.0895970i	−0.840324	+	0.542085i	$0.817635\pi$
$824$	−27.9579			−0.973960
$825$		0			0
$826$	74.6315			2.59676
$827$	5.72786	+	7.88372i	0.199177	+	0.274144i	0.896909	−	0.442215i	$-0.145807\pi$
$827$	5.72786	+	7.88372i	0.199177	+	0.274144i	−0.697732	+	0.716359i	$0.745807\pi$
$828$	29.2782	+	9.51307i	1.01749	+	0.330602i
$829$	−7.24188	+	22.2882i	−0.251521	+	0.774101i	0.742974	+	0.669320i	$0.233414\pi$
$829$	−7.24188	+	22.2882i	−0.251521	+	0.774101i	−0.994495	+	0.104782i	$0.966586\pi$
$830$		0			0
$831$	−3.62045	−	11.1426i	−0.125592	−	0.386532i
$832$		−	18.1859i		−	0.630484i
$833$	−3.92087	+	1.27397i	−0.135850	+	0.0441404i
$834$	15.8948	+	11.5483i	0.550393	+	0.399884i
$835$		0			0
$836$	−4.87115	+	3.53910i	−0.168472	+	0.122402i
$837$	−10.3805	+	14.2876i	−0.358803	+	0.493850i
$838$	19.4743	−	26.8041i	0.672728	−	0.925931i
$839$	34.5304	−	25.0878i	1.19212	−	0.866126i	0.198634	−	0.980074i	$-0.436350\pi$
$839$	34.5304	−	25.0878i	1.19212	−	0.866126i	0.993487	+	0.113948i	$0.0363496\pi$
$840$		0			0
$841$	10.7551	+	7.81406i	0.370866	+	0.269450i
$842$	33.9420	−	11.0284i	1.16972	−	0.380065i
$843$			0.873305i			0.0300782i
$844$	3.34057	+	10.2812i	0.114987	+	0.353894i
$845$		0			0
$846$	9.50329	−	29.2481i	0.326730	−	1.00557i
$847$	20.2106	+	6.56683i	0.694446	+	0.225639i
$848$	2.46776	+	3.39659i	0.0847434	+	0.116639i
$849$	4.10371			0.140839
$850$		0			0
$851$	−12.7187			−0.435993
$852$	11.5915	+	15.9543i	0.397117	+	0.546585i
$853$	16.1309	+	5.24124i	0.552310	+	0.179456i	0.571858	−	0.820352i	$-0.306223\pi$
$853$	16.1309	+	5.24124i	0.552310	+	0.179456i	−0.0195480	+	0.999809i	$0.506223\pi$
$854$	−30.9232	+	95.1719i	−1.05817	+	3.25672i
$855$		0			0
$856$	5.35323	+	16.4755i	0.182969	+	0.563122i
$857$			39.3176i			1.34306i	0.740976	+	0.671531i	$0.234363\pi$
$857$			39.3176i			1.34306i	−0.740976	+	0.671531i	$0.765637\pi$
$858$	2.97718	−	0.967343i	0.101639	−	0.0330246i
$859$	0.572020	+	0.415597i	0.0195171	+	0.0141800i	0.597501	−	0.801868i	$-0.296160\pi$
$859$	0.572020	+	0.415597i	0.0195171	+	0.0141800i	−0.577984	+	0.816048i	$0.696160\pi$
$860$		0			0
$861$	2.13939	−	1.55436i	0.0729101	−	0.0529723i
$862$	−16.9728	+	23.3611i	−0.578096	+	0.795681i
$863$	0.534537	−	0.735728i	0.0181959	−	0.0250445i	−0.799822	−	0.600237i	$-0.795073\pi$
$863$	0.534537	−	0.735728i	0.0181959	−	0.0250445i	0.818018	+	0.575193i	$0.195073\pi$
$864$	11.3931	−	8.27757i	0.387601	−	0.281609i
$865$		0			0
$866$	42.0264	+	30.5339i	1.42811	+	1.03759i
$867$	−6.11524	+	1.98696i	−0.207684	+	0.0674807i
$868$		−	65.1571i		−	2.21158i
$869$	5.29764	+	16.3045i	0.179710	+	0.553091i
$870$		0			0
$871$	4.71472	−	14.5104i	0.159752	−	0.491666i
$872$	29.6012	+	9.61803i	1.00242	+	0.325708i
$873$	−16.2395	−	22.3517i	−0.549624	−	0.756492i
$874$	6.94501			0.234918
$875$		0			0
$876$	0.423589			0.0143117
$877$	19.7856	+	27.2326i	0.668113	+	0.919578i	0.999716	−	0.0238407i	$-0.00758944\pi$
$877$	19.7856	+	27.2326i	0.668113	+	0.919578i	−0.331603	+	0.943419i	$0.607589\pi$
$878$	26.7450	+	8.68997i	0.902600	+	0.293272i
$879$	−0.923306	+	2.84164i	−0.0311423	+	0.0958463i
$880$		0			0
$881$	−6.15819	−	18.9529i	−0.207475	−	0.638541i	−0.999603	−	0.0281862i	$-0.991027\pi$
$881$	−6.15819	−	18.9529i	−0.207475	−	0.638541i	0.792128	−	0.610355i	$-0.208973\pi$
$882$			14.1991i			0.478109i
$883$	−14.8442	+	4.82317i	−0.499547	+	0.162313i	−0.547943	−	0.836516i	$-0.684589\pi$
$883$	−14.8442	+	4.82317i	−0.499547	+	0.162313i	0.0483963	+	0.998828i	$0.484589\pi$
$884$	−7.15845	−	5.20091i	−0.240765	−	0.174926i
$885$		0			0
$886$	38.6916	−	28.1111i	1.29987	−	0.944410i
$887$	−27.5652	+	37.9403i	−0.925550	+	1.27391i	0.0360196	+	0.999351i	$0.488532\pi$
$887$	−27.5652	+	37.9403i	−0.925550	+	1.27391i	−0.961570	+	0.274560i	$0.911468\pi$
$888$	3.28198	−	4.51725i	0.110136	−	0.151589i
$889$	−27.9028	+	20.2725i	−0.935828	+	0.679919i
$890$		0			0
$891$	−11.3603	−	8.25376i	−0.380585	−	0.276511i
$892$	91.0152	−	29.5726i	3.04742	−	0.990165i
$893$		−	4.33588i		−	0.145095i
$894$	2.13975	+	6.58549i	0.0715641	+	0.220252i
$895$		0			0
$896$	−17.9695	+	55.3045i	−0.600319	+	1.84759i
$897$	−2.14612	−	0.697318i	−0.0716570	−	0.0232828i
$898$	35.2287	+	48.4882i	1.17560	+	1.61807i
$899$	25.5220			0.851208
$900$		0			0
$901$	−17.6811			−0.589044
$902$	−4.97938	−	6.85353i	−0.165795	−	0.228198i
$903$	−4.92855	−	1.60138i	−0.164012	−	0.0532907i
$904$	−10.1877	+	31.3546i	−0.338839	+	1.04284i
$905$		0			0
$906$	1.59940	+	4.92244i	0.0531364	+	0.163537i
$907$		−	1.43447i		−	0.0476308i	−0.999716	−	0.0238154i	$-0.992419\pi$
$907$		−	1.43447i		−	0.0476308i	0.999716	−	0.0238154i	$-0.00758139\pi$
$908$	−37.1501	+	12.0708i	−1.23287	+	0.400583i
$909$	−20.9782	−	15.2416i	−0.695804	−	0.505531i
$910$		0			0
$911$	2.27438	−	1.65244i	0.0753537	−	0.0547476i	−0.549471	−	0.835513i	$-0.685171\pi$
$911$	2.27438	−	1.65244i	0.0753537	−	0.0547476i	0.624824	+	0.780765i	$0.285171\pi$
$912$	−0.111381	+	0.153302i	−0.00368818	+	0.00507635i
$913$	−14.8335	+	20.4166i	−0.490919	+	0.675692i
$914$	−15.8829	+	11.5396i	−0.525359	+	0.381695i
$915$		0			0
$916$	44.2220	+	32.1291i	1.46114	+	1.06158i
$917$	23.0624	−	7.49342i	0.761587	−	0.247455i
$918$		−	11.7805i		−	0.388814i
$919$	−0.306618	−	0.943673i	−0.0101144	−	0.0311289i	0.945872	−	0.324540i	$-0.105210\pi$
$919$	−0.306618	−	0.943673i	−0.0101144	−	0.0311289i	−0.955986	+	0.293411i	$0.905210\pi$
$920$		0			0
$921$	−4.20684	+	12.9473i	−0.138620	+	0.426629i
$922$	−32.4717	−	10.5507i	−1.06940	−	0.347469i
$923$	10.4525	+	14.3866i	0.344048	+	0.473541i
$924$	−9.60977			−0.316138
$925$		0			0
$926$	−51.2477			−1.68410
$927$	−14.8142	−	20.3900i	−0.486563	−	0.669697i
$928$	−19.3556	−	6.28900i	−0.635377	−	0.206447i
$929$	−10.2973	+	31.6918i	−0.337843	+	1.03977i	0.627461	+	0.778648i	$0.284094\pi$
$929$	−10.2973	+	31.6918i	−0.337843	+	1.03977i	−0.965305	+	0.261127i	$0.915906\pi$
$930$		0			0
$931$	0.618628	+	1.90394i	0.0202747	+	0.0623992i
$932$		−	75.0355i		−	2.45787i
$933$	3.53943	−	1.15003i	0.115876	−	0.0376503i
$934$	−53.2475	−	38.6866i	−1.74231	−	1.26586i
$935$		0			0
$936$	−9.85937	+	7.16325i	−0.322264	+	0.234138i
$937$	−7.85724	+	10.8146i	−0.256685	+	0.353296i	−0.917838	−	0.396954i	$-0.870067\pi$
$937$	−7.85724	+	10.8146i	−0.256685	+	0.353296i	0.661154	+	0.750251i	$0.270067\pi$
$938$	−44.0509	+	60.6309i	−1.43831	+	1.97967i
$939$	8.22553	−	5.97620i	0.268430	−	0.195026i
$940$		0			0
$941$	1.73924	+	1.26363i	0.0566976	+	0.0411932i	0.615773	−	0.787924i	$-0.288844\pi$
$941$	1.73924	+	1.26363i	0.0566976	+	0.0411932i	−0.559075	+	0.829117i	$0.688844\pi$
$942$	1.53226	−	0.497860i	0.0499236	−	0.0162212i
$943$			6.10671i			0.198862i
$944$	−1.45311	−	4.47221i	−0.0472947	−	0.145558i
$945$		0			0
$946$	−5.13004	+	15.7886i	−0.166792	+	0.513333i
$947$	−33.2093	−	10.7903i	−1.07916	−	0.350639i	−0.285109	−	0.958495i	$-0.592030\pi$
$947$	−33.2093	−	10.7903i	−1.07916	−	0.350639i	−0.794047	+	0.607856i	$0.792030\pi$
$948$	7.97436	+	10.9758i	0.258995	+	0.356476i
$949$	0.381966			0.0123991
$950$		0			0
$951$	1.90903			0.0619046
$952$	10.2162	+	14.0614i	0.331108	+	0.455732i
$953$	−7.87364	−	2.55830i	−0.255052	−	0.0828715i	0.178700	−	0.983904i	$-0.442811\pi$
$953$	−7.87364	−	2.55830i	−0.255052	−	0.0828715i	−0.433752	+	0.901032i	$0.642811\pi$
$954$	−18.8182	+	57.9164i	−0.609261	+	1.87511i
$955$		0			0
$956$	−6.83151	−	21.0252i	−0.220947	−	0.680004i
$957$		−	3.76415i		−	0.121678i
$958$	−55.0313	+	17.8807i	−1.77798	+	0.577701i
$959$	22.9326	+	16.6615i	0.740532	+	0.538028i
$960$		0			0
$961$	−8.47296	+	6.15597i	−0.273321	+	0.198580i
$962$	7.40066	−	10.1861i	0.238607	−	0.328414i
$963$	−9.17926	+	12.6342i	−0.295797	+	0.407130i
$964$	70.7120	−	51.3753i	2.27748	−	1.65469i
$965$		0			0
$966$	8.96746	+	6.51524i	0.288523	+	0.209624i
$967$	28.0439	−	9.11201i	0.901831	−	0.293023i	0.178838	−	0.983878i	$-0.442766\pi$
$967$	28.0439	−	9.11201i	0.901831	−	0.293023i	0.722993	+	0.690856i	$0.242766\pi$
$968$		−	21.5438i		−	0.692443i
$969$	−0.246603	−	0.758967i	−0.00792204	−	0.0243815i
$970$		0			0
$971$	6.75716	−	20.7964i	0.216848	−	0.667388i	−0.782170	−	0.623065i	$-0.785887\pi$
$971$	6.75716	−	20.7964i	0.216848	−	0.667388i	0.999017	−	0.0443227i	$-0.0141130\pi$
$972$	−36.6449	−	11.9067i	−1.17539	−	0.381906i
$973$	−31.9678	−	43.9998i	−1.02484	−	1.41057i
$974$	3.38260			0.108385
$975$		0			0
$976$	6.30517			0.201823
$977$	8.13976	+	11.2034i	0.260414	+	0.358429i	0.919124	−	0.393967i	$-0.128898\pi$
$977$	8.13976	+	11.2034i	0.260414	+	0.358429i	−0.658710	+	0.752397i	$0.728898\pi$
$978$	4.65149	+	1.51136i	0.148738	+	0.0483279i
$979$	2.94676	−	9.06919i	0.0941788	−	0.289853i
$980$		0			0
$981$	8.67045	+	26.6849i	0.276826	+	0.851983i
$982$			46.3440i			1.47890i
$983$	−2.79171	+	0.907082i	−0.0890418	+	0.0289314i	−0.353199	−	0.935548i	$-0.614906\pi$
$983$	−2.79171	+	0.907082i	−0.0890418	+	0.0289314i	0.264157	+	0.964480i	$0.414906\pi$
$984$	−2.16889	−	1.57579i	−0.0691417	−	0.0502344i
$985$		0			0
$986$	−13.7732	+	10.0068i	−0.438629	+	0.318682i
$987$	4.06757	−	5.59853i	0.129472	−	0.178203i
$988$	−2.52552	+	3.47608i	−0.0803474	+	0.110589i
$989$	9.68158	−	7.03408i	0.307856	−	0.223671i
$990$		0			0
$991$	−25.5760	−	18.5821i	−0.812450	−	0.590279i	0.102090	−	0.994775i	$-0.467447\pi$
$991$	−25.5760	−	18.5821i	−0.812450	−	0.590279i	−0.914540	+	0.404496i	$0.867447\pi$
$992$	31.4526	−	10.2196i	0.998623	−	0.324472i
$993$			5.52970i			0.175480i
$994$	−26.9927	−	83.0750i	−0.856156	−	2.63498i
$995$		0			0
$996$	−6.17144	+	18.9937i	−0.195549	+	0.601839i
$997$	11.4968	+	3.73554i	0.364108	+	0.118306i	0.485356	−	0.874316i	$-0.338690\pi$
$997$	11.4968	+	3.73554i	0.364108	+	0.118306i	−0.121249	+	0.992622i	$0.538690\pi$
$998$	−0.848347	−	1.16765i	−0.0268540	−	0.0369613i
$999$	10.4762			0.331453

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	125.2.e.b.74.2		8
5.2	odd	4		125.2.d.b.51.1		16
5.3	odd	4		125.2.d.b.51.4		16
5.4	even	2		25.2.e.a.14.1	yes	8
15.14	odd	2		225.2.m.a.64.2		8
20.19	odd	2		400.2.y.c.289.1		8
25.2	odd	20		625.2.d.o.126.4		16
25.3	odd	20		625.2.a.f.1.1		8
25.4	even	10		625.2.b.c.624.8		8
25.6	even	5		625.2.e.i.124.1		8
25.8	odd	20		625.2.d.o.501.1		16
25.9	even	10	inner	125.2.e.b.49.2		8
25.11	even	5		625.2.e.a.499.2		8
25.12	odd	20		125.2.d.b.76.1		16
25.13	odd	20		125.2.d.b.76.4		16
25.14	even	10		625.2.e.i.499.1		8
25.16	even	5		25.2.e.a.9.1	✓	8
25.17	odd	20		625.2.d.o.501.4		16
25.19	even	10		625.2.e.a.124.2		8
25.21	even	5		625.2.b.c.624.1		8
25.22	odd	20		625.2.a.f.1.8		8
25.23	odd	20		625.2.d.o.126.1		16
75.41	odd	10		225.2.m.a.109.2		8
75.47	even	20		5625.2.a.x.1.1		8
75.53	even	20		5625.2.a.x.1.8		8
100.3	even	20		10000.2.a.bj.1.5		8
100.47	even	20		10000.2.a.bj.1.4		8
100.91	odd	10		400.2.y.c.209.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.2.e.a.9.1	✓	8	25.16	even	5
25.2.e.a.14.1	yes	8	5.4	even	2
125.2.d.b.51.1		16	5.2	odd	4
125.2.d.b.51.4		16	5.3	odd	4
125.2.d.b.76.1		16	25.12	odd	20
125.2.d.b.76.4		16	25.13	odd	20
125.2.e.b.49.2		8	25.9	even	10	inner
125.2.e.b.74.2		8	1.1	even	1	trivial
225.2.m.a.64.2		8	15.14	odd	2
225.2.m.a.109.2		8	75.41	odd	10
400.2.y.c.209.1		8	100.91	odd	10
400.2.y.c.289.1		8	20.19	odd	2
625.2.a.f.1.1		8	25.3	odd	20
625.2.a.f.1.8		8	25.22	odd	20
625.2.b.c.624.1		8	25.21	even	5
625.2.b.c.624.8		8	25.4	even	10
625.2.d.o.126.1		16	25.23	odd	20
625.2.d.o.126.4		16	25.2	odd	20
625.2.d.o.501.1		16	25.8	odd	20
625.2.d.o.501.4		16	25.17	odd	20
625.2.e.a.124.2		8	25.19	even	10
625.2.e.a.499.2		8	25.11	even	5
625.2.e.i.124.1		8	25.6	even	5
625.2.e.i.499.1		8	25.14	even	10
5625.2.a.x.1.1		8	75.47	even	20
5625.2.a.x.1.8		8	75.53	even	20
10000.2.a.bj.1.4		8	100.47	even	20
10000.2.a.bj.1.5		8	100.3	even	20

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:	\( N \)	\(=\)	\( 125 = 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	125.e (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.35736 + 1.86824i) q^{2} +(0.451659 + 0.146753i) q^{3} +(-1.02988 + 3.16963i) q^{4} +(0.338893 + 1.04301i) q^{6} -3.03582i q^{7} +(-2.92705 + 0.951057i) q^{8} +(-2.24459 - 1.63079i) q^{9} +O(q^{10})\)	\(q+(1.35736 + 1.86824i) q^{2} +(0.451659 + 0.146753i) q^{3} +(-1.02988 + 3.16963i) q^{4} +(0.338893 + 1.04301i) q^{6} -3.03582i q^{7} +(-2.92705 + 0.951057i) q^{8} +(-2.24459 - 1.63079i) q^{9} +(-1.61803 + 1.17557i) q^{11} +(-0.930307 + 1.28046i) q^{12} +(-0.838893 + 1.15464i) q^{13} +(5.67164 - 4.12069i) q^{14} +(-0.357358 - 0.259635i) q^{16} +(1.76920 - 0.574848i) q^{17} -6.40701i q^{18} +(-0.279141 - 0.859107i) q^{19} +(0.445515 - 1.37116i) q^{21} +(-4.39250 - 1.42721i) q^{22} +(1.95693 + 2.69348i) q^{23} -1.46160 q^{24} -3.29582 q^{26} +(-1.61189 - 2.21858i) q^{27} +(9.62243 + 3.12652i) q^{28} +(-1.22466 + 3.76910i) q^{29} +(-1.99006 - 6.12477i) q^{31} +5.13532i q^{32} +(-0.903319 + 0.293506i) q^{33} +(3.47539 + 2.52502i) q^{34} +(7.48066 - 5.43502i) q^{36} +(-2.24547 + 3.09062i) q^{37} +(1.22613 - 1.68762i) q^{38} +(-0.548341 + 0.398393i) q^{39} +(1.48391 + 1.07813i) q^{41} +(3.16637 - 1.02882i) q^{42} -3.59445i q^{43} +(-2.05975 - 6.33927i) q^{44} +(-2.37582 + 7.31203i) q^{46} +(4.56502 + 1.48326i) q^{47} +(-0.123302 - 0.169710i) q^{48} -2.21619 q^{49} +0.883436 q^{51} +(-2.79582 - 3.84812i) q^{52} +(-9.03953 - 2.93712i) q^{53} +(1.95693 - 6.02280i) q^{54} +(2.88723 + 8.88599i) q^{56} -0.428989i q^{57} +(-8.70390 + 2.82807i) q^{58} +(8.61248 + 6.25734i) q^{59} +(-11.5481 + 8.39016i) q^{61} +(8.74134 - 12.0314i) q^{62} +(-4.95078 + 6.81417i) q^{63} +(-10.3087 + 7.48973i) q^{64} +(-1.77447 - 1.28923i) q^{66} +(-10.1670 + 3.30345i) q^{67} +6.19974i q^{68} +(0.488588 + 1.50372i) q^{69} +(3.85030 - 11.8500i) q^{71} +(8.12101 + 2.63868i) q^{72} +(-0.157310 - 0.216518i) q^{73} -8.82193 q^{74} +3.01054 q^{76} +(3.56882 + 4.91206i) q^{77} +(-1.48859 - 0.483672i) q^{78} +(2.64882 - 8.15223i) q^{79} +(2.16963 + 6.67743i) q^{81} +4.23572i q^{82} +(12.0006 - 3.89923i) q^{83} +(3.88723 + 2.82424i) q^{84} +(6.71531 - 4.87896i) q^{86} +(-1.10626 + 1.52263i) q^{87} +(3.61803 - 4.97980i) q^{88} +(-3.85736 + 2.80253i) q^{89} +(3.50527 + 2.54673i) q^{91} +(-10.5527 + 3.42879i) q^{92} -3.05836i q^{93} +(3.42527 + 10.5419i) q^{94} +(-0.753624 + 2.31942i) q^{96} +(9.47067 + 3.07721i) q^{97} +(-3.00816 - 4.14037i) q^{98} +5.54893 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 5 q^{2} + 5 q^{3} - q^{4} - 9 q^{6} - 10 q^{8} + q^{9}+O(q^{10}) \) 8 * q + 5 * q^2 + 5 * q^3 - q^4 - 9 * q^6 - 10 * q^8 + q^9	\( 8 q + 5 q^{2} + 5 q^{3} - q^{4} - 9 q^{6} - 10 q^{8} + q^{9} - 4 q^{11} - 15 q^{12} + 5 q^{13} + 13 q^{14} + 3 q^{16} + 10 q^{17} - 5 q^{19} - 4 q^{21} - 5 q^{23} - 20 q^{24} + 6 q^{26} + 5 q^{27} + 15 q^{28} - 5 q^{29} - 9 q^{31} - 10 q^{33} + 13 q^{34} + 23 q^{36} - 30 q^{37} - 15 q^{38} - 3 q^{39} - 4 q^{41} + 15 q^{42} - 2 q^{44} - 19 q^{46} + 30 q^{48} + 14 q^{49} - 4 q^{51} + 10 q^{52} + 10 q^{53} - 5 q^{54} + 10 q^{56} - 20 q^{58} - 9 q^{61} + 30 q^{62} - 10 q^{63} + 4 q^{64} + 12 q^{66} - 20 q^{67} + 17 q^{69} + 6 q^{71} - 5 q^{72} - 15 q^{73} - 12 q^{74} - 20 q^{76} - 10 q^{77} - 25 q^{78} + 15 q^{79} + 28 q^{81} + 45 q^{83} + 18 q^{84} - 9 q^{86} + 20 q^{87} + 20 q^{88} - 25 q^{89} + 6 q^{91} - 30 q^{92} - 27 q^{94} + 16 q^{96} + 60 q^{97} + 10 q^{98} - 8 q^{99}+O(q^{100}) \) 8 * q + 5 * q^2 + 5 * q^3 - q^4 - 9 * q^6 - 10 * q^8 + q^9 - 4 * q^11 - 15 * q^12 + 5 * q^13 + 13 * q^14 + 3 * q^16 + 10 * q^17 - 5 * q^19 - 4 * q^21 - 5 * q^23 - 20 * q^24 + 6 * q^26 + 5 * q^27 + 15 * q^28 - 5 * q^29 - 9 * q^31 - 10 * q^33 + 13 * q^34 + 23 * q^36 - 30 * q^37 - 15 * q^38 - 3 * q^39 - 4 * q^41 + 15 * q^42 - 2 * q^44 - 19 * q^46 + 30 * q^48 + 14 * q^49 - 4 * q^51 + 10 * q^52 + 10 * q^53 - 5 * q^54 + 10 * q^56 - 20 * q^58 - 9 * q^61 + 30 * q^62 - 10 * q^63 + 4 * q^64 + 12 * q^66 - 20 * q^67 + 17 * q^69 + 6 * q^71 - 5 * q^72 - 15 * q^73 - 12 * q^74 - 20 * q^76 - 10 * q^77 - 25 * q^78 + 15 * q^79 + 28 * q^81 + 45 * q^83 + 18 * q^84 - 9 * q^86 + 20 * q^87 + 20 * q^88 - 25 * q^89 + 6 * q^91 - 30 * q^92 - 27 * q^94 + 16 * q^96 + 60 * q^97 + 10 * q^98 - 8 * q^99

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