LMFDB - Embedded newform 950.2.n.a.39.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(39,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([3, 0]))

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

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

chi := DirichletCharacter("950.39");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.n (of order $10$, 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			39.17
Character	$\chi$	$=$	950.39
Dual form			950.2.n.a.609.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.587785 + 0.809017i) q^{2} +(-0.284260 - 0.0923618i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(0.810167 - 2.08414i) q^{5} +(-0.0923618 - 0.284260i) q^{6} +5.14607i q^{7} +(-0.951057 + 0.309017i) q^{8} +(-2.35478 - 1.71085i) q^{9} +O(q^{10})$	\(q+(0.587785 + 0.809017i) q^{2} +(-0.284260 - 0.0923618i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(0.810167 - 2.08414i) q^{5} +(-0.0923618 - 0.284260i) q^{6} +5.14607i q^{7} +(-0.951057 + 0.309017i) q^{8} +(-2.35478 - 1.71085i) q^{9} +(2.16231 - 0.569586i) q^{10} +(-2.82121 + 2.04973i) q^{11} +(0.175683 - 0.241806i) q^{12} +(-0.0727292 + 0.100103i) q^{13} +(-4.16326 + 3.02478i) q^{14} +(-0.422793 + 0.517609i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-2.72208 + 0.884457i) q^{17} -2.91067i q^{18} +(0.309017 + 0.951057i) q^{19} +(1.73178 + 1.41455i) q^{20} +(0.475300 - 1.46282i) q^{21} +(-3.31653 - 1.07761i) q^{22} +(0.274593 + 0.377945i) q^{23} +0.298889 q^{24} +(-3.68726 - 3.37700i) q^{25} -0.123734 q^{26} +(1.03840 + 1.42924i) q^{27} +(-4.89420 - 1.59022i) q^{28} +(-1.73155 + 5.32915i) q^{29} +(-0.667266 - 0.0378037i) q^{30} +(-0.0477733 - 0.147031i) q^{31} -1.00000i q^{32} +(0.991276 - 0.322085i) q^{33} +(-2.31554 - 1.68234i) q^{34} +(10.7251 + 4.16917i) q^{35} +(2.35478 - 1.71085i) q^{36} +(-5.01328 + 6.90019i) q^{37} +(-0.587785 + 0.809017i) q^{38} +(0.0299197 - 0.0217380i) q^{39} +(-0.126481 + 2.23249i) q^{40} +(-5.14648 - 3.73914i) q^{41} +(1.46282 - 0.475300i) q^{42} +0.721671i q^{43} +(-1.07761 - 3.31653i) q^{44} +(-5.47340 + 3.52161i) q^{45} +(-0.144362 + 0.444300i) q^{46} +(11.8830 + 3.86101i) q^{47} +(0.175683 + 0.241806i) q^{48} -19.4820 q^{49} +(0.564734 - 4.96801i) q^{50} +0.855469 q^{51} +(-0.0727292 - 0.100103i) q^{52} +(9.27451 + 3.01347i) q^{53} +(-0.545920 + 1.68017i) q^{54} +(1.98627 + 7.54042i) q^{55} +(-1.59022 - 4.89420i) q^{56} -0.298889i q^{57} +(-5.32915 + 1.73155i) q^{58} +(-2.24269 - 1.62941i) q^{59} +(-0.361625 - 0.562050i) q^{60} +(4.39526 - 3.19334i) q^{61} +(0.0908703 - 0.125072i) q^{62} +(8.80413 - 12.1178i) q^{63} +(0.809017 - 0.587785i) q^{64} +(0.149706 + 0.232678i) q^{65} +(0.843229 + 0.612642i) q^{66} +(-11.9876 + 3.89502i) q^{67} -2.86216i q^{68} +(-0.0431482 - 0.132797i) q^{69} +(2.93113 + 11.1274i) q^{70} +(-3.22889 + 9.93750i) q^{71} +(2.76821 + 0.899445i) q^{72} +(-3.61941 - 4.98169i) q^{73} -8.52911 q^{74} +(0.736236 + 1.30051i) q^{75} -1.00000 q^{76} +(-10.5481 - 14.5182i) q^{77} +(0.0351728 + 0.0114283i) q^{78} +(-0.669662 + 2.06101i) q^{79} +(-1.88046 + 1.20990i) q^{80} +(2.53517 + 7.80244i) q^{81} -6.36140i q^{82} +(0.474706 - 0.154241i) q^{83} +(1.24435 + 0.904074i) q^{84} +(-0.362009 + 6.38975i) q^{85} +(-0.583844 + 0.424188i) q^{86} +(0.984420 - 1.35494i) q^{87} +(2.04973 - 2.82121i) q^{88} +(5.60096 - 4.06934i) q^{89} +(-6.06623 - 2.35813i) q^{90} +(-0.515138 - 0.374270i) q^{91} +(-0.444300 + 0.144362i) q^{92} +0.0462076i q^{93} +(3.86101 + 11.8830i) q^{94} +(2.23249 + 0.126481i) q^{95} +(-0.0923618 + 0.284260i) q^{96} +(12.8207 + 4.16571i) q^{97} +(-11.4512 - 15.7613i) q^{98} +10.1501 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 22 q^{4} + 10 q^{5} + 2 q^{6} + 24 q^{9}+O(q^{10}) $ 88 * q + 22 * q^4 + 10 * q^5 + 2 * q^6 + 24 * q^9	$ 88 q + 22 q^{4} + 10 q^{5} + 2 q^{6} + 24 q^{9} + 26 q^{11} + 10 q^{12} - 10 q^{14} + 12 q^{15} - 22 q^{16} - 40 q^{17} - 22 q^{19} + 10 q^{23} + 8 q^{24} + 6 q^{25} - 28 q^{26} - 30 q^{27} - 10 q^{28} - 4 q^{29} - 4 q^{30} + 2 q^{31} - 8 q^{34} - 48 q^{35} - 24 q^{36} + 50 q^{37} + 8 q^{39} + 32 q^{41} + 10 q^{42} + 4 q^{44} - 8 q^{45} + 10 q^{46} + 10 q^{48} - 56 q^{49} + 28 q^{50} - 60 q^{51} - 70 q^{53} - 8 q^{54} + 4 q^{55} + 10 q^{56} - 60 q^{58} - 28 q^{59} - 12 q^{60} - 58 q^{61} + 60 q^{63} + 22 q^{64} - 24 q^{65} + 4 q^{66} - 70 q^{67} - 8 q^{69} - 4 q^{70} + 48 q^{71} + 40 q^{73} + 52 q^{74} + 108 q^{75} - 88 q^{76} - 50 q^{78} - 20 q^{79} + 24 q^{81} - 80 q^{83} + 30 q^{85} + 20 q^{86} + 70 q^{87} + 10 q^{88} - 62 q^{89} - 104 q^{90} + 20 q^{91} - 10 q^{92} - 10 q^{94} + 2 q^{96} - 10 q^{97} + 60 q^{98} + 156 q^{99}+O(q^{100}) $ 88 * q + 22 * q^4 + 10 * q^5 + 2 * q^6 + 24 * q^9 + 26 * q^11 + 10 * q^12 - 10 * q^14 + 12 * q^15 - 22 * q^16 - 40 * q^17 - 22 * q^19 + 10 * q^23 + 8 * q^24 + 6 * q^25 - 28 * q^26 - 30 * q^27 - 10 * q^28 - 4 * q^29 - 4 * q^30 + 2 * q^31 - 8 * q^34 - 48 * q^35 - 24 * q^36 + 50 * q^37 + 8 * q^39 + 32 * q^41 + 10 * q^42 + 4 * q^44 - 8 * q^45 + 10 * q^46 + 10 * q^48 - 56 * q^49 + 28 * q^50 - 60 * q^51 - 70 * q^53 - 8 * q^54 + 4 * q^55 + 10 * q^56 - 60 * q^58 - 28 * q^59 - 12 * q^60 - 58 * q^61 + 60 * q^63 + 22 * q^64 - 24 * q^65 + 4 * q^66 - 70 * q^67 - 8 * q^69 - 4 * q^70 + 48 * q^71 + 40 * q^73 + 52 * q^74 + 108 * q^75 - 88 * q^76 - 50 * q^78 - 20 * q^79 + 24 * q^81 - 80 * q^83 + 30 * q^85 + 20 * q^86 + 70 * q^87 + 10 * q^88 - 62 * q^89 - 104 * q^90 + 20 * q^91 - 10 * q^92 - 10 * q^94 + 2 * q^96 - 10 * q^97 + 60 * q^98 + 156 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$1$

Coefficient data

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

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

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

$2$	0.587785	+	0.809017i	0.415627	+	0.572061i
$2$	0.587785	+	0.809017i	0.415627	+	0.572061i
$3$	−0.284260	−	0.0923618i	−0.164118	−	0.0533251i	0.225806	−	0.974172i	$-0.427499\pi$
$3$	−0.284260	−	0.0923618i	−0.164118	−	0.0533251i	−0.389923	+	0.920847i	$0.627499\pi$
$4$	−0.309017	+	0.951057i	−0.154508	+	0.475528i
$5$	0.810167	−	2.08414i	0.362318	−	0.932055i
$5$	0.810167	−	2.08414i	0.362318	−	0.932055i
$6$	−0.0923618	−	0.284260i	−0.0377065	−	0.116049i
$7$			5.14607i			1.94503i	0.232839	+	0.972515i	$0.425199\pi$
$7$			5.14607i			1.94503i	−0.232839	+	0.972515i	$0.574801\pi$
$8$	−0.951057	+	0.309017i	−0.336249	+	0.109254i
$9$	−2.35478	−	1.71085i	−0.784926	−	0.570282i
$10$	2.16231	−	0.569586i	0.683782	−	0.180119i
$11$	−2.82121	+	2.04973i	−0.850628	+	0.618017i	−0.925319	−	0.379189i	$-0.876203\pi$
$11$	−2.82121	+	2.04973i	−0.850628	+	0.618017i	0.0746913	+	0.997207i	$0.476203\pi$
$12$	0.175683	−	0.241806i	0.0507152	−	0.0698035i
$13$	−0.0727292	+	0.100103i	−0.0201715	+	0.0277636i	−0.818984	−	0.573817i	$-0.805462\pi$
$13$	−0.0727292	+	0.100103i	−0.0201715	+	0.0277636i	0.798812	+	0.601581i	$0.205462\pi$
$14$	−4.16326	+	3.02478i	−1.11268	+	0.808407i
$15$	−0.422793	+	0.517609i	−0.109165	+	0.133646i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−2.72208	+	0.884457i	−0.660201	+	0.214512i	−0.619907	−	0.784675i	$-0.712830\pi$
$17$	−2.72208	+	0.884457i	−0.660201	+	0.214512i	−0.0402945	+	0.999188i	$0.512830\pi$
$18$		−	2.91067i		−	0.686050i
$19$	0.309017	+	0.951057i	0.0708934	+	0.218187i
$19$	0.309017	+	0.951057i	0.0708934	+	0.218187i
$20$	1.73178	+	1.41455i	0.387237	+	0.316303i
$21$	0.475300	−	1.46282i	0.103719	−	0.319214i
$22$	−3.31653	−	1.07761i	−0.707088	−	0.229747i
$23$	0.274593	+	0.377945i	0.0572566	+	0.0788069i	0.836685	−	0.547684i	$-0.184490\pi$
$23$	0.274593	+	0.377945i	0.0572566	+	0.0788069i	−0.779429	+	0.626491i	$0.784490\pi$
$24$	0.298889			0.0610105
$25$	−3.68726	−	3.37700i	−0.737452	−	0.675400i
$26$	−0.123734			−0.0242663
$27$	1.03840	+	1.42924i	0.199840	+	0.275057i
$28$	−4.89420	−	1.59022i	−0.924917	−	0.300524i
$29$	−1.73155	+	5.32915i	−0.321540	+	0.989598i	0.651438	+	0.758702i	$0.274166\pi$
$29$	−1.73155	+	5.32915i	−0.321540	+	0.989598i	−0.972978	+	0.230897i	$0.925834\pi$
$30$	−0.667266	−	0.0378037i	−0.121826	−	0.00690198i
$31$	−0.0477733	−	0.147031i	−0.00858035	−	0.0264076i	0.946675	−	0.322191i	$-0.104419\pi$
$31$	−0.0477733	−	0.147031i	−0.00858035	−	0.0264076i	−0.955255	+	0.295783i	$0.904419\pi$
$32$		−	1.00000i		−	0.176777i
$33$	0.991276	−	0.322085i	0.172559	−	0.0560678i
$34$	−2.31554	−	1.68234i	−0.397112	−	0.288519i
$35$	10.7251	+	4.16917i	1.81287	+	0.704719i
$36$	2.35478	−	1.71085i	0.392463	−	0.285141i
$37$	−5.01328	+	6.90019i	−0.824179	+	1.13438i	0.164800	+	0.986327i	$0.447302\pi$
$37$	−5.01328	+	6.90019i	−0.824179	+	1.13438i	−0.988979	+	0.148058i	$0.952698\pi$
$38$	−0.587785	+	0.809017i	−0.0953514	+	0.131240i
$39$	0.0299197	−	0.0217380i	0.00479099	−	0.00348086i
$40$	−0.126481	+	2.23249i	−0.0199984	+	0.352987i
$41$	−5.14648	−	3.73914i	−0.803746	−	0.583955i	0.108265	−	0.994122i	$-0.465471\pi$
$41$	−5.14648	−	3.73914i	−0.803746	−	0.583955i	−0.912011	+	0.410167i	$0.865471\pi$
$42$	1.46282	−	0.475300i	0.225718	−	0.0733404i
$43$			0.721671i			0.110054i	0.998485	+	0.0550269i	$0.0175245\pi$
$43$			0.721671i			0.110054i	−0.998485	+	0.0550269i	$0.982476\pi$
$44$	−1.07761	−	3.31653i	−0.162455	−	0.499986i
$45$	−5.47340	+	3.52161i	−0.815927	+	0.524971i
$46$	−0.144362	+	0.444300i	−0.0212850	+	0.0655085i
$47$	11.8830	+	3.86101i	1.73331	+	0.563186i	0.993921	−	0.110093i	$-0.0351147\pi$
$47$	11.8830	+	3.86101i	1.73331	+	0.563186i	0.739388	+	0.673279i	$0.235115\pi$
$48$	0.175683	+	0.241806i	0.0253576	+	0.0349017i
$49$	−19.4820			−2.78314
$50$	0.564734	−	4.96801i	0.0798654	−	0.702582i
$51$	0.855469			0.119790
$52$	−0.0727292	−	0.100103i	−0.0100857	−	0.0138818i
$53$	9.27451	+	3.01347i	1.27395	+	0.413932i	0.866446	−	0.499271i	$-0.166399\pi$
$53$	9.27451	+	3.01347i	1.27395	+	0.413932i	0.407506	+	0.913203i	$0.366399\pi$
$54$	−0.545920	+	1.68017i	−0.0742902	+	0.228642i
$55$	1.98627	+	7.54042i	0.267828	+	1.01675i
$56$	−1.59022	−	4.89420i	−0.212502	−	0.654015i
$57$		−	0.298889i		−	0.0395888i
$58$	−5.32915	+	1.73155i	−0.699752	+	0.227363i
$59$	−2.24269	−	1.62941i	−0.291973	−	0.212131i	0.432150	−	0.901802i	$-0.357755\pi$
$59$	−2.24269	−	1.62941i	−0.291973	−	0.212131i	−0.724123	+	0.689671i	$0.757755\pi$
$60$	−0.361625	−	0.562050i	−0.0466856	−	0.0725604i
$61$	4.39526	−	3.19334i	0.562756	−	0.408866i	−0.269711	−	0.962941i	$-0.586928\pi$
$61$	4.39526	−	3.19334i	0.562756	−	0.408866i	0.832466	+	0.554075i	$0.186928\pi$
$62$	0.0908703	−	0.125072i	0.0115405	−	0.0158842i
$63$	8.80413	−	12.1178i	1.10922	−	1.52671i
$64$	0.809017	−	0.587785i	0.101127	−	0.0734732i
$65$	0.149706	+	0.232678i	0.0185687	+	0.0288602i
$66$	0.843229	+	0.612642i	0.103794	+	0.0754110i
$67$	−11.9876	+	3.89502i	−1.46452	+	0.475852i	−0.929448	−	0.368952i	$-0.879717\pi$
$67$	−11.9876	+	3.89502i	−1.46452	+	0.475852i	−0.535075	+	0.844805i	$0.679717\pi$
$68$		−	2.86216i		−	0.347088i
$69$	−0.0431482	−	0.132797i	−0.00519443	−	0.0159868i
$70$	2.93113	+	11.1274i	0.350337	+	1.32998i
$71$	−3.22889	+	9.93750i	−0.383199	+	1.17936i	0.554580	+	0.832130i	$0.312879\pi$
$71$	−3.22889	+	9.93750i	−0.383199	+	1.17936i	−0.937779	+	0.347234i	$0.887121\pi$
$72$	2.76821	+	0.899445i	0.326236	+	0.106001i
$73$	−3.61941	−	4.98169i	−0.423620	−	0.583063i	0.542854	−	0.839827i	$-0.317344\pi$
$73$	−3.61941	−	4.98169i	−0.423620	−	0.583063i	−0.966474	+	0.256764i	$0.917344\pi$
$74$	−8.52911			−0.991489
$75$	0.736236	+	1.30051i	0.0850132	+	0.150170i
$76$	−1.00000			−0.114708
$77$	−10.5481	−	14.5182i	−1.20206	−	1.65450i
$78$	0.0351728	+	0.0114283i	0.00398253	+	0.00129400i
$79$	−0.669662	+	2.06101i	−0.0753429	+	0.231882i	−0.981634	−	0.190771i	$-0.938901\pi$
$79$	−0.669662	+	2.06101i	−0.0753429	+	0.231882i	0.906292	+	0.422653i	$0.138901\pi$
$80$	−1.88046	+	1.20990i	−0.210242	+	0.135271i
$81$	2.53517	+	7.80244i	0.281685	+	0.866938i
$82$		−	6.36140i		−	0.702499i
$83$	0.474706	−	0.154241i	0.0521058	−	0.0169302i	−0.282848	−	0.959165i	$-0.591279\pi$
$83$	0.474706	−	0.154241i	0.0521058	−	0.0169302i	0.334954	+	0.942235i	$0.391279\pi$
$84$	1.24435	+	0.904074i	0.135770	+	0.0986426i
$85$	−0.362009	+	6.38975i	−0.0392654	+	0.693065i
$86$	−0.583844	+	0.424188i	−0.0629575	+	0.0457413i
$87$	0.984420	−	1.35494i	0.105541	−	0.145265i
$88$	2.04973	−	2.82121i	0.218502	−	0.300742i
$89$	5.60096	−	4.06934i	0.593701	−	0.431349i	−0.249936	−	0.968262i	$-0.580410\pi$
$89$	5.60096	−	4.06934i	0.593701	−	0.431349i	0.843637	+	0.536913i	$0.180410\pi$
$90$	−6.06623	−	2.35813i	−0.639436	−	0.248568i
$91$	−0.515138	−	0.374270i	−0.0540011	−	0.0392341i
$92$	−0.444300	+	0.144362i	−0.0463215	+	0.0150508i
$93$			0.0462076i			0.00479150i
$94$	3.86101	+	11.8830i	0.398233	+	1.22564i
$95$	2.23249	+	0.126481i	0.229048	+	0.0129767i
$96$	−0.0923618	+	0.284260i	−0.00942663	+	0.0290122i
$97$	12.8207	+	4.16571i	1.30175	+	0.422964i	0.876190	−	0.481966i	$-0.160077\pi$
$97$	12.8207	+	4.16571i	1.30175	+	0.422964i	0.425560	+	0.904930i	$0.360077\pi$
$98$	−11.4512	−	15.7613i	−1.15675	−	1.59213i
$99$	10.1501			1.02012
$100$	4.35114	−	2.46324i	0.435114	−	0.246324i
$101$	10.2096			1.01589			0.507945	−	0.861389i	$-0.330405\pi$
$101$	10.2096			1.01589			0.507945	+	0.861389i	$0.330405\pi$
$102$	0.502832	+	0.692089i	0.0497878	+	0.0685270i
$103$	−6.85348	−	2.22683i	−0.675294	−	0.219416i	−0.0487599	−	0.998811i	$-0.515527\pi$
$103$	−6.85348	−	2.22683i	−0.675294	−	0.219416i	−0.626534	+	0.779394i	$0.715527\pi$
$104$	0.0382360	−	0.117678i	0.00374935	−	0.0115393i
$105$	−2.66365	−	2.17572i	−0.259946	−	0.212329i
$106$	3.01347	+	9.27451i	0.292694	+	0.900820i
$107$		−	13.1721i		−	1.27340i	−0.771113	−	0.636699i	$-0.780300\pi$
$107$		−	13.1721i		−	1.27340i	0.771113	−	0.636699i	$-0.219700\pi$
$108$	−1.68017	+	0.545920i	−0.161674	+	0.0525311i
$109$	−3.37018	−	2.44858i	−0.322804	−	0.234531i	0.414567	−	0.910019i	$-0.363933\pi$
$109$	−3.37018	−	2.44858i	−0.322804	−	0.234531i	−0.737371	+	0.675488i	$0.763933\pi$
$110$	−4.93283	+	6.03907i	−0.470327	+	0.575803i
$111$	2.06239	−	1.49842i	0.195754	−	0.142223i
$112$	3.02478	−	4.16326i	0.285815	−	0.393391i
$113$	4.13492	−	5.69123i	0.388980	−	0.535386i	−0.568955	−	0.822368i	$-0.692652\pi$
$113$	4.13492	−	5.69123i	0.388980	−	0.535386i	0.957936	+	0.286983i	$0.0926523\pi$
$114$	0.241806	−	0.175683i	0.0226472	−	0.0164542i
$115$	1.01015	−	0.266091i	0.0941974	−	0.0248131i
$116$	−4.53325	−	3.29360i	−0.420901	−	0.305803i
$117$	0.342522	−	0.111292i	0.0316662	−	0.0102890i
$118$		−	2.77211i		−	0.255194i
$119$	−4.55148	−	14.0080i	−0.417233	−	1.28411i
$120$	0.242150	−	0.622926i	0.0221052	−	0.0568651i
$121$	0.358658	−	1.10383i	0.0326052	−	0.100349i
$122$	5.16694	+	1.67884i	0.467793	+	0.151995i
$123$	1.11759	+	1.53823i	0.100769	+	0.138697i
$124$	0.154598			0.0138833
$125$	−10.0254	+	4.94882i	−0.896701	+	0.442636i
$126$	14.9785			1.33439
$127$	−3.99799	−	5.50276i	−0.354764	−	0.488291i	0.593916	−	0.804527i	$-0.297581\pi$
$127$	−3.99799	−	5.50276i	−0.354764	−	0.488291i	−0.948681	+	0.316236i	$0.897581\pi$
$128$	0.951057	+	0.309017i	0.0840623	+	0.0273135i
$129$	0.0666548	−	0.205142i	0.00586863	−	0.0180618i
$130$	−0.100246	+	0.257879i	−0.00879211	+	0.0226175i
$131$	1.17482	+	3.61572i	0.102644	+	0.315907i	0.989170	−	0.146772i	$-0.0468883\pi$
$131$	1.17482	+	3.61572i	0.102644	+	0.315907i	−0.886526	+	0.462679i	$0.846888\pi$
$132$			1.04229i			0.0907196i
$133$	−4.89420	+	1.59022i	−0.424381	+	0.137890i
$134$	−10.1973	−	7.40877i	−0.880912	−	0.640020i
$135$	3.82000	−	1.00625i	0.328773	−	0.0866042i
$136$	2.31554	−	1.68234i	0.198556	−	0.144259i
$137$	1.66635	−	2.29353i	0.142366	−	0.195949i	−0.731880	−	0.681434i	$-0.761357\pi$
$137$	1.66635	−	2.29353i	0.142366	−	0.195949i	0.874245	+	0.485484i	$0.161357\pi$
$138$	0.0820728	−	0.112963i	0.00698650	−	0.00961609i
$139$	3.73171	−	2.71125i	0.316519	−	0.229965i	−0.418169	−	0.908369i	$-0.637328\pi$
$139$	3.73171	−	2.71125i	0.316519	−	0.229965i	0.734689	+	0.678404i	$0.237328\pi$
$140$	−7.27936	+	8.91184i	−0.615218	+	0.753188i
$141$	−3.02125	−	2.19506i	−0.254435	−	0.184858i
$142$	−9.93750	+	3.22889i	−0.833936	+	0.270962i
$143$		−	0.431488i		−	0.0360828i
$144$	0.899445	+	2.76821i	0.0749538	+	0.230684i
$145$	9.70384	+	7.92628i	0.805860	+	0.658242i
$146$	1.90284	−	5.85633i	0.157480	−	0.484673i
$147$	5.53796	+	1.79939i	0.456763	+	0.148411i
$148$	−5.01328	−	6.90019i	−0.412089	−	0.567192i
$149$	−1.14328			−0.0936612			−0.0468306	−	0.998903i	$-0.514912\pi$
$149$	−1.14328			−0.0936612			−0.0468306	+	0.998903i	$0.514912\pi$
$150$	−0.619385	+	1.36005i	−0.0505726	+	0.111047i
$151$	15.1535			1.23318			0.616588	−	0.787286i	$-0.288515\pi$
$151$	15.1535			1.23318			0.616588	+	0.787286i	$0.288515\pi$
$152$	−0.587785	−	0.809017i	−0.0476757	−	0.0656199i
$153$	7.92306	+	2.57436i	0.640542	+	0.208125i
$154$	5.54544	−	17.0671i	0.446864	−	1.37531i
$155$	−0.345138	−	0.0195537i	−0.0277221	−	0.00157059i
$156$	0.0114283	+	0.0351728i	0.000914998	+	0.00281607i
$157$		−	8.63401i		−	0.689069i	−0.938774	−	0.344534i	$-0.888037\pi$
$157$		−	8.63401i		−	0.689069i	0.938774	−	0.344534i	$-0.111963\pi$
$158$	−2.06101	+	0.669662i	−0.163965	+	0.0532755i
$159$	−2.35804	−	1.71322i	−0.187005	−	0.135867i
$160$	−2.08414	−	0.810167i	−0.164766	−	0.0640493i
$161$	−1.94493	+	1.41307i	−0.153282	+	0.111366i
$162$	−4.82217	+	6.63715i	−0.378866	+	0.521464i
$163$	0.414515	−	0.570531i	0.0324673	−	0.0446874i	−0.792475	−	0.609905i	$-0.791208\pi$
$163$	0.414515	−	0.570531i	0.0324673	−	0.0446874i	0.824942	+	0.565217i	$0.191208\pi$
$164$	5.14648	−	3.73914i	0.401873	−	0.291978i
$165$	0.131830	−	2.32690i	0.0102629	−	0.181149i
$166$	0.403809	+	0.293385i	0.0313417	+	0.0227711i
$167$	23.9182	−	7.77149i	1.85085	−	0.601376i	0.854161	−	0.520008i	$-0.174071\pi$
$167$	23.9182	−	7.77149i	1.85085	−	0.601376i	0.996684	−	0.0813680i	$-0.0259289\pi$
$168$			1.53810i			0.118667i
$169$	4.01249	+	12.3492i	0.308653	+	0.949936i
$170$	−5.38220	+	3.46293i	−0.412796	+	0.265594i
$171$	0.899445	−	2.76821i	0.0687823	−	0.211690i
$172$	−0.686350	−	0.223009i	−0.0523337	−	0.0170043i
$173$	8.37360	+	11.5253i	0.636633	+	0.876250i	0.998430	−	0.0560069i	$-0.0178369\pi$
$173$	8.37360	+	11.5253i	0.636633	+	0.876250i	−0.361798	+	0.932257i	$0.617837\pi$
$174$	1.67479			0.126966
$175$	17.3783	−	18.9749i	1.31367	−	1.43437i
$176$	3.48721			0.262858
$177$	0.487012	+	0.670314i	0.0366060	+	0.0503839i
$178$	6.58433	+	2.13938i	0.493516	+	0.160353i
$179$	−2.67047	+	8.21886i	−0.199600	+	0.614306i	0.800292	+	0.599611i	$0.204678\pi$
$179$	−2.67047	+	8.21886i	−0.199600	+	0.614306i	−0.999892	+	0.0146957i	$0.995322\pi$
$180$	−1.65788	−	6.29375i	−0.123571	−	0.469109i
$181$	2.64452	+	8.13899i	0.196565	+	0.604966i	0.999955	+	0.00951207i	$0.00302783\pi$
$181$	2.64452	+	8.13899i	0.196565	+	0.604966i	−0.803389	+	0.595454i	$0.796972\pi$
$182$		−	0.636745i		−	0.0471987i
$183$	−1.54434	+	0.501787i	−0.114161	+	0.0370932i
$184$	−0.377945	−	0.274593i	−0.0278624	−	0.0202432i
$185$	10.3194	+	16.0387i	0.758694	+	1.17919i
$186$	−0.0373827	+	0.0271601i	−0.00274103	+	0.00199148i
$187$	5.86667	−	8.07477i	0.429013	−	0.590486i
$188$	−7.34408	+	10.1083i	−0.535622	+	0.737221i
$189$	−7.35494	+	5.34368i	−0.534994	+	0.388696i
$190$	1.20990	+	1.88046i	0.0877753	+	0.136423i
$191$	21.2448	+	15.4352i	1.53722	+	1.11685i	0.952051	+	0.305939i	$0.0989703\pi$
$191$	21.2448	+	15.4352i	1.53722	+	1.11685i	0.585165	+	0.810914i	$0.301030\pi$
$192$	−0.284260	+	0.0923618i	−0.0205147	+	0.00666564i
$193$			1.75458i			0.126297i	0.998004	+	0.0631486i	$0.0201142\pi$
$193$			1.75458i			0.126297i	−0.998004	+	0.0631486i	$0.979886\pi$
$194$	4.16571	+	12.8207i	0.299081	+	0.920476i
$195$	−0.0210649	−	0.0799682i	−0.00150849	−	0.00572664i
$196$	6.02027	−	18.5285i	0.430019	−	1.32346i
$197$	8.79199	+	2.85669i	0.626403	+	0.203531i	0.604981	−	0.796240i	$-0.293181\pi$
$197$	8.79199	+	2.85669i	0.626403	+	0.203531i	0.0214219	+	0.999771i	$0.493181\pi$
$198$	5.96608	+	8.21161i	0.423991	+	0.583573i
$199$	3.62576			0.257024			0.128512	−	0.991708i	$-0.458980\pi$
$199$	3.62576			0.257024			0.128512	+	0.991708i	$0.458980\pi$
$200$	4.55034	+	2.07229i	0.321758	+	0.146533i
$201$	3.76736			0.265729
$202$	6.00103	+	8.25971i	0.422231	+	0.581151i
$203$	−27.4242	−	8.91065i	−1.92480	−	0.625405i
$204$	−0.264355	+	0.813600i	−0.0185085	+	0.0569634i
$205$	−11.9624	+	7.69665i	−0.835490	+	0.537557i
$206$	−2.22683	−	6.85348i	−0.155151	−	0.477505i
$207$		−	1.35976i		−	0.0945100i
$208$	0.117678	−	0.0382360i	0.00815953	−	0.00265119i
$209$	−2.82121	−	2.04973i	−0.195147	−	0.141783i
$210$	0.194541	−	3.43380i	0.0134246	−	0.236954i
$211$	−12.9585	+	9.41493i	−0.892102	+	0.648150i	−0.936425	−	0.350867i	$-0.885887\pi$
$211$	−12.9585	+	9.41493i	−0.892102	+	0.648150i	0.0443230	+	0.999017i	$0.485887\pi$
$212$	−5.73196	+	7.88937i	−0.393673	+	0.541844i
$213$	1.83569	−	2.52661i	0.125779	−	0.173120i
$214$	10.6565	−	7.74238i	0.728461	−	0.529258i
$215$	1.50406	+	0.584674i	0.102576	+	0.0398745i
$216$	−1.42924	−	1.03840i	−0.0972472	−	0.0706542i
$217$	0.756633	−	0.245845i	0.0513636	−	0.0166890i
$218$		−	4.16577i		−	0.282141i
$219$	0.568737	+	1.75039i	0.0384317	+	0.118281i
$220$	−7.78516	−	0.441065i	−0.524875	−	0.0297366i
$221$	0.109438	−	0.336815i	0.00736158	−	0.0226566i
$222$	2.42449	+	0.787764i	0.162721	+	0.0528712i
$223$	6.03895	+	8.31190i	0.404398	+	0.556606i	0.961841	−	0.273609i	$-0.0882174\pi$
$223$	6.03895	+	8.31190i	0.404398	+	0.556606i	−0.557443	+	0.830215i	$0.688217\pi$
$224$	5.14607			0.343836
$225$	2.90515	+	14.2604i	0.193676	+	0.950694i
$226$	7.03474			0.467944
$227$	−11.7182	−	16.1287i	−0.777763	−	1.07050i	−0.995525	−	0.0944967i	$-0.969876\pi$
$227$	−11.7182	−	16.1287i	−0.777763	−	1.07050i	0.217762	−	0.976002i	$-0.430124\pi$
$228$	0.284260	+	0.0923618i	0.0188256	+	0.00611681i
$229$	−7.94770	+	24.4605i	−0.525199	+	1.61640i	0.238723	+	0.971088i	$0.423271\pi$
$229$	−7.94770	+	24.4605i	−0.525199	+	1.61640i	−0.763922	+	0.645308i	$0.776729\pi$
$230$	0.809026	+	0.660828i	0.0533456	+	0.0435737i
$231$	1.65747	+	5.10117i	0.109054	+	0.335632i
$232$		−	5.60340i		−	0.367881i
$233$	15.7334	−	5.11208i	1.03073	−	0.334903i	0.255649	−	0.966770i	$-0.417711\pi$
$233$	15.7334	−	5.11208i	1.03073	−	0.334903i	0.775077	+	0.631867i	$0.217711\pi$
$234$	0.291367	+	0.211690i	0.0190472	+	0.0138386i
$235$	17.6741	−	21.6377i	1.15293	−	1.41149i
$236$	2.24269	−	1.62941i	0.145986	−	0.106065i
$237$	0.380717	−	0.524012i	0.0247302	−	0.0340382i
$238$	8.65742	−	11.9159i	0.561177	−	0.772395i
$239$	−19.8771	+	14.4416i	−1.28574	+	0.934148i	−0.999710	−	0.0240711i	$-0.992337\pi$
$239$	−19.8771	+	14.4416i	−1.28574	+	0.934148i	−0.286034	+	0.958219i	$0.592337\pi$
$240$	0.646290	−	0.170243i	0.0417178	−	0.0109891i
$241$	0.00893884	+	0.00649445i	0.000575801	+	0.000418344i	0.588073	−	0.808808i	$-0.299887\pi$
$241$	0.00893884	+	0.00649445i	0.000575801	+	0.000418344i	−0.587497	+	0.809226i	$0.699887\pi$
$242$	1.10383	−	0.358658i	0.0709572	−	0.0230554i
$243$		−	7.75197i		−	0.497289i
$244$	1.67884	+	5.16694i	0.107477	+	0.330779i
$245$	−15.7837	+	40.6032i	−1.00838	+	2.59404i
$246$	−0.587550	+	1.80829i	−0.0374609	+	0.115293i
$247$	−0.117678	−	0.0382360i	−0.00748769	−	0.00243290i
$248$	0.0908703	+	0.125072i	0.00577027	+	0.00794209i
$249$	−0.149186			−0.00945429
$250$	−9.89648	−	5.20190i	−0.625908	−	0.328997i
$251$	2.64376			0.166873			0.0834364	−	0.996513i	$-0.473410\pi$
$251$	2.64376			0.166873			0.0834364	+	0.996513i	$0.473410\pi$
$252$	8.80413	+	12.1178i	0.554608	+	0.763353i
$253$	−1.54937	−	0.503421i	−0.0974080	−	0.0316498i
$254$	2.10187	−	6.46888i	0.131883	−	0.405894i
$255$	0.693073	−	1.78292i	0.0434019	−	0.111651i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$			2.66002i			0.165927i	0.996553	+	0.0829636i	$0.0264385\pi$
$257$			2.66002i			0.165927i	−0.996553	+	0.0829636i	$0.973561\pi$
$258$	0.205142	−	0.0666548i	0.0127716	−	0.00414975i
$259$	−35.5089	−	25.7987i	−2.20641	−	1.60305i
$260$	−0.267552	+	0.0704774i	−0.0165928	+	0.00437082i
$261$	13.1948	−	9.58656i	0.816735	−	0.593393i
$262$	−2.23464	+	3.07572i	−0.138056	+	0.190018i
$263$	−10.9351	+	15.0509i	−0.674287	+	0.928077i	−0.999848	−	0.0174442i	$-0.994447\pi$
$263$	−10.9351	+	15.0509i	−0.674287	+	0.928077i	0.325560	+	0.945521i	$0.394447\pi$
$264$	−0.843229	+	0.612642i	−0.0518972	+	0.0377055i
$265$	13.7944	−	16.8879i	0.847382	−	1.03742i
$266$	−4.16326	−	3.02478i	−0.255266	−	0.185461i
$267$	−1.96798	+	0.639436i	−0.120439	+	0.0391329i
$268$		−	12.6045i		−	0.769945i
$269$	−4.60885	−	14.1846i	−0.281007	−	0.864849i	−0.987567	−	0.157197i	$-0.949754\pi$
$269$	−4.60885	−	14.1846i	−0.281007	−	0.864849i	0.706561	−	0.707652i	$-0.250246\pi$
$270$	3.05941	+	2.49899i	0.186190	+	0.152084i
$271$	−2.79710	+	8.60858i	−0.169912	+	0.522934i	−0.999365	−	0.0356424i	$-0.988652\pi$
$271$	−2.79710	+	8.60858i	−0.169912	+	0.522934i	0.829453	+	0.558576i	$0.188652\pi$
$272$	2.72208	+	0.884457i	0.165050	+	0.0536281i
$273$	0.111865	+	0.153969i	0.00677038	+	0.00931863i
$274$	2.83496			0.171266
$275$	17.3245	+	1.96935i	1.04471	+	0.118756i
$276$	0.139631			0.00840477
$277$	−17.9086	−	24.6491i	−1.07603	−	1.48102i	−0.863822	−	0.503797i	$-0.831936\pi$
$277$	−17.9086	−	24.6491i	−1.07603	−	1.48102i	−0.212204	−	0.977225i	$-0.568064\pi$
$278$	4.38689	+	1.42539i	0.263108	+	0.0854890i
$279$	−0.139052	+	0.427959i	−0.00832484	+	0.0256212i
$280$	−11.4885	−	0.650879i	−0.686571	−	0.0388975i
$281$	−10.0916	−	31.0588i	−0.602014	−	1.85281i	−0.516140	−	0.856504i	$-0.672632\pi$
$281$	−10.0916	−	31.0588i	−0.602014	−	1.85281i	−0.0858741	−	0.996306i	$-0.527368\pi$
$282$		−	3.73447i		−	0.222384i
$283$	−12.6354	+	4.10550i	−0.751098	+	0.244047i	−0.659454	−	0.751745i	$-0.729212\pi$
$283$	−12.6354	+	4.10550i	−0.751098	+	0.244047i	−0.0916446	+	0.995792i	$0.529212\pi$
$284$	−8.45334	−	6.14171i	−0.501614	−	0.364444i
$285$	−0.622926	−	0.242150i	−0.0368989	−	0.0143437i
$286$	0.349081	−	0.253622i	0.0206416	−	0.0149970i
$287$	19.2419	−	26.4842i	1.13581	−	1.56331i
$288$	−1.71085	+	2.35478i	−0.100813	+	0.138757i
$289$	−7.12584	+	5.17722i	−0.419167	+	0.304542i
$290$	−0.708723	+	12.5095i	−0.0416176	+	0.734585i
$291$	−3.25968	−	2.36829i	−0.191086	−	0.138832i
$292$	5.85633	−	1.90284i	0.342716	−	0.111355i
$293$			24.3647i			1.42340i	0.702482	+	0.711702i	$0.252075\pi$
$293$			24.3647i			1.42340i	−0.702482	+	0.711702i	$0.747925\pi$
$294$	1.79939	+	5.53796i	0.104943	+	0.322981i
$295$	−5.21286	+	3.35397i	−0.303504	+	0.195276i
$296$	2.63564	−	8.11167i	0.153193	−	0.471481i
$297$	−5.85910	−	1.90374i	−0.339979	−	0.110466i
$298$	−0.672003	−	0.924933i	−0.0389281	−	0.0535799i
$299$	−0.0578044			−0.00334291
$300$	−1.46437	+	0.298322i	−0.0845452	+	0.0172236i
$301$	−3.71377			−0.214058
$302$	8.90701	+	12.2594i	0.512541	+	0.705452i
$303$	−2.90218	−	0.942974i	−0.166726	−	0.0541724i
$304$	0.309017	−	0.951057i	0.0177233	−	0.0545468i
$305$	−3.09447	−	11.7475i	−0.177189	−	0.672658i
$306$	2.57436	+	7.92306i	0.147166	+	0.452931i
$307$			5.96080i			0.340201i	0.985427	+	0.170100i	$0.0544092\pi$
$307$			5.96080i			0.340201i	−0.985427	+	0.170100i	$0.945591\pi$
$308$	17.0671	−	5.54544i	0.972489	−	0.315981i
$309$	1.74250	+	1.26600i	0.0991273	+	0.0720202i
$310$	−0.187048	−	0.290716i	−0.0106236	−	0.0165115i
$311$	6.67333	−	4.84846i	0.378410	−	0.274931i	−0.382280	−	0.924047i	$-0.624861\pi$
$311$	6.67333	−	4.84846i	0.378410	−	0.274931i	0.760690	+	0.649116i	$0.224861\pi$
$312$	−0.0217380	+	0.0299197i	−0.00123067	+	0.00169387i
$313$	0.567270	−	0.780781i	0.0320640	−	0.0441323i	−0.792684	−	0.609633i	$-0.791317\pi$
$313$	0.567270	−	0.780781i	0.0320640	−	0.0441323i	0.824748	+	0.565500i	$0.191317\pi$
$314$	6.98506	−	5.07494i	0.394190	−	0.286396i
$315$	−18.1224	−	28.1665i	−1.02108	−	1.58700i
$316$	−1.75320	−	1.27377i	−0.0986251	−	0.0716553i
$317$	4.85642	−	1.57795i	0.272764	−	0.0886264i	−0.169441	−	0.985540i	$-0.554196\pi$
$317$	4.85642	−	1.57795i	0.272764	−	0.0886264i	0.442205	+	0.896914i	$0.354196\pi$
$318$		−	2.91470i		−	0.163448i
$319$	−6.03827	−	18.5839i	−0.338078	−	1.04050i
$320$	−0.569586	−	2.16231i	−0.0318408	−	0.120877i
$321$	−1.21660	+	3.74431i	−0.0679040	+	0.208987i
$322$	−2.28640	−	0.742896i	−0.127416	−	0.0414000i
$323$	−1.68234	−	2.31554i	−0.0936078	−	0.128840i
$324$	−8.20397			−0.455776
$325$	0.606220	−	0.123500i	0.0336270	−	0.00685053i
$326$	0.705215			0.0390583
$327$	0.731852	+	1.00731i	0.0404715	+	0.0557043i
$328$	6.05005	+	1.96578i	0.334058	+	0.108542i
$329$	−19.8690	+	61.1506i	−1.09542	+	3.37134i
$330$	1.95999	−	1.26106i	0.107894	−	0.0694193i
$331$	−8.44374	−	25.9872i	−0.464110	−	1.42838i	−0.860098	−	0.510129i	$-0.829598\pi$
$331$	−8.44374	−	25.9872i	−0.464110	−	1.42838i	0.395988	−	0.918256i	$-0.370402\pi$
$332$			0.499136i			0.0273936i
$333$	23.6103	−	7.67147i	1.29384	−	0.420394i
$334$	20.3460	+	14.7823i	1.11329	+	0.808849i
$335$	−1.59423	+	28.1395i	−0.0871023	+	1.53743i
$336$	−1.24435	+	0.904074i	−0.0678849	+	0.0493213i
$337$	12.4047	−	17.0737i	0.675730	−	0.930062i	−0.324143	−	0.946008i	$-0.605076\pi$
$337$	12.4047	−	17.0737i	0.675730	−	0.930062i	0.999873	+	0.0159458i	$0.00507593\pi$
$338$	−7.63221	+	10.5048i	−0.415137	+	0.571388i
$339$	−1.70105	+	1.23588i	−0.0923881	+	0.0671239i
$340$	−5.96514	−	2.31883i	−0.323505	−	0.125756i
$341$	0.436153	+	0.316884i	0.0236190	+	0.0171602i
$342$	2.76821	−	0.899445i	0.149688	−	0.0486364i
$343$		−	64.2333i		−	3.46827i
$344$	−0.223009	−	0.686350i	−0.0120238	−	0.0370055i
$345$	−0.311723	−	0.0176606i	−0.0167826	−	0.000950814i
$346$	−4.40226	+	13.5488i	−0.236667	+	0.728386i
$347$	26.1062	+	8.48242i	1.40145	+	0.455360i	0.909661	−	0.415352i	$-0.136341\pi$
$347$	26.1062	+	8.48242i	1.40145	+	0.455360i	0.491794	+	0.870712i	$0.336341\pi$
$348$	0.984420	+	1.35494i	0.0527704	+	0.0726323i
$349$	−20.0469			−1.07309			−0.536544	−	0.843872i	$-0.680271\pi$
$349$	−20.0469			−1.07309			−0.536544	+	0.843872i	$0.680271\pi$
$350$	25.5657	+	2.90616i	1.36654	+	0.155341i
$351$	−0.218593			−0.0116676
$352$	2.04973	+	2.82121i	0.109251	+	0.150371i
$353$	−1.25597	−	0.408089i	−0.0668485	−	0.0217204i	0.275402	−	0.961329i	$-0.411189\pi$
$353$	−1.25597	−	0.408089i	−0.0668485	−	0.0217204i	−0.342250	+	0.939609i	$0.611189\pi$
$354$	−0.256037	+	0.788001i	−0.0136082	+	0.0418818i
$355$	18.0952	+	14.7805i	0.960392	+	0.784467i
$356$	2.13938	+	6.58433i	0.113387	+	0.348969i
$357$			4.40230i			0.232995i
$358$	−8.21886	+	2.67047i	−0.434380	+	0.141139i
$359$	17.5883	+	12.7786i	0.928275	+	0.674431i	0.945570	−	0.325419i	$-0.105505\pi$
$359$	17.5883	+	12.7786i	0.928275	+	0.674431i	−0.0172948	+	0.999850i	$0.505505\pi$
$360$	4.11728	−	5.04062i	0.217000	−	0.265664i
$361$	−0.809017	+	0.587785i	−0.0425798	+	0.0309361i
$362$	−5.03017	+	6.92344i	−0.264380	+	0.363888i
$363$	−0.203904	+	0.280650i	−0.0107022	+	0.0147303i
$364$	0.515138	−	0.374270i	0.0270006	−	0.0196171i
$365$	−13.3149	+	3.50735i	−0.696931	+	0.183583i
$366$	−1.31370	−	0.954456i	−0.0686680	−	0.0498902i
$367$	−11.0027	+	3.57500i	−0.574337	+	0.186614i	−0.581762	−	0.813359i	$-0.697637\pi$
$367$	−11.0027	+	3.57500i	−0.574337	+	0.186614i	0.00742486	+	0.999972i	$0.497637\pi$
$368$		−	0.467165i		−	0.0243527i
$369$	5.72173	+	17.6097i	0.297862	+	0.916723i
$370$	−6.91000	+	17.7758i	−0.359234	+	0.924122i
$371$	−15.5075	+	47.7272i	−0.805110	+	2.47787i
$372$	−0.0439460	−	0.0142789i	−0.00227849	−	0.000740328i
$373$	−16.0507	−	22.0919i	−0.831075	−	1.14388i	−0.987722	−	0.156222i	$-0.950069\pi$
$373$	−16.0507	−	22.0919i	−0.831075	−	1.14388i	0.156647	−	0.987655i	$-0.449931\pi$
$374$	9.98097			0.516104
$375$	3.30691	−	0.480787i	0.170768	−	0.0248277i
$376$	−12.4945			−0.644355
$377$	−0.407531	−	0.560918i	−0.0209889	−	0.0288888i
$378$	−8.64626	−	2.80934i	−0.444715	−	0.144497i
$379$	4.48108	−	13.7914i	0.230178	−	0.708415i	−0.767547	−	0.640993i	$-0.778523\pi$
$379$	4.48108	−	13.7914i	0.230178	−	0.708415i	0.997725	−	0.0674216i	$-0.0214773\pi$
$380$	−0.810167	+	2.08414i	−0.0415607	+	0.106914i
$381$	0.628225	+	1.93348i	0.0321849	+	0.0990551i
$382$			26.2600i			1.34358i
$383$	28.6012	−	9.29309i	1.46145	−	0.474855i	0.532939	−	0.846154i	$-0.321087\pi$
$383$	28.6012	−	9.29309i	1.46145	−	0.474855i	0.928513	+	0.371299i	$0.121087\pi$
$384$	−0.241806	−	0.175683i	−0.0123396	−	0.00896526i
$385$	−38.8035	+	10.2215i	−1.97761	+	0.520934i
$386$	−1.41948	+	1.03131i	−0.0722498	+	0.0524925i
$387$	1.23467	−	1.69938i	0.0627617	−	0.0863841i
$388$	−7.92366	+	10.9060i	−0.402263	+	0.553667i
$389$	−3.56384	+	2.58928i	−0.180694	+	0.131282i	−0.674456	−	0.738315i	$-0.735622\pi$
$389$	−3.56384	+	2.58928i	−0.180694	+	0.131282i	0.493762	+	0.869597i	$0.335622\pi$
$390$	0.0523140	−	0.0640460i	0.00264902	−	0.00324310i
$391$	−1.08174	−	0.785930i	−0.0547059	−	0.0397462i
$392$	18.5285	−	6.02027i	0.935830	−	0.304070i
$393$		−	1.13631i		−	0.0573195i
$394$	2.85669	+	8.79199i	0.143918	+	0.442934i
$395$	3.75289	+	3.06543i	0.188828	+	0.154238i
$396$	−3.13655	+	9.65332i	−0.157618	+	0.485098i
$397$	28.2376	+	9.17496i	1.41721	+	0.460478i	0.914713	−	0.404104i	$-0.132417\pi$
$397$	28.2376	+	9.17496i	1.41721	+	0.460478i	0.502492	+	0.864582i	$0.332417\pi$
$398$	2.13117	+	2.93330i	0.106826	+	0.147033i
$399$	1.53810			0.0770015
$400$	0.998104	+	4.89937i	0.0499052	+	0.244968i
$401$	−26.1481			−1.30577			−0.652886	−	0.757456i	$-0.726442\pi$
$401$	−26.1481			−1.30577			−0.652886	+	0.757456i	$0.726442\pi$
$402$	2.21440	+	3.04786i	0.110444	+	0.152013i
$403$	0.0181928	+	0.00591120i	0.000906249	+	0.000294458i
$404$	−3.15493	+	9.70988i	−0.156964	+	0.483084i
$405$	18.3153	+	1.03764i	0.910093	+	0.0515610i
$406$	−8.91065	−	27.4242i	−0.442228	−	1.36104i
$407$		−	29.7428i		−	1.47430i
$408$	−0.813600	+	0.264355i	−0.0402792	+	0.0130875i
$409$	−15.9368	−	11.5787i	−0.788023	−	0.572532i	0.119353	−	0.992852i	$-0.461918\pi$
$409$	−15.9368	−	11.5787i	−0.788023	−	0.572532i	−0.907376	+	0.420320i	$0.861918\pi$
$410$	−13.2580	−	5.15380i	−0.654768	−	0.254528i
$411$	−0.685510	+	0.498052i	−0.0338137	+	0.0245671i
$412$	4.23568	−	5.82992i	0.208677	−	0.287220i
$413$	8.38503	−	11.5410i	0.412601	−	0.567896i
$414$	1.10007	−	0.799248i	0.0540655	−	0.0392809i
$415$	0.0631311	−	1.11431i	0.00309898	−	0.0546995i
$416$	0.100103	+	0.0727292i	0.00490796	+	0.00356584i
$417$	−1.31119	+	0.426032i	−0.0642094	+	0.0208629i
$418$		−	3.48721i		−	0.170565i
$419$	−2.26295	−	6.96465i	−0.110553	−	0.340246i	0.880441	−	0.474156i	$-0.157247\pi$
$419$	−2.26295	−	6.96465i	−0.110553	−	0.340246i	−0.990993	+	0.133910i	$0.957247\pi$
$420$	2.89235	−	1.86095i	0.141132	−	0.0908050i
$421$	−0.152800	+	0.470271i	−0.00744703	+	0.0229196i	−0.954711	−	0.297535i	$-0.903836\pi$
$421$	−0.152800	+	0.470271i	−0.00744703	+	0.0229196i	0.947264	+	0.320454i	$0.103836\pi$
$422$	−15.2337	−	4.94972i	−0.741563	−	0.240949i
$423$	−21.3762	−	29.4218i	−1.03934	−	1.43054i
$424$	−9.75179			−0.473589
$425$	13.0238	+	5.93124i	0.631748	+	0.287707i
$426$	3.12306			0.151313
$427$	16.4332	+	22.6183i	0.795257	+	1.09458i
$428$	12.5274	+	4.07041i	0.605536	+	0.196751i
$429$	−0.0398530	+	0.122655i	−0.00192412	+	0.00592183i
$430$	0.411054	+	1.56047i	0.0198228	+	0.0752528i
$431$	4.29007	+	13.2035i	0.206645	+	0.635989i	0.999642	+	0.0267625i	$0.00851978\pi$
$431$	4.29007	+	13.2035i	0.206645	+	0.635989i	−0.792997	+	0.609226i	$0.791480\pi$
$432$		−	1.76663i		−	0.0849972i
$433$	−27.2108	+	8.84132i	−1.30767	+	0.424887i	−0.878242	−	0.478216i	$-0.841284\pi$
$433$	−27.2108	+	8.84132i	−1.30767	+	0.424887i	−0.429424	+	0.903103i	$0.641284\pi$
$434$	0.643630	+	0.467625i	0.0308952	+	0.0224467i
$435$	−2.02633	−	3.14939i	−0.0971551	−	0.151002i
$436$	3.37018	−	2.44858i	0.161402	−	0.117266i
$437$	−0.274593	+	0.377945i	−0.0131356	+	0.0180795i
$438$	−1.08180	+	1.48897i	−0.0516905	+	0.0711459i
$439$	3.54897	−	2.57848i	0.169383	−	0.123064i	−0.499864	−	0.866104i	$-0.666617\pi$
$439$	3.54897	−	2.57848i	0.169383	−	0.123064i	0.669247	+	0.743040i	$0.266617\pi$
$440$	−4.21917	−	6.55758i	−0.201141	−	0.312620i
$441$	45.8758	+	33.3307i	2.18456	+	1.58718i
$442$	0.336815	−	0.109438i	0.0160206	−	0.00520542i
$443$			35.5144i			1.68734i	0.536864	+	0.843669i	$0.319609\pi$
$443$			35.5144i			1.68734i	−0.536864	+	0.843669i	$0.680391\pi$
$444$	0.787764	+	2.42449i	0.0373856	+	0.115061i
$445$	−3.94334	−	14.9700i	−0.186932	−	0.709647i
$446$	−3.17487	+	9.77123i	−0.150334	+	0.462681i
$447$	0.324989	+	0.105595i	0.0153715	+	0.00499449i
$448$	3.02478	+	4.16326i	0.142908	+	0.196695i
$449$	23.0821			1.08931			0.544657	−	0.838659i	$-0.316660\pi$
$449$	23.0821			1.08931			0.544657	+	0.838659i	$0.316660\pi$
$450$	−9.82932	+	10.7324i	−0.463358	+	0.505929i
$451$	22.1836			1.04458
$452$	4.13492	+	5.69123i	0.194490	+	0.267693i
$453$	−4.30754	−	1.39960i	−0.202386	−	0.0657592i
$454$	6.16061	−	18.9604i	0.289132	−	0.889856i
$455$	−1.19738	+	0.770397i	−0.0561339	+	0.0361168i
$456$	0.0923618	+	0.284260i	0.00432524	+	0.0133117i
$457$			1.30674i			0.0611267i	0.999533	+	0.0305634i	$0.00973014\pi$
$457$			1.30674i			0.0611267i	−0.999533	+	0.0305634i	$0.990270\pi$
$458$	−24.4605	+	7.94770i	−1.14296	+	0.371372i
$459$	−4.09071	−	2.97207i	−0.190938	−	0.138724i
$460$	−0.0590874	+	1.04294i	−0.00275497	+	0.0486274i
$461$	−10.9758	+	7.97441i	−0.511196	+	0.371405i	−0.813277	−	0.581877i	$-0.802319\pi$
$461$	−10.9758	+	7.97441i	−0.511196	+	0.371405i	0.302081	+	0.953282i	$0.402319\pi$
$462$	−3.15270	+	4.33932i	−0.146677	+	0.201883i
$463$	−17.5861	+	24.2051i	−0.817293	+	1.12491i	0.172864	+	0.984946i	$0.444698\pi$
$463$	−17.5861	+	24.2051i	−0.817293	+	1.12491i	−0.990157	+	0.139962i	$0.955302\pi$
$464$	4.53325	−	3.29360i	0.210451	−	0.152901i
$465$	0.0963029	+	0.0374359i	0.00446594	+	0.00173605i
$466$	13.3836	+	9.72375i	0.619983	+	0.450444i
$467$	−26.5332	+	8.62117i	−1.22781	+	0.398940i	−0.849921	−	0.526910i	$-0.823350\pi$
$467$	−26.5332	+	8.62117i	−1.22781	+	0.398940i	−0.377891	+	0.925850i	$0.623350\pi$
$468$			0.360149i			0.0166479i
$469$	−20.0440	−	61.6892i	−0.925548	−	2.84854i
$470$	27.8938	+	1.58031i	1.28665	+	0.0728945i
$471$	−0.797452	+	2.45431i	−0.0367447	+	0.113088i
$472$	2.63643	+	0.856630i	0.121352	+	0.0394296i
$473$	−1.47923	−	2.03599i	−0.0680152	−	0.0936148i
$474$	0.647714			0.0297505
$475$	2.07229	−	4.55034i	0.0950833	−	0.208784i
$476$	14.7289			0.675098
$477$	−16.6838	−	22.9633i	−0.763900	−	1.05142i
$478$	−23.3670	−	7.59239i	−1.06878	−	0.347268i
$479$	−11.0141	+	33.8979i	−0.503247	+	1.54884i	0.300451	+	0.953797i	$0.402863\pi$
$479$	−11.0141	+	33.8979i	−0.503247	+	1.54884i	−0.803698	+	0.595038i	$0.797137\pi$
$480$	0.517609	+	0.422793i	0.0236255	+	0.0192978i
$481$	−0.326119	−	1.00369i	−0.0148698	−	0.0457644i
$482$			0.0110490i			0.000503269i
$483$	0.683380	−	0.222044i	0.0310949	−	0.0101033i
$484$	0.938978	+	0.682207i	0.0426808	+	0.0310094i
$485$	19.0689	−	23.3453i	0.865873	−	1.06005i
$486$	6.27148	−	4.55650i	0.284480	−	0.206687i
$487$	−5.21420	+	7.17673i	−0.236278	+	0.325209i	−0.910647	−	0.413186i	$-0.864416\pi$
$487$	−5.21420	+	7.17673i	−0.236278	+	0.325209i	0.674369	+	0.738395i	$0.264416\pi$
$488$	−3.19334	+	4.39526i	−0.144556	+	0.198964i
$489$	−0.170525	+	0.123894i	−0.00771143	+	0.00560268i
$490$	−42.1261	+	11.0967i	−1.90306	+	0.501297i
$491$	−33.0167	−	23.9881i	−1.49002	−	1.08257i	−0.974150	−	0.225902i	$-0.927467\pi$
$491$	−33.0167	−	23.9881i	−1.49002	−	1.08257i	−0.515874	−	0.856664i	$-0.672533\pi$
$492$	−1.80829	+	0.587550i	−0.0815242	+	0.0264888i
$493$		−	16.0379i		−	0.722308i
$494$	−0.0382360	−	0.117678i	−0.00172032	−	0.00529460i
$495$	8.22328	−	21.1542i	0.369609	−	0.950811i
$496$	−0.0477733	+	0.147031i	−0.00214509	+	0.00660190i
$497$	−51.1390	−	16.6161i	−2.29390	−	0.745333i
$498$	−0.0876894	−	0.120694i	−0.00392946	−	0.00540843i
$499$	3.85045			0.172370			0.0861848	−	0.996279i	$-0.472532\pi$
$499$	3.85045			0.172370			0.0861848	+	0.996279i	$0.472532\pi$
$500$	−1.60858	−	11.0640i	−0.0719379	−	0.494798i
$501$	−7.51678			−0.335825
$502$	1.55397	+	2.13885i	0.0693569	+	0.0954615i
$503$	−11.9046	−	3.86805i	−0.530802	−	0.172468i	0.0313402	−	0.999509i	$-0.490022\pi$
$503$	−11.9046	−	3.86805i	−0.530802	−	0.172468i	−0.562142	+	0.827041i	$0.690022\pi$
$504$	−4.62861	+	14.2454i	−0.206174	+	0.634540i
$505$	8.27146	−	21.2781i	0.368075	−	0.946865i
$506$	−0.503421	−	1.54937i	−0.0223798	−	0.0688779i
$507$		−	3.88098i		−	0.172360i
$508$	6.46888	−	2.10187i	0.287010	−	0.0932553i
$509$	−25.2851	−	18.3707i	−1.12074	−	0.814267i	−0.136421	−	0.990651i	$-0.543560\pi$
$509$	−25.2851	−	18.3707i	−1.12074	−	0.814267i	−0.984321	+	0.176384i	$0.943560\pi$
$510$	1.84979	−	0.487264i	0.0819100	−	0.0215764i
$511$	25.6361	−	18.6257i	1.13408	−	0.823954i
$512$	−0.587785	+	0.809017i	−0.0259767	+	0.0357538i
$513$	−1.03840	+	1.42924i	−0.0458465	+	0.0631023i
$514$	−2.15200	+	1.56352i	−0.0949206	+	0.0689638i
$515$	−10.1935	+	12.4795i	−0.449179	+	0.549912i
$516$	0.174505	+	0.126785i	0.00768214	+	0.00558140i
$517$	−41.4384	+	13.4642i	−1.82246	+	0.592153i
$518$		−	43.8914i		−	1.92848i
$519$	−1.31579	−	4.04958i	−0.0577566	−	0.177757i
$520$	−0.214280	−	0.175028i	−0.00939681	−	0.00767550i
$521$	3.81576	−	11.7437i	0.167172	−	0.514501i	−0.832018	−	0.554748i	$-0.812815\pi$
$521$	3.81576	−	11.7437i	0.167172	−	0.514501i	0.999190	+	0.0402472i	$0.0128145\pi$
$522$	15.5114	+	5.03995i	0.678914	+	0.220593i
$523$	23.9055	+	32.9031i	1.04532	+	1.43875i	0.892801	+	0.450451i	$0.148737\pi$
$523$	23.9055	+	32.9031i	1.04532	+	1.43875i	0.152514	+	0.988301i	$0.451263\pi$
$524$	−3.80179			−0.166082
$525$	−6.69251	+	3.78872i	−0.292085	+	0.165353i
$526$	−18.6039			−0.811169
$527$	0.260086	+	0.357977i	0.0113295	+	0.0155937i
$528$	−0.991276	−	0.322085i	−0.0431397	−	0.0140170i
$529$	7.03995	−	21.6667i	0.306085	−	0.942032i
$530$	21.7708	+	1.23342i	0.945662	+	0.0535761i
$531$	2.49336	+	7.67378i	0.108203	+	0.333014i
$532$		−	5.14607i		−	0.223110i
$533$	0.748599	−	0.243235i	0.0324254	−	0.0105357i
$534$	−1.67407	−	1.21628i	−0.0724439	−	0.0526336i
$535$	−27.4525	−	10.6716i	−1.18688	−	0.461374i
$536$	10.1973	−	7.40877i	0.440456	−	0.320010i
$537$	1.51822	−	2.08965i	0.0655159	−	0.0901749i
$538$	8.76655	−	12.0661i	0.377953	−	0.520208i
$539$	54.9629	−	39.9329i	2.36742	−	1.72003i
$540$	−0.223445	+	3.94399i	−0.00961555	+	0.169722i
$541$	5.85544	+	4.25422i	0.251745	+	0.182903i	0.706500	−	0.707713i	$-0.250273\pi$
$541$	5.85544	+	4.25422i	0.251745	+	0.182903i	−0.454755	+	0.890617i	$0.650273\pi$
$542$	−8.60858	+	2.79710i	−0.369770	+	0.120146i
$543$		−	2.55784i		−	0.109768i
$544$	0.884457	+	2.72208i	0.0379208	+	0.116708i
$545$	−7.83358	+	5.04015i	−0.335553	+	0.215896i
$546$	−0.0588109	+	0.181001i	−0.00251688	+	0.00774615i
$547$	−6.21146	−	2.01822i	−0.265583	−	0.0862930i	0.173199	−	0.984887i	$-0.444590\pi$
$547$	−6.21146	−	2.01822i	−0.265583	−	0.0862930i	−0.438781	+	0.898594i	$0.644590\pi$
$548$	1.66635	+	2.29353i	0.0711828	+	0.0979747i
$549$	−15.8132			−0.674890
$550$	8.58984	+	15.1734i	0.366272	+	0.646994i
$551$	−5.60340			−0.238713
$552$	0.0820728	+	0.112963i	0.00349325	+	0.00480804i
$553$	−10.6061	−	3.44613i	−0.451017	−	0.146544i
$554$	9.41513	−	28.9768i	0.400010	−	1.23111i
$555$	−1.45202	−	5.51228i	−0.0616349	−	0.233983i
$556$	1.42539	+	4.38689i	0.0604498	+	0.186045i
$557$		−	35.9467i		−	1.52311i	−0.648101	−	0.761554i	$-0.724437\pi$
$557$		−	35.9467i		−	1.52311i	0.648101	−	0.761554i	$-0.275563\pi$
$558$	−0.427959	+	0.139052i	−0.0181169	+	0.00588655i
$559$	−0.0722416	−	0.0524866i	−0.00305549	−	0.00221995i
$560$	−6.22622	−	9.67700i	−0.263106	−	0.408928i
$561$	−2.41346	+	1.75348i	−0.101896	+	0.0740321i
$562$	19.1954	−	26.4202i	0.809708	−	1.11447i
$563$	−17.3215	+	23.8410i	−0.730014	+	1.00478i	0.269118	+	0.963107i	$0.413268\pi$
$563$	−17.3215	+	23.8410i	−0.730014	+	1.00478i	−0.999131	+	0.0416704i	$0.986732\pi$
$564$	3.02125	−	2.19506i	0.127217	−	0.0924289i
$565$	−8.51133	−	13.2286i	−0.358074	−	0.556531i
$566$	−10.7483	−	7.80913i	−0.451786	−	0.328242i
$567$	−40.1519	+	13.0461i	−1.68622	+	0.547886i
$568$		−	10.4489i		−	0.438426i
$569$	9.44213	+	29.0599i	0.395835	+	1.21825i	0.928309	+	0.371808i	$0.121262\pi$
$569$	9.44213	+	29.0599i	0.395835	+	1.21825i	−0.532475	+	0.846446i	$0.678738\pi$
$570$	−0.170243	−	0.646290i	−0.00713070	−	0.0270701i
$571$	−10.1763	+	31.3194i	−0.425865	+	1.31068i	0.476299	+	0.879284i	$0.341978\pi$
$571$	−10.1763	+	31.3194i	−0.425865	+	1.31068i	−0.902164	+	0.431394i	$0.858022\pi$
$572$	0.410369	+	0.133337i	0.0171584	+	0.00557510i
$573$	−4.61342	−	6.34982i	−0.192728	−	0.265268i
$574$	32.7362			1.36638
$575$	0.263824	−	2.32088i	0.0110022	−	0.0967873i
$576$	−2.91067			−0.121278
$577$	19.3497	+	26.6325i	0.805537	+	1.10873i	0.991997	+	0.126264i	$0.0402986\pi$
$577$	19.3497	+	26.6325i	0.805537	+	1.10873i	−0.186460	+	0.982463i	$0.559701\pi$
$578$	−8.37692	−	2.72183i	−0.348434	−	0.113213i
$579$	0.162056	−	0.498757i	0.00673481	−	0.0207276i
$580$	−10.5370	+	6.77954i	−0.437525	+	0.281505i
$581$	0.793736	+	2.44287i	0.0329297	+	0.101347i
$582$		−	4.02918i		−	0.167015i
$583$	−32.3422	+	10.5086i	−1.33948	+	0.435222i
$584$	4.98169	+	3.61941i	0.206144	+	0.149772i
$585$	0.0455520	−	0.804029i	0.00188334	−	0.0332425i
$586$	−19.7115	+	14.3212i	−0.814274	+	0.591605i
$587$	16.4347	−	22.6204i	0.678331	−	0.933642i	−0.321582	−	0.946882i	$-0.604214\pi$
$587$	16.4347	−	22.6204i	0.678331	−	0.933642i	0.999912	+	0.0132398i	$0.00421447\pi$
$588$	−3.42265	+	4.71087i	−0.141148	+	0.194273i
$589$	0.125072	−	0.0908703i	0.00515351	−	0.00374425i
$590$	−5.77746	−	2.24587i	−0.237854	−	0.0924612i
$591$	−2.23536	−	1.62409i	−0.0919506	−	0.0668060i
$592$	8.11167	−	2.63564i	0.333387	−	0.108324i
$593$			36.3126i			1.49118i	0.666404	+	0.745591i	$0.267833\pi$
$593$			36.3126i			1.49118i	−0.666404	+	0.745591i	$0.732167\pi$
$594$	−1.90374	−	5.85910i	−0.0781113	−	0.240402i
$595$	−32.8821	−	1.86292i	−1.34803	−	0.0763724i
$596$	0.353293	−	1.08732i	0.0144714	−	0.0445385i
$597$	−1.03066	−	0.334882i	−0.0421821	−	0.0137058i
$598$	−0.0339766	−	0.0467647i	−0.00138940	−	0.00191235i
$599$	23.7237			0.969323			0.484661	−	0.874702i	$-0.338943\pi$
$599$	23.7237			0.969323			0.484661	+	0.874702i	$0.338943\pi$
$600$	−1.10208	−	1.00935i	−0.0449923	−	0.0412065i
$601$	−34.8638			−1.42212			−0.711062	−	0.703130i	$-0.751785\pi$
$601$	−34.8638			−1.42212			−0.711062	+	0.703130i	$0.751785\pi$
$602$	−2.18290	−	3.00450i	−0.0889683	−	0.122454i
$603$	34.8920	+	11.3371i	1.42091	+	0.461682i
$604$	−4.68269	+	14.4118i	−0.190536	+	0.586410i
$605$	−2.00997	−	1.64178i	−0.0817169	−	0.0667480i
$606$	−0.942974	−	2.90218i	−0.0383057	−	0.117893i
$607$		−	33.2663i		−	1.35024i	−0.737709	−	0.675119i	$-0.764092\pi$
$607$		−	33.2663i		−	1.35024i	0.737709	−	0.675119i	$-0.235908\pi$
$608$	0.951057	−	0.309017i	0.0385704	−	0.0125323i
$609$	6.97260	+	5.06589i	0.282544	+	0.205280i
$610$	7.68502	−	9.40847i	0.311157	−	0.380938i
$611$	−1.25074	+	0.908715i	−0.0505995	+	0.0367627i
$612$	−4.89672	+	6.73976i	−0.197938	+	0.272439i
$613$	−18.3271	+	25.2251i	−0.740225	+	1.01883i	0.258381	+	0.966043i	$0.416811\pi$
$613$	−18.3271	+	25.2251i	−0.740225	+	1.01883i	−0.998606	+	0.0527888i	$0.983189\pi$
$614$	−4.82239	+	3.50367i	−0.194616	+	0.141397i
$615$	4.11131	−	1.08298i	0.165784	−	0.0436702i
$616$	14.5182	+	10.5481i	0.584953	+	0.424993i
$617$	−16.4860	+	5.35663i	−0.663702	+	0.215650i	−0.621446	−	0.783457i	$-0.713455\pi$
$617$	−16.4860	+	5.35663i	−0.663702	+	0.215650i	−0.0422561	+	0.999107i	$0.513455\pi$
$618$			2.15385i			0.0866404i
$619$	3.44710	+	10.6091i	0.138551	+	0.426415i	0.996125	−	0.0879444i	$-0.0280298\pi$
$619$	3.44710	+	10.6091i	0.138551	+	0.426415i	−0.857575	+	0.514359i	$0.828030\pi$
$620$	0.125250	−	0.322203i	0.00503016	−	0.0129400i
$621$	−0.255035	+	0.784916i	−0.0102342	+	0.0314976i
$622$	7.84498	+	2.54899i	0.314555	+	0.102205i
$623$	20.9411	+	28.8229i	0.838987	+	1.15477i
$624$	−0.0369828			−0.00148050
$625$	2.19175	+	24.9037i	0.0876700	+	0.996150i
$626$	0.965098			0.0385731
$627$	0.612642	+	0.843229i	0.0244666	+	0.0336753i
$628$	8.21143	+	2.66805i	0.327672	+	0.106467i
$629$	7.54363	−	23.2169i	0.300784	−	0.925719i
$630$	12.1351	−	31.2172i	0.483473	−	1.24372i
$631$	8.54725	+	26.3057i	0.340261	+	1.04721i	0.964072	+	0.265640i	$0.0855833\pi$
$631$	8.54725	+	26.3057i	0.340261	+	1.04721i	−0.623812	+	0.781575i	$0.714417\pi$
$632$		−	2.16707i		−	0.0862015i
$633$	4.55318	−	1.47942i	0.180973	−	0.0588015i
$634$	4.13112	+	3.00144i	0.164068	+	0.119202i
$635$	−14.7076	+	3.87420i	−0.583651	+	0.153743i
$636$	2.35804	−	1.71322i	0.0935026	−	0.0679336i
$637$	1.41691	−	1.95021i	0.0561401	−	0.0772702i
$638$	11.4855	−	15.8084i	0.454714	−	0.625860i
$639$	24.6048	−	17.8765i	0.973353	−	0.707182i
$640$	1.41455	−	1.73178i	0.0559149	−	0.0684545i
$641$	27.0155	+	19.6279i	1.06705	+	0.775257i	0.975380	−	0.220532i	$-0.0707794\pi$
$641$	27.0155	+	19.6279i	1.06705	+	0.775257i	0.0916703	+	0.995789i	$0.470779\pi$
$642$	−3.74431	+	1.21660i	−0.147776	+	0.0480154i
$643$			17.2137i			0.678843i	0.940634	+	0.339421i	$0.110231\pi$
$643$			17.2137i			0.678843i	−0.940634	+	0.339421i	$0.889769\pi$
$644$	−0.742896	−	2.28640i	−0.0292742	−	0.0900968i
$645$	−0.373544	−	0.305118i	−0.0147083	−	0.0120140i
$646$	0.884457	−	2.72208i	0.0347985	−	0.107099i
$647$	−22.6113	−	7.34685i	−0.888941	−	0.288834i	−0.171276	−	0.985223i	$-0.554789\pi$
$647$	−22.6113	−	7.34685i	−0.888941	−	0.288834i	−0.717665	+	0.696389i	$0.754789\pi$
$648$	−4.82217	−	6.63715i	−0.189433	−	0.260732i
$649$	9.66694			0.379460
$650$	0.456241	+	0.417851i	0.0178952	+	0.0163895i
$651$	−0.237787			−0.00931962
$652$	0.414515	+	0.570531i	0.0162337	+	0.0223437i
$653$	−30.3922	−	9.87501i	−1.18934	−	0.386439i	−0.353509	−	0.935431i	$-0.615012\pi$
$653$	−30.3922	−	9.87501i	−1.18934	−	0.386439i	−0.835828	+	0.548992i	$0.815012\pi$
$654$	−0.384758	+	1.18416i	−0.0150452	+	0.0463044i
$655$	8.48746	+	0.480854i	0.331633	+	0.0187885i
$656$	1.96578	+	6.05005i	0.0767509	+	0.236215i
$657$			17.9230i			0.699244i
$658$	−61.1506	+	19.8690i	−2.38390	+	0.774575i
$659$	6.70264	+	4.86975i	0.261098	+	0.189699i	0.710631	−	0.703565i	$-0.248410\pi$
$659$	6.70264	+	4.86975i	0.261098	+	0.189699i	−0.449533	+	0.893264i	$0.648410\pi$
$660$	2.17227	+	0.844428i	0.0845556	+	0.0328693i
$661$	−27.7469	+	20.1593i	−1.07923	+	0.784105i	−0.977548	−	0.210712i	$-0.932422\pi$
$661$	−27.7469	+	20.1593i	−1.07923	+	0.784105i	−0.101680	+	0.994817i	$0.532422\pi$
$662$	16.0610	−	22.1060i	0.624227	−	0.859174i
$663$	−0.0622176	+	0.0856352i	−0.00241633	+	0.00332580i
$664$	−0.403809	+	0.293385i	−0.0156708	+	0.0113855i
$665$	−0.650879	+	11.4885i	−0.0252400	+	0.445506i
$666$	20.0842	+	14.5920i	0.778245	+	0.565428i
$667$	−2.48959	+	0.808918i	−0.0963974	+	0.0313214i
$668$			25.1491i			0.973047i
$669$	−0.948932	−	2.92051i	−0.0366878	−	0.112914i
$670$	−23.7024	+	15.2502i	−0.915704	+	0.589168i
$671$	−5.85447	+	18.0182i	−0.226009	+	0.695585i
$672$	−1.46282	−	0.475300i	−0.0564296	−	0.0183351i
$673$	26.0914	+	35.9117i	1.00575	+	1.38429i	0.921731	+	0.387830i	$0.126775\pi$
$673$	26.0914	+	35.9117i	1.00575	+	1.38429i	0.0840172	+	0.996464i	$0.473225\pi$
$674$	21.1042			0.812904
$675$	0.997677	−	8.77664i	0.0384006	−	0.337813i
$676$	−12.9847			−0.499411
$677$	11.5854	+	15.9460i	0.445264	+	0.612854i	0.971372	−	0.237564i	$-0.0763490\pi$
$677$	11.5854	+	15.9460i	0.445264	+	0.612854i	−0.526107	+	0.850418i	$0.676349\pi$
$678$	−1.99970	−	0.649741i	−0.0767980	−	0.0249532i
$679$	−21.4370	+	65.9764i	−0.822678	+	2.53194i
$680$	−1.63025	−	6.18888i	−0.0625172	−	0.237333i
$681$	1.84134	+	5.66706i	0.0705602	+	0.217162i
$682$			0.539115i			0.0206438i
$683$	19.0135	−	6.17786i	0.727531	−	0.236389i	0.0782460	−	0.996934i	$-0.475068\pi$
$683$	19.0135	−	6.17786i	0.727531	−	0.236389i	0.649285	+	0.760545i	$0.275068\pi$
$684$	2.35478	+	1.71085i	0.0900372	+	0.0654158i
$685$	−3.43001	−	5.33104i	−0.131054	−	0.203688i
$686$	51.9658	−	37.7554i	1.98406	−	1.44151i
$687$	4.51843	−	6.21909i	0.172389	−	0.237273i
$688$	0.424188	−	0.583844i	0.0161720	−	0.0222589i
$689$	−0.976186	+	0.709240i	−0.0371897	+	0.0270199i
$690$	−0.168939	−	0.262570i	−0.00643139	−	0.00999588i
$691$	5.33659	+	3.87726i	0.203013	+	0.147498i	0.684647	−	0.728875i	$-0.259956\pi$
$691$	5.33659	+	3.87726i	0.203013	+	0.147498i	−0.481634	+	0.876373i	$0.659956\pi$
$692$	−13.5488	+	4.40226i	−0.515047	+	0.167349i
$693$			52.2331i			1.98417i
$694$	8.48242	+	26.1062i	0.321988	+	0.990978i
$695$	−2.62730	−	9.97396i	−0.0996592	−	0.378334i
$696$	−0.517540	+	1.59282i	−0.0196173	+	0.0603759i
$697$	17.3162	+	5.62639i	0.655900	+	0.213115i
$698$	−11.7833	−	16.2183i	−0.446005	−	0.613873i
$699$	−4.94453			−0.187019
$700$	12.6760	+	22.3913i	0.479108	+	0.846311i
$701$	−44.5160			−1.68135			−0.840674	−	0.541542i	$-0.817841\pi$
$701$	−44.5160			−1.68135			−0.840674	+	0.541542i	$0.817841\pi$
$702$	−0.128486	−	0.176846i	−0.00484939	−	0.00667461i
$703$	−8.11167	−	2.63564i	−0.305937	−	0.0994050i
$704$	−1.07761	+	3.31653i	−0.0406139	+	0.124997i
$705$	−7.02253	+	4.51833i	−0.264484	+	0.170170i
$706$	−0.408089	−	1.25597i	−0.0153586	−	0.0472690i
$707$			52.5391i			1.97594i
$708$	−0.788001	+	0.256037i	−0.0296149	+	0.00962246i
$709$	−11.2220	−	8.15323i	−0.421449	−	0.306201i	0.356771	−	0.934192i	$-0.383878\pi$
$709$	−11.2220	−	8.15323i	−0.421449	−	0.306201i	−0.778221	+	0.627991i	$0.783878\pi$
$710$	−1.32159	+	23.3271i	−0.0495982	+	0.875449i
$711$	5.10297	−	3.70753i	0.191376	−	0.139043i
$712$	−4.06934	+	5.60096i	−0.152505	+	0.209905i
$713$	0.0424514	−	0.0584294i	0.00158982	−	0.00218820i
$714$	−3.56154	+	2.58761i	−0.133287	+	0.0968388i
$715$	−0.899280	−	0.349577i	−0.0336312	−	0.0130734i
$716$	−6.99138	−	5.07954i	−0.261280	−	0.189831i
$717$	6.98413	−	2.26928i	0.260827	−	0.0847479i
$718$			21.7403i			0.811342i
$719$	4.62373	+	14.2304i	0.172436	+	0.530703i	0.999507	−	0.0313940i	$-0.00999467\pi$
$719$	4.62373	+	14.2304i	0.172436	+	0.530703i	−0.827071	+	0.562097i	$0.809995\pi$
$720$	6.49803	+	0.368143i	0.242167	+	0.0137199i
$721$	11.4594	−	35.2685i	0.426771	−	1.31347i
$722$	−0.951057	−	0.309017i	−0.0353947	−	0.0115004i
$723$	−0.00194112	−	0.00267172i	−7.21910e−5	−	9.93623e-5i
$724$	−8.55784			−0.318050
$725$	24.3812	−	13.8025i	0.905495	−	0.512613i
$726$	−0.346903			−0.0128748
$727$	12.4662	+	17.1582i	0.462345	+	0.636363i	0.974993	−	0.222236i	$-0.0713354\pi$
$727$	12.4662	+	17.1582i	0.462345	+	0.636363i	−0.512648	+	0.858599i	$0.671335\pi$
$728$	0.605581	+	0.196765i	0.0224443	+	0.00729260i
$729$	6.88951	−	21.2037i	0.255167	−	0.785324i
$730$	−10.6638	−	8.71038i	−0.394684	−	0.322386i
$731$	−0.638287	−	1.96445i	−0.0236079	−	0.0726577i
$732$		−	1.62382i		−	0.0600180i
$733$	47.8150	−	15.5360i	1.76609	−	0.573837i	0.768286	−	0.640107i	$-0.221110\pi$
$733$	47.8150	−	15.5360i	1.76609	−	0.573837i	0.997802	+	0.0662701i	$0.0211099\pi$
$734$	−9.35947	−	6.80006i	−0.345464	−	0.250995i
$735$	8.23686	−	10.0841i	0.303821	−	0.371956i
$736$	0.377945	−	0.274593i	0.0139312	−	0.0101216i
$737$	25.8359	−	35.5601i	0.951679	−	1.30987i
$738$	−10.8834	+	14.9797i	−0.400623	+	0.551410i
$739$	38.0861	−	27.6712i	1.40102	−	1.01790i	0.406467	−	0.913666i	$-0.366761\pi$
$739$	38.0861	−	27.6712i	1.40102	−	1.01790i	0.994553	−	0.104235i	$-0.0332393\pi$
$740$	−18.4426	+	4.85806i	−0.677962	+	0.178586i
$741$	0.0299197	+	0.0217380i	0.00109913	+	0.000798564i
$742$	−47.7272	+	15.5075i	−1.75212	+	0.569299i
$743$		−	1.05172i		−	0.0385840i	−0.999814	−	0.0192920i	$-0.993859\pi$
$743$		−	1.05172i		−	0.0385840i	0.999814	−	0.0192920i	$-0.00614121\pi$
$744$	−0.0142789	−	0.0439460i	−0.000523491	−	0.00161114i
$745$	−0.926248	+	2.38275i	−0.0339351	+	0.0872973i
$746$	8.43836	−	25.9706i	0.308950	−	0.950852i
$747$	−1.38171	−	0.448945i	−0.0505541	−	0.0164260i
$748$	5.86667	+	8.07477i	0.214507	+	0.295243i
$749$	67.7846			2.47680
$750$	2.33272	+	2.39275i	0.0851789	+	0.0873708i
$751$	4.23454			0.154521			0.0772603	−	0.997011i	$-0.475383\pi$
$751$	4.23454			0.154521			0.0772603	+	0.997011i	$0.475383\pi$
$752$	−7.34408	−	10.1083i	−0.267811	−	0.368610i
$753$	−0.751517	−	0.244183i	−0.0273868	−	0.00889851i
$754$	0.214252	−	0.659399i	0.00780259	−	0.0240139i
$755$	12.2769	−	31.5820i	0.446801	−	1.14939i
$756$	−2.80934	−	8.64626i	−0.102175	−	0.314461i
$757$			51.8590i			1.88485i	0.334422	+	0.942423i	$0.391459\pi$
$757$			51.8590i			1.88485i	−0.334422	+	0.942423i	$0.608541\pi$
$758$	13.7914	−	4.48108i	0.500925	−	0.162760i
$759$	0.393927	+	0.286205i	0.0142987	+	0.0103886i
$760$	−2.16231	+	0.569586i	−0.0784351	+	0.0206611i
$761$	−3.45148	+	2.50765i	−0.125116	+	0.0909023i	−0.648583	−	0.761144i	$-0.724638\pi$
$761$	−3.45148	+	2.50765i	−0.125116	+	0.0909023i	0.523467	+	0.852046i	$0.324638\pi$
$762$	−1.19496	+	1.64471i	−0.0432887	+	0.0595817i
$763$	12.6005	−	17.3432i	0.456170	−	0.627864i
$764$	−21.2448	+	15.4352i	−0.768608	+	0.558426i
$765$	11.7843	−	14.4271i	0.426063	−	0.521613i
$766$	24.3296	+	17.6765i	0.879065	+	0.638678i
$767$	0.326218	−	0.105994i	0.0117790	−	0.00382724i
$768$		−	0.298889i		−	0.0107852i
$769$	−6.36222	−	19.5809i	−0.229427	−	0.706105i	−0.997812	−	0.0661164i	$-0.978939\pi$
$769$	−6.36222	−	19.5809i	−0.229427	−	0.706105i	0.768385	−	0.639988i	$-0.221061\pi$
$770$	−31.0775	−	25.3847i	−1.11995	−	0.914800i
$771$	0.245684	−	0.756137i	0.00884809	−	0.0272316i
$772$	−1.66870	−	0.542194i	−0.0600579	−	0.0195140i
$773$	1.98592	+	2.73339i	0.0714287	+	0.0983132i	0.843237	−	0.537543i	$-0.180647\pi$
$773$	1.98592	+	2.73339i	0.0714287	+	0.0983132i	−0.771808	+	0.635856i	$0.780647\pi$
$774$	2.10054			0.0755025
$775$	−0.320372	+	0.703473i	−0.0115081	+	0.0252695i
$776$	−13.4805			−0.483923
$777$	7.71095	+	10.6132i	0.276629	+	0.380747i
$778$	−4.18955	−	1.36127i	−0.150203	−	0.0488038i
$779$	1.96578	−	6.05005i	0.0704314	−	0.216766i
$780$	0.0825637	+	0.00467762i	0.00295626	+	0.000167486i
$781$	−11.2598	−	34.6542i	−0.402908	−	1.24002i
$782$		−	1.33710i		−	0.0478147i
$783$	−9.41465	+	3.05901i	−0.336452	+	0.109320i
$784$	15.7613	+	11.4512i	0.562903	+	0.408973i
$785$	−17.9945	−	6.99499i	−0.642250	−	0.249662i
$786$	0.919298	−	0.667909i	0.0327903	−	0.0238235i
$787$	17.9454	−	24.6997i	0.639684	−	0.880449i	−0.358915	−	0.933370i	$-0.616853\pi$
$787$	17.9454	−	24.6997i	0.639684	−	0.880449i	0.998599	+	0.0529212i	$0.0168532\pi$
$788$	−5.43375	+	7.47891i	−0.193569	+	0.266425i
$789$	4.49854	−	3.26838i	0.160152	−	0.116357i
$790$	−0.274093	+	4.83796i	−0.00975180	+	0.172127i
$791$	29.2874	+	21.2786i	1.04134	+	0.756579i
$792$	−9.65332	+	3.13655i	−0.343016	+	0.111453i
$793$			0.672229i			0.0238716i
$794$	9.17496	+	28.2376i	0.325607	+	1.00212i
$795$	−5.48100	+	3.52650i	−0.194391	+	0.125072i
$796$	−1.12042	+	3.44831i	−0.0397123	+	0.122222i
$797$	−35.0249	−	11.3803i	−1.24065	−	0.403110i	−0.386085	−	0.922463i	$-0.626173\pi$
$797$	−35.0249	−	11.3803i	−1.24065	−	0.403110i	−0.854560	+	0.519353i	$0.826173\pi$
$798$	0.904074	+	1.24435i	0.0320039	+	0.0440496i
$799$	−35.7613			−1.26514
$800$	−3.37700	+	3.68726i	−0.119395	+	0.130364i
$801$	−20.1510			−0.712002
$802$	−15.3694	−	21.1542i	−0.542714	−	0.746982i
$803$	20.4223	+	6.63559i	0.720686	+	0.234165i
$804$	−1.16418	+	3.58297i	−0.0410574	+	0.126362i
$805$	1.36932	+	5.19832i	0.0482622	+	0.183217i
$806$	0.00591120	+	0.0181928i	0.000208213	+	0.000640815i
$807$			4.45779i			0.156922i
$808$	−9.70988	+	3.15493i	−0.341592	+	0.110990i
$809$	−30.1225	−	21.8853i	−1.05905	−	0.769446i	−0.0851388	−	0.996369i	$-0.527133\pi$
$809$	−30.1225	−	21.8853i	−1.05905	−	0.769446i	−0.973913	+	0.226923i	$0.927133\pi$
$810$	9.92597	+	15.4273i	0.348763	+	0.542059i
$811$	13.2861	−	9.65292i	0.466538	−	0.338960i	−0.329552	−	0.944137i	$-0.606898\pi$
$811$	13.2861	−	9.65292i	0.466538	−	0.338960i	0.796091	+	0.605177i	$0.206898\pi$
$812$	16.9491	−	23.3284i	0.594796	−	0.818666i
$813$	1.59021	−	2.18873i	0.0557710	−	0.0767622i
$814$	24.0624	−	17.4824i	0.843388	−	0.612757i
$815$	−0.853239	−	1.32613i	−0.0298877	−	0.0464524i
$816$	−0.692089	−	0.502832i	−0.0242280	−	0.0176026i
$817$	−0.686350	+	0.223009i	−0.0240124	+	0.00780209i
$818$		−	19.6989i		−	0.688757i
$819$	0.572717	+	1.76264i	0.0200124	+	0.0615917i
$820$	−3.62337	−	13.7553i	−0.126534	−	0.480356i
$821$	1.89104	−	5.82004i	0.0659979	−	0.203121i	−0.912619	−	0.408810i	$-0.865944\pi$
$821$	1.89104	−	5.82004i	0.0659979	−	0.203121i	0.978617	+	0.205690i	$0.0659437\pi$
$822$	−0.805866	−	0.261842i	−0.0281078	−	0.00913278i
$823$	−7.43770	−	10.2371i	−0.259262	−	0.356844i	0.659466	−	0.751734i	$-0.270782\pi$
$823$	−7.43770	−	10.2371i	−0.259262	−	0.356844i	−0.918728	+	0.394891i	$0.870782\pi$
$824$	7.20618			0.251039
$825$	−4.74277	−	2.15993i	−0.165122	−	0.0751990i
$826$	14.2655			0.496359
$827$	−13.4691	−	18.5386i	−0.468365	−	0.644649i	0.507852	−	0.861444i	$-0.330440\pi$
$827$	−13.4691	−	18.5386i	−0.468365	−	0.644649i	−0.976217	+	0.216795i	$0.930440\pi$
$828$	1.29321	+	0.420189i	0.0449422	+	0.0146026i
$829$	−3.42404	+	10.5381i	−0.118922	+	0.366004i	−0.992745	−	0.120241i	$-0.961633\pi$
$829$	−3.42404	+	10.5381i	−0.118922	+	0.366004i	0.873823	+	0.486244i	$0.161633\pi$
$830$	0.938607	−	0.603903i	0.0325795	−	0.0209618i
$831$	2.81408	+	8.66084i	0.0976193	+	0.300441i
$832$			0.123734i			0.00428972i
$833$	53.0316	−	17.2310i	1.83744	−	0.597019i
$834$	−1.11537	−	0.810361i	−0.0386220	−	0.0280605i
$835$	3.18088	−	56.1450i	0.110079	−	1.94298i
$836$	2.82121	−	2.04973i	0.0975737	−	0.0708914i
$837$	0.160534	−	0.220957i	0.00554888	−	0.00763738i
$838$	4.30439	−	5.92449i	0.148693	−	0.204658i
$839$	−2.18360	+	1.58648i	−0.0753864	+	0.0547714i	−0.624840	−	0.780753i	$-0.714836\pi$
$839$	−2.18360	+	1.58648i	−0.0753864	+	0.0547714i	0.549454	+	0.835524i	$0.314836\pi$
$840$	3.20562	+	1.24612i	0.110604	+	0.0429952i
$841$	−1.94010	−	1.40956i	−0.0669000	−	0.0486057i
$842$	−0.470271	+	0.152800i	−0.0162066	+	0.00526584i
$843$			9.76085i			0.336182i
$844$	−4.94972	−	15.2337i	−0.170376	−	0.524365i
$845$	28.9882	+	1.64231i	0.997223	+	0.0564973i
$846$	11.2381	−	34.5874i	0.386374	−	1.18914i
$847$	5.68041	+	1.84568i	0.195181	+	0.0634182i
$848$	−5.73196	−	7.88937i	−0.196836	−	0.270922i
$849$	3.97094			0.136282
$850$	2.85674	+	14.0228i	0.0979853	+	0.480978i
$851$	−3.98450			−0.136587
$852$	1.83569	+	2.52661i	0.0628897	+	0.0865602i
$853$	46.8384	+	15.2187i	1.60372	+	0.521079i	0.968023	−	0.250861i	$-0.0807139\pi$
$853$	46.8384	+	15.2187i	1.60372	+	0.521079i	0.635694	+	0.771941i	$0.280714\pi$
$854$	−8.63943	+	26.5894i	−0.295635	+	0.909871i
$855$	−5.04062	−	4.11728i	−0.172386	−	0.140808i
$856$	4.07041	+	12.5274i	0.139124	+	0.428179i
$857$			1.94660i			0.0664946i	0.999447	+	0.0332473i	$0.0105849\pi$
$857$			1.94660i			0.0664946i	−0.999447	+	0.0332473i	$0.989415\pi$
$858$	−0.122655	+	0.0398530i	−0.00418737	+	0.00136056i
$859$	19.3642	+	14.0689i	0.660697	+	0.480025i	0.866898	−	0.498485i	$-0.166110\pi$
$859$	19.3642	+	14.0689i	0.660697	+	0.480025i	−0.206201	+	0.978510i	$0.566110\pi$
$860$	−1.02084	+	1.24977i	−0.0348103	+	0.0426169i
$861$	−7.91582	+	5.75118i	−0.269770	+	0.196000i
$862$	−8.16019	+	11.2315i	−0.277937	+	0.382548i
$863$	32.8316	−	45.1888i	1.11760	−	1.53825i	0.307886	−	0.951423i	$-0.400379\pi$
$863$	32.8316	−	45.1888i	1.11760	−	1.53825i	0.809715	−	0.586823i	$-0.199621\pi$
$864$	1.42924	−	1.03840i	0.0486236	−	0.0353271i
$865$	30.8042	−	8.11433i	1.04738	−	0.275896i
$866$	−23.1469	−	16.8172i	−0.786563	−	0.571471i
$867$	2.50377	−	0.813524i	0.0850325	−	0.0276287i
$868$			0.795571i			0.0270034i
$869$	−2.33525	−	7.18717i	−0.0792180	−	0.243808i
$870$	1.35686	−	3.49050i	0.0460020	−	0.118339i
$871$	0.481948	−	1.48328i	0.0163302	−	0.0502591i
$872$	3.96188	+	1.28729i	0.134166	+	0.0435932i
$873$	−23.0631	−	31.7437i	−0.780568	−	1.07436i
$874$	−0.467165			−0.0158021
$875$	−25.4670	−	51.5915i	−0.860940	−	1.74411i
$876$	−1.84047			−0.0621838
$877$	−8.53552	−	11.7481i	−0.288224	−	0.396706i	0.640212	−	0.768198i	$-0.278846\pi$
$877$	−8.53552	−	11.7481i	−0.288224	−	0.396706i	−0.928436	+	0.371492i	$0.878846\pi$
$878$	4.17207	+	1.35559i	0.140800	+	0.0457488i
$879$	2.25037	−	6.92593i	0.0759031	−	0.233606i
$880$	2.82522	−	7.26783i	0.0952383	−	0.244998i
$881$	11.6038	+	35.7128i	0.390942	+	1.20320i	0.932077	+	0.362260i	$0.117995\pi$
$881$	11.6038	+	35.7128i	0.390942	+	1.20320i	−0.541135	+	0.840936i	$0.682005\pi$
$882$			56.7056i			1.90938i
$883$	16.8562	−	5.47691i	0.567256	−	0.184313i	−0.0113275	−	0.999936i	$-0.503606\pi$
$883$	16.8562	−	5.47691i	0.567256	−	0.184313i	0.578583	+	0.815623i	$0.303606\pi$
$884$	0.286512	+	0.208163i	0.00963643	+	0.00700128i
$885$	1.79159	−	0.471933i	0.0602235	−	0.0158638i
$886$	−28.7317	+	20.8748i	−0.965261	+	0.701303i
$887$	8.15917	−	11.2301i	0.273958	−	0.377071i	−0.649763	−	0.760137i	$-0.725132\pi$
$887$	8.15917	−	11.2301i	0.273958	−	0.377071i	0.923721	+	0.383066i	$0.125132\pi$
$888$	−1.49842	+	2.06239i	−0.0502835	+	0.0692093i
$889$	28.3176	−	20.5739i	0.949741	−	0.690027i
$890$	9.79316	−	11.9894i	0.328268	−	0.401885i
$891$	−23.1451	−	16.8159i	−0.775391	−	0.563355i
$892$	−9.77123	+	3.17487i	−0.327165	+	0.106302i
$893$			12.4945i			0.418112i
$894$	0.105595	+	0.324989i	0.00353164	+	0.0108693i
$895$	14.9657	+	12.2243i	0.500248	+	0.408613i
$896$	−1.59022	+	4.89420i	−0.0531256	+	0.163504i
$897$	0.0164315	+	0.00533891i	0.000548631	+	0.000178261i
$898$	13.5673	+	18.6738i	0.452748	+	0.623154i
$899$	0.866273			0.0288918
$900$	−14.4602	−	1.64375i	−0.482007	−	0.0547917i
$901$	−27.9112			−0.929858
$902$	13.0392	+	17.9469i	0.434157	+	0.597566i
$903$	1.05568	+	0.343010i	0.0351307	+	0.0114147i
$904$	−2.17386	+	6.69044i	−0.0723014	+	0.222521i
$905$	19.1053	+	1.08240i	0.635081	+	0.0359803i
$906$	−1.39960	−	4.30754i	−0.0464988	−	0.143108i
$907$			35.4701i			1.17777i	0.808218	+	0.588883i	$0.200432\pi$
$907$			35.4701i			1.17777i	−0.808218	+	0.588883i	$0.799568\pi$
$908$	18.9604	−	6.16061i	0.629223	−	0.204447i
$909$	−24.0413	−	17.4670i	−0.797398	−	0.579344i
$910$	−1.32706	−	0.515870i	−0.0439918	−	0.0171009i
$911$	16.0768	−	11.6805i	0.532649	−	0.386992i	−0.288699	−	0.957420i	$-0.593223\pi$
$911$	16.0768	−	11.6805i	0.532649	−	0.386992i	0.821348	+	0.570428i	$0.193223\pi$
$912$	−0.175683	+	0.241806i	−0.00581743	+	0.00800701i
$913$	−1.02309	+	1.40817i	−0.0338595	+	0.0466035i
$914$	−1.05717	+	0.768083i	−0.0349682	+	0.0254059i
$915$	−0.205382	+	3.62515i	−0.00678971	+	0.119844i
$916$	−20.8074	−	15.1174i	−0.687494	−	0.499494i
$917$	−18.6067	+	6.04570i	−0.614449	+	0.199647i
$918$		−	5.05639i		−	0.166886i
$919$	−2.86848	−	8.82828i	−0.0946225	−	0.291218i	0.892533	−	0.450983i	$-0.148926\pi$
$919$	−2.86848	−	8.82828i	−0.0946225	−	0.291218i	−0.987155	+	0.159765i	$0.948926\pi$
$920$	−0.878487	+	0.565222i	−0.0289629	+	0.0186348i
$921$	0.550550	−	1.69442i	0.0181412	−	0.0558330i
$922$	−12.9029	−	4.19240i	−0.424933	−	0.138069i
$923$	−0.759941	−	1.04597i	−0.0250138	−	0.0344285i
$924$	−5.36369			−0.176452
$925$	41.7872	−	8.51294i	1.37396	−	0.279904i
$926$	−29.9192			−0.983205
$927$	12.3287	+	16.9689i	0.404926	+	0.557333i
$928$	5.32915	+	1.73155i	0.174938	+	0.0568408i
$929$	−14.4318	+	44.4164i	−0.473490	+	1.45725i	0.374492	+	0.927230i	$0.377817\pi$
$929$	−14.4318	+	44.4164i	−0.473490	+	1.45725i	−0.847983	+	0.530024i	$0.822183\pi$
$930$	0.0263192	+	0.0999150i	0.000863041	+	0.00327634i
$931$	−6.02027	−	18.5285i	−0.197306	−	0.607247i
$932$			16.5430i			0.541885i
$933$	−2.34478	+	0.761864i	−0.0767645	+	0.0249423i
$934$	−22.5705	−	16.3984i	−0.738530	−	0.536573i
$935$	−12.0760	−	18.7689i	−0.394926	−	0.613807i
$936$	−0.291367	+	0.211690i	−0.00952362	+	0.00691932i
$937$	−3.96416	+	5.45619i	−0.129503	+	0.178246i	−0.868845	−	0.495085i	$-0.835137\pi$
$937$	−3.96416	+	5.45619i	−0.129503	+	0.178246i	0.739341	+	0.673331i	$0.235137\pi$
$938$	38.1260	−	52.4760i	1.24486	−	1.71340i
$939$	−0.233367	+	0.169551i	−0.00761564	+	0.00553308i
$940$	15.1171	+	23.4955i	0.493065	+	0.766337i
$941$	−0.731861	−	0.531728i	−0.0238580	−	0.0173339i	0.575792	−	0.817596i	$-0.304694\pi$
$941$	−0.731861	−	0.531728i	−0.0238580	−	0.0173339i	−0.599650	+	0.800262i	$0.704694\pi$
$942$	−2.45431	+	0.797452i	−0.0799656	+	0.0259824i
$943$		−	2.97183i		−	0.0967760i
$944$	0.856630	+	2.63643i	0.0278809	+	0.0858086i
$945$	5.17823	+	19.6580i	0.168448	+	0.639474i
$946$	0.777678	−	2.39345i	0.0252845	−	0.0778177i
$947$	41.5920	+	13.5141i	1.35156	+	0.439148i	0.893216	−	0.449628i	$-0.148443\pi$
$947$	41.5920	+	13.5141i	1.35156	+	0.439148i	0.458342	+	0.888776i	$0.348443\pi$
$948$	0.380717	+	0.524012i	0.0123651	+	0.0170191i
$949$	0.761920			0.0247330
$950$	4.89937	−	0.998104i	0.158956	−	0.0323828i
$951$	−1.52623			−0.0494914
$952$	8.65742	+	11.9159i	0.280589	+	0.386197i
$953$	−3.39444	−	1.10292i	−0.109957	−	0.0357271i	0.253522	−	0.967330i	$-0.418411\pi$
$953$	−3.39444	−	1.10292i	−0.109957	−	0.0357271i	−0.363479	+	0.931603i	$0.618411\pi$
$954$	8.77120	−	26.9950i	0.283978	−	0.873995i
$955$	49.3809	−	31.7719i	1.59793	−	1.02811i
$956$	−7.59239	−	23.3670i	−0.245555	−	0.755742i
$957$			5.84036i			0.188792i
$958$	−33.8979	+	11.0141i	−1.09519	+	0.355849i
$959$	11.8027	+	8.57513i	0.381128	+	0.276905i
$960$	−0.0378037	+	0.667266i	−0.00122011	+	0.0215359i
$961$	25.0602	−	18.2073i	0.808393	−	0.587332i
$962$	0.620316	−	0.853791i	0.0199998	−	0.0275273i
$963$	−22.5355	+	31.0174i	−0.726196	+	0.999523i
$964$	−0.00893884	+	0.00649445i	−0.000287901	+	0.000209172i
$965$	3.65678	+	1.42150i	0.117716	+	0.0457597i
$966$	0.581318	+	0.422352i	0.0187036	+	0.0135890i
$967$	46.6891	−	15.1702i	1.50142	−	0.487841i	0.560988	−	0.827824i	$-0.310421\pi$
$967$	46.6891	−	15.1702i	1.50142	−	0.487841i	0.940431	+	0.339983i	$0.110421\pi$
$968$			1.16064i			0.0373044i
$969$	0.264355	+	0.813600i	0.00849229	+	0.0261366i
$970$	30.0951	+	1.70503i	0.966296	+	0.0547452i
$971$	−3.77109	+	11.6062i	−0.121020	+	0.372461i	−0.993155	−	0.116804i	$-0.962735\pi$
$971$	−3.77109	+	11.6062i	−0.121020	+	0.372461i	0.872135	+	0.489265i	$0.162735\pi$
$972$	7.37257	+	2.39549i	0.236475	+	0.0768354i
$973$	13.9523	+	19.2036i	0.447289	+	0.615640i
$974$	−8.87093			−0.284243
$975$	−0.183731	−	0.0208855i	−0.00588410	−	0.000668870i
$976$	−5.43284			−0.173901
$977$	21.9445	+	30.2041i	0.702068	+	0.966314i	0.999931	+	0.0117054i	$0.00372602\pi$
$977$	21.9445	+	30.2041i	0.702068	+	0.966314i	−0.297863	+	0.954609i	$0.596274\pi$
$978$	−0.200465	−	0.0651349i	−0.00641016	−	0.00208279i
$979$	−7.46046	+	22.9609i	−0.238437	+	0.733835i
$980$	−33.7385	−	27.5583i	−1.07774	−	0.880316i
$981$	3.74688	+	11.5317i	0.119629	+	0.368179i
$982$		−	40.8109i		−	1.30233i
$983$	18.9315	−	6.15121i	0.603820	−	0.196193i	0.00887660	−	0.999961i	$-0.497174\pi$
$983$	18.9315	−	6.15121i	0.603820	−	0.196193i	0.594943	+	0.803768i	$0.297174\pi$
$984$	−1.53823	−	1.11759i	−0.0490369	−	0.0356274i
$985$	13.0767	−	16.0093i	0.416659	−	0.510099i
$986$	12.9749	−	9.42681i	0.413205	−	0.300211i
$987$	11.2960	−	15.5475i	0.359554	−	0.494884i
$988$	0.0727292	−	0.100103i	0.00231382	−	0.00318471i
$989$	−0.272752	+	0.198166i	−0.00867300	+	0.00630130i
$990$	21.9476	−	5.78136i	0.697542	−	0.183744i
$991$	−39.5448	−	28.7310i	−1.25618	−	0.912671i	−0.257620	−	0.966246i	$-0.582938\pi$
$991$	−39.5448	−	28.7310i	−1.25618	−	0.912671i	−0.998564	+	0.0535757i	$0.982938\pi$
$992$	−0.147031	+	0.0477733i	−0.00466825	+	0.00151681i
$993$			8.16700i			0.259172i
$994$	−16.6161	−	51.1390i	−0.527030	−	1.62203i
$995$	2.93747	−	7.55659i	0.0931242	−	0.239560i
$996$	0.0461010	−	0.141884i	0.00146077	−	0.00449578i
$997$	−16.6259	−	5.40208i	−0.526547	−	0.171085i	0.0336675	−	0.999433i	$-0.489281\pi$
$997$	−16.6259	−	5.40208i	−0.526547	−	0.171085i	−0.560214	+	0.828348i	$0.689281\pi$
$998$	2.26323	+	3.11508i	0.0716414	+	0.0986060i
$999$	−15.0678			−0.476724

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.n.a.39.17	✓	88
25.9	even	10	inner	950.2.n.a.609.17	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.n.a.39.17	✓	88	1.1	even	1	trivial
950.2.n.a.609.17	yes	88	25.9	even	10	inner

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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.n (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.587785 + 0.809017i) q^{2} +(-0.284260 - 0.0923618i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(0.810167 - 2.08414i) q^{5} +(-0.0923618 - 0.284260i) q^{6} +5.14607i q^{7} +(-0.951057 + 0.309017i) q^{8} +(-2.35478 - 1.71085i) q^{9} +O(q^{10})\)	\(q+(0.587785 + 0.809017i) q^{2} +(-0.284260 - 0.0923618i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(0.810167 - 2.08414i) q^{5} +(-0.0923618 - 0.284260i) q^{6} +5.14607i q^{7} +(-0.951057 + 0.309017i) q^{8} +(-2.35478 - 1.71085i) q^{9} +(2.16231 - 0.569586i) q^{10} +(-2.82121 + 2.04973i) q^{11} +(0.175683 - 0.241806i) q^{12} +(-0.0727292 + 0.100103i) q^{13} +(-4.16326 + 3.02478i) q^{14} +(-0.422793 + 0.517609i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-2.72208 + 0.884457i) q^{17} -2.91067i q^{18} +(0.309017 + 0.951057i) q^{19} +(1.73178 + 1.41455i) q^{20} +(0.475300 - 1.46282i) q^{21} +(-3.31653 - 1.07761i) q^{22} +(0.274593 + 0.377945i) q^{23} +0.298889 q^{24} +(-3.68726 - 3.37700i) q^{25} -0.123734 q^{26} +(1.03840 + 1.42924i) q^{27} +(-4.89420 - 1.59022i) q^{28} +(-1.73155 + 5.32915i) q^{29} +(-0.667266 - 0.0378037i) q^{30} +(-0.0477733 - 0.147031i) q^{31} -1.00000i q^{32} +(0.991276 - 0.322085i) q^{33} +(-2.31554 - 1.68234i) q^{34} +(10.7251 + 4.16917i) q^{35} +(2.35478 - 1.71085i) q^{36} +(-5.01328 + 6.90019i) q^{37} +(-0.587785 + 0.809017i) q^{38} +(0.0299197 - 0.0217380i) q^{39} +(-0.126481 + 2.23249i) q^{40} +(-5.14648 - 3.73914i) q^{41} +(1.46282 - 0.475300i) q^{42} +0.721671i q^{43} +(-1.07761 - 3.31653i) q^{44} +(-5.47340 + 3.52161i) q^{45} +(-0.144362 + 0.444300i) q^{46} +(11.8830 + 3.86101i) q^{47} +(0.175683 + 0.241806i) q^{48} -19.4820 q^{49} +(0.564734 - 4.96801i) q^{50} +0.855469 q^{51} +(-0.0727292 - 0.100103i) q^{52} +(9.27451 + 3.01347i) q^{53} +(-0.545920 + 1.68017i) q^{54} +(1.98627 + 7.54042i) q^{55} +(-1.59022 - 4.89420i) q^{56} -0.298889i q^{57} +(-5.32915 + 1.73155i) q^{58} +(-2.24269 - 1.62941i) q^{59} +(-0.361625 - 0.562050i) q^{60} +(4.39526 - 3.19334i) q^{61} +(0.0908703 - 0.125072i) q^{62} +(8.80413 - 12.1178i) q^{63} +(0.809017 - 0.587785i) q^{64} +(0.149706 + 0.232678i) q^{65} +(0.843229 + 0.612642i) q^{66} +(-11.9876 + 3.89502i) q^{67} -2.86216i q^{68} +(-0.0431482 - 0.132797i) q^{69} +(2.93113 + 11.1274i) q^{70} +(-3.22889 + 9.93750i) q^{71} +(2.76821 + 0.899445i) q^{72} +(-3.61941 - 4.98169i) q^{73} -8.52911 q^{74} +(0.736236 + 1.30051i) q^{75} -1.00000 q^{76} +(-10.5481 - 14.5182i) q^{77} +(0.0351728 + 0.0114283i) q^{78} +(-0.669662 + 2.06101i) q^{79} +(-1.88046 + 1.20990i) q^{80} +(2.53517 + 7.80244i) q^{81} -6.36140i q^{82} +(0.474706 - 0.154241i) q^{83} +(1.24435 + 0.904074i) q^{84} +(-0.362009 + 6.38975i) q^{85} +(-0.583844 + 0.424188i) q^{86} +(0.984420 - 1.35494i) q^{87} +(2.04973 - 2.82121i) q^{88} +(5.60096 - 4.06934i) q^{89} +(-6.06623 - 2.35813i) q^{90} +(-0.515138 - 0.374270i) q^{91} +(-0.444300 + 0.144362i) q^{92} +0.0462076i q^{93} +(3.86101 + 11.8830i) q^{94} +(2.23249 + 0.126481i) q^{95} +(-0.0923618 + 0.284260i) q^{96} +(12.8207 + 4.16571i) q^{97} +(-11.4512 - 15.7613i) q^{98} +10.1501 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 22 q^{4} + 10 q^{5} + 2 q^{6} + 24 q^{9}+O(q^{10}) \) 88 * q + 22 * q^4 + 10 * q^5 + 2 * q^6 + 24 * q^9	\( 88 q + 22 q^{4} + 10 q^{5} + 2 q^{6} + 24 q^{9} + 26 q^{11} + 10 q^{12} - 10 q^{14} + 12 q^{15} - 22 q^{16} - 40 q^{17} - 22 q^{19} + 10 q^{23} + 8 q^{24} + 6 q^{25} - 28 q^{26} - 30 q^{27} - 10 q^{28} - 4 q^{29} - 4 q^{30} + 2 q^{31} - 8 q^{34} - 48 q^{35} - 24 q^{36} + 50 q^{37} + 8 q^{39} + 32 q^{41} + 10 q^{42} + 4 q^{44} - 8 q^{45} + 10 q^{46} + 10 q^{48} - 56 q^{49} + 28 q^{50} - 60 q^{51} - 70 q^{53} - 8 q^{54} + 4 q^{55} + 10 q^{56} - 60 q^{58} - 28 q^{59} - 12 q^{60} - 58 q^{61} + 60 q^{63} + 22 q^{64} - 24 q^{65} + 4 q^{66} - 70 q^{67} - 8 q^{69} - 4 q^{70} + 48 q^{71} + 40 q^{73} + 52 q^{74} + 108 q^{75} - 88 q^{76} - 50 q^{78} - 20 q^{79} + 24 q^{81} - 80 q^{83} + 30 q^{85} + 20 q^{86} + 70 q^{87} + 10 q^{88} - 62 q^{89} - 104 q^{90} + 20 q^{91} - 10 q^{92} - 10 q^{94} + 2 q^{96} - 10 q^{97} + 60 q^{98} + 156 q^{99}+O(q^{100}) \) 88 * q + 22 * q^4 + 10 * q^5 + 2 * q^6 + 24 * q^9 + 26 * q^11 + 10 * q^12 - 10 * q^14 + 12 * q^15 - 22 * q^16 - 40 * q^17 - 22 * q^19 + 10 * q^23 + 8 * q^24 + 6 * q^25 - 28 * q^26 - 30 * q^27 - 10 * q^28 - 4 * q^29 - 4 * q^30 + 2 * q^31 - 8 * q^34 - 48 * q^35 - 24 * q^36 + 50 * q^37 + 8 * q^39 + 32 * q^41 + 10 * q^42 + 4 * q^44 - 8 * q^45 + 10 * q^46 + 10 * q^48 - 56 * q^49 + 28 * q^50 - 60 * q^51 - 70 * q^53 - 8 * q^54 + 4 * q^55 + 10 * q^56 - 60 * q^58 - 28 * q^59 - 12 * q^60 - 58 * q^61 + 60 * q^63 + 22 * q^64 - 24 * q^65 + 4 * q^66 - 70 * q^67 - 8 * q^69 - 4 * q^70 + 48 * q^71 + 40 * q^73 + 52 * q^74 + 108 * q^75 - 88 * q^76 - 50 * q^78 - 20 * q^79 + 24 * q^81 - 80 * q^83 + 30 * q^85 + 20 * q^86 + 70 * q^87 + 10 * q^88 - 62 * q^89 - 104 * q^90 + 20 * q^91 - 10 * q^92 - 10 * q^94 + 2 * q^96 - 10 * q^97 + 60 * q^98 + 156 * q^99

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