LMFDB - Embedded newform 343.3.l.a.10.63

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [343,3,Mod(3,343)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(343, base_ring=CyclotomicField(294))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("343.3");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 343 = 7^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	343.l (of order $294$, degree $84$, 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:	$9.34607306756$
Analytic rank:	$0$
Dimension:	$5376$
Relative dimension:	$64$ over $\Q(\zeta_{294})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{294}]$

Embedding invariants

Embedding label			10.63
Character	$\chi$	$=$	343.10
Dual form			343.3.l.a.103.63

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.48678 + 1.77191i) q^{2} +(-2.49496 + 2.36509i) q^{3} +(6.65993 + 9.12553i) q^{4} +(-0.650784 + 0.00695434i) q^{5} +(-12.8901 + 3.82572i) q^{6} +(6.87965 + 1.29244i) q^{7} +(4.55518 + 28.1754i) q^{8} +(0.150514 - 2.81444i) q^{9} +(-2.28147 - 1.12889i) q^{10} +(9.65685 - 8.58360i) q^{11} +(-38.1990 - 7.01645i) q^{12} +(-13.6527 - 8.27636i) q^{13} +(21.6978 + 16.6966i) q^{14} +(1.60723 - 1.55651i) q^{15} +(-20.2610 + 63.2760i) q^{16} +(14.3480 - 1.69432i) q^{17} +(5.51176 - 9.54665i) q^{18} +(-20.5436 + 11.8609i) q^{19} +(-4.39764 - 5.89244i) q^{20} +(-20.2212 + 13.0464i) q^{21} +(48.8808 - 12.8180i) q^{22} +(-11.7728 - 34.2302i) q^{23} +(-78.0024 - 59.5230i) q^{24} +(-24.5708 + 0.525192i) q^{25} +(-32.9391 - 53.0493i) q^{26} +(-13.7754 - 16.1814i) q^{27} +(34.0238 + 71.3881i) q^{28} +(38.8126 - 7.55874i) q^{29} +(8.36207 - 2.57936i) q^{30} +(31.1243 - 12.2154i) q^{31} +(-102.471 + 103.572i) q^{32} +(-3.79241 + 44.2550i) q^{33} +(53.0307 + 19.5158i) q^{34} +(-4.48615 - 0.793259i) q^{35} +(26.6857 - 17.3705i) q^{36} +(34.2557 + 14.7282i) q^{37} +(-92.6477 + 4.95474i) q^{38} +(53.6373 - 11.6408i) q^{39} +(-3.16038 - 18.3044i) q^{40} +(11.0467 - 7.70572i) q^{41} +(-93.6240 + 9.65985i) q^{42} +(-7.37434 + 45.6129i) q^{43} +(142.644 + 30.9577i) q^{44} +(-0.0783798 + 1.83264i) q^{45} +(19.6039 - 140.214i) q^{46} +(70.2429 + 17.6199i) q^{47} +(-99.1033 - 205.790i) q^{48} +(45.6592 + 17.7831i) q^{49} +(-86.6037 - 41.7062i) q^{50} +(-31.7905 + 38.1617i) q^{51} +(-15.4000 - 179.708i) q^{52} +(-0.888830 + 3.24765i) q^{53} +(-19.3599 - 80.8299i) q^{54} +(-6.22483 + 5.65323i) q^{55} +(-5.07709 + 199.724i) q^{56} +(23.2034 - 78.1799i) q^{57} +(148.724 + 42.4168i) q^{58} +(-54.1781 + 25.3812i) q^{59} +(24.9081 + 4.30054i) q^{60} +(-0.420454 - 9.83087i) q^{61} +(130.169 + 12.5572i) q^{62} +(4.67299 - 19.1678i) q^{63} +(-288.592 + 95.8191i) q^{64} +(8.94253 + 5.29118i) q^{65} +(-91.6395 + 147.588i) q^{66} +(-40.3448 + 6.08100i) q^{67} +(111.019 + 119.650i) q^{68} +(110.330 + 57.5591i) q^{69} +(-14.2367 - 10.7150i) q^{70} +(-14.6330 - 2.84978i) q^{71} +(79.9836 - 8.57948i) q^{72} +(-0.532651 + 0.133611i) q^{73} +(93.3450 + 112.052i) q^{74} +(60.0610 - 59.4226i) q^{75} +(-245.056 - 108.479i) q^{76} +(77.5296 - 46.5712i) q^{77} +(207.648 + 54.4517i) q^{78} +(-4.78325 - 63.8281i) q^{79} +(12.7455 - 41.3199i) q^{80} +(97.8611 + 10.4971i) q^{81} +(52.1715 - 7.29433i) q^{82} +(-24.9011 + 2.40218i) q^{83} +(-253.727 - 97.6407i) q^{84} +(-9.32569 + 1.20242i) q^{85} +(-106.535 + 145.976i) q^{86} +(-78.9585 + 110.654i) q^{87} +(285.835 + 232.986i) q^{88} +(-12.5010 + 5.21725i) q^{89} +(-3.52057 + 6.25114i) q^{90} +(-83.2292 - 74.5838i) q^{91} +(233.963 - 335.404i) q^{92} +(-48.7633 + 104.089i) q^{93} +(213.701 + 185.901i) q^{94} +(13.2870 - 7.86173i) q^{95} +(10.7036 - 500.761i) q^{96} +(-12.6640 - 10.0992i) q^{97} +(127.694 + 142.910i) q^{98} +(-22.7045 - 28.4706i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5376 q - 84 q^{2} - 84 q^{3} - 84 q^{4} - 84 q^{5} - 112 q^{6} - 84 q^{7} - 84 q^{8} - 28 q^{9} - 84 q^{10} - 119 q^{11} - 119 q^{12} - 84 q^{13} + 21 q^{14} - 168 q^{15} - 84 q^{16} - 35 q^{17} - 42 q^{18}+ \cdots + 42 q^{99}+O(q^{100}) $ 5376 * q - 84 * q^2 - 84 * q^3 - 84 * q^4 - 84 * q^5 - 112 * q^6 - 84 * q^7 - 84 * q^8 - 28 * q^9 - 84 * q^10 - 119 * q^11 - 119 * q^12 - 84 * q^13 + 21 * q^14 - 168 * q^15 - 84 * q^16 - 35 * q^17 - 42 * q^18 - 126 * q^19 - 420 * q^20 - 84 * q^21 + 28 * q^22 - 147 * q^23 - 210 * q^24 - 84 * q^25 - 196 * q^26 + 21 * q^27 + 126 * q^28 - 336 * q^29 - 91 * q^30 - 77 * q^31 - 84 * q^33 - 616 * q^34 + 56 * q^35 + 420 * q^36 - 539 * q^37 - 532 * q^38 - 441 * q^39 - 364 * q^40 - 280 * q^41 - 700 * q^42 - 84 * q^43 - 112 * q^44 - 315 * q^45 - 252 * q^46 - 7 * q^47 - 98 * q^48 - 28 * q^49 + 56 * q^50 + 84 * q^51 + 84 * q^52 + 371 * q^53 + 798 * q^54 + 1267 * q^55 - 42 * q^56 - 735 * q^57 - 868 * q^58 + 1400 * q^59 + 406 * q^60 + 637 * q^61 + 336 * q^62 + 735 * q^63 - 420 * q^64 - 84 * q^65 + 1372 * q^66 - 91 * q^67 - 77 * q^68 + 84 * q^69 - 1078 * q^70 + 679 * q^71 + 273 * q^72 + 294 * q^73 - 1428 * q^74 - 1344 * q^75 - 231 * q^76 - 714 * q^77 + 5040 * q^78 - 91 * q^79 - 1148 * q^80 - 784 * q^81 - 224 * q^82 - 1414 * q^83 - 1246 * q^84 + 364 * q^85 - 1582 * q^86 - 952 * q^87 - 1974 * q^88 - 910 * q^89 - 287 * q^90 + 1456 * q^91 - 6384 * q^92 - 154 * q^93 - 770 * q^94 - 1358 * q^95 - 4284 * q^96 + 3430 * q^97 + 7 * q^98 + 42 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/343\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{223}{294}\right)$

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 $

$2$	3.48678	+	1.77191i	1.74339	+	0.885957i	0.966635	+	0.256157i	$0.0824565\pi$
$2$	3.48678	+	1.77191i	1.74339	+	0.885957i	0.776757	+	0.629800i	$0.216863\pi$
$3$	−2.49496	+	2.36509i	−0.831652	+	0.788364i	−0.979669	−	0.200621i	$-0.935704\pi$
$3$	−2.49496	+	2.36509i	−0.831652	+	0.788364i	0.148017	+	0.988985i	$0.452711\pi$
$4$	6.65993	+	9.12553i	1.66498	+	2.28138i
$5$	−0.650784	+	0.00695434i	−0.130157	+	0.00139087i	−0.0757412	−	0.997128i	$-0.524132\pi$
$5$	−0.650784	+	0.00695434i	−0.130157	+	0.00139087i	−0.0544156	+	0.998518i	$0.517330\pi$
$6$	−12.8901	+	3.82572i	−2.14835	+	0.637620i
$7$	6.87965	+	1.29244i	0.982807	+	0.184635i
$7$	6.87965	+	1.29244i	0.982807	+	0.184635i
$8$	4.55518	+	28.1754i	0.569398	+	3.52193i
$9$	0.150514	−	2.81444i	0.0167238	−	0.312716i
$10$	−2.28147	−	1.12889i	−0.228147	−	0.112889i
$11$	9.65685	−	8.58360i	0.877896	−	0.780327i	−0.0987660	−	0.995111i	$-0.531490\pi$
$11$	9.65685	−	8.58360i	0.877896	−	0.780327i	0.976662	+	0.214783i	$0.0689045\pi$
$12$	−38.1990	−	7.01645i	−3.18325	−	0.584704i
$13$	−13.6527	−	8.27636i	−1.05021	−	0.636643i	−0.115956	−	0.993254i	$-0.536993\pi$
$13$	−13.6527	−	8.27636i	−1.05021	−	0.636643i	−0.934253	+	0.356612i	$0.883932\pi$
$14$	21.6978	+	16.6966i	1.54984	+	1.19262i
$15$	1.60723	−	1.55651i	0.107149	−	0.103768i
$16$	−20.2610	+	63.2760i	−1.26631	+	3.95475i
$17$	14.3480	−	1.69432i	0.844003	−	0.0996657i	0.315844	−	0.948811i	$-0.397712\pi$
$17$	14.3480	−	1.69432i	0.844003	−	0.0996657i	0.528159	+	0.849146i	$0.322883\pi$
$18$	5.51176	−	9.54665i	0.306209	−	0.530369i
$19$	−20.5436	+	11.8609i	−1.08124	+	0.624256i	−0.931232	−	0.364428i	$-0.881265\pi$
$19$	−20.5436	+	11.8609i	−1.08124	+	0.624256i	−0.150012	+	0.988684i	$0.547931\pi$
$20$	−4.39764	−	5.89244i	−0.219882	−	0.294622i
$21$	−20.2212	+	13.0464i	−0.962913	+	0.621258i
$22$	48.8808	−	12.8180i	2.22185	−	0.582639i
$23$	−11.7728	−	34.2302i	−0.511859	−	1.48827i	−0.839443	−	0.543447i	$-0.817119\pi$
$23$	−11.7728	−	34.2302i	−0.511859	−	1.48827i	0.327584	−	0.944822i	$-0.393766\pi$
$24$	−78.0024	−	59.5230i	−3.25010	−	2.48012i
$25$	−24.5708	+	0.525192i	−0.982833	+	0.0210077i
$26$	−32.9391	−	53.0493i	−1.26689	−	2.04036i
$27$	−13.7754	−	16.1814i	−0.510201	−	0.599311i
$28$	34.0238	+	71.3881i	1.21513	+	2.54957i
$29$	38.8126	−	7.55874i	1.33836	−	0.260646i	0.529334	−	0.848414i	$-0.322442\pi$
$29$	38.8126	−	7.55874i	1.33836	−	0.260646i	0.809030	+	0.587767i	$0.199993\pi$
$30$	8.36207	−	2.57936i	0.278736	−	0.0859786i
$31$	31.1243	−	12.2154i	1.00401	−	0.394045i	0.194343	−	0.980934i	$-0.437742\pi$
$31$	31.1243	−	12.2154i	1.00401	−	0.394045i	0.809668	+	0.586888i	$0.199647\pi$
$32$	−102.471	+	103.572i	−3.20222	+	3.23663i
$33$	−3.79241	+	44.2550i	−0.114921	+	1.34106i
$34$	53.0307	+	19.5158i	1.55973	+	0.573994i
$35$	−4.48615	−	0.793259i	−0.128176	−	0.0226645i
$36$	26.6857	−	17.3705i	0.741269	−	0.482513i
$37$	34.2557	+	14.7282i	0.925829	+	0.398061i	0.804094	−	0.594502i	$-0.202651\pi$
$37$	34.2557	+	14.7282i	0.925829	+	0.398061i	0.121735	+	0.992563i	$0.461154\pi$
$38$	−92.6477	+	4.95474i	−2.43810	+	0.130388i
$39$	53.6373	−	11.6408i	1.37531	−	0.298482i
$40$	−3.16038	−	18.3044i	−0.0790095	−	0.457611i
$41$	11.0467	−	7.70572i	0.269433	−	0.187945i	−0.429630	−	0.903005i	$-0.641356\pi$
$41$	11.0467	−	7.70572i	0.269433	−	0.187945i	0.699063	+	0.715061i	$0.253601\pi$
$42$	−93.6240	+	9.65985i	−2.22914	+	0.229996i
$43$	−7.37434	+	45.6129i	−0.171496	+	1.06076i	0.746852	+	0.664991i	$0.231564\pi$
$43$	−7.37434	+	45.6129i	−0.171496	+	1.06076i	−0.918348	+	0.395774i	$0.870476\pi$
$44$	142.644	+	30.9577i	3.24191	+	0.703585i
$45$	−0.0783798	+	1.83264i	−0.00174177	+	0.0407253i
$46$	19.6039	−	140.214i	0.426172	−	3.04812i
$47$	70.2429	+	17.6199i	1.49453	+	0.374891i	0.902382	−	0.430938i	$-0.141817\pi$
$47$	70.2429	+	17.6199i	1.49453	+	0.374891i	0.592149	+	0.805829i	$0.298280\pi$
$48$	−99.1033	−	205.790i	−2.06465	−	4.28729i
$49$	45.6592	+	17.7831i	0.931820	+	0.362921i
$50$	−86.6037	−	41.7062i	−1.73207	−	0.834123i
$51$	−31.7905	+	38.1617i	−0.623343	+	0.748268i
$52$	−15.4000	−	179.708i	−0.296154	−	3.45593i
$53$	−0.888830	+	3.24765i	−0.0167704	+	0.0612764i	−0.972428	−	0.233205i	$-0.925079\pi$
$53$	−0.888830	+	3.24765i	−0.0167704	+	0.0612764i	0.955657	+	0.294481i	$0.0951468\pi$
$54$	−19.3599	−	80.8299i	−0.358516	−	1.49685i
$55$	−6.22483	+	5.65323i	−0.113179	+	0.102786i
$56$	−5.07709	+	199.724i	−0.0906623	+	3.56651i
$57$	23.2034	−	78.1799i	0.407077	−	1.37158i
$58$	148.724	+	42.4168i	2.56421	+	0.731325i
$59$	−54.1781	+	25.3812i	−0.918272	+	0.430190i	−0.824795	−	0.565431i	$-0.808710\pi$
$59$	−54.1781	+	25.3812i	−0.918272	+	0.430190i	−0.0934770	+	0.995621i	$0.529798\pi$
$60$	24.9081	+	4.30054i	0.415134	+	0.0716757i
$61$	−0.420454	−	9.83087i	−0.00689269	−	0.161162i	−0.999278	−	0.0379903i	$-0.987904\pi$
$61$	−0.420454	−	9.83087i	−0.00689269	−	0.161162i	0.992385	−	0.123171i	$-0.0393065\pi$
$62$	130.169	+	12.5572i	2.09949	+	0.202536i
$63$	4.67299	−	19.1678i	0.0741745	−	0.304251i
$64$	−288.592	+	95.8191i	−4.50925	+	1.49717i
$65$	8.94253	+	5.29118i	0.137577	+	0.0814027i
$66$	−91.6395	+	147.588i	−1.38848	+	2.23618i
$67$	−40.3448	+	6.08100i	−0.602161	+	0.0907612i	−0.443046	−	0.896499i	$-0.646102\pi$
$67$	−40.3448	+	6.08100i	−0.602161	+	0.0907612i	−0.159115	+	0.987260i	$0.550864\pi$
$68$	111.019	+	119.650i	1.63263	+	1.75955i
$69$	110.330	+	57.5591i	1.59899	+	0.834190i
$70$	−14.2367	−	10.7150i	−0.203381	−	0.153072i
$71$	−14.6330	−	2.84978i	−0.206099	−	0.0401378i	0.0870528	−	0.996204i	$-0.472255\pi$
$71$	−14.6330	−	2.84978i	−0.206099	−	0.0401378i	−0.293152	+	0.956066i	$0.594704\pi$
$72$	79.9836	−	8.57948i	1.11088	−	0.119159i
$73$	−0.532651	+	0.133611i	−0.00729659	+	0.00183029i	−0.246951	−	0.969028i	$-0.579429\pi$
$73$	−0.532651	+	0.133611i	−0.00729659	+	0.00183029i	0.239654	+	0.970858i	$0.422966\pi$
$74$	93.3450	+	112.052i	1.26142	+	1.51422i
$75$	60.0610	−	59.4226i	0.800813	−	0.792301i
$76$	−245.056	−	108.479i	−3.22442	−	1.42736i
$77$	77.5296	−	46.5712i	1.00688	−	0.604821i
$78$	207.648	+	54.4517i	2.66215	+	0.698099i
$79$	−4.78325	−	63.8281i	−0.0605475	−	0.807950i	−0.941986	−	0.335652i	$-0.891044\pi$
$79$	−4.78325	−	63.8281i	−0.0605475	−	0.807950i	0.881439	−	0.472298i	$-0.156576\pi$
$80$	12.7455	−	41.3199i	0.159319	−	0.516499i
$81$	97.8611	+	10.4971i	1.20816	+	0.129594i
$82$	52.1715	−	7.29433i	0.636238	−	0.0889552i
$83$	−24.9011	+	2.40218i	−0.300013	+	0.0289419i	−0.244933	−	0.969540i	$-0.578766\pi$
$83$	−24.9011	+	2.40218i	−0.300013	+	0.0289419i	−0.0550800	+	0.998482i	$0.517541\pi$
$84$	−253.727	−	97.6407i	−3.02056	−	1.16239i
$85$	−9.32569	+	1.20242i	−0.109714	+	0.0141461i
$86$	−106.535	+	145.976i	−1.23878	+	1.69739i
$87$	−78.9585	+	110.654i	−0.907569	+	1.27189i
$88$	285.835	+	232.986i	3.24813	+	2.64757i
$89$	−12.5010	+	5.21725i	−0.140461	+	0.0586208i	−0.454264	−	0.890867i	$-0.650098\pi$
$89$	−12.5010	+	5.21725i	−0.140461	+	0.0586208i	0.313803	+	0.949488i	$0.398397\pi$
$90$	−3.52057	+	6.25114i	−0.0391175	+	0.0694571i
$91$	−83.2292	−	74.5838i	−0.914606	−	0.819602i
$92$	233.963	−	335.404i	2.54308	−	3.64569i
$93$	−48.7633	+	104.089i	−0.524337	+	1.11923i
$94$	213.701	+	185.901i	2.27342	+	1.97767i
$95$	13.2870	−	7.86173i	0.139863	−	0.0827551i
$96$	10.7036	−	500.761i	0.111496	−	5.21626i
$97$	−12.6640	−	10.0992i	−0.130557	−	0.104116i	0.556034	−	0.831159i	$-0.312322\pi$
$97$	−12.6640	−	10.0992i	−0.130557	−	0.104116i	−0.686591	+	0.727044i	$0.740894\pi$
$98$	127.694	+	142.910i	1.30300	+	1.45827i
$99$	−22.7045	−	28.4706i	−0.229339	−	0.287582i
$100$	−168.433	−	220.724i	−1.68433	−	2.20724i
$101$	−72.2363	−	48.1273i	−0.715210	−	0.476508i	0.143054	−	0.989715i	$-0.454308\pi$
$101$	−72.2363	−	48.1273i	−0.715210	−	0.476508i	−0.858265	+	0.513207i	$0.828457\pi$
$102$	−178.466	+	76.7315i	−1.74967	+	0.752270i
$103$	105.142	−	52.0249i	1.02079	−	0.505096i	0.145843	−	0.989308i	$-0.453411\pi$
$103$	105.142	−	52.0249i	1.02079	−	0.505096i	0.874951	+	0.484212i	$0.160894\pi$
$104$	170.999	−	422.371i	1.64422	−	4.06126i
$105$	13.0689	−	8.63102i	0.124466	−	0.0822002i
$106$	−8.85372	+	9.74893i	−0.0835257	+	0.0919710i
$107$	6.18521	−	11.2623i	0.0578057	−	0.105255i	−0.846028	−	0.533138i	$-0.821013\pi$
$107$	6.18521	−	11.2623i	0.0578057	−	0.105255i	0.903834	+	0.427883i	$0.140741\pi$
$108$	55.9205	−	233.475i	0.517783	−	2.16181i
$109$	−81.0207	−	147.525i	−0.743309	−	1.35344i	−0.928719	−	0.370783i	$-0.879089\pi$
$109$	−81.0207	−	147.525i	−0.743309	−	1.35344i	0.185410	−	0.982661i	$-0.440639\pi$
$110$	−31.7217	+	8.68171i	−0.288379	+	0.0789247i
$111$	−120.300	+	44.2715i	−1.08378	+	0.398843i
$112$	−221.170	+	409.131i	−1.97473	+	3.65295i
$113$	−98.6088	−	12.7142i	−0.872644	−	0.112515i	−0.321485	−	0.946915i	$-0.604182\pi$
$113$	−98.6088	−	12.7142i	−0.872644	−	0.112515i	−0.551160	+	0.834400i	$0.685814\pi$
$114$	219.433	−	231.482i	1.92485	−	2.03054i
$115$	7.89958	+	22.1946i	0.0686920	+	0.192996i
$116$	327.467	+	303.845i	2.82299	+	2.61935i
$117$	−25.3482	+	37.1790i	−0.216652	+	0.317770i
$118$	−233.881	−	7.50010i	−1.98204	−	0.0635601i
$119$	100.899	+	6.88774i	0.847894	+	0.0578802i
$120$	51.1767	+	38.1941i	0.426472	+	0.318285i
$121$	5.38666	−	45.6161i	0.0445179	−	0.376992i
$122$	15.9534	−	35.0231i	0.130766	−	0.287075i
$123$	−9.33636	+	45.3520i	−0.0759054	+	0.368715i
$124$	318.758	+	202.673i	2.57063	+	1.63446i
$125$	32.2488	−	1.03416i	0.257991	−	0.00827325i
$126$	50.2575	−	58.5540i	0.398869	−	0.464714i
$127$	41.3927	+	35.2381i	0.325927	+	0.277466i	0.796172	−	0.605070i	$-0.206855\pi$
$127$	41.3927	+	35.2381i	0.325927	+	0.277466i	−0.470245	+	0.882536i	$0.655835\pi$
$128$	−599.764	−	90.3999i	−4.68566	−	0.706249i
$129$	−89.4800	−	131.243i	−0.693644	−	1.01739i
$130$	21.8051	+	34.2946i	0.167732	+	0.263804i
$131$	92.8949	+	244.338i	0.709122	+	1.86517i	0.417732	+	0.908570i	$0.362825\pi$
$131$	92.8949	+	244.338i	0.709122	+	1.86517i	0.291389	+	0.956605i	$0.405882\pi$
$132$	−429.108	+	260.128i	−3.25082	+	1.97067i
$133$	−156.663	+	55.0471i	−1.17791	+	0.413888i
$134$	−151.449	−	50.2844i	−1.13021	−	0.375257i
$135$	9.07736	+	10.4348i	0.0672397	+	0.0772948i
$136$	113.096	+	396.544i	0.831588	+	2.91577i
$137$	1.41652	−	132.557i	0.0103395	−	0.967568i	−0.869952	−	0.493136i	$-0.835851\pi$
$137$	1.41652	−	132.557i	0.0103395	−	0.967568i	0.880292	−	0.474432i	$-0.157347\pi$
$138$	282.707	+	396.192i	2.04860	+	2.87096i
$139$	8.00287	−	124.651i	0.0575746	−	0.896771i	−0.862754	−	0.505624i	$-0.831262\pi$
$139$	8.00287	−	124.651i	0.0575746	−	0.896771i	0.920328	−	0.391146i	$-0.127921\pi$
$140$	−22.6386	−	46.2216i	−0.161704	−	0.330154i
$141$	−216.926	+	122.170i	−1.53848	+	0.866455i
$142$	−45.9726	−	35.8650i	−0.323751	−	0.252571i
$143$	−202.883	+	37.2659i	−1.41876	+	0.260601i
$144$	175.037	+	66.5474i	1.21554	+	0.462135i
$145$	−25.2060	+	5.18903i	−0.173835	+	0.0357864i
$146$	−2.09399	−	0.477939i	−0.0143424	−	0.00327355i
$147$	−155.976	+	63.6200i	−1.06106	+	0.432789i
$148$	93.7374	+	410.691i	0.633361	+	2.77494i
$149$	64.4579	−	29.3613i	0.432603	−	0.197056i	−0.186350	−	0.982483i	$-0.559666\pi$
$149$	64.4579	−	29.3613i	0.432603	−	0.197056i	0.618953	+	0.785428i	$0.287557\pi$
$150$	314.711	−	100.771i	2.09808	−	0.671805i
$151$	−6.78854	−	3.63438i	−0.0449572	−	0.0240687i	0.449354	−	0.893354i	$-0.351654\pi$
$151$	−6.78854	−	3.63438i	−0.0449572	−	0.0240687i	−0.494311	+	0.869285i	$0.664580\pi$
$152$	−427.765	−	524.797i	−2.81424	−	3.45261i
$153$	−2.60896	−	40.6367i	−0.0170521	−	0.265600i
$154$	352.849	−	25.0080i	2.29123	−	0.162390i
$155$	−20.1703	+	8.16604i	−0.130131	+	0.0526841i
$156$	463.449	+	411.942i	2.97083	+	2.64065i
$157$	−108.639	−	139.256i	−0.691970	−	0.886983i	0.305910	−	0.952060i	$-0.401039\pi$
$157$	−108.639	−	139.256i	−0.691970	−	0.886983i	−0.997880	+	0.0650774i	$0.979271\pi$
$158$	96.4197	−	231.030i	0.610251	−	1.46222i
$159$	−5.46340	−	10.2049i	−0.0343610	−	0.0641818i
$160$	65.9663	−	68.1156i	0.412289	−	0.425723i
$161$	−36.7519	−	250.707i	−0.228273	−	1.55719i
$162$	322.620	+	210.003i	1.99148	+	1.29631i
$163$	13.4631	+	20.2073i	0.0825956	+	0.123971i	0.871197	−	0.490933i	$-0.163344\pi$
$163$	13.4631	+	20.2073i	0.0825956	+	0.123971i	−0.788601	+	0.614905i	$0.789194\pi$
$164$	143.889	+	49.4878i	0.877374	+	0.301755i
$165$	2.16027	−	28.8269i	0.0130926	−	0.174708i
$166$	−91.0811	−	35.7467i	−0.548681	−	0.215342i
$167$	−91.8654	+	40.6661i	−0.550092	+	0.243510i	−0.661084	−	0.750312i	$-0.729903\pi$
$167$	−91.8654	+	40.6661i	−0.550092	+	0.243510i	0.110992	+	0.993821i	$0.464597\pi$
$168$	−459.699	−	510.311i	−2.73631	−	3.03757i
$169$	39.7296	+	76.1542i	0.235086	+	0.450617i
$170$	−34.6473	−	12.3318i	−0.203807	−	0.0725398i
$171$	30.2896	+	59.6041i	0.177132	+	0.348562i
$172$	−465.355	+	236.484i	−2.70555	+	1.37491i
$173$	−22.5970	+	63.4884i	−0.130619	+	0.366985i	−0.989372	−	0.145403i	$-0.953552\pi$
$173$	−22.5970	+	63.4884i	−0.130619	+	0.366985i	0.858754	+	0.512388i	$0.171239\pi$
$174$	−471.381	+	245.919i	−2.70908	+	1.41333i
$175$	−169.717	−	28.1433i	−0.969814	−	0.160819i
$176$	347.478	+	784.960i	1.97431	+	4.46000i
$177$	75.1430	−	191.461i	0.424536	−	1.08170i
$178$	−52.8328	−	3.95927i	−0.296814	−	0.0222431i
$179$	−48.7058	+	141.616i	−0.272099	+	0.791149i	0.722872	+	0.690982i	$0.242822\pi$
$179$	−48.7058	+	141.616i	−0.272099	+	0.791149i	−0.994971	+	0.100166i	$0.968063\pi$
$180$	−17.2458	+	11.4900i	−0.0958101	+	0.0638333i
$181$	64.6453	−	99.3125i	0.357156	−	0.548688i	−0.613335	−	0.789822i	$-0.710173\pi$
$181$	64.6453	−	99.3125i	0.357156	−	0.548688i	0.970492	+	0.241135i	$0.0775196\pi$
$182$	−158.046	−	407.533i	−0.868385	−	2.23919i
$183$	24.2999	+	23.5332i	0.132786	+	0.128596i
$184$	910.823	−	487.627i	4.95012	−	2.65015i
$185$	−22.3955	−	9.34668i	−0.121057	−	0.0505226i
$186$	−354.464	+	276.531i	−1.90572	+	1.48673i
$187$	124.014	−	139.520i	0.663174	−	0.746094i
$188$	307.022	+	758.351i	1.63310	+	4.03378i
$189$	−73.8566	−	129.126i	−0.390775	−	0.683208i
$190$	60.2592	−	3.86877i	0.317153	−	0.0203619i
$191$	−258.635	+	210.815i	−1.35411	+	1.10374i	−0.369449	+	0.929251i	$0.620454\pi$
$191$	−258.635	+	210.815i	−1.35411	+	1.10374i	−0.984659	+	0.174491i	$0.944172\pi$
$192$	493.403	−	921.611i	2.56981	−	4.80006i
$193$	−101.499	−	316.986i	−0.525902	−	1.64241i	−0.745263	−	0.666771i	$-0.767676\pi$
$193$	−101.499	−	316.986i	−0.525902	−	1.64241i	0.219361	−	0.975644i	$-0.429603\pi$
$194$	−26.2618	−	57.6534i	−0.135370	−	0.297182i
$195$	−34.8253	+	7.94865i	−0.178591	+	0.0407623i
$196$	141.806	+	535.099i	0.723502	+	2.73010i
$197$	36.3440	−	159.234i	0.184488	−	0.808293i	−0.794971	−	0.606647i	$-0.792514\pi$
$197$	36.3440	−	159.234i	0.184488	−	0.808293i	0.979459	−	0.201645i	$-0.0646288\pi$
$198$	−28.7184	−	139.501i	−0.145042	−	0.704552i
$199$	75.4092	−	198.346i	0.378941	−	0.996713i	−0.601321	−	0.799008i	$-0.705359\pi$
$199$	75.4092	−	198.346i	0.378941	−	0.996713i	0.980261	−	0.197705i	$-0.0633489\pi$
$200$	−126.722	−	689.901i	−0.633610	−	3.44950i
$201$	86.2763	−	110.591i	0.429236	−	0.550204i
$202$	−166.595	−	295.806i	−0.824727	−	1.46439i
$203$	276.786	−	1.83846i	1.36348	−	0.00905644i
$204$	−559.968	−	35.9512i	−2.74494	−	0.176231i
$205$	−7.13545	+	5.09159i	−0.0348071	+	0.0248370i
$206$	458.790	+	4.90268i	2.22714	+	0.0237994i
$207$	−98.1108	+	27.9816i	−0.473965	+	0.135177i
$208$	800.313	−	696.202i	3.84766	−	3.34713i
$209$	−96.5778	+	290.877i	−0.462095	+	1.39176i
$210$	60.8618	−	6.93757i	0.289818	−	0.0330360i
$211$	35.1559	+	57.9934i	0.166616	+	0.274850i	0.927336	−	0.374230i	$-0.122093\pi$
$211$	35.1559	+	57.9934i	0.166616	+	0.274850i	−0.760720	+	0.649080i	$0.775154\pi$
$212$	−35.5561	+	13.5181i	−0.167717	+	0.0637646i
$213$	43.2487	−	27.4984i	0.203046	−	0.129100i
$214$	41.5223	−	28.3094i	0.194029	−	0.132287i
$215$	4.48189	−	29.7354i	0.0208460	−	0.138304i
$216$	393.168	−	461.838i	1.82022	−	2.13814i
$217$	229.912	−	43.8112i	1.05950	−	0.201895i
$218$	−21.0992	−	657.951i	−0.0967854	−	3.01812i
$219$	1.01294	−	1.59312i	0.00462529	−	0.00727453i
$220$	−93.0457	−	19.1548i	−0.422935	−	0.0870673i
$221$	−209.913	−	95.6175i	−0.949830	−	0.432658i
$222$	−497.906	−	58.7962i	−2.24282	−	0.264848i
$223$	−129.822	+	173.950i	−0.582161	+	0.780043i	−0.991186	−	0.132480i	$-0.957706\pi$
$223$	−129.822	+	173.950i	−0.582161	+	0.780043i	0.409024	+	0.912524i	$0.365869\pi$
$224$	−838.827	+	580.101i	−3.74476	+	2.58974i
$225$	−2.22014	+	69.2322i	−0.00986729	+	0.307698i
$226$	−321.299	−	219.058i	−1.42168	−	0.969283i
$227$	−214.923	+	231.632i	−0.946797	+	1.02040i	0.0529651	+	0.998596i	$0.483133\pi$
$227$	−214.923	+	231.632i	−0.946797	+	1.02040i	−0.999762	+	0.0218082i	$0.993058\pi$
$228$	867.967	−	308.930i	3.80687	−	1.35495i
$229$	197.471	+	187.192i	0.862317	+	0.817433i	0.984556	−	0.175067i	$-0.0560143\pi$
$229$	197.471	+	187.192i	0.862317	+	0.817433i	−0.122239	+	0.992501i	$0.539008\pi$
$230$	−11.7828	+	91.3851i	−0.0512296	+	0.397327i
$231$	−83.2876	+	299.558i	−0.360552	+	1.29679i
$232$	389.769	+	1059.13i	1.68004	+	4.56521i
$233$	−92.1072	−	336.546i	−0.395310	−	1.44440i	−0.836984	−	0.547228i	$-0.815683\pi$
$233$	−92.1072	−	336.546i	−0.395310	−	1.44440i	0.441674	−	0.897176i	$-0.354385\pi$
$234$	−154.262	+	84.7204i	−0.659239	+	0.362053i
$235$	−45.8355	−	10.9782i	−0.195045	−	0.0467159i
$236$	−592.439	−	325.367i	−2.51034	−	1.37867i
$237$	162.893	+	147.935i	0.687313	+	0.624200i
$238$	339.610	+	202.801i	1.42693	+	0.852105i
$239$	254.155	+	102.896i	1.06341	+	0.430527i	0.839092	−	0.543989i	$-0.183087\pi$
$239$	254.155	+	102.896i	1.06341	+	0.430527i	0.224318	+	0.974516i	$0.427985\pi$
$240$	65.9260	+	133.236i	0.274691	+	0.555149i
$241$	65.7502	+	152.925i	0.272823	+	0.634544i	0.998572	−	0.0534145i	$-0.0170104\pi$
$241$	65.7502	+	152.925i	0.272823	+	0.634544i	−0.725750	+	0.687959i	$0.758507\pi$
$242$	99.6099	−	149.509i	0.411611	−	0.617805i
$243$	−116.940	+	89.2359i	−0.481234	+	0.367226i
$244$	86.9117	−	69.3098i	0.356196	−	0.284056i
$245$	−29.8379	−	11.2554i	−0.121787	−	0.0459406i
$246$	−112.914	+	141.589i	−0.458999	+	0.575567i
$247$	378.641	+	8.09332i	1.53296	+	0.0327665i
$248$	485.951	+	821.298i	1.95948	+	3.31169i
$249$	56.4457	−	64.8866i	0.226689	−	0.260589i
$250$	114.277	+	53.5363i	0.457108	+	0.214145i
$251$	−185.574	−	129.448i	−0.739339	−	0.515731i	0.141039	−	0.990004i	$-0.454956\pi$
$251$	−185.574	−	129.448i	−0.739339	−	0.515731i	−0.880378	+	0.474273i	$0.842711\pi$
$252$	206.039	−	85.0129i	0.817613	−	0.337353i
$253$	−407.506	−	229.503i	−1.61070	−	0.907127i
$254$	81.8885	+	196.212i	0.322396	+	0.772489i
$255$	20.4234	−	25.0561i	0.0800916	−	0.0982592i
$256$	−940.958	−	671.432i	−3.67562	−	2.62278i
$257$	215.035	+	156.935i	0.836711	+	0.610642i	0.922641	−	0.385659i	$-0.126026\pi$
$257$	215.035	+	156.935i	0.836711	+	0.610642i	−0.0859307	+	0.996301i	$0.527386\pi$
$258$	−79.4460	−	616.167i	−0.307930	−	2.38825i
$259$	216.632	+	145.599i	0.836416	+	0.562157i
$260$	11.2718	+	116.844i	0.0433532	+	0.449401i
$261$	−15.4318	−	110.373i	−0.0591256	−	0.422886i
$262$	−109.041	+	1016.56i	−0.416188	+	3.87998i
$263$	−342.030	−	105.502i	−1.30049	−	0.401150i	−0.434260	−	0.900787i	$-0.642990\pi$
$263$	−342.030	−	105.502i	−1.30049	−	0.401150i	−0.866234	+	0.499638i	$0.833466\pi$
$264$	−1264.18	+	94.7371i	−4.78856	+	0.358853i
$265$	0.555851	−	2.11970i	0.00209755	−	0.00799887i
$266$	−643.787	−	85.6551i	−2.42025	−	0.322012i
$267$	18.8502	−	42.5828i	0.0705999	−	0.159486i
$268$	−324.186	−	327.669i	−1.20965	−	1.22264i
$269$	−310.087	+	258.317i	−1.15274	+	0.960286i	−0.999610	−	0.0279202i	$-0.991112\pi$
$269$	−310.087	+	258.317i	−1.15274	+	0.960286i	−0.153128	+	0.988206i	$0.548935\pi$
$270$	13.1612	+	52.4682i	0.0487453	+	0.194327i
$271$	16.7168	+	155.845i	0.0616857	+	0.575075i	0.982655	+	0.185441i	$0.0593713\pi$
$271$	16.7168	+	155.845i	0.0616857	+	0.575075i	−0.920970	+	0.389634i	$0.872602\pi$
$272$	−183.497	+	942.216i	−0.674620	+	3.46403i
$273$	384.051	−	10.7614i	1.40678	−	0.0394190i
$274$	239.819	−	459.687i	0.875250	−	1.67769i
$275$	−232.769	+	215.978i	−0.846432	+	0.785374i
$276$	209.533	+	1390.16i	0.759178	+	5.03681i
$277$	−253.838	−	157.612i	−0.916382	−	0.568995i	−0.0139861	−	0.999902i	$-0.504452\pi$
$277$	−253.838	−	157.612i	−0.916382	−	0.568995i	−0.902396	+	0.430907i	$0.858194\pi$
$278$	248.775	−	420.451i	0.894876	−	1.51241i
$279$	−29.6949	−	89.4362i	−0.106433	−	0.320560i
$280$	1.91514	−	130.013i	0.00683978	−	0.464331i
$281$	24.0018	−	248.804i	0.0854157	−	0.885423i	−0.848800	−	0.528714i	$-0.822674\pi$
$281$	24.0018	−	248.804i	0.0854157	−	0.885423i	0.934216	−	0.356709i	$-0.116101\pi$
$282$	−972.848	+	41.6075i	−3.44982	+	0.147544i
$283$	2.19584	−	12.7180i	0.00775915	−	0.0449398i	−0.981284	−	0.192565i	$-0.938319\pi$
$283$	2.19584	−	12.7180i	0.00775915	−	0.0449398i	0.989043	+	0.147625i	$0.0471629\pi$
$284$	−71.4492	−	152.514i	−0.251582	−	0.537019i
$285$	−14.5567	+	51.0396i	−0.0510762	+	0.179086i
$286$	−773.442	−	229.554i	−2.70434	−	0.802635i
$287$	85.9569	−	38.7354i	0.299501	−	0.134967i
$288$	276.074	+	303.988i	0.958590	+	1.05551i
$289$	−78.0553	+	18.6953i	−0.270087	+	0.0646897i
$290$	−97.0825	−	26.5699i	−0.334767	−	0.0916204i
$291$	55.4817	−	4.75447i	0.190659	−	0.0163384i
$292$	−4.76669	−	3.97088i	−0.0163243	−	0.0135989i
$293$	64.0362	−	132.973i	0.218554	−	0.453831i	−0.762649	−	0.646813i	$-0.776101\pi$
$293$	64.0362	−	132.973i	0.218554	−	0.453831i	0.981202	+	0.192982i	$0.0618157\pi$
$294$	−656.585	−	54.5474i	−2.23328	−	0.185535i
$295$	35.0817	−	16.8945i	0.118921	−	0.0572694i
$296$	−258.934	+	1032.26i	−0.874775	+	3.48736i
$297$	−271.922	−	38.0186i	−0.915562	−	0.128009i
$298$	276.776	+	11.8374i	0.928780	+	0.0397228i
$299$	−122.571	+	564.771i	−0.409937	+	1.88887i
$300$	942.265	+	152.338i	3.14088	+	0.507794i
$301$	−109.685	+	304.270i	−0.364402	+	1.01086i
$302$	−17.2304	−	24.7010i	−0.0570541	−	0.0817914i
$303$	294.052	−	50.7700i	0.970468	−	0.167558i
$304$	−334.274	−	1540.23i	−1.09958	−	5.06656i
$305$	0.341992	+	6.39485i	0.00112129	+	0.0209667i
$306$	62.9079	−	146.314i	0.205581	−	0.478152i
$307$	45.5965	+	70.0485i	0.148523	+	0.228171i	0.904548	−	0.426371i	$-0.140208\pi$
$307$	45.5965	+	70.0485i	0.148523	+	0.228171i	−0.756025	+	0.654542i	$0.772861\pi$
$308$	941.329	+	397.338i	3.05626	+	1.29006i
$309$	−139.280	+	378.470i	−0.450745	+	1.22482i
$310$	−84.7989	−	7.26679i	−0.273545	−	0.0234413i
$311$	−37.1307	−	36.7360i	−0.119391	−	0.118122i	0.641139	−	0.767425i	$-0.278462\pi$
$311$	−37.1307	−	36.7360i	−0.119391	−	0.118122i	−0.760530	+	0.649303i	$0.775061\pi$
$312$	572.312	+	1458.23i	1.83433	+	4.67380i
$313$	−77.0221	−	249.699i	−0.246077	−	0.797762i	−0.991378	−	0.131034i	$-0.958170\pi$
$313$	−77.0221	−	249.699i	−0.246077	−	0.797762i	0.745301	−	0.666728i	$-0.232306\pi$
$314$	−132.051	−	678.056i	−0.420546	−	2.15942i
$315$	−2.90781	+	12.5066i	−0.00923114	+	0.0397036i
$316$	550.609	−	468.740i	1.74243	−	1.48336i
$317$	174.774	−	108.519i	0.551336	−	0.342332i	−0.223290	−	0.974752i	$-0.571680\pi$
$317$	174.774	−	108.519i	0.551336	−	0.342332i	0.774626	+	0.632420i	$0.217938\pi$
$318$	−0.967480	−	45.2630i	−0.00304239	−	0.142337i
$319$	309.926	−	406.145i	0.971554	−	1.27318i
$320$	187.145	−	64.3645i	0.584827	−	0.201139i
$321$	11.2045	+	42.7274i	0.0349048	+	0.133107i
$322$	316.086	−	939.284i	0.981634	−	2.91703i
$323$	−274.665	+	204.988i	−0.850356	+	0.634637i
$324$	555.956	+	962.944i	1.71591	+	2.97205i
$325$	339.805	+	196.187i	1.04555	+	0.603651i
$326$	11.1372	+	94.3140i	0.0341633	+	0.289307i
$327$	551.054	+	176.448i	1.68518	+	0.539596i
$328$	267.432	+	276.145i	0.815341	+	0.841907i
$329$	460.474	+	212.004i	1.39962	+	0.644388i
$330$	58.6111	−	96.6852i	0.177610	−	0.292985i
$331$	23.1493	−	126.029i	0.0699374	−	0.380753i	−0.929976	−	0.367619i	$-0.880173\pi$
$331$	23.1493	−	126.029i	0.0699374	−	0.380753i	0.999914	−	0.0131341i	$-0.00418082\pi$
$332$	−187.761	−	211.237i	−0.565544	−	0.636257i
$333$	46.6077	−	94.1938i	0.139963	−	0.282864i
$334$	−392.372	−	20.9838i	−1.17477	−	0.0628257i
$335$	26.2135	−	4.23799i	0.0782491	−	0.0126507i
$336$	−415.824	−	1543.85i	−1.23757	−	4.59479i
$337$	133.286	+	449.084i	0.395507	+	1.33259i	0.887023	+	0.461726i	$0.152770\pi$
$337$	133.286	+	449.084i	0.395507	+	1.33259i	−0.491516	+	0.870869i	$0.663557\pi$
$338$	3.58979	+	335.931i	0.0106207	+	0.993878i
$339$	276.095	−	201.498i	0.814439	−	0.594388i
$340$	−73.0812	−	77.0939i	−0.214945	−	0.226747i
$341$	195.711	−	385.121i	0.573933	−	1.12939i
$342$			261.497i			0.764611i
$343$	291.135	+	181.354i	0.848791	+	0.528728i
$344$	−1318.75			−3.83359
$345$	−72.2013	−	36.6913i	−0.209279	−	0.106352i
$346$	−191.287	+	181.330i	−0.552853	+	0.524077i
$347$	122.924	+	168.433i	0.354249	+	0.485396i	0.947561	−	0.319576i	$-0.103541\pi$
$347$	122.924	+	168.433i	0.354249	+	0.485396i	−0.593312	+	0.804973i	$0.702180\pi$
$348$	−1535.63	+	16.4099i	−4.41274	+	0.0471550i
$349$	596.866	−	177.147i	1.71022	−	0.507584i	0.726480	−	0.687188i	$-0.241155\pi$
$349$	596.866	−	177.147i	1.71022	−	0.507584i	0.983739	+	0.179604i	$0.0574815\pi$
$350$	−541.901	−	398.854i	−1.54829	−	1.13958i
$351$	54.1490	+	334.930i	0.154271	+	0.954218i
$352$	−100.528	+	1879.75i	−0.285591	+	5.34020i
$353$	−31.2637	−	15.4695i	−0.0885658	−	0.0438230i	0.398662	−	0.917098i	$-0.369475\pi$
$353$	−31.2637	−	15.4695i	−0.0885658	−	0.0438230i	−0.487228	+	0.873275i	$0.661992\pi$
$354$	601.260	−	534.437i	1.69847	−	1.50971i
$355$	9.54276	+	1.75283i	0.0268810	+	0.00493755i
$356$	−130.866	−	79.3318i	−0.367601	−	0.222842i
$357$	−268.029	+	221.452i	−0.750783	+	0.620313i
$358$	−420.757	+	407.481i	−1.17530	+	1.13821i
$359$	−102.626	+	320.506i	−0.285867	+	0.892775i	0.698342	+	0.715764i	$0.253922\pi$
$359$	−102.626	+	320.506i	−0.285867	+	0.892775i	−0.984209	+	0.177011i	$0.943357\pi$
$360$	−51.9924	+	6.13962i	−0.144423	+	0.0170545i
$361$	100.860	−	174.696i	0.279392	−	0.483921i
$362$	401.377	−	231.735i	1.10878	−	0.640153i
$363$	94.4467	+	126.550i	0.260184	+	0.348623i
$364$	126.316	−	1256.23i	0.347023	−	3.45119i
$365$	0.345711	−	0.0906562i	0.000947155	−	0.000248373i
$366$	43.0298	+	125.112i	0.117568	+	0.341837i
$367$	−437.293	−	333.694i	−1.19153	−	0.909249i	−0.194110	−	0.980980i	$-0.562182\pi$
$367$	−437.293	−	333.694i	−1.19153	−	0.909249i	−0.997424	+	0.0717309i	$0.977148\pi$
$368$	2404.48	−	51.3949i	6.53391	−	0.139660i
$369$	−20.0246	−	32.2502i	−0.0542672	−	0.0873989i
$370$	−61.5267	−	72.2727i	−0.166288	−	0.195332i
$371$	−10.3122	+	21.1939i	−0.0277958	+	0.0571265i
$372$	−1274.63	+	248.233i	−3.42642	+	0.667294i
$373$	118.985	−	36.7020i	0.318995	−	0.0983968i	−0.131123	−	0.991366i	$-0.541858\pi$
$373$	118.985	−	36.7020i	0.318995	−	0.0983968i	0.450118	+	0.892969i	$0.351382\pi$
$374$	679.626	−	266.733i	1.81718	−	0.713191i
$375$	−78.0135	+	78.8516i	−0.208036	+	0.210271i
$376$	−176.478	+	2059.39i	−0.469356	+	5.47709i
$377$	−592.456	−	218.029i	−1.57150	−	0.578327i
$378$	−28.7210	−	581.103i	−0.0759816	−	1.53731i
$379$	−342.513	+	222.951i	−0.903729	+	0.588262i	−0.911315	−	0.411709i	$-0.864932\pi$
$379$	−342.513	+	222.951i	−0.903729	+	0.588262i	0.00758638	+	0.999971i	$0.497585\pi$
$380$	160.233	+	68.8922i	0.421666	+	0.181295i
$381$	−186.614	+	9.98001i	−0.489801	+	0.0261943i
$382$	−1275.35	+	276.786i	−3.33861	+	0.724572i
$383$	−93.0156	−	538.732i	−0.242861	−	1.40661i	−0.811658	−	0.584133i	$-0.801435\pi$
$383$	−93.0156	−	538.732i	−0.242861	−	1.40661i	0.568797	−	0.822478i	$-0.307409\pi$
$384$	1710.19	−	1192.95i	4.45362	−	3.10665i
$385$	−50.1311	+	30.8470i	−0.130211	+	0.0801220i
$386$	207.767	−	1285.11i	0.538255	−	3.32930i
$387$	127.265	+	27.6200i	0.328850	+	0.0713696i
$388$	7.81925	−	182.826i	0.0201527	−	0.471201i
$389$	20.5952	−	147.304i	0.0529439	−	0.378672i	−0.945628	−	0.325250i	$-0.894552\pi$
$389$	20.5952	−	147.304i	0.0529439	−	0.378672i	0.998572	−	0.0534226i	$-0.0170130\pi$
$390$	−135.513	−	33.9923i	−0.347469	−	0.0871596i
$391$	−226.913	−	471.190i	−0.580340	−	1.20509i
$392$	−293.061	+	1367.47i	−0.747605	+	3.48845i
$393$	−809.650	−	389.907i	−2.06018	−	0.992130i
$394$	408.872	−	490.815i	1.03775	−	1.24572i
$395$	3.55675	+	41.5050i	0.00900442	+	0.105076i
$396$	108.599	−	396.803i	0.274239	−	1.00203i
$397$	70.5275	+	294.461i	0.177651	+	0.741716i	0.987831	+	0.155534i	$0.0497098\pi$
$397$	70.5275	+	294.461i	0.177651	+	0.741716i	−0.810179	+	0.586182i	$0.800630\pi$
$398$	614.388	−	557.971i	1.54369	−	1.40194i
$399$	260.674	−	507.861i	0.653319	−	1.27284i
$400$	464.598	−	1565.38i	1.16150	−	3.91346i
$401$	313.826	+	89.5045i	0.782609	+	0.223203i	0.641839	−	0.766839i	$-0.278172\pi$
$401$	313.826	+	89.5045i	0.782609	+	0.223203i	0.140769	+	0.990042i	$0.455042\pi$
$402$	496.785	−	232.733i	1.23578	−	0.578937i
$403$	−526.031	−	90.8227i	−1.30529	−	0.225367i
$404$	−41.9014	−	979.719i	−0.103716	−	2.42505i
$405$	−63.7594	−	6.15079i	−0.157431	−	0.0151871i
$406$	968.351	+	484.031i	2.38510	+	1.19219i
$407$	457.223	−	151.809i	1.12340	−	0.372994i
$408$	−1220.03	−	721.877i	−2.99028	−	1.76931i
$409$	−45.8058	+	73.7716i	−0.111995	+	0.180371i	−0.900752	−	0.434335i	$-0.856984\pi$
$409$	−45.8058	+	73.7716i	−0.111995	+	0.180371i	0.788757	+	0.614705i	$0.210725\pi$
$410$	−33.9016	+	5.10985i	−0.0826869	+	0.0124630i
$411$	309.975	+	334.074i	0.754197	+	0.812831i
$412$	1174.99	+	612.992i	2.85192	+	1.48785i
$413$	−405.530	+	104.592i	−0.981913	+	0.253249i
$414$	−391.672	−	76.2782i	−0.946068	−	0.184247i
$415$	16.1885	−	1.73647i	0.0390085	−	0.00418426i
$416$	2256.21	−	565.952i	5.42358	−	1.36046i
$417$	274.845	+	329.926i	0.659100	+	0.791191i
$418$	−852.155	+	843.098i	−2.03865	+	2.01698i
$419$	63.4702	+	28.0964i	0.151480	+	0.0670558i	0.479133	−	0.877743i	$-0.340951\pi$
$419$	63.4702	+	28.0964i	0.151480	+	0.0670558i	−0.327652	+	0.944798i	$0.606257\pi$
$420$	165.801	+	61.7785i	0.394763	+	0.147092i
$421$	−348.862	−	91.4824i	−0.828651	−	0.217298i	−0.185118	−	0.982716i	$-0.559267\pi$
$421$	−348.862	−	91.4824i	−0.828651	−	0.217298i	−0.643533	+	0.765419i	$0.722532\pi$
$422$	19.8218	+	264.504i	0.0469711	+	0.626786i
$423$	60.1626	−	195.042i	0.142228	−	0.461093i
$424$	−95.5527	−	10.2495i	−0.225360	−	0.0241734i
$425$	−351.653	+	49.1662i	−0.827420	+	0.115685i
$426$	199.524	−	19.2478i	0.468366	−	0.0451827i
$427$	9.81327	−	68.1763i	0.0229819	−	0.159664i
$428$	143.967	−	18.5625i	0.336372	−	0.0433704i
$429$	418.047	−	572.814i	0.974469	−	1.33523i
$430$	68.3160	−	95.7395i	0.158874	−	0.222650i
$431$	399.158	+	325.356i	0.926121	+	0.754887i	0.969735	−	0.244162i	$-0.0785127\pi$
$431$	399.158	+	325.356i	0.926121	+	0.754887i	−0.0436131	+	0.999048i	$0.513887\pi$
$432$	1303.00	−	543.802i	3.01620	−	1.25880i
$433$	−58.4458	+	103.776i	−0.134979	+	0.239669i	−0.930528	−	0.366220i	$-0.880652\pi$
$433$	−58.4458	+	103.776i	−0.134979	+	0.239669i	0.795549	+	0.605889i	$0.207182\pi$
$434$	879.285	+	254.625i	2.02600	+	0.586693i
$435$	50.6154	−	72.5610i	0.116357	−	0.166807i
$436$	806.656	−	1721.87i	1.85013	−	3.94924i
$437$	647.855	+	563.577i	1.48251	+	1.28965i
$438$	6.35477	−	3.76003i	0.0145086	−	0.00858455i
$439$	−13.0417	+	610.148i	−0.0297077	+	1.38986i	0.703907	+	0.710292i	$0.251437\pi$
$439$	−13.0417	+	610.148i	−0.0297077	+	1.38986i	−0.733615	+	0.679566i	$0.762168\pi$
$440$	−187.637	−	149.636i	−0.426448	−	0.340081i
$441$	56.9219	−	125.828i	0.129075	−	0.285325i
$442$	−562.494	−	705.345i	−1.27261	−	1.59580i
$443$	−298.392	−	391.030i	−0.673571	−	0.882687i	0.324429	−	0.945910i	$-0.394828\pi$
$443$	−298.392	−	391.030i	−0.673571	−	0.882687i	−0.997999	+	0.0632234i	$0.979862\pi$
$444$	−1205.19	−	802.957i	−2.71440	−	1.80846i
$445$	8.09917	−	3.48224i	0.0182004	−	0.00782526i
$446$	−760.885	+	376.491i	−1.70602	+	0.844151i
$447$	−91.3774	+	225.704i	−0.204424	+	0.504930i
$448$	−2109.25	+	286.213i	−4.70815	+	0.638869i
$449$	109.181	−	120.221i	0.243166	−	0.267752i	−0.606489	−	0.795092i	$-0.707423\pi$
$449$	109.181	−	120.221i	0.243166	−	0.267752i	0.849655	+	0.527339i	$0.176810\pi$
$450$	−130.415	+	237.464i	−0.289810	+	0.527697i
$451$	40.5338	−	169.234i	0.0898755	−	0.375241i
$452$	−540.704	−	984.534i	−1.19625	−	2.17817i
$453$	25.5327	−	6.98790i	0.0563637	−	0.0154258i
$454$	−1159.82	+	426.825i	−2.55467	+	0.940144i
$455$	54.6829	+	47.9592i	0.120182	+	0.105405i
$456$	2308.45	+	297.641i	5.06238	+	0.652722i
$457$	−161.132	+	169.979i	−0.352585	+	0.371945i	−0.877802	−	0.479023i	$-0.840991\pi$
$457$	−161.132	+	169.979i	−0.352585	+	0.371945i	0.525217	+	0.850968i	$0.323984\pi$
$458$	356.849	+	1002.60i	0.779146	+	2.18908i
$459$	−225.067	−	208.831i	−0.490342	−	0.454971i
$460$	−149.927	+	219.902i	−0.325928	+	0.478049i
$461$	−73.3034	−	2.35070i	−0.159010	−	0.00509913i	−0.0475548	−	0.998869i	$-0.515143\pi$
$461$	−73.3034	−	2.35070i	−0.159010	−	0.00509913i	−0.111455	+	0.993770i	$0.535551\pi$
$462$	−821.197	+	896.915i	−1.77748	+	1.94137i
$463$	−441.084	−	329.190i	−0.952665	−	0.710993i	0.00466480	−	0.999989i	$-0.498515\pi$
$463$	−441.084	−	329.190i	−0.952665	−	0.710993i	−0.957330	+	0.288996i	$0.906678\pi$
$464$	−308.095	+	2609.05i	−0.663998	+	5.62296i
$465$	31.0105	−	68.0785i	0.0666893	−	0.146405i
$466$	275.173	−	1336.67i	0.590500	−	2.86839i
$467$	174.380	+	110.874i	0.373405	+	0.237418i	0.709954	−	0.704248i	$-0.248716\pi$
$467$	174.380	+	110.874i	0.373405	+	0.237418i	−0.336549	+	0.941666i	$0.609260\pi$
$468$	−508.096	+	16.2937i	−1.08568	+	0.0348155i
$469$	−285.417	−	10.3082i	−0.608566	−	0.0219792i
$470$	−140.366	−	119.495i	−0.298651	−	0.254245i
$471$	600.404	+	90.4964i	1.27474	+	0.192137i
$472$	−961.917	−	1410.87i	−2.03796	−	2.98914i
$473$	320.310	+	503.775i	0.677188	+	1.06506i
$474$	305.845	+	804.451i	0.645242	+	1.69716i
$475$	498.545	−	302.221i	1.04957	−	0.636254i
$476$	609.128	+	966.632i	1.27968	+	2.03074i
$477$	9.00654	+	2.99038i	0.0188816	+	0.00626914i
$478$	703.861	+	809.117i	1.47251	+	1.69271i
$479$	−4.28503	−	15.0244i	−0.00894579	−	0.0313663i	0.957053	−	0.289914i	$-0.0936268\pi$
$479$	−4.28503	−	15.0244i	−0.00894579	−	0.0313663i	−0.965998	+	0.258548i	$0.916756\pi$
$480$	−3.48326	+	325.962i	−0.00725679	+	0.679087i
$481$	−345.787	−	484.593i	−0.718892	−	1.00747i
$482$	−41.7135	+	649.721i	−0.0865424	+	1.34797i
$483$	684.640	+	538.582i	1.41747	+	1.11508i
$484$	452.146	−	254.644i	0.934186	−	0.526124i
$485$	8.31177	+	6.48434i	0.0171377	+	0.0133698i
$486$	−565.863	+	103.939i	−1.16433	+	0.213865i
$487$	473.791	+	180.131i	0.972877	+	0.369878i	0.789898	−	0.613238i	$-0.210133\pi$
$487$	473.791	+	180.131i	0.972877	+	0.369878i	0.182979	+	0.983117i	$0.441426\pi$
$488$	275.073	−	56.6279i	0.563675	−	0.116041i
$489$	−81.3820	−	18.5749i	−0.166425	−	0.0379855i
$490$	−84.0947	−	92.1156i	−0.171622	−	0.187991i
$491$	185.783	+	813.968i	0.378377	+	1.65778i	0.702441	+	0.711742i	$0.252093\pi$
$491$	185.783	+	813.968i	0.378377	+	1.65778i	−0.324065	+	0.946035i	$0.605050\pi$
$492$	−476.041	+	216.842i	−0.967562	+	0.440735i
$493$	544.077	−	174.214i	1.10361	−	0.353375i
$494$	1305.90	+	699.140i	2.64352	+	1.41526i
$495$	14.9737	+	18.3703i	0.0302500	+	0.0371117i
$496$	142.331	+	2216.92i	0.286958	+	4.46960i
$497$	−96.9869	−	38.5179i	−0.195145	−	0.0775007i
$498$	311.787	−	126.229i	0.626079	−	0.253471i
$499$	−84.2636	−	74.8987i	−0.168865	−	0.150098i	0.575667	−	0.817684i	$-0.304742\pi$
$499$	−84.2636	−	74.8987i	−0.168865	−	0.150098i	−0.744532	+	0.667587i	$0.767327\pi$
$500$	224.212	+	287.400i	0.448424	+	0.574801i
$501$	133.021	−	318.730i	0.265511	−	0.636188i
$502$	−417.685	−	780.180i	−0.832042	−	1.55414i
$503$	533.868	−	551.262i	1.06137	−	1.09595i	0.0661948	−	0.997807i	$-0.478914\pi$
$503$	533.868	−	551.262i	1.06137	−	1.09595i	0.995172	−	0.0981421i	$-0.0312900\pi$
$504$	561.348	+	44.3506i	1.11379	+	0.0879971i
$505$	47.3449	+	30.8181i	0.0937523	+	0.0610260i
$506$	−1014.23	−	1522.29i	−2.00440	−	3.00849i
$507$	−279.235	−	96.0372i	−0.550760	−	0.189422i
$508$	−45.8941	+	612.414i	−0.0903427	+	1.20554i
$509$	90.2692	+	35.4281i	0.177346	+	0.0696033i	0.452353	−	0.891839i	$-0.350585\pi$
$509$	90.2692	+	35.4281i	0.177346	+	0.0696033i	−0.275007	+	0.961442i	$0.588680\pi$
$510$	115.609	−	51.1767i	0.226685	−	0.100347i
$511$	−3.83714	+	0.230776i	−0.00750907	+	0.000451617i
$512$	−969.008	−	1857.41i	−1.89259	−	3.62775i
$513$	474.923	+	169.036i	0.925775	+	0.329505i
$514$	471.704	+	928.222i	0.917712	+	1.80588i
$515$	−68.0628	+	34.5881i	−0.132161	+	0.0671614i
$516$	601.732	−	1690.62i	1.16615	−	3.27640i
$517$	829.567	−	432.785i	1.60458	−	0.837108i
$518$	497.359	+	891.524i	0.960153	+	1.72109i
$519$	−93.7774	−	211.845i	−0.180689	−	0.408179i
$520$	−108.346	+	276.062i	−0.208358	+	0.530888i
$521$	462.832	+	34.6845i	0.888354	+	0.0665729i	0.511084	−	0.859531i	$-0.329244\pi$
$521$	462.832	+	34.6845i	0.888354	+	0.0665729i	0.377270	+	0.926103i	$0.376863\pi$
$522$	141.765	−	412.192i	0.271580	−	0.789640i
$523$	−342.748	+	228.355i	−0.655349	+	0.436625i	−0.837346	−	0.546674i	$-0.815894\pi$
$523$	−342.748	+	228.355i	−0.655349	+	0.436625i	0.181997	+	0.983299i	$0.441744\pi$
$524$	−1611.04	+	2474.99i	−3.07450	+	4.72326i
$525$	489.999	−	331.181i	0.933331	−	0.630821i
$526$	−1005.64	−	973.912i	−1.91187	−	1.85154i
$527$	425.877	−	228.002i	0.808115	−	0.432641i
$528$	−2723.45	−	1136.62i	−5.15804	−	2.15269i
$529$	−616.019	+	480.580i	−1.16450	+	0.908469i
$530$	5.69406	−	6.40602i	0.0107435	−	0.0120868i
$531$	63.2793	+	156.301i	0.119170	+	0.294353i
$532$	−1545.70	−	1063.02i	−2.90544	−	1.99816i
$533$	−214.593	+	13.7773i	−0.402614	+	0.0258487i
$534$	141.180	−	115.076i	0.264381	−	0.215499i
$535$	−3.94692	+	7.37232i	−0.00737742	+	0.0137800i
$536$	−355.113	−	1109.03i	−0.662524	−	2.06909i
$537$	−213.415	−	468.518i	−0.397421	−	0.872473i
$538$	−1538.92	+	351.249i	−2.86045	+	0.652878i
$539$	593.567	−	220.191i	1.10124	−	0.408518i
$540$	−34.7685	+	152.331i	−0.0643861	+	0.282094i
$541$	−135.945	−	660.363i	−0.251285	−	1.22063i	−0.891708	−	0.452611i	$-0.850493\pi$
$541$	−135.945	−	660.363i	−0.251285	−	1.22063i	0.640423	−	0.768022i	$-0.278759\pi$
$542$	−217.857	+	573.020i	−0.401949	+	1.05723i
$543$	73.5961	+	400.672i	0.135536	+	0.737886i
$544$	−1294.78	+	1659.67i	−2.38010	+	3.05087i
$545$	53.7529	+	95.4438i	0.0986292	+	0.175126i
$546$	1358.17	+	642.982i	2.48749	+	1.17762i
$547$	−618.338	−	39.6986i	−1.13042	−	0.0725752i	−0.512405	−	0.858744i	$-0.671245\pi$
$547$	−618.338	−	39.6986i	−1.13042	−	0.0725752i	−0.618012	+	0.786169i	$0.712062\pi$
$548$	1219.09	−	869.893i	2.22461	−	1.58740i
$549$	−27.7317	−	0.296343i	−0.0505131	−	0.000539787i
$550$	−1194.31	+	340.622i	−2.17147	+	0.619312i
$551$	−707.698	+	615.635i	−1.28439	+	1.11730i
$552$	−1119.18	+	3370.79i	−2.02750	+	6.10650i
$553$	49.5871	−	445.297i	0.0896693	−	0.805238i
$554$	−605.804	−	999.337i	−1.09351	−	1.80386i
$555$	77.9815	−	29.6478i	0.140507	−	0.0534195i
$556$	1190.81	−	757.138i	2.14174	−	1.36176i
$557$	292.510	−	199.430i	0.525153	−	0.358043i	−0.271541	−	0.962427i	$-0.587533\pi$
$557$	292.510	−	199.430i	0.525153	−	0.358043i	0.796693	+	0.604384i	$0.206581\pi$
$558$	54.9337	−	364.462i	0.0984476	−	0.653157i
$559$	478.188	−	561.707i	0.855435	−	1.00484i
$560$	141.088	−	267.794i	0.251944	−	0.478203i
$561$	20.5684	+	641.399i	0.0366638	+	1.14331i
$562$	524.548	−	824.996i	0.933360	−	1.46797i
$563$	189.229	+	38.9554i	0.336107	+	0.0691926i	0.366700	−	0.930339i	$-0.380488\pi$
$563$	189.229	+	38.9554i	0.336107	+	0.0691926i	−0.0305923	+	0.999532i	$0.509739\pi$
$564$	−2559.58	−	1165.92i	−4.53826	−	2.06723i
$565$	64.2614	+	7.58844i	0.113737	+	0.0134309i
$566$	30.1915	−	40.4539i	0.0533420	−	0.0714734i
$567$	659.683	+	198.696i	1.16346	+	0.350435i
$568$	13.6377	−	425.273i	0.0240100	−	0.748720i
$569$	79.1579	+	53.9690i	0.139118	+	0.0948488i	0.630879	−	0.775881i	$-0.282694\pi$
$569$	79.1579	+	53.9690i	0.139118	+	0.0948488i	−0.491761	+	0.870730i	$0.663647\pi$
$570$	−141.194	+	152.171i	−0.247709	+	0.266966i
$571$	106.425	−	37.8791i	0.186383	−	0.0663381i	−0.240481	−	0.970654i	$-0.577305\pi$
$571$	106.425	−	37.8791i	0.186383	−	0.0663381i	0.426864	+	0.904316i	$0.359618\pi$
$572$	−1691.26	−	1603.23i	−2.95675	−	2.80285i
$573$	146.686	−	1137.67i	0.255997	−	1.98546i
$574$	368.349	+	17.2463i	0.641723	+	0.0300458i
$575$	307.244	+	834.881i	0.534337	+	1.45197i
$576$	226.240	+	826.647i	0.392778	+	1.43515i
$577$	391.589	−	215.060i	0.678664	−	0.372721i	−0.104510	−	0.994524i	$-0.533327\pi$
$577$	391.589	−	215.060i	0.678664	−	0.372721i	0.783174	+	0.621803i	$0.213599\pi$
$578$	−305.288	−	73.1208i	−0.528181	−	0.126507i
$579$	1002.94	+	550.811i	1.73219	+	0.951314i
$580$	−215.223	−	195.460i	−0.371074	−	0.337000i
$581$	−174.415	−	15.6571i	−0.300198	−	0.0269485i
$582$	201.877	+	81.7311i	0.346868	+	0.140431i
$583$	19.2932	+	38.9915i	0.0330931	+	0.0668807i
$584$	−6.19087	−	14.3990i	−0.0106008	−	0.0246559i
$585$	16.2377	−	24.3718i	0.0277567	−	0.0416612i
$586$	458.897	−	350.180i	0.783100	−	0.597577i
$587$	−411.452	+	328.122i	−0.700941	+	0.558982i	−0.907807	−	0.419387i	$-0.862245\pi$
$587$	−411.452	+	328.122i	−0.700941	+	0.558982i	0.206866	+	0.978369i	$0.433673\pi$
$588$	−1619.36	−	999.662i	−2.75401	−	1.70011i
$589$	−494.522	+	620.111i	−0.839595	+	1.05282i
$590$	152.258	+	3.25446i	0.258064	+	0.00551603i
$591$	285.925	+	483.238i	0.483799	+	0.817661i
$592$	−1626.00	+	1869.15i	−2.74662	+	3.15736i
$593$	843.468	+	395.146i	1.42237	+	0.666351i	0.973802	−	0.227396i	$-0.0730211\pi$
$593$	843.468	+	395.146i	1.42237	+	0.666351i	0.448572	+	0.893747i	$0.351933\pi$
$594$	−880.768	−	614.385i	−1.48277	−	1.03432i
$595$	−65.7116	−	3.78074i	−0.110440	−	0.00635419i
$596$	697.222	+	392.668i	1.16984	+	0.658840i
$597$	280.964	+	673.214i	0.470626	+	1.12766i
$598$	−1428.10	+	1752.05i	−2.38813	+	2.92985i
$599$	−69.0621	−	49.2801i	−0.115296	−	0.0822706i	0.521742	−	0.853104i	$-0.325282\pi$
$599$	−69.0621	−	49.2801i	−0.115296	−	0.0822706i	−0.637037	+	0.770833i	$0.719840\pi$
$600$	1947.84	+	1421.56i	3.24641	+	2.36927i
$601$	−83.4219	−	647.004i	−0.138805	−	1.07655i	−0.902415	−	0.430868i	$-0.858208\pi$
$601$	−83.4219	−	647.004i	−0.138805	−	1.07655i	0.763610	−	0.645678i	$-0.223425\pi$
$602$	−921.588	+	866.571i	−1.53088	+	1.43949i
$603$	11.0421	+	114.463i	0.0183120	+	0.189823i
$604$	−12.0455	−	86.1537i	−0.0199429	−	0.142639i
$605$	−3.18832	+	29.7237i	−0.00526996	+	0.0491300i
$606$	1115.25	+	344.011i	1.84035	+	0.567674i
$607$	495.195	−	37.1097i	0.815807	−	0.0611363i	0.339711	−	0.940530i	$-0.389671\pi$
$607$	495.195	−	37.1097i	0.815807	−	0.0611363i	0.476096	+	0.879393i	$0.342052\pi$
$608$	876.675	−	3343.14i	1.44190	−	5.49859i
$609$	−686.221	+	659.211i	−1.12680	+	1.08245i
$610$	−10.1387	+	22.9034i	−0.0166208	+	0.0375466i
$611$	−813.178	−	821.915i	−1.33090	−	1.34520i
$612$	353.456	−	294.446i	0.577543	−	0.481121i
$613$	−137.761	−	549.196i	−0.224733	−	0.895915i	−0.972679	−	0.232155i	$-0.925422\pi$
$613$	−137.761	−	549.196i	−0.224733	−	0.895915i	0.747946	−	0.663760i	$-0.231040\pi$
$614$	34.8653	+	325.037i	0.0567838	+	0.529376i
$615$	5.76056	−	29.5793i	0.00936677	−	0.0480964i
$616$	1665.33	+	1972.29i	2.70345	+	3.20177i
$617$	−230.627	+	442.069i	−0.373787	+	0.716481i	−0.997894	−	0.0648583i	$-0.979340\pi$
$617$	−230.627	+	442.069i	−0.373787	+	0.716481i	0.624107	+	0.781339i	$0.285463\pi$
$618$	−1156.26	+	1072.85i	−1.87096	+	1.73600i
$619$	−147.964	−	981.678i	−0.239038	−	1.58591i	−0.710288	−	0.703911i	$-0.751435\pi$
$619$	−147.964	−	981.678i	−0.239038	−	1.58591i	0.471251	−	0.881999i	$-0.343803\pi$
$620$	−208.852	−	129.679i	−0.336858	−	0.209160i
$621$	−391.718	+	662.035i	−0.630785	+	1.06608i
$622$	−64.3736	−	193.883i	−0.103495	−	0.311709i
$623$	−92.7455	+	19.7360i	−0.148869	+	0.0316790i
$624$	−350.163	+	3629.81i	−0.561159	+	5.81700i
$625$	592.870	−	25.3563i	0.948592	−	0.0405701i
$626$	173.887	−	1007.12i	0.277774	−	1.60883i
$627$	−446.994	−	954.141i	−0.712908	−	1.52176i
$628$	547.258	−	1918.83i	0.871430	−	3.05546i
$629$	516.456	+	153.282i	0.821075	+	0.243691i
$630$	−32.2996	+	38.4555i	−0.0512692	+	0.0610405i
$631$	584.343	+	643.427i	0.926059	+	1.01969i	0.999749	+	0.0224124i	$0.00713469\pi$
$631$	584.343	+	643.427i	0.926059	+	1.01969i	−0.0736901	+	0.997281i	$0.523478\pi$
$632$	1776.59	−	425.519i	2.81107	−	0.673289i
$633$	−224.872	−	61.5439i	−0.355248	−	0.0972257i
$634$	801.685	−	68.6999i	1.26449	−	0.108359i
$635$	−27.1828	−	22.6446i	−0.0428075	−	0.0356607i
$636$	56.7394	−	117.820i	0.0892128	−	0.185252i
$637$	−476.192	−	620.680i	−0.747555	−	0.974379i
$638$	1800.30	−	866.979i	2.82179	−	1.35890i
$639$	−10.2230	+	40.7548i	−0.0159985	+	0.0637791i
$640$	390.946	+	54.6599i	0.610853	+	0.0854060i
$641$	−741.987	−	31.7339i	−1.15755	−	0.0495069i	−0.543943	−	0.839122i	$-0.683069\pi$
$641$	−741.987	−	31.7339i	−1.15755	−	0.0495069i	−0.613603	+	0.789615i	$0.710280\pi$
$642$	−36.6419	+	168.835i	−0.0570746	+	0.262982i
$643$	−607.197	−	98.1669i	−0.944319	−	0.152670i	−0.331998	−	0.943280i	$-0.607723\pi$
$643$	−607.197	−	98.1669i	−0.944319	−	0.152670i	−0.612320	+	0.790610i	$0.709764\pi$
$644$	2043.07	−	2005.07i	3.17248	−	3.11347i
$645$	59.1449	+	84.7886i	0.0916975	+	0.131455i
$646$	−1320.92	+	228.065i	−2.04476	+	0.353042i
$647$	54.6781	+	251.940i	0.0845102	+	0.389398i	0.999914	−	0.0131400i	$-0.00418270\pi$
$647$	54.6781	+	251.940i	0.0845102	+	0.389398i	−0.915403	+	0.402538i	$0.868128\pi$
$648$	150.014	+	2805.09i	0.231504	+	4.32885i
$649$	−305.327	+	710.146i	−0.470458	+	1.09422i
$650$	837.201	+	1286.17i	1.28800	+	1.97872i
$651$	−470.003	+	653.071i	−0.721971	+	1.00318i
$652$	−94.7393	+	257.437i	−0.145306	+	0.394842i
$653$	77.7856	+	6.66579i	0.119120	+	0.0102079i	0.144789	−	0.989463i	$-0.453750\pi$
$653$	77.7856	+	6.66579i	0.119120	+	0.0102079i	−0.0256686	+	0.999671i	$0.508171\pi$
$654$	1608.76	+	1591.66i	2.45987	+	2.43373i
$655$	−62.1537	−	158.365i	−0.0948912	−	0.241779i
$656$	263.769	+	855.120i	0.402088	+	1.30354i
$657$	0.295869	+	1.51922i	0.000450333	+	0.00231237i
$658$	1229.92	+	1555.13i	1.86918	+	2.36342i
$659$	−701.997	+	597.619i	−1.06525	+	0.906857i	−0.995875	−	0.0907339i	$-0.971079\pi$
$659$	−701.997	+	597.619i	−1.06525	+	0.906857i	−0.0693707	+	0.997591i	$0.522099\pi$
$660$	277.448	−	172.271i	0.420375	−	0.261017i
$661$	8.39699	+	392.848i	0.0127035	+	0.594324i	0.960940	+	0.276758i	$0.0892600\pi$
$661$	8.39699	+	392.848i	0.0127035	+	0.594324i	−0.948236	+	0.317566i	$0.897135\pi$
$662$	304.030	−	398.419i	0.459260	−	0.601841i
$663$	749.867	−	257.901i	1.13102	−	0.388991i
$664$	−181.111	−	690.655i	−0.272758	−	1.04014i
$665$	101.571	−	36.9133i	0.152738	−	0.0555087i
$666$	329.415	−	245.848i	0.494616	−	0.369142i
$667$	−715.668	−	1239.57i	−1.07297	−	1.85843i
$668$	−982.917	−	567.488i	−1.47143	−	0.849532i
$669$	−87.5069	−	741.038i	−0.130802	−	1.10768i
$670$	98.9100	+	31.6711i	0.147627	+	0.0472702i
$671$	−88.4445	−	91.3262i	−0.131810	−	0.136105i
$672$	720.843	−	3431.23i	1.07268	−	5.10600i
$673$	561.857	−	926.842i	0.834854	−	1.37718i	−0.0896364	−	0.995975i	$-0.528570\pi$
$673$	561.857	−	926.842i	0.834854	−	1.37718i	0.924491	−	0.381205i	$-0.124491\pi$
$674$	−331.000	+	1802.03i	−0.491098	+	2.67364i
$675$	346.972	+	390.356i	0.514032	+	0.578304i
$676$	−430.351	+	869.736i	−0.636615	+	1.28659i
$677$	−1220.80	−	65.2875i	−1.80325	−	0.0964364i	−0.878669	−	0.477431i	$-0.841568\pi$
$677$	−1220.80	−	65.2875i	−1.80325	−	0.0964364i	−0.924577	+	0.380995i	$0.875582\pi$
$678$	1319.72	−	213.362i	1.94649	−	0.314693i
$679$	−74.0713	−	85.8466i	−0.109089	−	0.126431i
$680$	−76.3588	−	257.278i	−0.112292	−	0.378350i
$681$	−11.6075	−	1086.22i	−0.0170448	−	1.59504i
$682$	1364.80	−	996.052i	2.00118	−	1.46049i
$683$	−8.17494	−	8.62381i	−0.0119692	−	0.0126264i	0.719730	−	0.694254i	$-0.244266\pi$
$683$	−8.17494	−	8.62381i	−0.0119692	−	0.0126264i	−0.731699	+	0.681628i	$0.761272\pi$
$684$	−342.192	+	673.368i	−0.500281	+	0.984456i
$685$			86.2757i			0.125950i
$686$	693.783	+	1148.21i	1.01135	+	1.67377i
$687$	−935.407			−1.36158
$688$	−2736.79	−	1390.78i	−3.97789	−	2.02149i
$689$	39.0137	−	36.9830i	0.0566236	−	0.0536763i
$690$	−186.737	−	255.869i	−0.270633	−	0.370825i
$691$	−93.6438	+	1.00069i	−0.135519	+	0.00144817i	−0.0784206	−	0.996920i	$-0.524988\pi$
$691$	−93.6438	+	1.00069i	−0.135519	+	0.00144817i	−0.0570987	+	0.998369i	$0.518185\pi$
$692$	−729.861	+	216.619i	−1.05471	+	0.313033i
$693$	−119.403	−	225.212i	−0.172298	−	0.324981i
$694$	130.162	+	805.099i	0.187554	+	1.16009i
$695$	−4.34127	+	81.1766i	−0.00624643	+	0.116801i
$696$	−3477.39	−	1720.64i	−4.99625	−	2.47218i
$697$	145.443	−	129.279i	0.208670	−	0.185479i
$698$	2395.03	+	439.924i	3.43128	+	0.630263i
$699$	1025.77	+	621.825i	1.46748	+	0.889593i
$700$	−873.484	−	1736.19i	−1.24783	−	2.48028i
$701$	−130.288	+	126.177i	−0.185861	+	0.179996i	−0.782767	−	0.622315i	$-0.786192\pi$
$701$	−130.288	+	126.177i	−0.185861	+	0.179996i	0.596906	+	0.802311i	$0.296396\pi$
$702$	−404.662	+	1263.78i	−0.576442	+	1.80025i
$703$	−878.426	+	103.731i	−1.24954	+	0.147554i
$704$	−1964.42	+	3402.47i	−2.79037	+	4.83305i
$705$	140.322	−	81.0150i	0.199038	−	0.114915i
$706$	−81.5992	−	109.336i	−0.115580	−	0.154866i
$707$	−434.758	−	424.460i	−0.614934	−	0.600368i
$708$	2247.63	−	589.399i	3.17462	−	0.832484i
$709$	336.045	+	977.075i	0.473970	+	1.37810i	0.884621	+	0.466310i	$0.154417\pi$
$709$	336.045	+	977.075i	0.473970	+	1.37810i	−0.410652	+	0.911792i	$0.634699\pi$
$710$	30.1677	+	23.0207i	0.0424897	+	0.0324235i
$711$	−180.360	+	3.85513i	−0.253671	+	0.00542213i
$712$	−203.943	−	328.455i	−0.286436	−	0.461314i
$713$	−784.555	−	921.583i	−1.10036	−	1.29254i
$714$	−1326.95	+	297.229i	−1.85848	+	0.416287i
$715$	131.774	−	25.6630i	0.184299	−	0.0358923i
$716$	−1616.70	+	498.684i	−2.25795	+	0.696487i
$717$	−877.464	+	344.379i	−1.22380	+	0.480306i
$718$	−925.746	+	935.691i	−1.28934	+	1.30319i
$719$	107.378	−	1253.03i	0.149343	−	1.74274i	−0.408469	−	0.912772i	$-0.633937\pi$
$719$	107.378	−	1253.03i	0.149343	−	1.74274i	0.557812	−	0.829968i	$-0.311641\pi$
$720$	−114.374	−	42.0907i	−0.158853	−	0.0584593i
$721$	790.577	−	222.023i	1.09650	−	0.307938i
$722$	661.224	−	430.409i	0.915823	−	0.596135i
$723$	−525.726	−	226.036i	−0.727145	−	0.312636i
$724$	1336.81	−	71.4919i	1.84643	−	0.0987457i
$725$	−949.687	+	206.109i	−1.30991	+	0.284288i
$726$	105.080	+	608.604i	0.144738	+	0.838298i
$727$	−487.823	+	340.284i	−0.671009	+	0.468067i	−0.857564	−	0.514378i	$-0.828023\pi$
$727$	−487.823	+	340.284i	−0.671009	+	0.468067i	0.186555	+	0.982445i	$0.440268\pi$
$728$	1722.31	−	2684.76i	2.36580	−	3.68786i
$729$	−60.6650	+	375.234i	−0.0832167	+	0.514725i
$730$	1.36606	+	0.296473i	0.00187131	+	0.000406127i
$731$	−28.5247	+	666.950i	−0.0390214	+	0.912380i
$732$	−52.9168	+	378.479i	−0.0722908	+	0.517048i
$733$	421.856	+	105.819i	0.575520	+	0.144365i	0.520110	−	0.854099i	$-0.325891\pi$
$733$	421.856	+	105.819i	0.575520	+	0.144365i	0.0554100	+	0.998464i	$0.482353\pi$
$734$	−933.468	−	1938.37i	−1.27175	−	2.64083i
$735$	101.064	−	42.4876i	0.137503	−	0.0578063i
$736$	4751.66	+	2288.28i	6.45606	+	3.10907i
$737$	−337.407	+	405.027i	−0.457811	+	0.549562i
$738$	−12.6769	−	147.931i	−0.0171774	−	0.200449i
$739$	−304.583	+	1112.90i	−0.412156	+	1.50596i	0.396700	+	0.917948i	$0.370155\pi$
$739$	−304.583	+	1112.90i	−0.412156	+	1.50596i	−0.808856	+	0.588007i	$0.799913\pi$
$740$	−63.8589	−	266.619i	−0.0862958	−	0.360296i
$741$	−963.834	+	875.329i	−1.30072	+	1.18128i
$742$	−73.5105	+	55.6263i	−0.0990707	+	0.0749681i
$743$	194.138	−	654.116i	0.261290	−	0.880371i	−0.720989	−	0.692946i	$-0.756312\pi$
$743$	194.138	−	654.116i	0.261290	−	0.880371i	0.982279	−	0.187425i	$-0.0600142\pi$
$744$	−3154.87	−	899.782i	−4.24042	−	1.20938i
$745$	−41.7440	+	19.5561i	−0.0560322	+	0.0262498i
$746$	479.908	+	82.8593i	0.643308	+	0.111071i
$747$	3.01281	+	70.4441i	0.00403321	+	0.0943027i
$748$	2099.11	+	202.499i	2.80630	+	0.270721i
$749$	57.1080	−	69.4864i	0.0762456	−	0.0927722i
$750$	−411.734	+	136.705i	−0.548979	+	0.182274i
$751$	805.518	+	476.614i	1.07259	+	0.634639i	0.934566	−	0.355789i	$-0.115788\pi$
$751$	805.518	+	476.614i	1.07259	+	0.634639i	0.138027	+	0.990428i	$0.455924\pi$
$752$	−2538.11	+	4087.70i	−3.37515	+	5.43577i
$753$	769.156	−	115.932i	1.02146	−	0.153960i
$754$	−1679.44	−	1810.00i	−2.22737	−	2.40053i
$755$	4.44315	+	2.31799i	0.00588496	+	0.00307018i
$756$	686.467	−	1533.95i	0.908025	−	2.02904i
$757$	682.257	+	132.869i	0.901264	+	0.175521i	0.620454	−	0.784243i	$-0.286948\pi$
$757$	682.257	+	132.869i	0.901264	+	0.175521i	0.280809	+	0.959764i	$0.409397\pi$
$758$	−1589.32	+	170.479i	−2.09673	+	0.224907i
$759$	1559.51	−	391.189i	2.05469	−	0.515401i
$760$	282.032	+	338.555i	0.371095	+	0.445467i
$761$	−41.9572	+	41.5112i	−0.0551343	+	0.0545483i	−0.730357	−	0.683066i	$-0.760646\pi$
$761$	−41.9572	+	41.5112i	−0.0551343	+	0.0545483i	0.675223	+	0.737614i	$0.264048\pi$
$762$	−668.368	−	295.867i	−0.877123	−	0.388276i
$763$	−366.726	−	1119.64i	−0.480637	−	1.46742i
$764$	−3646.29	−	956.169i	−4.77262	−	1.25153i
$765$	1.98047	+	26.4276i	0.00258886	+	0.0345459i
$766$	630.262	−	2043.26i	0.822796	−	2.66744i
$767$	949.742	+	101.875i	1.23826	+	0.132822i
$768$	3935.65	−	550.260i	5.12454	−	0.716485i
$769$	1307.79	−	126.161i	1.70064	−	0.164059i	0.800406	−	0.599458i	$-0.204617\pi$
$769$	1307.79	−	126.161i	1.70064	−	0.164059i	0.900238	+	0.435399i	$0.143393\pi$
$770$	−229.455	+	18.7287i	−0.297993	+	0.0243229i
$771$	−907.668	+	117.031i	−1.17726	+	0.151791i
$772$	2216.69	−	3037.34i	2.87136	−	3.93438i
$773$	−797.036	+	1116.98i	−1.03109	+	1.44500i	−0.140565	+	0.990071i	$0.544892\pi$
$773$	−797.036	+	1116.98i	−1.03109	+	1.44500i	−0.890530	+	0.454925i	$0.849666\pi$
$774$	394.805	+	321.807i	0.510083	+	0.415772i
$775$	−758.335	+	316.489i	−0.978497	+	0.408373i
$776$	226.863	−	402.818i	0.292349	−	0.519095i
$777$	−884.841	+	149.092i	−1.13879	+	0.191881i
$778$	332.820	−	477.123i	0.427790	−	0.613269i
$779$	−135.543	+	289.327i	−0.173997	+	0.371409i
$780$	−304.470	−	264.862i	−0.390346	−	0.339567i
$781$	−165.770	+	98.0841i	−0.212254	+	0.125588i
$782$	43.7113	−	2045.01i	0.0558968	−	2.61510i
$783$	−656.971	−	523.917i	−0.839043	−	0.669114i
$784$	−2050.35	+	2528.83i	−2.61524	+	3.22554i
$785$	71.6692	+	89.8703i	0.0912983	+	0.114484i
$786$	−2132.19	−	2794.15i	−2.71272	−	3.55490i
$787$	−720.293	−	479.894i	−0.915239	−	0.609776i	0.00548782	−	0.999985i	$-0.498253\pi$
$787$	−720.293	−	479.894i	−0.915239	−	0.609776i	−0.920726	+	0.390209i	$0.872403\pi$
$788$	1695.14	−	728.827i	2.15119	−	0.924907i
$789$	1102.87	−	545.709i	1.39781	−	0.691647i
$790$	−61.1417	+	151.021i	−0.0773946	+	0.191166i
$791$	−661.962	−	214.916i	−0.836867	−	0.271701i
$792$	698.747	−	769.399i	0.882257	−	0.971463i
$793$	−75.6234	+	137.698i	−0.0953637	+	0.173642i
$794$	−275.846	+	1151.69i	−0.347413	+	1.45049i
$795$	3.62646	+	6.60320i	0.00456159	+	0.00830591i
$796$	2312.23	−	632.821i	2.90482	−	0.795001i
$797$	−1350.89	+	497.139i	−1.69496	+	0.623763i	−0.995830	−	0.0912273i	$-0.970921\pi$
$797$	−1350.89	+	497.139i	−1.69496	+	0.623763i	−0.699135	+	0.714990i	$0.746431\pi$
$798$	1808.80	−	1308.91i	2.26667	−	1.64024i
$799$	1037.70	+	133.797i	1.29875	+	0.167455i
$800$	2463.41	−	2598.67i	3.07926	−	3.24833i
$801$	12.8021	+	35.9686i	0.0159826	+	0.0449046i
$802$	935.650	+	868.156i	1.16665	+	1.08249i
$803$	−3.99687	+	5.86233i	−0.00497742	+	0.00730053i
$804$	1583.80	+	50.7893i	1.96990	+	0.0631707i
$805$	25.6610	+	162.901i	0.0318771	+	0.202361i
$806$	−1673.23	−	1248.76i	−2.07596	−	1.54933i
$807$	162.709	−	1377.87i	0.201622	−	1.70740i
$808$	1026.96	−	2254.51i	1.27099	−	2.79024i
$809$	−243.674	+	1183.66i	−0.301204	+	1.46312i	0.500677	+	0.865634i	$0.333085\pi$
$809$	−243.674	+	1183.66i	−0.301204	+	1.46312i	−0.801881	+	0.597484i	$0.796167\pi$
$810$	−211.417	−	134.423i	−0.261008	−	0.165954i
$811$	−1470.15	+	47.1449i	−1.81276	+	0.0581318i	−0.919891	−	0.392175i	$-0.871723\pi$
$811$	−1470.15	+	47.1449i	−1.81276	+	0.0581318i	−0.892874	+	0.450307i	$0.851315\pi$
$812$	1860.15	+	2513.58i	2.29083	+	3.09554i
$813$	−410.296	−	349.290i	−0.504669	−	0.429631i
$814$	1863.23	+	280.837i	2.28898	+	0.345009i
$815$	−8.90209	−	13.0570i	−0.0109228	−	0.0160208i
$816$	−1770.61	−	2784.77i	−2.16987	−	3.41271i
$817$	−389.513	−	1024.52i	−0.476760	−	1.25400i
$818$	−290.432	+	176.062i	−0.355051	+	0.215234i
$819$	−222.439	+	223.018i	−0.271598	+	0.272305i
$820$	−93.9851	−	31.2052i	−0.114616	−	0.0380551i
$821$	705.368	+	810.849i	0.859157	+	0.987636i	0.999997	−	0.00239613i	$-0.000762713\pi$
$821$	705.368	+	810.849i	0.859157	+	0.987636i	−0.140840	+	0.990032i	$0.544980\pi$
$822$	488.866	+	1714.09i	0.594728	+	2.08527i
$823$	−5.92236	+	554.211i	−0.00719606	+	0.673404i	0.937953	+	0.346763i	$0.112719\pi$
$823$	−5.92236	+	554.211i	−0.00719606	+	0.673404i	−0.945149	+	0.326640i	$0.894083\pi$
$824$	1944.76	+	2725.43i	2.36015	+	3.30756i
$825$	69.9402	−	1089.37i	0.0847760	−	1.32045i
$826$	−1599.32	−	353.876i	−1.93623	−	0.428421i
$827$	−274.102	+	154.372i	−0.331442	+	0.186665i	−0.647481	−	0.762082i	$-0.724178\pi$
$827$	−274.102	+	154.372i	−0.331442	+	0.186665i	0.316039	+	0.948746i	$0.397647\pi$
$828$	−908.759	−	708.958i	−1.09753	−	0.856230i
$829$	−1399.95	+	257.145i	−1.68872	+	0.310187i	−0.937009	−	0.349304i	$-0.886418\pi$
$829$	−1399.95	+	257.145i	−1.68872	+	0.310187i	−0.751712	+	0.659491i	$0.770772\pi$
$830$	59.5227	+	22.6300i	0.0717141	+	0.0272650i
$831$	1006.08	−	207.116i	1.21069	−	0.249237i
$832$	4733.10	+	1080.30i	5.68882	+	1.29844i
$833$	685.250	+	177.792i	0.822629	+	0.213436i
$834$	373.722	+	1637.38i	0.448108	+	1.96329i
$835$	59.5017	−	27.1037i	0.0712596	−	0.0324595i
$836$	−3297.61	+	1055.90i	−3.94451	+	1.26303i
$837$	−626.414	−	335.363i	−0.748403	−	0.400673i
$838$	171.523	+	210.430i	0.204681	+	0.251110i
$839$	46.0542	+	717.331i	0.0548917	+	0.854983i	0.929192	+	0.369597i	$0.120504\pi$
$839$	46.0542	+	717.331i	0.0548917	+	0.854983i	−0.874300	+	0.485385i	$0.838679\pi$
$840$	302.714	+	328.905i	0.360374	+	0.391554i
$841$	669.743	−	271.149i	0.796365	−	0.322412i
$842$	−1054.31	−	937.133i	−1.25215	−	1.11298i
$843$	528.561	+	677.521i	0.627000	+	0.803702i
$844$	−295.084	+	707.048i	−0.349626	+	0.837735i
$845$	−26.3850	−	49.2837i	−0.0312248	−	0.0583239i
$846$	555.373	−	573.468i	0.656469	−	0.677858i
$847$	96.0146	−	306.861i	0.113358	−	0.362291i
$848$	−187.490	−	122.042i	−0.221097	−	0.143918i
$849$	24.6006	+	36.9241i	0.0289760	+	0.0434913i
$850$	−1313.26	−	451.668i	−1.54501	−	0.531374i
$851$	100.867	−	1345.97i	0.118527	−	1.58163i
$852$	538.971	+	211.531i	0.632595	+	0.248275i
$853$	−1406.28	+	622.517i	−1.64862	+	0.729797i	−0.999522	−	0.0309057i	$-0.990161\pi$
$853$	−1406.28	+	622.517i	−1.64862	+	0.729797i	−0.649101	+	0.760702i	$0.724855\pi$
$854$	155.019	−	220.328i	0.181522	−	0.257995i
$855$	−20.1265	−	38.5787i	−0.0235398	−	0.0451213i
$856$	345.494	+	122.969i	0.403614	+	0.143656i
$857$	28.3171	+	55.7225i	0.0330421	+	0.0650205i	0.907419	−	0.420227i	$-0.138049\pi$
$857$	28.3171	+	55.7225i	0.0330421	+	0.0650205i	−0.874377	+	0.485247i	$0.838730\pi$
$858$	2472.62	−	1256.54i	2.88184	−	1.46449i
$859$	335.459	−	942.504i	0.390523	−	1.09721i	−0.570633	−	0.821205i	$-0.693302\pi$
$859$	335.459	−	942.504i	0.390523	−	1.09721i	0.961156	−	0.276005i	$-0.0890108\pi$
$860$	301.201	−	157.136i	0.350233	−	0.182717i
$861$	−122.846	+	299.939i	−0.142678	+	0.348361i
$862$	815.276	+	1841.72i	0.945795	+	2.13657i
$863$	−250.006	+	637.005i	−0.289694	+	0.738129i	0.709739	+	0.704465i	$0.248813\pi$
$863$	−250.006	+	637.005i	−0.289694	+	0.738129i	−0.999433	+	0.0336641i	$0.989282\pi$
$864$	3087.52	+	231.378i	3.57352	+	0.267799i
$865$	14.2643	−	41.4744i	0.0164905	−	0.0479473i
$866$	−387.671	+	258.285i	−0.447657	+	0.298251i
$867$	150.528	−	231.252i	0.173620	−	0.266726i
$868$	1931.00	+	1806.29i	2.22466	+	2.08098i
$869$	−594.066	−	575.321i	−0.683620	−	0.662049i
$870$	305.057	−	163.318i	0.350640	−	0.187722i
$871$	601.145	+	250.886i	0.690178	+	0.288043i
$872$	3787.53	−	2954.80i	4.34349	−	3.38853i
$873$	−30.3298	+	34.1221i	−0.0347420	+	0.0390860i
$874$	1260.32	+	3113.02i	1.44201	+	3.56180i
$875$	223.197	+	34.5652i	0.255082	+	0.0395030i
$876$	21.2842	−	1.36649i	0.0242970	−	0.00155992i
$877$	−446.088	+	363.609i	−0.508652	+	0.414606i	−0.851157	−	0.524910i	$-0.824099\pi$
$877$	−446.088	+	363.609i	−0.508652	+	0.414606i	0.342505	+	0.939516i	$0.388725\pi$
$878$	−1126.60	+	2104.34i	−1.28315	+	2.39675i
$879$	154.725	+	483.212i	0.176024	+	0.549730i
$880$	−231.592	−	508.423i	−0.263173	−	0.577753i
$881$	640.240	−	146.131i	0.726720	−	0.165869i	0.156872	−	0.987619i	$-0.449859\pi$
$881$	640.240	−	146.131i	0.726720	−	0.165869i	0.569848	+	0.821750i	$0.307002\pi$
$882$	421.432	−	337.876i	0.477814	−	0.383079i
$883$	−31.1911	+	136.657i	−0.0353240	+	0.154765i	−0.989514	−	0.144437i	$-0.953863\pi$
$883$	−31.1911	+	136.657i	−0.0353240	+	0.154765i	0.954190	+	0.299201i	$0.0967202\pi$
$884$	−525.442	−	2552.37i	−0.594392	−	2.88730i
$885$	−47.5703	+	125.122i	−0.0537518	+	0.141381i
$886$	−347.556	−	1892.16i	−0.392275	−	2.13562i
$887$	−1015.17	+	1301.27i	−1.14450	+	1.46704i	−0.283118	+	0.959085i	$0.591369\pi$
$887$	−1015.17	+	1301.27i	−1.14450	+	1.46704i	−0.861381	+	0.507959i	$0.830400\pi$
$888$	−1795.36	−	3187.84i	−2.02180	−	3.58991i
$889$	239.224	+	295.924i	0.269093	+	0.332873i
$890$	34.4103	+	2.20921i	0.0386633	+	0.00248226i
$891$	1035.13	−	738.631i	1.16177	−	0.828991i
$892$	−2451.99	−	26.2022i	−2.74887	−	0.0293747i
$893$	−1652.03	+	471.166i	−1.84998	+	0.527622i
$894$	−718.541	+	625.068i	−0.803737	+	0.699181i
$895$	30.7121	−	92.4999i	0.0343152	−	0.103352i
$896$	−4009.33	−	1397.08i	−4.47470	−	1.55924i
$897$	−1029.93	−	1698.97i	−1.14819	−	1.89406i
$898$	593.713	−	225.724i	0.661150	−	0.251363i
$899$	1115.68	−	709.372i	1.24103	−	0.789068i
$900$	−646.566	+	440.822i	−0.718407	+	0.489802i
$901$	−7.25042	+	48.1034i	−0.00804708	+	0.0533889i
$902$	441.201	−	518.259i	0.489136	−	0.574567i
$903$	−445.967	−	1018.55i	−0.493873	−	1.12797i
$904$	−90.9533	−	2836.26i	−0.100612	−	3.13745i
$905$	−41.3795	+	65.0805i	−0.0457232	+	0.0719122i
$906$	101.409	+	20.8765i	0.111931	+	0.0230425i
$907$	90.9886	+	41.4463i	0.100318	+	0.0456960i	0.464060	−	0.885804i	$-0.346392\pi$
$907$	90.9886	+	41.4463i	0.100318	+	0.0456960i	−0.363742	+	0.931500i	$0.618501\pi$
$908$	−3545.14	−	418.634i	−3.90434	−	0.461051i
$909$	−146.324	+	196.061i	−0.160972	+	0.215688i
$910$	105.688	+	264.117i	0.116141	+	0.290238i
$911$	−22.4729	+	700.789i	−0.0246684	+	0.769253i	0.910182	+	0.414210i	$0.135942\pi$
$911$	−22.4729	+	700.789i	−0.0246684	+	0.769253i	−0.934850	+	0.355043i	$0.884466\pi$
$912$	4476.79	+	3052.22i	4.90876	+	3.34674i
$913$	−219.847	+	236.938i	−0.240796	+	0.259516i
$914$	−863.019	+	307.169i	−0.944222	+	0.336071i
$915$	−15.9777	−	15.1460i	−0.0174619	−	0.0165530i
$916$	−393.088	+	3048.71i	−0.429135	+	3.32829i
$917$	323.292	+	1801.02i	0.352554	+	1.96404i
$918$	−414.728	−	1126.95i	−0.451773	−	1.22761i
$919$	387.376	+	1415.41i	0.421519	+	1.54017i	0.791525	+	0.611137i	$0.209287\pi$
$919$	387.376	+	1415.41i	0.421519	+	1.54017i	−0.370006	+	0.929029i	$0.620644\pi$
$920$	−589.358	+	323.674i	−0.640606	+	0.351820i
$921$	−279.432	−	66.9279i	−0.303401	−	0.0726687i
$922$	−251.428	−	138.084i	−0.272699	−	0.149766i
$923$	176.195	+	160.015i	0.190894	+	0.173364i
$924$	−3288.31	+	1234.99i	−3.55878	+	1.33657i
$925$	−849.425	−	343.894i	−0.918298	−	0.371778i
$926$	−954.669	−	1929.38i	−1.03096	−	2.08356i
$927$	−130.596	−	303.746i	−0.140880	−	0.327665i
$928$	−3194.29	+	4794.45i	−3.44213	+	5.16643i
$929$	499.913	−	381.479i	0.538120	−	0.410634i	−0.301779	−	0.953378i	$-0.597580\pi$
$929$	499.913	−	381.479i	0.538120	−	0.410634i	0.839898	+	0.542744i	$0.182614\pi$
$930$	228.756	−	182.427i	0.245974	−	0.196158i
$931$	−1148.93	+	176.228i	−1.23408	+	0.189288i
$932$	2457.73	−	3081.90i	2.63705	−	3.30676i
$933$	179.524	+	3.83725i	0.192415	+	0.00411281i
$934$	411.566	+	695.581i	0.440649	+	0.744734i
$935$	−79.7358	+	91.6596i	−0.0852789	+	0.0980316i
$936$	−1163.00	−	544.840i	−1.24252	−	0.582094i
$937$	−716.101	−	499.521i	−0.764249	−	0.533107i	0.124103	−	0.992269i	$-0.460395\pi$
$937$	−716.101	−	499.521i	−0.764249	−	0.533107i	−0.888352	+	0.459162i	$0.848150\pi$
$938$	−976.924	−	541.678i	−1.04150	−	0.577482i
$939$	782.729	+	440.825i	0.833577	+	0.469462i
$940$	−205.079	−	491.388i	−0.218169	−	0.522753i
$941$	1147.89	−	1408.27i	1.21986	−	1.49657i	0.407727	−	0.913104i	$-0.366322\pi$
$941$	1147.89	−	1408.27i	1.21986	−	1.49657i	0.812137	−	0.583467i	$-0.198304\pi$
$942$	1933.13	+	1379.41i	2.05215	+	1.46434i
$943$	−393.819	−	287.414i	−0.417624	−	0.304787i
$944$	−508.319	−	3942.42i	−0.538474	−	4.17630i
$945$	48.9627	+	83.5197i	0.0518123	+	0.0883807i
$946$	224.205	+	2324.12i	0.237003	+	2.45678i
$947$	145.742	+	1042.40i	0.153899	+	1.10074i	0.900309	+	0.435251i	$0.143340\pi$
$947$	145.742	+	1042.40i	0.153899	+	1.10074i	−0.746410	+	0.665486i	$0.768224\pi$
$948$	−265.131	+	2471.73i	−0.279674	+	2.60731i
$949$	8.37794	+	2.58425i	0.00882818	+	0.00272313i
$950$	2273.83	−	170.400i	2.39350	−	0.179368i
$951$	−179.394	+	684.106i	−0.188637	+	0.719355i
$952$	265.550	+	2874.26i	0.278939	+	3.01918i
$953$	172.297	−	389.222i	0.180794	−	0.408418i	−0.800922	−	0.598769i	$-0.795657\pi$
$953$	172.297	−	389.222i	0.180794	−	0.408418i	0.981716	+	0.190352i	$0.0609628\pi$
$954$	26.1052	+	26.3856i	0.0273639	+	0.0276579i
$955$	166.849	−	138.993i	0.174711	−	0.145543i
$956$	753.674	+	3004.58i	0.788362	+	3.14287i
$957$	187.320	+	1746.32i	0.195736	+	1.82478i
$958$	11.6810	−	59.9797i	0.0121932	−	0.0626093i
$959$	181.067	−	910.114i	0.188809	−	0.949024i
$960$	−314.690	+	603.201i	−0.327802	+	0.628334i
$961$	115.046	−	106.747i	0.119715	−	0.111079i
$962$	−347.027	−	2302.38i	−0.360735	−	2.39332i
$963$	−30.7660	−	19.1031i	−0.0319481	−	0.0198370i
$964$	−957.632	+	1618.48i	−0.993394	+	1.67892i
$965$	68.2584	+	205.584i	0.0707341	+	0.213040i
$966$	1432.87	+	3091.04i	1.48330	+	3.19984i
$967$	53.4091	−	553.642i	0.0552318	−	0.572535i	−0.925710	−	0.378234i	$-0.876532\pi$
$967$	53.4091	−	553.642i	0.0552318	−	0.572535i	0.980942	−	0.194301i	$-0.0622440\pi$
$968$	1309.79	−	56.0181i	1.35309	−	0.0578699i
$969$	200.462	−	1161.04i	0.206875	−	1.19819i
$970$	17.4917	+	37.3373i	0.0180326	+	0.0384920i
$971$	−355.057	+	1244.92i	−0.365662	+	1.28210i	0.533988	+	0.845492i	$0.320693\pi$
$971$	−355.057	+	1244.92i	−0.365662	+	1.28210i	−0.899650	+	0.436613i	$0.856178\pi$
$972$	−1593.14	−	472.835i	−1.63903	−	0.486456i
$973$	216.162	−	847.213i	0.222160	−	0.870722i
$974$	1332.83	+	1467.59i	1.36841	+	1.50677i
$975$	−1311.80	+	314.194i	−1.34543	+	0.322250i
$976$	630.577	+	172.579i	0.646083	+	0.176823i
$977$	260.985	−	22.3649i	0.267129	−	0.0228914i	0.0489536	−	0.998801i	$-0.484411\pi$
$977$	260.985	−	22.3649i	0.267129	−	0.0228914i	0.218175	+	0.975910i	$0.429990\pi$
$978$	−250.848	−	208.969i	−0.256491	−	0.213669i
$979$	−75.9375	+	157.686i	−0.0775664	+	0.161068i
$980$	−96.0067	−	347.248i	−0.0979660	−	0.354334i
$981$	−427.396	+	205.823i	−0.435674	+	0.209810i
$982$	−794.497	+	3167.32i	−0.809060	+	3.22538i
$983$	−344.379	−	48.1492i	−0.350335	−	0.0489818i	−0.0388828	−	0.999244i	$-0.512380\pi$
$983$	−344.379	−	48.1492i	−0.350335	−	0.0489818i	−0.311452	+	0.950262i	$0.600815\pi$
$984$	−1320.34	−	56.4694i	−1.34181	−	0.0573876i
$985$	−22.5448	+	103.879i	−0.0228881	+	0.105461i
$986$	2205.77	+	356.612i	2.23709	+	0.361676i
$987$	−1650.27	+	560.124i	−1.67201	+	0.567502i
$988$	2447.87	+	3509.20i	2.47760	+	3.55183i
$989$	1648.15	−	284.565i	1.66649	−	0.287730i
$990$	19.6596	+	90.5855i	0.0198582	+	0.0915005i
$991$	−14.9063	−	278.730i	−0.0150417	−	0.281261i	−0.996142	−	0.0877597i	$-0.972029\pi$
$991$	−14.9063	−	278.730i	−0.0150417	−	0.281261i	0.981100	−	0.193501i	$-0.0619844\pi$
$992$	−1924.17	+	4475.34i	−1.93969	+	4.51143i
$993$	240.315	+	369.188i	0.242009	+	0.371790i
$994$	−269.922	−	306.156i	−0.271551	−	0.308004i
$995$	−47.6958	+	129.605i	−0.0479354	+	0.130256i
$996$	968.050	+	82.9564i	0.971937	+	0.0832895i
$997$	−252.860	−	250.172i	−0.253621	−	0.250925i	0.565227	−	0.824935i	$-0.308788\pi$
$997$	−252.860	−	250.172i	−0.253621	−	0.250925i	−0.818848	+	0.574010i	$0.805387\pi$
$998$	−161.095	−	410.464i	−0.161418	−	0.411286i
$999$	−233.563	−	757.193i	−0.233797	−	0.757951i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	343.3.l.a.10.63	✓	5376
343.103	odd	294	inner	343.3.l.a.103.63	yes	5376

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
343.3.l.a.10.63	✓	5376	1.1	even	1	trivial
343.3.l.a.103.63	yes	5376	343.103	odd	294	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:	\( N \)	\(=\)	\( 343 = 7^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	343.l (of order \(294\), degree \(84\), minimal)

\(f(q)\)	\(=\)	\(q+(3.48678 + 1.77191i) q^{2} +(-2.49496 + 2.36509i) q^{3} +(6.65993 + 9.12553i) q^{4} +(-0.650784 + 0.00695434i) q^{5} +(-12.8901 + 3.82572i) q^{6} +(6.87965 + 1.29244i) q^{7} +(4.55518 + 28.1754i) q^{8} +(0.150514 - 2.81444i) q^{9} +(-2.28147 - 1.12889i) q^{10} +(9.65685 - 8.58360i) q^{11} +(-38.1990 - 7.01645i) q^{12} +(-13.6527 - 8.27636i) q^{13} +(21.6978 + 16.6966i) q^{14} +(1.60723 - 1.55651i) q^{15} +(-20.2610 + 63.2760i) q^{16} +(14.3480 - 1.69432i) q^{17} +(5.51176 - 9.54665i) q^{18} +(-20.5436 + 11.8609i) q^{19} +(-4.39764 - 5.89244i) q^{20} +(-20.2212 + 13.0464i) q^{21} +(48.8808 - 12.8180i) q^{22} +(-11.7728 - 34.2302i) q^{23} +(-78.0024 - 59.5230i) q^{24} +(-24.5708 + 0.525192i) q^{25} +(-32.9391 - 53.0493i) q^{26} +(-13.7754 - 16.1814i) q^{27} +(34.0238 + 71.3881i) q^{28} +(38.8126 - 7.55874i) q^{29} +(8.36207 - 2.57936i) q^{30} +(31.1243 - 12.2154i) q^{31} +(-102.471 + 103.572i) q^{32} +(-3.79241 + 44.2550i) q^{33} +(53.0307 + 19.5158i) q^{34} +(-4.48615 - 0.793259i) q^{35} +(26.6857 - 17.3705i) q^{36} +(34.2557 + 14.7282i) q^{37} +(-92.6477 + 4.95474i) q^{38} +(53.6373 - 11.6408i) q^{39} +(-3.16038 - 18.3044i) q^{40} +(11.0467 - 7.70572i) q^{41} +(-93.6240 + 9.65985i) q^{42} +(-7.37434 + 45.6129i) q^{43} +(142.644 + 30.9577i) q^{44} +(-0.0783798 + 1.83264i) q^{45} +(19.6039 - 140.214i) q^{46} +(70.2429 + 17.6199i) q^{47} +(-99.1033 - 205.790i) q^{48} +(45.6592 + 17.7831i) q^{49} +(-86.6037 - 41.7062i) q^{50} +(-31.7905 + 38.1617i) q^{51} +(-15.4000 - 179.708i) q^{52} +(-0.888830 + 3.24765i) q^{53} +(-19.3599 - 80.8299i) q^{54} +(-6.22483 + 5.65323i) q^{55} +(-5.07709 + 199.724i) q^{56} +(23.2034 - 78.1799i) q^{57} +(148.724 + 42.4168i) q^{58} +(-54.1781 + 25.3812i) q^{59} +(24.9081 + 4.30054i) q^{60} +(-0.420454 - 9.83087i) q^{61} +(130.169 + 12.5572i) q^{62} +(4.67299 - 19.1678i) q^{63} +(-288.592 + 95.8191i) q^{64} +(8.94253 + 5.29118i) q^{65} +(-91.6395 + 147.588i) q^{66} +(-40.3448 + 6.08100i) q^{67} +(111.019 + 119.650i) q^{68} +(110.330 + 57.5591i) q^{69} +(-14.2367 - 10.7150i) q^{70} +(-14.6330 - 2.84978i) q^{71} +(79.9836 - 8.57948i) q^{72} +(-0.532651 + 0.133611i) q^{73} +(93.3450 + 112.052i) q^{74} +(60.0610 - 59.4226i) q^{75} +(-245.056 - 108.479i) q^{76} +(77.5296 - 46.5712i) q^{77} +(207.648 + 54.4517i) q^{78} +(-4.78325 - 63.8281i) q^{79} +(12.7455 - 41.3199i) q^{80} +(97.8611 + 10.4971i) q^{81} +(52.1715 - 7.29433i) q^{82} +(-24.9011 + 2.40218i) q^{83} +(-253.727 - 97.6407i) q^{84} +(-9.32569 + 1.20242i) q^{85} +(-106.535 + 145.976i) q^{86} +(-78.9585 + 110.654i) q^{87} +(285.835 + 232.986i) q^{88} +(-12.5010 + 5.21725i) q^{89} +(-3.52057 + 6.25114i) q^{90} +(-83.2292 - 74.5838i) q^{91} +(233.963 - 335.404i) q^{92} +(-48.7633 + 104.089i) q^{93} +(213.701 + 185.901i) q^{94} +(13.2870 - 7.86173i) q^{95} +(10.7036 - 500.761i) q^{96} +(-12.6640 - 10.0992i) q^{97} +(127.694 + 142.910i) q^{98} +(-22.7045 - 28.4706i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5376 q - 84 q^{2} - 84 q^{3} - 84 q^{4} - 84 q^{5} - 112 q^{6} - 84 q^{7} - 84 q^{8} - 28 q^{9} - 84 q^{10} - 119 q^{11} - 119 q^{12} - 84 q^{13} + 21 q^{14} - 168 q^{15} - 84 q^{16} - 35 q^{17} - 42 q^{18}+ \cdots + 42 q^{99}+O(q^{100}) \) 5376 * q - 84 * q^2 - 84 * q^3 - 84 * q^4 - 84 * q^5 - 112 * q^6 - 84 * q^7 - 84 * q^8 - 28 * q^9 - 84 * q^10 - 119 * q^11 - 119 * q^12 - 84 * q^13 + 21 * q^14 - 168 * q^15 - 84 * q^16 - 35 * q^17 - 42 * q^18 - 126 * q^19 - 420 * q^20 - 84 * q^21 + 28 * q^22 - 147 * q^23 - 210 * q^24 - 84 * q^25 - 196 * q^26 + 21 * q^27 + 126 * q^28 - 336 * q^29 - 91 * q^30 - 77 * q^31 - 84 * q^33 - 616 * q^34 + 56 * q^35 + 420 * q^36 - 539 * q^37 - 532 * q^38 - 441 * q^39 - 364 * q^40 - 280 * q^41 - 700 * q^42 - 84 * q^43 - 112 * q^44 - 315 * q^45 - 252 * q^46 - 7 * q^47 - 98 * q^48 - 28 * q^49 + 56 * q^50 + 84 * q^51 + 84 * q^52 + 371 * q^53 + 798 * q^54 + 1267 * q^55 - 42 * q^56 - 735 * q^57 - 868 * q^58 + 1400 * q^59 + 406 * q^60 + 637 * q^61 + 336 * q^62 + 735 * q^63 - 420 * q^64 - 84 * q^65 + 1372 * q^66 - 91 * q^67 - 77 * q^68 + 84 * q^69 - 1078 * q^70 + 679 * q^71 + 273 * q^72 + 294 * q^73 - 1428 * q^74 - 1344 * q^75 - 231 * q^76 - 714 * q^77 + 5040 * q^78 - 91 * q^79 - 1148 * q^80 - 784 * q^81 - 224 * q^82 - 1414 * q^83 - 1246 * q^84 + 364 * q^85 - 1582 * q^86 - 952 * q^87 - 1974 * q^88 - 910 * q^89 - 287 * q^90 + 1456 * q^91 - 6384 * q^92 - 154 * q^93 - 770 * q^94 - 1358 * q^95 - 4284 * q^96 + 3430 * q^97 + 7 * q^98 + 42 * q^99

Introduction

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