LMFDB - Embedded newform 56.3.j.a.5.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [56,3,Mod(5,56)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(56, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

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

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

chi := DirichletCharacter("56.5");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 56 = 2^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	56.j (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.52588948042$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			5.4
Character	$\chi$	$=$	56.5
Dual form			56.3.j.a.45.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.61426 + 1.18075i) q^{2} +(-0.455431 - 0.788830i) q^{3} +(1.21166 - 3.81207i) q^{4} +(3.17251 - 5.49495i) q^{5} +(1.66660 + 0.735624i) q^{6} +(3.79106 + 5.88455i) q^{7} +(2.54518 + 7.58433i) q^{8} +(4.08516 - 7.07571i) q^{9} +O(q^{10})$	\(q+(-1.61426 + 1.18075i) q^{2} +(-0.455431 - 0.788830i) q^{3} +(1.21166 - 3.81207i) q^{4} +(3.17251 - 5.49495i) q^{5} +(1.66660 + 0.735624i) q^{6} +(3.79106 + 5.88455i) q^{7} +(2.54518 + 7.58433i) q^{8} +(4.08516 - 7.07571i) q^{9} +(1.36692 + 12.6162i) q^{10} +(11.4442 - 6.60732i) q^{11} +(-3.55890 + 0.780346i) q^{12} -19.4243 q^{13} +(-13.0679 - 5.02288i) q^{14} -5.77945 q^{15} +(-13.0638 - 9.23784i) q^{16} +(13.7930 - 7.96338i) q^{17} +(1.76014 + 16.2456i) q^{18} +(-8.22725 + 14.2500i) q^{19} +(-17.1032 - 18.7518i) q^{20} +(2.91534 - 5.67051i) q^{21} +(-10.6723 + 24.1787i) q^{22} +(-11.9607 + 20.7166i) q^{23} +(4.82359 - 5.46186i) q^{24} +(-7.62967 - 13.2150i) q^{25} +(31.3559 - 22.9353i) q^{26} -15.6398 q^{27} +(27.0258 - 7.32173i) q^{28} +16.6618i q^{29} +(9.32952 - 6.82409i) q^{30} +(-11.1360 + 6.42939i) q^{31} +(31.9959 - 0.512817i) q^{32} +(-10.4241 - 6.01837i) q^{33} +(-12.8627 + 29.1410i) q^{34} +(44.3625 - 2.16288i) q^{35} +(-22.0233 - 24.1463i) q^{36} +(41.1844 + 23.7778i) q^{37} +(-3.54481 - 32.7175i) q^{38} +(8.84646 + 15.3225i) q^{39} +(49.7502 + 10.0757i) q^{40} -6.49499i q^{41} +(1.98934 + 12.5960i) q^{42} +33.2928i q^{43} +(-11.3211 - 51.6320i) q^{44} +(-25.9205 - 44.8956i) q^{45} +(-5.15343 - 47.5645i) q^{46} +(-18.9713 - 10.9531i) q^{47} +(-1.33743 + 14.5123i) q^{48} +(-20.2558 + 44.6173i) q^{49} +(27.9198 + 12.3236i) q^{50} +(-12.5635 - 7.25355i) q^{51} +(-23.5356 + 74.0470i) q^{52} +(-32.2028 + 18.5923i) q^{53} +(25.2467 - 18.4667i) q^{54} -83.8473i q^{55} +(-34.9814 + 43.7299i) q^{56} +14.9878 q^{57} +(-19.6734 - 26.8964i) q^{58} +(-27.3428 - 47.3591i) q^{59} +(-7.00270 + 22.0317i) q^{60} +(-5.12340 + 8.87399i) q^{61} +(10.3849 - 23.5276i) q^{62} +(57.1245 - 2.78508i) q^{63} +(-51.0441 + 38.6070i) q^{64} +(-61.6240 + 106.736i) q^{65} +(23.9334 - 2.59309i) q^{66} +(-14.8386 + 8.56706i) q^{67} +(-13.6446 - 62.2287i) q^{68} +21.7892 q^{69} +(-69.0587 + 55.8725i) q^{70} +32.0568 q^{71} +(64.0620 + 12.9743i) q^{72} +(92.8082 - 53.5828i) q^{73} +(-94.5579 + 10.2450i) q^{74} +(-6.94958 + 12.0370i) q^{75} +(44.3535 + 48.6290i) q^{76} +(82.2668 + 42.2953i) q^{77} +(-32.3725 - 14.2890i) q^{78} +(29.1542 - 50.4965i) q^{79} +(-92.2065 + 42.4777i) q^{80} +(-29.6436 - 51.3443i) q^{81} +(7.66897 + 10.4846i) q^{82} -36.3441 q^{83} +(-18.0840 - 17.9842i) q^{84} -101.056i q^{85} +(-39.3105 - 53.7432i) q^{86} +(13.1433 - 7.58829i) q^{87} +(79.2397 + 69.9799i) q^{88} +(0.929882 + 0.536867i) q^{89} +(94.8528 + 41.8674i) q^{90} +(-73.6388 - 114.303i) q^{91} +(64.4808 + 70.6965i) q^{92} +(10.1434 + 5.85629i) q^{93} +(43.5575 - 4.71928i) q^{94} +(52.2021 + 90.4167i) q^{95} +(-14.9765 - 25.0058i) q^{96} +169.517i q^{97} +(-19.9838 - 95.9408i) q^{98} -107.968i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 2 q^{2} - 4 q^{4} - 4 q^{7} - 20 q^{8} - 32 q^{9}+O(q^{10}) $ 28 * q - 2 * q^2 - 4 * q^4 - 4 * q^7 - 20 * q^8 - 32 * q^9	$ 28 q - 2 q^{2} - 4 q^{4} - 4 q^{7} - 20 q^{8} - 32 q^{9} + 24 q^{10} - 18 q^{12} + 24 q^{14} + 28 q^{15} + 16 q^{16} - 6 q^{17} - 42 q^{18} - 92 q^{22} + 30 q^{23} - 30 q^{24} - 32 q^{25} - 30 q^{26} - 42 q^{28} + 22 q^{30} - 6 q^{31} + 88 q^{32} - 6 q^{33} + 256 q^{36} + 6 q^{38} - 20 q^{39} + 102 q^{40} + 18 q^{42} - 42 q^{44} + 68 q^{46} - 294 q^{47} - 20 q^{49} + 400 q^{50} - 168 q^{52} + 330 q^{54} - 96 q^{56} + 124 q^{57} - 22 q^{58} - 62 q^{60} + 432 q^{63} - 520 q^{64} - 52 q^{65} - 306 q^{66} - 456 q^{68} - 324 q^{70} - 136 q^{71} + 96 q^{72} + 234 q^{73} - 138 q^{74} - 956 q^{78} - 162 q^{79} + 276 q^{80} - 18 q^{81} - 642 q^{82} + 504 q^{84} + 168 q^{86} + 48 q^{87} + 50 q^{88} - 150 q^{89} + 1020 q^{92} + 618 q^{94} + 290 q^{95} + 1044 q^{96} + 424 q^{98}+O(q^{100}) $ 28 * q - 2 * q^2 - 4 * q^4 - 4 * q^7 - 20 * q^8 - 32 * q^9 + 24 * q^10 - 18 * q^12 + 24 * q^14 + 28 * q^15 + 16 * q^16 - 6 * q^17 - 42 * q^18 - 92 * q^22 + 30 * q^23 - 30 * q^24 - 32 * q^25 - 30 * q^26 - 42 * q^28 + 22 * q^30 - 6 * q^31 + 88 * q^32 - 6 * q^33 + 256 * q^36 + 6 * q^38 - 20 * q^39 + 102 * q^40 + 18 * q^42 - 42 * q^44 + 68 * q^46 - 294 * q^47 - 20 * q^49 + 400 * q^50 - 168 * q^52 + 330 * q^54 - 96 * q^56 + 124 * q^57 - 22 * q^58 - 62 * q^60 + 432 * q^63 - 520 * q^64 - 52 * q^65 - 306 * q^66 - 456 * q^68 - 324 * q^70 - 136 * q^71 + 96 * q^72 + 234 * q^73 - 138 * q^74 - 956 * q^78 - 162 * q^79 + 276 * q^80 - 18 * q^81 - 642 * q^82 + 504 * q^84 + 168 * q^86 + 48 * q^87 + 50 * q^88 - 150 * q^89 + 1020 * q^92 + 618 * q^94 + 290 * q^95 + 1044 * q^96 + 424 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/56\mathbb{Z}\right)^\times$.

$n$	$15$	$17$	$29$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	−1.61426	+	1.18075i	−0.807129	+	0.590375i
$2$	−1.61426	+	1.18075i	−0.807129	+	0.590375i
$3$	−0.455431	−	0.788830i	−0.151810	−	0.262943i	0.780083	−	0.625677i	$-0.215177\pi$
$3$	−0.455431	−	0.788830i	−0.151810	−	0.262943i	−0.931893	+	0.362733i	$0.881844\pi$
$4$	1.21166	−	3.81207i	0.302914	−	0.953018i
$5$	3.17251	−	5.49495i	0.634503	−	1.09899i	−0.352118	−	0.935956i	$-0.614538\pi$
$5$	3.17251	−	5.49495i	0.634503	−	1.09899i	0.986620	−	0.163035i	$-0.0521283\pi$
$6$	1.66660	+	0.735624i	0.277766	+	0.122604i
$7$	3.79106	+	5.88455i	0.541579	+	0.840650i
$7$	3.79106	+	5.88455i	0.541579	+	0.840650i
$8$	2.54518	+	7.58433i	0.318148	+	0.948041i
$9$	4.08516	−	7.07571i	0.453907	−	0.786190i
$10$	1.36692	+	12.6162i	0.136692	+	1.26162i
$11$	11.4442	−	6.60732i	1.04038	−	0.600666i	0.120442	−	0.992720i	$-0.461569\pi$
$11$	11.4442	−	6.60732i	1.04038	−	0.600666i	0.919942	+	0.392054i	$0.128236\pi$
$12$	−3.55890	+	0.780346i	−0.296575	+	0.0650289i
$13$	−19.4243			−1.49418			−0.747090	−	0.664723i	$-0.768550\pi$
$13$	−19.4243			−1.49418			−0.747090	+	0.664723i	$0.768550\pi$
$14$	−13.0679	−	5.02288i	−0.933423	−	0.358777i
$15$	−5.77945			−0.385296
$16$	−13.0638	−	9.23784i	−0.816486	−	0.577365i
$17$	13.7930	−	7.96338i	0.811352	−	0.468434i	−0.0360732	−	0.999349i	$-0.511485\pi$
$17$	13.7930	−	7.96338i	0.811352	−	0.468434i	0.847425	+	0.530915i	$0.178152\pi$
$18$	1.76014	+	16.2456i	0.0977858	+	0.902532i
$19$	−8.22725	+	14.2500i	−0.433013	+	0.750001i	−0.997131	−	0.0756934i	$-0.975883\pi$
$19$	−8.22725	+	14.2500i	−0.433013	+	0.750001i	0.564118	+	0.825694i	$0.309216\pi$
$20$	−17.1032	−	18.7518i	−0.855158	−	0.937592i
$21$	2.91534	−	5.67051i	0.138826	−	0.270024i
$22$	−10.6723	+	24.1787i	−0.485105	+	1.09903i
$23$	−11.9607	+	20.7166i	−0.520032	+	0.900721i	0.479697	+	0.877434i	$0.340746\pi$
$23$	−11.9607	+	20.7166i	−0.520032	+	0.900721i	−0.999729	+	0.0232870i	$0.992587\pi$
$24$	4.82359	−	5.46186i	0.200983	−	0.227577i
$25$	−7.62967	−	13.2150i	−0.305187	−	0.528599i
$26$	31.3559	−	22.9353i	1.20600	−	0.882127i
$27$	−15.6398			−0.579252
$28$	27.0258	−	7.32173i	0.965206	−	0.261490i
$29$			16.6618i			0.574544i	0.957849	+	0.287272i	$0.0927483\pi$
$29$			16.6618i			0.574544i	−0.957849	+	0.287272i	$0.907252\pi$
$30$	9.32952	−	6.82409i	0.310984	−	0.227470i
$31$	−11.1360	+	6.42939i	−0.359227	+	0.207400i	−0.668741	−	0.743495i	$-0.733167\pi$
$31$	−11.1360	+	6.42939i	−0.359227	+	0.207400i	0.309515	+	0.950895i	$0.399833\pi$
$32$	31.9959	−	0.512817i	0.999872	−	0.0160255i
$33$	−10.4241	−	6.01837i	−0.315882	−	0.182375i
$34$	−12.8627	+	29.1410i	−0.378314	+	0.857089i
$35$	44.3625	−	2.16288i	1.26750	−	0.0617964i
$36$	−22.0233	−	24.1463i	−0.611759	−	0.670730i
$37$	41.1844	+	23.7778i	1.11309	+	0.642644i	0.939628	−	0.342196i	$-0.111171\pi$
$37$	41.1844	+	23.7778i	1.11309	+	0.642644i	0.173463	+	0.984840i	$0.444504\pi$
$38$	−3.54481	−	32.7175i	−0.0932845	−	0.860987i
$39$	8.84646	+	15.3225i	0.226832	+	0.392885i
$40$	49.7502	+	10.0757i	1.24375	+	0.251893i
$41$		−	6.49499i		−	0.158415i	−0.996858	−	0.0792073i	$-0.974761\pi$
$41$		−	6.49499i		−	0.158415i	0.996858	−	0.0792073i	$-0.0252389\pi$
$42$	1.98934	+	12.5960i	0.0473652	+	0.299904i
$43$			33.2928i			0.774252i	0.922027	+	0.387126i	$0.126532\pi$
$43$			33.2928i			0.774252i	−0.922027	+	0.387126i	$0.873468\pi$
$44$	−11.3211	−	51.6320i	−0.257299	−	1.17345i
$45$	−25.9205	−	44.8956i	−0.576010	−	0.997679i
$46$	−5.15343	−	47.5645i	−0.112031	−	1.03401i
$47$	−18.9713	−	10.9531i	−0.403645	−	0.233045i	0.284411	−	0.958703i	$-0.408202\pi$
$47$	−18.9713	−	10.9531i	−0.403645	−	0.233045i	−0.688056	+	0.725658i	$0.741535\pi$
$48$	−1.33743	+	14.5123i	−0.0278631	+	0.302340i
$49$	−20.2558	+	44.6173i	−0.413383	+	0.910557i
$50$	27.9198	+	12.3236i	0.558397	+	0.246473i
$51$	−12.5635	−	7.25355i	−0.246343	−	0.142226i
$52$	−23.5356	+	74.0470i	−0.452608	+	1.42398i
$53$	−32.2028	+	18.5923i	−0.607601	+	0.350798i	−0.772026	−	0.635591i	$-0.780756\pi$
$53$	−32.2028	+	18.5923i	−0.607601	+	0.350798i	0.164425	+	0.986390i	$0.447423\pi$
$54$	25.2467	−	18.4667i	0.467531	−	0.341976i
$55$		−	83.8473i		−	1.52450i
$56$	−34.9814	+	43.7299i	−0.624668	+	0.780890i
$57$	14.9878			0.262944
$58$	−19.6734	−	26.8964i	−0.339196	−	0.463731i
$59$	−27.3428	−	47.3591i	−0.463437	−	0.802696i	0.535693	−	0.844413i	$-0.320051\pi$
$59$	−27.3428	−	47.3591i	−0.463437	−	0.802696i	−0.999129	+	0.0417169i	$0.986717\pi$
$60$	−7.00270	+	22.0317i	−0.116712	+	0.367194i
$61$	−5.12340	+	8.87399i	−0.0839902	+	0.145475i	−0.904960	−	0.425496i	$-0.860100\pi$
$61$	−5.12340	+	8.87399i	−0.0839902	+	0.145475i	0.820970	+	0.570971i	$0.193433\pi$
$62$	10.3849	−	23.5276i	0.167499	−	0.379477i
$63$	57.1245	−	2.78508i	0.906737	−	0.0442076i
$64$	−51.0441	+	38.6070i	−0.797564	+	0.603234i
$65$	−61.6240	+	106.736i	−0.948061	+	1.64209i
$66$	23.9334	−	2.59309i	0.362627	−	0.0392892i
$67$	−14.8386	+	8.56706i	−0.221471	+	0.127867i	−0.606631	−	0.794983i	$-0.707480\pi$
$67$	−14.8386	+	8.56706i	−0.221471	+	0.127867i	0.385160	+	0.922850i	$0.374146\pi$
$68$	−13.6446	−	62.2287i	−0.200656	−	0.915128i
$69$	21.7892			0.315785
$70$	−69.0587	+	55.8725i	−0.986552	+	0.798178i
$71$	32.0568			0.451505			0.225752	−	0.974185i	$-0.427516\pi$
$71$	32.0568			0.451505			0.225752	+	0.974185i	$0.427516\pi$
$72$	64.0620	+	12.9743i	0.889750	+	0.180198i
$73$	92.8082	−	53.5828i	1.27135	−	0.734011i	0.296104	−	0.955156i	$-0.404313\pi$
$73$	92.8082	−	53.5828i	1.27135	−	0.734011i	0.975241	+	0.221144i	$0.0709792\pi$
$74$	−94.5579	+	10.2450i	−1.27781	+	0.138446i
$75$	−6.94958	+	12.0370i	−0.0926611	+	0.160494i
$76$	44.3535	+	48.6290i	0.583598	+	0.639855i
$77$	82.2668	+	42.2953i	1.06840	+	0.549290i
$78$	−32.3725	−	14.2890i	−0.415032	−	0.183193i
$79$	29.1542	−	50.4965i	0.369040	−	0.639196i	−0.620376	−	0.784305i	$-0.713020\pi$
$79$	29.1542	−	50.4965i	0.369040	−	0.639196i	0.989416	+	0.145109i	$0.0463532\pi$
$80$	−92.2065	+	42.4777i	−1.15258	+	0.530971i
$81$	−29.6436	−	51.3443i	−0.365971	−	0.633880i
$82$	7.66897	+	10.4846i	0.0935240	+	0.127861i
$83$	−36.3441			−0.437880			−0.218940	−	0.975738i	$-0.570260\pi$
$83$	−36.3441			−0.437880			−0.218940	+	0.975738i	$0.570260\pi$
$84$	−18.0840	−	17.9842i	−0.215286	−	0.214098i
$85$		−	101.056i		−	1.18889i
$86$	−39.3105	−	53.7432i	−0.457099	−	0.624921i
$87$	13.1433	−	7.58829i	0.151072	−	0.0872217i
$88$	79.2397	+	69.9799i	0.900452	+	0.795226i
$89$	0.929882	+	0.536867i	0.0104481	+	0.00603222i	0.505215	−	0.862994i	$-0.331413\pi$
$89$	0.929882	+	0.536867i	0.0104481	+	0.00603222i	−0.494767	+	0.869026i	$0.664747\pi$
$90$	94.8528	+	41.8674i	1.05392	+	0.465193i
$91$	−73.6388	−	114.303i	−0.809217	−	1.25608i
$92$	64.4808	+	70.6965i	0.700878	+	0.768440i
$93$	10.1434	+	5.85629i	0.109069	+	0.0629709i
$94$	43.5575	−	4.71928i	0.463377	−	0.0502051i
$95$	52.2021	+	90.4167i	0.549496	+	0.951755i
$96$	−14.9765	−	25.0058i	−0.156005	−	0.260477i
$97$			169.517i			1.74760i	0.486286	+	0.873799i	$0.338351\pi$
$97$			169.517i			1.74760i	−0.486286	+	0.873799i	$0.661649\pi$
$98$	−19.9838	−	95.9408i	−0.203917	−	0.978988i
$99$		−	107.968i		−	1.09059i
$100$	−59.6210	+	13.0728i	−0.596210	+	0.130728i
$101$	−14.0630	−	24.3579i	−0.139238	−	0.241167i	0.787971	−	0.615713i	$-0.211132\pi$
$101$	−14.0630	−	24.3579i	−0.139238	−	0.241167i	−0.927208	+	0.374546i	$0.877799\pi$
$102$	28.8454	−	3.12528i	0.282798	−	0.0306400i
$103$	−144.029	−	83.1551i	−1.39834	−	0.807331i	−0.404120	−	0.914706i	$-0.632422\pi$
$103$	−144.029	−	83.1551i	−1.39834	−	0.807331i	−0.994219	+	0.107374i	$0.965756\pi$
$104$	−49.4385	−	147.321i	−0.475370	−	1.41654i
$105$	−21.9102	−	34.0094i	−0.208669	−	0.323899i
$106$	30.0308	−	68.0363i	0.283309	−	0.641852i
$107$	171.112	+	98.7918i	1.59918	+	0.923288i	0.991645	+	0.128996i	$0.0411753\pi$
$107$	171.112	+	98.7918i	1.59918	+	0.923288i	0.607536	+	0.794292i	$0.292158\pi$
$108$	−18.9501	+	59.6201i	−0.175464	+	0.552038i
$109$	9.97643	−	5.75990i	0.0915269	−	0.0528431i	−0.453538	−	0.891237i	$-0.649838\pi$
$109$	9.97643	−	5.75990i	0.0915269	−	0.0528431i	0.545065	+	0.838394i	$0.316505\pi$
$110$	99.0027	+	135.351i	0.900025	+	1.23046i
$111$		−	43.3167i		−	0.390240i
$112$	4.83497	−	111.896i	0.0431693	−	0.999068i
$113$	−14.7908			−0.130892			−0.0654460	−	0.997856i	$-0.520847\pi$
$113$	−14.7908			−0.130892			−0.0654460	+	0.997856i	$0.520847\pi$
$114$	−24.1942	+	17.6968i	−0.212229	+	0.155235i
$115$	75.8911	+	131.447i	0.659923	+	1.14302i
$116$	63.5158	+	20.1883i	0.547550	+	0.174037i
$117$	−79.3516	+	137.441i	−0.678219	+	1.17471i
$118$	100.058	+	44.1648i	0.847945	+	0.374278i
$119$	99.1509	+	50.9758i	0.833201	+	0.428368i
$120$	−14.7097	−	43.8332i	−0.122581	−	0.365277i
$121$	26.8135	−	46.4423i	0.221599	−	0.383821i
$122$	−2.20748	−	20.3744i	−0.0180941	−	0.167003i
$123$	−5.12345	+	2.95802i	−0.0416541	+	0.0240490i
$124$	11.0163	+	50.2415i	0.0888408	+	0.405174i
$125$	61.8047			0.494438
$126$	−88.9251	+	71.9456i	−0.705755	+	0.570997i
$127$	−70.2656			−0.553272			−0.276636	−	0.960975i	$-0.589220\pi$
$127$	−70.2656			−0.553272			−0.276636	+	0.960975i	$0.589220\pi$
$128$	36.8131	−	122.592i	0.287602	−	0.957750i
$129$	26.2624	−	15.1626i	0.203584	−	0.117540i
$130$	−26.5515	−	245.062i	−0.204242	−	1.88509i
$131$	−71.0646	+	123.088i	−0.542478	+	0.939600i	0.456283	+	0.889835i	$0.349181\pi$
$131$	−71.0646	+	123.088i	−0.542478	+	0.939600i	−0.998761	+	0.0497649i	$0.984153\pi$
$132$	−35.5729	+	32.4453i	−0.269492	+	0.245798i
$133$	−115.045	+	5.60897i	−0.864999	+	0.0421727i
$134$	13.8377	−	31.3501i	0.103267	−	0.233956i
$135$	−49.6175	+	85.9400i	−0.367537	+	0.636593i
$136$	95.5026	+	84.3423i	0.702225	+	0.620164i
$137$	−126.537	−	219.168i	−0.923626	−	1.59977i	−0.793756	−	0.608236i	$-0.791877\pi$
$137$	−126.537	−	219.168i	−0.923626	−	1.59977i	−0.129870	−	0.991531i	$-0.541456\pi$
$138$	−35.1733	+	25.7276i	−0.254879	+	0.186432i
$139$	−49.1909			−0.353892			−0.176946	−	0.984221i	$-0.556622\pi$
$139$	−49.1909			−0.353892			−0.176946	+	0.984221i	$0.556622\pi$
$140$	45.5070	−	171.734i	0.325050	−	1.22667i
$141$			19.9535i			0.141514i
$142$	−51.7480	+	37.8511i	−0.364423	+	0.266557i
$143$	−222.296	+	128.343i	−1.55452	+	0.897503i
$144$	−118.732	+	54.6975i	−0.824528	+	0.379844i
$145$	91.5556	+	52.8597i	0.631418	+	0.364549i
$146$	−86.5484	+	196.080i	−0.592797	+	1.34301i
$147$	44.4206	−	4.34174i	0.302181	−	0.0295356i
$148$	140.544	−	128.187i	0.949622	−	0.866131i
$149$	−36.1077	−	20.8468i	−0.242334	−	0.139911i	0.373915	−	0.927463i	$-0.378015\pi$
$149$	−36.1077	−	20.8468i	−0.242334	−	0.139911i	−0.616249	+	0.787551i	$0.711348\pi$
$150$	−2.99431	−	27.6366i	−0.0199621	−	0.184244i
$151$	48.8145	+	84.5492i	0.323275	+	0.559928i	0.981162	−	0.193188i	$-0.0618829\pi$
$151$	48.8145	+	84.5492i	0.323275	+	0.559928i	−0.657887	+	0.753117i	$0.728550\pi$
$152$	−129.017	−	26.1293i	−0.848794	−	0.171903i
$153$		−	130.127i		−	0.850503i
$154$	−182.740	+	28.8610i	−1.18662	+	0.187409i
$155$			81.5892i			0.526382i
$156$	69.1294	−	15.1577i	0.443137	−	0.0971648i
$157$	−14.0827	−	24.3919i	−0.0896986	−	0.155363i	0.817685	−	0.575666i	$-0.195257\pi$
$157$	−14.0827	−	24.3919i	−0.0896986	−	0.155363i	−0.907384	+	0.420303i	$0.861924\pi$
$158$	12.5614	+	115.938i	0.0795027	+	0.733786i
$159$	29.3324	+	16.9350i	0.184480	+	0.106510i
$160$	98.6895	−	177.443i	0.616809	−	1.10902i
$161$	−167.251	+	8.15428i	−1.03883	+	0.0506477i
$162$	108.477	+	47.8811i	0.669612	+	0.295563i
$163$	−209.952	−	121.216i	−1.28805	−	0.743655i	−0.309743	−	0.950820i	$-0.600243\pi$
$163$	−209.952	−	121.216i	−1.28805	−	0.743655i	−0.978306	+	0.207165i	$0.933576\pi$
$164$	−24.7594	−	7.86970i	−0.150972	−	0.0479860i
$165$	−66.1413	+	38.1867i	−0.400856	+	0.231434i
$166$	58.6687	−	42.9133i	0.353426	−	0.258514i
$167$			60.1108i			0.359945i	0.983672	+	0.179972i	$0.0576008\pi$
$167$			60.1108i			0.359945i	−0.983672	+	0.179972i	$0.942399\pi$
$168$	50.4271	+	7.67845i	0.300161	+	0.0457051i
$169$	208.305			1.23257
$170$	119.322	+	163.130i	0.701892	+	0.959588i
$171$	67.2193	+	116.427i	0.393096	+	0.680861i
$172$	126.915	+	40.3395i	0.737876	+	0.234532i
$173$	69.6820	−	120.693i	0.402786	−	0.697646i	−0.591275	−	0.806470i	$-0.701375\pi$
$173$	69.6820	−	120.693i	0.402786	−	0.697646i	0.994061	+	0.108824i	$0.0347085\pi$
$174$	−12.2568	+	27.7684i	−0.0704414	+	0.159589i
$175$	48.8397	−	94.9959i	0.279084	−	0.542834i
$176$	−210.542	−	19.4032i	−1.19626	−	0.110246i
$177$	−24.9055	+	43.1376i	−0.140709	+	0.243715i
$178$	−2.13498	+	0.231316i	−0.0119942	+	0.00129953i
$179$	252.643	−	145.863i	1.41141	−	0.814879i	0.415891	−	0.909415i	$-0.363470\pi$
$179$	252.643	−	145.863i	1.41141	−	0.814879i	0.995522	+	0.0945354i	$0.0301365\pi$
$180$	−202.552	+	44.4127i	−1.12529	+	0.246737i
$181$	166.844			0.921791			0.460895	−	0.887455i	$-0.347528\pi$
$181$	166.844			0.921791			0.460895	+	0.887455i	$0.347528\pi$
$182$	253.836	+	97.5662i	1.39470	+	0.536078i
$183$	9.33343			0.0510024
$184$	−187.564	−	37.9866i	−1.01937	−	0.206449i
$185$	261.316	−	150.871i	1.41252	−	0.815518i
$186$	−23.2889	+	2.52325i	−0.125209	+	0.0135659i
$187$	105.233	−	182.269i	0.562745	−	0.974703i
$188$	−64.7407	+	59.0486i	−0.344365	+	0.314088i
$189$	−59.2914	−	92.0332i	−0.313711	−	0.486948i
$190$	−191.027	−	84.3182i	−1.00541	−	0.443780i
$191$	65.6781	−	113.758i	0.343864	−	0.595590i	−0.641283	−	0.767305i	$-0.721597\pi$
$191$	65.6781	−	113.758i	0.343864	−	0.595590i	0.985147	+	0.171715i	$0.0549307\pi$
$192$	53.7014	+	22.6823i	0.279695	+	0.118137i
$193$	40.7196	+	70.5284i	0.210982	+	0.365432i	0.952022	−	0.306029i	$-0.0990004\pi$
$193$	40.7196	+	70.5284i	0.210982	+	0.365432i	−0.741040	+	0.671461i	$0.765667\pi$
$194$	−200.157	−	273.644i	−1.03174	−	1.41054i
$195$	112.262			0.575702
$196$	145.541	+	131.277i	0.742558	+	0.669782i
$197$			2.09549i			0.0106370i	0.999986	+	0.00531851i	$0.00169294\pi$
$197$			2.09549i			0.0106370i	−0.999986	+	0.00531851i	$0.998307\pi$
$198$	127.483	+	174.288i	0.643855	+	0.880244i
$199$	−109.937	+	63.4721i	−0.552447	+	0.318955i	−0.750108	−	0.661315i	$-0.769999\pi$
$199$	−109.937	+	63.4721i	−0.552447	+	0.318955i	0.197662	+	0.980270i	$0.436665\pi$
$200$	80.8079	−	91.5005i	0.404039	−	0.457502i
$201$	13.5159	+	7.80341i	0.0672433	+	0.0388230i
$202$	51.4619	+	22.7149i	0.254762	+	0.112450i
$203$	−98.0469	+	63.1657i	−0.482990	+	0.311161i
$204$	−42.8737	+	39.1042i	−0.210165	+	0.191687i
$205$	−35.6897	−	20.6055i	−0.174096	−	0.100514i
$206$	330.685	−	35.8284i	1.60527	−	0.173924i
$207$	97.7231	+	169.261i	0.472092	+	0.817687i
$208$	253.755	+	179.439i	1.21998	+	0.862687i
$209$			217.440i			1.04038i
$210$	75.5254	+	29.0295i	0.359645	+	0.138236i
$211$		−	7.16822i		−	0.0339726i	−0.999856	−	0.0169863i	$-0.994593\pi$
$211$		−	7.16822i		−	0.0339726i	0.999856	−	0.0169863i	$-0.00540717\pi$
$212$	31.8565	+	145.287i	0.150266	+	0.685316i
$213$	−14.5997	−	25.2874i	−0.0685432	−	0.118720i
$214$	−392.868	+	42.5657i	−1.83583	+	0.198905i
$215$	182.943	+	105.622i	0.850896	+	0.491265i
$216$	−39.8062	−	118.617i	−0.184288	−	0.549155i
$217$	−80.0513	−	41.1563i	−0.368900	−	0.189660i
$218$	−9.30353	+	21.0776i	−0.0426768	+	0.0966864i
$219$	−84.5355	−	48.8066i	−0.386007	−	0.222861i
$220$	−319.632	−	101.594i	−1.45287	−	0.461791i
$221$	−267.920	+	154.683i	−1.21231	+	0.699925i
$222$	51.1462	+	69.9243i	0.230388	+	0.314974i
$223$		−	279.720i		−	1.25435i	−0.778878	−	0.627175i	$-0.784211\pi$
$223$		−	279.720i		−	1.25435i	0.778878	−	0.627175i	$-0.215789\pi$
$224$	124.316	+	186.337i	0.554982	+	0.831863i
$225$	−124.674			−0.554106
$226$	23.8762	−	17.4642i	0.105647	−	0.0772754i
$227$	−152.392	−	263.950i	−0.671330	−	1.16278i	−0.977527	−	0.210809i	$-0.932390\pi$
$227$	−152.392	−	263.950i	−0.671330	−	1.16278i	0.306198	−	0.951968i	$-0.400943\pi$
$228$	18.1600	−	57.1345i	0.0796493	−	0.250590i
$229$	207.344	−	359.130i	0.905433	−	1.56826i	0.0850971	−	0.996373i	$-0.472880\pi$
$229$	207.344	−	359.130i	0.905433	−	1.56826i	0.820335	−	0.571883i	$-0.193787\pi$
$230$	−277.714	−	122.581i	−1.20745	−	0.532962i
$231$	−4.10305	−	84.1572i	−0.0177621	−	0.364317i
$232$	−126.368	+	42.4072i	−0.544691	+	0.182790i
$233$	82.4628	−	142.830i	0.353918	−	0.613004i	−0.633014	−	0.774140i	$-0.718183\pi$
$233$	82.4628	−	142.830i	0.353918	−	0.613004i	0.986932	+	0.161136i	$0.0515159\pi$
$234$	−34.1896	−	315.560i	−0.146110	−	1.34855i
$235$	−120.373	+	69.4976i	−0.512227	+	0.295735i
$236$	−213.666	+	46.8497i	−0.905365	+	0.198516i
$237$	−53.1109			−0.224097
$238$	−220.245	+	34.7843i	−0.925398	+	0.146153i
$239$	−19.1182			−0.0799926			−0.0399963	−	0.999200i	$-0.512735\pi$
$239$	−19.1182			−0.0799926			−0.0399963	+	0.999200i	$0.512735\pi$
$240$	75.5014	+	53.3896i	0.314589	+	0.222457i
$241$	−303.376	+	175.154i	−1.25882	+	0.726780i	−0.972845	−	0.231457i	$-0.925651\pi$
$241$	−303.376	+	175.154i	−1.25882	+	0.726780i	−0.285975	+	0.958237i	$0.592317\pi$
$242$	11.5529	+	106.630i	0.0477393	+	0.440619i
$243$	−97.3804	+	168.668i	−0.400743	+	0.694106i
$244$	27.6205	+	30.2830i	0.113199	+	0.124111i
$245$	180.908	+	252.854i	0.738401	+	1.03206i
$246$	4.77788	−	10.8245i	0.0194223	−	0.0440022i
$247$	159.809	−	276.797i	0.647000	−	1.12064i
$248$	−77.1058	−	68.0953i	−0.310910	−	0.274578i
$249$	16.5522	+	28.6693i	0.0664748	+	0.115138i
$250$	−99.7687	+	72.9760i	−0.399075	+	0.291904i
$251$	−88.3204			−0.351874			−0.175937	−	0.984401i	$-0.556296\pi$
$251$	−88.3204			−0.351874			−0.175937	+	0.984401i	$0.556296\pi$
$252$	58.5982	−	221.137i	0.232533	−	0.877528i
$253$			316.114i			1.24946i
$254$	113.427	−	82.9661i	0.446562	−	0.326638i
$255$	−79.7158	+	46.0240i	−0.312611	+	0.180486i
$256$	85.3247	+	241.362i	0.333300	+	0.942821i
$257$	74.5499	+	43.0414i	0.290077	+	0.167476i	0.637977	−	0.770056i	$-0.279772\pi$
$257$	74.5499	+	43.0414i	0.290077	+	0.167476i	−0.347899	+	0.937532i	$0.613105\pi$
$258$	−24.4910	+	55.4857i	−0.0949265	+	0.215061i
$259$	16.2106	+	332.495i	0.0625893	+	1.28376i
$260$	332.218	+	364.242i	1.27776	+	1.40093i
$261$	117.894	+	68.0661i	0.451701	+	0.260789i
$262$	−30.6191	−	282.605i	−0.116867	−	1.07864i
$263$	−159.605	−	276.444i	−0.606863	−	1.05112i	−0.991754	−	0.128156i	$-0.959094\pi$
$263$	−159.605	−	276.444i	−0.606863	−	1.05112i	0.384891	−	0.922962i	$-0.374239\pi$
$264$	19.1140	−	94.3778i	0.0724015	−	0.357492i
$265$			235.937i			0.890330i
$266$	179.089	−	144.894i	0.673268	−	0.544713i
$267$		−	0.978025i		−	0.00366302i
$268$	14.6790	+	66.9461i	0.0547723	+	0.249799i
$269$	28.7340	+	49.7687i	0.106818	+	0.185014i	0.914479	−	0.404632i	$-0.132601\pi$
$269$	28.7340	+	49.7687i	0.106818	+	0.185014i	−0.807662	+	0.589646i	$0.799267\pi$
$270$	−21.3783	−	197.315i	−0.0791790	−	0.730797i
$271$	26.7398	+	15.4382i	0.0986709	+	0.0569677i	0.548523	−	0.836135i	$-0.315190\pi$
$271$	26.7398	+	15.4382i	0.0986709	+	0.0569677i	−0.449853	+	0.893103i	$0.648523\pi$
$272$	−253.753	−	23.3855i	−0.932915	−	0.0859759i
$273$	−56.6286	+	110.146i	−0.207431	+	0.403465i
$274$	463.046	+	204.385i	1.68995	+	0.745932i
$275$	−174.631	−	100.823i	−0.635023	−	0.366631i
$276$	26.4010	−	83.0618i	0.0956557	−	0.300949i
$277$	308.465	−	178.092i	1.11359	−	0.642933i	0.173834	−	0.984775i	$-0.444384\pi$
$277$	308.465	−	178.092i	1.11359	−	0.642933i	0.939757	+	0.341842i	$0.111051\pi$
$278$	79.4068	−	58.0822i	0.285636	−	0.208929i
$279$			105.060i			0.376561i
$280$	129.315	+	330.955i	0.461838	+	1.18198i
$281$	−294.160			−1.04683			−0.523416	−	0.852077i	$-0.675343\pi$
$281$	−294.160			−1.04683			−0.523416	+	0.852077i	$0.675343\pi$
$282$	−23.5601	−	32.2101i	−0.0835466	−	0.114220i
$283$	207.501	+	359.402i	0.733219	+	1.26997i	0.955501	+	0.294989i	$0.0953161\pi$
$283$	207.501	+	359.402i	0.733219	+	1.26997i	−0.222282	+	0.974982i	$0.571351\pi$
$284$	38.8419	−	122.203i	0.136767	−	0.430292i
$285$	47.5490	−	82.3572i	0.166838	−	0.288973i
$286$	207.303	−	469.655i	0.724835	−	1.64215i
$287$	38.2201	−	24.6229i	0.133171	−	0.0857940i
$288$	127.080	−	228.489i	0.441250	−	0.793363i
$289$	−17.6691	+	30.6037i	−0.0611386	+	0.105895i
$290$	−210.208	+	22.7752i	−0.724857	+	0.0785353i
$291$	133.720	−	77.2034i	0.459520	−	0.265304i
$292$	−91.8100	−	418.715i	−0.314418	−	1.43396i
$293$	−370.564			−1.26472			−0.632362	−	0.774673i	$-0.717915\pi$
$293$	−370.564			−1.26472			−0.632362	+	0.774673i	$0.717915\pi$
$294$	−66.5798	+	59.4583i	−0.226462	+	0.202239i
$295$	−346.981			−1.17621
$296$	−75.5171	+	372.875i	−0.255125	+	1.25971i
$297$	−178.986	+	103.337i	−0.602645	+	0.347937i
$298$	82.9021	−	8.98210i	0.278195	−	0.0301413i
$299$	232.329	−	402.406i	0.777021	−	1.34584i
$300$	37.4655	+	41.0770i	0.124885	+	0.136923i
$301$	−195.913	+	126.215i	−0.650875	+	0.419319i
$302$	−178.631	−	78.8464i	−0.591492	−	0.261081i
$303$	−12.8095	+	22.1867i	−0.0422755	+	0.0732233i
$304$	239.118	−	110.157i	0.786573	−	0.362359i
$305$	32.5081	+	56.3057i	0.106584	+	0.184609i
$306$	153.647	+	210.058i	0.502116	+	0.686465i
$307$	−160.327			−0.522239			−0.261120	−	0.965306i	$-0.584092\pi$
$307$	−160.327			−0.522239			−0.261120	+	0.965306i	$0.584092\pi$
$308$	260.912	−	262.360i	0.847116	−	0.851817i
$309$			151.486i			0.490245i
$310$	−96.3366	−	131.706i	−0.310763	−	0.424858i
$311$	409.490	−	236.419i	1.31669	−	0.760191i	0.333495	−	0.942752i	$-0.391772\pi$
$311$	409.490	−	236.419i	1.31669	−	0.760191i	0.983195	+	0.182561i	$0.0584387\pi$
$312$	−93.6951	+	106.093i	−0.300305	+	0.340042i
$313$	200.063	+	115.506i	0.639179	+	0.369030i	0.784298	−	0.620384i	$-0.213023\pi$
$313$	200.063	+	115.506i	0.639179	+	0.369030i	−0.145119	+	0.989414i	$0.546357\pi$
$314$	51.5339	+	22.7467i	0.164121	+	0.0724418i
$315$	165.924	−	322.732i	0.526743	−	1.02455i
$316$	−157.171	−	172.322i	−0.497378	−	0.545323i
$317$	−195.132	−	112.659i	−0.615557	−	0.355392i	0.159580	−	0.987185i	$-0.448986\pi$
$317$	−195.132	−	112.659i	−0.615557	−	0.355392i	−0.775137	+	0.631793i	$0.782319\pi$
$318$	−67.3461	+	7.29667i	−0.211780	+	0.0229455i
$319$	110.090	+	190.681i	0.345109	+	0.597746i
$320$	50.2055	+	402.966i	0.156892	+	1.25927i
$321$		−	179.972i		−	0.560659i
$322$	260.359	−	210.645i	0.808568	−	0.654178i
$323$			262.067i			0.811353i
$324$	−231.646	+	50.7920i	−0.714956	+	0.156766i
$325$	148.201	+	256.692i	0.456004	+	0.789822i
$326$	482.042	−	52.2273i	1.47866	−	0.160207i
$327$	−9.08716	−	5.24648i	−0.0277895	−	0.0160443i
$328$	49.2602	−	16.5309i	0.150183	−	0.0503992i
$329$	−7.46732	−	153.161i	−0.0226970	−	0.465536i
$330$	61.6801	−	139.740i	0.186909	−	0.423453i
$331$	17.9257	+	10.3494i	0.0541561	+	0.0312671i	0.526834	−	0.849968i	$-0.323379\pi$
$331$	17.9257	+	10.3494i	0.0541561	+	0.0312671i	−0.472677	+	0.881236i	$0.656712\pi$
$332$	−44.0365	+	138.546i	−0.132640	+	0.417308i
$333$	336.490	−	194.273i	1.01048	−	0.583401i
$334$	−70.9758	−	97.0343i	−0.212503	−	0.290522i
$335$			108.716i			0.324527i
$336$	−90.4686	+	47.1468i	−0.269252	+	0.140318i
$337$	34.9645			0.103752			0.0518762	−	0.998654i	$-0.483480\pi$
$337$	34.9645			0.103752			0.0518762	+	0.998654i	$0.483480\pi$
$338$	−336.258	+	245.956i	−0.994846	+	0.727682i
$339$	6.73619	+	11.6674i	0.0198708	+	0.0344172i
$340$	−385.232	−	122.445i	−1.13303	−	0.360132i
$341$	−84.9621	+	147.159i	−0.249156	+	0.431550i
$342$	−245.981	−	108.574i	−0.719243	−	0.317469i
$343$	−339.343	+	49.9505i	−0.989339	+	0.145628i
$344$	−252.504	+	84.7363i	−0.734023	+	0.246326i
$345$	69.1264	−	119.730i	0.200366	−	0.347045i
$346$	30.0234	+	277.106i	0.0867727	+	0.800886i
$347$	−379.958	+	219.369i	−1.09498	+	0.632188i	−0.934898	−	0.354916i	$-0.884509\pi$
$347$	−379.958	+	219.369i	−1.09498	+	0.632188i	−0.160083	+	0.987104i	$0.551176\pi$
$348$	−13.0019	−	59.2976i	−0.0373619	−	0.170395i
$349$	435.121			1.24677			0.623383	−	0.781917i	$-0.285758\pi$
$349$	435.121			1.24677			0.623383	+	0.781917i	$0.285758\pi$
$350$	33.3267	+	211.015i	0.0952191	+	0.602901i
$351$	303.793			0.865507
$352$	362.780	−	217.276i	1.03062	−	0.617261i
$353$	243.447	−	140.554i	0.689653	−	0.398171i	−0.113829	−	0.993500i	$-0.536312\pi$
$353$	243.447	−	140.554i	0.689653	−	0.398171i	0.803482	+	0.595329i	$0.202978\pi$
$354$	−10.7309	−	99.0424i	−0.0303131	−	0.279781i
$355$	101.701	−	176.151i	0.286481	−	0.496200i
$356$	3.17327	−	2.89428i	0.00891369	−	0.00812999i
$357$	−4.94514	−	101.429i	−0.0138519	−	0.284115i
$358$	−235.602	+	533.769i	−0.658107	+	1.49098i
$359$	−131.965	+	228.570i	−0.367590	+	0.636685i	−0.989188	−	0.146652i	$-0.953150\pi$
$359$	−131.965	+	228.570i	−0.367590	+	0.636685i	0.621598	+	0.783336i	$0.286484\pi$
$360$	274.531	−	310.857i	0.762585	−	0.863491i
$361$	45.1247	+	78.1583i	0.124999	+	0.216505i
$362$	−269.329	+	197.001i	−0.744004	+	0.544202i
$363$	−48.8468			−0.134564
$364$	−524.958	+	142.220i	−1.44219	+	0.390714i
$365$		−	679.969i		−	1.86293i
$366$	−15.0666	+	11.0205i	−0.0411655	+	0.0301105i
$367$	−134.181	+	77.4694i	−0.365615	+	0.211088i	−0.671541	−	0.740967i	$-0.734367\pi$
$367$	−134.181	+	77.4694i	−0.365615	+	0.211088i	0.305926	+	0.952055i	$0.401034\pi$
$368$	347.629	−	160.146i	0.944643	−	0.435178i
$369$	−45.9567	−	26.5331i	−0.124544	−	0.0719055i
$370$	−243.691	+	552.094i	−0.658623	+	1.49214i
$371$	−231.490	−	119.015i	−0.623962	−	0.320794i
$372$	34.6149	−	31.5715i	0.0930508	−	0.0848697i
$373$	−506.505	−	292.431i	−1.35792	−	0.783997i	−0.368579	−	0.929597i	$-0.620155\pi$
$373$	−506.505	−	292.431i	−1.35792	−	0.783997i	−0.989344	+	0.145600i	$0.953489\pi$
$374$	45.3411	+	418.484i	0.121233	+	1.11894i
$375$	−28.1478	−	48.7534i	−0.0750608	−	0.130009i
$376$	34.7864	−	171.762i	0.0925171	−	0.456815i
$377$		−	323.644i		−	0.858472i
$378$	204.380	+	78.5570i	0.540688	+	0.207823i
$379$			128.176i			0.338195i	0.985599	+	0.169098i	$0.0540853\pi$
$379$			128.176i			0.338195i	−0.985599	+	0.169098i	$0.945915\pi$
$380$	407.926	−	89.4442i	1.07349	−	0.235380i
$381$	32.0011	+	55.4276i	0.0839925	+	0.145479i
$382$	28.2982	+	261.184i	0.0740791	+	0.683727i
$383$	−216.437	−	124.960i	−0.565110	−	0.326266i	0.190084	−	0.981768i	$-0.439124\pi$
$383$	−216.437	−	124.960i	−0.565110	−	0.326266i	−0.755194	+	0.655502i	$0.772457\pi$
$384$	−113.470	+	26.7929i	−0.295495	+	0.0697733i
$385$	493.403	−	317.870i	1.28157	−	0.825636i
$386$	−149.008	−	65.7713i	−0.386032	−	0.170392i
$387$	235.571	+	136.007i	0.608709	+	0.351439i
$388$	646.211	+	205.396i	1.66549	+	0.529372i
$389$	−187.428	+	108.212i	−0.481821	+	0.278179i	−0.721175	−	0.692753i	$-0.756398\pi$
$389$	−187.428	+	108.212i	−0.481821	+	0.278179i	0.239354	+	0.970932i	$0.423064\pi$
$390$	−181.220	+	132.553i	−0.464666	+	0.339880i
$391$			380.991i			0.974402i
$392$	−389.947	−	40.0675i	−0.994763	−	0.102213i
$393$	129.460			0.329415
$394$	−2.47425	−	3.38266i	−0.00627983	−	0.00858544i
$395$	−184.984	−	320.401i	−0.468314	−	0.811143i
$396$	−411.582	−	130.820i	−1.03935	−	0.330354i
$397$	−349.941	+	606.116i	−0.881463	+	1.52674i	−0.0317493	+	0.999496i	$0.510108\pi$
$397$	−349.941	+	606.116i	−0.881463	+	1.52674i	−0.849714	+	0.527244i	$0.823226\pi$
$398$	102.522	−	232.268i	0.257592	−	0.583589i
$399$	56.8196	+	88.1964i	0.142405	+	0.221044i
$400$	−22.4055	+	243.119i	−0.0560137	+	0.607798i
$401$	90.4903	−	156.734i	0.225662	−	0.390858i	−0.730856	−	0.682532i	$-0.760879\pi$
$401$	90.4903	−	156.734i	0.225662	−	0.390858i	0.956518	+	0.291674i	$0.0942123\pi$
$402$	−31.0320	+	3.36220i	−0.0771941	+	0.00836368i
$403$	216.310	−	124.887i	0.536749	−	0.309892i
$404$	−109.893	+	24.0959i	−0.272013	+	0.0596433i
$405$	−376.179			−0.928837
$406$	83.6901	−	217.735i	0.206133	−	0.536292i
$407$	628.431			1.54406
$408$	23.0369	−	113.747i	0.0564629	−	0.278793i
$409$	−310.767	+	179.421i	−0.759821	+	0.438683i	−0.829232	−	0.558905i	$-0.811222\pi$
$409$	−310.767	+	179.421i	−0.759821	+	0.438683i	0.0694104	+	0.997588i	$0.477888\pi$
$410$	81.9423	−	8.87812i	0.199859	−	0.0216539i
$411$	−115.258	+	199.632i	−0.280432	+	0.485723i
$412$	−491.507	+	448.293i	−1.19298	+	1.08809i
$413$	175.029	−	340.441i	0.423798	−	0.824312i
$414$	−357.606	−	157.845i	−0.863782	−	0.381268i
$415$	−115.302	+	199.709i	−0.277836	+	0.481226i
$416$	−621.499	+	9.96114i	−1.49399	+	0.0239450i
$417$	22.4031	+	38.8033i	0.0537245	+	0.0930535i
$418$	−256.743	−	351.005i	−0.614218	−	0.839725i
$419$	780.890			1.86370			0.931849	−	0.362846i	$-0.118195\pi$
$419$	780.890			1.86370			0.931849	+	0.362846i	$0.118195\pi$
$420$	−156.194	+	42.3156i	−0.371890	+	0.100751i
$421$		−	114.961i		−	0.273068i	−0.990635	−	0.136534i	$-0.956404\pi$
$421$		−	114.961i		−	0.273068i	0.990635	−	0.136534i	$-0.0435962\pi$
$422$	8.46388	+	11.5714i	0.0200566	+	0.0274203i
$423$	−155.002	+	89.4904i	−0.366435	+	0.211561i
$424$	−222.972	−	196.916i	−0.525878	−	0.464425i
$425$	−210.472	−	121.516i	−0.495228	−	0.285920i
$426$	53.4258	+	23.5818i	0.125413	+	0.0553563i
$427$	−71.6425	+	3.49290i	−0.167781	+	0.00818010i
$428$	583.931	−	532.591i	1.36432	−	1.24437i
$429$	202.482	+	116.903i	0.471985	+	0.272501i
$430$	−420.030	+	45.5085i	−0.976813	+	0.105834i
$431$	−154.856	−	268.219i	−0.359295	−	0.622317i	0.628548	−	0.777771i	$-0.283649\pi$
$431$	−154.856	−	268.219i	−0.359295	−	0.622317i	−0.987843	+	0.155453i	$0.950316\pi$
$432$	204.315	+	144.478i	0.472952	+	0.334440i
$433$		−	595.775i		−	1.37592i	−0.725747	−	0.687962i	$-0.758506\pi$
$433$		−	595.775i		−	1.37592i	0.725747	−	0.687962i	$-0.241494\pi$
$434$	177.819	−	28.0838i	0.409721	−	0.0647092i
$435$		−	96.2958i		−	0.221370i
$436$	−9.86914	−	45.0099i	−0.0226356	−	0.103234i
$437$	−196.808	−	340.881i	−0.450361	−	0.780048i
$438$	194.091	−	21.0289i	0.443129	−	0.0480113i
$439$	698.796	+	403.450i	1.59179	+	0.919020i	0.993000	+	0.118113i	$0.0376846\pi$
$439$	698.796	+	403.450i	1.59179	+	0.919020i	0.598789	+	0.800907i	$0.295649\pi$
$440$	635.925	−	213.407i	1.44529	−	0.485015i
$441$	232.951	+	325.593i	0.528233	+	0.738306i
$442$	249.849	−	566.045i	0.565269	−	1.28065i
$443$	385.214	+	222.403i	0.869557	+	0.502039i	0.867201	−	0.497958i	$-0.165917\pi$
$443$	385.214	+	222.403i	0.869557	+	0.502039i	0.00235617	+	0.999997i	$0.499250\pi$
$444$	−165.126	−	52.4849i	−0.371906	−	0.118209i
$445$	5.90012	−	3.40644i	0.0132587	−	0.00765491i
$446$	330.280	+	451.540i	0.740538	+	1.01242i
$447$			37.9772i			0.0849601i
$448$	−420.696	−	154.010i	−0.939053	−	0.343773i
$449$	262.420			0.584455			0.292228	−	0.956349i	$-0.405604\pi$
$449$	262.420			0.584455			0.292228	+	0.956349i	$0.405604\pi$
$450$	201.256	−	147.209i	0.447235	−	0.327131i
$451$	−42.9145	−	74.3302i	−0.0951542	−	0.164812i
$452$	−17.9213	+	56.3836i	−0.0396490	+	0.124742i
$453$	44.4633	−	77.0127i	0.0981530	−	0.170006i
$454$	557.659	+	246.147i	1.22832	+	0.542174i
$455$	−861.712	+	42.0124i	−1.89387	+	0.0923350i
$456$	38.1466	+	113.672i	0.0836549	+	0.249281i
$457$	−194.738	+	337.296i	−0.426122	+	0.738065i	−0.996524	−	0.0833004i	$-0.973454\pi$
$457$	−194.738	+	337.296i	−0.426122	+	0.738065i	0.570403	+	0.821365i	$0.306787\pi$
$458$	89.3368	+	824.551i	0.195058	+	1.80033i
$459$	−215.720	+	124.546i	−0.469978	+	0.271342i
$460$	593.040	−	130.034i	1.28922	−	0.282682i
$461$	158.714			0.344283			0.172141	−	0.985072i	$-0.444931\pi$
$461$	158.714			0.344283			0.172141	+	0.985072i	$0.444931\pi$
$462$	105.992	+	131.007i	0.229420	+	0.283564i
$463$	−528.844			−1.14221			−0.571106	−	0.820877i	$-0.693485\pi$
$463$	−528.844			−1.14221			−0.571106	+	0.820877i	$0.693485\pi$
$464$	153.919	−	217.666i	0.331721	−	0.469107i
$465$	64.3601	−	37.1583i	0.138409	−	0.0799103i
$466$	35.5301	+	327.932i	0.0762449	+	0.703717i
$467$	−218.449	+	378.365i	−0.467771	+	0.810203i	−0.999322	−	0.0368236i	$-0.988276\pi$
$467$	−218.449	+	378.365i	−0.467771	+	0.810203i	0.531551	+	0.847026i	$0.321609\pi$
$468$	427.788	+	469.025i	0.914078	+	1.00219i
$469$	−106.667	−	54.8401i	−0.227435	−	0.116930i
$470$	112.254	−	254.318i	0.238839	−	0.541102i
$471$	−12.8274	+	22.2177i	−0.0272344	+	0.0471713i
$472$	289.595	−	327.914i	0.613548	−	0.694733i
$473$	219.977	+	381.011i	0.465067	+	0.805519i
$474$	85.7346	−	62.7107i	0.180875	−	0.132301i
$475$	251.085			0.528600
$476$	314.460	−	316.205i	0.660631	−	0.664296i
$477$			303.811i			0.636920i
$478$	30.8617	−	22.5739i	0.0645643	−	0.0472256i
$479$	472.737	−	272.935i	0.986925	−	0.569802i	0.0825716	−	0.996585i	$-0.473687\pi$
$479$	472.737	−	272.935i	0.986925	−	0.569802i	0.904354	+	0.426783i	$0.140353\pi$
$480$	−184.919	+	2.96380i	−0.385247	+	0.00617458i
$481$	−799.980	−	461.869i	−1.66316	−	0.960226i
$482$	282.913	−	640.955i	0.586957	−	1.32978i
$483$	82.6039	+	128.219i	0.171023	+	0.265464i
$484$	−144.553	−	158.487i	−0.298663	−	0.327453i
$485$	931.488	+	537.795i	1.92059	+	1.10886i
$486$	−41.9576	−	387.255i	−0.0863324	−	0.796822i
$487$	−324.115	−	561.384i	−0.665534	−	1.15274i	−0.979140	−	0.203185i	$-0.934871\pi$
$487$	−324.115	−	561.384i	−0.665534	−	1.15274i	0.313606	−	0.949553i	$-0.398463\pi$
$488$	−80.3433	−	16.2716i	−0.164638	−	0.0333435i
$489$			220.822i			0.451579i
$490$	−590.589	−	194.563i	−1.20528	−	0.397068i
$491$		−	732.074i		−	1.49098i	−0.666514	−	0.745492i	$-0.732214\pi$
$491$		−	732.074i		−	1.49098i	0.666514	−	0.745492i	$-0.267786\pi$
$492$	5.06834	+	23.1151i	0.0103015	+	0.0469818i
$493$	132.684	+	229.815i	0.269136	+	0.466157i
$494$	68.8557	+	635.516i	0.139384	+	1.28647i
$495$	−593.279	−	342.530i	−1.19854	−	0.691980i
$496$	204.872	+	18.8807i	0.413049	+	0.0380659i
$497$	121.529	+	188.640i	0.244526	+	0.379557i
$498$	−60.5709	−	26.7356i	−0.121628	−	0.0536859i
$499$	23.1264	+	13.3520i	0.0463454	+	0.0267575i	0.522994	−	0.852337i	$-0.324815\pi$
$499$	23.1264	+	13.3520i	0.0463454	+	0.0267575i	−0.476648	+	0.879094i	$0.658148\pi$
$500$	74.8860	−	235.604i	0.149772	−	0.471208i
$501$	47.4172	−	27.3763i	0.0946451	−	0.0546434i
$502$	142.572	−	104.284i	0.284008	−	0.207738i
$503$			616.414i			1.22548i	0.790286	+	0.612738i	$0.209932\pi$
$503$			616.414i			1.22548i	−0.790286	+	0.612738i	$0.790068\pi$
$504$	166.515	+	426.162i	0.330387	+	0.845560i
$505$	−178.460			−0.353387
$506$	−373.251	−	510.289i	−0.737651	−	1.00848i
$507$	−94.8687	−	164.317i	−0.187118	−	0.324097i
$508$	−85.1377	+	267.857i	−0.167594	+	0.527278i
$509$	−66.3763	+	114.967i	−0.130405	+	0.225869i	−0.923833	−	0.382796i	$-0.874961\pi$
$509$	−66.3763	+	114.967i	−0.130405	+	0.225869i	0.793428	+	0.608665i	$0.208295\pi$
$510$	74.3391	−	168.419i	0.145763	−	0.330233i
$511$	667.152	+	342.999i	1.30558	+	0.671230i
$512$	−422.725	−	288.874i	−0.825634	−	0.564206i
$513$	128.673	−	222.868i	0.250824	−	0.434440i
$514$	−171.164	+	18.5449i	−0.333004	+	0.0360796i
$515$	−913.867	+	527.621i	−1.77450	+	1.02451i
$516$	−25.9799	−	118.486i	−0.0503487	−	0.229624i
$517$	−289.483			−0.559928
$518$	−418.761	−	517.591i	−0.808420	−	0.999211i
$519$	−126.942			−0.244589
$520$	−966.364	−	195.714i	−1.85839	−	0.376374i
$521$	−585.480	+	338.027i	−1.12376	+	0.648804i	−0.942359	−	0.334605i	$-0.891397\pi$
$521$	−585.480	+	338.027i	−1.12376	+	0.648804i	−0.181403	+	0.983409i	$0.558064\pi$
$522$	−270.680	+	29.3271i	−0.518544	+	0.0561822i
$523$	−186.224	+	322.550i	−0.356069	+	0.616730i	−0.987300	−	0.158865i	$-0.949217\pi$
$523$	−186.224	+	322.550i	−0.356069	+	0.616730i	0.631231	+	0.775595i	$0.282550\pi$
$524$	383.113	+	420.043i	0.731131	+	0.801609i
$525$	−97.1787	+	4.73791i	−0.185102	+	0.00902459i
$526$	584.055	+	257.798i	1.11037	+	0.490110i
$527$	−102.399	+	177.361i	−0.194306	+	0.336548i
$528$	80.5817	+	174.919i	0.152617	+	0.331286i
$529$	−21.6179	−	37.4433i	−0.0408656	−	0.0707813i
$530$	−278.583	−	380.864i	−0.525629	−	0.718611i
$531$	−446.799			−0.841429
$532$	−118.013	+	445.355i	−0.221829	+	0.837134i
$533$			126.161i			0.236700i
$534$	1.15480	+	1.57878i	0.00216255	+	0.00295653i
$535$	1085.71	−	626.836i	2.02937	−	1.17166i
$536$	−102.742	−	90.7360i	−0.191683	−	0.169284i
$537$	−230.123	−	132.862i	−0.428534	−	0.247414i
$538$	−105.148	−	46.4119i	−0.195443	−	0.0862674i
$539$	62.9892	+	644.447i	0.116863	+	1.19563i
$540$	267.490	+	293.275i	0.495352	+	0.543102i
$541$	−60.3373	−	34.8357i	−0.111529	−	0.0643914i	0.443198	−	0.896424i	$-0.353844\pi$
$541$	−60.3373	−	34.8357i	−0.111529	−	0.0643914i	−0.554727	+	0.832032i	$0.687177\pi$
$542$	−61.3936	+	6.65176i	−0.113272	+	0.0122726i
$543$	−75.9860	−	131.612i	−0.139937	−	0.242379i
$544$	437.235	−	261.869i	0.803741	−	0.481377i
$545$		−	73.0934i		−	0.134116i
$546$	−38.6416	−	244.668i	−0.0707722	−	0.448110i
$547$		−	466.463i		−	0.852765i	−0.904543	−	0.426383i	$-0.859788\pi$
$547$		−	466.463i		−	0.852765i	0.904543	−	0.426383i	$-0.140212\pi$
$548$	−988.803	+	216.811i	−1.80439	+	0.395640i
$549$	41.8599	+	72.5034i	0.0762475	+	0.132065i
$550$	400.947	−	43.4410i	0.728995	−	0.0789837i
$551$	−237.430	−	137.081i	−0.430908	−	0.248785i
$552$	55.4574	+	165.256i	0.100466	+	0.299377i
$553$	407.674	−	19.8760i	0.737204	−	0.0359421i
$554$	−287.659	+	651.707i	−0.519241	+	1.17637i
$555$	−238.023	−	137.423i	−0.428870	−	0.247608i
$556$	−59.6025	+	187.519i	−0.107199	+	0.337265i
$557$	−118.835	+	68.6094i	−0.213348	+	0.123177i	−0.602866	−	0.797842i	$-0.705975\pi$
$557$	−118.835	+	68.6094i	−0.213348	+	0.123177i	0.389518	+	0.921019i	$0.372642\pi$
$558$	−124.050	−	169.595i	−0.222312	−	0.303933i
$559$		−	646.692i		−	1.15687i
$560$	−599.522	−	381.558i	−1.07058	−	0.681354i
$561$	−191.706			−0.341722
$562$	474.850	−	347.329i	0.844929	−	0.618024i
$563$	−84.5632	−	146.468i	−0.150201	−	0.260156i	0.781100	−	0.624406i	$-0.214659\pi$
$563$	−84.5632	−	146.468i	−0.150201	−	0.260156i	−0.931301	+	0.364250i	$0.881325\pi$
$564$	76.0643	+	24.1768i	0.134866	+	0.0428667i
$565$	−46.9240	+	81.2747i	−0.0830513	+	0.143849i
$566$	−759.324	−	335.161i	−1.34156	−	0.592157i
$567$	189.757	−	369.088i	0.334669	−	0.650949i
$568$	81.5905	+	243.130i	0.143645	+	0.428045i
$569$	−372.466	+	645.129i	−0.654597	+	1.13379i	0.327398	+	0.944887i	$0.393828\pi$
$569$	−372.466	+	645.129i	−0.654597	+	1.13379i	−0.981995	+	0.188908i	$0.939505\pi$
$570$	20.4871	+	189.089i	0.0359422	+	0.331735i
$571$	767.828	−	443.306i	1.34471	−	0.776367i	0.357213	−	0.934023i	$-0.383727\pi$
$571$	767.828	−	443.306i	1.34471	−	0.776367i	0.987494	+	0.157655i	$0.0503935\pi$
$572$	219.906	+	1002.92i	0.384450	+	1.75335i
$573$	−119.647			−0.208809
$574$	−32.6236	+	84.8761i	−0.0568355	+	0.147868i
$575$	365.026			0.634827
$576$	64.6484	+	518.889i	0.112237	+	0.900849i
$577$	−207.900	+	120.031i	−0.360311	+	0.208026i	−0.669217	−	0.743067i	$-0.733370\pi$
$577$	−207.900	+	120.031i	−0.360311	+	0.208026i	0.308906	+	0.951093i	$0.400037\pi$
$578$	−7.61293	−	70.2650i	−0.0131712	−	0.121566i
$579$	37.0900	−	64.2417i	0.0640586	−	0.110953i
$580$	312.439	−	284.969i	0.538687	−	0.491326i
$581$	−137.782	−	213.868i	−0.237147	−	0.368104i
$582$	−124.701	+	282.516i	−0.214263	+	0.485423i
$583$	−245.691	+	425.549i	−0.421425	+	0.729930i
$584$	642.604	+	567.510i	1.10035	+	0.971763i
$585$	503.488	+	872.067i	0.860663	+	1.49071i
$586$	598.186	−	437.544i	1.02080	−	0.746662i
$587$	190.873			0.325168			0.162584	−	0.986695i	$-0.448017\pi$
$587$	190.873			0.325168			0.162584	+	0.986695i	$0.448017\pi$
$588$	37.2715	−	174.595i	0.0633868	−	0.296931i
$589$		−	211.585i		−	0.359227i
$590$	560.117	−	409.698i	0.949351	−	0.694404i
$591$	1.65299	−	0.954353i	0.00279693	−	0.00161481i
$592$	−318.368	−	691.083i	−0.537784	−	1.16737i
$593$	637.548	+	368.089i	1.07512	+	0.620723i	0.929577	−	0.368629i	$-0.120173\pi$
$593$	637.548	+	368.089i	1.07512	+	0.620723i	0.145547	+	0.989351i	$0.453506\pi$
$594$	166.913	−	378.150i	0.280998	−	0.636617i
$595$	594.667	−	383.108i	0.999441	−	0.643879i
$596$	−123.220	+	112.386i	−0.206744	+	0.188567i
$597$	100.137	+	57.8144i	0.167734	+	0.0968415i
$598$	100.102	+	923.910i	0.167395	+	1.54500i
$599$	−558.330	−	967.057i	−0.932104	−	1.61445i	−0.779718	−	0.626131i	$-0.784638\pi$
$599$	−558.330	−	967.057i	−0.932104	−	1.61445i	−0.152386	−	0.988321i	$-0.548696\pi$
$600$	−108.981	−	22.0715i	−0.181635	−	0.0367858i
$601$			183.100i			0.304659i	0.988330	+	0.152329i	$0.0486774\pi$
$601$			183.100i			0.304659i	−0.988330	+	0.152329i	$0.951323\pi$
$602$	167.226	−	435.068i	0.277784	−	0.722705i
$603$			139.991i			0.232158i
$604$	381.454	−	83.6398i	0.631546	−	0.138477i
$605$	−170.132	−	294.678i	−0.281210	−	0.487071i
$606$	−5.51912	−	50.9398i	−0.00910746	−	0.0840591i
$607$	394.026	+	227.491i	0.649136	+	0.374779i	0.788125	−	0.615515i	$-0.211052\pi$
$607$	394.026	+	227.491i	0.649136	+	0.374779i	−0.138989	+	0.990294i	$0.544385\pi$
$608$	−255.931	+	460.161i	−0.420938	+	0.756844i
$609$	94.4807	+	48.5748i	0.155141	+	0.0797615i
$610$	−118.959	−	52.5079i	−0.195015	−	0.0860786i
$611$	368.505	+	212.757i	0.603118	+	0.348211i
$612$	−496.053	−	157.669i	−0.810544	−	0.257629i
$613$	232.853	−	134.438i	0.379859	−	0.219312i	−0.297898	−	0.954598i	$-0.596286\pi$
$613$	232.853	−	134.438i	0.379859	−	0.219312i	0.677757	+	0.735286i	$0.262952\pi$
$614$	258.810	−	189.307i	0.421514	−	0.308317i
$615$			37.5375i			0.0610366i
$616$	−111.398	+	731.588i	−0.180841	+	1.18764i
$617$	−184.934			−0.299731			−0.149866	−	0.988706i	$-0.547884\pi$
$617$	−184.934			−0.299731			−0.149866	+	0.988706i	$0.547884\pi$
$618$	−178.867	−	244.537i	−0.289429	−	0.395691i
$619$	−496.809	−	860.498i	−0.802599	−	1.39014i	−0.917900	−	0.396812i	$-0.870116\pi$
$619$	−496.809	−	860.498i	−0.802599	−	1.39014i	0.115301	−	0.993331i	$-0.463217\pi$
$620$	311.024	+	98.8581i	0.501652	+	0.159449i
$621$	187.064	−	324.004i	0.301229	−	0.521745i
$622$	−381.871	+	865.148i	−0.613940	+	1.39091i
$623$	0.366012	+	7.50723i	0.000587499	+	0.0120501i
$624$	25.9787	−	281.892i	0.0416325	−	0.451750i
$625$	386.818	−	669.988i	0.618909	−	1.07198i
$626$	−459.337	+	49.7674i	−0.733766	+	0.0795006i
$627$	171.524	−	99.0292i	0.273562	−	0.157941i
$628$	−110.047	+	24.1296i	−0.175234	+	0.0384229i
$629$	757.408			1.20415
$630$	113.222	+	716.887i	0.179717	+	1.13792i
$631$	805.857			1.27711			0.638555	−	0.769576i	$-0.279532\pi$
$631$	805.857			1.27711			0.638555	+	0.769576i	$0.279532\pi$
$632$	457.185	+	92.5920i	0.723393	+	0.146506i
$633$	−5.65451	+	3.26463i	−0.00893287	+	0.00515740i
$634$	448.015	−	48.5406i	0.706648	−	0.0765625i
$635$	−222.918	+	386.106i	−0.351053	+	0.608041i
$636$	100.098	−	91.2976i	0.157387	−	0.143550i
$637$	393.455	−	866.662i	0.617669	−	1.36054i
$638$	−402.860	−	177.820i	−0.631442	−	0.278714i
$639$	130.957	−	226.825i	0.204941	−	0.354969i
$640$	−556.847	−	591.211i	−0.870074	−	0.923767i
$641$	−2.75221	−	4.76696i	−0.00429361	−	0.00743676i	0.863871	−	0.503714i	$-0.168033\pi$
$641$	−2.75221	−	4.76696i	−0.00429361	−	0.00743676i	−0.868164	+	0.496277i	$0.834700\pi$
$642$	212.501	+	290.520i	0.330999	+	0.452524i
$643$	−1024.08			−1.59266			−0.796331	−	0.604861i	$-0.793229\pi$
$643$	−1024.08			−1.59266			−0.796331	+	0.604861i	$0.793229\pi$
$644$	−171.567	+	647.455i	−0.266408	+	1.00536i
$645$		−	192.414i		−	0.298317i
$646$	−309.436	−	423.044i	−0.479003	−	0.654866i
$647$	395.404	−	228.287i	0.611134	−	0.352839i	−0.162275	−	0.986746i	$-0.551883\pi$
$647$	395.404	−	228.287i	0.611134	−	0.352839i	0.773409	+	0.633907i	$0.218550\pi$
$648$	313.963	−	355.507i	0.484511	−	0.548623i
$649$	−625.834	−	361.325i	−0.964304	−	0.556741i
$650$	−542.325	−	239.379i	−0.834346	−	0.368275i
$651$	3.99255	+	81.8908i	0.00613295	+	0.125792i
$652$	−716.473	+	653.480i	−1.09888	+	1.00227i
$653$	−24.4603	−	14.1222i	−0.0374584	−	0.0216266i	0.481154	−	0.876636i	$-0.340218\pi$
$653$	−24.4603	−	14.1222i	−0.0374584	−	0.0216266i	−0.518612	+	0.855010i	$0.673551\pi$
$654$	20.8638	−	2.26051i	0.0319018	−	0.00345644i
$655$	450.907	+	780.994i	0.688407	+	1.19236i
$656$	−59.9997	+	84.8492i	−0.0914630	+	0.129343i
$657$		−	875.579i		−	1.33269i
$658$	192.900	+	238.425i	0.293160	+	0.362348i
$659$			132.188i			0.200589i	0.994958	+	0.100295i	$0.0319785\pi$
$659$			132.188i			0.200589i	−0.994958	+	0.100295i	$0.968021\pi$
$660$	65.4299	+	298.404i	0.0991362	+	0.452128i
$661$	346.924	+	600.889i	0.524847	+	0.909061i	0.999581	+	0.0289321i	$0.00921065\pi$
$661$	346.924	+	600.889i	0.524847	+	0.909061i	−0.474735	+	0.880129i	$0.657456\pi$
$662$	−41.1567	+	4.45917i	−0.0621703	+	0.00673590i
$663$	244.038	+	140.895i	0.368082	+	0.212512i
$664$	−92.5022	−	275.645i	−0.139311	−	0.415129i
$665$	−334.160	+	649.960i	−0.502497	+	0.977384i
$666$	−313.794	+	710.917i	−0.471162	+	1.06744i
$667$	−345.175	−	199.287i	−0.517504	−	0.298781i
$668$	229.147	+	72.8336i	0.343034	+	0.109032i
$669$	−220.652	+	127.393i	−0.329823	+	0.190424i
$670$	−128.367	−	175.496i	−0.191592	−	0.261935i
$671$			135.408i			0.201800i
$672$	90.3711	−	182.928i	0.134481	−	0.272214i
$673$	532.137			0.790694			0.395347	−	0.918532i	$-0.370624\pi$
$673$	532.137			0.790694			0.395347	+	0.918532i	$0.370624\pi$
$674$	−56.4418	+	41.2844i	−0.0837415	+	0.0612528i
$675$	119.327	+	206.680i	0.176780	+	0.306192i
$676$	252.394	−	794.074i	0.373364	−	1.17467i
$677$	−143.115	+	247.883i	−0.211396	+	0.366149i	−0.952152	−	0.305626i	$-0.901134\pi$
$677$	−143.115	+	247.883i	−0.211396	+	0.366149i	0.740756	+	0.671775i	$0.234468\pi$
$678$	−24.6503	−	10.8805i	−0.0363573	−	0.0160479i
$679$	−997.531	+	642.649i	−1.46912	+	0.946464i
$680$	766.440	−	257.205i	1.12712	−	0.378243i
$681$	−138.808	+	240.423i	−0.203830	+	0.353043i
$682$	−36.6070	−	337.871i	−0.0536759	−	0.495412i
$683$	387.838	−	223.918i	0.567844	−	0.327845i	−0.188443	−	0.982084i	$-0.560344\pi$
$683$	387.838	−	223.918i	0.567844	−	0.327845i	0.756288	+	0.654239i	$0.227011\pi$
$684$	525.276	−	115.175i	0.767947	−	0.168385i
$685$	−1605.76			−2.34417
$686$	488.809	−	481.313i	0.712549	−	0.701622i
$687$	−377.724			−0.549817
$688$	307.554	−	434.930i	0.447026	−	0.632166i
$689$	625.519	−	361.143i	0.907865	−	0.524156i
$690$	29.7840	+	274.897i	0.0431652	+	0.398401i
$691$	510.366	−	883.980i	0.738591	−	1.27928i	−0.214539	−	0.976715i	$-0.568825\pi$
$691$	510.366	−	883.980i	0.738591	−	1.27928i	0.953130	−	0.302561i	$-0.0978417\pi$
$692$	−375.659	−	411.871i	−0.542860	−	0.595189i
$693$	635.343	−	409.313i	0.916801	−	0.590639i
$694$	354.331	−	802.754i	0.510563	−	1.15671i
$695$	−156.059	+	270.302i	−0.224545	+	0.388924i
$696$	91.0042	+	80.3696i	0.130753	+	0.115474i
$697$	−51.7221	−	89.5854i	−0.0742068	−	0.128530i
$698$	−702.398	+	513.770i	−1.00630	+	0.736060i
$699$	−150.225			−0.214914
$700$	−302.954	−	301.283i	−0.432792	−	0.430404i
$701$			1311.02i			1.87021i	0.354369	+	0.935106i	$0.384696\pi$
$701$			1311.02i			1.87021i	−0.354369	+	0.935106i	$0.615304\pi$
$702$	−490.400	+	358.704i	−0.698576	+	0.510974i
$703$	−677.669	+	391.252i	−0.963967	+	0.556546i
$704$	−329.071	+	779.092i	−0.467431	+	1.10666i
$705$	109.644	+	63.3028i	0.155523	+	0.0897912i
$706$	−227.027	+	514.342i	−0.321568	+	0.728530i
$707$	90.0213	−	175.096i	0.127329	−	0.247661i
$708$	134.267	+	147.210i	0.189642	+	0.207923i
$709$	−465.495	−	268.754i	−0.656552	−	0.379061i	0.134410	−	0.990926i	$-0.457086\pi$
$709$	−465.495	−	268.754i	−0.656552	−	0.379061i	−0.790962	+	0.611865i	$0.790419\pi$
$710$	43.8190	+	404.436i	0.0617169	+	0.569628i
$711$	−238.199	−	412.573i	−0.335020	−	0.580271i
$712$	−1.70506	+	8.41895i	−0.00239475	+	0.0118244i
$713$		−	307.601i		−	0.431417i
$714$	127.745	+	157.894i	0.178915	+	0.221140i
$715$			1628.68i			2.27787i
$716$	−249.926	−	1139.83i	−0.349058	−	1.59194i
$717$	8.70704	+	15.0810i	0.0121437	+	0.0210335i
$718$	−56.8587	−	524.788i	−0.0791904	−	0.730903i
$719$	−233.275	−	134.681i	−0.324443	−	0.187318i	0.328928	−	0.944355i	$-0.393313\pi$
$719$	−233.275	−	134.681i	−0.324443	−	0.187318i	−0.653371	+	0.757037i	$0.726646\pi$
$720$	−76.1187	+	825.955i	−0.105720	+	1.14716i
$721$	−56.6914	−	1162.79i	−0.0786288	−	1.61275i
$722$	−165.128	−	72.8866i	−0.228710	−	0.100951i
$723$	276.334	+	159.541i	0.382204	+	0.220666i
$724$	202.158	−	636.022i	0.279223	−	0.878483i
$725$	220.185	−	127.124i	0.303703	−	0.175343i
$726$	78.8513	−	57.6759i	0.108611	−	0.0794434i
$727$			460.316i			0.633172i	0.948564	+	0.316586i	$0.102537\pi$
$727$			460.316i			0.633172i	−0.948564	+	0.316586i	$0.897463\pi$
$728$	679.491	−	849.424i	0.933367	−	1.16679i
$729$	−356.185			−0.488594
$730$	802.874	+	1097.64i	1.09983	+	1.50362i
$731$	265.124	+	459.208i	0.362686	+	0.628191i
$732$	11.3089	−	35.5797i	0.0154493	−	0.0486062i
$733$	−33.3410	+	57.7484i	−0.0454857	+	0.0787836i	−0.887872	−	0.460091i	$-0.847817\pi$
$733$	−33.3410	+	57.7484i	−0.0454857	+	0.0787836i	0.842386	+	0.538874i	$0.181150\pi$
$734$	125.130	−	283.490i	0.170478	−	0.386226i
$735$	117.067	−	257.863i	0.159275	−	0.350834i
$736$	−372.070	+	668.979i	−0.505530	+	0.908939i
$737$	−113.211	+	196.087i	−0.153610	+	0.266061i
$738$	105.515	−	11.4321i	0.142974	−	0.0154907i
$739$	−808.772	+	466.944i	−1.09441	+	0.631860i	−0.934748	−	0.355311i	$-0.884375\pi$
$739$	−808.772	+	466.944i	−1.09441	+	0.631860i	−0.159665	+	0.987171i	$0.551042\pi$
$740$	−258.506	−	1178.96i	−0.349332	−	1.59319i
$741$	−291.128			−0.392885
$742$	514.211	−	81.2119i	0.693007	−	0.109450i
$743$	−1198.23			−1.61269			−0.806345	−	0.591446i	$-0.798557\pi$
$743$	−1198.23			−1.61269			−0.806345	+	0.591446i	$0.798557\pi$
$744$	−18.5993	+	91.8361i	−0.0249990	+	0.123436i
$745$	−229.104	+	132.273i	−0.307523	+	0.177548i
$746$	1162.92	−	125.997i	1.55887	−	0.168897i
$747$	−148.471	+	257.160i	−0.198757	+	0.344257i
$748$	−567.318	−	622.005i	−0.758446	−	0.831557i
$749$	67.3518	+	1381.44i	0.0899222	+	1.84438i
$750$	103.003	+	45.4651i	0.137338	+	0.0606201i
$751$	84.2993	−	146.011i	0.112249	−	0.194422i	−0.804427	−	0.594051i	$-0.797528\pi$
$751$	84.2993	−	146.011i	0.112249	−	0.194422i	0.916677	+	0.399629i	$0.130861\pi$
$752$	146.654	+	318.343i	0.195019	+	0.423328i
$753$	40.2239	+	69.6698i	0.0534182	+	0.0925230i
$754$	382.143	+	522.445i	0.506821	+	0.692897i
$755$	619.458			0.820474
$756$	−422.678	+	114.511i	−0.559098	+	0.151469i
$757$		−	209.207i		−	0.276364i	−0.990407	−	0.138182i	$-0.955874\pi$
$757$		−	209.207i		−	0.276364i	0.990407	−	0.138182i	$-0.0441259\pi$
$758$	−151.344	−	206.909i	−0.199662	−	0.272967i
$759$	249.360	−	143.968i	0.328538	−	0.189681i
$760$	−552.886	+	626.045i	−0.727482	+	0.823743i
$761$	479.127	+	276.624i	0.629602	+	0.363501i	0.780598	−	0.625033i	$-0.214915\pi$
$761$	479.127	+	276.624i	0.629602	+	0.363501i	−0.150996	+	0.988534i	$0.548248\pi$
$762$	−117.104	−	51.6891i	−0.153680	−	0.0678334i
$763$	71.7156	+	36.8707i	0.0939916	+	0.0483233i
$764$	−354.073	−	388.205i	−0.463447	−	0.508121i
$765$	−715.041	−	412.829i	−0.934695	−	0.539646i
$766$	496.932	−	53.8405i	0.648736	−	0.0702879i
$767$	531.115	+	919.919i	0.692458	+	1.19937i
$768$	151.534	−	177.231i	0.197310	−	0.230769i
$769$		−	219.524i		−	0.285467i	−0.989761	−	0.142734i	$-0.954411\pi$
$769$		−	219.524i		−	0.285467i	0.989761	−	0.142734i	$-0.0455892\pi$
$770$	−421.155	+	1095.71i	−0.546955	+	1.42300i
$771$		−	78.4096i		−	0.101699i
$772$	318.197	−	69.7698i	0.412173	−	0.0903755i
$773$	−333.337	−	577.357i	−0.431225	−	0.746904i	0.565754	−	0.824574i	$-0.308585\pi$
$773$	−333.337	−	577.357i	−0.431225	−	0.746904i	−0.996979	+	0.0776701i	$0.975252\pi$
$774$	−540.862	+	58.6002i	−0.698788	+	0.0757108i
$775$	169.928	+	98.1082i	0.219262	+	0.126591i
$776$	−1285.67	+	431.452i	−1.65680	+	0.555995i
$777$	254.899	−	164.216i	0.328055	−	0.211346i
$778$	174.786	−	395.988i	0.224661	−	0.508981i
$779$	92.5538	+	53.4359i	0.118811	+	0.0685956i
$780$	136.023	−	427.951i	0.174388	−	0.548655i
$781$	366.866	−	211.810i	0.469738	−	0.271204i
$782$	−449.856	−	615.018i	−0.575263	−	0.786468i
$783$		−	260.587i		−	0.332806i
$784$	676.784	−	395.751i	0.863246	−	0.504784i
$785$	−178.710			−0.227656
$786$	−208.982	+	152.860i	−0.265881	+	0.194479i
$787$	459.932	+	796.626i	0.584412	+	1.01223i	0.994948	+	0.100387i	$0.0320081\pi$
$787$	459.932	+	796.626i	0.584412	+	1.01223i	−0.410536	+	0.911844i	$0.634659\pi$
$788$	7.98816	+	2.53901i	0.0101373	+	0.00322210i
$789$	−145.378	+	251.803i	−0.184256	+	0.319141i
$790$	676.926	+	298.791i	0.856868	+	0.378216i
$791$	−56.0727	−	87.0371i	−0.0708884	−	0.110034i
$792$	818.865	−	274.798i	1.03392	−	0.346967i
$793$	99.5187	−	172.371i	0.125496	−	0.217366i
$794$	−150.776	−	1391.62i	−0.189895	−	1.75267i
$795$	186.115	−	107.453i	0.234106	−	0.135161i
$796$	108.755	+	495.994i	0.136626	+	0.623108i
$797$	1016.13			1.27494			0.637470	−	0.770476i	$-0.279981\pi$
$797$	1016.13			1.27494			0.637470	+	0.770476i	$0.279981\pi$
$798$	−195.859	−	75.2819i	−0.245438	−	0.0943383i
$799$	−348.895			−0.436664
$800$	−250.895	−	418.912i	−0.313619	−	0.523640i
$801$	7.59744	−	4.38638i	0.00948494	−	0.00547613i
$802$	38.9889	+	359.855i	0.0486146	+	0.448697i
$803$	708.078	−	1226.43i	0.881791	−	1.52731i
$804$	46.1238	−	42.0686i	0.0573679	−	0.0523241i
$805$	−485.800	+	944.909i	−0.603478	+	1.17380i
$806$	−201.720	+	457.007i	−0.250273	+	0.567007i
$807$	26.1727	−	45.3325i	0.0324321	−	0.0561741i
$808$	148.945	−	168.654i	0.184338	−	0.208730i
$809$	−565.950	−	980.254i	−0.699567	−	1.21169i	−0.968617	−	0.248560i	$-0.920043\pi$
$809$	−565.950	−	980.254i	−0.699567	−	1.21169i	0.269049	−	0.963126i	$-0.413291\pi$
$810$	607.250	−	444.174i	0.749691	−	0.548362i
$811$	481.066			0.593176			0.296588	−	0.955006i	$-0.404151\pi$
$811$	481.066			0.593176			0.296588	+	0.955006i	$0.404151\pi$
$812$	121.993	+	450.297i	0.150238	+	0.554553i
$813$		−	28.1242i		−	0.0345931i
$814$	−1014.45	+	742.021i	−1.24625	+	0.911573i
$815$	−1332.15	+	769.117i	−1.63454	+	0.943702i
$816$	97.1199	+	210.818i	0.119019	+	0.258356i
$817$	−474.423	−	273.908i	−0.580690	−	0.335261i
$818$	289.806	−	656.570i	0.354286	−	0.802653i
$819$	−1109.60	+	54.0983i	−1.35483	+	0.0660541i
$820$	−121.793	+	111.085i	−0.148528	+	0.135469i
$821$	−630.185	−	363.838i	−0.767582	−	0.443164i	0.0644292	−	0.997922i	$-0.479477\pi$
$821$	−630.185	−	363.838i	−0.767582	−	0.443164i	−0.832011	+	0.554758i	$0.812811\pi$
$822$	−49.6602	−	458.348i	−0.0604138	−	0.557601i
$823$	313.323	+	542.692i	0.380709	+	0.659407i	0.991164	−	0.132644i	$-0.0423468\pi$
$823$	313.323	+	542.692i	0.380709	+	0.659407i	−0.610455	+	0.792051i	$0.709013\pi$
$824$	264.096	−	1304.01i	0.320505	−	1.58253i
$825$			183.673i			0.222633i
$826$	119.434	+	756.224i	0.144593	+	0.915526i
$827$		−	1468.52i		−	1.77572i	−0.460116	−	0.887859i	$-0.652192\pi$
$827$		−	1468.52i		−	1.77572i	0.460116	−	0.887859i	$-0.347808\pi$
$828$	763.643	−	167.441i	0.922274	−	0.202223i
$829$	−409.352	−	709.019i	−0.493790	−	0.855270i	0.506184	−	0.862425i	$-0.331056\pi$
$829$	−409.352	−	709.019i	−0.493790	−	0.855270i	−0.999974	+	0.00715566i	$0.997722\pi$
$830$	−49.6793	−	458.525i	−0.0598546	−	0.552439i
$831$	−280.969	−	162.218i	−0.338110	−	0.195208i
$832$	991.498	−	749.915i	1.19170	−	0.901341i
$833$	75.9169	+	776.710i	0.0911367	+	0.932425i
$834$	−81.9814	−	36.1861i	−0.0982990	−	0.0433886i
$835$	330.306	+	190.702i	0.395576	+	0.228386i
$836$	828.899	+	263.463i	0.991505	+	0.315147i
$837$	174.165	−	100.554i	0.208083	−	0.120137i
$838$	−1260.56	+	922.036i	−1.50424	+	1.10028i
$839$			1108.84i			1.32162i	0.750555	+	0.660808i	$0.229786\pi$
$839$			1108.84i			1.32162i	−0.750555	+	0.660808i	$0.770214\pi$
$840$	202.173	−	252.734i	0.240682	−	0.300874i
$841$	563.386			0.669900
$842$	135.741	+	185.577i	0.161212	+	0.220401i
$843$	133.970	+	232.042i	0.158920	+	0.275258i
$844$	−27.3258	−	8.68541i	−0.0323765	−	0.0102908i
$845$	660.850	−	1144.63i	0.782072	−	1.35459i
$846$	144.547	−	327.479i	0.170860	−	0.387091i
$847$	374.943	−	18.2802i	0.442672	−	0.0215823i
$848$	592.443	+	54.5986i	0.698636	+	0.0643852i
$849$	189.005	−	327.366i	0.222621	−	0.385590i
$850$	483.236	−	52.3567i	0.568513	−	0.0615961i
$851$	−985.191	+	568.800i	−1.15769	+	0.668390i
$852$	−114.087	+	25.0154i	−0.133905	+	0.0293608i
$853$	610.400			0.715592			0.357796	−	0.933800i	$-0.383528\pi$
$853$	610.400			0.715592			0.357796	+	0.933800i	$0.383528\pi$
$854$	111.525	−	90.2304i	0.130592	−	0.105656i
$855$	853.017			0.997680
$856$	−313.757	+	1549.22i	−0.366539	+	1.80983i
$857$	384.614	−	222.057i	0.448791	−	0.259110i	−0.258529	−	0.966004i	$-0.583238\pi$
$857$	384.614	−	222.057i	0.448791	−	0.259110i	0.707319	+	0.706894i	$0.249904\pi$
$858$	−464.891	+	50.3690i	−0.541830	+	0.0587052i
$859$	40.7547	−	70.5892i	0.0474443	−	0.0821760i	−0.841328	−	0.540525i	$-0.818226\pi$
$859$	40.7547	−	70.5892i	0.0474443	−	0.0821760i	0.888772	+	0.458349i	$0.151559\pi$
$860$	624.302	−	569.413i	0.725932	−	0.662108i
$861$	−36.8299	−	18.9351i	−0.0427757	−	0.0219920i
$862$	566.677	+	250.128i	0.657398	+	0.290171i
$863$	525.730	−	910.592i	0.609189	−	1.05515i	−0.382185	−	0.924086i	$-0.624828\pi$
$863$	525.730	−	910.592i	0.609189	−	1.05515i	0.991374	−	0.131061i	$-0.0418384\pi$
$864$	−500.410	+	8.02036i	−0.579178	+	0.00928283i
$865$	−442.134	−	765.799i	−0.511138	−	0.885317i
$866$	703.462	+	961.734i	0.812311	+	1.11055i
$867$	32.1882			0.0371259
$868$	−253.885	+	255.294i	−0.292495	+	0.294118i
$869$		−	770.524i		−	0.886679i
$870$	113.701	+	155.446i	0.130691	+	0.178674i
$871$	288.230	−	166.409i	0.330918	−	0.191056i
$872$	69.0768	+	61.0046i	0.0792165	+	0.0699594i
$873$	1199.45	+	692.505i	1.37395	+	0.793248i
$874$	720.194	+	317.889i	0.824020	+	0.363717i
$875$	234.305	+	363.693i	0.267777	+	0.415649i
$876$	−288.482	+	263.119i	−0.329318	+	0.300364i
$877$	1350.68	+	779.814i	1.54011	+	0.889183i	0.998831	+	0.0483410i	$0.0153934\pi$
$877$	1350.68	+	779.814i	1.54011	+	0.889183i	0.541280	+	0.840842i	$0.317940\pi$
$878$	−1604.41	+	173.831i	−1.82735	+	0.197986i
$879$	168.767	+	292.312i	0.191998	+	0.332551i
$880$	−774.568	+	1095.36i	−0.880190	+	1.24473i
$881$			1515.22i			1.71989i	0.510389	+	0.859944i	$0.329501\pi$
$881$			1515.22i			1.71989i	−0.510389	+	0.859944i	$0.670499\pi$
$882$	−760.487	−	250.534i	−0.862230	−	0.284052i
$883$			763.828i			0.865037i	0.901625	+	0.432519i	$0.142375\pi$
$883$			763.828i			0.865037i	−0.901625	+	0.432519i	$0.857625\pi$
$884$	265.038	+	1208.75i	0.299817	+	1.36737i
$885$	158.026	+	273.709i	0.178561	+	0.309276i
$886$	−884.437	+	95.8252i	−0.998236	+	0.108155i
$887$	496.554	+	286.686i	0.559813	+	0.323208i	0.753070	−	0.657940i	$-0.228572\pi$
$887$	496.554	+	286.686i	0.559813	+	0.323208i	−0.193258	+	0.981148i	$0.561905\pi$
$888$	328.528	−	110.249i	0.369964	−	0.124154i
$889$	−266.381	−	413.481i	−0.299641	−	0.465108i
$890$	−5.50216	+	12.4654i	−0.00618221	+	0.0140061i
$891$	−678.496	−	391.730i	−0.761500	−	0.439652i
$892$	−1066.31	−	338.925i	−1.19542	−	0.379960i
$893$	312.163	−	180.228i	0.349567	−	0.201823i
$894$	−44.8416	−	61.3049i	−0.0501583	−	0.0685737i
$895$		−	1851.01i		−	2.06817i
$896$	860.959	−	248.125i	0.960892	−	0.276925i
$897$	−423.240			−0.471840
$898$	−423.614	+	309.853i	−0.471731	+	0.345048i
$899$	−107.125	−	185.546i	−0.119160	−	0.206391i
$900$	−151.062	+	475.266i	−0.167846	+	0.528073i
$901$	−296.115	+	512.887i	−0.328652	+	0.569242i
$902$	157.041	+	69.3167i	0.174103	+	0.0768477i
$903$	188.787	+	97.0600i	0.209067	+	0.107486i
$904$	−37.6452	−	112.178i	−0.0416430	−	0.124091i
$905$	529.315	−	916.800i	0.584878	−	1.01304i
$906$	19.1576	+	176.818i	0.0211452	+	0.195164i
$907$	885.036	−	510.976i	0.975784	−	0.563369i	0.0747894	−	0.997199i	$-0.476172\pi$
$907$	885.036	−	510.976i	0.975784	−	0.563369i	0.900995	+	0.433830i	$0.142838\pi$
$908$	−1190.84	+	261.112i	−1.31150	+	0.287568i
$909$	−229.799			−0.252804
$910$	1341.42	−	1085.29i	1.47409	−	1.19262i
$911$	630.111			0.691669			0.345835	−	0.938295i	$-0.387596\pi$
$911$	630.111			0.691669			0.345835	+	0.938295i	$0.387596\pi$
$912$	−195.797	−	138.455i	−0.214690	−	0.151814i
$913$	−415.930	+	240.137i	−0.455564	+	0.263020i
$914$	−83.9052	−	774.419i	−0.0918000	−	0.847285i
$915$	29.6104	−	51.2868i	0.0323611	−	0.0560511i
$916$	−1117.80	−	1225.55i	−1.22031	−	1.33794i
$917$	−993.725	+	48.4486i	−1.08367	+	0.0528339i
$918$	201.170	−	455.760i	0.219139	−	0.496471i
$919$	421.489	−	730.041i	0.458639	−	0.794386i	−0.540250	−	0.841504i	$-0.681670\pi$
$919$	421.489	−	730.041i	0.458639	−	0.794386i	0.998889	+	0.0471182i	$0.0150038\pi$
$920$	−803.783	+	910.140i	−0.873677	+	0.989283i
$921$	73.0182	+	126.471i	0.0792814	+	0.137319i
$922$	−256.206	+	187.402i	−0.277881	+	0.203256i
$923$	−622.683			−0.674630
$924$	−325.785	−	86.3284i	−0.352581	−	0.0934290i
$925$		−	725.668i		−	0.784506i
$926$	853.690	−	624.433i	0.921911	−	0.674333i
$927$	−1176.76	+	679.405i	−1.26943	+	0.732907i
$928$	8.54444	+	533.108i	0.00920737	+	0.574470i
$929$	670.867	+	387.325i	0.722139	+	0.416927i	0.815540	−	0.578701i	$-0.196440\pi$
$929$	670.867	+	387.325i	0.722139	+	0.416927i	−0.0934003	+	0.995629i	$0.529774\pi$
$930$	−60.0190	+	135.976i	−0.0645366	+	0.146211i
$931$	−469.148	−	655.723i	−0.503918	−	0.704321i
$932$	−444.561	−	487.415i	−0.476997	−	0.522977i
$933$	−372.990	−	215.346i	−0.399774	−	0.230810i
$934$	−94.1214	−	868.712i	−0.100772	−	0.930098i
$935$	−667.708	−	1156.50i	−0.714126	−	1.23690i
$936$	−1244.36	−	252.016i	−1.32945	−	0.269248i
$937$			1586.27i			1.69293i	0.532447	+	0.846463i	$0.321273\pi$
$937$			1586.27i			1.69293i	−0.532447	+	0.846463i	$0.678727\pi$
$938$	236.941	−	37.4212i	0.252602	−	0.0398947i
$939$		−	210.421i		−	0.224090i
$940$	119.079	+	543.079i	0.126680	+	0.577744i
$941$	410.023	+	710.181i	0.435731	+	0.754708i	0.997355	−	0.0726842i	$-0.0231565\pi$
$941$	410.023	+	710.181i	0.435731	+	0.754708i	−0.561624	+	0.827393i	$0.689823\pi$
$942$	−5.52684	−	51.0110i	−0.00586713	−	0.0541518i
$943$	134.554	+	77.6849i	0.142687	+	0.0823805i
$944$	−80.2954	+	871.277i	−0.0850587	+	0.922963i
$945$	−693.821	+	33.8270i	−0.734202	+	0.0357957i
$946$	−804.977	−	355.312i	−0.850928	−	0.375594i
$947$	−551.949	−	318.668i	−0.582839	−	0.336502i	0.179422	−	0.983772i	$-0.442577\pi$
$947$	−551.949	−	318.668i	−0.582839	−	0.336502i	−0.762261	+	0.647270i	$0.775911\pi$
$948$	−64.3521	+	202.462i	−0.0678820	+	0.213568i
$949$	−1802.74	+	1040.81i	−1.89962	+	1.09675i
$950$	−405.316	+	296.469i	−0.426648	+	0.312072i
$951$			205.234i			0.215809i
$952$	−134.261	+	881.736i	−0.141030	+	0.926193i
$953$	−350.626			−0.367918			−0.183959	−	0.982934i	$-0.558891\pi$
$953$	−350.626			−0.367918			−0.183959	+	0.982934i	$0.558891\pi$
$954$	−358.725	−	490.429i	−0.376022	−	0.514076i
$955$	−416.729	−	721.796i	−0.436365	−	0.755807i
$956$	−23.1647	+	72.8801i	−0.0242309	+	0.0762344i
$957$	100.277	−	173.684i	0.104782	−	0.181488i
$958$	−440.852	+	998.772i	−0.460179	+	1.04256i
$959$	809.997	−	1575.49i	0.844627	−	1.64285i
$960$	295.007	−	223.127i	0.307299	−	0.232424i
$961$	−397.826	+	689.055i	−0.413971	+	0.717019i
$962$	1836.73	−	199.002i	1.90928	−	0.206863i
$963$	1398.04	−	807.161i	1.45176	−	0.838174i
$964$	300.113	+	1368.72i	0.311320	+	1.41983i
$965$	516.734			0.535475
$966$	−284.739	−	109.444i	−0.294761	−	0.113296i
$967$	−649.816			−0.671992			−0.335996	−	0.941863i	$-0.609073\pi$
$967$	−649.816			−0.671992			−0.335996	+	0.941863i	$0.609073\pi$
$968$	420.479	+	85.1582i	0.434379	+	0.0879733i
$969$	206.726	−	119.354i	0.213340	−	0.123172i
$970$	−2138.66	+	231.716i	−2.20481	+	0.238882i
$971$	−485.305	+	840.573i	−0.499799	+	0.865677i	−1.00000		0.000232071i	$-0.999926\pi$
$971$	−485.305	+	840.573i	−0.499799	+	0.865677i	0.500201	+	0.865909i	$0.333259\pi$
$972$	524.982	+	575.589i	0.540105	+	0.592169i
$973$	−186.486	−	289.466i	−0.191660	−	0.297499i
$974$	1186.06	+	523.519i	1.21772	+	0.537494i
$975$	134.991	−	233.811i	0.138452	−	0.239807i
$976$	148.907	−	68.5987i	0.152569	−	0.0702856i
$977$	300.437	+	520.373i	0.307510	+	0.532623i	0.977817	−	0.209461i	$-0.0671709\pi$
$977$	300.437	+	520.373i	0.307510	+	0.532623i	−0.670307	+	0.742084i	$0.733838\pi$
$978$	−260.736	−	356.464i	−0.266601	−	0.364482i
$979$	14.1890			0.0144934
$980$	1183.09	−	383.264i	1.20724	−	0.391085i
$981$		−	94.1205i		−	0.0959434i
$982$	864.396	+	1181.76i	0.880241	+	1.20342i
$983$	1098.66	−	634.311i	1.11766	−	0.645281i	0.176857	−	0.984236i	$-0.443407\pi$
$983$	1098.66	−	634.311i	1.11766	−	0.645281i	0.940802	+	0.338955i	$0.110074\pi$
$984$	−35.4747	−	31.3292i	−0.0360516	−	0.0318386i
$985$	11.5146	+	6.64797i	0.0116900	+	0.00674921i
$986$	−485.541	−	214.315i	−0.492435	−	0.217358i
$987$	−117.417	+	75.6449i	−0.118964	+	0.0766413i
$988$	−861.537	−	944.586i	−0.872001	−	0.956059i
$989$	−689.714	−	398.207i	−0.697385	−	0.402636i
$990$	1362.15	−	147.583i	1.37591	−	0.149074i
$991$	774.555	+	1341.57i	0.781590	+	1.35375i	0.931015	+	0.364980i	$0.118924\pi$
$991$	774.555	+	1341.57i	0.781590	+	1.35375i	−0.149426	+	0.988773i	$0.547742\pi$
$992$	−353.010	+	211.425i	−0.355857	+	0.213130i
$993$		−	18.8538i		−	0.0189867i
$994$	−418.916	−	161.018i	−0.421445	−	0.161990i
$995$			805.464i			0.809512i
$996$	129.345	−	28.3610i	0.129864	−	0.0284749i
$997$	470.469	+	814.876i	0.471885	+	0.817328i	0.999483	−	0.0321661i	$-0.0102406\pi$
$997$	470.469	+	814.876i	0.471885	+	0.817328i	−0.527598	+	0.849494i	$0.676907\pi$
$998$	−53.0973	+	5.75288i	−0.0532037	+	0.00576441i
$999$	−644.116	−	371.881i	−0.644761	−	0.372253i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	56.3.j.a.5.4	✓	28
4.3	odd	2		224.3.n.a.145.9		28
7.2	even	3		392.3.h.a.293.28		28
7.3	odd	6	inner	56.3.j.a.45.6	yes	28
7.4	even	3		392.3.j.e.325.6		28
7.5	odd	6		392.3.h.a.293.27		28
7.6	odd	2		392.3.j.e.117.4		28
8.3	odd	2		224.3.n.a.145.6		28
8.5	even	2	inner	56.3.j.a.5.6	yes	28
28.3	even	6		224.3.n.a.17.6		28
28.19	even	6		1568.3.h.a.881.18		28
28.23	odd	6		1568.3.h.a.881.12		28
56.3	even	6		224.3.n.a.17.9		28
56.5	odd	6		392.3.h.a.293.26		28
56.13	odd	2		392.3.j.e.117.6		28
56.19	even	6		1568.3.h.a.881.11		28
56.37	even	6		392.3.h.a.293.25		28
56.45	odd	6	inner	56.3.j.a.45.4	yes	28
56.51	odd	6		1568.3.h.a.881.17		28
56.53	even	6		392.3.j.e.325.4		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.3.j.a.5.4	✓	28	1.1	even	1	trivial
56.3.j.a.5.6	yes	28	8.5	even	2	inner
56.3.j.a.45.4	yes	28	56.45	odd	6	inner
56.3.j.a.45.6	yes	28	7.3	odd	6	inner
224.3.n.a.17.6		28	28.3	even	6
224.3.n.a.17.9		28	56.3	even	6
224.3.n.a.145.6		28	8.3	odd	2
224.3.n.a.145.9		28	4.3	odd	2
392.3.h.a.293.25		28	56.37	even	6
392.3.h.a.293.26		28	56.5	odd	6
392.3.h.a.293.27		28	7.5	odd	6
392.3.h.a.293.28		28	7.2	even	3
392.3.j.e.117.4		28	7.6	odd	2
392.3.j.e.117.6		28	56.13	odd	2
392.3.j.e.325.4		28	56.53	even	6
392.3.j.e.325.6		28	7.4	even	3
1568.3.h.a.881.11		28	56.19	even	6
1568.3.h.a.881.12		28	28.23	odd	6
1568.3.h.a.881.17		28	56.51	odd	6
1568.3.h.a.881.18		28	28.19	even	6

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:	\( N \)	\(=\)	\( 56 = 2^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	56.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.61426 + 1.18075i) q^{2} +(-0.455431 - 0.788830i) q^{3} +(1.21166 - 3.81207i) q^{4} +(3.17251 - 5.49495i) q^{5} +(1.66660 + 0.735624i) q^{6} +(3.79106 + 5.88455i) q^{7} +(2.54518 + 7.58433i) q^{8} +(4.08516 - 7.07571i) q^{9} +O(q^{10})\)	\(q+(-1.61426 + 1.18075i) q^{2} +(-0.455431 - 0.788830i) q^{3} +(1.21166 - 3.81207i) q^{4} +(3.17251 - 5.49495i) q^{5} +(1.66660 + 0.735624i) q^{6} +(3.79106 + 5.88455i) q^{7} +(2.54518 + 7.58433i) q^{8} +(4.08516 - 7.07571i) q^{9} +(1.36692 + 12.6162i) q^{10} +(11.4442 - 6.60732i) q^{11} +(-3.55890 + 0.780346i) q^{12} -19.4243 q^{13} +(-13.0679 - 5.02288i) q^{14} -5.77945 q^{15} +(-13.0638 - 9.23784i) q^{16} +(13.7930 - 7.96338i) q^{17} +(1.76014 + 16.2456i) q^{18} +(-8.22725 + 14.2500i) q^{19} +(-17.1032 - 18.7518i) q^{20} +(2.91534 - 5.67051i) q^{21} +(-10.6723 + 24.1787i) q^{22} +(-11.9607 + 20.7166i) q^{23} +(4.82359 - 5.46186i) q^{24} +(-7.62967 - 13.2150i) q^{25} +(31.3559 - 22.9353i) q^{26} -15.6398 q^{27} +(27.0258 - 7.32173i) q^{28} +16.6618i q^{29} +(9.32952 - 6.82409i) q^{30} +(-11.1360 + 6.42939i) q^{31} +(31.9959 - 0.512817i) q^{32} +(-10.4241 - 6.01837i) q^{33} +(-12.8627 + 29.1410i) q^{34} +(44.3625 - 2.16288i) q^{35} +(-22.0233 - 24.1463i) q^{36} +(41.1844 + 23.7778i) q^{37} +(-3.54481 - 32.7175i) q^{38} +(8.84646 + 15.3225i) q^{39} +(49.7502 + 10.0757i) q^{40} -6.49499i q^{41} +(1.98934 + 12.5960i) q^{42} +33.2928i q^{43} +(-11.3211 - 51.6320i) q^{44} +(-25.9205 - 44.8956i) q^{45} +(-5.15343 - 47.5645i) q^{46} +(-18.9713 - 10.9531i) q^{47} +(-1.33743 + 14.5123i) q^{48} +(-20.2558 + 44.6173i) q^{49} +(27.9198 + 12.3236i) q^{50} +(-12.5635 - 7.25355i) q^{51} +(-23.5356 + 74.0470i) q^{52} +(-32.2028 + 18.5923i) q^{53} +(25.2467 - 18.4667i) q^{54} -83.8473i q^{55} +(-34.9814 + 43.7299i) q^{56} +14.9878 q^{57} +(-19.6734 - 26.8964i) q^{58} +(-27.3428 - 47.3591i) q^{59} +(-7.00270 + 22.0317i) q^{60} +(-5.12340 + 8.87399i) q^{61} +(10.3849 - 23.5276i) q^{62} +(57.1245 - 2.78508i) q^{63} +(-51.0441 + 38.6070i) q^{64} +(-61.6240 + 106.736i) q^{65} +(23.9334 - 2.59309i) q^{66} +(-14.8386 + 8.56706i) q^{67} +(-13.6446 - 62.2287i) q^{68} +21.7892 q^{69} +(-69.0587 + 55.8725i) q^{70} +32.0568 q^{71} +(64.0620 + 12.9743i) q^{72} +(92.8082 - 53.5828i) q^{73} +(-94.5579 + 10.2450i) q^{74} +(-6.94958 + 12.0370i) q^{75} +(44.3535 + 48.6290i) q^{76} +(82.2668 + 42.2953i) q^{77} +(-32.3725 - 14.2890i) q^{78} +(29.1542 - 50.4965i) q^{79} +(-92.2065 + 42.4777i) q^{80} +(-29.6436 - 51.3443i) q^{81} +(7.66897 + 10.4846i) q^{82} -36.3441 q^{83} +(-18.0840 - 17.9842i) q^{84} -101.056i q^{85} +(-39.3105 - 53.7432i) q^{86} +(13.1433 - 7.58829i) q^{87} +(79.2397 + 69.9799i) q^{88} +(0.929882 + 0.536867i) q^{89} +(94.8528 + 41.8674i) q^{90} +(-73.6388 - 114.303i) q^{91} +(64.4808 + 70.6965i) q^{92} +(10.1434 + 5.85629i) q^{93} +(43.5575 - 4.71928i) q^{94} +(52.2021 + 90.4167i) q^{95} +(-14.9765 - 25.0058i) q^{96} +169.517i q^{97} +(-19.9838 - 95.9408i) q^{98} -107.968i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 2 q^{2} - 4 q^{4} - 4 q^{7} - 20 q^{8} - 32 q^{9}+O(q^{10}) \) 28 * q - 2 * q^2 - 4 * q^4 - 4 * q^7 - 20 * q^8 - 32 * q^9	\( 28 q - 2 q^{2} - 4 q^{4} - 4 q^{7} - 20 q^{8} - 32 q^{9} + 24 q^{10} - 18 q^{12} + 24 q^{14} + 28 q^{15} + 16 q^{16} - 6 q^{17} - 42 q^{18} - 92 q^{22} + 30 q^{23} - 30 q^{24} - 32 q^{25} - 30 q^{26} - 42 q^{28} + 22 q^{30} - 6 q^{31} + 88 q^{32} - 6 q^{33} + 256 q^{36} + 6 q^{38} - 20 q^{39} + 102 q^{40} + 18 q^{42} - 42 q^{44} + 68 q^{46} - 294 q^{47} - 20 q^{49} + 400 q^{50} - 168 q^{52} + 330 q^{54} - 96 q^{56} + 124 q^{57} - 22 q^{58} - 62 q^{60} + 432 q^{63} - 520 q^{64} - 52 q^{65} - 306 q^{66} - 456 q^{68} - 324 q^{70} - 136 q^{71} + 96 q^{72} + 234 q^{73} - 138 q^{74} - 956 q^{78} - 162 q^{79} + 276 q^{80} - 18 q^{81} - 642 q^{82} + 504 q^{84} + 168 q^{86} + 48 q^{87} + 50 q^{88} - 150 q^{89} + 1020 q^{92} + 618 q^{94} + 290 q^{95} + 1044 q^{96} + 424 q^{98}+O(q^{100}) \) 28 * q - 2 * q^2 - 4 * q^4 - 4 * q^7 - 20 * q^8 - 32 * q^9 + 24 * q^10 - 18 * q^12 + 24 * q^14 + 28 * q^15 + 16 * q^16 - 6 * q^17 - 42 * q^18 - 92 * q^22 + 30 * q^23 - 30 * q^24 - 32 * q^25 - 30 * q^26 - 42 * q^28 + 22 * q^30 - 6 * q^31 + 88 * q^32 - 6 * q^33 + 256 * q^36 + 6 * q^38 - 20 * q^39 + 102 * q^40 + 18 * q^42 - 42 * q^44 + 68 * q^46 - 294 * q^47 - 20 * q^49 + 400 * q^50 - 168 * q^52 + 330 * q^54 - 96 * q^56 + 124 * q^57 - 22 * q^58 - 62 * q^60 + 432 * q^63 - 520 * q^64 - 52 * q^65 - 306 * q^66 - 456 * q^68 - 324 * q^70 - 136 * q^71 + 96 * q^72 + 234 * q^73 - 138 * q^74 - 956 * q^78 - 162 * q^79 + 276 * q^80 - 18 * q^81 - 642 * q^82 + 504 * q^84 + 168 * q^86 + 48 * q^87 + 50 * q^88 - 150 * q^89 + 1020 * q^92 + 618 * q^94 + 290 * q^95 + 1044 * q^96 + 424 * q^98

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