LMFDB - Embedded newform 56.3.j.a.5.6

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			5.6
Character	$\chi$	$=$	56.5
Dual form			56.3.j.a.45.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.215431 + 1.98836i) q^{2} +(0.455431 + 0.788830i) q^{3} +(-3.90718 - 0.856711i) q^{4} +(-3.17251 + 5.49495i) q^{5} +(-1.66660 + 0.735624i) q^{6} +(3.79106 + 5.88455i) q^{7} +(2.54518 - 7.58433i) q^{8} +(4.08516 - 7.07571i) q^{9} +O(q^{10})$	\(q+(-0.215431 + 1.98836i) q^{2} +(0.455431 + 0.788830i) q^{3} +(-3.90718 - 0.856711i) 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} +(-10.2425 - 7.49189i) q^{10} +(-11.4442 + 6.60732i) q^{11} +(-1.10365 - 3.47227i) q^{12} +19.4243 q^{13} +(-12.5173 + 6.27028i) q^{14} -5.77945 q^{15} +(14.5321 + 6.69465i) q^{16} +(13.7930 - 7.96338i) q^{17} +(13.1890 + 9.64712i) 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} +(7.14190 - 1.44643i) q^{24} +(-7.62967 - 13.2150i) q^{25} +(-4.18461 + 38.6227i) q^{26} +15.6398 q^{27} +(-9.77098 - 26.2398i) q^{28} -16.6618i q^{29} +(1.24507 - 11.4916i) q^{30} +(-11.1360 + 6.42939i) q^{31} +(-16.4421 + 27.4528i) 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} +(26.5618 + 19.4287i) q^{38} +(8.84646 + 15.3225i) q^{39} +(33.6009 + 38.0470i) q^{40} -6.49499i q^{41} +(-10.6470 - 7.01837i) q^{42} -33.2928i q^{43} +(50.3752 - 16.0116i) q^{44} +(25.9205 + 44.8956i) q^{45} +(-38.6154 - 28.2453i) 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} +(-75.8944 - 16.6411i) q^{52} +(32.2028 - 18.5923i) q^{53} +(-3.36930 + 31.0976i) q^{54} -83.8473i q^{55} +(54.2793 - 13.7754i) q^{56} +14.9878 q^{57} +(33.1296 + 3.58946i) q^{58} +(27.3428 + 47.3591i) q^{59} +(22.5813 + 4.95132i) 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} +(14.2124 - 19.4304i) q^{66} +(14.8386 - 8.56706i) q^{67} +(-60.7140 + 19.2978i) q^{68} -21.7892 q^{69} +(5.25648 - 88.6747i) q^{70} +32.0568 q^{71} +(-43.2670 - 48.9922i) q^{72} +(92.8082 - 53.5828i) q^{73} +(56.1514 - 76.7671i) 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} +(-82.8900 + 58.6143i) q^{80} +(-29.6436 - 51.3443i) q^{81} +(12.9144 + 1.39922i) q^{82} +36.3441 q^{83} +(16.2488 - 19.6581i) q^{84} +101.056i q^{85} +(66.1983 + 7.17232i) q^{86} +(13.1433 - 7.58829i) q^{87} +(20.9845 + 103.614i) 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} +(25.8657 - 35.3622i) q^{94} +(52.2021 + 90.4167i) q^{95} +(-29.1439 - 0.467106i) q^{96} +169.517i q^{97} +(-84.3517 - 49.8878i) 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 $

$2$	−0.215431	+	1.98836i	−0.107716	+	0.994182i
$2$	−0.215431	+	1.98836i	−0.107716	+	0.994182i
$3$	0.455431	+	0.788830i	0.151810	+	0.262943i	0.931893	−	0.362733i	$-0.118156\pi$
$3$	0.455431	+	0.788830i	0.151810	+	0.262943i	−0.780083	+	0.625677i	$0.784823\pi$
$4$	−3.90718	−	0.856711i	−0.976795	−	0.214178i
$5$	−3.17251	+	5.49495i	−0.634503	+	1.09899i	0.352118	+	0.935956i	$0.385462\pi$
$5$	−3.17251	+	5.49495i	−0.634503	+	1.09899i	−0.986620	+	0.163035i	$0.947872\pi$
$6$	−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
$10$	−10.2425	−	7.49189i	−1.02425	−	0.749189i
$11$	−11.4442	+	6.60732i	−1.04038	+	0.600666i	−0.919942	−	0.392054i	$-0.871764\pi$
$11$	−11.4442	+	6.60732i	−1.04038	+	0.600666i	−0.120442	+	0.992720i	$0.538431\pi$
$12$	−1.10365	−	3.47227i	−0.0919710	−	0.289356i
$13$	19.4243			1.49418			0.747090	−	0.664723i	$-0.231450\pi$
$13$	19.4243			1.49418			0.747090	+	0.664723i	$0.231450\pi$
$14$	−12.5173	+	6.27028i	−0.894095	+	0.447877i
$15$	−5.77945			−0.385296
$16$	14.5321	+	6.69465i	0.908256	+	0.418415i
$17$	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	$0.178152\pi$
$18$	13.1890	+	9.64712i	0.732723	+	0.535951i
$19$	8.22725	−	14.2500i	0.433013	−	0.750001i	−0.564118	−	0.825694i	$-0.690784\pi$
$19$	8.22725	−	14.2500i	0.433013	−	0.750001i	0.997131	+	0.0756934i	$0.0241170\pi$
$20$	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	$0.992587\pi$
$24$	7.14190	−	1.44643i	0.297579	−	0.0602677i
$25$	−7.62967	−	13.2150i	−0.305187	−	0.528599i
$26$	−4.18461	+	38.6227i	−0.160947	+	1.48549i
$27$	15.6398			0.579252
$28$	−9.77098	−	26.2398i	−0.348963	−	0.937136i
$29$		−	16.6618i		−	0.574544i	−0.957849	−	0.287272i	$-0.907252\pi$
$29$		−	16.6618i		−	0.574544i	0.957849	−	0.287272i	$-0.0927483\pi$
$30$	1.24507	−	11.4916i	0.0415024	−	0.383055i
$31$	−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	$0.399833\pi$
$32$	−16.4421	+	27.4528i	−0.513814	+	0.857901i
$33$	−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	−0.173463	−	0.984840i	$-0.555496\pi$
$37$	−41.1844	−	23.7778i	−1.11309	−	0.642644i	−0.939628	+	0.342196i	$0.888829\pi$
$38$	26.5618	+	19.4287i	0.698995	+	0.511281i
$39$	8.84646	+	15.3225i	0.226832	+	0.392885i
$40$	33.6009	+	38.0470i	0.840023	+	0.951176i
$41$		−	6.49499i		−	0.158415i	−0.996858	−	0.0792073i	$-0.974761\pi$
$41$		−	6.49499i		−	0.158415i	0.996858	−	0.0792073i	$-0.0252389\pi$
$42$	−10.6470	−	7.01837i	−0.253499	−	0.167104i
$43$		−	33.2928i		−	0.774252i	−0.922027	−	0.387126i	$-0.873468\pi$
$43$		−	33.2928i		−	0.774252i	0.922027	−	0.387126i	$-0.126532\pi$
$44$	50.3752	−	16.0116i	1.14489	−	0.363900i
$45$	25.9205	+	44.8956i	0.576010	+	0.997679i
$46$	−38.6154	−	28.2453i	−0.839465	−	0.614028i
$47$	−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
$52$	−75.8944	−	16.6411i	−1.45951	−	0.320020i
$53$	32.2028	−	18.5923i	0.607601	−	0.350798i	−0.164425	−	0.986390i	$-0.552577\pi$
$53$	32.2028	−	18.5923i	0.607601	−	0.350798i	0.772026	+	0.635591i	$0.219244\pi$
$54$	−3.36930	+	31.0976i	−0.0623945	+	0.575882i
$55$		−	83.8473i		−	1.52450i
$56$	54.2793	−	13.7754i	0.969273	−	0.245989i
$57$	14.9878			0.262944
$58$	33.1296	+	3.58946i	0.571201	+	0.0618873i
$59$	27.3428	+	47.3591i	0.463437	+	0.802696i	0.999129	−	0.0417169i	$-0.0132827\pi$
$59$	27.3428	+	47.3591i	0.463437	+	0.802696i	−0.535693	+	0.844413i	$0.679949\pi$
$60$	22.5813	+	4.95132i	0.376356	+	0.0825219i
$61$	5.12340	−	8.87399i	0.0839902	−	0.145475i	−0.820970	−	0.570971i	$-0.806567\pi$
$61$	5.12340	−	8.87399i	0.0839902	−	0.145475i	0.904960	+	0.425496i	$0.139900\pi$
$62$	−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
$66$	14.2124	−	19.4304i	0.215339	−	0.294400i
$67$	14.8386	−	8.56706i	0.221471	−	0.127867i	−0.385160	−	0.922850i	$-0.625854\pi$
$67$	14.8386	−	8.56706i	0.221471	−	0.127867i	0.606631	+	0.794983i	$0.292520\pi$
$68$	−60.7140	+	19.2978i	−0.892853	+	0.283791i
$69$	−21.7892			−0.315785
$70$	5.25648	−	88.6747i	0.0750926	−	1.26678i
$71$	32.0568			0.451505			0.225752	−	0.974185i	$-0.427516\pi$
$71$	32.0568			0.451505			0.225752	+	0.974185i	$0.427516\pi$
$72$	−43.2670	−	48.9922i	−0.600931	−	0.680447i
$73$	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	$0.0709792\pi$
$74$	56.1514	−	76.7671i	0.758802	−	1.03739i
$75$	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	$0.0463532\pi$
$80$	−82.8900	+	58.6143i	−1.03613	+	0.732679i
$81$	−29.6436	−	51.3443i	−0.365971	−	0.633880i
$82$	12.9144	+	1.39922i	0.157493	+	0.0170637i
$83$	36.3441			0.437880			0.218940	−	0.975738i	$-0.429740\pi$
$83$	36.3441			0.437880			0.218940	+	0.975738i	$0.429740\pi$
$84$	16.2488	−	19.6581i	0.193438	−	0.234025i
$85$			101.056i			1.18889i
$86$	66.1983	+	7.17232i	0.769747	+	0.0833990i
$87$	13.1433	−	7.58829i	0.151072	−	0.0872217i
$88$	20.9845	+	103.614i	0.238460	+	1.17743i
$89$	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
$94$	25.8657	−	35.3622i	0.275167	−	0.376194i
$95$	52.2021	+	90.4167i	0.549496	+	0.951755i
$96$	−29.1439	−	0.467106i	−0.303582	−	0.00486569i
$97$			169.517i			1.74760i	0.486286	+	0.873799i	$0.338351\pi$
$97$			169.517i			1.74760i	−0.486286	+	0.873799i	$0.661649\pi$
$98$	−84.3517	−	49.8878i	−0.860731	−	0.509059i
$99$			107.968i			1.09059i
$100$	18.4891	+	58.1697i	0.184891	+	0.581697i
$101$	14.0630	+	24.3579i	0.139238	+	0.241167i	0.927208	−	0.374546i	$-0.122201\pi$
$101$	14.0630	+	24.3579i	0.139238	+	0.241167i	−0.787971	+	0.615713i	$0.788868\pi$
$102$	−17.1293	+	23.4182i	−0.167934	+	0.229590i
$103$	−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	$-0.958825\pi$
$107$	−171.112	−	98.7918i	−1.59918	−	0.923288i	−0.607536	−	0.794292i	$-0.707842\pi$
$108$	−61.1075	−	13.3988i	−0.565811	−	0.124063i
$109$	−9.97643	+	5.75990i	−0.0915269	+	0.0528431i	−0.545065	−	0.838394i	$-0.683495\pi$
$109$	−9.97643	+	5.75990i	−0.0915269	+	0.0528431i	0.453538	+	0.891237i	$0.350162\pi$
$110$	166.719	+	18.0633i	1.51563	+	0.164212i
$111$		−	43.3167i		−	0.390240i
$112$	15.6970	+	110.895i	0.140152	+	0.990130i
$113$	−14.7908			−0.130892			−0.0654460	−	0.997856i	$-0.520847\pi$
$113$	−14.7908			−0.130892			−0.0654460	+	0.997856i	$0.520847\pi$
$114$	−3.22884	+	29.8012i	−0.0283231	+	0.261414i
$115$	−75.8911	−	131.447i	−0.659923	−	1.14302i
$116$	−14.2743	+	65.1005i	−0.123054	+	0.561211i
$117$	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
$122$	16.5410	+	12.0989i	0.135582	+	0.0991715i
$123$	5.12345	−	2.95802i	0.0416541	−	0.0240490i
$124$	49.0186	−	15.5804i	0.395311	−	0.125648i
$125$	−61.8047			−0.494438
$126$	−6.76864	+	114.184i	−0.0537194	+	0.906224i
$127$	−70.2656			−0.553272			−0.276636	−	0.960975i	$-0.589220\pi$
$127$	−70.2656			−0.553272			−0.276636	+	0.960975i	$0.589220\pi$
$128$	87.7612	−	93.1771i	0.685635	−	0.727946i
$129$	26.2624	−	15.1626i	0.203584	−	0.117540i
$130$	−198.954	−	145.525i	−1.53041	−	1.11942i
$131$	71.0646	−	123.088i	0.542478	−	0.939600i	−0.456283	−	0.889835i	$-0.650819\pi$
$131$	71.0646	−	123.088i	0.542478	−	0.939600i	0.998761	−	0.0497649i	$-0.0158472\pi$
$132$	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
$136$	−25.2913	−	124.879i	−0.185965	−	0.918226i
$137$	−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	$-0.541456\pi$
$138$	4.69407	−	43.3248i	0.0340150	−	0.313948i
$139$	49.1909			0.353892			0.176946	−	0.984221i	$-0.443378\pi$
$139$	49.1909			0.353892			0.176946	+	0.984221i	$0.443378\pi$
$140$	175.185	+	29.5551i	1.25132	+	0.211108i
$141$		−	19.9535i		−	0.141514i
$142$	−6.90605	+	63.7407i	−0.0486341	+	0.448878i
$143$	−222.296	+	128.343i	−1.55452	+	0.897503i
$144$	106.735	−	75.4762i	0.741218	−	0.524140i
$145$	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	0.616249	−	0.787551i	$-0.288652\pi$
$149$	36.1077	+	20.8468i	0.242334	+	0.139911i	−0.373915	+	0.927463i	$0.621985\pi$
$150$	22.4368	+	16.4115i	0.149579	+	0.109410i
$151$	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	$0.728550\pi$
$152$	−87.1370	−	98.6670i	−0.573269	−	0.649125i
$153$		−	130.127i		−	0.850503i
$154$	101.821	−	154.465i	0.661177	−	1.00302i
$155$		−	81.5892i		−	0.526382i
$156$	−21.4377	−	67.4466i	−0.137421	−	0.432350i
$157$	14.0827	+	24.3919i	0.0896986	+	0.155363i	0.907384	−	0.420303i	$-0.138076\pi$
$157$	14.0827	+	24.3919i	0.0896986	+	0.155363i	−0.817685	+	0.575666i	$0.804743\pi$
$158$	94.1246	+	68.8476i	0.595726	+	0.435744i
$159$	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	0.978306	−	0.207165i	$-0.0664237\pi$
$163$	209.952	+	121.216i	1.28805	+	0.743655i	0.309743	+	0.950820i	$0.399757\pi$
$164$	−5.56433	+	25.3771i	−0.0339289	+	0.154738i
$165$	66.1413	−	38.1867i	0.400856	−	0.231434i
$166$	−7.82965	+	72.2652i	−0.0471665	+	0.435333i
$167$			60.1108i			0.359945i	0.983672	+	0.179972i	$0.0576008\pi$
$167$			60.1108i			0.359945i	−0.983672	+	0.179972i	$0.942399\pi$
$168$	35.5869	+	36.5434i	0.211827	+	0.217520i
$169$	208.305			1.23257
$170$	−200.936	−	21.7706i	−1.18197	−	0.128062i
$171$	−67.2193	−	116.427i	−0.393096	−	0.680861i
$172$	−28.5223	+	130.081i	−0.165828	+	0.756285i
$173$	−69.6820	+	120.693i	−0.402786	+	0.697646i	−0.994061	−	0.108824i	$-0.965292\pi$
$173$	−69.6820	+	120.693i	−0.402786	+	0.697646i	0.591275	+	0.806470i	$0.298625\pi$
$174$	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
$178$	−1.26781	+	1.73328i	−0.00712255	+	0.00973755i
$179$	−252.643	+	145.863i	−1.41141	+	0.814879i	−0.995522	−	0.0945354i	$-0.969863\pi$
$179$	−252.643	+	145.863i	−1.41141	+	0.814879i	−0.415891	+	0.909415i	$0.636530\pi$
$180$	−62.8134	−	197.621i	−0.348963	−	1.09790i
$181$	−166.844			−0.921791			−0.460895	−	0.887455i	$-0.652472\pi$
$181$	−166.844			−0.921791			−0.460895	+	0.887455i	$0.652472\pi$
$182$	−243.141	+	121.796i	−1.33594	+	0.669209i
$183$	9.33343			0.0510024
$184$	126.679	+	143.442i	0.688474	+	0.779574i
$185$	261.316	−	150.871i	1.41252	−	0.815518i
$186$	13.8296	−	18.9071i	0.0743529	−	0.101651i
$187$	−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	$0.0549307\pi$
$192$	7.20727	−	57.8480i	0.0375379	−	0.301292i
$193$	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	$0.765667\pi$
$194$	−337.062	−	36.5193i	−1.73743	−	0.188244i
$195$	−112.262			−0.575702
$196$	117.367	−	156.974i	0.598812	−	0.800890i
$197$		−	2.09549i		−	0.0106370i	−0.999986	−	0.00531851i	$-0.998307\pi$
$197$		−	2.09549i		−	0.0106370i	0.999986	−	0.00531851i	$-0.00169294\pi$
$198$	−214.680	−	23.2597i	−1.08424	−	0.117473i
$199$	−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	$0.436665\pi$
$200$	−119.646	+	24.2314i	−0.598228	+	0.121157i
$201$	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
$206$	196.371	−	268.468i	0.953257	−	1.30324i
$207$	97.7231	+	169.261i	0.472092	+	0.817687i
$208$	282.276	+	130.039i	1.35710	+	0.625188i
$209$			217.440i			1.04038i
$210$	72.3432	−	36.2388i	0.344492	−	0.172566i
$211$			7.16822i			0.0339726i	0.999856	+	0.0169863i	$0.00540717\pi$
$211$			7.16822i			0.0339726i	−0.999856	+	0.0169863i	$0.994593\pi$
$212$	−141.750	+	45.0550i	−0.668634	+	0.212523i
$213$	14.5997	+	25.2874i	0.0685432	+	0.118720i
$214$	233.297	−	318.951i	1.09017	−	1.49042i
$215$	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
$220$	−71.8329	+	327.606i	−0.326513	+	1.48912i
$221$	267.920	−	154.683i	1.21231	−	0.699925i
$222$	86.1293	+	9.33176i	0.387970	+	0.0420350i
$223$		−	279.720i		−	1.25435i	−0.778878	−	0.627175i	$-0.784211\pi$
$223$		−	279.720i		−	1.25435i	0.778878	−	0.627175i	$-0.215789\pi$
$224$	−223.880	+	7.32121i	−0.999466	+	0.0326840i
$225$	−124.674			−0.554106
$226$	3.18640	−	29.4095i	0.0140991	−	0.130130i
$227$	152.392	+	263.950i	0.671330	+	1.16278i	0.977527	+	0.210809i	$0.0676098\pi$
$227$	152.392	+	263.950i	0.671330	+	1.16278i	−0.306198	+	0.951968i	$0.599057\pi$
$228$	−58.5600	−	12.8402i	−0.256842	−	0.0563167i
$229$	−207.344	+	359.130i	−0.905433	+	1.56826i	−0.0850971	+	0.996373i	$0.527120\pi$
$229$	−207.344	+	359.130i	−0.905433	+	1.56826i	−0.820335	+	0.571883i	$0.806213\pi$
$230$	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	$0.0515159\pi$
$234$	256.188	+	187.389i	1.09482	+	0.800808i
$235$	120.373	−	69.4976i	0.512227	−	0.295735i
$236$	−66.2601	−	208.465i	−0.280763	−	0.883327i
$237$	53.1109			0.224097
$238$	−122.719	+	186.166i	−0.515625	+	0.782211i
$239$	−19.1182			−0.0799926			−0.0399963	−	0.999200i	$-0.512735\pi$
$239$	−19.1182			−0.0799926			−0.0399963	+	0.999200i	$0.512735\pi$
$240$	−83.9875	−	38.6914i	−0.349948	−	0.161214i
$241$	−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	$0.592317\pi$
$242$	86.5677	+	63.3201i	0.357718	+	0.261653i
$243$	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
$248$	20.4194	+	100.823i	0.0823362	+	0.406545i
$249$	16.5522	+	28.6693i	0.0664748	+	0.115138i
$250$	13.3147	−	122.890i	0.0532587	−	0.491561i
$251$	88.3204			0.351874			0.175937	−	0.984401i	$-0.443704\pi$
$251$	88.3204			0.351874			0.175937	+	0.984401i	$0.443704\pi$
$252$	−225.581	−	38.0573i	−0.895164	−	0.151021i
$253$		−	316.114i		−	1.24946i
$254$	15.1374	−	139.714i	0.0595961	−	0.550053i
$255$	−79.7158	+	46.0240i	−0.312611	+	0.180486i
$256$	166.363	+	194.574i	0.649857	+	0.760056i
$257$	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
$262$	229.433	+	167.819i	0.875699	+	0.640531i
$263$	−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	$-0.374239\pi$
$264$	−72.1765	+	63.7421i	−0.273396	+	0.241447i
$265$			235.937i			0.890330i
$266$	−13.6316	+	229.959i	−0.0512466	+	0.864509i
$267$			0.978025i			0.00366302i
$268$	−65.3165	+	20.7607i	−0.243718	+	0.0774651i
$269$	−28.7340	−	49.7687i	−0.106818	−	0.185014i	0.807662	−	0.589646i	$-0.200733\pi$
$269$	−28.7340	−	49.7687i	−0.106818	−	0.185014i	−0.914479	+	0.404632i	$0.867399\pi$
$270$	−160.191	−	117.172i	−0.593300	−	0.433970i
$271$	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
$276$	85.1341	+	18.6670i	0.308457	+	0.0676341i
$277$	−308.465	+	178.092i	−1.11359	+	0.642933i	−0.939757	−	0.341842i	$-0.888949\pi$
$277$	−308.465	+	178.092i	−1.11359	+	0.642933i	−0.173834	+	0.984775i	$0.555616\pi$
$278$	−10.5973	+	97.8095i	−0.0381197	+	0.351833i
$279$			105.060i			0.376561i
$280$	−96.5066	+	341.965i	−0.344666	+	1.22130i
$281$	−294.160			−1.04683			−0.523416	−	0.852077i	$-0.675343\pi$
$281$	−294.160			−1.04683			−0.523416	+	0.852077i	$0.675343\pi$
$282$	39.6749	+	4.29861i	0.140691	+	0.0152433i
$283$	−207.501	−	359.402i	−0.733219	−	1.26997i	−0.955501	−	0.294989i	$-0.904684\pi$
$283$	−207.501	−	359.402i	−0.733219	−	1.26997i	0.222282	−	0.974982i	$-0.428649\pi$
$284$	−125.252	−	27.4635i	−0.441028	−	0.0967023i
$285$	−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
$290$	−124.828	+	170.658i	−0.430442	+	0.588477i
$291$	−133.720	+	77.2034i	−0.459520	+	0.265304i
$292$	−408.523	+	129.848i	−1.39905	+	0.444685i
$293$	370.564			1.26472			0.632362	−	0.774673i	$-0.282085\pi$
$293$	370.564			1.26472			0.632362	+	0.774673i	$0.282085\pi$
$294$	0.936631	−	89.2596i	0.00318582	−	0.303604i
$295$	−346.981			−1.17621
$296$	−285.161	+	251.837i	−0.963380	+	0.850801i
$297$	−178.986	+	103.337i	−0.602645	+	0.347937i
$298$	−49.2298	+	67.3042i	−0.165201	+	0.225853i
$299$	−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
$304$	214.958	−	152.004i	0.707099	−	0.500013i
$305$	32.5081	+	56.3057i	0.106584	+	0.184609i
$306$	258.740	+	28.0334i	0.845554	+	0.0916124i
$307$	160.327			0.522239			0.261120	−	0.965306i	$-0.415908\pi$
$307$	160.327			0.522239			0.261120	+	0.965306i	$0.415908\pi$
$308$	285.196	+	235.734i	0.925962	+	0.765371i
$309$		−	151.486i		−	0.490245i
$310$	162.229	+	17.5769i	0.523320	+	0.0566996i
$311$	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	$0.0584387\pi$
$312$	138.727	−	28.0959i	0.444637	−	0.0900508i
$313$	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	0.775137	−	0.631793i	$-0.217681\pi$
$317$	195.132	+	112.659i	0.615557	+	0.355392i	−0.159580	+	0.987185i	$0.551014\pi$
$318$	−39.9921	+	54.6751i	−0.125761	+	0.171934i
$319$	110.090	+	190.681i	0.345109	+	0.597746i
$320$	374.082	−	158.004i	1.16901	−	0.493762i
$321$		−	179.972i		−	0.560659i
$322$	19.8175	−	334.313i	0.0615451	−	1.03824i
$323$		−	262.067i		−	0.811353i
$324$	71.8357	+	226.007i	0.221715	+	0.697553i
$325$	−148.201	−	256.692i	−0.456004	−	0.789822i
$326$	−286.251	+	391.347i	−0.878072	+	1.20045i
$327$	−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	0.472677	−	0.881236i	$-0.343288\pi$
$331$	−17.9257	−	10.3494i	−0.0541561	−	0.0312671i	−0.526834	+	0.849968i	$0.676621\pi$
$332$	−142.003	−	31.1364i	−0.427719	−	0.0937842i
$333$	−336.490	+	194.273i	−1.01048	+	0.583401i
$334$	−119.522	−	12.9497i	−0.357851	−	0.0387717i
$335$			108.716i			0.324527i
$336$	−80.3281	+	62.8871i	−0.239072	+	0.187164i
$337$	34.9645			0.103752			0.0518762	−	0.998654i	$-0.483480\pi$
$337$	34.9645			0.103752			0.0518762	+	0.998654i	$0.483480\pi$
$338$	−44.8754	+	414.186i	−0.132768	+	1.22540i
$339$	−6.73619	−	11.6674i	−0.0198708	−	0.0344172i
$340$	86.5756	−	394.843i	0.254634	−	1.16130i
$341$	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
$346$	−224.969	−	164.554i	−0.650201	−	0.475590i
$347$	379.958	−	219.369i	1.09498	−	0.632188i	0.160083	−	0.987104i	$-0.448824\pi$
$347$	379.958	−	219.369i	1.09498	−	0.632188i	0.934898	+	0.354916i	$0.115491\pi$
$348$	−57.8542	+	18.3888i	−0.166248	+	0.0528414i
$349$	−435.121			−1.24677			−0.623383	−	0.781917i	$-0.714242\pi$
$349$	−435.121			−1.24677			−0.623383	+	0.781917i	$0.714242\pi$
$350$	178.365	+	117.576i	0.509614	+	0.335932i
$351$	303.793			0.865507
$352$	6.77670	−	422.814i	0.0192520	−	1.20118i
$353$	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	$0.202978\pi$
$354$	−80.4078	−	58.8144i	−0.227141	−	0.166142i
$355$	−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	$0.286484\pi$
$360$	406.475	−	82.3220i	1.12910	−	0.228672i
$361$	45.1247	+	78.1583i	0.124999	+	0.216505i
$362$	35.9434	−	331.747i	0.0992912	−	0.916427i
$363$	48.8468			0.134564
$364$	−189.795	−	509.691i	−0.521414	−	1.40025i
$365$			679.969i			1.86293i
$366$	−2.01071	+	18.5583i	−0.00549375	+	0.0507056i
$367$	−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	$0.401034\pi$
$368$	−312.505	+	220.982i	−0.849197	+	0.600496i
$369$	−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	0.989344	−	0.145600i	$-0.0465112\pi$
$373$	506.505	+	292.431i	1.35792	+	0.783997i	0.368579	+	0.929597i	$0.379845\pi$
$374$	−339.747	−	248.509i	−0.908415	−	0.664462i
$375$	−28.1478	−	48.7534i	−0.0750608	−	0.130009i
$376$	−131.357	+	116.007i	−0.349355	+	0.308529i
$377$		−	323.644i		−	0.858472i
$378$	−195.769	+	98.0660i	−0.517907	+	0.259434i
$379$		−	128.176i		−	0.338195i	−0.985599	−	0.169098i	$-0.945915\pi$
$379$		−	128.176i		−	0.338195i	0.985599	−	0.169098i	$-0.0540853\pi$
$380$	−126.502	−	397.996i	−0.332900	−	1.04736i
$381$	−32.0011	−	55.4276i	−0.0839925	−	0.145479i
$382$	212.043	+	155.099i	0.555085	+	0.406018i
$383$	−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
$388$	145.227	−	662.334i	0.374297	−	1.70705i
$389$	187.428	−	108.212i	0.481821	−	0.278179i	−0.239354	−	0.970932i	$-0.576936\pi$
$389$	187.428	−	108.212i	0.481821	−	0.278179i	0.721175	+	0.692753i	$0.243602\pi$
$390$	24.1847	−	223.218i	0.0620121	−	0.572353i
$391$			380.991i			0.974402i
$392$	286.838	+	267.186i	0.731729	+	0.681596i
$393$	129.460			0.329415
$394$	4.16660	+	0.451434i	0.0105751	+	0.00114577i
$395$	184.984	+	320.401i	0.468314	+	0.811143i
$396$	92.4974	−	421.850i	0.233579	−	1.06528i
$397$	349.941	−	606.116i	0.881463	−	1.52674i	0.0317493	−	0.999496i	$-0.489892\pi$
$397$	349.941	−	606.116i	0.881463	−	1.52674i	0.849714	−	0.527244i	$-0.176774\pi$
$398$	−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	$0.0942123\pi$
$402$	−18.4278	+	25.1934i	−0.0458402	+	0.0626703i
$403$	−216.310	+	124.887i	−0.536749	+	0.309892i
$404$	−34.0791	−	107.218i	−0.0843541	−	0.265392i
$405$	376.179			0.928837
$406$	104.474	+	208.561i	0.257325	+	0.513697i
$407$	628.431			1.54406
$408$	86.9897	−	76.8242i	0.213210	−	0.188295i
$409$	−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	$0.477888\pi$
$410$	−48.6598	+	66.5250i	−0.118682	+	0.162256i
$411$	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
$416$	−319.376	+	533.253i	−0.767731	+	1.28186i
$417$	22.4031	+	38.8033i	0.0537245	+	0.0930535i
$418$	−432.351	−	46.8435i	−1.03433	−	0.112066i
$419$	−780.890			−1.86370			−0.931849	−	0.362846i	$-0.881805\pi$
$419$	−780.890			−1.86370			−0.931849	+	0.362846i	$0.881805\pi$
$420$	56.4708	+	151.652i	0.134454	+	0.361075i
$421$			114.961i			0.273068i	0.990635	+	0.136534i	$0.0435962\pi$
$421$			114.961i			0.273068i	−0.990635	+	0.136534i	$0.956404\pi$
$422$	−14.2530	−	1.54426i	−0.0337749	−	0.00365938i
$423$	−155.002	+	89.4904i	−0.366435	+	0.211561i
$424$	−59.0482	−	291.558i	−0.139265	−	0.687636i
$425$	−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
$430$	−249.426	+	341.002i	−0.580061	+	0.793028i
$431$	−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	$0.950316\pi$
$432$	227.279	+	104.703i	0.526109	+	0.242368i
$433$		−	595.775i		−	1.37592i	−0.725747	−	0.687962i	$-0.758506\pi$
$433$		−	595.775i		−	1.37592i	0.725747	−	0.687962i	$-0.241494\pi$
$434$	99.0792	−	150.305i	0.228293	−	0.346324i
$435$			96.2958i			0.221370i
$436$	43.9143	−	13.9580i	0.100721	−	0.0320138i
$437$	196.808	+	340.881i	0.450361	+	0.780048i
$438$	−115.257	+	157.573i	−0.263144	+	0.359755i
$439$	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	−0.00235617	−	0.999997i	$-0.500750\pi$
$443$	−385.214	−	222.403i	−0.869557	−	0.502039i	−0.867201	+	0.497958i	$0.834083\pi$
$444$	−37.1099	+	169.246i	−0.0835808	+	0.381185i
$445$	−5.90012	+	3.40644i	−0.0132587	+	0.00765491i
$446$	556.185	+	60.2605i	1.24705	+	0.135113i
$447$			37.9772i			0.0849601i
$448$	33.6736	−	446.733i	0.0751642	−	0.997171i
$449$	262.420			0.584455			0.292228	−	0.956349i	$-0.405604\pi$
$449$	262.420			0.584455			0.292228	+	0.956349i	$0.405604\pi$
$450$	26.8586	−	247.897i	0.0596859	−	0.550882i
$451$	42.9145	+	74.3302i	0.0951542	+	0.164812i
$452$	57.7903	+	12.6714i	0.127855	+	0.0280342i
$453$	−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	$0.306787\pi$
$458$	−669.413	−	489.643i	−1.46160	−	1.06909i
$459$	215.720	−	124.546i	0.469978	−	0.271342i
$460$	183.908	+	578.605i	0.399800	+	1.25784i
$461$	−158.714			−0.344283			−0.172141	−	0.985072i	$-0.555069\pi$
$461$	−158.714			−0.344283			−0.172141	+	0.985072i	$0.555069\pi$
$462$	168.219	+	9.97173i	0.364110	+	0.0215838i
$463$	−528.844			−1.14221			−0.571106	−	0.820877i	$-0.693485\pi$
$463$	−528.844			−1.14221			−0.571106	+	0.820877i	$0.693485\pi$
$464$	111.545	−	242.130i	0.240398	−	0.521833i
$465$	64.3601	−	37.1583i	0.138409	−	0.0799103i
$466$	266.233	+	194.736i	0.571314	+	0.417889i
$467$	218.449	−	378.365i	0.467771	−	0.810203i	−0.531551	−	0.847026i	$-0.678391\pi$
$467$	218.449	−	378.365i	0.467771	−	0.810203i	0.999322	+	0.0368236i	$0.0117240\pi$
$468$	−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
$472$	428.779	−	86.8392i	0.908430	−	0.183981i
$473$	219.977	+	381.011i	0.465067	+	0.805519i
$474$	−11.4417	+	105.604i	−0.0241387	+	0.222793i
$475$	−251.085			−0.528600
$476$	−343.729	−	284.115i	−0.722119	−	0.596881i
$477$		−	303.811i		−	0.636920i
$478$	4.11866	−	38.0140i	0.00861645	−	0.0795272i
$479$	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	$0.140353\pi$
$480$	95.0260	−	158.662i	0.197971	−	0.330546i
$481$	−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
$486$	314.394	+	229.964i	0.646902	+	0.473177i
$487$	−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	$-0.398463\pi$
$488$	−54.2633	−	61.4435i	−0.111195	−	0.125909i
$489$			220.822i			0.451579i
$490$	541.738	−	305.239i	1.10559	−	0.622936i
$491$			732.074i			1.49098i	0.666514	+	0.745492i	$0.267786\pi$
$491$			732.074i			1.49098i	−0.666514	+	0.745492i	$0.732214\pi$
$492$	−22.5524	+	7.16822i	−0.0458382	+	0.0145695i
$493$	−132.684	−	229.815i	−0.269136	−	0.466157i
$494$	515.946	+	377.389i	1.04442	+	0.763945i
$495$	−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	0.476648	−	0.879094i	$-0.341852\pi$
$499$	−23.1264	−	13.3520i	−0.0463454	−	0.0267575i	−0.522994	+	0.852337i	$0.675185\pi$
$500$	241.482	+	52.9488i	0.482964	+	0.105898i
$501$	−47.4172	+	27.3763i	−0.0946451	+	0.0546434i
$502$	−19.0270	+	175.613i	−0.0379023	+	0.349827i
$503$			616.414i			1.22548i	0.790286	+	0.612738i	$0.209932\pi$
$503$			616.414i			1.22548i	−0.790286	+	0.612738i	$0.790068\pi$
$504$	124.269	−	440.339i	0.246566	−	0.873689i
$505$	−178.460			−0.353387
$506$	628.549	+	68.1007i	1.24219	+	0.134586i
$507$	94.8687	+	164.317i	0.187118	+	0.324097i
$508$	274.540	+	60.1973i	0.540433	+	0.118499i
$509$	66.3763	−	114.967i	0.130405	−	0.225869i	−0.793428	−	0.608665i	$-0.791705\pi$
$509$	66.3763	−	114.967i	0.130405	−	0.225869i	0.923833	+	0.382796i	$0.125039\pi$
$510$	−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
$514$	−101.642	+	138.960i	−0.197748	+	0.270350i
$515$	913.867	−	527.621i	1.77450	−	1.02451i
$516$	−115.602	+	36.7437i	−0.224035	+	0.0712087i
$517$	289.483			0.559928
$518$	664.612	+	39.3971i	1.28304	+	0.0760561i
$519$	−126.942			−0.244589
$520$	652.676	+	739.039i	1.25515	+	1.42123i
$521$	−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	$0.558064\pi$
$522$	160.738	−	219.752i	0.307927	−	0.420981i
$523$	186.224	−	322.550i	0.356069	−	0.616730i	−0.631231	−	0.775595i	$-0.717450\pi$
$523$	186.224	−	322.550i	0.356069	−	0.616730i	0.987300	+	0.158865i	$0.0507833\pi$
$524$	−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
$528$	−111.193	−	157.245i	−0.210594	−	0.297813i
$529$	−21.6179	−	37.4433i	−0.0408656	−	0.0707813i
$530$	−469.129	−	50.8283i	−0.885150	−	0.0959024i
$531$	446.799			0.841429
$532$	−454.306	−	76.6450i	−0.853959	−	0.144069i
$533$		−	126.161i		−	0.236700i
$534$	−1.94467	−	0.210697i	−0.00364170	−	0.000394564i
$535$	1085.71	−	626.836i	2.02937	−	1.17166i
$536$	−27.2085	−	134.345i	−0.0507622	−	0.250644i
$537$	−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	0.554727	−	0.832032i	$-0.312823\pi$
$541$	60.3373	+	34.8357i	0.111529	+	0.0643914i	−0.443198	+	0.896424i	$0.646156\pi$
$542$	−36.4574	+	49.8426i	−0.0672646	+	0.0919605i
$543$	−75.9860	−	131.612i	−0.139937	−	0.242379i
$544$	−8.16752	+	509.591i	−0.0150138	+	0.936748i
$545$		−	73.0934i		−	0.134116i
$546$	−206.810	−	136.327i	−0.378774	−	0.249683i
$547$			466.463i			0.852765i	0.904543	+	0.426383i	$0.140212\pi$
$547$			466.463i			0.852765i	−0.904543	+	0.426383i	$0.859788\pi$
$548$	306.638	+	964.734i	0.559558	+	1.76046i
$549$	−41.8599	−	72.5034i	−0.0762475	−	0.132065i
$550$	−238.095	+	325.510i	−0.432899	+	0.591836i
$551$	−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
$556$	−192.198	−	42.1424i	−0.345679	−	0.0757957i
$557$	118.835	−	68.6094i	0.213348	−	0.123177i	−0.389518	−	0.921019i	$-0.627358\pi$
$557$	118.835	−	68.6094i	0.213348	−	0.123177i	0.602866	+	0.797842i	$0.294025\pi$
$558$	−208.898	−	22.6333i	−0.374370	−	0.0405615i
$559$		−	646.692i		−	1.15687i
$560$	−659.159	−	265.560i	−1.17707	−	0.474214i
$561$	−191.706			−0.341722
$562$	63.3712	−	584.897i	0.112760	−	1.04074i
$563$	84.5632	+	146.468i	0.150201	+	0.260156i	0.931301	−	0.364250i	$-0.118675\pi$
$563$	84.5632	+	146.468i	0.150201	+	0.260156i	−0.781100	+	0.624406i	$0.785341\pi$
$564$	−17.0944	+	77.9620i	−0.0303092	+	0.138231i
$565$	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	$0.939505\pi$
$570$	−153.513	−	112.287i	−0.269320	−	0.196995i
$571$	−767.828	+	443.306i	−1.34471	+	0.776367i	−0.987494	−	0.157655i	$-0.949606\pi$
$571$	−767.828	+	443.306i	−1.34471	+	0.776367i	−0.357213	+	0.934023i	$0.616273\pi$
$572$	978.505	−	311.015i	1.71067	−	0.543732i
$573$	119.647			0.208809
$574$	40.7255	+	81.3000i	0.0709503	+	0.141638i
$575$	365.026			0.634827
$576$	−481.696	+	203.458i	−0.836277	+	0.353225i
$577$	−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	$0.400037\pi$
$578$	−57.0448	−	41.7255i	−0.0986935	−	0.0721894i
$579$	−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
$584$	−170.176	−	840.266i	−0.291398	−	1.43881i
$585$	503.488	+	872.067i	0.860663	+	1.49071i
$586$	−79.8311	+	736.817i	−0.136231	+	1.25737i
$587$	−190.873			−0.325168			−0.162584	−	0.986695i	$-0.551983\pi$
$587$	−190.873			−0.325168			−0.162584	+	0.986695i	$0.551983\pi$
$588$	177.279	+	21.0917i	0.301495	+	0.0358702i
$589$			211.585i			0.359227i
$590$	74.7506	−	689.925i	0.126696	−	1.16936i
$591$	1.65299	−	0.954353i	0.00279693	−	0.00161481i
$592$	−439.311	−	621.256i	−0.742080	−	1.04942i
$593$	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
$598$	−750.078	−	548.646i	−1.25431	−	0.917468i
$599$	−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	$-0.548696\pi$
$600$	−73.6049	−	83.3444i	−0.122675	−	0.138907i
$601$			183.100i			0.304659i	0.988330	+	0.152329i	$0.0486774\pi$
$601$			183.100i			0.304659i	−0.988330	+	0.152329i	$0.951323\pi$
$602$	208.756	+	416.737i	0.346770	+	0.692255i
$603$		−	139.991i		−	0.232158i
$604$	−118.293	−	372.169i	−0.195849	−	0.616173i
$605$	170.132	+	294.678i	0.281210	+	0.487071i
$606$	−41.3556	−	30.2496i	−0.0682436	−	0.0499168i
$607$	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
$612$	−111.481	+	508.429i	−0.182159	+	0.830767i
$613$	−232.853	+	134.438i	−0.379859	+	0.219312i	−0.677757	−	0.735286i	$-0.737048\pi$
$613$	−232.853	+	134.438i	−0.379859	+	0.219312i	0.297898	+	0.954598i	$0.403714\pi$
$614$	−34.5395	+	318.789i	−0.0562533	+	0.519201i
$615$			37.5375i			0.0610366i
$616$	−530.166	+	516.289i	−0.860658	+	0.838132i
$617$	−184.934			−0.299731			−0.149866	−	0.988706i	$-0.547884\pi$
$617$	−184.934			−0.299731			−0.149866	+	0.988706i	$0.547884\pi$
$618$	301.209	+	32.6348i	0.487393	+	0.0528071i
$619$	496.809	+	860.498i	0.802599	+	1.39014i	0.917900	+	0.396812i	$0.129884\pi$
$619$	496.809	+	860.498i	0.802599	+	1.39014i	−0.115301	+	0.993331i	$0.536783\pi$
$620$	−69.8984	+	318.784i	−0.112739	+	0.514167i
$621$	−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
$626$	−272.769	+	372.914i	−0.435732	+	0.595710i
$627$	−171.524	+	99.0292i	−0.273562	+	0.157941i
$628$	−34.1267	−	107.368i	−0.0543419	−	0.170969i
$629$	−757.408			−1.20415
$630$	−605.963	−	399.444i	−0.961846	−	0.634038i
$631$	805.857			1.27711			0.638555	−	0.769576i	$-0.279532\pi$
$631$	805.857			1.27711			0.638555	+	0.769576i	$0.279532\pi$
$632$	−308.779	−	349.637i	−0.488575	−	0.553224i
$633$	−5.65451	+	3.26463i	−0.00893287	+	0.00515740i
$634$	−266.045	+	363.722i	−0.419629	+	0.573694i
$635$	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
$640$	233.580	+	777.849i	0.364969	+	1.21539i
$641$	−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	$0.834700\pi$
$642$	357.849	+	38.7715i	0.557397	+	0.0603917i
$643$	1024.08			1.59266			0.796331	−	0.604861i	$-0.206771\pi$
$643$	1024.08			1.59266			0.796331	+	0.604861i	$0.206771\pi$
$644$	660.467	+	111.426i	1.02557	+	0.173022i
$645$			192.414i			0.298317i
$646$	521.084	+	56.4574i	0.806632	+	0.0873954i
$647$	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	$0.218550\pi$
$648$	−464.860	+	94.1465i	−0.717377	+	0.145288i
$649$	−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	0.518612	−	0.855010i	$-0.326449\pi$
$653$	24.4603	+	14.1222i	0.0374584	+	0.0216266i	−0.481154	+	0.876636i	$0.659782\pi$
$654$	12.3896	−	16.9383i	0.0189443	−	0.0258996i
$655$	450.907	+	780.994i	0.688407	+	1.19236i
$656$	43.4817	−	94.3859i	0.0662831	−	0.143881i
$657$		−	875.579i		−	1.33269i
$658$	306.149	+	18.1480i	0.465272	+	0.0275805i
$659$		−	132.188i		−	0.200589i	−0.994958	−	0.100295i	$-0.968021\pi$
$659$		−	132.188i		−	0.200589i	0.994958	−	0.100295i	$-0.0319785\pi$
$660$	−291.141	+	92.5382i	−0.441122	+	0.140209i
$661$	−346.924	−	600.889i	−0.524847	−	0.909061i	−0.999581	−	0.0289321i	$-0.990789\pi$
$661$	−346.924	−	600.889i	−0.524847	−	0.909061i	0.474735	−	0.880129i	$-0.342544\pi$
$662$	24.4401	−	33.4132i	0.0369186	−	0.0504731i
$663$	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
$668$	51.4976	−	234.864i	0.0770922	−	0.351592i
$669$	220.652	−	127.393i	0.329823	−	0.190424i
$670$	−216.168	−	23.4209i	−0.322638	−	0.0349566i
$671$			135.408i			0.201800i
$672$	−107.737	−	173.269i	−0.160323	−	0.257841i
$673$	532.137			0.790694			0.395347	−	0.918532i	$-0.370624\pi$
$673$	532.137			0.790694			0.395347	+	0.918532i	$0.370624\pi$
$674$	−7.53246	+	69.5222i	−0.0111757	+	0.103149i
$675$	−119.327	−	206.680i	−0.176780	−	0.306192i
$676$	−813.885	−	178.457i	−1.20397	−	0.263990i
$677$	143.115	−	247.883i	0.211396	−	0.366149i	−0.740756	−	0.671775i	$-0.765532\pi$
$677$	143.115	−	247.883i	0.211396	−	0.366149i	0.952152	+	0.305626i	$0.0988657\pi$
$678$	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
$682$	274.301	+	200.638i	0.402202	+	0.294191i
$683$	−387.838	+	223.918i	−0.567844	+	0.327845i	−0.756288	−	0.654239i	$-0.772989\pi$
$683$	−387.838	+	223.918i	−0.567844	+	0.327845i	0.188443	+	0.982084i	$0.439656\pi$
$684$	162.893	+	512.490i	0.238148	+	0.749254i
$685$	1605.76			2.34417
$686$	−26.2146	−	685.499i	−0.0382138	−	0.999270i
$687$	−377.724			−0.549817
$688$	222.884	−	483.815i	0.323959	−	0.703219i
$689$	625.519	−	361.143i	0.907865	−	0.524156i
$690$	223.176	+	163.242i	0.323443	+	0.236583i
$691$	−510.366	+	883.980i	−0.738591	+	1.27928i	0.214539	+	0.976715i	$0.431175\pi$
$691$	−510.366	+	883.980i	−0.738591	+	1.27928i	−0.953130	+	0.302561i	$0.902158\pi$
$692$	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
$696$	−24.1000	−	118.997i	−0.0346264	−	0.170972i
$697$	−51.7221	−	89.5854i	−0.0742068	−	0.128530i
$698$	93.7387	−	865.180i	0.134296	−	1.23951i
$699$	150.225			0.214914
$700$	−272.209	+	329.324i	−0.388870	+	0.470463i
$701$		−	1311.02i		−	1.87021i	−0.354369	−	0.935106i	$-0.615304\pi$
$701$		−	1311.02i		−	1.87021i	0.354369	−	0.935106i	$-0.384696\pi$
$702$	−65.4465	+	604.051i	−0.0932287	+	0.860472i
$703$	−677.669	+	391.252i	−0.963967	+	0.556546i
$704$	839.249	+	104.562i	1.19212	+	0.148526i
$705$	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	0.790962	−	0.611865i	$-0.209581\pi$
$709$	465.495	+	268.754i	0.656552	+	0.379061i	−0.134410	+	0.990926i	$0.542914\pi$
$710$	−328.342	−	240.166i	−0.462454	−	0.338263i
$711$	−238.199	−	412.573i	−0.335020	−	0.580271i
$712$	6.43850	−	5.68610i	0.00904283	−	0.00798610i
$713$		−	307.601i		−	0.431417i
$714$	−202.743	−	12.0183i	−0.283954	−	0.0168323i
$715$		−	1628.68i		−	2.27787i
$716$	1112.08	−	353.472i	1.55319	−	0.493677i
$717$	−8.70704	−	15.0810i	−0.0121437	−	0.0210335i
$718$	−426.050	−	311.635i	−0.593385	−	0.434032i
$719$	−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
$724$	651.890	+	142.937i	0.900400	+	0.197427i
$725$	−220.185	+	127.124i	−0.303703	+	0.175343i
$726$	−10.5231	+	97.1252i	−0.0144947	+	0.133781i
$727$			460.316i			0.633172i	0.948564	+	0.316586i	$0.102537\pi$
$727$			460.316i			0.633172i	−0.948564	+	0.316586i	$0.897463\pi$
$728$	1054.34	−	267.578i	1.44827	−	0.367552i
$729$	−356.185			−0.488594
$730$	−1352.03	−	146.487i	−1.85209	−	0.200666i
$731$	−265.124	−	459.208i	−0.362686	−	0.628191i
$732$	−36.4674	−	7.99605i	−0.0498188	−	0.0109236i
$733$	33.3410	−	57.7484i	0.0454857	−	0.0787836i	−0.842386	−	0.538874i	$-0.818850\pi$
$733$	33.3410	−	57.7484i	0.0454857	−	0.0787836i	0.887872	+	0.460091i	$0.152183\pi$
$734$	−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
$738$	62.6580	−	85.6626i	0.0849024	−	0.116074i
$739$	808.772	−	466.944i	1.09441	−	0.631860i	0.159665	−	0.987171i	$-0.448958\pi$
$739$	808.772	−	466.944i	1.09441	−	0.631860i	0.934748	+	0.355311i	$0.115625\pi$
$740$	−1150.26	+	365.607i	−1.55441	+	0.494064i
$741$	291.128			0.392885
$742$	−286.514	+	434.647i	−0.386138	+	0.585778i
$743$	−1198.23			−1.61269			−0.806345	−	0.591446i	$-0.798557\pi$
$743$	−1198.23			−1.61269			−0.806345	+	0.591446i	$0.798557\pi$
$744$	−70.2328	+	62.0255i	−0.0943989	+	0.0833676i
$745$	−229.104	+	132.273i	−0.307523	+	0.177548i
$746$	−690.576	+	944.117i	−0.925705	+	1.26557i
$747$	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	$0.130861\pi$
$752$	−202.366	−	286.178i	−0.269103	−	0.380555i
$753$	40.2239	+	69.6698i	0.0534182	+	0.0925230i
$754$	643.522	+	69.7230i	0.853477	+	0.0924708i
$755$	−619.458			−0.820474
$756$	−152.816	−	410.386i	−0.202138	−	0.542838i
$757$			209.207i			0.276364i	0.990407	+	0.138182i	$0.0441259\pi$
$757$			209.207i			0.276364i	−0.990407	+	0.138182i	$0.955874\pi$
$758$	254.860	+	27.6131i	0.336227	+	0.0364289i
$759$	249.360	−	143.968i	0.328538	−	0.189681i
$760$	818.614	−	165.791i	1.07712	−	0.218146i
$761$	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
$766$	295.093	−	403.435i	0.385239	−	0.526678i
$767$	531.115	+	919.919i	0.692458	+	1.19937i
$768$	−77.7191	+	219.848i	−0.101197	+	0.286260i
$769$		−	219.524i		−	0.285467i	−0.989761	−	0.142734i	$-0.954411\pi$
$769$		−	219.524i		−	0.285467i	0.989761	−	0.142734i	$-0.0455892\pi$
$770$	525.746	+	1049.54i	0.682787	+	1.36304i
$771$			78.4096i			0.101699i
$772$	−98.6763	−	310.452i	−0.127819	−	0.402140i
$773$	333.337	+	577.357i	0.431225	+	0.746904i	0.996979	−	0.0776701i	$-0.0247481\pi$
$773$	333.337	+	577.357i	0.431225	+	0.746904i	−0.565754	+	0.824574i	$0.691415\pi$
$774$	321.180	−	439.100i	0.414961	−	0.567312i
$775$	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
$780$	438.628	+	96.1761i	0.562343	+	0.123303i
$781$	−366.866	+	211.810i	−0.469738	+	0.271204i
$782$	−757.549	−	82.0774i	−0.968733	−	0.104958i
$783$		−	260.587i		−	0.332806i
$784$	−593.056	+	512.777i	−0.756449	+	0.654053i
$785$	−178.710			−0.227656
$786$	−27.8898	+	257.414i	−0.0354832	+	0.327499i
$787$	−459.932	−	796.626i	−0.584412	−	1.01223i	−0.994948	−	0.100387i	$-0.967992\pi$
$787$	−459.932	−	796.626i	−0.584412	−	1.01223i	0.410536	−	0.911844i	$-0.365341\pi$
$788$	−1.79523	+	8.18746i	−0.00227821	+	0.0103902i
$789$	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
$794$	1129.79	+	826.386i	1.42291	+	1.04079i
$795$	−186.115	+	107.453i	−0.234106	+	0.135161i
$796$	483.920	−	153.813i	0.607940	−	0.193232i
$797$	−1016.13			−1.27494			−0.637470	−	0.770476i	$-0.720019\pi$
$797$	−1016.13			−1.27494			−0.637470	+	0.770476i	$0.720019\pi$
$798$	−187.607	+	93.9777i	−0.235097	+	0.117767i
$799$	−348.895			−0.436664
$800$	488.236	+	7.82525i	0.610295	+	0.00978156i
$801$	7.59744	−	4.38638i	0.00948494	−	0.00547613i
$802$	292.149	+	213.693i	0.364276	+	0.266450i
$803$	−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
$808$	220.531	−	44.6634i	0.272934	−	0.0552765i
$809$	−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	$-0.413291\pi$
$810$	−81.0407	+	747.981i	−0.100050	+	0.923433i
$811$	−481.066			−0.593176			−0.296588	−	0.955006i	$-0.595849\pi$
$811$	−481.066			−0.593176			−0.296588	+	0.955006i	$0.595849\pi$
$812$	−437.202	+	162.802i	−0.538426	+	0.200495i
$813$			28.1242i			0.0345931i
$814$	−135.384	+	1249.55i	−0.166319	+	1.53507i
$815$	−1332.15	+	769.117i	−1.63454	+	0.943702i
$816$	134.014	+	189.518i	0.164233	+	0.232252i
$817$	−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	0.832011	−	0.554758i	$-0.187189\pi$
$821$	630.185	+	363.838i	0.767582	+	0.443164i	−0.0644292	+	0.997922i	$0.520523\pi$
$822$	372.111	+	272.181i	0.452690	+	0.331120i
$823$	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	$0.709013\pi$
$824$	−997.256	+	880.718i	−1.21026	+	1.06883i
$825$			183.673i			0.222633i
$826$	−639.213	−	421.362i	−0.773866	−	0.510124i
$827$			1468.52i			1.77572i	0.460116	+	0.887859i	$0.347808\pi$
$827$			1468.52i			1.77572i	−0.460116	+	0.887859i	$0.652192\pi$
$828$	−236.813	−	745.055i	−0.286007	−	0.899824i
$829$	409.352	+	709.019i	0.493790	+	0.855270i	0.999974	−	0.00715566i	$-0.00227774\pi$
$829$	409.352	+	709.019i	0.493790	+	0.855270i	−0.506184	+	0.862425i	$0.668944\pi$
$830$	−372.254	−	272.286i	−0.448499	−	0.328055i
$831$	−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
$836$	186.284	−	849.579i	0.222827	−	1.01624i
$837$	−174.165	+	100.554i	−0.208083	+	0.120137i
$838$	168.228	−	1552.69i	0.200749	−	1.85285i
$839$			1108.84i			1.32162i	0.750555	+	0.660808i	$0.229786\pi$
$839$			1108.84i			1.32162i	−0.750555	+	0.660808i	$0.770214\pi$
$840$	−313.704	+	79.6141i	−0.373457	+	0.0947787i
$841$	563.386			0.669900
$842$	−228.585	−	24.7663i	−0.271479	−	0.0294136i
$843$	−133.970	−	232.042i	−0.158920	−	0.275258i
$844$	6.14109	−	28.0075i	0.00727618	−	0.0331843i
$845$	−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
$850$	286.960	−	392.316i	0.337600	−	0.461549i
$851$	985.191	−	568.800i	1.15769	−	0.668390i
$852$	−35.3796	−	111.310i	−0.0415254	−	0.130646i
$853$	−610.400			−0.715592			−0.357796	−	0.933800i	$-0.616472\pi$
$853$	−610.400			−0.715592			−0.357796	+	0.933800i	$0.616472\pi$
$854$	−8.48887	+	143.204i	−0.00994013	+	0.167686i
$855$	853.017			0.997680
$856$	−1184.78	+	1046.33i	−1.38409	+	1.22235i
$857$	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	$0.249904\pi$
$858$	276.066	−	377.423i	0.321755	−	0.439886i
$859$	−40.7547	+	70.5892i	−0.0474443	+	0.0821760i	−0.888772	−	0.458349i	$-0.848441\pi$
$859$	−40.7547	+	70.5892i	−0.0474443	+	0.0821760i	0.841328	+	0.540525i	$0.181774\pi$
$860$	−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	$-0.0418384\pi$
$864$	−257.151	+	429.357i	−0.297628	+	0.496941i
$865$	−442.134	−	765.799i	−0.511138	−	0.885317i
$866$	1184.62	+	128.349i	1.36792	+	0.148208i
$867$	−32.1882			−0.0371259
$868$	277.516	+	229.386i	0.319719	+	0.264269i
$869$			770.524i			0.886679i
$870$	−191.471	−	20.7451i	−0.220082	−	0.0238450i
$871$	288.230	−	166.409i	0.330918	−	0.191056i
$872$	18.2931	+	90.3245i	0.0209784	+	0.103583i
$873$	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	$-0.984607\pi$
$877$	−1350.68	−	779.814i	−1.54011	−	0.889183i	−0.541280	−	0.840842i	$-0.682060\pi$
$878$	−952.747	+	1302.54i	−1.08513	+	1.48354i
$879$	168.767	+	292.312i	0.191998	+	0.332551i
$880$	561.328	−	1218.48i	0.637873	−	1.38463i
$881$			1515.22i			1.71989i	0.510389	+	0.859944i	$0.329501\pi$
$881$			1515.22i			1.71989i	−0.510389	+	0.859944i	$0.670499\pi$
$882$	−697.582	+	393.048i	−0.790910	+	0.445633i
$883$		−	763.828i		−	0.865037i	−0.901625	−	0.432519i	$-0.857625\pi$
$883$		−	763.828i		−	0.865037i	0.901625	−	0.432519i	$-0.142375\pi$
$884$	−1179.33	+	374.846i	−1.33408	+	0.424034i
$885$	−158.026	−	273.709i	−0.178561	−	0.309276i
$886$	525.206	−	718.033i	0.592783	−	0.810421i
$887$	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
$892$	−239.639	+	1092.92i	−0.268654	+	1.22524i
$893$	−312.163	+	180.228i	−0.349567	+	0.201823i
$894$	−75.5124	−	8.18146i	−0.0844658	−	0.00915153i
$895$		−	1851.01i		−	2.06817i
$896$	881.013	+	163.195i	0.983273	+	0.182138i
$897$	−423.240			−0.471840
$898$	−56.5335	+	521.787i	−0.0629549	+	0.581055i
$899$	107.125	+	185.546i	0.119160	+	0.206391i
$900$	487.123	+	106.809i	0.541248	+	0.118677i
$901$	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
$906$	−143.550	−	105.000i	−0.158444	−	0.115894i
$907$	−885.036	+	510.976i	−0.975784	+	0.563369i	−0.900995	−	0.433830i	$-0.857162\pi$
$907$	−885.036	+	510.976i	−0.975784	+	0.563369i	−0.0747894	+	0.997199i	$0.523828\pi$
$908$	−369.293	−	1161.86i	−0.406710	−	1.27958i
$909$	229.799			0.252804
$910$	102.104	−	1722.45i	0.112202	−	1.89280i
$911$	630.111			0.691669			0.345835	−	0.938295i	$-0.387596\pi$
$911$	630.111			0.691669			0.345835	+	0.938295i	$0.387596\pi$
$912$	217.804	+	100.338i	0.238820	+	0.110020i
$913$	−415.930	+	240.137i	−0.455564	+	0.263020i
$914$	−628.714	−	459.873i	−0.687871	−	0.503144i
$915$	−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	$0.0150038\pi$
$920$	−1190.10	+	241.026i	−1.29358	+	0.261985i
$921$	73.0182	+	126.471i	0.0792814	+	0.137319i
$922$	34.1920	−	315.582i	0.0370846	−	0.342280i
$923$	622.683			0.674630
$924$	−56.0670	+	332.332i	−0.0606786	+	0.359667i
$925$			725.668i			0.784506i
$926$	113.929	−	1051.53i	0.123034	−	1.13557i
$927$	−1176.76	+	679.405i	−1.26943	+	0.732907i
$928$	457.413	+	273.954i	0.492902	+	0.295209i
$929$	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
$934$	705.266	+	515.867i	0.755103	+	0.552321i
$935$	−667.708	−	1156.50i	−0.714126	−	1.23690i
$936$	−840.434	−	951.641i	−0.897900	−	1.01671i
$937$			1586.27i			1.69293i	0.532447	+	0.846463i	$0.321273\pi$
$937$			1586.27i			1.69293i	−0.532447	+	0.846463i	$0.678727\pi$
$938$	−132.022	+	200.279i	−0.140748	+	0.213517i
$939$			210.421i			0.224090i
$940$	−529.860	+	168.414i	−0.563681	+	0.179164i
$941$	−410.023	−	710.181i	−0.435731	−	0.754708i	0.561624	−	0.827393i	$-0.310177\pi$
$941$	−410.023	−	710.181i	−0.435731	−	0.754708i	−0.997355	+	0.0726842i	$0.976843\pi$
$942$	−41.4134	−	30.2919i	−0.0439633	−	0.0321570i
$943$	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	0.762261	−	0.647270i	$-0.224089\pi$
$947$	551.949	+	318.668i	0.582839	+	0.336502i	−0.179422	+	0.983772i	$0.557423\pi$
$948$	−207.514	−	45.5007i	−0.218896	−	0.0479965i
$949$	1802.74	−	1040.81i	1.89962	−	1.09675i
$950$	54.0915	−	499.248i	0.0569384	−	0.525524i
$951$			205.234i			0.215809i
$952$	638.974	−	622.250i	0.671192	−	0.653624i
$953$	−350.626			−0.367918			−0.183959	−	0.982934i	$-0.558891\pi$
$953$	−350.626			−0.367918			−0.183959	+	0.982934i	$0.558891\pi$
$954$	604.086	+	65.4503i	0.633214	+	0.0686062i
$955$	416.729	+	721.796i	0.436365	+	0.755807i
$956$	74.6983	+	16.3788i	0.0781363	+	0.0171326i
$957$	−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
$962$	1090.70	−	1491.15i	1.13379	−	1.55005i
$963$	−1398.04	+	807.161i	−1.45176	+	0.838174i
$964$	1335.40	−	424.453i	1.38527	−	0.440304i
$965$	−516.734			−0.535475
$966$	272.742	−	136.624i	0.282342	−	0.141433i
$967$	−649.816			−0.671992			−0.335996	−	0.941863i	$-0.609073\pi$
$967$	−649.816			−0.671992			−0.335996	+	0.941863i	$0.609073\pi$
$968$	−283.989	−	321.566i	−0.293377	−	0.332197i
$969$	206.726	−	119.354i	0.213340	−	0.123172i
$970$	1270.00	−	1736.28i	1.30928	−	1.78998i
$971$	485.305	−	840.573i	0.499799	−	0.865677i	−0.500201	−	0.865909i	$-0.666741\pi$
$971$	485.305	−	840.573i	0.499799	−	0.865677i	1.00000		0.000232071i	$7.38706e-5\pi$
$972$	−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
$976$	133.862	−	94.6583i	0.137154	−	0.0969860i
$977$	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	$0.733838\pi$
$978$	−439.074	−	47.5719i	−0.448951	−	0.0486421i
$979$	−14.1890			−0.0144934
$980$	490.218	+	1142.93i	0.500223	+	1.16626i
$981$			94.1205i			0.0959434i
$982$	−1455.63	−	157.712i	−1.48231	−	0.160602i
$983$	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	$0.110074\pi$
$984$	−9.39453	−	46.3866i	−0.00954728	−	0.0471409i
$985$	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
$990$	808.885	−	1105.86i	0.817055	−	1.11703i
$991$	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	$0.547742\pi$
$992$	6.59420	−	411.428i	0.00664738	−	0.414746i
$993$		−	18.8538i		−	0.0189867i
$994$	−401.266	+	201.005i	−0.403688	+	0.202219i
$995$		−	805.464i		−	0.809512i
$996$	−40.1112	−	126.197i	−0.0402723	−	0.126703i
$997$	−470.469	−	814.876i	−0.471885	−	0.817328i	0.527598	−	0.849494i	$-0.323093\pi$
$997$	−470.469	−	814.876i	−0.471885	−	0.817328i	−0.999483	+	0.0321661i	$0.989759\pi$
$998$	31.5308	−	43.1072i	0.0315940	−	0.0431936i
$999$	−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.5.6	yes	28
4.3	odd	2		224.3.n.a.145.6		28
7.2	even	3		392.3.h.a.293.25		28
7.3	odd	6	inner	56.3.j.a.45.4	yes	28
7.4	even	3		392.3.j.e.325.4		28
7.5	odd	6		392.3.h.a.293.26		28
7.6	odd	2		392.3.j.e.117.6		28
8.3	odd	2		224.3.n.a.145.9		28
8.5	even	2	inner	56.3.j.a.5.4	✓	28
28.3	even	6		224.3.n.a.17.9		28
28.19	even	6		1568.3.h.a.881.11		28
28.23	odd	6		1568.3.h.a.881.17		28
56.3	even	6		224.3.n.a.17.6		28
56.5	odd	6		392.3.h.a.293.27		28
56.13	odd	2		392.3.j.e.117.4		28
56.19	even	6		1568.3.h.a.881.18		28
56.37	even	6		392.3.h.a.293.28		28
56.45	odd	6	inner	56.3.j.a.45.6	yes	28
56.51	odd	6		1568.3.h.a.881.12		28
56.53	even	6		392.3.j.e.325.6		28

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

\(f(q)\)	\(=\)	\(q+(-0.215431 + 1.98836i) q^{2} +(0.455431 + 0.788830i) q^{3} +(-3.90718 - 0.856711i) q^{4} +(-3.17251 + 5.49495i) q^{5} +(-1.66660 + 0.735624i) q^{6} +(3.79106 + 5.88455i) q^{7} +(2.54518 - 7.58433i) q^{8} +(4.08516 - 7.07571i) q^{9} +O(q^{10})\)	\(q+(-0.215431 + 1.98836i) q^{2} +(0.455431 + 0.788830i) q^{3} +(-3.90718 - 0.856711i) 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} +(-10.2425 - 7.49189i) q^{10} +(-11.4442 + 6.60732i) q^{11} +(-1.10365 - 3.47227i) q^{12} +19.4243 q^{13} +(-12.5173 + 6.27028i) q^{14} -5.77945 q^{15} +(14.5321 + 6.69465i) q^{16} +(13.7930 - 7.96338i) q^{17} +(13.1890 + 9.64712i) 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} +(7.14190 - 1.44643i) q^{24} +(-7.62967 - 13.2150i) q^{25} +(-4.18461 + 38.6227i) q^{26} +15.6398 q^{27} +(-9.77098 - 26.2398i) q^{28} -16.6618i q^{29} +(1.24507 - 11.4916i) q^{30} +(-11.1360 + 6.42939i) q^{31} +(-16.4421 + 27.4528i) 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} +(26.5618 + 19.4287i) q^{38} +(8.84646 + 15.3225i) q^{39} +(33.6009 + 38.0470i) q^{40} -6.49499i q^{41} +(-10.6470 - 7.01837i) q^{42} -33.2928i q^{43} +(50.3752 - 16.0116i) q^{44} +(25.9205 + 44.8956i) q^{45} +(-38.6154 - 28.2453i) 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} +(-75.8944 - 16.6411i) q^{52} +(32.2028 - 18.5923i) q^{53} +(-3.36930 + 31.0976i) q^{54} -83.8473i q^{55} +(54.2793 - 13.7754i) q^{56} +14.9878 q^{57} +(33.1296 + 3.58946i) q^{58} +(27.3428 + 47.3591i) q^{59} +(22.5813 + 4.95132i) 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} +(14.2124 - 19.4304i) q^{66} +(14.8386 - 8.56706i) q^{67} +(-60.7140 + 19.2978i) q^{68} -21.7892 q^{69} +(5.25648 - 88.6747i) q^{70} +32.0568 q^{71} +(-43.2670 - 48.9922i) q^{72} +(92.8082 - 53.5828i) q^{73} +(56.1514 - 76.7671i) 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} +(-82.8900 + 58.6143i) q^{80} +(-29.6436 - 51.3443i) q^{81} +(12.9144 + 1.39922i) q^{82} +36.3441 q^{83} +(16.2488 - 19.6581i) q^{84} +101.056i q^{85} +(66.1983 + 7.17232i) q^{86} +(13.1433 - 7.58829i) q^{87} +(20.9845 + 103.614i) 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} +(25.8657 - 35.3622i) q^{94} +(52.2021 + 90.4167i) q^{95} +(-29.1439 - 0.467106i) q^{96} +169.517i q^{97} +(-84.3517 - 49.8878i) 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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