LMFDB - Embedded newform 56.3.j.a.45.6

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			45.6
Character	$\chi$	$=$	56.45
Dual form			56.3.j.a.5.6

$q$-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 $\left(\mathbb{Z}/56\mathbb{Z}\right)^\times$.

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

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	−0.780083	−	0.625677i	$-0.784823\pi$
$3$	0.455431	−	0.788830i	0.151810	−	0.262943i	0.931893	+	0.362733i	$0.118156\pi$
$4$	−3.90718	+	0.856711i	−0.976795	+	0.214178i
$5$	−3.17251	−	5.49495i	−0.634503	−	1.09899i	−0.986620	−	0.163035i	$-0.947872\pi$
$5$	−3.17251	−	5.49495i	−0.634503	−	1.09899i	0.352118	−	0.935956i	$-0.385462\pi$
$6$	−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	−0.120442	−	0.992720i	$-0.538431\pi$
$11$	−11.4442	−	6.60732i	−1.04038	−	0.600666i	−0.919942	+	0.392054i	$0.871764\pi$
$12$	−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	0.847425	−	0.530915i	$-0.178152\pi$
$17$	13.7930	+	7.96338i	0.811352	+	0.468434i	−0.0360732	+	0.999349i	$0.511485\pi$
$18$	13.1890	−	9.64712i	0.732723	−	0.535951i
$19$	8.22725	+	14.2500i	0.433013	+	0.750001i	0.997131	−	0.0756934i	$-0.0241170\pi$
$19$	8.22725	+	14.2500i	0.433013	+	0.750001i	−0.564118	+	0.825694i	$0.690784\pi$
$20$	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	−0.999729	−	0.0232870i	$-0.992587\pi$
$23$	−11.9607	−	20.7166i	−0.520032	−	0.900721i	0.479697	−	0.877434i	$-0.340746\pi$
$24$	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	$0.0927483\pi$
$29$			16.6618i			0.574544i	−0.957849	+	0.287272i	$0.907252\pi$
$30$	1.24507	+	11.4916i	0.0415024	+	0.383055i
$31$	−11.1360	−	6.42939i	−0.359227	−	0.207400i	0.309515	−	0.950895i	$-0.399833\pi$
$31$	−11.1360	−	6.42939i	−0.359227	−	0.207400i	−0.668741	+	0.743495i	$0.733167\pi$
$32$	−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	−0.939628	−	0.342196i	$-0.888829\pi$
$37$	−41.1844	+	23.7778i	−1.11309	+	0.642644i	−0.173463	+	0.984840i	$0.555496\pi$
$38$	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	$0.0252389\pi$
$41$			6.49499i			0.158415i	−0.996858	+	0.0792073i	$0.974761\pi$
$42$	−10.6470	+	7.01837i	−0.253499	+	0.167104i
$43$			33.2928i			0.774252i	0.922027	+	0.387126i	$0.126532\pi$
$43$			33.2928i			0.774252i	−0.922027	+	0.387126i	$0.873468\pi$
$44$	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	−0.688056	−	0.725658i	$-0.741535\pi$
$47$	−18.9713	+	10.9531i	−0.403645	+	0.233045i	0.284411	+	0.958703i	$0.408202\pi$
$48$	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	0.772026	−	0.635591i	$-0.219244\pi$
$53$	32.2028	+	18.5923i	0.607601	+	0.350798i	−0.164425	+	0.986390i	$0.552577\pi$
$54$	−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	−0.535693	−	0.844413i	$-0.679949\pi$
$59$	27.3428	−	47.3591i	0.463437	−	0.802696i	0.999129	+	0.0417169i	$0.0132827\pi$
$60$	22.5813	−	4.95132i	0.376356	−	0.0825219i
$61$	5.12340	+	8.87399i	0.0839902	+	0.145475i	0.904960	−	0.425496i	$-0.139900\pi$
$61$	5.12340	+	8.87399i	0.0839902	+	0.145475i	−0.820970	+	0.570971i	$0.806567\pi$
$62$	−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	0.606631	−	0.794983i	$-0.292520\pi$
$67$	14.8386	+	8.56706i	0.221471	+	0.127867i	−0.385160	+	0.922850i	$0.625854\pi$
$68$	−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	0.975241	−	0.221144i	$-0.0709792\pi$
$73$	92.8082	+	53.5828i	1.27135	+	0.734011i	0.296104	+	0.955156i	$0.404313\pi$
$74$	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	0.989416	−	0.145109i	$-0.0463532\pi$
$79$	29.1542	+	50.4965i	0.369040	+	0.639196i	−0.620376	+	0.784305i	$0.713020\pi$
$80$	−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	−0.494767	−	0.869026i	$-0.664747\pi$
$89$	0.929882	−	0.536867i	0.0104481	−	0.00603222i	0.505215	+	0.862994i	$0.331413\pi$
$90$	−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	$-0.661649\pi$
$97$		−	169.517i		−	1.74760i	0.486286	−	0.873799i	$-0.338351\pi$
$98$	−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	−0.787971	−	0.615713i	$-0.788868\pi$
$101$	14.0630	−	24.3579i	0.139238	−	0.241167i	0.927208	+	0.374546i	$0.122201\pi$
$102$	−17.1293	−	23.4182i	−0.167934	−	0.229590i
$103$	−144.029	+	83.1551i	−1.39834	+	0.807331i	−0.994219	−	0.107374i	$-0.965756\pi$
$103$	−144.029	+	83.1551i	−1.39834	+	0.807331i	−0.404120	+	0.914706i	$0.632422\pi$
$104$	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	−0.607536	+	0.794292i	$0.707842\pi$
$107$	−171.112	+	98.7918i	−1.59918	+	0.923288i	−0.991645	+	0.128996i	$0.958825\pi$
$108$	−61.1075	+	13.3988i	−0.565811	+	0.124063i
$109$	−9.97643	−	5.75990i	−0.0915269	−	0.0528431i	0.453538	−	0.891237i	$-0.350162\pi$
$109$	−9.97643	−	5.75990i	−0.0915269	−	0.0528431i	−0.545065	+	0.838394i	$0.683495\pi$
$110$	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	0.998761	+	0.0497649i	$0.0158472\pi$
$131$	71.0646	+	123.088i	0.542478	+	0.939600i	−0.456283	+	0.889835i	$0.650819\pi$
$132$	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	−0.129870	+	0.991531i	$0.541456\pi$
$137$	−126.537	+	219.168i	−0.923626	+	1.59977i	−0.793756	+	0.608236i	$0.791877\pi$
$138$	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	−0.373915	−	0.927463i	$-0.621985\pi$
$149$	36.1077	−	20.8468i	0.242334	−	0.139911i	0.616249	+	0.787551i	$0.288652\pi$
$150$	22.4368	−	16.4115i	0.149579	−	0.109410i
$151$	48.8145	−	84.5492i	0.323275	−	0.559928i	−0.657887	−	0.753117i	$-0.728550\pi$
$151$	48.8145	−	84.5492i	0.323275	−	0.559928i	0.981162	+	0.193188i	$0.0618829\pi$
$152$	−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	−0.817685	−	0.575666i	$-0.804743\pi$
$157$	14.0827	−	24.3919i	0.0896986	−	0.155363i	0.907384	+	0.420303i	$0.138076\pi$
$158$	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	0.309743	−	0.950820i	$-0.399757\pi$
$163$	209.952	−	121.216i	1.28805	−	0.743655i	0.978306	+	0.207165i	$0.0664237\pi$
$164$	−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	$-0.942399\pi$
$167$		−	60.1108i		−	0.359945i	0.983672	−	0.179972i	$-0.0576008\pi$
$168$	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	0.591275	−	0.806470i	$-0.298625\pi$
$173$	−69.6820	−	120.693i	−0.402786	−	0.697646i	−0.994061	+	0.108824i	$0.965292\pi$
$174$	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	−0.415891	−	0.909415i	$-0.636530\pi$
$179$	−252.643	−	145.863i	−1.41141	−	0.814879i	−0.995522	+	0.0945354i	$0.969863\pi$
$180$	−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	0.985147	−	0.171715i	$-0.0549307\pi$
$191$	65.6781	+	113.758i	0.343864	+	0.595590i	−0.641283	+	0.767305i	$0.721597\pi$
$192$	7.20727	+	57.8480i	0.0375379	+	0.301292i
$193$	40.7196	−	70.5284i	0.210982	−	0.365432i	−0.741040	−	0.671461i	$-0.765667\pi$
$193$	40.7196	−	70.5284i	0.210982	−	0.365432i	0.952022	+	0.306029i	$0.0990004\pi$
$194$	−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	$0.00169294\pi$
$197$			2.09549i			0.0106370i	−0.999986	+	0.00531851i	$0.998307\pi$
$198$	−214.680	+	23.2597i	−1.08424	+	0.117473i
$199$	−109.937	−	63.4721i	−0.552447	−	0.318955i	0.197662	−	0.980270i	$-0.436665\pi$
$199$	−109.937	−	63.4721i	−0.552447	−	0.318955i	−0.750108	+	0.661315i	$0.769999\pi$
$200$	−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	$-0.994593\pi$
$211$		−	7.16822i		−	0.0339726i	0.999856	−	0.0169863i	$-0.00540717\pi$
$212$	−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	$0.215789\pi$
$223$			279.720i			1.25435i	−0.778878	+	0.627175i	$0.784211\pi$
$224$	−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	−0.306198	−	0.951968i	$-0.599057\pi$
$227$	152.392	−	263.950i	0.671330	−	1.16278i	0.977527	−	0.210809i	$-0.0676098\pi$
$228$	−58.5600	+	12.8402i	−0.256842	+	0.0563167i
$229$	−207.344	−	359.130i	−0.905433	−	1.56826i	−0.820335	−	0.571883i	$-0.806213\pi$
$229$	−207.344	−	359.130i	−0.905433	−	1.56826i	−0.0850971	−	0.996373i	$-0.527120\pi$
$230$	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	0.986932	−	0.161136i	$-0.0515159\pi$
$233$	82.4628	+	142.830i	0.353918	+	0.613004i	−0.633014	+	0.774140i	$0.718183\pi$
$234$	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	−0.285975	−	0.958237i	$-0.592317\pi$
$241$	−303.376	−	175.154i	−1.25882	−	0.726780i	−0.972845	+	0.231457i	$0.925651\pi$
$242$	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	−0.347899	−	0.937532i	$-0.613105\pi$
$257$	74.5499	−	43.0414i	0.290077	−	0.167476i	0.637977	+	0.770056i	$0.279772\pi$
$258$	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	0.384891	+	0.922962i	$0.374239\pi$
$263$	−159.605	+	276.444i	−0.606863	+	1.05112i	−0.991754	+	0.128156i	$0.959094\pi$
$264$	−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	−0.914479	−	0.404632i	$-0.867399\pi$
$269$	−28.7340	+	49.7687i	−0.106818	+	0.185014i	0.807662	+	0.589646i	$0.200733\pi$
$270$	−160.191	+	117.172i	−0.593300	+	0.433970i
$271$	26.7398	−	15.4382i	0.0986709	−	0.0569677i	−0.449853	−	0.893103i	$-0.648523\pi$
$271$	26.7398	−	15.4382i	0.0986709	−	0.0569677i	0.548523	+	0.836135i	$0.315190\pi$
$272$	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	−0.173834	−	0.984775i	$-0.555616\pi$
$277$	−308.465	−	178.092i	−1.11359	−	0.642933i	−0.939757	+	0.341842i	$0.888949\pi$
$278$	−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	0.222282	+	0.974982i	$0.428649\pi$
$283$	−207.501	+	359.402i	−0.733219	+	1.26997i	−0.955501	+	0.294989i	$0.904684\pi$
$284$	−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	0.983195	−	0.182561i	$-0.0584387\pi$
$311$	409.490	+	236.419i	1.31669	+	0.760191i	0.333495	+	0.942752i	$0.391772\pi$
$312$	138.727	+	28.0959i	0.444637	+	0.0900508i
$313$	200.063	−	115.506i	0.639179	−	0.369030i	−0.145119	−	0.989414i	$-0.546357\pi$
$313$	200.063	−	115.506i	0.639179	−	0.369030i	0.784298	+	0.620384i	$0.213023\pi$
$314$	−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	$-0.551014\pi$
$317$	195.132	−	112.659i	0.615557	−	0.355392i	0.775137	+	0.631793i	$0.217681\pi$
$318$	−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	−0.526834	−	0.849968i	$-0.676621\pi$
$331$	−17.9257	+	10.3494i	−0.0541561	+	0.0312671i	0.472677	+	0.881236i	$0.343288\pi$
$332$	−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	0.934898	−	0.354916i	$-0.115491\pi$
$347$	379.958	+	219.369i	1.09498	+	0.632188i	0.160083	+	0.987104i	$0.448824\pi$
$348$	−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	0.803482	−	0.595329i	$-0.202978\pi$
$353$	243.447	+	140.554i	0.689653	+	0.398171i	−0.113829	+	0.993500i	$0.536312\pi$
$354$	−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	0.621598	−	0.783336i	$-0.286484\pi$
$359$	−131.965	−	228.570i	−0.367590	−	0.636685i	−0.989188	+	0.146652i	$0.953150\pi$
$360$	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	0.305926	−	0.952055i	$-0.401034\pi$
$367$	−134.181	−	77.4694i	−0.365615	−	0.211088i	−0.671541	+	0.740967i	$0.734367\pi$
$368$	−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	0.368579	−	0.929597i	$-0.379845\pi$
$373$	506.505	−	292.431i	1.35792	−	0.783997i	0.989344	+	0.145600i	$0.0465112\pi$
$374$	−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	$0.0540853\pi$
$379$			128.176i			0.338195i	−0.985599	+	0.169098i	$0.945915\pi$
$380$	−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	−0.755194	−	0.655502i	$-0.772457\pi$
$383$	−216.437	+	124.960i	−0.565110	+	0.326266i	0.190084	+	0.981768i	$0.439124\pi$
$384$	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	0.721175	−	0.692753i	$-0.243602\pi$
$389$	187.428	+	108.212i	0.481821	+	0.278179i	−0.239354	+	0.970932i	$0.576936\pi$
$390$	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	0.849714	+	0.527244i	$0.176774\pi$
$397$	349.941	+	606.116i	0.881463	+	1.52674i	0.0317493	+	0.999496i	$0.489892\pi$
$398$	−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	0.956518	−	0.291674i	$-0.0942123\pi$
$401$	90.4903	+	156.734i	0.225662	+	0.390858i	−0.730856	+	0.682532i	$0.760879\pi$
$402$	−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	0.0694104	−	0.997588i	$-0.477888\pi$
$409$	−310.767	−	179.421i	−0.759821	−	0.438683i	−0.829232	+	0.558905i	$0.811222\pi$
$410$	−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	$-0.956404\pi$
$421$		−	114.961i		−	0.273068i	0.990635	−	0.136534i	$-0.0435962\pi$
$422$	−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	−0.987843	−	0.155453i	$-0.950316\pi$
$431$	−154.856	+	268.219i	−0.359295	+	0.622317i	0.628548	+	0.777771i	$0.283649\pi$
$432$	227.279	−	104.703i	0.526109	−	0.242368i
$433$			595.775i			1.37592i	0.725747	+	0.687962i	$0.241494\pi$
$433$			595.775i			1.37592i	−0.725747	+	0.687962i	$0.758506\pi$
$434$	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	0.598789	−	0.800907i	$-0.295649\pi$
$439$	698.796	−	403.450i	1.59179	−	0.919020i	0.993000	−	0.118113i	$-0.0376846\pi$
$440$	−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	$-0.834083\pi$
$443$	−385.214	+	222.403i	−0.869557	+	0.502039i	−0.00235617	+	0.999997i	$0.500750\pi$
$444$	−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	0.570403	−	0.821365i	$-0.306787\pi$
$457$	−194.738	−	337.296i	−0.426122	−	0.738065i	−0.996524	+	0.0833004i	$0.973454\pi$
$458$	−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	0.999322	−	0.0368236i	$-0.0117240\pi$
$467$	218.449	+	378.365i	0.467771	+	0.810203i	−0.531551	+	0.847026i	$0.678391\pi$
$468$	−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	0.904354	−	0.426783i	$-0.140353\pi$
$479$	472.737	+	272.935i	0.986925	+	0.569802i	0.0825716	+	0.996585i	$0.473687\pi$
$480$	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	0.313606	+	0.949553i	$0.398463\pi$
$487$	−324.115	+	561.384i	−0.665534	+	1.15274i	−0.979140	+	0.203185i	$0.934871\pi$
$488$	−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	$-0.732214\pi$
$491$		−	732.074i		−	1.49098i	0.666514	−	0.745492i	$-0.267786\pi$
$492$	−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	−0.522994	−	0.852337i	$-0.675185\pi$
$499$	−23.1264	+	13.3520i	−0.0463454	+	0.0267575i	0.476648	+	0.879094i	$0.341852\pi$
$500$	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	$-0.790068\pi$
$503$		−	616.414i		−	1.22548i	0.790286	−	0.612738i	$-0.209932\pi$
$504$	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	0.923833	−	0.382796i	$-0.125039\pi$
$509$	66.3763	+	114.967i	0.130405	+	0.225869i	−0.793428	+	0.608665i	$0.791705\pi$
$510$	−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	−0.181403	−	0.983409i	$-0.558064\pi$
$521$	−585.480	−	338.027i	−1.12376	−	0.648804i	−0.942359	+	0.334605i	$0.891397\pi$
$522$	160.738	+	219.752i	0.307927	+	0.420981i
$523$	186.224	+	322.550i	0.356069	+	0.616730i	0.987300	−	0.158865i	$-0.0507833\pi$
$523$	186.224	+	322.550i	0.356069	+	0.616730i	−0.631231	+	0.775595i	$0.717450\pi$
$524$	−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	−0.443198	−	0.896424i	$-0.646156\pi$
$541$	60.3373	−	34.8357i	0.111529	−	0.0643914i	0.554727	+	0.832032i	$0.312823\pi$
$542$	−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	$-0.859788\pi$
$547$		−	466.463i		−	0.852765i	0.904543	−	0.426383i	$-0.140212\pi$
$548$	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	0.602866	−	0.797842i	$-0.294025\pi$
$557$	118.835	+	68.6094i	0.213348	+	0.123177i	−0.389518	+	0.921019i	$0.627358\pi$
$558$	−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	−0.781100	−	0.624406i	$-0.785341\pi$
$563$	84.5632	−	146.468i	0.150201	−	0.260156i	0.931301	+	0.364250i	$0.118675\pi$
$564$	−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	−0.981995	−	0.188908i	$-0.939505\pi$
$569$	−372.466	−	645.129i	−0.654597	−	1.13379i	0.327398	−	0.944887i	$-0.393828\pi$
$570$	−153.513	+	112.287i	−0.269320	+	0.196995i
$571$	−767.828	−	443.306i	−1.34471	−	0.776367i	−0.357213	−	0.934023i	$-0.616273\pi$
$571$	−767.828	−	443.306i	−1.34471	−	0.776367i	−0.987494	+	0.157655i	$0.949606\pi$
$572$	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	0.308906	−	0.951093i	$-0.400037\pi$
$577$	−207.900	−	120.031i	−0.360311	−	0.208026i	−0.669217	+	0.743067i	$0.733370\pi$
$578$	−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	0.145547	−	0.989351i	$-0.453506\pi$
$593$	637.548	−	368.089i	1.07512	−	0.620723i	0.929577	+	0.368629i	$0.120173\pi$
$594$	−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	−0.152386	+	0.988321i	$0.548696\pi$
$599$	−558.330	+	967.057i	−0.932104	+	1.61445i	−0.779718	+	0.626131i	$0.784638\pi$
$600$	−73.6049	+	83.3444i	−0.122675	+	0.138907i
$601$		−	183.100i		−	0.304659i	−0.988330	−	0.152329i	$-0.951323\pi$
$601$		−	183.100i		−	0.304659i	0.988330	−	0.152329i	$-0.0486774\pi$
$602$	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	−0.138989	−	0.990294i	$-0.544385\pi$
$607$	394.026	−	227.491i	0.649136	−	0.374779i	0.788125	+	0.615515i	$0.211052\pi$
$608$	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	0.297898	−	0.954598i	$-0.403714\pi$
$613$	−232.853	−	134.438i	−0.379859	−	0.219312i	−0.677757	+	0.735286i	$0.737048\pi$
$614$	−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	−0.115301	−	0.993331i	$-0.536783\pi$
$619$	496.809	−	860.498i	0.802599	−	1.39014i	0.917900	−	0.396812i	$-0.129884\pi$
$620$	−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	−0.868164	−	0.496277i	$-0.834700\pi$
$641$	−2.75221	+	4.76696i	−0.00429361	+	0.00743676i	0.863871	+	0.503714i	$0.168033\pi$
$642$	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	0.773409	−	0.633907i	$-0.218550\pi$
$647$	395.404	+	228.287i	0.611134	+	0.352839i	−0.162275	+	0.986746i	$0.551883\pi$
$648$	−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	−0.481154	−	0.876636i	$-0.659782\pi$
$653$	24.4603	−	14.1222i	0.0374584	−	0.0216266i	0.518612	+	0.855010i	$0.326449\pi$
$654$	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	$0.0319785\pi$
$659$			132.188i			0.200589i	−0.994958	+	0.100295i	$0.968021\pi$
$660$	−291.141	−	92.5382i	−0.441122	−	0.140209i
$661$	−346.924	+	600.889i	−0.524847	+	0.909061i	0.474735	+	0.880129i	$0.342544\pi$
$661$	−346.924	+	600.889i	−0.524847	+	0.909061i	−0.999581	+	0.0289321i	$0.990789\pi$
$662$	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	0.952152	−	0.305626i	$-0.0988657\pi$
$677$	143.115	+	247.883i	0.211396	+	0.366149i	−0.740756	+	0.671775i	$0.765532\pi$
$678$	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	0.188443	−	0.982084i	$-0.439656\pi$
$683$	−387.838	−	223.918i	−0.567844	−	0.327845i	−0.756288	+	0.654239i	$0.772989\pi$
$684$	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	−0.953130	−	0.302561i	$-0.902158\pi$
$691$	−510.366	−	883.980i	−0.738591	−	1.27928i	0.214539	−	0.976715i	$-0.431175\pi$
$692$	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	$0.384696\pi$
$701$			1311.02i			1.87021i	−0.354369	+	0.935106i	$0.615304\pi$
$702$	−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	−0.134410	−	0.990926i	$-0.542914\pi$
$709$	465.495	−	268.754i	0.656552	−	0.379061i	0.790962	+	0.611865i	$0.209581\pi$
$710$	−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	−0.653371	−	0.757037i	$-0.726646\pi$
$719$	−233.275	+	134.681i	−0.324443	+	0.187318i	0.328928	+	0.944355i	$0.393313\pi$
$720$	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	$-0.897463\pi$
$727$		−	460.316i		−	0.633172i	0.948564	−	0.316586i	$-0.102537\pi$
$728$	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	0.887872	−	0.460091i	$-0.152183\pi$
$733$	33.3410	+	57.7484i	0.0454857	+	0.0787836i	−0.842386	+	0.538874i	$0.818850\pi$
$734$	−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	0.934748	−	0.355311i	$-0.115625\pi$
$739$	808.772	+	466.944i	1.09441	+	0.631860i	0.159665	+	0.987171i	$0.448958\pi$
$740$	−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	0.916677	−	0.399629i	$-0.130861\pi$
$751$	84.2993	+	146.011i	0.112249	+	0.194422i	−0.804427	+	0.594051i	$0.797528\pi$
$752$	−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	$-0.955874\pi$
$757$		−	209.207i		−	0.276364i	0.990407	−	0.138182i	$-0.0441259\pi$
$758$	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	−0.150996	−	0.988534i	$-0.548248\pi$
$761$	479.127	−	276.624i	0.629602	−	0.363501i	0.780598	+	0.625033i	$0.214915\pi$
$762$	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	$0.0455892\pi$
$769$			219.524i			0.285467i	−0.989761	+	0.142734i	$0.954411\pi$
$770$	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	−0.565754	−	0.824574i	$-0.691415\pi$
$773$	333.337	−	577.357i	0.431225	−	0.746904i	0.996979	+	0.0776701i	$0.0247481\pi$
$774$	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	0.410536	+	0.911844i	$0.365341\pi$
$787$	−459.932	+	796.626i	−0.584412	+	1.01223i	−0.994948	+	0.100387i	$0.967992\pi$
$788$	−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	0.269049	+	0.963126i	$0.413291\pi$
$809$	−565.950	+	980.254i	−0.699567	+	1.21169i	−0.968617	+	0.248560i	$0.920043\pi$
$810$	−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	−0.0644292	−	0.997922i	$-0.520523\pi$
$821$	630.185	−	363.838i	0.767582	−	0.443164i	0.832011	+	0.554758i	$0.187189\pi$
$822$	372.111	−	272.181i	0.452690	−	0.331120i
$823$	313.323	−	542.692i	0.380709	−	0.659407i	−0.610455	−	0.792051i	$-0.709013\pi$
$823$	313.323	−	542.692i	0.380709	−	0.659407i	0.991164	+	0.132644i	$0.0423468\pi$
$824$	−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	$-0.652192\pi$
$827$		−	1468.52i		−	1.77572i	0.460116	−	0.887859i	$-0.347808\pi$
$828$	−236.813	+	745.055i	−0.286007	+	0.899824i
$829$	409.352	−	709.019i	0.493790	−	0.855270i	−0.506184	−	0.862425i	$-0.668944\pi$
$829$	409.352	−	709.019i	0.493790	−	0.855270i	0.999974	+	0.00715566i	$0.00227774\pi$
$830$	−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	$-0.770214\pi$
$839$		−	1108.84i		−	1.32162i	0.750555	−	0.660808i	$-0.229786\pi$
$840$	−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	0.707319	−	0.706894i	$-0.249904\pi$
$857$	384.614	+	222.057i	0.448791	+	0.259110i	−0.258529	+	0.966004i	$0.583238\pi$
$858$	276.066	+	377.423i	0.321755	+	0.439886i
$859$	−40.7547	−	70.5892i	−0.0474443	−	0.0821760i	0.841328	−	0.540525i	$-0.181774\pi$
$859$	−40.7547	−	70.5892i	−0.0474443	−	0.0821760i	−0.888772	+	0.458349i	$0.848441\pi$
$860$	−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	0.991374	+	0.131061i	$0.0418384\pi$
$863$	525.730	+	910.592i	0.609189	+	1.05515i	−0.382185	+	0.924086i	$0.624828\pi$
$864$	−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	−0.541280	+	0.840842i	$0.682060\pi$
$877$	−1350.68	+	779.814i	−1.54011	+	0.889183i	−0.998831	+	0.0483410i	$0.984607\pi$
$878$	−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	$-0.670499\pi$
$881$		−	1515.22i		−	1.71989i	0.510389	−	0.859944i	$-0.329501\pi$
$882$	−697.582	−	393.048i	−0.790910	−	0.445633i
$883$			763.828i			0.865037i	0.901625	+	0.432519i	$0.142375\pi$
$883$			763.828i			0.865037i	−0.901625	+	0.432519i	$0.857625\pi$
$884$	−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	−0.193258	−	0.981148i	$-0.561905\pi$
$887$	496.554	−	286.686i	0.559813	−	0.323208i	0.753070	+	0.657940i	$0.228572\pi$
$888$	−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	−0.0747894	−	0.997199i	$-0.523828\pi$
$907$	−885.036	−	510.976i	−0.975784	−	0.563369i	−0.900995	+	0.433830i	$0.857162\pi$
$908$	−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	0.998889	−	0.0471182i	$-0.0150038\pi$
$919$	421.489	+	730.041i	0.458639	+	0.794386i	−0.540250	+	0.841504i	$0.681670\pi$
$920$	−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	−0.0934003	−	0.995629i	$-0.529774\pi$
$929$	670.867	−	387.325i	0.722139	−	0.416927i	0.815540	+	0.578701i	$0.196440\pi$
$930$	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	$-0.678727\pi$
$937$		−	1586.27i		−	1.69293i	0.532447	−	0.846463i	$-0.321273\pi$
$938$	−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	−0.997355	−	0.0726842i	$-0.976843\pi$
$941$	−410.023	+	710.181i	−0.435731	+	0.754708i	0.561624	+	0.827393i	$0.310177\pi$
$942$	−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	−0.179422	−	0.983772i	$-0.557423\pi$
$947$	551.949	−	318.668i	0.582839	−	0.336502i	0.762261	+	0.647270i	$0.224089\pi$
$948$	−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	1.00000		0.000232071i	$-7.38706e-5\pi$
$971$	485.305	+	840.573i	0.499799	+	0.865677i	−0.500201	+	0.865909i	$0.666741\pi$
$972$	−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	−0.670307	−	0.742084i	$-0.733838\pi$
$977$	300.437	−	520.373i	0.307510	−	0.532623i	0.977817	+	0.209461i	$0.0671709\pi$
$978$	−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	0.940802	−	0.338955i	$-0.110074\pi$
$983$	1098.66	+	634.311i	1.11766	+	0.645281i	0.176857	+	0.984236i	$0.443407\pi$
$984$	−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	−0.149426	−	0.988773i	$-0.547742\pi$
$991$	774.555	−	1341.57i	0.781590	−	1.35375i	0.931015	−	0.364980i	$-0.118924\pi$
$992$	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	−0.999483	−	0.0321661i	$-0.989759\pi$
$997$	−470.469	+	814.876i	−0.471885	+	0.817328i	0.527598	+	0.849494i	$0.323093\pi$
$998$	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.45.6	yes	28
4.3	odd	2		224.3.n.a.17.6		28
7.2	even	3		392.3.j.e.117.4		28
7.3	odd	6		392.3.h.a.293.28		28
7.4	even	3		392.3.h.a.293.27		28
7.5	odd	6	inner	56.3.j.a.5.4	✓	28
7.6	odd	2		392.3.j.e.325.6		28
8.3	odd	2		224.3.n.a.17.9		28
8.5	even	2	inner	56.3.j.a.45.4	yes	28
28.3	even	6		1568.3.h.a.881.12		28
28.11	odd	6		1568.3.h.a.881.18		28
28.19	even	6		224.3.n.a.145.9		28
56.3	even	6		1568.3.h.a.881.17		28
56.5	odd	6	inner	56.3.j.a.5.6	yes	28
56.11	odd	6		1568.3.h.a.881.11		28
56.13	odd	2		392.3.j.e.325.4		28
56.19	even	6		224.3.n.a.145.6		28
56.37	even	6		392.3.j.e.117.6		28
56.45	odd	6		392.3.h.a.293.25		28
56.53	even	6		392.3.h.a.293.26		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.3.j.a.5.4	✓	28	7.5	odd	6	inner
56.3.j.a.5.6	yes	28	56.5	odd	6	inner
56.3.j.a.45.4	yes	28	8.5	even	2	inner
56.3.j.a.45.6	yes	28	1.1	even	1	trivial
224.3.n.a.17.6		28	4.3	odd	2
224.3.n.a.17.9		28	8.3	odd	2
224.3.n.a.145.6		28	56.19	even	6
224.3.n.a.145.9		28	28.19	even	6
392.3.h.a.293.25		28	56.45	odd	6
392.3.h.a.293.26		28	56.53	even	6
392.3.h.a.293.27		28	7.4	even	3
392.3.h.a.293.28		28	7.3	odd	6
392.3.j.e.117.4		28	7.2	even	3
392.3.j.e.117.6		28	56.37	even	6
392.3.j.e.325.4		28	56.13	odd	2
392.3.j.e.325.6		28	7.6	odd	2
1568.3.h.a.881.11		28	56.11	odd	6
1568.3.h.a.881.12		28	28.3	even	6
1568.3.h.a.881.17		28	56.3	even	6
1568.3.h.a.881.18		28	28.11	odd	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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