LMFDB - Embedded newform 42.3.h.b.11.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [42,3,Mod(11,42)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(42, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

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

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

chi := DirichletCharacter("42.11");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 42 = 2 \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	42.h (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:	$1.14441711031$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.4857532416.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 7x^{6} - 2x^{5} + 98x^{4} - 98x^{3} + 67x^{2} - 30x + 9 $ x^8 - 2x^7 - 7x^6 - 2x^5 + 98x^4 - 98x^3 + 67x^2 - 30*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.4
Root			$2.91089 - 1.10325i$ of defining polynomial
Character	$\chi$	$=$	42.11
Dual form			42.3.h.b.23.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22474 - 0.707107i) q^{2} +(-0.598836 + 2.93963i) q^{3} +(1.00000 - 1.73205i) q^{4} +(5.32177 - 3.07253i) q^{5} +(1.34521 + 4.02373i) q^{6} +(-4.69042 + 5.19615i) q^{7} -2.82843i q^{8} +(-8.28279 - 3.52071i) q^{9} +O(q^{10})$	\(q+(1.22474 - 0.707107i) q^{2} +(-0.598836 + 2.93963i) q^{3} +(1.00000 - 1.73205i) q^{4} +(5.32177 - 3.07253i) q^{5} +(1.34521 + 4.02373i) q^{6} +(-4.69042 + 5.19615i) q^{7} -2.82843i q^{8} +(-8.28279 - 3.52071i) q^{9} +(4.34521 - 7.52612i) q^{10} +(-15.5862 - 8.99867i) q^{11} +(4.49274 + 3.97684i) q^{12} +1.38083 q^{13} +(-2.07033 + 9.68059i) q^{14} +(5.84521 + 17.4840i) q^{15} +(-2.00000 - 3.46410i) q^{16} +(5.32177 + 3.07253i) q^{17} +(-12.6338 + 1.54485i) q^{18} +(7.53562 + 13.0521i) q^{19} -12.2901i q^{20} +(-12.4660 - 16.8997i) q^{21} -25.4521 q^{22} +(22.9346 - 13.2413i) q^{23} +(8.31452 + 1.69376i) q^{24} +(6.38083 - 11.0519i) q^{25} +(1.69117 - 0.976395i) q^{26} +(15.3096 - 22.2400i) q^{27} +(4.30958 + 13.3202i) q^{28} +19.0241i q^{29} +(19.5219 + 17.2802i) q^{30} +(-9.22604 + 15.9800i) q^{31} +(-4.89898 - 2.82843i) q^{32} +(35.7863 - 40.4287i) q^{33} +8.69042 q^{34} +(-8.99601 + 42.0642i) q^{35} +(-14.3808 + 10.8255i) q^{36} +(0.500000 + 0.866025i) q^{37} +(18.4584 + 10.6570i) q^{38} +(-0.826891 + 4.05913i) q^{39} +(-8.69042 - 15.0522i) q^{40} -11.4145i q^{41} +(-27.2175 - 11.8831i) q^{42} +54.1425 q^{43} +(-31.1723 + 17.9973i) q^{44} +(-54.8966 + 6.71271i) q^{45} +(18.7260 - 32.4345i) q^{46} +(-46.4967 + 26.8449i) q^{47} +(11.3808 - 3.80482i) q^{48} +(-5.00000 - 48.7442i) q^{49} -18.0477i q^{50} +(-12.2189 + 13.8041i) q^{51} +(1.38083 - 2.39167i) q^{52} +(-35.4740 - 20.4809i) q^{53} +(3.02430 - 38.0638i) q^{54} -110.595 q^{55} +(14.6969 + 13.2665i) q^{56} +(-42.8808 + 14.3359i) q^{57} +(13.4521 + 23.2997i) q^{58} +(47.2550 + 27.2827i) q^{59} +(36.1283 + 7.35975i) q^{60} +(35.8808 + 62.1474i) q^{61} +26.0952i q^{62} +(57.1439 - 26.5251i) q^{63} -8.00000 q^{64} +(7.34847 - 4.24264i) q^{65} +(15.2416 - 74.8196i) q^{66} +(-10.9877 + 19.0313i) q^{67} +(10.6435 - 6.14505i) q^{68} +(25.1904 + 75.3486i) q^{69} +(18.7260 + 57.8790i) q^{70} -109.433i q^{71} +(-9.95806 + 23.4273i) q^{72} +(7.11917 - 12.3308i) q^{73} +(1.22474 + 0.707107i) q^{74} +(28.6674 + 25.3755i) q^{75} +30.1425 q^{76} +(119.864 - 38.7805i) q^{77} +(1.85751 + 5.55610i) q^{78} +(-46.3685 - 80.3127i) q^{79} +(-21.2871 - 12.2901i) q^{80} +(56.2093 + 58.3225i) q^{81} +(-8.07125 - 13.9798i) q^{82} -35.6924i q^{83} +(-41.7371 + 4.69196i) q^{84} +37.7617 q^{85} +(66.3107 - 38.2845i) q^{86} +(-55.9238 - 11.3923i) q^{87} +(-25.4521 + 44.0843i) q^{88} +(-138.876 + 80.1802i) q^{89} +(-62.4877 + 47.0391i) q^{90} +(-6.47667 + 7.17501i) q^{91} -52.9652i q^{92} +(-41.4502 - 36.6905i) q^{93} +(-37.9644 + 65.7562i) q^{94} +(80.2057 + 46.3068i) q^{95} +(11.2482 - 12.7074i) q^{96} +118.904 q^{97} +(-40.5911 - 56.1637i) q^{98} +(97.4152 + 129.408i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{3} + 8 q^{4} - 8 q^{6} - 10 q^{9}+O(q^{10}) $ 8 * q - 2 * q^3 + 8 * q^4 - 8 * q^6 - 10 * q^9	$ 8 q - 2 q^{3} + 8 q^{4} - 8 q^{6} - 10 q^{9} + 16 q^{10} + 4 q^{12} - 64 q^{13} + 28 q^{15} - 16 q^{16} - 40 q^{18} + 4 q^{19} + 26 q^{21} - 16 q^{22} - 8 q^{24} - 24 q^{25} + 160 q^{27} + 72 q^{28} + 52 q^{30} + 20 q^{31} - 106 q^{33} + 32 q^{34} - 40 q^{36} + 4 q^{37} - 72 q^{39} - 32 q^{40} - 88 q^{42} + 208 q^{43} - 58 q^{45} + 56 q^{46} + 16 q^{48} - 40 q^{49} + 14 q^{51} - 64 q^{52} - 32 q^{54} - 472 q^{55} - 268 q^{57} - 80 q^{58} + 28 q^{60} + 212 q^{61} + 178 q^{63} - 64 q^{64} + 224 q^{66} + 156 q^{67} + 164 q^{69} + 56 q^{70} + 80 q^{72} + 132 q^{73} + 164 q^{75} + 16 q^{76} + 240 q^{78} - 52 q^{79} + 98 q^{81} + 48 q^{82} - 124 q^{84} + 152 q^{85} - 260 q^{87} - 16 q^{88} - 256 q^{90} - 352 q^{91} - 210 q^{93} - 360 q^{94} + 16 q^{96} + 576 q^{97} - 140 q^{99}+O(q^{100}) $ 8 * q - 2 * q^3 + 8 * q^4 - 8 * q^6 - 10 * q^9 + 16 * q^10 + 4 * q^12 - 64 * q^13 + 28 * q^15 - 16 * q^16 - 40 * q^18 + 4 * q^19 + 26 * q^21 - 16 * q^22 - 8 * q^24 - 24 * q^25 + 160 * q^27 + 72 * q^28 + 52 * q^30 + 20 * q^31 - 106 * q^33 + 32 * q^34 - 40 * q^36 + 4 * q^37 - 72 * q^39 - 32 * q^40 - 88 * q^42 + 208 * q^43 - 58 * q^45 + 56 * q^46 + 16 * q^48 - 40 * q^49 + 14 * q^51 - 64 * q^52 - 32 * q^54 - 472 * q^55 - 268 * q^57 - 80 * q^58 + 28 * q^60 + 212 * q^61 + 178 * q^63 - 64 * q^64 + 224 * q^66 + 156 * q^67 + 164 * q^69 + 56 * q^70 + 80 * q^72 + 132 * q^73 + 164 * q^75 + 16 * q^76 + 240 * q^78 - 52 * q^79 + 98 * q^81 + 48 * q^82 - 124 * q^84 + 152 * q^85 - 260 * q^87 - 16 * q^88 - 256 * q^90 - 352 * q^91 - 210 * q^93 - 360 * q^94 + 16 * q^96 + 576 * q^97 - 140 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/42\mathbb{Z}\right)^\times$.

$n$	$29$	$31$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	1.22474	−	0.707107i	0.612372	−	0.353553i
$2$	1.22474	−	0.707107i	0.612372	−	0.353553i
$3$	−0.598836	+	2.93963i	−0.199612	+	0.979875i
$3$	−0.598836	+	2.93963i	−0.199612	+	0.979875i
$4$	1.00000	−	1.73205i	0.250000	−	0.433013i
$5$	5.32177	−	3.07253i	1.06435	−	0.614505i	0.137721	−	0.990471i	$-0.456022\pi$
$5$	5.32177	−	3.07253i	1.06435	−	0.614505i	0.926633	+	0.375966i	$0.122689\pi$
$6$	1.34521	+	4.02373i	0.224201	+	0.670622i
$7$	−4.69042	+	5.19615i	−0.670059	+	0.742307i
$7$	−4.69042	+	5.19615i	−0.670059	+	0.742307i
$8$		−	2.82843i		−	0.353553i
$9$	−8.28279	−	3.52071i	−0.920310	−	0.391189i
$10$	4.34521	−	7.52612i	0.434521	−	0.752612i
$11$	−15.5862	−	8.99867i	−1.41692	−	0.818061i	−0.420896	−	0.907109i	$-0.638284\pi$
$11$	−15.5862	−	8.99867i	−1.41692	−	0.818061i	−0.996027	+	0.0890483i	$0.971617\pi$
$12$	4.49274	+	3.97684i	0.374395	+	0.331403i
$13$	1.38083			0.106218			0.0531089	−	0.998589i	$-0.483087\pi$
$13$	1.38083			0.106218			0.0531089	+	0.998589i	$0.483087\pi$
$14$	−2.07033	+	9.68059i	−0.147881	+	0.691470i
$15$	5.84521	+	17.4840i	0.389681	+	1.16560i
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	5.32177	+	3.07253i	0.313045	+	0.180737i	0.648288	−	0.761395i	$-0.275485\pi$
$17$	5.32177	+	3.07253i	0.313045	+	0.180737i	−0.335243	+	0.942132i	$0.608818\pi$
$18$	−12.6338	+	1.54485i	−0.701879	+	0.0858251i
$19$	7.53562	+	13.0521i	0.396612	+	0.686952i	0.993305	−	0.115517i	$-0.0368526\pi$
$19$	7.53562	+	13.0521i	0.396612	+	0.686952i	−0.596694	+	0.802469i	$0.703519\pi$
$20$		−	12.2901i		−	0.614505i
$21$	−12.4660	−	16.8997i	−0.593617	−	0.804748i
$22$	−25.4521			−1.15691
$23$	22.9346	−	13.2413i	0.997157	−	0.575709i	0.0897514	−	0.995964i	$-0.471393\pi$
$23$	22.9346	−	13.2413i	0.997157	−	0.575709i	0.907406	+	0.420255i	$0.138059\pi$
$24$	8.31452	+	1.69376i	0.346438	+	0.0705735i
$25$	6.38083	−	11.0519i	0.255233	−	0.442077i
$26$	1.69117	−	0.976395i	0.0650449	−	0.0375537i
$27$	15.3096	−	22.2400i	0.567022	−	0.823703i
$28$	4.30958	+	13.3202i	0.153914	+	0.475721i
$29$			19.0241i			0.656004i	0.944677	+	0.328002i	$0.106375\pi$
$29$			19.0241i			0.656004i	−0.944677	+	0.328002i	$0.893625\pi$
$30$	19.5219	+	17.2802i	0.650730	+	0.576006i
$31$	−9.22604	+	15.9800i	−0.297614	+	0.515483i	−0.975590	−	0.219602i	$-0.929524\pi$
$31$	−9.22604	+	15.9800i	−0.297614	+	0.515483i	0.677975	+	0.735085i	$0.262858\pi$
$32$	−4.89898	−	2.82843i	−0.153093	−	0.0883883i
$33$	35.7863	−	40.4287i	1.08443	−	1.22511i
$34$	8.69042			0.255600
$35$	−8.99601	+	42.0642i	−0.257029	+	1.20183i
$36$	−14.3808	+	10.8255i	−0.399468	+	0.300709i
$37$	0.500000	+	0.866025i	0.0135135	+	0.0234061i	0.872703	−	0.488251i	$-0.162365\pi$
$37$	0.500000	+	0.866025i	0.0135135	+	0.0234061i	−0.859190	+	0.511657i	$0.829032\pi$
$38$	18.4584	+	10.6570i	0.485748	+	0.280447i
$39$	−0.826891	+	4.05913i	−0.0212023	+	0.104080i
$40$	−8.69042	−	15.0522i	−0.217260	−	0.376306i
$41$		−	11.4145i		−	0.278402i	−0.990264	−	0.139201i	$-0.955547\pi$
$41$		−	11.4145i		−	0.278402i	0.990264	−	0.139201i	$-0.0444534\pi$
$42$	−27.2175	−	11.8831i	−0.648036	−	0.282930i
$43$	54.1425			1.25913			0.629564	−	0.776949i	$-0.283234\pi$
$43$	54.1425			1.25913			0.629564	+	0.776949i	$0.283234\pi$
$44$	−31.1723	+	17.9973i	−0.708461	+	0.409030i
$45$	−54.8966	+	6.71271i	−1.21992	+	0.149171i
$46$	18.7260	−	32.4345i	0.407088	−	0.705097i
$47$	−46.4967	+	26.8449i	−0.989291	+	0.571167i	−0.905062	−	0.425279i	$-0.860176\pi$
$47$	−46.4967	+	26.8449i	−0.989291	+	0.571167i	−0.0842287	+	0.996446i	$0.526843\pi$
$48$	11.3808	−	3.80482i	0.237101	−	0.0792671i
$49$	−5.00000	−	48.7442i	−0.102041	−	0.994780i
$50$		−	18.0477i		−	0.360954i
$51$	−12.2189	+	13.8041i	−0.239587	+	0.270668i
$52$	1.38083	−	2.39167i	0.0265545	−	0.0459937i
$53$	−35.4740	−	20.4809i	−0.669320	−	0.386432i	0.126499	−	0.991967i	$-0.459626\pi$
$53$	−35.4740	−	20.4809i	−0.669320	−	0.386432i	−0.795819	+	0.605535i	$0.792959\pi$
$54$	3.02430	−	38.0638i	0.0560055	−	0.704885i
$55$	−110.595			−2.01081
$56$	14.6969	+	13.2665i	0.262445	+	0.236902i
$57$	−42.8808	+	14.3359i	−0.752295	+	0.251506i
$58$	13.4521	+	23.2997i	0.231932	+	0.401719i
$59$	47.2550	+	27.2827i	0.800932	+	0.462418i	0.843797	−	0.536662i	$-0.180315\pi$
$59$	47.2550	+	27.2827i	0.800932	+	0.462418i	−0.0428648	+	0.999081i	$0.513648\pi$
$60$	36.1283	+	7.35975i	0.602138	+	0.122663i
$61$	35.8808	+	62.1474i	0.588210	+	1.01881i	0.994467	+	0.105051i	$0.0335006\pi$
$61$	35.8808	+	62.1474i	0.588210	+	1.01881i	−0.406256	+	0.913759i	$0.633166\pi$
$62$			26.0952i			0.420890i
$63$	57.1439	−	26.5251i	0.907045	−	0.421033i
$64$	−8.00000			−0.125000
$65$	7.34847	−	4.24264i	0.113053	−	0.0652714i
$66$	15.2416	−	74.8196i	0.230934	−	1.13363i
$67$	−10.9877	+	19.0313i	−0.163996	+	0.284049i	−0.936298	−	0.351206i	$-0.885772\pi$
$67$	−10.9877	+	19.0313i	−0.163996	+	0.284049i	0.772303	+	0.635255i	$0.219105\pi$
$68$	10.6435	−	6.14505i	0.156523	−	0.0903684i
$69$	25.1904	+	75.3486i	0.365078	+	1.09201i
$70$	18.7260	+	57.8790i	0.267515	+	0.826843i
$71$		−	109.433i		−	1.54131i	−0.637252	−	0.770655i	$-0.719929\pi$
$71$		−	109.433i		−	1.54131i	0.637252	−	0.770655i	$-0.280071\pi$
$72$	−9.95806	+	23.4273i	−0.138306	+	0.325379i
$73$	7.11917	−	12.3308i	0.0975229	−	0.168915i	−0.813136	−	0.582074i	$-0.802241\pi$
$73$	7.11917	−	12.3308i	0.0975229	−	0.168915i	0.910659	+	0.413159i	$0.135575\pi$
$74$	1.22474	+	0.707107i	0.0165506	+	0.00955550i
$75$	28.6674	+	25.3755i	0.382233	+	0.338341i
$76$	30.1425			0.396612
$77$	119.864	−	38.7805i	1.55668	−	0.503643i
$78$	1.85751	+	5.55610i	0.0238142	+	0.0712320i
$79$	−46.3685	−	80.3127i	−0.586943	−	1.01662i	−0.994630	−	0.103494i	$-0.966998\pi$
$79$	−46.3685	−	80.3127i	−0.586943	−	1.01662i	0.407687	−	0.913122i	$-0.366336\pi$
$80$	−21.2871	−	12.2901i	−0.266089	−	0.153626i
$81$	56.2093	+	58.3225i	0.693942	+	0.720031i
$82$	−8.07125	−	13.9798i	−0.0984298	−	0.170485i
$83$		−	35.6924i		−	0.430029i	−0.976611	−	0.215014i	$-0.931020\pi$
$83$		−	35.6924i		−	0.430029i	0.976611	−	0.215014i	$-0.0689799\pi$
$84$	−41.7371	+	4.69196i	−0.496870	+	0.0558566i
$85$	37.7617			0.444255
$86$	66.3107	−	38.2845i	0.771055	−	0.445169i
$87$	−55.9238	−	11.3923i	−0.642802	−	0.130946i
$88$	−25.4521	+	44.0843i	−0.289228	+	0.500958i
$89$	−138.876	+	80.1802i	−1.56041	+	0.900901i	−0.563190	+	0.826327i	$0.690426\pi$
$89$	−138.876	+	80.1802i	−1.56041	+	0.900901i	−0.997216	+	0.0745732i	$0.976241\pi$
$90$	−62.4877	+	47.0391i	−0.694308	+	0.522657i
$91$	−6.47667	+	7.17501i	−0.0711722	+	0.0788463i
$92$		−	52.9652i		−	0.575709i
$93$	−41.4502	−	36.6905i	−0.445701	−	0.394521i
$94$	−37.9644	+	65.7562i	−0.403876	+	0.699534i
$95$	80.2057	+	46.3068i	0.844271	+	0.487440i
$96$	11.2482	−	12.7074i	0.117169	−	0.132369i
$97$	118.904			1.22582			0.612908	−	0.790154i	$-0.290000\pi$
$97$	118.904			1.22582			0.612908	+	0.790154i	$0.290000\pi$
$98$	−40.5911	−	56.1637i	−0.414195	−	0.573099i
$99$	97.4152	+	129.408i	0.983992	+	1.30715i
$100$	−12.7617	−	22.1038i	−0.127617	−	0.221038i
$101$	−27.6290	−	15.9516i	−0.273554	−	0.157936i	0.356948	−	0.934124i	$-0.383817\pi$
$101$	−27.6290	−	15.9516i	−0.273554	−	0.157936i	−0.630502	+	0.776188i	$0.717151\pi$
$102$	−5.20413	+	25.5466i	−0.0510209	+	0.250457i
$103$	−93.7494	−	162.379i	−0.910188	−	1.57649i	−0.813798	−	0.581148i	$-0.802604\pi$
$103$	−93.7494	−	162.379i	−0.910188	−	1.57649i	−0.0963903	−	0.995344i	$-0.530730\pi$
$104$		−	3.90558i		−	0.0375537i
$105$	−118.266	−	51.6344i	−1.12634	−	0.491756i
$106$	−57.9288			−0.546498
$107$	−22.1763	+	12.8035i	−0.207255	+	0.119659i	−0.600035	−	0.799974i	$-0.704847\pi$
$107$	−22.1763	+	12.8035i	−0.207255	+	0.119659i	0.392780	+	0.919632i	$0.371513\pi$
$108$	−23.2112	−	48.7570i	−0.214918	−	0.451453i
$109$	−23.8096	+	41.2394i	−0.218437	+	0.378343i	−0.954330	−	0.298754i	$-0.903429\pi$
$109$	−23.8096	+	41.2394i	−0.218437	+	0.378343i	0.735894	+	0.677097i	$0.236762\pi$
$110$	−135.450	+	78.2022i	−1.23136	+	0.710929i
$111$	−2.84521	+	0.951206i	−0.0256325	+	0.00856942i
$112$	27.3808	+	5.85577i	0.244472	+	0.0522837i
$113$		−	100.374i		−	0.888269i	−0.895960	−	0.444134i	$-0.853511\pi$
$113$		−	100.374i		−	0.888269i	0.895960	−	0.444134i	$-0.146489\pi$
$114$	−42.3811	+	47.8791i	−0.371764	+	0.419992i
$115$	81.3685	−	140.934i	0.707552	−	1.22552i
$116$	32.9507	+	19.0241i	0.284058	+	0.164001i
$117$	−11.4371	−	4.86150i	−0.0977533	−	0.0415513i
$118$	77.1671			0.653958
$119$	−40.9266	+	13.2413i	−0.343921	+	0.111272i
$120$	49.4521	−	16.5327i	0.412101	−	0.137773i
$121$	101.452	+	175.720i	0.838447	+	1.45223i
$122$	87.8897	+	50.7432i	0.720408	+	0.415928i
$123$	33.5543	+	6.83539i	0.272799	+	0.0555723i
$124$	18.4521	+	31.9599i	0.148807	+	0.257741i
$125$			75.2052i			0.601642i
$126$	51.2306	−	72.8933i	0.406592	−	0.578518i
$127$	−40.6192			−0.319836			−0.159918	−	0.987130i	$-0.551123\pi$
$127$	−40.6192			−0.319836			−0.159918	+	0.987130i	$0.551123\pi$
$128$	−9.79796	+	5.65685i	−0.0765466	+	0.0441942i
$129$	−32.4225	+	159.159i	−0.251337	+	1.23379i
$130$	6.00000	−	10.3923i	0.0461538	−	0.0799408i
$131$	55.8853	−	32.2654i	0.426606	−	0.246301i	−0.271294	−	0.962497i	$-0.587452\pi$
$131$	55.8853	−	32.2654i	0.426606	−	0.246301i	0.697900	+	0.716196i	$0.254118\pi$
$132$	−34.2383	−	102.412i	−0.259381	−	0.775851i
$133$	−103.166	−	22.0634i	−0.775683	−	0.165891i
$134$			31.0779i			0.231925i
$135$	13.1412	−	165.395i	0.0973422	−	1.22515i
$136$	8.69042	−	15.0522i	0.0639001	−	0.110678i
$137$	51.4528	+	29.7063i	0.375568	+	0.216834i	0.675888	−	0.737004i	$-0.263760\pi$
$137$	51.4528	+	29.7063i	0.375568	+	0.216834i	−0.300320	+	0.953838i	$0.597094\pi$
$138$	84.1313	+	74.4704i	0.609647	+	0.539641i
$139$	−59.6658			−0.429251			−0.214625	−	0.976696i	$-0.568853\pi$
$139$	−59.6658			−0.429251			−0.214625	+	0.976696i	$0.568853\pi$
$140$	63.8613	+	57.6457i	0.456152	+	0.411755i
$141$	−51.0700	−	152.758i	−0.362198	−	1.08339i
$142$	−77.3808	−	134.028i	−0.544935	−	0.943856i
$143$	−21.5218	−	12.4256i	−0.150502	−	0.0868926i
$144$	4.36950	+	35.7338i	0.0303438	+	0.248152i
$145$	58.4521	+	101.242i	0.403118	+	0.698220i
$146$		−	20.1360i		−	0.137918i
$147$	146.284	+	14.4917i	0.995129	+	0.0985827i
$148$	2.00000			0.0135135
$149$	−1.26837	+	0.732296i	−0.00851258	+	0.00491474i	−0.504250	−	0.863558i	$-0.668231\pi$
$149$	−1.26837	+	0.732296i	−0.00851258	+	0.00491474i	0.495738	+	0.868472i	$0.334898\pi$
$150$	53.0535	+	10.8076i	0.353690	+	0.0720508i
$151$	−85.9877	+	148.935i	−0.569455	+	0.986325i	0.427165	+	0.904174i	$0.359512\pi$
$151$	−85.9877	+	148.935i	−0.569455	+	0.986325i	−0.996620	+	0.0821512i	$0.973821\pi$
$152$	36.9169	−	21.3140i	0.242874	−	0.140223i
$153$	−33.2617	−	44.1855i	−0.217396	−	0.288794i
$154$	119.381	−	132.253i	0.775200	−	0.858785i
$155$			113.389i			0.731542i
$156$	6.20372	+	5.49134i	0.0397675	+	0.0352009i
$157$	0.500000	−	0.866025i	0.00318471	−	0.00551609i	−0.864429	−	0.502756i	$-0.832320\pi$
$157$	0.500000	−	0.866025i	0.00318471	−	0.00551609i	0.867613	+	0.497239i	$0.165653\pi$
$158$	−113.579	−	65.5750i	−0.718856	−	0.415032i
$159$	81.4493	−	92.0155i	0.512260	−	0.578714i
$160$	−34.7617			−0.217260
$161$	−38.7690	+	181.279i	−0.240802	+	1.12596i
$162$	110.082	+	31.6843i	0.679520	+	0.195582i
$163$	124.963	+	216.442i	0.766645	+	1.32787i	0.939373	+	0.342898i	$0.111409\pi$
$163$	124.963	+	216.442i	0.766645	+	1.32787i	−0.172728	+	0.984970i	$0.555258\pi$
$164$	−19.7704	−	11.4145i	−0.120551	−	0.0696004i
$165$	66.2280	−	325.107i	0.401382	−	1.97034i
$166$	−25.2383	−	43.7141i	−0.152038	−	0.263338i
$167$			26.9048i			0.161107i	0.996750	+	0.0805534i	$0.0256688\pi$
$167$			26.9048i			0.161107i	−0.996750	+	0.0805534i	$0.974331\pi$
$168$	−47.7996	+	35.2590i	−0.284521	+	0.209875i
$169$	−167.093			−0.988718
$170$	46.2484	−	26.7015i	0.272049	−	0.157068i
$171$	−16.4635	−	134.638i	−0.0962776	−	0.787359i
$172$	54.1425	−	93.7776i	0.314782	−	0.545218i
$173$	79.0682	−	45.6501i	0.457042	−	0.263873i	−0.253758	−	0.967268i	$-0.581667\pi$
$173$	79.0682	−	45.6501i	0.457042	−	0.263873i	0.710800	+	0.703395i	$0.248333\pi$
$174$	−76.5479	+	25.5914i	−0.439931	+	0.147077i
$175$	27.4987	+	84.9939i	0.157136	+	0.485679i
$176$			71.9894i			0.409030i
$177$	−108.499	+	122.574i	−0.612988	+	0.692509i
$178$	−113.392	+	196.400i	−0.637033	+	1.10337i
$179$	−209.210	−	120.788i	−1.16877	−	0.674791i	−0.215381	−	0.976530i	$-0.569099\pi$
$179$	−209.210	−	120.788i	−1.16877	−	0.674791i	−0.953390	+	0.301739i	$0.902433\pi$
$180$	−43.2698	+	101.796i	−0.240388	+	0.565535i
$181$	−19.9067			−0.109982			−0.0549909	−	0.998487i	$-0.517513\pi$
$181$	−19.9067			−0.109982			−0.0549909	+	0.998487i	$0.517513\pi$
$182$	−2.85877	+	13.3673i	−0.0157076	+	0.0734465i
$183$	−204.177	+	68.2601i	−1.11572	+	0.373006i
$184$	−37.4521	−	64.8689i	−0.203544	−	0.352548i
$185$	5.32177	+	3.07253i	0.0287663	+	0.0166082i
$186$	−76.7100	−	15.6267i	−0.412420	−	0.0840147i
$187$	−55.2973	−	95.7777i	−0.295707	−	0.512180i
$188$			107.379i			0.571167i
$189$	43.7540	+	183.866i	0.231503	+	0.972834i
$190$	130.975			0.689344
$191$	−86.0376	+	49.6738i	−0.450458	+	0.260072i	−0.708024	−	0.706189i	$-0.750413\pi$
$191$	−86.0376	+	49.6738i	−0.450458	+	0.260072i	0.257565	+	0.966261i	$0.417080\pi$
$192$	4.79069	−	23.5170i	0.0249515	−	0.122484i
$193$	192.426	−	333.292i	0.997027	−	1.72690i	0.431784	−	0.901977i	$-0.357884\pi$
$193$	192.426	−	333.292i	0.997027	−	1.72690i	0.565243	−	0.824924i	$-0.308782\pi$
$194$	145.627	−	84.0779i	0.750656	−	0.433391i
$195$	8.07125	+	24.1424i	0.0413910	+	0.123807i
$196$	−89.4275	−	40.0840i	−0.456263	−	0.204510i
$197$			105.628i			0.536184i	0.963393	+	0.268092i	$0.0863931\pi$
$197$			105.628i			0.536184i	−0.963393	+	0.268092i	$0.913607\pi$
$198$	210.814	+	89.6093i	1.06472	+	0.452572i
$199$	−20.6069	+	35.6921i	−0.103552	+	0.179358i	−0.913146	−	0.407633i	$-0.866354\pi$
$199$	−20.6069	+	35.6921i	−0.103552	+	0.179358i	0.809594	+	0.586991i	$0.199688\pi$
$200$	−31.2596	−	18.0477i	−0.156298	−	0.0902386i
$201$	−49.3649	−	43.6963i	−0.245597	−	0.217395i
$202$	−45.1179			−0.223356
$203$	−98.8522	−	89.2310i	−0.486957	−	0.439562i
$204$	11.6904	+	34.9679i	0.0573060	+	0.171411i
$205$	−35.0712	−	60.7452i	−0.171079	−	0.296318i
$206$	−229.638	−	132.582i	−1.11475	−	0.643600i
$207$	−236.581	+	28.9290i	−1.14291	+	0.139753i
$208$	−2.76166	−	4.78334i	−0.0132772	−	0.0229968i
$209$		−	271.242i		−	1.29781i
$210$	−181.356	+	20.3875i	−0.863602	+	0.0970834i
$211$	249.858			1.18416			0.592079	−	0.805880i	$-0.298307\pi$
$211$	249.858			1.18416			0.592079	+	0.805880i	$0.298307\pi$
$212$	−70.9479	+	40.9618i	−0.334660	+	0.193216i
$213$	321.692	+	65.5324i	1.51029	+	0.307664i
$214$	−18.1069	+	31.3620i	−0.0846115	+	0.146551i
$215$	288.134	−	166.354i	1.34016	−	0.773741i
$216$	−62.9042	−	43.3020i	−0.291223	−	0.200472i
$217$	−39.7604	−	122.893i	−0.183228	−	0.566325i
$218$			67.3437i			0.308916i
$219$	31.9846	+	28.3118i	0.146048	+	0.129278i
$220$	−110.595	+	191.555i	−0.502703	+	0.870706i
$221$	7.34847	+	4.24264i	0.0332510	+	0.0191975i
$222$	−2.81205	+	3.17685i	−0.0126669	+	0.0143101i
$223$	170.427			0.764249			0.382124	−	0.924111i	$-0.375193\pi$
$223$	170.427			0.764249			0.382124	+	0.924111i	$0.375193\pi$
$224$	37.6752	−	12.1893i	0.168193	−	0.0544167i
$225$	−91.7617	+	69.0758i	−0.407830	+	0.307003i
$226$	−70.9754	−	122.933i	−0.314050	−	0.543951i
$227$	297.130	+	171.548i	1.30894	+	0.755718i	0.981920	−	0.189298i	$-0.0606212\pi$
$227$	297.130	+	171.548i	1.30894	+	0.755718i	0.327023	+	0.945016i	$0.393955\pi$
$228$	−18.0504	+	88.6076i	−0.0791684	+	0.388630i
$229$	134.903	+	233.659i	0.589096	+	1.02034i	0.994351	+	0.106140i	$0.0338492\pi$
$229$	134.903	+	233.659i	0.589096	+	1.02034i	−0.405256	+	0.914203i	$0.632817\pi$
$230$		−	230.145i		−	1.00063i
$231$	42.2214	+	375.578i	0.182776	+	1.62588i
$232$	53.8083			0.231932
$233$	271.907	−	156.986i	1.16698	−	0.673758i	0.214015	−	0.976830i	$-0.431346\pi$
$233$	271.907	−	156.986i	1.16698	−	0.673758i	0.952967	+	0.303073i	$0.0980126\pi$
$234$	−17.4452	+	2.13318i	−0.0745520	+	0.00911616i
$235$	−164.963	+	285.724i	−0.701971	+	1.21585i
$236$	94.5100	−	54.5654i	0.400466	−	0.231209i
$237$	263.856	−	88.2120i	1.11332	−	0.372203i
$238$	−40.7617	+	45.1567i	−0.171267	+	0.189734i
$239$			59.6992i			0.249788i	0.992170	+	0.124894i	$0.0398590\pi$
$239$			59.6992i			0.249788i	−0.992170	+	0.124894i	$0.960141\pi$
$240$	48.8758	−	55.2163i	0.203649	−	0.230068i
$241$	154.642	−	267.849i	0.641670	−	1.11141i	−0.343390	−	0.939193i	$-0.611575\pi$
$241$	154.642	−	267.849i	0.641670	−	1.11141i	0.985060	−	0.172212i	$-0.0550915\pi$
$242$	248.506	+	143.475i	1.02688	+	0.592872i
$243$	−205.106	+	130.309i	−0.844060	+	0.536249i
$244$	143.523			0.588210
$245$	−176.377	−	244.043i	−0.719905	−	0.996094i
$246$	45.9288	−	15.3548i	0.186702	−	0.0624180i
$247$	10.4054	+	18.0227i	0.0421272	+	0.0729665i
$248$	45.1982	+	26.0952i	0.182251	+	0.105223i
$249$	104.922	+	21.3739i	0.421375	+	0.0858389i
$250$	53.1781	+	92.1072i	0.212712	+	0.368429i
$251$			70.2069i			0.279709i	0.990172	+	0.139854i	$0.0446634\pi$
$251$			70.2069i			0.279709i	−0.990172	+	0.139854i	$0.955337\pi$
$252$	11.2011	−	125.501i	0.0444487	−	0.498020i
$253$	−476.617			−1.88386
$254$	−49.7481	+	28.7221i	−0.195859	+	0.113079i
$255$	−22.6130	+	111.005i	−0.0886786	+	0.435314i
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	−60.5797	+	34.9757i	−0.235719	+	0.136092i	−0.613207	−	0.789922i	$-0.710121\pi$
$257$	−60.5797	+	34.9757i	−0.235719	+	0.136092i	0.377489	+	0.926014i	$0.376788\pi$
$258$	72.8329	+	217.855i	0.282298	+	0.844399i
$259$	−6.84521	−	1.46394i	−0.0264294	−	0.00565229i
$260$		−	16.9706i		−	0.0652714i
$261$	66.9783	−	157.573i	0.256622	−	0.603727i
$262$	45.6302	−	79.0338i	0.174161	−	0.301656i
$263$	−113.418	−	65.4820i	−0.431248	−	0.248981i	0.268630	−	0.963243i	$-0.413429\pi$
$263$	−113.418	−	65.4820i	−0.431248	−	0.248981i	−0.699878	+	0.714262i	$0.746762\pi$
$264$	−114.350	−	101.219i	−0.433143	−	0.383405i
$265$	−251.712			−0.949858
$266$	−141.953	+	45.9272i	−0.533658	+	0.172658i
$267$	−152.536	−	456.258i	−0.571294	−	1.70883i
$268$	21.9754	+	38.0625i	0.0819978	+	0.142024i
$269$	−302.059	−	174.394i	−1.12290	−	0.648304i	−0.180757	−	0.983528i	$-0.557855\pi$
$269$	−302.059	−	174.394i	−1.12290	−	0.648304i	−0.942139	+	0.335223i	$0.891188\pi$
$270$	−100.857	−	211.859i	−0.373546	−	0.784663i
$271$	−38.5110	−	66.7031i	−0.142107	−	0.246137i	0.786183	−	0.617994i	$-0.212054\pi$
$271$	−38.5110	−	66.7031i	−0.142107	−	0.246137i	−0.928290	+	0.371857i	$0.878721\pi$
$272$		−	24.5802i		−	0.0903684i
$273$	−17.2134	−	23.3356i	−0.0630527	−	0.0854786i
$274$	84.0221			0.306650
$275$	−198.905	+	114.838i	−0.723292	+	0.417593i
$276$	155.698	+	31.7175i	0.564123	+	0.114918i
$277$	−3.64249	+	6.30899i	−0.0131498	+	0.0227761i	−0.872525	−	0.488569i	$-0.837519\pi$
$277$	−3.64249	+	6.30899i	−0.0131498	+	0.0227761i	0.859376	+	0.511345i	$0.170852\pi$
$278$	−73.0754	+	42.1901i	−0.262861	+	0.151763i
$279$	132.678	−	99.8766i	0.475549	−	0.357981i
$280$	118.975	+	25.4445i	0.424912	+	0.0908734i
$281$			167.048i			0.594475i	0.954804	+	0.297238i	$0.0960653\pi$
$281$			167.048i			0.594475i	−0.954804	+	0.297238i	$0.903935\pi$
$282$	−170.564	−	150.978i	−0.604838	−	0.535384i
$283$	60.7248	−	105.178i	0.214575	−	0.371655i	−0.738566	−	0.674181i	$-0.764497\pi$
$283$	60.7248	−	105.178i	0.214575	−	0.371655i	0.953141	+	0.302526i	$0.0978300\pi$
$284$	−189.544	−	109.433i	−0.667407	−	0.385328i
$285$	−184.155	+	208.045i	−0.646157	+	0.729981i
$286$	−35.1450			−0.122885
$287$	59.3113	+	53.5386i	0.206660	+	0.186546i
$288$	30.6192	+	40.6751i	0.106317	+	0.141233i
$289$	−125.619	−	217.579i	−0.434668	−	0.752868i
$290$	143.178	+	82.6637i	0.493716	+	0.285047i
$291$	−71.2041	+	349.534i	−0.244687	+	1.20115i
$292$	−14.2383	−	24.6615i	−0.0487614	−	0.0844573i
$293$			477.594i			1.63001i	0.579451	+	0.815007i	$0.303267\pi$
$293$			477.594i			1.63001i	−0.579451	+	0.815007i	$0.696733\pi$
$294$	189.408	−	85.6898i	0.644244	−	0.291462i
$295$	335.307			1.13663
$296$	2.44949	−	1.41421i	0.00827530	−	0.00477775i
$297$	−438.748	+	208.870i	−1.47726	+	0.703265i
$298$	−1.03562	+	1.79375i	−0.00347525	+	0.00601930i
$299$	31.6688	−	18.2840i	0.105916	−	0.0611506i
$300$	72.6192	−	24.2779i	0.242064	−	0.0809264i
$301$	−253.951	+	281.333i	−0.843690	+	0.934660i
$302$			243.210i			0.805331i
$303$	63.4369	−	71.6664i	0.209363	−	0.236523i
$304$	30.1425	−	52.2083i	0.0991529	−	0.171738i
$305$	381.899	+	220.490i	1.25213	+	0.722917i
$306$	−71.9809	−	30.5964i	−0.235232	−	0.0999882i
$307$	−123.381			−0.401892			−0.200946	−	0.979602i	$-0.564402\pi$
$307$	−123.381			−0.401892			−0.200946	+	0.979602i	$0.564402\pi$
$308$	52.6942	−	246.391i	0.171085	−	0.799971i
$309$	533.473	−	178.350i	1.72645	−	0.577184i
$310$	80.1781	+	138.873i	0.258639	+	0.447976i
$311$	−345.012	−	199.193i	−1.10936	−	0.640492i	−0.170700	−	0.985323i	$-0.554603\pi$
$311$	−345.012	−	199.193i	−1.10936	−	0.640492i	−0.938665	+	0.344831i	$0.887936\pi$
$312$	11.4809	+	2.33880i	0.0367979	+	0.00749616i
$313$	26.5492	+	45.9845i	0.0848217	+	0.146915i	0.905315	−	0.424740i	$-0.139635\pi$
$313$	26.5492	+	45.9845i	0.0848217	+	0.146915i	−0.820494	+	0.571656i	$0.806301\pi$
$314$		−	1.41421i		−	0.00450386i
$315$	222.608	−	316.736i	0.706691	−	1.00551i
$316$	−185.474			−0.586943
$317$	−319.789	+	184.630i	−1.00880	+	0.582430i	−0.910840	−	0.412760i	$-0.864565\pi$
$317$	−319.789	+	184.630i	−1.00880	+	0.582430i	−0.0979592	+	0.995190i	$0.531231\pi$
$318$	34.6898	−	170.289i	0.109087	−	0.535499i
$319$	171.192	−	296.513i	0.536651	−	0.929507i
$320$	−42.5742	+	24.5802i	−0.133044	+	0.0768131i
$321$	−24.3575	−	72.8572i	−0.0758801	−	0.226969i
$322$	80.7014	+	249.434i	0.250626	+	0.774641i
$323$			92.6136i			0.286729i
$324$	157.227	−	39.0348i	0.485268	−	0.120478i
$325$	8.81085	−	15.2608i	0.0271103	−	0.0469564i
$326$	306.096	+	176.725i	0.938944	+	0.542100i
$327$	−106.970	−	94.6869i	−0.327127	−	0.289562i
$328$	−32.2850			−0.0984298
$329$	78.5987	−	367.517i	0.238902	−	1.11707i
$330$	−148.773	−	445.003i	−0.450826	−	1.34849i
$331$	68.2506	+	118.214i	0.206195	+	0.357141i	0.950513	−	0.310685i	$-0.100558\pi$
$331$	68.2506	+	118.214i	0.206195	+	0.357141i	−0.744318	+	0.667826i	$0.767225\pi$
$332$	−61.8210	−	35.6924i	−0.186208	−	0.107507i
$333$	−1.09238	−	8.93346i	−0.00328041	−	0.0268272i
$334$	19.0246	+	32.9516i	0.0569599	+	0.0986574i
$335$			135.040i			0.403104i
$336$	−33.6104	+	76.9827i	−0.100031	+	0.229115i
$337$	157.381			0.467005			0.233503	−	0.972356i	$-0.424981\pi$
$337$	157.381			0.467005			0.233503	+	0.972356i	$0.424981\pi$
$338$	−204.647	+	118.153i	−0.605464	+	0.349565i
$339$	295.063	+	60.1078i	0.870392	+	0.177309i
$340$	37.7617	−	65.4051i	0.111064	−	0.192368i
$341$	287.597	−	166.044i	0.843393	−	0.486933i
$342$	−115.367	−	153.256i	−0.337331	−	0.448118i
$343$	276.735	+	202.650i	0.806806	+	0.590816i
$344$		−	153.138i		−	0.445169i
$345$	365.568	+	323.590i	1.05962	+	0.937941i
$346$	64.5589	−	111.819i	0.186587	−	0.323177i
$347$	231.779	+	133.818i	0.667951	+	0.385642i	0.795300	−	0.606216i	$-0.207313\pi$
$347$	231.779	+	133.818i	0.667951	+	0.385642i	−0.127349	+	0.991858i	$0.540647\pi$
$348$	−75.6558	+	85.4705i	−0.217402	+	0.245605i
$349$	−190.236			−0.545088			−0.272544	−	0.962143i	$-0.587865\pi$
$349$	−190.236			−0.545088			−0.272544	+	0.962143i	$0.587865\pi$
$350$	93.7787	+	84.6513i	0.267939	+	0.241861i
$351$	21.1400	−	30.7097i	0.0602278	−	0.0874919i
$352$	50.9042	+	88.1686i	0.144614	+	0.250479i
$353$	91.4632	+	52.8063i	0.259103	+	0.149593i	0.623925	−	0.781484i	$-0.285537\pi$
$353$	91.4632	+	52.8063i	0.259103	+	0.149593i	−0.364823	+	0.931077i	$0.618870\pi$
$354$	−46.2104	+	226.842i	−0.130538	+	0.640797i
$355$	−336.236	−	582.377i	−0.947143	−	1.64050i
$356$			320.721i			0.900901i
$357$	−14.4162	−	128.238i	−0.0403814	−	0.359211i
$358$	−341.639			−0.954298
$359$	337.140	−	194.648i	0.939110	−	0.542195i	0.0494286	−	0.998778i	$-0.484260\pi$
$359$	337.140	−	194.648i	0.939110	−	0.542195i	0.889681	+	0.456582i	$0.150927\pi$
$360$	18.9864	+	155.271i	0.0527400	+	0.431308i
$361$	66.9288	−	115.924i	0.185398	−	0.321119i
$362$	−24.3806	+	14.0762i	−0.0673498	+	0.0388844i
$363$	−577.305	+	193.004i	−1.59037	+	0.531690i
$364$	5.95081	+	18.3929i	0.0163484	+	0.0505301i
$365$		−	87.4953i		−	0.239713i
$366$	−201.797	+	227.976i	−0.551359	+	0.622885i
$367$	−183.749	+	318.263i	−0.500679	+	0.867202i	0.499320	+	0.866418i	$0.333583\pi$
$367$	−183.749	+	318.263i	−0.500679	+	0.867202i	−1.00000		0.000784762i	$0.999750\pi$
$368$	−91.7385	−	52.9652i	−0.249289	−	0.143927i
$369$	−40.1870	+	94.5437i	−0.108908	+	0.256216i
$370$	8.69042			0.0234876
$371$	272.810	−	88.2642i	0.735336	−	0.237909i
$372$	−105.000	+	35.1034i	−0.282258	+	0.0943641i
$373$	−114.738	−	198.733i	−0.307609	−	0.532795i	0.670229	−	0.742154i	$-0.266196\pi$
$373$	−114.738	−	198.733i	−0.307609	−	0.532795i	−0.977839	+	0.209359i	$0.932862\pi$
$374$	−135.450	−	78.2022i	−0.362166	−	0.209097i
$375$	−221.075	−	45.0356i	−0.589534	−	0.120095i
$376$	75.9288	+	131.512i	0.201938	+	0.349767i
$377$			26.2691i			0.0696793i
$378$	183.600	+	194.250i	0.485715	+	0.513888i
$379$	368.899			0.973348			0.486674	−	0.873584i	$-0.338210\pi$
$379$	368.899			0.973348			0.486674	+	0.873584i	$0.338210\pi$
$380$	160.411	−	92.6136i	0.422135	−	0.243720i
$381$	24.3242	−	119.405i	0.0638431	−	0.313399i
$382$	−70.2494	+	121.675i	−0.183899	+	0.318522i
$383$	−530.557	+	306.317i	−1.38527	+	0.799783i	−0.992777	−	0.119974i	$-0.961719\pi$
$383$	−530.557	+	306.317i	−1.38527	+	0.799783i	−0.392488	+	0.919757i	$0.628386\pi$
$384$	−10.7617	−	32.1899i	−0.0280252	−	0.0838277i
$385$	518.735	−	574.666i	1.34736	−	1.49264i
$386$		−	544.264i		−	1.41001i
$387$	−448.451	−	190.620i	−1.15879	−	0.492557i
$388$	118.904	−	205.948i	0.306454	−	0.530794i
$389$	227.816	+	131.530i	0.585645	+	0.338123i	0.763374	−	0.645957i	$-0.223542\pi$
$389$	227.816	+	131.530i	0.585645	+	0.338123i	−0.177728	+	0.984080i	$0.556875\pi$
$390$	26.9565	+	23.8610i	0.0691191	+	0.0611821i
$391$	162.737			0.416207
$392$	−137.870	+	14.1421i	−0.351708	+	0.0360769i
$393$	61.3821	+	183.604i	0.156189	+	0.467185i
$394$	74.6904	+	129.368i	0.189570	+	0.328344i
$395$	−493.525	−	284.937i	−1.24943	−	0.721360i
$396$	321.557	−	39.3197i	0.812013	−	0.0992922i
$397$	301.665	+	522.498i	0.759860	+	1.31612i	0.942921	+	0.333015i	$0.108066\pi$
$397$	301.665	+	522.498i	0.759860	+	1.31612i	−0.183061	+	0.983102i	$0.558601\pi$
$398$			58.2850i			0.146445i
$399$	126.638	−	290.056i	0.317388	−	0.726959i
$400$	−51.0467			−0.127617
$401$	−591.240	+	341.353i	−1.47441	+	0.851254i	−0.999584	−	0.0288241i	$-0.990824\pi$
$401$	−591.240	+	341.353i	−1.47441	+	0.851254i	−0.474830	+	0.880078i	$0.657490\pi$
$402$	−91.3574	−	18.6106i	−0.227257	−	0.0462949i
$403$	−12.7396	+	22.0656i	−0.0316119	+	0.0547535i
$404$	−55.2579	+	31.9032i	−0.136777	+	0.0789682i
$405$	478.330	+	137.675i	1.18106	+	0.339938i
$406$	−184.165	−	39.3862i	−0.453607	−	0.0970102i
$407$		−	17.9973i		−	0.0442195i
$408$	39.0438	+	34.5604i	0.0956956	+	0.0847068i
$409$	−307.284	+	532.231i	−0.751305	+	1.30130i	0.195886	+	0.980627i	$0.437242\pi$
$409$	−307.284	+	532.231i	−0.751305	+	1.30130i	−0.947190	+	0.320672i	$0.896091\pi$
$410$	−85.9067	−	49.5982i	−0.209528	−	0.120971i
$411$	−118.137	+	133.463i	−0.287438	+	0.324727i
$412$	−374.997			−0.910188
$413$	−363.411	+	117.577i	−0.879929	+	0.284690i
$414$	−269.296	+	202.719i	−0.650473	+	0.489659i
$415$	−109.666	−	189.947i	−0.264255	−	0.457703i
$416$	−6.76467	−	3.90558i	−0.0162612	−	0.00938842i
$417$	35.7300	−	175.395i	0.0856835	−	0.420612i
$418$	−191.797	−	332.203i	−0.458845	−	0.794743i
$419$		−	775.997i		−	1.85202i	−0.377498	−	0.926010i	$-0.623216\pi$
$419$		−	775.997i		−	1.85202i	0.377498	−	0.926010i	$-0.376784\pi$
$420$	−207.699	+	153.208i	−0.494522	+	0.364781i
$421$	−161.194			−0.382884			−0.191442	−	0.981504i	$-0.561316\pi$
$421$	−161.194			−0.382884			−0.191442	+	0.981504i	$0.561316\pi$
$422$	306.012	−	176.676i	0.725146	−	0.418663i
$423$	479.635	−	58.6494i	1.13389	−	0.138651i
$424$	−57.9288	+	100.336i	−0.136624	+	0.236640i
$425$	67.9146	−	39.2105i	0.159799	−	0.0922601i
$426$	440.329	−	147.210i	1.03364	−	0.345564i
$427$	−491.224	−	105.055i	−1.15041	−	0.246030i
$428$			51.2140i			0.119659i
$429$	49.4148	−	55.8252i	0.115186	−	0.130129i
$430$	235.260	−	407.483i	0.547117	−	0.947635i
$431$	414.182	+	239.128i	0.960979	+	0.554821i	0.896474	−	0.443096i	$-0.146120\pi$
$431$	414.182	+	239.128i	0.960979	+	0.554821i	0.0645047	+	0.997917i	$0.479453\pi$
$432$	−107.661	−	8.55400i	−0.249215	−	0.0198009i
$433$	−97.5674			−0.225329			−0.112664	−	0.993633i	$-0.535939\pi$
$433$	−97.5674			−0.225329			−0.112664	+	0.993633i	$0.535939\pi$
$434$	−135.595	−	122.397i	−0.312430	−	0.282021i
$435$	−332.617	+	111.200i	−0.764636	+	0.255632i
$436$	47.6192	+	82.4788i	0.109218	+	0.189172i
$437$	345.653	+	199.563i	0.790969	+	0.456666i
$438$	59.1924	+	12.0582i	0.135143	+	0.0275301i
$439$	118.056	+	204.480i	0.268921	+	0.465785i	0.968584	−	0.248688i	$-0.0799995\pi$
$439$	118.056	+	204.480i	0.268921	+	0.465785i	−0.699662	+	0.714474i	$0.746666\pi$
$440$			312.809i			0.710929i
$441$	−130.200	+	421.342i	−0.295238	+	0.955424i
$442$	12.0000			0.0271493
$443$	400.063	−	230.976i	0.903076	−	0.521391i	0.0248789	−	0.999690i	$-0.492080\pi$
$443$	400.063	−	230.976i	0.903076	−	0.521391i	0.878197	+	0.478299i	$0.158747\pi$
$444$	−1.19767	+	5.87925i	−0.00269746	+	0.0132416i
$445$	−492.711	+	853.401i	−1.10722	+	1.91775i
$446$	208.730	−	120.510i	0.468005	−	0.270203i
$447$	−1.39313	−	4.16707i	−0.00311662	−	0.00932231i
$448$	37.5233	−	41.5692i	0.0837574	−	0.0927884i
$449$		−	296.954i		−	0.661367i	−0.943742	−	0.330683i	$-0.892721\pi$
$449$		−	296.954i		−	0.661367i	0.943742	−	0.330683i	$-0.107279\pi$
$450$	−63.5407	+	149.485i	−0.141202	+	0.332190i
$451$	−102.715	+	177.908i	−0.227749	+	0.394474i
$452$	−173.854	−	100.374i	−0.384632	−	0.222067i
$453$	−386.321	−	341.959i	−0.852805	−	0.754877i
$454$	485.211			1.06875
$455$	−12.4220	+	58.0835i	−0.0273010	+	0.127656i
$456$	40.5479	+	121.285i	0.0889209	+	0.265977i
$457$	181.547	+	314.448i	0.397257	+	0.688070i	0.993386	−	0.114819i	$-0.0366287\pi$
$457$	181.547	+	314.448i	0.397257	+	0.688070i	−0.596129	+	0.802889i	$0.703295\pi$
$458$	330.443	+	190.781i	0.721492	+	0.416553i
$459$	149.807	−	71.3170i	0.326377	−	0.155375i
$460$	−162.737	−	281.869i	−0.353776	−	0.612758i
$461$		−	616.559i		−	1.33744i	−0.743515	−	0.668719i	$-0.766843\pi$
$461$		−	616.559i		−	1.33744i	0.743515	−	0.668719i	$-0.233157\pi$
$462$	317.284	+	430.133i	0.686763	+	0.931023i
$463$	352.049			0.760365			0.380183	−	0.924911i	$-0.375861\pi$
$463$	352.049			0.760365			0.380183	+	0.924911i	$0.375861\pi$
$464$	65.9015	−	38.0482i	0.142029	−	0.0820005i
$465$	−333.321	−	67.9014i	−0.716820	−	0.146024i
$466$	222.011	−	384.534i	0.476419	−	0.825181i
$467$	449.723	−	259.648i	0.963005	−	0.555991i	0.0659085	−	0.997826i	$-0.479005\pi$
$467$	449.723	−	259.648i	0.963005	−	0.555991i	0.897097	+	0.441834i	$0.145672\pi$
$468$	−19.8575	+	14.9482i	−0.0424306	+	0.0319406i
$469$	−47.3524	−	146.358i	−0.100965	−	0.312065i
$470$			466.586i			0.992736i
$471$	2.24637	+	1.98842i	0.00476937	+	0.00422170i
$472$	77.1671	−	133.657i	0.163490	−	0.283172i
$473$	−843.873	−	487.210i	−1.78409	−	1.03004i
$474$	260.781	−	294.612i	0.550171	−	0.621544i
$475$	192.334			0.404914
$476$	−17.9920	+	84.1283i	−0.0377983	+	0.176740i
$477$	221.716	+	294.532i	0.464814	+	0.617468i
$478$	42.2137	+	73.1163i	0.0883133	+	0.152963i
$479$	206.358	+	119.141i	0.430809	+	0.248728i	0.699691	−	0.714445i	$-0.253321\pi$
$479$	206.358	+	119.141i	0.430809	+	0.248728i	−0.268882	+	0.963173i	$0.586654\pi$
$480$	20.8165	−	102.186i	0.0433678	−	0.212888i
$481$	0.690416	+	1.19584i	0.00143538	+	0.00248614i
$482$		−	437.395i		−	0.907459i
$483$	−509.676	−	222.523i	−1.05523	−	0.460710i
$484$	405.808			0.838447
$485$	632.781	−	365.336i	1.30470	−	0.753270i
$486$	−159.061	+	304.627i	−0.327286	+	0.626804i
$487$	149.391	−	258.752i	0.306757	−	0.531318i	−0.670894	−	0.741553i	$-0.734089\pi$
$487$	149.391	−	258.752i	0.306757	−	0.531318i	0.977651	+	0.210235i	$0.0674228\pi$
$488$	175.779	−	101.486i	0.360204	−	0.207964i
$489$	−711.092	+	237.731i	−1.45418	+	0.486158i
$490$	−388.581	−	174.173i	−0.793022	−	0.355456i
$491$			474.060i			0.965499i	0.875758	+	0.482750i	$0.160362\pi$
$491$			474.060i			0.965499i	−0.875758	+	0.482750i	$0.839638\pi$
$492$	45.3935	−	51.2823i	0.0922632	−	0.104232i
$493$	−58.4521	+	101.242i	−0.118564	+	0.205359i
$494$	25.4880	+	14.7155i	0.0515951	+	0.0297885i
$495$	916.032	+	389.371i	1.85057	+	0.786608i
$496$	73.8083			0.148807
$497$	568.631	+	513.286i	1.14413	+	1.03277i
$498$	143.617	−	48.0137i	0.288387	−	0.0964130i
$499$	−239.415	−	414.679i	−0.479790	−	0.831021i	0.519941	−	0.854202i	$-0.325954\pi$
$499$	−239.415	−	414.679i	−0.479790	−	0.831021i	−0.999731	+	0.0231814i	$0.992620\pi$
$500$	130.259	+	75.2052i	0.260519	+	0.150410i
$501$	−79.0901	−	16.1116i	−0.157865	−	0.0321588i
$502$	49.6438	+	85.9855i	0.0988920	+	0.171286i
$503$			879.634i			1.74877i	0.485229	+	0.874387i	$0.338736\pi$
$503$			879.634i			1.74877i	−0.485229	+	0.874387i	$0.661264\pi$
$504$	−75.0242	−	161.627i	−0.148858	−	0.320689i
$505$	−196.047			−0.388211
$506$	−583.734	+	337.019i	−1.15362	+	0.666045i
$507$	100.061	−	491.192i	0.197360	−	0.968820i
$508$	−40.6192	+	70.3545i	−0.0799590	+	0.138493i
$509$	−363.095	+	209.633i	−0.713349	+	0.411852i	−0.812300	−	0.583240i	$-0.801785\pi$
$509$	−363.095	+	209.633i	−0.713349	+	0.411852i	0.0989507	+	0.995092i	$0.468451\pi$
$510$	50.7973	+	151.943i	0.0996025	+	0.297927i
$511$	30.6807	+	94.8287i	0.0600404	+	0.185575i
$512$			22.6274i			0.0441942i
$513$	405.645	+	32.2299i	0.790732	+	0.0628262i
$514$	−49.4631	+	85.6726i	−0.0962317	+	0.166678i
$515$	−997.825	−	576.095i	−1.93752	−	1.11863i
$516$	243.248	+	215.316i	0.471412	+	0.417279i
$517$	966.272			1.86900
$518$	−9.41880	+	3.04734i	−0.0181830	+	0.00588289i
$519$	86.8452	+	259.768i	0.167332	+	0.500516i
$520$	−12.0000	−	20.7846i	−0.0230769	−	0.0399704i
$521$	−29.3534	−	16.9472i	−0.0563404	−	0.0325282i	0.471565	−	0.881831i	$-0.343689\pi$
$521$	−29.3534	−	16.9472i	−0.0563404	−	0.0325282i	−0.527906	+	0.849303i	$0.677023\pi$
$522$	−29.3895	−	240.347i	−0.0563016	−	0.460435i
$523$	250.676	+	434.183i	0.479303	+	0.830178i	0.999718	−	0.0237359i	$-0.00755609\pi$
$523$	250.676	+	434.183i	0.479303	+	0.830178i	−0.520415	+	0.853913i	$0.674223\pi$
$524$		−	129.062i		−	0.246301i
$525$	−266.317	+	29.9386i	−0.507271	+	0.0570259i
$526$	−185.211			−0.352113
$527$	−98.1977	+	56.6945i	−0.186333	+	0.107580i
$528$	−211.622	−	43.1098i	−0.400799	−	0.0816473i
$529$	86.1646	−	149.241i	0.162882	−	0.282120i
$530$	−308.284	+	177.988i	−0.581667	+	0.335826i
$531$	−295.349	−	392.348i	−0.556213	−	0.738885i
$532$	−141.381	+	156.625i	−0.265753	+	0.294408i
$533$		−	15.7615i		−	0.0295712i
$534$	−509.441	−	450.941i	−0.954009	−	0.844459i
$535$	−78.6781	+	136.274i	−0.147062	+	0.254719i
$536$	53.8285	+	31.0779i	0.100426	+	0.0579812i
$537$	480.353	−	542.667i	0.894511	−	1.01055i
$538$	−493.260			−0.916841
$539$	−360.702	+	804.728i	−0.669207	+	1.49300i
$540$	−273.332	−	188.156i	−0.506170	−	0.348438i
$541$	−464.758	−	804.984i	−0.859072	−	1.48796i	−0.872815	−	0.488050i	$-0.837708\pi$
$541$	−464.758	−	804.984i	−0.859072	−	1.48796i	0.0137436	−	0.999906i	$-0.495625\pi$
$542$	−94.3324	−	54.4628i	−0.174045	−	0.100485i
$543$	11.9208	−	58.5182i	0.0219537	−	0.107768i
$544$	−17.3808	−	30.1045i	−0.0319501	−	0.0553391i
$545$			292.622i			0.536922i
$546$	−37.5828	−	16.4085i	−0.0688330	−	0.0300522i
$547$	−905.754			−1.65586			−0.827929	−	0.560833i	$-0.810481\pi$
$547$	−905.754			−1.65586			−0.827929	+	0.560833i	$0.810481\pi$
$548$	102.906	−	59.4126i	0.187784	−	0.108417i
$549$	−78.3907	−	641.080i	−0.142788	−	1.16772i
$550$	−162.405	+	281.294i	−0.295283	+	0.511444i
$551$	−248.304	+	143.359i	−0.450643	+	0.260179i
$552$	213.118	−	71.2493i	0.386083	−	0.129075i
$553$	634.805	+	135.762i	1.14793	+	0.245501i
$554$			10.3025i			0.0185966i
$555$	−12.2189	+	13.8041i	−0.0220161	+	0.0248722i
$556$	−59.6658	+	103.344i	−0.107313	+	0.185871i
$557$	−366.706	−	211.718i	−0.658358	−	0.380103i	0.133293	−	0.991077i	$-0.457445\pi$
$557$	−366.706	−	211.718i	−0.658358	−	0.380103i	−0.791651	+	0.610973i	$0.790778\pi$
$558$	91.8734	−	216.141i	0.164648	−	0.387349i
$559$	74.7617			0.133742
$560$	163.707	−	52.9652i	0.292333	−	0.0945808i
$561$	314.665	−	105.198i	0.560899	−	0.187519i
$562$	118.120	+	204.591i	0.210179	+	0.364040i
$563$	560.655	+	323.694i	0.995834	+	0.574945i	0.907013	−	0.421102i	$-0.138357\pi$
$563$	560.655	+	323.694i	0.995834	+	0.574945i	0.0888212	+	0.996048i	$0.471690\pi$
$564$	−315.655	−	64.3027i	−0.559673	−	0.114012i
$565$	−308.403	−	534.169i	−0.545846	−	0.945433i
$566$		−	171.756i		−	0.303455i
$567$	−566.698	+	18.5150i	−0.999467	+	0.0326544i
$568$	−309.523			−0.544935
$569$	−566.134	+	326.858i	−0.994964	+	0.574443i	−0.906754	−	0.421659i	$-0.861448\pi$
$569$	−566.134	+	326.858i	−0.994964	+	0.574443i	−0.0882095	+	0.996102i	$0.528114\pi$
$570$	−78.4328	+	385.019i	−0.137601	+	0.675471i
$571$	288.916	−	500.418i	0.505983	−	0.876389i	−0.493993	−	0.869466i	$-0.664463\pi$
$571$	288.916	−	500.418i	0.505983	−	0.876389i	0.999976	−	0.00692274i	$-0.00220359\pi$
$572$	−43.0437	+	24.8513i	−0.0752512	+	0.0434463i
$573$	−94.5000	−	282.665i	−0.164921	−	0.493306i
$574$	110.499	+	23.6317i	0.192506	+	0.0411702i
$575$		−	337.962i		−	0.587760i
$576$	66.2623	+	28.1656i	0.115039	+	0.0488987i
$577$	466.259	−	807.584i	0.808075	−	1.39963i	−0.106121	−	0.994353i	$-0.533843\pi$
$577$	466.259	−	807.584i	0.808075	−	1.39963i	0.914196	−	0.405273i	$-0.132824\pi$
$578$	−307.703	−	177.652i	−0.532358	−	0.307357i
$579$	864.522	+	765.248i	1.49313	+	1.32167i
$580$	233.808			0.403118
$581$	185.463	+	167.412i	0.319214	+	0.288145i
$582$	159.951	+	478.438i	0.274830	+	0.822059i
$583$	368.602	+	638.437i	0.632250	+	1.09509i
$584$	−34.8767	−	20.1360i	−0.0597203	−	0.0344795i
$585$	−75.8029	+	9.26912i	−0.129578	+	0.0158446i
$586$	337.710	+	584.931i	0.576297	+	0.998175i
$587$		−	170.852i		−	0.291060i	−0.989354	−	0.145530i	$-0.953511\pi$
$587$		−	170.852i		−	0.291060i	0.989354	−	0.145530i	$-0.0464888\pi$
$588$	171.384	−	238.880i	0.291470	−	0.406258i
$589$	−278.096			−0.472149
$590$	410.666	−	237.098i	0.696043	−	0.401861i
$591$	−310.507	−	63.2539i	−0.525393	−	0.107029i
$592$	2.00000	−	3.46410i	0.00337838	−	0.00585152i
$593$	132.575	−	76.5421i	0.223566	−	0.129076i	−0.384034	−	0.923319i	$-0.625466\pi$
$593$	132.575	−	76.5421i	0.223566	−	0.129076i	0.607600	+	0.794243i	$0.292132\pi$
$594$	−389.661	+	566.054i	−0.655995	+	0.952952i
$595$	−177.118	+	196.215i	−0.297677	+	0.329774i
$596$			2.92919i			0.00491474i
$597$	−92.5814	−	81.9502i	−0.155078	−	0.137270i
$598$	25.8575	−	44.7865i	0.0432400	−	0.0748938i
$599$	624.046	+	360.293i	1.04181	+	0.601491i	0.920347	−	0.391104i	$-0.127907\pi$
$599$	624.046	+	360.293i	1.04181	+	0.601491i	0.121467	+	0.992595i	$0.461240\pi$
$600$	71.7729	−	81.0838i	0.119621	−	0.135140i
$601$	−110.422			−0.183731			−0.0918656	−	0.995771i	$-0.529283\pi$
$601$	−110.422			−0.183731			−0.0918656	+	0.995771i	$0.529283\pi$
$602$	−112.093	+	524.131i	−0.186201	+	0.870650i
$603$	158.012	−	118.947i	0.262044	−	0.197260i
$604$	171.975	+	297.870i	0.284727	+	0.493162i
$605$	1079.81	+	623.428i	1.78481	+	1.03046i
$606$	27.0182	−	132.630i	0.0445845	−	0.218861i
$607$	−179.084	−	310.182i	−0.295031	−	0.511008i	0.679961	−	0.733248i	$-0.261996\pi$
$607$	−179.084	−	310.182i	−0.295031	−	0.511008i	−0.974992	+	0.222240i	$0.928663\pi$
$608$		−	85.2558i		−	0.140223i
$609$	321.502	−	237.154i	0.527918	−	0.389415i
$610$	623.639			1.02236
$611$	−64.2041	+	37.0682i	−0.105080	+	0.0606682i
$612$	−109.793	+	13.4254i	−0.179401	+	0.0219369i
$613$	−79.4754	+	137.655i	−0.129650	+	0.224560i	−0.923541	−	0.383500i	$-0.874719\pi$
$613$	−79.4754	+	137.655i	−0.129650	+	0.224560i	0.793891	+	0.608060i	$0.208052\pi$
$614$	−151.110	+	87.2434i	−0.246108	+	0.142090i
$615$	199.570	−	66.7199i	0.324504	−	0.108488i
$616$	−109.688	−	339.027i	−0.178065	−	0.550368i
$617$		−	382.473i		−	0.619892i	−0.950754	−	0.309946i	$-0.899689\pi$
$617$		−	382.473i		−	0.619892i	0.950754	−	0.309946i	$-0.100311\pi$
$618$	527.256	−	595.655i	0.853165	−	0.963844i
$619$	−512.128	+	887.031i	−0.827347	+	1.43301i	0.0727657	+	0.997349i	$0.476817\pi$
$619$	−512.128	+	887.031i	−0.827347	+	1.43301i	−0.900112	+	0.435658i	$0.856516\pi$
$620$	196.395	+	113.389i	0.316767	+	0.182885i
$621$	56.6331	−	712.784i	0.0911966	−	1.14780i
$622$	−563.403			−0.905792
$623$	234.758	−	1097.70i	0.376819	−	1.76196i
$624$	15.7150	−	5.25382i	0.0251843	−	0.00841958i
$625$	390.591	+	676.523i	0.624945	+	1.08244i
$626$	65.0320	+	37.5462i	0.103885	+	0.0599780i
$627$	797.351	+	162.430i	1.27169	+	0.259058i
$628$	−1.00000	−	1.73205i	−0.00159236	−	0.00275804i
$629$			6.14505i			0.00976956i
$630$	48.6710	−	545.329i	0.0772556	−	0.865601i
$631$	−75.8524			−0.120210			−0.0601049	−	0.998192i	$-0.519144\pi$
$631$	−75.8524			−0.120210			−0.0601049	+	0.998192i	$0.519144\pi$
$632$	−227.158	+	131.150i	−0.359428	+	0.207516i
$633$	−149.624	+	734.487i	−0.236372	+	1.16033i
$634$	−261.107	+	452.250i	−0.411840	+	0.713329i
$635$	−216.166	+	124.803i	−0.340419	+	0.196541i
$636$	−77.9262	−	233.090i	−0.122525	−	0.366493i
$637$	−6.90416	−	67.3076i	−0.0108386	−	0.105663i
$638$		−	484.203i		−	0.758939i
$639$	−385.281	+	906.411i	−0.602944	+	1.41848i
$640$	−34.7617	+	60.2090i	−0.0543151	+	0.0940765i
$641$	−31.8631	−	18.3962i	−0.0497084	−	0.0286992i	0.474940	−	0.880018i	$-0.342470\pi$
$641$	−31.8631	−	18.3962i	−0.0497084	−	0.0286992i	−0.524648	+	0.851319i	$0.675803\pi$
$642$	−81.3495	−	72.0081i	−0.126713	−	0.112162i
$643$	−105.277			−0.163728			−0.0818642	−	0.996643i	$-0.526087\pi$
$643$	−105.277			−0.163728			−0.0818642	+	0.996643i	$0.526087\pi$
$644$	275.215	+	248.429i	0.427353	+	0.385759i
$645$	316.474	+	946.625i	0.490658	+	1.46764i
$646$	65.4877	+	113.428i	0.101374	+	0.175585i
$647$	−814.321	−	470.149i	−1.25861	−	0.726659i	−0.285807	−	0.958287i	$-0.592261\pi$
$647$	−814.321	−	470.149i	−1.25861	−	0.726659i	−0.972804	+	0.231628i	$0.925595\pi$
$648$	164.961	−	158.984i	0.254569	−	0.245345i
$649$	−491.016	−	850.464i	−0.756573	−	1.31042i
$650$		−	24.9209i		−	0.0383398i
$651$	385.068	−	43.2882i	0.591503	−	0.0664949i
$652$	499.852			0.766645
$653$	987.877	−	570.351i	1.51283	−	0.873432i	0.512941	−	0.858424i	$-0.328556\pi$
$653$	987.877	−	570.351i	1.51283	−	0.873432i	0.999887	−	0.0150077i	$-0.00477727\pi$
$654$	−197.965	−	40.3278i	−0.302699	−	0.0616633i
$655$	198.273	−	343.418i	0.302706	−	0.524303i
$656$	−39.5409	+	22.8289i	−0.0602757	+	0.0348002i
$657$	−102.380	+	77.0686i	−0.155829	+	0.117304i
$658$	−163.611	−	505.693i	−0.248648	−	0.768530i
$659$			69.5711i			0.105571i	0.998606	+	0.0527854i	$0.0168099\pi$
$659$			69.5711i			0.105571i	−0.998606	+	0.0527854i	$0.983190\pi$
$660$	−496.873	−	439.817i	−0.752838	−	0.666389i
$661$	271.399	−	470.077i	0.410589	−	0.711160i	−0.584366	−	0.811491i	$-0.698657\pi$
$661$	271.399	−	470.077i	0.410589	−	0.711160i	0.994954	+	0.100330i	$0.0319899\pi$
$662$	167.179	+	96.5210i	0.252537	+	0.145802i
$663$	−16.8723	+	19.0611i	−0.0254484	+	0.0287498i
$664$	−100.953			−0.152038
$665$	−616.815	+	199.563i	−0.927542	+	0.300095i
$666$	−7.65479	−	10.1688i	−0.0114937	−	0.0152684i
$667$	251.904	+	436.311i	0.377667	+	0.654139i
$668$	46.6006	+	26.9048i	0.0697613	+	0.0402767i
$669$	−102.058	+	500.993i	−0.152553	+	0.748868i
$670$	95.4877	+	165.390i	0.142519	+	0.246850i
$671$		−	1291.52i		−	1.92477i
$672$	13.2709	+	118.050i	0.0197483	+	0.175670i
$673$	−419.858			−0.623860			−0.311930	−	0.950105i	$-0.600975\pi$
$673$	−419.858			−0.623860			−0.311930	+	0.950105i	$0.600975\pi$
$674$	192.751	−	111.285i	0.285981	−	0.165111i
$675$	−148.107	−	311.110i	−0.219417	−	0.460904i
$676$	−167.093	+	289.414i	−0.247179	+	0.428127i
$677$	−665.772	+	384.384i	−0.983415	+	0.567775i	−0.903299	−	0.429011i	$-0.858862\pi$
$677$	−665.772	+	384.384i	−0.983415	+	0.567775i	−0.0801156	+	0.996786i	$0.525529\pi$
$678$	403.880	−	135.024i	0.595693	−	0.199151i
$679$	−557.710	+	617.844i	−0.821370	+	0.909932i
$680$		−	106.806i		−	0.157068i
$681$	−682.219	+	770.722i	−1.00179	+	1.13175i
$682$	234.822	−	406.723i	0.344314	−	0.596369i
$683$	248.489	+	143.465i	0.363820	+	0.210052i	0.670755	−	0.741679i	$-0.265970\pi$
$683$	248.489	+	143.465i	0.363820	+	0.210052i	−0.306935	+	0.951730i	$0.599303\pi$
$684$	−249.664	−	106.123i	−0.365006	−	0.155150i
$685$	365.093			0.532983
$686$	482.224	+	52.5136i	0.702951	+	0.0765505i
$687$	−767.654	+	256.641i	−1.11740	+	0.373567i
$688$	−108.285	−	187.555i	−0.157391	−	0.272609i
$689$	−48.9836	−	28.2807i	−0.0710937	−	0.0410460i
$690$	676.540	+	137.819i	0.980493	+	0.199738i
$691$	−451.464	−	781.959i	−0.653349	−	1.13163i	−0.982305	−	0.187289i	$-0.940030\pi$
$691$	−451.464	−	781.959i	−0.653349	−	1.13163i	0.328956	−	0.944345i	$-0.393303\pi$
$692$		−	182.600i		−	0.263873i
$693$	−1129.34	−	100.795i	−1.62964	−	0.145447i
$694$	378.494			0.545380
$695$	−317.528	+	183.325i	−0.456875	+	0.263777i
$696$	−32.2223	+	158.176i	−0.0462965	+	0.227265i
$697$	35.0712	−	60.7452i	0.0503174	−	0.0871523i
$698$	−232.990	+	134.517i	−0.333797	+	0.192718i
$699$	298.651	+	893.313i	0.427255	+	1.27799i
$700$	174.712	+	37.3647i	0.249589	+	0.0533781i
$701$		−	671.817i		−	0.958370i	−0.877714	−	0.479185i	$-0.840932\pi$
$701$		−	671.817i		−	0.958370i	0.877714	−	0.479185i	$-0.159068\pi$
$702$	4.17604	−	52.5597i	0.00594878	−	0.0748714i
$703$	−7.53562	+	13.0521i	−0.0107192	+	0.0185663i
$704$	124.689	+	71.9894i	0.177115	+	0.102258i
$705$	−741.137	−	656.032i	−1.05126	−	0.930541i
$706$	149.359			0.211556
$707$	212.478	−	68.7447i	0.300535	−	0.0972344i
$708$	103.806	+	310.500i	0.146618	+	0.438559i
$709$	−368.640	−	638.503i	−0.519944	−	0.900569i	−0.999731	−	0.0231840i	$-0.992620\pi$
$709$	−368.640	−	638.503i	−0.519944	−	0.900569i	0.479788	−	0.877385i	$-0.340714\pi$
$710$	−823.606	−	475.509i	−1.16001	−	0.669731i
$711$	101.304	+	828.463i	0.142481	+	1.16521i
$712$	226.784	+	392.801i	0.318516	+	0.551687i
$713$			488.659i			0.685357i
$714$	−108.334	−	146.865i	−0.151729	−	0.205694i
$715$	−152.712			−0.213584
$716$	−418.420	+	241.575i	−0.584386	+	0.337395i
$717$	−175.493	−	35.7500i	−0.244761	−	0.0498606i
$718$	275.274	−	476.788i	0.383390	−	0.664051i
$719$	−998.376	+	576.413i	−1.38856	+	0.801686i	−0.993153	−	0.116819i	$-0.962730\pi$
$719$	−998.376	+	576.413i	−1.38856	+	0.801686i	−0.395409	+	0.918505i	$0.629397\pi$
$720$	133.047	+	176.742i	0.184787	+	0.245475i
$721$	1283.47	+	274.487i	1.78012	+	0.380704i
$722$		−	189.303i		−	0.262193i
$723$	694.769	+	614.988i	0.960953	+	0.850606i
$724$	−19.9067	+	34.4794i	−0.0274954	+	0.0476235i
$725$	210.253	+	121.390i	0.290004	+	0.167434i
$726$	−570.577	+	644.596i	−0.785918	+	0.887873i
$727$	−101.386			−0.139458			−0.0697290	−	0.997566i	$-0.522213\pi$
$727$	−101.386			−0.139458			−0.0697290	+	0.997566i	$0.522213\pi$
$728$	20.2940	+	18.3188i	0.0278764	+	0.0251632i
$729$	−260.233	−	680.970i	−0.356973	−	0.934115i
$730$	−61.8685	−	107.159i	−0.0847514	−	0.146794i
$731$	288.134	+	166.354i	0.394164	+	0.227571i
$732$	−85.9469	+	421.905i	−0.117414	+	0.576373i
$733$	710.166	+	1230.04i	0.968848	+	1.67809i	0.698900	+	0.715220i	$0.253673\pi$
$733$	710.166	+	1230.04i	0.968848	+	1.67809i	0.269949	+	0.962875i	$0.412993\pi$
$734$			519.722i			0.708068i
$735$	823.016	−	372.340i	1.11975	−	0.506585i
$736$	−149.808			−0.203544
$737$	342.512	−	197.749i	0.464738	−	0.268317i
$738$	17.6337	+	144.208i	0.0238939	+	0.195404i
$739$	323.059	−	559.555i	0.437157	−	0.757178i	−0.560312	−	0.828282i	$-0.689319\pi$
$739$	323.059	−	559.555i	0.437157	−	0.757178i	0.997469	+	0.0711036i	$0.0226521\pi$
$740$	10.6435	−	6.14505i	0.0143832	−	0.00830412i
$741$	−59.2112	+	19.7954i	−0.0799072	+	0.0267144i
$742$	271.710	−	301.007i	0.366186	−	0.405669i
$743$		−	693.562i		−	0.933462i	−0.884399	−	0.466731i	$-0.845432\pi$
$743$		−	693.562i		−	0.933462i	0.884399	−	0.466731i	$-0.154568\pi$
$744$	−103.776	+	117.239i	−0.139484	+	0.157579i
$745$	−4.50000	+	7.79423i	−0.00604027	+	0.0104621i
$746$	−281.050	−	162.265i	−0.376743	−	0.217513i
$747$	−125.662	+	295.633i	−0.168223	+	0.395760i
$748$	−221.189			−0.295707
$749$	37.4872	−	175.285i	0.0500496	−	0.234026i
$750$	−302.606	+	101.167i	−0.403474	+	0.134889i
$751$	−662.651	−	1147.75i	−0.882358	−	1.52829i	−0.848712	−	0.528855i	$-0.822621\pi$
$751$	−662.651	−	1147.75i	−0.882358	−	1.52829i	−0.0336462	−	0.999434i	$-0.510712\pi$
$752$	185.987	+	107.379i	0.247323	+	0.142792i
$753$	−206.382	−	42.0424i	−0.274080	−	0.0558332i
$754$	18.5751	+	32.1729i	0.0246354	+	0.0426697i
$755$			1056.80i			1.39973i
$756$	362.219	+	108.082i	0.479125	+	0.142965i
$757$	999.091			1.31980			0.659901	−	0.751352i	$-0.270598\pi$
$757$	999.091			1.31980			0.659901	+	0.751352i	$0.270598\pi$
$758$	451.807	−	260.851i	0.596052	−	0.344131i
$759$	285.415	−	1401.07i	0.376041	−	1.84595i
$760$	130.975	−	226.856i	0.172336	−	0.298495i
$761$	1153.89	−	666.196i	1.51627	−	0.875422i	0.516458	−	0.856313i	$-0.327250\pi$
$761$	1153.89	−	666.196i	1.51627	−	0.875422i	0.999817	−	0.0191090i	$-0.00608295\pi$
$762$	−54.6412	−	163.441i	−0.0717076	−	0.214489i
$763$	−102.609	−	317.148i	−0.134482	−	0.415660i
$764$			198.695i			0.260072i
$765$	−312.772	−	132.948i	−0.408852	−	0.173788i
$766$	−433.198	+	750.320i	−0.565532	+	0.979530i
$767$	65.2512	+	37.6728i	0.0850733	+	0.0491171i
$768$	−35.9420	−	31.8147i	−0.0467994	−	0.0414254i
$769$	−1379.09			−1.79336			−0.896678	−	0.442683i	$-0.854027\pi$
$769$	−1379.09			−1.79336			−0.896678	+	0.442683i	$0.854027\pi$
$770$	228.967	−	1070.62i	0.297360	−	1.39042i
$771$	−66.5382	−	199.026i	−0.0863011	−	0.258140i
$772$	−384.852	−	666.584i	−0.498514	−	0.863451i
$773$	−1202.86	−	694.472i	−1.55609	−	0.898411i	−0.997625	−	0.0688859i	$-0.978056\pi$
$773$	−1202.86	−	694.472i	−1.55609	−	0.898411i	−0.558469	−	0.829525i	$-0.688611\pi$
$774$	−684.027	+	83.6422i	−0.883755	+	0.108065i
$775$	117.740	+	203.931i	0.151922	+	0.263137i
$776$		−	336.312i		−	0.433391i
$777$	8.40260	−	19.2457i	0.0108142	−	0.0247692i
$778$	372.022			0.478177
$779$	148.983	−	86.0151i	0.191248	−	0.110417i
$780$	49.8871	+	10.1626i	0.0639578	+	0.0130289i
$781$	−984.752	+	1705.64i	−1.26089	+	2.18392i
$782$	199.311	−	115.072i	0.254874	−	0.147152i
$783$	423.096	+	291.251i	0.540352	+	0.371968i
$784$	−158.855	+	114.809i	−0.202621	+	0.146440i
$785$		−	6.14505i		−	0.00782809i
$786$	205.005	+	181.464i	0.260820	+	0.230870i
$787$	−23.2235	+	40.2243i	−0.0295089	+	0.0511109i	−0.880403	−	0.474227i	$-0.842728\pi$
$787$	−23.2235	+	40.2243i	−0.0295089	+	0.0511109i	0.850894	+	0.525338i	$0.176061\pi$
$788$	182.953	+	105.628i	0.232174	+	0.134046i
$789$	260.412	−	294.194i	0.330053	−	0.372870i
$790$	−805.924			−1.02016
$791$	521.561	+	470.798i	0.659369	+	0.595193i
$792$	366.022	−	275.532i	0.462149	−	0.347894i
$793$	49.5454	+	85.8151i	0.0624784	+	0.108216i
$794$	738.924	+	426.618i	0.930635	+	0.537302i
$795$	150.734	−	739.940i	0.189603	−	0.930743i
$796$	41.2137	+	71.3843i	0.0517761	+	0.0896788i
$797$			422.335i			0.529906i	0.964261	+	0.264953i	$0.0853565\pi$
$797$			422.335i			0.529906i	−0.964261	+	0.264953i	$0.914644\pi$
$798$	−50.0021	−	444.791i	−0.0626593	−	0.557383i
$799$	−329.926			−0.412924
$800$	−62.5191	+	36.0954i	−0.0781489	+	0.0451193i
$801$	1432.57	−	175.174i	1.78848	−	0.218694i
$802$	−482.746	+	836.140i	−0.601927	+	1.04257i
$803$	−221.921	+	128.126i	−0.276365	+	0.159559i
$804$	−125.049	+	41.8063i	−0.155534	+	0.0519978i
$805$	350.665	+	1083.84i	0.435608	+	1.34639i
$806$			36.0330i			0.0447060i
$807$	693.536	−	783.507i	0.859401	−	0.970889i
$808$	−45.1179	+	78.1465i	−0.0558390	+	0.0967160i
$809$	1077.00	+	621.805i	1.33127	+	0.768609i	0.985494	−	0.169708i	$-0.0542825\pi$
$809$	1077.00	+	621.805i	1.33127	+	0.768609i	0.345776	+	0.938317i	$0.387616\pi$
$810$	683.183	−	169.614i	0.843436	−	0.209400i
$811$	1110.32			1.36907			0.684537	−	0.728978i	$-0.260004\pi$
$811$	1110.32			1.36907			0.684537	+	0.728978i	$0.260004\pi$
$812$	−253.405	+	81.9860i	−0.312075	+	0.100968i
$813$	219.144	−	73.2638i	0.269550	−	0.0901154i
$814$	−12.7260	−	22.0421i	−0.0156340	−	0.0270788i
$815$	1330.05	+	767.905i	1.63196	+	0.942214i
$816$	72.2566	+	14.7195i	0.0885497	+	0.0180386i
$817$	407.997	+	706.672i	0.499385	+	0.864960i
$818$			869.130i			1.06251i
$819$	78.9060	−	36.6267i	0.0963444	−	0.0447212i
$820$	−140.285			−0.171079
$821$	−1129.90	+	652.348i	−1.37625	+	0.794577i	−0.991706	−	0.128530i	$-0.958974\pi$
$821$	−1129.90	+	652.348i	−1.37625	+	0.794577i	−0.384542	+	0.923107i	$0.625641\pi$
$822$	−50.3154	+	246.993i	−0.0612110	+	0.300479i
$823$	516.010	−	893.755i	0.626986	−	1.08597i	−0.361167	−	0.932501i	$-0.617622\pi$
$823$	516.010	−	893.755i	0.626986	−	1.08597i	0.988153	−	0.153471i	$-0.0490452\pi$
$824$	−459.276	+	265.163i	−0.557374	+	0.321800i
$825$	−218.469	−	653.476i	−0.264811	−	0.792092i
$826$	−361.946	+	400.972i	−0.438191	+	0.485438i
$827$		−	1109.55i		−	1.34166i	−0.741613	−	0.670828i	$-0.765939\pi$
$827$		−	1109.55i		−	1.34166i	0.741613	−	0.670828i	$-0.234061\pi$
$828$	−186.475	+	438.700i	−0.225211	+	0.529831i
$829$	365.615	−	633.264i	0.441032	−	0.763889i	−0.556735	−	0.830690i	$-0.687946\pi$
$829$	365.615	−	633.264i	0.441032	−	0.763889i	0.997766	+	0.0668010i	$0.0212793\pi$
$830$	−268.625	−	155.091i	−0.323645	−	0.186856i
$831$	−16.3648	−	14.4856i	−0.0196929	−	0.0174315i
$832$	−11.0467			−0.0132772
$833$	123.159	−	274.768i	0.147850	−	0.329854i
$834$	−80.2629	−	240.079i	−0.0962385	−	0.287865i
$835$	82.6658	+	143.181i	0.0990010	+	0.171475i
$836$	−469.805	−	271.242i	−0.561968	−	0.324453i
$837$	214.147	+	449.834i	0.255851	+	0.537436i
$838$	−548.712	−	950.398i	−0.654788	−	1.13413i
$839$			636.854i			0.759064i	0.925179	+	0.379532i	$0.123915\pi$
$839$			636.854i			0.759064i	−0.925179	+	0.379532i	$0.876085\pi$
$840$	−146.044	+	334.506i	−0.173862	+	0.398221i
$841$	479.083			0.569659
$842$	−197.422	+	113.982i	−0.234468	+	0.135370i
$843$	−491.057	−	100.034i	−0.582511	−	0.118664i
$844$	249.858	−	432.766i	0.296040	−	0.512756i
$845$	−889.232	+	513.399i	−1.05235	+	0.607572i
$846$	545.959	−	410.984i	0.645342	−	0.485796i
$847$	−1388.92	−	297.040i	−1.63981	−	0.350697i
$848$			163.847i			0.193216i
$849$	272.821	+	241.493i	0.321344	+	0.284444i
$850$	55.4521	−	96.0458i	0.0652377	−	0.112995i
$851$	22.9346	+	13.2413i	0.0269502	+	0.0155597i
$852$	435.198	−	491.655i	0.510795	−	0.577059i
$853$	620.427			0.727348			0.363674	−	0.931526i	$-0.381522\pi$
$853$	620.427			0.727348			0.363674	+	0.931526i	$0.381522\pi$
$854$	−675.909	+	218.682i	−0.791462	+	0.256068i
$855$	−501.295	−	665.930i	−0.586310	−	0.778866i
$856$	36.2137	+	62.7240i	0.0423058	+	0.0732757i
$857$	−1069.50	−	617.473i	−1.24795	−	0.720506i	−0.277252	−	0.960797i	$-0.589424\pi$
$857$	−1069.50	−	617.473i	−1.24795	−	0.720506i	−0.970701	+	0.240292i	$0.922757\pi$
$858$	21.0461	−	103.313i	0.0245293	−	0.120412i
$859$	89.1031	+	154.331i	0.103729	+	0.179664i	0.913218	−	0.407471i	$-0.133589\pi$
$859$	89.1031	+	154.331i	0.103729	+	0.179664i	−0.809489	+	0.587135i	$0.800256\pi$
$860$		−	665.417i		−	0.773741i
$861$	−192.901	+	142.292i	−0.224043	+	0.165264i
$862$	676.356			0.784636
$863$	−94.5869	+	54.6097i	−0.109602	+	0.0632790i	−0.553799	−	0.832650i	$-0.686822\pi$
$863$	−94.5869	+	54.6097i	−0.109602	+	0.0632790i	0.444197	+	0.895929i	$0.353489\pi$
$864$	−137.905	+	65.6512i	−0.159613	+	0.0759851i
$865$	280.522	−	485.878i	0.324303	−	0.561709i
$866$	−119.495	+	68.9906i	−0.137985	+	0.0796658i
$867$	714.825	−	238.979i	0.824481	−	0.275639i
$868$	−252.617	−	54.0256i	−0.291033	−	0.0622415i
$869$			1669.02i			1.92062i
$870$	−328.740	+	371.387i	−0.377862	+	0.426882i
$871$	−15.1722	+	26.2790i	−0.0174192	+	0.0301710i
$872$	116.643	+	67.3437i	0.133765	+	0.0772290i
$873$	−984.858	−	418.626i	−1.12813	−	0.479526i
$874$	564.450			0.645823
$875$	−390.778	−	352.744i	−0.446603	−	0.403136i
$876$	81.0221	−	27.0872i	0.0924909	−	0.0309214i
$877$	−1.09204	−	1.89146i	−0.00124519	−	0.00215674i	0.865402	−	0.501078i	$-0.167063\pi$
$877$	−1.09204	−	1.89146i	−0.00124519	−	0.00215674i	−0.866647	+	0.498921i	$0.833730\pi$
$878$	289.178	+	166.957i	0.329360	+	0.190156i
$879$	−1403.95	−	286.000i	−1.59721	−	0.325370i
$880$	221.189	+	383.111i	0.251351	+	0.435353i
$881$		−	360.009i		−	0.408637i	−0.978904	−	0.204318i	$-0.934502\pi$
$881$		−	360.009i		−	0.408637i	0.978904	−	0.204318i	$-0.0654978\pi$
$882$	138.472	+	608.102i	0.156997	+	0.689458i
$883$	108.718			0.123123			0.0615615	−	0.998103i	$-0.480392\pi$
$883$	108.718			0.123123			0.0615615	+	0.998103i	$0.480392\pi$
$884$	14.6969	−	8.48528i	0.0166255	−	0.00959873i
$885$	−200.794	+	985.677i	−0.226886	+	1.11376i
$886$	326.650	−	565.774i	0.368679	−	0.638571i
$887$	920.522	−	531.464i	1.03779	−	0.599170i	0.118585	−	0.992944i	$-0.462164\pi$
$887$	920.522	−	531.464i	1.03779	−	0.599170i	0.919207	+	0.393774i	$0.128831\pi$
$888$	2.69042	+	8.04746i	0.00302975	+	0.00906246i
$889$	190.521	−	211.063i	0.214309	−	0.237417i
$890$			1393.60i			1.56584i
$891$	−351.261	−	1414.83i	−0.394232	−	1.58792i
$892$	170.427	−	295.189i	0.191062	−	0.330929i
$893$	−700.763	−	404.586i	−0.784729	−	0.453063i
$894$	−4.65279	−	4.11851i	−0.00520447	−	0.00460683i
$895$	−1484.49			−1.65865
$896$	16.5626	−	77.4447i	0.0184851	−	0.0864338i
$897$	34.7837	+	104.044i	0.0387778	+	0.115991i
$898$	−209.978	−	363.692i	−0.233828	−	0.405003i
$899$	−304.005	−	175.517i	−0.338159	−	0.195236i
$900$	27.8811	+	228.012i	0.0309790	+	0.253346i
$901$	−125.856	−	217.989i	−0.139685	−	0.241942i
$902$			290.522i			0.322086i
$903$	−674.938	−	914.992i	−0.747439	−	1.01328i
$904$	−283.902			−0.314050
$905$	−105.939	+	61.1638i	−0.117060	+	0.0675844i
$906$	−714.946	−	145.643i	−0.789124	−	0.160754i
$907$	−421.229	+	729.589i	−0.464420	+	0.804398i	−0.999175	−	0.0406085i	$-0.987070\pi$
$907$	−421.229	+	729.589i	−0.464420	+	0.804398i	0.534756	+	0.845007i	$0.320404\pi$
$908$	594.260	−	343.096i	0.654471	−	0.377859i
$909$	172.684	+	229.397i	0.189971	+	0.252362i
$910$	25.8575	+	79.9211i	0.0284148	+	0.0878254i
$911$			579.417i			0.636023i	0.948087	+	0.318012i	$0.103015\pi$
$911$			579.417i			0.636023i	−0.948087	+	0.318012i	$0.896985\pi$
$912$	135.423	+	119.872i	0.148490	+	0.131438i
$913$	−321.184	+	556.307i	−0.351790	+	0.609318i
$914$	444.697	+	256.746i	0.486539	+	0.280903i
$915$	−876.852	+	990.603i	−0.958308	+	1.08263i
$916$	539.612			0.589096
$917$	−94.4695	+	441.727i	−0.103020	+	0.481709i
$918$	133.047	−	193.275i	0.144931	−	0.210539i
$919$	579.865	+	1004.36i	0.630974	+	1.09288i	0.987353	+	0.158537i	$0.0506777\pi$
$919$	579.865	+	1004.36i	0.630974	+	1.09288i	−0.356379	+	0.934341i	$0.615989\pi$
$920$	−398.623	−	230.145i	−0.433286	−	0.250158i
$921$	73.8848	−	362.693i	0.0802224	−	0.393804i
$922$	−435.973	−	755.127i	−0.472856	−	0.819010i
$923$		−	151.109i		−	0.163715i
$924$	692.742	+	302.449i	0.749721	+	0.327326i
$925$	12.7617			0.0137964
$926$	431.170	−	248.936i	0.465627	−	0.268830i
$927$	204.819	+	1675.01i	0.220948	+	1.80692i
$928$	53.8083	−	93.1987i	0.0579831	−	0.100430i
$929$	753.773	−	435.191i	0.811381	−	0.468451i	−0.0360543	−	0.999350i	$-0.511479\pi$
$929$	753.773	−	435.191i	0.811381	−	0.468451i	0.847435	+	0.530899i	$0.178146\pi$
$930$	−456.247	+	152.532i	−0.490588	+	0.164013i
$931$	598.536	−	432.579i	0.642895	−	0.464639i
$932$		−	627.942i		−	0.673758i
$933$	792.158	−	894.923i	0.849044	−	0.959189i
$934$	367.198	−	636.005i	0.393145	−	0.680947i
$935$	−588.559	−	339.805i	−0.629475	−	0.363427i
$936$	−13.7504	+	32.3491i	−0.0146906	+	0.0345610i
$937$	−1339.70			−1.42978			−0.714888	−	0.699239i	$-0.753522\pi$
$937$	−1339.70			−1.42978			−0.714888	+	0.699239i	$0.753522\pi$
$938$	−161.486	−	145.768i	−0.172159	−	0.155403i
$939$	−151.076	+	50.5075i	−0.160890	+	0.0537886i
$940$	329.926	+	571.449i	0.350985	+	0.607924i
$941$	438.385	+	253.102i	0.465871	+	0.268971i	0.714510	−	0.699625i	$-0.246650\pi$
$941$	438.385	+	253.102i	0.465871	+	0.268971i	−0.248638	+	0.968596i	$0.579983\pi$
$942$	4.15726	+	0.846882i	0.00441322	+	0.000899025i
$943$	−151.142	−	261.786i	−0.160278	−	0.277610i
$944$		−	218.261i		−	0.231209i
$945$	797.781	+	844.056i	0.844213	+	0.893181i
$946$	−1378.04			−1.45670
$947$	−622.268	+	359.267i	−0.657094	+	0.379373i	−0.791169	−	0.611598i	$-0.790527\pi$
$947$	−622.268	+	359.267i	−0.657094	+	0.379373i	0.134075	+	0.990971i	$0.457194\pi$
$948$	111.069	−	545.224i	0.117161	−	0.575131i
$949$	9.83037	−	17.0267i	0.0103587	−	0.0179417i
$950$	235.560	−	136.001i	0.247958	−	0.143159i
$951$	−351.243	−	1050.62i	−0.369341	−	1.10476i
$952$	37.4521	+	115.758i	0.0393404	+	0.121595i
$953$			1620.84i			1.70078i	0.526152	+	0.850391i	$0.323634\pi$
$953$			1620.84i			1.70078i	−0.526152	+	0.850391i	$0.676366\pi$
$954$	479.812	+	203.950i	0.502947	+	0.213784i
$955$	−305.248	+	528.705i	−0.319632	+	0.553618i
$956$	103.402	+	59.6992i	0.108161	+	0.0624469i
$957$	769.120	+	680.802i	0.803679	+	0.711392i
$958$	336.980			0.351754
$959$	−395.693	+	128.022i	−0.412610	+	0.133495i
$960$	−46.7617	−	139.872i	−0.0487101	−	0.145700i
$961$	310.260	+	537.387i	0.322852	+	0.559195i
$962$	1.69117	+	0.976395i	0.00175797	+	0.00101496i
$963$	228.759	−	27.9724i	0.237548	−	0.0290472i
$964$	−309.285	−	535.697i	−0.320835	−	0.555703i
$965$		−	2364.94i		−	2.45071i
$966$	−781.571	+	87.8618i	−0.809079	+	0.0909542i
$967$	−713.562			−0.737914			−0.368957	−	0.929447i	$-0.620285\pi$
$967$	−713.562			−0.737914			−0.368957	+	0.929447i	$0.620285\pi$
$968$	497.012	−	286.950i	0.513442	−	0.296436i
$969$	−272.249	−	55.4603i	−0.280959	−	0.0572346i
$970$	516.663	−	894.887i	0.532643	−	0.922564i
$971$	792.718	−	457.676i	0.816394	−	0.471345i	−0.0327775	−	0.999463i	$-0.510435\pi$
$971$	792.718	−	457.676i	0.816394	−	0.471345i	0.849171	+	0.528117i	$0.177102\pi$
$972$	20.5946	+	485.563i	0.0211878	+	0.499551i
$973$	279.858	−	310.033i	0.287623	−	0.318636i
$974$		−	422.540i		−	0.433820i
$975$	39.5849	+	35.0393i	0.0405999	+	0.0359378i
$976$	143.523	−	248.590i	0.147053	−	0.254703i
$977$	−487.838	−	281.653i	−0.499322	−	0.288284i	0.229111	−	0.973400i	$-0.426418\pi$
$977$	−487.838	−	281.653i	−0.499322	−	0.288284i	−0.728434	+	0.685116i	$0.759751\pi$
$978$	−702.805	+	793.978i	−0.718614	+	0.811839i
$979$	2886.06			2.94797
$980$	−599.072	+	61.4505i	−0.611298	+	0.0627046i
$981$	342.402	−	257.751i	0.349033	−	0.262743i
$982$	335.211	+	580.603i	0.341356	+	0.591245i
$983$	604.195	+	348.832i	0.614644	+	0.354865i	0.774781	−	0.632230i	$-0.217860\pi$
$983$	604.195	+	348.832i	0.614644	+	0.354865i	−0.160137	+	0.987095i	$0.551194\pi$
$984$	19.3334	−	94.9058i	0.0196478	−	0.0964489i
$985$	324.545	+	562.129i	0.329488	+	0.570689i
$986$			165.327i			0.167675i
$987$	1033.30	+	451.133i	1.04691	+	0.457075i
$988$	41.6217			0.0421272
$989$	1241.74	−	716.918i	1.25555	−	0.724891i
$990$	1397.23	−	170.852i	1.41135	−	0.172578i
$991$	42.3931	−	73.4271i	0.0427781	−	0.0740939i	−0.843844	−	0.536589i	$-0.819712\pi$
$991$	42.3931	−	73.4271i	0.0427781	−	0.0740939i	0.886622	+	0.462495i	$0.153046\pi$
$992$	90.3964	−	52.1904i	0.0911254	−	0.0526113i
$993$	−388.374	+	129.841i	−0.391112	+	0.130756i
$994$	1059.38	+	226.562i	1.06577	+	0.227930i
$995$			253.261i			0.254533i
$996$	141.943	−	160.357i	0.142513	−	0.161001i
$997$	455.645	−	789.200i	0.457016	−	0.791575i	−0.541786	−	0.840517i	$-0.682252\pi$
$997$	455.645	−	789.200i	0.457016	−	0.791575i	0.998802	+	0.0489417i	$0.0155848\pi$
$998$	−586.445	−	338.584i	−0.587620	−	0.339263i
$999$	26.9152	+	2.13850i	0.0269421	+	0.00214064i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	42.3.h.b.11.4	yes	8
3.2	odd	2	inner	42.3.h.b.11.1	✓	8
4.3	odd	2		336.3.bn.g.305.2		8
7.2	even	3	inner	42.3.h.b.23.1	yes	8
7.3	odd	6		294.3.b.e.197.3		4
7.4	even	3		294.3.b.i.197.4		4
7.5	odd	6		294.3.h.h.275.2		8
7.6	odd	2		294.3.h.h.263.3		8
12.11	even	2		336.3.bn.g.305.4		8
21.2	odd	6	inner	42.3.h.b.23.4	yes	8
21.5	even	6		294.3.h.h.275.3		8
21.11	odd	6		294.3.b.i.197.2		4
21.17	even	6		294.3.b.e.197.1		4
21.20	even	2		294.3.h.h.263.2		8
28.23	odd	6		336.3.bn.g.65.4		8
84.23	even	6		336.3.bn.g.65.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.3.h.b.11.1	✓	8	3.2	odd	2	inner
42.3.h.b.11.4	yes	8	1.1	even	1	trivial
42.3.h.b.23.1	yes	8	7.2	even	3	inner
42.3.h.b.23.4	yes	8	21.2	odd	6	inner
294.3.b.e.197.1		4	21.17	even	6
294.3.b.e.197.3		4	7.3	odd	6
294.3.b.i.197.2		4	21.11	odd	6
294.3.b.i.197.4		4	7.4	even	3
294.3.h.h.263.2		8	21.20	even	2
294.3.h.h.263.3		8	7.6	odd	2
294.3.h.h.275.2		8	7.5	odd	6
294.3.h.h.275.3		8	21.5	even	6
336.3.bn.g.65.2		8	84.23	even	6
336.3.bn.g.65.4		8	28.23	odd	6
336.3.bn.g.305.2		8	4.3	odd	2
336.3.bn.g.305.4		8	12.11	even	2

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:	\( N \)	\(=\)	\( 42 = 2 \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	42.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.22474 - 0.707107i) q^{2} +(-0.598836 + 2.93963i) q^{3} +(1.00000 - 1.73205i) q^{4} +(5.32177 - 3.07253i) q^{5} +(1.34521 + 4.02373i) q^{6} +(-4.69042 + 5.19615i) q^{7} -2.82843i q^{8} +(-8.28279 - 3.52071i) q^{9} +O(q^{10})\)	\(q+(1.22474 - 0.707107i) q^{2} +(-0.598836 + 2.93963i) q^{3} +(1.00000 - 1.73205i) q^{4} +(5.32177 - 3.07253i) q^{5} +(1.34521 + 4.02373i) q^{6} +(-4.69042 + 5.19615i) q^{7} -2.82843i q^{8} +(-8.28279 - 3.52071i) q^{9} +(4.34521 - 7.52612i) q^{10} +(-15.5862 - 8.99867i) q^{11} +(4.49274 + 3.97684i) q^{12} +1.38083 q^{13} +(-2.07033 + 9.68059i) q^{14} +(5.84521 + 17.4840i) q^{15} +(-2.00000 - 3.46410i) q^{16} +(5.32177 + 3.07253i) q^{17} +(-12.6338 + 1.54485i) q^{18} +(7.53562 + 13.0521i) q^{19} -12.2901i q^{20} +(-12.4660 - 16.8997i) q^{21} -25.4521 q^{22} +(22.9346 - 13.2413i) q^{23} +(8.31452 + 1.69376i) q^{24} +(6.38083 - 11.0519i) q^{25} +(1.69117 - 0.976395i) q^{26} +(15.3096 - 22.2400i) q^{27} +(4.30958 + 13.3202i) q^{28} +19.0241i q^{29} +(19.5219 + 17.2802i) q^{30} +(-9.22604 + 15.9800i) q^{31} +(-4.89898 - 2.82843i) q^{32} +(35.7863 - 40.4287i) q^{33} +8.69042 q^{34} +(-8.99601 + 42.0642i) q^{35} +(-14.3808 + 10.8255i) q^{36} +(0.500000 + 0.866025i) q^{37} +(18.4584 + 10.6570i) q^{38} +(-0.826891 + 4.05913i) q^{39} +(-8.69042 - 15.0522i) q^{40} -11.4145i q^{41} +(-27.2175 - 11.8831i) q^{42} +54.1425 q^{43} +(-31.1723 + 17.9973i) q^{44} +(-54.8966 + 6.71271i) q^{45} +(18.7260 - 32.4345i) q^{46} +(-46.4967 + 26.8449i) q^{47} +(11.3808 - 3.80482i) q^{48} +(-5.00000 - 48.7442i) q^{49} -18.0477i q^{50} +(-12.2189 + 13.8041i) q^{51} +(1.38083 - 2.39167i) q^{52} +(-35.4740 - 20.4809i) q^{53} +(3.02430 - 38.0638i) q^{54} -110.595 q^{55} +(14.6969 + 13.2665i) q^{56} +(-42.8808 + 14.3359i) q^{57} +(13.4521 + 23.2997i) q^{58} +(47.2550 + 27.2827i) q^{59} +(36.1283 + 7.35975i) q^{60} +(35.8808 + 62.1474i) q^{61} +26.0952i q^{62} +(57.1439 - 26.5251i) q^{63} -8.00000 q^{64} +(7.34847 - 4.24264i) q^{65} +(15.2416 - 74.8196i) q^{66} +(-10.9877 + 19.0313i) q^{67} +(10.6435 - 6.14505i) q^{68} +(25.1904 + 75.3486i) q^{69} +(18.7260 + 57.8790i) q^{70} -109.433i q^{71} +(-9.95806 + 23.4273i) q^{72} +(7.11917 - 12.3308i) q^{73} +(1.22474 + 0.707107i) q^{74} +(28.6674 + 25.3755i) q^{75} +30.1425 q^{76} +(119.864 - 38.7805i) q^{77} +(1.85751 + 5.55610i) q^{78} +(-46.3685 - 80.3127i) q^{79} +(-21.2871 - 12.2901i) q^{80} +(56.2093 + 58.3225i) q^{81} +(-8.07125 - 13.9798i) q^{82} -35.6924i q^{83} +(-41.7371 + 4.69196i) q^{84} +37.7617 q^{85} +(66.3107 - 38.2845i) q^{86} +(-55.9238 - 11.3923i) q^{87} +(-25.4521 + 44.0843i) q^{88} +(-138.876 + 80.1802i) q^{89} +(-62.4877 + 47.0391i) q^{90} +(-6.47667 + 7.17501i) q^{91} -52.9652i q^{92} +(-41.4502 - 36.6905i) q^{93} +(-37.9644 + 65.7562i) q^{94} +(80.2057 + 46.3068i) q^{95} +(11.2482 - 12.7074i) q^{96} +118.904 q^{97} +(-40.5911 - 56.1637i) q^{98} +(97.4152 + 129.408i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{3} + 8 q^{4} - 8 q^{6} - 10 q^{9}+O(q^{10}) \) 8 * q - 2 * q^3 + 8 * q^4 - 8 * q^6 - 10 * q^9	\( 8 q - 2 q^{3} + 8 q^{4} - 8 q^{6} - 10 q^{9} + 16 q^{10} + 4 q^{12} - 64 q^{13} + 28 q^{15} - 16 q^{16} - 40 q^{18} + 4 q^{19} + 26 q^{21} - 16 q^{22} - 8 q^{24} - 24 q^{25} + 160 q^{27} + 72 q^{28} + 52 q^{30} + 20 q^{31} - 106 q^{33} + 32 q^{34} - 40 q^{36} + 4 q^{37} - 72 q^{39} - 32 q^{40} - 88 q^{42} + 208 q^{43} - 58 q^{45} + 56 q^{46} + 16 q^{48} - 40 q^{49} + 14 q^{51} - 64 q^{52} - 32 q^{54} - 472 q^{55} - 268 q^{57} - 80 q^{58} + 28 q^{60} + 212 q^{61} + 178 q^{63} - 64 q^{64} + 224 q^{66} + 156 q^{67} + 164 q^{69} + 56 q^{70} + 80 q^{72} + 132 q^{73} + 164 q^{75} + 16 q^{76} + 240 q^{78} - 52 q^{79} + 98 q^{81} + 48 q^{82} - 124 q^{84} + 152 q^{85} - 260 q^{87} - 16 q^{88} - 256 q^{90} - 352 q^{91} - 210 q^{93} - 360 q^{94} + 16 q^{96} + 576 q^{97} - 140 q^{99}+O(q^{100}) \) 8 * q - 2 * q^3 + 8 * q^4 - 8 * q^6 - 10 * q^9 + 16 * q^10 + 4 * q^12 - 64 * q^13 + 28 * q^15 - 16 * q^16 - 40 * q^18 + 4 * q^19 + 26 * q^21 - 16 * q^22 - 8 * q^24 - 24 * q^25 + 160 * q^27 + 72 * q^28 + 52 * q^30 + 20 * q^31 - 106 * q^33 + 32 * q^34 - 40 * q^36 + 4 * q^37 - 72 * q^39 - 32 * q^40 - 88 * q^42 + 208 * q^43 - 58 * q^45 + 56 * q^46 + 16 * q^48 - 40 * q^49 + 14 * q^51 - 64 * q^52 - 32 * q^54 - 472 * q^55 - 268 * q^57 - 80 * q^58 + 28 * q^60 + 212 * q^61 + 178 * q^63 - 64 * q^64 + 224 * q^66 + 156 * q^67 + 164 * q^69 + 56 * q^70 + 80 * q^72 + 132 * q^73 + 164 * q^75 + 16 * q^76 + 240 * q^78 - 52 * q^79 + 98 * q^81 + 48 * q^82 - 124 * q^84 + 152 * q^85 - 260 * q^87 - 16 * q^88 - 256 * q^90 - 352 * q^91 - 210 * q^93 - 360 * q^94 + 16 * q^96 + 576 * q^97 - 140 * q^99

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