LMFDB - Embedded newform 63.3.j.a.23.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,3,Mod(11,63)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(63, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 4]))

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

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

chi := DirichletCharacter("63.11");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	63.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:	$1.71662566547$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{6})$
Coefficient field:	6.0.63369648.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 12x^{4} + 17x^{3} + 118x^{2} + 33x + 9 $ x^6 - x^5 + 12x^4 + 17x^3 + 118x^2 + 33x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			23.2
Root			$1.98253 + 3.43384i$ of defining polynomial
Character	$\chi$	$=$	63.23
Dual form			63.3.j.a.11.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.03435i q^{2} +3.00000 q^{3} +2.93011 q^{4} +(-2.10422 + 1.21487i) q^{5} -3.10306i q^{6} +(-4.75661 + 5.13563i) q^{7} -7.16819i q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-1.03435i q^{2} +3.00000 q^{3} +2.93011 q^{4} +(-2.10422 + 1.21487i) q^{5} -3.10306i q^{6} +(-4.75661 + 5.13563i) q^{7} -7.16819i q^{8} +9.00000 q^{9} +(1.25661 + 2.17651i) q^{10} +(-11.6036 - 6.69935i) q^{11} +8.79033 q^{12} +(5.06928 - 8.78025i) q^{13} +(5.31206 + 4.92002i) q^{14} +(-6.31267 + 3.64462i) q^{15} +4.30600 q^{16} +(-18.6650 + 10.7762i) q^{17} -9.30919i q^{18} +(-10.4301 + 18.0655i) q^{19} +(-6.16561 + 3.55971i) q^{20} +(-14.2698 + 15.4069i) q^{21} +(-6.92950 + 12.0022i) q^{22} +(14.5825 - 8.41921i) q^{23} -21.5046i q^{24} +(-9.54816 + 16.5379i) q^{25} +(-9.08189 - 5.24343i) q^{26} +27.0000 q^{27} +(-13.9374 + 15.0480i) q^{28} +(-8.10422 + 4.67898i) q^{29} +(3.76983 + 6.52954i) q^{30} +12.1373 q^{31} -33.1267i q^{32} +(-34.8108 - 20.0980i) q^{33} +(11.1465 + 19.3062i) q^{34} +(3.76983 - 16.5852i) q^{35} +26.3710 q^{36} +(22.0957 - 38.2709i) q^{37} +(18.6861 + 10.7884i) q^{38} +(15.2078 - 26.3407i) q^{39} +(8.70845 + 15.0835i) q^{40} +(43.0384 + 24.8483i) q^{41} +(15.9362 + 14.7601i) q^{42} +(-25.8121 - 44.7078i) q^{43} +(-33.9999 - 19.6298i) q^{44} +(-18.9380 + 10.9339i) q^{45} +(-8.70845 - 15.0835i) q^{46} +63.4096i q^{47} +12.9180 q^{48} +(-3.74933 - 48.8563i) q^{49} +(17.1061 + 9.87619i) q^{50} +(-55.9950 + 32.3287i) q^{51} +(14.8535 - 25.7271i) q^{52} +(46.1222 - 26.6286i) q^{53} -27.9276i q^{54} +32.5554 q^{55} +(36.8132 + 34.0963i) q^{56} +(-31.2903 + 54.1964i) q^{57} +(4.83972 + 8.38264i) q^{58} -12.7712i q^{59} +(-18.4968 + 10.6791i) q^{60} +60.6916 q^{61} -12.5543i q^{62} +(-42.8095 + 46.2206i) q^{63} -17.0408 q^{64} +24.6341i q^{65} +(-20.7885 + 36.0067i) q^{66} -78.7615 q^{67} +(-54.6905 + 31.5756i) q^{68} +(43.7475 - 25.2576i) q^{69} +(-17.1550 - 3.89934i) q^{70} -9.91233i q^{71} -64.5137i q^{72} +(-49.3794 - 85.5276i) q^{73} +(-39.5857 - 22.8548i) q^{74} +(-28.6445 + 49.6137i) q^{75} +(-30.5614 + 52.9339i) q^{76} +(89.5992 - 27.7256i) q^{77} +(-27.2457 - 15.7303i) q^{78} +53.3734 q^{79} +(-9.06077 + 5.23124i) q^{80} +81.0000 q^{81} +(25.7019 - 44.5170i) q^{82} +(-81.5565 + 47.0867i) q^{83} +(-41.8122 + 45.1439i) q^{84} +(26.1835 - 45.3512i) q^{85} +(-46.2437 + 26.6988i) q^{86} +(-24.3127 + 14.0369i) q^{87} +(-48.0222 + 83.1769i) q^{88} +(17.1421 + 9.89697i) q^{89} +(11.3095 + 19.5886i) q^{90} +(20.9795 + 67.7981i) q^{91} +(42.7283 - 24.6692i) q^{92} +36.4120 q^{93} +65.5880 q^{94} -50.6851i q^{95} -99.3801i q^{96} +(-35.2144 - 60.9931i) q^{97} +(-50.5348 + 3.87813i) q^{98} +(-104.433 - 60.2941i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 18 q^{3} - 26 q^{4} - 15 q^{5} - 2 q^{7} + 54 q^{9}+O(q^{10}) $ 6 * q + 18 * q^3 - 26 * q^4 - 15 * q^5 - 2 * q^7 + 54 * q^9	\( 6 q + 18 q^{3} - 26 q^{4} - 15 q^{5} - 2 q^{7} + 54 q^{9} - 19 q^{10} - 9 q^{11} - 78 q^{12} + 11 q^{13} - 24 q^{14} - 45 q^{15} + 94 q^{16} + 33 q^{17} - 19 q^{19} + 45 q^{20} - 6 q^{21} + 65 q^{22} + 15 q^{23} - 26 q^{25} + 81 q^{26} + 162 q^{27} - 42 q^{28} - 51 q^{29} - 57 q^{30} - 92 q^{31} - 27 q^{33} + 93 q^{34} - 57 q^{35} - 234 q^{36} + 7 q^{37} - 21 q^{38} + 33 q^{39} + 57 q^{40} - 27 q^{41} - 72 q^{42} - 99 q^{43} - 273 q^{44} - 135 q^{45} - 57 q^{46} + 282 q^{48} + 6 q^{49} + 294 q^{50} + 99 q^{51} + 63 q^{52} + 45 q^{53} + 166 q^{55} + 360 q^{56} - 57 q^{57} - 7 q^{58} + 135 q^{60} + 44 q^{61} - 18 q^{63} - 138 q^{64} + 195 q^{66} - 196 q^{67} - 567 q^{68} + 45 q^{69} - 257 q^{70} - 101 q^{73} - 411 q^{74} - 78 q^{75} - 99 q^{76} + 105 q^{77} + 243 q^{78} + 180 q^{79} + 93 q^{80} + 486 q^{81} + 151 q^{82} + 99 q^{83} - 126 q^{84} - 159 q^{85} + 249 q^{86} - 153 q^{87} - 495 q^{88} - 243 q^{89} - 171 q^{90} + 177 q^{91} + 147 q^{92} - 276 q^{93} + 888 q^{94} - 161 q^{97} + 360 q^{98} - 81 q^{99}+O(q^{100}) \) 6 * q + 18 * q^3 - 26 * q^4 - 15 * q^5 - 2 * q^7 + 54 * q^9 - 19 * q^10 - 9 * q^11 - 78 * q^12 + 11 * q^13 - 24 * q^14 - 45 * q^15 + 94 * q^16 + 33 * q^17 - 19 * q^19 + 45 * q^20 - 6 * q^21 + 65 * q^22 + 15 * q^23 - 26 * q^25 + 81 * q^26 + 162 * q^27 - 42 * q^28 - 51 * q^29 - 57 * q^30 - 92 * q^31 - 27 * q^33 + 93 * q^34 - 57 * q^35 - 234 * q^36 + 7 * q^37 - 21 * q^38 + 33 * q^39 + 57 * q^40 - 27 * q^41 - 72 * q^42 - 99 * q^43 - 273 * q^44 - 135 * q^45 - 57 * q^46 + 282 * q^48 + 6 * q^49 + 294 * q^50 + 99 * q^51 + 63 * q^52 + 45 * q^53 + 166 * q^55 + 360 * q^56 - 57 * q^57 - 7 * q^58 + 135 * q^60 + 44 * q^61 - 18 * q^63 - 138 * q^64 + 195 * q^66 - 196 * q^67 - 567 * q^68 + 45 * q^69 - 257 * q^70 - 101 * q^73 - 411 * q^74 - 78 * q^75 - 99 * q^76 + 105 * q^77 + 243 * q^78 + 180 * q^79 + 93 * q^80 + 486 * q^81 + 151 * q^82 + 99 * q^83 - 126 * q^84 - 159 * q^85 + 249 * q^86 - 153 * q^87 - 495 * q^88 - 243 * q^89 - 171 * q^90 + 177 * q^91 + 147 * q^92 - 276 * q^93 + 888 * q^94 - 161 * q^97 + 360 * q^98 - 81 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$		−	1.03435i		−	0.517177i	−0.965988	−	0.258589i	$-0.916743\pi$
$2$		−	1.03435i		−	0.517177i	0.965988	−	0.258589i	$-0.0832574\pi$
$3$	3.00000			1.00000
$3$	3.00000			1.00000
$4$	2.93011			0.732528
$5$	−2.10422	+	1.21487i	−0.420845	+	0.242975i	−0.695439	−	0.718586i	$-0.744790\pi$
$5$	−2.10422	+	1.21487i	−0.420845	+	0.242975i	0.274594	+	0.961560i	$0.411457\pi$
$6$		−	3.10306i		−	0.517177i
$7$	−4.75661	+	5.13563i	−0.679516	+	0.733661i
$7$	−4.75661	+	5.13563i	−0.679516	+	0.733661i
$8$		−	7.16819i		−	0.896024i
$9$	9.00000			1.00000
$10$	1.25661	+	2.17651i	0.125661	+	0.217651i
$11$	−11.6036	−	6.69935i	−1.05487	−	0.609032i	−0.130864	−	0.991400i	$-0.541775\pi$
$11$	−11.6036	−	6.69935i	−1.05487	−	0.609032i	−0.924010	+	0.382369i	$0.875108\pi$
$12$	8.79033			0.732528
$13$	5.06928	−	8.78025i	0.389944	−	0.675404i	−0.602497	−	0.798121i	$-0.705828\pi$
$13$	5.06928	−	8.78025i	0.389944	−	0.675404i	0.992442	+	0.122717i	$0.0391609\pi$
$14$	5.31206	+	4.92002i	0.379433	+	0.351430i
$15$	−6.31267	+	3.64462i	−0.420845	+	0.242975i
$16$	4.30600			0.269125
$17$	−18.6650	+	10.7762i	−1.09794	+	0.633897i	−0.935679	−	0.352851i	$-0.885212\pi$
$17$	−18.6650	+	10.7762i	−1.09794	+	0.633897i	−0.162262	+	0.986748i	$0.551879\pi$
$18$		−	9.30919i		−	0.517177i
$19$	−10.4301	+	18.0655i	−0.548953	+	0.950815i	0.449393	+	0.893334i	$0.351640\pi$
$19$	−10.4301	+	18.0655i	−0.548953	+	0.950815i	−0.998347	+	0.0574809i	$0.981693\pi$
$20$	−6.16561	+	3.55971i	−0.308280	+	0.177986i
$21$	−14.2698	+	15.4069i	−0.679516	+	0.733661i
$22$	−6.92950	+	12.0022i	−0.314977	+	0.545557i
$23$	14.5825	−	8.41921i	0.634022	−	0.366053i	−0.148286	−	0.988944i	$-0.547376\pi$
$23$	14.5825	−	8.41921i	0.634022	−	0.366053i	0.782308	+	0.622892i	$0.214042\pi$
$24$		−	21.5046i		−	0.896024i
$25$	−9.54816	+	16.5379i	−0.381927	+	0.661516i
$26$	−9.08189	−	5.24343i	−0.349303	−	0.201670i
$27$	27.0000			1.00000
$28$	−13.9374	+	15.0480i	−0.497764	+	0.537427i
$29$	−8.10422	+	4.67898i	−0.279456	+	0.161344i	−0.633177	−	0.774007i	$-0.718250\pi$
$29$	−8.10422	+	4.67898i	−0.279456	+	0.161344i	0.353721	+	0.935351i	$0.384916\pi$
$30$	3.76983	+	6.52954i	0.125661	+	0.217651i
$31$	12.1373			0.391527			0.195763	−	0.980651i	$-0.437282\pi$
$31$	12.1373			0.391527			0.195763	+	0.980651i	$0.437282\pi$
$32$		−	33.1267i		−	1.03521i
$33$	−34.8108	−	20.0980i	−1.05487	−	0.609032i
$34$	11.1465	+	19.3062i	0.327837	+	0.567830i
$35$	3.76983	−	16.5852i	0.107709	−	0.473862i
$36$	26.3710			0.732528
$37$	22.0957	−	38.2709i	0.597182	−	1.03435i	−0.396053	−	0.918227i	$-0.629621\pi$
$37$	22.0957	−	38.2709i	0.597182	−	1.03435i	0.993235	−	0.116121i	$-0.0370462\pi$
$38$	18.6861	+	10.7884i	0.491740	+	0.283906i
$39$	15.2078	−	26.3407i	0.389944	−	0.675404i
$40$	8.70845	+	15.0835i	0.217711	+	0.377087i
$41$	43.0384	+	24.8483i	1.04972	+	0.606055i	0.922570	−	0.385829i	$-0.126084\pi$
$41$	43.0384	+	24.8483i	1.04972	+	0.606055i	0.127148	+	0.991884i	$0.459418\pi$
$42$	15.9362	+	14.7601i	0.379433	+	0.351430i
$43$	−25.8121	−	44.7078i	−0.600280	−	1.03972i	−0.992778	−	0.119963i	$-0.961722\pi$
$43$	−25.8121	−	44.7078i	−0.600280	−	1.03972i	0.392498	−	0.919753i	$-0.371611\pi$
$44$	−33.9999	−	19.6298i	−0.772724	−	0.446133i
$45$	−18.9380	+	10.9339i	−0.420845	+	0.242975i
$46$	−8.70845	−	15.0835i	−0.189314	−	0.327902i
$47$			63.4096i			1.34914i	0.738211	+	0.674570i	$0.235671\pi$
$47$			63.4096i			1.34914i	−0.738211	+	0.674570i	$0.764329\pi$
$48$	12.9180			0.269125
$49$	−3.74933	−	48.8563i	−0.0765169	−	0.997068i
$50$	17.1061	+	9.87619i	0.342121	+	0.197524i
$51$	−55.9950	+	32.3287i	−1.09794	+	0.633897i
$52$	14.8535	−	25.7271i	0.285645	−	0.494752i
$53$	46.1222	−	26.6286i	0.870229	−	0.502427i	0.00280492	−	0.999996i	$-0.499107\pi$
$53$	46.1222	−	26.6286i	0.870229	−	0.502427i	0.867424	+	0.497569i	$0.165774\pi$
$54$		−	27.9276i		−	0.517177i
$55$	32.5554			0.591917
$56$	36.8132	+	34.0963i	0.657378	+	0.608862i
$57$	−31.2903	+	54.1964i	−0.548953	+	0.950815i
$58$	4.83972	+	8.38264i	0.0834434	+	0.144528i
$59$		−	12.7712i		−	0.216461i	−0.994126	−	0.108230i	$-0.965482\pi$
$59$		−	12.7712i		−	0.216461i	0.994126	−	0.108230i	$-0.0345184\pi$
$60$	−18.4968	+	10.6791i	−0.308280	+	0.177986i
$61$	60.6916			0.994944			0.497472	−	0.867480i	$-0.334262\pi$
$61$	60.6916			0.994944			0.497472	+	0.867480i	$0.334262\pi$
$62$		−	12.5543i		−	0.202489i
$63$	−42.8095	+	46.2206i	−0.679516	+	0.733661i
$64$	−17.0408			−0.266262
$65$			24.6341i			0.378987i
$66$	−20.7885	+	36.0067i	−0.314977	+	0.545557i
$67$	−78.7615			−1.17554			−0.587772	−	0.809027i	$-0.699995\pi$
$67$	−78.7615			−1.17554			−0.587772	+	0.809027i	$0.699995\pi$
$68$	−54.6905	+	31.5756i	−0.804272	+	0.464347i
$69$	43.7475	−	25.2576i	0.634022	−	0.366053i
$70$	−17.1550	−	3.89934i	−0.245071	−	0.0557049i
$71$		−	9.91233i		−	0.139610i	−0.997561	−	0.0698051i	$-0.977762\pi$
$71$		−	9.91233i		−	0.139610i	0.997561	−	0.0698051i	$-0.0222378\pi$
$72$		−	64.5137i		−	0.896024i
$73$	−49.3794	−	85.5276i	−0.676430	−	1.17161i	−0.976049	−	0.217552i	$-0.930193\pi$
$73$	−49.3794	−	85.5276i	−0.676430	−	1.17161i	0.299619	−	0.954059i	$-0.403140\pi$
$74$	−39.5857	−	22.8548i	−0.534942	−	0.308849i
$75$	−28.6445	+	49.6137i	−0.381927	+	0.661516i
$76$	−30.5614	+	52.9339i	−0.402123	+	0.696498i
$77$	89.5992	−	27.7256i	1.16363	−	0.360073i
$78$	−27.2457	−	15.7303i	−0.349303	−	0.201670i
$79$	53.3734			0.675613			0.337807	−	0.941216i	$-0.390315\pi$
$79$	53.3734			0.675613			0.337807	+	0.941216i	$0.390315\pi$
$80$	−9.06077	+	5.23124i	−0.113260	+	0.0653905i
$81$	81.0000			1.00000
$82$	25.7019	−	44.5170i	0.313438	−	0.542890i
$83$	−81.5565	+	47.0867i	−0.982608	+	0.567309i	−0.903057	−	0.429521i	$-0.858682\pi$
$83$	−81.5565	+	47.0867i	−0.982608	+	0.567309i	−0.0795518	+	0.996831i	$0.525349\pi$
$84$	−41.8122	+	45.1439i	−0.497764	+	0.537427i
$85$	26.1835	−	45.3512i	0.308042	−	0.533544i
$86$	−46.2437	+	26.6988i	−0.537717	+	0.310451i
$87$	−24.3127	+	14.0369i	−0.279456	+	0.161344i
$88$	−48.0222	+	83.1769i	−0.545707	+	0.945192i
$89$	17.1421	+	9.89697i	0.192607	+	0.111202i	0.593203	−	0.805053i	$-0.297863\pi$
$89$	17.1421	+	9.89697i	0.192607	+	0.111202i	−0.400595	+	0.916255i	$0.631197\pi$
$90$	11.3095	+	19.5886i	0.125661	+	0.217651i
$91$	20.9795	+	67.7981i	0.230544	+	0.745034i
$92$	42.7283	−	24.6692i	0.464438	−	0.268144i
$93$	36.4120			0.391527
$94$	65.5880			0.697745
$95$		−	50.6851i		−	0.533527i
$96$		−	99.3801i		−	1.03521i
$97$	−35.2144	−	60.9931i	−0.363035	−	0.628795i	0.625424	−	0.780285i	$-0.284926\pi$
$97$	−35.2144	−	60.9931i	−0.363035	−	0.628795i	−0.988459	+	0.151490i	$0.951593\pi$
$98$	−50.5348	+	3.87813i	−0.515661	+	0.0395728i
$99$	−104.433	−	60.2941i	−1.05487	−	0.609032i
$100$	−27.9772	+	48.4579i	−0.279772	+	0.484579i
$101$	60.6824	+	35.0350i	0.600816	+	0.346881i	0.769363	−	0.638812i	$-0.220574\pi$
$101$	60.6824	+	35.0350i	0.600816	+	0.346881i	−0.168546	+	0.985694i	$0.553907\pi$
$102$	33.4394	+	57.9187i	0.327837	+	0.567830i
$103$	−0.851106	−	1.47416i	−0.00826317	−	0.0143122i	0.861864	−	0.507139i	$-0.169297\pi$
$103$	−0.851106	−	1.47416i	−0.00826317	−	0.0143122i	−0.870127	+	0.492827i	$0.835964\pi$
$104$	−62.9385	−	36.3376i	−0.605178	−	0.349400i
$105$	11.3095	−	49.7555i	0.107709	−	0.473862i
$106$	−27.5434	−	47.7067i	−0.259844	−	0.450063i
$107$	37.6471	+	21.7355i	0.351842	+	0.203136i	0.665496	−	0.746401i	$-0.268220\pi$
$107$	37.6471	+	21.7355i	0.351842	+	0.203136i	−0.313654	+	0.949537i	$0.601553\pi$
$108$	79.1130			0.732528
$109$	71.8669	+	124.477i	0.659329	+	1.14199i	0.980790	+	0.195069i	$0.0624930\pi$
$109$	71.8669	+	124.477i	0.659329	+	1.14199i	−0.321460	+	0.946923i	$0.604174\pi$
$110$		−	33.6739i		−	0.306126i
$111$	66.2872	−	114.813i	0.597182	−	1.03435i
$112$	−20.4819	+	22.1140i	−0.182874	+	0.197446i
$113$	186.805	+	107.852i	1.65314	+	0.954440i	0.975770	+	0.218797i	$0.0702132\pi$
$113$	186.805	+	107.852i	1.65314	+	0.954440i	0.677369	+	0.735644i	$0.263120\pi$
$114$	56.0583	+	32.3653i	0.491740	+	0.283906i
$115$	−20.4566	+	35.4318i	−0.177883	+	0.308102i
$116$	−23.7463	+	13.7099i	−0.204709	+	0.118189i
$117$	45.6235	−	79.0222i	0.389944	−	0.675404i
$118$	−13.2099			−0.111948
$119$	33.4394	−	147.115i	0.281003	−	1.23626i
$120$	26.1253	+	45.2504i	0.217711	+	0.377087i
$121$	29.2625	+	50.6842i	0.241839	+	0.418878i
$122$		−	62.7766i		−	0.514562i
$123$	129.115	+	74.5448i	1.04972	+	0.606055i
$124$	35.5637			0.286804
$125$		−	107.143i		−	0.857143i
$126$	47.8085	+	44.2802i	0.379433	+	0.351430i
$127$	5.13708			0.0404495			0.0202247	−	0.999795i	$-0.493562\pi$
$127$	5.13708			0.0404495			0.0202247	+	0.999795i	$0.493562\pi$
$128$		−	114.881i		−	0.897504i
$129$	−77.4362	−	134.123i	−0.600280	−	1.03972i
$130$	25.4804			0.196003
$131$	−140.012	+	80.8358i	−1.06879	+	0.617067i	−0.927851	−	0.372951i	$-0.878346\pi$
$131$	−140.012	+	80.8358i	−1.06879	+	0.617067i	−0.140941	+	0.990018i	$0.545013\pi$
$132$	−102.000	−	58.8895i	−0.772724	−	0.446133i
$133$	−43.1656	−	139.496i	−0.324553	−	1.04884i
$134$			81.4673i			0.607965i
$135$	−56.8140	+	32.8016i	−0.420845	+	0.242975i
$136$	77.2461	+	133.794i	0.567986	+	0.983781i
$137$	−157.261	−	90.7948i	−1.14789	−	0.662736i	−0.199519	−	0.979894i	$-0.563938\pi$
$137$	−157.261	−	90.7948i	−1.14789	−	0.662736i	−0.948373	+	0.317158i	$0.897271\pi$
$138$	−26.1253	−	45.2504i	−0.189314	−	0.327902i
$139$	−61.9625	+	107.322i	−0.445773	+	0.772102i	−0.998106	−	0.0615220i	$-0.980405\pi$
$139$	−61.9625	+	107.322i	−0.445773	+	0.772102i	0.552332	+	0.833624i	$0.313738\pi$
$140$	11.0460	−	48.5964i	0.0789001	−	0.347117i
$141$			190.229i			1.34914i
$142$	−10.2529			−0.0722033
$143$	−117.644	+	67.9217i	−0.822684	+	0.474977i
$144$	38.7540			0.269125
$145$	11.3687	−	19.6912i	0.0784050	−	0.135801i
$146$	−88.4658	+	51.0758i	−0.605930	+	0.349834i
$147$	−11.2480	−	146.569i	−0.0765169	−	0.997068i
$148$	64.7429	−	112.138i	0.437452	−	0.757689i
$149$	−99.2479	+	57.3008i	−0.666093	+	0.384569i	−0.794595	−	0.607140i	$-0.792317\pi$
$149$	−99.2479	+	57.3008i	−0.666093	+	0.384569i	0.128502	+	0.991709i	$0.458983\pi$
$150$	51.3182	+	29.6286i	0.342121	+	0.197524i
$151$	−133.431	+	231.108i	−0.883646	+	1.53052i	−0.0363884	+	0.999338i	$0.511585\pi$
$151$	−133.431	+	231.108i	−0.883646	+	1.53052i	−0.847258	+	0.531182i	$0.821748\pi$
$152$	129.497	+	74.7650i	0.851953	+	0.491875i
$153$	−167.985	+	96.9862i	−1.09794	+	0.633897i
$154$	−28.6781	−	92.6773i	−0.186222	−	0.601801i
$155$	−25.5397	+	14.7453i	−0.164772	+	0.0951312i
$156$	44.5606	−	77.1813i	0.285645	−	0.494752i
$157$	−73.3060			−0.466917			−0.233459	−	0.972367i	$-0.575004\pi$
$157$	−73.3060			−0.466917			−0.233459	+	0.972367i	$0.575004\pi$
$158$		−	55.2071i		−	0.349412i
$159$	138.366	−	79.8859i	0.870229	−	0.502427i
$160$	40.2447	+	69.7059i	0.251530	+	0.435662i
$161$	−26.1253	+	114.937i	−0.162269	+	0.713895i
$162$		−	83.7827i		−	0.517177i
$163$	−42.5107	+	73.6306i	−0.260802	+	0.451722i	−0.966455	−	0.256835i	$-0.917320\pi$
$163$	−42.5107	+	73.6306i	−0.260802	+	0.451722i	0.705654	+	0.708557i	$0.250653\pi$
$164$	126.107	+	72.8081i	0.768948	+	0.443952i
$165$	97.6663			0.591917
$166$	48.7043	+	84.3583i	0.293399	+	0.508183i
$167$	−171.888	−	99.2398i	−1.02927	−	0.594251i	−0.112496	−	0.993652i	$-0.535885\pi$
$167$	−171.888	−	99.2398i	−1.02927	−	0.594251i	−0.916776	+	0.399402i	$0.869218\pi$
$168$	110.439	+	102.289i	0.657378	+	0.608862i
$169$	33.1048	+	57.3393i	0.195887	+	0.339286i
$170$	−46.9092	−	27.0831i	−0.275937	−	0.159312i
$171$	−93.8710	+	162.589i	−0.548953	+	0.950815i
$172$	−75.6322	−	130.999i	−0.439722	−	0.761621i
$173$		−	216.257i		−	1.25004i	−0.780608	−	0.625020i	$-0.785091\pi$
$173$		−	216.257i		−	1.25004i	0.780608	−	0.625020i	$-0.214909\pi$
$174$	14.5192	+	25.1479i	0.0834434	+	0.144528i
$175$	−39.5156	−	127.700i	−0.225804	−	0.729715i
$176$	−49.9651	−	28.8474i	−0.283893	−	0.163905i
$177$		−	38.3135i		−	0.216461i
$178$	10.2370	−	17.7310i	0.0575111	−	0.0996121i
$179$	94.1411	−	54.3524i	0.525928	−	0.303645i	−0.213429	−	0.976959i	$-0.568463\pi$
$179$	94.1411	−	54.3524i	0.525928	−	0.303645i	0.739357	+	0.673314i	$0.235130\pi$
$180$	−55.4905	+	32.0374i	−0.308280	+	0.177986i
$181$	11.3972			0.0629679			0.0314839	−	0.999504i	$-0.489977\pi$
$181$	11.3972			0.0629679			0.0314839	+	0.999504i	$0.489977\pi$
$182$	70.1273	−	21.7002i	0.385315	−	0.119232i
$183$	182.075			0.994944
$184$	−60.3505	−	104.530i	−0.327992	−	0.568099i
$185$			107.374i			0.580400i
$186$		−	37.6629i		−	0.202489i
$187$	288.775			1.54425
$188$			185.797i			0.988283i
$189$	−128.428	+	138.662i	−0.679516	+	0.733661i
$190$	−52.4263			−0.275928
$191$			276.449i			1.44738i	0.690127	+	0.723688i	$0.257555\pi$
$191$			276.449i			1.44738i	−0.690127	+	0.723688i	$0.742445\pi$
$192$	−51.1223			−0.266262
$193$	129.200			0.669428			0.334714	−	0.942320i	$-0.391360\pi$
$193$	129.200			0.669428			0.334714	+	0.942320i	$0.391360\pi$
$194$	−63.0885	+	36.4241i	−0.325198	+	0.187753i
$195$			73.9024i			0.378987i
$196$	−10.9859	−	143.155i	−0.0560507	−	0.730380i
$197$		−	263.349i		−	1.33680i	−0.743804	−	0.668398i	$-0.766980\pi$
$197$		−	263.349i		−	1.33680i	0.743804	−	0.668398i	$-0.233020\pi$
$198$	−62.3655	+	108.020i	−0.314977	+	0.545557i
$199$	−79.6728	−	137.997i	−0.400366	−	0.693454i	0.593404	−	0.804905i	$-0.297784\pi$
$199$	−79.6728	−	137.997i	−0.400366	−	0.693454i	−0.993770	+	0.111451i	$0.964450\pi$
$200$	118.547	+	68.4431i	0.592734	+	0.342215i
$201$	−236.284			−1.17554
$202$	36.2386	−	62.7672i	0.179399	−	0.310728i
$203$	14.5192	−	63.8763i	0.0715229	−	0.314662i
$204$	−164.072	+	94.7267i	−0.804272	+	0.464347i
$205$	−120.750			−0.589024
$206$	−1.52480	+	0.880346i	−0.00740196	+	0.00427352i
$207$	131.242	−	75.7729i	0.634022	−	0.366053i
$208$	21.8283	−	37.8077i	0.104944	−	0.181768i
$209$	242.054	−	139.750i	1.15815	−	0.668660i
$210$	−51.4649	−	11.6980i	−0.245071	−	0.0557049i
$211$	19.7206	−	34.1571i	0.0934626	−	0.161882i	−0.815503	−	0.578752i	$-0.803540\pi$
$211$	19.7206	−	34.1571i	0.0934626	−	0.161882i	0.908966	+	0.416870i	$0.136873\pi$
$212$	135.143	−	78.0249i	0.637467	−	0.368042i
$213$		−	29.7370i		−	0.139610i
$214$	22.4823	−	38.9404i	0.105057	−	0.181964i
$215$	108.629	+	62.7168i	0.505250	+	0.291706i
$216$		−	193.541i		−	0.896024i
$217$	−57.7326	+	62.3328i	−0.266049	+	0.287248i
$218$	128.753	−	74.3358i	0.590612	−	0.340990i
$219$	−148.138	−	256.583i	−0.676430	−	1.17161i
$220$	95.3911			0.433596
$221$			218.511i			0.988738i
$222$	−118.757	−	68.5644i	−0.534942	−	0.308849i
$223$	−11.6007	−	20.0931i	−0.0520212	−	0.0901034i	0.838842	−	0.544375i	$-0.183233\pi$
$223$	−11.6007	−	20.0931i	−0.0520212	−	0.0901034i	−0.890863	+	0.454271i	$0.849900\pi$
$224$	170.126	+	157.571i	0.759492	+	0.703441i
$225$	−85.9335	+	148.841i	−0.381927	+	0.661516i
$226$	111.557	−	193.222i	0.493615	−	0.854966i
$227$	−11.0605	−	6.38581i	−0.0487249	−	0.0281313i	0.475440	−	0.879748i	$-0.342289\pi$
$227$	−11.0605	−	6.38581i	−0.0487249	−	0.0281313i	−0.524165	+	0.851617i	$0.675622\pi$
$228$	−91.6842	+	158.802i	−0.402123	+	0.696498i
$229$	8.91397	+	15.4394i	0.0389256	+	0.0674211i	0.884832	−	0.465910i	$-0.154273\pi$
$229$	8.91397	+	15.4394i	0.0389256	+	0.0674211i	−0.845906	+	0.533332i	$0.820940\pi$
$230$	36.6490	+	21.1593i	0.159344	+	0.0919971i
$231$	268.798	−	83.1769i	1.16363	−	0.360073i
$232$	33.5398	+	58.0926i	0.144568	+	0.250399i
$233$	258.535	+	149.265i	1.10959	+	0.640623i	0.938723	−	0.344672i	$-0.112010\pi$
$233$	258.535	+	149.265i	1.10959	+	0.640623i	0.170867	+	0.985294i	$0.445343\pi$
$234$	−81.7370	−	47.1909i	−0.349303	−	0.201670i
$235$	−77.0346	−	133.428i	−0.327807	−	0.567778i
$236$		−	37.4210i		−	0.158563i
$237$	160.120			0.675613
$238$	−152.169	−	34.5881i	−0.639365	−	0.145328i
$239$	−70.2626	−	40.5661i	−0.293986	−	0.169733i	0.345752	−	0.938326i	$-0.387624\pi$
$239$	−70.2626	−	40.5661i	−0.293986	−	0.169733i	−0.639738	+	0.768593i	$0.720957\pi$
$240$	−27.1823	+	15.6937i	−0.113260	+	0.0653905i
$241$	113.409	−	196.431i	0.470579	−	0.815066i	−0.528855	−	0.848712i	$-0.677379\pi$
$241$	113.409	−	196.431i	0.470579	−	0.815066i	0.999434	+	0.0336460i	$0.0107119\pi$
$242$	52.4254	−	30.2678i	0.216634	−	0.125074i
$243$	243.000			1.00000
$244$	177.833			0.728824
$245$	67.2437	+	98.2497i	0.274464	+	0.401019i
$246$	77.1057	−	133.551i	0.313438	−	0.542890i
$247$	105.746	+	183.158i	0.428123	+	0.741530i
$248$		−	87.0027i		−	0.350817i
$249$	−244.669	+	141.260i	−0.982608	+	0.567309i
$250$	−110.824			−0.443295
$251$		−	205.123i		−	0.817225i	−0.912708	−	0.408612i	$-0.866013\pi$
$251$		−	205.123i		−	0.817225i	0.912708	−	0.408612i	$-0.133987\pi$
$252$	−125.437	+	135.432i	−0.497764	+	0.537427i
$253$	−225.613			−0.891750
$254$		−	5.31356i		−	0.0209195i
$255$	78.5506	−	136.054i	0.308042	−	0.533544i
$256$	−186.990			−0.730431
$257$	−380.278	+	219.554i	−1.47968	+	0.854294i	−0.999735	−	0.0230036i	$-0.992677\pi$
$257$	−380.278	+	219.554i	−1.47968	+	0.854294i	−0.479946	+	0.877298i	$0.659344\pi$
$258$	−138.731	+	80.0964i	−0.537717	+	0.310451i
$259$	91.4444	+	295.515i	0.353067	+	1.14099i
$260$			72.1807i			0.277618i
$261$	−72.9380	+	42.1108i	−0.279456	+	0.161344i
$262$	83.6129	+	144.822i	0.319133	+	0.552755i
$263$	−335.114	−	193.478i	−1.27420	−	0.735658i	−0.298421	−	0.954434i	$-0.596460\pi$
$263$	−335.114	−	193.478i	−1.27420	−	0.735658i	−0.975775	+	0.218777i	$0.929793\pi$
$264$	−144.067	+	249.531i	−0.545707	+	0.945192i
$265$	−64.7009	+	112.065i	−0.244154	+	0.422887i
$266$	−144.288	+	44.6485i	−0.542436	+	0.167852i
$267$	51.4262	+	29.6909i	0.192607	+	0.111202i
$268$	−230.780			−0.861119
$269$	144.432	−	83.3879i	0.536922	−	0.309992i	−0.206909	−	0.978360i	$-0.566340\pi$
$269$	144.432	−	83.3879i	0.536922	−	0.309992i	0.743831	+	0.668368i	$0.233007\pi$
$270$	33.9285	+	58.7658i	0.125661	+	0.217651i
$271$	−83.5934	+	144.788i	−0.308463	+	0.534273i	−0.978026	−	0.208482i	$-0.933148\pi$
$271$	−83.5934	+	144.788i	−0.308463	+	0.534273i	0.669564	+	0.742755i	$0.266481\pi$
$272$	−80.3714	+	46.4024i	−0.295483	+	0.170597i
$273$	62.9385	+	203.394i	0.230544	+	0.745034i
$274$	−93.9140	+	162.664i	−0.342752	+	0.593663i
$275$	221.586	−	127.933i	0.805769	−	0.465211i
$276$	128.185	−	74.0077i	0.464438	−	0.268144i
$277$	182.478	−	316.061i	0.658764	−	1.14101i	−0.322172	−	0.946681i	$-0.604413\pi$
$277$	182.478	−	316.061i	0.658764	−	1.14101i	0.980936	−	0.194332i	$-0.0622537\pi$
$278$	111.009	+	64.0912i	0.399314	+	0.230544i
$279$	109.236			0.391527
$280$	−118.886	−	27.0229i	−0.424592	−	0.0965102i
$281$	−377.213	+	217.784i	−1.34239	+	0.775031i	−0.987158	−	0.159746i	$-0.948933\pi$
$281$	−377.213	+	217.784i	−1.34239	+	0.775031i	−0.355235	+	0.934777i	$0.615599\pi$
$282$	196.764			0.697745
$283$	−105.178			−0.371655			−0.185827	−	0.982582i	$-0.559497\pi$
$283$	−105.178			−0.371655			−0.185827	+	0.982582i	$0.559497\pi$
$284$		−	29.0442i		−	0.102268i
$285$		−	152.055i		−	0.533527i
$286$	70.2551	+	121.685i	0.245647	+	0.425474i
$287$	−332.328	+	102.836i	−1.15794	+	0.358313i
$288$		−	298.140i		−	1.03521i
$289$	87.7547	−	151.996i	0.303650	−	0.525936i
$290$	−20.3677	−	11.7593i	−0.0702334	−	0.0405493i
$291$	−105.643	−	182.979i	−0.363035	−	0.628795i
$292$	−144.687	−	250.605i	−0.495504	−	0.858237i
$293$	332.511	+	191.975i	1.13485	+	0.655206i	0.945150	−	0.326636i	$-0.105915\pi$
$293$	332.511	+	191.975i	1.13485	+	0.655206i	0.189700	+	0.981842i	$0.439248\pi$
$294$	−151.604	+	11.6344i	−0.515661	+	0.0395728i
$295$	15.5154	+	26.8734i	0.0525945	+	0.0910963i
$296$	−274.333	−	158.386i	−0.926801	−	0.535089i
$297$	−313.298	−	180.882i	−1.05487	−	0.609032i
$298$	59.2693	+	102.657i	0.198890	+	0.344488i
$299$		−	170.717i		−	0.570961i
$300$	−83.9315	+	145.374i	−0.279772	+	0.484579i
$301$	352.380	+	80.0964i	1.17070	+	0.266101i
$302$	239.048	+	138.014i	0.791550	+	0.457002i
$303$	182.047	+	105.105i	0.600816	+	0.346881i
$304$	−44.9120	+	77.7899i	−0.147737	+	0.255888i
$305$	−127.709	+	73.7326i	−0.418717	+	0.241746i
$306$	100.318	+	173.756i	0.327837	+	0.567830i
$307$	184.470			0.600878			0.300439	−	0.953801i	$-0.402867\pi$
$307$	184.470			0.600878			0.300439	+	0.953801i	$0.402867\pi$
$308$	262.536	−	81.2392i	0.852388	−	0.263764i
$309$	−2.55332	−	4.42248i	−0.00826317	−	0.0143122i
$310$	15.2519	+	26.4171i	0.0491997	+	0.0852163i
$311$		−	271.172i		−	0.871937i	−0.899962	−	0.435969i	$-0.856406\pi$
$311$		−	271.172i		−	0.871937i	0.899962	−	0.435969i	$-0.143594\pi$
$312$	−188.815	−	109.013i	−0.605178	−	0.349400i
$313$	−534.947			−1.70910			−0.854548	−	0.519373i	$-0.826165\pi$
$313$	−534.947			−1.70910			−0.854548	+	0.519373i	$0.826165\pi$
$314$			75.8244i			0.241479i
$315$	33.9285	−	149.267i	0.107709	−	0.473862i
$316$	156.390			0.494905
$317$			63.4096i			0.200030i	0.994986	+	0.100015i	$0.0318891\pi$
$317$			63.4096i			0.200030i	−0.994986	+	0.100015i	$0.968111\pi$
$318$	−82.6303	−	143.120i	−0.259844	−	0.450063i
$319$	125.384			0.393054
$320$	35.8575	−	20.7024i	0.112055	−	0.0646949i
$321$	112.941	+	65.2066i	0.351842	+	0.203136i
$322$	118.886	+	27.0229i	0.369210	+	0.0839219i
$323$		−	449.590i		−	1.39192i
$324$	237.339			0.732528
$325$	96.8046	+	167.670i	0.297860	+	0.515909i
$326$	76.1601	+	43.9711i	0.233620	+	0.134881i
$327$	215.601	+	373.431i	0.659329	+	1.14199i
$328$	178.117	−	308.508i	0.543040	−	0.940572i
$329$	−325.648	−	301.615i	−0.989812	−	0.916762i
$330$		−	101.022i		−	0.306126i
$331$	240.938			0.727911			0.363955	−	0.931416i	$-0.381426\pi$
$331$	240.938			0.727911			0.363955	+	0.931416i	$0.381426\pi$
$332$	−238.970	+	137.969i	−0.719788	+	0.415570i
$333$	198.861	−	344.438i	0.597182	−	1.03435i
$334$	−102.649	+	177.794i	−0.307333	+	0.532316i
$335$	165.732	−	95.6852i	0.494721	−	0.285627i
$336$	−61.4458	+	66.3420i	−0.182874	+	0.197446i
$337$	−56.5389	+	97.9282i	−0.167771	+	0.290588i	−0.937636	−	0.347619i	$-0.886990\pi$
$337$	−56.5389	+	97.9282i	−0.167771	+	0.290588i	0.769865	+	0.638207i	$0.220324\pi$
$338$	59.3091	−	34.2421i	0.175471	−	0.101308i
$339$	560.414	+	323.555i	1.65314	+	0.954440i
$340$	76.7207	−	132.884i	0.225649	−	0.390836i
$341$	−140.837	−	81.3122i	−0.413012	−	0.238452i
$342$	168.175	+	97.0959i	0.491740	+	0.283906i
$343$	268.742	+	213.135i	0.783504	+	0.621386i
$344$	−320.474	+	185.026i	−0.931610	+	0.537866i
$345$	−61.3697	+	106.295i	−0.177883	+	0.308102i
$346$	−223.686			−0.646493
$347$			123.868i			0.356968i	0.983943	+	0.178484i	$0.0571193\pi$
$347$			123.868i			0.356968i	−0.983943	+	0.178484i	$0.942881\pi$
$348$	−71.2388	+	41.1298i	−0.204709	+	0.118189i
$349$	−188.289	−	326.126i	−0.539510	−	0.934459i	−0.998930	−	0.0462398i	$-0.985276\pi$
$349$	−188.289	−	326.126i	−0.539510	−	0.934459i	0.459420	−	0.888219i	$-0.348057\pi$
$350$	−132.087	+	40.8732i	−0.377392	+	0.116780i
$351$	136.871	−	237.067i	0.389944	−	0.675404i
$352$	−221.927	+	384.389i	−0.630475	+	1.09201i
$353$	28.2606	+	16.3162i	0.0800583	+	0.0462217i	0.539495	−	0.841989i	$-0.318615\pi$
$353$	28.2606	+	16.3162i	0.0800583	+	0.0462217i	−0.459436	+	0.888211i	$0.651949\pi$
$354$	−39.6298			−0.111948
$355$	12.0422	+	20.8578i	0.0339218	+	0.0587542i
$356$	50.2281	+	28.9992i	0.141090	+	0.0814585i
$357$	100.318	−	441.344i	0.281003	−	1.23626i
$358$	−56.2196	−	97.3752i	−0.157038	−	0.271998i
$359$	−474.466	−	273.933i	−1.32163	−	0.763045i	−0.337643	−	0.941274i	$-0.609630\pi$
$359$	−474.466	−	273.933i	−1.32163	−	0.763045i	−0.983989	+	0.178229i	$0.942963\pi$
$360$	78.3760	+	135.751i	0.217711	+	0.377087i
$361$	−37.0744	−	64.2148i	−0.102699	−	0.177880i
$362$		−	11.7887i		−	0.0325655i
$363$	87.7876	+	152.053i	0.241839	+	0.418878i
$364$	61.4723	+	198.656i	0.168880	+	0.545758i
$365$	207.810	+	119.979i	0.569344	+	0.328711i
$366$		−	188.330i		−	0.514562i
$367$	−281.676	+	487.877i	−0.767509	+	1.32936i	0.171401	+	0.985201i	$0.445171\pi$
$367$	−281.676	+	487.877i	−0.767509	+	1.32936i	−0.938910	+	0.344163i	$0.888163\pi$
$368$	62.7922	−	36.2531i	0.170631	−	0.0985138i
$369$	387.346	+	223.634i	1.04972	+	0.606055i
$370$	111.063			0.300170
$371$	−82.6303	+	363.528i	−0.222723	+	0.979860i
$372$	106.691			0.286804
$373$	−144.476	−	250.240i	−0.387336	−	0.670885i	0.604755	−	0.796412i	$-0.293271\pi$
$373$	−144.476	−	250.240i	−0.387336	−	0.670885i	−0.992090	+	0.125527i	$0.959938\pi$
$374$		−	298.696i		−	0.798652i
$375$		−	321.429i		−	0.857143i
$376$	454.532			1.20886
$377$			94.8761i			0.251661i
$378$	143.426	+	132.841i	0.379433	+	0.351430i
$379$	267.813			0.706632			0.353316	−	0.935504i	$-0.385054\pi$
$379$	267.813			0.706632			0.353316	+	0.935504i	$0.385054\pi$
$380$		−	148.513i		−	0.390823i
$381$	15.4112			0.0404495
$382$	285.946			0.748550
$383$	602.618	−	347.922i	1.57342	−	0.908412i	0.577669	−	0.816271i	$-0.303962\pi$
$383$	602.618	−	347.922i	1.57342	−	0.908412i	0.995746	−	0.0921406i	$-0.0293709\pi$
$384$		−	344.642i		−	0.897504i
$385$	−154.854	+	167.193i	−0.402217	+	0.434267i
$386$		−	133.638i		−	0.346213i
$387$	−232.309	−	402.370i	−0.600280	−	1.03972i
$388$	−103.182	−	178.717i	−0.265933	−	0.460610i
$389$	320.094	+	184.806i	0.822863	+	0.475080i	0.851403	−	0.524512i	$-0.175752\pi$
$389$	320.094	+	184.806i	0.822863	+	0.475080i	−0.0285396	+	0.999593i	$0.509086\pi$
$390$	76.4413			0.196003
$391$	−181.455	+	314.289i	−0.464079	+	0.803808i
$392$	−350.212	+	26.8759i	−0.893397	+	0.0685609i
$393$	−420.035	+	242.507i	−1.06879	+	0.617067i
$394$	−272.396			−0.691361
$395$	−112.310	+	64.8420i	−0.284328	+	0.164157i
$396$	−305.999	−	176.669i	−0.772724	−	0.446133i
$397$	−54.5947	+	94.5607i	−0.137518	+	0.238188i	−0.926557	−	0.376156i	$-0.877246\pi$
$397$	−54.5947	+	94.5607i	−0.137518	+	0.238188i	0.789038	+	0.614344i	$0.210579\pi$
$398$	−142.738	+	82.4099i	−0.358638	+	0.207060i
$399$	−129.497	−	418.487i	−0.324553	−	1.04884i
$400$	−41.1143	+	71.2121i	−0.102786	+	0.178030i
$401$	298.605	−	172.400i	0.744650	−	0.429924i	−0.0791073	−	0.996866i	$-0.525207\pi$
$401$	298.605	−	172.400i	0.744650	−	0.429924i	0.823758	+	0.566942i	$0.191874\pi$
$402$			244.402i			0.607965i
$403$	61.5275	−	106.569i	0.152674	−	0.264439i
$404$	177.806	+	102.657i	0.440115	+	0.254100i
$405$	−170.442	+	98.4048i	−0.420845	+	0.242975i
$406$	−66.0708	−	15.0180i	−0.162736	−	0.0369900i
$407$	−512.780	+	296.054i	−1.25990	+	0.727405i
$408$	231.738	+	401.383i	0.567986	+	0.983781i
$409$	309.048			0.755619			0.377810	−	0.925883i	$-0.376677\pi$
$409$	309.048			0.755619			0.377810	+	0.925883i	$0.376677\pi$
$410$			124.898i			0.304630i
$411$	−471.783	−	272.384i	−1.14789	−	0.662736i
$412$	−2.49384	−	4.31945i	−0.00605300	−	0.0104841i
$413$	65.5880	+	60.7475i	0.158809	+	0.147088i
$414$	−78.3760	−	135.751i	−0.189314	−	0.327902i
$415$	114.409	−	198.162i	0.275684	−	0.477498i
$416$	−290.861	−	167.928i	−0.699184	−	0.403674i
$417$	−185.887	+	321.967i	−0.445773	+	0.772102i
$418$	−144.551	−	250.370i	−0.345816	−	0.598970i
$419$	308.758	+	178.261i	0.736892	+	0.425445i	0.820938	−	0.571017i	$-0.193451\pi$
$419$	308.758	+	178.261i	0.736892	+	0.425445i	−0.0840460	+	0.996462i	$0.526784\pi$
$420$	33.1381	−	145.789i	0.0789001	−	0.347117i
$421$	169.209	+	293.079i	0.401922	+	0.696149i	0.993958	−	0.109763i	$-0.0350090\pi$
$421$	169.209	+	293.079i	0.401922	+	0.696149i	−0.592036	+	0.805911i	$0.701676\pi$
$422$	−35.3306	−	20.3981i	−0.0837217	−	0.0483367i
$423$			570.686i			1.34914i
$424$	−190.879	−	330.612i	−0.450187	−	0.779746i
$425$		−	411.573i		−	0.968408i
$426$	−30.7586			−0.0722033
$427$	−288.686	+	311.689i	−0.676080	+	0.729951i
$428$	110.310	+	63.6876i	0.257734	+	0.148803i
$429$	−352.932	+	203.765i	−0.822684	+	0.474977i
$430$	64.8714	−	112.361i	0.150864	−	0.261304i
$431$	114.233	−	65.9527i	0.265043	−	0.153022i	−0.361590	−	0.932337i	$-0.617766\pi$
$431$	114.233	−	65.9527i	0.265043	−	0.153022i	0.626633	+	0.779315i	$0.284433\pi$
$432$	116.262			0.269125
$433$	−823.233			−1.90123			−0.950615	−	0.310371i	$-0.899547\pi$
$433$	−823.233			−1.90123			−0.950615	+	0.310371i	$0.899547\pi$
$434$	64.4742	+	59.7159i	0.148558	+	0.137594i
$435$	34.1062	−	59.0736i	0.0784050	−	0.135801i
$436$	210.578	+	364.732i	0.482977	+	0.836541i
$437$			351.253i			0.803783i
$438$	−265.398	+	153.227i	−0.605930	+	0.349834i
$439$	−465.031			−1.05930			−0.529648	−	0.848218i	$-0.677676\pi$
$439$	−465.031			−1.05930			−0.529648	+	0.848218i	$0.677676\pi$
$440$		−	233.364i		−	0.530372i
$441$	−33.7439	−	439.707i	−0.0765169	−	0.997068i
$442$	226.018			0.511353
$443$			374.603i			0.845605i	0.906222	+	0.422802i	$0.138954\pi$
$443$			374.603i			0.845605i	−0.906222	+	0.422802i	$0.861046\pi$
$444$	194.229	−	336.414i	0.437452	−	0.757689i
$445$	−48.0943			−0.108077
$446$	−20.7833	+	11.9993i	−0.0465994	+	0.0269042i
$447$	−297.744	+	171.902i	−0.666093	+	0.384569i
$448$	81.0562	−	87.5149i	0.180929	−	0.195346i
$449$		−	92.1792i		−	0.205299i	−0.994718	−	0.102649i	$-0.967268\pi$
$449$		−	92.1792i		−	0.205299i	0.994718	−	0.102649i	$-0.0327320\pi$
$450$	153.954	+	88.8857i	0.342121	+	0.197524i
$451$	−332.934	−	576.659i	−0.738213	−	1.27862i
$452$	547.359	+	316.018i	1.21097	+	0.699154i
$453$	−400.292	+	693.325i	−0.883646	+	1.53052i
$454$	−6.60519	+	11.4405i	−0.0145489	+	0.0251994i
$455$	−126.512	−	117.175i	−0.278048	−	0.257527i
$456$	388.490	+	224.295i	0.851953	+	0.491875i
$457$	728.091			1.59320			0.796598	−	0.604509i	$-0.206631\pi$
$457$	728.091			1.59320			0.796598	+	0.604509i	$0.206631\pi$
$458$	15.9699	−	9.22020i	0.0348687	−	0.0201314i
$459$	−503.955	+	290.958i	−1.09794	+	0.633897i
$460$	−59.9400	+	103.819i	−0.130304	+	0.225694i
$461$	−79.2568	+	45.7589i	−0.171924	+	0.0992601i	−0.583493	−	0.812119i	$-0.698314\pi$
$461$	−79.2568	+	45.7589i	−0.171924	+	0.0992601i	0.411569	+	0.911379i	$0.364981\pi$
$462$	−86.0344	−	278.032i	−0.186222	−	0.601801i
$463$	149.652	−	259.206i	0.323223	−	0.559839i	−0.657928	−	0.753081i	$-0.728567\pi$
$463$	149.652	−	259.206i	0.323223	−	0.559839i	0.981151	+	0.193242i	$0.0619002\pi$
$464$	−34.8967	+	20.1476i	−0.0752085	+	0.0434216i
$465$	−76.6190	+	44.2360i	−0.164772	+	0.0951312i
$466$	154.393	−	267.416i	0.331315	−	0.573855i
$467$	579.122	+	334.356i	1.24009	+	0.715966i	0.969112	−	0.246620i	$-0.0793199\pi$
$467$	579.122	+	334.356i	1.24009	+	0.715966i	0.270977	+	0.962586i	$0.412653\pi$
$468$	133.682	−	231.544i	0.285645	−	0.494752i
$469$	374.637	−	404.489i	0.798801	−	0.862451i
$470$	−138.012	+	79.6811i	−0.293642	+	0.169534i
$471$	−219.918			−0.466917
$472$	−91.5462			−0.193954
$473$			691.696i			1.46236i
$474$		−	165.621i		−	0.349412i
$475$	−199.177	−	344.984i	−0.419320	−	0.726283i
$476$	97.9810	−	431.063i	0.205842	−	0.905594i
$477$	415.099	−	239.658i	0.870229	−	0.502427i
$478$	−41.9598	+	72.6764i	−0.0877819	+	0.152043i
$479$	501.007	+	289.256i	1.04594	+	0.603876i	0.921511	−	0.388352i	$-0.126956\pi$
$479$	501.007	+	289.256i	1.04594	+	0.603876i	0.124432	+	0.992228i	$0.460289\pi$
$480$	120.734	+	209.118i	0.251530	+	0.435662i
$481$	−224.019	−	388.012i	−0.465735	−	0.806677i
$482$	−203.179	−	117.306i	−0.421534	−	0.243373i
$483$	−78.3760	+	344.811i	−0.162269	+	0.713895i
$484$	85.7425	+	148.510i	0.177154	+	0.306840i
$485$	148.198	+	85.5620i	0.305562	+	0.176417i
$486$		−	251.348i		−	0.517177i
$487$	323.525	+	560.361i	0.664322	+	1.15064i	0.979469	+	0.201596i	$0.0646130\pi$
$487$	323.525	+	560.361i	0.664322	+	1.15064i	−0.315147	+	0.949043i	$0.602054\pi$
$488$		−	435.049i		−	0.891493i
$489$	−127.532	+	220.892i	−0.260802	+	0.451722i
$490$	101.625	−	69.5538i	0.207398	−	0.141947i
$491$	−151.574	−	87.5114i	−0.308705	−	0.178231i	0.337642	−	0.941275i	$-0.390371\pi$
$491$	−151.574	−	87.5114i	−0.308705	−	0.178231i	−0.646347	+	0.763044i	$0.723704\pi$
$492$	378.322	+	218.424i	0.768948	+	0.443952i
$493$	100.844	−	174.666i	0.204551	−	0.354292i
$494$	189.450	−	109.379i	0.383502	−	0.221415i
$495$	292.999			0.591917
$496$	52.2633			0.105370
$497$	50.9060	+	47.1491i	0.102427	+	0.0948674i
$498$	146.113	+	253.075i	0.293399	+	0.508183i
$499$	−419.790	−	727.097i	−0.841262	−	1.45711i	−0.888828	−	0.458241i	$-0.848480\pi$
$499$	−419.790	−	727.097i	−0.841262	−	1.45711i	0.0475658	−	0.998868i	$-0.484854\pi$
$500$		−	313.941i		−	0.627881i
$501$	−515.665	−	297.720i	−1.02927	−	0.594251i
$502$	−212.170			−0.422650
$503$		−	92.3885i		−	0.183675i	−0.995774	−	0.0918375i	$-0.970726\pi$
$503$		−	92.3885i		−	0.183675i	0.995774	−	0.0918375i	$-0.0292740\pi$
$504$	331.318	+	306.867i	0.657378	+	0.608862i
$505$	−170.253			−0.337134
$506$			233.364i			0.461193i
$507$	99.3145	+	172.018i	0.195887	+	0.339286i
$508$	15.0522			0.0296304
$509$	−36.2020	+	20.9012i	−0.0711237	+	0.0410633i	−0.535140	−	0.844763i	$-0.679741\pi$
$509$	−36.2020	+	20.9012i	−0.0711237	+	0.0410633i	0.464016	+	0.885827i	$0.346408\pi$
$510$	−140.728	−	81.2492i	−0.275937	−	0.159312i
$511$	674.116	+	153.227i	1.31921	+	0.299858i
$512$		−	266.108i		−	0.519742i
$513$	−281.613	+	487.768i	−0.548953	+	0.950815i
$514$	227.096	+	393.342i	0.441822	+	0.765257i
$515$	3.58184	+	2.06797i	0.00695502	+	0.00401548i
$516$	−226.897	−	392.996i	−0.439722	−	0.761621i
$517$	424.803	−	735.780i	0.821669	−	1.42317i
$518$	305.667	−	94.5859i	0.590091	−	0.182598i
$519$		−	648.771i		−	1.25004i
$520$	176.582			0.339581
$521$	270.213	−	156.008i	0.518643	−	0.299439i	−0.217736	−	0.976008i	$-0.569867\pi$
$521$	270.213	−	156.008i	0.518643	−	0.299439i	0.736379	+	0.676569i	$0.236534\pi$
$522$	43.5575	+	75.4437i	0.0834434	+	0.144528i
$523$	285.621	−	494.709i	0.546120	−	0.945907i	−0.452416	−	0.891807i	$-0.649438\pi$
$523$	285.621	−	494.709i	0.546120	−	0.945907i	0.998536	−	0.0540998i	$-0.0172289\pi$
$524$	−410.250	+	236.858i	−0.782920	+	0.452019i
$525$	−118.547	−	383.101i	−0.225804	−	0.729715i
$526$	−200.125	+	346.626i	−0.380465	+	0.658985i
$527$	−226.543	+	130.795i	−0.429873	+	0.248188i
$528$	−149.895	−	86.5421i	−0.283893	−	0.163905i
$529$	−122.734	+	212.581i	−0.232011	+	0.401855i
$530$	115.915	+	66.9236i	0.218708	+	0.126271i
$531$		−	114.941i		−	0.216461i
$532$	−126.480	−	408.738i	−0.237744	−	0.768304i
$533$	436.348	−	251.925i	0.818663	−	0.472656i
$534$	30.7109	−	53.1929i	0.0575111	−	0.0996121i
$535$	−105.624			−0.197428
$536$			564.577i			1.05332i
$537$	282.423	−	163.057i	0.525928	−	0.303645i
$538$	−86.2526	−	149.394i	−0.160321	−	0.277684i
$539$	−283.800	+	592.028i	−0.526531	+	1.09838i
$540$	−166.471	+	96.1123i	−0.308280	+	0.177986i
$541$	140.132	−	242.716i	0.259024	−	0.448643i	−0.706956	−	0.707257i	$-0.749932\pi$
$541$	140.132	−	242.716i	0.259024	−	0.448643i	0.965981	+	0.258614i	$0.0832657\pi$
$542$	149.762	+	86.4652i	0.276314	+	0.159530i
$543$	34.1916			0.0629679
$544$	356.981	+	618.309i	0.656215	+	1.13660i
$545$	−302.448	−	174.618i	−0.554950	−	0.320401i
$546$	210.382	−	65.1007i	0.385315	−	0.119232i
$547$	−14.2455	−	24.6738i	−0.0260429	−	0.0451076i	0.852710	−	0.522384i	$-0.174957\pi$
$547$	−14.2455	−	24.6738i	−0.0260429	−	0.0451076i	−0.878753	+	0.477277i	$0.841624\pi$
$548$	−460.793	−	266.039i	−0.840862	−	0.485472i
$549$	546.224			0.994944
$550$	−132.328	−	229.199i	−0.240596	−	0.416725i
$551$		−	195.209i		−	0.354281i
$552$	−181.051	−	313.590i	−0.327992	−	0.568099i
$553$	−253.877	+	274.106i	−0.459090	+	0.495671i
$554$	−326.919	−	188.747i	−0.590106	−	0.340698i
$555$			322.122i			0.580400i
$556$	−181.557	+	314.466i	−0.326541	+	0.565586i
$557$	−50.1553	+	28.9571i	−0.0900453	+	0.0519877i	−0.544347	−	0.838860i	$-0.683222\pi$
$557$	−50.1553	+	28.9571i	−0.0900453	+	0.0519877i	0.454301	+	0.890848i	$0.349889\pi$
$558$		−	112.989i		−	0.202489i
$559$	−523.394			−0.936304
$560$	16.2329	−	71.4157i	0.0289873	−	0.127528i
$561$	866.326			1.54425
$562$	225.266	+	390.171i	0.400828	+	0.694255i
$563$		−	577.538i		−	1.02582i	−0.858442	−	0.512911i	$-0.828567\pi$
$563$		−	577.538i		−	1.02582i	0.858442	−	0.512911i	$-0.171433\pi$
$564$			557.391i			0.988283i
$565$	−524.105			−0.927620
$566$			108.792i			0.192211i
$567$	−385.285	+	415.986i	−0.679516	+	0.733661i
$568$	−71.0535			−0.125094
$569$		−	318.457i		−	0.559678i	−0.960047	−	0.279839i	$-0.909719\pi$
$569$		−	318.457i		−	0.559678i	0.960047	−	0.279839i	$-0.0902810\pi$
$570$	−157.279			−0.275928
$571$	540.531			0.946639			0.473320	−	0.880891i	$-0.343056\pi$
$571$	540.531			0.946639			0.473320	+	0.880891i	$0.343056\pi$
$572$	−344.710	+	199.018i	−0.602639	+	0.347934i
$573$			829.347i			1.44738i
$574$	106.369	+	343.745i	0.185311	+	0.598859i
$575$			321.552i			0.559221i
$576$	−153.367			−0.266262
$577$	96.2355	+	166.685i	0.166786	+	0.288882i	0.937288	−	0.348556i	$-0.113328\pi$
$577$	96.2355	+	166.685i	0.166786	+	0.288882i	−0.770502	+	0.637437i	$0.779994\pi$
$578$	−157.217	−	90.7695i	−0.272002	−	0.157041i
$579$	387.599			0.669428
$580$	33.3116	−	57.6974i	0.0574339	−	0.0994783i
$581$	146.113	−	642.817i	0.251485	−	1.10640i
$582$	−189.265	+	109.272i	−0.325198	+	0.187753i
$583$	−713.578			−1.22398
$584$	−613.078	+	353.961i	−1.04979	+	0.606097i
$585$			221.707i			0.378987i
$586$	198.571	−	343.934i	0.338858	−	0.586919i
$587$	337.215	−	194.691i	0.574473	−	0.331672i	−0.184461	−	0.982840i	$-0.559054\pi$
$587$	337.215	−	194.691i	0.574473	−	0.331672i	0.758934	+	0.651168i	$0.225721\pi$
$588$	−32.9578	−	429.464i	−0.0560507	−	0.730380i
$589$	−126.594	+	219.267i	−0.214930	+	0.372270i
$590$	27.7966	−	16.0484i	0.0471129	−	0.0272007i
$591$		−	790.047i		−	1.33680i
$592$	95.1441	−	164.794i	0.160716	−	0.278369i
$593$	−20.9074	−	12.0709i	−0.0352570	−	0.0203557i	0.482268	−	0.876024i	$-0.339813\pi$
$593$	−20.9074	−	12.0709i	−0.0352570	−	0.0203557i	−0.517525	+	0.855668i	$0.673147\pi$
$594$	−187.097	+	324.061i	−0.314977	+	0.545557i
$595$	108.362	+	350.187i	0.182121	+	0.588550i
$596$	−290.807	+	167.898i	−0.487932	+	0.281708i
$597$	−239.018	−	413.992i	−0.400366	−	0.693454i
$598$	−176.582			−0.295288
$599$		−	97.3663i		−	0.162548i	−0.996692	−	0.0812740i	$-0.974101\pi$
$599$		−	97.3663i		−	0.162548i	0.996692	−	0.0812740i	$-0.0258989\pi$
$600$	355.641	+	205.329i	0.592734	+	0.342215i
$601$	279.480	+	484.073i	0.465024	+	0.805446i	0.999203	−	0.0399261i	$-0.0127122\pi$
$601$	279.480	+	484.073i	0.465024	+	0.805446i	−0.534178	+	0.845372i	$0.679379\pi$
$602$	82.8481	−	364.486i	0.137621	−	0.605459i
$603$	−708.853			−1.17554
$604$	−390.966	+	677.174i	−0.647295	+	1.12115i
$605$	−123.150	−	71.1006i	−0.203553	−	0.117522i
$606$	108.716	−	188.301i	0.179399	−	0.310728i
$607$	223.834	+	387.691i	0.368754	+	0.638700i	0.989371	−	0.145413i	$-0.0464512\pi$
$607$	223.834	+	387.691i	0.368754	+	0.638700i	−0.620617	+	0.784114i	$0.713118\pi$
$608$	598.450	+	345.515i	0.984292	+	0.568281i
$609$	43.5575	−	191.629i	0.0715229	−	0.314662i
$610$	76.2656	+	132.096i	0.125026	+	0.216551i
$611$	556.752	+	321.441i	0.911214	+	0.526090i
$612$	−492.215	+	284.180i	−0.804272	+	0.464347i
$613$	306.529	+	530.923i	0.500047	+	0.866107i	1.00000		5.41150e-5i	$1.72253e-5\pi$
$613$	306.529	+	530.923i	0.500047	+	0.866107i	−0.499953	+	0.866052i	$0.666649\pi$
$614$		−	190.807i		−	0.310761i
$615$	−362.250			−0.589024
$616$	−198.743	−	642.264i	−0.322634	−	1.04264i
$617$	48.7599	+	28.1515i	0.0790273	+	0.0456264i	0.538993	−	0.842310i	$-0.318805\pi$
$617$	48.7599	+	28.1515i	0.0790273	+	0.0456264i	−0.459966	+	0.887937i	$0.652138\pi$
$618$	−4.57441	+	2.64104i	−0.00740196	+	0.00427352i
$619$	234.852	−	406.776i	0.379406	−	0.657150i	−0.611570	−	0.791190i	$-0.709462\pi$
$619$	234.852	−	406.776i	0.379406	−	0.657150i	0.990976	+	0.134040i	$0.0427952\pi$
$620$	−74.8340	+	43.2055i	−0.120700	+	0.0696862i
$621$	393.727	−	227.319i	0.634022	−	0.366053i
$622$	−280.488			−0.450946
$623$	−132.365	+	40.9592i	−0.212464	+	0.0657450i
$624$	65.4849	−	113.423i	0.104944	−	0.181768i
$625$	−108.539	−	187.995i	−0.173662	−	0.300792i
$626$			553.325i			0.883905i
$627$	726.162	−	419.250i	1.15815	−	0.668660i
$628$	−214.795			−0.342030
$629$			952.435i			1.51421i
$630$	−154.395	−	35.0941i	−0.245071	−	0.0557049i
$631$	−107.630			−0.170571			−0.0852856	−	0.996357i	$-0.527180\pi$
$631$	−107.630			−0.170571			−0.0852856	+	0.996357i	$0.527180\pi$
$632$		−	382.591i		−	0.605366i
$633$	59.1618	−	102.471i	0.0934626	−	0.161882i
$634$	65.5880			0.103451
$635$	−10.8096	+	6.24090i	−0.0170229	+	0.00982820i
$636$	405.429	−	234.075i	0.637467	−	0.368042i
$637$	−447.977	−	214.746i	−0.703261	−	0.337122i
$638$		−	129.692i		−	0.203279i
$639$		−	89.2110i		−	0.139610i
$640$	139.565	+	241.734i	0.218071	+	0.377710i
$641$	−836.048	−	482.692i	−1.30429	−	0.753030i	−0.323151	−	0.946348i	$-0.604742\pi$
$641$	−836.048	−	482.692i	−1.30429	−	0.753030i	−0.981136	+	0.193317i	$0.938075\pi$
$642$	67.4468	−	116.821i	0.105057	−	0.181964i
$643$	−100.415	+	173.923i	−0.156166	+	0.270487i	−0.933483	−	0.358622i	$-0.883247\pi$
$643$	−100.415	+	173.923i	−0.156166	+	0.270487i	0.777317	+	0.629109i	$0.216580\pi$
$644$	−76.5501	+	336.779i	−0.118867	+	0.522948i
$645$	325.886	+	188.150i	0.505250	+	0.291706i
$646$	−465.035			−0.719868
$647$	−658.907	+	380.420i	−1.01840	+	0.587975i	−0.913641	−	0.406522i	$-0.866741\pi$
$647$	−658.907	+	380.420i	−1.01840	+	0.587975i	−0.104762	+	0.994497i	$0.533408\pi$
$648$		−	580.623i		−	0.896024i
$649$	−85.5586	+	148.192i	−0.131831	+	0.228339i
$650$	173.431	−	100.130i	0.266816	−	0.154047i
$651$	−173.198	+	186.998i	−0.266049	+	0.287248i
$652$	−124.561	+	215.746i	−0.191044	+	0.330899i
$653$	−277.656	+	160.305i	−0.425201	+	0.245490i	−0.697300	−	0.716779i	$-0.745616\pi$
$653$	−277.656	+	160.305i	−0.425201	+	0.245490i	0.272099	+	0.962269i	$0.412282\pi$
$654$	386.260	−	223.008i	0.590612	−	0.340990i
$655$	196.411	−	340.193i	0.299863	−	0.519379i
$656$	185.323	+	106.996i	0.282505	+	0.163104i
$657$	−444.414	−	769.748i	−0.676430	−	1.17161i
$658$	−311.976	+	336.835i	−0.474128	+	0.511908i
$659$	580.208	−	334.984i	0.880438	−	0.508321i	0.00963502	−	0.999954i	$-0.496933\pi$
$659$	580.208	−	334.984i	0.880438	−	0.508321i	0.870803	+	0.491633i	$0.163600\pi$
$660$	286.173			0.433596
$661$	455.530			0.689152			0.344576	−	0.938758i	$-0.388023\pi$
$661$	455.530			0.689152			0.344576	+	0.938758i	$0.388023\pi$
$662$		−	249.216i		−	0.376459i
$663$			655.533i			0.988738i
$664$	337.526	+	584.613i	0.508323	+	0.880441i
$665$	260.300	+	241.089i	0.391428	+	0.362540i
$666$	−356.271	−	205.693i	−0.534942	−	0.308849i
$667$	−78.7865	+	136.462i	−0.118121	+	0.204591i
$668$	−503.652	−	290.784i	−0.753970	−	0.435305i
$669$	−34.8022	−	60.2792i	−0.0520212	−	0.0901034i
$670$	−98.9724	−	171.425i	−0.147720	−	0.255859i
$671$	−704.241	−	406.594i	−1.04954	−	0.605952i
$672$	510.379	+	472.712i	0.759492	+	0.703441i
$673$	17.2731	+	29.9178i	0.0256658	+	0.0444544i	0.878573	−	0.477608i	$-0.158496\pi$
$673$	17.2731	+	29.9178i	0.0256658	+	0.0444544i	−0.852907	+	0.522063i	$0.825163\pi$
$674$	101.292	+	58.4812i	0.150286	+	0.0867674i
$675$	−257.800	+	446.523i	−0.381927	+	0.661516i
$676$	97.0008	+	168.010i	0.143492	+	0.248536i
$677$		−	514.084i		−	0.759356i	−0.925119	−	0.379678i	$-0.876035\pi$
$677$		−	514.084i		−	0.759356i	0.925119	−	0.379678i	$-0.123965\pi$
$678$	334.671	−	579.667i	0.493615	−	0.854966i
$679$	480.739	+	109.272i	0.708010	+	0.160931i
$680$	−325.086	−	187.689i	−0.478068	−	0.276013i
$681$	−33.1816	−	19.1574i	−0.0487249	−	0.0281313i
$682$	−84.1057	+	145.675i	−0.123322	+	0.213600i
$683$	169.023	−	97.5857i	0.247472	−	0.142878i	−0.371134	−	0.928579i	$-0.621031\pi$
$683$	169.023	−	97.5857i	0.247472	−	0.142878i	0.618606	+	0.785701i	$0.287698\pi$
$684$	−275.052	+	476.405i	−0.402123	+	0.696498i
$685$	441.217			0.644112
$686$	220.458	−	277.975i	0.321367	−	0.405211i
$687$	26.7419	+	46.3183i	0.0389256	+	0.0674211i
$688$	−111.147	−	192.512i	−0.161550	−	0.279813i
$689$		−	539.952i		−	0.783675i
$690$	109.947	+	63.4780i	0.159344	+	0.0919971i
$691$	466.772			0.675502			0.337751	−	0.941235i	$-0.390334\pi$
$691$	466.772			0.675502			0.337751	+	0.941235i	$0.390334\pi$
$692$		−	633.657i		−	0.915690i
$693$	806.393	−	249.531i	1.16363	−	0.360073i
$694$	128.123			0.184616
$695$		−	301.106i		−	0.433247i
$696$	100.619	+	174.278i	0.144568	+	0.250399i
$697$	−1071.08			−1.53670
$698$	−337.330	+	194.758i	−0.483281	+	0.279022i
$699$	775.604	+	447.795i	1.10959	+	0.640623i
$700$	−115.785	−	374.176i	−0.165407	−	0.534537i
$701$		−	129.972i		−	0.185409i	−0.995694	−	0.0927044i	$-0.970449\pi$
$701$		−	129.972i		−	0.185409i	0.995694	−	0.0927044i	$-0.0295512\pi$
$702$	−245.211	−	141.573i	−0.349303	−	0.201670i
$703$	460.922	+	798.340i	0.655649	+	1.13562i
$704$	197.734	+	114.162i	0.280873	+	0.162162i
$705$	−231.104	−	400.284i	−0.327807	−	0.567778i
$706$	16.8768	−	29.2314i	0.0239048	−	0.0414043i
$707$	−468.570	+	144.994i	−0.662757	+	0.205084i
$708$		−	112.263i		−	0.158563i
$709$	500.798			0.706345			0.353172	−	0.935558i	$-0.385103\pi$
$709$	500.798			0.706345			0.353172	+	0.935558i	$0.385103\pi$
$710$	21.5743	−	12.4559i	0.0303863	−	0.0175436i
$711$	480.361			0.675613
$712$	70.9433	−	122.877i	0.0996395	−	0.172581i
$713$	176.993	−	102.187i	0.248237	−	0.143319i
$714$	−456.507	−	103.764i	−0.639365	−	0.145328i
$715$	165.033	−	285.845i	0.230815	−	0.399783i
$716$	275.844	−	159.259i	0.385257	−	0.222428i
$717$	−210.788	−	121.698i	−0.293986	−	0.169733i
$718$	−283.344	+	490.766i	−0.394629	+	0.683518i
$719$	−649.800	−	375.162i	−0.903756	−	0.521784i	−0.0253388	−	0.999679i	$-0.508066\pi$
$719$	−649.800	−	375.162i	−0.903756	−	0.521784i	−0.878417	+	0.477895i	$0.841400\pi$
$720$	−81.5470	+	47.0812i	−0.113260	+	0.0653905i
$721$	11.6191	+	2.64104i	0.0161153	+	0.00366302i
$722$	−66.4209	+	38.3481i	−0.0919957	+	0.0531137i
$723$	340.228	−	589.293i	0.470579	−	0.815066i
$724$	33.3950			0.0461257
$725$		−	178.702i		−	0.246486i
$726$	157.276	−	90.8035i	0.216634	−	0.125074i
$727$	−8.82404	−	15.2837i	−0.0121376	−	0.0210230i	0.859893	−	0.510475i	$-0.170530\pi$
$727$	−8.82404	−	15.2837i	−0.0121376	−	0.0210230i	−0.872030	+	0.489452i	$0.837197\pi$
$728$	485.990	−	150.385i	0.667569	−	0.206573i
$729$	729.000			1.00000
$730$	124.101	−	214.950i	0.170002	−	0.294452i
$731$	963.564	+	556.314i	1.31814	+	0.761031i
$732$	533.499			0.728824
$733$	353.143	+	611.662i	0.481778	+	0.834464i	0.999781	−	0.0209148i	$-0.00665789\pi$
$733$	353.143	+	611.662i	0.481778	+	0.834464i	−0.518003	+	0.855379i	$0.673325\pi$
$734$	504.637	+	291.353i	0.687517	+	0.396938i
$735$	201.731	+	294.749i	0.274464	+	0.401019i
$736$	−278.901	−	483.070i	−0.378941	−	0.656345i
$737$	913.917	+	527.650i	1.24005	+	0.715944i
$738$	231.317	−	400.653i	0.313438	−	0.542890i
$739$	−524.821	−	909.016i	−0.710177	−	1.23006i	−0.964791	−	0.263019i	$-0.915282\pi$
$739$	−524.821	−	909.016i	−0.710177	−	1.23006i	0.254614	−	0.967043i	$-0.418052\pi$
$740$			314.618i			0.425159i
$741$	317.239	+	549.474i	0.428123	+	0.741530i
$742$	376.017	+	85.4691i	0.506761	+	0.115187i
$743$	738.043	+	426.109i	0.993328	+	0.573498i	0.906268	−	0.422705i	$-0.138919\pi$
$743$	738.043	+	426.109i	0.993328	+	0.573498i	0.0870609	+	0.996203i	$0.472253\pi$
$744$		−	261.008i		−	0.350817i
$745$	139.226	−	241.147i	0.186881	−	0.323688i
$746$	−258.837	+	149.440i	−0.346966	+	0.200321i
$747$	−734.008	+	423.780i	−0.982608	+	0.567309i
$748$	846.143			1.13121
$749$	−290.698	+	89.9538i	−0.388115	+	0.120098i
$750$	−332.471			−0.443295
$751$	93.1953	+	161.419i	0.124095	+	0.214939i	0.921379	−	0.388666i	$-0.127064\pi$
$751$	93.1953	+	161.419i	0.124095	+	0.214939i	−0.797284	+	0.603605i	$0.793731\pi$
$752$			273.041i			0.363087i
$753$		−	615.370i		−	0.817225i
$754$	98.1355			0.130153
$755$		−	648.405i		−	0.858815i
$756$	−376.310	+	406.295i	−0.497764	+	0.537427i
$757$	619.209			0.817978			0.408989	−	0.912539i	$-0.365881\pi$
$757$	619.209			0.817978			0.408989	+	0.912539i	$0.365881\pi$
$758$		−	277.014i		−	0.365454i
$759$	−676.839			−0.891750
$760$	−363.320			−0.478053
$761$	−917.262	+	529.582i	−1.20534	+	0.695902i	−0.961737	−	0.273973i	$-0.911662\pi$
$761$	−917.262	+	529.582i	−1.20534	+	0.695902i	−0.243601	+	0.969876i	$0.578329\pi$
$762$		−	15.9407i		−	0.0209195i
$763$	−981.111	−	223.008i	−1.28586	−	0.292277i
$764$			810.026i			1.06024i
$765$	235.652	−	408.161i	0.308042	−	0.533544i
$766$	−359.874	−	623.321i	−0.469810	−	0.813734i
$767$	−112.134	−	64.7406i	−0.146198	−	0.0844076i
$768$	−560.971			−0.730431
$769$	0.501476	−	0.868581i	0.000652114	−	0.00112949i	−0.865699	−	0.500565i	$-0.833126\pi$
$769$	0.501476	−	0.868581i	0.000652114	−	0.00112949i	0.866351	+	0.499435i	$0.166459\pi$
$770$	172.936	+	160.173i	0.224593	+	0.208017i
$771$	−1140.83	+	658.661i	−1.47968	+	0.854294i
$772$	378.569			0.490375
$773$	952.452	−	549.899i	1.23215	−	0.711382i	0.264673	−	0.964338i	$-0.414736\pi$
$773$	952.452	−	549.899i	1.23215	−	0.711382i	0.967478	+	0.252956i	$0.0814027\pi$
$774$	−416.193	+	240.289i	−0.537717	+	0.310451i
$775$	−115.889	+	200.726i	−0.149535	+	0.259001i
$776$	−437.210	+	252.423i	−0.563415	+	0.325288i
$777$	274.333	+	886.545i	0.353067	+	1.14099i
$778$	191.155	−	331.090i	0.245701	−	0.425566i
$779$	−897.791	+	518.340i	−1.15249	+	0.665392i
$780$			216.542i			0.277618i
$781$	−66.4062	+	115.019i	−0.0850271	+	0.147271i
$782$	325.086	+	187.689i	0.415711	+	0.240011i
$783$	−218.814	+	126.332i	−0.279456	+	0.161344i
$784$	−16.1446	−	210.375i	−0.0205926	−	0.268336i
$785$	154.252	−	89.0575i	0.196500	−	0.113449i
$786$	250.839	+	434.465i	0.319133	+	0.552755i
$787$	−815.686			−1.03645			−0.518225	−	0.855245i	$-0.673407\pi$
$787$	−815.686			−1.03645			−0.518225	+	0.855245i	$0.673407\pi$
$788$		−	771.642i		−	0.979241i
$789$	−1005.34	−	580.434i	−1.27420	−	0.735658i
$790$	67.0696	+	116.168i	0.0848982	+	0.147048i
$791$	−1442.44	+	446.351i	−1.82357	+	0.564287i
$792$	−432.200	+	748.592i	−0.545707	+	0.945192i
$793$	307.662	−	532.887i	0.387973	−	0.671989i
$794$	97.8093	+	56.4702i	0.123186	+	0.0711212i
$795$	−194.103	+	336.196i	−0.244154	+	0.422887i
$796$	−233.450	−	404.347i	−0.293279	−	0.507974i
$797$	−372.316	−	214.957i	−0.467147	−	0.269707i	0.247898	−	0.968786i	$-0.420260\pi$
$797$	−372.316	−	214.957i	−0.467147	−	0.269707i	−0.715045	+	0.699079i	$0.753594\pi$
$798$	−432.864	+	133.946i	−0.542436	+	0.167852i
$799$	−683.317	−	1183.54i	−0.855215	−	1.48128i
$800$	547.846	+	316.299i	0.684808	+	0.395374i
$801$	154.278	+	89.0727i	0.192607	+	0.111202i
$802$	−178.322	−	308.863i	−0.222347	−	0.385116i
$803$			1323.24i			1.64787i
$804$	−692.339			−0.861119
$805$	−84.6606	−	273.592i	−0.105168	−	0.339866i
$806$	−110.230	−	63.6413i	−0.136762	−	0.0789594i
$807$	433.296	−	250.164i	0.536922	−	0.309992i
$808$	251.138	−	434.983i	0.310814	−	0.538346i
$809$	−31.8045	+	18.3624i	−0.0393134	+	0.0226976i	−0.519528	−	0.854453i	$-0.673892\pi$
$809$	−31.8045	+	18.3624i	−0.0393134	+	0.0226976i	0.480214	+	0.877151i	$0.340559\pi$
$810$	101.785	+	176.297i	0.125661	+	0.217651i
$811$	−176.943			−0.218178			−0.109089	−	0.994032i	$-0.534793\pi$
$811$	−176.943			−0.218178			−0.109089	+	0.994032i	$0.534793\pi$
$812$	42.5427	−	187.165i	0.0523925	−	0.230498i
$813$	−250.780	+	434.364i	−0.308463	+	0.534273i
$814$	306.225	+	530.397i	0.376197	+	0.651593i
$815$		−	206.580i		−	0.253473i
$816$	−241.114	+	139.207i	−0.295483	+	0.170597i
$817$	1076.89			1.31810
$818$		−	319.665i		−	0.390789i
$819$	188.815	+	610.183i	0.230544	+	0.745034i
$820$	−353.811			−0.431477
$821$			25.1313i			0.0306105i	0.999883	+	0.0153053i	$0.00487201\pi$
$821$			25.1313i			0.0306105i	−0.999883	+	0.0153053i	$0.995128\pi$
$822$	−281.742	+	487.991i	−0.342752	+	0.593663i
$823$	−358.406			−0.435488			−0.217744	−	0.976006i	$-0.569870\pi$
$823$	−358.406			−0.435488			−0.217744	+	0.976006i	$0.569870\pi$
$824$	−10.5671	+	6.10089i	−0.0128241	+	0.00740400i
$825$	664.759	−	383.799i	0.805769	−	0.465211i
$826$	62.8344	−	67.8412i	0.0760708	−	0.0821322i
$827$			620.301i			0.750061i	0.927012	+	0.375031i	$0.122368\pi$
$827$			620.301i			0.750061i	−0.927012	+	0.375031i	$0.877632\pi$
$828$	384.555	−	222.023i	0.464438	−	0.268144i
$829$	−451.062	−	781.263i	−0.544104	−	0.942416i	−0.998663	−	0.0516989i	$-0.983536\pi$
$829$	−451.062	−	781.263i	−0.544104	−	0.942416i	0.454559	−	0.890717i	$-0.349797\pi$
$830$	−204.969	−	118.339i	−0.246951	−	0.142577i
$831$	547.433	−	948.182i	0.658764	−	1.14101i
$832$	−86.3843	+	149.622i	−0.103827	+	0.179834i
$833$	596.469	+	871.500i	0.716049	+	1.04622i
$834$	333.027	+	192.274i	0.399314	+	0.230544i
$835$	482.255			0.577551
$836$	709.245	−	409.483i	0.848379	−	0.489812i
$837$	327.708			0.391527
$838$	184.385	−	319.365i	0.220030	−	0.381104i
$839$	820.992	−	474.000i	0.978537	−	0.564958i	0.0767087	−	0.997054i	$-0.475559\pi$
$839$	820.992	−	474.000i	0.978537	−	0.564958i	0.901828	+	0.432095i	$0.142226\pi$
$840$	−356.657	−	81.0686i	−0.424592	−	0.0965102i
$841$	−376.714	+	652.488i	−0.447936	+	0.775848i
$842$	303.147	−	175.022i	0.360032	−	0.207865i
$843$	−1131.64	+	653.351i	−1.34239	+	0.775031i
$844$	57.7836	−	100.084i	0.0684640	−	0.118583i
$845$	−139.320	−	80.4364i	−0.164876	−	0.0951910i
$846$	590.292			0.697745
$847$	−399.486	−	90.8035i	−0.471648	−	0.107206i
$848$	198.602	−	114.663i	0.234200	−	0.135216i
$849$	−315.535			−0.371655
$850$	−425.713			−0.500838
$851$		−	744.114i		−	0.874399i
$852$		−	87.1327i		−	0.102268i
$853$	502.340	+	870.078i	0.588910	+	1.02002i	0.994376	+	0.105911i	$0.0337760\pi$
$853$	502.340	+	870.078i	0.588910	+	1.02002i	−0.405466	+	0.914110i	$0.632891\pi$
$854$	322.397	+	298.604i	0.377514	+	0.349653i
$855$		−	456.166i		−	0.533527i
$856$	155.805	−	269.861i	0.182015	−	0.315259i
$857$	−103.121	−	59.5367i	−0.120327	−	0.0694711i	0.438628	−	0.898669i	$-0.355464\pi$
$857$	−103.121	−	59.5367i	−0.120327	−	0.0694711i	−0.558956	+	0.829198i	$0.688798\pi$
$858$	210.765	+	365.056i	0.245647	+	0.425474i
$859$	−174.849	−	302.847i	−0.203549	−	0.352558i	0.746120	−	0.665811i	$-0.231914\pi$
$859$	−174.849	−	302.847i	−0.203549	−	0.352558i	−0.949670	+	0.313254i	$0.898581\pi$
$860$	318.294	+	183.767i	0.370109	+	0.213683i
$861$	−996.985	+	308.508i	−1.15794	+	0.358313i
$862$	−68.2184	−	118.158i	−0.0791397	−	0.137074i
$863$	−580.996	−	335.438i	−0.673229	−	0.388689i	0.124070	−	0.992273i	$-0.460405\pi$
$863$	−580.996	−	335.438i	−0.673229	−	0.388689i	−0.797299	+	0.603585i	$0.793739\pi$
$864$		−	894.421i		−	1.03521i
$865$	262.725	+	455.053i	0.303728	+	0.526073i
$866$			851.515i			0.983273i
$867$	263.264	−	455.987i	0.303650	−	0.525936i
$868$	−169.163	+	182.642i	−0.194888	+	0.210417i
$869$	−619.325	−	357.567i	−0.712687	−	0.411470i
$870$	−61.1031	−	35.2779i	−0.0702334	−	0.0405493i
$871$	−399.264	+	691.545i	−0.458397	+	0.793967i
$872$	892.276	−	515.156i	1.02325	−	0.590775i
$873$	−316.929	−	548.938i	−0.363035	−	0.628795i
$874$	363.320			0.415698
$875$	550.246	+	509.637i	0.628853	+	0.582442i
$876$	−434.061	−	751.816i	−0.495504	−	0.858237i
$877$	−78.8477	−	136.568i	−0.0899062	−	0.155722i	0.817565	−	0.575836i	$-0.195323\pi$
$877$	−78.8477	−	136.568i	−0.0899062	−	0.155722i	−0.907471	+	0.420114i	$0.861990\pi$
$878$			481.006i			0.547843i
$879$	997.533	+	575.926i	1.13485	+	0.655206i
$880$	140.184			0.159300
$881$		−	169.327i		−	0.192199i	−0.995372	−	0.0960995i	$-0.969363\pi$
$881$		−	169.327i		−	0.192199i	0.995372	−	0.0960995i	$-0.0306367\pi$
$882$	−454.813	+	34.9032i	−0.515661	+	0.0395728i
$883$	−944.394			−1.06953			−0.534764	−	0.845001i	$-0.679600\pi$
$883$	−944.394			−1.06953			−0.534764	+	0.845001i	$0.679600\pi$
$884$			640.262i			0.724278i
$885$	46.5461	+	80.6202i	0.0525945	+	0.0910963i
$886$	387.472			0.437327
$887$	950.157	−	548.574i	1.07120	−	0.618459i	0.142693	−	0.989767i	$-0.454424\pi$
$887$	950.157	−	548.574i	1.07120	−	0.618459i	0.928510	+	0.371307i	$0.121090\pi$
$888$	−822.999	−	475.159i	−0.926801	−	0.535089i
$889$	−24.4351	+	26.3821i	−0.0274860	+	0.0296762i
$890$			49.7465i			0.0558950i
$891$	−939.893	−	542.647i	−1.05487	−	0.609032i
$892$	−33.9914	−	58.8749i	−0.0381070	−	0.0660032i
$893$	−1145.52	−	661.369i	−1.28278	−	0.740615i
$894$	177.808	+	307.972i	0.198890	+	0.344488i
$895$	−132.063	+	228.739i	−0.147556	+	0.255574i
$896$	589.984	+	546.442i	0.658464	+	0.609868i
$897$		−	512.152i		−	0.570961i
$898$	−95.3460			−0.106176
$899$	−98.3637	+	56.7903i	−0.109415	+	0.0631705i
$900$	−251.795	+	436.121i	−0.279772	+	0.484579i
$901$	−573.913	+	994.047i	−0.636974	+	1.10327i
$902$	−596.470	+	344.372i	−0.661275	+	0.381787i
$903$	1057.14	+	240.289i	1.17070	+	0.266101i
$904$	773.102	−	1339.05i	0.855201	−	1.48125i
$905$	−23.9822	+	13.8461i	−0.0264997	+	0.0152996i
$906$	717.144	+	414.043i	0.791550	+	0.457002i
$907$	−166.934	+	289.137i	−0.184050	+	0.318784i	−0.943256	−	0.332066i	$-0.892254\pi$
$907$	−166.934	+	289.137i	−0.184050	+	0.318784i	0.759206	+	0.650851i	$0.225588\pi$
$908$	−32.4086	−	18.7111i	−0.0356923	−	0.0206070i
$909$	546.142	+	315.315i	0.600816	+	0.346881i
$910$	−121.200	+	130.858i	−0.133187	+	0.143800i
$911$	789.460	−	455.795i	0.866586	−	0.500324i	0.000374020	−	1.00000i	$-0.499881\pi$
$911$	789.460	−	455.795i	0.866586	−	0.500324i	0.866212	+	0.499676i	$0.166548\pi$
$912$	−134.736	+	233.370i	−0.147737	+	0.255888i
$913$	1261.80			1.38204
$914$		−	753.104i		−	0.823965i
$915$	−383.126	+	221.198i	−0.418717	+	0.241746i
$916$	26.1189	+	45.2393i	0.0285141	+	0.0493879i
$917$	250.839	−	1103.55i	0.273543	−	1.20344i
$918$	300.954	+	521.268i	0.327837	+	0.567830i
$919$	−422.629	+	732.014i	−0.459879	+	0.796534i	−0.998954	−	0.0457240i	$-0.985441\pi$
$919$	−422.629	+	732.014i	−0.459879	+	0.796534i	0.539075	+	0.842258i	$0.318774\pi$
$920$	253.982	+	146.636i	0.276067	+	0.159387i
$921$	553.409			0.600878
$922$	47.3309	+	81.9796i	0.0513351	+	0.0889149i
$923$	−87.0327	−	50.2484i	−0.0942933	−	0.0544403i
$924$	787.607	−	243.718i	0.852388	−	0.263764i
$925$	421.947	+	730.834i	0.456159	+	0.790091i
$926$	−268.110	−	154.794i	−0.289536	−	0.167164i
$927$	−7.65996	−	13.2674i	−0.00826317	−	0.0143122i
$928$	154.999	+	268.466i	0.167025	+	0.289295i
$929$			907.807i			0.977188i	0.872511	+	0.488594i	$0.162490\pi$
$929$			907.807i			0.977188i	−0.872511	+	0.488594i	$0.837510\pi$
$930$	45.7557	+	79.2512i	0.0491997	+	0.0852163i
$931$	921.719	+	441.844i	0.990032	+	0.474590i
$932$	757.535	+	437.363i	0.812806	+	0.469274i
$933$		−	813.517i		−	0.871937i
$934$	345.843	−	599.017i	0.370281	−	0.641346i
$935$	−607.647	+	350.825i	−0.649890	+	0.375214i
$936$	−566.446	−	327.038i	−0.605178	−	0.349400i
$937$	265.251			0.283085			0.141543	−	0.989932i	$-0.454794\pi$
$937$	265.251			0.283085			0.141543	+	0.989932i	$0.454794\pi$
$938$	−418.385	−	387.508i	−0.446040	−	0.413121i
$939$	−1604.84			−1.70910
$940$	−225.720	−	390.959i	−0.240128	−	0.415913i
$941$			1025.92i			1.09024i	0.838357	+	0.545121i	$0.183516\pi$
$941$			1025.92i			1.09024i	−0.838357	+	0.545121i	$0.816484\pi$
$942$			227.473i			0.241479i
$943$	836.811			0.887392
$944$		−	54.9926i		−	0.0582549i
$945$	101.785	−	447.800i	0.107709	−	0.473862i
$946$	715.459			0.756299
$947$			613.355i			0.647682i	0.946112	+	0.323841i	$0.104974\pi$
$947$			613.355i			0.647682i	−0.946112	+	0.323841i	$0.895026\pi$
$948$	469.170			0.494905
$949$	−1001.27			−1.05508
$950$	−356.836	+	206.019i	−0.375617	+	0.216863i
$951$			190.229i			0.200030i
$952$	−1054.55	−	239.700i	−1.10772	−	0.251785i
$953$		−	943.403i		−	0.989929i	−0.868913	−	0.494965i	$-0.835181\pi$
$953$		−	943.403i		−	0.989929i	0.868913	−	0.494965i	$-0.164819\pi$
$954$	−247.891	−	429.360i	−0.259844	−	0.450063i
$955$	−335.850	−	581.710i	−0.351676	−	0.609120i
$956$	−205.877	−	118.863i	−0.215353	−	0.124334i
$957$	376.153			0.393054
$958$	299.194	−	518.219i	0.312311	−	0.540938i
$959$	1214.32	−	375.759i	1.26623	−	0.391824i
$960$	107.573	−	62.1071i	0.112055	−	0.0646949i
$961$	−813.685			−0.846707
$962$	−401.342	+	231.715i	−0.417195	+	0.240868i
$963$	338.824	+	195.620i	0.351842	+	0.203136i
$964$	332.302	−	575.564i	0.344712	−	0.597058i
$965$	−271.865	+	156.961i	−0.281725	+	0.162654i
$966$	356.657	+	81.0686i	0.369210	+	0.0839219i
$967$	443.072	−	767.423i	0.458192	−	0.793613i	−0.540673	−	0.841233i	$-0.681830\pi$
$967$	443.072	−	767.423i	0.458192	−	0.793613i	0.998866	+	0.0476203i	$0.0151637\pi$
$968$	363.314	−	209.760i	0.375325	−	0.216694i
$969$		−	1348.77i		−	1.39192i
$970$	88.5015	−	153.289i	0.0912386	−	0.158030i
$971$	−736.011	−	424.936i	−0.757993	−	0.437628i	0.0705816	−	0.997506i	$-0.477514\pi$
$971$	−736.011	−	424.936i	−0.757993	−	0.437628i	−0.828575	+	0.559878i	$0.810848\pi$
$972$	712.017			0.732528
$973$	−256.435	−	828.706i	−0.263551	−	0.851702i
$974$	579.612	−	334.639i	0.595084	−	0.343572i
$975$	290.414	+	503.011i	0.297860	+	0.515909i
$976$	261.338			0.267764
$977$		−	800.908i		−	0.819763i	−0.912139	−	0.409881i	$-0.865570\pi$
$977$		−	800.908i		−	0.819763i	0.912139	−	0.409881i	$-0.134430\pi$
$978$	228.480	+	131.913i	0.233620	+	0.134881i
$979$	−132.606	−	229.681i	−0.135451	−	0.234608i
$980$	197.032	+	287.882i	0.201053	+	0.293758i
$981$	646.802	+	1120.29i	0.659329	+	1.14199i
$982$	−90.5178	+	156.781i	−0.0921770	+	0.159655i
$983$	−404.645	−	233.622i	−0.411643	−	0.237662i	0.279853	−	0.960043i	$-0.409714\pi$
$983$	−404.645	−	233.622i	−0.411643	−	0.237662i	−0.691495	+	0.722381i	$0.743048\pi$
$984$	534.351	−	925.523i	0.543040	−	0.940572i
$985$	319.936	+	554.145i	0.324808	+	0.562584i
$986$	−180.667	−	104.308i	−0.183232	−	0.105789i
$987$	−976.944	−	904.844i	−0.989812	−	0.916762i
$988$	309.848	+	536.673i	0.313612	+	0.543191i
$989$	−752.809	−	434.634i	−0.761182	−	0.439468i
$990$		−	303.065i		−	0.306126i
$991$	638.604	+	1106.09i	0.644403	+	1.11614i	0.984439	+	0.175727i	$0.0562275\pi$
$991$	638.604	+	1106.09i	0.644403	+	1.11614i	−0.340036	+	0.940412i	$0.610439\pi$
$992$		−	402.070i		−	0.405312i
$993$	722.815			0.727911
$994$	48.7689	−	52.6549i	0.0490632	−	0.0529727i
$995$	335.298	+	193.585i	0.336983	+	0.194557i
$996$	−716.909	+	413.907i	−0.719788	+	0.415570i
$997$	−342.562	+	593.335i	−0.343593	+	0.595120i	−0.985097	−	0.171999i	$-0.944977\pi$
$997$	−342.562	+	593.335i	−0.343593	+	0.595120i	0.641504	+	0.767120i	$0.278311\pi$
$998$	−752.076	+	434.211i	−0.753584	+	0.435082i
$999$	596.584	−	1033.31i	0.597182	−	1.03435i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.3.j.a.23.2	yes	6
3.2	odd	2		189.3.j.a.44.2		6
7.2	even	3		441.3.r.b.50.2		6
7.3	odd	6		441.3.n.c.410.2		6
7.4	even	3		63.3.n.a.32.2	yes	6
7.5	odd	6		441.3.r.c.50.2		6
7.6	odd	2		441.3.j.c.275.2		6
9.2	odd	6		63.3.n.a.2.2	yes	6
9.7	even	3		189.3.n.a.170.2		6
21.11	odd	6		189.3.n.a.179.2		6
63.2	odd	6		441.3.r.b.344.2		6
63.11	odd	6	inner	63.3.j.a.11.2	✓	6
63.20	even	6		441.3.n.c.128.2		6
63.25	even	3		189.3.j.a.116.2		6
63.38	even	6		441.3.j.c.263.2		6
63.47	even	6		441.3.r.c.344.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.3.j.a.11.2	✓	6	63.11	odd	6	inner
63.3.j.a.23.2	yes	6	1.1	even	1	trivial
63.3.n.a.2.2	yes	6	9.2	odd	6
63.3.n.a.32.2	yes	6	7.4	even	3
189.3.j.a.44.2		6	3.2	odd	2
189.3.j.a.116.2		6	63.25	even	3
189.3.n.a.170.2		6	9.7	even	3
189.3.n.a.179.2		6	21.11	odd	6
441.3.j.c.263.2		6	63.38	even	6
441.3.j.c.275.2		6	7.6	odd	2
441.3.n.c.128.2		6	63.20	even	6
441.3.n.c.410.2		6	7.3	odd	6
441.3.r.b.50.2		6	7.2	even	3
441.3.r.b.344.2		6	63.2	odd	6
441.3.r.c.50.2		6	7.5	odd	6
441.3.r.c.344.2		6	63.47	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	63.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.03435i q^{2} +3.00000 q^{3} +2.93011 q^{4} +(-2.10422 + 1.21487i) q^{5} -3.10306i q^{6} +(-4.75661 + 5.13563i) q^{7} -7.16819i q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-1.03435i q^{2} +3.00000 q^{3} +2.93011 q^{4} +(-2.10422 + 1.21487i) q^{5} -3.10306i q^{6} +(-4.75661 + 5.13563i) q^{7} -7.16819i q^{8} +9.00000 q^{9} +(1.25661 + 2.17651i) q^{10} +(-11.6036 - 6.69935i) q^{11} +8.79033 q^{12} +(5.06928 - 8.78025i) q^{13} +(5.31206 + 4.92002i) q^{14} +(-6.31267 + 3.64462i) q^{15} +4.30600 q^{16} +(-18.6650 + 10.7762i) q^{17} -9.30919i q^{18} +(-10.4301 + 18.0655i) q^{19} +(-6.16561 + 3.55971i) q^{20} +(-14.2698 + 15.4069i) q^{21} +(-6.92950 + 12.0022i) q^{22} +(14.5825 - 8.41921i) q^{23} -21.5046i q^{24} +(-9.54816 + 16.5379i) q^{25} +(-9.08189 - 5.24343i) q^{26} +27.0000 q^{27} +(-13.9374 + 15.0480i) q^{28} +(-8.10422 + 4.67898i) q^{29} +(3.76983 + 6.52954i) q^{30} +12.1373 q^{31} -33.1267i q^{32} +(-34.8108 - 20.0980i) q^{33} +(11.1465 + 19.3062i) q^{34} +(3.76983 - 16.5852i) q^{35} +26.3710 q^{36} +(22.0957 - 38.2709i) q^{37} +(18.6861 + 10.7884i) q^{38} +(15.2078 - 26.3407i) q^{39} +(8.70845 + 15.0835i) q^{40} +(43.0384 + 24.8483i) q^{41} +(15.9362 + 14.7601i) q^{42} +(-25.8121 - 44.7078i) q^{43} +(-33.9999 - 19.6298i) q^{44} +(-18.9380 + 10.9339i) q^{45} +(-8.70845 - 15.0835i) q^{46} +63.4096i q^{47} +12.9180 q^{48} +(-3.74933 - 48.8563i) q^{49} +(17.1061 + 9.87619i) q^{50} +(-55.9950 + 32.3287i) q^{51} +(14.8535 - 25.7271i) q^{52} +(46.1222 - 26.6286i) q^{53} -27.9276i q^{54} +32.5554 q^{55} +(36.8132 + 34.0963i) q^{56} +(-31.2903 + 54.1964i) q^{57} +(4.83972 + 8.38264i) q^{58} -12.7712i q^{59} +(-18.4968 + 10.6791i) q^{60} +60.6916 q^{61} -12.5543i q^{62} +(-42.8095 + 46.2206i) q^{63} -17.0408 q^{64} +24.6341i q^{65} +(-20.7885 + 36.0067i) q^{66} -78.7615 q^{67} +(-54.6905 + 31.5756i) q^{68} +(43.7475 - 25.2576i) q^{69} +(-17.1550 - 3.89934i) q^{70} -9.91233i q^{71} -64.5137i q^{72} +(-49.3794 - 85.5276i) q^{73} +(-39.5857 - 22.8548i) q^{74} +(-28.6445 + 49.6137i) q^{75} +(-30.5614 + 52.9339i) q^{76} +(89.5992 - 27.7256i) q^{77} +(-27.2457 - 15.7303i) q^{78} +53.3734 q^{79} +(-9.06077 + 5.23124i) q^{80} +81.0000 q^{81} +(25.7019 - 44.5170i) q^{82} +(-81.5565 + 47.0867i) q^{83} +(-41.8122 + 45.1439i) q^{84} +(26.1835 - 45.3512i) q^{85} +(-46.2437 + 26.6988i) q^{86} +(-24.3127 + 14.0369i) q^{87} +(-48.0222 + 83.1769i) q^{88} +(17.1421 + 9.89697i) q^{89} +(11.3095 + 19.5886i) q^{90} +(20.9795 + 67.7981i) q^{91} +(42.7283 - 24.6692i) q^{92} +36.4120 q^{93} +65.5880 q^{94} -50.6851i q^{95} -99.3801i q^{96} +(-35.2144 - 60.9931i) q^{97} +(-50.5348 + 3.87813i) q^{98} +(-104.433 - 60.2941i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 18 q^{3} - 26 q^{4} - 15 q^{5} - 2 q^{7} + 54 q^{9}+O(q^{10}) \) 6 * q + 18 * q^3 - 26 * q^4 - 15 * q^5 - 2 * q^7 + 54 * q^9	\( 6 q + 18 q^{3} - 26 q^{4} - 15 q^{5} - 2 q^{7} + 54 q^{9} - 19 q^{10} - 9 q^{11} - 78 q^{12} + 11 q^{13} - 24 q^{14} - 45 q^{15} + 94 q^{16} + 33 q^{17} - 19 q^{19} + 45 q^{20} - 6 q^{21} + 65 q^{22} + 15 q^{23} - 26 q^{25} + 81 q^{26} + 162 q^{27} - 42 q^{28} - 51 q^{29} - 57 q^{30} - 92 q^{31} - 27 q^{33} + 93 q^{34} - 57 q^{35} - 234 q^{36} + 7 q^{37} - 21 q^{38} + 33 q^{39} + 57 q^{40} - 27 q^{41} - 72 q^{42} - 99 q^{43} - 273 q^{44} - 135 q^{45} - 57 q^{46} + 282 q^{48} + 6 q^{49} + 294 q^{50} + 99 q^{51} + 63 q^{52} + 45 q^{53} + 166 q^{55} + 360 q^{56} - 57 q^{57} - 7 q^{58} + 135 q^{60} + 44 q^{61} - 18 q^{63} - 138 q^{64} + 195 q^{66} - 196 q^{67} - 567 q^{68} + 45 q^{69} - 257 q^{70} - 101 q^{73} - 411 q^{74} - 78 q^{75} - 99 q^{76} + 105 q^{77} + 243 q^{78} + 180 q^{79} + 93 q^{80} + 486 q^{81} + 151 q^{82} + 99 q^{83} - 126 q^{84} - 159 q^{85} + 249 q^{86} - 153 q^{87} - 495 q^{88} - 243 q^{89} - 171 q^{90} + 177 q^{91} + 147 q^{92} - 276 q^{93} + 888 q^{94} - 161 q^{97} + 360 q^{98} - 81 q^{99}+O(q^{100}) \) 6 * q + 18 * q^3 - 26 * q^4 - 15 * q^5 - 2 * q^7 + 54 * q^9 - 19 * q^10 - 9 * q^11 - 78 * q^12 + 11 * q^13 - 24 * q^14 - 45 * q^15 + 94 * q^16 + 33 * q^17 - 19 * q^19 + 45 * q^20 - 6 * q^21 + 65 * q^22 + 15 * q^23 - 26 * q^25 + 81 * q^26 + 162 * q^27 - 42 * q^28 - 51 * q^29 - 57 * q^30 - 92 * q^31 - 27 * q^33 + 93 * q^34 - 57 * q^35 - 234 * q^36 + 7 * q^37 - 21 * q^38 + 33 * q^39 + 57 * q^40 - 27 * q^41 - 72 * q^42 - 99 * q^43 - 273 * q^44 - 135 * q^45 - 57 * q^46 + 282 * q^48 + 6 * q^49 + 294 * q^50 + 99 * q^51 + 63 * q^52 + 45 * q^53 + 166 * q^55 + 360 * q^56 - 57 * q^57 - 7 * q^58 + 135 * q^60 + 44 * q^61 - 18 * q^63 - 138 * q^64 + 195 * q^66 - 196 * q^67 - 567 * q^68 + 45 * q^69 - 257 * q^70 - 101 * q^73 - 411 * q^74 - 78 * q^75 - 99 * q^76 + 105 * q^77 + 243 * q^78 + 180 * q^79 + 93 * q^80 + 486 * q^81 + 151 * q^82 + 99 * q^83 - 126 * q^84 - 159 * q^85 + 249 * q^86 - 153 * q^87 - 495 * q^88 - 243 * q^89 - 171 * q^90 + 177 * q^91 + 147 * q^92 - 276 * q^93 + 888 * q^94 - 161 * q^97 + 360 * q^98 - 81 * q^99

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