LMFDB - Embedded newform 156.3.n.d.43.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [156,3,Mod(43,156)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(156, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 1]))

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

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

chi := DirichletCharacter("156.43");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 156 = 2^{2} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	156.n (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:	$4.25069212402$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{142})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 142x^{2} + 20164 $ x^4 + 142*x^2 + 20164
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			43.2
Root			$5.95819 + 10.3199i$ of defining polynomial
Character	$\chi$	$=$	156.43
Dual form			156.3.n.d.127.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.73205i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-2.00000 + 3.46410i) q^{4} -1.73205i q^{5} +3.46410i q^{6} +(6.95819 + 12.0519i) q^{7} +8.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(-1.00000 - 1.73205i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-2.00000 + 3.46410i) q^{4} -1.73205i q^{5} +3.46410i q^{6} +(6.95819 + 12.0519i) q^{7} +8.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(-3.00000 + 1.73205i) q^{10} +(2.95819 - 5.12373i) q^{11} +(6.00000 - 3.46410i) q^{12} +(1.45819 - 12.9180i) q^{13} +(13.9164 - 24.1039i) q^{14} +(-1.50000 + 2.59808i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(0.541812 + 0.938447i) q^{17} +(3.00000 - 5.19615i) q^{18} +(9.95819 + 17.2481i) q^{19} +(6.00000 + 3.46410i) q^{20} -24.1039i q^{21} -11.8328 q^{22} +(23.8746 + 13.7840i) q^{23} +(-12.0000 - 6.92820i) q^{24} +22.0000 q^{25} +(-23.8328 + 10.3923i) q^{26} -5.19615i q^{27} -55.6655 q^{28} +(15.4164 - 26.7019i) q^{29} +6.00000 q^{30} -8.16725 q^{31} +(-16.0000 + 27.7128i) q^{32} +(-8.87456 + 5.12373i) q^{33} +(1.08362 - 1.87689i) q^{34} +(20.8746 - 12.0519i) q^{35} -12.0000 q^{36} +(7.37456 + 4.25771i) q^{37} +(19.9164 - 34.4962i) q^{38} +(-13.3746 + 18.1141i) q^{39} -13.8564i q^{40} +(49.1237 + 28.3616i) q^{41} +(-41.7491 + 24.1039i) q^{42} +(-23.8746 + 13.7840i) q^{43} +(11.8328 + 20.4949i) q^{44} +(4.50000 - 2.59808i) q^{45} -55.1359i q^{46} +0.0836247 q^{47} +27.7128i q^{48} +(-72.3328 + 125.284i) q^{49} +(-22.0000 - 38.1051i) q^{50} -1.87689i q^{51} +(41.8328 + 30.8872i) q^{52} -48.8328 q^{53} +(-9.00000 + 5.19615i) q^{54} +(-8.87456 - 5.12373i) q^{55} +(55.6655 + 96.4155i) q^{56} -34.4962i q^{57} -61.6655 q^{58} +(28.0000 + 48.4974i) q^{59} +(-6.00000 - 10.3923i) q^{60} +(16.2909 + 28.2167i) q^{61} +(8.16725 + 14.1461i) q^{62} +(-20.8746 + 36.1558i) q^{63} +64.0000 q^{64} +(-22.3746 - 2.52566i) q^{65} +(17.7491 + 10.2475i) q^{66} +(51.7073 - 89.5597i) q^{67} -4.33450 q^{68} +(-23.8746 - 41.3520i) q^{69} +(-41.7491 - 24.1039i) q^{70} +(-61.8746 - 107.170i) q^{71} +(12.0000 + 20.7846i) q^{72} -43.5910i q^{73} -17.0308i q^{74} +(-33.0000 - 19.0526i) q^{75} -79.6655 q^{76} +82.3345 q^{77} +(44.7491 + 5.05131i) q^{78} +48.2077i q^{79} +(-24.0000 + 13.8564i) q^{80} +(-4.50000 + 7.79423i) q^{81} -113.446i q^{82} -133.247 q^{83} +(83.4983 + 48.2077i) q^{84} +(1.62544 - 0.938447i) q^{85} +(47.7491 + 27.5680i) q^{86} +(-46.2491 + 26.7019i) q^{87} +(23.6655 - 40.9899i) q^{88} +(-107.749 - 62.2090i) q^{89} +(-9.00000 - 5.19615i) q^{90} +(165.833 - 72.3116i) q^{91} +(-95.4983 + 55.1359i) q^{92} +(12.2509 + 7.07305i) q^{93} +(-0.0836247 - 0.144842i) q^{94} +(29.8746 - 17.2481i) q^{95} +(48.0000 - 27.7128i) q^{96} +(68.4983 - 39.5475i) q^{97} +289.331 q^{98} +17.7491 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - 6 q^{3} - 8 q^{4} + 4 q^{7} + 32 q^{8} + 6 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 - 6 * q^3 - 8 * q^4 + 4 * q^7 + 32 * q^8 + 6 * q^9	\( 4 q - 4 q^{2} - 6 q^{3} - 8 q^{4} + 4 q^{7} + 32 q^{8} + 6 q^{9} - 12 q^{10} - 12 q^{11} + 24 q^{12} - 18 q^{13} + 8 q^{14} - 6 q^{15} - 32 q^{16} + 26 q^{17} + 12 q^{18} + 16 q^{19} + 24 q^{20} + 48 q^{22} + 24 q^{23} - 48 q^{24} + 88 q^{25} - 32 q^{28} + 14 q^{29} + 24 q^{30} - 128 q^{31} - 64 q^{32} + 36 q^{33} + 52 q^{34} + 12 q^{35} - 48 q^{36} - 42 q^{37} + 32 q^{38} + 18 q^{39} - 18 q^{41} - 24 q^{42} - 24 q^{43} - 48 q^{44} + 18 q^{45} + 48 q^{47} - 194 q^{49} - 88 q^{50} + 72 q^{52} - 100 q^{53} - 36 q^{54} + 36 q^{55} + 32 q^{56} - 56 q^{58} + 112 q^{59} - 24 q^{60} - 54 q^{61} + 128 q^{62} - 12 q^{63} + 256 q^{64} - 18 q^{65} - 72 q^{66} + 40 q^{67} - 208 q^{68} - 24 q^{69} - 24 q^{70} - 176 q^{71} + 48 q^{72} - 132 q^{75} - 128 q^{76} + 520 q^{77} + 36 q^{78} - 96 q^{80} - 18 q^{81} - 104 q^{83} + 48 q^{84} + 78 q^{85} + 48 q^{86} - 42 q^{87} - 96 q^{88} - 288 q^{89} - 36 q^{90} + 568 q^{91} - 96 q^{92} + 192 q^{93} - 48 q^{94} + 48 q^{95} + 192 q^{96} - 12 q^{97} + 776 q^{98} - 72 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 - 6 * q^3 - 8 * q^4 + 4 * q^7 + 32 * q^8 + 6 * q^9 - 12 * q^10 - 12 * q^11 + 24 * q^12 - 18 * q^13 + 8 * q^14 - 6 * q^15 - 32 * q^16 + 26 * q^17 + 12 * q^18 + 16 * q^19 + 24 * q^20 + 48 * q^22 + 24 * q^23 - 48 * q^24 + 88 * q^25 - 32 * q^28 + 14 * q^29 + 24 * q^30 - 128 * q^31 - 64 * q^32 + 36 * q^33 + 52 * q^34 + 12 * q^35 - 48 * q^36 - 42 * q^37 + 32 * q^38 + 18 * q^39 - 18 * q^41 - 24 * q^42 - 24 * q^43 - 48 * q^44 + 18 * q^45 + 48 * q^47 - 194 * q^49 - 88 * q^50 + 72 * q^52 - 100 * q^53 - 36 * q^54 + 36 * q^55 + 32 * q^56 - 56 * q^58 + 112 * q^59 - 24 * q^60 - 54 * q^61 + 128 * q^62 - 12 * q^63 + 256 * q^64 - 18 * q^65 - 72 * q^66 + 40 * q^67 - 208 * q^68 - 24 * q^69 - 24 * q^70 - 176 * q^71 + 48 * q^72 - 132 * q^75 - 128 * q^76 + 520 * q^77 + 36 * q^78 - 96 * q^80 - 18 * q^81 - 104 * q^83 + 48 * q^84 + 78 * q^85 + 48 * q^86 - 42 * q^87 - 96 * q^88 - 288 * q^89 - 36 * q^90 + 568 * q^91 - 96 * q^92 + 192 * q^93 - 48 * q^94 + 48 * q^95 + 192 * q^96 - 12 * q^97 + 776 * q^98 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/156\mathbb{Z}\right)^\times$.

$n$	$53$	$79$	$145$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−1.00000	−	1.73205i	−0.500000	−	0.866025i
$2$	−1.00000	−	1.73205i	−0.500000	−	0.866025i
$3$	−1.50000	−	0.866025i	−0.500000	−	0.288675i
$3$	−1.50000	−	0.866025i	−0.500000	−	0.288675i
$4$	−2.00000	+	3.46410i	−0.500000	+	0.866025i
$5$		−	1.73205i		−	0.346410i	−0.984886	−	0.173205i	$-0.944588\pi$
$5$		−	1.73205i		−	0.346410i	0.984886	−	0.173205i	$-0.0554123\pi$
$6$			3.46410i			0.577350i
$7$	6.95819	+	12.0519i	0.994027	+	1.72170i	0.591528	+	0.806284i	$0.298525\pi$
$7$	6.95819	+	12.0519i	0.994027	+	1.72170i	0.402499	+	0.915421i	$0.368142\pi$
$8$	8.00000			1.00000
$9$	1.50000	+	2.59808i	0.166667	+	0.288675i
$10$	−3.00000	+	1.73205i	−0.300000	+	0.173205i
$11$	2.95819	−	5.12373i	0.268926	−	0.465794i	−0.699659	−	0.714477i	$-0.746665\pi$
$11$	2.95819	−	5.12373i	0.268926	−	0.465794i	0.968585	+	0.248684i	$0.0799979\pi$
$12$	6.00000	−	3.46410i	0.500000	−	0.288675i
$13$	1.45819	−	12.9180i	0.112168	−	0.993689i
$13$	1.45819	−	12.9180i	0.112168	−	0.993689i
$14$	13.9164	−	24.1039i	0.994027	−	1.72170i
$15$	−1.50000	+	2.59808i	−0.100000	+	0.173205i
$16$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$17$	0.541812	+	0.938447i	0.0318713	+	0.0552027i	0.881521	−	0.472145i	$-0.156520\pi$
$17$	0.541812	+	0.938447i	0.0318713	+	0.0552027i	−0.849650	+	0.527347i	$0.823187\pi$
$18$	3.00000	−	5.19615i	0.166667	−	0.288675i
$19$	9.95819	+	17.2481i	0.524115	+	0.907794i	0.999606	+	0.0280733i	$0.00893719\pi$
$19$	9.95819	+	17.2481i	0.524115	+	0.907794i	−0.475491	+	0.879721i	$0.657729\pi$
$20$	6.00000	+	3.46410i	0.300000	+	0.173205i
$21$		−	24.1039i		−	1.14780i
$22$	−11.8328			−0.537852
$23$	23.8746	+	13.7840i	1.03802	+	0.599304i	0.919273	−	0.393620i	$-0.128778\pi$
$23$	23.8746	+	13.7840i	1.03802	+	0.599304i	0.118751	+	0.992924i	$0.462111\pi$
$24$	−12.0000	−	6.92820i	−0.500000	−	0.288675i
$25$	22.0000			0.880000
$26$	−23.8328	+	10.3923i	−0.916644	+	0.399704i
$27$		−	5.19615i		−	0.192450i
$28$	−55.6655			−1.98805
$29$	15.4164	−	26.7019i	0.531599	−	0.920757i	−0.467721	−	0.883876i	$-0.654925\pi$
$29$	15.4164	−	26.7019i	0.531599	−	0.920757i	0.999320	−	0.0368803i	$-0.0117420\pi$
$30$	6.00000			0.200000
$31$	−8.16725			−0.263460			−0.131730	−	0.991286i	$-0.542053\pi$
$31$	−8.16725			−0.263460			−0.131730	+	0.991286i	$0.542053\pi$
$32$	−16.0000	+	27.7128i	−0.500000	+	0.866025i
$33$	−8.87456	+	5.12373i	−0.268926	+	0.155265i
$34$	1.08362	−	1.87689i	0.0318713	−	0.0552027i
$35$	20.8746	−	12.0519i	0.596416	−	0.344341i
$36$	−12.0000			−0.333333
$37$	7.37456	+	4.25771i	0.199313	+	0.115073i	0.596335	−	0.802736i	$-0.296623\pi$
$37$	7.37456	+	4.25771i	0.199313	+	0.115073i	−0.397022	+	0.917809i	$0.629956\pi$
$38$	19.9164	−	34.4962i	0.524115	−	0.907794i
$39$	−13.3746	+	18.1141i	−0.342938	+	0.464464i
$40$		−	13.8564i		−	0.346410i
$41$	49.1237	+	28.3616i	1.19814	+	0.691746i	0.960140	−	0.279520i	$-0.0901752\pi$
$41$	49.1237	+	28.3616i	1.19814	+	0.691746i	0.237999	+	0.971265i	$0.423509\pi$
$42$	−41.7491	+	24.1039i	−0.994027	+	0.573902i
$43$	−23.8746	+	13.7840i	−0.555222	+	0.320558i	−0.751226	−	0.660045i	$-0.770537\pi$
$43$	−23.8746	+	13.7840i	−0.555222	+	0.320558i	0.196003	+	0.980603i	$0.437204\pi$
$44$	11.8328	+	20.4949i	0.268926	+	0.465794i
$45$	4.50000	−	2.59808i	0.100000	−	0.0577350i
$46$		−	55.1359i		−	1.19861i
$47$	0.0836247			0.00177925			0.000889625	−	1.00000i	$-0.499717\pi$
$47$	0.0836247			0.00177925			0.000889625		1.00000i	$0.499717\pi$
$48$			27.7128i			0.577350i
$49$	−72.3328	+	125.284i	−1.47618	+	2.55682i
$50$	−22.0000	−	38.1051i	−0.440000	−	0.762102i
$51$		−	1.87689i		−	0.0368018i
$52$	41.8328	+	30.8872i	0.804476	+	0.593985i
$53$	−48.8328			−0.921373			−0.460686	−	0.887563i	$-0.652397\pi$
$53$	−48.8328			−0.921373			−0.460686	+	0.887563i	$0.652397\pi$
$54$	−9.00000	+	5.19615i	−0.166667	+	0.0962250i
$55$	−8.87456	−	5.12373i	−0.161356	−	0.0931588i
$56$	55.6655	+	96.4155i	0.994027	+	1.72170i
$57$		−	34.4962i		−	0.605196i
$58$	−61.6655			−1.06320
$59$	28.0000	+	48.4974i	0.474576	+	0.821990i	0.999576	−	0.0291121i	$-0.00926797\pi$
$59$	28.0000	+	48.4974i	0.474576	+	0.821990i	−0.525000	+	0.851102i	$0.675935\pi$
$60$	−6.00000	−	10.3923i	−0.100000	−	0.173205i
$61$	16.2909	+	28.2167i	0.267065	+	0.462569i	0.968102	−	0.250555i	$-0.0806130\pi$
$61$	16.2909	+	28.2167i	0.267065	+	0.462569i	−0.701038	+	0.713124i	$0.747280\pi$
$62$	8.16725	+	14.1461i	0.131730	+	0.228163i
$63$	−20.8746	+	36.1558i	−0.331342	+	0.573902i
$64$	64.0000			1.00000
$65$	−22.3746	−	2.52566i	−0.344224	−	0.0388562i
$66$	17.7491	+	10.2475i	0.268926	+	0.155265i
$67$	51.7073	−	89.5597i	0.771751	−	1.33671i	−0.164852	−	0.986318i	$-0.552715\pi$
$67$	51.7073	−	89.5597i	0.771751	−	1.33671i	0.936603	−	0.350393i	$-0.113952\pi$
$68$	−4.33450			−0.0637426
$69$	−23.8746	−	41.3520i	−0.346008	−	0.599304i
$70$	−41.7491	−	24.1039i	−0.596416	−	0.344341i
$71$	−61.8746	−	107.170i	−0.871473	−	1.50944i	−0.860473	−	0.509496i	$-0.829832\pi$
$71$	−61.8746	−	107.170i	−0.871473	−	1.50944i	−0.0109994	−	0.999940i	$-0.503501\pi$
$72$	12.0000	+	20.7846i	0.166667	+	0.288675i
$73$		−	43.5910i		−	0.597136i	−0.954388	−	0.298568i	$-0.903491\pi$
$73$		−	43.5910i		−	0.597136i	0.954388	−	0.298568i	$-0.0965090\pi$
$74$		−	17.0308i		−	0.230146i
$75$	−33.0000	−	19.0526i	−0.440000	−	0.254034i
$76$	−79.6655			−1.04823
$77$	82.3345			1.06928
$78$	44.7491	+	5.05131i	0.573707	+	0.0647604i
$79$			48.2077i			0.610225i	0.952316	+	0.305112i	$0.0986940\pi$
$79$			48.2077i			0.610225i	−0.952316	+	0.305112i	$0.901306\pi$
$80$	−24.0000	+	13.8564i	−0.300000	+	0.173205i
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$		−	113.446i		−	1.38349i
$83$	−133.247			−1.60539			−0.802695	−	0.596390i	$-0.796601\pi$
$83$	−133.247			−1.60539			−0.802695	+	0.596390i	$0.796601\pi$
$84$	83.4983	+	48.2077i	0.994027	+	0.573902i
$85$	1.62544	−	0.938447i	0.0191228	−	0.0110405i
$86$	47.7491	+	27.5680i	0.555222	+	0.320558i
$87$	−46.2491	+	26.7019i	−0.531599	+	0.306919i
$88$	23.6655	−	40.9899i	0.268926	−	0.465794i
$89$	−107.749	−	62.2090i	−1.21066	−	0.698977i	−0.247760	−	0.968821i	$-0.579695\pi$
$89$	−107.749	−	62.2090i	−1.21066	−	0.698977i	−0.962904	+	0.269844i	$0.913028\pi$
$90$	−9.00000	−	5.19615i	−0.100000	−	0.0577350i
$91$	165.833	−	72.3116i	1.82234	−	0.794633i
$92$	−95.4983	+	55.1359i	−1.03802	+	0.599304i
$93$	12.2509	+	7.07305i	0.131730	+	0.0760543i
$94$	−0.0836247	−	0.144842i	−0.000889625	−	0.00154088i
$95$	29.8746	−	17.2481i	0.314469	−	0.181559i
$96$	48.0000	−	27.7128i	0.500000	−	0.288675i
$97$	68.4983	−	39.5475i	0.706168	−	0.407706i	−0.103473	−	0.994632i	$-0.532995\pi$
$97$	68.4983	−	39.5475i	0.706168	−	0.407706i	0.809640	+	0.586926i	$0.199662\pi$
$98$	289.331			2.95236
$99$	17.7491			0.179284
$100$	−44.0000	+	76.2102i	−0.440000	+	0.762102i
$101$	−38.5836	+	66.8288i	−0.382016	+	0.661671i	−0.991350	−	0.131242i	$-0.958103\pi$
$101$	−38.5836	+	66.8288i	−0.382016	+	0.661671i	0.609334	+	0.792913i	$0.291437\pi$
$102$	−3.25087	+	1.87689i	−0.0318713	+	0.0184009i
$103$			52.1064i			0.505887i	0.967481	+	0.252944i	$0.0813987\pi$
$103$			52.1064i			0.505887i	−0.967481	+	0.252944i	$0.918601\pi$
$104$	11.6655	−	103.344i	0.112168	−	0.993689i
$105$	−41.7491			−0.397611
$106$	48.8328	+	84.5808i	0.460686	+	0.797932i
$107$	−9.12544	−	5.26857i	−0.0852845	−	0.0492390i	0.456751	−	0.889594i	$-0.349013\pi$
$107$	−9.12544	−	5.26857i	−0.0852845	−	0.0492390i	−0.542036	+	0.840355i	$0.682346\pi$
$108$	18.0000	+	10.3923i	0.166667	+	0.0962250i
$109$			48.7871i			0.447588i	0.974636	+	0.223794i	$0.0718443\pi$
$109$			48.7871i			0.447588i	−0.974636	+	0.223794i	$0.928156\pi$
$110$			20.4949i			0.186318i
$111$	−7.37456	−	12.7731i	−0.0664375	−	0.115073i
$112$	111.331	−	192.831i	0.994027	−	1.72170i
$113$	−68.2073	−	118.139i	−0.603605	−	1.04547i	−0.992270	−	0.124095i	$-0.960397\pi$
$113$	−68.2073	−	118.139i	−0.603605	−	1.04547i	0.388666	−	0.921379i	$-0.372936\pi$
$114$	−59.7491	+	34.4962i	−0.524115	+	0.302598i
$115$	23.8746	−	41.3520i	0.207605	−	0.359582i
$116$	61.6655	+	106.808i	0.531599	+	0.920757i
$117$	35.7491	−	15.5885i	0.305548	−	0.133235i
$118$	56.0000	−	96.9948i	0.474576	−	0.821990i
$119$	−7.54006	+	13.0598i	−0.0633619	+	0.109746i
$120$	−12.0000	+	20.7846i	−0.100000	+	0.173205i
$121$	42.9983	+	74.4752i	0.355357	+	0.615497i
$122$	32.5819	−	56.4335i	0.267065	−	0.462569i
$123$	−49.1237	−	85.0847i	−0.399380	−	0.691746i
$124$	16.3345	−	28.2922i	0.131730	−	0.228163i
$125$		−	81.4064i		−	0.651251i
$126$	83.4983			0.662685
$127$	−143.498	−	82.8488i	−1.12991	−	0.652352i	−0.185996	−	0.982551i	$-0.559551\pi$
$127$	−143.498	−	82.8488i	−1.12991	−	0.652352i	−0.943912	+	0.330198i	$0.892884\pi$
$128$	−64.0000	−	110.851i	−0.500000	−	0.866025i
$129$	47.7491			0.370148
$130$	18.0000	+	41.2795i	0.138462	+	0.317535i
$131$			124.997i			0.954178i	0.878855	+	0.477089i	$0.158308\pi$
$131$			124.997i			0.954178i	−0.878855	+	0.477089i	$0.841692\pi$
$132$		−	40.9899i		−	0.310529i
$133$	−138.582	+	240.031i	−1.04197	+	1.80474i
$134$	−206.829			−1.54350
$135$	−9.00000			−0.0666667
$136$	4.33450	+	7.50757i	0.0318713	+	0.0552027i
$137$	220.124	−	127.088i	1.60674	−	0.927653i	0.616650	−	0.787238i	$-0.288490\pi$
$137$	220.124	−	127.088i	1.60674	−	0.927653i	0.990093	−	0.140415i	$-0.0448438\pi$
$138$	−47.7491	+	82.7039i	−0.346008	+	0.599304i
$139$	35.4983	−	20.4949i	0.255383	−	0.147446i	−0.366844	−	0.930283i	$-0.619562\pi$
$139$	35.4983	−	20.4949i	0.255383	−	0.147446i	0.622227	+	0.782837i	$0.286228\pi$
$140$			96.4155i			0.688682i
$141$	−0.125437	−	0.0724211i	−0.000889625	−	0.000513625i
$142$	−123.749	+	214.340i	−0.871473	+	1.50944i
$143$	−61.8746	−	45.6851i	−0.432689	−	0.319476i
$144$	24.0000	−	41.5692i	0.166667	−	0.288675i
$145$	−46.2491	−	26.7019i	−0.318959	−	0.184151i
$146$	−75.5017	+	43.5910i	−0.517135	+	0.298568i
$147$	216.998	−	125.284i	1.47618	−	0.852272i
$148$	−29.4983	+	17.0308i	−0.199313	+	0.115073i
$149$	−66.9983	+	38.6815i	−0.449653	+	0.259607i	−0.707684	−	0.706530i	$-0.750260\pi$
$149$	−66.9983	+	38.6815i	−0.449653	+	0.259607i	0.258031	+	0.966137i	$0.416926\pi$
$150$			76.2102i			0.508068i
$151$	−49.4146			−0.327249			−0.163625	−	0.986523i	$-0.552319\pi$
$151$	−49.4146			−0.327249			−0.163625	+	0.986523i	$0.552319\pi$
$152$	79.6655	+	137.985i	0.524115	+	0.907794i
$153$	−1.62544	+	2.81534i	−0.0106238	+	0.0184009i
$154$	−82.3345	−	142.608i	−0.534640	−	0.926023i
$155$			14.1461i			0.0912651i
$156$	−36.0000	−	82.5591i	−0.230769	−	0.529225i
$157$	217.913			1.38798			0.693990	−	0.719985i	$-0.255851\pi$
$157$	217.913			1.38798			0.693990	+	0.719985i	$0.255851\pi$
$158$	83.4983	−	48.2077i	0.528470	−	0.305112i
$159$	73.2491	+	42.2904i	0.460686	+	0.265977i
$160$	48.0000	+	27.7128i	0.300000	+	0.173205i
$161$			383.646i			2.38290i
$162$	18.0000			0.111111
$163$	−55.9164	−	96.8500i	−0.343045	−	0.594172i	0.641951	−	0.766745i	$-0.278125\pi$
$163$	−55.9164	−	96.8500i	−0.343045	−	0.594172i	−0.984997	+	0.172574i	$0.944792\pi$
$164$	−196.495	+	113.446i	−1.19814	+	0.691746i
$165$	8.87456	+	15.3712i	0.0537852	+	0.0931588i
$166$	133.247	+	230.791i	0.802695	+	1.39031i
$167$	−35.9164	+	62.2090i	−0.215068	+	0.372509i	−0.953294	−	0.302045i	$-0.902331\pi$
$167$	−35.9164	+	62.2090i	−0.215068	+	0.372509i	0.738226	+	0.674554i	$0.235664\pi$
$168$		−	192.831i		−	1.14780i
$169$	−164.747	−	37.6736i	−0.974837	−	0.222921i
$170$	−3.25087	−	1.87689i	−0.0191228	−	0.0110405i
$171$	−29.8746	+	51.7443i	−0.174705	+	0.302598i
$172$		−	110.272i		−	0.641116i
$173$	−93.8328	−	162.523i	−0.542386	−	0.939440i	−0.998766	−	0.0496552i	$-0.984188\pi$
$173$	−93.8328	−	162.523i	−0.542386	−	0.939440i	0.456381	−	0.889785i	$-0.349146\pi$
$174$	92.4983	+	53.4039i	0.531599	+	0.306919i
$175$	153.080	+	265.143i	0.874744	+	1.51510i
$176$	−94.6620			−0.537852
$177$		−	96.9948i		−	0.547993i
$178$			248.836i			1.39795i
$179$	−45.1254	−	26.0532i	−0.252097	−	0.145549i	0.368627	−	0.929577i	$-0.379828\pi$
$179$	−45.1254	−	26.0532i	−0.252097	−	0.145549i	−0.620724	+	0.784029i	$0.713161\pi$
$180$			20.7846i			0.115470i
$181$	64.7491			0.357730			0.178865	−	0.983874i	$-0.442757\pi$
$181$	64.7491			0.357730			0.178865	+	0.983874i	$0.442757\pi$
$182$	−291.080	−	214.919i	−1.59934	−	1.18087i
$183$		−	56.4335i		−	0.308380i
$184$	190.997	+	110.272i	1.03802	+	0.599304i
$185$	7.37456	−	12.7731i	0.0398625	−	0.0690439i
$186$		−	28.2922i		−	0.152109i
$187$	6.41113			0.0342841
$188$	−0.167249	+	0.289685i	−0.000889625	+	0.00154088i
$189$	62.6237	−	36.1558i	0.331342	−	0.191301i
$190$	−59.7491	−	34.4962i	−0.314469	−	0.181559i
$191$	−226.997	+	131.056i	−1.18846	+	0.686160i	−0.957957	−	0.286911i	$-0.907372\pi$
$191$	−226.997	+	131.056i	−1.18846	+	0.686160i	−0.230506	+	0.973071i	$0.574038\pi$
$192$	−96.0000	−	55.4256i	−0.500000	−	0.288675i
$193$	−34.2491	−	19.7737i	−0.177457	−	0.102455i	0.408641	−	0.912695i	$-0.366003\pi$
$193$	−34.2491	−	19.7737i	−0.177457	−	0.102455i	−0.586097	+	0.810241i	$0.699336\pi$
$194$	−136.997	−	79.0950i	−0.706168	−	0.407706i
$195$	31.3746	+	23.1654i	0.160895	+	0.118797i
$196$	−289.331	−	501.136i	−1.47618	−	2.55682i
$197$	−310.495	−	179.264i	−1.57612	−	0.909971i	−0.995394	−	0.0958684i	$-0.969437\pi$
$197$	−310.495	−	179.264i	−1.57612	−	0.909971i	−0.580721	−	0.814102i	$-0.697229\pi$
$198$	−17.7491	−	30.7424i	−0.0896420	−	0.155265i
$199$	−289.871	+	167.357i	−1.45664	+	0.840991i	−0.998844	−	0.0480674i	$-0.984694\pi$
$199$	−289.871	+	167.357i	−1.45664	+	0.840991i	−0.457794	+	0.889058i	$0.651360\pi$
$200$	176.000			0.880000
$201$	−155.122	+	89.5597i	−0.771751	+	0.445571i
$202$	154.334			0.764032
$203$	429.080			2.11370
$204$	6.50175	+	3.75379i	0.0318713	+	0.0184009i
$205$	49.1237	−	85.0847i	0.239628	−	0.415047i
$206$	90.2509	−	52.1064i	0.438111	−	0.252944i
$207$			82.7039i			0.399536i
$208$	−190.662	+	83.1384i	−0.916644	+	0.399704i
$209$	117.833			0.563793
$210$	41.7491	+	72.3116i	0.198805	+	0.344341i
$211$	204.251	+	117.924i	0.968014	+	0.558883i	0.898630	−	0.438707i	$-0.144563\pi$
$211$	204.251	+	117.924i	0.968014	+	0.558883i	0.0693835	+	0.997590i	$0.477897\pi$
$212$	97.6655	−	169.162i	0.460686	−	0.797932i
$213$			214.340i			1.00629i
$214$			21.0743i			0.0984780i
$215$	23.8746	+	41.3520i	0.111044	+	0.192335i
$216$		−	41.5692i		−	0.192450i
$217$	−56.8293	−	98.4312i	−0.261886	−	0.453600i
$218$	84.5017	−	48.7871i	0.387623	−	0.223794i
$219$	−37.7509	+	65.3864i	−0.172378	+	0.298568i
$220$	35.4983	−	20.4949i	0.161356	−	0.0931588i
$221$	12.9129	−	5.63068i	0.0584293	−	0.0254782i
$222$	−14.7491	+	25.5462i	−0.0664375	+	0.115073i
$223$	22.3345	−	38.6845i	0.100155	−	0.173473i	−0.811594	−	0.584222i	$-0.801400\pi$
$223$	22.3345	−	38.6845i	0.100155	−	0.173473i	0.911748	+	0.410749i	$0.134733\pi$
$224$	−445.324			−1.98805
$225$	33.0000	+	57.1577i	0.146667	+	0.254034i
$226$	−136.415	+	236.277i	−0.603605	+	1.04547i
$227$	−63.0418	−	109.192i	−0.277717	−	0.481020i	0.693100	−	0.720842i	$-0.256244\pi$
$227$	−63.0418	−	109.192i	−0.277717	−	0.481020i	−0.970817	+	0.239821i	$0.922911\pi$
$228$	119.498	+	68.9923i	0.524115	+	0.302598i
$229$		−	190.526i		−	0.831989i	−0.909367	−	0.415995i	$-0.863433\pi$
$229$		−	190.526i		−	0.831989i	0.909367	−	0.415995i	$-0.136567\pi$
$230$	−95.4983			−0.415210
$231$	−123.502	−	71.3038i	−0.534640	−	0.308674i
$232$	123.331	−	213.616i	0.531599	−	0.920757i
$233$	264.662			1.13589			0.567944	−	0.823067i	$-0.307739\pi$
$233$	264.662			1.13589			0.567944	+	0.823067i	$0.307739\pi$
$234$	−62.7491	−	46.3308i	−0.268159	−	0.197995i
$235$		−	0.144842i		−	0.000616350i
$236$	−224.000			−0.949153
$237$	41.7491	−	72.3116i	0.176157	−	0.305112i
$238$	30.1603			0.126724
$239$	−69.2544			−0.289767			−0.144884	−	0.989449i	$-0.546281\pi$
$239$	−69.2544			−0.289767			−0.144884	+	0.989449i	$0.546281\pi$
$240$	48.0000			0.200000
$241$	204.497	−	118.066i	0.848533	−	0.489901i	−0.0116225	−	0.999932i	$-0.503700\pi$
$241$	204.497	−	118.066i	0.848533	−	0.489901i	0.860156	+	0.510032i	$0.170366\pi$
$242$	85.9965	−	148.950i	0.355357	−	0.615497i
$243$	13.5000	−	7.79423i	0.0555556	−	0.0320750i
$244$	−130.328			−0.534129
$245$	216.998	+	125.284i	0.885707	+	0.511363i
$246$	−98.2474	+	170.169i	−0.399380	+	0.691746i
$247$	237.331	−	103.489i	0.960854	−	0.418982i
$248$	−65.3380			−0.263460
$249$	199.871	+	115.396i	0.802695	+	0.463436i
$250$	−141.000	+	81.4064i	−0.564000	+	0.325626i
$251$	250.746	−	144.768i	0.998987	−	0.576765i	0.0910383	−	0.995847i	$-0.470981\pi$
$251$	250.746	−	144.768i	0.998987	−	0.576765i	0.907948	+	0.419082i	$0.137648\pi$
$252$	−83.4983	−	144.623i	−0.331342	−	0.573902i
$253$	141.251	−	81.5512i	0.558304	−	0.322337i
$254$			331.395i			1.30470i
$255$	−3.25087			−0.0127485
$256$	−128.000	+	221.703i	−0.500000	+	0.866025i
$257$	27.0401	−	46.8348i	0.105214	−	0.182236i	−0.808611	−	0.588343i	$-0.799780\pi$
$257$	27.0401	−	46.8348i	0.105214	−	0.182236i	0.913826	+	0.406107i	$0.133114\pi$
$258$	−47.7491	−	82.7039i	−0.185074	−	0.320558i
$259$			118.504i			0.457543i
$260$	53.4983	−	72.4564i	0.205763	−	0.278679i
$261$	92.4983			0.354399
$262$	216.502	−	124.997i	0.826343	−	0.477089i
$263$	−6.12544	−	3.53652i	−0.0232906	−	0.0134469i	0.488309	−	0.872671i	$-0.337614\pi$
$263$	−6.12544	−	3.53652i	−0.0232906	−	0.0134469i	−0.511600	+	0.859224i	$0.670947\pi$
$264$	−70.9965	+	40.9899i	−0.268926	+	0.155265i
$265$			84.5808i			0.319173i
$266$	554.328			2.08394
$267$	107.749	+	186.627i	0.403555	+	0.698977i
$268$	206.829	+	358.239i	0.771751	+	1.33671i
$269$	186.662	+	323.308i	0.693911	+	1.20189i	0.970546	+	0.240914i	$0.0774471\pi$
$269$	186.662	+	323.308i	0.693911	+	1.20189i	−0.276636	+	0.960975i	$0.589220\pi$
$270$	9.00000	+	15.5885i	0.0333333	+	0.0577350i
$271$	46.3345	−	80.2537i	0.170976	−	0.296139i	−0.767785	−	0.640707i	$-0.778641\pi$
$271$	46.3345	−	80.2537i	0.170976	−	0.296139i	0.938761	+	0.344568i	$0.111975\pi$
$272$	8.66900	−	15.0151i	0.0318713	−	0.0552027i
$273$	−311.373	−	35.1480i	−1.14056	−	0.128747i
$274$	−440.247	−	254.177i	−1.60674	−	0.927653i
$275$	65.0801	−	112.722i	0.236655	−	0.409899i
$276$	190.997			0.692016
$277$	−120.706	−	209.068i	−0.435760	−	0.754759i	0.561597	−	0.827411i	$-0.310187\pi$
$277$	−120.706	−	209.068i	−0.435760	−	0.754759i	−0.997357	+	0.0726520i	$0.976854\pi$
$278$	−70.9965	−	40.9899i	−0.255383	−	0.147446i
$279$	−12.2509	−	21.2191i	−0.0439099	−	0.0760543i
$280$	166.997	−	96.4155i	0.596416	−	0.344341i
$281$			89.3485i			0.317966i	0.987281	+	0.158983i	$0.0508215\pi$
$281$			89.3485i			0.317966i	−0.987281	+	0.158983i	$0.949178\pi$
$282$			0.289685i			0.00102725i
$283$	−113.875	−	65.7455i	−0.402384	−	0.232316i	0.285128	−	0.958489i	$-0.407964\pi$
$283$	−113.875	−	65.7455i	−0.402384	−	0.232316i	−0.687512	+	0.726173i	$0.741297\pi$
$284$	494.997			1.74295
$285$	−59.7491			−0.209646
$286$	−17.2544	+	152.855i	−0.0603300	+	0.534458i
$287$			789.381i			2.75046i
$288$	−96.0000			−0.333333
$289$	143.913	−	249.264i	0.497968	−	0.862507i
$290$			106.808i			0.368303i
$291$	−136.997			−0.470778
$292$	151.003	+	87.1819i	0.517135	+	0.298568i
$293$	−341.744	+	197.306i	−1.16636	+	0.673399i	−0.952820	−	0.303535i	$-0.901833\pi$
$293$	−341.744	+	197.306i	−1.16636	+	0.673399i	−0.213541	+	0.976934i	$0.568500\pi$
$294$	−433.997	−	250.568i	−1.47618	−	0.852272i
$295$	84.0000	−	48.4974i	0.284746	−	0.164398i
$296$	58.9965	+	34.0616i	0.199313	+	0.115073i
$297$	−26.6237	−	15.3712i	−0.0896420	−	0.0517549i
$298$	133.997	+	77.3629i	0.449653	+	0.259607i
$299$	212.875	−	288.311i	0.711955	−	0.964251i
$300$	132.000	−	76.2102i	0.440000	−	0.254034i
$301$	−332.247	−	191.823i	−1.10381	−	0.637286i
$302$	49.4146	+	85.5886i	0.163625	+	0.283406i
$303$	115.751	−	66.8288i	0.382016	−	0.220557i
$304$	159.331	−	275.969i	0.524115	−	0.907794i
$305$	48.8728	−	28.2167i	0.160239	−	0.0925139i
$306$	6.50175			0.0212475
$307$	−150.913			−0.491573			−0.245786	−	0.969324i	$-0.579046\pi$
$307$	−150.913			−0.491573			−0.245786	+	0.969324i	$0.579046\pi$
$308$	−164.669	+	285.215i	−0.534640	+	0.926023i
$309$	45.1254	−	78.1595i	0.146037	−	0.252944i
$310$	24.5017	−	14.1461i	0.0790379	−	0.0456326i
$311$		−	42.5831i		−	0.136923i	−0.997654	−	0.0684616i	$-0.978191\pi$
$311$		−	42.5831i		−	0.136923i	0.997654	−	0.0684616i	$-0.0218091\pi$
$312$	−106.997	+	144.913i	−0.342938	+	0.464464i
$313$	−276.990			−0.884951			−0.442475	−	0.896781i	$-0.645900\pi$
$313$	−276.990			−0.884951			−0.442475	+	0.896781i	$0.645900\pi$
$314$	−217.913	−	377.436i	−0.693990	−	1.20203i
$315$	62.6237	+	36.1558i	0.198805	+	0.114780i
$316$	−166.997	−	96.4155i	−0.528470	−	0.305112i
$317$		−	93.2350i		−	0.294117i	−0.989128	−	0.147058i	$-0.953019\pi$
$317$		−	93.2350i		−	0.294117i	0.989128	−	0.147058i	$-0.0469805\pi$
$318$		−	169.162i		−	0.531955i
$319$	−91.2091	−	157.979i	−0.285922	−	0.495231i
$320$		−	110.851i		−	0.346410i
$321$	9.12544	+	15.8057i	0.0284282	+	0.0492390i
$322$	664.495	−	383.646i	2.06365	−	1.19145i
$323$	−10.7909	+	18.6905i	−0.0334085	+	0.0578652i
$324$	−18.0000	−	31.1769i	−0.0555556	−	0.0962250i
$325$	32.0801	−	284.195i	0.0987081	−	0.874447i
$326$	−111.833	+	193.700i	−0.343045	+	0.594172i
$327$	42.2509	−	73.1807i	0.129208	−	0.223794i
$328$	392.990	+	226.893i	1.19814	+	0.691746i
$329$	0.581876	+	1.00784i	0.00176862	+	0.00306334i
$330$	17.7491	−	30.7424i	0.0537852	−	0.0931588i
$331$	−157.164	−	272.216i	−0.474815	−	0.822404i	0.524769	−	0.851245i	$-0.324152\pi$
$331$	−157.164	−	272.216i	−0.474815	−	0.822404i	−0.999584	+	0.0288410i	$0.990818\pi$
$332$	266.495	−	461.582i	0.802695	−	1.39031i
$333$			25.5462i			0.0767154i
$334$	143.666			0.430136
$335$	−155.122	−	89.5597i	−0.463051	−	0.267342i
$336$	−333.993	+	192.831i	−0.994027	+	0.573902i
$337$	−138.826			−0.411946			−0.205973	−	0.978558i	$-0.566036\pi$
$337$	−138.826			−0.411946			−0.205973	+	0.978558i	$0.566036\pi$
$338$	99.4948	+	323.024i	0.294363	+	0.955694i
$339$			236.277i			0.696982i
$340$			7.50757i			0.0220811i
$341$	−24.1603	+	41.8468i	−0.0708512	+	0.122718i
$342$	119.498			0.349410
$343$	−1331.32			−3.88139
$344$	−190.997	+	110.272i	−0.555222	+	0.320558i
$345$	−71.6237	+	41.3520i	−0.207605	+	0.119861i
$346$	−187.666	+	325.046i	−0.542386	+	0.939440i
$347$	463.118	−	267.382i	1.33464	−	0.770552i	0.348629	−	0.937261i	$-0.386647\pi$
$347$	463.118	−	267.382i	1.33464	−	0.770552i	0.986006	+	0.166709i	$0.0533140\pi$
$348$		−	213.616i		−	0.613838i
$349$	210.753	+	121.678i	0.603876	+	0.348648i	0.770565	−	0.637362i	$-0.219974\pi$
$349$	210.753	+	121.678i	0.603876	+	0.348648i	−0.166689	+	0.986010i	$0.553308\pi$
$350$	306.160	−	530.285i	0.874744	−	1.51510i
$351$	−67.1237	−	7.57697i	−0.191236	−	0.0215868i
$352$	94.6620	+	163.959i	0.268926	+	0.465794i
$353$	226.615	+	130.836i	0.641969	+	0.370641i	0.785372	−	0.619023i	$-0.212471\pi$
$353$	226.615	+	130.836i	0.641969	+	0.370641i	−0.143404	+	0.989664i	$0.545805\pi$
$354$	−168.000	+	96.9948i	−0.474576	+	0.273997i
$355$	−185.624	+	107.170i	−0.522884	+	0.301887i
$356$	430.997	−	248.836i	1.21066	−	0.698977i
$357$	22.6202	−	13.0598i	0.0633619	−	0.0365820i
$358$			104.213i			0.291097i
$359$	408.585			1.13812			0.569060	−	0.822296i	$-0.307307\pi$
$359$	408.585			1.13812			0.569060	+	0.822296i	$0.307307\pi$
$360$	36.0000	−	20.7846i	0.100000	−	0.0577350i
$361$	−17.8310	+	30.8842i	−0.0493934	+	0.0855518i
$362$	−64.7491	−	112.149i	−0.178865	−	0.309803i
$363$		−	148.950i		−	0.410331i
$364$	−81.1707	+	719.085i	−0.222997	+	1.97551i
$365$	−75.5017			−0.206854
$366$	−97.7456	+	56.4335i	−0.267065	+	0.154190i
$367$	195.125	+	112.656i	0.531677	+	0.306964i	0.741699	−	0.670733i	$-0.234020\pi$
$367$	195.125	+	112.656i	0.531677	+	0.306964i	−0.210022	+	0.977697i	$0.567354\pi$
$368$		−	441.088i		−	1.19861i
$369$			170.169i			0.461164i
$370$	−29.4983			−0.0797250
$371$	−339.787	−	588.529i	−0.915869	−	1.58633i
$372$	−49.0035	+	28.2922i	−0.131730	+	0.0760543i
$373$	254.371	+	440.584i	0.681960	+	1.18119i	0.974382	+	0.224900i	$0.0722055\pi$
$373$	254.371	+	440.584i	0.681960	+	1.18119i	−0.292422	+	0.956289i	$0.594461\pi$
$374$	−6.41113	−	11.1044i	−0.0171421	−	0.0296909i
$375$	−70.5000	+	122.110i	−0.188000	+	0.325626i
$376$	0.668998			0.00177925
$377$	−322.455	−	238.085i	−0.855317	−	0.631524i
$378$	−125.247	−	72.3116i	−0.331342	−	0.191301i
$379$	130.084	−	225.311i	0.343229	−	0.594489i	−0.641802	−	0.766871i	$-0.721813\pi$
$379$	130.084	−	225.311i	0.343229	−	0.594489i	0.985030	+	0.172381i	$0.0551461\pi$
$380$			137.985i			0.363118i
$381$	143.498	+	248.546i	0.376636	+	0.652352i
$382$	453.993	+	262.113i	1.18846	+	0.686160i
$383$	−196.913	−	341.063i	−0.514133	−	0.890504i	−0.999866	−	0.0163968i	$-0.994780\pi$
$383$	−196.913	−	341.063i	−0.514133	−	0.890504i	0.485733	−	0.874107i	$-0.338553\pi$
$384$			221.703i			0.577350i
$385$		−	142.608i		−	0.370409i
$386$			79.0950i			0.204909i
$387$	−71.6237	−	41.3520i	−0.185074	−	0.106853i
$388$			316.380i			0.815412i
$389$	−354.331			−0.910877			−0.455438	−	0.890267i	$-0.650517\pi$
$389$	−354.331			−0.910877			−0.455438	+	0.890267i	$0.650517\pi$
$390$	8.74913	−	77.5078i	0.0224337	−	0.198738i
$391$			29.8733i			0.0764024i
$392$	−578.662	+	1002.27i	−1.47618	+	2.55682i
$393$	108.251	−	187.496i	0.275448	−	0.477089i
$394$			717.057i			1.81994i
$395$	83.4983			0.211388
$396$	−35.4983	+	61.4848i	−0.0896420	+	0.155265i
$397$	−592.746	+	342.222i	−1.49306	+	0.862020i	−0.999968	−	0.00795644i	$-0.997467\pi$
$397$	−592.746	+	342.222i	−1.49306	+	0.862020i	−0.493094	+	0.869976i	$0.664134\pi$
$398$	579.742	+	334.714i	1.45664	+	0.840991i
$399$	415.746	−	240.031i	1.04197	−	0.601581i
$400$	−176.000	−	304.841i	−0.440000	−	0.762102i
$401$	339.120	+	195.791i	0.845686	+	0.488257i	0.859193	−	0.511652i	$-0.170966\pi$
$401$	339.120	+	195.791i	0.845686	+	0.488257i	−0.0135068	+	0.999909i	$0.504299\pi$
$402$	310.244	+	179.119i	0.771751	+	0.445571i
$403$	−11.9094	+	105.504i	−0.0295518	+	0.261797i
$404$	−154.334	−	267.315i	−0.382016	−	0.661671i
$405$	13.5000	+	7.79423i	0.0333333	+	0.0192450i
$406$	−429.080	−	743.189i	−1.05685	−	1.83051i
$407$	43.6307	−	25.1902i	0.107201	−	0.0618923i
$408$		−	15.0151i		−	0.0368018i
$409$	−334.500	+	193.124i	−0.817848	+	0.472185i	−0.849674	−	0.527308i	$-0.823201\pi$
$409$	−334.500	+	193.124i	−0.817848	+	0.472185i	0.0318255	+	0.999493i	$0.489868\pi$
$410$	−196.495			−0.479256
$411$	−440.247			−1.07116
$412$	−180.502	−	104.213i	−0.438111	−	0.252944i
$413$	−389.659	+	674.908i	−0.943483	+	1.63416i
$414$	143.247	−	82.7039i	0.346008	−	0.199768i
$415$			230.791i			0.556123i
$416$	334.662	+	247.098i	0.804476	+	0.593985i
$417$	−70.9965			−0.170255
$418$	−117.833	−	204.092i	−0.281897	−	0.488259i
$419$	−400.746	−	231.371i	−0.956433	−	0.552197i	−0.0613600	−	0.998116i	$-0.519544\pi$
$419$	−400.746	−	231.371i	−0.956433	−	0.552197i	−0.895074	+	0.445919i	$0.852877\pi$
$420$	83.4983	−	144.623i	0.198805	−	0.344341i
$421$		−	474.431i		−	1.12691i	−0.826145	−	0.563457i	$-0.809471\pi$
$421$		−	474.431i		−	1.12691i	0.826145	−	0.563457i	$-0.190529\pi$
$422$		−	471.697i		−	1.11777i
$423$	0.125437	+	0.217263i	0.000296542	+	0.000513625i
$424$	−390.662			−0.921373
$425$	11.9199	+	20.6458i	0.0280468	+	0.0485784i
$426$	371.247	−	214.340i	0.871473	−	0.503145i
$427$	−226.711	+	392.675i	−0.530939	+	0.919613i
$428$	36.5017	−	21.0743i	0.0852845	−	0.0492390i
$429$	53.2474	+	122.113i	0.124120	+	0.284645i
$430$	47.7491	−	82.7039i	0.111044	−	0.192335i
$431$	−138.794	+	240.399i	−0.322029	+	0.557770i	−0.980907	−	0.194480i	$-0.937698\pi$
$431$	−138.794	+	240.399i	−0.322029	+	0.557770i	0.658878	+	0.752250i	$0.271031\pi$
$432$	−72.0000	+	41.5692i	−0.166667	+	0.0962250i
$433$	−220.584	−	382.062i	−0.509431	−	0.882360i	−0.999940	−	0.0109244i	$-0.996523\pi$
$433$	−220.584	−	382.062i	−0.509431	−	0.882360i	0.490509	−	0.871436i	$-0.336811\pi$
$434$	−113.659	+	196.862i	−0.261886	+	0.453600i
$435$	46.2491	+	80.1058i	0.106320	+	0.184151i
$436$	−169.003	−	97.5742i	−0.387623	−	0.223794i
$437$			549.054i			1.25642i
$438$	151.003			0.344757
$439$	169.369	+	97.7854i	0.385807	+	0.222746i	0.680342	−	0.732895i	$-0.261831\pi$
$439$	169.369	+	97.7854i	0.385807	+	0.222746i	−0.294535	+	0.955641i	$0.595165\pi$
$440$	−70.9965	−	40.9899i	−0.161356	−	0.0931588i
$441$	−433.997			−0.984119
$442$	−22.6655	−	16.7351i	−0.0512794	−	0.0378622i
$443$			188.510i			0.425530i	0.977103	+	0.212765i	$0.0682469\pi$
$443$			188.510i			0.425530i	−0.977103	+	0.212765i	$0.931753\pi$
$444$	58.9965			0.132875
$445$	−107.749	+	186.627i	−0.242133	+	0.419386i
$446$	−89.3380			−0.200309
$447$	133.997			0.299768
$448$	445.324	+	771.324i	0.994027	+	1.72170i
$449$	196.746	−	113.591i	0.438186	−	0.252987i	−0.264642	−	0.964347i	$-0.585254\pi$
$449$	196.746	−	113.591i	0.438186	−	0.252987i	0.702828	+	0.711360i	$0.251920\pi$
$450$	66.0000	−	114.315i	0.146667	−	0.254034i
$451$	290.634	−	167.798i	0.644422	−	0.372057i
$452$	545.659			1.20721
$453$	74.1219	+	42.7943i	0.163625	+	0.0944687i
$454$	−126.084	+	218.383i	−0.277717	+	0.481020i
$455$	−125.247	−	287.231i	−0.275269	−	0.631276i
$456$		−	275.969i		−	0.605196i
$457$	139.490	+	80.5343i	0.305229	+	0.176224i	0.644789	−	0.764360i	$-0.276945\pi$
$457$	139.490	+	80.5343i	0.305229	+	0.176224i	−0.339561	+	0.940584i	$0.610278\pi$
$458$	−330.000	+	190.526i	−0.720524	+	0.415995i
$459$	4.87631	−	2.81534i	0.0106238	−	0.00613364i
$460$	95.4983	+	165.408i	0.207605	+	0.359582i
$461$	69.4965	−	40.1238i	0.150752	−	0.0870365i	−0.422727	−	0.906257i	$-0.638927\pi$
$461$	69.4965	−	40.1238i	0.150752	−	0.0870365i	0.573478	+	0.819221i	$0.305594\pi$
$462$			285.215i			0.617349i
$463$	595.073			1.28526			0.642628	−	0.766179i	$-0.277844\pi$
$463$	595.073			1.28526			0.642628	+	0.766179i	$0.277844\pi$
$464$	−493.324			−1.06320
$465$	12.2509	−	21.2191i	0.0263460	−	0.0456326i
$466$	−264.662	−	458.408i	−0.567944	−	0.983708i
$467$			236.850i			0.507174i	0.967313	+	0.253587i	$0.0816105\pi$
$467$			236.850i			0.507174i	−0.967313	+	0.253587i	$0.918390\pi$
$468$	−17.4983	+	155.016i	−0.0373894	+	0.331230i
$469$	1439.16			3.06856
$470$	−0.250874	+	0.144842i	−0.000533775	+	0.000308175i
$471$	−326.869	−	188.718i	−0.693990	−	0.400675i
$472$	224.000	+	387.979i	0.474576	+	0.821990i
$473$			163.102i			0.344825i
$474$	−166.997			−0.352313
$475$	219.080	+	379.458i	0.461221	+	0.798859i
$476$	−30.1603	−	52.2391i	−0.0633619	−	0.109746i
$477$	−73.2491	−	126.871i	−0.153562	−	0.265977i
$478$	69.2544	+	119.952i	0.144884	+	0.250946i
$479$	−146.251	+	253.314i	−0.305325	+	0.528839i	−0.977334	−	0.211704i	$-0.932099\pi$
$479$	−146.251	+	253.314i	−0.305325	+	0.528839i	0.672008	+	0.740544i	$0.265432\pi$
$480$	−48.0000	−	83.1384i	−0.100000	−	0.173205i
$481$	65.7544	−	89.0558i	0.136703	−	0.185147i
$482$	−408.993	−	236.132i	−0.848533	−	0.489901i
$483$	332.247	−	575.469i	0.687883	−	1.19145i
$484$	−343.986			−0.710715
$485$	−68.4983	−	118.642i	−0.141234	−	0.244624i
$486$	−27.0000	−	15.5885i	−0.0555556	−	0.0320750i
$487$	−285.537	−	494.564i	−0.586317	−	1.01553i	−0.994710	−	0.102725i	$-0.967244\pi$
$487$	−285.537	−	494.564i	−0.586317	−	1.01553i	0.408392	−	0.912806i	$-0.366090\pi$
$488$	130.328	+	225.734i	0.267065	+	0.462569i
$489$			193.700i			0.396115i
$490$		−	501.136i		−	1.02273i
$491$	103.369	+	59.6803i	0.210528	+	0.121548i	0.601557	−	0.798830i	$-0.294547\pi$
$491$	103.369	+	59.6803i	0.210528	+	0.121548i	−0.391029	+	0.920378i	$0.627881\pi$
$492$	392.990			0.798759
$493$	33.4111			0.0677711
$494$	−416.578	−	307.581i	−0.843276	−	0.622633i
$495$		−	30.7424i		−	0.0621058i
$496$	65.3380	+	113.169i	0.131730	+	0.228163i
$497$	861.070	−	1491.42i	1.73253	−	3.00084i
$498$		−	461.582i		−	0.926872i
$499$	25.3240			0.0507495			0.0253748	−	0.999678i	$-0.491922\pi$
$499$	25.3240			0.0507495			0.0253748	+	0.999678i	$0.491922\pi$
$500$	282.000	+	162.813i	0.564000	+	0.325626i
$501$	107.749	−	62.2090i	0.215068	−	0.124170i
$502$	−501.491	−	289.536i	−0.998987	−	0.576765i
$503$	−400.118	+	231.008i	−0.795464	+	0.459261i	−0.841883	−	0.539661i	$-0.818553\pi$
$503$	−400.118	+	231.008i	−0.795464	+	0.459261i	0.0464185	+	0.998922i	$0.485219\pi$
$504$	−166.997	+	289.246i	−0.331342	+	0.573902i
$505$	115.751	+	66.8288i	0.229210	+	0.132334i
$506$	−282.502	−	163.102i	−0.558304	−	0.322337i
$507$	214.495	+	199.186i	0.423067	+	0.392871i
$508$	573.993	−	331.395i	1.12991	−	0.652352i
$509$	−148.239	−	85.5856i	−0.291235	−	0.168145i	0.347264	−	0.937768i	$-0.387111\pi$
$509$	−148.239	−	85.5856i	−0.291235	−	0.168145i	−0.638499	+	0.769623i	$0.720444\pi$
$510$	3.25087	+	5.63068i	0.00637426	+	0.0110405i
$511$	525.355	−	303.314i	1.02809	−	0.593570i
$512$	512.000			1.00000
$513$	89.6237	−	51.7443i	0.174705	−	0.100866i
$514$	−108.160			−0.210429
$515$	90.2509			0.175244
$516$	−95.4983	+	165.408i	−0.185074	+	0.320558i
$517$	0.247378	−	0.428471i	0.000478487	−	0.000828763i
$518$	205.254	−	118.504i	0.396244	−	0.228772i
$519$			325.046i			0.626293i
$520$	−178.997	−	20.2052i	−0.344224	−	0.0388562i
$521$	−228.080			−0.437774			−0.218887	−	0.975750i	$-0.570243\pi$
$521$	−228.080			−0.437774			−0.218887	+	0.975750i	$0.570243\pi$
$522$	−92.4983	−	160.212i	−0.177200	−	0.306919i
$523$	556.620	+	321.365i	1.06428	+	0.614464i	0.926614	−	0.376014i	$-0.122706\pi$
$523$	556.620	+	321.365i	1.06428	+	0.614464i	0.137669	+	0.990478i	$0.456039\pi$
$524$	−433.003	−	249.995i	−0.826343	−	0.477089i
$525$		−	530.285i		−	1.01007i
$526$			14.1461i			0.0268937i
$527$	−4.42512	−	7.66453i	−0.00839681	−	0.0145437i
$528$	141.993	+	81.9797i	0.268926	+	0.155265i
$529$	115.497	+	200.046i	0.218330	+	0.378158i
$530$	146.498	−	84.5808i	0.276412	−	0.159586i
$531$	−84.0000	+	145.492i	−0.158192	+	0.273997i
$532$	−554.328	−	960.123i	−1.04197	−	1.80474i
$533$	438.005	−	593.221i	0.821773	−	1.11299i
$534$	215.498	−	373.254i	0.403555	−	0.698977i
$535$	−9.12544	+	15.8057i	−0.0170569	+	0.0295434i
$536$	413.659	−	716.478i	0.771751	−	1.33671i
$537$	45.1254	+	78.1595i	0.0840325	+	0.145549i
$538$	373.324	−	646.616i	0.693911	−	1.20189i
$539$	427.948	+	741.227i	0.793966	+	1.37519i
$540$	18.0000	−	31.1769i	0.0333333	−	0.0577350i
$541$		−	633.478i		−	1.17094i	−0.810694	−	0.585469i	$-0.800910\pi$
$541$		−	633.478i		−	1.17094i	0.810694	−	0.585469i	$-0.199090\pi$
$542$	−185.338			−0.341952
$543$	−97.1237	−	56.0744i	−0.178865	−	0.103268i
$544$	−34.6760			−0.0637426
$545$	84.5017			0.155049
$546$	250.495	+	574.461i	0.458782	+	1.05213i
$547$		−	632.036i		−	1.15546i	−0.816229	−	0.577729i	$-0.803939\pi$
$547$		−	632.036i		−	1.15546i	0.816229	−	0.577729i	$-0.196061\pi$
$548$			1016.71i			1.85531i
$549$	−48.8728	+	84.6502i	−0.0890215	+	0.154190i
$550$	−260.321			−0.473310
$551$	614.077			1.11448
$552$	−190.997	−	330.816i	−0.346008	−	0.599304i
$553$	−580.997	+	335.438i	−1.05063	+	0.606580i
$554$	−241.411	+	418.136i	−0.435760	+	0.754759i
$555$	−22.1237	+	12.7731i	−0.0398625	+	0.0230146i
$556$			163.959i			0.294891i
$557$	−347.493	−	200.625i	−0.623865	−	0.360189i	0.154507	−	0.987992i	$-0.450621\pi$
$557$	−347.493	−	200.625i	−0.623865	−	0.360189i	−0.778372	+	0.627803i	$0.783954\pi$
$558$	−24.5017	+	42.4383i	−0.0439099	+	0.0760543i
$559$	143.247	+	328.510i	0.256256	+	0.587675i
$560$	−333.993	−	192.831i	−0.596416	−	0.344341i
$561$	−9.61670	−	5.55220i	−0.0171421	−	0.00989697i
$562$	154.756	−	89.3485i	0.275367	−	0.158983i
$563$	−811.986	+	468.800i	−1.44225	+	0.832683i	−0.998000	−	0.0632206i	$-0.979863\pi$
$563$	−811.986	+	468.800i	−1.44225	+	0.832683i	−0.444249	+	0.895903i	$0.646529\pi$
$564$	0.501748	−	0.289685i	0.000889625	−	0.000513625i
$565$	−204.622	+	118.139i	−0.362163	+	0.209095i
$566$			262.982i			0.464633i
$567$	−125.247			−0.220895
$568$	−494.997	−	857.359i	−0.871473	−	1.50944i
$569$	173.909	−	301.220i	0.305640	−	0.529385i	−0.671763	−	0.740766i	$-0.734463\pi$
$569$	173.909	−	301.220i	0.305640	−	0.529385i	0.977404	+	0.211381i	$0.0677961\pi$
$570$	59.7491	+	103.489i	0.104823	+	0.181559i
$571$			526.109i			0.921382i	0.887561	+	0.460691i	$0.152398\pi$
$571$			526.109i			0.921382i	−0.887561	+	0.460691i	$0.847602\pi$
$572$	282.007	−	122.970i	0.493019	−	0.214982i
$573$	453.993			0.792309
$574$	1367.25	−	789.381i	2.38196	−	1.37523i
$575$	525.240	+	303.248i	0.913462	+	0.527387i
$576$	96.0000	+	166.277i	0.166667	+	0.288675i
$577$			976.858i			1.69300i	0.532392	+	0.846498i	$0.321293\pi$
$577$			976.858i			1.69300i	−0.532392	+	0.846498i	$0.678707\pi$
$578$	−575.652			−0.995937
$579$	34.2491	+	59.3212i	0.0591522	+	0.102455i
$580$	184.997	−	106.808i	0.318959	−	0.184151i
$581$	−927.160	−	1605.89i	−1.59580	−	2.76401i
$582$	136.997	+	237.285i	0.235389	+	0.407706i
$583$	−144.456	+	250.206i	−0.247781	+	0.429170i
$584$		−	348.728i		−	0.597136i
$585$	−27.0000	−	61.9193i	−0.0461538	−	0.105845i
$586$	683.488	+	394.612i	1.16636	+	0.673399i
$587$	−418.990	+	725.711i	−0.713781	+	1.23631i	0.249647	+	0.968337i	$0.419686\pi$
$587$	−418.990	+	725.711i	−0.713781	+	1.23631i	−0.963428	+	0.267968i	$0.913648\pi$
$588$			1002.27i			1.70454i
$589$	−81.3310	−	140.869i	−0.138083	−	0.239167i
$590$	−168.000	−	96.9948i	−0.284746	−	0.164398i
$591$	310.495	+	537.793i	0.525372	+	0.909971i
$592$		−	136.247i		−	0.230146i
$593$			669.000i			1.12816i	0.825719	+	0.564081i	$0.190769\pi$
$593$			669.000i			1.12816i	−0.825719	+	0.564081i	$0.809231\pi$
$594$			61.4848i			0.103510i
$595$	22.6202	+	13.0598i	0.0380171	+	0.0219492i
$596$		−	309.452i		−	0.519214i
$597$	579.742			0.971092
$598$	−712.244	−	80.3985i	−1.19104	−	0.134446i
$599$			973.690i			1.62553i	0.582594	+	0.812763i	$0.302038\pi$
$599$			973.690i			1.62553i	−0.582594	+	0.812763i	$0.697962\pi$
$600$	−264.000	−	152.420i	−0.440000	−	0.254034i
$601$	−438.995	+	760.361i	−0.730441	+	1.26516i	0.226255	+	0.974068i	$0.427352\pi$
$601$	−438.995	+	760.361i	−0.730441	+	1.26516i	−0.956695	+	0.291092i	$0.905981\pi$
$602$			767.292i			1.27457i
$603$	310.244			0.514501
$604$	98.8293	−	171.177i	0.163625	−	0.283406i
$605$	128.995	−	74.4752i	0.213214	−	0.123099i
$606$	−231.502	−	133.658i	−0.382016	−	0.220557i
$607$	865.986	−	499.977i	1.42667	−	0.823686i	0.429810	−	0.902920i	$-0.358581\pi$
$607$	865.986	−	499.977i	1.42667	−	0.823686i	0.996856	+	0.0792338i	$0.0252474\pi$
$608$	−637.324			−1.04823
$609$	−643.620	−	371.594i	−1.05685	−	0.610171i
$610$	−97.7456	−	56.4335i	−0.160239	−	0.0925139i
$611$	0.121941	−	1.08026i	0.000199575	−	0.00176802i
$612$	−6.50175	−	11.2614i	−0.0106238	−	0.0184009i
$613$	−579.622	−	334.645i	−0.945550	−	0.545913i	−0.0538540	−	0.998549i	$-0.517151\pi$
$613$	−579.622	−	334.645i	−0.945550	−	0.545913i	−0.891696	+	0.452635i	$0.850484\pi$
$614$	150.913	+	261.389i	0.245786	+	0.425715i
$615$	−147.371	+	85.0847i	−0.239628	+	0.138349i
$616$	658.676			1.06928
$617$	−266.618	+	153.932i	−0.432121	+	0.249485i	−0.700250	−	0.713898i	$-0.746928\pi$
$617$	−266.618	+	153.932i	−0.432121	+	0.249485i	0.268129	+	0.963383i	$0.413595\pi$
$618$	−180.502			−0.292074
$619$	−406.174			−0.656178			−0.328089	−	0.944647i	$-0.606405\pi$
$619$	−406.174			−0.656178			−0.328089	+	0.944647i	$0.606405\pi$
$620$	−49.0035	−	28.2922i	−0.0790379	−	0.0456326i
$621$	71.6237	−	124.056i	0.115336	−	0.199768i
$622$	−73.7561	+	42.5831i	−0.118579	+	0.0684616i
$623$		−	1731.45i		−	2.77921i
$624$	357.993	+	40.4105i	0.573707	+	0.0647604i
$625$	409.000			0.654400
$626$	276.990	+	479.760i	0.442475	+	0.766390i
$627$	−176.749	−	102.046i	−0.281897	−	0.162753i
$628$	−435.826	+	754.872i	−0.693990	+	1.20203i
$629$			9.22751i			0.0146701i
$630$		−	144.623i		−	0.229561i
$631$	−346.655	−	600.424i	−0.549374	−	0.951544i	−0.998318	−	0.0579836i	$-0.981533\pi$
$631$	−346.655	−	600.424i	−0.549374	−	0.951544i	0.448944	−	0.893560i	$-0.351800\pi$
$632$			385.662i			0.610225i
$633$	−204.251	−	353.773i	−0.322671	−	0.558883i
$634$	−161.488	+	93.2350i	−0.254713	+	0.147058i
$635$	−143.498	+	248.546i	−0.225981	+	0.391411i
$636$	−292.997	+	169.162i	−0.460686	+	0.265977i
$637$	1512.94	+	1117.08i	2.37510	+	1.75366i
$638$	−182.418	+	315.957i	−0.285922	+	0.495231i
$639$	185.624	−	321.510i	0.290491	−	0.503145i
$640$	−192.000	+	110.851i	−0.300000	+	0.173205i
$641$	584.538	+	1012.45i	0.911916	+	1.57949i	0.811354	+	0.584554i	$0.198731\pi$
$641$	584.538	+	1012.45i	0.911916	+	1.57949i	0.100562	+	0.994931i	$0.467936\pi$
$642$	18.2509	−	31.6114i	0.0284282	−	0.0492390i
$643$	−433.666	−	751.131i	−0.674441	−	1.16817i	−0.976632	−	0.214919i	$-0.931051\pi$
$643$	−433.666	−	751.131i	−0.674441	−	1.16817i	0.302191	−	0.953247i	$-0.402282\pi$
$644$	−1328.99	−	767.292i	−2.06365	−	1.19145i
$645$		−	82.7039i		−	0.128223i
$646$	43.1638			0.0668170
$647$	−478.746	−	276.404i	−0.739947	−	0.427209i	0.0821031	−	0.996624i	$-0.473836\pi$
$647$	−478.746	−	276.404i	−0.739947	−	0.427209i	−0.822050	+	0.569415i	$0.807170\pi$
$648$	−36.0000	+	62.3538i	−0.0555556	+	0.0962250i
$649$	331.317			0.510504
$650$	−524.321	+	228.631i	−0.806647	+	0.351740i
$651$			196.862i			0.302400i
$652$	447.331			0.686090
$653$	−211.826	+	366.893i	−0.324389	+	0.561858i	−0.981388	−	0.192033i	$-0.938492\pi$
$653$	−211.826	+	366.893i	−0.324389	+	0.561858i	0.657000	+	0.753891i	$0.271825\pi$
$654$	−169.003			−0.258415
$655$	216.502			0.330537
$656$		−	907.570i		−	1.38349i
$657$	113.253	−	65.3864i	0.172378	−	0.0995227i
$658$	1.16375	−	2.01568i	0.00176862	−	0.00306334i
$659$	−43.7561	+	25.2626i	−0.0663978	+	0.0383348i	−0.532831	−	0.846221i	$-0.678872\pi$
$659$	−43.7561	+	25.2626i	−0.0663978	+	0.0383348i	0.466434	+	0.884556i	$0.345539\pi$
$660$	−70.9965			−0.107570
$661$	695.357	+	401.465i	1.05198	+	0.607359i	0.923202	−	0.384314i	$-0.125562\pi$
$661$	695.357	+	401.465i	1.05198	+	0.607359i	0.128775	+	0.991674i	$0.458895\pi$
$662$	−314.328	+	544.431i	−0.474815	+	0.822404i
$663$	−24.2456	−	2.73686i	−0.0365696	−	0.00412800i
$664$	−1065.98			−1.60539
$665$	415.746	+	240.031i	0.625181	+	0.360949i
$666$	44.2474	−	25.5462i	0.0664375	−	0.0383577i
$667$	736.118	−	424.998i	1.10363	−	0.637179i
$668$	−143.666	−	248.836i	−0.215068	−	0.372509i
$669$	−67.0035	+	38.6845i	−0.100155	+	0.0578243i
$670$			358.239i			0.534685i
$671$	192.767			0.287283
$672$	667.986	+	385.662i	0.994027	+	0.573902i
$673$	14.9111	−	25.8268i	0.0221562	−	0.0383757i	−0.854735	−	0.519065i	$-0.826280\pi$
$673$	14.9111	−	25.8268i	0.0221562	−	0.0383757i	0.876891	+	0.480689i	$0.159614\pi$
$674$	138.826	+	240.453i	0.205973	+	0.356756i
$675$		−	114.315i		−	0.169356i
$676$	460.000	−	495.354i	0.680473	−	0.732773i
$677$	−135.331			−0.199898			−0.0999490	−	0.994993i	$-0.531868\pi$
$677$	−135.331			−0.199898			−0.0999490	+	0.994993i	$0.531868\pi$
$678$	409.244	−	236.277i	0.603605	−	0.348491i
$679$	953.247	+	550.358i	1.40390	+	0.810541i
$680$	13.0035	−	7.50757i	0.0191228	−	0.0110405i
$681$			218.383i			0.320680i
$682$	96.6410			0.141702
$683$	−389.164	−	674.051i	−0.569786	−	0.986898i	−0.996587	−	0.0825524i	$-0.973693\pi$
$683$	−389.164	−	674.051i	−0.569786	−	0.986898i	0.426801	−	0.904346i	$-0.359641\pi$
$684$	−119.498	−	206.977i	−0.174705	−	0.302598i
$685$	−220.124	−	381.265i	−0.321348	−	0.556592i
$686$	1331.32	+	2305.91i	1.94070	+	3.36138i
$687$	−165.000	+	285.788i	−0.240175	+	0.415995i
$688$	381.993	+	220.544i	0.555222	+	0.320558i
$689$	−71.2073	+	630.820i	−0.103349	+	0.915558i
$690$	143.247	+	82.7039i	0.207605	+	0.119861i
$691$	−324.035	+	561.245i	−0.468936	+	0.812221i	−0.999369	−	0.0355055i	$-0.988696\pi$
$691$	−324.035	+	561.245i	−0.468936	+	0.812221i	0.530433	+	0.847727i	$0.322029\pi$
$692$	750.662			1.08477
$693$	123.502	+	213.911i	0.178213	+	0.308674i
$694$	−926.237	−	534.763i	−1.33464	−	0.770552i
$695$	−35.4983	−	61.4848i	−0.0510766	−	0.0884673i
$696$	−369.993	+	213.616i	−0.531599	+	0.306919i
$697$			61.4666i			0.0881874i
$698$		−	486.712i		−	0.697296i
$699$	−396.993	−	229.204i	−0.567944	−	0.327903i
$700$	−1224.64			−1.74949
$701$	−924.321			−1.31857			−0.659287	−	0.751891i	$-0.729142\pi$
$701$	−924.321			−1.31857			−0.659287	+	0.751891i	$0.729142\pi$
$702$	54.0000	+	123.839i	0.0769231	+	0.176408i
$703$			169.596i			0.241246i
$704$	189.324	−	327.919i	0.268926	−	0.465794i
$705$	−0.125437	+	0.217263i	−0.000177925	+	0.000308175i
$706$		−	523.345i		−	0.741282i
$707$	−1073.89			−1.51894
$708$	336.000	+	193.990i	0.474576	+	0.273997i
$709$	−641.880	+	370.589i	−0.905331	+	0.522693i	−0.878926	−	0.476958i	$-0.841739\pi$
$709$	−641.880	+	370.589i	−0.905331	+	0.522693i	−0.0264052	+	0.999651i	$0.508406\pi$
$710$	371.247	+	214.340i	0.522884	+	0.301887i
$711$	−125.247	+	72.3116i	−0.176157	+	0.101704i
$712$	−861.993	−	497.672i	−1.21066	−	0.698977i
$713$	−194.990	−	112.577i	−0.273478	−	0.157892i
$714$	−45.2404	−	26.1195i	−0.0633619	−	0.0365820i
$715$	−79.1289	+	107.170i	−0.110670	+	0.149888i
$716$	180.502	−	104.213i	0.252097	−	0.145549i
$717$	103.882	+	59.9760i	0.144884	+	0.0836486i
$718$	−408.585	−	707.691i	−0.569060	−	0.985642i
$719$	−337.756	+	195.004i	−0.469758	+	0.271215i	−0.716138	−	0.697958i	$-0.754092\pi$
$719$	−337.756	+	195.004i	−0.469758	+	0.271215i	0.246380	+	0.969173i	$0.420759\pi$
$720$	−72.0000	−	41.5692i	−0.100000	−	0.0577350i
$721$	−627.983	+	362.566i	−0.870988	+	0.502865i
$722$	71.3240			0.0987867
$723$	−408.993			−0.565689
$724$	−129.498	+	224.298i	−0.178865	+	0.309803i
$725$	339.160	−	587.443i	0.467807	−	0.810266i
$726$	−257.990	+	148.950i	−0.355357	+	0.205166i
$727$		−	316.827i		−	0.435800i	−0.975971	−	0.217900i	$-0.930079\pi$
$727$		−	316.827i		−	0.435800i	0.975971	−	0.217900i	$-0.0699206\pi$
$728$	1326.66	−	578.493i	1.82234	−	0.794633i
$729$	−27.0000			−0.0370370
$730$	75.5017	+	130.773i	0.103427	+	0.179141i
$731$	−25.8711	−	14.9367i	−0.0353913	−	0.0204332i
$732$	195.491	+	112.867i	0.267065	+	0.154190i
$733$		−	668.723i		−	0.912309i	−0.889901	−	0.456155i	$-0.849226\pi$
$733$		−	668.723i		−	0.912309i	0.889901	−	0.456155i	$-0.150774\pi$
$734$		−	450.623i		−	0.613928i
$735$	−216.998	−	375.852i	−0.295236	−	0.511363i
$736$	−763.986	+	441.088i	−1.03802	+	0.599304i
$737$	−305.920	−	529.869i	−0.415088	−	0.718954i
$738$	294.742	−	170.169i	0.399380	−	0.230582i
$739$	−54.6620	+	94.6774i	−0.0739675	+	0.128116i	−0.900637	−	0.434573i	$-0.856899\pi$
$739$	−54.6620	+	94.6774i	−0.0739675	+	0.128116i	0.826669	+	0.562688i	$0.190233\pi$
$740$	29.4983	+	51.0925i	0.0398625	+	0.0690439i
$741$	−445.620	−	50.3019i	−0.601377	−	0.0678838i
$742$	−679.575	+	1177.06i	−0.915869	+	1.58633i
$743$	541.240	−	937.456i	0.728453	−	1.26172i	−0.229084	−	0.973407i	$-0.573573\pi$
$743$	541.240	−	937.456i	0.728453	−	1.26172i	0.957537	−	0.288311i	$-0.0930935\pi$
$744$	98.0070	+	56.5844i	0.131730	+	0.0760543i
$745$	66.9983	+	116.044i	0.0899305	+	0.155764i
$746$	508.742	−	881.167i	0.681960	−	1.18119i
$747$	−199.871	−	346.187i	−0.267565	−	0.463436i
$748$	−12.8223	+	22.2088i	−0.0171421	+	0.0296909i
$749$		−	146.639i		−	0.195780i
$750$	282.000			0.376000
$751$	−59.6132	−	34.4177i	−0.0793784	−	0.0458292i	0.459785	−	0.888030i	$-0.347926\pi$
$751$	−59.6132	−	34.4177i	−0.0793784	−	0.0458292i	−0.539164	+	0.842201i	$0.681260\pi$
$752$	−0.668998	−	1.15874i	−0.000889625	−	0.00154088i
$753$	−501.491			−0.665991
$754$	−89.9199	+	796.592i	−0.119257	+	1.05649i
$755$			85.5886i			0.113362i
$756$			289.246i			0.382601i
$757$	−307.502	+	532.609i	−0.406211	+	0.703578i	−0.994462	−	0.105101i	$-0.966484\pi$
$757$	−307.502	+	532.609i	−0.406211	+	0.703578i	0.588251	+	0.808679i	$0.299817\pi$
$758$	−520.334			−0.686457
$759$	−282.502			−0.372203
$760$	238.997	−	137.985i	0.314469	−	0.181559i
$761$	1057.23	−	610.394i	1.38927	−	0.802095i	0.396036	−	0.918235i	$-0.370386\pi$
$761$	1057.23	−	610.394i	1.38927	−	0.802095i	0.993233	+	0.116140i	$0.0370523\pi$
$762$	286.997	−	497.093i	0.376636	−	0.652352i
$763$	−587.979	+	339.470i	−0.770615	+	0.444915i
$764$		−	1048.45i		−	1.37232i
$765$	4.87631	+	2.81534i	0.00637426	+	0.00368018i
$766$	−393.826	+	682.126i	−0.514133	+	0.890504i
$767$	667.317	−	290.985i	0.870035	−	0.379380i
$768$	384.000	−	221.703i	0.500000	−	0.288675i
$769$	−509.990	−	294.443i	−0.663185	−	0.382890i	0.130304	−	0.991474i	$-0.458405\pi$
$769$	−509.990	−	294.443i	−0.663185	−	0.382890i	−0.793490	+	0.608584i	$0.791738\pi$
$770$	−247.003	+	142.608i	−0.320784	+	0.185205i
$771$	−81.1202	+	46.8348i	−0.105214	+	0.0607455i
$772$	136.997	−	79.0950i	0.177457	−	0.102455i
$773$	−931.495	+	537.799i	−1.20504	+	0.695729i	−0.961671	−	0.274205i	$-0.911585\pi$
$773$	−931.495	+	537.799i	−1.20504	+	0.695729i	−0.243367	+	0.969934i	$0.578252\pi$
$774$			165.408i			0.213705i
$775$	−179.679			−0.231844
$776$	547.986	−	316.380i	0.706168	−	0.407706i
$777$	102.627	−	177.755i	0.132081	−	0.228772i
$778$	354.331	+	613.719i	0.455438	+	0.788842i
$779$			1129.72i			1.45022i
$780$	−142.997	+	62.3538i	−0.183329	+	0.0799408i
$781$	−732.146			−0.937447
$782$	51.7421	−	29.8733i	0.0661664	−	0.0382012i
$783$	−138.747	−	80.1058i	−0.177200	−	0.102306i
$784$	2314.65			2.95236
$785$		−	377.436i		−	0.480810i
$786$	−433.003			−0.550895
$787$	129.080	+	223.573i	0.164015	+	0.284083i	0.936305	−	0.351187i	$-0.114222\pi$
$787$	129.080	+	223.573i	0.164015	+	0.284083i	−0.772290	+	0.635270i	$0.780889\pi$
$788$	1241.98	−	717.057i	1.57612	−	0.909971i
$789$	6.12544	+	10.6096i	0.00776355	+	0.0134469i
$790$	−83.4983	−	144.623i	−0.105694	−	0.183067i
$791$	949.199	−	1644.06i	1.20000	−	2.07846i
$792$	141.993			0.179284
$793$	388.258	−	169.300i	0.489606	−	0.213494i
$794$	1185.49	+	684.444i	1.49306	+	0.862020i
$795$	73.2491	−	126.871i	0.0921373	−	0.159586i
$796$		−	1338.86i		−	1.68198i
$797$	291.662	+	505.173i	0.365950	+	0.633844i	0.988928	−	0.148395i	$-0.0474108\pi$
$797$	291.662	+	505.173i	0.365950	+	0.633844i	−0.622978	+	0.782239i	$0.714078\pi$
$798$	−831.491	−	480.062i	−1.04197	−	0.601581i
$799$	0.0453089	+	0.0784773i	5.67070e−5	+	9.82194e-5i
$800$	−352.000	+	609.682i	−0.440000	+	0.762102i
$801$		−	373.254i		−	0.465985i
$802$		−	783.165i		−	0.976514i
$803$	−223.348	−	128.950i	−0.278142	−	0.160586i
$804$		−	716.478i		−	0.891141i
$805$	664.495			0.825459
$806$	194.648	−	84.8765i	0.241499	−	0.105306i
$807$		−	646.616i		−	0.801259i
$808$	−308.669	+	534.630i	−0.382016	+	0.661671i
$809$	31.2944	−	54.2036i	0.0386829	−	0.0670007i	−0.846036	−	0.533126i	$-0.821017\pi$
$809$	31.2944	−	54.2036i	0.0386829	−	0.0670007i	0.884719	+	0.466125i	$0.154350\pi$
$810$		−	31.1769i		−	0.0384900i
$811$	−57.1707			−0.0704941			−0.0352471	−	0.999379i	$-0.511222\pi$
$811$	−57.1707			−0.0704941			−0.0352471	+	0.999379i	$0.511222\pi$
$812$	−858.160	+	1486.38i	−1.05685	+	1.83051i
$813$	−139.003	+	80.2537i	−0.170976	+	0.0987130i
$814$	−87.2614	−	50.3804i	−0.107201	−	0.0618923i
$815$	−167.749	+	96.8500i	−0.205827	+	0.118834i
$816$	−26.0070	+	15.0151i	−0.0318713	+	0.0184009i
$817$	−475.495	−	274.527i	−0.582001	−	0.336018i
$818$	669.000	+	386.247i	0.817848	+	0.472185i
$819$	436.620	+	322.379i	0.533114	+	0.393625i
$820$	196.495	+	340.339i	0.239628	+	0.415047i
$821$	630.993	+	364.304i	0.768566	+	0.443732i	0.832363	−	0.554231i	$-0.186988\pi$
$821$	630.993	+	364.304i	0.768566	+	0.443732i	−0.0637966	+	0.997963i	$0.520321\pi$
$822$	440.247	+	762.531i	0.535581	+	0.927653i
$823$	−343.484	+	198.311i	−0.417356	+	0.240961i	−0.693946	−	0.720027i	$-0.744129\pi$
$823$	−343.484	+	198.311i	−0.417356	+	0.240961i	0.276589	+	0.960988i	$0.410796\pi$
$824$			416.851i			0.505887i
$825$	−195.240	+	112.722i	−0.236655	+	0.136633i
$826$	1558.63			1.88697
$827$	426.815			0.516101			0.258050	−	0.966131i	$-0.416920\pi$
$827$	426.815			0.516101			0.258050	+	0.966131i	$0.416920\pi$
$828$	−286.495	−	165.408i	−0.346008	−	0.199768i
$829$	−233.866	+	405.067i	−0.282106	+	0.488622i	−0.971903	−	0.235381i	$-0.924366\pi$
$829$	−233.866	+	405.067i	−0.282106	+	0.488622i	0.689797	+	0.724003i	$0.257700\pi$
$830$	399.742	−	230.791i	0.481617	−	0.278062i
$831$			418.136i			0.503172i
$832$	93.3240	−	826.749i	0.112168	−	0.993689i
$833$	−156.763			−0.188191
$834$	70.9965	+	122.970i	0.0851277	+	0.147446i
$835$	107.749	+	62.2090i	0.129041	+	0.0745018i
$836$	−235.666	+	408.185i	−0.281897	+	0.488259i
$837$			42.4383i			0.0507028i
$838$			925.482i			1.10439i
$839$	−462.997	−	801.933i	−0.551843	−	0.955821i	−0.998142	−	0.0609364i	$-0.980591\pi$
$839$	−462.997	−	801.933i	−0.551843	−	0.955821i	0.446298	−	0.894884i	$-0.352742\pi$
$840$	−333.993			−0.397611
$841$	−54.8293	−	94.9671i	−0.0651953	−	0.112922i
$842$	−821.739	+	474.431i	−0.975937	+	0.563457i
$843$	77.3781	−	134.023i	0.0917889	−	0.158983i
$844$	−817.003	+	471.697i	−0.968014	+	0.558883i
$845$	−65.2526	+	285.351i	−0.0772220	+	0.337693i
$846$	0.250874	−	0.434527i	0.000296542	−	0.000513625i
$847$	−598.380	+	1036.42i	−0.706470	+	1.22364i
$848$	390.662	+	676.646i	0.460686	+	0.797932i
$849$	113.875	+	197.237i	0.134128	+	0.232316i
$850$	23.8397	−	41.2916i	0.0280468	−	0.0485784i
$851$	117.376	+	203.302i	0.137928	+	0.238897i
$852$	−742.495	−	428.680i	−0.871473	−	0.503145i
$853$			546.887i			0.641134i	0.947226	+	0.320567i	$0.103873\pi$
$853$			546.887i			0.641134i	−0.947226	+	0.320567i	$0.896127\pi$
$854$	906.843			1.06188
$855$	89.6237	+	51.7443i	0.104823	+	0.0605196i
$856$	−73.0035	−	42.1486i	−0.0852845	−	0.0492390i
$857$	1075.91			1.25543			0.627716	−	0.778442i	$-0.283990\pi$
$857$	1075.91			1.25543			0.627716	+	0.778442i	$0.283990\pi$
$858$	158.258	−	214.340i	0.184450	−	0.249813i
$859$		−	175.957i		−	0.204839i	−0.994741	−	0.102420i	$-0.967342\pi$
$859$		−	175.957i		−	0.204839i	0.994741	−	0.102420i	$-0.0326585\pi$
$860$	−190.997			−0.222089
$861$	683.624	−	1184.07i	0.793988	−	1.37523i
$862$	555.178			0.644058
$863$	1291.07			1.49602			0.748011	−	0.663687i	$-0.231009\pi$
$863$	1291.07			1.49602			0.748011	+	0.663687i	$0.231009\pi$
$864$	144.000	+	83.1384i	0.166667	+	0.0962250i
$865$	−281.498	+	162.523i	−0.325432	+	0.187888i
$866$	−441.167	+	764.124i	−0.509431	+	0.882360i
$867$	−431.739	+	249.264i	−0.497968	+	0.287502i
$868$	454.634			0.523772
$869$	247.003	+	142.608i	0.284239	+	0.164105i
$870$	92.4983	−	160.212i	0.106320	−	0.184151i
$871$	−1081.53	−	798.548i	−1.24171	−	0.916817i
$872$			390.297i			0.447588i
$873$	205.495	+	118.642i	0.235389	+	0.135902i
$874$	950.990	−	549.054i	1.08809	−	0.628208i
$875$	981.104	−	566.441i	1.12126	−	0.647361i
$876$	−151.003	−	261.546i	−0.172378	−	0.298568i
$877$	1040.36	−	600.650i	1.18627	−	0.684892i	0.228812	−	0.973471i	$-0.426516\pi$
$877$	1040.36	−	600.650i	1.18627	−	0.684892i	0.957456	+	0.288578i	$0.0931826\pi$
$878$		−	391.142i		−	0.445492i
$879$	683.488			0.777574
$880$			163.959i			0.186318i
$881$	−373.204	+	646.408i	−0.423614	+	0.733721i	−0.996290	−	0.0860611i	$-0.972572\pi$
$881$	−373.204	+	646.408i	−0.423614	+	0.733721i	0.572676	+	0.819782i	$0.305905\pi$
$882$	433.997	+	751.704i	0.492060	+	0.852272i
$883$		−	1266.12i		−	1.43389i	−0.697131	−	0.716944i	$-0.745540\pi$
$883$		−	1266.12i		−	1.43389i	0.697131	−	0.716944i	$-0.254460\pi$
$884$	−6.32051	+	55.9929i	−0.00714990	+	0.0633404i
$885$	−168.000			−0.189831
$886$	326.509	−	188.510i	0.368520	−	0.212765i
$887$	−1062.98	−	613.713i	−1.19840	−	0.691898i	−0.238203	−	0.971215i	$-0.576558\pi$
$887$	−1062.98	−	613.713i	−1.19840	−	0.691898i	−0.960199	+	0.279318i	$0.909892\pi$
$888$	−58.9965	−	102.185i	−0.0664375	−	0.115073i
$889$		−	2305.91i		−	2.59382i
$890$	430.997			0.484266
$891$	26.6237	+	46.1136i	0.0298807	+	0.0517549i
$892$	89.3380	+	154.738i	0.100155	+	0.173473i
$893$	0.832751	+	1.44237i	0.000932531	+	0.00161519i
$894$	−133.997	−	232.089i	−0.149884	−	0.259607i
$895$	−45.1254	+	78.1595i	−0.0504195	+	0.0873291i
$896$	890.648	−	1542.65i	0.994027	−	1.72170i
$897$	−568.997	+	248.112i	−0.634333	+	0.276602i
$898$	−393.491	−	227.182i	−0.438186	−	0.252987i
$899$	−125.909	+	218.081i	−0.140055	+	0.242582i
$900$	−264.000			−0.293333
$901$	−26.4582	−	45.8269i	−0.0293654	−	0.0508623i
$902$	−581.268	−	335.595i	−0.644422	−	0.372057i
$903$	332.247	+	575.469i	0.367937	+	0.637286i
$904$	−545.659	−	945.108i	−0.603605	−	1.04547i
$905$		−	112.149i		−	0.123921i
$906$		−	171.177i		−	0.188937i
$907$	229.735	+	132.638i	0.253291	+	0.146238i	0.621270	−	0.783596i	$-0.286617\pi$
$907$	229.735	+	132.638i	0.253291	+	0.146238i	−0.367979	+	0.929834i	$0.619950\pi$
$908$	504.334			0.555434
$909$	−231.502			−0.254677
$910$	−372.251	+	504.166i	−0.409067	+	0.554028i
$911$			67.2785i			0.0738512i	0.999318	+	0.0369256i	$0.0117565\pi$
$911$			67.2785i			0.0738512i	−0.999318	+	0.0369256i	$0.988244\pi$
$912$	−477.993	+	275.969i	−0.524115	+	0.302598i
$913$	−394.171	+	682.724i	−0.431731	+	0.747781i
$914$		−	322.137i		−	0.352448i
$915$	−97.7456			−0.106826
$916$	660.000	+	381.051i	0.720524	+	0.415995i
$917$	−1506.46	+	869.755i	−1.64281	+	0.948479i
$918$	−9.75262	−	5.63068i	−0.0106238	−	0.00613364i
$919$	756.732	−	436.899i	0.823429	−	0.475407i	−0.0281682	−	0.999603i	$-0.508967\pi$
$919$	756.732	−	436.899i	0.823429	−	0.475407i	0.851598	+	0.524196i	$0.175634\pi$
$920$	190.997	−	330.816i	0.207605	−	0.359582i
$921$	226.369	+	130.694i	0.245786	+	0.141905i
$922$	−138.993	−	80.2476i	−0.150752	−	0.0870365i
$923$	−1474.64	+	643.019i	−1.59766	+	0.696662i
$924$	494.007	−	285.215i	0.534640	−	0.308674i
$925$	162.240	+	93.6695i	0.175395	+	0.101264i
$926$	−595.073	−	1030.70i	−0.642628	−	1.11306i
$927$	−135.376	+	78.1595i	−0.146037	+	0.0843145i
$928$	493.324	+	854.462i	0.531599	+	0.920757i
$929$	1255.09	−	724.628i	1.35101	−	0.780008i	0.362623	−	0.931936i	$-0.381881\pi$
$929$	1255.09	−	724.628i	1.35101	−	0.780008i	0.988392	+	0.151928i	$0.0485481\pi$
$930$	−49.0035			−0.0526919
$931$	−2881.21			−3.09475
$932$	−529.324	+	916.816i	−0.567944	+	0.983708i
$933$	−36.8781	+	63.8747i	−0.0395263	+	0.0684616i
$934$	410.237	−	236.850i	0.439226	−	0.253587i
$935$		−	11.1044i		−	0.0118764i
$936$	285.993	−	124.708i	0.305548	−	0.133235i
$937$	601.641			0.642093			0.321046	−	0.947063i	$-0.395965\pi$
$937$	601.641			0.642093			0.321046	+	0.947063i	$0.395965\pi$
$938$	−1439.16	−	2492.69i	−1.53428	−	2.65745i
$939$	415.484	+	239.880i	0.442475	+	0.255463i
$940$	0.501748	+	0.289685i	0.000533775	+	0.000308175i
$941$			532.301i			0.565676i	0.959168	+	0.282838i	$0.0912758\pi$
$941$			532.301i			0.565676i	−0.959168	+	0.282838i	$0.908724\pi$
$942$			754.872i			0.801351i
$943$	781.871	+	1354.24i	0.829132	+	1.43610i
$944$	448.000	−	775.959i	0.474576	−	0.821990i
$945$	−62.6237	−	108.467i	−0.0662685	−	0.114780i
$946$	282.502	−	163.102i	0.298628	−	0.172413i
$947$	−215.491	+	373.242i	−0.227551	+	0.394131i	−0.957082	−	0.289818i	$-0.906405\pi$
$947$	−215.491	+	373.242i	−0.227551	+	0.394131i	0.729530	+	0.683948i	$0.239739\pi$
$948$	166.997	+	289.246i	0.176157	+	0.305112i
$949$	−563.106	−	63.5638i	−0.593368	−	0.0669798i
$950$	438.160	−	758.916i	0.461221	−	0.798859i
$951$	−80.7439	+	139.853i	−0.0849042	+	0.147058i
$952$	−60.3205	+	104.478i	−0.0633619	+	0.109746i
$953$	−410.578	−	711.143i	−0.430827	−	0.746215i	0.566117	−	0.824325i	$-0.308445\pi$
$953$	−410.578	−	711.143i	−0.430827	−	0.746215i	−0.996945	+	0.0781099i	$0.975112\pi$
$954$	−146.498	+	253.742i	−0.153562	+	0.265977i
$955$	226.997	+	393.169i	0.237693	+	0.411696i
$956$	138.509	−	239.904i	0.144884	−	0.250946i
$957$			315.957i			0.330154i
$958$	585.003			0.610651
$959$	3063.32	+	1768.61i	3.19429	+	1.84422i
$960$	−96.0000	+	166.277i	−0.100000	+	0.173205i
$961$	−894.296			−0.930589
$962$	−220.003	−	24.8341i	−0.228694	−	0.0258151i
$963$		−	31.6114i		−	0.0328260i
$964$			944.529i			0.979802i
$965$	−34.2491	+	59.3212i	−0.0354913	+	0.0614728i
$966$	−1328.99			−1.37577
$967$	1678.08			1.73535			0.867675	−	0.497132i	$-0.165613\pi$
$967$	1678.08			1.73535			0.867675	+	0.497132i	$0.165613\pi$
$968$	343.986	+	595.801i	0.355357	+	0.615497i
$969$	32.3728	−	18.6905i	0.0334085	−	0.0192884i
$970$	−136.997	+	237.285i	−0.141234	+	0.244624i
$971$	582.732	−	336.440i	0.600136	−	0.346488i	−0.168959	−	0.985623i	$-0.554041\pi$
$971$	582.732	−	336.440i	0.600136	−	0.346488i	0.769095	+	0.639135i	$0.220707\pi$
$972$			62.3538i			0.0641500i
$973$	494.007	+	285.215i	0.507715	+	0.293130i
$974$	−571.073	+	989.128i	−0.586317	+	1.01553i
$975$	−294.240	+	398.510i	−0.301785	+	0.408729i
$976$	260.655	−	451.468i	0.267065	−	0.462569i
$977$	−599.106	−	345.894i	−0.613210	−	0.354037i	0.161011	−	0.986953i	$-0.448525\pi$
$977$	−599.106	−	345.894i	−0.613210	−	0.354037i	−0.774221	+	0.632916i	$0.781858\pi$
$978$	335.498	−	193.700i	0.343045	−	0.198057i
$979$	−637.484	+	368.052i	−0.651159	+	0.375947i
$980$	−867.993	+	501.136i	−0.885707	+	0.511363i
$981$	−126.753	+	73.1807i	−0.129208	+	0.0745980i
$982$		−	238.721i		−	0.243097i
$983$	294.007			0.299092			0.149546	−	0.988755i	$-0.452219\pi$
$983$	294.007			0.299092			0.149546	+	0.988755i	$0.452219\pi$
$984$	−392.990	−	680.678i	−0.399380	−	0.691746i
$985$	−310.495	+	537.793i	−0.315223	+	0.545982i
$986$	−33.4111	−	57.8698i	−0.0338855	−	0.0586915i
$987$		−	2.01568i		−	0.00204223i
$988$	−116.167	+	1029.12i	−0.117578	+	1.04162i
$989$	−759.993			−0.768446
$990$	−53.2474	+	30.7424i	−0.0537852	+	0.0310529i
$991$	−676.380	−	390.508i	−0.682523	−	0.394055i	0.118282	−	0.992980i	$-0.462261\pi$
$991$	−676.380	−	390.508i	−0.682523	−	0.394055i	−0.800805	+	0.598925i	$0.795595\pi$
$992$	130.676	−	226.337i	0.131730	−	0.228163i
$993$			544.431i			0.548269i
$994$	−3444.28			−3.46507
$995$	289.871	+	502.071i	0.291328	+	0.504594i
$996$	−799.484	+	461.582i	−0.802695	+	0.463436i
$997$	437.873	+	758.418i	0.439190	+	0.760700i	0.997627	−	0.0688470i	$-0.0219320\pi$
$997$	437.873	+	758.418i	0.439190	+	0.760700i	−0.558437	+	0.829547i	$0.688599\pi$
$998$	−25.3240	−	43.8625i	−0.0253748	−	0.0439504i
$999$	22.1237	−	38.3194i	0.0221458	−	0.0383577i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	156.3.n.d.43.2	yes	4
4.3	odd	2		156.3.n.c.43.1	✓	4
13.10	even	6		156.3.n.c.127.1	yes	4
52.23	odd	6	inner	156.3.n.d.127.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
156.3.n.c.43.1	✓	4	4.3	odd	2
156.3.n.c.127.1	yes	4	13.10	even	6
156.3.n.d.43.2	yes	4	1.1	even	1	trivial
156.3.n.d.127.2	yes	4	52.23	odd	6	inner

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:	\( N \)	\(=\)	\( 156 = 2^{2} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	156.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.73205i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-2.00000 + 3.46410i) q^{4} -1.73205i q^{5} +3.46410i q^{6} +(6.95819 + 12.0519i) q^{7} +8.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(-1.00000 - 1.73205i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-2.00000 + 3.46410i) q^{4} -1.73205i q^{5} +3.46410i q^{6} +(6.95819 + 12.0519i) q^{7} +8.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(-3.00000 + 1.73205i) q^{10} +(2.95819 - 5.12373i) q^{11} +(6.00000 - 3.46410i) q^{12} +(1.45819 - 12.9180i) q^{13} +(13.9164 - 24.1039i) q^{14} +(-1.50000 + 2.59808i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(0.541812 + 0.938447i) q^{17} +(3.00000 - 5.19615i) q^{18} +(9.95819 + 17.2481i) q^{19} +(6.00000 + 3.46410i) q^{20} -24.1039i q^{21} -11.8328 q^{22} +(23.8746 + 13.7840i) q^{23} +(-12.0000 - 6.92820i) q^{24} +22.0000 q^{25} +(-23.8328 + 10.3923i) q^{26} -5.19615i q^{27} -55.6655 q^{28} +(15.4164 - 26.7019i) q^{29} +6.00000 q^{30} -8.16725 q^{31} +(-16.0000 + 27.7128i) q^{32} +(-8.87456 + 5.12373i) q^{33} +(1.08362 - 1.87689i) q^{34} +(20.8746 - 12.0519i) q^{35} -12.0000 q^{36} +(7.37456 + 4.25771i) q^{37} +(19.9164 - 34.4962i) q^{38} +(-13.3746 + 18.1141i) q^{39} -13.8564i q^{40} +(49.1237 + 28.3616i) q^{41} +(-41.7491 + 24.1039i) q^{42} +(-23.8746 + 13.7840i) q^{43} +(11.8328 + 20.4949i) q^{44} +(4.50000 - 2.59808i) q^{45} -55.1359i q^{46} +0.0836247 q^{47} +27.7128i q^{48} +(-72.3328 + 125.284i) q^{49} +(-22.0000 - 38.1051i) q^{50} -1.87689i q^{51} +(41.8328 + 30.8872i) q^{52} -48.8328 q^{53} +(-9.00000 + 5.19615i) q^{54} +(-8.87456 - 5.12373i) q^{55} +(55.6655 + 96.4155i) q^{56} -34.4962i q^{57} -61.6655 q^{58} +(28.0000 + 48.4974i) q^{59} +(-6.00000 - 10.3923i) q^{60} +(16.2909 + 28.2167i) q^{61} +(8.16725 + 14.1461i) q^{62} +(-20.8746 + 36.1558i) q^{63} +64.0000 q^{64} +(-22.3746 - 2.52566i) q^{65} +(17.7491 + 10.2475i) q^{66} +(51.7073 - 89.5597i) q^{67} -4.33450 q^{68} +(-23.8746 - 41.3520i) q^{69} +(-41.7491 - 24.1039i) q^{70} +(-61.8746 - 107.170i) q^{71} +(12.0000 + 20.7846i) q^{72} -43.5910i q^{73} -17.0308i q^{74} +(-33.0000 - 19.0526i) q^{75} -79.6655 q^{76} +82.3345 q^{77} +(44.7491 + 5.05131i) q^{78} +48.2077i q^{79} +(-24.0000 + 13.8564i) q^{80} +(-4.50000 + 7.79423i) q^{81} -113.446i q^{82} -133.247 q^{83} +(83.4983 + 48.2077i) q^{84} +(1.62544 - 0.938447i) q^{85} +(47.7491 + 27.5680i) q^{86} +(-46.2491 + 26.7019i) q^{87} +(23.6655 - 40.9899i) q^{88} +(-107.749 - 62.2090i) q^{89} +(-9.00000 - 5.19615i) q^{90} +(165.833 - 72.3116i) q^{91} +(-95.4983 + 55.1359i) q^{92} +(12.2509 + 7.07305i) q^{93} +(-0.0836247 - 0.144842i) q^{94} +(29.8746 - 17.2481i) q^{95} +(48.0000 - 27.7128i) q^{96} +(68.4983 - 39.5475i) q^{97} +289.331 q^{98} +17.7491 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - 6 q^{3} - 8 q^{4} + 4 q^{7} + 32 q^{8} + 6 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 - 6 * q^3 - 8 * q^4 + 4 * q^7 + 32 * q^8 + 6 * q^9	\( 4 q - 4 q^{2} - 6 q^{3} - 8 q^{4} + 4 q^{7} + 32 q^{8} + 6 q^{9} - 12 q^{10} - 12 q^{11} + 24 q^{12} - 18 q^{13} + 8 q^{14} - 6 q^{15} - 32 q^{16} + 26 q^{17} + 12 q^{18} + 16 q^{19} + 24 q^{20} + 48 q^{22} + 24 q^{23} - 48 q^{24} + 88 q^{25} - 32 q^{28} + 14 q^{29} + 24 q^{30} - 128 q^{31} - 64 q^{32} + 36 q^{33} + 52 q^{34} + 12 q^{35} - 48 q^{36} - 42 q^{37} + 32 q^{38} + 18 q^{39} - 18 q^{41} - 24 q^{42} - 24 q^{43} - 48 q^{44} + 18 q^{45} + 48 q^{47} - 194 q^{49} - 88 q^{50} + 72 q^{52} - 100 q^{53} - 36 q^{54} + 36 q^{55} + 32 q^{56} - 56 q^{58} + 112 q^{59} - 24 q^{60} - 54 q^{61} + 128 q^{62} - 12 q^{63} + 256 q^{64} - 18 q^{65} - 72 q^{66} + 40 q^{67} - 208 q^{68} - 24 q^{69} - 24 q^{70} - 176 q^{71} + 48 q^{72} - 132 q^{75} - 128 q^{76} + 520 q^{77} + 36 q^{78} - 96 q^{80} - 18 q^{81} - 104 q^{83} + 48 q^{84} + 78 q^{85} + 48 q^{86} - 42 q^{87} - 96 q^{88} - 288 q^{89} - 36 q^{90} + 568 q^{91} - 96 q^{92} + 192 q^{93} - 48 q^{94} + 48 q^{95} + 192 q^{96} - 12 q^{97} + 776 q^{98} - 72 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 - 6 * q^3 - 8 * q^4 + 4 * q^7 + 32 * q^8 + 6 * q^9 - 12 * q^10 - 12 * q^11 + 24 * q^12 - 18 * q^13 + 8 * q^14 - 6 * q^15 - 32 * q^16 + 26 * q^17 + 12 * q^18 + 16 * q^19 + 24 * q^20 + 48 * q^22 + 24 * q^23 - 48 * q^24 + 88 * q^25 - 32 * q^28 + 14 * q^29 + 24 * q^30 - 128 * q^31 - 64 * q^32 + 36 * q^33 + 52 * q^34 + 12 * q^35 - 48 * q^36 - 42 * q^37 + 32 * q^38 + 18 * q^39 - 18 * q^41 - 24 * q^42 - 24 * q^43 - 48 * q^44 + 18 * q^45 + 48 * q^47 - 194 * q^49 - 88 * q^50 + 72 * q^52 - 100 * q^53 - 36 * q^54 + 36 * q^55 + 32 * q^56 - 56 * q^58 + 112 * q^59 - 24 * q^60 - 54 * q^61 + 128 * q^62 - 12 * q^63 + 256 * q^64 - 18 * q^65 - 72 * q^66 + 40 * q^67 - 208 * q^68 - 24 * q^69 - 24 * q^70 - 176 * q^71 + 48 * q^72 - 132 * q^75 - 128 * q^76 + 520 * q^77 + 36 * q^78 - 96 * q^80 - 18 * q^81 - 104 * q^83 + 48 * q^84 + 78 * q^85 + 48 * q^86 - 42 * q^87 - 96 * q^88 - 288 * q^89 - 36 * q^90 + 568 * q^91 - 96 * q^92 + 192 * q^93 - 48 * q^94 + 48 * q^95 + 192 * q^96 - 12 * q^97 + 776 * q^98 - 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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