LMFDB - Embedded newform 156.3.n.d.43.1

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			43.1
Root			$-5.95819 - 10.3199i$ of defining polynomial
Character	$\chi$	$=$	156.43
Dual form			156.3.n.d.127.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.73205i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-2.00000 + 3.46410i) q^{4} -1.73205i q^{5} +3.46410i q^{6} +(-4.95819 - 8.58783i) q^{7} +8.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(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} +(-4.95819 - 8.58783i) q^{7} +8.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(-3.00000 + 1.73205i) q^{10} +(-8.95819 + 15.5160i) q^{11} +(6.00000 - 3.46410i) q^{12} +(-10.4582 + 7.72181i) q^{13} +(-9.91638 + 17.1757i) q^{14} +(-1.50000 + 2.59808i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(12.4582 + 21.5782i) q^{17} +(3.00000 - 5.19615i) q^{18} +(-1.95819 - 3.39168i) q^{19} +(6.00000 + 3.46410i) q^{20} +17.1757i q^{21} +35.8328 q^{22} +(-11.8746 - 6.85578i) q^{23} +(-12.0000 - 6.92820i) q^{24} +22.0000 q^{25} +(23.8328 + 10.3923i) q^{26} -5.19615i q^{27} +39.6655 q^{28} +(-8.41638 + 14.5776i) q^{29} +6.00000 q^{30} -55.8328 q^{31} +(-16.0000 + 27.7128i) q^{32} +(26.8746 - 15.5160i) q^{33} +(24.9164 - 43.1564i) q^{34} +(-14.8746 + 8.58783i) q^{35} -12.0000 q^{36} +(-28.3746 - 16.3821i) q^{37} +(-3.91638 + 6.78336i) q^{38} +(22.3746 - 2.52566i) q^{39} -13.8564i q^{40} +(-58.1237 - 33.5577i) q^{41} +(29.7491 - 17.1757i) q^{42} +(11.8746 - 6.85578i) q^{43} +(-35.8328 - 62.0641i) q^{44} +(4.50000 - 2.59808i) q^{45} +27.4231i q^{46} +23.9164 q^{47} +27.7128i q^{48} +(-24.6672 + 42.7249i) q^{49} +(-22.0000 - 38.1051i) q^{50} -43.1564i q^{51} +(-5.83275 - 51.6718i) q^{52} -1.16725 q^{53} +(-9.00000 + 5.19615i) q^{54} +(26.8746 + 15.5160i) q^{55} +(-39.6655 - 68.7027i) q^{56} +6.78336i q^{57} +33.6655 q^{58} +(28.0000 + 48.4974i) q^{59} +(-6.00000 - 10.3923i) q^{60} +(-43.2909 - 74.9821i) q^{61} +(55.8328 + 96.7052i) q^{62} +(14.8746 - 25.7635i) q^{63} +64.0000 q^{64} +(13.3746 + 18.1141i) q^{65} +(-53.7491 - 31.0321i) q^{66} +(-31.7073 + 54.9187i) q^{67} -99.6655 q^{68} +(11.8746 + 20.5673i) q^{69} +(29.7491 + 17.1757i) q^{70} +(-26.1254 - 45.2506i) q^{71} +(12.0000 + 20.7846i) q^{72} -126.150i q^{73} +65.5282i q^{74} +(-33.0000 - 19.0526i) q^{75} +15.6655 q^{76} +177.666 q^{77} +(-26.7491 - 36.2282i) q^{78} -34.3513i q^{79} +(-24.0000 + 13.8564i) q^{80} +(-4.50000 + 7.79423i) q^{81} +134.231i q^{82} +81.2474 q^{83} +(-59.4983 - 34.3513i) q^{84} +(37.3746 - 21.5782i) q^{85} +(-23.7491 - 13.7116i) q^{86} +(25.2491 - 14.5776i) q^{87} +(-71.6655 + 124.128i) q^{88} +(-36.2509 - 20.9295i) q^{89} +(-9.00000 - 5.19615i) q^{90} +(118.167 + 51.5270i) q^{91} +(47.4983 - 27.4231i) q^{92} +(83.7491 + 48.3526i) q^{93} +(-23.9164 - 41.4244i) q^{94} +(-5.87456 + 3.39168i) q^{95} +(48.0000 - 27.7128i) q^{96} +(-74.4983 + 43.0116i) q^{97} +98.6690 q^{98} -53.7491 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
$7$	−4.95819	−	8.58783i	−0.708313	−	1.22683i	−0.965483	−	0.260467i	$-0.916123\pi$
$7$	−4.95819	−	8.58783i	−0.708313	−	1.22683i	0.257170	−	0.966366i	$-0.417210\pi$
$8$	8.00000			1.00000
$9$	1.50000	+	2.59808i	0.166667	+	0.288675i
$10$	−3.00000	+	1.73205i	−0.300000	+	0.173205i
$11$	−8.95819	+	15.5160i	−0.814381	+	1.41055i	0.0953911	+	0.995440i	$0.469590\pi$
$11$	−8.95819	+	15.5160i	−0.814381	+	1.41055i	−0.909772	+	0.415109i	$0.863743\pi$
$12$	6.00000	−	3.46410i	0.500000	−	0.288675i
$13$	−10.4582	+	7.72181i	−0.804476	+	0.593985i
$13$	−10.4582	+	7.72181i	−0.804476	+	0.593985i
$14$	−9.91638	+	17.1757i	−0.708313	+	1.22683i
$15$	−1.50000	+	2.59808i	−0.100000	+	0.173205i
$16$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$17$	12.4582	+	21.5782i	0.732835	+	1.26931i	0.955667	+	0.294450i	$0.0951364\pi$
$17$	12.4582	+	21.5782i	0.732835	+	1.26931i	−0.222832	+	0.974857i	$0.571530\pi$
$18$	3.00000	−	5.19615i	0.166667	−	0.288675i
$19$	−1.95819	−	3.39168i	−0.103063	−	0.178509i	0.809882	−	0.586592i	$-0.199531\pi$
$19$	−1.95819	−	3.39168i	−0.103063	−	0.178509i	−0.912945	+	0.408083i	$0.866198\pi$
$20$	6.00000	+	3.46410i	0.300000	+	0.173205i
$21$			17.1757i			0.817889i
$22$	35.8328			1.62876
$23$	−11.8746	−	6.85578i	−0.516285	−	0.298077i	0.219128	−	0.975696i	$-0.429679\pi$
$23$	−11.8746	−	6.85578i	−0.516285	−	0.298077i	−0.735414	+	0.677619i	$0.763012\pi$
$24$	−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
$28$	39.6655			1.41663
$29$	−8.41638	+	14.5776i	−0.290220	+	0.502676i	−0.973862	−	0.227142i	$-0.927062\pi$
$29$	−8.41638	+	14.5776i	−0.290220	+	0.502676i	0.683642	+	0.729818i	$0.260395\pi$
$30$	6.00000			0.200000
$31$	−55.8328			−1.80106			−0.900528	−	0.434798i	$-0.856820\pi$
$31$	−55.8328			−1.80106			−0.900528	+	0.434798i	$0.856820\pi$
$32$	−16.0000	+	27.7128i	−0.500000	+	0.866025i
$33$	26.8746	−	15.5160i	0.814381	−	0.470183i
$34$	24.9164	−	43.1564i	0.732835	−	1.26931i
$35$	−14.8746	+	8.58783i	−0.424988	+	0.245367i
$36$	−12.0000			−0.333333
$37$	−28.3746	−	16.3821i	−0.766880	−	0.442758i	0.0648804	−	0.997893i	$-0.479333\pi$
$37$	−28.3746	−	16.3821i	−0.766880	−	0.442758i	−0.831761	+	0.555135i	$0.812667\pi$
$38$	−3.91638	+	6.78336i	−0.103063	+	0.178509i
$39$	22.3746	−	2.52566i	0.573707	−	0.0647604i
$40$		−	13.8564i		−	0.346410i
$41$	−58.1237	−	33.5577i	−1.41765	−	0.818481i	−0.421559	−	0.906801i	$-0.638517\pi$
$41$	−58.1237	−	33.5577i	−1.41765	−	0.818481i	−0.996092	+	0.0883199i	$0.971850\pi$
$42$	29.7491	−	17.1757i	0.708313	−	0.408944i
$43$	11.8746	−	6.85578i	0.276153	−	0.159437i	−0.355528	−	0.934666i	$-0.615699\pi$
$43$	11.8746	−	6.85578i	0.276153	−	0.159437i	0.631680	+	0.775229i	$0.282366\pi$
$44$	−35.8328	−	62.0641i	−0.814381	−	1.41055i
$45$	4.50000	−	2.59808i	0.100000	−	0.0577350i
$46$			27.4231i			0.596155i
$47$	23.9164			0.508859			0.254430	−	0.967091i	$-0.418112\pi$
$47$	23.9164			0.508859			0.254430	+	0.967091i	$0.418112\pi$
$48$			27.7128i			0.577350i
$49$	−24.6672	+	42.7249i	−0.503413	+	0.871937i
$50$	−22.0000	−	38.1051i	−0.440000	−	0.762102i
$51$		−	43.1564i		−	0.846204i
$52$	−5.83275	−	51.6718i	−0.112168	−	0.993689i
$53$	−1.16725			−0.0220236			−0.0110118	−	0.999939i	$-0.503505\pi$
$53$	−1.16725			−0.0220236			−0.0110118	+	0.999939i	$0.503505\pi$
$54$	−9.00000	+	5.19615i	−0.166667	+	0.0962250i
$55$	26.8746	+	15.5160i	0.488628	+	0.282110i
$56$	−39.6655	−	68.7027i	−0.708313	−	1.22683i
$57$			6.78336i			0.119006i
$58$	33.6655			0.580440
$59$	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
$61$	−43.2909	−	74.9821i	−0.709688	−	1.22921i	−0.964973	−	0.262349i	$-0.915503\pi$
$61$	−43.2909	−	74.9821i	−0.709688	−	1.22921i	0.255286	−	0.966866i	$-0.417831\pi$
$62$	55.8328	+	96.7052i	0.900528	+	1.55976i
$63$	14.8746	−	25.7635i	0.236104	−	0.408944i
$64$	64.0000			1.00000
$65$	13.3746	+	18.1141i	0.205763	+	0.278679i
$66$	−53.7491	−	31.0321i	−0.814381	−	0.470183i
$67$	−31.7073	+	54.9187i	−0.473243	+	0.819682i	−0.999531	−	0.0306250i	$-0.990250\pi$
$67$	−31.7073	+	54.9187i	−0.473243	+	0.819682i	0.526287	+	0.850307i	$0.323584\pi$
$68$	−99.6655			−1.46567
$69$	11.8746	+	20.5673i	0.172095	+	0.298077i
$70$	29.7491	+	17.1757i	0.424988	+	0.245367i
$71$	−26.1254	−	45.2506i	−0.367964	−	0.637332i	0.621283	−	0.783586i	$-0.286612\pi$
$71$	−26.1254	−	45.2506i	−0.367964	−	0.637332i	−0.989247	+	0.146254i	$0.953278\pi$
$72$	12.0000	+	20.7846i	0.166667	+	0.288675i
$73$		−	126.150i		−	1.72808i	−0.503421	−	0.864041i	$-0.667926\pi$
$73$		−	126.150i		−	1.72808i	0.503421	−	0.864041i	$-0.332074\pi$
$74$			65.5282i			0.885517i
$75$	−33.0000	−	19.0526i	−0.440000	−	0.254034i
$76$	15.6655			0.206125
$77$	177.666			2.30734
$78$	−26.7491	−	36.2282i	−0.342938	−	0.464464i
$79$		−	34.3513i		−	0.434827i	−0.976080	−	0.217413i	$-0.930238\pi$
$79$		−	34.3513i		−	0.434827i	0.976080	−	0.217413i	$-0.0697620\pi$
$80$	−24.0000	+	13.8564i	−0.300000	+	0.173205i
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$			134.231i			1.63696i
$83$	81.2474			0.978884			0.489442	−	0.872036i	$-0.337200\pi$
$83$	81.2474			0.978884			0.489442	+	0.872036i	$0.337200\pi$
$84$	−59.4983	−	34.3513i	−0.708313	−	0.408944i
$85$	37.3746	−	21.5782i	0.439701	−	0.253861i
$86$	−23.7491	−	13.7116i	−0.276153	−	0.159437i
$87$	25.2491	−	14.5776i	0.290220	−	0.167559i
$88$	−71.6655	+	124.128i	−0.814381	+	1.41055i
$89$	−36.2509	−	20.9295i	−0.407313	−	0.235162i	0.282321	−	0.959320i	$-0.408896\pi$
$89$	−36.2509	−	20.9295i	−0.407313	−	0.235162i	−0.689635	+	0.724157i	$0.742229\pi$
$90$	−9.00000	−	5.19615i	−0.100000	−	0.0577350i
$91$	118.167	+	51.5270i	1.29854	+	0.566231i
$92$	47.4983	−	27.4231i	0.516285	−	0.298077i
$93$	83.7491	+	48.3526i	0.900528	+	0.519920i
$94$	−23.9164	−	41.4244i	−0.254430	−	0.440685i
$95$	−5.87456	+	3.39168i	−0.0618375	+	0.0357019i
$96$	48.0000	−	27.7128i	0.500000	−	0.288675i
$97$	−74.4983	+	43.0116i	−0.768023	+	0.443418i	−0.832169	−	0.554522i	$-0.812901\pi$
$97$	−74.4983	+	43.0116i	−0.768023	+	0.443418i	0.0641458	+	0.997941i	$0.479568\pi$
$98$	98.6690			1.00683
$99$	−53.7491			−0.542920
$100$	−44.0000	+	76.2102i	−0.440000	+	0.762102i
$101$	−62.4164	+	108.108i	−0.617984	+	1.07038i	0.371869	+	0.928285i	$0.378717\pi$
$101$	−62.4164	+	108.108i	−0.617984	+	1.07038i	−0.989853	+	0.142094i	$0.954616\pi$
$102$	−74.7491	+	43.1564i	−0.732835	+	0.423102i
$103$			93.3859i			0.906659i	0.891343	+	0.453330i	$0.149764\pi$
$103$			93.3859i			0.906659i	−0.891343	+	0.453330i	$0.850236\pi$
$104$	−83.6655	+	61.7745i	−0.804476	+	0.593985i
$105$	29.7491			0.283325
$106$	1.16725	+	2.02174i	0.0110118	+	0.0190730i
$107$	−44.8746	−	25.9083i	−0.419388	−	0.242134i	0.275427	−	0.961322i	$-0.411181\pi$
$107$	−44.8746	−	25.9083i	−0.419388	−	0.242134i	−0.694816	+	0.719188i	$0.744514\pi$
$108$	18.0000	+	10.3923i	0.166667	+	0.0962250i
$109$			131.346i			1.20501i	0.798115	+	0.602505i	$0.205831\pi$
$109$			131.346i			1.20501i	−0.798115	+	0.602505i	$0.794169\pi$
$110$		−	62.0641i		−	0.564219i
$111$	28.3746	+	49.1462i	0.255627	+	0.442758i
$112$	−79.3310	+	137.405i	−0.708313	+	1.22683i
$113$	15.2073	+	26.3398i	0.134578	+	0.233096i	0.925436	−	0.378904i	$-0.123699\pi$
$113$	15.2073	+	26.3398i	0.134578	+	0.233096i	−0.790858	+	0.611999i	$0.790365\pi$
$114$	11.7491	−	6.78336i	0.103063	−	0.0595032i
$115$	−11.8746	+	20.5673i	−0.103257	+	0.178846i
$116$	−33.6655	−	58.3104i	−0.290220	−	0.502676i
$117$	−35.7491	−	15.5885i	−0.305548	−	0.133235i
$118$	56.0000	−	96.9948i	0.474576	−	0.821990i
$119$	123.540	−	213.978i	1.03815	−	1.79813i
$120$	−12.0000	+	20.7846i	−0.100000	+	0.173205i
$121$	−99.9983	−	173.202i	−0.826432	−	1.43142i
$122$	−86.5819	+	149.964i	−0.709688	+	1.22921i
$123$	58.1237	+	100.673i	0.472550	+	0.818481i
$124$	111.666	−	193.410i	0.900528	−	1.55976i
$125$		−	81.4064i		−	0.651251i
$126$	−59.4983			−0.472208
$127$	−0.501748	−	0.289685i	−0.00395077	−	0.00228098i	0.498023	−	0.867164i	$-0.334059\pi$
$127$	−0.501748	−	0.289685i	−0.00395077	−	0.00228098i	−0.501974	+	0.864883i	$0.667393\pi$
$128$	−64.0000	−	110.851i	−0.500000	−	0.866025i
$129$	−23.7491			−0.184102
$130$	18.0000	−	41.2795i	0.138462	−	0.317535i
$131$			207.556i			1.58440i	0.610261	+	0.792200i	$0.291064\pi$
$131$			207.556i			1.58440i	−0.610261	+	0.792200i	$0.708936\pi$
$132$			124.128i			0.940366i
$133$	−19.4181	+	33.6332i	−0.146001	+	0.252881i
$134$	126.829			0.946487
$135$	−9.00000			−0.0666667
$136$	99.6655	+	172.626i	0.732835	+	1.26931i
$137$	112.876	−	65.1692i	0.823915	−	0.475687i	−0.0278499	−	0.999612i	$-0.508866\pi$
$137$	112.876	−	65.1692i	0.823915	−	0.475687i	0.851765	+	0.523925i	$0.175533\pi$
$138$	23.7491	−	41.1347i	0.172095	−	0.298077i
$139$	−107.498	+	62.0641i	−0.773369	+	0.446505i	−0.834075	−	0.551651i	$-0.813998\pi$
$139$	−107.498	+	62.0641i	−0.773369	+	0.446505i	0.0607063	+	0.998156i	$0.480665\pi$
$140$		−	68.7027i		−	0.490733i
$141$	−35.8746	−	20.7122i	−0.254430	−	0.146895i
$142$	−52.2509	+	90.5012i	−0.367964	+	0.637332i
$143$	−26.1254	−	231.443i	−0.182695	−	1.61848i
$144$	24.0000	−	41.5692i	0.166667	−	0.288675i
$145$	25.2491	+	14.5776i	0.174132	+	0.100535i
$146$	−218.498	+	126.150i	−1.49656	+	0.864041i
$147$	74.0017	−	42.7249i	0.503413	−	0.290646i
$148$	113.498	−	65.5282i	0.766880	−	0.442758i
$149$	75.9983	−	43.8776i	0.510055	−	0.294481i	−0.222801	−	0.974864i	$-0.571520\pi$
$149$	75.9983	−	43.8776i	0.510055	−	0.294481i	0.732856	+	0.680383i	$0.238187\pi$
$150$			76.2102i			0.508068i
$151$	117.415			0.777580			0.388790	−	0.921326i	$-0.372893\pi$
$151$	117.415			0.777580			0.388790	+	0.921326i	$0.372893\pi$
$152$	−15.6655	−	27.1334i	−0.103063	−	0.178509i
$153$	−37.3746	+	64.7346i	−0.244278	+	0.423102i
$154$	−177.666	−	307.726i	−1.15367	−	1.99822i
$155$			96.7052i			0.623904i
$156$	−36.0000	+	82.5591i	−0.230769	+	0.529225i
$157$	−91.9129			−0.585432			−0.292716	−	0.956199i	$-0.594559\pi$
$157$	−91.9129			−0.585432			−0.292716	+	0.956199i	$0.594559\pi$
$158$	−59.4983	+	34.3513i	−0.376571	+	0.217413i
$159$	1.75087	+	1.01087i	0.0110118	+	0.00635766i
$160$	48.0000	+	27.7128i	0.300000	+	0.173205i
$161$			135.969i			0.844528i
$162$	18.0000			0.111111
$163$	−32.0836	−	55.5705i	−0.196832	−	0.340923i	0.750668	−	0.660680i	$-0.229732\pi$
$163$	−32.0836	−	55.5705i	−0.196832	−	0.340923i	−0.947500	+	0.319757i	$0.896399\pi$
$164$	232.495	−	134.231i	1.41765	−	0.818481i
$165$	−26.8746	−	46.5481i	−0.162876	−	0.282110i
$166$	−81.2474	−	140.725i	−0.489442	−	0.847738i
$167$	−12.0836	+	20.9295i	−0.0723570	+	0.125326i	−0.899934	−	0.436026i	$-0.856385\pi$
$167$	−12.0836	+	20.9295i	−0.0723570	+	0.125326i	0.827577	+	0.561352i	$0.189719\pi$
$168$			137.405i			0.817889i
$169$	49.7474	−	161.512i	0.294363	−	0.955694i
$170$	−74.7491	−	43.1564i	−0.439701	−	0.253861i
$171$	5.87456	−	10.1750i	0.0343542	−	0.0595032i
$172$			54.8463i			0.318874i
$173$	−46.1672	−	79.9640i	−0.266863	−	0.462220i	0.701187	−	0.712977i	$-0.252654\pi$
$173$	−46.1672	−	79.9640i	−0.266863	−	0.462220i	−0.968050	+	0.250757i	$0.919320\pi$
$174$	−50.4983	−	29.1552i	−0.290220	−	0.167559i
$175$	−109.080	−	188.932i	−0.623315	−	1.07961i
$176$	286.662			1.62876
$177$		−	96.9948i		−	0.547993i
$178$			83.7178i			0.470325i
$179$	−80.8746	−	46.6930i	−0.451813	−	0.260854i	0.256782	−	0.966469i	$-0.417338\pi$
$179$	−80.8746	−	46.6930i	−0.451813	−	0.260854i	−0.708596	+	0.705615i	$0.750671\pi$
$180$			20.7846i			0.115470i
$181$	−6.74913			−0.0372880			−0.0186440	−	0.999826i	$-0.505935\pi$
$181$	−6.74913			−0.0372880			−0.0186440	+	0.999826i	$0.505935\pi$
$182$	−28.9199	−	256.199i	−0.158900	−	1.40769i
$183$			149.964i			0.819477i
$184$	−94.9965	−	54.8463i	−0.516285	−	0.298077i
$185$	−28.3746	+	49.1462i	−0.153376	+	0.265655i
$186$		−	193.410i		−	1.03984i
$187$	−446.411			−2.38723
$188$	−47.8328	+	82.8488i	−0.254430	+	0.440685i
$189$	−44.6237	+	25.7635i	−0.236104	+	0.136315i
$190$	11.7491	+	6.78336i	0.0618375	+	0.0357019i
$191$	58.9965	−	34.0616i	0.308882	−	0.178333i	−0.337544	−	0.941310i	$-0.609596\pi$
$191$	58.9965	−	34.0616i	0.308882	−	0.178333i	0.646426	+	0.762977i	$0.276263\pi$
$192$	−96.0000	−	55.4256i	−0.500000	−	0.288675i
$193$	37.2491	+	21.5058i	0.193001	+	0.111429i	0.593387	−	0.804918i	$-0.297791\pi$
$193$	37.2491	+	21.5058i	0.193001	+	0.111429i	−0.400386	+	0.916347i	$0.631124\pi$
$194$	148.997	+	86.0232i	0.768023	+	0.443418i
$195$	−4.37456	−	38.7539i	−0.0224337	−	0.198738i
$196$	−98.6690	−	170.900i	−0.503413	−	0.871937i
$197$	118.495	+	68.4130i	0.601496	+	0.347274i	0.769630	−	0.638490i	$-0.220441\pi$
$197$	118.495	+	68.4130i	0.601496	+	0.347274i	−0.168134	+	0.985764i	$0.553774\pi$
$198$	53.7491	+	93.0962i	0.271460	+	0.470183i
$199$	31.8711	−	18.4008i	0.160156	−	0.0924662i	−0.417780	−	0.908548i	$-0.637192\pi$
$199$	31.8711	−	18.4008i	0.160156	−	0.0924662i	0.577936	+	0.816082i	$0.303858\pi$
$200$	176.000			0.880000
$201$	95.1219	−	54.9187i	0.473243	−	0.273227i
$202$	249.666			1.23597
$203$	166.920			0.822265
$204$	149.498	+	86.3129i	0.732835	+	0.423102i
$205$	−58.1237	+	100.673i	−0.283530	+	0.491089i
$206$	161.749	−	93.3859i	0.785190	−	0.453330i
$207$		−	41.1347i		−	0.198718i
$208$	190.662	+	83.1384i	0.916644	+	0.399704i
$209$	70.1672			0.335728
$210$	−29.7491	−	51.5270i	−0.141663	−	0.245367i
$211$	275.749	+	159.204i	1.30687	+	0.754521i	0.981572	−	0.191092i	$-0.0612028\pi$
$211$	275.749	+	159.204i	1.30687	+	0.754521i	0.325296	+	0.945612i	$0.394536\pi$
$212$	2.33450	−	4.04347i	0.0110118	−	0.0190730i
$213$			90.5012i			0.424888i
$214$			103.633i			0.484268i
$215$	−11.8746	−	20.5673i	−0.0552305	−	0.0956621i
$216$		−	41.5692i		−	0.192450i
$217$	276.829	+	479.482i	1.27571	+	2.20960i
$218$	227.498	−	131.346i	1.04357	−	0.602505i
$219$	−109.249	+	189.225i	−0.498854	+	0.864041i
$220$	−107.498	+	62.0641i	−0.488628	+	0.282110i
$221$	−296.913	−	129.469i	−1.34350	−	0.585834i
$222$	56.7491	−	98.2924i	0.255627	−	0.442758i
$223$	117.666	−	203.803i	0.527648	−	0.913913i	−0.471833	−	0.881688i	$-0.656407\pi$
$223$	117.666	−	203.803i	0.527648	−	0.913913i	0.999481	−	0.0322250i	$-0.0102593\pi$
$224$	317.324			1.41663
$225$	33.0000	+	57.1577i	0.146667	+	0.254034i
$226$	30.4146	−	52.6797i	0.134578	−	0.233096i
$227$	−74.9582	−	129.831i	−0.330212	−	0.571944i	0.652341	−	0.757926i	$-0.273787\pi$
$227$	−74.9582	−	129.831i	−0.330212	−	0.571944i	−0.982553	+	0.185981i	$0.940454\pi$
$228$	−23.4983	−	13.5667i	−0.103063	−	0.0595032i
$229$		−	190.526i		−	0.831989i	−0.909367	−	0.415995i	$-0.863433\pi$
$229$		−	190.526i		−	0.831989i	0.909367	−	0.415995i	$-0.136567\pi$
$230$	47.4983			0.206514
$231$	−266.498	−	153.863i	−1.15367	−	0.666073i
$232$	−67.3310	+	116.621i	−0.290220	+	0.502676i
$233$	−116.662			−0.500695			−0.250348	−	0.968156i	$-0.580545\pi$
$233$	−116.662			−0.500695			−0.250348	+	0.968156i	$0.580545\pi$
$234$	8.74913	+	77.5078i	0.0373894	+	0.331230i
$235$		−	41.4244i		−	0.176274i
$236$	−224.000			−0.949153
$237$	−29.7491	+	51.5270i	−0.125524	+	0.217413i
$238$	−494.160			−2.07630
$239$	−426.746			−1.78555			−0.892773	−	0.450506i	$-0.851244\pi$
$239$	−426.746			−1.78555			−0.892773	+	0.450506i	$0.851244\pi$
$240$	48.0000			0.200000
$241$	−81.4965	+	47.0520i	−0.338160	+	0.195237i	−0.659458	−	0.751741i	$-0.729214\pi$
$241$	−81.4965	+	47.0520i	−0.338160	+	0.195237i	0.321298	+	0.946978i	$0.395881\pi$
$242$	−199.997	+	346.404i	−0.826432	+	1.43142i
$243$	13.5000	−	7.79423i	0.0555556	−	0.0320750i
$244$	346.328			1.41938
$245$	74.0017	+	42.7249i	0.302048	+	0.174387i
$246$	116.247	−	201.346i	0.472550	−	0.818481i
$247$	46.6690	+	20.3501i	0.188943	+	0.0823890i
$248$	−446.662			−1.80106
$249$	−121.871	−	70.3623i	−0.489442	−	0.282579i
$250$	−141.000	+	81.4064i	−0.564000	+	0.325626i
$251$	−106.746	+	61.6296i	−0.425281	+	0.245536i	−0.697334	−	0.716746i	$-0.745631\pi$
$251$	−106.746	+	61.6296i	−0.425281	+	0.245536i	0.272053	+	0.962282i	$0.412297\pi$
$252$	59.4983	+	103.054i	0.236104	+	0.408944i
$253$	212.749	−	122.831i	0.840906	−	0.485497i
$254$			1.15874i			0.00456196i
$255$	−74.7491			−0.293134
$256$	−128.000	+	221.703i	−0.500000	+	0.866025i
$257$	−104.040	+	180.203i	−0.404825	+	0.701178i	−0.994301	−	0.106608i	$-0.966001\pi$
$257$	−104.040	+	180.203i	−0.404825	+	0.701178i	0.589476	+	0.807786i	$0.299334\pi$
$258$	23.7491	+	41.1347i	0.0920509	+	0.159437i
$259$			324.901i			1.25445i
$260$	−89.4983	+	10.1026i	−0.344224	+	0.0388562i
$261$	−50.4983			−0.193480
$262$	359.498	−	207.556i	1.37213	−	0.792200i
$263$	−41.8746	−	24.1763i	−0.159219	−	0.0919251i	0.418274	−	0.908321i	$-0.362635\pi$
$263$	−41.8746	−	24.1763i	−0.159219	−	0.0919251i	−0.577492	+	0.816396i	$0.695969\pi$
$264$	214.997	−	124.128i	0.814381	−	0.470183i
$265$			2.02174i			0.00762919i
$266$	77.6725			0.292002
$267$	36.2509	+	62.7884i	0.135771	+	0.235162i
$268$	−126.829	−	219.675i	−0.473243	−	0.819682i
$269$	−194.662	−	337.164i	−0.723651	−	1.25340i	−0.959527	−	0.281617i	$-0.909129\pi$
$269$	−194.662	−	337.164i	−0.723651	−	1.25340i	0.235876	−	0.971783i	$-0.424204\pi$
$270$	9.00000	+	15.5885i	0.0333333	+	0.0577350i
$271$	141.666	−	245.372i	0.522751	−	0.905431i	−0.476899	−	0.878958i	$-0.658239\pi$
$271$	141.666	−	245.372i	0.522751	−	0.905431i	0.999650	−	0.0264728i	$-0.00842755\pi$
$272$	199.331	−	345.251i	0.732835	−	1.26931i
$273$	−132.627	−	179.626i	−0.485814	−	0.657972i
$274$	−225.753	−	130.338i	−0.823915	−	0.475687i
$275$	−197.080	+	341.353i	−0.716655	+	1.24128i
$276$	−94.9965			−0.344190
$277$	105.706	+	183.087i	0.381609	+	0.660965i	0.991292	−	0.131679i	$-0.0420369\pi$
$277$	105.706	+	183.087i	0.381609	+	0.660965i	−0.609684	+	0.792645i	$0.708704\pi$
$278$	214.997	+	124.128i	0.773369	+	0.446505i
$279$	−83.7491	−	145.058i	−0.300176	−	0.519920i
$280$	−118.997	+	68.7027i	−0.424988	+	0.245367i
$281$			378.305i			1.34628i	0.739514	+	0.673141i	$0.235055\pi$
$281$			378.305i			1.34628i	−0.739514	+	0.673141i	$0.764945\pi$
$282$			82.8488i			0.293790i
$283$	−78.1254	−	45.1057i	−0.276062	−	0.159384i	0.355578	−	0.934647i	$-0.384284\pi$
$283$	−78.1254	−	45.1057i	−0.276062	−	0.159384i	−0.631639	+	0.775263i	$0.717618\pi$
$284$	209.003			0.735928
$285$	11.7491			0.0412250
$286$	−374.746	+	276.694i	−1.31030	+	0.967460i
$287$			665.542i			2.31896i
$288$	−96.0000			−0.333333
$289$	−165.913	+	287.370i	−0.574093	+	0.994358i
$290$		−	58.3104i		−	0.201070i
$291$	148.997			0.512015
$292$	436.997	+	252.300i	1.49656	+	0.864041i
$293$	158.744	−	91.6508i	0.541788	−	0.312801i	−0.204015	−	0.978968i	$-0.565399\pi$
$293$	158.744	−	91.6508i	0.541788	−	0.312801i	0.745803	+	0.666166i	$0.232066\pi$
$294$	−148.003	−	85.4499i	−0.503413	−	0.290646i
$295$	84.0000	−	48.4974i	0.284746	−	0.164398i
$296$	−226.997	−	131.056i	−0.766880	−	0.442758i
$297$	80.6237	+	46.5481i	0.271460	+	0.156728i
$298$	−151.997	−	87.7552i	−0.510055	−	0.294481i
$299$	177.125	−	19.9940i	0.592393	−	0.0668697i
$300$	132.000	−	76.2102i	0.440000	−	0.254034i
$301$	−117.753	−	67.9845i	−0.391205	−	0.225862i
$302$	−117.415	−	203.368i	−0.388790	−	0.673404i
$303$	187.249	−	108.108i	0.617984	−	0.356793i
$304$	−31.3310	+	54.2669i	−0.103063	+	0.178509i
$305$	−129.873	+	74.9821i	−0.425813	+	0.245843i
$306$	149.498			0.488556
$307$	158.913			0.517632			0.258816	−	0.965927i	$-0.416668\pi$
$307$	158.913			0.517632			0.258816	+	0.965927i	$0.416668\pi$
$308$	−355.331	+	615.451i	−1.15367	+	1.99822i
$309$	80.8746	−	140.079i	0.261730	−	0.453330i
$310$	167.498	−	96.7052i	0.540317	−	0.311952i
$311$		−	331.540i		−	1.06604i	−0.846101	−	0.533022i	$-0.821056\pi$
$311$		−	331.540i		−	1.06604i	0.846101	−	0.533022i	$-0.178944\pi$
$312$	178.997	−	20.2052i	0.573707	−	0.0647604i
$313$	580.990			1.85620			0.928098	−	0.372335i	$-0.121443\pi$
$313$	580.990			1.85620			0.928098	+	0.372335i	$0.121443\pi$
$314$	91.9129	+	159.198i	0.292716	+	0.506999i
$315$	−44.6237	−	25.7635i	−0.141663	−	0.0817889i
$316$	118.997	+	68.7027i	0.376571	+	0.217413i
$317$			484.678i			1.52895i	0.644651	+	0.764477i	$0.277003\pi$
$317$			484.678i			1.52895i	−0.644651	+	0.764477i	$0.722997\pi$
$318$		−	4.04347i		−	0.0127153i
$319$	−150.791	−	261.178i	−0.472699	−	0.818738i
$320$		−	110.851i		−	0.346410i
$321$	44.8746	+	77.7250i	0.139796	+	0.242134i
$322$	235.505	−	135.969i	0.731383	−	0.422264i
$323$	48.7909	−	84.5084i	0.151056	−	0.261636i
$324$	−18.0000	−	31.1769i	−0.0555556	−	0.0962250i
$325$	−230.080	+	169.880i	−0.707939	+	0.522707i
$326$	−64.1672	+	111.141i	−0.196832	+	0.340923i
$327$	113.749	−	197.019i	0.347857	−	0.602505i
$328$	−464.990	−	268.462i	−1.41765	−	0.818481i
$329$	−118.582	−	205.390i	−0.360431	−	0.624285i
$330$	−53.7491	+	93.0962i	−0.162876	+	0.282110i
$331$	81.1638	+	140.580i	0.245208	+	0.424712i	0.962190	−	0.272379i	$-0.0878105\pi$
$331$	81.1638	+	140.580i	0.245208	+	0.424712i	−0.716982	+	0.697091i	$0.754477\pi$
$332$	−162.495	+	281.449i	−0.489442	+	0.847738i
$333$		−	98.2924i		−	0.295172i
$334$	48.3345			0.144714
$335$	95.1219	+	54.9187i	0.283946	+	0.163936i
$336$	237.993	−	137.405i	0.708313	−	0.408944i
$337$	480.826			1.42678			0.713391	−	0.700766i	$-0.247158\pi$
$337$	480.826			1.42678			0.713391	+	0.700766i	$0.247158\pi$
$338$	−329.495	+	75.3472i	−0.974837	+	0.222921i
$339$		−	52.6797i		−	0.155397i
$340$			172.626i			0.507723i
$341$	500.160	−	866.303i	1.46675	−	2.54048i
$342$	−23.4983			−0.0687083
$343$	3.31702			0.00967060
$344$	94.9965	−	54.8463i	0.276153	−	0.159437i
$345$	35.6237	−	20.5673i	0.103257	−	0.0596155i
$346$	−92.3345	+	159.928i	−0.266863	+	0.462220i
$347$	−73.1184	+	42.2150i	−0.210716	+	0.121657i	−0.601644	−	0.798764i	$-0.705487\pi$
$347$	−73.1184	+	42.2150i	−0.210716	+	0.121657i	0.390928	+	0.920421i	$0.372154\pi$
$348$			116.621i			0.335117i
$349$	425.247	+	245.517i	1.21847	+	0.703486i	0.964591	−	0.263749i	$-0.0849590\pi$
$349$	425.247	+	245.517i	1.21847	+	0.703486i	0.253882	+	0.967235i	$0.418292\pi$
$350$	−218.160	+	377.865i	−0.623315	+	1.07961i
$351$	40.1237	+	54.3423i	0.114313	+	0.154821i
$352$	−286.662	−	496.513i	−0.814381	−	1.41055i
$353$	−595.615	−	343.878i	−1.68729	−	0.974160i	−0.956577	−	0.291480i	$-0.905852\pi$
$353$	−595.615	−	343.878i	−1.68729	−	0.974160i	−0.730718	−	0.682680i	$-0.760814\pi$
$354$	−168.000	+	96.9948i	−0.474576	+	0.273997i
$355$	−78.3763	+	45.2506i	−0.220778	+	0.127466i
$356$	145.003	−	83.7178i	0.407313	−	0.235162i
$357$	−370.620	+	213.978i	−1.03815	+	0.599377i
$358$			186.772i			0.521709i
$359$	575.415			1.60283			0.801413	−	0.598111i	$-0.204082\pi$
$359$	575.415			1.60283			0.801413	+	0.598111i	$0.204082\pi$
$360$	36.0000	−	20.7846i	0.100000	−	0.0577350i
$361$	172.831	−	299.352i	0.478756	−	0.829230i
$362$	6.74913	+	11.6898i	0.0186440	+	0.0322923i
$363$			346.404i			0.954281i
$364$	−414.829	+	306.289i	−1.13964	+	0.841454i
$365$	−218.498			−0.598625
$366$	259.746	−	149.964i	0.709688	−	0.409738i
$367$	230.875	+	133.295i	0.629086	+	0.363203i	0.780398	−	0.625283i	$-0.215016\pi$
$367$	230.875	+	133.295i	0.629086	+	0.363203i	−0.151312	+	0.988486i	$0.548350\pi$
$368$			219.385i			0.596155i
$369$		−	201.346i		−	0.545654i
$370$	113.498			0.306752
$371$	5.78744	+	10.0241i	0.0155996	+	0.0270193i
$372$	−334.997	+	193.410i	−0.900528	+	0.519920i
$373$	−67.3711	−	116.690i	−0.180619	−	0.312842i	0.761472	−	0.648198i	$-0.224477\pi$
$373$	−67.3711	−	116.690i	−0.180619	−	0.312842i	−0.942092	+	0.335355i	$0.891144\pi$
$374$	446.411	+	773.207i	1.19361	+	2.06740i
$375$	−70.5000	+	122.110i	−0.188000	+	0.325626i
$376$	191.331			0.508859
$377$	−24.5453	−	217.445i	−0.0651069	−	0.576777i
$378$	89.2474	+	51.5270i	0.236104	+	0.136315i
$379$	153.916	−	266.591i	0.406112	−	0.703406i	−0.588338	−	0.808615i	$-0.700218\pi$
$379$	153.916	−	266.591i	0.406112	−	0.703406i	0.994450	+	0.105209i	$0.0335510\pi$
$380$		−	27.1334i		−	0.0714038i
$381$	0.501748	+	0.869054i	0.00131692	+	0.00228098i
$382$	−117.993	−	68.1233i	−0.308882	−	0.178333i
$383$	112.913	+	195.571i	0.294812	+	0.510629i	0.974941	−	0.222463i	$-0.0714097\pi$
$383$	112.913	+	195.571i	0.294812	+	0.510629i	−0.680129	+	0.733092i	$0.738076\pi$
$384$			221.703i			0.577350i
$385$		−	307.726i		−	0.799287i
$386$		−	86.0232i		−	0.222858i
$387$	35.6237	+	20.5673i	0.0920509	+	0.0531456i
$388$		−	344.093i		−	0.886837i
$389$	−163.669			−0.420743			−0.210371	−	0.977622i	$-0.567467\pi$
$389$	−163.669			−0.420743			−0.210371	+	0.977622i	$0.567467\pi$
$390$	−62.7491	+	46.3308i	−0.160895	+	0.118797i
$391$		−	341.642i		−	0.873766i
$392$	−197.338	+	341.799i	−0.503413	+	0.871937i
$393$	179.749	−	311.335i	0.457377	−	0.792200i
$394$		−	273.652i		−	0.694548i
$395$	−59.4983			−0.150628
$396$	107.498	−	186.192i	0.271460	−	0.470183i
$397$	−235.254	+	135.824i	−0.592580	+	0.342126i	−0.766117	−	0.642701i	$-0.777814\pi$
$397$	−235.254	+	135.824i	−0.592580	+	0.342126i	0.173537	+	0.984827i	$0.444480\pi$
$398$	−63.7421	−	36.8015i	−0.160156	−	0.0924662i
$399$	58.2544	−	33.6332i	0.146001	−	0.0842937i
$400$	−176.000	−	304.841i	−0.440000	−	0.762102i
$401$	−54.1202	−	31.2463i	−0.134963	−	0.0779210i	0.430998	−	0.902353i	$-0.358162\pi$
$401$	−54.1202	−	31.2463i	−0.134963	−	0.0779210i	−0.565961	+	0.824432i	$0.691495\pi$
$402$	−190.244	−	109.837i	−0.473243	−	0.273227i
$403$	583.909	−	431.130i	1.44891	−	1.06980i
$404$	−249.666	−	432.433i	−0.617984	−	1.07038i
$405$	13.5000	+	7.79423i	0.0333333	+	0.0192450i
$406$	−166.920	−	289.114i	−0.411133	−	0.712103i
$407$	508.369	−	293.507i	1.24906	−	0.721148i
$408$		−	345.251i		−	0.846204i
$409$	−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	$0.489868\pi$
$410$	232.495			0.567060
$411$	−225.753			−0.549276
$412$	−323.498	−	186.772i	−0.785190	−	0.453330i
$413$	277.659	−	480.919i	0.672297	−	1.16445i
$414$	−71.2474	+	41.1347i	−0.172095	+	0.0993592i
$415$		−	140.725i		−	0.339095i
$416$	−46.6620	−	413.375i	−0.112168	−	0.993689i
$417$	214.997			0.515579
$418$	−70.1672	−	121.533i	−0.167864	−	0.290749i
$419$	−43.2544	−	24.9729i	−0.103232	−	0.0596012i	0.447495	−	0.894286i	$-0.352316\pi$
$419$	−43.2544	−	24.9729i	−0.103232	−	0.0596012i	−0.550727	+	0.834685i	$0.685650\pi$
$420$	−59.4983	+	103.054i	−0.141663	+	0.245367i
$421$			62.2029i			0.147750i	0.997267	+	0.0738752i	$0.0235367\pi$
$421$			62.2029i			0.147750i	−0.997267	+	0.0738752i	$0.976463\pi$
$422$		−	636.815i		−	1.50904i
$423$	35.8746	+	62.1366i	0.0848098	+	0.146895i
$424$	−9.33800			−0.0220236
$425$	274.080	+	474.721i	0.644894	+	1.11699i
$426$	156.753	−	90.5012i	0.367964	−	0.212444i
$427$	−429.289	+	743.551i	−1.00536	+	1.74134i
$428$	179.498	−	103.633i	0.419388	−	0.242134i
$429$	−161.247	+	369.790i	−0.375868	+	0.861981i
$430$	−23.7491	+	41.1347i	−0.0552305	+	0.0956621i
$431$	−365.206	+	632.555i	−0.847345	+	1.46764i	0.0362246	+	0.999344i	$0.488467\pi$
$431$	−365.206	+	632.555i	−0.847345	+	1.46764i	−0.883569	+	0.468300i	$0.844867\pi$
$432$	−72.0000	+	41.5692i	−0.166667	+	0.0962250i
$433$	−244.416	−	423.342i	−0.564472	−	0.977694i	−0.997099	−	0.0761210i	$-0.975746\pi$
$433$	−244.416	−	423.342i	−0.564472	−	0.977694i	0.432627	−	0.901573i	$-0.357587\pi$
$434$	553.659	−	958.965i	1.27571	−	2.20960i
$435$	−25.2491	−	43.7328i	−0.0580440	−	0.100535i
$436$	−454.997	−	262.692i	−1.04357	−	0.602505i
$437$			53.6996i			0.122882i
$438$	436.997			0.997709
$439$	−295.369	−	170.532i	−0.672823	−	0.388455i	0.124322	−	0.992242i	$-0.460324\pi$
$439$	−295.369	−	170.532i	−0.672823	−	0.388455i	−0.797145	+	0.603787i	$0.793658\pi$
$440$	214.997	+	124.128i	0.488628	+	0.282110i
$441$	−148.003			−0.335609
$442$	72.6655	+	643.737i	0.164402	+	1.45642i
$443$			601.305i			1.35735i	0.734440	+	0.678674i	$0.237445\pi$
$443$			601.305i			1.35735i	−0.734440	+	0.678674i	$0.762555\pi$
$444$	−226.997			−0.511253
$445$	−36.2509	+	62.7884i	−0.0814626	+	0.141097i
$446$	−470.662			−1.05530
$447$	−151.997			−0.340037
$448$	−317.324	−	549.621i	−0.708313	−	1.22683i
$449$	−160.746	+	92.8065i	−0.358008	+	0.206696i	−0.668207	−	0.743976i	$-0.732938\pi$
$449$	−160.746	+	92.8065i	−0.358008	+	0.206696i	0.310199	+	0.950672i	$0.399604\pi$
$450$	66.0000	−	114.315i	0.146667	−	0.254034i
$451$	1041.37	−	601.233i	2.30902	−	1.33311i
$452$	−121.659			−0.269156
$453$	−176.122	−	101.684i	−0.388790	−	0.224468i
$454$	−149.916	+	259.663i	−0.330212	+	0.571944i
$455$	89.2474	−	204.672i	0.196148	−	0.449828i
$456$			54.2669i			0.119006i
$457$	−718.490	−	414.820i	−1.57219	−	0.907703i	−0.995901	−	0.0904550i	$-0.971168\pi$
$457$	−718.490	−	414.820i	−1.57219	−	0.907703i	−0.576287	−	0.817248i	$-0.695499\pi$
$458$	−330.000	+	190.526i	−0.720524	+	0.415995i
$459$	112.124	−	64.7346i	0.244278	−	0.141034i
$460$	−47.4983	−	82.2694i	−0.103257	−	0.178846i
$461$	−216.497	+	124.994i	−0.469624	+	0.271137i	−0.716082	−	0.698016i	$-0.754066\pi$
$461$	−216.497	+	124.994i	−0.469624	+	0.271137i	0.246459	+	0.969153i	$0.420733\pi$
$462$			615.451i			1.33215i
$463$	−239.073			−0.516357			−0.258178	−	0.966097i	$-0.583122\pi$
$463$	−239.073			−0.516357			−0.258178	+	0.966097i	$0.583122\pi$
$464$	269.324			0.580440
$465$	83.7491	−	145.058i	0.180106	−	0.311952i
$466$	116.662	+	202.065i	0.250348	+	0.433615i
$467$		−	382.343i		−	0.818721i	−0.912373	−	0.409360i	$-0.865752\pi$
$467$		−	382.343i		−	0.818721i	0.912373	−	0.409360i	$-0.134248\pi$
$468$	125.498	−	92.6617i	0.268159	−	0.197995i
$469$	628.843			1.34082
$470$	−71.7491	+	41.4244i	−0.152658	+	0.0881370i
$471$	137.869	+	79.5989i	0.292716	+	0.169000i
$472$	224.000	+	387.979i	0.474576	+	0.821990i
$473$			245.662i			0.519369i
$474$	118.997			0.251047
$475$	−43.0801	−	74.6170i	−0.0906950	−	0.157088i
$476$	494.160	+	855.911i	1.03815	+	1.79813i
$477$	−1.75087	−	3.03260i	−0.00367060	−	0.00635766i
$478$	426.746	+	739.145i	0.892773	+	1.54633i
$479$	−217.749	+	377.153i	−0.454591	+	0.787375i	−0.998665	−	0.0516627i	$-0.983548\pi$
$479$	−217.749	+	377.153i	−0.454591	+	0.787375i	0.544074	+	0.839038i	$0.316881\pi$
$480$	−48.0000	−	83.1384i	−0.100000	−	0.173205i
$481$	423.246	−	47.7762i	0.879929	−	0.0993269i
$482$	162.993	+	94.1041i	0.338160	+	0.195237i
$483$	117.753	−	203.954i	0.243794	−	0.422264i
$484$	799.986			1.65286
$485$	74.4983	+	129.035i	0.153605	+	0.266051i
$486$	−27.0000	−	15.5885i	−0.0555556	−	0.0320750i
$487$	131.537	+	227.828i	0.270096	+	0.467819i	0.968886	−	0.247507i	$-0.0796114\pi$
$487$	131.537	+	227.828i	0.270096	+	0.467819i	−0.698790	+	0.715326i	$0.746278\pi$
$488$	−346.328	−	599.857i	−0.709688	−	1.22921i
$489$			111.141i			0.227282i
$490$		−	170.900i		−	0.348775i
$491$	−361.369	−	208.637i	−0.735986	−	0.424922i	0.0846218	−	0.996413i	$-0.473032\pi$
$491$	−361.369	−	208.637i	−0.735986	−	0.424922i	−0.820608	+	0.571491i	$0.806365\pi$
$492$	−464.990			−0.945101
$493$	−419.411			−0.850733
$494$	−11.4216	−	101.183i	−0.0231207	−	0.204824i
$495$			93.0962i			0.188073i
$496$	446.662	+	773.641i	0.900528	+	1.55976i
$497$	−259.070	+	448.722i	−0.521267	+	0.902861i
$498$			281.449i			0.565159i
$499$	−737.324			−1.47760			−0.738802	−	0.673923i	$-0.764608\pi$
$499$	−737.324			−1.47760			−0.738802	+	0.673923i	$0.764608\pi$
$500$	282.000	+	162.813i	0.564000	+	0.325626i
$501$	36.2509	−	20.9295i	0.0723570	−	0.0417754i
$502$	213.491	+	123.259i	0.425281	+	0.245536i
$503$	136.118	−	78.5880i	0.270613	−	0.156239i	−0.358553	−	0.933509i	$-0.616730\pi$
$503$	136.118	−	78.5880i	0.270613	−	0.156239i	0.629166	+	0.777271i	$0.283396\pi$
$504$	118.997	−	206.108i	0.236104	−	0.408944i
$505$	187.249	+	108.108i	0.370790	+	0.214076i
$506$	−425.498	−	245.662i	−0.840906	−	0.485497i
$507$	−214.495	+	199.186i	−0.423067	+	0.392871i
$508$	2.00699	−	1.15874i	0.00395077	−	0.00228098i
$509$	781.239	+	451.048i	1.53485	+	0.886146i	0.999128	+	0.0417516i	$0.0132938\pi$
$509$	781.239	+	451.048i	1.53485	+	0.886146i	0.535722	+	0.844394i	$0.320040\pi$
$510$	74.7491	+	129.469i	0.146567	+	0.253861i
$511$	−1083.36	+	625.475i	−2.12007	+	1.22402i
$512$	512.000			1.00000
$513$	−17.6237	+	10.1750i	−0.0343542	+	0.0198344i
$514$	416.160			0.809650
$515$	161.749			0.314076
$516$	47.4983	−	82.2694i	0.0920509	−	0.159437i
$517$	−214.247	+	371.087i	−0.414405	+	0.717770i
$518$	562.746	−	324.901i	1.08638	−	0.627223i
$519$			159.928i			0.308147i
$520$	106.997	+	144.913i	0.205763	+	0.278679i
$521$	34.0801			0.0654129			0.0327065	−	0.999465i	$-0.489587\pi$
$521$	34.0801			0.0654129			0.0327065	+	0.999465i	$0.489587\pi$
$522$	50.4983	+	87.4655i	0.0967399	+	0.167559i
$523$	163.380	+	94.3274i	0.312390	+	0.180358i	0.647995	−	0.761644i	$-0.275608\pi$
$523$	163.380	+	94.3274i	0.312390	+	0.180358i	−0.335606	+	0.942003i	$0.608941\pi$
$524$	−718.997	−	415.113i	−1.37213	−	0.792200i
$525$			377.865i			0.719742i
$526$			96.7052i			0.183850i
$527$	−695.575	−	1204.77i	−1.31988	−	2.28609i
$528$	−429.993	−	248.257i	−0.814381	−	0.470183i
$529$	−170.497	−	295.309i	−0.322300	−	0.558239i
$530$	3.50175	−	2.02174i	0.00660707	−	0.00381459i
$531$	−84.0000	+	145.492i	−0.158192	+	0.273997i
$532$	−77.6725	−	134.533i	−0.146001	−	0.252881i
$533$	866.995	−	97.8669i	1.62663	−	0.183615i
$534$	72.5017	−	125.577i	0.135771	−	0.235162i
$535$	−44.8746	+	77.7250i	−0.0838777	+	0.145280i
$536$	−253.659	+	439.349i	−0.473243	+	0.819682i
$537$	80.8746	+	140.079i	0.150604	+	0.260854i
$538$	−389.324	+	674.329i	−0.723651	+	1.25340i
$539$	−441.948	−	765.476i	−0.819940	−	1.42018i
$540$	18.0000	−	31.1769i	0.0333333	−	0.0577350i
$541$			976.424i			1.80485i	0.430847	+	0.902425i	$0.358215\pi$
$541$			976.424i			1.80485i	−0.430847	+	0.902425i	$0.641785\pi$
$542$	−566.662			−1.04550
$543$	10.1237	+	5.84491i	0.0186440	+	0.0107641i
$544$	−797.324			−1.46567
$545$	227.498			0.417428
$546$	−178.495	+	409.343i	−0.326913	+	0.749713i
$547$			895.307i			1.63676i	0.574678	+	0.818380i	$0.305127\pi$
$547$			895.307i			1.63676i	−0.574678	+	0.818380i	$0.694873\pi$
$548$			521.353i			0.951375i
$549$	129.873	−	224.946i	0.236563	−	0.409738i
$550$	788.321			1.43331
$551$	65.9234			0.119643
$552$	94.9965	+	164.539i	0.172095	+	0.298077i
$553$	−295.003	+	170.320i	−0.533460	+	0.307993i
$554$	211.411	−	366.175i	0.381609	−	0.660965i
$555$	85.1237	−	49.1462i	0.153376	−	0.0885517i
$556$		−	496.513i		−	0.893009i
$557$	224.493	+	129.611i	0.403040	+	0.232695i	0.687795	−	0.725905i	$-0.258579\pi$
$557$	224.493	+	129.611i	0.403040	+	0.232695i	−0.284755	+	0.958600i	$0.591912\pi$
$558$	−167.498	+	290.115i	−0.300176	+	0.519920i
$559$	−71.2474	+	163.392i	−0.127455	+	0.292294i
$560$	237.993	+	137.405i	0.424988	+	0.245367i
$561$	669.617	+	386.603i	1.19361	+	0.689133i
$562$	655.244	−	378.305i	1.16591	−	0.673141i
$563$	331.986	−	191.672i	0.589673	−	0.340448i	−0.175295	−	0.984516i	$-0.556088\pi$
$563$	331.986	−	191.672i	0.589673	−	0.340448i	0.764968	+	0.644068i	$0.222755\pi$
$564$	143.498	−	82.8488i	0.254430	−	0.146895i
$565$	45.6219	−	26.3398i	0.0807468	−	0.0466192i
$566$			180.423i			0.318768i
$567$	89.2474			0.157403
$568$	−209.003	−	362.005i	−0.367964	−	0.637332i
$569$	−421.909	+	730.768i	−0.741493	+	1.28430i	0.210323	+	0.977632i	$0.432549\pi$
$569$	−421.909	+	730.768i	−0.741493	+	1.28430i	−0.951816	+	0.306671i	$0.900785\pi$
$570$	−11.7491	−	20.3501i	−0.0206125	−	0.0357019i
$571$			402.270i			0.704501i	0.935906	+	0.352251i	$0.114584\pi$
$571$			402.270i			0.704501i	−0.935906	+	0.352251i	$0.885416\pi$
$572$	853.993	+	372.385i	1.49299	+	0.651022i
$573$	−117.993			−0.205921
$574$	1152.75	−	665.542i	2.00828	−	1.15948i
$575$	−261.240	−	150.827i	−0.454331	−	0.262308i
$576$	96.0000	+	166.277i	0.166667	+	0.288675i
$577$		−	509.205i		−	0.882504i	−0.897383	−	0.441252i	$-0.854535\pi$
$577$		−	509.205i		−	0.882504i	0.897383	−	0.441252i	$-0.145465\pi$
$578$	663.652			1.14819
$579$	−37.2491	−	64.5174i	−0.0643336	−	0.111429i
$580$	−100.997	+	58.3104i	−0.174132	+	0.100535i
$581$	−402.840	−	697.739i	−0.693356	−	1.20093i
$582$	−148.997	−	258.070i	−0.256008	−	0.443418i
$583$	10.4564	−	18.1111i	0.0179356	−	0.0310653i
$584$		−	1009.20i		−	1.72808i
$585$	−27.0000	+	61.9193i	−0.0461538	+	0.105845i
$586$	−317.488	−	183.302i	−0.541788	−	0.312801i
$587$	438.990	−	760.352i	0.747853	−	1.29532i	−0.200997	−	0.979592i	$-0.564418\pi$
$587$	438.990	−	760.352i	0.747853	−	1.29532i	0.948850	−	0.315727i	$-0.102248\pi$
$588$			341.799i			0.581292i
$589$	109.331	+	189.367i	0.185621	+	0.321506i
$590$	−168.000	−	96.9948i	−0.284746	−	0.164398i
$591$	−118.495	−	205.239i	−0.200499	−	0.347274i
$592$			524.226i			0.885517i
$593$			297.484i			0.501660i	0.968031	+	0.250830i	$0.0807035\pi$
$593$			297.484i			0.501660i	−0.968031	+	0.250830i	$0.919297\pi$
$594$		−	186.192i		−	0.313455i
$595$	−370.620	−	213.978i	−0.622891	−	0.359626i
$596$			351.021i			0.588961i
$597$	−63.7421			−0.106771
$598$	−211.756	−	286.796i	−0.354107	−	0.479592i
$599$			65.5404i			0.109416i	0.998502	+	0.0547081i	$0.0174228\pi$
$599$			65.5404i			0.109416i	−0.998502	+	0.0547081i	$0.982577\pi$
$600$	−264.000	−	152.420i	−0.440000	−	0.254034i
$601$	−10.0052	+	17.3296i	−0.0166477	+	0.0288346i	−0.874229	−	0.485513i	$-0.838633\pi$
$601$	−10.0052	+	17.3296i	−0.0166477	+	0.0288346i	0.857582	+	0.514348i	$0.171966\pi$
$602$			271.938i			0.451724i
$603$	−190.244			−0.315496
$604$	−234.829	+	406.736i	−0.388790	+	0.673404i
$605$	−299.995	+	173.202i	−0.495859	+	0.286284i
$606$	−374.498	−	216.217i	−0.617984	−	0.356793i
$607$	−277.986	+	160.495i	−0.457967	+	0.264407i	−0.711189	−	0.703001i	$-0.751843\pi$
$607$	−277.986	+	160.495i	−0.457967	+	0.264407i	0.253222	+	0.967408i	$0.418510\pi$
$608$	125.324			0.206125
$609$	−250.380	−	144.557i	−0.411133	−	0.237368i
$610$	259.746	+	149.964i	0.425813	+	0.245843i
$611$	−250.122	+	184.678i	−0.409365	+	0.302255i
$612$	−149.498	−	258.939i	−0.244278	−	0.423102i
$613$	−329.378	−	190.167i	−0.537321	−	0.310223i	0.206671	−	0.978410i	$-0.433737\pi$
$613$	−329.378	−	190.167i	−0.537321	−	0.310223i	−0.743993	+	0.668188i	$0.767070\pi$
$614$	−158.913	−	275.245i	−0.258816	−	0.448282i
$615$	174.371	−	100.673i	0.283530	−	0.163696i
$616$	1421.32			2.30734
$617$	269.618	−	155.664i	0.436983	−	0.252292i	−0.265334	−	0.964157i	$-0.585482\pi$
$617$	269.618	−	155.664i	0.436983	−	0.252292i	0.702317	+	0.711864i	$0.252149\pi$
$618$	−323.498			−0.523460
$619$	−1025.83			−1.65723			−0.828615	−	0.559818i	$-0.810871\pi$
$619$	−1025.83			−1.65723			−0.828615	+	0.559818i	$0.810871\pi$
$620$	−334.997	−	193.410i	−0.540317	−	0.311952i
$621$	−35.6237	+	61.7020i	−0.0573650	+	0.0993592i
$622$	−574.244	+	331.540i	−0.923222	+	0.533022i
$623$			415.089i			0.666274i
$624$	−213.993	−	289.826i	−0.342938	−	0.464464i
$625$	409.000			0.654400
$626$	−580.990	−	1006.30i	−0.928098	−	1.60751i
$627$	−105.251	−	60.7666i	−0.167864	−	0.0969165i
$628$	183.826	−	318.396i	0.292716	−	0.506999i
$629$		−	816.363i		−	1.29787i
$630$			103.054i			0.163578i
$631$	606.655	+	1050.76i	0.961418	+	1.66523i	0.718944	+	0.695068i	$0.244626\pi$
$631$	606.655	+	1050.76i	0.961418	+	1.66523i	0.242474	+	0.970158i	$0.422041\pi$
$632$		−	274.811i		−	0.434827i
$633$	−275.749	−	477.611i	−0.435623	−	0.754521i
$634$	839.488	−	484.678i	1.32411	−	0.764477i
$635$	−0.501748	+	0.869054i	−0.000790155	+	0.00136859i
$636$	−7.00350	+	4.04347i	−0.0110118	+	0.00635766i
$637$	−71.9390	−	637.301i	−0.112934	−	1.00047i
$638$	−301.582	+	522.355i	−0.472699	+	0.818738i
$639$	78.3763	−	135.752i	0.122655	−	0.212444i
$640$	−192.000	+	110.851i	−0.300000	+	0.173205i
$641$	310.462	+	537.735i	0.484340	+	0.838901i	0.999838	−	0.0179896i	$-0.00572659\pi$
$641$	310.462	+	537.735i	0.484340	+	0.838901i	−0.515499	+	0.856890i	$0.672393\pi$
$642$	89.7491	−	155.450i	0.139796	−	0.242134i
$643$	−338.334	−	586.013i	−0.526181	−	0.911373i	−0.999535	−	0.0305000i	$-0.990290\pi$
$643$	−338.334	−	586.013i	−0.526181	−	0.911373i	0.473354	−	0.880873i	$-0.343043\pi$
$644$	−471.010	−	271.938i	−0.731383	−	0.422264i
$645$			41.1347i			0.0637747i
$646$	−195.164			−0.302111
$647$	−121.254	−	70.0062i	−0.187410	−	0.108201i	0.403359	−	0.915042i	$-0.367842\pi$
$647$	−121.254	−	70.0062i	−0.187410	−	0.108201i	−0.590770	+	0.806840i	$0.701176\pi$
$648$	−36.0000	+	62.3538i	−0.0555556	+	0.0962250i
$649$	−1003.32			−1.54594
$650$	524.321	+	228.631i	0.806647	+	0.351740i
$651$		−	958.965i		−	1.47306i
$652$	256.669			0.393664
$653$	407.826	−	706.375i	0.624542	−	1.08174i	−0.364088	−	0.931365i	$-0.618619\pi$
$653$	407.826	−	706.375i	0.624542	−	1.08174i	0.988629	−	0.150373i	$-0.0480476\pi$
$654$	−454.997			−0.695713
$655$	359.498			0.548852
$656$			1073.85i			1.63696i
$657$	327.747	−	189.225i	0.498854	−	0.288014i
$658$	−237.164	+	410.780i	−0.360431	+	0.624285i
$659$	−544.244	+	314.219i	−0.825863	+	0.476812i	−0.852434	−	0.522835i	$-0.824875\pi$
$659$	−544.244	+	314.219i	−0.825863	+	0.476812i	0.0265709	+	0.999647i	$0.491541\pi$
$660$	214.997			0.325752
$661$	−770.357	−	444.766i	−1.16544	−	0.672868i	−0.212840	−	0.977087i	$-0.568271\pi$
$661$	−770.357	−	444.766i	−1.16544	−	0.672868i	−0.952602	+	0.304219i	$0.901605\pi$
$662$	162.328	−	281.159i	0.245208	−	0.424712i
$663$	333.246	+	451.338i	0.502633	+	0.680751i
$664$	649.979			0.978884
$665$	58.2544	+	33.6332i	0.0876006	+	0.0505762i
$666$	−170.247	+	98.2924i	−0.255627	+	0.147586i
$667$	199.882	−	115.402i	0.299672	−	0.173016i
$668$	−48.3345	−	83.7178i	−0.0723570	−	0.125326i
$669$	−352.997	+	203.803i	−0.527648	+	0.304638i
$670$		−	219.675i		−	0.327873i
$671$	1551.23			2.31182
$672$	−475.986	−	274.811i	−0.708313	−	0.408944i
$673$	−437.911	+	758.484i	−0.650685	+	1.12702i	0.332272	+	0.943184i	$0.392185\pi$
$673$	−437.911	+	758.484i	−0.650685	+	1.12702i	−0.982957	+	0.183836i	$0.941148\pi$
$674$	−480.826	−	832.815i	−0.713391	−	1.23563i
$675$		−	114.315i		−	0.169356i
$676$	460.000	+	495.354i	0.680473	+	0.732773i
$677$	55.3310			0.0817297			0.0408648	−	0.999165i	$-0.486989\pi$
$677$	55.3310			0.0817297			0.0408648	+	0.999165i	$0.486989\pi$
$678$	−91.2439	+	52.6797i	−0.134578	+	0.0776986i
$679$	738.753	+	426.519i	1.08800	+	0.628158i
$680$	298.997	−	172.626i	0.439701	−	0.253861i
$681$			259.663i			0.381296i
$682$	−2000.64			−2.93349
$683$	−150.836	−	261.256i	−0.220844	−	0.382513i	0.734221	−	0.678911i	$-0.237548\pi$
$683$	−150.836	−	261.256i	−0.220844	−	0.382513i	−0.955064	+	0.296398i	$0.904214\pi$
$684$	23.4983	+	40.7002i	0.0343542	+	0.0595032i
$685$	−112.876	−	195.508i	−0.164783	−	0.285412i
$686$	−3.31702	−	5.74524i	−0.00483530	−	0.00837499i
$687$	−165.000	+	285.788i	−0.240175	+	0.415995i
$688$	−189.993	−	109.693i	−0.276153	−	0.159437i
$689$	12.2073	−	9.01328i	0.0177174	−	0.0130817i
$690$	−71.2474	−	41.1347i	−0.103257	−	0.0596155i
$691$	236.035	−	408.824i	0.341584	−	0.591642i	−0.643143	−	0.765746i	$-0.722370\pi$
$691$	236.035	−	408.824i	0.341584	−	0.591642i	0.984727	+	0.174105i	$0.0557031\pi$
$692$	369.338			0.533725
$693$	266.498	+	461.589i	0.384557	+	0.666073i
$694$	146.237	+	84.4299i	0.210716	+	0.121657i
$695$	107.498	+	186.192i	0.154674	+	0.267903i
$696$	201.993	−	116.621i	0.290220	−	0.167559i
$697$		−	1672.27i		−	2.39925i
$698$		−	982.067i		−	1.40697i
$699$	174.993	+	101.032i	0.250348	+	0.144538i
$700$	872.641			1.24663
$701$	124.321			0.177347			0.0886737	−	0.996061i	$-0.471737\pi$
$701$	124.321			0.177347			0.0886737	+	0.996061i	$0.471737\pi$
$702$	54.0000	−	123.839i	0.0769231	−	0.176408i
$703$			128.317i			0.182527i
$704$	−573.324	+	993.026i	−0.814381	+	1.41055i
$705$	−35.8746	+	62.1366i	−0.0508859	+	0.0881370i
$706$			1375.51i			1.94832i
$707$	1237.89			1.75090
$708$	336.000	+	193.990i	0.474576	+	0.273997i
$709$	−1035.12	+	597.627i	−1.45997	+	0.842915i	−0.999009	−	0.0445042i	$-0.985829\pi$
$709$	−1035.12	+	597.627i	−1.45997	+	0.842915i	−0.460963	+	0.887419i	$0.652496\pi$
$710$	156.753	+	90.5012i	0.220778	+	0.127466i
$711$	89.2474	−	51.5270i	0.125524	−	0.0724712i
$712$	−290.007	−	167.436i	−0.407313	−	0.235162i
$713$	662.990	+	382.777i	0.929859	+	0.536854i
$714$	741.240	+	427.955i	1.03815	+	0.599377i
$715$	−400.871	+	45.2506i	−0.560659	+	0.0632875i
$716$	323.498	−	186.772i	0.451813	−	0.260854i
$717$	640.118	+	369.573i	0.892773	+	0.515443i
$718$	−575.415	−	996.647i	−0.801413	−	1.38809i
$719$	−838.244	+	483.960i	−1.16585	+	0.673102i	−0.952698	−	0.303918i	$-0.901705\pi$
$719$	−838.244	+	483.960i	−1.16585	+	0.673102i	−0.213149	+	0.977020i	$0.568372\pi$
$720$	−72.0000	−	41.5692i	−0.100000	−	0.0577350i
$721$	801.983	−	463.025i	1.11232	−	0.642198i
$722$	−691.324			−0.957512
$723$	162.993			0.225440
$724$	13.4983	−	23.3797i	0.0186440	−	0.0322923i
$725$	−185.160	+	320.707i	−0.255393	+	0.442354i
$726$	599.990	−	346.404i	0.826432	−	0.477141i
$727$		−	770.901i		−	1.06039i	−0.847877	−	0.530194i	$-0.822119\pi$
$727$		−	770.901i		−	1.06039i	0.847877	−	0.530194i	$-0.177881\pi$
$728$	945.338	+	412.216i	1.29854	+	0.566231i
$729$	−27.0000			−0.0370370
$730$	218.498	+	378.450i	0.299313	+	0.518425i
$731$	295.871	+	170.821i	0.404748	+	0.233682i
$732$	−519.491	−	299.928i	−0.709688	−	0.409738i
$733$		−	1205.36i		−	1.64442i	−0.569188	−	0.822208i	$-0.692742\pi$
$733$		−	1205.36i		−	1.64442i	0.569188	−	0.822208i	$-0.307258\pi$
$734$		−	533.182i		−	0.726406i
$735$	−74.0017	−	128.175i	−0.100683	−	0.174387i
$736$	379.986	−	219.385i	0.516285	−	0.298077i
$737$	−568.080	−	983.944i	−0.770801	−	1.33507i
$738$	−348.742	+	201.346i	−0.472550	+	0.272827i
$739$	326.662	−	565.795i	0.442032	−	0.765623i	−0.555808	−	0.831311i	$-0.687591\pi$
$739$	326.662	−	565.795i	0.442032	−	0.765623i	0.997840	+	0.0656882i	$0.0209243\pi$
$740$	−113.498	−	196.585i	−0.153376	−	0.265655i
$741$	−52.3798	−	70.9417i	−0.0706880	−	0.0957377i
$742$	11.5749	−	20.0483i	0.0155996	−	0.0270193i
$743$	−245.240	+	424.769i	−0.330068	+	0.571694i	−0.982525	−	0.186132i	$-0.940405\pi$
$743$	−245.240	+	424.769i	−0.330068	+	0.571694i	0.652457	+	0.757826i	$0.273738\pi$
$744$	669.993	+	386.821i	0.900528	+	0.519920i
$745$	−75.9983	−	131.633i	−0.102011	−	0.176688i
$746$	−134.742	+	233.380i	−0.180619	+	0.312842i
$747$	121.871	+	211.087i	0.163147	+	0.282579i
$748$	892.822	−	1546.41i	1.19361	−	2.06740i
$749$			513.834i			0.686026i
$750$	282.000			0.376000
$751$	905.613	+	522.856i	1.20588	+	0.696213i	0.961856	−	0.273557i	$-0.0882002\pi$
$751$	905.613	+	522.856i	1.20588	+	0.696213i	0.244021	+	0.969770i	$0.421534\pi$
$752$	−191.331	−	331.395i	−0.254430	−	0.440685i
$753$	213.491			0.283521
$754$	−352.080	+	259.959i	−0.466950	+	0.344773i
$755$		−	203.368i		−	0.269362i
$756$		−	206.108i		−	0.272630i
$757$	−450.498	+	780.286i	−0.595110	+	1.03076i	0.398421	+	0.917202i	$0.369558\pi$
$757$	−450.498	+	780.286i	−0.595110	+	1.03076i	−0.993531	+	0.113558i	$0.963775\pi$
$758$	−615.666			−0.812224
$759$	−425.498			−0.560604
$760$	−46.9965	+	27.1334i	−0.0618375	+	0.0357019i
$761$	−301.233	+	173.917i	−0.395839	+	0.228538i	−0.684687	−	0.728837i	$-0.740061\pi$
$761$	−301.233	+	173.917i	−0.395839	+	0.228538i	0.288848	+	0.957375i	$0.406728\pi$
$762$	1.00350	−	1.73811i	0.00131692	−	0.00228098i
$763$	1127.98	−	651.239i	1.47835	−	0.853524i
$764$			272.493i			0.356666i
$765$	112.124	+	64.7346i	0.146567	+	0.0846204i
$766$	225.826	−	391.142i	0.294812	−	0.510629i
$767$	−667.317	−	290.985i	−0.870035	−	0.379380i
$768$	384.000	−	221.703i	0.500000	−	0.288675i
$769$	347.990	+	200.912i	0.452522	+	0.261264i	0.708895	−	0.705314i	$-0.249194\pi$
$769$	347.990	+	200.912i	0.452522	+	0.261264i	−0.256373	+	0.966578i	$0.582527\pi$
$770$	−532.997	+	307.726i	−0.692203	+	0.399644i
$771$	312.120	−	180.203i	0.404825	−	0.233726i
$772$	−148.997	+	86.0232i	−0.193001	+	0.111429i
$773$	−502.505	+	290.122i	−0.650071	+	0.375319i	−0.788484	−	0.615056i	$-0.789133\pi$
$773$	−502.505	+	290.122i	−0.650071	+	0.375319i	0.138412	+	0.990375i	$0.455800\pi$
$774$		−	82.2694i		−	0.106291i
$775$	−1228.32			−1.58493
$776$	−595.986	+	344.093i	−0.768023	+	0.443418i
$777$	281.373	−	487.352i	0.362127	−	0.627223i
$778$	163.669	+	283.483i	0.210371	+	0.364374i
$779$			262.849i			0.337419i
$780$	142.997	+	62.3538i	0.183329	+	0.0799408i
$781$	936.146			1.19865
$782$	−591.742	+	341.642i	−0.756703	+	0.436883i
$783$	75.7474	+	43.7328i	0.0967399	+	0.0558528i
$784$	789.352			1.00683
$785$			159.198i			0.202800i
$786$	−718.997			−0.914754
$787$	−133.080	−	230.502i	−0.169098	−	0.292886i	0.769005	−	0.639243i	$-0.220752\pi$
$787$	−133.080	−	230.502i	−0.169098	−	0.292886i	−0.938103	+	0.346356i	$0.887419\pi$
$788$	−473.979	+	273.652i	−0.601496	+	0.347274i
$789$	41.8746	+	72.5289i	0.0530730	+	0.0919251i
$790$	59.4983	+	103.054i	0.0753142	+	0.130448i
$791$	150.801	−	261.196i	0.190647	−	0.330210i
$792$	−429.993			−0.542920
$793$	1031.74	+	449.893i	1.30106	+	0.567330i
$794$	470.509	+	271.648i	0.592580	+	0.342126i
$795$	1.75087	−	3.03260i	0.00220236	−	0.00381459i
$796$			147.206i			0.184932i
$797$	−89.6620	−	155.299i	−0.112499	−	0.194855i	0.804278	−	0.594253i	$-0.202552\pi$
$797$	−89.6620	−	155.299i	−0.112499	−	0.194855i	−0.916777	+	0.399399i	$0.869219\pi$
$798$	−116.509	−	67.2664i	−0.146001	−	0.0842937i
$799$	297.955	+	516.073i	0.372910	+	0.645898i
$800$	−352.000	+	609.682i	−0.440000	+	0.762102i
$801$		−	125.577i		−	0.156775i
$802$			124.985i			0.155842i
$803$	1957.35	+	1130.08i	2.43754	+	1.40732i
$804$			439.349i			0.546455i
$805$	235.505			0.292553
$806$	−1330.65	−	580.231i	−1.65093	−	0.719890i
$807$			674.329i			0.835600i
$808$	−499.331	+	864.867i	−0.617984	+	1.07038i
$809$	257.706	−	446.359i	0.318548	−	0.551742i	−0.661637	−	0.749824i	$-0.730138\pi$
$809$	257.706	−	446.359i	0.318548	−	0.551742i	0.980185	+	0.198082i	$0.0634714\pi$
$810$		−	31.1769i		−	0.0384900i
$811$	−390.829			−0.481910			−0.240955	−	0.970536i	$-0.577461\pi$
$811$	−390.829			−0.481910			−0.240955	+	0.970536i	$0.577461\pi$
$812$	−333.840	+	578.227i	−0.411133	+	0.712103i
$813$	−424.997	+	245.372i	−0.522751	+	0.301810i
$814$	−1016.74	−	587.014i	−1.24906	−	0.721148i
$815$	−96.2509	+	55.5705i	−0.118099	+	0.0681846i
$816$	−597.993	+	345.251i	−0.732835	+	0.423102i
$817$	−46.5052	−	26.8498i	−0.0569220	−	0.0328639i
$818$	669.000	+	386.247i	0.817848	+	0.472185i
$819$	43.3798	+	384.298i	0.0529668	+	0.469228i
$820$	−232.495	−	402.693i	−0.283530	−	0.491089i
$821$	59.0070	+	34.0677i	0.0718721	+	0.0414954i	0.535505	−	0.844532i	$-0.320121\pi$
$821$	59.0070	+	34.0677i	0.0718721	+	0.0414954i	−0.463633	+	0.886027i	$0.653454\pi$
$822$	225.753	+	391.015i	0.274638	+	0.475687i
$823$	943.484	−	544.721i	1.14640	−	0.661872i	0.198390	−	0.980123i	$-0.436429\pi$
$823$	943.484	−	544.721i	1.14640	−	0.661872i	0.948007	+	0.318251i	$0.103095\pi$
$824$			747.087i			0.906659i
$825$	591.240	−	341.353i	0.716655	−	0.413761i
$826$	−1110.63			−1.34459
$827$	−1050.82			−1.27064			−0.635318	−	0.772251i	$-0.719131\pi$
$827$	−1050.82			−1.27064			−0.635318	+	0.772251i	$0.719131\pi$
$828$	142.495	+	82.2694i	0.172095	+	0.0993592i
$829$	516.866	−	895.238i	0.623481	−	1.07990i	−0.365351	−	0.930870i	$-0.619051\pi$
$829$	516.866	−	895.238i	0.623481	−	1.07990i	0.988832	−	0.149031i	$-0.0476155\pi$
$830$	−243.742	+	140.725i	−0.293665	+	0.169548i
$831$		−	366.175i		−	0.440644i
$832$	−669.324	+	494.196i	−0.804476	+	0.593985i
$833$	−1229.24			−1.47567
$834$	−214.997	−	372.385i	−0.257790	−	0.446505i
$835$	36.2509	+	20.9295i	0.0434142	+	0.0250652i
$836$	−140.334	+	243.066i	−0.167864	+	0.290749i
$837$			290.115i			0.346613i
$838$			99.8917i			0.119202i
$839$	−177.003	−	306.579i	−0.210970	−	0.365410i	0.741049	−	0.671451i	$-0.234329\pi$
$839$	−177.003	−	306.579i	−0.210970	−	0.365410i	−0.952018	+	0.306041i	$0.900995\pi$
$840$	237.993			0.283325
$841$	278.829	+	482.946i	0.331545	+	0.574253i
$842$	107.739	−	62.2029i	0.127956	−	0.0738752i
$843$	327.622	−	567.458i	0.388638	−	0.673141i
$844$	−1103.00	+	636.815i	−1.30687	+	0.754521i
$845$	−279.747	−	86.1650i	−0.331062	−	0.101970i
$846$	71.7491	−	124.273i	0.0848098	−	0.146895i
$847$	−991.620	+	1717.54i	−1.17074	+	2.02779i
$848$	9.33800	+	16.1739i	0.0110118	+	0.0190730i
$849$	78.1254	+	135.317i	0.0920205	+	0.159384i
$850$	548.160	−	949.441i	0.644894	−	1.11699i
$851$	224.624	+	389.060i	0.263953	+	0.457179i
$852$	−313.505	−	181.002i	−0.367964	−	0.212444i
$853$		−	72.3056i		−	0.0847662i	−0.999101	−	0.0423831i	$-0.986505\pi$
$853$		−	72.3056i		−	0.0847662i	0.999101	−	0.0423831i	$-0.0134950\pi$
$854$	1717.16			2.01072
$855$	−17.6237	−	10.1750i	−0.0206125	−	0.0119006i
$856$	−358.997	−	207.267i	−0.419388	−	0.242134i
$857$	194.094			0.226481			0.113240	−	0.993568i	$-0.463877\pi$
$857$	194.094			0.226481			0.113240	+	0.993568i	$0.463877\pi$
$858$	801.742	−	90.5012i	0.934431	−	0.105479i
$859$		−	960.268i		−	1.11789i	−0.829204	−	0.558945i	$-0.811206\pi$
$859$		−	960.268i		−	1.11789i	0.829204	−	0.558945i	$-0.188794\pi$
$860$	94.9965			0.110461
$861$	576.376	−	998.313i	0.669427	−	1.15948i
$862$	1460.82			1.69469
$863$	−115.066			−0.133333			−0.0666664	−	0.997775i	$-0.521236\pi$
$863$	−115.066			−0.133333			−0.0666664	+	0.997775i	$0.521236\pi$
$864$	144.000	+	83.1384i	0.166667	+	0.0962250i
$865$	−138.502	+	79.9640i	−0.160118	+	0.0924440i
$866$	−488.833	+	846.683i	−0.564472	+	0.977694i
$867$	497.739	−	287.370i	0.574093	−	0.331453i
$868$	−2214.63			−2.55142
$869$	532.997	+	307.726i	0.613345	+	0.354115i
$870$	−50.4983	+	87.4655i	−0.0580440	+	0.100535i
$871$	−92.4704	−	819.188i	−0.106166	−	0.940514i
$872$			1050.77i			1.20501i
$873$	−223.495	−	129.035i	−0.256008	−	0.147806i
$874$	93.0105	−	53.6996i	0.106419	−	0.0614412i
$875$	−699.104	+	403.628i	−0.798977	+	0.461289i
$876$	−436.997	−	756.900i	−0.498854	−	0.864041i
$877$	−425.357	+	245.580i	−0.485014	+	0.280023i	−0.722504	−	0.691367i	$-0.757009\pi$
$877$	−425.357	+	245.580i	−0.485014	+	0.280023i	0.237490	+	0.971390i	$0.423675\pi$
$878$			682.126i			0.776909i
$879$	−317.488			−0.361192
$880$		−	496.513i		−	0.564219i
$881$	−3.79618	+	6.57518i	−0.00430895	+	0.00746332i	−0.868172	−	0.496264i	$-0.834705\pi$
$881$	−3.79618	+	6.57518i	−0.00430895	+	0.00746332i	0.863863	+	0.503727i	$0.168038\pi$
$882$	148.003	+	256.350i	0.167804	+	0.290646i
$883$		−	770.769i		−	0.872898i	−0.899729	−	0.436449i	$-0.856236\pi$
$883$		−	770.769i		−	0.872898i	0.899729	−	0.436449i	$-0.143764\pi$
$884$	1042.32	−	769.598i	1.17910	−	0.870586i
$885$	−168.000			−0.189831
$886$	1041.49	−	601.305i	1.17550	−	0.678674i
$887$	366.983	+	211.877i	0.413735	+	0.238870i	0.692393	−	0.721521i	$-0.256556\pi$
$887$	366.983	+	211.877i	0.413735	+	0.238870i	−0.278659	+	0.960390i	$0.589890\pi$
$888$	226.997	+	393.169i	0.255627	+	0.442758i
$889$			5.74524i			0.00646259i
$890$	145.003			0.162925
$891$	−80.6237	−	139.644i	−0.0904867	−	0.156728i
$892$	470.662	+	815.211i	0.527648	+	0.913913i
$893$	−46.8328	−	81.1167i	−0.0524443	−	0.0908362i
$894$	151.997	+	263.266i	0.170018	+	0.294481i
$895$	−80.8746	+	140.079i	−0.0903626	+	0.156513i
$896$	−634.648	+	1099.24i	−0.708313	+	1.22683i
$897$	−283.003	−	123.404i	−0.315500	−	0.137574i
$898$	321.491	+	185.613i	0.358008	+	0.206696i
$899$	469.909	−	813.907i	0.522702	−	0.905347i
$900$	−264.000			−0.293333
$901$	−14.5418	−	25.1872i	−0.0161396	−	0.0279547i
$902$	−2082.73	−	1202.47i	−2.30902	−	1.33311i
$903$	117.753	+	203.954i	0.130402	+	0.225862i
$904$	121.659	+	210.719i	0.134578	+	0.233096i
$905$			11.6898i			0.0129169i
$906$			406.736i			0.448936i
$907$	−985.735	−	569.114i	−1.08681	−	0.627469i	−0.154083	−	0.988058i	$-0.549242\pi$
$907$	−985.735	−	569.114i	−1.08681	−	0.627469i	−0.932725	+	0.360589i	$0.882576\pi$
$908$	599.666			0.660425
$909$	−374.498			−0.411989
$910$	−443.749	+	50.0907i	−0.487636	+	0.0550447i
$911$			1470.78i			1.61447i	0.590230	+	0.807235i	$0.299037\pi$
$911$			1470.78i			1.61447i	−0.590230	+	0.807235i	$0.700963\pi$
$912$	93.9930	−	54.2669i	0.103063	−	0.0595032i
$913$	−727.829	+	1260.64i	−0.797184	+	1.38076i
$914$			1659.28i			1.81541i
$915$	259.746			0.283875
$916$	660.000	+	381.051i	0.720524	+	0.415995i
$917$	1782.46	−	1029.10i	1.94379	−	1.12225i
$918$	−224.247	−	129.469i	−0.244278	−	0.141034i
$919$	−744.732	+	429.971i	−0.810372	+	0.467868i	−0.847085	−	0.531457i	$-0.821645\pi$
$919$	−744.732	+	429.971i	−0.810372	+	0.467868i	0.0367132	+	0.999326i	$0.488311\pi$
$920$	−94.9965	+	164.539i	−0.103257	+	0.178846i
$921$	−238.369	−	137.623i	−0.258816	−	0.149427i
$922$	432.993	+	249.989i	0.469624	+	0.271137i
$923$	622.641	+	271.504i	0.674584	+	0.294153i
$924$	1065.99	−	615.451i	1.15367	−	0.666073i
$925$	−624.240	−	360.405i	−0.674854	−	0.389627i
$926$	239.073	+	414.087i	0.258178	+	0.447178i
$927$	−242.624	+	140.079i	−0.261730	+	0.151110i
$928$	−269.324	−	466.483i	−0.290220	−	0.502676i
$929$	−1426.09	+	823.355i	−1.53508	+	0.886281i	−0.535967	+	0.844239i	$0.680053\pi$
$929$	−1426.09	+	823.355i	−1.53508	+	0.886281i	−0.999116	+	0.0420419i	$0.986614\pi$
$930$	−334.997			−0.360211
$931$	193.212			0.207532
$932$	233.324	−	404.129i	0.250348	−	0.433615i
$933$	−287.122	+	497.310i	−0.307741	+	0.533022i
$934$	−662.237	+	382.343i	−0.709033	+	0.409360i
$935$			773.207i			0.826959i
$936$	−285.993	−	124.708i	−0.305548	−	0.133235i
$937$	−1495.64			−1.59620			−0.798101	−	0.602524i	$-0.794162\pi$
$937$	−1495.64			−1.59620			−0.798101	+	0.602524i	$0.794162\pi$
$938$	−628.843	−	1089.19i	−0.670409	−	1.16118i
$939$	−871.484	−	503.152i	−0.928098	−	0.535838i
$940$	143.498	+	82.8488i	0.152658	+	0.0881370i
$941$		−	788.644i		−	0.838092i	−0.907965	−	0.419046i	$-0.862365\pi$
$941$		−	788.644i		−	0.838092i	0.907965	−	0.419046i	$-0.137635\pi$
$942$		−	318.396i		−	0.338000i
$943$	460.129	+	796.967i	0.487942	+	0.845140i
$944$	448.000	−	775.959i	0.474576	−	0.821990i
$945$	44.6237	+	77.2905i	0.0472208	+	0.0817889i
$946$	425.498	−	245.662i	0.449787	−	0.259684i
$947$	499.491	−	865.144i	0.527446	−	0.913563i	−0.472042	−	0.881576i	$-0.656483\pi$
$947$	499.491	−	865.144i	0.527446	−	0.913563i	0.999488	−	0.0319872i	$-0.0101836\pi$
$948$	−118.997	−	206.108i	−0.125524	−	0.217413i
$949$	974.106	+	1319.30i	1.02646	+	1.39020i
$950$	−86.1603	+	149.234i	−0.0906950	+	0.157088i
$951$	419.744	−	727.018i	0.441371	−	0.764477i
$952$	988.321	−	1711.82i	1.03815	−	1.79813i
$953$	−5.42162	−	9.39052i	−0.00568900	−	0.00985364i	0.863167	−	0.504919i	$-0.168478\pi$
$953$	−5.42162	−	9.39052i	−0.00568900	−	0.00985364i	−0.868856	+	0.495065i	$0.835144\pi$
$954$	−3.50175	+	6.06521i	−0.00367060	+	0.00635766i
$955$	−58.9965	−	102.185i	−0.0617764	−	0.107000i
$956$	853.491	−	1478.29i	0.892773	−	1.54633i
$957$			522.355i			0.545826i
$958$	870.997			0.909182
$959$	−1119.32	−	646.242i	−1.16718	−	0.673871i
$960$	−96.0000	+	166.277i	−0.100000	+	0.173205i
$961$	2156.30			2.24380
$962$	−505.997	−	685.307i	−0.525984	−	0.712377i
$963$		−	155.450i		−	0.161423i
$964$		−	376.416i		−	0.390473i
$965$	37.2491	−	64.5174i	0.0386001	−	0.0668574i
$966$	−471.010			−0.487588
$967$	1701.92			1.76000			0.879998	−	0.474977i	$-0.157544\pi$
$967$	1701.92			1.76000			0.879998	+	0.474977i	$0.157544\pi$
$968$	−799.986	−	1385.62i	−0.826432	−	1.43142i
$969$	−146.373	+	84.5084i	−0.151056	+	0.0872120i
$970$	148.997	−	258.070i	0.153605	−	0.266051i
$971$	−918.732	+	530.430i	−0.946171	+	0.546272i	−0.891889	−	0.452254i	$-0.850620\pi$
$971$	−918.732	+	530.430i	−0.946171	+	0.546272i	−0.0542813	+	0.998526i	$0.517287\pi$
$972$			62.3538i			0.0641500i
$973$	1065.99	+	615.451i	1.09557	+	0.632530i
$974$	263.073	−	455.656i	0.270096	−	0.467819i
$975$	492.240	−	55.5644i	0.504862	−	0.0569891i
$976$	−692.655	+	1199.71i	−0.709688	+	1.22921i
$977$	938.106	+	541.616i	0.960191	+	0.554366i	0.896232	−	0.443586i	$-0.146294\pi$
$977$	938.106	+	541.616i	0.960191	+	0.554366i	0.0639589	+	0.997953i	$0.479627\pi$
$978$	192.502	−	111.141i	0.196832	−	0.113641i
$979$	649.484	−	374.980i	0.663416	−	0.383023i
$980$	−296.007	+	170.900i	−0.302048	+	0.174387i
$981$	−341.247	+	197.019i	−0.347857	+	0.200835i
$982$			834.547i			0.849844i
$983$	865.993			0.880969			0.440485	−	0.897760i	$-0.354807\pi$
$983$	865.993			0.880969			0.440485	+	0.897760i	$0.354807\pi$
$984$	464.990	+	805.385i	0.472550	+	0.818481i
$985$	118.495	−	205.239i	0.120299	−	0.208364i
$986$	419.411	+	726.441i	0.425366	+	0.736756i
$987$			410.780i			0.416190i
$988$	−163.833	+	120.966i	−0.165823	+	0.122435i
$989$	−188.007			−0.190098
$990$	161.247	−	93.0962i	0.162876	−	0.0940366i
$991$	−1069.62	−	617.546i	−1.07933	−	0.623154i	−0.148617	−	0.988895i	$-0.547482\pi$
$991$	−1069.62	−	617.546i	−1.07933	−	0.623154i	−0.930717	+	0.365741i	$0.880816\pi$
$992$	893.324	−	1547.28i	0.900528	−	1.55976i
$993$		−	281.159i		−	0.283141i
$994$	1036.28			1.04253
$995$	−31.8711	−	55.2023i	−0.0320312	−	0.0554797i
$996$	487.484	−	281.449i	0.489442	−	0.282579i
$997$	259.127	+	448.821i	0.259907	+	0.450172i	0.966217	−	0.257731i	$-0.0829748\pi$
$997$	259.127	+	448.821i	0.259907	+	0.450172i	−0.706310	+	0.707903i	$0.749641\pi$
$998$	737.324	+	1277.08i	0.738802	+	1.27964i
$999$	−85.1237	+	147.439i	−0.0852089	+	0.147586i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.73205i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-2.00000 + 3.46410i) q^{4} -1.73205i q^{5} +3.46410i q^{6} +(-4.95819 - 8.58783i) q^{7} +8.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(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} +(-4.95819 - 8.58783i) q^{7} +8.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(-3.00000 + 1.73205i) q^{10} +(-8.95819 + 15.5160i) q^{11} +(6.00000 - 3.46410i) q^{12} +(-10.4582 + 7.72181i) q^{13} +(-9.91638 + 17.1757i) q^{14} +(-1.50000 + 2.59808i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(12.4582 + 21.5782i) q^{17} +(3.00000 - 5.19615i) q^{18} +(-1.95819 - 3.39168i) q^{19} +(6.00000 + 3.46410i) q^{20} +17.1757i q^{21} +35.8328 q^{22} +(-11.8746 - 6.85578i) q^{23} +(-12.0000 - 6.92820i) q^{24} +22.0000 q^{25} +(23.8328 + 10.3923i) q^{26} -5.19615i q^{27} +39.6655 q^{28} +(-8.41638 + 14.5776i) q^{29} +6.00000 q^{30} -55.8328 q^{31} +(-16.0000 + 27.7128i) q^{32} +(26.8746 - 15.5160i) q^{33} +(24.9164 - 43.1564i) q^{34} +(-14.8746 + 8.58783i) q^{35} -12.0000 q^{36} +(-28.3746 - 16.3821i) q^{37} +(-3.91638 + 6.78336i) q^{38} +(22.3746 - 2.52566i) q^{39} -13.8564i q^{40} +(-58.1237 - 33.5577i) q^{41} +(29.7491 - 17.1757i) q^{42} +(11.8746 - 6.85578i) q^{43} +(-35.8328 - 62.0641i) q^{44} +(4.50000 - 2.59808i) q^{45} +27.4231i q^{46} +23.9164 q^{47} +27.7128i q^{48} +(-24.6672 + 42.7249i) q^{49} +(-22.0000 - 38.1051i) q^{50} -43.1564i q^{51} +(-5.83275 - 51.6718i) q^{52} -1.16725 q^{53} +(-9.00000 + 5.19615i) q^{54} +(26.8746 + 15.5160i) q^{55} +(-39.6655 - 68.7027i) q^{56} +6.78336i q^{57} +33.6655 q^{58} +(28.0000 + 48.4974i) q^{59} +(-6.00000 - 10.3923i) q^{60} +(-43.2909 - 74.9821i) q^{61} +(55.8328 + 96.7052i) q^{62} +(14.8746 - 25.7635i) q^{63} +64.0000 q^{64} +(13.3746 + 18.1141i) q^{65} +(-53.7491 - 31.0321i) q^{66} +(-31.7073 + 54.9187i) q^{67} -99.6655 q^{68} +(11.8746 + 20.5673i) q^{69} +(29.7491 + 17.1757i) q^{70} +(-26.1254 - 45.2506i) q^{71} +(12.0000 + 20.7846i) q^{72} -126.150i q^{73} +65.5282i q^{74} +(-33.0000 - 19.0526i) q^{75} +15.6655 q^{76} +177.666 q^{77} +(-26.7491 - 36.2282i) q^{78} -34.3513i q^{79} +(-24.0000 + 13.8564i) q^{80} +(-4.50000 + 7.79423i) q^{81} +134.231i q^{82} +81.2474 q^{83} +(-59.4983 - 34.3513i) q^{84} +(37.3746 - 21.5782i) q^{85} +(-23.7491 - 13.7116i) q^{86} +(25.2491 - 14.5776i) q^{87} +(-71.6655 + 124.128i) q^{88} +(-36.2509 - 20.9295i) q^{89} +(-9.00000 - 5.19615i) q^{90} +(118.167 + 51.5270i) q^{91} +(47.4983 - 27.4231i) q^{92} +(83.7491 + 48.3526i) q^{93} +(-23.9164 - 41.4244i) q^{94} +(-5.87456 + 3.39168i) q^{95} +(48.0000 - 27.7128i) q^{96} +(-74.4983 + 43.0116i) q^{97} +98.6690 q^{98} -53.7491 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

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Database

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