LMFDB - Embedded newform 57.3.g.b.46.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [57,3,Mod(31,57)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(57, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("57.31");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 57 = 3 \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	57.g (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.55313750685$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{6})$
Coefficient field:	6.0.92607408.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 20x^{4} - 35x^{3} + 94x^{2} - 77x + 43 $ x^6 - 3x^5 + 20x^4 - 35x^3 + 94x^2 - 77*x + 43
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			46.3
Root			$0.500000 + 2.69511i$ of defining polynomial
Character	$\chi$	$=$	57.46
Dual form			57.3.g.b.31.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.08403 + 1.78057i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(4.34085 + 7.51857i) q^{4} +(2.32722 - 4.03087i) q^{5} +(-3.08403 - 5.34170i) q^{6} -10.6817 q^{7} +16.6722i q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(3.08403 + 1.78057i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(4.34085 + 7.51857i) q^{4} +(2.32722 - 4.03087i) q^{5} +(-3.08403 - 5.34170i) q^{6} -10.6817 q^{7} +16.6722i q^{8} +(1.50000 + 2.59808i) q^{9} +(14.3545 - 8.28756i) q^{10} -6.37280 q^{11} -15.0371i q^{12} +(15.3770 - 8.87792i) q^{13} +(-32.9427 - 19.0195i) q^{14} +(-6.98167 + 4.03087i) q^{15} +(-12.3225 + 21.3432i) q^{16} +(-5.84976 + 10.1321i) q^{17} +10.6834i q^{18} +(-3.88643 - 18.5983i) q^{19} +40.4085 q^{20} +(16.0225 + 9.25062i) q^{21} +(-19.6539 - 11.3472i) q^{22} +(13.9817 + 24.2170i) q^{23} +(14.4385 - 25.0082i) q^{24} +(1.66807 + 2.88918i) q^{25} +63.2310 q^{26} -5.19615i q^{27} +(-46.3676 - 80.3110i) q^{28} +(-33.2498 + 19.1968i) q^{29} -28.7089 q^{30} +42.9440i q^{31} +(-18.2521 + 10.5379i) q^{32} +(9.55920 + 5.51901i) q^{33} +(-36.0817 + 20.8318i) q^{34} +(-24.8587 + 43.0565i) q^{35} +(-13.0225 + 22.5557i) q^{36} -33.9790i q^{37} +(21.1296 - 64.2778i) q^{38} -30.7540 q^{39} +(67.2032 + 38.7998i) q^{40} +(16.3728 + 9.45284i) q^{41} +(32.9427 + 57.0585i) q^{42} +(26.5089 - 45.9148i) q^{43} +(-27.6634 - 47.9143i) q^{44} +13.9633 q^{45} +99.5813i q^{46} +(-12.0272 - 20.8318i) q^{47} +(36.9675 - 21.3432i) q^{48} +65.0986 q^{49} +11.8804i q^{50} +(17.5493 - 10.1321i) q^{51} +(133.499 + 77.0754i) q^{52} +(-13.3224 + 7.69168i) q^{53} +(9.25210 - 16.0251i) q^{54} +(-14.8309 + 25.6879i) q^{55} -178.087i q^{56} +(-10.2769 + 31.2632i) q^{57} -136.725 q^{58} +(25.6539 + 14.8113i) q^{59} +(-60.6127 - 34.9948i) q^{60} +(-21.3403 - 36.9626i) q^{61} +(-76.4648 + 132.441i) q^{62} +(-16.0225 - 27.7519i) q^{63} +23.5266 q^{64} -82.6436i q^{65} +(19.6539 + 34.0416i) q^{66} +(-15.1585 + 8.75178i) q^{67} -101.572 q^{68} -48.4339i q^{69} +(-153.330 + 88.5252i) q^{70} +(-74.6028 - 43.0719i) q^{71} +(-43.3155 + 25.0082i) q^{72} +(46.2352 - 80.0817i) q^{73} +(60.5019 - 104.792i) q^{74} -5.77836i q^{75} +(122.962 - 109.953i) q^{76} +68.0723 q^{77} +(-94.8465 - 54.7596i) q^{78} +(-26.3908 - 15.2367i) q^{79} +(57.3545 + 99.3409i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(33.6629 + 58.3058i) q^{82} +77.1154 q^{83} +160.622i q^{84} +(27.2274 + 47.1592i) q^{85} +(163.509 - 94.4019i) q^{86} +66.4996 q^{87} -106.248i q^{88} +(-76.8129 + 44.3479i) q^{89} +(43.0634 + 24.8627i) q^{90} +(-164.253 + 94.8312i) q^{91} +(-121.385 + 210.244i) q^{92} +(37.1906 - 64.4160i) q^{93} -85.6613i q^{94} +(-84.0118 - 27.6166i) q^{95} +36.5042 q^{96} +(-1.82351 - 1.05281i) q^{97} +(200.766 + 115.912i) q^{98} +(-9.55920 - 16.5570i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} - 9 q^{3} + 5 q^{4} + 4 q^{5} - 3 q^{6} - 22 q^{7} + 9 q^{9}+O(q^{10}) $ 6 * q + 3 * q^2 - 9 * q^3 + 5 * q^4 + 4 * q^5 - 3 * q^6 - 22 * q^7 + 9 * q^9	$ 6 q + 3 q^{2} - 9 q^{3} + 5 q^{4} + 4 q^{5} - 3 q^{6} - 22 q^{7} + 9 q^{9} + 54 q^{10} - 36 q^{11} - 3 q^{13} - 57 q^{14} - 12 q^{15} - 23 q^{16} + 38 q^{17} - 10 q^{19} + 32 q^{20} + 33 q^{21} + 36 q^{22} + 54 q^{23} + 39 q^{24} - 21 q^{25} + 118 q^{26} - 101 q^{28} - 102 q^{29} - 108 q^{30} - 63 q^{32} + 54 q^{33} - 150 q^{34} - 24 q^{35} - 15 q^{36} + 119 q^{38} + 6 q^{39} + 30 q^{40} + 96 q^{41} + 57 q^{42} + 107 q^{43} - 94 q^{44} + 24 q^{45} - 50 q^{47} + 69 q^{48} - 48 q^{49} - 114 q^{51} + 399 q^{52} - 90 q^{53} + 9 q^{54} + 148 q^{55} - 3 q^{57} - 116 q^{58} - 48 q^{60} + 27 q^{61} - 121 q^{62} - 33 q^{63} + 46 q^{64} - 36 q^{66} - 39 q^{67} - 388 q^{68} - 354 q^{70} + 84 q^{71} - 117 q^{72} - 77 q^{73} + 219 q^{74} + 215 q^{76} + 260 q^{77} - 177 q^{78} + 9 q^{79} + 312 q^{80} - 27 q^{81} - 4 q^{82} - 348 q^{83} + 68 q^{85} + 249 q^{86} + 204 q^{87} - 72 q^{89} + 162 q^{90} - 393 q^{91} - 118 q^{92} + 129 q^{93} + 104 q^{95} + 126 q^{96} - 228 q^{97} + 540 q^{98} - 54 q^{99}+O(q^{100}) $ 6 * q + 3 * q^2 - 9 * q^3 + 5 * q^4 + 4 * q^5 - 3 * q^6 - 22 * q^7 + 9 * q^9 + 54 * q^10 - 36 * q^11 - 3 * q^13 - 57 * q^14 - 12 * q^15 - 23 * q^16 + 38 * q^17 - 10 * q^19 + 32 * q^20 + 33 * q^21 + 36 * q^22 + 54 * q^23 + 39 * q^24 - 21 * q^25 + 118 * q^26 - 101 * q^28 - 102 * q^29 - 108 * q^30 - 63 * q^32 + 54 * q^33 - 150 * q^34 - 24 * q^35 - 15 * q^36 + 119 * q^38 + 6 * q^39 + 30 * q^40 + 96 * q^41 + 57 * q^42 + 107 * q^43 - 94 * q^44 + 24 * q^45 - 50 * q^47 + 69 * q^48 - 48 * q^49 - 114 * q^51 + 399 * q^52 - 90 * q^53 + 9 * q^54 + 148 * q^55 - 3 * q^57 - 116 * q^58 - 48 * q^60 + 27 * q^61 - 121 * q^62 - 33 * q^63 + 46 * q^64 - 36 * q^66 - 39 * q^67 - 388 * q^68 - 354 * q^70 + 84 * q^71 - 117 * q^72 - 77 * q^73 + 219 * q^74 + 215 * q^76 + 260 * q^77 - 177 * q^78 + 9 * q^79 + 312 * q^80 - 27 * q^81 - 4 * q^82 - 348 * q^83 + 68 * q^85 + 249 * q^86 + 204 * q^87 - 72 * q^89 + 162 * q^90 - 393 * q^91 - 118 * q^92 + 129 * q^93 + 104 * q^95 + 126 * q^96 - 228 * q^97 + 540 * q^98 - 54 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/57\mathbb{Z}\right)^\times$.

$n$	$20$	$40$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	3.08403	+	1.78057i	1.54202	+	0.890284i	0.998711	+	0.0507494i	$0.0161610\pi$
$2$	3.08403	+	1.78057i	1.54202	+	0.890284i	0.543306	+	0.839535i	$0.317172\pi$
$3$	−1.50000	−	0.866025i	−0.500000	−	0.288675i
$3$	−1.50000	−	0.866025i	−0.500000	−	0.288675i
$4$	4.34085	+	7.51857i	1.08521	+	1.87964i
$5$	2.32722	−	4.03087i	0.465445	−	0.806174i	−0.533777	−	0.845625i	$-0.679228\pi$
$5$	2.32722	−	4.03087i	0.465445	−	0.806174i	0.999221	+	0.0394517i	$0.0125611\pi$
$6$	−3.08403	−	5.34170i	−0.514006	−	0.890284i
$7$	−10.6817			−1.52596			−0.762978	−	0.646424i	$-0.776264\pi$
$7$	−10.6817			−1.52596			−0.762978	+	0.646424i	$0.776264\pi$
$8$			16.6722i			2.08402i
$9$	1.50000	+	2.59808i	0.166667	+	0.288675i
$10$	14.3545	−	8.28756i	1.43545	−	0.828756i
$11$	−6.37280			−0.579346			−0.289673	−	0.957126i	$-0.593547\pi$
$11$	−6.37280			−0.579346			−0.289673	+	0.957126i	$0.593547\pi$
$12$		−	15.0371i		−	1.25309i
$13$	15.3770	−	8.87792i	1.18285	−	0.682917i	0.226176	−	0.974087i	$-0.427378\pi$
$13$	15.3770	−	8.87792i	1.18285	−	0.682917i	0.956671	+	0.291170i	$0.0940444\pi$
$14$	−32.9427	−	19.0195i	−2.35305	−	1.35853i
$15$	−6.98167	+	4.03087i	−0.465445	+	0.268725i
$16$	−12.3225	+	21.3432i	−0.770157	+	1.33395i
$17$	−5.84976	+	10.1321i	−0.344104	+	0.596005i	−0.985191	−	0.171463i	$-0.945151\pi$
$17$	−5.84976	+	10.1321i	−0.344104	+	0.596005i	0.641087	+	0.767468i	$0.278484\pi$
$18$			10.6834i			0.593523i
$19$	−3.88643	−	18.5983i	−0.204549	−	0.978856i
$19$	−3.88643	−	18.5983i	−0.204549	−	0.978856i
$20$	40.4085			2.02042
$21$	16.0225	+	9.25062i	0.762978	+	0.440506i
$22$	−19.6539	−	11.3472i	−0.893361	−	0.515782i
$23$	13.9817	+	24.2170i	0.607899	+	1.05291i	0.991586	+	0.129448i	$0.0413206\pi$
$23$	13.9817	+	24.2170i	0.607899	+	1.05291i	−0.383688	+	0.923463i	$0.625346\pi$
$24$	14.4385	−	25.0082i	0.601604	−	1.04201i
$25$	1.66807	+	2.88918i	0.0667228	+	0.115567i
$26$	63.2310			2.43196
$27$		−	5.19615i		−	0.192450i
$28$	−46.3676	−	80.3110i	−1.65599	−	2.86825i
$29$	−33.2498	+	19.1968i	−1.14655	+	0.661958i	−0.948043	−	0.318142i	$-0.896941\pi$
$29$	−33.2498	+	19.1968i	−1.14655	+	0.661958i	−0.198502	+	0.980100i	$0.563608\pi$
$30$	−28.7089			−0.956965
$31$			42.9440i			1.38529i	0.721278	+	0.692645i	$0.243555\pi$
$31$			42.9440i			1.38529i	−0.721278	+	0.692645i	$0.756445\pi$
$32$	−18.2521	+	10.5379i	−0.570378	+	0.329308i
$33$	9.55920	+	5.51901i	0.289673	+	0.167243i
$34$	−36.0817	+	20.8318i	−1.06123	+	0.612700i
$35$	−24.8587	+	43.0565i	−0.710248	+	1.23019i
$36$	−13.0225	+	22.5557i	−0.361737	+	0.626547i
$37$		−	33.9790i		−	0.918351i	−0.888346	−	0.459176i	$-0.848145\pi$
$37$		−	33.9790i		−	0.918351i	0.888346	−	0.459176i	$-0.151855\pi$
$38$	21.1296	−	64.2778i	0.556043	−	1.69152i
$39$	−30.7540			−0.788565
$40$	67.2032	+	38.7998i	1.68008	+	0.969995i
$41$	16.3728	+	9.45284i	0.399337	+	0.230557i	0.686198	−	0.727415i	$-0.259278\pi$
$41$	16.3728	+	9.45284i	0.399337	+	0.230557i	−0.286861	+	0.957972i	$0.592612\pi$
$42$	32.9427	+	57.0585i	0.784350	+	1.35853i
$43$	26.5089	−	45.9148i	0.616486	−	1.06779i	−0.373635	−	0.927576i	$-0.621889\pi$
$43$	26.5089	−	45.9148i	0.616486	−	1.06779i	0.990122	−	0.140210i	$-0.0447778\pi$
$44$	−27.6634	−	47.9143i	−0.628713	−	1.08896i
$45$	13.9633			0.310296
$46$			99.5813i			2.16481i
$47$	−12.0272	−	20.8318i	−0.255899	−	0.443230i	0.709240	−	0.704967i	$-0.249038\pi$
$47$	−12.0272	−	20.8318i	−0.255899	−	0.443230i	−0.965139	+	0.261737i	$0.915705\pi$
$48$	36.9675	−	21.3432i	0.770157	−	0.444650i
$49$	65.0986			1.32854
$50$			11.8804i			0.237609i
$51$	17.5493	−	10.1321i	0.344104	−	0.198668i
$52$	133.499	+	77.0754i	2.56728	+	1.48222i
$53$	−13.3224	+	7.69168i	−0.251366	+	0.145126i	−0.620389	−	0.784294i	$-0.713025\pi$
$53$	−13.3224	+	7.69168i	−0.251366	+	0.145126i	0.369024	+	0.929420i	$0.379692\pi$
$54$	9.25210	−	16.0251i	0.171335	−	0.296761i
$55$	−14.8309	+	25.6879i	−0.269653	+	0.467053i
$56$		−	178.087i		−	3.18012i
$57$	−10.2769	+	31.2632i	−0.180297	+	0.548476i
$58$	−136.725			−2.35732
$59$	25.6539	+	14.8113i	0.434813	+	0.251039i	0.701395	−	0.712773i	$-0.252561\pi$
$59$	25.6539	+	14.8113i	0.434813	+	0.251039i	−0.266582	+	0.963812i	$0.585894\pi$
$60$	−60.6127	−	34.9948i	−1.01021	−	0.583246i
$61$	−21.3403	−	36.9626i	−0.349842	−	0.605944i	0.636379	−	0.771376i	$-0.280431\pi$
$61$	−21.3403	−	36.9626i	−0.349842	−	0.605944i	−0.986221	+	0.165433i	$0.947098\pi$
$62$	−76.4648	+	132.441i	−1.23330	+	2.13614i
$63$	−16.0225	−	27.7519i	−0.254326	−	0.440506i
$64$	23.5266			0.367603
$65$		−	82.6436i		−	1.27144i
$66$	19.6539	+	34.0416i	0.297787	+	0.515782i
$67$	−15.1585	+	8.75178i	−0.226247	+	0.130624i	−0.608839	−	0.793294i	$-0.708365\pi$
$67$	−15.1585	+	8.75178i	−0.226247	+	0.130624i	0.382593	+	0.923917i	$0.375031\pi$
$68$	−101.572			−1.49370
$69$		−	48.4339i		−	0.701941i
$70$	−153.330	+	88.5252i	−2.19043	+	1.26465i
$71$	−74.6028	−	43.0719i	−1.05074	−	0.606647i	−0.127886	−	0.991789i	$-0.540819\pi$
$71$	−74.6028	−	43.0719i	−1.05074	−	0.606647i	−0.922857	+	0.385142i	$0.874153\pi$
$72$	−43.3155	+	25.0082i	−0.601604	+	0.347336i
$73$	46.2352	−	80.0817i	0.633359	−	1.09701i	−0.353502	−	0.935434i	$-0.615009\pi$
$73$	46.2352	−	80.0817i	0.633359	−	1.09701i	0.986860	−	0.161576i	$-0.0516576\pi$
$74$	60.5019	−	104.792i	0.817593	−	1.41611i
$75$		−	5.77836i		−	0.0770448i
$76$	122.962	−	109.953i	1.61792	−	1.44674i
$77$	68.0723			0.884056
$78$	−94.8465	−	54.7596i	−1.21598	−	0.702047i
$79$	−26.3908	−	15.2367i	−0.334060	−	0.192870i	0.323582	−	0.946200i	$-0.395113\pi$
$79$	−26.3908	−	15.2367i	−0.334060	−	0.192870i	−0.657642	+	0.753330i	$0.728446\pi$
$80$	57.3545	+	99.3409i	0.716931	+	1.24176i
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$	33.6629	+	58.3058i	0.410523	+	0.711046i
$83$	77.1154			0.929101			0.464551	−	0.885547i	$-0.346216\pi$
$83$	77.1154			0.929101			0.464551	+	0.885547i	$0.346216\pi$
$84$			160.622i			1.91217i
$85$	27.2274	+	47.1592i	0.320322	+	0.554815i
$86$	163.509	−	94.4019i	1.90127	−	1.09770i
$87$	66.4996			0.764364
$88$		−	106.248i		−	1.20737i
$89$	−76.8129	+	44.3479i	−0.863066	+	0.498291i	−0.865038	−	0.501707i	$-0.832706\pi$
$89$	−76.8129	+	44.3479i	−0.863066	+	0.498291i	0.00197195	+	0.999998i	$0.499372\pi$
$90$	43.0634	+	24.8627i	0.478482	+	0.276252i
$91$	−164.253	+	94.8312i	−1.80497	+	1.04210i
$92$	−121.385	+	210.244i	−1.31940	+	2.28526i
$93$	37.1906	−	64.4160i	0.399899	−	0.692645i
$94$		−	85.6613i		−	0.911291i
$95$	−84.0118	−	27.6166i	−0.884334	−	0.290702i
$96$	36.5042			0.380252
$97$	−1.82351	−	1.05281i	−0.0187991	−	0.0108537i	0.490571	−	0.871401i	$-0.336788\pi$
$97$	−1.82351	−	1.05281i	−0.0187991	−	0.0108537i	−0.509370	+	0.860548i	$0.670122\pi$
$98$	200.766	+	115.912i	2.04864	+	1.18278i
$99$	−9.55920	−	16.5570i	−0.0965576	−	0.167243i
$100$	−14.4817	+	25.0830i	−0.144817	+	0.250830i
$101$	−13.7690	−	23.8486i	−0.136327	−	0.236125i	0.789777	−	0.613395i	$-0.210196\pi$
$101$	−13.7690	−	23.8486i	−0.136327	−	0.236125i	−0.926104	+	0.377269i	$0.876863\pi$
$102$	72.1635			0.707485
$103$		−	102.351i		−	0.993696i	−0.867837	−	0.496848i	$-0.834491\pi$
$103$		−	102.351i		−	0.993696i	0.867837	−	0.496848i	$-0.165509\pi$
$104$	148.014	+	256.368i	1.42321	+	2.46508i
$105$	74.5760	−	43.0565i	0.710248	−	0.410062i
$106$	−54.7823			−0.516814
$107$		−	0.549592i		−	0.00513638i	−0.999997	−	0.00256819i	$-0.999183\pi$
$107$		−	0.549592i		−	0.00513638i	0.999997	−	0.00256819i	$-0.000817481\pi$
$108$	39.0676	−	22.5557i	0.361737	−	0.208849i
$109$	80.7219	+	46.6048i	0.740568	+	0.427567i	0.822276	−	0.569089i	$-0.192704\pi$
$109$	80.7219	+	46.6048i	0.740568	+	0.427567i	−0.0817076	+	0.996656i	$0.526037\pi$
$110$	−91.4782	+	52.8150i	−0.831620	+	0.480136i
$111$	−29.4267	+	50.9685i	−0.265105	+	0.459176i
$112$	131.625	−	227.982i	1.17523	−	2.03555i
$113$			55.4186i			0.490430i	0.969469	+	0.245215i	$0.0788586\pi$
$113$			55.4186i			0.490430i	−0.969469	+	0.245215i	$0.921141\pi$
$114$	−87.3606	+	78.1179i	−0.766321	+	0.685244i
$115$	130.154			1.13177
$116$	−288.665	−	166.661i	−2.48849	−	1.43673i
$117$	46.1310	+	26.6338i	0.394282	+	0.227639i
$118$	52.7451	+	91.3572i	0.446992	+	0.774214i
$119$	62.4854	−	108.228i	0.525087	−	0.909478i
$120$	−67.2032	−	116.399i	−0.560027	−	0.969995i
$121$	−80.3874			−0.664359
$122$		−	151.992i		−	1.24583i
$123$	−16.3728	−	28.3585i	−0.133112	−	0.230557i
$124$	−322.877	+	186.413i	−2.60385	+	1.50333i
$125$	131.889			1.05511
$126$		−	114.117i		−	0.905690i
$127$	−82.7181	+	47.7573i	−0.651324	+	0.376042i	−0.788963	−	0.614441i	$-0.789382\pi$
$127$	−82.7181	+	47.7573i	−0.651324	+	0.376042i	0.137640	+	0.990482i	$0.456048\pi$
$128$	145.565	+	84.0422i	1.13723	+	0.656580i
$129$	−79.5267	+	45.9148i	−0.616486	+	0.355929i
$130$	147.153	−	254.876i	1.13194	−	1.96058i
$131$	−84.0762	+	145.624i	−0.641803	+	1.11164i	0.343227	+	0.939252i	$0.388480\pi$
$131$	−84.0762	+	145.624i	−0.641803	+	1.11164i	−0.985030	+	0.172383i	$0.944853\pi$
$132$			95.8287i			0.725975i
$133$	41.5136	+	198.661i	0.312133	+	1.49369i
$134$	−62.3326			−0.465168
$135$	−20.9450	−	12.0926i	−0.155148	−	0.0895748i
$136$	−168.924	−	97.5281i	−1.24209	−	0.717119i
$137$	59.3774	+	102.845i	0.433412	+	0.750691i	0.997165	−	0.0752526i	$-0.0239763\pi$
$137$	59.3774	+	102.845i	0.433412	+	0.750691i	−0.563753	+	0.825943i	$0.690643\pi$
$138$	86.2399	−	149.372i	0.624927	−	1.08240i
$139$	−55.1822	−	95.5784i	−0.396994	−	0.687614i	0.596359	−	0.802718i	$-0.296613\pi$
$139$	−55.1822	−	95.5784i	−0.396994	−	0.687614i	−0.993354	+	0.115104i	$0.963280\pi$
$140$	−431.631			−3.08308
$141$			41.6636i			0.295487i
$142$	−153.385	−	265.671i	−1.08018	−	1.87092i
$143$	−97.9947	+	56.5772i	−0.685277	+	0.395645i
$144$	−73.9351			−0.513438
$145$			178.701i			1.23242i
$146$	285.182	−	164.650i	1.95330	−	1.12774i
$147$	−97.6479	−	56.3770i	−0.664271	−	0.383517i
$148$	255.473	−	147.498i	1.72617	−	0.996605i
$149$	28.8719	−	50.0077i	0.193771	−	0.335622i	−0.752726	−	0.658334i	$-0.771261\pi$
$149$	28.8719	−	50.0077i	0.193771	−	0.335622i	0.946497	+	0.322712i	$0.104595\pi$
$150$	10.2888	−	17.8207i	0.0685918	−	0.118804i
$151$			205.459i			1.36066i	0.732908	+	0.680328i	$0.238163\pi$
$151$			205.459i			1.36066i	−0.732908	+	0.680328i	$0.761837\pi$
$152$	310.073	−	64.7951i	2.03996	−	0.426284i
$153$	−35.0986			−0.229402
$154$	209.937	+	121.207i	1.36323	+	0.787061i
$155$	173.102	+	99.9403i	1.11678	+	0.644776i
$156$	−133.499	−	231.226i	−0.855760	−	1.48222i
$157$	−55.6080	+	96.3159i	−0.354191	+	0.613477i	−0.986979	−	0.160848i	$-0.948577\pi$
$157$	−55.6080	+	96.3159i	−0.354191	+	0.613477i	0.632788	+	0.774325i	$0.281910\pi$
$158$	−54.2600	−	93.9811i	−0.343418	−	0.594817i
$159$	26.6448			0.167577
$160$			98.0958i			0.613099i
$161$	−149.348	−	258.678i	−0.927627	−	1.60670i
$162$	−27.7563	+	16.0251i	−0.171335	+	0.0989205i
$163$	69.1905			0.424481			0.212241	−	0.977217i	$-0.431924\pi$
$163$	69.1905			0.424481			0.212241	+	0.977217i	$0.431924\pi$
$164$			164.133i			1.00081i
$165$	44.4928	−	25.6879i	0.269653	−	0.155684i
$166$	237.827	+	137.309i	1.43269	+	0.827164i
$167$	181.817	−	104.972i	1.08873	−	0.628577i	0.155490	−	0.987837i	$-0.450304\pi$
$167$	181.817	−	104.972i	1.08873	−	0.628577i	0.933237	+	0.359261i	$0.116971\pi$
$168$	−154.228	+	267.130i	−0.918022	+	1.59006i
$169$	73.1350	−	126.674i	0.432751	−	0.749547i
$170$			193.921i			1.14071i
$171$	42.4901	−	37.9946i	0.248480	−	0.222191i
$172$	460.285			2.67607
$173$	−264.781	−	152.871i	−1.53053	−	0.883649i	−0.999337	−	0.0363949i	$-0.988413\pi$
$173$	−264.781	−	152.871i	−1.53053	−	0.883649i	−0.531188	−	0.847254i	$-0.678254\pi$
$174$	205.087	+	118.407i	1.17866	+	0.680501i
$175$	−17.8178	−	30.8613i	−0.101816	−	0.176351i
$176$	78.5290	−	136.016i	0.446187	−	0.772819i
$177$	−25.6539	−	44.4339i	−0.144938	−	0.251039i
$178$	−315.858			−1.77448
$179$			303.001i			1.69274i	0.532593	+	0.846371i	$0.321218\pi$
$179$			303.001i			1.69274i	−0.532593	+	0.846371i	$0.678782\pi$
$180$	60.6127	+	104.984i	0.336737	+	0.583246i
$181$	−62.8763	+	36.3016i	−0.347383	+	0.200561i	−0.663532	−	0.748148i	$-0.730943\pi$
$181$	−62.8763	+	36.3016i	−0.347383	+	0.200561i	0.316149	+	0.948709i	$0.397610\pi$
$182$	−675.414			−3.71107
$183$			73.9251i			0.403962i
$184$	−403.749	+	233.104i	−2.19429	+	1.26687i
$185$	−136.965	−	79.0767i	−0.740350	−	0.427442i
$186$	229.394	−	132.441i	1.23330	−	0.712048i
$187$	37.2794	−	64.5698i	0.199355	−	0.345293i
$188$	104.417	−	180.855i	0.555409	−	0.961997i
$189$			55.5037i			0.293670i
$190$	−209.922	−	234.759i	−1.10485	−	1.23558i
$191$	−48.5734			−0.254311			−0.127156	−	0.991883i	$-0.540585\pi$
$191$	−48.5734			−0.254311			−0.127156	+	0.991883i	$0.540585\pi$
$192$	−35.2899	−	20.3747i	−0.183802	−	0.106118i
$193$	9.48401	+	5.47559i	0.0491399	+	0.0283710i	0.524369	−	0.851491i	$-0.324301\pi$
$193$	9.48401	+	5.47559i	0.0491399	+	0.0283710i	−0.475229	+	0.879862i	$0.657635\pi$
$194$	−3.74919	−	6.49378i	−0.0193257	−	0.0334731i
$195$	−71.5715	+	123.965i	−0.367033	+	0.635720i
$196$	282.583	+	489.448i	1.44175	+	2.49718i
$197$	104.442			0.530163			0.265082	−	0.964226i	$-0.414601\pi$
$197$	104.442			0.530163			0.265082	+	0.964226i	$0.414601\pi$
$198$		−	68.0833i		−	0.343855i
$199$	−140.643	−	243.602i	−0.706751	−	1.22413i	−0.966056	−	0.258333i	$-0.916827\pi$
$199$	−140.643	−	243.602i	−0.706751	−	1.22413i	0.259305	−	0.965795i	$-0.416506\pi$
$200$	−48.1689	+	27.8103i	−0.240844	+	0.139052i
$201$	30.3171			0.150831
$202$		−	98.0667i		−	0.485479i
$203$	355.164	−	205.054i	1.74958	−	1.01012i
$204$	152.358	+	87.9637i	0.746851	+	0.431194i
$205$	76.2063	−	43.9977i	0.371738	−	0.214623i
$206$	182.242	−	315.653i	0.884672	−	1.53230i
$207$	−41.9450	+	72.6509i	−0.202633	+	0.350970i
$208$			437.593i			2.10381i
$209$	24.7674	+	118.523i	0.118504	+	0.567096i
$210$	306.660			1.46029
$211$	89.2808	+	51.5463i	0.423132	+	0.244295i	0.696416	−	0.717638i	$-0.254777\pi$
$211$	89.2808	+	51.5463i	0.423132	+	0.244295i	−0.273285	+	0.961933i	$0.588110\pi$
$212$	−115.661	−	66.7768i	−0.545570	−	0.314985i
$213$	74.6028	+	129.216i	0.350248	+	0.606647i
$214$	0.978587	−	1.69496i	0.00457284	−	0.00792038i
$215$	−123.384	−	213.708i	−0.573880	−	0.993990i
$216$	86.6310			0.401070
$217$		−	458.715i		−	2.11389i
$218$	165.966	+	287.462i	0.761313	+	1.31863i
$219$	−138.706	+	80.0817i	−0.633359	+	0.365670i
$220$	−257.515			−1.17052
$221$			207.735i			0.939977i
$222$	−181.506	+	104.792i	−0.817593	+	0.472038i
$223$	−68.9560	−	39.8118i	−0.309220	−	0.178528i	0.337357	−	0.941377i	$-0.390467\pi$
$223$	−68.9560	−	39.8118i	−0.309220	−	0.178528i	−0.646577	+	0.762848i	$0.723800\pi$
$224$	194.963	−	112.562i	0.870372	−	0.502510i
$225$	−5.00421	+	8.66754i	−0.0222409	+	0.0385224i
$226$	−98.6766	+	170.913i	−0.436622	+	0.756252i
$227$			131.031i			0.577228i	0.957446	+	0.288614i	$0.0931944\pi$
$227$			131.031i			0.577228i	−0.957446	+	0.288614i	$0.906806\pi$
$228$	−279.665	+	58.4407i	−1.22660	+	0.256319i
$229$	30.3537			0.132549			0.0662745	−	0.997801i	$-0.478889\pi$
$229$	30.3537			0.132549			0.0662745	+	0.997801i	$0.478889\pi$
$230$	401.399	+	231.748i	1.74521	+	1.00760i
$231$	−102.108	−	58.9524i	−0.442028	−	0.255205i
$232$	−320.052	−	554.346i	−1.37953	−	2.38942i
$233$	−47.0484	+	81.4902i	−0.201924	+	0.349743i	−0.949148	−	0.314829i	$-0.898053\pi$
$233$	−47.0484	+	81.4902i	−0.201924	+	0.349743i	0.747224	+	0.664572i	$0.231386\pi$
$234$	94.8465	+	164.279i	0.405327	+	0.702047i
$235$	−111.960			−0.476427
$236$			257.175i			1.08972i
$237$	26.3908	+	45.7101i	0.111353	+	0.192870i
$238$	385.414	−	222.519i	1.61939	−	0.934954i
$239$	375.297			1.57028			0.785141	−	0.619317i	$-0.212591\pi$
$239$	375.297			1.57028			0.785141	+	0.619317i	$0.212591\pi$
$240$		−	198.682i		−	0.827840i
$241$	0.482424	−	0.278528i	0.00200176	−	0.00115572i	−0.498999	−	0.866603i	$-0.666299\pi$
$241$	0.482424	−	0.278528i	0.00200176	−	0.00115572i	0.501001	+	0.865447i	$0.332965\pi$
$242$	−247.917	−	143.135i	−1.02445	−	0.591468i
$243$	13.5000	−	7.79423i	0.0555556	−	0.0320750i
$244$	185.270	−	320.898i	0.759305	−	1.31515i
$245$	151.499	−	262.404i	0.618363	−	1.07104i
$246$		−	116.612i		−	0.474031i
$247$	−224.876	−	251.482i	−0.910428	−	1.01815i
$248$	−715.969			−2.88697
$249$	−115.673	−	66.7839i	−0.464551	−	0.268208i
$250$	406.750	+	234.837i	1.62700	+	0.939350i
$251$	117.309	+	203.185i	0.467367	+	0.809504i	0.999305	−	0.0372799i	$-0.0118693\pi$
$251$	117.309	+	203.185i	0.467367	+	0.809504i	−0.531938	+	0.846783i	$0.678536\pi$
$252$	139.103	−	240.933i	0.551995	−	0.956084i
$253$	−89.1024	−	154.330i	−0.352183	−	0.610000i
$254$	−340.141			−1.33914
$255$		−	94.3185i		−	0.369876i
$256$	252.232	+	436.879i	0.985283	+	1.70656i
$257$	−11.0702	+	6.39141i	−0.0430749	+	0.0248693i	−0.521383	−	0.853323i	$-0.674584\pi$
$257$	−11.0702	+	6.39141i	−0.0430749	+	0.0248693i	0.478308	+	0.878192i	$0.341250\pi$
$258$	−327.018			−1.26751
$259$			362.953i			1.40136i
$260$	621.361	−	358.743i	2.38985	−	1.37978i
$261$	−99.7494	−	57.5904i	−0.382182	−	0.220653i
$262$	−518.588	+	299.407i	−1.97934	+	1.14277i
$263$	106.457	−	184.389i	0.404780	−	0.701099i	−0.589516	−	0.807757i	$-0.700681\pi$
$263$	106.457	−	184.389i	0.404780	−	0.701099i	0.994296	+	0.106657i	$0.0340148\pi$
$264$	−92.0138	+	159.372i	−0.348537	+	0.603684i
$265$			71.6010i			0.270193i
$266$	−225.700	+	686.595i	−0.848497	+	2.58119i
$267$	153.626			0.575377
$268$	−131.602	−	75.9803i	−0.491051	−	0.283508i
$269$	−438.717	−	253.293i	−1.63092	−	0.941610i	−0.983811	−	0.179211i	$-0.942646\pi$
$269$	−438.717	−	253.293i	−1.63092	−	0.941610i	−0.647106	−	0.762400i	$-0.724021\pi$
$270$	−43.0634	−	74.5880i	−0.159494	−	0.276252i
$271$	110.063	−	190.635i	0.406136	−	0.703449i	−0.588317	−	0.808631i	$-0.700209\pi$
$271$	110.063	−	190.635i	0.406136	−	0.703449i	0.994453	+	0.105182i	$0.0335425\pi$
$272$	−144.168	−	249.706i	−0.530028	−	0.918035i
$273$	328.505			1.20332
$274$			422.902i			1.54344i
$275$	−10.6303	−	18.4122i	−0.0386556	−	0.0669534i
$276$	364.154	−	210.244i	1.31940	−	0.761754i
$277$	262.083			0.946148			0.473074	−	0.881023i	$-0.343144\pi$
$277$	262.083			0.946148			0.473074	+	0.881023i	$0.343144\pi$
$278$		−	393.023i		−	1.41375i
$279$	−111.572	+	64.4160i	−0.399899	+	0.230882i
$280$	−717.844	−	414.448i	−2.56373	−	1.48017i
$281$	−346.203	+	199.880i	−1.23204	+	0.711317i	−0.967454	−	0.253046i	$-0.918568\pi$
$281$	−346.203	+	199.880i	−1.23204	+	0.711317i	−0.264583	+	0.964363i	$0.585234\pi$
$282$	−74.1849	+	128.492i	−0.263067	+	0.455645i
$283$	41.2358	−	71.4225i	0.145710	−	0.252376i	−0.783928	−	0.620852i	$-0.786787\pi$
$283$	41.2358	−	71.4225i	0.145710	−	0.252376i	0.929637	+	0.368475i	$0.120120\pi$
$284$		−	747.875i		−	2.63336i
$285$	102.101	+	114.181i	0.358249	+	0.400636i
$286$	−402.959			−1.40895
$287$	−174.889	−	100.972i	−0.609370	−	0.351820i
$288$	−54.7563	−	31.6136i	−0.190126	−	0.109769i
$289$	76.0605	+	131.741i	0.263185	+	0.455850i
$290$	−318.189	+	551.120i	−1.09720	+	1.90041i
$291$	1.82351	+	3.15842i	0.00626637	+	0.0108537i
$292$	802.800			2.74931
$293$		−	223.552i		−	0.762977i	−0.924374	−	0.381489i	$-0.875412\pi$
$293$		−	223.552i		−	0.762977i	0.924374	−	0.381489i	$-0.124588\pi$
$294$	−200.766	−	347.737i	−0.682878	−	1.18278i
$295$	119.405	−	68.9384i	0.404762	−	0.233690i
$296$	566.503			1.91386
$297$			33.1141i			0.111495i
$298$	178.084	−	102.817i	0.597598	−	0.345023i
$299$	429.993	+	248.256i	1.43810	+	0.830289i
$300$	43.4450	−	25.0830i	0.144817	−	0.0836099i
$301$	−283.160	+	490.448i	−0.940731	+	1.62939i
$302$	−365.834	+	633.643i	−1.21137	+	2.09816i
$303$			47.6973i			0.157417i
$304$	444.838	+	146.229i	1.46328	+	0.481015i
$305$	−198.655			−0.651328
$306$	−108.245	−	62.4954i	−0.353743	−	0.204233i
$307$	339.034	+	195.741i	1.10434	+	0.637594i	0.937359	−	0.348366i	$-0.113263\pi$
$307$	339.034	+	195.741i	1.10434	+	0.637594i	0.166986	+	0.985959i	$0.446597\pi$
$308$	295.492	+	511.806i	0.959388	+	1.66171i
$309$	−88.6383	+	153.526i	−0.286855	+	0.496848i
$310$	355.901	+	616.439i	1.14807	+	1.98851i
$311$	375.828			1.20845			0.604224	−	0.796814i	$-0.293483\pi$
$311$	375.828			1.20845			0.604224	+	0.796814i	$0.293483\pi$
$312$		−	512.736i		−	1.64338i
$313$	75.3935	+	130.585i	0.240874	+	0.417206i	0.960963	−	0.276675i	$-0.0892327\pi$
$313$	75.3935	+	130.585i	0.240874	+	0.417206i	−0.720090	+	0.693881i	$0.755899\pi$
$314$	−342.994	+	198.028i	−1.09234	+	0.630661i
$315$	−149.152			−0.473499
$316$		−	264.561i		−	0.837218i
$317$	−438.163	+	252.973i	−1.38222	+	0.798024i	−0.992422	−	0.122878i	$-0.960788\pi$
$317$	−438.163	+	252.973i	−1.38222	+	0.798024i	−0.389796	+	0.920901i	$0.627454\pi$
$318$	82.1734	+	47.4428i	0.258407	+	0.149191i
$319$	211.895	−	122.337i	0.664246	−	0.383503i
$320$	54.7517	−	94.8327i	0.171099	−	0.296352i
$321$	−0.475961	+	0.824389i	−0.00148274	+	0.00256819i
$322$		−	1063.70i		−	3.30341i
$323$	211.174	+	69.4179i	0.653789	+	0.214916i
$324$	−78.1352			−0.241158
$325$	51.2998	+	29.6180i	0.157846	+	0.0911322i
$326$	213.386	+	123.198i	0.654558	+	0.377909i
$327$	−80.7219	−	139.814i	−0.246856	−	0.427567i
$328$	−157.599	+	272.970i	−0.480485	+	0.832225i
$329$	128.471	+	222.519i	0.390491	+	0.676349i
$330$	182.956			0.554413
$331$		−	443.028i		−	1.33845i	−0.743058	−	0.669227i	$-0.766626\pi$
$331$		−	443.028i		−	1.33845i	0.743058	−	0.669227i	$-0.233374\pi$
$332$	334.746	+	579.797i	1.00827	+	1.74638i
$333$	88.2800	−	50.9685i	0.265105	−	0.153059i
$334$	747.642			2.23845
$335$			81.4694i			0.243192i
$336$	−394.876	+	227.982i	−1.17523	+	0.678517i
$337$	168.764	+	97.4357i	0.500782	+	0.289127i	0.729037	−	0.684475i	$-0.239968\pi$
$337$	168.764	+	97.4357i	0.500782	+	0.289127i	−0.228254	+	0.973602i	$0.573302\pi$
$338$	451.102	−	260.444i	1.33462	−	0.770543i
$339$	47.9939	−	83.1279i	0.141575	−	0.245215i
$340$	−236.380	+	409.422i	−0.695235	+	1.20418i
$341$		−	273.674i		−	0.802562i
$342$	198.693	−	41.5203i	0.580974	−	0.121404i
$343$	−171.960			−0.501341
$344$	765.498	+	441.961i	2.22529	+	1.28477i
$345$	−195.231	−	112.717i	−0.565886	−	0.326715i
$346$	−544.396	−	942.921i	−1.57340	−	2.72520i
$347$	262.446	−	454.570i	0.756329	−	1.31000i	−0.188382	−	0.982096i	$-0.560324\pi$
$347$	262.446	−	454.570i	0.756329	−	1.31000i	0.944711	−	0.327905i	$-0.106342\pi$
$348$	288.665	+	499.982i	0.829496	+	1.43673i
$349$	−369.064			−1.05749			−0.528745	−	0.848781i	$-0.677337\pi$
$349$	−369.064			−1.05749			−0.528745	+	0.848781i	$0.677337\pi$
$350$		−	126.903i		−	0.362581i
$351$	−46.1310	−	79.9013i	−0.131427	−	0.227639i
$352$	116.317	−	67.1557i	0.330446	−	0.190783i
$353$	323.725			0.917067			0.458533	−	0.888677i	$-0.348375\pi$
$353$	323.725			0.917067			0.458533	+	0.888677i	$0.348375\pi$
$354$		−	182.714i		−	0.516142i
$355$	−347.235	+	200.476i	−0.978126	+	0.564721i
$356$	−666.866	−	385.015i	−1.87322	−	1.08150i
$357$	−187.456	+	108.228i	−0.525087	+	0.303159i
$358$	−539.514	+	934.465i	−1.50702	+	2.61024i
$359$	−6.25614	+	10.8359i	−0.0174266	+	0.0301837i	−0.874607	−	0.484832i	$-0.838881\pi$
$359$	−6.25614	+	10.8359i	−0.0174266	+	0.0301837i	0.857181	+	0.515016i	$0.172214\pi$
$360$			232.799i			0.646663i
$361$	−330.791	+	144.562i	−0.916320	+	0.400448i
$362$	−258.550			−0.714227
$363$	120.581	+	69.6175i	0.332179	+	0.191784i
$364$	−1425.99	−	823.296i	−3.91756	−	2.26180i
$365$	−215.199	−	372.736i	−0.589587	−	1.02119i
$366$	−131.629	+	227.988i	−0.359641	+	0.622917i
$367$	−44.3159	−	76.7574i	−0.120752	−	0.209148i	0.799313	−	0.600916i	$-0.205197\pi$
$367$	−44.3159	−	76.7574i	−0.120752	−	0.209148i	−0.920064	+	0.391767i	$0.871864\pi$
$368$	−689.157			−1.87271
$369$			56.7171i			0.153705i
$370$	−281.603	−	487.750i	−0.761089	−	1.31824i
$371$	142.306	−	82.1602i	0.383573	−	0.221456i
$372$	645.755			1.73590
$373$		−	406.489i		−	1.08978i	−0.838507	−	0.544892i	$-0.816571\pi$
$373$		−	406.489i		−	1.08978i	0.838507	−	0.544892i	$-0.183429\pi$
$374$	229.942	−	132.757i	0.614818	−	0.354965i
$375$	−197.834	−	114.219i	−0.527556	−	0.304585i
$376$	347.311	−	200.520i	0.923699	−	0.533298i
$377$	−340.855	+	590.378i	−0.904125	+	1.56599i
$378$	−98.8281	+	171.175i	−0.261450	+	0.452845i
$379$			433.800i			1.14459i	0.820047	+	0.572296i	$0.193947\pi$
$379$			433.800i			1.14459i	−0.820047	+	0.572296i	$0.806053\pi$
$380$	−157.045	−	751.528i	−0.413275	−	1.97770i
$381$	165.436			0.434216
$382$	−149.802	−	86.4883i	−0.392152	−	0.226409i
$383$	−355.819	−	205.432i	−0.929031	−	0.536377i	−0.0425263	−	0.999095i	$-0.513541\pi$
$383$	−355.819	−	205.432i	−0.929031	−	0.536377i	−0.886505	+	0.462719i	$0.846874\pi$
$384$	−145.565	−	252.127i	−0.379076	−	0.656580i
$385$	158.419	−	274.391i	0.411479	−	0.712703i
$386$	19.4993	+	33.7738i	0.0505164	+	0.0874970i
$387$	159.053			0.410991
$388$		−	18.2803i		−	0.0471141i
$389$	−94.6013	−	163.854i	−0.243191	−	0.421219i	0.718430	−	0.695599i	$-0.244861\pi$
$389$	−94.6013	−	163.854i	−0.243191	−	0.421219i	−0.961621	+	0.274380i	$0.911528\pi$
$390$	−441.458	+	254.876i	−1.13194	+	0.653528i
$391$	−327.158			−0.836721
$392$			1085.33i			2.76871i
$393$	252.228	−	145.624i	0.641803	−	0.370545i
$394$	322.103	+	185.966i	0.817521	+	0.471996i
$395$	−122.834	+	70.9185i	−0.310973	+	0.179540i
$396$	82.9901	−	143.743i	0.209571	−	0.362987i
$397$	−220.839	+	382.504i	−0.556269	+	0.963487i	0.441534	+	0.897244i	$0.354434\pi$
$397$	−220.839	+	382.504i	−0.556269	+	0.963487i	−0.997804	+	0.0662425i	$0.978899\pi$
$398$		−	1001.70i		−	2.51684i
$399$	109.775	−	333.943i	0.275125	−	0.836951i
$400$	−82.2192			−0.205548
$401$	320.526	+	185.056i	0.799316	+	0.461485i	0.843232	−	0.537550i	$-0.180650\pi$
$401$	320.526	+	185.056i	0.799316	+	0.461485i	−0.0439159	+	0.999035i	$0.513983\pi$
$402$	93.4988	+	53.9816i	0.232584	+	0.134283i
$403$	381.254	+	660.351i	0.946039	+	1.63859i
$404$	119.538	−	207.047i	0.295887	−	0.512491i
$405$	20.9450	+	36.2778i	0.0517161	+	0.0895748i
$406$	1460.45			3.59717
$407$			216.541i			0.532043i
$408$	168.924	+	292.584i	0.414029	+	0.717119i
$409$	418.387	−	241.556i	1.02295	−	0.590602i	0.107995	−	0.994151i	$-0.465557\pi$
$409$	418.387	−	241.556i	1.02295	−	0.590602i	0.914958	+	0.403550i	$0.132224\pi$
$410$	313.364			0.764302
$411$		−	205.689i		−	0.500461i
$412$	769.531	−	444.289i	1.86779	−	1.07837i
$413$	−274.028	−	158.210i	−0.663505	−	0.383075i
$414$	−258.720	+	149.372i	−0.624927	+	0.360802i
$415$	179.465	−	310.842i	0.432445	−	0.749017i
$416$	−187.109	+	324.082i	−0.449780	+	0.779042i
$417$			191.157i			0.458409i
$418$	−134.655	+	409.630i	−0.322141	+	0.979975i
$419$	−295.264			−0.704687			−0.352344	−	0.935871i	$-0.614615\pi$
$419$	−295.264			−0.704687			−0.352344	+	0.935871i	$0.614615\pi$
$420$	647.446	+	373.803i	1.54154	+	0.890008i
$421$	−449.581	−	259.566i	−1.06789	−	0.616545i	−0.140284	−	0.990111i	$-0.544802\pi$
$421$	−449.581	−	259.566i	−1.06789	−	0.616545i	−0.927604	+	0.373566i	$0.878135\pi$
$422$	183.563	+	317.941i	0.434984	+	0.753415i
$423$	36.0817	−	62.4954i	0.0852996	−	0.147743i
$424$	−128.237	−	222.113i	−0.302446	−	0.523851i
$425$	−39.0312			−0.0918382
$426$			531.341i			1.24728i
$427$	227.951	+	394.823i	0.533843	+	0.924644i
$428$	4.13215	−	2.38570i	0.00965455	−	0.00557406i
$429$	195.989			0.456852
$430$		−	878.777i		−	2.04367i
$431$	−195.895	+	113.100i	−0.454514	+	0.262414i	−0.709735	−	0.704469i	$-0.751185\pi$
$431$	−195.895	+	113.100i	−0.454514	+	0.262414i	0.255221	+	0.966883i	$0.417852\pi$
$432$	110.903	+	64.0297i	0.256719	+	0.148217i
$433$	−251.769	+	145.359i	−0.581452	+	0.335702i	−0.761710	−	0.647918i	$-0.775640\pi$
$433$	−251.769	+	145.359i	−0.581452	+	0.335702i	0.180258	+	0.983619i	$0.442307\pi$
$434$	816.773	−	1414.69i	1.88197	−	3.25966i
$435$	154.759	−	268.051i	0.355769	−	0.616210i
$436$			809.218i			1.85600i
$437$	396.055	−	354.152i	0.906304	−	0.810417i
$438$	−570.364			−1.30220
$439$	251.921	+	145.447i	0.573852	+	0.331314i	0.758686	−	0.651456i	$-0.225842\pi$
$439$	251.921	+	145.447i	0.573852	+	0.331314i	−0.184834	+	0.982770i	$0.559175\pi$
$440$	−428.273	−	247.264i	−0.973348	−	0.561963i
$441$	97.6479	+	169.131i	0.221424	+	0.383517i
$442$	−369.886	+	640.662i	−0.836847	+	1.44946i
$443$	−217.722	−	377.106i	−0.491473	−	0.851256i	0.508479	−	0.861074i	$-0.330208\pi$
$443$	−217.722	−	377.106i	−0.491473	−	0.851256i	−0.999952	+	0.00981853i	$0.996875\pi$
$444$	−510.947			−1.15078
$445$			412.830i			0.927708i
$446$	−141.775	−	245.562i	−0.317882	−	0.550587i
$447$	−86.6158	+	50.0077i	−0.193771	+	0.111874i
$448$	−251.304			−0.560947
$449$			263.736i			0.587385i	0.955900	+	0.293692i	$0.0948842\pi$
$449$			263.736i			0.587385i	−0.955900	+	0.293692i	$0.905116\pi$
$450$	−30.8663	+	17.8207i	−0.0685918	+	0.0396015i
$451$	−104.341	−	60.2411i	−0.231354	−	0.133572i
$452$	−416.669	+	240.564i	−0.921833	+	0.532221i
$453$	177.933	−	308.189i	0.392788	−	0.680328i
$454$	−233.309	+	404.103i	−0.513897	+	0.890096i
$455$			882.774i			1.94016i
$456$	−521.224	−	171.339i	−1.14303	−	0.375743i
$457$	641.042			1.40272			0.701359	−	0.712809i	$-0.252577\pi$
$457$	641.042			1.40272			0.701359	+	0.712809i	$0.252577\pi$
$458$	93.6119	+	54.0469i	0.204393	+	0.118006i
$459$	52.6479	+	30.3963i	0.114701	+	0.0662228i
$460$	564.978	+	978.570i	1.22821	+	2.12733i
$461$	−323.490	+	560.302i	−0.701714	+	1.21540i	0.266150	+	0.963932i	$0.414248\pi$
$461$	−323.490	+	560.302i	−0.701714	+	1.21540i	−0.967864	+	0.251473i	$0.919085\pi$
$462$	−209.937	−	363.622i	−0.454410	−	0.787061i
$463$	−407.362			−0.879831			−0.439916	−	0.898039i	$-0.644992\pi$
$463$	−407.362			−0.879831			−0.439916	+	0.898039i	$0.644992\pi$
$464$		−	946.211i		−	2.03925i
$465$	−173.102	−	299.821i	−0.372262	−	0.644776i
$466$	−290.198	+	167.546i	−0.622742	+	0.359540i
$467$	146.962			0.314694			0.157347	−	0.987543i	$-0.449706\pi$
$467$	146.962			0.314694			0.157347	+	0.987543i	$0.449706\pi$
$468$			462.452i			0.988146i
$469$	161.919	−	93.4838i	0.345242	−	0.199326i
$470$	−345.290	−	199.353i	−0.734659	−	0.424155i
$471$	166.824	−	96.3159i	0.354191	−	0.204492i
$472$	−246.936	+	427.706i	−0.523170	+	0.906158i
$473$	−168.936	+	292.606i	−0.357159	+	0.618617i
$474$			187.962i			0.396545i
$475$	47.2509	−	42.2518i	0.0994757	−	0.0889512i
$476$	1084.96			2.27932
$477$	−39.9672	−	23.0751i	−0.0837886	−	0.0483754i
$478$	1157.43	+	668.242i	2.42140	+	1.39800i
$479$	−309.698	−	536.413i	−0.646552	−	1.11986i	−0.983941	−	0.178495i	$-0.942877\pi$
$479$	−309.698	−	536.413i	−0.646552	−	1.11986i	0.337389	−	0.941365i	$-0.390456\pi$
$480$	84.9534	−	147.144i	0.176986	−	0.306549i
$481$	−301.663	−	522.495i	−0.627158	−	1.08627i
$482$	1.98375			0.00411566
$483$			517.356i			1.07113i
$484$	−348.949	−	604.398i	−0.720970	−	1.24876i
$485$	−8.48745	+	4.90023i	−0.0174999	+	0.0101036i
$486$	55.5126			0.114224
$487$			343.861i			0.706080i	0.935608	+	0.353040i	$0.114852\pi$
$487$			343.861i			0.706080i	−0.935608	+	0.353040i	$0.885148\pi$
$488$	616.245	−	355.789i	1.26280	−	0.729077i
$489$	−103.786	−	59.9207i	−0.212241	−	0.122537i
$490$	934.456	−	539.508i	1.90705	−	1.10104i
$491$	−250.993	+	434.733i	−0.511187	+	0.885402i	0.488729	+	0.872436i	$0.337461\pi$
$491$	−250.993	+	434.733i	−0.511187	+	0.885402i	−0.999916	+	0.0129665i	$0.995873\pi$
$492$	142.144	−	246.200i	0.288910	−	0.500407i
$493$		−	449.187i		−	0.911129i
$494$	−245.743	−	1175.99i	−0.497455	−	2.38054i
$495$	−88.9856			−0.179769
$496$	−916.564	−	529.178i	−1.84791	−	1.06689i
$497$	796.884	+	460.081i	1.60339	+	0.925717i
$498$	−237.827	−	411.928i	−0.477563	−	0.827164i
$499$	453.717	−	785.861i	0.909253	−	1.57487i	0.0941479	−	0.995558i	$-0.469987\pi$
$499$	453.717	−	785.861i	0.909253	−	1.57487i	0.815105	−	0.579314i	$-0.196679\pi$
$500$	572.510	+	991.616i	1.14502	+	1.98323i
$501$	−363.635			−0.725818
$502$			835.508i			1.66436i
$503$	183.800	+	318.352i	0.365408	+	0.632906i	0.988842	−	0.148971i	$-0.0475960\pi$
$503$	183.800	+	318.352i	0.365408	+	0.632906i	−0.623433	+	0.781877i	$0.714263\pi$
$504$	462.683	−	267.130i	0.918022	−	0.530020i
$505$	−128.174			−0.253810
$506$		−	634.612i		−	1.25417i
$507$	−219.405	+	126.674i	−0.432751	+	0.249849i
$508$	−718.133	−	414.614i	−1.41365	−	0.816170i
$509$	406.585	−	234.742i	0.798791	−	0.461182i	−0.0442573	−	0.999020i	$-0.514092\pi$
$509$	406.585	−	234.742i	0.798791	−	0.461182i	0.843048	+	0.537838i	$0.180759\pi$
$510$	167.941	−	290.881i	0.329295	−	0.570356i
$511$	−493.870	+	855.408i	−0.966478	+	1.67399i
$512$			1124.13i			2.19557i
$513$	−96.6395	+	20.1945i	−0.188381	+	0.0393654i
$514$	−45.5214			−0.0885630
$515$	−412.562	−	238.193i	−0.801092	−	0.462511i
$516$	−690.427	−	398.618i	−1.33804	−	0.772516i
$517$	76.6473	+	132.757i	0.148254	+	0.256783i
$518$	−646.263	+	1119.36i	−1.24761	+	2.16093i
$519$	264.781	+	458.614i	0.510175	+	0.883649i
$520$	1377.85			2.64970
$521$		−	691.695i		−	1.32763i	−0.747897	−	0.663815i	$-0.768936\pi$
$521$		−	691.695i		−	1.32763i	0.747897	−	0.663815i	$-0.231064\pi$
$522$	−205.087	−	355.221i	−0.392887	−	0.680501i
$523$	−70.7545	+	40.8501i	−0.135286	+	0.0781073i	−0.566115	−	0.824326i	$-0.691554\pi$
$523$	−70.7545	+	40.8501i	−0.135286	+	0.0781073i	0.430830	+	0.902433i	$0.358221\pi$
$524$	−1459.85			−2.78597
$525$			61.7227i			0.117567i
$526$	656.635	−	379.108i	1.24836	−	0.720738i
$527$	−435.113	−	251.212i	−0.825640	−	0.476684i
$528$	−235.587	+	136.016i	−0.446187	+	0.257606i
$529$	−126.474	+	219.060i	−0.239081	+	0.414101i
$530$	−127.491	+	220.820i	−0.240548	+	0.416642i
$531$			88.8679i			0.167359i
$532$	−1313.44	+	1174.48i	−2.46888	+	2.20767i
$533$	335.686			0.629806
$534$	473.787	+	273.541i	0.887242	+	0.512249i
$535$	−2.21533	−	1.27902i	−0.00414081	−	0.00239070i
$536$	−145.911	−	252.725i	−0.272222	−	0.471502i
$537$	262.406	−	454.501i	0.488653	−	0.846371i
$538$	−902.012	−	1562.33i	−1.67660	−	2.90396i
$539$	−414.860			−0.769685
$540$		−	209.969i		−	0.388831i
$541$	373.182	+	646.370i	0.689800	+	1.19477i	0.971902	+	0.235384i	$0.0756349\pi$
$541$	373.182	+	646.370i	0.689800	+	1.19477i	−0.282102	+	0.959384i	$0.591032\pi$
$542$	678.876	−	391.949i	1.25254	−	0.723153i
$543$	125.753			0.231588
$544$		−	246.576i		−	0.453264i
$545$	375.716	−	216.920i	0.689387	−	0.398018i
$546$	1013.12	+	584.926i	1.85553	+	1.07129i
$547$	404.687	−	233.646i	0.739830	−	0.427141i	−0.0821772	−	0.996618i	$-0.526187\pi$
$547$	404.687	−	233.646i	0.739830	−	0.427141i	0.822008	+	0.569476i	$0.192854\pi$
$548$	−515.496	+	892.866i	−0.940687	+	1.62932i
$549$	64.0210	−	110.888i	0.116614	−	0.201981i
$550$		−	75.7117i		−	0.137658i
$551$	486.250	+	543.782i	0.882487	+	0.986900i
$552$	807.498			1.46286
$553$	281.898	+	162.754i	0.509761	+	0.294311i
$554$	808.273	+	466.657i	1.45898	+	0.842341i
$555$	136.965	+	237.230i	0.246783	+	0.427442i
$556$	479.075	−	829.782i	0.861645	−	1.49241i
$557$	386.099	+	668.743i	0.693175	+	1.20061i	0.970792	+	0.239923i	$0.0771222\pi$
$557$	386.099	+	668.743i	0.693175	+	1.20061i	−0.277617	+	0.960692i	$0.589544\pi$
$558$	−458.789			−0.822202
$559$		−	941.376i		−	1.68404i
$560$	−612.643	−	1061.13i	−1.09401	−	1.89487i
$561$	−111.838	+	64.5698i	−0.199355	+	0.115098i
$562$	−1423.60			−2.53310
$563$		−	195.273i		−	0.346844i	−0.984848	−	0.173422i	$-0.944518\pi$
$563$		−	195.273i		−	0.346844i	0.984848	−	0.173422i	$-0.0554825\pi$
$564$	−313.251	+	180.855i	−0.555409	+	0.320666i
$565$	223.385	+	128.971i	0.395372	+	0.228268i
$566$	254.345	−	146.846i	0.449373	−	0.259446i
$567$	48.0676	−	83.2556i	0.0847753	−	0.146835i
$568$	718.102	−	1243.79i	1.26426	−	2.18977i
$569$		−	579.517i		−	1.01848i	−0.860624	−	0.509242i	$-0.829926\pi$
$569$		−	579.517i		−	1.01848i	0.860624	−	0.509242i	$-0.170074\pi$
$570$	111.575	+	533.937i	0.195746	+	0.936731i
$571$	−145.886			−0.255492			−0.127746	−	0.991807i	$-0.540774\pi$
$571$	−145.886			−0.255492			−0.127746	+	0.991807i	$0.540774\pi$
$572$	−850.760	−	491.186i	−1.48734	−	0.858717i
$573$	72.8602	+	42.0658i	0.127156	+	0.0734133i
$574$	−359.576	−	622.805i	−0.626440	−	1.08503i
$575$	−46.6448	+	80.7911i	−0.0811214	+	0.140506i
$576$	35.2899	+	61.1240i	0.0612672	+	0.106118i
$577$	−1037.54			−1.79817			−0.899084	−	0.437777i	$-0.855766\pi$
$577$	−1037.54			−1.79817			−0.899084	+	0.437777i	$0.855766\pi$
$578$			541.724i			0.937239i
$579$	−9.48401	−	16.4268i	−0.0163800	−	0.0283710i
$580$	−1343.57	+	775.713i	−2.31651	+	1.33744i
$581$	−823.723			−1.41777
$582$			12.9876i			0.0223154i
$583$	84.9009	−	49.0176i	0.145628	−	0.0840782i
$584$	1335.13	+	770.840i	2.28619	+	1.31993i
$585$	214.714	−	123.965i	0.367033	−	0.211907i
$586$	398.050	−	689.443i	0.679266	−	1.17652i
$587$	441.521	−	764.737i	0.752165	−	1.30279i	−0.194606	−	0.980882i	$-0.562343\pi$
$587$	441.521	−	764.737i	0.752165	−	1.30279i	0.946771	−	0.321907i	$-0.104324\pi$
$588$		−	978.896i		−	1.66479i
$589$	798.684	−	166.899i	1.35600	−	0.283360i
$590$	490.998			0.832201
$591$	−156.663	−	90.4495i	−0.265082	−	0.153045i
$592$	725.221	+	418.707i	1.22504	+	0.707275i
$593$	119.583	+	207.125i	0.201658	+	0.349283i	0.949063	−	0.315087i	$-0.102034\pi$
$593$	119.583	+	207.125i	0.201658	+	0.349283i	−0.747404	+	0.664369i	$0.768700\pi$
$594$	−58.9618	+	102.125i	−0.0992624	+	0.171927i
$595$	−290.835	−	503.741i	−0.488798	−	0.846623i
$596$	501.315			0.841132
$597$			487.203i			0.816086i
$598$	884.075	+	1531.26i	1.47839	+	2.56064i
$599$	−793.604	+	458.187i	−1.32488	+	0.764920i	−0.984503	−	0.175368i	$-0.943888\pi$
$599$	−793.604	+	458.187i	−1.32488	+	0.764920i	−0.340378	+	0.940289i	$0.610555\pi$
$600$	96.3377			0.160563
$601$		−	789.891i		−	1.31429i	−0.753762	−	0.657147i	$-0.771763\pi$
$601$		−	789.891i		−	1.31429i	0.753762	−	0.657147i	$-0.228237\pi$
$602$	−1746.55	+	1008.37i	−2.90125	+	1.67504i
$603$	−45.4756	−	26.2553i	−0.0754155	−	0.0435412i
$604$	−1544.76	+	891.867i	−2.55755	+	1.47660i
$605$	−187.079	+	324.031i	−0.309222	+	0.535588i
$606$	−84.9283	+	147.100i	−0.140146	+	0.242739i
$607$		−	653.712i		−	1.07696i	−0.842640	−	0.538478i	$-0.819000\pi$
$607$		−	653.712i		−	1.07696i	0.842640	−	0.538478i	$-0.181000\pi$
$608$	266.921	+	298.503i	0.439015	+	0.490959i
$609$	−710.329			−1.16639
$610$	−612.659	−	353.719i	−1.00436	−	0.579867i
$611$	−369.886	−	213.554i	−0.605379	−	0.349515i
$612$	−152.358	−	263.891i	−0.248950	−	0.431194i
$613$	528.343	−	915.118i	0.861898	−	1.49285i	−0.00819687	−	0.999966i	$-0.502609\pi$
$613$	528.343	−	915.118i	0.861898	−	1.49285i	0.870095	−	0.492885i	$-0.164057\pi$
$614$	697.061	+	1207.35i	1.13528	+	1.96636i
$615$	−152.413			−0.247825
$616$			1134.91i			1.84239i
$617$	−501.032	−	867.813i	−0.812045	−	1.40650i	−0.911430	−	0.411455i	$-0.865021\pi$
$617$	−501.032	−	867.813i	−0.812045	−	1.40650i	0.0993850	−	0.995049i	$-0.468312\pi$
$618$	−546.727	+	315.653i	−0.884672	+	0.510766i
$619$	252.948			0.408640			0.204320	−	0.978904i	$-0.434502\pi$
$619$	252.948			0.408640			0.204320	+	0.978904i	$0.434502\pi$
$620$			1735.30i			2.79887i
$621$	125.835	−	72.6509i	0.202633	−	0.116990i
$622$	1159.07	+	669.187i	1.86345	+	1.07586i
$623$	820.491	−	473.711i	1.31700	−	0.760371i
$624$	378.967	−	656.390i	0.607319	−	1.05191i
$625$	265.233	−	459.398i	0.424373	−	0.735036i
$626$			536.973i			0.857784i
$627$	65.4929	−	199.234i	0.104454	−	0.317757i
$628$	−965.543			−1.53749
$629$	344.278	+	198.769i	0.547342	+	0.316008i
$630$	−459.990	−	265.575i	−0.730143	−	0.421548i
$631$	−605.640	−	1049.00i	−0.959809	−	1.66244i	−0.722957	−	0.690893i	$-0.757217\pi$
$631$	−605.640	−	1049.00i	−0.959809	−	1.66244i	−0.236853	−	0.971546i	$-0.576116\pi$
$632$	254.029	−	439.991i	0.401944	−	0.696188i
$633$	−89.2808	−	154.639i	−0.141044	−	0.244295i
$634$	−1801.75			−2.84187
$635$			444.568i			0.700107i
$636$	115.661	+	200.331i	0.181857	+	0.314985i
$637$	1001.02	−	577.940i	1.57146	−	0.907284i
$638$	871.320			1.36571
$639$		−	258.432i		−	0.404431i
$640$	677.526	−	391.170i	1.05863	−	0.611203i
$641$	89.1040	+	51.4442i	0.139008	+	0.0802562i	0.567891	−	0.823104i	$-0.307759\pi$
$641$	89.1040	+	51.4442i	0.139008	+	0.0802562i	−0.428883	+	0.903360i	$0.641093\pi$
$642$	−2.93576	+	1.69496i	−0.00457284	+	0.00264013i
$643$	−384.990	+	666.822i	−0.598740	+	1.03705i	0.394267	+	0.918996i	$0.370998\pi$
$643$	−384.990	+	666.822i	−0.598740	+	1.03705i	−0.993007	+	0.118052i	$0.962335\pi$
$644$	1296.59	−	2245.76i	2.01334	−	3.48721i
$645$			427.416i			0.662660i
$646$	527.665	+	590.097i	0.816818	+	0.913463i
$647$	−790.984			−1.22254			−0.611270	−	0.791422i	$-0.709341\pi$
$647$	−790.984			−1.22254			−0.611270	+	0.791422i	$0.709341\pi$
$648$	−129.947	−	75.0247i	−0.200535	−	0.115779i
$649$	−163.488	−	94.3896i	−0.251907	−	0.145438i
$650$	105.474	+	182.686i	0.162267	+	0.281055i
$651$	−397.259	+	688.072i	−0.610228	+	1.05695i
$652$	300.345	+	520.213i	0.460652	+	0.797873i
$653$	320.503			0.490816			0.245408	−	0.969420i	$-0.421078\pi$
$653$	320.503			0.490816			0.245408	+	0.969420i	$0.421078\pi$
$654$		−	574.924i		−	0.879088i
$655$	391.328	+	677.800i	0.597447	+	1.03481i
$656$	−403.508	+	232.966i	−0.615104	+	0.355130i
$657$	277.411			0.422239
$658$			915.008i			1.39059i
$659$	−616.112	+	355.713i	−0.934920	+	0.539776i	−0.888364	−	0.459139i	$-0.848158\pi$
$659$	−616.112	+	355.713i	−0.934920	+	0.539776i	−0.0465558	+	0.998916i	$0.514825\pi$
$660$	386.273	+	223.015i	0.585262	+	0.337901i
$661$	−410.779	+	237.163i	−0.621451	+	0.358795i	−0.777434	−	0.628965i	$-0.783479\pi$
$661$	−410.779	+	237.163i	−0.621451	+	0.358795i	0.155983	+	0.987760i	$0.450146\pi$
$662$	788.842	−	1366.31i	1.19160	−	2.06392i
$663$	179.904	−	311.602i	0.271348	−	0.469989i
$664$			1285.68i			1.93626i
$665$	897.388	+	294.993i	1.34946	+	0.443598i
$666$	363.012			0.545062
$667$	−929.776	−	536.806i	−1.39397	−	0.804807i
$668$	1578.48	+	911.338i	2.36300	+	1.36428i
$669$	68.9560	+	119.435i	0.103073	+	0.178528i
$670$	−145.062	+	251.254i	−0.216510	+	0.375006i
$671$	135.998	+	235.555i	0.202679	+	0.351051i
$672$	−389.927			−0.580248
$673$			648.662i			0.963836i	0.876216	+	0.481918i	$0.160060\pi$
$673$			648.662i			0.963836i	−0.876216	+	0.481918i	$0.839940\pi$
$674$	346.982	+	600.990i	0.514810	+	0.891677i
$675$	15.0126	−	8.66754i	0.0222409	−	0.0128408i
$676$	1269.87			1.87851
$677$		−	860.699i		−	1.27134i	−0.771960	−	0.635671i	$-0.780723\pi$
$677$		−	860.699i		−	1.27134i	0.771960	−	0.635671i	$-0.219277\pi$
$678$	296.030	−	170.913i	0.436622	−	0.252084i
$679$	19.4782	+	11.2458i	0.0286866	+	0.0165622i
$680$	−786.246	+	453.939i	−1.15624	+	0.667558i
$681$	113.476	−	196.546i	0.166631	−	0.288614i
$682$	487.295	−	844.019i	0.714509	−	1.23757i
$683$		−	194.789i		−	0.285196i	−0.989781	−	0.142598i	$-0.954454\pi$
$683$		−	194.789i		−	0.285196i	0.989781	−	0.142598i	$-0.0455456\pi$
$684$	470.108	+	154.536i	0.687293	+	0.225929i
$685$	552.738			0.806916
$686$	−530.331	−	306.187i	−0.773077	−	0.446336i
$687$	−45.5306	−	26.2871i	−0.0662745	−	0.0382636i
$688$	653.313	+	1131.57i	0.949583	+	1.64473i
$689$	−136.572	+	236.550i	−0.198218	+	0.343324i
$690$	−401.399	−	695.243i	−0.581738	−	1.00760i
$691$	719.067			1.04062			0.520309	−	0.853978i	$-0.325817\pi$
$691$	719.067			1.04062			0.520309	+	0.853978i	$0.325817\pi$
$692$		−	2654.36i		−	3.83579i
$693$	102.108	+	176.857i	0.147343	+	0.255205i
$694$	1618.79	−	934.607i	2.33255	−	1.34670i
$695$	−513.685			−0.739115
$696$			1108.69i			1.59295i
$697$	−191.554	+	110.594i	−0.274826	+	0.158671i
$698$	−1138.21	−	657.144i	−1.63067	−	0.941467i
$699$	141.145	−	81.4902i	0.201924	−	0.116581i
$700$	154.689	−	267.929i	0.220984	−	0.382755i
$701$	242.353	−	419.767i	0.345724	−	0.598812i	−0.639761	−	0.768574i	$-0.720967\pi$
$701$	242.353	−	419.767i	0.345724	−	0.598812i	0.985485	+	0.169762i	$0.0542999\pi$
$702$		−	328.558i		−	0.468031i
$703$	−631.951	+	132.057i	−0.898934	+	0.187848i
$704$	−149.931			−0.212969
$705$	167.941	+	96.9605i	0.238213	+	0.137533i
$706$	998.378	+	576.414i	1.41413	+	0.816450i
$707$	147.076	+	254.744i	0.208029	+	0.360317i
$708$	222.720	−	385.762i	0.314576	−	0.544861i
$709$	620.485	+	1074.71i	0.875156	+	1.51581i	0.856597	+	0.515987i	$0.172575\pi$
$709$	620.485	+	1074.71i	0.875156	+	1.51581i	0.0185591	+	0.999828i	$0.494092\pi$
$710$	−1427.84			−2.01105
$711$		−	91.4203i		−	0.128580i
$712$	−739.375	−	1280.64i	−1.03845	−	1.79865i
$713$	−1039.97	+	600.429i	−1.45859	+	0.842116i
$714$	−770.828			−1.07959
$715$			526.671i			0.736603i
$716$	−2278.13	+	1315.28i	−3.18175	+	1.83698i
$717$	−562.946	−	325.017i	−0.785141	−	0.453301i
$718$	−38.5883	+	22.2790i	−0.0537441	+	0.0310292i
$719$	65.3191	−	113.136i	0.0908471	−	0.157352i	−0.817021	−	0.576608i	$-0.804376\pi$
$719$	65.3191	−	113.136i	0.0908471	−	0.157352i	0.907868	+	0.419256i	$0.137709\pi$
$720$	−172.063	+	298.023i	−0.238977	+	0.413920i
$721$			1093.28i			1.51634i
$722$	−1277.57	−	143.163i	−1.76949	−	0.198287i
$723$	−0.964848			−0.00133451
$724$	−545.873	−	315.160i	−0.753968	−	0.435303i
$725$	−110.926	−	64.0432i	−0.153001	−	0.0883354i
$726$	247.917	+	429.406i	0.341484	+	0.591468i
$727$	−566.505	+	981.216i	−0.779237	+	1.34968i	0.153145	+	0.988204i	$0.451060\pi$
$727$	−566.505	+	981.216i	−0.779237	+	1.34968i	−0.932382	+	0.361475i	$0.882273\pi$
$728$	−1581.04	−	2738.44i	−2.17176	−	3.76160i
$729$	−27.0000			−0.0370370
$730$		−	1532.71i		−	2.09960i
$731$	310.142	+	537.181i	0.424271	+	0.734858i
$732$	−555.811	+	320.898i	−0.759305	+	0.438385i
$733$	−837.144			−1.14208			−0.571040	−	0.820922i	$-0.693460\pi$
$733$	−837.144			−1.14208			−0.571040	+	0.820922i	$0.693460\pi$
$734$		−	315.630i		−	0.430014i
$735$	−454.497	+	262.404i	−0.618363	+	0.357012i
$736$	−510.390	−	294.674i	−0.693464	−	0.400372i
$737$	96.6023	−	55.7734i	0.131075	−	0.0756762i
$738$	−100.989	+	174.917i	−0.136841	+	0.237015i
$739$	144.463	−	250.216i	0.195484	−	0.338588i	−0.751575	−	0.659647i	$-0.770706\pi$
$739$	144.463	−	250.216i	0.195484	−	0.338588i	0.947059	+	0.321060i	$0.104039\pi$
$740$		−	1373.04i		−	1.85546i
$741$	119.523	+	571.972i	0.161300	+	0.771892i
$742$	585.167			0.788635
$743$	−66.4928	−	38.3896i	−0.0894923	−	0.0516684i	0.454586	−	0.890703i	$-0.349787\pi$
$743$	−66.4928	−	38.3896i	−0.0894923	−	0.0516684i	−0.544078	+	0.839034i	$0.683121\pi$
$744$	1073.95	+	620.047i	1.44349	+	0.833397i
$745$	−134.383	−	232.758i	−0.180380	−	0.312427i
$746$	723.782	−	1253.63i	0.970217	−	1.68046i
$747$	115.673	+	200.352i	0.154850	+	0.268208i
$748$	647.296			0.865370
$749$			5.87058i			0.00783789i
$750$	−406.750	−	704.512i	−0.542334	−	0.939350i
$751$	923.318	−	533.078i	1.22945	−	0.709824i	0.262536	−	0.964922i	$-0.415441\pi$
$751$	923.318	−	533.078i	1.22945	−	0.709824i	0.966915	+	0.255098i	$0.0821078\pi$
$752$	592.824			0.788329
$753$		−	406.371i		−	0.539669i
$754$	−2102.42	+	1213.83i	−2.78835	+	1.60986i
$755$	828.179	+	478.149i	1.09693	+	0.633310i
$756$	−417.308	+	240.933i	−0.551995	+	0.318695i
$757$	4.94030	−	8.55684i	0.00652615	−	0.0113036i	−0.862744	−	0.505641i	$-0.831256\pi$
$757$	4.94030	−	8.55684i	0.00652615	−	0.0113036i	0.869270	+	0.494338i	$0.164589\pi$
$758$	−772.411	+	1337.85i	−1.01901	+	1.76498i
$759$			308.660i			0.406666i
$760$	460.429	−	1400.66i	0.605827	−	1.84297i
$761$	1147.50			1.50788			0.753940	−	0.656944i	$-0.228151\pi$
$761$	1147.50			1.50788			0.753940	+	0.656944i	$0.228151\pi$
$762$	510.211	+	294.570i	0.669568	+	0.386575i
$763$	−862.247	−	497.819i	−1.13007	−	0.652449i
$764$	−210.850	−	365.203i	−0.275982	−	0.478014i
$765$	−81.6822	+	141.478i	−0.106774	+	0.184938i
$766$	−731.572	−	1267.12i	−0.955055	−	1.65420i
$767$	525.975			0.685756
$768$		−	873.759i		−	1.13771i
$769$	299.227	+	518.276i	0.389112	+	0.673961i	0.992330	−	0.123615i	$-0.0394486\pi$
$769$	299.227	+	518.276i	0.389112	+	0.673961i	−0.603218	+	0.797576i	$0.706115\pi$
$770$	977.142	−	564.153i	1.26902	−	0.732667i
$771$	22.1405			0.0287166
$772$			95.0749i			0.123154i
$773$	858.414	−	495.605i	1.11050	−	0.641145i	0.171538	−	0.985177i	$-0.445126\pi$
$773$	858.414	−	495.605i	1.11050	−	0.641145i	0.938958	+	0.344032i	$0.111793\pi$
$774$	490.527	+	283.206i	0.633755	+	0.365899i
$775$	−124.073	+	71.6336i	−0.160094	+	0.0924305i
$776$	17.5525	−	30.4019i	0.0226193	−	0.0391777i
$777$	314.327	−	544.430i	0.404539	−	0.700682i
$778$		−	673.776i		−	0.866036i
$779$	112.175	−	341.244i	0.143998	−	0.438053i
$780$	−1242.72			−1.59323
$781$	475.429	+	274.489i	0.608744	+	0.351458i
$782$	−1008.97	−	582.527i	−1.29024	−	0.744919i
$783$	99.7494	+	172.771i	0.127394	+	0.220653i
$784$	−802.178	+	1389.41i	−1.02319	+	1.77221i
$785$	258.824	+	448.297i	0.329713	+	0.571079i
$786$	1037.18			1.31956
$787$			1226.83i			1.55887i	0.626480	+	0.779437i	$0.284495\pi$
$787$			1226.83i			1.55887i	−0.626480	+	0.779437i	$0.715505\pi$
$788$	453.367	+	785.255i	0.575339	+	0.996517i
$789$	−319.371	+	184.389i	−0.404780	+	0.233700i
$790$	−505.101			−0.639368
$791$		−	591.965i		−	0.748375i
$792$	276.041	−	159.372i	0.348537	−	0.201228i
$793$	−656.302	−	378.916i	−0.827619	−	0.477826i
$794$	−1362.15	+	786.438i	−1.71555	+	0.990476i
$795$	62.0083	−	107.402i	0.0779979	−	0.135096i
$796$	1221.02	−	2114.87i	1.53395	−	2.65688i
$797$			788.636i			0.989506i	0.869034	+	0.494753i	$0.164741\pi$
$797$			788.636i			0.989506i	−0.869034	+	0.494753i	$0.835259\pi$
$798$	933.159	−	834.431i	1.16937	−	1.04565i
$799$	281.426			0.352223
$800$	−60.8916	−	35.1558i	−0.0761144	−	0.0439447i
$801$	−230.439	−	133.044i	−0.287689	−	0.166097i
$802$	659.008	+	1141.44i	0.821706	+	1.42324i
$803$	−294.648	+	510.345i	−0.366934	+	0.635548i
$804$	131.602	+	227.941i	0.163684	+	0.283508i
$805$	−1390.26			−1.72704
$806$			2715.39i			3.36897i
$807$	438.717	+	759.880i	0.543639	+	0.941610i
$808$	397.608	−	229.559i	0.492089	−	0.284108i
$809$	640.524			0.791748			0.395874	−	0.918305i	$-0.370442\pi$
$809$	640.524			0.791748			0.395874	+	0.918305i	$0.370442\pi$
$810$			149.176i			0.184168i
$811$	−811.945	+	468.777i	−1.00117	+	0.578023i	−0.908593	−	0.417683i	$-0.862842\pi$
$811$	−811.945	+	468.777i	−1.00117	+	0.578023i	−0.0925727	+	0.995706i	$0.529509\pi$
$812$	3083.43	+	1780.22i	3.79732	+	2.19239i
$813$	−330.189	+	190.635i	−0.406136	+	0.234483i
$814$	−385.567	+	667.821i	−0.473669	+	0.820419i
$815$	161.022	−	278.898i	0.197573	−	0.342206i
$816$			499.411i			0.612023i
$817$	−956.961	−	314.576i	−1.17131	−	0.385037i
$818$	1720.43			2.10321
$819$	−492.758	−	284.494i	−0.601658	−	0.347367i
$820$	661.600	+	381.975i	0.806829	+	0.465823i
$821$	−671.718	−	1163.45i	−0.818170	−	1.41711i	−0.907029	−	0.421068i	$-0.861655\pi$
$821$	−671.718	−	1163.45i	−0.818170	−	1.41711i	0.0888591	−	0.996044i	$-0.471678\pi$
$822$	366.244	−	634.353i	0.445552	−	0.771719i
$823$	435.019	+	753.475i	0.528577	+	0.915522i	0.999445	+	0.0333184i	$0.0106075\pi$
$823$	435.019	+	753.475i	0.528577	+	0.915522i	−0.470868	+	0.882204i	$0.656059\pi$
$824$	1706.41			2.07088
$825$			36.8244i			0.0446356i
$826$	−563.407	−	975.850i	−0.682091	−	1.18142i
$827$	583.285	−	336.760i	0.705303	−	0.407207i	−0.104017	−	0.994576i	$-0.533170\pi$
$827$	583.285	−	336.760i	0.705303	−	0.407207i	0.809319	+	0.587369i	$0.199836\pi$
$828$	−728.307			−0.879598
$829$			516.908i			0.623532i	0.950159	+	0.311766i	$0.100920\pi$
$829$			516.908i			0.623532i	−0.950159	+	0.311766i	$0.899080\pi$
$830$	1106.95	−	639.098i	1.33368	−	0.769998i
$831$	−393.125	−	226.971i	−0.473074	−	0.273129i
$832$	361.769	−	208.867i	0.434819	−	0.251043i
$833$	−380.811	+	659.584i	−0.457156	+	0.791818i
$834$	−340.368	+	589.534i	−0.408115	+	0.706875i
$835$		−	977.176i		−	1.17027i
$836$	−783.612	+	700.706i	−0.937335	+	0.838165i
$837$	223.144			0.266599
$838$	−910.605	−	525.738i	−1.08664	−	0.627372i
$839$	−1050.53	−	606.526i	−1.25213	−	0.722915i	−0.280595	−	0.959826i	$-0.590532\pi$
$839$	−1050.53	−	606.526i	−1.25213	−	0.722915i	−0.971531	+	0.236911i	$0.923865\pi$
$840$	717.844	+	1243.34i	0.854577	+	1.48017i
$841$	316.533	−	548.252i	0.376377	−	0.651905i
$842$	−924.348	−	1601.02i	−1.09780	−	1.90145i
$843$	692.405			0.821358
$844$			895.018i			1.06045i
$845$	−340.403	−	589.595i	−0.402844	−	0.697745i
$846$	222.555	−	128.492i	0.263067	−	0.151882i
$847$	858.673			1.01378
$848$		−	379.124i		−	0.447080i
$849$	−123.707	+	71.4225i	−0.145710	+	0.0841255i
$850$	−120.374	−	69.4978i	−0.141616	−	0.0817621i
$851$	822.868	−	475.083i	0.966942	−	0.558264i
$852$	−647.679	+	1121.81i	−0.760186	+	1.31668i
$853$	−267.766	+	463.785i	−0.313911	+	0.543710i	−0.979205	−	0.202871i	$-0.934973\pi$
$853$	−267.766	+	463.785i	−0.313911	+	0.543710i	0.665294	+	0.746581i	$0.268306\pi$
$854$			1623.53i			1.90109i
$855$	−54.2675	−	259.694i	−0.0634707	−	0.303736i
$856$	9.16289			0.0107043
$857$	655.156	+	378.254i	0.764476	+	0.441370i	0.830901	−	0.556421i	$-0.187826\pi$
$857$	655.156	+	378.254i	0.764476	+	0.441370i	−0.0664245	+	0.997791i	$0.521159\pi$
$858$	604.438	+	348.972i	0.704473	+	0.406728i
$859$	538.135	+	932.077i	0.626466	+	1.08507i	0.988255	+	0.152812i	$0.0488328\pi$
$859$	538.135	+	932.077i	0.626466	+	1.08507i	−0.361789	+	0.932260i	$0.617834\pi$
$860$	1071.18	−	1855.35i	1.24556	−	2.15738i
$861$	174.889	+	302.917i	0.203123	+	0.351820i
$862$	−805.531			−0.934491
$863$			939.206i			1.08830i	0.838987	+	0.544152i	$0.183148\pi$
$863$			939.206i			1.08830i	−0.838987	+	0.544152i	$0.816852\pi$
$864$	54.7563	+	94.8407i	0.0633754	+	0.109769i
$865$	−1232.41	+	711.531i	−1.42475	+	0.822579i
$866$	−1035.29			−1.19548
$867$		−	263.481i		−	0.303900i
$868$	3448.88	−	1991.21i	3.97336	−	2.29402i
$869$	168.183	+	97.1006i	0.193536	+	0.111738i
$870$	954.567	−	551.120i	1.09720	−	0.633471i
$871$	−155.395	+	269.152i	−0.178410	+	0.309015i
$872$	−777.003	+	1345.81i	−0.891058	+	1.54336i
$873$		−	6.31684i		−	0.00723578i
$874$	1852.04	−	387.015i	2.11904	−	0.442809i
$875$	−1408.80			−1.61005
$876$	−1204.20	−	695.245i	−1.37466	−	0.793658i
$877$	−1011.30	−	583.873i	−1.15313	−	0.665761i	−0.203484	−	0.979078i	$-0.565226\pi$
$877$	−1011.30	−	583.873i	−1.15313	−	0.665761i	−0.949649	+	0.313317i	$0.898560\pi$
$878$	517.955	+	897.125i	0.589926	+	1.02178i
$879$	−193.602	+	335.328i	−0.220252	+	0.381489i
$880$	−365.509	−	633.080i	−0.415351	−	0.719409i
$881$	68.2541			0.0774734			0.0387367	−	0.999249i	$-0.487667\pi$
$881$	68.2541			0.0774734			0.0387367	+	0.999249i	$0.487667\pi$
$882$			695.475i			0.788520i
$883$	−134.599	−	233.133i	−0.152434	−	0.264023i	0.779688	−	0.626169i	$-0.215378\pi$
$883$	−134.599	−	233.133i	−0.152434	−	0.264023i	−0.932122	+	0.362145i	$0.882044\pi$
$884$	−1561.87	+	901.746i	−1.76682	+	1.02007i
$885$	−238.810			−0.269842
$886$		−	1550.68i		−	1.75020i
$887$	795.589	−	459.333i	0.896943	−	0.517850i	0.0207361	−	0.999785i	$-0.493399\pi$
$887$	795.589	−	459.333i	0.896943	−	0.517850i	0.876207	+	0.481935i	$0.160066\pi$
$888$	−849.754	−	490.606i	−0.956931	−	0.552484i
$889$	883.569	−	510.129i	0.993891	−	0.573823i
$890$	−735.072	+	1273.18i	−0.825924	+	1.43054i
$891$	28.6776	−	49.6711i	0.0321859	−	0.0557476i
$892$		−	691.268i		−	0.774964i
$893$	−340.693	+	304.647i	−0.381515	+	0.341150i
$894$	−356.168			−0.398398
$895$	1221.36	+	705.151i	1.36464	+	0.787878i
$896$	−1554.88	−	897.713i	−1.73536	−	1.00191i
$897$	−429.993	−	744.769i	−0.479367	−	0.830289i
$898$	−469.600	+	813.370i	−0.522939	+	0.905758i
$899$	−824.387	−	1427.88i	−0.917005	−	1.58830i
$900$	−86.8900			−0.0965445
$901$		−	179.978i		−	0.199754i
$902$	−214.527	−	371.571i	−0.237835	−	0.411942i
$903$	849.480	−	490.448i	0.940731	−	0.543131i
$904$	−923.947			−1.02207
$905$			337.928i			0.373401i
$906$	1097.50	−	633.643i	1.21137	−	0.699385i
$907$	654.944	+	378.132i	0.722099	+	0.416904i	0.815525	−	0.578722i	$-0.196448\pi$
$907$	654.944	+	378.132i	0.722099	+	0.416904i	−0.0934255	+	0.995626i	$0.529782\pi$
$908$	−985.164	+	568.784i	−1.08498	+	0.626415i
$909$	41.3071	−	71.5459i	0.0454423	−	0.0787084i
$910$	−1571.84	+	2722.50i	−1.72730	+	2.99176i
$911$		−	945.788i		−	1.03819i	−0.854718	−	0.519093i	$-0.826270\pi$
$911$		−	945.788i		−	1.03819i	0.854718	−	0.519093i	$-0.173730\pi$
$912$	−540.619	−	604.584i	−0.592784	−	0.662921i
$913$	−491.441			−0.538271
$914$	1977.00	+	1141.42i	2.16301	+	1.24882i
$915$	297.982	+	172.040i	0.325664	+	0.188022i
$916$	131.761	+	228.216i	0.143844	+	0.249145i
$917$	898.076	−	1555.51i	0.979363	−	1.69631i
$918$	108.245	+	187.486i	0.117914	+	0.204233i
$919$	1224.77			1.33272			0.666362	−	0.745628i	$-0.267850\pi$
$919$	1224.77			1.33272			0.666362	+	0.745628i	$0.267850\pi$
$920$			2169.94i			2.35863i
$921$	−339.034	−	587.224i	−0.368115	−	0.637594i
$922$	−1995.31	+	1151.99i	−2.16411	+	1.24945i
$923$	−1529.56			−1.65716
$924$		−	1023.61i		−	1.10781i
$925$	98.1715	−	56.6793i	0.106131	−	0.0612749i
$926$	−1256.32	−	725.336i	−1.35671	−	0.783300i
$927$	265.915	−	153.526i	0.286855	−	0.165616i
$928$	404.586	−	700.764i	0.435976	−	0.755133i
$929$	−529.236	+	916.663i	−0.569683	+	0.986721i	0.426914	+	0.904292i	$0.359601\pi$
$929$	−529.236	+	916.663i	−0.569683	+	0.986721i	−0.996597	+	0.0824281i	$0.973733\pi$
$930$		−	1232.88i		−	1.32567i
$931$	−253.001	−	1210.72i	−0.271752	−	1.30045i
$932$	−816.920			−0.876523
$933$	−563.741	−	325.476i	−0.604224	−	0.348849i
$934$	453.236	+	261.676i	0.485263	+	0.280167i
$935$	−173.515	−	300.537i	−0.185577	−	0.321429i
$936$	−444.042	+	769.104i	−0.474404	+	0.821692i
$937$	−96.5921	−	167.302i	−0.103087	−	0.178551i	0.809868	−	0.586612i	$-0.199539\pi$
$937$	−96.5921	−	167.302i	−0.103087	−	0.178551i	−0.912955	+	0.408061i	$0.866205\pi$
$938$	665.817			0.709827
$939$		−	261.171i		−	0.278137i
$940$	−486.003	−	841.781i	−0.517024	−	0.895512i
$941$	178.549	−	103.085i	0.189744	−	0.109549i	−0.402119	−	0.915587i	$-0.631726\pi$
$941$	178.549	−	103.085i	0.189744	−	0.109549i	0.591863	+	0.806039i	$0.298393\pi$
$942$	685.988			0.728225
$943$			528.666i			0.560621i
$944$	−632.242	+	365.025i	−0.669748	+	0.386679i
$945$	223.728	+	129.169i	0.236749	+	0.136687i
$946$	−1042.01	+	601.605i	−1.10149	+	0.635946i
$947$	553.455	−	958.612i	0.584430	−	1.01226i	−0.410517	−	0.911853i	$-0.634652\pi$
$947$	553.455	−	958.612i	0.584430	−	1.01226i	0.994946	−	0.100409i	$-0.0320151\pi$
$948$	−229.117	+	396.841i	−0.241684	+	0.418609i
$949$		−	1641.89i		−	1.73013i
$950$	220.956	−	46.1725i	0.232585	−	0.0486026i
$951$	876.326			0.921478
$952$	1804.39	+	1041.77i	1.89537	+	1.09429i
$953$	729.970	+	421.448i	0.765970	+	0.442233i	0.831435	−	0.555622i	$-0.187520\pi$
$953$	729.970	+	421.448i	0.765970	+	0.442233i	−0.0654649	+	0.997855i	$0.520853\pi$
$954$	−82.1734	−	142.329i	−0.0861356	−	0.149191i
$955$	−113.041	+	195.793i	−0.118368	+	0.205019i
$956$	1629.11	+	2821.70i	1.70409	+	2.95157i
$957$	−423.789			−0.442831
$958$		−	2205.76i		−	2.30246i
$959$	−634.251	−	1098.55i	−0.661367	−	1.14552i
$960$	−164.255	+	94.8327i	−0.171099	+	0.0987841i
$961$	−883.189			−0.919031
$962$		−	2148.53i		−	2.23339i
$963$	1.42788	−	0.824389i	0.00148274	−	0.000856063i
$964$	4.18826	+	2.41809i	0.00434467	+	0.00250839i
$965$	44.1428	−	25.4859i	0.0457438	−	0.0264102i
$966$	−921.188	+	1595.54i	−0.953611	+	1.65170i
$967$	−404.649	+	700.873i	−0.418458	+	0.724791i	−0.995785	−	0.0917223i	$-0.970763\pi$
$967$	−404.649	+	700.873i	−0.418458	+	0.724791i	0.577326	+	0.816514i	$0.304096\pi$
$968$		−	1340.23i		−	1.38454i
$969$	−256.643	−	287.009i	−0.264854	−	0.296191i
$970$	−34.9008			−0.0359802
$971$	−29.7562	−	17.1798i	−0.0306449	−	0.0176929i	0.484599	−	0.874736i	$-0.338965\pi$
$971$	−29.7562	−	17.1798i	−0.0306449	−	0.0176929i	−0.515244	+	0.857043i	$0.672299\pi$
$972$	117.203	+	67.6671i	0.120579	+	0.0696164i
$973$	589.439	+	1020.94i	0.605796	+	1.04927i
$974$	−612.268	+	1060.48i	−0.628612	+	1.08879i
$975$	−51.2998	−	88.8539i	−0.0526152	−	0.0911322i
$976$	1051.87			1.07773
$977$			1293.09i			1.32353i	0.749711	+	0.661765i	$0.230192\pi$
$977$			1293.09i			1.32353i	−0.749711	+	0.661765i	$0.769808\pi$
$978$	−213.386	−	369.595i	−0.218186	−	0.377909i
$979$	489.513	−	282.621i	0.500013	−	0.288683i
$980$	2630.53			2.68422
$981$			279.629i			0.285045i
$982$	−1548.14	+	893.820i	−1.57652	+	0.910204i
$983$	405.649	+	234.202i	0.412665	+	0.238252i	0.691934	−	0.721961i	$-0.256759\pi$
$983$	405.649	+	234.202i	0.412665	+	0.238252i	−0.279269	+	0.960213i	$0.590092\pi$
$984$	472.798	−	272.970i	0.480485	−	0.277408i
$985$	243.060	−	420.992i	0.246762	−	0.427403i
$986$	799.808	−	1385.31i	0.811164	−	1.40498i
$987$		−	445.038i		−	0.450900i
$988$	914.637	−	2782.39i	0.925746	−	2.81618i
$989$	1482.56			1.49904
$990$	−274.435	−	158.445i	−0.277207	−	0.160045i
$991$	1362.49	+	786.632i	1.37486	+	0.793776i	0.991535	−	0.129838i	$-0.0414456\pi$
$991$	1362.49	+	786.632i	1.37486	+	0.793776i	0.383325	+	0.923614i	$0.374779\pi$
$992$	−452.538	−	783.819i	−0.456187	−	0.790140i
$993$	−383.674	+	664.542i	−0.386378	+	0.669227i
$994$	1638.41	+	2837.81i	1.64830	+	2.85494i
$995$	−1309.23			−1.31581
$996$		−	1159.59i		−	1.16425i
$997$	121.379	+	210.235i	0.121744	+	0.210867i	0.920456	−	0.390847i	$-0.127818\pi$
$997$	121.379	+	210.235i	0.121744	+	0.210867i	−0.798711	+	0.601714i	$0.794485\pi$
$998$	2798.56	−	1615.75i	2.80417	−	1.61899i
$999$	−176.560			−0.176737

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	57.3.g.b.46.3	yes	6
3.2	odd	2		171.3.p.c.46.1		6
4.3	odd	2		912.3.be.f.673.2		6
19.12	odd	6	inner	57.3.g.b.31.3	✓	6
57.50	even	6		171.3.p.c.145.1		6
76.31	even	6		912.3.be.f.145.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
57.3.g.b.31.3	✓	6	19.12	odd	6	inner
57.3.g.b.46.3	yes	6	1.1	even	1	trivial
171.3.p.c.46.1		6	3.2	odd	2
171.3.p.c.145.1		6	57.50	even	6
912.3.be.f.145.2		6	76.31	even	6
912.3.be.f.673.2		6	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 57 = 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	57.g (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(3.08403 + 1.78057i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(4.34085 + 7.51857i) q^{4} +(2.32722 - 4.03087i) q^{5} +(-3.08403 - 5.34170i) q^{6} -10.6817 q^{7} +16.6722i q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(3.08403 + 1.78057i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(4.34085 + 7.51857i) q^{4} +(2.32722 - 4.03087i) q^{5} +(-3.08403 - 5.34170i) q^{6} -10.6817 q^{7} +16.6722i q^{8} +(1.50000 + 2.59808i) q^{9} +(14.3545 - 8.28756i) q^{10} -6.37280 q^{11} -15.0371i q^{12} +(15.3770 - 8.87792i) q^{13} +(-32.9427 - 19.0195i) q^{14} +(-6.98167 + 4.03087i) q^{15} +(-12.3225 + 21.3432i) q^{16} +(-5.84976 + 10.1321i) q^{17} +10.6834i q^{18} +(-3.88643 - 18.5983i) q^{19} +40.4085 q^{20} +(16.0225 + 9.25062i) q^{21} +(-19.6539 - 11.3472i) q^{22} +(13.9817 + 24.2170i) q^{23} +(14.4385 - 25.0082i) q^{24} +(1.66807 + 2.88918i) q^{25} +63.2310 q^{26} -5.19615i q^{27} +(-46.3676 - 80.3110i) q^{28} +(-33.2498 + 19.1968i) q^{29} -28.7089 q^{30} +42.9440i q^{31} +(-18.2521 + 10.5379i) q^{32} +(9.55920 + 5.51901i) q^{33} +(-36.0817 + 20.8318i) q^{34} +(-24.8587 + 43.0565i) q^{35} +(-13.0225 + 22.5557i) q^{36} -33.9790i q^{37} +(21.1296 - 64.2778i) q^{38} -30.7540 q^{39} +(67.2032 + 38.7998i) q^{40} +(16.3728 + 9.45284i) q^{41} +(32.9427 + 57.0585i) q^{42} +(26.5089 - 45.9148i) q^{43} +(-27.6634 - 47.9143i) q^{44} +13.9633 q^{45} +99.5813i q^{46} +(-12.0272 - 20.8318i) q^{47} +(36.9675 - 21.3432i) q^{48} +65.0986 q^{49} +11.8804i q^{50} +(17.5493 - 10.1321i) q^{51} +(133.499 + 77.0754i) q^{52} +(-13.3224 + 7.69168i) q^{53} +(9.25210 - 16.0251i) q^{54} +(-14.8309 + 25.6879i) q^{55} -178.087i q^{56} +(-10.2769 + 31.2632i) q^{57} -136.725 q^{58} +(25.6539 + 14.8113i) q^{59} +(-60.6127 - 34.9948i) q^{60} +(-21.3403 - 36.9626i) q^{61} +(-76.4648 + 132.441i) q^{62} +(-16.0225 - 27.7519i) q^{63} +23.5266 q^{64} -82.6436i q^{65} +(19.6539 + 34.0416i) q^{66} +(-15.1585 + 8.75178i) q^{67} -101.572 q^{68} -48.4339i q^{69} +(-153.330 + 88.5252i) q^{70} +(-74.6028 - 43.0719i) q^{71} +(-43.3155 + 25.0082i) q^{72} +(46.2352 - 80.0817i) q^{73} +(60.5019 - 104.792i) q^{74} -5.77836i q^{75} +(122.962 - 109.953i) q^{76} +68.0723 q^{77} +(-94.8465 - 54.7596i) q^{78} +(-26.3908 - 15.2367i) q^{79} +(57.3545 + 99.3409i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(33.6629 + 58.3058i) q^{82} +77.1154 q^{83} +160.622i q^{84} +(27.2274 + 47.1592i) q^{85} +(163.509 - 94.4019i) q^{86} +66.4996 q^{87} -106.248i q^{88} +(-76.8129 + 44.3479i) q^{89} +(43.0634 + 24.8627i) q^{90} +(-164.253 + 94.8312i) q^{91} +(-121.385 + 210.244i) q^{92} +(37.1906 - 64.4160i) q^{93} -85.6613i q^{94} +(-84.0118 - 27.6166i) q^{95} +36.5042 q^{96} +(-1.82351 - 1.05281i) q^{97} +(200.766 + 115.912i) q^{98} +(-9.55920 - 16.5570i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - 9 q^{3} + 5 q^{4} + 4 q^{5} - 3 q^{6} - 22 q^{7} + 9 q^{9}+O(q^{10}) \) 6 * q + 3 * q^2 - 9 * q^3 + 5 * q^4 + 4 * q^5 - 3 * q^6 - 22 * q^7 + 9 * q^9	\( 6 q + 3 q^{2} - 9 q^{3} + 5 q^{4} + 4 q^{5} - 3 q^{6} - 22 q^{7} + 9 q^{9} + 54 q^{10} - 36 q^{11} - 3 q^{13} - 57 q^{14} - 12 q^{15} - 23 q^{16} + 38 q^{17} - 10 q^{19} + 32 q^{20} + 33 q^{21} + 36 q^{22} + 54 q^{23} + 39 q^{24} - 21 q^{25} + 118 q^{26} - 101 q^{28} - 102 q^{29} - 108 q^{30} - 63 q^{32} + 54 q^{33} - 150 q^{34} - 24 q^{35} - 15 q^{36} + 119 q^{38} + 6 q^{39} + 30 q^{40} + 96 q^{41} + 57 q^{42} + 107 q^{43} - 94 q^{44} + 24 q^{45} - 50 q^{47} + 69 q^{48} - 48 q^{49} - 114 q^{51} + 399 q^{52} - 90 q^{53} + 9 q^{54} + 148 q^{55} - 3 q^{57} - 116 q^{58} - 48 q^{60} + 27 q^{61} - 121 q^{62} - 33 q^{63} + 46 q^{64} - 36 q^{66} - 39 q^{67} - 388 q^{68} - 354 q^{70} + 84 q^{71} - 117 q^{72} - 77 q^{73} + 219 q^{74} + 215 q^{76} + 260 q^{77} - 177 q^{78} + 9 q^{79} + 312 q^{80} - 27 q^{81} - 4 q^{82} - 348 q^{83} + 68 q^{85} + 249 q^{86} + 204 q^{87} - 72 q^{89} + 162 q^{90} - 393 q^{91} - 118 q^{92} + 129 q^{93} + 104 q^{95} + 126 q^{96} - 228 q^{97} + 540 q^{98} - 54 q^{99}+O(q^{100}) \) 6 * q + 3 * q^2 - 9 * q^3 + 5 * q^4 + 4 * q^5 - 3 * q^6 - 22 * q^7 + 9 * q^9 + 54 * q^10 - 36 * q^11 - 3 * q^13 - 57 * q^14 - 12 * q^15 - 23 * q^16 + 38 * q^17 - 10 * q^19 + 32 * q^20 + 33 * q^21 + 36 * q^22 + 54 * q^23 + 39 * q^24 - 21 * q^25 + 118 * q^26 - 101 * q^28 - 102 * q^29 - 108 * q^30 - 63 * q^32 + 54 * q^33 - 150 * q^34 - 24 * q^35 - 15 * q^36 + 119 * q^38 + 6 * q^39 + 30 * q^40 + 96 * q^41 + 57 * q^42 + 107 * q^43 - 94 * q^44 + 24 * q^45 - 50 * q^47 + 69 * q^48 - 48 * q^49 - 114 * q^51 + 399 * q^52 - 90 * q^53 + 9 * q^54 + 148 * q^55 - 3 * q^57 - 116 * q^58 - 48 * q^60 + 27 * q^61 - 121 * q^62 - 33 * q^63 + 46 * q^64 - 36 * q^66 - 39 * q^67 - 388 * q^68 - 354 * q^70 + 84 * q^71 - 117 * q^72 - 77 * q^73 + 219 * q^74 + 215 * q^76 + 260 * q^77 - 177 * q^78 + 9 * q^79 + 312 * q^80 - 27 * q^81 - 4 * q^82 - 348 * q^83 + 68 * q^85 + 249 * q^86 + 204 * q^87 - 72 * q^89 + 162 * q^90 - 393 * q^91 - 118 * q^92 + 129 * q^93 + 104 * q^95 + 126 * q^96 - 228 * q^97 + 540 * q^98 - 54 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more