LMFDB - Embedded newform 171.3.p.c.46.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [171,3,Mod(46,171)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(171, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("171.46");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 171 = 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	171.p (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:	$4.65941252056$
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:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 57)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			46.1
Root			$0.500000 + 2.69511i$ of defining polynomial
Character	$\chi$	$=$	171.46
Dual form			171.3.p.c.145.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.08403 - 1.78057i) q^{2} +(4.34085 + 7.51857i) q^{4} +(-2.32722 + 4.03087i) q^{5} -10.6817 q^{7} -16.6722i q^{8} +O(q^{10})$	\(q+(-3.08403 - 1.78057i) q^{2} +(4.34085 + 7.51857i) q^{4} +(-2.32722 + 4.03087i) q^{5} -10.6817 q^{7} -16.6722i q^{8} +(14.3545 - 8.28756i) q^{10} +6.37280 q^{11} +(15.3770 - 8.87792i) q^{13} +(32.9427 + 19.0195i) q^{14} +(-12.3225 + 21.3432i) q^{16} +(5.84976 - 10.1321i) q^{17} +(-3.88643 - 18.5983i) q^{19} -40.4085 q^{20} +(-19.6539 - 11.3472i) q^{22} +(-13.9817 - 24.2170i) q^{23} +(1.66807 + 2.88918i) q^{25} -63.2310 q^{26} +(-46.3676 - 80.3110i) q^{28} +(33.2498 - 19.1968i) q^{29} +42.9440i q^{31} +(18.2521 - 10.5379i) q^{32} +(-36.0817 + 20.8318i) q^{34} +(24.8587 - 43.0565i) q^{35} -33.9790i q^{37} +(-21.1296 + 64.2778i) q^{38} +(67.2032 + 38.7998i) q^{40} +(-16.3728 - 9.45284i) q^{41} +(26.5089 - 45.9148i) q^{43} +(27.6634 + 47.9143i) q^{44} +99.5813i q^{46} +(12.0272 + 20.8318i) q^{47} +65.0986 q^{49} -11.8804i q^{50} +(133.499 + 77.0754i) q^{52} +(13.3224 - 7.69168i) q^{53} +(-14.8309 + 25.6879i) q^{55} +178.087i q^{56} -136.725 q^{58} +(-25.6539 - 14.8113i) q^{59} +(-21.3403 - 36.9626i) q^{61} +(76.4648 - 132.441i) q^{62} +23.5266 q^{64} +82.6436i q^{65} +(-15.1585 + 8.75178i) q^{67} +101.572 q^{68} +(-153.330 + 88.5252i) q^{70} +(74.6028 + 43.0719i) q^{71} +(46.2352 - 80.0817i) q^{73} +(-60.5019 + 104.792i) q^{74} +(122.962 - 109.953i) q^{76} -68.0723 q^{77} +(-26.3908 - 15.2367i) q^{79} +(-57.3545 - 99.3409i) q^{80} +(33.6629 + 58.3058i) q^{82} -77.1154 q^{83} +(27.2274 + 47.1592i) q^{85} +(-163.509 + 94.4019i) q^{86} -106.248i q^{88} +(76.8129 - 44.3479i) q^{89} +(-164.253 + 94.8312i) q^{91} +(121.385 - 210.244i) q^{92} -85.6613i q^{94} +(84.0118 + 27.6166i) q^{95} +(-1.82351 - 1.05281i) q^{97} +(-200.766 - 115.912i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} + 5 q^{4} - 4 q^{5} - 22 q^{7}+O(q^{10}) $ 6 * q - 3 * q^2 + 5 * q^4 - 4 * q^5 - 22 * q^7	$ 6 q - 3 q^{2} + 5 q^{4} - 4 q^{5} - 22 q^{7} + 54 q^{10} + 36 q^{11} - 3 q^{13} + 57 q^{14} - 23 q^{16} - 38 q^{17} - 10 q^{19} - 32 q^{20} + 36 q^{22} - 54 q^{23} - 21 q^{25} - 118 q^{26} - 101 q^{28} + 102 q^{29} + 63 q^{32} - 150 q^{34} + 24 q^{35} - 119 q^{38} + 30 q^{40} - 96 q^{41} + 107 q^{43} + 94 q^{44} + 50 q^{47} - 48 q^{49} + 399 q^{52} + 90 q^{53} + 148 q^{55} - 116 q^{58} + 27 q^{61} + 121 q^{62} + 46 q^{64} - 39 q^{67} + 388 q^{68} - 354 q^{70} - 84 q^{71} - 77 q^{73} - 219 q^{74} + 215 q^{76} - 260 q^{77} + 9 q^{79} - 312 q^{80} - 4 q^{82} + 348 q^{83} + 68 q^{85} - 249 q^{86} + 72 q^{89} - 393 q^{91} + 118 q^{92} - 104 q^{95} - 228 q^{97} - 540 q^{98}+O(q^{100}) $ 6 * q - 3 * q^2 + 5 * q^4 - 4 * q^5 - 22 * q^7 + 54 * q^10 + 36 * q^11 - 3 * q^13 + 57 * q^14 - 23 * q^16 - 38 * q^17 - 10 * q^19 - 32 * q^20 + 36 * q^22 - 54 * q^23 - 21 * q^25 - 118 * q^26 - 101 * q^28 + 102 * q^29 + 63 * q^32 - 150 * q^34 + 24 * q^35 - 119 * q^38 + 30 * q^40 - 96 * q^41 + 107 * q^43 + 94 * q^44 + 50 * q^47 - 48 * q^49 + 399 * q^52 + 90 * q^53 + 148 * q^55 - 116 * q^58 + 27 * q^61 + 121 * q^62 + 46 * q^64 - 39 * q^67 + 388 * q^68 - 354 * q^70 - 84 * q^71 - 77 * q^73 - 219 * q^74 + 215 * q^76 - 260 * q^77 + 9 * q^79 - 312 * q^80 - 4 * q^82 + 348 * q^83 + 68 * q^85 - 249 * q^86 + 72 * q^89 - 393 * q^91 + 118 * q^92 - 104 * q^95 - 228 * q^97 - 540 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/171\mathbb{Z}\right)^\times$.

$n$	$20$	$154$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$

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	$-0.983839\pi$
$2$	−3.08403	−	1.78057i	−1.54202	−	0.890284i	−0.543306	−	0.839535i	$-0.682828\pi$
$3$		0			0
$3$		0			0
$4$	4.34085	+	7.51857i	1.08521	+	1.87964i
$5$	−2.32722	+	4.03087i	−0.465445	+	0.806174i	−0.999221	−	0.0394517i	$-0.987439\pi$
$5$	−2.32722	+	4.03087i	−0.465445	+	0.806174i	0.533777	+	0.845625i	$0.320772\pi$
$6$		0			0
$7$	−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
$9$		0			0
$10$	14.3545	−	8.28756i	1.43545	−	0.828756i
$11$	6.37280			0.579346			0.289673	−	0.957126i	$-0.406453\pi$
$11$	6.37280			0.579346			0.289673	+	0.957126i	$0.406453\pi$
$12$		0			0
$13$	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
$15$		0			0
$16$	−12.3225	+	21.3432i	−0.770157	+	1.33395i
$17$	5.84976	−	10.1321i	0.344104	−	0.596005i	−0.641087	−	0.767468i	$-0.721516\pi$
$17$	5.84976	−	10.1321i	0.344104	−	0.596005i	0.985191	+	0.171463i	$0.0548495\pi$
$18$		0			0
$19$	−3.88643	−	18.5983i	−0.204549	−	0.978856i
$19$	−3.88643	−	18.5983i	−0.204549	−	0.978856i
$20$	−40.4085			−2.02042
$21$		0			0
$22$	−19.6539	−	11.3472i	−0.893361	−	0.515782i
$23$	−13.9817	−	24.2170i	−0.607899	−	1.05291i	−0.991586	−	0.129448i	$-0.958679\pi$
$23$	−13.9817	−	24.2170i	−0.607899	−	1.05291i	0.383688	−	0.923463i	$-0.374654\pi$
$24$		0			0
$25$	1.66807	+	2.88918i	0.0667228	+	0.115567i
$26$	−63.2310			−2.43196
$27$		0			0
$28$	−46.3676	−	80.3110i	−1.65599	−	2.86825i
$29$	33.2498	−	19.1968i	1.14655	−	0.661958i	0.198502	−	0.980100i	$-0.436392\pi$
$29$	33.2498	−	19.1968i	1.14655	−	0.661958i	0.948043	+	0.318142i	$0.103059\pi$
$30$		0			0
$31$			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
$33$		0			0
$34$	−36.0817	+	20.8318i	−1.06123	+	0.612700i
$35$	24.8587	−	43.0565i	0.710248	−	1.23019i
$36$		0			0
$37$		−	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
$39$		0			0
$40$	67.2032	+	38.7998i	1.68008	+	0.969995i
$41$	−16.3728	−	9.45284i	−0.399337	−	0.230557i	0.286861	−	0.957972i	$-0.407388\pi$
$41$	−16.3728	−	9.45284i	−0.399337	−	0.230557i	−0.686198	+	0.727415i	$0.740722\pi$
$42$		0			0
$43$	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
$45$		0			0
$46$			99.5813i			2.16481i
$47$	12.0272	+	20.8318i	0.255899	+	0.443230i	0.965139	−	0.261737i	$-0.0842952\pi$
$47$	12.0272	+	20.8318i	0.255899	+	0.443230i	−0.709240	+	0.704967i	$0.750962\pi$
$48$		0			0
$49$	65.0986			1.32854
$50$		−	11.8804i		−	0.237609i
$51$		0			0
$52$	133.499	+	77.0754i	2.56728	+	1.48222i
$53$	13.3224	−	7.69168i	0.251366	−	0.145126i	−0.369024	−	0.929420i	$-0.620308\pi$
$53$	13.3224	−	7.69168i	0.251366	−	0.145126i	0.620389	+	0.784294i	$0.286975\pi$
$54$		0			0
$55$	−14.8309	+	25.6879i	−0.269653	+	0.467053i
$56$			178.087i			3.18012i
$57$		0			0
$58$	−136.725			−2.35732
$59$	−25.6539	−	14.8113i	−0.434813	−	0.251039i	0.266582	−	0.963812i	$-0.414106\pi$
$59$	−25.6539	−	14.8113i	−0.434813	−	0.251039i	−0.701395	+	0.712773i	$0.747439\pi$
$60$		0			0
$61$	−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
$63$		0			0
$64$	23.5266			0.367603
$65$			82.6436i			1.27144i
$66$		0			0
$67$	−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
$69$		0			0
$70$	−153.330	+	88.5252i	−2.19043	+	1.26465i
$71$	74.6028	+	43.0719i	1.05074	+	0.606647i	0.922857	−	0.385142i	$-0.125847\pi$
$71$	74.6028	+	43.0719i	1.05074	+	0.606647i	0.127886	+	0.991789i	$0.459181\pi$
$72$		0			0
$73$	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
$75$		0			0
$76$	122.962	−	109.953i	1.61792	−	1.44674i
$77$	−68.0723			−0.884056
$78$		0			0
$79$	−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
$81$		0			0
$82$	33.6629	+	58.3058i	0.410523	+	0.711046i
$83$	−77.1154			−0.929101			−0.464551	−	0.885547i	$-0.653784\pi$
$83$	−77.1154			−0.929101			−0.464551	+	0.885547i	$0.653784\pi$
$84$		0			0
$85$	27.2274	+	47.1592i	0.320322	+	0.554815i
$86$	−163.509	+	94.4019i	−1.90127	+	1.09770i
$87$		0			0
$88$		−	106.248i		−	1.20737i
$89$	76.8129	−	44.3479i	0.863066	−	0.498291i	−0.00197195	−	0.999998i	$-0.500628\pi$
$89$	76.8129	−	44.3479i	0.863066	−	0.498291i	0.865038	+	0.501707i	$0.167294\pi$
$90$		0			0
$91$	−164.253	+	94.8312i	−1.80497	+	1.04210i
$92$	121.385	−	210.244i	1.31940	−	2.28526i
$93$		0			0
$94$		−	85.6613i		−	0.911291i
$95$	84.0118	+	27.6166i	0.884334	+	0.290702i
$96$		0			0
$97$	−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
$99$		0			0
$100$	−14.4817	+	25.0830i	−0.144817	+	0.250830i
$101$	13.7690	+	23.8486i	0.136327	+	0.236125i	0.926104	−	0.377269i	$-0.123137\pi$
$101$	13.7690	+	23.8486i	0.136327	+	0.236125i	−0.789777	+	0.613395i	$0.789804\pi$
$102$		0			0
$103$		−	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
$105$		0			0
$106$	−54.7823			−0.516814
$107$			0.549592i			0.00513638i	0.999997	+	0.00256819i	$0.000817481\pi$
$107$			0.549592i			0.00513638i	−0.999997	+	0.00256819i	$0.999183\pi$
$108$		0			0
$109$	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
$111$		0			0
$112$	131.625	−	227.982i	1.17523	−	2.03555i
$113$		−	55.4186i		−	0.490430i	−0.969469	−	0.245215i	$-0.921141\pi$
$113$		−	55.4186i		−	0.490430i	0.969469	−	0.245215i	$-0.0788586\pi$
$114$		0			0
$115$	130.154			1.13177
$116$	288.665	+	166.661i	2.48849	+	1.43673i
$117$		0			0
$118$	52.7451	+	91.3572i	0.446992	+	0.774214i
$119$	−62.4854	+	108.228i	−0.525087	+	0.909478i
$120$		0			0
$121$	−80.3874			−0.664359
$122$			151.992i			1.24583i
$123$		0			0
$124$	−322.877	+	186.413i	−2.60385	+	1.50333i
$125$	−131.889			−1.05511
$126$		0			0
$127$	−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
$129$		0			0
$130$	147.153	−	254.876i	1.13194	−	1.96058i
$131$	84.0762	−	145.624i	0.641803	−	1.11164i	−0.343227	−	0.939252i	$-0.611520\pi$
$131$	84.0762	−	145.624i	0.641803	−	1.11164i	0.985030	−	0.172383i	$-0.0551466\pi$
$132$		0			0
$133$	41.5136	+	198.661i	0.312133	+	1.49369i
$134$	62.3326			0.465168
$135$		0			0
$136$	−168.924	−	97.5281i	−1.24209	−	0.717119i
$137$	−59.3774	−	102.845i	−0.433412	−	0.750691i	0.563753	−	0.825943i	$-0.309357\pi$
$137$	−59.3774	−	102.845i	−0.433412	−	0.750691i	−0.997165	+	0.0752526i	$0.976024\pi$
$138$		0			0
$139$	−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
$141$		0			0
$142$	−153.385	−	265.671i	−1.08018	−	1.87092i
$143$	97.9947	−	56.5772i	0.685277	−	0.395645i
$144$		0			0
$145$			178.701i			1.23242i
$146$	−285.182	+	164.650i	−1.95330	+	1.12774i
$147$		0			0
$148$	255.473	−	147.498i	1.72617	−	0.996605i
$149$	−28.8719	+	50.0077i	−0.193771	+	0.335622i	−0.946497	−	0.322712i	$-0.895405\pi$
$149$	−28.8719	+	50.0077i	−0.193771	+	0.335622i	0.752726	+	0.658334i	$0.228739\pi$
$150$		0			0
$151$			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
$153$		0			0
$154$	209.937	+	121.207i	1.36323	+	0.787061i
$155$	−173.102	−	99.9403i	−1.11678	−	0.644776i
$156$		0			0
$157$	−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
$159$		0			0
$160$			98.0958i			0.613099i
$161$	149.348	+	258.678i	0.927627	+	1.60670i
$162$		0			0
$163$	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
$165$		0			0
$166$	237.827	+	137.309i	1.43269	+	0.827164i
$167$	−181.817	+	104.972i	−1.08873	+	0.628577i	−0.933237	−	0.359261i	$-0.883029\pi$
$167$	−181.817	+	104.972i	−1.08873	+	0.628577i	−0.155490	+	0.987837i	$0.549696\pi$
$168$		0			0
$169$	73.1350	−	126.674i	0.432751	−	0.749547i
$170$		−	193.921i		−	1.14071i
$171$		0			0
$172$	460.285			2.67607
$173$	264.781	+	152.871i	1.53053	+	0.883649i	0.999337	+	0.0363949i	$0.0115874\pi$
$173$	264.781	+	152.871i	1.53053	+	0.883649i	0.531188	+	0.847254i	$0.321746\pi$
$174$		0			0
$175$	−17.8178	−	30.8613i	−0.101816	−	0.176351i
$176$	−78.5290	+	136.016i	−0.446187	+	0.772819i
$177$		0			0
$178$	−315.858			−1.77448
$179$		−	303.001i		−	1.69274i	−0.532593	−	0.846371i	$-0.678782\pi$
$179$		−	303.001i		−	1.69274i	0.532593	−	0.846371i	$-0.321218\pi$
$180$		0			0
$181$	−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
$183$		0			0
$184$	−403.749	+	233.104i	−2.19429	+	1.26687i
$185$	136.965	+	79.0767i	0.740350	+	0.427442i
$186$		0			0
$187$	37.2794	−	64.5698i	0.199355	−	0.345293i
$188$	−104.417	+	180.855i	−0.555409	+	0.961997i
$189$		0			0
$190$	−209.922	−	234.759i	−1.10485	−	1.23558i
$191$	48.5734			0.254311			0.127156	−	0.991883i	$-0.459415\pi$
$191$	48.5734			0.254311			0.127156	+	0.991883i	$0.459415\pi$
$192$		0			0
$193$	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
$195$		0			0
$196$	282.583	+	489.448i	1.44175	+	2.49718i
$197$	−104.442			−0.530163			−0.265082	−	0.964226i	$-0.585399\pi$
$197$	−104.442			−0.530163			−0.265082	+	0.964226i	$0.585399\pi$
$198$		0			0
$199$	−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
$201$		0			0
$202$		−	98.0667i		−	0.485479i
$203$	−355.164	+	205.054i	−1.74958	+	1.01012i
$204$		0			0
$205$	76.2063	−	43.9977i	0.371738	−	0.214623i
$206$	−182.242	+	315.653i	−0.884672	+	1.53230i
$207$		0			0
$208$			437.593i			2.10381i
$209$	−24.7674	−	118.523i	−0.118504	−	0.567096i
$210$		0			0
$211$	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
$213$		0			0
$214$	0.978587	−	1.69496i	0.00457284	−	0.00792038i
$215$	123.384	+	213.708i	0.573880	+	0.993990i
$216$		0			0
$217$		−	458.715i		−	2.11389i
$218$	−165.966	−	287.462i	−0.761313	−	1.31863i
$219$		0			0
$220$	−257.515			−1.17052
$221$		−	207.735i		−	0.939977i
$222$		0			0
$223$	−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
$225$		0			0
$226$	−98.6766	+	170.913i	−0.436622	+	0.756252i
$227$		−	131.031i		−	0.577228i	−0.957446	−	0.288614i	$-0.906806\pi$
$227$		−	131.031i		−	0.577228i	0.957446	−	0.288614i	$-0.0931944\pi$
$228$		0			0
$229$	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
$231$		0			0
$232$	−320.052	−	554.346i	−1.37953	−	2.38942i
$233$	47.0484	−	81.4902i	0.201924	−	0.349743i	−0.747224	−	0.664572i	$-0.768614\pi$
$233$	47.0484	−	81.4902i	0.201924	−	0.349743i	0.949148	+	0.314829i	$0.101947\pi$
$234$		0			0
$235$	−111.960			−0.476427
$236$		−	257.175i		−	1.08972i
$237$		0			0
$238$	385.414	−	222.519i	1.61939	−	0.934954i
$239$	−375.297			−1.57028			−0.785141	−	0.619317i	$-0.787409\pi$
$239$	−375.297			−1.57028			−0.785141	+	0.619317i	$0.787409\pi$
$240$		0			0
$241$	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
$243$		0			0
$244$	185.270	−	320.898i	0.759305	−	1.31515i
$245$	−151.499	+	262.404i	−0.618363	+	1.07104i
$246$		0			0
$247$	−224.876	−	251.482i	−0.910428	−	1.01815i
$248$	715.969			2.88697
$249$		0			0
$250$	406.750	+	234.837i	1.62700	+	0.939350i
$251$	−117.309	−	203.185i	−0.467367	−	0.809504i	0.531938	−	0.846783i	$-0.321464\pi$
$251$	−117.309	−	203.185i	−0.467367	−	0.809504i	−0.999305	+	0.0372799i	$0.988131\pi$
$252$		0			0
$253$	−89.1024	−	154.330i	−0.352183	−	0.610000i
$254$	340.141			1.33914
$255$		0			0
$256$	252.232	+	436.879i	0.985283	+	1.70656i
$257$	11.0702	−	6.39141i	0.0430749	−	0.0248693i	−0.478308	−	0.878192i	$-0.658750\pi$
$257$	11.0702	−	6.39141i	0.0430749	−	0.0248693i	0.521383	+	0.853323i	$0.325416\pi$
$258$		0			0
$259$			362.953i			1.40136i
$260$	−621.361	+	358.743i	−2.38985	+	1.37978i
$261$		0			0
$262$	−518.588	+	299.407i	−1.97934	+	1.14277i
$263$	−106.457	+	184.389i	−0.404780	+	0.701099i	−0.994296	−	0.106657i	$-0.965985\pi$
$263$	−106.457	+	184.389i	−0.404780	+	0.701099i	0.589516	+	0.807757i	$0.299319\pi$
$264$		0			0
$265$			71.6010i			0.270193i
$266$	225.700	−	686.595i	0.848497	−	2.58119i
$267$		0			0
$268$	−131.602	−	75.9803i	−0.491051	−	0.283508i
$269$	438.717	+	253.293i	1.63092	+	0.941610i	0.983811	+	0.179211i	$0.0573544\pi$
$269$	438.717	+	253.293i	1.63092	+	0.941610i	0.647106	+	0.762400i	$0.275979\pi$
$270$		0			0
$271$	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
$273$		0			0
$274$			422.902i			1.54344i
$275$	10.6303	+	18.4122i	0.0386556	+	0.0669534i
$276$		0			0
$277$	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
$279$		0			0
$280$	−717.844	−	414.448i	−2.56373	−	1.48017i
$281$	346.203	−	199.880i	1.23204	−	0.711317i	0.264583	−	0.964363i	$-0.414766\pi$
$281$	346.203	−	199.880i	1.23204	−	0.711317i	0.967454	+	0.253046i	$0.0814322\pi$
$282$		0			0
$283$	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
$285$		0			0
$286$	−402.959			−1.40895
$287$	174.889	+	100.972i	0.609370	+	0.351820i
$288$		0			0
$289$	76.0605	+	131.741i	0.263185	+	0.455850i
$290$	318.189	−	551.120i	1.09720	−	1.90041i
$291$		0			0
$292$	802.800			2.74931
$293$			223.552i			0.762977i	0.924374	+	0.381489i	$0.124588\pi$
$293$			223.552i			0.762977i	−0.924374	+	0.381489i	$0.875412\pi$
$294$		0			0
$295$	119.405	−	68.9384i	0.404762	−	0.233690i
$296$	−566.503			−1.91386
$297$		0			0
$298$	178.084	−	102.817i	0.597598	−	0.345023i
$299$	−429.993	−	248.256i	−1.43810	−	0.830289i
$300$		0			0
$301$	−283.160	+	490.448i	−0.940731	+	1.62939i
$302$	365.834	−	633.643i	1.21137	−	2.09816i
$303$		0			0
$304$	444.838	+	146.229i	1.46328	+	0.481015i
$305$	198.655			0.651328
$306$		0			0
$307$	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
$309$		0			0
$310$	355.901	+	616.439i	1.14807	+	1.98851i
$311$	−375.828			−1.20845			−0.604224	−	0.796814i	$-0.706517\pi$
$311$	−375.828			−1.20845			−0.604224	+	0.796814i	$0.706517\pi$
$312$		0			0
$313$	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
$315$		0			0
$316$		−	264.561i		−	0.837218i
$317$	438.163	−	252.973i	1.38222	−	0.798024i	0.389796	−	0.920901i	$-0.372546\pi$
$317$	438.163	−	252.973i	1.38222	−	0.798024i	0.992422	+	0.122878i	$0.0392123\pi$
$318$		0			0
$319$	211.895	−	122.337i	0.664246	−	0.383503i
$320$	−54.7517	+	94.8327i	−0.171099	+	0.296352i
$321$		0			0
$322$		−	1063.70i		−	3.30341i
$323$	−211.174	−	69.4179i	−0.653789	−	0.214916i
$324$		0			0
$325$	51.2998	+	29.6180i	0.157846	+	0.0911322i
$326$	−213.386	−	123.198i	−0.654558	−	0.377909i
$327$		0			0
$328$	−157.599	+	272.970i	−0.480485	+	0.832225i
$329$	−128.471	−	222.519i	−0.390491	−	0.676349i
$330$		0			0
$331$		−	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
$333$		0			0
$334$	747.642			2.23845
$335$		−	81.4694i		−	0.243192i
$336$		0			0
$337$	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
$339$		0			0
$340$	−236.380	+	409.422i	−0.695235	+	1.20418i
$341$			273.674i			0.802562i
$342$		0			0
$343$	−171.960			−0.501341
$344$	−765.498	−	441.961i	−2.22529	−	1.28477i
$345$		0			0
$346$	−544.396	−	942.921i	−1.57340	−	2.72520i
$347$	−262.446	+	454.570i	−0.756329	+	1.31000i	0.188382	+	0.982096i	$0.439676\pi$
$347$	−262.446	+	454.570i	−0.756329	+	1.31000i	−0.944711	+	0.327905i	$0.893658\pi$
$348$		0			0
$349$	−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
$351$		0			0
$352$	116.317	−	67.1557i	0.330446	−	0.190783i
$353$	−323.725			−0.917067			−0.458533	−	0.888677i	$-0.651625\pi$
$353$	−323.725			−0.917067			−0.458533	+	0.888677i	$0.651625\pi$
$354$		0			0
$355$	−347.235	+	200.476i	−0.978126	+	0.564721i
$356$	666.866	+	385.015i	1.87322	+	1.08150i
$357$		0			0
$358$	−539.514	+	934.465i	−1.50702	+	2.61024i
$359$	6.25614	−	10.8359i	0.0174266	−	0.0301837i	−0.857181	−	0.515016i	$-0.827786\pi$
$359$	6.25614	−	10.8359i	0.0174266	−	0.0301837i	0.874607	+	0.484832i	$0.161119\pi$
$360$		0			0
$361$	−330.791	+	144.562i	−0.916320	+	0.400448i
$362$	258.550			0.714227
$363$		0			0
$364$	−1425.99	−	823.296i	−3.91756	−	2.26180i
$365$	215.199	+	372.736i	0.589587	+	1.02119i
$366$		0			0
$367$	−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
$369$		0			0
$370$	−281.603	−	487.750i	−0.761089	−	1.31824i
$371$	−142.306	+	82.1602i	−0.383573	+	0.221456i
$372$		0			0
$373$		−	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
$375$		0			0
$376$	347.311	−	200.520i	0.923699	−	0.533298i
$377$	340.855	−	590.378i	0.904125	−	1.56599i
$378$		0			0
$379$			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
$381$		0			0
$382$	−149.802	−	86.4883i	−0.392152	−	0.226409i
$383$	355.819	+	205.432i	0.929031	+	0.536377i	0.886505	−	0.462719i	$-0.153126\pi$
$383$	355.819	+	205.432i	0.929031	+	0.536377i	0.0425263	+	0.999095i	$0.486459\pi$
$384$		0			0
$385$	158.419	−	274.391i	0.411479	−	0.712703i
$386$	−19.4993	−	33.7738i	−0.0505164	−	0.0874970i
$387$		0			0
$388$		−	18.2803i		−	0.0471141i
$389$	94.6013	+	163.854i	0.243191	+	0.421219i	0.961621	−	0.274380i	$-0.0884725\pi$
$389$	94.6013	+	163.854i	0.243191	+	0.421219i	−0.718430	+	0.695599i	$0.755139\pi$
$390$		0			0
$391$	−327.158			−0.836721
$392$		−	1085.33i		−	2.76871i
$393$		0			0
$394$	322.103	+	185.966i	0.817521	+	0.471996i
$395$	122.834	−	70.9185i	0.310973	−	0.179540i
$396$		0			0
$397$	−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
$399$		0			0
$400$	−82.2192			−0.205548
$401$	−320.526	−	185.056i	−0.799316	−	0.461485i	0.0439159	−	0.999035i	$-0.486017\pi$
$401$	−320.526	−	185.056i	−0.799316	−	0.461485i	−0.843232	+	0.537550i	$0.819350\pi$
$402$		0			0
$403$	381.254	+	660.351i	0.946039	+	1.63859i
$404$	−119.538	+	207.047i	−0.295887	+	0.512491i
$405$		0			0
$406$	1460.45			3.59717
$407$		−	216.541i		−	0.532043i
$408$		0			0
$409$	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
$411$		0			0
$412$	769.531	−	444.289i	1.86779	−	1.07837i
$413$	274.028	+	158.210i	0.663505	+	0.383075i
$414$		0			0
$415$	179.465	−	310.842i	0.432445	−	0.749017i
$416$	187.109	−	324.082i	0.449780	−	0.779042i
$417$		0			0
$418$	−134.655	+	409.630i	−0.322141	+	0.979975i
$419$	295.264			0.704687			0.352344	−	0.935871i	$-0.385385\pi$
$419$	295.264			0.704687			0.352344	+	0.935871i	$0.385385\pi$
$420$		0			0
$421$	−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
$423$		0			0
$424$	−128.237	−	222.113i	−0.302446	−	0.523851i
$425$	39.0312			0.0918382
$426$		0			0
$427$	227.951	+	394.823i	0.533843	+	0.924644i
$428$	−4.13215	+	2.38570i	−0.00965455	+	0.00557406i
$429$		0			0
$430$		−	878.777i		−	2.04367i
$431$	195.895	−	113.100i	0.454514	−	0.262414i	−0.255221	−	0.966883i	$-0.582148\pi$
$431$	195.895	−	113.100i	0.454514	−	0.262414i	0.709735	+	0.704469i	$0.248815\pi$
$432$		0			0
$433$	−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
$435$		0			0
$436$			809.218i			1.85600i
$437$	−396.055	+	354.152i	−0.906304	+	0.810417i
$438$		0			0
$439$	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
$441$		0			0
$442$	−369.886	+	640.662i	−0.836847	+	1.44946i
$443$	217.722	+	377.106i	0.491473	+	0.851256i	0.999952	−	0.00981853i	$-0.00312539\pi$
$443$	217.722	+	377.106i	0.491473	+	0.851256i	−0.508479	+	0.861074i	$0.669792\pi$
$444$		0			0
$445$			412.830i			0.927708i
$446$	141.775	+	245.562i	0.317882	+	0.550587i
$447$		0			0
$448$	−251.304			−0.560947
$449$		−	263.736i		−	0.587385i	−0.955900	−	0.293692i	$-0.905116\pi$
$449$		−	263.736i		−	0.587385i	0.955900	−	0.293692i	$-0.0948842\pi$
$450$		0			0
$451$	−104.341	−	60.2411i	−0.231354	−	0.133572i
$452$	416.669	−	240.564i	0.921833	−	0.532221i
$453$		0			0
$454$	−233.309	+	404.103i	−0.513897	+	0.890096i
$455$		−	882.774i		−	1.94016i
$456$		0			0
$457$	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
$459$		0			0
$460$	564.978	+	978.570i	1.22821	+	2.12733i
$461$	323.490	−	560.302i	0.701714	−	1.21540i	−0.266150	−	0.963932i	$-0.585752\pi$
$461$	323.490	−	560.302i	0.701714	−	1.21540i	0.967864	−	0.251473i	$-0.0809150\pi$
$462$		0			0
$463$	−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
$465$		0			0
$466$	−290.198	+	167.546i	−0.622742	+	0.359540i
$467$	−146.962			−0.314694			−0.157347	−	0.987543i	$-0.550294\pi$
$467$	−146.962			−0.314694			−0.157347	+	0.987543i	$0.550294\pi$
$468$		0			0
$469$	161.919	−	93.4838i	0.345242	−	0.199326i
$470$	345.290	+	199.353i	0.734659	+	0.424155i
$471$		0			0
$472$	−246.936	+	427.706i	−0.523170	+	0.906158i
$473$	168.936	−	292.606i	0.357159	−	0.618617i
$474$		0			0
$475$	47.2509	−	42.2518i	0.0994757	−	0.0889512i
$476$	−1084.96			−2.27932
$477$		0			0
$478$	1157.43	+	668.242i	2.42140	+	1.39800i
$479$	309.698	+	536.413i	0.646552	+	1.11986i	0.983941	+	0.178495i	$0.0571230\pi$
$479$	309.698	+	536.413i	0.646552	+	1.11986i	−0.337389	+	0.941365i	$0.609544\pi$
$480$		0			0
$481$	−301.663	−	522.495i	−0.627158	−	1.08627i
$482$	−1.98375			−0.00411566
$483$		0			0
$484$	−348.949	−	604.398i	−0.720970	−	1.24876i
$485$	8.48745	−	4.90023i	0.0174999	−	0.0101036i
$486$		0			0
$487$			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
$489$		0			0
$490$	934.456	−	539.508i	1.90705	−	1.10104i
$491$	250.993	−	434.733i	0.511187	−	0.885402i	−0.488729	−	0.872436i	$-0.662539\pi$
$491$	250.993	−	434.733i	0.511187	−	0.885402i	0.999916	−	0.0129665i	$-0.00412747\pi$
$492$		0			0
$493$		−	449.187i		−	0.911129i
$494$	245.743	+	1175.99i	0.497455	+	2.38054i
$495$		0			0
$496$	−916.564	−	529.178i	−1.84791	−	1.06689i
$497$	−796.884	−	460.081i	−1.60339	−	0.925717i
$498$		0			0
$499$	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
$501$		0			0
$502$			835.508i			1.66436i
$503$	−183.800	−	318.352i	−0.365408	−	0.632906i	0.623433	−	0.781877i	$-0.285737\pi$
$503$	−183.800	−	318.352i	−0.365408	−	0.632906i	−0.988842	+	0.148971i	$0.952404\pi$
$504$		0			0
$505$	−128.174			−0.253810
$506$			634.612i			1.25417i
$507$		0			0
$508$	−718.133	−	414.614i	−1.41365	−	0.816170i
$509$	−406.585	+	234.742i	−0.798791	+	0.461182i	−0.843048	−	0.537838i	$-0.819241\pi$
$509$	−406.585	+	234.742i	−0.798791	+	0.461182i	0.0442573	+	0.999020i	$0.485908\pi$
$510$		0			0
$511$	−493.870	+	855.408i	−0.966478	+	1.67399i
$512$		−	1124.13i		−	2.19557i
$513$		0			0
$514$	−45.5214			−0.0885630
$515$	412.562	+	238.193i	0.801092	+	0.462511i
$516$		0			0
$517$	76.6473	+	132.757i	0.148254	+	0.256783i
$518$	646.263	−	1119.36i	1.24761	−	2.16093i
$519$		0			0
$520$	1377.85			2.64970
$521$			691.695i			1.32763i	0.747897	+	0.663815i	$0.231064\pi$
$521$			691.695i			1.32763i	−0.747897	+	0.663815i	$0.768936\pi$
$522$		0			0
$523$	−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
$525$		0			0
$526$	656.635	−	379.108i	1.24836	−	0.720738i
$527$	435.113	+	251.212i	0.825640	+	0.476684i
$528$		0			0
$529$	−126.474	+	219.060i	−0.239081	+	0.414101i
$530$	127.491	−	220.820i	0.240548	−	0.416642i
$531$		0			0
$532$	−1313.44	+	1174.48i	−2.46888	+	2.20767i
$533$	−335.686			−0.629806
$534$		0			0
$535$	−2.21533	−	1.27902i	−0.00414081	−	0.00239070i
$536$	145.911	+	252.725i	0.272222	+	0.471502i
$537$		0			0
$538$	−902.012	−	1562.33i	−1.67660	−	2.90396i
$539$	414.860			0.769685
$540$		0			0
$541$	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
$543$		0			0
$544$		−	246.576i		−	0.453264i
$545$	−375.716	+	216.920i	−0.689387	+	0.398018i
$546$		0			0
$547$	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
$549$		0			0
$550$		−	75.7117i		−	0.137658i
$551$	−486.250	−	543.782i	−0.882487	−	0.986900i
$552$		0			0
$553$	281.898	+	162.754i	0.509761	+	0.294311i
$554$	−808.273	−	466.657i	−1.45898	−	0.842341i
$555$		0			0
$556$	479.075	−	829.782i	0.861645	−	1.49241i
$557$	−386.099	−	668.743i	−0.693175	−	1.20061i	−0.970792	−	0.239923i	$-0.922878\pi$
$557$	−386.099	−	668.743i	−0.693175	−	1.20061i	0.277617	−	0.960692i	$-0.410456\pi$
$558$		0			0
$559$		−	941.376i		−	1.68404i
$560$	612.643	+	1061.13i	1.09401	+	1.89487i
$561$		0			0
$562$	−1423.60			−2.53310
$563$			195.273i			0.346844i	0.984848	+	0.173422i	$0.0554825\pi$
$563$			195.273i			0.346844i	−0.984848	+	0.173422i	$0.944518\pi$
$564$		0			0
$565$	223.385	+	128.971i	0.395372	+	0.228268i
$566$	−254.345	+	146.846i	−0.449373	+	0.259446i
$567$		0			0
$568$	718.102	−	1243.79i	1.26426	−	2.18977i
$569$			579.517i			1.01848i	0.860624	+	0.509242i	$0.170074\pi$
$569$			579.517i			1.01848i	−0.860624	+	0.509242i	$0.829926\pi$
$570$		0			0
$571$	−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
$573$		0			0
$574$	−359.576	−	622.805i	−0.626440	−	1.08503i
$575$	46.6448	−	80.7911i	0.0811214	−	0.140506i
$576$		0			0
$577$	−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
$579$		0			0
$580$	−1343.57	+	775.713i	−2.31651	+	1.33744i
$581$	823.723			1.41777
$582$		0			0
$583$	84.9009	−	49.0176i	0.145628	−	0.0840782i
$584$	−1335.13	−	770.840i	−2.28619	−	1.31993i
$585$		0			0
$586$	398.050	−	689.443i	0.679266	−	1.17652i
$587$	−441.521	+	764.737i	−0.752165	+	1.30279i	0.194606	+	0.980882i	$0.437657\pi$
$587$	−441.521	+	764.737i	−0.752165	+	1.30279i	−0.946771	+	0.321907i	$0.895676\pi$
$588$		0			0
$589$	798.684	−	166.899i	1.35600	−	0.283360i
$590$	−490.998			−0.832201
$591$		0			0
$592$	725.221	+	418.707i	1.22504	+	0.707275i
$593$	−119.583	−	207.125i	−0.201658	−	0.349283i	0.747404	−	0.664369i	$-0.231300\pi$
$593$	−119.583	−	207.125i	−0.201658	−	0.349283i	−0.949063	+	0.315087i	$0.897966\pi$
$594$		0			0
$595$	−290.835	−	503.741i	−0.488798	−	0.846623i
$596$	−501.315			−0.841132
$597$		0			0
$598$	884.075	+	1531.26i	1.47839	+	2.56064i
$599$	793.604	−	458.187i	1.32488	−	0.764920i	0.340378	−	0.940289i	$-0.389445\pi$
$599$	793.604	−	458.187i	1.32488	−	0.764920i	0.984503	+	0.175368i	$0.0561116\pi$
$600$		0			0
$601$		−	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
$603$		0			0
$604$	−1544.76	+	891.867i	−2.55755	+	1.47660i
$605$	187.079	−	324.031i	0.309222	−	0.535588i
$606$		0			0
$607$		−	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
$609$		0			0
$610$	−612.659	−	353.719i	−1.00436	−	0.579867i
$611$	369.886	+	213.554i	0.605379	+	0.349515i
$612$		0			0
$613$	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
$615$		0			0
$616$			1134.91i			1.84239i
$617$	501.032	+	867.813i	0.812045	+	1.40650i	0.911430	+	0.411455i	$0.134979\pi$
$617$	501.032	+	867.813i	0.812045	+	1.40650i	−0.0993850	+	0.995049i	$0.531688\pi$
$618$		0			0
$619$	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
$621$		0			0
$622$	1159.07	+	669.187i	1.86345	+	1.07586i
$623$	−820.491	+	473.711i	−1.31700	+	0.760371i
$624$		0			0
$625$	265.233	−	459.398i	0.424373	−	0.735036i
$626$		−	536.973i		−	0.857784i
$627$		0			0
$628$	−965.543			−1.53749
$629$	−344.278	−	198.769i	−0.547342	−	0.316008i
$630$		0			0
$631$	−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
$633$		0			0
$634$	−1801.75			−2.84187
$635$		−	444.568i		−	0.700107i
$636$		0			0
$637$	1001.02	−	577.940i	1.57146	−	0.907284i
$638$	−871.320			−1.36571
$639$		0			0
$640$	677.526	−	391.170i	1.05863	−	0.611203i
$641$	−89.1040	−	51.4442i	−0.139008	−	0.0802562i	0.428883	−	0.903360i	$-0.358907\pi$
$641$	−89.1040	−	51.4442i	−0.139008	−	0.0802562i	−0.567891	+	0.823104i	$0.692241\pi$
$642$		0			0
$643$	−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
$645$		0			0
$646$	527.665	+	590.097i	0.816818	+	0.913463i
$647$	790.984			1.22254			0.611270	−	0.791422i	$-0.290659\pi$
$647$	790.984			1.22254			0.611270	+	0.791422i	$0.290659\pi$
$648$		0			0
$649$	−163.488	−	94.3896i	−0.251907	−	0.145438i
$650$	−105.474	−	182.686i	−0.162267	−	0.281055i
$651$		0			0
$652$	300.345	+	520.213i	0.460652	+	0.797873i
$653$	−320.503			−0.490816			−0.245408	−	0.969420i	$-0.578922\pi$
$653$	−320.503			−0.490816			−0.245408	+	0.969420i	$0.578922\pi$
$654$		0			0
$655$	391.328	+	677.800i	0.597447	+	1.03481i
$656$	403.508	−	232.966i	0.615104	−	0.355130i
$657$		0			0
$658$			915.008i			1.39059i
$659$	616.112	−	355.713i	0.934920	−	0.539776i	0.0465558	−	0.998916i	$-0.485175\pi$
$659$	616.112	−	355.713i	0.934920	−	0.539776i	0.888364	+	0.459139i	$0.151842\pi$
$660$		0			0
$661$	−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
$663$		0			0
$664$			1285.68i			1.93626i
$665$	−897.388	−	294.993i	−1.34946	−	0.443598i
$666$		0			0
$667$	−929.776	−	536.806i	−1.39397	−	0.804807i
$668$	−1578.48	−	911.338i	−2.36300	−	1.36428i
$669$		0			0
$670$	−145.062	+	251.254i	−0.216510	+	0.375006i
$671$	−135.998	−	235.555i	−0.202679	−	0.351051i
$672$		0			0
$673$			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
$675$		0			0
$676$	1269.87			1.87851
$677$			860.699i			1.27134i	0.771960	+	0.635671i	$0.219277\pi$
$677$			860.699i			1.27134i	−0.771960	+	0.635671i	$0.780723\pi$
$678$		0			0
$679$	19.4782	+	11.2458i	0.0286866	+	0.0165622i
$680$	786.246	−	453.939i	1.15624	−	0.667558i
$681$		0			0
$682$	487.295	−	844.019i	0.714509	−	1.23757i
$683$			194.789i			0.285196i	0.989781	+	0.142598i	$0.0455456\pi$
$683$			194.789i			0.285196i	−0.989781	+	0.142598i	$0.954454\pi$
$684$		0			0
$685$	552.738			0.806916
$686$	530.331	+	306.187i	0.773077	+	0.446336i
$687$		0			0
$688$	653.313	+	1131.57i	0.949583	+	1.64473i
$689$	136.572	−	236.550i	0.198218	−	0.343324i
$690$		0			0
$691$	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
$693$		0			0
$694$	1618.79	−	934.607i	2.33255	−	1.34670i
$695$	513.685			0.739115
$696$		0			0
$697$	−191.554	+	110.594i	−0.274826	+	0.158671i
$698$	1138.21	+	657.144i	1.63067	+	0.941467i
$699$		0			0
$700$	154.689	−	267.929i	0.220984	−	0.382755i
$701$	−242.353	+	419.767i	−0.345724	+	0.598812i	−0.985485	−	0.169762i	$-0.945700\pi$
$701$	−242.353	+	419.767i	−0.345724	+	0.598812i	0.639761	+	0.768574i	$0.279033\pi$
$702$		0			0
$703$	−631.951	+	132.057i	−0.898934	+	0.187848i
$704$	149.931			0.212969
$705$		0			0
$706$	998.378	+	576.414i	1.41413	+	0.816450i
$707$	−147.076	−	254.744i	−0.208029	−	0.360317i
$708$		0			0
$709$	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
$711$		0			0
$712$	−739.375	−	1280.64i	−1.03845	−	1.79865i
$713$	1039.97	−	600.429i	1.45859	−	0.842116i
$714$		0			0
$715$			526.671i			0.736603i
$716$	2278.13	−	1315.28i	3.18175	−	1.83698i
$717$		0			0
$718$	−38.5883	+	22.2790i	−0.0537441	+	0.0310292i
$719$	−65.3191	+	113.136i	−0.0908471	+	0.157352i	−0.907868	−	0.419256i	$-0.862291\pi$
$719$	−65.3191	+	113.136i	−0.0908471	+	0.157352i	0.817021	+	0.576608i	$0.195624\pi$
$720$		0			0
$721$			1093.28i			1.51634i
$722$	1277.57	+	143.163i	1.76949	+	0.198287i
$723$		0			0
$724$	−545.873	−	315.160i	−0.753968	−	0.435303i
$725$	110.926	+	64.0432i	0.153001	+	0.0883354i
$726$		0			0
$727$	−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
$729$		0			0
$730$		−	1532.71i		−	2.09960i
$731$	−310.142	−	537.181i	−0.424271	−	0.734858i
$732$		0			0
$733$	−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
$735$		0			0
$736$	−510.390	−	294.674i	−0.693464	−	0.400372i
$737$	−96.6023	+	55.7734i	−0.131075	+	0.0756762i
$738$		0			0
$739$	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
$741$		0			0
$742$	585.167			0.788635
$743$	66.4928	+	38.3896i	0.0894923	+	0.0516684i	0.544078	−	0.839034i	$-0.316879\pi$
$743$	66.4928	+	38.3896i	0.0894923	+	0.0516684i	−0.454586	+	0.890703i	$0.650213\pi$
$744$		0			0
$745$	−134.383	−	232.758i	−0.180380	−	0.312427i
$746$	−723.782	+	1253.63i	−0.970217	+	1.68046i
$747$		0			0
$748$	647.296			0.865370
$749$		−	5.87058i		−	0.00783789i
$750$		0			0
$751$	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
$753$		0			0
$754$	−2102.42	+	1213.83i	−2.78835	+	1.60986i
$755$	−828.179	−	478.149i	−1.09693	−	0.633310i
$756$		0			0
$757$	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
$759$		0			0
$760$	460.429	−	1400.66i	0.605827	−	1.84297i
$761$	−1147.50			−1.50788			−0.753940	−	0.656944i	$-0.771849\pi$
$761$	−1147.50			−1.50788			−0.753940	+	0.656944i	$0.771849\pi$
$762$		0			0
$763$	−862.247	−	497.819i	−1.13007	−	0.652449i
$764$	210.850	+	365.203i	0.275982	+	0.478014i
$765$		0			0
$766$	−731.572	−	1267.12i	−0.955055	−	1.65420i
$767$	−525.975			−0.685756
$768$		0			0
$769$	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
$771$		0			0
$772$			95.0749i			0.123154i
$773$	−858.414	+	495.605i	−1.11050	+	0.641145i	−0.938958	−	0.344032i	$-0.888207\pi$
$773$	−858.414	+	495.605i	−1.11050	+	0.641145i	−0.171538	+	0.985177i	$0.554874\pi$
$774$		0			0
$775$	−124.073	+	71.6336i	−0.160094	+	0.0924305i
$776$	−17.5525	+	30.4019i	−0.0226193	+	0.0391777i
$777$		0			0
$778$		−	673.776i		−	0.866036i
$779$	−112.175	+	341.244i	−0.143998	+	0.438053i
$780$		0			0
$781$	475.429	+	274.489i	0.608744	+	0.351458i
$782$	1008.97	+	582.527i	1.29024	+	0.744919i
$783$		0			0
$784$	−802.178	+	1389.41i	−1.02319	+	1.77221i
$785$	−258.824	−	448.297i	−0.329713	−	0.571079i
$786$		0			0
$787$			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
$789$		0			0
$790$	−505.101			−0.639368
$791$			591.965i			0.748375i
$792$		0			0
$793$	−656.302	−	378.916i	−0.827619	−	0.477826i
$794$	1362.15	−	786.438i	1.71555	−	0.990476i
$795$		0			0
$796$	1221.02	−	2114.87i	1.53395	−	2.65688i
$797$		−	788.636i		−	0.989506i	−0.869034	−	0.494753i	$-0.835259\pi$
$797$		−	788.636i		−	0.989506i	0.869034	−	0.494753i	$-0.164741\pi$
$798$		0			0
$799$	281.426			0.352223
$800$	60.8916	+	35.1558i	0.0761144	+	0.0439447i
$801$		0			0
$802$	659.008	+	1141.44i	0.821706	+	1.42324i
$803$	294.648	−	510.345i	0.366934	−	0.635548i
$804$		0			0
$805$	−1390.26			−1.72704
$806$		−	2715.39i		−	3.36897i
$807$		0			0
$808$	397.608	−	229.559i	0.492089	−	0.284108i
$809$	−640.524			−0.791748			−0.395874	−	0.918305i	$-0.629558\pi$
$809$	−640.524			−0.791748			−0.395874	+	0.918305i	$0.629558\pi$
$810$		0			0
$811$	−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
$813$		0			0
$814$	−385.567	+	667.821i	−0.473669	+	0.820419i
$815$	−161.022	+	278.898i	−0.197573	+	0.342206i
$816$		0			0
$817$	−956.961	−	314.576i	−1.17131	−	0.385037i
$818$	−1720.43			−2.10321
$819$		0			0
$820$	661.600	+	381.975i	0.806829	+	0.465823i
$821$	671.718	+	1163.45i	0.818170	+	1.41711i	0.907029	+	0.421068i	$0.138345\pi$
$821$	671.718	+	1163.45i	0.818170	+	1.41711i	−0.0888591	+	0.996044i	$0.528322\pi$
$822$		0			0
$823$	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
$825$		0			0
$826$	−563.407	−	975.850i	−0.682091	−	1.18142i
$827$	−583.285	+	336.760i	−0.705303	+	0.407207i	−0.809319	−	0.587369i	$-0.800164\pi$
$827$	−583.285	+	336.760i	−0.705303	+	0.407207i	0.104017	+	0.994576i	$0.466830\pi$
$828$		0			0
$829$			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
$831$		0			0
$832$	361.769	−	208.867i	0.434819	−	0.251043i
$833$	380.811	−	659.584i	0.457156	−	0.791818i
$834$		0			0
$835$		−	977.176i		−	1.17027i
$836$	783.612	−	700.706i	0.937335	−	0.838165i
$837$		0			0
$838$	−910.605	−	525.738i	−1.08664	−	0.627372i
$839$	1050.53	+	606.526i	1.25213	+	0.722915i	0.971531	−	0.236911i	$-0.0761350\pi$
$839$	1050.53	+	606.526i	1.25213	+	0.722915i	0.280595	+	0.959826i	$0.409468\pi$
$840$		0			0
$841$	316.533	−	548.252i	0.376377	−	0.651905i
$842$	924.348	+	1601.02i	1.09780	+	1.90145i
$843$		0			0
$844$			895.018i			1.06045i
$845$	340.403	+	589.595i	0.402844	+	0.697745i
$846$		0			0
$847$	858.673			1.01378
$848$			379.124i			0.447080i
$849$		0			0
$850$	−120.374	−	69.4978i	−0.141616	−	0.0817621i
$851$	−822.868	+	475.083i	−0.966942	+	0.558264i
$852$		0			0
$853$	−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
$855$		0			0
$856$	9.16289			0.0107043
$857$	−655.156	−	378.254i	−0.764476	−	0.441370i	0.0664245	−	0.997791i	$-0.478841\pi$
$857$	−655.156	−	378.254i	−0.764476	−	0.441370i	−0.830901	+	0.556421i	$0.812174\pi$
$858$		0			0
$859$	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
$861$		0			0
$862$	−805.531			−0.934491
$863$		−	939.206i		−	1.08830i	−0.838987	−	0.544152i	$-0.816852\pi$
$863$		−	939.206i		−	1.08830i	0.838987	−	0.544152i	$-0.183148\pi$
$864$		0			0
$865$	−1232.41	+	711.531i	−1.42475	+	0.822579i
$866$	1035.29			1.19548
$867$		0			0
$868$	3448.88	−	1991.21i	3.97336	−	2.29402i
$869$	−168.183	−	97.1006i	−0.193536	−	0.111738i
$870$		0			0
$871$	−155.395	+	269.152i	−0.178410	+	0.309015i
$872$	777.003	−	1345.81i	0.891058	−	1.54336i
$873$		0			0
$874$	1852.04	−	387.015i	2.11904	−	0.442809i
$875$	1408.80			1.61005
$876$		0			0
$877$	−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
$879$		0			0
$880$	−365.509	−	633.080i	−0.415351	−	0.719409i
$881$	−68.2541			−0.0774734			−0.0387367	−	0.999249i	$-0.512333\pi$
$881$	−68.2541			−0.0774734			−0.0387367	+	0.999249i	$0.512333\pi$
$882$		0			0
$883$	−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
$885$		0			0
$886$		−	1550.68i		−	1.75020i
$887$	−795.589	+	459.333i	−0.896943	+	0.517850i	−0.876207	−	0.481935i	$-0.839934\pi$
$887$	−795.589	+	459.333i	−0.896943	+	0.517850i	−0.0207361	+	0.999785i	$0.506601\pi$
$888$		0			0
$889$	883.569	−	510.129i	0.993891	−	0.573823i
$890$	735.072	−	1273.18i	0.825924	−	1.43054i
$891$		0			0
$892$		−	691.268i		−	0.774964i
$893$	340.693	−	304.647i	0.381515	−	0.341150i
$894$		0			0
$895$	1221.36	+	705.151i	1.36464	+	0.787878i
$896$	1554.88	+	897.713i	1.73536	+	1.00191i
$897$		0			0
$898$	−469.600	+	813.370i	−0.522939	+	0.905758i
$899$	824.387	+	1427.88i	0.917005	+	1.58830i
$900$		0			0
$901$		−	179.978i		−	0.199754i
$902$	214.527	+	371.571i	0.237835	+	0.411942i
$903$		0			0
$904$	−923.947			−1.02207
$905$		−	337.928i		−	0.373401i
$906$		0			0
$907$	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
$909$		0			0
$910$	−1571.84	+	2722.50i	−1.72730	+	2.99176i
$911$			945.788i			1.03819i	0.854718	+	0.519093i	$0.173730\pi$
$911$			945.788i			1.03819i	−0.854718	+	0.519093i	$0.826270\pi$
$912$		0			0
$913$	−491.441			−0.538271
$914$	−1977.00	−	1141.42i	−2.16301	−	1.24882i
$915$		0			0
$916$	131.761	+	228.216i	0.143844	+	0.249145i
$917$	−898.076	+	1555.51i	−0.979363	+	1.69631i
$918$		0			0
$919$	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
$921$		0			0
$922$	−1995.31	+	1151.99i	−2.16411	+	1.24945i
$923$	1529.56			1.65716
$924$		0			0
$925$	98.1715	−	56.6793i	0.106131	−	0.0612749i
$926$	1256.32	+	725.336i	1.35671	+	0.783300i
$927$		0			0
$928$	404.586	−	700.764i	0.435976	−	0.755133i
$929$	529.236	−	916.663i	0.569683	−	0.986721i	−0.426914	−	0.904292i	$-0.640399\pi$
$929$	529.236	−	916.663i	0.569683	−	0.986721i	0.996597	−	0.0824281i	$-0.0262675\pi$
$930$		0			0
$931$	−253.001	−	1210.72i	−0.271752	−	1.30045i
$932$	816.920			0.876523
$933$		0			0
$934$	453.236	+	261.676i	0.485263	+	0.280167i
$935$	173.515	+	300.537i	0.185577	+	0.321429i
$936$		0			0
$937$	−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
$939$		0			0
$940$	−486.003	−	841.781i	−0.517024	−	0.895512i
$941$	−178.549	+	103.085i	−0.189744	+	0.109549i	−0.591863	−	0.806039i	$-0.701607\pi$
$941$	−178.549	+	103.085i	−0.189744	+	0.109549i	0.402119	+	0.915587i	$0.368274\pi$
$942$		0			0
$943$			528.666i			0.560621i
$944$	632.242	−	365.025i	0.669748	−	0.386679i
$945$		0			0
$946$	−1042.01	+	601.605i	−1.10149	+	0.635946i
$947$	−553.455	+	958.612i	−0.584430	+	1.01226i	0.410517	+	0.911853i	$0.365348\pi$
$947$	−553.455	+	958.612i	−0.584430	+	1.01226i	−0.994946	+	0.100409i	$0.967985\pi$
$948$		0			0
$949$		−	1641.89i		−	1.73013i
$950$	−220.956	+	46.1725i	−0.232585	+	0.0486026i
$951$		0			0
$952$	1804.39	+	1041.77i	1.89537	+	1.09429i
$953$	−729.970	−	421.448i	−0.765970	−	0.442233i	0.0654649	−	0.997855i	$-0.479147\pi$
$953$	−729.970	−	421.448i	−0.765970	−	0.442233i	−0.831435	+	0.555622i	$0.812480\pi$
$954$		0			0
$955$	−113.041	+	195.793i	−0.118368	+	0.205019i
$956$	−1629.11	−	2821.70i	−1.70409	−	2.95157i
$957$		0			0
$958$		−	2205.76i		−	2.30246i
$959$	634.251	+	1098.55i	0.661367	+	1.14552i
$960$		0			0
$961$	−883.189			−0.919031
$962$			2148.53i			2.23339i
$963$		0			0
$964$	4.18826	+	2.41809i	0.00434467	+	0.00250839i
$965$	−44.1428	+	25.4859i	−0.0457438	+	0.0264102i
$966$		0			0
$967$	−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
$969$		0			0
$970$	−34.9008			−0.0359802
$971$	29.7562	+	17.1798i	0.0306449	+	0.0176929i	0.515244	−	0.857043i	$-0.327701\pi$
$971$	29.7562	+	17.1798i	0.0306449	+	0.0176929i	−0.484599	+	0.874736i	$0.661035\pi$
$972$		0			0
$973$	589.439	+	1020.94i	0.605796	+	1.04927i
$974$	612.268	−	1060.48i	0.628612	−	1.08879i
$975$		0			0
$976$	1051.87			1.07773
$977$		−	1293.09i		−	1.32353i	−0.749711	−	0.661765i	$-0.769808\pi$
$977$		−	1293.09i		−	1.32353i	0.749711	−	0.661765i	$-0.230192\pi$
$978$		0			0
$979$	489.513	−	282.621i	0.500013	−	0.288683i
$980$	−2630.53			−2.68422
$981$		0			0
$982$	−1548.14	+	893.820i	−1.57652	+	0.910204i
$983$	−405.649	−	234.202i	−0.412665	−	0.238252i	0.279269	−	0.960213i	$-0.409908\pi$
$983$	−405.649	−	234.202i	−0.412665	−	0.238252i	−0.691934	+	0.721961i	$0.743241\pi$
$984$		0			0
$985$	243.060	−	420.992i	0.246762	−	0.427403i
$986$	−799.808	+	1385.31i	−0.811164	+	1.40498i
$987$		0			0
$988$	914.637	−	2782.39i	0.925746	−	2.81618i
$989$	−1482.56			−1.49904
$990$		0			0
$991$	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
$993$		0			0
$994$	1638.41	+	2837.81i	1.64830	+	2.85494i
$995$	1309.23			1.31581
$996$		0			0
$997$	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
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	171.3.p.c.46.1		6
3.2	odd	2		57.3.g.b.46.3	yes	6
12.11	even	2		912.3.be.f.673.2		6
19.12	odd	6	inner	171.3.p.c.145.1		6
57.50	even	6		57.3.g.b.31.3	✓	6
228.107	odd	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	57.50	even	6
57.3.g.b.46.3	yes	6	3.2	odd	2
171.3.p.c.46.1		6	1.1	even	1	trivial
171.3.p.c.145.1		6	19.12	odd	6	inner
912.3.be.f.145.2		6	228.107	odd	6
912.3.be.f.673.2		6	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 171 = 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	171.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.08403 - 1.78057i) q^{2} +(4.34085 + 7.51857i) q^{4} +(-2.32722 + 4.03087i) q^{5} -10.6817 q^{7} -16.6722i q^{8} +O(q^{10})\)	\(q+(-3.08403 - 1.78057i) q^{2} +(4.34085 + 7.51857i) q^{4} +(-2.32722 + 4.03087i) q^{5} -10.6817 q^{7} -16.6722i q^{8} +(14.3545 - 8.28756i) q^{10} +6.37280 q^{11} +(15.3770 - 8.87792i) q^{13} +(32.9427 + 19.0195i) q^{14} +(-12.3225 + 21.3432i) q^{16} +(5.84976 - 10.1321i) q^{17} +(-3.88643 - 18.5983i) q^{19} -40.4085 q^{20} +(-19.6539 - 11.3472i) q^{22} +(-13.9817 - 24.2170i) q^{23} +(1.66807 + 2.88918i) q^{25} -63.2310 q^{26} +(-46.3676 - 80.3110i) q^{28} +(33.2498 - 19.1968i) q^{29} +42.9440i q^{31} +(18.2521 - 10.5379i) q^{32} +(-36.0817 + 20.8318i) q^{34} +(24.8587 - 43.0565i) q^{35} -33.9790i q^{37} +(-21.1296 + 64.2778i) q^{38} +(67.2032 + 38.7998i) q^{40} +(-16.3728 - 9.45284i) q^{41} +(26.5089 - 45.9148i) q^{43} +(27.6634 + 47.9143i) q^{44} +99.5813i q^{46} +(12.0272 + 20.8318i) q^{47} +65.0986 q^{49} -11.8804i q^{50} +(133.499 + 77.0754i) q^{52} +(13.3224 - 7.69168i) q^{53} +(-14.8309 + 25.6879i) q^{55} +178.087i q^{56} -136.725 q^{58} +(-25.6539 - 14.8113i) q^{59} +(-21.3403 - 36.9626i) q^{61} +(76.4648 - 132.441i) q^{62} +23.5266 q^{64} +82.6436i q^{65} +(-15.1585 + 8.75178i) q^{67} +101.572 q^{68} +(-153.330 + 88.5252i) q^{70} +(74.6028 + 43.0719i) q^{71} +(46.2352 - 80.0817i) q^{73} +(-60.5019 + 104.792i) q^{74} +(122.962 - 109.953i) q^{76} -68.0723 q^{77} +(-26.3908 - 15.2367i) q^{79} +(-57.3545 - 99.3409i) q^{80} +(33.6629 + 58.3058i) q^{82} -77.1154 q^{83} +(27.2274 + 47.1592i) q^{85} +(-163.509 + 94.4019i) q^{86} -106.248i q^{88} +(76.8129 - 44.3479i) q^{89} +(-164.253 + 94.8312i) q^{91} +(121.385 - 210.244i) q^{92} -85.6613i q^{94} +(84.0118 + 27.6166i) q^{95} +(-1.82351 - 1.05281i) q^{97} +(-200.766 - 115.912i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} + 5 q^{4} - 4 q^{5} - 22 q^{7}+O(q^{10}) \) 6 * q - 3 * q^2 + 5 * q^4 - 4 * q^5 - 22 * q^7	\( 6 q - 3 q^{2} + 5 q^{4} - 4 q^{5} - 22 q^{7} + 54 q^{10} + 36 q^{11} - 3 q^{13} + 57 q^{14} - 23 q^{16} - 38 q^{17} - 10 q^{19} - 32 q^{20} + 36 q^{22} - 54 q^{23} - 21 q^{25} - 118 q^{26} - 101 q^{28} + 102 q^{29} + 63 q^{32} - 150 q^{34} + 24 q^{35} - 119 q^{38} + 30 q^{40} - 96 q^{41} + 107 q^{43} + 94 q^{44} + 50 q^{47} - 48 q^{49} + 399 q^{52} + 90 q^{53} + 148 q^{55} - 116 q^{58} + 27 q^{61} + 121 q^{62} + 46 q^{64} - 39 q^{67} + 388 q^{68} - 354 q^{70} - 84 q^{71} - 77 q^{73} - 219 q^{74} + 215 q^{76} - 260 q^{77} + 9 q^{79} - 312 q^{80} - 4 q^{82} + 348 q^{83} + 68 q^{85} - 249 q^{86} + 72 q^{89} - 393 q^{91} + 118 q^{92} - 104 q^{95} - 228 q^{97} - 540 q^{98}+O(q^{100}) \) 6 * q - 3 * q^2 + 5 * q^4 - 4 * q^5 - 22 * q^7 + 54 * q^10 + 36 * q^11 - 3 * q^13 + 57 * q^14 - 23 * q^16 - 38 * q^17 - 10 * q^19 - 32 * q^20 + 36 * q^22 - 54 * q^23 - 21 * q^25 - 118 * q^26 - 101 * q^28 + 102 * q^29 + 63 * q^32 - 150 * q^34 + 24 * q^35 - 119 * q^38 + 30 * q^40 - 96 * q^41 + 107 * q^43 + 94 * q^44 + 50 * q^47 - 48 * q^49 + 399 * q^52 + 90 * q^53 + 148 * q^55 - 116 * q^58 + 27 * q^61 + 121 * q^62 + 46 * q^64 - 39 * q^67 + 388 * q^68 - 354 * q^70 - 84 * q^71 - 77 * q^73 - 219 * q^74 + 215 * q^76 - 260 * q^77 + 9 * q^79 - 312 * q^80 - 4 * q^82 + 348 * q^83 + 68 * q^85 - 249 * q^86 + 72 * q^89 - 393 * q^91 + 118 * q^92 - 104 * q^95 - 228 * q^97 - 540 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more