LMFDB - Embedded newform 171.3.p.c.145.1

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			145.1
Root			$0.500000 - 2.69511i$ of defining polynomial
Character	$\chi$	$=$	171.145
Dual form			171.3.p.c.46.1

$q$-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 $\left(\mathbb{Z}/171\mathbb{Z}\right)^\times$.

$n$	$20$	$154$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−3.08403	+	1.78057i	−1.54202	+	0.890284i	−0.543306	+	0.839535i	$0.682828\pi$
$2$	−3.08403	+	1.78057i	−1.54202	+	0.890284i	−0.998711	+	0.0507494i	$0.983839\pi$
$3$		0			0
$3$		0			0
$4$	4.34085	−	7.51857i	1.08521	−	1.87964i
$5$	−2.32722	−	4.03087i	−0.465445	−	0.806174i	0.533777	−	0.845625i	$-0.320772\pi$
$5$	−2.32722	−	4.03087i	−0.465445	−	0.806174i	−0.999221	+	0.0394517i	$0.987439\pi$
$6$		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	0.956671	−	0.291170i	$-0.0940444\pi$
$13$	15.3770	+	8.87792i	1.18285	+	0.682917i	0.226176	+	0.974087i	$0.427378\pi$
$14$	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	0.985191	−	0.171463i	$-0.0548495\pi$
$17$	5.84976	+	10.1321i	0.344104	+	0.596005i	−0.641087	+	0.767468i	$0.721516\pi$
$18$		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	0.383688	+	0.923463i	$0.374654\pi$
$23$	−13.9817	+	24.2170i	−0.607899	+	1.05291i	−0.991586	+	0.129448i	$0.958679\pi$
$24$		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	0.948043	−	0.318142i	$-0.103059\pi$
$29$	33.2498	+	19.1968i	1.14655	+	0.661958i	0.198502	+	0.980100i	$0.436392\pi$
$30$		0			0
$31$		−	42.9440i		−	1.38529i	−0.721278	−	0.692645i	$-0.756445\pi$
$31$		−	42.9440i		−	1.38529i	0.721278	−	0.692645i	$-0.243555\pi$
$32$	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	$0.151855\pi$
$37$			33.9790i			0.918351i	−0.888346	+	0.459176i	$0.848145\pi$
$38$	−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	−0.686198	−	0.727415i	$-0.740722\pi$
$41$	−16.3728	+	9.45284i	−0.399337	+	0.230557i	0.286861	+	0.957972i	$0.407388\pi$
$42$		0			0
$43$	26.5089	+	45.9148i	0.616486	+	1.06779i	0.990122	+	0.140210i	$0.0447778\pi$
$43$	26.5089	+	45.9148i	0.616486	+	1.06779i	−0.373635	+	0.927576i	$0.621889\pi$
$44$	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	−0.709240	−	0.704967i	$-0.750962\pi$
$47$	12.0272	−	20.8318i	0.255899	−	0.443230i	0.965139	+	0.261737i	$0.0842952\pi$
$48$		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	0.620389	−	0.784294i	$-0.286975\pi$
$53$	13.3224	+	7.69168i	0.251366	+	0.145126i	−0.369024	+	0.929420i	$0.620308\pi$
$54$		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	−0.701395	−	0.712773i	$-0.747439\pi$
$59$	−25.6539	+	14.8113i	−0.434813	+	0.251039i	0.266582	+	0.963812i	$0.414106\pi$
$60$		0			0
$61$	−21.3403	+	36.9626i	−0.349842	+	0.605944i	−0.986221	−	0.165433i	$-0.947098\pi$
$61$	−21.3403	+	36.9626i	−0.349842	+	0.605944i	0.636379	+	0.771376i	$0.280431\pi$
$62$	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	0.382593	−	0.923917i	$-0.375031\pi$
$67$	−15.1585	−	8.75178i	−0.226247	−	0.130624i	−0.608839	+	0.793294i	$0.708365\pi$
$68$	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	0.127886	−	0.991789i	$-0.459181\pi$
$71$	74.6028	−	43.0719i	1.05074	−	0.606647i	0.922857	+	0.385142i	$0.125847\pi$
$72$		0			0
$73$	46.2352	+	80.0817i	0.633359	+	1.09701i	0.986860	+	0.161576i	$0.0516576\pi$
$73$	46.2352	+	80.0817i	0.633359	+	1.09701i	−0.353502	+	0.935434i	$0.615009\pi$
$74$	−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	−0.657642	−	0.753330i	$-0.728446\pi$
$79$	−26.3908	+	15.2367i	−0.334060	+	0.192870i	0.323582	+	0.946200i	$0.395113\pi$
$80$	−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	0.865038	−	0.501707i	$-0.167294\pi$
$89$	76.8129	+	44.3479i	0.863066	+	0.498291i	−0.00197195	+	0.999998i	$0.500628\pi$
$90$		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	−0.509370	−	0.860548i	$-0.670122\pi$
$97$	−1.82351	+	1.05281i	−0.0187991	+	0.0108537i	0.490571	+	0.871401i	$0.336788\pi$
$98$	−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	−0.789777	−	0.613395i	$-0.789804\pi$
$101$	13.7690	−	23.8486i	0.136327	−	0.236125i	0.926104	+	0.377269i	$0.123137\pi$
$102$		0			0
$103$			102.351i			0.993696i	0.867837	+	0.496848i	$0.165509\pi$
$103$			102.351i			0.993696i	−0.867837	+	0.496848i	$0.834491\pi$
$104$	−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	$-0.999183\pi$
$107$		−	0.549592i		−	0.00513638i	0.999997	−	0.00256819i	$-0.000817481\pi$
$108$		0			0
$109$	80.7219	−	46.6048i	0.740568	−	0.427567i	−0.0817076	−	0.996656i	$-0.526037\pi$
$109$	80.7219	−	46.6048i	0.740568	−	0.427567i	0.822276	+	0.569089i	$0.192704\pi$
$110$	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	$0.0788586\pi$
$113$			55.4186i			0.490430i	−0.969469	+	0.245215i	$0.921141\pi$
$114$		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	0.137640	−	0.990482i	$-0.456048\pi$
$127$	−82.7181	−	47.7573i	−0.651324	−	0.376042i	−0.788963	+	0.614441i	$0.789382\pi$
$128$	−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	0.985030	+	0.172383i	$0.0551466\pi$
$131$	84.0762	+	145.624i	0.641803	+	1.11164i	−0.343227	+	0.939252i	$0.611520\pi$
$132$		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	−0.997165	−	0.0752526i	$-0.976024\pi$
$137$	−59.3774	+	102.845i	−0.433412	+	0.750691i	0.563753	+	0.825943i	$0.309357\pi$
$138$		0			0
$139$	−55.1822	+	95.5784i	−0.396994	+	0.687614i	−0.993354	−	0.115104i	$-0.963280\pi$
$139$	−55.1822	+	95.5784i	−0.396994	+	0.687614i	0.596359	+	0.802718i	$0.296613\pi$
$140$	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	0.752726	−	0.658334i	$-0.228739\pi$
$149$	−28.8719	−	50.0077i	−0.193771	−	0.335622i	−0.946497	+	0.322712i	$0.895405\pi$
$150$		0			0
$151$		−	205.459i		−	1.36066i	−0.732908	−	0.680328i	$-0.761837\pi$
$151$		−	205.459i		−	1.36066i	0.732908	−	0.680328i	$-0.238163\pi$
$152$	−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	0.632788	−	0.774325i	$-0.281910\pi$
$157$	−55.6080	−	96.3159i	−0.354191	−	0.613477i	−0.986979	+	0.160848i	$0.948577\pi$
$158$	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	−0.155490	−	0.987837i	$-0.549696\pi$
$167$	−181.817	−	104.972i	−1.08873	−	0.628577i	−0.933237	+	0.359261i	$0.883029\pi$
$168$		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	0.531188	−	0.847254i	$-0.321746\pi$
$173$	264.781	−	152.871i	1.53053	−	0.883649i	0.999337	−	0.0363949i	$-0.0115874\pi$
$174$		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	$0.321218\pi$
$179$			303.001i			1.69274i	−0.532593	+	0.846371i	$0.678782\pi$
$180$		0			0
$181$	−62.8763	−	36.3016i	−0.347383	−	0.200561i	0.316149	−	0.948709i	$-0.397610\pi$
$181$	−62.8763	−	36.3016i	−0.347383	−	0.200561i	−0.663532	+	0.748148i	$0.730943\pi$
$182$	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	−0.475229	−	0.879862i	$-0.657635\pi$
$193$	9.48401	−	5.47559i	0.0491399	−	0.0283710i	0.524369	+	0.851491i	$0.324301\pi$
$194$	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	0.259305	+	0.965795i	$0.416506\pi$
$199$	−140.643	+	243.602i	−0.706751	+	1.22413i	−0.966056	+	0.258333i	$0.916827\pi$
$200$	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	−0.273285	−	0.961933i	$-0.588110\pi$
$211$	89.2808	−	51.5463i	0.423132	−	0.244295i	0.696416	+	0.717638i	$0.254777\pi$
$212$	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	−0.646577	−	0.762848i	$-0.723800\pi$
$223$	−68.9560	+	39.8118i	−0.309220	+	0.178528i	0.337357	+	0.941377i	$0.390467\pi$
$224$	−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	$0.0931944\pi$
$227$			131.031i			0.577228i	−0.957446	+	0.288614i	$0.906806\pi$
$228$		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	0.949148	−	0.314829i	$-0.101947\pi$
$233$	47.0484	+	81.4902i	0.201924	+	0.349743i	−0.747224	+	0.664572i	$0.768614\pi$
$234$		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	0.501001	−	0.865447i	$-0.332965\pi$
$241$	0.482424	+	0.278528i	0.00200176	+	0.00115572i	−0.498999	+	0.866603i	$0.666299\pi$
$242$	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	−0.999305	−	0.0372799i	$-0.988131\pi$
$251$	−117.309	+	203.185i	−0.467367	+	0.809504i	0.531938	+	0.846783i	$0.321464\pi$
$252$		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	0.521383	−	0.853323i	$-0.325416\pi$
$257$	11.0702	+	6.39141i	0.0430749	+	0.0248693i	−0.478308	+	0.878192i	$0.658750\pi$
$258$		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	0.589516	−	0.807757i	$-0.299319\pi$
$263$	−106.457	−	184.389i	−0.404780	−	0.701099i	−0.994296	+	0.106657i	$0.965985\pi$
$264$		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	0.647106	−	0.762400i	$-0.275979\pi$
$269$	438.717	−	253.293i	1.63092	−	0.941610i	0.983811	−	0.179211i	$-0.0573544\pi$
$270$		0			0
$271$	110.063	+	190.635i	0.406136	+	0.703449i	0.994453	−	0.105182i	$-0.0335425\pi$
$271$	110.063	+	190.635i	0.406136	+	0.703449i	−0.588317	+	0.808631i	$0.700209\pi$
$272$	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	0.967454	−	0.253046i	$-0.0814322\pi$
$281$	346.203	+	199.880i	1.23204	+	0.711317i	0.264583	+	0.964363i	$0.414766\pi$
$282$		0			0
$283$	41.2358	+	71.4225i	0.145710	+	0.252376i	0.929637	−	0.368475i	$-0.120120\pi$
$283$	41.2358	+	71.4225i	0.145710	+	0.252376i	−0.783928	+	0.620852i	$0.786787\pi$
$284$		−	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	$-0.875412\pi$
$293$		−	223.552i		−	0.762977i	0.924374	−	0.381489i	$-0.124588\pi$
$294$		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	0.166986	−	0.985959i	$-0.446597\pi$
$307$	339.034	−	195.741i	1.10434	−	0.637594i	0.937359	+	0.348366i	$0.113263\pi$
$308$	−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	−0.720090	−	0.693881i	$-0.755899\pi$
$313$	75.3935	−	130.585i	0.240874	−	0.417206i	0.960963	+	0.276675i	$0.0892327\pi$
$314$	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	0.992422	−	0.122878i	$-0.0392123\pi$
$317$	438.163	+	252.973i	1.38222	+	0.798024i	0.389796	+	0.920901i	$0.372546\pi$
$318$		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	$0.233374\pi$
$331$			443.028i			1.33845i	−0.743058	+	0.669227i	$0.766626\pi$
$332$	−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	−0.228254	−	0.973602i	$-0.573302\pi$
$337$	168.764	−	97.4357i	0.500782	−	0.289127i	0.729037	+	0.684475i	$0.239968\pi$
$338$	−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	−0.944711	−	0.327905i	$-0.893658\pi$
$347$	−262.446	−	454.570i	−0.756329	−	1.31000i	0.188382	−	0.982096i	$-0.439676\pi$
$348$		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	0.874607	−	0.484832i	$-0.161119\pi$
$359$	6.25614	+	10.8359i	0.0174266	+	0.0301837i	−0.857181	+	0.515016i	$0.827786\pi$
$360$		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	−0.920064	−	0.391767i	$-0.871864\pi$
$367$	−44.3159	+	76.7574i	−0.120752	+	0.209148i	0.799313	+	0.600916i	$0.205197\pi$
$368$	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	$0.183429\pi$
$373$			406.489i			1.08978i	−0.838507	+	0.544892i	$0.816571\pi$
$374$	−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	$-0.806053\pi$
$379$		−	433.800i		−	1.14459i	0.820047	−	0.572296i	$-0.193947\pi$
$380$	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	0.0425263	−	0.999095i	$-0.486459\pi$
$383$	355.819	−	205.432i	0.929031	−	0.536377i	0.886505	+	0.462719i	$0.153126\pi$
$384$		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	−0.718430	−	0.695599i	$-0.755139\pi$
$389$	94.6013	−	163.854i	0.243191	−	0.421219i	0.961621	+	0.274380i	$0.0884725\pi$
$390$		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	−0.997804	−	0.0662425i	$-0.978899\pi$
$397$	−220.839	−	382.504i	−0.556269	−	0.963487i	0.441534	−	0.897244i	$-0.354434\pi$
$398$		−	1001.70i		−	2.51684i
$399$		0			0
$400$	−82.2192			−0.205548
$401$	−320.526	+	185.056i	−0.799316	+	0.461485i	−0.843232	−	0.537550i	$-0.819350\pi$
$401$	−320.526	+	185.056i	−0.799316	+	0.461485i	0.0439159	+	0.999035i	$0.486017\pi$
$402$		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	0.914958	−	0.403550i	$-0.132224\pi$
$409$	418.387	+	241.556i	1.02295	+	0.590602i	0.107995	+	0.994151i	$0.465557\pi$
$410$	−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	−0.927604	−	0.373566i	$-0.878135\pi$
$421$	−449.581	+	259.566i	−1.06789	+	0.616545i	−0.140284	+	0.990111i	$0.544802\pi$
$422$	−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	0.709735	−	0.704469i	$-0.248815\pi$
$431$	195.895	+	113.100i	0.454514	+	0.262414i	−0.255221	+	0.966883i	$0.582148\pi$
$432$		0			0
$433$	−251.769	−	145.359i	−0.581452	−	0.335702i	0.180258	−	0.983619i	$-0.442307\pi$
$433$	−251.769	−	145.359i	−0.581452	−	0.335702i	−0.761710	+	0.647918i	$0.775640\pi$
$434$	−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	−0.184834	−	0.982770i	$-0.559175\pi$
$439$	251.921	−	145.447i	0.573852	−	0.331314i	0.758686	+	0.651456i	$0.225842\pi$
$440$	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	−0.508479	−	0.861074i	$-0.669792\pi$
$443$	217.722	−	377.106i	0.491473	−	0.851256i	0.999952	+	0.00981853i	$0.00312539\pi$
$444$		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	$0.0948842\pi$
$449$			263.736i			0.587385i	−0.955900	+	0.293692i	$0.905116\pi$
$450$		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	0.967864	+	0.251473i	$0.0809150\pi$
$461$	323.490	+	560.302i	0.701714	+	1.21540i	−0.266150	+	0.963932i	$0.585752\pi$
$462$		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	−0.337389	−	0.941365i	$-0.609544\pi$
$479$	309.698	−	536.413i	0.646552	−	1.11986i	0.983941	−	0.178495i	$-0.0571230\pi$
$480$		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	$-0.885148\pi$
$487$		−	343.861i		−	0.706080i	0.935608	−	0.353040i	$-0.114852\pi$
$488$	−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	0.999916	+	0.0129665i	$0.00412747\pi$
$491$	250.993	+	434.733i	0.511187	+	0.885402i	−0.488729	+	0.872436i	$0.662539\pi$
$492$		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	0.815105	+	0.579314i	$0.196679\pi$
$499$	453.717	+	785.861i	0.909253	+	1.57487i	0.0941479	+	0.995558i	$0.469987\pi$
$500$	−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	−0.988842	−	0.148971i	$-0.952404\pi$
$503$	−183.800	+	318.352i	−0.365408	+	0.632906i	0.623433	+	0.781877i	$0.285737\pi$
$504$		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	0.0442573	−	0.999020i	$-0.485908\pi$
$509$	−406.585	−	234.742i	−0.798791	−	0.461182i	−0.843048	+	0.537838i	$0.819241\pi$
$510$		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	$-0.768936\pi$
$521$		−	691.695i		−	1.32763i	0.747897	−	0.663815i	$-0.231064\pi$
$522$		0			0
$523$	−70.7545	−	40.8501i	−0.135286	−	0.0781073i	0.430830	−	0.902433i	$-0.358221\pi$
$523$	−70.7545	−	40.8501i	−0.135286	−	0.0781073i	−0.566115	+	0.824326i	$0.691554\pi$
$524$	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	−0.282102	−	0.959384i	$-0.591032\pi$
$541$	373.182	−	646.370i	0.689800	−	1.19477i	0.971902	−	0.235384i	$-0.0756349\pi$
$542$	−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	0.822008	−	0.569476i	$-0.192854\pi$
$547$	404.687	+	233.646i	0.739830	+	0.427141i	−0.0821772	+	0.996618i	$0.526187\pi$
$548$	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	0.277617	+	0.960692i	$0.410456\pi$
$557$	−386.099	+	668.743i	−0.693175	+	1.20061i	−0.970792	+	0.239923i	$0.922878\pi$
$558$		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	$-0.944518\pi$
$563$		−	195.273i		−	0.346844i	0.984848	−	0.173422i	$-0.0554825\pi$
$564$		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	$-0.829926\pi$
$569$		−	579.517i		−	1.01848i	0.860624	−	0.509242i	$-0.170074\pi$
$570$		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	−0.946771	−	0.321907i	$-0.895676\pi$
$587$	−441.521	−	764.737i	−0.752165	−	1.30279i	0.194606	−	0.980882i	$-0.437657\pi$
$588$		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	−0.949063	−	0.315087i	$-0.897966\pi$
$593$	−119.583	+	207.125i	−0.201658	+	0.349283i	0.747404	+	0.664369i	$0.231300\pi$
$594$		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	0.984503	−	0.175368i	$-0.0561116\pi$
$599$	793.604	+	458.187i	1.32488	+	0.764920i	0.340378	+	0.940289i	$0.389445\pi$
$600$		0			0
$601$			789.891i			1.31429i	0.753762	+	0.657147i	$0.228237\pi$
$601$			789.891i			1.31429i	−0.753762	+	0.657147i	$0.771763\pi$
$602$	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	$0.181000\pi$
$607$			653.712i			1.07696i	−0.842640	+	0.538478i	$0.819000\pi$
$608$	−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	0.870095	+	0.492885i	$0.164057\pi$
$613$	528.343	+	915.118i	0.861898	+	1.49285i	−0.00819687	+	0.999966i	$0.502609\pi$
$614$	−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	−0.0993850	−	0.995049i	$-0.531688\pi$
$617$	501.032	−	867.813i	0.812045	−	1.40650i	0.911430	−	0.411455i	$-0.134979\pi$
$618$		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	−0.236853	+	0.971546i	$0.576116\pi$
$631$	−605.640	+	1049.00i	−0.959809	+	1.66244i	−0.722957	+	0.690893i	$0.757217\pi$
$632$	−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	−0.567891	−	0.823104i	$-0.692241\pi$
$641$	−89.1040	+	51.4442i	−0.139008	+	0.0802562i	0.428883	+	0.903360i	$0.358907\pi$
$642$		0			0
$643$	−384.990	−	666.822i	−0.598740	−	1.03705i	−0.993007	−	0.118052i	$-0.962335\pi$
$643$	−384.990	−	666.822i	−0.598740	−	1.03705i	0.394267	−	0.918996i	$-0.370998\pi$
$644$	−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	0.888364	−	0.459139i	$-0.151842\pi$
$659$	616.112	+	355.713i	0.934920	+	0.539776i	0.0465558	+	0.998916i	$0.485175\pi$
$660$		0			0
$661$	−410.779	−	237.163i	−0.621451	−	0.358795i	0.155983	−	0.987760i	$-0.450146\pi$
$661$	−410.779	−	237.163i	−0.621451	−	0.358795i	−0.777434	+	0.628965i	$0.783479\pi$
$662$	−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	$-0.839940\pi$
$673$		−	648.662i		−	0.963836i	0.876216	−	0.481918i	$-0.160060\pi$
$674$	−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	$-0.780723\pi$
$677$		−	860.699i		−	1.27134i	0.771960	−	0.635671i	$-0.219277\pi$
$678$		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	$-0.954454\pi$
$683$		−	194.789i		−	0.285196i	0.989781	−	0.142598i	$-0.0455456\pi$
$684$		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	0.639761	−	0.768574i	$-0.279033\pi$
$701$	−242.353	−	419.767i	−0.345724	−	0.598812i	−0.985485	+	0.169762i	$0.945700\pi$
$702$		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	0.0185591	−	0.999828i	$-0.494092\pi$
$709$	620.485	−	1074.71i	0.875156	−	1.51581i	0.856597	−	0.515987i	$-0.172575\pi$
$710$	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	0.817021	−	0.576608i	$-0.195624\pi$
$719$	−65.3191	−	113.136i	−0.0908471	−	0.157352i	−0.907868	+	0.419256i	$0.862291\pi$
$720$		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	−0.932382	−	0.361475i	$-0.882273\pi$
$727$	−566.505	−	981.216i	−0.779237	−	1.34968i	0.153145	−	0.988204i	$-0.451060\pi$
$728$	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	0.947059	−	0.321060i	$-0.104039\pi$
$739$	144.463	+	250.216i	0.195484	+	0.338588i	−0.751575	+	0.659647i	$0.770706\pi$
$740$		−	1373.04i		−	1.85546i
$741$		0			0
$742$	585.167			0.788635
$743$	66.4928	−	38.3896i	0.0894923	−	0.0516684i	−0.454586	−	0.890703i	$-0.650213\pi$
$743$	66.4928	−	38.3896i	0.0894923	−	0.0516684i	0.544078	+	0.839034i	$0.316879\pi$
$744$		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	0.966915	−	0.255098i	$-0.0821078\pi$
$751$	923.318	+	533.078i	1.22945	+	0.709824i	0.262536	+	0.964922i	$0.415441\pi$
$752$	−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	0.869270	−	0.494338i	$-0.164589\pi$
$757$	4.94030	+	8.55684i	0.00652615	+	0.0113036i	−0.862744	+	0.505641i	$0.831256\pi$
$758$	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	−0.603218	−	0.797576i	$-0.706115\pi$
$769$	299.227	−	518.276i	0.389112	−	0.673961i	0.992330	+	0.123615i	$0.0394486\pi$
$770$	−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	−0.171538	−	0.985177i	$-0.554874\pi$
$773$	−858.414	−	495.605i	−1.11050	−	0.641145i	−0.938958	+	0.344032i	$0.888207\pi$
$774$		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	$-0.715505\pi$
$787$		−	1226.83i		−	1.55887i	0.626480	−	0.779437i	$-0.284495\pi$
$788$	−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	$0.164741\pi$
$797$			788.636i			0.989506i	−0.869034	+	0.494753i	$0.835259\pi$
$798$		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	−0.0925727	−	0.995706i	$-0.529509\pi$
$811$	−811.945	−	468.777i	−1.00117	−	0.578023i	−0.908593	+	0.417683i	$0.862842\pi$
$812$	−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	−0.0888591	−	0.996044i	$-0.528322\pi$
$821$	671.718	−	1163.45i	0.818170	−	1.41711i	0.907029	−	0.421068i	$-0.138345\pi$
$822$		0			0
$823$	435.019	−	753.475i	0.528577	−	0.915522i	−0.470868	−	0.882204i	$-0.656059\pi$
$823$	435.019	−	753.475i	0.528577	−	0.915522i	0.999445	−	0.0333184i	$-0.0106075\pi$
$824$	−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	0.104017	−	0.994576i	$-0.466830\pi$
$827$	−583.285	−	336.760i	−0.705303	−	0.407207i	−0.809319	+	0.587369i	$0.800164\pi$
$828$		0			0
$829$		−	516.908i		−	0.623532i	−0.950159	−	0.311766i	$-0.899080\pi$
$829$		−	516.908i		−	0.623532i	0.950159	−	0.311766i	$-0.100920\pi$
$830$	−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	0.280595	−	0.959826i	$-0.409468\pi$
$839$	1050.53	−	606.526i	1.25213	−	0.722915i	0.971531	+	0.236911i	$0.0761350\pi$
$840$		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	0.665294	−	0.746581i	$-0.268306\pi$
$853$	−267.766	−	463.785i	−0.313911	−	0.543710i	−0.979205	+	0.202871i	$0.934973\pi$
$854$			1623.53i			1.90109i
$855$		0			0
$856$	9.16289			0.0107043
$857$	−655.156	+	378.254i	−0.764476	+	0.441370i	−0.830901	−	0.556421i	$-0.812174\pi$
$857$	−655.156	+	378.254i	−0.764476	+	0.441370i	0.0664245	+	0.997791i	$0.478841\pi$
$858$		0			0
$859$	538.135	−	932.077i	0.626466	−	1.08507i	−0.361789	−	0.932260i	$-0.617834\pi$
$859$	538.135	−	932.077i	0.626466	−	1.08507i	0.988255	−	0.152812i	$-0.0488328\pi$
$860$	−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	$0.183148\pi$
$863$			939.206i			1.08830i	−0.838987	+	0.544152i	$0.816852\pi$
$864$		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	−0.949649	−	0.313317i	$-0.898560\pi$
$877$	−1011.30	+	583.873i	−1.15313	+	0.665761i	−0.203484	+	0.979078i	$0.565226\pi$
$878$	−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	−0.932122	−	0.362145i	$-0.882044\pi$
$883$	−134.599	+	233.133i	−0.152434	+	0.264023i	0.779688	+	0.626169i	$0.215378\pi$
$884$	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	−0.0207361	−	0.999785i	$-0.506601\pi$
$887$	−795.589	−	459.333i	−0.896943	−	0.517850i	−0.876207	+	0.481935i	$0.839934\pi$
$888$		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	−0.0934255	−	0.995626i	$-0.529782\pi$
$907$	654.944	−	378.132i	0.722099	−	0.416904i	0.815525	+	0.578722i	$0.196448\pi$
$908$	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	$-0.826270\pi$
$911$		−	945.788i		−	1.03819i	0.854718	−	0.519093i	$-0.173730\pi$
$912$		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	0.996597	+	0.0824281i	$0.0262675\pi$
$929$	529.236	+	916.663i	0.569683	+	0.986721i	−0.426914	+	0.904292i	$0.640399\pi$
$930$		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	−0.912955	−	0.408061i	$-0.866205\pi$
$937$	−96.5921	+	167.302i	−0.103087	+	0.178551i	0.809868	+	0.586612i	$0.199539\pi$
$938$	−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	0.402119	−	0.915587i	$-0.368274\pi$
$941$	−178.549	−	103.085i	−0.189744	−	0.109549i	−0.591863	+	0.806039i	$0.701607\pi$
$942$		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	−0.994946	−	0.100409i	$-0.967985\pi$
$947$	−553.455	−	958.612i	−0.584430	−	1.01226i	0.410517	−	0.911853i	$-0.365348\pi$
$948$		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	−0.831435	−	0.555622i	$-0.812480\pi$
$953$	−729.970	+	421.448i	−0.765970	+	0.442233i	0.0654649	+	0.997855i	$0.479147\pi$
$954$		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	0.577326	−	0.816514i	$-0.304096\pi$
$967$	−404.649	−	700.873i	−0.418458	−	0.724791i	−0.995785	+	0.0917223i	$0.970763\pi$
$968$		−	1340.23i		−	1.38454i
$969$		0			0
$970$	−34.9008			−0.0359802
$971$	29.7562	−	17.1798i	0.0306449	−	0.0176929i	−0.484599	−	0.874736i	$-0.661035\pi$
$971$	29.7562	−	17.1798i	0.0306449	−	0.0176929i	0.515244	+	0.857043i	$0.327701\pi$
$972$		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	$0.230192\pi$
$977$			1293.09i			1.32353i	−0.749711	+	0.661765i	$0.769808\pi$
$978$		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	−0.691934	−	0.721961i	$-0.743241\pi$
$983$	−405.649	+	234.202i	−0.412665	+	0.238252i	0.279269	+	0.960213i	$0.409908\pi$
$984$		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	0.383325	−	0.923614i	$-0.374779\pi$
$991$	1362.49	−	786.632i	1.37486	−	0.793776i	0.991535	+	0.129838i	$0.0414456\pi$
$992$	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	−0.798711	−	0.601714i	$-0.794485\pi$
$997$	121.379	−	210.235i	0.121744	−	0.210867i	0.920456	+	0.390847i	$0.127818\pi$
$998$	−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.145.1		6
3.2	odd	2		57.3.g.b.31.3	✓	6
12.11	even	2		912.3.be.f.145.2		6
19.8	odd	6	inner	171.3.p.c.46.1		6
57.8	even	6		57.3.g.b.46.3	yes	6
228.179	odd	6		912.3.be.f.673.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
57.3.g.b.31.3	✓	6	3.2	odd	2
57.3.g.b.46.3	yes	6	57.8	even	6
171.3.p.c.46.1		6	19.8	odd	6	inner
171.3.p.c.145.1		6	1.1	even	1	trivial
912.3.be.f.145.2		6	12.11	even	2
912.3.be.f.673.2		6	228.179	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 171 = 3^{2} \cdot 19 \)
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

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