LMFDB - Embedded newform 171.3.p.f.46.2

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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.19163381760000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 14x^{6} + 177x^{4} - 266x^{2} + 361 $ x^8 - 14x^6 + 177x^4 - 266*x^2 + 361
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			46.2
Root			$-1.06868 - 0.617004i$ of defining polynomial
Character	$\chi$	$=$	171.46
Dual form			171.3.p.f.145.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.06868 - 0.617004i) q^{2} +(-1.23861 - 2.14534i) q^{4} +(4.08850 - 7.08149i) q^{5} -10.4772 q^{7} +7.99294i q^{8} +O(q^{10})$	\(q+(-1.06868 - 0.617004i) q^{2} +(-1.23861 - 2.14534i) q^{4} +(4.08850 - 7.08149i) q^{5} -10.4772 q^{7} +7.99294i q^{8} +(-8.73861 + 5.04524i) q^{10} +3.90227 q^{11} +(-2.02277 + 1.16785i) q^{13} +(11.1968 + 6.46449i) q^{14} +(-0.0227744 + 0.0394465i) q^{16} +(-2.13736 + 3.70202i) q^{17} +(-17.4772 + 7.45296i) q^{19} -20.2563 q^{20} +(-4.17029 - 2.40772i) q^{22} +(-20.0701 - 34.7623i) q^{23} +(-20.9317 - 36.2547i) q^{25} +2.88227 q^{26} +(12.9772 + 22.4772i) q^{28} +(-10.6868 + 6.17004i) q^{29} +22.2148i q^{31} +(27.7370 - 16.0140i) q^{32} +(4.56832 - 2.63752i) q^{34} +(-42.8361 + 74.1944i) q^{35} -62.2749i q^{37} +(23.2761 + 2.81867i) q^{38} +(56.6020 + 32.6792i) q^{40} +(44.7873 + 25.8579i) q^{41} +(6.67029 - 11.5533i) q^{43} +(-4.83341 - 8.37171i) q^{44} +49.5332i q^{46} +(-24.1586 - 41.8438i) q^{47} +60.7723 q^{49} +51.6597i q^{50} +(5.01087 + 2.89303i) q^{52} +(67.7396 - 39.1095i) q^{53} +(15.9545 - 27.6339i) q^{55} -83.7439i q^{56} +15.2277 q^{58} +(-82.7011 - 47.7475i) q^{59} +(18.8861 + 32.7117i) q^{61} +(13.7066 - 23.7406i) q^{62} -39.3406 q^{64} +19.0990i q^{65} +(-52.6247 + 30.3829i) q^{67} +10.5895 q^{68} +(91.5564 - 52.8601i) q^{70} +(78.8877 + 45.5459i) q^{71} +(41.7950 - 72.3911i) q^{73} +(-38.4239 + 66.5521i) q^{74} +(37.6366 + 28.2633i) q^{76} -40.8850 q^{77} +(0.466357 + 0.269251i) q^{79} +(0.186227 + 0.322554i) q^{80} +(-31.9089 - 55.2678i) q^{82} +54.0816 q^{83} +(17.4772 + 30.2714i) q^{85} +(-14.2568 + 8.23119i) q^{86} +31.1907i q^{88} +(81.6811 - 47.1586i) q^{89} +(21.1931 - 12.2358i) q^{91} +(-49.7180 + 86.1142i) q^{92} +59.6237i q^{94} +(-18.6776 + 154.236i) q^{95} +(-126.909 - 73.2709i) q^{97} +(-64.9462 - 37.4967i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 12 q^{4} - 40 q^{7}+O(q^{10}) $ 8 * q + 12 * q^4 - 40 * q^7	$ 8 q + 12 q^{4} - 40 q^{7} - 48 q^{10} - 60 q^{13} - 44 q^{16} - 96 q^{19} + 120 q^{22} - 36 q^{25} + 60 q^{28} + 168 q^{34} + 168 q^{40} - 100 q^{43} + 48 q^{49} - 420 q^{52} + 40 q^{55} + 560 q^{58} - 68 q^{61} - 8 q^{64} - 180 q^{67} + 360 q^{70} - 60 q^{73} + 564 q^{76} + 420 q^{79} - 80 q^{82} + 96 q^{85} + 60 q^{91} - 840 q^{97}+O(q^{100}) $ 8 * q + 12 * q^4 - 40 * q^7 - 48 * q^10 - 60 * q^13 - 44 * q^16 - 96 * q^19 + 120 * q^22 - 36 * q^25 + 60 * q^28 + 168 * q^34 + 168 * q^40 - 100 * q^43 + 48 * q^49 - 420 * q^52 + 40 * q^55 + 560 * q^58 - 68 * q^61 - 8 * q^64 - 180 * q^67 + 360 * q^70 - 60 * q^73 + 564 * q^76 + 420 * q^79 - 80 * q^82 + 96 * q^85 + 60 * q^91 - 840 * q^97

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 $

$2$	−1.06868	−	0.617004i	−0.534341	−	0.308502i	0.208441	−	0.978035i	$-0.433161\pi$
$2$	−1.06868	−	0.617004i	−0.534341	−	0.308502i	−0.742782	+	0.669533i	$0.766494\pi$
$3$		0			0
$3$		0			0
$4$	−1.23861	−	2.14534i	−0.309653	−	0.536335i
$5$	4.08850	−	7.08149i	0.817700	−	1.41630i	−0.0896726	−	0.995971i	$-0.528582\pi$
$5$	4.08850	−	7.08149i	0.817700	−	1.41630i	0.907373	−	0.420327i	$-0.138085\pi$
$6$		0			0
$7$	−10.4772			−1.49675			−0.748373	−	0.663278i	$-0.769165\pi$
$7$	−10.4772			−1.49675			−0.748373	+	0.663278i	$0.769165\pi$
$8$			7.99294i			0.999118i
$9$		0			0
$10$	−8.73861	+	5.04524i	−0.873861	+	0.504524i
$11$	3.90227			0.354752			0.177376	−	0.984143i	$-0.443239\pi$
$11$	3.90227			0.354752			0.177376	+	0.984143i	$0.443239\pi$
$12$		0			0
$13$	−2.02277	+	1.16785i	−0.155598	+	0.0898346i	−0.575777	−	0.817607i	$-0.695300\pi$
$13$	−2.02277	+	1.16785i	−0.155598	+	0.0898346i	0.420179	+	0.907441i	$0.361967\pi$
$14$	11.1968	+	6.46449i	0.799773	+	0.461749i
$15$		0			0
$16$	−0.0227744	+	0.0394465i	−0.00142340	+	0.00246540i
$17$	−2.13736	+	3.70202i	−0.125727	+	0.217766i	−0.922017	−	0.387149i	$-0.873460\pi$
$17$	−2.13736	+	3.70202i	−0.125727	+	0.217766i	0.796290	+	0.604915i	$0.206793\pi$
$18$		0			0
$19$	−17.4772	+	7.45296i	−0.919854	+	0.392261i
$19$	−17.4772	+	7.45296i	−0.919854	+	0.392261i
$20$	−20.2563			−1.01281
$21$		0			0
$22$	−4.17029	−	2.40772i	−0.189559	−	0.109442i
$23$	−20.0701	−	34.7623i	−0.872611	−	1.51141i	−0.859286	−	0.511495i	$-0.829092\pi$
$23$	−20.0701	−	34.7623i	−0.872611	−	1.51141i	−0.0133248	−	0.999911i	$-0.504242\pi$
$24$		0			0
$25$	−20.9317	−	36.2547i	−0.837267	−	1.45019i
$26$	2.88227			0.110857
$27$		0			0
$28$	12.9772	+	22.4772i	0.463472	+	0.802758i
$29$	−10.6868	+	6.17004i	−0.368511	+	0.212760i	−0.672808	−	0.739817i	$-0.734912\pi$
$29$	−10.6868	+	6.17004i	−0.368511	+	0.212760i	0.304297	+	0.952577i	$0.401579\pi$
$30$		0			0
$31$			22.2148i			0.716608i	0.933605	+	0.358304i	$0.116645\pi$
$31$			22.2148i			0.716608i	−0.933605	+	0.358304i	$0.883355\pi$
$32$	27.7370	−	16.0140i	0.866783	−	0.500437i
$33$		0			0
$34$	4.56832	−	2.63752i	0.134362	−	0.0775742i
$35$	−42.8361	+	74.1944i	−1.22389	+	2.11984i
$36$		0			0
$37$		−	62.2749i		−	1.68311i	−0.540174	−	0.841553i	$-0.681642\pi$
$37$		−	62.2749i		−	1.68311i	0.540174	−	0.841553i	$-0.318358\pi$
$38$	23.2761	+	2.81867i	0.612529	+	0.0741756i
$39$		0			0
$40$	56.6020	+	32.6792i	1.41505	+	0.816979i
$41$	44.7873	+	25.8579i	1.09237	+	0.630682i	0.934207	−	0.356731i	$-0.116109\pi$
$41$	44.7873	+	25.8579i	1.09237	+	0.630682i	0.158166	+	0.987413i	$0.449442\pi$
$42$		0			0
$43$	6.67029	−	11.5533i	0.155123	−	0.268681i	−0.777981	−	0.628288i	$-0.783756\pi$
$43$	6.67029	−	11.5533i	0.155123	−	0.268681i	0.933104	+	0.359607i	$0.117089\pi$
$44$	−4.83341	−	8.37171i	−0.109850	−	0.190266i
$45$		0			0
$46$			49.5332i			1.07681i
$47$	−24.1586	−	41.8438i	−0.514012	−	0.890294i	−0.999868	−	0.0162556i	$-0.994825\pi$
$47$	−24.1586	−	41.8438i	−0.514012	−	0.890294i	0.485856	−	0.874039i	$-0.338508\pi$
$48$		0			0
$49$	60.7723			1.24025
$50$			51.6597i			1.03319i
$51$		0			0
$52$	5.01087	+	2.89303i	0.0963629	+	0.0556351i
$53$	67.7396	−	39.1095i	1.27811	−	0.737915i	0.301606	−	0.953433i	$-0.402477\pi$
$53$	67.7396	−	39.1095i	1.27811	−	0.737915i	0.976500	+	0.215518i	$0.0691440\pi$
$54$		0			0
$55$	15.9545	−	27.6339i	0.290081	−	0.502435i
$56$		−	83.7439i		−	1.49543i
$57$		0			0
$58$	15.2277			0.262547
$59$	−82.7011	−	47.7475i	−1.40171	−	0.809280i	−0.407146	−	0.913363i	$-0.633476\pi$
$59$	−82.7011	−	47.7475i	−1.40171	−	0.809280i	−0.994569	+	0.104083i	$0.966809\pi$
$60$		0			0
$61$	18.8861	+	32.7117i	0.309609	+	0.536258i	0.978277	−	0.207303i	$-0.0664686\pi$
$61$	18.8861	+	32.7117i	0.309609	+	0.536258i	−0.668668	+	0.743561i	$0.733135\pi$
$62$	13.7066	−	23.7406i	0.221075	−	0.382913i
$63$		0			0
$64$	−39.3406			−0.614697
$65$			19.0990i			0.293831i
$66$		0			0
$67$	−52.6247	+	30.3829i	−0.785444	+	0.453476i	−0.838356	−	0.545123i	$-0.816483\pi$
$67$	−52.6247	+	30.3829i	−0.785444	+	0.453476i	0.0529122	+	0.998599i	$0.483150\pi$
$68$	10.5895			0.155727
$69$		0			0
$70$	91.5564	−	52.8601i	1.30795	−	0.755145i
$71$	78.8877	+	45.5459i	1.11110	+	0.641491i	0.939113	−	0.343609i	$-0.111650\pi$
$71$	78.8877	+	45.5459i	1.11110	+	0.641491i	0.171982	+	0.985100i	$0.444983\pi$
$72$		0			0
$73$	41.7950	−	72.3911i	0.572535	−	0.991659i	−0.423770	−	0.905770i	$-0.639294\pi$
$73$	41.7950	−	72.3911i	0.572535	−	0.991659i	0.996305	−	0.0858893i	$-0.0273731\pi$
$74$	−38.4239	+	66.5521i	−0.519241	+	0.899353i
$75$		0			0
$76$	37.6366	+	28.2633i	0.495219	+	0.371885i
$77$	−40.8850			−0.530974
$78$		0			0
$79$	0.466357	+	0.269251i	0.00590325	+	0.00340825i	0.502949	−	0.864316i	$-0.332248\pi$
$79$	0.466357	+	0.269251i	0.00590325	+	0.00340825i	−0.497045	+	0.867724i	$0.665582\pi$
$80$	0.186227	+	0.322554i	0.00232783	+	0.00403192i
$81$		0			0
$82$	−31.9089	−	55.2678i	−0.389133	−	0.673998i
$83$	54.0816			0.651586			0.325793	−	0.945441i	$-0.394369\pi$
$83$	54.0816			0.651586			0.325793	+	0.945441i	$0.394369\pi$
$84$		0			0
$85$	17.4772	+	30.2714i	0.205614	+	0.356135i
$86$	−14.2568	+	8.23119i	−0.165777	+	0.0957115i
$87$		0			0
$88$			31.1907i			0.354439i
$89$	81.6811	−	47.1586i	0.917766	−	0.529872i	0.0348441	−	0.999393i	$-0.488907\pi$
$89$	81.6811	−	47.1586i	0.917766	−	0.529872i	0.882922	+	0.469521i	$0.155573\pi$
$90$		0			0
$91$	21.1931	−	12.2358i	0.232891	−	0.134460i
$92$	−49.7180	+	86.1142i	−0.540414	+	0.936024i
$93$		0			0
$94$			59.6237i			0.634294i
$95$	−18.6776	+	154.236i	−0.196606	+	1.62354i
$96$		0			0
$97$	−126.909	−	73.2709i	−1.30834	−	0.755370i	−0.326520	−	0.945190i	$-0.605876\pi$
$97$	−126.909	−	73.2709i	−1.30834	−	0.755370i	−0.981819	+	0.189820i	$0.939209\pi$
$98$	−64.9462	−	37.4967i	−0.662716	−	0.382619i
$99$		0			0
$100$	−51.8525	+	89.8111i	−0.518525	+	0.898111i
$101$	−59.3764	−	102.843i	−0.587885	−	1.01825i	−0.994509	−	0.104651i	$-0.966627\pi$
$101$	−59.3764	−	102.843i	−0.587885	−	1.01825i	0.406624	−	0.913596i	$-0.366706\pi$
$102$		0			0
$103$			26.1248i			0.253639i	0.991926	+	0.126819i	$0.0404769\pi$
$103$			26.1248i			0.253639i	−0.991926	+	0.126819i	$0.959523\pi$
$104$	−9.33456	−	16.1679i	−0.0897553	−	0.155461i
$105$		0			0
$106$	−96.5228			−0.910592
$107$		−	120.708i		−	1.12811i	−0.825737	−	0.564056i	$-0.809240\pi$
$107$		−	120.708i		−	1.12811i	0.825737	−	0.564056i	$-0.190760\pi$
$108$		0			0
$109$	−91.9545	−	53.0899i	−0.843619	−	0.487064i	0.0148739	−	0.999889i	$-0.495265\pi$
$109$	−91.9545	−	53.0899i	−0.843619	−	0.487064i	−0.858493	+	0.512826i	$0.828599\pi$
$110$	−34.1005	+	19.6879i	−0.310004	+	0.178981i
$111$		0			0
$112$	0.238613	−	0.413289i	0.00213047	−	0.00369008i
$113$			101.609i			0.899194i	0.893232	+	0.449597i	$0.148432\pi$
$113$			101.609i			0.899194i	−0.893232	+	0.449597i	$0.851568\pi$
$114$		0			0
$115$	−328.226			−2.85414
$116$	26.4737	+	15.2846i	0.228221	+	0.131764i
$117$		0			0
$118$	58.9208	+	102.054i	0.499329	+	0.864863i
$119$	22.3936	−	38.7869i	0.188182	−	0.325941i
$120$		0			0
$121$	−105.772			−0.874151
$122$		−	46.6112i		−	0.382059i
$123$		0			0
$124$	47.6584	−	27.5156i	0.384342	−	0.221900i
$125$	−137.892			−1.10313
$126$		0			0
$127$	95.7267	−	55.2678i	0.753754	−	0.435180i	−0.0732950	−	0.997310i	$-0.523351\pi$
$127$	95.7267	−	55.2678i	0.753754	−	0.435180i	0.827049	+	0.562130i	$0.190018\pi$
$128$	−68.9056	−	39.7827i	−0.538325	−	0.310802i
$129$		0			0
$130$	11.7842	−	20.4108i	0.0906474	−	0.157006i
$131$	28.1582	−	48.7714i	0.214948	−	0.372301i	−0.738309	−	0.674463i	$-0.764375\pi$
$131$	28.1582	−	48.7714i	0.214948	−	0.372301i	0.953256	+	0.302162i	$0.0977085\pi$
$132$		0			0
$133$	183.113	−	78.0863i	1.37679	−	0.587115i
$134$	74.9855			0.559593
$135$		0			0
$136$	−29.5901	−	17.0838i	−0.217574	−	0.125616i
$137$	69.9658	+	121.184i	0.510700	+	0.884558i	0.999923	+	0.0123992i	$0.00394687\pi$
$137$	69.9658	+	121.184i	0.510700	+	0.884558i	−0.489224	+	0.872158i	$0.662720\pi$
$138$		0			0
$139$	85.1475	+	147.480i	0.612572	+	1.06101i	0.990805	+	0.135296i	$0.0431984\pi$
$139$	85.1475	+	147.480i	0.612572	+	1.06101i	−0.378233	+	0.925710i	$0.623468\pi$
$140$	212.230			1.51593
$141$		0			0
$142$	−56.2039	−	97.3481i	−0.395802	−	0.685550i
$143$	−7.89342	+	4.55727i	−0.0551987	+	0.0318690i
$144$		0			0
$145$			100.905i			0.695895i
$146$	−89.3312	+	51.5754i	−0.611857	+	0.353256i
$147$		0			0
$148$	−133.601	+	77.1345i	−0.902709	+	0.521179i
$149$	59.4652	−	102.997i	0.399096	−	0.691254i	−0.594519	−	0.804082i	$-0.702657\pi$
$149$	59.4652	−	102.997i	0.399096	−	0.691254i	0.993615	+	0.112828i	$0.0359908\pi$
$150$		0			0
$151$		−	150.898i		−	0.999322i	−0.866221	−	0.499661i	$-0.833458\pi$
$151$		−	150.898i		−	0.999322i	0.866221	−	0.499661i	$-0.166542\pi$
$152$	−59.5711	−	139.694i	−0.391915	−	0.919043i
$153$		0			0
$154$	43.6931	+	25.2262i	0.283721	+	0.163807i
$155$	157.314	+	90.8254i	1.01493	+	0.585970i
$156$		0			0
$157$	5.11387	−	8.85749i	0.0325724	−	0.0564171i	−0.849280	−	0.527943i	$-0.822963\pi$
$157$	5.11387	−	8.85749i	0.0325724	−	0.0564171i	0.881852	+	0.471526i	$0.156297\pi$
$158$	−0.332258	−	0.575488i	−0.00210290	−	0.00364233i
$159$		0			0
$160$		−	261.893i		−	1.63683i
$161$	210.278	+	364.213i	1.30608	+	2.26219i
$162$		0			0
$163$	−42.8851			−0.263099			−0.131549	−	0.991310i	$-0.541995\pi$
$163$	−42.8851			−0.263099			−0.131549	+	0.991310i	$0.541995\pi$
$164$		−	128.112i		−	0.781170i
$165$		0			0
$166$	−57.7961	−	33.3686i	−0.348169	−	0.201016i
$167$	1.48133	−	0.855246i	0.00887024	−	0.00512123i	−0.495558	−	0.868575i	$-0.665037\pi$
$167$	1.48133	−	0.855246i	0.00887024	−	0.00512123i	0.504429	+	0.863453i	$0.331703\pi$
$168$		0			0
$169$	−81.7723	+	141.634i	−0.483860	+	0.838069i
$170$		−	43.1341i		−	0.253730i
$171$		0			0
$172$	−33.0476			−0.192137
$173$	−176.089	−	101.665i	−1.01786	−	0.587660i	−0.104374	−	0.994538i	$-0.533284\pi$
$173$	−176.089	−	101.665i	−1.01786	−	0.587660i	−0.913482	+	0.406879i	$0.866617\pi$
$174$		0			0
$175$	219.306	+	379.849i	1.25318	+	2.17057i
$176$	−0.0888721	+	0.153931i	−0.000504955	+	0.000874607i
$177$		0			0
$178$	−116.388			−0.653866
$179$		−	34.9725i		−	0.195377i	−0.995217	−	0.0976885i	$-0.968855\pi$
$179$		−	34.9725i		−	0.195377i	0.995217	−	0.0976885i	$-0.0311449\pi$
$180$		0			0
$181$	100.295	−	57.9054i	0.554116	−	0.319919i	−0.196664	−	0.980471i	$-0.563011\pi$
$181$	100.295	−	57.9054i	0.554116	−	0.319919i	0.750781	+	0.660552i	$0.229678\pi$
$182$	−30.1982			−0.165924
$183$		0			0
$184$	277.854	−	160.419i	1.51007	−	0.871841i
$185$	−440.999	−	254.611i	−2.38378	−	1.37628i
$186$		0			0
$187$	−8.34058	+	14.4463i	−0.0446020	+	0.0772530i
$188$	−59.8462	+	103.657i	−0.318331	+	0.551365i
$189$		0			0
$190$	115.125	−	153.305i	0.605920	−	0.806870i
$191$	175.247			0.917523			0.458761	−	0.888559i	$-0.348293\pi$
$191$	175.247			0.917523			0.458761	+	0.888559i	$0.348293\pi$
$192$		0			0
$193$	290.884	+	167.942i	1.50717	+	0.870166i	0.999965	+	0.00834091i	$0.00265502\pi$
$193$	290.884	+	167.942i	1.50717	+	0.870166i	0.507206	+	0.861825i	$0.330678\pi$
$194$	90.4168	+	156.607i	0.466066	+	0.807250i
$195$		0			0
$196$	−75.2733	−	130.377i	−0.384047	−	0.665190i
$197$	−243.998			−1.23857			−0.619284	−	0.785167i	$-0.712577\pi$
$197$	−243.998			−1.23857			−0.619284	+	0.785167i	$0.712577\pi$
$198$		0			0
$199$	169.738	+	293.994i	0.852953	+	1.47736i	0.878531	+	0.477685i	$0.158524\pi$
$199$	169.738	+	293.994i	0.852953	+	1.47736i	−0.0255788	+	0.999673i	$0.508143\pi$
$200$	289.782	−	167.306i	1.44891	−	0.836529i
$201$		0			0
$202$			146.542i			0.725454i
$203$	111.968	−	64.6449i	0.551568	−	0.318448i
$204$		0			0
$205$	366.226	−	211.440i	1.78647	−	1.03142i
$206$	16.1191	−	27.9191i	0.0782481	−	0.135530i
$207$		0			0
$208$		−	0.106388i		−	0.000511483i
$209$	−68.2009	+	29.0835i	−0.326320	+	0.139155i
$210$		0			0
$211$	−85.0782	−	49.1199i	−0.403214	−	0.232796i	0.284656	−	0.958630i	$-0.408121\pi$
$211$	−85.0782	−	49.1199i	−0.403214	−	0.232796i	−0.687870	+	0.725834i	$0.741454\pi$
$212$	−167.806	−	96.8830i	−0.791539	−	0.456995i
$213$		0			0
$214$	−74.4772	+	128.998i	−0.348024	+	0.602796i
$215$	−54.5430	−	94.4712i	−0.253688	−	0.439401i
$216$		0			0
$217$		−	232.750i		−	1.07258i
$218$	65.5134	+	113.472i	0.300520	+	0.520516i
$219$		0			0
$220$	−79.0455			−0.359298
$221$		−	9.98447i		−	0.0451786i
$222$		0			0
$223$	57.3535	+	33.1131i	0.257191	+	0.148489i	0.623052	−	0.782180i	$-0.285892\pi$
$223$	57.3535	+	33.1131i	0.257191	+	0.148489i	−0.365862	+	0.930669i	$0.619226\pi$
$224$	−290.607	+	167.782i	−1.29735	+	0.749028i
$225$		0			0
$226$	62.6931	−	108.588i	0.277403	−	0.480476i
$227$			375.221i			1.65296i	0.562968	+	0.826479i	$0.309659\pi$
$227$			375.221i			1.65296i	−0.562968	+	0.826479i	$0.690341\pi$
$228$		0			0
$229$	40.4534			0.176652			0.0883262	−	0.996092i	$-0.471848\pi$
$229$	40.4534			0.176652			0.0883262	+	0.996092i	$0.471848\pi$
$230$	350.769	+	202.516i	1.52508	+	0.880506i
$231$		0			0
$232$	−49.3168	−	85.4191i	−0.212572	−	0.368186i
$233$	−134.459	+	232.890i	−0.577078	+	0.999529i	0.418734	+	0.908109i	$0.362474\pi$
$233$	−134.459	+	232.890i	−0.577078	+	0.999529i	−0.995812	+	0.0914198i	$0.970859\pi$
$234$		0			0
$235$	−395.089			−1.68123
$236$			236.563i			1.00238i
$237$		0			0
$238$	−47.8634	+	27.6339i	−0.201107	+	0.116109i
$239$	−58.1786			−0.243425			−0.121713	−	0.992565i	$-0.538839\pi$
$239$	−58.1786			−0.243425			−0.121713	+	0.992565i	$0.538839\pi$
$240$		0			0
$241$	125.159	−	72.2608i	0.519334	−	0.299837i	−0.217328	−	0.976099i	$-0.569734\pi$
$241$	125.159	−	72.2608i	0.519334	−	0.299837i	0.736662	+	0.676261i	$0.236401\pi$
$242$	113.037	+	65.2619i	0.467095	+	0.269677i
$243$		0			0
$244$	46.7852	−	81.0343i	0.191743	−	0.332108i
$245$	248.467	−	430.358i	1.01415	−	1.75656i
$246$		0			0
$247$	26.6486	−	35.4864i	0.107889	−	0.143670i
$248$	−177.562			−0.715976
$249$		0			0
$250$	147.362	+	85.0797i	0.589449	+	0.340319i
$251$	−46.8273	−	81.1072i	−0.186563	−	0.323136i	0.757539	−	0.652790i	$-0.226401\pi$
$251$	−46.8273	−	81.1072i	−0.186563	−	0.323136i	−0.944102	+	0.329653i	$0.893068\pi$
$252$		0			0
$253$	−78.3188	−	135.652i	−0.309561	−	0.536175i
$254$	−136.402			−0.537015
$255$		0			0
$256$	127.773	+	221.310i	0.499114	+	0.864492i
$257$	358.565	−	207.018i	1.39519	−	0.805516i	0.401310	−	0.915942i	$-0.368555\pi$
$257$	358.565	−	207.018i	1.39519	−	0.805516i	0.993884	+	0.110427i	$0.0352218\pi$
$258$		0			0
$259$			652.469i			2.51918i
$260$	40.9739	−	23.6563i	0.157592	−	0.0909857i
$261$		0			0
$262$	−60.1843	+	34.7474i	−0.229711	+	0.132624i
$263$	85.7696	−	148.557i	0.326120	−	0.564857i	−0.655618	−	0.755093i	$-0.727592\pi$
$263$	85.7696	−	148.557i	0.326120	−	0.564857i	0.981738	+	0.190236i	$0.0609252\pi$
$264$		0			0
$265$		−	639.597i		−	2.41357i
$266$	−243.869	−	29.5319i	−0.916800	−	0.111022i
$267$		0			0
$268$	130.363	+	75.2653i	0.486430	+	0.280841i
$269$	5.85341	+	3.37947i	0.0217599	+	0.0125631i	0.510840	−	0.859676i	$-0.329334\pi$
$269$	5.85341	+	3.37947i	0.0217599	+	0.0125631i	−0.489081	+	0.872239i	$0.662668\pi$
$270$		0			0
$271$	−123.499	+	213.906i	−0.455716	+	0.789323i	−0.998729	−	0.0504013i	$-0.983950\pi$
$271$	−123.499	+	213.906i	−0.455716	+	0.789323i	0.543013	+	0.839724i	$0.317283\pi$
$272$	−0.0973545	−	0.168623i	−0.000357921	−	0.000619937i
$273$		0			0
$274$		−	172.677i		−	0.630207i
$275$	−81.6811	−	141.476i	−0.297022	−	0.514458i
$276$		0			0
$277$	67.6356			0.244172			0.122086	−	0.992520i	$-0.461042\pi$
$277$	67.6356			0.244172			0.122086	+	0.992520i	$0.461042\pi$
$278$		−	210.145i		−	0.755918i
$279$		0			0
$280$	−593.032	−	342.387i	−2.11797	−	1.22281i
$281$	22.1270	−	12.7750i	0.0787439	−	0.0454628i	−0.460111	−	0.887861i	$-0.652190\pi$
$281$	22.1270	−	12.7750i	0.0787439	−	0.0454628i	0.538855	+	0.842399i	$0.318857\pi$
$282$		0			0
$283$	0.477226	−	0.826579i	0.00168631	−	0.00292077i	−0.865181	−	0.501460i	$-0.832797\pi$
$283$	0.477226	−	0.826579i	0.00168631	−	0.00292077i	0.866867	+	0.498539i	$0.166130\pi$
$284$		−	225.655i		−	0.794559i
$285$		0			0
$286$	11.2474			0.0393266
$287$	−469.246	−	270.920i	−1.63501	−	0.943971i
$288$		0			0
$289$	135.363	+	234.456i	0.468385	+	0.811267i
$290$	62.2586	−	107.835i	0.214685	−	0.371845i
$291$		0			0
$292$	−207.071			−0.709149
$293$			297.002i			1.01366i	0.862046	+	0.506830i	$0.169183\pi$
$293$			297.002i			1.01366i	−0.862046	+	0.506830i	$0.830817\pi$
$294$		0			0
$295$	−676.247	+	390.432i	−2.29236	+	1.32350i
$296$	497.760			1.68162
$297$		0			0
$298$	−127.099	+	73.3806i	−0.426506	+	0.246243i
$299$	81.1944	+	46.8776i	0.271553	+	0.156781i
$300$		0			0
$301$	−69.8861	+	121.046i	−0.232180	+	0.402147i
$302$	−93.1044	+	161.262i	−0.308293	+	0.533979i
$303$		0			0
$304$	0.104041	−	0.859152i	0.000342240	−	0.00282616i
$305$	308.864			1.01267
$306$		0			0
$307$	47.8634	+	27.6339i	0.155907	+	0.0900128i	0.575924	−	0.817503i	$-0.304643\pi$
$307$	47.8634	+	27.6339i	0.155907	+	0.0900128i	−0.420017	+	0.907516i	$0.637976\pi$
$308$	50.6407	+	87.7123i	0.164418	+	0.284780i
$309$		0			0
$310$	−112.079	−	194.127i	−0.361546	−	0.626216i
$311$	110.770			0.356175			0.178088	−	0.984015i	$-0.443009\pi$
$311$	110.770			0.356175			0.178088	+	0.984015i	$0.443009\pi$
$312$		0			0
$313$	−105.727	−	183.124i	−0.337785	−	0.585061i	0.646231	−	0.763142i	$-0.276344\pi$
$313$	−105.727	−	183.124i	−0.337785	−	0.585061i	−0.984016	+	0.178081i	$0.943011\pi$
$314$	−10.9302	+	6.31056i	−0.0348096	+	0.0200973i
$315$		0			0
$316$		−	1.33399i		−	0.00422150i
$317$	−143.470	+	82.8324i	−0.452587	+	0.261301i	−0.708922	−	0.705287i	$-0.750818\pi$
$317$	−143.470	+	82.8324i	−0.452587	+	0.261301i	0.256335	+	0.966588i	$0.417485\pi$
$318$		0			0
$319$	−41.7029	+	24.0772i	−0.130730	+	0.0754770i
$320$	−160.844	+	278.590i	−0.502637	+	0.870594i
$321$		0			0
$322$		−	518.970i		−	1.61171i
$323$	9.76417	−	80.6308i	0.0302296	−	0.249631i
$324$		0			0
$325$	84.6801	+	48.8901i	0.260554	+	0.150431i
$326$	45.8305	+	26.4603i	0.140584	+	0.0811664i
$327$		0			0
$328$	−206.681	+	357.982i	−0.630125	+	1.09141i
$329$	253.115	+	438.407i	0.769345	+	1.33255i
$330$		0			0
$331$			358.233i			1.08227i	0.840934	+	0.541137i	$0.182006\pi$
$331$			358.233i			1.08227i	−0.840934	+	0.541137i	$0.817994\pi$
$332$	−66.9862	−	116.024i	−0.201766	−	0.349468i
$333$		0			0
$334$	−2.11076			−0.00631964
$335$			496.882i			1.48323i
$336$		0			0
$337$	−550.179	−	317.646i	−1.63258	−	0.942570i	−0.983294	−	0.182025i	$-0.941735\pi$
$337$	−550.179	−	317.646i	−1.63258	−	0.942570i	−0.649285	−	0.760545i	$-0.724932\pi$
$338$	174.777	−	100.908i	0.517092	−	0.298543i
$339$		0			0
$340$	43.2950	−	74.9892i	0.127338	−	0.220556i
$341$			86.6884i			0.254218i
$342$		0			0
$343$	−123.341			−0.359594
$344$	92.3447	+	53.3153i	0.268444	+	0.154986i
$345$		0			0
$346$	125.455	+	217.295i	0.362588	+	0.628021i
$347$	74.7992	−	129.556i	0.215560	−	0.373360i	−0.737886	−	0.674926i	$-0.764176\pi$
$347$	74.7992	−	129.556i	0.215560	−	0.373360i	0.953446	+	0.301565i	$0.0975091\pi$
$348$		0			0
$349$	211.863			0.607058			0.303529	−	0.952822i	$-0.401835\pi$
$349$	211.863			0.607058			0.303529	+	0.952822i	$0.401835\pi$
$350$		−	541.250i		−	1.54643i
$351$		0			0
$352$	108.238	−	62.4910i	0.307493	−	0.177531i
$353$	−154.974			−0.439019			−0.219509	−	0.975610i	$-0.570446\pi$
$353$	−154.974			−0.439019			−0.219509	+	0.975610i	$0.570446\pi$
$354$		0			0
$355$	645.065	−	372.429i	1.81709	−	1.04909i
$356$	−202.343	−	116.823i	−0.568378	−	0.328153i
$357$		0			0
$358$	−21.5782	+	37.3745i	−0.0602742	+	0.104398i
$359$	−124.695	+	215.978i	−0.347340	+	0.601610i	−0.985776	−	0.168064i	$-0.946248\pi$
$359$	−124.695	+	215.978i	−0.347340	+	0.601610i	0.638436	+	0.769675i	$0.279582\pi$
$360$		0			0
$361$	249.907	−	260.514i	0.692263	−	0.721646i
$362$	−142.911			−0.394783
$363$		0			0
$364$	−52.5000	−	30.3109i	−0.144231	−	0.0832717i
$365$	−341.758	−	591.942i	−0.936323	−	1.62176i
$366$		0			0
$367$	−326.714	−	565.885i	−0.890228	−	1.54192i	−0.839601	−	0.543203i	$-0.817211\pi$
$367$	−326.714	−	565.885i	−0.890228	−	1.54192i	−0.0506268	−	0.998718i	$-0.516122\pi$
$368$	1.82834			0.00496830
$369$		0			0
$370$	314.192	+	544.197i	0.849168	+	1.47080i
$371$	−709.723	+	409.759i	−1.91300	+	1.10447i
$372$		0			0
$373$			324.494i			0.869956i	0.900441	+	0.434978i	$0.143244\pi$
$373$			324.494i			0.869956i	−0.900441	+	0.434978i	$0.856756\pi$
$374$	17.8269	−	10.2923i	0.0476654	−	0.0275196i
$375$		0			0
$376$	334.455	−	193.098i	0.889509	−	0.513558i
$377$	14.4113	−	24.9612i	0.0382264	−	0.0662100i
$378$		0			0
$379$			21.4534i			0.0566053i	0.999599	+	0.0283026i	$0.00901021\pi$
$379$			21.4534i			0.0566053i	−0.999599	+	0.0283026i	$0.990990\pi$
$380$	354.024	−	150.969i	0.931641	−	0.397287i
$381$		0			0
$382$	−187.283	−	108.128i	−0.490270	−	0.283057i
$383$	185.197	+	106.924i	0.483544	+	0.279174i	0.721892	−	0.692006i	$-0.243273\pi$
$383$	185.197	+	106.924i	0.483544	+	0.279174i	−0.238348	+	0.971180i	$0.576606\pi$
$384$		0			0
$385$	−167.158	+	289.527i	−0.434178	+	0.752018i
$386$	−207.242	−	358.953i	−0.536896	−	0.929930i
$387$		0			0
$388$			363.017i			0.935611i
$389$	−188.727	−	326.885i	−0.485160	−	0.840321i	0.514695	−	0.857373i	$-0.327905\pi$
$389$	−188.727	−	326.885i	−0.485160	−	0.840321i	−0.999855	+	0.0170523i	$0.994572\pi$
$390$		0			0
$391$	171.588			0.438844
$392$			485.749i			1.23916i
$393$		0			0
$394$	260.756	+	150.548i	0.661818	+	0.382101i
$395$	3.81340	−	2.20167i	0.00965418	−	0.00557385i
$396$		0			0
$397$	132.294	−	229.140i	0.333234	−	0.577179i	−0.649910	−	0.760011i	$-0.725193\pi$
$397$	132.294	−	229.140i	0.333234	−	0.577179i	0.983144	+	0.182833i	$0.0585267\pi$
$398$		−	418.915i		−	1.05255i
$399$		0			0
$400$	1.90683			0.00476707
$401$	424.726	+	245.216i	1.05917	+	0.611510i	0.925202	−	0.379476i	$-0.123896\pi$
$401$	424.726	+	245.216i	1.05917	+	0.611510i	0.133965	+	0.990986i	$0.457229\pi$
$402$		0			0
$403$	−25.9436	−	44.9356i	−0.0643761	−	0.111503i
$404$	−147.089	+	254.765i	−0.364081	+	0.630607i
$405$		0			0
$406$	−159.545			−0.392967
$407$		−	243.014i		−	0.597086i
$408$		0			0
$409$	−364.046	+	210.182i	−0.890087	+	0.513892i	−0.873971	−	0.485978i	$-0.838463\pi$
$409$	−364.046	+	210.182i	−0.890087	+	0.513892i	−0.0161160	+	0.999870i	$0.505130\pi$
$410$	−521.838			−1.27278
$411$		0			0
$412$	56.0466	−	32.3585i	0.136035	−	0.0785401i
$413$	866.479	+	500.262i	2.09801	+	1.21129i
$414$		0			0
$415$	221.113	−	382.979i	0.532802	−	0.922840i
$416$	−37.4039	+	64.7854i	−0.0899131	+	0.155734i
$417$		0			0
$418$	90.8297	+	10.9992i	0.217296	+	0.0263140i
$419$	−646.178			−1.54219			−0.771095	−	0.636720i	$-0.780291\pi$
$419$	−646.178			−1.54219			−0.771095	+	0.636720i	$0.780291\pi$
$420$		0			0
$421$	468.113	+	270.265i	1.11191	+	0.641960i	0.939323	−	0.343035i	$-0.111455\pi$
$421$	468.113	+	270.265i	1.11191	+	0.641960i	0.172584	+	0.984995i	$0.444788\pi$
$422$	60.6143	+	104.987i	0.143636	+	0.248785i
$423$		0			0
$424$	312.600	+	541.439i	0.737264	+	1.27698i
$425$	178.954			0.421069
$426$		0			0
$427$	−197.874	−	342.728i	−0.463406	−	0.802642i
$428$	−258.960	+	149.510i	−0.605046	+	0.349323i
$429$		0			0
$430$			134.613i			0.313053i
$431$	198.483	−	114.594i	0.460517	−	0.265880i	−0.251745	−	0.967794i	$-0.581004\pi$
$431$	198.483	−	114.594i	0.460517	−	0.265880i	0.712262	+	0.701914i	$0.247671\pi$
$432$		0			0
$433$	238.975	−	137.972i	0.551906	−	0.318643i	−0.197985	−	0.980205i	$-0.563440\pi$
$433$	238.975	−	137.972i	0.551906	−	0.318643i	0.749890	+	0.661562i	$0.230106\pi$
$434$	−143.608	+	248.736i	−0.330893	+	0.573123i
$435$		0			0
$436$			263.031i			0.603283i
$437$	609.851	+	457.968i	1.39554	+	1.04798i
$438$		0			0
$439$	10.6486	+	6.14794i	0.0242564	+	0.0140044i	0.512079	−	0.858938i	$-0.328875\pi$
$439$	10.6486	+	6.14794i	0.0242564	+	0.0140044i	−0.487823	+	0.872943i	$0.662209\pi$
$440$	220.876	+	127.523i	0.501992	+	0.289825i
$441$		0			0
$442$	−6.16046	+	10.6702i	−0.0139377	+	0.0241408i
$443$	−31.4933	−	54.5480i	−0.0710910	−	0.123133i	0.828289	−	0.560301i	$-0.189315\pi$
$443$	−31.4933	−	54.5480i	−0.0710910	−	0.123133i	−0.899380	+	0.437168i	$0.855981\pi$
$444$		0			0
$445$		−	771.232i		−	1.73311i
$446$	−40.8618	−	70.7747i	−0.0916183	−	0.158688i
$447$		0			0
$448$	412.180			0.920045
$449$		−	679.936i		−	1.51433i	−0.653222	−	0.757167i	$-0.726583\pi$
$449$		−	679.936i		−	1.51433i	0.653222	−	0.757167i	$-0.273417\pi$
$450$		0			0
$451$	174.772	+	100.905i	0.387522	+	0.223736i
$452$	217.986	−	125.854i	0.482269	−	0.278438i
$453$		0			0
$454$	231.513	−	400.992i	0.509940	−	0.883243i
$455$		−	200.105i		−	0.439790i
$456$		0			0
$457$	−434.089			−0.949867			−0.474933	−	0.880022i	$-0.657528\pi$
$457$	−434.089			−0.949867			−0.474933	+	0.880022i	$0.657528\pi$
$458$	−43.2318	−	24.9599i	−0.0943926	−	0.0544976i
$459$		0			0
$460$	406.545	+	704.156i	0.883792	+	1.53077i
$461$	265.088	−	459.146i	0.575028	−	0.995978i	−0.421010	−	0.907056i	$-0.638324\pi$
$461$	265.088	−	459.146i	0.575028	−	0.995978i	0.996039	−	0.0889223i	$-0.0283423\pi$
$462$		0			0
$463$	−450.022			−0.971969			−0.485985	−	0.873967i	$-0.661539\pi$
$463$	−450.022			−0.971969			−0.485985	+	0.873967i	$0.661539\pi$
$464$		−	0.562076i		−	0.00121137i
$465$		0			0
$466$	287.388	−	165.924i	0.616713	−	0.356059i
$467$	733.340			1.57032			0.785161	−	0.619292i	$-0.212580\pi$
$467$	733.340			1.57032			0.785161	+	0.619292i	$0.212580\pi$
$468$		0			0
$469$	551.361	−	318.329i	1.17561	−	0.678739i
$470$	422.224	+	243.771i	0.898350	+	0.518663i
$471$		0			0
$472$	381.643	−	661.026i	0.808566	−	1.40048i
$473$	26.0293	−	45.0841i	0.0550302	−	0.0953152i
$474$		0			0
$475$	636.033	+	477.629i	1.33902	+	1.00554i
$476$	−110.948			−0.233084
$477$		0			0
$478$	62.1744	+	35.8964i	0.130072	+	0.0750971i
$479$	131.657	+	228.037i	0.274859	+	0.476069i	0.970099	−	0.242708i	$-0.0780356\pi$
$479$	131.657	+	228.037i	0.274859	+	0.476069i	−0.695241	+	0.718777i	$0.744702\pi$
$480$		0			0
$481$	72.7277	+	125.968i	0.151201	+	0.261888i
$482$	−178.341			−0.370002
$483$		0			0
$484$	131.011	+	226.917i	0.270684	+	0.468838i
$485$	−1037.73	+	599.136i	−2.13966	+	1.23533i
$486$		0			0
$487$		−	307.749i		−	0.631929i	−0.948771	−	0.315964i	$-0.897672\pi$
$487$		−	307.749i		−	0.631929i	0.948771	−	0.315964i	$-0.102328\pi$
$488$	−261.463	+	150.956i	−0.535785	+	0.309336i
$489$		0			0
$490$	−531.065	+	306.611i	−1.08381	+	0.625736i
$491$	296.882	−	514.214i	0.604647	−	1.04728i	−0.387460	−	0.921887i	$-0.626647\pi$
$491$	296.882	−	514.214i	0.604647	−	1.04728i	0.992107	−	0.125393i	$-0.0400193\pi$
$492$		0			0
$493$		−	52.7505i		−	0.106999i
$494$	−50.3741	+	21.4814i	−0.101972	+	0.0434847i
$495$		0			0
$496$	−0.876297	−	0.505930i	−0.00176673	−	0.00102002i
$497$	−826.525	−	477.194i	−1.66303	−	0.960149i
$498$		0			0
$499$	327.577	−	567.380i	0.656467	−	1.13703i	−0.325057	−	0.945695i	$-0.605383\pi$
$499$	327.577	−	567.380i	0.656467	−	1.13703i	0.981524	−	0.191340i	$-0.0612833\pi$
$500$	170.794	+	295.825i	0.341589	+	0.591649i
$501$		0			0
$502$			115.570i			0.230220i
$503$	−383.121	−	663.586i	−0.761673	−	1.31926i	−0.941988	−	0.335647i	$-0.891045\pi$
$503$	−383.121	−	663.586i	−0.761673	−	1.31926i	0.180315	−	0.983609i	$-0.442288\pi$
$504$		0			0
$505$	−971.041			−1.92285
$506$			193.292i			0.382000i
$507$		0			0
$508$	−237.137	−	136.911i	−0.466804	−	0.269510i
$509$	757.837	−	437.537i	1.48887	−	0.859602i	0.488955	−	0.872309i	$-0.337378\pi$
$509$	757.837	−	437.537i	1.48887	−	0.859602i	0.999919	+	0.0127070i	$0.00404489\pi$
$510$		0			0
$511$	−437.896	+	758.458i	−0.856939	+	1.48426i
$512$			2.91512i			0.00569359i
$513$		0			0
$514$	−510.922			−0.994012
$515$	185.003	+	106.811i	0.359228	+	0.207401i
$516$		0			0
$517$	−94.2733	−	163.286i	−0.182347	−	0.315834i
$518$	402.576	−	697.281i	0.777173	−	1.34610i
$519$		0			0
$520$	−152.657			−0.293572
$521$			445.728i			0.855525i	0.903891	+	0.427762i	$0.140698\pi$
$521$			445.728i			0.855525i	−0.903891	+	0.427762i	$0.859302\pi$
$522$		0			0
$523$	764.415	−	441.335i	1.46160	−	0.843853i	0.462510	−	0.886614i	$-0.346949\pi$
$523$	764.415	−	441.335i	1.46160	−	0.843853i	0.999085	+	0.0427611i	$0.0136154\pi$
$524$	−139.508			−0.266237
$525$		0			0
$526$	−183.321	+	105.840i	−0.348519	+	0.201217i
$527$	−82.2398	−	47.4812i	−0.156053	−	0.0900971i
$528$		0			0
$529$	−541.114	+	937.237i	−1.02290	+	1.77171i
$530$	−394.633	+	683.525i	−0.744591	+	1.28967i
$531$		0			0
$532$	−394.328	−	296.121i	−0.741217	−	0.556618i
$533$	−120.793			−0.226628
$534$		0			0
$535$	−854.792	−	493.514i	−1.59774	−	0.922457i
$536$	−242.849	−	420.627i	−0.453076	−	0.784751i
$537$		0			0
$538$	−4.17029	−	7.22315i	−0.00775147	−	0.0134259i
$539$	237.150			0.439981
$540$		0			0
$541$	−72.3654	−	125.341i	−0.133762	−	0.231683i	0.791362	−	0.611348i	$-0.209373\pi$
$541$	−72.3654	−	125.341i	−0.133762	−	0.231683i	−0.925124	+	0.379665i	$0.876039\pi$
$542$	263.962	−	152.399i	0.487015	−	0.281178i
$543$		0			0
$544$			136.911i			0.251674i
$545$	−751.912	+	434.116i	−1.37965	+	0.796544i
$546$		0			0
$547$	−91.2148	+	52.6629i	−0.166755	+	0.0962758i	−0.581055	−	0.813865i	$-0.697360\pi$
$547$	−91.2148	+	52.6629i	−0.166755	+	0.0962758i	0.414300	+	0.910140i	$0.364026\pi$
$548$	173.321	−	300.201i	0.316279	−	0.547812i
$549$		0			0
$550$			201.590i			0.366528i
$551$	140.791	−	187.484i	0.255519	−	0.340261i
$552$		0			0
$553$	−4.88613	−	2.82101i	−0.00883567	−	0.00510128i
$554$	−72.2809	−	41.7314i	−0.130471	−	0.0753275i
$555$		0			0
$556$	210.930	−	365.341i	0.379370	−	0.657088i
$557$	298.372	+	516.795i	0.535676	+	0.927819i	0.999130	+	0.0416975i	$0.0132766\pi$
$557$	298.372	+	516.795i	0.535676	+	0.927819i	−0.463454	+	0.886121i	$0.653390\pi$
$558$		0			0
$559$			31.1596i			0.0557416i
$560$	−1.95114	−	3.37947i	−0.00348417	−	0.00603477i
$561$		0			0
$562$	−31.5290			−0.0561014
$563$			709.552i			1.26031i	0.776471	+	0.630153i	$0.217008\pi$
$563$			709.552i			1.26031i	−0.776471	+	0.630153i	$0.782992\pi$
$564$		0			0
$565$	719.542	+	415.428i	1.27353	+	0.735271i
$566$	−1.02000	+	0.588900i	−0.00180213	+	0.00104046i
$567$		0			0
$568$	−364.046	+	630.545i	−0.640925	+	1.11012i
$569$		−	275.069i		−	0.483425i	−0.970348	−	0.241712i	$-0.922291\pi$
$569$		−	275.069i		−	0.483425i	0.970348	−	0.241712i	$-0.0777090\pi$
$570$		0			0
$571$	−924.109			−1.61840			−0.809202	−	0.587531i	$-0.800100\pi$
$571$	−924.109			−1.61840			−0.809202	+	0.587531i	$0.800100\pi$
$572$	19.5538	+	11.2894i	0.0341849	+	0.0197367i
$573$		0			0
$574$	334.317	+	579.054i	0.582433	+	1.00880i
$575$	−840.200	+	1455.27i	−1.46122	+	2.53090i
$576$		0			0
$577$	−443.905			−0.769332			−0.384666	−	0.923056i	$-0.625683\pi$
$577$	−443.905			−0.769332			−0.384666	+	0.923056i	$0.625683\pi$
$578$		−	334.079i		−	0.577991i
$579$		0			0
$580$	216.475	−	124.982i	0.373233	−	0.215486i
$581$	−566.626			−0.975259
$582$		0			0
$583$	264.339	−	152.616i	0.453411	−	0.261777i
$584$	578.618	+	334.065i	0.990785	+	0.572030i
$585$		0			0
$586$	183.252	−	317.401i	0.312716	−	0.541640i
$587$	255.163	−	441.955i	0.434690	−	0.752905i	−0.562580	−	0.826743i	$-0.690191\pi$
$587$	255.163	−	441.955i	0.434690	−	0.752905i	0.997270	+	0.0738374i	$0.0235246\pi$
$588$		0			0
$589$	−165.566	−	388.254i	−0.281097	−	0.659174i
$590$	963.591			1.63321
$591$		0			0
$592$	2.45653	+	1.41828i	0.00414954	+	0.00239574i
$593$	−57.1501	−	98.9869i	−0.0963746	−	0.166926i	0.813807	−	0.581135i	$-0.197391\pi$
$593$	−57.1501	−	98.9869i	−0.0963746	−	0.166926i	−0.910181	+	0.414210i	$0.864058\pi$
$594$		0			0
$595$	−183.113	−	317.161i	−0.307753	−	0.533043i
$596$	−294.618			−0.494325
$597$		0			0
$598$	−57.8473	−	100.194i	−0.0967346	−	0.167549i
$599$	530.087	−	306.046i	0.884954	−	0.510928i	0.0126651	−	0.999920i	$-0.495968\pi$
$599$	530.087	−	306.046i	0.884954	−	0.510928i	0.872288	+	0.488992i	$0.162635\pi$
$600$		0			0
$601$			46.8204i			0.0779041i	0.999241	+	0.0389520i	$0.0124020\pi$
$601$			46.8204i			0.0779041i	−0.999241	+	0.0389520i	$0.987598\pi$
$602$	149.372	−	86.2400i	0.248126	−	0.143256i
$603$		0			0
$604$	−323.727	+	186.904i	−0.535971	+	0.309443i
$605$	−432.450	+	749.025i	−0.714793	+	1.23806i
$606$		0			0
$607$			177.626i			0.292629i	0.989238	+	0.146315i	$0.0467412\pi$
$607$			177.626i			0.292629i	−0.989238	+	0.146315i	$0.953259\pi$
$608$	−365.415	+	486.603i	−0.601012	+	0.800334i
$609$		0			0
$610$	−330.077	−	190.570i	−0.541110	−	0.312410i
$611$	97.7346	+	56.4271i	0.159958	+	0.0923520i
$612$		0			0
$613$	−194.067	+	336.134i	−0.316586	+	0.548343i	−0.979773	−	0.200110i	$-0.935870\pi$
$613$	−194.067	+	336.134i	−0.316586	+	0.548343i	0.663187	+	0.748454i	$0.269203\pi$
$614$	−34.1005	−	59.0637i	−0.0555382	−	0.0961950i
$615$		0			0
$616$		−	326.792i		−	0.530506i
$617$	−113.174	−	196.024i	−0.183427	−	0.317705i	0.759618	−	0.650369i	$-0.225386\pi$
$617$	−113.174	−	196.024i	−0.183427	−	0.317705i	−0.943045	+	0.332664i	$0.892052\pi$
$618$		0			0
$619$	−168.929			−0.272906			−0.136453	−	0.990647i	$-0.543570\pi$
$619$	−168.929			−0.272906			−0.136453	+	0.990647i	$0.543570\pi$
$620$		−	449.990i		−	0.725790i
$621$		0			0
$622$	−118.378	−	68.3458i	−0.190319	−	0.109881i
$623$	−855.792	+	494.092i	−1.37366	+	0.793084i
$624$		0			0
$625$	−40.4783	+	70.1104i	−0.0647652	+	0.112177i
$626$			260.935i			0.416829i
$627$		0			0
$628$	−25.3364			−0.0403446
$629$	230.543	+	133.104i	0.366523	+	0.211612i
$630$		0			0
$631$	−355.351	−	615.487i	−0.563156	−	0.975415i	−0.997219	−	0.0745321i	$-0.976254\pi$
$631$	−355.351	−	615.487i	−0.563156	−	0.975415i	0.434063	−	0.900883i	$-0.357080\pi$
$632$	−2.15211	+	3.72757i	−0.00340524	+	0.00589805i
$633$		0			0
$634$	204.432			0.322447
$635$		−	903.850i		−	1.42339i
$636$		0			0
$637$	−122.929	+	70.9728i	−0.192980	+	0.111417i
$638$	59.4228			0.0931392
$639$		0			0
$640$	−563.442	+	325.303i	−0.880377	+	0.508286i
$641$	−901.332	−	520.385i	−1.40613	−	0.811832i	−0.411122	−	0.911580i	$-0.634863\pi$
$641$	−901.332	−	520.385i	−1.40613	−	0.811832i	−0.995013	+	0.0997480i	$0.968196\pi$
$642$		0			0
$643$	7.89596	−	13.6762i	0.0122799	−	0.0212694i	−0.859820	−	0.510597i	$-0.829424\pi$
$643$	7.89596	−	13.6762i	0.0122799	−	0.0212694i	0.872100	+	0.489328i	$0.162758\pi$
$644$	520.907	−	902.238i	0.808862	−	1.40099i
$645$		0			0
$646$	−60.1843	+	80.1441i	−0.0931645	+	0.124062i
$647$	214.998			0.332299			0.166150	−	0.986101i	$-0.446867\pi$
$647$	214.998			0.332299			0.166150	+	0.986101i	$0.446867\pi$
$648$		0			0
$649$	−322.723	−	186.324i	−0.497261	−	0.287094i
$650$	−60.3307	−	104.496i	−0.0928165	−	0.160763i
$651$		0			0
$652$	53.1180	+	92.0031i	0.0814694	+	0.141109i
$653$	−371.833			−0.569423			−0.284712	−	0.958613i	$-0.591898\pi$
$653$	−371.833			−0.569423			−0.284712	+	0.958613i	$0.591898\pi$
$654$		0			0
$655$	−230.249	−	398.804i	−0.351526	−	0.608861i
$656$	−2.04001	+	1.17780i	−0.00310977	+	0.00179543i
$657$		0			0
$658$		−	624.691i		−	0.949378i
$659$	113.255	−	65.3877i	0.171859	−	0.0992226i	−0.411603	−	0.911363i	$-0.635031\pi$
$659$	113.255	−	65.3877i	0.171859	−	0.0992226i	0.583462	+	0.812140i	$0.301698\pi$
$660$		0			0
$661$	−194.222	+	112.134i	−0.293830	+	0.169643i	−0.639668	−	0.768652i	$-0.720928\pi$
$661$	−194.222	+	112.134i	−0.293830	+	0.169643i	0.345838	+	0.938294i	$0.387595\pi$
$662$	221.031	−	382.837i	0.333884	−	0.578303i
$663$		0			0
$664$			432.272i			0.651011i
$665$	195.689	−	1615.97i	0.294270	−	2.43003i
$666$		0			0
$667$	428.970	+	247.666i	0.643133	+	0.371313i
$668$	−3.66959	−	2.11864i	−0.00549339	−	0.00317161i
$669$		0			0
$670$	306.578	−	531.009i	0.457579	−	0.792551i
$671$	73.6989	+	127.650i	0.109834	+	0.190239i
$672$		0			0
$673$		−	101.375i		−	0.150631i	−0.997160	−	0.0753154i	$-0.976004\pi$
$673$		−	101.375i		−	0.150631i	0.997160	−	0.0753154i	$-0.0239964\pi$
$674$	391.978	+	678.925i	0.581569	+	1.00731i
$675$		0			0
$676$	405.137			0.599315
$677$			60.9135i			0.0899756i	0.998988	+	0.0449878i	$0.0143249\pi$
$677$			60.9135i			0.0899756i	−0.998988	+	0.0449878i	$0.985675\pi$
$678$		0			0
$679$	1329.65	+	767.676i	1.95825	+	1.13060i
$680$	−241.958	+	139.694i	−0.355821	+	0.205433i
$681$		0			0
$682$	53.4871	−	92.6423i	0.0784268	−	0.135839i
$683$			118.773i			0.173898i	0.996213	+	0.0869492i	$0.0277118\pi$
$683$			118.773i			0.173898i	−0.996213	+	0.0869492i	$0.972288\pi$
$684$		0			0
$685$	1144.22			1.67040
$686$	131.812	+	76.1016i	0.192146	+	0.110935i
$687$		0			0
$688$	0.303824	+	0.526239i	0.000441605	+	0.000764882i
$689$	−91.3480	+	158.219i	−0.132580	+	0.229636i
$690$		0			0
$691$	−55.9089			−0.0809101			−0.0404551	−	0.999181i	$-0.512881\pi$
$691$	−55.9089			−0.0809101			−0.0404551	+	0.999181i	$0.512881\pi$
$692$			503.695i			0.727883i
$693$		0			0
$694$	−159.873	+	92.3028i	−0.230365	+	0.133001i
$695$	1392.50			2.00360
$696$		0			0
$697$	−191.453	+	110.536i	−0.274682	+	0.158588i
$698$	−226.415	−	130.720i	−0.324376	−	0.187279i
$699$		0			0
$700$	543.270	−	940.972i	0.776100	−	1.34425i
$701$	16.5402	−	28.6485i	0.0235952	−	0.0408681i	−0.853987	−	0.520295i	$-0.825822\pi$
$701$	16.5402	−	28.6485i	0.0235952	−	0.0408681i	0.877582	+	0.479427i	$0.159155\pi$
$702$		0			0
$703$	464.132	+	1088.39i	0.660217	+	1.54821i
$704$	−153.518			−0.218065
$705$		0			0
$706$	165.617	+	95.6193i	0.234586	+	0.135438i
$707$	622.100	+	1077.51i	0.879915	+	1.52406i
$708$		0			0
$709$	371.042	+	642.664i	0.523332	+	0.906438i	0.999631	+	0.0271545i	$0.00864459\pi$
$709$	371.042	+	642.664i	0.523332	+	0.906438i	−0.476299	+	0.879283i	$0.658022\pi$
$710$	−919.159			−1.29459
$711$		0			0
$712$	376.936	+	652.873i	0.529405	+	0.916956i
$713$	772.240	−	445.853i	1.08309	−	0.625320i
$714$		0			0
$715$			74.5296i			0.104237i
$716$	−75.0279	+	43.3174i	−0.104788	+	0.0604991i
$717$		0			0
$718$	266.519	−	153.875i	0.371196	−	0.214310i
$719$	672.563	−	1164.91i	0.935414	−	1.62018i	0.161520	−	0.986869i	$-0.448360\pi$
$719$	672.563	−	1164.91i	0.935414	−	1.62018i	0.773894	−	0.633315i	$-0.218306\pi$
$720$		0			0
$721$		−	273.715i		−	0.379633i
$722$	−427.809	+	124.213i	−0.592533	+	0.172040i
$723$		0			0
$724$	−248.453	−	143.445i	−0.343168	−	0.198128i
$725$	447.386	+	258.298i	0.617084	+	0.356274i
$726$		0			0
$727$	107.104	−	185.510i	0.147323	−	0.255171i	−0.782914	−	0.622130i	$-0.786268\pi$
$727$	107.104	−	185.510i	0.147323	−	0.255171i	0.930237	+	0.366958i	$0.119601\pi$
$728$	97.8002	+	169.395i	0.134341	+	0.232685i
$729$		0			0
$730$			843.464i			1.15543i
$731$	28.5137	+	49.3871i	0.0390064	+	0.0675610i
$732$		0			0
$733$	503.818			0.687337			0.343668	−	0.939091i	$-0.388330\pi$
$733$	503.818			0.687337			0.343668	+	0.939091i	$0.388330\pi$
$734$			806.334i			1.09855i
$735$		0			0
$736$	−1113.37	−	642.803i	−1.51273	−	0.873374i
$737$	−205.356	+	118.562i	−0.278638	+	0.160872i
$738$		0			0
$739$	708.464	−	1227.10i	0.958680	−	1.66048i	0.232966	−	0.972485i	$-0.425157\pi$
$739$	708.464	−	1227.10i	0.958680	−	1.66048i	0.725713	−	0.687997i	$-0.241510\pi$
$740$			1261.46i			1.70467i
$741$		0			0
$742$	1011.29			1.36293
$743$	539.026	+	311.207i	0.725472	+	0.418852i	0.816764	−	0.576973i	$-0.195766\pi$
$743$	539.026	+	311.207i	0.725472	+	0.418852i	−0.0912911	+	0.995824i	$0.529099\pi$
$744$		0			0
$745$	−486.247	−	842.205i	−0.652681	−	1.13048i
$746$	200.214	−	346.780i	0.268383	−	0.464853i
$747$		0			0
$748$	41.3230			0.0552446
$749$			1264.68i			1.68850i
$750$		0			0
$751$	−484.987	+	280.007i	−0.645788	+	0.372846i	−0.786841	−	0.617156i	$-0.788285\pi$
$751$	−484.987	+	280.007i	−0.645788	+	0.372846i	0.141052	+	0.990002i	$0.454951\pi$
$752$	2.20079			0.00292658
$753$		0			0
$754$	−30.8023	+	17.7837i	−0.0408518	+	0.0235858i
$755$	−1068.58	−	616.945i	−1.41534	−	0.817146i
$756$		0			0
$757$	−686.860	+	1189.68i	−0.907345	+	1.57157i	−0.0896071	+	0.995977i	$0.528561\pi$
$757$	−686.860	+	1189.68i	−0.907345	+	1.57157i	−0.817738	+	0.575591i	$0.804772\pi$
$758$	13.2368	−	22.9269i	0.0174628	−	0.0302465i
$759$		0			0
$760$	−1232.80	−	149.289i	−1.62211	−	0.196433i
$761$	−1196.22			−1.57191			−0.785953	−	0.618286i	$-0.787827\pi$
$761$	−1196.22			−1.57191			−0.785953	+	0.618286i	$0.787827\pi$
$762$		0			0
$763$	963.428	+	556.235i	1.26268	+	0.729011i
$764$	−217.063	−	375.964i	−0.284114	−	0.492100i
$765$		0			0
$766$	−131.945	−	228.535i	−0.172251	−	0.298348i
$767$	223.048			0.290805
$768$		0			0
$769$	73.0921	+	126.599i	0.0950483	+	0.164628i	0.909629	−	0.415422i	$-0.136366\pi$
$769$	73.0921	+	126.599i	0.0950483	+	0.164628i	−0.814580	+	0.580051i	$0.803033\pi$
$770$	357.278	−	206.275i	0.463998	−	0.267889i
$771$		0			0
$772$		−	832.060i		−	1.07780i
$773$	486.540	−	280.904i	0.629418	−	0.363395i	−0.151109	−	0.988517i	$-0.548284\pi$
$773$	486.540	−	280.904i	0.629418	−	0.363395i	0.780527	+	0.625123i	$0.214951\pi$
$774$		0			0
$775$	805.393	−	464.994i	1.03922	−	0.599992i
$776$	585.650	−	1014.38i	0.754704	−	1.30719i
$777$		0			0
$778$			465.781i			0.598691i
$779$	−975.476	−	118.127i	−1.25222	−	0.151640i
$780$		0			0
$781$	307.842	+	177.732i	0.394163	+	0.227570i
$782$	−183.373	−	105.870i	−0.234492	−	0.135384i
$783$		0			0
$784$	−1.38405	+	2.39725i	−0.00176537	+	0.00305772i
$785$	−41.8161	−	72.4277i	−0.0532690	−	0.0922646i
$786$		0			0
$787$			1067.08i			1.35589i	0.735114	+	0.677944i	$0.237129\pi$
$787$			1067.08i			1.35589i	−0.735114	+	0.677944i	$0.762871\pi$
$788$	302.219	+	523.459i	0.383527	+	0.664288i
$789$		0			0
$790$	−5.43375			−0.00687817
$791$		−	1064.58i		−	1.34587i
$792$		0			0
$793$	−76.4048	−	44.1123i	−0.0963490	−	0.0556271i
$794$	−282.760	+	163.252i	−0.356121	+	0.205607i
$795$		0			0
$796$	420.478	−	728.290i	0.528239	−	0.914937i
$797$		−	396.451i		−	0.497429i	−0.968577	−	0.248715i	$-0.919992\pi$
$797$		−	396.451i		−	0.497429i	0.968577	−	0.248715i	$-0.0800081\pi$
$798$		0			0
$799$	206.542			0.258501
$800$	−1161.17	−	670.399i	−1.45146	−	0.837999i
$801$		0			0
$802$	−302.598	−	524.115i	−0.377304	−	0.653510i
$803$	163.096	−	282.490i	0.203108	−	0.351793i
$804$		0			0
$805$	3438.89			4.27192
$806$			64.0291i			0.0794406i
$807$		0			0
$808$	822.018	−	474.592i	1.01735	−	0.587366i
$809$	−227.128			−0.280751			−0.140376	−	0.990098i	$-0.544831\pi$
$809$	−227.128			−0.280751			−0.140376	+	0.990098i	$0.544831\pi$
$810$		0			0
$811$	−692.720	+	399.942i	−0.854156	+	0.493147i	−0.862051	−	0.506822i	$-0.830820\pi$
$811$	−692.720	+	399.942i	−0.854156	+	0.493147i	0.00789497	+	0.999969i	$0.497487\pi$
$812$	−277.370	−	160.140i	−0.341589	−	0.197217i
$813$		0			0
$814$	−149.940	+	259.705i	−0.184202	+	0.319047i
$815$	−175.336	+	303.690i	−0.215136	+	0.372626i
$816$		0			0
$817$	−30.4720	+	251.633i	−0.0372975	+	0.307996i
$818$	518.732			0.634146
$819$		0			0
$820$	−907.224	−	523.786i	−1.10637	−	0.638763i
$821$	−73.4787	−	127.269i	−0.0894990	−	0.155017i	0.817800	−	0.575502i	$-0.195193\pi$
$821$	−73.4787	−	127.269i	−0.0894990	−	0.155017i	−0.907299	+	0.420485i	$0.861860\pi$
$822$		0			0
$823$	−307.863	−	533.235i	−0.374075	−	0.647916i	0.616114	−	0.787657i	$-0.288706\pi$
$823$	−307.863	−	533.235i	−0.374075	−	0.647916i	−0.990188	+	0.139741i	$0.955373\pi$
$824$	−208.814			−0.253415
$825$		0			0
$826$	−617.327	−	1069.24i	−0.747369	−	1.29448i
$827$	410.031	−	236.731i	0.495805	−	0.286253i	−0.231174	−	0.972912i	$-0.574257\pi$
$827$	410.031	−	236.731i	0.495805	−	0.286253i	0.726980	+	0.686659i	$0.240923\pi$
$828$		0			0
$829$			264.846i			0.319476i	0.987159	+	0.159738i	$0.0510650\pi$
$829$			264.846i			0.319476i	−0.987159	+	0.159738i	$0.948935\pi$
$830$	−472.599	+	272.855i	−0.569396	+	0.328741i
$831$		0			0
$832$	79.5771	−	45.9439i	0.0956456	−	0.0552210i
$833$	−129.892	+	224.980i	−0.155933	+	0.270084i
$834$		0			0
$835$		−	13.9867i		−	0.0167505i
$836$	146.869	+	110.291i	0.175680	+	0.131927i
$837$		0			0
$838$	690.558	+	398.694i	0.824055	+	0.475769i
$839$	−264.910	−	152.946i	−0.315745	−	0.182296i	0.333749	−	0.942662i	$-0.391686\pi$
$839$	−264.910	−	152.946i	−0.315745	−	0.182296i	−0.649495	+	0.760366i	$0.725019\pi$
$840$		0			0
$841$	−344.361	+	596.451i	−0.409466	+	0.709217i
$842$	−333.509	−	577.655i	−0.396092	−	0.686051i
$843$		0			0
$844$			243.362i			0.288344i
$845$	668.652	+	1158.14i	0.791304	+	1.37058i
$846$		0			0
$847$	1108.20			1.30838
$848$			3.56278i			0.00420140i
$849$		0			0
$850$	−191.245	−	110.416i	−0.224995	−	0.129901i
$851$	−2164.82	+	1249.86i	−2.54386	+	1.46870i
$852$		0			0
$853$	−578.769	+	1002.46i	−0.678510	+	1.17521i	0.296919	+	0.954903i	$0.404041\pi$
$853$	−578.769	+	1002.46i	−0.678510	+	1.17521i	−0.975430	+	0.220311i	$0.929293\pi$
$854$			488.357i			0.571846i
$855$		0			0
$856$	964.812			1.12712
$857$	787.565	+	454.701i	0.918979	+	0.530573i	0.883309	−	0.468791i	$-0.155310\pi$
$857$	787.565	+	454.701i	0.918979	+	0.530573i	0.0356701	+	0.999364i	$0.488643\pi$
$858$		0			0
$859$	−556.807	−	964.418i	−0.648204	−	1.12272i	−0.983552	−	0.180627i	$-0.942187\pi$
$859$	−556.807	−	964.418i	−0.648204	−	1.12272i	0.335348	−	0.942094i	$-0.391146\pi$
$860$	−135.115	+	234.026i	−0.157111	+	0.272124i
$861$		0			0
$862$	−282.820			−0.328097
$863$			511.832i			0.593085i	0.955020	+	0.296542i	$0.0958336\pi$
$863$			511.832i			0.593085i	−0.955020	+	0.296542i	$0.904166\pi$
$864$		0			0
$865$	−1439.88	+	831.316i	−1.66460	+	0.961059i
$866$	−340.518			−0.393208
$867$		0			0
$868$	−499.328	+	288.287i	−0.575262	+	0.332128i
$869$	1.81985	+	1.05069i	0.00209419	+	0.00120908i
$870$		0			0
$871$	70.9653	−	122.916i	0.0814757	−	0.141120i
$872$	424.345	−	734.987i	0.486634	−	0.842875i
$873$		0			0
$874$	−369.169	−	865.703i	−0.422390	−	0.990506i
$875$	1444.72			1.65111
$876$		0			0
$877$	−270.775	−	156.332i	−0.308752	−	0.178258i	0.337616	−	0.941284i	$-0.390379\pi$
$877$	−270.775	−	156.332i	−0.308752	−	0.178258i	−0.646368	+	0.763026i	$0.723713\pi$
$878$	−7.58661	−	13.1404i	−0.00864079	−	0.0149663i
$879$		0			0
$880$	0.726707	+	1.25869i	0.000825803	+	0.00143033i
$881$	858.585			0.974557			0.487279	−	0.873246i	$-0.337990\pi$
$881$	858.585			0.974557			0.487279	+	0.873246i	$0.337990\pi$
$882$		0			0
$883$	−544.512	−	943.122i	−0.616661	−	1.06809i	−0.990091	−	0.140430i	$-0.955151\pi$
$883$	−544.512	−	943.122i	−0.616661	−	1.06809i	0.373429	−	0.927659i	$-0.378182\pi$
$884$	−21.4201	+	12.3669i	−0.0242309	+	0.0139897i
$885$		0			0
$886$			77.7259i			0.0877268i
$887$	−241.738	+	139.567i	−0.272534	+	0.157348i	−0.630039	−	0.776564i	$-0.716961\pi$
$887$	−241.738	+	139.567i	−0.272534	+	0.157348i	0.357505	+	0.933911i	$0.383628\pi$
$888$		0			0
$889$	−1002.95	+	579.054i	−1.12818	+	0.651354i
$890$	−475.853	+	824.202i	−0.534667	+	0.926070i
$891$		0			0
$892$		−	164.057i		−	0.183921i
$893$	734.085	+	551.262i	0.822043	+	0.617314i
$894$		0			0
$895$	−247.657	−	142.985i	−0.276712	−	0.159760i
$896$	721.940	+	416.812i	0.805737	+	0.465192i
$897$		0			0
$898$	−419.523	+	726.635i	−0.467175	+	0.809170i
$899$	−137.066	−	237.406i	−0.152465	−	0.264078i
$900$		0			0
$901$			334.365i			0.371104i
$902$	−124.517	−	215.670i	−0.138046	−	0.239102i
$903$		0			0
$904$	−812.154			−0.898401
$905$		−	946.984i		−	1.04639i
$906$		0			0
$907$	224.436	+	129.578i	0.247449	+	0.142864i	0.618595	−	0.785710i	$-0.287702\pi$
$907$	224.436	+	129.578i	0.247449	+	0.142864i	−0.371147	+	0.928574i	$0.621035\pi$
$908$	804.977	−	464.754i	0.886539	−	0.511844i
$909$		0			0
$910$	−123.465	+	213.848i	−0.135676	+	0.234998i
$911$			922.079i			1.01216i	0.862486	+	0.506081i	$0.168906\pi$
$911$			922.079i			1.01216i	−0.862486	+	0.506081i	$0.831094\pi$
$912$		0			0
$913$	211.041			0.231152
$914$	463.903	+	267.835i	0.507553	+	0.293036i
$915$		0			0
$916$	−50.1061	−	86.7863i	−0.0547010	−	0.0947449i
$917$	−295.020	+	510.989i	−0.321723	+	0.557240i
$918$		0			0
$919$	434.655			0.472965			0.236483	−	0.971636i	$-0.424005\pi$
$919$	434.655			0.472965			0.236483	+	0.971636i	$0.424005\pi$
$920$		−	2623.49i		−	2.85162i
$921$		0			0
$922$	−566.590	+	327.121i	−0.614522	+	0.354795i
$923$	−212.763			−0.230512
$924$		0			0
$925$	−2257.76	+	1303.52i	−2.44082	+	1.40921i
$926$	480.930	+	277.665i	0.519363	+	0.299854i
$927$		0			0
$928$	−197.614	+	342.277i	−0.212946	+	0.368833i
$929$	−223.539	+	387.180i	−0.240623	+	0.416771i	−0.960892	−	0.276924i	$-0.910685\pi$
$929$	−223.539	+	387.180i	−0.240623	+	0.416771i	0.720269	+	0.693695i	$0.244018\pi$
$930$		0			0
$931$	−1062.13	+	452.933i	−1.14085	+	0.486502i
$932$	666.172			0.714776
$933$		0			0
$934$	−783.707	−	452.473i	−0.839087	−	0.484447i
$935$	68.2009	+	118.127i	0.0729422	+	0.126340i
$936$		0			0
$937$	296.047	+	512.768i	0.315952	+	0.547244i	0.979639	−	0.200766i	$-0.0643430\pi$
$937$	296.047	+	512.768i	0.315952	+	0.547244i	−0.663688	+	0.748010i	$0.731010\pi$
$938$	−785.640			−0.837569
$939$		0			0
$940$	489.362	+	847.600i	0.520598	+	0.901703i
$941$	534.341	−	308.502i	0.567844	−	0.327845i	−0.188444	−	0.982084i	$-0.560344\pi$
$941$	534.341	−	308.502i	0.567844	−	0.327845i	0.756288	+	0.654239i	$0.227011\pi$
$942$		0			0
$943$		−	2075.88i		−	2.20136i
$944$	3.76694	−	2.17485i	0.00399040	−	0.00230386i
$945$		0			0
$946$	−55.6341	+	32.1203i	−0.0588098	+	0.0339539i
$947$	−469.361	+	812.957i	−0.495629	+	0.858455i	−0.999987	−	0.00503973i	$-0.998396\pi$
$947$	−469.361	+	812.957i	−0.495629	+	0.858455i	0.504358	+	0.863495i	$0.331729\pi$
$948$		0			0
$949$			195.241i			0.205734i
$950$	−385.018	−	902.868i	−0.405282	−	0.950387i
$951$		0			0
$952$	310.022	+	178.991i	0.325653	+	0.188016i
$953$	−1138.99	−	657.596i	−1.19516	−	0.690028i	−0.235690	−	0.971828i	$-0.575735\pi$
$953$	−1138.99	−	657.596i	−1.19516	−	0.690028i	−0.959473	+	0.281801i	$0.909068\pi$
$954$		0			0
$955$	716.497	−	1241.01i	0.750259	−	1.29949i
$956$	72.0608	+	124.813i	0.0753774	+	0.130557i
$957$		0			0
$958$		−	324.932i		−	0.339178i
$959$	−733.048	−	1269.68i	−0.764388	−	1.32396i
$960$		0			0
$961$	467.501			0.486474
$962$		−	179.493i		−	0.186583i
$963$		0			0
$964$	−310.048	−	179.006i	−0.321627	−	0.185691i
$965$	2378.56	−	1373.26i	2.46483	−	1.42307i
$966$		0			0
$967$	105.759	−	183.181i	0.109368	−	0.189432i	−0.806146	−	0.591717i	$-0.798450\pi$
$967$	105.759	−	183.181i	0.109368	−	0.189432i	0.915515	+	0.402285i	$0.131784\pi$
$968$		−	845.432i		−	0.873380i
$969$		0			0
$970$	1478.68			1.52441
$971$	−840.225	−	485.104i	−0.865319	−	0.499592i	0.000470648	−	1.00000i	$-0.499850\pi$
$971$	−840.225	−	485.104i	−0.865319	−	0.499592i	−0.865790	+	0.500408i	$0.833184\pi$
$972$		0			0
$973$	−892.110	−	1545.18i	−0.916865	−	1.58806i
$974$	−189.882	+	328.886i	−0.194951	+	0.337665i
$975$		0			0
$976$	−1.72048			−0.00176279
$977$			957.081i			0.979612i	0.871831	+	0.489806i	$0.162932\pi$
$977$			957.081i			0.979612i	−0.871831	+	0.489806i	$0.837068\pi$
$978$		0			0
$979$	318.742	−	184.026i	0.325579	−	0.187973i
$980$	−1231.02			−1.25614
$981$		0			0
$982$	−634.545	+	366.354i	−0.646176	+	0.373070i
$983$	−408.211	−	235.681i	−0.415271	−	0.239757i	0.277781	−	0.960644i	$-0.410401\pi$
$983$	−408.211	−	235.681i	−0.415271	−	0.239757i	−0.693052	+	0.720888i	$0.743734\pi$
$984$		0			0
$985$	−997.586	+	1727.87i	−1.01278	+	1.75418i
$986$	−32.5472	+	56.3735i	−0.0330094	+	0.0571739i
$987$		0			0
$988$	−109.138	−	13.2163i	−0.110463	−	0.0133768i
$989$	−535.492			−0.541448
$990$		0			0
$991$	584.759	+	337.611i	0.590070	+	0.340677i	0.765125	−	0.643882i	$-0.222677\pi$
$991$	584.759	+	337.611i	0.590070	+	0.340677i	−0.175055	+	0.984559i	$0.556010\pi$
$992$	355.748	+	616.174i	0.358617	+	0.621143i
$993$		0			0
$994$	588.861	+	1019.94i	0.592416	+	1.02609i
$995$	2775.89			2.78984
$996$		0			0
$997$	−352.522	−	610.586i	−0.353582	−	0.612423i	0.633292	−	0.773913i	$-0.281703\pi$
$997$	−352.522	−	610.586i	−0.353582	−	0.612423i	−0.986874	+	0.161490i	$0.948370\pi$
$998$	−700.151	+	404.233i	−0.701555	+	0.405043i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	171.3.p.f.46.2	✓	8
3.2	odd	2	inner	171.3.p.f.46.3	yes	8
19.12	odd	6	inner	171.3.p.f.145.2	yes	8
57.50	even	6	inner	171.3.p.f.145.3	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
171.3.p.f.46.2	✓	8	1.1	even	1	trivial
171.3.p.f.46.3	yes	8	3.2	odd	2	inner
171.3.p.f.145.2	yes	8	19.12	odd	6	inner
171.3.p.f.145.3	yes	8	57.50	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.06868 - 0.617004i) q^{2} +(-1.23861 - 2.14534i) q^{4} +(4.08850 - 7.08149i) q^{5} -10.4772 q^{7} +7.99294i q^{8} +O(q^{10})\)	\(q+(-1.06868 - 0.617004i) q^{2} +(-1.23861 - 2.14534i) q^{4} +(4.08850 - 7.08149i) q^{5} -10.4772 q^{7} +7.99294i q^{8} +(-8.73861 + 5.04524i) q^{10} +3.90227 q^{11} +(-2.02277 + 1.16785i) q^{13} +(11.1968 + 6.46449i) q^{14} +(-0.0227744 + 0.0394465i) q^{16} +(-2.13736 + 3.70202i) q^{17} +(-17.4772 + 7.45296i) q^{19} -20.2563 q^{20} +(-4.17029 - 2.40772i) q^{22} +(-20.0701 - 34.7623i) q^{23} +(-20.9317 - 36.2547i) q^{25} +2.88227 q^{26} +(12.9772 + 22.4772i) q^{28} +(-10.6868 + 6.17004i) q^{29} +22.2148i q^{31} +(27.7370 - 16.0140i) q^{32} +(4.56832 - 2.63752i) q^{34} +(-42.8361 + 74.1944i) q^{35} -62.2749i q^{37} +(23.2761 + 2.81867i) q^{38} +(56.6020 + 32.6792i) q^{40} +(44.7873 + 25.8579i) q^{41} +(6.67029 - 11.5533i) q^{43} +(-4.83341 - 8.37171i) q^{44} +49.5332i q^{46} +(-24.1586 - 41.8438i) q^{47} +60.7723 q^{49} +51.6597i q^{50} +(5.01087 + 2.89303i) q^{52} +(67.7396 - 39.1095i) q^{53} +(15.9545 - 27.6339i) q^{55} -83.7439i q^{56} +15.2277 q^{58} +(-82.7011 - 47.7475i) q^{59} +(18.8861 + 32.7117i) q^{61} +(13.7066 - 23.7406i) q^{62} -39.3406 q^{64} +19.0990i q^{65} +(-52.6247 + 30.3829i) q^{67} +10.5895 q^{68} +(91.5564 - 52.8601i) q^{70} +(78.8877 + 45.5459i) q^{71} +(41.7950 - 72.3911i) q^{73} +(-38.4239 + 66.5521i) q^{74} +(37.6366 + 28.2633i) q^{76} -40.8850 q^{77} +(0.466357 + 0.269251i) q^{79} +(0.186227 + 0.322554i) q^{80} +(-31.9089 - 55.2678i) q^{82} +54.0816 q^{83} +(17.4772 + 30.2714i) q^{85} +(-14.2568 + 8.23119i) q^{86} +31.1907i q^{88} +(81.6811 - 47.1586i) q^{89} +(21.1931 - 12.2358i) q^{91} +(-49.7180 + 86.1142i) q^{92} +59.6237i q^{94} +(-18.6776 + 154.236i) q^{95} +(-126.909 - 73.2709i) q^{97} +(-64.9462 - 37.4967i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 12 q^{4} - 40 q^{7}+O(q^{10}) \) 8 * q + 12 * q^4 - 40 * q^7	\( 8 q + 12 q^{4} - 40 q^{7} - 48 q^{10} - 60 q^{13} - 44 q^{16} - 96 q^{19} + 120 q^{22} - 36 q^{25} + 60 q^{28} + 168 q^{34} + 168 q^{40} - 100 q^{43} + 48 q^{49} - 420 q^{52} + 40 q^{55} + 560 q^{58} - 68 q^{61} - 8 q^{64} - 180 q^{67} + 360 q^{70} - 60 q^{73} + 564 q^{76} + 420 q^{79} - 80 q^{82} + 96 q^{85} + 60 q^{91} - 840 q^{97}+O(q^{100}) \) 8 * q + 12 * q^4 - 40 * q^7 - 48 * q^10 - 60 * q^13 - 44 * q^16 - 96 * q^19 + 120 * q^22 - 36 * q^25 + 60 * q^28 + 168 * q^34 + 168 * q^40 - 100 * q^43 + 48 * q^49 - 420 * q^52 + 40 * q^55 + 560 * q^58 - 68 * q^61 - 8 * q^64 - 180 * q^67 + 360 * q^70 - 60 * q^73 + 564 * q^76 + 420 * q^79 - 80 * q^82 + 96 * q^85 + 60 * q^91 - 840 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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