LMFDB - Embedded newform 189.2.g.b.100.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [189,2,Mod(100,189)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("189.100"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(189, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.g (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [10] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.991381711347.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 9x^{8} - 8x^{7} + 40x^{6} - 36x^{5} + 90x^{4} - 3x^{3} + 36x^{2} - 9x + 9 $ x^10 - 2x^9 + 9x^8 - 8x^7 + 40x^6 - 36x^5 + 90x^4 - 3x^3 + 36x^2 - 9*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			100.4
Root			$-0.335166 - 0.580525i$ of defining polynomial
Character	$\chi$	$=$	189.100
Dual form			189.2.g.b.172.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.335166 + 0.580525i) q^{2} +(0.775327 - 1.34291i) q^{4} -1.42494 q^{5} +(2.21529 + 1.44655i) q^{7} +2.38012 q^{8} +(-0.477591 - 0.827212i) q^{10} +4.93077 q^{11} +(-1.37730 - 2.38556i) q^{13} +(-0.0972697 + 1.77086i) q^{14} +(-0.752918 - 1.30409i) q^{16} +(-0.559839 - 0.969670i) q^{17} +(-2.00752 + 3.47713i) q^{19} +(-1.10479 + 1.91356i) q^{20} +(1.65263 + 2.86244i) q^{22} -5.43661 q^{23} -2.96955 q^{25} +(0.923251 - 1.59912i) q^{26} +(3.66015 - 1.85337i) q^{28} +(-3.40555 + 5.89858i) q^{29} +(-1.25292 + 2.17012i) q^{31} +(2.88483 - 4.99666i) q^{32} +(0.375279 - 0.650002i) q^{34} +(-3.15664 - 2.06124i) q^{35} +(0.709787 - 1.22939i) q^{37} -2.69142 q^{38} -3.39152 q^{40} +(-0.124384 - 0.215440i) q^{41} +(-0.498313 + 0.863104i) q^{43} +(3.82296 - 6.62156i) q^{44} +(-1.82217 - 3.15609i) q^{46} +(-4.73790 - 8.20628i) q^{47} +(2.81498 + 6.40905i) q^{49} +(-0.995294 - 1.72390i) q^{50} -4.27144 q^{52} +(0.410229 + 0.710537i) q^{53} -7.02604 q^{55} +(5.27265 + 3.44296i) q^{56} -4.56570 q^{58} +(-3.29204 + 5.70197i) q^{59} +(-0.0376322 - 0.0651809i) q^{61} -1.67974 q^{62} +0.855913 q^{64} +(1.96257 + 3.39927i) q^{65} +(6.29385 - 10.9013i) q^{67} -1.73623 q^{68} +(0.138603 - 2.52337i) q^{70} -0.0804951 q^{71} +(5.34551 + 9.25869i) q^{73} +0.951587 q^{74} +(3.11297 + 5.39183i) q^{76} +(10.9231 + 7.13261i) q^{77} +(0.922457 + 1.59774i) q^{79} +(1.07286 + 1.85825i) q^{80} +(0.0833788 - 0.144416i) q^{82} +(7.23583 - 12.5328i) q^{83} +(0.797736 + 1.38172i) q^{85} -0.668072 q^{86} +11.7358 q^{88} +(-6.76292 + 11.7137i) q^{89} +(0.399711 - 7.27703i) q^{91} +(-4.21515 + 7.30085i) q^{92} +(3.17597 - 5.50094i) q^{94} +(2.86059 - 4.95469i) q^{95} +(2.70160 - 4.67930i) q^{97} +(-2.77712 + 3.78226i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 2 q^{2} - 4 q^{4} + 8 q^{5} - q^{7} + 6 q^{8} - 7 q^{10} + 8 q^{11} - 8 q^{13} - 16 q^{14} + 2 q^{16} - 12 q^{17} + q^{19} - 5 q^{20} - q^{22} + 6 q^{23} + 2 q^{25} - 11 q^{26} - 2 q^{28} - 7 q^{29}+ \cdots - 59 q^{98}+O(q^{100}) $ 10 * q - 2 * q^2 - 4 * q^4 + 8 * q^5 - q^7 + 6 * q^8 - 7 * q^10 + 8 * q^11 - 8 * q^13 - 16 * q^14 + 2 * q^16 - 12 * q^17 + q^19 - 5 * q^20 - q^22 + 6 * q^23 + 2 * q^25 - 11 * q^26 - 2 * q^28 - 7 * q^29 - 3 * q^31 + 2 * q^32 + 3 * q^34 - 5 * q^35 + 40 * q^38 + 6 * q^40 - 5 * q^41 - 7 * q^43 + 10 * q^44 + 3 * q^46 - 27 * q^47 + 25 * q^49 - 19 * q^50 + 20 * q^52 + 21 * q^53 + 4 * q^55 + 45 * q^56 + 20 * q^58 - 30 * q^59 - 14 * q^61 + 12 * q^62 - 50 * q^64 + 11 * q^65 - 2 * q^67 + 54 * q^68 - 29 * q^70 + 6 * q^71 + 15 * q^73 - 72 * q^74 + 5 * q^76 + 31 * q^77 - 4 * q^79 - 20 * q^80 - 5 * q^82 - 9 * q^83 - 6 * q^85 - 16 * q^86 + 36 * q^88 - 28 * q^89 - 4 * q^91 - 27 * q^92 - 3 * q^94 + 14 * q^95 - 12 * q^97 - 59 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.335166	+	0.580525i	0.236998	+	0.410493i	0.959852	−	0.280508i	$-0.0905031\pi$
$2$	0.335166	+	0.580525i	0.236998	+	0.410493i	−0.722853	+	0.691002i	$0.757170\pi$
$3$		0			0
$3$		0			0
$4$	0.775327	−	1.34291i	0.387664	−	0.671453i
$5$	−1.42494			−0.637251			−0.318626	−	0.947881i	$-0.603221\pi$
$5$	−1.42494			−0.637251			−0.318626	+	0.947881i	$0.603221\pi$
$6$		0			0
$7$	2.21529	+	1.44655i	0.837299	+	0.546745i
$7$	2.21529	+	1.44655i	0.837299	+	0.546745i
$8$	2.38012			0.841499
$9$		0			0
$10$	−0.477591	−	0.827212i	−0.151028	−	0.261587i
$11$	4.93077			1.48668			0.743342	−	0.668911i	$-0.233239\pi$
$11$	4.93077			1.48668			0.743342	+	0.668911i	$0.233239\pi$
$12$		0			0
$13$	−1.37730	−	2.38556i	−0.381995	−	0.661635i	0.609352	−	0.792900i	$-0.291429\pi$
$13$	−1.37730	−	2.38556i	−0.381995	−	0.661635i	−0.991347	+	0.131265i	$0.958096\pi$
$14$	−0.0972697	+	1.77086i	−0.0259964	+	0.473283i
$15$		0			0
$16$	−0.752918	−	1.30409i	−0.188230	−	0.326023i
$17$	−0.559839	−	0.969670i	−0.135781	−	0.235180i	0.790115	−	0.612959i	$-0.210021\pi$
$17$	−0.559839	−	0.969670i	−0.135781	−	0.235180i	−0.925896	+	0.377780i	$0.876688\pi$
$18$		0			0
$19$	−2.00752	+	3.47713i	−0.460557	+	0.797709i	−0.998989	−	0.0449606i	$-0.985684\pi$
$19$	−2.00752	+	3.47713i	−0.460557	+	0.797709i	0.538431	+	0.842669i	$0.319017\pi$
$20$	−1.10479	+	1.91356i	−0.247039	+	0.427884i
$21$		0			0
$22$	1.65263	+	2.86244i	0.352342	+	0.610274i
$23$	−5.43661			−1.13361			−0.566806	−	0.823851i	$-0.691821\pi$
$23$	−5.43661			−1.13361			−0.566806	+	0.823851i	$0.691821\pi$
$24$		0			0
$25$	−2.96955			−0.593911
$26$	0.923251	−	1.59912i	0.181064	−	0.313613i
$27$		0			0
$28$	3.66015	−	1.85337i	0.691704	−	0.350254i
$29$	−3.40555	+	5.89858i	−0.632394	+	1.09534i	0.354667	+	0.934993i	$0.384594\pi$
$29$	−3.40555	+	5.89858i	−0.632394	+	1.09534i	−0.987061	+	0.160346i	$0.948739\pi$
$30$		0			0
$31$	−1.25292	+	2.17012i	−0.225031	+	0.389765i	−0.956329	−	0.292294i	$-0.905582\pi$
$31$	−1.25292	+	2.17012i	−0.225031	+	0.389765i	0.731298	+	0.682058i	$0.238915\pi$
$32$	2.88483	−	4.99666i	0.509970	−	0.883294i
$33$		0			0
$34$	0.375279	−	0.650002i	0.0643597	−	0.111474i
$35$	−3.15664	−	2.06124i	−0.533570	−	0.348414i
$36$		0			0
$37$	0.709787	−	1.22939i	0.116688	−	0.202110i	−0.801765	−	0.597639i	$-0.796106\pi$
$37$	0.709787	−	1.22939i	0.116688	−	0.202110i	0.918453	+	0.395529i	$0.129439\pi$
$38$	−2.69142			−0.436605
$39$		0			0
$40$	−3.39152			−0.536247
$41$	−0.124384	−	0.215440i	−0.0194256	−	0.0336460i	0.856149	−	0.516729i	$-0.172850\pi$
$41$	−0.124384	−	0.215440i	−0.0194256	−	0.0336460i	−0.875575	+	0.483083i	$0.839517\pi$
$42$		0			0
$43$	−0.498313	+	0.863104i	−0.0759921	+	0.131622i	−0.901517	−	0.432743i	$-0.857546\pi$
$43$	−0.498313	+	0.863104i	−0.0759921	+	0.131622i	0.825525	+	0.564365i	$0.190879\pi$
$44$	3.82296	−	6.62156i	0.576333	−	0.998238i
$45$		0			0
$46$	−1.82217	−	3.15609i	−0.268664	−	0.465340i
$47$	−4.73790	−	8.20628i	−0.691093	−	1.19701i	−0.971480	−	0.237122i	$-0.923796\pi$
$47$	−4.73790	−	8.20628i	−0.691093	−	1.19701i	0.280387	−	0.959887i	$-0.409537\pi$
$48$		0			0
$49$	2.81498	+	6.40905i	0.402140	+	0.915578i
$50$	−0.995294	−	1.72390i	−0.140756	−	0.243796i
$51$		0			0
$52$	−4.27144			−0.592342
$53$	0.410229	+	0.710537i	0.0563493	+	0.0975998i	0.892824	−	0.450406i	$-0.148721\pi$
$53$	0.410229	+	0.710537i	0.0563493	+	0.0975998i	−0.836475	+	0.548005i	$0.815387\pi$
$54$		0			0
$55$	−7.02604			−0.947392
$56$	5.27265	+	3.44296i	0.704587	+	0.460085i
$57$		0			0
$58$	−4.56570			−0.599506
$59$	−3.29204	+	5.70197i	−0.428586	+	0.742334i	−0.996748	−	0.0805836i	$-0.974322\pi$
$59$	−3.29204	+	5.70197i	−0.428586	+	0.742334i	0.568161	+	0.822917i	$0.307655\pi$
$60$		0			0
$61$	−0.0376322	−	0.0651809i	−0.00481831	−	0.00834556i	0.863606	−	0.504167i	$-0.168200\pi$
$61$	−0.0376322	−	0.0651809i	−0.00481831	−	0.00834556i	−0.868425	+	0.495821i	$0.834867\pi$
$62$	−1.67974			−0.213328
$63$		0			0
$64$	0.855913			0.106989
$65$	1.96257	+	3.39927i	0.243427	+	0.421628i
$66$		0			0
$67$	6.29385	−	10.9013i	0.768916	−	1.33180i	−0.169235	−	0.985576i	$-0.554130\pi$
$67$	6.29385	−	10.9013i	0.768916	−	1.33180i	0.938151	−	0.346226i	$-0.112537\pi$
$68$	−1.73623			−0.210549
$69$		0			0
$70$	0.138603	−	2.52337i	0.0165663	−	0.301600i
$71$	−0.0804951			−0.00955301			−0.00477651	−	0.999989i	$-0.501520\pi$
$71$	−0.0804951			−0.00955301			−0.00477651	+	0.999989i	$0.501520\pi$
$72$		0			0
$73$	5.34551	+	9.25869i	0.625644	+	1.08365i	0.988416	+	0.151769i	$0.0484971\pi$
$73$	5.34551	+	9.25869i	0.625644	+	1.08365i	−0.362772	+	0.931878i	$0.618170\pi$
$74$	0.951587			0.110620
$75$		0			0
$76$	3.11297	+	5.39183i	0.357083	+	0.618485i
$77$	10.9231	+	7.13261i	1.24480	+	0.812837i
$78$		0			0
$79$	0.922457	+	1.59774i	0.103785	+	0.179760i	0.913241	−	0.407420i	$-0.133571\pi$
$79$	0.922457	+	1.59774i	0.103785	+	0.179760i	−0.809456	+	0.587180i	$0.800238\pi$
$80$	1.07286	+	1.85825i	0.119950	+	0.207759i
$81$		0			0
$82$	0.0833788	−	0.144416i	0.00920765	−	0.0159481i
$83$	7.23583	−	12.5328i	0.794236	−	1.37566i	−0.129088	−	0.991633i	$-0.541205\pi$
$83$	7.23583	−	12.5328i	0.794236	−	1.37566i	0.923323	−	0.384023i	$-0.125462\pi$
$84$		0			0
$85$	0.797736	+	1.38172i	0.0865266	+	0.149868i
$86$	−0.668072			−0.0720400
$87$		0			0
$88$	11.7358			1.25104
$89$	−6.76292	+	11.7137i	−0.716868	+	1.24165i	0.245366	+	0.969430i	$0.421092\pi$
$89$	−6.76292	+	11.7137i	−0.716868	+	1.24165i	−0.962235	+	0.272222i	$0.912242\pi$
$90$		0			0
$91$	0.399711	−	7.27703i	0.0419011	−	0.762840i
$92$	−4.21515	+	7.30085i	−0.439460	+	0.761167i
$93$		0			0
$94$	3.17597	−	5.50094i	0.327576	−	0.567378i
$95$	2.86059	−	4.95469i	0.293491	−	0.508341i
$96$		0			0
$97$	2.70160	−	4.67930i	0.274306	−	0.475111i	−0.695654	−	0.718377i	$-0.744885\pi$
$97$	2.70160	−	4.67930i	0.274306	−	0.475111i	0.969960	+	0.243266i	$0.0782187\pi$
$98$	−2.77712	+	3.78226i	−0.280532	+	0.382066i
$99$		0			0
$100$	−2.30238	+	3.98783i	−0.230238	+	0.398783i
$101$	5.13540			0.510991			0.255496	−	0.966810i	$-0.417761\pi$
$101$	5.13540			0.510991			0.255496	+	0.966810i	$0.417761\pi$
$102$		0			0
$103$	−14.2112			−1.40027			−0.700137	−	0.714009i	$-0.746878\pi$
$103$	−14.2112			−1.40027			−0.700137	+	0.714009i	$0.746878\pi$
$104$	−3.27814	−	5.67791i	−0.321448	−	0.556765i
$105$		0			0
$106$	−0.274990	+	0.476296i	−0.0267094	+	0.0462620i
$107$	−3.83015	+	6.63401i	−0.370274	+	0.641334i	−0.989608	−	0.143794i	$-0.954070\pi$
$107$	−3.83015	+	6.63401i	−0.370274	+	0.641334i	0.619333	+	0.785128i	$0.287403\pi$
$108$		0			0
$109$	−0.849394	−	1.47119i	−0.0813572	−	0.140915i	0.822476	−	0.568800i	$-0.192592\pi$
$109$	−0.849394	−	1.47119i	−0.0813572	−	0.140915i	−0.903833	+	0.427885i	$0.859259\pi$
$110$	−2.35489	−	4.07880i	−0.224530	−	0.388898i
$111$		0			0
$112$	0.218507	−	3.97807i	0.0206469	−	0.375892i
$113$	0.300351	+	0.520224i	0.0282547	+	0.0489385i	0.879807	−	0.475331i	$-0.157672\pi$
$113$	0.300351	+	0.520224i	0.0282547	+	0.0489385i	−0.851552	+	0.524270i	$0.824338\pi$
$114$		0			0
$115$	7.74683			0.722395
$116$	5.28083	+	9.14666i	0.490312	+	0.849246i
$117$		0			0
$118$	−4.41352			−0.406297
$119$	0.162473	−	2.95793i	0.0148939	−	0.271153i
$120$		0			0
$121$	13.3125			1.21023
$122$	0.0252261	−	0.0436929i	0.00228386	−	0.00395577i
$123$		0			0
$124$	1.94284	+	3.36510i	0.174472	+	0.302195i
$125$	11.3561			1.01572
$126$		0			0
$127$	7.25977			0.644200			0.322100	−	0.946706i	$-0.395611\pi$
$127$	7.25977			0.644200			0.322100	+	0.946706i	$0.395611\pi$
$128$	−5.48278	−	9.49645i	−0.484614	−	0.839375i
$129$		0			0
$130$	−1.31557	+	2.27864i	−0.115384	+	0.199850i
$131$	20.4530			1.78698			0.893492	−	0.449079i	$-0.148248\pi$
$131$	20.4530			1.78698			0.893492	+	0.449079i	$0.148248\pi$
$132$		0			0
$133$	−9.47708	+	4.79886i	−0.821767	+	0.416114i
$134$	8.43794			0.728927
$135$		0			0
$136$	−1.33248	−	2.30793i	−0.114260	−	0.197903i
$137$	−12.2116			−1.04331			−0.521655	−	0.853157i	$-0.674685\pi$
$137$	−12.2116			−1.04331			−0.521655	+	0.853157i	$0.674685\pi$
$138$		0			0
$139$	−1.24092	−	2.14933i	−0.105253	−	0.182304i	0.808588	−	0.588375i	$-0.200232\pi$
$139$	−1.24092	−	2.14933i	−0.105253	−	0.182304i	−0.913842	+	0.406071i	$0.866899\pi$
$140$	−5.21549	+	2.64094i	−0.440789	+	0.223200i
$141$		0			0
$142$	−0.0269793	−	0.0467294i	−0.00226405	−	0.00392145i
$143$	−6.79117	−	11.7626i	−0.567906	−	0.983642i
$144$		0			0
$145$	4.85269	−	8.40511i	0.402994	−	0.698006i
$146$	−3.58327	+	6.20640i	−0.296553	+	0.513645i
$147$		0			0
$148$	−1.10063	−	1.90635i	−0.0904715	−	0.156701i
$149$	8.55593			0.700929			0.350465	−	0.936576i	$-0.386024\pi$
$149$	8.55593			0.700929			0.350465	+	0.936576i	$0.386024\pi$
$150$		0			0
$151$	−17.6592			−1.43709			−0.718544	−	0.695482i	$-0.755191\pi$
$151$	−17.6592			−1.43709			−0.718544	+	0.695482i	$0.755191\pi$
$152$	−4.77814	+	8.27599i	−0.387559	+	0.671271i
$153$		0			0
$154$	−0.479615	+	8.73173i	−0.0386485	+	0.703623i
$155$	1.78533	−	3.09228i	0.143401	−	0.248378i
$156$		0			0
$157$	−3.16074	+	5.47457i	−0.252255	+	0.436918i	−0.964146	−	0.265371i	$-0.914505\pi$
$157$	−3.16074	+	5.47457i	−0.252255	+	0.436918i	0.711891	+	0.702289i	$0.247839\pi$
$158$	−0.618353	+	1.07102i	−0.0491936	+	0.0852057i
$159$		0			0
$160$	−4.11070	+	7.11993i	−0.324979	+	0.562880i
$161$	−12.0436	−	7.86433i	−0.949172	−	0.619796i
$162$		0			0
$163$	−4.01134	+	6.94784i	−0.314192	+	0.544197i	−0.979265	−	0.202581i	$-0.935067\pi$
$163$	−4.01134	+	6.94784i	−0.314192	+	0.544197i	0.665073	+	0.746778i	$0.268400\pi$
$164$	−0.385754			−0.0301223
$165$		0			0
$166$	9.70083			0.752930
$167$	−1.06038	−	1.83663i	−0.0820545	−	0.142123i	0.822078	−	0.569375i	$-0.192815\pi$
$167$	−1.06038	−	1.83663i	−0.0820545	−	0.142123i	−0.904132	+	0.427253i	$0.859482\pi$
$168$		0			0
$169$	2.70608	−	4.68706i	0.208160	−	0.360543i
$170$	−0.534749	+	0.926212i	−0.0410133	+	0.0710372i
$171$		0			0
$172$	0.772712	+	1.33838i	0.0589187	+	0.102050i
$173$	−9.14404	−	15.8379i	−0.695208	−	1.20414i	−0.970110	−	0.242664i	$-0.921979\pi$
$173$	−9.14404	−	15.8379i	−0.695208	−	1.20414i	0.274902	−	0.961472i	$-0.411354\pi$
$174$		0			0
$175$	−6.57841	−	4.29561i	−0.497281	−	0.324718i
$176$	−3.71247	−	6.43018i	−0.279838	−	0.484693i
$177$		0			0
$178$	−9.06681			−0.679586
$179$	−3.81276	−	6.60389i	−0.284979	−	0.493598i	0.687625	−	0.726066i	$-0.258653\pi$
$179$	−3.81276	−	6.60389i	−0.284979	−	0.493598i	−0.972604	+	0.232468i	$0.925320\pi$
$180$		0			0
$181$	15.5305			1.15438			0.577188	−	0.816611i	$-0.304150\pi$
$181$	15.5305			1.15438			0.577188	+	0.816611i	$0.304150\pi$
$182$	4.35847	−	2.20697i	0.323071	−	0.163592i
$183$		0			0
$184$	−12.9398			−0.953933
$185$	−1.01140	+	1.75180i	−0.0743597	+	0.128795i
$186$		0			0
$187$	−2.76044	−	4.78122i	−0.201863	−	0.349638i
$188$	−14.6937			−1.07165
$189$		0			0
$190$	3.83510			0.278227
$191$	7.41624	+	12.8453i	0.536620	+	0.929454i	0.999083	+	0.0428150i	$0.0136326\pi$
$191$	7.41624	+	12.8453i	0.536620	+	0.929454i	−0.462463	+	0.886639i	$0.653034\pi$
$192$		0			0
$193$	−8.28387	+	14.3481i	−0.596286	+	1.03280i	0.397078	+	0.917785i	$0.370024\pi$
$193$	−8.28387	+	14.3481i	−0.596286	+	1.03280i	−0.993364	+	0.115013i	$0.963309\pi$
$194$	3.62194			0.260040
$195$		0			0
$196$	10.7893	+	1.18885i	0.770663	+	0.0849178i
$197$	4.03740			0.287653			0.143826	−	0.989603i	$-0.454059\pi$
$197$	4.03740			0.287653			0.143826	+	0.989603i	$0.454059\pi$
$198$		0			0
$199$	−12.6407	−	21.8943i	−0.896076	−	1.55205i	−0.832468	−	0.554074i	$-0.813073\pi$
$199$	−12.6407	−	21.8943i	−0.896076	−	1.55205i	−0.0636081	−	0.997975i	$-0.520261\pi$
$200$	−7.06789			−0.499775
$201$		0			0
$202$	1.72121	+	2.98123i	0.121104	+	0.209758i
$203$	−16.0769	+	8.14075i	−1.12837	+	0.571368i
$204$		0			0
$205$	0.177240	+	0.306988i	0.0123790	+	0.0214410i
$206$	−4.76312	−	8.24997i	−0.331862	−	0.574803i
$207$		0			0
$208$	−2.07399	+	3.59226i	−0.143805	+	0.249078i
$209$	−9.89864	+	17.1449i	−0.684703	+	1.18594i
$210$		0			0
$211$	−3.76246	−	6.51678i	−0.259019	−	0.448634i	0.706961	−	0.707253i	$-0.250066\pi$
$211$	−3.76246	−	6.51678i	−0.259019	−	0.448634i	−0.965979	+	0.258619i	$0.916732\pi$
$212$	1.27225			0.0873782
$213$		0			0
$214$	−5.13495			−0.351018
$215$	0.710065	−	1.22987i	0.0484261	−	0.0838764i
$216$		0			0
$217$	−5.91476	+	2.99502i	−0.401520	+	0.203315i
$218$	0.569377	−	0.986190i	0.0385631	−	0.0667932i
$219$		0			0
$220$	−5.44748	+	9.43531i	−0.367269	+	0.636129i
$221$	−1.54214	+	2.67106i	−0.103735	+	0.179675i
$222$		0			0
$223$	6.49230	−	11.2450i	0.434757	−	0.753020i	−0.562519	−	0.826784i	$-0.690168\pi$
$223$	6.49230	−	11.2450i	0.434757	−	0.753020i	0.997276	+	0.0737638i	$0.0235011\pi$
$224$	13.6186	−	6.89599i	0.909934	−	0.460758i
$225$		0			0
$226$	−0.201335	+	0.348723i	−0.0133926	+	0.0231967i
$227$	28.9665			1.92257			0.961286	−	0.275551i	$-0.0888603\pi$
$227$	28.9665			1.92257			0.961286	+	0.275551i	$0.0888603\pi$
$228$		0			0
$229$	15.4358			1.02003			0.510013	−	0.860167i	$-0.329640\pi$
$229$	15.4358			1.02003			0.510013	+	0.860167i	$0.329640\pi$
$230$	2.59648	+	4.49723i	0.171207	+	0.296538i
$231$		0			0
$232$	−8.10561	+	14.0393i	−0.532159	+	0.921727i
$233$	2.47324	−	4.28378i	0.162027	−	0.280640i	−0.773568	−	0.633713i	$-0.781530\pi$
$233$	2.47324	−	4.28378i	0.162027	−	0.280640i	0.935596	+	0.353073i	$0.114863\pi$
$234$		0			0
$235$	6.75121	+	11.6934i	0.440400	+	0.762795i
$236$	5.10481	+	8.84179i	0.332295	+	0.575551i
$237$		0			0
$238$	1.77161	−	0.897080i	0.114836	−	0.0581491i
$239$	−6.51732	−	11.2883i	−0.421571	−	0.730182i	0.574523	−	0.818489i	$-0.305188\pi$
$239$	−6.51732	−	11.2883i	−0.421571	−	0.730182i	−0.996093	+	0.0883069i	$0.971854\pi$
$240$		0			0
$241$	14.5825			0.939339			0.469670	−	0.882842i	$-0.344373\pi$
$241$	14.5825			0.939339			0.469670	+	0.882842i	$0.344373\pi$
$242$	4.46191	+	7.72826i	0.286823	+	0.496791i
$243$		0			0
$244$	−0.116709			−0.00747154
$245$	−4.01117	−	9.13249i	−0.256265	−	0.583453i
$246$		0			0
$247$	11.0599			0.703722
$248$	−2.98209	+	5.16514i	−0.189363	+	0.327987i
$249$		0			0
$250$	3.80619	+	6.59251i	0.240724	+	0.416947i
$251$	14.0715			0.888187			0.444094	−	0.895980i	$-0.353526\pi$
$251$	14.0715			0.888187			0.444094	+	0.895980i	$0.353526\pi$
$252$		0			0
$253$	−26.8067			−1.68532
$254$	2.43323	+	4.21448i	0.152674	+	0.264440i
$255$		0			0
$256$	4.53120	−	7.84826i	0.283200	−	0.490517i
$257$	8.36215			0.521617			0.260808	−	0.965391i	$-0.416011\pi$
$257$	8.36215			0.521617			0.260808	+	0.965391i	$0.416011\pi$
$258$		0			0
$259$	3.35075	−	1.69670i	0.208206	−	0.105428i
$260$	6.08653			0.377471
$261$		0			0
$262$	6.85515	+	11.8735i	0.423512	+	0.733545i
$263$	−3.27066			−0.201678			−0.100839	−	0.994903i	$-0.532153\pi$
$263$	−3.27066			−0.201678			−0.100839	+	0.994903i	$0.532153\pi$
$264$		0			0
$265$	−0.584551	−	1.01247i	−0.0359087	−	0.0621956i
$266$	−5.96226	−	3.89327i	−0.365569	−	0.238712i
$267$		0			0
$268$	−9.75958	−	16.9041i	−0.596161	−	1.03258i
$269$	7.69349	+	13.3255i	0.469081	+	0.812471i	0.999375	−	0.0353420i	$-0.0112521\pi$
$269$	7.69349	+	13.3255i	0.469081	+	0.812471i	−0.530295	+	0.847813i	$0.677919\pi$
$270$		0			0
$271$	4.06308	−	7.03747i	0.246815	−	0.427496i	−0.715825	−	0.698279i	$-0.753949\pi$
$271$	4.06308	−	7.03747i	0.246815	−	0.427496i	0.962640	+	0.270783i	$0.0872827\pi$
$272$	−0.843026	+	1.46016i	−0.0511160	+	0.0885355i
$273$		0			0
$274$	−4.09293	−	7.08915i	−0.247263	−	0.428271i
$275$	−14.6422			−0.882958
$276$		0			0
$277$	12.8457			0.771826			0.385913	−	0.922535i	$-0.373887\pi$
$277$	12.8457			0.771826			0.385913	+	0.922535i	$0.373887\pi$
$278$	0.831826	−	1.44077i	0.0498896	−	0.0864114i
$279$		0			0
$280$	−7.51319	−	4.90601i	−0.448999	−	0.293190i
$281$	0.724081	−	1.25415i	0.0431951	−	0.0748161i	−0.843620	−	0.536941i	$-0.819580\pi$
$281$	0.724081	−	1.25415i	0.0431951	−	0.0748161i	0.886815	+	0.462125i	$0.152913\pi$
$282$		0			0
$283$	8.71926	−	15.1022i	0.518306	−	0.897732i	−0.481468	−	0.876464i	$-0.659896\pi$
$283$	8.71926	−	15.1022i	0.518306	−	0.897732i	0.999774	−	0.0212686i	$-0.00677053\pi$
$284$	−0.0624100	+	0.108097i	−0.00370335	+	0.00641440i
$285$		0			0
$286$	4.55234	−	7.88489i	0.269186	−	0.466243i
$287$	0.0360979	−	0.657189i	0.00213079	−	0.0387926i
$288$		0			0
$289$	7.87316	−	13.6367i	0.463127	−	0.802160i
$290$	6.50584			0.382036
$291$		0			0
$292$	16.5781			0.970158
$293$	0.900048	+	1.55893i	0.0525814	+	0.0910736i	0.891118	−	0.453772i	$-0.149922\pi$
$293$	0.900048	+	1.55893i	0.0525814	+	0.0910736i	−0.838537	+	0.544845i	$0.816588\pi$
$294$		0			0
$295$	4.69094	−	8.12495i	0.273117	−	0.473053i
$296$	1.68938	−	2.92609i	0.0981931	−	0.170075i
$297$		0			0
$298$	2.86766	+	4.96693i	0.166119	+	0.287727i
$299$	7.48786	+	12.9693i	0.433034	+	0.750037i
$300$		0			0
$301$	−2.35243	+	1.19119i	−0.135592	+	0.0686589i
$302$	−5.91878	−	10.2516i	−0.340588	−	0.589915i
$303$		0			0
$304$	6.04600			0.346762
$305$	0.0536236	+	0.0928787i	0.00307048	+	0.00531822i
$306$		0			0
$307$	1.06478			0.0607699			0.0303850	−	0.999538i	$-0.490327\pi$
$307$	1.06478			0.0607699			0.0303850	+	0.999538i	$0.490327\pi$
$308$	18.0474	−	9.13855i	1.02835	−	0.520717i
$309$		0			0
$310$	2.39353			0.135943
$311$	−8.46463	+	14.6612i	−0.479985	+	0.831359i	−0.999736	−	0.0229591i	$-0.992691\pi$
$311$	−8.46463	+	14.6612i	−0.479985	+	0.831359i	0.519751	+	0.854318i	$0.326025\pi$
$312$		0			0
$313$	4.13928	+	7.16944i	0.233966	+	0.405241i	0.958972	−	0.283502i	$-0.0914963\pi$
$313$	4.13928	+	7.16944i	0.233966	+	0.405241i	−0.725006	+	0.688743i	$0.758163\pi$
$314$	−4.23750			−0.239136
$315$		0			0
$316$	2.86082			0.160934
$317$	3.27371	+	5.67023i	0.183870	+	0.318472i	0.943195	−	0.332239i	$-0.107804\pi$
$317$	3.27371	+	5.67023i	0.183870	+	0.318472i	−0.759325	+	0.650711i	$0.774471\pi$
$318$		0			0
$319$	−16.7920	+	29.0846i	−0.940171	+	1.62842i
$320$	−1.21962			−0.0681790
$321$		0			0
$322$	0.528817	−	9.62750i	0.0294698	−	0.536519i
$323$	4.49556			0.250140
$324$		0			0
$325$	4.08997	+	7.08404i	0.226871	+	0.392952i
$326$	−5.37786			−0.297852
$327$		0			0
$328$	−0.296049	−	0.512773i	−0.0163466	−	0.0283131i
$329$	1.37500	−	25.0329i	0.0758062	−	1.38011i
$330$		0			0
$331$	13.3629	+	23.1453i	0.734493	+	1.27218i	0.954946	+	0.296781i	$0.0959131\pi$
$331$	13.3629	+	23.1453i	0.734493	+	1.27218i	−0.220453	+	0.975398i	$0.570754\pi$
$332$	−11.2203	−	19.4341i	−0.615792	−	1.06658i
$333$		0			0
$334$	0.710806	−	1.23115i	0.0388936	−	0.0673657i
$335$	−8.96834	+	15.5336i	−0.489993	+	0.848692i
$336$		0			0
$337$	−4.76164	−	8.24740i	−0.259383	−	0.449264i	0.706694	−	0.707520i	$-0.250186\pi$
$337$	−4.76164	−	8.24740i	−0.259383	−	0.449264i	−0.966077	+	0.258255i	$0.916853\pi$
$338$	3.62794			0.197334
$339$		0			0
$340$	2.47403			0.134173
$341$	−6.17786	+	10.7004i	−0.334550	+	0.579457i
$342$		0			0
$343$	−3.03502	+	18.2699i	−0.163876	+	0.986481i
$344$	−1.18605	+	2.05429i	−0.0639473	+	0.110760i
$345$		0			0
$346$	6.12955	−	10.6167i	0.329526	−	0.570757i
$347$	−9.35156	+	16.1974i	−0.502018	+	0.869521i	0.497979	+	0.867189i	$0.334076\pi$
$347$	−9.35156	+	16.1974i	−0.502018	+	0.869521i	−0.999997	+	0.00233189i	$0.999258\pi$
$348$		0			0
$349$	−15.0542	+	26.0747i	−0.805834	+	1.39574i	0.109893	+	0.993943i	$0.464949\pi$
$349$	−15.0542	+	26.0747i	−0.805834	+	1.39574i	−0.915727	+	0.401801i	$0.868384\pi$
$350$	0.288848	−	5.25868i	0.0154396	−	0.281088i
$351$		0			0
$352$	14.2244	−	24.6374i	0.758164	−	1.31318i
$353$	−6.25933			−0.333150			−0.166575	−	0.986029i	$-0.553271\pi$
$353$	−6.25933			−0.333150			−0.166575	+	0.986029i	$0.553271\pi$
$354$		0			0
$355$	0.114700			0.00608767
$356$	10.4870	+	18.1639i	0.555807	+	0.962686i
$357$		0			0
$358$	2.55582	−	4.42680i	0.135079	−	0.233964i
$359$	5.09755	−	8.82921i	0.269038	−	0.465988i	−0.699575	−	0.714559i	$-0.746628\pi$
$359$	5.09755	−	8.82921i	0.269038	−	0.465988i	0.968614	+	0.248571i	$0.0799608\pi$
$360$		0			0
$361$	1.43970	+	2.49364i	0.0757739	+	0.131244i
$362$	5.20532	+	9.01587i	0.273585	+	0.473864i
$363$		0			0
$364$	−9.46246	−	6.17885i	−0.495968	−	0.323860i
$365$	−7.61701	−	13.1931i	−0.398693	−	0.690556i
$366$		0			0
$367$	−28.6557			−1.49581			−0.747906	−	0.663804i	$-0.768941\pi$
$367$	−28.6557			−1.49581			−0.747906	+	0.663804i	$0.768941\pi$
$368$	4.09332	+	7.08984i	0.213379	+	0.369584i
$369$		0			0
$370$	−1.35595			−0.0704926
$371$	−0.119054	+	2.16746i	−0.00618097	+	0.112529i
$372$		0			0
$373$	−16.0734			−0.832249			−0.416124	−	0.909308i	$-0.636612\pi$
$373$	−16.0734			−0.832249			−0.416124	+	0.909308i	$0.636612\pi$
$374$	1.85041	−	3.20501i	0.0956826	−	0.165727i
$375$		0			0
$376$	−11.2768	−	19.5319i	−0.581555	−	1.00728i
$377$	18.7619			0.966286
$378$		0			0
$379$	−1.01893			−0.0523388			−0.0261694	−	0.999658i	$-0.508331\pi$
$379$	−1.01893			−0.0523388			−0.0261694	+	0.999658i	$0.508331\pi$
$380$	−4.43579	−	7.68302i	−0.227551	−	0.394130i
$381$		0			0
$382$	−4.97135	+	8.61063i	−0.254356	+	0.440558i
$383$	11.5865			0.592044			0.296022	−	0.955181i	$-0.404340\pi$
$383$	11.5865			0.592044			0.296022	+	0.955181i	$0.404340\pi$
$384$		0			0
$385$	−15.5647	−	10.1635i	−0.793250	−	0.517981i
$386$	−11.1059			−0.565275
$387$		0			0
$388$	−4.18924	−	7.25598i	−0.212677	−	0.368367i
$389$	−17.8135			−0.903181			−0.451590	−	0.892225i	$-0.649143\pi$
$389$	−17.8135			−0.903181			−0.451590	+	0.892225i	$0.649143\pi$
$390$		0			0
$391$	3.04363	+	5.27172i	0.153923	+	0.266602i
$392$	6.70000	+	15.2543i	0.338401	+	0.770458i
$393$		0			0
$394$	1.35320	+	2.34381i	0.0681732	+	0.118079i
$395$	−1.31444	−	2.27668i	−0.0661369	−	0.114552i
$396$		0			0
$397$	−6.54229	+	11.3316i	−0.328348	+	0.568715i	−0.982184	−	0.187921i	$-0.939825\pi$
$397$	−6.54229	+	11.3316i	−0.328348	+	0.568715i	0.653836	+	0.756636i	$0.273159\pi$
$398$	8.47348	−	14.6765i	0.424737	−	0.735666i
$399$		0			0
$400$	2.23583	+	3.87257i	0.111792	+	0.193629i
$401$	−14.1033			−0.704285			−0.352143	−	0.935946i	$-0.614547\pi$
$401$	−14.1033			−0.704285			−0.352143	+	0.935946i	$0.614547\pi$
$402$		0			0
$403$	6.90259			0.343842
$404$	3.98161	−	6.89636i	0.198093	−	0.343107i
$405$		0			0
$406$	−10.1143	−	6.60452i	−0.501966	−	0.327777i
$407$	3.49980	−	6.06183i	0.173479	−	0.300474i
$408$		0			0
$409$	1.32300	−	2.29150i	0.0654179	−	0.113307i	−0.831461	−	0.555583i	$-0.812495\pi$
$409$	1.32300	−	2.29150i	0.0654179	−	0.113307i	0.896879	+	0.442275i	$0.145829\pi$
$410$	−0.118810	+	0.205784i	−0.00586759	+	0.0101630i
$411$		0			0
$412$	−11.0183	+	19.0843i	−0.542835	+	0.940217i
$413$	−15.5410	+	7.86940i	−0.764722	+	0.387228i
$414$		0			0
$415$	−10.3106	+	17.8585i	−0.506128	+	0.876639i
$416$	−15.8931			−0.779224
$417$		0			0
$418$	−13.2708			−0.649094
$419$	−16.7567	−	29.0235i	−0.818619	−	1.41789i	−0.906700	−	0.421776i	$-0.861407\pi$
$419$	−16.7567	−	29.0235i	−0.818619	−	1.41789i	0.0880816	−	0.996113i	$-0.471926\pi$
$420$		0			0
$421$	−2.41950	+	4.19071i	−0.117919	+	0.204242i	−0.918943	−	0.394390i	$-0.870956\pi$
$421$	−2.41950	+	4.19071i	−0.117919	+	0.204242i	0.801024	+	0.598633i	$0.204289\pi$
$422$	2.52210	−	4.36841i	0.122774	−	0.212651i
$423$		0			0
$424$	0.976394	+	1.69116i	0.0474179	+	0.0821302i
$425$	1.66247	+	2.87949i	0.0806418	+	0.139676i
$426$		0			0
$427$	0.0109214	−	0.198831i	0.000528522	−	0.00962212i
$428$	5.93923	+	10.2871i	0.287084	+	0.497244i
$429$		0			0
$430$	0.951960			0.0459076
$431$	−17.6643	−	30.5954i	−0.850858	−	1.47373i	−0.880435	−	0.474166i	$-0.842749\pi$
$431$	−17.6643	−	30.5954i	−0.850858	−	1.47373i	0.0295774	−	0.999562i	$-0.490584\pi$
$432$		0			0
$433$	5.47404			0.263066			0.131533	−	0.991312i	$-0.458010\pi$
$433$	5.47404			0.263066			0.131533	+	0.991312i	$0.458010\pi$
$434$	−3.72111	−	2.42983i	−0.178619	−	0.116636i
$435$		0			0
$436$	−2.63423			−0.126157
$437$	10.9141	−	18.9038i	0.522093	−	0.904292i
$438$		0			0
$439$	−3.19906	−	5.54093i	−0.152683	−	0.264454i	0.779530	−	0.626365i	$-0.215458\pi$
$439$	−3.19906	−	5.54093i	−0.152683	−	0.264454i	−0.932213	+	0.361911i	$0.882125\pi$
$440$	−16.7228			−0.797229
$441$		0			0
$442$	−2.06749			−0.0983404
$443$	−3.19341	−	5.53115i	−0.151723	−	0.262793i	0.780138	−	0.625608i	$-0.215149\pi$
$443$	−3.19341	−	5.53115i	−0.151723	−	0.262793i	−0.931861	+	0.362815i	$0.881816\pi$
$444$		0			0
$445$	9.63674	−	16.6913i	0.456825	−	0.791245i
$446$	8.70400			0.412146
$447$		0			0
$448$	1.89609	+	1.23812i	0.0895819	+	0.0584957i
$449$	11.7460			0.554327			0.277163	−	0.960823i	$-0.410606\pi$
$449$	11.7460			0.554327			0.277163	+	0.960823i	$0.410606\pi$
$450$		0			0
$451$	−0.613311	−	1.06229i	−0.0288797	−	0.0500210i
$452$	0.931482			0.0438132
$453$		0			0
$454$	9.70859	+	16.8158i	0.455647	+	0.789203i
$455$	−0.569564	+	10.3693i	−0.0267016	+	0.486121i
$456$		0			0
$457$	−5.26120	−	9.11266i	−0.246108	−	0.426272i	0.716334	−	0.697757i	$-0.245819\pi$
$457$	−5.26120	−	9.11266i	−0.246108	−	0.426272i	−0.962443	+	0.271485i	$0.912485\pi$
$458$	5.17356	+	8.96087i	0.241745	+	0.418714i
$459$		0			0
$460$	6.00633	−	10.4033i	0.280046	−	0.485055i
$461$	3.54278	−	6.13627i	0.165004	−	0.285794i	−0.771653	−	0.636044i	$-0.780570\pi$
$461$	3.54278	−	6.13627i	0.165004	−	0.285794i	0.936657	+	0.350249i	$0.113903\pi$
$462$		0			0
$463$	16.3760	+	28.3641i	0.761059	+	1.31819i	0.942305	+	0.334755i	$0.108654\pi$
$463$	16.3760	+	28.3641i	0.761059	+	1.31819i	−0.181246	+	0.983438i	$0.558013\pi$
$464$	10.2564			0.476141
$465$		0			0
$466$	3.31579			0.153601
$467$	−1.96216	+	3.39856i	−0.0907978	+	0.157266i	−0.907847	−	0.419301i	$-0.862275\pi$
$467$	−1.96216	+	3.39856i	−0.0907978	+	0.157266i	0.817049	+	0.576568i	$0.195608\pi$
$468$		0			0
$469$	29.7119	−	15.0450i	1.37197	−	0.694716i
$470$	−4.52555	+	7.83849i	−0.208748	+	0.361563i
$471$		0			0
$472$	−7.83544	+	13.5714i	−0.360655	+	0.624673i
$473$	−2.45707	+	4.25577i	−0.112976	+	0.195681i
$474$		0			0
$475$	5.96145	−	10.3255i	0.273530	−	0.473768i
$476$	−3.84626	−	2.51155i	−0.176293	−	0.115117i
$477$		0			0
$478$	4.36878	−	7.56694i	0.199823	−	0.346104i
$479$	−16.0865			−0.735010			−0.367505	−	0.930022i	$-0.619788\pi$
$479$	−16.0865			−0.735010			−0.367505	+	0.930022i	$0.619788\pi$
$480$		0			0
$481$	−3.91036			−0.178297
$482$	4.88755	+	8.46549i	0.222622	+	0.385592i
$483$		0			0
$484$	10.3216	−	17.8775i	0.469162	−	0.812612i
$485$	−3.84961	+	6.66771i	−0.174802	+	0.302765i
$486$		0			0
$487$	−1.75172	−	3.03407i	−0.0793781	−	0.137487i	0.823604	−	0.567166i	$-0.191960\pi$
$487$	−1.75172	−	3.03407i	−0.0793781	−	0.137487i	−0.902982	+	0.429679i	$0.858627\pi$
$488$	−0.0895692	−	0.155138i	−0.00405461	−	0.00702279i
$489$		0			0
$490$	3.95723	−	5.38949i	0.178769	−	0.243472i
$491$	20.5546	+	35.6017i	0.927618	+	1.60668i	0.787296	+	0.616575i	$0.211480\pi$
$491$	20.5546	+	35.6017i	0.927618	+	1.60668i	0.140321	+	0.990106i	$0.455186\pi$
$492$		0			0
$493$	7.62624			0.343468
$494$	3.70689	+	6.42053i	0.166781	+	0.288873i
$495$		0			0
$496$	3.77338			0.169430
$497$	−0.178320	−	0.116440i	−0.00799873	−	0.00522306i
$498$		0			0
$499$	11.8297			0.529571			0.264785	−	0.964307i	$-0.414699\pi$
$499$	11.8297			0.529571			0.264785	+	0.964307i	$0.414699\pi$
$500$	8.80470	−	15.2502i	0.393758	−	0.682009i
$501$		0			0
$502$	4.71631	+	8.16888i	0.210499	+	0.364595i
$503$	−21.8595			−0.974665			−0.487332	−	0.873217i	$-0.662030\pi$
$503$	−21.8595			−0.974665			−0.487332	+	0.873217i	$0.662030\pi$
$504$		0			0
$505$	−7.31762			−0.325630
$506$	−8.98470	−	15.5620i	−0.399419	−	0.691813i
$507$		0			0
$508$	5.62869	−	9.74918i	0.249733	−	0.432550i
$509$	−16.8966			−0.748930			−0.374465	−	0.927241i	$-0.622174\pi$
$509$	−16.8966			−0.748930			−0.374465	+	0.927241i	$0.622174\pi$
$510$		0			0
$511$	−1.55134	+	28.2432i	−0.0686271	+	1.24941i
$512$	−15.8563			−0.700756
$513$		0			0
$514$	2.80271	+	4.85444i	0.123622	+	0.214120i
$515$	20.2501			0.892326
$516$		0			0
$517$	−23.3615	−	40.4633i	−1.02744	−	1.77957i
$518$	2.10804	+	1.37652i	0.0926218	+	0.0604807i
$519$		0			0
$520$	4.67115	+	8.09067i	0.204843	+	0.354799i
$521$	17.2466	+	29.8720i	0.755587	+	1.30872i	0.945082	+	0.326834i	$0.105982\pi$
$521$	17.2466	+	29.8720i	0.755587	+	1.30872i	−0.189495	+	0.981882i	$0.560685\pi$
$522$		0			0
$523$	0.995615	−	1.72445i	0.0435352	−	0.0754051i	−0.843437	−	0.537229i	$-0.819471\pi$
$523$	0.995615	−	1.72445i	0.0435352	−	0.0754051i	0.886972	+	0.461823i	$0.152805\pi$
$524$	15.8577	−	27.4664i	0.692749	−	1.19988i
$525$		0			0
$526$	−1.09622	−	1.89870i	−0.0477972	−	0.0827873i
$527$	2.80573			0.122220
$528$		0			0
$529$	6.55673			0.285075
$530$	0.391843	−	0.678693i	0.0170206	−	0.0294805i
$531$		0			0
$532$	−0.903426	+	16.4475i	−0.0391685	+	0.713090i
$533$	−0.342629	+	0.593452i	−0.0148409	+	0.0257052i
$534$		0			0
$535$	5.45772	−	9.45305i	0.235958	−	0.408691i
$536$	14.9801	−	25.9463i	0.647042	−	1.12071i
$537$		0			0
$538$	−5.15720	+	8.93253i	−0.222343	+	0.385109i
$539$	13.8800	+	31.6016i	0.597856	+	1.36118i
$540$		0			0
$541$	−15.0681	+	26.0988i	−0.647830	+	1.12207i	0.335810	+	0.941930i	$0.390990\pi$
$541$	−15.0681	+	26.0988i	−0.647830	+	1.12207i	−0.983640	+	0.180145i	$0.942343\pi$
$542$	5.44724			0.233979
$543$		0			0
$544$	−6.46015			−0.276977
$545$	1.21033	+	2.09636i	0.0518450	+	0.0897982i
$546$		0			0
$547$	7.68070	−	13.3034i	0.328403	−	0.568810i	−0.653792	−	0.756674i	$-0.726823\pi$
$547$	7.68070	−	13.3034i	0.328403	−	0.568810i	0.982195	+	0.187864i	$0.0601563\pi$
$548$	−9.46800	+	16.3991i	−0.404453	+	0.700533i
$549$		0			0
$550$	−4.90757	−	8.50016i	−0.209260	−	0.362448i
$551$	−13.6734	−	23.6831i	−0.582508	−	1.00893i
$552$		0			0
$553$	−0.267709	+	4.87384i	−0.0113842	+	0.207257i
$554$	4.30546	+	7.45728i	0.182921	+	0.316829i
$555$		0			0
$556$	−3.84846			−0.163211
$557$	11.6412	+	20.1631i	0.493252	+	0.854338i	0.999970	−	0.00777438i	$-0.00247469\pi$
$557$	11.6412	+	20.1631i	0.493252	+	0.854338i	−0.506718	+	0.862112i	$0.669141\pi$
$558$		0			0
$559$	2.74531			0.116114
$560$	−0.311358	+	5.66850i	−0.0131573	+	0.239538i
$561$		0			0
$562$	0.970751			0.0409487
$563$	2.27942	−	3.94808i	0.0960663	−	0.166392i	−0.813987	−	0.580883i	$-0.802707\pi$
$563$	2.27942	−	3.94808i	0.0960663	−	0.166392i	0.910053	+	0.414492i	$0.136041\pi$
$564$		0			0
$565$	−0.427982	−	0.741286i	−0.0180053	−	0.0311861i
$566$	11.6896			0.491351
$567$		0			0
$568$	−0.191588			−0.00803885
$569$	9.09976	+	15.7612i	0.381482	+	0.660746i	0.991274	−	0.131815i	$-0.0420806\pi$
$569$	9.09976	+	15.7612i	0.381482	+	0.660746i	−0.609793	+	0.792561i	$0.708747\pi$
$570$		0			0
$571$	8.52275	−	14.7618i	0.356666	−	0.617763i	−0.630736	−	0.775998i	$-0.717247\pi$
$571$	8.52275	−	14.7618i	0.356666	−	0.617763i	0.987402	+	0.158234i	$0.0505801\pi$
$572$	−21.0615			−0.880625
$573$		0			0
$574$	0.393614	−	0.199312i	0.0164291	−	0.00831912i
$575$	16.1443			0.673264
$576$		0			0
$577$	−5.70473	−	9.88088i	−0.237491	−	0.411346i	0.722503	−	0.691368i	$-0.242992\pi$
$577$	−5.70473	−	9.88088i	−0.237491	−	0.411346i	−0.959994	+	0.280022i	$0.909658\pi$
$578$	10.5553			0.439041
$579$		0			0
$580$	−7.52485	−	13.0334i	−0.312452	−	0.541183i
$581$	34.1588	−	17.2968i	1.41715	−	0.717592i
$582$		0			0
$583$	2.02275	+	3.50350i	0.0837736	+	0.145100i
$584$	12.7229	+	22.0368i	0.526479	+	0.911889i
$585$		0			0
$586$	−0.603332	+	1.04500i	−0.0249234	+	0.0431686i
$587$	−2.52544	+	4.37420i	−0.104236	+	0.180543i	−0.913426	−	0.407005i	$-0.866573\pi$
$587$	−2.52544	+	4.37420i	−0.104236	+	0.180543i	0.809190	+	0.587548i	$0.199906\pi$
$588$		0			0
$589$	−5.03052	−	8.71312i	−0.207279	−	0.359018i
$590$	6.28899			0.258913
$591$		0			0
$592$	−2.13765			−0.0878567
$593$	9.98892	−	17.3013i	0.410196	−	0.710480i	−0.584715	−	0.811239i	$-0.698794\pi$
$593$	9.98892	−	17.3013i	0.410196	−	0.710480i	0.994911	+	0.100759i	$0.0321271\pi$
$594$		0			0
$595$	−0.231513	+	4.21487i	−0.00949113	+	0.172793i
$596$	6.63365	−	11.4898i	0.271725	−	0.470641i
$597$		0			0
$598$	−5.01935	+	8.69378i	−0.205257	+	0.355515i
$599$	2.19660	−	3.80463i	0.0897508	−	0.155453i	−0.817655	−	0.575709i	$-0.804726\pi$
$599$	2.19660	−	3.80463i	0.0897508	−	0.155453i	0.907406	+	0.420256i	$0.138060\pi$
$600$		0			0
$601$	12.1778	−	21.0926i	0.496743	−	0.860385i	−0.503250	−	0.864141i	$-0.667862\pi$
$601$	12.1778	−	21.0926i	0.496743	−	0.860385i	0.999993	+	0.00375637i	$0.00119569\pi$
$602$	−1.47997	−	0.966399i	−0.0603191	−	0.0393875i
$603$		0			0
$604$	−13.6917	+	23.7147i	−0.557107	+	0.964937i
$605$	−18.9695			−0.771221
$606$		0			0
$607$	13.1256			0.532752			0.266376	−	0.963869i	$-0.414174\pi$
$607$	13.1256			0.532752			0.266376	+	0.963869i	$0.414174\pi$
$608$	11.5827	+	20.0618i	0.469741	+	0.813615i
$609$		0			0
$610$	−0.0359456	+	0.0622597i	−0.00145540	+	0.00252082i
$611$	−13.0510	+	22.6051i	−0.527988	+	0.914502i
$612$		0			0
$613$	−23.2403	−	40.2534i	−0.938667	−	1.62582i	−0.767960	−	0.640497i	$-0.778728\pi$
$613$	−23.2403	−	40.2534i	−0.938667	−	1.62582i	−0.170707	−	0.985322i	$-0.554605\pi$
$614$	0.356877	+	0.618129i	0.0144024	+	0.0249456i
$615$		0			0
$616$	25.9982	+	16.9765i	1.04750	+	0.684002i
$617$	−14.1948	−	24.5862i	−0.571463	−	0.989803i	−0.996416	−	0.0845873i	$-0.973043\pi$
$617$	−14.1948	−	24.5862i	−0.571463	−	0.989803i	0.424953	−	0.905215i	$-0.360291\pi$
$618$		0			0
$619$	31.9212			1.28302			0.641511	−	0.767114i	$-0.278308\pi$
$619$	31.9212			1.28302			0.641511	+	0.767114i	$0.278308\pi$
$620$	−2.76843	−	4.79506i	−0.111183	−	0.192574i
$621$		0			0
$622$	−11.3482			−0.455023
$623$	−31.9263	+	16.1663i	−1.27910	+	0.647691i
$624$		0			0
$625$	−1.33399			−0.0533594
$626$	−2.77469	+	4.80591i	−0.110899	+	0.192083i
$627$		0			0
$628$	4.90122	+	8.48916i	0.195580	+	0.338754i
$629$	−1.58947			−0.0633762
$630$		0			0
$631$	38.7184			1.54135			0.770677	−	0.637226i	$-0.219918\pi$
$631$	38.7184			1.54135			0.770677	+	0.637226i	$0.219918\pi$
$632$	2.19556	+	3.80282i	0.0873346	+	0.151268i
$633$		0			0
$634$	−2.19447	+	3.80094i	−0.0871537	+	0.150955i
$635$	−10.3447			−0.410517
$636$		0			0
$637$	11.4121	−	15.5425i	0.452163	−	0.615816i
$638$	−22.5124			−0.891276
$639$		0			0
$640$	7.81261	+	13.5318i	0.308821	+	0.534893i
$641$	40.4001			1.59571			0.797854	−	0.602851i	$-0.205968\pi$
$641$	40.4001			1.59571			0.797854	+	0.602851i	$0.205968\pi$
$642$		0			0
$643$	6.27355	+	10.8661i	0.247405	+	0.428517i	0.962805	−	0.270198i	$-0.0870890\pi$
$643$	6.27355	+	10.8661i	0.247405	+	0.428517i	−0.715400	+	0.698715i	$0.753756\pi$
$644$	−19.8988	+	10.0761i	−0.784123	+	0.397052i
$645$		0			0
$646$	1.50676	+	2.60979i	0.0592827	+	0.102681i
$647$	−17.2774	−	29.9253i	−0.679245	−	1.17649i	−0.975209	−	0.221287i	$-0.928974\pi$
$647$	−17.2774	−	29.9253i	−0.679245	−	1.17649i	0.295964	−	0.955199i	$-0.404359\pi$
$648$		0			0
$649$	−16.2323	+	28.1151i	−0.637173	+	1.10362i
$650$	−2.74164	+	4.74866i	−0.107536	+	0.186258i
$651$		0			0
$652$	6.22019	+	10.7737i	0.243602	+	0.421930i
$653$	22.2944			0.872446			0.436223	−	0.899839i	$-0.356316\pi$
$653$	22.2944			0.872446			0.436223	+	0.899839i	$0.356316\pi$
$654$		0			0
$655$	−29.1442			−1.13876
$656$	−0.187302	+	0.324417i	−0.00731293	+	0.0126664i
$657$		0			0
$658$	14.9931	−	7.59195i	0.584490	−	0.295965i
$659$	−3.57493	+	6.19196i	−0.139259	+	0.241204i	−0.927217	−	0.374526i	$-0.877806\pi$
$659$	−3.57493	+	6.19196i	−0.139259	+	0.241204i	0.787957	+	0.615730i	$0.211139\pi$
$660$		0			0
$661$	−21.4530	+	37.1577i	−0.834425	+	1.44527i	0.0600736	+	0.998194i	$0.480866\pi$
$661$	−21.4530	+	37.1577i	−0.834425	+	1.44527i	−0.894498	+	0.447072i	$0.852467\pi$
$662$	−8.95760	+	15.5150i	−0.348147	+	0.603008i
$663$		0			0
$664$	17.2221	−	29.8296i	0.668349	−	1.15761i
$665$	13.5043	−	6.83807i	0.523672	−	0.265169i
$666$		0			0
$667$	18.5146	−	32.0683i	0.716889	−	1.24169i
$668$	−3.28856			−0.127238
$669$		0			0
$670$	−12.0235			−0.464510
$671$	−0.185556	−	0.321392i	−0.00716331	−	0.0124072i
$672$		0			0
$673$	−18.8270	+	32.6094i	−0.725729	+	1.25700i	0.232944	+	0.972490i	$0.425164\pi$
$673$	−18.8270	+	32.6094i	−0.725729	+	1.25700i	−0.958673	+	0.284510i	$0.908169\pi$
$674$	3.19188	−	5.52850i	0.122947	−	0.212950i
$675$		0			0
$676$	−4.19619	−	7.26801i	−0.161392	−	0.279539i
$677$	−13.1808	−	22.8298i	−0.506580	−	0.877422i	−0.999971	−	0.00761453i	$-0.997576\pi$
$677$	−13.1808	−	22.8298i	−0.506580	−	0.877422i	0.493391	−	0.869808i	$-0.335757\pi$
$678$		0			0
$679$	12.7537	−	6.45800i	0.489440	−	0.247835i
$680$	1.89871	+	3.28866i	0.0728121	+	0.126114i
$681$		0			0
$682$	−8.28244			−0.317151
$683$	−1.96588	−	3.40500i	−0.0752222	−	0.130289i	0.825961	−	0.563728i	$-0.190633\pi$
$683$	−1.96588	−	3.40500i	−0.0752222	−	0.130289i	−0.901183	+	0.433439i	$0.857300\pi$
$684$		0			0
$685$	17.4008			0.664850
$686$	−11.6234	+	4.36155i	−0.443782	+	0.166525i
$687$		0			0
$688$	1.50076			0.0572158
$689$	1.13002	−	1.95725i	0.0430503	−	0.0745653i
$690$		0			0
$691$	−9.95052	−	17.2348i	−0.378536	−	0.655643i	0.612314	−	0.790615i	$-0.290239\pi$
$691$	−9.95052	−	17.2348i	−0.378536	−	0.655643i	−0.990849	+	0.134972i	$0.956906\pi$
$692$	−28.3585			−1.07803
$693$		0			0
$694$	−12.5373			−0.475910
$695$	1.76823	+	3.06266i	0.0670727	+	0.116173i
$696$		0			0
$697$	−0.139270	+	0.241223i	−0.00527524	+	0.00913699i
$698$	−20.1827			−0.763925
$699$		0			0
$700$	−10.8690	+	5.50368i	−0.410810	+	0.208020i
$701$	−43.7908			−1.65396			−0.826979	−	0.562234i	$-0.809942\pi$
$701$	−43.7908			−1.65396			−0.826979	+	0.562234i	$0.809942\pi$
$702$		0			0
$703$	2.84983	+	4.93604i	0.107483	+	0.186166i
$704$	4.22031			0.159059
$705$		0			0
$706$	−2.09792	−	3.63370i	−0.0789561	−	0.136756i
$707$	11.3764	+	7.42861i	0.427853	+	0.279382i
$708$		0			0
$709$	−22.3172	−	38.6545i	−0.838139	−	1.45170i	−0.891449	−	0.453121i	$-0.850310\pi$
$709$	−22.3172	−	38.6545i	−0.838139	−	1.45170i	0.0533097	−	0.998578i	$-0.483023\pi$
$710$	0.0384437	+	0.0665865i	0.00144277	+	0.00249895i
$711$		0			0
$712$	−16.0966	+	27.8801i	−0.603244	+	1.04485i
$713$	6.81163	−	11.7981i	0.255097	−	0.441842i
$714$		0			0
$715$	9.67699	+	16.7610i	0.361899	+	0.626827i
$716$	−11.8245			−0.441904
$717$		0			0
$718$	6.83411			0.255047
$719$	19.5096	−	33.7917i	0.727586	−	1.26022i	−0.230315	−	0.973116i	$-0.573976\pi$
$719$	19.5096	−	33.7917i	0.727586	−	1.26022i	0.957901	−	0.287100i	$-0.0926912\pi$
$720$		0			0
$721$	−31.4819	−	20.5572i	−1.17245	−	0.765592i
$722$	−0.965081	+	1.67157i	−0.0359166	+	0.0622094i
$723$		0			0
$724$	12.0413	−	20.8561i	0.447510	−	0.775109i
$725$	10.1130	−	17.5162i	0.375586	−	0.650534i
$726$		0			0
$727$	−11.2554	+	19.4949i	−0.417439	+	0.723025i	−0.995681	−	0.0928402i	$-0.970405\pi$
$727$	−11.2554	+	19.4949i	−0.417439	+	0.723025i	0.578242	+	0.815865i	$0.303739\pi$
$728$	0.951361	−	17.3202i	0.0352598	−	0.641929i
$729$		0			0
$730$	5.10593	−	8.84373i	0.188979	−	0.327321i
$731$	1.11590			0.0412731
$732$		0			0
$733$	−0.897039			−0.0331329			−0.0165664	−	0.999863i	$-0.505274\pi$
$733$	−0.897039			−0.0331329			−0.0165664	+	0.999863i	$0.505274\pi$
$734$	−9.60441	−	16.6353i	−0.354505	−	0.614021i
$735$		0			0
$736$	−15.6837	+	27.1649i	−0.578108	+	1.00131i
$737$	31.0335	−	53.7517i	1.14314	−	1.97997i
$738$		0			0
$739$	1.79032	+	3.10092i	0.0658578	+	0.114069i	0.897074	−	0.441880i	$-0.145688\pi$
$739$	1.79032	+	3.10092i	0.0658578	+	0.114069i	−0.831216	+	0.555949i	$0.812355\pi$
$740$	1.56833	+	2.71643i	0.0576531	+	0.0998581i
$741$		0			0
$742$	−1.29817	+	0.657346i	−0.0476572	+	0.0241319i
$743$	24.7964	+	42.9486i	0.909691	+	1.57563i	0.814493	+	0.580173i	$0.197015\pi$
$743$	24.7964	+	42.9486i	0.909691	+	1.57563i	0.0951977	+	0.995458i	$0.469652\pi$
$744$		0			0
$745$	−12.1917			−0.446668
$746$	−5.38726	−	9.33101i	−0.197242	−	0.341633i
$747$		0			0
$748$	−8.56098			−0.313020
$749$	−18.0813	+	9.15573i	−0.660676	+	0.334543i
$750$		0			0
$751$	−42.9030			−1.56555			−0.782776	−	0.622304i	$-0.786197\pi$
$751$	−42.9030			−1.56555			−0.782776	+	0.622304i	$0.786197\pi$
$752$	−7.13450	+	12.3573i	−0.260168	+	0.450625i
$753$		0			0
$754$	6.28835	+	10.8917i	0.229008	+	0.396654i
$755$	25.1633			0.915786
$756$		0			0
$757$	13.8029			0.501677			0.250838	−	0.968029i	$-0.419294\pi$
$757$	13.8029			0.501677			0.250838	+	0.968029i	$0.419294\pi$
$758$	−0.341510	−	0.591513i	−0.0124042	−	0.0214847i
$759$		0			0
$760$	6.80856	−	11.7928i	0.246972	−	0.427769i
$761$	−40.7197			−1.47609			−0.738044	−	0.674752i	$-0.764251\pi$
$761$	−40.7197			−1.47609			−0.738044	+	0.674752i	$0.764251\pi$
$762$		0			0
$763$	0.246505	−	4.48781i	0.00892410	−	0.162470i
$764$	23.0001			0.832113
$765$		0			0
$766$	3.88342	+	6.72627i	0.140313	+	0.243030i
$767$	18.1365			0.654871
$768$		0			0
$769$	5.57381	+	9.65413i	0.200997	+	0.348137i	0.948850	−	0.315728i	$-0.102249\pi$
$769$	5.57381	+	9.65413i	0.200997	+	0.348137i	−0.747853	+	0.663864i	$0.768915\pi$
$770$	0.683421	−	12.4422i	0.0246288	−	0.448385i
$771$		0			0
$772$	12.8454	+	22.2489i	0.462317	+	0.800756i
$773$	0.462831	+	0.801647i	0.0166469	+	0.0288332i	0.874229	−	0.485514i	$-0.161368\pi$
$773$	0.462831	+	0.801647i	0.0166469	+	0.0288332i	−0.857582	+	0.514347i	$0.828034\pi$
$774$		0			0
$775$	3.72061	−	6.44428i	0.133648	−	0.231485i
$776$	6.43012	−	11.1373i	0.230828	−	0.399806i
$777$		0			0
$778$	−5.97049	−	10.3412i	−0.214052	−	0.370750i
$779$	0.998817			0.0357863
$780$		0			0
$781$	−0.396903			−0.0142023
$782$	−2.04024	+	3.53381i	−0.0729590	+	0.126369i
$783$		0			0
$784$	6.23854	−	8.49648i	0.222805	−	0.303446i
$785$	4.50386	−	7.80092i	0.160750	−	0.278427i
$786$		0			0
$787$	−11.5120	+	19.9393i	−0.410358	+	0.710761i	−0.994929	−	0.100582i	$-0.967930\pi$
$787$	−11.5120	+	19.9393i	−0.410358	+	0.710761i	0.584571	+	0.811343i	$0.301263\pi$
$788$	3.13030	−	5.42184i	0.111512	−	0.193145i
$789$		0			0
$790$	0.881115	−	1.52614i	0.0313487	−	0.0542975i
$791$	−0.0871659	+	1.58692i	−0.00309926	+	0.0564243i
$792$		0			0
$793$	−0.103662	+	0.179548i	−0.00368114	+	0.00637593i
$794$	−8.77102			−0.311272
$795$		0			0
$796$	−39.2027			−1.38950
$797$	−11.3925	−	19.7325i	−0.403544	−	0.698960i	0.590606	−	0.806960i	$-0.298889\pi$
$797$	−11.3925	−	19.7325i	−0.403544	−	0.698960i	−0.994151	+	0.108000i	$0.965555\pi$
$798$		0			0
$799$	−5.30492	+	9.18839i	−0.187675	+	0.325062i
$800$	−8.56664	+	14.8379i	−0.302877	+	0.524598i
$801$		0			0
$802$	−4.72695	−	8.18732i	−0.166914	−	0.289104i
$803$	26.3575	+	45.6525i	0.930135	+	1.61104i
$804$		0			0
$805$	17.1614	+	11.2062i	0.604861	+	0.394966i
$806$	2.31352	+	4.00713i	0.0814901	+	0.141145i
$807$		0			0
$808$	12.2229			0.429999
$809$	−6.73753	−	11.6697i	−0.236879	−	0.410286i	0.722938	−	0.690913i	$-0.242791\pi$
$809$	−6.73753	−	11.6697i	−0.236879	−	0.410286i	−0.959817	+	0.280627i	$0.909458\pi$
$810$		0			0
$811$	−30.7348			−1.07924			−0.539622	−	0.841907i	$-0.681433\pi$
$811$	−30.7348			−1.07924			−0.539622	+	0.841907i	$0.681433\pi$
$812$	−1.53257	+	27.9014i	−0.0537825	+	0.979149i
$813$		0			0
$814$	4.69206			0.164457
$815$	5.71590	−	9.90023i	0.200219	−	0.346790i
$816$		0			0
$817$	−2.00075	−	3.46540i	−0.0699974	−	0.121239i
$818$	1.77369			0.0620158
$819$		0			0
$820$	0.549675			0.0191955
$821$	−8.49319	−	14.7106i	−0.296414	−	0.513405i	0.678899	−	0.734232i	$-0.262458\pi$
$821$	−8.49319	−	14.7106i	−0.296414	−	0.513405i	−0.975313	+	0.220827i	$0.929124\pi$
$822$		0			0
$823$	9.29157	−	16.0935i	0.323884	−	0.560983i	−0.657402	−	0.753540i	$-0.728345\pi$
$823$	9.29157	−	16.0935i	0.323884	−	0.560983i	0.981286	+	0.192557i	$0.0616780\pi$
$824$	−33.8244			−1.17833
$825$		0			0
$826$	−9.77720	−	6.38438i	−0.340192	−	0.222141i
$827$	−14.5419			−0.505670			−0.252835	−	0.967509i	$-0.581363\pi$
$827$	−14.5419			−0.505670			−0.252835	+	0.967509i	$0.581363\pi$
$828$		0			0
$829$	4.78717	+	8.29161i	0.166265	+	0.287980i	0.937104	−	0.349051i	$-0.113496\pi$
$829$	4.78717	+	8.29161i	0.166265	+	0.287980i	−0.770839	+	0.637030i	$0.780163\pi$
$830$	−13.8231			−0.479806
$831$		0			0
$832$	−1.17885	−	2.04183i	−0.0408693	−	0.0707877i
$833$	4.63872	−	6.31764i	0.160722	−	0.218893i
$834$		0			0
$835$	1.51097	+	2.61708i	0.0522894	+	0.0905678i
$836$	15.3494	+	26.5859i	0.530869	+	0.919492i
$837$		0			0
$838$	11.2326	−	19.4554i	0.388023	−	0.672075i
$839$	−21.2303	+	36.7720i	−0.732952	+	1.26951i	0.222664	+	0.974895i	$0.428525\pi$
$839$	−21.2303	+	36.7720i	−0.732952	+	1.26951i	−0.955616	+	0.294615i	$0.904809\pi$
$840$		0			0
$841$	−8.69551	−	15.0611i	−0.299845	−	0.519347i
$842$	−3.24375			−0.111787
$843$		0			0
$844$	−11.6686			−0.401648
$845$	−3.85599	+	6.67877i	−0.132650	+	0.229757i
$846$		0			0
$847$	29.4911	+	19.2572i	1.01332	+	0.661687i
$848$	0.617738	−	1.06995i	0.0212132	−	0.0367423i
$849$		0			0
$850$	−1.11441	+	1.93021i	−0.0382239	+	0.0662058i
$851$	−3.85883	+	6.68370i	−0.132279	+	0.229114i
$852$		0			0
$853$	7.14039	−	12.3675i	0.244482	−	0.423456i	−0.717504	−	0.696555i	$-0.754715\pi$
$853$	7.14039	−	12.3675i	0.244482	−	0.423456i	0.961986	+	0.273099i	$0.0880486\pi$
$854$	0.119087	−	0.0603014i	0.00407507	−	0.00206347i
$855$		0			0
$856$	−9.11621	+	15.7897i	−0.311586	+	0.539682i
$857$	−34.7790			−1.18803			−0.594013	−	0.804455i	$-0.702457\pi$
$857$	−34.7790			−1.18803			−0.594013	+	0.804455i	$0.702457\pi$
$858$		0			0
$859$	−12.6486			−0.431564			−0.215782	−	0.976442i	$-0.569230\pi$
$859$	−12.6486			−0.431564			−0.215782	+	0.976442i	$0.569230\pi$
$860$	−1.10107	−	1.90710i	−0.0375460	−	0.0650316i
$861$		0			0
$862$	11.8409	−	20.5091i	0.403304	−	0.698543i
$863$	−13.2398	+	22.9321i	−0.450690	+	0.780617i	−0.998429	−	0.0560318i	$-0.982155\pi$
$863$	−13.2398	+	22.9321i	−0.450690	+	0.780617i	0.547739	+	0.836649i	$0.315489\pi$
$864$		0			0
$865$	13.0297	+	22.5681i	0.443022	+	0.767337i
$866$	1.83471	+	3.17782i	0.0623461	+	0.107987i
$867$		0			0
$868$	−0.563839	+	10.2651i	−0.0191379	+	0.348420i
$869$	4.54843	+	7.87811i	0.154295	+	0.267247i
$870$		0			0
$871$	−34.6741			−1.17489
$872$	−2.02166	−	3.50162i	−0.0684621	−	0.118580i
$873$		0			0
$874$	14.6322			0.494941
$875$	25.1570	+	16.4272i	0.850463	+	0.555341i
$876$		0			0
$877$	28.4534			0.960805			0.480402	−	0.877048i	$-0.340491\pi$
$877$	28.4534			0.960805			0.480402	+	0.877048i	$0.340491\pi$
$878$	2.14443	−	3.71427i	0.0723711	−	0.125350i
$879$		0			0
$880$	5.29004	+	9.16261i	0.178327	+	0.308872i
$881$	20.3637			0.686071			0.343036	−	0.939322i	$-0.388545\pi$
$881$	20.3637			0.686071			0.343036	+	0.939322i	$0.388545\pi$
$882$		0			0
$883$	49.1950			1.65554			0.827772	−	0.561065i	$-0.189608\pi$
$883$	49.1950			1.65554			0.827772	+	0.561065i	$0.189608\pi$
$884$	2.39132	+	4.14189i	0.0804288	+	0.139307i
$885$		0			0
$886$	2.14065	−	3.70771i	0.0719164	−	0.124563i
$887$	4.21692			0.141590			0.0707952	−	0.997491i	$-0.477446\pi$
$887$	4.21692			0.141590			0.0707952	+	0.997491i	$0.477446\pi$
$888$		0			0
$889$	16.0825	+	10.5016i	0.539388	+	0.352213i
$890$	12.9196			0.433067
$891$		0			0
$892$	−10.0673	−	17.4371i	−0.337078	−	0.583837i
$893$	38.0457			1.27315
$894$		0			0
$895$	5.43294	+	9.41013i	0.181603	+	0.314546i
$896$	1.59117	−	28.9685i	0.0531574	−	0.967768i
$897$		0			0
$898$	3.93685	+	6.81883i	0.131375	+	0.227547i
$899$	−8.53374	−	14.7809i	−0.284616	−	0.492970i
$900$		0			0
$901$	0.459325	−	0.795574i	0.0153023	−	0.0265044i
$902$	0.411122	−	0.712084i	0.0136889	−	0.0237098i
$903$		0			0
$904$	0.714872	+	1.23819i	0.0237763	+	0.0411817i
$905$	−22.1301			−0.735628
$906$		0			0
$907$	47.9851			1.59332			0.796659	−	0.604429i	$-0.206599\pi$
$907$	47.9851			1.59332			0.796659	+	0.604429i	$0.206599\pi$
$908$	22.4585	−	38.8993i	0.745311	−	1.29092i
$909$		0			0
$910$	−6.21054	+	3.14480i	−0.205878	+	0.104249i
$911$	12.8667	−	22.2858i	0.426294	−	0.738362i	−0.570247	−	0.821474i	$-0.693152\pi$
$911$	12.8667	−	22.2858i	0.426294	−	0.738362i	0.996540	+	0.0831113i	$0.0264857\pi$
$912$		0			0
$913$	35.6782	−	61.7965i	1.18078	−	2.04517i
$914$	3.52675	−	6.10852i	0.116655	−	0.202052i
$915$		0			0
$916$	11.9678	−	20.7288i	0.395427	−	0.684900i
$917$	45.3092	+	29.5863i	1.49624	+	0.977024i
$918$		0			0
$919$	1.13478	−	1.96550i	0.0374330	−	0.0648359i	−0.846702	−	0.532068i	$-0.821415\pi$
$919$	1.13478	−	1.96550i	0.0374330	−	0.0648359i	0.884135	+	0.467232i	$0.154749\pi$
$920$	18.4384			0.607895
$921$		0			0
$922$	4.74968			0.156422
$923$	0.110866	+	0.192026i	0.00364920	+	0.00632060i
$924$		0			0
$925$	−2.10775	+	3.65073i	−0.0693024	+	0.120035i
$926$	−10.9774	+	19.0134i	−0.360740	+	0.624819i
$927$		0			0
$928$	19.6488	+	34.0328i	0.645004	+	1.11718i
$929$	22.9248	+	39.7069i	0.752138	+	1.30274i	0.946785	+	0.321868i	$0.104311\pi$
$929$	22.9248	+	39.7069i	0.752138	+	1.30274i	−0.194647	+	0.980873i	$0.562356\pi$
$930$		0			0
$931$	−27.9362	−	3.07824i	−0.915573	−	0.100885i
$932$	−3.83514	−	6.64266i	−0.125624	−	0.217587i
$933$		0			0
$934$	−2.63060			−0.0860757
$935$	3.93346	+	6.81294i	0.128638	+	0.222807i
$936$		0			0
$937$	−56.2075			−1.83622			−0.918110	−	0.396325i	$-0.870285\pi$
$937$	−56.2075			−1.83622			−0.918110	+	0.396325i	$0.870285\pi$
$938$	18.6925	+	12.2059i	0.610330	+	0.398537i
$939$		0			0
$940$	20.9376			0.682908
$941$	−17.6402	+	30.5536i	−0.575053	+	0.996020i	0.420983	+	0.907068i	$0.361685\pi$
$941$	−17.6402	+	30.5536i	−0.575053	+	0.996020i	−0.996036	+	0.0889519i	$0.971648\pi$
$942$		0			0
$943$	0.676229	+	1.17126i	0.0220210	+	0.0381415i
$944$	9.91453			0.322691
$945$		0			0
$946$	−3.29411			−0.107101
$947$	−25.3565	−	43.9188i	−0.823976	−	1.42717i	−0.902699	−	0.430272i	$-0.858418\pi$
$947$	−25.3565	−	43.9188i	−0.823976	−	1.42717i	0.0787236	−	0.996896i	$-0.474916\pi$
$948$		0			0
$949$	14.7248	−	25.5040i	0.477986	−	0.827896i
$950$	7.99230			0.259305
$951$		0			0
$952$	0.386705	−	7.04023i	0.0125332	−	0.228175i
$953$	−25.9988			−0.842184			−0.421092	−	0.907018i	$-0.638353\pi$
$953$	−25.9988			−0.842184			−0.421092	+	0.907018i	$0.638353\pi$
$954$		0			0
$955$	−10.5677	−	18.3038i	−0.341962	−	0.592296i
$956$	−20.2122			−0.653710
$957$		0			0
$958$	−5.39165	−	9.33861i	−0.174196	−	0.301717i
$959$	−27.0522	−	17.6647i	−0.873562	−	0.570424i
$960$		0			0
$961$	12.3604	+	21.4088i	0.398722	+	0.690607i
$962$	−1.31062	−	2.27006i	−0.0422562	−	0.0731898i
$963$		0			0
$964$	11.3062	−	19.5829i	0.364148	−	0.630722i
$965$	11.8040	−	20.4451i	0.379984	−	0.658152i
$966$		0			0
$967$	−12.9810	−	22.4838i	−0.417442	−	0.723031i	0.578239	−	0.815867i	$-0.303740\pi$
$967$	−12.9810	−	22.4838i	−0.417442	−	0.723031i	−0.995681	+	0.0928360i	$0.970407\pi$
$968$	31.6854			1.01841
$969$		0			0
$970$	−5.16103			−0.165711
$971$	3.97206	−	6.87981i	0.127469	−	0.220783i	−0.795226	−	0.606313i	$-0.792648\pi$
$971$	3.97206	−	6.87981i	0.127469	−	0.220783i	0.922696	+	0.385530i	$0.125981\pi$
$972$		0			0
$973$	0.360130	−	6.55643i	0.0115452	−	0.210189i
$974$	1.17424	−	2.03384i	0.0376249	−	0.0651683i
$975$		0			0
$976$	−0.0566680	+	0.0981518i	−0.00181390	+	0.00314176i
$977$	−26.1274	+	45.2540i	−0.835889	+	1.44780i	0.0574149	+	0.998350i	$0.481714\pi$
$977$	−26.1274	+	45.2540i	−0.835889	+	1.44780i	−0.893304	+	0.449452i	$0.851619\pi$
$978$		0			0
$979$	−33.3464	+	57.7577i	−1.06576	+	1.84594i
$980$	−15.3740	−	1.69404i	−0.491106	−	0.0541140i
$981$		0			0
$982$	−13.7784	+	23.8650i	−0.439688	+	0.761562i
$983$	38.8379			1.23874			0.619369	−	0.785100i	$-0.287389\pi$
$983$	38.8379			1.23874			0.619369	+	0.785100i	$0.287389\pi$
$984$		0			0
$985$	−5.75304			−0.183307
$986$	2.55606	+	4.42722i	0.0814015	+	0.140991i
$987$		0			0
$988$	8.57501	−	14.8524i	0.272807	−	0.472516i
$989$	2.70914	−	4.69236i	0.0861455	−	0.149208i
$990$		0			0
$991$	−15.4689	−	26.7929i	−0.491385	−	0.851104i	0.508565	−	0.861023i	$-0.330176\pi$
$991$	−15.4689	−	26.7929i	−0.491385	−	0.851104i	−0.999951	+	0.00991892i	$0.996843\pi$
$992$	7.22890	+	12.5208i	0.229518	+	0.397536i
$993$		0			0
$994$	0.00782973	−	0.142546i	0.000248344	−	0.00452128i
$995$	18.0122	+	31.1981i	0.571025	+	0.989045i
$996$		0			0
$997$	47.0670			1.49063			0.745313	−	0.666714i	$-0.232300\pi$
$997$	47.0670			1.49063			0.745313	+	0.666714i	$0.232300\pi$
$998$	3.96492	+	6.86745i	0.125507	+	0.217385i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.g.b.100.4		10
3.2	odd	2		63.2.g.b.16.2	yes	10
4.3	odd	2		3024.2.t.i.289.1		10
7.2	even	3		1323.2.f.e.883.4		10
7.3	odd	6		1323.2.h.f.802.2		10
7.4	even	3		189.2.h.b.46.2		10
7.5	odd	6		1323.2.f.f.883.4		10
7.6	odd	2		1323.2.g.f.667.4		10
9.2	odd	6		567.2.e.f.163.2		10
9.4	even	3		189.2.h.b.37.2		10
9.5	odd	6		63.2.h.b.58.4	yes	10
9.7	even	3		567.2.e.e.163.4		10
12.11	even	2		1008.2.t.i.961.4		10
21.2	odd	6		441.2.f.e.295.2		10
21.5	even	6		441.2.f.f.295.2		10
21.11	odd	6		63.2.h.b.25.4	yes	10
21.17	even	6		441.2.h.f.214.4		10
21.20	even	2		441.2.g.f.79.2		10
28.11	odd	6		3024.2.q.i.2881.5		10
36.23	even	6		1008.2.q.i.625.1		10
36.31	odd	6		3024.2.q.i.2305.5		10
63.2	odd	6		3969.2.a.z.1.4		5
63.4	even	3	inner	189.2.g.b.172.4		10
63.5	even	6		441.2.f.f.148.2		10
63.11	odd	6		567.2.e.f.487.2		10
63.13	odd	6		1323.2.h.f.226.2		10
63.16	even	3		3969.2.a.bc.1.2		5
63.23	odd	6		441.2.f.e.148.2		10
63.25	even	3		567.2.e.e.487.4		10
63.31	odd	6		1323.2.g.f.361.4		10
63.32	odd	6		63.2.g.b.4.2	✓	10
63.40	odd	6		1323.2.f.f.442.4		10
63.41	even	6		441.2.h.f.373.4		10
63.47	even	6		3969.2.a.ba.1.4		5
63.58	even	3		1323.2.f.e.442.4		10
63.59	even	6		441.2.g.f.67.2		10
63.61	odd	6		3969.2.a.bb.1.2		5
84.11	even	6		1008.2.q.i.529.1		10
252.67	odd	6		3024.2.t.i.1873.1		10
252.95	even	6		1008.2.t.i.193.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.g.b.4.2	✓	10	63.32	odd	6
63.2.g.b.16.2	yes	10	3.2	odd	2
63.2.h.b.25.4	yes	10	21.11	odd	6
63.2.h.b.58.4	yes	10	9.5	odd	6
189.2.g.b.100.4		10	1.1	even	1	trivial
189.2.g.b.172.4		10	63.4	even	3	inner
189.2.h.b.37.2		10	9.4	even	3
189.2.h.b.46.2		10	7.4	even	3
441.2.f.e.148.2		10	63.23	odd	6
441.2.f.e.295.2		10	21.2	odd	6
441.2.f.f.148.2		10	63.5	even	6
441.2.f.f.295.2		10	21.5	even	6
441.2.g.f.67.2		10	63.59	even	6
441.2.g.f.79.2		10	21.20	even	2
441.2.h.f.214.4		10	21.17	even	6
441.2.h.f.373.4		10	63.41	even	6
567.2.e.e.163.4		10	9.7	even	3
567.2.e.e.487.4		10	63.25	even	3
567.2.e.f.163.2		10	9.2	odd	6
567.2.e.f.487.2		10	63.11	odd	6
1008.2.q.i.529.1		10	84.11	even	6
1008.2.q.i.625.1		10	36.23	even	6
1008.2.t.i.193.4		10	252.95	even	6
1008.2.t.i.961.4		10	12.11	even	2
1323.2.f.e.442.4		10	63.58	even	3
1323.2.f.e.883.4		10	7.2	even	3
1323.2.f.f.442.4		10	63.40	odd	6
1323.2.f.f.883.4		10	7.5	odd	6
1323.2.g.f.361.4		10	63.31	odd	6
1323.2.g.f.667.4		10	7.6	odd	2
1323.2.h.f.226.2		10	63.13	odd	6
1323.2.h.f.802.2		10	7.3	odd	6
3024.2.q.i.2305.5		10	36.31	odd	6
3024.2.q.i.2881.5		10	28.11	odd	6
3024.2.t.i.289.1		10	4.3	odd	2
3024.2.t.i.1873.1		10	252.67	odd	6
3969.2.a.z.1.4		5	63.2	odd	6
3969.2.a.ba.1.4		5	63.47	even	6
3969.2.a.bb.1.2		5	63.61	odd	6
3969.2.a.bc.1.2		5	63.16	even	3

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.335166 + 0.580525i) q^{2} +(0.775327 - 1.34291i) q^{4} -1.42494 q^{5} +(2.21529 + 1.44655i) q^{7} +2.38012 q^{8} +(-0.477591 - 0.827212i) q^{10} +4.93077 q^{11} +(-1.37730 - 2.38556i) q^{13} +(-0.0972697 + 1.77086i) q^{14} +(-0.752918 - 1.30409i) q^{16} +(-0.559839 - 0.969670i) q^{17} +(-2.00752 + 3.47713i) q^{19} +(-1.10479 + 1.91356i) q^{20} +(1.65263 + 2.86244i) q^{22} -5.43661 q^{23} -2.96955 q^{25} +(0.923251 - 1.59912i) q^{26} +(3.66015 - 1.85337i) q^{28} +(-3.40555 + 5.89858i) q^{29} +(-1.25292 + 2.17012i) q^{31} +(2.88483 - 4.99666i) q^{32} +(0.375279 - 0.650002i) q^{34} +(-3.15664 - 2.06124i) q^{35} +(0.709787 - 1.22939i) q^{37} -2.69142 q^{38} -3.39152 q^{40} +(-0.124384 - 0.215440i) q^{41} +(-0.498313 + 0.863104i) q^{43} +(3.82296 - 6.62156i) q^{44} +(-1.82217 - 3.15609i) q^{46} +(-4.73790 - 8.20628i) q^{47} +(2.81498 + 6.40905i) q^{49} +(-0.995294 - 1.72390i) q^{50} -4.27144 q^{52} +(0.410229 + 0.710537i) q^{53} -7.02604 q^{55} +(5.27265 + 3.44296i) q^{56} -4.56570 q^{58} +(-3.29204 + 5.70197i) q^{59} +(-0.0376322 - 0.0651809i) q^{61} -1.67974 q^{62} +0.855913 q^{64} +(1.96257 + 3.39927i) q^{65} +(6.29385 - 10.9013i) q^{67} -1.73623 q^{68} +(0.138603 - 2.52337i) q^{70} -0.0804951 q^{71} +(5.34551 + 9.25869i) q^{73} +0.951587 q^{74} +(3.11297 + 5.39183i) q^{76} +(10.9231 + 7.13261i) q^{77} +(0.922457 + 1.59774i) q^{79} +(1.07286 + 1.85825i) q^{80} +(0.0833788 - 0.144416i) q^{82} +(7.23583 - 12.5328i) q^{83} +(0.797736 + 1.38172i) q^{85} -0.668072 q^{86} +11.7358 q^{88} +(-6.76292 + 11.7137i) q^{89} +(0.399711 - 7.27703i) q^{91} +(-4.21515 + 7.30085i) q^{92} +(3.17597 - 5.50094i) q^{94} +(2.86059 - 4.95469i) q^{95} +(2.70160 - 4.67930i) q^{97} +(-2.77712 + 3.78226i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2 q^{2} - 4 q^{4} + 8 q^{5} - q^{7} + 6 q^{8} - 7 q^{10} + 8 q^{11} - 8 q^{13} - 16 q^{14} + 2 q^{16} - 12 q^{17} + q^{19} - 5 q^{20} - q^{22} + 6 q^{23} + 2 q^{25} - 11 q^{26} - 2 q^{28} - 7 q^{29}+ \cdots - 59 q^{98}+O(q^{100}) \) 10 * q - 2 * q^2 - 4 * q^4 + 8 * q^5 - q^7 + 6 * q^8 - 7 * q^10 + 8 * q^11 - 8 * q^13 - 16 * q^14 + 2 * q^16 - 12 * q^17 + q^19 - 5 * q^20 - q^22 + 6 * q^23 + 2 * q^25 - 11 * q^26 - 2 * q^28 - 7 * q^29 - 3 * q^31 + 2 * q^32 + 3 * q^34 - 5 * q^35 + 40 * q^38 + 6 * q^40 - 5 * q^41 - 7 * q^43 + 10 * q^44 + 3 * q^46 - 27 * q^47 + 25 * q^49 - 19 * q^50 + 20 * q^52 + 21 * q^53 + 4 * q^55 + 45 * q^56 + 20 * q^58 - 30 * q^59 - 14 * q^61 + 12 * q^62 - 50 * q^64 + 11 * q^65 - 2 * q^67 + 54 * q^68 - 29 * q^70 + 6 * q^71 + 15 * q^73 - 72 * q^74 + 5 * q^76 + 31 * q^77 - 4 * q^79 - 20 * q^80 - 5 * q^82 - 9 * q^83 - 6 * q^85 - 16 * q^86 + 36 * q^88 - 28 * q^89 - 4 * q^91 - 27 * q^92 - 3 * q^94 + 14 * q^95 - 12 * q^97 - 59 * q^98

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