LMFDB - Embedded newform 1323.2.g.f.667.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(361,1323)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1323, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 4]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1323.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.g (of order $3$, degree $2$, not 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:	$10.5642081874$
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			667.4
Root			$-0.335166 - 0.580525i$ of defining polynomial
Character	$\chi$	$=$	1323.667
Dual form			1323.2.g.f.361.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

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	$-0.396779\pi$
$5$	1.42494			0.637251			0.318626	+	0.947881i	$0.396779\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	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	0.991347	−	0.131265i	$-0.0419038\pi$
$13$	1.37730	+	2.38556i	0.381995	+	0.661635i	−0.609352	+	0.792900i	$0.708571\pi$
$14$		0			0
$15$		0			0
$16$	−0.752918	−	1.30409i	−0.188230	−	0.326023i
$17$	0.559839	+	0.969670i	0.135781	+	0.235180i	0.925896	−	0.377780i	$-0.123312\pi$
$17$	0.559839	+	0.969670i	0.135781	+	0.235180i	−0.790115	+	0.612959i	$0.789979\pi$
$18$		0			0
$19$	2.00752	−	3.47713i	0.460557	−	0.797709i	−0.538431	−	0.842669i	$-0.680983\pi$
$19$	2.00752	−	3.47713i	0.460557	−	0.797709i	0.998989	+	0.0449606i	$0.0143162\pi$
$20$	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
$28$		0			0
$29$	−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	−0.731298	−	0.682058i	$-0.761085\pi$
$31$	1.25292	−	2.17012i	0.225031	−	0.389765i	0.956329	+	0.292294i	$0.0944184\pi$
$32$	2.88483	−	4.99666i	0.509970	−	0.883294i
$33$		0			0
$34$	−0.375279	+	0.650002i	−0.0643597	+	0.111474i
$35$		0			0
$36$		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	0.875575	−	0.483083i	$-0.160483\pi$
$41$	0.124384	+	0.215440i	0.0194256	+	0.0336460i	−0.856149	+	0.516729i	$0.827150\pi$
$42$		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	$0.0762040\pi$
$47$	4.73790	+	8.20628i	0.691093	+	1.19701i	−0.280387	+	0.959887i	$0.590463\pi$
$48$		0			0
$49$		0			0
$50$	−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
$56$		0			0
$57$		0			0
$58$	−4.56570			−0.599506
$59$	3.29204	−	5.70197i	0.428586	−	0.742334i	−0.568161	−	0.822917i	$-0.692345\pi$
$59$	3.29204	−	5.70197i	0.428586	−	0.742334i	0.996748	+	0.0805836i	$0.0256784\pi$
$60$		0			0
$61$	0.0376322	+	0.0651809i	0.00481831	+	0.00834556i	0.868425	−	0.495821i	$-0.165133\pi$
$61$	0.0376322	+	0.0651809i	0.00481831	+	0.00834556i	−0.863606	+	0.504167i	$0.831800\pi$
$62$	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			0
$71$	−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	$-0.951503\pi$
$73$	−5.34551	−	9.25869i	−0.625644	−	1.08365i	0.362772	−	0.931878i	$-0.381830\pi$
$74$	0.951587			0.110620
$75$		0			0
$76$	−3.11297	−	5.39183i	−0.357083	−	0.618485i
$77$		0			0
$78$		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	$0.458795\pi$
$83$	−7.23583	+	12.5328i	−0.794236	+	1.37566i	−0.923323	+	0.384023i	$0.874538\pi$
$84$		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	$-0.578908\pi$
$89$	6.76292	−	11.7137i	0.716868	−	1.24165i	0.962235	−	0.272222i	$-0.0877584\pi$
$90$		0			0
$91$		0			0
$92$	−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	−0.969960	−	0.243266i	$-0.921781\pi$
$97$	−2.70160	+	4.67930i	−0.274306	+	0.475111i	0.695654	+	0.718377i	$0.255115\pi$
$98$		0			0
$99$		0			0
$100$	−2.30238	+	3.98783i	−0.230238	+	0.398783i
$101$	−5.13540			−0.510991			−0.255496	−	0.966810i	$-0.582239\pi$
$101$	−5.13540			−0.510991			−0.255496	+	0.966810i	$0.582239\pi$
$102$		0			0
$103$	14.2112			1.40027			0.700137	−	0.714009i	$-0.253122\pi$
$103$	14.2112			1.40027			0.700137	+	0.714009i	$0.253122\pi$
$104$	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			0
$113$	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			0
$120$		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	$-0.851752\pi$
$131$	−20.4530			−1.78698			−0.893492	+	0.449079i	$0.851752\pi$
$132$		0			0
$133$		0			0
$134$	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	0.913842	−	0.406071i	$-0.133101\pi$
$139$	1.24092	+	2.14933i	0.105253	+	0.182304i	−0.808588	+	0.588375i	$0.799768\pi$
$140$		0			0
$141$		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			0
$155$	1.78533	−	3.09228i	0.143401	−	0.248378i
$156$		0			0
$157$	3.16074	−	5.47457i	0.252255	−	0.436918i	−0.711891	−	0.702289i	$-0.752161\pi$
$157$	3.16074	−	5.47457i	0.252255	−	0.436918i	0.964146	+	0.265371i	$0.0854946\pi$
$158$	−0.618353	+	1.07102i	−0.0491936	+	0.0852057i
$159$		0			0
$160$	4.11070	−	7.11993i	0.324979	−	0.562880i
$161$		0			0
$162$		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	0.904132	−	0.427253i	$-0.140518\pi$
$167$	1.06038	+	1.83663i	0.0820545	+	0.142123i	−0.822078	+	0.569375i	$0.807185\pi$
$168$		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	$0.0780212\pi$
$173$	9.14404	+	15.8379i	0.695208	+	1.20414i	−0.274902	+	0.961472i	$0.588646\pi$
$174$		0			0
$175$		0			0
$176$	−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	$-0.695850\pi$
$181$	−15.5305			−1.15438			−0.577188	+	0.816611i	$0.695850\pi$
$182$		0			0
$183$		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
$196$		0			0
$197$	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	$0.186927\pi$
$199$	12.6407	+	21.8943i	0.896076	+	1.55205i	0.0636081	+	0.997975i	$0.479739\pi$
$200$	−7.06789			−0.499775
$201$		0			0
$202$	−1.72121	−	2.98123i	−0.121104	−	0.209758i
$203$		0			0
$204$		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
$217$		0			0
$218$	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	−0.997276	−	0.0737638i	$-0.976499\pi$
$223$	−6.49230	+	11.2450i	−0.434757	+	0.753020i	0.562519	+	0.826784i	$0.309832\pi$
$224$		0			0
$225$		0			0
$226$	−0.201335	+	0.348723i	−0.0133926	+	0.0231967i
$227$	−28.9665			−1.92257			−0.961286	−	0.275551i	$-0.911140\pi$
$227$	−28.9665			−1.92257			−0.961286	+	0.275551i	$0.911140\pi$
$228$		0			0
$229$	−15.4358			−1.02003			−0.510013	−	0.860167i	$-0.670360\pi$
$229$	−15.4358			−1.02003			−0.510013	+	0.860167i	$0.670360\pi$
$230$	−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
$238$		0			0
$239$	−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	$-0.655627\pi$
$241$	−14.5825			−0.939339			−0.469670	+	0.882842i	$0.655627\pi$
$242$	4.46191	+	7.72826i	0.286823	+	0.496791i
$243$		0			0
$244$	0.116709			0.00747154
$245$		0			0
$246$		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	$-0.646474\pi$
$251$	−14.0715			−0.888187			−0.444094	+	0.895980i	$0.646474\pi$
$252$		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	$-0.583989\pi$
$257$	−8.36215			−0.521617			−0.260808	+	0.965391i	$0.583989\pi$
$258$		0			0
$259$		0			0
$260$	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
$266$		0			0
$267$		0			0
$268$	−9.75958	−	16.9041i	−0.596161	−	1.03258i
$269$	−7.69349	−	13.3255i	−0.469081	−	0.812471i	0.530295	−	0.847813i	$-0.322081\pi$
$269$	−7.69349	−	13.3255i	−0.469081	−	0.812471i	−0.999375	+	0.0353420i	$0.988748\pi$
$270$		0			0
$271$	−4.06308	+	7.03747i	−0.246815	+	0.427496i	−0.962640	−	0.270783i	$-0.912717\pi$
$271$	−4.06308	+	7.03747i	−0.246815	+	0.427496i	0.715825	+	0.698279i	$0.246051\pi$
$272$	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
$280$		0			0
$281$	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	$0.340104\pi$
$283$	−8.71926	+	15.1022i	−0.518306	+	0.897732i	−0.999774	+	0.0212686i	$0.993229\pi$
$284$	−0.0624100	+	0.108097i	−0.00370335	+	0.00641440i
$285$		0			0
$286$	−4.55234	+	7.88489i	−0.269186	+	0.466243i
$287$		0			0
$288$		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	0.838537	−	0.544845i	$-0.183412\pi$
$293$	−0.900048	−	1.55893i	−0.0525814	−	0.0910736i	−0.891118	+	0.453772i	$0.850078\pi$
$294$		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
$301$		0			0
$302$	−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	$-0.509673\pi$
$307$	−1.06478			−0.0607699			−0.0303850	+	0.999538i	$0.509673\pi$
$308$		0			0
$309$		0			0
$310$	2.39353			0.135943
$311$	8.46463	−	14.6612i	0.479985	−	0.831359i	−0.519751	−	0.854318i	$-0.673975\pi$
$311$	8.46463	−	14.6612i	0.479985	−	0.831359i	0.999736	+	0.0229591i	$0.00730874\pi$
$312$		0			0
$313$	−4.13928	−	7.16944i	−0.233966	−	0.405241i	0.725006	−	0.688743i	$-0.241837\pi$
$313$	−4.13928	−	7.16944i	−0.233966	−	0.405241i	−0.958972	+	0.283502i	$0.908504\pi$
$314$	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			0
$323$	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
$329$		0			0
$330$		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
$343$		0			0
$344$	−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	$-0.535051\pi$
$349$	15.0542	−	26.0747i	0.805834	−	1.39574i	0.915727	−	0.401801i	$-0.131616\pi$
$350$		0			0
$351$		0			0
$352$	14.2244	−	24.6374i	0.758164	−	1.31318i
$353$	6.25933			0.333150			0.166575	−	0.986029i	$-0.446729\pi$
$353$	6.25933			0.333150			0.166575	+	0.986029i	$0.446729\pi$
$354$		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
$364$		0			0
$365$	−7.61701	−	13.1931i	−0.398693	−	0.690556i
$366$		0			0
$367$	28.6557			1.49581			0.747906	−	0.663804i	$-0.231059\pi$
$367$	28.6557			1.49581			0.747906	+	0.663804i	$0.231059\pi$
$368$	4.09332	+	7.08984i	0.213379	+	0.369584i
$369$		0			0
$370$	1.35595			0.0704926
$371$		0			0
$372$		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	$-0.595660\pi$
$383$	−11.5865			−0.592044			−0.296022	+	0.955181i	$0.595660\pi$
$384$		0			0
$385$		0			0
$386$	−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
$392$		0			0
$393$		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	−0.653836	−	0.756636i	$-0.726841\pi$
$397$	6.54229	−	11.3316i	0.328348	−	0.568715i	0.982184	+	0.187921i	$0.0601748\pi$
$398$	−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
$406$		0			0
$407$	3.49980	−	6.06183i	0.173479	−	0.300474i
$408$		0			0
$409$	−1.32300	+	2.29150i	−0.0654179	+	0.113307i	−0.896879	−	0.442275i	$-0.854171\pi$
$409$	−1.32300	+	2.29150i	−0.0654179	+	0.113307i	0.831461	+	0.555583i	$0.187505\pi$
$410$	−0.118810	+	0.205784i	−0.00586759	+	0.0101630i
$411$		0			0
$412$	11.0183	−	19.0843i	0.542835	−	0.940217i
$413$		0			0
$414$		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	$0.138593\pi$
$419$	16.7567	+	29.0235i	0.818619	+	1.41789i	−0.0880816	+	0.996113i	$0.528074\pi$
$420$		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			0
$428$	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	$-0.541990\pi$
$433$	−5.47404			−0.263066			−0.131533	+	0.991312i	$0.541990\pi$
$434$		0			0
$435$		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	0.932213	−	0.361911i	$-0.117875\pi$
$439$	3.19906	+	5.54093i	0.152683	+	0.264454i	−0.779530	+	0.626365i	$0.784542\pi$
$440$	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
$448$		0			0
$449$	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			0
$456$		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	−0.936657	−	0.350249i	$-0.886097\pi$
$461$	−3.54278	+	6.13627i	−0.165004	+	0.285794i	0.771653	+	0.636044i	$0.219430\pi$
$462$		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	−0.817049	−	0.576568i	$-0.804392\pi$
$467$	1.96216	−	3.39856i	0.0907978	−	0.157266i	0.907847	+	0.419301i	$0.137725\pi$
$468$		0			0
$469$		0			0
$470$	−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
$476$		0			0
$477$		0			0
$478$	4.36878	−	7.56694i	0.199823	−	0.346104i
$479$	16.0865			0.735010			0.367505	−	0.930022i	$-0.380212\pi$
$479$	16.0865			0.735010			0.367505	+	0.930022i	$0.380212\pi$
$480$		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
$490$		0			0
$491$	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			0
$498$		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	$-0.337970\pi$
$503$	21.8595			0.974665			0.487332	+	0.873217i	$0.337970\pi$
$504$		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	$-0.377826\pi$
$509$	16.8966			0.748930			0.374465	+	0.927241i	$0.377826\pi$
$510$		0			0
$511$		0			0
$512$	−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
$518$		0			0
$519$		0			0
$520$	4.67115	+	8.09067i	0.204843	+	0.354799i
$521$	−17.2466	−	29.8720i	−0.755587	−	1.30872i	−0.945082	−	0.326834i	$-0.894018\pi$
$521$	−17.2466	−	29.8720i	−0.755587	−	1.30872i	0.189495	−	0.981882i	$-0.439315\pi$
$522$		0			0
$523$	−0.995615	+	1.72445i	−0.0435352	+	0.0754051i	−0.886972	−	0.461823i	$-0.847195\pi$
$523$	−0.995615	+	1.72445i	−0.0435352	+	0.0754051i	0.843437	+	0.537229i	$0.180529\pi$
$524$	−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			0
$533$	−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
$539$		0			0
$540$		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			0
$554$	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			0
$561$		0			0
$562$	0.970751			0.0409487
$563$	−2.27942	+	3.94808i	−0.0960663	+	0.166392i	−0.910053	−	0.414492i	$-0.863959\pi$
$563$	−2.27942	+	3.94808i	−0.0960663	+	0.166392i	0.813987	+	0.580883i	$0.197293\pi$
$564$		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			0
$575$	16.1443			0.673264
$576$		0			0
$577$	5.70473	+	9.88088i	0.237491	+	0.411346i	0.959994	−	0.280022i	$-0.0903417\pi$
$577$	5.70473	+	9.88088i	0.237491	+	0.411346i	−0.722503	+	0.691368i	$0.757008\pi$
$578$	10.5553			0.439041
$579$		0			0
$580$	7.52485	+	13.0334i	0.312452	+	0.541183i
$581$		0			0
$582$		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	−0.809190	−	0.587548i	$-0.800094\pi$
$587$	2.52544	−	4.37420i	0.104236	−	0.180543i	0.913426	+	0.407005i	$0.133427\pi$
$588$		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	−0.994911	−	0.100759i	$-0.967873\pi$
$593$	−9.98892	+	17.3013i	−0.410196	+	0.710480i	0.584715	+	0.811239i	$0.301206\pi$
$594$		0			0
$595$		0			0
$596$	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	−0.999993	−	0.00375637i	$-0.998804\pi$
$601$	−12.1778	+	21.0926i	−0.496743	+	0.860385i	0.503250	+	0.864141i	$0.332138\pi$
$602$		0			0
$603$		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	$-0.585826\pi$
$607$	−13.1256			−0.532752			−0.266376	+	0.963869i	$0.585826\pi$
$608$	−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
$616$		0			0
$617$	−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	$-0.721692\pi$
$619$	−31.9212			−1.28302			−0.641511	+	0.767114i	$0.721692\pi$
$620$	−2.76843	−	4.79506i	−0.111183	−	0.192574i
$621$		0			0
$622$	11.3482			0.455023
$623$		0			0
$624$		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
$637$		0			0
$638$	−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	0.715400	−	0.698715i	$-0.246244\pi$
$643$	−6.27355	−	10.8661i	−0.247405	−	0.428517i	−0.962805	+	0.270198i	$0.912911\pi$
$644$		0			0
$645$		0			0
$646$	1.50676	+	2.60979i	0.0592827	+	0.102681i
$647$	17.2774	+	29.9253i	0.679245	+	1.17649i	0.975209	+	0.221287i	$0.0710258\pi$
$647$	17.2774	+	29.9253i	0.679245	+	1.17649i	−0.295964	+	0.955199i	$0.595641\pi$
$648$		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
$658$		0			0
$659$	−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	$-0.519134\pi$
$661$	21.4530	−	37.1577i	0.834425	−	1.44527i	0.894498	−	0.447072i	$-0.147533\pi$
$662$	−8.95760	+	15.5150i	−0.348147	+	0.603008i
$663$		0			0
$664$	−17.2221	+	29.8296i	−0.668349	+	1.15761i
$665$		0			0
$666$		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	$0.00242380\pi$
$677$	13.1808	+	22.8298i	0.506580	+	0.877422i	−0.493391	+	0.869808i	$0.664243\pi$
$678$		0			0
$679$		0			0
$680$	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
$686$		0			0
$687$		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	0.990849	−	0.134972i	$-0.0430944\pi$
$691$	9.95052	+	17.2348i	0.378536	+	0.655643i	−0.612314	+	0.790615i	$0.709761\pi$
$692$	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
$700$		0			0
$701$	−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
$707$		0			0
$708$		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	$0.426024\pi$
$719$	−19.5096	+	33.7917i	−0.727586	+	1.26022i	−0.957901	+	0.287100i	$0.907309\pi$
$720$		0			0
$721$		0			0
$722$	−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	−0.578242	−	0.815865i	$-0.696261\pi$
$727$	11.2554	−	19.4949i	0.417439	−	0.723025i	0.995681	+	0.0928402i	$0.0295946\pi$
$728$		0			0
$729$		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	$-0.494726\pi$
$733$	0.897039			0.0331329			0.0165664	+	0.999863i	$0.494726\pi$
$734$	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
$742$		0			0
$743$	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
$749$		0			0
$750$		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	$-0.235749\pi$
$761$	40.7197			1.47609			0.738044	+	0.674752i	$0.235749\pi$
$762$		0			0
$763$		0			0
$764$	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	0.747853	−	0.663864i	$-0.231085\pi$
$769$	−5.57381	−	9.65413i	−0.200997	−	0.348137i	−0.948850	+	0.315728i	$0.897751\pi$
$770$		0			0
$771$		0			0
$772$	12.8454	+	22.2489i	0.462317	+	0.800756i
$773$	−0.462831	−	0.801647i	−0.0166469	−	0.0288332i	0.857582	−	0.514347i	$-0.171966\pi$
$773$	−0.462831	−	0.801647i	−0.0166469	−	0.0288332i	−0.874229	+	0.485514i	$0.838632\pi$
$774$		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
$784$		0			0
$785$	4.50386	−	7.80092i	0.160750	−	0.278427i
$786$		0			0
$787$	11.5120	−	19.9393i	0.410358	−	0.710761i	−0.584571	−	0.811343i	$-0.698737\pi$
$787$	11.5120	−	19.9393i	0.410358	−	0.710761i	0.994929	+	0.100582i	$0.0320704\pi$
$788$	3.13030	−	5.42184i	0.111512	−	0.193145i
$789$		0			0
$790$	−0.881115	+	1.52614i	−0.0313487	+	0.0542975i
$791$		0			0
$792$		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	0.994151	−	0.108000i	$-0.0344447\pi$
$797$	11.3925	+	19.7325i	0.403544	+	0.698960i	−0.590606	+	0.806960i	$0.701111\pi$
$798$		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
$805$		0			0
$806$	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	$-0.318567\pi$
$811$	30.7348			1.07924			0.539622	+	0.841907i	$0.318567\pi$
$812$		0			0
$813$		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
$826$		0			0
$827$	−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	0.770839	−	0.637030i	$-0.219837\pi$
$829$	−4.78717	−	8.29161i	−0.166265	−	0.287980i	−0.937104	+	0.349051i	$0.886504\pi$
$830$	−13.8231			−0.479806
$831$		0			0
$832$	1.17885	+	2.04183i	0.0408693	+	0.0707877i
$833$		0			0
$834$		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	$-0.571475\pi$
$839$	21.2303	−	36.7720i	0.732952	−	1.26951i	0.955616	−	0.294615i	$-0.0951913\pi$
$840$		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
$847$		0			0
$848$	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	−0.961986	−	0.273099i	$-0.911951\pi$
$853$	−7.14039	+	12.3675i	−0.244482	+	0.423456i	0.717504	+	0.696555i	$0.245285\pi$
$854$		0			0
$855$		0			0
$856$	−9.11621	+	15.7897i	−0.311586	+	0.539682i
$857$	34.7790			1.18803			0.594013	−	0.804455i	$-0.297543\pi$
$857$	34.7790			1.18803			0.594013	+	0.804455i	$0.297543\pi$
$858$		0			0
$859$	12.6486			0.431564			0.215782	−	0.976442i	$-0.430770\pi$
$859$	12.6486			0.431564			0.215782	+	0.976442i	$0.430770\pi$
$860$	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			0
$869$	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
$875$		0			0
$876$		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	$-0.611455\pi$
$881$	−20.3637			−0.686071			−0.343036	+	0.939322i	$0.611455\pi$
$882$		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	$-0.522554\pi$
$887$	−4.21692			−0.141590			−0.0707952	+	0.997491i	$0.522554\pi$
$888$		0			0
$889$		0			0
$890$	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
$896$		0			0
$897$		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
$910$		0			0
$911$	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
$917$		0			0
$918$		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	$-0.895689\pi$
$929$	−22.9248	−	39.7069i	−0.752138	−	1.30274i	0.194647	−	0.980873i	$-0.437644\pi$
$930$		0			0
$931$		0			0
$932$	−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	$-0.129715\pi$
$937$	56.2075			1.83622			0.918110	+	0.396325i	$0.129715\pi$
$938$		0			0
$939$		0			0
$940$	20.9376			0.682908
$941$	17.6402	−	30.5536i	0.575053	−	0.996020i	−0.420983	−	0.907068i	$-0.638315\pi$
$941$	17.6402	−	30.5536i	0.575053	−	0.996020i	0.996036	−	0.0889519i	$-0.0283517\pi$
$942$		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			0
$953$	−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
$959$		0			0
$960$		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	−0.922696	−	0.385530i	$-0.874019\pi$
$971$	−3.97206	+	6.87981i	−0.127469	+	0.220783i	0.795226	+	0.606313i	$0.207352\pi$
$972$		0			0
$973$		0			0
$974$	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
$980$		0			0
$981$		0			0
$982$	−13.7784	+	23.8650i	−0.439688	+	0.761562i
$983$	−38.8379			−1.23874			−0.619369	−	0.785100i	$-0.712611\pi$
$983$	−38.8379			−1.23874			−0.619369	+	0.785100i	$0.712611\pi$
$984$		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			0
$995$	18.0122	+	31.1981i	0.571025	+	0.989045i
$996$		0			0
$997$	−47.0670			−1.49063			−0.745313	−	0.666714i	$-0.767700\pi$
$997$	−47.0670			−1.49063			−0.745313	+	0.666714i	$0.767700\pi$
$998$	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	1323.2.g.f.667.4		10
3.2	odd	2		441.2.g.f.79.2		10
7.2	even	3		1323.2.f.f.883.4		10
7.3	odd	6		189.2.h.b.46.2		10
7.4	even	3		1323.2.h.f.802.2		10
7.5	odd	6		1323.2.f.e.883.4		10
7.6	odd	2		189.2.g.b.100.4		10
9.4	even	3		1323.2.h.f.226.2		10
9.5	odd	6		441.2.h.f.373.4		10
21.2	odd	6		441.2.f.f.295.2		10
21.5	even	6		441.2.f.e.295.2		10
21.11	odd	6		441.2.h.f.214.4		10
21.17	even	6		63.2.h.b.25.4	yes	10
21.20	even	2		63.2.g.b.16.2	yes	10
28.3	even	6		3024.2.q.i.2881.5		10
28.27	even	2		3024.2.t.i.289.1		10
63.2	odd	6		3969.2.a.ba.1.4		5
63.4	even	3	inner	1323.2.g.f.361.4		10
63.5	even	6		441.2.f.e.148.2		10
63.13	odd	6		189.2.h.b.37.2		10
63.16	even	3		3969.2.a.bb.1.2		5
63.20	even	6		567.2.e.f.163.2		10
63.23	odd	6		441.2.f.f.148.2		10
63.31	odd	6		189.2.g.b.172.4		10
63.32	odd	6		441.2.g.f.67.2		10
63.34	odd	6		567.2.e.e.163.4		10
63.38	even	6		567.2.e.f.487.2		10
63.40	odd	6		1323.2.f.e.442.4		10
63.41	even	6		63.2.h.b.58.4	yes	10
63.47	even	6		3969.2.a.z.1.4		5
63.52	odd	6		567.2.e.e.487.4		10
63.58	even	3		1323.2.f.f.442.4		10
63.59	even	6		63.2.g.b.4.2	✓	10
63.61	odd	6		3969.2.a.bc.1.2		5
84.59	odd	6		1008.2.q.i.529.1		10
84.83	odd	2		1008.2.t.i.961.4		10
252.31	even	6		3024.2.t.i.1873.1		10
252.59	odd	6		1008.2.t.i.193.4		10
252.139	even	6		3024.2.q.i.2305.5		10
252.167	odd	6		1008.2.q.i.625.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.g.b.4.2	✓	10	63.59	even	6
63.2.g.b.16.2	yes	10	21.20	even	2
63.2.h.b.25.4	yes	10	21.17	even	6
63.2.h.b.58.4	yes	10	63.41	even	6
189.2.g.b.100.4		10	7.6	odd	2
189.2.g.b.172.4		10	63.31	odd	6
189.2.h.b.37.2		10	63.13	odd	6
189.2.h.b.46.2		10	7.3	odd	6
441.2.f.e.148.2		10	63.5	even	6
441.2.f.e.295.2		10	21.5	even	6
441.2.f.f.148.2		10	63.23	odd	6
441.2.f.f.295.2		10	21.2	odd	6
441.2.g.f.67.2		10	63.32	odd	6
441.2.g.f.79.2		10	3.2	odd	2
441.2.h.f.214.4		10	21.11	odd	6
441.2.h.f.373.4		10	9.5	odd	6
567.2.e.e.163.4		10	63.34	odd	6
567.2.e.e.487.4		10	63.52	odd	6
567.2.e.f.163.2		10	63.20	even	6
567.2.e.f.487.2		10	63.38	even	6
1008.2.q.i.529.1		10	84.59	odd	6
1008.2.q.i.625.1		10	252.167	odd	6
1008.2.t.i.193.4		10	252.59	odd	6
1008.2.t.i.961.4		10	84.83	odd	2
1323.2.f.e.442.4		10	63.40	odd	6
1323.2.f.e.883.4		10	7.5	odd	6
1323.2.f.f.442.4		10	63.58	even	3
1323.2.f.f.883.4		10	7.2	even	3
1323.2.g.f.361.4		10	63.4	even	3	inner
1323.2.g.f.667.4		10	1.1	even	1	trivial
1323.2.h.f.226.2		10	9.4	even	3
1323.2.h.f.802.2		10	7.4	even	3
3024.2.q.i.2305.5		10	252.139	even	6
3024.2.q.i.2881.5		10	28.3	even	6
3024.2.t.i.289.1		10	28.27	even	2
3024.2.t.i.1873.1		10	252.31	even	6
3969.2.a.z.1.4		5	63.47	even	6
3969.2.a.ba.1.4		5	63.2	odd	6
3969.2.a.bb.1.2		5	63.16	even	3
3969.2.a.bc.1.2		5	63.61	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1323 = 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1323.g (of order \(3\), degree \(2\), not minimal)

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

Introduction

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