LMFDB - Embedded newform 243.2.e.a.55.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [243,2,Mod(28,243)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(243, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("243.28");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 243 = 3^{5} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	243.e (of order $9$, degree $6$, 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:	$1.94036476912$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	12.0.1952986685049.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 27 x^{10} - 80 x^{9} + 186 x^{8} - 330 x^{7} + 463 x^{6} - 504 x^{5} + 420 x^{4} + \cdots + 3 $ x^12 - 6x^11 + 27x^10 - 80x^9 + 186x^8 - 330x^7 + 463x^6 - 504x^5 + 420x^4 - 258x^3 + 108x^2 - 27*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			55.2
Root			$0.500000 - 1.68614i$ of defining polynomial
Character	$\chi$	$=$	243.55
Dual form			243.2.e.a.190.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.990741 - 0.360600i) q^{2} +(-0.680553 + 0.571052i) q^{4} +(0.303153 + 1.71926i) q^{5} +(1.88389 + 1.58077i) q^{7} +(-1.52266 + 2.63732i) q^{8} +O(q^{10})$	\(q+(0.990741 - 0.360600i) q^{2} +(-0.680553 + 0.571052i) q^{4} +(0.303153 + 1.71926i) q^{5} +(1.88389 + 1.58077i) q^{7} +(-1.52266 + 2.63732i) q^{8} +(0.920313 + 1.59403i) q^{10} +(0.217792 - 1.23516i) q^{11} +(4.27469 + 1.55586i) q^{13} +(2.43648 + 0.886805i) q^{14} +(-0.249003 + 1.41216i) q^{16} +(-3.32358 - 5.75662i) q^{17} +(-0.124578 + 0.215776i) q^{19} +(-1.18810 - 0.996935i) q^{20} +(-0.229623 - 1.30226i) q^{22} +(-0.645010 + 0.541228i) q^{23} +(1.83449 - 0.667701i) q^{25} +4.79615 q^{26} -2.18479 q^{28} +(-0.481483 + 0.175245i) q^{29} +(-0.628159 + 0.527088i) q^{31} +(-0.795096 - 4.50921i) q^{32} +(-5.36865 - 4.50483i) q^{34} +(-2.14666 + 3.71812i) q^{35} +(-1.30403 - 2.25865i) q^{37} +(-0.0456159 + 0.258701i) q^{38} +(-4.99584 - 1.81834i) q^{40} +(-7.66114 - 2.78843i) q^{41} +(0.751401 - 4.26141i) q^{43} +(0.557121 + 0.964962i) q^{44} +(-0.443871 + 0.768808i) q^{46} +(4.06182 + 3.40828i) q^{47} +(-0.165332 - 0.937642i) q^{49} +(1.57674 - 1.32304i) q^{50} +(-3.79763 + 1.38222i) q^{52} +10.4841 q^{53} +2.18959 q^{55} +(-7.03752 + 2.56145i) q^{56} +(-0.413831 + 0.347246i) q^{58} +(0.522022 + 2.96053i) q^{59} +(2.20864 + 1.85327i) q^{61} +(-0.432275 + 0.748722i) q^{62} +(-3.84771 - 6.66442i) q^{64} +(-1.37905 + 7.82099i) q^{65} +(-9.47799 - 3.44971i) q^{67} +(5.54920 + 2.01975i) q^{68} +(-0.786028 + 4.45779i) q^{70} +(0.0447378 + 0.0774882i) q^{71} +(2.66057 - 4.60824i) q^{73} +(-2.10643 - 1.76750i) q^{74} +(-0.0384370 - 0.217987i) q^{76} +(2.36280 - 1.98263i) q^{77} +(-4.48884 + 1.63380i) q^{79} -2.50337 q^{80} -8.59571 q^{82} +(7.55575 - 2.75007i) q^{83} +(8.88960 - 7.45926i) q^{85} +(-0.792220 - 4.49291i) q^{86} +(2.92588 + 2.45511i) q^{88} +(3.35189 - 5.80564i) q^{89} +(5.59359 + 9.68839i) q^{91} +(0.129895 - 0.736669i) q^{92} +(5.25324 + 1.91202i) q^{94} +(-0.408742 - 0.148770i) q^{95} +(0.953429 - 5.40716i) q^{97} +(-0.501915 - 0.869342i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{2} + 3 q^{4} - 6 q^{5} + 3 q^{7} - 6 q^{8}+O(q^{10}) $ 12 * q - 3 * q^2 + 3 * q^4 - 6 * q^5 + 3 * q^7 - 6 * q^8	$ 12 q - 3 q^{2} + 3 q^{4} - 6 q^{5} + 3 q^{7} - 6 q^{8} - 3 q^{10} + 6 q^{11} + 3 q^{13} + 21 q^{14} + 9 q^{16} - 9 q^{17} - 3 q^{19} - 24 q^{20} + 12 q^{22} + 12 q^{23} + 12 q^{25} + 30 q^{26} - 12 q^{28} + 24 q^{29} + 12 q^{31} - 27 q^{32} - 12 q^{35} - 3 q^{37} + 30 q^{38} - 15 q^{40} - 6 q^{41} - 15 q^{43} - 3 q^{44} - 3 q^{46} - 12 q^{47} - 33 q^{49} - 21 q^{50} - 45 q^{52} + 18 q^{53} - 12 q^{55} - 30 q^{56} - 51 q^{58} + 3 q^{59} - 33 q^{61} + 12 q^{62} + 12 q^{64} - 21 q^{65} - 6 q^{67} - 9 q^{68} - 15 q^{70} - 27 q^{71} + 6 q^{73} + 21 q^{74} + 6 q^{76} + 12 q^{77} + 21 q^{79} - 42 q^{80} - 12 q^{82} + 6 q^{83} + 36 q^{85} + 21 q^{86} + 42 q^{88} - 9 q^{89} + 6 q^{91} + 3 q^{92} + 48 q^{94} - 3 q^{95} + 39 q^{97} + 45 q^{98}+O(q^{100}) $ 12 * q - 3 * q^2 + 3 * q^4 - 6 * q^5 + 3 * q^7 - 6 * q^8 - 3 * q^10 + 6 * q^11 + 3 * q^13 + 21 * q^14 + 9 * q^16 - 9 * q^17 - 3 * q^19 - 24 * q^20 + 12 * q^22 + 12 * q^23 + 12 * q^25 + 30 * q^26 - 12 * q^28 + 24 * q^29 + 12 * q^31 - 27 * q^32 - 12 * q^35 - 3 * q^37 + 30 * q^38 - 15 * q^40 - 6 * q^41 - 15 * q^43 - 3 * q^44 - 3 * q^46 - 12 * q^47 - 33 * q^49 - 21 * q^50 - 45 * q^52 + 18 * q^53 - 12 * q^55 - 30 * q^56 - 51 * q^58 + 3 * q^59 - 33 * q^61 + 12 * q^62 + 12 * q^64 - 21 * q^65 - 6 * q^67 - 9 * q^68 - 15 * q^70 - 27 * q^71 + 6 * q^73 + 21 * q^74 + 6 * q^76 + 12 * q^77 + 21 * q^79 - 42 * q^80 - 12 * q^82 + 6 * q^83 + 36 * q^85 + 21 * q^86 + 42 * q^88 - 9 * q^89 + 6 * q^91 + 3 * q^92 + 48 * q^94 - 3 * q^95 + 39 * q^97 + 45 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/243\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{8}{9}\right)$

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 $

$2$	0.990741	−	0.360600i	0.700560	−	0.254983i	0.0329100	−	0.999458i	$-0.489523\pi$
$2$	0.990741	−	0.360600i	0.700560	−	0.254983i	0.667650	+	0.744475i	$0.267300\pi$
$3$		0			0
$3$		0			0
$4$	−0.680553	+	0.571052i	−0.340277	+	0.285526i
$5$	0.303153	+	1.71926i	0.135574	+	0.768879i	0.974458	+	0.224569i	$0.0720973\pi$
$5$	0.303153	+	1.71926i	0.135574	+	0.768879i	−0.838884	+	0.544310i	$0.816792\pi$
$6$		0			0
$7$	1.88389	+	1.58077i	0.712044	+	0.597476i	0.925172	−	0.379548i	$-0.123921\pi$
$7$	1.88389	+	1.58077i	0.712044	+	0.597476i	−0.213128	+	0.977024i	$0.568365\pi$
$8$	−1.52266	+	2.63732i	−0.538340	+	0.932432i
$9$		0			0
$10$	0.920313	+	1.59403i	0.291029	+	0.504076i
$11$	0.217792	−	1.23516i	0.0656667	−	0.372414i	−0.934210	−	0.356723i	$-0.883894\pi$
$11$	0.217792	−	1.23516i	0.0656667	−	0.372414i	0.999877	−	0.0156913i	$-0.00499490\pi$
$12$		0			0
$13$	4.27469	+	1.55586i	1.18559	+	0.431518i	0.858171	−	0.513363i	$-0.171601\pi$
$13$	4.27469	+	1.55586i	1.18559	+	0.431518i	0.327414	+	0.944881i	$0.393823\pi$
$14$	2.43648	+	0.886805i	0.651176	+	0.237009i
$15$		0			0
$16$	−0.249003	+	1.41216i	−0.0622506	+	0.353041i
$17$	−3.32358	−	5.75662i	−0.806088	−	1.39618i	−0.915554	−	0.402194i	$-0.868248\pi$
$17$	−3.32358	−	5.75662i	−0.806088	−	1.39618i	0.109467	−	0.993990i	$-0.465086\pi$
$18$		0			0
$19$	−0.124578	+	0.215776i	−0.0285802	+	0.0495023i	−0.879962	−	0.475045i	$-0.842432\pi$
$19$	−0.124578	+	0.215776i	−0.0285802	+	0.0495023i	0.851382	+	0.524547i	$0.175765\pi$
$20$	−1.18810	−	0.996935i	−0.265667	−	0.222921i
$21$		0			0
$22$	−0.229623	−	1.30226i	−0.0489559	−	0.277642i
$23$	−0.645010	+	0.541228i	−0.134494	+	0.112854i	−0.707553	−	0.706660i	$-0.750201\pi$
$23$	−0.645010	+	0.541228i	−0.134494	+	0.112854i	0.573059	+	0.819514i	$0.305757\pi$
$24$		0			0
$25$	1.83449	−	0.667701i	0.366899	−	0.133540i
$26$	4.79615			0.940603
$27$		0			0
$28$	−2.18479			−0.412887
$29$	−0.481483	+	0.175245i	−0.0894091	+	0.0325422i	−0.386337	−	0.922358i	$-0.626260\pi$
$29$	−0.481483	+	0.175245i	−0.0894091	+	0.0325422i	0.296928	+	0.954900i	$0.404038\pi$
$30$		0			0
$31$	−0.628159	+	0.527088i	−0.112821	+	0.0946678i	−0.697453	−	0.716631i	$-0.745683\pi$
$31$	−0.628159	+	0.527088i	−0.112821	+	0.0946678i	0.584632	+	0.811299i	$0.301239\pi$
$32$	−0.795096	−	4.50921i	−0.140554	−	0.797124i
$33$		0			0
$34$	−5.36865	−	4.50483i	−0.920716	−	0.772572i
$35$	−2.14666	+	3.71812i	−0.362852	+	0.628478i
$36$		0			0
$37$	−1.30403	−	2.25865i	−0.214381	−	0.371319i	0.738700	−	0.674035i	$-0.235440\pi$
$37$	−1.30403	−	2.25865i	−0.214381	−	0.371319i	−0.953081	+	0.302715i	$0.902107\pi$
$38$	−0.0456159	+	0.258701i	−0.00739988	+	0.0419668i
$39$		0			0
$40$	−4.99584	−	1.81834i	−0.789912	−	0.287504i
$41$	−7.66114	−	2.78843i	−1.19647	−	0.435479i	−0.334478	−	0.942403i	$-0.608560\pi$
$41$	−7.66114	−	2.78843i	−1.19647	−	0.435479i	−0.861991	+	0.506924i	$0.830782\pi$
$42$		0			0
$43$	0.751401	−	4.26141i	0.114588	−	0.649858i	−0.872366	−	0.488853i	$-0.837415\pi$
$43$	0.751401	−	4.26141i	0.114588	−	0.649858i	0.986954	−	0.161005i	$-0.0514735\pi$
$44$	0.557121	+	0.964962i	0.0839891	+	0.145473i
$45$		0			0
$46$	−0.443871	+	0.768808i	−0.0654452	+	0.113354i
$47$	4.06182	+	3.40828i	0.592478	+	0.497148i	0.889018	−	0.457872i	$-0.151388\pi$
$47$	4.06182	+	3.40828i	0.592478	+	0.497148i	−0.296540	+	0.955020i	$0.595833\pi$
$48$		0			0
$49$	−0.165332	−	0.937642i	−0.0236188	−	0.133949i
$50$	1.57674	−	1.32304i	0.222984	−	0.187106i
$51$		0			0
$52$	−3.79763	+	1.38222i	−0.526637	+	0.191680i
$53$	10.4841			1.44010			0.720052	−	0.693920i	$-0.244118\pi$
$53$	10.4841			1.44010			0.720052	+	0.693920i	$0.244118\pi$
$54$		0			0
$55$	2.18959			0.295244
$56$	−7.03752	+	2.56145i	−0.940428	+	0.342288i
$57$		0			0
$58$	−0.413831	+	0.347246i	−0.0543387	+	0.0455956i
$59$	0.522022	+	2.96053i	0.0679614	+	0.385428i	0.999749	+	0.0224233i	$0.00713815\pi$
$59$	0.522022	+	2.96053i	0.0679614	+	0.385428i	−0.931787	+	0.363005i	$0.881751\pi$
$60$		0			0
$61$	2.20864	+	1.85327i	0.282787	+	0.237287i	0.773137	−	0.634239i	$-0.218687\pi$
$61$	2.20864	+	1.85327i	0.282787	+	0.237287i	−0.490350	+	0.871526i	$0.663131\pi$
$62$	−0.432275	+	0.748722i	−0.0548990	+	0.0950878i
$63$		0			0
$64$	−3.84771	−	6.66442i	−0.480963	−	0.833053i
$65$	−1.37905	+	7.82099i	−0.171050	+	0.970074i
$66$		0			0
$67$	−9.47799	−	3.44971i	−1.15792	−	0.421449i	−0.309566	−	0.950878i	$-0.600184\pi$
$67$	−9.47799	−	3.44971i	−1.15792	−	0.421449i	−0.848354	+	0.529429i	$0.822406\pi$
$68$	5.54920	+	2.01975i	0.672940	+	0.244930i
$69$		0			0
$70$	−0.786028	+	4.45779i	−0.0939483	+	0.532807i
$71$	0.0447378	+	0.0774882i	0.00530940	+	0.00919615i	0.868668	−	0.495395i	$-0.164977\pi$
$71$	0.0447378	+	0.0774882i	0.00530940	+	0.00919615i	−0.863358	+	0.504591i	$0.831643\pi$
$72$		0			0
$73$	2.66057	−	4.60824i	0.311396	−	0.539354i	−0.667269	−	0.744817i	$-0.732537\pi$
$73$	2.66057	−	4.60824i	0.311396	−	0.539354i	0.978665	+	0.205463i	$0.0658701\pi$
$74$	−2.10643	−	1.76750i	−0.244867	−	0.205468i
$75$		0			0
$76$	−0.0384370	−	0.217987i	−0.00440903	−	0.0250049i
$77$	2.36280	−	1.98263i	0.269266	−	0.225941i
$78$		0			0
$79$	−4.48884	+	1.63380i	−0.505034	+	0.183817i	−0.581957	−	0.813220i	$-0.697713\pi$
$79$	−4.48884	+	1.63380i	−0.505034	+	0.183817i	0.0769231	+	0.997037i	$0.475490\pi$
$80$	−2.50337			−0.279885
$81$		0			0
$82$	−8.59571			−0.949238
$83$	7.55575	−	2.75007i	0.829351	−	0.301859i	0.107759	−	0.994177i	$-0.465633\pi$
$83$	7.55575	−	2.75007i	0.829351	−	0.301859i	0.721593	+	0.692318i	$0.243410\pi$
$84$		0			0
$85$	8.88960	−	7.45926i	0.964212	−	0.809070i
$86$	−0.792220	−	4.49291i	−0.0854273	−	0.484482i
$87$		0			0
$88$	2.92588	+	2.45511i	0.311900	+	0.261715i
$89$	3.35189	−	5.80564i	0.355299	−	0.615396i	−0.631870	−	0.775074i	$-0.717712\pi$
$89$	3.35189	−	5.80564i	0.355299	−	0.615396i	0.987169	+	0.159678i	$0.0510457\pi$
$90$		0			0
$91$	5.59359	+	9.68839i	0.586368	+	1.01562i
$92$	0.129895	−	0.736669i	0.0135424	−	0.0768030i
$93$		0			0
$94$	5.25324	+	1.91202i	0.541831	+	0.197210i
$95$	−0.408742	−	0.148770i	−0.0419360	−	0.0152635i
$96$		0			0
$97$	0.953429	−	5.40716i	0.0968060	−	0.549014i	−0.897373	−	0.441273i	$-0.854527\pi$
$97$	0.953429	−	5.40716i	0.0968060	−	0.549014i	0.994179	−	0.107741i	$-0.0343618\pi$
$98$	−0.501915	−	0.869342i	−0.0507010	−	0.0878168i
$99$		0			0
$100$	−0.867179	+	1.50200i	−0.0867179	+	0.150200i
$101$	−3.83441	−	3.21745i	−0.381538	−	0.320148i	0.431768	−	0.901985i	$-0.357890\pi$
$101$	−3.83441	−	3.21745i	−0.381538	−	0.320148i	−0.813306	+	0.581836i	$0.802334\pi$
$102$		0			0
$103$	2.01765	+	11.4426i	0.198805	+	1.12748i	0.906896	+	0.421356i	$0.138446\pi$
$103$	2.01765	+	11.4426i	0.198805	+	1.12748i	−0.708091	+	0.706121i	$0.750443\pi$
$104$	−10.6122	+	8.90467i	−1.04061	+	0.873175i
$105$		0			0
$106$	10.3870	−	3.78057i	1.00888	−	0.367202i
$107$	−19.4581			−1.88109			−0.940544	−	0.339673i	$-0.889684\pi$
$107$	−19.4581			−1.88109			−0.940544	+	0.339673i	$0.889684\pi$
$108$		0			0
$109$	6.31515			0.604881			0.302441	−	0.953168i	$-0.402199\pi$
$109$	6.31515			0.604881			0.302441	+	0.953168i	$0.402199\pi$
$110$	2.16932	−	0.789566i	0.206836	−	0.0752822i
$111$		0			0
$112$	−2.70140	+	2.26675i	−0.255259	+	0.214188i
$113$	1.20090	+	6.81066i	0.112971	+	0.640693i	0.987735	+	0.156142i	$0.0499058\pi$
$113$	1.20090	+	6.81066i	0.112971	+	0.640693i	−0.874763	+	0.484551i	$0.838983\pi$
$114$		0			0
$115$	−1.12605	−	0.944868i	−0.105005	−	0.0881094i
$116$	0.227600	−	0.394215i	0.0211322	−	0.0366020i
$117$		0			0
$118$	1.58476	+	2.74488i	0.145889	+	0.252687i
$119$	2.83863	−	16.0987i	0.260217	−	1.47576i
$120$		0			0
$121$	8.85844	+	3.22421i	0.805312	+	0.293110i
$122$	2.85648	+	1.03967i	0.258613	+	0.0941276i
$123$		0			0
$124$	0.126501	−	0.717423i	0.0113601	−	0.0644265i
$125$	6.06855	+	10.5110i	0.542788	+	0.940136i
$126$		0			0
$127$	−6.01162	+	10.4124i	−0.533445	+	0.923954i	0.465792	+	0.884894i	$0.345770\pi$
$127$	−6.01162	+	10.4124i	−0.533445	+	0.923954i	−0.999237	+	0.0390598i	$0.987564\pi$
$128$	0.799814	+	0.671124i	0.0706943	+	0.0593195i
$129$		0			0
$130$	1.45397	+	8.24586i	0.127521	+	0.723210i
$131$	10.7896	−	9.05353i	0.942690	−	0.791011i	−0.0353614	−	0.999375i	$-0.511258\pi$
$131$	10.7896	−	9.05353i	0.942690	−	0.791011i	0.978051	+	0.208364i	$0.0668138\pi$
$132$		0			0
$133$	−0.575784	+	0.209568i	−0.0499268	+	0.0181719i
$134$	−10.6342			−0.918655
$135$		0			0
$136$	20.2427			1.73580
$137$	2.12196	−	0.772329i	0.181291	−	0.0659846i	−0.249780	−	0.968303i	$-0.580358\pi$
$137$	2.12196	−	0.772329i	0.181291	−	0.0659846i	0.431071	+	0.902318i	$0.358136\pi$
$138$		0			0
$139$	−6.10928	+	5.12629i	−0.518182	+	0.434806i	−0.863997	−	0.503496i	$-0.832047\pi$
$139$	−6.10928	+	5.12629i	−0.518182	+	0.434806i	0.345815	+	0.938303i	$0.387602\pi$
$140$	−0.662326	−	3.75624i	−0.0559768	−	0.317460i
$141$		0			0
$142$	0.0722659	+	0.0606383i	0.00606442	+	0.00508865i
$143$	2.85273	−	4.94107i	0.238557	−	0.413193i
$144$		0			0
$145$	−0.447256	−	0.774670i	−0.0371426	−	0.0643328i
$146$	0.974203	−	5.52498i	0.0806256	−	0.457250i
$147$		0			0
$148$	2.17727	+	0.792461i	0.178970	+	0.0651399i
$149$	−0.100489	−	0.0365751i	−0.00823240	−	0.00299635i	0.337901	−	0.941182i	$-0.390283\pi$
$149$	−0.100489	−	0.0365751i	−0.00823240	−	0.00299635i	−0.346133	+	0.938185i	$0.612505\pi$
$150$		0			0
$151$	−3.51801	+	19.9516i	−0.286292	+	1.62364i	0.414344	+	0.910121i	$0.364011\pi$
$151$	−3.51801	+	19.9516i	−0.286292	+	1.62364i	−0.700635	+	0.713520i	$0.747100\pi$
$152$	−0.379379	−	0.657104i	−0.0307717	−	0.0532982i
$153$		0			0
$154$	1.62599	−	2.81630i	0.131026	−	0.226944i
$155$	−1.09663	−	0.920184i	−0.0880836	−	0.0739109i
$156$		0			0
$157$	−3.60317	−	20.4346i	−0.287564	−	1.63086i	−0.695979	−	0.718062i	$-0.745029\pi$
$157$	−3.60317	−	20.4346i	−0.287564	−	1.63086i	0.408415	−	0.912797i	$-0.366082\pi$
$158$	−3.85813	+	3.23735i	−0.306936	+	0.257550i
$159$		0			0
$160$	7.51149	−	2.73396i	0.593836	−	0.216139i
$161$	−2.07069			−0.163193
$162$		0			0
$163$	−20.1346			−1.57706			−0.788531	−	0.614995i	$-0.789158\pi$
$163$	−20.1346			−1.57706			−0.788531	+	0.614995i	$0.789158\pi$
$164$	6.80615	−	2.47724i	0.531471	−	0.193440i
$165$		0			0
$166$	6.49412	−	5.44921i	0.504041	−	0.422941i
$167$	3.44910	+	19.5608i	0.266900	+	1.51366i	0.763570	+	0.645724i	$0.223445\pi$
$167$	3.44910	+	19.5608i	0.266900	+	1.51366i	−0.496671	+	0.867939i	$0.665444\pi$
$168$		0			0
$169$	5.89369	+	4.94540i	0.453361	+	0.380415i
$170$	6.11748	−	10.5958i	0.469189	−	0.812660i
$171$		0			0
$172$	1.92212	+	3.32920i	0.146560	+	0.253849i
$173$	−3.28631	+	18.6376i	−0.249854	+	1.41699i	0.559091	+	0.829106i	$0.311150\pi$
$173$	−3.28631	+	18.6376i	−0.249854	+	1.41699i	−0.808945	+	0.587884i	$0.799961\pi$
$174$		0			0
$175$	4.51147	+	1.64204i	0.341035	+	0.124127i
$176$	1.69002	+	0.615115i	0.127390	+	0.0463661i
$177$		0			0
$178$	1.22734	−	6.96057i	0.0919928	−	0.521717i
$179$	5.45683	+	9.45151i	0.407863	+	0.706439i	0.994650	−	0.103302i	$-0.0329409\pi$
$179$	5.45683	+	9.45151i	0.407863	+	0.706439i	−0.586787	+	0.809741i	$0.699608\pi$
$180$		0			0
$181$	8.97393	−	15.5433i	0.667027	−	1.15532i	−0.311704	−	0.950179i	$-0.600900\pi$
$181$	8.97393	−	15.5433i	0.667027	−	1.15532i	0.978731	−	0.205146i	$-0.0657668\pi$
$182$	9.03544	+	7.58163i	0.669751	+	0.561988i
$183$		0			0
$184$	−0.445261	−	2.52520i	−0.0328251	−	0.186160i
$185$	3.48789	−	2.92669i	0.256435	−	0.215174i
$186$		0			0
$187$	−7.83419	+	2.85141i	−0.572892	+	0.208516i
$188$	−4.71059			−0.343555
$189$		0			0
$190$	−0.458604			−0.0332706
$191$	−25.3398	+	9.22293i	−1.83352	+	0.667348i	−0.841666	+	0.539998i	$0.818425\pi$
$191$	−25.3398	+	9.22293i	−1.83352	+	0.667348i	−0.991858	+	0.127350i	$0.959353\pi$
$192$		0			0
$193$	−13.1413	+	11.0269i	−0.945935	+	0.793734i	−0.978608	−	0.205733i	$-0.934042\pi$
$193$	−13.1413	+	11.0269i	−0.945935	+	0.793734i	0.0326735	+	0.999466i	$0.489598\pi$
$194$	−1.00522	−	5.70091i	−0.0721709	−	0.409301i
$195$		0			0
$196$	0.647959	+	0.543702i	0.0462828	+	0.0388359i
$197$	1.25612	−	2.17567i	0.0894951	−	0.155010i	−0.817803	−	0.575499i	$-0.804808\pi$
$197$	1.25612	−	2.17567i	0.0894951	−	0.155010i	0.907298	+	0.420489i	$0.138141\pi$
$198$		0			0
$199$	−9.26942	−	16.0551i	−0.657092	−	1.13812i	−0.981365	−	0.192153i	$-0.938453\pi$
$199$	−9.26942	−	16.0551i	−0.657092	−	1.13812i	0.324273	−	0.945964i	$-0.394880\pi$
$200$	−1.03236	+	5.85482i	−0.0729991	+	0.413998i
$201$		0			0
$202$	−4.95912	−	1.80497i	−0.348922	−	0.126997i
$203$	−1.18408	−	0.430971i	−0.0831064	−	0.0302483i
$204$		0			0
$205$	2.47155	−	14.0168i	0.172620	−	0.978979i
$206$	6.12519	+	10.6091i	0.426762	+	0.739173i
$207$		0			0
$208$	−3.26154	+	5.64915i	−0.226147	+	0.391698i
$209$	0.239385	+	0.200868i	0.0165586	+	0.0138943i
$210$		0			0
$211$	−0.640967	−	3.63510i	−0.0441260	−	0.250251i	0.954763	−	0.297366i	$-0.0961082\pi$
$211$	−0.640967	−	3.63510i	−0.0441260	−	0.250251i	−0.998889	+	0.0471155i	$0.984997\pi$
$212$	−7.13500	+	5.98697i	−0.490034	+	0.411187i
$213$		0			0
$214$	−19.2780	+	7.01660i	−1.31781	+	0.479645i
$215$	7.55427			0.515197
$216$		0			0
$217$	−2.01659			−0.136895
$218$	6.25668	−	2.27724i	0.423756	−	0.154234i
$219$		0			0
$220$	−1.49013	+	1.25037i	−0.100465	+	0.0842999i
$221$	−5.25080	−	29.7788i	−0.353207	−	2.00314i
$222$		0			0
$223$	−16.2716	−	13.6535i	−1.08963	−	0.914305i	−0.0929417	−	0.995672i	$-0.529627\pi$
$223$	−16.2716	−	13.6535i	−1.08963	−	0.914305i	−0.996684	+	0.0813669i	$0.974071\pi$
$224$	5.63017	−	9.75174i	0.376181	−	0.651565i
$225$		0			0
$226$	3.64571	+	6.31456i	0.242509	+	0.420038i
$227$	2.49012	−	14.1222i	0.165275	−	0.937323i	−0.783505	−	0.621386i	$-0.786570\pi$
$227$	2.49012	−	14.1222i	0.165275	−	0.937323i	0.948780	−	0.315937i	$-0.102319\pi$
$228$		0			0
$229$	−15.8675	−	5.77529i	−1.04855	−	0.381642i	−0.240436	−	0.970665i	$-0.577290\pi$
$229$	−15.8675	−	5.77529i	−1.04855	−	0.381642i	−0.808116	+	0.589023i	$0.799513\pi$
$230$	−1.45634	−	0.530066i	−0.0960285	−	0.0349515i
$231$		0			0
$232$	0.270955	−	1.53666i	0.0177890	−	0.100887i
$233$	2.79972	+	4.84926i	0.183416	+	0.317686i	0.943042	−	0.332675i	$-0.107951\pi$
$233$	2.79972	+	4.84926i	0.183416	+	0.317686i	−0.759626	+	0.650361i	$0.774618\pi$
$234$		0			0
$235$	−4.62837	+	8.01658i	−0.301922	+	0.522944i
$236$	−2.04588	−	1.71670i	−0.133176	−	0.111748i
$237$		0			0
$238$	−2.99284	−	16.9732i	−0.193997	−	1.10021i
$239$	4.04033	−	3.39024i	0.261347	−	0.219296i	−0.502693	−	0.864465i	$-0.667657\pi$
$239$	4.04033	−	3.39024i	0.261347	−	0.219296i	0.764040	+	0.645169i	$0.223213\pi$
$240$		0			0
$241$	8.36559	−	3.04483i	0.538875	−	0.196135i	−0.0582216	−	0.998304i	$-0.518543\pi$
$241$	8.36559	−	3.04483i	0.538875	−	0.196135i	0.597097	+	0.802169i	$0.296321\pi$
$242$	9.93907			0.638907
$243$		0			0
$244$	−2.56141			−0.163977
$245$	1.56193	−	0.568497i	0.0997883	−	0.0363200i
$246$		0			0
$247$	−0.868249	+	0.728548i	−0.0552454	+	0.0463564i
$248$	−0.433628	−	2.45923i	−0.0275354	−	0.156161i
$249$		0			0
$250$	9.80265	+	8.22540i	0.619974	+	0.520220i
$251$	−3.89010	+	6.73786i	−0.245541	+	0.425290i	−0.962284	−	0.272048i	$-0.912299\pi$
$251$	−3.89010	+	6.73786i	−0.245541	+	0.425290i	0.716742	+	0.697338i	$0.245632\pi$
$252$		0			0
$253$	0.528024	+	0.914565i	0.0331966	+	0.0574982i
$254$	−2.20123	+	12.4838i	−0.138118	+	0.783305i
$255$		0			0
$256$	15.4971	+	5.64047i	0.968566	+	0.352529i
$257$	−19.2041	−	6.98971i	−1.19792	−	0.436006i	−0.335420	−	0.942069i	$-0.608878\pi$
$257$	−19.2041	−	6.98971i	−1.19792	−	0.436006i	−0.862497	+	0.506062i	$0.831101\pi$
$258$		0			0
$259$	1.11376	−	6.31643i	0.0692054	−	0.392484i
$260$	−3.52767	−	6.11011i	−0.218777	−	0.378933i
$261$		0			0
$262$	7.42498	−	12.8604i	0.458717	−	0.794520i
$263$	−8.64084	−	7.25052i	−0.532817	−	0.447086i	0.336256	−	0.941771i	$-0.390839\pi$
$263$	−8.64084	−	7.25052i	−0.532817	−	0.447086i	−0.869073	+	0.494684i	$0.835284\pi$
$264$		0			0
$265$	3.17829	+	18.0250i	0.195241	+	1.10726i
$266$	−0.494883	+	0.415256i	−0.0303432	+	0.0254610i
$267$		0			0
$268$	8.42024	−	3.06472i	0.514348	−	0.187207i
$269$	0.307761			0.0187645			0.00938226	−	0.999956i	$-0.497013\pi$
$269$	0.307761			0.0187645			0.00938226	+	0.999956i	$0.497013\pi$
$270$		0			0
$271$	−2.22251			−0.135008			−0.0675040	−	0.997719i	$-0.521504\pi$
$271$	−2.22251			−0.135008			−0.0675040	+	0.997719i	$0.521504\pi$
$272$	8.95687	−	3.26003i	0.543090	−	0.197669i
$273$		0			0
$274$	1.82381	−	1.53036i	0.110180	−	0.0924523i
$275$	−0.425179	−	2.41131i	−0.0256393	−	0.145408i
$276$		0			0
$277$	−17.8716	−	14.9961i	−1.07380	−	0.901026i	−0.0784094	−	0.996921i	$-0.524984\pi$
$277$	−17.8716	−	14.9961i	−1.07380	−	0.901026i	−0.995391	+	0.0958953i	$0.969429\pi$
$278$	−4.20417	+	7.28184i	−0.252149	+	0.436735i
$279$		0			0
$280$	−6.53725	−	11.3228i	−0.390675	−	0.676670i
$281$	−1.25469	+	7.11568i	−0.0748484	+	0.424486i	0.924241	+	0.381811i	$0.124699\pi$
$281$	−1.25469	+	7.11568i	−0.0748484	+	0.424486i	−0.999089	+	0.0426756i	$0.986412\pi$
$282$		0			0
$283$	−6.69088	−	2.43528i	−0.397732	−	0.144763i	0.135408	−	0.990790i	$-0.456766\pi$
$283$	−6.69088	−	2.43528i	−0.397732	−	0.144763i	−0.533139	+	0.846027i	$0.678988\pi$
$284$	−0.0746962	−	0.0271872i	−0.00443241	−	0.00161326i
$285$		0			0
$286$	1.04456	−	5.92401i	0.0617663	−	0.350294i
$287$	−10.0249	−	17.3636i	−0.591751	−	1.02494i
$288$		0			0
$289$	−13.5924	+	23.5428i	−0.799555	+	1.38487i
$290$	−0.722461	−	0.606217i	−0.0424244	−	0.0355983i
$291$		0			0
$292$	0.820886	+	4.65548i	0.0480387	+	0.272441i
$293$	−0.423228	+	0.355131i	−0.0247253	+	0.0207469i	−0.655067	−	0.755571i	$-0.727359\pi$
$293$	−0.423228	+	0.355131i	−0.0247253	+	0.0207469i	0.630341	+	0.776318i	$0.282915\pi$
$294$		0			0
$295$	−4.93169	+	1.79499i	−0.287134	+	0.104508i
$296$	7.94236			0.461640
$297$		0			0
$298$	−0.112748			−0.00653131
$299$	−3.59929	+	1.31004i	−0.208152	+	0.0757613i
$300$		0			0
$301$	8.15187	−	6.84023i	0.469866	−	0.394265i
$302$	3.70913	+	21.0355i	0.213436	+	1.21046i
$303$		0			0
$304$	−0.273690	−	0.229653i	−0.0156972	−	0.0131715i
$305$	−2.51670	+	4.35906i	−0.144106	+	0.249599i
$306$		0			0
$307$	−3.36438	−	5.82728i	−0.192015	−	0.332580i	0.753903	−	0.656986i	$-0.228169\pi$
$307$	−3.36438	−	5.82728i	−0.192015	−	0.332580i	−0.945918	+	0.324406i	$0.894836\pi$
$308$	−0.475830	+	2.69857i	−0.0271129	+	0.153765i
$309$		0			0
$310$	−1.41830	−	0.516218i	−0.0805539	−	0.0293192i
$311$	14.4933	+	5.27513i	0.821840	+	0.299125i	0.718505	−	0.695521i	$-0.244827\pi$
$311$	14.4933	+	5.27513i	0.821840	+	0.299125i	0.103335	+	0.994647i	$0.467049\pi$
$312$		0			0
$313$	−4.09130	+	23.2029i	−0.231254	+	1.31151i	0.619107	+	0.785307i	$0.287495\pi$
$313$	−4.09130	+	23.2029i	−0.231254	+	1.31151i	−0.850361	+	0.526200i	$0.823616\pi$
$314$	−10.9385	−	18.9461i	−0.617297	−	1.06919i
$315$		0			0
$316$	2.12191	−	3.67525i	0.119367	−	0.206749i
$317$	−5.55539	−	4.66152i	−0.312022	−	0.261817i	0.473305	−	0.880898i	$-0.343061\pi$
$317$	−5.55539	−	4.66152i	−0.312022	−	0.261817i	−0.785327	+	0.619081i	$0.787505\pi$
$318$		0			0
$319$	0.111593	+	0.632874i	0.00624800	+	0.0354342i
$320$	10.2915	−	8.63556i	0.575310	−	0.482743i
$321$		0			0
$322$	−2.05152	+	0.746691i	−0.114327	+	0.0416115i
$323$	1.65618			0.0921525
$324$		0			0
$325$	8.88074			0.492615
$326$	−19.9482	+	7.26054i	−1.10483	+	0.402124i
$327$		0			0
$328$	19.0192	−	15.9590i	1.05016	−	0.881190i
$329$	2.26433	+	12.8416i	0.124836	+	0.707983i
$330$		0			0
$331$	22.2417	+	18.6630i	1.22251	+	1.02581i	0.998689	+	0.0511815i	$0.0162987\pi$
$331$	22.2417	+	18.6630i	1.22251	+	1.02581i	0.223825	+	0.974629i	$0.428146\pi$
$332$	−3.57166	+	6.18629i	−0.196020	+	0.339517i
$333$		0			0
$334$	10.4708	+	18.1360i	0.572938	+	0.992357i
$335$	3.05768	−	17.3410i	0.167059	−	0.947438i
$336$		0			0
$337$	1.08919	+	0.396434i	0.0593321	+	0.0215951i	0.371516	−	0.928427i	$-0.378838\pi$
$337$	1.08919	+	0.396434i	0.0593321	+	0.0215951i	−0.312184	+	0.950022i	$0.601060\pi$
$338$	7.62244	+	2.77434i	0.414606	+	0.150904i
$339$		0			0
$340$	−1.79022	+	10.1528i	−0.0970883	+	0.550615i
$341$	0.514230	+	0.890672i	0.0278471	+	0.0482326i
$342$		0			0
$343$	9.77810	−	16.9362i	0.527968	−	0.914467i
$344$	10.0946	+	8.47033i	0.544262	+	0.456690i
$345$		0			0
$346$	3.46484	+	19.6501i	0.186271	+	1.05640i
$347$	−4.51178	+	3.78583i	−0.242205	+	0.203234i	−0.755807	−	0.654794i	$-0.772755\pi$
$347$	−4.51178	+	3.78583i	−0.242205	+	0.203234i	0.513602	+	0.858029i	$0.328311\pi$
$348$		0			0
$349$	28.7477	−	10.4633i	1.53883	−	0.560089i	0.573066	−	0.819509i	$-0.305754\pi$
$349$	28.7477	−	10.4633i	1.53883	−	0.560089i	0.965764	+	0.259421i	$0.0835316\pi$
$350$	5.06182			0.270566
$351$		0			0
$352$	−5.74276			−0.306090
$353$	34.7322	−	12.6415i	1.84861	−	0.672839i	0.862664	−	0.505778i	$-0.168794\pi$
$353$	34.7322	−	12.6415i	1.84861	−	0.672839i	0.985947	−	0.167061i	$-0.0534278\pi$
$354$		0			0
$355$	−0.119660	+	0.100407i	−0.00635091	+	0.00532904i
$356$	1.03418	+	5.86514i	0.0548116	+	0.310852i
$357$		0			0
$358$	8.81452	+	7.39626i	0.465862	+	0.390905i
$359$	−13.1880	+	22.8423i	−0.696037	+	1.20557i	0.273792	+	0.961789i	$0.411722\pi$
$359$	−13.1880	+	22.8423i	−0.696037	+	1.20557i	−0.969830	+	0.243783i	$0.921611\pi$
$360$		0			0
$361$	9.46896	+	16.4007i	0.498366	+	0.863196i
$362$	3.28592	−	18.6354i	0.172704	−	0.979455i
$363$		0			0
$364$	−9.33931	−	3.39923i	−0.489513	−	0.178168i
$365$	8.72935	+	3.17722i	0.456915	+	0.166303i
$366$		0			0
$367$	−1.96450	+	11.1413i	−0.102546	+	0.581569i	0.889626	+	0.456690i	$0.150965\pi$
$367$	−1.96450	+	11.1413i	−0.102546	+	0.581569i	−0.992172	+	0.124879i	$0.960146\pi$
$368$	−0.603693	−	1.04563i	−0.0314697	−	0.0545071i
$369$		0			0
$370$	2.40023	−	4.15733i	0.124782	−	0.216129i
$371$	19.7509	+	16.5730i	1.02542	+	0.860428i
$372$		0			0
$373$	1.01481	+	5.75529i	0.0525451	+	0.297998i	0.999743	−	0.0226503i	$-0.00721043\pi$
$373$	1.01481	+	5.75529i	0.0525451	+	0.297998i	−0.947198	+	0.320648i	$0.896099\pi$
$374$	−6.73343	+	5.65002i	−0.348177	+	0.292156i
$375$		0			0
$376$	−15.1735	+	5.52269i	−0.782511	+	0.284811i
$377$	−2.33085			−0.120045
$378$		0			0
$379$	24.3265			1.24957			0.624783	−	0.780798i	$-0.285187\pi$
$379$	24.3265			1.24957			0.624783	+	0.780798i	$0.285187\pi$
$380$	0.363126	−	0.132167i	0.0186280	−	0.00678002i
$381$		0			0
$382$	−21.7794	+	18.2751i	−1.11433	+	0.935035i
$383$	0.662650	+	3.75808i	0.0338598	+	0.192029i	0.997046	−	0.0768065i	$-0.0244724\pi$
$383$	0.662650	+	3.75808i	0.0338598	+	0.192029i	−0.963186	+	0.268835i	$0.913361\pi$
$384$		0			0
$385$	4.12495	+	3.46124i	0.210227	+	0.176401i
$386$	−9.04337	+	15.6636i	−0.460295	+	0.797255i
$387$		0			0
$388$	2.43891	+	4.22432i	0.123817	+	0.214457i
$389$	−1.88267	+	10.6771i	−0.0954550	+	0.541352i	0.899152	+	0.437637i	$0.144184\pi$
$389$	−1.88267	+	10.6771i	−0.0954550	+	0.541352i	−0.994607	+	0.103716i	$0.966927\pi$
$390$		0			0
$391$	5.25939	+	1.91426i	0.265979	+	0.0968083i
$392$	2.72460	+	0.991674i	0.137613	+	0.0500871i
$393$		0			0
$394$	0.459946	−	2.60848i	0.0231718	−	0.131414i
$395$	−4.16974	−	7.22221i	−0.209802	−	0.363389i
$396$		0			0
$397$	5.25461	−	9.10124i	0.263721	−	0.456778i	−0.703507	−	0.710689i	$-0.748383\pi$
$397$	5.25461	−	9.10124i	0.263721	−	0.456778i	0.967228	+	0.253910i	$0.0817168\pi$
$398$	−14.9731	−	12.5639i	−0.750533	−	0.629772i
$399$		0			0
$400$	0.486110	+	2.75687i	0.0243055	+	0.137843i
$401$	−11.0047	+	9.23401i	−0.549547	+	0.461125i	−0.874788	−	0.484507i	$-0.838999\pi$
$401$	−11.0047	+	9.23401i	−0.549547	+	0.461125i	0.325241	+	0.945631i	$0.394555\pi$
$402$		0			0
$403$	−3.50526	+	1.27581i	−0.174609	+	0.0635527i
$404$	4.44685			0.221239
$405$		0			0
$406$	−1.32853			−0.0659338
$407$	−3.07380	+	1.11877i	−0.152362	+	0.0554554i
$408$		0			0
$409$	13.5454	−	11.3659i	0.669777	−	0.562009i	−0.243223	−	0.969971i	$-0.578205\pi$
$409$	13.5454	−	11.3659i	0.669777	−	0.562009i	0.912999	+	0.407961i	$0.133760\pi$
$410$	−2.60581	−	14.7783i	−0.128692	−	0.729849i
$411$		0			0
$412$	−7.90746	−	6.63514i	−0.389572	−	0.326890i
$413$	−3.69650	+	6.40252i	−0.181893	+	0.315047i
$414$		0			0
$415$	7.01864	+	12.1566i	0.344532	+	0.596746i
$416$	3.61691	−	20.5125i	0.177334	−	1.00571i
$417$		0			0
$418$	0.309602	+	0.112686i	0.0151431	+	0.00551164i
$419$	8.58293	+	3.12393i	0.419304	+	0.152614i	0.543051	−	0.839700i	$-0.317269\pi$
$419$	8.58293	+	3.12393i	0.419304	+	0.152614i	−0.123747	+	0.992314i	$0.539491\pi$
$420$		0			0
$421$	4.20140	−	23.8273i	0.204764	−	1.16127i	−0.693047	−	0.720892i	$-0.743732\pi$
$421$	4.20140	−	23.8273i	0.204764	−	1.16127i	0.897811	−	0.440381i	$-0.145157\pi$
$422$	−1.94585	−	3.37031i	−0.0947226	−	0.164064i
$423$		0			0
$424$	−15.9637	+	27.6499i	−0.775265	+	1.34280i
$425$	−9.94080	−	8.34132i	−0.482199	−	0.404613i
$426$		0			0
$427$	1.23124	+	6.98271i	0.0595839	+	0.337917i
$428$	13.2423	−	11.1116i	0.640090	−	0.537099i
$429$		0			0
$430$	7.48433	−	2.72407i	0.360926	−	0.131366i
$431$	29.5332			1.42256			0.711282	−	0.702907i	$-0.248115\pi$
$431$	29.5332			1.42256			0.711282	+	0.702907i	$0.248115\pi$
$432$		0			0
$433$	0.669754			0.0321863			0.0160932	−	0.999870i	$-0.494877\pi$
$433$	0.669754			0.0321863			0.0160932	+	0.999870i	$0.494877\pi$
$434$	−1.99792	+	0.727183i	−0.0959032	+	0.0349059i
$435$		0			0
$436$	−4.29779	+	3.60628i	−0.205827	+	0.172709i
$437$	−0.0364296	−	0.206603i	−0.00174266	−	0.00988314i
$438$		0			0
$439$	−4.86352	−	4.08097i	−0.232123	−	0.194774i	0.519306	−	0.854588i	$-0.326191\pi$
$439$	−4.86352	−	4.08097i	−0.232123	−	0.194774i	−0.751429	+	0.659814i	$0.770635\pi$
$440$	−3.33399	+	5.77464i	−0.158942	+	0.275295i
$441$		0			0
$442$	−15.9404	−	27.6096i	−0.758209	−	1.31326i
$443$	−2.66618	+	15.1207i	−0.126674	+	0.718404i	0.853625	+	0.520887i	$0.174399\pi$
$443$	−2.66618	+	15.1207i	−0.126674	+	0.718404i	−0.980299	+	0.197517i	$0.936712\pi$
$444$		0			0
$445$	10.9976	+	4.00278i	0.521334	+	0.189750i
$446$	−21.0444	−	7.65953i	−0.996480	−	0.362689i
$447$		0			0
$448$	3.28628	−	18.6374i	0.155262	−	0.880535i
$449$	−16.0199	−	27.7473i	−0.756027	−	1.30948i	−0.944862	−	0.327468i	$-0.893805\pi$
$449$	−16.0199	−	27.7473i	−0.756027	−	1.30948i	0.188836	−	0.982009i	$-0.439529\pi$
$450$		0			0
$451$	−5.11268	+	8.85543i	−0.240747	+	0.416986i
$452$	−4.70652	−	3.94924i	−0.221376	−	0.185757i
$453$		0			0
$454$	−2.62540	−	14.8894i	−0.123216	−	0.698793i
$455$	−14.9612	+	12.5539i	−0.701391	+	0.588537i
$456$		0			0
$457$	−18.0121	+	6.55586i	−0.842569	+	0.306670i	−0.727007	−	0.686630i	$-0.759089\pi$
$457$	−18.0121	+	6.55586i	−0.842569	+	0.306670i	−0.115562	+	0.993300i	$0.536867\pi$
$458$	−17.8031			−0.831886
$459$		0			0
$460$	1.30591			0.0608882
$461$	−4.90547	+	1.78545i	−0.228471	+	0.0831565i	−0.453719	−	0.891145i	$-0.649903\pi$
$461$	−4.90547	+	1.78545i	−0.228471	+	0.0831565i	0.225248	+	0.974301i	$0.427681\pi$
$462$		0			0
$463$	1.30028	−	1.09106i	0.0604289	−	0.0507059i	−0.612073	−	0.790801i	$-0.709664\pi$
$463$	1.30028	−	1.09106i	0.0604289	−	0.0507059i	0.672502	+	0.740095i	$0.265220\pi$
$464$	−0.127585	−	0.723569i	−0.00592297	−	0.0335908i
$465$		0			0
$466$	4.52245	+	3.79478i	0.209498	+	0.175790i
$467$	9.84136	−	17.0457i	0.455404	−	0.788783i	−0.543307	−	0.839534i	$-0.682828\pi$
$467$	9.84136	−	17.0457i	0.455404	−	0.788783i	0.998711	+	0.0507511i	$0.0161615\pi$
$468$		0			0
$469$	−12.4023	−	21.4814i	−0.572685	−	0.991920i
$470$	−1.69474	+	9.61135i	−0.0781725	+	0.443338i
$471$		0			0
$472$	−8.60272	−	3.13113i	−0.395972	−	0.144122i
$473$	−5.09986	−	1.85620i	−0.234492	−	0.0853481i
$474$		0			0
$475$	−0.0844641	+	0.479020i	−0.00387548	+	0.0219789i
$476$	7.26134	+	12.5770i	0.332823	+	0.576467i
$477$		0			0
$478$	2.78040	−	4.81579i	0.127173	−	0.220269i
$479$	22.4094	+	18.8037i	1.02391	+	0.859165i	0.990114	−	0.140264i	$-0.0447951\pi$
$479$	22.4094	+	18.8037i	1.02391	+	0.859165i	0.0337985	+	0.999429i	$0.489240\pi$
$480$		0			0
$481$	−2.06019	−	11.6839i	−0.0939365	−	0.532740i
$482$	7.19017	−	6.03327i	0.327503	−	0.274808i
$483$		0			0
$484$	−7.86983	+	2.86438i	−0.357719	+	0.130199i
$485$	9.58538			0.435250
$486$		0			0
$487$	−20.5056			−0.929199			−0.464600	−	0.885521i	$-0.653802\pi$
$487$	−20.5056			−0.929199			−0.464600	+	0.885521i	$0.653802\pi$
$488$	−8.25065	+	3.00299i	−0.373489	+	0.135939i
$489$		0			0
$490$	1.34247	−	1.12647i	0.0606467	−	0.0508886i
$491$	−3.04353	−	17.2607i	−0.137353	−	0.778965i	−0.973193	−	0.229992i	$-0.926130\pi$
$491$	−3.04353	−	17.2607i	−0.137353	−	0.778965i	0.835840	−	0.548973i	$-0.184981\pi$
$492$		0			0
$493$	2.60907	+	2.18927i	0.117507	+	0.0985997i
$494$	−0.597496	+	1.03489i	−0.0268826	+	0.0465620i
$495$		0			0
$496$	−0.587922	−	1.01831i	−0.0263985	−	0.0457235i
$497$	−0.0382100	+	0.216700i	−0.00171395	+	0.00972031i
$498$		0			0
$499$	17.9538	+	6.53463i	0.803720	+	0.292530i	0.711027	−	0.703164i	$-0.248230\pi$
$499$	17.9538	+	6.53463i	0.803720	+	0.292530i	0.0926931	+	0.995695i	$0.470452\pi$
$500$	−10.1323	−	3.68787i	−0.453131	−	0.164926i
$501$		0			0
$502$	−1.42441	+	8.07825i	−0.0635747	+	0.360550i
$503$	−5.48381	−	9.49824i	−0.244511	−	0.423506i	0.717483	−	0.696576i	$-0.245294\pi$
$503$	−5.48381	−	9.49824i	−0.244511	−	0.423506i	−0.961994	+	0.273070i	$0.911961\pi$
$504$		0			0
$505$	4.36924	−	7.56774i	0.194429	−	0.336760i
$506$	0.852928	+	0.715691i	0.0379173	+	0.0318164i
$507$		0			0
$508$	−1.85481	−	10.5192i	−0.0822940	−	0.466712i
$509$	15.2438	−	12.7911i	0.675669	−	0.566954i	−0.239068	−	0.971003i	$-0.576842\pi$
$509$	15.2438	−	12.7911i	0.675669	−	0.566954i	0.914737	+	0.404049i	$0.132397\pi$
$510$		0			0
$511$	12.2968	−	4.47567i	0.543979	−	0.197992i
$512$	15.2994			0.676143
$513$		0			0
$514$	−21.5468			−0.950387
$515$	−19.0613	+	6.93774i	−0.839940	+	0.305713i
$516$		0			0
$517$	5.09439	−	4.27470i	0.224051	−	0.188001i
$518$	−1.17426	−	6.65956i	−0.0515941	−	0.292604i
$519$		0			0
$520$	−18.5266	−	15.5457i	−0.812445	−	0.681722i
$521$	17.5583	−	30.4119i	0.769244	−	1.33237i	−0.168729	−	0.985662i	$-0.553966\pi$
$521$	17.5583	−	30.4119i	0.769244	−	1.33237i	0.937973	−	0.346708i	$-0.112700\pi$
$522$		0			0
$523$	7.12269	+	12.3369i	0.311453	+	0.539453i	0.978677	−	0.205404i	$-0.0658509\pi$
$523$	7.12269	+	12.3369i	0.311453	+	0.539453i	−0.667224	+	0.744857i	$0.732518\pi$
$524$	−2.17285	+	12.3228i	−0.0949212	+	0.538325i
$525$		0			0
$526$	−11.1754	−	4.06750i	−0.487269	−	0.177352i
$527$	5.12199	+	1.86425i	0.223117	+	0.0812080i
$528$		0			0
$529$	−3.87080	+	21.9524i	−0.168296	+	0.954451i
$530$	9.64867	+	16.7120i	0.419111	+	0.725922i
$531$		0			0
$532$	0.272177	−	0.471425i	0.0118004	−	0.0204389i
$533$	−28.4106	−	23.8393i	−1.23060	−	1.03260i
$534$		0			0
$535$	−5.89878	−	33.4537i	−0.255027	−	1.44633i
$536$	23.5297	−	19.7437i	1.01633	−	0.852800i
$537$		0			0
$538$	0.304911	−	0.110979i	0.0131457	−	0.00478463i
$539$	−1.19414			−0.0514354
$540$		0			0
$541$	−13.2368			−0.569094			−0.284547	−	0.958662i	$-0.591843\pi$
$541$	−13.2368			−0.569094			−0.284547	+	0.958662i	$0.591843\pi$
$542$	−2.20194	+	0.801439i	−0.0945813	+	0.0344248i
$543$		0			0
$544$	−23.3152	+	19.5638i	−0.999633	+	0.838792i
$545$	1.91445	+	10.8574i	0.0820062	+	0.465080i
$546$		0			0
$547$	−12.4903	−	10.4806i	−0.534046	−	0.448118i	0.335450	−	0.942058i	$-0.391112\pi$
$547$	−12.4903	−	10.4806i	−0.534046	−	0.448118i	−0.869496	+	0.493940i	$0.835556\pi$
$548$	−1.00306	+	1.73736i	−0.0428488	+	0.0742163i
$549$		0			0
$550$	−1.29076	−	2.23567i	−0.0550383	−	0.0953291i
$551$	0.0221685	−	0.125724i	0.000944411	−	0.00535602i
$552$		0			0
$553$	−11.0392	−	4.01792i	−0.469433	−	0.170859i
$554$	−23.1137	−	8.41271i	−0.982008	−	0.357422i
$555$		0			0
$556$	1.23031	−	6.97743i	0.0521767	−	0.295909i
$557$	15.4486	+	26.7577i	0.654577	+	1.13376i	0.982000	+	0.188883i	$0.0604867\pi$
$557$	15.4486	+	26.7577i	0.654577	+	1.13376i	−0.327422	+	0.944878i	$0.606180\pi$
$558$		0			0
$559$	9.84215	−	17.0471i	0.416279	−	0.721016i
$560$	−4.71608	−	3.95726i	−0.199291	−	0.167225i
$561$		0			0
$562$	1.32285	+	7.50224i	0.0558010	+	0.316463i
$563$	−20.5116	+	17.2112i	−0.864459	+	0.725368i	−0.962924	−	0.269773i	$-0.913051\pi$
$563$	−20.5116	+	17.2112i	−0.864459	+	0.725368i	0.0984645	+	0.995141i	$0.468607\pi$
$564$		0			0
$565$	−11.3453	+	4.12934i	−0.477299	+	0.173723i
$566$	−7.50710			−0.315547
$567$		0			0
$568$	−0.272481			−0.0114331
$569$	17.9111	−	6.51912i	0.750874	−	0.273296i	0.0619006	−	0.998082i	$-0.480284\pi$
$569$	17.9111	−	6.51912i	0.750874	−	0.273296i	0.688974	+	0.724786i	$0.258062\pi$
$570$		0			0
$571$	−14.3819	+	12.0678i	−0.601863	+	0.505023i	−0.892044	−	0.451949i	$-0.850729\pi$
$571$	−14.3819	+	12.0678i	−0.601863	+	0.505023i	0.290181	+	0.956972i	$0.406284\pi$
$572$	0.880174	+	4.99171i	0.0368019	+	0.208714i
$573$		0			0
$574$	−16.1934	−	13.5879i	−0.675899	−	0.567147i
$575$	−0.821889	+	1.42355i	−0.0342751	+	0.0593663i
$576$		0			0
$577$	2.42981	+	4.20856i	0.101154	+	0.175204i	0.912161	−	0.409833i	$-0.134413\pi$
$577$	2.42981	+	4.20856i	0.101154	+	0.175204i	−0.811006	+	0.585038i	$0.801080\pi$
$578$	−4.97705	+	28.2262i	−0.207018	+	1.17406i
$579$		0			0
$580$	0.746758	+	0.271798i	0.0310074	+	0.0112858i
$581$	18.5815	+	6.76310i	0.770889	+	0.280580i
$582$		0			0
$583$	2.28335	−	12.9495i	0.0945669	−	0.536315i
$584$	8.10226	+	14.0335i	0.335274	+	0.580712i
$585$		0			0
$586$	−0.291249	+	0.504459i	−0.0120314	+	0.0208390i
$587$	25.1242	+	21.0817i	1.03699	+	0.870136i	0.991666	−	0.128837i	$-0.0411243\pi$
$587$	25.1242	+	21.0817i	1.03699	+	0.870136i	0.0453217	+	0.998972i	$0.485569\pi$
$588$		0			0
$589$	−0.0354779	−	0.201205i	−0.00146184	−	0.00829051i
$590$	−4.23875	+	3.55674i	−0.174507	+	0.146428i
$591$		0			0
$592$	3.51429	−	1.27910i	0.144436	−	0.0525705i
$593$	−17.3446			−0.712258			−0.356129	−	0.934437i	$-0.615904\pi$
$593$	−17.3446			−0.712258			−0.356129	+	0.934437i	$0.615904\pi$
$594$		0			0
$595$	28.5384			1.16996
$596$	0.0892745	−	0.0324933i	0.00365683	−	0.00133098i
$597$		0			0
$598$	−3.09357	+	2.59581i	−0.126505	+	0.106151i
$599$	−4.23839	−	24.0371i	−0.173176	−	0.982129i	−0.940228	−	0.340545i	$-0.889388\pi$
$599$	−4.23839	−	24.0371i	−0.173176	−	0.982129i	0.767052	−	0.641584i	$-0.221723\pi$
$600$		0			0
$601$	6.02897	+	5.05891i	0.245927	+	0.206357i	0.757416	−	0.652933i	$-0.226461\pi$
$601$	6.02897	+	5.05891i	0.245927	+	0.206357i	−0.511489	+	0.859290i	$0.670906\pi$
$602$	5.60981	−	9.71647i	0.228639	−	0.396014i
$603$		0			0
$604$	−8.99922	−	15.5871i	−0.366173	−	0.634230i
$605$	−2.85781	+	16.2074i	−0.116186	+	0.658925i
$606$		0			0
$607$	9.62007	+	3.50142i	0.390467	+	0.142118i	0.529790	−	0.848129i	$-0.322271\pi$
$607$	9.62007	+	3.50142i	0.390467	+	0.142118i	−0.139324	+	0.990247i	$0.544493\pi$
$608$	1.07203	+	0.390187i	0.0434765	+	0.0158242i
$609$		0			0
$610$	−0.921524	+	5.22622i	−0.0373114	+	0.211604i
$611$	12.0602	+	20.8889i	0.487905	+	0.845076i
$612$		0			0
$613$	−1.11753	+	1.93563i	−0.0451368	+	0.0781792i	−0.887711	−	0.460401i	$-0.847706\pi$
$613$	−1.11753	+	1.93563i	−0.0451368	+	0.0781792i	0.842574	+	0.538580i	$0.181039\pi$
$614$	−5.43455	−	4.56013i	−0.219321	−	0.184032i
$615$		0			0
$616$	1.63108	+	9.25031i	0.0657181	+	0.372706i
$617$	−26.0269	+	21.8391i	−1.04780	+	0.879211i	−0.992861	−	0.119279i	$-0.961942\pi$
$617$	−26.0269	+	21.8391i	−1.04780	+	0.879211i	−0.0549420	+	0.998490i	$0.517497\pi$
$618$		0			0
$619$	27.1157	−	9.86932i	1.08987	−	0.396682i	0.266300	−	0.963890i	$-0.414199\pi$
$619$	27.1157	−	9.86932i	1.08987	−	0.396682i	0.823574	+	0.567209i	$0.191977\pi$
$620$	1.27179			0.0510763
$621$		0			0
$622$	16.2613			0.652020
$623$	15.4920	−	5.63862i	0.620673	−	0.225907i
$624$		0			0
$625$	−8.75410	+	7.34556i	−0.350164	+	0.293823i
$626$	4.31356	+	24.4634i	0.172405	+	0.977755i
$627$		0			0
$628$	14.1214	+	11.8492i	0.563504	+	0.472836i
$629$	−8.66811	+	15.0136i	−0.345620	+	0.598632i
$630$		0			0
$631$	1.57039	+	2.71999i	0.0625162	+	0.108281i	0.895590	−	0.444881i	$-0.146754\pi$
$631$	1.57039	+	2.71999i	0.0625162	+	0.108281i	−0.833073	+	0.553163i	$0.813421\pi$
$632$	2.52610	−	14.3262i	0.100483	−	0.569866i
$633$		0			0
$634$	−7.18490	−	2.61509i	−0.285349	−	0.103858i
$635$	−19.7242	−	7.17901i	−0.782730	−	0.284890i
$636$		0			0
$637$	0.752098	−	4.26536i	0.0297992	−	0.169000i
$638$	0.338774	+	0.586774i	0.0134122	+	0.0232306i
$639$		0			0
$640$	−0.911374	+	1.57855i	−0.0360252	+	0.0623975i
$641$	24.3775	+	20.4551i	0.962853	+	0.807929i	0.981415	−	0.191898i	$-0.0614644\pi$
$641$	24.3775	+	20.4551i	0.962853	+	0.807929i	−0.0185622	+	0.999828i	$0.505909\pi$
$642$		0			0
$643$	−2.23087	−	12.6519i	−0.0879769	−	0.498942i	−0.996674	−	0.0814867i	$-0.974033\pi$
$643$	−2.23087	−	12.6519i	−0.0879769	−	0.498942i	0.908698	−	0.417455i	$-0.137078\pi$
$644$	1.40921	−	1.18247i	0.0555308	−	0.0465959i
$645$		0			0
$646$	1.64085	−	0.597220i	0.0645584	−	0.0234973i
$647$	−28.2444			−1.11040			−0.555200	−	0.831717i	$-0.687358\pi$
$647$	−28.2444			−1.11040			−0.555200	+	0.831717i	$0.687358\pi$
$648$		0			0
$649$	3.77042			0.148002
$650$	8.79852	−	3.20240i	0.345106	−	0.125608i
$651$		0			0
$652$	13.7027	−	11.4979i	0.536637	−	0.450292i
$653$	−4.51320	−	25.5956i	−0.176615	−	1.00163i	−0.936263	−	0.351300i	$-0.885740\pi$
$653$	−4.51320	−	25.5956i	−0.176615	−	1.00163i	0.759648	−	0.650335i	$-0.225371\pi$
$654$		0			0
$655$	18.8363	+	15.8055i	0.735996	+	0.617574i
$656$	5.84536	−	10.1245i	0.228223	−	0.395294i
$657$		0			0
$658$	6.87407	+	11.9062i	0.267979	+	0.464153i
$659$	8.26875	−	46.8944i	0.322105	−	1.82675i	−0.207181	−	0.978303i	$-0.566429\pi$
$659$	8.26875	−	46.8944i	0.322105	−	1.82675i	0.529286	−	0.848443i	$-0.322460\pi$
$660$		0			0
$661$	0.823648	+	0.299783i	0.0320362	+	0.0116602i	0.357989	−	0.933726i	$-0.383463\pi$
$661$	0.823648	+	0.299783i	0.0320362	+	0.0116602i	−0.325952	+	0.945386i	$0.605685\pi$
$662$	28.7656	+	10.4698i	1.11801	+	0.406922i
$663$		0			0
$664$	−4.25200	+	24.1143i	−0.165010	+	0.935817i
$665$	−0.534854	−	0.926394i	−0.0207407	−	0.0359240i
$666$		0			0
$667$	0.215714	−	0.373627i	0.00835246	−	0.0144669i
$668$	−13.5176	−	11.3426i	−0.523010	−	0.438857i
$669$		0			0
$670$	−3.22379	−	18.2830i	−0.124546	−	0.706334i
$671$	2.77010	−	2.32439i	0.106939	−	0.0897322i
$672$		0			0
$673$	−35.0876	+	12.7708i	−1.35253	+	0.492280i	−0.913736	−	0.406309i	$-0.866816\pi$
$673$	−35.0876	+	12.7708i	−1.35253	+	0.492280i	−0.438792	+	0.898589i	$0.644593\pi$
$674$	1.22206			0.0470721
$675$		0			0
$676$	−6.83505			−0.262886
$677$	−12.8918	+	4.69223i	−0.495472	+	0.180337i	−0.577656	−	0.816280i	$-0.696033\pi$
$677$	−12.8918	+	4.69223i	−0.495472	+	0.180337i	0.0821842	+	0.996617i	$0.473810\pi$
$678$		0			0
$679$	10.3437	−	8.67936i	0.396953	−	0.333083i
$680$	6.13663	+	34.8026i	0.235329	+	1.33462i
$681$		0			0
$682$	0.830645	+	0.696994i	0.0318070	+	0.0266893i
$683$	24.9943	−	43.2914i	0.956381	−	1.65650i	0.225206	−	0.974311i	$-0.427694\pi$
$683$	24.9943	−	43.2914i	0.956381	−	1.65650i	0.731175	−	0.682190i	$-0.238972\pi$
$684$		0			0
$685$	1.97112	+	3.41407i	0.0753125	+	0.130445i
$686$	3.58038	−	20.3053i	0.136699	−	0.775261i
$687$		0			0
$688$	5.83070	+	2.12220i	0.222293	+	0.0809082i
$689$	44.8163	+	16.3118i	1.70737	+	0.621430i
$690$		0			0
$691$	4.13544	−	23.4533i	0.157320	−	0.892204i	−0.799315	−	0.600913i	$-0.794804\pi$
$691$	4.13544	−	23.4533i	0.157320	−	0.892204i	0.956634	−	0.291291i	$-0.0940849\pi$
$692$	−8.40653	−	14.5605i	−0.319568	−	0.553508i
$693$		0			0
$694$	−3.10483	+	5.37773i	−0.117858	+	0.204136i
$695$	−10.6655	−	8.94941i	−0.404565	−	0.339471i
$696$		0			0
$697$	9.41054	+	53.3698i	0.356450	+	2.02153i
$698$	24.7085	−	20.7329i	0.935230	−	0.784751i
$699$		0			0
$700$	−4.00799	+	1.45879i	−0.151488	+	0.0551370i
$701$	−34.4493			−1.30113			−0.650565	−	0.759450i	$-0.725468\pi$
$701$	−34.4493			−1.30113			−0.650565	+	0.759450i	$0.725468\pi$
$702$		0			0
$703$	0.649815			0.0245082
$704$	−9.06962	+	3.30107i	−0.341824	+	0.124414i
$705$		0			0
$706$	29.8521	−	25.0489i	1.12350	−	0.942728i
$707$	−2.13755	−	12.1227i	−0.0803909	−	0.455920i
$708$		0			0
$709$	11.8915	+	9.97817i	0.446595	+	0.374738i	0.838171	−	0.545408i	$-0.183625\pi$
$709$	11.8915	+	9.97817i	0.446595	+	0.374738i	−0.391575	+	0.920146i	$0.628070\pi$
$710$	−0.0823456	+	0.142627i	−0.00309038	+	0.00535269i
$711$		0			0
$712$	10.2075	+	17.6800i	0.382543	+	0.662585i
$713$	0.119894	−	0.679954i	0.00449008	−	0.0254645i
$714$		0			0
$715$	9.35981	+	3.40669i	0.350037	+	0.127403i
$716$	−9.11097	−	3.31612i	−0.340493	−	0.123929i
$717$		0			0
$718$	−4.82897	+	27.3864i	−0.180216	+	1.02205i
$719$	6.02686	+	10.4388i	0.224764	+	0.389303i	0.956249	−	0.292555i	$-0.0945056\pi$
$719$	6.02686	+	10.4388i	0.224764	+	0.389303i	−0.731485	+	0.681858i	$0.761172\pi$
$720$		0			0
$721$	−14.2872	+	24.7461i	−0.532083	+	0.921594i
$722$	15.2954	+	12.8344i	0.569236	+	0.477645i
$723$		0			0
$724$	2.76880	+	15.7026i	0.102902	+	0.583584i
$725$	−0.766265	+	0.642973i	−0.0284584	+	0.0238794i
$726$		0			0
$727$	29.7227	−	10.8182i	1.10235	−	0.401224i	0.274171	−	0.961681i	$-0.411597\pi$
$727$	29.7227	−	10.8182i	1.10235	−	0.401224i	0.828184	+	0.560457i	$0.189374\pi$
$728$	−34.0685			−1.26266
$729$		0			0
$730$	9.79423			0.362501
$731$	−27.0286	+	9.83761i	−0.999690	+	0.363857i
$732$		0			0
$733$	−14.5784	+	12.2328i	−0.538466	+	0.451827i	−0.871013	−	0.491260i	$-0.836537\pi$
$733$	−14.5784	+	12.2328i	−0.538466	+	0.451827i	0.332547	+	0.943087i	$0.392092\pi$
$734$	2.07123	+	11.7465i	0.0764503	+	0.433571i
$735$		0			0
$736$	2.95336	+	2.47816i	0.108862	+	0.0913462i
$737$	−6.32516	+	10.9555i	−0.232990	+	0.403551i
$738$		0			0
$739$	−8.30036	−	14.3767i	−0.305334	−	0.528854i	0.672002	−	0.740550i	$-0.265435\pi$
$739$	−8.30036	−	14.3767i	−0.305334	−	0.528854i	−0.977336	+	0.211696i	$0.932101\pi$
$740$	−0.702405	+	3.98354i	−0.0258209	+	0.146438i
$741$		0			0
$742$	25.5443	+	9.29737i	0.937761	+	0.341317i
$743$	−31.2951	−	11.3905i	−1.14811	−	0.417876i	−0.303271	−	0.952904i	$-0.598079\pi$
$743$	−31.2951	−	11.3905i	−1.14811	−	0.417876i	−0.844834	+	0.535028i	$0.820301\pi$
$744$		0			0
$745$	0.0324187	−	0.183855i	0.00118773	−	0.00673594i
$746$	3.08078	+	5.33606i	0.112795	+	0.195367i
$747$		0			0
$748$	3.70328	−	6.41426i	0.135405	−	0.234529i
$749$	−36.6570	−	30.7589i	−1.33942	−	1.12390i
$750$		0			0
$751$	4.82422	+	27.3595i	0.176038	+	0.998364i	0.936938	+	0.349494i	$0.113647\pi$
$751$	4.82422	+	27.3595i	0.176038	+	0.998364i	−0.760900	+	0.648869i	$0.775242\pi$
$752$	−5.82445	+	4.88729i	−0.212396	+	0.178221i
$753$		0			0
$754$	−2.30926	+	0.840504i	−0.0840985	+	0.0306093i
$755$	−35.3686			−1.28720
$756$		0			0
$757$	−3.12036			−0.113411			−0.0567057	−	0.998391i	$-0.518060\pi$
$757$	−3.12036			−0.113411			−0.0567057	+	0.998391i	$0.518060\pi$
$758$	24.1012	−	8.77213i	0.875396	−	0.318618i
$759$		0			0
$760$	1.01473	−	0.851456i	0.0368080	−	0.0308855i
$761$	7.63343	+	43.2914i	0.276712	+	1.56931i	0.733471	+	0.679720i	$0.237899\pi$
$761$	7.63343	+	43.2914i	0.276712	+	1.56931i	−0.456760	+	0.889590i	$0.650990\pi$
$762$		0			0
$763$	11.8971	+	9.98282i	0.430702	+	0.361402i
$764$	11.9783	−	20.7470i	0.433360	−	0.750602i
$765$		0			0
$766$	2.01168	+	3.48433i	0.0726849	+	0.125894i
$767$	−2.37469	+	13.4675i	−0.0857452	+	0.486285i
$768$		0			0
$769$	−3.48894	−	1.26987i	−0.125815	−	0.0457927i	0.278346	−	0.960481i	$-0.410214\pi$
$769$	−3.48894	−	1.26987i	−0.125815	−	0.0457927i	−0.404160	+	0.914688i	$0.632436\pi$
$770$	5.33488	+	1.94174i	0.192256	+	0.0699754i
$771$		0			0
$772$	2.64645	−	15.0088i	0.0952479	−	0.540178i
$773$	−4.48452	−	7.76741i	−0.161297	−	0.279374i	0.774037	−	0.633140i	$-0.218234\pi$
$773$	−4.48452	−	7.76741i	−0.161297	−	0.279374i	−0.935334	+	0.353766i	$0.884901\pi$
$774$		0			0
$775$	−0.800417	+	1.38636i	−0.0287518	+	0.0497996i
$776$	12.8087	+	10.7477i	0.459804	+	0.385821i
$777$		0			0
$778$	1.98494	+	11.2572i	0.0711636	+	0.403589i
$779$	1.55608	−	1.30571i	0.0557525	−	0.0467819i

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:	\( N \)	\(=\)	\( 243 = 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	243.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.990741 - 0.360600i) q^{2} +(-0.680553 + 0.571052i) q^{4} +(0.303153 + 1.71926i) q^{5} +(1.88389 + 1.58077i) q^{7} +(-1.52266 + 2.63732i) q^{8} +O(q^{10})\)	\(q+(0.990741 - 0.360600i) q^{2} +(-0.680553 + 0.571052i) q^{4} +(0.303153 + 1.71926i) q^{5} +(1.88389 + 1.58077i) q^{7} +(-1.52266 + 2.63732i) q^{8} +(0.920313 + 1.59403i) q^{10} +(0.217792 - 1.23516i) q^{11} +(4.27469 + 1.55586i) q^{13} +(2.43648 + 0.886805i) q^{14} +(-0.249003 + 1.41216i) q^{16} +(-3.32358 - 5.75662i) q^{17} +(-0.124578 + 0.215776i) q^{19} +(-1.18810 - 0.996935i) q^{20} +(-0.229623 - 1.30226i) q^{22} +(-0.645010 + 0.541228i) q^{23} +(1.83449 - 0.667701i) q^{25} +4.79615 q^{26} -2.18479 q^{28} +(-0.481483 + 0.175245i) q^{29} +(-0.628159 + 0.527088i) q^{31} +(-0.795096 - 4.50921i) q^{32} +(-5.36865 - 4.50483i) q^{34} +(-2.14666 + 3.71812i) q^{35} +(-1.30403 - 2.25865i) q^{37} +(-0.0456159 + 0.258701i) q^{38} +(-4.99584 - 1.81834i) q^{40} +(-7.66114 - 2.78843i) q^{41} +(0.751401 - 4.26141i) q^{43} +(0.557121 + 0.964962i) q^{44} +(-0.443871 + 0.768808i) q^{46} +(4.06182 + 3.40828i) q^{47} +(-0.165332 - 0.937642i) q^{49} +(1.57674 - 1.32304i) q^{50} +(-3.79763 + 1.38222i) q^{52} +10.4841 q^{53} +2.18959 q^{55} +(-7.03752 + 2.56145i) q^{56} +(-0.413831 + 0.347246i) q^{58} +(0.522022 + 2.96053i) q^{59} +(2.20864 + 1.85327i) q^{61} +(-0.432275 + 0.748722i) q^{62} +(-3.84771 - 6.66442i) q^{64} +(-1.37905 + 7.82099i) q^{65} +(-9.47799 - 3.44971i) q^{67} +(5.54920 + 2.01975i) q^{68} +(-0.786028 + 4.45779i) q^{70} +(0.0447378 + 0.0774882i) q^{71} +(2.66057 - 4.60824i) q^{73} +(-2.10643 - 1.76750i) q^{74} +(-0.0384370 - 0.217987i) q^{76} +(2.36280 - 1.98263i) q^{77} +(-4.48884 + 1.63380i) q^{79} -2.50337 q^{80} -8.59571 q^{82} +(7.55575 - 2.75007i) q^{83} +(8.88960 - 7.45926i) q^{85} +(-0.792220 - 4.49291i) q^{86} +(2.92588 + 2.45511i) q^{88} +(3.35189 - 5.80564i) q^{89} +(5.59359 + 9.68839i) q^{91} +(0.129895 - 0.736669i) q^{92} +(5.25324 + 1.91202i) q^{94} +(-0.408742 - 0.148770i) q^{95} +(0.953429 - 5.40716i) q^{97} +(-0.501915 - 0.869342i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} + 3 q^{4} - 6 q^{5} + 3 q^{7} - 6 q^{8}+O(q^{10}) \) 12 * q - 3 * q^2 + 3 * q^4 - 6 * q^5 + 3 * q^7 - 6 * q^8	\( 12 q - 3 q^{2} + 3 q^{4} - 6 q^{5} + 3 q^{7} - 6 q^{8} - 3 q^{10} + 6 q^{11} + 3 q^{13} + 21 q^{14} + 9 q^{16} - 9 q^{17} - 3 q^{19} - 24 q^{20} + 12 q^{22} + 12 q^{23} + 12 q^{25} + 30 q^{26} - 12 q^{28} + 24 q^{29} + 12 q^{31} - 27 q^{32} - 12 q^{35} - 3 q^{37} + 30 q^{38} - 15 q^{40} - 6 q^{41} - 15 q^{43} - 3 q^{44} - 3 q^{46} - 12 q^{47} - 33 q^{49} - 21 q^{50} - 45 q^{52} + 18 q^{53} - 12 q^{55} - 30 q^{56} - 51 q^{58} + 3 q^{59} - 33 q^{61} + 12 q^{62} + 12 q^{64} - 21 q^{65} - 6 q^{67} - 9 q^{68} - 15 q^{70} - 27 q^{71} + 6 q^{73} + 21 q^{74} + 6 q^{76} + 12 q^{77} + 21 q^{79} - 42 q^{80} - 12 q^{82} + 6 q^{83} + 36 q^{85} + 21 q^{86} + 42 q^{88} - 9 q^{89} + 6 q^{91} + 3 q^{92} + 48 q^{94} - 3 q^{95} + 39 q^{97} + 45 q^{98}+O(q^{100}) \) 12 * q - 3 * q^2 + 3 * q^4 - 6 * q^5 + 3 * q^7 - 6 * q^8 - 3 * q^10 + 6 * q^11 + 3 * q^13 + 21 * q^14 + 9 * q^16 - 9 * q^17 - 3 * q^19 - 24 * q^20 + 12 * q^22 + 12 * q^23 + 12 * q^25 + 30 * q^26 - 12 * q^28 + 24 * q^29 + 12 * q^31 - 27 * q^32 - 12 * q^35 - 3 * q^37 + 30 * q^38 - 15 * q^40 - 6 * q^41 - 15 * q^43 - 3 * q^44 - 3 * q^46 - 12 * q^47 - 33 * q^49 - 21 * q^50 - 45 * q^52 + 18 * q^53 - 12 * q^55 - 30 * q^56 - 51 * q^58 + 3 * q^59 - 33 * q^61 + 12 * q^62 + 12 * q^64 - 21 * q^65 - 6 * q^67 - 9 * q^68 - 15 * q^70 - 27 * q^71 + 6 * q^73 + 21 * q^74 + 6 * q^76 + 12 * q^77 + 21 * q^79 - 42 * q^80 - 12 * q^82 + 6 * q^83 + 36 * q^85 + 21 * q^86 + 42 * q^88 - 9 * q^89 + 6 * q^91 + 3 * q^92 + 48 * q^94 - 3 * q^95 + 39 * q^97 + 45 * q^98

Introduction

L-functions

Modular forms

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