LMFDB - Embedded newform 726.2.e.e.493.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [726,2,Mod(487,726)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(726, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 8]))

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

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

chi := DirichletCharacter("726.487");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 726 = 2 \cdot 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	726.e (of order $5$, degree $4$, 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:	$5.79713918674$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 66)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			493.1
Root			$-0.309017 - 0.951057i$ of defining polynomial
Character	$\chi$	$=$	726.493
Dual form			726.2.e.e.511.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 - 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-1.23607 - 3.80423i) q^{5} +(0.309017 + 0.951057i) q^{6} +(1.61803 + 1.17557i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(0.309017 - 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-1.23607 - 3.80423i) q^{5} +(0.309017 + 0.951057i) q^{6} +(1.61803 + 1.17557i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.309017 - 0.951057i) q^{9} -4.00000 q^{10} +1.00000 q^{12} +(1.23607 - 3.80423i) q^{13} +(1.61803 - 1.17557i) q^{14} +(3.23607 + 2.35114i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-0.618034 - 1.90211i) q^{17} +(-0.809017 - 0.587785i) q^{18} +(-1.23607 + 3.80423i) q^{20} -2.00000 q^{21} -6.00000 q^{23} +(0.309017 - 0.951057i) q^{24} +(-8.89919 + 6.46564i) q^{25} +(-3.23607 - 2.35114i) q^{26} +(0.309017 + 0.951057i) q^{27} +(-0.618034 - 1.90211i) q^{28} +(-8.09017 - 5.87785i) q^{29} +(3.23607 - 2.35114i) q^{30} +(-2.47214 + 7.60845i) q^{31} +1.00000 q^{32} -2.00000 q^{34} +(2.47214 - 7.60845i) q^{35} +(-0.809017 + 0.587785i) q^{36} +(1.61803 + 1.17557i) q^{37} +(1.23607 + 3.80423i) q^{39} +(3.23607 + 2.35114i) q^{40} +(-1.61803 + 1.17557i) q^{41} +(-0.618034 + 1.90211i) q^{42} +4.00000 q^{43} -4.00000 q^{45} +(-1.85410 + 5.70634i) q^{46} +(1.61803 - 1.17557i) q^{47} +(-0.809017 - 0.587785i) q^{48} +(-0.927051 - 2.85317i) q^{49} +(3.39919 + 10.4616i) q^{50} +(1.61803 + 1.17557i) q^{51} +(-3.23607 + 2.35114i) q^{52} +(1.23607 - 3.80423i) q^{53} +1.00000 q^{54} -2.00000 q^{56} +(-8.09017 + 5.87785i) q^{58} +(-1.23607 - 3.80423i) q^{60} +(-2.47214 - 7.60845i) q^{61} +(6.47214 + 4.70228i) q^{62} +(1.61803 - 1.17557i) q^{63} +(0.309017 - 0.951057i) q^{64} -16.0000 q^{65} -12.0000 q^{67} +(-0.618034 + 1.90211i) q^{68} +(4.85410 - 3.52671i) q^{69} +(-6.47214 - 4.70228i) q^{70} +(0.618034 + 1.90211i) q^{71} +(0.309017 + 0.951057i) q^{72} +(4.85410 + 3.52671i) q^{73} +(1.61803 - 1.17557i) q^{74} +(3.39919 - 10.4616i) q^{75} +4.00000 q^{78} +(3.09017 - 9.51057i) q^{79} +(3.23607 - 2.35114i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(0.618034 + 1.90211i) q^{82} +(1.23607 + 3.80423i) q^{83} +(1.61803 + 1.17557i) q^{84} +(-6.47214 + 4.70228i) q^{85} +(1.23607 - 3.80423i) q^{86} +10.0000 q^{87} +10.0000 q^{89} +(-1.23607 + 3.80423i) q^{90} +(6.47214 - 4.70228i) q^{91} +(4.85410 + 3.52671i) q^{92} +(-2.47214 - 7.60845i) q^{93} +(-0.618034 - 1.90211i) q^{94} +(-0.809017 + 0.587785i) q^{96} +(-0.618034 + 1.90211i) q^{97} -3.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} - q^{3} - q^{4} + 4 q^{5} - q^{6} + 2 q^{7} - q^{8} - q^{9}+O(q^{10}) $ 4 * q - q^2 - q^3 - q^4 + 4 * q^5 - q^6 + 2 * q^7 - q^8 - q^9	$ 4 q - q^{2} - q^{3} - q^{4} + 4 q^{5} - q^{6} + 2 q^{7} - q^{8} - q^{9} - 16 q^{10} + 4 q^{12} - 4 q^{13} + 2 q^{14} + 4 q^{15} - q^{16} + 2 q^{17} - q^{18} + 4 q^{20} - 8 q^{21} - 24 q^{23} - q^{24} - 11 q^{25} - 4 q^{26} - q^{27} + 2 q^{28} - 10 q^{29} + 4 q^{30} + 8 q^{31} + 4 q^{32} - 8 q^{34} - 8 q^{35} - q^{36} + 2 q^{37} - 4 q^{39} + 4 q^{40} - 2 q^{41} + 2 q^{42} + 16 q^{43} - 16 q^{45} + 6 q^{46} + 2 q^{47} - q^{48} + 3 q^{49} - 11 q^{50} + 2 q^{51} - 4 q^{52} - 4 q^{53} + 4 q^{54} - 8 q^{56} - 10 q^{58} + 4 q^{60} + 8 q^{61} + 8 q^{62} + 2 q^{63} - q^{64} - 64 q^{65} - 48 q^{67} + 2 q^{68} + 6 q^{69} - 8 q^{70} - 2 q^{71} - q^{72} + 6 q^{73} + 2 q^{74} - 11 q^{75} + 16 q^{78} - 10 q^{79} + 4 q^{80} - q^{81} - 2 q^{82} - 4 q^{83} + 2 q^{84} - 8 q^{85} - 4 q^{86} + 40 q^{87} + 40 q^{89} + 4 q^{90} + 8 q^{91} + 6 q^{92} + 8 q^{93} + 2 q^{94} - q^{96} + 2 q^{97} - 12 q^{98}+O(q^{100}) $ 4 * q - q^2 - q^3 - q^4 + 4 * q^5 - q^6 + 2 * q^7 - q^8 - q^9 - 16 * q^10 + 4 * q^12 - 4 * q^13 + 2 * q^14 + 4 * q^15 - q^16 + 2 * q^17 - q^18 + 4 * q^20 - 8 * q^21 - 24 * q^23 - q^24 - 11 * q^25 - 4 * q^26 - q^27 + 2 * q^28 - 10 * q^29 + 4 * q^30 + 8 * q^31 + 4 * q^32 - 8 * q^34 - 8 * q^35 - q^36 + 2 * q^37 - 4 * q^39 + 4 * q^40 - 2 * q^41 + 2 * q^42 + 16 * q^43 - 16 * q^45 + 6 * q^46 + 2 * q^47 - q^48 + 3 * q^49 - 11 * q^50 + 2 * q^51 - 4 * q^52 - 4 * q^53 + 4 * q^54 - 8 * q^56 - 10 * q^58 + 4 * q^60 + 8 * q^61 + 8 * q^62 + 2 * q^63 - q^64 - 64 * q^65 - 48 * q^67 + 2 * q^68 + 6 * q^69 - 8 * q^70 - 2 * q^71 - q^72 + 6 * q^73 + 2 * q^74 - 11 * q^75 + 16 * q^78 - 10 * q^79 + 4 * q^80 - q^81 - 2 * q^82 - 4 * q^83 + 2 * q^84 - 8 * q^85 - 4 * q^86 + 40 * q^87 + 40 * q^89 + 4 * q^90 + 8 * q^91 + 6 * q^92 + 8 * q^93 + 2 * q^94 - q^96 + 2 * q^97 - 12 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/726\mathbb{Z}\right)^\times$.

$n$	$485$	$607$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	−1.23607	−	3.80423i	−0.552786	−	1.70130i	−0.701719	−	0.712454i	$-0.747584\pi$
$5$	−1.23607	−	3.80423i	−0.552786	−	1.70130i	0.148932	−	0.988847i	$-0.452416\pi$
$6$	0.309017	+	0.951057i	0.126156	+	0.388267i
$7$	1.61803	+	1.17557i	0.611559	+	0.444324i	0.849963	−	0.526842i	$-0.176624\pi$
$7$	1.61803	+	1.17557i	0.611559	+	0.444324i	−0.238404	+	0.971166i	$0.576624\pi$
$8$	−0.809017	+	0.587785i	−0.286031	+	0.207813i
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$	−4.00000			−1.26491
$11$		0			0
$11$		0			0
$12$	1.00000			0.288675
$13$	1.23607	−	3.80423i	0.342824	−	1.05510i	−0.619915	−	0.784669i	$-0.712833\pi$
$13$	1.23607	−	3.80423i	0.342824	−	1.05510i	0.962739	−	0.270434i	$-0.0871670\pi$
$14$	1.61803	−	1.17557i	0.432438	−	0.314184i
$15$	3.23607	+	2.35114i	0.835549	+	0.607062i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−0.618034	−	1.90211i	−0.149895	−	0.461330i	0.847713	−	0.530456i	$-0.177979\pi$
$17$	−0.618034	−	1.90211i	−0.149895	−	0.461330i	−0.997608	+	0.0691254i	$0.977979\pi$
$18$	−0.809017	−	0.587785i	−0.190687	−	0.138542i
$19$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$19$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$20$	−1.23607	+	3.80423i	−0.276393	+	0.850651i
$21$	−2.00000			−0.436436
$22$		0			0
$23$	−6.00000			−1.25109			−0.625543	−	0.780189i	$-0.715123\pi$
$23$	−6.00000			−1.25109			−0.625543	+	0.780189i	$0.715123\pi$
$24$	0.309017	−	0.951057i	0.0630778	−	0.194134i
$25$	−8.89919	+	6.46564i	−1.77984	+	1.29313i
$26$	−3.23607	−	2.35114i	−0.634645	−	0.461097i
$27$	0.309017	+	0.951057i	0.0594703	+	0.183031i
$28$	−0.618034	−	1.90211i	−0.116797	−	0.359466i
$29$	−8.09017	−	5.87785i	−1.50231	−	1.09149i	−0.969451	−	0.245284i	$-0.921119\pi$
$29$	−8.09017	−	5.87785i	−1.50231	−	1.09149i	−0.532855	−	0.846206i	$-0.678881\pi$
$30$	3.23607	−	2.35114i	0.590822	−	0.429258i
$31$	−2.47214	+	7.60845i	−0.444009	+	1.36652i	0.439558	+	0.898214i	$0.355135\pi$
$31$	−2.47214	+	7.60845i	−0.444009	+	1.36652i	−0.883567	+	0.468304i	$0.844865\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	−2.00000			−0.342997
$35$	2.47214	−	7.60845i	0.417867	−	1.28606i
$36$	−0.809017	+	0.587785i	−0.134836	+	0.0979642i
$37$	1.61803	+	1.17557i	0.266003	+	0.193263i	0.712789	−	0.701378i	$-0.247432\pi$
$37$	1.61803	+	1.17557i	0.266003	+	0.193263i	−0.446786	+	0.894641i	$0.647432\pi$
$38$		0			0
$39$	1.23607	+	3.80423i	0.197929	+	0.609164i
$40$	3.23607	+	2.35114i	0.511667	+	0.371748i
$41$	−1.61803	+	1.17557i	−0.252694	+	0.183593i	−0.706920	−	0.707293i	$-0.749916\pi$
$41$	−1.61803	+	1.17557i	−0.252694	+	0.183593i	0.454226	+	0.890887i	$0.349916\pi$
$42$	−0.618034	+	1.90211i	−0.0953647	+	0.293502i
$43$	4.00000			0.609994			0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000			0.609994			0.304997	+	0.952353i	$0.401344\pi$
$44$		0			0
$45$	−4.00000			−0.596285
$46$	−1.85410	+	5.70634i	−0.273372	+	0.841354i
$47$	1.61803	−	1.17557i	0.236015	−	0.171475i	−0.463491	−	0.886101i	$-0.653403\pi$
$47$	1.61803	−	1.17557i	0.236015	−	0.171475i	0.699506	+	0.714627i	$0.253403\pi$
$48$	−0.809017	−	0.587785i	−0.116772	−	0.0848395i
$49$	−0.927051	−	2.85317i	−0.132436	−	0.407596i
$50$	3.39919	+	10.4616i	0.480718	+	1.47950i
$51$	1.61803	+	1.17557i	0.226570	+	0.164613i
$52$	−3.23607	+	2.35114i	−0.448762	+	0.326045i
$53$	1.23607	−	3.80423i	0.169787	−	0.522551i	−0.829570	−	0.558403i	$-0.811414\pi$
$53$	1.23607	−	3.80423i	0.169787	−	0.522551i	0.999357	+	0.0358519i	$0.0114145\pi$
$54$	1.00000			0.136083
$55$		0			0
$56$	−2.00000			−0.267261
$57$		0			0
$58$	−8.09017	+	5.87785i	−1.06229	+	0.771800i
$59$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$59$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$60$	−1.23607	−	3.80423i	−0.159576	−	0.491123i
$61$	−2.47214	−	7.60845i	−0.316525	−	0.974162i	−0.975122	−	0.221667i	$-0.928850\pi$
$61$	−2.47214	−	7.60845i	−0.316525	−	0.974162i	0.658598	−	0.752495i	$-0.271150\pi$
$62$	6.47214	+	4.70228i	0.821962	+	0.597190i
$63$	1.61803	−	1.17557i	0.203853	−	0.148108i
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	−16.0000			−1.98456
$66$		0			0
$67$	−12.0000			−1.46603			−0.733017	−	0.680211i	$-0.761888\pi$
$67$	−12.0000			−1.46603			−0.733017	+	0.680211i	$0.761888\pi$
$68$	−0.618034	+	1.90211i	−0.0749476	+	0.230665i
$69$	4.85410	−	3.52671i	0.584365	−	0.424566i
$70$	−6.47214	−	4.70228i	−0.773568	−	0.562030i
$71$	0.618034	+	1.90211i	0.0733471	+	0.225739i	0.981009	−	0.193963i	$-0.0621343\pi$
$71$	0.618034	+	1.90211i	0.0733471	+	0.225739i	−0.907662	+	0.419703i	$0.862134\pi$
$72$	0.309017	+	0.951057i	0.0364180	+	0.112083i
$73$	4.85410	+	3.52671i	0.568130	+	0.412770i	0.834425	−	0.551121i	$-0.185800\pi$
$73$	4.85410	+	3.52671i	0.568130	+	0.412770i	−0.266296	+	0.963891i	$0.585800\pi$
$74$	1.61803	−	1.17557i	0.188093	−	0.136657i
$75$	3.39919	−	10.4616i	0.392504	−	1.20800i
$76$		0			0
$77$		0			0
$78$	4.00000			0.452911
$79$	3.09017	−	9.51057i	0.347671	−	1.07002i	−0.612467	−	0.790496i	$-0.709823\pi$
$79$	3.09017	−	9.51057i	0.347671	−	1.07002i	0.960138	−	0.279526i	$-0.0901773\pi$
$80$	3.23607	−	2.35114i	0.361803	−	0.262866i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	0.618034	+	1.90211i	0.0682504	+	0.210053i
$83$	1.23607	+	3.80423i	0.135676	+	0.417568i	0.995695	−	0.0926948i	$-0.0295481\pi$
$83$	1.23607	+	3.80423i	0.135676	+	0.417568i	−0.860018	+	0.510263i	$0.829548\pi$
$84$	1.61803	+	1.17557i	0.176542	+	0.128265i
$85$	−6.47214	+	4.70228i	−0.702002	+	0.510034i
$86$	1.23607	−	3.80423i	0.133289	−	0.410220i
$87$	10.0000			1.07211
$88$		0			0
$89$	10.0000			1.06000			0.529999	−	0.847998i	$-0.322192\pi$
$89$	10.0000			1.06000			0.529999	+	0.847998i	$0.322192\pi$
$90$	−1.23607	+	3.80423i	−0.130293	+	0.401001i
$91$	6.47214	−	4.70228i	0.678464	−	0.492933i
$92$	4.85410	+	3.52671i	0.506075	+	0.367685i
$93$	−2.47214	−	7.60845i	−0.256349	−	0.788960i
$94$	−0.618034	−	1.90211i	−0.0637453	−	0.196188i
$95$		0			0
$96$	−0.809017	+	0.587785i	−0.0825700	+	0.0599906i
$97$	−0.618034	+	1.90211i	−0.0627518	+	0.193130i	−0.977517	−	0.210855i	$-0.932375\pi$
$97$	−0.618034	+	1.90211i	−0.0627518	+	0.193130i	0.914766	+	0.403985i	$0.132375\pi$
$98$	−3.00000			−0.303046
$99$		0			0
$100$	11.0000			1.10000
$101$	0.618034	−	1.90211i	0.0614967	−	0.189267i	−0.915588	−	0.402117i	$-0.868274\pi$
$101$	0.618034	−	1.90211i	0.0614967	−	0.189267i	0.977085	+	0.212850i	$0.0682745\pi$
$102$	1.61803	−	1.17557i	0.160209	−	0.116399i
$103$	−3.23607	−	2.35114i	−0.318859	−	0.231665i	0.416829	−	0.908985i	$-0.363141\pi$
$103$	−3.23607	−	2.35114i	−0.318859	−	0.231665i	−0.735689	+	0.677320i	$0.763141\pi$
$104$	1.23607	+	3.80423i	0.121206	+	0.373035i
$105$	2.47214	+	7.60845i	0.241256	+	0.742509i
$106$	−3.23607	−	2.35114i	−0.314315	−	0.228363i
$107$	9.70820	−	7.05342i	0.938527	−	0.681880i	−0.00953827	−	0.999955i	$-0.503036\pi$
$107$	9.70820	−	7.05342i	0.938527	−	0.681880i	0.948066	+	0.318074i	$0.103036\pi$
$108$	0.309017	−	0.951057i	0.0297352	−	0.0915155i
$109$	20.0000			1.91565			0.957826	−	0.287348i	$-0.0927736\pi$
$109$	20.0000			1.91565			0.957826	+	0.287348i	$0.0927736\pi$
$110$		0			0
$111$	−2.00000			−0.189832
$112$	−0.618034	+	1.90211i	−0.0583987	+	0.179733i
$113$	4.85410	−	3.52671i	0.456636	−	0.331765i	−0.335575	−	0.942014i	$-0.608930\pi$
$113$	4.85410	−	3.52671i	0.456636	−	0.331765i	0.792210	+	0.610249i	$0.208930\pi$
$114$		0			0
$115$	7.41641	+	22.8254i	0.691584	+	2.12848i
$116$	3.09017	+	9.51057i	0.286915	+	0.883034i
$117$	−3.23607	−	2.35114i	−0.299175	−	0.217363i
$118$		0			0
$119$	1.23607	−	3.80423i	0.113310	−	0.348733i
$120$	−4.00000			−0.365148
$121$		0			0
$122$	−8.00000			−0.724286
$123$	0.618034	−	1.90211i	0.0557262	−	0.171508i
$124$	6.47214	−	4.70228i	0.581215	−	0.422277i
$125$	19.4164	+	14.1068i	1.73666	+	1.26175i
$126$	−0.618034	−	1.90211i	−0.0550588	−	0.169454i
$127$	−6.79837	−	20.9232i	−0.603258	−	1.85664i	−0.508348	−	0.861152i	$-0.669744\pi$
$127$	−6.79837	−	20.9232i	−0.603258	−	1.85664i	−0.0949102	−	0.995486i	$-0.530256\pi$
$128$	−0.809017	−	0.587785i	−0.0715077	−	0.0519534i
$129$	−3.23607	+	2.35114i	−0.284920	+	0.207006i
$130$	−4.94427	+	15.2169i	−0.433641	+	1.33461i
$131$	12.0000			1.04844			0.524222	−	0.851581i	$-0.324356\pi$
$131$	12.0000			1.04844			0.524222	+	0.851581i	$0.324356\pi$
$132$		0			0
$133$		0			0
$134$	−3.70820	+	11.4127i	−0.320340	+	0.985905i
$135$	3.23607	−	2.35114i	0.278516	−	0.202354i
$136$	1.61803	+	1.17557i	0.138745	+	0.100804i
$137$	−0.618034	−	1.90211i	−0.0528022	−	0.162508i	0.921178	−	0.389141i	$-0.127228\pi$
$137$	−0.618034	−	1.90211i	−0.0528022	−	0.162508i	−0.973980	+	0.226633i	$0.927228\pi$
$138$	−1.85410	−	5.70634i	−0.157832	−	0.485756i
$139$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$139$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$140$	−6.47214	+	4.70228i	−0.546995	+	0.397415i
$141$	−0.618034	+	1.90211i	−0.0520479	+	0.160187i
$142$	2.00000			0.167836
$143$		0			0
$144$	1.00000			0.0833333
$145$	−12.3607	+	38.0423i	−1.02650	+	3.15924i
$146$	4.85410	−	3.52671i	0.401728	−	0.291873i
$147$	2.42705	+	1.76336i	0.200180	+	0.145439i
$148$	−0.618034	−	1.90211i	−0.0508021	−	0.156353i
$149$	−3.09017	−	9.51057i	−0.253157	−	0.779136i	−0.994187	−	0.107665i	$-0.965663\pi$
$149$	−3.09017	−	9.51057i	−0.253157	−	0.779136i	0.741031	−	0.671471i	$-0.234337\pi$
$150$	−8.89919	−	6.46564i	−0.726616	−	0.527917i
$151$	−1.61803	+	1.17557i	−0.131674	+	0.0956666i	−0.651673	−	0.758500i	$-0.725932\pi$
$151$	−1.61803	+	1.17557i	−0.131674	+	0.0956666i	0.519999	+	0.854167i	$0.325932\pi$
$152$		0			0
$153$	−2.00000			−0.161690
$154$		0			0
$155$	32.0000			2.57030
$156$	1.23607	−	3.80423i	0.0989646	−	0.304582i
$157$	−14.5623	+	10.5801i	−1.16220	+	0.844387i	−0.990054	−	0.140685i	$-0.955069\pi$
$157$	−14.5623	+	10.5801i	−1.16220	+	0.844387i	−0.172144	+	0.985072i	$0.555069\pi$
$158$	−8.09017	−	5.87785i	−0.643619	−	0.467617i
$159$	1.23607	+	3.80423i	0.0980266	+	0.301695i
$160$	−1.23607	−	3.80423i	−0.0977198	−	0.300750i
$161$	−9.70820	−	7.05342i	−0.765114	−	0.555888i
$162$	−0.809017	+	0.587785i	−0.0635624	+	0.0461808i
$163$	1.23607	−	3.80423i	0.0968163	−	0.297970i	−0.890906	−	0.454187i	$-0.849930\pi$
$163$	1.23607	−	3.80423i	0.0968163	−	0.297970i	0.987723	+	0.156217i	$0.0499299\pi$
$164$	2.00000			0.156174
$165$		0			0
$166$	4.00000			0.310460
$167$	−3.70820	+	11.4127i	−0.286949	+	0.883140i	0.698858	+	0.715260i	$0.253692\pi$
$167$	−3.70820	+	11.4127i	−0.286949	+	0.883140i	−0.985808	+	0.167879i	$0.946308\pi$
$168$	1.61803	−	1.17557i	0.124834	−	0.0906972i
$169$	−2.42705	−	1.76336i	−0.186696	−	0.135643i
$170$	2.47214	+	7.60845i	0.189604	+	0.583542i
$171$		0			0
$172$	−3.23607	−	2.35114i	−0.246748	−	0.179273i
$173$	4.85410	−	3.52671i	0.369051	−	0.268131i	−0.387767	−	0.921758i	$-0.626753\pi$
$173$	4.85410	−	3.52671i	0.369051	−	0.268131i	0.756817	+	0.653627i	$0.226753\pi$
$174$	3.09017	−	9.51057i	0.234265	−	0.720994i
$175$	−22.0000			−1.66304
$176$		0			0
$177$		0			0
$178$	3.09017	−	9.51057i	0.231618	−	0.712847i
$179$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$179$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$180$	3.23607	+	2.35114i	0.241202	+	0.175244i
$181$	0.618034	+	1.90211i	0.0459381	+	0.141383i	0.971395	−	0.237471i	$-0.0763184\pi$
$181$	0.618034	+	1.90211i	0.0459381	+	0.141383i	−0.925457	+	0.378854i	$0.876318\pi$
$182$	−2.47214	−	7.60845i	−0.183247	−	0.563976i
$183$	6.47214	+	4.70228i	0.478434	+	0.347603i
$184$	4.85410	−	3.52671i	0.357849	−	0.259993i
$185$	2.47214	−	7.60845i	0.181755	−	0.559385i
$186$	−8.00000			−0.586588
$187$		0			0
$188$	−2.00000			−0.145865
$189$	−0.618034	+	1.90211i	−0.0449554	+	0.138358i
$190$		0			0
$191$	−17.7984	−	12.9313i	−1.28785	−	0.935674i	−0.288086	−	0.957605i	$-0.593019\pi$
$191$	−17.7984	−	12.9313i	−1.28785	−	0.935674i	−0.999760	+	0.0219304i	$0.993019\pi$
$192$	0.309017	+	0.951057i	0.0223014	+	0.0686366i
$193$	4.32624	+	13.3148i	0.311409	+	0.958420i	0.977207	+	0.212287i	$0.0680913\pi$
$193$	4.32624	+	13.3148i	0.311409	+	0.958420i	−0.665798	+	0.746132i	$0.731909\pi$
$194$	1.61803	+	1.17557i	0.116168	+	0.0844010i
$195$	12.9443	−	9.40456i	0.926959	−	0.673475i
$196$	−0.927051	+	2.85317i	−0.0662179	+	0.203798i
$197$	18.0000			1.28245			0.641223	−	0.767354i	$-0.278427\pi$
$197$	18.0000			1.28245			0.641223	+	0.767354i	$0.278427\pi$
$198$		0			0
$199$	20.0000			1.41776			0.708881	−	0.705328i	$-0.249200\pi$
$199$	20.0000			1.41776			0.708881	+	0.705328i	$0.249200\pi$
$200$	3.39919	−	10.4616i	0.240359	−	0.739748i
$201$	9.70820	−	7.05342i	0.684764	−	0.497510i
$202$	−1.61803	−	1.17557i	−0.113844	−	0.0827129i
$203$	−6.18034	−	19.0211i	−0.433775	−	1.33502i
$204$	−0.618034	−	1.90211i	−0.0432710	−	0.133175i
$205$	6.47214	+	4.70228i	0.452034	+	0.328422i
$206$	−3.23607	+	2.35114i	−0.225468	+	0.163812i
$207$	−1.85410	+	5.70634i	−0.128869	+	0.396618i
$208$	4.00000			0.277350
$209$		0			0
$210$	8.00000			0.552052
$211$	3.70820	−	11.4127i	0.255283	−	0.785681i	−0.738490	−	0.674264i	$-0.764461\pi$
$211$	3.70820	−	11.4127i	0.255283	−	0.785681i	0.993774	−	0.111417i	$-0.0355390\pi$
$212$	−3.23607	+	2.35114i	−0.222254	+	0.161477i
$213$	−1.61803	−	1.17557i	−0.110866	−	0.0805488i
$214$	−3.70820	−	11.4127i	−0.253488	−	0.780155i
$215$	−4.94427	−	15.2169i	−0.337197	−	1.03778i
$216$	−0.809017	−	0.587785i	−0.0550466	−	0.0399937i
$217$	−12.9443	+	9.40456i	−0.878714	+	0.638423i
$218$	6.18034	−	19.0211i	0.418585	−	1.28827i
$219$	−6.00000			−0.405442
$220$		0			0
$221$	−8.00000			−0.538138
$222$	−0.618034	+	1.90211i	−0.0414797	+	0.127661i
$223$	12.9443	−	9.40456i	0.866813	−	0.629776i	−0.0629172	−	0.998019i	$-0.520040\pi$
$223$	12.9443	−	9.40456i	0.866813	−	0.629776i	0.929730	+	0.368243i	$0.120040\pi$
$224$	1.61803	+	1.17557i	0.108109	+	0.0785461i
$225$	3.39919	+	10.4616i	0.226612	+	0.697441i
$226$	−1.85410	−	5.70634i	−0.123333	−	0.379580i
$227$	9.70820	+	7.05342i	0.644356	+	0.468152i	0.861344	−	0.508022i	$-0.169623\pi$
$227$	9.70820	+	7.05342i	0.644356	+	0.468152i	−0.216988	+	0.976174i	$0.569623\pi$
$228$		0			0
$229$	3.09017	−	9.51057i	0.204204	−	0.628476i	−0.795541	−	0.605900i	$-0.792813\pi$
$229$	3.09017	−	9.51057i	0.204204	−	0.628476i	0.999745	−	0.0225760i	$-0.00718678\pi$
$230$	24.0000			1.58251
$231$		0			0
$232$	10.0000			0.656532
$233$	−1.85410	+	5.70634i	−0.121466	+	0.373835i	−0.993241	−	0.116073i	$-0.962969\pi$
$233$	−1.85410	+	5.70634i	−0.121466	+	0.373835i	0.871774	+	0.489907i	$0.162969\pi$
$234$	−3.23607	+	2.35114i	−0.211548	+	0.153699i
$235$	−6.47214	−	4.70228i	−0.422196	−	0.306743i
$236$		0			0
$237$	3.09017	+	9.51057i	0.200728	+	0.617778i
$238$	−3.23607	−	2.35114i	−0.209763	−	0.152402i
$239$	16.1803	−	11.7557i	1.04662	−	0.760413i	0.0750525	−	0.997180i	$-0.476088\pi$
$239$	16.1803	−	11.7557i	1.04662	−	0.760413i	0.971567	+	0.236766i	$0.0760876\pi$
$240$	−1.23607	+	3.80423i	−0.0797878	+	0.245562i
$241$	−18.0000			−1.15948			−0.579741	−	0.814801i	$-0.696846\pi$
$241$	−18.0000			−1.15948			−0.579741	+	0.814801i	$0.696846\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$	−2.47214	+	7.60845i	−0.158262	+	0.487081i
$245$	−9.70820	+	7.05342i	−0.620234	+	0.450627i
$246$	−1.61803	−	1.17557i	−0.103162	−	0.0749516i
$247$		0			0
$248$	−2.47214	−	7.60845i	−0.156981	−	0.483137i
$249$	−3.23607	−	2.35114i	−0.205077	−	0.148998i
$250$	19.4164	−	14.1068i	1.22800	−	0.892195i
$251$	−2.47214	+	7.60845i	−0.156040	+	0.480241i	−0.998265	−	0.0588851i	$-0.981245\pi$
$251$	−2.47214	+	7.60845i	−0.156040	+	0.480241i	0.842225	+	0.539126i	$0.181245\pi$
$252$	−2.00000			−0.125988
$253$		0			0
$254$	−22.0000			−1.38040
$255$	2.47214	−	7.60845i	0.154811	−	0.476460i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−14.5623	−	10.5801i	−0.908372	−	0.659971i	0.0322308	−	0.999480i	$-0.489739\pi$
$257$	−14.5623	−	10.5801i	−0.908372	−	0.659971i	−0.940603	+	0.339510i	$0.889739\pi$
$258$	1.23607	+	3.80423i	0.0769542	+	0.236841i
$259$	1.23607	+	3.80423i	0.0768055	+	0.236383i
$260$	12.9443	+	9.40456i	0.802770	+	0.583246i
$261$	−8.09017	+	5.87785i	−0.500769	+	0.363830i
$262$	3.70820	−	11.4127i	0.229094	−	0.705078i
$263$	−16.0000			−0.986602			−0.493301	−	0.869859i	$-0.664210\pi$
$263$	−16.0000			−0.986602			−0.493301	+	0.869859i	$0.664210\pi$
$264$		0			0
$265$	−16.0000			−0.982872
$266$		0			0
$267$	−8.09017	+	5.87785i	−0.495110	+	0.359719i
$268$	9.70820	+	7.05342i	0.593023	+	0.430856i
$269$	−6.18034	−	19.0211i	−0.376822	−	1.15974i	−0.942241	−	0.334935i	$-0.891286\pi$
$269$	−6.18034	−	19.0211i	−0.376822	−	1.15974i	0.565419	−	0.824804i	$-0.308714\pi$
$270$	−1.23607	−	3.80423i	−0.0752247	−	0.231518i
$271$	−17.7984	−	12.9313i	−1.08117	−	0.785519i	−0.103287	−	0.994652i	$-0.532936\pi$
$271$	−17.7984	−	12.9313i	−1.08117	−	0.785519i	−0.977887	+	0.209133i	$0.932936\pi$
$272$	1.61803	−	1.17557i	0.0981077	−	0.0712794i
$273$	−2.47214	+	7.60845i	−0.149620	+	0.460484i
$274$	−2.00000			−0.120824
$275$		0			0
$276$	−6.00000			−0.361158
$277$	2.47214	−	7.60845i	0.148536	−	0.457148i	−0.848913	−	0.528533i	$-0.822742\pi$
$277$	2.47214	−	7.60845i	0.148536	−	0.457148i	0.997449	+	0.0713858i	$0.0227421\pi$
$278$		0			0
$279$	6.47214	+	4.70228i	0.387477	+	0.281518i
$280$	2.47214	+	7.60845i	0.147738	+	0.454692i
$281$	6.79837	+	20.9232i	0.405557	+	1.24818i	0.920429	+	0.390909i	$0.127839\pi$
$281$	6.79837	+	20.9232i	0.405557	+	1.24818i	−0.514872	+	0.857267i	$0.672161\pi$
$282$	1.61803	+	1.17557i	0.0963525	+	0.0700042i
$283$	−3.23607	+	2.35114i	−0.192364	+	0.139761i	−0.679799	−	0.733399i	$-0.737933\pi$
$283$	−3.23607	+	2.35114i	−0.192364	+	0.139761i	0.487434	+	0.873160i	$0.337933\pi$
$284$	0.618034	−	1.90211i	0.0366736	−	0.112870i
$285$		0			0
$286$		0			0
$287$	−4.00000			−0.236113
$288$	0.309017	−	0.951057i	0.0182090	−	0.0560415i
$289$	10.5172	−	7.64121i	0.618660	−	0.449483i
$290$	32.3607	+	23.5114i	1.90028	+	1.38064i
$291$	−0.618034	−	1.90211i	−0.0362298	−	0.111504i
$292$	−1.85410	−	5.70634i	−0.108503	−	0.333938i
$293$	−11.3262	−	8.22899i	−0.661686	−	0.480743i	0.205546	−	0.978647i	$-0.434103\pi$
$293$	−11.3262	−	8.22899i	−0.661686	−	0.480743i	−0.867232	+	0.497905i	$0.834103\pi$
$294$	2.42705	−	1.76336i	0.141548	−	0.102841i
$295$		0			0
$296$	−2.00000			−0.116248
$297$		0			0
$298$	−10.0000			−0.579284
$299$	−7.41641	+	22.8254i	−0.428902	+	1.32002i
$300$	−8.89919	+	6.46564i	−0.513795	+	0.373294i
$301$	6.47214	+	4.70228i	0.373048	+	0.271035i
$302$	0.618034	+	1.90211i	0.0355639	+	0.109454i
$303$	0.618034	+	1.90211i	0.0355051	+	0.109274i
$304$		0			0
$305$	−25.8885	+	18.8091i	−1.48237	+	1.07701i
$306$	−0.618034	+	1.90211i	−0.0353307	+	0.108737i
$307$	8.00000			0.456584			0.228292	−	0.973593i	$-0.426686\pi$
$307$	8.00000			0.456584			0.228292	+	0.973593i	$0.426686\pi$
$308$		0			0
$309$	4.00000			0.227552
$310$	9.88854	−	30.4338i	0.561632	−	1.72852i
$311$	−1.61803	+	1.17557i	−0.0917503	+	0.0666605i	−0.632715	−	0.774385i	$-0.718059\pi$
$311$	−1.61803	+	1.17557i	−0.0917503	+	0.0666605i	0.540964	+	0.841046i	$0.318059\pi$
$312$	−3.23607	−	2.35114i	−0.183206	−	0.133107i
$313$	−1.85410	−	5.70634i	−0.104800	−	0.322541i	0.884883	−	0.465813i	$-0.154238\pi$
$313$	−1.85410	−	5.70634i	−0.104800	−	0.322541i	−0.989683	+	0.143271i	$0.954238\pi$
$314$	5.56231	+	17.1190i	0.313899	+	0.966082i
$315$	−6.47214	−	4.70228i	−0.364664	−	0.264944i
$316$	−8.09017	+	5.87785i	−0.455108	+	0.330655i
$317$	−9.88854	+	30.4338i	−0.555396	+	1.70933i	0.139499	+	0.990222i	$0.455451\pi$
$317$	−9.88854	+	30.4338i	−0.555396	+	1.70933i	−0.694895	+	0.719111i	$0.744549\pi$
$318$	4.00000			0.224309
$319$		0			0
$320$	−4.00000			−0.223607
$321$	−3.70820	+	11.4127i	−0.206972	+	0.636994i
$322$	−9.70820	+	7.05342i	−0.541017	+	0.393072i
$323$		0			0
$324$	0.309017	+	0.951057i	0.0171676	+	0.0528365i
$325$	13.5967	+	41.8465i	0.754212	+	2.32123i
$326$	−3.23607	−	2.35114i	−0.179229	−	0.130218i
$327$	−16.1803	+	11.7557i	−0.894775	+	0.650092i
$328$	0.618034	−	1.90211i	0.0341252	−	0.105027i
$329$	4.00000			0.220527
$330$		0			0
$331$	−28.0000			−1.53902			−0.769510	−	0.638635i	$-0.779499\pi$
$331$	−28.0000			−1.53902			−0.769510	+	0.638635i	$0.779499\pi$
$332$	1.23607	−	3.80423i	0.0678380	−	0.208784i
$333$	1.61803	−	1.17557i	0.0886677	−	0.0644209i
$334$	9.70820	+	7.05342i	0.531209	+	0.385946i
$335$	14.8328	+	45.6507i	0.810403	+	2.49416i
$336$	−0.618034	−	1.90211i	−0.0337165	−	0.103769i
$337$	17.7984	+	12.9313i	0.969539	+	0.704411i	0.955347	−	0.295488i	$-0.0954822\pi$
$337$	17.7984	+	12.9313i	0.969539	+	0.704411i	0.0141927	+	0.999899i	$0.495482\pi$
$338$	−2.42705	+	1.76336i	−0.132014	+	0.0959139i
$339$	−1.85410	+	5.70634i	−0.100701	+	0.309926i
$340$	8.00000			0.433861
$341$		0			0
$342$		0			0
$343$	6.18034	−	19.0211i	0.333707	−	1.02704i
$344$	−3.23607	+	2.35114i	−0.174477	+	0.126765i
$345$	−19.4164	−	14.1068i	−1.04534	−	0.759487i
$346$	−1.85410	−	5.70634i	−0.0996771	−	0.306775i
$347$	−3.70820	−	11.4127i	−0.199067	−	0.612665i	−0.999905	−	0.0137839i	$-0.995612\pi$
$347$	−3.70820	−	11.4127i	−0.199067	−	0.612665i	0.800838	−	0.598881i	$-0.204388\pi$
$348$	−8.09017	−	5.87785i	−0.433679	−	0.315086i
$349$	16.1803	−	11.7557i	0.866114	−	0.629268i	−0.0634276	−	0.997986i	$-0.520203\pi$
$349$	16.1803	−	11.7557i	0.866114	−	0.629268i	0.929541	+	0.368718i	$0.120203\pi$
$350$	−6.79837	+	20.9232i	−0.363388	+	1.11839i
$351$	4.00000			0.213504
$352$		0			0
$353$	−6.00000			−0.319348			−0.159674	−	0.987170i	$-0.551044\pi$
$353$	−6.00000			−0.319348			−0.159674	+	0.987170i	$0.551044\pi$
$354$		0			0
$355$	6.47214	−	4.70228i	0.343505	−	0.249571i
$356$	−8.09017	−	5.87785i	−0.428778	−	0.311526i
$357$	1.23607	+	3.80423i	0.0654197	+	0.201341i
$358$		0			0
$359$	16.1803	+	11.7557i	0.853966	+	0.620442i	0.926237	−	0.376943i	$-0.123025\pi$
$359$	16.1803	+	11.7557i	0.853966	+	0.620442i	−0.0722709	+	0.997385i	$0.523025\pi$
$360$	3.23607	−	2.35114i	0.170556	−	0.123916i
$361$	−5.87132	+	18.0701i	−0.309017	+	0.951057i
$362$	2.00000			0.105118
$363$		0			0
$364$	−8.00000			−0.419314
$365$	7.41641	−	22.8254i	0.388193	−	1.19473i
$366$	6.47214	−	4.70228i	0.338304	−	0.245792i
$367$	−6.47214	−	4.70228i	−0.337843	−	0.245457i	0.405908	−	0.913914i	$-0.366955\pi$
$367$	−6.47214	−	4.70228i	−0.337843	−	0.245457i	−0.743751	+	0.668457i	$0.766955\pi$
$368$	−1.85410	−	5.70634i	−0.0966517	−	0.297463i
$369$	0.618034	+	1.90211i	0.0321736	+	0.0990200i
$370$	−6.47214	−	4.70228i	−0.336470	−	0.244460i
$371$	6.47214	−	4.70228i	0.336017	−	0.244130i
$372$	−2.47214	+	7.60845i	−0.128174	+	0.394480i
$373$	4.00000			0.207112			0.103556	−	0.994624i	$-0.466978\pi$
$373$	4.00000			0.207112			0.103556	+	0.994624i	$0.466978\pi$
$374$		0			0
$375$	−24.0000			−1.23935
$376$	−0.618034	+	1.90211i	−0.0318727	+	0.0980940i
$377$	−32.3607	+	23.5114i	−1.66666	+	1.21090i
$378$	1.61803	+	1.17557i	0.0832227	+	0.0604648i
$379$	−6.18034	−	19.0211i	−0.317463	−	0.977050i	−0.974729	−	0.223391i	$-0.928287\pi$
$379$	−6.18034	−	19.0211i	−0.317463	−	0.977050i	0.657266	−	0.753659i	$-0.271713\pi$
$380$		0			0
$381$	17.7984	+	12.9313i	0.911838	+	0.662489i
$382$	−17.7984	+	12.9313i	−0.910644	+	0.661622i
$383$	−1.85410	+	5.70634i	−0.0947402	+	0.291580i	−0.987186	−	0.159575i	$-0.948988\pi$
$383$	−1.85410	+	5.70634i	−0.0947402	+	0.291580i	0.892446	+	0.451155i	$0.148988\pi$
$384$	1.00000			0.0510310
$385$		0			0
$386$	14.0000			0.712581
$387$	1.23607	−	3.80423i	0.0628329	−	0.193380i
$388$	1.61803	−	1.17557i	0.0821432	−	0.0596806i
$389$	16.1803	+	11.7557i	0.820376	+	0.596038i	0.916820	−	0.399300i	$-0.130747\pi$
$389$	16.1803	+	11.7557i	0.820376	+	0.596038i	−0.0964443	+	0.995338i	$0.530747\pi$
$390$	−4.94427	−	15.2169i	−0.250363	−	0.770538i
$391$	3.70820	+	11.4127i	0.187532	+	0.577164i
$392$	2.42705	+	1.76336i	0.122585	+	0.0890629i
$393$	−9.70820	+	7.05342i	−0.489714	+	0.355798i
$394$	5.56231	−	17.1190i	0.280225	−	0.862444i
$395$	−40.0000			−2.01262
$396$		0			0
$397$	18.0000			0.903394			0.451697	−	0.892171i	$-0.350819\pi$
$397$	18.0000			0.903394			0.451697	+	0.892171i	$0.350819\pi$
$398$	6.18034	−	19.0211i	0.309792	−	0.953443i
$399$		0			0
$400$	−8.89919	−	6.46564i	−0.444959	−	0.323282i
$401$	−5.56231	−	17.1190i	−0.277768	−	0.854883i	−0.988474	−	0.151393i	$-0.951624\pi$
$401$	−5.56231	−	17.1190i	−0.277768	−	0.854883i	0.710705	−	0.703490i	$-0.248376\pi$
$402$	−3.70820	−	11.4127i	−0.184948	−	0.569213i
$403$	25.8885	+	18.8091i	1.28960	+	0.936949i
$404$	−1.61803	+	1.17557i	−0.0805002	+	0.0584868i
$405$	−1.23607	+	3.80423i	−0.0614207	+	0.189034i
$406$	−20.0000			−0.992583
$407$		0			0
$408$	−2.00000			−0.0990148
$409$	−3.09017	+	9.51057i	−0.152799	+	0.470267i	−0.997931	−	0.0642902i	$-0.979522\pi$
$409$	−3.09017	+	9.51057i	−0.152799	+	0.470267i	0.845132	+	0.534557i	$0.179522\pi$
$410$	6.47214	−	4.70228i	0.319636	−	0.232229i
$411$	1.61803	+	1.17557i	0.0798117	+	0.0579866i
$412$	1.23607	+	3.80423i	0.0608967	+	0.187421i
$413$		0			0
$414$	4.85410	+	3.52671i	0.238566	+	0.173328i
$415$	12.9443	−	9.40456i	0.635409	−	0.461652i
$416$	1.23607	−	3.80423i	0.0606032	−	0.186518i
$417$		0			0
$418$		0			0
$419$		0			0			−	1.00000i	$-0.5\pi$
$419$		0			0				1.00000i	$0.5\pi$
$420$	2.47214	−	7.60845i	0.120628	−	0.371254i
$421$	14.5623	−	10.5801i	0.709723	−	0.515644i	−0.173361	−	0.984858i	$-0.555463\pi$
$421$	14.5623	−	10.5801i	0.709723	−	0.515644i	0.883084	+	0.469214i	$0.155463\pi$
$422$	−9.70820	−	7.05342i	−0.472588	−	0.343355i
$423$	−0.618034	−	1.90211i	−0.0300498	−	0.0924839i
$424$	1.23607	+	3.80423i	0.0600288	+	0.184750i
$425$	17.7984	+	12.9313i	0.863348	+	0.627259i
$426$	−1.61803	+	1.17557i	−0.0783940	+	0.0569566i
$427$	4.94427	−	15.2169i	0.239270	−	0.736398i
$428$	−12.0000			−0.580042
$429$		0			0
$430$	−16.0000			−0.771589
$431$	9.88854	−	30.4338i	0.476314	−	1.46594i	−0.367862	−	0.929880i	$-0.619910\pi$
$431$	9.88854	−	30.4338i	0.476314	−	1.46594i	0.844177	−	0.536065i	$-0.180090\pi$
$432$	−0.809017	+	0.587785i	−0.0389238	+	0.0282798i
$433$	4.85410	+	3.52671i	0.233273	+	0.169483i	0.698281	−	0.715824i	$-0.253949\pi$
$433$	4.85410	+	3.52671i	0.233273	+	0.169483i	−0.465008	+	0.885307i	$0.653949\pi$
$434$	4.94427	+	15.2169i	0.237333	+	0.730435i
$435$	−12.3607	−	38.0423i	−0.592649	−	1.82399i
$436$	−16.1803	−	11.7557i	−0.774898	−	0.562996i
$437$		0			0
$438$	−1.85410	+	5.70634i	−0.0885924	+	0.272659i
$439$	10.0000			0.477274			0.238637	−	0.971109i	$-0.423299\pi$
$439$	10.0000			0.477274			0.238637	+	0.971109i	$0.423299\pi$
$440$		0			0
$441$	−3.00000			−0.142857
$442$	−2.47214	+	7.60845i	−0.117588	+	0.361897i
$443$	−19.4164	+	14.1068i	−0.922501	+	0.670236i	−0.944145	−	0.329529i	$-0.893110\pi$
$443$	−19.4164	+	14.1068i	−0.922501	+	0.670236i	0.0216440	+	0.999766i	$0.493110\pi$
$444$	1.61803	+	1.17557i	0.0767885	+	0.0557901i
$445$	−12.3607	−	38.0423i	−0.585952	−	1.80338i
$446$	−4.94427	−	15.2169i	−0.234118	−	0.720541i
$447$	8.09017	+	5.87785i	0.382652	+	0.278013i
$448$	1.61803	−	1.17557i	0.0764449	−	0.0555405i
$449$	9.27051	−	28.5317i	0.437502	−	1.34649i	−0.452998	−	0.891512i	$-0.649646\pi$
$449$	9.27051	−	28.5317i	0.437502	−	1.34649i	0.890500	−	0.454982i	$-0.150354\pi$
$450$	11.0000			0.518545
$451$		0			0
$452$	−6.00000			−0.282216
$453$	0.618034	−	1.90211i	0.0290378	−	0.0893691i
$454$	9.70820	−	7.05342i	0.455629	−	0.331034i
$455$	−25.8885	−	18.8091i	−1.21367	−	0.881786i
$456$		0			0
$457$	−0.618034	−	1.90211i	−0.0289104	−	0.0889771i	0.935560	−	0.353167i	$-0.114895\pi$
$457$	−0.618034	−	1.90211i	−0.0289104	−	0.0889771i	−0.964471	+	0.264190i	$0.914895\pi$
$458$	−8.09017	−	5.87785i	−0.378029	−	0.274654i
$459$	1.61803	−	1.17557i	0.0755234	−	0.0548709i
$460$	7.41641	−	22.8254i	0.345792	−	1.06424i
$461$	−18.0000			−0.838344			−0.419172	−	0.907907i	$-0.637680\pi$
$461$	−18.0000			−0.838344			−0.419172	+	0.907907i	$0.637680\pi$
$462$		0			0
$463$	4.00000			0.185896			0.0929479	−	0.995671i	$-0.470371\pi$
$463$	4.00000			0.185896			0.0929479	+	0.995671i	$0.470371\pi$
$464$	3.09017	−	9.51057i	0.143458	−	0.441517i
$465$	−25.8885	+	18.8091i	−1.20055	+	0.872252i
$466$	4.85410	+	3.52671i	0.224862	+	0.163372i
$467$	8.65248	+	26.6296i	0.400389	+	1.23227i	0.924685	+	0.380734i	$0.124329\pi$
$467$	8.65248	+	26.6296i	0.400389	+	1.23227i	−0.524296	+	0.851536i	$0.675671\pi$
$468$	1.23607	+	3.80423i	0.0571373	+	0.175850i
$469$	−19.4164	−	14.1068i	−0.896566	−	0.651394i
$470$	−6.47214	+	4.70228i	−0.298537	+	0.216900i
$471$	5.56231	−	17.1190i	0.256298	−	0.788803i
$472$		0			0
$473$		0			0
$474$	10.0000			0.459315
$475$		0			0
$476$	−3.23607	+	2.35114i	−0.148325	+	0.107764i
$477$	−3.23607	−	2.35114i	−0.148169	−	0.107651i
$478$	−6.18034	−	19.0211i	−0.282682	−	0.870006i
$479$	12.3607	+	38.0423i	0.564774	+	1.73820i	0.668622	+	0.743602i	$0.266884\pi$
$479$	12.3607	+	38.0423i	0.564774	+	1.73820i	−0.103848	+	0.994593i	$0.533116\pi$
$480$	3.23607	+	2.35114i	0.147706	+	0.107314i
$481$	6.47214	−	4.70228i	0.295104	−	0.214406i
$482$	−5.56231	+	17.1190i	−0.253356	+	0.779750i
$483$	12.0000			0.546019
$484$		0			0
$485$	8.00000			0.363261
$486$	0.309017	−	0.951057i	0.0140173	−	0.0431408i
$487$	−22.6525	+	16.4580i	−1.02648	+	0.745783i	−0.967601	−	0.252482i	$-0.918753\pi$
$487$	−22.6525	+	16.4580i	−1.02648	+	0.745783i	−0.0588802	+	0.998265i	$0.518753\pi$
$488$	6.47214	+	4.70228i	0.292980	+	0.212862i
$489$	1.23607	+	3.80423i	0.0558969	+	0.172033i
$490$	3.70820	+	11.4127i	0.167520	+	0.515572i
$491$	−9.70820	−	7.05342i	−0.438125	−	0.318317i	0.346764	−	0.937952i	$-0.387280\pi$
$491$	−9.70820	−	7.05342i	−0.438125	−	0.318317i	−0.784890	+	0.619636i	$0.787280\pi$
$492$	−1.61803	+	1.17557i	−0.0729466	+	0.0529988i
$493$	−6.18034	+	19.0211i	−0.278349	+	0.856669i
$494$		0			0
$495$		0			0
$496$	−8.00000			−0.359211
$497$	−1.23607	+	3.80423i	−0.0554452	+	0.170643i
$498$	−3.23607	+	2.35114i	−0.145012	+	0.105357i
$499$	16.1803	+	11.7557i	0.724331	+	0.526258i	0.887765	−	0.460297i	$-0.152257\pi$
$499$	16.1803	+	11.7557i	0.724331	+	0.526258i	−0.163434	+	0.986554i	$0.552257\pi$
$500$	−7.41641	−	22.8254i	−0.331672	−	1.02078i
$501$	−3.70820	−	11.4127i	−0.165670	−	0.509881i
$502$	6.47214	+	4.70228i	0.288866	+	0.209873i
$503$	−3.23607	+	2.35114i	−0.144289	+	0.104832i	−0.657588	−	0.753378i	$-0.728423\pi$
$503$	−3.23607	+	2.35114i	−0.144289	+	0.104832i	0.513299	+	0.858210i	$0.328423\pi$
$504$	−0.618034	+	1.90211i	−0.0275294	+	0.0847268i
$505$	−8.00000			−0.355995
$506$		0			0
$507$	3.00000			0.133235
$508$	−6.79837	+	20.9232i	−0.301629	+	0.928319i
$509$	16.1803	−	11.7557i	0.717181	−	0.521062i	−0.168301	−	0.985736i	$-0.553828\pi$
$509$	16.1803	−	11.7557i	0.717181	−	0.521062i	0.885482	+	0.464673i	$0.153828\pi$
$510$	−6.47214	−	4.70228i	−0.286591	−	0.208221i
$511$	3.70820	+	11.4127i	0.164041	+	0.504867i
$512$	0.309017	+	0.951057i	0.0136568	+	0.0420312i
$513$		0			0
$514$	−14.5623	+	10.5801i	−0.642316	+	0.466670i
$515$	−4.94427	+	15.2169i	−0.217871	+	0.670537i
$516$	4.00000			0.176090
$517$		0			0
$518$	4.00000			0.175750
$519$	−1.85410	+	5.70634i	−0.0813860	+	0.250480i
$520$	12.9443	−	9.40456i	0.567644	−	0.412417i
$521$	14.5623	+	10.5801i	0.637986	+	0.463524i	0.859158	−	0.511711i	$-0.170988\pi$
$521$	14.5623	+	10.5801i	0.637986	+	0.463524i	−0.221172	+	0.975235i	$0.570988\pi$
$522$	3.09017	+	9.51057i	0.135253	+	0.416266i
$523$	13.5967	+	41.8465i	0.594544	+	1.82982i	0.556982	+	0.830525i	$0.311959\pi$
$523$	13.5967	+	41.8465i	0.594544	+	1.82982i	0.0375627	+	0.999294i	$0.488041\pi$
$524$	−9.70820	−	7.05342i	−0.424105	−	0.308130i
$525$	17.7984	−	12.9313i	0.776785	−	0.564367i
$526$	−4.94427	+	15.2169i	−0.215580	+	0.663489i
$527$	16.0000			0.696971
$528$		0			0
$529$	13.0000			0.565217
$530$	−4.94427	+	15.2169i	−0.214765	+	0.660980i
$531$		0			0
$532$		0			0
$533$	2.47214	+	7.60845i	0.107080	+	0.329559i
$534$	3.09017	+	9.51057i	0.133725	+	0.411562i
$535$	−38.8328	−	28.2137i	−1.67889	−	1.21978i
$536$	9.70820	−	7.05342i	0.419331	−	0.304661i
$537$		0			0
$538$	−20.0000			−0.862261
$539$		0			0
$540$	−4.00000			−0.172133
$541$	3.70820	−	11.4127i	0.159428	−	0.490669i	−0.839154	−	0.543893i	$-0.816950\pi$
$541$	3.70820	−	11.4127i	0.159428	−	0.490669i	0.998583	+	0.0532238i	$0.0169497\pi$
$542$	−17.7984	+	12.9313i	−0.764506	+	0.555446i
$543$	−1.61803	−	1.17557i	−0.0694365	−	0.0504486i
$544$	−0.618034	−	1.90211i	−0.0264980	−	0.0815524i
$545$	−24.7214	−	76.0845i	−1.05895	−	3.25910i
$546$	6.47214	+	4.70228i	0.276982	+	0.201239i
$547$	25.8885	−	18.8091i	1.10691	−	0.804220i	0.124739	−	0.992190i	$-0.460191\pi$
$547$	25.8885	−	18.8091i	1.10691	−	0.804220i	0.982175	+	0.187969i	$0.0601906\pi$
$548$	−0.618034	+	1.90211i	−0.0264011	+	0.0812542i
$549$	−8.00000			−0.341432
$550$		0			0
$551$		0			0
$552$	−1.85410	+	5.70634i	−0.0789158	+	0.242878i
$553$	16.1803	−	11.7557i	0.688058	−	0.499903i
$554$	−6.47214	−	4.70228i	−0.274975	−	0.199781i
$555$	2.47214	+	7.60845i	0.104936	+	0.322961i
$556$		0			0
$557$	−30.7426	−	22.3358i	−1.30261	−	0.946400i	−0.302630	−	0.953108i	$-0.597865\pi$
$557$	−30.7426	−	22.3358i	−1.30261	−	0.946400i	−0.999978	+	0.00670815i	$0.997865\pi$
$558$	6.47214	−	4.70228i	0.273987	−	0.199063i
$559$	4.94427	−	15.2169i	0.209120	−	0.643606i
$560$	8.00000			0.338062
$561$		0			0
$562$	22.0000			0.928014
$563$	−11.1246	+	34.2380i	−0.468846	+	1.44296i	0.385233	+	0.922819i	$0.374121\pi$
$563$	−11.1246	+	34.2380i	−0.468846	+	1.44296i	−0.854080	+	0.520142i	$0.825879\pi$
$564$	1.61803	−	1.17557i	0.0681315	−	0.0495004i
$565$	−19.4164	−	14.1068i	−0.816854	−	0.593479i
$566$	1.23607	+	3.80423i	0.0519558	+	0.159904i
$567$	−0.618034	−	1.90211i	−0.0259550	−	0.0798812i
$568$	−1.61803	−	1.17557i	−0.0678912	−	0.0493258i
$569$	8.09017	−	5.87785i	0.339158	−	0.246412i	−0.405149	−	0.914251i	$-0.632780\pi$
$569$	8.09017	−	5.87785i	0.339158	−	0.246412i	0.744306	+	0.667838i	$0.232780\pi$
$570$		0			0
$571$	32.0000			1.33916			0.669579	−	0.742741i	$-0.266474\pi$
$571$	32.0000			1.33916			0.669579	+	0.742741i	$0.266474\pi$
$572$		0			0
$573$	22.0000			0.919063
$574$	−1.23607	+	3.80423i	−0.0515925	+	0.158785i
$575$	53.3951	−	38.7938i	2.22673	−	1.61781i
$576$	−0.809017	−	0.587785i	−0.0337090	−	0.0244911i
$577$	−0.618034	−	1.90211i	−0.0257291	−	0.0791860i	0.937367	−	0.348342i	$-0.113255\pi$
$577$	−0.618034	−	1.90211i	−0.0257291	−	0.0791860i	−0.963097	+	0.269156i	$0.913255\pi$
$578$	−4.01722	−	12.3637i	−0.167094	−	0.514264i
$579$	−11.3262	−	8.22899i	−0.470702	−	0.341985i
$580$	32.3607	−	23.5114i	1.34370	−	0.976258i
$581$	−2.47214	+	7.60845i	−0.102561	+	0.315652i
$582$	−2.00000			−0.0829027
$583$		0			0
$584$	−6.00000			−0.248282
$585$	−4.94427	+	15.2169i	−0.204420	+	0.629142i
$586$	−11.3262	+	8.22899i	−0.467883	+	0.339937i
$587$	−6.47214	−	4.70228i	−0.267134	−	0.194084i	0.446152	−	0.894957i	$-0.352794\pi$
$587$	−6.47214	−	4.70228i	−0.267134	−	0.194084i	−0.713286	+	0.700873i	$0.752794\pi$
$588$	−0.927051	−	2.85317i	−0.0382309	−	0.117663i
$589$		0			0
$590$		0			0
$591$	−14.5623	+	10.5801i	−0.599013	+	0.435209i
$592$	−0.618034	+	1.90211i	−0.0254010	+	0.0781764i
$593$	14.0000			0.574911			0.287456	−	0.957794i	$-0.407191\pi$
$593$	14.0000			0.574911			0.287456	+	0.957794i	$0.407191\pi$
$594$		0			0
$595$	−16.0000			−0.655936
$596$	−3.09017	+	9.51057i	−0.126578	+	0.389568i
$597$	−16.1803	+	11.7557i	−0.662217	+	0.481129i
$598$	19.4164	+	14.1068i	0.793996	+	0.576872i
$599$	−9.27051	−	28.5317i	−0.378783	−	1.16577i	−0.940891	−	0.338710i	$-0.890010\pi$
$599$	−9.27051	−	28.5317i	−0.378783	−	1.16577i	0.562108	−	0.827064i	$-0.309990\pi$
$600$	3.39919	+	10.4616i	0.138771	+	0.427094i
$601$	−33.9787	−	24.6870i	−1.38602	−	1.00700i	−0.996289	−	0.0860746i	$-0.972568\pi$
$601$	−33.9787	−	24.6870i	−1.38602	−	1.00700i	−0.389732	−	0.920928i	$-0.627432\pi$
$602$	6.47214	−	4.70228i	0.263785	−	0.191651i
$603$	−3.70820	+	11.4127i	−0.151010	+	0.464760i
$604$	2.00000			0.0813788
$605$		0			0
$606$	2.00000			0.0812444
$607$	−6.79837	+	20.9232i	−0.275937	+	0.849248i	0.713032	+	0.701131i	$0.247321\pi$
$607$	−6.79837	+	20.9232i	−0.275937	+	0.849248i	−0.988970	+	0.148117i	$0.952679\pi$
$608$		0			0
$609$	16.1803	+	11.7557i	0.655660	+	0.476365i
$610$	9.88854	+	30.4338i	0.400375	+	1.23223i
$611$	−2.47214	−	7.60845i	−0.100012	−	0.307805i
$612$	1.61803	+	1.17557i	0.0654051	+	0.0475196i
$613$	12.9443	−	9.40456i	0.522814	−	0.379847i	−0.294849	−	0.955544i	$-0.595269\pi$
$613$	12.9443	−	9.40456i	0.522814	−	0.379847i	0.817663	+	0.575697i	$0.195269\pi$
$614$	2.47214	−	7.60845i	0.0997673	−	0.307052i
$615$	−8.00000			−0.322591
$616$		0			0
$617$	−22.0000			−0.885687			−0.442843	−	0.896599i	$-0.646030\pi$
$617$	−22.0000			−0.885687			−0.442843	+	0.896599i	$0.646030\pi$
$618$	1.23607	−	3.80423i	0.0497219	−	0.153028i
$619$	16.1803	−	11.7557i	0.650343	−	0.472502i	−0.213045	−	0.977042i	$-0.568338\pi$
$619$	16.1803	−	11.7557i	0.650343	−	0.472502i	0.863388	+	0.504541i	$0.168338\pi$
$620$	−25.8885	−	18.8091i	−1.03971	−	0.755393i
$621$	−1.85410	−	5.70634i	−0.0744025	−	0.228988i
$622$	0.618034	+	1.90211i	0.0247809	+	0.0762678i
$623$	16.1803	+	11.7557i	0.648252	+	0.470982i
$624$	−3.23607	+	2.35114i	−0.129546	+	0.0941210i
$625$	12.6697	−	38.9933i	0.506788	−	1.55973i
$626$	−6.00000			−0.239808
$627$		0			0
$628$	18.0000			0.718278
$629$	1.23607	−	3.80423i	0.0492853	−	0.151684i
$630$	−6.47214	+	4.70228i	−0.257856	+	0.187343i
$631$	38.8328	+	28.2137i	1.54591	+	1.12317i	0.946489	+	0.322735i	$0.104602\pi$
$631$	38.8328	+	28.2137i	1.54591	+	1.12317i	0.599421	+	0.800434i	$0.295398\pi$
$632$	3.09017	+	9.51057i	0.122920	+	0.378310i
$633$	3.70820	+	11.4127i	0.147388	+	0.453613i
$634$	25.8885	+	18.8091i	1.02817	+	0.747006i
$635$	−71.1935	+	51.7251i	−2.82523	+	2.05265i
$636$	1.23607	−	3.80423i	0.0490133	−	0.150847i
$637$	−12.0000			−0.475457
$638$		0			0
$639$	2.00000			0.0791188
$640$	−1.23607	+	3.80423i	−0.0488599	+	0.150375i
$641$	14.5623	−	10.5801i	0.575177	−	0.417890i	−0.261805	−	0.965121i	$-0.584318\pi$
$641$	14.5623	−	10.5801i	0.575177	−	0.417890i	0.836982	+	0.547230i	$0.184318\pi$
$642$	9.70820	+	7.05342i	0.383152	+	0.278376i
$643$	13.5967	+	41.8465i	0.536203	+	1.65026i	0.741034	+	0.671467i	$0.234335\pi$
$643$	13.5967	+	41.8465i	0.536203	+	1.65026i	−0.204831	+	0.978797i	$0.565665\pi$
$644$	3.70820	+	11.4127i	0.146124	+	0.449723i
$645$	12.9443	+	9.40456i	0.509680	+	0.370304i
$646$		0			0
$647$	−6.79837	+	20.9232i	−0.267272	+	0.822578i	0.723890	+	0.689916i	$0.242352\pi$
$647$	−6.79837	+	20.9232i	−0.267272	+	0.822578i	−0.991161	+	0.132662i	$0.957648\pi$
$648$	1.00000			0.0392837
$649$		0			0
$650$	44.0000			1.72582
$651$	4.94427	−	15.2169i	0.193781	−	0.596397i
$652$	−3.23607	+	2.35114i	−0.126734	+	0.0920778i
$653$	−19.4164	−	14.1068i	−0.759823	−	0.552044i	0.139033	−	0.990288i	$-0.455601\pi$
$653$	−19.4164	−	14.1068i	−0.759823	−	0.552044i	−0.898856	+	0.438244i	$0.855601\pi$
$654$	6.18034	+	19.0211i	0.241670	+	0.743785i
$655$	−14.8328	−	45.6507i	−0.579566	−	1.78372i
$656$	−1.61803	−	1.17557i	−0.0631736	−	0.0458983i
$657$	4.85410	−	3.52671i	0.189377	−	0.137590i
$658$	1.23607	−	3.80423i	0.0481869	−	0.148304i
$659$	−20.0000			−0.779089			−0.389545	−	0.921008i	$-0.627368\pi$
$659$	−20.0000			−0.779089			−0.389545	+	0.921008i	$0.627368\pi$
$660$		0			0
$661$	42.0000			1.63361			0.816805	−	0.576913i	$-0.195743\pi$
$661$	42.0000			1.63361			0.816805	+	0.576913i	$0.195743\pi$
$662$	−8.65248	+	26.6296i	−0.336288	+	1.03499i
$663$	6.47214	−	4.70228i	0.251357	−	0.182622i
$664$	−3.23607	−	2.35114i	−0.125584	−	0.0912420i
$665$		0			0
$666$	−0.618034	−	1.90211i	−0.0239483	−	0.0737054i
$667$	48.5410	+	35.2671i	1.87952	+	1.36555i
$668$	9.70820	−	7.05342i	0.375622	−	0.272905i
$669$	−4.94427	+	15.2169i	−0.191157	+	0.588320i
$670$	48.0000			1.85440
$671$		0			0
$672$	−2.00000			−0.0771517
$673$	4.32624	−	13.3148i	0.166764	−	0.513247i	−0.832398	−	0.554179i	$-0.813032\pi$
$673$	4.32624	−	13.3148i	0.166764	−	0.513247i	0.999162	+	0.0409312i	$0.0130324\pi$
$674$	17.7984	−	12.9313i	0.685568	−	0.498094i
$675$	−8.89919	−	6.46564i	−0.342530	−	0.248863i
$676$	0.927051	+	2.85317i	0.0356558	+	0.109737i
$677$	−6.79837	−	20.9232i	−0.261283	−	0.804146i	−0.992526	−	0.122029i	$-0.961060\pi$
$677$	−6.79837	−	20.9232i	−0.261283	−	0.804146i	0.731244	−	0.682116i	$-0.238940\pi$
$678$	4.85410	+	3.52671i	0.186421	+	0.135443i
$679$	−3.23607	+	2.35114i	−0.124189	+	0.0902285i
$680$	2.47214	−	7.60845i	0.0948021	−	0.291771i
$681$	−12.0000			−0.459841
$682$		0			0
$683$	−16.0000			−0.612223			−0.306111	−	0.951996i	$-0.599028\pi$
$683$	−16.0000			−0.612223			−0.306111	+	0.951996i	$0.599028\pi$
$684$		0			0
$685$	−6.47214	+	4.70228i	−0.247288	+	0.179665i
$686$	−16.1803	−	11.7557i	−0.617768	−	0.448835i
$687$	3.09017	+	9.51057i	0.117897	+	0.362851i
$688$	1.23607	+	3.80423i	0.0471246	+	0.145035i
$689$	−12.9443	−	9.40456i	−0.493137	−	0.358285i
$690$	−19.4164	+	14.1068i	−0.739170	+	0.537038i
$691$	16.0689	−	49.4549i	0.611289	−	1.88135i	0.165520	−	0.986206i	$-0.447070\pi$
$691$	16.0689	−	49.4549i	0.611289	−	1.88135i	0.445769	−	0.895148i	$-0.352930\pi$
$692$	−6.00000			−0.228086
$693$		0			0
$694$	−12.0000			−0.455514
$695$		0			0
$696$	−8.09017	+	5.87785i	−0.306657	+	0.222799i
$697$	3.23607	+	2.35114i	0.122575	+	0.0890558i
$698$	−6.18034	−	19.0211i	−0.233929	−	0.719960i
$699$	−1.85410	−	5.70634i	−0.0701286	−	0.215834i
$700$	17.7984	+	12.9313i	0.672715	+	0.488756i
$701$	14.5623	−	10.5801i	0.550011	−	0.399606i	−0.277779	−	0.960645i	$-0.589598\pi$
$701$	14.5623	−	10.5801i	0.550011	−	0.399606i	0.827789	+	0.561039i	$0.189598\pi$
$702$	1.23607	−	3.80423i	0.0466524	−	0.143581i
$703$		0			0
$704$		0			0
$705$	8.00000			0.301297
$706$	−1.85410	+	5.70634i	−0.0697800	+	0.214761i
$707$	3.23607	−	2.35114i	0.121705	−	0.0884238i
$708$		0			0
$709$	3.09017	+	9.51057i	0.116054	+	0.357177i	0.992165	−	0.124932i	$-0.0398711\pi$
$709$	3.09017	+	9.51057i	0.116054	+	0.357177i	−0.876112	+	0.482108i	$0.839871\pi$
$710$	−2.47214	−	7.60845i	−0.0927776	−	0.285540i
$711$	−8.09017	−	5.87785i	−0.303405	−	0.220437i
$712$	−8.09017	+	5.87785i	−0.303192	+	0.220282i
$713$	14.8328	−	45.6507i	0.555493	−	1.70963i
$714$	4.00000			0.149696
$715$		0			0
$716$		0			0
$717$	−6.18034	+	19.0211i	−0.230809	+	0.710357i
$718$	16.1803	−	11.7557i	0.603845	−	0.438719i
$719$	−8.09017	−	5.87785i	−0.301712	−	0.219207i	0.426620	−	0.904431i	$-0.359704\pi$
$719$	−8.09017	−	5.87785i	−0.301712	−	0.219207i	−0.728332	+	0.685224i	$0.759704\pi$
$720$	−1.23607	−	3.80423i	−0.0460655	−	0.141775i
$721$	−2.47214	−	7.60845i	−0.0920672	−	0.283354i
$722$	15.3713	+	11.1679i	0.572061	+	0.415627i
$723$	14.5623	−	10.5801i	0.541578	−	0.393479i
$724$	0.618034	−	1.90211i	0.0229691	−	0.0706915i
$725$	110.000			4.08530
$726$		0			0
$727$	28.0000			1.03846			0.519231	−	0.854634i	$-0.326218\pi$
$727$	28.0000			1.03846			0.519231	+	0.854634i	$0.326218\pi$
$728$	−2.47214	+	7.60845i	−0.0916235	+	0.281988i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	−19.4164	−	14.1068i	−0.718633	−	0.522118i
$731$	−2.47214	−	7.60845i	−0.0914353	−	0.281409i
$732$	−2.47214	−	7.60845i	−0.0913728	−	0.281216i
$733$	−3.23607	−	2.35114i	−0.119527	−	0.0868414i	0.526416	−	0.850227i	$-0.323536\pi$
$733$	−3.23607	−	2.35114i	−0.119527	−	0.0868414i	−0.645943	+	0.763386i	$0.723536\pi$
$734$	−6.47214	+	4.70228i	−0.238891	+	0.173564i
$735$	3.70820	−	11.4127i	0.136779	−	0.420963i
$736$	−6.00000			−0.221163
$737$		0			0
$738$	2.00000			0.0736210
$739$	6.18034	−	19.0211i	0.227347	−	0.699704i	−0.770697	−	0.637201i	$-0.780092\pi$
$739$	6.18034	−	19.0211i	0.227347	−	0.699704i	0.998045	−	0.0625022i	$-0.0199080\pi$
$740$	−6.47214	+	4.70228i	−0.237920	+	0.172859i
$741$		0			0
$742$	−2.47214	−	7.60845i	−0.0907550	−	0.279315i
$743$	13.5967	+	41.8465i	0.498816	+	1.53520i	0.810924	+	0.585152i	$0.198965\pi$
$743$	13.5967	+	41.8465i	0.498816	+	1.53520i	−0.312107	+	0.950047i	$0.601035\pi$
$744$	6.47214	+	4.70228i	0.237280	+	0.172394i
$745$	−32.3607	+	23.5114i	−1.18560	+	0.861391i
$746$	1.23607	−	3.80423i	0.0452557	−	0.139283i
$747$	4.00000			0.146352
$748$		0			0
$749$	24.0000			0.876941
$750$	−7.41641	+	22.8254i	−0.270809	+	0.833464i
$751$	6.47214	−	4.70228i	0.236172	−	0.171589i	−0.463404	−	0.886147i	$-0.653372\pi$
$751$	6.47214	−	4.70228i	0.236172	−	0.171589i	0.699576	+	0.714558i	$0.253372\pi$
$752$	1.61803	+	1.17557i	0.0590036	+	0.0428686i
$753$	−2.47214	−	7.60845i	−0.0900896	−	0.277267i
$754$	12.3607	+	38.0423i	0.450149	+	1.38542i
$755$	6.47214	+	4.70228i	0.235545	+	0.171134i
$756$	1.61803	−	1.17557i	0.0588473	−	0.0427551i
$757$	−12.9787	+	39.9444i	−0.471719	+	1.45180i	0.378612	+	0.925555i	$0.376401\pi$
$757$	−12.9787	+	39.9444i	−0.471719	+	1.45180i	−0.850331	+	0.526248i	$0.823599\pi$
$758$	−20.0000			−0.726433
$759$		0			0
$760$		0			0
$761$	6.79837	−	20.9232i	0.246441	−	0.758467i	−0.748955	−	0.662621i	$-0.769444\pi$
$761$	6.79837	−	20.9232i	0.246441	−	0.758467i	0.995396	−	0.0958464i	$-0.0305558\pi$
$762$	17.7984	−	12.9313i	0.644767	−	0.468451i
$763$	32.3607	+	23.5114i	1.17154	+	0.851170i
$764$	6.79837	+	20.9232i	0.245957	+	0.756976i
$765$	2.47214	+	7.60845i	0.0893803	+	0.275084i
$766$	4.85410	+	3.52671i	0.175386	+	0.127425i
$767$		0			0
$768$	0.309017	−	0.951057i	0.0111507	−	0.0343183i
$769$	−50.0000			−1.80305			−0.901523	−	0.432731i	$-0.857550\pi$
$769$	−50.0000			−1.80305			−0.901523	+	0.432731i	$0.857550\pi$
$770$		0			0
$771$	18.0000			0.648254
$772$	4.32624	−	13.3148i	0.155705	−	0.479210i
$773$	−3.23607	+	2.35114i	−0.116393	+	0.0845647i	−0.644459	−	0.764639i	$-0.722917\pi$
$773$	−3.23607	+	2.35114i	−0.116393	+	0.0845647i	0.528066	+	0.849203i	$0.322917\pi$
$774$	−3.23607	−	2.35114i	−0.116318	−	0.0845100i
$775$	−27.1935	−	83.6930i	−0.976819	−	3.00634i
$776$	−0.618034	−	1.90211i	−0.0221861	−	0.0682819i
$777$	−3.23607	−	2.35114i	−0.116093	−	0.0843467i
$778$	16.1803	−	11.7557i	0.580093	−	0.421462i
$779$		0			0
$780$	−16.0000			−0.572892
$781$		0			0
$782$	12.0000			0.429119
$783$	3.09017	−	9.51057i	0.110434	−	0.339880i
$784$	2.42705	−	1.76336i	0.0866804	−	0.0629770i
$785$	58.2492	+	42.3205i	2.07900	+	1.51048i
$786$	3.70820	+	11.4127i	0.132267	+	0.407077i
$787$	−16.0689	−	49.4549i	−0.572794	−	1.76288i	−0.643571	−	0.765386i	$-0.722548\pi$
$787$	−16.0689	−	49.4549i	−0.572794	−	1.76288i	0.0707776	−	0.997492i	$-0.477452\pi$
$788$	−14.5623	−	10.5801i	−0.518761	−	0.376902i
$789$	12.9443	−	9.40456i	0.460828	−	0.334811i
$790$	−12.3607	+	38.0423i	−0.439773	+	1.35348i
$791$	12.0000			0.426671
$792$		0			0
$793$	−32.0000			−1.13635
$794$	5.56231	−	17.1190i	0.197399	−	0.607531i
$795$	12.9443	−	9.40456i	0.459086	−	0.333546i
$796$	−16.1803	−	11.7557i	−0.573497	−	0.416670i
$797$	8.65248	+	26.6296i	0.306486	+	0.943268i	0.979118	+	0.203291i	$0.0651637\pi$
$797$	8.65248	+	26.6296i	0.306486	+	0.943268i	−0.672632	+	0.739977i	$0.734836\pi$
$798$		0			0
$799$	−3.23607	−	2.35114i	−0.114484	−	0.0831774i
$800$	−8.89919	+	6.46564i	−0.314634	+	0.228595i
$801$	3.09017	−	9.51057i	0.109186	−	0.336039i
$802$	−18.0000			−0.635602
$803$		0			0
$804$	−12.0000			−0.423207
$805$	−14.8328	+	45.6507i	−0.522788	+	1.60898i
$806$	25.8885	−	18.8091i	0.911885	−	0.662523i
$807$	16.1803	+	11.7557i	0.569575	+	0.413820i
$808$	0.618034	+	1.90211i	0.0217424	+	0.0669161i
$809$	3.09017	+	9.51057i	0.108645	+	0.334374i	0.990569	−	0.137018i	$-0.0437518\pi$
$809$	3.09017	+	9.51057i	0.108645	+	0.334374i	−0.881924	+	0.471392i	$0.843752\pi$
$810$	3.23607	+	2.35114i	0.113704	+	0.0826107i
$811$	−9.70820	+	7.05342i	−0.340901	+	0.247679i	−0.745042	−	0.667018i	$-0.767571\pi$
$811$	−9.70820	+	7.05342i	−0.340901	+	0.247679i	0.404141	+	0.914697i	$0.367571\pi$
$812$	−6.18034	+	19.0211i	−0.216887	+	0.667511i
$813$	22.0000			0.771574
$814$		0			0
$815$	−16.0000			−0.560456
$816$	−0.618034	+	1.90211i	−0.0216355	+	0.0665873i
$817$		0			0
$818$	8.09017	+	5.87785i	0.282866	+	0.205514i
$819$	−2.47214	−	7.60845i	−0.0863834	−	0.265861i
$820$	−2.47214	−	7.60845i	−0.0863307	−	0.265699i
$821$	30.7426	+	22.3358i	1.07293	+	0.779526i	0.976436	−	0.215808i	$-0.0692385\pi$
$821$	30.7426	+	22.3358i	1.07293	+	0.779526i	0.0964899	+	0.995334i	$0.469238\pi$
$822$	1.61803	−	1.17557i	0.0564354	−	0.0410027i
$823$	7.41641	−	22.8254i	0.258520	−	0.795642i	−0.734596	−	0.678505i	$-0.762628\pi$
$823$	7.41641	−	22.8254i	0.258520	−	0.795642i	0.993116	−	0.117137i	$-0.0373717\pi$
$824$	4.00000			0.139347
$825$		0			0
$826$		0			0
$827$	−3.70820	+	11.4127i	−0.128947	+	0.396858i	−0.994600	−	0.103787i	$-0.966904\pi$
$827$	−3.70820	+	11.4127i	−0.128947	+	0.396858i	0.865653	+	0.500645i	$0.166904\pi$
$828$	4.85410	−	3.52671i	0.168692	−	0.122562i
$829$	−24.2705	−	17.6336i	−0.842950	−	0.612439i	0.0802434	−	0.996775i	$-0.474430\pi$
$829$	−24.2705	−	17.6336i	−0.842950	−	0.612439i	−0.923193	+	0.384337i	$0.874430\pi$
$830$	−4.94427	−	15.2169i	−0.171618	−	0.528186i
$831$	2.47214	+	7.60845i	0.0857574	+	0.263934i
$832$	−3.23607	−	2.35114i	−0.112190	−	0.0815111i
$833$	−4.85410	+	3.52671i	−0.168185	+	0.122193i
$834$		0			0
$835$	48.0000			1.66111
$836$		0			0
$837$	−8.00000			−0.276520
$838$		0			0
$839$	−24.2705	+	17.6336i	−0.837911	+	0.608778i	−0.921786	−	0.387698i	$-0.873270\pi$
$839$	−24.2705	+	17.6336i	−0.837911	+	0.608778i	0.0838753	+	0.996476i	$0.473270\pi$
$840$	−6.47214	−	4.70228i	−0.223310	−	0.162244i
$841$	21.9402	+	67.5250i	0.756559	+	2.32845i
$842$	−5.56231	−	17.1190i	−0.191690	−	0.589960i
$843$	−17.7984	−	12.9313i	−0.613009	−	0.445377i
$844$	−9.70820	+	7.05342i	−0.334170	+	0.242789i
$845$	−3.70820	+	11.4127i	−0.127566	+	0.392608i
$846$	−2.00000			−0.0687614
$847$		0			0
$848$	4.00000			0.137361
$849$	1.23607	−	3.80423i	0.0424217	−	0.130561i
$850$	17.7984	−	12.9313i	0.610479	−	0.443539i
$851$	−9.70820	−	7.05342i	−0.332793	−	0.241788i
$852$	0.618034	+	1.90211i	0.0211735	+	0.0651653i
$853$	7.41641	+	22.8254i	0.253933	+	0.781525i	0.994038	+	0.109034i	$0.0347758\pi$
$853$	7.41641	+	22.8254i	0.253933	+	0.781525i	−0.740105	+	0.672491i	$0.765224\pi$
$854$	−12.9443	−	9.40456i	−0.442944	−	0.321818i
$855$		0			0
$856$	−3.70820	+	11.4127i	−0.126744	+	0.390077i
$857$	−22.0000			−0.751506			−0.375753	−	0.926720i	$-0.622616\pi$
$857$	−22.0000			−0.751506			−0.375753	+	0.926720i	$0.622616\pi$
$858$		0			0
$859$	−20.0000			−0.682391			−0.341196	−	0.939992i	$-0.610832\pi$
$859$	−20.0000			−0.682391			−0.341196	+	0.939992i	$0.610832\pi$
$860$	−4.94427	+	15.2169i	−0.168598	+	0.518892i
$861$	3.23607	−	2.35114i	0.110285	−	0.0801267i
$862$	−25.8885	−	18.8091i	−0.881767	−	0.640641i
$863$	16.6869	+	51.3571i	0.568029	+	1.74821i	0.658775	+	0.752340i	$0.271075\pi$
$863$	16.6869	+	51.3571i	0.568029	+	1.74821i	−0.0907454	+	0.995874i	$0.528925\pi$
$864$	0.309017	+	0.951057i	0.0105130	+	0.0323556i
$865$	−19.4164	−	14.1068i	−0.660178	−	0.479647i
$866$	4.85410	−	3.52671i	0.164949	−	0.119843i
$867$	−4.01722	+	12.3637i	−0.136432	+	0.419894i
$868$	16.0000			0.543075
$869$		0			0
$870$	−40.0000			−1.35613
$871$	−14.8328	+	45.6507i	−0.502591	+	1.54682i
$872$	−16.1803	+	11.7557i	−0.547935	+	0.398098i
$873$	1.61803	+	1.17557i	0.0547622	+	0.0397870i
$874$		0			0
$875$	14.8328	+	45.6507i	0.501441	+	1.54328i
$876$	4.85410	+	3.52671i	0.164005	+	0.119157i
$877$	−22.6525	+	16.4580i	−0.764920	+	0.555747i	−0.900415	−	0.435031i	$-0.856737\pi$
$877$	−22.6525	+	16.4580i	−0.764920	+	0.555747i	0.135496	+	0.990778i	$0.456737\pi$
$878$	3.09017	−	9.51057i	0.104288	−	0.320966i
$879$	14.0000			0.472208
$880$		0			0
$881$	−38.0000			−1.28025			−0.640126	−	0.768270i	$-0.721118\pi$
$881$	−38.0000			−1.28025			−0.640126	+	0.768270i	$0.721118\pi$
$882$	−0.927051	+	2.85317i	−0.0312154	+	0.0960712i
$883$	−35.5967	+	25.8626i	−1.19793	+	0.870344i	−0.994079	−	0.108659i	$-0.965344\pi$
$883$	−35.5967	+	25.8626i	−1.19793	+	0.870344i	−0.203847	+	0.979003i	$0.565344\pi$
$884$	6.47214	+	4.70228i	0.217681	+	0.158155i
$885$		0			0
$886$	7.41641	+	22.8254i	0.249159	+	0.766833i
$887$	9.70820	+	7.05342i	0.325970	+	0.236831i	0.738718	−	0.674014i	$-0.235431\pi$
$887$	9.70820	+	7.05342i	0.325970	+	0.236831i	−0.412749	+	0.910845i	$0.635431\pi$
$888$	1.61803	−	1.17557i	0.0542977	−	0.0394496i
$889$	13.5967	−	41.8465i	0.456020	−	1.40349i
$890$	−40.0000			−1.34080
$891$		0			0
$892$	−16.0000			−0.535720
$893$		0			0
$894$	8.09017	−	5.87785i	0.270576	−	0.196585i
$895$		0			0
$896$	−0.618034	−	1.90211i	−0.0206471	−	0.0635451i
$897$	−7.41641	−	22.8254i	−0.247627	−	0.762116i
$898$	−24.2705	−	17.6336i	−0.809917	−	0.588439i
$899$	64.7214	−	47.0228i	2.15858	−	1.56830i
$900$	3.39919	−	10.4616i	0.113306	−	0.348721i
$901$	−8.00000			−0.266519
$902$		0			0
$903$	−8.00000			−0.266223
$904$	−1.85410	+	5.70634i	−0.0616665	+	0.189790i
$905$	6.47214	−	4.70228i	0.215141	−	0.156309i
$906$	−1.61803	−	1.17557i	−0.0537556	−	0.0390557i
$907$	−3.70820	−	11.4127i	−0.123129	−	0.378952i	0.870427	−	0.492298i	$-0.163843\pi$
$907$	−3.70820	−	11.4127i	−0.123129	−	0.378952i	−0.993556	+	0.113346i	$0.963843\pi$
$908$	−3.70820	−	11.4127i	−0.123061	−	0.378743i
$909$	−1.61803	−	1.17557i	−0.0536668	−	0.0389912i
$910$	−25.8885	+	18.8091i	−0.858197	+	0.623517i
$911$	0.618034	−	1.90211i	0.0204764	−	0.0630198i	−0.940296	−	0.340357i	$-0.889452\pi$
$911$	0.618034	−	1.90211i	0.0204764	−	0.0630198i	0.960773	+	0.277337i	$0.0894520\pi$
$912$		0			0
$913$		0			0
$914$	−2.00000			−0.0661541
$915$	9.88854	−	30.4338i	0.326905	−	1.00611i
$916$	−8.09017	+	5.87785i	−0.267307	+	0.194210i
$917$	19.4164	+	14.1068i	0.641186	+	0.465849i
$918$	−0.618034	−	1.90211i	−0.0203982	−	0.0627791i
$919$	−3.09017	−	9.51057i	−0.101935	−	0.313725i	0.887064	−	0.461647i	$-0.152741\pi$
$919$	−3.09017	−	9.51057i	−0.101935	−	0.313725i	−0.988999	+	0.147923i	$0.952741\pi$
$920$	−19.4164	−	14.1068i	−0.640140	−	0.465089i
$921$	−6.47214	+	4.70228i	−0.213264	+	0.154945i
$922$	−5.56231	+	17.1190i	−0.183185	+	0.563785i
$923$	8.00000			0.263323
$924$		0			0
$925$	−22.0000			−0.723356
$926$	1.23607	−	3.80423i	0.0406197	−	0.125015i
$927$	−3.23607	+	2.35114i	−0.106286	+	0.0772216i
$928$	−8.09017	−	5.87785i	−0.265573	−	0.192950i
$929$	9.27051	+	28.5317i	0.304156	+	0.936095i	0.979991	+	0.199042i	$0.0637830\pi$
$929$	9.27051	+	28.5317i	0.304156	+	0.936095i	−0.675835	+	0.737053i	$0.736217\pi$
$930$	9.88854	+	30.4338i	0.324258	+	0.997964i
$931$		0			0
$932$	4.85410	−	3.52671i	0.159001	−	0.115521i
$933$	0.618034	−	1.90211i	0.0202335	−	0.0622724i
$934$	28.0000			0.916188
$935$		0			0
$936$	4.00000			0.130744
$937$	17.9230	−	55.1613i	0.585518	−	1.80204i	−0.0116601	−	0.999932i	$-0.503712\pi$
$937$	17.9230	−	55.1613i	0.585518	−	1.80204i	0.597178	−	0.802108i	$-0.296288\pi$
$938$	−19.4164	+	14.1068i	−0.633968	+	0.460605i
$939$	4.85410	+	3.52671i	0.158408	+	0.115090i
$940$	2.47214	+	7.60845i	0.0806322	+	0.248160i
$941$	12.9787	+	39.9444i	0.423094	+	1.30215i	0.904808	+	0.425821i	$0.140015\pi$
$941$	12.9787	+	39.9444i	0.423094	+	1.30215i	−0.481714	+	0.876329i	$0.659985\pi$
$942$	−14.5623	−	10.5801i	−0.474466	−	0.344719i
$943$	9.70820	−	7.05342i	0.316143	−	0.229691i
$944$		0			0
$945$	8.00000			0.260240
$946$		0			0
$947$	28.0000			0.909878			0.454939	−	0.890523i	$-0.349661\pi$
$947$	28.0000			0.909878			0.454939	+	0.890523i	$0.349661\pi$
$948$	3.09017	−	9.51057i	0.100364	−	0.308889i
$949$	19.4164	−	14.1068i	0.630283	−	0.457928i
$950$		0			0
$951$	−9.88854	−	30.4338i	−0.320658	−	0.986884i
$952$	1.23607	+	3.80423i	0.0400612	+	0.123296i
$953$	4.85410	+	3.52671i	0.157240	+	0.114241i	0.663623	−	0.748067i	$-0.269018\pi$
$953$	4.85410	+	3.52671i	0.157240	+	0.114241i	−0.506383	+	0.862309i	$0.669018\pi$
$954$	−3.23607	+	2.35114i	−0.104772	+	0.0761210i
$955$	−27.1935	+	83.6930i	−0.879961	+	2.70824i
$956$	−20.0000			−0.646846
$957$		0			0
$958$	40.0000			1.29234
$959$	1.23607	−	3.80423i	0.0399147	−	0.122845i
$960$	3.23607	−	2.35114i	0.104444	−	0.0758827i
$961$	−26.6976	−	19.3969i	−0.861212	−	0.625707i
$962$	−2.47214	−	7.60845i	−0.0797049	−	0.245306i
$963$	−3.70820	−	11.4127i	−0.119495	−	0.367768i
$964$	14.5623	+	10.5801i	0.469020	+	0.340763i
$965$	45.3050	−	32.9160i	1.45842	−	1.05960i
$966$	3.70820	−	11.4127i	0.119310	−	0.367197i
$967$	−22.0000			−0.707472			−0.353736	−	0.935345i	$-0.615089\pi$
$967$	−22.0000			−0.707472			−0.353736	+	0.935345i	$0.615089\pi$
$968$		0			0
$969$		0			0
$970$	2.47214	−	7.60845i	0.0793755	−	0.244293i
$971$	−25.8885	+	18.8091i	−0.830803	+	0.603614i	−0.919786	−	0.392419i	$-0.871638\pi$
$971$	−25.8885	+	18.8091i	−0.830803	+	0.603614i	0.0889835	+	0.996033i	$0.471638\pi$
$972$	−0.809017	−	0.587785i	−0.0259492	−	0.0188532i
$973$		0			0
$974$	8.65248	+	26.6296i	0.277243	+	0.853267i
$975$	−35.5967	−	25.8626i	−1.14001	−	0.828265i
$976$	6.47214	−	4.70228i	0.207168	−	0.150516i
$977$	11.7426	−	36.1401i	0.375681	−	1.15623i	−0.567338	−	0.823485i	$-0.692027\pi$
$977$	11.7426	−	36.1401i	0.375681	−	1.15623i	0.943018	−	0.332741i	$-0.107973\pi$
$978$	4.00000			0.127906
$979$		0			0
$980$	12.0000			0.383326
$981$	6.18034	−	19.0211i	0.197323	−	0.607298i
$982$	−9.70820	+	7.05342i	−0.309801	+	0.225084i
$983$	37.2148	+	27.0381i	1.18697	+	0.862382i	0.992940	−	0.118614i	$-0.0378451\pi$
$983$	37.2148	+	27.0381i	1.18697	+	0.862382i	0.194027	+	0.980996i	$0.437845\pi$
$984$	0.618034	+	1.90211i	0.0197022	+	0.0606371i
$985$	−22.2492	−	68.4761i	−0.708919	−	2.18183i
$986$	16.1803	+	11.7557i	0.515287	+	0.374378i
$987$	−3.23607	+	2.35114i	−0.103005	+	0.0748376i
$988$		0			0
$989$	−24.0000			−0.763156
$990$		0			0
$991$	−8.00000			−0.254128			−0.127064	−	0.991894i	$-0.540555\pi$
$991$	−8.00000			−0.254128			−0.127064	+	0.991894i	$0.540555\pi$
$992$	−2.47214	+	7.60845i	−0.0784904	+	0.241569i
$993$	22.6525	−	16.4580i	0.718855	−	0.522278i
$994$	3.23607	+	2.35114i	0.102642	+	0.0745737i
$995$	−24.7214	−	76.0845i	−0.783720	−	2.41204i
$996$	1.23607	+	3.80423i	0.0391663	+	0.120542i
$997$	42.0689	+	30.5648i	1.33233	+	0.967998i	0.999689	+	0.0249463i	$0.00794146\pi$
$997$	42.0689	+	30.5648i	1.33233	+	0.967998i	0.332646	+	0.943052i	$0.392059\pi$
$998$	16.1803	−	11.7557i	0.512180	−	0.372120i
$999$	−0.618034	+	1.90211i	−0.0195537	+	0.0601802i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	726.2.e.e.493.1		4
11.2	odd	10		726.2.e.m.487.1		4
11.3	even	5	inner	726.2.e.e.565.1		4
11.4	even	5		66.2.a.c.1.1	✓	1
11.5	even	5	inner	726.2.e.e.511.1		4
11.6	odd	10		726.2.e.m.511.1		4
11.7	odd	10		726.2.a.d.1.1		1
11.8	odd	10		726.2.e.m.565.1		4
11.9	even	5	inner	726.2.e.e.487.1		4
11.10	odd	2		726.2.e.m.493.1		4
33.26	odd	10		198.2.a.c.1.1		1
33.29	even	10		2178.2.a.m.1.1		1
44.7	even	10		5808.2.a.b.1.1		1
44.15	odd	10		528.2.a.a.1.1		1
55.4	even	10		1650.2.a.c.1.1		1
55.37	odd	20		1650.2.c.m.199.2		2
55.48	odd	20		1650.2.c.m.199.1		2
77.48	odd	10		3234.2.a.s.1.1		1
88.37	even	10		2112.2.a.n.1.1		1
88.59	odd	10		2112.2.a.bd.1.1		1
99.4	even	15		1782.2.e.l.1189.1		2
99.59	odd	30		1782.2.e.n.1189.1		2
99.70	even	15		1782.2.e.l.595.1		2
99.92	odd	30		1782.2.e.n.595.1		2
132.59	even	10		1584.2.a.s.1.1		1
165.59	odd	10		4950.2.a.bo.1.1		1
165.92	even	20		4950.2.c.d.199.1		2
165.158	even	20		4950.2.c.d.199.2		2
231.125	even	10		9702.2.a.a.1.1		1
264.59	even	10		6336.2.a.d.1.1		1
264.125	odd	10		6336.2.a.c.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
66.2.a.c.1.1	✓	1	11.4	even	5
198.2.a.c.1.1		1	33.26	odd	10
528.2.a.a.1.1		1	44.15	odd	10
726.2.a.d.1.1		1	11.7	odd	10
726.2.e.e.487.1		4	11.9	even	5	inner
726.2.e.e.493.1		4	1.1	even	1	trivial
726.2.e.e.511.1		4	11.5	even	5	inner
726.2.e.e.565.1		4	11.3	even	5	inner
726.2.e.m.487.1		4	11.2	odd	10
726.2.e.m.493.1		4	11.10	odd	2
726.2.e.m.511.1		4	11.6	odd	10
726.2.e.m.565.1		4	11.8	odd	10
1584.2.a.s.1.1		1	132.59	even	10
1650.2.a.c.1.1		1	55.4	even	10
1650.2.c.m.199.1		2	55.48	odd	20
1650.2.c.m.199.2		2	55.37	odd	20
1782.2.e.l.595.1		2	99.70	even	15
1782.2.e.l.1189.1		2	99.4	even	15
1782.2.e.n.595.1		2	99.92	odd	30
1782.2.e.n.1189.1		2	99.59	odd	30
2112.2.a.n.1.1		1	88.37	even	10
2112.2.a.bd.1.1		1	88.59	odd	10
2178.2.a.m.1.1		1	33.29	even	10
3234.2.a.s.1.1		1	77.48	odd	10
4950.2.a.bo.1.1		1	165.59	odd	10
4950.2.c.d.199.1		2	165.92	even	20
4950.2.c.d.199.2		2	165.158	even	20
5808.2.a.b.1.1		1	44.7	even	10
6336.2.a.c.1.1		1	264.125	odd	10
6336.2.a.d.1.1		1	264.59	even	10
9702.2.a.a.1.1		1	231.125	even	10

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:	\( N \)	\(=\)	\( 726 = 2 \cdot 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	726.e (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 - 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-1.23607 - 3.80423i) q^{5} +(0.309017 + 0.951057i) q^{6} +(1.61803 + 1.17557i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.309017 - 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-1.23607 - 3.80423i) q^{5} +(0.309017 + 0.951057i) q^{6} +(1.61803 + 1.17557i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.309017 - 0.951057i) q^{9} -4.00000 q^{10} +1.00000 q^{12} +(1.23607 - 3.80423i) q^{13} +(1.61803 - 1.17557i) q^{14} +(3.23607 + 2.35114i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-0.618034 - 1.90211i) q^{17} +(-0.809017 - 0.587785i) q^{18} +(-1.23607 + 3.80423i) q^{20} -2.00000 q^{21} -6.00000 q^{23} +(0.309017 - 0.951057i) q^{24} +(-8.89919 + 6.46564i) q^{25} +(-3.23607 - 2.35114i) q^{26} +(0.309017 + 0.951057i) q^{27} +(-0.618034 - 1.90211i) q^{28} +(-8.09017 - 5.87785i) q^{29} +(3.23607 - 2.35114i) q^{30} +(-2.47214 + 7.60845i) q^{31} +1.00000 q^{32} -2.00000 q^{34} +(2.47214 - 7.60845i) q^{35} +(-0.809017 + 0.587785i) q^{36} +(1.61803 + 1.17557i) q^{37} +(1.23607 + 3.80423i) q^{39} +(3.23607 + 2.35114i) q^{40} +(-1.61803 + 1.17557i) q^{41} +(-0.618034 + 1.90211i) q^{42} +4.00000 q^{43} -4.00000 q^{45} +(-1.85410 + 5.70634i) q^{46} +(1.61803 - 1.17557i) q^{47} +(-0.809017 - 0.587785i) q^{48} +(-0.927051 - 2.85317i) q^{49} +(3.39919 + 10.4616i) q^{50} +(1.61803 + 1.17557i) q^{51} +(-3.23607 + 2.35114i) q^{52} +(1.23607 - 3.80423i) q^{53} +1.00000 q^{54} -2.00000 q^{56} +(-8.09017 + 5.87785i) q^{58} +(-1.23607 - 3.80423i) q^{60} +(-2.47214 - 7.60845i) q^{61} +(6.47214 + 4.70228i) q^{62} +(1.61803 - 1.17557i) q^{63} +(0.309017 - 0.951057i) q^{64} -16.0000 q^{65} -12.0000 q^{67} +(-0.618034 + 1.90211i) q^{68} +(4.85410 - 3.52671i) q^{69} +(-6.47214 - 4.70228i) q^{70} +(0.618034 + 1.90211i) q^{71} +(0.309017 + 0.951057i) q^{72} +(4.85410 + 3.52671i) q^{73} +(1.61803 - 1.17557i) q^{74} +(3.39919 - 10.4616i) q^{75} +4.00000 q^{78} +(3.09017 - 9.51057i) q^{79} +(3.23607 - 2.35114i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(0.618034 + 1.90211i) q^{82} +(1.23607 + 3.80423i) q^{83} +(1.61803 + 1.17557i) q^{84} +(-6.47214 + 4.70228i) q^{85} +(1.23607 - 3.80423i) q^{86} +10.0000 q^{87} +10.0000 q^{89} +(-1.23607 + 3.80423i) q^{90} +(6.47214 - 4.70228i) q^{91} +(4.85410 + 3.52671i) q^{92} +(-2.47214 - 7.60845i) q^{93} +(-0.618034 - 1.90211i) q^{94} +(-0.809017 + 0.587785i) q^{96} +(-0.618034 + 1.90211i) q^{97} -3.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} - q^{3} - q^{4} + 4 q^{5} - q^{6} + 2 q^{7} - q^{8} - q^{9}+O(q^{10}) \) 4 * q - q^2 - q^3 - q^4 + 4 * q^5 - q^6 + 2 * q^7 - q^8 - q^9	\( 4 q - q^{2} - q^{3} - q^{4} + 4 q^{5} - q^{6} + 2 q^{7} - q^{8} - q^{9} - 16 q^{10} + 4 q^{12} - 4 q^{13} + 2 q^{14} + 4 q^{15} - q^{16} + 2 q^{17} - q^{18} + 4 q^{20} - 8 q^{21} - 24 q^{23} - q^{24} - 11 q^{25} - 4 q^{26} - q^{27} + 2 q^{28} - 10 q^{29} + 4 q^{30} + 8 q^{31} + 4 q^{32} - 8 q^{34} - 8 q^{35} - q^{36} + 2 q^{37} - 4 q^{39} + 4 q^{40} - 2 q^{41} + 2 q^{42} + 16 q^{43} - 16 q^{45} + 6 q^{46} + 2 q^{47} - q^{48} + 3 q^{49} - 11 q^{50} + 2 q^{51} - 4 q^{52} - 4 q^{53} + 4 q^{54} - 8 q^{56} - 10 q^{58} + 4 q^{60} + 8 q^{61} + 8 q^{62} + 2 q^{63} - q^{64} - 64 q^{65} - 48 q^{67} + 2 q^{68} + 6 q^{69} - 8 q^{70} - 2 q^{71} - q^{72} + 6 q^{73} + 2 q^{74} - 11 q^{75} + 16 q^{78} - 10 q^{79} + 4 q^{80} - q^{81} - 2 q^{82} - 4 q^{83} + 2 q^{84} - 8 q^{85} - 4 q^{86} + 40 q^{87} + 40 q^{89} + 4 q^{90} + 8 q^{91} + 6 q^{92} + 8 q^{93} + 2 q^{94} - q^{96} + 2 q^{97} - 12 q^{98}+O(q^{100}) \) 4 * q - q^2 - q^3 - q^4 + 4 * q^5 - q^6 + 2 * q^7 - q^8 - q^9 - 16 * q^10 + 4 * q^12 - 4 * q^13 + 2 * q^14 + 4 * q^15 - q^16 + 2 * q^17 - q^18 + 4 * q^20 - 8 * q^21 - 24 * q^23 - q^24 - 11 * q^25 - 4 * q^26 - q^27 + 2 * q^28 - 10 * q^29 + 4 * q^30 + 8 * q^31 + 4 * q^32 - 8 * q^34 - 8 * q^35 - q^36 + 2 * q^37 - 4 * q^39 + 4 * q^40 - 2 * q^41 + 2 * q^42 + 16 * q^43 - 16 * q^45 + 6 * q^46 + 2 * q^47 - q^48 + 3 * q^49 - 11 * q^50 + 2 * q^51 - 4 * q^52 - 4 * q^53 + 4 * q^54 - 8 * q^56 - 10 * q^58 + 4 * q^60 + 8 * q^61 + 8 * q^62 + 2 * q^63 - q^64 - 64 * q^65 - 48 * q^67 + 2 * q^68 + 6 * q^69 - 8 * q^70 - 2 * q^71 - q^72 + 6 * q^73 + 2 * q^74 - 11 * q^75 + 16 * q^78 - 10 * q^79 + 4 * q^80 - q^81 - 2 * q^82 - 4 * q^83 + 2 * q^84 - 8 * q^85 - 4 * q^86 + 40 * q^87 + 40 * q^89 + 4 * q^90 + 8 * q^91 + 6 * q^92 + 8 * q^93 + 2 * q^94 - q^96 + 2 * q^97 - 12 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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