LMFDB - Embedded newform 726.2.e.c.493.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [726,2,Mod(487,726)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage: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")

magma://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:traces = [4,-1,-1,-1,0,-1,2,-1,-1,10] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

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.c.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} +(1.11803 + 3.44095i) q^{5} +(0.309017 + 0.951057i) q^{6} +(0.500000 + 0.363271i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.309017 - 0.951057i) q^{9} +3.61803 q^{10} +1.00000 q^{12} +(-1.00000 + 3.07768i) q^{13} +(0.500000 - 0.363271i) q^{14} +(-2.92705 - 2.12663i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-1.23607 - 3.80423i) q^{17} +(-0.809017 - 0.587785i) q^{18} +(-4.61803 + 3.35520i) q^{19} +(1.11803 - 3.44095i) q^{20} -0.618034 q^{21} -5.70820 q^{23} +(0.309017 - 0.951057i) q^{24} +(-6.54508 + 4.75528i) q^{25} +(2.61803 + 1.90211i) q^{26} +(0.309017 + 0.951057i) q^{27} +(-0.190983 - 0.587785i) q^{28} +(5.54508 + 4.02874i) q^{29} +(-2.92705 + 2.12663i) q^{30} +(-1.04508 + 3.21644i) q^{31} +1.00000 q^{32} -4.00000 q^{34} +(-0.690983 + 2.12663i) q^{35} +(-0.809017 + 0.587785i) q^{36} +(7.23607 + 5.25731i) q^{37} +(1.76393 + 5.42882i) q^{38} +(-1.00000 - 3.07768i) q^{39} +(-2.92705 - 2.12663i) q^{40} +(-4.61803 + 3.35520i) q^{41} +(-0.190983 + 0.587785i) q^{42} +4.76393 q^{43} +3.61803 q^{45} +(-1.76393 + 5.42882i) q^{46} +(-3.23607 + 2.35114i) q^{47} +(-0.809017 - 0.587785i) q^{48} +(-2.04508 - 6.29412i) q^{49} +(2.50000 + 7.69421i) q^{50} +(3.23607 + 2.35114i) q^{51} +(2.61803 - 1.90211i) q^{52} +(0.427051 - 1.31433i) q^{53} +1.00000 q^{54} -0.618034 q^{56} +(1.76393 - 5.42882i) q^{57} +(5.54508 - 4.02874i) q^{58} +(-8.35410 - 6.06961i) q^{59} +(1.11803 + 3.44095i) q^{60} +(1.14590 + 3.52671i) q^{61} +(2.73607 + 1.98787i) q^{62} +(0.500000 - 0.363271i) q^{63} +(0.309017 - 0.951057i) q^{64} -11.7082 q^{65} +4.94427 q^{67} +(-1.23607 + 3.80423i) q^{68} +(4.61803 - 3.35520i) q^{69} +(1.80902 + 1.31433i) q^{70} +(1.85410 + 5.70634i) q^{71} +(0.309017 + 0.951057i) q^{72} +(11.7812 + 8.55951i) q^{73} +(7.23607 - 5.25731i) q^{74} +(2.50000 - 7.69421i) q^{75} +5.70820 q^{76} -3.23607 q^{78} +(2.11803 - 6.51864i) q^{79} +(-2.92705 + 2.12663i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(1.76393 + 5.42882i) q^{82} +(-0.500000 - 1.53884i) q^{83} +(0.500000 + 0.363271i) q^{84} +(11.7082 - 8.50651i) q^{85} +(1.47214 - 4.53077i) q^{86} -6.85410 q^{87} +6.76393 q^{89} +(1.11803 - 3.44095i) q^{90} +(-1.61803 + 1.17557i) q^{91} +(4.61803 + 3.35520i) q^{92} +(-1.04508 - 3.21644i) q^{93} +(1.23607 + 3.80423i) q^{94} +(-16.7082 - 12.1392i) q^{95} +(-0.809017 + 0.587785i) q^{96} +(-2.97214 + 9.14729i) q^{97} -6.61803 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} - q^{3} - q^{4} - q^{6} + 2 q^{7} - q^{8} - q^{9} + 10 q^{10} + 4 q^{12} - 4 q^{13} + 2 q^{14} - 5 q^{15} - q^{16} + 4 q^{17} - q^{18} - 14 q^{19} + 2 q^{21} + 4 q^{23} - q^{24} - 15 q^{25}+ \cdots - 22 q^{98}+O(q^{100}) $ 4 * q - q^2 - q^3 - q^4 - q^6 + 2 * q^7 - q^8 - q^9 + 10 * q^10 + 4 * q^12 - 4 * q^13 + 2 * q^14 - 5 * q^15 - q^16 + 4 * q^17 - q^18 - 14 * q^19 + 2 * q^21 + 4 * q^23 - q^24 - 15 * q^25 + 6 * q^26 - q^27 - 3 * q^28 + 11 * q^29 - 5 * q^30 + 7 * q^31 + 4 * q^32 - 16 * q^34 - 5 * q^35 - q^36 + 20 * q^37 + 16 * q^38 - 4 * q^39 - 5 * q^40 - 14 * q^41 - 3 * q^42 + 28 * q^43 + 10 * q^45 - 16 * q^46 - 4 * q^47 - q^48 + 3 * q^49 + 10 * q^50 + 4 * q^51 + 6 * q^52 - 5 * q^53 + 4 * q^54 + 2 * q^56 + 16 * q^57 + 11 * q^58 - 20 * q^59 + 18 * q^61 + 2 * q^62 + 2 * q^63 - q^64 - 20 * q^65 - 16 * q^67 + 4 * q^68 + 14 * q^69 + 5 * q^70 - 6 * q^71 - q^72 + 27 * q^73 + 20 * q^74 + 10 * q^75 - 4 * q^76 - 4 * q^78 + 4 * q^79 - 5 * q^80 - q^81 + 16 * q^82 - 2 * q^83 + 2 * q^84 + 20 * q^85 - 12 * q^86 - 14 * q^87 + 36 * q^89 - 2 * q^91 + 14 * q^92 + 7 * q^93 - 4 * q^94 - 40 * q^95 - q^96 + 6 * q^97 - 22 * q^98

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
$5$	1.11803	+	3.44095i	0.500000	+	1.53884i	0.809017	+	0.587785i	$0.200000\pi$
$5$	1.11803	+	3.44095i	0.500000	+	1.53884i	−0.309017	+	0.951057i	$0.600000\pi$
$6$	0.309017	+	0.951057i	0.126156	+	0.388267i
$7$	0.500000	+	0.363271i	0.188982	+	0.137304i	0.678253	−	0.734828i	$-0.262737\pi$
$7$	0.500000	+	0.363271i	0.188982	+	0.137304i	−0.489271	+	0.872132i	$0.662737\pi$
$8$	−0.809017	+	0.587785i	−0.286031	+	0.207813i
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$	3.61803			1.14412
$11$		0			0
$11$		0			0
$12$	1.00000			0.288675
$13$	−1.00000	+	3.07768i	−0.277350	+	0.853596i	0.711238	+	0.702951i	$0.248135\pi$
$13$	−1.00000	+	3.07768i	−0.277350	+	0.853596i	−0.988588	+	0.150644i	$0.951865\pi$
$14$	0.500000	−	0.363271i	0.133631	−	0.0970883i
$15$	−2.92705	−	2.12663i	−0.755761	−	0.549093i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−1.23607	−	3.80423i	−0.299791	−	0.922660i	−0.981570	−	0.191103i	$-0.938794\pi$
$17$	−1.23607	−	3.80423i	−0.299791	−	0.922660i	0.681780	−	0.731558i	$-0.261206\pi$
$18$	−0.809017	−	0.587785i	−0.190687	−	0.138542i
$19$	−4.61803	+	3.35520i	−1.05945	+	0.769735i	−0.973986	−	0.226606i	$-0.927237\pi$
$19$	−4.61803	+	3.35520i	−1.05945	+	0.769735i	−0.0854632	+	0.996341i	$0.527237\pi$
$20$	1.11803	−	3.44095i	0.250000	−	0.769421i
$21$	−0.618034			−0.134866
$22$		0			0
$23$	−5.70820			−1.19024			−0.595121	−	0.803636i	$-0.702896\pi$
$23$	−5.70820			−1.19024			−0.595121	+	0.803636i	$0.702896\pi$
$24$	0.309017	−	0.951057i	0.0630778	−	0.194134i
$25$	−6.54508	+	4.75528i	−1.30902	+	0.951057i
$26$	2.61803	+	1.90211i	0.513439	+	0.373035i
$27$	0.309017	+	0.951057i	0.0594703	+	0.183031i
$28$	−0.190983	−	0.587785i	−0.0360924	−	0.111081i
$29$	5.54508	+	4.02874i	1.02970	+	0.748118i	0.968248	−	0.249992i	$-0.0804280\pi$
$29$	5.54508	+	4.02874i	1.02970	+	0.748118i	0.0614485	+	0.998110i	$0.480428\pi$
$30$	−2.92705	+	2.12663i	−0.534404	+	0.388267i
$31$	−1.04508	+	3.21644i	−0.187703	+	0.577690i	−0.999984	−	0.00557557i	$-0.998225\pi$
$31$	−1.04508	+	3.21644i	−0.187703	+	0.577690i	0.812282	+	0.583265i	$0.198225\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	−4.00000			−0.685994
$35$	−0.690983	+	2.12663i	−0.116797	+	0.359466i
$36$	−0.809017	+	0.587785i	−0.134836	+	0.0979642i
$37$	7.23607	+	5.25731i	1.18960	+	0.864297i	0.993222	−	0.116231i	$-0.0370814\pi$
$37$	7.23607	+	5.25731i	1.18960	+	0.864297i	0.196380	+	0.980528i	$0.437081\pi$
$38$	1.76393	+	5.42882i	0.286148	+	0.880672i
$39$	−1.00000	−	3.07768i	−0.160128	−	0.492824i
$40$	−2.92705	−	2.12663i	−0.462807	−	0.336249i
$41$	−4.61803	+	3.35520i	−0.721216	+	0.523994i	−0.886772	−	0.462206i	$-0.847058\pi$
$41$	−4.61803	+	3.35520i	−0.721216	+	0.523994i	0.165557	+	0.986200i	$0.447058\pi$
$42$	−0.190983	+	0.587785i	−0.0294693	+	0.0906972i
$43$	4.76393			0.726493			0.363246	−	0.931693i	$-0.381668\pi$
$43$	4.76393			0.726493			0.363246	+	0.931693i	$0.381668\pi$
$44$		0			0
$45$	3.61803			0.539345
$46$	−1.76393	+	5.42882i	−0.260078	+	0.800437i
$47$	−3.23607	+	2.35114i	−0.472029	+	0.342949i	−0.798232	−	0.602351i	$-0.794231\pi$
$47$	−3.23607	+	2.35114i	−0.472029	+	0.342949i	0.326202	+	0.945300i	$0.394231\pi$
$48$	−0.809017	−	0.587785i	−0.116772	−	0.0848395i
$49$	−2.04508	−	6.29412i	−0.292155	−	0.899161i
$50$	2.50000	+	7.69421i	0.353553	+	1.08813i
$51$	3.23607	+	2.35114i	0.453140	+	0.329226i
$52$	2.61803	−	1.90211i	0.363056	−	0.263776i
$53$	0.427051	−	1.31433i	0.0586600	−	0.180537i	−0.917433	−	0.397890i	$-0.869742\pi$
$53$	0.427051	−	1.31433i	0.0586600	−	0.180537i	0.976093	+	0.217354i	$0.0697424\pi$
$54$	1.00000			0.136083
$55$		0			0
$56$	−0.618034			−0.0825883
$57$	1.76393	−	5.42882i	0.233639	−	0.719065i
$58$	5.54508	−	4.02874i	0.728105	−	0.528999i
$59$	−8.35410	−	6.06961i	−1.08761	−	0.790196i	−0.108617	−	0.994084i	$-0.534642\pi$
$59$	−8.35410	−	6.06961i	−1.08761	−	0.790196i	−0.978994	+	0.203888i	$0.934642\pi$
$60$	1.11803	+	3.44095i	0.144338	+	0.444225i
$61$	1.14590	+	3.52671i	0.146717	+	0.451549i	0.997228	−	0.0744087i	$-0.0237069\pi$
$61$	1.14590	+	3.52671i	0.146717	+	0.451549i	−0.850511	+	0.525958i	$0.823707\pi$
$62$	2.73607	+	1.98787i	0.347481	+	0.252460i
$63$	0.500000	−	0.363271i	0.0629941	−	0.0457679i
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	−11.7082			−1.45222
$66$		0			0
$67$	4.94427			0.604039			0.302019	−	0.953302i	$-0.402339\pi$
$67$	4.94427			0.604039			0.302019	+	0.953302i	$0.402339\pi$
$68$	−1.23607	+	3.80423i	−0.149895	+	0.461330i
$69$	4.61803	−	3.35520i	0.555946	−	0.403918i
$70$	1.80902	+	1.31433i	0.216219	+	0.157092i
$71$	1.85410	+	5.70634i	0.220041	+	0.677218i	0.998757	+	0.0498409i	$0.0158714\pi$
$71$	1.85410	+	5.70634i	0.220041	+	0.677218i	−0.778716	+	0.627377i	$0.784129\pi$
$72$	0.309017	+	0.951057i	0.0364180	+	0.112083i
$73$	11.7812	+	8.55951i	1.37888	+	1.00181i	0.996984	+	0.0776093i	$0.0247287\pi$
$73$	11.7812	+	8.55951i	1.37888	+	1.00181i	0.381896	+	0.924205i	$0.375271\pi$
$74$	7.23607	−	5.25731i	0.841176	−	0.611150i
$75$	2.50000	−	7.69421i	0.288675	−	0.888451i
$76$	5.70820			0.654776
$77$		0			0
$78$	−3.23607			−0.366413
$79$	2.11803	−	6.51864i	0.238297	−	0.733404i	−0.758369	−	0.651825i	$-0.774004\pi$
$79$	2.11803	−	6.51864i	0.238297	−	0.733404i	0.996667	−	0.0815791i	$-0.0259963\pi$
$80$	−2.92705	+	2.12663i	−0.327254	+	0.237764i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	1.76393	+	5.42882i	0.194794	+	0.599513i
$83$	−0.500000	−	1.53884i	−0.0548821	−	0.168910i	0.919858	−	0.392251i	$-0.128304\pi$
$83$	−0.500000	−	1.53884i	−0.0548821	−	0.168910i	−0.974740	+	0.223341i	$0.928304\pi$
$84$	0.500000	+	0.363271i	0.0545545	+	0.0396361i
$85$	11.7082	−	8.50651i	1.26993	−	0.922660i
$86$	1.47214	−	4.53077i	0.158745	−	0.488565i
$87$	−6.85410			−0.734837
$88$		0			0
$89$	6.76393			0.716975			0.358488	−	0.933534i	$-0.383293\pi$
$89$	6.76393			0.716975			0.358488	+	0.933534i	$0.383293\pi$
$90$	1.11803	−	3.44095i	0.117851	−	0.362708i
$91$	−1.61803	+	1.17557i	−0.169616	+	0.123233i
$92$	4.61803	+	3.35520i	0.481463	+	0.349804i
$93$	−1.04508	−	3.21644i	−0.108370	−	0.333529i
$94$	1.23607	+	3.80423i	0.127491	+	0.392376i
$95$	−16.7082	−	12.1392i	−1.71423	−	1.24546i
$96$	−0.809017	+	0.587785i	−0.0825700	+	0.0599906i
$97$	−2.97214	+	9.14729i	−0.301775	+	0.928767i	0.679086	+	0.734058i	$0.262376\pi$
$97$	−2.97214	+	9.14729i	−0.301775	+	0.928767i	−0.980861	+	0.194709i	$0.937624\pi$
$98$	−6.61803			−0.668522
$99$		0			0
$100$	8.09017			0.809017
$101$	0.645898	−	1.98787i	0.0642693	−	0.197800i	−0.913766	−	0.406242i	$-0.866839\pi$
$101$	0.645898	−	1.98787i	0.0642693	−	0.197800i	0.978035	+	0.208441i	$0.0668391\pi$
$102$	3.23607	−	2.35114i	0.320418	−	0.232798i
$103$	7.97214	+	5.79210i	0.785518	+	0.570712i	0.906630	−	0.421927i	$-0.138646\pi$
$103$	7.97214	+	5.79210i	0.785518	+	0.570712i	−0.121112	+	0.992639i	$0.538646\pi$
$104$	−1.00000	−	3.07768i	−0.0980581	−	0.301792i
$105$	−0.690983	−	2.12663i	−0.0674330	−	0.207538i
$106$	−1.11803	−	0.812299i	−0.108593	−	0.0788975i
$107$	0.881966	−	0.640786i	0.0852629	−	0.0619471i	−0.544337	−	0.838867i	$-0.683219\pi$
$107$	0.881966	−	0.640786i	0.0852629	−	0.0619471i	0.629600	+	0.776919i	$0.283219\pi$
$108$	0.309017	−	0.951057i	0.0297352	−	0.0915155i
$109$	2.94427			0.282010			0.141005	−	0.990009i	$-0.454967\pi$
$109$	2.94427			0.282010			0.141005	+	0.990009i	$0.454967\pi$
$110$		0			0
$111$	−8.94427			−0.848953
$112$	−0.190983	+	0.587785i	−0.0180462	+	0.0555405i
$113$	−5.61803	+	4.08174i	−0.528500	+	0.383978i	−0.819796	−	0.572655i	$-0.805913\pi$
$113$	−5.61803	+	4.08174i	−0.528500	+	0.383978i	0.291296	+	0.956633i	$0.405913\pi$
$114$	−4.61803	−	3.35520i	−0.432519	−	0.314243i
$115$	−6.38197	−	19.6417i	−0.595121	−	1.83160i
$116$	−2.11803	−	6.51864i	−0.196655	−	0.605240i
$117$	2.61803	+	1.90211i	0.242037	+	0.175850i
$118$	−8.35410	+	6.06961i	−0.769057	+	0.558753i
$119$	0.763932	−	2.35114i	0.0700295	−	0.215529i
$120$	3.61803			0.330280
$121$		0			0
$122$	3.70820			0.335725
$123$	1.76393	−	5.42882i	0.159048	−	0.489501i
$124$	2.73607	−	1.98787i	0.245706	−	0.178516i
$125$	−9.04508	−	6.57164i	−0.809017	−	0.587785i
$126$	−0.190983	−	0.587785i	−0.0170141	−	0.0523641i
$127$	−1.23607	−	3.80423i	−0.109683	−	0.337570i	0.881118	−	0.472897i	$-0.156792\pi$
$127$	−1.23607	−	3.80423i	−0.109683	−	0.337570i	−0.990801	+	0.135326i	$0.956792\pi$
$128$	−0.809017	−	0.587785i	−0.0715077	−	0.0519534i
$129$	−3.85410	+	2.80017i	−0.339335	+	0.246541i
$130$	−3.61803	+	11.1352i	−0.317323	+	0.976618i
$131$	−3.85410			−0.336734			−0.168367	−	0.985724i	$-0.553849\pi$
$131$	−3.85410			−0.336734			−0.168367	+	0.985724i	$0.553849\pi$
$132$		0			0
$133$	−3.52786			−0.305905
$134$	1.52786	−	4.70228i	0.131987	−	0.406215i
$135$	−2.92705	+	2.12663i	−0.251920	+	0.183031i
$136$	3.23607	+	2.35114i	0.277491	+	0.201609i
$137$	−4.38197	−	13.4863i	−0.374377	−	1.15221i	−0.943898	−	0.330236i	$-0.892872\pi$
$137$	−4.38197	−	13.4863i	−0.374377	−	1.15221i	0.569522	−	0.821976i	$-0.307128\pi$
$138$	−1.76393	−	5.42882i	−0.150156	−	0.462132i
$139$	−12.7082	−	9.23305i	−1.07790	−	0.783137i	−0.100581	−	0.994929i	$-0.532070\pi$
$139$	−12.7082	−	9.23305i	−1.07790	−	0.783137i	−0.977315	+	0.211792i	$0.932070\pi$
$140$	1.80902	−	1.31433i	0.152890	−	0.111081i
$141$	1.23607	−	3.80423i	0.104096	−	0.320374i
$142$	6.00000			0.503509
$143$		0			0
$144$	1.00000			0.0833333
$145$	−7.66312	+	23.5847i	−0.636387	+	1.95860i
$146$	11.7812	−	8.55951i	0.975015	−	0.708390i
$147$	5.35410	+	3.88998i	0.441599	+	0.320840i
$148$	−2.76393	−	8.50651i	−0.227194	−	0.699231i
$149$	−1.86475	−	5.73910i	−0.152766	−	0.470165i	0.845162	−	0.534511i	$-0.179504\pi$
$149$	−1.86475	−	5.73910i	−0.152766	−	0.470165i	−0.997928	+	0.0643455i	$0.979504\pi$
$150$	−6.54508	−	4.75528i	−0.534404	−	0.388267i
$151$	16.0172	−	11.6372i	1.30346	−	0.947021i	0.303480	−	0.952838i	$-0.401851\pi$
$151$	16.0172	−	11.6372i	1.30346	−	0.947021i	0.999983	+	0.00581658i	$0.00185149\pi$
$152$	1.76393	−	5.42882i	0.143074	−	0.440336i
$153$	−4.00000			−0.323381
$154$		0			0
$155$	−12.2361			−0.982825
$156$	−1.00000	+	3.07768i	−0.0800641	+	0.246412i
$157$	14.5623	−	10.5801i	1.16220	−	0.844387i	0.172144	−	0.985072i	$-0.444931\pi$
$157$	14.5623	−	10.5801i	1.16220	−	0.844387i	0.990054	+	0.140685i	$0.0449305\pi$
$158$	−5.54508	−	4.02874i	−0.441143	−	0.320509i
$159$	0.427051	+	1.31433i	0.0338673	+	0.104233i
$160$	1.11803	+	3.44095i	0.0883883	+	0.272031i
$161$	−2.85410	−	2.07363i	−0.224935	−	0.163425i
$162$	−0.809017	+	0.587785i	−0.0635624	+	0.0461808i
$163$	0.145898	−	0.449028i	0.0114276	−	0.0351706i	−0.945180	−	0.326549i	$-0.894114\pi$
$163$	0.145898	−	0.449028i	0.0114276	−	0.0351706i	0.956608	+	0.291379i	$0.0941140\pi$
$164$	5.70820			0.445736
$165$		0			0
$166$	−1.61803			−0.125584
$167$	1.94427	−	5.98385i	0.150452	−	0.463044i	−0.847219	−	0.531243i	$-0.821725\pi$
$167$	1.94427	−	5.98385i	0.150452	−	0.463044i	0.997672	+	0.0681985i	$0.0217251\pi$
$168$	0.500000	−	0.363271i	0.0385758	−	0.0280270i
$169$	2.04508	+	1.48584i	0.157314	+	0.114295i
$170$	−4.47214	−	13.7638i	−0.342997	−	1.05564i
$171$	1.76393	+	5.42882i	0.134891	+	0.415153i
$172$	−3.85410	−	2.80017i	−0.293873	−	0.213511i
$173$	−11.5902	+	8.42075i	−0.881184	+	0.640218i	−0.933565	−	0.358409i	$-0.883319\pi$
$173$	−11.5902	+	8.42075i	−0.881184	+	0.640218i	0.0523802	+	0.998627i	$0.483319\pi$
$174$	−2.11803	+	6.51864i	−0.160568	+	0.494177i
$175$	−5.00000			−0.377964
$176$		0			0
$177$	10.3262			0.776168
$178$	2.09017	−	6.43288i	0.156665	−	0.482165i
$179$	15.0172	−	10.9106i	1.12244	−	0.815500i	0.137863	−	0.990451i	$-0.455977\pi$
$179$	15.0172	−	10.9106i	1.12244	−	0.815500i	0.984577	+	0.174951i	$0.0559767\pi$
$180$	−2.92705	−	2.12663i	−0.218169	−	0.158509i
$181$	6.61803	+	20.3682i	0.491915	+	1.51396i	0.821710	+	0.569905i	$0.193020\pi$
$181$	6.61803	+	20.3682i	0.491915	+	1.51396i	−0.329796	+	0.944052i	$0.606980\pi$
$182$	0.618034	+	1.90211i	0.0458117	+	0.140994i
$183$	−3.00000	−	2.17963i	−0.221766	−	0.161123i
$184$	4.61803	−	3.35520i	0.340446	−	0.247348i
$185$	−10.0000	+	30.7768i	−0.735215	+	2.26276i
$186$	−3.38197			−0.247978
$187$		0			0
$188$	4.00000			0.291730
$189$	−0.190983	+	0.587785i	−0.0138920	+	0.0427551i
$190$	−16.7082	+	12.1392i	−1.21214	+	0.880672i
$191$	2.47214	+	1.79611i	0.178877	+	0.129962i	0.673621	−	0.739077i	$-0.264738\pi$
$191$	2.47214	+	1.79611i	0.178877	+	0.129962i	−0.494744	+	0.869039i	$0.664738\pi$
$192$	0.309017	+	0.951057i	0.0223014	+	0.0686366i
$193$	1.42705	+	4.39201i	0.102721	+	0.316144i	0.989189	−	0.146647i	$-0.0468481\pi$
$193$	1.42705	+	4.39201i	0.102721	+	0.316144i	−0.886468	+	0.462791i	$0.846848\pi$
$194$	7.78115	+	5.65334i	0.558654	+	0.405886i
$195$	9.47214	−	6.88191i	0.678314	−	0.492824i
$196$	−2.04508	+	6.29412i	−0.146077	+	0.449580i
$197$	25.5066			1.81727			0.908634	−	0.417593i	$-0.137126\pi$
$197$	25.5066			1.81727			0.908634	+	0.417593i	$0.137126\pi$
$198$		0			0
$199$	−0.381966			−0.0270769			−0.0135384	−	0.999908i	$-0.504310\pi$
$199$	−0.381966			−0.0270769			−0.0135384	+	0.999908i	$0.504310\pi$
$200$	2.50000	−	7.69421i	0.176777	−	0.544063i
$201$	−4.00000	+	2.90617i	−0.282138	+	0.204985i
$202$	−1.69098	−	1.22857i	−0.118977	−	0.0864420i
$203$	1.30902	+	4.02874i	0.0918750	+	0.282762i
$204$	−1.23607	−	3.80423i	−0.0865421	−	0.266349i
$205$	−16.7082	−	12.1392i	−1.16695	−	0.847840i
$206$	7.97214	−	5.79210i	0.555445	−	0.403554i
$207$	−1.76393	+	5.42882i	−0.122602	+	0.377329i
$208$	−3.23607			−0.224381
$209$		0			0
$210$	−2.23607			−0.154303
$211$	2.85410	−	8.78402i	0.196484	−	0.604717i	−0.803472	−	0.595343i	$-0.797016\pi$
$211$	2.85410	−	8.78402i	0.196484	−	0.604717i	0.999956	−	0.00937395i	$-0.00298386\pi$
$212$	−1.11803	+	0.812299i	−0.0767869	+	0.0557889i
$213$	−4.85410	−	3.52671i	−0.332598	−	0.241646i
$214$	−0.336881	−	1.03681i	−0.0230287	−	0.0708751i
$215$	5.32624	+	16.3925i	0.363246	+	1.11796i
$216$	−0.809017	−	0.587785i	−0.0550466	−	0.0399937i
$217$	−1.69098	+	1.22857i	−0.114791	+	0.0834008i
$218$	0.909830	−	2.80017i	0.0616215	−	0.189651i
$219$	−14.5623			−0.984029
$220$		0			0
$221$	12.9443			0.870726
$222$	−2.76393	+	8.50651i	−0.185503	+	0.570919i
$223$	1.07295	−	0.779543i	0.0718500	−	0.0522021i	−0.551280	−	0.834320i	$-0.685861\pi$
$223$	1.07295	−	0.779543i	0.0718500	−	0.0522021i	0.623130	+	0.782118i	$0.285861\pi$
$224$	0.500000	+	0.363271i	0.0334077	+	0.0242721i
$225$	2.50000	+	7.69421i	0.166667	+	0.512947i
$226$	2.14590	+	6.60440i	0.142743	+	0.439318i
$227$	4.07295	+	2.95917i	0.270331	+	0.196407i	0.714689	−	0.699442i	$-0.246568\pi$
$227$	4.07295	+	2.95917i	0.270331	+	0.196407i	−0.444358	+	0.895849i	$0.646568\pi$
$228$	−4.61803	+	3.35520i	−0.305837	+	0.222203i
$229$	−1.67376	+	5.15131i	−0.110605	+	0.340408i	−0.991005	−	0.133824i	$-0.957274\pi$
$229$	−1.67376	+	5.15131i	−0.110605	+	0.340408i	0.880400	+	0.474232i	$0.157274\pi$
$230$	−20.6525			−1.36178
$231$		0			0
$232$	−6.85410			−0.449994
$233$	5.23607	−	16.1150i	0.343026	−	1.05573i	−0.619606	−	0.784913i	$-0.712708\pi$
$233$	5.23607	−	16.1150i	0.343026	−	1.05573i	0.962632	−	0.270813i	$-0.0872925\pi$
$234$	2.61803	−	1.90211i	0.171146	−	0.124345i
$235$	−11.7082	−	8.50651i	−0.763759	−	0.554903i
$236$	3.19098	+	9.82084i	0.207715	+	0.639282i
$237$	2.11803	+	6.51864i	0.137581	+	0.423431i
$238$	−2.00000	−	1.45309i	−0.129641	−	0.0941895i
$239$	−6.09017	+	4.42477i	−0.393940	+	0.286214i	−0.767068	−	0.641565i	$-0.778285\pi$
$239$	−6.09017	+	4.42477i	−0.393940	+	0.286214i	0.373128	+	0.927780i	$0.378285\pi$
$240$	1.11803	−	3.44095i	0.0721688	−	0.222113i
$241$	−8.61803			−0.555136			−0.277568	−	0.960706i	$-0.589528\pi$
$241$	−8.61803			−0.555136			−0.277568	+	0.960706i	$0.589528\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$	1.14590	−	3.52671i	0.0733586	−	0.225775i
$245$	19.3713	−	14.0741i	1.23759	−	0.899161i
$246$	−4.61803	−	3.35520i	−0.294435	−	0.213920i
$247$	−5.70820	−	17.5680i	−0.363204	−	1.11783i
$248$	−1.04508	−	3.21644i	−0.0663630	−	0.204244i
$249$	1.30902	+	0.951057i	0.0829556	+	0.0602708i
$250$	−9.04508	+	6.57164i	−0.572061	+	0.415627i
$251$	4.73607	−	14.5761i	0.298938	−	0.920036i	−0.682932	−	0.730482i	$-0.739296\pi$
$251$	4.73607	−	14.5761i	0.298938	−	0.920036i	0.981870	−	0.189555i	$-0.0607044\pi$
$252$	−0.618034			−0.0389325
$253$		0			0
$254$	−4.00000			−0.250982
$255$	−4.47214	+	13.7638i	−0.280056	+	0.861924i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−6.70820	−	4.87380i	−0.418446	−	0.304019i	0.358566	−	0.933504i	$-0.383266\pi$
$257$	−6.70820	−	4.87380i	−0.418446	−	0.304019i	−0.777012	+	0.629485i	$0.783266\pi$
$258$	1.47214	+	4.53077i	0.0916512	+	0.282073i
$259$	1.70820	+	5.25731i	0.106143	+	0.326673i
$260$	9.47214	+	6.88191i	0.587437	+	0.426798i
$261$	5.54508	−	4.02874i	0.343232	−	0.249373i
$262$	−1.19098	+	3.66547i	−0.0735792	+	0.226453i
$263$	17.2361			1.06282			0.531411	−	0.847114i	$-0.321662\pi$
$263$	17.2361			1.06282			0.531411	+	0.847114i	$0.321662\pi$
$264$		0			0
$265$	5.00000			0.307148
$266$	−1.09017	+	3.35520i	−0.0668426	+	0.205720i
$267$	−5.47214	+	3.97574i	−0.334889	+	0.243311i
$268$	−4.00000	−	2.90617i	−0.244339	−	0.177523i
$269$	1.85410	+	5.70634i	0.113047	+	0.347922i	0.991535	−	0.129843i	$-0.0414473\pi$
$269$	1.85410	+	5.70634i	0.113047	+	0.347922i	−0.878488	+	0.477764i	$0.841447\pi$
$270$	1.11803	+	3.44095i	0.0680414	+	0.209410i
$271$	21.4164	+	15.5599i	1.30095	+	0.945199i	0.999964	−	0.00842890i	$-0.00268304\pi$
$271$	21.4164	+	15.5599i	1.30095	+	0.945199i	0.300990	+	0.953627i	$0.402683\pi$
$272$	3.23607	−	2.35114i	0.196215	−	0.142559i
$273$	0.618034	−	1.90211i	0.0374051	−	0.115121i
$274$	−14.1803			−0.856666
$275$		0			0
$276$	−5.70820			−0.343594
$277$	−4.85410	+	14.9394i	−0.291655	+	0.897621i	0.692670	+	0.721255i	$0.256434\pi$
$277$	−4.85410	+	14.9394i	−0.291655	+	0.897621i	−0.984325	+	0.176366i	$0.943566\pi$
$278$	−12.7082	+	9.23305i	−0.762187	+	0.553762i
$279$	2.73607	+	1.98787i	0.163804	+	0.119011i
$280$	−0.690983	−	2.12663i	−0.0412941	−	0.127090i
$281$	−6.56231	−	20.1967i	−0.391474	−	1.20483i	−0.931673	−	0.363297i	$-0.881651\pi$
$281$	−6.56231	−	20.1967i	−0.391474	−	1.20483i	0.540199	−	0.841537i	$-0.318349\pi$
$282$	−3.23607	−	2.35114i	−0.192705	−	0.140008i
$283$	−6.09017	+	4.42477i	−0.362023	+	0.263025i	−0.753895	−	0.656994i	$-0.771827\pi$
$283$	−6.09017	+	4.42477i	−0.362023	+	0.263025i	0.391872	+	0.920020i	$0.371827\pi$
$284$	1.85410	−	5.70634i	0.110021	−	0.338609i
$285$	20.6525			1.22335
$286$		0			0
$287$	−3.52786			−0.208243
$288$	0.309017	−	0.951057i	0.0182090	−	0.0560415i
$289$	0.809017	−	0.587785i	0.0475892	−	0.0345756i
$290$	20.0623	+	14.5761i	1.17810	+	0.855939i
$291$	−2.97214	−	9.14729i	−0.174230	−	0.536224i
$292$	−4.50000	−	13.8496i	−0.263343	−	0.810485i
$293$	4.35410	+	3.16344i	0.254369	+	0.184810i	0.707661	−	0.706552i	$-0.249750\pi$
$293$	4.35410	+	3.16344i	0.254369	+	0.184810i	−0.453292	+	0.891362i	$0.649750\pi$
$294$	5.35410	−	3.88998i	0.312258	−	0.226868i
$295$	11.5451	−	35.5321i	0.672181	−	2.06876i
$296$	−8.94427			−0.519875
$297$		0			0
$298$	−6.03444			−0.349566
$299$	5.70820	−	17.5680i	0.330114	−	1.01599i
$300$	−6.54508	+	4.75528i	−0.377881	+	0.274546i
$301$	2.38197	+	1.73060i	0.137294	+	0.0997501i
$302$	−6.11803	−	18.8294i	−0.352053	−	1.08351i
$303$	0.645898	+	1.98787i	0.0371059	+	0.114200i
$304$	−4.61803	−	3.35520i	−0.264862	−	0.192434i
$305$	−10.8541	+	7.88597i	−0.621504	+	0.451549i
$306$	−1.23607	+	3.80423i	−0.0706613	+	0.217473i
$307$	17.2361			0.983714			0.491857	−	0.870676i	$-0.336318\pi$
$307$	17.2361			0.983714			0.491857	+	0.870676i	$0.336318\pi$
$308$		0			0
$309$	−9.85410			−0.560580
$310$	−3.78115	+	11.6372i	−0.214755	+	0.660948i
$311$	−13.3262	+	9.68208i	−0.755662	+	0.549020i	−0.897577	−	0.440859i	$-0.854674\pi$
$311$	−13.3262	+	9.68208i	−0.755662	+	0.549020i	0.141915	+	0.989879i	$0.454674\pi$
$312$	2.61803	+	1.90211i	0.148217	+	0.107686i
$313$	6.79180	+	20.9030i	0.383895	+	1.18151i	0.937279	+	0.348581i	$0.113336\pi$
$313$	6.79180	+	20.9030i	0.383895	+	1.18151i	−0.553384	+	0.832926i	$0.686664\pi$
$314$	−5.56231	−	17.1190i	−0.313899	−	0.966082i
$315$	1.80902	+	1.31433i	0.101927	+	0.0740540i
$316$	−5.54508	+	4.02874i	−0.311935	+	0.226634i
$317$	−2.79837	+	8.61251i	−0.157172	+	0.483727i	−0.998375	−	0.0569940i	$-0.981848\pi$
$317$	−2.79837	+	8.61251i	−0.157172	+	0.483727i	0.841202	+	0.540721i	$0.181848\pi$
$318$	1.38197			0.0774968
$319$		0			0
$320$	3.61803			0.202254
$321$	−0.336881	+	1.03681i	−0.0188029	+	0.0578693i
$322$	−2.85410	+	2.07363i	−0.159053	+	0.115559i
$323$	18.4721	+	13.4208i	1.02782	+	0.746753i
$324$	0.309017	+	0.951057i	0.0171676	+	0.0528365i
$325$	−8.09017	−	24.8990i	−0.448762	−	1.38115i
$326$	−0.381966	−	0.277515i	−0.0211551	−	0.0153701i
$327$	−2.38197	+	1.73060i	−0.131723	+	0.0957024i
$328$	1.76393	−	5.42882i	0.0973969	−	0.299757i
$329$	−2.47214			−0.136293
$330$		0			0
$331$	−16.3607			−0.899264			−0.449632	−	0.893214i	$-0.648445\pi$
$331$	−16.3607			−0.899264			−0.449632	+	0.893214i	$0.648445\pi$
$332$	−0.500000	+	1.53884i	−0.0274411	+	0.0844549i
$333$	7.23607	−	5.25731i	0.396534	−	0.288099i
$334$	−5.09017	−	3.69822i	−0.278522	−	0.202358i
$335$	5.52786	+	17.0130i	0.302019	+	0.929520i
$336$	−0.190983	−	0.587785i	−0.0104190	−	0.0320663i
$337$	16.0902	+	11.6902i	0.876487	+	0.636805i	0.932320	−	0.361635i	$-0.117781\pi$
$337$	16.0902	+	11.6902i	0.876487	+	0.636805i	−0.0558324	+	0.998440i	$0.517781\pi$
$338$	2.04508	−	1.48584i	0.111238	−	0.0808191i
$339$	2.14590	−	6.60440i	0.116549	−	0.358702i
$340$	−14.4721			−0.784862
$341$		0			0
$342$	5.70820			0.308664
$343$	2.60081	−	8.00448i	0.140431	−	0.432201i
$344$	−3.85410	+	2.80017i	−0.207799	+	0.150975i
$345$	16.7082	+	12.1392i	0.899539	+	0.653554i
$346$	4.42705	+	13.6251i	0.238000	+	0.732488i
$347$	10.6074	+	32.6462i	0.569435	+	1.75254i	0.654393	+	0.756155i	$0.272924\pi$
$347$	10.6074	+	32.6462i	0.569435	+	1.75254i	−0.0849581	+	0.996385i	$0.527076\pi$
$348$	5.54508	+	4.02874i	0.297248	+	0.215963i
$349$	−9.94427	+	7.22494i	−0.532305	+	0.386742i	−0.821219	−	0.570613i	$-0.806706\pi$
$349$	−9.94427	+	7.22494i	−0.532305	+	0.386742i	0.288914	+	0.957355i	$0.406706\pi$
$350$	−1.54508	+	4.75528i	−0.0825883	+	0.254181i
$351$	−3.23607			−0.172729
$352$		0			0
$353$	6.76393			0.360008			0.180004	−	0.983666i	$-0.442389\pi$
$353$	6.76393			0.360008			0.180004	+	0.983666i	$0.442389\pi$
$354$	3.19098	−	9.82084i	0.169599	−	0.521972i
$355$	−17.5623	+	12.7598i	−0.932110	+	0.677218i
$356$	−5.47214	−	3.97574i	−0.290023	−	0.210714i
$357$	0.763932	+	2.35114i	0.0404316	+	0.124436i
$358$	−5.73607	−	17.6538i	−0.303161	−	0.933032i
$359$	−22.7984	−	16.5640i	−1.20325	−	0.874214i	−0.208651	−	0.977990i	$-0.566907\pi$
$359$	−22.7984	−	16.5640i	−1.20325	−	0.874214i	−0.994601	+	0.103776i	$0.966907\pi$
$360$	−2.92705	+	2.12663i	−0.154269	+	0.112083i
$361$	4.19756	−	12.9188i	0.220924	−	0.679935i
$362$	21.4164			1.12562
$363$		0			0
$364$	2.00000			0.104828
$365$	−16.2812	+	50.1082i	−0.852194	+	2.62278i
$366$	−3.00000	+	2.17963i	−0.156813	+	0.113931i
$367$	15.3992	+	11.1882i	0.803831	+	0.584017i	0.912036	−	0.410111i	$-0.134510\pi$
$367$	15.3992	+	11.1882i	0.803831	+	0.584017i	−0.108204	+	0.994129i	$0.534510\pi$
$368$	−1.76393	−	5.42882i	−0.0919513	−	0.282997i
$369$	1.76393	+	5.42882i	0.0918266	+	0.282613i
$370$	26.1803	+	19.0211i	1.36105	+	0.988861i
$371$	0.690983	−	0.502029i	0.0358741	−	0.0260640i
$372$	−1.04508	+	3.21644i	−0.0541851	+	0.166765i
$373$		0			0			−	1.00000i	$-0.5\pi$
$373$		0			0				1.00000i	$0.5\pi$
$374$		0			0
$375$	11.1803			0.577350
$376$	1.23607	−	3.80423i	0.0637453	−	0.196188i
$377$	−17.9443	+	13.0373i	−0.924177	+	0.671454i
$378$	0.500000	+	0.363271i	0.0257172	+	0.0186847i
$379$	8.09017	+	24.8990i	0.415564	+	1.27897i	0.911745	+	0.410756i	$0.134735\pi$
$379$	8.09017	+	24.8990i	0.415564	+	1.27897i	−0.496181	+	0.868219i	$0.665265\pi$
$380$	6.38197	+	19.6417i	0.327388	+	1.00760i
$381$	3.23607	+	2.35114i	0.165789	+	0.120453i
$382$	2.47214	−	1.79611i	0.126485	−	0.0918971i
$383$	7.50658	−	23.1029i	0.383568	−	1.18050i	−0.553945	−	0.832553i	$-0.686878\pi$
$383$	7.50658	−	23.1029i	0.383568	−	1.18050i	0.937514	−	0.347949i	$-0.113122\pi$
$384$	1.00000			0.0510310
$385$		0			0
$386$	4.61803			0.235052
$387$	1.47214	−	4.53077i	0.0748329	−	0.230312i
$388$	7.78115	−	5.65334i	0.395028	−	0.287005i
$389$	−15.3262	−	11.1352i	−0.777071	−	0.564575i	0.127027	−	0.991899i	$-0.459456\pi$
$389$	−15.3262	−	11.1352i	−0.777071	−	0.564575i	−0.904099	+	0.427324i	$0.859456\pi$
$390$	−3.61803	−	11.1352i	−0.183206	−	0.563851i
$391$	7.05573	+	21.7153i	0.356824	+	1.09819i
$392$	5.35410	+	3.88998i	0.270423	+	0.196474i
$393$	3.11803	−	2.26538i	0.157284	−	0.114274i
$394$	7.88197	−	24.2582i	0.397088	−	1.22211i
$395$	24.7984			1.24774
$396$		0			0
$397$	4.94427			0.248146			0.124073	−	0.992273i	$-0.460404\pi$
$397$	4.94427			0.248146			0.124073	+	0.992273i	$0.460404\pi$
$398$	−0.118034	+	0.363271i	−0.00591651	+	0.0182091i
$399$	2.85410	−	2.07363i	0.142884	−	0.103811i
$400$	−6.54508	−	4.75528i	−0.327254	−	0.237764i
$401$	−0.527864	−	1.62460i	−0.0263603	−	0.0811286i	0.937011	−	0.349300i	$-0.113581\pi$
$401$	−0.527864	−	1.62460i	−0.0263603	−	0.0811286i	−0.963371	+	0.268171i	$0.913581\pi$
$402$	1.52786	+	4.70228i	0.0762029	+	0.234529i
$403$	−8.85410	−	6.43288i	−0.441054	−	0.320445i
$404$	−1.69098	+	1.22857i	−0.0841295	+	0.0611237i
$405$	1.11803	−	3.44095i	0.0555556	−	0.170982i
$406$	4.23607			0.210233
$407$		0			0
$408$	−4.00000			−0.198030
$409$	9.26393	−	28.5115i	0.458072	−	1.40980i	−0.409418	−	0.912347i	$-0.634268\pi$
$409$	9.26393	−	28.5115i	0.458072	−	1.40980i	0.867490	−	0.497454i	$-0.165732\pi$
$410$	−16.7082	+	12.1392i	−0.825159	+	0.599513i
$411$	11.4721	+	8.33499i	0.565879	+	0.411135i
$412$	−3.04508	−	9.37181i	−0.150021	−	0.461716i
$413$	−1.97214	−	6.06961i	−0.0970425	−	0.298666i
$414$	4.61803	+	3.35520i	0.226964	+	0.164899i
$415$	4.73607	−	3.44095i	0.232484	−	0.168910i
$416$	−1.00000	+	3.07768i	−0.0490290	+	0.150896i
$417$	15.7082			0.769234
$418$		0			0
$419$	12.0902			0.590643			0.295322	−	0.955398i	$-0.404573\pi$
$419$	12.0902			0.590643			0.295322	+	0.955398i	$0.404573\pi$
$420$	−0.690983	+	2.12663i	−0.0337165	+	0.103769i
$421$	7.76393	−	5.64083i	0.378391	−	0.274917i	−0.382291	−	0.924042i	$-0.624865\pi$
$421$	7.76393	−	5.64083i	0.378391	−	0.274917i	0.760682	+	0.649125i	$0.224865\pi$
$422$	−7.47214	−	5.42882i	−0.363738	−	0.264271i
$423$	1.23607	+	3.80423i	0.0600997	+	0.184968i
$424$	0.427051	+	1.31433i	0.0207394	+	0.0638294i
$425$	26.1803	+	19.0211i	1.26993	+	0.922660i
$426$	−4.85410	+	3.52671i	−0.235182	+	0.170870i
$427$	−0.708204	+	2.17963i	−0.0342724	+	0.105480i
$428$	−1.09017			−0.0526954
$429$		0			0
$430$	17.2361			0.831197
$431$	−10.5279	+	32.4014i	−0.507109	+	1.56072i	0.290086	+	0.957001i	$0.406316\pi$
$431$	−10.5279	+	32.4014i	−0.507109	+	1.56072i	−0.797195	+	0.603722i	$0.793684\pi$
$432$	−0.809017	+	0.587785i	−0.0389238	+	0.0282798i
$433$	−5.97214	−	4.33901i	−0.287003	−	0.208520i	0.434963	−	0.900448i	$-0.356761\pi$
$433$	−5.97214	−	4.33901i	−0.287003	−	0.208520i	−0.721966	+	0.691929i	$0.756761\pi$
$434$	0.645898	+	1.98787i	0.0310041	+	0.0954208i
$435$	−7.66312	−	23.5847i	−0.367418	−	1.13080i
$436$	−2.38197	−	1.73060i	−0.114075	−	0.0828807i
$437$	26.3607	−	19.1522i	1.26100	−	0.916172i
$438$	−4.50000	+	13.8496i	−0.215018	+	0.661758i
$439$	−29.9230			−1.42815			−0.714073	−	0.700071i	$-0.753152\pi$
$439$	−29.9230			−1.42815			−0.714073	+	0.700071i	$0.753152\pi$
$440$		0			0
$441$	−6.61803			−0.315144
$442$	4.00000	−	12.3107i	0.190261	−	0.585562i
$443$	−0.118034	+	0.0857567i	−0.00560796	+	0.00407442i	−0.590586	−	0.806975i	$-0.701103\pi$
$443$	−0.118034	+	0.0857567i	−0.00560796	+	0.00407442i	0.584978	+	0.811049i	$0.301103\pi$
$444$	7.23607	+	5.25731i	0.343409	+	0.249501i
$445$	7.56231	+	23.2744i	0.358488	+	1.10331i
$446$	−0.409830	−	1.26133i	−0.0194060	−	0.0597256i
$447$	4.88197	+	3.54696i	0.230909	+	0.167765i
$448$	0.500000	−	0.363271i	0.0236228	−	0.0171630i
$449$	0.145898	−	0.449028i	0.00688535	−	0.0211909i	−0.947555	−	0.319593i	$-0.896454\pi$
$449$	0.145898	−	0.449028i	0.00688535	−	0.0211909i	0.954440	+	0.298402i	$0.0964537\pi$
$450$	8.09017			0.381374
$451$		0			0
$452$	6.94427			0.326631
$453$	−6.11803	+	18.8294i	−0.287450	+	0.884681i
$454$	4.07295	−	2.95917i	0.191153	−	0.138881i
$455$	−5.85410	−	4.25325i	−0.274445	−	0.199396i
$456$	1.76393	+	5.42882i	0.0826037	+	0.254228i
$457$	8.68034	+	26.7153i	0.406049	+	1.24969i	0.920016	+	0.391881i	$0.128175\pi$
$457$	8.68034	+	26.7153i	0.406049	+	1.24969i	−0.513967	+	0.857810i	$0.671825\pi$
$458$	4.38197	+	3.18368i	0.204756	+	0.148764i
$459$	3.23607	−	2.35114i	0.151047	−	0.109742i
$460$	−6.38197	+	19.6417i	−0.297561	+	0.915798i
$461$	−22.0000			−1.02464			−0.512321	−	0.858794i	$-0.671214\pi$
$461$	−22.0000			−1.02464			−0.512321	+	0.858794i	$0.671214\pi$
$462$		0			0
$463$	−7.74265			−0.359831			−0.179916	−	0.983682i	$-0.557582\pi$
$463$	−7.74265			−0.359831			−0.179916	+	0.983682i	$0.557582\pi$
$464$	−2.11803	+	6.51864i	−0.0983273	+	0.302620i
$465$	9.89919	−	7.19218i	0.459064	−	0.333529i
$466$	−13.7082	−	9.95959i	−0.635020	−	0.461369i
$467$	3.95492	+	12.1720i	0.183012	+	0.563252i	0.999908	−	0.0135319i	$-0.00430748\pi$
$467$	3.95492	+	12.1720i	0.183012	+	0.563252i	−0.816897	+	0.576784i	$0.804307\pi$
$468$	−1.00000	−	3.07768i	−0.0462250	−	0.142266i
$469$	2.47214	+	1.79611i	0.114153	+	0.0829367i
$470$	−11.7082	+	8.50651i	−0.540059	+	0.392376i
$471$	−5.56231	+	17.1190i	−0.256298	+	0.788803i
$472$	10.3262			0.475304
$473$		0			0
$474$	6.85410			0.314819
$475$	14.2705	−	43.9201i	0.654776	−	2.01519i
$476$	−2.00000	+	1.45309i	−0.0916698	+	0.0666020i
$477$	−1.11803	−	0.812299i	−0.0511913	−	0.0371926i
$478$	2.32624	+	7.15942i	0.106400	+	0.327464i
$479$	−2.70820	−	8.33499i	−0.123741	−	0.380836i	0.869929	−	0.493178i	$-0.164165\pi$
$479$	−2.70820	−	8.33499i	−0.123741	−	0.380836i	−0.993670	+	0.112342i	$0.964165\pi$
$480$	−2.92705	−	2.12663i	−0.133601	−	0.0970668i
$481$	−23.4164	+	17.0130i	−1.06770	+	0.775727i
$482$	−2.66312	+	8.19624i	−0.121302	+	0.373328i
$483$	3.52786			0.160523
$484$		0			0
$485$	−34.7984			−1.58011
$486$	0.309017	−	0.951057i	0.0140173	−	0.0431408i
$487$	−2.50000	+	1.81636i	−0.113286	+	0.0823070i	−0.642986	−	0.765878i	$-0.722305\pi$
$487$	−2.50000	+	1.81636i	−0.113286	+	0.0823070i	0.529700	+	0.848185i	$0.322305\pi$
$488$	−3.00000	−	2.17963i	−0.135804	−	0.0986671i
$489$	0.145898	+	0.449028i	0.00659774	+	0.0203057i
$490$	−7.39919	−	22.7724i	−0.334261	−	1.02875i
$491$	−23.7082	−	17.2250i	−1.06994	−	0.777354i	−0.0940355	−	0.995569i	$-0.529977\pi$
$491$	−23.7082	−	17.2250i	−1.06994	−	0.777354i	−0.975901	+	0.218215i	$0.929977\pi$
$492$	−4.61803	+	3.35520i	−0.208197	+	0.151264i
$493$	8.47214	−	26.0746i	0.381566	−	1.17434i
$494$	−18.4721			−0.831101
$495$		0			0
$496$	−3.38197			−0.151855
$497$	−1.14590	+	3.52671i	−0.0514006	+	0.158195i
$498$	1.30902	−	0.951057i	0.0586585	−	0.0426179i
$499$	−30.1803	−	21.9273i	−1.35106	−	0.981601i	−0.998958	−	0.0456382i	$-0.985468\pi$
$499$	−30.1803	−	21.9273i	−1.35106	−	0.981601i	−0.352100	−	0.935963i	$-0.614532\pi$
$500$	3.45492	+	10.6331i	0.154508	+	0.475528i
$501$	1.94427	+	5.98385i	0.0868637	+	0.267339i
$502$	−12.3992	−	9.00854i	−0.553403	−	0.402071i
$503$	−3.70820	+	2.69417i	−0.165341	+	0.120127i	−0.667379	−	0.744719i	$-0.732584\pi$
$503$	−3.70820	+	2.69417i	−0.165341	+	0.120127i	0.502038	+	0.864846i	$0.332584\pi$
$504$	−0.190983	+	0.587785i	−0.00850706	+	0.0261820i
$505$	7.56231			0.336518
$506$		0			0
$507$	−2.52786			−0.112266
$508$	−1.23607	+	3.80423i	−0.0548416	+	0.168785i
$509$	−18.8262	+	13.6781i	−0.834458	+	0.606269i	−0.920817	−	0.389995i	$-0.872477\pi$
$509$	−18.8262	+	13.6781i	−0.834458	+	0.606269i	0.0863588	+	0.996264i	$0.472477\pi$
$510$	11.7082	+	8.50651i	0.518448	+	0.376675i
$511$	2.78115	+	8.55951i	0.123031	+	0.378650i
$512$	0.309017	+	0.951057i	0.0136568	+	0.0420312i
$513$	−4.61803	−	3.35520i	−0.203891	−	0.148136i
$514$	−6.70820	+	4.87380i	−0.295886	+	0.214974i
$515$	−11.0172	+	33.9075i	−0.485477	+	1.49414i
$516$	4.76393			0.209720
$517$		0			0
$518$	5.52786			0.242880
$519$	4.42705	−	13.6251i	0.194326	−	0.598074i
$520$	9.47214	−	6.88191i	0.415381	−	0.301792i
$521$	22.6525	+	16.4580i	0.992423	+	0.721038i	0.960450	−	0.278451i	$-0.0898211\pi$
$521$	22.6525	+	16.4580i	0.992423	+	0.721038i	0.0319726	+	0.999489i	$0.489821\pi$
$522$	−2.11803	−	6.51864i	−0.0927038	−	0.285313i
$523$	−4.52786	−	13.9353i	−0.197990	−	0.609350i	−0.999929	−	0.0119436i	$-0.996198\pi$
$523$	−4.52786	−	13.9353i	−0.197990	−	0.609350i	0.801939	−	0.597406i	$-0.203802\pi$
$524$	3.11803	+	2.26538i	0.136212	+	0.0989638i
$525$	4.04508	−	2.93893i	0.176542	−	0.128265i
$526$	5.32624	−	16.3925i	0.232235	−	0.714746i
$527$	13.5279			0.589283
$528$		0			0
$529$	9.58359			0.416678
$530$	1.54508	−	4.75528i	0.0671142	−	0.206556i
$531$	−8.35410	+	6.06961i	−0.362537	+	0.263399i
$532$	2.85410	+	2.07363i	0.123741	+	0.0899031i
$533$	−5.70820	−	17.5680i	−0.247250	−	0.760957i
$534$	2.09017	+	6.43288i	0.0904505	+	0.278378i
$535$	3.19098	+	2.31838i	0.137958	+	0.100233i
$536$	−4.00000	+	2.90617i	−0.172774	+	0.125527i
$537$	−5.73607	+	17.6538i	−0.247530	+	0.761818i
$538$	6.00000			0.258678
$539$		0			0
$540$	3.61803			0.155695
$541$	1.38197	−	4.25325i	0.0594154	−	0.182862i	−0.916944	−	0.399017i	$-0.869352\pi$
$541$	1.38197	−	4.25325i	0.0594154	−	0.182862i	0.976359	+	0.216155i	$0.0693516\pi$
$542$	21.4164	−	15.5599i	0.919913	−	0.668356i
$543$	−17.3262	−	12.5882i	−0.743540	−	0.540213i
$544$	−1.23607	−	3.80423i	−0.0529960	−	0.163105i
$545$	3.29180	+	10.1311i	0.141005	+	0.433969i
$546$	−1.61803	−	1.17557i	−0.0692455	−	0.0503098i
$547$	−34.8885	+	25.3480i	−1.49173	+	1.08380i	−0.518191	+	0.855265i	$0.673395\pi$
$547$	−34.8885	+	25.3480i	−1.49173	+	1.08380i	−0.973535	+	0.228538i	$0.926605\pi$
$548$	−4.38197	+	13.4863i	−0.187188	+	0.576106i
$549$	3.70820			0.158262
$550$		0			0
$551$	−39.1246			−1.66676
$552$	−1.76393	+	5.42882i	−0.0750779	+	0.231066i
$553$	3.42705	−	2.48990i	0.145733	−	0.105881i
$554$	12.7082	+	9.23305i	0.539920	+	0.392275i
$555$	−10.0000	−	30.7768i	−0.424476	−	1.30640i
$556$	4.85410	+	14.9394i	0.205860	+	0.633571i
$557$	−1.88197	−	1.36733i	−0.0797415	−	0.0579356i	0.547200	−	0.837002i	$-0.315694\pi$
$557$	−1.88197	−	1.36733i	−0.0797415	−	0.0579356i	−0.626942	+	0.779066i	$0.715694\pi$
$558$	2.73607	−	1.98787i	0.115827	−	0.0841532i
$559$	−4.76393	+	14.6619i	−0.201493	+	0.620131i
$560$	−2.23607			−0.0944911
$561$		0			0
$562$	−21.2361			−0.895789
$563$	−2.47214	+	7.60845i	−0.104188	+	0.320658i	−0.989539	−	0.144265i	$-0.953918\pi$
$563$	−2.47214	+	7.60845i	−0.104188	+	0.320658i	0.885351	+	0.464923i	$0.153918\pi$
$564$	−3.23607	+	2.35114i	−0.136263	+	0.0990009i
$565$	−20.3262	−	14.7679i	−0.855131	−	0.621289i
$566$	2.32624	+	7.15942i	0.0977791	+	0.300933i
$567$	−0.190983	−	0.587785i	−0.00802053	−	0.0246847i
$568$	−4.85410	−	3.52671i	−0.203674	−	0.147978i
$569$	−6.09017	+	4.42477i	−0.255313	+	0.185496i	−0.708078	−	0.706134i	$-0.750438\pi$
$569$	−6.09017	+	4.42477i	−0.255313	+	0.185496i	0.452765	+	0.891630i	$0.350438\pi$
$570$	6.38197	−	19.6417i	0.267311	−	0.822699i
$571$	−32.6525			−1.36646			−0.683232	−	0.730202i	$-0.739426\pi$
$571$	−32.6525			−1.36646			−0.683232	+	0.730202i	$0.739426\pi$
$572$		0			0
$573$	−3.05573			−0.127655
$574$	−1.09017	+	3.35520i	−0.0455028	+	0.140043i
$575$	37.3607	−	27.1441i	1.55805	−	1.13199i
$576$	−0.809017	−	0.587785i	−0.0337090	−	0.0244911i
$577$	−14.7533	−	45.4060i	−0.614187	−	1.89027i	−0.413037	−	0.910714i	$-0.635532\pi$
$577$	−14.7533	−	45.4060i	−0.614187	−	1.89027i	−0.201150	−	0.979560i	$-0.564468\pi$
$578$	−0.309017	−	0.951057i	−0.0128534	−	0.0395587i
$579$	−3.73607	−	2.71441i	−0.155266	−	0.112807i
$580$	20.0623	−	14.5761i	0.833042	−	0.605240i
$581$	0.309017	−	0.951057i	0.0128202	−	0.0394565i
$582$	−9.61803			−0.398680
$583$		0			0
$584$	−14.5623			−0.602593
$585$	−3.61803	+	11.1352i	−0.149587	+	0.460382i
$586$	4.35410	−	3.16344i	0.179866	−	0.130681i
$587$	37.0517	+	26.9196i	1.52929	+	1.11109i	0.956634	+	0.291292i	$0.0940853\pi$
$587$	37.0517	+	26.9196i	1.52929	+	1.11109i	0.572652	+	0.819799i	$0.305915\pi$
$588$	−2.04508	−	6.29412i	−0.0843379	−	0.259565i
$589$	−5.96556	−	18.3601i	−0.245807	−	0.756515i
$590$	−30.2254	−	21.9601i	−1.24436	−	0.904081i
$591$	−20.6353	+	14.9924i	−0.848821	+	0.616705i
$592$	−2.76393	+	8.50651i	−0.113597	+	0.349615i
$593$	−27.8885			−1.14525			−0.572623	−	0.819819i	$-0.694074\pi$
$593$	−27.8885			−1.14525			−0.572623	+	0.819819i	$0.694074\pi$
$594$		0			0
$595$	8.94427			0.366679
$596$	−1.86475	+	5.73910i	−0.0763829	+	0.235083i
$597$	0.309017	−	0.224514i	0.0126472	−	0.00918875i
$598$	−14.9443	−	10.8576i	−0.611117	−	0.444002i
$599$	−3.81966	−	11.7557i	−0.156067	−	0.480325i	0.842200	−	0.539165i	$-0.181260\pi$
$599$	−3.81966	−	11.7557i	−0.156067	−	0.480325i	−0.998267	+	0.0588396i	$0.981260\pi$
$600$	2.50000	+	7.69421i	0.102062	+	0.314115i
$601$	−7.20820	−	5.23707i	−0.294029	−	0.213624i	0.430984	−	0.902359i	$-0.358166\pi$
$601$	−7.20820	−	5.23707i	−0.294029	−	0.213624i	−0.725013	+	0.688735i	$0.758166\pi$
$602$	2.38197	−	1.73060i	0.0970817	−	0.0705340i
$603$	1.52786	−	4.70228i	0.0622194	−	0.191492i
$604$	−19.7984			−0.805584
$605$		0			0
$606$	2.09017			0.0849073
$607$	−10.1803	+	31.3319i	−0.413207	+	1.27172i	0.500637	+	0.865657i	$0.333099\pi$
$607$	−10.1803	+	31.3319i	−0.413207	+	1.27172i	−0.913845	+	0.406064i	$0.866901\pi$
$608$	−4.61803	+	3.35520i	−0.187286	+	0.136071i
$609$	−3.42705	−	2.48990i	−0.138871	−	0.100896i
$610$	4.14590	+	12.7598i	0.167863	+	0.516628i
$611$	−4.00000	−	12.3107i	−0.161823	−	0.498039i
$612$	3.23607	+	2.35114i	0.130810	+	0.0950392i
$613$	28.0344	−	20.3682i	1.13230	−	0.822664i	0.146272	−	0.989244i	$-0.453272\pi$
$613$	28.0344	−	20.3682i	1.13230	−	0.822664i	0.986028	+	0.166580i	$0.0532724\pi$
$614$	5.32624	−	16.3925i	0.214949	−	0.661546i
$615$	20.6525			0.832788
$616$		0			0
$617$	25.1246			1.01148			0.505739	−	0.862686i	$-0.331220\pi$
$617$	25.1246			1.01148			0.505739	+	0.862686i	$0.331220\pi$
$618$	−3.04508	+	9.37181i	−0.122491	+	0.376989i
$619$	−3.23607	+	2.35114i	−0.130069	+	0.0945003i	−0.650917	−	0.759149i	$-0.725616\pi$
$619$	−3.23607	+	2.35114i	−0.130069	+	0.0945003i	0.520849	+	0.853649i	$0.325616\pi$
$620$	9.89919	+	7.19218i	0.397561	+	0.288845i
$621$	−1.76393	−	5.42882i	−0.0707842	−	0.217851i
$622$	5.09017	+	15.6659i	0.204097	+	0.628147i
$623$	3.38197	+	2.45714i	0.135496	+	0.0984433i
$624$	2.61803	−	1.90211i	0.104805	−	0.0761455i
$625$		0			0
$626$	21.9787			0.878446
$627$		0			0
$628$	−18.0000			−0.718278
$629$	11.0557	−	34.0260i	0.440821	−	1.35671i
$630$	1.80902	−	1.31433i	0.0720730	−	0.0523641i
$631$	−22.0172	−	15.9964i	−0.876492	−	0.636809i	0.0558293	−	0.998440i	$-0.482220\pi$
$631$	−22.0172	−	15.9964i	−0.876492	−	0.636809i	−0.932321	+	0.361632i	$0.882220\pi$
$632$	2.11803	+	6.51864i	0.0842509	+	0.259298i
$633$	2.85410	+	8.78402i	0.113440	+	0.349134i
$634$	7.32624	+	5.32282i	0.290962	+	0.211396i
$635$	11.7082	−	8.50651i	0.464626	−	0.337570i
$636$	0.427051	−	1.31433i	0.0169337	−	0.0521165i
$637$	21.4164			0.848549
$638$		0			0
$639$	6.00000			0.237356
$640$	1.11803	−	3.44095i	0.0441942	−	0.136016i
$641$	−1.76393	+	1.28157i	−0.0696711	+	0.0506190i	−0.622076	−	0.782957i	$-0.713710\pi$
$641$	−1.76393	+	1.28157i	−0.0696711	+	0.0506190i	0.552405	+	0.833576i	$0.313710\pi$
$642$	0.881966	+	0.640786i	0.0348084	+	0.0252898i
$643$	1.85410	+	5.70634i	0.0731186	+	0.225036i	0.980936	−	0.194329i	$-0.0622528\pi$
$643$	1.85410	+	5.70634i	0.0731186	+	0.225036i	−0.907818	+	0.419365i	$0.862253\pi$
$644$	1.09017	+	3.35520i	0.0429587	+	0.132213i
$645$	−13.9443	−	10.1311i	−0.549055	−	0.398912i
$646$	18.4721	−	13.4208i	0.726776	−	0.528034i
$647$	−5.18034	+	15.9434i	−0.203660	+	0.626802i	0.796106	+	0.605158i	$0.206890\pi$
$647$	−5.18034	+	15.9434i	−0.203660	+	0.626802i	−0.999766	+	0.0216438i	$0.993110\pi$
$648$	1.00000			0.0392837
$649$		0			0
$650$	−26.1803			−1.02688
$651$	0.645898	−	1.98787i	0.0253147	−	0.0779108i
$652$	−0.381966	+	0.277515i	−0.0149589	+	0.0108683i
$653$	−13.3992	−	9.73508i	−0.524351	−	0.380963i	0.293890	−	0.955839i	$-0.405050\pi$
$653$	−13.3992	−	9.73508i	−0.524351	−	0.380963i	−0.818240	+	0.574876i	$0.805050\pi$
$654$	0.909830	+	2.80017i	0.0355772	+	0.109495i
$655$	−4.30902	−	13.2618i	−0.168367	−	0.518181i
$656$	−4.61803	−	3.35520i	−0.180304	−	0.130998i
$657$	11.7812	−	8.55951i	0.459627	−	0.333938i
$658$	−0.763932	+	2.35114i	−0.0297812	+	0.0916570i
$659$	18.9230			0.737135			0.368567	−	0.929601i	$-0.379848\pi$
$659$	18.9230			0.737135			0.368567	+	0.929601i	$0.379848\pi$
$660$		0			0
$661$	37.5967			1.46234			0.731172	−	0.682193i	$-0.238974\pi$
$661$	37.5967			1.46234			0.731172	+	0.682193i	$0.238974\pi$
$662$	−5.05573	+	15.5599i	−0.196496	+	0.604754i
$663$	−10.4721	+	7.60845i	−0.406704	+	0.295488i
$664$	1.30902	+	0.951057i	0.0507997	+	0.0369082i
$665$	−3.94427	−	12.1392i	−0.152952	−	0.470739i
$666$	−2.76393	−	8.50651i	−0.107100	−	0.329620i
$667$	−31.6525	−	22.9969i	−1.22559	−	0.890442i
$668$	−5.09017	+	3.69822i	−0.196945	+	0.143089i
$669$	−0.409830	+	1.26133i	−0.0158449	+	0.0487657i
$670$	17.8885			0.691095
$671$		0			0
$672$	−0.618034			−0.0238412
$673$	10.7361	−	33.0422i	0.413845	−	1.27368i	−0.499435	−	0.866351i	$-0.666459\pi$
$673$	10.7361	−	33.0422i	0.413845	−	1.27368i	0.913280	−	0.407333i	$-0.133541\pi$
$674$	16.0902	−	11.6902i	0.619770	−	0.450289i
$675$	−6.54508	−	4.75528i	−0.251920	−	0.183031i
$676$	−0.781153	−	2.40414i	−0.0300443	−	0.0924670i
$677$	−13.6418	−	41.9852i	−0.524298	−	1.61362i	−0.765699	−	0.643199i	$-0.777607\pi$
$677$	−13.6418	−	41.9852i	−0.524298	−	1.61362i	0.241401	−	0.970425i	$-0.422393\pi$
$678$	−5.61803	−	4.08174i	−0.215759	−	0.156758i
$679$	−4.80902	+	3.49396i	−0.184553	+	0.134086i
$680$	−4.47214	+	13.7638i	−0.171499	+	0.527818i
$681$	−5.03444			−0.192920
$682$		0			0
$683$	41.4508			1.58607			0.793036	−	0.609174i	$-0.208499\pi$
$683$	41.4508			1.58607			0.793036	+	0.609174i	$0.208499\pi$
$684$	1.76393	−	5.42882i	0.0674456	−	0.207576i
$685$	41.5066	−	30.1563i	1.58588	−	1.15221i
$686$	−6.80902	−	4.94704i	−0.259969	−	0.188879i
$687$	−1.67376	−	5.15131i	−0.0638580	−	0.196535i
$688$	1.47214	+	4.53077i	0.0561247	+	0.172734i
$689$	3.61803	+	2.62866i	0.137836	+	0.100144i
$690$	16.7082	−	12.1392i	0.636070	−	0.462132i
$691$	−10.8541	+	33.4055i	−0.412909	+	1.27080i	0.501198	+	0.865333i	$0.332893\pi$
$691$	−10.8541	+	33.4055i	−0.412909	+	1.27080i	−0.914107	+	0.405472i	$0.867107\pi$
$692$	14.3262			0.544602
$693$		0			0
$694$	34.3262			1.30301
$695$	17.5623	−	54.0512i	0.666176	−	2.05028i
$696$	5.54508	−	4.02874i	0.210186	−	0.152709i
$697$	18.4721	+	13.4208i	0.699682	+	0.508349i
$698$	3.79837	+	11.6902i	0.143771	+	0.442480i
$699$	5.23607	+	16.1150i	0.198046	+	0.609524i
$700$	4.04508	+	2.93893i	0.152890	+	0.111081i
$701$	41.9787	−	30.4993i	1.58551	−	1.15194i	0.675505	−	0.737356i	$-0.263926\pi$
$701$	41.9787	−	30.4993i	1.58551	−	1.15194i	0.910009	−	0.414588i	$-0.136074\pi$
$702$	−1.00000	+	3.07768i	−0.0377426	+	0.116160i
$703$	−51.0557			−1.92560
$704$		0			0
$705$	14.4721			0.545052
$706$	2.09017	−	6.43288i	0.0786646	−	0.242105i
$707$	1.04508	−	0.759299i	0.0393045	−	0.0285564i
$708$	−8.35410	−	6.06961i	−0.313966	−	0.228110i
$709$	−10.0557	−	30.9483i	−0.377651	−	1.16229i	−0.941673	−	0.336530i	$-0.890747\pi$
$709$	−10.0557	−	30.9483i	−0.377651	−	1.16229i	0.564022	−	0.825760i	$-0.309253\pi$
$710$	6.70820	+	20.6457i	0.251754	+	0.774820i
$711$	−5.54508	−	4.02874i	−0.207957	−	0.151090i
$712$	−5.47214	+	3.97574i	−0.205077	+	0.148997i
$713$	5.96556	−	18.3601i	0.223412	−	0.687591i
$714$	2.47214			0.0925174
$715$		0			0
$716$	−18.5623			−0.693706
$717$	2.32624	−	7.15942i	0.0868749	−	0.267374i
$718$	−22.7984	+	16.5640i	−0.850828	+	0.618163i
$719$	−15.3262	−	11.1352i	−0.571572	−	0.415272i	0.264104	−	0.964494i	$-0.414924\pi$
$719$	−15.3262	−	11.1352i	−0.571572	−	0.415272i	−0.835676	+	0.549223i	$0.814924\pi$
$720$	1.11803	+	3.44095i	0.0416667	+	0.128237i
$721$	1.88197	+	5.79210i	0.0700881	+	0.215709i
$722$	−10.9894	−	7.98424i	−0.408982	−	0.297142i
$723$	6.97214	−	5.06555i	0.259297	−	0.188390i
$724$	6.61803	−	20.3682i	0.245957	−	0.756979i
$725$	−55.4508			−2.05939
$726$		0			0
$727$	−4.58359			−0.169996			−0.0849980	−	0.996381i	$-0.527088\pi$
$727$	−4.58359			−0.169996			−0.0849980	+	0.996381i	$0.527088\pi$
$728$	0.618034	−	1.90211i	0.0229059	−	0.0704970i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	42.6246	+	30.9686i	1.57761	+	1.14620i
$731$	−5.88854	−	18.1231i	−0.217796	−	0.670306i
$732$	1.14590	+	3.52671i	0.0423536	+	0.130351i
$733$	15.1803	+	11.0292i	0.560699	+	0.407371i	0.831715	−	0.555203i	$-0.187360\pi$
$733$	15.1803	+	11.0292i	0.560699	+	0.407371i	−0.271016	+	0.962575i	$0.587360\pi$
$734$	15.3992	−	11.1882i	0.568394	−	0.412963i
$735$	−7.39919	+	22.7724i	−0.272923	+	0.839971i
$736$	−5.70820			−0.210407
$737$		0			0
$738$	5.70820			0.210122
$739$	−13.1246	+	40.3934i	−0.482797	+	1.48590i	0.352350	+	0.935868i	$0.385383\pi$
$739$	−13.1246	+	40.3934i	−0.482797	+	1.48590i	−0.835147	+	0.550027i	$0.814617\pi$
$740$	26.1803	−	19.0211i	0.962408	−	0.699231i
$741$	14.9443	+	10.8576i	0.548992	+	0.398866i
$742$	−0.263932	−	0.812299i	−0.00968925	−	0.0298204i
$743$	13.2705	+	40.8424i	0.486848	+	1.49836i	0.829287	+	0.558823i	$0.188747\pi$
$743$	13.2705	+	40.8424i	0.486848	+	1.49836i	−0.342439	+	0.939540i	$0.611253\pi$
$744$	2.73607	+	1.98787i	0.100309	+	0.0728788i
$745$	17.6631	−	12.8330i	0.647127	−	0.470165i
$746$		0			0
$747$	−1.61803			−0.0592008
$748$		0			0
$749$	0.673762			0.0246187
$750$	3.45492	−	10.6331i	0.126156	−	0.388267i
$751$	−28.1803	+	20.4742i	−1.02832	+	0.747115i	−0.967971	−	0.251063i	$-0.919220\pi$
$751$	−28.1803	+	20.4742i	−1.02832	+	0.747115i	−0.0603444	+	0.998178i	$0.519220\pi$
$752$	−3.23607	−	2.35114i	−0.118007	−	0.0857373i
$753$	4.73607	+	14.5761i	0.172592	+	0.531183i
$754$	6.85410	+	21.0948i	0.249612	+	0.768226i
$755$	57.9508	+	42.1038i	2.10905	+	1.53231i
$756$	0.500000	−	0.363271i	0.0181848	−	0.0132120i
$757$	−7.21478	+	22.2048i	−0.262226	+	0.807048i	0.730094	+	0.683347i	$0.239476\pi$
$757$	−7.21478	+	22.2048i	−0.262226	+	0.807048i	−0.992320	+	0.123701i	$0.960524\pi$
$758$	26.1803			0.950913
$759$		0			0
$760$	20.6525			0.749144
$761$	−9.83282	+	30.2623i	−0.356439	+	1.09701i	0.598731	+	0.800950i	$0.295672\pi$
$761$	−9.83282	+	30.2623i	−0.356439	+	1.09701i	−0.955170	+	0.296057i	$0.904328\pi$
$762$	3.23607	−	2.35114i	0.117230	−	0.0851729i
$763$	1.47214	+	1.06957i	0.0532949	+	0.0387210i
$764$	−0.944272	−	2.90617i	−0.0341626	−	0.105142i
$765$	−4.47214	−	13.7638i	−0.161690	−	0.497632i
$766$	−19.6525	−	14.2784i	−0.710073	−	0.515898i
$767$	27.0344	−	19.6417i	0.976157	−	0.709220i
$768$	0.309017	−	0.951057i	0.0111507	−	0.0343183i
$769$	21.4377			0.773063			0.386532	−	0.922276i	$-0.373673\pi$
$769$	21.4377			0.773063			0.386532	+	0.922276i	$0.373673\pi$
$770$		0			0
$771$	8.29180			0.298622
$772$	1.42705	−	4.39201i	0.0513607	−	0.158072i
$773$	−10.4894	+	7.62096i	−0.377276	+	0.274107i	−0.760222	−	0.649664i	$-0.774910\pi$
$773$	−10.4894	+	7.62096i	−0.377276	+	0.274107i	0.382946	+	0.923771i	$0.374910\pi$
$774$	−3.85410	−	2.80017i	−0.138533	−	0.100650i
$775$	−8.45492	−	26.0216i	−0.303710	−	0.934722i
$776$	−2.97214	−	9.14729i	−0.106693	−	0.328369i
$777$	−4.47214	−	3.24920i	−0.160437	−	0.116564i
$778$	−15.3262	+	11.1352i	−0.549472	+	0.399215i
$779$	10.0689	−	30.9888i	0.360755	−	1.11029i
$780$	−11.7082			−0.419221
$781$		0			0
$782$	22.8328			0.816500
$783$	−2.11803	+	6.51864i	−0.0756924	+	0.232957i
$784$	5.35410	−	3.88998i	0.191218	−	0.138928i
$785$	52.6869	+	38.2793i	1.88048	+	1.36625i
$786$	−1.19098	−	3.66547i	−0.0424810	−	0.130743i
$787$	−10.4164	−	32.0584i	−0.371305	−	1.14276i	−0.945938	−	0.324348i	$-0.894855\pi$
$787$	−10.4164	−	32.0584i	−0.371305	−	1.14276i	0.574633	−	0.818411i	$-0.305145\pi$
$788$	−20.6353	−	14.9924i	−0.735101	−	0.534082i
$789$	−13.9443	+	10.1311i	−0.496429	+	0.360677i
$790$	7.66312	−	23.5847i	0.272642	−	0.839104i
$791$	−4.29180			−0.152599
$792$		0			0
$793$	−12.0000			−0.426132
$794$	1.52786	−	4.70228i	0.0542219	−	0.166878i
$795$	−4.04508	+	2.93893i	−0.143464	+	0.104233i
$796$	0.309017	+	0.224514i	0.0109528	+	0.00795769i
$797$	−9.77458	−	30.0830i	−0.346233	−	1.06560i	−0.960920	−	0.276825i	$-0.910718\pi$
$797$	−9.77458	−	30.0830i	−0.346233	−	1.06560i	0.614687	−	0.788771i	$-0.289282\pi$
$798$	−1.09017	−	3.35520i	−0.0385916	−	0.118773i
$799$	12.9443	+	9.40456i	0.457935	+	0.332710i
$800$	−6.54508	+	4.75528i	−0.231404	+	0.168125i
$801$	2.09017	−	6.43288i	0.0738525	−	0.227295i
$802$	−1.70820			−0.0603188
$803$		0			0
$804$	4.94427			0.174371
$805$	3.94427	−	12.1392i	0.139017	−	0.427851i
$806$	−8.85410	+	6.43288i	−0.311872	+	0.226589i
$807$	−4.85410	−	3.52671i	−0.170872	−	0.124146i
$808$	0.645898	+	1.98787i	0.0227226	+	0.0699330i
$809$	6.47214	+	19.9192i	0.227548	+	0.700321i	0.998023	+	0.0628508i	$0.0200192\pi$
$809$	6.47214	+	19.9192i	0.227548	+	0.700321i	−0.770475	+	0.637471i	$0.779981\pi$
$810$	−2.92705	−	2.12663i	−0.102846	−	0.0747221i
$811$	35.7426	−	25.9686i	1.25509	−	0.911879i	0.256588	−	0.966521i	$-0.417402\pi$
$811$	35.7426	−	25.9686i	1.25509	−	0.911879i	0.998506	+	0.0546417i	$0.0174016\pi$
$812$	1.30902	−	4.02874i	0.0459375	−	0.141381i
$813$	−26.4721			−0.928418
$814$		0			0
$815$	1.70820			0.0598358
$816$	−1.23607	+	3.80423i	−0.0432710	+	0.133175i
$817$	−22.0000	+	15.9839i	−0.769683	+	0.559207i
$818$	−24.2533	−	17.6210i	−0.847996	−	0.616105i
$819$	0.618034	+	1.90211i	0.0215959	+	0.0664652i
$820$	6.38197	+	19.6417i	0.222868	+	0.685917i
$821$	19.7705	+	14.3641i	0.689996	+	0.501311i	0.876659	−	0.481113i	$-0.159767\pi$
$821$	19.7705	+	14.3641i	0.689996	+	0.501311i	−0.186663	+	0.982424i	$0.559767\pi$
$822$	11.4721	−	8.33499i	0.400137	−	0.290716i
$823$	5.29837	−	16.3067i	0.184690	−	0.568416i	−0.815253	−	0.579105i	$-0.803402\pi$
$823$	5.29837	−	16.3067i	0.184690	−	0.568416i	0.999943	+	0.0106882i	$0.00340224\pi$
$824$	−9.85410			−0.343284
$825$		0			0
$826$	−6.38197			−0.222057
$827$	−13.7533	+	42.3283i	−0.478249	+	1.47190i	0.363277	+	0.931681i	$0.381658\pi$
$827$	−13.7533	+	42.3283i	−0.478249	+	1.47190i	−0.841526	+	0.540217i	$0.818342\pi$
$828$	4.61803	−	3.35520i	0.160488	−	0.116601i
$829$	−40.2705	−	29.2582i	−1.39865	−	1.01618i	−0.994853	−	0.101333i	$-0.967689\pi$
$829$	−40.2705	−	29.2582i	−1.39865	−	1.01618i	−0.403800	−	0.914847i	$-0.632311\pi$
$830$	−1.80902	−	5.56758i	−0.0627919	−	0.193254i
$831$	−4.85410	−	14.9394i	−0.168387	−	0.518242i
$832$	2.61803	+	1.90211i	0.0907640	+	0.0659439i
$833$	−21.4164	+	15.5599i	−0.742035	+	0.539120i
$834$	4.85410	−	14.9394i	0.168084	−	0.517309i
$835$	22.7639			0.787778
$836$		0			0
$837$	−3.38197			−0.116898
$838$	3.73607	−	11.4984i	0.129060	−	0.397207i
$839$	20.2361	−	14.7024i	0.698627	−	0.507582i	−0.180858	−	0.983509i	$-0.557887\pi$
$839$	20.2361	−	14.7024i	0.698627	−	0.507582i	0.879485	+	0.475927i	$0.157887\pi$
$840$	1.80902	+	1.31433i	0.0624170	+	0.0453486i
$841$	5.55573	+	17.0988i	0.191577	+	0.589613i
$842$	−2.96556	−	9.12705i	−0.102200	−	0.314539i
$843$	17.1803	+	12.4822i	0.591722	+	0.429911i
$844$	−7.47214	+	5.42882i	−0.257202	+	0.186868i
$845$	−2.82624	+	8.69827i	−0.0972255	+	0.299229i
$846$	4.00000			0.137523
$847$		0			0
$848$	1.38197			0.0474569
$849$	2.32624	−	7.15942i	0.0798363	−	0.245711i
$850$	26.1803	−	19.0211i	0.897978	−	0.652419i
$851$	−41.3050	−	30.0098i	−1.41592	−	1.02872i
$852$	1.85410	+	5.70634i	0.0635205	+	0.195496i
$853$	−4.18034	−	12.8658i	−0.143132	−	0.440515i	0.853634	−	0.520873i	$-0.174394\pi$
$853$	−4.18034	−	12.8658i	−0.143132	−	0.440515i	−0.996766	+	0.0803580i	$0.974394\pi$
$854$	1.85410	+	1.34708i	0.0634461	+	0.0460963i
$855$	−16.7082	+	12.1392i	−0.571409	+	0.415153i
$856$	−0.336881	+	1.03681i	−0.0115144	+	0.0354375i
$857$	−20.1803			−0.689347			−0.344674	−	0.938723i	$-0.612010\pi$
$857$	−20.1803			−0.689347			−0.344674	+	0.938723i	$0.612010\pi$
$858$		0			0
$859$	−51.9574			−1.77276			−0.886382	−	0.462954i	$-0.846789\pi$
$859$	−51.9574			−1.77276			−0.886382	+	0.462954i	$0.846789\pi$
$860$	5.32624	−	16.3925i	0.181623	−	0.558979i
$861$	2.85410	−	2.07363i	0.0972675	−	0.0706690i
$862$	27.5623	+	20.0252i	0.938776	+	0.682061i
$863$	2.20163	+	6.77591i	0.0749442	+	0.230655i	0.981510	−	0.191409i	$-0.0613058\pi$
$863$	2.20163	+	6.77591i	0.0749442	+	0.230655i	−0.906566	+	0.422064i	$0.861306\pi$
$864$	0.309017	+	0.951057i	0.0105130	+	0.0323556i
$865$	−41.9336	−	30.4666i	−1.42579	−	1.03589i
$866$	−5.97214	+	4.33901i	−0.202941	+	0.147446i
$867$	−0.309017	+	0.951057i	−0.0104948	+	0.0322996i
$868$	2.09017			0.0709450
$869$		0			0
$870$	−24.7984			−0.840744
$871$	−4.94427	+	15.2169i	−0.167530	+	0.515605i
$872$	−2.38197	+	1.73060i	−0.0806635	+	0.0586055i
$873$	7.78115	+	5.65334i	0.263352	+	0.191337i
$874$	−10.0689	−	30.9888i	−0.340585	−	1.04821i
$875$	−2.13525	−	6.57164i	−0.0721848	−	0.222162i
$876$	11.7812	+	8.55951i	0.398048	+	0.289199i
$877$	−23.3262	+	16.9475i	−0.787671	+	0.572277i	−0.907271	−	0.420546i	$-0.861839\pi$
$877$	−23.3262	+	16.9475i	−0.787671	+	0.572277i	0.119600	+	0.992822i	$0.461839\pi$
$878$	−9.24671	+	28.4585i	−0.312061	+	0.960426i
$879$	−5.38197			−0.181529
$880$		0			0
$881$	−24.0689			−0.810901			−0.405451	−	0.914117i	$-0.632885\pi$
$881$	−24.0689			−0.810901			−0.405451	+	0.914117i	$0.632885\pi$
$882$	−2.04508	+	6.29412i	−0.0688616	+	0.211934i
$883$	45.7426	−	33.2340i	1.53936	−	1.11841i	0.588629	−	0.808403i	$-0.299668\pi$
$883$	45.7426	−	33.2340i	1.53936	−	1.11841i	0.950734	−	0.310009i	$-0.100332\pi$
$884$	−10.4721	−	7.60845i	−0.352216	−	0.255900i
$885$	11.5451	+	35.5321i	0.388084	+	1.19440i
$886$	0.0450850	+	0.138757i	0.00151466	+	0.00466164i
$887$	−47.7426	−	34.6871i	−1.60304	−	1.16468i	−0.881352	−	0.472460i	$-0.843366\pi$
$887$	−47.7426	−	34.6871i	−1.60304	−	1.16468i	−0.721689	−	0.692217i	$-0.756634\pi$
$888$	7.23607	−	5.25731i	0.242827	−	0.176424i
$889$	0.763932	−	2.35114i	0.0256215	−	0.0788547i
$890$	24.4721			0.820308
$891$		0			0
$892$	−1.32624			−0.0444057
$893$	7.05573	−	21.7153i	0.236111	−	0.726675i
$894$	4.88197	−	3.54696i	0.163277	−	0.118628i
$895$	54.3328	+	39.4751i	1.81615	+	1.31951i
$896$	−0.190983	−	0.587785i	−0.00638029	−	0.0196365i
$897$	5.70820	+	17.5680i	0.190591	+	0.586580i
$898$	−0.381966	−	0.277515i	−0.0127464	−	0.00926078i
$899$	−18.7533	+	13.6251i	−0.625457	+	0.454421i
$900$	2.50000	−	7.69421i	0.0833333	−	0.256474i
$901$	−5.52786			−0.184160
$902$		0			0
$903$	−2.94427			−0.0979792
$904$	2.14590	−	6.60440i	0.0713715	−	0.219659i
$905$	−62.6869	+	45.5447i	−2.08378	+	1.51396i
$906$	16.0172	+	11.6372i	0.532137	+	0.386620i
$907$	−0.527864	−	1.62460i	−0.0175274	−	0.0539439i	0.941910	−	0.335865i	$-0.109028\pi$
$907$	−0.527864	−	1.62460i	−0.0175274	−	0.0539439i	−0.959438	+	0.281921i	$0.909028\pi$
$908$	−1.55573	−	4.78804i	−0.0516286	−	0.158897i
$909$	−1.69098	−	1.22857i	−0.0560864	−	0.0407491i
$910$	−5.85410	+	4.25325i	−0.194062	+	0.140994i
$911$	8.20163	−	25.2420i	0.271732	−	0.836305i	−0.718334	−	0.695699i	$-0.755095\pi$
$911$	8.20163	−	25.2420i	0.271732	−	0.836305i	0.990066	−	0.140606i	$-0.0449052\pi$
$912$	5.70820			0.189018
$913$		0			0
$914$	28.0902			0.929140
$915$	4.14590	−	12.7598i	0.137059	−	0.421825i
$916$	4.38197	−	3.18368i	0.144784	−	0.105192i
$917$	−1.92705	−	1.40008i	−0.0636368	−	0.0462349i
$918$	−1.23607	−	3.80423i	−0.0407963	−	0.125558i
$919$	−15.3541	−	47.2551i	−0.506485	−	1.55880i	−0.798260	−	0.602314i	$-0.794246\pi$
$919$	−15.3541	−	47.2551i	−0.506485	−	1.55880i	0.291774	−	0.956487i	$-0.405754\pi$
$920$	16.7082	+	12.1392i	0.550853	+	0.400218i
$921$	−13.9443	+	10.1311i	−0.459479	+	0.333831i
$922$	−6.79837	+	20.9232i	−0.223893	+	0.689070i
$923$	−19.4164			−0.639099
$924$		0			0
$925$	−72.3607			−2.37920
$926$	−2.39261	+	7.36369i	−0.0786260	+	0.241986i
$927$	7.97214	−	5.79210i	0.261839	−	0.190237i
$928$	5.54508	+	4.02874i	0.182026	+	0.132250i
$929$	8.09017	+	24.8990i	0.265430	+	0.816909i	0.991594	+	0.129388i	$0.0413012\pi$
$929$	8.09017	+	24.8990i	0.265430	+	0.816909i	−0.726164	+	0.687521i	$0.758699\pi$
$930$	−3.78115	−	11.6372i	−0.123989	−	0.381599i
$931$	30.5623	+	22.2048i	1.00164	+	0.727733i
$932$	−13.7082	+	9.95959i	−0.449027	+	0.326237i
$933$	5.09017	−	15.6659i	0.166645	−	0.512880i
$934$	12.7984			0.418776
$935$		0			0
$936$	−3.23607			−0.105774
$937$	−1.06637	+	3.28195i	−0.0348368	+	0.107217i	−0.966963	−	0.254917i	$-0.917952\pi$
$937$	−1.06637	+	3.28195i	−0.0348368	+	0.107217i	0.932126	+	0.362134i	$0.117952\pi$
$938$	2.47214	−	1.79611i	0.0807181	−	0.0586451i
$939$	−17.7812	−	12.9188i	−0.580266	−	0.421588i
$940$	4.47214	+	13.7638i	0.145865	+	0.448926i
$941$	−11.6738	−	35.9281i	−0.380554	−	1.17122i	−0.939655	−	0.342124i	$-0.888854\pi$
$941$	−11.6738	−	35.9281i	−0.380554	−	1.17122i	0.559101	−	0.829100i	$-0.311146\pi$
$942$	14.5623	+	10.5801i	0.474466	+	0.344719i
$943$	26.3607	−	19.1522i	0.858422	−	0.623680i
$944$	3.19098	−	9.82084i	0.103858	−	0.319641i
$945$	−2.23607			−0.0727393
$946$		0			0
$947$	31.9230			1.03736			0.518679	−	0.854969i	$-0.326424\pi$
$947$	31.9230			1.03736			0.518679	+	0.854969i	$0.326424\pi$
$948$	2.11803	−	6.51864i	0.0687905	−	0.211716i
$949$	−38.1246	+	27.6992i	−1.23758	+	0.899153i
$950$	−37.3607	−	27.1441i	−1.21214	−	0.880672i
$951$	−2.79837	−	8.61251i	−0.0907435	−	0.279280i
$952$	0.763932	+	2.35114i	0.0247592	+	0.0762009i
$953$	−14.1803	−	10.3026i	−0.459346	−	0.333735i	0.333929	−	0.942598i	$-0.391626\pi$
$953$	−14.1803	−	10.3026i	−0.459346	−	0.333735i	−0.793275	+	0.608864i	$0.791626\pi$
$954$	−1.11803	+	0.812299i	−0.0361977	+	0.0262992i
$955$	−3.41641	+	10.5146i	−0.110552	+	0.340245i
$956$	7.52786			0.243469
$957$		0			0
$958$	−8.76393			−0.283150
$959$	2.70820	−	8.33499i	0.0874525	−	0.269151i
$960$	−2.92705	+	2.12663i	−0.0944702	+	0.0686366i
$961$	15.8262	+	11.4984i	0.510524	+	0.370917i
$962$	8.94427	+	27.5276i	0.288375	+	0.887527i
$963$	−0.336881	−	1.03681i	−0.0108558	−	0.0334108i
$964$	6.97214	+	5.06555i	0.224557	+	0.163150i
$965$	−13.5172	+	9.82084i	−0.435135	+	0.316144i
$966$	1.09017	−	3.35520i	0.0350756	−	0.107952i
$967$	19.6180			0.630873			0.315437	−	0.948947i	$-0.397849\pi$
$967$	19.6180			0.630873			0.315437	+	0.948947i	$0.397849\pi$
$968$		0			0
$969$	−22.8328			−0.733496
$970$	−10.7533	+	33.0952i	−0.345267	+	1.06262i
$971$	4.47214	−	3.24920i	0.143518	−	0.104272i	−0.513710	−	0.857964i	$-0.671729\pi$
$971$	4.47214	−	3.24920i	0.143518	−	0.104272i	0.657227	+	0.753692i	$0.271729\pi$
$972$	−0.809017	−	0.587785i	−0.0259492	−	0.0188532i
$973$	−3.00000	−	9.23305i	−0.0961756	−	0.295998i
$974$	0.954915	+	2.93893i	0.0305975	+	0.0941693i
$975$	21.1803	+	15.3884i	0.678314	+	0.492824i
$976$	−3.00000	+	2.17963i	−0.0960277	+	0.0697682i
$977$	−5.87539	+	18.0826i	−0.187970	+	0.578513i	−0.999987	−	0.00512122i	$-0.998370\pi$
$977$	−5.87539	+	18.0826i	−0.187970	+	0.578513i	0.812017	+	0.583634i	$0.198370\pi$
$978$	0.472136			0.0150972
$979$		0			0
$980$	−23.9443			−0.764872
$981$	0.909830	−	2.80017i	0.0290486	−	0.0894025i
$982$	−23.7082	+	17.2250i	−0.756559	+	0.549672i
$983$	15.8541	+	11.5187i	0.505667	+	0.367389i	0.811178	−	0.584800i	$-0.198827\pi$
$983$	15.8541	+	11.5187i	0.505667	+	0.367389i	−0.305510	+	0.952189i	$0.598827\pi$
$984$	1.76393	+	5.42882i	0.0562321	+	0.173065i
$985$	28.5172	+	87.7670i	0.908634	+	2.79649i
$986$	−22.1803	−	16.1150i	−0.706366	−	0.513205i
$987$	2.00000	−	1.45309i	0.0636607	−	0.0462522i
$988$	−5.70820	+	17.5680i	−0.181602	+	0.558914i
$989$	−27.1935			−0.864703
$990$		0			0
$991$	55.3951			1.75968			0.879842	−	0.475266i	$-0.157648\pi$
$991$	55.3951			1.75968			0.879842	+	0.475266i	$0.157648\pi$
$992$	−1.04508	+	3.21644i	−0.0331815	+	0.102122i
$993$	13.2361	−	9.61657i	0.420034	−	0.305173i
$994$	3.00000	+	2.17963i	0.0951542	+	0.0691336i
$995$	−0.427051	−	1.31433i	−0.0135384	−	0.0416670i
$996$	−0.500000	−	1.53884i	−0.0158431	−	0.0487601i
$997$	19.9443	+	14.4904i	0.631641	+	0.458914i	0.856968	−	0.515369i	$-0.172345\pi$
$997$	19.9443	+	14.4904i	0.631641	+	0.458914i	−0.225327	+	0.974283i	$0.572345\pi$
$998$	−30.1803	+	21.9273i	−0.955342	+	0.694097i
$999$	−2.76393	+	8.50651i	−0.0874469	+	0.269134i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	726.2.e.c.493.1		4
11.2	odd	10		726.2.e.j.487.1		4
11.3	even	5		726.2.e.a.565.1		4
11.4	even	5		726.2.a.m.1.2		2
11.5	even	5	inner	726.2.e.c.511.1		4
11.6	odd	10		66.2.e.b.49.1	yes	4
11.7	odd	10		726.2.a.k.1.2		2
11.8	odd	10		726.2.e.j.565.1		4
11.9	even	5		726.2.e.a.487.1		4
11.10	odd	2		66.2.e.b.31.1	✓	4
33.17	even	10		198.2.f.a.181.1		4
33.26	odd	10		2178.2.a.o.1.1		2
33.29	even	10		2178.2.a.v.1.1		2
33.32	even	2		198.2.f.a.163.1		4
44.7	even	10		5808.2.a.bz.1.2		2
44.15	odd	10		5808.2.a.by.1.2		2
44.39	even	10		528.2.y.g.49.1		4
44.43	even	2		528.2.y.g.97.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
66.2.e.b.31.1	✓	4	11.10	odd	2
66.2.e.b.49.1	yes	4	11.6	odd	10
198.2.f.a.163.1		4	33.32	even	2
198.2.f.a.181.1		4	33.17	even	10
528.2.y.g.49.1		4	44.39	even	10
528.2.y.g.97.1		4	44.43	even	2
726.2.a.k.1.2		2	11.7	odd	10
726.2.a.m.1.2		2	11.4	even	5
726.2.e.a.487.1		4	11.9	even	5
726.2.e.a.565.1		4	11.3	even	5
726.2.e.c.493.1		4	1.1	even	1	trivial
726.2.e.c.511.1		4	11.5	even	5	inner
726.2.e.j.487.1		4	11.2	odd	10
726.2.e.j.565.1		4	11.8	odd	10
2178.2.a.o.1.1		2	33.26	odd	10
2178.2.a.v.1.1		2	33.29	even	10
5808.2.a.by.1.2		2	44.15	odd	10
5808.2.a.bz.1.2		2	44.7	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 $\F_{q}$
Belyi maps

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} +(1.11803 + 3.44095i) q^{5} +(0.309017 + 0.951057i) q^{6} +(0.500000 + 0.363271i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.309017 - 0.951057i) q^{9} +3.61803 q^{10} +1.00000 q^{12} +(-1.00000 + 3.07768i) q^{13} +(0.500000 - 0.363271i) q^{14} +(-2.92705 - 2.12663i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-1.23607 - 3.80423i) q^{17} +(-0.809017 - 0.587785i) q^{18} +(-4.61803 + 3.35520i) q^{19} +(1.11803 - 3.44095i) q^{20} -0.618034 q^{21} -5.70820 q^{23} +(0.309017 - 0.951057i) q^{24} +(-6.54508 + 4.75528i) q^{25} +(2.61803 + 1.90211i) q^{26} +(0.309017 + 0.951057i) q^{27} +(-0.190983 - 0.587785i) q^{28} +(5.54508 + 4.02874i) q^{29} +(-2.92705 + 2.12663i) q^{30} +(-1.04508 + 3.21644i) q^{31} +1.00000 q^{32} -4.00000 q^{34} +(-0.690983 + 2.12663i) q^{35} +(-0.809017 + 0.587785i) q^{36} +(7.23607 + 5.25731i) q^{37} +(1.76393 + 5.42882i) q^{38} +(-1.00000 - 3.07768i) q^{39} +(-2.92705 - 2.12663i) q^{40} +(-4.61803 + 3.35520i) q^{41} +(-0.190983 + 0.587785i) q^{42} +4.76393 q^{43} +3.61803 q^{45} +(-1.76393 + 5.42882i) q^{46} +(-3.23607 + 2.35114i) q^{47} +(-0.809017 - 0.587785i) q^{48} +(-2.04508 - 6.29412i) q^{49} +(2.50000 + 7.69421i) q^{50} +(3.23607 + 2.35114i) q^{51} +(2.61803 - 1.90211i) q^{52} +(0.427051 - 1.31433i) q^{53} +1.00000 q^{54} -0.618034 q^{56} +(1.76393 - 5.42882i) q^{57} +(5.54508 - 4.02874i) q^{58} +(-8.35410 - 6.06961i) q^{59} +(1.11803 + 3.44095i) q^{60} +(1.14590 + 3.52671i) q^{61} +(2.73607 + 1.98787i) q^{62} +(0.500000 - 0.363271i) q^{63} +(0.309017 - 0.951057i) q^{64} -11.7082 q^{65} +4.94427 q^{67} +(-1.23607 + 3.80423i) q^{68} +(4.61803 - 3.35520i) q^{69} +(1.80902 + 1.31433i) q^{70} +(1.85410 + 5.70634i) q^{71} +(0.309017 + 0.951057i) q^{72} +(11.7812 + 8.55951i) q^{73} +(7.23607 - 5.25731i) q^{74} +(2.50000 - 7.69421i) q^{75} +5.70820 q^{76} -3.23607 q^{78} +(2.11803 - 6.51864i) q^{79} +(-2.92705 + 2.12663i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(1.76393 + 5.42882i) q^{82} +(-0.500000 - 1.53884i) q^{83} +(0.500000 + 0.363271i) q^{84} +(11.7082 - 8.50651i) q^{85} +(1.47214 - 4.53077i) q^{86} -6.85410 q^{87} +6.76393 q^{89} +(1.11803 - 3.44095i) q^{90} +(-1.61803 + 1.17557i) q^{91} +(4.61803 + 3.35520i) q^{92} +(-1.04508 - 3.21644i) q^{93} +(1.23607 + 3.80423i) q^{94} +(-16.7082 - 12.1392i) q^{95} +(-0.809017 + 0.587785i) q^{96} +(-2.97214 + 9.14729i) q^{97} -6.61803 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} - q^{3} - q^{4} - q^{6} + 2 q^{7} - q^{8} - q^{9} + 10 q^{10} + 4 q^{12} - 4 q^{13} + 2 q^{14} - 5 q^{15} - q^{16} + 4 q^{17} - q^{18} - 14 q^{19} + 2 q^{21} + 4 q^{23} - q^{24} - 15 q^{25}+ \cdots - 22 q^{98}+O(q^{100}) \) 4 * q - q^2 - q^3 - q^4 - q^6 + 2 * q^7 - q^8 - q^9 + 10 * q^10 + 4 * q^12 - 4 * q^13 + 2 * q^14 - 5 * q^15 - q^16 + 4 * q^17 - q^18 - 14 * q^19 + 2 * q^21 + 4 * q^23 - q^24 - 15 * q^25 + 6 * q^26 - q^27 - 3 * q^28 + 11 * q^29 - 5 * q^30 + 7 * q^31 + 4 * q^32 - 16 * q^34 - 5 * q^35 - q^36 + 20 * q^37 + 16 * q^38 - 4 * q^39 - 5 * q^40 - 14 * q^41 - 3 * q^42 + 28 * q^43 + 10 * q^45 - 16 * q^46 - 4 * q^47 - q^48 + 3 * q^49 + 10 * q^50 + 4 * q^51 + 6 * q^52 - 5 * q^53 + 4 * q^54 + 2 * q^56 + 16 * q^57 + 11 * q^58 - 20 * q^59 + 18 * q^61 + 2 * q^62 + 2 * q^63 - q^64 - 20 * q^65 - 16 * q^67 + 4 * q^68 + 14 * q^69 + 5 * q^70 - 6 * q^71 - q^72 + 27 * q^73 + 20 * q^74 + 10 * q^75 - 4 * q^76 - 4 * q^78 + 4 * q^79 - 5 * q^80 - q^81 + 16 * q^82 - 2 * q^83 + 2 * q^84 + 20 * q^85 - 12 * q^86 - 14 * q^87 + 36 * q^89 - 2 * q^91 + 14 * q^92 + 7 * q^93 - 4 * q^94 - 40 * q^95 - q^96 + 6 * q^97 - 22 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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