LMFDB - Embedded newform 66.2.e.b.31.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [66,2,Mod(25,66)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(66, 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("66.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 66 = 2 \cdot 3 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	66.e (of order $5$, degree $4$, 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:	$0.527012653340$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			31.1
Root			$-0.309017 + 0.951057i$ of defining polynomial
Character	$\chi$	$=$	66.31
Dual form			66.2.e.b.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 + 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(1.11803 + 3.44095i) q^{5} +(-0.309017 - 0.951057i) q^{6} +(-0.500000 - 0.363271i) q^{7} +(0.809017 - 0.587785i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(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} +(1.23607 - 3.07768i) q^{11} +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} +(2.54508 + 2.12663i) q^{22} -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} +(0.809017 + 3.21644i) q^{33} -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} +(-2.80902 + 1.76336i) q^{44} +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} +(11.9721 + 0.812299i) q^{55} -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} +(-3.30902 - 0.224514i) q^{66} +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} +(-1.73607 + 1.08981i) q^{77} -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} +(-0.809017 - 3.21644i) q^{88} +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} +(-2.54508 - 2.12663i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} - q^{3} - q^{4} + q^{6} - 2 q^{7} + q^{8} - q^{9}+O(q^{10}) $ 4 * q + q^2 - q^3 - q^4 + q^6 - 2 * q^7 + q^8 - q^9	\( 4 q + q^{2} - q^{3} - q^{4} + q^{6} - 2 q^{7} + q^{8} - q^{9} - 10 q^{10} - 4 q^{11} + 4 q^{12} + 4 q^{13} + 2 q^{14} - 5 q^{15} - q^{16} - 4 q^{17} + q^{18} + 14 q^{19} - 2 q^{21} - q^{22} + 4 q^{23} + q^{24} - 15 q^{25} + 6 q^{26} - q^{27} + 3 q^{28} - 11 q^{29} + 5 q^{30} + 7 q^{31} - 4 q^{32} + q^{33} - 16 q^{34} + 5 q^{35} - q^{36} + 20 q^{37} + 16 q^{38} + 4 q^{39} + 5 q^{40} + 14 q^{41} - 3 q^{42} - 28 q^{43} - 9 q^{44} + 10 q^{45} + 16 q^{46} - 4 q^{47} - q^{48} + 3 q^{49} - 10 q^{50} - 4 q^{51} - 6 q^{52} - 5 q^{53} - 4 q^{54} + 30 q^{55} + 2 q^{56} - 16 q^{57} + 11 q^{58} - 20 q^{59} - 18 q^{61} - 2 q^{62} - 2 q^{63} - q^{64} + 20 q^{65} - 11 q^{66} - 16 q^{67} - 4 q^{68} + 14 q^{69} + 5 q^{70} - 6 q^{71} + q^{72} - 27 q^{73} - 20 q^{74} + 10 q^{75} + 4 q^{76} + 2 q^{77} - 4 q^{78} - 4 q^{79} - 5 q^{80} - q^{81} + 16 q^{82} + 2 q^{83} - 2 q^{84} - 20 q^{85} - 12 q^{86} + 14 q^{87} - q^{88} + 36 q^{89} - 2 q^{91} + 14 q^{92} + 7 q^{93} + 4 q^{94} + 40 q^{95} + q^{96} + 6 q^{97} + 22 q^{98} + q^{99}+O(q^{100}) \) 4 * q + q^2 - q^3 - q^4 + q^6 - 2 * q^7 + q^8 - q^9 - 10 * q^10 - 4 * q^11 + 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 - q^22 + 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 + q^33 - 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 - 9 * q^44 + 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 + 30 * q^55 + 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 - 11 * q^66 - 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 + 2 * q^77 - 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 - q^88 + 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 + q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/66\mathbb{Z}\right)^\times$.

$n$	$13$	$23$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$

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	0.489271	−	0.872132i	$-0.337263\pi$
$7$	−0.500000	−	0.363271i	−0.188982	−	0.137304i	−0.678253	+	0.734828i	$0.737263\pi$
$8$	0.809017	−	0.587785i	0.286031	−	0.207813i
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$	−3.61803			−1.14412
$11$	1.23607	−	3.07768i	0.372689	−	0.927957i
$11$	1.23607	−	3.07768i	0.372689	−	0.927957i
$12$	1.00000			0.288675
$13$	1.00000	−	3.07768i	0.277350	−	0.853596i	−0.711238	−	0.702951i	$-0.751865\pi$
$13$	1.00000	−	3.07768i	0.277350	−	0.853596i	0.988588	−	0.150644i	$-0.0481349\pi$
$14$	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	$0.0612063\pi$
$17$	1.23607	+	3.80423i	0.299791	+	0.922660i	−0.681780	+	0.731558i	$0.738794\pi$
$18$	0.809017	+	0.587785i	0.190687	+	0.138542i
$19$	4.61803	−	3.35520i	1.05945	−	0.769735i	0.0854632	−	0.996341i	$-0.472763\pi$
$19$	4.61803	−	3.35520i	1.05945	−	0.769735i	0.973986	+	0.226606i	$0.0727630\pi$
$20$	1.11803	−	3.44095i	0.250000	−	0.769421i
$21$	0.618034			0.134866
$22$	2.54508	+	2.12663i	0.542614	+	0.453398i
$23$	−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	−0.0614485	−	0.998110i	$-0.519572\pi$
$29$	−5.54508	−	4.02874i	−1.02970	−	0.748118i	−0.968248	+	0.249992i	$0.919572\pi$
$30$	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
$33$	0.809017	+	3.21644i	0.140832	+	0.559910i
$34$	−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	−0.165557	−	0.986200i	$-0.552942\pi$
$41$	4.61803	−	3.35520i	0.721216	−	0.523994i	0.886772	+	0.462206i	$0.152942\pi$
$42$	−0.190983	+	0.587785i	−0.0294693	+	0.0906972i
$43$	−4.76393			−0.726493			−0.363246	−	0.931693i	$-0.618332\pi$
$43$	−4.76393			−0.726493			−0.363246	+	0.931693i	$0.618332\pi$
$44$	−2.80902	+	1.76336i	−0.423475	+	0.265836i
$45$	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
$55$	11.9721	+	0.812299i	1.61432	+	0.109530i
$56$	−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	0.850511	−	0.525958i	$-0.176293\pi$
$61$	−1.14590	−	3.52671i	−0.146717	−	0.451549i	−0.997228	+	0.0744087i	$0.976293\pi$
$62$	−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
$66$	−3.30902	−	0.224514i	−0.407312	−	0.0276358i
$67$	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	$-0.975271\pi$
$73$	−11.7812	−	8.55951i	−1.37888	−	1.00181i	−0.381896	−	0.924205i	$-0.624729\pi$
$74$	−7.23607	+	5.25731i	−0.841176	+	0.611150i
$75$	2.50000	−	7.69421i	0.288675	−	0.888451i
$76$	−5.70820			−0.654776
$77$	−1.73607	+	1.08981i	−0.197843	+	0.124196i
$78$	−3.23607			−0.366413
$79$	−2.11803	+	6.51864i	−0.238297	+	0.733404i	0.758369	+	0.651825i	$0.225996\pi$
$79$	−2.11803	+	6.51864i	−0.238297	+	0.733404i	−0.996667	+	0.0815791i	$0.974004\pi$
$80$	−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	0.974740	−	0.223341i	$-0.0716964\pi$
$83$	0.500000	+	1.53884i	0.0548821	+	0.168910i	−0.919858	+	0.392251i	$0.871696\pi$
$84$	−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
$88$	−0.809017	−	3.21644i	−0.0862415	−	0.342874i
$89$	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
$99$	−2.54508	−	2.12663i	−0.255791	−	0.213734i
$100$	8.09017			0.809017
$101$	−0.645898	+	1.98787i	−0.0642693	+	0.197800i	−0.978035	−	0.208441i	$-0.933161\pi$
$101$	−0.645898	+	1.98787i	−0.0642693	+	0.197800i	0.913766	+	0.406242i	$0.133161\pi$
$102$	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	−0.629600	−	0.776919i	$-0.716781\pi$
$107$	−0.881966	+	0.640786i	−0.0852629	+	0.0619471i	0.544337	+	0.838867i	$0.316781\pi$
$108$	0.309017	−	0.951057i	0.0297352	−	0.0915155i
$109$	−2.94427			−0.282010			−0.141005	−	0.990009i	$-0.545033\pi$
$109$	−2.94427			−0.282010			−0.141005	+	0.990009i	$0.545033\pi$
$110$	−4.47214	+	11.1352i	−0.426401	+	1.06170i
$111$	−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
$121$	−7.94427	−	7.60845i	−0.722207	−	0.691677i
$122$	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	0.990801	−	0.135326i	$-0.0432083\pi$
$127$	1.23607	+	3.80423i	0.109683	+	0.337570i	−0.881118	+	0.472897i	$0.843208\pi$
$128$	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	$-0.446151\pi$
$131$	3.85410			0.336734			0.168367	+	0.985724i	$0.446151\pi$
$132$	1.23607	−	3.07768i	0.107586	−	0.267878i
$133$	−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	0.977315	−	0.211792i	$-0.0679299\pi$
$139$	12.7082	+	9.23305i	1.07790	+	0.783137i	0.100581	+	0.994929i	$0.467930\pi$
$140$	−1.80902	+	1.31433i	−0.152890	+	0.111081i
$141$	1.23607	−	3.80423i	0.104096	−	0.320374i
$142$	−6.00000			−0.503509
$143$	−8.23607	−	6.88191i	−0.688735	−	0.575494i
$144$	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	0.997928	−	0.0643455i	$-0.0204960\pi$
$149$	1.86475	+	5.73910i	0.152766	+	0.470165i	−0.845162	+	0.534511i	$0.820496\pi$
$150$	6.54508	+	4.75528i	0.534404	+	0.388267i
$151$	−16.0172	+	11.6372i	−1.30346	+	0.947021i	−0.999983	−	0.00581658i	$-0.998149\pi$
$151$	−16.0172	+	11.6372i	−1.30346	+	0.947021i	−0.303480	+	0.952838i	$0.598149\pi$
$152$	1.76393	−	5.42882i	0.143074	−	0.440336i
$153$	4.00000			0.323381
$154$	−0.500000	−	1.98787i	−0.0402911	−	0.160187i
$155$	−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
$165$	−10.1631	+	6.37988i	−0.791198	+	0.496673i
$166$	−1.61803			−0.125584
$167$	−1.94427	+	5.98385i	−0.150452	+	0.463044i	−0.997672	−	0.0681985i	$-0.978275\pi$
$167$	−1.94427	+	5.98385i	−0.150452	+	0.463044i	0.847219	+	0.531243i	$0.178275\pi$
$168$	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	−0.0523802	−	0.998627i	$-0.516681\pi$
$173$	11.5902	−	8.42075i	0.881184	−	0.640218i	0.933565	+	0.358409i	$0.116681\pi$
$174$	−2.11803	+	6.51864i	−0.160568	+	0.494177i
$175$	5.00000			0.377964
$176$	3.30902	+	0.224514i	0.249427	+	0.0169234i
$177$	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
$187$	13.2361	+	0.898056i	0.967917	+	0.0656724i
$188$	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	0.886468	−	0.462791i	$-0.153152\pi$
$193$	−1.42705	−	4.39201i	−0.102721	−	0.316144i	−0.989189	+	0.146647i	$0.953152\pi$
$194$	−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	$-0.862874\pi$
$197$	−25.5066			−1.81727			−0.908634	+	0.417593i	$0.862874\pi$
$198$	2.80902	−	1.76336i	0.199628	−	0.125316i
$199$	−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
$209$	−4.61803	−	18.3601i	−0.319436	−	1.26999i
$210$	−2.23607			−0.154303
$211$	−2.85410	+	8.78402i	−0.196484	+	0.604717i	0.803472	+	0.595343i	$0.202984\pi$
$211$	−2.85410	+	8.78402i	−0.196484	+	0.604717i	−0.999956	+	0.00937395i	$0.997016\pi$
$212$	−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
$220$	−9.20820	−	7.69421i	−0.620817	−	0.518743i
$221$	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	0.444358	−	0.895849i	$-0.353432\pi$
$227$	−4.07295	−	2.95917i	−0.270331	−	0.196407i	−0.714689	+	0.699442i	$0.753432\pi$
$228$	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
$231$	0.763932	−	1.90211i	0.0502630	−	0.125150i
$232$	−6.85410			−0.449994
$233$	−5.23607	+	16.1150i	−0.343026	+	1.05573i	0.619606	+	0.784913i	$0.287292\pi$
$233$	−5.23607	+	16.1150i	−0.343026	+	1.05573i	−0.962632	+	0.270813i	$0.912708\pi$
$234$	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	−0.373128	−	0.927780i	$-0.621715\pi$
$239$	6.09017	−	4.42477i	0.393940	−	0.286214i	0.767068	+	0.641565i	$0.221715\pi$
$240$	1.11803	−	3.44095i	0.0721688	−	0.222113i
$241$	8.61803			0.555136			0.277568	−	0.960706i	$-0.410472\pi$
$241$	8.61803			0.555136			0.277568	+	0.960706i	$0.410472\pi$
$242$	9.69098	−	5.20431i	0.622960	−	0.334546i
$243$	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
$253$	−7.05573	+	17.5680i	−0.443590	+	1.10449i
$254$	−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	$-0.678338\pi$
$263$	−17.2361			−1.06282			−0.531411	+	0.847114i	$0.678338\pi$
$264$	2.54508	+	2.12663i	0.156639	+	0.130885i
$265$	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	−0.300990	−	0.953627i	$-0.597317\pi$
$271$	−21.4164	−	15.5599i	−1.30095	−	0.945199i	−0.999964	+	0.00842890i	$0.997317\pi$
$272$	−3.23607	+	2.35114i	−0.196215	+	0.142559i
$273$	0.618034	−	1.90211i	0.0374051	−	0.115121i
$274$	14.1803			0.856666
$275$	6.54508	+	26.0216i	0.394683	+	1.56916i
$276$	−5.70820			−0.343594
$277$	4.85410	−	14.9394i	0.291655	−	0.897621i	−0.692670	−	0.721255i	$-0.743566\pi$
$277$	4.85410	−	14.9394i	0.291655	−	0.897621i	0.984325	−	0.176366i	$-0.0564343\pi$
$278$	−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	$0.118349\pi$
$281$	6.56231	+	20.1967i	0.391474	+	1.20483i	−0.540199	+	0.841537i	$0.681651\pi$
$282$	3.23607	+	2.35114i	0.192705	+	0.140008i
$283$	6.09017	−	4.42477i	0.362023	−	0.263025i	−0.391872	−	0.920020i	$-0.628173\pi$
$283$	6.09017	−	4.42477i	0.362023	−	0.263025i	0.753895	+	0.656994i	$0.228173\pi$
$284$	1.85410	−	5.70634i	0.110021	−	0.338609i
$285$	−20.6525			−1.22335
$286$	9.09017	−	5.70634i	0.537513	−	0.337423i
$287$	−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	0.453292	−	0.891362i	$-0.350250\pi$
$293$	−4.35410	−	3.16344i	−0.254369	−	0.184810i	−0.707661	+	0.706552i	$0.750250\pi$
$294$	−5.35410	+	3.88998i	−0.312258	+	0.226868i
$295$	11.5451	−	35.5321i	0.672181	−	2.06876i
$296$	8.94427			0.519875
$297$	3.30902	+	0.224514i	0.192009	+	0.0130276i
$298$	−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	$-0.663682\pi$
$307$	−17.2361			−0.983714			−0.491857	+	0.870676i	$0.663682\pi$
$308$	2.04508	+	0.138757i	0.116530	+	0.00790643i
$309$	−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
$319$	−19.2533	+	12.0862i	−1.07798	+	0.676698i
$320$	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
$330$	−2.92705	−	11.6372i	−0.161129	−	0.640606i
$331$	−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	0.0558324	−	0.998440i	$-0.482219\pi$
$337$	−16.0902	−	11.6902i	−0.876487	−	0.636805i	−0.932320	+	0.361635i	$0.882219\pi$
$338$	−2.04508	+	1.48584i	−0.111238	+	0.0808191i
$339$	2.14590	−	6.60440i	0.116549	−	0.358702i
$340$	14.4721			0.784862
$341$	8.60739	+	7.19218i	0.466116	+	0.389478i
$342$	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	$-0.727076\pi$
$347$	−10.6074	−	32.6462i	−0.569435	−	1.75254i	0.0849581	−	0.996385i	$-0.472924\pi$
$348$	−5.54508	−	4.02874i	−0.297248	−	0.215963i
$349$	9.94427	−	7.22494i	0.532305	−	0.386742i	−0.288914	−	0.957355i	$-0.593294\pi$
$349$	9.94427	−	7.22494i	0.532305	−	0.386742i	0.821219	+	0.570613i	$0.193294\pi$
$350$	−1.54508	+	4.75528i	−0.0825883	+	0.254181i
$351$	3.23607			0.172729
$352$	−1.23607	+	3.07768i	−0.0658826	+	0.164041i
$353$	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	0.994601	−	0.103776i	$-0.0330926\pi$
$359$	22.7984	+	16.5640i	1.20325	+	0.874214i	0.208651	+	0.977990i	$0.433093\pi$
$360$	2.92705	−	2.12663i	0.154269	−	0.112083i
$361$	4.19756	−	12.9188i	0.220924	−	0.679935i
$362$	−21.4164			−1.12562
$363$	10.8992	+	1.48584i	0.572059	+	0.0779864i
$364$	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	$0.5\pi$
$374$	−4.94427	+	12.3107i	−0.255662	+	0.636573i
$375$	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
$385$	−5.69098	−	4.75528i	−0.290039	−	0.242352i
$386$	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
$396$	0.809017	+	3.21644i	0.0406546	+	0.161632i
$397$	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
$407$	25.1246	−	15.7719i	1.24538	−	0.781786i
$408$	−4.00000			−0.198030
$409$	−9.26393	+	28.5115i	−0.458072	+	1.40980i	0.409418	+	0.912347i	$0.365732\pi$
$409$	−9.26393	+	28.5115i	−0.458072	+	1.40980i	−0.867490	+	0.497454i	$0.834268\pi$
$410$	−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
$418$	18.8885	+	1.28157i	0.923869	+	0.0626837i
$419$	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
$429$	10.7082	+	0.726543i	0.516997	+	0.0350778i
$430$	17.2361			0.831197
$431$	10.5279	−	32.4014i	0.507109	−	1.56072i	−0.290086	−	0.957001i	$-0.593684\pi$
$431$	10.5279	−	32.4014i	0.507109	−	1.56072i	0.797195	−	0.603722i	$-0.206316\pi$
$432$	−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	$-0.246848\pi$
$439$	29.9230			1.42815			0.714073	+	0.700071i	$0.246848\pi$
$440$	10.1631	−	6.37988i	0.484508	−	0.304149i
$441$	−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
$451$	−4.61803	−	18.3601i	−0.217455	−	0.864543i
$452$	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	$-0.871825\pi$
$457$	−8.68034	−	26.7153i	−0.406049	−	1.24969i	0.513967	−	0.857810i	$-0.328175\pi$
$458$	−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	$-0.328786\pi$
$461$	22.0000			1.02464			0.512321	+	0.858794i	$0.328786\pi$
$462$	1.57295	+	1.31433i	0.0731802	+	0.0611481i
$463$	−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
$473$	−5.88854	+	14.6619i	−0.270756	+	0.674154i
$474$	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	0.993670	−	0.112342i	$-0.0358352\pi$
$479$	2.70820	+	8.33499i	0.123741	+	0.380836i	−0.869929	+	0.493178i	$0.835835\pi$
$480$	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
$484$	1.95492	+	10.8249i	0.0888598	+	0.492041i
$485$	−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	0.975901	−	0.218215i	$-0.0700233\pi$
$491$	23.7082	+	17.2250i	1.06994	+	0.777354i	0.0940355	+	0.995569i	$0.470023\pi$
$492$	4.61803	−	3.35520i	0.208197	−	0.151264i
$493$	8.47214	−	26.0746i	0.381566	−	1.17434i
$494$	18.4721			0.831101
$495$	4.47214	−	11.1352i	0.201008	−	0.500488i
$496$	−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	−0.502038	−	0.864846i	$-0.667416\pi$
$503$	3.70820	−	2.69417i	0.165341	−	0.120127i	0.667379	+	0.744719i	$0.267416\pi$
$504$	−0.190983	+	0.587785i	−0.00850706	+	0.0261820i
$505$	−7.56231			−0.336518
$506$	−14.5279	−	12.1392i	−0.645842	−	0.539654i
$507$	−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
$517$	3.23607	+	12.8658i	0.142322	+	0.565836i
$518$	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	$0.00380186\pi$
$523$	4.52786	+	13.9353i	0.197990	+	0.609350i	−0.801939	+	0.597406i	$0.796198\pi$
$524$	−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
$528$	−2.80902	+	1.76336i	−0.122247	+	0.0767402i
$529$	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
$539$	−21.8992	−	1.48584i	−0.943265	−	0.0639997i
$540$	3.61803			0.155695
$541$	−1.38197	+	4.25325i	−0.0594154	+	0.182862i	−0.976359	−	0.216155i	$-0.930648\pi$
$541$	−1.38197	+	4.25325i	−0.0594154	+	0.182862i	0.916944	+	0.399017i	$0.130648\pi$
$542$	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	$-0.326605\pi$
$547$	34.8885	−	25.3480i	1.49173	−	1.08380i	0.973535	−	0.228538i	$-0.0733945\pi$
$548$	−4.38197	+	13.4863i	−0.187188	+	0.576106i
$549$	−3.70820			−0.158262
$550$	−26.7705	−	1.81636i	−1.14150	−	0.0774497i
$551$	−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	0.626942	−	0.779066i	$-0.284306\pi$
$557$	1.88197	+	1.36733i	0.0797415	+	0.0579356i	−0.547200	+	0.837002i	$0.684306\pi$
$558$	−2.73607	+	1.98787i	−0.115827	+	0.0841532i
$559$	−4.76393	+	14.6619i	−0.201493	+	0.620131i
$560$	2.23607			0.0944911
$561$	−11.2361	+	7.05342i	−0.474387	+	0.297796i
$562$	−21.2361			−0.895789
$563$	2.47214	−	7.60845i	0.104188	−	0.320658i	−0.885351	−	0.464923i	$-0.846082\pi$
$563$	2.47214	−	7.60845i	0.104188	−	0.320658i	0.989539	+	0.144265i	$0.0460819\pi$
$564$	−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	−0.452765	−	0.891630i	$-0.649562\pi$
$569$	6.09017	−	4.42477i	0.255313	−	0.185496i	0.708078	+	0.706134i	$0.249562\pi$
$570$	6.38197	−	19.6417i	0.267311	−	0.822699i
$571$	32.6525			1.36646			0.683232	−	0.730202i	$-0.260574\pi$
$571$	32.6525			1.36646			0.683232	+	0.730202i	$0.260574\pi$
$572$	2.61803	+	10.4086i	0.109466	+	0.435206i
$573$	−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
$583$	−3.51722	−	2.93893i	−0.145668	−	0.121718i
$584$	−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	$-0.305926\pi$
$593$	27.8885			1.14525			0.572623	+	0.819819i	$0.305926\pi$
$594$	−1.23607	+	3.07768i	−0.0507165	+	0.126279i
$595$	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	0.725013	−	0.688735i	$-0.241834\pi$
$601$	7.20820	+	5.23707i	0.294029	+	0.213624i	−0.430984	+	0.902359i	$0.641834\pi$
$602$	−2.38197	+	1.73060i	−0.0970817	+	0.0705340i
$603$	1.52786	−	4.70228i	0.0622194	−	0.191492i
$604$	19.7984			0.805584
$605$	17.2984	−	35.8424i	0.703279	−	1.45720i
$606$	2.09017			0.0849073
$607$	10.1803	−	31.3319i	0.413207	−	1.27172i	−0.500637	−	0.865657i	$-0.666901\pi$
$607$	10.1803	−	31.3319i	0.413207	−	1.27172i	0.913845	−	0.406064i	$-0.133099\pi$
$608$	−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	−0.986028	−	0.166580i	$-0.946728\pi$
$613$	−28.0344	+	20.3682i	−1.13230	+	0.822664i	−0.146272	+	0.989244i	$0.546728\pi$
$614$	5.32624	−	16.3925i	0.214949	−	0.661546i
$615$	−20.6525			−0.832788
$616$	−0.763932	+	1.90211i	−0.0307797	+	0.0766383i
$617$	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
$627$	14.5279	+	12.1392i	0.580187	+	0.484794i
$628$	−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
$638$	−5.54508	−	22.0458i	−0.219532	−	0.872802i
$639$	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
$649$	−29.0066	+	18.2088i	−1.13861	+	0.714759i
$650$	−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	$-0.620152\pi$
$659$	−18.9230			−0.737135			−0.368567	+	0.929601i	$0.620152\pi$
$660$	11.9721	+	0.812299i	0.466015	+	0.0316187i
$661$	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
$671$	−12.2705	−	0.832544i	−0.473698	−	0.0321400i
$672$	−0.618034			−0.0238412
$673$	−10.7361	+	33.0422i	−0.413845	+	1.27368i	0.499435	+	0.866351i	$0.333541\pi$
$673$	−10.7361	+	33.0422i	−0.413845	+	1.27368i	−0.913280	+	0.407333i	$0.866459\pi$
$674$	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	$0.222393\pi$
$677$	13.6418	+	41.9852i	0.524298	+	1.61362i	−0.241401	+	0.970425i	$0.577607\pi$
$678$	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
$682$	−9.50000	+	5.96361i	−0.363774	+	0.228358i
$683$	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
$693$	0.500000	+	1.98787i	0.0189934	+	0.0755129i
$694$	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	$0.736074\pi$
$701$	−41.9787	+	30.4993i	−1.58551	+	1.15194i	−0.910009	+	0.414588i	$0.863926\pi$
$702$	−1.00000	+	3.07768i	−0.0377426	+	0.116160i
$703$	51.0557			1.92560
$704$	−2.54508	−	2.12663i	−0.0959215	−	0.0801503i
$705$	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
$715$	14.4721	−	36.0341i	0.541227	−	1.34760i
$716$	−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
$726$	−4.78115	+	9.90659i	−0.177445	+	0.367668i
$727$	−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	0.271016	−	0.962575i	$-0.412640\pi$
$733$	−15.1803	−	11.0292i	−0.560699	−	0.407371i	−0.831715	+	0.555203i	$0.812640\pi$
$734$	−15.3992	+	11.1882i	−0.568394	+	0.412963i
$735$	−7.39919	+	22.7724i	−0.272923	+	0.839971i
$736$	5.70820			0.210407
$737$	6.11146	−	15.2169i	0.225118	−	0.560522i
$738$	5.70820			0.210122
$739$	13.1246	−	40.3934i	0.482797	−	1.48590i	−0.352350	−	0.935868i	$-0.614617\pi$
$739$	13.1246	−	40.3934i	0.482797	−	1.48590i	0.835147	−	0.550027i	$-0.185383\pi$
$740$	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	$-0.811253\pi$
$743$	−13.2705	−	40.8424i	−0.486848	−	1.49836i	0.342439	−	0.939540i	$-0.388747\pi$
$744$	−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
$748$	−10.1803	−	8.50651i	−0.372230	−	0.311029i
$749$	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
$759$	−4.61803	−	18.3601i	−0.167624	−	0.666429i
$760$	20.6525			0.749144
$761$	9.83282	−	30.2623i	0.356439	−	1.09701i	−0.598731	−	0.800950i	$-0.704328\pi$
$761$	9.83282	−	30.2623i	0.356439	−	1.09701i	0.955170	−	0.296057i	$-0.0956719\pi$
$762$	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	$-0.626327\pi$
$769$	−21.4377			−0.773063			−0.386532	+	0.922276i	$0.626327\pi$
$770$	6.28115	−	3.94298i	0.226357	−	0.142095i
$771$	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
$781$	19.8541	+	1.34708i	0.710436	+	0.0482025i
$782$	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	$0.105145\pi$
$787$	10.4164	+	32.0584i	0.371305	+	1.14276i	−0.574633	+	0.818411i	$0.694855\pi$
$788$	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
$792$	−3.30902	−	0.224514i	−0.117581	−	0.00797776i
$793$	−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
$803$	−40.9058	+	25.6785i	−1.44353	+	0.906176i
$804$	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	$-0.979981\pi$
$809$	−6.47214	−	19.9192i	−0.227548	−	0.700321i	0.770475	−	0.637471i	$-0.220019\pi$
$810$	2.92705	+	2.12663i	0.102846	+	0.0747221i
$811$	−35.7426	+	25.9686i	−1.25509	+	0.911879i	−0.998506	−	0.0546417i	$-0.982598\pi$
$811$	−35.7426	+	25.9686i	−1.25509	+	0.911879i	−0.256588	+	0.966521i	$0.582598\pi$
$812$	1.30902	−	4.02874i	0.0459375	−	0.141381i
$813$	26.4721			0.928418
$814$	7.23607	+	28.7687i	0.253624	+	1.00834i
$815$	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	0.186663	−	0.982424i	$-0.440233\pi$
$821$	−19.7705	−	14.3641i	−0.689996	−	0.501311i	−0.876659	+	0.481113i	$0.840233\pi$
$822$	−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
$825$	−20.5902	−	17.2048i	−0.716858	−	0.598993i
$826$	−6.38197			−0.222057
$827$	13.7533	−	42.3283i	0.478249	−	1.47190i	−0.363277	−	0.931681i	$-0.618342\pi$
$827$	13.7533	−	42.3283i	0.478249	−	1.47190i	0.841526	−	0.540217i	$-0.181658\pi$
$828$	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
$836$	−7.05573	+	17.5680i	−0.244027	+	0.607604i
$837$	−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
$847$	1.20820	+	6.69015i	0.0415144	+	0.229876i
$848$	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	0.996766	−	0.0803580i	$-0.0256064\pi$
$853$	4.18034	+	12.8658i	0.143132	+	0.440515i	−0.853634	+	0.520873i	$0.825606\pi$
$854$	−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	$-0.387990\pi$
$857$	20.1803			0.689347			0.344674	+	0.938723i	$0.387990\pi$
$858$	−4.00000	+	9.95959i	−0.136558	+	0.340015i
$859$	−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
$869$	17.4443	+	14.5761i	0.591756	+	0.494461i
$870$	−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	−0.119600	−	0.992822i	$-0.538161\pi$
$877$	23.3262	−	16.9475i	0.787671	−	0.572277i	0.907271	+	0.420546i	$0.138161\pi$
$878$	−9.24671	+	28.4585i	−0.312061	+	0.960426i
$879$	5.38197			0.181529
$880$	2.92705	+	11.6372i	0.0986709	+	0.392290i
$881$	−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	$0.156634\pi$
$887$	47.7426	+	34.6871i	1.60304	+	1.16468i	0.721689	+	0.692217i	$0.243366\pi$
$888$	−7.23607	+	5.25731i	−0.242827	+	0.176424i
$889$	0.763932	−	2.35114i	0.0256215	−	0.0788547i
$890$	−24.4721			−0.820308
$891$	−2.80902	+	1.76336i	−0.0941056	+	0.0590746i
$892$	−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
$902$	18.8885	+	1.28157i	0.628920	+	0.0426717i
$903$	−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
$913$	5.35410	+	0.363271i	0.177195	+	0.0120225i
$914$	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	$0.205754\pi$
$919$	15.3541	+	47.2551i	0.506485	+	1.55880i	−0.291774	+	0.956487i	$0.594246\pi$
$920$	−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
$924$	−1.73607	+	1.08981i	−0.0571124	+	0.0358522i
$925$	−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
$935$	11.7082	+	46.5488i	0.382899	+	1.52231i
$936$	−3.23607			−0.105774
$937$	1.06637	−	3.28195i	0.0348368	−	0.107217i	−0.932126	−	0.362134i	$-0.882048\pi$
$937$	1.06637	−	3.28195i	0.0348368	−	0.107217i	0.966963	+	0.254917i	$0.0820483\pi$
$938$	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	$0.111146\pi$
$941$	11.6738	+	35.9281i	0.380554	+	1.17122i	−0.559101	+	0.829100i	$0.688854\pi$
$942$	−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
$946$	−12.1246	−	10.1311i	−0.394205	−	0.329391i
$947$	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	0.793275	−	0.608864i	$-0.208374\pi$
$953$	14.1803	+	10.3026i	0.459346	+	0.333735i	−0.333929	+	0.942598i	$0.608374\pi$
$954$	1.11803	−	0.812299i	0.0361977	−	0.0262992i
$955$	−3.41641	+	10.5146i	−0.110552	+	0.340245i
$956$	−7.52786			−0.243469
$957$	8.47214	−	21.0948i	0.273865	−	0.681897i
$958$	−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	$-0.602151\pi$
$967$	−19.6180			−0.630873			−0.315437	+	0.948947i	$0.602151\pi$
$968$	−10.8992	−	1.48584i	−0.350313	−	0.0477567i
$969$	−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
$979$	8.36068	−	20.8172i	0.267208	−	0.665322i
$980$	−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
$990$	9.20820	+	7.69421i	0.292656	+	0.244538i
$991$	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	0.225327	−	0.974283i	$-0.427655\pi$
$997$	−19.9443	−	14.4904i	−0.631641	−	0.458914i	−0.856968	+	0.515369i	$0.827655\pi$
$998$	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	66.2.e.b.31.1	✓	4
3.2	odd	2		198.2.f.a.163.1		4
4.3	odd	2		528.2.y.g.97.1		4
11.2	odd	10		726.2.e.a.487.1		4
11.3	even	5		726.2.e.j.565.1		4
11.4	even	5		726.2.a.k.1.2		2
11.5	even	5	inner	66.2.e.b.49.1	yes	4
11.6	odd	10		726.2.e.c.511.1		4
11.7	odd	10		726.2.a.m.1.2		2
11.8	odd	10		726.2.e.a.565.1		4
11.9	even	5		726.2.e.j.487.1		4
11.10	odd	2		726.2.e.c.493.1		4
33.5	odd	10		198.2.f.a.181.1		4
33.26	odd	10		2178.2.a.v.1.1		2
33.29	even	10		2178.2.a.o.1.1		2
44.7	even	10		5808.2.a.by.1.2		2
44.15	odd	10		5808.2.a.bz.1.2		2
44.27	odd	10		528.2.y.g.49.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
66.2.e.b.31.1	✓	4	1.1	even	1	trivial
66.2.e.b.49.1	yes	4	11.5	even	5	inner
198.2.f.a.163.1		4	3.2	odd	2
198.2.f.a.181.1		4	33.5	odd	10
528.2.y.g.49.1		4	44.27	odd	10
528.2.y.g.97.1		4	4.3	odd	2
726.2.a.k.1.2		2	11.4	even	5
726.2.a.m.1.2		2	11.7	odd	10
726.2.e.a.487.1		4	11.2	odd	10
726.2.e.a.565.1		4	11.8	odd	10
726.2.e.c.493.1		4	11.10	odd	2
726.2.e.c.511.1		4	11.6	odd	10
726.2.e.j.487.1		4	11.9	even	5
726.2.e.j.565.1		4	11.3	even	5
2178.2.a.o.1.1		2	33.29	even	10
2178.2.a.v.1.1		2	33.26	odd	10
5808.2.a.by.1.2		2	44.7	even	10
5808.2.a.bz.1.2		2	44.15	odd	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:	\( N \)	\(=\)	\( 66 = 2 \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	66.e (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 + 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(1.11803 + 3.44095i) q^{5} +(-0.309017 - 0.951057i) q^{6} +(-0.500000 - 0.363271i) q^{7} +(0.809017 - 0.587785i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(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} +(1.23607 - 3.07768i) q^{11} +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} +(2.54508 + 2.12663i) q^{22} -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} +(0.809017 + 3.21644i) q^{33} -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} +(-2.80902 + 1.76336i) q^{44} +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} +(11.9721 + 0.812299i) q^{55} -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} +(-3.30902 - 0.224514i) q^{66} +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} +(-1.73607 + 1.08981i) q^{77} -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} +(-0.809017 - 3.21644i) q^{88} +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} +(-2.54508 - 2.12663i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} - q^{3} - q^{4} + q^{6} - 2 q^{7} + q^{8} - q^{9}+O(q^{10}) \) 4 * q + q^2 - q^3 - q^4 + q^6 - 2 * q^7 + q^8 - q^9	\( 4 q + q^{2} - q^{3} - q^{4} + q^{6} - 2 q^{7} + q^{8} - q^{9} - 10 q^{10} - 4 q^{11} + 4 q^{12} + 4 q^{13} + 2 q^{14} - 5 q^{15} - q^{16} - 4 q^{17} + q^{18} + 14 q^{19} - 2 q^{21} - q^{22} + 4 q^{23} + q^{24} - 15 q^{25} + 6 q^{26} - q^{27} + 3 q^{28} - 11 q^{29} + 5 q^{30} + 7 q^{31} - 4 q^{32} + q^{33} - 16 q^{34} + 5 q^{35} - q^{36} + 20 q^{37} + 16 q^{38} + 4 q^{39} + 5 q^{40} + 14 q^{41} - 3 q^{42} - 28 q^{43} - 9 q^{44} + 10 q^{45} + 16 q^{46} - 4 q^{47} - q^{48} + 3 q^{49} - 10 q^{50} - 4 q^{51} - 6 q^{52} - 5 q^{53} - 4 q^{54} + 30 q^{55} + 2 q^{56} - 16 q^{57} + 11 q^{58} - 20 q^{59} - 18 q^{61} - 2 q^{62} - 2 q^{63} - q^{64} + 20 q^{65} - 11 q^{66} - 16 q^{67} - 4 q^{68} + 14 q^{69} + 5 q^{70} - 6 q^{71} + q^{72} - 27 q^{73} - 20 q^{74} + 10 q^{75} + 4 q^{76} + 2 q^{77} - 4 q^{78} - 4 q^{79} - 5 q^{80} - q^{81} + 16 q^{82} + 2 q^{83} - 2 q^{84} - 20 q^{85} - 12 q^{86} + 14 q^{87} - q^{88} + 36 q^{89} - 2 q^{91} + 14 q^{92} + 7 q^{93} + 4 q^{94} + 40 q^{95} + q^{96} + 6 q^{97} + 22 q^{98} + q^{99}+O(q^{100}) \) 4 * q + q^2 - q^3 - q^4 + q^6 - 2 * q^7 + q^8 - q^9 - 10 * q^10 - 4 * q^11 + 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 - q^22 + 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 + q^33 - 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 - 9 * q^44 + 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 + 30 * q^55 + 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 - 11 * q^66 - 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 + 2 * q^77 - 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 - q^88 + 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 + q^99

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