LMFDB - Embedded newform 546.2.l.l.295.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(211,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("546.211");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.l (of order $3$, degree $2$, 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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{17})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 5x^{2} + 4x + 16 $ x^4 - x^3 + 5x^2 + 4x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			295.2
Root			$-0.780776 - 1.35234i$ of defining polynomial
Character	$\chi$	$=$	546.295
Dual form			546.2.l.l.211.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +1.56155 q^{5} +(0.500000 + 0.866025i) q^{6} +(-0.500000 - 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +1.56155 q^{5} +(0.500000 + 0.866025i) q^{6} +(-0.500000 - 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.780776 + 1.35234i) q^{10} +(1.28078 - 2.21837i) q^{11} -1.00000 q^{12} +(-0.500000 - 3.57071i) q^{13} +1.00000 q^{14} +(0.780776 - 1.35234i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.0615528 - 0.106613i) q^{17} +1.00000 q^{18} +(1.28078 + 2.21837i) q^{19} +(-0.780776 - 1.35234i) q^{20} -1.00000 q^{21} +(1.28078 + 2.21837i) q^{22} +(0.561553 - 0.972638i) q^{23} +(0.500000 - 0.866025i) q^{24} -2.56155 q^{25} +(3.34233 + 1.35234i) q^{26} -1.00000 q^{27} +(-0.500000 + 0.866025i) q^{28} +(3.06155 - 5.30277i) q^{29} +(0.780776 + 1.35234i) q^{30} +(-0.500000 - 0.866025i) q^{32} +(-1.28078 - 2.21837i) q^{33} +0.123106 q^{34} +(-0.780776 - 1.35234i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(1.21922 - 2.11176i) q^{37} -2.56155 q^{38} +(-3.34233 - 1.35234i) q^{39} +1.56155 q^{40} +(5.62311 - 9.73950i) q^{41} +(0.500000 - 0.866025i) q^{42} +(4.00000 + 6.92820i) q^{43} -2.56155 q^{44} +(-0.780776 - 1.35234i) q^{45} +(0.561553 + 0.972638i) q^{46} -0.315342 q^{47} +(0.500000 + 0.866025i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(1.28078 - 2.21837i) q^{50} -0.123106 q^{51} +(-2.84233 + 2.21837i) q^{52} +7.00000 q^{53} +(0.500000 - 0.866025i) q^{54} +(2.00000 - 3.46410i) q^{55} +(-0.500000 - 0.866025i) q^{56} +2.56155 q^{57} +(3.06155 + 5.30277i) q^{58} +(-2.56155 - 4.43674i) q^{59} -1.56155 q^{60} +(5.62311 + 9.73950i) q^{61} +(-0.500000 + 0.866025i) q^{63} +1.00000 q^{64} +(-0.780776 - 5.57586i) q^{65} +2.56155 q^{66} +(-4.56155 + 7.90084i) q^{67} +(-0.0615528 + 0.106613i) q^{68} +(-0.561553 - 0.972638i) q^{69} +1.56155 q^{70} +(5.68466 + 9.84612i) q^{71} +(-0.500000 - 0.866025i) q^{72} -2.43845 q^{73} +(1.21922 + 2.11176i) q^{74} +(-1.28078 + 2.21837i) q^{75} +(1.28078 - 2.21837i) q^{76} -2.56155 q^{77} +(2.84233 - 2.21837i) q^{78} -6.56155 q^{79} +(-0.780776 + 1.35234i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(5.62311 + 9.73950i) q^{82} -5.12311 q^{83} +(0.500000 + 0.866025i) q^{84} +(-0.0961180 - 0.166481i) q^{85} -8.00000 q^{86} +(-3.06155 - 5.30277i) q^{87} +(1.28078 - 2.21837i) q^{88} +(-1.71922 + 2.97778i) q^{89} +1.56155 q^{90} +(-2.84233 + 2.21837i) q^{91} -1.12311 q^{92} +(0.157671 - 0.273094i) q^{94} +(2.00000 + 3.46410i) q^{95} -1.00000 q^{96} +(0.438447 + 0.759413i) q^{97} +(-0.500000 - 0.866025i) q^{98} -2.56155 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} + 4 q^{8} - 2 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 + 2 * q^6 - 2 * q^7 + 4 * q^8 - 2 * q^9	\( 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} + 4 q^{8} - 2 q^{9} + q^{10} + q^{11} - 4 q^{12} - 2 q^{13} + 4 q^{14} - q^{15} - 2 q^{16} + 8 q^{17} + 4 q^{18} + q^{19} + q^{20} - 4 q^{21} + q^{22} - 6 q^{23} + 2 q^{24} - 2 q^{25} + q^{26} - 4 q^{27} - 2 q^{28} + 4 q^{29} - q^{30} - 2 q^{32} - q^{33} - 16 q^{34} + q^{35} - 2 q^{36} + 9 q^{37} - 2 q^{38} - q^{39} - 2 q^{40} + 6 q^{41} + 2 q^{42} + 16 q^{43} - 2 q^{44} + q^{45} - 6 q^{46} - 26 q^{47} + 2 q^{48} - 2 q^{49} + q^{50} + 16 q^{51} + q^{52} + 28 q^{53} + 2 q^{54} + 8 q^{55} - 2 q^{56} + 2 q^{57} + 4 q^{58} - 2 q^{59} + 2 q^{60} + 6 q^{61} - 2 q^{63} + 4 q^{64} + q^{65} + 2 q^{66} - 10 q^{67} + 8 q^{68} + 6 q^{69} - 2 q^{70} - 2 q^{71} - 2 q^{72} - 18 q^{73} + 9 q^{74} - q^{75} + q^{76} - 2 q^{77} - q^{78} - 18 q^{79} + q^{80} - 2 q^{81} + 6 q^{82} - 4 q^{83} + 2 q^{84} - 21 q^{85} - 32 q^{86} - 4 q^{87} + q^{88} - 11 q^{89} - 2 q^{90} + q^{91} + 12 q^{92} + 13 q^{94} + 8 q^{95} - 4 q^{96} + 10 q^{97} - 2 q^{98} - 2 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 + 2 * q^6 - 2 * q^7 + 4 * q^8 - 2 * q^9 + q^10 + q^11 - 4 * q^12 - 2 * q^13 + 4 * q^14 - q^15 - 2 * q^16 + 8 * q^17 + 4 * q^18 + q^19 + q^20 - 4 * q^21 + q^22 - 6 * q^23 + 2 * q^24 - 2 * q^25 + q^26 - 4 * q^27 - 2 * q^28 + 4 * q^29 - q^30 - 2 * q^32 - q^33 - 16 * q^34 + q^35 - 2 * q^36 + 9 * q^37 - 2 * q^38 - q^39 - 2 * q^40 + 6 * q^41 + 2 * q^42 + 16 * q^43 - 2 * q^44 + q^45 - 6 * q^46 - 26 * q^47 + 2 * q^48 - 2 * q^49 + q^50 + 16 * q^51 + q^52 + 28 * q^53 + 2 * q^54 + 8 * q^55 - 2 * q^56 + 2 * q^57 + 4 * q^58 - 2 * q^59 + 2 * q^60 + 6 * q^61 - 2 * q^63 + 4 * q^64 + q^65 + 2 * q^66 - 10 * q^67 + 8 * q^68 + 6 * q^69 - 2 * q^70 - 2 * q^71 - 2 * q^72 - 18 * q^73 + 9 * q^74 - q^75 + q^76 - 2 * q^77 - q^78 - 18 * q^79 + q^80 - 2 * q^81 + 6 * q^82 - 4 * q^83 + 2 * q^84 - 21 * q^85 - 32 * q^86 - 4 * q^87 + q^88 - 11 * q^89 - 2 * q^90 + q^91 + 12 * q^92 + 13 * q^94 + 8 * q^95 - 4 * q^96 + 10 * q^97 - 2 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	1.56155			0.698348			0.349174	−	0.937058i	$-0.386462\pi$
$5$	1.56155			0.698348			0.349174	+	0.937058i	$0.386462\pi$
$6$	0.500000	+	0.866025i	0.204124	+	0.353553i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$8$	1.00000			0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−0.780776	+	1.35234i	−0.246903	+	0.427649i
$11$	1.28078	−	2.21837i	0.386169	−	0.668864i	−0.605762	−	0.795646i	$-0.707132\pi$
$11$	1.28078	−	2.21837i	0.386169	−	0.668864i	0.991931	+	0.126782i	$0.0404650\pi$
$12$	−1.00000			−0.288675
$13$	−0.500000	−	3.57071i	−0.138675	−	0.990338i
$13$	−0.500000	−	3.57071i	−0.138675	−	0.990338i
$14$	1.00000			0.267261
$15$	0.780776	−	1.35234i	0.201596	−	0.349174i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−0.0615528	−	0.106613i	−0.0149287	−	0.0258574i	0.858465	−	0.512873i	$-0.171419\pi$
$17$	−0.0615528	−	0.106613i	−0.0149287	−	0.0258574i	−0.873393	+	0.487016i	$0.838085\pi$
$18$	1.00000			0.235702
$19$	1.28078	+	2.21837i	0.293830	+	0.508929i	0.974712	−	0.223464i	$-0.0717366\pi$
$19$	1.28078	+	2.21837i	0.293830	+	0.508929i	−0.680882	+	0.732393i	$0.738403\pi$
$20$	−0.780776	−	1.35234i	−0.174587	−	0.302393i
$21$	−1.00000			−0.218218
$22$	1.28078	+	2.21837i	0.273062	+	0.472958i
$23$	0.561553	−	0.972638i	0.117092	−	0.202809i	−0.801522	−	0.597965i	$-0.795976\pi$
$23$	0.561553	−	0.972638i	0.117092	−	0.202809i	0.918614	+	0.395156i	$0.129309\pi$
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$	−2.56155			−0.512311
$26$	3.34233	+	1.35234i	0.655485	+	0.265217i
$27$	−1.00000			−0.192450
$28$	−0.500000	+	0.866025i	−0.0944911	+	0.163663i
$29$	3.06155	−	5.30277i	0.568516	−	0.984699i	−0.428197	−	0.903685i	$-0.640851\pi$
$29$	3.06155	−	5.30277i	0.568516	−	0.984699i	0.996713	−	0.0810133i	$-0.0258156\pi$
$30$	0.780776	+	1.35234i	0.142550	+	0.246903i
$31$		0			0			−	1.00000i	$-0.5\pi$
$31$		0			0				1.00000i	$0.5\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−1.28078	−	2.21837i	−0.222955	−	0.386169i
$34$	0.123106			0.0211124
$35$	−0.780776	−	1.35234i	−0.131975	−	0.228588i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	1.21922	−	2.11176i	0.200439	−	0.347171i	−0.748231	−	0.663438i	$-0.769096\pi$
$37$	1.21922	−	2.11176i	0.200439	−	0.347171i	0.948670	+	0.316268i	$0.102430\pi$
$38$	−2.56155			−0.415539
$39$	−3.34233	−	1.35234i	−0.535201	−	0.216548i
$40$	1.56155			0.246903
$41$	5.62311	−	9.73950i	0.878182	−	1.52106i	0.0248471	−	0.999691i	$-0.492090\pi$
$41$	5.62311	−	9.73950i	0.878182	−	1.52106i	0.853335	−	0.521364i	$-0.174577\pi$
$42$	0.500000	−	0.866025i	0.0771517	−	0.133631i
$43$	4.00000	+	6.92820i	0.609994	+	1.05654i	0.991241	+	0.132068i	$0.0421616\pi$
$43$	4.00000	+	6.92820i	0.609994	+	1.05654i	−0.381246	+	0.924473i	$0.624505\pi$
$44$	−2.56155			−0.386169
$45$	−0.780776	−	1.35234i	−0.116391	−	0.201596i
$46$	0.561553	+	0.972638i	0.0827964	+	0.143408i
$47$	−0.315342			−0.0459973			−0.0229986	−	0.999735i	$-0.507321\pi$
$47$	−0.315342			−0.0459973			−0.0229986	+	0.999735i	$0.507321\pi$
$48$	0.500000	+	0.866025i	0.0721688	+	0.125000i
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	1.28078	−	2.21837i	0.181129	−	0.313725i
$51$	−0.123106			−0.0172382
$52$	−2.84233	+	2.21837i	−0.394160	+	0.307633i
$53$	7.00000			0.961524			0.480762	−	0.876851i	$-0.340360\pi$
$53$	7.00000			0.961524			0.480762	+	0.876851i	$0.340360\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$	2.00000	−	3.46410i	0.269680	−	0.467099i
$56$	−0.500000	−	0.866025i	−0.0668153	−	0.115728i
$57$	2.56155			0.339286
$58$	3.06155	+	5.30277i	0.402002	+	0.696287i
$59$	−2.56155	−	4.43674i	−0.333486	−	0.577614i	0.649707	−	0.760185i	$-0.274892\pi$
$59$	−2.56155	−	4.43674i	−0.333486	−	0.577614i	−0.983193	+	0.182570i	$0.941558\pi$
$60$	−1.56155			−0.201596
$61$	5.62311	+	9.73950i	0.719965	+	1.24702i	0.961013	+	0.276503i	$0.0891755\pi$
$61$	5.62311	+	9.73950i	0.719965	+	1.24702i	−0.241048	+	0.970513i	$0.577491\pi$
$62$		0			0
$63$	−0.500000	+	0.866025i	−0.0629941	+	0.109109i
$64$	1.00000			0.125000
$65$	−0.780776	−	5.57586i	−0.0968434	−	0.691600i
$66$	2.56155			0.315305
$67$	−4.56155	+	7.90084i	−0.557282	+	0.965241i	0.440440	+	0.897782i	$0.354823\pi$
$67$	−4.56155	+	7.90084i	−0.557282	+	0.965241i	−0.997722	+	0.0674592i	$0.978511\pi$
$68$	−0.0615528	+	0.106613i	−0.00746437	+	0.0129287i
$69$	−0.561553	−	0.972638i	−0.0676030	−	0.117092i
$70$	1.56155			0.186641
$71$	5.68466	+	9.84612i	0.674645	+	1.16852i	0.976573	+	0.215188i	$0.0690365\pi$
$71$	5.68466	+	9.84612i	0.674645	+	1.16852i	−0.301928	+	0.953331i	$0.597630\pi$
$72$	−0.500000	−	0.866025i	−0.0589256	−	0.102062i
$73$	−2.43845			−0.285399			−0.142699	−	0.989766i	$-0.545578\pi$
$73$	−2.43845			−0.285399			−0.142699	+	0.989766i	$0.545578\pi$
$74$	1.21922	+	2.11176i	0.141732	+	0.245487i
$75$	−1.28078	+	2.21837i	−0.147891	+	0.256155i
$76$	1.28078	−	2.21837i	0.146915	−	0.254464i
$77$	−2.56155			−0.291916
$78$	2.84233	−	2.21837i	0.321830	−	0.251181i
$79$	−6.56155			−0.738232			−0.369116	−	0.929383i	$-0.620340\pi$
$79$	−6.56155			−0.738232			−0.369116	+	0.929383i	$0.620340\pi$
$80$	−0.780776	+	1.35234i	−0.0872935	+	0.151197i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	5.62311	+	9.73950i	0.620968	+	1.07555i
$83$	−5.12311			−0.562334			−0.281167	−	0.959659i	$-0.590721\pi$
$83$	−5.12311			−0.562334			−0.281167	+	0.959659i	$0.590721\pi$
$84$	0.500000	+	0.866025i	0.0545545	+	0.0944911i
$85$	−0.0961180	−	0.166481i	−0.0104255	−	0.0180574i
$86$	−8.00000			−0.862662
$87$	−3.06155	−	5.30277i	−0.328233	−	0.568516i
$88$	1.28078	−	2.21837i	0.136531	−	0.236479i
$89$	−1.71922	+	2.97778i	−0.182237	+	0.315644i	−0.942642	−	0.333805i	$-0.891667\pi$
$89$	−1.71922	+	2.97778i	−0.182237	+	0.315644i	0.760405	+	0.649449i	$0.225001\pi$
$90$	1.56155			0.164602
$91$	−2.84233	+	2.21837i	−0.297957	+	0.232548i
$92$	−1.12311			−0.117092
$93$		0			0
$94$	0.157671	−	0.273094i	0.0162625	−	0.0281675i
$95$	2.00000	+	3.46410i	0.205196	+	0.355409i
$96$	−1.00000			−0.102062
$97$	0.438447	+	0.759413i	0.0445176	+	0.0771067i	0.887426	−	0.460951i	$-0.152492\pi$
$97$	0.438447	+	0.759413i	0.0445176	+	0.0771067i	−0.842908	+	0.538058i	$0.819158\pi$
$98$	−0.500000	−	0.866025i	−0.0505076	−	0.0874818i
$99$	−2.56155			−0.257446
$100$	1.28078	+	2.21837i	0.128078	+	0.221837i
$101$	2.90388	−	5.02967i	0.288947	−	0.500471i	−0.684612	−	0.728908i	$-0.740028\pi$
$101$	2.90388	−	5.02967i	0.288947	−	0.500471i	0.973559	+	0.228437i	$0.0733615\pi$
$102$	0.0615528	−	0.106613i	0.00609464	−	0.0105562i
$103$	6.24621			0.615457			0.307729	−	0.951474i	$-0.400431\pi$
$103$	6.24621			0.615457			0.307729	+	0.951474i	$0.400431\pi$
$104$	−0.500000	−	3.57071i	−0.0490290	−	0.350137i
$105$	−1.56155			−0.152392
$106$	−3.50000	+	6.06218i	−0.339950	+	0.588811i
$107$	−6.96543	+	12.0645i	−0.673374	+	1.16632i	0.303567	+	0.952810i	$0.401822\pi$
$107$	−6.96543	+	12.0645i	−0.673374	+	1.16632i	−0.976941	+	0.213508i	$0.931511\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$	−12.2462			−1.17297			−0.586487	−	0.809959i	$-0.699490\pi$
$109$	−12.2462			−1.17297			−0.586487	+	0.809959i	$0.699490\pi$
$110$	2.00000	+	3.46410i	0.190693	+	0.330289i
$111$	−1.21922	−	2.11176i	−0.115724	−	0.200439i
$112$	1.00000			0.0944911
$113$	−0.780776	−	1.35234i	−0.0734493	−	0.127218i	0.826962	−	0.562258i	$-0.190067\pi$
$113$	−0.780776	−	1.35234i	−0.0734493	−	0.127218i	−0.900411	+	0.435041i	$0.856734\pi$
$114$	−1.28078	+	2.21837i	−0.119956	+	0.207769i
$115$	0.876894	−	1.51883i	0.0817708	−	0.141631i
$116$	−6.12311			−0.568516
$117$	−2.84233	+	2.21837i	−0.262773	+	0.205088i
$118$	5.12311			0.471620
$119$	−0.0615528	+	0.106613i	−0.00564254	+	0.00977316i
$120$	0.780776	−	1.35234i	0.0712748	−	0.123452i
$121$	2.21922	+	3.84381i	0.201748	+	0.349437i
$122$	−11.2462			−1.01818
$123$	−5.62311	−	9.73950i	−0.507018	−	0.878182i
$124$		0			0
$125$	−11.8078			−1.05612
$126$	−0.500000	−	0.866025i	−0.0445435	−	0.0771517i
$127$	−6.24621	+	10.8188i	−0.554262	+	0.960009i	0.443699	+	0.896176i	$0.353666\pi$
$127$	−6.24621	+	10.8188i	−0.554262	+	0.960009i	−0.997961	+	0.0638334i	$0.979667\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	8.00000			0.704361
$130$	5.21922	+	2.11176i	0.457756	+	0.185213i
$131$	14.2462			1.24470			0.622349	−	0.782740i	$-0.286179\pi$
$131$	14.2462			1.24470			0.622349	+	0.782740i	$0.286179\pi$
$132$	−1.28078	+	2.21837i	−0.111477	+	0.193084i
$133$	1.28078	−	2.21837i	0.111057	−	0.192357i
$134$	−4.56155	−	7.90084i	−0.394058	−	0.682529i
$135$	−1.56155			−0.134397
$136$	−0.0615528	−	0.106613i	−0.00527811	−	0.00914195i
$137$	−6.21922	−	10.7720i	−0.531344	−	0.920315i	−0.999331	−	0.0365795i	$-0.988354\pi$
$137$	−6.21922	−	10.7720i	−0.531344	−	0.920315i	0.467987	−	0.883736i	$-0.344980\pi$
$138$	1.12311			0.0956051
$139$	2.71922	+	4.70983i	0.230642	+	0.399483i	0.957997	−	0.286778i	$-0.0925842\pi$
$139$	2.71922	+	4.70983i	0.230642	+	0.399483i	−0.727356	+	0.686261i	$0.759251\pi$
$140$	−0.780776	+	1.35234i	−0.0659877	+	0.114294i
$141$	−0.157671	+	0.273094i	−0.0132783	+	0.0229986i
$142$	−11.3693			−0.954092
$143$	−8.56155	−	3.46410i	−0.715953	−	0.289683i
$144$	1.00000			0.0833333
$145$	4.78078	−	8.28055i	0.397022	−	0.687662i
$146$	1.21922	−	2.11176i	0.100904	−	0.174770i
$147$	0.500000	+	0.866025i	0.0412393	+	0.0714286i
$148$	−2.43845			−0.200439
$149$	7.78078	+	13.4767i	0.637426	+	1.10405i	0.985996	+	0.166771i	$0.0533342\pi$
$149$	7.78078	+	13.4767i	0.637426	+	1.10405i	−0.348570	+	0.937283i	$0.613332\pi$
$150$	−1.28078	−	2.21837i	−0.104575	−	0.181129i
$151$	−21.9309			−1.78471			−0.892354	−	0.451335i	$-0.850948\pi$
$151$	−21.9309			−1.78471			−0.892354	+	0.451335i	$0.850948\pi$
$152$	1.28078	+	2.21837i	0.103885	+	0.179934i
$153$	−0.0615528	+	0.106613i	−0.00497625	+	0.00861912i
$154$	1.28078	−	2.21837i	0.103208	−	0.178761i
$155$		0			0
$156$	0.500000	+	3.57071i	0.0400320	+	0.285886i
$157$	−1.31534			−0.104976			−0.0524878	−	0.998622i	$-0.516715\pi$
$157$	−1.31534			−0.104976			−0.0524878	+	0.998622i	$0.516715\pi$
$158$	3.28078	−	5.68247i	0.261005	−	0.452073i
$159$	3.50000	−	6.06218i	0.277568	−	0.480762i
$160$	−0.780776	−	1.35234i	−0.0617258	−	0.106912i
$161$	−1.12311			−0.0885131
$162$	−0.500000	−	0.866025i	−0.0392837	−	0.0680414i
$163$	−12.2462	−	21.2111i	−0.959197	−	1.66138i	−0.724457	−	0.689320i	$-0.757909\pi$
$163$	−12.2462	−	21.2111i	−0.959197	−	1.66138i	−0.234741	−	0.972058i	$-0.575424\pi$
$164$	−11.2462			−0.878182
$165$	−2.00000	−	3.46410i	−0.155700	−	0.269680i
$166$	2.56155	−	4.43674i	0.198815	−	0.344358i
$167$	−6.24621	+	10.8188i	−0.483346	+	0.837180i	−0.999817	−	0.0191244i	$-0.993912\pi$
$167$	−6.24621	+	10.8188i	−0.483346	+	0.837180i	0.516471	+	0.856305i	$0.327245\pi$
$168$	−1.00000			−0.0771517
$169$	−12.5000	+	3.57071i	−0.961538	+	0.274670i
$170$	0.192236			0.0147438
$171$	1.28078	−	2.21837i	0.0979434	−	0.169643i
$172$	4.00000	−	6.92820i	0.304997	−	0.528271i
$173$	9.00000	+	15.5885i	0.684257	+	1.18517i	0.973670	+	0.227964i	$0.0732068\pi$
$173$	9.00000	+	15.5885i	0.684257	+	1.18517i	−0.289412	+	0.957205i	$0.593460\pi$
$174$	6.12311			0.464191
$175$	1.28078	+	2.21837i	0.0968176	+	0.167693i
$176$	1.28078	+	2.21837i	0.0965422	+	0.167216i
$177$	−5.12311			−0.385076
$178$	−1.71922	−	2.97778i	−0.128861	−	0.223194i
$179$	0.876894	−	1.51883i	0.0655422	−	0.113522i	−0.831392	−	0.555686i	$-0.812456\pi$
$179$	0.876894	−	1.51883i	0.0655422	−	0.113522i	0.896934	+	0.442164i	$0.145789\pi$
$180$	−0.780776	+	1.35234i	−0.0581956	+	0.100798i
$181$	13.2462			0.984583			0.492292	−	0.870430i	$-0.336159\pi$
$181$	13.2462			0.984583			0.492292	+	0.870430i	$0.336159\pi$
$182$	−0.500000	−	3.57071i	−0.0370625	−	0.264679i
$183$	11.2462			0.831344
$184$	0.561553	−	0.972638i	0.0413982	−	0.0717038i
$185$	1.90388	−	3.29762i	0.139976	−	0.242446i
$186$		0			0
$187$	−0.315342			−0.0230601
$188$	0.157671	+	0.273094i	0.0114993	+	0.0199174i
$189$	0.500000	+	0.866025i	0.0363696	+	0.0629941i
$190$	−4.00000			−0.290191
$191$	2.56155	+	4.43674i	0.185347	+	0.321031i	0.943694	−	0.330821i	$-0.107326\pi$
$191$	2.56155	+	4.43674i	0.185347	+	0.321031i	−0.758346	+	0.651852i	$0.773992\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	−0.0615528	+	0.106613i	−0.00443067	+	0.00767414i	−0.868232	−	0.496158i	$-0.834744\pi$
$193$	−0.0615528	+	0.106613i	−0.00443067	+	0.00767414i	0.863802	+	0.503832i	$0.168077\pi$
$194$	−0.876894			−0.0629573
$195$	−5.21922	−	2.11176i	−0.373756	−	0.151226i
$196$	1.00000			0.0714286
$197$	−6.28078	+	10.8786i	−0.447487	+	0.775070i	−0.998222	−	0.0596103i	$-0.981014\pi$
$197$	−6.28078	+	10.8786i	−0.447487	+	0.775070i	0.550735	+	0.834680i	$0.314348\pi$
$198$	1.28078	−	2.21837i	0.0910208	−	0.157653i
$199$	8.00000	+	13.8564i	0.567105	+	0.982255i	0.996850	+	0.0793045i	$0.0252700\pi$
$199$	8.00000	+	13.8564i	0.567105	+	0.982255i	−0.429745	+	0.902950i	$0.641397\pi$
$200$	−2.56155			−0.181129
$201$	4.56155	+	7.90084i	0.321747	+	0.557282i
$202$	2.90388	+	5.02967i	0.204316	+	0.353886i
$203$	−6.12311			−0.429758
$204$	0.0615528	+	0.106613i	0.00430956	+	0.00746437i
$205$	8.78078	−	15.2088i	0.613276	−	1.06223i
$206$	−3.12311	+	5.40938i	−0.217597	+	0.376889i
$207$	−1.12311			−0.0780612
$208$	3.34233	+	1.35234i	0.231749	+	0.0937682i
$209$	6.56155			0.453872
$210$	0.780776	−	1.35234i	0.0538787	−	0.0933206i
$211$	−2.56155	+	4.43674i	−0.176345	+	0.305438i	−0.940626	−	0.339445i	$-0.889761\pi$
$211$	−2.56155	+	4.43674i	−0.176345	+	0.305438i	0.764281	+	0.644883i	$0.223094\pi$
$212$	−3.50000	−	6.06218i	−0.240381	−	0.416352i
$213$	11.3693			0.779013
$214$	−6.96543	−	12.0645i	−0.476147	−	0.824711i
$215$	6.24621	+	10.8188i	0.425988	+	0.737833i
$216$	−1.00000			−0.0680414
$217$		0			0
$218$	6.12311	−	10.6055i	0.414709	−	0.718297i
$219$	−1.21922	+	2.11176i	−0.0823875	+	0.142699i
$220$	−4.00000			−0.269680
$221$	−0.349907	+	0.273094i	−0.0235373	+	0.0183703i
$222$	2.43845			0.163658
$223$	−4.87689	+	8.44703i	−0.326581	+	0.565655i	−0.981831	−	0.189757i	$-0.939230\pi$
$223$	−4.87689	+	8.44703i	−0.326581	+	0.565655i	0.655250	+	0.755412i	$0.272563\pi$
$224$	−0.500000	+	0.866025i	−0.0334077	+	0.0578638i
$225$	1.28078	+	2.21837i	0.0853851	+	0.147891i
$226$	1.56155			0.103873
$227$	5.43845	+	9.41967i	0.360962	+	0.625205i	0.988119	−	0.153688i	$-0.0491149\pi$
$227$	5.43845	+	9.41967i	0.360962	+	0.625205i	−0.627157	+	0.778893i	$0.715782\pi$
$228$	−1.28078	−	2.21837i	−0.0848215	−	0.146915i
$229$	17.0540			1.12696			0.563479	−	0.826130i	$-0.309462\pi$
$229$	17.0540			1.12696			0.563479	+	0.826130i	$0.309462\pi$
$230$	0.876894	+	1.51883i	0.0578207	+	0.100148i
$231$	−1.28078	+	2.21837i	−0.0842689	+	0.145958i
$232$	3.06155	−	5.30277i	0.201001	−	0.348144i
$233$	1.36932			0.0897069			0.0448535	−	0.998994i	$-0.485718\pi$
$233$	1.36932			0.0897069			0.0448535	+	0.998994i	$0.485718\pi$
$234$	−0.500000	−	3.57071i	−0.0326860	−	0.233425i
$235$	−0.492423			−0.0321221
$236$	−2.56155	+	4.43674i	−0.166743	+	0.288807i
$237$	−3.28078	+	5.68247i	−0.213109	+	0.369116i
$238$	−0.0615528	−	0.106613i	−0.00398988	−	0.00691067i
$239$	19.3693			1.25290			0.626448	−	0.779463i	$-0.284508\pi$
$239$	19.3693			1.25290			0.626448	+	0.779463i	$0.284508\pi$
$240$	0.780776	+	1.35234i	0.0503989	+	0.0872935i
$241$	0.0961180	+	0.166481i	0.00619150	+	0.0107240i	0.869105	−	0.494628i	$-0.164696\pi$
$241$	0.0961180	+	0.166481i	0.00619150	+	0.0107240i	−0.862913	+	0.505352i	$0.831363\pi$
$242$	−4.43845			−0.285314
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	5.62311	−	9.73950i	0.359982	−	0.623508i
$245$	−0.780776	+	1.35234i	−0.0498820	+	0.0863981i
$246$	11.2462			0.717032
$247$	7.28078	−	5.68247i	0.463265	−	0.361567i
$248$		0			0
$249$	−2.56155	+	4.43674i	−0.162332	+	0.281167i
$250$	5.90388	−	10.2258i	0.373394	−	0.646738i
$251$	6.80776	+	11.7914i	0.429702	+	0.744266i	0.996847	−	0.0793522i	$-0.0252852\pi$
$251$	6.80776	+	11.7914i	0.429702	+	0.744266i	−0.567144	+	0.823618i	$0.691952\pi$
$252$	1.00000			0.0629941
$253$	−1.43845	−	2.49146i	−0.0904344	−	0.156637i
$254$	−6.24621	−	10.8188i	−0.391922	−	0.678829i
$255$	−0.192236			−0.0120383
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	12.1847	−	21.1044i	0.760058	−	1.31646i	−0.182762	−	0.983157i	$-0.558504\pi$
$257$	12.1847	−	21.1044i	0.760058	−	1.31646i	0.942820	−	0.333302i	$-0.108163\pi$
$258$	−4.00000	+	6.92820i	−0.249029	+	0.431331i
$259$	−2.43845			−0.151518
$260$	−4.43845	+	3.46410i	−0.275261	+	0.214834i
$261$	−6.12311			−0.379011
$262$	−7.12311	+	12.3376i	−0.440067	+	0.762218i
$263$	−2.56155	+	4.43674i	−0.157952	+	0.273581i	−0.934130	−	0.356933i	$-0.883822\pi$
$263$	−2.56155	+	4.43674i	−0.157952	+	0.273581i	0.776178	+	0.630514i	$0.217156\pi$
$264$	−1.28078	−	2.21837i	−0.0788263	−	0.136531i
$265$	10.9309			0.671478
$266$	1.28078	+	2.21837i	0.0785294	+	0.136017i
$267$	1.71922	+	2.97778i	0.105215	+	0.182237i
$268$	9.12311			0.557282
$269$	−13.5616	−	23.4893i	−0.826862	−	1.43217i	−0.900488	−	0.434882i	$-0.856790\pi$
$269$	−13.5616	−	23.4893i	−0.826862	−	1.43217i	0.0736251	−	0.997286i	$-0.476543\pi$
$270$	0.780776	−	1.35234i	0.0475165	−	0.0823011i
$271$	11.3693	−	19.6922i	0.690637	−	1.19622i	−0.280993	−	0.959710i	$-0.590664\pi$
$271$	11.3693	−	19.6922i	0.690637	−	1.19622i	0.971630	−	0.236508i	$-0.0760030\pi$
$272$	0.123106			0.00746437
$273$	0.500000	+	3.57071i	0.0302614	+	0.216109i
$274$	12.4384			0.751434
$275$	−3.28078	+	5.68247i	−0.197838	+	0.342666i
$276$	−0.561553	+	0.972638i	−0.0338015	+	0.0585459i
$277$	9.78078	+	16.9408i	0.587670	+	1.01787i	0.994537	+	0.104387i	$0.0332879\pi$
$277$	9.78078	+	16.9408i	0.587670	+	1.01787i	−0.406867	+	0.913487i	$0.633379\pi$
$278$	−5.43845			−0.326176
$279$		0			0
$280$	−0.780776	−	1.35234i	−0.0466603	−	0.0808180i
$281$	12.9309			0.771391			0.385696	−	0.922626i	$-0.373962\pi$
$281$	12.9309			0.771391			0.385696	+	0.922626i	$0.373962\pi$
$282$	−0.157671	−	0.273094i	−0.00938916	−	0.0162625i
$283$	10.0000	−	17.3205i	0.594438	−	1.02960i	−0.399188	−	0.916869i	$-0.630708\pi$
$283$	10.0000	−	17.3205i	0.594438	−	1.02960i	0.993626	−	0.112728i	$-0.0359589\pi$
$284$	5.68466	−	9.84612i	0.337322	−	0.584260i
$285$	4.00000			0.236940
$286$	7.28078	−	5.68247i	0.430521	−	0.336012i
$287$	−11.2462			−0.663843
$288$	−0.500000	+	0.866025i	−0.0294628	+	0.0510310i
$289$	8.49242	−	14.7093i	0.499554	−	0.865253i
$290$	4.78078	+	8.28055i	0.280737	+	0.486251i
$291$	0.876894			0.0514045
$292$	1.21922	+	2.11176i	0.0713497	+	0.123581i
$293$	3.46543	+	6.00231i	0.202453	+	0.350659i	0.949318	−	0.314317i	$-0.101775\pi$
$293$	3.46543	+	6.00231i	0.202453	+	0.350659i	−0.746865	+	0.664975i	$0.768442\pi$
$294$	−1.00000			−0.0583212
$295$	−4.00000	−	6.92820i	−0.232889	−	0.403376i
$296$	1.21922	−	2.11176i	0.0708659	−	0.122743i
$297$	−1.28078	+	2.21837i	−0.0743182	+	0.128723i
$298$	−15.5616			−0.901457
$299$	−3.75379	−	1.51883i	−0.217087	−	0.0878360i
$300$	2.56155			0.147891
$301$	4.00000	−	6.92820i	0.230556	−	0.399335i
$302$	10.9654	−	18.9927i	0.630990	−	1.09291i
$303$	−2.90388	−	5.02967i	−0.166824	−	0.288947i
$304$	−2.56155			−0.146915
$305$	8.78078	+	15.2088i	0.502786	+	0.870851i
$306$	−0.0615528	−	0.106613i	−0.00351874	−	0.00609464i
$307$	−9.93087			−0.566785			−0.283392	−	0.959004i	$-0.591460\pi$
$307$	−9.93087			−0.566785			−0.283392	+	0.959004i	$0.591460\pi$
$308$	1.28078	+	2.21837i	0.0729790	+	0.126403i
$309$	3.12311	−	5.40938i	0.177667	−	0.307729i
$310$		0			0
$311$	21.9309			1.24359			0.621793	−	0.783182i	$-0.286405\pi$
$311$	21.9309			1.24359			0.621793	+	0.783182i	$0.286405\pi$
$312$	−3.34233	−	1.35234i	−0.189222	−	0.0765614i
$313$	−6.00000			−0.339140			−0.169570	−	0.985518i	$-0.554238\pi$
$313$	−6.00000			−0.339140			−0.169570	+	0.985518i	$0.554238\pi$
$314$	0.657671	−	1.13912i	0.0371145	−	0.0642842i
$315$	−0.780776	+	1.35234i	−0.0439918	+	0.0761960i
$316$	3.28078	+	5.68247i	0.184558	+	0.319664i
$317$	12.4384			0.698613			0.349306	−	0.937009i	$-0.386417\pi$
$317$	12.4384			0.698613			0.349306	+	0.937009i	$0.386417\pi$
$318$	3.50000	+	6.06218i	0.196270	+	0.339950i
$319$	−7.84233	−	13.5833i	−0.439086	−	0.760520i
$320$	1.56155			0.0872935
$321$	6.96543	+	12.0645i	0.388773	+	0.673374i
$322$	0.561553	−	0.972638i	0.0312941	−	0.0542030i
$323$	0.157671	−	0.273094i	0.00877304	−	0.0151953i
$324$	1.00000			0.0555556
$325$	1.28078	+	9.14657i	0.0710447	+	0.507361i
$326$	24.4924			1.35651
$327$	−6.12311	+	10.6055i	−0.338609	+	0.586487i
$328$	5.62311	−	9.73950i	0.310484	−	0.537774i
$329$	0.157671	+	0.273094i	0.00869267	+	0.0150561i
$330$	4.00000			0.220193
$331$	−9.68466	−	16.7743i	−0.532317	−	0.922000i	−0.999288	−	0.0377275i	$-0.987988\pi$
$331$	−9.68466	−	16.7743i	−0.532317	−	0.922000i	0.466971	−	0.884273i	$-0.345345\pi$
$332$	2.56155	+	4.43674i	0.140583	+	0.243498i
$333$	−2.43845			−0.133626
$334$	−6.24621	−	10.8188i	−0.341777	−	0.591976i
$335$	−7.12311	+	12.3376i	−0.389177	+	0.674074i
$336$	0.500000	−	0.866025i	0.0272772	−	0.0472456i
$337$	−13.4924			−0.734979			−0.367490	−	0.930028i	$-0.619783\pi$
$337$	−13.4924			−0.734979			−0.367490	+	0.930028i	$0.619783\pi$
$338$	3.15767	−	12.6107i	0.171755	−	0.685930i
$339$	−1.56155			−0.0848119
$340$	−0.0961180	+	0.166481i	−0.00521273	+	0.00902871i
$341$		0			0
$342$	1.28078	+	2.21837i	0.0692565	+	0.119956i
$343$	1.00000			0.0539949
$344$	4.00000	+	6.92820i	0.215666	+	0.373544i
$345$	−0.876894	−	1.51883i	−0.0472104	−	0.0817708i
$346$	−18.0000			−0.967686
$347$	−7.52699	−	13.0371i	−0.404070	−	0.699870i	0.590143	−	0.807299i	$-0.299071\pi$
$347$	−7.52699	−	13.0371i	−0.404070	−	0.699870i	−0.994213	+	0.107429i	$0.965738\pi$
$348$	−3.06155	+	5.30277i	−0.164116	+	0.284258i
$349$	9.00000	−	15.5885i	0.481759	−	0.834431i	−0.518022	−	0.855367i	$-0.673331\pi$
$349$	9.00000	−	15.5885i	0.481759	−	0.834431i	0.999781	+	0.0209364i	$0.00666475\pi$
$350$	−2.56155			−0.136921
$351$	0.500000	+	3.57071i	0.0266880	+	0.190591i
$352$	−2.56155			−0.136531
$353$	16.9039	−	29.2784i	0.899703	−	1.55833i	0.0718288	−	0.997417i	$-0.477116\pi$
$353$	16.9039	−	29.2784i	0.899703	−	1.55833i	0.827874	−	0.560914i	$-0.189550\pi$
$354$	2.56155	−	4.43674i	0.136145	−	0.235810i
$355$	8.87689	+	15.3752i	0.471137	+	0.816033i
$356$	3.43845			0.182237
$357$	0.0615528	+	0.106613i	0.00325772	+	0.00564254i
$358$	0.876894	+	1.51883i	0.0463453	+	0.0802724i
$359$	−1.75379			−0.0925614			−0.0462807	−	0.998928i	$-0.514737\pi$
$359$	−1.75379			−0.0925614			−0.0462807	+	0.998928i	$0.514737\pi$
$360$	−0.780776	−	1.35234i	−0.0411505	−	0.0712748i
$361$	6.21922	−	10.7720i	0.327328	−	0.566948i
$362$	−6.62311	+	11.4716i	−0.348103	+	0.602932i
$363$	4.43845			0.232958
$364$	3.34233	+	1.35234i	0.175186	+	0.0708821i
$365$	−3.80776			−0.199307
$366$	−5.62311	+	9.73950i	−0.293924	+	0.509092i
$367$	−6.80776	+	11.7914i	−0.355362	+	0.615506i	−0.987180	−	0.159611i	$-0.948976\pi$
$367$	−6.80776	+	11.7914i	−0.355362	+	0.615506i	0.631818	+	0.775117i	$0.282309\pi$
$368$	0.561553	+	0.972638i	0.0292730	+	0.0507023i
$369$	−11.2462			−0.585454
$370$	1.90388	+	3.29762i	0.0989781	+	0.171435i
$371$	−3.50000	−	6.06218i	−0.181711	−	0.314733i
$372$		0			0
$373$	1.53457	+	2.65794i	0.0794568	+	0.137623i	0.903016	−	0.429608i	$-0.141348\pi$
$373$	1.53457	+	2.65794i	0.0794568	+	0.137623i	−0.823559	+	0.567231i	$0.808015\pi$
$374$	0.157671	−	0.273094i	0.00815296	−	0.0141213i
$375$	−5.90388	+	10.2258i	−0.304875	+	0.528059i
$376$	−0.315342			−0.0162625
$377$	−20.4654	−	8.28055i	−1.05402	−	0.426470i
$378$	−1.00000			−0.0514344
$379$	−18.8078	+	32.5760i	−0.966090	+	1.67332i	−0.259432	+	0.965761i	$0.583535\pi$
$379$	−18.8078	+	32.5760i	−0.966090	+	1.67332i	−0.706658	+	0.707556i	$0.749798\pi$
$380$	2.00000	−	3.46410i	0.102598	−	0.177705i
$381$	6.24621	+	10.8188i	0.320003	+	0.554262i
$382$	−5.12311			−0.262121
$383$	6.40388	+	11.0918i	0.327223	+	0.566767i	0.981960	−	0.189090i	$-0.0605538\pi$
$383$	6.40388	+	11.0918i	0.327223	+	0.566767i	−0.654737	+	0.755857i	$0.727220\pi$
$384$	0.500000	+	0.866025i	0.0255155	+	0.0441942i
$385$	−4.00000			−0.203859
$386$	−0.0615528	−	0.106613i	−0.00313296	−	0.00542644i
$387$	4.00000	−	6.92820i	0.203331	−	0.352180i
$388$	0.438447	−	0.759413i	0.0222588	−	0.0385533i
$389$	−5.31534			−0.269499			−0.134749	−	0.990880i	$-0.543023\pi$
$389$	−5.31534			−0.269499			−0.134749	+	0.990880i	$0.543023\pi$
$390$	4.43845	−	3.46410i	0.224750	−	0.175412i
$391$	−0.138261			−0.00699214
$392$	−0.500000	+	0.866025i	−0.0252538	+	0.0437409i
$393$	7.12311	−	12.3376i	0.359313	−	0.622349i
$394$	−6.28078	−	10.8786i	−0.316421	−	0.548057i
$395$	−10.2462			−0.515543
$396$	1.28078	+	2.21837i	0.0643614	+	0.111477i
$397$	−13.9654	−	24.1888i	−0.700905	−	1.21400i	−0.968149	−	0.250374i	$-0.919446\pi$
$397$	−13.9654	−	24.1888i	−0.700905	−	1.21400i	0.267244	−	0.963629i	$-0.413887\pi$
$398$	−16.0000			−0.802008
$399$	−1.28078	−	2.21837i	−0.0641190	−	0.111057i
$400$	1.28078	−	2.21837i	0.0640388	−	0.110918i
$401$	0.903882	−	1.56557i	0.0451377	−	0.0781808i	−0.842574	−	0.538581i	$-0.818961\pi$
$401$	0.903882	−	1.56557i	0.0451377	−	0.0781808i	0.887712	+	0.460400i	$0.152294\pi$
$402$	−9.12311			−0.455019
$403$		0			0
$404$	−5.80776			−0.288947
$405$	−0.780776	+	1.35234i	−0.0387971	+	0.0671985i
$406$	3.06155	−	5.30277i	0.151942	−	0.263172i
$407$	−3.12311	−	5.40938i	−0.154807	−	0.268133i
$408$	−0.123106			−0.00609464
$409$	5.78078	+	10.0126i	0.285841	+	0.495091i	0.972813	−	0.231593i	$-0.0743937\pi$
$409$	5.78078	+	10.0126i	0.285841	+	0.495091i	−0.686972	+	0.726684i	$0.741060\pi$
$410$	8.78078	+	15.2088i	0.433652	+	0.751107i
$411$	−12.4384			−0.613543
$412$	−3.12311	−	5.40938i	−0.153864	−	0.266501i
$413$	−2.56155	+	4.43674i	−0.126046	+	0.218318i
$414$	0.561553	−	0.972638i	0.0275988	−	0.0478025i
$415$	−8.00000			−0.392705
$416$	−2.84233	+	2.21837i	−0.139357	+	0.108765i
$417$	5.43845			0.266322
$418$	−3.28078	+	5.68247i	−0.160468	+	0.277939i
$419$	−11.6847	+	20.2384i	−0.570833	+	0.988712i	0.425648	+	0.904889i	$0.360046\pi$
$419$	−11.6847	+	20.2384i	−0.570833	+	0.988712i	−0.996481	+	0.0838227i	$0.973287\pi$
$420$	0.780776	+	1.35234i	0.0380980	+	0.0659877i
$421$	−22.3002			−1.08684			−0.543422	−	0.839459i	$-0.682872\pi$
$421$	−22.3002			−1.08684			−0.543422	+	0.839459i	$0.682872\pi$
$422$	−2.56155	−	4.43674i	−0.124694	−	0.215977i
$423$	0.157671	+	0.273094i	0.00766622	+	0.0132783i
$424$	7.00000			0.339950
$425$	0.157671	+	0.273094i	0.00764816	+	0.0132470i
$426$	−5.68466	+	9.84612i	−0.275423	+	0.477046i
$427$	5.62311	−	9.73950i	0.272121	−	0.471328i
$428$	13.9309			0.673374
$429$	−7.28078	+	5.68247i	−0.351519	+	0.274352i
$430$	−12.4924			−0.602438
$431$	−9.68466	+	16.7743i	−0.466494	+	0.807991i	−0.999268	−	0.0382670i	$-0.987816\pi$
$431$	−9.68466	+	16.7743i	−0.466494	+	0.807991i	0.532774	+	0.846258i	$0.321150\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	10.6577	+	18.4596i	0.512175	+	0.887113i	0.999900	+	0.0141160i	$0.00449340\pi$
$433$	10.6577	+	18.4596i	0.512175	+	0.887113i	−0.487725	+	0.872997i	$0.662173\pi$
$434$		0			0
$435$	−4.78078	−	8.28055i	−0.229221	−	0.397022i
$436$	6.12311	+	10.6055i	0.293244	+	0.507913i
$437$	2.87689			0.137621
$438$	−1.21922	−	2.11176i	−0.0582568	−	0.100904i
$439$	13.1231	−	22.7299i	0.626332	−	1.08484i	−0.361950	−	0.932197i	$-0.617889\pi$
$439$	13.1231	−	22.7299i	0.626332	−	1.08484i	0.988282	−	0.152641i	$-0.0487777\pi$
$440$	2.00000	−	3.46410i	0.0953463	−	0.165145i
$441$	1.00000			0.0476190
$442$	−0.0615528	−	0.439575i	−0.00292777	−	0.0209085i
$443$	−27.0540			−1.28537			−0.642687	−	0.766129i	$-0.722180\pi$
$443$	−27.0540			−1.28537			−0.642687	+	0.766129i	$0.722180\pi$
$444$	−1.21922	+	2.11176i	−0.0578618	+	0.100220i
$445$	−2.68466	+	4.64996i	−0.127265	+	0.220429i
$446$	−4.87689	−	8.44703i	−0.230928	−	0.399978i
$447$	15.5616			0.736036
$448$	−0.500000	−	0.866025i	−0.0236228	−	0.0409159i
$449$	3.31534	+	5.74234i	0.156461	+	0.270998i	0.933590	−	0.358343i	$-0.116658\pi$
$449$	3.31534	+	5.74234i	0.156461	+	0.270998i	−0.777129	+	0.629341i	$0.783325\pi$
$450$	−2.56155			−0.120753
$451$	−14.4039	−	24.9483i	−0.678252	−	1.17477i
$452$	−0.780776	+	1.35234i	−0.0367246	+	0.0636089i
$453$	−10.9654	+	18.9927i	−0.515201	+	0.892354i
$454$	−10.8769			−0.510478
$455$	−4.43845	+	3.46410i	−0.208078	+	0.162400i
$456$	2.56155			0.119956
$457$	−14.4654	+	25.0549i	−0.676665	+	1.17202i	0.299315	+	0.954154i	$0.403242\pi$
$457$	−14.4654	+	25.0549i	−0.676665	+	1.17202i	−0.975979	+	0.217863i	$0.930091\pi$
$458$	−8.52699	+	14.7692i	−0.398440	+	0.690118i
$459$	0.0615528	+	0.106613i	0.00287304	+	0.00497625i
$460$	−1.75379			−0.0817708
$461$	−3.02699	−	5.24290i	−0.140981	−	0.244186i	0.786885	−	0.617099i	$-0.211692\pi$
$461$	−3.02699	−	5.24290i	−0.140981	−	0.244186i	−0.927866	+	0.372913i	$0.878359\pi$
$462$	−1.28078	−	2.21837i	−0.0595871	−	0.103208i
$463$	12.3153			0.572342			0.286171	−	0.958178i	$-0.407617\pi$
$463$	12.3153			0.572342			0.286171	+	0.958178i	$0.407617\pi$
$464$	3.06155	+	5.30277i	0.142129	+	0.246175i
$465$		0			0
$466$	−0.684658	+	1.18586i	−0.0317162	+	0.0549341i
$467$	−36.9848			−1.71145			−0.855727	−	0.517427i	$-0.826890\pi$
$467$	−36.9848			−1.71145			−0.855727	+	0.517427i	$0.826890\pi$
$468$	3.34233	+	1.35234i	0.154499	+	0.0625121i
$469$	9.12311			0.421266
$470$	0.246211	−	0.426450i	0.0113569	−	0.0196707i
$471$	−0.657671	+	1.13912i	−0.0303039	+	0.0524878i
$472$	−2.56155	−	4.43674i	−0.117905	−	0.204217i
$473$	20.4924			0.942243
$474$	−3.28078	−	5.68247i	−0.150691	−	0.261005i
$475$	−3.28078	−	5.68247i	−0.150532	−	0.260730i
$476$	0.123106			0.00564254
$477$	−3.50000	−	6.06218i	−0.160254	−	0.277568i
$478$	−9.68466	+	16.7743i	−0.442966	+	0.767240i
$479$	0.965435	−	1.67218i	0.0441118	−	0.0764040i	−0.843126	−	0.537715i	$-0.819288\pi$
$479$	0.965435	−	1.67218i	0.0441118	−	0.0764040i	0.887238	+	0.461311i	$0.152621\pi$
$480$	−1.56155			−0.0712748
$481$	−8.15009	−	3.29762i	−0.371612	−	0.150359i
$482$	−0.192236			−0.00875611
$483$	−0.561553	+	0.972638i	−0.0255515	+	0.0442566i
$484$	2.21922	−	3.84381i	0.100874	−	0.174719i
$485$	0.684658	+	1.18586i	0.0310887	+	0.0538473i
$486$	−1.00000			−0.0453609
$487$	−11.8423	−	20.5115i	−0.536627	−	0.929466i	−0.999083	−	0.0428230i	$-0.986365\pi$
$487$	−11.8423	−	20.5115i	−0.536627	−	0.929466i	0.462456	−	0.886642i	$-0.346968\pi$
$488$	5.62311	+	9.73950i	0.254546	+	0.440887i
$489$	−24.4924			−1.10759
$490$	−0.780776	−	1.35234i	−0.0352719	−	0.0610927i
$491$	8.24621	−	14.2829i	0.372146	−	0.644576i	−0.617749	−	0.786375i	$-0.711955\pi$
$491$	8.24621	−	14.2829i	0.372146	−	0.644576i	0.989895	+	0.141799i	$0.0452886\pi$
$492$	−5.62311	+	9.73950i	−0.253509	+	0.439091i
$493$	−0.753789			−0.0339489
$494$	1.28078	+	9.14657i	0.0576249	+	0.411524i
$495$	−4.00000			−0.179787
$496$		0			0
$497$	5.68466	−	9.84612i	0.254992	−	0.441659i
$498$	−2.56155	−	4.43674i	−0.114786	−	0.198815i
$499$	30.2462			1.35401			0.677003	−	0.735980i	$-0.263278\pi$
$499$	30.2462			1.35401			0.677003	+	0.735980i	$0.263278\pi$
$500$	5.90388	+	10.2258i	0.264030	+	0.457313i
$501$	6.24621	+	10.8188i	0.279060	+	0.483346i
$502$	−13.6155			−0.607691
$503$	14.2462	+	24.6752i	0.635207	+	1.10021i	0.986471	+	0.163935i	$0.0524186\pi$
$503$	14.2462	+	24.6752i	0.635207	+	1.10021i	−0.351264	+	0.936276i	$0.614248\pi$
$504$	−0.500000	+	0.866025i	−0.0222718	+	0.0385758i
$505$	4.53457	−	7.85410i	0.201786	−	0.349503i
$506$	2.87689			0.127894
$507$	−3.15767	+	12.6107i	−0.140237	+	0.560060i
$508$	12.4924			0.554262
$509$	20.9039	−	36.2066i	0.926548	−	1.60483i	0.137496	−	0.990502i	$-0.456094\pi$
$509$	20.9039	−	36.2066i	0.926548	−	1.60483i	0.789052	−	0.614326i	$-0.210572\pi$
$510$	0.0961180	−	0.166481i	0.00425618	−	0.00737191i
$511$	1.21922	+	2.11176i	0.0539353	+	0.0934186i
$512$	1.00000			0.0441942
$513$	−1.28078	−	2.21837i	−0.0565477	−	0.0979434i
$514$	12.1847	+	21.1044i	0.537442	+	0.930877i
$515$	9.75379			0.429803
$516$	−4.00000	−	6.92820i	−0.176090	−	0.304997i
$517$	−0.403882	+	0.699544i	−0.0177627	+	0.0307659i
$518$	1.21922	−	2.11176i	0.0535696	−	0.0927853i
$519$	18.0000			0.790112
$520$	−0.780776	−	5.57586i	−0.0342393	−	0.244518i
$521$	25.8769			1.13369			0.566844	−	0.823825i	$-0.308164\pi$
$521$	25.8769			1.13369			0.566844	+	0.823825i	$0.308164\pi$
$522$	3.06155	−	5.30277i	0.134001	−	0.232096i
$523$	8.40388	−	14.5560i	0.367476	−	0.636487i	−0.621694	−	0.783260i	$-0.713555\pi$
$523$	8.40388	−	14.5560i	0.367476	−	0.636487i	0.989170	+	0.146773i	$0.0468886\pi$
$524$	−7.12311	−	12.3376i	−0.311174	−	0.538970i
$525$	2.56155			0.111795
$526$	−2.56155	−	4.43674i	−0.111689	−	0.193451i
$527$		0			0
$528$	2.56155			0.111477
$529$	10.8693	+	18.8262i	0.472579	+	0.818531i
$530$	−5.46543	+	9.46641i	−0.237403	+	0.411195i
$531$	−2.56155	+	4.43674i	−0.111162	+	0.192538i
$532$	−2.56155			−0.111057
$533$	−37.5885	−	15.2088i	−1.62814	−	0.658764i
$534$	−3.43845			−0.148796
$535$	−10.8769	+	18.8393i	−0.470249	+	0.814495i
$536$	−4.56155	+	7.90084i	−0.197029	+	0.341264i
$537$	−0.876894	−	1.51883i	−0.0378408	−	0.0655422i
$538$	27.1231			1.16936
$539$	1.28078	+	2.21837i	0.0551669	+	0.0955520i
$540$	0.780776	+	1.35234i	0.0335993	+	0.0581956i
$541$	19.1771			0.824487			0.412244	−	0.911074i	$-0.364745\pi$
$541$	19.1771			0.824487			0.412244	+	0.911074i	$0.364745\pi$
$542$	11.3693	+	19.6922i	0.488354	+	0.845854i
$543$	6.62311	−	11.4716i	0.284225	−	0.492292i
$544$	−0.0615528	+	0.106613i	−0.00263906	+	0.00457098i
$545$	−19.1231			−0.819144
$546$	−3.34233	−	1.35234i	−0.143038	−	0.0578750i
$547$	−33.6155			−1.43730			−0.718648	−	0.695374i	$-0.755239\pi$
$547$	−33.6155			−1.43730			−0.718648	+	0.695374i	$0.755239\pi$
$548$	−6.21922	+	10.7720i	−0.265672	+	0.460158i
$549$	5.62311	−	9.73950i	0.239988	−	0.415672i
$550$	−3.28078	−	5.68247i	−0.139893	−	0.242301i
$551$	15.6847			0.668189
$552$	−0.561553	−	0.972638i	−0.0239013	−	0.0413982i
$553$	3.28078	+	5.68247i	0.139513	+	0.241643i
$554$	−19.5616			−0.831091
$555$	−1.90388	−	3.29762i	−0.0808153	−	0.139976i
$556$	2.71922	−	4.70983i	0.115321	−	0.199741i
$557$	−6.06155	+	10.4989i	−0.256836	+	0.444853i	−0.965393	−	0.260801i	$-0.916013\pi$
$557$	−6.06155	+	10.4989i	−0.256836	+	0.444853i	0.708556	+	0.705654i	$0.249347\pi$
$558$		0			0
$559$	22.7386	−	17.7470i	0.961742	−	0.750616i
$560$	1.56155			0.0659877
$561$	−0.157671	+	0.273094i	−0.00665687	+	0.0115300i
$562$	−6.46543	+	11.1985i	−0.272728	+	0.472379i
$563$	2.87689	+	4.98293i	0.121247	+	0.210005i	0.920260	−	0.391309i	$-0.127977\pi$
$563$	2.87689	+	4.98293i	0.121247	+	0.210005i	−0.799013	+	0.601314i	$0.794644\pi$
$564$	0.315342			0.0132783
$565$	−1.21922	−	2.11176i	−0.0512931	−	0.0888423i
$566$	10.0000	+	17.3205i	0.420331	+	0.728035i
$567$	1.00000			0.0419961
$568$	5.68466	+	9.84612i	0.238523	+	0.413134i
$569$	11.0000	−	19.0526i	0.461144	−	0.798725i	−0.537874	−	0.843025i	$-0.680772\pi$
$569$	11.0000	−	19.0526i	0.461144	−	0.798725i	0.999018	+	0.0443003i	$0.0141058\pi$
$570$	−2.00000	+	3.46410i	−0.0837708	+	0.145095i
$571$	−21.1231			−0.883974			−0.441987	−	0.897021i	$-0.645726\pi$
$571$	−21.1231			−0.883974			−0.441987	+	0.897021i	$0.645726\pi$
$572$	1.28078	+	9.14657i	0.0535520	+	0.382437i
$573$	5.12311			0.214021
$574$	5.62311	−	9.73950i	0.234704	−	0.406519i
$575$	−1.43845	+	2.49146i	−0.0599874	+	0.103901i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−35.5616			−1.48045			−0.740223	−	0.672361i	$-0.765280\pi$
$577$	−35.5616			−1.48045			−0.740223	+	0.672361i	$0.765280\pi$
$578$	8.49242	+	14.7093i	0.353238	+	0.611827i
$579$	0.0615528	+	0.106613i	0.00255805	+	0.00443067i
$580$	−9.56155			−0.397022
$581$	2.56155	+	4.43674i	0.106271	+	0.184067i
$582$	−0.438447	+	0.759413i	−0.0181742	+	0.0314787i
$583$	8.96543	−	15.5286i	0.371310	−	0.643128i
$584$	−2.43845			−0.100904
$585$	−4.43845	+	3.46410i	−0.183507	+	0.143223i
$586$	−6.93087			−0.286312
$587$	−1.12311	+	1.94528i	−0.0463555	+	0.0802901i	−0.888272	−	0.459317i	$-0.848094\pi$
$587$	−1.12311	+	1.94528i	−0.0463555	+	0.0802901i	0.841917	+	0.539608i	$0.181427\pi$
$588$	0.500000	−	0.866025i	0.0206197	−	0.0357143i
$589$		0			0
$590$	8.00000			0.329355
$591$	6.28078	+	10.8786i	0.258357	+	0.447487i
$592$	1.21922	+	2.11176i	0.0501098	+	0.0867927i
$593$	−33.9848			−1.39559			−0.697795	−	0.716297i	$-0.745835\pi$
$593$	−33.9848			−1.39559			−0.697795	+	0.716297i	$0.745835\pi$
$594$	−1.28078	−	2.21837i	−0.0525509	−	0.0910208i
$595$	−0.0961180	+	0.166481i	−0.00394045	+	0.00682506i
$596$	7.78078	−	13.4767i	0.318713	−	0.552027i
$597$	16.0000			0.654836
$598$	3.19224	−	2.49146i	0.130540	−	0.101884i
$599$	23.8617			0.974964			0.487482	−	0.873133i	$-0.337915\pi$
$599$	23.8617			0.974964			0.487482	+	0.873133i	$0.337915\pi$
$600$	−1.28078	+	2.21837i	−0.0522875	+	0.0905646i
$601$	−14.1501	+	24.5087i	−0.577194	+	0.999730i	0.418605	+	0.908168i	$0.362519\pi$
$601$	−14.1501	+	24.5087i	−0.577194	+	0.999730i	−0.995799	+	0.0915616i	$0.970814\pi$
$602$	4.00000	+	6.92820i	0.163028	+	0.282372i
$603$	9.12311			0.371522
$604$	10.9654	+	18.9927i	0.446177	+	0.772802i
$605$	3.46543	+	6.00231i	0.140890	+	0.244029i
$606$	5.80776			0.235924
$607$	24.4924	+	42.4221i	0.994117	+	1.72186i	0.590861	+	0.806774i	$0.298788\pi$
$607$	24.4924	+	42.4221i	0.994117	+	1.72186i	0.403256	+	0.915087i	$0.367878\pi$
$608$	1.28078	−	2.21837i	0.0519423	−	0.0899668i
$609$	−3.06155	+	5.30277i	−0.124060	+	0.214879i
$610$	−17.5616			−0.711046
$611$	0.157671	+	1.12599i	0.00637868	+	0.0455529i
$612$	0.123106			0.00497625
$613$	−10.7808	+	18.6729i	−0.435431	+	0.754189i	−0.997331	−	0.0730162i	$-0.976738\pi$
$613$	−10.7808	+	18.6729i	−0.435431	+	0.754189i	0.561899	+	0.827206i	$0.310071\pi$
$614$	4.96543	−	8.60039i	0.200389	−	0.347083i
$615$	−8.78078	−	15.2088i	−0.354075	−	0.613276i
$616$	−2.56155			−0.103208
$617$	−11.5885	−	20.0719i	−0.466537	−	0.808066i	0.532732	−	0.846284i	$-0.321165\pi$
$617$	−11.5885	−	20.0719i	−0.466537	−	0.808066i	−0.999269	+	0.0382179i	$0.987832\pi$
$618$	3.12311	+	5.40938i	0.125630	+	0.217597i
$619$	2.06913			0.0831654			0.0415827	−	0.999135i	$-0.486760\pi$
$619$	2.06913			0.0831654			0.0415827	+	0.999135i	$0.486760\pi$
$620$		0			0
$621$	−0.561553	+	0.972638i	−0.0225343	+	0.0390306i
$622$	−10.9654	+	18.9927i	−0.439674	+	0.761537i
$623$	3.43845			0.137758
$624$	2.84233	−	2.21837i	0.113784	−	0.0888059i
$625$	−5.63068			−0.225227
$626$	3.00000	−	5.19615i	0.119904	−	0.207680i
$627$	3.28078	−	5.68247i	0.131022	−	0.226936i
$628$	0.657671	+	1.13912i	0.0262439	+	0.0454558i
$629$	−0.300187			−0.0119692
$630$	−0.780776	−	1.35234i	−0.0311069	−	0.0538787i
$631$	5.03457	+	8.72012i	0.200423	+	0.347143i	0.948665	−	0.316283i	$-0.102435\pi$
$631$	5.03457	+	8.72012i	0.200423	+	0.347143i	−0.748242	+	0.663426i	$0.769102\pi$
$632$	−6.56155			−0.261005
$633$	2.56155	+	4.43674i	0.101813	+	0.176345i
$634$	−6.21922	+	10.7720i	−0.246997	+	0.427811i
$635$	−9.75379	+	16.8941i	−0.387067	+	0.670420i
$636$	−7.00000			−0.277568
$637$	3.34233	+	1.35234i	0.132428	+	0.0535818i
$638$	15.6847			0.620962
$639$	5.68466	−	9.84612i	0.224882	−	0.389506i
$640$	−0.780776	+	1.35234i	−0.0308629	+	0.0534561i
$641$	−4.21922	−	7.30791i	−0.166649	−	0.288645i	0.770590	−	0.637331i	$-0.219961\pi$
$641$	−4.21922	−	7.30791i	−0.166649	−	0.288645i	−0.937240	+	0.348686i	$0.886628\pi$
$642$	−13.9309			−0.549808
$643$	−23.8423	−	41.2961i	−0.940250	−	1.62856i	−0.764994	−	0.644037i	$-0.777258\pi$
$643$	−23.8423	−	41.2961i	−0.940250	−	1.62856i	−0.175256	−	0.984523i	$-0.556075\pi$
$644$	0.561553	+	0.972638i	0.0221283	+	0.0383273i
$645$	12.4924			0.491889
$646$	0.157671	+	0.273094i	0.00620347	+	0.0107447i
$647$	4.47301	−	7.74748i	0.175852	−	0.304585i	−0.764604	−	0.644501i	$-0.777065\pi$
$647$	4.47301	−	7.74748i	0.175852	−	0.304585i	0.940456	+	0.339916i	$0.110399\pi$
$648$	−0.500000	+	0.866025i	−0.0196419	+	0.0340207i
$649$	−13.1231			−0.515127
$650$	−8.56155	−	3.46410i	−0.335812	−	0.135873i
$651$		0			0
$652$	−12.2462	+	21.2111i	−0.479599	+	0.830689i
$653$	−10.2808	+	17.8068i	−0.402318	+	0.696835i	−0.994005	−	0.109333i	$-0.965129\pi$
$653$	−10.2808	+	17.8068i	−0.402318	+	0.696835i	0.591687	+	0.806168i	$0.298462\pi$
$654$	−6.12311	−	10.6055i	−0.239432	−	0.414709i
$655$	22.2462			0.869231
$656$	5.62311	+	9.73950i	0.219545	+	0.380264i
$657$	1.21922	+	2.11176i	0.0475664	+	0.0823875i
$658$	−0.315342			−0.0122933
$659$	−1.03457	−	1.79192i	−0.0403009	−	0.0698033i	0.845171	−	0.534495i	$-0.179498\pi$
$659$	−1.03457	−	1.79192i	−0.0403009	−	0.0698033i	−0.885472	+	0.464692i	$0.846165\pi$
$660$	−2.00000	+	3.46410i	−0.0778499	+	0.134840i
$661$	10.0270	−	17.3673i	0.390005	−	0.675508i	−0.602445	−	0.798160i	$-0.705807\pi$
$661$	10.0270	−	17.3673i	0.390005	−	0.675508i	0.992450	+	0.122653i	$0.0391401\pi$
$662$	19.3693			0.752810
$663$	0.0615528	+	0.439575i	0.00239051	+	0.0170717i
$664$	−5.12311			−0.198815
$665$	2.00000	−	3.46410i	0.0775567	−	0.134332i
$666$	1.21922	−	2.11176i	0.0472440	−	0.0818289i
$667$	−3.43845	−	5.95557i	−0.133137	−	0.230600i
$668$	12.4924			0.483346
$669$	4.87689	+	8.44703i	0.188552	+	0.326581i
$670$	−7.12311	−	12.3376i	−0.275190	−	0.476642i
$671$	28.8078			1.11211
$672$	0.500000	+	0.866025i	0.0192879	+	0.0334077i
$673$	1.37689	−	2.38485i	0.0530754	−	0.0919293i	−0.838267	−	0.545260i	$-0.816431\pi$
$673$	1.37689	−	2.38485i	0.0530754	−	0.0919293i	0.891342	+	0.453331i	$0.149764\pi$
$674$	6.74621	−	11.6848i	0.259854	−	0.450081i
$675$	2.56155			0.0985942
$676$	9.34233	+	9.03996i	0.359320	+	0.347691i
$677$	−24.7386			−0.950783			−0.475391	−	0.879774i	$-0.657694\pi$
$677$	−24.7386			−0.950783			−0.475391	+	0.879774i	$0.657694\pi$
$678$	0.780776	−	1.35234i	0.0299855	−	0.0519365i
$679$	0.438447	−	0.759413i	0.0168261	−	0.0291436i
$680$	−0.0961180	−	0.166481i	−0.00368596	−	0.00638426i
$681$	10.8769			0.416803
$682$		0			0
$683$	−20.2462	−	35.0675i	−0.774700	−	1.34182i	−0.934963	−	0.354745i	$-0.884568\pi$
$683$	−20.2462	−	35.0675i	−0.774700	−	1.34182i	0.160263	−	0.987074i	$-0.448766\pi$
$684$	−2.56155			−0.0979434
$685$	−9.71165	−	16.8211i	−0.371063	−	0.642700i
$686$	−0.500000	+	0.866025i	−0.0190901	+	0.0330650i
$687$	8.52699	−	14.7692i	0.325325	−	0.563479i
$688$	−8.00000			−0.304997
$689$	−3.50000	−	24.9950i	−0.133339	−	0.952234i
$690$	1.75379			0.0667656
$691$	16.4924	−	28.5657i	0.627401	−	1.08669i	−0.360670	−	0.932694i	$-0.617452\pi$
$691$	16.4924	−	28.5657i	0.627401	−	1.08669i	0.988071	−	0.153997i	$-0.0492148\pi$
$692$	9.00000	−	15.5885i	0.342129	−	0.592584i
$693$	1.28078	+	2.21837i	0.0486527	+	0.0842689i
$694$	15.0540			0.571441
$695$	4.24621	+	7.35465i	0.161068	+	0.278978i
$696$	−3.06155	−	5.30277i	−0.116048	−	0.201001i
$697$	−1.38447			−0.0524406
$698$	9.00000	+	15.5885i	0.340655	+	0.590032i
$699$	0.684658	−	1.18586i	0.0258962	−	0.0448535i
$700$	1.28078	−	2.21837i	0.0484088	−	0.0838465i
$701$	−39.3002			−1.48435			−0.742174	−	0.670207i	$-0.766205\pi$
$701$	−39.3002			−1.48435			−0.742174	+	0.670207i	$0.766205\pi$
$702$	−3.34233	−	1.35234i	−0.126148	−	0.0510410i
$703$	6.24621			0.235580
$704$	1.28078	−	2.21837i	0.0482711	−	0.0836080i
$705$	−0.246211	+	0.426450i	−0.00927285	+	0.0160611i
$706$	16.9039	+	29.2784i	0.636186	+	1.10191i
$707$	−5.80776			−0.218423
$708$	2.56155	+	4.43674i	0.0962690	+	0.166743i
$709$	19.1501	+	33.1689i	0.719197	+	1.24569i	0.961318	+	0.275440i	$0.0888234\pi$
$709$	19.1501	+	33.1689i	0.719197	+	1.24569i	−0.242122	+	0.970246i	$0.577843\pi$
$710$	−17.7538			−0.666288
$711$	3.28078	+	5.68247i	0.123039	+	0.213109i
$712$	−1.71922	+	2.97778i	−0.0644306	+	0.111597i
$713$		0			0
$714$	−0.123106			−0.00460711
$715$	−13.3693	−	5.40938i	−0.499984	−	0.202299i
$716$	−1.75379			−0.0655422
$717$	9.68466	−	16.7743i	0.361680	−	0.626448i
$718$	0.876894	−	1.51883i	0.0327254	−	0.0566821i
$719$	−0.403882	−	0.699544i	−0.0150623	−	0.0260886i	0.858396	−	0.512988i	$-0.171461\pi$
$719$	−0.403882	−	0.699544i	−0.0150623	−	0.0260886i	−0.873458	+	0.486899i	$0.838128\pi$
$720$	1.56155			0.0581956
$721$	−3.12311	−	5.40938i	−0.116311	−	0.201456i
$722$	6.21922	+	10.7720i	0.231456	+	0.400893i
$723$	0.192236			0.00714933
$724$	−6.62311	−	11.4716i	−0.246146	−	0.426337i
$725$	−7.84233	+	13.5833i	−0.291257	+	0.504472i
$726$	−2.21922	+	3.84381i	−0.0823631	+	0.142657i
$727$	40.0000			1.48352			0.741759	−	0.670667i	$-0.233992\pi$
$727$	40.0000			1.48352			0.741759	+	0.670667i	$0.233992\pi$
$728$	−2.84233	+	2.21837i	−0.105344	+	0.0822183i
$729$	1.00000			0.0370370
$730$	1.90388	−	3.29762i	0.0704658	−	0.122050i
$731$	0.492423	−	0.852901i	0.0182129	−	0.0315457i
$732$	−5.62311	−	9.73950i	−0.207836	−	0.359982i
$733$	−28.8617			−1.06603			−0.533016	−	0.846105i	$-0.678942\pi$
$733$	−28.8617			−1.06603			−0.533016	+	0.846105i	$0.678942\pi$
$734$	−6.80776	−	11.7914i	−0.251279	−	0.435228i
$735$	0.780776	+	1.35234i	0.0287994	+	0.0498820i
$736$	−1.12311			−0.0413982
$737$	11.6847	+	20.2384i	0.430410	+	0.745492i
$738$	5.62311	−	9.73950i	0.206989	−	0.358516i
$739$	−7.68466	+	13.3102i	−0.282685	+	0.489624i	−0.972045	−	0.234794i	$-0.924558\pi$
$739$	−7.68466	+	13.3102i	−0.282685	+	0.489624i	0.689360	+	0.724419i	$0.257892\pi$
$740$	−3.80776			−0.139976
$741$	−1.28078	−	9.14657i	−0.0470505	−	0.336008i
$742$	7.00000			0.256978
$743$	2.24621	−	3.89055i	0.0824055	−	0.142731i	−0.821877	−	0.569665i	$-0.807073\pi$
$743$	2.24621	−	3.89055i	0.0824055	−	0.142731i	0.904283	+	0.426934i	$0.140406\pi$
$744$		0			0
$745$	12.1501	+	21.0446i	0.445145	+	0.771014i
$746$	−3.06913			−0.112369
$747$	2.56155	+	4.43674i	0.0937223	+	0.162332i
$748$	0.157671	+	0.273094i	0.00576501	+	0.00998530i
$749$	13.9309			0.509023
$750$	−5.90388	−	10.2258i	−0.215579	−	0.373394i
$751$	20.4039	−	35.3406i	0.744548	−	1.28960i	−0.205857	−	0.978582i	$-0.565998\pi$
$751$	20.4039	−	35.3406i	0.744548	−	1.28960i	0.950406	−	0.311013i	$-0.100668\pi$
$752$	0.157671	−	0.273094i	0.00574966	−	0.00995871i
$753$	13.6155			0.496177
$754$	17.4039	−	13.5833i	0.633812	−	0.494675i
$755$	−34.2462			−1.24635
$756$	0.500000	−	0.866025i	0.0181848	−	0.0314970i
$757$	−26.3693	+	45.6730i	−0.958409	+	1.66001i	−0.232043	+	0.972706i	$0.574541\pi$
$757$	−26.3693	+	45.6730i	−0.958409	+	1.66001i	−0.726366	+	0.687308i	$0.758792\pi$
$758$	−18.8078	−	32.5760i	−0.683129	−	1.18321i
$759$	−2.87689			−0.104425
$760$	2.00000	+	3.46410i	0.0725476	+	0.125656i
$761$	−25.4924	−	44.1542i	−0.924100	−	1.60059i	−0.793003	−	0.609218i	$-0.791483\pi$
$761$	−25.4924	−	44.1542i	−0.924100	−	1.60059i	−0.131097	−	0.991370i	$-0.541850\pi$
$762$	−12.4924			−0.452553
$763$	6.12311	+	10.6055i	0.221671	+	0.383946i
$764$	2.56155	−	4.43674i	0.0926737	−	0.160516i
$765$	−0.0961180	+	0.166481i	−0.00347515	+	0.00601914i
$766$	−12.8078			−0.462763
$767$	−14.5616	+	11.3649i	−0.525787	+	0.410364i
$768$	−1.00000			−0.0360844
$769$	−2.43845	+	4.22351i	−0.0879327	+	0.152304i	−0.906637	−	0.421911i	$-0.861359\pi$
$769$	−2.43845	+	4.22351i	−0.0879327	+	0.152304i	0.818704	+	0.574215i	$0.194693\pi$
$770$	2.00000	−	3.46410i	0.0720750	−	0.124838i
$771$	−12.1847	−	21.1044i	−0.438820	−	0.760058i
$772$	0.123106			0.00443067
$773$	−10.3693	−	17.9602i	−0.372958	−	0.645983i	0.617061	−	0.786915i	$-0.288323\pi$
$773$	−10.3693	−	17.9602i	−0.372958	−	0.645983i	−0.990019	+	0.140933i	$0.954990\pi$
$774$	4.00000	+	6.92820i	0.143777	+	0.249029i
$775$		0			0
$776$	0.438447	+	0.759413i	0.0157393	+	0.0272613i
$777$	−1.21922	+	2.11176i	−0.0437394	+	0.0757589i
$778$	2.65767	−	4.60322i	0.0952821	−	0.165033i
$779$	28.8078			1.03215
$780$	0.780776	+	5.57586i	0.0279563	+	0.199648i
$781$	29.1231			1.04211
$782$	0.0691303	−	0.119737i	0.00247209	−	0.00428179i
$783$	−3.06155	+	5.30277i	−0.109411	+	0.189505i
$784$	−0.500000	−	0.866025i	−0.0178571	−	0.0309295i
$785$	−2.05398			−0.0733095
$786$	7.12311	+	12.3376i	0.254073	+	0.440067i
$787$	0.0885405	+	0.153357i	0.00315613	+	0.00546657i	0.867599	−	0.497264i	$-0.165662\pi$
$787$	0.0885405	+	0.153357i	0.00315613	+	0.00546657i	−0.864443	+	0.502731i	$0.832329\pi$
$788$	12.5616			0.447487
$789$	2.56155	+	4.43674i	0.0911937	+	0.157952i
$790$	5.12311	−	8.87348i	0.182272	−	0.315704i
$791$	−0.780776	+	1.35234i	−0.0277612	+	0.0480838i
$792$	−2.56155			−0.0910208
$793$	31.9654	−	24.9483i	1.13513	−	0.885939i
$794$	27.9309			0.991229
$795$	5.46543	−	9.46641i	0.193839	−	0.335739i
$796$	8.00000	−	13.8564i	0.283552	−	0.491127i
$797$	−25.2462	−	43.7277i	−0.894267	−	1.54892i	−0.834710	−	0.550690i	$-0.814364\pi$
$797$	−25.2462	−	43.7277i	−0.894267	−	1.54892i	−0.0595571	−	0.998225i	$-0.518969\pi$
$798$	2.56155			0.0906780
$799$	0.0194102	+	0.0336194i	0.000686682	+	0.00118937i
$800$	1.28078	+	2.21837i	0.0452823	+	0.0784312i
$801$	3.43845			0.121492
$802$	0.903882	+	1.56557i	0.0319172	+	0.0552822i
$803$	−3.12311	+	5.40938i	−0.110212	+	0.190893i
$804$	4.56155	−	7.90084i	0.160874	−	0.278641i
$805$	−1.75379			−0.0618129
$806$		0			0
$807$	−27.1231			−0.954779
$808$	2.90388	−	5.02967i	0.102158	−	0.176943i
$809$	−4.46543	+	7.73436i	−0.156996	+	0.271926i	−0.933784	−	0.357837i	$-0.883514\pi$
$809$	−4.46543	+	7.73436i	−0.156996	+	0.271926i	0.776788	+	0.629762i	$0.216848\pi$
$810$	−0.780776	−	1.35234i	−0.0274337	−	0.0475165i
$811$	24.0000			0.842754			0.421377	−	0.906886i	$-0.361547\pi$
$811$	24.0000			0.842754			0.421377	+	0.906886i	$0.361547\pi$
$812$	3.06155	+	5.30277i	0.107439	+	0.186091i
$813$	−11.3693	−	19.6922i	−0.398739	−	0.690637i
$814$	6.24621			0.218930
$815$	−19.1231	−	33.1222i	−0.669853	−	1.16022i
$816$	0.0615528	−	0.106613i	0.00215478	−	0.00373219i
$817$	−10.2462	+	17.7470i	−0.358470	+	0.620887i
$818$	−11.5616			−0.404240
$819$	3.34233	+	1.35234i	0.116790	+	0.0472547i
$820$	−17.5616			−0.613276
$821$	−13.6501	+	23.6427i	−0.476392	+	0.825134i	−0.999634	−	0.0270494i	$-0.991389\pi$
$821$	−13.6501	+	23.6427i	−0.476392	+	0.825134i	0.523243	+	0.852184i	$0.324722\pi$
$822$	6.21922	−	10.7720i	0.216920	−	0.375717i
$823$	19.1231	+	33.1222i	0.666590	+	1.15457i	0.978852	+	0.204571i	$0.0655799\pi$
$823$	19.1231	+	33.1222i	0.666590	+	1.15457i	−0.312262	+	0.949996i	$0.601087\pi$
$824$	6.24621			0.217597
$825$	3.28078	+	5.68247i	0.114222	+	0.197838i
$826$	−2.56155	−	4.43674i	−0.0891278	−	0.154374i
$827$	34.2462			1.19086			0.595429	−	0.803408i	$-0.296982\pi$
$827$	34.2462			1.19086			0.595429	+	0.803408i	$0.296982\pi$
$828$	0.561553	+	0.972638i	0.0195153	+	0.0338015i
$829$	0.184658	−	0.319838i	0.00641345	−	0.0111084i	−0.862801	−	0.505544i	$-0.831292\pi$
$829$	0.184658	−	0.319838i	0.00641345	−	0.0111084i	0.869214	+	0.494436i	$0.164625\pi$
$830$	4.00000	−	6.92820i	0.138842	−	0.240481i
$831$	19.5616			0.678583
$832$	−0.500000	−	3.57071i	−0.0173344	−	0.123792i
$833$	0.123106			0.00426536
$834$	−2.71922	+	4.70983i	−0.0941590	+	0.163088i
$835$	−9.75379	+	16.8941i	−0.337544	+	0.584643i
$836$	−3.28078	−	5.68247i	−0.113468	−	0.196532i
$837$		0			0
$838$	−11.6847	−	20.2384i	−0.403640	−	0.699125i
$839$	−9.12311	−	15.8017i	−0.314965	−	0.545535i	0.664465	−	0.747319i	$-0.268659\pi$
$839$	−9.12311	−	15.8017i	−0.314965	−	0.545535i	−0.979430	+	0.201784i	$0.935326\pi$
$840$	−1.56155			−0.0538787
$841$	−4.24621	−	7.35465i	−0.146421	−	0.253609i
$842$	11.1501	−	19.3125i	0.384258	−	0.665554i
$843$	6.46543	−	11.1985i	0.222681	−	0.385696i
$844$	5.12311			0.176345
$845$	−19.5194	+	5.57586i	−0.671488	+	0.191815i
$846$	−0.315342			−0.0108417
$847$	2.21922	−	3.84381i	0.0762534	−	0.132075i
$848$	−3.50000	+	6.06218i	−0.120190	+	0.208176i
$849$	−10.0000	−	17.3205i	−0.343199	−	0.594438i
$850$	−0.315342			−0.0108161
$851$	−1.36932	−	2.37173i	−0.0469396	−	0.0813017i
$852$	−5.68466	−	9.84612i	−0.194753	−	0.337322i
$853$	30.3693			1.03983			0.519913	−	0.854219i	$-0.325964\pi$
$853$	30.3693			1.03983			0.519913	+	0.854219i	$0.325964\pi$
$854$	5.62311	+	9.73950i	0.192419	+	0.333279i
$855$	2.00000	−	3.46410i	0.0683986	−	0.118470i
$856$	−6.96543	+	12.0645i	−0.238074	+	0.412356i
$857$	16.4384			0.561527			0.280763	−	0.959777i	$-0.409412\pi$
$857$	16.4384			0.561527			0.280763	+	0.959777i	$0.409412\pi$
$858$	−1.28078	−	9.14657i	−0.0437250	−	0.312259i
$859$	17.9309			0.611793			0.305897	−	0.952065i	$-0.401044\pi$
$859$	17.9309			0.611793			0.305897	+	0.952065i	$0.401044\pi$
$860$	6.24621	−	10.8188i	0.212994	−	0.368916i
$861$	−5.62311	+	9.73950i	−0.191635	+	0.331921i
$862$	−9.68466	−	16.7743i	−0.329861	−	0.571336i
$863$	41.1231			1.39985			0.699923	−	0.714218i	$-0.253217\pi$
$863$	41.1231			1.39985			0.699923	+	0.714218i	$0.253217\pi$
$864$	0.500000	+	0.866025i	0.0170103	+	0.0294628i
$865$	14.0540	+	24.3422i	0.477849	+	0.827660i
$866$	−21.3153			−0.724325
$867$	−8.49242	−	14.7093i	−0.288418	−	0.499554i
$868$		0			0
$869$	−8.40388	+	14.5560i	−0.285082	+	0.493777i
$870$	9.56155			0.324167
$871$	30.4924	+	12.3376i	1.03320	+	0.418043i
$872$	−12.2462			−0.414709
$873$	0.438447	−	0.759413i	0.0148392	−	0.0257022i
$874$	−1.43845	+	2.49146i	−0.0486562	+	0.0842750i
$875$	5.90388	+	10.2258i	0.199588	+	0.345696i
$876$	2.43845			0.0823875
$877$	14.2732	+	24.7219i	0.481972	+	0.834799i	0.999786	−	0.0206937i	$-0.00658747\pi$
$877$	14.2732	+	24.7219i	0.481972	+	0.834799i	−0.517814	+	0.855493i	$0.673254\pi$
$878$	13.1231	+	22.7299i	0.442883	+	0.767096i
$879$	6.93087			0.233772
$880$	2.00000	+	3.46410i	0.0674200	+	0.116775i
$881$	−9.97301	+	17.2738i	−0.335999	+	0.581968i	−0.983676	−	0.179947i	$-0.942407\pi$
$881$	−9.97301	+	17.2738i	−0.335999	+	0.581968i	0.647677	+	0.761915i	$0.275741\pi$
$882$	−0.500000	+	0.866025i	−0.0168359	+	0.0291606i
$883$	−20.0000			−0.673054			−0.336527	−	0.941674i	$-0.609252\pi$
$883$	−20.0000			−0.673054			−0.336527	+	0.941674i	$0.609252\pi$
$884$	0.411460	+	0.166481i	0.0138389	+	0.00559937i
$885$	−8.00000			−0.268917
$886$	13.5270	−	23.4294i	0.454448	−	0.787127i
$887$	4.47301	−	7.74748i	0.150189	−	0.260135i	−0.781108	−	0.624396i	$-0.785345\pi$
$887$	4.47301	−	7.74748i	0.150189	−	0.260135i	0.931297	+	0.364261i	$0.118678\pi$
$888$	−1.21922	−	2.11176i	−0.0409145	−	0.0708659i
$889$	12.4924			0.418982
$890$	−2.68466	−	4.64996i	−0.0899900	−	0.155867i
$891$	1.28078	+	2.21837i	0.0429076	+	0.0743182i
$892$	9.75379			0.326581
$893$	−0.403882	−	0.699544i	−0.0135154	−	0.0234094i
$894$	−7.78078	+	13.4767i	−0.260228	+	0.450728i
$895$	1.36932	−	2.37173i	0.0457712	−	0.0792781i
$896$	1.00000			0.0334077
$897$	−3.19224	+	2.49146i	−0.106586	+	0.0831875i
$898$	−6.63068			−0.221269
$899$		0			0
$900$	1.28078	−	2.21837i	0.0426925	−	0.0739457i
$901$	−0.430870	−	0.746288i	−0.0143544	−	0.0248625i
$902$	28.8078			0.959194
$903$	−4.00000	−	6.92820i	−0.133112	−	0.230556i
$904$	−0.780776	−	1.35234i	−0.0259682	−	0.0449783i
$905$	20.6847			0.687581
$906$	−10.9654	−	18.9927i	−0.364302	−	0.630990i
$907$	0.561553	−	0.972638i	0.0186461	−	0.0322959i	−0.856552	−	0.516061i	$-0.827398\pi$
$907$	0.561553	−	0.972638i	0.0186461	−	0.0322959i	0.875198	+	0.483765i	$0.160731\pi$
$908$	5.43845	−	9.41967i	0.180481	−	0.312603i
$909$	−5.80776			−0.192631
$910$	−0.780776	−	5.57586i	−0.0258825	−	0.184838i
$911$	13.6155			0.451103			0.225551	−	0.974231i	$-0.427582\pi$
$911$	13.6155			0.451103			0.225551	+	0.974231i	$0.427582\pi$
$912$	−1.28078	+	2.21837i	−0.0424107	+	0.0734576i
$913$	−6.56155	+	11.3649i	−0.217156	+	0.376125i
$914$	−14.4654	−	25.0549i	−0.478474	−	0.828741i
$915$	17.5616			0.580567
$916$	−8.52699	−	14.7692i	−0.281740	−	0.487987i
$917$	−7.12311	−	12.3376i	−0.235226	−	0.407423i
$918$	−0.123106			−0.00406309
$919$	22.9654	+	39.7773i	0.757560	+	1.31213i	0.944092	+	0.329683i	$0.106942\pi$
$919$	22.9654	+	39.7773i	0.757560	+	1.31213i	−0.186532	+	0.982449i	$0.559725\pi$
$920$	0.876894	−	1.51883i	0.0289104	−	0.0500742i
$921$	−4.96543	+	8.60039i	−0.163617	+	0.283392i
$922$	6.05398			0.199377
$923$	32.3153	−	25.2213i	1.06367	−	0.830171i
$924$	2.56155			0.0842689
$925$	−3.12311	+	5.40938i	−0.102687	+	0.177859i
$926$	−6.15767	+	10.6654i	−0.202354	+	0.350487i
$927$	−3.12311	−	5.40938i	−0.102576	−	0.177667i
$928$	−6.12311			−0.201001
$929$	1.37689	+	2.38485i	0.0451744	+	0.0782444i	0.887729	−	0.460367i	$-0.152282\pi$
$929$	1.37689	+	2.38485i	0.0451744	+	0.0782444i	−0.842554	+	0.538612i	$0.818949\pi$
$930$		0			0
$931$	−2.56155			−0.0839515
$932$	−0.684658	−	1.18586i	−0.0224267	−	0.0388442i
$933$	10.9654	−	18.9927i	0.358992	−	0.621793i
$934$	18.4924	−	32.0298i	0.605091	−	1.04805i
$935$	−0.492423			−0.0161039
$936$	−2.84233	+	2.21837i	−0.0929044	+	0.0725097i
$937$	−34.4384			−1.12506			−0.562528	−	0.826779i	$-0.690171\pi$
$937$	−34.4384			−1.12506			−0.562528	+	0.826779i	$0.690171\pi$
$938$	−4.56155	+	7.90084i	−0.148940	+	0.257972i
$939$	−3.00000	+	5.19615i	−0.0979013	+	0.169570i
$940$	0.246211	+	0.426450i	0.00803053	+	0.0139093i
$941$	−10.6307			−0.346550			−0.173275	−	0.984873i	$-0.555435\pi$
$941$	−10.6307			−0.346550			−0.173275	+	0.984873i	$0.555435\pi$
$942$	−0.657671	−	1.13912i	−0.0214281	−	0.0371145i
$943$	−6.31534	−	10.9385i	−0.205656	−	0.356206i
$944$	5.12311			0.166743
$945$	0.780776	+	1.35234i	0.0253987	+	0.0439918i
$946$	−10.2462	+	17.7470i	−0.333133	+	0.577003i
$947$	−29.2808	+	50.7158i	−0.951497	+	1.64804i	−0.209310	+	0.977849i	$0.567122\pi$
$947$	−29.2808	+	50.7158i	−0.951497	+	1.64804i	−0.742187	+	0.670192i	$0.766212\pi$
$948$	6.56155			0.213109
$949$	1.21922	+	8.70700i	0.0395777	+	0.282641i
$950$	6.56155			0.212885
$951$	6.21922	−	10.7720i	0.201672	−	0.349306i
$952$	−0.0615528	+	0.106613i	−0.00199494	+	0.00345533i
$953$	−6.43845	−	11.1517i	−0.208562	−	0.361240i	0.742700	−	0.669624i	$-0.233545\pi$
$953$	−6.43845	−	11.1517i	−0.208562	−	0.361240i	−0.951262	+	0.308385i	$0.900212\pi$
$954$	7.00000			0.226633
$955$	4.00000	+	6.92820i	0.129437	+	0.224191i
$956$	−9.68466	−	16.7743i	−0.313224	−	0.542520i
$957$	−15.6847			−0.507013
$958$	0.965435	+	1.67218i	0.0311918	+	0.0540258i
$959$	−6.21922	+	10.7720i	−0.200829	+	0.347846i
$960$	0.780776	−	1.35234i	0.0251995	−	0.0436467i
$961$	−31.0000			−1.00000
$962$	6.93087	−	5.40938i	0.223460	−	0.174405i
$963$	13.9309			0.448916
$964$	0.0961180	−	0.166481i	0.00309575	−	0.00536200i
$965$	−0.0961180	+	0.166481i	−0.00309415	+	0.00535922i
$966$	−0.561553	−	0.972638i	−0.0180677	−	0.0312941i
$967$	−28.4924			−0.916255			−0.458127	−	0.888887i	$-0.651480\pi$
$967$	−28.4924			−0.916255			−0.458127	+	0.888887i	$0.651480\pi$
$968$	2.21922	+	3.84381i	0.0713285	+	0.123545i
$969$	−0.157671	−	0.273094i	−0.00506512	−	0.00877304i
$970$	−1.36932			−0.0439661
$971$	−20.8078	−	36.0401i	−0.667753	−	1.15658i	−0.978531	−	0.206100i	$-0.933923\pi$
$971$	−20.8078	−	36.0401i	−0.667753	−	1.15658i	0.310778	−	0.950482i	$-0.399410\pi$
$972$	0.500000	−	0.866025i	0.0160375	−	0.0277778i
$973$	2.71922	−	4.70983i	0.0871743	−	0.150990i
$974$	23.6847			0.758905
$975$	8.56155	+	3.46410i	0.274189	+	0.110940i
$976$	−11.2462			−0.359982
$977$	20.5885	−	35.6604i	0.658686	−	1.14088i	−0.322270	−	0.946648i	$-0.604446\pi$
$977$	20.5885	−	35.6604i	0.658686	−	1.14088i	0.980956	−	0.194230i	$-0.0622207\pi$
$978$	12.2462	−	21.2111i	0.391591	−	0.678255i
$979$	4.40388	+	7.62775i	0.140749	+	0.243784i
$980$	1.56155			0.0498820
$981$	6.12311	+	10.6055i	0.195496	+	0.338609i
$982$	8.24621	+	14.2829i	0.263147	+	0.455784i
$983$	18.7386			0.597670			0.298835	−	0.954305i	$-0.403402\pi$
$983$	18.7386			0.597670			0.298835	+	0.954305i	$0.403402\pi$
$984$	−5.62311	−	9.73950i	−0.179258	−	0.310484i
$985$	−9.80776	+	16.9875i	−0.312501	+	0.541268i
$986$	0.376894	−	0.652800i	0.0120028	−	0.0207894i
$987$	0.315342			0.0100374
$988$	−8.56155	−	3.46410i	−0.272379	−	0.110208i
$989$	8.98485			0.285701
$990$	2.00000	−	3.46410i	0.0635642	−	0.110096i
$991$	14.3348	−	24.8285i	0.455358	−	0.788704i	−0.543350	−	0.839506i	$-0.682844\pi$
$991$	14.3348	−	24.8285i	0.455358	−	0.788704i	0.998709	+	0.0508022i	$0.0161778\pi$
$992$		0			0
$993$	−19.3693			−0.614667
$994$	5.68466	+	9.84612i	0.180306	+	0.312300i
$995$	12.4924	+	21.6375i	0.396036	+	0.685955i
$996$	5.12311			0.162332
$997$	20.9924	+	36.3599i	0.664837	+	1.15153i	0.979330	+	0.202271i	$0.0648322\pi$
$997$	20.9924	+	36.3599i	0.664837	+	1.15153i	−0.314493	+	0.949260i	$0.601834\pi$
$998$	−15.1231	+	26.1940i	−0.478714	+	0.829156i
$999$	−1.21922	+	2.11176i	−0.0385745	+	0.0668130i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.l.l.295.2	yes	4
3.2	odd	2		1638.2.r.y.1387.1		4
13.3	even	3	inner	546.2.l.l.211.2	✓	4
13.4	even	6		7098.2.a.bi.1.1		2
13.9	even	3		7098.2.a.bt.1.2		2
39.29	odd	6		1638.2.r.y.757.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.l.l.211.2	✓	4	13.3	even	3	inner
546.2.l.l.295.2	yes	4	1.1	even	1	trivial
1638.2.r.y.757.1		4	39.29	odd	6
1638.2.r.y.1387.1		4	3.2	odd	2
7098.2.a.bi.1.1		2	13.4	even	6
7098.2.a.bt.1.2		2	13.9	even	3

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.l (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +1.56155 q^{5} +(0.500000 + 0.866025i) q^{6} +(-0.500000 - 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +1.56155 q^{5} +(0.500000 + 0.866025i) q^{6} +(-0.500000 - 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.780776 + 1.35234i) q^{10} +(1.28078 - 2.21837i) q^{11} -1.00000 q^{12} +(-0.500000 - 3.57071i) q^{13} +1.00000 q^{14} +(0.780776 - 1.35234i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.0615528 - 0.106613i) q^{17} +1.00000 q^{18} +(1.28078 + 2.21837i) q^{19} +(-0.780776 - 1.35234i) q^{20} -1.00000 q^{21} +(1.28078 + 2.21837i) q^{22} +(0.561553 - 0.972638i) q^{23} +(0.500000 - 0.866025i) q^{24} -2.56155 q^{25} +(3.34233 + 1.35234i) q^{26} -1.00000 q^{27} +(-0.500000 + 0.866025i) q^{28} +(3.06155 - 5.30277i) q^{29} +(0.780776 + 1.35234i) q^{30} +(-0.500000 - 0.866025i) q^{32} +(-1.28078 - 2.21837i) q^{33} +0.123106 q^{34} +(-0.780776 - 1.35234i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(1.21922 - 2.11176i) q^{37} -2.56155 q^{38} +(-3.34233 - 1.35234i) q^{39} +1.56155 q^{40} +(5.62311 - 9.73950i) q^{41} +(0.500000 - 0.866025i) q^{42} +(4.00000 + 6.92820i) q^{43} -2.56155 q^{44} +(-0.780776 - 1.35234i) q^{45} +(0.561553 + 0.972638i) q^{46} -0.315342 q^{47} +(0.500000 + 0.866025i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(1.28078 - 2.21837i) q^{50} -0.123106 q^{51} +(-2.84233 + 2.21837i) q^{52} +7.00000 q^{53} +(0.500000 - 0.866025i) q^{54} +(2.00000 - 3.46410i) q^{55} +(-0.500000 - 0.866025i) q^{56} +2.56155 q^{57} +(3.06155 + 5.30277i) q^{58} +(-2.56155 - 4.43674i) q^{59} -1.56155 q^{60} +(5.62311 + 9.73950i) q^{61} +(-0.500000 + 0.866025i) q^{63} +1.00000 q^{64} +(-0.780776 - 5.57586i) q^{65} +2.56155 q^{66} +(-4.56155 + 7.90084i) q^{67} +(-0.0615528 + 0.106613i) q^{68} +(-0.561553 - 0.972638i) q^{69} +1.56155 q^{70} +(5.68466 + 9.84612i) q^{71} +(-0.500000 - 0.866025i) q^{72} -2.43845 q^{73} +(1.21922 + 2.11176i) q^{74} +(-1.28078 + 2.21837i) q^{75} +(1.28078 - 2.21837i) q^{76} -2.56155 q^{77} +(2.84233 - 2.21837i) q^{78} -6.56155 q^{79} +(-0.780776 + 1.35234i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(5.62311 + 9.73950i) q^{82} -5.12311 q^{83} +(0.500000 + 0.866025i) q^{84} +(-0.0961180 - 0.166481i) q^{85} -8.00000 q^{86} +(-3.06155 - 5.30277i) q^{87} +(1.28078 - 2.21837i) q^{88} +(-1.71922 + 2.97778i) q^{89} +1.56155 q^{90} +(-2.84233 + 2.21837i) q^{91} -1.12311 q^{92} +(0.157671 - 0.273094i) q^{94} +(2.00000 + 3.46410i) q^{95} -1.00000 q^{96} +(0.438447 + 0.759413i) q^{97} +(-0.500000 - 0.866025i) q^{98} -2.56155 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} + 4 q^{8} - 2 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 + 2 * q^6 - 2 * q^7 + 4 * q^8 - 2 * q^9	\( 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} + 4 q^{8} - 2 q^{9} + q^{10} + q^{11} - 4 q^{12} - 2 q^{13} + 4 q^{14} - q^{15} - 2 q^{16} + 8 q^{17} + 4 q^{18} + q^{19} + q^{20} - 4 q^{21} + q^{22} - 6 q^{23} + 2 q^{24} - 2 q^{25} + q^{26} - 4 q^{27} - 2 q^{28} + 4 q^{29} - q^{30} - 2 q^{32} - q^{33} - 16 q^{34} + q^{35} - 2 q^{36} + 9 q^{37} - 2 q^{38} - q^{39} - 2 q^{40} + 6 q^{41} + 2 q^{42} + 16 q^{43} - 2 q^{44} + q^{45} - 6 q^{46} - 26 q^{47} + 2 q^{48} - 2 q^{49} + q^{50} + 16 q^{51} + q^{52} + 28 q^{53} + 2 q^{54} + 8 q^{55} - 2 q^{56} + 2 q^{57} + 4 q^{58} - 2 q^{59} + 2 q^{60} + 6 q^{61} - 2 q^{63} + 4 q^{64} + q^{65} + 2 q^{66} - 10 q^{67} + 8 q^{68} + 6 q^{69} - 2 q^{70} - 2 q^{71} - 2 q^{72} - 18 q^{73} + 9 q^{74} - q^{75} + q^{76} - 2 q^{77} - q^{78} - 18 q^{79} + q^{80} - 2 q^{81} + 6 q^{82} - 4 q^{83} + 2 q^{84} - 21 q^{85} - 32 q^{86} - 4 q^{87} + q^{88} - 11 q^{89} - 2 q^{90} + q^{91} + 12 q^{92} + 13 q^{94} + 8 q^{95} - 4 q^{96} + 10 q^{97} - 2 q^{98} - 2 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 + 2 * q^6 - 2 * q^7 + 4 * q^8 - 2 * q^9 + q^10 + q^11 - 4 * q^12 - 2 * q^13 + 4 * q^14 - q^15 - 2 * q^16 + 8 * q^17 + 4 * q^18 + q^19 + q^20 - 4 * q^21 + q^22 - 6 * q^23 + 2 * q^24 - 2 * q^25 + q^26 - 4 * q^27 - 2 * q^28 + 4 * q^29 - q^30 - 2 * q^32 - q^33 - 16 * q^34 + q^35 - 2 * q^36 + 9 * q^37 - 2 * q^38 - q^39 - 2 * q^40 + 6 * q^41 + 2 * q^42 + 16 * q^43 - 2 * q^44 + q^45 - 6 * q^46 - 26 * q^47 + 2 * q^48 - 2 * q^49 + q^50 + 16 * q^51 + q^52 + 28 * q^53 + 2 * q^54 + 8 * q^55 - 2 * q^56 + 2 * q^57 + 4 * q^58 - 2 * q^59 + 2 * q^60 + 6 * q^61 - 2 * q^63 + 4 * q^64 + q^65 + 2 * q^66 - 10 * q^67 + 8 * q^68 + 6 * q^69 - 2 * q^70 - 2 * q^71 - 2 * q^72 - 18 * q^73 + 9 * q^74 - q^75 + q^76 - 2 * q^77 - q^78 - 18 * q^79 + q^80 - 2 * q^81 + 6 * q^82 - 4 * q^83 + 2 * q^84 - 21 * q^85 - 32 * q^86 - 4 * q^87 + q^88 - 11 * q^89 - 2 * q^90 + q^91 + 12 * q^92 + 13 * q^94 + 8 * q^95 - 4 * q^96 + 10 * q^97 - 2 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

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