LMFDB - Embedded newform 403.2.k.b.157.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(66,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("403.66");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.k (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:	$3.21797120146$
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			157.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	403.157
Dual form			403.2.k.b.326.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 - 0.587785i) q^{2} +(-1.61803 + 1.17557i) q^{3} +(-0.309017 - 0.951057i) q^{4} -3.23607 q^{5} +2.00000 q^{6} +(0.809017 + 2.48990i) q^{7} +(-0.927051 + 2.85317i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.809017 - 0.587785i) q^{2} +(-1.61803 + 1.17557i) q^{3} +(-0.309017 - 0.951057i) q^{4} -3.23607 q^{5} +2.00000 q^{6} +(0.809017 + 2.48990i) q^{7} +(-0.927051 + 2.85317i) q^{8} +(0.309017 - 0.951057i) q^{9} +(2.61803 + 1.90211i) q^{10} +(-0.500000 - 1.53884i) q^{11} +(1.61803 + 1.17557i) q^{12} +(0.809017 - 0.587785i) q^{13} +(0.809017 - 2.48990i) q^{14} +(5.23607 - 3.80423i) q^{15} +(0.809017 - 0.587785i) q^{16} +(1.42705 - 4.39201i) q^{17} +(-0.809017 + 0.587785i) q^{18} +(1.00000 + 3.07768i) q^{20} +(-4.23607 - 3.07768i) q^{21} +(-0.500000 + 1.53884i) q^{22} +(1.61803 - 4.97980i) q^{23} +(-1.85410 - 5.70634i) q^{24} +5.47214 q^{25} -1.00000 q^{26} +(-1.23607 - 3.80423i) q^{27} +(2.11803 - 1.53884i) q^{28} +(-2.50000 - 1.81636i) q^{29} -6.47214 q^{30} +(3.23607 + 4.53077i) q^{31} +5.00000 q^{32} +(2.61803 + 1.90211i) q^{33} +(-3.73607 + 2.71441i) q^{34} +(-2.61803 - 8.05748i) q^{35} -1.00000 q^{36} +3.23607 q^{37} +(-0.618034 + 1.90211i) q^{39} +(3.00000 - 9.23305i) q^{40} +(1.61803 + 4.97980i) q^{42} +(7.85410 + 5.70634i) q^{43} +(-1.30902 + 0.951057i) q^{44} +(-1.00000 + 3.07768i) q^{45} +(-4.23607 + 3.07768i) q^{46} +(9.59017 - 6.96767i) q^{47} +(-0.618034 + 1.90211i) q^{48} +(0.118034 - 0.0857567i) q^{49} +(-4.42705 - 3.21644i) q^{50} +(2.85410 + 8.78402i) q^{51} +(-0.809017 - 0.587785i) q^{52} +(-0.618034 + 1.90211i) q^{53} +(-1.23607 + 3.80423i) q^{54} +(1.61803 + 4.97980i) q^{55} -7.85410 q^{56} +(0.954915 + 2.93893i) q^{58} +(-6.54508 + 4.75528i) q^{59} +(-5.23607 - 3.80423i) q^{60} -10.3820 q^{61} +(0.0450850 - 5.56758i) q^{62} +2.61803 q^{63} +(-5.66312 - 4.11450i) q^{64} +(-2.61803 + 1.90211i) q^{65} +(-1.00000 - 3.07768i) q^{66} +6.61803 q^{67} -4.61803 q^{68} +(3.23607 + 9.95959i) q^{69} +(-2.61803 + 8.05748i) q^{70} +(0.500000 - 1.53884i) q^{71} +(2.42705 + 1.76336i) q^{72} +(-2.38197 - 7.33094i) q^{73} +(-2.61803 - 1.90211i) q^{74} +(-8.85410 + 6.43288i) q^{75} +(3.42705 - 2.48990i) q^{77} +(1.61803 - 1.17557i) q^{78} +(3.76393 - 11.5842i) q^{79} +(-2.61803 + 1.90211i) q^{80} +(8.89919 + 6.46564i) q^{81} +(1.92705 + 1.40008i) q^{83} +(-1.61803 + 4.97980i) q^{84} +(-4.61803 + 14.2128i) q^{85} +(-3.00000 - 9.23305i) q^{86} +6.18034 q^{87} +4.85410 q^{88} +(-1.23607 - 3.80423i) q^{89} +(2.61803 - 1.90211i) q^{90} +(2.11803 + 1.53884i) q^{91} -5.23607 q^{92} +(-10.5623 - 3.52671i) q^{93} -11.8541 q^{94} +(-8.09017 + 5.87785i) q^{96} +(2.52786 + 7.77997i) q^{97} -0.145898 q^{98} -1.61803 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} - 2 q^{3} + q^{4} - 4 q^{5} + 8 q^{6} + q^{7} + 3 q^{8} - q^{9}+O(q^{10}) $ 4 * q - q^2 - 2 * q^3 + q^4 - 4 * q^5 + 8 * q^6 + q^7 + 3 * q^8 - q^9	$ 4 q - q^{2} - 2 q^{3} + q^{4} - 4 q^{5} + 8 q^{6} + q^{7} + 3 q^{8} - q^{9} + 6 q^{10} - 2 q^{11} + 2 q^{12} + q^{13} + q^{14} + 12 q^{15} + q^{16} - q^{17} - q^{18} + 4 q^{20} - 8 q^{21} - 2 q^{22} + 2 q^{23} + 6 q^{24} + 4 q^{25} - 4 q^{26} + 4 q^{27} + 4 q^{28} - 10 q^{29} - 8 q^{30} + 4 q^{31} + 20 q^{32} + 6 q^{33} - 6 q^{34} - 6 q^{35} - 4 q^{36} + 4 q^{37} + 2 q^{39} + 12 q^{40} + 2 q^{42} + 18 q^{43} - 3 q^{44} - 4 q^{45} - 8 q^{46} + 16 q^{47} + 2 q^{48} - 4 q^{49} - 11 q^{50} - 2 q^{51} - q^{52} + 2 q^{53} + 4 q^{54} + 2 q^{55} - 18 q^{56} + 15 q^{58} - 15 q^{59} - 12 q^{60} - 46 q^{61} - 11 q^{62} + 6 q^{63} - 7 q^{64} - 6 q^{65} - 4 q^{66} + 22 q^{67} - 14 q^{68} + 4 q^{69} - 6 q^{70} + 2 q^{71} + 3 q^{72} - 14 q^{73} - 6 q^{74} - 22 q^{75} + 7 q^{77} + 2 q^{78} + 24 q^{79} - 6 q^{80} + 11 q^{81} + q^{83} - 2 q^{84} - 14 q^{85} - 12 q^{86} - 20 q^{87} + 6 q^{88} + 4 q^{89} + 6 q^{90} + 4 q^{91} - 12 q^{92} - 2 q^{93} - 34 q^{94} - 10 q^{96} + 28 q^{97} - 14 q^{98} - 2 q^{99}+O(q^{100}) $ 4 * q - q^2 - 2 * q^3 + q^4 - 4 * q^5 + 8 * q^6 + q^7 + 3 * q^8 - q^9 + 6 * q^10 - 2 * q^11 + 2 * q^12 + q^13 + q^14 + 12 * q^15 + q^16 - q^17 - q^18 + 4 * q^20 - 8 * q^21 - 2 * q^22 + 2 * q^23 + 6 * q^24 + 4 * q^25 - 4 * q^26 + 4 * q^27 + 4 * q^28 - 10 * q^29 - 8 * q^30 + 4 * q^31 + 20 * q^32 + 6 * q^33 - 6 * q^34 - 6 * q^35 - 4 * q^36 + 4 * q^37 + 2 * q^39 + 12 * q^40 + 2 * q^42 + 18 * q^43 - 3 * q^44 - 4 * q^45 - 8 * q^46 + 16 * q^47 + 2 * q^48 - 4 * q^49 - 11 * q^50 - 2 * q^51 - q^52 + 2 * q^53 + 4 * q^54 + 2 * q^55 - 18 * q^56 + 15 * q^58 - 15 * q^59 - 12 * q^60 - 46 * q^61 - 11 * q^62 + 6 * q^63 - 7 * q^64 - 6 * q^65 - 4 * q^66 + 22 * q^67 - 14 * q^68 + 4 * q^69 - 6 * q^70 + 2 * q^71 + 3 * q^72 - 14 * q^73 - 6 * q^74 - 22 * q^75 + 7 * q^77 + 2 * q^78 + 24 * q^79 - 6 * q^80 + 11 * q^81 + q^83 - 2 * q^84 - 14 * q^85 - 12 * q^86 - 20 * q^87 + 6 * q^88 + 4 * q^89 + 6 * q^90 + 4 * q^91 - 12 * q^92 - 2 * q^93 - 34 * q^94 - 10 * q^96 + 28 * q^97 - 14 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i	0.263792	−	0.964580i	$-0.415027\pi$
$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i	−0.835853	+	0.548953i	$0.815027\pi$
$3$	−1.61803	+	1.17557i	−0.934172	+	0.678716i	−0.947011	−	0.321202i	$-0.895913\pi$
$3$	−1.61803	+	1.17557i	−0.934172	+	0.678716i	0.0128385	+	0.999918i	$0.495913\pi$
$4$	−0.309017	−	0.951057i	−0.154508	−	0.475528i
$5$	−3.23607			−1.44721			−0.723607	−	0.690212i	$-0.757517\pi$
$5$	−3.23607			−1.44721			−0.723607	+	0.690212i	$0.757517\pi$
$6$	2.00000			0.816497
$7$	0.809017	+	2.48990i	0.305780	+	0.941093i	0.979385	+	0.202002i	$0.0647447\pi$
$7$	0.809017	+	2.48990i	0.305780	+	0.941093i	−0.673605	+	0.739091i	$0.735255\pi$
$8$	−0.927051	+	2.85317i	−0.327762	+	1.00875i
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$	2.61803	+	1.90211i	0.827895	+	0.601501i
$11$	−0.500000	−	1.53884i	−0.150756	−	0.463978i	0.846950	−	0.531672i	$-0.178436\pi$
$11$	−0.500000	−	1.53884i	−0.150756	−	0.463978i	−0.997706	+	0.0676935i	$0.978436\pi$
$12$	1.61803	+	1.17557i	0.467086	+	0.339358i
$13$	0.809017	−	0.587785i	0.224381	−	0.163022i
$13$	0.809017	−	0.587785i	0.224381	−	0.163022i
$14$	0.809017	−	2.48990i	0.216219	−	0.665453i
$15$	5.23607	−	3.80423i	1.35195	−	0.982247i
$16$	0.809017	−	0.587785i	0.202254	−	0.146946i
$17$	1.42705	−	4.39201i	0.346111	−	1.06522i	−0.614876	−	0.788624i	$-0.710794\pi$
$17$	1.42705	−	4.39201i	0.346111	−	1.06522i	0.960987	−	0.276595i	$-0.0892061\pi$
$18$	−0.809017	+	0.587785i	−0.190687	+	0.138542i
$19$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$19$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$20$	1.00000	+	3.07768i	0.223607	+	0.688191i
$21$	−4.23607	−	3.07768i	−0.924386	−	0.671606i
$22$	−0.500000	+	1.53884i	−0.106600	+	0.328082i
$23$	1.61803	−	4.97980i	0.337383	−	1.03836i	−0.628153	−	0.778090i	$-0.716189\pi$
$23$	1.61803	−	4.97980i	0.337383	−	1.03836i	0.965536	−	0.260269i	$-0.0838113\pi$
$24$	−1.85410	−	5.70634i	−0.378467	−	1.16480i
$25$	5.47214			1.09443
$26$	−1.00000			−0.196116
$27$	−1.23607	−	3.80423i	−0.237881	−	0.732124i
$28$	2.11803	−	1.53884i	0.400271	−	0.290814i
$29$	−2.50000	−	1.81636i	−0.464238	−	0.337289i	0.330953	−	0.943647i	$-0.392630\pi$
$29$	−2.50000	−	1.81636i	−0.464238	−	0.337289i	−0.795192	+	0.606358i	$0.792630\pi$
$30$	−6.47214			−1.18164
$31$	3.23607	+	4.53077i	0.581215	+	0.813750i
$31$	3.23607	+	4.53077i	0.581215	+	0.813750i
$32$	5.00000			0.883883
$33$	2.61803	+	1.90211i	0.455741	+	0.331115i
$34$	−3.73607	+	2.71441i	−0.640730	+	0.465518i
$35$	−2.61803	−	8.05748i	−0.442529	−	1.36196i
$36$	−1.00000			−0.166667
$37$	3.23607			0.532006			0.266003	−	0.963972i	$-0.414297\pi$
$37$	3.23607			0.532006			0.266003	+	0.963972i	$0.414297\pi$
$38$		0			0
$39$	−0.618034	+	1.90211i	−0.0989646	+	0.304582i
$40$	3.00000	−	9.23305i	0.474342	−	1.45987i
$41$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$41$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$42$	1.61803	+	4.97980i	0.249668	+	0.768399i
$43$	7.85410	+	5.70634i	1.19774	+	0.870209i	0.994060	−	0.108829i	$-0.0347102\pi$
$43$	7.85410	+	5.70634i	1.19774	+	0.870209i	0.203679	+	0.979038i	$0.434710\pi$
$44$	−1.30902	+	0.951057i	−0.197342	+	0.143377i
$45$	−1.00000	+	3.07768i	−0.149071	+	0.458794i
$46$	−4.23607	+	3.07768i	−0.624574	+	0.453780i
$47$	9.59017	−	6.96767i	1.39887	−	1.01634i	0.404045	−	0.914739i	$-0.367604\pi$
$47$	9.59017	−	6.96767i	1.39887	−	1.01634i	0.994825	−	0.101599i	$-0.0323960\pi$
$48$	−0.618034	+	1.90211i	−0.0892055	+	0.274546i
$49$	0.118034	−	0.0857567i	0.0168620	−	0.0122510i
$50$	−4.42705	−	3.21644i	−0.626080	−	0.454873i
$51$	2.85410	+	8.78402i	0.399654	+	1.23001i
$52$	−0.809017	−	0.587785i	−0.112190	−	0.0815111i
$53$	−0.618034	+	1.90211i	−0.0848935	+	0.261275i	−0.984488	−	0.175450i	$-0.943862\pi$
$53$	−0.618034	+	1.90211i	−0.0848935	+	0.261275i	0.899595	+	0.436726i	$0.143862\pi$
$54$	−1.23607	+	3.80423i	−0.168208	+	0.517690i
$55$	1.61803	+	4.97980i	0.218176	+	0.671476i
$56$	−7.85410			−1.04955
$57$		0			0
$58$	0.954915	+	2.93893i	0.125386	+	0.385900i
$59$	−6.54508	+	4.75528i	−0.852097	+	0.619085i	−0.925724	−	0.378201i	$-0.876543\pi$
$59$	−6.54508	+	4.75528i	−0.852097	+	0.619085i	0.0736261	+	0.997286i	$0.476543\pi$
$60$	−5.23607	−	3.80423i	−0.675973	−	0.491123i
$61$	−10.3820			−1.32927			−0.664637	−	0.747166i	$-0.731414\pi$
$61$	−10.3820			−1.32927			−0.664637	+	0.747166i	$0.731414\pi$
$62$	0.0450850	−	5.56758i	0.00572580	−	0.707084i
$63$	2.61803			0.329841
$64$	−5.66312	−	4.11450i	−0.707890	−	0.514312i
$65$	−2.61803	+	1.90211i	−0.324727	+	0.235928i
$66$	−1.00000	−	3.07768i	−0.123091	−	0.378837i
$67$	6.61803			0.808522			0.404261	−	0.914644i	$-0.367529\pi$
$67$	6.61803			0.808522			0.404261	+	0.914644i	$0.367529\pi$
$68$	−4.61803			−0.560019
$69$	3.23607	+	9.95959i	0.389577	+	1.19899i
$70$	−2.61803	+	8.05748i	−0.312915	+	0.963053i
$71$	0.500000	−	1.53884i	0.0593391	−	0.182627i	−0.916993	−	0.398903i	$-0.869391\pi$
$71$	0.500000	−	1.53884i	0.0593391	−	0.182627i	0.976332	+	0.216276i	$0.0693911\pi$
$72$	2.42705	+	1.76336i	0.286031	+	0.207813i
$73$	−2.38197	−	7.33094i	−0.278788	−	0.858021i	−0.988192	−	0.153219i	$-0.951036\pi$
$73$	−2.38197	−	7.33094i	−0.278788	−	0.858021i	0.709404	−	0.704802i	$-0.248964\pi$
$74$	−2.61803	−	1.90211i	−0.304340	−	0.221116i
$75$	−8.85410	+	6.43288i	−1.02238	+	0.742805i
$76$		0			0
$77$	3.42705	−	2.48990i	0.390549	−	0.283750i
$78$	1.61803	−	1.17557i	0.183206	−	0.133107i
$79$	3.76393	−	11.5842i	0.423475	−	1.30332i	−0.480971	−	0.876736i	$-0.659716\pi$
$79$	3.76393	−	11.5842i	0.423475	−	1.30332i	0.904447	−	0.426587i	$-0.140284\pi$
$80$	−2.61803	+	1.90211i	−0.292705	+	0.212663i
$81$	8.89919	+	6.46564i	0.988799	+	0.718404i
$82$		0			0
$83$	1.92705	+	1.40008i	0.211521	+	0.153679i	0.688502	−	0.725235i	$-0.258269\pi$
$83$	1.92705	+	1.40008i	0.211521	+	0.153679i	−0.476980	+	0.878914i	$0.658269\pi$
$84$	−1.61803	+	4.97980i	−0.176542	+	0.543340i
$85$	−4.61803	+	14.2128i	−0.500896	+	1.54160i
$86$	−3.00000	−	9.23305i	−0.323498	−	0.995625i
$87$	6.18034			0.662602
$88$	4.85410			0.517449
$89$	−1.23607	−	3.80423i	−0.131023	−	0.403247i	0.863927	−	0.503617i	$-0.167998\pi$
$89$	−1.23607	−	3.80423i	−0.131023	−	0.403247i	−0.994950	+	0.100369i	$0.967998\pi$
$90$	2.61803	−	1.90211i	0.275965	−	0.200500i
$91$	2.11803	+	1.53884i	0.222030	+	0.161314i
$92$	−5.23607			−0.545898
$93$	−10.5623	−	3.52671i	−1.09526	−	0.365703i
$94$	−11.8541			−1.22266
$95$		0			0
$96$	−8.09017	+	5.87785i	−0.825700	+	0.599906i
$97$	2.52786	+	7.77997i	0.256666	+	0.789936i	0.993497	+	0.113859i	$0.0363212\pi$
$97$	2.52786	+	7.77997i	0.256666	+	0.789936i	−0.736831	+	0.676077i	$0.763679\pi$
$98$	−0.145898			−0.0147379
$99$	−1.61803			−0.162619
$100$	−1.69098	−	5.20431i	−0.169098	−	0.520431i
$101$	−5.26393	+	16.2007i	−0.523781	+	1.61203i	0.242933	+	0.970043i	$0.421890\pi$
$101$	−5.26393	+	16.2007i	−0.523781	+	1.61203i	−0.766714	+	0.641989i	$0.778110\pi$
$102$	2.85410	−	8.78402i	0.282598	−	0.869748i
$103$	−13.9443	−	10.1311i	−1.37397	−	0.998248i	−0.997415	−	0.0718532i	$-0.977109\pi$
$103$	−13.9443	−	10.1311i	−1.37397	−	0.998248i	−0.376555	−	0.926394i	$-0.622891\pi$
$104$	0.927051	+	2.85317i	0.0909048	+	0.279776i
$105$	13.7082	+	9.95959i	1.33778	+	0.971957i
$106$	1.61803	−	1.17557i	0.157157	−	0.114182i
$107$	1.85410	−	5.70634i	0.179243	−	0.551653i	−0.820559	−	0.571562i	$-0.806338\pi$
$107$	1.85410	−	5.70634i	0.179243	−	0.551653i	0.999802	+	0.0199092i	$0.00633772\pi$
$108$	−3.23607	+	2.35114i	−0.311391	+	0.226239i
$109$	8.85410	−	6.43288i	0.848069	−	0.616158i	−0.0765438	−	0.997066i	$-0.524389\pi$
$109$	8.85410	−	6.43288i	0.848069	−	0.616158i	0.924613	+	0.380908i	$0.124389\pi$
$110$	1.61803	−	4.97980i	0.154273	−	0.474805i
$111$	−5.23607	+	3.80423i	−0.496986	+	0.361081i
$112$	2.11803	+	1.53884i	0.200135	+	0.145407i
$113$	4.97214	+	15.3027i	0.467739	+	1.43955i	0.855505	+	0.517795i	$0.173247\pi$
$113$	4.97214	+	15.3027i	0.467739	+	1.43955i	−0.387765	+	0.921758i	$0.626753\pi$
$114$		0			0
$115$	−5.23607	+	16.1150i	−0.488266	+	1.50273i
$116$	−0.954915	+	2.93893i	−0.0886616	+	0.272872i
$117$	−0.309017	−	0.951057i	−0.0285686	−	0.0879252i
$118$	8.09017			0.744761
$119$	12.0902			1.10830
$120$	6.00000	+	18.4661i	0.547723	+	1.68572i
$121$	6.78115	−	4.92680i	0.616468	−	0.447891i
$122$	8.39919	+	6.10237i	0.760427	+	0.552482i
$123$		0			0
$124$	3.30902	−	4.47777i	0.297158	−	0.402115i
$125$	−1.52786			−0.136656
$126$	−2.11803	−	1.53884i	−0.188689	−	0.137091i
$127$	7.23607	−	5.25731i	0.642097	−	0.466511i	−0.218473	−	0.975843i	$-0.570108\pi$
$127$	7.23607	−	5.25731i	0.642097	−	0.466511i	0.860570	+	0.509332i	$0.170108\pi$
$128$	−0.927051	−	2.85317i	−0.0819405	−	0.252187i
$129$	−19.4164			−1.70952
$130$	3.23607			0.283822
$131$	−5.47214	−	16.8415i	−0.478103	−	1.47145i	−0.841727	−	0.539903i	$-0.818461\pi$
$131$	−5.47214	−	16.8415i	−0.478103	−	1.47145i	0.363624	−	0.931546i	$-0.381539\pi$
$132$	1.00000	−	3.07768i	0.0870388	−	0.267878i
$133$		0			0
$134$	−5.35410	−	3.88998i	−0.462524	−	0.336043i
$135$	4.00000	+	12.3107i	0.344265	+	1.05954i
$136$	11.2082	+	8.14324i	0.961096	+	0.698277i
$137$	5.23607	−	3.80423i	0.447347	−	0.325017i	−0.341200	−	0.939991i	$-0.610833\pi$
$137$	5.23607	−	3.80423i	0.447347	−	0.325017i	0.788548	+	0.614974i	$0.210833\pi$
$138$	3.23607	−	9.95959i	0.275472	−	0.847817i
$139$	4.61803	−	3.35520i	0.391697	−	0.284584i	−0.374454	−	0.927246i	$-0.622170\pi$
$139$	4.61803	−	3.35520i	0.391697	−	0.284584i	0.766150	+	0.642661i	$0.222170\pi$
$140$	−6.85410	+	4.97980i	−0.579277	+	0.420870i
$141$	−7.32624	+	22.5478i	−0.616981	+	1.89887i
$142$	−1.30902	+	0.951057i	−0.109850	+	0.0798109i
$143$	−1.30902	−	0.951057i	−0.109466	−	0.0795313i
$144$	−0.309017	−	0.951057i	−0.0257514	−	0.0792547i
$145$	8.09017	+	5.87785i	0.671852	+	0.488129i
$146$	−2.38197	+	7.33094i	−0.197133	+	0.606713i
$147$	−0.0901699	+	0.277515i	−0.00743709	+	0.0228890i
$148$	−1.00000	−	3.07768i	−0.0821995	−	0.252984i
$149$	1.70820			0.139942			0.0699708	−	0.997549i	$-0.477709\pi$
$149$	1.70820			0.139942			0.0699708	+	0.997549i	$0.477709\pi$
$150$	10.9443			0.893596
$151$	−0.263932	−	0.812299i	−0.0214785	−	0.0661040i	0.939743	−	0.341882i	$-0.111064\pi$
$151$	−0.263932	−	0.812299i	−0.0214785	−	0.0661040i	−0.961221	+	0.275778i	$0.911064\pi$
$152$		0			0
$153$	−3.73607	−	2.71441i	−0.302043	−	0.219447i
$154$	−4.23607			−0.341352
$155$	−10.4721	−	14.6619i	−0.841142	−	1.17767i
$156$	2.00000			0.160128
$157$	−10.3992	−	7.55545i	−0.829945	−	0.602991i	0.0895984	−	0.995978i	$-0.471442\pi$
$157$	−10.3992	−	7.55545i	−0.829945	−	0.602991i	−0.919544	+	0.392987i	$0.871442\pi$
$158$	−9.85410	+	7.15942i	−0.783950	+	0.569573i
$159$	−1.23607	−	3.80423i	−0.0980266	−	0.301695i
$160$	−16.1803			−1.27917
$161$	13.7082			1.08036
$162$	−3.39919	−	10.4616i	−0.267065	−	0.821943i
$163$	3.79180	−	11.6699i	0.296996	−	0.914061i	−0.685547	−	0.728028i	$-0.740437\pi$
$163$	3.79180	−	11.6699i	0.296996	−	0.914061i	0.982544	−	0.186033i	$-0.0595630\pi$
$164$		0			0
$165$	−8.47214	−	6.15537i	−0.659555	−	0.479195i
$166$	−0.736068	−	2.26538i	−0.0571300	−	0.175828i
$167$	4.35410	+	3.16344i	0.336931	+	0.244794i	0.743366	−	0.668885i	$-0.233228\pi$
$167$	4.35410	+	3.16344i	0.336931	+	0.244794i	−0.406435	+	0.913680i	$0.633228\pi$
$168$	12.7082	−	9.23305i	0.980459	−	0.712345i
$169$	0.309017	−	0.951057i	0.0237705	−	0.0731582i
$170$	12.0902	−	8.78402i	0.927274	−	0.673704i
$171$		0			0
$172$	3.00000	−	9.23305i	0.228748	−	0.704014i
$173$	2.54508	−	1.84911i	0.193499	−	0.140585i	−0.486817	−	0.873504i	$-0.661842\pi$
$173$	2.54508	−	1.84911i	0.193499	−	0.140585i	0.680317	+	0.732918i	$0.261842\pi$
$174$	−5.00000	−	3.63271i	−0.379049	−	0.275395i
$175$	4.42705	+	13.6251i	0.334654	+	1.02996i
$176$	−1.30902	−	0.951057i	−0.0986709	−	0.0716886i
$177$	5.00000	−	15.3884i	0.375823	−	1.15666i
$178$	−1.23607	+	3.80423i	−0.0926472	+	0.285139i
$179$	−4.47214	−	13.7638i	−0.334263	−	1.02876i	−0.967084	−	0.254458i	$-0.918103\pi$
$179$	−4.47214	−	13.7638i	−0.334263	−	1.02876i	0.632821	−	0.774298i	$-0.281897\pi$
$180$	3.23607			0.241202
$181$	−2.14590			−0.159503			−0.0797517	−	0.996815i	$-0.525413\pi$
$181$	−2.14590			−0.159503			−0.0797517	+	0.996815i	$0.525413\pi$
$182$	−0.809017	−	2.48990i	−0.0599683	−	0.184564i
$183$	16.7984	−	12.2047i	1.24177	−	0.902200i
$184$	12.7082	+	9.23305i	0.936861	+	0.680670i
$185$	−10.4721			−0.769927
$186$	6.47214	+	9.06154i	0.474560	+	0.664424i
$187$	−7.47214			−0.546417
$188$	−9.59017	−	6.96767i	−0.699435	−	0.508169i
$189$	8.47214	−	6.15537i	0.616257	−	0.447737i
$190$		0			0
$191$	−23.1246			−1.67324			−0.836619	−	0.547785i	$-0.815471\pi$
$191$	−23.1246			−1.67324			−0.836619	+	0.547785i	$0.815471\pi$
$192$	14.0000			1.01036
$193$	2.76393	+	8.50651i	0.198952	+	0.612312i	0.999908	+	0.0135880i	$0.00432532\pi$
$193$	2.76393	+	8.50651i	0.198952	+	0.612312i	−0.800955	+	0.598724i	$0.795675\pi$
$194$	2.52786	−	7.77997i	0.181490	−	0.558569i
$195$	2.00000	−	6.15537i	0.143223	−	0.440795i
$196$	−0.118034	−	0.0857567i	−0.00843100	−	0.00612548i
$197$	−3.70820	−	11.4127i	−0.264199	−	0.813120i	−0.991877	−	0.127201i	$-0.959401\pi$
$197$	−3.70820	−	11.4127i	−0.264199	−	0.813120i	0.727678	−	0.685919i	$-0.240599\pi$
$198$	1.30902	+	0.951057i	0.0930278	+	0.0675886i
$199$	21.4164	−	15.5599i	1.51817	−	1.10301i	0.555783	−	0.831327i	$-0.312418\pi$
$199$	21.4164	−	15.5599i	1.51817	−	1.10301i	0.962386	−	0.271687i	$-0.0875816\pi$
$200$	−5.07295	+	15.6129i	−0.358712	+	1.10400i
$201$	−10.7082	+	7.77997i	−0.755298	+	0.548756i
$202$	13.7812	−	10.0126i	0.969639	−	0.704484i
$203$	2.50000	−	7.69421i	0.175466	−	0.540028i
$204$	7.47214	−	5.42882i	0.523154	−	0.380094i
$205$		0			0
$206$	5.32624	+	16.3925i	0.371097	+	1.14212i
$207$	−4.23607	−	3.07768i	−0.294427	−	0.213914i
$208$	0.309017	−	0.951057i	0.0214265	−	0.0659439i
$209$		0			0
$210$	−5.23607	−	16.1150i	−0.361323	−	1.11204i
$211$	−13.7082			−0.943712			−0.471856	−	0.881676i	$-0.656416\pi$
$211$	−13.7082			−0.943712			−0.471856	+	0.881676i	$0.656416\pi$
$212$	2.00000			0.137361
$213$	1.00000	+	3.07768i	0.0685189	+	0.210879i
$214$	−4.85410	+	3.52671i	−0.331820	+	0.241081i
$215$	−25.4164	−	18.4661i	−1.73338	−	1.25938i
$216$	12.0000			0.816497
$217$	−8.66312	+	11.7229i	−0.588091	+	0.795806i
$218$	−10.9443			−0.741240
$219$	12.4721	+	9.06154i	0.842789	+	0.612322i
$220$	4.23607	−	3.07768i	0.285596	−	0.207497i
$221$	−1.42705	−	4.39201i	−0.0959938	−	0.295439i
$222$	6.47214			0.434381
$223$	2.90983			0.194857			0.0974283	−	0.995243i	$-0.468938\pi$
$223$	2.90983			0.194857			0.0974283	+	0.995243i	$0.468938\pi$
$224$	4.04508	+	12.4495i	0.270274	+	0.831817i
$225$	1.69098	−	5.20431i	0.112732	−	0.346954i
$226$	4.97214	−	15.3027i	0.330742	−	1.01792i
$227$	−8.54508	−	6.20837i	−0.567157	−	0.412064i	0.266914	−	0.963720i	$-0.413996\pi$
$227$	−8.54508	−	6.20837i	−0.567157	−	0.412064i	−0.834071	+	0.551656i	$0.813996\pi$
$228$		0			0
$229$	−13.3262	−	9.68208i	−0.880623	−	0.639810i	0.0527935	−	0.998605i	$-0.483187\pi$
$229$	−13.3262	−	9.68208i	−0.880623	−	0.639810i	−0.933416	+	0.358796i	$0.883187\pi$
$230$	13.7082	−	9.95959i	0.903892	−	0.656716i
$231$	−2.61803	+	8.05748i	−0.172254	+	0.530143i
$232$	7.50000	−	5.44907i	0.492399	−	0.357749i
$233$	21.4443	−	15.5802i	1.40486	−	1.02069i	0.410816	−	0.911718i	$-0.365244\pi$
$233$	21.4443	−	15.5802i	1.40486	−	1.02069i	0.994045	−	0.108973i	$-0.0347562\pi$
$234$	−0.309017	+	0.951057i	−0.0202011	+	0.0621725i
$235$	−31.0344	+	22.5478i	−2.02446	+	1.47086i
$236$	6.54508	+	4.75528i	0.426049	+	0.309543i
$237$	7.52786	+	23.1684i	0.488987	+	1.50495i
$238$	−9.78115	−	7.10642i	−0.634018	−	0.460641i
$239$	−8.13525	+	25.0377i	−0.526226	+	1.61956i	0.235653	+	0.971837i	$0.424277\pi$
$239$	−8.13525	+	25.0377i	−0.526226	+	1.61956i	−0.761879	+	0.647720i	$0.775723\pi$
$240$	2.00000	−	6.15537i	0.129099	−	0.397327i
$241$	6.61803	+	20.3682i	0.426305	+	1.31203i	0.901739	+	0.432281i	$0.142291\pi$
$241$	6.61803	+	20.3682i	0.426305	+	1.31203i	−0.475434	+	0.879751i	$0.657709\pi$
$242$	−8.38197			−0.538813
$243$	−10.0000			−0.641500
$244$	3.20820	+	9.87384i	0.205384	+	0.632108i
$245$	−0.381966	+	0.277515i	−0.0244029	+	0.0177298i
$246$		0			0
$247$		0			0
$248$	−15.9271	+	5.03280i	−1.01137	+	0.319583i
$249$	−4.76393			−0.301902
$250$	1.23607	+	0.898056i	0.0781758	+	0.0567980i
$251$	23.5623	−	17.1190i	1.48724	−	1.08054i	0.512107	−	0.858922i	$-0.328865\pi$
$251$	23.5623	−	17.1190i	1.48724	−	1.08054i	0.975133	−	0.221621i	$-0.0711348\pi$
$252$	−0.809017	−	2.48990i	−0.0509633	−	0.156849i
$253$	−8.47214			−0.532639
$254$	−8.94427			−0.561214
$255$	−9.23607	−	28.4257i	−0.578385	−	1.78009i
$256$	−5.25329	+	16.1680i	−0.328331	+	1.01050i
$257$	−6.26393	+	19.2784i	−0.390733	+	1.20255i	0.541502	+	0.840700i	$0.317856\pi$
$257$	−6.26393	+	19.2784i	−0.390733	+	1.20255i	−0.932235	+	0.361854i	$0.882144\pi$
$258$	15.7082	+	11.4127i	0.977950	+	0.710522i
$259$	2.61803	+	8.05748i	0.162677	+	0.500667i
$260$	2.61803	+	1.90211i	0.162364	+	0.117964i
$261$	−2.50000	+	1.81636i	−0.154746	+	0.112430i
$262$	−5.47214	+	16.8415i	−0.338070	+	1.04047i
$263$	10.6180	−	7.71445i	0.654736	−	0.475694i	−0.210145	−	0.977670i	$-0.567394\pi$
$263$	10.6180	−	7.71445i	0.654736	−	0.475694i	0.864881	+	0.501977i	$0.167394\pi$
$264$	−7.85410	+	5.70634i	−0.483387	+	0.351201i
$265$	2.00000	−	6.15537i	0.122859	−	0.378121i
$266$		0			0
$267$	6.47214	+	4.70228i	0.396088	+	0.287775i
$268$	−2.04508	−	6.29412i	−0.124923	−	0.384475i
$269$	0.854102	+	0.620541i	0.0520755	+	0.0378351i	0.613519	−	0.789680i	$-0.289754\pi$
$269$	0.854102	+	0.620541i	0.0520755	+	0.0378351i	−0.561443	+	0.827515i	$0.689754\pi$
$270$	4.00000	−	12.3107i	0.243432	−	0.749207i
$271$	1.68034	−	5.17155i	0.102073	−	0.314150i	−0.886959	−	0.461848i	$-0.847187\pi$
$271$	1.68034	−	5.17155i	0.102073	−	0.314150i	0.989032	+	0.147699i	$0.0471865\pi$
$272$	−1.42705	−	4.39201i	−0.0865277	−	0.266305i
$273$	−5.23607			−0.316901
$274$	−6.47214			−0.390996
$275$	−2.73607	−	8.42075i	−0.164991	−	0.507790i
$276$	8.47214	−	6.15537i	0.509963	−	0.370510i
$277$	5.78115	+	4.20025i	0.347356	+	0.252369i	0.747759	−	0.663970i	$-0.231130\pi$
$277$	5.78115	+	4.20025i	0.347356	+	0.252369i	−0.400403	+	0.916339i	$0.631130\pi$
$278$	−5.70820			−0.342355
$279$	5.30902	−	1.67760i	0.317843	−	0.100435i
$280$	25.4164			1.51892
$281$	11.7082	+	8.50651i	0.698453	+	0.507456i	0.879428	−	0.476032i	$-0.157925\pi$
$281$	11.7082	+	8.50651i	0.698453	+	0.507456i	−0.180975	+	0.983488i	$0.557925\pi$
$282$	19.1803	−	13.9353i	1.14217	−	0.829837i
$283$	−2.23607	−	6.88191i	−0.132920	−	0.409087i	0.862340	−	0.506329i	$-0.168998\pi$
$283$	−2.23607	−	6.88191i	−0.132920	−	0.409087i	−0.995261	+	0.0972421i	$0.968998\pi$
$284$	−1.61803			−0.0960127
$285$		0			0
$286$	0.500000	+	1.53884i	0.0295656	+	0.0909936i
$287$		0			0
$288$	1.54508	−	4.75528i	0.0910450	−	0.280208i
$289$	−3.50000	−	2.54290i	−0.205882	−	0.149582i
$290$	−3.09017	−	9.51057i	−0.181461	−	0.558480i
$291$	−13.2361	−	9.61657i	−0.775912	−	0.563733i
$292$	−6.23607	+	4.53077i	−0.364938	+	0.265143i
$293$	−7.09017	+	21.8213i	−0.414212	+	1.27481i	0.498742	+	0.866751i	$0.333796\pi$
$293$	−7.09017	+	21.8213i	−0.414212	+	1.27481i	−0.912954	+	0.408063i	$0.866204\pi$
$294$	0.236068	−	0.171513i	0.0137678	−	0.0100029i
$295$	21.1803	−	15.3884i	1.23317	−	0.895948i
$296$	−3.00000	+	9.23305i	−0.174371	+	0.536660i
$297$	−5.23607	+	3.80423i	−0.303827	+	0.220744i
$298$	−1.38197	−	1.00406i	−0.0800551	−	0.0581635i
$299$	−1.61803	−	4.97980i	−0.0935733	−	0.287989i
$300$	8.85410	+	6.43288i	0.511192	+	0.371403i
$301$	−7.85410	+	24.1724i	−0.452703	+	1.39328i
$302$	−0.263932	+	0.812299i	−0.0151876	+	0.0467426i
$303$	−10.5279	−	32.4014i	−0.604810	−	1.86141i
$304$		0			0
$305$	33.5967			1.92374
$306$	1.42705	+	4.39201i	0.0815791	+	0.251075i
$307$	10.8262	−	7.86572i	0.617886	−	0.448920i	−0.234296	−	0.972165i	$-0.575279\pi$
$307$	10.8262	−	7.86572i	0.617886	−	0.448920i	0.852182	+	0.523245i	$0.175279\pi$
$308$	−3.42705	−	2.48990i	−0.195274	−	0.141875i
$309$	34.4721			1.96105
$310$	−0.145898	+	18.0171i	−0.00828645	+	1.02330i
$311$	2.65248			0.150408			0.0752041	−	0.997168i	$-0.476039\pi$
$311$	2.65248			0.150408			0.0752041	+	0.997168i	$0.476039\pi$
$312$	−4.85410	−	3.52671i	−0.274809	−	0.199661i
$313$	2.38197	−	1.73060i	0.134637	−	0.0978193i	−0.518428	−	0.855121i	$-0.673483\pi$
$313$	2.38197	−	1.73060i	0.134637	−	0.0978193i	0.653065	+	0.757302i	$0.273483\pi$
$314$	3.97214	+	12.2250i	0.224161	+	0.689895i
$315$	−8.47214			−0.477351
$316$	−12.1803			−0.685198
$317$	−3.18034	−	9.78808i	−0.178626	−	0.549753i	0.821155	−	0.570706i	$-0.193330\pi$
$317$	−3.18034	−	9.78808i	−0.178626	−	0.549753i	−0.999780	+	0.0209522i	$0.993330\pi$
$318$	−1.23607	+	3.80423i	−0.0693153	+	0.213330i
$319$	−1.54508	+	4.75528i	−0.0865082	+	0.266245i
$320$	18.3262	+	13.3148i	1.02447	+	0.744319i
$321$	3.70820	+	11.4127i	0.206972	+	0.636994i
$322$	−11.0902	−	8.05748i	−0.618031	−	0.449026i
$323$		0			0
$324$	3.39919	−	10.4616i	0.188844	−	0.581201i
$325$	4.42705	−	3.21644i	0.245569	−	0.178416i
$326$	−9.92705	+	7.21242i	−0.549809	+	0.399459i
$327$	−6.76393	+	20.8172i	−0.374046	+	1.15120i
$328$		0			0
$329$	25.1074	+	18.2416i	1.38422	+	1.00569i
$330$	3.23607	+	9.95959i	0.178140	+	0.548258i
$331$	26.5795	+	19.3112i	1.46094	+	1.06144i	0.983116	+	0.182983i	$0.0585754\pi$
$331$	26.5795	+	19.3112i	1.46094	+	1.06144i	0.477827	+	0.878454i	$0.341425\pi$
$332$	0.736068	−	2.26538i	0.0403970	−	0.124329i
$333$	1.00000	−	3.07768i	0.0547997	−	0.168656i
$334$	−1.66312	−	5.11855i	−0.0910018	−	0.280075i
$335$	−21.4164			−1.17010
$336$	−5.23607			−0.285651
$337$	−3.80902	−	11.7229i	−0.207490	−	0.638590i	−0.999602	−	0.0282134i	$-0.991018\pi$
$337$	−3.80902	−	11.7229i	−0.207490	−	0.638590i	0.792112	−	0.610376i	$-0.208982\pi$
$338$	−0.809017	+	0.587785i	−0.0440047	+	0.0319713i
$339$	−26.0344	−	18.9151i	−1.41400	−	1.02733i
$340$	14.9443			0.810467
$341$	5.35410	−	7.24518i	0.289941	−	0.392349i
$342$		0			0
$343$	15.1353	+	10.9964i	0.817227	+	0.593750i
$344$	−23.5623	+	17.1190i	−1.27039	+	0.922996i
$345$	−10.4721	−	32.2299i	−0.563801	−	1.73520i
$346$	−3.14590			−0.169125
$347$	32.9443			1.76854			0.884271	−	0.466975i	$-0.154656\pi$
$347$	32.9443			1.76854			0.884271	+	0.466975i	$0.154656\pi$
$348$	−1.90983	−	5.87785i	−0.102378	−	0.315086i
$349$	−5.61803	+	17.2905i	−0.300726	+	0.925541i	0.680511	+	0.732738i	$0.261758\pi$
$349$	−5.61803	+	17.2905i	−0.300726	+	0.925541i	−0.981237	+	0.192803i	$0.938242\pi$
$350$	4.42705	−	13.6251i	0.236636	−	0.728290i
$351$	−3.23607	−	2.35114i	−0.172729	−	0.125495i
$352$	−2.50000	−	7.69421i	−0.133250	−	0.410103i
$353$	−17.7082	−	12.8658i	−0.942513	−	0.684775i	0.00651157	−	0.999979i	$-0.497927\pi$
$353$	−17.7082	−	12.8658i	−0.942513	−	0.684775i	−0.949024	+	0.315203i	$0.897927\pi$
$354$	−13.0902	+	9.51057i	−0.695735	+	0.505481i
$355$	−1.61803	+	4.97980i	−0.0858763	+	0.264300i
$356$	−3.23607	+	2.35114i	−0.171511	+	0.124610i
$357$	−19.5623	+	14.2128i	−1.03535	+	0.752224i
$358$	−4.47214	+	13.7638i	−0.236360	+	0.727440i
$359$	−4.07295	+	2.95917i	−0.214962	+	0.156179i	−0.690056	−	0.723756i	$-0.742414\pi$
$359$	−4.07295	+	2.95917i	−0.214962	+	0.156179i	0.475094	+	0.879935i	$0.342414\pi$
$360$	−7.85410	−	5.70634i	−0.413948	−	0.300750i
$361$	−5.87132	−	18.0701i	−0.309017	−	0.951057i
$362$	1.73607	+	1.26133i	0.0912457	+	0.0662939i
$363$	−5.18034	+	15.9434i	−0.271897	+	0.836814i
$364$	0.809017	−	2.48990i	0.0424040	−	0.130506i
$365$	7.70820	+	23.7234i	0.403466	+	1.24174i
$366$	−20.7639			−1.08535
$367$	−20.9443			−1.09328			−0.546641	−	0.837367i	$-0.684094\pi$
$367$	−20.9443			−1.09328			−0.546641	+	0.837367i	$0.684094\pi$
$368$	−1.61803	−	4.97980i	−0.0843459	−	0.259590i
$369$		0			0
$370$	8.47214	+	6.15537i	0.440445	+	0.320002i
$371$	−5.23607			−0.271843
$372$	−0.0901699	+	11.1352i	−0.00467509	+	0.577331i
$373$	−7.88854			−0.408453			−0.204227	−	0.978924i	$-0.565468\pi$
$373$	−7.88854			−0.408453			−0.204227	+	0.978924i	$0.565468\pi$
$374$	6.04508	+	4.39201i	0.312584	+	0.227105i
$375$	2.47214	−	1.79611i	0.127661	−	0.0927508i
$376$	10.9894	+	33.8218i	0.566733	+	1.74422i
$377$	−3.09017			−0.159152
$378$	−10.4721			−0.538629
$379$	−11.4443	−	35.2218i	−0.587853	−	1.80922i	−0.587499	−	0.809225i	$-0.699887\pi$
$379$	−11.4443	−	35.2218i	−0.587853	−	1.80922i	−0.000353677	−	1.00000i	$-0.500113\pi$
$380$		0			0
$381$	−5.52786	+	17.0130i	−0.283201	+	0.871603i
$382$	18.7082	+	13.5923i	0.957195	+	0.695443i
$383$	5.46149	+	16.8087i	0.279069	+	0.858887i	0.988114	+	0.153723i	$0.0491264\pi$
$383$	5.46149	+	16.8087i	0.279069	+	0.858887i	−0.709045	+	0.705164i	$0.750874\pi$
$384$	4.85410	+	3.52671i	0.247710	+	0.179972i
$385$	−11.0902	+	8.05748i	−0.565207	+	0.410647i
$386$	2.76393	−	8.50651i	0.140680	−	0.432970i
$387$	7.85410	−	5.70634i	0.399246	−	0.290070i
$388$	6.61803	−	4.80828i	0.335980	−	0.244104i
$389$	0.791796	−	2.43690i	0.0401457	−	0.123556i	−0.928975	−	0.370142i	$-0.879309\pi$
$389$	0.791796	−	2.43690i	0.0401457	−	0.123556i	0.969121	+	0.246587i	$0.0793090\pi$
$390$	−5.23607	+	3.80423i	−0.265139	+	0.192634i
$391$	−19.5623	−	14.2128i	−0.989308	−	0.718775i
$392$	0.135255	+	0.416272i	0.00683140	+	0.0210249i
$393$	28.6525	+	20.8172i	1.44533	+	1.05009i
$394$	−3.70820	+	11.4127i	−0.186817	+	0.574962i
$395$	−12.1803	+	37.4872i	−0.612859	+	1.88619i
$396$	0.500000	+	1.53884i	0.0251259	+	0.0773297i
$397$	−24.3607			−1.22263			−0.611314	−	0.791388i	$-0.709359\pi$
$397$	−24.3607			−1.22263			−0.611314	+	0.791388i	$0.709359\pi$
$398$	−26.4721			−1.32693
$399$		0			0
$400$	4.42705	−	3.21644i	0.221353	−	0.160822i
$401$	−27.2705	−	19.8132i	−1.36182	−	0.989423i	−0.998327	−	0.0578282i	$-0.981582\pi$
$401$	−27.2705	−	19.8132i	−1.36182	−	0.989423i	−0.363498	−	0.931595i	$-0.618418\pi$
$402$	13.2361			0.660155
$403$	5.28115	+	1.76336i	0.263073	+	0.0878390i
$404$	17.0344			0.847495
$405$	−28.7984	−	20.9232i	−1.43100	−	1.03968i
$406$	−6.54508	+	4.75528i	−0.324827	+	0.236001i
$407$	−1.61803	−	4.97980i	−0.0802030	−	0.246839i
$408$	−27.7082			−1.37176
$409$	−15.0557			−0.744458			−0.372229	−	0.928141i	$-0.621406\pi$
$409$	−15.0557			−0.744458			−0.372229	+	0.928141i	$0.621406\pi$
$410$		0			0
$411$	−4.00000	+	12.3107i	−0.197305	+	0.607244i
$412$	−5.32624	+	16.3925i	−0.262405	+	0.807599i
$413$	−17.1353	−	12.4495i	−0.843171	−	0.612599i
$414$	1.61803	+	4.97980i	0.0795220	+	0.244744i
$415$	−6.23607	−	4.53077i	−0.306117	−	0.222407i
$416$	4.04508	−	2.93893i	0.198327	−	0.144093i
$417$	−3.52786	+	10.8576i	−0.172760	+	0.531701i
$418$		0			0
$419$	2.52786	−	1.83660i	0.123494	−	0.0897238i	−0.524324	−	0.851519i	$-0.675682\pi$
$419$	2.52786	−	1.83660i	0.123494	−	0.0897238i	0.647818	+	0.761795i	$0.275682\pi$
$420$	5.23607	−	16.1150i	0.255494	−	0.786330i
$421$	−12.6180	+	9.16754i	−0.614965	+	0.446798i	−0.851159	−	0.524907i	$-0.824100\pi$
$421$	−12.6180	+	9.16754i	−0.614965	+	0.446798i	0.236194	+	0.971706i	$0.424100\pi$
$422$	11.0902	+	8.05748i	0.539861	+	0.392232i
$423$	−3.66312	−	11.2739i	−0.178107	−	0.548157i
$424$	−4.85410	−	3.52671i	−0.235736	−	0.171272i
$425$	7.80902	−	24.0337i	0.378793	−	1.16580i
$426$	1.00000	−	3.07768i	0.0484502	−	0.149114i
$427$	−8.39919	−	25.8500i	−0.406465	−	1.25097i
$428$	−6.00000			−0.290021
$429$	3.23607			0.156239
$430$	9.70820	+	29.8788i	0.468171	+	1.44088i
$431$	−1.64590	+	1.19581i	−0.0792801	+	0.0576004i	−0.626719	−	0.779245i	$-0.715603\pi$
$431$	−1.64590	+	1.19581i	−0.0792801	+	0.0576004i	0.547439	+	0.836845i	$0.315603\pi$
$432$	−3.23607	−	2.35114i	−0.155695	−	0.113119i
$433$	22.7984			1.09562			0.547810	−	0.836603i	$-0.315462\pi$
$433$	22.7984			1.09562			0.547810	+	0.836603i	$0.315462\pi$
$434$	13.8992	−	4.39201i	0.667182	−	0.210823i
$435$	−20.0000			−0.958927
$436$	−8.85410	−	6.43288i	−0.424035	−	0.308079i
$437$		0			0
$438$	−4.76393	−	14.6619i	−0.227629	−	0.700571i
$439$	17.1246			0.817313			0.408657	−	0.912688i	$-0.365997\pi$
$439$	17.1246			0.817313			0.408657	+	0.912688i	$0.365997\pi$
$440$	−15.7082			−0.748859
$441$	−0.0450850	−	0.138757i	−0.00214690	−	0.00660749i
$442$	−1.42705	+	4.39201i	−0.0678779	+	0.208907i
$443$	−2.90983	+	8.95554i	−0.138250	+	0.425490i	−0.996081	−	0.0884412i	$-0.971811\pi$
$443$	−2.90983	+	8.95554i	−0.138250	+	0.425490i	0.857831	+	0.513932i	$0.171811\pi$
$444$	5.23607	+	3.80423i	0.248493	+	0.180541i
$445$	4.00000	+	12.3107i	0.189618	+	0.583585i
$446$	−2.35410	−	1.71036i	−0.111470	−	0.0809877i
$447$	−2.76393	+	2.00811i	−0.130729	+	0.0949805i
$448$	5.66312	−	17.4293i	0.267557	−	0.823456i
$449$	−8.09017	+	5.87785i	−0.381799	+	0.277393i	−0.762087	−	0.647475i	$-0.775825\pi$
$449$	−8.09017	+	5.87785i	−0.381799	+	0.277393i	0.380288	+	0.924868i	$0.375825\pi$
$450$	−4.42705	+	3.21644i	−0.208693	+	0.151624i
$451$		0			0
$452$	13.0172	−	9.45756i	0.612279	−	0.444846i
$453$	1.38197	+	1.00406i	0.0649304	+	0.0471747i
$454$	3.26393	+	10.0453i	0.153184	+	0.471452i
$455$	−6.85410	−	4.97980i	−0.321325	−	0.233456i
$456$		0			0
$457$	6.38197	−	19.6417i	0.298536	−	0.918799i	−0.683475	−	0.729974i	$-0.739532\pi$
$457$	6.38197	−	19.6417i	0.298536	−	0.918799i	0.982011	−	0.188825i	$-0.0604678\pi$
$458$	5.09017	+	15.6659i	0.237848	+	0.732021i
$459$	−18.4721			−0.862205
$460$	16.9443			0.790031
$461$	5.52786	+	17.0130i	0.257458	+	0.792375i	0.993335	+	0.115260i	$0.0367701\pi$
$461$	5.52786	+	17.0130i	0.257458	+	0.792375i	−0.735877	+	0.677115i	$0.763230\pi$
$462$	6.85410	−	4.97980i	0.318882	−	0.231681i
$463$	−5.82624	−	4.23301i	−0.270768	−	0.196725i	0.444113	−	0.895971i	$-0.353519\pi$
$463$	−5.82624	−	4.23301i	−0.270768	−	0.196725i	−0.714881	+	0.699246i	$0.753519\pi$
$464$	−3.09017			−0.143458
$465$	34.1803	+	11.4127i	1.58508	+	0.529250i
$466$	−26.5066			−1.22789
$467$	4.38197	+	3.18368i	0.202773	+	0.147323i	0.684538	−	0.728977i	$-0.260004\pi$
$467$	4.38197	+	3.18368i	0.202773	+	0.147323i	−0.481765	+	0.876301i	$0.660004\pi$
$468$	−0.809017	+	0.587785i	−0.0373968	+	0.0271704i
$469$	5.35410	+	16.4782i	0.247229	+	0.760894i
$470$	38.3607			1.76945
$471$	25.7082			1.18457
$472$	−7.50000	−	23.0826i	−0.345215	−	1.06246i
$473$	4.85410	−	14.9394i	0.223192	−	0.686914i
$474$	7.52786	−	23.1684i	0.345766	−	1.06416i
$475$		0			0
$476$	−3.73607	−	11.4984i	−0.171242	−	0.527030i
$477$	1.61803	+	1.17557i	0.0740847	+	0.0538257i
$478$	21.2984	−	15.4742i	0.974165	−	0.707772i
$479$	8.89919	−	27.3889i	0.406614	−	1.25143i	−0.512926	−	0.858433i	$-0.671438\pi$
$479$	8.89919	−	27.3889i	0.406614	−	1.25143i	0.919540	−	0.392997i	$-0.128562\pi$
$480$	26.1803	−	19.0211i	1.19496	−	0.868192i
$481$	2.61803	−	1.90211i	0.119372	−	0.0867289i
$482$	6.61803	−	20.3682i	0.301443	−	0.927747i
$483$	−22.1803	+	16.1150i	−1.00924	+	0.733256i
$484$	−6.78115	−	4.92680i	−0.308234	−	0.223945i
$485$	−8.18034	−	25.1765i	−0.371450	−	1.14321i
$486$	8.09017	+	5.87785i	0.366978	+	0.266625i
$487$	−13.2361	+	40.7364i	−0.599783	+	1.84594i	−0.0704764	+	0.997513i	$0.522452\pi$
$487$	−13.2361	+	40.7364i	−0.599783	+	1.84594i	−0.529307	+	0.848430i	$0.677548\pi$
$488$	9.62461	−	29.6215i	0.435686	−	1.34090i
$489$	7.58359	+	23.3399i	0.342942	+	1.05547i
$490$	0.472136			0.0213289
$491$	13.7082			0.618643			0.309321	−	0.950958i	$-0.399898\pi$
$491$	13.7082			0.618643			0.309321	+	0.950958i	$0.399898\pi$
$492$		0			0
$493$	−11.5451	+	8.38800i	−0.519964	+	0.377776i
$494$		0			0
$495$	5.23607			0.235344
$496$	5.28115	+	1.76336i	0.237131	+	0.0791770i
$497$	4.23607			0.190014
$498$	3.85410	+	2.80017i	0.172706	+	0.125479i
$499$	21.7082	−	15.7719i	0.971793	−	0.706049i	0.0159332	−	0.999873i	$-0.494928\pi$
$499$	21.7082	−	15.7719i	0.971793	−	0.706049i	0.955859	+	0.293824i	$0.0949281\pi$
$500$	0.472136	+	1.45309i	0.0211146	+	0.0649839i
$501$	−10.7639			−0.480897
$502$	−29.1246			−1.29990
$503$	7.67376	+	23.6174i	0.342156	+	1.05305i	0.963089	+	0.269184i	$0.0867541\pi$
$503$	7.67376	+	23.6174i	0.342156	+	1.05305i	−0.620933	+	0.783864i	$0.713246\pi$
$504$	−2.42705	+	7.46969i	−0.108109	+	0.332727i
$505$	17.0344	−	52.4266i	0.758023	−	2.33295i
$506$	6.85410	+	4.97980i	0.304702	+	0.221379i
$507$	0.618034	+	1.90211i	0.0274479	+	0.0844758i
$508$	−7.23607	−	5.25731i	−0.321049	−	0.233255i
$509$	3.00000	−	2.17963i	0.132973	−	0.0966103i	−0.519311	−	0.854586i	$-0.673811\pi$
$509$	3.00000	−	2.17963i	0.132973	−	0.0966103i	0.652283	+	0.757975i	$0.273811\pi$
$510$	−9.23607	+	28.4257i	−0.408980	+	1.25871i
$511$	16.3262	−	11.8617i	0.722230	−	0.524731i
$512$	8.89919	−	6.46564i	0.393292	−	0.285744i
$513$		0			0
$514$	16.3992	−	11.9147i	0.723337	−	0.525535i
$515$	45.1246	+	32.7849i	1.98843	+	1.44468i
$516$	6.00000	+	18.4661i	0.264135	+	0.812925i
$517$	−15.5172	−	11.2739i	−0.682447	−	0.495826i
$518$	2.61803	−	8.05748i	0.115030	−	0.354025i
$519$	−1.94427	+	5.98385i	−0.0853441	+	0.262662i
$520$	−3.00000	−	9.23305i	−0.131559	−	0.404896i
$521$	4.32624			0.189536			0.0947680	−	0.995499i	$-0.469789\pi$
$521$	4.32624			0.189536			0.0947680	+	0.995499i	$0.469789\pi$
$522$	3.09017			0.135253
$523$	10.2361	+	31.5034i	0.447592	+	1.37755i	0.879616	+	0.475684i	$0.157800\pi$
$523$	10.2361	+	31.5034i	0.447592	+	1.37755i	−0.432024	+	0.901862i	$0.642200\pi$
$524$	−14.3262	+	10.4086i	−0.625845	+	0.454703i
$525$	−23.1803	−	16.8415i	−1.01167	−	0.735023i
$526$	−13.1246			−0.572260
$527$	24.5172	−	7.74721i	1.06799	−	0.337474i
$528$	3.23607			0.140832
$529$	−3.57295	−	2.59590i	−0.155346	−	0.112865i
$530$	−5.23607	+	3.80423i	−0.227440	+	0.165245i
$531$	2.50000	+	7.69421i	0.108491	+	0.333900i
$532$		0			0
$533$		0			0
$534$	−2.47214	−	7.60845i	−0.106980	−	0.329250i
$535$	−6.00000	+	18.4661i	−0.259403	+	0.798359i
$536$	−6.13525	+	18.8824i	−0.265003	+	0.815594i
$537$	23.4164	+	17.0130i	1.01049	+	0.734166i
$538$	−0.326238	−	1.00406i	−0.0140651	−	0.0432880i
$539$	−0.190983	−	0.138757i	−0.00822622	−	0.00597670i
$540$	10.4721	−	7.60845i	0.450649	−	0.327416i
$541$	5.94427	−	18.2946i	0.255564	−	0.786546i	−0.738154	−	0.674633i	$-0.764302\pi$
$541$	5.94427	−	18.2946i	0.255564	−	0.786546i	0.993718	−	0.111913i	$-0.0356979\pi$
$542$	−4.39919	+	3.19620i	−0.188961	+	0.137288i
$543$	3.47214	−	2.52265i	0.149004	−	0.108257i
$544$	7.13525	−	21.9601i	0.305922	−	0.941530i
$545$	−28.6525	+	20.8172i	−1.22734	+	0.891713i
$546$	4.23607	+	3.07768i	0.181287	+	0.131713i
$547$	−11.4721	−	35.3076i	−0.490513	−	1.50964i	−0.823834	−	0.566831i	$-0.808169\pi$
$547$	−11.4721	−	35.3076i	−0.490513	−	1.50964i	0.333321	−	0.942813i	$-0.391831\pi$
$548$	−5.23607	−	3.80423i	−0.223674	−	0.162508i
$549$	−3.20820	+	9.87384i	−0.136923	+	0.421405i
$550$	−2.73607	+	8.42075i	−0.116666	+	0.359062i
$551$		0			0
$552$	−31.4164			−1.33717
$553$	31.8885			1.35604
$554$	−2.20820	−	6.79615i	−0.0938176	−	0.288741i
$555$	16.9443	−	12.3107i	0.719244	−	0.522562i
$556$	−4.61803	−	3.35520i	−0.195848	−	0.142292i
$557$	5.81966			0.246587			0.123293	−	0.992370i	$-0.460654\pi$
$557$	5.81966			0.246587			0.123293	+	0.992370i	$0.460654\pi$
$558$	−5.28115	−	1.76336i	−0.223569	−	0.0746488i
$559$	9.70820			0.410613
$560$	−6.85410	−	4.97980i	−0.289639	−	0.210435i
$561$	12.0902	−	8.78402i	0.510447	−	0.370862i
$562$	−4.47214	−	13.7638i	−0.188646	−	0.580592i
$563$	−11.5279			−0.485842			−0.242921	−	0.970046i	$-0.578106\pi$
$563$	−11.5279			−0.485842			−0.242921	+	0.970046i	$0.578106\pi$
$564$	23.7082			0.998295
$565$	−16.0902	−	49.5205i	−0.676919	−	2.08334i
$566$	−2.23607	+	6.88191i	−0.0939889	+	0.289268i
$567$	−8.89919	+	27.3889i	−0.373731	+	1.15022i
$568$	3.92705	+	2.85317i	0.164775	+	0.119716i
$569$	−5.97214	−	18.3803i	−0.250365	−	0.770544i	−0.994708	−	0.102746i	$-0.967237\pi$
$569$	−5.97214	−	18.3803i	−0.250365	−	0.770544i	0.744343	−	0.667798i	$-0.232763\pi$
$570$		0			0
$571$	−19.9443	+	14.4904i	−0.834642	+	0.606403i	−0.920869	−	0.389873i	$-0.872519\pi$
$571$	−19.9443	+	14.4904i	−0.834642	+	0.606403i	0.0862269	+	0.996276i	$0.472519\pi$
$572$	−0.500000	+	1.53884i	−0.0209061	+	0.0643422i
$573$	37.4164	−	27.1846i	1.56309	−	1.13565i
$574$		0			0
$575$	8.85410	−	27.2501i	0.369242	−	1.13641i
$576$	−5.66312	+	4.11450i	−0.235963	+	0.171437i
$577$	−18.7082	−	13.5923i	−0.778833	−	0.565855i	0.125796	−	0.992056i	$-0.459852\pi$
$577$	−18.7082	−	13.5923i	−0.778833	−	0.565855i	−0.904628	+	0.426201i	$0.859852\pi$
$578$	1.33688	+	4.11450i	0.0556069	+	0.171141i
$579$	−14.4721	−	10.5146i	−0.601441	−	0.436973i
$580$	3.09017	−	9.51057i	0.128312	−	0.394905i
$581$	−1.92705	+	5.93085i	−0.0799475	+	0.246053i
$582$	5.05573	+	15.5599i	0.209567	+	0.644980i
$583$	3.23607			0.134024
$584$	23.1246			0.956903
$585$	1.00000	+	3.07768i	0.0413449	+	0.127247i
$586$	18.5623	−	13.4863i	0.766802	−	0.557114i
$587$	12.0000	+	8.71851i	0.495293	+	0.359851i	0.807216	−	0.590256i	$-0.200973\pi$
$587$	12.0000	+	8.71851i	0.495293	+	0.359851i	−0.311923	+	0.950107i	$0.600973\pi$
$588$	0.291796			0.0120335
$589$		0			0
$590$	−26.1803			−1.07783
$591$	19.4164	+	14.1068i	0.798684	+	0.580278i
$592$	2.61803	−	1.90211i	0.107601	−	0.0781764i
$593$	14.7639	+	45.4387i	0.606282	+	1.86594i	0.487726	+	0.872997i	$0.337827\pi$
$593$	14.7639	+	45.4387i	0.606282	+	1.86594i	0.118556	+	0.992947i	$0.462173\pi$
$594$	6.47214			0.265555
$595$	−39.1246			−1.60395
$596$	−0.527864	−	1.62460i	−0.0216222	−	0.0665461i
$597$	−16.3607	+	50.3530i	−0.669598	+	2.06081i
$598$	−1.61803	+	4.97980i	−0.0661663	+	0.203639i
$599$	5.47214	+	3.97574i	0.223585	+	0.162444i	0.693939	−	0.720034i	$-0.255874\pi$
$599$	5.47214	+	3.97574i	0.223585	+	0.162444i	−0.470354	+	0.882478i	$0.655874\pi$
$600$	−10.1459	−	31.2259i	−0.414205	−	1.27479i
$601$	−29.1976	−	21.2133i	−1.19099	−	0.865307i	−0.197624	−	0.980278i	$-0.563323\pi$
$601$	−29.1976	−	21.2133i	−1.19099	−	0.865307i	−0.993369	+	0.114970i	$0.963323\pi$
$602$	20.5623	−	14.9394i	0.838057	−	0.608884i
$603$	2.04508	−	6.29412i	0.0832823	−	0.256317i
$604$	−0.690983	+	0.502029i	−0.0281157	+	0.0204273i
$605$	−21.9443	+	15.9434i	−0.892162	+	0.648193i
$606$	−10.5279	+	32.4014i	−0.427665	+	1.31622i
$607$	2.09017	−	1.51860i	0.0848374	−	0.0616380i	−0.544558	−	0.838723i	$-0.683303\pi$
$607$	2.09017	−	1.51860i	0.0848374	−	0.0616380i	0.629395	+	0.777085i	$0.283303\pi$
$608$		0			0
$609$	5.00000	+	15.3884i	0.202610	+	0.623570i
$610$	−27.1803	−	19.7477i	−1.10050	−	0.799560i
$611$	3.66312	−	11.2739i	0.148194	−	0.456094i
$612$	−1.42705	+	4.39201i	−0.0576851	+	0.177537i
$613$	11.6180	+	35.7566i	0.469248	+	1.44420i	0.853561	+	0.520994i	$0.174439\pi$
$613$	11.6180	+	35.7566i	0.469248	+	1.44420i	−0.384313	+	0.923203i	$0.625561\pi$
$614$	−13.3820			−0.540052
$615$		0			0
$616$	3.92705	+	12.0862i	0.158225	+	0.486968i
$617$	27.1246	−	19.7072i	1.09200	−	0.793381i	0.112261	−	0.993679i	$-0.464191\pi$
$617$	27.1246	−	19.7072i	1.09200	−	0.793381i	0.979735	+	0.200297i	$0.0641909\pi$
$618$	−27.8885	−	20.2622i	−1.12184	−	0.815066i
$619$	12.1459			0.488185			0.244092	−	0.969752i	$-0.421510\pi$
$619$	12.1459			0.488185			0.244092	+	0.969752i	$0.421510\pi$
$620$	−10.7082	+	14.4904i	−0.430052	+	0.581947i
$621$	−20.9443			−0.840465
$622$	−2.14590	−	1.55909i	−0.0860427	−	0.0625137i
$623$	8.47214	−	6.15537i	0.339429	−	0.246610i
$624$	0.618034	+	1.90211i	0.0247412	+	0.0761455i
$625$	−22.4164			−0.896656
$626$	−2.94427			−0.117677
$627$		0			0
$628$	−3.97214	+	12.2250i	−0.158505	+	0.487830i
$629$	4.61803	−	14.2128i	0.184133	−	0.566703i
$630$	6.85410	+	4.97980i	0.273074	+	0.198400i
$631$	8.38854	+	25.8173i	0.333943	+	1.02777i	0.967241	+	0.253862i	$0.0817008\pi$
$631$	8.38854	+	25.8173i	0.333943	+	1.02777i	−0.633298	+	0.773908i	$0.718299\pi$
$632$	29.5623	+	21.4783i	1.17593	+	0.854360i
$633$	22.1803	−	16.1150i	0.881589	−	0.640512i
$634$	−3.18034	+	9.78808i	−0.126307	+	0.388734i
$635$	−23.4164	+	17.0130i	−0.929252	+	0.675141i
$636$	−3.23607	+	2.35114i	−0.128318	+	0.0932288i
$637$	0.0450850	−	0.138757i	0.00178633	−	0.00549776i
$638$	4.04508	−	2.93893i	0.160146	−	0.116353i
$639$	−1.30902	−	0.951057i	−0.0517839	−	0.0376232i
$640$	3.00000	+	9.23305i	0.118585	+	0.364968i
$641$	−18.2082	−	13.2290i	−0.719181	−	0.522515i	0.166942	−	0.985967i	$-0.446611\pi$
$641$	−18.2082	−	13.2290i	−0.719181	−	0.522515i	−0.886122	+	0.463451i	$0.846611\pi$
$642$	3.70820	−	11.4127i	0.146351	−	0.450422i
$643$	6.00000	−	18.4661i	0.236617	−	0.728232i	−0.760286	−	0.649589i	$-0.774941\pi$
$643$	6.00000	−	18.4661i	0.236617	−	0.728232i	0.996903	−	0.0786434i	$-0.0250588\pi$
$644$	−4.23607	−	13.0373i	−0.166924	−	0.513741i
$645$	62.8328			2.47404
$646$		0			0
$647$	3.61803	+	11.1352i	0.142240	+	0.437768i	0.996646	−	0.0818374i	$-0.0260788\pi$
$647$	3.61803	+	11.1352i	0.142240	+	0.437768i	−0.854406	+	0.519606i	$0.826079\pi$
$648$	−26.6976	+	19.3969i	−1.04878	+	0.761983i
$649$	10.5902	+	7.69421i	0.415701	+	0.302024i
$650$	−5.47214			−0.214635
$651$	0.236068	−	29.1522i	0.00925223	−	1.14257i
$652$	−12.2705			−0.480550
$653$	29.7984	+	21.6498i	1.16610	+	0.847222i	0.990537	−	0.137247i	$-0.0438252\pi$
$653$	29.7984	+	21.6498i	1.16610	+	0.847222i	0.175564	+	0.984468i	$0.443825\pi$
$654$	17.7082	−	12.8658i	0.692446	−	0.503091i
$655$	17.7082	+	54.5002i	0.691917	+	2.12950i
$656$		0			0
$657$	−7.70820			−0.300726
$658$	−9.59017	−	29.5155i	−0.373864	−	1.15063i
$659$	7.90983	−	24.3440i	0.308123	−	0.948306i	−0.670370	−	0.742027i	$-0.733865\pi$
$659$	7.90983	−	24.3440i	0.308123	−	0.948306i	0.978493	−	0.206279i	$-0.0661354\pi$
$660$	−3.23607	+	9.95959i	−0.125964	+	0.387677i
$661$	−33.7426	−	24.5155i	−1.31244	−	0.953541i	−0.999994	−	0.00360475i	$-0.998853\pi$
$661$	−33.7426	−	24.5155i	−1.31244	−	0.953541i	−0.312443	−	0.949936i	$-0.601147\pi$
$662$	−10.1525	−	31.2461i	−0.394587	−	1.21441i
$663$	7.47214	+	5.42882i	0.290194	+	0.210838i
$664$	−5.78115	+	4.20025i	−0.224352	+	0.163001i
$665$		0			0
$666$	−2.61803	+	1.90211i	−0.101447	+	0.0737054i
$667$	−13.0902	+	9.51057i	−0.506853	+	0.368251i
$668$	1.66312	−	5.11855i	0.0643480	−	0.198043i
$669$	−4.70820	+	3.42071i	−0.182030	+	0.132252i
$670$	17.3262	+	12.5882i	0.669371	+	0.486326i
$671$	5.19098	+	15.9762i	0.200396	+	0.616754i
$672$	−21.1803	−	15.3884i	−0.817049	−	0.593621i
$673$	9.68034	−	29.7930i	0.373150	−	1.14844i	−0.571569	−	0.820554i	$-0.693665\pi$
$673$	9.68034	−	29.7930i	0.373150	−	1.14844i	0.944719	−	0.327883i	$-0.106335\pi$
$674$	−3.80902	+	11.7229i	−0.146718	+	0.451551i
$675$	−6.76393	−	20.8172i	−0.260344	−	0.801256i
$676$	−1.00000			−0.0384615
$677$	45.0344			1.73081			0.865407	−	0.501069i	$-0.167060\pi$
$677$	45.0344			1.73081			0.865407	+	0.501069i	$0.167060\pi$
$678$	9.94427	+	30.6053i	0.381907	+	1.17539i
$679$	−17.3262	+	12.5882i	−0.664920	+	0.483093i
$680$	−36.2705	−	26.3521i	−1.39091	−	1.01056i
$681$	21.1246			0.809497
$682$	−8.59017	+	2.71441i	−0.328935	+	0.103940i
$683$	12.5836			0.481498			0.240749	−	0.970587i	$-0.422607\pi$
$683$	12.5836			0.481498			0.240749	+	0.970587i	$0.422607\pi$
$684$		0			0
$685$	−16.9443	+	12.3107i	−0.647407	+	0.470369i
$686$	−5.78115	−	17.7926i	−0.220725	−	0.679323i
$687$	32.9443			1.25690
$688$	9.70820			0.370122
$689$	0.618034	+	1.90211i	0.0235452	+	0.0724647i
$690$	−10.4721	+	32.2299i	−0.398667	+	1.22697i
$691$	0.263932	−	0.812299i	0.0100404	−	0.0309013i	−0.945911	−	0.324427i	$-0.894829\pi$
$691$	0.263932	−	0.812299i	0.0100404	−	0.0309013i	0.955951	+	0.293526i	$0.0948286\pi$
$692$	−2.54508	−	1.84911i	−0.0967496	−	0.0702927i
$693$	−1.30902	−	4.02874i	−0.0497254	−	0.153039i
$694$	−26.6525	−	19.3642i	−1.01171	−	0.735053i
$695$	−14.9443	+	10.8576i	−0.566869	+	0.411854i
$696$	−5.72949	+	17.6336i	−0.217176	+	0.668398i
$697$		0			0
$698$	14.7082	−	10.6861i	0.556714	−	0.404476i
$699$	−16.3820	+	50.4185i	−0.619623	+	1.90700i
$700$	11.5902	−	8.42075i	0.438067	−	0.318274i
$701$	−0.545085	−	0.396027i	−0.0205876	−	0.0149577i	0.577444	−	0.816430i	$-0.304050\pi$
$701$	−0.545085	−	0.396027i	−0.0205876	−	0.0149577i	−0.598031	+	0.801473i	$0.704050\pi$
$702$	1.23607	+	3.80423i	0.0466524	+	0.143581i
$703$		0			0
$704$	−3.50000	+	10.7719i	−0.131911	+	0.405981i
$705$	23.7082	−	72.9663i	0.892903	−	2.74807i
$706$	6.76393	+	20.8172i	0.254564	+	0.783467i
$707$	−44.5967			−1.67723
$708$	−16.1803			−0.608094
$709$	−10.1459	−	31.2259i	−0.381037	−	1.17271i	−0.939314	−	0.343057i	$-0.888537\pi$
$709$	−10.1459	−	31.2259i	−0.381037	−	1.17271i	0.558277	−	0.829654i	$-0.311463\pi$
$710$	4.23607	−	3.07768i	0.158977	−	0.115503i
$711$	−9.85410	−	7.15942i	−0.369558	−	0.268499i
$712$	12.0000			0.449719
$713$	27.7984	−	8.78402i	1.04106	−	0.328964i
$714$	24.1803			0.904926
$715$	4.23607	+	3.07768i	0.158420	+	0.115099i
$716$	−11.7082	+	8.50651i	−0.437556	+	0.317903i
$717$	−16.2705	−	50.0755i	−0.607633	−	1.87010i
$718$	5.03444			0.187884
$719$	−40.2492			−1.50104			−0.750521	−	0.660846i	$-0.770198\pi$
$719$	−40.2492			−1.50104			−0.750521	+	0.660846i	$0.770198\pi$
$720$	1.00000	+	3.07768i	0.0372678	+	0.114698i
$721$	13.9443	−	42.9161i	0.519312	−	1.59828i
$722$	−5.87132	+	18.0701i	−0.218508	+	0.672499i
$723$	−34.6525	−	25.1765i	−1.28874	−	0.936324i
$724$	0.663119	+	2.04087i	0.0246446	+	0.0758483i
$725$	−13.6803	−	9.93935i	−0.508075	−	0.369138i
$726$	13.5623	−	9.85359i	0.503344	−	0.365701i
$727$	2.29180	−	7.05342i	0.0849980	−	0.261597i	−0.899520	−	0.436879i	$-0.856084\pi$
$727$	2.29180	−	7.05342i	0.0849980	−	0.261597i	0.984518	+	0.175282i	$0.0560838\pi$
$728$	−6.35410	+	4.61653i	−0.235499	+	0.171100i
$729$	−10.5172	+	7.64121i	−0.389527	+	0.283008i
$730$	7.70820	−	23.7234i	0.285293	−	0.878043i
$731$	36.2705	−	26.3521i	1.34151	−	0.974666i
$732$	−16.7984	−	12.2047i	−0.620886	−	0.451100i
$733$	−7.00000	−	21.5438i	−0.258551	−	0.795738i	−0.993109	−	0.117192i	$-0.962611\pi$
$733$	−7.00000	−	21.5438i	−0.258551	−	0.795738i	0.734558	−	0.678546i	$-0.237389\pi$
$734$	16.9443	+	12.3107i	0.625424	+	0.454397i
$735$	0.291796	−	0.898056i	0.0107631	−	0.0331253i
$736$	8.09017	−	24.8990i	0.298208	−	0.917789i
$737$	−3.30902	−	10.1841i	−0.121889	−	0.375136i
$738$		0			0
$739$	32.2148			1.18504			0.592520	−	0.805556i	$-0.298133\pi$
$739$	32.2148			1.18504			0.592520	+	0.805556i	$0.298133\pi$
$740$	3.23607	+	9.95959i	0.118960	+	0.366122i
$741$		0			0
$742$	4.23607	+	3.07768i	0.155511	+	0.112985i
$743$	15.5623			0.570926			0.285463	−	0.958390i	$-0.407853\pi$
$743$	15.5623			0.570926			0.285463	+	0.958390i	$0.407853\pi$
$744$	19.8541	−	26.8666i	0.727887	−	0.984978i
$745$	−5.52786			−0.202525
$746$	6.38197	+	4.63677i	0.233660	+	0.169764i
$747$	1.92705	−	1.40008i	0.0705071	−	0.0512264i
$748$	2.30902	+	7.10642i	0.0844260	+	0.259837i
$749$	15.7082			0.573965
$750$	−3.05573			−0.111579
$751$	13.7426	+	42.2955i	0.501476	+	1.54339i	0.806615	+	0.591077i	$0.201297\pi$
$751$	13.7426	+	42.2955i	0.501476	+	1.54339i	−0.305139	+	0.952308i	$0.598703\pi$
$752$	3.66312	−	11.2739i	0.133580	−	0.411118i
$753$	−18.0000	+	55.3983i	−0.655956	+	2.01883i
$754$	2.50000	+	1.81636i	0.0910446	+	0.0661478i
$755$	0.854102	+	2.62866i	0.0310840	+	0.0956666i
$756$	−8.47214	−	6.15537i	−0.308129	−	0.223869i
$757$	−3.60081	+	2.61614i	−0.130874	+	0.0950854i	−0.651296	−	0.758824i	$-0.725774\pi$
$757$	−3.60081	+	2.61614i	−0.130874	+	0.0950854i	0.520422	+	0.853909i	$0.325774\pi$
$758$	−11.4443	+	35.2218i	−0.415675	+	1.27932i
$759$	13.7082	−	9.95959i	0.497576	−	0.361510i
$760$		0			0
$761$	−13.2016	+	40.6304i	−0.478559	+	1.47285i	0.362539	+	0.931969i	$0.381910\pi$
$761$	−13.2016	+	40.6304i	−0.478559	+	1.47285i	−0.841098	+	0.540883i	$0.818090\pi$
$762$	14.4721	−	10.5146i	0.524270	−	0.380905i
$763$	23.1803	+	16.8415i	0.839185	+	0.609703i
$764$	7.14590	+	21.9928i	0.258530	+	0.795672i
$765$	12.0902	+	8.78402i	0.437121	+	0.317587i
$766$	5.46149	−	16.8087i	0.197332	−	0.607325i
$767$	−2.50000	+	7.69421i	−0.0902698	+	0.277822i
$768$	−10.5066	−	32.3359i	−0.379123	−	1.16682i
$769$	24.1803			0.871965			0.435983	−	0.899955i	$-0.356401\pi$
$769$	24.1803			0.871965			0.435983	+	0.899955i	$0.356401\pi$
$770$	13.7082			0.494009
$771$	−12.5279	−	38.5568i	−0.451180	−	1.38859i
$772$	7.23607	−	5.25731i	0.260432	−	0.189215i
$773$	15.0000	+	10.8981i	0.539513	+	0.391979i	0.823904	−	0.566729i	$-0.191792\pi$
$773$	15.0000	+	10.8981i	0.539513	+	0.391979i	−0.284391	+	0.958708i	$0.591792\pi$
$774$	−9.70820			−0.348954
$775$	17.7082	+	24.7930i	0.636097	+	0.890590i
$776$	−24.5410			−0.880971
$777$	−13.7082	−	9.95959i	−0.491779	−	0.357298i
$778$	−2.07295	+	1.50609i	−0.0743188	+	0.0539958i
$779$		0			0
$780$	−6.47214			−0.231740
$781$	−2.61803			−0.0936806
$782$	7.47214	+	22.9969i	0.267203	+	0.822366i
$783$	−3.81966	+	11.7557i	−0.136504	+	0.420115i
$784$	0.0450850	−	0.138757i	0.00161018	−	0.00495562i
$785$	33.6525	+	24.4500i	1.20111	+	0.872656i
$786$	−10.9443	−	33.6830i	−0.390369	−	1.20143i
$787$	−9.48936	−	6.89442i	−0.338259	−	0.245760i	0.405668	−	0.914021i	$-0.367039\pi$
$787$	−9.48936	−	6.89442i	−0.338259	−	0.245760i	−0.743927	+	0.668261i	$0.767039\pi$
$788$	−9.70820	+	7.05342i	−0.345840	+	0.251268i
$789$	−8.11146	+	24.9645i	−0.288775	+	0.888760i
$790$	31.8885	−	23.1684i	1.13454	−	0.824294i
$791$	−34.0795	+	24.7602i	−1.21173	+	0.880372i
$792$	1.50000	−	4.61653i	0.0533002	−	0.164041i
$793$	−8.39919	+	6.10237i	−0.298264	+	0.216701i
$794$	19.7082	+	14.3188i	0.699418	+	0.508157i
$795$	4.00000	+	12.3107i	0.141865	+	0.436617i
$796$	−21.4164	−	15.5599i	−0.759084	−	0.551507i
$797$	−10.0836	+	31.0341i	−0.357179	+	1.09928i	0.597556	+	0.801827i	$0.296139\pi$
$797$	−10.0836	+	31.0341i	−0.357179	+	1.09928i	−0.954735	+	0.297457i	$0.903861\pi$
$798$		0			0
$799$	−16.9164	−	52.0633i	−0.598459	−	1.84187i
$800$	27.3607			0.967346
$801$	−4.00000			−0.141333
$802$	10.4164	+	32.0584i	0.367816	+	1.13202i
$803$	−10.0902	+	7.33094i	−0.356074	+	0.258703i
$804$	10.7082	+	7.77997i	0.377649	+	0.274378i
$805$	−44.3607			−1.56351
$806$	−3.23607	−	4.53077i	−0.113986	−	0.159590i
$807$	−2.11146			−0.0743268
$808$	−41.3435	−	30.0378i	−1.45446	−	1.05673i
$809$	23.8156	−	17.3030i	0.837312	−	0.608343i	−0.0843067	−	0.996440i	$-0.526868\pi$
$809$	23.8156	−	17.3030i	0.837312	−	0.608343i	0.921618	+	0.388097i	$0.126868\pi$
$810$	11.0000	+	33.8545i	0.386501	+	1.18953i
$811$	−31.0557			−1.09051			−0.545257	−	0.838269i	$-0.683568\pi$
$811$	−31.0557			−1.09051			−0.545257	+	0.838269i	$0.683568\pi$
$812$	−8.09017			−0.283909
$813$	3.36068	+	10.3431i	0.117864	+	0.362749i
$814$	−1.61803	+	4.97980i	−0.0567121	+	0.174542i
$815$	−12.2705	+	37.7647i	−0.429817	+	1.32284i
$816$	7.47214	+	5.42882i	0.261577	+	0.190047i
$817$		0			0
$818$	12.1803	+	8.84953i	0.425876	+	0.309417i
$819$	2.11803	−	1.53884i	0.0740101	−	0.0537715i
$820$		0			0
$821$	−15.6180	+	11.3472i	−0.545073	+	0.396019i	−0.825966	−	0.563720i	$-0.809370\pi$
$821$	−15.6180	+	11.3472i	−0.545073	+	0.396019i	0.280893	+	0.959739i	$0.409370\pi$
$822$	10.4721	−	7.60845i	0.365258	−	0.265375i
$823$	−2.38197	+	7.33094i	−0.0830301	+	0.255540i	−0.983950	−	0.178445i	$-0.942893\pi$
$823$	−2.38197	+	7.33094i	−0.0830301	+	0.255540i	0.900920	+	0.433986i	$0.142893\pi$
$824$	41.8328	−	30.3933i	1.45732	−	1.05880i
$825$	14.3262	+	10.4086i	0.498776	+	0.362382i
$826$	6.54508	+	20.1437i	0.227733	+	0.700889i
$827$	−27.2984	−	19.8334i	−0.949257	−	0.689676i	0.00137366	−	0.999999i	$-0.499563\pi$
$827$	−27.2984	−	19.8334i	−0.949257	−	0.689676i	−0.950631	+	0.310323i	$0.899563\pi$
$828$	−1.61803	+	4.97980i	−0.0562306	+	0.173060i
$829$	2.84346	−	8.75127i	0.0987574	−	0.303944i	−0.889457	−	0.457018i	$-0.848917\pi$
$829$	2.84346	−	8.75127i	0.0987574	−	0.303944i	0.988215	+	0.153074i	$0.0489174\pi$
$830$	2.38197	+	7.33094i	0.0826792	+	0.254461i
$831$	−14.2918			−0.495777
$832$	−7.00000			−0.242681
$833$	−0.208204	−	0.640786i	−0.00721384	−	0.0222019i
$834$	9.23607	−	6.71040i	0.319819	−	0.232362i
$835$	−14.0902	−	10.2371i	−0.487610	−	0.354270i
$836$		0			0
$837$	13.2361	−	17.9111i	0.457505	−	0.619097i
$838$	−3.12461			−0.107938
$839$	−15.3541	−	11.1554i	−0.530082	−	0.385127i	0.290306	−	0.956934i	$-0.406243\pi$
$839$	−15.3541	−	11.1554i	−0.530082	−	0.385127i	−0.820389	+	0.571806i	$0.806243\pi$
$840$	−41.1246	+	29.8788i	−1.41893	+	1.03092i
$841$	−6.01064	−	18.4989i	−0.207264	−	0.637892i
$842$	15.5967			0.537499
$843$	−28.9443			−0.996894
$844$	4.23607	+	13.0373i	0.145811	+	0.448762i
$845$	−1.00000	+	3.07768i	−0.0344010	+	0.105876i
$846$	−3.66312	+	11.2739i	−0.125941	+	0.387605i
$847$	17.7533	+	12.8985i	0.610010	+	0.443198i
$848$	0.618034	+	1.90211i	0.0212234	+	0.0653188i
$849$	11.7082	+	8.50651i	0.401825	+	0.291943i
$850$	−20.4443	+	14.8536i	−0.701233	+	0.509475i
$851$	5.23607	−	16.1150i	0.179490	−	0.552414i
$852$	2.61803	−	1.90211i	0.0896924	−	0.0651653i
$853$	−0.236068	+	0.171513i	−0.00808281	+	0.00587251i	−0.591819	−	0.806071i	$-0.701590\pi$
$853$	−0.236068	+	0.171513i	−0.00808281	+	0.00587251i	0.583737	+	0.811943i	$0.301590\pi$
$854$	−8.39919	+	25.8500i	−0.287414	+	0.884570i
$855$		0			0
$856$	14.5623	+	10.5801i	0.497729	+	0.361622i
$857$	7.62868	+	23.4787i	0.260591	+	0.802016i	0.992676	+	0.120803i	$0.0385470\pi$
$857$	7.62868	+	23.4787i	0.260591	+	0.802016i	−0.732086	+	0.681212i	$0.761453\pi$
$858$	−2.61803	−	1.90211i	−0.0893782	−	0.0649371i
$859$	5.14590	−	15.8374i	0.175576	−	0.540367i	−0.824084	−	0.566468i	$-0.808309\pi$
$859$	5.14590	−	15.8374i	0.175576	−	0.540367i	0.999659	+	0.0261016i	$0.00830936\pi$
$860$	−9.70820	+	29.8788i	−0.331047	+	1.01886i
$861$		0			0
$862$	2.03444			0.0692934
$863$	6.25735			0.213003			0.106501	−	0.994313i	$-0.466035\pi$
$863$	6.25735			0.213003			0.106501	+	0.994313i	$0.466035\pi$
$864$	−6.18034	−	19.0211i	−0.210259	−	0.647112i
$865$	−8.23607	+	5.98385i	−0.280035	+	0.203457i
$866$	−18.4443	−	13.4005i	−0.626762	−	0.455369i
$867$	8.65248			0.293853
$868$	13.8262	+	4.61653i	0.469293	+	0.156695i
$869$	−19.7082			−0.668555
$870$	16.1803	+	11.7557i	0.548565	+	0.398556i
$871$	5.35410	−	3.88998i	0.181417	−	0.131807i
$872$	10.1459	+	31.2259i	0.343583	+	1.05744i
$873$	8.18034			0.276863
$874$		0			0
$875$	−1.23607	−	3.80423i	−0.0417867	−	0.128606i
$876$	4.76393	−	14.6619i	0.160958	−	0.495379i
$877$	4.70820	−	14.4904i	0.158985	−	0.489305i	−0.839558	−	0.543270i	$-0.817186\pi$
$877$	4.70820	−	14.4904i	0.158985	−	0.489305i	0.998543	+	0.0539652i	$0.0171860\pi$
$878$	−13.8541	−	10.0656i	−0.467553	−	0.339697i
$879$	−14.1803	−	43.6426i	−0.478291	−	1.47203i
$880$	4.23607	+	3.07768i	0.142798	+	0.103749i
$881$	−38.9058	+	28.2667i	−1.31077	+	0.952329i	−0.310770	+	0.950485i	$0.600587\pi$
$881$	−38.9058	+	28.2667i	−1.31077	+	0.952329i	−0.999998	+	0.00184400i	$0.999413\pi$
$882$	−0.0450850	+	0.138757i	−0.00151809	+	0.00467220i
$883$	32.8885	−	23.8949i	1.10679	−	0.804128i	0.124633	−	0.992203i	$-0.460225\pi$
$883$	32.8885	−	23.8949i	1.10679	−	0.804128i	0.982155	+	0.188075i	$0.0602247\pi$
$884$	−3.73607	+	2.71441i	−0.125658	+	0.0912956i
$885$	−16.1803	+	49.7980i	−0.543896	+	1.67394i
$886$	7.61803	−	5.53483i	0.255933	−	0.185946i
$887$	−33.2705	−	24.1724i	−1.11711	−	0.811631i	−0.133345	−	0.991070i	$-0.542572\pi$
$887$	−33.2705	−	24.1724i	−1.11711	−	0.811631i	−0.983769	+	0.179439i	$0.942572\pi$
$888$	−6.00000	−	18.4661i	−0.201347	−	0.619682i
$889$	18.9443	+	13.7638i	0.635370	+	0.461624i
$890$	4.00000	−	12.3107i	0.134080	−	0.412657i
$891$	5.50000	−	16.9273i	0.184257	−	0.567085i
$892$	−0.899187	−	2.76741i	−0.0301070	−	0.0926598i
$893$		0			0
$894$	3.41641			0.114262
$895$	14.4721	+	44.5407i	0.483750	+	1.48883i
$896$	6.35410	−	4.61653i	0.212276	−	0.154227i
$897$	8.47214	+	6.15537i	0.282876	+	0.205522i
$898$	10.0000			0.333704
$899$	0.139320	−	17.2048i	0.00464659	−	0.573811i
$900$	−5.47214			−0.182405
$901$	7.47214	+	5.42882i	0.248933	+	0.180860i
$902$		0			0
$903$	−15.7082	−	48.3449i	−0.522736	−	1.60882i
$904$	−48.2705			−1.60545
$905$	6.94427			0.230835
$906$	−0.527864	−	1.62460i	−0.0175371	−	0.0539737i
$907$	0.0344419	−	0.106001i	0.00114362	−	0.00351971i	−0.950483	−	0.310776i	$-0.899411\pi$
$907$	0.0344419	−	0.106001i	0.00114362	−	0.00351971i	0.951627	+	0.307257i	$0.0994110\pi$
$908$	−3.26393	+	10.0453i	−0.108317	+	0.333367i
$909$	13.7812	+	10.0126i	0.457092	+	0.332097i
$910$	2.61803	+	8.05748i	0.0867870	+	0.267103i
$911$	41.4164	+	30.0908i	1.37219	+	0.996952i	0.997563	+	0.0697753i	$0.0222282\pi$
$911$	41.4164	+	30.0908i	1.37219	+	0.996952i	0.374624	+	0.927177i	$0.377772\pi$
$912$		0			0
$913$	1.19098	−	3.66547i	0.0394158	−	0.121309i
$914$	−16.7082	+	12.1392i	−0.552658	+	0.401530i
$915$	−54.3607	+	39.4953i	−1.79711	+	1.30568i
$916$	−5.09017	+	15.6659i	−0.168184	+	0.517617i
$917$	37.5066	−	27.2501i	1.23858	−	0.899878i
$918$	14.9443	+	10.8576i	0.493234	+	0.358356i
$919$	4.94427	+	15.2169i	0.163096	+	0.501959i	0.998891	−	0.0470830i	$-0.0149925\pi$
$919$	4.94427	+	15.2169i	0.163096	+	0.501959i	−0.835794	+	0.549042i	$0.814993\pi$
$920$	−41.1246	−	29.8788i	−1.35584	−	0.985074i
$921$	−8.27051	+	25.4540i	−0.272523	+	0.838738i
$922$	5.52786	−	17.0130i	0.182051	−	0.560294i
$923$	−0.500000	−	1.53884i	−0.0164577	−	0.0506516i
$924$	8.47214			0.278713
$925$	17.7082			0.582242
$926$	2.22542	+	6.84915i	0.0731320	+	0.225077i
$927$	−13.9443	+	10.1311i	−0.457990	+	0.332749i
$928$	−12.5000	−	9.08178i	−0.410333	−	0.298124i
$929$	−51.5967			−1.69283			−0.846417	−	0.532520i	$-0.821245\pi$
$929$	−51.5967			−1.69283			−0.846417	+	0.532520i	$0.821245\pi$
$930$	−20.9443	−	29.3238i	−0.686790	−	0.961564i
$931$		0			0
$932$	−21.4443	−	15.5802i	−0.702430	−	0.510346i
$933$	−4.29180	+	3.11817i	−0.140507	+	0.102084i
$934$	−1.67376	−	5.15131i	−0.0547672	−	0.168556i
$935$	24.1803			0.790782
$936$	3.00000			0.0980581
$937$	−12.1697	−	37.4545i	−0.397567	−	1.22358i	−0.926945	−	0.375198i	$-0.877575\pi$
$937$	−12.1697	−	37.4545i	−0.397567	−	1.22358i	0.529378	−	0.848386i	$-0.322425\pi$
$938$	5.35410	−	16.4782i	0.174818	−	0.538033i
$939$	−1.81966	+	5.60034i	−0.0593824	+	0.182760i
$940$	31.0344	+	22.5478i	1.01223	+	0.735430i
$941$	−13.5279	−	41.6345i	−0.440996	−	1.35725i	−0.886816	−	0.462123i	$-0.847088\pi$
$941$	−13.5279	−	41.6345i	−0.440996	−	1.35725i	0.445820	−	0.895123i	$-0.352912\pi$
$942$	−20.7984	−	15.1109i	−0.677648	−	0.492340i
$943$		0			0
$944$	−2.50000	+	7.69421i	−0.0813681	+	0.250425i
$945$	−27.4164	+	19.9192i	−0.891856	+	0.647971i
$946$	−12.7082	+	9.23305i	−0.413179	+	0.300192i
$947$	13.5000	−	41.5487i	0.438691	−	1.35015i	−0.450565	−	0.892743i	$-0.648778\pi$
$947$	13.5000	−	41.5487i	0.438691	−	1.35015i	0.889257	−	0.457409i	$-0.151222\pi$
$948$	19.7082	−	14.3188i	0.640093	−	0.465055i
$949$	−6.23607	−	4.53077i	−0.202431	−	0.147075i
$950$		0			0
$951$	16.6525	+	12.0987i	0.539994	+	0.392328i
$952$	−11.2082	+	34.4953i	−0.363260	+	1.11800i
$953$	−8.77458	+	27.0054i	−0.284236	+	0.874790i	0.702390	+	0.711792i	$0.252116\pi$
$953$	−8.77458	+	27.0054i	−0.284236	+	0.874790i	−0.986626	+	0.162997i	$0.947884\pi$
$954$	−0.618034	−	1.90211i	−0.0200096	−	0.0615832i
$955$	74.8328			2.42153
$956$	26.3262			0.851451
$957$	−3.09017	−	9.51057i	−0.0998910	−	0.307433i
$958$	−23.2984	+	16.9273i	−0.752736	+	0.546895i
$959$	13.7082	+	9.95959i	0.442661	+	0.321612i
$960$	−45.3050			−1.46221
$961$	−10.0557	+	29.3238i	−0.324378	+	0.945927i
$962$	−3.23607			−0.104335
$963$	−4.85410	−	3.52671i	−0.156421	−	0.113647i
$964$	17.3262	−	12.5882i	0.558041	−	0.405440i
$965$	−8.94427	−	27.5276i	−0.287926	−	0.886146i
$966$	27.4164			0.882108
$967$	26.6180			0.855978			0.427989	−	0.903784i	$-0.359222\pi$
$967$	26.6180			0.855978			0.427989	+	0.903784i	$0.359222\pi$
$968$	7.77051	+	23.9152i	0.249754	+	0.768663i
$969$		0			0
$970$	−8.18034	+	25.1765i	−0.262655	+	0.808369i
$971$	31.0344	+	22.5478i	0.995943	+	0.723595i	0.961214	−	0.275802i	$-0.0889434\pi$
$971$	31.0344	+	22.5478i	0.995943	+	0.723595i	0.0347282	+	0.999397i	$0.488943\pi$
$972$	3.09017	+	9.51057i	0.0991172	+	0.305052i
$973$	12.0902	+	8.78402i	0.387593	+	0.281603i
$974$	34.6525	−	25.1765i	1.11034	−	0.806707i
$975$	−3.38197	+	10.4086i	−0.108310	+	0.333343i
$976$	−8.39919	+	6.10237i	−0.268851	+	0.195332i
$977$	44.2148	−	32.1239i	1.41456	−	1.02774i	0.421916	−	0.906635i	$-0.361358\pi$
$977$	44.2148	−	32.1239i	1.41456	−	1.02774i	0.992640	−	0.121100i	$-0.0386423\pi$
$978$	7.58359	−	23.3399i	0.242497	−	0.746328i
$979$	−5.23607	+	3.80423i	−0.167345	+	0.121584i
$980$	0.381966	+	0.277515i	0.0122015	+	0.00886488i
$981$	−3.38197	−	10.4086i	−0.107978	−	0.332322i
$982$	−11.0902	−	8.05748i	−0.353902	−	0.257125i
$983$	−3.95492	+	12.1720i	−0.126142	+	0.388226i	−0.994107	−	0.108399i	$-0.965428\pi$
$983$	−3.95492	+	12.1720i	−0.126142	+	0.388226i	0.867965	+	0.496625i	$0.165428\pi$
$984$		0			0
$985$	12.0000	+	36.9322i	0.382352	+	1.17676i
$986$	14.2705			0.454466
$987$	−62.0689			−1.97567
$988$		0			0
$989$	41.1246	−	29.8788i	1.30769	−	0.950090i
$990$	−4.23607	−	3.07768i	−0.134631	−	0.0978152i
$991$	7.70820			0.244859			0.122430	−	0.992477i	$-0.460931\pi$
$991$	7.70820			0.244859			0.122430	+	0.992477i	$0.460931\pi$
$992$	16.1803	+	22.6538i	0.513726	+	0.719260i
$993$	−65.7082			−2.08519
$994$	−3.42705	−	2.48990i	−0.108699	−	0.0789748i
$995$	−69.3050	+	50.3530i	−2.19711	+	1.59630i
$996$	1.47214	+	4.53077i	0.0466464	+	0.143563i
$997$	−26.5066			−0.839472			−0.419736	−	0.907646i	$-0.637877\pi$
$997$	−26.5066			−0.839472			−0.419736	+	0.907646i	$0.637877\pi$
$998$	−26.8328			−0.849378
$999$	−4.00000	−	12.3107i	−0.126554	−	0.389494i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.k.b.157.1	✓	4
31.16	even	5	inner	403.2.k.b.326.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.k.b.157.1	✓	4	1.1	even	1	trivial
403.2.k.b.326.1	yes	4	31.16	even	5	inner

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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.k (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{2} +(-1.61803 + 1.17557i) q^{3} +(-0.309017 - 0.951057i) q^{4} -3.23607 q^{5} +2.00000 q^{6} +(0.809017 + 2.48990i) q^{7} +(-0.927051 + 2.85317i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.809017 - 0.587785i) q^{2} +(-1.61803 + 1.17557i) q^{3} +(-0.309017 - 0.951057i) q^{4} -3.23607 q^{5} +2.00000 q^{6} +(0.809017 + 2.48990i) q^{7} +(-0.927051 + 2.85317i) q^{8} +(0.309017 - 0.951057i) q^{9} +(2.61803 + 1.90211i) q^{10} +(-0.500000 - 1.53884i) q^{11} +(1.61803 + 1.17557i) q^{12} +(0.809017 - 0.587785i) q^{13} +(0.809017 - 2.48990i) q^{14} +(5.23607 - 3.80423i) q^{15} +(0.809017 - 0.587785i) q^{16} +(1.42705 - 4.39201i) q^{17} +(-0.809017 + 0.587785i) q^{18} +(1.00000 + 3.07768i) q^{20} +(-4.23607 - 3.07768i) q^{21} +(-0.500000 + 1.53884i) q^{22} +(1.61803 - 4.97980i) q^{23} +(-1.85410 - 5.70634i) q^{24} +5.47214 q^{25} -1.00000 q^{26} +(-1.23607 - 3.80423i) q^{27} +(2.11803 - 1.53884i) q^{28} +(-2.50000 - 1.81636i) q^{29} -6.47214 q^{30} +(3.23607 + 4.53077i) q^{31} +5.00000 q^{32} +(2.61803 + 1.90211i) q^{33} +(-3.73607 + 2.71441i) q^{34} +(-2.61803 - 8.05748i) q^{35} -1.00000 q^{36} +3.23607 q^{37} +(-0.618034 + 1.90211i) q^{39} +(3.00000 - 9.23305i) q^{40} +(1.61803 + 4.97980i) q^{42} +(7.85410 + 5.70634i) q^{43} +(-1.30902 + 0.951057i) q^{44} +(-1.00000 + 3.07768i) q^{45} +(-4.23607 + 3.07768i) q^{46} +(9.59017 - 6.96767i) q^{47} +(-0.618034 + 1.90211i) q^{48} +(0.118034 - 0.0857567i) q^{49} +(-4.42705 - 3.21644i) q^{50} +(2.85410 + 8.78402i) q^{51} +(-0.809017 - 0.587785i) q^{52} +(-0.618034 + 1.90211i) q^{53} +(-1.23607 + 3.80423i) q^{54} +(1.61803 + 4.97980i) q^{55} -7.85410 q^{56} +(0.954915 + 2.93893i) q^{58} +(-6.54508 + 4.75528i) q^{59} +(-5.23607 - 3.80423i) q^{60} -10.3820 q^{61} +(0.0450850 - 5.56758i) q^{62} +2.61803 q^{63} +(-5.66312 - 4.11450i) q^{64} +(-2.61803 + 1.90211i) q^{65} +(-1.00000 - 3.07768i) q^{66} +6.61803 q^{67} -4.61803 q^{68} +(3.23607 + 9.95959i) q^{69} +(-2.61803 + 8.05748i) q^{70} +(0.500000 - 1.53884i) q^{71} +(2.42705 + 1.76336i) q^{72} +(-2.38197 - 7.33094i) q^{73} +(-2.61803 - 1.90211i) q^{74} +(-8.85410 + 6.43288i) q^{75} +(3.42705 - 2.48990i) q^{77} +(1.61803 - 1.17557i) q^{78} +(3.76393 - 11.5842i) q^{79} +(-2.61803 + 1.90211i) q^{80} +(8.89919 + 6.46564i) q^{81} +(1.92705 + 1.40008i) q^{83} +(-1.61803 + 4.97980i) q^{84} +(-4.61803 + 14.2128i) q^{85} +(-3.00000 - 9.23305i) q^{86} +6.18034 q^{87} +4.85410 q^{88} +(-1.23607 - 3.80423i) q^{89} +(2.61803 - 1.90211i) q^{90} +(2.11803 + 1.53884i) q^{91} -5.23607 q^{92} +(-10.5623 - 3.52671i) q^{93} -11.8541 q^{94} +(-8.09017 + 5.87785i) q^{96} +(2.52786 + 7.77997i) q^{97} -0.145898 q^{98} -1.61803 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} - 2 q^{3} + q^{4} - 4 q^{5} + 8 q^{6} + q^{7} + 3 q^{8} - q^{9}+O(q^{10}) \) 4 * q - q^2 - 2 * q^3 + q^4 - 4 * q^5 + 8 * q^6 + q^7 + 3 * q^8 - q^9	\( 4 q - q^{2} - 2 q^{3} + q^{4} - 4 q^{5} + 8 q^{6} + q^{7} + 3 q^{8} - q^{9} + 6 q^{10} - 2 q^{11} + 2 q^{12} + q^{13} + q^{14} + 12 q^{15} + q^{16} - q^{17} - q^{18} + 4 q^{20} - 8 q^{21} - 2 q^{22} + 2 q^{23} + 6 q^{24} + 4 q^{25} - 4 q^{26} + 4 q^{27} + 4 q^{28} - 10 q^{29} - 8 q^{30} + 4 q^{31} + 20 q^{32} + 6 q^{33} - 6 q^{34} - 6 q^{35} - 4 q^{36} + 4 q^{37} + 2 q^{39} + 12 q^{40} + 2 q^{42} + 18 q^{43} - 3 q^{44} - 4 q^{45} - 8 q^{46} + 16 q^{47} + 2 q^{48} - 4 q^{49} - 11 q^{50} - 2 q^{51} - q^{52} + 2 q^{53} + 4 q^{54} + 2 q^{55} - 18 q^{56} + 15 q^{58} - 15 q^{59} - 12 q^{60} - 46 q^{61} - 11 q^{62} + 6 q^{63} - 7 q^{64} - 6 q^{65} - 4 q^{66} + 22 q^{67} - 14 q^{68} + 4 q^{69} - 6 q^{70} + 2 q^{71} + 3 q^{72} - 14 q^{73} - 6 q^{74} - 22 q^{75} + 7 q^{77} + 2 q^{78} + 24 q^{79} - 6 q^{80} + 11 q^{81} + q^{83} - 2 q^{84} - 14 q^{85} - 12 q^{86} - 20 q^{87} + 6 q^{88} + 4 q^{89} + 6 q^{90} + 4 q^{91} - 12 q^{92} - 2 q^{93} - 34 q^{94} - 10 q^{96} + 28 q^{97} - 14 q^{98} - 2 q^{99}+O(q^{100}) \) 4 * q - q^2 - 2 * q^3 + q^4 - 4 * q^5 + 8 * q^6 + q^7 + 3 * q^8 - q^9 + 6 * q^10 - 2 * q^11 + 2 * q^12 + q^13 + q^14 + 12 * q^15 + q^16 - q^17 - q^18 + 4 * q^20 - 8 * q^21 - 2 * q^22 + 2 * q^23 + 6 * q^24 + 4 * q^25 - 4 * q^26 + 4 * q^27 + 4 * q^28 - 10 * q^29 - 8 * q^30 + 4 * q^31 + 20 * q^32 + 6 * q^33 - 6 * q^34 - 6 * q^35 - 4 * q^36 + 4 * q^37 + 2 * q^39 + 12 * q^40 + 2 * q^42 + 18 * q^43 - 3 * q^44 - 4 * q^45 - 8 * q^46 + 16 * q^47 + 2 * q^48 - 4 * q^49 - 11 * q^50 - 2 * q^51 - q^52 + 2 * q^53 + 4 * q^54 + 2 * q^55 - 18 * q^56 + 15 * q^58 - 15 * q^59 - 12 * q^60 - 46 * q^61 - 11 * q^62 + 6 * q^63 - 7 * q^64 - 6 * q^65 - 4 * q^66 + 22 * q^67 - 14 * q^68 + 4 * q^69 - 6 * q^70 + 2 * q^71 + 3 * q^72 - 14 * q^73 - 6 * q^74 - 22 * q^75 + 7 * q^77 + 2 * q^78 + 24 * q^79 - 6 * q^80 + 11 * q^81 + q^83 - 2 * q^84 - 14 * q^85 - 12 * q^86 - 20 * q^87 + 6 * q^88 + 4 * q^89 + 6 * q^90 + 4 * q^91 - 12 * q^92 - 2 * q^93 - 34 * q^94 - 10 * q^96 + 28 * q^97 - 14 * q^98 - 2 * q^99

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