LMFDB - Embedded newform 546.2.bm.b.205.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(205,546)]

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, 2, 5]))

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

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

chi := DirichletCharacter("546.205");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bm (of order $6$, 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:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 56 x^{18} + 1306 x^{16} + 16508 x^{14} + 123139 x^{12} + 552164 x^{10} + 1447090 x^{8} + \cdots + 576 $ x^20 + 56x^18 + 1306x^16 + 16508x^14 + 123139x^12 + 552164x^10 + 1447090x^8 + 2035844x^6 + 1263505x^4 + 215520*x^2 + 576
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			205.4
Root			$-2.62249i$ of defining polynomial
Character	$\chi$	$=$	546.205
Dual form			546.2.bm.b.277.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(-0.500000 + 0.866025i) q^{3} -1.00000 q^{4} +(2.27114 + 1.31124i) q^{5} +(0.866025 + 0.500000i) q^{6} +(-0.116897 - 2.64317i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(-0.500000 + 0.866025i) q^{3} -1.00000 q^{4} +(2.27114 + 1.31124i) q^{5} +(0.866025 + 0.500000i) q^{6} +(-0.116897 - 2.64317i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.31124 - 2.27114i) q^{10} +(-4.33943 - 2.50537i) q^{11} +(0.500000 - 0.866025i) q^{12} +(3.59427 - 0.285022i) q^{13} +(-2.64317 + 0.116897i) q^{14} +(-2.27114 + 1.31124i) q^{15} +1.00000 q^{16} +6.89718 q^{17} +(-0.866025 + 0.500000i) q^{18} +(2.62699 - 1.51669i) q^{19} +(-2.27114 - 1.31124i) q^{20} +(2.34750 + 1.22035i) q^{21} +(-2.50537 + 4.33943i) q^{22} +4.99967 q^{23} +(-0.866025 - 0.500000i) q^{24} +(0.938722 + 1.62591i) q^{25} +(-0.285022 - 3.59427i) q^{26} +1.00000 q^{27} +(0.116897 + 2.64317i) q^{28} +(2.18859 + 3.79075i) q^{29} +(1.31124 + 2.27114i) q^{30} +(-4.93016 + 2.84643i) q^{31} -1.00000i q^{32} +(4.33943 - 2.50537i) q^{33} -6.89718i q^{34} +(3.20035 - 6.15629i) q^{35} +(0.500000 + 0.866025i) q^{36} +4.28366i q^{37} +(-1.51669 - 2.62699i) q^{38} +(-1.55030 + 3.25524i) q^{39} +(-1.31124 + 2.27114i) q^{40} +(4.95053 - 2.85819i) q^{41} +(1.22035 - 2.34750i) q^{42} +(6.44053 - 11.1553i) q^{43} +(4.33943 + 2.50537i) q^{44} -2.62249i q^{45} -4.99967i q^{46} +(-0.499608 - 0.288449i) q^{47} +(-0.500000 + 0.866025i) q^{48} +(-6.97267 + 0.617955i) q^{49} +(1.62591 - 0.938722i) q^{50} +(-3.44859 + 5.97313i) q^{51} +(-3.59427 + 0.285022i) q^{52} +(-3.49408 - 6.05193i) q^{53} -1.00000i q^{54} +(-6.57031 - 11.3801i) q^{55} +(2.64317 - 0.116897i) q^{56} +3.03338i q^{57} +(3.79075 - 2.18859i) q^{58} +10.4885i q^{59} +(2.27114 - 1.31124i) q^{60} +(-7.15751 - 12.3972i) q^{61} +(2.84643 + 4.93016i) q^{62} +(-2.23060 + 1.42282i) q^{63} -1.00000 q^{64} +(8.53682 + 4.06564i) q^{65} +(-2.50537 - 4.33943i) q^{66} +(-2.14699 - 1.23956i) q^{67} -6.89718 q^{68} +(-2.49983 + 4.32984i) q^{69} +(-6.15629 - 3.20035i) q^{70} +(2.82667 + 1.63198i) q^{71} +(0.866025 - 0.500000i) q^{72} +(-4.20527 + 2.42791i) q^{73} +4.28366 q^{74} -1.87744 q^{75} +(-2.62699 + 1.51669i) q^{76} +(-6.11485 + 11.7627i) q^{77} +(3.25524 + 1.55030i) q^{78} +(-3.69502 + 6.39996i) q^{79} +(2.27114 + 1.31124i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-2.85819 - 4.95053i) q^{82} +9.16995i q^{83} +(-2.34750 - 1.22035i) q^{84} +(15.6645 + 9.04389i) q^{85} +(-11.1553 - 6.44053i) q^{86} -4.37718 q^{87} +(2.50537 - 4.33943i) q^{88} +15.4247i q^{89} -2.62249 q^{90} +(-1.17352 - 9.46693i) q^{91} -4.99967 q^{92} -5.69286i q^{93} +(-0.288449 + 0.499608i) q^{94} +7.95501 q^{95} +(0.866025 + 0.500000i) q^{96} +(-12.1886 - 7.03709i) q^{97} +(0.617955 + 6.97267i) q^{98} +5.01074i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 10 q^{3} - 20 q^{4} - 10 q^{9}+O(q^{10}) $ 20 * q - 10 * q^3 - 20 * q^4 - 10 * q^9	$ 20 q - 10 q^{3} - 20 q^{4} - 10 q^{9} + 4 q^{10} + 6 q^{11} + 10 q^{12} + 8 q^{13} + 4 q^{14} + 20 q^{16} - 8 q^{17} - 12 q^{19} + 6 q^{21} - 10 q^{22} - 16 q^{23} + 6 q^{25} + 8 q^{26} + 20 q^{27} + 8 q^{29} + 4 q^{30} + 12 q^{31} - 6 q^{33} + 10 q^{35} + 10 q^{36} + 6 q^{38} - 10 q^{39} - 4 q^{40} - 18 q^{41} - 2 q^{42} + 18 q^{43} - 6 q^{44} - 6 q^{47} - 10 q^{48} - 20 q^{49} + 12 q^{50} + 4 q^{51} - 8 q^{52} + 18 q^{53} - 12 q^{55} - 4 q^{56} + 24 q^{58} - 6 q^{61} - 6 q^{63} - 20 q^{64} - 6 q^{65} - 10 q^{66} + 24 q^{67} + 8 q^{68} + 8 q^{69} + 42 q^{70} - 6 q^{71} + 24 q^{73} + 36 q^{74} - 12 q^{75} + 12 q^{76} - 34 q^{77} + 2 q^{78} - 10 q^{81} + 18 q^{82} - 6 q^{84} - 36 q^{86} - 16 q^{87} + 10 q^{88} - 8 q^{90} - 10 q^{91} + 16 q^{92} - 16 q^{94} - 80 q^{95} - 96 q^{97} - 12 q^{98}+O(q^{100}) $ 20 * q - 10 * q^3 - 20 * q^4 - 10 * q^9 + 4 * q^10 + 6 * q^11 + 10 * q^12 + 8 * q^13 + 4 * q^14 + 20 * q^16 - 8 * q^17 - 12 * q^19 + 6 * q^21 - 10 * q^22 - 16 * q^23 + 6 * q^25 + 8 * q^26 + 20 * q^27 + 8 * q^29 + 4 * q^30 + 12 * q^31 - 6 * q^33 + 10 * q^35 + 10 * q^36 + 6 * q^38 - 10 * q^39 - 4 * q^40 - 18 * q^41 - 2 * q^42 + 18 * q^43 - 6 * q^44 - 6 * q^47 - 10 * q^48 - 20 * q^49 + 12 * q^50 + 4 * q^51 - 8 * q^52 + 18 * q^53 - 12 * q^55 - 4 * q^56 + 24 * q^58 - 6 * q^61 - 6 * q^63 - 20 * q^64 - 6 * q^65 - 10 * q^66 + 24 * q^67 + 8 * q^68 + 8 * q^69 + 42 * q^70 - 6 * q^71 + 24 * q^73 + 36 * q^74 - 12 * q^75 + 12 * q^76 - 34 * q^77 + 2 * q^78 - 10 * q^81 + 18 * q^82 - 6 * q^84 - 36 * q^86 - 16 * q^87 + 10 * q^88 - 8 * q^90 - 10 * q^91 + 16 * q^92 - 16 * q^94 - 80 * q^95 - 96 * q^97 - 12 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	−1.00000			−0.500000
$5$	2.27114	+	1.31124i	1.01569	+	0.586406i	0.912851	−	0.408292i	$-0.133876\pi$
$5$	2.27114	+	1.31124i	1.01569	+	0.586406i	0.102834	+	0.994699i	$0.467209\pi$
$6$	0.866025	+	0.500000i	0.353553	+	0.204124i
$7$	−0.116897	−	2.64317i	−0.0441828	−	0.999023i
$7$	−0.116897	−	2.64317i	−0.0441828	−	0.999023i
$8$			1.00000i			0.353553i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	1.31124	−	2.27114i	0.414652	−	0.718198i
$11$	−4.33943	−	2.50537i	−1.30839	−	0.755398i	−0.326560	−	0.945176i	$-0.605890\pi$
$11$	−4.33943	−	2.50537i	−1.30839	−	0.755398i	−0.981827	+	0.189779i	$0.939223\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	3.59427	−	0.285022i	0.996871	−	0.0790510i
$13$	3.59427	−	0.285022i	0.996871	−	0.0790510i
$14$	−2.64317	+	0.116897i	−0.706416	+	0.0312420i
$15$	−2.27114	+	1.31124i	−0.586406	+	0.338562i
$16$	1.00000			0.250000
$17$	6.89718			1.67281			0.836406	−	0.548110i	$-0.184653\pi$
$17$	6.89718			1.67281			0.836406	+	0.548110i	$0.184653\pi$
$18$	−0.866025	+	0.500000i	−0.204124	+	0.117851i
$19$	2.62699	−	1.51669i	0.602672	−	0.347953i	−0.167420	−	0.985886i	$-0.553544\pi$
$19$	2.62699	−	1.51669i	0.602672	−	0.347953i	0.770092	+	0.637933i	$0.220210\pi$
$20$	−2.27114	−	1.31124i	−0.507843	−	0.293203i
$21$	2.34750	+	1.22035i	0.512266	+	0.266302i
$22$	−2.50537	+	4.33943i	−0.534147	+	0.925169i
$23$	4.99967			1.04250			0.521251	−	0.853403i	$-0.325465\pi$
$23$	4.99967			1.04250			0.521251	+	0.853403i	$0.325465\pi$
$24$	−0.866025	−	0.500000i	−0.176777	−	0.102062i
$25$	0.938722	+	1.62591i	0.187744	+	0.325183i
$26$	−0.285022	−	3.59427i	−0.0558975	−	0.704894i
$27$	1.00000			0.192450
$28$	0.116897	+	2.64317i	0.0220914	+	0.499512i
$29$	2.18859	+	3.79075i	0.406411	+	0.703924i	0.994485	−	0.104883i	$-0.0334468\pi$
$29$	2.18859	+	3.79075i	0.406411	+	0.703924i	−0.588074	+	0.808807i	$0.700113\pi$
$30$	1.31124	+	2.27114i	0.239399	+	0.414652i
$31$	−4.93016	+	2.84643i	−0.885484	+	0.511234i	−0.872463	−	0.488681i	$-0.837478\pi$
$31$	−4.93016	+	2.84643i	−0.885484	+	0.511234i	−0.0130211	+	0.999915i	$0.504145\pi$
$32$		−	1.00000i		−	0.176777i
$33$	4.33943	−	2.50537i	0.755398	−	0.436129i
$34$		−	6.89718i		−	1.18286i
$35$	3.20035	−	6.15629i	0.540958	−	1.04060i
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$			4.28366i			0.704230i	0.935957	+	0.352115i	$0.114537\pi$
$37$			4.28366i			0.704230i	−0.935957	+	0.352115i	$0.885463\pi$
$38$	−1.51669	−	2.62699i	−0.246040	−	0.426153i
$39$	−1.55030	+	3.25524i	−0.248246	+	0.521255i
$40$	−1.31124	+	2.27114i	−0.207326	+	0.359099i
$41$	4.95053	−	2.85819i	0.773143	−	0.446374i	−0.0608516	−	0.998147i	$-0.519382\pi$
$41$	4.95053	−	2.85819i	0.773143	−	0.446374i	0.833995	+	0.551772i	$0.186048\pi$
$42$	1.22035	−	2.34750i	0.188304	−	0.362227i
$43$	6.44053	−	11.1553i	0.982172	−	1.70117i	0.328285	−	0.944579i	$-0.393529\pi$
$43$	6.44053	−	11.1553i	0.982172	−	1.70117i	0.653886	−	0.756593i	$-0.273137\pi$
$44$	4.33943	+	2.50537i	0.654194	+	0.377699i
$45$		−	2.62249i		−	0.390937i
$46$		−	4.99967i		−	0.737161i
$47$	−0.499608	−	0.288449i	−0.0728753	−	0.0420746i	0.463120	−	0.886296i	$-0.346730\pi$
$47$	−0.499608	−	0.288449i	−0.0728753	−	0.0420746i	−0.535995	+	0.844221i	$0.680063\pi$
$48$	−0.500000	+	0.866025i	−0.0721688	+	0.125000i
$49$	−6.97267	+	0.617955i	−0.996096	+	0.0882793i
$50$	1.62591	−	0.938722i	0.229939	−	0.132755i
$51$	−3.44859	+	5.97313i	−0.482899	+	0.836406i
$52$	−3.59427	+	0.285022i	−0.498435	+	0.0395255i
$53$	−3.49408	−	6.05193i	−0.479949	−	0.831296i	0.519786	−	0.854296i	$-0.326012\pi$
$53$	−3.49408	−	6.05193i	−0.479949	−	0.831296i	−0.999735	+	0.0229999i	$0.992678\pi$
$54$		−	1.00000i		−	0.136083i
$55$	−6.57031	−	11.3801i	−0.885940	−	1.53449i
$56$	2.64317	−	0.116897i	0.353208	−	0.0156210i
$57$			3.03338i			0.401781i
$58$	3.79075	−	2.18859i	0.497750	−	0.287376i
$59$			10.4885i			1.36549i	0.730657	+	0.682744i	$0.239214\pi$
$59$			10.4885i			1.36549i	−0.730657	+	0.682744i	$0.760786\pi$
$60$	2.27114	−	1.31124i	0.293203	−	0.169281i
$61$	−7.15751	−	12.3972i	−0.916425	−	1.58730i	−0.804801	−	0.593545i	$-0.797728\pi$
$61$	−7.15751	−	12.3972i	−0.916425	−	1.58730i	−0.111624	−	0.993750i	$-0.535605\pi$
$62$	2.84643	+	4.93016i	0.361497	+	0.626132i
$63$	−2.23060	+	1.42282i	−0.281029	+	0.179258i
$64$	−1.00000			−0.125000
$65$	8.53682	+	4.06564i	1.05886	+	0.504280i
$66$	−2.50537	−	4.33943i	−0.308390	−	0.534147i
$67$	−2.14699	−	1.23956i	−0.262296	−	0.151437i	0.363085	−	0.931756i	$-0.381723\pi$
$67$	−2.14699	−	1.23956i	−0.262296	−	0.151437i	−0.625382	+	0.780319i	$0.715057\pi$
$68$	−6.89718			−0.836406
$69$	−2.49983	+	4.32984i	−0.300945	+	0.521251i
$70$	−6.15629	−	3.20035i	−0.735817	−	0.382515i
$71$	2.82667	+	1.63198i	0.335463	+	0.193680i	0.658264	−	0.752787i	$-0.271291\pi$
$71$	2.82667	+	1.63198i	0.335463	+	0.193680i	−0.322801	+	0.946467i	$0.604624\pi$
$72$	0.866025	−	0.500000i	0.102062	−	0.0589256i
$73$	−4.20527	+	2.42791i	−0.492189	+	0.284166i	−0.725482	−	0.688241i	$-0.758383\pi$
$73$	−4.20527	+	2.42791i	−0.492189	+	0.284166i	0.233293	+	0.972406i	$0.425050\pi$
$74$	4.28366			0.497966
$75$	−1.87744			−0.216789
$76$	−2.62699	+	1.51669i	−0.301336	+	0.173976i
$77$	−6.11485	+	11.7627i	−0.696852	+	1.34049i
$78$	3.25524	+	1.55030i	0.368583	+	0.175537i
$79$	−3.69502	+	6.39996i	−0.415722	+	0.720052i	−0.995504	−	0.0947200i	$-0.969804\pi$
$79$	−3.69502	+	6.39996i	−0.415722	+	0.720052i	0.579782	+	0.814772i	$0.303138\pi$
$80$	2.27114	+	1.31124i	0.253921	+	0.146602i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−2.85819	−	4.95053i	−0.315634	−	0.546695i
$83$			9.16995i			1.00653i	0.864131	+	0.503266i	$0.167869\pi$
$83$			9.16995i			1.00653i	−0.864131	+	0.503266i	$0.832131\pi$
$84$	−2.34750	−	1.22035i	−0.256133	−	0.133151i
$85$	15.6645	+	9.04389i	1.69905	+	0.980947i
$86$	−11.1553	−	6.44053i	−1.20291	−	0.694500i
$87$	−4.37718			−0.469283
$88$	2.50537	−	4.33943i	0.267073	−	0.462585i
$89$			15.4247i			1.63501i	0.575918	+	0.817507i	$0.304645\pi$
$89$			15.4247i			1.63501i	−0.575918	+	0.817507i	$0.695355\pi$
$90$	−2.62249			−0.276435
$91$	−1.17352	−	9.46693i	−0.123018	−	0.992404i
$92$	−4.99967			−0.521251
$93$		−	5.69286i		−	0.590322i
$94$	−0.288449	+	0.499608i	−0.0297512	+	0.0515306i
$95$	7.95501			0.816167
$96$	0.866025	+	0.500000i	0.0883883	+	0.0510310i
$97$	−12.1886	−	7.03709i	−1.23756	−	0.714508i	−0.268969	−	0.963149i	$-0.586683\pi$
$97$	−12.1886	−	7.03709i	−1.23756	−	0.714508i	−0.968596	+	0.248641i	$0.920016\pi$
$98$	0.617955	+	6.97267i	0.0624229	+	0.704346i
$99$			5.01074i			0.503598i
$100$	−0.938722	−	1.62591i	−0.0938722	−	0.162591i
$101$	4.61704	−	7.99696i	0.459413	−	0.795727i	−0.539517	−	0.841975i	$-0.681393\pi$
$101$	4.61704	−	7.99696i	0.459413	−	0.795727i	0.998930	+	0.0462480i	$0.0147264\pi$
$102$	5.97313	+	3.44859i	0.591428	+	0.341461i
$103$	−2.43903	+	4.22453i	−0.240325	+	0.416255i	−0.960807	−	0.277219i	$-0.910587\pi$
$103$	−2.43903	+	4.22453i	−0.240325	+	0.416255i	0.720482	+	0.693474i	$0.243921\pi$
$104$	0.285022	+	3.59427i	0.0279487	+	0.352447i
$105$	3.73133	+	5.84973i	0.364140	+	0.570875i
$106$	−6.05193	+	3.49408i	−0.587815	+	0.339375i
$107$	−0.172747			−0.0167001			−0.00835006	−	0.999965i	$-0.502658\pi$
$107$	−0.172747			−0.0167001			−0.00835006	+	0.999965i	$0.502658\pi$
$108$	−1.00000			−0.0962250
$109$	−10.9212	+	6.30538i	−1.04606	+	0.603946i	−0.921545	−	0.388271i	$-0.873072\pi$
$109$	−10.9212	+	6.30538i	−1.04606	+	0.603946i	−0.124520	+	0.992217i	$0.539739\pi$
$110$	−11.3801	+	6.57031i	−1.08505	+	0.626454i
$111$	−3.70976	−	2.14183i	−0.352115	−	0.203294i
$112$	−0.116897	−	2.64317i	−0.0110457	−	0.249756i
$113$	−6.33262	+	10.9684i	−0.595722	+	1.03182i	0.397722	+	0.917506i	$0.369801\pi$
$113$	−6.33262	+	10.9684i	−0.595722	+	1.03182i	−0.993444	+	0.114316i	$0.963533\pi$
$114$	3.03338			0.284102
$115$	11.3550	+	6.55579i	1.05885	+	0.611330i
$116$	−2.18859	−	3.79075i	−0.203205	−	0.351962i
$117$	−2.04397	−	2.97022i	−0.188965	−	0.274597i
$118$	10.4885			0.965546
$119$	−0.806258	−	18.2304i	−0.0739095	−	1.67118i
$120$	−1.31124	−	2.27114i	−0.119700	−	0.207326i
$121$	7.05376	+	12.2175i	0.641251	+	1.11068i
$122$	−12.3972	+	7.15751i	−1.12239	+	0.648011i
$123$			5.71638i			0.515429i
$124$	4.93016	−	2.84643i	0.442742	−	0.255617i
$125$		−	8.18887i		−	0.732434i
$126$	1.42282	+	2.23060i	0.126755	+	0.198718i
$127$	3.67120	+	6.35871i	0.325767	+	0.564244i	0.981667	−	0.190603i	$-0.0610443\pi$
$127$	3.67120	+	6.35871i	0.325767	+	0.564244i	−0.655901	+	0.754847i	$0.727711\pi$
$128$			1.00000i			0.0883883i
$129$	6.44053	+	11.1553i	0.567057	+	0.982172i
$130$	4.06564	−	8.53682i	0.356580	−	0.748729i
$131$	5.41067	−	9.37156i	0.472733	−	0.818797i	−0.526780	−	0.850001i	$-0.676601\pi$
$131$	5.41067	−	9.37156i	0.472733	−	0.818797i	0.999513	+	0.0312046i	$0.00993434\pi$
$132$	−4.33943	+	2.50537i	−0.377699	+	0.218065i
$133$	−4.31596	−	6.76627i	−0.374241	−	0.586710i
$134$	−1.23956	+	2.14699i	−0.107082	+	0.185471i
$135$	2.27114	+	1.31124i	0.195469	+	0.112854i
$136$			6.89718i			0.591428i
$137$			13.8123i			1.18006i	0.807380	+	0.590031i	$0.200885\pi$
$137$			13.8123i			1.18006i	−0.807380	+	0.590031i	$0.799115\pi$
$138$	4.32984	+	2.49983i	0.368580	+	0.212800i
$139$	5.75709	−	9.97158i	0.488310	−	0.845778i	−0.511599	−	0.859224i	$-0.670947\pi$
$139$	5.75709	−	9.97158i	0.488310	−	0.845778i	0.999910	+	0.0134459i	$0.00428009\pi$
$140$	−3.20035	+	6.15629i	−0.270479	+	0.520301i
$141$	0.499608	−	0.288449i	0.0420746	−	0.0242918i
$142$	1.63198	−	2.82667i	0.136952	−	0.237209i
$143$	−16.3112	−	7.76814i	−1.36401	−	0.649604i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$			11.4791i			0.953288i
$146$	2.42791	+	4.20527i	0.200935	+	0.348030i
$147$	2.95117	−	6.34749i	0.243408	−	0.523532i
$148$		−	4.28366i		−	0.352115i
$149$	14.2970	−	8.25436i	1.17125	−	0.676223i	0.217278	−	0.976110i	$-0.430282\pi$
$149$	14.2970	−	8.25436i	1.17125	−	0.676223i	0.953975	+	0.299886i	$0.0969488\pi$
$150$			1.87744i			0.153293i
$151$	−5.69210	+	3.28634i	−0.463217	+	0.267438i	−0.713396	−	0.700761i	$-0.752844\pi$
$151$	−5.69210	+	3.28634i	−0.463217	+	0.267438i	0.250179	+	0.968200i	$0.419510\pi$
$152$	1.51669	+	2.62699i	0.123020	+	0.213077i
$153$	−3.44859	−	5.97313i	−0.278802	−	0.482899i
$154$	11.7627	+	6.11485i	0.947866	+	0.492749i
$155$	−14.9295			−1.19916
$156$	1.55030	−	3.25524i	0.124123	−	0.260628i
$157$	4.40621	+	7.63178i	0.351654	+	0.609083i	0.986539	−	0.163524i	$-0.0522860\pi$
$157$	4.40621	+	7.63178i	0.351654	+	0.609083i	−0.634885	+	0.772606i	$0.718953\pi$
$158$	6.39996	+	3.69502i	0.509153	+	0.293960i
$159$	6.98817			0.554198
$160$	1.31124	−	2.27114i	0.103663	−	0.179549i
$161$	−0.584445	−	13.2150i	−0.0460607	−	1.04148i
$162$	0.866025	+	0.500000i	0.0680414	+	0.0392837i
$163$	−8.11055	+	4.68263i	−0.635268	+	0.366772i	−0.782789	−	0.622287i	$-0.786204\pi$
$163$	−8.11055	+	4.68263i	−0.635268	+	0.366772i	0.147522	+	0.989059i	$0.452870\pi$
$164$	−4.95053	+	2.85819i	−0.386572	+	0.223187i
$165$	13.1406			1.02300
$166$	9.16995			0.711726
$167$	−2.26138	+	1.30561i	−0.174991	+	0.101031i	−0.584937	−	0.811079i	$-0.698881\pi$
$167$	−2.26138	+	1.30561i	−0.174991	+	0.101031i	0.409946	+	0.912110i	$0.365547\pi$
$168$	−1.22035	+	2.34750i	−0.0941519	+	0.181113i
$169$	12.8375	−	2.04889i	0.987502	−	0.157607i
$170$	9.04389	−	15.6645i	0.693635	−	1.20141i
$171$	−2.62699	−	1.51669i	−0.200891	−	0.115984i
$172$	−6.44053	+	11.1553i	−0.491086	+	0.850586i
$173$	2.49748	+	4.32576i	0.189880	+	0.328881i	0.945210	−	0.326463i	$-0.105857\pi$
$173$	2.49748	+	4.32576i	0.189880	+	0.328881i	−0.755330	+	0.655344i	$0.772524\pi$
$174$			4.37718i			0.331833i
$175$	4.18783	−	2.67126i	0.316570	−	0.201929i
$176$	−4.33943	−	2.50537i	−0.327097	−	0.188849i
$177$	−9.08332	−	5.24426i	−0.682744	−	0.394183i
$178$	15.4247			1.15613
$179$	3.76120	−	6.51459i	0.281125	−	0.486923i	−0.690537	−	0.723297i	$-0.742626\pi$
$179$	3.76120	−	6.51459i	0.281125	−	0.486923i	0.971662	+	0.236374i	$0.0759590\pi$
$180$			2.62249i			0.195469i
$181$	−7.14351			−0.530973			−0.265487	−	0.964115i	$-0.585533\pi$
$181$	−7.14351			−0.530973			−0.265487	+	0.964115i	$0.585533\pi$
$182$	−9.46693	+	1.17352i	−0.701736	+	0.0869871i
$183$	14.3150			1.05820
$184$			4.99967i			0.368580i
$185$	−5.61693	+	9.72880i	−0.412965	+	0.715276i
$186$	−5.69286			−0.417421
$187$	−29.9298	−	17.2800i	−2.18869	−	1.26364i
$188$	0.499608	+	0.288449i	0.0364376	+	0.0210373i
$189$	−0.116897	−	2.64317i	−0.00850298	−	0.192262i
$190$		−	7.95501i		−	0.577117i
$191$	−3.96451	−	6.86674i	−0.286862	−	0.496860i	0.686197	−	0.727416i	$-0.259279\pi$
$191$	−3.96451	−	6.86674i	−0.286862	−	0.496860i	−0.973059	+	0.230556i	$0.925945\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	−9.33627	−	5.39030i	−0.672040	−	0.388002i	0.124809	−	0.992181i	$-0.460168\pi$
$193$	−9.33627	−	5.39030i	−0.672040	−	0.388002i	−0.796849	+	0.604178i	$0.793501\pi$
$194$	−7.03709	+	12.1886i	−0.505234	+	0.875090i
$195$	−7.78936	+	5.36029i	−0.557807	+	0.383858i
$196$	6.97267	−	0.617955i	0.498048	−	0.0441396i
$197$	−16.5289	+	9.54296i	−1.17763	+	0.679908i	−0.955466	−	0.295100i	$-0.904647\pi$
$197$	−16.5289	+	9.54296i	−1.17763	+	0.679908i	−0.222169	+	0.975008i	$0.571314\pi$
$198$	5.01074			0.356098
$199$	−23.5141			−1.66687			−0.833436	−	0.552615i	$-0.813630\pi$
$199$	−23.5141			−1.66687			−0.833436	+	0.552615i	$0.813630\pi$
$200$	−1.62591	+	0.938722i	−0.114970	+	0.0663777i
$201$	2.14699	−	1.23956i	0.151437	−	0.0874320i
$202$	−7.99696	−	4.61704i	−0.562664	−	0.324854i
$203$	9.76375	−	6.22794i	0.685281	−	0.437115i
$204$	3.44859	−	5.97313i	0.241450	−	0.418203i
$205$	14.9911			1.04703
$206$	4.22453	+	2.43903i	0.294337	+	0.169936i
$207$	−2.49983	−	4.32984i	−0.173750	−	0.300945i
$208$	3.59427	−	0.285022i	0.249218	−	0.0197627i
$209$	−15.1995			−1.05137
$210$	5.84973	−	3.73133i	0.403670	−	0.257486i
$211$	2.44732	+	4.23888i	0.168480	+	0.291816i	0.937886	−	0.346944i	$-0.112781\pi$
$211$	2.44732	+	4.23888i	0.168480	+	0.291816i	−0.769406	+	0.638761i	$0.779447\pi$
$212$	3.49408	+	6.05193i	0.239975	+	0.415648i
$213$	−2.82667	+	1.63198i	−0.193680	+	0.111821i
$214$			0.172747i			0.0118088i
$215$	29.2547	−	16.8902i	1.99515	−	1.15190i
$216$			1.00000i			0.0680414i
$217$	8.09992	+	12.6985i	0.549858	+	0.862031i
$218$	6.30538	+	10.9212i	0.427054	+	0.739680i
$219$		−	4.85582i		−	0.328126i
$220$	6.57031	+	11.3801i	0.442970	+	0.767246i
$221$	24.7903	−	1.96585i	1.66758	−	0.132237i
$222$	−2.14183	+	3.70976i	−0.143750	+	0.248983i
$223$	−8.72547	+	5.03765i	−0.584301	+	0.337346i	−0.762841	−	0.646587i	$-0.776196\pi$
$223$	−8.72547	+	5.03765i	−0.584301	+	0.337346i	0.178540	+	0.983933i	$0.442863\pi$
$224$	−2.64317	+	0.116897i	−0.176604	+	0.00781049i
$225$	0.938722	−	1.62591i	0.0625815	−	0.108394i
$226$	10.9684	+	6.33262i	0.729608	+	0.421239i
$227$			14.3178i			0.950307i	0.879903	+	0.475154i	$0.157608\pi$
$227$			14.3178i			0.950307i	−0.879903	+	0.475154i	$0.842392\pi$
$228$		−	3.03338i		−	0.200891i
$229$	13.3945	+	7.73332i	0.885134	+	0.511032i	0.872348	−	0.488886i	$-0.162597\pi$
$229$	13.3945	+	7.73332i	0.885134	+	0.511032i	0.0127863	+	0.999918i	$0.495930\pi$
$230$	6.55579	−	11.3550i	0.432276	−	0.748723i
$231$	−7.12938	−	11.1770i	−0.469079	−	0.735391i
$232$	−3.79075	+	2.18859i	−0.248875	+	0.143688i
$233$	2.31317	−	4.00653i	0.151541	−	0.262477i	−0.780253	−	0.625464i	$-0.784910\pi$
$233$	2.31317	−	4.00653i	0.151541	−	0.262477i	0.931794	+	0.362987i	$0.118243\pi$
$234$	−2.97022	+	2.04397i	−0.194169	+	0.133619i
$235$	−0.756453	−	1.31022i	−0.0493456	−	0.0854690i
$236$		−	10.4885i		−	0.682744i
$237$	−3.69502	−	6.39996i	−0.240017	−	0.415722i
$238$	−18.2304	+	0.806258i	−1.18170	+	0.0522619i
$239$			8.48540i			0.548875i	0.961605	+	0.274437i	$0.0884916\pi$
$239$			8.48540i			0.548875i	−0.961605	+	0.274437i	$0.911508\pi$
$240$	−2.27114	+	1.31124i	−0.146602	+	0.0846404i
$241$		−	4.25892i		−	0.274341i	−0.990547	−	0.137170i	$-0.956199\pi$
$241$		−	4.25892i		−	0.274341i	0.990547	−	0.137170i	$-0.0438008\pi$
$242$	12.2175	−	7.05376i	0.785369	−	0.453433i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	7.15751	+	12.3972i	0.458213	+	0.793648i
$245$	−16.6462	−	7.73941i	−1.06349	−	0.494453i
$246$	5.71638			0.364463
$247$	9.00980	−	6.20014i	0.573280	−	0.394506i
$248$	−2.84643	−	4.93016i	−0.180749	−	0.313066i
$249$	−7.94141	−	4.58497i	−0.503266	−	0.290561i
$250$	−8.18887			−0.517909
$251$	−1.00766	+	1.74531i	−0.0636027	+	0.110163i	−0.896073	−	0.443906i	$-0.853592\pi$
$251$	−1.00766	+	1.74531i	−0.0636027	+	0.110163i	0.832471	+	0.554069i	$0.186926\pi$
$252$	2.23060	−	1.42282i	0.140515	−	0.0896292i
$253$	−21.6957	−	12.5260i	−1.36400	−	0.787504i
$254$	6.35871	−	3.67120i	0.398981	−	0.230352i
$255$	−15.6645	+	9.04389i	−0.980947	+	0.566350i
$256$	1.00000			0.0625000
$257$	−22.9955			−1.43442			−0.717211	−	0.696856i	$-0.754582\pi$
$257$	−22.9955			−1.43442			−0.717211	+	0.696856i	$0.754582\pi$
$258$	11.1553	−	6.44053i	0.694500	−	0.400970i
$259$	11.3224	−	0.500746i	0.703542	−	0.0311148i
$260$	−8.53682	−	4.06564i	−0.529431	−	0.252140i
$261$	2.18859	−	3.79075i	0.135470	−	0.234641i
$262$	−9.37156	−	5.41067i	−0.578977	−	0.334272i
$263$	−11.0191	+	19.0857i	−0.679470	+	1.17688i	0.295671	+	0.955290i	$0.404457\pi$
$263$	−11.0191	+	19.0857i	−0.679470	+	1.17688i	−0.975141	+	0.221586i	$0.928876\pi$
$264$	2.50537	+	4.33943i	0.154195	+	0.267073i
$265$		−	18.3264i		−	1.12578i
$266$	−6.76627	+	4.31596i	−0.414867	+	0.264628i
$267$	−13.3582	−	7.71235i	−0.817507	−	0.471988i
$268$	2.14699	+	1.23956i	0.131148	+	0.0757184i
$269$	4.37283			0.266616			0.133308	−	0.991075i	$-0.457440\pi$
$269$	4.37283			0.266616			0.133308	+	0.991075i	$0.457440\pi$
$270$	1.31124	−	2.27114i	0.0797998	−	0.138217i
$271$			15.5078i			0.942032i	0.882125	+	0.471016i	$0.156113\pi$
$271$			15.5078i			0.942032i	−0.882125	+	0.471016i	$0.843887\pi$
$272$	6.89718			0.418203
$273$	8.78537	+	3.71717i	0.531715	+	0.224973i
$274$	13.8123			0.834430
$275$		−	9.40739i		−	0.567287i
$276$	2.49983	−	4.32984i	0.150472	−	0.260626i
$277$	28.7587			1.72794			0.863972	−	0.503539i	$-0.167969\pi$
$277$	28.7587			1.72794			0.863972	+	0.503539i	$0.167969\pi$
$278$	−9.97158	−	5.75709i	−0.598056	−	0.345288i
$279$	4.93016	+	2.84643i	0.295161	+	0.170411i
$280$	6.15629	+	3.20035i	0.367909	+	0.191257i
$281$		−	13.5100i		−	0.805941i	−0.915213	−	0.402970i	$-0.867978\pi$
$281$		−	13.5100i		−	0.805941i	0.915213	−	0.402970i	$-0.132022\pi$
$282$	−0.288449	−	0.499608i	−0.0171769	−	0.0297512i
$283$	9.50356	−	16.4607i	0.564928	−	0.978484i	−0.432128	−	0.901812i	$-0.642237\pi$
$283$	9.50356	−	16.4607i	0.564928	−	0.978484i	0.997056	−	0.0766722i	$-0.0244295\pi$
$284$	−2.82667	−	1.63198i	−0.167732	−	0.0968400i
$285$	−3.97750	+	6.88924i	−0.235607	+	0.408083i
$286$	−7.76814	+	16.3112i	−0.459340	+	0.964499i
$287$	−8.13338	−	12.7510i	−0.480098	−	0.752666i
$288$	−0.866025	+	0.500000i	−0.0510310	+	0.0294628i
$289$	30.5711			1.79830
$290$	11.4791			0.674076
$291$	12.1886	−	7.03709i	0.714508	−	0.412522i
$292$	4.20527	−	2.42791i	0.246095	−	0.142083i
$293$	−7.14308	−	4.12406i	−0.417303	−	0.240930i	0.276620	−	0.960979i	$-0.410786\pi$
$293$	−7.14308	−	4.12406i	−0.417303	−	0.240930i	−0.693923	+	0.720049i	$0.744119\pi$
$294$	−6.34749	−	2.95117i	−0.370193	−	0.172116i
$295$	−13.7530	+	23.8209i	−0.800731	+	1.38691i
$296$	−4.28366			−0.248983
$297$	−4.33943	−	2.50537i	−0.251799	−	0.145376i
$298$	−8.25436	−	14.2970i	−0.478162	−	0.828201i
$299$	17.9701	−	1.42502i	1.03924	−	0.0824109i
$300$	1.87744			0.108394
$301$	−30.2383	−	15.7194i	−1.74291	−	0.906050i
$302$	3.28634	+	5.69210i	0.189107	+	0.327544i
$303$	4.61704	+	7.99696i	0.265242	+	0.459413i
$304$	2.62699	−	1.51669i	0.150668	−	0.0869882i
$305$		−	37.5410i		−	2.14959i
$306$	−5.97313	+	3.44859i	−0.341461	+	0.197143i
$307$		−	2.94195i		−	0.167906i	−0.996470	−	0.0839531i	$-0.973245\pi$
$307$		−	2.94195i		−	0.167906i	0.996470	−	0.0839531i	$-0.0267546\pi$
$308$	6.11485	−	11.7627i	0.348426	−	0.670243i
$309$	−2.43903	−	4.22453i	−0.138752	−	0.240325i
$310$			14.9295i			0.847937i
$311$	7.47126	+	12.9406i	0.423656	+	0.733794i	0.996294	−	0.0860145i	$-0.0274131\pi$
$311$	7.47126	+	12.9406i	0.423656	+	0.733794i	−0.572638	+	0.819809i	$0.694080\pi$
$312$	−3.25524	−	1.55030i	−0.184292	−	0.0877683i
$313$	12.1929	−	21.1187i	0.689182	−	1.19370i	−0.282921	−	0.959143i	$-0.591303\pi$
$313$	12.1929	−	21.1187i	0.689182	−	1.19370i	0.972103	−	0.234555i	$-0.0753632\pi$
$314$	7.63178	−	4.40621i	0.430686	−	0.248657i
$315$	−6.93168	+	0.306560i	−0.390556	+	0.0172727i
$316$	3.69502	−	6.39996i	0.207861	−	0.360026i
$317$	−24.6493	−	14.2313i	−1.38444	−	0.799309i	−0.391762	−	0.920067i	$-0.628134\pi$
$317$	−24.6493	−	14.2313i	−1.38444	−	0.799309i	−0.992682	+	0.120758i	$0.961468\pi$
$318$		−	6.98817i		−	0.391877i
$319$		−	21.9329i		−	1.22801i
$320$	−2.27114	−	1.31124i	−0.126961	−	0.0733008i
$321$	0.0863737	−	0.149604i	0.00482091	−	0.00835006i
$322$	−13.2150	+	0.584445i	−0.736441	+	0.0325698i
$323$	18.1188	−	10.4609i	1.00816	−	0.582060i
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$	3.83744	+	5.57642i	0.212863	+	0.309324i
$326$	4.68263	+	8.11055i	0.259347	+	0.449202i
$327$		−	12.6108i		−	0.697377i
$328$	2.85819	+	4.95053i	0.157817	+	0.273347i
$329$	−0.704016	+	1.35427i	−0.0388136	+	0.0746631i
$330$		−	13.1406i		−	0.723367i
$331$	−5.43590	+	3.13842i	−0.298784	+	0.172503i	−0.641897	−	0.766791i	$-0.721852\pi$
$331$	−5.43590	+	3.13842i	−0.298784	+	0.172503i	0.343112	+	0.939294i	$0.388519\pi$
$332$		−	9.16995i		−	0.503266i
$333$	3.70976	−	2.14183i	0.203294	−	0.117372i
$334$	1.30561	+	2.26138i	0.0714397	+	0.123737i
$335$	−3.25074	−	5.63045i	−0.177607	−	0.307624i
$336$	2.34750	+	1.22035i	0.128067	+	0.0665755i
$337$	9.99063			0.544224			0.272112	−	0.962266i	$-0.412278\pi$
$337$	9.99063			0.544224			0.272112	+	0.962266i	$0.412278\pi$
$338$	−2.04889	−	12.8375i	−0.111445	−	0.698269i
$339$	−6.33262	−	10.9684i	−0.343941	−	0.595722i
$340$	−15.6645	−	9.04389i	−0.849525	−	0.490474i
$341$	28.5255			1.54474
$342$	−1.51669	+	2.62699i	−0.0820133	+	0.142051i
$343$	2.44844	+	18.3577i	0.132203	+	0.991223i
$344$	11.1553	+	6.44053i	0.601455	+	0.347250i
$345$	−11.3550	+	6.55579i	−0.611330	+	0.352952i
$346$	4.32576	−	2.49748i	0.232554	−	0.134265i
$347$	−3.90930			−0.209862			−0.104931	−	0.994479i	$-0.533462\pi$
$347$	−3.90930			−0.209862			−0.104931	+	0.994479i	$0.533462\pi$
$348$	4.37718			0.234641
$349$	13.3325	−	7.69750i	0.713671	−	0.412038i	−0.0987480	−	0.995112i	$-0.531484\pi$
$349$	13.3325	−	7.69750i	0.713671	−	0.412038i	0.812419	+	0.583074i	$0.198150\pi$
$350$	−2.67126	−	4.18783i	−0.142785	−	0.223849i
$351$	3.59427	−	0.285022i	0.191848	−	0.0152134i
$352$	−2.50537	+	4.33943i	−0.133537	+	0.231292i
$353$	26.0531	+	15.0418i	1.38667	+	0.800594i	0.992938	−	0.118632i	$-0.0378509\pi$
$353$	26.0531	+	15.0418i	1.38667	+	0.800594i	0.393731	+	0.919226i	$0.371184\pi$
$354$	−5.24426	+	9.08332i	−0.278729	+	0.482773i
$355$	4.27984	+	7.41290i	0.227150	+	0.393436i
$356$		−	15.4247i		−	0.817507i
$357$	16.1911	+	8.41696i	0.856925	+	0.445473i
$358$	−6.51459	−	3.76120i	−0.344307	−	0.198786i
$359$	7.23357	+	4.17631i	0.381773	+	0.220417i	0.678590	−	0.734518i	$-0.262592\pi$
$359$	7.23357	+	4.17631i	0.381773	+	0.220417i	−0.296816	+	0.954935i	$0.595925\pi$
$360$	2.62249			0.138217
$361$	−4.89930	+	8.48583i	−0.257858	+	0.446623i
$362$			7.14351i			0.375455i
$363$	−14.1075			−0.740453
$364$	1.17352	+	9.46693i	0.0615092	+	0.496202i
$365$	−12.7343			−0.666546
$366$		−	14.3150i		−	0.748258i
$367$	−6.18199	+	10.7075i	−0.322697	+	0.558928i	−0.981044	−	0.193787i	$-0.937923\pi$
$367$	−6.18199	+	10.7075i	−0.322697	+	0.558928i	0.658346	+	0.752715i	$0.271256\pi$
$368$	4.99967			0.260626
$369$	−4.95053	−	2.85819i	−0.257714	−	0.148791i
$370$	9.72880	+	5.61693i	0.505776	+	0.292010i
$371$	−15.5878	+	9.94290i	−0.809279	+	0.516210i
$372$			5.69286i			0.295161i
$373$	11.3199	+	19.6066i	0.586122	+	1.01519i	0.994735	+	0.102485i	$0.0326792\pi$
$373$	11.3199	+	19.6066i	0.586122	+	1.01519i	−0.408613	+	0.912708i	$0.633987\pi$
$374$	−17.2800	+	29.9298i	−0.893527	+	1.54763i
$375$	7.09177	+	4.09443i	0.366217	+	0.211436i
$376$	0.288449	−	0.499608i	0.0148756	−	0.0257653i
$377$	8.94683	+	13.0012i	0.460785	+	0.669594i
$378$	−2.64317	+	0.116897i	−0.135950	+	0.00601252i
$379$	9.43601	−	5.44788i	0.484695	−	0.279839i	−0.237676	−	0.971344i	$-0.576386\pi$
$379$	9.43601	−	5.44788i	0.484695	−	0.279839i	0.722371	+	0.691506i	$0.243052\pi$
$380$	−7.95501			−0.408083
$381$	−7.34240			−0.376163
$382$	−6.86674	+	3.96451i	−0.351333	+	0.202842i
$383$	−1.09953	+	0.634815i	−0.0561835	+	0.0324375i	−0.527829	−	0.849351i	$-0.676994\pi$
$383$	−1.09953	+	0.634815i	−0.0561835	+	0.0324375i	0.471645	+	0.881788i	$0.343660\pi$
$384$	−0.866025	−	0.500000i	−0.0441942	−	0.0255155i
$385$	−29.3115	+	18.6967i	−1.49385	+	0.952873i
$386$	−5.39030	+	9.33627i	−0.274359	+	0.475204i
$387$	−12.8811			−0.654781
$388$	12.1886	+	7.03709i	0.618782	+	0.357254i
$389$	15.3303	+	26.5529i	0.777279	+	1.34629i	0.933505	+	0.358565i	$0.116734\pi$
$389$	15.3303	+	26.5529i	0.777279	+	1.34629i	−0.156226	+	0.987721i	$0.549933\pi$
$390$	5.36029	+	7.78936i	0.271429	+	0.394429i
$391$	34.4836			1.74391
$392$	−0.617955	−	6.97267i	−0.0312114	−	0.352173i
$393$	5.41067	+	9.37156i	0.272932	+	0.472733i
$394$	9.54296	+	16.5289i	0.480767	+	0.832714i
$395$	−16.7838	+	9.69014i	−0.844486	+	0.487564i
$396$		−	5.01074i		−	0.251799i
$397$	22.9046	−	13.2240i	1.14955	−	0.663692i	0.200772	−	0.979638i	$-0.435655\pi$
$397$	22.9046	−	13.2240i	1.14955	−	0.663692i	0.948777	+	0.315946i	$0.102322\pi$
$398$			23.5141i			1.17866i
$399$	8.01774	−	0.354592i	0.401389	−	0.0177518i
$400$	0.938722	+	1.62591i	0.0469361	+	0.0812957i
$401$			21.9134i			1.09430i	0.837034	+	0.547151i	$0.184288\pi$
$401$			21.9134i			1.09430i	−0.837034	+	0.547151i	$0.815712\pi$
$402$	−1.23956	−	2.14699i	−0.0618238	−	0.107082i
$403$	−16.9090	+	11.6360i	−0.842299	+	0.579633i
$404$	−4.61704	+	7.99696i	−0.229707	+	0.397863i
$405$	−2.27114	+	1.31124i	−0.112854	+	0.0651562i
$406$	−6.22794	−	9.76375i	−0.309087	−	0.484567i
$407$	10.7322	−	18.5886i	0.531973	−	0.921405i
$408$	−5.97313	−	3.44859i	−0.295714	−	0.170731i
$409$		−	10.3492i		−	0.511737i	−0.966712	−	0.255868i	$-0.917639\pi$
$409$		−	10.3492i		−	0.511737i	0.966712	−	0.255868i	$-0.0823614\pi$
$410$		−	14.9911i		−	0.740360i
$411$	−11.9618	−	6.90614i	−0.590031	−	0.340655i
$412$	2.43903	−	4.22453i	0.120163	−	0.208128i
$413$	27.7229	−	1.22607i	1.36416	−	0.0603311i
$414$	−4.32984	+	2.49983i	−0.212800	+	0.122860i
$415$	−12.0240	+	20.8262i	−0.590237	+	1.02232i
$416$	−0.285022	−	3.59427i	−0.0139744	−	0.176223i
$417$	5.75709	+	9.97158i	0.281926	+	0.488310i
$418$			15.1995i			0.743432i
$419$	−8.98405	−	15.5608i	−0.438900	−	0.760197i	0.558705	−	0.829366i	$-0.311298\pi$
$419$	−8.98405	−	15.5608i	−0.438900	−	0.760197i	−0.997605	+	0.0691697i	$0.977965\pi$
$420$	−3.73133	−	5.84973i	−0.182070	−	0.285437i
$421$		−	7.16224i		−	0.349066i	−0.984651	−	0.174533i	$-0.944158\pi$
$421$		−	7.16224i		−	0.349066i	0.984651	−	0.174533i	$-0.0558416\pi$
$422$	4.23888	−	2.44732i	0.206345	−	0.119133i
$423$			0.576897i			0.0280497i
$424$	6.05193	−	3.49408i	0.293908	−	0.169688i
$425$	6.47454	+	11.2142i	0.314061	+	0.543970i
$426$	1.63198	+	2.82667i	0.0790695	+	0.136952i
$427$	−31.9311	+	20.3677i	−1.54525	+	0.985661i
$428$	0.172747			0.00835006
$429$	14.8830	−	10.2418i	0.718557	−	0.494479i
$430$	−16.8902	−	29.2547i	−0.814519	−	1.41079i
$431$	27.5193	+	15.8883i	1.32556	+	0.765311i	0.984609	−	0.174771i	$-0.0559185\pi$
$431$	27.5193	+	15.8883i	1.32556	+	0.765311i	0.340949	+	0.940082i	$0.389252\pi$
$432$	1.00000			0.0481125
$433$	2.56335	−	4.43985i	0.123187	−	0.213365i	−0.797836	−	0.602874i	$-0.794022\pi$
$433$	2.56335	−	4.43985i	0.123187	−	0.213365i	0.921023	+	0.389509i	$0.127355\pi$
$434$	12.6985	−	8.09992i	0.609548	−	0.388808i
$435$	−9.94119	−	5.73955i	−0.476644	−	0.275190i
$436$	10.9212	−	6.30538i	0.523032	−	0.301973i
$437$	13.1341	−	7.58295i	0.628287	−	0.362742i
$438$	−4.85582			−0.232020
$439$	36.3198			1.73345			0.866725	−	0.498787i	$-0.166221\pi$
$439$	36.3198			1.73345			0.866725	+	0.498787i	$0.166221\pi$
$440$	11.3801	−	6.57031i	0.542525	−	0.313227i
$441$	4.02150	+	5.72953i	0.191500	+	0.272835i
$442$	−1.96585	−	24.7903i	−0.0935060	−	1.17916i
$443$	7.15190	−	12.3874i	0.339797	−	0.588545i	−0.644598	−	0.764522i	$-0.722975\pi$
$443$	7.15190	−	12.3874i	0.339797	−	0.588545i	0.984394	+	0.175977i	$0.0563084\pi$
$444$	3.70976	+	2.14183i	0.176057	+	0.101647i
$445$	−20.2255	+	35.0317i	−0.958783	+	1.66066i
$446$	5.03765	+	8.72547i	0.238540	+	0.413163i
$447$			16.5087i			0.780835i
$448$	0.116897	+	2.64317i	0.00552285	+	0.124878i
$449$	−5.30462	−	3.06262i	−0.250340	−	0.144534i	0.369580	−	0.929199i	$-0.379502\pi$
$449$	−5.30462	−	3.06262i	−0.250340	−	0.144534i	−0.619920	+	0.784665i	$0.712835\pi$
$450$	−1.62591	−	0.938722i	−0.0766463	−	0.0442518i
$451$	−28.6433			−1.34876
$452$	6.33262	−	10.9684i	0.297861	−	0.515911i
$453$		−	6.57267i		−	0.308811i
$454$	14.3178			0.671969
$455$	9.74823	−	23.0395i	0.457004	−	1.08011i
$456$	−3.03338			−0.142051
$457$			21.4549i			1.00362i	0.864979	+	0.501808i	$0.167332\pi$
$457$			21.4549i			1.00362i	−0.864979	+	0.501808i	$0.832668\pi$
$458$	7.73332	−	13.3945i	0.361354	−	0.625884i
$459$	6.89718			0.321933
$460$	−11.3550	−	6.55579i	−0.529427	−	0.305665i
$461$	−23.6097	−	13.6311i	−1.09961	−	0.634862i	−0.163494	−	0.986544i	$-0.552277\pi$
$461$	−23.6097	−	13.6311i	−1.09961	−	0.634862i	−0.936120	+	0.351682i	$0.885610\pi$
$462$	−11.1770	+	7.12938i	−0.520000	+	0.331689i
$463$			26.5768i			1.23513i	0.786521	+	0.617564i	$0.211880\pi$
$463$			26.5768i			1.23513i	−0.786521	+	0.617564i	$0.788120\pi$
$464$	2.18859	+	3.79075i	0.101603	+	0.175981i
$465$	7.46473	−	12.9293i	0.346169	−	0.599582i
$466$	−4.00653	−	2.31317i	−0.185599	−	0.107156i
$467$	−9.69582	+	16.7937i	−0.448669	+	0.777118i	−0.998300	−	0.0582902i	$-0.981435\pi$
$467$	−9.69582	+	16.7937i	−0.448669	+	0.777118i	0.549631	+	0.835408i	$0.314768\pi$
$468$	2.04397	+	2.97022i	0.0944826	+	0.137298i
$469$	−3.02540	+	5.81975i	−0.139700	+	0.268731i
$470$	−1.31022	+	0.756453i	−0.0604357	+	0.0348926i
$471$	−8.81242			−0.406055
$472$	−10.4885			−0.482773
$473$	−55.8965	+	32.2718i	−2.57012	+	1.48386i
$474$	−6.39996	+	3.69502i	−0.293960	+	0.169718i
$475$	4.93202	+	2.84750i	0.226297	+	0.130652i
$476$	0.806258	+	18.2304i	0.0369548	+	0.835589i
$477$	−3.49408	+	6.05193i	−0.159983	+	0.277099i
$478$	8.48540			0.388113
$479$	−21.3818	−	12.3448i	−0.976960	−	0.564048i	−0.0756092	−	0.997138i	$-0.524090\pi$
$479$	−21.3818	−	12.3448i	−0.976960	−	0.564048i	−0.901351	+	0.433089i	$0.857423\pi$
$480$	1.31124	+	2.27114i	0.0598498	+	0.103663i
$481$	1.22094	+	15.3966i	0.0556700	+	0.702026i
$482$	−4.25892			−0.193988
$483$	11.7367	+	6.10134i	0.534039	+	0.277620i
$484$	−7.05376	−	12.2175i	−0.320626	−	0.555340i
$485$	−18.4547	−	31.9645i	−0.837984	−	1.45143i
$486$	−0.866025	+	0.500000i	−0.0392837	+	0.0226805i
$487$		−	26.2566i		−	1.18980i	−0.803799	−	0.594901i	$-0.797191\pi$
$487$		−	26.2566i		−	1.18980i	0.803799	−	0.594901i	$-0.202809\pi$
$488$	12.3972	−	7.15751i	0.561194	−	0.324005i
$489$		−	9.36526i		−	0.423512i
$490$	−7.73941	+	16.6462i	−0.349631	+	0.751999i
$491$	−11.0510	−	19.1408i	−0.498723	−	0.863813i	0.501276	−	0.865287i	$-0.332864\pi$
$491$	−11.0510	−	19.1408i	−0.498723	−	0.863813i	−0.999999	+	0.00147433i	$0.999531\pi$
$492$		−	5.71638i		−	0.257714i
$493$	15.0951	+	26.1455i	0.679849	+	1.17753i
$494$	−6.20014	−	9.00980i	−0.278958	−	0.405370i
$495$	−6.57031	+	11.3801i	−0.295313	+	0.511498i
$496$	−4.93016	+	2.84643i	−0.221371	+	0.127809i
$497$	3.98316	−	7.66212i	0.178669	−	0.343693i
$498$	−4.58497	+	7.94141i	−0.205458	+	0.355863i
$499$	−28.1585	−	16.2573i	−1.26055	−	0.727778i	−0.287368	−	0.957820i	$-0.592780\pi$
$499$	−28.1585	−	16.2573i	−1.26055	−	0.727778i	−0.973181	+	0.230042i	$0.926114\pi$
$500$			8.18887i			0.366217i
$501$		−	2.61122i		−	0.116661i
$502$	1.74531	+	1.00766i	0.0778971	+	0.0449739i
$503$	9.95552	−	17.2435i	0.443895	−	0.768848i	−0.554080	−	0.832464i	$-0.686930\pi$
$503$	9.95552	−	17.2435i	0.443895	−	0.768848i	0.997974	+	0.0636154i	$0.0202631\pi$
$504$	−1.42282	−	2.23060i	−0.0633774	−	0.0993589i
$505$	20.9719	−	12.1081i	0.933238	−	0.538805i
$506$	−12.5260	+	21.6957i	−0.556850	+	0.964492i
$507$	−4.64437	+	12.1421i	−0.206264	+	0.539248i
$508$	−3.67120	−	6.35871i	−0.162883	−	0.282122i
$509$			2.71278i			0.120242i	0.998191	+	0.0601209i	$0.0191486\pi$
$509$			2.71278i			0.120242i	−0.998191	+	0.0601209i	$0.980851\pi$
$510$	9.04389	+	15.6645i	0.400470	+	0.693635i
$511$	6.90896	+	10.8314i	0.305634	+	0.479153i
$512$		−	1.00000i		−	0.0441942i
$513$	2.62699	−	1.51669i	0.115984	−	0.0669636i
$514$			22.9955i			1.01429i
$515$	−11.0788	+	6.39634i	−0.488189	+	0.281856i
$516$	−6.44053	−	11.1553i	−0.283529	−	0.491086i
$517$	1.44534	+	2.50341i	0.0635660	+	0.110100i
$518$	−0.500746	−	11.3224i	−0.0220015	−	0.497479i
$519$	−4.99495			−0.219254
$520$	−4.06564	+	8.53682i	−0.178290	+	0.374365i
$521$	−2.90626	−	5.03379i	−0.127326	−	0.220534i	0.795314	−	0.606198i	$-0.207306\pi$
$521$	−2.90626	−	5.03379i	−0.127326	−	0.220534i	−0.922640	+	0.385663i	$0.873973\pi$
$522$	−3.79075	−	2.18859i	−0.165917	−	0.0957920i
$523$	−39.2972			−1.71834			−0.859172	−	0.511686i	$-0.829021\pi$
$523$	−39.2972			−1.71834			−0.859172	+	0.511686i	$0.829021\pi$
$524$	−5.41067	+	9.37156i	−0.236366	+	0.409398i
$525$	0.219467	+	4.96240i	0.00957833	+	0.216577i
$526$	19.0857	+	11.0191i	0.832177	+	0.480458i
$527$	−34.0042	+	19.6324i	−1.48125	+	0.855199i
$528$	4.33943	−	2.50537i	0.188849	−	0.109032i
$529$	1.99668			0.0868123
$530$	−18.3264			−0.796047
$531$	9.08332	−	5.24426i	0.394183	−	0.227581i
$532$	4.31596	+	6.76627i	0.187120	+	0.293355i
$533$	16.9789	−	11.6841i	0.735437	−	0.506095i
$534$	−7.71235	+	13.3582i	−0.333746	+	0.578065i
$535$	−0.392334	−	0.226514i	−0.0169621	−	0.00979306i
$536$	1.23956	−	2.14699i	0.0535410	−	0.0927357i
$537$	3.76120	+	6.51459i	0.162308	+	0.281125i
$538$		−	4.37283i		−	0.188526i
$539$	31.8056	+	14.7876i	1.36996	+	0.636945i
$540$	−2.27114	−	1.31124i	−0.0977344	−	0.0564270i
$541$	−20.1625	−	11.6408i	−0.866854	−	0.500478i	−0.000552417	−	1.00000i	$-0.500176\pi$
$541$	−20.1625	−	11.6408i	−0.866854	−	0.500478i	−0.866301	+	0.499522i	$0.833509\pi$
$542$	15.5078			0.666117
$543$	3.57176	−	6.18646i	0.153279	−	0.265487i
$544$		−	6.89718i		−	0.295714i
$545$	−33.0716			−1.41663
$546$	3.71717	−	8.78537i	0.159080	−	0.375979i
$547$	−9.23824			−0.394999			−0.197499	−	0.980303i	$-0.563282\pi$
$547$	−9.23824			−0.394999			−0.197499	+	0.980303i	$0.563282\pi$
$548$		−	13.8123i		−	0.590031i
$549$	−7.15751	+	12.3972i	−0.305475	+	0.529098i
$550$	−9.40739			−0.401132
$551$	11.4988	+	6.63883i	0.489865	+	0.282824i
$552$	−4.32984	−	2.49983i	−0.184290	−	0.106400i
$553$	17.3481	+	9.01842i	0.737716	+	0.383502i
$554$		−	28.7587i		−	1.22184i
$555$	−5.61693	−	9.72880i	−0.238425	−	0.412965i
$556$	−5.75709	+	9.97158i	−0.244155	+	0.422889i
$557$	−20.6490	−	11.9217i	−0.874926	−	0.505139i	−0.00594396	−	0.999982i	$-0.501892\pi$
$557$	−20.6490	−	11.9217i	−0.874926	−	0.505139i	−0.868982	+	0.494844i	$0.835225\pi$
$558$	2.84643	−	4.93016i	0.120499	−	0.208711i
$559$	19.9695	−	41.9309i	0.844619	−	1.77349i
$560$	3.20035	−	6.15629i	0.135239	−	0.260151i
$561$	29.9298	−	17.2800i	1.26364	−	0.729562i
$562$	−13.5100			−0.569886
$563$	−2.08096			−0.0877022			−0.0438511	−	0.999038i	$-0.513963\pi$
$563$	−2.08096			−0.0877022			−0.0438511	+	0.999038i	$0.513963\pi$
$564$	−0.499608	+	0.288449i	−0.0210373	+	0.0121459i
$565$	−28.7645	+	16.6072i	−1.21013	+	0.698671i
$566$	−16.4607	−	9.50356i	−0.691893	−	0.399465i
$567$	2.34750	+	1.22035i	0.0985857	+	0.0512498i
$568$	−1.63198	+	2.82667i	−0.0684762	+	0.118604i
$569$	−35.3688			−1.48274			−0.741370	−	0.671097i	$-0.765823\pi$
$569$	−35.3688			−1.48274			−0.741370	+	0.671097i	$0.765823\pi$
$570$	6.88924	+	3.97750i	0.288559	+	0.166599i
$571$	18.0174	+	31.2071i	0.754006	+	1.30598i	0.945867	+	0.324555i	$0.105214\pi$
$571$	18.0174	+	31.2071i	0.754006	+	1.30598i	−0.191861	+	0.981422i	$0.561452\pi$
$572$	16.3112	+	7.76814i	0.682004	+	0.324802i
$573$	7.92903			0.331240
$574$	−12.7510	+	8.13338i	−0.532215	+	0.339481i
$575$	4.69330	+	8.12903i	0.195724	+	0.339004i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	34.4738	−	19.9034i	1.43516	−	0.828591i	0.437654	−	0.899143i	$-0.355809\pi$
$577$	34.4738	−	19.9034i	1.43516	−	0.828591i	0.997508	+	0.0705519i	$0.0224760\pi$
$578$		−	30.5711i		−	1.27159i
$579$	9.33627	−	5.39030i	0.388002	−	0.224013i
$580$		−	11.4791i		−	0.476644i
$581$	24.2377	−	1.07194i	1.00555	−	0.0444714i
$582$	−7.03709	−	12.1886i	−0.291697	−	0.505234i
$583$			35.0159i			1.45021i
$584$	−2.42791	−	4.20527i	−0.100468	−	0.174015i
$585$	−0.747468	−	9.42593i	−0.0309040	−	0.389714i
$586$	−4.12406	+	7.14308i	−0.170363	+	0.295078i
$587$	12.1473	−	7.01325i	0.501373	−	0.289468i	−0.227907	−	0.973683i	$-0.573188\pi$
$587$	12.1473	−	7.01325i	0.501373	−	0.289468i	0.729280	+	0.684215i	$0.239855\pi$
$588$	−2.95117	+	6.34749i	−0.121704	+	0.261766i
$589$	−8.63432	+	14.9551i	−0.355771	+	0.616213i
$590$	23.8209	+	13.7530i	0.980691	+	0.566202i
$591$		−	19.0859i		−	0.785090i
$592$			4.28366i			0.176057i
$593$	−15.5416	−	8.97292i	−0.638215	−	0.368474i	0.145711	−	0.989327i	$-0.453453\pi$
$593$	−15.5416	−	8.97292i	−0.638215	−	0.368474i	−0.783927	+	0.620853i	$0.786786\pi$
$594$	−2.50537	+	4.33943i	−0.102797	+	0.178049i
$595$	22.0734	−	42.4610i	0.904921	−	1.74073i
$596$	−14.2970	+	8.25436i	−0.585627	+	0.338112i
$597$	11.7571	−	20.3638i	0.481185	−	0.833436i
$598$	−1.42502	−	17.9701i	−0.0582733	−	0.734854i
$599$	15.2420	+	26.4000i	0.622772	+	1.07867i	0.988967	+	0.148135i	$0.0473270\pi$
$599$	15.2420	+	26.4000i	0.622772	+	1.07867i	−0.366195	+	0.930538i	$0.619340\pi$
$600$		−	1.87744i		−	0.0766463i
$601$	−7.94423	−	13.7598i	−0.324052	−	0.561274i	0.657268	−	0.753657i	$-0.271712\pi$
$601$	−7.94423	−	13.7598i	−0.324052	−	0.561274i	−0.981320	+	0.192383i	$0.938379\pi$
$602$	−15.7194	+	30.2383i	−0.640674	+	1.23242i
$603$			2.47913i			0.100958i
$604$	5.69210	−	3.28634i	0.231608	−	0.133719i
$605$			36.9968i			1.50413i
$606$	7.99696	−	4.61704i	0.324854	−	0.187555i
$607$	−2.14571	−	3.71649i	−0.0870919	−	0.150848i	0.819189	−	0.573524i	$-0.194424\pi$
$607$	−2.14571	−	3.71649i	−0.0870919	−	0.150848i	−0.906281	+	0.422676i	$0.861091\pi$
$608$	−1.51669	−	2.62699i	−0.0615100	−	0.106538i
$609$	0.511678	+	11.5696i	0.0207342	+	0.468825i
$610$	−37.5410			−1.51999
$611$	−1.87794	−	0.894362i	−0.0759733	−	0.0361820i
$612$	3.44859	+	5.97313i	0.139401	+	0.241450i
$613$	7.24626	+	4.18363i	0.292674	+	0.168975i	0.639147	−	0.769085i	$-0.279288\pi$
$613$	7.24626	+	4.18363i	0.292674	+	0.168975i	−0.346473	+	0.938060i	$0.612621\pi$
$614$	−2.94195			−0.118728
$615$	−7.49557	+	12.9827i	−0.302251	+	0.523513i
$616$	−11.7627	−	6.11485i	−0.473933	−	0.246374i
$617$	22.4455	+	12.9589i	0.903621	+	0.521706i	0.878373	−	0.477976i	$-0.158629\pi$
$617$	22.4455	+	12.9589i	0.903621	+	0.521706i	0.0252476	+	0.999681i	$0.491963\pi$
$618$	−4.22453	+	2.43903i	−0.169936	+	0.0981123i
$619$	4.60270	−	2.65737i	0.184998	−	0.106809i	−0.404641	−	0.914476i	$-0.632603\pi$
$619$	4.60270	−	2.65737i	0.184998	−	0.106809i	0.589639	+	0.807667i	$0.299270\pi$
$620$	14.9295			0.599582
$621$	4.99967			0.200630
$622$	12.9406	−	7.47126i	0.518871	−	0.299570i
$623$	40.7701	−	1.80310i	1.63342	−	0.0722395i
$624$	−1.55030	+	3.25524i	−0.0620616	+	0.130314i
$625$	15.4312	−	26.7276i	0.617248	−	1.06911i
$626$	−21.1187	−	12.1929i	−0.844072	−	0.487325i
$627$	7.59975	−	13.1631i	0.303505	−	0.525686i
$628$	−4.40621	−	7.63178i	−0.175827	−	0.304541i
$629$			29.5452i			1.17804i
$630$	0.306560	+	6.93168i	0.0122136	+	0.276165i
$631$	4.21716	+	2.43478i	0.167883	+	0.0969271i	0.581587	−	0.813484i	$-0.302432\pi$
$631$	4.21716	+	2.43478i	0.167883	+	0.0969271i	−0.413704	+	0.910411i	$0.635765\pi$
$632$	−6.39996	−	3.69502i	−0.254577	−	0.146980i
$633$	−4.89463			−0.194544
$634$	−14.2313	+	24.6493i	−0.565197	+	0.978950i
$635$			19.2554i			0.764126i
$636$	−6.98817			−0.277099
$637$	−24.8855	+	4.20846i	−0.986000	+	0.166745i
$638$	−21.9329			−0.868333
$639$		−	3.26395i		−	0.129120i
$640$	−1.31124	+	2.27114i	−0.0518315	+	0.0897747i
$641$	−19.2157			−0.758975			−0.379487	−	0.925197i	$-0.623900\pi$
$641$	−19.2157			−0.758975			−0.379487	+	0.925197i	$0.623900\pi$
$642$	−0.149604	−	0.0863737i	−0.00590439	−	0.00340890i
$643$	−12.2082	−	7.04841i	−0.481444	−	0.277962i	0.239574	−	0.970878i	$-0.422992\pi$
$643$	−12.2082	−	7.04841i	−0.481444	−	0.277962i	−0.721018	+	0.692916i	$0.756326\pi$
$644$	0.584445	+	13.2150i	0.0230303	+	0.520742i
$645$			33.7804i			1.33010i
$646$	−10.4609	−	18.1188i	−0.411578	−	0.712875i
$647$	14.0919	−	24.4080i	0.554012	−	0.959576i	−0.443968	−	0.896043i	$-0.646430\pi$
$647$	14.0919	−	24.4080i	0.554012	−	0.959576i	0.997980	−	0.0635335i	$-0.0202370\pi$
$648$	−0.866025	−	0.500000i	−0.0340207	−	0.0196419i
$649$	26.2776	−	45.5142i	1.03149	−	1.78659i
$650$	5.57642	−	3.83744i	0.218725	−	0.150517i
$651$	−15.0472	+	0.665477i	−0.589746	+	0.0260821i
$652$	8.11055	−	4.68263i	0.317634	−	0.183386i
$653$	−44.4096			−1.73788			−0.868941	−	0.494915i	$-0.835199\pi$
$653$	−44.4096			−1.73788			−0.868941	+	0.494915i	$0.835199\pi$
$654$	−12.6108			−0.493120
$655$	24.5768	−	14.1894i	0.960295	−	0.554427i
$656$	4.95053	−	2.85819i	0.193286	−	0.111594i
$657$	4.20527	+	2.42791i	0.164063	+	0.0947218i
$658$	1.35427	+	0.704016i	0.0527948	+	0.0274454i
$659$	−8.69801	+	15.0654i	−0.338826	+	0.586864i	−0.984212	−	0.176992i	$-0.943363\pi$
$659$	−8.69801	+	15.0654i	−0.338826	+	0.586864i	0.645386	+	0.763857i	$0.276697\pi$
$660$	−13.1406			−0.511498
$661$	0.685760	+	0.395924i	0.0266730	+	0.0153997i	0.513277	−	0.858223i	$-0.328431\pi$
$661$	0.685760	+	0.395924i	0.0266730	+	0.0153997i	−0.486604	+	0.873623i	$0.661765\pi$
$662$	3.13842	+	5.43590i	0.121978	+	0.211272i
$663$	−10.6927	+	22.4520i	−0.415269	+	0.871962i
$664$	−9.16995			−0.355863
$665$	−0.929914	−	21.0264i	−0.0360605	−	0.815370i
$666$	−2.14183	−	3.70976i	−0.0829943	−	0.143750i
$667$	10.9422	+	18.9525i	0.423685	+	0.733843i
$668$	2.26138	−	1.30561i	0.0874954	−	0.0505155i
$669$		−	10.0753i		−	0.389534i
$670$	−5.63045	+	3.25074i	−0.217523	+	0.125587i
$671$			71.7289i			2.76906i
$672$	1.22035	−	2.34750i	0.0470760	−	0.0905567i
$673$	10.4137	+	18.0371i	0.401420	+	0.695280i	0.993898	−	0.110307i	$-0.0351834\pi$
$673$	10.4137	+	18.0371i	0.401420	+	0.695280i	−0.592477	+	0.805587i	$0.701850\pi$
$674$		−	9.99063i		−	0.384825i
$675$	0.938722	+	1.62591i	0.0361314	+	0.0625815i
$676$	−12.8375	+	2.04889i	−0.493751	+	0.0788036i
$677$	−14.2416	+	24.6671i	−0.547347	+	0.948034i	0.451108	+	0.892470i	$0.351029\pi$
$677$	−14.2416	+	24.6671i	−0.547347	+	0.948034i	−0.998455	+	0.0555641i	$0.982304\pi$
$678$	−10.9684	+	6.33262i	−0.421239	+	0.243203i
$679$	−17.1754	+	33.0391i	−0.659132	+	1.26793i
$680$	−9.04389	+	15.6645i	−0.346817	+	0.600705i
$681$	−12.3996	−	7.15891i	−0.475154	−	0.274330i
$682$		−	28.5255i		−	1.09230i
$683$			8.18235i			0.313089i	0.987671	+	0.156544i	$0.0500355\pi$
$683$			8.18235i			0.313089i	−0.987671	+	0.156544i	$0.949965\pi$
$684$	2.62699	+	1.51669i	0.100445	+	0.0579921i
$685$	−18.1113	+	31.3696i	−0.691996	+	1.19857i
$686$	18.3577	−	2.44844i	0.700900	−	0.0934819i
$687$	−13.3945	+	7.73332i	−0.511032	+	0.295045i
$688$	6.44053	−	11.1553i	0.245543	−	0.425293i
$689$	−14.2836	−	20.7564i	−0.544162	−	0.790755i
$690$	6.55579	+	11.3550i	0.249574	+	0.432276i
$691$		−	1.27080i		−	0.0483434i	−0.999708	−	0.0241717i	$-0.992305\pi$
$691$		−	1.27080i		−	0.0483434i	0.999708	−	0.0241717i	$-0.00769484\pi$
$692$	−2.49748	−	4.32576i	−0.0949398	−	0.164441i
$693$	13.2442	−	0.585739i	0.503107	−	0.0222504i
$694$			3.90930i			0.148395i
$695$	26.1503	−	15.0979i	0.991939	−	0.572696i
$696$		−	4.37718i		−	0.165917i
$697$	34.1447	−	19.7135i	1.29332	−	0.746701i
$698$	−7.69750	−	13.3325i	−0.291355	−	0.504641i
$699$	2.31317	+	4.00653i	0.0874922	+	0.151541i
$700$	−4.18783	+	2.67126i	−0.158285	+	0.100964i
$701$	13.9585			0.527207			0.263604	−	0.964631i	$-0.415089\pi$
$701$	13.9585			0.527207			0.263604	+	0.964631i	$0.415089\pi$
$702$	−0.285022	−	3.59427i	−0.0107575	−	0.135657i
$703$	6.49699	+	11.2531i	0.245039	+	0.424419i
$704$	4.33943	+	2.50537i	0.163548	+	0.0944247i
$705$	1.51291			0.0569793
$706$	15.0418	−	26.0531i	0.566105	−	0.980523i
$707$	−21.6770	−	11.2688i	−0.815248	−	0.423807i
$708$	9.08332	+	5.24426i	0.341372	+	0.197091i
$709$	1.91883	−	1.10784i	0.0720631	−	0.0416057i	−0.463535	−	0.886078i	$-0.653419\pi$
$709$	1.91883	−	1.10784i	0.0720631	−	0.0416057i	0.535599	+	0.844473i	$0.320086\pi$
$710$	7.41290	−	4.27984i	0.278201	−	0.160619i
$711$	7.39004			0.277148
$712$	−15.4247			−0.578065
$713$	−24.6492	+	14.2312i	−0.923119	+	0.532963i
$714$	8.41696	−	16.1911i	0.314997	−	0.605938i
$715$	−26.8590	−	39.0305i	−1.00447	−	1.45966i
$716$	−3.76120	+	6.51459i	−0.140563	+	0.243462i
$717$	−7.34857	−	4.24270i	−0.274437	−	0.158446i
$718$	4.17631	−	7.23357i	0.155858	−	0.269955i
$719$	−3.05336	−	5.28857i	−0.113871	−	0.197231i	0.803457	−	0.595363i	$-0.202992\pi$
$719$	−3.05336	−	5.28857i	−0.113871	−	0.197231i	−0.917328	+	0.398132i	$0.869658\pi$
$720$		−	2.62249i		−	0.0977344i
$721$	11.4513	+	5.95294i	0.426467	+	0.221699i
$722$	8.48583	+	4.89930i	0.315810	+	0.182333i
$723$	3.68833	+	2.12946i	0.137170	+	0.0791954i
$724$	7.14351			0.265487
$725$	−4.10896	+	7.11692i	−0.152603	+	0.264316i
$726$			14.1075i			0.523580i
$727$	6.95455			0.257930			0.128965	−	0.991649i	$-0.458835\pi$
$727$	6.95455			0.257930			0.128965	+	0.991649i	$0.458835\pi$
$728$	9.46693	−	1.17352i	0.350868	−	0.0434935i
$729$	1.00000			0.0370370
$730$			12.7343i			0.471319i
$731$	44.4215	−	76.9403i	1.64299	−	2.84574i
$732$	−14.3150			−0.529098
$733$	−13.1539	−	7.59443i	−0.485852	−	0.280506i	0.237000	−	0.971510i	$-0.423836\pi$
$733$	−13.1539	−	7.59443i	−0.485852	−	0.280506i	−0.722852	+	0.691003i	$0.757169\pi$
$734$	10.7075	+	6.18199i	0.395222	+	0.228181i
$735$	15.0256	−	10.5463i	0.554229	−	0.389007i
$736$		−	4.99967i		−	0.184290i
$737$	6.21113	+	10.7580i	0.228790	+	0.396276i
$738$	−2.85819	+	4.95053i	−0.105211	+	0.182232i
$739$	−41.6744	−	24.0607i	−1.53302	−	0.885088i	−0.999221	−	0.0394745i	$-0.987432\pi$
$739$	−41.6744	−	24.0607i	−1.53302	−	0.885088i	−0.533796	−	0.845613i	$-0.679235\pi$
$740$	5.61693	−	9.72880i	0.206482	−	0.357638i
$741$	0.864582	+	10.9028i	0.0317612	+	0.400524i
$742$	9.94290	+	15.5878i	0.365015	+	0.572247i
$743$	35.6831	−	20.6017i	1.30909	−	0.755802i	0.327143	−	0.944975i	$-0.393914\pi$
$743$	35.6831	−	20.6017i	1.30909	−	0.755802i	0.981944	+	0.189173i	$0.0605807\pi$
$744$	5.69286			0.208711
$745$	43.2939			1.58617
$746$	19.6066	−	11.3199i	0.717849	−	0.414451i
$747$	7.94141	−	4.58497i	0.290561	−	0.167755i
$748$	29.9298	+	17.2800i	1.09434	+	0.631819i
$749$	0.0201936	+	0.456600i	0.000737858	+	0.0166838i
$750$	4.09443	−	7.09177i	0.149508	−	0.258955i
$751$	42.7215			1.55893			0.779465	−	0.626446i	$-0.215491\pi$
$751$	42.7215			1.55893			0.779465	+	0.626446i	$0.215491\pi$
$752$	−0.499608	−	0.288449i	−0.0182188	−	0.0105186i
$753$	−1.00766	−	1.74531i	−0.0367210	−	0.0636027i
$754$	13.0012	−	8.94683i	0.473475	−	0.325824i
$755$	−17.2368			−0.627310
$756$	0.116897	+	2.64317i	0.00425149	+	0.0961311i
$757$	−21.7752	−	37.7157i	−0.791432	−	1.37080i	−0.925080	−	0.379772i	$-0.876003\pi$
$757$	−21.7752	−	37.7157i	−0.791432	−	1.37080i	0.133648	−	0.991029i	$-0.457331\pi$
$758$	−5.44788	−	9.43601i	−0.197876	−	0.342731i
$759$	21.6957	−	12.5260i	0.787504	−	0.454666i
$760$			7.95501i			0.288559i
$761$	−8.26994	+	4.77465i	−0.299785	+	0.173081i	−0.642346	−	0.766414i	$-0.722039\pi$
$761$	−8.26994	+	4.77465i	−0.299785	+	0.173081i	0.342561	+	0.939496i	$0.388706\pi$
$762$			7.34240i			0.265987i
$763$	17.9428	+	28.1296i	0.649574	+	1.01836i
$764$	3.96451	+	6.86674i	0.143431	+	0.248430i
$765$		−	18.0878i		−	0.653965i
$766$	0.634815	+	1.09953i	0.0229368	+	0.0397277i
$767$	2.98946	+	37.6985i	0.107943	+	1.36122i
$768$	−0.500000	+	0.866025i	−0.0180422	+	0.0312500i
$769$	−22.0605	+	12.7366i	−0.795521	+	0.459294i	−0.841903	−	0.539630i	$-0.818564\pi$
$769$	−22.0605	+	12.7366i	−0.795521	+	0.459294i	0.0463817	+	0.998924i	$0.485231\pi$
$770$	18.6967	+	29.3115i	0.673783	+	1.05631i
$771$	11.4978	−	19.9147i	0.414082	−	0.717211i
$772$	9.33627	+	5.39030i	0.336020	+	0.194001i
$773$			17.0573i			0.613508i	0.951789	+	0.306754i	$0.0992429\pi$
$773$			17.0573i			0.613508i	−0.951789	+	0.306754i	$0.900757\pi$
$774$			12.8811i			0.463000i
$775$	−9.25611	−	5.34402i	−0.332489	−	0.191963i
$776$	7.03709	−	12.1886i	0.252617	−	0.437545i
$777$	−5.22756	+	10.0559i	−0.187538	+	0.360753i
$778$	26.5529	−	15.3303i	0.951968	−	0.549619i
$779$	8.66999	−	15.0169i	0.310634	−	0.538035i
$780$	7.78936	−	5.36029i	0.278904	−	0.191929i
$781$	−8.17741	−	14.1637i	−0.292611	−	0.506817i
$782$		−	34.4836i		−	1.23313i
$783$	2.18859	+	3.79075i	0.0782138	+	0.135470i
$784$	−6.97267	+	0.617955i	−0.249024	+	0.0220698i
$785$			23.1105i			0.824848i
$786$	9.37156	−	5.41067i	0.334272	−	0.192992i
$787$		−	39.5049i		−	1.40820i	−0.710102	−	0.704099i	$-0.751351\pi$
$787$		−	39.5049i		−	1.40820i	0.710102	−	0.704099i	$-0.248649\pi$
$788$	16.5289	−	9.54296i	0.588817	−	0.339954i
$789$	−11.0191	−	19.0857i	−0.392292	−	0.679470i
$790$	9.69014	+	16.7838i	0.344760	+	0.597141i
$791$	29.7316	+	15.4560i	1.05713	+	0.549552i
$792$	−5.01074			−0.178049
$793$	−29.2595	−	42.5187i	−1.03903	−	1.50988i
$794$	−13.2240	−	22.9046i	−0.469301	−	0.812854i
$795$	15.8711	+	9.16319i	0.562890	+	0.324985i
$796$	23.5141			0.833436
$797$	−8.76369	+	15.1792i	−0.310426	+	0.537673i	−0.978455	−	0.206462i	$-0.933805\pi$
$797$	−8.76369	+	15.1792i	−0.310426	+	0.537673i	0.668029	+	0.744135i	$0.267138\pi$
$798$	−0.354592	−	8.01774i	−0.0125524	−	0.283825i
$799$	−3.44589	−	1.98948i	−0.121907	−	0.0703828i
$800$	1.62591	−	0.938722i	0.0574848	−	0.0331888i
$801$	13.3582	−	7.71235i	0.471988	−	0.272502i
$802$	21.9134			0.773788
$803$	24.3313			0.858632
$804$	−2.14699	+	1.23956i	−0.0757184	+	0.0437160i
$805$	16.0007	−	30.7794i	0.563950	−	1.08483i
$806$	11.6360	+	16.9090i	0.409862	+	0.595595i
$807$	−2.18641	+	3.78698i	−0.0769654	+	0.133308i
$808$	7.99696	+	4.61704i	0.281332	+	0.162427i
$809$	−3.60911	+	6.25117i	−0.126890	+	0.219779i	−0.922470	−	0.386069i	$-0.873833\pi$
$809$	−3.60911	+	6.25117i	−0.126890	+	0.219779i	0.795580	+	0.605848i	$0.207166\pi$
$810$	1.31124	+	2.27114i	0.0460724	+	0.0797998i
$811$			33.6889i			1.18298i	0.806314	+	0.591488i	$0.201459\pi$
$811$			33.6889i			1.18298i	−0.806314	+	0.591488i	$0.798541\pi$
$812$	−9.76375	+	6.22794i	−0.342640	+	0.218558i
$813$	−13.4302	−	7.75390i	−0.471016	−	0.271941i
$814$	−18.5886	−	10.7322i	−0.651532	−	0.376162i
$815$	−24.5603			−0.860309
$816$	−3.44859	+	5.97313i	−0.120725	+	0.209102i
$817$		−	39.0732i		−	1.36700i
$818$	−10.3492			−0.361852
$819$	−7.61185	+	5.74977i	−0.265979	+	0.200913i
$820$	−14.9911			−0.523513
$821$			6.36019i			0.221972i	0.993822	+	0.110986i	$0.0354009\pi$
$821$			6.36019i			0.221972i	−0.993822	+	0.110986i	$0.964599\pi$
$822$	−6.90614	+	11.9618i	−0.240879	+	0.417215i
$823$	−9.89209			−0.344817			−0.172408	−	0.985026i	$-0.555155\pi$
$823$	−9.89209			−0.344817			−0.172408	+	0.985026i	$0.555155\pi$
$824$	−4.22453	−	2.43903i	−0.147168	−	0.0849678i
$825$	8.14704	+	4.70369i	0.283643	+	0.163762i
$826$	−1.22607	−	27.7229i	−0.0426605	−	0.964603i
$827$		−	0.161968i		−	0.00563219i	−0.999996	−	0.00281610i	$-0.999104\pi$
$827$		−	0.161968i		−	0.00563219i	0.999996	−	0.00281610i	$-0.000896393\pi$
$828$	2.49983	+	4.32984i	0.0868752	+	0.150472i
$829$	−1.24938	+	2.16399i	−0.0433928	+	0.0751586i	−0.886906	−	0.461950i	$-0.847150\pi$
$829$	−1.24938	+	2.16399i	−0.0433928	+	0.0751586i	0.843513	+	0.537108i	$0.180483\pi$
$830$	20.8262	+	12.0240i	0.722890	+	0.417361i
$831$	−14.3794	+	24.9058i	−0.498815	+	0.863972i
$832$	−3.59427	+	0.285022i	−0.124609	+	0.00988137i
$833$	−48.0918	+	4.26215i	−1.66628	+	0.147675i
$834$	9.97158	−	5.75709i	0.345288	−	0.199352i
$835$	−6.84788			−0.236981
$836$	15.1995			0.525686
$837$	−4.93016	+	2.84643i	−0.170411	+	0.0983871i
$838$	−15.5608	+	8.98405i	−0.537540	+	0.310349i
$839$	33.8670	+	19.5531i	1.16922	+	0.675048i	0.953496	−	0.301407i	$-0.0974563\pi$
$839$	33.8670	+	19.5531i	1.16922	+	0.675048i	0.215722	+	0.976455i	$0.430790\pi$
$840$	−5.84973	+	3.73133i	−0.201835	+	0.128743i
$841$	4.92015	−	8.52195i	0.169660	−	0.293860i
$842$	−7.16224			−0.246827
$843$	11.7000	+	6.75501i	0.402970	+	0.232655i
$844$	−2.44732	−	4.23888i	−0.0842401	−	0.145908i
$845$	31.8424	+	12.1798i	1.09541	+	0.418998i
$846$	0.576897			0.0198341
$847$	31.4683	−	20.0725i	1.08126	−	0.689698i
$848$	−3.49408	−	6.05193i	−0.119987	−	0.207824i
$849$	9.50356	+	16.4607i	0.326161	+	0.564928i
$850$	11.2142	−	6.47454i	0.384645	−	0.222075i
$851$			21.4169i			0.734161i
$852$	2.82667	−	1.63198i	0.0968400	−	0.0559106i
$853$		−	3.18625i		−	0.109095i	−0.998511	−	0.0545476i	$-0.982628\pi$
$853$		−	3.18625i		−	0.109095i	0.998511	−	0.0545476i	$-0.0173717\pi$
$854$	20.3677	+	31.9311i	0.696968	+	1.09266i
$855$	−3.97750	−	6.88924i	−0.136028	−	0.235607i
$856$		−	0.172747i		−	0.00590439i
$857$	−21.1932	−	36.7078i	−0.723947	−	1.25391i	−0.959406	−	0.282029i	$-0.908993\pi$
$857$	−21.1932	−	36.7078i	−0.723947	−	1.25391i	0.235459	−	0.971884i	$-0.424341\pi$
$858$	−10.2418	−	14.8830i	−0.349650	−	0.508097i
$859$	6.71141	−	11.6245i	0.228990	−	0.396623i	−0.728519	−	0.685026i	$-0.759791\pi$
$859$	6.71141	−	11.6245i	0.228990	−	0.396623i	0.957509	+	0.288403i	$0.0931242\pi$
$860$	−29.2547	+	16.8902i	−0.997577	+	0.575952i
$861$	15.1094	−	0.668226i	0.514925	−	0.0227731i
$862$	15.8883	−	27.5193i	0.541157	−	0.937311i
$863$	34.2623	+	19.7813i	1.16630	+	0.673365i	0.952806	−	0.303579i	$-0.0981818\pi$
$863$	34.2623	+	19.7813i	1.16630	+	0.673365i	0.213496	+	0.976944i	$0.431515\pi$
$864$		−	1.00000i		−	0.0340207i
$865$			13.0992i			0.445386i
$866$	−4.43985	−	2.56335i	−0.150872	−	0.0871061i
$867$	−15.2856	+	26.4754i	−0.519125	+	0.899150i
$868$	−8.09992	−	12.6985i	−0.274929	−	0.431016i
$869$	32.0685	−	18.5148i	1.08785	−	0.628071i
$870$	−5.73955	+	9.94119i	−0.194589	+	0.337038i
$871$	−8.07015	−	3.84338i	−0.273447	−	0.130228i
$872$	−6.30538	−	10.9212i	−0.213527	−	0.369840i
$873$			14.0742i			0.476339i
$874$	−7.58295	−	13.1341i	−0.256497	−	0.444266i
$875$	−21.6445	+	0.957251i	−0.731719	+	0.0323610i
$876$			4.85582i			0.164063i
$877$	−23.9925	+	13.8521i	−0.810169	+	0.467752i	−0.847015	−	0.531569i	$-0.821602\pi$
$877$	−23.9925	+	13.8521i	−0.810169	+	0.467752i	0.0368453	+	0.999321i	$0.488269\pi$
$878$		−	36.3198i		−	1.22573i
$879$	7.14308	−	4.12406i	0.240930	−	0.139101i
$880$	−6.57031	−	11.3801i	−0.221485	−	0.383623i
$881$	18.7398	+	32.4583i	0.631360	+	1.09355i	0.987274	+	0.159029i	$0.0508364\pi$
$881$	18.7398	+	32.4583i	0.631360	+	1.09355i	−0.355914	+	0.934519i	$0.615830\pi$
$882$	5.72953	−	4.02150i	0.192923	−	0.135411i
$883$	25.4665			0.857015			0.428508	−	0.903538i	$-0.359040\pi$
$883$	25.4665			0.857015			0.428508	+	0.903538i	$0.359040\pi$
$884$	−24.7903	+	1.96585i	−0.833789	+	0.0661187i
$885$	−13.7530	−	23.8209i	−0.462302	−	0.800731i
$886$	−12.3874	−	7.15190i	−0.416164	−	0.240273i
$887$	−29.7764			−0.999793			−0.499896	−	0.866085i	$-0.666629\pi$
$887$	−29.7764			−0.999793			−0.499896	+	0.866085i	$0.666629\pi$
$888$	2.14183	−	3.70976i	0.0718751	−	0.124491i
$889$	16.3780	−	10.4469i	0.549300	−	0.350378i
$890$	35.0317	+	20.2255i	1.17426	+	0.677962i
$891$	4.33943	−	2.50537i	0.145376	−	0.0839331i
$892$	8.72547	−	5.03765i	0.292150	−	0.168673i
$893$	−1.74995			−0.0585598
$894$	16.5087			0.552134
$895$	17.0844	−	9.86371i	0.571070	−	0.329707i
$896$	2.64317	−	0.116897i	0.0883020	−	0.00390524i
$897$	−7.75097	+	16.2751i	−0.258797	+	0.543410i
$898$	−3.06262	+	5.30462i	−0.102201	+	0.177017i
$899$	−21.5802	−	12.4593i	−0.719741	−	0.415542i
$900$	−0.938722	+	1.62591i	−0.0312907	+	0.0541971i
$901$	−24.0993	−	41.7413i	−0.802865	−	1.39060i
$902$			28.6433i			0.953718i
$903$	28.7325	−	18.3274i	0.956158	−	0.609898i
$904$	−10.9684	−	6.33262i	−0.364804	−	0.210620i
$905$	−16.2239	−	9.36689i	−0.539302	−	0.311366i
$906$	−6.57267			−0.218362
$907$	−22.6569	+	39.2429i	−0.752311	+	1.30304i	0.194389	+	0.980924i	$0.437727\pi$
$907$	−22.6569	+	39.2429i	−0.752311	+	1.30304i	−0.946700	+	0.322116i	$0.895606\pi$
$908$		−	14.3178i		−	0.475154i
$909$	−9.23409			−0.306275
$910$	−23.0395	−	9.74823i	−0.763753	−	0.323151i
$911$	−44.3887			−1.47066			−0.735332	−	0.677707i	$-0.762974\pi$
$911$	−44.3887			−1.47066			−0.735332	+	0.677707i	$0.762974\pi$
$912$			3.03338i			0.100445i
$913$	22.9741	−	39.7923i	0.760332	−	1.31693i
$914$	21.4549			0.709664
$915$	32.5114	+	18.7705i	1.07479	+	0.620533i
$916$	−13.3945	−	7.73332i	−0.442567	−	0.255516i
$917$	−25.4031	−	13.2058i	−0.838884	−	0.436094i
$918$		−	6.89718i		−	0.227641i
$919$	14.6659	+	25.4021i	0.483784	+	0.837938i	0.999827	−	0.0186247i	$-0.00592876\pi$
$919$	14.6659	+	25.4021i	0.483784	+	0.837938i	−0.516043	+	0.856563i	$0.672595\pi$
$920$	−6.55579	+	11.3550i	−0.216138	+	0.374362i
$921$	2.54781	+	1.47098i	0.0839531	+	0.0484704i
$922$	−13.6311	+	23.6097i	−0.448915	+	0.777544i
$923$	10.6249	+	5.06010i	0.349724	+	0.166555i
$924$	7.12938	+	11.1770i	0.234539	+	0.367695i
$925$	−6.96487	+	4.02117i	−0.229003	+	0.132215i
$926$	26.5768			0.873367
$927$	4.87807			0.160217
$928$	3.79075	−	2.18859i	0.124437	−	0.0718440i
$929$	24.1786	−	13.9595i	0.793275	−	0.457997i	−0.0478394	−	0.998855i	$-0.515234\pi$
$929$	24.1786	−	13.9595i	0.793275	−	0.457997i	0.841114	+	0.540858i	$0.181900\pi$
$930$	−12.9293	−	7.46473i	−0.423968	−	0.244778i
$931$	−17.3799	+	12.1987i	−0.569602	+	0.399798i
$932$	−2.31317	+	4.00653i	−0.0757705	+	0.131238i
$933$	−14.9425			−0.489196
$934$	16.7937	+	9.69582i	0.549505	+	0.317257i
$935$	−45.3166	−	78.4906i	−1.48201	−	2.56692i
$936$	2.97022	−	2.04397i	0.0970846	−	0.0668093i
$937$	−38.6927			−1.26404			−0.632018	−	0.774953i	$-0.717773\pi$
$937$	−38.6927			−1.26404			−0.632018	+	0.774953i	$0.717773\pi$
$938$	5.81975	+	3.02540i	0.190021	+	0.0987827i
$939$	12.1929	+	21.1187i	0.397899	+	0.689182i
$940$	0.756453	+	1.31022i	0.0246728	+	0.0427345i
$941$	−2.94391	+	1.69967i	−0.0959688	+	0.0554076i	−0.547216	−	0.836991i	$-0.684312\pi$
$941$	−2.94391	+	1.69967i	−0.0959688	+	0.0554076i	0.451247	+	0.892399i	$0.350979\pi$
$942$			8.81242i			0.287124i
$943$	24.7510	−	14.2900i	0.806004	−	0.465347i
$944$			10.4885i			0.341372i
$945$	3.20035	−	6.15629i	0.104107	−	0.200264i
$946$	32.2718	+	55.8965i	1.04925	+	1.81735i
$947$			20.8303i			0.676893i	0.940986	+	0.338446i	$0.109901\pi$
$947$			20.8303i			0.676893i	−0.940986	+	0.338446i	$0.890099\pi$
$948$	3.69502	+	6.39996i	0.120009	+	0.207861i
$949$	−14.4228	+	9.92516i	−0.468185	+	0.322184i
$950$	2.84750	−	4.93202i	0.0923852	−	0.160016i
$951$	24.6493	−	14.2313i	0.799309	−	0.461481i
$952$	18.2304	−	0.806258i	0.590851	−	0.0261310i
$953$	−12.1372	+	21.0222i	−0.393162	+	0.680977i	−0.992865	−	0.119246i	$-0.961952\pi$
$953$	−12.1372	+	21.0222i	−0.393162	+	0.680977i	0.599703	+	0.800223i	$0.295286\pi$
$954$	6.05193	+	3.49408i	0.195938	+	0.113125i
$955$		−	20.7938i		−	0.672871i
$956$		−	8.48540i		−	0.274437i
$957$	18.9945	+	10.9665i	0.614004	+	0.354495i
$958$	−12.3448	+	21.3818i	−0.398842	+	0.690815i
$959$	36.5082	−	1.61461i	1.17891	−	0.0521385i
$960$	2.27114	−	1.31124i	0.0733008	−	0.0423202i
$961$	0.704348	−	1.21997i	0.0227209	−	0.0393537i
$962$	15.3966	−	1.22094i	0.496407	−	0.0393647i
$963$	0.0863737	+	0.149604i	0.00278335	+	0.00482091i
$964$			4.25892i			0.137170i
$965$	−14.1360	−	24.4843i	−0.455054	−	0.788176i
$966$	6.10134	−	11.7367i	0.196307	−	0.377623i
$967$		−	47.4200i		−	1.52492i	−0.647033	−	0.762462i	$-0.723990\pi$
$967$		−	47.4200i		−	1.52492i	0.647033	−	0.762462i	$-0.276010\pi$
$968$	−12.2175	+	7.05376i	−0.392685	+	0.226717i
$969$			20.9218i			0.672105i
$970$	−31.9645	+	18.4547i	−1.02632	+	0.592544i
$971$	−16.4564	−	28.5033i	−0.528110	−	0.914713i	−0.999463	−	0.0327685i	$-0.989568\pi$
$971$	−16.4564	−	28.5033i	−0.528110	−	0.914713i	0.471353	−	0.881945i	$-0.343766\pi$
$972$	0.500000	+	0.866025i	0.0160375	+	0.0277778i
$973$	−27.0295	−	14.0513i	−0.866527	−	0.450465i
$974$	−26.2566			−0.841317
$975$	−6.74804	+	0.535114i	−0.216110	+	0.0171374i
$976$	−7.15751	−	12.3972i	−0.229106	−	0.396824i
$977$	−41.2955	−	23.8420i	−1.32116	−	0.762773i	−0.337247	−	0.941416i	$-0.609496\pi$
$977$	−41.2955	−	23.8420i	−1.32116	−	0.762773i	−0.983914	+	0.178643i	$0.942829\pi$
$978$	−9.36526			−0.299468
$979$	38.6446	−	66.9344i	1.23509	−	2.13923i
$980$	16.6462	+	7.73941i	0.531744	+	0.247226i
$981$	10.9212	+	6.30538i	0.348688	+	0.201315i
$982$	−19.1408	+	11.0510i	−0.610808	+	0.352650i
$983$	−24.8943	+	14.3727i	−0.794003	+	0.458418i	−0.841370	−	0.540459i	$-0.818250\pi$
$983$	−24.8943	+	14.3727i	−0.794003	+	0.458418i	0.0473666	+	0.998878i	$0.484917\pi$
$984$	−5.71638			−0.182232
$985$	−50.0526			−1.59481
$986$	26.1455	−	15.0951i	0.832642	−	0.480726i
$987$	−0.820821	−	1.28683i	−0.0261270	−	0.0409602i
$988$	−9.00980	+	6.20014i	−0.286640	+	0.197253i
$989$	32.2005	−	55.7729i	1.02392	−	1.77348i
$990$	11.3801	+	6.57031i	0.361683	+	0.208818i
$991$	−4.36019	+	7.55207i	−0.138506	+	0.239899i	−0.926931	−	0.375231i	$-0.877563\pi$
$991$	−4.36019	+	7.55207i	−0.138506	+	0.239899i	0.788425	+	0.615130i	$0.210897\pi$
$992$	2.84643	+	4.93016i	0.0903743	+	0.156533i
$993$		−	6.27684i		−	0.199189i
$994$	−7.66212	−	3.98316i	−0.243028	−	0.126338i
$995$	−53.4039	−	30.8328i	−1.69302	−	0.977464i
$996$	7.94141	+	4.58497i	0.251633	+	0.145280i
$997$	−0.882019			−0.0279338			−0.0139669	−	0.999902i	$-0.504446\pi$
$997$	−0.882019			−0.0279338			−0.0139669	+	0.999902i	$0.504446\pi$
$998$	−16.2573	+	28.1585i	−0.514617	+	0.891342i
$999$			4.28366i			0.135529i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bm.b.205.4	yes	20
3.2	odd	2		1638.2.dt.b.1297.7		20
7.4	even	3		546.2.bd.b.361.7	yes	20
13.4	even	6		546.2.bd.b.121.7	✓	20
21.11	odd	6		1638.2.cr.b.361.4		20
39.17	odd	6		1638.2.cr.b.667.4		20
91.4	even	6	inner	546.2.bm.b.277.9	yes	20
273.95	odd	6		1638.2.dt.b.1369.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bd.b.121.7	✓	20	13.4	even	6
546.2.bd.b.361.7	yes	20	7.4	even	3
546.2.bm.b.205.4	yes	20	1.1	even	1	trivial
546.2.bm.b.277.9	yes	20	91.4	even	6	inner
1638.2.cr.b.361.4		20	21.11	odd	6
1638.2.cr.b.667.4		20	39.17	odd	6
1638.2.dt.b.1297.7		20	3.2	odd	2
1638.2.dt.b.1369.2		20	273.95	odd	6

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.bm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-0.500000 + 0.866025i) q^{3} -1.00000 q^{4} +(2.27114 + 1.31124i) q^{5} +(0.866025 + 0.500000i) q^{6} +(-0.116897 - 2.64317i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(-0.500000 + 0.866025i) q^{3} -1.00000 q^{4} +(2.27114 + 1.31124i) q^{5} +(0.866025 + 0.500000i) q^{6} +(-0.116897 - 2.64317i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.31124 - 2.27114i) q^{10} +(-4.33943 - 2.50537i) q^{11} +(0.500000 - 0.866025i) q^{12} +(3.59427 - 0.285022i) q^{13} +(-2.64317 + 0.116897i) q^{14} +(-2.27114 + 1.31124i) q^{15} +1.00000 q^{16} +6.89718 q^{17} +(-0.866025 + 0.500000i) q^{18} +(2.62699 - 1.51669i) q^{19} +(-2.27114 - 1.31124i) q^{20} +(2.34750 + 1.22035i) q^{21} +(-2.50537 + 4.33943i) q^{22} +4.99967 q^{23} +(-0.866025 - 0.500000i) q^{24} +(0.938722 + 1.62591i) q^{25} +(-0.285022 - 3.59427i) q^{26} +1.00000 q^{27} +(0.116897 + 2.64317i) q^{28} +(2.18859 + 3.79075i) q^{29} +(1.31124 + 2.27114i) q^{30} +(-4.93016 + 2.84643i) q^{31} -1.00000i q^{32} +(4.33943 - 2.50537i) q^{33} -6.89718i q^{34} +(3.20035 - 6.15629i) q^{35} +(0.500000 + 0.866025i) q^{36} +4.28366i q^{37} +(-1.51669 - 2.62699i) q^{38} +(-1.55030 + 3.25524i) q^{39} +(-1.31124 + 2.27114i) q^{40} +(4.95053 - 2.85819i) q^{41} +(1.22035 - 2.34750i) q^{42} +(6.44053 - 11.1553i) q^{43} +(4.33943 + 2.50537i) q^{44} -2.62249i q^{45} -4.99967i q^{46} +(-0.499608 - 0.288449i) q^{47} +(-0.500000 + 0.866025i) q^{48} +(-6.97267 + 0.617955i) q^{49} +(1.62591 - 0.938722i) q^{50} +(-3.44859 + 5.97313i) q^{51} +(-3.59427 + 0.285022i) q^{52} +(-3.49408 - 6.05193i) q^{53} -1.00000i q^{54} +(-6.57031 - 11.3801i) q^{55} +(2.64317 - 0.116897i) q^{56} +3.03338i q^{57} +(3.79075 - 2.18859i) q^{58} +10.4885i q^{59} +(2.27114 - 1.31124i) q^{60} +(-7.15751 - 12.3972i) q^{61} +(2.84643 + 4.93016i) q^{62} +(-2.23060 + 1.42282i) q^{63} -1.00000 q^{64} +(8.53682 + 4.06564i) q^{65} +(-2.50537 - 4.33943i) q^{66} +(-2.14699 - 1.23956i) q^{67} -6.89718 q^{68} +(-2.49983 + 4.32984i) q^{69} +(-6.15629 - 3.20035i) q^{70} +(2.82667 + 1.63198i) q^{71} +(0.866025 - 0.500000i) q^{72} +(-4.20527 + 2.42791i) q^{73} +4.28366 q^{74} -1.87744 q^{75} +(-2.62699 + 1.51669i) q^{76} +(-6.11485 + 11.7627i) q^{77} +(3.25524 + 1.55030i) q^{78} +(-3.69502 + 6.39996i) q^{79} +(2.27114 + 1.31124i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-2.85819 - 4.95053i) q^{82} +9.16995i q^{83} +(-2.34750 - 1.22035i) q^{84} +(15.6645 + 9.04389i) q^{85} +(-11.1553 - 6.44053i) q^{86} -4.37718 q^{87} +(2.50537 - 4.33943i) q^{88} +15.4247i q^{89} -2.62249 q^{90} +(-1.17352 - 9.46693i) q^{91} -4.99967 q^{92} -5.69286i q^{93} +(-0.288449 + 0.499608i) q^{94} +7.95501 q^{95} +(0.866025 + 0.500000i) q^{96} +(-12.1886 - 7.03709i) q^{97} +(0.617955 + 6.97267i) q^{98} +5.01074i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 10 q^{3} - 20 q^{4} - 10 q^{9}+O(q^{10}) \) 20 * q - 10 * q^3 - 20 * q^4 - 10 * q^9	\( 20 q - 10 q^{3} - 20 q^{4} - 10 q^{9} + 4 q^{10} + 6 q^{11} + 10 q^{12} + 8 q^{13} + 4 q^{14} + 20 q^{16} - 8 q^{17} - 12 q^{19} + 6 q^{21} - 10 q^{22} - 16 q^{23} + 6 q^{25} + 8 q^{26} + 20 q^{27} + 8 q^{29} + 4 q^{30} + 12 q^{31} - 6 q^{33} + 10 q^{35} + 10 q^{36} + 6 q^{38} - 10 q^{39} - 4 q^{40} - 18 q^{41} - 2 q^{42} + 18 q^{43} - 6 q^{44} - 6 q^{47} - 10 q^{48} - 20 q^{49} + 12 q^{50} + 4 q^{51} - 8 q^{52} + 18 q^{53} - 12 q^{55} - 4 q^{56} + 24 q^{58} - 6 q^{61} - 6 q^{63} - 20 q^{64} - 6 q^{65} - 10 q^{66} + 24 q^{67} + 8 q^{68} + 8 q^{69} + 42 q^{70} - 6 q^{71} + 24 q^{73} + 36 q^{74} - 12 q^{75} + 12 q^{76} - 34 q^{77} + 2 q^{78} - 10 q^{81} + 18 q^{82} - 6 q^{84} - 36 q^{86} - 16 q^{87} + 10 q^{88} - 8 q^{90} - 10 q^{91} + 16 q^{92} - 16 q^{94} - 80 q^{95} - 96 q^{97} - 12 q^{98}+O(q^{100}) \) 20 * q - 10 * q^3 - 20 * q^4 - 10 * q^9 + 4 * q^10 + 6 * q^11 + 10 * q^12 + 8 * q^13 + 4 * q^14 + 20 * q^16 - 8 * q^17 - 12 * q^19 + 6 * q^21 - 10 * q^22 - 16 * q^23 + 6 * q^25 + 8 * q^26 + 20 * q^27 + 8 * q^29 + 4 * q^30 + 12 * q^31 - 6 * q^33 + 10 * q^35 + 10 * q^36 + 6 * q^38 - 10 * q^39 - 4 * q^40 - 18 * q^41 - 2 * q^42 + 18 * q^43 - 6 * q^44 - 6 * q^47 - 10 * q^48 - 20 * q^49 + 12 * q^50 + 4 * q^51 - 8 * q^52 + 18 * q^53 - 12 * q^55 - 4 * q^56 + 24 * q^58 - 6 * q^61 - 6 * q^63 - 20 * q^64 - 6 * q^65 - 10 * q^66 + 24 * q^67 + 8 * q^68 + 8 * q^69 + 42 * q^70 - 6 * q^71 + 24 * q^73 + 36 * q^74 - 12 * q^75 + 12 * q^76 - 34 * q^77 + 2 * q^78 - 10 * q^81 + 18 * q^82 - 6 * q^84 - 36 * q^86 - 16 * q^87 + 10 * q^88 - 8 * q^90 - 10 * q^91 + 16 * q^92 - 16 * q^94 - 80 * q^95 - 96 * q^97 - 12 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more