LMFDB - Embedded newform 546.2.by.b.397.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(19,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 10, 5]))

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

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

chi := DirichletCharacter("546.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.by (of order $12$, 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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			397.7
Character	$\chi$	$=$	546.397
Dual form			546.2.by.b.535.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 - 0.965926i) q^{2} +1.00000i q^{3} +(-0.866025 - 0.500000i) q^{4} +(-0.382567 - 1.42776i) q^{5} +(0.965926 + 0.258819i) q^{6} +(-1.00882 + 2.44587i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(0.258819 - 0.965926i) q^{2} +1.00000i q^{3} +(-0.866025 - 0.500000i) q^{4} +(-0.382567 - 1.42776i) q^{5} +(0.965926 + 0.258819i) q^{6} +(-1.00882 + 2.44587i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.00000 q^{9} -1.47812 q^{10} +(4.12568 - 4.12568i) q^{11} +(0.500000 - 0.866025i) q^{12} +(2.68146 + 2.41035i) q^{13} +(2.10143 + 1.60748i) q^{14} +(1.42776 - 0.382567i) q^{15} +(0.500000 + 0.866025i) q^{16} +(3.47189 - 6.01349i) q^{17} +(-0.258819 + 0.965926i) q^{18} +(3.76741 - 3.76741i) q^{19} +(-0.382567 + 1.42776i) q^{20} +(-2.44587 - 1.00882i) q^{21} +(-2.91730 - 5.05291i) q^{22} +(0.666449 - 0.384774i) q^{23} +(-0.707107 - 0.707107i) q^{24} +(2.43799 - 1.40757i) q^{25} +(3.02223 - 1.96624i) q^{26} -1.00000i q^{27} +(2.09660 - 1.61378i) q^{28} +(-4.35699 + 7.54652i) q^{29} -1.47812i q^{30} +(-0.379148 - 0.101593i) q^{31} +(0.965926 - 0.258819i) q^{32} +(4.12568 + 4.12568i) q^{33} +(-4.91000 - 4.91000i) q^{34} +(3.87805 + 0.504639i) q^{35} +(0.866025 + 0.500000i) q^{36} +(-5.66482 - 1.51788i) q^{37} +(-2.66396 - 4.61411i) q^{38} +(-2.41035 + 2.68146i) q^{39} +(1.28009 + 0.739062i) q^{40} +(1.70135 + 6.34954i) q^{41} +(-1.60748 + 2.10143i) q^{42} +(0.142904 - 0.0825059i) q^{43} +(-5.63579 + 1.51010i) q^{44} +(0.382567 + 1.42776i) q^{45} +(-0.199174 - 0.743327i) q^{46} +(12.0638 - 3.23250i) q^{47} +(-0.866025 + 0.500000i) q^{48} +(-4.96457 - 4.93488i) q^{49} +(-0.728614 - 2.71922i) q^{50} +(6.01349 + 3.47189i) q^{51} +(-1.11703 - 3.42815i) q^{52} +(-4.44772 - 7.70367i) q^{53} +(-0.965926 - 0.258819i) q^{54} +(-7.46883 - 4.31213i) q^{55} +(-1.01615 - 2.44283i) q^{56} +(3.76741 + 3.76741i) q^{57} +(6.16171 + 6.16171i) q^{58} +(0.842719 - 0.225806i) q^{59} +(-1.42776 - 0.382567i) q^{60} +5.64703i q^{61} +(-0.196262 + 0.339935i) q^{62} +(1.00882 - 2.44587i) q^{63} -1.00000i q^{64} +(2.41556 - 4.75059i) q^{65} +(5.05291 - 2.91730i) q^{66} +(-3.38202 - 3.38202i) q^{67} +(-6.01349 + 3.47189i) q^{68} +(0.384774 + 0.666449i) q^{69} +(1.49116 - 3.61530i) q^{70} +(-1.36236 + 5.08439i) q^{71} +(0.707107 - 0.707107i) q^{72} +(-2.39782 + 8.94879i) q^{73} +(-2.93233 + 5.07894i) q^{74} +(1.40757 + 2.43799i) q^{75} +(-5.14638 + 1.37897i) q^{76} +(5.92883 + 14.2529i) q^{77} +(1.96624 + 3.02223i) q^{78} +(-3.96454 + 6.86679i) q^{79} +(1.04519 - 1.04519i) q^{80} +1.00000 q^{81} +6.57353 q^{82} +(9.29167 - 9.29167i) q^{83} +(1.61378 + 2.09660i) q^{84} +(-9.91405 - 2.65646i) q^{85} +(-0.0427082 - 0.159389i) q^{86} +(-7.54652 - 4.35699i) q^{87} +5.83459i q^{88} +(-2.30793 + 8.61332i) q^{89} +1.47812 q^{90} +(-8.60051 + 4.12689i) q^{91} -0.769549 q^{92} +(0.101593 - 0.379148i) q^{93} -12.4894i q^{94} +(-6.82024 - 3.93766i) q^{95} +(0.258819 + 0.965926i) q^{96} +(-0.852159 - 0.228335i) q^{97} +(-6.05165 + 3.51817i) q^{98} +(-4.12568 + 4.12568i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{7} - 40 q^{9}+O(q^{10}) $ 40 * q - 4 * q^7 - 40 * q^9	$ 40 q - 4 q^{7} - 40 q^{9} - 4 q^{11} + 20 q^{12} + 4 q^{14} + 20 q^{16} + 8 q^{17} + 8 q^{19} - 8 q^{21} - 4 q^{22} + 24 q^{23} + 24 q^{25} - 8 q^{26} + 4 q^{28} - 12 q^{29} + 24 q^{31} - 4 q^{33} + 8 q^{34} + 28 q^{35} - 8 q^{37} - 8 q^{38} - 16 q^{39} - 20 q^{41} - 12 q^{42} - 24 q^{43} + 8 q^{44} - 4 q^{46} - 16 q^{47} + 4 q^{49} - 16 q^{50} - 24 q^{51} - 4 q^{52} - 4 q^{53} - 24 q^{55} + 12 q^{56} + 8 q^{57} + 24 q^{58} - 12 q^{59} - 32 q^{62} + 4 q^{63} - 4 q^{65} - 24 q^{67} + 24 q^{68} + 8 q^{69} + 52 q^{70} - 28 q^{71} + 108 q^{73} + 20 q^{74} - 36 q^{75} - 4 q^{76} + 12 q^{77} + 4 q^{78} + 40 q^{81} - 48 q^{82} - 60 q^{83} - 8 q^{84} - 4 q^{85} - 20 q^{86} - 36 q^{87} - 60 q^{89} - 40 q^{91} - 16 q^{92} - 48 q^{95} + 48 q^{97} - 8 q^{98} + 4 q^{99}+O(q^{100}) $ 40 * q - 4 * q^7 - 40 * q^9 - 4 * q^11 + 20 * q^12 + 4 * q^14 + 20 * q^16 + 8 * q^17 + 8 * q^19 - 8 * q^21 - 4 * q^22 + 24 * q^23 + 24 * q^25 - 8 * q^26 + 4 * q^28 - 12 * q^29 + 24 * q^31 - 4 * q^33 + 8 * q^34 + 28 * q^35 - 8 * q^37 - 8 * q^38 - 16 * q^39 - 20 * q^41 - 12 * q^42 - 24 * q^43 + 8 * q^44 - 4 * q^46 - 16 * q^47 + 4 * q^49 - 16 * q^50 - 24 * q^51 - 4 * q^52 - 4 * q^53 - 24 * q^55 + 12 * q^56 + 8 * q^57 + 24 * q^58 - 12 * q^59 - 32 * q^62 + 4 * q^63 - 4 * q^65 - 24 * q^67 + 24 * q^68 + 8 * q^69 + 52 * q^70 - 28 * q^71 + 108 * q^73 + 20 * q^74 - 36 * q^75 - 4 * q^76 + 12 * q^77 + 4 * q^78 + 40 * q^81 - 48 * q^82 - 60 * q^83 - 8 * q^84 - 4 * q^85 - 20 * q^86 - 36 * q^87 - 60 * q^89 - 40 * q^91 - 16 * q^92 - 48 * q^95 + 48 * q^97 - 8 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{11}{12}\right)$

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 $

$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	−0.382567	−	1.42776i	−0.171089	−	0.638513i	−0.997185	−	0.0749833i	$-0.976110\pi$
$5$	−0.382567	−	1.42776i	−0.171089	−	0.638513i	0.826096	−	0.563530i	$-0.190557\pi$
$6$	0.965926	+	0.258819i	0.394338	+	0.105662i
$7$	−1.00882	+	2.44587i	−0.381297	+	0.924453i
$7$	−1.00882	+	2.44587i	−0.381297	+	0.924453i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−1.00000			−0.333333
$10$	−1.47812			−0.467424
$11$	4.12568	−	4.12568i	1.24394	−	1.24394i	0.285587	−	0.958353i	$-0.407811\pi$
$11$	4.12568	−	4.12568i	1.24394	−	1.24394i	0.958353	−	0.285587i	$-0.0921885\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	2.68146	+	2.41035i	0.743702	+	0.668511i
$13$	2.68146	+	2.41035i	0.743702	+	0.668511i
$14$	2.10143	+	1.60748i	0.561631	+	0.429617i
$15$	1.42776	−	0.382567i	0.368646	−	0.0987783i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	3.47189	−	6.01349i	0.842057	−	1.45849i	−0.0460951	−	0.998937i	$-0.514678\pi$
$17$	3.47189	−	6.01349i	0.842057	−	1.45849i	0.888152	−	0.459549i	$-0.151989\pi$
$18$	−0.258819	+	0.965926i	−0.0610042	+	0.227671i
$19$	3.76741	−	3.76741i	0.864303	−	0.864303i	−0.127532	−	0.991834i	$-0.540705\pi$
$19$	3.76741	−	3.76741i	0.864303	−	0.864303i	0.991834	+	0.127532i	$0.0407055\pi$
$20$	−0.382567	+	1.42776i	−0.0855445	+	0.319257i
$21$	−2.44587	−	1.00882i	−0.533733	−	0.220142i
$22$	−2.91730	−	5.05291i	−0.621970	−	1.07728i
$23$	0.666449	−	0.384774i	0.138964	−	0.0802310i	−0.428906	−	0.903349i	$-0.641101\pi$
$23$	0.666449	−	0.384774i	0.138964	−	0.0802310i	0.567870	+	0.823118i	$0.307768\pi$
$24$	−0.707107	−	0.707107i	−0.144338	−	0.144338i
$25$	2.43799	−	1.40757i	0.487598	−	0.281515i
$26$	3.02223	−	1.96624i	0.592709	−	0.385612i
$27$		−	1.00000i		−	0.192450i
$28$	2.09660	−	1.61378i	0.396220	−	0.304975i
$29$	−4.35699	+	7.54652i	−0.809072	+	1.40135i	0.104435	+	0.994532i	$0.466697\pi$
$29$	−4.35699	+	7.54652i	−0.809072	+	1.40135i	−0.913507	+	0.406823i	$0.866637\pi$
$30$		−	1.47812i		−	0.269867i
$31$	−0.379148	−	0.101593i	−0.0680971	−	0.0182466i	0.224610	−	0.974449i	$-0.427889\pi$
$31$	−0.379148	−	0.101593i	−0.0680971	−	0.0182466i	−0.292707	+	0.956202i	$0.594556\pi$
$32$	0.965926	−	0.258819i	0.170753	−	0.0457532i
$33$	4.12568	+	4.12568i	0.718189	+	0.718189i
$34$	−4.91000	−	4.91000i	−0.842057	−	0.842057i
$35$	3.87805	+	0.504639i	0.655511	+	0.0852995i
$36$	0.866025	+	0.500000i	0.144338	+	0.0833333i
$37$	−5.66482	−	1.51788i	−0.931291	−	0.249539i	−0.238886	−	0.971048i	$-0.576782\pi$
$37$	−5.66482	−	1.51788i	−0.931291	−	0.249539i	−0.692405	+	0.721509i	$0.743449\pi$
$38$	−2.66396	−	4.61411i	−0.432151	−	0.748508i
$39$	−2.41035	+	2.68146i	−0.385965	+	0.429377i
$40$	1.28009	+	0.739062i	0.202401	+	0.116856i
$41$	1.70135	+	6.34954i	0.265707	+	0.991632i	0.961816	+	0.273696i	$0.0882462\pi$
$41$	1.70135	+	6.34954i	0.265707	+	0.991632i	−0.696109	+	0.717936i	$0.745087\pi$
$42$	−1.60748	+	2.10143i	−0.248040	+	0.324258i
$43$	0.142904	−	0.0825059i	0.0217927	−	0.0125820i	−0.489064	−	0.872248i	$-0.662662\pi$
$43$	0.142904	−	0.0825059i	0.0217927	−	0.0125820i	0.510857	+	0.859666i	$0.329328\pi$
$44$	−5.63579	+	1.51010i	−0.849627	+	0.227657i
$45$	0.382567	+	1.42776i	0.0570297	+	0.212838i
$46$	−0.199174	−	0.743327i	−0.0293666	−	0.109598i
$47$	12.0638	−	3.23250i	1.75969	−	0.471508i	0.773041	−	0.634355i	$-0.218734\pi$
$47$	12.0638	−	3.23250i	1.75969	−	0.471508i	0.986651	+	0.162847i	$0.0520678\pi$
$48$	−0.866025	+	0.500000i	−0.125000	+	0.0721688i
$49$	−4.96457	−	4.93488i	−0.709225	−	0.704982i
$50$	−0.728614	−	2.71922i	−0.103042	−	0.384556i
$51$	6.01349	+	3.47189i	0.842057	+	0.486162i
$52$	−1.11703	−	3.42815i	−0.154905	−	0.475399i
$53$	−4.44772	−	7.70367i	−0.610941	−	1.05818i	−0.991082	−	0.133252i	$-0.957458\pi$
$53$	−4.44772	−	7.70367i	−0.610941	−	1.05818i	0.380141	−	0.924928i	$-0.375875\pi$
$54$	−0.965926	−	0.258819i	−0.131446	−	0.0352208i
$55$	−7.46883	−	4.31213i	−1.00710	−	0.581447i
$56$	−1.01615	−	2.44283i	−0.135789	−	0.326437i
$57$	3.76741	+	3.76741i	0.499005	+	0.499005i
$58$	6.16171	+	6.16171i	0.809072	+	0.809072i
$59$	0.842719	−	0.225806i	0.109713	−	0.0293974i	−0.203545	−	0.979066i	$-0.565246\pi$
$59$	0.842719	−	0.225806i	0.109713	−	0.0293974i	0.313258	+	0.949668i	$0.398580\pi$
$60$	−1.42776	−	0.382567i	−0.184323	−	0.0493892i
$61$			5.64703i			0.723028i	0.932367	+	0.361514i	$0.117740\pi$
$61$			5.64703i			0.723028i	−0.932367	+	0.361514i	$0.882260\pi$
$62$	−0.196262	+	0.339935i	−0.0249253	+	0.0431718i
$63$	1.00882	−	2.44587i	0.127099	−	0.308151i
$64$		−	1.00000i		−	0.125000i
$65$	2.41556	−	4.75059i	0.299614	−	0.589238i
$66$	5.05291	−	2.91730i	0.621970	−	0.359094i
$67$	−3.38202	−	3.38202i	−0.413180	−	0.413180i	0.469665	−	0.882845i	$-0.344375\pi$
$67$	−3.38202	−	3.38202i	−0.413180	−	0.413180i	−0.882845	+	0.469665i	$0.844375\pi$
$68$	−6.01349	+	3.47189i	−0.729243	+	0.421029i
$69$	0.384774	+	0.666449i	0.0463214	+	0.0802310i
$70$	1.49116	−	3.61530i	0.178227	−	0.432111i
$71$	−1.36236	+	5.08439i	−0.161682	+	0.603406i	0.836758	+	0.547573i	$0.184448\pi$
$71$	−1.36236	+	5.08439i	−0.161682	+	0.603406i	−0.998440	+	0.0558333i	$0.982218\pi$
$72$	0.707107	−	0.707107i	0.0833333	−	0.0833333i
$73$	−2.39782	+	8.94879i	−0.280644	+	1.04738i	0.671321	+	0.741167i	$0.265727\pi$
$73$	−2.39782	+	8.94879i	−0.280644	+	1.04738i	−0.951964	+	0.306209i	$0.900939\pi$
$74$	−2.93233	+	5.07894i	−0.340876	+	0.590415i
$75$	1.40757	+	2.43799i	0.162533	+	0.281515i
$76$	−5.14638	+	1.37897i	−0.590330	+	0.158178i
$77$	5.92883	+	14.2529i	0.675653	+	1.62427i
$78$	1.96624	+	3.02223i	0.222633	+	0.342200i
$79$	−3.96454	+	6.86679i	−0.446046	+	0.772574i	−0.998124	−	0.0612181i	$-0.980501\pi$
$79$	−3.96454	+	6.86679i	−0.446046	+	0.772574i	0.552079	+	0.833792i	$0.313835\pi$
$80$	1.04519	−	1.04519i	0.116856	−	0.116856i
$81$	1.00000			0.111111
$82$	6.57353			0.725925
$83$	9.29167	−	9.29167i	1.01989	−	1.01989i	0.0200956	−	0.999798i	$-0.493603\pi$
$83$	9.29167	−	9.29167i	1.01989	−	1.01989i	0.999798	−	0.0200956i	$-0.00639705\pi$
$84$	1.61378	+	2.09660i	0.176078	+	0.228758i
$85$	−9.91405	−	2.65646i	−1.07533	−	0.288134i
$86$	−0.0427082	−	0.159389i	−0.00460534	−	0.0171874i
$87$	−7.54652	−	4.35699i	−0.809072	−	0.467118i
$88$			5.83459i			0.621970i
$89$	−2.30793	+	8.61332i	−0.244640	+	0.913010i	0.728924	+	0.684595i	$0.240021\pi$
$89$	−2.30793	+	8.61332i	−0.244640	+	0.913010i	−0.973564	+	0.228415i	$0.926646\pi$
$90$	1.47812			0.155808
$91$	−8.60051	+	4.12689i	−0.901578	+	0.432616i
$92$	−0.769549			−0.0802310
$93$	0.101593	−	0.379148i	0.0105347	−	0.0393159i
$94$		−	12.4894i		−	1.28818i
$95$	−6.82024	−	3.93766i	−0.699741	−	0.403996i
$96$	0.258819	+	0.965926i	0.0264156	+	0.0985844i
$97$	−0.852159	−	0.228335i	−0.0865237	−	0.0231839i	0.215297	−	0.976549i	$-0.430928\pi$
$97$	−0.852159	−	0.228335i	−0.0865237	−	0.0231839i	−0.301821	+	0.953365i	$0.597595\pi$
$98$	−6.05165	+	3.51817i	−0.611309	+	0.355389i
$99$	−4.12568	+	4.12568i	−0.414647	+	0.414647i
$100$	−2.81515			−0.281515
$101$	−11.9682			−1.19088			−0.595439	−	0.803401i	$-0.703022\pi$
$101$	−11.9682			−1.19088			−0.595439	+	0.803401i	$0.703022\pi$
$102$	4.91000	−	4.91000i	0.486162	−	0.486162i
$103$	6.40446	−	11.0928i	0.631050	−	1.09301i	−0.356288	−	0.934376i	$-0.615958\pi$
$103$	6.40446	−	11.0928i	0.631050	−	1.09301i	0.987337	−	0.158634i	$-0.0507090\pi$
$104$	−3.60045	+	0.191699i	−0.353053	+	0.0187977i
$105$	−0.504639	+	3.87805i	−0.0492477	+	0.378459i
$106$	−8.59233	+	2.30231i	−0.834561	+	0.223620i
$107$	−1.32962	−	2.30297i	−0.128539	−	0.222636i	0.794572	−	0.607170i	$-0.207695\pi$
$107$	−1.32962	−	2.30297i	−0.128539	−	0.222636i	−0.923111	+	0.384534i	$0.874362\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	−3.87980	+	14.4796i	−0.371617	+	1.38689i	0.486607	+	0.873621i	$0.338234\pi$
$109$	−3.87980	+	14.4796i	−0.371617	+	1.38689i	−0.858225	+	0.513274i	$0.828432\pi$
$110$	−6.09827	+	6.09827i	−0.581447	+	0.581447i
$111$	1.51788	−	5.66482i	0.144071	−	0.537681i
$112$	−2.62260	+	0.349274i	−0.247812	+	0.0330033i
$113$	4.95793	+	8.58738i	0.466403	+	0.807833i	0.999264	−	0.0383697i	$-0.0122165\pi$
$113$	4.95793	+	8.58738i	0.466403	+	0.807833i	−0.532861	+	0.846203i	$0.678883\pi$
$114$	4.61411	−	2.66396i	0.432151	−	0.249503i
$115$	−0.804326	−	0.804326i	−0.0750038	−	0.0750038i
$116$	7.54652	−	4.35699i	0.700677	−	0.404536i
$117$	−2.68146	−	2.41035i	−0.247901	−	0.222837i
$118$		−	0.872447i		−	0.0803153i
$119$	11.2057	+	14.5583i	1.02723	+	1.33456i
$120$	−0.739062	+	1.28009i	−0.0674668	+	0.116856i
$121$		−	23.0425i		−	2.09477i
$122$	5.45461	+	1.46156i	0.493837	+	0.132323i
$123$	−6.34954	+	1.70135i	−0.572519	+	0.153406i
$124$	0.277556	+	0.277556i	0.0249253	+	0.0249253i
$125$	−8.16833	−	8.16833i	−0.730598	−	0.730598i
$126$	−2.10143	−	1.60748i	−0.187210	−	0.143206i
$127$	−9.01558	−	5.20515i	−0.800003	−	0.461882i	0.0434689	−	0.999055i	$-0.486159\pi$
$127$	−9.01558	−	5.20515i	−0.800003	−	0.461882i	−0.843472	+	0.537173i	$0.819492\pi$
$128$	−0.965926	−	0.258819i	−0.0853766	−	0.0228766i
$129$	0.0825059	+	0.142904i	0.00726424	+	0.0125820i
$130$	−3.96353	−	3.56280i	−0.347624	−	0.312478i
$131$	−3.41500	−	1.97165i	−0.298370	−	0.172264i	0.343340	−	0.939211i	$-0.388442\pi$
$131$	−3.41500	−	1.97165i	−0.298370	−	0.172264i	−0.641710	+	0.766947i	$0.721775\pi$
$132$	−1.51010	−	5.63579i	−0.131438	−	0.490532i
$133$	5.41397	+	13.0152i	0.469451	+	1.12856i
$134$	−4.14211	+	2.39145i	−0.357824	+	0.206590i
$135$	−1.42776	+	0.382567i	−0.122882	+	0.0329261i
$136$	1.79718	+	6.70718i	0.154107	+	0.575136i
$137$	−0.739423	−	2.75957i	−0.0631732	−	0.235766i	0.927119	−	0.374767i	$-0.122277\pi$
$137$	−0.739423	−	2.75957i	−0.0631732	−	0.235766i	−0.990292	+	0.139002i	$0.955611\pi$
$138$	0.743327	−	0.199174i	0.0632762	−	0.0169548i
$139$	−8.27684	+	4.77864i	−0.702033	+	0.405319i	−0.808104	−	0.589040i	$-0.799506\pi$
$139$	−8.27684	+	4.77864i	−0.702033	+	0.405319i	0.106071	+	0.994359i	$0.466173\pi$
$140$	−3.10617	−	2.37606i	−0.262520	−	0.200813i
$141$	3.23250	+	12.0638i	0.272225	+	1.01596i
$142$	4.55854	+	2.63188i	0.382544	+	0.220862i
$143$	21.0072	−	1.11849i	1.75671	−	0.0935326i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	12.4415	+	3.33368i	1.03321	+	0.276847i
$146$	8.02326	+	4.63223i	0.664010	+	0.383366i
$147$	4.93488	−	4.96457i	0.407022	−	0.409471i
$148$	4.14694	+	4.14694i	0.340876	+	0.340876i
$149$	7.38712	+	7.38712i	0.605176	+	0.605176i	0.941682	−	0.336505i	$-0.109245\pi$
$149$	7.38712	+	7.38712i	0.605176	+	0.605176i	−0.336505	+	0.941682i	$0.609245\pi$
$150$	2.71922	−	0.728614i	0.222024	−	0.0594911i
$151$	4.33716	+	1.16214i	0.352953	+	0.0945734i	0.430939	−	0.902381i	$-0.358182\pi$
$151$	4.33716	+	1.16214i	0.352953	+	0.0945734i	−0.0779863	+	0.996954i	$0.524849\pi$
$152$			5.32792i			0.432151i
$153$	−3.47189	+	6.01349i	−0.280686	+	0.486162i
$154$	15.3018	−	2.03787i	1.23305	−	0.164217i
$155$			0.580198i			0.0466027i
$156$	3.42815	−	1.11703i	0.274472	−	0.0894342i
$157$	12.7423	−	7.35677i	1.01695	−	0.587134i	0.103728	−	0.994606i	$-0.466923\pi$
$157$	12.7423	−	7.35677i	1.01695	−	0.587134i	0.913218	+	0.407472i	$0.133590\pi$
$158$	5.60671	+	5.60671i	0.446046	+	0.446046i
$159$	7.70367	−	4.44772i	0.610941	−	0.352727i
$160$	−0.739062	−	1.28009i	−0.0584280	−	0.101200i
$161$	0.268784	+	2.01821i	0.0211831	+	0.159058i
$162$	0.258819	−	0.965926i	0.0203347	−	0.0758903i
$163$	−16.2530	+	16.2530i	−1.27303	+	1.27303i	−0.328542	+	0.944489i	$0.606557\pi$
$163$	−16.2530	+	16.2530i	−1.27303	+	1.27303i	−0.944489	+	0.328542i	$0.893443\pi$
$164$	1.70135	−	6.34954i	0.132853	−	0.495816i
$165$	4.31213	−	7.46883i	0.335699	−	0.581447i
$166$	−6.57021	−	11.3799i	−0.509947	−	0.883254i
$167$	−0.821354	+	0.220081i	−0.0635583	+	0.0170304i	−0.290458	−	0.956888i	$-0.593808\pi$
$167$	−0.821354	+	0.220081i	−0.0635583	+	0.0170304i	0.226900	+	0.973918i	$0.427141\pi$
$168$	2.44283	−	1.01615i	0.188469	−	0.0783977i
$169$	1.38041	+	12.9265i	0.106185	+	0.994346i
$170$	−5.13189	+	8.88869i	−0.393598	+	0.681731i
$171$	−3.76741	+	3.76741i	−0.288101	+	0.288101i
$172$	−0.165012			−0.0125820
$173$	9.23304			0.701975			0.350988	−	0.936380i	$-0.385846\pi$
$173$	9.23304			0.701975			0.350988	+	0.936380i	$0.385846\pi$
$174$	−6.16171	+	6.16171i	−0.467118	+	0.467118i
$175$	0.983259	+	7.38299i	0.0743274	+	0.558102i
$176$	5.63579	+	1.51010i	0.424813	+	0.113828i
$177$	0.225806	+	0.842719i	0.0169726	+	0.0633426i
$178$	7.72249	+	4.45858i	0.578825	+	0.334185i
$179$			10.4418i			0.780454i	0.920719	+	0.390227i	$0.127604\pi$
$179$			10.4418i			0.780454i	−0.920719	+	0.390227i	$0.872396\pi$
$180$	0.382567	−	1.42776i	0.0285148	−	0.106419i
$181$	1.21138			0.0900414			0.0450207	−	0.998986i	$-0.485665\pi$
$181$	1.21138			0.0900414			0.0450207	+	0.998986i	$0.485665\pi$
$182$	1.76029	+	9.37557i	0.130482	+	0.694964i
$183$	−5.64703			−0.417440
$184$	−0.199174	+	0.743327i	−0.0146833	+	0.0547988i
$185$			8.66869i			0.637335i
$186$	−0.339935	−	0.196262i	−0.0249253	−	0.0143906i
$187$	−10.4858	−	39.1337i	−0.766800	−	2.86174i
$188$	−12.0638	−	3.23250i	−0.879846	−	0.235754i
$189$	2.44587	+	1.00882i	0.177911	+	0.0733807i
$190$	−5.56870	+	5.56870i	−0.403996	+	0.403996i
$191$	−24.8840			−1.80054			−0.900271	−	0.435329i	$-0.856632\pi$
$191$	−24.8840			−1.80054			−0.900271	+	0.435329i	$0.856632\pi$
$192$	1.00000			0.0721688
$193$	−13.1115	+	13.1115i	−0.943787	+	0.943787i	−0.998502	−	0.0547154i	$-0.982575\pi$
$193$	−13.1115	+	13.1115i	−0.943787	+	0.943787i	0.0547154	+	0.998502i	$0.482575\pi$
$194$	−0.441110	+	0.764025i	−0.0316699	+	0.0548538i
$195$	4.75059	+	2.41556i	0.340197	+	0.172982i
$196$	1.83201	+	6.75602i	0.130858	+	0.482573i
$197$	0.939199	−	0.251658i	0.0669152	−	0.0179299i	−0.225206	−	0.974311i	$-0.572306\pi$
$197$	0.939199	−	0.251658i	0.0669152	−	0.0179299i	0.292121	+	0.956381i	$0.405639\pi$
$198$	2.91730	+	5.05291i	0.207323	+	0.359094i
$199$	−0.585830	+	1.01469i	−0.0415284	+	0.0719293i	−0.886043	−	0.463604i	$-0.846556\pi$
$199$	−0.585830	+	1.01469i	−0.0415284	+	0.0719293i	0.844514	+	0.535533i	$0.179889\pi$
$200$	−0.728614	+	2.71922i	−0.0515208	+	0.192278i
$201$	3.38202	−	3.38202i	0.238549	−	0.238549i
$202$	−3.09759	+	11.5604i	−0.217946	+	0.813384i
$203$	−14.0624	−	18.2697i	−0.986989	−	1.28228i
$204$	−3.47189	−	6.01349i	−0.243081	−	0.421029i
$205$	8.41473	−	4.85825i	0.587710	−	0.339315i
$206$	−9.05727	−	9.05727i	−0.631050	−	0.631050i
$207$	−0.666449	+	0.384774i	−0.0463214	+	0.0267437i
$208$	−0.746698	+	3.52738i	−0.0517742	+	0.244580i
$209$		−	31.0863i		−	2.15028i
$210$	3.61530	+	1.49116i	0.249480	+	0.102900i
$211$	8.43264	−	14.6058i	0.580527	−	1.00550i	−0.414890	−	0.909871i	$-0.636180\pi$
$211$	8.43264	−	14.6058i	0.580527	−	1.00550i	0.995417	−	0.0956302i	$-0.0304866\pi$
$212$			8.89544i			0.610941i
$213$	−5.08439	−	1.36236i	−0.348377	−	0.0933473i
$214$	−2.56863	+	0.688262i	−0.175588	+	0.0470486i
$215$	−0.172469	−	0.172469i	−0.0117623	−	0.0117623i
$216$	0.707107	+	0.707107i	0.0481125	+	0.0481125i
$217$	0.630974	−	0.824860i	0.0428333	−	0.0559951i
$218$	12.9821	+	7.49520i	0.879256	+	0.507639i
$219$	−8.94879	−	2.39782i	−0.604703	−	0.162030i
$220$	4.31213	+	7.46883i	0.290724	+	0.503548i
$221$	23.8044	−	7.75643i	1.60125	−	0.521754i
$222$	−5.07894	−	2.93233i	−0.340876	−	0.196805i
$223$	−0.0655089	−	0.244483i	−0.00438680	−	0.0163718i	0.963698	−	0.266996i	$-0.0860309\pi$
$223$	−0.0655089	−	0.244483i	−0.00438680	−	0.0163718i	−0.968085	+	0.250624i	$0.919364\pi$
$224$	−0.341405	+	2.62363i	−0.0228111	+	0.175299i
$225$	−2.43799	+	1.40757i	−0.162533	+	0.0938383i
$226$	9.57798	−	2.56641i	0.637118	−	0.170715i
$227$	−0.432323	−	1.61345i	−0.0286943	−	0.107088i	0.950093	−	0.311965i	$-0.100987\pi$
$227$	−0.432323	−	1.61345i	−0.0286943	−	0.107088i	−0.978788	+	0.204877i	$0.934321\pi$
$228$	−1.37897	−	5.14638i	−0.0913243	−	0.340827i
$229$	25.9161	−	6.94421i	1.71259	−	0.458886i	0.736531	−	0.676404i	$-0.236463\pi$
$229$	25.9161	−	6.94421i	1.71259	−	0.458886i	0.976056	+	0.217517i	$0.0697959\pi$
$230$	−0.985094	+	0.568744i	−0.0649552	+	0.0375019i
$231$	−14.2529	+	5.92883i	−0.937775	+	0.390088i
$232$	−2.25534	−	8.41705i	−0.148071	−	0.552607i
$233$	−14.5436	−	8.39675i	−0.952783	−	0.550089i	−0.0588383	−	0.998268i	$-0.518740\pi$
$233$	−14.5436	−	8.39675i	−0.952783	−	0.550089i	−0.893944	+	0.448178i	$0.852073\pi$
$234$	−3.02223	+	1.96624i	−0.197570	+	0.128537i
$235$	−9.23045	−	15.9876i	−0.602128	−	1.04292i
$236$	−0.842719	−	0.225806i	−0.0548563	−	0.0146987i
$237$	−6.86679	−	3.96454i	−0.446046	−	0.257525i
$238$	16.9625	−	7.05593i	1.09952	−	0.457368i
$239$	−1.66598	−	1.66598i	−0.107763	−	0.107763i	0.651169	−	0.758933i	$-0.274279\pi$
$239$	−1.66598	−	1.66598i	−0.107763	−	0.107763i	−0.758933	+	0.651169i	$0.774279\pi$
$240$	1.04519	+	1.04519i	0.0674668	+	0.0674668i
$241$	14.3501	−	3.84511i	0.924373	−	0.247685i	0.234919	−	0.972015i	$-0.424517\pi$
$241$	14.3501	−	3.84511i	0.924373	−	0.247685i	0.689454	+	0.724330i	$0.257851\pi$
$242$	−22.2573	−	5.96384i	−1.43076	−	0.383370i
$243$			1.00000i			0.0641500i
$244$	2.82351	−	4.89047i	0.180757	−	0.313080i
$245$	−5.14653	+	8.97613i	−0.328800	+	0.573464i
$246$			6.57353i			0.419113i
$247$	19.1829	−	1.02136i	1.22058	−	0.0649875i
$248$	0.339935	−	0.196262i	0.0215859	−	0.0124626i
$249$	9.29167	+	9.29167i	0.588836	+	0.588836i
$250$	−10.0041	+	5.77588i	−0.632716	+	0.365299i
$251$	−5.71406	−	9.89703i	−0.360668	−	0.624695i	0.627403	−	0.778695i	$-0.284118\pi$
$251$	−5.71406	−	9.89703i	−0.360668	−	0.624695i	−0.988071	+	0.154000i	$0.950785\pi$
$252$	−2.09660	+	1.61378i	−0.132073	+	0.101658i
$253$	1.16210	−	4.33701i	0.0730605	−	0.272666i
$254$	−7.36119	+	7.36119i	−0.461882	+	0.461882i
$255$	2.65646	−	9.91405i	0.166354	−	0.620842i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−4.76323	−	8.25015i	−0.297122	−	0.514630i	0.678354	−	0.734735i	$-0.262693\pi$
$257$	−4.76323	−	8.25015i	−0.297122	−	0.514630i	−0.975476	+	0.220105i	$0.929360\pi$
$258$	0.159389	−	0.0427082i	0.00992313	−	0.00265889i
$259$	9.42732	−	12.3242i	0.585785	−	0.765786i
$260$	−4.46724	+	2.90635i	−0.277046	+	0.180244i
$261$	4.35699	−	7.54652i	0.269691	−	0.467118i
$262$	−2.78834	+	2.78834i	−0.172264	+	0.172264i
$263$	23.1506			1.42753			0.713763	−	0.700387i	$-0.246989\pi$
$263$	23.1506			1.42753			0.713763	+	0.700387i	$0.246989\pi$
$264$	−5.83459			−0.359094
$265$	−9.29744	+	9.29744i	−0.571137	+	0.571137i
$266$	13.9730	−	1.86091i	0.856738	−	0.114099i
$267$	−8.61332	−	2.30793i	−0.527126	−	0.141243i
$268$	1.23791	+	4.61993i	0.0756171	+	0.282207i
$269$	−23.8047	−	13.7436i	−1.45140	−	0.837965i	−0.452837	−	0.891593i	$-0.649588\pi$
$269$	−23.8047	−	13.7436i	−1.45140	−	0.837965i	−0.998561	+	0.0536283i	$0.982921\pi$
$270$			1.47812i			0.0899558i
$271$	−7.23129	+	26.9875i	−0.439270	+	1.63938i	0.291368	+	0.956611i	$0.405890\pi$
$271$	−7.23129	+	26.9875i	−0.439270	+	1.63938i	−0.730638	+	0.682765i	$0.760777\pi$
$272$	6.94378			0.421029
$273$	−4.12689	−	8.60051i	−0.249771	−	0.520527i
$274$	−2.85691			−0.172592
$275$	4.25117	−	15.8656i	0.256355	−	0.956730i
$276$		−	0.769549i		−	0.0463214i
$277$	−7.25671	−	4.18966i	−0.436013	−	0.251732i	0.265892	−	0.964003i	$-0.414334\pi$
$277$	−7.25671	−	4.18966i	−0.436013	−	0.251732i	−0.701905	+	0.712271i	$0.747667\pi$
$278$	2.47361	+	9.23162i	0.148357	+	0.553676i
$279$	0.379148	+	0.101593i	0.0226990	+	0.00608218i
$280$	−3.09903	+	2.38537i	−0.185203	+	0.142553i
$281$	−2.04772	+	2.04772i	−0.122156	+	0.122156i	−0.765542	−	0.643386i	$-0.777529\pi$
$281$	−2.04772	+	2.04772i	−0.122156	+	0.122156i	0.643386	+	0.765542i	$0.277529\pi$
$282$	12.4894			0.743734
$283$	0.899767			0.0534856			0.0267428	−	0.999642i	$-0.491486\pi$
$283$	0.899767			0.0534856			0.0267428	+	0.999642i	$0.491486\pi$
$284$	3.72203	−	3.72203i	0.220862	−	0.220862i
$285$	3.93766	−	6.82024i	0.233247	−	0.403996i
$286$	4.35668	−	20.5809i	0.257616	−	1.21697i
$287$	−17.2465	−	2.24423i	−1.01803	−	0.132473i
$288$	−0.965926	+	0.258819i	−0.0569177	+	0.0152511i
$289$	−15.6081	−	27.0339i	−0.918121	−	1.59023i
$290$	6.44017	−	11.1547i	0.378180	−	0.655027i
$291$	0.228335	−	0.852159i	0.0133853	−	0.0499545i
$292$	6.55097	−	6.55097i	0.383366	−	0.383366i
$293$	−8.10572	+	30.2510i	−0.473541	+	1.76728i	0.153348	+	0.988172i	$0.450994\pi$
$293$	−8.10572	+	30.2510i	−0.473541	+	1.76728i	−0.626889	+	0.779108i	$0.715672\pi$
$294$	−3.51817	−	6.05165i	−0.205184	−	0.352939i
$295$	−0.644793	−	1.11681i	−0.0375413	−	0.0650234i
$296$	5.07894	−	2.93233i	0.295207	−	0.170438i
$297$	−4.12568	−	4.12568i	−0.239396	−	0.239396i
$298$	9.04733	−	5.22348i	0.524098	−	0.302588i
$299$	2.71449	+	0.574621i	0.156983	+	0.0332312i
$300$		−	2.81515i		−	0.162533i
$301$	0.0576343	+	0.432759i	0.00332199	+	0.0249438i
$302$	2.24508	−	3.88859i	0.129190	−	0.223763i
$303$		−	11.9682i		−	0.687553i
$304$	5.14638	+	1.37897i	0.295165	+	0.0790892i
$305$	8.06259	−	2.16036i	0.461663	−	0.123702i
$306$	4.91000	+	4.91000i	0.280686	+	0.280686i
$307$	−6.31072	−	6.31072i	−0.360172	−	0.360172i	0.503704	−	0.863876i	$-0.331970\pi$
$307$	−6.31072	−	6.31072i	−0.360172	−	0.360172i	−0.863876	+	0.503704i	$0.831970\pi$
$308$	1.99196	−	15.3078i	0.113502	−	0.872244i
$309$	11.0928	+	6.40446i	0.631050	+	0.364337i
$310$	0.560429	+	0.150166i	0.0318302	+	0.00852888i
$311$	0.856069	+	1.48276i	0.0485432	+	0.0840793i	0.889276	−	0.457371i	$-0.151209\pi$
$311$	0.856069	+	1.48276i	0.0485432	+	0.0840793i	−0.840733	+	0.541450i	$0.817875\pi$
$312$	−0.191699	−	3.60045i	−0.0108528	−	0.203835i
$313$	−10.9749	−	6.33634i	−0.620336	−	0.358151i	0.156664	−	0.987652i	$-0.449926\pi$
$313$	−10.9749	−	6.33634i	−0.620336	−	0.358151i	−0.777000	+	0.629501i	$0.783259\pi$
$314$	−3.80814	−	14.2122i	−0.214906	−	0.802040i
$315$	−3.87805	−	0.504639i	−0.218504	−	0.0284332i
$316$	6.86679	−	3.96454i	0.386287	−	0.223023i
$317$	13.3185	−	3.56867i	0.748039	−	0.200436i	0.135391	−	0.990792i	$-0.456771\pi$
$317$	13.3185	−	3.56867i	0.748039	−	0.200436i	0.612648	+	0.790356i	$0.290104\pi$
$318$	−2.30231	−	8.59233i	−0.129107	−	0.481834i
$319$	13.1590	+	49.1101i	0.736763	+	2.74964i
$320$	−1.42776	+	0.382567i	−0.0798141	+	0.0213861i
$321$	2.30297	−	1.32962i	0.128539	−	0.0742121i
$322$	2.01901	+	0.262728i	0.112515	+	0.0146412i
$323$	−9.57525	−	35.7353i	−0.532781	−	1.98837i
$324$	−0.866025	−	0.500000i	−0.0481125	−	0.0277778i
$325$	9.93011	+	2.10207i	0.550823	+	0.116602i
$326$	11.4926	+	19.9058i	0.636516	+	1.10248i
$327$	−14.4796	−	3.87980i	−0.800724	−	0.214553i
$328$	−5.69284	−	3.28676i	−0.314335	−	0.181481i
$329$	−4.26394	+	32.7676i	−0.235079	+	1.80654i
$330$	−6.09827	−	6.09827i	−0.335699	−	0.335699i
$331$	18.1988	+	18.1988i	1.00030	+	1.00030i	1.00000		0.000297733i	$9.47714e-5\pi$
$331$	18.1988	+	18.1988i	1.00030	+	1.00030i	0.000297733		1.00000i	$0.499905\pi$
$332$	−12.6927	+	3.40099i	−0.696600	+	0.186653i
$333$	5.66482	+	1.51788i	0.310430	+	0.0831795i
$334$			0.850328i			0.0465279i
$335$	−3.53486	+	6.12256i	−0.193130	+	0.334511i
$336$	−0.349274	−	2.62260i	−0.0190545	−	0.143074i
$337$			33.5630i			1.82829i	0.405383	+	0.914147i	$0.367138\pi$
$337$			33.5630i			1.82829i	−0.405383	+	0.914147i	$0.632862\pi$
$338$	12.8433	+	2.01225i	0.698584	+	0.109452i
$339$	−8.58738	+	4.95793i	−0.466403	+	0.269278i
$340$	7.25758	+	7.25758i	0.393598	+	0.393598i
$341$	−1.98338	+	1.14511i	−0.107406	+	0.0620110i
$342$	2.66396	+	4.61411i	0.144050	+	0.249503i
$343$	17.0784	−	7.16432i	0.922148	−	0.386837i
$344$	−0.0427082	+	0.159389i	−0.00230267	+	0.00859368i
$345$	0.804326	−	0.804326i	0.0433035	−	0.0433035i
$346$	2.38969	−	8.91843i	0.128470	−	0.479458i
$347$	14.7530	−	25.5529i	0.791983	−	1.37175i	−0.132755	−	0.991149i	$-0.542382\pi$
$347$	14.7530	−	25.5529i	0.791983	−	1.37175i	0.924738	−	0.380605i	$-0.124284\pi$
$348$	4.35699	+	7.54652i	0.233559	+	0.404536i
$349$	−18.0248	+	4.82973i	−0.964844	+	0.258529i	−0.706650	−	0.707564i	$-0.749794\pi$
$349$	−18.0248	+	4.82973i	−0.964844	+	0.258529i	−0.258195	+	0.966093i	$0.583128\pi$
$350$	7.38591	+	0.961105i	0.394794	+	0.0513732i
$351$	2.41035	−	2.68146i	0.128655	−	0.143126i
$352$	2.91730	−	5.05291i	0.155492	−	0.269321i
$353$	−17.2943	+	17.2943i	−0.920481	+	0.920481i	−0.997063	−	0.0765819i	$-0.975599\pi$
$353$	−17.2943	+	17.2943i	−0.920481	+	0.920481i	0.0765819	+	0.997063i	$0.475599\pi$
$354$	0.872447			0.0463700
$355$	7.78048			0.412945
$356$	6.30539	−	6.30539i	0.334185	−	0.334185i
$357$	−14.5583	+	11.2057i	−0.770508	+	0.593070i
$358$	10.0860	+	2.70253i	0.533060	+	0.142833i
$359$	−6.21830	−	23.2070i	−0.328189	−	1.22482i	−0.911067	−	0.412259i	$-0.864740\pi$
$359$	−6.21830	−	23.2070i	−0.328189	−	1.22482i	0.582877	−	0.812560i	$-0.301927\pi$
$360$	−1.28009	−	0.739062i	−0.0674668	−	0.0389520i
$361$		−	9.38674i		−	0.494039i
$362$	0.313529	−	1.17011i	0.0164787	−	0.0614994i
$363$	23.0425			1.20942
$364$	9.51171	+	0.726263i	0.498549	+	0.0380665i
$365$	13.6940			0.716779
$366$	−1.46156	+	5.45461i	−0.0763969	+	0.285117i
$367$			7.06387i			0.368731i	0.982858	+	0.184366i	$0.0590230\pi$
$367$			7.06387i			0.368731i	−0.982858	+	0.184366i	$0.940977\pi$
$368$	0.666449	+	0.384774i	0.0347410	+	0.0200577i
$369$	−1.70135	−	6.34954i	−0.0885690	−	0.330544i
$370$	8.37331	+	2.24362i	0.435308	+	0.116640i
$371$	23.3291	−	3.10695i	1.21119	−	0.161305i
$372$	−0.277556	+	0.277556i	−0.0143906	+	0.0143906i
$373$	−11.2090			−0.580381			−0.290191	−	0.956969i	$-0.593719\pi$
$373$	−11.2090			−0.580381			−0.290191	+	0.956969i	$0.593719\pi$
$374$	−40.5142			−2.09494
$375$	8.16833	−	8.16833i	0.421811	−	0.421811i
$376$	−6.24471	+	10.8161i	−0.322046	+	0.557800i
$377$	−29.8728	+	9.73379i	−1.53853	+	0.501316i
$378$	1.60748	−	2.10143i	0.0826799	−	0.108086i
$379$	3.13887	−	0.841057i	0.161233	−	0.0432022i	−0.177300	−	0.984157i	$-0.556736\pi$
$379$	3.13887	−	0.841057i	0.161233	−	0.0432022i	0.338532	+	0.940955i	$0.390070\pi$
$380$	3.93766	+	6.82024i	0.201998	+	0.349871i
$381$	5.20515	−	9.01558i	0.266668	−	0.461882i
$382$	−6.44045	+	24.0361i	−0.329522	+	1.22979i
$383$	4.20655	−	4.20655i	0.214945	−	0.214945i	−0.591419	−	0.806364i	$-0.701432\pi$
$383$	4.20655	−	4.20655i	0.214945	−	0.214945i	0.806364	+	0.591419i	$0.201432\pi$
$384$	0.258819	−	0.965926i	0.0132078	−	0.0492922i
$385$	18.0816	−	13.9176i	0.921523	−	0.709309i
$386$	9.27123	+	16.0582i	0.471893	+	0.817343i
$387$	−0.142904	+	0.0825059i	−0.00726424	+	0.00419401i
$388$	0.623824	+	0.623824i	0.0316699	+	0.0316699i
$389$	8.00851	−	4.62372i	0.406048	−	0.234432i	−0.283042	−	0.959107i	$-0.591344\pi$
$389$	8.00851	−	4.62372i	0.406048	−	0.234432i	0.689090	+	0.724676i	$0.258010\pi$
$390$	3.56280	−	3.96353i	0.180409	−	0.200701i
$391$		−	5.34358i		−	0.270236i
$392$	6.99997	−	0.0210005i	0.353552	−	0.00106069i
$393$	1.97165	−	3.41500i	0.0994567	−	0.172264i
$394$		−	0.972331i		−	0.0489853i
$395$	11.3208	+	3.03340i	0.569612	+	0.152627i
$396$	5.63579	−	1.51010i	0.283209	−	0.0758856i
$397$	7.19597	+	7.19597i	0.361155	+	0.361155i	0.864238	−	0.503083i	$-0.167801\pi$
$397$	7.19597	+	7.19597i	0.361155	+	0.361155i	−0.503083	+	0.864238i	$0.667801\pi$
$398$	0.828489	+	0.828489i	0.0415284	+	0.0415284i
$399$	−13.0152	+	5.41397i	−0.651576	+	0.271038i
$400$	2.43799	+	1.40757i	0.121899	+	0.0703787i
$401$	10.7267	+	2.87422i	0.535668	+	0.143532i	0.516504	−	0.856285i	$-0.327233\pi$
$401$	10.7267	+	2.87422i	0.535668	+	0.143532i	0.0191636	+	0.999816i	$0.493900\pi$
$402$	−2.39145	−	4.14211i	−0.119275	−	0.206590i
$403$	−0.771796	−	1.18630i	−0.0384459	−	0.0590937i
$404$	10.3647	+	5.98408i	0.515665	+	0.297719i
$405$	−0.382567	−	1.42776i	−0.0190099	−	0.0709459i
$406$	−21.2868	+	8.85471i	−1.05645	+	0.439452i
$407$	−29.6336	+	17.1089i	−1.46888	+	0.848059i
$408$	−6.70718	+	1.79718i	−0.332055	+	0.0889738i
$409$	3.35256	+	12.5119i	0.165773	+	0.618675i	0.997940	+	0.0641495i	$0.0204334\pi$
$409$	3.35256	+	12.5119i	0.165773	+	0.618675i	−0.832167	+	0.554525i	$0.812900\pi$
$410$	−2.51481	−	9.38541i	−0.124198	−	0.463512i
$411$	2.75957	−	0.739423i	0.136119	−	0.0364731i
$412$	−11.0928	+	6.40446i	−0.546505	+	0.315525i
$413$	−0.297857	+	2.28898i	−0.0146566	+	0.112633i
$414$	0.199174	+	0.743327i	0.00978886	+	0.0365325i
$415$	−16.8210	−	9.71158i	−0.825708	−	0.476723i
$416$	3.21393	+	1.63421i	0.157576	+	0.0801237i
$417$	−4.77864	−	8.27684i	−0.234011	−	0.405319i
$418$	−30.0270	−	8.04571i	−1.46867	−	0.393529i
$419$	19.5436	+	11.2835i	0.954768	+	0.551236i	0.894559	−	0.446950i	$-0.147490\pi$
$419$	19.5436	+	11.2835i	0.954768	+	0.551236i	0.0602092	+	0.998186i	$0.480823\pi$
$420$	2.37606	−	3.10617i	0.115940	−	0.151566i
$421$	−14.4017	−	14.4017i	−0.701895	−	0.701895i	0.262922	−	0.964817i	$-0.415314\pi$
$421$	−14.4017	−	14.4017i	−0.701895	−	0.701895i	−0.964817	+	0.262922i	$0.915314\pi$
$422$	−11.9255	−	11.9255i	−0.580527	−	0.580527i
$423$	−12.0638	+	3.23250i	−0.586564	+	0.157169i
$424$	8.59233	+	2.30231i	0.417280	+	0.111810i
$425$		−	19.5478i		−	0.948206i
$426$	−2.63188	+	4.55854i	−0.127515	+	0.220862i
$427$	−13.8119	−	5.69682i	−0.668405	−	0.275688i
$428$			2.65924i			0.128539i
$429$	1.11849	+	21.0072i	0.0540011	+	1.01424i
$430$	−0.211230	+	0.121954i	−0.0101864	+	0.00588114i
$431$	−1.31565	−	1.31565i	−0.0633728	−	0.0633728i	0.674710	−	0.738083i	$-0.264269\pi$
$431$	−1.31565	−	1.31565i	−0.0633728	−	0.0633728i	−0.738083	+	0.674710i	$0.764269\pi$
$432$	0.866025	−	0.500000i	0.0416667	−	0.0240563i
$433$	16.6576	+	28.8518i	0.800514	+	1.38653i	0.919279	+	0.393608i	$0.128773\pi$
$433$	16.6576	+	28.8518i	0.800514	+	1.38653i	−0.118765	+	0.992922i	$0.537894\pi$
$434$	−0.633446	−	0.822963i	−0.0304064	−	0.0395035i
$435$	−3.33368	+	12.4415i	−0.159838	+	0.596522i
$436$	10.5998	−	10.5998i	0.507639	−	0.507639i
$437$	1.06118	−	3.96039i	0.0507632	−	0.189451i
$438$	−4.63223	+	8.02326i	−0.221337	+	0.383366i
$439$	12.1665	+	21.0730i	0.580675	+	1.00576i	0.995399	+	0.0958117i	$0.0305447\pi$
$439$	12.1665	+	21.0730i	0.580675	+	1.00576i	−0.414724	+	0.909947i	$0.636122\pi$
$440$	8.33039	−	2.23212i	0.397136	−	0.106412i
$441$	4.96457	+	4.93488i	0.236408	+	0.234994i
$442$	−1.33112	−	25.0008i	−0.0633148	−	1.18916i
$443$	15.5729	−	26.9730i	0.739890	−	1.28153i	−0.212655	−	0.977127i	$-0.568211\pi$
$443$	15.5729	−	26.9730i	0.739890	−	1.28153i	0.952545	−	0.304399i	$-0.0984556\pi$
$444$	−4.14694	+	4.14694i	−0.196805	+	0.196805i
$445$	13.1807			0.624824
$446$	−0.253107			−0.0119850
$447$	−7.38712	+	7.38712i	−0.349399	+	0.349399i
$448$	2.44587	+	1.00882i	0.115557	+	0.0476621i
$449$	−11.1005	−	2.97437i	−0.523866	−	0.140369i	−0.0128116	−	0.999918i	$-0.504078\pi$
$449$	−11.1005	−	2.97437i	−0.523866	−	0.140369i	−0.511054	+	0.859549i	$0.670745\pi$
$450$	0.728614	+	2.71922i	0.0343472	+	0.128185i
$451$	33.2154	+	19.1769i	1.56405	+	0.903007i
$452$		−	9.91586i		−	0.466403i
$453$	−1.16214	+	4.33716i	−0.0546020	+	0.203777i
$454$	−1.67037			−0.0783942
$455$	9.18247	+	10.7006i	0.430481	+	0.501654i
$456$	−5.32792			−0.249503
$457$	−9.87919	+	36.8696i	−0.462129	+	1.72469i	0.204108	+	0.978948i	$0.434571\pi$
$457$	−9.87919	+	36.8696i	−0.462129	+	1.72469i	−0.666237	+	0.745740i	$0.732096\pi$
$458$		−	26.8304i		−	1.25370i
$459$	−6.01349	−	3.47189i	−0.280686	−	0.162054i
$460$	0.294404	+	1.09873i	0.0137266	+	0.0512285i
$461$	6.32045	+	1.69356i	0.294373	+	0.0788770i	0.402983	−	0.915207i	$-0.367973\pi$
$461$	6.32045	+	1.69356i	0.294373	+	0.0788770i	−0.108610	+	0.994084i	$0.534640\pi$
$462$	2.03787	+	15.3018i	0.0948105	+	0.711903i
$463$	−10.5716	+	10.5716i	−0.491304	+	0.491304i	−0.908717	−	0.417413i	$-0.862937\pi$
$463$	−10.5716	+	10.5716i	−0.491304	+	0.491304i	0.417413	+	0.908717i	$0.362937\pi$
$464$	−8.71398			−0.404536
$465$	−0.580198			−0.0269061
$466$	−11.8748	+	11.8748i	−0.550089	+	0.550089i
$467$	−0.763124	+	1.32177i	−0.0353132	+	0.0611642i	−0.883142	−	0.469106i	$-0.844576\pi$
$467$	−0.763124	+	1.32177i	−0.0353132	+	0.0611642i	0.847829	+	0.530270i	$0.177910\pi$
$468$	1.11703	+	3.42815i	0.0516349	+	0.158466i
$469$	11.6838	−	4.86015i	0.539509	−	0.224421i
$470$	−17.8319	+	4.77803i	−0.822523	+	0.220394i
$471$	7.35677	+	12.7423i	0.338982	+	0.587134i
$472$	−0.436223	+	0.755561i	−0.0200788	+	0.0347775i
$473$	0.249185	−	0.929971i	0.0114575	−	0.0427601i
$474$	−5.60671	+	5.60671i	−0.257525	+	0.257525i
$475$	3.88200	−	14.4878i	0.178118	−	0.664746i
$476$	−2.42528	−	18.2107i	−0.111163	−	0.834688i
$477$	4.44772	+	7.70367i	0.203647	+	0.352727i
$478$	−2.04040	+	1.17803i	−0.0933257	+	0.0538816i
$479$	2.47503	+	2.47503i	0.113087	+	0.113087i	0.761386	−	0.648299i	$-0.224519\pi$
$479$	2.47503	+	2.47503i	0.113087	+	0.113087i	−0.648299	+	0.761386i	$0.724519\pi$
$480$	1.28009	−	0.739062i	0.0584280	−	0.0337334i
$481$	−11.5313	−	17.7244i	−0.525783	−	0.808161i
$482$		−	14.8563i		−	0.676688i
$483$	−2.01821	+	0.268784i	−0.0918320	+	0.0122301i
$484$	−11.5212	+	19.9554i	−0.523693	+	0.907063i
$485$			1.30403i			0.0592130i
$486$	0.965926	+	0.258819i	0.0438153	+	0.0117403i
$487$	−4.22270	+	1.13147i	−0.191349	+	0.0512718i	−0.353221	−	0.935540i	$-0.614914\pi$
$487$	−4.22270	+	1.13147i	−0.191349	+	0.0512718i	0.161872	+	0.986812i	$0.448247\pi$
$488$	−3.99305	−	3.99305i	−0.180757	−	0.180757i
$489$	−16.2530	−	16.2530i	−0.734985	−	0.734985i
$490$	7.33826	+	7.29436i	0.331509	+	0.329526i
$491$	0.333214	+	0.192381i	0.0150377	+	0.00868203i	0.507500	−	0.861652i	$-0.330570\pi$
$491$	0.333214	+	0.192381i	0.0150377	+	0.00868203i	−0.492462	+	0.870334i	$0.663903\pi$
$492$	6.34954	+	1.70135i	0.286259	+	0.0767030i
$493$	30.2540	+	52.4014i	1.36257	+	2.36004i
$494$	3.97835	−	18.7936i	0.178994	−	0.845565i
$495$	7.46883	+	4.31213i	0.335699	+	0.193816i
$496$	−0.101593	−	0.379148i	−0.00456164	−	0.0170243i
$497$	−11.0614	−	8.46138i	−0.496172	−	0.379545i
$498$	11.3799	−	6.57021i	0.509947	−	0.294418i
$499$	8.20014	−	2.19722i	0.367089	−	0.0983612i	−0.0705590	−	0.997508i	$-0.522478\pi$
$499$	8.20014	−	2.19722i	0.367089	−	0.0983612i	0.437648	+	0.899146i	$0.355812\pi$
$500$	2.98982	+	11.1581i	0.133709	+	0.499007i
$501$	−0.220081	−	0.821354i	−0.00983250	−	0.0366954i
$502$	−11.0387	+	2.95781i	−0.492682	+	0.132014i
$503$	6.42502	−	3.70948i	0.286477	−	0.165398i	−0.349875	−	0.936796i	$-0.613776\pi$
$503$	6.42502	−	3.70948i	0.286477	−	0.165398i	0.636352	+	0.771399i	$0.280443\pi$
$504$	1.01615	+	2.44283i	0.0452629	+	0.108812i
$505$	4.57862	+	17.0877i	0.203746	+	0.760391i
$506$	−3.88846	−	2.24500i	−0.172863	−	0.0998025i
$507$	−12.9265	+	1.38041i	−0.574086	+	0.0613060i
$508$	5.20515	+	9.01558i	0.230941	+	0.400002i
$509$	11.8661	+	3.17952i	0.525957	+	0.140930i	0.512021	−	0.858973i	$-0.328897\pi$
$509$	11.8661	+	3.17952i	0.525957	+	0.140930i	0.0139366	+	0.999903i	$0.495564\pi$
$510$	−8.88869	−	5.13189i	−0.393598	−	0.227244i
$511$	−19.4686	−	14.8925i	−0.861241	−	0.658803i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−3.76741	−	3.76741i	−0.166335	−	0.166335i
$514$	−9.20185	+	2.46563i	−0.405876	+	0.108754i
$515$	−18.2880	−	4.90026i	−0.805867	−	0.215931i
$516$		−	0.165012i		−	0.00726424i
$517$	36.4353	−	63.1078i	1.60242	−	2.77548i
$518$	−9.46425	−	12.2958i	−0.415835	−	0.540247i
$519$			9.23304i			0.405285i
$520$	1.65111	+	5.06724i	0.0724061	+	0.222213i
$521$	−9.80499	+	5.66091i	−0.429564	+	0.248009i	−0.699161	−	0.714964i	$-0.746443\pi$
$521$	−9.80499	+	5.66091i	−0.429564	+	0.248009i	0.269597	+	0.962973i	$0.413110\pi$
$522$	−6.16171	−	6.16171i	−0.269691	−	0.269691i
$523$	0.607906	−	0.350975i	0.0265819	−	0.0153471i	−0.486650	−	0.873597i	$-0.661781\pi$
$523$	0.607906	−	0.350975i	0.0265819	−	0.0153471i	0.513232	+	0.858250i	$0.328448\pi$
$524$	1.97165	+	3.41500i	0.0861320	+	0.149185i
$525$	−7.38299	+	0.983259i	−0.322220	+	0.0429129i
$526$	5.99181	−	22.3617i	0.261255	−	0.975018i
$527$	−1.92729	+	1.92729i	−0.0839540	+	0.0839540i
$528$	−1.51010	+	5.63579i	−0.0657189	+	0.245266i
$529$	−11.2039	+	19.4057i	−0.487126	+	0.843727i
$530$	6.57428	+	11.3870i	0.285568	+	0.494619i
$531$	−0.842719	+	0.225806i	−0.0365709	+	0.00979914i
$532$	1.81898	−	13.9785i	0.0788627	−	0.606045i
$533$	−10.7425	+	21.1269i	−0.465310	+	0.915106i
$534$	−4.45858	+	7.72249i	−0.192942	+	0.334185i
$535$	−2.77942	+	2.77942i	−0.120165	+	0.120165i
$536$	4.78290			0.206590
$537$	−10.4418			−0.450596
$538$	−19.4365	+	19.4365i	−0.837965	+	0.837965i
$539$	−40.8420	+	0.122529i	−1.75919	+	0.00527771i
$540$	1.42776	+	0.382567i	0.0614409	+	0.0164631i
$541$	−2.08100	−	7.76639i	−0.0894691	−	0.333903i	0.906654	−	0.421875i	$-0.138628\pi$
$541$	−2.08100	−	7.76639i	−0.0894691	−	0.333903i	−0.996123	+	0.0879721i	$0.971961\pi$
$542$	24.1964	+	13.9698i	1.03932	+	0.600053i
$543$			1.21138i			0.0519854i
$544$	1.79718	−	6.70718i	0.0770536	−	0.287568i
$545$	22.1577			0.949130
$546$	−9.37557	+	1.76029i	−0.401237	+	0.0753336i
$547$	13.2526			0.566641			0.283321	−	0.959025i	$-0.408564\pi$
$547$	13.2526			0.566641			0.283321	+	0.959025i	$0.408564\pi$
$548$	−0.739423	+	2.75957i	−0.0315866	+	0.117883i
$549$		−	5.64703i		−	0.241009i
$550$	−14.2247	−	8.21262i	−0.606542	−	0.350187i
$551$	12.0163	+	44.8454i	0.511911	+	1.91048i
$552$	−0.743327	−	0.199174i	−0.0316381	−	0.00847740i
$553$	−12.7958	−	16.6241i	−0.544132	−	0.706928i
$554$	−5.92508	+	5.92508i	−0.251732	+	0.251732i
$555$	−8.66869			−0.367965
$556$	9.55728			0.405319
$557$	5.97510	−	5.97510i	0.253173	−	0.253173i	−0.569097	−	0.822270i	$-0.692707\pi$
$557$	5.97510	−	5.97510i	0.253173	−	0.253173i	0.822270	+	0.569097i	$0.192707\pi$
$558$	0.196262	−	0.339935i	0.00830842	−	0.0143906i
$559$	0.582060	+	0.123214i	0.0246185	+	0.00521139i
$560$	1.50200	+	3.61081i	0.0634710	+	0.152585i
$561$	39.1337	−	10.4858i	1.65222	−	0.442712i
$562$	1.44795	+	2.50793i	0.0610782	+	0.105791i
$563$	−6.08867	+	10.5459i	−0.256607	+	0.444456i	−0.965331	−	0.261030i	$-0.915938\pi$
$563$	−6.08867	+	10.5459i	−0.256607	+	0.444456i	0.708724	+	0.705486i	$0.249271\pi$
$564$	3.23250	−	12.0638i	0.136113	−	0.507980i
$565$	10.3640	−	10.3640i	0.436016	−	0.436016i
$566$	0.232877	−	0.869108i	0.00978854	−	0.0365313i
$567$	−1.00882	+	2.44587i	−0.0423663	+	0.102717i
$568$	−2.63188	−	4.55854i	−0.110431	−	0.191272i
$569$	−15.5153	+	8.95779i	−0.650437	+	0.375530i	−0.788624	−	0.614876i	$-0.789206\pi$
$569$	−15.5153	+	8.95779i	−0.650437	+	0.375530i	0.138187	+	0.990406i	$0.455873\pi$
$570$	−5.56870	−	5.56870i	−0.233247	−	0.233247i
$571$	−32.2814	+	18.6377i	−1.35093	+	0.779962i	−0.988380	−	0.152001i	$-0.951428\pi$
$571$	−32.2814	+	18.6377i	−1.35093	+	0.779962i	−0.362554	+	0.931963i	$0.618095\pi$
$572$	−18.7520	−	9.53495i	−0.784060	−	0.398676i
$573$		−	24.8840i		−	1.03954i
$574$	−6.63149	+	16.0780i	−0.276793	+	0.671083i
$575$	1.08320	−	1.87615i	0.0451724	−	0.0782409i
$576$			1.00000i			0.0416667i
$577$	3.72390	+	0.997816i	0.155028	+	0.0415396i	0.335498	−	0.942041i	$-0.391095\pi$
$577$	3.72390	+	0.997816i	0.155028	+	0.0415396i	−0.180470	+	0.983580i	$0.557762\pi$
$578$	−30.1525	+	8.07933i	−1.25418	+	0.336056i
$579$	−13.1115	−	13.1115i	−0.544895	−	0.544895i
$580$	−9.10778	−	9.10778i	−0.378180	−	0.378180i
$581$	13.3526	+	32.0998i	0.553961	+	1.33173i
$582$	−0.764025	−	0.441110i	−0.0316699	−	0.0182846i
$583$	−50.1328	−	13.4330i	−2.07629	−	0.556339i
$584$	−4.63223	−	8.02326i	−0.191683	−	0.332005i
$585$	−2.41556	+	4.75059i	−0.0998713	+	0.196413i
$586$	27.1223	+	15.6591i	1.12041	+	0.646870i
$587$	8.69926	+	32.4661i	0.359057	+	1.34002i	0.875302	+	0.483577i	$0.160663\pi$
$587$	8.69926	+	32.4661i	0.359057	+	1.34002i	−0.516245	+	0.856441i	$0.672671\pi$
$588$	−6.75602	+	1.83201i	−0.278613	+	0.0755508i
$589$	−1.81115	+	1.04567i	−0.0746270	+	0.0430859i
$590$	−1.24564	+	0.333769i	−0.0512823	+	0.0137411i
$591$	0.251658	+	0.939199i	0.0103518	+	0.0386335i
$592$	−1.51788	−	5.66482i	−0.0623847	−	0.232823i
$593$	−46.3688	+	12.4245i	−1.90414	+	0.510212i	−0.908387	+	0.418130i	$0.862686\pi$
$593$	−46.3688	+	12.4245i	−1.90414	+	0.510212i	−0.995751	+	0.0920820i	$0.970648\pi$
$594$	−5.05291	+	2.91730i	−0.207323	+	0.119698i
$595$	16.4988	−	21.5686i	0.676386	−	0.884226i
$596$	−2.70387	−	10.0910i	−0.110755	−	0.413343i
$597$	−1.01469	−	0.585830i	−0.0415284	−	0.0239764i
$598$	1.25760	−	2.47328i	0.0514272	−	0.101140i
$599$	8.59552	+	14.8879i	0.351204	+	0.608302i	0.986461	−	0.163998i	$-0.0524392\pi$
$599$	8.59552	+	14.8879i	0.351204	+	0.608302i	−0.635257	+	0.772301i	$0.719106\pi$
$600$	−2.71922	−	0.728614i	−0.111012	−	0.0297455i
$601$	−8.13421	−	4.69629i	−0.331801	−	0.191566i	0.324839	−	0.945769i	$-0.394690\pi$
$601$	−8.13421	−	4.69629i	−0.331801	−	0.191566i	−0.656641	+	0.754204i	$0.728023\pi$
$602$	0.432930	+	0.0563358i	0.0176449	+	0.00229607i
$603$	3.38202	+	3.38202i	0.137727	+	0.137727i
$604$	−3.17502	−	3.17502i	−0.129190	−	0.129190i
$605$	−32.8991	+	8.81529i	−1.33754	+	0.358393i
$606$	−11.5604	−	3.09759i	−0.469608	−	0.125831i
$607$		−	7.92139i		−	0.321519i	−0.986994	−	0.160760i	$-0.948606\pi$
$607$		−	7.92139i		−	0.321519i	0.986994	−	0.160760i	$-0.0513944\pi$
$608$	2.66396	−	4.61411i	0.108038	−	0.187127i
$609$	18.2697	−	14.0624i	0.740325	−	0.569838i
$610$		−	8.34701i		−	0.337960i
$611$	40.1401	+	20.4103i	1.62390	+	0.825713i
$612$	6.01349	−	3.47189i	0.243081	−	0.140343i
$613$	−15.6552	−	15.6552i	−0.632307	−	0.632307i	0.316339	−	0.948646i	$-0.397546\pi$
$613$	−15.6552	−	15.6552i	−0.632307	−	0.632307i	−0.948646	+	0.316339i	$0.897546\pi$
$614$	−7.72903	+	4.46236i	−0.311918	+	0.180086i
$615$	4.85825	+	8.41473i	0.195903	+	0.339315i
$616$	−14.2707	−	5.88604i	−0.574982	−	0.237155i
$617$	12.1595	−	45.3797i	0.489521	−	1.82692i	−0.0692532	−	0.997599i	$-0.522062\pi$
$617$	12.1595	−	45.3797i	0.489521	−	1.82692i	0.558775	−	0.829320i	$-0.311272\pi$
$618$	9.05727	−	9.05727i	0.364337	−	0.364337i
$619$	−6.76879	+	25.2615i	−0.272061	+	1.01534i	0.685725	+	0.727861i	$0.259485\pi$
$619$	−6.76879	+	25.2615i	−0.272061	+	1.01534i	−0.957786	+	0.287483i	$0.907181\pi$
$620$	0.290099	−	0.502466i	0.0116507	−	0.0201795i
$621$	−0.384774	−	0.666449i	−0.0154405	−	0.0267437i
$622$	1.65380	−	0.443134i	0.0663113	−	0.0177681i
$623$	−18.7388	−	14.3342i	−0.750754	−	0.574286i
$624$	−3.52738	−	0.746698i	−0.141208	−	0.0298919i
$625$	−1.49960	+	2.59739i	−0.0599840	+	0.103895i
$626$	−8.96094	+	8.96094i	−0.358151	+	0.358151i
$627$	31.0863			1.24147
$628$	−14.7135			−0.587134
$629$	−28.7954	+	28.7954i	−1.14815	+	1.14815i
$630$	−1.49116	+	3.61530i	−0.0594091	+	0.144037i
$631$	−30.2532	−	8.10633i	−1.20436	−	0.322708i	−0.399814	−	0.916596i	$-0.630925\pi$
$631$	−30.2532	−	8.10633i	−1.20436	−	0.322708i	−0.804547	+	0.593888i	$0.797592\pi$
$632$	−2.05220	−	7.65891i	−0.0816320	−	0.304655i
$633$	14.6058	+	8.43264i	0.580527	+	0.335167i
$634$		−	13.7883i		−	0.547603i
$635$	−3.98263	+	14.8634i	−0.158046	+	0.589836i
$636$	−8.89544			−0.352727
$637$	−1.41750	−	25.1990i	−0.0561634	−	0.998422i
$638$	50.8425			2.01287
$639$	1.36236	−	5.08439i	0.0538941	−	0.201135i
$640$			1.47812i			0.0584280i
$641$	−22.3360	−	12.8957i	−0.882218	−	0.509349i	−0.0108290	−	0.999941i	$-0.503447\pi$
$641$	−22.3360	−	12.8957i	−0.882218	−	0.509349i	−0.871389	+	0.490592i	$0.836780\pi$
$642$	−0.688262	−	2.56863i	−0.0271635	−	0.101376i
$643$	17.7658	+	4.76034i	0.700616	+	0.187730i	0.591507	−	0.806300i	$-0.298533\pi$
$643$	17.7658	+	4.76034i	0.700616	+	0.187730i	0.109110	+	0.994030i	$0.465200\pi$
$644$	0.776334	−	1.88222i	0.0305918	−	0.0741697i
$645$	0.172469	−	0.172469i	0.00679096	−	0.00679096i
$646$	−36.9959			−1.45559
$647$	3.70498			0.145658			0.0728289	−	0.997344i	$-0.476797\pi$
$647$	3.70498			0.145658			0.0728289	+	0.997344i	$0.476797\pi$
$648$	−0.707107	+	0.707107i	−0.0277778	+	0.0277778i
$649$	2.54519	−	4.40839i	0.0999073	−	0.173045i
$650$	4.60054	−	9.04769i	0.180448	−	0.354880i
$651$	0.824860	+	0.630974i	0.0323288	+	0.0247298i
$652$	22.2020	−	5.94900i	0.869497	−	0.232981i
$653$	6.05347	+	10.4849i	0.236891	+	0.410307i	0.959820	−	0.280615i	$-0.0905384\pi$
$653$	6.05347	+	10.4849i	0.236891	+	0.410307i	−0.722930	+	0.690921i	$0.757205\pi$
$654$	−7.49520	+	12.9821i	−0.293085	+	0.507639i
$655$	−1.50858	+	5.63009i	−0.0589450	+	0.219986i
$656$	−4.64819	+	4.64819i	−0.181481	+	0.181481i
$657$	2.39782	−	8.94879i	0.0935479	−	0.349125i
$658$	30.5475	+	12.5995i	1.19087	+	0.491181i
$659$	6.59589	+	11.4244i	0.256939	+	0.445032i	0.965420	−	0.260698i	$-0.0839526\pi$
$659$	6.59589	+	11.4244i	0.256939	+	0.445032i	−0.708481	+	0.705730i	$0.750619\pi$
$660$	−7.46883	+	4.31213i	−0.290724	+	0.167849i
$661$	−8.93254	−	8.93254i	−0.347436	−	0.347436i	0.511718	−	0.859154i	$-0.329009\pi$
$661$	−8.93254	−	8.93254i	−0.347436	−	0.347436i	−0.859154	+	0.511718i	$0.829009\pi$
$662$	22.2889	−	12.8685i	0.866283	−	0.500149i
$663$	7.75643	+	23.8044i	0.301235	+	0.924485i
$664$			13.1404i			0.509947i
$665$	16.5114	−	12.7090i	0.640284	−	0.492835i
$666$	2.93233	−	5.07894i	0.113625	−	0.196805i
$667$			6.70583i			0.259651i
$668$	0.821354	+	0.220081i	0.0317791	+	0.00851519i
$669$	0.244483	−	0.0655089i	0.00945225	−	0.00253272i
$670$	4.99905	+	4.99905i	0.193130	+	0.193130i
$671$	23.2978	+	23.2978i	0.899403	+	0.899403i
$672$	−2.62363	−	0.341405i	−0.101209	−	0.0131700i
$673$	33.2503	+	19.1971i	1.28170	+	0.739993i	0.977160	−	0.212505i	$-0.0681623\pi$
$673$	33.2503	+	19.1971i	1.28170	+	0.739993i	0.304545	+	0.952498i	$0.401496\pi$
$674$	32.4194	+	8.68675i	1.24875	+	0.334601i
$675$	−1.40757	−	2.43799i	−0.0541775	−	0.0938383i
$676$	5.26778	−	11.8849i	0.202607	−	0.457111i
$677$	−30.8327	−	17.8013i	−1.18500	−	0.684158i	−0.227831	−	0.973701i	$-0.573163\pi$
$677$	−30.8327	−	17.8013i	−1.18500	−	0.684158i	−0.957165	+	0.289543i	$0.906497\pi$
$678$	2.56641	+	9.57798i	0.0985625	+	0.367840i
$679$	1.41815	−	1.85392i	0.0544237	−	0.0711471i
$680$	8.88869	−	5.13189i	0.340866	−	0.196799i
$681$	1.61345	−	0.432323i	0.0618276	−	0.0165666i
$682$	0.592751	+	2.21218i	0.0226976	+	0.0847086i
$683$	4.33967	+	16.1959i	0.166053	+	0.619718i	0.997904	+	0.0647182i	$0.0206149\pi$
$683$	4.33967	+	16.1959i	0.166053	+	0.619718i	−0.831851	+	0.554999i	$0.812718\pi$
$684$	5.14638	−	1.37897i	0.196777	−	0.0527261i
$685$	−3.65712	+	2.11144i	−0.139731	+	0.0806738i
$686$	−2.49998	−	18.3508i	−0.0954498	−	0.700635i
$687$	6.94421	+	25.9161i	0.264938	+	0.988763i
$688$	0.142904	+	0.0825059i	0.00544818	+	0.00314551i
$689$	6.64221	−	31.3776i	0.253048	−	1.19539i
$690$	−0.568744	−	0.985094i	−0.0216517	−	0.0375019i
$691$	1.39827	+	0.374666i	0.0531928	+	0.0142530i	0.285317	−	0.958433i	$-0.407901\pi$
$691$	1.39827	+	0.374666i	0.0531928	+	0.0142530i	−0.232125	+	0.972686i	$0.574568\pi$
$692$	−7.99605	−	4.61652i	−0.303964	−	0.175494i
$693$	−5.92883	−	14.2529i	−0.225218	−	0.541425i
$694$	−20.8639	−	20.8639i	−0.791983	−	0.791983i
$695$	9.98919	+	9.98919i	0.378911	+	0.378911i
$696$	8.41705	−	2.25534i	0.319048	−	0.0854885i
$697$	44.0898	+	11.8138i	1.67002	+	0.447481i
$698$			18.6606i			0.706315i
$699$	8.39675	−	14.5436i	0.317594	−	0.550089i
$700$	2.83997	−	6.88549i	0.107341	−	0.260247i
$701$		−	22.7118i		−	0.857812i	−0.903349	−	0.428906i	$-0.858899\pi$
$701$		−	22.7118i		−	0.857812i	0.903349	−	0.428906i	$-0.141101\pi$
$702$	−1.96624	−	3.02223i	−0.0742110	−	0.114067i
$703$	−27.0602	+	15.6232i	−1.02059	+	0.589240i
$704$	−4.12568	−	4.12568i	−0.155492	−	0.155492i
$705$	15.9876	−	9.23045i	0.602128	−	0.347639i
$706$	12.2289	+	21.1811i	0.460241	+	0.797160i
$707$	12.0737	−	29.2726i	0.454078	−	1.10091i
$708$	0.225806	−	0.842719i	0.00848630	−	0.0316713i
$709$	15.5796	−	15.5796i	0.585105	−	0.585105i	−0.351197	−	0.936302i	$-0.614225\pi$
$709$	15.5796	−	15.5796i	0.585105	−	0.585105i	0.936302	+	0.351197i	$0.114225\pi$
$710$	2.01374	−	7.51537i	0.0755742	−	0.282047i
$711$	3.96454	−	6.86679i	0.148682	−	0.257525i
$712$	−4.45858	−	7.72249i	−0.167092	−	0.289413i
$713$	−0.291773	+	0.0781804i	−0.0109270	+	0.00292788i
$714$	7.05593	+	16.9625i	0.264062	+	0.634806i
$715$	−9.63358	−	29.5653i	−0.360275	−	1.10568i
$716$	5.22088	−	9.04284i	0.195114	−	0.337947i
$717$	1.66598	−	1.66598i	0.0622171	−	0.0622171i
$718$	−24.0257			−0.896630
$719$	22.5463			0.840835			0.420417	−	0.907331i	$-0.361884\pi$
$719$	22.5463			0.840835			0.420417	+	0.907331i	$0.361884\pi$
$720$	−1.04519	+	1.04519i	−0.0389520	+	0.0389520i
$721$	20.6707	+	26.8551i	0.769819	+	1.00014i
$722$	−9.06689	−	2.42947i	−0.337435	−	0.0904154i
$723$	3.84511	+	14.3501i	0.143001	+	0.533687i
$724$	−1.04909	−	0.605691i	−0.0389890	−	0.0225103i
$725$			24.5311i			0.911063i
$726$	5.96384	−	22.2573i	0.221339	−	0.826047i
$727$	22.2011			0.823394			0.411697	−	0.911321i	$-0.364936\pi$
$727$	22.2011			0.823394			0.411697	+	0.911321i	$0.364936\pi$
$728$	3.16333	−	8.99963i	0.117241	−	0.333549i
$729$	−1.00000			−0.0370370
$730$	3.54428	−	13.2274i	0.131180	−	0.489569i
$731$		−	1.14581i		−	0.0423791i
$732$	4.89047	+	2.82351i	0.180757	+	0.104360i
$733$	−6.11108	−	22.8069i	−0.225718	−	0.842390i	−0.982116	−	0.188279i	$-0.939709\pi$
$733$	−6.11108	−	22.8069i	−0.225718	−	0.842390i	0.756398	−	0.654112i	$-0.226957\pi$
$734$	6.82318	+	1.82827i	0.251848	+	0.0674825i
$735$	−8.97613	−	5.14653i	−0.331090	−	0.189833i
$736$	0.544153	−	0.544153i	0.0200577	−	0.0200577i
$737$	−27.9063			−1.02794
$738$	−6.57353			−0.241975
$739$	−17.7024	+	17.7024i	−0.651192	+	0.651192i	−0.953280	−	0.302088i	$-0.902316\pi$
$739$	−17.7024	+	17.7024i	−0.651192	+	0.651192i	0.302088	+	0.953280i	$0.402316\pi$
$740$	4.33434	−	7.50731i	0.159334	−	0.275974i
$741$	1.02136	+	19.1829i	0.0375205	+	0.704702i
$742$	3.03694	−	23.3383i	0.111490	−	0.856778i
$743$	−13.5455	+	3.62950i	−0.496936	+	0.133154i	−0.498578	−	0.866845i	$-0.666144\pi$
$743$	−13.5455	+	3.62950i	−0.496936	+	0.133154i	0.00164161	+	0.999999i	$0.499477\pi$
$744$	0.196262	+	0.339935i	0.00719530	+	0.0124626i
$745$	7.72095	−	13.3731i	0.282874	−	0.489952i
$746$	−2.90111	+	10.8271i	−0.106217	+	0.396408i
$747$	−9.29167	+	9.29167i	−0.339965	+	0.339965i
$748$	−10.4858	+	39.1337i	−0.383400	+	1.43087i
$749$	6.97411	−	0.928804i	0.254828	−	0.0339378i
$750$	−5.77588	−	10.0041i	−0.210905	−	0.365299i
$751$	−27.8132	+	16.0580i	−1.01492	+	0.585964i	−0.912628	−	0.408791i	$-0.865951\pi$
$751$	−27.8132	+	16.0580i	−1.01492	+	0.585964i	−0.102291	+	0.994755i	$0.532617\pi$
$752$	8.83135	+	8.83135i	0.322046	+	0.322046i
$753$	9.89703	−	5.71406i	0.360668	−	0.208232i
$754$	1.67046	+	31.3742i	0.0608346	+	1.14258i
$755$		−	6.63701i		−	0.241545i
$756$	−1.61378	−	2.09660i	−0.0586925	−	0.0762525i
$757$	1.29840	−	2.24889i	0.0471910	−	0.0817372i	−0.841465	−	0.540312i	$-0.818306\pi$
$757$	1.29840	−	2.24889i	0.0471910	−	0.0817372i	0.888656	+	0.458574i	$0.151640\pi$
$758$		−	3.24959i		−	0.118031i
$759$	4.33701	+	1.16210i	0.157424	+	0.0421815i
$760$	7.60698	−	2.03829i	0.275934	−	0.0739364i
$761$	−10.2208	−	10.2208i	−0.370504	−	0.370504i	0.497157	−	0.867661i	$-0.334377\pi$
$761$	−10.2208	−	10.2208i	−0.370504	−	0.370504i	−0.867661	+	0.497157i	$0.834377\pi$
$762$	−7.36119	−	7.36119i	−0.266668	−	0.266668i
$763$	−31.5013	−	24.0968i	−1.14042	−	0.872362i
$764$	21.5502	+	12.4420i	0.779658	+	0.450136i
$765$	9.91405	+	2.65646i	0.358443	+	0.0960445i
$766$	−2.97448	−	5.15195i	−0.107472	−	0.186148i
$767$	2.80399	+	1.42576i	0.101246	+	0.0514812i
$768$	−0.866025	−	0.500000i	−0.0312500	−	0.0180422i
$769$	5.20930	+	19.4414i	0.187852	+	0.701074i	0.994002	+	0.109363i	$0.0348809\pi$
$769$	5.20930	+	19.4414i	0.187852	+	0.701074i	−0.806150	+	0.591712i	$0.798452\pi$
$770$	−8.76354	−	21.0676i	−0.315816	−	0.759225i
$771$	8.25015	−	4.76323i	0.297122	−	0.171543i
$772$	17.9106	−	4.79914i	0.644618	−	0.172725i
$773$	−6.98843	−	26.0812i	−0.251356	−	0.938075i	−0.970081	−	0.242780i	$-0.921941\pi$
$773$	−6.98843	−	26.0812i	−0.251356	−	0.938075i	0.718725	−	0.695294i	$-0.244726\pi$
$774$	0.0427082	+	0.159389i	0.00153511	+	0.00572912i
$775$	−1.06736	+	0.285998i	−0.0383407	+	0.0102733i
$776$	0.764025	−	0.441110i	0.0274269	−	0.0158349i
$777$	12.3242	+	9.42732i	0.442127	+	0.338203i
$778$	−2.39341	−	8.93234i	−0.0858080	−	0.320240i
$779$	30.3310	+	17.5116i	1.08672	+	0.627419i
$780$	−2.90635	−	4.46724i	−0.104064	−	0.159953i
$781$	15.3559	+	26.5972i	0.549478	+	0.951724i
$782$	−5.16150	−	1.38302i	−0.184575	−	0.0494567i
$783$	7.54652	+	4.35699i	0.269691	+	0.155706i
$784$	1.79144	−	6.76689i	0.0639800	−	0.241674i
$785$	−15.3785	−	15.3785i	−0.548881	−	0.548881i
$786$	−2.78834	−	2.78834i	−0.0994567	−	0.0994567i
$787$	28.8301	−	7.72500i	1.02768	−	0.275367i	0.294682	−	0.955595i	$-0.404786\pi$
$787$	28.8301	−	7.72500i	1.02768	−	0.275367i	0.733000	+	0.680229i	$0.238120\pi$
$788$	−0.939199	−	0.251658i	−0.0334576	−	0.00896493i
$789$			23.1506i			0.824182i
$790$	5.86009	−	10.1500i	0.208492	−	0.361120i
$791$	−26.0053	+	3.46335i	−0.924641	+	0.123143i
$792$		−	5.83459i		−	0.207323i
$793$	−13.6113	+	15.1422i	−0.483352	+	0.537717i
$794$	8.81322	−	5.08832i	0.312770	−	0.180578i
$795$	−9.29744	−	9.29744i	−0.329746	−	0.329746i
$796$	1.01469	−	0.585830i	0.0359647	−	0.0207642i
$797$	−8.82062	−	15.2778i	−0.312442	−	0.541166i	0.666448	−	0.745551i	$-0.267814\pi$
$797$	−8.82062	−	15.2778i	−0.312442	−	0.541166i	−0.978891	+	0.204385i	$0.934480\pi$
$798$	1.86091	+	13.9730i	0.0658753	+	0.494638i
$799$	22.4458	−	83.7687i	0.794074	−	2.96352i
$800$	1.99061	−	1.99061i	0.0703787	−	0.0703787i
$801$	2.30793	−	8.61332i	0.0815468	−	0.304337i
$802$	5.55257	−	9.61733i	0.196068	−	0.339600i
$803$	27.0272	+	46.8125i	0.953769	+	1.65198i
$804$	−4.61993	+	1.23791i	−0.162932	+	0.0436576i
$805$	2.77870	−	1.15586i	0.0979362	−	0.0407387i
$806$	−1.34563	+	0.438461i	−0.0473978	+	0.0154441i
$807$	13.7436	−	23.8047i	0.483799	−	0.837965i
$808$	8.46277	−	8.46277i	0.297719	−	0.297719i
$809$	−11.9756			−0.421041			−0.210520	−	0.977589i	$-0.567516\pi$
$809$	−11.9756			−0.421041			−0.210520	+	0.977589i	$0.567516\pi$
$810$	−1.47812			−0.0519360
$811$	20.9279	−	20.9279i	0.734877	−	0.734877i	−0.236704	−	0.971582i	$-0.576067\pi$
$811$	20.9279	−	20.9279i	0.734877	−	0.734877i	0.971582	+	0.236704i	$0.0760673\pi$
$812$	3.04357	+	22.8532i	0.106808	+	0.801991i
$813$	−26.9875	−	7.23129i	−0.946494	−	0.253612i
$814$	8.85624	+	33.0519i	0.310411	+	1.15847i
$815$	29.4232	+	16.9875i	1.03065	+	0.595045i
$816$			6.94378i			0.243081i
$817$	0.227546	−	0.849212i	0.00796082	−	0.0297102i
$818$	12.9533			0.452901
$819$	8.60051	−	4.12689i	0.300526	−	0.144205i
$820$	−9.71649			−0.339315
$821$	−2.26668	+	8.45935i	−0.0791076	+	0.295233i	−0.994133	−	0.108162i	$-0.965503\pi$
$821$	−2.26668	+	8.45935i	−0.0791076	+	0.295233i	0.915026	+	0.403396i	$0.132170\pi$
$822$		−	2.85691i		−	0.0996463i
$823$	−37.2224	−	21.4904i	−1.29749	−	0.749108i	−0.317522	−	0.948251i	$-0.602851\pi$
$823$	−37.2224	−	21.4904i	−1.29749	−	0.749108i	−0.979970	+	0.199143i	$0.936184\pi$
$824$	3.31519	+	12.3725i	0.115490	+	0.431015i
$825$	15.8656	+	4.25117i	0.552368	+	0.148007i
$826$	2.13389	+	0.880140i	0.0742476	+	0.0306240i
$827$	38.0028	−	38.0028i	1.32149	−	1.32149i	0.408915	−	0.912572i	$-0.365907\pi$
$827$	38.0028	−	38.0028i	1.32149	−	1.32149i	0.912572	−	0.408915i	$-0.134093\pi$
$828$	0.769549			0.0267437
$829$	−25.7479			−0.894262			−0.447131	−	0.894468i	$-0.647554\pi$
$829$	−25.7479			−0.894262			−0.447131	+	0.894468i	$0.647554\pi$
$830$	−13.7342	+	13.7342i	−0.476723	+	0.476723i
$831$	4.18966	−	7.25671i	0.145338	−	0.251732i
$832$	2.41035	−	2.68146i	0.0835639	−	0.0929627i
$833$	−46.9123	+	12.7211i	−1.62541	+	0.440759i
$834$	−9.23162	+	2.47361i	−0.319665	+	0.0856539i
$835$	0.628445	+	1.08850i	0.0217482	+	0.0376691i
$836$	−15.5431	+	26.9215i	−0.537570	+	0.931099i
$837$	−0.101593	+	0.379148i	−0.00351155	+	0.0131053i
$838$	15.9573	−	15.9573i	0.551236	−	0.551236i
$839$	−4.51723	+	16.8585i	−0.155952	+	0.582021i	0.843070	+	0.537804i	$0.180746\pi$
$839$	−4.51723	+	16.8585i	−0.155952	+	0.582021i	−0.999022	+	0.0442169i	$0.985921\pi$
$840$	−2.38537	−	3.09903i	−0.0823029	−	0.106927i
$841$	−23.4667	−	40.6455i	−0.809196	−	1.40157i
$842$	−17.6384	+	10.1835i	−0.607859	+	0.350947i
$843$	−2.04772	−	2.04772i	−0.0705271	−	0.0705271i
$844$	−14.6058	+	8.43264i	−0.502751	+	0.290263i
$845$	17.9278	−	6.91614i	0.616736	−	0.237922i
$846$			12.4894i			0.429395i
$847$	56.3590	+	23.2457i	1.93652	+	0.798731i
$848$	4.44772	−	7.70367i	0.152735	−	0.264545i
$849$			0.899767i			0.0308799i
$850$	−18.8817	−	5.05934i	−0.647637	−	0.173534i
$851$	−4.35936	+	1.16809i	−0.149437	+	0.0400415i
$852$	3.72203	+	3.72203i	0.127515	+	0.127515i
$853$	29.2570	+	29.2570i	1.00174	+	1.00174i	0.999998	+	0.00174344i	$0.000554955\pi$
$853$	29.2570	+	29.2570i	1.00174	+	1.00174i	0.00174344	+	0.999998i	$0.499445\pi$
$854$	−9.07749	+	11.8668i	−0.310625	+	0.406074i
$855$	6.82024	+	3.93766i	0.233247	+	0.134665i
$856$	2.56863	+	0.688262i	0.0877939	+	0.0235243i
$857$	17.5657	+	30.4247i	0.600032	+	1.03929i	0.992815	+	0.119656i	$0.0381790\pi$
$857$	17.5657	+	30.4247i	0.600032	+	1.03929i	−0.392783	+	0.919631i	$0.628488\pi$
$858$	20.5809	+	4.35668i	0.702619	+	0.148735i
$859$	−16.7019	−	9.64284i	−0.569861	−	0.329009i	0.187233	−	0.982316i	$-0.440048\pi$
$859$	−16.7019	−	9.64284i	−0.569861	−	0.329009i	−0.757094	+	0.653306i	$0.773381\pi$
$860$	0.0631280	+	0.235597i	0.00215265	+	0.00803379i
$861$	2.24423	−	17.2465i	0.0764833	−	0.587760i
$862$	−1.61134	+	0.930307i	−0.0548824	+	0.0316864i
$863$	−10.6461	+	2.85260i	−0.362396	+	0.0971038i	−0.435422	−	0.900226i	$-0.643401\pi$
$863$	−10.6461	+	2.85260i	−0.362396	+	0.0971038i	0.0730262	+	0.997330i	$0.476734\pi$
$864$	−0.258819	−	0.965926i	−0.00880520	−	0.0328615i
$865$	−3.53225	−	13.1826i	−0.120100	−	0.448220i
$866$	32.1800	−	8.62261i	1.09352	−	0.293008i
$867$	27.0339	−	15.6081i	0.918121	−	0.530077i
$868$	−0.958869	+	0.398863i	−0.0325461	+	0.0135383i
$869$	11.9737	+	44.6866i	0.406181	+	1.51589i
$870$	11.1547	+	6.44017i	0.378180	+	0.218342i
$871$	−0.916878	−	17.2206i	−0.0310672	−	0.583498i
$872$	−7.49520	−	12.9821i	−0.253819	−	0.439628i
$873$	0.852159	+	0.228335i	0.0288412	+	0.00772798i
$874$	−3.55079	−	2.05005i	−0.120107	−	0.0693439i
$875$	28.2190	−	11.7383i	0.953978	−	0.396828i
$876$	6.55097	+	6.55097i	0.221337	+	0.221337i
$877$	−26.9855	−	26.9855i	−0.911236	−	0.911236i	0.0851336	−	0.996370i	$-0.472868\pi$
$877$	−26.9855	−	26.9855i	−0.911236	−	0.911236i	−0.996370	+	0.0851336i	$0.972868\pi$
$878$	23.5039	−	6.29784i	0.793217	−	0.212542i
$879$	−30.2510	−	8.10572i	−1.02034	−	0.273399i
$880$		−	8.62426i		−	0.290724i
$881$	−6.45418	+	11.1790i	−0.217447	+	0.376629i	−0.954027	−	0.299721i	$-0.903106\pi$
$881$	−6.45418	+	11.1790i	−0.217447	+	0.376629i	0.736580	+	0.676351i	$0.236440\pi$
$882$	6.05165	−	3.51817i	0.203770	−	0.118463i
$883$		−	28.8060i		−	0.969399i	−0.874681	−	0.484700i	$-0.838929\pi$
$883$		−	28.8060i		−	0.969399i	0.874681	−	0.484700i	$-0.161071\pi$
$884$	−24.4934	−	5.18491i	−0.823802	−	0.174387i
$885$	1.11681	−	0.644793i	0.0375413	−	0.0216745i
$886$	−22.0234	−	22.0234i	−0.739890	−	0.739890i
$887$	−1.11304	+	0.642613i	−0.0373722	+	0.0215768i	−0.518570	−	0.855035i	$-0.673535\pi$
$887$	−1.11304	+	0.642613i	−0.0373722	+	0.0215768i	0.481197	+	0.876612i	$0.340202\pi$
$888$	2.93233	+	5.07894i	0.0984025	+	0.170438i
$889$	21.8262	−	16.7999i	0.732027	−	0.563451i
$890$	3.41141	−	12.7316i	0.114351	−	0.426763i
$891$	4.12568	−	4.12568i	0.138216	−	0.138216i
$892$	−0.0655089	+	0.244483i	−0.00219340	+	0.00818589i
$893$	33.2713	−	57.6276i	1.11338	−	1.92843i
$894$	5.22348	+	9.04733i	0.174699	+	0.302588i
$895$	14.9083	−	3.99467i	0.498330	−	0.133527i
$896$	1.60748	−	2.10143i	0.0537022	−	0.0702038i
$897$	−0.574621	+	2.71449i	−0.0191860	+	0.0906343i
$898$	−5.74605	+	9.95245i	−0.191748	+	0.332118i
$899$	2.41862	−	2.41862i	0.0806653	−	0.0806653i
$900$	2.81515			0.0938383
$901$	−61.7680			−2.05779
$902$	27.1203	−	27.1203i	0.903007	−	0.903007i
$903$	−0.432759	+	0.0576343i	−0.0144013	+	0.00191795i
$904$	−9.57798	−	2.56641i	−0.318559	−	0.0853576i
$905$	−0.463435	−	1.72956i	−0.0154051	−	0.0574926i
$906$	3.88859	+	2.24508i	0.129190	+	0.0745877i
$907$		−	40.3811i		−	1.34083i	−0.741986	−	0.670415i	$-0.766116\pi$
$907$		−	40.3811i		−	1.34083i	0.741986	−	0.670415i	$-0.233884\pi$
$908$	−0.432323	+	1.61345i	−0.0143471	+	0.0535442i
$909$	11.9682			0.396959
$910$	12.7126	−	6.10006i	0.421419	−	0.202215i
$911$	15.9440			0.528249			0.264124	−	0.964489i	$-0.414917\pi$
$911$	15.9440			0.528249			0.264124	+	0.964489i	$0.414917\pi$
$912$	−1.37897	+	5.14638i	−0.0456622	+	0.170414i
$913$		−	76.6690i		−	2.53737i
$914$	33.0564	+	19.0851i	1.09341	+	0.631280i
$915$	2.16036	+	8.06259i	0.0714195	+	0.266541i
$916$	−25.9161	−	6.94421i	−0.856294	−	0.229443i
$917$	8.26752	−	6.36362i	0.273018	−	0.210145i
$918$	−4.91000	+	4.91000i	−0.162054	+	0.162054i
$919$	46.8890			1.54672			0.773362	−	0.633964i	$-0.218573\pi$
$919$	46.8890			1.54672			0.773362	+	0.633964i	$0.218573\pi$
$920$	1.13749			0.0375019
$921$	6.31072	−	6.31072i	0.207945	−	0.207945i
$922$	3.27171	−	5.66676i	0.107748	−	0.186625i
$923$	−15.9083	+	10.3498i	−0.523627	+	0.340668i
$924$	15.3078	+	1.99196i	0.503591	+	0.0655306i
$925$	−15.9473	+	4.27307i	−0.524344	+	0.140498i
$926$	7.47525	+	12.9475i	0.245652	+	0.425482i
$927$	−6.40446	+	11.0928i	−0.210350	+	0.364337i
$928$	−2.25534	+	8.41705i	−0.0740353	+	0.276303i
$929$	18.1178	−	18.1178i	0.594426	−	0.594426i	−0.344398	−	0.938824i	$-0.611917\pi$
$929$	18.1178	−	18.1178i	0.594426	−	0.594426i	0.938824	+	0.344398i	$0.111917\pi$
$930$	−0.150166	+	0.560429i	−0.00492415	+	0.0183772i
$931$	−37.2953	+	0.111889i	−1.22230	+	0.00366701i
$932$	8.39675	+	14.5436i	0.275045	+	0.476391i
$933$	−1.48276	+	0.856069i	−0.0485432	+	0.0280264i
$934$	1.07922	+	1.07922i	0.0353132	+	0.0353132i
$935$	−51.8619	+	29.9425i	−1.69607	+	0.979224i
$936$	3.60045	−	0.191699i	0.117684	−	0.00626588i
$937$			9.10555i			0.297465i	0.988877	+	0.148733i	$0.0475194\pi$
$937$			9.10555i			0.297465i	−0.988877	+	0.148733i	$0.952481\pi$
$938$	−1.67054	−	12.5436i	−0.0545452	−	0.409564i
$939$	6.33634	−	10.9749i	0.206779	−	0.358151i
$940$			18.4609i			0.602128i
$941$	−9.85714	−	2.64121i	−0.321333	−	0.0861010i	0.0945468	−	0.995520i	$-0.469860\pi$
$941$	−9.85714	−	2.64121i	−0.321333	−	0.0861010i	−0.415880	+	0.909419i	$0.636526\pi$
$942$	14.2122	−	3.80814i	0.463058	−	0.124076i
$943$	3.57701	+	3.57701i	0.116483	+	0.116483i
$944$	0.616913	+	0.616913i	0.0200788	+	0.0200788i
$945$	0.504639	−	3.87805i	0.0164159	−	0.126153i
$946$	−0.833789	−	0.481388i	−0.0271088	−	0.0156513i
$947$	1.13320	+	0.303640i	0.0368240	+	0.00986696i	0.277184	−	0.960817i	$-0.410599\pi$
$947$	1.13320	+	0.303640i	0.0368240	+	0.00986696i	−0.240360	+	0.970684i	$0.577265\pi$
$948$	3.96454	+	6.86679i	0.128762	+	0.223023i
$949$	−27.9994	+	18.2162i	−0.908898	+	0.591322i
$950$	−12.9894	−	7.49944i	−0.421432	−	0.243314i
$951$	3.56867	+	13.3185i	0.115722	+	0.431881i
$952$	−18.2179	−	2.37064i	−0.590446	−	0.0768329i
$953$	−33.2954	+	19.2231i	−1.07855	+	0.622698i	−0.930504	−	0.366283i	$-0.880630\pi$
$953$	−33.2954	+	19.2231i	−1.07855	+	0.622698i	−0.148042	+	0.988981i	$0.547297\pi$
$954$	8.59233	−	2.30231i	0.278187	−	0.0745400i
$955$	9.51979	+	35.5283i	0.308053	+	1.14967i
$956$	0.609791	+	2.27577i	0.0197220	+	0.0736037i
$957$	−49.1101	+	13.1590i	−1.58750	+	0.425370i
$958$	3.03129	−	1.75011i	0.0979364	−	0.0565436i
$959$	7.49549	+	0.975363i	0.242042	+	0.0314961i
$960$	−0.382567	−	1.42776i	−0.0123473	−	0.0460807i
$961$	−26.7134	−	15.4230i	−0.861721	−	0.497515i
$962$	−20.1049	+	6.55101i	−0.648209	+	0.211213i
$963$	1.32962	+	2.30297i	0.0428464	+	0.0742121i
$964$	−14.3501	−	3.84511i	−0.462187	−	0.123843i
$965$	23.7361	+	13.7040i	0.764092	+	0.441148i
$966$	−0.262728	+	2.01901i	−0.00845312	+	0.0649607i
$967$	16.9249	+	16.9249i	0.544268	+	0.544268i	0.924777	−	0.380509i	$-0.124251\pi$
$967$	16.9249	+	16.9249i	0.544268	+	0.544268i	−0.380509	+	0.924777i	$0.624251\pi$
$968$	16.2935	+	16.2935i	0.523693	+	0.523693i
$969$	35.7353	−	9.57525i	1.14798	−	0.307601i
$970$	1.25960	+	0.337508i	0.0404432	+	0.0108367i
$971$		−	23.3288i		−	0.748655i	−0.927296	−	0.374328i	$-0.877874\pi$
$971$		−	23.3288i		−	0.748655i	0.927296	−	0.374328i	$-0.122126\pi$
$972$	0.500000	−	0.866025i	0.0160375	−	0.0277778i
$973$	−3.33811	−	25.0649i	−0.107015	−	0.803543i
$974$			4.37167i			0.140077i
$975$	−2.10207	+	9.93011i	−0.0673200	+	0.318018i
$976$	−4.89047	+	2.82351i	−0.156540	+	0.0903785i
$977$	−23.5713	−	23.5713i	−0.754113	−	0.754113i	0.221131	−	0.975244i	$-0.429025\pi$
$977$	−23.5713	−	23.5713i	−0.754113	−	0.754113i	−0.975244	+	0.221131i	$0.929025\pi$
$978$	−19.9058	+	11.4926i	−0.636516	+	0.367493i
$979$	26.0140	+	45.0576i	0.831412	+	1.44005i
$980$	8.94509	−	5.20030i	0.285741	−	0.166117i
$981$	3.87980	−	14.4796i	0.123872	−	0.462298i
$982$	0.272068	−	0.272068i	0.00868203	−	0.00868203i
$983$	8.00802	−	29.8863i	0.255416	−	0.953226i	−0.712442	−	0.701731i	$-0.752411\pi$
$983$	8.00802	−	29.8863i	0.255416	−	0.953226i	0.967858	−	0.251495i	$-0.0809223\pi$
$984$	3.28676	−	5.69284i	0.104778	−	0.181481i
$985$	−0.718613	−	1.24467i	−0.0228969	−	0.0396586i
$986$	58.4462	−	15.6606i	1.86131	−	0.498735i
$987$	−32.7676	−	4.26394i	−1.04300	−	0.135723i
$988$	−17.1236	−	8.70694i	−0.544773	−	0.277005i
$989$	0.0634923	−	0.109972i	0.00201894	−	0.00349690i
$990$	6.09827	−	6.09827i	0.193816	−	0.193816i
$991$	−46.4827			−1.47657			−0.738285	−	0.674488i	$-0.764364\pi$
$991$	−46.4827			−1.47657			−0.738285	+	0.674488i	$0.764364\pi$
$992$	−0.392523			−0.0124626
$993$	−18.1988	+	18.1988i	−0.577522	+	0.577522i
$994$	−11.0360	+	8.49453i	−0.350040	+	0.269430i
$995$	1.67285	+	0.448238i	0.0530329	+	0.0142101i
$996$	−3.40099	−	12.6927i	−0.107764	−	0.402182i
$997$	−50.9890	−	29.4385i	−1.61484	−	0.932327i	−0.988227	−	0.152994i	$-0.951109\pi$
$997$	−50.9890	−	29.4385i	−1.61484	−	0.932327i	−0.626610	−	0.779333i	$-0.715558\pi$
$998$		−	8.48941i		−	0.268728i
$999$	−1.51788	+	5.66482i	−0.0480237	+	0.179227i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.by.b.397.7	✓	40
7.3	odd	6		546.2.cg.b.241.7	yes	40
13.2	odd	12		546.2.cg.b.145.7	yes	40
91.80	even	12	inner	546.2.by.b.535.7	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.by.b.397.7	✓	40	1.1	even	1	trivial
546.2.by.b.535.7	yes	40	91.80	even	12	inner
546.2.cg.b.145.7	yes	40	13.2	odd	12
546.2.cg.b.241.7	yes	40	7.3	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.by (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 - 0.965926i) q^{2} +1.00000i q^{3} +(-0.866025 - 0.500000i) q^{4} +(-0.382567 - 1.42776i) q^{5} +(0.965926 + 0.258819i) q^{6} +(-1.00882 + 2.44587i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(0.258819 - 0.965926i) q^{2} +1.00000i q^{3} +(-0.866025 - 0.500000i) q^{4} +(-0.382567 - 1.42776i) q^{5} +(0.965926 + 0.258819i) q^{6} +(-1.00882 + 2.44587i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.00000 q^{9} -1.47812 q^{10} +(4.12568 - 4.12568i) q^{11} +(0.500000 - 0.866025i) q^{12} +(2.68146 + 2.41035i) q^{13} +(2.10143 + 1.60748i) q^{14} +(1.42776 - 0.382567i) q^{15} +(0.500000 + 0.866025i) q^{16} +(3.47189 - 6.01349i) q^{17} +(-0.258819 + 0.965926i) q^{18} +(3.76741 - 3.76741i) q^{19} +(-0.382567 + 1.42776i) q^{20} +(-2.44587 - 1.00882i) q^{21} +(-2.91730 - 5.05291i) q^{22} +(0.666449 - 0.384774i) q^{23} +(-0.707107 - 0.707107i) q^{24} +(2.43799 - 1.40757i) q^{25} +(3.02223 - 1.96624i) q^{26} -1.00000i q^{27} +(2.09660 - 1.61378i) q^{28} +(-4.35699 + 7.54652i) q^{29} -1.47812i q^{30} +(-0.379148 - 0.101593i) q^{31} +(0.965926 - 0.258819i) q^{32} +(4.12568 + 4.12568i) q^{33} +(-4.91000 - 4.91000i) q^{34} +(3.87805 + 0.504639i) q^{35} +(0.866025 + 0.500000i) q^{36} +(-5.66482 - 1.51788i) q^{37} +(-2.66396 - 4.61411i) q^{38} +(-2.41035 + 2.68146i) q^{39} +(1.28009 + 0.739062i) q^{40} +(1.70135 + 6.34954i) q^{41} +(-1.60748 + 2.10143i) q^{42} +(0.142904 - 0.0825059i) q^{43} +(-5.63579 + 1.51010i) q^{44} +(0.382567 + 1.42776i) q^{45} +(-0.199174 - 0.743327i) q^{46} +(12.0638 - 3.23250i) q^{47} +(-0.866025 + 0.500000i) q^{48} +(-4.96457 - 4.93488i) q^{49} +(-0.728614 - 2.71922i) q^{50} +(6.01349 + 3.47189i) q^{51} +(-1.11703 - 3.42815i) q^{52} +(-4.44772 - 7.70367i) q^{53} +(-0.965926 - 0.258819i) q^{54} +(-7.46883 - 4.31213i) q^{55} +(-1.01615 - 2.44283i) q^{56} +(3.76741 + 3.76741i) q^{57} +(6.16171 + 6.16171i) q^{58} +(0.842719 - 0.225806i) q^{59} +(-1.42776 - 0.382567i) q^{60} +5.64703i q^{61} +(-0.196262 + 0.339935i) q^{62} +(1.00882 - 2.44587i) q^{63} -1.00000i q^{64} +(2.41556 - 4.75059i) q^{65} +(5.05291 - 2.91730i) q^{66} +(-3.38202 - 3.38202i) q^{67} +(-6.01349 + 3.47189i) q^{68} +(0.384774 + 0.666449i) q^{69} +(1.49116 - 3.61530i) q^{70} +(-1.36236 + 5.08439i) q^{71} +(0.707107 - 0.707107i) q^{72} +(-2.39782 + 8.94879i) q^{73} +(-2.93233 + 5.07894i) q^{74} +(1.40757 + 2.43799i) q^{75} +(-5.14638 + 1.37897i) q^{76} +(5.92883 + 14.2529i) q^{77} +(1.96624 + 3.02223i) q^{78} +(-3.96454 + 6.86679i) q^{79} +(1.04519 - 1.04519i) q^{80} +1.00000 q^{81} +6.57353 q^{82} +(9.29167 - 9.29167i) q^{83} +(1.61378 + 2.09660i) q^{84} +(-9.91405 - 2.65646i) q^{85} +(-0.0427082 - 0.159389i) q^{86} +(-7.54652 - 4.35699i) q^{87} +5.83459i q^{88} +(-2.30793 + 8.61332i) q^{89} +1.47812 q^{90} +(-8.60051 + 4.12689i) q^{91} -0.769549 q^{92} +(0.101593 - 0.379148i) q^{93} -12.4894i q^{94} +(-6.82024 - 3.93766i) q^{95} +(0.258819 + 0.965926i) q^{96} +(-0.852159 - 0.228335i) q^{97} +(-6.05165 + 3.51817i) q^{98} +(-4.12568 + 4.12568i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{7} - 40 q^{9}+O(q^{10}) \) 40 * q - 4 * q^7 - 40 * q^9	\( 40 q - 4 q^{7} - 40 q^{9} - 4 q^{11} + 20 q^{12} + 4 q^{14} + 20 q^{16} + 8 q^{17} + 8 q^{19} - 8 q^{21} - 4 q^{22} + 24 q^{23} + 24 q^{25} - 8 q^{26} + 4 q^{28} - 12 q^{29} + 24 q^{31} - 4 q^{33} + 8 q^{34} + 28 q^{35} - 8 q^{37} - 8 q^{38} - 16 q^{39} - 20 q^{41} - 12 q^{42} - 24 q^{43} + 8 q^{44} - 4 q^{46} - 16 q^{47} + 4 q^{49} - 16 q^{50} - 24 q^{51} - 4 q^{52} - 4 q^{53} - 24 q^{55} + 12 q^{56} + 8 q^{57} + 24 q^{58} - 12 q^{59} - 32 q^{62} + 4 q^{63} - 4 q^{65} - 24 q^{67} + 24 q^{68} + 8 q^{69} + 52 q^{70} - 28 q^{71} + 108 q^{73} + 20 q^{74} - 36 q^{75} - 4 q^{76} + 12 q^{77} + 4 q^{78} + 40 q^{81} - 48 q^{82} - 60 q^{83} - 8 q^{84} - 4 q^{85} - 20 q^{86} - 36 q^{87} - 60 q^{89} - 40 q^{91} - 16 q^{92} - 48 q^{95} + 48 q^{97} - 8 q^{98} + 4 q^{99}+O(q^{100}) \) 40 * q - 4 * q^7 - 40 * q^9 - 4 * q^11 + 20 * q^12 + 4 * q^14 + 20 * q^16 + 8 * q^17 + 8 * q^19 - 8 * q^21 - 4 * q^22 + 24 * q^23 + 24 * q^25 - 8 * q^26 + 4 * q^28 - 12 * q^29 + 24 * q^31 - 4 * q^33 + 8 * q^34 + 28 * q^35 - 8 * q^37 - 8 * q^38 - 16 * q^39 - 20 * q^41 - 12 * q^42 - 24 * q^43 + 8 * q^44 - 4 * q^46 - 16 * q^47 + 4 * q^49 - 16 * q^50 - 24 * q^51 - 4 * q^52 - 4 * q^53 - 24 * q^55 + 12 * q^56 + 8 * q^57 + 24 * q^58 - 12 * q^59 - 32 * q^62 + 4 * q^63 - 4 * q^65 - 24 * q^67 + 24 * q^68 + 8 * q^69 + 52 * q^70 - 28 * q^71 + 108 * q^73 + 20 * q^74 - 36 * q^75 - 4 * q^76 + 12 * q^77 + 4 * q^78 + 40 * q^81 - 48 * q^82 - 60 * q^83 - 8 * q^84 - 4 * q^85 - 20 * q^86 - 36 * q^87 - 60 * q^89 - 40 * q^91 - 16 * q^92 - 48 * q^95 + 48 * q^97 - 8 * q^98 + 4 * q^99

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