LMFDB - Embedded newform 546.2.by.a.397.4

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:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			397.4
Character	$\chi$	$=$	546.397
Dual form			546.2.by.a.535.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 + 0.965926i) q^{2} -1.00000i q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.782522 + 2.92041i) q^{5} +(0.965926 + 0.258819i) q^{6} +(1.58056 + 2.12175i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(-0.258819 + 0.965926i) q^{2} -1.00000i q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.782522 + 2.92041i) q^{5} +(0.965926 + 0.258819i) q^{6} +(1.58056 + 2.12175i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000 q^{9} -3.02343 q^{10} +(-1.55872 + 1.55872i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(1.15303 - 3.41621i) q^{13} +(-2.45853 + 0.977554i) q^{14} +(2.92041 - 0.782522i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-2.40096 + 4.15859i) q^{17} +(0.258819 - 0.965926i) q^{18} +(-2.01814 + 2.01814i) q^{19} +(0.782522 - 2.92041i) q^{20} +(2.12175 - 1.58056i) q^{21} +(-1.10218 - 1.90904i) q^{22} +(-0.721017 + 0.416279i) q^{23} +(-0.707107 - 0.707107i) q^{24} +(-3.58634 + 2.07057i) q^{25} +(3.00138 + 1.99792i) q^{26} +1.00000i q^{27} +(-0.307929 - 2.62777i) q^{28} +(0.310629 - 0.538026i) q^{29} +3.02343i q^{30} +(2.04496 + 0.547944i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(1.55872 + 1.55872i) q^{33} +(-3.39547 - 3.39547i) q^{34} +(-4.95957 + 6.27620i) q^{35} +(0.866025 + 0.500000i) q^{36} +(3.98822 + 1.06864i) q^{37} +(-1.42704 - 2.47170i) q^{38} +(-3.41621 - 1.15303i) q^{39} +(2.61837 + 1.51172i) q^{40} +(2.82732 + 10.5517i) q^{41} +(0.977554 + 2.45853i) q^{42} +(-5.69185 + 3.28619i) q^{43} +(2.12926 - 0.570532i) q^{44} +(-0.782522 - 2.92041i) q^{45} +(-0.215482 - 0.804190i) q^{46} +(3.82672 - 1.02537i) q^{47} +(0.866025 - 0.500000i) q^{48} +(-2.00366 + 6.70711i) q^{49} +(-1.07181 - 4.00004i) q^{50} +(4.15859 + 2.40096i) q^{51} +(-2.70666 + 2.38201i) q^{52} +(5.61789 + 9.73048i) q^{53} +(-0.965926 - 0.258819i) q^{54} +(-5.77185 - 3.33238i) q^{55} +(2.61793 + 0.382681i) q^{56} +(2.01814 + 2.01814i) q^{57} +(0.439296 + 0.439296i) q^{58} +(-7.61175 + 2.03956i) q^{59} +(-2.92041 - 0.782522i) q^{60} -7.60468i q^{61} +(-1.05855 + 1.83346i) q^{62} +(-1.58056 - 2.12175i) q^{63} -1.00000i q^{64} +(10.8790 + 0.694061i) q^{65} +(-1.90904 + 1.10218i) q^{66} +(-5.74537 - 5.74537i) q^{67} +(4.15859 - 2.40096i) q^{68} +(0.416279 + 0.721017i) q^{69} +(-4.77872 - 6.41497i) q^{70} +(2.25799 - 8.42695i) q^{71} +(-0.707107 + 0.707107i) q^{72} +(4.17659 - 15.5872i) q^{73} +(-2.06446 + 3.57574i) q^{74} +(2.07057 + 3.58634i) q^{75} +(2.75683 - 0.738690i) q^{76} +(-5.77088 - 0.843569i) q^{77} +(1.99792 - 3.00138i) q^{78} +(0.859183 - 1.48815i) q^{79} +(-2.13789 + 2.13789i) q^{80} +1.00000 q^{81} -10.9239 q^{82} +(12.5964 - 12.5964i) q^{83} +(-2.62777 + 0.307929i) q^{84} +(-14.0236 - 3.75761i) q^{85} +(-1.70106 - 6.34844i) q^{86} +(-0.538026 - 0.310629i) q^{87} +2.20437i q^{88} +(1.91835 - 7.15939i) q^{89} +3.02343 q^{90} +(9.07079 - 2.95309i) q^{91} +0.832559 q^{92} +(0.547944 - 2.04496i) q^{93} +3.96171i q^{94} +(-7.47303 - 4.31456i) q^{95} +(0.258819 + 0.965926i) q^{96} +(11.7346 + 3.14428i) q^{97} +(-5.95999 - 3.67132i) q^{98} +(1.55872 - 1.55872i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 8 q^{7} - 32 q^{9}+O(q^{10}) $ 32 * q + 8 * q^7 - 32 * q^9	$ 32 q + 8 q^{7} - 32 q^{9} - 4 q^{11} - 16 q^{12} + 4 q^{14} + 16 q^{16} - 8 q^{17} - 12 q^{19} - 8 q^{21} - 4 q^{22} - 24 q^{23} - 24 q^{25} + 8 q^{26} - 4 q^{28} - 12 q^{29} - 28 q^{31} + 4 q^{33} - 8 q^{34} - 44 q^{35} - 36 q^{37} + 8 q^{38} - 20 q^{39} - 28 q^{41} + 12 q^{42} + 84 q^{43} + 8 q^{44} - 4 q^{46} + 16 q^{47} + 24 q^{49} - 16 q^{50} + 8 q^{52} - 4 q^{53} + 48 q^{55} + 12 q^{56} + 12 q^{57} + 24 q^{58} + 12 q^{59} - 40 q^{62} - 8 q^{63} - 4 q^{65} + 8 q^{67} - 8 q^{69} + 60 q^{70} + 20 q^{71} + 4 q^{73} + 20 q^{74} + 8 q^{75} + 36 q^{76} - 12 q^{77} - 20 q^{78} + 32 q^{81} - 48 q^{82} + 12 q^{83} - 16 q^{84} - 4 q^{85} + 52 q^{86} - 36 q^{87} - 36 q^{89} - 16 q^{92} + 4 q^{93} - 48 q^{95} + 76 q^{97} + 8 q^{98} + 4 q^{99}+O(q^{100}) $ 32 * q + 8 * q^7 - 32 * q^9 - 4 * q^11 - 16 * q^12 + 4 * q^14 + 16 * q^16 - 8 * q^17 - 12 * q^19 - 8 * q^21 - 4 * q^22 - 24 * q^23 - 24 * q^25 + 8 * q^26 - 4 * q^28 - 12 * q^29 - 28 * q^31 + 4 * q^33 - 8 * q^34 - 44 * q^35 - 36 * q^37 + 8 * q^38 - 20 * q^39 - 28 * q^41 + 12 * q^42 + 84 * q^43 + 8 * q^44 - 4 * q^46 + 16 * q^47 + 24 * q^49 - 16 * q^50 + 8 * q^52 - 4 * q^53 + 48 * q^55 + 12 * q^56 + 12 * q^57 + 24 * q^58 + 12 * q^59 - 40 * q^62 - 8 * q^63 - 4 * q^65 + 8 * q^67 - 8 * q^69 + 60 * q^70 + 20 * q^71 + 4 * q^73 + 20 * q^74 + 8 * q^75 + 36 * q^76 - 12 * q^77 - 20 * q^78 + 32 * q^81 - 48 * q^82 + 12 * q^83 - 16 * q^84 - 4 * q^85 + 52 * q^86 - 36 * q^87 - 36 * q^89 - 16 * q^92 + 4 * q^93 - 48 * q^95 + 76 * 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
$5$	0.782522	+	2.92041i	0.349955	+	1.30605i	0.886716	+	0.462314i	$0.152981\pi$
$5$	0.782522	+	2.92041i	0.349955	+	1.30605i	−0.536762	+	0.843734i	$0.680353\pi$
$6$	0.965926	+	0.258819i	0.394338	+	0.105662i
$7$	1.58056	+	2.12175i	0.597395	+	0.801947i
$7$	1.58056	+	2.12175i	0.597395	+	0.801947i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−1.00000			−0.333333
$10$	−3.02343			−0.956093
$11$	−1.55872	+	1.55872i	−0.469973	+	0.469973i	−0.901906	−	0.431933i	$-0.857832\pi$
$11$	−1.55872	+	1.55872i	−0.469973	+	0.469973i	0.431933	+	0.901906i	$0.357832\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	1.15303	−	3.41621i	0.319793	−	0.947487i
$13$	1.15303	−	3.41621i	0.319793	−	0.947487i
$14$	−2.45853	+	0.977554i	−0.657071	+	0.261262i
$15$	2.92041	−	0.782522i	0.754047	−	0.202046i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−2.40096	+	4.15859i	−0.582319	+	1.00861i	0.412885	+	0.910783i	$0.364521\pi$
$17$	−2.40096	+	4.15859i	−0.582319	+	1.00861i	−0.995204	+	0.0978228i	$0.968812\pi$
$18$	0.258819	−	0.965926i	0.0610042	−	0.227671i
$19$	−2.01814	+	2.01814i	−0.462993	+	0.462993i	−0.899635	−	0.436642i	$-0.856168\pi$
$19$	−2.01814	+	2.01814i	−0.462993	+	0.462993i	0.436642	+	0.899635i	$0.356168\pi$
$20$	0.782522	−	2.92041i	0.174977	−	0.653024i
$21$	2.12175	−	1.58056i	0.463004	−	0.344906i
$22$	−1.10218	−	1.90904i	−0.234986	−	0.407008i
$23$	−0.721017	+	0.416279i	−0.150342	+	0.0868002i	−0.573284	−	0.819357i	$-0.694331\pi$
$23$	−0.721017	+	0.416279i	−0.150342	+	0.0868002i	0.422942	+	0.906157i	$0.360998\pi$
$24$	−0.707107	−	0.707107i	−0.144338	−	0.144338i
$25$	−3.58634	+	2.07057i	−0.717268	+	0.414115i
$26$	3.00138	+	1.99792i	0.588620	+	0.391825i
$27$			1.00000i			0.192450i
$28$	−0.307929	−	2.62777i	−0.0581931	−	0.496602i
$29$	0.310629	−	0.538026i	0.0576824	−	0.0999089i	−0.835742	−	0.549122i	$-0.814962\pi$
$29$	0.310629	−	0.538026i	0.0576824	−	0.0999089i	0.893425	+	0.449213i	$0.148296\pi$
$30$			3.02343i			0.552001i
$31$	2.04496	+	0.547944i	0.367285	+	0.0984137i	0.437741	−	0.899101i	$-0.355779\pi$
$31$	2.04496	+	0.547944i	0.367285	+	0.0984137i	−0.0704559	+	0.997515i	$0.522445\pi$
$32$	−0.965926	+	0.258819i	−0.170753	+	0.0457532i
$33$	1.55872	+	1.55872i	0.271339	+	0.271339i
$34$	−3.39547	−	3.39547i	−0.582319	−	0.582319i
$35$	−4.95957	+	6.27620i	−0.838320	+	1.06087i
$36$	0.866025	+	0.500000i	0.144338	+	0.0833333i
$37$	3.98822	+	1.06864i	0.655660	+	0.175684i	0.571287	−	0.820751i	$-0.306444\pi$
$37$	3.98822	+	1.06864i	0.655660	+	0.175684i	0.0843734	+	0.996434i	$0.473111\pi$
$38$	−1.42704	−	2.47170i	−0.231496	−	0.400963i
$39$	−3.41621	−	1.15303i	−0.547032	−	0.184633i
$40$	2.61837	+	1.51172i	0.414001	+	0.239023i
$41$	2.82732	+	10.5517i	0.441553	+	1.64790i	0.724881	+	0.688874i	$0.241895\pi$
$41$	2.82732	+	10.5517i	0.441553	+	1.64790i	−0.283329	+	0.959023i	$0.591439\pi$
$42$	0.977554	+	2.45853i	0.150840	+	0.379360i
$43$	−5.69185	+	3.28619i	−0.867999	+	0.501140i	−0.866683	−	0.498860i	$-0.833752\pi$
$43$	−5.69185	+	3.28619i	−0.867999	+	0.501140i	−0.00131639	+	0.999999i	$0.500419\pi$
$44$	2.12926	−	0.570532i	0.320997	−	0.0860110i
$45$	−0.782522	−	2.92041i	−0.116652	−	0.435349i
$46$	−0.215482	−	0.804190i	−0.0317711	−	0.118571i
$47$	3.82672	−	1.02537i	0.558184	−	0.149565i	0.0313122	−	0.999510i	$-0.490031\pi$
$47$	3.82672	−	1.02537i	0.558184	−	0.149565i	0.526872	+	0.849945i	$0.323365\pi$
$48$	0.866025	−	0.500000i	0.125000	−	0.0721688i
$49$	−2.00366	+	6.70711i	−0.286237	+	0.958159i
$50$	−1.07181	−	4.00004i	−0.151577	−	0.565691i
$51$	4.15859	+	2.40096i	0.582319	+	0.336202i
$52$	−2.70666	+	2.38201i	−0.375346	+	0.330326i
$53$	5.61789	+	9.73048i	0.771677	+	1.33658i	0.936643	+	0.350285i	$0.113915\pi$
$53$	5.61789	+	9.73048i	0.771677	+	1.33658i	−0.164966	+	0.986299i	$0.552751\pi$
$54$	−0.965926	−	0.258819i	−0.131446	−	0.0352208i
$55$	−5.77185	−	3.33238i	−0.778276	−	0.449338i
$56$	2.61793	+	0.382681i	0.349836	+	0.0511378i
$57$	2.01814	+	2.01814i	0.267309	+	0.267309i
$58$	0.439296	+	0.439296i	0.0576824	+	0.0576824i
$59$	−7.61175	+	2.03956i	−0.990966	+	0.265528i	−0.717656	−	0.696398i	$-0.754785\pi$
$59$	−7.61175	+	2.03956i	−0.990966	+	0.265528i	−0.273310	+	0.961926i	$0.588118\pi$
$60$	−2.92041	−	0.782522i	−0.377024	−	0.101023i
$61$		−	7.60468i		−	0.973679i	−0.873491	−	0.486839i	$-0.838150\pi$
$61$		−	7.60468i		−	0.973679i	0.873491	−	0.486839i	$-0.161850\pi$
$62$	−1.05855	+	1.83346i	−0.134436	+	0.232849i
$63$	−1.58056	−	2.12175i	−0.199132	−	0.267316i
$64$		−	1.00000i		−	0.125000i
$65$	10.8790	+	0.694061i	1.34938	+	0.0860876i
$66$	−1.90904	+	1.10218i	−0.234986	+	0.135669i
$67$	−5.74537	−	5.74537i	−0.701909	−	0.701909i	0.262911	−	0.964820i	$-0.415317\pi$
$67$	−5.74537	−	5.74537i	−0.701909	−	0.701909i	−0.964820	+	0.262911i	$0.915317\pi$
$68$	4.15859	−	2.40096i	0.504303	−	0.291159i
$69$	0.416279	+	0.721017i	0.0501141	+	0.0868002i
$70$	−4.77872	−	6.41497i	−0.571166	−	0.766736i
$71$	2.25799	−	8.42695i	0.267975	−	1.00009i	−0.692430	−	0.721485i	$-0.743460\pi$
$71$	2.25799	−	8.42695i	0.267975	−	1.00009i	0.960404	−	0.278610i	$-0.0898736\pi$
$72$	−0.707107	+	0.707107i	−0.0833333	+	0.0833333i
$73$	4.17659	−	15.5872i	0.488832	−	1.82435i	−0.0733125	−	0.997309i	$-0.523357\pi$
$73$	4.17659	−	15.5872i	0.488832	−	1.82435i	0.562145	−	0.827039i	$-0.309976\pi$
$74$	−2.06446	+	3.57574i	−0.239988	+	0.415672i
$75$	2.07057	+	3.58634i	0.239089	+	0.414115i
$76$	2.75683	−	0.738690i	0.316230	−	0.0847336i
$77$	−5.77088	−	0.843569i	−0.657653	−	0.0961336i
$78$	1.99792	−	3.00138i	0.226220	−	0.339840i
$79$	0.859183	−	1.48815i	0.0966657	−	0.167430i	−0.813637	−	0.581373i	$-0.802516\pi$
$79$	0.859183	−	1.48815i	0.0966657	−	0.167430i	0.910303	+	0.413944i	$0.135849\pi$
$80$	−2.13789	+	2.13789i	−0.239023	+	0.239023i
$81$	1.00000			0.111111
$82$	−10.9239			−1.20634
$83$	12.5964	−	12.5964i	1.38264	−	1.38264i	0.542730	−	0.839907i	$-0.317391\pi$
$83$	12.5964	−	12.5964i	1.38264	−	1.38264i	0.839907	−	0.542730i	$-0.182609\pi$
$84$	−2.62777	+	0.307929i	−0.286713	+	0.0335978i
$85$	−14.0236	−	3.75761i	−1.52107	−	0.407570i
$86$	−1.70106	−	6.34844i	−0.183430	−	0.684569i
$87$	−0.538026	−	0.310629i	−0.0576824	−	0.0333030i
$88$			2.20437i			0.234986i
$89$	1.91835	−	7.15939i	0.203345	−	0.758894i	−0.786603	−	0.617459i	$-0.788162\pi$
$89$	1.91835	−	7.15939i	0.203345	−	0.758894i	0.989948	−	0.141434i	$-0.0451714\pi$
$90$	3.02343			0.318698
$91$	9.07079	−	2.95309i	0.950877	−	0.309568i
$92$	0.832559			0.0868002
$93$	0.547944	−	2.04496i	0.0568192	−	0.212052i
$94$			3.96171i			0.408619i
$95$	−7.47303	−	4.31456i	−0.766717	−	0.442664i
$96$	0.258819	+	0.965926i	0.0264156	+	0.0985844i
$97$	11.7346	+	3.14428i	1.19147	+	0.319254i	0.799467	−	0.600710i	$-0.205115\pi$
$97$	11.7346	+	3.14428i	1.19147	+	0.319254i	0.392004	+	0.919964i	$0.371782\pi$
$98$	−5.95999	−	3.67132i	−0.602050	−	0.370859i
$99$	1.55872	−	1.55872i	0.156658	−	0.156658i
$100$	4.14115			0.414115
$101$	12.6134			1.25508			0.627542	−	0.778583i	$-0.284061\pi$
$101$	12.6134			1.25508			0.627542	+	0.778583i	$0.284061\pi$
$102$	−3.39547	+	3.39547i	−0.336202	+	0.336202i
$103$	−7.11234	+	12.3189i	−0.700799	+	1.21382i	0.267387	+	0.963589i	$0.413840\pi$
$103$	−7.11234	+	12.3189i	−0.700799	+	1.21382i	−0.968186	+	0.250231i	$0.919494\pi$
$104$	−1.60031	−	3.23094i	−0.156924	−	0.316820i
$105$	6.27620	+	4.95957i	0.612495	+	0.484004i
$106$	−10.8529	+	2.90804i	−1.05413	+	0.282453i
$107$	−5.94911	−	10.3042i	−0.575122	−	0.996141i	−0.996028	−	0.0890370i	$-0.971621\pi$
$107$	−5.94911	−	10.3042i	−0.575122	−	0.996141i	0.420906	−	0.907104i	$-0.361712\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	0.0602948	−	0.225023i	0.00577519	−	0.0215533i	−0.962978	−	0.269580i	$-0.913115\pi$
$109$	0.0602948	−	0.225023i	0.00577519	−	0.0215533i	0.968753	+	0.248026i	$0.0797819\pi$
$110$	4.71270	−	4.71270i	0.449338	−	0.449338i
$111$	1.06864	−	3.98822i	0.101431	−	0.378546i
$112$	−1.04721	+	2.42968i	−0.0989522	+	0.229583i
$113$	1.85838	+	3.21881i	0.174822	+	0.302800i	0.940100	−	0.340900i	$-0.110732\pi$
$113$	1.85838	+	3.21881i	0.174822	+	0.302800i	−0.765278	+	0.643700i	$0.777398\pi$
$114$	−2.47170	+	1.42704i	−0.231496	+	0.133654i
$115$	−1.77992	−	1.77992i	−0.165978	−	0.165978i
$116$	−0.538026	+	0.310629i	−0.0499544	+	0.0288412i
$117$	−1.15303	+	3.41621i	−0.106598	+	0.315829i
$118$		−	7.88027i		−	0.725437i
$119$	−12.6184	+	1.47865i	−1.15672	+	0.135548i
$120$	1.51172	−	2.61837i	0.138000	−	0.239023i
$121$			6.14076i			0.558251i
$122$	7.34555	+	1.96823i	0.665035	+	0.178196i
$123$	10.5517	−	2.82732i	0.951414	−	0.254930i
$124$	−1.49701	−	1.49701i	−0.134436	−	0.134436i
$125$	1.83613	+	1.83613i	0.164229	+	0.164229i
$126$	2.45853	−	0.977554i	0.219024	−	0.0870874i
$127$	−10.5916	−	6.11504i	−0.939849	−	0.542622i	−0.0499361	−	0.998752i	$-0.515902\pi$
$127$	−10.5916	−	6.11504i	−0.939849	−	0.542622i	−0.889913	+	0.456130i	$0.849235\pi$
$128$	0.965926	+	0.258819i	0.0853766	+	0.0228766i
$129$	3.28619	+	5.69185i	0.289333	+	0.501140i
$130$	−3.48611	+	10.3287i	−0.305752	+	0.905887i
$131$	2.13475	+	1.23250i	0.186514	+	0.107684i	0.590349	−	0.807148i	$-0.298990\pi$
$131$	2.13475	+	1.23250i	0.186514	+	0.107684i	−0.403836	+	0.914831i	$0.632323\pi$
$132$	−0.570532	−	2.12926i	−0.0496585	−	0.185328i
$133$	−7.47178	−	1.09220i	−0.647885	−	0.0947058i
$134$	7.03661	−	4.06259i	0.607871	−	0.350954i
$135$	−2.92041	+	0.782522i	−0.251349	+	0.0673488i
$136$	1.24283	+	4.63830i	0.106572	+	0.397731i
$137$	0.181127	+	0.675975i	0.0154747	+	0.0577525i	0.973231	−	0.229827i	$-0.0738161\pi$
$137$	0.181127	+	0.675975i	0.0154747	+	0.0577525i	−0.957757	+	0.287580i	$0.907149\pi$
$138$	−0.804190	+	0.215482i	−0.0684572	+	0.0183430i
$139$	14.3429	−	8.28090i	1.21655	−	0.702377i	0.252374	−	0.967630i	$-0.418789\pi$
$139$	14.3429	−	8.28090i	1.21655	−	0.702377i	0.964179	+	0.265253i	$0.0854554\pi$
$140$	7.43321	−	2.95557i	0.628221	−	0.249791i
$141$	−1.02537	−	3.82672i	−0.0863514	−	0.322268i
$142$	7.55540	+	4.36211i	0.634035	+	0.366060i
$143$	3.52768	+	7.12219i	0.294999	+	0.595587i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	1.81433	+	0.486149i	0.150672	+	0.0403724i
$146$	13.9751	+	8.06855i	1.15659	+	0.667758i
$147$	6.70711	+	2.00366i	0.553193	+	0.165259i
$148$	−2.91958	−	2.91958i	−0.239988	−	0.239988i
$149$	3.44321	+	3.44321i	0.282079	+	0.282079i	0.833937	−	0.551859i	$-0.186081\pi$
$149$	3.44321	+	3.44321i	0.282079	+	0.282079i	−0.551859	+	0.833937i	$0.686081\pi$
$150$	−4.00004	+	1.07181i	−0.326602	+	0.0875127i
$151$	1.68502	+	0.451500i	0.137125	+	0.0367425i	0.326729	−	0.945118i	$-0.394054\pi$
$151$	1.68502	+	0.451500i	0.137125	+	0.0367425i	−0.189604	+	0.981861i	$0.560720\pi$
$152$			2.85408i			0.231496i
$153$	2.40096	−	4.15859i	0.194106	−	0.336202i
$154$	2.30844	−	5.35591i	0.186019	−	0.431592i
$155$			6.40089i			0.514132i
$156$	2.38201	+	2.70666i	0.190714	+	0.216706i
$157$	19.2885	−	11.1362i	1.53939	−	0.888768i	0.540517	−	0.841333i	$-0.318229\pi$
$157$	19.2885	−	11.1362i	1.53939	−	0.888768i	0.998874	−	0.0474350i	$-0.0151047\pi$
$158$	1.21507	+	1.21507i	0.0966657	+	0.0966657i
$159$	9.73048	−	5.61789i	0.771677	−	0.445528i
$160$	−1.51172	−	2.61837i	−0.119512	−	0.207000i
$161$	−2.02285	−	0.871865i	−0.159423	−	0.0687126i
$162$	−0.258819	+	0.965926i	−0.0203347	+	0.0758903i
$163$	1.80913	−	1.80913i	0.141702	−	0.141702i	−0.632697	−	0.774399i	$-0.718052\pi$
$163$	1.80913	−	1.80913i	0.141702	−	0.141702i	0.774399	+	0.632697i	$0.218052\pi$
$164$	2.82732	−	10.5517i	0.220776	−	0.823948i
$165$	−3.33238	+	5.77185i	−0.259425	+	0.449338i
$166$	8.90702	+	15.4274i	0.691319	+	1.19740i
$167$	10.4744	−	2.80660i	0.810533	−	0.217182i	0.170329	−	0.985387i	$-0.445517\pi$
$167$	10.4744	−	2.80660i	0.810533	−	0.217182i	0.640203	+	0.768206i	$0.278850\pi$
$168$	0.382681	−	2.61793i	0.0295245	−	0.201978i
$169$	−10.3410	−	7.87800i	−0.795465	−	0.606000i
$170$	7.25915	−	12.5732i	0.556751	−	0.964322i
$171$	2.01814	−	2.01814i	0.154331	−	0.154331i
$172$	6.57238			0.501140
$173$	−12.9730			−0.986316			−0.493158	−	0.869940i	$-0.664158\pi$
$173$	−12.9730			−0.986316			−0.493158	+	0.869940i	$0.664158\pi$
$174$	0.439296	−	0.439296i	0.0333030	−	0.0333030i
$175$	−10.0617	−	4.33666i	−0.760591	−	0.327820i
$176$	−2.12926	−	0.570532i	−0.160499	−	0.0430055i
$177$	2.03956	+	7.61175i	0.153303	+	0.572134i
$178$	6.41893	+	3.70597i	0.481119	+	0.277774i
$179$		−	4.24905i		−	0.317589i	−0.987312	−	0.158795i	$-0.949239\pi$
$179$		−	4.24905i		−	0.317589i	0.987312	−	0.158795i	$-0.0507607\pi$
$180$	−0.782522	+	2.92041i	−0.0583258	+	0.217675i
$181$	14.5375			1.08056			0.540280	−	0.841485i	$-0.318318\pi$
$181$	14.5375			1.08056			0.540280	+	0.841485i	$0.318318\pi$
$182$	0.504769	+	9.52603i	0.0374160	+	0.706116i
$183$	−7.60468			−0.562154
$184$	−0.215482	+	0.804190i	−0.0158855	+	0.0592857i
$185$			12.4835i			0.917805i
$186$	1.83346	+	1.05855i	0.134436	+	0.0776164i
$187$	−2.73965	−	10.2245i	−0.200343	−	0.747691i
$188$	−3.82672	−	1.02537i	−0.279092	−	0.0747825i
$189$	−2.12175	+	1.58056i	−0.154335	+	0.114969i
$190$	6.10171	−	6.10171i	0.442664	−	0.442664i
$191$	−13.1278			−0.949892			−0.474946	−	0.880015i	$-0.657532\pi$
$191$	−13.1278			−0.949892			−0.474946	+	0.880015i	$0.657532\pi$
$192$	−1.00000			−0.0721688
$193$	−8.80972	+	8.80972i	−0.634137	+	0.634137i	−0.949103	−	0.314966i	$-0.898007\pi$
$193$	−8.80972	+	8.80972i	−0.634137	+	0.634137i	0.314966	+	0.949103i	$0.398007\pi$
$194$	−6.07429	+	10.5210i	−0.436108	+	0.755362i
$195$	0.694061	−	10.8790i	0.0497027	−	0.779063i
$196$	5.08878	−	4.80670i	0.363484	−	0.343336i
$197$	−23.1200	+	6.19498i	−1.64723	+	0.441374i	−0.958835	−	0.283963i	$-0.908351\pi$
$197$	−23.1200	+	6.19498i	−1.64723	+	0.441374i	−0.688394	+	0.725337i	$0.741684\pi$
$198$	1.10218	+	1.90904i	0.0783288	+	0.135669i
$199$	8.69068	−	15.0527i	0.616066	−	1.06706i	−0.374130	−	0.927376i	$-0.622059\pi$
$199$	8.69068	−	15.0527i	0.616066	−	1.06706i	0.990196	−	0.139682i	$-0.0446079\pi$
$200$	−1.07181	+	4.00004i	−0.0757883	+	0.282846i
$201$	−5.74537	+	5.74537i	−0.405247	+	0.405247i
$202$	−3.26460	+	12.1836i	−0.229696	+	0.857238i
$203$	1.63253	−	0.191304i	0.114581	−	0.0134269i
$204$	−2.40096	−	4.15859i	−0.168101	−	0.291159i
$205$	−28.6028	+	16.5139i	−1.99771	+	1.15338i
$206$	−10.0584	−	10.0584i	−0.700799	−	0.700799i
$207$	0.721017	−	0.416279i	0.0501141	−	0.0289334i
$208$	3.53504	−	0.709554i	0.245111	−	0.0491987i
$209$		−	6.29144i		−	0.435188i
$210$	−6.41497	+	4.77872i	−0.442675	+	0.329763i
$211$	10.0120	−	17.3414i	0.689258	−	1.19383i	−0.282821	−	0.959173i	$-0.591270\pi$
$211$	10.0120	−	17.3414i	0.689258	−	1.19383i	0.972078	−	0.234657i	$-0.0753965\pi$
$212$		−	11.2358i		−	0.771677i
$213$	−8.42695	−	2.25799i	−0.577405	−	0.154715i
$214$	11.4928	−	3.07949i	0.785632	−	0.210509i
$215$	−14.0510	−	14.0510i	−0.958273	−	0.958273i
$216$	0.707107	+	0.707107i	0.0481125	+	0.0481125i
$217$	2.06957	+	5.20495i	0.140492	+	0.353335i
$218$	0.201750	+	0.116481i	0.0136643	+	0.00788906i
$219$	−15.5872	−	4.17659i	−1.05329	−	0.282228i
$220$	3.33238	+	5.77185i	0.224669	+	0.389138i
$221$	11.4382	+	12.9972i	0.769420	+	0.874285i
$222$	3.57574	+	2.06446i	0.239988	+	0.138557i
$223$	2.41674	+	9.01938i	0.161837	+	0.603983i	0.998423	+	0.0561468i	$0.0178815\pi$
$223$	2.41674	+	9.01938i	0.161837	+	0.603983i	−0.836586	+	0.547836i	$0.815452\pi$
$224$	−2.07585	−	1.64038i	−0.138699	−	0.109602i
$225$	3.58634	−	2.07057i	0.239089	−	0.138038i
$226$	−3.59011	+	0.961968i	−0.238811	+	0.0639892i
$227$	6.64348	+	24.7938i	0.440944	+	1.64562i	0.726430	+	0.687241i	$0.241178\pi$
$227$	6.64348	+	24.7938i	0.440944	+	1.64562i	−0.285486	+	0.958383i	$0.592155\pi$
$228$	−0.738690	−	2.75683i	−0.0489209	−	0.182575i
$229$	1.69771	−	0.454900i	0.112188	−	0.0300606i	−0.202288	−	0.979326i	$-0.564838\pi$
$229$	1.69771	−	0.454900i	0.112188	−	0.0300606i	0.314476	+	0.949265i	$0.398171\pi$
$230$	2.17995	−	1.25859i	0.143741	−	0.0829891i
$231$	−0.843569	+	5.77088i	−0.0555028	+	0.379696i
$232$	−0.160794	−	0.600090i	−0.0105566	−	0.0393978i
$233$	−2.03170	−	1.17300i	−0.133101	−	0.0768459i	0.431971	−	0.901887i	$-0.357818\pi$
$233$	−2.03170	−	1.17300i	−0.133101	−	0.0768459i	−0.565072	+	0.825042i	$0.691152\pi$
$234$	−3.00138	−	1.99792i	−0.196207	−	0.130608i
$235$	5.98898	+	10.3732i	0.390678	+	0.676674i
$236$	7.61175	+	2.03956i	0.495483	+	0.132764i
$237$	−1.48815	−	0.859183i	−0.0966657	−	0.0558100i
$238$	1.83760	−	12.5711i	0.119114	−	0.814863i
$239$	7.68798	+	7.68798i	0.497294	+	0.497294i	0.910595	−	0.413300i	$-0.135624\pi$
$239$	7.68798	+	7.68798i	0.497294	+	0.497294i	−0.413300	+	0.910595i	$0.635624\pi$
$240$	2.13789	+	2.13789i	0.138000	+	0.138000i
$241$	3.98230	−	1.06705i	0.256522	−	0.0687349i	−0.128266	−	0.991740i	$-0.540941\pi$
$241$	3.98230	−	1.06705i	0.256522	−	0.0687349i	0.384788	+	0.923005i	$0.374274\pi$
$242$	−5.93152	−	1.58935i	−0.381293	−	0.102167i
$243$		−	1.00000i		−	0.0641500i
$244$	−3.80234	+	6.58584i	−0.243420	+	0.421615i
$245$	−21.1554	−	0.603056i	−1.35157	−	0.0385278i
$246$			10.9239i			0.696483i
$247$	4.56742	+	9.22137i	0.290618	+	0.586742i
$248$	1.83346	−	1.05855i	0.116425	−	0.0672178i
$249$	−12.5964	−	12.5964i	−0.798266	−	0.798266i
$250$	−2.24879	+	1.29834i	−0.142226	+	0.0821143i
$251$	−12.8869	−	22.3207i	−0.813412	−	1.40887i	−0.910463	−	0.413591i	$-0.864274\pi$
$251$	−12.8869	−	22.3207i	−0.813412	−	1.40887i	0.0970512	−	0.995279i	$-0.469059\pi$
$252$	0.307929	+	2.62777i	0.0193977	+	0.165534i
$253$	0.475002	−	1.77273i	0.0298631	−	0.111451i
$254$	8.64797	−	8.64797i	0.542622	−	0.542622i
$255$	−3.75761	+	14.0236i	−0.235311	+	0.878192i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	0.367121	+	0.635872i	0.0229004	+	0.0396646i	0.877248	−	0.480037i	$-0.159377\pi$
$257$	0.367121	+	0.635872i	0.0229004	+	0.0396646i	−0.854348	+	0.519701i	$0.826043\pi$
$258$	−6.34844	+	1.70106i	−0.395236	+	0.105903i
$259$	4.03623	+	10.1511i	0.250799	+	0.630757i
$260$	−9.07448	−	6.04059i	−0.562775	−	0.374621i
$261$	−0.310629	+	0.538026i	−0.0192275	+	0.0333030i
$262$	−1.74301	+	1.74301i	−0.107684	+	0.107684i
$263$	−10.6412			−0.656167			−0.328083	−	0.944649i	$-0.606403\pi$
$263$	−10.6412			−0.656167			−0.328083	+	0.944649i	$0.606403\pi$
$264$	2.20437			0.135669
$265$	−24.0209	+	24.0209i	−1.47559	+	1.47559i
$266$	2.98882	−	6.93450i	0.183257	−	0.425182i
$267$	−7.15939	−	1.91835i	−0.438147	−	0.117401i
$268$	2.10295	+	7.84832i	0.128458	+	0.479412i
$269$	−26.5319	−	15.3182i	−1.61768	−	0.933968i	−0.987518	−	0.157505i	$-0.949655\pi$
$269$	−26.5319	−	15.3182i	−1.61768	−	0.933968i	−0.630162	−	0.776464i	$-0.717012\pi$
$270$		−	3.02343i		−	0.184000i
$271$	−2.39530	+	8.93937i	−0.145504	+	0.543028i	0.854228	+	0.519898i	$0.174030\pi$
$271$	−2.39530	+	8.93937i	−0.145504	+	0.543028i	−0.999732	+	0.0231305i	$0.992637\pi$
$272$	−4.80193			−0.291159
$273$	−2.95309	−	9.07079i	−0.178729	−	0.548989i
$274$	−0.699821			−0.0422777
$275$	2.36266	−	8.81756i	0.142474	−	0.531719i
$276$		−	0.832559i		−	0.0501141i
$277$	15.5648	+	8.98632i	0.935196	+	0.539935i	0.888451	−	0.458971i	$-0.151782\pi$
$277$	15.5648	+	8.98632i	0.935196	+	0.539935i	0.0467446	+	0.998907i	$0.485115\pi$
$278$	4.28651	+	15.9975i	0.257088	+	0.959465i
$279$	−2.04496	−	0.547944i	−0.122428	−	0.0328046i
$280$	0.931003	+	7.94489i	0.0556380	+	0.474798i
$281$	17.1750	−	17.1750i	1.02458	−	1.02458i	0.0248857	−	0.999690i	$-0.492078\pi$
$281$	17.1750	−	17.1750i	1.02458	−	1.02458i	0.999690	−	0.0248857i	$-0.00792219\pi$
$282$	3.96171			0.235916
$283$	23.2881			1.38433			0.692167	−	0.721738i	$-0.256656\pi$
$283$	23.2881			1.38433			0.692167	+	0.721738i	$0.256656\pi$
$284$	−6.16895	+	6.16895i	−0.366060	+	0.366060i
$285$	−4.31456	+	7.47303i	−0.255572	+	0.442664i
$286$	−7.79254	+	1.56412i	−0.460782	+	0.0924882i
$287$	−17.9193	+	22.6764i	−1.05774	+	1.33855i
$288$	0.965926	−	0.258819i	0.0569177	−	0.0152511i
$289$	−3.02924	−	5.24680i	−0.178191	−	0.308635i
$290$	−0.939167	+	1.62668i	−0.0551498	+	0.0955222i
$291$	3.14428	−	11.7346i	0.184321	−	0.687896i
$292$	−11.4106	+	11.4106i	−0.667758	+	0.667758i
$293$	−0.988549	+	3.68932i	−0.0577517	+	0.215532i	−0.988771	−	0.149437i	$-0.952254\pi$
$293$	−0.988549	+	3.68932i	−0.0577517	+	0.215532i	0.931020	+	0.364969i	$0.118920\pi$
$294$	−3.67132	+	5.95999i	−0.214116	+	0.347593i
$295$	−11.9127	−	20.6334i	−0.693586	−	1.20133i
$296$	3.57574	−	2.06446i	0.207836	−	0.119994i
$297$	−1.55872	−	1.55872i	−0.0904463	−	0.0904463i
$298$	−4.21705	+	2.43472i	−0.244287	+	0.141039i
$299$	0.590745	+	2.94313i	0.0341637	+	0.170206i
$300$		−	4.14115i		−	0.239089i
$301$	−15.9688	−	6.88267i	−0.920426	−	0.396711i
$302$	−0.872230	+	1.51075i	−0.0501912	+	0.0869337i
$303$		−	12.6134i		−	0.724623i
$304$	−2.75683	−	0.738690i	−0.158115	−	0.0423668i
$305$	22.2088	−	5.95083i	1.27167	−	0.340743i
$306$	3.39547	+	3.39547i	0.194106	+	0.194106i
$307$	5.02364	+	5.02364i	0.286714	+	0.286714i	0.835779	−	0.549065i	$-0.185016\pi$
$307$	5.02364	+	5.02364i	0.286714	+	0.286714i	−0.549065	+	0.835779i	$0.685016\pi$
$308$	4.57594	+	3.61599i	0.260739	+	0.206040i
$309$	12.3189	+	7.11234i	0.700799	+	0.404607i
$310$	−6.18279	−	1.65667i	−0.351159	−	0.0940927i
$311$	1.10966	+	1.92199i	0.0629230	+	0.108986i	0.895771	−	0.444516i	$-0.146624\pi$
$311$	1.10966	+	1.92199i	0.0629230	+	0.108986i	−0.832848	+	0.553502i	$0.813291\pi$
$312$	−3.23094	+	1.60031i	−0.182916	+	0.0905999i
$313$	9.33736	+	5.39093i	0.527779	+	0.304713i	0.740111	−	0.672484i	$-0.234773\pi$
$313$	9.33736	+	5.39093i	0.527779	+	0.304713i	−0.212333	+	0.977197i	$0.568106\pi$
$314$	5.76454	+	21.5135i	0.325312	+	1.21408i
$315$	4.95957	−	6.27620i	0.279440	−	0.353624i
$316$	−1.48815	+	0.859183i	−0.0837149	+	0.0483328i
$317$	−20.5329	+	5.50177i	−1.15324	+	0.309010i	−0.784263	−	0.620428i	$-0.786959\pi$
$317$	−20.5329	+	5.50177i	−1.15324	+	0.309010i	−0.368978	+	0.929438i	$0.620292\pi$
$318$	2.90804	+	10.8529i	0.163075	+	0.608603i
$319$	0.354448	+	1.32282i	0.0198453	+	0.0740636i
$320$	2.92041	−	0.782522i	0.163256	−	0.0437443i
$321$	−10.3042	+	5.94911i	−0.575122	+	0.332047i
$322$	1.36571	−	1.72827i	0.0761080	−	0.0963127i
$323$	−3.54713	−	13.2381i	−0.197368	−	0.736587i
$324$	−0.866025	−	0.500000i	−0.0481125	−	0.0277778i
$325$	2.93837	+	14.6391i	0.162991	+	0.812033i
$326$	1.27925	+	2.21572i	0.0708510	+	0.122718i
$327$	−0.225023	−	0.0602948i	−0.0124438	−	0.00333431i
$328$	9.46038	+	5.46195i	0.522362	+	0.301586i
$329$	8.22393	+	6.49869i	0.453400	+	0.358285i
$330$	−4.71270	−	4.71270i	−0.259425	−	0.259425i
$331$	−17.2588	−	17.2588i	−0.948629	−	0.948629i	0.0501147	−	0.998743i	$-0.484041\pi$
$331$	−17.2588	−	17.2588i	−0.948629	−	0.948629i	−0.998743	+	0.0501147i	$0.984041\pi$
$332$	−17.2070	+	4.61061i	−0.944359	+	0.253040i
$333$	−3.98822	−	1.06864i	−0.218553	−	0.0585612i
$334$			10.8439i			0.593351i
$335$	12.2830	−	21.2747i	0.671090	−	1.16236i
$336$	2.42968	+	1.04721i	0.132550	+	0.0571301i
$337$			28.2173i			1.53709i	0.639794	+	0.768547i	$0.279020\pi$
$337$			28.2173i			1.53709i	−0.639794	+	0.768547i	$0.720980\pi$
$338$	10.2860	−	7.94970i	0.559486	−	0.432407i
$339$	3.21881	−	1.85838i	0.174822	−	0.100933i
$340$	10.2660	+	10.2660i	0.556751	+	0.556751i
$341$	−4.04161	+	2.33343i	−0.218866	+	0.126362i
$342$	1.42704	+	2.47170i	0.0771655	+	0.133654i
$343$	−17.3977	+	6.34972i	−0.939389	+	0.342852i
$344$	−1.70106	+	6.34844i	−0.0917149	+	0.342285i
$345$	−1.77992	+	1.77992i	−0.0958276	+	0.0958276i
$346$	3.35765	−	12.5309i	0.180508	−	0.673666i
$347$	−0.985719	+	1.70732i	−0.0529162	+	0.0916535i	−0.891270	−	0.453473i	$-0.850185\pi$
$347$	−0.985719	+	1.70732i	−0.0529162	+	0.0916535i	0.838354	+	0.545126i	$0.183518\pi$
$348$	0.310629	+	0.538026i	0.0166515	+	0.0288412i
$349$	26.2589	−	7.03605i	1.40561	−	0.376631i	0.525252	−	0.850947i	$-0.323971\pi$
$349$	26.2589	−	7.03605i	1.40561	−	0.376631i	0.880355	+	0.474316i	$0.157304\pi$
$350$	6.79304	−	8.59641i	0.363103	−	0.459498i
$351$	3.41621	+	1.15303i	0.182344	+	0.0615442i
$352$	1.10218	−	1.90904i	0.0587466	−	0.101752i
$353$	6.65588	−	6.65588i	0.354257	−	0.354257i	−0.507434	−	0.861691i	$-0.669406\pi$
$353$	6.65588	−	6.65588i	0.354257	−	0.354257i	0.861691	+	0.507434i	$0.169406\pi$
$354$	−7.88027			−0.418831
$355$	26.3771			1.39995
$356$	−5.24104	+	5.24104i	−0.277774	+	0.277774i
$357$	1.47865	+	12.6184i	0.0782586	+	0.667834i
$358$	4.10427	+	1.09974i	0.216917	+	0.0581228i
$359$	−1.22341	−	4.56581i	−0.0645689	−	0.240974i	0.926097	−	0.377285i	$-0.123142\pi$
$359$	−1.22341	−	4.56581i	−0.0645689	−	0.240974i	−0.990666	+	0.136310i	$0.956476\pi$
$360$	−2.61837	−	1.51172i	−0.138000	−	0.0796745i
$361$			10.8542i			0.571275i
$362$	−3.76257	+	14.0421i	−0.197756	+	0.738036i
$363$	6.14076			0.322306
$364$	−9.33208	−	1.97795i	−0.489134	−	0.103673i
$365$	48.7894			2.55375
$366$	1.96823	−	7.34555i	0.102881	−	0.383958i
$367$			32.9526i			1.72011i	0.510198	+	0.860057i	$0.329572\pi$
$367$			32.9526i			1.72011i	−0.510198	+	0.860057i	$0.670428\pi$
$368$	−0.721017	−	0.416279i	−0.0375856	−	0.0217001i
$369$	−2.82732	−	10.5517i	−0.147184	−	0.549299i
$370$	−12.0581	−	3.23097i	−0.626872	−	0.167970i
$371$	−11.7662	+	27.2994i	−0.610873	+	1.41731i
$372$	−1.49701	+	1.49701i	−0.0776164	+	0.0776164i
$373$	−15.3975			−0.797250			−0.398625	−	0.917114i	$-0.630512\pi$
$373$	−15.3975			−0.797250			−0.398625	+	0.917114i	$0.630512\pi$
$374$	10.5852			0.547348
$375$	1.83613	−	1.83613i	0.0948175	−	0.0948175i
$376$	1.98085	−	3.43094i	0.102155	−	0.176937i
$377$	−1.47985	−	1.68154i	−0.0762160	−	0.0866035i
$378$	−0.977554	−	2.45853i	−0.0502799	−	0.126453i
$379$	13.5428	−	3.62878i	0.695647	−	0.186398i	0.106367	−	0.994327i	$-0.466078\pi$
$379$	13.5428	−	3.62878i	0.695647	−	0.186398i	0.589280	+	0.807929i	$0.299411\pi$
$380$	4.31456	+	7.47303i	0.221332	+	0.383359i
$381$	−6.11504	+	10.5916i	−0.313283	+	0.542622i
$382$	3.39771	−	12.6804i	0.173842	−	0.648788i
$383$	−15.3754	+	15.3754i	−0.785645	+	0.785645i	−0.980777	−	0.195132i	$-0.937486\pi$
$383$	−15.3754	+	15.3754i	−0.785645	+	0.785645i	0.195132	+	0.980777i	$0.437486\pi$
$384$	0.258819	−	0.965926i	0.0132078	−	0.0492922i
$385$	−2.05227	−	17.5135i	−0.104593	−	0.892568i
$386$	−6.22941	−	10.7897i	−0.317069	−	0.549179i
$387$	5.69185	−	3.28619i	0.289333	−	0.167047i
$388$	−8.59034	−	8.59034i	−0.436108	−	0.436108i
$389$	15.8249	−	9.13651i	0.802354	−	0.463239i	−0.0419397	−	0.999120i	$-0.513354\pi$
$389$	15.8249	−	9.13651i	0.802354	−	0.463239i	0.844294	+	0.535881i	$0.180020\pi$
$390$	10.3287	+	3.48611i	0.523014	+	0.176526i
$391$		−	3.99788i		−	0.202182i
$392$	3.32584	+	6.15945i	0.167980	+	0.311099i
$393$	1.23250	−	2.13475i	0.0621712	−	0.107684i
$394$		−	23.9356i		−	1.20586i
$395$	5.01834	+	1.34466i	0.252500	+	0.0676572i
$396$	−2.12926	+	0.570532i	−0.106999	+	0.0286703i
$397$	−15.9002	−	15.9002i	−0.798008	−	0.798008i	0.184773	−	0.982781i	$-0.440845\pi$
$397$	−15.9002	−	15.9002i	−0.798008	−	0.798008i	−0.982781	+	0.184773i	$0.940845\pi$
$398$	12.2905	+	12.2905i	0.616066	+	0.616066i
$399$	−1.09220	+	7.47178i	−0.0546784	+	0.374057i
$400$	−3.58634	−	2.07057i	−0.179317	−	0.103529i
$401$	32.7852	+	8.78477i	1.63722	+	0.438691i	0.955994	−	0.293386i	$-0.0947822\pi$
$401$	32.7852	+	8.78477i	1.63722	+	0.438691i	0.681222	+	0.732077i	$0.261449\pi$
$402$	−4.06259	−	7.03661i	−0.202624	−	0.350954i
$403$	4.22979	−	6.35421i	0.210701	−	0.316526i
$404$	−10.9236	−	6.30672i	−0.543467	−	0.313771i
$405$	0.782522	+	2.92041i	0.0388838	+	0.145116i
$406$	−0.237744	+	1.62641i	−0.0117990	+	0.0807174i
$407$	−7.88226	+	4.55082i	−0.390709	+	0.225576i
$408$	4.63830	−	1.24283i	0.229630	−	0.0615292i
$409$	−0.656867	−	2.45146i	−0.0324800	−	0.121217i	0.947782	−	0.318918i	$-0.103319\pi$
$409$	−0.656867	−	2.45146i	−0.0324800	−	0.121217i	−0.980262	+	0.197701i	$0.936653\pi$
$410$	−8.54820	−	31.9023i	−0.422166	−	1.57554i
$411$	0.675975	−	0.181127i	0.0333434	−	0.00893434i
$412$	12.3189	−	7.11234i	0.606910	−	0.350400i
$413$	−16.3583	−	12.9266i	−0.804938	−	0.636076i
$414$	0.215482	+	0.804190i	0.0105904	+	0.0395238i
$415$	46.6437	+	26.9298i	2.28965	+	1.32193i
$416$	−0.229560	+	3.59824i	−0.0112551	+	0.176418i
$417$	−8.28090	−	14.3429i	−0.405518	−	0.702377i
$418$	6.07706	+	1.62834i	0.297239	+	0.0796449i
$419$	−30.0008	−	17.3210i	−1.46564	−	0.846185i	−0.466374	−	0.884588i	$-0.654440\pi$
$419$	−30.0008	−	17.3210i	−1.46564	−	0.846185i	−0.999262	+	0.0384023i	$0.987773\pi$
$420$	−2.95557	−	7.43321i	−0.144217	−	0.362704i
$421$	13.6090	+	13.6090i	0.663260	+	0.663260i	0.956147	−	0.292887i	$-0.0946160\pi$
$421$	13.6090	+	13.6090i	0.663260	+	0.663260i	−0.292887	+	0.956147i	$0.594616\pi$
$422$	14.1592	+	14.1592i	0.689258	+	0.689258i
$423$	−3.82672	+	1.02537i	−0.186061	+	0.0498550i
$424$	10.8529	+	2.90804i	0.527065	+	0.141227i
$425$		−	19.8855i		−	0.964587i
$426$	4.36211	−	7.55540i	0.211345	−	0.366060i
$427$	16.1352	−	12.0196i	0.780839	−	0.581671i
$428$			11.8982i			0.575122i
$429$	7.12219	−	3.52768i	0.343863	−	0.170318i
$430$	17.2089	−	9.93558i	0.829888	−	0.479136i
$431$	−18.5610	−	18.5610i	−0.894052	−	0.894052i	0.100850	−	0.994902i	$-0.467844\pi$
$431$	−18.5610	−	18.5610i	−0.894052	−	0.894052i	−0.994902	+	0.100850i	$0.967844\pi$
$432$	−0.866025	+	0.500000i	−0.0416667	+	0.0240563i
$433$	−2.23696	−	3.87452i	−0.107501	−	0.186198i	0.807256	−	0.590201i	$-0.200952\pi$
$433$	−2.23696	−	3.87452i	−0.107501	−	0.186198i	−0.914757	+	0.404004i	$0.867618\pi$
$434$	−5.56324	+	0.651915i	−0.267044	+	0.0312929i
$435$	0.486149	−	1.81433i	0.0233090	−	0.0869905i
$436$	−0.164728	+	0.164728i	−0.00788906	+	0.00788906i
$437$	0.615003	−	2.29522i	0.0294196	−	0.109795i
$438$	8.06855	−	13.9751i	0.385530	−	0.667758i
$439$	−3.81710	−	6.61141i	−0.182180	−	0.315546i	0.760442	−	0.649405i	$-0.224982\pi$
$439$	−3.81710	−	6.61141i	−0.182180	−	0.315546i	−0.942623	+	0.333860i	$0.891649\pi$
$440$	−6.43766	+	1.72497i	−0.306904	+	0.0822345i
$441$	2.00366	−	6.70711i	0.0954125	−	0.319386i
$442$	−15.5148	+	7.68458i	−0.737961	+	0.365518i
$443$	−0.344592	+	0.596852i	−0.0163721	+	0.0283573i	−0.874095	−	0.485754i	$-0.838545\pi$
$443$	−0.344592	+	0.596852i	−0.0163721	+	0.0283573i	0.857723	+	0.514112i	$0.171878\pi$
$444$	−2.91958	+	2.91958i	−0.138557	+	0.138557i
$445$	22.4095			1.06231
$446$	−9.33755			−0.442146
$447$	3.44321	−	3.44321i	0.162858	−	0.162858i
$448$	2.12175	−	1.58056i	0.100243	−	0.0746744i
$449$	−9.38986	−	2.51601i	−0.443135	−	0.118738i	0.0303504	−	0.999539i	$-0.490338\pi$
$449$	−9.38986	−	2.51601i	−0.443135	−	0.118738i	−0.473485	+	0.880802i	$0.657004\pi$
$450$	1.07181	+	4.00004i	0.0505255	+	0.188564i
$451$	−20.8542	−	12.0402i	−0.981984	−	0.566949i
$452$		−	3.71676i		−	0.174822i
$453$	0.451500	−	1.68502i	0.0212133	−	0.0791691i
$454$	−25.6685			−1.20468
$455$	15.7223	+	24.1796i	0.737074	+	1.13356i
$456$	2.85408			0.133654
$457$	−2.67009	+	9.96493i	−0.124902	+	0.466140i	−0.999836	−	0.0181018i	$-0.994238\pi$
$457$	−2.67009	+	9.96493i	−0.124902	+	0.466140i	0.874934	+	0.484241i	$0.160904\pi$
$458$			1.75760i			0.0821272i
$459$	−4.15859	−	2.40096i	−0.194106	−	0.112067i
$460$	0.651495	+	2.43141i	0.0303761	+	0.113365i
$461$	−15.6819	−	4.20195i	−0.730379	−	0.195704i	−0.125581	−	0.992083i	$-0.540079\pi$
$461$	−15.6819	−	4.20195i	−0.730379	−	0.195704i	−0.604798	+	0.796379i	$0.706746\pi$
$462$	−5.35591	−	2.30844i	−0.249179	−	0.107398i
$463$	−4.30031	+	4.30031i	−0.199852	+	0.199852i	−0.799937	−	0.600084i	$-0.795134\pi$
$463$	−4.30031	+	4.30031i	−0.199852	+	0.199852i	0.600084	+	0.799937i	$0.295134\pi$
$464$	0.621259			0.0288412
$465$	6.40089			0.296834
$466$	1.65887	−	1.65887i	0.0768459	−	0.0768459i
$467$	−13.5301	+	23.4348i	−0.626097	+	1.08443i	0.362230	+	0.932089i	$0.382015\pi$
$467$	−13.5301	+	23.4348i	−0.626097	+	1.08443i	−0.988328	+	0.152344i	$0.951318\pi$
$468$	2.70666	−	2.38201i	0.125115	−	0.110109i
$469$	3.10935	−	21.2711i	0.143576	−	0.982210i
$470$	−11.5698	+	3.10013i	−0.533676	+	0.142998i
$471$	−11.1362	−	19.2885i	−0.513130	−	0.888768i
$472$	−3.94013	+	6.82451i	−0.181359	+	0.314124i
$473$	3.74976	−	13.9943i	0.172414	−	0.643458i
$474$	1.21507	−	1.21507i	0.0558100	−	0.0558100i
$475$	3.05902	−	11.4164i	0.140358	−	0.523822i
$476$	11.6671	+	5.02863i	0.534763	+	0.230487i
$477$	−5.61789	−	9.73048i	−0.257226	−	0.445528i
$478$	−9.41582	+	5.43623i	−0.430670	+	0.248647i
$479$	8.00963	+	8.00963i	0.365969	+	0.365969i	0.866005	−	0.500035i	$-0.166680\pi$
$479$	8.00963	+	8.00963i	0.365969	+	0.365969i	−0.500035	+	0.866005i	$0.666680\pi$
$480$	−2.61837	+	1.51172i	−0.119512	+	0.0690001i
$481$	8.24925	−	12.3925i	0.376134	−	0.565047i
$482$			4.12278i			0.187787i
$483$	−0.871865	+	2.02285i	−0.0396712	+	0.0920429i
$484$	3.07038	−	5.31806i	0.139563	−	0.241730i
$485$			36.7304i			1.66784i
$486$	0.965926	+	0.258819i	0.0438153	+	0.0117403i
$487$	20.3392	−	5.44988i	0.921658	−	0.246958i	0.233364	−	0.972389i	$-0.425027\pi$
$487$	20.3392	−	5.44988i	0.921658	−	0.246958i	0.688294	+	0.725432i	$0.258360\pi$
$488$	−5.37732	−	5.37732i	−0.243420	−	0.243420i
$489$	−1.80913	−	1.80913i	−0.0818117	−	0.0818117i
$490$	6.05794	−	20.2785i	0.273670	−	0.916089i
$491$	18.2551	+	10.5396i	0.823841	+	0.475645i	0.851739	−	0.523966i	$-0.175548\pi$
$491$	18.2551	+	10.5396i	0.823841	+	0.475645i	−0.0278979	+	0.999611i	$0.508881\pi$
$492$	−10.5517	−	2.82732i	−0.475707	−	0.127465i
$493$	1.49162	+	2.58356i	0.0671791	+	0.116358i
$494$	−10.0893	+	2.02512i	−0.453939	+	0.0911146i
$495$	5.77185	+	3.33238i	0.259425	+	0.149779i
$496$	0.547944	+	2.04496i	0.0246034	+	0.0918212i
$497$	21.4488	−	8.52839i	0.962110	−	0.382551i
$498$	15.4274	−	8.90702i	0.691319	−	0.399133i
$499$	−15.2390	+	4.08327i	−0.682190	+	0.182792i	−0.583240	−	0.812300i	$-0.698215\pi$
$499$	−15.2390	+	4.08327i	−0.682190	+	0.182792i	−0.0989503	+	0.995092i	$0.531548\pi$
$500$	−0.672071	−	2.50820i	−0.0300559	−	0.112170i
$501$	−2.80660	−	10.4744i	−0.125390	−	0.467961i
$502$	24.8955	−	6.67073i	1.11114	−	0.297729i
$503$	−12.4612	+	7.19450i	−0.555619	+	0.320787i	−0.751385	−	0.659864i	$-0.770614\pi$
$503$	−12.4612	+	7.19450i	−0.555619	+	0.320787i	0.195766	+	0.980651i	$0.437281\pi$
$504$	−2.61793	−	0.382681i	−0.116612	−	0.0170459i
$505$	9.87029	+	36.8364i	0.439222	+	1.63920i
$506$	1.58939	+	0.917633i	0.0706568	+	0.0407937i
$507$	−7.87800	+	10.3410i	−0.349874	+	0.459262i
$508$	6.11504	+	10.5916i	0.271311	+	0.469925i
$509$	9.77396	+	2.61892i	0.433223	+	0.116082i	0.468839	−	0.883284i	$-0.344673\pi$
$509$	9.77396	+	2.61892i	0.433223	+	0.116082i	−0.0356156	+	0.999366i	$0.511339\pi$
$510$	−12.5732	−	7.25915i	−0.556751	−	0.321441i
$511$	39.6736	−	15.7749i	1.75506	−	0.697839i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−2.01814	−	2.01814i	−0.0891030	−	0.0891030i
$514$	−0.709223	+	0.190036i	−0.0312825	+	0.00838212i
$515$	−41.5419	−	11.1311i	−1.83055	−	0.490496i
$516$		−	6.57238i		−	0.289333i
$517$	−4.36653	+	7.56306i	−0.192040	+	0.332623i
$518$	−10.8498	+	1.27141i	−0.476715	+	0.0558626i
$519$			12.9730i			0.569450i
$520$	8.18341	−	7.20186i	0.358866	−	0.315822i
$521$	−1.89410	+	1.09356i	−0.0829818	+	0.0479096i	−0.540917	−	0.841076i	$-0.681923\pi$
$521$	−1.89410	+	1.09356i	−0.0829818	+	0.0479096i	0.457935	+	0.888986i	$0.348589\pi$
$522$	−0.439296	−	0.439296i	−0.0192275	−	0.0192275i
$523$	0.666614	−	0.384870i	0.0291490	−	0.0168292i	−0.485355	−	0.874317i	$-0.661310\pi$
$523$	0.666614	−	0.384870i	0.0291490	−	0.0168292i	0.514504	+	0.857488i	$0.327976\pi$
$524$	−1.23250	−	2.13475i	−0.0538418	−	0.0932568i
$525$	−4.33666	+	10.0617i	−0.189267	+	0.439127i
$526$	2.75415	−	10.2786i	0.120087	−	0.448170i
$527$	−7.18854	+	7.18854i	−0.313138	+	0.313138i
$528$	−0.570532	+	2.12926i	−0.0248292	+	0.0926640i
$529$	−11.1534	+	19.3183i	−0.484931	+	0.839926i
$530$	−16.9853	−	29.4194i	−0.737795	−	1.27790i
$531$	7.61175	−	2.03956i	0.330322	−	0.0885095i
$532$	5.92465	+	4.68176i	0.256866	+	0.202980i
$533$	39.3068	+	2.50770i	1.70257	+	0.108620i
$534$	3.70597	−	6.41893i	0.160373	−	0.277774i
$535$	25.4371	−	25.4371i	1.09974	−	1.09974i
$536$	−8.12518			−0.350954
$537$	−4.24905			−0.183360
$538$	21.6632	−	21.6632i	0.933968	−	0.933968i
$539$	−7.33138	−	13.5777i	−0.315785	−	0.584832i
$540$	2.92041	+	0.782522i	0.125675	+	0.0336744i
$541$	−7.89555	−	29.4666i	−0.339456	−	1.26687i	−0.898956	−	0.438038i	$-0.855674\pi$
$541$	−7.89555	−	29.4666i	−0.339456	−	1.26687i	0.559500	−	0.828830i	$-0.310993\pi$
$542$	−8.01482	−	4.62736i	−0.344266	−	0.198762i
$543$		−	14.5375i		−	0.623862i
$544$	1.24283	−	4.63830i	0.0532859	−	0.198866i
$545$	0.704343			0.0301707
$546$	9.52603	−	0.504769i	0.407676	−	0.0216021i
$547$	−22.4927			−0.961719			−0.480860	−	0.876798i	$-0.659675\pi$
$547$	−22.4927			−0.961719			−0.480860	+	0.876798i	$0.659675\pi$
$548$	0.181127	−	0.675975i	0.00773736	−	0.0288762i
$549$			7.60468i			0.324560i
$550$	7.90561	+	4.56431i	0.337096	+	0.194623i
$551$	0.458918	+	1.71270i	0.0195505	+	0.0729636i
$552$	0.804190	+	0.215482i	0.0342286	+	0.00917152i
$553$	4.51547	−	0.529135i	0.192018	−	0.0225011i
$554$	−12.7086	+	12.7086i	−0.539935	+	0.539935i
$555$	12.4835			0.529895
$556$	−16.5618			−0.702377
$557$	13.3438	−	13.3438i	0.565394	−	0.565394i	−0.365441	−	0.930835i	$-0.619082\pi$
$557$	13.3438	−	13.3438i	0.565394	−	0.565394i	0.930835	+	0.365441i	$0.119082\pi$
$558$	1.05855	−	1.83346i	0.0448119	−	0.0776164i
$559$	4.66346	+	23.2337i	0.197243	+	0.982679i
$560$	−7.91514	−	1.15701i	−0.334476	−	0.0488926i
$561$	−10.2245	+	2.73965i	−0.431680	+	0.115668i
$562$	12.1446	+	21.0350i	0.512288	+	0.887309i
$563$	4.60236	−	7.97152i	0.193966	−	0.335959i	−0.752595	−	0.658484i	$-0.771198\pi$
$563$	4.60236	−	7.97152i	0.193966	−	0.335959i	0.946561	+	0.322524i	$0.104531\pi$
$564$	−1.02537	+	3.82672i	−0.0431757	+	0.161134i
$565$	−7.94602	+	7.94602i	−0.334292	+	0.334292i
$566$	−6.02740	+	22.4946i	−0.253351	+	0.945517i
$567$	1.58056	+	2.12175i	0.0663773	+	0.0891052i
$568$	−4.36211	−	7.55540i	−0.183030	−	0.317017i
$569$	−19.3789	+	11.1884i	−0.812407	+	0.469043i	−0.847791	−	0.530330i	$-0.822068\pi$
$569$	−19.3789	+	11.1884i	−0.812407	+	0.469043i	0.0353840	+	0.999374i	$0.488735\pi$
$570$	−6.10171	−	6.10171i	−0.255572	−	0.255572i
$571$	−12.4979	+	7.21569i	−0.523023	+	0.301967i	−0.738170	−	0.674614i	$-0.764310\pi$
$571$	−12.4979	+	7.21569i	−0.523023	+	0.301967i	0.215148	+	0.976581i	$0.430977\pi$
$572$	0.506036	−	7.93184i	0.0211584	−	0.331647i
$573$			13.1278i			0.548420i
$574$	−17.2659	−	23.1778i	−0.720664	−	0.967424i
$575$	1.72387	−	2.98584i	0.0718905	−	0.124518i
$576$			1.00000i			0.0416667i
$577$	20.1531	+	5.40001i	0.838985	+	0.224805i	0.652630	−	0.757677i	$-0.273666\pi$
$577$	20.1531	+	5.40001i	0.838985	+	0.224805i	0.186355	+	0.982482i	$0.440332\pi$
$578$	5.85205	−	1.56805i	0.243413	−	0.0652223i
$579$	8.80972	+	8.80972i	0.366119	+	0.366119i
$580$	−1.32818	−	1.32818i	−0.0551498	−	0.0551498i
$581$	46.6359	+	6.81709i	1.93478	+	0.282820i
$582$	10.5210	+	6.07429i	0.436108	+	0.251787i
$583$	−23.9239	−	6.41038i	−0.990825	−	0.265491i
$584$	−8.06855	−	13.9751i	−0.333879	−	0.578295i
$585$	−10.8790	−	0.694061i	−0.449792	−	0.0286959i
$586$	−3.30775	−	1.90973i	−0.136642	−	0.0788902i
$587$	−2.08827	−	7.79352i	−0.0861920	−	0.321673i	0.909345	−	0.416042i	$-0.136583\pi$
$587$	−2.08827	−	7.79352i	−0.0861920	−	0.321673i	−0.995537	+	0.0943694i	$0.969917\pi$
$588$	−4.80670	−	5.08878i	−0.198225	−	0.209858i
$589$	−5.23283	+	3.02118i	−0.215615	+	0.124485i
$590$	23.0136	−	6.16648i	0.947456	−	0.253870i
$591$	6.19498	+	23.1200i	0.254827	+	0.951028i
$592$	1.06864	+	3.98822i	0.0439209	+	0.163915i
$593$	19.3983	−	5.19777i	0.796594	−	0.213447i	0.162506	−	0.986708i	$-0.448042\pi$
$593$	19.3983	−	5.19777i	0.796594	−	0.213447i	0.634088	+	0.773261i	$0.281376\pi$
$594$	1.90904	−	1.10218i	0.0783288	−	0.0452232i
$595$	−14.1924	−	35.6937i	−0.581832	−	1.46330i
$596$	−1.26030	−	4.70351i	−0.0516240	−	0.192663i
$597$	−15.0527	−	8.69068i	−0.616066	−	0.355686i
$598$	−2.99574	−	0.191123i	−0.122505	−	0.00781558i
$599$	5.28465	+	9.15328i	0.215925	+	0.373993i	0.953558	−	0.301209i	$-0.0973900\pi$
$599$	5.28465	+	9.15328i	0.215925	+	0.373993i	−0.737633	+	0.675201i	$0.764057\pi$
$600$	4.00004	+	1.07181i	0.163301	+	0.0437564i
$601$	−21.1744	−	12.2251i	−0.863723	−	0.498671i	0.00153438	−	0.999999i	$-0.499512\pi$
$601$	−21.1744	−	12.2251i	−0.863723	−	0.498671i	−0.865257	+	0.501328i	$0.832845\pi$
$602$	10.7812	−	13.6433i	0.439408	−	0.556060i
$603$	5.74537	+	5.74537i	0.233970	+	0.233970i
$604$	−1.23352	−	1.23352i	−0.0501912	−	0.0501912i
$605$	−17.9336	+	4.80528i	−0.729103	+	0.195363i
$606$	12.1836	+	3.26460i	0.494927	+	0.132615i
$607$			14.4840i			0.587888i	0.955823	+	0.293944i	$0.0949680\pi$
$607$			14.4840i			0.587888i	−0.955823	+	0.293944i	$0.905032\pi$
$608$	1.42704	−	2.47170i	0.0578741	−	0.100241i
$609$	−0.191304	−	1.63253i	−0.00775201	−	0.0661533i
$610$			22.9922i			0.930928i
$611$	0.909452	−	14.2552i	0.0367925	−	0.576702i
$612$	−4.15859	+	2.40096i	−0.168101	+	0.0970532i
$613$	12.1745	+	12.1745i	0.491724	+	0.491724i	0.908849	−	0.417125i	$-0.136962\pi$
$613$	12.1745	+	12.1745i	0.491724	+	0.491724i	−0.417125	+	0.908849i	$0.636962\pi$
$614$	−6.15268	+	3.55225i	−0.248302	+	0.143357i
$615$	16.5139	+	28.6028i	0.665903	+	1.15338i
$616$	−4.67712	+	3.48413i	−0.188447	+	0.140380i
$617$	4.78436	−	17.8555i	0.192611	−	0.718835i	−0.800261	−	0.599652i	$-0.795306\pi$
$617$	4.78436	−	17.8555i	0.192611	−	0.718835i	0.992872	−	0.119183i	$-0.0380275\pi$
$618$	−10.0584	+	10.0584i	−0.404607	+	0.404607i
$619$	12.2093	−	45.5656i	0.490732	−	1.83144i	−0.0619980	−	0.998076i	$-0.519747\pi$
$619$	12.2093	−	45.5656i	0.490732	−	1.83144i	0.552730	−	0.833360i	$-0.313586\pi$
$620$	3.20045	−	5.54333i	0.128533	−	0.222626i
$621$	−0.416279	−	0.721017i	−0.0167047	−	0.0289334i
$622$	−2.14370	+	0.574402i	−0.0859545	+	0.0230314i
$623$	18.2225	−	7.24557i	0.730070	−	0.290288i
$624$	−0.709554	−	3.53504i	−0.0284049	−	0.141515i
$625$	−14.2783	+	24.7308i	−0.571133	+	0.989231i
$626$	−7.62392	+	7.62392i	−0.304713	+	0.304713i
$627$	−6.29144			−0.251256
$628$	−22.2725			−0.888768
$629$	−14.0196	+	14.0196i	−0.558999	+	0.558999i
$630$	4.77872	+	6.41497i	0.190389	+	0.255579i
$631$	−41.8739	−	11.2201i	−1.66697	−	0.446664i	−0.702680	−	0.711506i	$-0.748013\pi$
$631$	−41.8739	−	11.2201i	−1.66697	−	0.446664i	−0.964292	+	0.264842i	$0.914680\pi$
$632$	−0.444746	−	1.65982i	−0.0176910	−	0.0660239i
$633$	−17.3414	−	10.0120i	−0.689258	−	0.397943i
$634$		−	21.2572i		−	0.844231i
$635$	9.57031	−	35.7169i	0.379786	−	1.41738i
$636$	−11.2358			−0.445528
$637$	20.6026	+	14.5784i	0.816307	+	0.577619i
$638$	−1.36948			−0.0542183
$639$	−2.25799	+	8.42695i	−0.0893249	+	0.333365i
$640$			3.02343i			0.119512i
$641$	−1.53774	−	0.887817i	−0.0607373	−	0.0350667i	0.469324	−	0.883026i	$-0.344498\pi$
$641$	−1.53774	−	0.887817i	−0.0607373	−	0.0350667i	−0.530061	+	0.847959i	$0.677831\pi$
$642$	−3.07949	−	11.4928i	−0.121538	−	0.453585i
$643$	−42.7011	−	11.4417i	−1.68397	−	0.451218i	−0.715145	−	0.698976i	$-0.753639\pi$
$643$	−42.7011	−	11.4417i	−1.68397	−	0.451218i	−0.968822	+	0.247759i	$0.920306\pi$
$644$	1.31591	+	1.76648i	0.0518541	+	0.0696092i
$645$	−14.0510	+	14.0510i	−0.553259	+	0.553259i
$646$	13.7051			0.539219
$647$	−17.0267			−0.669390			−0.334695	−	0.942326i	$-0.608633\pi$
$647$	−17.0267			−0.669390			−0.334695	+	0.942326i	$0.608633\pi$
$648$	0.707107	−	0.707107i	0.0277778	−	0.0277778i
$649$	8.68550	−	15.0437i	0.340936	−	0.590518i
$650$	−14.9008	−	0.950644i	−0.584458	−	0.0372873i
$651$	5.20495	−	2.06957i	0.203998	−	0.0811130i
$652$	−2.47132	+	0.662188i	−0.0967843	+	0.0259333i
$653$	−11.8401	−	20.5077i	−0.463339	−	0.802527i	0.535786	−	0.844354i	$-0.320016\pi$
$653$	−11.8401	−	20.5077i	−0.463339	−	0.802527i	−0.999125	+	0.0418269i	$0.986682\pi$
$654$	0.116481	−	0.201750i	0.00455475	−	0.00788906i
$655$	−1.92891	+	7.19879i	−0.0753688	+	0.281280i
$656$	−7.72437	+	7.72437i	−0.301586	+	0.301586i
$657$	−4.17659	+	15.5872i	−0.162944	+	0.608116i
$658$	−8.40577	+	6.26172i	−0.327691	+	0.244107i
$659$	5.15795	+	8.93383i	0.200925	+	0.348013i	0.948827	−	0.315797i	$-0.102272\pi$
$659$	5.15795	+	8.93383i	0.200925	+	0.348013i	−0.747902	+	0.663810i	$0.768939\pi$
$660$	5.77185	−	3.33238i	0.224669	−	0.129713i
$661$	31.7013	+	31.7013i	1.23304	+	1.23304i	0.962791	+	0.270249i	$0.0871060\pi$
$661$	31.7013	+	31.7013i	1.23304	+	1.23304i	0.270249	+	0.962791i	$0.412894\pi$
$662$	21.1376	−	12.2038i	0.821537	−	0.474314i
$663$	12.9972	−	11.4382i	0.504769	−	0.444225i
$664$		−	17.8140i		−	0.691319i
$665$	−2.65715	−	22.6753i	−0.103040	−	0.879312i
$666$	2.06446	−	3.57574i	0.0799961	−	0.138557i
$667$			0.517234i			0.0200274i
$668$	−10.4744	−	2.80660i	−0.405266	−	0.108591i
$669$	9.01938	−	2.41674i	0.348709	−	0.0934364i
$670$	17.3707	+	17.3707i	0.671090	+	0.671090i
$671$	11.8536	+	11.8536i	0.457603	+	0.457603i
$672$	−1.64038	+	2.07585i	−0.0632789	+	0.0800778i
$673$	−14.3604	−	8.29101i	−0.553555	−	0.319595i	0.197000	−	0.980404i	$-0.436880\pi$
$673$	−14.3604	−	8.29101i	−0.553555	−	0.319595i	−0.750554	+	0.660809i	$0.770213\pi$
$674$	−27.2558	−	7.30317i	−1.04985	−	0.281308i
$675$	−2.07057	−	3.58634i	−0.0796964	−	0.138038i
$676$	5.01661	+	11.9931i	0.192946	+	0.461272i
$677$	−33.8180	−	19.5248i	−1.29973	−	0.750400i	−0.319374	−	0.947629i	$-0.603473\pi$
$677$	−33.8180	−	19.5248i	−1.29973	−	0.750400i	−0.980358	+	0.197229i	$0.936806\pi$
$678$	0.961968	+	3.59011i	0.0369442	+	0.137878i
$679$	11.8759	+	29.8677i	0.455755	+	1.14622i
$680$	−12.5732	+	7.25915i	−0.482161	+	0.278376i
$681$	24.7938	−	6.64348i	0.950101	−	0.254579i
$682$	−1.20787	−	4.50783i	−0.0462518	−	0.172614i
$683$	9.34323	+	34.8694i	0.357509	+	1.33424i	0.877298	+	0.479946i	$0.159344\pi$
$683$	9.34323	+	34.8694i	0.357509	+	1.33424i	−0.519789	+	0.854295i	$0.673990\pi$
$684$	−2.75683	+	0.738690i	−0.105410	+	0.0282445i
$685$	−1.83239	+	1.05793i	−0.0700120	+	0.0404215i
$686$	−1.63049	−	18.4483i	−0.0622524	−	0.704361i
$687$	−0.454900	−	1.69771i	−0.0173555	−	0.0647717i
$688$	−5.69185	−	3.28619i	−0.217000	−	0.125285i
$689$	39.7190	−	7.97239i	1.51317	−	0.303724i
$690$	−1.25859	−	2.17995i	−0.0479138	−	0.0829891i
$691$	−21.2588	−	5.69627i	−0.808722	−	0.216696i	−0.169312	−	0.985562i	$-0.554155\pi$
$691$	−21.2588	−	5.69627i	−0.808722	−	0.216696i	−0.639410	+	0.768866i	$0.720821\pi$
$692$	11.2349	+	6.48648i	0.427087	+	0.246579i
$693$	5.77088	+	0.843569i	0.219218	+	0.0320445i
$694$	−1.39402	−	1.39402i	−0.0529162	−	0.0529162i
$695$	35.4073	+	35.4073i	1.34308	+	1.34308i
$696$	−0.600090	+	0.160794i	−0.0227463	+	0.00609486i
$697$	−50.6684	−	13.5766i	−1.91920	−	0.514249i
$698$			27.1852i			1.02898i
$699$	−1.17300	+	2.03170i	−0.0443670	+	0.0768459i
$700$	6.54533	+	8.78649i	0.247390	+	0.332098i
$701$		−	40.1037i		−	1.51470i	−0.653011	−	0.757348i	$-0.726495\pi$
$701$		−	40.1037i		−	1.51470i	0.653011	−	0.757348i	$-0.273505\pi$
$702$	−1.99792	+	3.00138i	−0.0754068	+	0.113280i
$703$	−10.2055	+	5.89212i	−0.384906	+	0.222226i
$704$	1.55872	+	1.55872i	0.0587466	+	0.0587466i
$705$	10.3732	−	5.98898i	0.390678	−	0.225558i
$706$	4.70641	+	8.15175i	0.177128	+	0.306795i
$707$	19.9363	+	26.7626i	0.749781	+	1.00651i
$708$	2.03956	−	7.61175i	0.0766515	−	0.286067i
$709$	33.4508	−	33.4508i	1.25627	−	1.25627i	0.303411	−	0.952860i	$-0.401874\pi$
$709$	33.4508	−	33.4508i	1.25627	−	1.25627i	0.952860	−	0.303411i	$-0.0981257\pi$
$710$	−6.82689	+	25.4783i	−0.256209	+	0.956184i
$711$	−0.859183	+	1.48815i	−0.0322219	+	0.0558100i
$712$	−3.70597	−	6.41893i	−0.138887	−	0.240560i
$713$	−1.70255	+	0.456196i	−0.0637608	+	0.0170847i
$714$	−12.5711	−	1.83760i	−0.470462	−	0.0687706i
$715$	−18.0392	+	15.8755i	−0.674629	+	0.593712i
$716$	−2.12453	+	3.67979i	−0.0793973	+	0.137520i
$717$	7.68798	−	7.68798i	0.287113	−	0.287113i
$718$	4.72688			0.176405
$719$	49.3147			1.83913			0.919564	−	0.392940i	$-0.128542\pi$
$719$	49.3147			1.83913			0.919564	+	0.392940i	$0.128542\pi$
$720$	2.13789	−	2.13789i	0.0796745	−	0.0796745i
$721$	−37.3792	+	4.38019i	−1.39207	+	0.163127i
$722$	−10.4844	−	2.80928i	−0.390188	−	0.104551i
$723$	−1.06705	−	3.98230i	−0.0396841	−	0.148103i
$724$	−12.5898	−	7.26873i	−0.467896	−	0.270140i
$725$			2.57272i			0.0955486i
$726$	−1.58935	+	5.93152i	−0.0589862	+	0.220139i
$727$	18.2225			0.675836			0.337918	−	0.941175i	$-0.390277\pi$
$727$	18.2225			0.675836			0.337918	+	0.941175i	$0.390277\pi$
$728$	4.32587	−	8.50217i	0.160327	−	0.315111i
$729$	−1.00000			−0.0370370
$730$	−12.6276	+	47.1270i	−0.467370	+	1.74425i
$731$		−	31.5601i		−	1.16729i
$732$	6.58584	+	3.80234i	0.243420	+	0.140538i
$733$	−12.0316	−	44.9025i	−0.444397	−	1.65851i	−0.717524	−	0.696533i	$-0.754725\pi$
$733$	−12.0316	−	44.9025i	−0.444397	−	1.65851i	0.273128	−	0.961978i	$-0.411942\pi$
$734$	−31.8298	−	8.52877i	−1.17486	−	0.314803i
$735$	−0.603056	+	21.1554i	−0.0222440	+	0.780330i
$736$	0.588708	−	0.588708i	0.0217001	−	0.0217001i
$737$	17.9109			0.659756
$738$	10.9239			0.402115
$739$	20.6157	−	20.6157i	0.758361	−	0.758361i	−0.217663	−	0.976024i	$-0.569843\pi$
$739$	20.6157	−	20.6157i	0.758361	−	0.758361i	0.976024	+	0.217663i	$0.0698435\pi$
$740$	6.24175	−	10.8110i	0.229451	−	0.397421i
$741$	9.22137	−	4.56742i	0.338755	−	0.167788i
$742$	−23.3238	−	18.4309i	−0.856245	−	0.676620i
$743$	3.58181	−	0.959744i	0.131404	−	0.0352096i	−0.192518	−	0.981294i	$-0.561665\pi$
$743$	3.58181	−	0.959744i	0.131404	−	0.0352096i	0.323922	+	0.946084i	$0.394999\pi$
$744$	−1.05855	−	1.83346i	−0.0388082	−	0.0672178i
$745$	−7.36120	+	12.7500i	−0.269694	+	0.467123i
$746$	3.98515	−	14.8728i	0.145907	−	0.544532i
$747$	−12.5964	+	12.5964i	−0.460879	+	0.460879i
$748$	−2.73965	+	10.2245i	−0.100172	+	0.373846i
$749$	12.4600	−	28.9089i	0.455277	−	1.05631i
$750$	1.29834	+	2.24879i	0.0474087	+	0.0821143i
$751$	−36.7338	+	21.2083i	−1.34043	+	0.773900i	−0.986871	−	0.161511i	$-0.948363\pi$
$751$	−36.7338	+	21.2083i	−1.34043	+	0.773900i	−0.353563	+	0.935411i	$0.615030\pi$
$752$	2.80135	+	2.80135i	0.102155	+	0.102155i
$753$	−22.3207	+	12.8869i	−0.813412	+	0.469623i
$754$	2.00725	−	0.994208i	0.0730998	−	0.0362069i
$755$			5.27426i			0.191950i
$756$	2.62777	−	0.307929i	0.0955711	−	0.0111993i
$757$	−13.6306	+	23.6089i	−0.495412	+	0.858080i	−0.999986	−	0.00528912i	$-0.998316\pi$
$757$	−13.6306	+	23.6089i	−0.495412	+	0.858080i	0.504574	+	0.863369i	$0.331650\pi$
$758$			14.0205i			0.509249i
$759$	−1.77273	−	0.475002i	−0.0643460	−	0.0172415i
$760$	−8.33509	+	2.23338i	−0.302345	+	0.0810132i
$761$	−8.48747	−	8.48747i	−0.307671	−	0.307671i	0.536335	−	0.844005i	$-0.319808\pi$
$761$	−8.48747	−	8.48747i	−0.307671	−	0.307671i	−0.844005	+	0.536335i	$0.819808\pi$
$762$	−8.64797	−	8.64797i	−0.313283	−	0.313283i
$763$	0.572743	−	0.227732i	0.0207347	−	0.00824446i
$764$	11.3690	+	6.56388i	0.411315	+	0.237473i
$765$	14.0236	+	3.75761i	0.507024	+	0.135857i
$766$	−10.8720	−	18.8309i	−0.392823	−	0.680389i
$767$	−1.80900	+	28.3551i	−0.0653191	+	1.02384i
$768$	0.866025	+	0.500000i	0.0312500	+	0.0180422i
$769$	13.5023	+	50.3911i	0.486904	+	1.81715i	0.571329	+	0.820721i	$0.306428\pi$
$769$	13.5023	+	50.3911i	0.486904	+	1.81715i	−0.0844245	+	0.996430i	$0.526905\pi$
$770$	17.4479	+	2.55047i	0.628778	+	0.0919127i
$771$	0.635872	−	0.367121i	0.0229004	−	0.0132215i
$772$	12.0343	−	3.22458i	0.433124	−	0.116055i
$773$	0.564178	+	2.10554i	0.0202921	+	0.0757310i	0.975329	−	0.220755i	$-0.0708520\pi$
$773$	0.564178	+	2.10554i	0.0202921	+	0.0757310i	−0.955037	+	0.296486i	$0.904185\pi$
$774$	1.70106	+	6.34844i	0.0611433	+	0.228190i
$775$	−8.46846	+	2.26912i	−0.304196	+	0.0815091i
$776$	10.5210	−	6.07429i	0.377681	−	0.218054i
$777$	10.1511	−	4.03623i	0.364168	−	0.144799i
$778$	4.72940	+	17.6504i	0.169557	+	0.632797i
$779$	−27.0007	−	15.5889i	−0.967400	−	0.558529i
$780$	−6.04059	+	9.07448i	−0.216288	+	0.324919i
$781$	9.61569	+	16.6549i	0.344077	+	0.595958i
$782$	3.86166	+	1.03473i	0.138093	+	0.0370018i
$783$	0.538026	+	0.310629i	0.0192275	+	0.0111010i
$784$	−6.81036	+	1.61833i	−0.243227	+	0.0577976i
$785$	47.6161	+	47.6161i	1.69949	+	1.69949i
$786$	1.74301	+	1.74301i	0.0621712	+	0.0621712i
$787$	39.7914	−	10.6621i	1.41841	−	0.380062i	0.533490	−	0.845806i	$-0.320880\pi$
$787$	39.7914	−	10.6621i	1.41841	−	0.380062i	0.884919	+	0.465744i	$0.154213\pi$
$788$	23.1200	+	6.19498i	0.823615	+	0.220687i
$789$			10.6412i			0.378838i
$790$	−2.59768	+	4.49932i	−0.0924214	+	0.160079i
$791$	−3.89223	+	9.03054i	−0.138392	+	0.321089i
$792$		−	2.20437i		−	0.0783288i
$793$	−25.9792	−	8.76842i	−0.922549	−	0.311376i
$794$	19.4737	−	11.2431i	0.691095	−	0.399004i
$795$	24.0209	+	24.0209i	0.851933	+	0.851933i
$796$	−15.0527	+	8.69068i	−0.533529	+	0.308033i
$797$	13.3815	+	23.1774i	0.473997	+	0.820987i	0.999557	−	0.0297695i	$-0.00947732\pi$
$797$	13.3815	+	23.1774i	0.473997	+	0.820987i	−0.525560	+	0.850757i	$0.676144\pi$
$798$	−6.93450	−	2.98882i	−0.245479	−	0.105803i
$799$	−4.92373	+	18.3756i	−0.174189	+	0.650082i
$800$	2.92823	−	2.92823i	0.103529	−	0.103529i
$801$	−1.91835	+	7.15939i	−0.0677816	+	0.252965i
$802$	−16.9709	+	29.3944i	−0.599263	+	1.03795i
$803$	17.7860	+	30.8063i	0.627656	+	1.08713i
$804$	7.84832	−	2.10295i	0.276789	−	0.0741654i
$805$	0.963278	−	6.58981i	0.0339511	−	0.232260i
$806$	5.04295	+	5.73026i	0.177630	+	0.201840i
$807$	−15.3182	+	26.5319i	−0.539227	+	0.933968i
$808$	8.91905	−	8.91905i	0.313771	−	0.313771i
$809$	−34.1049			−1.19907			−0.599533	−	0.800350i	$-0.704647\pi$
$809$	−34.1049			−1.19907			−0.599533	+	0.800350i	$0.704647\pi$
$810$	−3.02343			−0.106233
$811$	−27.4078	+	27.4078i	−0.962416	+	0.962416i	−0.999319	−	0.0369025i	$-0.988251\pi$
$811$	−27.4078	+	27.4078i	−0.962416	+	0.962416i	0.0369025	+	0.999319i	$0.488251\pi$
$812$	−1.50946	−	0.650589i	−0.0529717	−	0.0228312i
$813$	8.93937	+	2.39530i	0.313518	+	0.0840068i
$814$	−2.35568	−	8.79151i	−0.0825665	−	0.308142i
$815$	6.69909	+	3.86772i	0.234659	+	0.135480i
$816$			4.80193i			0.168101i
$817$	4.85495	−	18.1189i	0.169853	−	0.633901i
$818$	2.53794			0.0887370
$819$	−9.07079	+	2.95309i	−0.316959	+	0.103189i
$820$	33.0277			1.15338
$821$	9.14574	−	34.1324i	0.319189	−	1.19123i	−0.600838	−	0.799371i	$-0.705166\pi$
$821$	9.14574	−	34.1324i	0.319189	−	1.19123i	0.920026	−	0.391857i	$-0.128167\pi$
$822$			0.699821i			0.0244091i
$823$	35.5786	+	20.5413i	1.24019	+	0.716025i	0.969133	−	0.246538i	$-0.0792930\pi$
$823$	35.5786	+	20.5413i	1.24019	+	0.716025i	0.271058	+	0.962563i	$0.412626\pi$
$824$	3.68162	+	13.7400i	0.128255	+	0.478655i
$825$	−8.81756	−	2.36266i	−0.306988	−	0.0822572i
$826$	16.7200	−	12.4552i	0.581762	−	0.433373i
$827$	9.78086	−	9.78086i	0.340114	−	0.340114i	−0.516296	−	0.856410i	$-0.672690\pi$
$827$	9.78086	−	9.78086i	0.340114	−	0.340114i	0.856410	+	0.516296i	$0.172690\pi$
$828$	−0.832559			−0.0289334
$829$	−11.8864			−0.412833			−0.206417	−	0.978464i	$-0.566180\pi$
$829$	−11.8864			−0.412833			−0.206417	+	0.978464i	$0.566180\pi$
$830$	−38.0844	+	38.0844i	−1.32193	+	1.32193i
$831$	8.98632	−	15.5648i	0.311732	−	0.539935i
$832$	−3.41621	−	1.15303i	−0.118436	−	0.0399741i
$833$	−23.0814	−	24.4359i	−0.799723	−	0.846655i
$834$	15.9975	−	4.28651i	0.553947	−	0.148430i
$835$	16.3929	+	28.3933i	0.567299	+	0.982591i
$836$	−3.14572	+	5.44855i	−0.108797	+	0.188442i
$837$	−0.547944	+	2.04496i	−0.0189397	+	0.0706840i
$838$	24.4956	−	24.4956i	0.846185	−	0.846185i
$839$	−4.10667	+	15.3263i	−0.141778	+	0.529122i	0.858100	+	0.513483i	$0.171645\pi$
$839$	−4.10667	+	15.3263i	−0.141778	+	0.529122i	−0.999878	+	0.0156394i	$0.995022\pi$
$840$	7.94489	−	0.931003i	0.274125	−	0.0321226i
$841$	14.3070	+	24.7805i	0.493345	+	0.854499i
$842$	−16.6675	+	9.62299i	−0.574400	+	0.331630i
$843$	−17.1750	−	17.1750i	−0.591539	−	0.591539i
$844$	−17.3414	+	10.0120i	−0.596915	+	0.344629i
$845$	14.9149	−	36.3648i	0.513088	−	1.25099i
$846$		−	3.96171i		−	0.136206i
$847$	−13.0292	+	9.70584i	−0.447688	+	0.333497i
$848$	−5.61789	+	9.73048i	−0.192919	+	0.334146i
$849$		−	23.2881i		−	0.799245i
$850$	19.2079	+	5.14674i	0.658825	+	0.176532i
$851$	−3.32043	+	0.889707i	−0.113823	+	0.0304987i
$852$	6.16895	+	6.16895i	0.211345	+	0.211345i
$853$	−23.9541	−	23.9541i	−0.820171	−	0.820171i	0.165961	−	0.986132i	$-0.446927\pi$
$853$	−23.9541	−	23.9541i	−0.820171	−	0.820171i	−0.986132	+	0.165961i	$0.946927\pi$
$854$	7.43398	+	18.6964i	0.254386	+	0.639776i
$855$	7.47303	+	4.31456i	0.255572	+	0.147555i
$856$	−11.4928	−	3.07949i	−0.392816	−	0.105255i
$857$	−6.80356	−	11.7841i	−0.232405	−	0.402537i	0.726110	−	0.687578i	$-0.241326\pi$
$857$	−6.80356	−	11.7841i	−0.232405	−	0.402537i	−0.958515	+	0.285041i	$0.907993\pi$
$858$	1.56412	+	7.79254i	0.0533981	+	0.266033i
$859$	25.4005	+	14.6650i	0.866654	+	0.500363i	0.866235	−	0.499637i	$-0.166533\pi$
$859$	25.4005	+	14.6650i	0.866654	+	0.500363i	0.000419425		1.00000i	$0.499866\pi$
$860$	5.14304	+	19.1941i	0.175376	+	0.654512i
$861$	22.6764	+	17.9193i	0.772811	+	0.610689i
$862$	22.7325	−	13.1246i	0.774272	−	0.447026i
$863$	−1.12885	+	0.302475i	−0.0384265	+	0.0102964i	−0.277981	−	0.960587i	$-0.589665\pi$
$863$	−1.12885	+	0.302475i	−0.0384265	+	0.0102964i	0.239555	+	0.970883i	$0.422999\pi$
$864$	−0.258819	−	0.965926i	−0.00880520	−	0.0328615i
$865$	−10.1516	−	37.8864i	−0.345166	−	1.28818i
$866$	4.32147	−	1.15793i	0.146849	−	0.0393482i
$867$	−5.24680	+	3.02924i	−0.178191	+	0.102878i
$868$	0.810171	−	5.54240i	0.0274990	−	0.188121i
$869$	0.980384	+	3.65884i	0.0332572	+	0.124118i
$870$	1.62668	+	0.939167i	0.0551498	+	0.0318407i
$871$	−26.2520	+	13.0028i	−0.889515	+	0.440584i
$872$	−0.116481	−	0.201750i	−0.00394453	−	0.00683213i
$873$	−11.7346	−	3.14428i	−0.397157	−	0.106418i
$874$	2.05784	+	1.18809i	0.0696074	+	0.0401879i
$875$	−0.993700	+	6.79793i	−0.0335932	+	0.229812i
$876$	11.4106	+	11.4106i	0.385530	+	0.385530i
$877$	4.38328	+	4.38328i	0.148013	+	0.148013i	0.777230	−	0.629217i	$-0.216624\pi$
$877$	4.38328	+	4.38328i	0.148013	+	0.148013i	−0.629217	+	0.777230i	$0.716624\pi$
$878$	7.37407	−	1.97588i	0.248863	−	0.0666826i
$879$	3.68932	+	0.988549i	0.124438	+	0.0333429i
$880$		−	6.66476i		−	0.224669i
$881$	2.51876	−	4.36262i	0.0848592	−	0.146980i	−0.820472	−	0.571687i	$-0.806289\pi$
$881$	2.51876	−	4.36262i	0.0848592	−	0.146980i	0.905331	+	0.424706i	$0.139623\pi$
$882$	5.95999	+	3.67132i	0.200683	+	0.123620i
$883$			0.666737i			0.0224375i	0.999937	+	0.0112187i	$0.00357111\pi$
$883$			0.666737i			0.0224375i	−0.999937	+	0.0112187i	$0.996429\pi$
$884$	−3.40722	−	16.9750i	−0.114597	−	0.570932i
$885$	−20.6334	+	11.9127i	−0.693586	+	0.400442i
$886$	−0.487327	−	0.487327i	−0.0163721	−	0.0163721i
$887$	−22.2768	+	12.8615i	−0.747983	+	0.431848i	−0.824965	−	0.565184i	$-0.808805\pi$
$887$	−22.2768	+	12.8615i	−0.747983	+	0.431848i	0.0769814	+	0.997033i	$0.475472\pi$
$888$	−2.06446	−	3.57574i	−0.0692786	−	0.119994i
$889$	−3.76600	−	32.1379i	−0.126307	−	1.07787i
$890$	−5.80001	+	21.6459i	−0.194417	+	0.725573i
$891$	−1.55872	+	1.55872i	−0.0522192	+	0.0522192i
$892$	2.41674	−	9.01938i	0.0809183	−	0.301991i
$893$	−5.65352	+	9.79218i	−0.189188	+	0.327683i
$894$	2.43472	+	4.21705i	0.0814291	+	0.141039i
$895$	12.4090	−	3.32498i	0.414787	−	0.111142i
$896$	0.977554	+	2.45853i	0.0326578	+	0.0821339i
$897$	2.94313	−	0.590745i	0.0982683	−	0.0197244i
$898$	4.86055	−	8.41872i	0.162199	−	0.280936i
$899$	0.930031	−	0.930031i	0.0310183	−	0.0310183i
$900$	−4.14115			−0.138038
$901$	−53.9534			−1.79745
$902$	17.0274	−	17.0274i	0.566949	−	0.566949i
$903$	−6.88267	+	15.9688i	−0.229041	+	0.531408i
$904$	3.59011	+	0.961968i	0.119405	+	0.0319946i
$905$	11.3759	+	42.4554i	0.378147	+	1.41126i
$906$	1.51075	+	0.872230i	0.0501912	+	0.0289779i
$907$			59.5047i			1.97582i	0.155022	+	0.987911i	$0.450455\pi$
$907$			59.5047i			1.97582i	−0.155022	+	0.987911i	$0.549545\pi$
$908$	6.64348	−	24.7938i	0.220472	−	0.822812i
$909$	−12.6134			−0.418361
$910$	−27.4249	+	8.92846i	−0.909128	+	0.295976i
$911$	−21.2475			−0.703960			−0.351980	−	0.936008i	$-0.614491\pi$
$911$	−21.2475			−0.703960			−0.351980	+	0.936008i	$0.614491\pi$
$912$	−0.738690	+	2.75683i	−0.0244605	+	0.0912877i
$913$			39.2687i			1.29960i
$914$	−8.93431	−	5.15823i	−0.295521	−	0.170619i
$915$	−5.95083	−	22.2088i	−0.196728	−	0.734200i
$916$	−1.69771	−	0.454900i	−0.0560939	−	0.0150303i
$917$	0.759042	+	6.47743i	0.0250658	+	0.213904i
$918$	3.39547	−	3.39547i	0.112067	−	0.112067i
$919$	15.6889			0.517528			0.258764	−	0.965941i	$-0.416685\pi$
$919$	15.6889			0.517528			0.258764	+	0.965941i	$0.416685\pi$
$920$	−2.51719			−0.0829891
$921$	5.02364	−	5.02364i	0.165535	−	0.165535i
$922$	8.11755	−	14.0600i	0.267337	−	0.463042i
$923$	−26.1847	−	17.4303i	−0.861881	−	0.573726i
$924$	3.61599	−	4.57594i	0.118957	−	0.150538i
$925$	−16.5158	+	4.42540i	−0.543037	+	0.145506i
$926$	−3.04078	−	5.26678i	−0.0999262	−	0.173077i
$927$	7.11234	−	12.3189i	0.233600	−	0.404607i
$928$	−0.160794	+	0.600090i	−0.00527831	+	0.0196989i
$929$	31.2181	−	31.2181i	1.02423	−	1.02423i	0.0245349	−	0.999699i	$-0.492190\pi$
$929$	31.2181	−	31.2181i	1.02423	−	1.02423i	0.999699	−	0.0245349i	$-0.00781050\pi$
$930$	−1.65667	+	6.18279i	−0.0543244	+	0.202742i
$931$	−9.49221	−	17.5795i	−0.311095	−	0.576146i
$932$	1.17300	+	2.03170i	0.0384229	+	0.0665505i
$933$	1.92199	−	1.10966i	0.0629230	−	0.0363286i
$934$	−19.1344	−	19.1344i	−0.626097	−	0.626097i
$935$	27.7160	−	16.0018i	0.906410	−	0.523316i
$936$	1.60031	+	3.23094i	0.0523079	+	0.105607i
$937$		−	41.7209i		−	1.36296i	−0.731836	−	0.681481i	$-0.761336\pi$
$937$		−	41.7209i		−	1.36296i	0.731836	−	0.681481i	$-0.238664\pi$
$938$	19.7416	+	8.50878i	0.644586	+	0.277821i
$939$	5.39093	−	9.33736i	0.175926	−	0.304713i
$940$		−	11.9780i		−	0.390678i
$941$	−48.7954	−	13.0747i	−1.59068	−	0.426223i	−0.648472	−	0.761239i	$-0.724592\pi$
$941$	−48.7954	−	13.0747i	−1.59068	−	0.426223i	−0.942212	+	0.335016i	$0.891258\pi$
$942$	21.5135	−	5.76454i	0.700949	−	0.187819i
$943$	−6.43099	−	6.43099i	−0.209422	−	0.209422i
$944$	−5.57219	−	5.57219i	−0.181359	−	0.181359i
$945$	−6.27620	−	4.95957i	−0.204165	−	0.161335i
$946$	12.5469	+	7.24398i	0.407936	+	0.235522i
$947$	−45.1503	−	12.0980i	−1.46719	−	0.393132i	−0.565222	−	0.824939i	$-0.691209\pi$
$947$	−45.1503	−	12.0980i	−1.46719	−	0.393132i	−0.901966	+	0.431807i	$0.857876\pi$
$948$	0.859183	+	1.48815i	0.0279050	+	0.0483328i
$949$	−48.4336	−	32.2407i	−1.57222	−	1.04658i
$950$	10.2357	+	5.90958i	0.332090	+	0.191732i
$951$	5.50177	+	20.5329i	0.178407	+	0.665824i
$952$	−7.87696	+	9.96809i	−0.255294	+	0.323068i
$953$	−48.4304	+	27.9613i	−1.56881	+	0.905755i	−0.572506	+	0.819901i	$0.694028\pi$
$953$	−48.4304	+	27.9613i	−1.56881	+	0.905755i	−0.996308	+	0.0858539i	$0.972638\pi$
$954$	10.8529	−	2.90804i	0.351377	−	0.0941511i
$955$	−10.2728	−	38.3385i	−0.332419	−	1.24060i
$956$	−2.81400	−	10.5020i	−0.0910112	−	0.339658i
$957$	1.32282	−	0.354448i	0.0427606	−	0.0114577i
$958$	−9.80976	+	5.66367i	−0.316939	+	0.182985i
$959$	−1.14797	+	1.45273i	−0.0370699	+	0.0469110i
$960$	−0.782522	−	2.92041i	−0.0252558	−	0.0942559i
$961$	−22.9652	−	13.2590i	−0.740812	−	0.427708i
$962$	9.83513	+	11.1756i	0.317097	+	0.360315i
$963$	5.94911	+	10.3042i	0.191707	+	0.332047i
$964$	−3.98230	−	1.06705i	−0.128261	−	0.0343675i
$965$	−32.6218	−	18.8342i	−1.05013	−	0.606294i
$966$	−1.72827	−	1.36571i	−0.0556062	−	0.0439410i
$967$	−9.57079	−	9.57079i	−0.307776	−	0.307776i	0.536270	−	0.844046i	$-0.319833\pi$
$967$	−9.57079	−	9.57079i	−0.307776	−	0.307776i	−0.844046	+	0.536270i	$0.819833\pi$
$968$	4.34217	+	4.34217i	0.139563	+	0.139563i
$969$	−13.2381	+	3.54713i	−0.425269	+	0.113950i
$970$	−35.4789	−	9.50653i	−1.13916	−	0.305236i
$971$		−	29.7111i		−	0.953474i	−0.879046	−	0.476737i	$-0.841819\pi$
$971$		−	29.7111i		−	0.953474i	0.879046	−	0.476737i	$-0.158181\pi$
$972$	−0.500000	+	0.866025i	−0.0160375	+	0.0277778i
$973$	40.2399	+	17.3437i	1.29003	+	0.556014i
$974$			21.0567i			0.674701i
$975$	14.6391	−	2.93837i	0.468828	−	0.0941030i
$976$	6.58584	−	3.80234i	0.210808	−	0.121710i
$977$	−0.648179	−	0.648179i	−0.0207371	−	0.0207371i	0.696662	−	0.717399i	$-0.254668\pi$
$977$	−0.648179	−	0.648179i	−0.0207371	−	0.0207371i	−0.717399	+	0.696662i	$0.754668\pi$
$978$	2.21572	−	1.27925i	0.0708510	−	0.0409058i
$979$	8.16933	+	14.1497i	0.261093	+	0.452226i
$980$	18.0196	+	11.1000i	0.575616	+	0.354576i
$981$	−0.0602948	+	0.225023i	−0.00192506	+	0.00718444i
$982$	−14.9052	+	14.9052i	−0.475645	+	0.475645i
$983$	−13.9200	+	51.9502i	−0.443980	+	1.65696i	0.274636	+	0.961548i	$0.411443\pi$
$983$	−13.9200	+	51.9502i	−0.443980	+	1.65696i	−0.718616	+	0.695407i	$0.755224\pi$
$984$	5.46195	−	9.46038i	0.174121	−	0.301586i
$985$	−36.1838	−	62.6721i	−1.15291	−	1.99690i
$986$	−2.88159	+	0.772119i	−0.0917684	+	0.0245893i
$987$	6.49869	−	8.22393i	0.206856	−	0.261771i
$988$	0.655184	−	10.2696i	0.0208442	−	0.326721i
$989$	2.73595	−	4.73880i	0.0869981	−	0.150685i
$990$	−4.71270	+	4.71270i	−0.149779	+	0.149779i
$991$	8.93986			0.283984			0.141992	−	0.989868i	$-0.454649\pi$
$991$	8.93986			0.283984			0.141992	+	0.989868i	$0.454649\pi$
$992$	−2.11709			−0.0672178
$993$	−17.2588	+	17.2588i	−0.547691	+	0.547691i
$994$	2.68644	+	22.9253i	0.0852087	+	0.727145i
$995$	50.7607	+	13.6013i	1.60922	+	0.431190i
$996$	4.61061	+	17.2070i	0.146093	+	0.545226i
$997$	−31.7216	−	18.3145i	−1.00463	−	0.580026i	−0.0950184	−	0.995476i	$-0.530291\pi$
$997$	−31.7216	−	18.3145i	−1.00463	−	0.580026i	−0.909616	+	0.415449i	$0.863624\pi$
$998$		−	15.7765i		−	0.499398i
$999$	−1.06864	+	3.98822i	−0.0338103	+	0.126182i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.by.a.397.4	✓	32
7.3	odd	6		546.2.cg.a.241.4	yes	32
13.2	odd	12		546.2.cg.a.145.4	yes	32
91.80	even	12	inner	546.2.by.a.535.4	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.by.a.397.4	✓	32	1.1	even	1	trivial
546.2.by.a.535.4	yes	32	91.80	even	12	inner
546.2.cg.a.145.4	yes	32	13.2	odd	12
546.2.cg.a.241.4	yes	32	7.3	odd	6

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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)

\(f(q)\)	\(=\)	\(q+(-0.258819 + 0.965926i) q^{2} -1.00000i q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.782522 + 2.92041i) q^{5} +(0.965926 + 0.258819i) q^{6} +(1.58056 + 2.12175i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(-0.258819 + 0.965926i) q^{2} -1.00000i q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.782522 + 2.92041i) q^{5} +(0.965926 + 0.258819i) q^{6} +(1.58056 + 2.12175i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000 q^{9} -3.02343 q^{10} +(-1.55872 + 1.55872i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(1.15303 - 3.41621i) q^{13} +(-2.45853 + 0.977554i) q^{14} +(2.92041 - 0.782522i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-2.40096 + 4.15859i) q^{17} +(0.258819 - 0.965926i) q^{18} +(-2.01814 + 2.01814i) q^{19} +(0.782522 - 2.92041i) q^{20} +(2.12175 - 1.58056i) q^{21} +(-1.10218 - 1.90904i) q^{22} +(-0.721017 + 0.416279i) q^{23} +(-0.707107 - 0.707107i) q^{24} +(-3.58634 + 2.07057i) q^{25} +(3.00138 + 1.99792i) q^{26} +1.00000i q^{27} +(-0.307929 - 2.62777i) q^{28} +(0.310629 - 0.538026i) q^{29} +3.02343i q^{30} +(2.04496 + 0.547944i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(1.55872 + 1.55872i) q^{33} +(-3.39547 - 3.39547i) q^{34} +(-4.95957 + 6.27620i) q^{35} +(0.866025 + 0.500000i) q^{36} +(3.98822 + 1.06864i) q^{37} +(-1.42704 - 2.47170i) q^{38} +(-3.41621 - 1.15303i) q^{39} +(2.61837 + 1.51172i) q^{40} +(2.82732 + 10.5517i) q^{41} +(0.977554 + 2.45853i) q^{42} +(-5.69185 + 3.28619i) q^{43} +(2.12926 - 0.570532i) q^{44} +(-0.782522 - 2.92041i) q^{45} +(-0.215482 - 0.804190i) q^{46} +(3.82672 - 1.02537i) q^{47} +(0.866025 - 0.500000i) q^{48} +(-2.00366 + 6.70711i) q^{49} +(-1.07181 - 4.00004i) q^{50} +(4.15859 + 2.40096i) q^{51} +(-2.70666 + 2.38201i) q^{52} +(5.61789 + 9.73048i) q^{53} +(-0.965926 - 0.258819i) q^{54} +(-5.77185 - 3.33238i) q^{55} +(2.61793 + 0.382681i) q^{56} +(2.01814 + 2.01814i) q^{57} +(0.439296 + 0.439296i) q^{58} +(-7.61175 + 2.03956i) q^{59} +(-2.92041 - 0.782522i) q^{60} -7.60468i q^{61} +(-1.05855 + 1.83346i) q^{62} +(-1.58056 - 2.12175i) q^{63} -1.00000i q^{64} +(10.8790 + 0.694061i) q^{65} +(-1.90904 + 1.10218i) q^{66} +(-5.74537 - 5.74537i) q^{67} +(4.15859 - 2.40096i) q^{68} +(0.416279 + 0.721017i) q^{69} +(-4.77872 - 6.41497i) q^{70} +(2.25799 - 8.42695i) q^{71} +(-0.707107 + 0.707107i) q^{72} +(4.17659 - 15.5872i) q^{73} +(-2.06446 + 3.57574i) q^{74} +(2.07057 + 3.58634i) q^{75} +(2.75683 - 0.738690i) q^{76} +(-5.77088 - 0.843569i) q^{77} +(1.99792 - 3.00138i) q^{78} +(0.859183 - 1.48815i) q^{79} +(-2.13789 + 2.13789i) q^{80} +1.00000 q^{81} -10.9239 q^{82} +(12.5964 - 12.5964i) q^{83} +(-2.62777 + 0.307929i) q^{84} +(-14.0236 - 3.75761i) q^{85} +(-1.70106 - 6.34844i) q^{86} +(-0.538026 - 0.310629i) q^{87} +2.20437i q^{88} +(1.91835 - 7.15939i) q^{89} +3.02343 q^{90} +(9.07079 - 2.95309i) q^{91} +0.832559 q^{92} +(0.547944 - 2.04496i) q^{93} +3.96171i q^{94} +(-7.47303 - 4.31456i) q^{95} +(0.258819 + 0.965926i) q^{96} +(11.7346 + 3.14428i) q^{97} +(-5.95999 - 3.67132i) q^{98} +(1.55872 - 1.55872i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{7} - 32 q^{9}+O(q^{10}) \) 32 * q + 8 * q^7 - 32 * q^9	\( 32 q + 8 q^{7} - 32 q^{9} - 4 q^{11} - 16 q^{12} + 4 q^{14} + 16 q^{16} - 8 q^{17} - 12 q^{19} - 8 q^{21} - 4 q^{22} - 24 q^{23} - 24 q^{25} + 8 q^{26} - 4 q^{28} - 12 q^{29} - 28 q^{31} + 4 q^{33} - 8 q^{34} - 44 q^{35} - 36 q^{37} + 8 q^{38} - 20 q^{39} - 28 q^{41} + 12 q^{42} + 84 q^{43} + 8 q^{44} - 4 q^{46} + 16 q^{47} + 24 q^{49} - 16 q^{50} + 8 q^{52} - 4 q^{53} + 48 q^{55} + 12 q^{56} + 12 q^{57} + 24 q^{58} + 12 q^{59} - 40 q^{62} - 8 q^{63} - 4 q^{65} + 8 q^{67} - 8 q^{69} + 60 q^{70} + 20 q^{71} + 4 q^{73} + 20 q^{74} + 8 q^{75} + 36 q^{76} - 12 q^{77} - 20 q^{78} + 32 q^{81} - 48 q^{82} + 12 q^{83} - 16 q^{84} - 4 q^{85} + 52 q^{86} - 36 q^{87} - 36 q^{89} - 16 q^{92} + 4 q^{93} - 48 q^{95} + 76 q^{97} + 8 q^{98} + 4 q^{99}+O(q^{100}) \) 32 * q + 8 * q^7 - 32 * q^9 - 4 * q^11 - 16 * q^12 + 4 * q^14 + 16 * q^16 - 8 * q^17 - 12 * q^19 - 8 * q^21 - 4 * q^22 - 24 * q^23 - 24 * q^25 + 8 * q^26 - 4 * q^28 - 12 * q^29 - 28 * q^31 + 4 * q^33 - 8 * q^34 - 44 * q^35 - 36 * q^37 + 8 * q^38 - 20 * q^39 - 28 * q^41 + 12 * q^42 + 84 * q^43 + 8 * q^44 - 4 * q^46 + 16 * q^47 + 24 * q^49 - 16 * q^50 + 8 * q^52 - 4 * q^53 + 48 * q^55 + 12 * q^56 + 12 * q^57 + 24 * q^58 + 12 * q^59 - 40 * q^62 - 8 * q^63 - 4 * q^65 + 8 * q^67 - 8 * q^69 + 60 * q^70 + 20 * q^71 + 4 * q^73 + 20 * q^74 + 8 * q^75 + 36 * q^76 - 12 * q^77 - 20 * q^78 + 32 * q^81 - 48 * q^82 + 12 * q^83 - 16 * q^84 - 4 * q^85 + 52 * q^86 - 36 * q^87 - 36 * q^89 - 16 * q^92 + 4 * q^93 - 48 * q^95 + 76 * q^97 + 8 * q^98 + 4 * q^99

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