LMFDB - Embedded newform 546.2.bx.a.97.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(97,546)]

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, 6, 5]))

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

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

chi := DirichletCharacter("546.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bx (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			97.8
Character	$\chi$	$=$	546.97
Dual form			546.2.bx.a.349.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 + 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(0.0374438 + 0.0374438i) q^{5} +(0.258819 - 0.965926i) q^{6} +(-2.54217 - 0.733067i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.258819 + 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(0.0374438 + 0.0374438i) q^{5} +(0.258819 - 0.965926i) q^{6} +(-2.54217 - 0.733067i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +(-0.0264768 + 0.0458592i) q^{10} +(1.73753 - 0.465569i) q^{11} +1.00000 q^{12} +(-2.12463 + 2.91306i) q^{13} +(0.0501275 - 2.64528i) q^{14} +(-0.0137054 - 0.0511492i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-3.26497 - 5.65510i) q^{17} +(-0.707107 + 0.707107i) q^{18} +(1.60100 - 5.97500i) q^{19} +(-0.0511492 - 0.0137054i) q^{20} +(1.83505 + 1.90594i) q^{21} +(0.899410 + 1.55782i) q^{22} +(-6.84131 - 3.94983i) q^{23} +(0.258819 + 0.965926i) q^{24} -4.99720i q^{25} +(-3.36370 - 1.29828i) q^{26} -1.00000i q^{27} +(2.56811 - 0.636228i) q^{28} +(-3.18465 + 5.51598i) q^{29} +(0.0458592 - 0.0264768i) q^{30} +(-1.81281 - 1.81281i) q^{31} +(0.965926 + 0.258819i) q^{32} +(-1.73753 - 0.465569i) q^{33} +(4.61737 - 4.61737i) q^{34} +(-0.0677396 - 0.122637i) q^{35} +(-0.866025 - 0.500000i) q^{36} +(-4.19793 + 1.12483i) q^{37} +6.18577 q^{38} +(3.29652 - 1.46047i) q^{39} -0.0529536i q^{40} +(0.982767 - 0.263332i) q^{41} +(-1.36605 + 2.26581i) q^{42} +(9.47687 - 5.47148i) q^{43} +(-1.27196 + 1.27196i) q^{44} +(-0.0137054 + 0.0511492i) q^{45} +(2.04458 - 7.63049i) q^{46} +(-4.86100 + 4.86100i) q^{47} +(-0.866025 + 0.500000i) q^{48} +(5.92522 + 3.72716i) q^{49} +(4.82692 - 1.29337i) q^{50} +6.52995i q^{51} +(0.383455 - 3.58510i) q^{52} -4.52395 q^{53} +(0.965926 - 0.258819i) q^{54} +(0.0824923 + 0.0476270i) q^{55} +(1.27923 + 2.31594i) q^{56} +(-4.37400 + 4.37400i) q^{57} +(-6.15227 - 1.64850i) q^{58} +(9.90333 + 2.65359i) q^{59} +(0.0374438 + 0.0374438i) q^{60} +(-2.13293 + 1.23145i) q^{61} +(1.28185 - 2.22023i) q^{62} +(-0.636228 - 2.56811i) q^{63} +1.00000i q^{64} +(-0.188631 + 0.0295218i) q^{65} -1.79882i q^{66} +(-1.84174 - 6.87347i) q^{67} +(5.65510 + 3.26497i) q^{68} +(3.94983 + 6.84131i) q^{69} +(0.100926 - 0.0971723i) q^{70} +(-10.4733 - 2.80632i) q^{71} +(0.258819 - 0.965926i) q^{72} +(-3.17457 + 3.17457i) q^{73} +(-2.17301 - 3.76376i) q^{74} +(-2.49860 + 4.32770i) q^{75} +(1.60100 + 5.97500i) q^{76} +(-4.75837 - 0.0901704i) q^{77} +(2.26391 + 2.80619i) q^{78} +5.14192 q^{79} +(0.0511492 - 0.0137054i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(0.508717 + 0.881124i) q^{82} +(-6.12074 - 6.12074i) q^{83} +(-2.54217 - 0.733067i) q^{84} +(0.0894956 - 0.334002i) q^{85} +(7.73784 + 7.73784i) q^{86} +(5.51598 - 3.18465i) q^{87} +(-1.55782 - 0.899410i) q^{88} +(1.38055 + 5.15227i) q^{89} -0.0529536 q^{90} +(7.53664 - 5.84799i) q^{91} +7.89966 q^{92} +(0.663534 + 2.47634i) q^{93} +(-5.95349 - 3.43725i) q^{94} +(0.283674 - 0.163779i) q^{95} +(-0.707107 - 0.707107i) q^{96} +(-3.92607 + 14.6523i) q^{97} +(-2.06660 + 6.68799i) q^{98} +(1.27196 + 1.27196i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 8 q^{7} + 20 q^{9}+O(q^{10}) $ 40 * q - 8 * q^7 + 20 * q^9	$ 40 q - 8 q^{7} + 20 q^{9} + 8 q^{11} + 40 q^{12} - 8 q^{14} + 20 q^{16} + 16 q^{17} + 16 q^{19} + 4 q^{21} + 8 q^{22} + 32 q^{26} + 8 q^{28} - 8 q^{33} + 16 q^{34} - 32 q^{35} + 40 q^{37} - 16 q^{38} - 16 q^{39} - 4 q^{41} + 12 q^{42} + 24 q^{43} + 8 q^{44} - 4 q^{46} + 16 q^{47} - 4 q^{49} - 16 q^{50} - 8 q^{52} + 32 q^{53} - 72 q^{55} + 12 q^{56} + 8 q^{57} - 36 q^{58} + 84 q^{59} - 48 q^{61} - 4 q^{62} - 4 q^{63} - 16 q^{65} + 12 q^{68} - 8 q^{69} + 36 q^{70} - 40 q^{71} - 48 q^{73} + 8 q^{74} + 36 q^{75} + 16 q^{76} - 24 q^{77} - 8 q^{78} - 48 q^{79} - 20 q^{81} + 36 q^{83} - 8 q^{84} + 8 q^{85} - 8 q^{86} + 12 q^{89} - 48 q^{91} - 16 q^{92} - 24 q^{93} - 96 q^{95} + 8 q^{98} - 8 q^{99}+O(q^{100}) $ 40 * q - 8 * q^7 + 20 * q^9 + 8 * q^11 + 40 * q^12 - 8 * q^14 + 20 * q^16 + 16 * q^17 + 16 * q^19 + 4 * q^21 + 8 * q^22 + 32 * q^26 + 8 * q^28 - 8 * q^33 + 16 * q^34 - 32 * q^35 + 40 * q^37 - 16 * q^38 - 16 * q^39 - 4 * q^41 + 12 * q^42 + 24 * q^43 + 8 * q^44 - 4 * q^46 + 16 * q^47 - 4 * q^49 - 16 * q^50 - 8 * q^52 + 32 * q^53 - 72 * q^55 + 12 * q^56 + 8 * q^57 - 36 * q^58 + 84 * q^59 - 48 * q^61 - 4 * q^62 - 4 * q^63 - 16 * q^65 + 12 * q^68 - 8 * q^69 + 36 * q^70 - 40 * q^71 - 48 * q^73 + 8 * q^74 + 36 * q^75 + 16 * q^76 - 24 * q^77 - 8 * q^78 - 48 * q^79 - 20 * q^81 + 36 * q^83 - 8 * q^84 + 8 * q^85 - 8 * q^86 + 12 * q^89 - 48 * q^91 - 16 * q^92 - 24 * q^93 - 96 * q^95 + 8 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$	0.0374438	+	0.0374438i	0.0167454	+	0.0167454i	0.715430	−	0.698685i	$-0.246231\pi$
$5$	0.0374438	+	0.0374438i	0.0167454	+	0.0167454i	−0.698685	+	0.715430i	$0.746231\pi$
$6$	0.258819	−	0.965926i	0.105662	−	0.394338i
$7$	−2.54217	−	0.733067i	−0.960849	−	0.277073i
$7$	−2.54217	−	0.733067i	−0.960849	−	0.277073i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−0.0264768	+	0.0458592i	−0.00837270	+	0.0145019i
$11$	1.73753	−	0.465569i	0.523884	−	0.140374i	0.0128213	−	0.999918i	$-0.495919\pi$
$11$	1.73753	−	0.465569i	0.523884	−	0.140374i	0.511063	+	0.859544i	$0.329252\pi$
$12$	1.00000			0.288675
$13$	−2.12463	+	2.91306i	−0.589267	+	0.807938i
$13$	−2.12463	+	2.91306i	−0.589267	+	0.807938i
$14$	0.0501275	−	2.64528i	0.0133972	−	0.706980i
$15$	−0.0137054	−	0.0511492i	−0.00353872	−	0.0132067i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−3.26497	−	5.65510i	−0.791873	−	1.37156i	−0.924806	−	0.380439i	$-0.875773\pi$
$17$	−3.26497	−	5.65510i	−0.791873	−	1.37156i	0.132933	−	0.991125i	$-0.457560\pi$
$18$	−0.707107	+	0.707107i	−0.166667	+	0.166667i
$19$	1.60100	−	5.97500i	0.367294	−	1.37076i	−0.496991	−	0.867756i	$-0.665562\pi$
$19$	1.60100	−	5.97500i	0.367294	−	1.37076i	0.864285	−	0.503003i	$-0.167772\pi$
$20$	−0.0511492	−	0.0137054i	−0.0114373	−	0.00306462i
$21$	1.83505	+	1.90594i	0.400440	+	0.415910i
$22$	0.899410	+	1.55782i	0.191755	+	0.332129i
$23$	−6.84131	−	3.94983i	−1.42651	−	0.823597i	−0.429668	−	0.902987i	$-0.641369\pi$
$23$	−6.84131	−	3.94983i	−1.42651	−	0.823597i	−0.996844	+	0.0793904i	$0.974703\pi$
$24$	0.258819	+	0.965926i	0.0528312	+	0.197169i
$25$		−	4.99720i		−	0.999439i
$26$	−3.36370	−	1.29828i	−0.659675	−	0.254614i
$27$		−	1.00000i		−	0.192450i
$28$	2.56811	−	0.636228i	0.485328	−	0.120236i
$29$	−3.18465	+	5.51598i	−0.591375	+	1.02429i	0.402673	+	0.915344i	$0.368081\pi$
$29$	−3.18465	+	5.51598i	−0.591375	+	1.02429i	−0.994048	+	0.108947i	$0.965252\pi$
$30$	0.0458592	−	0.0264768i	0.00837270	−	0.00483398i
$31$	−1.81281	−	1.81281i	−0.325590	−	0.325590i	0.525317	−	0.850907i	$-0.323947\pi$
$31$	−1.81281	−	1.81281i	−0.325590	−	0.325590i	−0.850907	+	0.525317i	$0.823947\pi$
$32$	0.965926	+	0.258819i	0.170753	+	0.0457532i
$33$	−1.73753	−	0.465569i	−0.302464	−	0.0810451i
$34$	4.61737	−	4.61737i	0.791873	−	0.791873i
$35$	−0.0677396	−	0.122637i	−0.0114501	−	0.0207295i
$36$	−0.866025	−	0.500000i	−0.144338	−	0.0833333i
$37$	−4.19793	+	1.12483i	−0.690136	+	0.184921i	−0.586808	−	0.809726i	$-0.699616\pi$
$37$	−4.19793	+	1.12483i	−0.690136	+	0.184921i	−0.103328	+	0.994647i	$0.532949\pi$
$38$	6.18577			1.00347
$39$	3.29652	−	1.46047i	0.527865	−	0.233862i
$40$		−	0.0529536i		−	0.00837270i
$41$	0.982767	−	0.263332i	0.153482	−	0.0411255i	−0.181260	−	0.983435i	$-0.558017\pi$
$41$	0.982767	−	0.263332i	0.153482	−	0.0411255i	0.334742	+	0.942310i	$0.391351\pi$
$42$	−1.36605	+	2.26581i	−0.210786	+	0.349623i
$43$	9.47687	−	5.47148i	1.44521	−	0.834392i	0.447019	−	0.894524i	$-0.352486\pi$
$43$	9.47687	−	5.47148i	1.44521	−	0.834392i	0.998190	+	0.0601321i	$0.0191522\pi$
$44$	−1.27196	+	1.27196i	−0.191755	+	0.191755i
$45$	−0.0137054	+	0.0511492i	−0.00204308	+	0.00762488i
$46$	2.04458	−	7.63049i	0.301457	−	1.12505i
$47$	−4.86100	+	4.86100i	−0.709050	+	0.709050i	−0.966335	−	0.257285i	$-0.917172\pi$
$47$	−4.86100	+	4.86100i	−0.709050	+	0.709050i	0.257285	+	0.966335i	$0.417172\pi$
$48$	−0.866025	+	0.500000i	−0.125000	+	0.0721688i
$49$	5.92522	+	3.72716i	0.846461	+	0.532451i
$50$	4.82692	−	1.29337i	0.682630	−	0.182910i
$51$			6.52995i			0.914376i
$52$	0.383455	−	3.58510i	0.0531756	−	0.497164i
$53$	−4.52395			−0.621412			−0.310706	−	0.950506i	$-0.600565\pi$
$53$	−4.52395			−0.621412			−0.310706	+	0.950506i	$0.600565\pi$
$54$	0.965926	−	0.258819i	0.131446	−	0.0352208i
$55$	0.0824923	+	0.0476270i	0.0111233	+	0.00642202i
$56$	1.27923	+	2.31594i	0.170944	+	0.309481i
$57$	−4.37400	+	4.37400i	−0.579351	+	0.579351i
$58$	−6.15227	−	1.64850i	−0.807833	−	0.216458i
$59$	9.90333	+	2.65359i	1.28930	+	0.345468i	0.837396	−	0.546597i	$-0.184077\pi$
$59$	9.90333	+	2.65359i	1.28930	+	0.345468i	0.451908	+	0.892065i	$0.350744\pi$
$60$	0.0374438	+	0.0374438i	0.00483398	+	0.00483398i
$61$	−2.13293	+	1.23145i	−0.273094	+	0.157671i	−0.630293	−	0.776358i	$-0.717065\pi$
$61$	−2.13293	+	1.23145i	−0.273094	+	0.157671i	0.357199	+	0.934028i	$0.383732\pi$
$62$	1.28185	−	2.22023i	0.162795	−	0.281969i
$63$	−0.636228	−	2.56811i	−0.0801572	−	0.323552i
$64$			1.00000i			0.125000i
$65$	−0.188631	+	0.0295218i	−0.0233968	+	0.00366173i
$66$		−	1.79882i		−	0.221419i
$67$	−1.84174	−	6.87347i	−0.225004	−	0.839728i	−0.982403	−	0.186775i	$-0.940196\pi$
$67$	−1.84174	−	6.87347i	−0.225004	−	0.839728i	0.757398	−	0.652953i	$-0.226470\pi$
$68$	5.65510	+	3.26497i	0.685782	+	0.395936i
$69$	3.94983	+	6.84131i	0.475504	+	0.823597i
$70$	0.100926	−	0.0971723i	0.0120630	−	0.0116143i
$71$	−10.4733	−	2.80632i	−1.24295	−	0.333049i	−0.423344	−	0.905969i	$-0.639144\pi$
$71$	−10.4733	−	2.80632i	−1.24295	−	0.333049i	−0.819611	+	0.572921i	$0.805810\pi$
$72$	0.258819	−	0.965926i	0.0305021	−	0.113835i
$73$	−3.17457	+	3.17457i	−0.371555	+	0.371555i	−0.868043	−	0.496489i	$-0.834622\pi$
$73$	−3.17457	+	3.17457i	−0.371555	+	0.371555i	0.496489	+	0.868043i	$0.334622\pi$
$74$	−2.17301	−	3.76376i	−0.252607	−	0.437528i
$75$	−2.49860	+	4.32770i	−0.288513	+	0.499720i
$76$	1.60100	+	5.97500i	0.183647	+	0.685379i
$77$	−4.75837	−	0.0901704i	−0.542267	−	0.0102759i
$78$	2.26391	+	2.80619i	0.256337	+	0.317739i
$79$	5.14192			0.578512			0.289256	−	0.957252i	$-0.406592\pi$
$79$	5.14192			0.578512			0.289256	+	0.957252i	$0.406592\pi$
$80$	0.0511492	−	0.0137054i	0.00571866	−	0.00153231i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	0.508717	+	0.881124i	0.0561784	+	0.0973039i
$83$	−6.12074	−	6.12074i	−0.671839	−	0.671839i	0.286301	−	0.958140i	$-0.407574\pi$
$83$	−6.12074	−	6.12074i	−0.671839	−	0.671839i	−0.958140	+	0.286301i	$0.907574\pi$
$84$	−2.54217	−	0.733067i	−0.277373	−	0.0799842i
$85$	0.0894956	−	0.334002i	0.00970716	−	0.0362276i
$86$	7.73784	+	7.73784i	0.834392	+	0.834392i
$87$	5.51598	−	3.18465i	0.591375	−	0.341430i
$88$	−1.55782	−	0.899410i	−0.166065	−	0.0958774i
$89$	1.38055	+	5.15227i	0.146338	+	0.546139i	0.999692	+	0.0248085i	$0.00789760\pi$
$89$	1.38055	+	5.15227i	0.146338	+	0.546139i	−0.853355	+	0.521331i	$0.825436\pi$
$90$	−0.0529536			−0.00558180
$91$	7.53664	−	5.84799i	0.790055	−	0.613036i
$92$	7.89966			0.823597
$93$	0.663534	+	2.47634i	0.0688052	+	0.256785i
$94$	−5.95349	−	3.43725i	−0.614055	−	0.354525i
$95$	0.283674	−	0.163779i	0.0291044	−	0.0168034i
$96$	−0.707107	−	0.707107i	−0.0721688	−	0.0721688i
$97$	−3.92607	+	14.6523i	−0.398632	+	1.48771i	0.416873	+	0.908965i	$0.363126\pi$
$97$	−3.92607	+	14.6523i	−0.398632	+	1.48771i	−0.815505	+	0.578750i	$0.803541\pi$
$98$	−2.06660	+	6.68799i	−0.208758	+	0.675589i
$99$	1.27196	+	1.27196i	0.127837	+	0.127837i
$100$	2.49860	+	4.32770i	0.249860	+	0.432770i
$101$	−7.62081	+	13.1996i	−0.758299	+	1.31341i	0.185419	+	0.982660i	$0.440636\pi$
$101$	−7.62081	+	13.1996i	−0.758299	+	1.31341i	−0.943718	+	0.330752i	$0.892698\pi$
$102$	−6.30745	+	1.69008i	−0.624530	+	0.167342i
$103$	19.1901			1.89086			0.945429	−	0.325828i	$-0.105643\pi$
$103$	19.1901			1.89086			0.945429	+	0.325828i	$0.105643\pi$
$104$	3.56219	−	0.557504i	0.349301	−	0.0546678i
$105$	−0.00265443	+	0.140077i	−0.000259046	+	0.0136701i
$106$	−1.17088	−	4.36980i	−0.113726	−	0.424432i
$107$	−9.34489	+	16.1858i	−0.903405	+	1.56474i	−0.0803599	+	0.996766i	$0.525607\pi$
$107$	−9.34489	+	16.1858i	−0.903405	+	1.56474i	−0.823045	+	0.567977i	$0.807726\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$	14.5734	−	14.5734i	1.39588	−	1.39588i	0.584439	−	0.811437i	$-0.301315\pi$
$109$	14.5734	−	14.5734i	1.39588	−	1.39588i	0.811437	−	0.584439i	$-0.198685\pi$
$110$	−0.0246535	+	0.0920083i	−0.00235062	+	0.00877264i
$111$	4.19793	+	1.12483i	0.398450	+	0.106764i
$112$	−1.90594	+	1.83505i	−0.180094	+	0.173396i
$113$	3.90162	+	6.75781i	0.367034	+	0.635721i	0.989100	−	0.147243i	$-0.0470399\pi$
$113$	3.90162	+	6.75781i	0.367034	+	0.635721i	−0.622066	+	0.782964i	$0.713707\pi$
$114$	−5.35704	−	3.09289i	−0.501733	−	0.289675i
$115$	−0.108268	−	0.404062i	−0.0100960	−	0.0376789i
$116$		−	6.36930i		−	0.591375i
$117$	−3.58510	−	0.383455i	−0.331443	−	0.0354504i
$118$			10.2527i			0.943836i
$119$	4.15454	+	16.7697i	0.380846	+	1.53727i
$120$	−0.0264768	+	0.0458592i	−0.00241699	+	0.00418635i
$121$	−6.72404	+	3.88212i	−0.611276	+	0.352920i
$122$	−1.74153	−	1.74153i	−0.157671	−	0.157671i
$123$	−0.982767	−	0.263332i	−0.0886131	−	0.0237438i
$124$	2.47634	+	0.663534i	0.222382	+	0.0595871i
$125$	0.374333	−	0.374333i	0.0334814	−	0.0334814i
$126$	2.31594	−	1.27923i	0.206320	−	0.113963i
$127$	−7.24448	−	4.18260i	−0.642843	−	0.371146i	0.142866	−	0.989742i	$-0.454368\pi$
$127$	−7.24448	−	4.18260i	−0.642843	−	0.371146i	−0.785709	+	0.618596i	$0.787702\pi$
$128$	−0.965926	+	0.258819i	−0.0853766	+	0.0228766i
$129$	−10.9430			−0.963473
$130$	−0.0773371	−	0.174562i	−0.00678291	−	0.0153101i
$131$		−	8.99279i		−	0.785704i	−0.919602	−	0.392852i	$-0.871488\pi$
$131$		−	8.99279i		−	0.785704i	0.919602	−	0.392852i	$-0.128512\pi$
$132$	1.73753	−	0.465569i	0.151232	−	0.0405226i
$133$	−8.45008	+	14.0158i	−0.732715	+	1.21532i
$134$	6.16259	−	3.55797i	0.532366	−	0.307362i
$135$	0.0374438	−	0.0374438i	0.00322265	−	0.00322265i
$136$	−1.69008	+	6.30745i	−0.144923	+	0.540859i
$137$	5.44962	−	20.3383i	0.465593	−	1.73762i	−0.189324	−	0.981915i	$-0.560630\pi$
$137$	5.44962	−	20.3383i	0.465593	−	1.73762i	0.654917	−	0.755701i	$-0.272704\pi$
$138$	−5.58590	+	5.58590i	−0.475504	+	0.475504i
$139$	−4.84711	+	2.79848i	−0.411126	+	0.237364i	−0.691274	−	0.722593i	$-0.742950\pi$
$139$	−4.84711	+	2.79848i	−0.411126	+	0.237364i	0.280147	+	0.959957i	$0.409617\pi$
$140$	0.119983	+	0.0723372i	0.0101404	+	0.00611361i
$141$	6.64025	−	1.77925i	0.559210	−	0.149840i
$142$		−	10.8428i		−	0.909906i
$143$	−2.33537	+	6.05069i	−0.195294	+	0.505984i
$144$	1.00000			0.0833333
$145$	−0.325785	+	0.0872938i	−0.0270550	+	0.00724936i
$146$	−3.88803	−	2.24476i	−0.321776	−	0.185777i
$147$	−3.26782	−	6.19043i	−0.269525	−	0.510578i
$148$	3.07310	−	3.07310i	0.252607	−	0.252607i
$149$	−2.77611	−	0.743856i	−0.227428	−	0.0609390i	0.143305	−	0.989679i	$-0.454227\pi$
$149$	−2.77611	−	0.743856i	−0.227428	−	0.0609390i	−0.370733	+	0.928739i	$0.620894\pi$
$150$	−4.82692	−	1.29337i	−0.394116	−	0.105603i
$151$	2.06592	+	2.06592i	0.168122	+	0.168122i	0.786153	−	0.618031i	$-0.212070\pi$
$151$	2.06592	+	2.06592i	0.168122	+	0.168122i	−0.618031	+	0.786153i	$0.712070\pi$
$152$	−5.35704	+	3.09289i	−0.434513	+	0.250866i
$153$	3.26497	−	5.65510i	0.263958	−	0.457188i
$154$	−1.14446	−	4.61957i	−0.0922232	−	0.372256i
$155$		−	0.135757i		−	0.0109043i
$156$	−2.12463	+	2.91306i	−0.170107	+	0.233232i
$157$		−	7.42705i		−	0.592743i	−0.955073	−	0.296371i	$-0.904223\pi$
$157$		−	7.42705i		−	0.592743i	0.955073	−	0.296371i	$-0.0957766\pi$
$158$	1.33083	+	4.96672i	0.105875	+	0.395131i
$159$	3.91785	+	2.26197i	0.310706	+	0.179386i
$160$	0.0264768	+	0.0458592i	0.00209317	+	0.00362548i
$161$	14.4963	+	15.0563i	1.14246	+	1.18660i
$162$	−0.965926	−	0.258819i	−0.0758903	−	0.0203347i
$163$	2.08469	−	7.78018i	0.163286	−	0.609391i	−0.834967	−	0.550300i	$-0.814513\pi$
$163$	2.08469	−	7.78018i	0.163286	−	0.609391i	0.998253	−	0.0590905i	$-0.0188200\pi$
$164$	−0.719435	+	0.719435i	−0.0561784	+	0.0561784i
$165$	−0.0476270	−	0.0824923i	−0.00370776	−	0.00642202i
$166$	4.32802	−	7.49635i	0.335919	−	0.581829i
$167$	0.136199	+	0.508303i	0.0105394	+	0.0393337i	0.970995	−	0.239099i	$-0.0768519\pi$
$167$	0.136199	+	0.508303i	0.0105394	+	0.0393337i	−0.960456	+	0.278432i	$0.910185\pi$
$168$	0.0501275	−	2.64528i	0.00386742	−	0.204088i
$169$	−3.97187	−	12.3784i	−0.305528	−	0.952183i
$170$	0.345784			0.0265204
$171$	5.97500	−	1.60100i	0.456920	−	0.122431i
$172$	−5.47148	+	9.47687i	−0.417196	+	0.722605i
$173$	2.38636	+	4.13330i	0.181432	+	0.314249i	0.942368	−	0.334577i	$-0.108594\pi$
$173$	2.38636	+	4.13330i	0.181432	+	0.314249i	−0.760937	+	0.648826i	$0.775260\pi$
$174$	4.50378	+	4.50378i	0.341430	+	0.341430i
$175$	−3.66328	+	12.7037i	−0.276918	+	0.960310i
$176$	0.465569	−	1.73753i	0.0350936	−	0.130971i
$177$	−7.24974	−	7.24974i	−0.544924	−	0.544924i
$178$	−4.61940	+	2.66701i	−0.346238	+	0.199901i
$179$	−17.6975	−	10.2177i	−1.32278	−	0.763705i	−0.338605	−	0.940929i	$-0.609955\pi$
$179$	−17.6975	−	10.2177i	−1.32278	−	0.763705i	−0.984171	+	0.177224i	$0.943288\pi$
$180$	−0.0137054	−	0.0511492i	−0.00102154	−	0.00381244i
$181$	−12.6427			−0.939728			−0.469864	−	0.882739i	$-0.655697\pi$
$181$	−12.6427			−0.939728			−0.469864	+	0.882739i	$0.655697\pi$
$182$	7.59935	+	5.76627i	0.563302	+	0.427424i
$183$	2.46290			0.182062
$184$	2.04458	+	7.63049i	0.150729	+	0.562527i
$185$	−0.199305	−	0.115069i	−0.0146532	−	0.00846001i
$186$	−2.22023	+	1.28185i	−0.162795	+	0.0939897i
$187$	−8.30582	−	8.30582i	−0.607382	−	0.607382i
$188$	1.77925	−	6.64025i	0.129765	−	0.484290i
$189$	−0.733067	+	2.54217i	−0.0533228	+	0.184915i
$190$	0.231619	+	0.231619i	0.0168034	+	0.0168034i
$191$	1.26921	+	2.19834i	0.0918371	+	0.159067i	0.908284	−	0.418354i	$-0.137393\pi$
$191$	1.26921	+	2.19834i	0.0918371	+	0.159067i	−0.816447	+	0.577420i	$0.804059\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	4.10345	−	1.09951i	0.295372	−	0.0791448i	−0.108090	−	0.994141i	$-0.534473\pi$
$193$	4.10345	−	1.09951i	0.295372	−	0.0791448i	0.403462	+	0.914996i	$0.367807\pi$
$194$	−15.1692			−1.08908
$195$	0.178120	+	0.0687487i	0.0127554	+	0.00492320i
$196$	−6.99497	−	0.265202i	−0.499641	−	0.0189430i
$197$	−3.20097	−	11.9462i	−0.228060	−	0.851131i	−0.981156	−	0.193220i	$-0.938107\pi$
$197$	−3.20097	−	11.9462i	−0.228060	−	0.851131i	0.753096	−	0.657911i	$-0.228560\pi$
$198$	−0.899410	+	1.55782i	−0.0639183	+	0.110710i
$199$	2.63958	+	4.57189i	0.187115	+	0.324092i	0.944287	−	0.329123i	$-0.106753\pi$
$199$	2.63958	+	4.57189i	0.187115	+	0.324092i	−0.757172	+	0.653215i	$0.773420\pi$
$200$	−3.53355	+	3.53355i	−0.249860	+	0.249860i
$201$	−1.84174	+	6.87347i	−0.129906	+	0.484817i
$202$	−14.7223	−	3.94482i	−1.03586	−	0.277557i
$203$	12.1395	−	11.6880i	0.852026	−	0.820335i
$204$	−3.26497	−	5.65510i	−0.228594	−	0.395936i
$205$	0.0466587	+	0.0269384i	0.00325879	+	0.00188146i
$206$	4.96677	+	18.5362i	0.346051	+	1.29148i
$207$		−	7.89966i		−	0.549064i
$208$	1.46047	+	3.29652i	0.101265	+	0.228572i
$209$		−	11.1271i		−	0.769677i
$210$	−0.135991	+	0.0336906i	−0.00938426	+	0.00232487i
$211$	−10.3655	+	17.9535i	−0.713589	+	1.23597i	0.249912	+	0.968269i	$0.419598\pi$
$211$	−10.3655	+	17.9535i	−0.713589	+	1.23597i	−0.963501	+	0.267704i	$0.913735\pi$
$212$	3.91785	−	2.26197i	0.269079	−	0.155353i
$213$	7.66700	+	7.66700i	0.525334	+	0.525334i
$214$	−18.0529	−	4.83727i	−1.23407	−	0.330669i
$215$	0.559724	+	0.149978i	0.0381728	+	0.0102284i
$216$	−0.707107	+	0.707107i	−0.0481125	+	0.0481125i
$217$	3.27955	+	5.93737i	0.222630	+	0.403055i
$218$	17.8487	+	10.3049i	1.20886	+	0.697938i
$219$	4.33654	−	1.16197i	0.293036	−	0.0785188i
$220$	−0.0952540			−0.00642202
$221$	23.4105	+	2.50394i	1.57476	+	0.168433i
$222$			4.34602i			0.291686i
$223$	22.8651	−	6.12669i	1.53116	−	0.410274i	0.607764	−	0.794118i	$-0.292067\pi$
$223$	22.8651	−	6.12669i	1.53116	−	0.410274i	0.923398	+	0.383844i	$0.125400\pi$
$224$	−2.26581	−	1.36605i	−0.151391	−	0.0912731i
$225$	4.32770	−	2.49860i	0.288513	−	0.166573i
$226$	−5.51773	+	5.51773i	−0.367034	+	0.367034i
$227$	4.97806	−	18.5784i	0.330405	−	1.23309i	−0.578360	−	0.815781i	$-0.696307\pi$
$227$	4.97806	−	18.5784i	0.330405	−	1.23309i	0.908765	−	0.417307i	$-0.137026\pi$
$228$	1.60100	−	5.97500i	0.106029	−	0.395704i
$229$	18.7339	−	18.7339i	1.23797	−	1.23797i	0.277142	−	0.960829i	$-0.410613\pi$
$229$	18.7339	−	18.7339i	1.23797	−	1.23797i	0.960829	−	0.277142i	$-0.0893872\pi$
$230$	0.362272	−	0.209158i	0.0238875	−	0.0137915i
$231$	4.07579	+	2.45728i	0.268167	+	0.161677i
$232$	6.15227	−	1.64850i	0.403917	−	0.108229i
$233$			22.2718i			1.45907i	0.683942	+	0.729536i	$0.260264\pi$
$233$			22.2718i			1.45907i	−0.683942	+	0.729536i	$0.739736\pi$
$234$	−0.557504	−	3.56219i	−0.0364452	−	0.232868i
$235$	−0.364029			−0.0237466
$236$	−9.90333	+	2.65359i	−0.644652	+	0.172734i
$237$	−4.45304	−	2.57096i	−0.289256	−	0.167002i
$238$	−15.1230	+	8.35328i	−0.980277	+	0.541463i
$239$	12.8622	−	12.8622i	0.831985	−	0.831985i	−0.155804	−	0.987788i	$-0.549797\pi$
$239$	12.8622	−	12.8622i	0.831985	−	0.831985i	0.987788	+	0.155804i	$0.0497967\pi$
$240$	−0.0511492	−	0.0137054i	−0.00330167	−	0.000884680i
$241$	4.38024	+	1.17368i	0.282156	+	0.0756034i	0.397122	−	0.917766i	$-0.370009\pi$
$241$	4.38024	+	1.17368i	0.282156	+	0.0756034i	−0.114966	+	0.993369i	$0.536676\pi$
$242$	−5.49015	−	5.49015i	−0.352920	−	0.352920i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	1.23145	−	2.13293i	0.0788354	−	0.136547i
$245$	0.0823040	+	0.361422i	0.00525821	+	0.0230904i
$246$		−	1.01743i		−	0.0648693i
$247$	14.0040	+	17.3585i	0.891054	+	1.10449i
$248$			2.56370i			0.162795i
$249$	2.24035	+	8.36109i	0.141976	+	0.529863i
$250$	0.458463	+	0.264694i	0.0289957	+	0.0167407i
$251$	−6.82072	−	11.8138i	−0.430520	−	0.745682i	0.566398	−	0.824132i	$-0.308336\pi$
$251$	−6.82072	−	11.8138i	−0.430520	−	0.745682i	−0.996918	+	0.0784495i	$0.975003\pi$
$252$	1.83505	+	1.90594i	0.115597	+	0.120063i
$253$	−13.7259	−	3.67784i	−0.862938	−	0.231224i
$254$	2.16507	−	8.08016i	0.135849	−	0.506994i
$255$	−0.244506	+	0.244506i	−0.0153116	+	0.0153116i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−3.01610	+	5.22404i	−0.188139	+	0.325866i	−0.944630	−	0.328138i	$-0.893579\pi$
$257$	−3.01610	+	5.22404i	−0.188139	+	0.325866i	0.756491	+	0.654004i	$0.226912\pi$
$258$	−2.83224	−	10.5701i	−0.176328	−	0.658064i
$259$	11.4964	+	0.217855i	0.714353	+	0.0135369i
$260$	0.148598	−	0.119882i	0.00921566	−	0.00743477i
$261$	−6.36930			−0.394250
$262$	8.68637	−	2.32751i	0.536646	−	0.143794i
$263$	0.128688	−	0.222894i	0.00793522	−	0.0137442i	−0.862031	−	0.506856i	$-0.830807\pi$
$263$	0.128688	−	0.222894i	0.00793522	−	0.0137442i	0.869966	+	0.493112i	$0.164141\pi$
$264$	0.899410	+	1.55782i	0.0553548	+	0.0958774i
$265$	−0.169394	−	0.169394i	−0.0104058	−	0.0104058i
$266$	−15.7253	−	4.53459i	−0.964178	−	0.278034i
$267$	1.38055	−	5.15227i	0.0844881	−	0.315314i
$268$	5.03173	+	5.03173i	0.307362	+	0.307362i
$269$	8.18417	−	4.72513i	0.498998	−	0.288096i	−0.229302	−	0.973355i	$-0.573644\pi$
$269$	8.18417	−	4.72513i	0.498998	−	0.288096i	0.728299	+	0.685259i	$0.240311\pi$
$270$	0.0458592	+	0.0264768i	0.00279090	+	0.00161133i
$271$	−5.35914	−	20.0006i	−0.325544	−	1.21495i	−0.913764	−	0.406246i	$-0.866837\pi$
$271$	−5.35914	−	20.0006i	−0.325544	−	1.21495i	0.588219	−	0.808701i	$-0.299829\pi$
$272$	−6.52995			−0.395936
$273$	−9.45092	+	1.29619i	−0.571996	+	0.0784489i
$274$	21.0557			1.27202
$275$	−2.32654	−	8.68276i	−0.140296	−	0.523590i
$276$	−6.84131	−	3.94983i	−0.411798	−	0.237752i
$277$	10.7522	−	6.20781i	0.646039	−	0.372991i	−0.140898	−	0.990024i	$-0.544999\pi$
$277$	10.7522	−	6.20781i	0.646039	−	0.372991i	0.786937	+	0.617033i	$0.211666\pi$
$278$	−3.95765	−	3.95765i	−0.237364	−	0.237364i
$279$	0.663534	−	2.47634i	0.0397247	−	0.148255i
$280$	−0.0388186	+	0.134617i	−0.00231985	+	0.00804490i
$281$	−7.48838	−	7.48838i	−0.446720	−	0.446720i	0.447543	−	0.894262i	$-0.352299\pi$
$281$	−7.48838	−	7.48838i	−0.446720	−	0.446720i	−0.894262	+	0.447543i	$0.852299\pi$
$282$	3.43725	+	5.95349i	0.204685	+	0.354525i
$283$	12.5837	−	21.7956i	0.748025	−	1.29562i	−0.200744	−	0.979644i	$-0.564336\pi$
$283$	12.5837	−	21.7956i	0.748025	−	1.29562i	0.948768	−	0.315973i	$-0.102331\pi$
$284$	10.4733	−	2.80632i	0.621477	−	0.166524i
$285$	−0.327559			−0.0194029
$286$	−6.44895	−	0.689766i	−0.381335	−	0.0407867i
$287$	−2.69140	−	0.0510015i	−0.158868	−	0.00301052i
$288$	0.258819	+	0.965926i	0.0152511	+	0.0569177i
$289$	−12.8201	+	22.2051i	−0.754125	+	1.30618i
$290$	−0.168639	−	0.292091i	−0.00990281	−	0.0171522i
$291$	10.7262	−	10.7262i	0.628782	−	0.628782i
$292$	1.16197	−	4.33654i	0.0679992	−	0.253777i
$293$	−3.83933	−	1.02875i	−0.224296	−	0.0600999i	0.144921	−	0.989443i	$-0.453707\pi$
$293$	−3.83933	−	1.02875i	−0.224296	−	0.0600999i	−0.369217	+	0.929343i	$0.620374\pi$
$294$	5.13372	−	4.75867i	0.299405	−	0.277531i
$295$	0.271458	+	0.470179i	0.0158049	+	0.0273749i
$296$	3.76376	+	2.17301i	0.218764	+	0.126304i
$297$	−0.465569	−	1.73753i	−0.0270150	−	0.100821i
$298$		−	2.87404i		−	0.166489i
$299$	26.0414	−	11.5372i	1.50601	−	0.667215i
$300$		−	4.99720i		−	0.288513i
$301$	−28.1028	+	6.96222i	−1.61982	+	0.401296i
$302$	−1.46082	+	2.53022i	−0.0840610	+	0.145598i
$303$	13.1996	−	7.62081i	0.758299	−	0.437804i
$304$	−4.37400	−	4.37400i	−0.250866	−	0.250866i
$305$	−0.125975	−	0.0337550i	−0.00721332	−	0.00193280i
$306$	6.30745	+	1.69008i	0.360573	+	0.0966152i
$307$	5.25816	−	5.25816i	0.300099	−	0.300099i	−0.540954	−	0.841052i	$-0.681937\pi$
$307$	5.25816	−	5.25816i	0.300099	−	0.300099i	0.841052	+	0.540954i	$0.181937\pi$
$308$	4.16596	−	2.30110i	0.237378	−	0.131117i
$309$	−16.6191	−	9.59506i	−0.945429	−	0.545844i
$310$	0.131131	−	0.0351365i	0.00744775	−	0.00199562i
$311$	−0.482464			−0.0273580			−0.0136790	−	0.999906i	$-0.504354\pi$
$311$	−0.482464			−0.0273580			−0.0136790	+	0.999906i	$0.504354\pi$
$312$	−3.36370	−	1.29828i	−0.190432	−	0.0735007i
$313$			2.74394i			0.155097i	0.996989	+	0.0775484i	$0.0247092\pi$
$313$			2.74394i			0.155097i	−0.996989	+	0.0775484i	$0.975291\pi$
$314$	7.17398	−	1.92226i	0.404851	−	0.108479i
$315$	0.0723372	−	0.119983i	0.00407574	−	0.00676027i
$316$	−4.45304	+	2.57096i	−0.250503	+	0.144628i
$317$	2.83551	−	2.83551i	0.159258	−	0.159258i	−0.622980	−	0.782238i	$-0.714078\pi$
$317$	2.83551	−	2.83551i	0.159258	−	0.159258i	0.782238	+	0.622980i	$0.214078\pi$
$318$	−1.17088	+	4.36980i	−0.0656599	+	0.245046i
$319$	−2.96535	+	11.0668i	−0.166028	+	0.619624i
$320$	−0.0374438	+	0.0374438i	−0.00209317	+	0.00209317i
$321$	16.1858	−	9.34489i	0.903405	−	0.521581i
$322$	−10.7913	+	17.8992i	−0.601377	+	0.997481i
$323$	−39.0164	+	10.4544i	−2.17093	+	0.581700i
$324$		−	1.00000i		−	0.0555556i
$325$	14.5571	+	10.6172i	0.807485	+	0.588937i
$326$	8.05463			0.446105
$327$	−19.9076	+	5.33423i	−1.10089	+	0.294983i
$328$	−0.881124	−	0.508717i	−0.0486520	−	0.0280892i
$329$	15.9209	−	8.79404i	0.877749	−	0.484831i
$330$	0.0673547	−	0.0673547i	0.00370776	−	0.00370776i
$331$	−6.99923	−	1.87544i	−0.384712	−	0.103083i	0.0612790	−	0.998121i	$-0.480482\pi$
$331$	−6.99923	−	1.87544i	−0.384712	−	0.103083i	−0.445991	+	0.895037i	$0.647149\pi$
$332$	8.36109	+	2.24035i	0.458874	+	0.122955i
$333$	−3.07310	−	3.07310i	−0.168405	−	0.168405i
$334$	−0.455732	+	0.263117i	−0.0249366	+	0.0143971i
$335$	0.188407	−	0.326331i	0.0102938	−	0.0178294i
$336$	2.56811	−	0.636228i	0.140102	−	0.0347091i
$337$			20.6065i			1.12251i	0.827644	+	0.561254i	$0.189681\pi$
$337$			20.6065i			1.12251i	−0.827644	+	0.561254i	$0.810319\pi$
$338$	10.9286	−	7.04029i	0.594437	−	0.382941i
$339$		−	7.80325i		−	0.423814i
$340$	0.0894956	+	0.334002i	0.00485358	+	0.0181138i
$341$	−3.99379	−	2.30581i	−0.216276	−	0.124867i
$342$	3.09289	+	5.35704i	0.167244	+	0.289675i
$343$	−12.3306	−	13.8186i	−0.665793	−	0.746137i
$344$	−10.5701	−	2.83224i	−0.569900	−	0.152704i
$345$	−0.108268	+	0.404062i	−0.00582895	+	0.0217540i
$346$	−3.37482	+	3.37482i	−0.181432	+	0.181432i
$347$	5.87966	+	10.1839i	0.315637	+	0.546699i	0.979573	−	0.201090i	$-0.0644485\pi$
$347$	5.87966	+	10.1839i	0.315637	+	0.546699i	−0.663936	+	0.747790i	$0.731115\pi$
$348$	−3.18465	+	5.51598i	−0.170715	+	0.295687i
$349$	1.86752	+	6.96967i	0.0999659	+	0.373078i	0.997726	−	0.0674079i	$-0.0214729\pi$
$349$	1.86752	+	6.96967i	0.0999659	+	0.373078i	−0.897760	+	0.440486i	$0.854806\pi$
$350$	−13.2190	−	0.250497i	−0.706583	−	0.0133896i
$351$	2.91306	+	2.12463i	0.155488	+	0.113405i
$352$	1.79882			0.0958774
$353$	−9.00241	+	2.41219i	−0.479150	+	0.128388i	−0.490307	−	0.871550i	$-0.663115\pi$
$353$	−9.00241	+	2.41219i	−0.479150	+	0.128388i	0.0111567	+	0.999938i	$0.496449\pi$
$354$	5.12634	−	8.87908i	0.272462	−	0.471918i
$355$	−0.287082	−	0.497241i	−0.0152367	−	0.0263908i
$356$	−3.77172	−	3.77172i	−0.199901	−	0.199901i
$357$	4.78689	−	16.6002i	0.253349	−	0.878577i
$358$	5.28906	−	19.7390i	0.279535	−	1.04324i
$359$	−12.1364	−	12.1364i	−0.640535	−	0.640535i	0.310152	−	0.950687i	$-0.399620\pi$
$359$	−12.1364	−	12.1364i	−0.640535	−	0.640535i	−0.950687	+	0.310152i	$0.899620\pi$
$360$	0.0458592	−	0.0264768i	0.00241699	−	0.00139545i
$361$	−16.6829	−	9.63190i	−0.878049	−	0.506942i
$362$	−3.27218	−	12.2120i	−0.171982	−	0.641846i
$363$	7.76425			0.407517
$364$	−3.60293	+	8.83283i	−0.188845	+	0.462966i
$365$	−0.237736			−0.0124437
$366$	0.637444	+	2.37897i	0.0333197	+	0.124351i
$367$	−23.4736	−	13.5525i	−1.22531	−	0.707434i	−0.259266	−	0.965806i	$-0.583481\pi$
$367$	−23.4736	−	13.5525i	−1.22531	−	0.707434i	−0.966045	+	0.258372i	$0.916814\pi$
$368$	−6.84131	+	3.94983i	−0.356628	+	0.205899i
$369$	0.719435	+	0.719435i	0.0374523	+	0.0374523i
$370$	0.0595639	−	0.222295i	0.00309658	−	0.0115566i
$371$	11.5006	+	3.31636i	0.597083	+	0.172177i
$372$	−1.81281	−	1.81281i	−0.0939897	−	0.0939897i
$373$	3.73995	+	6.47779i	0.193647	+	0.335407i	0.946456	−	0.322832i	$-0.104635\pi$
$373$	3.73995	+	6.47779i	0.193647	+	0.335407i	−0.752809	+	0.658239i	$0.771302\pi$
$374$	5.87310	−	10.1725i	0.303691	−	0.526008i
$375$	−0.511349	+	0.137016i	−0.0264059	+	0.00707545i
$376$	6.87449			0.354525
$377$	−9.30218	−	20.9965i	−0.479086	−	1.08138i
$378$	−2.64528	−	0.0501275i	−0.136058	−	0.00257828i
$379$	6.84739	+	25.5548i	0.351727	+	1.31266i	0.884554	+	0.466438i	$0.154463\pi$
$379$	6.84739	+	25.5548i	0.351727	+	1.31266i	−0.532827	+	0.846224i	$0.678870\pi$
$380$	−0.163779	+	0.283674i	−0.00840171	+	0.0145522i
$381$	4.18260	+	7.24448i	0.214281	+	0.371146i
$382$	−1.79494	+	1.79494i	−0.0918371	+	0.0918371i
$383$	−4.56308	+	17.0297i	−0.233163	+	0.870175i	0.745806	+	0.666163i	$0.232065\pi$
$383$	−4.56308	+	17.0297i	−0.233163	+	0.870175i	−0.978968	+	0.204011i	$0.934602\pi$
$384$	0.965926	+	0.258819i	0.0492922	+	0.0132078i
$385$	−0.174796	−	0.181548i	−0.00890840	−	0.00925255i
$386$	2.12410	+	3.67905i	0.108114	+	0.187259i
$387$	9.47687	+	5.47148i	0.481737	+	0.278131i
$388$	−3.92607	−	14.6523i	−0.199316	−	0.743857i
$389$		−	8.71310i		−	0.441772i	−0.975300	−	0.220886i	$-0.929105\pi$
$389$		−	8.71310i		−	0.441772i	0.975300	−	0.220886i	$-0.0708949\pi$
$390$	−0.0203053	+	0.189844i	−0.00102820	+	0.00961313i
$391$			51.5844i			2.60873i
$392$	−1.55427	−	6.82527i	−0.0785023	−	0.344728i
$393$	−4.49640	+	7.78799i	−0.226813	+	0.392852i
$394$	10.7107	−	6.18380i	0.539595	−	0.311535i
$395$	0.192533	+	0.192533i	0.00968740	+	0.00968740i
$396$	−1.73753	−	0.465569i	−0.0873140	−	0.0233957i
$397$	1.54721	+	0.414574i	0.0776524	+	0.0208069i	0.297436	−	0.954742i	$-0.403868\pi$
$397$	1.54721	+	0.414574i	0.0776524	+	0.0208069i	−0.219784	+	0.975549i	$0.570535\pi$
$398$	−3.73293	+	3.73293i	−0.187115	+	0.187115i
$399$	14.3259	−	7.91301i	0.717191	−	0.396146i
$400$	−4.32770	−	2.49860i	−0.216385	−	0.124930i
$401$	18.0230	−	4.82925i	0.900026	−	0.241161i	0.220999	−	0.975274i	$-0.429068\pi$
$401$	18.0230	−	4.82925i	0.900026	−	0.241161i	0.679027	+	0.734113i	$0.262402\pi$
$402$	−7.11594			−0.354911
$403$	9.13238	−	1.42927i	0.454916	−	0.0711971i
$404$		−	15.2416i		−	0.758299i
$405$	−0.0511492	+	0.0137054i	−0.00254163	+	0.000681027i
$406$	14.4316	+	8.70079i	0.716231	+	0.431813i
$407$	−6.77033	+	3.90885i	−0.335593	+	0.193755i
$408$	4.61737	−	4.61737i	0.228594	−	0.228594i
$409$	−5.88757	+	21.9727i	−0.291121	+	1.08648i	0.653128	+	0.757248i	$0.273457\pi$
$409$	−5.88757	+	21.9727i	−0.291121	+	1.08648i	−0.944249	+	0.329232i	$0.893210\pi$
$410$	−0.0139444	+	0.0520410i	−0.000688662	+	0.00257012i
$411$	−14.8886	+	14.8886i	−0.734403	+	0.734403i
$412$	−16.6191	+	9.59506i	−0.818766	+	0.472715i
$413$	−23.2307	−	14.0057i	−1.14311	−	0.689174i
$414$	7.63049	−	2.04458i	0.375018	−	0.100486i
$415$		−	0.458368i		−	0.0225004i
$416$	−2.80619	+	2.26391i	−0.137585	+	0.110997i
$417$	5.59696			0.274084
$418$	10.7479	−	2.87990i	0.525699	−	0.140861i
$419$	7.58249	+	4.37775i	0.370429	+	0.213867i	0.673646	−	0.739054i	$-0.264727\pi$
$419$	7.58249	+	4.37775i	0.370429	+	0.213867i	−0.303217	+	0.952922i	$0.598061\pi$
$420$	−0.0677396	−	0.122637i	−0.00330536	−	0.00598409i
$421$	−5.68785	+	5.68785i	−0.277209	+	0.277209i	−0.831994	−	0.554785i	$-0.812801\pi$
$421$	−5.68785	+	5.68785i	−0.277209	+	0.277209i	0.554785	+	0.831994i	$0.312801\pi$
$422$	−20.0246	−	5.36557i	−0.974781	−	0.261192i
$423$	−6.64025	−	1.77925i	−0.322860	−	0.0865101i
$424$	3.19891	+	3.19891i	0.155353	+	0.155353i
$425$	−28.2597	+	16.3157i	−1.37079	+	0.791429i
$426$	−5.42139	+	9.39012i	−0.262667	+	0.454953i
$427$	6.32500	−	1.56696i	0.306088	−	0.0758307i
$428$		−	18.6898i		−	0.903405i
$429$	5.04784	−	4.07236i	0.243712	−	0.196615i
$430$			0.579469i			0.0279445i
$431$	−0.341932	−	1.27611i	−0.0164703	−	0.0614680i	0.957202	−	0.289422i	$-0.0934631\pi$
$431$	−0.341932	−	1.27611i	−0.0164703	−	0.0614680i	−0.973672	+	0.227954i	$0.926796\pi$
$432$	−0.866025	−	0.500000i	−0.0416667	−	0.0240563i
$433$	−9.23315	−	15.9923i	−0.443717	−	0.768540i	0.554245	−	0.832354i	$-0.313007\pi$
$433$	−9.23315	−	15.9923i	−0.443717	−	0.768540i	−0.997962	+	0.0638133i	$0.979674\pi$
$434$	−4.88625	+	4.70451i	−0.234547	+	0.225824i
$435$	0.325785	+	0.0872938i	0.0156202	+	0.00418542i
$436$	−5.33423	+	19.9076i	−0.255463	+	0.953402i
$437$	−34.5531	+	34.5531i	−1.65290	+	1.65290i
$438$	2.24476	+	3.88803i	0.107259	+	0.185777i
$439$	4.64434	−	8.04424i	0.221662	−	0.383931i	−0.733650	−	0.679527i	$-0.762185\pi$
$439$	4.64434	−	8.04424i	0.221662	−	0.383931i	0.955313	+	0.295596i	$0.0955184\pi$
$440$	−0.0246535	−	0.0920083i	−0.00117531	−	0.00438632i
$441$	−0.265202	+	6.99497i	−0.0126287	+	0.333094i
$442$	3.64047	+	23.2609i	0.173160	+	1.10641i
$443$	18.3552			0.872081			0.436040	−	0.899927i	$-0.356380\pi$
$443$	18.3552			0.872081			0.436040	+	0.899927i	$0.356380\pi$
$444$	−4.19793	+	1.12483i	−0.199225	+	0.0533822i
$445$	−0.141228	+	0.244614i	−0.00669484	+	0.0115958i
$446$	11.8359	+	20.5003i	0.560444	+	0.970718i
$447$	2.03225	+	2.03225i	0.0961222	+	0.0961222i
$448$	0.733067	−	2.54217i	0.0346342	−	0.120106i
$449$	8.10237	−	30.2385i	0.382375	−	1.42704i	−0.459889	−	0.887976i	$-0.652111\pi$
$449$	8.10237	−	30.2385i	0.382375	−	1.42704i	0.842264	−	0.539065i	$-0.181222\pi$
$450$	3.53355	+	3.53355i	0.166573	+	0.166573i
$451$	1.58498	−	0.915091i	0.0746340	−	0.0430899i
$452$	−6.75781	−	3.90162i	−0.317861	−	0.183517i
$453$	−0.756178	−	2.82210i	−0.0355284	−	0.132594i
$454$	19.2337			0.902684
$455$	0.501172	+	0.0632296i	0.0234953	+	0.00296425i
$456$	6.18577			0.289675
$457$	4.85179	+	18.1071i	0.226957	+	0.847016i	0.981611	+	0.190892i	$0.0611382\pi$
$457$	4.85179	+	18.1071i	0.226957	+	0.847016i	−0.754654	+	0.656123i	$0.772195\pi$
$458$	22.9442	+	13.2469i	1.07211	+	0.618985i
$459$	−5.65510	+	3.26497i	−0.263958	+	0.152396i
$460$	0.295794	+	0.295794i	0.0137915	+	0.0137915i
$461$	9.25430	−	34.5375i	0.431016	−	1.60857i	−0.319409	−	0.947617i	$-0.603484\pi$
$461$	9.25430	−	34.5375i	0.431016	−	1.60857i	0.750425	−	0.660956i	$-0.229849\pi$
$462$	−1.31866	+	4.57290i	−0.0613494	+	0.212751i
$463$	−25.6652	−	25.6652i	−1.19276	−	1.19276i	−0.976288	−	0.216476i	$-0.930544\pi$
$463$	−25.6652	−	25.6652i	−1.19276	−	1.19276i	−0.216476	−	0.976288i	$-0.569456\pi$
$464$	3.18465	+	5.51598i	0.147844	+	0.256073i
$465$	−0.0678785	+	0.117569i	−0.00314779	+	0.00545213i
$466$	−21.5129	+	5.76436i	−0.996565	+	0.267029i
$467$	−21.9730			−1.01679			−0.508395	−	0.861124i	$-0.669761\pi$
$467$	−21.9730			−1.01679			−0.508395	+	0.861124i	$0.669761\pi$
$468$	3.29652	−	1.46047i	0.152382	−	0.0675102i
$469$	−0.356705	+	18.8236i	−0.0164711	+	0.869194i
$470$	−0.0942177	−	0.351625i	−0.00434594	−	0.0162193i
$471$	−3.71352	+	6.43201i	−0.171110	+	0.296371i
$472$	−5.12634	−	8.87908i	−0.235959	−	0.408693i
$473$	13.9190	−	13.9190i	0.639995	−	0.639995i
$474$	1.33083	−	4.96672i	0.0611269	−	0.228129i
$475$	−29.8582	−	8.00049i	−1.36999	−	0.367088i
$476$	−11.9828	−	12.4457i	−0.549229	−	0.570447i
$477$	−2.26197	−	3.91785i	−0.103569	−	0.179386i
$478$	15.7529	+	9.09493i	0.720520	+	0.415992i
$479$	7.80424	+	29.1258i	0.356585	+	1.33079i	0.878479	+	0.477782i	$0.158559\pi$
$479$	7.80424	+	29.1258i	0.356585	+	1.33079i	−0.521894	+	0.853010i	$0.674774\pi$
$480$		−	0.0529536i		−	0.00241699i
$481$	5.64236	−	14.6187i	0.257269	−	0.666555i
$482$			4.53475i			0.206552i
$483$	−5.02599	−	20.2872i	−0.228690	−	0.923101i
$484$	3.88212	−	6.72404i	0.176460	−	0.305638i
$485$	−0.695645	+	0.401631i	−0.0315876	+	0.0182371i
$486$	0.707107	+	0.707107i	0.0320750	+	0.0320750i
$487$	7.94581	+	2.12907i	0.360059	+	0.0964775i	0.434313	−	0.900762i	$-0.356991\pi$
$487$	7.94581	+	2.12907i	0.360059	+	0.0964775i	−0.0742545	+	0.997239i	$0.523658\pi$
$488$	2.37897	+	0.637444i	0.107691	+	0.0288557i
$489$	−5.69549	+	5.69549i	−0.257559	+	0.257559i
$490$	−0.327805	+	0.173043i	−0.0148087	+	0.00781727i
$491$	0.705731	+	0.407454i	0.0318492	+	0.0183881i	0.515840	−	0.856685i	$-0.327480\pi$
$491$	0.705731	+	0.407454i	0.0318492	+	0.0183881i	−0.483991	+	0.875073i	$0.660813\pi$
$492$	0.982767	−	0.263332i	0.0443065	−	0.0118719i
$493$	41.5912			1.87317
$494$	−13.1425	+	18.0195i	−0.591309	+	0.810738i
$495$			0.0952540i			0.00428135i
$496$	−2.47634	+	0.663534i	−0.111191	+	0.0297935i
$497$	24.5677	+	14.8118i	1.10201	+	0.664399i
$498$	−7.49635	+	4.32802i	−0.335919	+	0.193943i
$499$	12.7028	−	12.7028i	0.568654	−	0.568654i	−0.363097	−	0.931751i	$-0.618281\pi$
$499$	12.7028	−	12.7028i	0.568654	−	0.568654i	0.931751	+	0.363097i	$0.118281\pi$
$500$	−0.137016	+	0.511349i	−0.00612752	+	0.0228682i
$501$	0.136199	−	0.508303i	0.00608494	−	0.0227093i
$502$	9.64595	−	9.64595i	0.430520	−	0.430520i
$503$	−8.76122	+	5.05829i	−0.390644	+	0.225538i	−0.682439	−	0.730943i	$-0.739081\pi$
$503$	−8.76122	+	5.05829i	−0.390644	+	0.225538i	0.291795	+	0.956481i	$0.405747\pi$
$504$	−1.36605	+	2.26581i	−0.0608487	+	0.100927i
$505$	−0.779597	+	0.208892i	−0.0346916	+	0.00929559i
$506$		−	14.2101i		−	0.631714i
$507$	−2.74945	+	12.7059i	−0.122107	+	0.564290i
$508$	8.36520			0.371146
$509$	−9.81044	+	2.62870i	−0.434840	+	0.116515i	−0.469597	−	0.882881i	$-0.655601\pi$
$509$	−9.81044	+	2.62870i	−0.434840	+	0.116515i	0.0347572	+	0.999396i	$0.488934\pi$
$510$	−0.299458	−	0.172892i	−0.0132602	−	0.00765579i
$511$	10.3974	−	5.74310i	0.459956	−	0.254060i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−5.97500	−	1.60100i	−0.263803	−	0.0706857i
$514$	−5.82665	−	1.56125i	−0.257003	−	0.0688637i
$515$	0.718552	+	0.718552i	0.0316632	+	0.0316632i
$516$	9.47687	−	5.47148i	0.417196	−	0.240868i
$517$	−6.18299	+	10.7092i	−0.271927	+	0.470992i
$518$	2.76506	+	11.1611i	0.121490	+	0.490389i
$519$		−	4.77272i		−	0.209499i
$520$	0.154257	+	0.112507i	0.00676462	+	0.00493376i
$521$			0.601825i			0.0263664i	0.999913	+	0.0131832i	$0.00419647\pi$
$521$			0.601825i			0.0263664i	−0.999913	+	0.0131832i	$0.995804\pi$
$522$	−1.64850	−	6.15227i	−0.0721528	−	0.269278i
$523$	20.6078	+	11.8979i	0.901118	+	0.520261i	0.877563	−	0.479462i	$-0.159168\pi$
$523$	20.6078	+	11.8979i	0.901118	+	0.520261i	0.0235553	+	0.999723i	$0.492501\pi$
$524$	4.49640	+	7.78799i	0.196426	+	0.340220i
$525$	9.52435	−	9.17009i	0.415677	−	0.400216i
$526$	0.248605	+	0.0666136i	0.0108397	+	0.00290449i
$527$	−4.33284	+	16.1704i	−0.188742	+	0.704393i
$528$	−1.27196	+	1.27196i	−0.0553548	+	0.0553548i
$529$	19.7023	+	34.1254i	0.856623	+	1.48371i
$530$	0.119780	−	0.207464i	0.00520289	−	0.00901168i
$531$	2.65359	+	9.90333i	0.115156	+	0.429768i
$532$	0.310078	−	16.3631i	0.0134436	−	0.709430i
$533$	−1.32092	+	3.42234i	−0.0572153	+	0.148238i
$534$	5.33402			0.230826
$535$	−0.955968	+	0.256151i	−0.0413301	+	0.0110744i
$536$	−3.55797	+	6.16259i	−0.153681	+	0.266183i
$537$	10.2177	+	17.6975i	0.440925	+	0.763705i
$538$	6.68235	+	6.68235i	0.288096	+	0.288096i
$539$	12.0305	+	3.71744i	0.518190	+	0.160121i
$540$	−0.0137054	+	0.0511492i	−0.000589786	+	0.00220111i
$541$	−26.6124	−	26.6124i	−1.14416	−	1.14416i	−0.987682	−	0.156476i	$-0.949987\pi$
$541$	−26.6124	−	26.6124i	−1.14416	−	1.14416i	−0.156476	−	0.987682i	$-0.550013\pi$
$542$	17.9320	−	10.3531i	0.770246	−	0.444702i
$543$	10.9489	+	6.32137i	0.469864	+	0.271276i
$544$	−1.69008	−	6.30745i	−0.0724614	−	0.270430i
$545$	1.09137			0.0467490
$546$	−3.69810	−	8.79341i	−0.158264	−	0.376323i
$547$	−20.5028			−0.876636			−0.438318	−	0.898820i	$-0.644426\pi$
$547$	−20.5028			−0.876636			−0.438318	+	0.898820i	$0.644426\pi$
$548$	5.44962	+	20.3383i	0.232796	+	0.868808i
$549$	−2.13293	−	1.23145i	−0.0910312	−	0.0525569i
$550$	7.78475	−	4.49453i	0.331943	−	0.191647i
$551$	27.8594	+	27.8594i	1.18685	+	1.18685i
$552$	2.04458	−	7.63049i	0.0870232	−	0.324775i
$553$	−13.0716	−	3.76938i	−0.555862	−	0.160290i
$554$	8.77916	+	8.77916i	0.372991	+	0.372991i
$555$	0.115069	+	0.199305i	0.00488439	+	0.00846001i
$556$	2.79848	−	4.84711i	0.118682	−	0.205563i
$557$	15.2351	−	4.08222i	0.645530	−	0.172969i	0.0788230	−	0.996889i	$-0.474884\pi$
$557$	15.2351	−	4.08222i	0.645530	−	0.172969i	0.566707	+	0.823919i	$0.308217\pi$
$558$	2.56370			0.108530
$559$	−4.19613	+	39.2316i	−0.177477	+	1.65932i
$560$	−0.140077	−	0.00265443i	−0.00591933	−	0.000112170i
$561$	3.04014	+	11.3460i	0.128355	+	0.479027i
$562$	5.29509	−	9.17136i	0.223360	−	0.386870i
$563$	−21.2677	−	36.8368i	−0.896328	−	1.55249i	−0.832152	−	0.554548i	$-0.812891\pi$
$563$	−21.2677	−	36.8368i	−0.896328	−	1.55249i	−0.0641762	−	0.997939i	$-0.520442\pi$
$564$	−4.86100	+	4.86100i	−0.204685	+	0.204685i
$565$	−0.106947	+	0.399130i	−0.00449928	+	0.0167915i
$566$	24.3099	+	6.51381i	1.02182	+	0.273796i
$567$	1.90594	−	1.83505i	0.0800419	−	0.0770647i
$568$	5.42139	+	9.39012i	0.227476	+	0.394001i
$569$	22.7077	+	13.1103i	0.951957	+	0.549613i	0.893688	−	0.448688i	$-0.148109\pi$
$569$	22.7077	+	13.1103i	0.951957	+	0.549613i	0.0582689	+	0.998301i	$0.481442\pi$
$570$	−0.0847785	−	0.316398i	−0.00355098	−	0.0132524i
$571$			38.7663i			1.62232i	0.584826	+	0.811159i	$0.301163\pi$
$571$			38.7663i			1.62232i	−0.584826	+	0.811159i	$0.698837\pi$
$572$	−1.00285	−	6.40773i	−0.0419312	−	0.267921i
$573$		−	2.53843i		−	0.106044i
$574$	−0.647321	−	2.61289i	−0.0270187	−	0.109060i
$575$	−19.7381	+	34.1874i	−0.823135	+	1.42571i
$576$	−0.866025	+	0.500000i	−0.0360844	+	0.0208333i
$577$	−20.1046	−	20.1046i	−0.836966	−	0.836966i	0.151492	−	0.988458i	$-0.451592\pi$
$577$	−20.1046	−	20.1046i	−0.836966	−	0.836966i	−0.988458	+	0.151492i	$0.951592\pi$
$578$	−24.7666	−	6.63618i	−1.03015	−	0.276029i
$579$	−4.10345	−	1.09951i	−0.170533	−	0.0456943i
$580$	0.238491	−	0.238491i	0.00990281	−	0.00990281i
$581$	11.0730	+	20.0469i	0.459387	+	0.831684i
$582$	13.1369	+	7.58458i	0.544541	+	0.314391i
$583$	−7.86048	+	2.10621i	−0.325548	+	0.0872302i
$584$	4.48951			0.185777
$585$	−0.119882	−	0.148598i	−0.00495651	−	0.00614377i
$586$		−	3.97477i		−	0.164196i
$587$	−1.21078	+	0.324428i	−0.0499744	+	0.0133906i	−0.283720	−	0.958907i	$-0.591568\pi$
$587$	−1.21078	+	0.324428i	−0.0499744	+	0.0133906i	0.233745	+	0.972298i	$0.424902\pi$
$588$	5.92522	+	3.72716i	0.244352	+	0.153705i
$589$	−13.7338	+	7.92923i	−0.565892	+	0.326718i
$590$	−0.383900	+	0.383900i	−0.0158049	+	0.0158049i
$591$	−3.20097	+	11.9462i	−0.131670	+	0.491400i
$592$	−1.12483	+	4.19793i	−0.0462303	+	0.172534i
$593$	−3.53595	+	3.53595i	−0.145204	+	0.145204i	−0.775972	−	0.630768i	$-0.782740\pi$
$593$	−3.53595	+	3.53595i	−0.145204	+	0.145204i	0.630768	+	0.775972i	$0.282740\pi$
$594$	1.55782	−	0.899410i	0.0639183	−	0.0369032i
$595$	−0.472359	+	0.783482i	−0.0193648	+	0.0321196i
$596$	2.77611	−	0.743856i	0.113714	−	0.0304695i
$597$		−	5.27916i		−	0.216062i
$598$	17.8841	+	22.1680i	0.731335	+	0.906516i
$599$	−22.0342			−0.900292			−0.450146	−	0.892955i	$-0.648628\pi$
$599$	−22.0342			−0.900292			−0.450146	+	0.892955i	$0.648628\pi$
$600$	4.82692	−	1.29337i	0.197058	−	0.0528016i
$601$	22.3561	+	12.9073i	0.911923	+	0.526499i	0.881050	−	0.473024i	$-0.156838\pi$
$601$	22.3561	+	12.9073i	0.911923	+	0.526499i	0.0308739	+	0.999523i	$0.490171\pi$
$602$	−13.9985	−	25.3432i	−0.570537	−	1.03291i
$603$	5.03173	−	5.03173i	0.204908	−	0.204908i
$604$	−2.82210	−	0.756178i	−0.114829	−	0.0307685i
$605$	−0.397135	−	0.106412i	−0.0161459	−	0.00432627i
$606$	10.7774	+	10.7774i	0.437804	+	0.437804i
$607$	−13.7868	+	7.95982i	−0.559590	+	0.323079i	−0.752981	−	0.658042i	$-0.771385\pi$
$607$	−13.7868	+	7.95982i	−0.559590	+	0.323079i	0.193391	+	0.981122i	$0.438051\pi$
$608$	3.09289	−	5.35704i	0.125433	−	0.217257i
$609$	−16.3571	+	4.05233i	−0.662823	+	0.164209i
$610$		−	0.130419i		−	0.00528052i
$611$	−3.83256	−	24.4882i	−0.155049	−	0.990689i
$612$			6.52995i			0.263958i
$613$	−2.53483	−	9.46013i	−0.102381	−	0.382091i	0.895654	−	0.444752i	$-0.146708\pi$
$613$	−2.53483	−	9.46013i	−0.102381	−	0.382091i	−0.998035	+	0.0626607i	$0.980041\pi$
$614$	6.43990	+	3.71808i	0.259893	+	0.150049i
$615$	−0.0269384	−	0.0466587i	−0.00108626	−	0.00188146i
$616$	3.30092	+	3.42844i	0.132998	+	0.138136i
$617$	25.2829	+	6.77454i	1.01785	+	0.272733i	0.728907	−	0.684613i	$-0.240029\pi$
$617$	25.2829	+	6.77454i	1.01785	+	0.272733i	0.288946	+	0.957345i	$0.406695\pi$
$618$	4.96677	−	18.5362i	0.199793	−	0.745636i
$619$	10.8941	−	10.8941i	0.437871	−	0.437871i	−0.453424	−	0.891295i	$-0.649798\pi$
$619$	10.8941	−	10.8941i	0.437871	−	0.437871i	0.891295	+	0.453424i	$0.149798\pi$
$620$	0.0678785	+	0.117569i	0.00272607	+	0.00472169i
$621$	−3.94983	+	6.84131i	−0.158501	+	0.274532i
$622$	−0.124871	−	0.466025i	−0.00500687	−	0.0186859i
$623$	0.267381	−	14.1100i	0.0107124	−	0.565304i
$624$	0.383455	−	3.58510i	0.0153505	−	0.143519i
$625$	−24.9579			−0.998318
$626$	−2.65044	+	0.710185i	−0.105933	+	0.0283847i
$627$	−5.56355	+	9.63634i	−0.222187	+	0.384838i
$628$	3.71352	+	6.43201i	0.148186	+	0.256665i
$629$	20.0672	+	20.0672i	0.800131	+	0.800131i
$630$	0.134617	+	0.0388186i	0.00536326	+	0.00154657i
$631$	5.57471	−	20.8051i	0.221926	−	0.828238i	−0.761687	−	0.647945i	$-0.775629\pi$
$631$	5.57471	−	20.8051i	0.221926	−	0.828238i	0.983613	−	0.180293i	$-0.0577047\pi$
$632$	−3.63589	−	3.63589i	−0.144628	−	0.144628i
$633$	17.9535	−	10.3655i	0.713589	−	0.411991i
$634$	3.47278	+	2.00501i	0.137922	+	0.0796291i
$635$	−0.114648	−	0.427874i	−0.00454968	−	0.0169796i
$636$	−4.52395			−0.179386
$637$	−23.4464	+	9.34170i	−0.928979	+	0.370132i
$638$	−11.4572			−0.453596
$639$	−2.80632	−	10.4733i	−0.111016	−	0.414318i
$640$	−0.0458592	−	0.0264768i	−0.00181274	−	0.00104659i
$641$	25.1435	−	14.5166i	0.993108	−	0.573371i	0.0869060	−	0.996217i	$-0.472302\pi$
$641$	25.1435	−	14.5166i	0.993108	−	0.573371i	0.906202	+	0.422845i	$0.138969\pi$
$642$	13.2157	+	13.2157i	0.521581	+	0.521581i
$643$	0.723318	−	2.69946i	0.0285249	−	0.106456i	−0.950196	−	0.311654i	$-0.899117\pi$
$643$	0.723318	−	2.69946i	0.0285249	−	0.106456i	0.978721	+	0.205198i	$0.0657837\pi$
$644$	−20.0823	−	5.79098i	−0.791352	−	0.228197i
$645$	−0.409746	−	0.409746i	−0.0161337	−	0.0161337i
$646$	−20.1964	−	34.9812i	−0.794617	−	1.37632i
$647$	−5.40323	+	9.35867i	−0.212423	+	0.367927i	−0.952472	−	0.304625i	$-0.901469\pi$
$647$	−5.40323	+	9.35867i	−0.212423	+	0.367927i	0.740049	+	0.672552i	$0.234802\pi$
$648$	0.965926	−	0.258819i	0.0379452	−	0.0101674i
$649$	18.4427			0.723940
$650$	−6.48777	+	16.8091i	−0.254471	+	0.659306i
$651$	0.128512	−	6.78169i	0.00503678	−	0.265795i
$652$	2.08469	+	7.78018i	0.0816429	+	0.304695i
$653$	11.9061	−	20.6220i	0.465923	−	0.807001i	−0.533320	−	0.845913i	$-0.679056\pi$
$653$	11.9061	−	20.6220i	0.465923	−	0.807001i	0.999243	+	0.0389120i	$0.0123892\pi$
$654$	−10.3049	−	17.8487i	−0.402955	−	0.697938i
$655$	0.336725	−	0.336725i	0.0131569	−	0.0131569i
$656$	0.263332	−	0.982767i	0.0102814	−	0.0383706i
$657$	−4.33654	−	1.16197i	−0.169184	−	0.0453328i
$658$	12.6150	+	13.1024i	0.491785	+	0.510783i
$659$	−4.48460	−	7.76755i	−0.174695	−	0.302581i	0.765361	−	0.643602i	$-0.222561\pi$
$659$	−4.48460	−	7.76755i	−0.174695	−	0.302581i	−0.940056	+	0.341021i	$0.889227\pi$
$660$	0.0824923	+	0.0476270i	0.00321101	+	0.00185388i
$661$	−2.54511	−	9.49849i	−0.0989934	−	0.369448i	0.898601	−	0.438766i	$-0.144584\pi$
$661$	−2.54511	−	9.49849i	−0.0989934	−	0.369448i	−0.997595	+	0.0693179i	$0.977918\pi$
$662$		−	7.24613i		−	0.281629i
$663$	−19.0222	−	13.8737i	−0.738759	−	0.538812i
$664$			8.65604i			0.335919i
$665$	−0.841209	+	0.208402i	−0.0326207	+	0.00808149i
$666$	2.17301	−	3.76376i	0.0842024	−	0.145843i
$667$	43.5744	−	25.1577i	1.68721	−	0.974109i
$668$	−0.372104	−	0.372104i	−0.0143971	−	0.0143971i
$669$	−22.8651	−	6.12669i	−0.884017	−	0.236872i
$670$	0.363975	+	0.0975268i	0.0140616	+	0.00376779i
$671$	−3.13270	+	3.13270i	−0.120936	+	0.120936i
$672$	1.27923	+	2.31594i	0.0493472	+	0.0893393i
$673$	3.44179	+	1.98712i	0.132671	+	0.0765977i	0.564867	−	0.825182i	$-0.308928\pi$
$673$	3.44179	+	1.98712i	0.132671	+	0.0765977i	−0.432195	+	0.901780i	$0.642261\pi$
$674$	−19.9044	+	5.33336i	−0.766687	+	0.205433i
$675$	−4.99720			−0.192342
$676$	9.62893	+	8.73406i	0.370343	+	0.335925i
$677$		−	9.40300i		−	0.361387i	−0.983539	−	0.180693i	$-0.942166\pi$
$677$		−	9.40300i		−	0.361387i	0.983539	−	0.180693i	$-0.0578341\pi$
$678$	7.53736	−	2.01963i	0.289471	−	0.0775634i
$679$	20.7218	−	34.3705i	0.795231	−	1.31902i
$680$	−0.299458	+	0.172892i	−0.0114837	+	0.00663011i
$681$	−13.6003	+	13.6003i	−0.521165	+	0.521165i
$682$	1.19358	−	4.45449i	0.0457044	−	0.170571i
$683$	−11.7755	+	43.9469i	−0.450578	+	1.68158i	0.250193	+	0.968196i	$0.419506\pi$
$683$	−11.7755	+	43.9469i	−0.450578	+	1.68158i	−0.700772	+	0.713386i	$0.747161\pi$
$684$	−4.37400	+	4.37400i	−0.167244	+	0.167244i
$685$	0.965598	−	0.557488i	0.0368936	−	0.0213005i
$686$	10.1564	−	15.4870i	0.387773	−	0.591297i
$687$	−25.5910	+	6.85708i	−0.976357	+	0.261614i
$688$		−	10.9430i		−	0.417196i
$689$	9.61173	−	13.1785i	0.366178	−	0.502062i
$690$	−0.418315			−0.0159250
$691$	5.93630	−	1.59063i	0.225828	−	0.0605103i	−0.144131	−	0.989559i	$-0.546039\pi$
$691$	5.93630	−	1.59063i	0.225828	−	0.0605103i	0.369958	+	0.929048i	$0.379372\pi$
$692$	−4.13330	−	2.38636i	−0.157124	−	0.0907158i
$693$	−2.30110	−	4.16596i	−0.0874115	−	0.158252i
$694$	−8.31510	+	8.31510i	−0.315637	+	0.315637i
$695$	−0.286280	−	0.0767086i	−0.0108592	−	0.00290972i
$696$	−6.15227	−	1.64850i	−0.233201	−	0.0624861i
$697$	−4.69788	−	4.69788i	−0.177945	−	0.177945i
$698$	−6.24884	+	3.60777i	−0.236522	+	0.136556i
$699$	11.1359	−	19.2879i	0.421198	−	0.729536i
$700$	−3.17936	−	12.8334i	−0.120168	−	0.485056i
$701$			35.3166i			1.33389i	0.745107	+	0.666945i	$0.232399\pi$
$701$			35.3166i			1.33389i	−0.745107	+	0.666945i	$0.767601\pi$
$702$	−1.29828	+	3.36370i	−0.0490005	+	0.126955i
$703$			26.8835i			1.01393i
$704$	0.465569	+	1.73753i	0.0175468	+	0.0654855i
$705$	0.315259	+	0.182015i	0.0118733	+	0.00685507i
$706$	−4.65999	−	8.07134i	−0.175381	−	0.303769i
$707$	29.0496	−	27.9691i	1.09252	−	1.05189i
$708$	9.90333	+	2.65359i	0.372190	+	0.0997280i
$709$	3.74654	−	13.9823i	0.140704	−	0.525116i	−0.859205	−	0.511632i	$-0.829041\pi$
$709$	3.74654	−	13.9823i	0.140704	−	0.525116i	0.999909	−	0.0134837i	$-0.00429214\pi$
$710$	0.405995	−	0.405995i	0.0152367	−	0.0152367i
$711$	2.57096	+	4.45304i	0.0964186	+	0.167002i
$712$	2.66701	−	4.61940i	0.0999504	−	0.173119i
$713$	5.24169	+	19.5623i	0.196303	+	0.732612i
$714$	17.2735	+	0.327330i	0.646445	+	0.0122500i
$715$	−0.314006	+	0.139116i	−0.0117432	+	0.00520263i
$716$	20.4353			0.763705
$717$	−17.5700	+	4.70788i	−0.656166	+	0.175819i
$718$	8.58173	−	14.8640i	0.320267	−	0.554719i
$719$	15.8830	+	27.5102i	0.592336	+	1.02596i	0.993917	+	0.110132i	$0.0351274\pi$
$719$	15.8830	+	27.5102i	0.592336	+	1.02596i	−0.401581	+	0.915823i	$0.631539\pi$
$720$	0.0374438	+	0.0374438i	0.00139545	+	0.00139545i
$721$	−48.7845	−	14.0676i	−1.81683	−	0.523907i
$722$	4.98584	−	18.6074i	0.185554	−	0.692496i
$723$	−3.20656	−	3.20656i	−0.119253	−	0.119253i
$724$	10.9489	−	6.32137i	0.406914	−	0.234932i
$725$	27.5644	+	15.9143i	1.02372	+	0.591043i
$726$	2.00954	+	7.49969i	0.0745809	+	0.278340i
$727$	−29.8284			−1.10627			−0.553137	−	0.833090i	$-0.686570\pi$
$727$	−29.8284			−1.10627			−0.553137	+	0.833090i	$0.686570\pi$
$728$	−9.46437	−	1.19406i	−0.350773	−	0.0442547i
$729$	−1.00000			−0.0370370
$730$	−0.0615306	−	0.229635i	−0.00227735	−	0.00849918i
$731$	−61.8835	−	35.7285i	−2.28884	−	1.32146i
$732$	−2.13293	+	1.23145i	−0.0788354	+	0.0455156i
$733$	−34.6231	−	34.6231i	−1.27884	−	1.27884i	−0.941320	−	0.337515i	$-0.890414\pi$
$733$	−34.6231	−	34.6231i	−1.27884	−	1.27884i	−0.337515	−	0.941320i	$-0.609586\pi$
$734$	7.01528	−	26.1814i	0.258939	−	0.966372i
$735$	0.109434	−	0.354153i	0.00403653	−	0.0130631i
$736$	−5.58590	−	5.58590i	−0.205899	−	0.205899i
$737$	−6.40015	−	11.0854i	−0.235752	−	0.408335i
$738$	−0.508717	+	0.881124i	−0.0187261	+	0.0324346i
$739$	−23.9569	+	6.41924i	−0.881270	+	0.236135i	−0.670955	−	0.741498i	$-0.734116\pi$
$739$	−23.9569	+	6.41924i	−0.881270	+	0.236135i	−0.210315	+	0.977634i	$0.567449\pi$
$740$	0.230137			0.00846001
$741$	−3.44859	−	22.0349i	−0.126687	−	0.809472i
$742$	−0.226774	+	11.9671i	−0.00832515	+	0.439326i
$743$	7.65203	+	28.5578i	0.280726	+	1.04768i	0.951906	+	0.306389i	$0.0991209\pi$
$743$	7.65203	+	28.5578i	0.280726	+	1.04768i	−0.671180	+	0.741294i	$0.734212\pi$
$744$	1.28185	−	2.22023i	0.0469949	−	0.0813975i
$745$	−0.0760953	−	0.131801i	−0.00278792	−	0.00482881i
$746$	−5.28909	+	5.28909i	−0.193647	+	0.193647i
$747$	2.24035	−	8.36109i	0.0819700	−	0.305916i
$748$	11.3460	+	3.04014i	0.414849	+	0.111159i
$749$	35.6216	−	34.2966i	1.30158	−	1.25317i
$750$	−0.264694	−	0.458463i	−0.00966525	−	0.0167407i
$751$	−13.0186	−	7.51627i	−0.475054	−	0.274273i	0.243299	−	0.969951i	$-0.421770\pi$
$751$	−13.0186	−	7.51627i	−0.475054	−	0.274273i	−0.718353	+	0.695679i	$0.755104\pi$
$752$	1.77925	+	6.64025i	0.0648826	+	0.242145i
$753$			13.6414i			0.497121i
$754$	17.8735	−	14.4195i	0.650915	−	0.525128i
$755$			0.154712i			0.00563054i
$756$	−0.636228	−	2.56811i	−0.0231394	−	0.0934014i
$757$	18.7307	−	32.4425i	0.680777	−	1.17914i	−0.293967	−	0.955816i	$-0.594975\pi$
$757$	18.7307	−	32.4425i	0.680777	−	1.17914i	0.974744	−	0.223325i	$-0.0716913\pi$
$758$	−22.9118	+	13.2281i	−0.832195	+	0.480468i
$759$	10.0480	+	10.0480i	0.364721	+	0.364721i
$760$	−0.316398	−	0.0847785i	−0.0114769	−	0.00307524i
$761$	14.5390	+	3.89572i	0.527039	+	0.141220i	0.512520	−	0.858675i	$-0.328712\pi$
$761$	14.5390	+	3.89572i	0.527039	+	0.141220i	0.0145182	+	0.999895i	$0.495379\pi$
$762$	−5.91509	+	5.91509i	−0.214281	+	0.214281i
$763$	−47.7312	+	26.3647i	−1.72799	+	0.954466i
$764$	−2.19834	−	1.26921i	−0.0795333	−	0.0459186i
$765$	0.334002	−	0.0894956i	0.0120759	−	0.00323572i
$766$	−17.6304			−0.637012
$767$	−28.7710	+	23.2111i	−1.03886	+	0.838105i
$768$			1.00000i			0.0360844i
$769$	29.2057	−	7.82566i	1.05319	−	0.282200i	0.309618	−	0.950861i	$-0.399799\pi$
$769$	29.2057	−	7.82566i	1.05319	−	0.282200i	0.743568	+	0.668661i	$0.233132\pi$
$770$	0.130122	−	0.215828i	0.00468926	−	0.00777789i
$771$	5.22404	−	3.01610i	0.188139	−	0.108622i
$772$	−3.00393	+	3.00393i	−0.108114	+	0.108114i
$773$	7.83189	−	29.2290i	0.281693	−	1.05129i	−0.669528	−	0.742786i	$-0.733504\pi$
$773$	7.83189	−	29.2290i	0.281693	−	1.05129i	0.951222	−	0.308508i	$-0.0998296\pi$
$774$	−2.83224	+	10.5701i	−0.101803	+	0.379934i
$775$	−9.05896	+	9.05896i	−0.325407	+	0.325407i
$776$	13.1369	−	7.58458i	0.471587	−	0.272271i
$777$	−9.84726	−	5.93688i	−0.353269	−	0.212984i
$778$	8.41621	−	2.25512i	0.301736	−	0.0808499i
$779$		−	6.29362i		−	0.225492i
$780$	−0.188631	+	0.0295218i	−0.00675406	+	0.00105705i
$781$	−19.5042			−0.697915
$782$	−49.8267	+	13.3510i	−1.78180	+	0.477432i
$783$	5.51598	+	3.18465i	0.197125	+	0.113810i
$784$	6.19043	−	3.26782i	0.221087	−	0.116708i
$785$	0.278097	−	0.278097i	0.00992571	−	0.00992571i
$786$	−8.68637	−	2.32751i	−0.309833	−	0.0830194i
$787$	21.7680	+	5.83271i	0.775945	+	0.207914i	0.624996	−	0.780628i	$-0.285101\pi$
$787$	21.7680	+	5.83271i	0.775945	+	0.207914i	0.150949	+	0.988542i	$0.451767\pi$
$788$	8.74522	+	8.74522i	0.311535	+	0.311535i
$789$	−0.222894	+	0.128688i	−0.00793522	+	0.00458140i
$790$	−0.136142	+	0.235804i	−0.00484370	+	0.00838954i
$791$	−4.96465	−	20.0396i	−0.176523	−	0.712528i
$792$		−	1.79882i		−	0.0639183i
$793$	0.944409	−	8.82973i	0.0335369	−	0.313553i
$794$			1.60179i			0.0568455i
$795$	0.0620025	+	0.231396i	0.00219900	+	0.00820679i
$796$	−4.57189	−	2.63958i	−0.162046	−	0.0935574i
$797$	0.581522	+	1.00723i	0.0205986	+	0.0356778i	0.876141	−	0.482055i	$-0.160109\pi$
$797$	0.581522	+	1.00723i	0.0205986	+	0.0356778i	−0.855542	+	0.517733i	$0.826776\pi$
$798$	11.3512	+	11.7897i	0.401828	+	0.417351i
$799$	43.3605	+	11.6184i	1.53398	+	0.411030i
$800$	1.29337	−	4.82692i	0.0457275	−	0.170657i
$801$	−3.77172	+	3.77172i	−0.133267	+	0.133267i
$802$	9.32940	+	16.1590i	0.329432	+	0.570594i
$803$	−4.03791	+	6.99387i	−0.142495	+	0.246808i
$804$	−1.84174	−	6.87347i	−0.0649532	−	0.242409i
$805$	−0.0209691	+	1.10656i	−0.000739065	+	0.0390011i
$806$	3.74420	+	8.45127i	0.131884	+	0.297683i
$807$	−9.45026			−0.332665
$808$	14.7223	−	3.94482i	0.517928	−	0.138778i
$809$	−11.6018	+	20.0949i	−0.407898	+	0.706501i	−0.994654	−	0.103263i	$-0.967072\pi$
$809$	−11.6018	+	20.0949i	−0.407898	+	0.706501i	0.586756	+	0.809764i	$0.300405\pi$
$810$	−0.0264768	−	0.0458592i	−0.000930300	−	0.00161133i
$811$	−20.1178	−	20.1178i	−0.706430	−	0.706430i	0.259352	−	0.965783i	$-0.416491\pi$
$811$	−20.1178	−	20.1178i	−0.706430	−	0.706430i	−0.965783	+	0.259352i	$0.916491\pi$
$812$	−4.66913	+	16.1918i	−0.163854	+	0.568222i
$813$	−5.35914	+	20.0006i	−0.187953	+	0.701450i
$814$	−5.52795	−	5.52795i	−0.193755	−	0.193755i
$815$	0.369379	−	0.213261i	0.0129388	−	0.00747020i
$816$	5.65510	+	3.26497i	0.197968	+	0.114297i
$817$	−17.5196	−	65.3841i	−0.612934	−	2.28750i
$818$	−22.7478			−0.795359
$819$	8.83283	+	3.60293i	0.308644	+	0.125896i
$820$	−0.0538768			−0.00188146
$821$	2.85633	+	10.6600i	0.0996865	+	0.372035i	0.997688	−	0.0679568i	$-0.0216480\pi$
$821$	2.85633	+	10.6600i	0.0996865	+	0.372035i	−0.898002	+	0.439992i	$0.854981\pi$
$822$	−18.2348	−	10.5279i	−0.636011	−	0.367201i
$823$	3.66847	−	2.11799i	0.127875	−	0.0738285i	−0.434698	−	0.900576i	$-0.643145\pi$
$823$	3.66847	−	2.11799i	0.127875	−	0.0738285i	0.562573	+	0.826748i	$0.309812\pi$
$824$	−13.5695	−	13.5695i	−0.472715	−	0.472715i
$825$	−2.32654	+	8.68276i	−0.0809997	+	0.302295i
$826$	7.51591	−	26.0640i	0.261512	−	0.906883i
$827$	−5.94692	−	5.94692i	−0.206795	−	0.206795i	0.596109	−	0.802904i	$-0.296713\pi$
$827$	−5.94692	−	5.94692i	−0.206795	−	0.206795i	−0.802904	+	0.596109i	$0.796713\pi$
$828$	3.94983	+	6.84131i	0.137266	+	0.237752i
$829$	16.9564	−	29.3693i	0.588919	−	1.02004i	−0.405455	−	0.914115i	$-0.632887\pi$
$829$	16.9564	−	29.3693i	0.588919	−	1.02004i	0.994374	−	0.105923i	$-0.0337798\pi$
$830$	0.442750	−	0.118634i	0.0153681	−	0.00411786i
$831$	−12.4156			−0.430693
$832$	−2.91306	−	2.12463i	−0.100992	−	0.0736584i
$833$	1.73176	−	45.6768i	0.0600019	−	1.58261i
$834$	1.44860	+	5.40625i	0.0501609	+	0.187203i
$835$	−0.0139330	+	0.0241327i	−0.000482171	+	0.000835145i
$836$	5.56355	+	9.63634i	0.192419	+	0.333280i
$837$	−1.81281	+	1.81281i	−0.0626598	+	0.0626598i
$838$	−2.26609	+	8.45717i	−0.0782808	+	0.292148i
$839$	−28.0717	−	7.52179i	−0.969142	−	0.259681i	−0.260677	−	0.965426i	$-0.583946\pi$
$839$	−28.0717	−	7.52179i	−0.969142	−	0.259681i	−0.708466	+	0.705745i	$0.750612\pi$
$840$	0.100926	−	0.0971723i	0.00348229	−	0.00335276i
$841$	−5.78401	−	10.0182i	−0.199449	−	0.345455i
$842$	−6.96616	−	4.02192i	−0.240070	−	0.138604i
$843$	2.74094	+	10.2293i	0.0944029	+	0.352317i
$844$		−	20.7310i		−	0.713589i
$845$	0.314772	−	0.612216i	0.0108285	−	0.0210609i
$846$		−	6.87449i		−	0.236350i
$847$	19.9395	−	4.93984i	0.685129	−	0.169735i
$848$	−2.26197	+	3.91785i	−0.0776765	+	0.134540i
$849$	−21.7956	+	12.5837i	−0.748025	+	0.431872i
$850$	−23.0739	−	23.0739i	−0.791429	−	0.791429i
$851$	33.1622	+	8.88579i	1.13679	+	0.304601i
$852$	−10.4733	−	2.80632i	−0.358810	−	0.0961429i
$853$	5.21859	−	5.21859i	0.178681	−	0.178681i	−0.612099	−	0.790781i	$-0.709675\pi$
$853$	5.21859	−	5.21859i	0.178681	−	0.178681i	0.790781	+	0.612099i	$0.209675\pi$
$854$	3.15060	+	5.70392i	0.107811	+	0.195184i
$855$	0.283674	+	0.163779i	0.00970146	+	0.00560114i
$856$	18.0529	−	4.83727i	0.617037	−	0.165335i
$857$	−27.8272			−0.950558			−0.475279	−	0.879835i	$-0.657653\pi$
$857$	−27.8272			−0.950558			−0.475279	+	0.879835i	$0.657653\pi$
$858$	5.24007	+	3.82183i	0.178893	+	0.130475i
$859$		−	32.7816i		−	1.11849i	−0.829001	−	0.559247i	$-0.811090\pi$
$859$		−	32.7816i		−	1.11849i	0.829001	−	0.559247i	$-0.188910\pi$
$860$	−0.559724	+	0.149978i	−0.0190864	+	0.00511419i
$861$	2.30532	+	1.38987i	0.0785650	+	0.0473665i
$862$	1.14413	−	0.660562i	0.0389691	−	0.0224988i
$863$	11.1705	−	11.1705i	0.380248	−	0.380248i	−0.490943	−	0.871192i	$-0.663348\pi$
$863$	11.1705	−	11.1705i	0.380248	−	0.380248i	0.871192	+	0.490943i	$0.163348\pi$
$864$	0.258819	−	0.965926i	0.00880520	−	0.0328615i
$865$	−0.0654121	+	0.244121i	−0.00222408	+	0.00830037i
$866$	13.0576	−	13.0576i	0.443717	−	0.443717i
$867$	22.2051	−	12.8201i	0.754125	−	0.435394i
$868$	−5.80886	−	3.50214i	−0.197166	−	0.118870i
$869$	8.93423	−	2.39392i	0.303073	−	0.0812081i
$870$			0.337277i			0.0114348i
$871$	23.9359	+	9.23850i	0.811036	+	0.313034i
$872$	−20.6099			−0.697938
$873$	−14.6523	+	3.92607i	−0.495905	+	0.132877i
$874$	−42.3188	−	24.4328i	−1.43145	−	0.826450i
$875$	−1.22603	+	0.677206i	−0.0414474	+	0.0228938i
$876$	−3.17457	+	3.17457i	−0.107259	+	0.107259i
$877$	36.9690	+	9.90582i	1.24835	+	0.334496i	0.821701	−	0.569919i	$-0.193026\pi$
$877$	36.9690	+	9.90582i	1.24835	+	0.334496i	0.426654	+	0.904415i	$0.359692\pi$
$878$	8.97218	+	2.40409i	0.302796	+	0.0811341i
$879$	2.81058	+	2.81058i	0.0947986	+	0.0947986i
$880$	0.0824923	−	0.0476270i	0.00278082	−	0.00160551i
$881$	−1.23157	+	2.13313i	−0.0414925	+	0.0718671i	−0.886026	−	0.463636i	$-0.846545\pi$
$881$	−1.23157	+	2.13313i	−0.0414925	+	0.0718671i	0.844533	+	0.535503i	$0.179878\pi$
$882$	−6.82527	+	1.55427i	−0.229819	+	0.0523349i
$883$		−	29.5254i		−	0.993610i	−0.867862	−	0.496805i	$-0.834506\pi$
$883$		−	29.5254i		−	0.993610i	0.867862	−	0.496805i	$-0.165494\pi$
$884$	−21.5261	+	9.53679i	−0.724001	+	0.320757i
$885$		−	0.542916i		−	0.0182499i
$886$	4.75067	+	17.7297i	0.159602	+	0.595642i
$887$	7.82728	+	4.51908i	0.262814	+	0.151736i	0.625618	−	0.780130i	$-0.284847\pi$
$887$	7.82728	+	4.51908i	0.262814	+	0.151736i	−0.362803	+	0.931866i	$0.618180\pi$
$888$	−2.17301	−	3.76376i	−0.0729214	−	0.126304i
$889$	15.3505	+	15.9436i	0.514840	+	0.534730i
$890$	−0.272831	−	0.0731049i	−0.00914532	−	0.00245048i
$891$	−0.465569	+	1.73753i	−0.0155971	+	0.0582093i
$892$	−16.7384	+	16.7384i	−0.560444	+	0.560444i
$893$	21.2620	+	36.8269i	0.711507	+	1.23237i
$894$	−1.43702	+	2.48899i	−0.0480611	+	0.0832443i
$895$	−0.280075	−	1.04525i	−0.00936186	−	0.0349389i
$896$	2.64528	+	0.0501275i	0.0883725	+	0.00167464i
$897$	−28.3211	−	3.02916i	−0.945614	−	0.101141i
$898$	31.3052			1.04467
$899$	15.7726	−	4.22625i	0.526045	−	0.140953i
$900$	−2.49860	+	4.32770i	−0.0832866	+	0.144257i
$901$	14.7706	+	25.5834i	0.492079	+	0.852306i
$902$	1.29413	+	1.29413i	0.0430899	+	0.0430899i
$903$	27.8188	+	8.02192i	0.925752	+	0.266953i
$904$	2.01963	−	7.53736i	0.0671719	−	0.250689i
$905$	−0.473393	−	0.473393i	−0.0157361	−	0.0157361i
$906$	2.53022	−	1.46082i	0.0840610	−	0.0485326i
$907$	−21.4216	−	12.3678i	−0.711292	−	0.410665i	0.100247	−	0.994963i	$-0.468037\pi$
$907$	−21.4216	−	12.3678i	−0.711292	−	0.410665i	−0.811539	+	0.584298i	$0.801370\pi$
$908$	4.97806	+	18.5784i	0.165203	+	0.616544i
$909$	−15.2416			−0.505532
$910$	0.0686378	+	0.500460i	0.00227532	+	0.0165901i
$911$	32.4077			1.07372			0.536858	−	0.843673i	$-0.319611\pi$
$911$	32.4077			1.07372			0.536858	+	0.843673i	$0.319611\pi$
$912$	1.60100	+	5.97500i	0.0530143	+	0.197852i
$913$	−13.4846	−	7.78532i	−0.446274	−	0.257657i
$914$	−16.2344	+	9.37294i	−0.536986	+	0.310029i
$915$	0.0922203	+	0.0922203i	0.00304871	+	0.00304871i
$916$	−6.85708	+	25.5910i	−0.226564	+	0.845550i
$917$	−6.59232	+	22.8612i	−0.217698	+	0.754943i
$918$	−4.61737	−	4.61737i	−0.152396	−	0.152396i
$919$	−12.5634	−	21.7605i	−0.414428	−	0.717811i	0.580940	−	0.813946i	$-0.302685\pi$
$919$	−12.5634	−	21.7605i	−0.414428	−	0.717811i	−0.995368	+	0.0961354i	$0.969352\pi$
$920$	−0.209158	+	0.362272i	−0.00689573	+	0.0119437i
$921$	−7.18278	+	1.92462i	−0.236681	+	0.0634184i
$922$	35.7559			1.17756
$923$	30.4269	−	24.5470i	1.00152	−	0.807976i
$924$	−4.75837	−	0.0901704i	−0.156539	−	0.00296639i
$925$	5.62101	+	20.9779i	0.184818	+	0.689748i
$926$	18.1480	−	31.4333i	0.596382	−	1.03296i
$927$	9.59506	+	16.6191i	0.315143	+	0.545844i
$928$	−4.50378	+	4.50378i	−0.147844	+	0.147844i
$929$	1.04368	−	3.89507i	0.0342421	−	0.127793i	−0.946689	−	0.322149i	$-0.895595\pi$
$929$	1.04368	−	3.89507i	0.0342421	−	0.127793i	0.980931	+	0.194356i	$0.0622615\pi$
$930$	−0.131131	−	0.0351365i	−0.00429996	−	0.00115217i
$931$	31.7560	−	29.4360i	1.04076	−	0.964727i
$932$	−11.1359	−	19.2879i	−0.364768	−	0.631797i
$933$	0.417826	+	0.241232i	0.0136790	+	0.00789759i
$934$	−5.68703	−	21.2243i	−0.186085	−	0.694480i
$935$		−	0.622004i		−	0.0203417i
$936$	2.26391	+	2.80619i	0.0739981	+	0.0917233i
$937$		−	1.23523i		−	0.0403533i	−0.999796	−	0.0201767i	$-0.993577\pi$
$937$		−	1.23523i		−	0.0403533i	0.999796	−	0.0201767i	$-0.00642287\pi$
$938$	−18.2746	+	4.52736i	−0.596685	+	0.147824i
$939$	1.37197	−	2.37632i	0.0447726	−	0.0775484i
$940$	0.315259	−	0.182015i	0.0102826	−	0.00593666i
$941$	−0.630850	−	0.630850i	−0.0205651	−	0.0205651i	0.696749	−	0.717315i	$-0.254629\pi$
$941$	−0.630850	−	0.630850i	−0.0205651	−	0.0205651i	−0.717315	+	0.696749i	$0.754629\pi$
$942$	−7.17398	−	1.92226i	−0.233741	−	0.0626306i
$943$	−7.76352	−	2.08023i	−0.252815	−	0.0677416i
$944$	7.24974	−	7.24974i	0.235959	−	0.235959i
$945$	−0.122637	+	0.0677396i	−0.00398939	+	0.00220357i
$946$	17.0472	+	9.84220i	0.554252	+	0.319997i
$947$	−23.8094	+	6.37971i	−0.773701	+	0.207313i	−0.624006	−	0.781420i	$-0.714496\pi$
$947$	−23.8094	+	6.37971i	−0.773701	+	0.207313i	−0.149695	+	0.988732i	$0.547829\pi$
$948$	5.14192			0.167002
$949$	−2.50292	−	15.9925i	−0.0812483	−	0.519138i
$950$		−	30.9115i		−	1.00290i
$951$	−3.87338	+	1.03787i	−0.125603	+	0.0336552i
$952$	8.92024	−	14.7956i	0.289107	−	0.479530i
$953$	10.1237	−	5.84491i	0.327938	−	0.189335i	−0.326987	−	0.945029i	$-0.606033\pi$
$953$	10.1237	−	5.84491i	0.327938	−	0.189335i	0.654925	+	0.755694i	$0.272700\pi$
$954$	3.19891	−	3.19891i	0.103569	−	0.103569i
$955$	−0.0347902	+	0.129839i	−0.00112578	+	0.00420148i
$956$	−4.70788	+	17.5700i	−0.152264	+	0.568256i
$957$	8.10148	−	8.10148i	0.261884	−	0.261884i
$958$	−26.1135	+	15.0766i	−0.843689	+	0.487104i
$959$	−28.7632	+	47.7083i	−0.928811	+	1.54058i
$960$	0.0511492	−	0.0137054i	0.00165083	−	0.000442340i
$961$		−	24.4275i		−	0.787982i
$962$	15.5809	+	1.66650i	0.502349	+	0.0537302i
$963$	−18.6898			−0.602270
$964$	−4.38024	+	1.17368i	−0.141078	+	0.0378017i
$965$	0.194819	+	0.112479i	0.00627144	+	0.00362082i
$966$	18.2951	−	10.1055i	0.588637	−	0.325138i
$967$	−11.5185	+	11.5185i	−0.370410	+	0.370410i	−0.867627	−	0.497216i	$-0.834356\pi$
$967$	−11.5185	+	11.5185i	−0.370410	+	0.370410i	0.497216	+	0.867627i	$0.334356\pi$
$968$	7.49969	+	2.00954i	0.241049	+	0.0645889i
$969$	39.0164	+	10.4544i	1.25339	+	0.335844i
$970$	−0.567992	−	0.567992i	−0.0182371	−	0.0182371i
$971$	22.9362	−	13.2422i	0.736059	−	0.424964i	−0.0845759	−	0.996417i	$-0.526954\pi$
$971$	22.9362	−	13.2422i	0.736059	−	0.424964i	0.820635	+	0.571453i	$0.193620\pi$
$972$	−0.500000	+	0.866025i	−0.0160375	+	0.0277778i
$973$	14.3736	−	3.56094i	0.460798	−	0.114159i
$974$			8.22610i			0.263581i
$975$	−7.29825	−	16.4733i	−0.233731	−	0.527569i
$976$			2.46290i			0.0788354i
$977$	2.80220	+	10.4580i	0.0896504	+	0.334580i	0.996154	−	0.0876178i	$-0.0279254\pi$
$977$	2.80220	+	10.4580i	0.0896504	+	0.334580i	−0.906504	+	0.422198i	$0.861259\pi$
$978$	−6.97552	−	4.02732i	−0.223052	−	0.128779i
$979$	4.79747	+	8.30946i	0.153328	+	0.265572i
$980$	−0.251989	−	0.271849i	−0.00804948	−	0.00868390i
$981$	19.9076	+	5.33423i	0.635601	+	0.170309i
$982$	−0.210914	+	0.787140i	−0.00673052	+	0.0251187i
$983$	−25.9807	+	25.9807i	−0.828657	+	0.828657i	−0.987331	−	0.158674i	$-0.949278\pi$
$983$	−25.9807	+	25.9807i	−0.828657	+	0.828657i	0.158674	+	0.987331i	$0.449278\pi$
$984$	0.508717	+	0.881124i	0.0162173	+	0.0280892i
$985$	0.327454	−	0.567168i	0.0104336	−	0.0180715i
$986$	10.7646	+	40.1740i	0.342815	+	1.27940i
$987$	−18.1849	−	0.344602i	−0.578833	−	0.0109688i
$988$	−20.8071	−	8.03088i	−0.661961	−	0.255496i
$989$	−86.4456			−2.74881
$990$	−0.0920083	+	0.0246535i	−0.00292421	+	0.000783541i
$991$	−7.49191	+	12.9764i	−0.237988	+	0.412208i	−0.960137	−	0.279530i	$-0.909821\pi$
$991$	−7.49191	+	12.9764i	−0.237988	+	0.412208i	0.722149	+	0.691738i	$0.243155\pi$
$992$	−1.28185	−	2.22023i	−0.0406987	−	0.0704923i
$993$	5.12379	+	5.12379i	0.162599	+	0.162599i
$994$	−7.94849	+	27.5642i	−0.252111	+	0.874282i
$995$	−0.0723530	+	0.270025i	−0.00229374	+	0.00856037i
$996$	−6.12074	−	6.12074i	−0.193943	−	0.193943i
$997$	−13.9113	+	8.03171i	−0.440576	+	0.254367i	−0.703842	−	0.710357i	$-0.748534\pi$
$997$	−13.9113	+	8.03171i	−0.440576	+	0.254367i	0.263266	+	0.964723i	$0.415200\pi$
$998$	15.5576	+	8.98221i	0.492469	+	0.284327i
$999$	1.12483	+	4.19793i	0.0355881	+	0.132817i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bx.a.97.8	✓	40
7.6	odd	2		546.2.bx.b.97.8	yes	40
13.11	odd	12		546.2.bx.b.349.8	yes	40
91.76	even	12	inner	546.2.bx.a.349.8	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bx.a.97.8	✓	40	1.1	even	1	trivial
546.2.bx.a.349.8	yes	40	91.76	even	12	inner
546.2.bx.b.97.8	yes	40	7.6	odd	2
546.2.bx.b.349.8	yes	40	13.11	odd	12

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.bx (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 + 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(0.0374438 + 0.0374438i) q^{5} +(0.258819 - 0.965926i) q^{6} +(-2.54217 - 0.733067i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.258819 + 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(0.0374438 + 0.0374438i) q^{5} +(0.258819 - 0.965926i) q^{6} +(-2.54217 - 0.733067i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +(-0.0264768 + 0.0458592i) q^{10} +(1.73753 - 0.465569i) q^{11} +1.00000 q^{12} +(-2.12463 + 2.91306i) q^{13} +(0.0501275 - 2.64528i) q^{14} +(-0.0137054 - 0.0511492i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-3.26497 - 5.65510i) q^{17} +(-0.707107 + 0.707107i) q^{18} +(1.60100 - 5.97500i) q^{19} +(-0.0511492 - 0.0137054i) q^{20} +(1.83505 + 1.90594i) q^{21} +(0.899410 + 1.55782i) q^{22} +(-6.84131 - 3.94983i) q^{23} +(0.258819 + 0.965926i) q^{24} -4.99720i q^{25} +(-3.36370 - 1.29828i) q^{26} -1.00000i q^{27} +(2.56811 - 0.636228i) q^{28} +(-3.18465 + 5.51598i) q^{29} +(0.0458592 - 0.0264768i) q^{30} +(-1.81281 - 1.81281i) q^{31} +(0.965926 + 0.258819i) q^{32} +(-1.73753 - 0.465569i) q^{33} +(4.61737 - 4.61737i) q^{34} +(-0.0677396 - 0.122637i) q^{35} +(-0.866025 - 0.500000i) q^{36} +(-4.19793 + 1.12483i) q^{37} +6.18577 q^{38} +(3.29652 - 1.46047i) q^{39} -0.0529536i q^{40} +(0.982767 - 0.263332i) q^{41} +(-1.36605 + 2.26581i) q^{42} +(9.47687 - 5.47148i) q^{43} +(-1.27196 + 1.27196i) q^{44} +(-0.0137054 + 0.0511492i) q^{45} +(2.04458 - 7.63049i) q^{46} +(-4.86100 + 4.86100i) q^{47} +(-0.866025 + 0.500000i) q^{48} +(5.92522 + 3.72716i) q^{49} +(4.82692 - 1.29337i) q^{50} +6.52995i q^{51} +(0.383455 - 3.58510i) q^{52} -4.52395 q^{53} +(0.965926 - 0.258819i) q^{54} +(0.0824923 + 0.0476270i) q^{55} +(1.27923 + 2.31594i) q^{56} +(-4.37400 + 4.37400i) q^{57} +(-6.15227 - 1.64850i) q^{58} +(9.90333 + 2.65359i) q^{59} +(0.0374438 + 0.0374438i) q^{60} +(-2.13293 + 1.23145i) q^{61} +(1.28185 - 2.22023i) q^{62} +(-0.636228 - 2.56811i) q^{63} +1.00000i q^{64} +(-0.188631 + 0.0295218i) q^{65} -1.79882i q^{66} +(-1.84174 - 6.87347i) q^{67} +(5.65510 + 3.26497i) q^{68} +(3.94983 + 6.84131i) q^{69} +(0.100926 - 0.0971723i) q^{70} +(-10.4733 - 2.80632i) q^{71} +(0.258819 - 0.965926i) q^{72} +(-3.17457 + 3.17457i) q^{73} +(-2.17301 - 3.76376i) q^{74} +(-2.49860 + 4.32770i) q^{75} +(1.60100 + 5.97500i) q^{76} +(-4.75837 - 0.0901704i) q^{77} +(2.26391 + 2.80619i) q^{78} +5.14192 q^{79} +(0.0511492 - 0.0137054i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(0.508717 + 0.881124i) q^{82} +(-6.12074 - 6.12074i) q^{83} +(-2.54217 - 0.733067i) q^{84} +(0.0894956 - 0.334002i) q^{85} +(7.73784 + 7.73784i) q^{86} +(5.51598 - 3.18465i) q^{87} +(-1.55782 - 0.899410i) q^{88} +(1.38055 + 5.15227i) q^{89} -0.0529536 q^{90} +(7.53664 - 5.84799i) q^{91} +7.89966 q^{92} +(0.663534 + 2.47634i) q^{93} +(-5.95349 - 3.43725i) q^{94} +(0.283674 - 0.163779i) q^{95} +(-0.707107 - 0.707107i) q^{96} +(-3.92607 + 14.6523i) q^{97} +(-2.06660 + 6.68799i) q^{98} +(1.27196 + 1.27196i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 8 q^{7} + 20 q^{9}+O(q^{10}) \) 40 * q - 8 * q^7 + 20 * q^9	\( 40 q - 8 q^{7} + 20 q^{9} + 8 q^{11} + 40 q^{12} - 8 q^{14} + 20 q^{16} + 16 q^{17} + 16 q^{19} + 4 q^{21} + 8 q^{22} + 32 q^{26} + 8 q^{28} - 8 q^{33} + 16 q^{34} - 32 q^{35} + 40 q^{37} - 16 q^{38} - 16 q^{39} - 4 q^{41} + 12 q^{42} + 24 q^{43} + 8 q^{44} - 4 q^{46} + 16 q^{47} - 4 q^{49} - 16 q^{50} - 8 q^{52} + 32 q^{53} - 72 q^{55} + 12 q^{56} + 8 q^{57} - 36 q^{58} + 84 q^{59} - 48 q^{61} - 4 q^{62} - 4 q^{63} - 16 q^{65} + 12 q^{68} - 8 q^{69} + 36 q^{70} - 40 q^{71} - 48 q^{73} + 8 q^{74} + 36 q^{75} + 16 q^{76} - 24 q^{77} - 8 q^{78} - 48 q^{79} - 20 q^{81} + 36 q^{83} - 8 q^{84} + 8 q^{85} - 8 q^{86} + 12 q^{89} - 48 q^{91} - 16 q^{92} - 24 q^{93} - 96 q^{95} + 8 q^{98} - 8 q^{99}+O(q^{100}) \) 40 * q - 8 * q^7 + 20 * q^9 + 8 * q^11 + 40 * q^12 - 8 * q^14 + 20 * q^16 + 16 * q^17 + 16 * q^19 + 4 * q^21 + 8 * q^22 + 32 * q^26 + 8 * q^28 - 8 * q^33 + 16 * q^34 - 32 * q^35 + 40 * q^37 - 16 * q^38 - 16 * q^39 - 4 * q^41 + 12 * q^42 + 24 * q^43 + 8 * q^44 - 4 * q^46 + 16 * q^47 - 4 * q^49 - 16 * q^50 - 8 * q^52 + 32 * q^53 - 72 * q^55 + 12 * q^56 + 8 * q^57 - 36 * q^58 + 84 * q^59 - 48 * q^61 - 4 * q^62 - 4 * q^63 - 16 * q^65 + 12 * q^68 - 8 * q^69 + 36 * q^70 - 40 * q^71 - 48 * q^73 + 8 * q^74 + 36 * q^75 + 16 * q^76 - 24 * q^77 - 8 * q^78 - 48 * q^79 - 20 * q^81 + 36 * q^83 - 8 * q^84 + 8 * q^85 - 8 * q^86 + 12 * q^89 - 48 * q^91 - 16 * q^92 - 24 * q^93 - 96 * q^95 + 8 * q^98 - 8 * q^99

Introduction

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