LMFDB - Embedded newform 546.2.cg.a.145.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(145,546)]

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, 1]))

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

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

chi := DirichletCharacter("546.145");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.cg (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			145.4
Character	$\chi$	$=$	546.145
Dual form			546.2.cg.a.241.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(0.866025 + 0.500000i) q^{3} -1.00000i q^{4} +(2.92041 - 0.782522i) q^{5} +(-0.965926 + 0.258819i) q^{6} +(2.42968 + 1.04721i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(0.866025 + 0.500000i) q^{3} -1.00000i q^{4} +(2.92041 - 0.782522i) q^{5} +(-0.965926 + 0.258819i) q^{6} +(2.42968 + 1.04721i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.51172 + 2.61837i) q^{10} +(2.12926 - 0.570532i) 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} -1.00000 q^{16} -4.80193 q^{17} +(-0.965926 - 0.258819i) q^{18} +(0.738690 - 2.75683i) q^{19} +(-0.782522 - 2.92041i) q^{20} +(1.58056 + 2.12175i) q^{21} +(-1.10218 + 1.90904i) q^{22} +0.832559i q^{23} +(0.258819 + 0.965926i) q^{24} +(3.58634 - 2.07057i) q^{25} +(3.23094 + 1.60031i) q^{26} +1.00000i q^{27} +(1.04721 - 2.42968i) q^{28} +(0.310629 + 0.538026i) q^{29} +(-2.61837 + 1.51172i) q^{30} +(0.547944 - 2.04496i) q^{31} +(0.707107 - 0.707107i) q^{32} +(2.12926 + 0.570532i) q^{33} +(3.39547 - 3.39547i) q^{34} +(7.91514 + 1.15701i) q^{35} +(0.866025 - 0.500000i) q^{36} +(-2.91958 - 2.91958i) q^{37} +(1.42704 + 2.47170i) q^{38} +(0.709554 - 3.53504i) q^{39} +(2.61837 + 1.51172i) q^{40} +(-2.82732 + 10.5517i) q^{41} +(-2.61793 - 0.382681i) q^{42} +(-5.69185 - 3.28619i) q^{43} +(-0.570532 - 2.12926i) q^{44} +(2.13789 + 2.13789i) q^{45} +(-0.588708 - 0.588708i) q^{46} +(1.02537 + 3.82672i) q^{47} +(-0.866025 - 0.500000i) q^{48} +(4.80670 + 5.08878i) q^{49} +(-1.07181 + 4.00004i) q^{50} +(-4.15859 - 2.40096i) q^{51} +(-3.41621 + 1.15303i) q^{52} +(5.61789 + 9.73048i) q^{53} +(-0.707107 - 0.707107i) q^{54} +(5.77185 - 3.33238i) q^{55} +(0.977554 + 2.45853i) q^{56} +(2.01814 - 2.01814i) q^{57} +(-0.600090 - 0.160794i) q^{58} +(-5.57219 + 5.57219i) q^{59} +(0.782522 - 2.92041i) q^{60} +(-6.58584 + 3.80234i) q^{61} +(1.05855 + 1.83346i) q^{62} +(0.307929 + 2.62777i) q^{63} +1.00000i q^{64} +(-6.04059 - 9.07448i) q^{65} +(-1.90904 + 1.10218i) q^{66} +(-2.10295 - 7.84832i) q^{67} +4.80193i q^{68} +(-0.416279 + 0.721017i) q^{69} +(-6.41497 + 4.77872i) q^{70} +(2.25799 + 8.42695i) q^{71} +(-0.258819 + 0.965926i) q^{72} +(15.5872 + 4.17659i) q^{73} +4.12891 q^{74} +4.14115 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} +(-2.92041 + 0.782522i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-5.46195 - 9.46038i) q^{82} +(-12.5964 - 12.5964i) q^{83} +(2.12175 - 1.58056i) q^{84} +(-14.0236 + 3.75761i) q^{85} +(6.34844 - 1.70106i) q^{86} +0.621259i q^{87} +(1.90904 + 1.10218i) q^{88} +(-5.24104 + 5.24104i) q^{89} -3.02343 q^{90} +(0.776002 - 9.50778i) q^{91} +0.832559 q^{92} +(1.49701 - 1.49701i) q^{93} +(-3.43094 - 1.98085i) q^{94} -8.62912i q^{95} +(0.965926 - 0.258819i) q^{96} +(-11.7346 + 3.14428i) q^{97} +(-6.99716 - 0.199461i) q^{98} +(1.55872 + 1.55872i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{7} + 16 q^{9}+O(q^{10}) $ 32 * q - 4 * q^7 + 16 * q^9	$ 32 q - 4 q^{7} + 16 q^{9} + 8 q^{11} + 16 q^{12} + 4 q^{14} - 32 q^{16} - 16 q^{17} + 24 q^{19} + 8 q^{21} - 4 q^{22} + 24 q^{25} - 8 q^{26} + 8 q^{28} - 12 q^{29} + 4 q^{31} + 8 q^{33} + 8 q^{34} + 40 q^{35} - 12 q^{37} - 8 q^{38} + 28 q^{39} + 28 q^{41} - 12 q^{42} + 84 q^{43} - 4 q^{44} - 40 q^{46} - 4 q^{47} - 36 q^{49} - 16 q^{50} - 20 q^{52} - 4 q^{53} - 48 q^{55} + 12 q^{56} + 12 q^{57} + 12 q^{58} - 24 q^{59} - 36 q^{61} + 40 q^{62} + 4 q^{63} + 44 q^{65} - 16 q^{67} + 8 q^{69} + 40 q^{70} + 20 q^{71} - 16 q^{73} - 40 q^{74} + 16 q^{75} - 36 q^{76} + 12 q^{77} - 20 q^{78} - 16 q^{81} - 24 q^{82} - 12 q^{83} - 8 q^{84} - 4 q^{85} - 20 q^{86} - 60 q^{89} - 48 q^{91} - 16 q^{92} - 32 q^{93} - 76 q^{97} - 8 q^{98} + 4 q^{99}+O(q^{100}) $ 32 * q - 4 * q^7 + 16 * q^9 + 8 * q^11 + 16 * q^12 + 4 * q^14 - 32 * q^16 - 16 * q^17 + 24 * q^19 + 8 * q^21 - 4 * q^22 + 24 * q^25 - 8 * q^26 + 8 * q^28 - 12 * q^29 + 4 * q^31 + 8 * q^33 + 8 * q^34 + 40 * q^35 - 12 * q^37 - 8 * q^38 + 28 * q^39 + 28 * q^41 - 12 * q^42 + 84 * q^43 - 4 * q^44 - 40 * q^46 - 4 * q^47 - 36 * q^49 - 16 * q^50 - 20 * q^52 - 4 * q^53 - 48 * q^55 + 12 * q^56 + 12 * q^57 + 12 * q^58 - 24 * q^59 - 36 * q^61 + 40 * q^62 + 4 * q^63 + 44 * q^65 - 16 * q^67 + 8 * q^69 + 40 * q^70 + 20 * q^71 - 16 * q^73 - 40 * q^74 + 16 * q^75 - 36 * q^76 + 12 * q^77 - 20 * q^78 - 16 * q^81 - 24 * q^82 - 12 * q^83 - 8 * q^84 - 4 * q^85 - 20 * q^86 - 60 * q^89 - 48 * q^91 - 16 * q^92 - 32 * q^93 - 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 $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$		−	1.00000i		−	0.500000i
$5$	2.92041	−	0.782522i	1.30605	−	0.349955i	0.462314	−	0.886716i	$-0.347019\pi$
$5$	2.92041	−	0.782522i	1.30605	−	0.349955i	0.843734	+	0.536762i	$0.180353\pi$
$6$	−0.965926	+	0.258819i	−0.394338	+	0.105662i
$7$	2.42968	+	1.04721i	0.918333	+	0.395809i
$7$	2.42968	+	1.04721i	0.918333	+	0.395809i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−1.51172	+	2.61837i	−0.478047	+	0.828001i
$11$	2.12926	−	0.570532i	0.641995	−	0.172022i	0.0768880	−	0.997040i	$-0.475502\pi$
$11$	2.12926	−	0.570532i	0.641995	−	0.172022i	0.565107	+	0.825018i	$0.308835\pi$
$12$	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
$16$	−1.00000			−0.250000
$17$	−4.80193			−1.16464			−0.582319	−	0.812960i	$-0.697855\pi$
$17$	−4.80193			−1.16464			−0.582319	+	0.812960i	$0.697855\pi$
$18$	−0.965926	−	0.258819i	−0.227671	−	0.0610042i
$19$	0.738690	−	2.75683i	0.169467	−	0.632460i	−0.827961	−	0.560786i	$-0.810499\pi$
$19$	0.738690	−	2.75683i	0.169467	−	0.632460i	0.997428	−	0.0716742i	$-0.0228342\pi$
$20$	−0.782522	−	2.92041i	−0.174977	−	0.653024i
$21$	1.58056	+	2.12175i	0.344906	+	0.463004i
$22$	−1.10218	+	1.90904i	−0.234986	+	0.407008i
$23$			0.832559i			0.173600i	0.996226	+	0.0868002i	$0.0276642\pi$
$23$			0.832559i			0.173600i	−0.996226	+	0.0868002i	$0.972336\pi$
$24$	0.258819	+	0.965926i	0.0528312	+	0.197169i
$25$	3.58634	−	2.07057i	0.717268	−	0.414115i
$26$	3.23094	+	1.60031i	0.633640	+	0.313847i
$27$			1.00000i			0.192450i
$28$	1.04721	−	2.42968i	0.197904	−	0.459167i
$29$	0.310629	+	0.538026i	0.0576824	+	0.0999089i	0.893425	−	0.449213i	$-0.148296\pi$
$29$	0.310629	+	0.538026i	0.0576824	+	0.0999089i	−0.835742	+	0.549122i	$0.814962\pi$
$30$	−2.61837	+	1.51172i	−0.478047	+	0.276000i
$31$	0.547944	−	2.04496i	0.0984137	−	0.367285i	−0.899101	−	0.437741i	$-0.855779\pi$
$31$	0.547944	−	2.04496i	0.0984137	−	0.367285i	0.997515	+	0.0704559i	$0.0224454\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	2.12926	+	0.570532i	0.370656	+	0.0993169i
$34$	3.39547	−	3.39547i	0.582319	−	0.582319i
$35$	7.91514	+	1.15701i	1.33790	+	0.195570i
$36$	0.866025	−	0.500000i	0.144338	−	0.0833333i
$37$	−2.91958	−	2.91958i	−0.479976	−	0.479976i	0.425148	−	0.905124i	$-0.360222\pi$
$37$	−2.91958	−	2.91958i	−0.479976	−	0.479976i	−0.905124	+	0.425148i	$0.860222\pi$
$38$	1.42704	+	2.47170i	0.231496	+	0.400963i
$39$	0.709554	−	3.53504i	0.113620	−	0.566060i
$40$	2.61837	+	1.51172i	0.414001	+	0.239023i
$41$	−2.82732	+	10.5517i	−0.441553	+	1.64790i	0.283329	+	0.959023i	$0.408561\pi$
$41$	−2.82732	+	10.5517i	−0.441553	+	1.64790i	−0.724881	+	0.688874i	$0.758105\pi$
$42$	−2.61793	−	0.382681i	−0.403955	−	0.0590489i
$43$	−5.69185	−	3.28619i	−0.867999	−	0.501140i	−0.00131639	−	0.999999i	$-0.500419\pi$
$43$	−5.69185	−	3.28619i	−0.867999	−	0.501140i	−0.866683	+	0.498860i	$0.833752\pi$
$44$	−0.570532	−	2.12926i	−0.0860110	−	0.320997i
$45$	2.13789	+	2.13789i	0.318698	+	0.318698i
$46$	−0.588708	−	0.588708i	−0.0868002	−	0.0868002i
$47$	1.02537	+	3.82672i	0.149565	+	0.558184i	0.999510	+	0.0313122i	$0.00996861\pi$
$47$	1.02537	+	3.82672i	0.149565	+	0.558184i	−0.849945	+	0.526872i	$0.823365\pi$
$48$	−0.866025	−	0.500000i	−0.125000	−	0.0721688i
$49$	4.80670	+	5.08878i	0.686671	+	0.726968i
$50$	−1.07181	+	4.00004i	−0.151577	+	0.565691i
$51$	−4.15859	−	2.40096i	−0.582319	−	0.336202i
$52$	−3.41621	+	1.15303i	−0.473744	+	0.159897i
$53$	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	$0.552751\pi$
$54$	−0.707107	−	0.707107i	−0.0962250	−	0.0962250i
$55$	5.77185	−	3.33238i	0.778276	−	0.449338i
$56$	0.977554	+	2.45853i	0.130631	+	0.328535i
$57$	2.01814	−	2.01814i	0.267309	−	0.267309i
$58$	−0.600090	−	0.160794i	−0.0787956	−	0.0211132i
$59$	−5.57219	+	5.57219i	−0.725437	+	0.725437i	−0.969707	−	0.244270i	$-0.921452\pi$
$59$	−5.57219	+	5.57219i	−0.725437	+	0.725437i	0.244270	+	0.969707i	$0.421452\pi$
$60$	0.782522	−	2.92041i	0.101023	−	0.377024i
$61$	−6.58584	+	3.80234i	−0.843231	+	0.486839i	−0.858361	−	0.513046i	$-0.828517\pi$
$61$	−6.58584	+	3.80234i	−0.843231	+	0.486839i	0.0151304	+	0.999886i	$0.495184\pi$
$62$	1.05855	+	1.83346i	0.134436	+	0.232849i
$63$	0.307929	+	2.62777i	0.0387954	+	0.331068i
$64$			1.00000i			0.125000i
$65$	−6.04059	−	9.07448i	−0.749243	−	1.12555i
$66$	−1.90904	+	1.10218i	−0.234986	+	0.135669i
$67$	−2.10295	−	7.84832i	−0.256916	−	0.958825i	−0.967014	−	0.254722i	$-0.918016\pi$
$67$	−2.10295	−	7.84832i	−0.256916	−	0.958825i	0.710098	−	0.704103i	$-0.248651\pi$
$68$			4.80193i			0.582319i
$69$	−0.416279	+	0.721017i	−0.0501141	+	0.0868002i
$70$	−6.41497	+	4.77872i	−0.766736	+	0.571166i
$71$	2.25799	+	8.42695i	0.267975	+	1.00009i	0.960404	+	0.278610i	$0.0898736\pi$
$71$	2.25799	+	8.42695i	0.267975	+	1.00009i	−0.692430	+	0.721485i	$0.743460\pi$
$72$	−0.258819	+	0.965926i	−0.0305021	+	0.113835i
$73$	15.5872	+	4.17659i	1.82435	+	0.488832i	0.997309	−	0.0733125i	$-0.0233570\pi$
$73$	15.5872	+	4.17659i	1.82435	+	0.488832i	0.827039	+	0.562145i	$0.190024\pi$
$74$	4.12891			0.479976
$75$	4.14115			0.478179
$76$	−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	$0.135849\pi$
$80$	−2.92041	+	0.782522i	−0.326512	+	0.0874886i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−5.46195	−	9.46038i	−0.603172	−	1.04472i
$83$	−12.5964	−	12.5964i	−1.38264	−	1.38264i	−0.839907	−	0.542730i	$-0.817391\pi$
$83$	−12.5964	−	12.5964i	−1.38264	−	1.38264i	−0.542730	−	0.839907i	$-0.682609\pi$
$84$	2.12175	−	1.58056i	0.231502	−	0.172453i
$85$	−14.0236	+	3.75761i	−1.52107	+	0.407570i
$86$	6.34844	−	1.70106i	0.684569	−	0.183430i
$87$			0.621259i			0.0666059i
$88$	1.90904	+	1.10218i	0.203504	+	0.117493i
$89$	−5.24104	+	5.24104i	−0.555549	+	0.555549i	−0.928037	−	0.372488i	$-0.878505\pi$
$89$	−5.24104	+	5.24104i	−0.555549	+	0.555549i	0.372488	+	0.928037i	$0.378505\pi$
$90$	−3.02343			−0.318698
$91$	0.776002	−	9.50778i	0.0813471	−	0.996686i
$92$	0.832559			0.0868002
$93$	1.49701	−	1.49701i	0.155233	−	0.155233i
$94$	−3.43094	−	1.98085i	−0.353875	−	0.204310i
$95$		−	8.62912i		−	0.885329i
$96$	0.965926	−	0.258819i	0.0985844	−	0.0264156i
$97$	−11.7346	+	3.14428i	−1.19147	+	0.319254i	−0.799467	−	0.600710i	$-0.794885\pi$
$97$	−11.7346	+	3.14428i	−1.19147	+	0.319254i	−0.392004	+	0.919964i	$0.628218\pi$
$98$	−6.99716	−	0.199461i	−0.706820	−	0.0201486i
$99$	1.55872	+	1.55872i	0.156658	+	0.156658i
$100$	−2.07057	−	3.58634i	−0.207057	−	0.358634i
$101$	6.30672	−	10.9236i	0.627542	−	1.08693i	−0.360501	−	0.932759i	$-0.617394\pi$
$101$	6.30672	−	10.9236i	0.627542	−	1.08693i	0.988043	−	0.154176i	$-0.0492723\pi$
$102$	4.63830	−	1.24283i	0.459260	−	0.123058i
$103$	7.11234	−	12.3189i	0.700799	−	1.21382i	−0.267387	−	0.963589i	$-0.586160\pi$
$103$	7.11234	−	12.3189i	0.700799	−	1.21382i	0.968186	−	0.250231i	$-0.0805065\pi$
$104$	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
$107$	11.8982			1.15024			0.575122	−	0.818067i	$-0.304954\pi$
$107$	11.8982			1.15024			0.575122	+	0.818067i	$0.304954\pi$
$108$	1.00000			0.0962250
$109$	−0.225023	−	0.0602948i	−0.0215533	−	0.00577519i	0.248026	−	0.968753i	$-0.420218\pi$
$109$	−0.225023	−	0.0602948i	−0.0215533	−	0.00577519i	−0.269580	+	0.962978i	$0.586885\pi$
$110$	−1.72497	+	6.43766i	−0.164469	+	0.613807i
$111$	−1.06864	−	3.98822i	−0.101431	−	0.378546i
$112$	−2.42968	−	1.04721i	−0.229583	−	0.0989522i
$113$	1.85838	−	3.21881i	0.174822	−	0.302800i	−0.765278	−	0.643700i	$-0.777398\pi$
$113$	1.85838	−	3.21881i	0.174822	−	0.302800i	0.940100	+	0.340900i	$0.110732\pi$
$114$			2.85408i			0.267309i
$115$	0.651495	+	2.43141i	0.0607523	+	0.226731i
$116$	0.538026	−	0.310629i	0.0499544	−	0.0288412i
$117$	2.38201	−	2.70666i	0.220217	−	0.250231i
$118$		−	7.88027i		−	0.725437i
$119$	−11.6671	−	5.02863i	−1.06953	−	0.460974i
$120$	1.51172	+	2.61837i	0.138000	+	0.239023i
$121$	−5.31806	+	3.07038i	−0.483460	+	0.279126i
$122$	1.96823	−	7.34555i	0.178196	−	0.665035i
$123$	−7.72437	+	7.72437i	−0.696483	+	0.696483i
$124$	−2.04496	−	0.547944i	−0.183642	−	0.0492068i
$125$	−1.83613	+	1.83613i	−0.164229	+	0.164229i
$126$	−2.07585	−	1.64038i	−0.184932	−	0.146136i
$127$	−10.5916	+	6.11504i	−0.939849	+	0.542622i	−0.889913	−	0.456130i	$-0.849235\pi$
$127$	−10.5916	+	6.11504i	−0.939849	+	0.542622i	−0.0499361	+	0.998752i	$0.515902\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	−3.28619	−	5.69185i	−0.289333	−	0.501140i
$130$	10.6880	+	2.14529i	0.937397	+	0.188154i
$131$	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
$133$	4.68176	−	5.92465i	0.405960	−	0.513732i
$134$	7.03661	+	4.06259i	0.607871	+	0.350954i
$135$	0.782522	+	2.92041i	0.0673488	+	0.251349i
$136$	−3.39547	−	3.39547i	−0.291159	−	0.291159i
$137$	0.494848	+	0.494848i	0.0422777	+	0.0422777i	0.727930	−	0.685652i	$-0.240483\pi$
$137$	0.494848	+	0.494848i	0.0422777	+	0.0422777i	−0.685652	+	0.727930i	$0.740483\pi$
$138$	−0.215482	−	0.804190i	−0.0183430	−	0.0684572i
$139$	−14.3429	−	8.28090i	−1.21655	−	0.702377i	−0.252374	−	0.967630i	$-0.581211\pi$
$139$	−14.3429	−	8.28090i	−1.21655	−	0.702377i	−0.964179	+	0.265253i	$0.914545\pi$
$140$	1.15701	−	7.91514i	0.0977851	−	0.668951i
$141$	−1.02537	+	3.82672i	−0.0863514	+	0.322268i
$142$	−7.55540	−	4.36211i	−0.634035	−	0.366060i
$143$	−4.40416	−	6.61615i	−0.368294	−	0.553271i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	1.32818	+	1.32818i	0.110300	+	0.110300i
$146$	−13.9751	+	8.06855i	−1.15659	+	0.667758i
$147$	1.61833	+	6.81036i	0.133478	+	0.561709i
$148$	−2.91958	+	2.91958i	−0.239988	+	0.239988i
$149$	−4.70351	−	1.26030i	−0.385327	−	0.103248i	0.0609551	−	0.998141i	$-0.480585\pi$
$149$	−4.70351	−	1.26030i	−0.385327	−	0.103248i	−0.446282	+	0.894893i	$0.647252\pi$
$150$	−2.92823	+	2.92823i	−0.239089	+	0.239089i
$151$	−0.451500	+	1.68502i	−0.0367425	+	0.137125i	−0.981861	−	0.189604i	$-0.939280\pi$
$151$	−0.451500	+	1.68502i	−0.0367425	+	0.137125i	0.945118	+	0.326729i	$0.105946\pi$
$152$	2.47170	−	1.42704i	0.200482	−	0.115748i
$153$	−2.40096	−	4.15859i	−0.194106	−	0.336202i
$154$	−4.67712	+	3.48413i	−0.376893	+	0.280760i
$155$		−	6.40089i		−	0.514132i
$156$	−3.53504	−	0.709554i	−0.283030	−	0.0568098i
$157$	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	$-0.0151047\pi$
$158$	0.444746	+	1.65982i	0.0353821	+	0.132048i
$159$			11.2358i			0.891056i
$160$	1.51172	−	2.61837i	0.119512	−	0.207000i
$161$	−0.871865	+	2.02285i	−0.0687126	+	0.159423i
$162$	−0.258819	−	0.965926i	−0.0203347	−	0.0758903i
$163$	0.662188	−	2.47132i	0.0518665	−	0.193569i	−0.935132	−	0.354301i	$-0.884719\pi$
$163$	0.662188	−	2.47132i	0.0518665	−	0.193569i	0.986998	+	0.160732i	$0.0513856\pi$
$164$	10.5517	+	2.82732i	0.823948	+	0.220776i
$165$	6.66476			0.518851
$166$	17.8140			1.38264
$167$	−10.4744	−	2.80660i	−0.810533	−	0.217182i	−0.170329	−	0.985387i	$-0.554483\pi$
$167$	−10.4744	−	2.80660i	−0.810533	−	0.217182i	−0.640203	+	0.768206i	$0.721150\pi$
$168$	−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
$171$	2.75683	−	0.738690i	0.210820	−	0.0564890i
$172$	−3.28619	+	5.69185i	−0.250570	+	0.434000i
$173$	−6.48648	−	11.2349i	−0.493158	−	0.854175i	0.506811	−	0.862057i	$-0.330824\pi$
$173$	−6.48648	−	11.2349i	−0.493158	−	0.854175i	−0.999969	+	0.00788246i	$0.997491\pi$
$174$	−0.439296	−	0.439296i	−0.0333030	−	0.0333030i
$175$	10.8820	−	1.27518i	0.822601	−	0.0963945i
$176$	−2.12926	+	0.570532i	−0.160499	+	0.0430055i
$177$	−7.61175	+	2.03956i	−0.572134	+	0.153303i
$178$		−	7.41194i		−	0.555549i
$179$	−3.67979	−	2.12453i	−0.275040	−	0.158795i	0.356136	−	0.934434i	$-0.384094\pi$
$179$	−3.67979	−	2.12453i	−0.275040	−	0.158795i	−0.631176	+	0.775640i	$0.717427\pi$
$180$	2.13789	−	2.13789i	0.159349	−	0.159349i
$181$	−14.5375			−1.08056			−0.540280	−	0.841485i	$-0.681682\pi$
$181$	−14.5375			−1.08056			−0.540280	+	0.841485i	$0.681682\pi$
$182$	6.17430	+	7.27173i	0.457669	+	0.539016i
$183$	−7.60468			−0.562154
$184$	−0.588708	+	0.588708i	−0.0434001	+	0.0434001i
$185$	−10.8110	−	6.24175i	−0.794842	−	0.458902i
$186$			2.11709i			0.155233i
$187$	−10.2245	+	2.73965i	−0.747691	+	0.200343i
$188$	3.82672	−	1.02537i	0.279092	−	0.0747825i
$189$	−1.04721	+	2.42968i	−0.0761734	+	0.176733i
$190$	6.10171	+	6.10171i	0.442664	+	0.442664i
$191$	6.56388	+	11.3690i	0.474946	+	0.822630i	0.999588	−	0.0286925i	$-0.00913435\pi$
$191$	6.56388	+	11.3690i	0.474946	+	0.822630i	−0.524643	+	0.851323i	$0.675801\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	12.0343	−	3.22458i	0.866247	−	0.232110i	0.201783	−	0.979430i	$-0.435326\pi$
$193$	12.0343	−	3.22458i	0.866247	−	0.232110i	0.664464	+	0.747320i	$0.268660\pi$
$194$	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	−0.688394	−	0.725337i	$-0.741684\pi$
$197$	−23.1200	−	6.19498i	−1.64723	−	0.441374i	−0.958835	+	0.283963i	$0.908351\pi$
$198$	−2.20437			−0.156658
$199$	17.3814			1.23213			0.616066	−	0.787694i	$-0.288725\pi$
$199$	17.3814			1.23213			0.616066	+	0.787694i	$0.288725\pi$
$200$	4.00004	+	1.07181i	0.282846	+	0.0757883i
$201$	2.10295	−	7.84832i	0.148331	−	0.553578i
$202$	3.26460	+	12.1836i	0.229696	+	0.857238i
$203$	0.191304	+	1.63253i	0.0134269	+	0.114581i
$204$	−2.40096	+	4.15859i	−0.168101	+	0.291159i
$205$			33.0277i			2.30676i
$206$	3.68162	+	13.7400i	0.256510	+	0.957310i
$207$	−0.721017	+	0.416279i	−0.0501141	+	0.0289334i
$208$	1.15303	+	3.41621i	0.0799483	+	0.236872i
$209$		−	6.29144i		−	0.435188i
$210$	−7.94489	+	0.931003i	−0.548249	+	0.0642453i
$211$	10.0120	+	17.3414i	0.689258	+	1.19383i	0.972078	+	0.234657i	$0.0753965\pi$
$211$	10.0120	+	17.3414i	0.689258	+	1.19383i	−0.282821	+	0.959173i	$0.591270\pi$
$212$	9.73048	−	5.61789i	0.668292	−	0.385839i
$213$	−2.25799	+	8.42695i	−0.154715	+	0.577405i
$214$	−8.41332	+	8.41332i	−0.575122	+	0.575122i
$215$	−19.1941	−	5.14304i	−1.30902	−	0.350752i
$216$	−0.707107	+	0.707107i	−0.0481125	+	0.0481125i
$217$	3.47283	−	4.39478i	0.235751	−	0.298337i
$218$	0.201750	−	0.116481i	0.0136643	−	0.00788906i
$219$	11.4106	+	11.4106i	0.771060	+	0.771060i
$220$	−3.33238	−	5.77185i	−0.224669	−	0.389138i
$221$	5.53677	+	16.4044i	0.372443	+	1.10348i
$222$	3.57574	+	2.06446i	0.239988	+	0.138557i
$223$	−2.41674	+	9.01938i	−0.161837	+	0.603983i	0.836586	+	0.547836i	$0.184548\pi$
$223$	−2.41674	+	9.01938i	−0.161837	+	0.603983i	−0.998423	+	0.0561468i	$0.982119\pi$
$224$	2.45853	−	0.977554i	0.164268	−	0.0653156i
$225$	3.58634	+	2.07057i	0.239089	+	0.138038i
$226$	0.961968	+	3.59011i	0.0639892	+	0.238811i
$227$	−18.1503	−	18.1503i	−1.20468	−	1.20468i	−0.972727	−	0.231953i	$-0.925488\pi$
$227$	−18.1503	−	18.1503i	−1.20468	−	1.20468i	−0.231953	−	0.972727i	$-0.574512\pi$
$228$	−2.01814	−	2.01814i	−0.133654	−	0.133654i
$229$	0.454900	+	1.69771i	0.0300606	+	0.112188i	0.979326	−	0.202288i	$-0.0648378\pi$
$229$	0.454900	+	1.69771i	0.0300606	+	0.112188i	−0.949265	+	0.314476i	$0.898171\pi$
$230$	−2.17995	−	1.25859i	−0.143741	−	0.0829891i
$231$	4.57594	+	3.61599i	0.301075	+	0.237915i
$232$	−0.160794	+	0.600090i	−0.0105566	+	0.0393978i
$233$	2.03170	+	1.17300i	0.133101	+	0.0768459i	0.565072	−	0.825042i	$-0.308848\pi$
$233$	2.03170	+	1.17300i	0.133101	+	0.0768459i	−0.431971	+	0.901887i	$0.642182\pi$
$234$	0.229560	+	3.59824i	0.0150068	+	0.235224i
$235$	5.98898	+	10.3732i	0.390678	+	0.676674i
$236$	5.57219	+	5.57219i	0.362719	+	0.362719i
$237$	1.48815	−	0.859183i	0.0966657	−	0.0558100i
$238$	11.8057	−	4.69414i	0.765250	−	0.304276i
$239$	7.68798	−	7.68798i	0.497294	−	0.497294i	−0.413300	−	0.910595i	$-0.635624\pi$
$239$	7.68798	−	7.68798i	0.497294	−	0.497294i	0.910595	+	0.413300i	$0.135624\pi$
$240$	−2.92041	−	0.782522i	−0.188512	−	0.0505116i
$241$	2.91524	−	2.91524i	0.187787	−	0.187787i	−0.606952	−	0.794739i	$-0.707608\pi$
$241$	2.91524	−	2.91524i	0.187787	−	0.187787i	0.794739	+	0.606952i	$0.207608\pi$
$242$	1.58935	−	5.93152i	0.102167	−	0.381293i
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	3.80234	+	6.58584i	0.243420	+	0.421615i
$245$	18.0196	+	11.1000i	1.15123	+	0.709152i
$246$		−	10.9239i		−	0.696483i
$247$	−10.2696	+	0.655184i	−0.653442	+	0.0416883i
$248$	1.83346	−	1.05855i	0.116425	−	0.0672178i
$249$	−4.61061	−	17.2070i	−0.292186	−	1.09045i
$250$		−	2.59668i		−	0.164229i
$251$	12.8869	−	22.3207i	0.813412	−	1.40887i	−0.0970512	−	0.995279i	$-0.530941\pi$
$251$	12.8869	−	22.3207i	0.813412	−	1.40887i	0.910463	−	0.413591i	$-0.135726\pi$
$252$	2.62777	−	0.307929i	0.165534	−	0.0193977i
$253$	0.475002	+	1.77273i	0.0298631	+	0.111451i
$254$	3.16538	−	11.8134i	0.198613	−	0.741236i
$255$	−14.0236	−	3.75761i	−0.878192	−	0.235311i
$256$	1.00000			0.0625000
$257$	0.734242			0.0458008			0.0229004	−	0.999738i	$-0.492710\pi$
$257$	0.734242			0.0458008			0.0229004	+	0.999738i	$0.492710\pi$
$258$	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
$262$	−2.38100	+	0.637987i	−0.147099	+	0.0394150i
$263$	5.32062	−	9.21558i	0.328083	−	0.568257i	−0.654048	−	0.756453i	$-0.726931\pi$
$263$	5.32062	−	9.21558i	0.328083	−	0.568257i	0.982131	+	0.188196i	$0.0602640\pi$
$264$	1.10218	+	1.90904i	0.0678347	+	0.117493i
$265$	24.0209	+	24.0209i	1.47559	+	1.47559i
$266$	0.878854	+	7.49987i	0.0538860	+	0.459846i
$267$	−7.15939	+	1.91835i	−0.438147	+	0.117401i
$268$	−7.84832	+	2.10295i	−0.479412	+	0.128458i
$269$			30.6364i			1.86794i	0.357356	+	0.933968i	$0.383678\pi$
$269$			30.6364i			1.86794i	−0.357356	+	0.933968i	$0.616322\pi$
$270$	−2.61837	−	1.51172i	−0.159349	−	0.0920001i
$271$	6.54408	−	6.54408i	0.397524	−	0.397524i	−0.479835	−	0.877359i	$-0.659303\pi$
$271$	6.54408	−	6.54408i	0.397524	−	0.397524i	0.877359	+	0.479835i	$0.159303\pi$
$272$	4.80193			0.291159
$273$	5.42593	−	7.84598i	0.328392	−	0.474860i
$274$	−0.699821			−0.0422777
$275$	6.45490	−	6.45490i	0.389245	−	0.389245i
$276$	0.721017	+	0.416279i	0.0434001	+	0.0250571i
$277$			17.9726i			1.07987i	0.841706	+	0.539935i	$0.181551\pi$
$277$			17.9726i			1.07987i	−0.841706	+	0.539935i	$0.818449\pi$
$278$	15.9975	−	4.28651i	0.959465	−	0.257088i
$279$	2.04496	−	0.547944i	0.122428	−	0.0328046i
$280$	4.77872	+	6.41497i	0.285583	+	0.383368i
$281$	17.1750	+	17.1750i	1.02458	+	1.02458i	0.999690	+	0.0248857i	$0.00792219\pi$
$281$	17.1750	+	17.1750i	1.02458	+	1.02458i	0.0248857	+	0.999690i	$0.492078\pi$
$282$	−1.98085	−	3.43094i	−0.117958	−	0.204310i
$283$	11.6440	−	20.1681i	0.692167	−	1.19887i	−0.278960	−	0.960303i	$-0.589990\pi$
$283$	11.6440	−	20.1681i	0.692167	−	1.19887i	0.971127	−	0.238565i	$-0.0766770\pi$
$284$	8.42695	−	2.25799i	0.500047	−	0.133987i
$285$	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
$289$	6.05848			0.356381
$290$	−1.87833			−0.110300
$291$	−11.7346	−	3.14428i	−0.687896	−	0.184321i
$292$	4.17659	−	15.5872i	0.244416	−	0.912174i
$293$	0.988549	+	3.68932i	0.0577517	+	0.215532i	0.988771	−	0.149437i	$-0.0477462\pi$
$293$	0.988549	+	3.68932i	0.0577517	+	0.215532i	−0.931020	+	0.364969i	$0.881080\pi$
$294$	−5.95999	−	3.67132i	−0.347593	−	0.214116i
$295$	−11.9127	+	20.6334i	−0.693586	+	1.20133i
$296$		−	4.12891i		−	0.239988i
$297$	0.570532	+	2.12926i	0.0331056	+	0.123552i
$298$	4.21705	−	2.43472i	0.244287	−	0.141039i
$299$	2.84420	−	0.959965i	0.164484	−	0.0555162i
$300$		−	4.14115i		−	0.239089i
$301$	−10.3880	−	13.9450i	−0.598757	−	0.803775i
$302$	−0.872230	−	1.51075i	−0.0501912	−	0.0869337i
$303$	10.9236	−	6.30672i	0.627542	−	0.362312i
$304$	−0.738690	+	2.75683i	−0.0423668	+	0.158115i
$305$	−16.2580	+	16.2580i	−0.930928	+	0.930928i
$306$	4.63830	+	1.24283i	0.265154	+	0.0710478i
$307$	−5.02364	+	5.02364i	−0.286714	+	0.286714i	−0.835779	−	0.549065i	$-0.814984\pi$
$307$	−5.02364	+	5.02364i	−0.286714	+	0.286714i	0.549065	+	0.835779i	$0.314984\pi$
$308$	0.843569	−	5.77088i	0.0480668	−	0.328826i
$309$	12.3189	−	7.11234i	0.700799	−	0.404607i
$310$	4.52611	+	4.52611i	0.257066	+	0.257066i
$311$	−1.10966	−	1.92199i	−0.0629230	−	0.108986i	0.832848	−	0.553502i	$-0.186709\pi$
$311$	−1.10966	−	1.92199i	−0.0629230	−	0.108986i	−0.895771	+	0.444516i	$0.853376\pi$
$312$	3.00138	−	1.99792i	0.169920	−	0.113110i
$313$	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
$315$	2.95557	+	7.43321i	0.166527	+	0.418814i
$316$	−1.48815	−	0.859183i	−0.0837149	−	0.0483328i
$317$	5.50177	+	20.5329i	0.309010	+	1.15324i	0.929438	+	0.368978i	$0.120292\pi$
$317$	5.50177	+	20.5329i	0.309010	+	1.15324i	−0.620428	+	0.784263i	$0.713041\pi$
$318$	−7.94490	−	7.94490i	−0.445528	−	0.445528i
$319$	0.968370	+	0.968370i	0.0542183	+	0.0542183i
$320$	0.782522	+	2.92041i	0.0437443	+	0.163256i
$321$	10.3042	+	5.94911i	0.575122	+	0.332047i
$322$	−0.813871	−	2.04687i	−0.0453552	−	0.114068i
$323$	−3.54713	+	13.2381i	−0.197368	+	0.736587i
$324$	0.866025	+	0.500000i	0.0481125	+	0.0277778i
$325$	−11.2087	−	9.86427i	−0.621746	−	0.547171i
$326$	1.27925	+	2.21572i	0.0708510	+	0.122718i
$327$	−0.164728	−	0.164728i	−0.00910950	−	0.00910950i
$328$	−9.46038	+	5.46195i	−0.522362	+	0.301586i
$329$	−1.51607	+	10.3715i	−0.0835836	+	0.571798i
$330$	−4.71270	+	4.71270i	−0.259425	+	0.259425i
$331$	23.5759	+	6.31715i	1.29585	+	0.347222i	0.839880	−	0.542772i	$-0.182625\pi$
$331$	23.5759	+	6.31715i	1.29585	+	0.347222i	0.455971	+	0.889995i	$0.349292\pi$
$332$	−12.5964	+	12.5964i	−0.691319	+	0.691319i
$333$	1.06864	−	3.98822i	0.0585612	−	0.218553i
$334$	9.39108	−	5.42194i	0.513857	−	0.296676i
$335$	−12.2830	−	21.2747i	−0.671090	−	1.16236i
$336$	−1.58056	−	2.12175i	−0.0862266	−	0.115751i
$337$		−	28.2173i		−	1.53709i	−0.639794	−	0.768547i	$-0.720980\pi$
$337$		−	28.2173i		−	1.53709i	0.639794	−	0.768547i	$-0.279020\pi$
$338$	1.74164	−	12.8828i	0.0947325	−	0.700732i
$339$	3.21881	−	1.85838i	0.174822	−	0.100933i
$340$	3.75761	+	14.0236i	0.203785	+	0.760536i
$341$		−	4.66685i		−	0.252724i
$342$	−1.42704	+	2.47170i	−0.0771655	+	0.133654i
$343$	6.34972	+	17.3977i	0.342852	+	0.939389i
$344$	−1.70106	−	6.34844i	−0.0917149	−	0.342285i
$345$	−0.651495	+	2.43141i	−0.0350753	+	0.130903i
$346$	12.5309	+	3.35765i	0.673666	+	0.180508i
$347$	1.97144			0.105832			0.0529162	−	0.998599i	$-0.483148\pi$
$347$	1.97144			0.105832			0.0529162	+	0.998599i	$0.483148\pi$
$348$	0.621259			0.0333030
$349$	−26.2589	−	7.03605i	−1.40561	−	0.376631i	−0.525252	−	0.850947i	$-0.676029\pi$
$349$	−26.2589	−	7.03605i	−1.40561	−	0.376631i	−0.880355	+	0.474316i	$0.842696\pi$
$350$	−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
$353$	9.09210	−	2.43622i	0.483923	−	0.129667i	−0.00860550	−	0.999963i	$-0.502739\pi$
$353$	9.09210	−	2.43622i	0.483923	−	0.129667i	0.492529	+	0.870296i	$0.336073\pi$
$354$	3.94013	−	6.82451i	0.209416	−	0.362719i
$355$	13.1885	+	22.8432i	0.699975	+	1.21239i
$356$	5.24104	+	5.24104i	0.277774	+	0.277774i
$357$	−7.58973	−	10.1885i	−0.401691	−	0.539232i
$358$	4.10427	−	1.09974i	0.216917	−	0.0581228i
$359$	4.56581	−	1.22341i	0.240974	−	0.0645689i	−0.136310	−	0.990666i	$-0.543524\pi$
$359$	4.56581	−	1.22341i	0.240974	−	0.0645689i	0.377285	+	0.926097i	$0.376858\pi$
$360$			3.02343i			0.159349i
$361$	9.40004	+	5.42712i	0.494739	+	0.285638i
$362$	10.2795	−	10.2795i	0.540280	−	0.540280i
$363$	−6.14076			−0.322306
$364$	−9.50778	−	0.776002i	−0.498343	−	0.0406736i
$365$	48.7894			2.55375
$366$	5.37732	−	5.37732i	0.281077	−	0.281077i
$367$	−28.5378	−	16.4763i	−1.48966	−	0.860057i	−0.489732	−	0.871873i	$-0.662905\pi$
$367$	−28.5378	−	16.4763i	−1.48966	−	0.860057i	−0.999930	+	0.0118165i	$0.996239\pi$
$368$		−	0.832559i		−	0.0434001i
$369$	−10.5517	+	2.82732i	−0.549299	+	0.147184i
$370$	12.0581	−	3.23097i	0.626872	−	0.167970i
$371$	3.45982	+	29.5251i	0.179625	+	1.53287i
$372$	−1.49701	−	1.49701i	−0.0776164	−	0.0776164i
$373$	7.69873	+	13.3346i	0.398625	+	0.690439i	0.993557	−	0.113338i	$-0.0361542\pi$
$373$	7.69873	+	13.3346i	0.398625	+	0.690439i	−0.594932	+	0.803776i	$0.702821\pi$
$374$	5.29260	−	9.16706i	0.273674	−	0.474017i
$375$	−2.50820	+	0.672071i	−0.129523	+	0.0347056i
$376$	−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	0.589280	−	0.807929i	$-0.299411\pi$
$379$	13.5428	+	3.62878i	0.695647	+	0.186398i	0.106367	+	0.994327i	$0.466078\pi$
$380$	−8.62912			−0.442664
$381$	−12.2301			−0.626566
$382$	−12.6804	−	3.39771i	−0.648788	−	0.173842i
$383$	5.62778	−	21.0032i	0.287566	−	1.07321i	−0.659378	−	0.751812i	$-0.729180\pi$
$383$	5.62778	−	21.0032i	0.287566	−	1.07321i	0.946944	−	0.321399i	$-0.104153\pi$
$384$	−0.258819	−	0.965926i	−0.0132078	−	0.0492922i
$385$	17.5135	−	2.05227i	0.892568	−	0.104593i
$386$	−6.22941	+	10.7897i	−0.317069	+	0.549179i
$387$		−	6.57238i		−	0.334093i
$388$	3.14428	+	11.7346i	0.159627	+	0.595735i
$389$	−15.8249	+	9.13651i	−0.802354	+	0.463239i	−0.844294	−	0.535881i	$-0.819980\pi$
$389$	−15.8249	+	9.13651i	−0.802354	+	0.463239i	0.0419397	+	0.999120i	$0.486646\pi$
$390$	8.18341	+	7.20186i	0.414383	+	0.364680i
$391$		−	3.99788i		−	0.202182i
$392$	−0.199461	+	6.99716i	−0.0100743	+	0.353410i
$393$	1.23250	+	2.13475i	0.0621712	+	0.107684i
$394$	20.7288	−	11.9678i	1.04430	−	0.602928i
$395$	1.34466	−	5.01834i	0.0676572	−	0.252500i
$396$	1.55872	−	1.55872i	0.0783288	−	0.0783288i
$397$	−21.7201	−	5.81988i	−1.09010	−	0.292091i	−0.331372	−	0.943500i	$-0.607512\pi$
$397$	−21.7201	−	5.81988i	−1.09010	−	0.292091i	−0.758727	+	0.651409i	$0.774178\pi$
$398$	−12.2905	+	12.2905i	−0.616066	+	0.616066i
$399$	7.01685	−	2.79002i	0.351282	−	0.139675i
$400$	−3.58634	+	2.07057i	−0.179317	+	0.103529i
$401$	−24.0004	−	24.0004i	−1.19853	−	1.19853i	−0.974608	−	0.223917i	$-0.928116\pi$
$401$	−24.0004	−	24.0004i	−1.19853	−	1.19853i	−0.223917	−	0.974608i	$-0.571884\pi$
$402$	4.06259	+	7.03661i	0.202624	+	0.350954i
$403$	−7.61780	+	0.486001i	−0.379470	+	0.0242094i
$404$	−10.9236	−	6.30672i	−0.543467	−	0.313771i
$405$	−0.782522	+	2.92041i	−0.0388838	+	0.145116i
$406$	−1.28964	−	1.01910i	−0.0640038	−	0.0505770i
$407$	−7.88226	−	4.55082i	−0.390709	−	0.225576i
$408$	−1.24283	−	4.63830i	−0.0615292	−	0.229630i
$409$	1.79460	+	1.79460i	0.0887370	+	0.0887370i	0.750082	−	0.661345i	$-0.230014\pi$
$409$	1.79460	+	1.79460i	0.0887370	+	0.0887370i	−0.661345	+	0.750082i	$0.730014\pi$
$410$	−23.3541	−	23.3541i	−1.15338	−	1.15338i
$411$	0.181127	+	0.675975i	0.00893434	+	0.0333434i
$412$	−12.3189	−	7.11234i	−0.606910	−	0.350400i
$413$	−19.3739	+	7.70338i	−0.953327	+	0.379059i
$414$	0.215482	−	0.804190i	0.0105904	−	0.0395238i
$415$	−46.6437	−	26.9298i	−2.28965	−	1.32193i
$416$	−3.23094	−	1.60031i	−0.158410	−	0.0784618i
$417$	−8.28090	−	14.3429i	−0.405518	−	0.702377i
$418$	4.44872	+	4.44872i	0.217594	+	0.217594i
$419$	30.0008	−	17.3210i	1.46564	−	0.846185i	0.466374	−	0.884588i	$-0.345560\pi$
$419$	30.0008	−	17.3210i	1.46564	−	0.846185i	0.999262	+	0.0384023i	$0.0122268\pi$
$420$	4.95957	−	6.27620i	0.242002	−	0.306247i
$421$	13.6090	−	13.6090i	0.663260	−	0.663260i	−0.292887	−	0.956147i	$-0.594616\pi$
$421$	13.6090	−	13.6090i	0.663260	−	0.663260i	0.956147	+	0.292887i	$0.0946160\pi$
$422$	−19.3418	−	5.18262i	−0.941544	−	0.252286i
$423$	−2.80135	+	2.80135i	−0.136206	+	0.136206i
$424$	−2.90804	+	10.8529i	−0.141227	+	0.527065i
$425$	−17.2213	+	9.94274i	−0.835357	+	0.482294i
$426$	−4.36211	−	7.55540i	−0.211345	−	0.366060i
$427$	−19.9833	+	2.34170i	−0.967062	+	0.113323i
$428$		−	11.8982i		−	0.575122i
$429$	−0.506036	−	7.93184i	−0.0244316	−	0.382953i
$430$	17.2089	−	9.93558i	0.829888	−	0.479136i
$431$	−6.79380	−	25.3548i	−0.327246	−	1.22130i	−0.912035	−	0.410112i	$-0.865490\pi$
$431$	−6.79380	−	25.3548i	−0.327246	−	1.22130i	0.584789	−	0.811185i	$-0.301177\pi$
$432$		−	1.00000i		−	0.0481125i
$433$	2.23696	−	3.87452i	0.107501	−	0.186198i	−0.807256	−	0.590201i	$-0.799048\pi$
$433$	2.23696	−	3.87452i	0.107501	−	0.186198i	0.914757	+	0.404004i	$0.132382\pi$
$434$	0.651915	+	5.56324i	0.0312929	+	0.267044i
$435$	0.486149	+	1.81433i	0.0233090	+	0.0869905i
$436$	−0.0602948	+	0.225023i	−0.00288760	+	0.0107767i
$437$	2.29522	+	0.615003i	0.109795	+	0.0294196i
$438$	−16.1371			−0.771060
$439$	−7.63420			−0.364361			−0.182180	−	0.983265i	$-0.558315\pi$
$439$	−7.63420			−0.364361			−0.182180	+	0.983265i	$0.558315\pi$
$440$	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	$0.171878\pi$
$444$	−3.98822	+	1.06864i	−0.189273	+	0.0507155i
$445$	−11.2048	+	19.4072i	−0.531157	+	0.919990i
$446$	−4.66878	−	8.08656i	−0.221073	−	0.382910i
$447$	−3.44321	−	3.44321i	−0.162858	−	0.162858i
$448$	−1.04721	+	2.42968i	−0.0494761	+	0.114792i
$449$	−9.38986	+	2.51601i	−0.443135	+	0.118738i	−0.473485	−	0.880802i	$-0.657004\pi$
$449$	−9.38986	+	2.51601i	−0.443135	+	0.118738i	0.0303504	+	0.999539i	$0.490338\pi$
$450$	−4.00004	+	1.07181i	−0.188564	+	0.0505255i
$451$			24.0803i			1.13390i
$452$	−3.21881	−	1.85838i	−0.151400	−	0.0874108i
$453$	−1.23352	+	1.23352i	−0.0579558	+	0.0579558i
$454$	25.6685			1.20468
$455$	−5.17380	−	28.3739i	−0.242551	−	1.33019i
$456$	2.85408			0.133654
$457$	−7.29483	+	7.29483i	−0.341238	+	0.341238i	−0.856833	−	0.515595i	$-0.827571\pi$
$457$	−7.29483	+	7.29483i	−0.341238	+	0.341238i	0.515595	+	0.856833i	$0.327571\pi$
$458$	−1.52213	−	0.878800i	−0.0711243	−	0.0410636i
$459$		−	4.80193i		−	0.224135i
$460$	2.43141	−	0.651495i	0.113365	−	0.0303761i
$461$	15.6819	−	4.20195i	0.730379	−	0.195704i	0.125581	−	0.992083i	$-0.459921\pi$
$461$	15.6819	−	4.20195i	0.730379	−	0.195704i	0.604798	+	0.796379i	$0.293254\pi$
$462$	−5.79257	+	0.678789i	−0.269495	+	0.0315801i
$463$	−4.30031	−	4.30031i	−0.199852	−	0.199852i	0.600084	−	0.799937i	$-0.295134\pi$
$463$	−4.30031	−	4.30031i	−0.199852	−	0.199852i	−0.799937	+	0.600084i	$0.795134\pi$
$464$	−0.310629	−	0.538026i	−0.0144206	−	0.0249772i
$465$	3.20045	−	5.54333i	0.148417	−	0.257066i
$466$	−2.26607	+	0.607190i	−0.104973	+	0.0281275i
$467$	13.5301	−	23.4348i	0.626097	−	1.08443i	−0.362230	−	0.932089i	$-0.617985\pi$
$467$	13.5301	−	23.4348i	0.626097	−	1.08443i	0.988328	−	0.152344i	$-0.0486820\pi$
$468$	−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
$471$	22.2725			1.02626
$472$	−7.88027			−0.362719
$473$	−13.9943	−	3.74976i	−0.643458	−	0.172414i
$474$	−0.444746	+	1.65982i	−0.0204279	+	0.0762378i
$475$	−3.05902	−	11.4164i	−0.140358	−	0.523822i
$476$	−5.02863	+	11.6671i	−0.230487	+	0.534763i
$477$	−5.61789	+	9.73048i	−0.257226	+	0.445528i
$478$			10.8725i			0.497294i
$479$	−2.93173	−	10.9414i	−0.133954	−	0.499924i	0.866046	−	0.499965i	$-0.166654\pi$
$479$	−2.93173	−	10.9414i	−0.133954	−	0.499924i	−1.00000		4.09367e-5i	$0.999987\pi$
$480$	2.61837	−	1.51172i	0.119512	−	0.0690001i
$481$	−6.60755	+	13.3403i	−0.301278	+	0.608265i
$482$			4.12278i			0.187787i
$483$	−1.76648	+	1.31591i	−0.0803777	+	0.0598759i
$484$	3.07038	+	5.31806i	0.139563	+	0.241730i
$485$	−31.8095	+	18.3652i	−1.44439	+	0.833921i
$486$	0.258819	−	0.965926i	0.0117403	−	0.0438153i
$487$	−14.8893	+	14.8893i	−0.674701	+	0.674701i	−0.958796	−	0.284095i	$-0.908307\pi$
$487$	−14.8893	+	14.8893i	−0.674701	+	0.674701i	0.284095	+	0.958796i	$0.408307\pi$
$488$	−7.34555	−	1.96823i	−0.332518	−	0.0890978i
$489$	1.80913	−	1.80913i	0.0818117	−	0.0818117i
$490$	−20.5907	+	4.89292i	−0.930191	+	0.221040i
$491$	18.2551	−	10.5396i	0.823841	−	0.475645i	−0.0278979	−	0.999611i	$-0.508881\pi$
$491$	18.2551	−	10.5396i	0.823841	−	0.475645i	0.851739	+	0.523966i	$0.175548\pi$
$492$	7.72437	+	7.72437i	0.348242	+	0.348242i
$493$	−1.49162	−	2.58356i	−0.0671791	−	0.116358i
$494$	6.79845	−	7.72502i	0.305877	−	0.347565i
$495$	5.77185	+	3.33238i	0.259425	+	0.149779i
$496$	−0.547944	+	2.04496i	−0.0246034	+	0.0918212i
$497$	−3.33859	+	22.8394i	−0.149756	+	1.02449i
$498$	15.4274	+	8.90702i	0.691319	+	0.399133i
$499$	4.08327	+	15.2390i	0.182792	+	0.682190i	0.995092	+	0.0989503i	$0.0315485\pi$
$499$	4.08327	+	15.2390i	0.182792	+	0.682190i	−0.812300	+	0.583240i	$0.801785\pi$
$500$	1.83613	+	1.83613i	0.0821143	+	0.0821143i
$501$	−7.66779	−	7.66779i	−0.342571	−	0.342571i
$502$	6.67073	+	24.8955i	0.297729	+	1.11114i
$503$	12.4612	+	7.19450i	0.555619	+	0.320787i	0.751385	−	0.659864i	$-0.229386\pi$
$503$	12.4612	+	7.19450i	0.555619	+	0.320787i	−0.195766	+	0.980651i	$0.562719\pi$
$504$	−1.64038	+	2.07585i	−0.0730682	+	0.0924659i
$505$	9.87029	−	36.8364i	0.439222	−	1.63920i
$506$	−1.58939	−	0.917633i	−0.0706568	−	0.0407937i
$507$	−12.8946	+	1.65203i	−0.572669	+	0.0733690i
$508$	6.11504	+	10.5916i	0.271311	+	0.469925i
$509$	7.15503	+	7.15503i	0.317141	+	0.317141i	0.847668	−	0.530527i	$-0.178006\pi$
$509$	7.15503	+	7.15503i	0.317141	+	0.317141i	−0.530527	+	0.847668i	$0.678006\pi$
$510$	12.5732	−	7.25915i	0.556751	−	0.321441i
$511$	33.4982	+	26.4709i	1.48187	+	1.17100i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	2.75683	+	0.738690i	0.121717	+	0.0326140i
$514$	−0.519187	+	0.519187i	−0.0229004	+	0.0229004i
$515$	11.1311	−	41.5419i	0.490496	−	1.83055i
$516$	−5.69185	+	3.28619i	−0.250570	+	0.144667i
$517$	4.36653	+	7.56306i	0.192040	+	0.332623i
$518$	10.0319	+	4.32384i	0.440778	+	0.189979i
$519$		−	12.9730i		−	0.569450i
$520$	2.14529	−	10.6880i	0.0940771	−	0.468698i
$521$	−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	$0.348589\pi$
$522$	−0.160794	−	0.600090i	−0.00703774	−	0.0262652i
$523$			0.769739i			0.0336583i	0.999858	+	0.0168292i	$0.00535714\pi$
$523$			0.769739i			0.0336583i	−0.999858	+	0.0168292i	$0.994643\pi$
$524$	1.23250	−	2.13475i	0.0538418	−	0.0932568i
$525$	10.0617	+	4.33666i	0.439127	+	0.189267i
$526$	2.75415	+	10.2786i	0.120087	+	0.448170i
$527$	−2.63119	+	9.81972i	−0.114616	+	0.427754i
$528$	−2.12926	−	0.570532i	−0.0926640	−	0.0248292i
$529$	22.3068			0.969863
$530$	−33.9707			−1.47559
$531$	−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
$535$	34.7477	−	9.31062i	1.50228	−	0.402533i
$536$	4.06259	−	7.03661i	0.175477	−	0.303935i
$537$	−2.12453	−	3.67979i	−0.0916801	−	0.158795i
$538$	−21.6632	−	21.6632i	−0.933968	−	0.933968i
$539$	13.1380	+	8.09293i	0.565894	+	0.348587i
$540$	2.92041	−	0.782522i	0.125675	−	0.0336744i
$541$	29.4666	−	7.89555i	1.26687	−	0.339456i	0.438038	−	0.898956i	$-0.355674\pi$
$541$	29.4666	−	7.89555i	1.26687	−	0.339456i	0.828830	+	0.559500i	$0.189007\pi$
$542$			9.25472i			0.397524i
$543$	−12.5898	−	7.26873i	−0.540280	−	0.311931i
$544$	−3.39547	+	3.39547i	−0.145580	+	0.145580i
$545$	−0.704343			−0.0301707
$546$	1.71123	+	9.38465i	0.0732340	+	0.401626i
$547$	−22.4927			−0.961719			−0.480860	−	0.876798i	$-0.659675\pi$
$547$	−22.4927			−0.961719			−0.480860	+	0.876798i	$0.659675\pi$
$548$	0.494848	−	0.494848i	0.0211389	−	0.0211389i
$549$	−6.58584	−	3.80234i	−0.281077	−	0.162280i
$550$			9.12861i			0.389245i
$551$	1.71270	−	0.458918i	0.0729636	−	0.0195505i
$552$	−0.804190	+	0.215482i	−0.0342286	+	0.00917152i
$553$	3.64595	−	2.71598i	0.155041	−	0.115495i
$554$	−12.7086	−	12.7086i	−0.539935	−	0.539935i
$555$	−6.24175	−	10.8110i	−0.264947	−	0.458902i
$556$	−8.28090	+	14.3429i	−0.351188	+	0.608276i
$557$	−18.2279	+	4.88416i	−0.772342	+	0.206949i	−0.623406	−	0.781898i	$-0.714252\pi$
$557$	−18.2279	+	4.88416i	−0.772342	+	0.206949i	−0.148936	+	0.988847i	$0.547585\pi$
$558$	−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
$562$	−24.2892			−1.02458
$563$	9.20471			0.387932			0.193966	−	0.981008i	$-0.437865\pi$
$563$	9.20471			0.387932			0.193966	+	0.981008i	$0.437865\pi$
$564$	3.82672	+	1.02537i	0.161134	+	0.0431757i
$565$	2.90845	−	10.8545i	0.122359	−	0.456651i
$566$	6.02740	+	22.4946i	0.253351	+	0.945517i
$567$	−2.12175	+	1.58056i	−0.0891052	+	0.0663773i
$568$	−4.36211	+	7.55540i	−0.183030	+	0.317017i
$569$			22.3769i			0.938087i	0.883175	+	0.469043i	$0.155401\pi$
$569$			22.3769i			0.938087i	−0.883175	+	0.469043i	$0.844599\pi$
$570$	2.23338	+	8.33509i	0.0935460	+	0.349118i
$571$	12.4979	−	7.21569i	0.523023	−	0.301967i	−0.215148	−	0.976581i	$-0.569023\pi$
$571$	12.4979	−	7.21569i	0.523023	−	0.301967i	0.738170	+	0.674614i	$0.235690\pi$
$572$	−6.61615	+	4.40416i	−0.276635	+	0.184147i
$573$			13.1278i			0.548420i
$574$	−3.36379	−	28.7055i	−0.140402	−	1.19815i
$575$	1.72387	+	2.98584i	0.0718905	+	0.124518i
$576$	−0.866025	+	0.500000i	−0.0360844	+	0.0208333i
$577$	5.40001	−	20.1531i	0.224805	−	0.838985i	−0.757677	−	0.652630i	$-0.773666\pi$
$577$	5.40001	−	20.1531i	0.224805	−	0.838985i	0.982482	−	0.186355i	$-0.0596675\pi$
$578$	−4.28400	+	4.28400i	−0.178191	+	0.178191i
$579$	12.0343	+	3.22458i	0.500128	+	0.134009i
$580$	1.32818	−	1.32818i	0.0551498	−	0.0551498i
$581$	−17.4142	−	43.7964i	−0.722462	−	1.81698i
$582$	10.5210	−	6.07429i	0.436108	−	0.251787i
$583$	17.5135	+	17.5135i	0.725334	+	0.725334i
$584$	8.06855	+	13.9751i	0.333879	+	0.578295i
$585$	4.83844	−	9.76854i	0.200045	−	0.403880i
$586$	−3.30775	−	1.90973i	−0.136642	−	0.0788902i
$587$	2.08827	−	7.79352i	0.0861920	−	0.321673i	−0.909345	−	0.416042i	$-0.863417\pi$
$587$	2.08827	−	7.79352i	0.0861920	−	0.321673i	0.995537	+	0.0943694i	$0.0300835\pi$
$588$	6.81036	−	1.61833i	0.280854	−	0.0667389i
$589$	−5.23283	−	3.02118i	−0.215615	−	0.124485i
$590$	−6.16648	−	23.0136i	−0.253870	−	0.947456i
$591$	−16.9250	−	16.9250i	−0.696201	−	0.696201i
$592$	2.91958	+	2.91958i	0.119994	+	0.119994i
$593$	5.19777	+	19.3983i	0.213447	+	0.796594i	0.986708	+	0.162506i	$0.0519577\pi$
$593$	5.19777	+	19.3983i	0.213447	+	0.796594i	−0.773261	+	0.634088i	$0.781376\pi$
$594$	−1.90904	−	1.10218i	−0.0783288	−	0.0452232i
$595$	−38.0079	−	5.55587i	−1.55817	−	0.227769i
$596$	−1.26030	+	4.70351i	−0.0516240	+	0.192663i
$597$	15.0527	+	8.69068i	0.616066	+	0.355686i
$598$	−1.33235	+	2.68995i	−0.0544840	+	0.110000i
$599$	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	$0.764057\pi$
$600$	2.92823	+	2.92823i	0.119545	+	0.119545i
$601$	21.1744	−	12.2251i	0.863723	−	0.498671i	−0.00153438	−	0.999999i	$-0.500488\pi$
$601$	21.1744	−	12.2251i	0.863723	−	0.498671i	0.865257	+	0.501328i	$0.167155\pi$
$602$	17.2060	+	2.51512i	0.701266	+	0.102509i
$603$	5.74537	−	5.74537i	0.233970	−	0.233970i
$604$	1.68502	+	0.451500i	0.0685625	+	0.0183713i
$605$	−13.1283	+	13.1283i	−0.533740	+	0.533740i
$606$	−3.26460	+	12.1836i	−0.132615	+	0.494927i
$607$	12.5435	−	7.24201i	0.509126	−	0.293944i	−0.223348	−	0.974739i	$-0.571699\pi$
$607$	12.5435	−	7.24201i	0.509126	−	0.293944i	0.732474	+	0.680795i	$0.238365\pi$
$608$	−1.42704	−	2.47170i	−0.0578741	−	0.100241i
$609$	−0.650589	+	1.50946i	−0.0263632	+	0.0611664i
$610$		−	22.9922i		−	0.930928i
$611$	11.8906	−	7.91519i	0.481043	−	0.320214i
$612$	−4.15859	+	2.40096i	−0.168101	+	0.0970532i
$613$	4.45618	+	16.6307i	0.179983	+	0.671707i	0.995649	+	0.0931834i	$0.0297043\pi$
$613$	4.45618	+	16.6307i	0.179983	+	0.671707i	−0.815666	+	0.578524i	$0.803629\pi$
$614$		−	7.10450i		−	0.286714i
$615$	−16.5139	+	28.6028i	−0.665903	+	1.15338i
$616$	3.48413	+	4.67712i	0.140380	+	0.188447i
$617$	4.78436	+	17.8555i	0.192611	+	0.718835i	0.992872	+	0.119183i	$0.0380275\pi$
$617$	4.78436	+	17.8555i	0.192611	+	0.718835i	−0.800261	+	0.599652i	$0.795306\pi$
$618$	−3.68162	+	13.7400i	−0.148096	+	0.552703i
$619$	45.5656	+	12.2093i	1.83144	+	0.490732i	0.998076	−	0.0619980i	$-0.0197472\pi$
$619$	45.5656	+	12.2093i	1.83144	+	0.490732i	0.833360	+	0.552730i	$0.186414\pi$
$620$	−6.40089			−0.257066
$621$	−0.832559			−0.0334094
$622$	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
$626$	−10.4145	+	2.79055i	−0.416246	+	0.111533i
$627$	3.14572	−	5.44855i	0.125628	−	0.217594i
$628$	−11.1362	−	19.2885i	−0.444384	−	0.769696i
$629$	14.0196	+	14.0196i	0.558999	+	0.558999i
$630$	−7.34598	−	3.16617i	−0.292671	−	0.126143i
$631$	−41.8739	+	11.2201i	−1.66697	+	0.446664i	−0.964292	−	0.264842i	$-0.914680\pi$
$631$	−41.8739	+	11.2201i	−1.66697	+	0.446664i	−0.702680	+	0.711506i	$0.748013\pi$
$632$	1.65982	−	0.444746i	0.0660239	−	0.0176910i
$633$			20.0241i			0.795886i
$634$	−18.4093	−	10.6286i	−0.731125	−	0.422115i
$635$	−26.1466	+	26.1466i	−1.03760	+	1.03760i
$636$	11.2358			0.445528
$637$	11.8421	−	22.2882i	0.469201	−	0.883092i
$638$	−1.36948			−0.0542183
$639$	−6.16895	+	6.16895i	−0.244040	+	0.244040i
$640$	−2.61837	−	1.51172i	−0.103500	−	0.0597558i
$641$		−	1.77563i		−	0.0701334i	−0.999385	−	0.0350667i	$-0.988836\pi$
$641$		−	1.77563i		−	0.0701334i	0.999385	−	0.0350667i	$-0.0111644\pi$
$642$	−11.4928	+	3.07949i	−0.453585	+	0.121538i
$643$	42.7011	−	11.4417i	1.68397	−	0.451218i	0.715145	−	0.698976i	$-0.246361\pi$
$643$	42.7011	−	11.4417i	1.68397	−	0.451218i	0.968822	+	0.247759i	$0.0796940\pi$
$644$	2.02285	+	0.871865i	0.0797115	+	0.0343563i
$645$	−14.0510	−	14.0510i	−0.553259	−	0.553259i
$646$	−6.85254	−	11.8689i	−0.269609	−	0.466977i
$647$	−8.51337	+	14.7456i	−0.334695	+	0.579709i	−0.983426	−	0.181309i	$-0.941967\pi$
$647$	−8.51337	+	14.7456i	−0.334695	+	0.579709i	0.648731	+	0.761018i	$0.275300\pi$
$648$	−0.965926	+	0.258819i	−0.0379452	+	0.0101674i
$649$	−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
$653$	23.6802			0.926679			0.463339	−	0.886181i	$-0.346651\pi$
$653$	23.6802			0.926679			0.463339	+	0.886181i	$0.346651\pi$
$654$	0.232961			0.00910950
$655$	7.19879	+	1.92891i	0.281280	+	0.0753688i
$656$	2.82732	−	10.5517i	0.110388	−	0.411974i
$657$	4.17659	+	15.5872i	0.162944	+	0.608116i
$658$	−6.26172	−	8.40577i	−0.244107	−	0.327691i
$659$	5.15795	−	8.93383i	0.200925	−	0.348013i	−0.747902	−	0.663810i	$-0.768939\pi$
$659$	5.15795	−	8.93383i	0.200925	−	0.348013i	0.948827	+	0.315797i	$0.102272\pi$
$660$		−	6.66476i		−	0.259425i
$661$	−11.6035	−	43.3048i	−0.451324	−	1.68436i	−0.698677	−	0.715438i	$-0.746227\pi$
$661$	−11.6035	−	43.3048i	−0.451324	−	1.68436i	0.247353	−	0.968925i	$-0.420439\pi$
$662$	−21.1376	+	12.2038i	−0.821537	+	0.474314i
$663$	−3.40722	+	16.9750i	−0.132326	+	0.659255i
$664$		−	17.8140i		−	0.691319i
$665$	9.03651	−	20.9660i	0.350421	−	0.813027i
$666$	2.06446	+	3.57574i	0.0799961	+	0.138557i
$667$	−0.447938	+	0.258617i	−0.0173442	+	0.0100137i
$668$	−2.80660	+	10.4744i	−0.108591	+	0.405266i
$669$	−6.60265	+	6.60265i	−0.255273	+	0.255273i
$670$	23.7289	+	6.35813i	0.916726	+	0.245636i
$671$	−11.8536	+	11.8536i	−0.457603	+	0.457603i
$672$	2.61793	+	0.382681i	0.100989	+	0.0147622i
$673$	−14.3604	+	8.29101i	−0.553555	+	0.319595i	−0.750554	−	0.660809i	$-0.770213\pi$
$673$	−14.3604	+	8.29101i	−0.553555	+	0.319595i	0.197000	+	0.980404i	$0.436880\pi$
$674$	19.9526	+	19.9526i	0.768547	+	0.768547i
$675$	2.07057	+	3.58634i	0.0796964	+	0.138038i
$676$	7.87800	+	10.3410i	0.303000	+	0.397732i
$677$	−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
$679$	−31.8041	−	4.64902i	−1.22053	−	0.178413i
$680$	−12.5732	−	7.25915i	−0.482161	−	0.278376i
$681$	−6.64348	−	24.7938i	−0.254579	−	0.950101i
$682$	3.29996	+	3.29996i	0.126362	+	0.126362i
$683$	25.5262	+	25.5262i	0.976732	+	0.976732i	0.999735	−	0.0230034i	$-0.00732287\pi$
$683$	25.5262	+	25.5262i	0.976732	+	0.976732i	−0.0230034	+	0.999735i	$0.507323\pi$
$684$	−0.738690	−	2.75683i	−0.0282445	−	0.105410i
$685$	1.83239	+	1.05793i	0.0700120	+	0.0404215i
$686$	−16.7920	−	7.81213i	−0.641121	−	0.298268i
$687$	−0.454900	+	1.69771i	−0.0173555	+	0.0647717i
$688$	5.69185	+	3.28619i	0.217000	+	0.125285i
$689$	26.7638	−	30.4115i	1.01962	−	1.15858i
$690$	−1.25859	−	2.17995i	−0.0479138	−	0.0829891i
$691$	−15.5625	−	15.5625i	−0.592026	−	0.592026i	0.346153	−	0.938178i	$-0.387488\pi$
$691$	−15.5625	−	15.5625i	−0.592026	−	0.592026i	−0.938178	+	0.346153i	$0.887488\pi$
$692$	−11.2349	+	6.48648i	−0.427087	+	0.246579i
$693$	2.15489	+	5.41951i	0.0818574	+	0.205870i
$694$	−1.39402	+	1.39402i	−0.0529162	+	0.0529162i
$695$	−48.3673	−	12.9600i	−1.83468	−	0.491600i
$696$	−0.439296	+	0.439296i	−0.0166515	+	0.0166515i
$697$	13.5766	−	50.6684i	0.514249	−	1.91920i
$698$	23.5431	−	13.5926i	0.891119	−	0.514488i
$699$	1.17300	+	2.03170i	0.0443670	+	0.0768459i
$700$	−1.27518	−	10.8820i	−0.0481972	−	0.411300i
$701$			40.1037i			1.51470i	0.653011	+	0.757348i	$0.273505\pi$
$701$			40.1037i			1.51470i	−0.653011	+	0.757348i	$0.726495\pi$
$702$	−1.60031	+	3.23094i	−0.0603999	+	0.121944i
$703$	−10.2055	+	5.89212i	−0.384906	+	0.222226i
$704$	0.570532	+	2.12926i	0.0215027	+	0.0802493i
$705$			11.9780i			0.451116i
$706$	−4.70641	+	8.15175i	−0.177128	+	0.306795i
$707$	26.7626	−	19.9363i	1.00651	−	0.749781i
$708$	2.03956	+	7.61175i	0.0766515	+	0.286067i
$709$	12.2438	−	45.6946i	0.459827	−	1.71610i	−0.213668	−	0.976906i	$-0.568541\pi$
$709$	12.2438	−	45.6946i	0.459827	−	1.71610i	0.673495	−	0.739192i	$-0.264792\pi$
$710$	−25.4783	−	6.82689i	−0.956184	−	0.256209i
$711$	1.71837			0.0644438
$712$	−7.41194			−0.277774
$713$	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
$717$	10.5020	−	2.81400i	0.392204	−	0.105091i
$718$	−2.36344	+	4.09359i	−0.0882027	+	0.152772i
$719$	24.6574	+	42.7078i	0.919564	+	1.59273i	0.800078	+	0.599896i	$0.204791\pi$
$719$	24.6574	+	42.7078i	0.919564	+	1.59273i	0.119486	+	0.992836i	$0.461875\pi$
$720$	−2.13789	−	2.13789i	−0.0796745	−	0.0796745i
$721$	30.1812	−	22.4829i	1.12401	−	0.837309i
$722$	−10.4844	+	2.80928i	−0.390188	+	0.104551i
$723$	3.98230	−	1.06705i	0.148103	−	0.0396841i
$724$			14.5375i			0.540280i
$725$	2.22804	+	1.28636i	0.0827475	+	0.0477743i
$726$	4.34217	−	4.34217i	0.161153	−	0.161153i
$727$	−18.2225			−0.675836			−0.337918	−	0.941175i	$-0.609723\pi$
$727$	−18.2225			−0.675836			−0.337918	+	0.941175i	$0.609723\pi$
$728$	7.27173	−	6.17430i	0.269508	−	0.228835i
$729$	−1.00000			−0.0370370
$730$	−34.4993	+	34.4993i	−1.27688	+	1.27688i
$731$	27.3318	+	15.7800i	1.01090	+	0.583646i
$732$			7.60468i			0.281077i
$733$	−44.9025	+	12.0316i	−1.65851	+	0.444397i	−0.961978	−	0.273128i	$-0.911942\pi$
$733$	−44.9025	+	12.0316i	−1.65851	+	0.444397i	−0.696533	+	0.717524i	$0.745275\pi$
$734$	31.8298	−	8.52877i	1.17486	−	0.314803i
$735$	10.0555	+	18.6227i	0.370901	+	0.686908i
$736$	0.588708	+	0.588708i	0.0217001	+	0.0217001i
$737$	−8.95544	−	15.5113i	−0.329878	−	0.571365i
$738$	5.46195	−	9.46038i	0.201057	−	0.348242i
$739$	−28.1616	+	7.54587i	−1.03594	+	0.277579i	−0.736430	−	0.676514i	$-0.763490\pi$
$739$	−28.1616	+	7.54587i	−1.03594	+	0.277579i	−0.299510	+	0.954093i	$0.596823\pi$
$740$	−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	0.323922	−	0.946084i	$-0.394999\pi$
$743$	3.58181	+	0.959744i	0.131404	+	0.0352096i	−0.192518	+	0.981294i	$0.561665\pi$
$744$	2.11709			0.0776164
$745$	−14.7224			−0.539387
$746$	−14.8728	−	3.98515i	−0.544532	−	0.145907i
$747$	4.61061	−	17.2070i	0.168693	−	0.629573i
$748$	2.73965	+	10.2245i	0.100172	+	0.373846i
$749$	28.9089	+	12.4600i	1.05631	+	0.455277i
$750$	1.29834	−	2.24879i	0.0474087	−	0.0821143i
$751$			42.4165i			1.54780i	0.633308	+	0.773900i	$0.281697\pi$
$751$			42.4165i			1.54780i	−0.633308	+	0.773900i	$0.718303\pi$
$752$	−1.02537	−	3.82672i	−0.0373912	−	0.139546i
$753$	22.3207	−	12.8869i	0.813412	−	0.469623i
$754$	0.142616	+	2.23544i	0.00519378	+	0.0814097i
$755$			5.27426i			0.191950i
$756$	2.42968	+	1.04721i	0.0883666	+	0.0380867i
$757$	−13.6306	−	23.6089i	−0.495412	−	0.858080i	0.504574	−	0.863369i	$-0.331650\pi$
$757$	−13.6306	−	23.6089i	−0.495412	−	0.858080i	−0.999986	+	0.00528912i	$0.998316\pi$
$758$	−12.1421	+	7.01027i	−0.441023	+	0.254624i
$759$	−0.475002	+	1.77273i	−0.0172415	+	0.0643460i
$760$	6.10171	−	6.10171i	0.221332	−	0.221332i
$761$	−11.5941	−	3.10663i	−0.420286	−	0.112615i	0.0424769	−	0.999097i	$-0.486475\pi$
$761$	−11.5941	−	3.10663i	−0.420286	−	0.112615i	−0.462763	+	0.886482i	$0.653142\pi$
$762$	8.64797	−	8.64797i	0.313283	−	0.313283i
$763$	−0.483593	−	0.382144i	−0.0175073	−	0.0138345i
$764$	11.3690	−	6.56388i	0.411315	−	0.237473i
$765$	−10.2660	−	10.2660i	−0.371168	−	0.371168i
$766$	10.8720	+	18.8309i	0.392823	+	0.680389i
$767$	25.4607	+	12.6109i	0.919332	+	0.455353i
$768$	0.866025	+	0.500000i	0.0312500	+	0.0180422i
$769$	−13.5023	+	50.3911i	−0.486904	+	1.81715i	0.0844245	+	0.996430i	$0.473095\pi$
$769$	−13.5023	+	50.3911i	−0.486904	+	1.81715i	−0.571329	+	0.820721i	$0.693572\pi$
$770$	−10.9327	+	13.8351i	−0.393988	+	0.498581i
$771$	0.635872	+	0.367121i	0.0229004	+	0.0132215i
$772$	−3.22458	−	12.0343i	−0.116055	−	0.433124i
$773$	−1.54136	−	1.54136i	−0.0554390	−	0.0554390i	0.678844	−	0.734283i	$-0.262481\pi$
$773$	−1.54136	−	1.54136i	−0.0554390	−	0.0554390i	−0.734283	+	0.678844i	$0.762481\pi$
$774$	4.64738	+	4.64738i	0.167047	+	0.167047i
$775$	−2.26912	−	8.46846i	−0.0815091	−	0.304196i
$776$	−10.5210	−	6.07429i	−0.377681	−	0.218054i
$777$	1.58006	−	10.8092i	0.0566842	−	0.387778i
$778$	4.72940	−	17.6504i	0.169557	−	0.632797i
$779$	27.0007	+	15.5889i	0.967400	+	0.558529i
$780$	−10.8790	+	0.694061i	−0.389532	+	0.0248514i
$781$	9.61569	+	16.6549i	0.344077	+	0.595958i
$782$	2.82693	+	2.82693i	0.101091	+	0.101091i
$783$	−0.538026	+	0.310629i	−0.0192275	+	0.0111010i
$784$	−4.80670	−	5.08878i	−0.171668	−	0.181742i
$785$	47.6161	−	47.6161i	1.69949	−	1.69949i
$786$	−2.38100	−	0.637987i	−0.0849274	−	0.0227562i
$787$	29.1293	−	29.1293i	1.03835	−	1.03835i	0.0391132	−	0.999235i	$-0.487547\pi$
$787$	29.1293	−	29.1293i	1.03835	−	1.03835i	0.999235	−	0.0391132i	$-0.0124533\pi$
$788$	−6.19498	+	23.1200i	−0.220687	+	0.823615i
$789$	9.21558	−	5.32062i	0.328083	−	0.189419i
$790$	2.59768	+	4.49932i	0.0924214	+	0.160079i
$791$	7.88604	−	5.87456i	0.280395	−	0.208875i
$792$			2.20437i			0.0783288i
$793$	20.5833	+	18.1144i	0.730934	+	0.643263i
$794$	19.4737	−	11.2431i	0.691095	−	0.399004i
$795$	8.79225	+	32.8131i	0.311829	+	1.16376i
$796$		−	17.3814i		−	0.616066i
$797$	−13.3815	+	23.1774i	−0.473997	+	0.820987i	−0.999557	−	0.0297695i	$-0.990523\pi$
$797$	−13.3815	+	23.1774i	−0.473997	+	0.820987i	0.525560	+	0.850757i	$0.323856\pi$
$798$	−2.98882	+	6.93450i	−0.105803	+	0.245479i
$799$	−4.92373	−	18.3756i	−0.174189	−	0.650082i
$800$	1.07181	−	4.00004i	0.0378941	−	0.141423i
$801$	−7.15939	−	1.91835i	−0.252965	−	0.0677816i
$802$	33.9418			1.19853
$803$	35.5721			1.25531
$804$	−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
$808$	12.1836	−	3.26460i	0.428619	−	0.114848i
$809$	17.0525	−	29.5357i	0.599533	−	1.03842i	−0.393357	−	0.919386i	$-0.628686\pi$
$809$	17.0525	−	29.5357i	0.599533	−	1.03842i	0.992890	−	0.119036i	$-0.0379803\pi$
$810$	−1.51172	−	2.61837i	−0.0531163	−	0.0920001i
$811$	27.4078	+	27.4078i	0.962416	+	0.962416i	0.999319	−	0.0369025i	$-0.0117491\pi$
$811$	27.4078	+	27.4078i	0.962416	+	0.962416i	−0.0369025	+	0.999319i	$0.511749\pi$
$812$	1.63253	−	0.191304i	0.0572904	−	0.00671344i
$813$	8.93937	−	2.39530i	0.313518	−	0.0840068i
$814$	8.79151	−	2.35568i	0.308142	−	0.0825665i
$815$		−	7.73544i		−	0.270961i
$816$	4.15859	+	2.40096i	0.145580	+	0.0840505i
$817$	−13.2640	+	13.2640i	−0.464048	+	0.464048i
$818$	−2.53794			−0.0887370
$819$	8.62198	−	4.08185i	0.301276	−	0.142631i
$820$	33.0277			1.15338
$821$	24.9866	−	24.9866i	0.872039	−	0.872039i	−0.120655	−	0.992694i	$-0.538500\pi$
$821$	24.9866	−	24.9866i	0.872039	−	0.872039i	0.992694	+	0.120655i	$0.0384996\pi$
$822$	−0.606063	−	0.349911i	−0.0211389	−	0.0122045i
$823$			41.0826i			1.43205i	0.698075	+	0.716025i	$0.254040\pi$
$823$			41.0826i			1.43205i	−0.698075	+	0.716025i	$0.745960\pi$
$824$	13.7400	−	3.68162i	0.478655	−	0.128255i
$825$	8.81756	−	2.36266i	0.306988	−	0.0822572i
$826$	8.25230	−	19.1465i	0.287134	−	0.666193i
$827$	9.78086	+	9.78086i	0.340114	+	0.340114i	0.856410	−	0.516296i	$-0.172690\pi$
$827$	9.78086	+	9.78086i	0.340114	+	0.340114i	−0.516296	+	0.856410i	$0.672690\pi$
$828$	0.416279	+	0.721017i	0.0144667	+	0.0250571i
$829$	−5.94322	+	10.2940i	−0.206417	+	0.357524i	−0.950583	−	0.310470i	$-0.899514\pi$
$829$	−5.94322	+	10.2940i	−0.206417	+	0.357524i	0.744167	+	0.667994i	$0.232847\pi$
$830$	52.0243	−	13.9399i	1.80579	−	0.483860i
$831$	−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
$835$	−32.7858			−1.13460
$836$	−6.29144			−0.217594
$837$	2.04496	+	0.547944i	0.0706840	+	0.0189397i
$838$	−8.96600	+	33.4616i	−0.309725	+	1.15591i
$839$	4.10667	+	15.3263i	0.141778	+	0.529122i	0.999878	+	0.0156394i	$0.00497837\pi$
$839$	4.10667	+	15.3263i	0.141778	+	0.529122i	−0.858100	+	0.513483i	$0.828355\pi$
$840$	0.931003	+	7.94489i	0.0321226	+	0.274125i
$841$	14.3070	−	24.7805i	0.493345	−	0.854499i
$842$			19.2460i			0.663260i
$843$	6.28650	+	23.4615i	0.216518	+	0.808058i
$844$	17.3414	−	10.0120i	0.596915	−	0.344629i
$845$	−24.0354	+	31.0991i	−0.826843	+	1.06984i
$846$		−	3.96171i		−	0.136206i
$847$	−16.1365	+	1.89092i	−0.554457	+	0.0649727i
$848$	−5.61789	−	9.73048i	−0.192919	−	0.334146i
$849$	20.1681	−	11.6440i	0.692167	−	0.399623i
$850$	5.14674	−	19.2079i	0.176532	−	0.658825i
$851$	2.43072	−	2.43072i	0.0833241	−	0.0833241i
$852$	8.42695	+	2.25799i	0.288703	+	0.0773576i
$853$	23.9541	−	23.9541i	0.820171	−	0.820171i	−0.165961	−	0.986132i	$-0.553073\pi$
$853$	23.9541	−	23.9541i	0.820171	−	0.820171i	0.986132	+	0.165961i	$0.0530726\pi$
$854$	12.4745	−	15.7862i	0.426870	−	0.540192i
$855$	7.47303	−	4.31456i	0.255572	−	0.147555i
$856$	8.41332	+	8.41332i	0.287561	+	0.287561i
$857$	6.80356	+	11.7841i	0.232405	+	0.402537i	0.958515	−	0.285041i	$-0.0920072\pi$
$857$	6.80356	+	11.7841i	0.232405	+	0.402537i	−0.726110	+	0.687578i	$0.758674\pi$
$858$	5.96648	+	5.25083i	0.203692	+	0.179260i
$859$	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
$861$	−26.8568	+	10.6787i	−0.915277	+	0.363929i
$862$	22.7325	+	13.1246i	0.774272	+	0.447026i
$863$	0.302475	+	1.12885i	0.0102964	+	0.0384265i	0.970883	−	0.239555i	$-0.0770014\pi$
$863$	0.302475	+	1.12885i	0.0102964	+	0.0384265i	−0.960587	+	0.277981i	$0.910335\pi$
$864$	0.707107	+	0.707107i	0.0240563	+	0.0240563i
$865$	−27.7348	−	27.7348i	−0.943010	−	0.943010i
$866$	1.15793	+	4.32147i	0.0393482	+	0.146849i
$867$	5.24680	+	3.02924i	0.178191	+	0.102878i
$868$	−4.39478	−	3.47283i	−0.149168	−	0.117876i
$869$	0.980384	−	3.65884i	0.0332572	−	0.124118i
$870$	−1.62668	−	0.939167i	−0.0551498	−	0.0318407i
$871$	−24.3868	+	16.2335i	−0.826315	+	0.550051i
$872$	−0.116481	−	0.201750i	−0.00394453	−	0.00683213i
$873$	−8.59034	−	8.59034i	−0.290739	−	0.290739i
$874$	−2.05784	+	1.18809i	−0.0696074	+	0.0401879i
$875$	−6.38403	+	2.53840i	−0.215820	+	0.0858135i
$876$	11.4106	−	11.4106i	0.385530	−	0.385530i
$877$	−5.98767	−	1.60439i	−0.202189	−	0.0541765i	0.156303	−	0.987709i	$-0.450042\pi$
$877$	−5.98767	−	1.60439i	−0.202189	−	0.0541765i	−0.358492	+	0.933533i	$0.616709\pi$
$878$	5.39820	−	5.39820i	0.182180	−	0.182180i
$879$	−0.988549	+	3.68932i	−0.0333429	+	0.124438i
$880$	−5.77185	+	3.33238i	−0.194569	+	0.112334i
$881$	−2.51876	−	4.36262i	−0.0848592	−	0.146980i	0.820472	−	0.571687i	$-0.193711\pi$
$881$	−2.51876	−	4.36262i	−0.0848592	−	0.146980i	−0.905331	+	0.424706i	$0.860377\pi$
$882$	−3.32584	−	6.15945i	−0.111987	−	0.207399i
$883$		−	0.666737i		−	0.0224375i	−0.999937	−	0.0112187i	$-0.996429\pi$
$883$		−	0.666737i		−	0.0224375i	0.999937	−	0.0112187i	$-0.00357111\pi$
$884$	16.4044	−	5.53677i	0.551740	−	0.186222i
$885$	−20.6334	+	11.9127i	−0.693586	+	0.400442i
$886$	−0.178374	−	0.665702i	−0.00599260	−	0.0223647i
$887$		−	25.7231i		−	0.863697i	−0.901946	−	0.431848i	$-0.857862\pi$
$887$		−	25.7231i		−	0.863697i	0.901946	−	0.431848i	$-0.142138\pi$
$888$	2.06446	−	3.57574i	0.0692786	−	0.119994i
$889$	−32.1379	+	3.76600i	−1.07787	+	0.126307i
$890$	−5.80001	−	21.6459i	−0.194417	−	0.725573i
$891$	−0.570532	+	2.12926i	−0.0191136	+	0.0713328i
$892$	9.01938	+	2.41674i	0.301991	+	0.0809183i
$893$	11.3070			0.378375
$894$	4.86943			0.162858
$895$	−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
$899$	1.27045	−	0.340415i	0.0423718	−	0.0113535i
$900$	2.07057	−	3.58634i	0.0690191	−	0.119545i
$901$	−26.9767	−	46.7250i	−0.898724	−	1.55664i
$902$	−17.0274	−	17.0274i	−0.566949	−	0.566949i
$903$	−2.02383	−	17.2707i	−0.0673488	−	0.574734i
$904$	3.59011	−	0.961968i	0.119405	−	0.0319946i
$905$	−42.4554	+	11.3759i	−1.41126	+	0.378147i
$906$		−	1.74446i		−	0.0579558i
$907$	51.5326	+	29.7524i	1.71111	+	0.987911i	0.933067	+	0.359702i	$0.117122\pi$
$907$	51.5326	+	29.7524i	1.71111	+	0.987911i	0.778045	+	0.628209i	$0.216212\pi$
$908$	−18.1503	+	18.1503i	−0.602340	+	0.602340i
$909$	12.6134			0.418361
$910$	23.7218	+	16.4049i	0.786369	+	0.543818i
$911$	−21.2475			−0.703960			−0.351980	−	0.936008i	$-0.614491\pi$
$911$	−21.2475			−0.703960			−0.351980	+	0.936008i	$0.614491\pi$
$912$	−2.01814	+	2.01814i	−0.0668272	+	0.0668272i
$913$	−34.0077	−	19.6343i	−1.12549	−	0.649802i
$914$		−	10.3165i		−	0.341238i
$915$	−22.2088	+	5.95083i	−0.734200	+	0.196728i
$916$	1.69771	−	0.454900i	0.0560939	−	0.0150303i
$917$	3.89607	+	5.23010i	0.128659	+	0.172713i
$918$	3.39547	+	3.39547i	0.112067	+	0.112067i
$919$	−7.84443	−	13.5870i	−0.258764	−	0.448192i	0.707147	−	0.707066i	$-0.249982\pi$
$919$	−7.84443	−	13.5870i	−0.258764	−	0.448192i	−0.965911	+	0.258874i	$0.916648\pi$
$920$	−1.25859	+	2.17995i	−0.0414946	+	0.0718707i
$921$	−6.86242	+	1.83878i	−0.226124	+	0.0605898i
$922$	−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
$926$	6.08156			0.199852
$927$	14.2247			0.467200
$928$	0.600090	+	0.160794i	0.0196989	+	0.00527831i
$929$	−11.4266	+	42.6448i	−0.374896	+	1.39913i	0.478602	+	0.878032i	$0.341144\pi$
$929$	−11.4266	+	42.6448i	−0.374896	+	1.39913i	−0.853497	+	0.521097i	$0.825523\pi$
$930$	1.65667	+	6.18279i	0.0543244	+	0.202742i
$931$	17.5795	−	9.49221i	0.576146	−	0.311095i
$932$	1.17300	−	2.03170i	0.0384229	−	0.0665505i
$933$		−	2.21932i		−	0.0726573i
$934$	7.00368	+	26.1381i	0.229167	+	0.855265i
$935$	−27.7160	+	16.0018i	−0.906410	+	0.523316i
$936$	3.59824	−	0.229560i	0.117612	−	0.00750342i
$937$		−	41.7209i		−	1.36296i	−0.731836	−	0.681481i	$-0.761336\pi$
$937$		−	41.7209i		−	1.36296i	0.731836	−	0.681481i	$-0.238664\pi$
$938$	12.8423	+	17.2396i	0.419317	+	0.562893i
$939$	5.39093	+	9.33736i	0.175926	+	0.304713i
$940$	10.3732	−	5.98898i	0.338337	−	0.195339i
$941$	−13.0747	+	48.7954i	−0.426223	+	1.59068i	0.335016	+	0.942212i	$0.391258\pi$
$941$	−13.0747	+	48.7954i	−0.426223	+	1.59068i	−0.761239	+	0.648472i	$0.775408\pi$
$942$	−15.7490	+	15.7490i	−0.513130	+	0.513130i
$943$	−8.78490	−	2.35391i	−0.286076	−	0.0766537i
$944$	5.57219	−	5.57219i	0.181359	−	0.181359i
$945$	−1.15701	+	7.91514i	−0.0376375	+	0.257479i
$946$	12.5469	−	7.24398i	0.407936	−	0.235522i
$947$	33.0523	+	33.0523i	1.07406	+	1.07406i	0.997029	+	0.0770268i	$0.0245427\pi$
$947$	33.0523	+	33.0523i	1.07406	+	1.07406i	0.0770268	+	0.997029i	$0.475457\pi$
$948$	−0.859183	−	1.48815i	−0.0279050	−	0.0483328i
$949$	−3.70444	−	58.0651i	−0.120251	−	1.88487i
$950$	10.2357	+	5.90958i	0.332090	+	0.191732i
$951$	−5.50177	+	20.5329i	−0.178407	+	0.665824i
$952$	−4.69414	−	11.8057i	−0.152138	−	0.382625i
$953$	−48.4304	−	27.9613i	−1.56881	−	0.905755i	−0.996308	−	0.0858539i	$-0.972638\pi$
$953$	−48.4304	−	27.9613i	−1.56881	−	0.905755i	−0.572506	−	0.819901i	$-0.694028\pi$
$954$	−2.90804	−	10.8529i	−0.0941511	−	0.351377i
$955$	28.0657	+	28.0657i	0.908185	+	0.908185i
$956$	−7.68798	−	7.68798i	−0.248647	−	0.248647i
$957$	0.354448	+	1.32282i	0.0114577	+	0.0427606i
$958$	9.80976	+	5.66367i	0.316939	+	0.182985i
$959$	0.684113	+	1.72053i	0.0220912	+	0.0555589i
$960$	−0.782522	+	2.92041i	−0.0252558	+	0.0942559i
$961$	22.9652	+	13.2590i	0.740812	+	0.427708i
$962$	−4.76076	−	14.1053i	−0.153493	−	0.454772i
$963$	5.94911	+	10.3042i	0.191707	+	0.332047i
$964$	−2.91524	−	2.91524i	−0.0938937	−	0.0938937i
$965$	32.6218	−	18.8342i	1.05013	−	0.606294i
$966$	0.318604	−	2.17958i	0.0102509	−	0.0701268i
$967$	−9.57079	+	9.57079i	−0.307776	+	0.307776i	−0.844046	−	0.536270i	$-0.819833\pi$
$967$	−9.57079	+	9.57079i	−0.307776	+	0.307776i	0.536270	+	0.844046i	$0.319833\pi$
$968$	−5.93152	−	1.58935i	−0.190646	−	0.0510835i
$969$	−9.69095	+	9.69095i	−0.311318	+	0.311318i
$970$	9.50653	−	35.4789i	0.305236	−	1.13916i
$971$	−25.7306	+	14.8555i	−0.825733	+	0.476737i	−0.852389	−	0.522908i	$-0.824847\pi$
$971$	−25.7306	+	14.8555i	−0.825733	+	0.476737i	0.0266567	+	0.999645i	$0.491514\pi$
$972$	0.500000	+	0.866025i	0.0160375	+	0.0277778i
$973$	−26.1769	−	35.1400i	−0.839194	−	1.12654i
$974$		−	21.0567i		−	0.674701i
$975$	−4.77487	−	14.1470i	−0.152918	−	0.453068i
$976$	6.58584	−	3.80234i	0.210808	−	0.121710i
$977$	−0.237250	−	0.885429i	−0.00759030	−	0.0283274i	0.962027	−	0.272955i	$-0.0880010\pi$
$977$	−0.237250	−	0.885429i	−0.00759030	−	0.0283274i	−0.969617	+	0.244628i	$0.921334\pi$
$978$			2.55850i			0.0818117i
$979$	−8.16933	+	14.1497i	−0.261093	+	0.452226i
$980$	11.1000	−	18.0196i	0.354576	−	0.575616i
$981$	−0.0602948	−	0.225023i	−0.00192506	−	0.00718444i
$982$	−5.45569	+	20.3609i	−0.174098	+	0.649743i
$983$	−51.9502	−	13.9200i	−1.65696	−	0.443980i	−0.695407	−	0.718616i	$-0.744776\pi$
$983$	−51.9502	−	13.9200i	−1.65696	−	0.443980i	−0.961548	+	0.274636i	$0.911443\pi$
$984$	−10.9239			−0.348242
$985$	−72.3675			−2.30582
$986$	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
$990$	−6.43766	+	1.72497i	−0.204602	+	0.0548230i
$991$	−4.46993	+	7.74214i	−0.141992	+	0.245937i	−0.928247	−	0.371965i	$-0.878684\pi$
$991$	−4.46993	+	7.74214i	−0.141992	+	0.245937i	0.786255	+	0.617903i	$0.212017\pi$
$992$	−1.05855	−	1.83346i	−0.0336089	−	0.0582123i
$993$	17.2588	+	17.2588i	0.547691	+	0.547691i
$994$	−13.7892	−	18.5106i	−0.437365	−	0.587122i
$995$	50.7607	−	13.6013i	1.60922	−	0.431190i
$996$	−17.2070	+	4.61061i	−0.545226	+	0.146093i
$997$			36.6290i			1.16005i	0.814598	+	0.580026i	$0.196958\pi$
$997$			36.6290i			1.16005i	−0.814598	+	0.580026i	$0.803042\pi$
$998$	−13.6629	−	7.88827i	−0.432491	−	0.249699i
$999$	2.91958	−	2.91958i	0.0923715	−	0.0923715i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.by.a.397.4	✓	32	13.7	odd	12
546.2.by.a.535.4	yes	32	7.3	odd	6
546.2.cg.a.145.4	yes	32	1.1	even	1	trivial
546.2.cg.a.241.4	yes	32	91.59	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.cg (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.866025 + 0.500000i) q^{3} -1.00000i q^{4} +(2.92041 - 0.782522i) q^{5} +(-0.965926 + 0.258819i) q^{6} +(2.42968 + 1.04721i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.866025 + 0.500000i) q^{3} -1.00000i q^{4} +(2.92041 - 0.782522i) q^{5} +(-0.965926 + 0.258819i) q^{6} +(2.42968 + 1.04721i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.51172 + 2.61837i) q^{10} +(2.12926 - 0.570532i) 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} -1.00000 q^{16} -4.80193 q^{17} +(-0.965926 - 0.258819i) q^{18} +(0.738690 - 2.75683i) q^{19} +(-0.782522 - 2.92041i) q^{20} +(1.58056 + 2.12175i) q^{21} +(-1.10218 + 1.90904i) q^{22} +0.832559i q^{23} +(0.258819 + 0.965926i) q^{24} +(3.58634 - 2.07057i) q^{25} +(3.23094 + 1.60031i) q^{26} +1.00000i q^{27} +(1.04721 - 2.42968i) q^{28} +(0.310629 + 0.538026i) q^{29} +(-2.61837 + 1.51172i) q^{30} +(0.547944 - 2.04496i) q^{31} +(0.707107 - 0.707107i) q^{32} +(2.12926 + 0.570532i) q^{33} +(3.39547 - 3.39547i) q^{34} +(7.91514 + 1.15701i) q^{35} +(0.866025 - 0.500000i) q^{36} +(-2.91958 - 2.91958i) q^{37} +(1.42704 + 2.47170i) q^{38} +(0.709554 - 3.53504i) q^{39} +(2.61837 + 1.51172i) q^{40} +(-2.82732 + 10.5517i) q^{41} +(-2.61793 - 0.382681i) q^{42} +(-5.69185 - 3.28619i) q^{43} +(-0.570532 - 2.12926i) q^{44} +(2.13789 + 2.13789i) q^{45} +(-0.588708 - 0.588708i) q^{46} +(1.02537 + 3.82672i) q^{47} +(-0.866025 - 0.500000i) q^{48} +(4.80670 + 5.08878i) q^{49} +(-1.07181 + 4.00004i) q^{50} +(-4.15859 - 2.40096i) q^{51} +(-3.41621 + 1.15303i) q^{52} +(5.61789 + 9.73048i) q^{53} +(-0.707107 - 0.707107i) q^{54} +(5.77185 - 3.33238i) q^{55} +(0.977554 + 2.45853i) q^{56} +(2.01814 - 2.01814i) q^{57} +(-0.600090 - 0.160794i) q^{58} +(-5.57219 + 5.57219i) q^{59} +(0.782522 - 2.92041i) q^{60} +(-6.58584 + 3.80234i) q^{61} +(1.05855 + 1.83346i) q^{62} +(0.307929 + 2.62777i) q^{63} +1.00000i q^{64} +(-6.04059 - 9.07448i) q^{65} +(-1.90904 + 1.10218i) q^{66} +(-2.10295 - 7.84832i) q^{67} +4.80193i q^{68} +(-0.416279 + 0.721017i) q^{69} +(-6.41497 + 4.77872i) q^{70} +(2.25799 + 8.42695i) q^{71} +(-0.258819 + 0.965926i) q^{72} +(15.5872 + 4.17659i) q^{73} +4.12891 q^{74} +4.14115 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} +(-2.92041 + 0.782522i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-5.46195 - 9.46038i) q^{82} +(-12.5964 - 12.5964i) q^{83} +(2.12175 - 1.58056i) q^{84} +(-14.0236 + 3.75761i) q^{85} +(6.34844 - 1.70106i) q^{86} +0.621259i q^{87} +(1.90904 + 1.10218i) q^{88} +(-5.24104 + 5.24104i) q^{89} -3.02343 q^{90} +(0.776002 - 9.50778i) q^{91} +0.832559 q^{92} +(1.49701 - 1.49701i) q^{93} +(-3.43094 - 1.98085i) q^{94} -8.62912i q^{95} +(0.965926 - 0.258819i) q^{96} +(-11.7346 + 3.14428i) q^{97} +(-6.99716 - 0.199461i) q^{98} +(1.55872 + 1.55872i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{7} + 16 q^{9}+O(q^{10}) \) 32 * q - 4 * q^7 + 16 * q^9	\( 32 q - 4 q^{7} + 16 q^{9} + 8 q^{11} + 16 q^{12} + 4 q^{14} - 32 q^{16} - 16 q^{17} + 24 q^{19} + 8 q^{21} - 4 q^{22} + 24 q^{25} - 8 q^{26} + 8 q^{28} - 12 q^{29} + 4 q^{31} + 8 q^{33} + 8 q^{34} + 40 q^{35} - 12 q^{37} - 8 q^{38} + 28 q^{39} + 28 q^{41} - 12 q^{42} + 84 q^{43} - 4 q^{44} - 40 q^{46} - 4 q^{47} - 36 q^{49} - 16 q^{50} - 20 q^{52} - 4 q^{53} - 48 q^{55} + 12 q^{56} + 12 q^{57} + 12 q^{58} - 24 q^{59} - 36 q^{61} + 40 q^{62} + 4 q^{63} + 44 q^{65} - 16 q^{67} + 8 q^{69} + 40 q^{70} + 20 q^{71} - 16 q^{73} - 40 q^{74} + 16 q^{75} - 36 q^{76} + 12 q^{77} - 20 q^{78} - 16 q^{81} - 24 q^{82} - 12 q^{83} - 8 q^{84} - 4 q^{85} - 20 q^{86} - 60 q^{89} - 48 q^{91} - 16 q^{92} - 32 q^{93} - 76 q^{97} - 8 q^{98} + 4 q^{99}+O(q^{100}) \) 32 * q - 4 * q^7 + 16 * q^9 + 8 * q^11 + 16 * q^12 + 4 * q^14 - 32 * q^16 - 16 * q^17 + 24 * q^19 + 8 * q^21 - 4 * q^22 + 24 * q^25 - 8 * q^26 + 8 * q^28 - 12 * q^29 + 4 * q^31 + 8 * q^33 + 8 * q^34 + 40 * q^35 - 12 * q^37 - 8 * q^38 + 28 * q^39 + 28 * q^41 - 12 * q^42 + 84 * q^43 - 4 * q^44 - 40 * q^46 - 4 * q^47 - 36 * q^49 - 16 * q^50 - 20 * q^52 - 4 * q^53 - 48 * q^55 + 12 * q^56 + 12 * q^57 + 12 * q^58 - 24 * q^59 - 36 * q^61 + 40 * q^62 + 4 * q^63 + 44 * q^65 - 16 * q^67 + 8 * q^69 + 40 * q^70 + 20 * q^71 - 16 * q^73 - 40 * q^74 + 16 * q^75 - 36 * q^76 + 12 * q^77 - 20 * q^78 - 16 * q^81 - 24 * q^82 - 12 * q^83 - 8 * q^84 - 4 * q^85 - 20 * q^86 - 60 * q^89 - 48 * q^91 - 16 * q^92 - 32 * q^93 - 76 * q^97 - 8 * q^98 + 4 * q^99

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