LMFDB - Embedded newform 546.2.cg.b.241.7

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:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			241.7
Character	$\chi$	$=$	546.241
Dual form			546.2.cg.b.145.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(-0.866025 + 0.500000i) q^{3} +1.00000i q^{4} +(-1.42776 - 0.382567i) q^{5} +(-0.965926 - 0.258819i) q^{6} +(0.349274 - 2.62260i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(-0.866025 + 0.500000i) q^{3} +1.00000i q^{4} +(-1.42776 - 0.382567i) q^{5} +(-0.965926 - 0.258819i) q^{6} +(0.349274 - 2.62260i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.500000 - 0.866025i) q^{9} +(-0.739062 - 1.28009i) q^{10} +(-5.63579 - 1.51010i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(-2.68146 - 2.41035i) q^{13} +(2.10143 - 1.60748i) q^{14} +(1.42776 - 0.382567i) q^{15} -1.00000 q^{16} +6.94378 q^{17} +(0.965926 - 0.258819i) q^{18} +(-1.37897 - 5.14638i) q^{19} +(0.382567 - 1.42776i) q^{20} +(1.00882 + 2.44587i) q^{21} +(-2.91730 - 5.05291i) q^{22} +0.769549i q^{23} +(0.258819 - 0.965926i) q^{24} +(-2.43799 - 1.40757i) q^{25} +(-0.191699 - 3.60045i) q^{26} +1.00000i q^{27} +(2.62260 + 0.349274i) q^{28} +(-4.35699 + 7.54652i) q^{29} +(1.28009 + 0.739062i) q^{30} +(-0.101593 - 0.379148i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(5.63579 - 1.51010i) q^{33} +(4.91000 + 4.91000i) q^{34} +(-1.50200 + 3.61081i) q^{35} +(0.866025 + 0.500000i) q^{36} +(4.14694 - 4.14694i) q^{37} +(2.66396 - 4.61411i) q^{38} +(3.52738 + 0.746698i) q^{39} +(1.28009 - 0.739062i) q^{40} +(-1.70135 - 6.34954i) q^{41} +(-1.01615 + 2.44283i) q^{42} +(0.142904 - 0.0825059i) q^{43} +(1.51010 - 5.63579i) q^{44} +(-1.04519 + 1.04519i) q^{45} +(-0.544153 + 0.544153i) q^{46} +(3.23250 - 12.0638i) q^{47} +(0.866025 - 0.500000i) q^{48} +(-6.75602 - 1.83201i) q^{49} +(-0.728614 - 2.71922i) q^{50} +(-6.01349 + 3.47189i) q^{51} +(2.41035 - 2.68146i) q^{52} +(-4.44772 + 7.70367i) q^{53} +(-0.707107 + 0.707107i) q^{54} +(7.46883 + 4.31213i) q^{55} +(1.60748 + 2.10143i) q^{56} +(3.76741 + 3.76741i) q^{57} +(-8.41705 + 2.25534i) q^{58} +(0.616913 + 0.616913i) q^{59} +(0.382567 + 1.42776i) q^{60} +(4.89047 + 2.82351i) q^{61} +(0.196262 - 0.339935i) q^{62} +(-2.09660 - 1.61378i) q^{63} -1.00000i q^{64} +(2.90635 + 4.46724i) q^{65} +(5.05291 + 2.91730i) q^{66} +(-1.23791 + 4.61993i) q^{67} +6.94378i q^{68} +(-0.384774 - 0.666449i) q^{69} +(-3.61530 + 1.49116i) q^{70} +(-1.36236 + 5.08439i) q^{71} +(0.258819 + 0.965926i) q^{72} +(-8.94879 + 2.39782i) q^{73} +5.86465 q^{74} +2.81515 q^{75} +(5.14638 - 1.37897i) q^{76} +(-5.92883 + 14.2529i) q^{77} +(1.96624 + 3.02223i) q^{78} +(-3.96454 - 6.86679i) q^{79} +(1.42776 + 0.382567i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(3.28676 - 5.69284i) q^{82} +(-9.29167 + 9.29167i) q^{83} +(-2.44587 + 1.00882i) q^{84} +(-9.91405 - 2.65646i) q^{85} +(0.159389 + 0.0427082i) q^{86} -8.71398i q^{87} +(5.05291 - 2.91730i) q^{88} +(6.30539 + 6.30539i) q^{89} -1.47812 q^{90} +(-7.25794 + 6.19050i) q^{91} -0.769549 q^{92} +(0.277556 + 0.277556i) q^{93} +(10.8161 - 6.24471i) q^{94} +7.87533i q^{95} +(0.965926 + 0.258819i) q^{96} +(0.852159 + 0.228335i) q^{97} +(-3.48180 - 6.07265i) q^{98} +(-4.12568 + 4.12568i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 4 q^{7} + 20 q^{9}+O(q^{10}) $ 40 * q + 4 * q^7 + 20 * q^9	$ 40 q + 4 q^{7} + 20 q^{9} + 8 q^{11} - 20 q^{12} + 4 q^{14} - 40 q^{16} + 16 q^{17} + 4 q^{19} + 4 q^{21} - 4 q^{22} - 24 q^{25} + 8 q^{26} - 4 q^{28} - 12 q^{29} - 8 q^{33} - 8 q^{34} - 32 q^{35} + 40 q^{37} + 8 q^{38} + 20 q^{39} + 20 q^{41} + 12 q^{42} - 24 q^{43} - 4 q^{44} + 32 q^{46} + 4 q^{47} + 32 q^{49} - 16 q^{50} + 24 q^{51} + 16 q^{52} - 4 q^{53} + 24 q^{55} + 12 q^{56} + 8 q^{57} + 12 q^{58} + 24 q^{59} + 60 q^{61} + 32 q^{62} - 4 q^{63} + 44 q^{65} - 12 q^{67} - 8 q^{69} - 24 q^{70} - 28 q^{71} + 60 q^{73} - 40 q^{74} - 72 q^{75} + 4 q^{76} - 12 q^{77} + 4 q^{78} - 20 q^{81} - 24 q^{82} + 60 q^{83} - 8 q^{84} - 4 q^{85} - 20 q^{86} - 36 q^{89} - 16 q^{92} - 24 q^{93} - 48 q^{97} - 88 q^{98} + 4 q^{99}+O(q^{100}) $ 40 * q + 4 * q^7 + 20 * q^9 + 8 * q^11 - 20 * q^12 + 4 * q^14 - 40 * q^16 + 16 * q^17 + 4 * q^19 + 4 * q^21 - 4 * q^22 - 24 * q^25 + 8 * q^26 - 4 * q^28 - 12 * q^29 - 8 * q^33 - 8 * q^34 - 32 * q^35 + 40 * q^37 + 8 * q^38 + 20 * q^39 + 20 * q^41 + 12 * q^42 - 24 * q^43 - 4 * q^44 + 32 * q^46 + 4 * q^47 + 32 * q^49 - 16 * q^50 + 24 * q^51 + 16 * q^52 - 4 * q^53 + 24 * q^55 + 12 * q^56 + 8 * q^57 + 12 * q^58 + 24 * q^59 + 60 * q^61 + 32 * q^62 - 4 * q^63 + 44 * q^65 - 12 * q^67 - 8 * q^69 - 24 * q^70 - 28 * q^71 + 60 * q^73 - 40 * q^74 - 72 * q^75 + 4 * q^76 - 12 * q^77 + 4 * q^78 - 20 * q^81 - 24 * q^82 + 60 * q^83 - 8 * q^84 - 4 * q^85 - 20 * q^86 - 36 * q^89 - 16 * q^92 - 24 * q^93 - 48 * q^97 - 88 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.707107	+	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
$5$	−1.42776	−	0.382567i	−0.638513	−	0.171089i	−0.0749833	−	0.997185i	$-0.523890\pi$
$5$	−1.42776	−	0.382567i	−0.638513	−	0.171089i	−0.563530	+	0.826096i	$0.690557\pi$
$6$	−0.965926	−	0.258819i	−0.394338	−	0.105662i
$7$	0.349274	−	2.62260i	0.132013	−	0.991248i
$7$	0.349274	−	2.62260i	0.132013	−	0.991248i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	−0.739062	−	1.28009i	−0.233712	−	0.404801i
$11$	−5.63579	−	1.51010i	−1.69925	−	0.455314i	−0.726502	−	0.687164i	$-0.758855\pi$
$11$	−5.63579	−	1.51010i	−1.69925	−	0.455314i	−0.972751	+	0.231851i	$0.925522\pi$
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	−2.68146	−	2.41035i	−0.743702	−	0.668511i
$13$	−2.68146	−	2.41035i	−0.743702	−	0.668511i
$14$	2.10143	−	1.60748i	0.561631	−	0.429617i
$15$	1.42776	−	0.382567i	0.368646	−	0.0987783i
$16$	−1.00000			−0.250000
$17$	6.94378			1.68411			0.842057	−	0.539388i	$-0.181344\pi$
$17$	6.94378			1.68411			0.842057	+	0.539388i	$0.181344\pi$
$18$	0.965926	−	0.258819i	0.227671	−	0.0610042i
$19$	−1.37897	−	5.14638i	−0.316357	−	1.18066i	−0.922720	−	0.385472i	$-0.874039\pi$
$19$	−1.37897	−	5.14638i	−0.316357	−	1.18066i	0.606363	−	0.795188i	$-0.292628\pi$
$20$	0.382567	−	1.42776i	0.0855445	−	0.319257i
$21$	1.00882	+	2.44587i	0.220142	+	0.533733i
$22$	−2.91730	−	5.05291i	−0.621970	−	1.07728i
$23$			0.769549i			0.160462i	0.996776	+	0.0802310i	$0.0255658\pi$
$23$			0.769549i			0.160462i	−0.996776	+	0.0802310i	$0.974434\pi$
$24$	0.258819	−	0.965926i	0.0528312	−	0.197169i
$25$	−2.43799	−	1.40757i	−0.487598	−	0.281515i
$26$	−0.191699	−	3.60045i	−0.0375953	−	0.706107i
$27$			1.00000i			0.192450i
$28$	2.62260	+	0.349274i	0.495624	+	0.0660066i
$29$	−4.35699	+	7.54652i	−0.809072	+	1.40135i	0.104435	+	0.994532i	$0.466697\pi$
$29$	−4.35699	+	7.54652i	−0.809072	+	1.40135i	−0.913507	+	0.406823i	$0.866637\pi$
$30$	1.28009	+	0.739062i	0.233712	+	0.134934i
$31$	−0.101593	−	0.379148i	−0.0182466	−	0.0680971i	0.956202	−	0.292707i	$-0.0945560\pi$
$31$	−0.101593	−	0.379148i	−0.0182466	−	0.0680971i	−0.974449	+	0.224610i	$0.927889\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	5.63579	−	1.51010i	0.981064	−	0.262875i
$34$	4.91000	+	4.91000i	0.842057	+	0.842057i
$35$	−1.50200	+	3.61081i	−0.253884	+	0.610339i
$36$	0.866025	+	0.500000i	0.144338	+	0.0833333i
$37$	4.14694	−	4.14694i	0.681752	−	0.681752i	−0.278643	−	0.960395i	$-0.589885\pi$
$37$	4.14694	−	4.14694i	0.681752	−	0.681752i	0.960395	+	0.278643i	$0.0898845\pi$
$38$	2.66396	−	4.61411i	0.432151	−	0.748508i
$39$	3.52738	+	0.746698i	0.564834	+	0.119567i
$40$	1.28009	−	0.739062i	0.202401	−	0.116856i
$41$	−1.70135	−	6.34954i	−0.265707	−	0.991632i	−0.961816	−	0.273696i	$-0.911754\pi$
$41$	−1.70135	−	6.34954i	−0.265707	−	0.991632i	0.696109	−	0.717936i	$-0.254913\pi$
$42$	−1.01615	+	2.44283i	−0.156795	+	0.376937i
$43$	0.142904	−	0.0825059i	0.0217927	−	0.0125820i	−0.489064	−	0.872248i	$-0.662662\pi$
$43$	0.142904	−	0.0825059i	0.0217927	−	0.0125820i	0.510857	+	0.859666i	$0.329328\pi$
$44$	1.51010	−	5.63579i	0.227657	−	0.849627i
$45$	−1.04519	+	1.04519i	−0.155808	+	0.155808i
$46$	−0.544153	+	0.544153i	−0.0802310	+	0.0802310i
$47$	3.23250	−	12.0638i	0.471508	−	1.75969i	−0.162847	−	0.986651i	$-0.552068\pi$
$47$	3.23250	−	12.0638i	0.471508	−	1.75969i	0.634355	−	0.773041i	$-0.281266\pi$
$48$	0.866025	−	0.500000i	0.125000	−	0.0721688i
$49$	−6.75602	−	1.83201i	−0.965145	−	0.261716i
$50$	−0.728614	−	2.71922i	−0.103042	−	0.384556i
$51$	−6.01349	+	3.47189i	−0.842057	+	0.486162i
$52$	2.41035	−	2.68146i	0.334256	−	0.371851i
$53$	−4.44772	+	7.70367i	−0.610941	+	1.05818i	0.380141	+	0.924928i	$0.375875\pi$
$53$	−4.44772	+	7.70367i	−0.610941	+	1.05818i	−0.991082	+	0.133252i	$0.957458\pi$
$54$	−0.707107	+	0.707107i	−0.0962250	+	0.0962250i
$55$	7.46883	+	4.31213i	1.00710	+	0.581447i
$56$	1.60748	+	2.10143i	0.214809	+	0.280815i
$57$	3.76741	+	3.76741i	0.499005	+	0.499005i
$58$	−8.41705	+	2.25534i	−1.10521	+	0.296141i
$59$	0.616913	+	0.616913i	0.0803153	+	0.0803153i	0.746123	−	0.665808i	$-0.231913\pi$
$59$	0.616913	+	0.616913i	0.0803153	+	0.0803153i	−0.665808	+	0.746123i	$0.731913\pi$
$60$	0.382567	+	1.42776i	0.0493892	+	0.184323i
$61$	4.89047	+	2.82351i	0.626160	+	0.361514i	0.779264	−	0.626696i	$-0.215593\pi$
$61$	4.89047	+	2.82351i	0.626160	+	0.361514i	−0.153103	+	0.988210i	$0.548927\pi$
$62$	0.196262	−	0.339935i	0.0249253	−	0.0431718i
$63$	−2.09660	−	1.61378i	−0.264146	−	0.203317i
$64$		−	1.00000i		−	0.125000i
$65$	2.90635	+	4.46724i	0.360488	+	0.554093i
$66$	5.05291	+	2.91730i	0.621970	+	0.359094i
$67$	−1.23791	+	4.61993i	−0.151234	+	0.564414i	0.848164	+	0.529733i	$0.177708\pi$
$67$	−1.23791	+	4.61993i	−0.151234	+	0.564414i	−0.999398	+	0.0346805i	$0.988959\pi$
$68$			6.94378i			0.842057i
$69$	−0.384774	−	0.666449i	−0.0463214	−	0.0802310i
$70$	−3.61530	+	1.49116i	−0.432111	+	0.178227i
$71$	−1.36236	+	5.08439i	−0.161682	+	0.603406i	0.836758	+	0.547573i	$0.184448\pi$
$71$	−1.36236	+	5.08439i	−0.161682	+	0.603406i	−0.998440	+	0.0558333i	$0.982218\pi$
$72$	0.258819	+	0.965926i	0.0305021	+	0.113835i
$73$	−8.94879	+	2.39782i	−1.04738	+	0.280644i	−0.741167	−	0.671321i	$-0.765727\pi$
$73$	−8.94879	+	2.39782i	−1.04738	+	0.280644i	−0.306209	+	0.951964i	$0.599061\pi$
$74$	5.86465			0.681752
$75$	2.81515			0.325065
$76$	5.14638	−	1.37897i	0.590330	−	0.158178i
$77$	−5.92883	+	14.2529i	−0.675653	+	1.62427i
$78$	1.96624	+	3.02223i	0.222633	+	0.342200i
$79$	−3.96454	−	6.86679i	−0.446046	−	0.772574i	0.552079	−	0.833792i	$-0.313835\pi$
$79$	−3.96454	−	6.86679i	−0.446046	−	0.772574i	−0.998124	+	0.0612181i	$0.980501\pi$
$80$	1.42776	+	0.382567i	0.159628	+	0.0427723i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	3.28676	−	5.69284i	0.362962	−	0.628669i
$83$	−9.29167	+	9.29167i	−1.01989	+	1.01989i	−0.0200956	+	0.999798i	$0.506397\pi$
$83$	−9.29167	+	9.29167i	−1.01989	+	1.01989i	−0.999798	+	0.0200956i	$0.993603\pi$
$84$	−2.44587	+	1.00882i	−0.266866	+	0.110071i
$85$	−9.91405	−	2.65646i	−1.07533	−	0.288134i
$86$	0.159389	+	0.0427082i	0.0171874	+	0.00460534i
$87$		−	8.71398i		−	0.934236i
$88$	5.05291	−	2.91730i	0.538642	−	0.310985i
$89$	6.30539	+	6.30539i	0.668370	+	0.668370i	0.957338	−	0.288969i	$-0.0933124\pi$
$89$	6.30539	+	6.30539i	0.668370	+	0.668370i	−0.288969	+	0.957338i	$0.593312\pi$
$90$	−1.47812			−0.155808
$91$	−7.25794	+	6.19050i	−0.760839	+	0.648941i
$92$	−0.769549			−0.0802310
$93$	0.277556	+	0.277556i	0.0287812	+	0.0287812i
$94$	10.8161	−	6.24471i	1.11560	−	0.644092i
$95$			7.87533i			0.807992i
$96$	0.965926	+	0.258819i	0.0985844	+	0.0264156i
$97$	0.852159	+	0.228335i	0.0865237	+	0.0231839i	0.301821	−	0.953365i	$-0.402405\pi$
$97$	0.852159	+	0.228335i	0.0865237	+	0.0231839i	−0.215297	+	0.976549i	$0.569072\pi$
$98$	−3.48180	−	6.07265i	−0.351715	−	0.613430i
$99$	−4.12568	+	4.12568i	−0.414647	+	0.414647i
$100$	1.40757	−	2.43799i	0.140757	−	0.243799i
$101$	−5.98408	−	10.3647i	−0.595439	−	1.03133i	−0.993485	−	0.113965i	$-0.963645\pi$
$101$	−5.98408	−	10.3647i	−0.595439	−	1.03133i	0.398046	−	0.917365i	$-0.369688\pi$
$102$	−6.70718	−	1.79718i	−0.664110	−	0.177948i
$103$	−6.40446	−	11.0928i	−0.631050	−	1.09301i	−0.987337	−	0.158634i	$-0.949291\pi$
$103$	−6.40446	−	11.0928i	−0.631050	−	1.09301i	0.356288	−	0.934376i	$-0.384042\pi$
$104$	3.60045	−	0.191699i	0.353053	−	0.0187977i
$105$	−0.504639	−	3.87805i	−0.0492477	−	0.378459i
$106$	−8.59233	+	2.30231i	−0.834561	+	0.223620i
$107$	2.65924			0.257078			0.128539	−	0.991704i	$-0.458971\pi$
$107$	2.65924			0.257078			0.128539	+	0.991704i	$0.458971\pi$
$108$	−1.00000			−0.0962250
$109$	14.4796	−	3.87980i	1.38689	−	0.371617i	0.513274	−	0.858225i	$-0.328432\pi$
$109$	14.4796	−	3.87980i	1.38689	−	0.371617i	0.873621	+	0.486607i	$0.161766\pi$
$110$	2.23212	+	8.33039i	0.212824	+	0.794272i
$111$	−1.51788	+	5.66482i	−0.144071	+	0.537681i
$112$	−0.349274	+	2.62260i	−0.0330033	+	0.247812i
$113$	4.95793	+	8.58738i	0.466403	+	0.807833i	0.999264	−	0.0383697i	$-0.0122165\pi$
$113$	4.95793	+	8.58738i	0.466403	+	0.807833i	−0.532861	+	0.846203i	$0.678883\pi$
$114$			5.32792i			0.499005i
$115$	0.294404	−	1.09873i	0.0274533	−	0.102457i
$116$	−7.54652	−	4.35699i	−0.700677	−	0.404536i
$117$	−3.42815	+	1.11703i	−0.316933	+	0.103270i
$118$			0.872447i			0.0803153i
$119$	2.42528	−	18.2107i	0.222325	−	1.66938i
$120$	−0.739062	+	1.28009i	−0.0674668	+	0.116856i
$121$	19.9554	+	11.5212i	1.81413	+	1.04739i
$122$	1.46156	+	5.45461i	0.132323	+	0.493837i
$123$	4.64819	+	4.64819i	0.419113	+	0.419113i
$124$	0.379148	−	0.101593i	0.0340485	−	0.00912328i
$125$	8.16833	+	8.16833i	0.730598	+	0.730598i
$126$	−0.341405	−	2.62363i	−0.0304147	−	0.233732i
$127$	−9.01558	−	5.20515i	−0.800003	−	0.461882i	0.0434689	−	0.999055i	$-0.486159\pi$
$127$	−9.01558	−	5.20515i	−0.800003	−	0.461882i	−0.843472	+	0.537173i	$0.819492\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	−0.0825059	+	0.142904i	−0.00726424	+	0.0125820i
$130$	−1.10371	+	5.21391i	−0.0968020	+	0.457290i
$131$	−3.41500	+	1.97165i	−0.298370	+	0.172264i	−0.641710	−	0.766947i	$-0.721775\pi$
$131$	−3.41500	+	1.97165i	−0.298370	+	0.172264i	0.343340	+	0.939211i	$0.388442\pi$
$132$	1.51010	+	5.63579i	0.131438	+	0.490532i
$133$	−13.9785	+	1.81898i	−1.21209	+	0.157725i
$134$	−4.14211	+	2.39145i	−0.357824	+	0.206590i
$135$	0.382567	−	1.42776i	0.0329261	−	0.122882i
$136$	−4.91000	+	4.91000i	−0.421029	+	0.421029i
$137$	−2.02014	+	2.02014i	−0.172592	+	0.172592i	−0.788117	−	0.615525i	$-0.788944\pi$
$137$	−2.02014	+	2.02014i	−0.172592	+	0.172592i	0.615525	+	0.788117i	$0.288944\pi$
$138$	0.199174	−	0.743327i	0.0169548	−	0.0632762i
$139$	8.27684	−	4.77864i	0.702033	−	0.405319i	−0.106071	−	0.994359i	$-0.533827\pi$
$139$	8.27684	−	4.77864i	0.702033	−	0.405319i	0.808104	+	0.589040i	$0.200494\pi$
$140$	−3.61081	−	1.50200i	−0.305169	−	0.126942i
$141$	3.23250	+	12.0638i	0.272225	+	1.01596i
$142$	−4.55854	+	2.63188i	−0.382544	+	0.220862i
$143$	11.4722	+	17.6335i	0.959356	+	1.47459i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	9.10778	−	9.10778i	0.756360	−	0.756360i
$146$	−8.02326	−	4.63223i	−0.664010	−	0.383366i
$147$	6.76689	−	1.79144i	0.558123	−	0.147756i
$148$	4.14694	+	4.14694i	0.340876	+	0.340876i
$149$	−10.0910	+	2.70387i	−0.826686	+	0.221510i	−0.647267	−	0.762263i	$-0.724088\pi$
$149$	−10.0910	+	2.70387i	−0.826686	+	0.221510i	−0.179419	+	0.983773i	$0.557422\pi$
$150$	1.99061	+	1.99061i	0.162533	+	0.162533i
$151$	−1.16214	−	4.33716i	−0.0945734	−	0.352953i	0.902381	−	0.430939i	$-0.141818\pi$
$151$	−1.16214	−	4.33716i	−0.0945734	−	0.352953i	−0.996954	+	0.0779863i	$0.975151\pi$
$152$	4.61411	+	2.66396i	0.374254	+	0.216076i
$153$	3.47189	−	6.01349i	0.280686	−	0.486162i
$154$	−14.2707	+	5.88604i	−1.14996	+	0.474311i
$155$			0.580198i			0.0466027i
$156$	−0.746698	+	3.52738i	−0.0597837	+	0.282417i
$157$	12.7423	+	7.35677i	1.01695	+	0.587134i	0.913218	−	0.407472i	$-0.133590\pi$
$157$	12.7423	+	7.35677i	1.01695	+	0.587134i	0.103728	+	0.994606i	$0.466923\pi$
$158$	2.05220	−	7.65891i	0.163264	−	0.609310i
$159$		−	8.89544i		−	0.705454i
$160$	0.739062	+	1.28009i	0.0584280	+	0.101200i
$161$	2.01821	+	0.268784i	0.159058	+	0.0211831i
$162$	0.258819	−	0.965926i	0.0203347	−	0.0758903i
$163$	−5.94900	−	22.2020i	−0.465962	−	1.73899i	−0.653681	−	0.756771i	$-0.726776\pi$
$163$	−5.94900	−	22.2020i	−0.465962	−	1.73899i	0.187719	−	0.982223i	$-0.439891\pi$
$164$	6.34954	−	1.70135i	0.495816	−	0.132853i
$165$	−8.62426			−0.671398
$166$	−13.1404			−1.01989
$167$	0.821354	−	0.220081i	0.0635583	−	0.0170304i	−0.226900	−	0.973918i	$-0.572859\pi$
$167$	0.821354	−	0.220081i	0.0635583	−	0.0170304i	0.290458	+	0.956888i	$0.406192\pi$
$168$	−2.44283	−	1.01615i	−0.188469	−	0.0783977i
$169$	1.38041	+	12.9265i	0.106185	+	0.994346i
$170$	−5.13189	−	8.88869i	−0.393598	−	0.681731i
$171$	−5.14638	−	1.37897i	−0.393553	−	0.105452i
$172$	0.0825059	+	0.142904i	0.00629101	+	0.0108964i
$173$	4.61652	−	7.99605i	0.350988	−	0.607928i	−0.635435	−	0.772154i	$-0.719179\pi$
$173$	4.61652	−	7.99605i	0.350988	−	0.607928i	0.986423	+	0.164226i	$0.0525126\pi$
$174$	6.16171	−	6.16171i	0.467118	−	0.467118i
$175$	−4.54302	+	5.90223i	−0.343420	+	0.446167i
$176$	5.63579	+	1.51010i	0.424813	+	0.113828i
$177$	−0.842719	−	0.225806i	−0.0633426	−	0.0169726i
$178$			8.91716i			0.668370i
$179$	9.04284	−	5.22088i	0.675893	−	0.390227i	−0.122413	−	0.992479i	$-0.539063\pi$
$179$	9.04284	−	5.22088i	0.675893	−	0.390227i	0.798306	+	0.602252i	$0.205730\pi$
$180$	−1.04519	−	1.04519i	−0.0779040	−	0.0779040i
$181$	−1.21138			−0.0900414			−0.0450207	−	0.998986i	$-0.514335\pi$
$181$	−1.21138			−0.0900414			−0.0450207	+	0.998986i	$0.514335\pi$
$182$	−9.50948	−	0.754796i	−0.704890	−	0.0559492i
$183$	−5.64703			−0.417440
$184$	−0.544153	−	0.544153i	−0.0401155	−	0.0401155i
$185$	−7.50731	+	4.33434i	−0.551948	+	0.318667i
$186$			0.392523i			0.0287812i
$187$	−39.1337	−	10.4858i	−2.86174	−	0.766800i
$188$	12.0638	+	3.23250i	0.879846	+	0.235754i
$189$	2.62260	+	0.349274i	0.190766	+	0.0254060i
$190$	−5.56870	+	5.56870i	−0.403996	+	0.403996i
$191$	12.4420	−	21.5502i	0.900271	−	1.55932i	0.0731296	−	0.997322i	$-0.476701\pi$
$191$	12.4420	−	21.5502i	0.900271	−	1.55932i	0.827142	−	0.561993i	$-0.189965\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	17.9106	+	4.79914i	1.28924	+	0.345450i	0.837370	−	0.546636i	$-0.184092\pi$
$193$	17.9106	+	4.79914i	1.28924	+	0.345450i	0.451866	+	0.892086i	$0.350759\pi$
$194$	0.441110	+	0.764025i	0.0316699	+	0.0548538i
$195$	−4.75059	−	2.41556i	−0.340197	−	0.172982i
$196$	1.83201	−	6.75602i	0.130858	−	0.482573i
$197$	0.939199	−	0.251658i	0.0669152	−	0.0179299i	−0.225206	−	0.974311i	$-0.572306\pi$
$197$	0.939199	−	0.251658i	0.0669152	−	0.0179299i	0.292121	+	0.956381i	$0.405639\pi$
$198$	−5.83459			−0.414647
$199$	−1.17166			−0.0830568			−0.0415284	−	0.999137i	$-0.513223\pi$
$199$	−1.17166			−0.0830568			−0.0415284	+	0.999137i	$0.513223\pi$
$200$	2.71922	−	0.728614i	0.192278	−	0.0515208i
$201$	−1.23791	−	4.61993i	−0.0873151	−	0.325865i
$202$	3.09759	−	11.5604i	0.217946	−	0.813384i
$203$	18.2697	+	14.0624i	1.28228	+	0.986989i
$204$	−3.47189	−	6.01349i	−0.243081	−	0.421029i
$205$			9.71649i			0.678629i
$206$	3.31519	−	12.3725i	0.230980	−	0.862030i
$207$	0.666449	+	0.384774i	0.0463214	+	0.0267437i
$208$	2.68146	+	2.41035i	0.185925	+	0.167128i
$209$			31.0863i			2.15028i
$210$	2.38537	−	3.09903i	0.164606	−	0.213854i
$211$	8.43264	−	14.6058i	0.580527	−	1.00550i	−0.414890	−	0.909871i	$-0.636180\pi$
$211$	8.43264	−	14.6058i	0.580527	−	1.00550i	0.995417	−	0.0956302i	$-0.0304866\pi$
$212$	−7.70367	−	4.44772i	−0.529090	−	0.305471i
$213$	−1.36236	−	5.08439i	−0.0933473	−	0.348377i
$214$	1.88037	+	1.88037i	0.128539	+	0.128539i
$215$	−0.235597	+	0.0631280i	−0.0160676	+	0.00430529i
$216$	−0.707107	−	0.707107i	−0.0481125	−	0.0481125i
$217$	−1.02984	+	0.134009i	−0.0699099	+	0.00909714i
$218$	12.9821	+	7.49520i	0.879256	+	0.507639i
$219$	6.55097	−	6.55097i	0.442673	−	0.442673i
$220$	−4.31213	+	7.46883i	−0.290724	+	0.503548i
$221$	−18.6194	−	16.7370i	−1.25248	−	1.12585i
$222$	−5.07894	+	2.93233i	−0.340876	+	0.196805i
$223$	0.0655089	+	0.244483i	0.00438680	+	0.0163718i	0.968085	−	0.250624i	$-0.0806357\pi$
$223$	0.0655089	+	0.244483i	0.00438680	+	0.0163718i	−0.963698	+	0.266996i	$0.913969\pi$
$224$	−2.10143	+	1.60748i	−0.140408	+	0.107404i
$225$	−2.43799	+	1.40757i	−0.162533	+	0.0938383i
$226$	−2.56641	+	9.57798i	−0.170715	+	0.637118i
$227$	1.18113	−	1.18113i	0.0783942	−	0.0783942i	−0.666822	−	0.745217i	$-0.732346\pi$
$227$	1.18113	−	1.18113i	0.0783942	−	0.0783942i	0.745217	+	0.666822i	$0.232346\pi$
$228$	−3.76741	+	3.76741i	−0.249503	+	0.249503i
$229$	6.94421	−	25.9161i	0.458886	−	1.71259i	−0.217517	−	0.976056i	$-0.569796\pi$
$229$	6.94421	−	25.9161i	0.458886	−	1.71259i	0.676404	−	0.736531i	$-0.263537\pi$
$230$	0.985094	−	0.568744i	0.0649552	−	0.0375019i
$231$	−1.99196	−	15.3078i	−0.131061	−	1.00718i
$232$	−2.25534	−	8.41705i	−0.148071	−	0.552607i
$233$	14.5436	−	8.39675i	0.952783	−	0.550089i	0.0588383	−	0.998268i	$-0.481260\pi$
$233$	14.5436	−	8.39675i	0.952783	−	0.550089i	0.893944	+	0.448178i	$0.147927\pi$
$234$	−3.21393	−	1.63421i	−0.210101	−	0.106832i
$235$	−9.23045	+	15.9876i	−0.602128	+	1.04292i
$236$	−0.616913	+	0.616913i	−0.0401576	+	0.0401576i
$237$	6.86679	+	3.96454i	0.446046	+	0.257525i
$238$	14.5919	−	11.1620i	0.945850	−	0.723525i
$239$	−1.66598	−	1.66598i	−0.107763	−	0.107763i	0.651169	−	0.758933i	$-0.274279\pi$
$239$	−1.66598	−	1.66598i	−0.107763	−	0.107763i	−0.758933	+	0.651169i	$0.774279\pi$
$240$	−1.42776	+	0.382567i	−0.0921614	+	0.0246946i
$241$	10.5050	+	10.5050i	0.676688	+	0.676688i	0.959249	−	0.282561i	$-0.0911840\pi$
$241$	10.5050	+	10.5050i	0.676688	+	0.676688i	−0.282561	+	0.959249i	$0.591184\pi$
$242$	5.96384	+	22.2573i	0.383370	+	1.43076i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	−2.82351	+	4.89047i	−0.180757	+	0.313080i
$245$	8.94509	+	5.20030i	0.571481	+	0.332235i
$246$			6.57353i			0.419113i
$247$	−8.70694	+	17.1236i	−0.554009	+	1.08955i
$248$	0.339935	+	0.196262i	0.0215859	+	0.0124626i
$249$	3.40099	−	12.6927i	0.215529	−	0.804365i
$250$			11.5518i			0.730598i
$251$	5.71406	+	9.89703i	0.360668	+	0.624695i	0.988071	−	0.154000i	$-0.0492154\pi$
$251$	5.71406	+	9.89703i	0.360668	+	0.624695i	−0.627403	+	0.778695i	$0.715882\pi$
$252$	1.61378	−	2.09660i	0.101658	−	0.132073i
$253$	1.16210	−	4.33701i	0.0730605	−	0.272666i
$254$	−2.69438	−	10.0556i	−0.169061	−	0.630943i
$255$	9.91405	−	2.65646i	0.620842	−	0.166354i
$256$	1.00000			0.0625000
$257$	−9.52645			−0.594244			−0.297122	−	0.954840i	$-0.596027\pi$
$257$	−9.52645			−0.594244			−0.297122	+	0.954840i	$0.596027\pi$
$258$	−0.159389	+	0.0427082i	−0.00992313	+	0.00265889i
$259$	−9.42732	−	12.3242i	−0.585785	−	0.765786i
$260$	−4.46724	+	2.90635i	−0.277046	+	0.180244i
$261$	4.35699	+	7.54652i	0.269691	+	0.467118i
$262$	−3.80894	−	1.02060i	−0.235317	−	0.0630530i
$263$	−11.5753	−	20.0490i	−0.713763	−	1.23627i	−0.963435	−	0.267943i	$-0.913656\pi$
$263$	−11.5753	−	20.0490i	−0.713763	−	1.23627i	0.249672	−	0.968330i	$-0.419677\pi$
$264$	−2.91730	+	5.05291i	−0.179547	+	0.310985i
$265$	9.29744	−	9.29744i	0.571137	−	0.571137i
$266$	−11.1705	−	8.59808i	−0.684907	−	0.527182i
$267$	−8.61332	−	2.30793i	−0.527126	−	0.141243i
$268$	−4.61993	−	1.23791i	−0.282207	−	0.0756171i
$269$		−	27.4873i		−	1.67593i	−0.545724	−	0.837965i	$-0.683745\pi$
$269$		−	27.4873i		−	1.67593i	0.545724	−	0.837965i	$-0.316255\pi$
$270$	1.28009	−	0.739062i	0.0779040	−	0.0449779i
$271$	19.7563	+	19.7563i	1.20011	+	1.20011i	0.974133	+	0.225973i	$0.0725562\pi$
$271$	19.7563	+	19.7563i	1.20011	+	1.20011i	0.225973	+	0.974133i	$0.427444\pi$
$272$	−6.94378			−0.421029
$273$	3.19031	−	8.99010i	0.193086	−	0.544106i
$274$	−2.85691			−0.172592
$275$	11.6144	+	11.6144i	0.700375	+	0.700375i
$276$	0.666449	−	0.384774i	0.0401155	−	0.0231607i
$277$			8.37932i			0.503465i	0.967797	+	0.251732i	$0.0810003\pi$
$277$			8.37932i			0.503465i	−0.967797	+	0.251732i	$0.919000\pi$
$278$	9.23162	+	2.47361i	0.553676	+	0.148357i
$279$	−0.379148	−	0.101593i	−0.0226990	−	0.00608218i
$280$	−1.49116	−	3.61530i	−0.0891137	−	0.216056i
$281$	−2.04772	+	2.04772i	−0.122156	+	0.122156i	−0.765542	−	0.643386i	$-0.777529\pi$
$281$	−2.04772	+	2.04772i	−0.122156	+	0.122156i	0.643386	+	0.765542i	$0.277529\pi$
$282$	−6.24471	+	10.8161i	−0.371867	+	0.644092i
$283$	0.449883	+	0.779221i	0.0267428	+	0.0463199i	0.879087	−	0.476661i	$-0.158153\pi$
$283$	0.449883	+	0.779221i	0.0267428	+	0.0463199i	−0.852344	+	0.522981i	$0.824820\pi$
$284$	−5.08439	−	1.36236i	−0.301703	−	0.0808411i
$285$	−3.93766	−	6.82024i	−0.233247	−	0.403996i
$286$	−4.35668	+	20.5809i	−0.257616	+	1.21697i
$287$	−17.2465	+	2.24423i	−1.01803	+	0.132473i
$288$	−0.965926	+	0.258819i	−0.0569177	+	0.0152511i
$289$	31.2161			1.83624
$290$	12.8803			0.756360
$291$	−0.852159	+	0.228335i	−0.0499545	+	0.0133853i
$292$	−2.39782	−	8.94879i	−0.140322	−	0.523688i
$293$	8.10572	−	30.2510i	0.473541	−	1.76728i	−0.153348	−	0.988172i	$-0.549006\pi$
$293$	8.10572	−	30.2510i	0.473541	−	1.76728i	0.626889	−	0.779108i	$-0.284328\pi$
$294$	6.05165	+	3.51817i	0.352939	+	0.205184i
$295$	−0.644793	−	1.11681i	−0.0375413	−	0.0650234i
$296$			5.86465i			0.340876i
$297$	1.51010	−	5.63579i	0.0876251	−	0.327021i
$298$	−9.04733	−	5.22348i	−0.524098	−	0.302588i
$299$	1.85488	−	2.06351i	0.107271	−	0.119336i
$300$			2.81515i			0.162533i
$301$	−0.166467	−	0.403597i	−0.00959498	−	0.0232630i
$302$	2.24508	−	3.88859i	0.129190	−	0.223763i
$303$	10.3647	+	5.98408i	0.595439	+	0.343777i
$304$	1.37897	+	5.14638i	0.0790892	+	0.295165i
$305$	−5.90223	−	5.90223i	−0.337960	−	0.337960i
$306$	6.70718	−	1.79718i	0.383424	−	0.102738i
$307$	6.31072	+	6.31072i	0.360172	+	0.360172i	0.863876	−	0.503704i	$-0.168030\pi$
$307$	6.31072	+	6.31072i	0.360172	+	0.360172i	−0.503704	+	0.863876i	$0.668030\pi$
$308$	−14.2529	−	5.92883i	−0.812137	−	0.337826i
$309$	11.0928	+	6.40446i	0.631050	+	0.364337i
$310$	−0.410262	+	0.410262i	−0.0233013	+	0.0233013i
$311$	−0.856069	+	1.48276i	−0.0485432	+	0.0840793i	−0.889276	−	0.457371i	$-0.848791\pi$
$311$	−0.856069	+	1.48276i	−0.0485432	+	0.0840793i	0.840733	+	0.541450i	$0.182125\pi$
$312$	−3.02223	+	1.96624i	−0.171100	+	0.111317i
$313$	−10.9749	+	6.33634i	−0.620336	+	0.358151i	−0.777000	−	0.629501i	$-0.783259\pi$
$313$	−10.9749	+	6.33634i	−0.620336	+	0.358151i	0.156664	+	0.987652i	$0.449926\pi$
$314$	3.80814	+	14.2122i	0.214906	+	0.802040i
$315$	2.37606	+	3.10617i	0.133876	+	0.175013i
$316$	6.86679	−	3.96454i	0.386287	−	0.223023i
$317$	−3.56867	+	13.3185i	−0.200436	+	0.748039i	0.790356	+	0.612648i	$0.209896\pi$
$317$	−3.56867	+	13.3185i	−0.200436	+	0.748039i	−0.990792	+	0.135391i	$0.956771\pi$
$318$	6.29002	−	6.29002i	0.352727	−	0.352727i
$319$	35.9511	−	35.9511i	2.01287	−	2.01287i
$320$	−0.382567	+	1.42776i	−0.0213861	+	0.0798141i
$321$	−2.30297	+	1.32962i	−0.128539	+	0.0742121i
$322$	1.23703	+	1.61715i	0.0689373	+	0.0901204i
$323$	−9.57525	−	35.7353i	−0.532781	−	1.98837i
$324$	0.866025	−	0.500000i	0.0481125	−	0.0277778i
$325$	3.14461	+	9.65076i	0.174432	+	0.535328i
$326$	11.4926	−	19.9058i	0.636516	−	1.10248i
$327$	−10.5998	+	10.5998i	−0.586171	+	0.586171i
$328$	5.69284	+	3.28676i	0.314335	+	0.181481i
$329$	−30.5096	−	12.6911i	−1.68205	−	0.699684i
$330$	−6.09827	−	6.09827i	−0.335699	−	0.335699i
$331$	−24.8601	+	6.66123i	−1.36643	+	0.366134i	−0.866174	−	0.499742i	$-0.833428\pi$
$331$	−24.8601	+	6.66123i	−1.36643	+	0.366134i	−0.500258	+	0.865876i	$0.666761\pi$
$332$	−9.29167	−	9.29167i	−0.509947	−	0.509947i
$333$	−1.51788	−	5.66482i	−0.0831795	−	0.310430i
$334$	0.736406	+	0.425164i	0.0402943	+	0.0232639i
$335$	3.53486	−	6.12256i	0.193130	−	0.334511i
$336$	−1.00882	−	2.44587i	−0.0550355	−	0.133433i
$337$			33.5630i			1.82829i	0.405383	+	0.914147i	$0.367138\pi$
$337$			33.5630i			1.82829i	−0.405383	+	0.914147i	$0.632862\pi$
$338$	−8.16432	+	10.1165i	−0.444081	+	0.550266i
$339$	−8.58738	−	4.95793i	−0.466403	−	0.269278i
$340$	2.65646	−	9.91405i	0.144067	−	0.537665i
$341$			2.29021i			0.124022i
$342$	−2.66396	−	4.61411i	−0.144050	−	0.249503i
$343$	−7.16432	+	17.0784i	−0.386837	+	0.922148i
$344$	−0.0427082	+	0.159389i	−0.00230267	+	0.00859368i
$345$	0.294404	+	1.09873i	0.0158502	+	0.0591536i
$346$	8.91843	−	2.38969i	0.479458	−	0.128470i
$347$	−29.5060			−1.58397			−0.791983	−	0.610544i	$-0.790951\pi$
$347$	−29.5060			−1.58397			−0.791983	+	0.610544i	$0.790951\pi$
$348$	8.71398			0.467118
$349$	18.0248	−	4.82973i	0.964844	−	0.258529i	0.258195	−	0.966093i	$-0.416872\pi$
$349$	18.0248	−	4.82973i	0.964844	−	0.258529i	0.706650	+	0.707564i	$0.250206\pi$
$350$	−7.38591	+	0.961105i	−0.394794	+	0.0513732i
$351$	2.41035	−	2.68146i	0.128655	−	0.143126i
$352$	2.91730	+	5.05291i	0.155492	+	0.269321i
$353$	−23.6244	−	6.33014i	−1.25740	−	0.336920i	−0.432210	−	0.901773i	$-0.642266\pi$
$353$	−23.6244	−	6.33014i	−1.25740	−	0.336920i	−0.825191	+	0.564854i	$0.808933\pi$
$354$	−0.436223	−	0.755561i	−0.0231850	−	0.0401576i
$355$	3.89024	−	6.73809i	0.206472	−	0.357621i
$356$	−6.30539	+	6.30539i	−0.334185	+	0.334185i
$357$	7.00501	+	16.9836i	0.370744	+	0.898867i
$358$	10.0860	+	2.70253i	0.533060	+	0.142833i
$359$	23.2070	+	6.21830i	1.22482	+	0.328189i	0.812560	−	0.582877i	$-0.198073\pi$
$359$	23.2070	+	6.21830i	1.22482	+	0.328189i	0.412259	+	0.911067i	$0.364740\pi$
$360$		−	1.47812i		−	0.0779040i
$361$	−8.12915	+	4.69337i	−0.427850	+	0.247019i
$362$	−0.856577	−	0.856577i	−0.0450207	−	0.0450207i
$363$	−23.0425			−1.20942
$364$	−6.19050	−	7.25794i	−0.324470	−	0.380420i
$365$	13.6940			0.716779
$366$	−3.99305	−	3.99305i	−0.208720	−	0.208720i
$367$	−6.11749	+	3.53194i	−0.319331	+	0.184366i	−0.651094	−	0.758997i	$-0.725690\pi$
$367$	−6.11749	+	3.53194i	−0.319331	+	0.184366i	0.331764	+	0.943363i	$0.392356\pi$
$368$		−	0.769549i		−	0.0401155i
$369$	−6.34954	−	1.70135i	−0.330544	−	0.0885690i
$370$	−8.37331	−	2.24362i	−0.435308	−	0.116640i
$371$	18.6501	+	14.3553i	0.968267	+	0.745288i
$372$	−0.277556	+	0.277556i	−0.0143906	+	0.0143906i
$373$	5.60451	−	9.70730i	0.290191	−	0.502625i	−0.683664	−	0.729797i	$-0.739615\pi$
$373$	5.60451	−	9.70730i	0.290191	−	0.502625i	0.973855	+	0.227172i	$0.0729479\pi$
$374$	−20.2571	−	35.0863i	−1.04747	−	1.81427i
$375$	−11.1581	−	2.98982i	−0.576204	−	0.154393i
$376$	6.24471	+	10.8161i	0.322046	+	0.557800i
$377$	29.8728	−	9.73379i	1.53853	−	0.501316i
$378$	1.60748	+	2.10143i	0.0826799	+	0.108086i
$379$	3.13887	−	0.841057i	0.161233	−	0.0432022i	−0.177300	−	0.984157i	$-0.556736\pi$
$379$	3.13887	−	0.841057i	0.161233	−	0.0432022i	0.338532	+	0.940955i	$0.390070\pi$
$380$	−7.87533			−0.403996
$381$	10.4103			0.533336
$382$	24.0361	−	6.44045i	1.22979	−	0.329522i
$383$	−1.53970	−	5.74625i	−0.0786752	−	0.293620i	0.915366	−	0.402622i	$-0.131901\pi$
$383$	−1.53970	−	5.74625i	−0.0786752	−	0.293620i	−0.994042	+	0.109002i	$0.965234\pi$
$384$	−0.258819	+	0.965926i	−0.0132078	+	0.0492922i
$385$	13.9176	−	18.0816i	0.709309	−	0.921523i
$386$	9.27123	+	16.0582i	0.471893	+	0.817343i
$387$		−	0.165012i		−	0.00838802i
$388$	−0.228335	+	0.852159i	−0.0115920	+	0.0432618i
$389$	−8.00851	−	4.62372i	−0.406048	−	0.234432i	0.283042	−	0.959107i	$-0.408656\pi$
$389$	−8.00851	−	4.62372i	−0.406048	−	0.234432i	−0.689090	+	0.724676i	$0.741990\pi$
$390$	−1.65111	−	5.06724i	−0.0836074	−	0.256590i
$391$			5.34358i			0.270236i
$392$	6.07265	−	3.48180i	0.306715	−	0.175857i
$393$	1.97165	−	3.41500i	0.0994567	−	0.172264i
$394$	0.842063	+	0.486165i	0.0424225	+	0.0244927i
$395$	3.03340	+	11.3208i	0.152627	+	0.569612i
$396$	−4.12568	−	4.12568i	−0.207323	−	0.207323i
$397$	9.82987	−	2.63391i	0.493347	−	0.132192i	−0.00356351	−	0.999994i	$-0.501134\pi$
$397$	9.82987	−	2.63391i	0.493347	−	0.132192i	0.496911	+	0.867802i	$0.334468\pi$
$398$	−0.828489	−	0.828489i	−0.0415284	−	0.0415284i
$399$	11.1962	−	8.56453i	0.560513	−	0.428763i
$400$	2.43799	+	1.40757i	0.121899	+	0.0703787i
$401$	−7.85252	+	7.85252i	−0.392136	+	0.392136i	−0.875448	−	0.483312i	$-0.839434\pi$
$401$	−7.85252	+	7.85252i	−0.392136	+	0.392136i	0.483312	+	0.875448i	$0.339434\pi$
$402$	2.39145	−	4.14211i	0.119275	−	0.206590i
$403$	−0.641465	+	1.26154i	−0.0319537	+	0.0628419i
$404$	10.3647	−	5.98408i	0.515665	−	0.297719i
$405$	0.382567	+	1.42776i	0.0190099	+	0.0709459i
$406$	2.97499	+	22.8623i	0.147646	+	1.13463i
$407$	−29.6336	+	17.1089i	−1.46888	+	0.848059i
$408$	1.79718	−	6.70718i	0.0889738	−	0.332055i
$409$	−9.15936	+	9.15936i	−0.452901	+	0.452901i	−0.896316	−	0.443415i	$-0.853767\pi$
$409$	−9.15936	+	9.15936i	−0.452901	+	0.452901i	0.443415	+	0.896316i	$0.353767\pi$
$410$	−6.87060	+	6.87060i	−0.339315	+	0.339315i
$411$	0.739423	−	2.75957i	0.0364731	−	0.136119i
$412$	11.0928	−	6.40446i	0.546505	−	0.315525i
$413$	1.83339	−	1.40244i	0.0902150	−	0.0690097i
$414$	0.199174	+	0.743327i	0.00978886	+	0.0365325i
$415$	16.8210	−	9.71158i	0.825708	−	0.476723i
$416$	0.191699	+	3.60045i	0.00939883	+	0.176527i
$417$	−4.77864	+	8.27684i	−0.234011	+	0.405319i
$418$	−21.9813	+	21.9813i	−1.07514	+	1.07514i
$419$	−19.5436	−	11.2835i	−0.954768	−	0.551236i	−0.0602092	−	0.998186i	$-0.519177\pi$
$419$	−19.5436	−	11.2835i	−0.954768	−	0.551236i	−0.894559	+	0.446950i	$0.852510\pi$
$420$	3.87805	−	0.504639i	0.189230	−	0.0246238i
$421$	−14.4017	−	14.4017i	−0.701895	−	0.701895i	0.262922	−	0.964817i	$-0.415314\pi$
$421$	−14.4017	−	14.4017i	−0.701895	−	0.701895i	−0.964817	+	0.262922i	$0.915314\pi$
$422$	16.2906	−	4.36505i	0.793014	−	0.212488i
$423$	−8.83135	−	8.83135i	−0.429395	−	0.429395i
$424$	−2.30231	−	8.59233i	−0.111810	−	0.417280i
$425$	−16.9289	−	9.77389i	−0.821171	−	0.474103i
$426$	2.63188	−	4.55854i	0.127515	−	0.220862i
$427$	9.11305	−	11.8395i	0.441011	−	0.572955i
$428$			2.65924i			0.128539i
$429$	−18.7520	−	9.53495i	−0.905355	−	0.460352i
$430$	−0.211230	−	0.121954i	−0.0101864	−	0.00588114i
$431$	−0.481562	+	1.79721i	−0.0231960	+	0.0865688i	−0.976554	−	0.215275i	$-0.930935\pi$
$431$	−0.481562	+	1.79721i	−0.0231960	+	0.0865688i	0.953358	+	0.301843i	$0.0976020\pi$
$432$		−	1.00000i		−	0.0481125i
$433$	−16.6576	−	28.8518i	−0.800514	−	1.38653i	−0.919279	−	0.393608i	$-0.871227\pi$
$433$	−16.6576	−	28.8518i	−0.800514	−	1.38653i	0.118765	−	0.992922i	$-0.462106\pi$
$434$	−0.822963	−	0.633446i	−0.0395035	−	0.0304064i
$435$	−3.33368	+	12.4415i	−0.159838	+	0.596522i
$436$	3.87980	+	14.4796i	0.185809	+	0.693447i
$437$	3.96039	−	1.06118i	0.189451	−	0.0507632i
$438$	9.26447			0.442673
$439$	24.3330			1.16135			0.580675	−	0.814135i	$-0.302789\pi$
$439$	24.3330			1.16135			0.580675	+	0.814135i	$0.302789\pi$
$440$	−8.33039	+	2.23212i	−0.397136	+	0.106412i
$441$	−4.96457	+	4.93488i	−0.236408	+	0.234994i
$442$	−1.33112	−	25.0008i	−0.0633148	−	1.18916i
$443$	15.5729	+	26.9730i	0.739890	+	1.28153i	0.952545	+	0.304399i	$0.0984556\pi$
$443$	15.5729	+	26.9730i	0.739890	+	1.28153i	−0.212655	+	0.977127i	$0.568211\pi$
$444$	−5.66482	−	1.51788i	−0.268841	−	0.0720356i
$445$	−6.59034	−	11.4148i	−0.312412	−	0.541113i
$446$	−0.126554	+	0.219197i	−0.00599248	+	0.0103793i
$447$	7.38712	−	7.38712i	0.349399	−	0.349399i
$448$	−2.62260	−	0.349274i	−0.123906	−	0.0165017i
$449$	−11.1005	−	2.97437i	−0.523866	−	0.140369i	−0.0128116	−	0.999918i	$-0.504078\pi$
$449$	−11.1005	−	2.97437i	−0.523866	−	0.140369i	−0.511054	+	0.859549i	$0.670745\pi$
$450$	−2.71922	−	0.728614i	−0.128185	−	0.0343472i
$451$			38.3539i			1.80601i
$452$	−8.58738	+	4.95793i	−0.403917	+	0.233201i
$453$	3.17502	+	3.17502i	0.149175	+	0.149175i
$454$	1.67037			0.0783942
$455$	12.7309	−	6.06189i	0.596832	−	0.284186i
$456$	−5.32792			−0.249503
$457$	−26.9904	−	26.9904i	−1.26256	−	1.26256i	−0.949848	−	0.312711i	$-0.898763\pi$
$457$	−26.9904	−	26.9904i	−1.26256	−	1.26256i	−0.312711	−	0.949848i	$-0.601237\pi$
$458$	23.2358	−	13.4152i	1.08574	−	0.626850i
$459$			6.94378i			0.324108i
$460$	1.09873	+	0.294404i	0.0512285	+	0.0137266i
$461$	−6.32045	−	1.69356i	−0.294373	−	0.0788770i	0.108610	−	0.994084i	$-0.465360\pi$
$461$	−6.32045	−	1.69356i	−0.294373	−	0.0788770i	−0.402983	+	0.915207i	$0.632027\pi$
$462$	9.41574	−	12.2328i	0.438060	−	0.569121i
$463$	−10.5716	+	10.5716i	−0.491304	+	0.491304i	−0.908717	−	0.417413i	$-0.862937\pi$
$463$	−10.5716	+	10.5716i	−0.491304	+	0.491304i	0.417413	+	0.908717i	$0.362937\pi$
$464$	4.35699	−	7.54652i	0.202268	−	0.350339i
$465$	−0.290099	−	0.502466i	−0.0134530	−	0.0233013i
$466$	16.2213	+	4.34648i	0.751436	+	0.201347i
$467$	0.763124	+	1.32177i	0.0353132	+	0.0611642i	0.883142	−	0.469106i	$-0.155424\pi$
$467$	0.763124	+	1.32177i	0.0353132	+	0.0611642i	−0.847829	+	0.530270i	$0.822090\pi$
$468$	−1.11703	−	3.42815i	−0.0516349	−	0.158466i
$469$	11.6838	+	4.86015i	0.539509	+	0.224421i
$470$	−17.8319	+	4.77803i	−0.822523	+	0.220394i
$471$	−14.7135			−0.677964
$472$	−0.872447			−0.0401576
$473$	−0.929971	+	0.249185i	−0.0427601	+	0.0114575i
$474$	2.05220	+	7.65891i	0.0942606	+	0.351785i
$475$	−3.88200	+	14.4878i	−0.178118	+	0.664746i
$476$	18.2107	+	2.42528i	0.834688	+	0.111163i
$477$	4.44772	+	7.70367i	0.203647	+	0.352727i
$478$		−	2.35605i		−	0.107763i
$479$	−0.905926	+	3.38096i	−0.0413928	+	0.154480i	−0.983529	−	0.180750i	$-0.942147\pi$
$479$	−0.905926	+	3.38096i	−0.0413928	+	0.154480i	0.942136	+	0.335230i	$0.108814\pi$
$480$	−1.28009	−	0.739062i	−0.0584280	−	0.0337334i
$481$	−21.1154	+	1.12425i	−0.962780	+	0.0512614i
$482$			14.8563i			0.676688i
$483$	−1.88222	+	0.776334i	−0.0856438	+	0.0353244i
$484$	−11.5212	+	19.9554i	−0.523693	+	0.907063i
$485$	−1.12932	−	0.652016i	−0.0512800	−	0.0296065i
$486$	0.258819	+	0.965926i	0.0117403	+	0.0438153i
$487$	3.09123	+	3.09123i	0.140077	+	0.140077i	0.773668	−	0.633591i	$-0.218420\pi$
$487$	3.09123	+	3.09123i	0.140077	+	0.140077i	−0.633591	+	0.773668i	$0.718420\pi$
$488$	−5.45461	+	1.46156i	−0.246919	+	0.0661616i
$489$	16.2530	+	16.2530i	0.734985	+	0.734985i
$490$	2.64797	+	10.0023i	0.119623	+	0.451858i
$491$	0.333214	+	0.192381i	0.0150377	+	0.00868203i	0.507500	−	0.861652i	$-0.330570\pi$
$491$	0.333214	+	0.192381i	0.0150377	+	0.00868203i	−0.492462	+	0.870334i	$0.663903\pi$
$492$	−4.64819	+	4.64819i	−0.209556	+	0.209556i
$493$	−30.2540	+	52.4014i	−1.36257	+	2.36004i
$494$	−18.2649	+	5.95146i	−0.821778	+	0.267769i
$495$	7.46883	−	4.31213i	0.335699	−	0.193816i
$496$	0.101593	+	0.379148i	0.00456164	+	0.0170243i
$497$	12.8585	+	5.34876i	0.576781	+	0.239925i
$498$	11.3799	−	6.57021i	0.509947	−	0.294418i
$499$	−2.19722	+	8.20014i	−0.0983612	+	0.367089i	−0.997508	−	0.0705590i	$-0.977522\pi$
$499$	−2.19722	+	8.20014i	−0.0983612	+	0.367089i	0.899146	+	0.437648i	$0.144188\pi$
$500$	−8.16833	+	8.16833i	−0.365299	+	0.365299i
$501$	−0.601273	+	0.601273i	−0.0268629	+	0.0268629i
$502$	−2.95781	+	11.0387i	−0.132014	+	0.492682i
$503$	−6.42502	+	3.70948i	−0.286477	+	0.165398i	−0.636352	−	0.771399i	$-0.719557\pi$
$503$	−6.42502	+	3.70948i	−0.286477	+	0.165398i	0.349875	+	0.936796i	$0.386224\pi$
$504$	2.62363	−	0.341405i	0.116866	−	0.0152074i
$505$	4.57862	+	17.0877i	0.203746	+	0.760391i
$506$	3.88846	−	2.24500i	0.172863	−	0.0998025i
$507$	−7.65872	−	10.5045i	−0.340136	−	0.466520i
$508$	5.20515	−	9.01558i	0.230941	−	0.400002i
$509$	8.68662	−	8.68662i	0.385028	−	0.385028i	−0.487882	−	0.872910i	$-0.662230\pi$
$509$	8.68662	−	8.68662i	0.385028	−	0.385028i	0.872910	+	0.487882i	$0.162230\pi$
$510$	8.88869	+	5.13189i	0.393598	+	0.227244i
$511$	3.16293	+	24.3066i	0.139920	+	1.07526i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	5.14638	−	1.37897i	0.227218	−	0.0608829i
$514$	−6.73622	−	6.73622i	−0.297122	−	0.297122i
$515$	4.90026	+	18.2880i	0.215931	+	0.805867i
$516$	−0.142904	−	0.0825059i	−0.00629101	−	0.00363212i
$517$	−36.4353	+	63.1078i	−1.60242	+	2.77548i
$518$	2.04837	−	15.3806i	0.0900003	−	0.675785i
$519$			9.23304i			0.405285i
$520$	−5.21391	−	1.10371i	−0.228645	−	0.0484010i
$521$	−9.80499	−	5.66091i	−0.429564	−	0.248009i	0.269597	−	0.962973i	$-0.413110\pi$
$521$	−9.80499	−	5.66091i	−0.429564	−	0.248009i	−0.699161	+	0.714964i	$0.746443\pi$
$522$	−2.25534	+	8.41705i	−0.0987137	+	0.368404i
$523$		−	0.701950i		−	0.0306941i	−0.999882	−	0.0153471i	$-0.995115\pi$
$523$		−	0.701950i		−	0.0306941i	0.999882	−	0.0153471i	$-0.00488531\pi$
$524$	−1.97165	−	3.41500i	−0.0861320	−	0.149185i
$525$	0.983259	−	7.38299i	0.0429129	−	0.322220i
$526$	5.99181	−	22.3617i	0.261255	−	0.975018i
$527$	−0.705436	−	2.63272i	−0.0307293	−	0.114683i
$528$	−5.63579	+	1.51010i	−0.245266	+	0.0657189i
$529$	22.4078			0.974252
$530$	13.1486			0.571137
$531$	0.842719	−	0.225806i	0.0365709	−	0.00979914i
$532$	−1.81898	−	13.9785i	−0.0788627	−	0.606045i
$533$	−10.7425	+	21.1269i	−0.465310	+	0.915106i
$534$	−4.45858	−	7.72249i	−0.192942	−	0.334185i
$535$	−3.79675	−	1.01734i	−0.164148	−	0.0439833i
$536$	−2.39145	−	4.14211i	−0.103295	−	0.178912i
$537$	−5.22088	+	9.04284i	−0.225298	+	0.390227i
$538$	19.4365	−	19.4365i	0.837965	−	0.837965i
$539$	35.3089	+	20.5271i	1.52086	+	0.884165i
$540$	1.42776	+	0.382567i	0.0614409	+	0.0164631i
$541$	7.76639	+	2.08100i	0.333903	+	0.0894691i	0.421875	−	0.906654i	$-0.361372\pi$
$541$	7.76639	+	2.08100i	0.333903	+	0.0894691i	−0.0879721	+	0.996123i	$0.528039\pi$
$542$			27.9396i			1.20011i
$543$	1.04909	−	0.605691i	0.0450207	−	0.0259927i
$544$	−4.91000	−	4.91000i	−0.210514	−	0.210514i
$545$	−22.1577			−0.949130
$546$	8.61285	−	4.10107i	0.368596	−	0.175510i
$547$	13.2526			0.566641			0.283321	−	0.959025i	$-0.408564\pi$
$547$	13.2526			0.566641			0.283321	+	0.959025i	$0.408564\pi$
$548$	−2.02014	−	2.02014i	−0.0862962	−	0.0862962i
$549$	4.89047	−	2.82351i	0.208720	−	0.120505i
$550$			16.4252i			0.700375i
$551$	44.8454	+	12.0163i	1.91048	+	0.511911i
$552$	0.743327	+	0.199174i	0.0316381	+	0.00847740i
$553$	−19.3935	+	7.99900i	−0.824696	+	0.340152i
$554$	−5.92508	+	5.92508i	−0.251732	+	0.251732i
$555$	4.33434	−	7.50731i	0.183983	−	0.318667i
$556$	4.77864	+	8.27684i	0.202659	+	0.351016i
$557$	−8.16213	−	2.18704i	−0.345841	−	0.0926677i	0.0817176	−	0.996656i	$-0.473959\pi$
$557$	−8.16213	−	2.18704i	−0.345841	−	0.0926677i	−0.427558	+	0.903988i	$0.640626\pi$
$558$	−0.196262	−	0.339935i	−0.00830842	−	0.0143906i
$559$	−0.582060	−	0.123214i	−0.0246185	−	0.00521139i
$560$	1.50200	−	3.61081i	0.0634710	−	0.152585i
$561$	39.1337	−	10.4858i	1.65222	−	0.442712i
$562$	−2.89591			−0.122156
$563$	−12.1773			−0.513214			−0.256607	−	0.966516i	$-0.582605\pi$
$563$	−12.1773			−0.513214			−0.256607	+	0.966516i	$0.582605\pi$
$564$	−12.0638	+	3.23250i	−0.507980	+	0.136113i
$565$	−3.79348	−	14.1574i	−0.159593	−	0.595608i
$566$	−0.232877	+	0.869108i	−0.00978854	+	0.0365313i
$567$	−2.44587	+	1.00882i	−0.102717	+	0.0423663i
$568$	−2.63188	−	4.55854i	−0.110431	−	0.191272i
$569$		−	17.9156i		−	0.751060i	−0.926810	−	0.375530i	$-0.877461\pi$
$569$		−	17.9156i		−	0.751060i	0.926810	−	0.375530i	$-0.122539\pi$
$570$	2.03829	−	7.60698i	0.0853744	−	0.318622i
$571$	32.2814	+	18.6377i	1.35093	+	0.779962i	0.988380	−	0.152001i	$-0.0485716\pi$
$571$	32.2814	+	18.6377i	1.35093	+	0.779962i	0.362554	+	0.931963i	$0.381905\pi$
$572$	−17.6335	+	11.4722i	−0.737294	+	0.479678i
$573$			24.8840i			1.03954i
$574$	−13.7820	−	10.6082i	−0.575251	−	0.442778i
$575$	1.08320	−	1.87615i	0.0451724	−	0.0782409i
$576$	−0.866025	−	0.500000i	−0.0360844	−	0.0208333i
$577$	0.997816	+	3.72390i	0.0415396	+	0.155028i	0.983580	−	0.180470i	$-0.0577620\pi$
$577$	0.997816	+	3.72390i	0.0415396	+	0.155028i	−0.942041	+	0.335498i	$0.891095\pi$
$578$	22.0731	+	22.0731i	0.918121	+	0.918121i
$579$	−17.9106	+	4.79914i	−0.744341	+	0.199446i
$580$	9.10778	+	9.10778i	0.378180	+	0.378180i
$581$	21.1230	+	27.6136i	0.876328	+	1.14561i
$582$	−0.764025	−	0.441110i	−0.0316699	−	0.0182846i
$583$	36.6997	−	36.6997i	1.51995	−	1.51995i
$584$	4.63223	−	8.02326i	0.191683	−	0.332005i
$585$	5.32192	−	0.283355i	0.220034	−	0.0117153i
$586$	27.1223	−	15.6591i	1.12041	−	0.646870i
$587$	−8.69926	−	32.4661i	−0.359057	−	1.34002i	−0.875302	−	0.483577i	$-0.839337\pi$
$587$	−8.69926	−	32.4661i	−0.359057	−	1.34002i	0.516245	−	0.856441i	$-0.327329\pi$
$588$	1.79144	+	6.76689i	0.0738778	+	0.279062i
$589$	−1.81115	+	1.04567i	−0.0746270	+	0.0430859i
$590$	0.333769	−	1.24564i	0.0137411	−	0.0512823i
$591$	−0.687542	+	0.687542i	−0.0282817	+	0.0282817i
$592$	−4.14694	+	4.14694i	−0.170438	+	0.170438i
$593$	−12.4245	+	46.3688i	−0.510212	+	1.90414i	−0.0920820	+	0.995751i	$0.529352\pi$
$593$	−12.4245	+	46.3688i	−0.510212	+	1.90414i	−0.418130	+	0.908387i	$0.637314\pi$
$594$	5.05291	−	2.91730i	0.207323	−	0.119698i
$595$	−10.4295	+	25.0727i	−0.427570	+	1.02788i
$596$	−2.70387	−	10.0910i	−0.110755	−	0.413343i
$597$	1.01469	−	0.585830i	0.0415284	−	0.0239764i
$598$	2.77072	−	0.147522i	0.113303	−	0.00603262i
$599$	8.59552	−	14.8879i	0.351204	−	0.608302i	−0.635257	−	0.772301i	$-0.719106\pi$
$599$	8.59552	−	14.8879i	0.351204	−	0.608302i	0.986461	+	0.163998i	$0.0524392\pi$
$600$	−1.99061	+	1.99061i	−0.0812663	+	0.0812663i
$601$	8.13421	+	4.69629i	0.331801	+	0.191566i	0.656641	−	0.754204i	$-0.271977\pi$
$601$	8.13421	+	4.69629i	0.331801	+	0.191566i	−0.324839	+	0.945769i	$0.605310\pi$
$602$	0.167677	−	0.403096i	0.00683399	−	0.0164290i
$603$	3.38202	+	3.38202i	0.137727	+	0.137727i
$604$	4.33716	−	1.16214i	0.176476	−	0.0472867i
$605$	−24.0838	−	24.0838i	−0.979147	−	0.979147i
$606$	3.09759	+	11.5604i	0.125831	+	0.469608i
$607$	−6.86013	−	3.96070i	−0.278444	−	0.160760i	0.354275	−	0.935141i	$-0.384728\pi$
$607$	−6.86013	−	3.96070i	−0.278444	−	0.160760i	−0.632719	+	0.774382i	$0.718061\pi$
$608$	−2.66396	+	4.61411i	−0.108038	+	0.187127i
$609$	−22.8532	−	3.04357i	−0.926060	−	0.123332i
$610$		−	8.34701i		−	0.337960i
$611$	−37.7459	+	24.5572i	−1.52704	+	0.993478i
$612$	6.01349	+	3.47189i	0.243081	+	0.140343i
$613$	−5.73019	+	21.3854i	−0.231440	+	0.863747i	0.748281	+	0.663382i	$0.230880\pi$
$613$	−5.73019	+	21.3854i	−0.231440	+	0.863747i	−0.979721	+	0.200365i	$0.935787\pi$
$614$			8.92471i			0.360172i
$615$	−4.85825	−	8.41473i	−0.195903	−	0.339315i
$616$	−5.88604	−	14.2707i	−0.237155	−	0.574982i
$617$	12.1595	−	45.3797i	0.489521	−	1.82692i	−0.0692532	−	0.997599i	$-0.522062\pi$
$617$	12.1595	−	45.3797i	0.489521	−	1.82692i	0.558775	−	0.829320i	$-0.311272\pi$
$618$	3.31519	+	12.3725i	0.133357	+	0.497693i
$619$	−25.2615	+	6.76879i	−1.01534	+	0.272061i	−0.727861	−	0.685725i	$-0.759485\pi$
$619$	−25.2615	+	6.76879i	−1.01534	+	0.272061i	−0.287483	+	0.957786i	$0.592819\pi$
$620$	−0.580198			−0.0233013
$621$	−0.769549			−0.0308809
$622$	−1.65380	+	0.443134i	−0.0663113	+	0.0177681i
$623$	18.7388	−	14.3342i	0.750754	−	0.574286i
$624$	−3.52738	−	0.746698i	−0.141208	−	0.0298919i
$625$	−1.49960	−	2.59739i	−0.0599840	−	0.103895i
$626$	−12.2409	−	3.27993i	−0.489244	−	0.131092i
$627$	−15.5431	−	26.9215i	−0.620733	−	1.07514i
$628$	−7.35677	+	12.7423i	−0.293567	+	0.508473i
$629$	28.7954	−	28.7954i	1.14815	−	1.14815i
$630$	−0.516271	+	3.87652i	−0.0205687	+	0.154444i
$631$	−30.2532	−	8.10633i	−1.20436	−	0.322708i	−0.399814	−	0.916596i	$-0.630925\pi$
$631$	−30.2532	−	8.10633i	−1.20436	−	0.322708i	−0.804547	+	0.593888i	$0.797592\pi$
$632$	7.65891	+	2.05220i	0.304655	+	0.0816320i
$633$			16.8653i			0.670334i
$634$	−11.9410	+	6.89414i	−0.474238	+	0.273801i
$635$	10.8808	+	10.8808i	0.431790	+	0.431790i
$636$	8.89544			0.352727
$637$	13.7002	+	21.1968i	0.542820	+	0.839849i
$638$	50.8425			2.01287
$639$	3.72203	+	3.72203i	0.147241	+	0.147241i
$640$	−1.28009	+	0.739062i	−0.0506001	+	0.0292140i
$641$			25.7914i			1.01870i	0.860560	+	0.509349i	$0.170114\pi$
$641$			25.7914i			1.01870i	−0.860560	+	0.509349i	$0.829886\pi$
$642$	−2.56863	−	0.688262i	−0.101376	−	0.0271635i
$643$	−17.7658	−	4.76034i	−0.700616	−	0.187730i	−0.109110	−	0.994030i	$-0.534800\pi$
$643$	−17.7658	−	4.76034i	−0.700616	−	0.187730i	−0.591507	+	0.806300i	$0.701467\pi$
$644$	−0.268784	+	2.01821i	−0.0105916	+	0.0795288i
$645$	0.172469	−	0.172469i	0.00679096	−	0.00679096i
$646$	18.4980	−	32.0394i	0.727793	−	1.26057i
$647$	1.85249	+	3.20861i	0.0728289	+	0.126143i	0.900140	−	0.435601i	$-0.143464\pi$
$647$	1.85249	+	3.20861i	0.0728289	+	0.126143i	−0.827311	+	0.561744i	$0.810131\pi$
$648$	0.965926	+	0.258819i	0.0379452	+	0.0101674i
$649$	−2.54519	−	4.40839i	−0.0999073	−	0.173045i
$650$	−4.60054	+	9.04769i	−0.180448	+	0.354880i
$651$	0.824860	−	0.630974i	0.0323288	−	0.0247298i
$652$	22.2020	−	5.94900i	0.869497	−	0.232981i
$653$	−12.1069			−0.473781			−0.236891	−	0.971536i	$-0.576128\pi$
$653$	−12.1069			−0.473781			−0.236891	+	0.971536i	$0.576128\pi$
$654$	−14.9904			−0.586171
$655$	5.63009	−	1.50858i	0.219986	−	0.0589450i
$656$	1.70135	+	6.34954i	0.0664267	+	0.247908i
$657$	−2.39782	+	8.94879i	−0.0935479	+	0.349125i
$658$	−12.5995	−	30.5475i	−0.491181	−	1.19087i
$659$	6.59589	+	11.4244i	0.256939	+	0.445032i	0.965420	−	0.260698i	$-0.0839526\pi$
$659$	6.59589	+	11.4244i	0.256939	+	0.445032i	−0.708481	+	0.705730i	$0.750619\pi$
$660$		−	8.62426i		−	0.335699i
$661$	3.26954	−	12.2021i	0.127170	−	0.474606i	−0.872737	−	0.488190i	$-0.837657\pi$
$661$	3.26954	−	12.2021i	0.127170	−	0.474606i	0.999908	+	0.0135839i	$0.00432402\pi$
$662$	−22.2889	−	12.8685i	−0.866283	−	0.500149i
$663$	24.4934	+	5.18491i	0.951244	+	0.201365i
$664$		−	13.1404i		−	0.509947i
$665$	20.6538	+	2.75065i	0.800920	+	0.106666i
$666$	2.93233	−	5.07894i	0.113625	−	0.196805i
$667$	−5.80742	−	3.35291i	−0.224864	−	0.129825i
$668$	0.220081	+	0.821354i	0.00851519	+	0.0317791i
$669$	−0.178974	−	0.178974i	−0.00691952	−	0.00691952i
$670$	6.82883	−	1.82978i	0.263821	−	0.0706905i
$671$	−23.2978	−	23.2978i	−0.899403	−	0.899403i
$672$	1.01615	−	2.44283i	0.0391989	−	0.0942344i
$673$	33.2503	+	19.1971i	1.28170	+	0.739993i	0.977160	−	0.212505i	$-0.0681623\pi$
$673$	33.2503	+	19.1971i	1.28170	+	0.739993i	0.304545	+	0.952498i	$0.401496\pi$
$674$	−23.7326	+	23.7326i	−0.914147	+	0.914147i
$675$	1.40757	−	2.43799i	0.0541775	−	0.0938383i
$676$	−12.9265	+	1.38041i	−0.497173	+	0.0530926i
$677$	−30.8327	+	17.8013i	−1.18500	+	0.684158i	−0.957165	−	0.289543i	$-0.906497\pi$
$677$	−30.8327	+	17.8013i	−1.18500	+	0.684158i	−0.227831	+	0.973701i	$0.573163\pi$
$678$	−2.56641	−	9.57798i	−0.0985625	−	0.367840i
$679$	0.896469	−	2.15512i	0.0344033	−	0.0827058i
$680$	8.88869	−	5.13189i	0.340866	−	0.196799i
$681$	−0.432323	+	1.61345i	−0.0165666	+	0.0618276i
$682$	−1.61943	+	1.61943i	−0.0620110	+	0.0620110i
$683$	11.8562	−	11.8562i	0.453665	−	0.453665i	−0.442904	−	0.896569i	$-0.646052\pi$
$683$	11.8562	−	11.8562i	0.453665	−	0.453665i	0.896569	+	0.442904i	$0.146052\pi$
$684$	1.37897	−	5.14638i	0.0527261	−	0.196777i
$685$	3.65712	−	2.11144i	0.139731	−	0.0806738i
$686$	−17.1422	+	7.01033i	−0.654493	+	0.267655i
$687$	6.94421	+	25.9161i	0.264938	+	0.988763i
$688$	−0.142904	+	0.0825059i	−0.00544818	+	0.00314551i
$689$	30.4949	−	9.93649i	1.16176	−	0.378550i
$690$	−0.568744	+	0.985094i	−0.0216517	+	0.0375019i
$691$	1.02361	−	1.02361i	0.0389398	−	0.0389398i	−0.687369	−	0.726309i	$-0.741234\pi$
$691$	1.02361	−	1.02361i	0.0389398	−	0.0389398i	0.726309	+	0.687369i	$0.241234\pi$
$692$	7.99605	+	4.61652i	0.303964	+	0.175494i
$693$	9.37900	+	12.2610i	0.356279	+	0.465756i
$694$	−20.8639	−	20.8639i	−0.791983	−	0.791983i
$695$	−13.6455	+	3.65630i	−0.517603	+	0.138691i
$696$	6.16171	+	6.16171i	0.233559	+	0.233559i
$697$	−11.8138	−	44.0898i	−0.447481	−	1.67002i
$698$	16.1606	+	9.33031i	0.611687	+	0.353158i
$699$	−8.39675	+	14.5436i	−0.317594	+	0.550089i
$700$	−5.90223	−	4.54302i	−0.223083	−	0.171710i
$701$		−	22.7118i		−	0.857812i	−0.903349	−	0.428906i	$-0.858899\pi$
$701$		−	22.7118i		−	0.857812i	0.903349	−	0.428906i	$-0.141101\pi$
$702$	3.60045	−	0.191699i	0.135890	−	0.00723522i
$703$	−27.0602	−	15.6232i	−1.02059	−	0.589240i
$704$	−1.51010	+	5.63579i	−0.0569142	+	0.212407i
$705$		−	18.4609i		−	0.695278i
$706$	−12.2289	−	21.1811i	−0.460241	−	0.797160i
$707$	−29.2726	+	12.0737i	−1.10091	+	0.454078i
$708$	0.225806	−	0.842719i	0.00848630	−	0.0316713i
$709$	5.70253	+	21.2821i	0.214163	+	0.799268i	0.986459	+	0.164005i	$0.0524414\pi$
$709$	5.70253	+	21.2821i	0.214163	+	0.799268i	−0.772296	+	0.635263i	$0.780892\pi$
$710$	7.51537	−	2.01374i	0.282047	−	0.0755742i
$711$	−7.92908			−0.297364
$712$	−8.91716			−0.334185
$713$	0.291773	−	0.0781804i	0.0109270	−	0.00292788i
$714$	−7.05593	+	16.9625i	−0.264062	+	0.634806i
$715$	−9.63358	−	29.5653i	−0.360275	−	1.10568i
$716$	5.22088	+	9.04284i	0.195114	+	0.337947i
$717$	2.27577	+	0.609791i	0.0849902	+	0.0227731i
$718$	12.0128	+	20.8068i	0.448315	+	0.776504i
$719$	11.2731	−	19.5257i	0.420417	−	0.728184i	−0.575563	−	0.817758i	$-0.695217\pi$
$719$	11.2731	−	19.5257i	0.420417	−	0.728184i	0.995980	+	0.0895733i	$0.0285503\pi$
$720$	1.04519	−	1.04519i	0.0389520	−	0.0389520i
$721$	−31.3290	+	12.9219i	−1.16675	+	0.481235i
$722$	−9.06689	−	2.42947i	−0.337435	−	0.0904154i
$723$	−14.3501	−	3.84511i	−0.533687	−	0.143001i
$724$		−	1.21138i		−	0.0450207i
$725$	21.2446	−	12.2656i	0.789004	−	0.455532i
$726$	−16.2935	−	16.2935i	−0.604709	−	0.604709i
$727$	−22.2011			−0.823394			−0.411697	−	0.911321i	$-0.635064\pi$
$727$	−22.2011			−0.823394			−0.411697	+	0.911321i	$0.635064\pi$
$728$	0.754796	−	9.50948i	0.0279746	−	0.352445i
$729$	−1.00000			−0.0370370
$730$	9.68315	+	9.68315i	0.358389	+	0.358389i
$731$	0.992297	−	0.572903i	0.0367014	−	0.0211896i
$732$		−	5.64703i		−	0.208720i
$733$	−22.8069	−	6.11108i	−0.842390	−	0.225718i	−0.188279	−	0.982116i	$-0.560291\pi$
$733$	−22.8069	−	6.11108i	−0.842390	−	0.225718i	−0.654112	+	0.756398i	$0.726957\pi$
$734$	−6.82318	−	1.82827i	−0.251848	−	0.0674825i
$735$	−10.3468	−	0.0310413i	−0.381648	−	0.00114498i
$736$	0.544153	−	0.544153i	0.0200577	−	0.0200577i
$737$	13.9531	−	24.1676i	0.513971	−	0.890223i
$738$	−3.28676	−	5.69284i	−0.120987	−	0.209556i
$739$	24.1819	+	6.47951i	0.889545	+	0.238353i	0.674521	−	0.738256i	$-0.264350\pi$
$739$	24.1819	+	6.47951i	0.889545	+	0.238353i	0.215024	+	0.976609i	$0.431017\pi$
$740$	−4.33434	−	7.50731i	−0.159334	−	0.275974i
$741$	−1.02136	−	19.1829i	−0.0375205	−	0.704702i
$742$	3.03694	+	23.3383i	0.111490	+	0.856778i
$743$	−13.5455	+	3.62950i	−0.496936	+	0.133154i	−0.498578	−	0.866845i	$-0.666144\pi$
$743$	−13.5455	+	3.62950i	−0.496936	+	0.133154i	0.00164161	+	0.999999i	$0.499477\pi$
$744$	−0.392523			−0.0143906
$745$	15.4419			0.565748
$746$	10.8271	−	2.90111i	0.396408	−	0.106217i
$747$	3.40099	+	12.6927i	0.124436	+	0.464400i
$748$	10.4858	−	39.1337i	0.383400	−	1.43087i
$749$	0.928804	−	6.97411i	0.0339378	−	0.254828i
$750$	−5.77588	−	10.0041i	−0.210905	−	0.365299i
$751$		−	32.1160i		−	1.17193i	−0.810337	−	0.585964i	$-0.800716\pi$
$751$		−	32.1160i		−	1.17193i	0.810337	−	0.585964i	$-0.199284\pi$
$752$	−3.23250	+	12.0638i	−0.117877	+	0.439923i
$753$	−9.89703	−	5.71406i	−0.360668	−	0.208232i
$754$	28.0061	+	14.2405i	1.01992	+	0.518607i
$755$			6.63701i			0.241545i
$756$	−0.349274	+	2.62260i	−0.0127030	+	0.0953829i
$757$	1.29840	−	2.24889i	0.0471910	−	0.0817372i	−0.841465	−	0.540312i	$-0.818306\pi$
$757$	1.29840	−	2.24889i	0.0471910	−	0.0817372i	0.888656	+	0.458574i	$0.151640\pi$
$758$	2.81423	+	1.62480i	0.102218	+	0.0590153i
$759$	1.16210	+	4.33701i	0.0421815	+	0.157424i
$760$	−5.56870	−	5.56870i	−0.201998	−	0.201998i
$761$	−13.9619	+	3.74108i	−0.506118	+	0.135614i	−0.502838	−	0.864381i	$-0.667711\pi$
$761$	−13.9619	+	3.74108i	−0.506118	+	0.135614i	−0.00328001	+	0.999995i	$0.501044\pi$
$762$	7.36119	+	7.36119i	0.266668	+	0.266668i
$763$	−5.11779	−	39.3293i	−0.185276	−	1.42382i
$764$	21.5502	+	12.4420i	0.779658	+	0.450136i
$765$	−7.25758	+	7.25758i	−0.262399	+	0.262399i
$766$	2.97448	−	5.15195i	0.107472	−	0.186148i
$767$	−0.167247	−	3.14120i	−0.00603895	−	0.113422i
$768$	−0.866025	+	0.500000i	−0.0312500	+	0.0180422i
$769$	−5.20930	−	19.4414i	−0.187852	−	0.701074i	−0.994002	−	0.109363i	$-0.965119\pi$
$769$	−5.20930	−	19.4414i	−0.187852	−	0.701074i	0.806150	−	0.591712i	$-0.201548\pi$
$770$	22.6269	−	2.94436i	0.815416	−	0.106107i
$771$	8.25015	−	4.76323i	0.297122	−	0.171543i
$772$	−4.79914	+	17.9106i	−0.172725	+	0.644618i
$773$	19.0927	−	19.0927i	0.686718	−	0.686718i	−0.274787	−	0.961505i	$-0.588607\pi$
$773$	19.0927	−	19.0927i	0.686718	−	0.686718i	0.961505	+	0.274787i	$0.0886073\pi$
$774$	0.116681	−	0.116681i	0.00419401	−	0.00419401i
$775$	−0.285998	+	1.06736i	−0.0102733	+	0.0383407i
$776$	−0.764025	+	0.441110i	−0.0274269	+	0.0158349i
$777$	14.3264	+	5.95937i	0.513956	+	0.213791i
$778$	−2.39341	−	8.93234i	−0.0858080	−	0.320240i
$779$	−30.3310	+	17.5116i	−1.08672	+	0.627419i
$780$	2.41556	−	4.75059i	0.0864911	−	0.170098i
$781$	15.3559	−	26.5972i	0.549478	−	0.951724i
$782$	−3.77848	+	3.77848i	−0.135118	+	0.135118i
$783$	−7.54652	−	4.35699i	−0.269691	−	0.155706i
$784$	6.75602	+	1.83201i	0.241286	+	0.0654289i
$785$	−15.3785	−	15.3785i	−0.548881	−	0.548881i
$786$	3.80894	−	1.02060i	0.135860	−	0.0364037i
$787$	21.1051	+	21.1051i	0.752315	+	0.752315i	0.974911	−	0.222596i	$-0.0714529\pi$
$787$	21.1051	+	21.1051i	0.752315	+	0.752315i	−0.222596	+	0.974911i	$0.571453\pi$
$788$	0.251658	+	0.939199i	0.00896493	+	0.0334576i
$789$	20.0490	+	11.5753i	0.713763	+	0.412091i
$790$	−5.86009	+	10.1500i	−0.208492	+	0.361120i
$791$	24.2529	−	10.0033i	0.862334	−	0.355676i
$792$		−	5.83459i		−	0.207323i
$793$	−6.30791	−	19.3589i	−0.224001	−	0.687454i
$794$	8.81322	+	5.08832i	0.312770	+	0.180578i
$795$	−3.40310	+	12.7005i	−0.120695	+	0.450442i
$796$		−	1.17166i		−	0.0415284i
$797$	8.82062	+	15.2778i	0.312442	+	0.541166i	0.978891	−	0.204385i	$-0.0655196\pi$
$797$	8.82062	+	15.2778i	0.312442	+	0.541166i	−0.666448	+	0.745551i	$0.732186\pi$
$798$	13.9730	+	1.86091i	0.494638	+	0.0658753i
$799$	22.4458	−	83.7687i	0.794074	−	2.96352i
$800$	0.728614	+	2.71922i	0.0257604	+	0.0961391i
$801$	8.61332	−	2.30793i	0.304337	−	0.0815468i
$802$	−11.1051			−0.392136
$803$	54.0544			1.90754
$804$	4.61993	−	1.23791i	0.162932	−	0.0436576i
$805$	−2.77870	−	1.15586i	−0.0979362	−	0.0407387i
$806$	−1.34563	+	0.438461i	−0.0473978	+	0.0154441i
$807$	13.7436	+	23.8047i	0.483799	+	0.837965i
$808$	11.5604	+	3.09759i	0.406692	+	0.108973i
$809$	5.98782	+	10.3712i	0.210520	+	0.364632i	0.951878	−	0.306479i	$-0.0991508\pi$
$809$	5.98782	+	10.3712i	0.210520	+	0.364632i	−0.741357	+	0.671111i	$0.765817\pi$
$810$	−0.739062	+	1.28009i	−0.0259680	+	0.0449779i
$811$	−20.9279	+	20.9279i	−0.734877	+	0.734877i	−0.971582	−	0.236704i	$-0.923933\pi$
$811$	−20.9279	+	20.9279i	−0.734877	+	0.734877i	0.236704	+	0.971582i	$0.423933\pi$
$812$	−14.0624	+	18.2697i	−0.493494	+	0.641141i
$813$	−26.9875	−	7.23129i	−0.946494	−	0.253612i
$814$	−33.0519	−	8.85624i	−1.15847	−	0.310411i
$815$			33.9750i			1.19009i
$816$	6.01349	−	3.47189i	0.210514	−	0.121541i
$817$	−0.621667	−	0.621667i	−0.0217494	−	0.0217494i
$818$	−12.9533			−0.452901
$819$	1.73216	+	9.38081i	0.0605265	+	0.327792i
$820$	−9.71649			−0.339315
$821$	−6.19268	−	6.19268i	−0.216126	−	0.216126i	0.590738	−	0.806864i	$-0.298837\pi$
$821$	−6.19268	−	6.19268i	−0.216126	−	0.216126i	−0.806864	+	0.590738i	$0.798837\pi$
$822$	2.47416	−	1.42846i	0.0862962	−	0.0498231i
$823$			42.9808i			1.49822i	0.662448	+	0.749108i	$0.269518\pi$
$823$			42.9808i			1.49822i	−0.662448	+	0.749108i	$0.730482\pi$
$824$	12.3725	+	3.31519i	0.431015	+	0.115490i
$825$	−15.8656	−	4.25117i	−0.552368	−	0.148007i
$826$	2.28808	+	0.304723i	0.0796123	+	0.0106027i
$827$	38.0028	−	38.0028i	1.32149	−	1.32149i	0.408915	−	0.912572i	$-0.365907\pi$
$827$	38.0028	−	38.0028i	1.32149	−	1.32149i	0.912572	−	0.408915i	$-0.134093\pi$
$828$	−0.384774	+	0.666449i	−0.0133718	+	0.0231607i
$829$	−12.8740	−	22.2983i	−0.447131	−	0.774454i	0.551067	−	0.834461i	$-0.314221\pi$
$829$	−12.8740	−	22.2983i	−0.447131	−	0.774454i	−0.998198	+	0.0600074i	$0.980888\pi$
$830$	18.7613	+	5.02708i	0.651215	+	0.174493i
$831$	−4.18966	−	7.25671i	−0.145338	−	0.251732i
$832$	−2.41035	+	2.68146i	−0.0835639	+	0.0929627i
$833$	−46.9123	−	12.7211i	−1.62541	−	0.440759i
$834$	−9.23162	+	2.47361i	−0.319665	+	0.0856539i
$835$	−1.25689			−0.0434965
$836$	−31.0863			−1.07514
$837$	0.379148	−	0.101593i	0.0131053	−	0.00351155i
$838$	−5.84078	−	21.7981i	−0.201766	−	0.753002i
$839$	4.51723	−	16.8585i	0.155952	−	0.582021i	−0.843070	−	0.537804i	$-0.819254\pi$
$839$	4.51723	−	16.8585i	0.155952	−	0.582021i	0.999022	−	0.0442169i	$-0.0140793\pi$
$840$	3.09903	+	2.38537i	0.106927	+	0.0823029i
$841$	−23.4667	−	40.6455i	−0.809196	−	1.40157i
$842$		−	20.3671i		−	0.701895i
$843$	0.749516	−	2.79723i	0.0258147	−	0.0963418i
$844$	14.6058	+	8.43264i	0.502751	+	0.290263i
$845$	2.97436	−	18.9840i	0.102321	−	0.653070i
$846$		−	12.4894i		−	0.429395i
$847$	37.1855	−	48.3108i	1.27771	−	1.65998i
$848$	4.44772	−	7.70367i	0.152735	−	0.264545i
$849$	−0.779221	−	0.449883i	−0.0267428	−	0.0154400i
$850$	−5.05934	−	18.8817i	−0.173534	−	0.647637i
$851$	3.19127	+	3.19127i	0.109395	+	0.109395i
$852$	5.08439	−	1.36236i	0.174188	−	0.0466736i
$853$	−29.2570	−	29.2570i	−1.00174	−	1.00174i	−0.999998	−	0.00174344i	$-0.999445\pi$
$853$	−29.2570	−	29.2570i	−1.00174	−	1.00174i	−0.00174344	−	0.999998i	$-0.500555\pi$
$854$	14.8157	−	1.92792i	0.506983	−	0.0659721i
$855$	6.82024	+	3.93766i	0.233247	+	0.134665i
$856$	−1.88037	+	1.88037i	−0.0642696	+	0.0642696i
$857$	−17.5657	+	30.4247i	−0.600032	+	1.03929i	0.392783	+	0.919631i	$0.371512\pi$
$857$	−17.5657	+	30.4247i	−0.600032	+	1.03929i	−0.992815	+	0.119656i	$0.961821\pi$
$858$	−6.51743	−	20.0019i	−0.222501	−	0.682853i
$859$	−16.7019	+	9.64284i	−0.569861	+	0.329009i	−0.757094	−	0.653306i	$-0.773381\pi$
$859$	−16.7019	+	9.64284i	−0.569861	+	0.329009i	0.187233	+	0.982316i	$0.440048\pi$
$860$	−0.0631280	−	0.235597i	−0.00215265	−	0.00803379i
$861$	13.8138	−	10.5668i	0.470773	−	0.360116i
$862$	−1.61134	+	0.930307i	−0.0548824	+	0.0316864i
$863$	2.85260	−	10.6461i	0.0971038	−	0.362396i	−0.900226	−	0.435422i	$-0.856599\pi$
$863$	2.85260	−	10.6461i	0.0971038	−	0.362396i	0.997330	+	0.0730262i	$0.0232657\pi$
$864$	0.707107	−	0.707107i	0.0240563	−	0.0240563i
$865$	−9.65030	+	9.65030i	−0.328120	+	0.328120i
$866$	8.62261	−	32.1800i	0.293008	−	1.09352i
$867$	−27.0339	+	15.6081i	−0.918121	+	0.530077i
$868$	−0.134009	−	1.02984i	−0.00454857	−	0.0349549i
$869$	11.9737	+	44.6866i	0.406181	+	1.51589i
$870$	−11.1547	+	6.44017i	−0.378180	+	0.218342i
$871$	14.4550	−	9.40434i	0.489790	−	0.318654i
$872$	−7.49520	+	12.9821i	−0.253819	+	0.439628i
$873$	0.623824	−	0.623824i	0.0211132	−	0.0211132i
$874$	3.55079	+	2.05005i	0.120107	+	0.0693439i
$875$	24.2752	−	18.5692i	0.820652	−	0.627755i
$876$	6.55097	+	6.55097i	0.221337	+	0.221337i
$877$	36.8629	−	9.87738i	1.24477	−	0.333535i	0.424457	−	0.905448i	$-0.360465\pi$
$877$	36.8629	−	9.87738i	1.24477	−	0.333535i	0.820315	+	0.571913i	$0.193798\pi$
$878$	17.2060	+	17.2060i	0.580675	+	0.580675i
$879$	8.10572	+	30.2510i	0.273399	+	1.02034i
$880$	−7.46883	−	4.31213i	−0.251774	−	0.145362i
$881$	6.45418	−	11.1790i	0.217447	−	0.376629i	−0.736580	−	0.676351i	$-0.763560\pi$
$881$	6.45418	−	11.1790i	0.217447	−	0.376629i	0.954027	+	0.299721i	$0.0968938\pi$
$882$	−6.99997	−	0.0210005i	−0.235701	−	0.000707123i
$883$		−	28.8060i		−	0.969399i	−0.874681	−	0.484700i	$-0.838929\pi$
$883$		−	28.8060i		−	0.969399i	0.874681	−	0.484700i	$-0.161071\pi$
$884$	16.7370	−	18.6194i	0.562925	−	0.626240i
$885$	1.11681	+	0.644793i	0.0375413	+	0.0216745i
$886$	−8.06111	+	30.0845i	−0.270818	+	1.01071i
$887$			1.28523i			0.0431537i	0.999767	+	0.0215768i	$0.00686866\pi$
$887$			1.28523i			0.0431537i	−0.999767	+	0.0215768i	$0.993131\pi$
$888$	−2.93233	−	5.07894i	−0.0984025	−	0.170438i
$889$	−16.7999	+	21.8262i	−0.563451	+	0.732027i
$890$	3.41141	−	12.7316i	0.114351	−	0.426763i
$891$	1.51010	+	5.63579i	0.0505904	+	0.188806i
$892$	−0.244483	+	0.0655089i	−0.00818589	+	0.00219340i
$893$	−66.5426			−2.22676
$894$	10.4470			0.349399
$895$	−14.9083	+	3.99467i	−0.498330	+	0.133527i
$896$	−1.60748	−	2.10143i	−0.0537022	−	0.0702038i
$897$	−0.574621	+	2.71449i	−0.0191860	+	0.0906343i
$898$	−5.74605	−	9.95245i	−0.191748	−	0.332118i
$899$	3.30389	+	0.885275i	0.110191	+	0.0295256i
$900$	−1.40757	−	2.43799i	−0.0469191	−	0.0812663i
$901$	−30.8840	+	53.4926i	−1.02889	+	1.78210i
$902$	−27.1203	+	27.1203i	−0.903007	+	0.903007i
$903$	0.345963	+	0.266292i	0.0115129	+	0.00886165i
$904$	−9.57798	−	2.56641i	−0.318559	−	0.0853576i
$905$	1.72956	+	0.463435i	0.0574926	+	0.0154051i
$906$			4.49016i			0.149175i
$907$	−34.9710	+	20.1905i	−1.16119	+	0.670415i	−0.951590	−	0.307371i	$-0.900551\pi$
$907$	−34.9710	+	20.1905i	−1.16119	+	0.670415i	−0.209604	+	0.977786i	$0.567217\pi$
$908$	1.18113	+	1.18113i	0.0391971	+	0.0391971i
$909$	−11.9682			−0.396959
$910$	13.2885	+	4.71568i	0.440509	+	0.156323i
$911$	15.9440			0.528249			0.264124	−	0.964489i	$-0.414917\pi$
$911$	15.9440			0.528249			0.264124	+	0.964489i	$0.414917\pi$
$912$	−3.76741	−	3.76741i	−0.124751	−	0.124751i
$913$	66.3973	−	38.3345i	2.19743	−	1.26869i
$914$		−	38.1702i		−	1.26256i
$915$	8.06259	+	2.16036i	0.266541	+	0.0714195i
$916$	25.9161	+	6.94421i	0.856294	+	0.229443i
$917$	3.97807	+	9.64482i	0.131368	+	0.318500i
$918$	−4.91000	+	4.91000i	−0.162054	+	0.162054i
$919$	−23.4445	+	40.6071i	−0.773362	+	1.33950i	0.162348	+	0.986734i	$0.448093\pi$
$919$	−23.4445	+	40.6071i	−0.773362	+	1.33950i	−0.935710	+	0.352769i	$0.885240\pi$
$920$	0.568744	+	0.985094i	0.0187509	+	0.0324776i
$921$	−8.62061	−	2.30989i	−0.284059	−	0.0761133i
$922$	−3.27171	−	5.66676i	−0.107748	−	0.186625i
$923$	15.9083	−	10.3498i	0.523627	−	0.340668i
$924$	15.3078	−	1.99196i	0.503591	−	0.0655306i
$925$	−15.9473	+	4.27307i	−0.524344	+	0.140498i
$926$	−14.9505			−0.491304
$927$	−12.8089			−0.420700
$928$	8.41705	−	2.25534i	0.276303	−	0.0740353i
$929$	−6.63158	−	24.7494i	−0.217575	−	0.812001i	−0.985244	−	0.171155i	$-0.945250\pi$
$929$	−6.63158	−	24.7494i	−0.217575	−	0.812001i	0.767669	−	0.640846i	$-0.221416\pi$
$930$	0.150166	−	0.560429i	0.00492415	−	0.0183772i
$931$	−0.111889	+	37.2953i	−0.00366701	+	1.22230i
$932$	8.39675	+	14.5436i	0.275045	+	0.476391i
$933$		−	1.71214i		−	0.0560529i
$934$	−0.395022	+	1.47424i	−0.0129255	+	0.0482387i
$935$	51.8619	+	29.9425i	1.69607	+	0.979224i
$936$	1.63421	−	3.21393i	0.0534158	−	0.105051i
$937$		−	9.10555i		−	0.297465i	−0.988877	−	0.148733i	$-0.952481\pi$
$937$		−	9.10555i		−	0.297465i	0.988877	−	0.148733i	$-0.0475194\pi$
$938$	4.82507	+	11.6984i	0.157544	+	0.381965i
$939$	6.33634	−	10.9749i	0.206779	−	0.358151i
$940$	−15.9876	−	9.23045i	−0.521458	−	0.301064i
$941$	−2.64121	−	9.85714i	−0.0861010	−	0.321333i	0.909419	−	0.415880i	$-0.136526\pi$
$941$	−2.64121	−	9.85714i	−0.0861010	−	0.321333i	−0.995520	+	0.0945468i	$0.969860\pi$
$942$	−10.4040	−	10.4040i	−0.338982	−	0.338982i
$943$	4.88628	−	1.30927i	0.159119	−	0.0426359i
$944$	−0.616913	−	0.616913i	−0.0200788	−	0.0200788i
$945$	−3.61081	−	1.50200i	−0.117460	−	0.0488600i
$946$	−0.833789	−	0.481388i	−0.0271088	−	0.0156513i
$947$	−0.829559	+	0.829559i	−0.0269570	+	0.0269570i	−0.720457	−	0.693500i	$-0.756068\pi$
$947$	−0.829559	+	0.829559i	−0.0269570	+	0.0269570i	0.693500	+	0.720457i	$0.256068\pi$
$948$	−3.96454	+	6.86679i	−0.128762	+	0.223023i
$949$	29.7754	+	15.1401i	0.966549	+	0.491468i
$950$	−12.9894	+	7.49944i	−0.421432	+	0.243314i
$951$	−3.56867	−	13.3185i	−0.115722	−	0.431881i
$952$	11.1620	+	14.5919i	0.361762	+	0.472925i
$953$	−33.2954	+	19.2231i	−1.07855	+	0.622698i	−0.930504	−	0.366283i	$-0.880630\pi$
$953$	−33.2954	+	19.2231i	−1.07855	+	0.622698i	−0.148042	+	0.988981i	$0.547297\pi$
$954$	−2.30231	+	8.59233i	−0.0745400	+	0.278187i
$955$	−26.0085	+	26.0085i	−0.841617	+	0.841617i
$956$	1.66598	−	1.66598i	0.0538816	−	0.0538816i
$957$	−13.1590	+	49.1101i	−0.425370	+	1.58750i
$958$	−3.03129	+	1.75011i	−0.0979364	+	0.0565436i
$959$	4.59243	+	6.00360i	0.148297	+	0.193866i
$960$	−0.382567	−	1.42776i	−0.0123473	−	0.0460807i
$961$	26.7134	−	15.4230i	0.861721	−	0.497515i
$962$	−15.7258	−	14.1359i	−0.507020	−	0.455759i
$963$	1.32962	−	2.30297i	0.0428464	−	0.0742121i
$964$	−10.5050	+	10.5050i	−0.338344	+	0.338344i
$965$	−23.7361	−	13.7040i	−0.764092	−	0.441148i
$966$	−1.87988	−	0.781977i	−0.0604841	−	0.0251597i
$967$	16.9249	+	16.9249i	0.544268	+	0.544268i	0.924777	−	0.380509i	$-0.124251\pi$
$967$	16.9249	+	16.9249i	0.544268	+	0.544268i	−0.380509	+	0.924777i	$0.624251\pi$
$968$	−22.2573	+	5.96384i	−0.715378	+	0.191685i
$969$	26.1601	+	26.1601i	0.840382	+	0.840382i
$970$	−0.337508	−	1.25960i	−0.0108367	−	0.0404432i
$971$	−20.2033	−	11.6644i	−0.648355	−	0.374328i	0.139471	−	0.990226i	$-0.455460\pi$
$971$	−20.2033	−	11.6644i	−0.648355	−	0.374328i	−0.787826	+	0.615898i	$0.788793\pi$
$972$	−0.500000	+	0.866025i	−0.0160375	+	0.0277778i
$973$	−9.64155	−	23.3759i	−0.309094	−	0.749396i
$974$			4.37167i			0.140077i
$975$	−7.54869	−	6.78550i	−0.241752	−	0.217310i
$976$	−4.89047	−	2.82351i	−0.156540	−	0.0903785i
$977$	−8.62770	+	32.1990i	−0.276025	+	1.03014i	0.679127	+	0.734021i	$0.262359\pi$
$977$	−8.62770	+	32.1990i	−0.276025	+	1.03014i	−0.955152	+	0.296117i	$0.904308\pi$
$978$			22.9852i			0.734985i
$979$	−26.0140	−	45.0576i	−0.831412	−	1.44005i
$980$	−5.20030	+	8.94509i	−0.166117	+	0.285741i
$981$	3.87980	−	14.4796i	0.123872	−	0.462298i
$982$	0.0995838	+	0.371652i	0.00317785	+	0.0118599i
$983$	29.8863	−	8.00802i	0.953226	−	0.255416i	0.251495	−	0.967858i	$-0.419078\pi$
$983$	29.8863	−	8.00802i	0.953226	−	0.255416i	0.701731	+	0.712442i	$0.252411\pi$
$984$	−6.57353			−0.209556
$985$	−1.43723			−0.0457938
$986$	−58.4462	+	15.6606i	−1.86131	+	0.498735i
$987$	32.7676	−	4.26394i	1.04300	−	0.135723i
$988$	−17.1236	−	8.70694i	−0.544773	−	0.277005i
$989$	0.0634923	+	0.109972i	0.00201894	+	0.00349690i
$990$	8.33039	+	2.23212i	0.264757	+	0.0709415i
$991$	23.2413	+	40.2552i	0.738285	+	1.27875i	0.953267	+	0.302130i	$0.0976976\pi$
$991$	23.2413	+	40.2552i	0.738285	+	1.27875i	−0.214981	+	0.976618i	$0.568969\pi$
$992$	−0.196262	+	0.339935i	−0.00623131	+	0.0107930i
$993$	18.1988	−	18.1988i	0.577522	−	0.577522i
$994$	5.31016	+	12.8745i	0.168428	+	0.408353i
$995$	1.67285	+	0.448238i	0.0530329	+	0.0142101i
$996$	12.6927	+	3.40099i	0.402182	+	0.107764i
$997$		−	58.8770i		−	1.86465i	−0.361617	−	0.932327i	$-0.617775\pi$
$997$		−	58.8770i		−	1.86465i	0.361617	−	0.932327i	$-0.382225\pi$
$998$	−7.35205	+	4.24471i	−0.232725	+	0.134364i
$999$	4.14694	+	4.14694i	0.131203	+	0.131203i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.by.b.397.7	✓	40	7.5	odd	6
546.2.by.b.535.7	yes	40	13.2	odd	12
546.2.cg.b.145.7	yes	40	91.54	even	12	inner
546.2.cg.b.241.7	yes	40	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(-0.866025 + 0.500000i) q^{3} +1.00000i q^{4} +(-1.42776 - 0.382567i) q^{5} +(-0.965926 - 0.258819i) q^{6} +(0.349274 - 2.62260i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(-0.866025 + 0.500000i) q^{3} +1.00000i q^{4} +(-1.42776 - 0.382567i) q^{5} +(-0.965926 - 0.258819i) q^{6} +(0.349274 - 2.62260i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.500000 - 0.866025i) q^{9} +(-0.739062 - 1.28009i) q^{10} +(-5.63579 - 1.51010i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(-2.68146 - 2.41035i) q^{13} +(2.10143 - 1.60748i) q^{14} +(1.42776 - 0.382567i) q^{15} -1.00000 q^{16} +6.94378 q^{17} +(0.965926 - 0.258819i) q^{18} +(-1.37897 - 5.14638i) q^{19} +(0.382567 - 1.42776i) q^{20} +(1.00882 + 2.44587i) q^{21} +(-2.91730 - 5.05291i) q^{22} +0.769549i q^{23} +(0.258819 - 0.965926i) q^{24} +(-2.43799 - 1.40757i) q^{25} +(-0.191699 - 3.60045i) q^{26} +1.00000i q^{27} +(2.62260 + 0.349274i) q^{28} +(-4.35699 + 7.54652i) q^{29} +(1.28009 + 0.739062i) q^{30} +(-0.101593 - 0.379148i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(5.63579 - 1.51010i) q^{33} +(4.91000 + 4.91000i) q^{34} +(-1.50200 + 3.61081i) q^{35} +(0.866025 + 0.500000i) q^{36} +(4.14694 - 4.14694i) q^{37} +(2.66396 - 4.61411i) q^{38} +(3.52738 + 0.746698i) q^{39} +(1.28009 - 0.739062i) q^{40} +(-1.70135 - 6.34954i) q^{41} +(-1.01615 + 2.44283i) q^{42} +(0.142904 - 0.0825059i) q^{43} +(1.51010 - 5.63579i) q^{44} +(-1.04519 + 1.04519i) q^{45} +(-0.544153 + 0.544153i) q^{46} +(3.23250 - 12.0638i) q^{47} +(0.866025 - 0.500000i) q^{48} +(-6.75602 - 1.83201i) q^{49} +(-0.728614 - 2.71922i) q^{50} +(-6.01349 + 3.47189i) q^{51} +(2.41035 - 2.68146i) q^{52} +(-4.44772 + 7.70367i) q^{53} +(-0.707107 + 0.707107i) q^{54} +(7.46883 + 4.31213i) q^{55} +(1.60748 + 2.10143i) q^{56} +(3.76741 + 3.76741i) q^{57} +(-8.41705 + 2.25534i) q^{58} +(0.616913 + 0.616913i) q^{59} +(0.382567 + 1.42776i) q^{60} +(4.89047 + 2.82351i) q^{61} +(0.196262 - 0.339935i) q^{62} +(-2.09660 - 1.61378i) q^{63} -1.00000i q^{64} +(2.90635 + 4.46724i) q^{65} +(5.05291 + 2.91730i) q^{66} +(-1.23791 + 4.61993i) q^{67} +6.94378i q^{68} +(-0.384774 - 0.666449i) q^{69} +(-3.61530 + 1.49116i) q^{70} +(-1.36236 + 5.08439i) q^{71} +(0.258819 + 0.965926i) q^{72} +(-8.94879 + 2.39782i) q^{73} +5.86465 q^{74} +2.81515 q^{75} +(5.14638 - 1.37897i) q^{76} +(-5.92883 + 14.2529i) q^{77} +(1.96624 + 3.02223i) q^{78} +(-3.96454 - 6.86679i) q^{79} +(1.42776 + 0.382567i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(3.28676 - 5.69284i) q^{82} +(-9.29167 + 9.29167i) q^{83} +(-2.44587 + 1.00882i) q^{84} +(-9.91405 - 2.65646i) q^{85} +(0.159389 + 0.0427082i) q^{86} -8.71398i q^{87} +(5.05291 - 2.91730i) q^{88} +(6.30539 + 6.30539i) q^{89} -1.47812 q^{90} +(-7.25794 + 6.19050i) q^{91} -0.769549 q^{92} +(0.277556 + 0.277556i) q^{93} +(10.8161 - 6.24471i) q^{94} +7.87533i q^{95} +(0.965926 + 0.258819i) q^{96} +(0.852159 + 0.228335i) q^{97} +(-3.48180 - 6.07265i) q^{98} +(-4.12568 + 4.12568i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 4 q^{7} + 20 q^{9}+O(q^{10}) \) 40 * q + 4 * q^7 + 20 * q^9	\( 40 q + 4 q^{7} + 20 q^{9} + 8 q^{11} - 20 q^{12} + 4 q^{14} - 40 q^{16} + 16 q^{17} + 4 q^{19} + 4 q^{21} - 4 q^{22} - 24 q^{25} + 8 q^{26} - 4 q^{28} - 12 q^{29} - 8 q^{33} - 8 q^{34} - 32 q^{35} + 40 q^{37} + 8 q^{38} + 20 q^{39} + 20 q^{41} + 12 q^{42} - 24 q^{43} - 4 q^{44} + 32 q^{46} + 4 q^{47} + 32 q^{49} - 16 q^{50} + 24 q^{51} + 16 q^{52} - 4 q^{53} + 24 q^{55} + 12 q^{56} + 8 q^{57} + 12 q^{58} + 24 q^{59} + 60 q^{61} + 32 q^{62} - 4 q^{63} + 44 q^{65} - 12 q^{67} - 8 q^{69} - 24 q^{70} - 28 q^{71} + 60 q^{73} - 40 q^{74} - 72 q^{75} + 4 q^{76} - 12 q^{77} + 4 q^{78} - 20 q^{81} - 24 q^{82} + 60 q^{83} - 8 q^{84} - 4 q^{85} - 20 q^{86} - 36 q^{89} - 16 q^{92} - 24 q^{93} - 48 q^{97} - 88 q^{98} + 4 q^{99}+O(q^{100}) \) 40 * q + 4 * q^7 + 20 * q^9 + 8 * q^11 - 20 * q^12 + 4 * q^14 - 40 * q^16 + 16 * q^17 + 4 * q^19 + 4 * q^21 - 4 * q^22 - 24 * q^25 + 8 * q^26 - 4 * q^28 - 12 * q^29 - 8 * q^33 - 8 * q^34 - 32 * q^35 + 40 * q^37 + 8 * q^38 + 20 * q^39 + 20 * q^41 + 12 * q^42 - 24 * q^43 - 4 * q^44 + 32 * q^46 + 4 * q^47 + 32 * q^49 - 16 * q^50 + 24 * q^51 + 16 * q^52 - 4 * q^53 + 24 * q^55 + 12 * q^56 + 8 * q^57 + 12 * q^58 + 24 * q^59 + 60 * q^61 + 32 * q^62 - 4 * q^63 + 44 * q^65 - 12 * q^67 - 8 * q^69 - 24 * q^70 - 28 * q^71 + 60 * q^73 - 40 * q^74 - 72 * q^75 + 4 * q^76 - 12 * q^77 + 4 * q^78 - 20 * q^81 - 24 * q^82 + 60 * q^83 - 8 * q^84 - 4 * q^85 - 20 * q^86 - 36 * q^89 - 16 * q^92 - 24 * q^93 - 48 * q^97 - 88 * q^98 + 4 * q^99

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