LMFDB - Embedded newform 546.2.cg.b.145.7

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			145.7
Character	$\chi$	$=$	546.145
Dual form			546.2.cg.b.241.7

$q$-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 $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

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

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
$5$	−1.42776	+	0.382567i	−0.638513	+	0.171089i	−0.563530	−	0.826096i	$-0.690557\pi$
$5$	−1.42776	+	0.382567i	−0.638513	+	0.171089i	−0.0749833	+	0.997185i	$0.523890\pi$
$6$	−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	−0.972751	−	0.231851i	$-0.925522\pi$
$11$	−5.63579	+	1.51010i	−1.69925	+	0.455314i	−0.726502	+	0.687164i	$0.758855\pi$
$12$	−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	0.606363	+	0.795188i	$0.292628\pi$
$19$	−1.37897	+	5.14638i	−0.316357	+	1.18066i	−0.922720	+	0.385472i	$0.874039\pi$
$20$	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	$-0.974434\pi$
$23$		−	0.769549i		−	0.160462i	0.996776	−	0.0802310i	$-0.0255658\pi$
$24$	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	−0.913507	−	0.406823i	$-0.866637\pi$
$29$	−4.35699	−	7.54652i	−0.809072	−	1.40135i	0.104435	−	0.994532i	$-0.466697\pi$
$30$	1.28009	−	0.739062i	0.233712	−	0.134934i
$31$	−0.101593	+	0.379148i	−0.0182466	+	0.0680971i	−0.974449	−	0.224610i	$-0.927889\pi$
$31$	−0.101593	+	0.379148i	−0.0182466	+	0.0680971i	0.956202	+	0.292707i	$0.0945560\pi$
$32$	−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	0.960395	−	0.278643i	$-0.0898845\pi$
$37$	4.14694	+	4.14694i	0.681752	+	0.681752i	−0.278643	+	0.960395i	$0.589885\pi$
$38$	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	0.696109	+	0.717936i	$0.254913\pi$
$41$	−1.70135	+	6.34954i	−0.265707	+	0.991632i	−0.961816	+	0.273696i	$0.911754\pi$
$42$	−1.01615	−	2.44283i	−0.156795	−	0.376937i
$43$	0.142904	+	0.0825059i	0.0217927	+	0.0125820i	0.510857	−	0.859666i	$-0.329328\pi$
$43$	0.142904	+	0.0825059i	0.0217927	+	0.0125820i	−0.489064	+	0.872248i	$0.662662\pi$
$44$	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	0.634355	+	0.773041i	$0.281266\pi$
$47$	3.23250	+	12.0638i	0.471508	+	1.75969i	−0.162847	+	0.986651i	$0.552068\pi$
$48$	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	−0.991082	−	0.133252i	$-0.957458\pi$
$53$	−4.44772	−	7.70367i	−0.610941	−	1.05818i	0.380141	−	0.924928i	$-0.375875\pi$
$54$	−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	−0.665808	−	0.746123i	$-0.731913\pi$
$59$	0.616913	−	0.616913i	0.0803153	−	0.0803153i	0.746123	+	0.665808i	$0.231913\pi$
$60$	0.382567	−	1.42776i	0.0493892	−	0.184323i
$61$	4.89047	−	2.82351i	0.626160	−	0.361514i	−0.153103	−	0.988210i	$-0.548927\pi$
$61$	4.89047	−	2.82351i	0.626160	−	0.361514i	0.779264	+	0.626696i	$0.215593\pi$
$62$	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	−0.999398	−	0.0346805i	$-0.988959\pi$
$67$	−1.23791	−	4.61993i	−0.151234	−	0.564414i	0.848164	−	0.529733i	$-0.177708\pi$
$68$		−	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	−0.998440	−	0.0558333i	$-0.982218\pi$
$71$	−1.36236	−	5.08439i	−0.161682	−	0.603406i	0.836758	−	0.547573i	$-0.184448\pi$
$72$	0.258819	−	0.965926i	0.0305021	−	0.113835i
$73$	−8.94879	−	2.39782i	−1.04738	−	0.280644i	−0.306209	−	0.951964i	$-0.599061\pi$
$73$	−8.94879	−	2.39782i	−1.04738	−	0.280644i	−0.741167	+	0.671321i	$0.765727\pi$
$74$	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	−0.998124	−	0.0612181i	$-0.980501\pi$
$79$	−3.96454	+	6.86679i	−0.446046	+	0.772574i	0.552079	+	0.833792i	$0.313835\pi$
$80$	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	−0.999798	−	0.0200956i	$-0.993603\pi$
$83$	−9.29167	−	9.29167i	−1.01989	−	1.01989i	−0.0200956	−	0.999798i	$-0.506397\pi$
$84$	−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	−0.288969	−	0.957338i	$-0.593312\pi$
$89$	6.30539	−	6.30539i	0.668370	−	0.668370i	0.957338	+	0.288969i	$0.0933124\pi$
$90$	−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	−0.215297	−	0.976549i	$-0.569072\pi$
$97$	0.852159	−	0.228335i	0.0865237	−	0.0231839i	0.301821	+	0.953365i	$0.402405\pi$
$98$	−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	0.398046	+	0.917365i	$0.369688\pi$
$101$	−5.98408	+	10.3647i	−0.595439	+	1.03133i	−0.993485	+	0.113965i	$0.963645\pi$
$102$	−6.70718	+	1.79718i	−0.664110	+	0.177948i
$103$	−6.40446	+	11.0928i	−0.631050	+	1.09301i	0.356288	+	0.934376i	$0.384042\pi$
$103$	−6.40446	+	11.0928i	−0.631050	+	1.09301i	−0.987337	+	0.158634i	$0.949291\pi$
$104$	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	0.873621	−	0.486607i	$-0.161766\pi$
$109$	14.4796	+	3.87980i	1.38689	+	0.371617i	0.513274	+	0.858225i	$0.328432\pi$
$110$	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	−0.532861	−	0.846203i	$-0.678883\pi$
$113$	4.95793	−	8.58738i	0.466403	−	0.807833i	0.999264	+	0.0383697i	$0.0122165\pi$
$114$		−	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	−0.843472	−	0.537173i	$-0.819492\pi$
$127$	−9.01558	+	5.20515i	−0.800003	+	0.461882i	0.0434689	+	0.999055i	$0.486159\pi$
$128$	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	0.343340	−	0.939211i	$-0.388442\pi$
$131$	−3.41500	−	1.97165i	−0.298370	−	0.172264i	−0.641710	+	0.766947i	$0.721775\pi$
$132$	1.51010	−	5.63579i	0.131438	−	0.490532i
$133$	−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	0.615525	−	0.788117i	$-0.288944\pi$
$137$	−2.02014	−	2.02014i	−0.172592	−	0.172592i	−0.788117	+	0.615525i	$0.788944\pi$
$138$	0.199174	+	0.743327i	0.0169548	+	0.0632762i
$139$	8.27684	+	4.77864i	0.702033	+	0.405319i	0.808104	−	0.589040i	$-0.200494\pi$
$139$	8.27684	+	4.77864i	0.702033	+	0.405319i	−0.106071	+	0.994359i	$0.533827\pi$
$140$	−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	−0.179419	−	0.983773i	$-0.557422\pi$
$149$	−10.0910	−	2.70387i	−0.826686	−	0.221510i	−0.647267	+	0.762263i	$0.724088\pi$
$150$	1.99061	−	1.99061i	0.162533	−	0.162533i
$151$	−1.16214	+	4.33716i	−0.0945734	+	0.352953i	−0.996954	−	0.0779863i	$-0.975151\pi$
$151$	−1.16214	+	4.33716i	−0.0945734	+	0.352953i	0.902381	+	0.430939i	$0.141818\pi$
$152$	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	0.103728	−	0.994606i	$-0.466923\pi$
$157$	12.7423	−	7.35677i	1.01695	−	0.587134i	0.913218	+	0.407472i	$0.133590\pi$
$158$	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	0.187719	+	0.982223i	$0.439891\pi$
$163$	−5.94900	+	22.2020i	−0.465962	+	1.73899i	−0.653681	+	0.756771i	$0.726776\pi$
$164$	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	0.290458	−	0.956888i	$-0.406192\pi$
$167$	0.821354	+	0.220081i	0.0635583	+	0.0170304i	−0.226900	+	0.973918i	$0.572859\pi$
$168$	−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	0.986423	−	0.164226i	$-0.0525126\pi$
$173$	4.61652	+	7.99605i	0.350988	+	0.607928i	−0.635435	+	0.772154i	$0.719179\pi$
$174$	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	0.798306	−	0.602252i	$-0.205730\pi$
$179$	9.04284	+	5.22088i	0.675893	+	0.390227i	−0.122413	+	0.992479i	$0.539063\pi$
$180$	−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	0.827142	+	0.561993i	$0.189965\pi$
$191$	12.4420	+	21.5502i	0.900271	+	1.55932i	0.0731296	+	0.997322i	$0.476701\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	17.9106	−	4.79914i	1.28924	−	0.345450i	0.451866	−	0.892086i	$-0.350759\pi$
$193$	17.9106	−	4.79914i	1.28924	−	0.345450i	0.837370	+	0.546636i	$0.184092\pi$
$194$	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	0.292121	−	0.956381i	$-0.405639\pi$
$197$	0.939199	+	0.251658i	0.0669152	+	0.0179299i	−0.225206	+	0.974311i	$0.572306\pi$
$198$	−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	0.995417	+	0.0956302i	$0.0304866\pi$
$211$	8.43264	+	14.6058i	0.580527	+	1.00550i	−0.414890	+	0.909871i	$0.636180\pi$
$212$	−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	−0.963698	−	0.266996i	$-0.913969\pi$
$223$	0.0655089	−	0.244483i	0.00438680	−	0.0163718i	0.968085	+	0.250624i	$0.0806357\pi$
$224$	−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	0.745217	−	0.666822i	$-0.232346\pi$
$227$	1.18113	+	1.18113i	0.0783942	+	0.0783942i	−0.666822	+	0.745217i	$0.732346\pi$
$228$	−3.76741	−	3.76741i	−0.249503	−	0.249503i
$229$	6.94421	+	25.9161i	0.458886	+	1.71259i	0.676404	+	0.736531i	$0.263537\pi$
$229$	6.94421	+	25.9161i	0.458886	+	1.71259i	−0.217517	+	0.976056i	$0.569796\pi$
$230$	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	0.893944	−	0.448178i	$-0.147927\pi$
$233$	14.5436	+	8.39675i	0.952783	+	0.550089i	0.0588383	+	0.998268i	$0.481260\pi$
$234$	−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	−0.758933	−	0.651169i	$-0.774279\pi$
$239$	−1.66598	+	1.66598i	−0.107763	+	0.107763i	0.651169	+	0.758933i	$0.274279\pi$
$240$	−1.42776	−	0.382567i	−0.0921614	−	0.0246946i
$241$	10.5050	−	10.5050i	0.676688	−	0.676688i	−0.282561	−	0.959249i	$-0.591184\pi$
$241$	10.5050	−	10.5050i	0.676688	−	0.676688i	0.959249	+	0.282561i	$0.0911840\pi$
$242$	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	−0.627403	−	0.778695i	$-0.715882\pi$
$251$	5.71406	−	9.89703i	0.360668	−	0.624695i	0.988071	+	0.154000i	$0.0492154\pi$
$252$	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	0.249672	+	0.968330i	$0.419677\pi$
$263$	−11.5753	+	20.0490i	−0.713763	+	1.23627i	−0.963435	+	0.267943i	$0.913656\pi$
$264$	−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	$0.316255\pi$
$269$			27.4873i			1.67593i	−0.545724	+	0.837965i	$0.683745\pi$
$270$	1.28009	+	0.739062i	0.0779040	+	0.0449779i
$271$	19.7563	−	19.7563i	1.20011	−	1.20011i	0.225973	−	0.974133i	$-0.427444\pi$
$271$	19.7563	−	19.7563i	1.20011	−	1.20011i	0.974133	−	0.225973i	$-0.0725562\pi$
$272$	−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	$-0.919000\pi$
$277$		−	8.37932i		−	0.503465i	0.967797	−	0.251732i	$-0.0810003\pi$
$278$	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	0.643386	−	0.765542i	$-0.277529\pi$
$281$	−2.04772	−	2.04772i	−0.122156	−	0.122156i	−0.765542	+	0.643386i	$0.777529\pi$
$282$	−6.24471	−	10.8161i	−0.371867	−	0.644092i
$283$	0.449883	−	0.779221i	0.0267428	−	0.0463199i	−0.852344	−	0.522981i	$-0.824820\pi$
$283$	0.449883	−	0.779221i	0.0267428	−	0.0463199i	0.879087	+	0.476661i	$0.158153\pi$
$284$	−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	0.626889	+	0.779108i	$0.284328\pi$
$293$	8.10572	+	30.2510i	0.473541	+	1.76728i	−0.153348	+	0.988172i	$0.549006\pi$
$294$	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	−0.503704	−	0.863876i	$-0.668030\pi$
$307$	6.31072	−	6.31072i	0.360172	−	0.360172i	0.863876	+	0.503704i	$0.168030\pi$
$308$	−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	0.840733	−	0.541450i	$-0.182125\pi$
$311$	−0.856069	−	1.48276i	−0.0485432	−	0.0840793i	−0.889276	+	0.457371i	$0.848791\pi$
$312$	−3.02223	−	1.96624i	−0.171100	−	0.111317i
$313$	−10.9749	−	6.33634i	−0.620336	−	0.358151i	0.156664	−	0.987652i	$-0.449926\pi$
$313$	−10.9749	−	6.33634i	−0.620336	−	0.358151i	−0.777000	+	0.629501i	$0.783259\pi$
$314$	3.80814	−	14.2122i	0.214906	−	0.802040i
$315$	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	−0.990792	−	0.135391i	$-0.956771\pi$
$317$	−3.56867	−	13.3185i	−0.200436	−	0.748039i	0.790356	−	0.612648i	$-0.209896\pi$
$318$	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	−0.500258	−	0.865876i	$-0.666761\pi$
$331$	−24.8601	−	6.66123i	−1.36643	−	0.366134i	−0.866174	+	0.499742i	$0.833428\pi$
$332$	−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	$-0.632862\pi$
$337$		−	33.5630i		−	1.82829i	0.405383	−	0.914147i	$-0.367138\pi$
$338$	−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	0.706650	−	0.707564i	$-0.250206\pi$
$349$	18.0248	+	4.82973i	0.964844	+	0.258529i	0.258195	+	0.966093i	$0.416872\pi$
$350$	−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	−0.825191	−	0.564854i	$-0.808933\pi$
$353$	−23.6244	+	6.33014i	−1.25740	+	0.336920i	−0.432210	+	0.901773i	$0.642266\pi$
$354$	−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	0.412259	−	0.911067i	$-0.364740\pi$
$359$	23.2070	−	6.21830i	1.22482	−	0.328189i	0.812560	+	0.582877i	$0.198073\pi$
$360$			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	0.331764	−	0.943363i	$-0.392356\pi$
$367$	−6.11749	−	3.53194i	−0.319331	−	0.184366i	−0.651094	+	0.758997i	$0.725690\pi$
$368$			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	0.973855	−	0.227172i	$-0.0729479\pi$
$373$	5.60451	+	9.70730i	0.290191	+	0.502625i	−0.683664	+	0.729797i	$0.739615\pi$
$374$	−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	0.338532	−	0.940955i	$-0.390070\pi$
$379$	3.13887	+	0.841057i	0.161233	+	0.0432022i	−0.177300	+	0.984157i	$0.556736\pi$
$380$	−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	−0.994042	−	0.109002i	$-0.965234\pi$
$383$	−1.53970	+	5.74625i	−0.0786752	+	0.293620i	0.915366	+	0.402622i	$0.131901\pi$
$384$	−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	−0.689090	−	0.724676i	$-0.741990\pi$
$389$	−8.00851	+	4.62372i	−0.406048	+	0.234432i	0.283042	+	0.959107i	$0.408656\pi$
$390$	−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	0.496911	−	0.867802i	$-0.334468\pi$
$397$	9.82987	+	2.63391i	0.493347	+	0.132192i	−0.00356351	+	0.999994i	$0.501134\pi$
$398$	−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	0.483312	−	0.875448i	$-0.339434\pi$
$401$	−7.85252	−	7.85252i	−0.392136	−	0.392136i	−0.875448	+	0.483312i	$0.839434\pi$
$402$	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	0.443415	−	0.896316i	$-0.353767\pi$
$409$	−9.15936	−	9.15936i	−0.452901	−	0.452901i	−0.896316	+	0.443415i	$0.853767\pi$
$410$	−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	−0.894559	−	0.446950i	$-0.852510\pi$
$419$	−19.5436	+	11.2835i	−0.954768	+	0.551236i	−0.0602092	+	0.998186i	$0.519177\pi$
$420$	3.87805	+	0.504639i	0.189230	+	0.0246238i
$421$	−14.4017	+	14.4017i	−0.701895	+	0.701895i	−0.964817	−	0.262922i	$-0.915314\pi$
$421$	−14.4017	+	14.4017i	−0.701895	+	0.701895i	0.262922	+	0.964817i	$0.415314\pi$
$422$	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	0.953358	−	0.301843i	$-0.0976020\pi$
$431$	−0.481562	−	1.79721i	−0.0231960	−	0.0865688i	−0.976554	+	0.215275i	$0.930935\pi$
$432$			1.00000i			0.0481125i
$433$	−16.6576	+	28.8518i	−0.800514	+	1.38653i	0.118765	+	0.992922i	$0.462106\pi$
$433$	−16.6576	+	28.8518i	−0.800514	+	1.38653i	−0.919279	+	0.393608i	$0.871227\pi$
$434$	−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	−0.212655	−	0.977127i	$-0.568211\pi$
$443$	15.5729	−	26.9730i	0.739890	−	1.28153i	0.952545	−	0.304399i	$-0.0984556\pi$
$444$	−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	−0.511054	−	0.859549i	$-0.670745\pi$
$449$	−11.1005	+	2.97437i	−0.523866	+	0.140369i	−0.0128116	+	0.999918i	$0.504078\pi$
$450$	−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	−0.312711	+	0.949848i	$0.601237\pi$
$457$	−26.9904	+	26.9904i	−1.26256	+	1.26256i	−0.949848	+	0.312711i	$0.898763\pi$
$458$	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	−0.402983	−	0.915207i	$-0.632027\pi$
$461$	−6.32045	+	1.69356i	−0.294373	+	0.0788770i	0.108610	+	0.994084i	$0.465360\pi$
$462$	9.41574	+	12.2328i	0.438060	+	0.569121i
$463$	−10.5716	−	10.5716i	−0.491304	−	0.491304i	0.417413	−	0.908717i	$-0.362937\pi$
$463$	−10.5716	−	10.5716i	−0.491304	−	0.491304i	−0.908717	+	0.417413i	$0.862937\pi$
$464$	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	−0.847829	−	0.530270i	$-0.822090\pi$
$467$	0.763124	−	1.32177i	0.0353132	−	0.0611642i	0.883142	+	0.469106i	$0.155424\pi$
$468$	−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	0.942136	−	0.335230i	$-0.108814\pi$
$479$	−0.905926	−	3.38096i	−0.0413928	−	0.154480i	−0.983529	+	0.180750i	$0.942147\pi$
$480$	−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	−0.633591	−	0.773668i	$-0.718420\pi$
$487$	3.09123	−	3.09123i	0.140077	−	0.140077i	0.773668	+	0.633591i	$0.218420\pi$
$488$	−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	−0.492462	−	0.870334i	$-0.663903\pi$
$491$	0.333214	−	0.192381i	0.0150377	−	0.00868203i	0.507500	+	0.861652i	$0.330570\pi$
$492$	−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	0.899146	−	0.437648i	$-0.144188\pi$
$499$	−2.19722	−	8.20014i	−0.0983612	−	0.367089i	−0.997508	+	0.0705590i	$0.977522\pi$
$500$	−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	0.349875	−	0.936796i	$-0.386224\pi$
$503$	−6.42502	−	3.70948i	−0.286477	−	0.165398i	−0.636352	+	0.771399i	$0.719557\pi$
$504$	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	0.872910	−	0.487882i	$-0.162230\pi$
$509$	8.68662	+	8.68662i	0.385028	+	0.385028i	−0.487882	+	0.872910i	$0.662230\pi$
$510$	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	−0.699161	−	0.714964i	$-0.746443\pi$
$521$	−9.80499	+	5.66091i	−0.429564	+	0.248009i	0.269597	+	0.962973i	$0.413110\pi$
$522$	−2.25534	−	8.41705i	−0.0987137	−	0.368404i
$523$			0.701950i			0.0306941i	0.999882	+	0.0153471i	$0.00488531\pi$
$523$			0.701950i			0.0306941i	−0.999882	+	0.0153471i	$0.995115\pi$
$524$	−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	−0.0879721	−	0.996123i	$-0.528039\pi$
$541$	7.76639	−	2.08100i	0.333903	−	0.0894691i	0.421875	+	0.906654i	$0.361372\pi$
$542$		−	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	−0.427558	−	0.903988i	$-0.640626\pi$
$557$	−8.16213	+	2.18704i	−0.345841	+	0.0926677i	0.0817176	+	0.996656i	$0.473959\pi$
$558$	−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	$0.122539\pi$
$569$			17.9156i			0.751060i	−0.926810	+	0.375530i	$0.877461\pi$
$570$	2.03829	+	7.60698i	0.0853744	+	0.318622i
$571$	32.2814	−	18.6377i	1.35093	−	0.779962i	0.362554	−	0.931963i	$-0.381905\pi$
$571$	32.2814	−	18.6377i	1.35093	−	0.779962i	0.988380	+	0.152001i	$0.0485716\pi$
$572$	−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	−0.942041	−	0.335498i	$-0.891095\pi$
$577$	0.997816	−	3.72390i	0.0415396	−	0.155028i	0.983580	+	0.180470i	$0.0577620\pi$
$578$	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	0.516245	+	0.856441i	$0.327329\pi$
$587$	−8.69926	+	32.4661i	−0.359057	+	1.34002i	−0.875302	+	0.483577i	$0.839337\pi$
$588$	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	−0.418130	−	0.908387i	$-0.637314\pi$
$593$	−12.4245	−	46.3688i	−0.510212	−	1.90414i	−0.0920820	−	0.995751i	$-0.529352\pi$
$594$	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	0.986461	−	0.163998i	$-0.0524392\pi$
$599$	8.59552	+	14.8879i	0.351204	+	0.608302i	−0.635257	+	0.772301i	$0.719106\pi$
$600$	−1.99061	−	1.99061i	−0.0812663	−	0.0812663i
$601$	8.13421	−	4.69629i	0.331801	−	0.191566i	−0.324839	−	0.945769i	$-0.605310\pi$
$601$	8.13421	−	4.69629i	0.331801	−	0.191566i	0.656641	+	0.754204i	$0.271977\pi$
$602$	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	−0.632719	−	0.774382i	$-0.718061\pi$
$607$	−6.86013	+	3.96070i	−0.278444	+	0.160760i	0.354275	+	0.935141i	$0.384728\pi$
$608$	−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	−0.979721	−	0.200365i	$-0.935787\pi$
$613$	−5.73019	−	21.3854i	−0.231440	−	0.863747i	0.748281	−	0.663382i	$-0.230880\pi$
$614$		−	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	0.558775	+	0.829320i	$0.311272\pi$
$617$	12.1595	+	45.3797i	0.489521	+	1.82692i	−0.0692532	+	0.997599i	$0.522062\pi$
$618$	3.31519	−	12.3725i	0.133357	−	0.497693i
$619$	−25.2615	−	6.76879i	−1.01534	−	0.272061i	−0.287483	−	0.957786i	$-0.592819\pi$
$619$	−25.2615	−	6.76879i	−1.01534	−	0.272061i	−0.727861	+	0.685725i	$0.759485\pi$
$620$	−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	−0.804547	−	0.593888i	$-0.797592\pi$
$631$	−30.2532	+	8.10633i	−1.20436	+	0.322708i	−0.399814	+	0.916596i	$0.630925\pi$
$632$	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	$-0.829886\pi$
$641$		−	25.7914i		−	1.01870i	0.860560	−	0.509349i	$-0.170114\pi$
$642$	−2.56863	+	0.688262i	−0.101376	+	0.0271635i
$643$	−17.7658	+	4.76034i	−0.700616	+	0.187730i	−0.591507	−	0.806300i	$-0.701467\pi$
$643$	−17.7658	+	4.76034i	−0.700616	+	0.187730i	−0.109110	+	0.994030i	$0.534800\pi$
$644$	−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	−0.827311	−	0.561744i	$-0.810131\pi$
$647$	1.85249	−	3.20861i	0.0728289	−	0.126143i	0.900140	+	0.435601i	$0.143464\pi$
$648$	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	−0.708481	−	0.705730i	$-0.750619\pi$
$659$	6.59589	−	11.4244i	0.256939	−	0.445032i	0.965420	+	0.260698i	$0.0839526\pi$
$660$			8.62426i			0.335699i
$661$	3.26954	+	12.2021i	0.127170	+	0.474606i	0.999908	−	0.0135839i	$-0.00432402\pi$
$661$	3.26954	+	12.2021i	0.127170	+	0.474606i	−0.872737	+	0.488190i	$0.837657\pi$
$662$	−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	0.304545	−	0.952498i	$-0.401496\pi$
$673$	33.2503	−	19.1971i	1.28170	−	0.739993i	0.977160	+	0.212505i	$0.0681623\pi$
$674$	−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	−0.227831	−	0.973701i	$-0.573163\pi$
$677$	−30.8327	−	17.8013i	−1.18500	−	0.684158i	−0.957165	+	0.289543i	$0.906497\pi$
$678$	−2.56641	+	9.57798i	−0.0985625	+	0.367840i
$679$	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	0.896569	−	0.442904i	$-0.146052\pi$
$683$	11.8562	+	11.8562i	0.453665	+	0.453665i	−0.442904	+	0.896569i	$0.646052\pi$
$684$	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	0.726309	−	0.687369i	$-0.241234\pi$
$691$	1.02361	+	1.02361i	0.0389398	+	0.0389398i	−0.687369	+	0.726309i	$0.741234\pi$
$692$	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	$0.141101\pi$
$701$			22.7118i			0.857812i	−0.903349	+	0.428906i	$0.858899\pi$
$702$	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	−0.772296	−	0.635263i	$-0.780892\pi$
$709$	5.70253	−	21.2821i	0.214163	−	0.799268i	0.986459	−	0.164005i	$-0.0524414\pi$
$710$	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	0.995980	−	0.0895733i	$-0.0285503\pi$
$719$	11.2731	+	19.5257i	0.420417	+	0.728184i	−0.575563	+	0.817758i	$0.695217\pi$
$720$	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	−0.654112	−	0.756398i	$-0.726957\pi$
$733$	−22.8069	+	6.11108i	−0.842390	+	0.225718i	−0.188279	+	0.982116i	$0.560291\pi$
$734$	−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	0.215024	−	0.976609i	$-0.431017\pi$
$739$	24.1819	−	6.47951i	0.889545	−	0.238353i	0.674521	+	0.738256i	$0.264350\pi$
$740$	−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	0.00164161	−	0.999999i	$-0.499477\pi$
$743$	−13.5455	−	3.62950i	−0.496936	−	0.133154i	−0.498578	+	0.866845i	$0.666144\pi$
$744$	−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	$0.199284\pi$
$751$			32.1160i			1.17193i	−0.810337	+	0.585964i	$0.800716\pi$
$752$	−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	0.888656	−	0.458574i	$-0.151640\pi$
$757$	1.29840	+	2.24889i	0.0471910	+	0.0817372i	−0.841465	+	0.540312i	$0.818306\pi$
$758$	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	−0.00328001	−	0.999995i	$-0.501044\pi$
$761$	−13.9619	−	3.74108i	−0.506118	−	0.135614i	−0.502838	+	0.864381i	$0.667711\pi$
$762$	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	0.806150	+	0.591712i	$0.201548\pi$
$769$	−5.20930	+	19.4414i	−0.187852	+	0.701074i	−0.994002	+	0.109363i	$0.965119\pi$
$770$	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	0.961505	−	0.274787i	$-0.0886073\pi$
$773$	19.0927	+	19.0927i	0.686718	+	0.686718i	−0.274787	+	0.961505i	$0.588607\pi$
$774$	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	−0.222596	−	0.974911i	$-0.571453\pi$
$787$	21.1051	−	21.1051i	0.752315	−	0.752315i	0.974911	+	0.222596i	$0.0714529\pi$
$788$	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	−0.666448	−	0.745551i	$-0.732186\pi$
$797$	8.82062	−	15.2778i	0.312442	−	0.541166i	0.978891	+	0.204385i	$0.0655196\pi$
$798$	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	−0.741357	−	0.671111i	$-0.765817\pi$
$809$	5.98782	−	10.3712i	0.210520	−	0.364632i	0.951878	+	0.306479i	$0.0991508\pi$
$810$	−0.739062	−	1.28009i	−0.0259680	−	0.0449779i
$811$	−20.9279	−	20.9279i	−0.734877	−	0.734877i	0.236704	−	0.971582i	$-0.423933\pi$
$811$	−20.9279	−	20.9279i	−0.734877	−	0.734877i	−0.971582	+	0.236704i	$0.923933\pi$
$812$	−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	−0.806864	−	0.590738i	$-0.798837\pi$
$821$	−6.19268	+	6.19268i	−0.216126	+	0.216126i	0.590738	+	0.806864i	$0.298837\pi$
$822$	2.47416	+	1.42846i	0.0862962	+	0.0498231i
$823$		−	42.9808i		−	1.49822i	−0.662448	−	0.749108i	$-0.730482\pi$
$823$		−	42.9808i		−	1.49822i	0.662448	−	0.749108i	$-0.269518\pi$
$824$	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	0.912572	+	0.408915i	$0.134093\pi$
$827$	38.0028	+	38.0028i	1.32149	+	1.32149i	0.408915	+	0.912572i	$0.365907\pi$
$828$	−0.384774	−	0.666449i	−0.0133718	−	0.0231607i
$829$	−12.8740	+	22.2983i	−0.447131	+	0.774454i	−0.998198	−	0.0600074i	$-0.980888\pi$
$829$	−12.8740	+	22.2983i	−0.447131	+	0.774454i	0.551067	+	0.834461i	$0.314221\pi$
$830$	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	0.999022	+	0.0442169i	$0.0140793\pi$
$839$	4.51723	+	16.8585i	0.155952	+	0.582021i	−0.843070	+	0.537804i	$0.819254\pi$
$840$	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	−0.00174344	+	0.999998i	$0.500555\pi$
$853$	−29.2570	+	29.2570i	−1.00174	+	1.00174i	−0.999998	+	0.00174344i	$0.999445\pi$
$854$	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	−0.992815	−	0.119656i	$-0.961821\pi$
$857$	−17.5657	−	30.4247i	−0.600032	−	1.03929i	0.392783	−	0.919631i	$-0.371512\pi$
$858$	−6.51743	+	20.0019i	−0.222501	+	0.682853i
$859$	−16.7019	−	9.64284i	−0.569861	−	0.329009i	0.187233	−	0.982316i	$-0.440048\pi$
$859$	−16.7019	−	9.64284i	−0.569861	−	0.329009i	−0.757094	+	0.653306i	$0.773381\pi$
$860$	−0.0631280	+	0.235597i	−0.00215265	+	0.00803379i
$861$	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	0.997330	−	0.0730262i	$-0.0232657\pi$
$863$	2.85260	+	10.6461i	0.0971038	+	0.362396i	−0.900226	+	0.435422i	$0.856599\pi$
$864$	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	0.820315	−	0.571913i	$-0.193798\pi$
$877$	36.8629	+	9.87738i	1.24477	+	0.333535i	0.424457	+	0.905448i	$0.360465\pi$
$878$	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	0.954027	−	0.299721i	$-0.0968938\pi$
$881$	6.45418	+	11.1790i	0.217447	+	0.376629i	−0.736580	+	0.676351i	$0.763560\pi$
$882$	−6.99997	+	0.0210005i	−0.235701	+	0.000707123i
$883$			28.8060i			0.969399i	0.874681	+	0.484700i	$0.161071\pi$
$883$			28.8060i			0.969399i	−0.874681	+	0.484700i	$0.838929\pi$
$884$	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	$-0.993131\pi$
$887$		−	1.28523i		−	0.0431537i	0.999767	−	0.0215768i	$-0.00686866\pi$
$888$	−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	−0.209604	−	0.977786i	$-0.567217\pi$
$907$	−34.9710	−	20.1905i	−1.16119	−	0.670415i	−0.951590	+	0.307371i	$0.900551\pi$
$908$	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	−0.935710	−	0.352769i	$-0.885240\pi$
$919$	−23.4445	−	40.6071i	−0.773362	−	1.33950i	0.162348	−	0.986734i	$-0.448093\pi$
$920$	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	0.767669	+	0.640846i	$0.221416\pi$
$929$	−6.63158	+	24.7494i	−0.217575	+	0.812001i	−0.985244	+	0.171155i	$0.945250\pi$
$930$	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	$0.0475194\pi$
$937$			9.10555i			0.297465i	−0.988877	+	0.148733i	$0.952481\pi$
$938$	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	−0.995520	−	0.0945468i	$-0.969860\pi$
$941$	−2.64121	+	9.85714i	−0.0861010	+	0.321333i	0.909419	+	0.415880i	$0.136526\pi$
$942$	−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	0.693500	−	0.720457i	$-0.256068\pi$
$947$	−0.829559	−	0.829559i	−0.0269570	−	0.0269570i	−0.720457	+	0.693500i	$0.756068\pi$
$948$	−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	−0.148042	−	0.988981i	$-0.547297\pi$
$953$	−33.2954	−	19.2231i	−1.07855	−	0.622698i	−0.930504	+	0.366283i	$0.880630\pi$
$954$	−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	−0.380509	−	0.924777i	$-0.624251\pi$
$967$	16.9249	−	16.9249i	0.544268	−	0.544268i	0.924777	+	0.380509i	$0.124251\pi$
$968$	−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	−0.787826	−	0.615898i	$-0.788793\pi$
$971$	−20.2033	+	11.6644i	−0.648355	+	0.374328i	0.139471	+	0.990226i	$0.455460\pi$
$972$	−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	−0.955152	−	0.296117i	$-0.904308\pi$
$977$	−8.62770	−	32.1990i	−0.276025	−	1.03014i	0.679127	−	0.734021i	$-0.262359\pi$
$978$		−	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	0.701731	−	0.712442i	$-0.252411\pi$
$983$	29.8863	+	8.00802i	0.953226	+	0.255416i	0.251495	+	0.967858i	$0.419078\pi$
$984$	−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	−0.214981	−	0.976618i	$-0.568969\pi$
$991$	23.2413	−	40.2552i	0.738285	−	1.27875i	0.953267	−	0.302130i	$-0.0976976\pi$
$992$	−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	$0.382225\pi$
$997$			58.8770i			1.86465i	−0.361617	+	0.932327i	$0.617775\pi$
$998$	−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.145.7	yes	40
7.3	odd	6		546.2.by.b.535.7	yes	40
13.7	odd	12		546.2.by.b.397.7	✓	40
91.59	even	12	inner	546.2.cg.b.241.7	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.by.b.397.7	✓	40	13.7	odd	12
546.2.by.b.535.7	yes	40	7.3	odd	6
546.2.cg.b.145.7	yes	40	1.1	even	1	trivial
546.2.cg.b.241.7	yes	40	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)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(-0.866025 - 0.500000i) q^{3} -1.00000i q^{4} +(-1.42776 + 0.382567i) q^{5} +(-0.965926 + 0.258819i) q^{6} +(0.349274 + 2.62260i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(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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