LMFDB - Embedded newform 546.2.bz.a.73.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(31,546)]

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, 2, 9]))

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

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

chi := DirichletCharacter("546.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bz (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			73.5
Character	$\chi$	$=$	546.73
Dual form			546.2.bz.a.187.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 + 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(3.26974 + 0.876125i) q^{5} +(0.707107 - 0.707107i) q^{6} +(-1.99861 - 1.73365i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.258819 + 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(3.26974 + 0.876125i) q^{5} +(0.707107 - 0.707107i) q^{6} +(-1.99861 - 1.73365i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.69254 + 2.93157i) q^{10} +(1.42558 + 5.32034i) q^{11} +(0.500000 + 0.866025i) q^{12} +(0.661484 - 3.54435i) q^{13} +(2.19186 - 1.48181i) q^{14} +(-2.39362 - 2.39362i) q^{15} +(0.500000 + 0.866025i) q^{16} +(1.21733 - 2.10848i) q^{17} +(-0.965926 + 0.258819i) q^{18} +(3.32142 + 0.889973i) q^{19} +(-2.39362 - 2.39362i) q^{20} +(0.864026 + 2.50069i) q^{21} -5.50802 q^{22} +(0.824738 - 0.476163i) q^{23} +(-0.965926 + 0.258819i) q^{24} +(5.59350 + 3.22941i) q^{25} +(3.25238 + 1.55629i) q^{26} -1.00000i q^{27} +(0.864026 + 2.50069i) q^{28} +9.96464 q^{29} +(2.93157 - 1.69254i) q^{30} +(0.160573 + 0.599266i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(1.42558 - 5.32034i) q^{33} +(1.72157 + 1.72157i) q^{34} +(-5.01606 - 7.41962i) q^{35} -1.00000i q^{36} +(2.34483 + 0.628295i) q^{37} +(-1.71930 + 2.97791i) q^{38} +(-2.34504 + 2.73876i) q^{39} +(2.93157 - 1.69254i) q^{40} +(-7.08960 + 7.08960i) q^{41} +(-2.63911 + 0.187359i) q^{42} +8.62938i q^{43} +(1.42558 - 5.32034i) q^{44} +(0.876125 + 3.26974i) q^{45} +(0.246480 + 0.919876i) q^{46} +(-0.140221 + 0.523310i) q^{47} -1.00000i q^{48} +(0.988921 + 6.92979i) q^{49} +(-4.56707 + 4.56707i) q^{50} +(-2.10848 + 1.21733i) q^{51} +(-2.34504 + 2.73876i) q^{52} +(2.63548 - 4.56479i) q^{53} +(0.965926 + 0.258819i) q^{54} +18.6451i q^{55} +(-2.63911 + 0.187359i) q^{56} +(-2.43145 - 2.43145i) q^{57} +(-2.57904 + 9.62511i) q^{58} +(8.99767 - 2.41092i) q^{59} +(0.876125 + 3.26974i) q^{60} +(12.1534 - 7.01679i) q^{61} -0.620406 q^{62} +(0.502077 - 2.59768i) q^{63} -1.00000i q^{64} +(5.26818 - 11.0096i) q^{65} +(4.77009 + 2.75401i) q^{66} +(-11.7728 + 3.15451i) q^{67} +(-2.10848 + 1.21733i) q^{68} -0.952325 q^{69} +(8.46506 - 2.92480i) q^{70} +(-8.83572 - 8.83572i) q^{71} +(0.965926 + 0.258819i) q^{72} +(-2.76813 + 0.741717i) q^{73} +(-1.21377 + 2.10232i) q^{74} +(-3.22941 - 5.59350i) q^{75} +(-2.43145 - 2.43145i) q^{76} +(6.37442 - 13.1048i) q^{77} +(-2.03850 - 2.97398i) q^{78} +(0.573562 + 0.993439i) q^{79} +(0.876125 + 3.26974i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-5.01311 - 8.68296i) q^{82} +(-2.46153 + 2.46153i) q^{83} +(0.502077 - 2.59768i) q^{84} +(5.82766 - 5.82766i) q^{85} +(-8.33534 - 2.23345i) q^{86} +(-8.62963 - 4.98232i) q^{87} +(4.77009 + 2.75401i) q^{88} +(-1.18691 + 4.42960i) q^{89} -3.38509 q^{90} +(-7.46672 + 5.93701i) q^{91} -0.952325 q^{92} +(0.160573 - 0.599266i) q^{93} +(-0.469187 - 0.270885i) q^{94} +(10.0805 + 5.81997i) q^{95} +(0.965926 + 0.258819i) q^{96} +(4.97742 - 4.97742i) q^{97} +(-6.94962 - 0.838339i) q^{98} +(-3.89476 + 3.89476i) 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} - 4 q^{11} + 20 q^{12} + 4 q^{14} + 20 q^{16} + 8 q^{17} + 32 q^{19} + 4 q^{21} + 8 q^{22} - 24 q^{23} - 48 q^{25} - 8 q^{26} + 4 q^{28} + 24 q^{29} - 4 q^{33} - 16 q^{34} - 8 q^{35} - 8 q^{37} + 16 q^{38} - 4 q^{39} - 8 q^{41} - 4 q^{44} + 44 q^{46} + 20 q^{47} + 16 q^{49} + 32 q^{50} - 12 q^{51} - 4 q^{52} - 4 q^{53} - 16 q^{57} + 12 q^{58} - 24 q^{59} - 12 q^{61} + 16 q^{62} - 8 q^{63} + 8 q^{65} - 12 q^{68} - 16 q^{69} + 4 q^{70} + 8 q^{71} + 12 q^{73} - 40 q^{74} - 36 q^{75} - 16 q^{76} + 48 q^{77} - 8 q^{78} - 20 q^{81} + 24 q^{83} - 8 q^{84} - 40 q^{85} + 16 q^{86} - 72 q^{87} - 24 q^{89} + 8 q^{91} - 16 q^{92} - 36 q^{94} - 32 q^{98} - 8 q^{99}+O(q^{100}) $ 40 * q - 4 * q^7 + 20 * q^9 - 4 * q^11 + 20 * q^12 + 4 * q^14 + 20 * q^16 + 8 * q^17 + 32 * q^19 + 4 * q^21 + 8 * q^22 - 24 * q^23 - 48 * q^25 - 8 * q^26 + 4 * q^28 + 24 * q^29 - 4 * q^33 - 16 * q^34 - 8 * q^35 - 8 * q^37 + 16 * q^38 - 4 * q^39 - 8 * q^41 - 4 * q^44 + 44 * q^46 + 20 * q^47 + 16 * q^49 + 32 * q^50 - 12 * q^51 - 4 * q^52 - 4 * q^53 - 16 * q^57 + 12 * q^58 - 24 * q^59 - 12 * q^61 + 16 * q^62 - 8 * q^63 + 8 * q^65 - 12 * q^68 - 16 * q^69 + 4 * q^70 + 8 * q^71 + 12 * q^73 - 40 * q^74 - 36 * q^75 - 16 * q^76 + 48 * q^77 - 8 * q^78 - 20 * q^81 + 24 * q^83 - 8 * q^84 - 40 * q^85 + 16 * q^86 - 72 * q^87 - 24 * q^89 + 8 * q^91 - 16 * q^92 - 36 * q^94 - 32 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	3.26974	+	0.876125i	1.46227	+	0.391815i	0.900274	−	0.435323i	$-0.143366\pi$
$5$	3.26974	+	0.876125i	1.46227	+	0.391815i	0.561999	+	0.827138i	$0.310032\pi$
$6$	0.707107	−	0.707107i	0.288675	−	0.288675i
$7$	−1.99861	−	1.73365i	−0.755405	−	0.655258i
$7$	−1.99861	−	1.73365i	−0.755405	−	0.655258i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−1.69254	+	2.93157i	−0.535229	+	0.927044i
$11$	1.42558	+	5.32034i	0.429829	+	1.60414i	0.753146	+	0.657853i	$0.228535\pi$
$11$	1.42558	+	5.32034i	0.429829	+	1.60414i	−0.323317	+	0.946291i	$0.604798\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	0.661484	−	3.54435i	0.183463	−	0.983027i
$13$	0.661484	−	3.54435i	0.183463	−	0.983027i
$14$	2.19186	−	1.48181i	0.585798	−	0.396031i
$15$	−2.39362	−	2.39362i	−0.618030	−	0.618030i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	1.21733	−	2.10848i	0.295247	−	0.511382i	−0.679795	−	0.733402i	$-0.737931\pi$
$17$	1.21733	−	2.10848i	0.295247	−	0.511382i	0.975042	+	0.222019i	$0.0712648\pi$
$18$	−0.965926	+	0.258819i	−0.227671	+	0.0610042i
$19$	3.32142	+	0.889973i	0.761987	+	0.204174i	0.618829	−	0.785526i	$-0.287608\pi$
$19$	3.32142	+	0.889973i	0.761987	+	0.204174i	0.143158	+	0.989700i	$0.454274\pi$
$20$	−2.39362	−	2.39362i	−0.535229	−	0.535229i
$21$	0.864026	+	2.50069i	0.188546	+	0.545696i
$22$	−5.50802			−1.17431
$23$	0.824738	−	0.476163i	0.171970	−	0.0992868i	−0.411545	−	0.911390i	$-0.635011\pi$
$23$	0.824738	−	0.476163i	0.171970	−	0.0992868i	0.583514	+	0.812103i	$0.301677\pi$
$24$	−0.965926	+	0.258819i	−0.197169	+	0.0528312i
$25$	5.59350	+	3.22941i	1.11870	+	0.645881i
$26$	3.25238	+	1.55629i	0.637844	+	0.305214i
$27$		−	1.00000i		−	0.192450i
$28$	0.864026	+	2.50069i	0.163286	+	0.472586i
$29$	9.96464			1.85039			0.925194	−	0.379495i	$-0.123902\pi$
$29$	9.96464			1.85039			0.925194	+	0.379495i	$0.123902\pi$
$30$	2.93157	−	1.69254i	0.535229	−	0.309015i
$31$	0.160573	+	0.599266i	0.0288398	+	0.107631i	0.978845	−	0.204601i	$-0.0655898\pi$
$31$	0.160573	+	0.599266i	0.0288398	+	0.107631i	−0.950006	+	0.312233i	$0.898923\pi$
$32$	−0.965926	+	0.258819i	−0.170753	+	0.0457532i
$33$	1.42558	−	5.32034i	0.248162	−	0.926153i
$34$	1.72157	+	1.72157i	0.295247	+	0.295247i
$35$	−5.01606	−	7.41962i	−0.847869	−	1.25415i
$36$		−	1.00000i		−	0.166667i
$37$	2.34483	+	0.628295i	0.385488	+	0.103291i	0.446358	−	0.894855i	$-0.352721\pi$
$37$	2.34483	+	0.628295i	0.385488	+	0.103291i	−0.0608701	+	0.998146i	$0.519388\pi$
$38$	−1.71930	+	2.97791i	−0.278907	+	0.483080i
$39$	−2.34504	+	2.73876i	−0.375507	+	0.438552i
$40$	2.93157	−	1.69254i	0.463522	−	0.267615i
$41$	−7.08960	+	7.08960i	−1.10721	+	1.10721i	−0.113694	+	0.993516i	$0.536268\pi$
$41$	−7.08960	+	7.08960i	−1.10721	+	1.10721i	−0.993516	+	0.113694i	$0.963732\pi$
$42$	−2.63911	+	0.187359i	−0.407223	+	0.0289101i
$43$			8.62938i			1.31597i	0.753032	+	0.657984i	$0.228590\pi$
$43$			8.62938i			1.31597i	−0.753032	+	0.657984i	$0.771410\pi$
$44$	1.42558	−	5.32034i	0.214914	−	0.802072i
$45$	0.876125	+	3.26974i	0.130605	+	0.487424i
$46$	0.246480	+	0.919876i	0.0363415	+	0.135628i
$47$	−0.140221	+	0.523310i	−0.0204533	+	0.0763326i	−0.975398	−	0.220451i	$-0.929247\pi$
$47$	−0.140221	+	0.523310i	−0.0204533	+	0.0763326i	0.954945	+	0.296783i	$0.0959139\pi$
$48$		−	1.00000i		−	0.144338i
$49$	0.988921	+	6.92979i	0.141274	+	0.989970i
$50$	−4.56707	+	4.56707i	−0.645881	+	0.645881i
$51$	−2.10848	+	1.21733i	−0.295247	+	0.170461i
$52$	−2.34504	+	2.73876i	−0.325198	+	0.379797i
$53$	2.63548	−	4.56479i	0.362012	−	0.627022i	−0.626280	−	0.779598i	$-0.715423\pi$
$53$	2.63548	−	4.56479i	0.362012	−	0.627022i	0.988292	+	0.152576i	$0.0487567\pi$
$54$	0.965926	+	0.258819i	0.131446	+	0.0352208i
$55$			18.6451i			2.51411i
$56$	−2.63911	+	0.187359i	−0.352666	+	0.0250369i
$57$	−2.43145	−	2.43145i	−0.322054	−	0.322054i
$58$	−2.57904	+	9.62511i	−0.338644	+	1.26384i
$59$	8.99767	−	2.41092i	1.17140	−	0.313875i	0.379888	−	0.925033i	$-0.375963\pi$
$59$	8.99767	−	2.41092i	1.17140	−	0.313875i	0.791509	+	0.611158i	$0.209296\pi$
$60$	0.876125	+	3.26974i	0.113107	+	0.422122i
$61$	12.1534	−	7.01679i	1.55609	−	0.898408i	0.558462	−	0.829530i	$-0.311392\pi$
$61$	12.1534	−	7.01679i	1.55609	−	0.898408i	0.997625	−	0.0688777i	$-0.0219418\pi$
$62$	−0.620406			−0.0787917
$63$	0.502077	−	2.59768i	0.0632558	−	0.327276i
$64$		−	1.00000i		−	0.125000i
$65$	5.26818	−	11.0096i	0.653437	−	1.36557i
$66$	4.77009	+	2.75401i	0.587157	+	0.338995i
$67$	−11.7728	+	3.15451i	−1.43828	+	0.385385i	−0.891929	−	0.452175i	$-0.850648\pi$
$67$	−11.7728	+	3.15451i	−1.43828	+	0.385385i	−0.546346	+	0.837559i	$0.683982\pi$
$68$	−2.10848	+	1.21733i	−0.255691	+	0.147623i
$69$	−0.952325			−0.114646
$70$	8.46506	−	2.92480i	1.01177	−	0.349581i
$71$	−8.83572	−	8.83572i	−1.04861	−	1.04861i	−0.998757	−	0.0498505i	$-0.984126\pi$
$71$	−8.83572	−	8.83572i	−1.04861	−	1.04861i	−0.0498505	−	0.998757i	$-0.515874\pi$
$72$	0.965926	+	0.258819i	0.113835	+	0.0305021i
$73$	−2.76813	+	0.741717i	−0.323985	+	0.0868114i	−0.417146	−	0.908840i	$-0.636970\pi$
$73$	−2.76813	+	0.741717i	−0.323985	+	0.0868114i	0.0931611	+	0.995651i	$0.470303\pi$
$74$	−1.21377	+	2.10232i	−0.141098	+	0.244389i
$75$	−3.22941	−	5.59350i	−0.372900	−	0.645881i
$76$	−2.43145	−	2.43145i	−0.278907	−	0.278907i
$77$	6.37442	−	13.1048i	0.726433	−	1.49343i
$78$	−2.03850	−	2.97398i	−0.230814	−	0.336736i
$79$	0.573562	+	0.993439i	0.0645308	+	0.111771i	0.896486	−	0.443073i	$-0.146112\pi$
$79$	0.573562	+	0.993439i	0.0645308	+	0.111771i	−0.831955	+	0.554843i	$0.812778\pi$
$80$	0.876125	+	3.26974i	0.0979538	+	0.365568i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−5.01311	−	8.68296i	−0.553605	−	0.958872i
$83$	−2.46153	+	2.46153i	−0.270188	+	0.270188i	−0.829176	−	0.558988i	$-0.811190\pi$
$83$	−2.46153	+	2.46153i	−0.270188	+	0.270188i	0.558988	+	0.829176i	$0.311190\pi$
$84$	0.502077	−	2.59768i	0.0547811	−	0.283430i
$85$	5.82766	−	5.82766i	0.632099	−	0.632099i
$86$	−8.33534	−	2.23345i	−0.898822	−	0.240839i
$87$	−8.62963	−	4.98232i	−0.925194	−	0.534161i
$88$	4.77009	+	2.75401i	0.508493	+	0.293579i
$89$	−1.18691	+	4.42960i	−0.125812	+	0.469536i	−0.999867	−	0.0162898i	$-0.994815\pi$
$89$	−1.18691	+	4.42960i	−0.125812	+	0.469536i	0.874055	+	0.485826i	$0.161481\pi$
$90$	−3.38509			−0.356819
$91$	−7.46672	+	5.93701i	−0.782725	+	0.622368i
$92$	−0.952325			−0.0992868
$93$	0.160573	−	0.599266i	0.0166506	−	0.0621410i
$94$	−0.469187	−	0.270885i	−0.0483929	−	0.0279397i
$95$	10.0805	+	5.81997i	1.03424	+	0.597116i
$96$	0.965926	+	0.258819i	0.0985844	+	0.0264156i
$97$	4.97742	−	4.97742i	0.505381	−	0.505381i	−0.407724	−	0.913105i	$-0.633678\pi$
$97$	4.97742	−	4.97742i	0.505381	−	0.505381i	0.913105	+	0.407724i	$0.133678\pi$
$98$	−6.94962	−	0.838339i	−0.702017	−	0.0846850i
$99$	−3.89476	+	3.89476i	−0.391438	+	0.391438i
$100$	−3.22941	−	5.59350i	−0.322941	−	0.559350i
$101$	5.02397	−	8.70177i	0.499903	−	0.865858i	−0.500097	−	0.865970i	$-0.666702\pi$
$101$	5.02397	−	8.70177i	0.499903	−	0.865858i	1.00000		0.000111484i	$3.54865e-5\pi$
$102$	−0.630138	−	2.35171i	−0.0623930	−	0.232854i
$103$	−5.49909	−	9.52470i	−0.541841	−	0.938496i	−0.998798	−	0.0490078i	$-0.984394\pi$
$103$	−5.49909	−	9.52470i	−0.541841	−	0.938496i	0.456957	−	0.889489i	$-0.348939\pi$
$104$	−2.03850	−	2.97398i	−0.199891	−	0.291622i
$105$	0.634226	+	8.93361i	0.0618941	+	0.871831i
$106$	3.72714	+	3.72714i	0.362012	+	0.362012i
$107$	−4.11637	−	7.12976i	−0.397945	−	0.689260i	0.595528	−	0.803335i	$-0.296943\pi$
$107$	−4.11637	−	7.12976i	−0.397945	−	0.689260i	−0.993472	+	0.114075i	$0.963610\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	−16.6992	+	4.47455i	−1.59950	+	0.428584i	−0.944891	−	0.327386i	$-0.893832\pi$
$109$	−16.6992	+	4.47455i	−1.59950	+	0.428584i	−0.654606	+	0.755970i	$0.727165\pi$
$110$	−18.0098	−	4.82572i	−1.71717	−	0.460114i
$111$	−1.71654	−	1.71654i	−0.162926	−	0.162926i
$112$	0.502077	−	2.59768i	0.0474418	−	0.245457i
$113$	−16.8069			−1.58106			−0.790530	−	0.612423i	$-0.790195\pi$
$113$	−16.8069			−1.58106			−0.790530	+	0.612423i	$0.790195\pi$
$114$	2.97791	−	1.71930i	0.278907	−	0.161027i
$115$	3.11386	−	0.834356i	0.290369	−	0.0778041i
$116$	−8.62963	−	4.98232i	−0.801241	−	0.462597i
$117$	3.40024	−	1.19931i	0.314352	−	0.110877i
$118$			9.31507i			0.857522i
$119$	−6.08835	+	2.10362i	−0.558118	+	0.192838i
$120$	−3.38509			−0.309015
$121$	−16.7475	+	9.66916i	−1.52250	+	0.879015i
$122$	3.63216	+	13.5554i	0.328840	+	1.22725i
$123$	9.68458	−	2.59498i	0.873229	−	0.233981i
$124$	0.160573	−	0.599266i	0.0144199	−	0.0538157i
$125$	3.49184	+	3.49184i	0.312320	+	0.312320i
$126$	2.37921	+	1.15730i	0.211957	+	0.103100i
$127$		−	7.36842i		−	0.653841i	−0.945052	−	0.326921i	$-0.893989\pi$
$127$		−	7.36842i		−	0.653841i	0.945052	−	0.326921i	$-0.106011\pi$
$128$	0.965926	+	0.258819i	0.0853766	+	0.0228766i
$129$	4.31469	−	7.47326i	0.379887	−	0.657984i
$130$	9.27093	+	7.93816i	0.813115	+	0.696223i
$131$	0.806298	−	0.465516i	0.0704466	−	0.0406724i	−0.464363	−	0.885645i	$-0.653717\pi$
$131$	0.806298	−	0.465516i	0.0704466	−	0.0406724i	0.534810	+	0.844973i	$0.320383\pi$
$132$	−3.89476	+	3.89476i	−0.338995	+	0.338995i
$133$	−5.09535	−	7.53690i	−0.441823	−	0.653532i
$134$		−	12.1881i		−	1.05289i
$135$	0.876125	−	3.26974i	0.0754048	−	0.281415i
$136$	−0.630138	−	2.35171i	−0.0540339	−	0.201657i
$137$	−4.05963	−	15.1507i	−0.346838	−	1.29442i	−0.890451	−	0.455080i	$-0.849611\pi$
$137$	−4.05963	−	15.1507i	−0.346838	−	1.29442i	0.543613	−	0.839336i	$-0.317056\pi$
$138$	0.246480	−	0.919876i	0.0209818	−	0.0783050i
$139$		−	10.9643i		−	0.929981i	−0.885316	−	0.464990i	$-0.846058\pi$
$139$		−	10.9643i		−	0.929981i	0.885316	−	0.464990i	$-0.153942\pi$
$140$	0.634226	+	8.93361i	0.0536019	+	0.755028i
$141$	0.383090	−	0.383090i	0.0322620	−	0.0322620i
$142$	10.8215	−	6.24780i	0.908120	−	0.524304i
$143$	19.8002	−	1.53344i	1.65577	−	0.128233i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	32.5818	+	8.73027i	2.70577	+	0.725010i
$146$		−	2.86577i		−	0.237173i
$147$	2.60847	−	6.49584i	0.215143	−	0.535768i
$148$	−1.71654	−	1.71654i	−0.141098	−	0.141098i
$149$	−4.49686	+	16.7825i	−0.368397	+	1.37488i	0.494360	+	0.869257i	$0.335403\pi$
$149$	−4.49686	+	16.7825i	−0.368397	+	1.37488i	−0.862757	+	0.505619i	$0.831264\pi$
$150$	6.23874	−	1.67166i	0.509391	−	0.136491i
$151$	−3.66242	−	13.6683i	−0.298044	−	1.11231i	−0.938770	−	0.344545i	$-0.888033\pi$
$151$	−3.66242	−	13.6683i	−0.298044	−	1.11231i	0.640726	−	0.767770i	$-0.278633\pi$
$152$	2.97791	−	1.71930i	0.241540	−	0.139453i
$153$	2.43467			0.196831
$154$	11.0084	+	9.54898i	0.887083	+	0.769479i
$155$			2.10013i			0.168686i
$156$	3.40024	−	1.19931i	0.272237	−	0.0960220i
$157$	−2.85914	−	1.65072i	−0.228184	−	0.131742i	0.381550	−	0.924348i	$-0.375390\pi$
$157$	−2.85914	−	1.65072i	−0.228184	−	0.131742i	−0.609734	+	0.792606i	$0.708724\pi$
$158$	−1.10804	+	0.296898i	−0.0881507	+	0.0236199i
$159$	−4.56479	+	2.63548i	−0.362012	+	0.209007i
$160$	−3.38509			−0.267615
$161$	−2.47383	−	0.478141i	−0.194965	−	0.0376828i
$162$	−0.707107	−	0.707107i	−0.0555556	−	0.0555556i
$163$	11.0786	+	2.96849i	0.867740	+	0.232510i	0.665110	−	0.746745i	$-0.268385\pi$
$163$	11.0786	+	2.96849i	0.867740	+	0.232510i	0.202630	+	0.979255i	$0.435051\pi$
$164$	9.68458	−	2.59498i	0.756239	−	0.202634i
$165$	9.32257	−	16.1472i	0.725761	−	1.25706i
$166$	−1.74056	−	3.01474i	−0.135094	−	0.233989i
$167$	5.95118	+	5.95118i	0.460516	+	0.460516i	0.898825	−	0.438308i	$-0.144422\pi$
$167$	5.95118	+	5.95118i	0.460516	+	0.460516i	−0.438308	+	0.898825i	$0.644422\pi$
$168$	2.37921	+	1.15730i	0.183560	+	0.0892874i
$169$	−12.1249	−	4.68906i	−0.932683	−	0.360697i
$170$	4.12078	+	7.13740i	0.316049	+	0.547414i
$171$	0.889973	+	3.32142i	0.0680579	+	0.253996i
$172$	4.31469	−	7.47326i	0.328992	−	0.569831i
$173$	10.3528	+	17.9316i	0.787109	+	1.36331i	0.927731	+	0.373250i	$0.121757\pi$
$173$	10.3528	+	17.9316i	0.787109	+	1.36331i	−0.140621	+	0.990063i	$0.544910\pi$
$174$	7.04607	−	7.04607i	0.534161	−	0.534161i
$175$	−5.58059	−	16.1515i	−0.421853	−	1.22094i
$176$	−3.89476	+	3.89476i	−0.293579	+	0.293579i
$177$	−8.99767	−	2.41092i	−0.676306	−	0.181216i
$178$	−3.97147	−	2.29293i	−0.297674	−	0.171862i
$179$	0.868634	+	0.501506i	0.0649248	+	0.0374843i	0.532111	−	0.846675i	$-0.321399\pi$
$179$	0.868634	+	0.501506i	0.0649248	+	0.0374843i	−0.467186	+	0.884159i	$0.654732\pi$
$180$	0.876125	−	3.26974i	0.0653025	−	0.243712i
$181$	−17.4276			−1.29538			−0.647692	−	0.761902i	$-0.724266\pi$
$181$	−17.4276			−1.29538			−0.647692	+	0.761902i	$0.724266\pi$
$182$	−3.80219	−	8.74891i	−0.281837	−	0.648512i
$183$	−14.0336			−1.03739
$184$	0.246480	−	0.919876i	0.0181707	−	0.0678141i
$185$	7.11653	+	4.10873i	0.523218	+	0.302080i
$186$	0.537288	+	0.310203i	0.0393958	+	0.0227452i
$187$	12.9533	+	3.47082i	0.947236	+	0.253811i
$188$	0.383090	−	0.383090i	0.0279397	−	0.0279397i
$189$	−1.73365	+	1.99861i	−0.126104	+	0.145378i
$190$	−8.23068	+	8.23068i	−0.597116	+	0.597116i
$191$	1.69029	+	2.92767i	0.122305	+	0.211839i	0.920676	−	0.390327i	$-0.127638\pi$
$191$	1.69029	+	2.92767i	0.122305	+	0.211839i	−0.798371	+	0.602166i	$0.794305\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	2.96618	+	11.0699i	0.213510	+	0.796830i	0.986686	+	0.162638i	$0.0520004\pi$
$193$	2.96618	+	11.0699i	0.213510	+	0.796830i	−0.773176	+	0.634192i	$0.781333\pi$
$194$	3.51957	+	6.09607i	0.252690	+	0.437673i
$195$	−10.0672	+	6.90049i	−0.720925	+	0.494154i
$196$	2.60847	−	6.49584i	0.186319	−	0.463988i
$197$	6.69585	+	6.69585i	0.477059	+	0.477059i	0.904190	−	0.427131i	$-0.140476\pi$
$197$	6.69585	+	6.69585i	0.477059	+	0.477059i	−0.427131	+	0.904190i	$0.640476\pi$
$198$	−2.75401	−	4.77009i	−0.195719	−	0.338995i
$199$	−2.99276	+	5.18362i	−0.212151	+	0.367457i	−0.952388	−	0.304890i	$-0.901380\pi$
$199$	−2.99276	+	5.18362i	−0.212151	+	0.367457i	0.740236	+	0.672347i	$0.234714\pi$
$200$	6.23874	−	1.67166i	0.441145	−	0.118204i
$201$	11.7728	+	3.15451i	0.830389	+	0.222502i
$202$	7.10496	+	7.10496i	0.499903	+	0.499903i
$203$	−19.9155	−	17.2752i	−1.39779	−	1.21248i
$204$	2.43467			0.170461
$205$	−29.3926	+	16.9698i	−2.05287	+	1.18522i
$206$	10.6234	−	2.84654i	0.740169	−	0.198328i
$207$	0.824738	+	0.476163i	0.0573232	+	0.0330956i
$208$	3.40024	−	1.19931i	0.235764	−	0.0831575i
$209$			18.9398i			1.31010i
$210$	−8.79336	−	1.69957i	−0.606799	−	0.117282i
$211$	−15.3770			−1.05860			−0.529299	−	0.848435i	$-0.677545\pi$
$211$	−15.3770			−1.05860			−0.529299	+	0.848435i	$0.677545\pi$
$212$	−4.56479	+	2.63548i	−0.313511	+	0.181006i
$213$	3.23410	+	12.0698i	0.221597	+	0.827010i
$214$	7.95222	−	2.13079i	0.543602	−	0.145658i
$215$	−7.56041	+	28.2158i	−0.515616	+	1.92430i
$216$	−0.707107	−	0.707107i	−0.0481125	−	0.0481125i
$217$	0.717994	−	1.47608i	0.0487406	−	0.100203i
$218$		−	17.2883i		−	1.17091i
$219$	2.76813	+	0.741717i	0.187053	+	0.0501206i
$220$	9.32257	−	16.1472i	0.628528	−	1.08864i
$221$	−6.66796	−	5.70939i	−0.448536	−	0.384055i
$222$	2.10232	−	1.21377i	0.141098	−	0.0814631i
$223$	−4.42968	+	4.42968i	−0.296633	+	0.296633i	−0.839694	−	0.543060i	$-0.817265\pi$
$223$	−4.42968	+	4.42968i	−0.296633	+	0.296633i	0.543060	+	0.839694i	$0.317265\pi$
$224$	2.37921	+	1.15730i	0.158968	+	0.0773252i
$225$			6.45881i			0.430588i
$226$	4.34994	−	16.2342i	0.289354	−	1.07988i
$227$	1.15694	+	4.31777i	0.0767890	+	0.286580i	0.993633	−	0.112665i	$-0.0359387\pi$
$227$	1.15694	+	4.31777i	0.0767890	+	0.286580i	−0.916844	+	0.399246i	$0.869272\pi$
$228$	0.889973	+	3.32142i	0.0589399	+	0.219967i
$229$	−3.94260	+	14.7140i	−0.260535	+	0.972328i	0.704393	+	0.709811i	$0.251219\pi$
$229$	−3.94260	+	14.7140i	−0.260535	+	0.972328i	−0.964927	+	0.262518i	$0.915447\pi$
$230$			3.22370i			0.212565i
$231$	−12.0728	+	8.16186i	−0.794332	+	0.537011i
$232$	7.04607	−	7.04607i	0.462597	−	0.462597i
$233$	−0.0969733	+	0.0559876i	−0.00635294	+	0.00366787i	−0.503173	−	0.864186i	$-0.667834\pi$
$233$	−0.0969733	+	0.0559876i	−0.00635294	+	0.00366787i	0.496820	+	0.867854i	$0.334501\pi$
$234$	0.278402	+	3.59479i	0.0181997	+	0.234999i
$235$	−0.916970	+	1.58824i	−0.0598165	+	0.103605i
$236$	−8.99767	−	2.41092i	−0.585698	−	0.156937i
$237$		−	1.14712i		−	0.0745138i
$238$	−0.456156	−	6.42535i	−0.0295682	−	0.416494i
$239$	−14.2293	−	14.2293i	−0.920414	−	0.920414i	0.0766447	−	0.997058i	$-0.475579\pi$
$239$	−14.2293	−	14.2293i	−0.920414	−	0.920414i	−0.997058	+	0.0766447i	$0.975579\pi$
$240$	0.876125	−	3.26974i	0.0565536	−	0.211061i
$241$	11.6854	−	3.13108i	0.752720	−	0.201691i	0.137996	−	0.990433i	$-0.455934\pi$
$241$	11.6854	−	3.13108i	0.752720	−	0.201691i	0.614724	+	0.788742i	$0.289267\pi$
$242$	−5.00513	−	18.6794i	−0.321742	−	1.20076i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	−14.0336			−0.898408
$245$	−2.83785	+	23.5251i	−0.181304	+	1.50296i
$246$			10.0262i			0.639248i
$247$	5.35145	−	11.1836i	0.340504	−	0.711595i
$248$	0.537288	+	0.310203i	0.0341178	+	0.0196979i
$249$	3.36251	−	0.900981i	0.213090	−	0.0570974i
$250$	−4.27662	+	2.46911i	−0.270477	+	0.156160i
$251$	23.8347			1.50443			0.752217	−	0.658916i	$-0.228985\pi$
$251$	23.8347			1.50443			0.752217	+	0.658916i	$0.228985\pi$
$252$	−1.73365	+	1.99861i	−0.109210	+	0.125901i
$253$	3.70908	+	3.70908i	0.233188	+	0.233188i
$254$	7.11734	+	1.90709i	0.446582	+	0.119661i
$255$	−7.96074	+	2.13307i	−0.498521	+	0.133578i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−10.4551	−	18.1088i	−0.652174	−	1.12960i	−0.982594	−	0.185765i	$-0.940524\pi$
$257$	−10.4551	−	18.1088i	−0.652174	−	1.12960i	0.330420	−	0.943834i	$-0.392810\pi$
$258$	6.10189	+	6.10189i	0.379887	+	0.379887i
$259$	−3.59717	−	5.32083i	−0.223517	−	0.330621i
$260$	−10.0672	+	6.90049i	−0.624339	+	0.427950i
$261$	4.98232	+	8.62963i	0.308398	+	0.534161i
$262$	0.240969	+	0.899309i	0.0148871	+	0.0555595i
$263$	2.95411	−	5.11667i	0.182158	−	0.315507i	−0.760457	−	0.649388i	$-0.775025\pi$
$263$	2.95411	−	5.11667i	0.182158	−	0.315507i	0.942615	+	0.333881i	$0.108358\pi$
$264$	−2.75401	−	4.77009i	−0.169498	−	0.293579i
$265$	12.6167	−	12.6167i	0.775037	−	0.775037i
$266$	8.59886	−	2.97103i	0.527230	−	0.182166i
$267$	3.24269	−	3.24269i	0.198449	−	0.198449i
$268$	11.7728	+	3.15451i	0.719138	+	0.192692i
$269$	−24.9013	−	14.3768i	−1.51826	−	0.876568i	−0.999769	−	0.0214854i	$-0.993160\pi$
$269$	−24.9013	−	14.3768i	−1.51826	−	0.876568i	−0.518491	−	0.855083i	$-0.673506\pi$
$270$	2.93157	+	1.69254i	0.178410	+	0.103005i
$271$	−0.580949	+	2.16813i	−0.0352901	+	0.131705i	−0.981324	−	0.192365i	$-0.938384\pi$
$271$	−0.580949	+	2.16813i	−0.0352901	+	0.131705i	0.946033	+	0.324069i	$0.105051\pi$
$272$	2.43467			0.147623
$273$	9.43487	−	1.40825i	0.571025	−	0.0852310i
$274$	15.6852			0.947578
$275$	−9.20757	+	34.3631i	−0.555237	+	2.07217i
$276$	0.824738	+	0.476163i	0.0496434	+	0.0286616i
$277$	−16.1792	−	9.34106i	−0.972114	−	0.561250i	−0.0722338	−	0.997388i	$-0.523013\pi$
$277$	−16.1792	−	9.34106i	−0.972114	−	0.561250i	−0.899880	+	0.436138i	$0.856346\pi$
$278$	10.5907	+	2.83777i	0.635189	+	0.170198i
$279$	−0.438693	+	0.438693i	−0.0262639	+	0.0262639i
$280$	−8.79336	−	1.69957i	−0.525504	−	0.101569i
$281$	−10.9100	+	10.9100i	−0.650837	+	0.650837i	−0.953195	−	0.302358i	$-0.902226\pi$
$281$	−10.9100	+	10.9100i	−0.650837	+	0.650837i	0.302358	+	0.953195i	$0.402226\pi$
$282$	0.270885	+	0.469187i	0.0161310	+	0.0279397i
$283$	−7.51710	+	13.0200i	−0.446845	+	0.773958i	−0.998179	−	0.0603265i	$-0.980786\pi$
$283$	−7.51710	+	13.0200i	−0.446845	+	0.773958i	0.551334	+	0.834285i	$0.314119\pi$
$284$	3.23410	+	12.0698i	0.191908	+	0.716212i
$285$	−5.81997	−	10.0805i	−0.344745	−	0.597116i
$286$	−3.64347	+	19.5224i	−0.215443	+	1.15438i
$287$	26.4603	−	1.87850i	1.56190	−	0.110884i
$288$	−0.707107	−	0.707107i	−0.0416667	−	0.0416667i
$289$	5.53620	+	9.58898i	0.325659	+	0.564057i
$290$	−16.8656	+	29.2121i	−0.990382	+	1.71539i
$291$	−6.79929	+	1.82186i	−0.398581	+	0.106800i
$292$	2.76813	+	0.741717i	0.161992	+	0.0434057i
$293$	−4.45840	−	4.45840i	−0.260462	−	0.260462i	0.564779	−	0.825242i	$-0.308961\pi$
$293$	−4.45840	−	4.45840i	−0.260462	−	0.260462i	−0.825242	+	0.564779i	$0.808961\pi$
$294$	5.59938	+	4.20083i	0.326562	+	0.244997i
$295$	31.5323			1.83588
$296$	2.10232	−	1.21377i	0.122195	−	0.0705492i
$297$	5.32034	−	1.42558i	0.308718	−	0.0827206i
$298$	−15.0468	−	8.68726i	−0.871637	−	0.503240i
$299$	−1.14214	−	3.23814i	−0.0660515	−	0.187266i
$300$			6.45881i			0.372900i
$301$	14.9603	−	17.2468i	0.862298	−	0.994089i
$302$	14.1505			0.814271
$303$	−8.70177	+	5.02397i	−0.499903	+	0.288619i
$304$	0.889973	+	3.32142i	0.0510435	+	0.190497i
$305$	45.8862	−	12.2952i	2.62744	−	0.704019i
$306$	−0.630138	+	2.35171i	−0.0360226	+	0.134438i
$307$	4.04928	+	4.04928i	0.231105	+	0.231105i	0.813154	−	0.582049i	$-0.197749\pi$
$307$	4.04928	+	4.04928i	0.231105	+	0.231105i	−0.582049	+	0.813154i	$0.697749\pi$
$308$	−12.0728	+	8.16186i	−0.687911	+	0.465065i
$309$			10.9982i			0.625664i
$310$	−2.02857	−	0.543553i	−0.115215	−	0.0308718i
$311$	−12.9438	+	22.4193i	−0.733975	+	1.27128i	0.221197	+	0.975229i	$0.429004\pi$
$311$	−12.9438	+	22.4193i	−0.733975	+	1.27128i	−0.955172	+	0.296052i	$0.904330\pi$
$312$	0.278402	+	3.59479i	0.0157614	+	0.203515i
$313$	6.49380	−	3.74920i	0.367051	−	0.211917i	−0.305118	−	0.952314i	$-0.598696\pi$
$313$	6.49380	−	3.74920i	0.367051	−	0.211917i	0.672169	+	0.740397i	$0.265363\pi$
$314$	2.33447	−	2.33447i	0.131742	−	0.131742i
$315$	3.91755	−	8.05385i	0.220729	−	0.453783i
$316$		−	1.14712i		−	0.0645308i
$317$	1.82674	−	6.81749i	0.102600	−	0.382908i	−0.895462	−	0.445138i	$-0.853155\pi$
$317$	1.82674	−	6.81749i	0.102600	−	0.382908i	0.998062	+	0.0622299i	$0.0198212\pi$
$318$	−1.36423	−	5.09136i	−0.0765021	−	0.285510i
$319$	14.2054	+	53.0153i	0.795350	+	2.96829i
$320$	0.876125	−	3.26974i	0.0489769	−	0.182784i
$321$			8.23274i			0.459507i
$322$	1.10212	−	2.26579i	0.0614189	−	0.126267i
$323$	5.91978	−	5.91978i	0.329385	−	0.329385i
$324$	0.866025	−	0.500000i	0.0481125	−	0.0277778i
$325$	15.1462	−	17.6891i	0.840158	−	0.981216i
$326$	−5.73468	+	9.93276i	−0.317615	+	0.550125i
$327$	16.6992	+	4.47455i	0.923470	+	0.247443i
$328$			10.0262i			0.553605i
$329$	1.18748	−	0.802802i	0.0654681	−	0.0442599i
$330$	13.1841	+	13.1841i	0.725761	+	0.725761i
$331$	1.29963	−	4.85028i	0.0714340	−	0.266595i	−0.920967	−	0.389640i	$-0.872599\pi$
$331$	1.29963	−	4.85028i	0.0714340	−	0.266595i	0.992401	+	0.123045i	$0.0392660\pi$
$332$	3.36251	−	0.900981i	0.184542	−	0.0494478i
$333$	0.628295	+	2.34483i	0.0344304	+	0.128496i
$334$	−7.28868	+	4.20812i	−0.398819	+	0.230258i
$335$	−41.2578			−2.25415
$336$	−1.73365	+	1.99861i	−0.0945783	+	0.109033i
$337$			12.7840i			0.696388i	0.937422	+	0.348194i	$0.113205\pi$
$337$			12.7840i			0.696388i	−0.937422	+	0.348194i	$0.886795\pi$
$338$	7.66744	−	10.4981i	0.417054	−	0.571022i
$339$	14.5552	+	8.40345i	0.790530	+	0.456413i
$340$	−7.96074	+	2.13307i	−0.431732	+	0.115682i
$341$	−2.95939	+	1.70861i	−0.160260	+	0.0925262i
$342$	−3.43859			−0.185938
$343$	10.0374	−	15.5644i	0.541966	−	0.840400i
$344$	6.10189	+	6.10189i	0.328992	+	0.328992i
$345$	−3.11386	−	0.834356i	−0.167645	−	0.0449202i
$346$	−20.0001	+	5.35901i	−1.07521	+	0.288102i
$347$	11.4847	−	19.8920i	0.616529	−	1.06786i	−0.373585	−	0.927596i	$-0.621871\pi$
$347$	11.4847	−	19.8920i	0.616529	−	1.06786i	0.990114	−	0.140264i	$-0.0447952\pi$
$348$	4.98232	+	8.62963i	0.267080	+	0.462597i
$349$	2.94528	+	2.94528i	0.157657	+	0.157657i	0.781528	−	0.623871i	$-0.214441\pi$
$349$	2.94528	+	2.94528i	0.157657	+	0.157657i	−0.623871	+	0.781528i	$0.714441\pi$
$350$	17.0455	−	1.21012i	0.911121	−	0.0646834i
$351$	−3.54435	−	0.661484i	−0.189184	−	0.0353074i
$352$	−2.75401	−	4.77009i	−0.146789	−	0.254247i
$353$	0.881264	+	3.28892i	0.0469050	+	0.175052i	0.985405	−	0.170228i	$-0.0544506\pi$
$353$	0.881264	+	3.28892i	0.0469050	+	0.175052i	−0.938500	+	0.345280i	$0.887784\pi$
$354$	4.65753	−	8.06709i	0.247545	−	0.428761i
$355$	−21.1493	−	36.6317i	−1.12249	−	1.94421i
$356$	3.24269	−	3.24269i	0.171862	−	0.171862i
$357$	6.32448	+	1.22239i	0.334727	+	0.0646958i
$358$	−0.709237	+	0.709237i	−0.0374843	+	0.0374843i
$359$	27.1628	+	7.27824i	1.43360	+	0.384131i	0.890286	−	0.455402i	$-0.150504\pi$
$359$	27.1628	+	7.27824i	1.43360	+	0.384131i	0.543309	+	0.839533i	$0.317171\pi$
$360$	2.93157	+	1.69254i	0.154507	+	0.0892049i
$361$	−6.21467	−	3.58804i	−0.327088	−	0.188844i
$362$	4.51060	−	16.8338i	0.237072	−	0.884764i
$363$	19.3383			1.01500
$364$	9.43487	−	1.40825i	0.494522	−	0.0738122i
$365$	−9.70090			−0.507768
$366$	3.63216	−	13.5554i	0.189856	−	0.708552i
$367$	−31.9566	−	18.4502i	−1.66812	−	0.963091i	−0.968649	−	0.248432i	$-0.920085\pi$
$367$	−31.9566	−	18.4502i	−1.66812	−	0.963091i	−0.699473	−	0.714659i	$-0.746582\pi$
$368$	0.824738	+	0.476163i	0.0429924	+	0.0248217i
$369$	−9.68458	−	2.59498i	−0.504159	−	0.135089i
$370$	−5.81062	+	5.81062i	−0.302080	+	0.302080i
$371$	−13.1811	+	4.55426i	−0.684327	+	0.236445i
$372$	−0.438693	+	0.438693i	−0.0227452	+	0.0227452i
$373$	5.52566	+	9.57072i	0.286108	+	0.495553i	0.972877	−	0.231322i	$-0.0743051\pi$
$373$	5.52566	+	9.57072i	0.286108	+	0.495553i	−0.686769	+	0.726875i	$0.740972\pi$
$374$	−6.70510	+	11.6136i	−0.346713	+	0.600524i
$375$	−1.27810	−	4.76995i	−0.0660010	−	0.246319i
$376$	0.270885	+	0.469187i	0.0139698	+	0.0241965i
$377$	6.59145	−	35.3182i	0.339477	−	1.81898i
$378$	−1.48181	−	2.19186i	−0.0762162	−	0.112737i
$379$	−18.9613	−	18.9613i	−0.973976	−	0.973976i	0.0256943	−	0.999670i	$-0.491820\pi$
$379$	−18.9613	−	18.9613i	−0.973976	−	0.973976i	−0.999670	+	0.0256943i	$0.991820\pi$
$380$	−5.81997	−	10.0805i	−0.298558	−	0.517118i
$381$	−3.68421	+	6.38123i	−0.188748	+	0.326921i
$382$	−3.26539	+	0.874958i	−0.167072	+	0.0447667i
$383$	20.9887	+	5.62391i	1.07247	+	0.287368i	0.751509	−	0.659723i	$-0.229326\pi$
$383$	20.9887	+	5.62391i	1.07247	+	0.287368i	0.320964	+	0.947091i	$0.395993\pi$
$384$	−0.707107	−	0.707107i	−0.0360844	−	0.0360844i
$385$	32.3241	−	37.2644i	1.64739	−	1.89917i
$386$	−11.4604			−0.583320
$387$	−7.47326	+	4.31469i	−0.379887	+	0.219328i
$388$	−6.79929	+	1.82186i	−0.345182	+	0.0924911i
$389$	19.4216	+	11.2131i	0.984714	+	0.568525i	0.903690	−	0.428187i	$-0.140848\pi$
$389$	19.4216	+	11.2131i	0.984714	+	0.568525i	0.0810239	+	0.996712i	$0.474181\pi$
$390$	−4.05978	−	11.5101i	−0.205575	−	0.582837i
$391$		−	2.31860i		−	0.117256i
$392$	5.59938	+	4.20083i	0.282811	+	0.212174i
$393$	−0.931033			−0.0469644
$394$	−8.20070	+	4.73468i	−0.413146	+	0.238530i
$395$	1.00502	+	3.75080i	0.0505683	+	0.188723i
$396$	5.32034	−	1.42558i	0.267357	−	0.0716382i
$397$	−3.96216	+	14.7870i	−0.198855	+	0.742137i	0.792380	+	0.610028i	$0.208842\pi$
$397$	−3.96216	+	14.7870i	−0.198855	+	0.742137i	−0.991235	+	0.132110i	$0.957825\pi$
$398$	−4.23241	−	4.23241i	−0.212151	−	0.212151i
$399$	0.644250	+	9.07482i	0.0322529	+	0.454309i
$400$			6.45881i			0.322941i
$401$	12.3810	+	3.31748i	0.618278	+	0.165667i	0.554345	−	0.832287i	$-0.312969\pi$
$401$	12.3810	+	3.31748i	0.618278	+	0.165667i	0.0639331	+	0.997954i	$0.479636\pi$
$402$	−6.09405	+	10.5552i	−0.303943	+	0.526445i
$403$	2.23023	−	0.172722i	0.111096	−	0.00860390i
$404$	−8.70177	+	5.02397i	−0.432929	+	0.249952i
$405$	−2.39362	+	2.39362i	−0.118940	+	0.118940i
$406$	21.8411	−	14.7657i	1.08395	−	0.732811i
$407$			13.3710i			0.662775i
$408$	−0.630138	+	2.35171i	−0.0311965	+	0.116427i
$409$	−3.37799	−	12.6068i	−0.167031	−	0.623368i	−0.997772	−	0.0667098i	$-0.978750\pi$
$409$	−3.37799	−	12.6068i	−0.167031	−	0.623368i	0.830741	−	0.556659i	$-0.187917\pi$
$410$	−8.78422	−	32.7831i	−0.433822	−	1.61904i
$411$	−4.05963	+	15.1507i	−0.200247	+	0.747331i
$412$			10.9982i			0.541841i
$413$	−22.1626	−	10.7803i	−1.09055	−	0.530464i
$414$	−0.673396	+	0.673396i	−0.0330956	+	0.0330956i
$415$	−10.2052	+	5.89196i	−0.500952	+	0.289225i
$416$	0.278402	+	3.59479i	0.0136498	+	0.176249i
$417$	−5.48216	+	9.49537i	−0.268462	+	0.464990i
$418$	−18.2945	−	4.90199i	−0.894813	−	0.239764i
$419$		−	2.56622i		−	0.125368i	−0.998033	−	0.0626841i	$-0.980034\pi$
$419$		−	2.56622i		−	0.125368i	0.998033	−	0.0626841i	$-0.0199661\pi$
$420$	3.91755	−	8.05385i	0.191157	−	0.392988i
$421$	−8.66134	−	8.66134i	−0.422128	−	0.422128i	0.463808	−	0.885936i	$-0.346483\pi$
$421$	−8.66134	−	8.66134i	−0.422128	−	0.422128i	−0.885936	+	0.463808i	$0.846483\pi$
$422$	3.97987	−	14.8531i	0.193737	−	0.723036i
$423$	−0.523310	+	0.140221i	−0.0254442	+	0.00681776i
$424$	−1.36423	−	5.09136i	−0.0662527	−	0.247259i
$425$	13.6183	−	7.86253i	0.660585	−	0.381389i
$426$	−12.4956			−0.605414
$427$	−36.4547	−	7.04593i	−1.76417	−	0.340977i
$428$			8.23274i			0.397945i
$429$	−17.9142	−	8.57208i	−0.864904	−	0.413864i
$430$	−25.2976	−	14.6056i	−1.21996	−	0.704344i
$431$	10.4371	−	2.79663i	0.502740	−	0.134709i	0.00146850	−	0.999999i	$-0.499533\pi$
$431$	10.4371	−	2.79663i	0.502740	−	0.134709i	0.501271	+	0.865290i	$0.332866\pi$
$432$	0.866025	−	0.500000i	0.0416667	−	0.0240563i
$433$	20.1982			0.970665			0.485333	−	0.874330i	$-0.338699\pi$
$433$	20.1982			0.970665			0.485333	+	0.874330i	$0.338699\pi$
$434$	1.23995	+	1.07557i	0.0595196	+	0.0516289i
$435$	−23.8516	−	23.8516i	−1.14359	−	1.14359i
$436$	16.6992	+	4.47455i	0.799748	+	0.214292i
$437$	3.16308	−	0.847544i	0.151310	−	0.0405435i
$438$	−1.43289	+	2.48183i	−0.0684660	+	0.118587i
$439$	2.25623	+	3.90791i	0.107684	+	0.186514i	0.914832	−	0.403835i	$-0.132323\pi$
$439$	2.25623	+	3.90791i	0.107684	+	0.186514i	−0.807148	+	0.590350i	$0.798990\pi$
$440$	13.1841	+	13.1841i	0.628528	+	0.628528i
$441$	−5.50692	+	4.32133i	−0.262234	+	0.205777i
$442$	7.24064	−	4.96306i	0.344402	−	0.236069i
$443$	7.71159	+	13.3569i	0.366389	+	0.634604i	0.988998	−	0.147929i	$-0.0472607\pi$
$443$	7.71159	+	13.3569i	0.366389	+	0.634604i	−0.622609	+	0.782533i	$0.713927\pi$
$444$	0.628295	+	2.34483i	0.0298176	+	0.111281i
$445$	−7.76176	+	13.4438i	−0.367943	+	0.637296i
$446$	−3.13225	−	5.42522i	−0.148317	−	0.256892i
$447$	12.2856	−	12.2856i	0.581091	−	0.581091i
$448$	−1.73365	+	1.99861i	−0.0819072	+	0.0944257i
$449$	18.0218	−	18.0218i	0.850503	−	0.850503i	−0.139692	−	0.990195i	$-0.544611\pi$
$449$	18.0218	−	18.0218i	0.850503	−	0.850503i	0.990195	+	0.139692i	$0.0446112\pi$
$450$	−6.23874	−	1.67166i	−0.294097	−	0.0788030i
$451$	−47.8259	−	27.6123i	−2.25204	−	1.30021i
$452$	14.5552	+	8.40345i	0.684619	+	0.395265i
$453$	−3.66242	+	13.6683i	−0.172076	+	0.642195i
$454$	−4.47008			−0.209791
$455$	−29.6158	+	12.8707i	−1.38841	+	0.603389i
$456$	−3.43859			−0.161027
$457$	−5.36235	+	20.0126i	−0.250840	+	0.936149i	0.719517	+	0.694475i	$0.244363\pi$
$457$	−5.36235	+	20.0126i	−0.250840	+	0.936149i	−0.970357	+	0.241674i	$0.922303\pi$
$458$	−13.1922	−	7.61653i	−0.616431	−	0.355897i
$459$	−2.10848	−	1.21733i	−0.0984156	−	0.0568203i
$460$	−3.11386	−	0.834356i	−0.145184	−	0.0389020i
$461$	15.2571	−	15.2571i	0.710592	−	0.710592i	−0.256067	−	0.966659i	$-0.582427\pi$
$461$	15.2571	−	15.2571i	0.710592	−	0.710592i	0.966659	+	0.256067i	$0.0824269\pi$
$462$	−4.75908	−	13.7739i	−0.221412	−	0.640818i
$463$	4.18978	−	4.18978i	0.194716	−	0.194716i	−0.603015	−	0.797730i	$-0.706034\pi$
$463$	4.18978	−	4.18978i	0.194716	−	0.194716i	0.797730	+	0.603015i	$0.206034\pi$
$464$	4.98232	+	8.62963i	0.231298	+	0.400621i
$465$	1.05006	−	1.81877i	0.0486956	−	0.0843432i
$466$	−0.0289813	−	0.108160i	−0.00134253	−	0.00501040i
$467$	−3.56716	−	6.17851i	−0.165069	−	0.285907i	0.771611	−	0.636095i	$-0.219451\pi$
$467$	−3.56716	−	6.17851i	−0.165069	−	0.285907i	−0.936680	+	0.350187i	$0.886118\pi$
$468$	−3.54435	−	0.661484i	−0.163838	−	0.0305771i
$469$	28.9981	+	14.1052i	1.33901	+	0.651320i
$470$	−1.29679	−	1.29679i	−0.0598165	−	0.0598165i
$471$	1.65072	+	2.85914i	0.0760613	+	0.131742i
$472$	4.65753	−	8.06709i	0.214380	−	0.371318i
$473$	−45.9112	+	12.3019i	−2.11100	+	0.565641i
$474$	1.10804	+	0.296898i	0.0508938	+	0.0136370i
$475$	15.7043	+	15.7043i	0.720562	+	0.720562i
$476$	6.32448	+	1.22239i	0.289882	+	0.0560282i
$477$	5.27097			0.241341
$478$	17.4272	−	10.0616i	0.797102	−	0.460207i
$479$	16.5968	−	4.44710i	0.758327	−	0.203193i	0.141119	−	0.989993i	$-0.454930\pi$
$479$	16.5968	−	4.44710i	0.758327	−	0.203193i	0.617209	+	0.786800i	$0.288263\pi$
$480$	2.93157	+	1.69254i	0.133807	+	0.0772537i
$481$	3.77797	−	7.89530i	0.172261	−	0.359995i
$482$			12.0976i			0.551030i
$483$	1.90333	+	1.65100i	0.0866046	+	0.0751230i
$484$	19.3383			0.879015
$485$	20.6357	−	11.9141i	0.937021	−	0.540989i
$486$	0.258819	+	0.965926i	0.0117403	+	0.0438153i
$487$	0.541400	−	0.145068i	0.0245332	−	0.00657365i	−0.246532	−	0.969135i	$-0.579291\pi$
$487$	0.541400	−	0.145068i	0.0245332	−	0.00657365i	0.271065	+	0.962561i	$0.412624\pi$
$488$	3.63216	−	13.5554i	0.164420	−	0.613624i
$489$	−8.11007	−	8.11007i	−0.366750	−	0.366750i
$490$	−21.9890	−	8.82989i	−0.993361	−	0.398894i
$491$			7.25820i			0.327558i	0.986497	+	0.163779i	$0.0523684\pi$
$491$			7.25820i			0.327558i	−0.986497	+	0.163779i	$0.947632\pi$
$492$	−9.68458	−	2.59498i	−0.436615	−	0.116991i
$493$	12.1303	−	21.0103i	0.546321	−	0.946256i
$494$	9.41747	+	8.06363i	0.423712	+	0.362800i
$495$	−16.1472	+	9.32257i	−0.725761	+	0.419018i
$496$	−0.438693	+	0.438693i	−0.0196979	+	0.0196979i
$497$	2.34116	+	32.9772i	0.105015	+	1.47923i
$498$			3.48112i			0.155993i
$499$	0.163296	−	0.609430i	0.00731015	−	0.0272818i	−0.962174	−	0.272434i	$-0.912171\pi$
$499$	0.163296	−	0.609430i	0.00731015	−	0.0272818i	0.969485	+	0.245152i	$0.0788380\pi$
$500$	−1.27810	−	4.76995i	−0.0571585	−	0.213318i
$501$	−2.17828	−	8.12946i	−0.0973185	−	0.363198i
$502$	−6.16888	+	23.0226i	−0.275330	+	1.02755i
$503$			2.16347i			0.0964643i	0.998836	+	0.0482322i	$0.0153587\pi$
$503$			2.16347i			0.0964643i	−0.998836	+	0.0482322i	$0.984641\pi$
$504$	−1.48181	−	2.19186i	−0.0660052	−	0.0976330i
$505$	24.0509	−	24.0509i	1.07025	−	1.07025i
$506$	−4.54268	+	2.62272i	−0.201947	+	0.116594i
$507$	8.15592	+	10.1233i	0.362217	+	0.449591i
$508$	−3.68421	+	6.38123i	−0.163460	+	0.283122i
$509$	−14.6115	−	3.91515i	−0.647645	−	0.173536i	−0.0799811	−	0.996796i	$-0.525486\pi$
$509$	−14.6115	−	3.91515i	−0.647645	−	0.173536i	−0.567664	+	0.823260i	$0.692153\pi$
$510$		−	8.24156i		−	0.364942i
$511$	6.81829	+	3.31655i	0.301624	+	0.146716i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	0.889973	−	3.32142i	0.0392933	−	0.146644i
$514$	20.1978	−	5.41198i	0.890886	−	0.238712i
$515$	−9.63578	−	35.9612i	−0.424603	−	1.58464i
$516$	−7.47326	+	4.31469i	−0.328992	+	0.189944i
$517$	−2.98408			−0.131240
$518$	6.07055	−	2.09746i	0.266725	−	0.0921573i
$519$		−	20.7056i		−	0.908876i
$520$	−4.05978	−	11.5101i	−0.178033	−	0.504752i
$521$	−9.00542	−	5.19928i	−0.394535	−	0.227785i	0.289588	−	0.957151i	$-0.406482\pi$
$521$	−9.00542	−	5.19928i	−0.394535	−	0.227785i	−0.684123	+	0.729367i	$0.739815\pi$
$522$	−9.62511	+	2.57904i	−0.421279	+	0.112881i
$523$	15.2792	−	8.82145i	0.668113	−	0.385735i	−0.127248	−	0.991871i	$-0.540615\pi$
$523$	15.2792	−	8.82145i	0.668113	−	0.385735i	0.795361	+	0.606136i	$0.207281\pi$
$524$	−0.931033			−0.0406724
$525$	−3.24282	+	16.7779i	−0.141528	+	0.732248i
$526$	4.17774	+	4.17774i	0.182158	+	0.182158i
$527$	1.45901	+	0.390942i	0.0635557	+	0.0170297i
$528$	5.32034	−	1.42558i	0.231538	−	0.0620405i
$529$	−11.0465	+	19.1332i	−0.480284	+	0.831877i
$530$	8.92134	+	15.4522i	0.387518	+	0.671202i
$531$	6.58675	+	6.58675i	0.285841	+	0.285841i
$532$	0.644250	+	9.07482i	0.0279318	+	0.393443i
$533$	20.4384	+	29.8177i	0.885285	+	1.29155i
$534$	2.29293	+	3.97147i	0.0992247	+	0.171862i
$535$	−7.21291	−	26.9190i	−0.311841	−	1.16381i
$536$	−6.09405	+	10.5552i	−0.263223	+	0.455915i
$537$	−0.501506	−	0.868634i	−0.0216416	−	0.0374843i
$538$	20.3318	−	20.3318i	0.876568	−	0.876568i
$539$	−35.4591	+	15.1404i	−1.52733	+	0.652142i
$540$	−2.39362	+	2.39362i	−0.103005	+	0.103005i
$541$	−9.53526	−	2.55496i	−0.409953	−	0.109846i	0.0479480	−	0.998850i	$-0.484732\pi$
$541$	−9.53526	−	2.55496i	−0.409953	−	0.109846i	−0.457901	+	0.889003i	$0.651398\pi$
$542$	−1.94389	−	1.12231i	−0.0834973	−	0.0482072i
$543$	15.0927	+	8.71380i	0.647692	+	0.373945i
$544$	−0.630138	+	2.35171i	−0.0270170	+	0.100829i
$545$	−58.5225			−2.50683
$546$	−1.08166	+	9.47787i	−0.0462909	+	0.405615i
$547$	1.20517			0.0515293			0.0257647	−	0.999668i	$-0.491798\pi$
$547$	1.20517			0.0515293			0.0257647	+	0.999668i	$0.491798\pi$
$548$	−4.05963	+	15.1507i	−0.173419	+	0.647208i
$549$	12.1534	+	7.01679i	0.518696	+	0.299469i
$550$	−30.8091	−	17.7877i	−1.31371	−	0.758468i
$551$	33.0968	+	8.86826i	1.40997	+	0.377801i
$552$	−0.673396	+	0.673396i	−0.0286616	+	0.0286616i
$553$	0.575945	−	2.97986i	0.0244917	−	0.126716i
$554$	13.2103	−	13.2103i	0.561250	−	0.561250i
$555$	−4.10873	−	7.11653i	−0.174406	−	0.302080i
$556$	−5.48216	+	9.49537i	−0.232495	+	0.402694i
$557$	−1.78013	−	6.64353i	−0.0754265	−	0.281495i	0.917903	−	0.396804i	$-0.129881\pi$
$557$	−1.78013	−	6.64353i	−0.0754265	−	0.281495i	−0.993330	+	0.115309i	$0.963214\pi$
$558$	−0.310203	−	0.537288i	−0.0131319	−	0.0227452i
$559$	30.5856	+	5.70819i	1.29363	+	0.241431i
$560$	3.91755	−	8.05385i	0.165547	−	0.340337i
$561$	−9.48245	−	9.48245i	−0.400349	−	0.400349i
$562$	−7.71454	−	13.3620i	−0.325418	−	0.563641i
$563$	−0.208837	+	0.361716i	−0.00880142	+	0.0152445i	−0.870393	−	0.492358i	$-0.836135\pi$
$563$	−0.208837	+	0.361716i	−0.00880142	+	0.0152445i	0.861591	+	0.507603i	$0.169468\pi$
$564$	−0.523310	+	0.140221i	−0.0220353	+	0.00590435i
$565$	−54.9542	−	14.7249i	−2.31194	−	0.619483i
$566$	−10.6308	−	10.6308i	−0.446845	−	0.446845i
$567$	2.50069	−	0.864026i	0.105019	−	0.0362857i
$568$	−12.4956			−0.524304
$569$	28.1918	−	16.2765i	1.18186	−	0.682348i	0.225417	−	0.974262i	$-0.427625\pi$
$569$	28.1918	−	16.2765i	1.18186	−	0.682348i	0.956445	+	0.291914i	$0.0942921\pi$
$570$	11.2433	−	3.01264i	0.470930	−	0.126185i
$571$	−31.6764	−	18.2884i	−1.32561	−	0.765344i	−0.340996	−	0.940065i	$-0.610764\pi$
$571$	−31.6764	−	18.2884i	−1.32561	−	0.765344i	−0.984618	+	0.174721i	$0.944098\pi$
$572$	−17.9142	−	8.57208i	−0.749029	−	0.358417i
$573$		−	3.38058i		−	0.141226i
$574$	−5.03393	+	26.0449i	−0.210112	+	1.08709i
$575$	6.15089			0.256510
$576$	0.866025	−	0.500000i	0.0360844	−	0.0208333i
$577$	4.59918	+	17.1644i	0.191466	+	0.714562i	0.993153	+	0.116818i	$0.0372694\pi$
$577$	4.59918	+	17.1644i	0.191466	+	0.714562i	−0.801687	+	0.597744i	$0.796064\pi$
$578$	−10.6951	+	2.86575i	−0.444858	+	0.119199i
$579$	2.96618	−	11.0699i	0.123270	−	0.460050i
$580$	−23.8516	−	23.8516i	−0.990382	−	0.990382i
$581$	9.18707	−	0.652219i	0.381144	−	0.0270586i
$582$		−	7.03914i		−	0.291782i
$583$	28.0434	+	7.51419i	1.16144	+	0.311206i
$584$	−1.43289	+	2.48183i	−0.0592933	+	0.102699i
$585$	12.1687	−	0.942414i	0.503112	−	0.0389640i
$586$	5.46040	−	3.15256i	0.225567	−	0.130231i
$587$	−3.24643	+	3.24643i	−0.133995	+	0.133995i	−0.770923	−	0.636928i	$-0.780205\pi$
$587$	−3.24643	+	3.24643i	−0.133995	+	0.133995i	0.636928	+	0.770923i	$0.280205\pi$
$588$	−5.50692	+	4.32133i	−0.227101	+	0.178209i
$589$			2.13332i			0.0879021i
$590$	−8.16116	+	30.4579i	−0.335990	+	1.25393i
$591$	−2.45085	−	9.14670i	−0.100815	−	0.376245i
$592$	0.628295	+	2.34483i	0.0258228	+	0.0963719i
$593$	−1.74404	+	6.50885i	−0.0716191	+	0.267286i	−0.992445	−	0.122687i	$-0.960849\pi$
$593$	−1.74404	+	6.50885i	−0.0716191	+	0.267286i	0.920826	+	0.389973i	$0.127516\pi$
$594$			5.50802i			0.225997i
$595$	−21.7504	+	1.54413i	−0.891679	+	0.0633031i
$596$	12.2856	−	12.2856i	0.503240	−	0.503240i
$597$	5.18362	−	2.99276i	0.212151	−	0.122486i
$598$	3.42341	−	0.265129i	0.139994	−	0.0108419i
$599$	6.27256	−	10.8644i	0.256290	−	0.443907i	−0.708955	−	0.705254i	$-0.750833\pi$
$599$	6.27256	−	10.8644i	0.256290	−	0.443907i	0.965245	+	0.261346i	$0.0841665\pi$
$600$	−6.23874	−	1.67166i	−0.254695	−	0.0682454i
$601$			35.8923i			1.46408i	0.681263	+	0.732039i	$0.261431\pi$
$601$			35.8923i			1.46408i	−0.681263	+	0.732039i	$0.738569\pi$
$602$	12.7871	+	18.9143i	0.521164	+	0.770891i
$603$	−8.61828	−	8.61828i	−0.350964	−	0.350964i
$604$	−3.66242	+	13.6683i	−0.149022	+	0.556157i
$605$	−63.2314	+	16.9428i	−2.57072	+	0.688822i
$606$	−2.60060	−	9.70556i	−0.105642	−	0.394261i
$607$	20.0726	−	11.5889i	0.814723	−	0.470381i	−0.0338702	−	0.999426i	$-0.510783\pi$
$607$	20.0726	−	11.5889i	0.814723	−	0.470381i	0.848593	+	0.529046i	$0.177450\pi$
$608$	−3.43859			−0.139453
$609$	8.60972	+	24.9185i	0.348883	+	1.00975i
$610$			47.5049i			1.92342i
$611$	1.76204	+	0.843152i	0.0712846	+	0.0341103i
$612$	−2.10848	−	1.21733i	−0.0852304	−	0.0492078i
$613$	−7.65088	+	2.05005i	−0.309016	+	0.0828006i	−0.409994	−	0.912088i	$-0.634469\pi$
$613$	−7.65088	+	2.05005i	−0.309016	+	0.0828006i	0.100978	+	0.994889i	$0.467803\pi$
$614$	−4.95933	+	2.86327i	−0.200142	+	0.115552i
$615$	33.9396			1.36858
$616$	−4.75908	−	13.7739i	−0.191749	−	0.554965i
$617$	−7.53021	−	7.53021i	−0.303155	−	0.303155i	0.539092	−	0.842247i	$-0.318767\pi$
$617$	−7.53021	−	7.53021i	−0.303155	−	0.303155i	−0.842247	+	0.539092i	$0.818767\pi$
$618$	−10.6234	−	2.84654i	−0.427337	−	0.114505i
$619$	−8.96181	+	2.40131i	−0.360205	+	0.0965168i	−0.434383	−	0.900728i	$-0.643034\pi$
$619$	−8.96181	+	2.40131i	−0.360205	+	0.0965168i	0.0741775	+	0.997245i	$0.476367\pi$
$620$	1.05006	−	1.81877i	0.0421716	−	0.0730434i
$621$	−0.476163	−	0.824738i	−0.0191077	−	0.0330956i
$622$	−18.3053	−	18.3053i	−0.733975	−	0.733975i
$623$	10.0515	−	6.79538i	0.402706	−	0.272251i
$624$	−3.54435	−	0.661484i	−0.141888	−	0.0264805i
$625$	−7.78890	−	13.4908i	−0.311556	−	0.539631i
$626$	1.94073	+	7.24289i	0.0775670	+	0.289484i
$627$	9.46992	−	16.4024i	0.378192	−	0.655048i
$628$	1.65072	+	2.85914i	0.0658710	+	0.114092i
$629$	4.17919	−	4.17919i	0.166635	−	0.166635i
$630$	6.76548	+	5.86855i	0.269543	+	0.233809i
$631$	−34.0998	+	34.0998i	−1.35749	+	1.35749i	−0.480497	+	0.876997i	$0.659544\pi$
$631$	−34.0998	+	34.0998i	−1.35749	+	1.35749i	−0.876997	+	0.480497i	$0.840456\pi$
$632$	1.10804	+	0.296898i	0.0440754	+	0.0118100i
$633$	13.3169	+	7.68851i	0.529299	+	0.305591i
$634$	6.11239	+	3.52899i	0.242754	+	0.140154i
$635$	6.45565	−	24.0928i	0.256185	−	0.956095i
$636$	5.27097			0.209007
$637$	25.2158	+	1.07886i	0.999086	+	0.0427461i
$638$	−54.8855			−2.17294
$639$	3.23410	−	12.0698i	0.127939	−	0.477475i
$640$	2.93157	+	1.69254i	0.115881	+	0.0669037i
$641$	−37.5455	−	21.6769i	−1.48296	−	0.856187i	−0.483146	−	0.875540i	$-0.660506\pi$
$641$	−37.5455	−	21.6769i	−1.48296	−	0.856187i	−0.999813	+	0.0193532i	$0.993839\pi$
$642$	−7.95222	−	2.13079i	−0.313849	−	0.0840956i
$643$	−17.2911	+	17.2911i	−0.681895	+	0.681895i	−0.960427	−	0.278532i	$-0.910152\pi$
$643$	−17.2911	+	17.2911i	−0.681895	+	0.681895i	0.278532	+	0.960427i	$0.410152\pi$
$644$	1.90333	+	1.65100i	0.0750018	+	0.0650584i
$645$	20.6554	−	20.6554i	0.813307	−	0.813307i
$646$	4.18591	+	7.25021i	0.164693	+	0.285256i
$647$	20.7092	−	35.8694i	0.814163	−	1.41017i	−0.0957651	−	0.995404i	$-0.530530\pi$
$647$	20.7092	−	35.8694i	0.814163	−	1.41017i	0.909928	−	0.414767i	$-0.136137\pi$
$648$	0.258819	+	0.965926i	0.0101674	+	0.0379452i
$649$	25.6538	+	44.4337i	1.00700	+	1.74418i
$650$	13.1663	+	19.2084i	0.516424	+	0.753414i
$651$	−1.35984	+	0.919325i	−0.0532964	+	0.0360312i
$652$	−8.11007	−	8.11007i	−0.317615	−	0.317615i
$653$	−21.4281	−	37.1145i	−0.838545	−	1.45240i	−0.891112	−	0.453784i	$-0.850074\pi$
$653$	−21.4281	−	37.1145i	−0.838545	−	1.45240i	0.0525670	−	0.998617i	$-0.483260\pi$
$654$	−8.64416	+	14.9721i	−0.338013	+	0.585456i
$655$	3.04424	−	0.815701i	0.118948	−	0.0318721i
$656$	−9.68458	−	2.59498i	−0.378119	−	0.101317i
$657$	−2.02641	−	2.02641i	−0.0790577	−	0.0790577i
$658$	0.468104	+	1.35480i	0.0182486	+	0.0528156i
$659$	7.74721			0.301789			0.150894	−	0.988550i	$-0.451785\pi$
$659$	7.74721			0.301789			0.150894	+	0.988550i	$0.451785\pi$
$660$	−16.1472	+	9.32257i	−0.628528	+	0.362881i
$661$	33.4785	−	8.97055i	1.30216	−	0.348914i	0.459896	−	0.887973i	$-0.347887\pi$
$661$	33.4785	−	8.97055i	1.30216	−	0.348914i	0.842268	+	0.539059i	$0.181220\pi$
$662$	4.34864	+	2.51069i	0.169015	+	0.0975807i
$663$	2.91993	+	8.27846i	0.113401	+	0.321509i
$664$			3.48112i			0.135094i
$665$	−10.0572	−	29.1079i	−0.390002	−	1.12876i
$666$	−2.42755			−0.0940655
$667$	8.21822	−	4.74479i	0.318211	−	0.183719i
$668$	−2.17828	−	8.12946i	−0.0842803	−	0.314538i
$669$	6.05105	−	1.62137i	0.233947	−	0.0626860i
$670$	10.6783	−	39.8519i	0.412538	−	1.53961i
$671$	54.6574	+	54.6574i	2.11003	+	2.11003i
$672$	−1.48181	−	2.19186i	−0.0571621	−	0.0845527i
$673$			15.3973i			0.593523i	0.954952	+	0.296761i	$0.0959066\pi$
$673$			15.3973i			0.593523i	−0.954952	+	0.296761i	$0.904093\pi$
$674$	−12.3484	−	3.30874i	−0.475642	−	0.127448i
$675$	3.22941	−	5.59350i	0.124300	−	0.215294i
$676$	8.15592	+	10.1233i	0.313689	+	0.389357i
$677$	−38.9245	+	22.4731i	−1.49599	+	0.863711i	−0.999989	−	0.00460997i	$-0.998533\pi$
$677$	−38.9245	+	22.4731i	−1.49599	+	0.863711i	−0.496002	+	0.868321i	$0.665199\pi$
$678$	−11.8843	+	11.8843i	−0.456413	+	0.456413i
$679$	−18.5771	+	1.31884i	−0.712922	+	0.0506126i
$680$		−	8.24156i		−	0.316049i
$681$	1.15694	−	4.31777i	0.0443342	−	0.165457i
$682$	−0.884440	−	3.30077i	−0.0338669	−	0.126393i
$683$	5.84412	+	21.8105i	0.223619	+	0.834557i	0.982953	+	0.183856i	$0.0588581\pi$
$683$	5.84412	+	21.8105i	0.223619	+	0.834557i	−0.759334	+	0.650701i	$0.774475\pi$
$684$	0.889973	−	3.32142i	0.0340290	−	0.126998i
$685$		−	53.0958i		−	2.02869i
$686$	12.4362	+	13.7237i	0.474817	+	0.523974i
$687$	10.7714	−	10.7714i	0.410954	−	0.410954i
$688$	−7.47326	+	4.31469i	−0.284915	+	0.164496i
$689$	−14.4359	−	12.3606i	−0.549964	−	0.470902i
$690$	1.61185	−	2.79181i	0.0613622	−	0.106282i
$691$	1.67010	+	0.447502i	0.0635336	+	0.0170238i	0.290446	−	0.956891i	$-0.406196\pi$
$691$	1.67010	+	0.447502i	0.0635336	+	0.0170238i	−0.226912	+	0.973915i	$0.572863\pi$
$692$		−	20.7056i		−	0.787109i
$693$	14.5363	−	1.03198i	0.552187	−	0.0392016i
$694$	16.2418	+	16.2418i	0.616529	+	0.616529i
$695$	9.60611	−	35.8505i	0.364380	−	1.35989i
$696$	−9.62511	+	2.57904i	−0.364839	+	0.0977582i
$697$	6.31790	+	23.5787i	0.239308	+	0.893108i
$698$	−3.60721	+	2.08262i	−0.136535	+	0.0788285i
$699$	0.111975			0.00423529
$700$	−3.24282	+	16.7779i	−0.122567	+	0.634145i
$701$			0.844039i			0.0318789i	0.999873	+	0.0159394i	$0.00507390\pi$
$701$			0.844039i			0.0318789i	−0.999873	+	0.0159394i	$0.994926\pi$
$702$	1.55629	−	3.25238i	0.0587384	−	0.122753i
$703$	7.22901	+	4.17367i	0.272647	+	0.157413i
$704$	5.32034	−	1.42558i	0.200518	−	0.0537286i
$705$	1.58824	−	0.916970i	0.0598165	−	0.0345351i
$706$	−3.40494			−0.128147
$707$	−25.1268	+	8.68168i	−0.944990	+	0.326508i
$708$	6.58675	+	6.58675i	0.247545	+	0.247545i
$709$	−4.80893	−	1.28855i	−0.180603	−	0.0483924i	0.167384	−	0.985892i	$-0.446468\pi$
$709$	−4.80893	−	1.28855i	−0.180603	−	0.0483924i	−0.347987	+	0.937499i	$0.613135\pi$
$710$	40.8574	−	10.9477i	1.53335	−	0.410860i
$711$	−0.573562	+	0.993439i	−0.0215103	+	0.0372569i
$712$	2.29293	+	3.97147i	0.0859311	+	0.148837i
$713$	0.417779	+	0.417779i	0.0156459	+	0.0156459i
$714$	−2.81763	+	5.79260i	−0.105447	+	0.216782i
$715$	66.0850	+	12.3335i	2.47144	+	0.461245i
$716$	−0.501506	−	0.868634i	−0.0187422	−	0.0324624i
$717$	5.20827	+	19.4375i	0.194506	+	0.725907i
$718$	−14.0605	+	24.3535i	−0.524732	+	0.908863i
$719$	7.92066	+	13.7190i	0.295391	+	0.511632i	0.975076	−	0.221872i	$-0.0712168\pi$
$719$	7.92066	+	13.7190i	0.295391	+	0.511632i	−0.679685	+	0.733504i	$0.737883\pi$
$720$	−2.39362	+	2.39362i	−0.0892049	+	0.0892049i
$721$	−5.52193	+	28.5697i	−0.205647	+	1.06399i
$722$	5.07426	−	5.07426i	0.188844	−	0.188844i
$723$	−11.6854	−	3.13108i	−0.434583	−	0.116446i
$724$	15.0927	+	8.71380i	0.560918	+	0.323846i
$725$	55.7372	+	32.1799i	2.07003	+	1.19513i
$726$	−5.00513	+	18.6794i	−0.185758	+	0.693257i
$727$	−45.6887			−1.69450			−0.847249	−	0.531195i	$-0.821743\pi$
$727$	−45.6887			−1.69450			−0.847249	+	0.531195i	$0.821743\pi$
$728$	−1.08166	+	9.47787i	−0.0400891	+	0.351273i
$729$	−1.00000			−0.0370370
$730$	2.51078	−	9.37035i	0.0929280	−	0.346812i
$731$	18.1949	+	10.5048i	0.672963	+	0.388535i
$732$	12.1534	+	7.01679i	0.449204	+	0.259348i
$733$	−0.742039	−	0.198829i	−0.0274078	−	0.00734390i	0.245089	−	0.969501i	$-0.421183\pi$
$733$	−0.742039	−	0.198829i	−0.0274078	−	0.00734390i	−0.272497	+	0.962157i	$0.587849\pi$
$734$	26.0925	−	26.0925i	0.963091	−	0.963091i
$735$	14.2202	−	18.9544i	0.524519	−	0.699143i
$736$	−0.673396	+	0.673396i	−0.0248217	+	0.0248217i
$737$	−33.5662	−	58.1383i	−1.23643	−	2.14155i
$738$	5.01311	−	8.68296i	0.184535	−	0.319624i
$739$	−4.38177	−	16.3530i	−0.161186	−	0.601555i	−0.998496	−	0.0548261i	$-0.982540\pi$
$739$	−4.38177	−	16.3530i	−0.161186	−	0.601555i	0.837310	−	0.546729i	$-0.184127\pi$
$740$	−4.10873	−	7.11653i	−0.151040	−	0.261609i
$741$	−10.2263	+	7.00956i	−0.375672	+	0.257503i
$742$	−0.987562	−	13.9107i	−0.0362546	−	0.510676i
$743$	24.9729	+	24.9729i	0.916168	+	0.916168i	0.996748	−	0.0805800i	$-0.0256773\pi$
$743$	24.9729	+	24.9729i	0.916168	+	0.916168i	−0.0805800	+	0.996748i	$0.525677\pi$
$744$	−0.310203	−	0.537288i	−0.0113726	−	0.0196979i
$745$	−29.4071	+	50.9347i	−1.07739	+	1.86610i
$746$	−10.6748	+	2.86029i	−0.390831	+	0.104723i
$747$	−3.36251	−	0.900981i	−0.123028	−	0.0329652i
$748$	−9.48245	−	9.48245i	−0.346713	−	0.346713i
$749$	−4.13347	+	21.3860i	−0.151034	+	0.781427i
$750$	4.93821			0.180318
$751$	−19.6538	+	11.3471i	−0.717178	+	0.414063i	−0.813713	−	0.581267i	$-0.802557\pi$
$751$	−19.6538	+	11.3471i	−0.717178	+	0.414063i	0.0965354	+	0.995330i	$0.469224\pi$
$752$	−0.523310	+	0.140221i	−0.0190832	+	0.00511332i
$753$	−20.6415	−	11.9174i	−0.752217	−	0.434292i
$754$	32.4088	+	15.5079i	1.18026	+	0.564764i
$755$		−	47.9007i		−	1.74329i
$756$	2.50069	−	0.864026i	0.0909493	−	0.0314243i
$757$	11.4156			0.414907			0.207454	−	0.978245i	$-0.433482\pi$
$757$	11.4156			0.414907			0.207454	+	0.978245i	$0.433482\pi$
$758$	23.2227	−	13.4076i	0.843488	−	0.486988i
$759$	−1.35762	−	5.06670i	−0.0492784	−	0.183909i
$760$	11.2433	−	3.01264i	0.407838	−	0.109280i
$761$	−1.59251	+	5.94332i	−0.0577284	+	0.215445i	−0.988764	−	0.149482i	$-0.952239\pi$
$761$	−1.59251	+	5.94332i	−0.0577284	+	0.215445i	0.931036	+	0.364927i	$0.118906\pi$
$762$	−5.21026	−	5.21026i	−0.188748	−	0.188748i
$763$	41.1326	+	20.0077i	1.48910	+	0.724328i
$764$		−	3.38058i		−	0.122305i
$765$	7.96074	+	2.13307i	0.287821	+	0.0771214i
$766$	−10.8646	+	18.8180i	−0.392552	+	0.679921i
$767$	−2.59333	−	33.4857i	−0.0936398	−	1.20910i
$768$	0.866025	−	0.500000i	0.0312500	−	0.0180422i
$769$	24.7530	−	24.7530i	0.892615	−	0.892615i	−0.102154	−	0.994769i	$-0.532573\pi$
$769$	24.7530	−	24.7530i	0.892615	−	0.892615i	0.994769	+	0.102154i	$0.0325734\pi$
$770$	27.6286	+	40.8675i	0.995665	+	1.47276i
$771$			20.9103i			0.753066i
$772$	2.96618	−	11.0699i	0.106755	−	0.398415i
$773$	5.74468	+	21.4394i	0.206622	+	0.771123i	0.988949	+	0.148256i	$0.0473658\pi$
$773$	5.74468	+	21.4394i	0.206622	+	0.771123i	−0.782327	+	0.622868i	$0.785967\pi$
$774$	−2.23345	−	8.33534i	−0.0802796	−	0.299607i
$775$	−1.03711	+	3.87055i	−0.0372541	+	0.139034i
$776$		−	7.03914i		−	0.252690i
$777$	0.454822	+	6.40656i	0.0163167	+	0.229834i
$778$	−15.8577	+	15.8577i	−0.568525	+	0.568525i
$779$	−29.8571	+	17.2380i	−1.06974	+	0.617616i
$780$	12.1687	−	0.942414i	0.435708	−	0.0337438i
$781$	34.4130	−	59.6051i	1.23139	−	2.13284i
$782$	2.23959	+	0.600097i	0.0800876	+	0.0214594i
$783$		−	9.96464i		−	0.356107i
$784$	−5.50692	+	4.32133i	−0.196676	+	0.154333i
$785$	−7.90240	−	7.90240i	−0.282049	−	0.282049i
$786$	0.240969	−	0.899309i	0.00859508	−	0.0320773i
$787$	10.6172	−	2.84488i	0.378464	−	0.101409i	−0.0645717	−	0.997913i	$-0.520568\pi$
$787$	10.6172	−	2.84488i	0.378464	−	0.101409i	0.443036	+	0.896504i	$0.353901\pi$
$788$	−2.45085	−	9.14670i	−0.0873079	−	0.325838i
$789$	−5.11667	+	2.95411i	−0.182158	+	0.105169i
$790$	−3.88312			−0.138155
$791$	33.5905	+	29.1373i	1.19434	+	1.03600i
$792$			5.50802i			0.195719i
$793$	−16.8307	−	47.7175i	−0.597675	−	1.69450i
$794$	−13.2576	−	7.65431i	−0.470496	−	0.271641i
$795$	−17.2347	+	4.61803i	−0.611252	+	0.163785i
$796$	5.18362	−	2.99276i	0.183729	−	0.106076i
$797$	−51.4534			−1.82257			−0.911286	−	0.411774i	$-0.864909\pi$
$797$	−51.4534			−1.82257			−0.911286	+	0.411774i	$0.864909\pi$
$798$	−8.93235	−	1.72644i	−0.316202	−	0.0611152i
$799$	0.932696	+	0.932696i	0.0329964	+	0.0329964i
$800$	−6.23874	−	1.67166i	−0.220573	−	0.0591022i
$801$	−4.42960	+	1.18691i	−0.156512	+	0.0419373i
$802$	−6.40888	+	11.1005i	−0.226305	+	0.391972i
$803$	−7.89238	−	13.6700i	−0.278516	−	0.482404i
$804$	−8.61828	−	8.61828i	−0.303943	−	0.303943i
$805$	−7.66988	−	3.73078i	−0.270328	−	0.131493i
$806$	−0.410389	+	2.19894i	−0.0144553	+	0.0774543i
$807$	14.3768	+	24.9013i	0.506087	+	0.876568i
$808$	−2.60060	−	9.70556i	−0.0914887	−	0.341440i
$809$	−22.4876	+	38.9497i	−0.790623	+	1.36940i	0.134958	+	0.990851i	$0.456910\pi$
$809$	−22.4876	+	38.9497i	−0.790623	+	1.36940i	−0.925582	+	0.378548i	$0.876423\pi$
$810$	−1.69254	−	2.93157i	−0.0594699	−	0.103005i
$811$	27.5353	−	27.5353i	0.966894	−	0.966894i	−0.0325753	−	0.999469i	$-0.510371\pi$
$811$	27.5353	−	27.5353i	0.966894	−	0.966894i	0.999469	+	0.0325753i	$0.0103709\pi$
$812$	8.60972	+	24.9185i	0.302142	+	0.874468i
$813$	1.58718	−	1.58718i	0.0556649	−	0.0556649i
$814$	−12.9154	−	3.46067i	−0.452684	−	0.121296i
$815$	33.6233	+	19.4124i	1.17777	+	0.679987i
$816$	−2.10848	−	1.21733i	−0.0738117	−	0.0426152i
$817$	−7.67991	+	28.6618i	−0.268686	+	1.00275i
$818$	13.0516			0.456337
$819$	−8.87496	−	3.49786i	−0.310116	−	0.122225i
$820$	33.9396			1.18522
$821$	−10.4376	+	38.9535i	−0.364274	+	1.35949i	0.504129	+	0.863628i	$0.331814\pi$
$821$	−10.4376	+	38.9535i	−0.364274	+	1.35949i	−0.868403	+	0.495859i	$0.834853\pi$
$822$	−13.5838	−	7.84260i	−0.473789	−	0.273542i
$823$	28.8404	+	16.6510i	1.00531	+	0.580418i	0.909816	−	0.415012i	$-0.136223\pi$
$823$	28.8404	+	16.6510i	1.00531	+	0.580418i	0.0954973	+	0.995430i	$0.469556\pi$
$824$	−10.6234	−	2.84654i	−0.370084	−	0.0991638i
$825$	25.1555	−	25.1555i	0.875803	−	0.875803i
$826$	16.1491	−	18.6172i	0.561898	−	0.647776i
$827$	−39.4707	+	39.4707i	−1.37253	+	1.37253i	−0.515852	+	0.856677i	$0.672525\pi$
$827$	−39.4707	+	39.4707i	−1.37253	+	1.37253i	−0.856677	+	0.515852i	$0.827475\pi$
$828$	−0.476163	−	0.824738i	−0.0165478	−	0.0286616i
$829$	25.3637	−	43.9312i	0.880918	−	1.52579i	0.0305961	−	0.999532i	$-0.490259\pi$
$829$	25.3637	−	43.9312i	0.880918	−	1.52579i	0.850322	−	0.526263i	$-0.176407\pi$
$830$	−3.04990	−	11.3824i	−0.105864	−	0.395088i
$831$	9.34106	+	16.1792i	0.324038	+	0.561250i
$832$	−3.54435	−	0.661484i	−0.122878	−	0.0229328i
$833$	15.8152	+	6.35075i	0.547964	+	0.220040i
$834$	−7.75294	−	7.75294i	−0.268462	−	0.268462i
$835$	14.2449	+	24.6728i	0.492963	+	0.853838i
$836$	9.46992	−	16.4024i	0.327524	−	0.567288i
$837$	0.599266	−	0.160573i	0.0207137	−	0.00555021i
$838$	2.47878	+	0.664188i	0.0856281	+	0.0229440i
$839$	−40.4977	−	40.4977i	−1.39814	−	1.39814i	−0.805388	−	0.592748i	$-0.798043\pi$
$839$	−40.4977	−	40.4977i	−1.39814	−	1.39814i	−0.592748	−	0.805388i	$-0.701957\pi$
$840$	6.76548	+	5.86855i	0.233431	+	0.202484i
$841$	70.2941			2.42394
$842$	10.6079	−	6.12449i	0.365574	−	0.211064i
$843$	14.9034	−	3.99334i	0.513299	−	0.137538i
$844$	13.3169	+	7.68851i	0.458386	+	0.264650i
$845$	−35.5370	−	25.9549i	−1.22251	−	0.892877i
$846$		−	0.541771i		−	0.0186265i
$847$	50.2347	+	9.70933i	1.72608	+	0.333616i
$848$	5.27097			0.181006
$849$	13.0200	−	7.51710i	0.446845	−	0.257986i
$850$	4.06995	+	15.1892i	0.139598	+	0.520987i
$851$	2.23304	−	0.598342i	0.0765477	−	0.0205109i
$852$	3.23410	−	12.0698i	0.110798	−	0.413505i
$853$	18.7260	+	18.7260i	0.641167	+	0.641167i	0.950842	−	0.309676i	$-0.100220\pi$
$853$	18.7260	+	18.7260i	0.641167	+	0.641167i	−0.309676	+	0.950842i	$0.600220\pi$
$854$	16.2410	−	33.3889i	0.555756	−	1.14254i
$855$			11.6399i			0.398077i
$856$	−7.95222	−	2.13079i	−0.271801	−	0.0728289i
$857$	17.0390	−	29.5124i	0.582041	−	1.00812i	−0.413196	−	0.910642i	$-0.635588\pi$
$857$	17.0390	−	29.5124i	0.582041	−	1.00812i	0.995237	−	0.0974823i	$-0.0310789\pi$
$858$	12.9165	−	15.0851i	0.440963	−	0.514998i
$859$	−17.5587	+	10.1375i	−0.599094	+	0.345887i	−0.768685	−	0.639627i	$-0.779089\pi$
$859$	−17.5587	+	10.1375i	−0.599094	+	0.345887i	0.169591	+	0.985515i	$0.445755\pi$
$860$	20.6554	−	20.6554i	0.704344	−	0.704344i
$861$	−23.8545	−	11.6033i	−0.812960	−	0.395440i
$862$			10.8053i			0.368031i
$863$	−5.34873	+	19.9617i	−0.182073	+	0.679505i	0.813165	+	0.582033i	$0.197743\pi$
$863$	−5.34873	+	19.9617i	−0.182073	+	0.679505i	−0.995238	+	0.0974726i	$0.968924\pi$
$864$	0.258819	+	0.965926i	0.00880520	+	0.0328615i
$865$	18.1407	+	67.7020i	0.616803	+	2.30194i
$866$	−5.22769	+	19.5100i	−0.177644	+	0.662977i
$867$		−	11.0724i		−	0.376038i
$868$	−1.35984	+	0.919325i	−0.0461560	+	0.0312039i
$869$	−4.46778	+	4.46778i	−0.151559	+	0.151559i
$870$	29.2121	−	16.8656i	0.990382	−	0.571797i
$871$	3.39319	+	43.8136i	0.114974	+	1.48457i
$872$	−8.64416	+	14.9721i	−0.292728	+	0.507020i
$873$	6.79929	+	1.82186i	0.230121	+	0.0616607i
$874$			3.27466i			0.110767i
$875$	−0.925217	−	13.0325i	−0.0312781	−	0.440578i
$876$	−2.02641	−	2.02641i	−0.0684660	−	0.0684660i
$877$	−7.65872	+	28.5827i	−0.258616	+	0.965170i	0.707426	+	0.706787i	$0.249856\pi$
$877$	−7.65872	+	28.5827i	−0.258616	+	0.965170i	−0.966043	+	0.258383i	$0.916810\pi$
$878$	−4.35871	+	1.16791i	−0.147099	+	0.0394151i
$879$	1.63189	+	6.09029i	0.0550422	+	0.205420i
$880$	−16.1472	+	9.32257i	−0.544321	+	0.314264i
$881$	28.6254			0.964413			0.482207	−	0.876058i	$-0.339835\pi$
$881$	28.6254			0.964413			0.482207	+	0.876058i	$0.339835\pi$
$882$	−2.74879	−	6.43771i	−0.0925565	−	0.216769i
$883$			33.5425i			1.12880i	0.825503	+	0.564398i	$0.190892\pi$
$883$			33.5425i			1.12880i	−0.825503	+	0.564398i	$0.809108\pi$
$884$	2.91993	+	8.27846i	0.0982080	+	0.278435i
$885$	−27.3078	−	15.7662i	−0.917941	−	0.529974i
$886$	−14.8976	+	3.99181i	−0.500496	+	0.134108i
$887$	27.3293	−	15.7786i	0.917627	−	0.529792i	0.0347498	−	0.999396i	$-0.488937\pi$
$887$	27.3293	−	15.7786i	0.917627	−	0.529792i	0.882877	+	0.469604i	$0.155603\pi$
$888$	−2.42755			−0.0814631
$889$	−12.7742	+	14.7266i	−0.428435	+	0.493915i
$890$	−10.9768	−	10.9768i	−0.367943	−	0.367943i
$891$	−5.32034	−	1.42558i	−0.178238	−	0.0477588i
$892$	6.05105	−	1.62137i	0.202604	−	0.0542876i
$893$	−0.931464	+	1.61334i	−0.0311702	+	0.0539885i
$894$	8.68726	+	15.0468i	0.290546	+	0.503240i
$895$	2.40083	+	2.40083i	0.0802508	+	0.0802508i
$896$	−1.48181	−	2.19186i	−0.0495039	−	0.0732248i
$897$	−0.629948	+	3.37538i	−0.0210333	+	0.112701i
$898$	12.7434	+	22.0722i	0.425252	+	0.736557i
$899$	1.60005	+	5.97148i	0.0533647	+	0.199160i
$900$	3.22941	−	5.59350i	0.107647	−	0.186450i
$901$	−6.41653	−	11.1138i	−0.213766	−	0.370253i
$902$	39.0497	−	39.0497i	1.30021	−	1.30021i
$903$	−21.5794	+	7.45601i	−0.718118	+	0.248120i
$904$	−11.8843	+	11.8843i	−0.395265	+	0.395265i
$905$	−56.9838	−	15.2688i	−1.89421	−	0.507551i
$906$	−12.2547	−	7.07526i	−0.407135	−	0.235060i
$907$	−39.5608	−	22.8404i	−1.31359	−	0.758404i	−0.330904	−	0.943664i	$-0.607354\pi$
$907$	−39.5608	−	22.8404i	−1.31359	−	0.758404i	−0.982689	+	0.185260i	$0.940687\pi$
$908$	1.15694	−	4.31777i	0.0383945	−	0.143290i
$909$	10.0479			0.333269
$910$	−4.76704	−	31.9379i	−0.158026	−	1.05873i
$911$	32.7618			1.08545			0.542724	−	0.839911i	$-0.317393\pi$
$911$	32.7618			1.08545			0.542724	+	0.839911i	$0.317393\pi$
$912$	0.889973	−	3.32142i	0.0294700	−	0.109983i
$913$	−16.6053	−	9.58706i	−0.549554	−	0.317285i
$914$	−17.9428	−	10.3593i	−0.593495	−	0.342654i
$915$	−45.8862	−	12.2952i	−1.51695	−	0.406466i
$916$	10.7714	−	10.7714i	0.355897	−	0.355897i
$917$	−2.41852	−	0.467450i	−0.0798666	−	0.0154366i
$918$	1.72157	−	1.72157i	0.0568203	−	0.0568203i
$919$	7.75658	+	13.4348i	0.255866	+	0.443173i	0.965130	−	0.261770i	$-0.0843061\pi$
$919$	7.75658	+	13.4348i	0.255866	+	0.443173i	−0.709264	+	0.704943i	$0.750973\pi$
$920$	1.61185	−	2.79181i	0.0531412	−	0.0920432i
$921$	−1.48214	−	5.53142i	−0.0488381	−	0.182266i
$922$	10.7884	+	18.6860i	0.355296	+	0.615390i
$923$	−37.1616	+	25.4722i	−1.22319	+	0.838429i
$924$	14.5363	−	1.03198i	0.478208	−	0.0339495i
$925$	11.0868	+	11.0868i	0.364531	+	0.364531i
$926$	2.96262	+	5.13141i	0.0973578	+	0.168629i
$927$	5.49909	−	9.52470i	0.180614	−	0.312832i
$928$	−9.62511	+	2.57904i	−0.315960	+	0.0846611i
$929$	−7.62845	−	2.04404i	−0.250281	−	0.0670627i	0.131497	−	0.991317i	$-0.458022\pi$
$929$	−7.62845	−	2.04404i	−0.250281	−	0.0670627i	−0.381778	+	0.924254i	$0.624688\pi$
$930$	1.48502	+	1.48502i	0.0486956	+	0.0486956i
$931$	−2.88270	+	23.8969i	−0.0944768	+	0.783189i
$932$	0.111975			0.00366787
$933$	22.4193	−	12.9438i	0.733975	−	0.423760i
$934$	6.89123	−	1.84650i	0.225488	−	0.0604193i
$935$	39.3130	+	22.6974i	1.28567	+	0.742283i
$936$	1.55629	−	3.25238i	0.0508689	−	0.106307i
$937$		−	30.2873i		−	0.989444i	−0.869051	−	0.494722i	$-0.835270\pi$
$937$		−	30.2873i		−	0.989444i	0.869051	−	0.494722i	$-0.164730\pi$
$938$	−21.1299	+	24.3593i	−0.689915	+	0.795359i
$939$	−7.49839			−0.244701
$940$	1.58824	−	0.916970i	0.0518026	−	0.0299083i
$941$	−1.17423	−	4.38229i	−0.0382788	−	0.142859i	0.944142	−	0.329540i	$-0.106894\pi$
$941$	−1.17423	−	4.38229i	−0.0382788	−	0.142859i	−0.982421	+	0.186681i	$0.940227\pi$
$942$	−3.18895	+	0.854477i	−0.103902	+	0.0278404i
$943$	−2.47126	+	9.22287i	−0.0804753	+	0.300338i
$944$	6.58675	+	6.58675i	0.214380	+	0.214380i
$945$	−7.41962	+	5.01606i	−0.241360	+	0.163173i
$946$		−	47.5308i		−	1.54536i
$947$	−36.1988	−	9.69944i	−1.17630	−	0.315189i	−0.382844	−	0.923813i	$-0.625055\pi$
$947$	−36.1988	−	9.69944i	−1.17630	−	0.315189i	−0.793459	+	0.608624i	$0.791722\pi$
$948$	−0.573562	+	0.993439i	−0.0186284	+	0.0322654i
$949$	0.797836	+	10.3018i	0.0258989	+	0.334412i
$950$	−19.2338	+	11.1046i	−0.624025	+	0.360281i
$951$	−4.99075	+	4.99075i	−0.161836	+	0.161836i
$952$	−2.81763	+	5.79260i	−0.0913200	+	0.187739i
$953$		−	50.3172i		−	1.62993i	−0.579507	−	0.814967i	$-0.696755\pi$
$953$		−	50.3172i		−	1.62993i	0.579507	−	0.814967i	$-0.303245\pi$
$954$	−1.36423	+	5.09136i	−0.0441685	+	0.164839i
$955$	2.96181	+	11.0536i	0.0958419	+	0.357687i
$956$	5.20827	+	19.4375i	0.168447	+	0.628654i
$957$	14.2054	−	53.0153i	0.459196	−	1.71374i
$958$			17.1823i			0.555134i
$959$	−18.1524	+	37.3185i	−0.586173	+	1.20508i
$960$	−2.39362	+	2.39362i	−0.0772537	+	0.0772537i
$961$	26.5135	−	15.3075i	0.855273	−	0.493792i
$962$	6.64846	+	5.69269i	0.214355	+	0.183540i
$963$	4.11637	−	7.12976i	0.132648	−	0.229753i
$964$	−11.6854	−	3.13108i	−0.376360	−	0.100845i
$965$			38.7945i			1.24884i
$966$	−2.08736	+	1.41117i	−0.0671597	+	0.0454036i
$967$	−14.2617	−	14.2617i	−0.458626	−	0.458626i	0.439578	−	0.898204i	$-0.355128\pi$
$967$	−14.2617	−	14.2617i	−0.458626	−	0.458626i	−0.898204	+	0.439578i	$0.855128\pi$
$968$	−5.00513	+	18.6794i	−0.160871	+	0.600378i
$969$	−8.08656	+	2.16679i	−0.259778	+	0.0696073i
$970$	6.16717	+	23.0162i	0.198016	+	0.739005i
$971$	35.8902	−	20.7212i	1.15177	−	0.664976i	0.202454	−	0.979292i	$-0.435108\pi$
$971$	35.8902	−	20.7212i	1.15177	−	0.664976i	0.949318	+	0.314316i	$0.101775\pi$
$972$	−1.00000			−0.0320750
$973$	−19.0083	+	21.9134i	−0.609377	+	0.702513i
$974$			0.560499i			0.0179595i
$975$	−21.9615	+	7.74615i	−0.703332	+	0.248075i
$976$	12.1534	+	7.01679i	0.389022	+	0.224602i
$977$	−26.7705	+	7.17314i	−0.856464	+	0.229489i	−0.660226	−	0.751067i	$-0.729539\pi$
$977$	−26.7705	+	7.17314i	−0.856464	+	0.229489i	−0.196239	+	0.980556i	$0.562873\pi$
$978$	9.93276	−	5.73468i	0.317615	−	0.183375i
$979$	−25.2590			−0.807281
$980$	14.2202	−	18.9544i	0.454247	−	0.605475i
$981$	−12.2247	−	12.2247i	−0.390304	−	0.390304i
$982$	−7.01088	−	1.87856i	−0.223726	−	0.0599473i
$983$	4.08359	−	1.09420i	0.130246	−	0.0348994i	−0.193107	−	0.981178i	$-0.561856\pi$
$983$	4.08359	−	1.09420i	0.130246	−	0.0348994i	0.323353	+	0.946278i	$0.395190\pi$
$984$	5.01311	−	8.68296i	0.159812	−	0.276803i
$985$	16.0273	+	27.7601i	0.510672	+	0.884510i
$986$	17.1548	+	17.1548i	0.546321	+	0.546321i
$987$	−1.42979	+	0.101505i	−0.0455108	+	0.00323095i
$988$	−10.2263	+	7.00956i	−0.325342	+	0.223004i
$989$	4.10899	+	7.11697i	0.130658	+	0.226307i
$990$	−4.82572	−	18.0098i	−0.153371	−	0.572390i
$991$	11.4502	−	19.8323i	0.363727	−	0.629994i	−0.624844	−	0.780750i	$-0.714837\pi$
$991$	11.4502	−	19.8323i	0.363727	−	0.629994i	0.988571	+	0.150756i	$0.0481706\pi$
$992$	−0.310203	−	0.537288i	−0.00984896	−	0.0170589i
$993$	−3.55065	+	3.55065i	−0.112676	+	0.112676i
$994$	−32.4595	−	6.27375i	−1.02955	−	0.198991i
$995$	−14.3271	+	14.3271i	−0.454199	+	0.454199i
$996$	−3.36251	−	0.900981i	−0.106545	−	0.0285487i
$997$	−40.8570	−	23.5888i	−1.29395	−	0.747064i	−0.314600	−	0.949224i	$-0.601871\pi$
$997$	−40.8570	−	23.5888i	−1.29395	−	0.747064i	−0.979352	+	0.202160i	$0.935204\pi$
$998$	0.546400	+	0.315464i	0.0172960	+	0.00998585i
$999$	0.628295	−	2.34483i	0.0198784	−	0.0741872i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bz.a.73.5	✓	40
7.5	odd	6		546.2.bz.b.229.10	yes	40
13.5	odd	4		546.2.bz.b.31.10	yes	40
91.5	even	12	inner	546.2.bz.a.187.5	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bz.a.73.5	✓	40	1.1	even	1	trivial
546.2.bz.a.187.5	yes	40	91.5	even	12	inner
546.2.bz.b.31.10	yes	40	13.5	odd	4
546.2.bz.b.229.10	yes	40	7.5	odd	6

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

\(f(q)\)	\(=\)	\(q+(-0.258819 + 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(3.26974 + 0.876125i) q^{5} +(0.707107 - 0.707107i) q^{6} +(-1.99861 - 1.73365i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.258819 + 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(3.26974 + 0.876125i) q^{5} +(0.707107 - 0.707107i) q^{6} +(-1.99861 - 1.73365i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.69254 + 2.93157i) q^{10} +(1.42558 + 5.32034i) q^{11} +(0.500000 + 0.866025i) q^{12} +(0.661484 - 3.54435i) q^{13} +(2.19186 - 1.48181i) q^{14} +(-2.39362 - 2.39362i) q^{15} +(0.500000 + 0.866025i) q^{16} +(1.21733 - 2.10848i) q^{17} +(-0.965926 + 0.258819i) q^{18} +(3.32142 + 0.889973i) q^{19} +(-2.39362 - 2.39362i) q^{20} +(0.864026 + 2.50069i) q^{21} -5.50802 q^{22} +(0.824738 - 0.476163i) q^{23} +(-0.965926 + 0.258819i) q^{24} +(5.59350 + 3.22941i) q^{25} +(3.25238 + 1.55629i) q^{26} -1.00000i q^{27} +(0.864026 + 2.50069i) q^{28} +9.96464 q^{29} +(2.93157 - 1.69254i) q^{30} +(0.160573 + 0.599266i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(1.42558 - 5.32034i) q^{33} +(1.72157 + 1.72157i) q^{34} +(-5.01606 - 7.41962i) q^{35} -1.00000i q^{36} +(2.34483 + 0.628295i) q^{37} +(-1.71930 + 2.97791i) q^{38} +(-2.34504 + 2.73876i) q^{39} +(2.93157 - 1.69254i) q^{40} +(-7.08960 + 7.08960i) q^{41} +(-2.63911 + 0.187359i) q^{42} +8.62938i q^{43} +(1.42558 - 5.32034i) q^{44} +(0.876125 + 3.26974i) q^{45} +(0.246480 + 0.919876i) q^{46} +(-0.140221 + 0.523310i) q^{47} -1.00000i q^{48} +(0.988921 + 6.92979i) q^{49} +(-4.56707 + 4.56707i) q^{50} +(-2.10848 + 1.21733i) q^{51} +(-2.34504 + 2.73876i) q^{52} +(2.63548 - 4.56479i) q^{53} +(0.965926 + 0.258819i) q^{54} +18.6451i q^{55} +(-2.63911 + 0.187359i) q^{56} +(-2.43145 - 2.43145i) q^{57} +(-2.57904 + 9.62511i) q^{58} +(8.99767 - 2.41092i) q^{59} +(0.876125 + 3.26974i) q^{60} +(12.1534 - 7.01679i) q^{61} -0.620406 q^{62} +(0.502077 - 2.59768i) q^{63} -1.00000i q^{64} +(5.26818 - 11.0096i) q^{65} +(4.77009 + 2.75401i) q^{66} +(-11.7728 + 3.15451i) q^{67} +(-2.10848 + 1.21733i) q^{68} -0.952325 q^{69} +(8.46506 - 2.92480i) q^{70} +(-8.83572 - 8.83572i) q^{71} +(0.965926 + 0.258819i) q^{72} +(-2.76813 + 0.741717i) q^{73} +(-1.21377 + 2.10232i) q^{74} +(-3.22941 - 5.59350i) q^{75} +(-2.43145 - 2.43145i) q^{76} +(6.37442 - 13.1048i) q^{77} +(-2.03850 - 2.97398i) q^{78} +(0.573562 + 0.993439i) q^{79} +(0.876125 + 3.26974i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-5.01311 - 8.68296i) q^{82} +(-2.46153 + 2.46153i) q^{83} +(0.502077 - 2.59768i) q^{84} +(5.82766 - 5.82766i) q^{85} +(-8.33534 - 2.23345i) q^{86} +(-8.62963 - 4.98232i) q^{87} +(4.77009 + 2.75401i) q^{88} +(-1.18691 + 4.42960i) q^{89} -3.38509 q^{90} +(-7.46672 + 5.93701i) q^{91} -0.952325 q^{92} +(0.160573 - 0.599266i) q^{93} +(-0.469187 - 0.270885i) q^{94} +(10.0805 + 5.81997i) q^{95} +(0.965926 + 0.258819i) q^{96} +(4.97742 - 4.97742i) q^{97} +(-6.94962 - 0.838339i) q^{98} +(-3.89476 + 3.89476i) 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	\( 40 q - 4 q^{7} + 20 q^{9} - 4 q^{11} + 20 q^{12} + 4 q^{14} + 20 q^{16} + 8 q^{17} + 32 q^{19} + 4 q^{21} + 8 q^{22} - 24 q^{23} - 48 q^{25} - 8 q^{26} + 4 q^{28} + 24 q^{29} - 4 q^{33} - 16 q^{34} - 8 q^{35} - 8 q^{37} + 16 q^{38} - 4 q^{39} - 8 q^{41} - 4 q^{44} + 44 q^{46} + 20 q^{47} + 16 q^{49} + 32 q^{50} - 12 q^{51} - 4 q^{52} - 4 q^{53} - 16 q^{57} + 12 q^{58} - 24 q^{59} - 12 q^{61} + 16 q^{62} - 8 q^{63} + 8 q^{65} - 12 q^{68} - 16 q^{69} + 4 q^{70} + 8 q^{71} + 12 q^{73} - 40 q^{74} - 36 q^{75} - 16 q^{76} + 48 q^{77} - 8 q^{78} - 20 q^{81} + 24 q^{83} - 8 q^{84} - 40 q^{85} + 16 q^{86} - 72 q^{87} - 24 q^{89} + 8 q^{91} - 16 q^{92} - 36 q^{94} - 32 q^{98} - 8 q^{99}+O(q^{100}) \) 40 * q - 4 * q^7 + 20 * q^9 - 4 * q^11 + 20 * q^12 + 4 * q^14 + 20 * q^16 + 8 * q^17 + 32 * q^19 + 4 * q^21 + 8 * q^22 - 24 * q^23 - 48 * q^25 - 8 * q^26 + 4 * q^28 + 24 * q^29 - 4 * q^33 - 16 * q^34 - 8 * q^35 - 8 * q^37 + 16 * q^38 - 4 * q^39 - 8 * q^41 - 4 * q^44 + 44 * q^46 + 20 * q^47 + 16 * q^49 + 32 * q^50 - 12 * q^51 - 4 * q^52 - 4 * q^53 - 16 * q^57 + 12 * q^58 - 24 * q^59 - 12 * q^61 + 16 * q^62 - 8 * q^63 + 8 * q^65 - 12 * q^68 - 16 * q^69 + 4 * q^70 + 8 * q^71 + 12 * q^73 - 40 * q^74 - 36 * q^75 - 16 * q^76 + 48 * q^77 - 8 * q^78 - 20 * q^81 + 24 * q^83 - 8 * q^84 - 40 * q^85 + 16 * q^86 - 72 * q^87 - 24 * q^89 + 8 * q^91 - 16 * q^92 - 36 * q^94 - 32 * q^98 - 8 * q^99

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