LMFDB - Embedded newform 546.2.bz.b.31.10

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			31.10
Character	$\chi$	$=$	546.31
Dual form			546.2.bz.b.229.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 + 0.258819i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.866025 + 0.500000i) q^{4} +(0.876125 - 3.26974i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(1.73365 - 1.99861i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.965926 + 0.258819i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.866025 + 0.500000i) q^{4} +(0.876125 - 3.26974i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(1.73365 - 1.99861i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +(1.69254 - 2.93157i) q^{10} +(-5.32034 + 1.42558i) 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} +(0.258819 + 0.965926i) q^{18} +(0.889973 - 3.32142i) q^{19} +(2.39362 - 2.39362i) q^{20} +(-2.50069 + 0.864026i) q^{21} -5.50802 q^{22} +(-0.824738 + 0.476163i) q^{23} +(-0.258819 - 0.965926i) q^{24} +(-5.59350 - 3.22941i) q^{25} +(0.278402 - 3.59479i) q^{26} -1.00000i q^{27} +(2.50069 - 0.864026i) q^{28} +9.96464 q^{29} +(-2.93157 + 1.69254i) q^{30} +(0.599266 - 0.160573i) q^{31} +(0.258819 + 0.965926i) q^{32} +(5.32034 + 1.42558i) q^{33} +(-1.72157 + 1.72157i) q^{34} +(-5.01606 - 7.41962i) q^{35} +1.00000i q^{36} +(-0.628295 + 2.34483i) q^{37} +(1.71930 - 2.97791i) q^{38} +(-1.19931 + 3.40024i) q^{39} +(2.93157 - 1.69254i) q^{40} +(7.08960 + 7.08960i) q^{41} +(-2.63911 + 0.187359i) q^{42} -8.62938i q^{43} +(-5.32034 - 1.42558i) q^{44} +(3.26974 - 0.876125i) q^{45} +(-0.919876 + 0.246480i) q^{46} +(-0.523310 - 0.140221i) q^{47} -1.00000i q^{48} +(-0.988921 - 6.92979i) q^{49} +(-4.56707 - 4.56707i) q^{50} +(2.10848 - 1.21733i) q^{51} +(1.19931 - 3.40024i) q^{52} +(2.63548 - 4.56479i) q^{53} +(0.258819 - 0.965926i) q^{54} +18.6451i q^{55} +(2.63911 - 0.187359i) q^{56} +(-2.43145 + 2.43145i) q^{57} +(9.62511 + 2.57904i) q^{58} +(2.41092 + 8.99767i) q^{59} +(-3.26974 + 0.876125i) q^{60} +(12.1534 - 7.01679i) q^{61} +0.620406 q^{62} +(2.59768 + 0.502077i) q^{63} +1.00000i q^{64} +(-12.1687 - 0.942414i) q^{65} +(4.77009 + 2.75401i) q^{66} +(3.15451 + 11.7728i) q^{67} +(-2.10848 + 1.21733i) q^{68} +0.952325 q^{69} +(-2.92480 - 8.46506i) q^{70} +(-8.83572 + 8.83572i) q^{71} +(-0.258819 + 0.965926i) q^{72} +(-0.741717 - 2.76813i) 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} +(3.26974 - 0.876125i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(5.01311 + 8.68296i) q^{82} +(2.46153 + 2.46153i) q^{83} +(-2.59768 - 0.502077i) q^{84} +(5.82766 + 5.82766i) q^{85} +(2.23345 - 8.33534i) q^{86} +(-8.62963 - 4.98232i) q^{87} +(-4.77009 - 2.75401i) q^{88} +(-4.42960 - 1.18691i) q^{89} +3.38509 q^{90} +(-8.23058 - 4.82261i) q^{91} -0.952325 q^{92} +(-0.599266 - 0.160573i) q^{93} +(-0.469187 - 0.270885i) q^{94} +(-10.0805 - 5.81997i) q^{95} +(0.258819 - 0.965926i) q^{96} +(-4.97742 - 4.97742i) q^{97} +(0.838339 - 6.94962i) 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} + 16 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} - 32 q^{37} - 16 q^{38} - 4 q^{39} + 8 q^{41} - 4 q^{44} - 28 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} - 24 q^{67} - 12 q^{68} + 16 q^{69} + 12 q^{70} + 8 q^{71} - 36 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} - 56 q^{86} - 72 q^{87} - 72 q^{89} - 24 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 + 16 * 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 - 32 * q^37 - 16 * q^38 - 4 * q^39 + 8 * q^41 - 4 * q^44 - 28 * 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 - 24 * q^67 - 12 * q^68 + 16 * q^69 + 12 * q^70 + 8 * q^71 - 36 * 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 - 56 * q^86 - 72 * q^87 - 72 * q^89 - 24 * 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 $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	0.876125	−	3.26974i	0.391815	−	1.46227i	−0.435323	−	0.900274i	$-0.643366\pi$
$5$	0.876125	−	3.26974i	0.391815	−	1.46227i	0.827138	−	0.561999i	$-0.189968\pi$
$6$	−0.707107	−	0.707107i	−0.288675	−	0.288675i
$7$	1.73365	−	1.99861i	0.655258	−	0.755405i
$7$	1.73365	−	1.99861i	0.655258	−	0.755405i
$8$	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
$11$	−5.32034	+	1.42558i	−1.60414	+	0.429829i	−0.946291	−	0.323317i	$-0.895202\pi$
$11$	−5.32034	+	1.42558i	−1.60414	+	0.429829i	−0.657853	+	0.753146i	$0.728535\pi$
$12$	−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	−0.975042	−	0.222019i	$-0.928735\pi$
$17$	−1.21733	+	2.10848i	−0.295247	+	0.511382i	0.679795	+	0.733402i	$0.262069\pi$
$18$	0.258819	+	0.965926i	0.0610042	+	0.227671i
$19$	0.889973	−	3.32142i	0.204174	−	0.761987i	−0.785526	−	0.618829i	$-0.787608\pi$
$19$	0.889973	−	3.32142i	0.204174	−	0.761987i	0.989700	−	0.143158i	$-0.0457258\pi$
$20$	2.39362	−	2.39362i	0.535229	−	0.535229i
$21$	−2.50069	+	0.864026i	−0.545696	+	0.188546i
$22$	−5.50802			−1.17431
$23$	−0.824738	+	0.476163i	−0.171970	+	0.0992868i	−0.583514	−	0.812103i	$-0.698323\pi$
$23$	−0.824738	+	0.476163i	−0.171970	+	0.0992868i	0.411545	+	0.911390i	$0.364989\pi$
$24$	−0.258819	−	0.965926i	−0.0528312	−	0.197169i
$25$	−5.59350	−	3.22941i	−1.11870	−	0.645881i
$26$	0.278402	−	3.59479i	0.0545991	−	0.704996i
$27$		−	1.00000i		−	0.192450i
$28$	2.50069	−	0.864026i	0.472586	−	0.163286i
$29$	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
$31$	0.599266	−	0.160573i	0.107631	−	0.0288398i	−0.204601	−	0.978845i	$-0.565590\pi$
$31$	0.599266	−	0.160573i	0.107631	−	0.0288398i	0.312233	+	0.950006i	$0.398923\pi$
$32$	0.258819	+	0.965926i	0.0457532	+	0.170753i
$33$	5.32034	+	1.42558i	0.926153	+	0.248162i
$34$	−1.72157	+	1.72157i	−0.295247	+	0.295247i
$35$	−5.01606	−	7.41962i	−0.847869	−	1.25415i
$36$			1.00000i			0.166667i
$37$	−0.628295	+	2.34483i	−0.103291	+	0.385488i	−0.998146	−	0.0608701i	$-0.980612\pi$
$37$	−0.628295	+	2.34483i	−0.103291	+	0.385488i	0.894855	+	0.446358i	$0.147279\pi$
$38$	1.71930	−	2.97791i	0.278907	−	0.483080i
$39$	−1.19931	+	3.40024i	−0.192044	+	0.544474i
$40$	2.93157	−	1.69254i	0.463522	−	0.267615i
$41$	7.08960	+	7.08960i	1.10721	+	1.10721i	0.993516	+	0.113694i	$0.0362685\pi$
$41$	7.08960	+	7.08960i	1.10721	+	1.10721i	0.113694	+	0.993516i	$0.463732\pi$
$42$	−2.63911	+	0.187359i	−0.407223	+	0.0289101i
$43$		−	8.62938i		−	1.31597i	−0.753032	−	0.657984i	$-0.771410\pi$
$43$		−	8.62938i		−	1.31597i	0.753032	−	0.657984i	$-0.228590\pi$
$44$	−5.32034	−	1.42558i	−0.802072	−	0.214914i
$45$	3.26974	−	0.876125i	0.487424	−	0.130605i
$46$	−0.919876	+	0.246480i	−0.135628	+	0.0363415i
$47$	−0.523310	−	0.140221i	−0.0763326	−	0.0204533i	0.220451	−	0.975398i	$-0.429247\pi$
$47$	−0.523310	−	0.140221i	−0.0763326	−	0.0204533i	−0.296783	+	0.954945i	$0.595914\pi$
$48$		−	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
$52$	1.19931	−	3.40024i	0.166315	−	0.471529i
$53$	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	$0.0487567\pi$
$54$	0.258819	−	0.965926i	0.0352208	−	0.131446i
$55$			18.6451i			2.51411i
$56$	2.63911	−	0.187359i	0.352666	−	0.0250369i
$57$	−2.43145	+	2.43145i	−0.322054	+	0.322054i
$58$	9.62511	+	2.57904i	1.26384	+	0.338644i
$59$	2.41092	+	8.99767i	0.313875	+	1.17140i	0.925033	+	0.379888i	$0.124037\pi$
$59$	2.41092	+	8.99767i	0.313875	+	1.17140i	−0.611158	+	0.791509i	$0.709296\pi$
$60$	−3.26974	+	0.876125i	−0.422122	+	0.113107i
$61$	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
$63$	2.59768	+	0.502077i	0.327276	+	0.0632558i
$64$			1.00000i			0.125000i
$65$	−12.1687	−	0.942414i	−1.50934	−	0.116892i
$66$	4.77009	+	2.75401i	0.587157	+	0.338995i
$67$	3.15451	+	11.7728i	0.385385	+	1.43828i	0.837559	+	0.546346i	$0.183982\pi$
$67$	3.15451	+	11.7728i	0.385385	+	1.43828i	−0.452175	+	0.891929i	$0.649352\pi$
$68$	−2.10848	+	1.21733i	−0.255691	+	0.147623i
$69$	0.952325			0.114646
$70$	−2.92480	−	8.46506i	−0.349581	−	1.01177i
$71$	−8.83572	+	8.83572i	−1.04861	+	1.04861i	−0.0498505	+	0.998757i	$0.515874\pi$
$71$	−8.83572	+	8.83572i	−1.04861	+	1.04861i	−0.998757	+	0.0498505i	$0.984126\pi$
$72$	−0.258819	+	0.965926i	−0.0305021	+	0.113835i
$73$	−0.741717	−	2.76813i	−0.0868114	−	0.323985i	0.908840	−	0.417146i	$-0.136970\pi$
$73$	−0.741717	−	2.76813i	−0.0868114	−	0.323985i	−0.995651	+	0.0931611i	$0.970303\pi$
$74$	−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	$0.812778\pi$
$80$	3.26974	−	0.876125i	0.365568	−	0.0979538i
$81$	−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	$-0.188810\pi$
$83$	2.46153	+	2.46153i	0.270188	+	0.270188i	−0.558988	+	0.829176i	$0.688810\pi$
$84$	−2.59768	−	0.502077i	−0.283430	−	0.0547811i
$85$	5.82766	+	5.82766i	0.632099	+	0.632099i
$86$	2.23345	−	8.33534i	0.240839	−	0.898822i
$87$	−8.62963	−	4.98232i	−0.925194	−	0.534161i
$88$	−4.77009	−	2.75401i	−0.508493	−	0.293579i
$89$	−4.42960	−	1.18691i	−0.469536	−	0.125812i	0.0162898	−	0.999867i	$-0.494815\pi$
$89$	−4.42960	−	1.18691i	−0.469536	−	0.125812i	−0.485826	+	0.874055i	$0.661481\pi$
$90$	3.38509			0.356819
$91$	−8.23058	−	4.82261i	−0.862799	−	0.505547i
$92$	−0.952325			−0.0992868
$93$	−0.599266	−	0.160573i	−0.0621410	−	0.0166506i
$94$	−0.469187	−	0.270885i	−0.0483929	−	0.0279397i
$95$	−10.0805	−	5.81997i	−1.03424	−	0.597116i
$96$	0.258819	−	0.965926i	0.0264156	−	0.0985844i
$97$	−4.97742	−	4.97742i	−0.505381	−	0.505381i	0.407724	−	0.913105i	$-0.366322\pi$
$97$	−4.97742	−	4.97742i	−0.505381	−	0.505381i	−0.913105	+	0.407724i	$0.866322\pi$
$98$	0.838339	−	6.94962i	0.0846850	−	0.702017i
$99$	−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	−1.00000		0.000111484i	$-0.999965\pi$
$101$	−5.02397	+	8.70177i	−0.499903	+	0.865858i	0.500097	+	0.865970i	$0.333298\pi$
$102$	2.35171	−	0.630138i	0.232854	−	0.0623930i
$103$	5.49909	+	9.52470i	0.541841	+	0.938496i	0.998798	+	0.0490078i	$0.0156059\pi$
$103$	5.49909	+	9.52470i	0.541841	+	0.938496i	−0.456957	+	0.889489i	$0.651061\pi$
$104$	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
$109$	4.47455	+	16.6992i	0.428584	+	1.59950i	0.755970	+	0.654606i	$0.227165\pi$
$109$	4.47455	+	16.6992i	0.428584	+	1.59950i	−0.327386	+	0.944891i	$0.606168\pi$
$110$	−4.82572	+	18.0098i	−0.460114	+	1.71717i
$111$	1.71654	−	1.71654i	0.162926	−	0.162926i
$112$	2.59768	+	0.502077i	0.245457	+	0.0474418i
$113$	−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
$115$	0.834356	+	3.11386i	0.0778041	+	0.290369i
$116$	8.62963	+	4.98232i	0.801241	+	0.462597i
$117$	2.73876	−	2.34504i	0.253198	−	0.216799i
$118$			9.31507i			0.857522i
$119$	2.10362	+	6.08835i	0.192838	+	0.558118i
$120$	−3.38509			−0.309015
$121$	16.7475	−	9.66916i	1.52250	−	0.879015i
$122$	13.5554	−	3.63216i	1.22725	−	0.328840i
$123$	−2.59498	−	9.68458i	−0.233981	−	0.873229i
$124$	0.599266	+	0.160573i	0.0538157	+	0.0144199i
$125$	−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	$0.106011\pi$
$127$			7.36842i			0.653841i	−0.945052	+	0.326921i	$0.893989\pi$
$128$	−0.258819	+	0.965926i	−0.0228766	+	0.0853766i
$129$	−4.31469	+	7.47326i	−0.379887	+	0.657984i
$130$	−11.5101	−	4.05978i	−1.00950	−	0.356067i
$131$	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
$135$	−3.26974	−	0.876125i	−0.281415	−	0.0754048i
$136$	−2.35171	+	0.630138i	−0.201657	+	0.0540339i
$137$	15.1507	−	4.05963i	1.29442	−	0.346838i	0.455080	−	0.890451i	$-0.349611\pi$
$137$	15.1507	−	4.05963i	1.29442	−	0.346838i	0.839336	+	0.543613i	$0.182944\pi$
$138$	0.919876	+	0.246480i	0.0783050	+	0.0209818i
$139$		−	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
$143$	8.57208	+	17.9142i	0.716834	+	1.49806i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	8.73027	−	32.5818i	0.725010	−	2.70577i
$146$		−	2.86577i		−	0.237173i
$147$	−2.60847	+	6.49584i	−0.215143	+	0.535768i
$148$	−1.71654	+	1.71654i	−0.141098	+	0.141098i
$149$	16.7825	+	4.49686i	1.37488	+	0.368397i	0.869257	−	0.494360i	$-0.164597\pi$
$149$	16.7825	+	4.49686i	1.37488	+	0.368397i	0.505619	+	0.862757i	$0.331264\pi$
$150$	1.67166	+	6.23874i	0.136491	+	0.509391i
$151$	13.6683	−	3.66242i	1.11231	−	0.298044i	0.344545	−	0.938770i	$-0.388033\pi$
$151$	13.6683	−	3.66242i	1.11231	−	0.298044i	0.767770	+	0.640726i	$0.221367\pi$
$152$	2.97791	−	1.71930i	0.241540	−	0.139453i
$153$	−2.43467			−0.196831
$154$	−9.54898	+	11.0084i	−0.769479	+	0.887083i
$155$		−	2.10013i		−	0.168686i
$156$	−2.73876	+	2.34504i	−0.219276	+	0.187753i
$157$	−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	$0.708724\pi$
$158$	0.296898	+	1.10804i	0.0236199	+	0.0881507i
$159$	−4.56479	+	2.63548i	−0.362012	+	0.209007i
$160$	3.38509			0.267615
$161$	−0.478141	+	2.47383i	−0.0376828	+	0.194965i
$162$	−0.707107	+	0.707107i	−0.0555556	+	0.0555556i
$163$	−2.96849	+	11.0786i	−0.232510	+	0.867740i	0.746745	+	0.665110i	$0.231615\pi$
$163$	−2.96849	+	11.0786i	−0.232510	+	0.867740i	−0.979255	+	0.202630i	$0.935051\pi$
$164$	2.59498	+	9.68458i	0.202634	+	0.756239i
$165$	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	$-0.855578\pi$
$167$	−5.95118	+	5.95118i	−0.460516	+	0.460516i	0.438308	+	0.898825i	$0.355578\pi$
$168$	−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
$171$	3.32142	−	0.889973i	0.253996	−	0.0680579i
$172$	4.31469	−	7.47326i	0.328992	−	0.569831i
$173$	−10.3528	−	17.9316i	−0.787109	−	1.36331i	−0.927731	−	0.373250i	$-0.878243\pi$
$173$	−10.3528	−	17.9316i	−0.787109	−	1.36331i	0.140621	−	0.990063i	$-0.455090\pi$
$174$	−7.04607	−	7.04607i	−0.534161	−	0.534161i
$175$	−16.1515	+	5.58059i	−1.22094	+	0.421853i
$176$	−3.89476	−	3.89476i	−0.293579	−	0.293579i
$177$	2.41092	−	8.99767i	0.181216	−	0.676306i
$178$	−3.97147	−	2.29293i	−0.297674	−	0.171862i
$179$	−0.868634	−	0.501506i	−0.0649248	−	0.0374843i	0.467186	−	0.884159i	$-0.345268\pi$
$179$	−0.868634	−	0.501506i	−0.0649248	−	0.0374843i	−0.532111	+	0.846675i	$0.678601\pi$
$180$	3.26974	+	0.876125i	0.243712	+	0.0653025i
$181$	17.4276			1.29538			0.647692	−	0.761902i	$-0.275734\pi$
$181$	17.4276			1.29538			0.647692	+	0.761902i	$0.275734\pi$
$182$	−6.70194	−	6.78852i	−0.496781	−	0.503198i
$183$	−14.0336			−1.03739
$184$	−0.919876	−	0.246480i	−0.0678141	−	0.0181707i
$185$	7.11653	+	4.10873i	0.523218	+	0.302080i
$186$	−0.537288	−	0.310203i	−0.0393958	−	0.0227452i
$187$	3.47082	−	12.9533i	0.253811	−	0.947236i
$188$	−0.383090	−	0.383090i	−0.0279397	−	0.0279397i
$189$	−1.99861	−	1.73365i	−0.145378	−	0.126104i
$190$	−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
$193$	−11.0699	+	2.96618i	−0.796830	+	0.213510i	−0.634192	−	0.773176i	$-0.718667\pi$
$193$	−11.0699	+	2.96618i	−0.796830	+	0.213510i	−0.162638	+	0.986686i	$0.552000\pi$
$194$	−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	−0.427131	−	0.904190i	$-0.640476\pi$
$197$	6.69585	−	6.69585i	0.477059	−	0.477059i	0.904190	+	0.427131i	$0.140476\pi$
$198$	−2.75401	−	4.77009i	−0.195719	−	0.338995i
$199$	2.99276	−	5.18362i	0.212151	−	0.367457i	−0.740236	−	0.672347i	$-0.765286\pi$
$199$	2.99276	−	5.18362i	0.212151	−	0.367457i	0.952388	+	0.304890i	$0.0986197\pi$
$200$	−1.67166	−	6.23874i	−0.118204	−	0.441145i
$201$	3.15451	−	11.7728i	0.222502	−	0.830389i
$202$	−7.10496	+	7.10496i	−0.499903	+	0.499903i
$203$	17.2752	−	19.9155i	1.21248	−	1.39779i
$204$	2.43467			0.170461
$205$	29.3926	−	16.9698i	2.05287	−	1.18522i
$206$	2.84654	+	10.6234i	0.198328	+	0.740169i
$207$	−0.824738	−	0.476163i	−0.0573232	−	0.0330956i
$208$	2.73876	−	2.34504i	0.189899	−	0.162599i
$209$			18.9398i			1.31010i
$210$	−1.69957	+	8.79336i	−0.117282	+	0.606799i
$211$	−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
$213$	12.0698	−	3.23410i	0.827010	−	0.221597i
$214$	−2.13079	−	7.95222i	−0.145658	−	0.543602i
$215$	−28.2158	−	7.56041i	−1.92430	−	0.515616i
$216$	0.707107	−	0.707107i	0.0481125	−	0.0481125i
$217$	0.717994	−	1.47608i	0.0487406	−	0.100203i
$218$			17.2883i			1.17091i
$219$	−0.741717	+	2.76813i	−0.0501206	+	0.187053i
$220$	−9.32257	+	16.1472i	−0.628528	+	1.08864i
$221$	8.27846	+	2.91993i	0.556869	+	0.196416i
$222$	2.10232	−	1.21377i	0.141098	−	0.0814631i
$223$	4.42968	+	4.42968i	0.296633	+	0.296633i	0.839694	−	0.543060i	$-0.182735\pi$
$223$	4.42968	+	4.42968i	0.296633	+	0.296633i	−0.543060	+	0.839694i	$0.682735\pi$
$224$	2.37921	+	1.15730i	0.158968	+	0.0773252i
$225$		−	6.45881i		−	0.430588i
$226$	−16.2342	−	4.34994i	−1.07988	−	0.289354i
$227$	4.31777	−	1.15694i	0.286580	−	0.0767890i	−0.112665	−	0.993633i	$-0.535939\pi$
$227$	4.31777	−	1.15694i	0.286580	−	0.0767890i	0.399246	+	0.916844i	$0.369272\pi$
$228$	−3.32142	+	0.889973i	−0.219967	+	0.0589399i
$229$	−14.7140	−	3.94260i	−0.972328	−	0.260535i	−0.262518	−	0.964927i	$-0.584553\pi$
$229$	−14.7140	−	3.94260i	−0.972328	−	0.260535i	−0.709811	+	0.704393i	$0.751219\pi$
$230$			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	−0.496820	−	0.867854i	$-0.665499\pi$
$233$	0.0969733	−	0.0559876i	0.00635294	−	0.00366787i	0.503173	+	0.864186i	$0.332166\pi$
$234$	3.25238	−	1.55629i	0.212615	−	0.101738i
$235$	−0.916970	+	1.58824i	−0.0598165	+	0.103605i
$236$	−2.41092	+	8.99767i	−0.156937	+	0.585698i
$237$		−	1.14712i		−	0.0745138i
$238$	0.456156	+	6.42535i	0.0295682	+	0.416494i
$239$	−14.2293	+	14.2293i	−0.920414	+	0.920414i	−0.997058	−	0.0766447i	$-0.975579\pi$
$239$	−14.2293	+	14.2293i	−0.920414	+	0.920414i	0.0766447	+	0.997058i	$0.475579\pi$
$240$	−3.26974	−	0.876125i	−0.211061	−	0.0565536i
$241$	3.13108	+	11.6854i	0.201691	+	0.752720i	0.990433	+	0.137996i	$0.0440661\pi$
$241$	3.13108	+	11.6854i	0.201691	+	0.752720i	−0.788742	+	0.614724i	$0.789267\pi$
$242$	18.6794	−	5.00513i	1.20076	−	0.321742i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	14.0336			0.898408
$245$	−23.5251	−	2.83785i	−1.50296	−	0.181304i
$246$		−	10.0262i		−	0.639248i
$247$	−12.3610	−	0.957310i	−0.786512	−	0.0609122i
$248$	0.537288	+	0.310203i	0.0341178	+	0.0196979i
$249$	−0.900981	−	3.36251i	−0.0570974	−	0.213090i
$250$	−4.27662	+	2.46911i	−0.270477	+	0.156160i
$251$	−23.8347			−1.50443			−0.752217	−	0.658916i	$-0.771015\pi$
$251$	−23.8347			−1.50443			−0.752217	+	0.658916i	$0.771015\pi$
$252$	1.99861	+	1.73365i	0.125901	+	0.109210i
$253$	3.70908	−	3.70908i	0.233188	−	0.233188i
$254$	−1.90709	+	7.11734i	−0.119661	+	0.446582i
$255$	−2.13307	−	7.96074i	−0.133578	−	0.498521i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	10.4551	+	18.1088i	0.652174	+	1.12960i	0.982594	+	0.185765i	$0.0594763\pi$
$257$	10.4551	+	18.1088i	0.652174	+	1.12960i	−0.330420	+	0.943834i	$0.607190\pi$
$258$	−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
$262$	0.899309	−	0.240969i	0.0555595	−	0.0148871i
$263$	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
$266$	−2.97103	−	8.59886i	−0.182166	−	0.527230i
$267$	3.24269	+	3.24269i	0.198449	+	0.198449i
$268$	−3.15451	+	11.7728i	−0.192692	+	0.719138i
$269$	−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
$271$	−2.16813	−	0.580949i	−0.131705	−	0.0352901i	0.192365	−	0.981324i	$-0.438384\pi$
$271$	−2.16813	−	0.580949i	−0.131705	−	0.0352901i	−0.324069	+	0.946033i	$0.605051\pi$
$272$	−2.43467			−0.147623
$273$	4.71658	+	8.29179i	0.285461	+	0.501842i
$274$	15.6852			0.947578
$275$	34.3631	+	9.20757i	2.07217	+	0.555237i
$276$	0.824738	+	0.476163i	0.0496434	+	0.0286616i
$277$	16.1792	+	9.34106i	0.972114	+	0.561250i	0.899880	−	0.436138i	$-0.143654\pi$
$277$	16.1792	+	9.34106i	0.972114	+	0.561250i	0.0722338	+	0.997388i	$0.476987\pi$
$278$	2.83777	−	10.5907i	0.170198	−	0.635189i
$279$	0.438693	+	0.438693i	0.0262639	+	0.0262639i
$280$	1.69957	−	8.79336i	0.101569	−	0.525504i
$281$	−10.9100	−	10.9100i	−0.650837	−	0.650837i	0.302358	−	0.953195i	$-0.402226\pi$
$281$	−10.9100	−	10.9100i	−0.650837	−	0.650837i	−0.953195	+	0.302358i	$0.902226\pi$
$282$	0.270885	+	0.469187i	0.0161310	+	0.0279397i
$283$	7.51710	−	13.0200i	0.446845	−	0.773958i	−0.551334	−	0.834285i	$-0.685881\pi$
$283$	7.51710	−	13.0200i	0.446845	−	0.773958i	0.998179	+	0.0603265i	$0.0192142\pi$
$284$	−12.0698	+	3.23410i	−0.716212	+	0.191908i
$285$	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
$291$	1.82186	+	6.79929i	0.106800	+	0.398581i
$292$	0.741717	−	2.76813i	0.0434057	−	0.161992i
$293$	4.45840	−	4.45840i	0.260462	−	0.260462i	−0.564779	−	0.825242i	$-0.691039\pi$
$293$	4.45840	−	4.45840i	0.260462	−	0.260462i	0.825242	+	0.564779i	$0.191039\pi$
$294$	−4.20083	+	5.59938i	−0.244997	+	0.326562i
$295$	31.5323			1.83588
$296$	−2.10232	+	1.21377i	−0.122195	+	0.0705492i
$297$	1.42558	+	5.32034i	0.0827206	+	0.308718i
$298$	15.0468	+	8.68726i	0.871637	+	0.503240i
$299$	2.23324	+	2.60819i	0.129152	+	0.150835i
$300$			6.45881i			0.372900i
$301$	−17.2468	−	14.9603i	−0.994089	−	0.862298i
$302$	14.1505			0.814271
$303$	8.70177	−	5.02397i	0.499903	−	0.288619i
$304$	3.32142	−	0.889973i	0.190497	−	0.0510435i
$305$	−12.2952	−	45.8862i	−0.704019	−	2.62744i
$306$	−2.35171	−	0.630138i	−0.134438	−	0.0360226i
$307$	−4.04928	+	4.04928i	−0.231105	+	0.231105i	−0.813154	−	0.582049i	$-0.802251\pi$
$307$	−4.04928	+	4.04928i	−0.231105	+	0.231105i	0.582049	+	0.813154i	$0.302251\pi$
$308$	−12.0728	+	8.16186i	−0.687911	+	0.465065i
$309$		−	10.9982i		−	0.625664i
$310$	0.543553	−	2.02857i	0.0308718	−	0.115215i
$311$	12.9438	−	22.4193i	0.733975	−	1.27128i	−0.221197	−	0.975229i	$-0.570996\pi$
$311$	12.9438	−	22.4193i	0.733975	−	1.27128i	0.955172	−	0.296052i	$-0.0956703\pi$
$312$	−3.25238	+	1.55629i	−0.184130	+	0.0881076i
$313$	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
$317$	−6.81749	−	1.82674i	−0.382908	−	0.102600i	0.0622299	−	0.998062i	$-0.480179\pi$
$317$	−6.81749	−	1.82674i	−0.382908	−	0.102600i	−0.445138	+	0.895462i	$0.646845\pi$
$318$	−5.09136	+	1.36423i	−0.285510	+	0.0765021i
$319$	−53.0153	+	14.2054i	−2.96829	+	0.795350i
$320$	3.26974	+	0.876125i	0.182784	+	0.0489769i
$321$			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
$325$	−7.74615	+	21.9615i	−0.429679	+	1.21821i
$326$	−5.73468	+	9.93276i	−0.317615	+	0.550125i
$327$	4.47455	−	16.6992i	0.247443	−	0.923470i
$328$			10.0262i			0.553605i
$329$	−1.18748	+	0.802802i	−0.0654681	+	0.0442599i
$330$	13.1841	−	13.1841i	0.725761	−	0.725761i
$331$	−4.85028	−	1.29963i	−0.266595	−	0.0714340i	0.123045	−	0.992401i	$-0.460734\pi$
$331$	−4.85028	−	1.29963i	−0.266595	−	0.0714340i	−0.389640	+	0.920967i	$0.627401\pi$
$332$	0.900981	+	3.36251i	0.0494478	+	0.184542i
$333$	−2.34483	+	0.628295i	−0.128496	+	0.0344304i
$334$	−7.28868	+	4.20812i	−0.398819	+	0.230258i
$335$	41.2578			2.25415
$336$	−1.99861	−	1.73365i	−0.109033	−	0.0945783i
$337$		−	12.7840i		−	0.696388i	−0.937422	−	0.348194i	$-0.886795\pi$
$337$		−	12.7840i		−	0.696388i	0.937422	−	0.348194i	$-0.113205\pi$
$338$	−12.9254	+	1.39114i	−0.703046	+	0.0756680i
$339$	14.5552	+	8.40345i	0.790530	+	0.456413i
$340$	2.13307	+	7.96074i	0.115682	+	0.431732i
$341$	−2.95939	+	1.70861i	−0.160260	+	0.0925262i
$342$	3.43859			0.185938
$343$	−15.5644	−	10.0374i	−0.840400	−	0.541966i
$344$	6.10189	−	6.10189i	0.328992	−	0.328992i
$345$	0.834356	−	3.11386i	0.0449202	−	0.167645i
$346$	−5.35901	−	20.0001i	−0.288102	−	1.07521i
$347$	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	$-0.785559\pi$
$349$	−2.94528	+	2.94528i	−0.157657	+	0.157657i	0.623871	+	0.781528i	$0.285559\pi$
$350$	−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
$353$	3.28892	−	0.881264i	0.175052	−	0.0469050i	−0.170228	−	0.985405i	$-0.554451\pi$
$353$	3.28892	−	0.881264i	0.175052	−	0.0469050i	0.345280	+	0.938500i	$0.387784\pi$
$354$	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
$357$	1.22239	−	6.32448i	0.0646958	−	0.334727i
$358$	−0.709237	−	0.709237i	−0.0374843	−	0.0374843i
$359$	−7.27824	+	27.1628i	−0.384131	+	1.43360i	0.455402	+	0.890286i	$0.349496\pi$
$359$	−7.27824	+	27.1628i	−0.384131	+	1.43360i	−0.839533	+	0.543309i	$0.817171\pi$
$360$	2.93157	+	1.69254i	0.154507	+	0.0892049i
$361$	6.21467	+	3.58804i	0.327088	+	0.188844i
$362$	16.8338	+	4.51060i	0.884764	+	0.237072i
$363$	−19.3383			−1.01500
$364$	−4.71658	−	8.29179i	−0.247216	−	0.434608i
$365$	−9.70090			−0.507768
$366$	−13.5554	−	3.63216i	−0.708552	−	0.189856i
$367$	−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
$369$	−2.59498	+	9.68458i	−0.135089	+	0.504159i
$370$	5.81062	+	5.81062i	0.302080	+	0.302080i
$371$	−4.55426	−	13.1811i	−0.236445	−	0.684327i
$372$	−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
$375$	4.76995	−	1.27810i	0.246319	−	0.0660010i
$376$	−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	−0.999670	−	0.0256943i	$-0.991820\pi$
$379$	−18.9613	+	18.9613i	−0.973976	+	0.973976i	0.0256943	+	0.999670i	$0.491820\pi$
$380$	−5.81997	−	10.0805i	−0.298558	−	0.517118i
$381$	3.68421	−	6.38123i	0.188748	−	0.326921i
$382$	0.874958	+	3.26539i	0.0447667	+	0.167072i
$383$	5.62391	−	20.9887i	0.287368	−	1.07247i	−0.659723	−	0.751509i	$-0.729326\pi$
$383$	5.62391	−	20.9887i	0.287368	−	1.07247i	0.947091	−	0.320964i	$-0.104007\pi$
$384$	0.707107	−	0.707107i	0.0360844	−	0.0360844i
$385$	37.2644	+	32.3241i	1.89917	+	1.64739i
$386$	−11.4604			−0.583320
$387$	7.47326	−	4.31469i	0.379887	−	0.219328i
$388$	−1.82186	−	6.79929i	−0.0924911	−	0.345182i
$389$	−19.4216	−	11.2131i	−0.984714	−	0.568525i	−0.0810239	−	0.996712i	$-0.525819\pi$
$389$	−19.4216	−	11.2131i	−0.984714	−	0.568525i	−0.903690	+	0.428187i	$0.859152\pi$
$390$	7.93816	+	9.27093i	0.401964	+	0.469452i
$391$		−	2.31860i		−	0.117256i
$392$	4.20083	−	5.59938i	0.212174	−	0.282811i
$393$	−0.931033			−0.0469644
$394$	8.20070	−	4.73468i	0.413146	−	0.238530i
$395$	3.75080	−	1.00502i	0.188723	−	0.0505683i
$396$	−1.42558	−	5.32034i	−0.0716382	−	0.267357i
$397$	−14.7870	−	3.96216i	−0.742137	−	0.198855i	−0.132110	−	0.991235i	$-0.542175\pi$
$397$	−14.7870	−	3.96216i	−0.742137	−	0.198855i	−0.610028	+	0.792380i	$0.708842\pi$
$398$	4.23241	−	4.23241i	0.212151	−	0.212151i
$399$	0.644250	+	9.07482i	0.0322529	+	0.454309i
$400$		−	6.45881i		−	0.322941i
$401$	−3.31748	+	12.3810i	−0.165667	+	0.618278i	0.832287	+	0.554345i	$0.187031\pi$
$401$	−3.31748	+	12.3810i	−0.165667	+	0.618278i	−0.997954	+	0.0639331i	$0.979636\pi$
$402$	6.09405	−	10.5552i	0.303943	−	0.526445i
$403$	−0.965532	−	2.01780i	−0.0480966	−	0.100514i
$404$	−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
$408$	2.35171	+	0.630138i	0.116427	+	0.0311965i
$409$	−12.6068	+	3.37799i	−0.623368	+	0.167031i	−0.556659	−	0.830741i	$-0.687917\pi$
$409$	−12.6068	+	3.37799i	−0.623368	+	0.167031i	−0.0667098	+	0.997772i	$0.521250\pi$
$410$	32.7831	−	8.78422i	1.61904	−	0.433822i
$411$	−15.1507	−	4.05963i	−0.747331	−	0.200247i
$412$			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
$416$	3.25238	−	1.55629i	0.159461	−	0.0763034i
$417$	−5.48216	+	9.49537i	−0.268462	+	0.464990i
$418$	−4.90199	+	18.2945i	−0.239764	+	0.894813i
$419$		−	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	−0.885936	−	0.463808i	$-0.846483\pi$
$421$	−8.66134	+	8.66134i	−0.422128	+	0.422128i	0.463808	+	0.885936i	$0.346483\pi$
$422$	−14.8531	−	3.97987i	−0.723036	−	0.193737i
$423$	−0.140221	−	0.523310i	−0.00681776	−	0.0254442i
$424$	5.09136	−	1.36423i	0.247259	−	0.0662527i
$425$	13.6183	−	7.86253i	0.660585	−	0.381389i
$426$	12.4956			0.605414
$427$	7.04593	−	36.4547i	0.340977	−	1.76417i
$428$		−	8.23274i		−	0.397945i
$429$	1.53344	−	19.8002i	0.0740353	−	0.955961i
$430$	−25.2976	−	14.6056i	−1.21996	−	0.704344i
$431$	−2.79663	−	10.4371i	−0.134709	−	0.502740i	−0.999999	−	0.00146850i	$-0.999533\pi$
$431$	−2.79663	−	10.4371i	−0.134709	−	0.502740i	0.865290	−	0.501271i	$-0.167134\pi$
$432$	0.866025	−	0.500000i	0.0416667	−	0.0240563i
$433$	−20.1982			−0.970665			−0.485333	−	0.874330i	$-0.661301\pi$
$433$	−20.1982			−0.970665			−0.485333	+	0.874330i	$0.661301\pi$
$434$	1.07557	−	1.23995i	0.0516289	−	0.0595196i
$435$	−23.8516	+	23.8516i	−1.14359	+	1.14359i
$436$	−4.47455	+	16.6992i	−0.214292	+	0.799748i
$437$	0.847544	+	3.16308i	0.0405435	+	0.151310i
$438$	−1.43289	+	2.48183i	−0.0684660	+	0.118587i
$439$	−2.25623	−	3.90791i	−0.107684	−	0.186514i	0.807148	−	0.590350i	$-0.201010\pi$
$439$	−2.25623	−	3.90791i	−0.107684	−	0.186514i	−0.914832	+	0.403835i	$0.867677\pi$
$440$	−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	$0.713927\pi$
$444$	2.34483	−	0.628295i	0.111281	−	0.0298176i
$445$	−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
$448$	1.99861	+	1.73365i	0.0944257	+	0.0819072i
$449$	18.0218	+	18.0218i	0.850503	+	0.850503i	0.990195	−	0.139692i	$-0.0446112\pi$
$449$	18.0218	+	18.0218i	0.850503	+	0.850503i	−0.139692	+	0.990195i	$0.544611\pi$
$450$	1.67166	−	6.23874i	0.0788030	−	0.294097i
$451$	−47.8259	−	27.6123i	−2.25204	−	1.30021i
$452$	−14.5552	−	8.40345i	−0.684619	−	0.395265i
$453$	−13.6683	−	3.66242i	−0.642195	−	0.172076i
$454$	4.47008			0.209791
$455$	−22.9797	+	22.6867i	−1.07731	+	1.06357i
$456$	−3.43859			−0.161027
$457$	20.0126	+	5.36235i	0.936149	+	0.250840i	0.694475	−	0.719517i	$-0.255637\pi$
$457$	20.0126	+	5.36235i	0.936149	+	0.250840i	0.241674	+	0.970357i	$0.422303\pi$
$458$	−13.1922	−	7.61653i	−0.616431	−	0.355897i
$459$	2.10848	+	1.21733i	0.0984156	+	0.0568203i
$460$	−0.834356	+	3.11386i	−0.0389020	+	0.145184i
$461$	−15.2571	−	15.2571i	−0.710592	−	0.710592i	0.256067	−	0.966659i	$-0.417573\pi$
$461$	−15.2571	−	15.2571i	−0.710592	−	0.710592i	−0.966659	+	0.256067i	$0.917573\pi$
$462$	13.7739	−	4.75908i	0.640818	−	0.221412i
$463$	4.18978	+	4.18978i	0.194716	+	0.194716i	0.797730	−	0.603015i	$-0.206034\pi$
$463$	4.18978	+	4.18978i	0.194716	+	0.194716i	−0.603015	+	0.797730i	$0.706034\pi$
$464$	4.98232	+	8.62963i	0.231298	+	0.400621i
$465$	−1.05006	+	1.81877i	−0.0486956	+	0.0843432i
$466$	0.108160	−	0.0289813i	0.00501040	−	0.00134253i
$467$	3.56716	+	6.17851i	0.165069	+	0.285907i	0.936680	−	0.350187i	$-0.113882\pi$
$467$	3.56716	+	6.17851i	0.165069	+	0.285907i	−0.771611	+	0.636095i	$0.780549\pi$
$468$	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
$473$	12.3019	+	45.9112i	0.565641	+	2.11100i
$474$	0.296898	−	1.10804i	0.0136370	−	0.0508938i
$475$	−15.7043	+	15.7043i	−0.720562	+	0.720562i
$476$	−1.22239	+	6.32448i	−0.0560282	+	0.289882i
$477$	5.27097			0.241341
$478$	−17.4272	+	10.0616i	−0.797102	+	0.460207i
$479$	4.44710	+	16.5968i	0.203193	+	0.758327i	0.989993	+	0.141119i	$0.0450699\pi$
$479$	4.44710	+	16.5968i	0.203193	+	0.758327i	−0.786800	+	0.617209i	$0.788263\pi$
$480$	−2.93157	−	1.69254i	−0.133807	−	0.0772537i
$481$	8.72651	+	0.675833i	0.397895	+	0.0308153i
$482$			12.0976i			0.551030i
$483$	1.65100	−	1.90333i	0.0751230	−	0.0866046i
$484$	19.3383			0.879015
$485$	−20.6357	+	11.9141i	−0.937021	+	0.540989i
$486$	0.965926	−	0.258819i	0.0438153	−	0.0117403i
$487$	−0.145068	−	0.541400i	−0.00657365	−	0.0245332i	0.962561	−	0.271065i	$-0.0873758\pi$
$487$	−0.145068	−	0.541400i	−0.00657365	−	0.0245332i	−0.969135	+	0.246532i	$0.920709\pi$
$488$	13.5554	+	3.63216i	0.613624	+	0.164420i
$489$	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	$-0.947632\pi$
$491$		−	7.25820i		−	0.327558i	0.986497	−	0.163779i	$-0.0523684\pi$
$492$	2.59498	−	9.68458i	0.116991	−	0.436615i
$493$	−12.1303	+	21.0103i	−0.546321	+	0.946256i
$494$	−11.6920	−	4.12395i	−0.526050	−	0.185545i
$495$	−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
$499$	−0.609430	−	0.163296i	−0.0272818	−	0.00731015i	0.245152	−	0.969485i	$-0.421162\pi$
$499$	−0.609430	−	0.163296i	−0.0272818	−	0.00731015i	−0.272434	+	0.962174i	$0.587829\pi$
$500$	−4.76995	+	1.27810i	−0.213318	+	0.0571585i
$501$	8.12946	−	2.17828i	0.363198	−	0.0973185i
$502$	−23.0226	−	6.16888i	−1.02755	−	0.275330i
$503$			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
$507$	12.8450	+	2.00159i	0.570466	+	0.0888937i
$508$	−3.68421	+	6.38123i	−0.163460	+	0.283122i
$509$	−3.91515	+	14.6115i	−0.173536	+	0.647645i	0.823260	+	0.567664i	$0.192153\pi$
$509$	−3.91515	+	14.6115i	−0.173536	+	0.647645i	−0.996796	+	0.0799811i	$0.974514\pi$
$510$		−	8.24156i		−	0.364942i
$511$	−6.81829	−	3.31655i	−0.301624	−	0.146716i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−3.32142	−	0.889973i	−0.146644	−	0.0392933i
$514$	5.41198	+	20.1978i	0.238712	+	0.890886i
$515$	35.9612	−	9.63578i	1.58464	−	0.424603i
$516$	−7.47326	+	4.31469i	−0.328992	+	0.189944i
$517$	2.98408			0.131240
$518$	2.09746	+	6.07055i	0.0921573	+	0.266725i
$519$			20.7056i			0.908876i
$520$	−7.93816	−	9.27093i	−0.348111	−	0.406557i
$521$	−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	$0.739815\pi$
$522$	2.57904	+	9.62511i	0.112881	+	0.421279i
$523$	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
$525$	16.7779	+	3.24282i	0.732248	+	0.141528i
$526$	4.17774	−	4.17774i	0.182158	−	0.182158i
$527$	−0.390942	+	1.45901i	−0.0170297	+	0.0635557i
$528$	1.42558	+	5.32034i	0.0620405	+	0.231538i
$529$	−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
$535$	−26.9190	+	7.21291i	−1.16381	+	0.311841i
$536$	−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
$539$	15.1404	+	35.4591i	0.652142	+	1.52733i
$540$	−2.39362	−	2.39362i	−0.103005	−	0.103005i
$541$	2.55496	−	9.53526i	0.109846	−	0.409953i	−0.889003	−	0.457901i	$-0.848602\pi$
$541$	2.55496	−	9.53526i	0.109846	−	0.409953i	0.998850	+	0.0479480i	$0.0152682\pi$
$542$	−1.94389	−	1.12231i	−0.0834973	−	0.0482072i
$543$	−15.0927	−	8.71380i	−0.647692	−	0.373945i
$544$	−2.35171	−	0.630138i	−0.100829	−	0.0270170i
$545$	58.5225			2.50683
$546$	2.40979	+	9.23000i	0.103130	+	0.395008i
$547$	1.20517			0.0515293			0.0257647	−	0.999668i	$-0.491798\pi$
$547$	1.20517			0.0515293			0.0257647	+	0.999668i	$0.491798\pi$
$548$	15.1507	+	4.05963i	0.647208	+	0.173419i
$549$	12.1534	+	7.01679i	0.518696	+	0.299469i
$550$	30.8091	+	17.7877i	1.31371	+	0.758468i
$551$	8.86826	−	33.0968i	0.377801	−	1.40997i
$552$	0.673396	+	0.673396i	0.0286616	+	0.0286616i
$553$	2.97986	+	0.575945i	0.126716	+	0.0244917i
$554$	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
$557$	6.64353	−	1.78013i	0.281495	−	0.0754265i	−0.115309	−	0.993330i	$-0.536786\pi$
$557$	6.64353	−	1.78013i	0.281495	−	0.0754265i	0.396804	+	0.917903i	$0.370119\pi$
$558$	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	−0.861591	−	0.507603i	$-0.830532\pi$
$563$	0.208837	−	0.361716i	0.00880142	−	0.0152445i	0.870393	+	0.492358i	$0.163865\pi$
$564$	0.140221	+	0.523310i	0.00590435	+	0.0220353i
$565$	−14.7249	+	54.9542i	−0.619483	+	2.31194i
$566$	10.6308	−	10.6308i	0.446845	−	0.446845i
$567$	0.864026	+	2.50069i	0.0362857	+	0.105019i
$568$	−12.4956			−0.524304
$569$	−28.1918	+	16.2765i	−1.18186	+	0.682348i	−0.956445	−	0.291914i	$-0.905708\pi$
$569$	−28.1918	+	16.2765i	−1.18186	+	0.682348i	−0.225417	+	0.974262i	$0.572375\pi$
$570$	3.01264	+	11.2433i	0.126185	+	0.470930i
$571$	31.6764	+	18.2884i	1.32561	+	0.765344i	0.984618	−	0.174721i	$-0.0559023\pi$
$571$	31.6764	+	18.2884i	1.32561	+	0.765344i	0.340996	+	0.940065i	$0.389236\pi$
$572$	−1.53344	+	19.8002i	−0.0641165	+	0.827887i
$573$		−	3.38058i		−	0.141226i
$574$	26.0449	+	5.03393i	1.08709	+	0.210112i
$575$	6.15089			0.256510
$576$	−0.866025	+	0.500000i	−0.0360844	+	0.0208333i
$577$	17.1644	−	4.59918i	0.714562	−	0.191466i	0.116818	−	0.993153i	$-0.462731\pi$
$577$	17.1644	−	4.59918i	0.714562	−	0.191466i	0.597744	+	0.801687i	$0.296064\pi$
$578$	2.86575	+	10.6951i	0.119199	+	0.444858i
$579$	11.0699	+	2.96618i	0.460050	+	0.123270i
$580$	23.8516	−	23.8516i	0.990382	−	0.990382i
$581$	9.18707	−	0.652219i	0.381144	−	0.0270586i
$582$			7.03914i			0.291782i
$583$	−7.51419	+	28.0434i	−0.311206	+	1.16144i
$584$	1.43289	−	2.48183i	0.0592933	−	0.102699i
$585$	−5.26818	−	11.0096i	−0.217812	−	0.455190i
$586$	5.46040	−	3.15256i	0.225567	−	0.130231i
$587$	3.24643	+	3.24643i	0.133995	+	0.133995i	0.770923	−	0.636928i	$-0.219795\pi$
$587$	3.24643	+	3.24643i	0.133995	+	0.133995i	−0.636928	+	0.770923i	$0.719795\pi$
$588$	−5.50692	+	4.32133i	−0.227101	+	0.178209i
$589$		−	2.13332i		−	0.0879021i
$590$	30.4579	+	8.16116i	1.25393	+	0.335990i
$591$	−9.14670	+	2.45085i	−0.376245	+	0.100815i
$592$	−2.34483	+	0.628295i	−0.0963719	+	0.0258228i
$593$	−6.50885	−	1.74404i	−0.267286	−	0.0716191i	0.122687	−	0.992445i	$-0.460849\pi$
$593$	−6.50885	−	1.74404i	−0.267286	−	0.0716191i	−0.389973	+	0.920826i	$0.627516\pi$
$594$			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
$598$	1.48209	+	3.09732i	0.0606074	+	0.126659i
$599$	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	$0.0841665\pi$
$600$	−1.67166	+	6.23874i	−0.0682454	+	0.254695i
$601$			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
$604$	13.6683	+	3.66242i	0.556157	+	0.149022i
$605$	−16.9428	−	63.2314i	−0.688822	−	2.57072i
$606$	9.70556	−	2.60060i	0.394261	−	0.105642i
$607$	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
$609$	−24.9185	+	8.60972i	−1.00975	+	0.348883i
$610$		−	47.5049i		−	1.92342i
$611$	−0.150830	+	1.94755i	−0.00610192	+	0.0787894i
$612$	−2.10848	−	1.21733i	−0.0852304	−	0.0492078i
$613$	2.05005	+	7.65088i	0.0828006	+	0.309016i	0.994889	−	0.100978i	$-0.0321973\pi$
$613$	2.05005	+	7.65088i	0.0828006	+	0.309016i	−0.912088	+	0.409994i	$0.865531\pi$
$614$	−4.95933	+	2.86327i	−0.200142	+	0.115552i
$615$	−33.9396			−1.36858
$616$	−13.7739	+	4.75908i	−0.554965	+	0.191749i
$617$	−7.53021	+	7.53021i	−0.303155	+	0.303155i	−0.842247	−	0.539092i	$-0.818767\pi$
$617$	−7.53021	+	7.53021i	−0.303155	+	0.303155i	0.539092	+	0.842247i	$0.318767\pi$
$618$	2.84654	−	10.6234i	0.114505	−	0.427337i
$619$	−2.40131	−	8.96181i	−0.0965168	−	0.360205i	0.900728	−	0.434383i	$-0.143034\pi$
$619$	−2.40131	−	8.96181i	−0.0965168	−	0.360205i	−0.997245	+	0.0741775i	$0.976367\pi$
$620$	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
$626$	7.24289	−	1.94073i	0.289484	−	0.0775670i
$627$	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
$630$	5.86855	−	6.76548i	0.233809	−	0.269543i
$631$	−34.0998	−	34.0998i	−1.35749	−	1.35749i	−0.876997	−	0.480497i	$-0.840456\pi$
$631$	−34.0998	−	34.0998i	−1.35749	−	1.35749i	−0.480497	−	0.876997i	$-0.659544\pi$
$632$	−0.296898	+	1.10804i	−0.0118100	+	0.0440754i
$633$	13.3169	+	7.68851i	0.529299	+	0.305591i
$634$	−6.11239	−	3.52899i	−0.242754	−	0.140154i
$635$	24.0928	+	6.45565i	0.956095	+	0.256185i
$636$	−5.27097			−0.209007
$637$	−23.9075	+	8.08903i	−0.947249	+	0.320499i
$638$	−54.8855			−2.17294
$639$	−12.0698	−	3.23410i	−0.477475	−	0.127939i
$640$	2.93157	+	1.69254i	0.115881	+	0.0669037i
$641$	37.5455	+	21.6769i	1.48296	+	0.856187i	0.999813	−	0.0193532i	$-0.00616071\pi$
$641$	37.5455	+	21.6769i	1.48296	+	0.856187i	0.483146	+	0.875540i	$0.339494\pi$
$642$	−2.13079	+	7.95222i	−0.0840956	+	0.313849i
$643$	17.2911	+	17.2911i	0.681895	+	0.681895i	0.960427	−	0.278532i	$-0.0898478\pi$
$643$	17.2911	+	17.2911i	0.681895	+	0.681895i	−0.278532	+	0.960427i	$0.589848\pi$
$644$	−1.65100	+	1.90333i	−0.0650584	+	0.0750018i
$645$	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	$0.469470\pi$
$647$	−20.7092	+	35.8694i	−0.814163	+	1.41017i	−0.909928	+	0.414767i	$0.863863\pi$
$648$	−0.965926	+	0.258819i	−0.0379452	+	0.0101674i
$649$	−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
$655$	−0.815701	−	3.04424i	−0.0318721	−	0.118948i
$656$	−2.59498	+	9.68458i	−0.101317	+	0.378119i
$657$	2.02641	−	2.02641i	0.0790577	−	0.0790577i
$658$	−1.35480	+	0.468104i	−0.0528156	+	0.0182486i
$659$	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
$661$	8.97055	+	33.4785i	0.348914	+	1.30216i	0.887973	+	0.459896i	$0.152113\pi$
$661$	8.97055	+	33.4785i	0.348914	+	1.30216i	−0.539059	+	0.842268i	$0.681220\pi$
$662$	−4.34864	−	2.51069i	−0.169015	−	0.0975807i
$663$	−5.70939	−	6.66796i	−0.221734	−	0.258962i
$664$			3.48112i			0.135094i
$665$	−29.1079	+	10.0572i	−1.12876	+	0.390002i
$666$	−2.42755			−0.0940655
$667$	−8.21822	+	4.74479i	−0.318211	+	0.183719i
$668$	−8.12946	+	2.17828i	−0.314538	+	0.0842803i
$669$	−1.62137	−	6.05105i	−0.0626860	−	0.233947i
$670$	39.8519	+	10.6783i	1.53961	+	0.412538i
$671$	−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	$-0.904093\pi$
$673$		−	15.3973i		−	0.593523i	0.954952	−	0.296761i	$-0.0959066\pi$
$674$	3.30874	−	12.3484i	0.127448	−	0.475642i
$675$	−3.22941	+	5.59350i	−0.124300	+	0.215294i
$676$	−12.8450	−	2.00159i	−0.494038	−	0.0769842i
$677$	−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
$681$	−4.31777	−	1.15694i	−0.165457	−	0.0443342i
$682$	−3.30077	+	0.884440i	−0.126393	+	0.0338669i
$683$	−21.8105	+	5.84412i	−0.834557	+	0.223619i	−0.650701	−	0.759334i	$-0.725525\pi$
$683$	−21.8105	+	5.84412i	−0.834557	+	0.223619i	−0.183856	+	0.982953i	$0.558858\pi$
$684$	3.32142	+	0.889973i	0.126998	+	0.0340290i
$685$		−	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
$689$	−17.9226	−	6.32155i	−0.682795	−	0.240832i
$690$	1.61185	−	2.79181i	0.0613622	−	0.106282i
$691$	0.447502	−	1.67010i	0.0170238	−	0.0635336i	−0.956891	−	0.290446i	$-0.906196\pi$
$691$	0.447502	−	1.67010i	0.0170238	−	0.0635336i	0.973915	+	0.226912i	$0.0728631\pi$
$692$		−	20.7056i		−	0.787109i
$693$	−14.5363	+	1.03198i	−0.552187	+	0.0392016i
$694$	16.2418	−	16.2418i	0.616529	−	0.616529i
$695$	−35.8505	−	9.60611i	−1.35989	−	0.364380i
$696$	−2.57904	−	9.62511i	−0.0977582	−	0.364839i
$697$	−23.5787	+	6.31790i	−0.893108	+	0.239308i
$698$	−3.60721	+	2.08262i	−0.136535	+	0.0788285i
$699$	−0.111975			−0.00423529
$700$	−16.7779	−	3.24282i	−0.634145	−	0.122567i
$701$		−	0.844039i		−	0.0318789i	−0.999873	−	0.0159394i	$-0.994926\pi$
$701$		−	0.844039i		−	0.0318789i	0.999873	−	0.0159394i	$-0.00507390\pi$
$702$	−3.59479	−	0.278402i	−0.135676	−	0.0105076i
$703$	7.22901	+	4.17367i	0.272647	+	0.157413i
$704$	−1.42558	−	5.32034i	−0.0537286	−	0.200518i
$705$	1.58824	−	0.916970i	0.0598165	−	0.0345351i
$706$	3.40494			0.128147
$707$	8.68168	+	25.1268i	0.326508	+	0.944990i
$708$	6.58675	−	6.58675i	0.247545	−	0.247545i
$709$	1.28855	−	4.80893i	0.0483924	−	0.180603i	−0.937499	−	0.347987i	$-0.886865\pi$
$709$	1.28855	−	4.80893i	0.0483924	−	0.180603i	0.985892	+	0.167384i	$0.0535320\pi$
$710$	10.9477	+	40.8574i	0.410860	+	1.53335i
$711$	−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
$717$	19.4375	−	5.20827i	0.725907	−	0.194506i
$718$	−14.0605	+	24.3535i	−0.524732	+	0.908863i
$719$	−7.92066	−	13.7190i	−0.295391	−	0.511632i	0.679685	−	0.733504i	$-0.262117\pi$
$719$	−7.92066	−	13.7190i	−0.295391	−	0.511632i	−0.975076	+	0.221872i	$0.928783\pi$
$720$	2.39362	+	2.39362i	0.0892049	+	0.0892049i
$721$	28.5697	+	5.52193i	1.06399	+	0.205647i
$722$	5.07426	+	5.07426i	0.188844	+	0.188844i
$723$	3.13108	−	11.6854i	0.116446	−	0.434583i
$724$	15.0927	+	8.71380i	0.560918	+	0.323846i
$725$	−55.7372	−	32.1799i	−2.07003	−	1.19513i
$726$	−18.6794	−	5.00513i	−0.693257	−	0.185758i
$727$	45.6887			1.69450			0.847249	−	0.531195i	$-0.178257\pi$
$727$	45.6887			1.69450			0.847249	+	0.531195i	$0.178257\pi$
$728$	−2.40979	−	9.23000i	−0.0893129	−	0.342087i
$729$	−1.00000			−0.0370370
$730$	−9.37035	−	2.51078i	−0.346812	−	0.0929280i
$731$	18.1949	+	10.5048i	0.672963	+	0.388535i
$732$	−12.1534	−	7.01679i	−0.449204	−	0.259348i
$733$	−0.198829	+	0.742039i	−0.00734390	+	0.0274078i	−0.969501	−	0.245089i	$-0.921183\pi$
$733$	−0.198829	+	0.742039i	−0.00734390	+	0.0274078i	0.962157	+	0.272497i	$0.0878495\pi$
$734$	−26.0925	−	26.0925i	−0.963091	−	0.963091i
$735$	18.9544	+	14.2202i	0.699143	+	0.524519i
$736$	−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
$739$	16.3530	−	4.38177i	0.601555	−	0.161186i	0.0548261	−	0.998496i	$-0.482540\pi$
$739$	16.3530	−	4.38177i	0.601555	−	0.161186i	0.546729	+	0.837310i	$0.315873\pi$
$740$	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	−0.0805800	−	0.996748i	$-0.525677\pi$
$743$	24.9729	−	24.9729i	0.916168	−	0.916168i	0.996748	+	0.0805800i	$0.0256773\pi$
$744$	−0.310203	−	0.537288i	−0.0113726	−	0.0196979i
$745$	29.4071	−	50.9347i	1.07739	−	1.86610i
$746$	2.86029	+	10.6748i	0.104723	+	0.390831i
$747$	−0.900981	+	3.36251i	−0.0329652	+	0.123028i
$748$	9.48245	−	9.48245i	0.346713	−	0.346713i
$749$	−21.3860	−	4.13347i	−0.781427	−	0.151034i
$750$	4.93821			0.180318
$751$	19.6538	−	11.3471i	0.717178	−	0.414063i	−0.0965354	−	0.995330i	$-0.530776\pi$
$751$	19.6538	−	11.3471i	0.717178	−	0.414063i	0.813713	+	0.581267i	$0.197443\pi$
$752$	−0.140221	−	0.523310i	−0.00511332	−	0.0190832i
$753$	20.6415	+	11.9174i	0.752217	+	0.434292i
$754$	2.77417	−	35.8208i	0.101029	−	1.30452i
$755$		−	47.9007i		−	1.74329i
$756$	−0.864026	−	2.50069i	−0.0314243	−	0.0909493i
$757$	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
$759$	−5.06670	+	1.35762i	−0.183909	+	0.0492784i
$760$	−3.01264	−	11.2433i	−0.109280	−	0.407838i
$761$	−5.94332	−	1.59251i	−0.215445	−	0.0577284i	0.149482	−	0.988764i	$-0.452239\pi$
$761$	−5.94332	−	1.59251i	−0.215445	−	0.0577284i	−0.364927	+	0.931036i	$0.618906\pi$
$762$	5.21026	−	5.21026i	0.188748	−	0.188748i
$763$	41.1326	+	20.0077i	1.48910	+	0.724328i
$764$			3.38058i			0.122305i
$765$	−2.13307	+	7.96074i	−0.0771214	+	0.287821i
$766$	10.8646	−	18.8180i	0.392552	−	0.679921i
$767$	30.2961	−	14.4970i	1.09393	−	0.523455i
$768$	0.866025	−	0.500000i	0.0312500	−	0.0180422i
$769$	−24.7530	−	24.7530i	−0.892615	−	0.892615i	0.102154	−	0.994769i	$-0.467427\pi$
$769$	−24.7530	−	24.7530i	−0.892615	−	0.892615i	−0.994769	+	0.102154i	$0.967427\pi$
$770$	27.6286	+	40.8675i	0.995665	+	1.47276i
$771$		−	20.9103i		−	0.753066i
$772$	−11.0699	−	2.96618i	−0.398415	−	0.106755i
$773$	21.4394	−	5.74468i	0.771123	−	0.206622i	0.148256	−	0.988949i	$-0.452634\pi$
$773$	21.4394	−	5.74468i	0.771123	−	0.206622i	0.622868	+	0.782327i	$0.285967\pi$
$774$	8.33534	−	2.23345i	0.299607	−	0.0802796i
$775$	−3.87055	−	1.03711i	−0.139034	−	0.0372541i
$776$		−	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
$780$	5.26818	+	11.0096i	0.188631	+	0.394206i
$781$	34.4130	−	59.6051i	1.23139	−	2.13284i
$782$	0.600097	−	2.23959i	0.0214594	−	0.0800876i
$783$		−	9.96464i		−	0.356107i
$784$	5.50692	−	4.32133i	0.196676	−	0.154333i
$785$	−7.90240	+	7.90240i	−0.282049	+	0.282049i
$786$	−0.899309	−	0.240969i	−0.0320773	−	0.00859508i
$787$	2.84488	+	10.6172i	0.101409	+	0.378464i	0.997913	−	0.0645717i	$-0.0205681\pi$
$787$	2.84488	+	10.6172i	0.101409	+	0.378464i	−0.896504	+	0.443036i	$0.853901\pi$
$788$	9.14670	−	2.45085i	0.325838	−	0.0873079i
$789$	−5.11667	+	2.95411i	−0.182158	+	0.105169i
$790$	3.88312			0.138155
$791$	−29.1373	+	33.5905i	−1.03600	+	1.19434i
$792$		−	5.50802i		−	0.195719i
$793$	−32.9093	−	38.4346i	−1.16864	−	1.36485i
$794$	−13.2576	−	7.65431i	−0.470496	−	0.271641i
$795$	4.61803	+	17.2347i	0.163785	+	0.611252i
$796$	5.18362	−	2.99276i	0.183729	−	0.106076i
$797$	51.4534			1.82257			0.911286	−	0.411774i	$-0.135091\pi$
$797$	51.4534			1.82257			0.911286	+	0.411774i	$0.135091\pi$
$798$	−1.72644	+	8.93235i	−0.0611152	+	0.316202i
$799$	0.932696	−	0.932696i	0.0329964	−	0.0329964i
$800$	1.67166	−	6.23874i	0.0591022	−	0.220573i
$801$	−1.18691	−	4.42960i	−0.0419373	−	0.156512i
$802$	−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
$808$	−9.70556	+	2.60060i	−0.341440	+	0.0914887i
$809$	−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	$-0.489629\pi$
$811$	−27.5353	−	27.5353i	−0.966894	−	0.966894i	−0.999469	+	0.0325753i	$0.989629\pi$
$812$	24.9185	−	8.60972i	0.874468	−	0.302142i
$813$	1.58718	+	1.58718i	0.0556649	+	0.0556649i
$814$	3.46067	−	12.9154i	0.121296	−	0.452684i
$815$	33.6233	+	19.4124i	1.17777	+	0.679987i
$816$	2.10848	+	1.21733i	0.0738117	+	0.0426152i
$817$	−28.6618	−	7.67991i	−1.00275	−	0.268686i
$818$	−13.0516			−0.456337
$819$	0.0612176	−	9.53920i	0.00213912	−	0.333326i
$820$	33.9396			1.18522
$821$	38.9535	+	10.4376i	1.35949	+	0.364274i	0.863628	−	0.504129i	$-0.168186\pi$
$821$	38.9535	+	10.4376i	1.35949	+	0.364274i	0.495859	+	0.868403i	$0.334853\pi$
$822$	−13.5838	−	7.84260i	−0.473789	−	0.273542i
$823$	−28.8404	−	16.6510i	−1.00531	−	0.580418i	−0.0954973	−	0.995430i	$-0.530444\pi$
$823$	−28.8404	−	16.6510i	−1.00531	−	0.580418i	−0.909816	+	0.415012i	$0.863777\pi$
$824$	−2.84654	+	10.6234i	−0.0991638	+	0.370084i
$825$	−25.1555	−	25.1555i	−0.875803	−	0.875803i
$826$	18.6172	+	16.1491i	0.647776	+	0.561898i
$827$	−39.4707	−	39.4707i	−1.37253	−	1.37253i	−0.856677	−	0.515852i	$-0.827475\pi$
$827$	−39.4707	−	39.4707i	−1.37253	−	1.37253i	−0.515852	−	0.856677i	$-0.672525\pi$
$828$	−0.476163	−	0.824738i	−0.0165478	−	0.0286616i
$829$	−25.3637	+	43.9312i	−0.880918	+	1.52579i	−0.0305961	+	0.999532i	$0.509741\pi$
$829$	−25.3637	+	43.9312i	−0.880918	+	1.52579i	−0.850322	+	0.526263i	$0.823593\pi$
$830$	11.3824	−	3.04990i	0.395088	−	0.105864i
$831$	−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
$837$	−0.160573	−	0.599266i	−0.00555021	−	0.0207137i
$838$	0.664188	−	2.47878i	0.0229440	−	0.0856281i
$839$	40.4977	−	40.4977i	1.39814	−	1.39814i	0.592748	−	0.805388i	$-0.298043\pi$
$839$	40.4977	−	40.4977i	1.39814	−	1.39814i	0.805388	−	0.592748i	$-0.201957\pi$
$840$	−5.86855	+	6.76548i	−0.202484	+	0.233431i
$841$	70.2941			2.42394
$842$	−10.6079	+	6.12449i	−0.365574	+	0.211064i
$843$	3.99334	+	14.9034i	0.137538	+	0.513299i
$844$	−13.3169	−	7.68851i	−0.458386	−	0.264650i
$845$	4.70913	+	43.7534i	0.161999	+	1.50516i
$846$		−	0.541771i		−	0.0186265i
$847$	9.70933	−	50.2347i	0.333616	−	1.72608i
$848$	5.27097			0.181006
$849$	−13.0200	+	7.51710i	−0.446845	+	0.257986i
$850$	15.1892	−	4.06995i	0.520987	−	0.139598i
$851$	−0.598342	−	2.23304i	−0.0205109	−	0.0765477i
$852$	12.0698	+	3.23410i	0.413505	+	0.110798i
$853$	−18.7260	+	18.7260i	−0.641167	+	0.641167i	−0.950842	−	0.309676i	$-0.899780\pi$
$853$	−18.7260	+	18.7260i	−0.641167	+	0.641167i	0.309676	+	0.950842i	$0.399780\pi$
$854$	16.2410	−	33.3889i	0.555756	−	1.14254i
$855$		−	11.6399i		−	0.398077i
$856$	2.13079	−	7.95222i	0.0728289	−	0.271801i
$857$	−17.0390	+	29.5124i	−0.582041	+	1.00812i	0.413196	+	0.910642i	$0.364412\pi$
$857$	−17.0390	+	29.5124i	−0.582041	+	1.00812i	−0.995237	+	0.0974823i	$0.968921\pi$
$858$	6.60585	−	18.7286i	0.225520	−	0.639384i
$859$	−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
$863$	19.9617	+	5.34873i	0.679505	+	0.182073i	0.582033	−	0.813165i	$-0.302257\pi$
$863$	19.9617	+	5.34873i	0.679505	+	0.182073i	0.0974726	+	0.995238i	$0.468924\pi$
$864$	0.965926	−	0.258819i	0.0328615	−	0.00880520i
$865$	−67.7020	+	18.1407i	−2.30194	+	0.616803i
$866$	−19.5100	−	5.22769i	−0.662977	−	0.177644i
$867$		−	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
$871$	39.6403	−	18.9682i	1.34316	−	0.642713i
$872$	−8.64416	+	14.9721i	−0.292728	+	0.507020i
$873$	1.82186	−	6.79929i	0.0616607	−	0.230121i
$874$			3.27466i			0.110767i
$875$	0.925217	+	13.0325i	0.0312781	+	0.440578i
$876$	−2.02641	+	2.02641i	−0.0684660	+	0.0684660i
$877$	28.5827	+	7.65872i	0.965170	+	0.258616i	0.706787	−	0.707426i	$-0.250144\pi$
$877$	28.5827	+	7.65872i	0.965170	+	0.258616i	0.258383	+	0.966043i	$0.416810\pi$
$878$	−1.16791	−	4.35871i	−0.0394151	−	0.147099i
$879$	−6.09029	+	1.63189i	−0.205420	+	0.0550422i
$880$	−16.1472	+	9.32257i	−0.544321	+	0.314264i
$881$	−28.6254			−0.964413			−0.482207	−	0.876058i	$-0.660165\pi$
$881$	−28.6254			−0.964413			−0.482207	+	0.876058i	$0.660165\pi$
$882$	6.43771	−	2.74879i	0.216769	−	0.0925565i
$883$		−	33.5425i		−	1.12880i	−0.825503	−	0.564398i	$-0.809108\pi$
$883$		−	33.5425i		−	1.12880i	0.825503	−	0.564398i	$-0.190892\pi$
$884$	5.70939	+	6.66796i	0.192028	+	0.224268i
$885$	−27.3078	−	15.7662i	−0.917941	−	0.529974i
$886$	3.99181	+	14.8976i	0.134108	+	0.500496i
$887$	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
$889$	14.7266	+	12.7742i	0.493915	+	0.428435i
$890$	−10.9768	+	10.9768i	−0.367943	+	0.367943i
$891$	1.42558	−	5.32034i	0.0477588	−	0.178238i
$892$	1.62137	+	6.05105i	0.0542876	+	0.202604i
$893$	−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
$899$	5.97148	−	1.60005i	0.199160	−	0.0533647i
$900$	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
$903$	7.45601	+	21.5794i	0.248120	+	0.718118i
$904$	−11.8843	−	11.8843i	−0.395265	−	0.395265i
$905$	15.2688	−	56.9838i	0.507551	−	1.89421i
$906$	−12.2547	−	7.07526i	−0.407135	−	0.235060i
$907$	39.5608	+	22.8404i	1.31359	+	0.758404i	0.982689	−	0.185260i	$-0.0593129\pi$
$907$	39.5608	+	22.8404i	1.31359	+	0.758404i	0.330904	+	0.943664i	$0.392646\pi$
$908$	4.31777	+	1.15694i	0.143290	+	0.0383945i
$909$	−10.0479			−0.333269
$910$	−28.0684	+	15.9660i	−0.930460	+	0.529269i
$911$	32.7618			1.08545			0.542724	−	0.839911i	$-0.317393\pi$
$911$	32.7618			1.08545			0.542724	+	0.839911i	$0.317393\pi$
$912$	−3.32142	−	0.889973i	−0.109983	−	0.0294700i
$913$	−16.6053	−	9.58706i	−0.549554	−	0.317285i
$914$	17.9428	+	10.3593i	0.593495	+	0.342654i
$915$	−12.2952	+	45.8862i	−0.406466	+	1.51695i
$916$	−10.7714	−	10.7714i	−0.355897	−	0.355897i
$917$	0.467450	−	2.41852i	0.0154366	−	0.0798666i
$918$	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
$921$	5.53142	−	1.48214i	0.182266	−	0.0488381i
$922$	−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
$928$	2.57904	+	9.62511i	0.0846611	+	0.315960i
$929$	−2.04404	+	7.62845i	−0.0670627	+	0.250281i	−0.991317	−	0.131497i	$-0.958022\pi$
$929$	−2.04404	+	7.62845i	−0.0670627	+	0.250281i	0.924254	+	0.381778i	$0.124688\pi$
$930$	−1.48502	+	1.48502i	−0.0486956	+	0.0486956i
$931$	−23.8969	−	2.88270i	−0.783189	−	0.0944768i
$932$	0.111975			0.00366787
$933$	−22.4193	+	12.9438i	−0.733975	+	0.423760i
$934$	1.84650	+	6.89123i	0.0604193	+	0.225488i
$935$	−39.3130	−	22.6974i	−1.28567	−	0.742283i
$936$	3.59479	+	0.278402i	0.117499	+	0.00909984i
$937$		−	30.2873i		−	0.989444i	−0.869051	−	0.494722i	$-0.835270\pi$
$937$		−	30.2873i		−	0.989444i	0.869051	−	0.494722i	$-0.164730\pi$
$938$	24.3593	+	21.1299i	0.795359	+	0.689915i
$939$	−7.49839			−0.244701
$940$	−1.58824	+	0.916970i	−0.0518026	+	0.0299083i
$941$	−4.38229	+	1.17423i	−0.142859	+	0.0382788i	−0.329540	−	0.944142i	$-0.606894\pi$
$941$	−4.38229	+	1.17423i	−0.142859	+	0.0382788i	0.186681	+	0.982421i	$0.440227\pi$
$942$	0.854477	+	3.18895i	0.0278404	+	0.103902i
$943$	−9.22287	−	2.47126i	−0.300338	−	0.0804753i
$944$	−6.58675	+	6.58675i	−0.214380	+	0.214380i
$945$	−7.41962	+	5.01606i	−0.241360	+	0.163173i
$946$			47.5308i			1.54536i
$947$	9.69944	−	36.1988i	0.315189	−	1.17630i	−0.608624	−	0.793459i	$-0.708278\pi$
$947$	9.69944	−	36.1988i	0.315189	−	1.17630i	0.923813	−	0.382844i	$-0.125055\pi$
$948$	0.573562	−	0.993439i	0.0186284	−	0.0322654i
$949$	−9.32058	+	4.45998i	−0.302559	+	0.144777i
$950$	−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	$0.303245\pi$
$953$			50.3172i			1.62993i	−0.579507	+	0.814967i	$0.696755\pi$
$954$	5.09136	+	1.36423i	0.164839	+	0.0441685i
$955$	11.0536	−	2.96181i	0.357687	−	0.0958419i
$956$	−19.4375	+	5.20827i	−0.628654	+	0.168447i
$957$	53.0153	+	14.2054i	1.71374	+	0.459196i
$958$			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
$962$	8.25425	+	2.91139i	0.266128	+	0.0938671i
$963$	4.11637	−	7.12976i	0.132648	−	0.229753i
$964$	−3.13108	+	11.6854i	−0.100845	+	0.376360i
$965$			38.7945i			1.24884i
$966$	2.08736	−	1.41117i	0.0671597	−	0.0454036i
$967$	−14.2617	+	14.2617i	−0.458626	+	0.458626i	−0.898204	−	0.439578i	$-0.855128\pi$
$967$	−14.2617	+	14.2617i	−0.458626	+	0.458626i	0.439578	+	0.898204i	$0.355128\pi$
$968$	18.6794	+	5.00513i	0.600378	+	0.160871i
$969$	−2.16679	−	8.08656i	−0.0696073	−	0.259778i
$970$	−23.0162	+	6.16717i	−0.739005	+	0.198016i
$971$	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
$973$	−21.9134	−	19.0083i	−0.702513	−	0.609377i
$974$		−	0.560499i		−	0.0179595i
$975$	17.6891	−	15.1462i	0.566505	−	0.485066i
$976$	12.1534	+	7.01679i	0.389022	+	0.224602i
$977$	7.17314	+	26.7705i	0.229489	+	0.856464i	0.980556	+	0.196239i	$0.0628727\pi$
$977$	7.17314	+	26.7705i	0.229489	+	0.856464i	−0.751067	+	0.660226i	$0.770461\pi$
$978$	9.93276	−	5.73468i	0.317615	−	0.183375i
$979$	25.2590			0.807281
$980$	−18.9544	−	14.2202i	−0.605475	−	0.454247i
$981$	−12.2247	+	12.2247i	−0.390304	+	0.390304i
$982$	1.87856	−	7.01088i	0.0599473	−	0.223726i
$983$	1.09420	+	4.08359i	0.0348994	+	0.130246i	0.981178	−	0.193107i	$-0.0618564\pi$
$983$	1.09420	+	4.08359i	0.0348994	+	0.130246i	−0.946278	+	0.323353i	$0.895190\pi$
$984$	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
$990$	−18.0098	+	4.82572i	−0.572390	+	0.153371i
$991$	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
$994$	−6.27375	+	32.4595i	−0.198991	+	1.02955i
$995$	−14.3271	−	14.3271i	−0.454199	−	0.454199i
$996$	0.900981	−	3.36251i	0.0285487	−	0.106545i
$997$	−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
$999$	2.34483	+	0.628295i	0.0741872	+	0.0198784i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bz.a.73.5	✓	40	13.8	odd	4
546.2.bz.a.187.5	yes	40	7.5	odd	6
546.2.bz.b.31.10	yes	40	1.1	even	1	trivial
546.2.bz.b.229.10	yes	40	91.47	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.bz (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 + 0.258819i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.866025 + 0.500000i) q^{4} +(0.876125 - 3.26974i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(1.73365 - 1.99861i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.965926 + 0.258819i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.866025 + 0.500000i) q^{4} +(0.876125 - 3.26974i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(1.73365 - 1.99861i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +(1.69254 - 2.93157i) q^{10} +(-5.32034 + 1.42558i) 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} +(0.258819 + 0.965926i) q^{18} +(0.889973 - 3.32142i) q^{19} +(2.39362 - 2.39362i) q^{20} +(-2.50069 + 0.864026i) q^{21} -5.50802 q^{22} +(-0.824738 + 0.476163i) q^{23} +(-0.258819 - 0.965926i) q^{24} +(-5.59350 - 3.22941i) q^{25} +(0.278402 - 3.59479i) q^{26} -1.00000i q^{27} +(2.50069 - 0.864026i) q^{28} +9.96464 q^{29} +(-2.93157 + 1.69254i) q^{30} +(0.599266 - 0.160573i) q^{31} +(0.258819 + 0.965926i) q^{32} +(5.32034 + 1.42558i) q^{33} +(-1.72157 + 1.72157i) q^{34} +(-5.01606 - 7.41962i) q^{35} +1.00000i q^{36} +(-0.628295 + 2.34483i) q^{37} +(1.71930 - 2.97791i) q^{38} +(-1.19931 + 3.40024i) q^{39} +(2.93157 - 1.69254i) q^{40} +(7.08960 + 7.08960i) q^{41} +(-2.63911 + 0.187359i) q^{42} -8.62938i q^{43} +(-5.32034 - 1.42558i) q^{44} +(3.26974 - 0.876125i) q^{45} +(-0.919876 + 0.246480i) q^{46} +(-0.523310 - 0.140221i) q^{47} -1.00000i q^{48} +(-0.988921 - 6.92979i) q^{49} +(-4.56707 - 4.56707i) q^{50} +(2.10848 - 1.21733i) q^{51} +(1.19931 - 3.40024i) q^{52} +(2.63548 - 4.56479i) q^{53} +(0.258819 - 0.965926i) q^{54} +18.6451i q^{55} +(2.63911 - 0.187359i) q^{56} +(-2.43145 + 2.43145i) q^{57} +(9.62511 + 2.57904i) q^{58} +(2.41092 + 8.99767i) q^{59} +(-3.26974 + 0.876125i) q^{60} +(12.1534 - 7.01679i) q^{61} +0.620406 q^{62} +(2.59768 + 0.502077i) q^{63} +1.00000i q^{64} +(-12.1687 - 0.942414i) q^{65} +(4.77009 + 2.75401i) q^{66} +(3.15451 + 11.7728i) q^{67} +(-2.10848 + 1.21733i) q^{68} +0.952325 q^{69} +(-2.92480 - 8.46506i) q^{70} +(-8.83572 + 8.83572i) q^{71} +(-0.258819 + 0.965926i) q^{72} +(-0.741717 - 2.76813i) 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} +(3.26974 - 0.876125i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(5.01311 + 8.68296i) q^{82} +(2.46153 + 2.46153i) q^{83} +(-2.59768 - 0.502077i) q^{84} +(5.82766 + 5.82766i) q^{85} +(2.23345 - 8.33534i) q^{86} +(-8.62963 - 4.98232i) q^{87} +(-4.77009 - 2.75401i) q^{88} +(-4.42960 - 1.18691i) q^{89} +3.38509 q^{90} +(-8.23058 - 4.82261i) q^{91} -0.952325 q^{92} +(-0.599266 - 0.160573i) q^{93} +(-0.469187 - 0.270885i) q^{94} +(-10.0805 - 5.81997i) q^{95} +(0.258819 - 0.965926i) q^{96} +(-4.97742 - 4.97742i) q^{97} +(0.838339 - 6.94962i) 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	\( 40 q + 4 q^{7} + 20 q^{9} - 4 q^{11} - 20 q^{12} + 4 q^{14} + 20 q^{16} - 8 q^{17} + 16 q^{19} + 4 q^{21} + 8 q^{22} + 24 q^{23} + 48 q^{25} + 8 q^{26} - 4 q^{28} + 24 q^{29} + 4 q^{33} + 16 q^{34} - 8 q^{35} - 32 q^{37} - 16 q^{38} - 4 q^{39} + 8 q^{41} - 4 q^{44} - 28 q^{46} - 20 q^{47} - 16 q^{49} + 32 q^{50} + 12 q^{51} + 4 q^{52} - 4 q^{53} - 16 q^{57} + 12 q^{58} + 24 q^{59} - 12 q^{61} - 16 q^{62} + 8 q^{63} + 8 q^{65} - 24 q^{67} - 12 q^{68} + 16 q^{69} + 12 q^{70} + 8 q^{71} - 36 q^{73} - 40 q^{74} + 36 q^{75} + 16 q^{76} - 48 q^{77} - 8 q^{78} - 20 q^{81} - 24 q^{83} - 8 q^{84} - 40 q^{85} - 56 q^{86} - 72 q^{87} - 72 q^{89} - 24 q^{91} - 16 q^{92} - 36 q^{94} + 32 q^{98} - 8 q^{99}+O(q^{100}) \) 40 * q + 4 * q^7 + 20 * q^9 - 4 * q^11 - 20 * q^12 + 4 * q^14 + 20 * q^16 - 8 * q^17 + 16 * 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 - 32 * q^37 - 16 * q^38 - 4 * q^39 + 8 * q^41 - 4 * q^44 - 28 * 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 - 24 * q^67 - 12 * q^68 + 16 * q^69 + 12 * q^70 + 8 * q^71 - 36 * 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 - 56 * q^86 - 72 * q^87 - 72 * q^89 - 24 * q^91 - 16 * q^92 - 36 * q^94 + 32 * q^98 - 8 * q^99

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