LMFDB - Embedded newform 546.2.cg.b.145.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 10, 1]))

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

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

chi := DirichletCharacter("546.145");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			145.4
Character	$\chi$	$=$	546.145
Dual form			546.2.cg.b.241.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(-0.866025 - 0.500000i) q^{3} -1.00000i q^{4} +(3.01304 - 0.807342i) q^{5} +(0.965926 - 0.258819i) q^{6} +(2.56888 + 0.633142i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.866025 - 0.500000i) q^{3} -1.00000i q^{4} +(3.01304 - 0.807342i) q^{5} +(0.965926 - 0.258819i) q^{6} +(2.56888 + 0.633142i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.55967 + 2.70142i) q^{10} +(-1.47840 + 0.396136i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(-0.598039 + 3.55561i) q^{13} +(-2.26417 + 1.36877i) q^{14} +(-3.01304 - 0.807342i) q^{15} -1.00000 q^{16} +3.46440 q^{17} +(-0.965926 - 0.258819i) q^{18} +(1.28965 - 4.81303i) q^{19} +(-0.807342 - 3.01304i) q^{20} +(-1.90814 - 1.83276i) q^{21} +(0.765275 - 1.32550i) q^{22} -7.42537i q^{23} +(-0.258819 - 0.965926i) q^{24} +(4.09650 - 2.36511i) q^{25} +(-2.09132 - 2.93707i) q^{26} -1.00000i q^{27} +(0.633142 - 2.56888i) q^{28} +(1.30096 + 2.25333i) q^{29} +(2.70142 - 1.55967i) q^{30} +(-2.72003 + 10.1513i) q^{31} +(0.707107 - 0.707107i) q^{32} +(1.47840 + 0.396136i) q^{33} +(-2.44970 + 2.44970i) q^{34} +(8.25130 - 0.166280i) q^{35} +(0.866025 - 0.500000i) q^{36} +(3.34550 + 3.34550i) q^{37} +(2.49141 + 4.31525i) q^{38} +(2.29572 - 2.78023i) q^{39} +(2.70142 + 1.55967i) q^{40} +(-0.819786 + 3.05948i) q^{41} +(2.64521 - 0.0533064i) q^{42} +(6.51981 + 3.76421i) q^{43} +(0.396136 + 1.47840i) q^{44} +(2.20570 + 2.20570i) q^{45} +(5.25053 + 5.25053i) q^{46} +(-2.52616 - 9.42774i) q^{47} +(0.866025 + 0.500000i) q^{48} +(6.19826 + 3.25293i) q^{49} +(-1.22427 + 4.56905i) q^{50} +(-3.00026 - 1.73220i) q^{51} +(3.55561 + 0.598039i) q^{52} +(-3.34211 - 5.78870i) q^{53} +(0.707107 + 0.707107i) q^{54} +(-4.13466 + 2.38715i) q^{55} +(1.36877 + 2.26417i) q^{56} +(-3.52339 + 3.52339i) q^{57} +(-2.51326 - 0.673426i) q^{58} +(6.02046 - 6.02046i) q^{59} +(-0.807342 + 3.01304i) q^{60} +(6.60836 - 3.81534i) q^{61} +(-5.25469 - 9.10138i) q^{62} +(0.736122 + 2.54128i) q^{63} +1.00000i q^{64} +(1.06868 + 11.1960i) q^{65} +(-1.32550 + 0.765275i) q^{66} +(0.779022 + 2.90735i) q^{67} -3.46440i q^{68} +(-3.71268 + 6.43056i) q^{69} +(-5.71697 + 5.95213i) q^{70} +(0.689184 + 2.57207i) q^{71} +(-0.258819 + 0.965926i) q^{72} +(-6.59087 - 1.76602i) q^{73} -4.73126 q^{74} -4.73023 q^{75} +(-4.81303 - 1.28965i) q^{76} +(-4.04863 + 0.0815882i) q^{77} +(0.342598 + 3.58924i) q^{78} +(7.33360 - 12.7022i) q^{79} +(-3.01304 + 0.807342i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-1.58370 - 2.74306i) q^{82} +(-5.39273 - 5.39273i) q^{83} +(-1.83276 + 1.90814i) q^{84} +(10.4384 - 2.79696i) q^{85} +(-7.27190 + 1.94850i) q^{86} -2.60192i q^{87} +(-1.32550 - 0.765275i) q^{88} +(-5.62087 + 5.62087i) q^{89} -3.11933 q^{90} +(-3.78749 + 8.75528i) q^{91} -7.42537 q^{92} +(7.43125 - 7.43125i) q^{93} +(8.45268 + 4.88016i) q^{94} -15.5431i q^{95} +(-0.965926 + 0.258819i) q^{96} +(-4.27487 + 1.14545i) q^{97} +(-6.68300 + 2.08267i) q^{98} +(-1.08226 - 1.08226i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 4 q^{7} + 20 q^{9}+O(q^{10}) $ 40 * q + 4 * q^7 + 20 * q^9	$ 40 q + 4 q^{7} + 20 q^{9} + 8 q^{11} - 20 q^{12} + 4 q^{14} - 40 q^{16} + 16 q^{17} + 4 q^{19} + 4 q^{21} - 4 q^{22} - 24 q^{25} + 8 q^{26} - 4 q^{28} - 12 q^{29} - 8 q^{33} - 8 q^{34} - 32 q^{35} + 40 q^{37} + 8 q^{38} + 20 q^{39} + 20 q^{41} + 12 q^{42} - 24 q^{43} - 4 q^{44} + 32 q^{46} + 4 q^{47} + 32 q^{49} - 16 q^{50} + 24 q^{51} + 16 q^{52} - 4 q^{53} + 24 q^{55} + 12 q^{56} + 8 q^{57} + 12 q^{58} + 24 q^{59} + 60 q^{61} + 32 q^{62} - 4 q^{63} + 44 q^{65} - 12 q^{67} - 8 q^{69} - 24 q^{70} - 28 q^{71} + 60 q^{73} - 40 q^{74} - 72 q^{75} + 4 q^{76} - 12 q^{77} + 4 q^{78} - 20 q^{81} - 24 q^{82} + 60 q^{83} - 8 q^{84} - 4 q^{85} - 20 q^{86} - 36 q^{89} - 16 q^{92} - 24 q^{93} - 48 q^{97} - 88 q^{98} + 4 q^{99}+O(q^{100}) $ 40 * q + 4 * q^7 + 20 * q^9 + 8 * q^11 - 20 * q^12 + 4 * q^14 - 40 * q^16 + 16 * q^17 + 4 * q^19 + 4 * q^21 - 4 * q^22 - 24 * q^25 + 8 * q^26 - 4 * q^28 - 12 * q^29 - 8 * q^33 - 8 * q^34 - 32 * q^35 + 40 * q^37 + 8 * q^38 + 20 * q^39 + 20 * q^41 + 12 * q^42 - 24 * q^43 - 4 * q^44 + 32 * q^46 + 4 * q^47 + 32 * q^49 - 16 * q^50 + 24 * q^51 + 16 * q^52 - 4 * q^53 + 24 * q^55 + 12 * q^56 + 8 * q^57 + 12 * q^58 + 24 * q^59 + 60 * q^61 + 32 * q^62 - 4 * q^63 + 44 * q^65 - 12 * q^67 - 8 * q^69 - 24 * q^70 - 28 * q^71 + 60 * q^73 - 40 * q^74 - 72 * q^75 + 4 * q^76 - 12 * q^77 + 4 * q^78 - 20 * q^81 - 24 * q^82 + 60 * q^83 - 8 * q^84 - 4 * q^85 - 20 * q^86 - 36 * q^89 - 16 * q^92 - 24 * q^93 - 48 * q^97 - 88 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$		−	1.00000i		−	0.500000i
$5$	3.01304	−	0.807342i	1.34747	−	0.361054i	0.488272	−	0.872692i	$-0.337627\pi$
$5$	3.01304	−	0.807342i	1.34747	−	0.361054i	0.859202	+	0.511637i	$0.170961\pi$
$6$	0.965926	−	0.258819i	0.394338	−	0.105662i
$7$	2.56888	+	0.633142i	0.970944	+	0.239305i
$7$	2.56888	+	0.633142i	0.970944	+	0.239305i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−1.55967	+	2.70142i	−0.493210	+	0.854264i
$11$	−1.47840	+	0.396136i	−0.445754	+	0.119439i	−0.474712	−	0.880141i	$-0.657448\pi$
$11$	−1.47840	+	0.396136i	−0.445754	+	0.119439i	0.0289580	+	0.999581i	$0.490781\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	−0.598039	+	3.55561i	−0.165866	+	0.986148i
$13$	−0.598039	+	3.55561i	−0.165866	+	0.986148i
$14$	−2.26417	+	1.36877i	−0.605125	+	0.365820i
$15$	−3.01304	−	0.807342i	−0.777964	−	0.208455i
$16$	−1.00000			−0.250000
$17$	3.46440			0.840241			0.420120	−	0.907468i	$-0.361988\pi$
$17$	3.46440			0.840241			0.420120	+	0.907468i	$0.361988\pi$
$18$	−0.965926	−	0.258819i	−0.227671	−	0.0610042i
$19$	1.28965	−	4.81303i	0.295866	−	1.10419i	−0.644662	−	0.764468i	$-0.723002\pi$
$19$	1.28965	−	4.81303i	0.295866	−	1.10419i	0.940527	−	0.339718i	$-0.110332\pi$
$20$	−0.807342	−	3.01304i	−0.180527	−	0.673737i
$21$	−1.90814	−	1.83276i	−0.416391	−	0.399940i
$22$	0.765275	−	1.32550i	0.163157	−	0.282597i
$23$		−	7.42537i		−	1.54830i	−0.633004	−	0.774148i	$-0.718179\pi$
$23$		−	7.42537i		−	1.54830i	0.633004	−	0.774148i	$-0.281821\pi$
$24$	−0.258819	−	0.965926i	−0.0528312	−	0.197169i
$25$	4.09650	−	2.36511i	0.819299	−	0.473023i
$26$	−2.09132	−	2.93707i	−0.410141	−	0.576007i
$27$		−	1.00000i		−	0.192450i
$28$	0.633142	−	2.56888i	0.119653	−	0.485472i
$29$	1.30096	+	2.25333i	0.241582	+	0.418432i	0.961165	−	0.275974i	$-0.0890004\pi$
$29$	1.30096	+	2.25333i	0.241582	+	0.418432i	−0.719583	+	0.694406i	$0.755667\pi$
$30$	2.70142	−	1.55967i	0.493210	−	0.284755i
$31$	−2.72003	+	10.1513i	−0.488531	+	1.82322i	0.0750732	+	0.997178i	$0.476081\pi$
$31$	−2.72003	+	10.1513i	−0.488531	+	1.82322i	−0.563604	+	0.826045i	$0.690586\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	1.47840	+	0.396136i	0.257356	+	0.0689584i
$34$	−2.44970	+	2.44970i	−0.420120	+	0.420120i
$35$	8.25130	−	0.166280i	1.39472	−	0.0281065i
$36$	0.866025	−	0.500000i	0.144338	−	0.0833333i
$37$	3.34550	+	3.34550i	0.549997	+	0.549997i	0.926440	−	0.376442i	$-0.122853\pi$
$37$	3.34550	+	3.34550i	0.549997	+	0.549997i	−0.376442	+	0.926440i	$0.622853\pi$
$38$	2.49141	+	4.31525i	0.404160	+	0.700026i
$39$	2.29572	−	2.78023i	0.367610	−	0.445193i
$40$	2.70142	+	1.55967i	0.427132	+	0.246605i
$41$	−0.819786	+	3.05948i	−0.128029	+	0.477811i	−0.999930	−	0.0118723i	$-0.996221\pi$
$41$	−0.819786	+	3.05948i	−0.128029	+	0.477811i	0.871900	+	0.489683i	$0.162888\pi$
$42$	2.64521	−	0.0533064i	0.408165	−	0.00822536i
$43$	6.51981	+	3.76421i	0.994261	+	0.574037i	0.906545	−	0.422109i	$-0.138710\pi$
$43$	6.51981	+	3.76421i	0.994261	+	0.574037i	0.0877159	+	0.996146i	$0.472043\pi$
$44$	0.396136	+	1.47840i	0.0597197	+	0.222877i
$45$	2.20570	+	2.20570i	0.328806	+	0.328806i
$46$	5.25053	+	5.25053i	0.774148	+	0.774148i
$47$	−2.52616	−	9.42774i	−0.368478	−	1.37518i	−0.862645	−	0.505810i	$-0.831194\pi$
$47$	−2.52616	−	9.42774i	−0.368478	−	1.37518i	0.494167	−	0.869367i	$-0.335473\pi$
$48$	0.866025	+	0.500000i	0.125000	+	0.0721688i
$49$	6.19826	+	3.25293i	0.885466	+	0.464704i
$50$	−1.22427	+	4.56905i	−0.173138	+	0.646161i
$51$	−3.00026	−	1.73220i	−0.420120	−	0.242557i
$52$	3.55561	+	0.598039i	0.493074	+	0.0829330i
$53$	−3.34211	−	5.78870i	−0.459074	−	0.795140i	0.539838	−	0.841769i	$-0.318485\pi$
$53$	−3.34211	−	5.78870i	−0.459074	−	0.795140i	−0.998912	+	0.0466291i	$0.985152\pi$
$54$	0.707107	+	0.707107i	0.0962250	+	0.0962250i
$55$	−4.13466	+	2.38715i	−0.557517	+	0.321883i
$56$	1.36877	+	2.26417i	0.182910	+	0.302562i
$57$	−3.52339	+	3.52339i	−0.466684	+	0.466684i
$58$	−2.51326	−	0.673426i	−0.330007	−	0.0884252i
$59$	6.02046	−	6.02046i	0.783797	−	0.783797i	−0.196672	−	0.980469i	$-0.563013\pi$
$59$	6.02046	−	6.02046i	0.783797	−	0.783797i	0.980469	+	0.196672i	$0.0630134\pi$
$60$	−0.807342	+	3.01304i	−0.104227	+	0.388982i
$61$	6.60836	−	3.81534i	0.846113	−	0.488504i	−0.0132242	−	0.999913i	$-0.504210\pi$
$61$	6.60836	−	3.81534i	0.846113	−	0.488504i	0.859338	+	0.511409i	$0.170876\pi$
$62$	−5.25469	−	9.10138i	−0.667346	−	1.15588i
$63$	0.736122	+	2.54128i	0.0927426	+	0.320172i
$64$			1.00000i			0.125000i
$65$	1.06868	+	11.1960i	0.132553	+	1.38870i
$66$	−1.32550	+	0.765275i	−0.163157	+	0.0941989i
$67$	0.779022	+	2.90735i	0.0951727	+	0.355189i	0.997046	−	0.0768122i	$-0.0244742\pi$
$67$	0.779022	+	2.90735i	0.0951727	+	0.355189i	−0.901873	+	0.432002i	$0.857808\pi$
$68$		−	3.46440i		−	0.420120i
$69$	−3.71268	+	6.43056i	−0.446955	+	0.774148i
$70$	−5.71697	+	5.95213i	−0.683309	+	0.711415i
$71$	0.689184	+	2.57207i	0.0817911	+	0.305248i	0.994687	−	0.102944i	$-0.0328261\pi$
$71$	0.689184	+	2.57207i	0.0817911	+	0.305248i	−0.912896	+	0.408192i	$0.866159\pi$
$72$	−0.258819	+	0.965926i	−0.0305021	+	0.113835i
$73$	−6.59087	−	1.76602i	−0.771403	−	0.206697i	−0.148412	−	0.988926i	$-0.547416\pi$
$73$	−6.59087	−	1.76602i	−0.771403	−	0.206697i	−0.622991	+	0.782229i	$0.714083\pi$
$74$	−4.73126			−0.549997
$75$	−4.73023			−0.546199
$76$	−4.81303	−	1.28965i	−0.552093	−	0.147933i
$77$	−4.04863	+	0.0815882i	−0.461385	+	0.00929784i
$78$	0.342598	+	3.58924i	0.0387916	+	0.406401i
$79$	7.33360	−	12.7022i	0.825095	−	1.42911i	−0.0767519	−	0.997050i	$-0.524455\pi$
$79$	7.33360	−	12.7022i	0.825095	−	1.42911i	0.901847	−	0.432056i	$-0.142212\pi$
$80$	−3.01304	+	0.807342i	−0.336868	+	0.0902636i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−1.58370	−	2.74306i	−0.174891	−	0.302920i
$83$	−5.39273	−	5.39273i	−0.591929	−	0.591929i	0.346223	−	0.938152i	$-0.387464\pi$
$83$	−5.39273	−	5.39273i	−0.591929	−	0.591929i	−0.938152	+	0.346223i	$0.887464\pi$
$84$	−1.83276	+	1.90814i	−0.199970	+	0.208195i
$85$	10.4384	−	2.79696i	1.13220	−	0.303373i
$86$	−7.27190	+	1.94850i	−0.784149	+	0.210112i
$87$		−	2.60192i		−	0.278955i
$88$	−1.32550	−	0.765275i	−0.141298	−	0.0815786i
$89$	−5.62087	+	5.62087i	−0.595811	+	0.595811i	−0.939195	−	0.343384i	$-0.888427\pi$
$89$	−5.62087	+	5.62087i	−0.595811	+	0.595811i	0.343384	+	0.939195i	$0.388427\pi$
$90$	−3.11933			−0.328806
$91$	−3.78749	+	8.75528i	−0.397037	+	0.917803i
$92$	−7.42537			−0.774148
$93$	7.43125	−	7.43125i	0.770585	−	0.770585i
$94$	8.45268	+	4.88016i	0.871828	+	0.503350i
$95$		−	15.5431i		−	1.59468i
$96$	−0.965926	+	0.258819i	−0.0985844	+	0.0264156i
$97$	−4.27487	+	1.14545i	−0.434048	+	0.116303i	−0.469226	−	0.883078i	$-0.655467\pi$
$97$	−4.27487	+	1.14545i	−0.434048	+	0.116303i	0.0351779	+	0.999381i	$0.488800\pi$
$98$	−6.68300	+	2.08267i	−0.675085	+	0.210381i
$99$	−1.08226	−	1.08226i	−0.108771	−	0.108771i
$100$	−2.36511	−	4.09650i	−0.236511	−	0.409650i
$101$	4.22380	−	7.31584i	0.420284	−	0.727954i	−0.575683	−	0.817673i	$-0.695264\pi$
$101$	4.22380	−	7.31584i	0.420284	−	0.727954i	0.995967	+	0.0897194i	$0.0285970\pi$
$102$	3.34635	−	0.896653i	0.331339	−	0.0887819i
$103$	−7.73745	+	13.4017i	−0.762394	+	1.32051i	0.179219	+	0.983809i	$0.442643\pi$
$103$	−7.73745	+	13.4017i	−0.762394	+	1.32051i	−0.941613	+	0.336696i	$0.890690\pi$
$104$	−2.93707	+	2.09132i	−0.288004	+	0.205071i
$105$	−7.22897	−	3.98165i	−0.705476	−	0.388569i
$106$	6.45646	+	1.73000i	0.627107	+	0.168033i
$107$	−19.7154			−1.90596			−0.952978	−	0.303041i	$-0.901998\pi$
$107$	−19.7154			−1.90596			−0.952978	+	0.303041i	$0.901998\pi$
$108$	−1.00000			−0.0962250
$109$	10.3670	+	2.77782i	0.992976	+	0.266067i	0.718500	−	0.695527i	$-0.244829\pi$
$109$	10.3670	+	2.77782i	0.992976	+	0.266067i	0.274476	+	0.961594i	$0.411496\pi$
$110$	1.23568	−	4.61161i	0.117817	−	0.439700i
$111$	−1.22454	−	4.57004i	−0.116228	−	0.433769i
$112$	−2.56888	−	0.633142i	−0.242736	−	0.0598263i
$113$	−0.926673	+	1.60505i	−0.0871741	+	0.150990i	−0.906316	−	0.422602i	$-0.861117\pi$
$113$	−0.926673	+	1.60505i	−0.0871741	+	0.150990i	0.819141	+	0.573592i	$0.194450\pi$
$114$		−	4.98282i		−	0.466684i
$115$	−5.99481	−	22.3729i	−0.559019	−	2.08629i
$116$	2.25333	−	1.30096i	0.209216	−	0.120791i
$117$	−3.37827	+	1.25989i	−0.312321	+	0.116477i
$118$			8.51422i			0.783797i
$119$	8.89962	+	2.19346i	0.815827	+	0.201074i
$120$	−1.55967	−	2.70142i	−0.142377	−	0.246605i
$121$	−7.49754	+	4.32871i	−0.681595	+	0.393519i
$122$	−1.97496	+	7.37066i	−0.178805	+	0.667309i
$123$	2.23970	−	2.23970i	0.201947	−	0.201947i
$124$	10.1513	+	2.72003i	0.911611	+	0.244266i
$125$	−0.595042	+	0.595042i	−0.0532222	+	0.0532222i
$126$	−2.31748	−	1.27644i	−0.206457	−	0.113715i
$127$	−9.01483	+	5.20472i	−0.799937	+	0.461844i	−0.843449	−	0.537209i	$-0.819479\pi$
$127$	−9.01483	+	5.20472i	−0.799937	+	0.461844i	0.0435122	+	0.999053i	$0.486145\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	−3.76421	−	6.51981i	−0.331420	−	0.574037i
$130$	−8.67245	−	7.16111i	−0.760624	−	0.628071i
$131$	0.294912	+	0.170268i	0.0257666	+	0.0148763i	0.512828	−	0.858491i	$-0.328598\pi$
$131$	0.294912	+	0.170268i	0.0257666	+	0.0148763i	−0.487061	+	0.873368i	$0.661931\pi$
$132$	0.396136	−	1.47840i	0.0344792	−	0.128678i
$133$	6.36028	−	11.5476i	0.551506	−	1.00130i
$134$	−2.60666	−	1.50496i	−0.225181	−	0.130008i
$135$	−0.807342	−	3.01304i	−0.0694850	−	0.259321i
$136$	2.44970	+	2.44970i	0.210060	+	0.210060i
$137$	11.7225	+	11.7225i	1.00152	+	1.00152i	0.999999	+	0.00152351i	$0.000484947\pi$
$137$	11.7225	+	11.7225i	1.00152	+	1.00152i	0.00152351	+	0.999999i	$0.499515\pi$
$138$	−1.92183	−	7.17236i	−0.163597	−	0.610551i
$139$	−17.9972	−	10.3907i	−1.52650	−	0.881327i	−0.999505	−	0.0314614i	$-0.989984\pi$
$139$	−17.9972	−	10.3907i	−1.52650	−	0.881327i	−0.526999	−	0.849866i	$-0.676683\pi$
$140$	−0.166280	−	8.25130i	−0.0140533	−	0.697362i
$141$	−2.52616	+	9.42774i	−0.212741	+	0.793959i
$142$	−2.30605	−	1.33140i	−0.193520	−	0.111729i
$143$	−0.524364	−	5.49351i	−0.0438495	−	0.459390i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	5.73905	+	5.73905i	0.476602	+	0.476602i
$146$	5.90921	−	3.41168i	0.489050	−	0.282353i
$147$	−3.74139	−	5.91625i	−0.308585	−	0.487964i
$148$	3.34550	−	3.34550i	0.274999	−	0.274999i
$149$	9.43017	+	2.52681i	0.772550	+	0.207004i	0.623498	−	0.781825i	$-0.285711\pi$
$149$	9.43017	+	2.52681i	0.772550	+	0.207004i	0.149052	+	0.988829i	$0.452378\pi$
$150$	3.34477	−	3.34477i	0.273100	−	0.273100i
$151$	−2.22644	+	8.30920i	−0.181185	+	0.676193i	0.814230	+	0.580543i	$0.197160\pi$
$151$	−2.22644	+	8.30920i	−0.181185	+	0.676193i	−0.995415	+	0.0956501i	$0.969507\pi$
$152$	4.31525	−	2.49141i	0.350013	−	0.202080i
$153$	1.73220	+	3.00026i	0.140040	+	0.242557i
$154$	2.80513	−	2.92051i	0.226043	−	0.235341i
$155$			32.7822i			2.63313i
$156$	−2.78023	−	2.29572i	−0.222596	−	0.183805i
$157$	−9.91398	+	5.72384i	−0.791222	+	0.456812i	−0.840392	−	0.541978i	$-0.817675\pi$
$157$	−9.91398	+	5.72384i	−0.791222	+	0.456812i	0.0491707	+	0.998790i	$0.484342\pi$
$158$	3.79615	+	14.1674i	0.302006	+	1.12710i
$159$			6.68422i			0.530093i
$160$	1.55967	−	2.70142i	0.123302	−	0.213566i
$161$	4.70131	−	19.0749i	0.370515	−	1.50331i
$162$	−0.258819	−	0.965926i	−0.0203347	−	0.0758903i
$163$	1.20844	−	4.50994i	0.0946519	−	0.353246i	−0.902315	−	0.431078i	$-0.858133\pi$
$163$	1.20844	−	4.50994i	0.0946519	−	0.353246i	0.996966	+	0.0778325i	$0.0247999\pi$
$164$	3.05948	+	0.819786i	0.238905	+	0.0640145i
$165$	4.77429			0.371678
$166$	7.62647			0.591929
$167$	−13.5903	−	3.64150i	−1.05165	−	0.281788i	−0.308715	−	0.951155i	$-0.599899\pi$
$167$	−13.5903	−	3.64150i	−1.05165	−	0.281788i	−0.742932	+	0.669367i	$0.766566\pi$
$168$	−0.0533064	−	2.64521i	−0.00411268	−	0.204083i
$169$	−12.2847	−	4.25278i	−0.944977	−	0.327137i
$170$	−5.40331	+	9.35880i	−0.414415	+	0.717787i
$171$	4.81303	−	1.28965i	0.368062	−	0.0986219i
$172$	3.76421	−	6.51981i	0.287018	−	0.497131i
$173$	−3.47694	−	6.02223i	−0.264347	−	0.457862i	0.703046	−	0.711145i	$-0.251823\pi$
$173$	−3.47694	−	6.02223i	−0.264347	−	0.457862i	−0.967392	+	0.253283i	$0.918490\pi$
$174$	1.83983	+	1.83983i	0.139477	+	0.139477i
$175$	12.0208	−	3.48202i	0.908691	−	0.263216i
$176$	1.47840	−	0.396136i	0.111438	−	0.0298598i
$177$	−8.22410	+	2.20364i	−0.618162	+	0.165636i
$178$		−	7.94911i		−	0.595811i
$179$	−3.56278	−	2.05697i	−0.266294	−	0.153745i	0.360908	−	0.932601i	$-0.382467\pi$
$179$	−3.56278	−	2.05697i	−0.266294	−	0.153745i	−0.627202	+	0.778856i	$0.715800\pi$
$180$	2.20570	−	2.20570i	0.164403	−	0.164403i
$181$	−4.55457			−0.338538			−0.169269	−	0.985570i	$-0.554141\pi$
$181$	−4.55457			−0.338538			−0.169269	+	0.985570i	$0.554141\pi$
$182$	−3.51276	−	8.86908i	−0.260383	−	0.657420i
$183$	−7.63067			−0.564076
$184$	5.25053	−	5.25053i	0.387074	−	0.387074i
$185$	12.7811	+	7.37918i	0.939686	+	0.542528i
$186$			10.5094i			0.770585i
$187$	−5.12177	+	1.37237i	−0.374541	+	0.100358i
$188$	−9.42774	+	2.52616i	−0.687589	+	0.184239i
$189$	0.633142	−	2.56888i	0.0460543	−	0.186858i
$190$	10.9906	+	10.9906i	0.797342	+	0.797342i
$191$	6.06829	+	10.5106i	0.439086	+	0.760519i	0.997619	−	0.0689631i	$-0.0219691\pi$
$191$	6.06829	+	10.5106i	0.439086	+	0.760519i	−0.558533	+	0.829482i	$0.688636\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	−9.81910	+	2.63102i	−0.706794	+	0.189385i	−0.594272	−	0.804264i	$-0.702560\pi$
$193$	−9.81910	+	2.63102i	−0.706794	+	0.189385i	−0.112522	+	0.993649i	$0.535893\pi$
$194$	2.21284	−	3.83275i	0.158872	−	0.275175i
$195$	4.67251	−	10.2304i	0.334605	−	0.732612i
$196$	3.25293	−	6.19826i	0.232352	−	0.442733i
$197$	−5.66778	−	1.51868i	−0.403813	−	0.108201i	0.0511952	−	0.998689i	$-0.483697\pi$
$197$	−5.66778	−	1.51868i	−0.403813	−	0.108201i	−0.455008	+	0.890487i	$0.650364\pi$
$198$	1.53055			0.108771
$199$	−11.9801			−0.849245			−0.424623	−	0.905370i	$-0.639593\pi$
$199$	−11.9801			−0.849245			−0.424623	+	0.905370i	$0.639593\pi$
$200$	4.56905	+	1.22427i	0.323080	+	0.0865691i
$201$	0.779022	−	2.90735i	0.0549480	−	0.205069i
$202$	2.18640	+	8.15976i	0.153835	+	0.574119i
$203$	1.91533	+	6.61221i	0.134430	+	0.464087i
$204$	−1.73220	+	3.00026i	−0.121278	+	0.210060i
$205$			9.88020i			0.690063i
$206$	−4.00520	−	14.9476i	−0.279056	−	1.04145i
$207$	6.43056	−	3.71268i	0.446955	−	0.258049i
$208$	0.598039	−	3.55561i	0.0414665	−	0.246537i
$209$			7.62646i			0.527533i
$210$	7.92711	−	2.29621i	0.547022	−	0.158453i
$211$	1.72829	+	2.99349i	0.118981	+	0.206080i	0.919364	−	0.393408i	$-0.128704\pi$
$211$	1.72829	+	2.99349i	0.118981	+	0.206080i	−0.800383	+	0.599488i	$0.795371\pi$
$212$	−5.78870	+	3.34211i	−0.397570	+	0.229537i
$213$	0.689184	−	2.57207i	0.0472221	−	0.176235i
$214$	13.9409	−	13.9409i	0.952978	−	0.952978i
$215$	22.6835	+	6.07802i	1.54700	+	0.414517i
$216$	0.707107	−	0.707107i	0.0481125	−	0.0481125i
$217$	−13.4146	+	24.3552i	−0.910643	+	1.65334i
$218$	−9.29477	+	5.36634i	−0.629521	+	0.363454i
$219$	4.82485	+	4.82485i	0.326033	+	0.326033i
$220$	2.38715	+	4.13466i	0.160941	+	0.278759i
$221$	−2.07185	+	12.3181i	−0.139367	+	0.828602i
$222$	4.09739	+	2.36563i	0.274999	+	0.158771i
$223$	2.65061	−	9.89222i	0.177498	−	0.662432i	−0.818614	−	0.574343i	$-0.805257\pi$
$223$	2.65061	−	9.89222i	0.177498	−	0.662432i	0.996113	−	0.0880887i	$-0.0280759\pi$
$224$	2.26417	−	1.36877i	0.151281	−	0.0914549i
$225$	4.09650	+	2.36511i	0.273100	+	0.157674i
$226$	−0.479681	−	1.79020i	−0.0319079	−	0.119082i
$227$	−4.59359	−	4.59359i	−0.304887	−	0.304887i	0.538035	−	0.842922i	$-0.319167\pi$
$227$	−4.59359	−	4.59359i	−0.304887	−	0.304887i	−0.842922	+	0.538035i	$0.819167\pi$
$228$	3.52339	+	3.52339i	0.233342	+	0.233342i
$229$	−6.19109	−	23.1055i	−0.409119	−	1.52685i	−0.796331	−	0.604862i	$-0.793228\pi$
$229$	−6.19109	−	23.1055i	−0.409119	−	1.52685i	0.387212	−	0.921991i	$-0.373438\pi$
$230$	20.0590	+	11.5811i	1.32265	+	0.763635i
$231$	3.54701	+	1.95366i	0.233376	+	0.128541i
$232$	−0.673426	+	2.51326i	−0.0442126	+	0.165004i
$233$	22.0693	+	12.7417i	1.44581	+	0.834737i	0.998228	−	0.0595070i	$-0.0189529\pi$
$233$	22.0693	+	12.7417i	1.44581	+	0.834737i	0.447579	+	0.894244i	$0.352286\pi$
$234$	1.49792	−	3.27967i	0.0979221	−	0.214399i
$235$	−15.2228	−	26.3667i	−0.993028	−	1.71997i
$236$	−6.02046	−	6.02046i	−0.391899	−	0.391899i
$237$	−12.7022	+	7.33360i	−0.825095	+	0.476369i
$238$	−7.84399	+	4.74198i	−0.508450	+	0.307377i
$239$	−8.18763	+	8.18763i	−0.529614	+	0.529614i	−0.920457	−	0.390843i	$-0.872183\pi$
$239$	−8.18763	+	8.18763i	−0.529614	+	0.529614i	0.390843	+	0.920457i	$0.372183\pi$
$240$	3.01304	+	0.807342i	0.194491	+	0.0521137i
$241$	4.68689	−	4.68689i	0.301909	−	0.301909i	−0.539851	−	0.841760i	$-0.681520\pi$
$241$	4.68689	−	4.68689i	0.301909	−	0.301909i	0.841760	+	0.539851i	$0.181520\pi$
$242$	2.24070	−	8.36242i	0.144038	−	0.537557i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	−3.81534	−	6.60836i	−0.244252	−	0.423057i
$245$	21.3019	+	4.79709i	1.36093	+	0.306475i
$246$			3.16741i			0.201947i
$247$	16.3420	+	7.46387i	1.03982	+	0.474914i
$248$	−9.10138	+	5.25469i	−0.577939	+	0.333673i
$249$	1.97387	+	7.36660i	0.125089	+	0.466839i
$250$		−	0.841516i		−	0.0532222i
$251$	−11.2754	+	19.5296i	−0.711697	+	1.23270i	0.252523	+	0.967591i	$0.418740\pi$
$251$	−11.2754	+	19.5296i	−0.711697	+	1.23270i	−0.964220	+	0.265105i	$0.914594\pi$
$252$	2.54128	−	0.736122i	0.160086	−	0.0463713i
$253$	2.94145	+	10.9777i	0.184928	+	0.690159i
$254$	2.69416	−	10.0547i	0.169047	−	0.630890i
$255$	−10.4384	−	2.79696i	−0.653677	−	0.175152i
$256$	1.00000			0.0625000
$257$	−19.9240			−1.24283			−0.621414	−	0.783482i	$-0.713441\pi$
$257$	−19.9240			−1.24283			−0.621414	+	0.783482i	$0.713441\pi$
$258$	7.27190	+	1.94850i	0.452729	+	0.121308i
$259$	6.47601	+	10.7124i	0.402400	+	0.665634i
$260$	11.1960	−	1.06868i	0.694348	−	0.0662765i
$261$	−1.30096	+	2.25333i	−0.0805274	+	0.139477i
$262$	−0.328932	+	0.0881370i	−0.0203215	+	0.00544512i
$263$	5.08726	−	8.81139i	0.313694	−	0.543333i	−0.665465	−	0.746429i	$-0.731767\pi$
$263$	5.08726	−	8.81139i	0.313694	−	0.543333i	0.979159	+	0.203095i	$0.0651002\pi$
$264$	0.765275	+	1.32550i	0.0470994	+	0.0815786i
$265$	−14.7434	−	14.7434i	−0.905679	−	0.905679i
$266$	3.66796	+	12.6628i	0.224897	+	0.776404i
$267$	7.67825	−	2.05738i	0.469901	−	0.125910i
$268$	2.90735	−	0.779022i	0.177595	−	0.0475864i
$269$		−	29.4833i		−	1.79763i	−0.438328	−	0.898815i	$-0.644429\pi$
$269$		−	29.4833i		−	1.79763i	0.438328	−	0.898815i	$-0.355571\pi$
$270$	2.70142	+	1.55967i	0.164403	+	0.0949182i
$271$	1.90329	−	1.90329i	0.115617	−	0.115617i	−0.646931	−	0.762548i	$-0.723948\pi$
$271$	1.90329	−	1.90329i	0.115617	−	0.115617i	0.762548	+	0.646931i	$0.223948\pi$
$272$	−3.46440			−0.210060
$273$	7.65770	−	5.68855i	0.463465	−	0.344287i
$274$	−16.5781			−1.00152
$275$	−5.11935	+	5.11935i	−0.308708	+	0.308708i
$276$	6.43056	+	3.71268i	0.387074	+	0.223477i
$277$			6.75444i			0.405835i	0.979196	+	0.202918i	$0.0650423\pi$
$277$			6.75444i			0.405835i	−0.979196	+	0.202918i	$0.934958\pi$
$278$	20.0733	−	5.37862i	1.20392	−	0.322588i
$279$	−10.1513	+	2.72003i	−0.607741	+	0.162844i
$280$	5.95213	+	5.71697i	0.355708	+	0.341654i
$281$	0.0630402	+	0.0630402i	0.00376067	+	0.00376067i	0.708985	−	0.705224i	$-0.249154\pi$
$281$	0.0630402	+	0.0630402i	0.00376067	+	0.00376067i	−0.705224	+	0.708985i	$0.749154\pi$
$282$	−4.88016	−	8.45268i	−0.290609	−	0.503350i
$283$	−14.3396	+	24.8368i	−0.852398	+	1.47640i	0.0266392	+	0.999645i	$0.491519\pi$
$283$	−14.3396	+	24.8368i	−0.852398	+	1.47640i	−0.879038	+	0.476752i	$0.841814\pi$
$284$	2.57207	−	0.689184i	0.152624	−	0.0408955i
$285$	−7.77153	+	13.4607i	−0.460346	+	0.797342i
$286$	4.25528	+	3.51372i	0.251620	+	0.207770i
$287$	−4.04302	+	7.34039i	−0.238652	+	0.433290i
$288$	0.965926	+	0.258819i	0.0569177	+	0.0152511i
$289$	−4.99792			−0.293995
$290$	−8.11625			−0.476602
$291$	4.27487	+	1.14545i	0.250598	+	0.0671474i
$292$	−1.76602	+	6.59087i	−0.103348	+	0.385701i
$293$	−3.19461	−	11.9224i	−0.186631	−	0.696516i	−0.994276	−	0.106847i	$-0.965925\pi$
$293$	−3.19461	−	11.9224i	−0.186631	−	0.696516i	0.807645	−	0.589670i	$-0.200742\pi$
$294$	6.82898	+	1.53786i	0.398274	+	0.0896897i
$295$	13.2793	−	23.0005i	0.773153	−	1.33914i
$296$			4.73126i			0.274999i
$297$	0.396136	+	1.47840i	0.0229861	+	0.0857854i
$298$	−8.45486	+	4.88142i	−0.489777	+	0.282773i
$299$	26.4017	+	4.44066i	1.52685	+	0.256810i
$300$			4.73023i			0.273100i
$301$	14.3653	+	13.7978i	0.828002	+	0.795290i
$302$	−4.30116	−	7.44982i	−0.247504	−	0.428689i
$303$	−7.31584	+	4.22380i	−0.420284	+	0.242651i
$304$	−1.28965	+	4.81303i	−0.0739664	+	0.276046i
$305$	16.8310	−	16.8310i	0.963739	−	0.963739i
$306$	−3.34635	−	0.896653i	−0.191298	−	0.0512582i
$307$	13.8751	−	13.8751i	0.791896	−	0.791896i	−0.189906	−	0.981802i	$-0.560818\pi$
$307$	13.8751	−	13.8751i	0.791896	−	0.791896i	0.981802	+	0.189906i	$0.0608184\pi$
$308$	0.0815882	+	4.04863i	0.00464892	+	0.230692i
$309$	13.4017	−	7.73745i	0.762394	−	0.440168i
$310$	−23.1805	−	23.1805i	−1.31657	−	1.31657i
$311$	13.1243	+	22.7319i	0.744209	+	1.28901i	0.950564	+	0.310530i	$0.100507\pi$
$311$	13.1243	+	22.7319i	0.744209	+	1.28901i	−0.206355	+	0.978477i	$0.566160\pi$
$312$	3.58924	−	0.342598i	0.203201	−	0.0193958i
$313$	11.1431	+	6.43346i	0.629845	+	0.363641i	0.780692	−	0.624916i	$-0.214867\pi$
$313$	11.1431	+	6.43346i	0.629845	+	0.363641i	−0.150847	+	0.988557i	$0.548200\pi$
$314$	2.96288	−	11.0576i	0.167205	−	0.624017i
$315$	4.26965	+	7.06269i	0.240568	+	0.397938i
$316$	−12.7022	−	7.33360i	−0.714553	−	0.412547i
$317$	0.559370	+	2.08760i	0.0314173	+	0.117251i	0.979854	−	0.199716i	$-0.0640021\pi$
$317$	0.559370	+	2.08760i	0.0314173	+	0.117251i	−0.948436	+	0.316967i	$0.897335\pi$
$318$	−4.72646	−	4.72646i	−0.265047	−	0.265047i
$319$	−2.81596	−	2.81596i	−0.157663	−	0.157663i
$320$	0.807342	+	3.01304i	0.0451318	+	0.168434i
$321$	17.0740	+	9.85768i	0.952978	+	0.550202i
$322$	10.1636	+	16.8123i	0.566397	+	0.936912i
$323$	4.46786	−	16.6743i	0.248598	−	0.927782i
$324$	0.866025	+	0.500000i	0.0481125	+	0.0277778i
$325$	5.95955	+	15.9800i	0.330576	+	0.886409i
$326$	2.33452	+	4.04350i	0.129297	+	0.223949i
$327$	−7.58915	−	7.58915i	−0.419681	−	0.419681i
$328$	−2.74306	+	1.58370i	−0.151460	+	0.0874455i
$329$	−0.520288	−	25.8181i	−0.0286844	−	1.42340i
$330$	−3.37594	+	3.37594i	−0.185839	+	0.185839i
$331$	17.8827	+	4.79165i	0.982921	+	0.263373i	0.714274	−	0.699866i	$-0.246757\pi$
$331$	17.8827	+	4.79165i	0.982921	+	0.263373i	0.268647	+	0.963239i	$0.413424\pi$
$332$	−5.39273	+	5.39273i	−0.295964	+	0.295964i
$333$	−1.22454	+	4.57004i	−0.0671044	+	0.250437i
$334$	12.1847	−	7.03485i	0.666718	−	0.384930i
$335$	4.69445	+	8.13103i	0.256485	+	0.444246i
$336$	1.90814	+	1.83276i	0.104098	+	0.0999850i
$337$		−	7.41532i		−	0.403938i	−0.979392	−	0.201969i	$-0.935266\pi$
$337$		−	7.41532i		−	0.403938i	0.979392	−	0.201969i	$-0.0647340\pi$
$338$	11.6938	−	5.67942i	0.636057	−	0.308920i
$339$	1.60505	−	0.926673i	0.0871741	−	0.0503300i
$340$	−2.79696	−	10.4384i	−0.151686	−	0.566101i
$341$		−	16.0851i		−	0.871059i
$342$	−2.49141	+	4.31525i	−0.134720	+	0.233342i
$343$	13.8630	+	12.2808i	0.748532	+	0.663098i
$344$	1.94850	+	7.27190i	0.105056	+	0.392075i
$345$	−5.99481	+	22.3729i	−0.322750	+	1.20452i
$346$	6.71693	+	1.79979i	0.361104	+	0.0967576i
$347$	−8.58941			−0.461104			−0.230552	−	0.973060i	$-0.574053\pi$
$347$	−8.58941			−0.461104			−0.230552	+	0.973060i	$0.574053\pi$
$348$	−2.60192			−0.139477
$349$	24.1386	+	6.46792i	1.29211	+	0.346220i	0.838462	−	0.544961i	$-0.183455\pi$
$349$	24.1386	+	6.46792i	1.29211	+	0.346220i	0.453649	+	0.891181i	$0.350122\pi$
$350$	−6.03786	+	10.9622i	−0.322737	+	0.585953i
$351$	3.55561	+	0.598039i	0.189784	+	0.0319209i
$352$	−0.765275	+	1.32550i	−0.0407893	+	0.0706492i
$353$	−19.8395	+	5.31599i	−1.05595	+	0.282941i	−0.744709	−	0.667389i	$-0.767412\pi$
$353$	−19.8395	+	5.31599i	−1.05595	+	0.282941i	−0.311243	+	0.950330i	$0.600745\pi$
$354$	4.25711	−	7.37353i	0.226263	−	0.391899i
$355$	4.15308	+	7.19334i	0.220423	+	0.381783i
$356$	5.62087	+	5.62087i	0.297905	+	0.297905i
$357$	−6.61057	−	6.34940i	−0.349869	−	0.336046i
$358$	3.97376	−	1.06477i	0.210020	−	0.0562746i
$359$	0.954577	−	0.255778i	0.0503807	−	0.0134995i	−0.233541	−	0.972347i	$-0.575031\pi$
$359$	0.954577	−	0.255778i	0.0503807	−	0.0134995i	0.283921	+	0.958848i	$0.408365\pi$
$360$			3.11933i			0.164403i
$361$	−5.04763	−	2.91425i	−0.265665	−	0.153382i
$362$	3.22056	−	3.22056i	0.169269	−	0.169269i
$363$	8.65741			0.454396
$364$	8.75528	+	3.78749i	0.458901	+	0.198519i
$365$	−21.2843			−1.11407
$366$	5.39570	−	5.39570i	0.282038	−	0.282038i
$367$	−27.7588	−	16.0266i	−1.44900	−	0.836580i	−0.450578	−	0.892737i	$-0.648782\pi$
$367$	−27.7588	−	16.0266i	−1.44900	−	0.836580i	−0.998422	+	0.0561571i	$0.982115\pi$
$368$			7.42537i			0.387074i
$369$	−3.05948	+	0.819786i	−0.159270	+	0.0426763i
$370$	−14.2555	+	3.81974i	−0.741107	+	0.198579i
$371$	−4.92040	−	16.9865i	−0.255454	−	0.881895i
$372$	−7.43125	−	7.43125i	−0.385292	−	0.385292i
$373$	−17.0271	−	29.4919i	−0.881632	−	1.52703i	−0.849526	−	0.527546i	$-0.823112\pi$
$373$	−17.0271	−	29.4919i	−0.881632	−	1.52703i	−0.0321054	−	0.999484i	$-0.510221\pi$
$374$	2.65122	−	4.59205i	0.137091	−	0.237449i
$375$	0.812842	−	0.217800i	0.0419750	−	0.0112472i
$376$	4.88016	−	8.45268i	0.251675	−	0.435914i
$377$	−8.78998	+	3.27812i	−0.452707	+	0.168832i
$378$	1.36877	+	2.26417i	0.0704020	+	0.116456i
$379$	34.3383	+	9.20093i	1.76384	+	0.472620i	0.987490	−	0.157679i	$-0.0504013\pi$
$379$	34.3383	+	9.20093i	1.76384	+	0.472620i	0.776352	+	0.630300i	$0.217068\pi$
$380$	−15.5431			−0.797342
$381$	10.4094			0.533291
$382$	−11.7230	−	3.14118i	−0.599802	−	0.160717i
$383$	−9.81817	+	36.6419i	−0.501685	+	1.87231i	−0.0128882	+	0.999917i	$0.504103\pi$
$383$	−9.81817	+	36.6419i	−0.501685	+	1.87231i	−0.488797	+	0.872398i	$0.662564\pi$
$384$	0.258819	+	0.965926i	0.0132078	+	0.0492922i
$385$	−12.1328	+	3.51446i	−0.618347	+	0.179114i
$386$	5.08274	−	8.80356i	0.258705	−	0.448090i
$387$			7.52842i			0.382691i
$388$	1.14545	+	4.27487i	0.0581514	+	0.217024i
$389$	−17.3048	+	9.99095i	−0.877390	+	0.506561i	−0.869797	−	0.493410i	$-0.835750\pi$
$389$	−17.3048	+	9.99095i	−0.877390	+	0.506561i	−0.00759279	+	0.999971i	$0.502417\pi$
$390$	3.93001	+	10.5379i	0.199004	+	0.533609i
$391$		−	25.7245i		−	1.30094i
$392$	2.08267	+	6.68300i	0.105191	+	0.337543i
$393$	−0.170268	−	0.294912i	−0.00858886	−	0.0148763i
$394$	5.08159	−	2.93386i	0.256007	−	0.147806i
$395$	11.8415	−	44.1929i	0.595808	−	2.22359i
$396$	−1.08226	+	1.08226i	−0.0543857	+	0.0543857i
$397$	−12.3207	−	3.30131i	−0.618356	−	0.165688i	−0.0639757	−	0.997951i	$-0.520378\pi$
$397$	−12.3207	−	3.30131i	−0.618356	−	0.165688i	−0.554380	+	0.832263i	$0.687045\pi$
$398$	8.47120	−	8.47120i	0.424623	−	0.424623i
$399$	−11.2820	+	6.82034i	−0.564804	+	0.341444i
$400$	−4.09650	+	2.36511i	−0.204825	+	0.118256i
$401$	8.42752	+	8.42752i	0.420850	+	0.420850i	0.885496	−	0.464646i	$-0.153818\pi$
$401$	8.42752	+	8.42752i	0.420850	+	0.420850i	−0.464646	+	0.885496i	$0.653818\pi$
$402$	1.50496	+	2.60666i	0.0750603	+	0.130008i
$403$	−34.4673	−	15.7422i	−1.71694	−	0.784175i
$404$	−7.31584	−	4.22380i	−0.363977	−	0.210142i
$405$	−0.807342	+	3.01304i	−0.0401172	+	0.149719i
$406$	−6.02988	−	3.32120i	−0.299258	−	0.164828i
$407$	−6.27126	−	3.62071i	−0.310855	−	0.179472i
$408$	−0.896653	−	3.34635i	−0.0443909	−	0.165669i
$409$	21.9236	+	21.9236i	1.08405	+	1.08405i	0.996127	+	0.0879228i	$0.0280229\pi$
$409$	21.9236	+	21.9236i	1.08405	+	1.08405i	0.0879228	+	0.996127i	$0.471977\pi$
$410$	−6.98635	−	6.98635i	−0.345031	−	0.345031i
$411$	−4.29074	−	16.0133i	−0.211647	−	0.789876i
$412$	13.4017	+	7.73745i	0.660253	+	0.381197i
$413$	19.2776	−	11.6540i	0.948590	−	0.573457i
$414$	−1.92183	+	7.17236i	−0.0944526	+	0.352502i
$415$	−20.6023	−	11.8947i	−1.01133	−	0.583890i
$416$	2.09132	+	2.93707i	0.102535	+	0.144002i
$417$	10.3907	+	17.9972i	0.508835	+	0.881327i
$418$	−5.39272	−	5.39272i	−0.263767	−	0.263767i
$419$	6.93782	−	4.00555i	0.338935	−	0.195684i	−0.320866	−	0.947125i	$-0.603974\pi$
$419$	6.93782	−	4.00555i	0.338935	−	0.195684i	0.659801	+	0.751441i	$0.270641\pi$
$420$	−3.98165	+	7.22897i	−0.194284	+	0.352738i
$421$	6.84792	−	6.84792i	0.333747	−	0.333747i	−0.520261	−	0.854008i	$-0.674165\pi$
$421$	6.84792	−	6.84792i	0.333747	−	0.333747i	0.854008	+	0.520261i	$0.174165\pi$
$422$	−3.33880	−	0.894630i	−0.162530	−	0.0435499i
$423$	6.90159	−	6.90159i	0.335567	−	0.335567i
$424$	1.73000	−	6.45646i	0.0840164	−	0.313553i
$425$	14.1919	−	8.19370i	0.688408	−	0.397453i
$426$	1.33140	+	2.30605i	0.0645066	+	0.111729i
$427$	19.3917	−	5.61711i	0.938431	−	0.271831i
$428$			19.7154i			0.952978i
$429$	−2.29264	+	5.01970i	−0.110690	+	0.242353i
$430$	−20.3374	+	11.7418i	−0.980758	+	0.566241i
$431$	1.34118	+	5.00536i	0.0646024	+	0.241100i	0.990675	−	0.136246i	$-0.0435037\pi$
$431$	1.34118	+	5.00536i	0.0646024	+	0.241100i	−0.926073	+	0.377345i	$0.876837\pi$
$432$			1.00000i			0.0481125i
$433$	5.71366	−	9.89634i	0.274581	−	0.475588i	−0.695448	−	0.718576i	$-0.744794\pi$
$433$	5.71366	−	9.89634i	0.274581	−	0.475588i	0.970029	+	0.242988i	$0.0781276\pi$
$434$	−7.73618	−	26.7073i	−0.371349	−	1.28199i
$435$	−2.10064	−	7.83969i	−0.100718	−	0.375884i
$436$	2.77782	−	10.3670i	0.133034	−	0.496488i
$437$	−35.7386	−	9.57612i	−1.70961	−	0.458088i
$438$	−6.82337			−0.326033
$439$	−25.9311			−1.23762			−0.618811	−	0.785540i	$-0.712385\pi$
$439$	−25.9311			−1.23762			−0.618811	+	0.785540i	$0.712385\pi$
$440$	−4.61161	−	1.23568i	−0.219850	−	0.0589086i
$441$	0.282014	+	6.99432i	0.0134292	+	0.333063i
$442$	−7.24516	−	10.1752i	−0.344617	−	0.483985i
$443$	18.8762	−	32.6945i	0.896833	−	1.55336i	0.0653141	−	0.997865i	$-0.479195\pi$
$443$	18.8762	−	32.6945i	0.896833	−	1.55336i	0.831519	−	0.555496i	$-0.187472\pi$
$444$	−4.57004	+	1.22454i	−0.216885	+	0.0581141i
$445$	−12.3979	+	21.4739i	−0.587719	+	1.01796i
$446$	5.12059	+	8.86912i	0.242467	+	0.419965i
$447$	−6.90337	−	6.90337i	−0.326518	−	0.326518i
$448$	−0.633142	+	2.56888i	−0.0299131	+	0.121368i
$449$	3.29660	−	0.883320i	0.155576	−	0.0416865i	−0.180190	−	0.983632i	$-0.557671\pi$
$449$	3.29660	−	0.883320i	0.155576	−	0.0416865i	0.335766	+	0.941945i	$0.391005\pi$
$450$	−4.56905	+	1.22427i	−0.215387	+	0.0577128i
$451$		−	4.84788i		−	0.228278i
$452$	1.60505	+	0.926673i	0.0754950	+	0.0435871i
$453$	6.08276	−	6.08276i	0.285793	−	0.285793i
$454$	6.49632			0.304887
$455$	−4.34337	+	29.4378i	−0.203620	+	1.38007i
$456$	−4.98282			−0.233342
$457$	−11.3894	+	11.3894i	−0.532772	+	0.532772i	−0.921396	−	0.388624i	$-0.872950\pi$
$457$	−11.3894	+	11.3894i	−0.532772	+	0.532772i	0.388624	+	0.921396i	$0.372950\pi$
$458$	20.7158	+	11.9603i	0.967986	+	0.558867i
$459$		−	3.46440i		−	0.161704i
$460$	−22.3729	+	5.99481i	−1.04314	+	0.279510i
$461$	−19.9854	+	5.35508i	−0.930814	+	0.249411i	−0.692202	−	0.721704i	$-0.743359\pi$
$461$	−19.9854	+	5.35508i	−0.930814	+	0.249411i	−0.238612	+	0.971115i	$0.576692\pi$
$462$	−3.88956	+	1.12667i	−0.180959	+	0.0524175i
$463$	−12.0105	−	12.0105i	−0.558176	−	0.558176i	0.370612	−	0.928788i	$-0.379148\pi$
$463$	−12.0105	−	12.0105i	−0.558176	−	0.558176i	−0.928788	+	0.370612i	$0.879148\pi$
$464$	−1.30096	−	2.25333i	−0.0603955	−	0.104608i
$465$	16.3911	−	28.3902i	0.760119	−	1.31657i
$466$	−24.6151	+	6.59559i	−1.14027	+	0.305535i
$467$	−1.96024	+	3.39524i	−0.0907092	+	0.157113i	−0.907810	−	0.419382i	$-0.862247\pi$
$467$	−1.96024	+	3.39524i	−0.0907092	+	0.157113i	0.817101	+	0.576495i	$0.195580\pi$
$468$	1.25989	+	3.37827i	0.0582383	+	0.156160i
$469$	0.160448	+	7.96186i	0.00740878	+	0.367644i
$470$	29.4082	+	7.87992i	1.35650	+	0.363473i
$471$	11.4477			0.527481
$472$	8.51422			0.391899
$473$	−11.1300	−	2.98228i	−0.511758	−	0.137125i
$474$	3.79615	−	14.1674i	0.174363	−	0.650732i
$475$	−6.10033	−	22.7667i	−0.279902	−	1.04461i
$476$	2.19346	−	8.89962i	0.100537	−	0.407914i
$477$	3.34211	−	5.78870i	0.153025	−	0.265047i
$478$		−	11.5791i		−	0.529614i
$479$	−2.00137	−	7.46923i	−0.0914451	−	0.341278i	0.905011	−	0.425387i	$-0.139862\pi$
$479$	−2.00137	−	7.46923i	−0.0914451	−	0.341278i	−0.996457	+	0.0841094i	$0.973195\pi$
$480$	−2.70142	+	1.55967i	−0.123302	+	0.0711887i
$481$	−13.8960	+	9.89456i	−0.633605	+	0.451153i
$482$			6.62826i			0.301909i
$483$	−13.6089	+	14.1687i	−0.619226	+	0.644696i
$484$	4.32871	+	7.49754i	0.196759	+	0.340797i
$485$	−11.9556	+	6.90257i	−0.542876	+	0.313430i
$486$	−0.258819	+	0.965926i	−0.0117403	+	0.0438153i
$487$	9.75715	−	9.75715i	0.442139	−	0.442139i	−0.450591	−	0.892730i	$-0.648787\pi$
$487$	9.75715	−	9.75715i	0.442139	−	0.442139i	0.892730	+	0.450591i	$0.148787\pi$
$488$	7.37066	+	1.97496i	0.333654	+	0.0894024i
$489$	−3.30151	+	3.30151i	−0.149299	+	0.149299i
$490$	−18.4547	+	11.6706i	−0.833700	+	0.527225i
$491$	−9.28265	+	5.35934i	−0.418920	+	0.241864i	−0.694615	−	0.719382i	$-0.744425\pi$
$491$	−9.28265	+	5.35934i	−0.418920	+	0.241864i	0.275695	+	0.961245i	$0.411092\pi$
$492$	−2.23970	−	2.23970i	−0.100973	−	0.100973i
$493$	4.50705	+	7.80643i	0.202987	+	0.351584i
$494$	−16.8333	+	6.27779i	−0.757366	+	0.282451i
$495$	−4.13466	−	2.38715i	−0.185839	−	0.107294i
$496$	2.72003	−	10.1513i	0.122133	−	0.455806i
$497$	0.141944	+	7.04368i	0.00636708	+	0.315952i
$498$	−6.60471	−	3.81323i	−0.295964	−	0.170875i
$499$	0.379762	+	1.41729i	0.0170005	+	0.0634467i	0.973905	−	0.226956i	$-0.0728774\pi$
$499$	0.379762	+	1.41729i	0.0170005	+	0.0634467i	−0.956905	+	0.290403i	$0.906211\pi$
$500$	0.595042	+	0.595042i	0.0266111	+	0.0266111i
$501$	9.94878	+	9.94878i	0.444478	+	0.444478i
$502$	−5.83658	−	21.7824i	−0.260499	−	0.972196i
$503$	−0.457260	−	0.263999i	−0.0203882	−	0.0117711i	0.489771	−	0.871851i	$-0.337080\pi$
$503$	−0.457260	−	0.263999i	−0.0203882	−	0.0117711i	−0.510159	+	0.860080i	$0.670414\pi$
$504$	−1.27644	+	2.31748i	−0.0568573	+	0.103229i
$505$	6.82011	−	25.4530i	0.303491	−	1.13264i
$506$	−9.84229	−	5.68245i	−0.437543	−	0.252616i
$507$	8.51247	+	9.82537i	0.378052	+	0.436360i
$508$	5.20472	+	9.01483i	0.230922	+	0.399968i
$509$	23.8161	+	23.8161i	1.05563	+	1.05563i	0.998359	+	0.0572703i	$0.0182397\pi$
$509$	23.8161	+	23.8161i	1.05563	+	1.05563i	0.0572703	+	0.998359i	$0.481760\pi$
$510$	9.35880	−	5.40331i	0.414415	−	0.239262i
$511$	−15.8130	−	8.70964i	−0.699526	−	0.385292i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−4.81303	−	1.28965i	−0.212501	−	0.0569394i
$514$	14.0884	−	14.0884i	0.621414	−	0.621414i
$515$	−12.4935	+	46.6266i	−0.550532	+	2.05461i
$516$	−6.51981	+	3.76421i	−0.287018	+	0.165710i
$517$	7.46933	+	12.9373i	0.328501	+	0.568980i
$518$	−12.1540	−	2.99556i	−0.534017	−	0.131617i
$519$			6.95387i			0.305241i
$520$	−7.16111	+	8.67245i	−0.314036	+	0.380312i
$521$	2.83563	−	1.63715i	0.124231	−	0.0717250i	−0.436597	−	0.899657i	$-0.643816\pi$
$521$	2.83563	−	1.63715i	0.124231	−	0.0717250i	0.560828	+	0.827932i	$0.310483\pi$
$522$	−0.673426	−	2.51326i	−0.0294751	−	0.110002i
$523$		−	36.6706i		−	1.60349i	−0.597665	−	0.801746i	$-0.703905\pi$
$523$		−	36.6706i		−	1.60349i	0.597665	−	0.801746i	$-0.296095\pi$
$524$	0.170268	−	0.294912i	0.00743817	−	0.0128833i
$525$	−12.1514	−	2.99490i	−0.530329	−	0.130708i
$526$	2.63336	+	9.82782i	0.114820	+	0.428514i
$527$	−9.42326	+	35.1681i	−0.410484	+	1.53195i
$528$	−1.47840	−	0.396136i	−0.0643390	−	0.0172396i
$529$	−32.1361			−1.39722
$530$	20.8503			0.905679
$531$	8.22410	+	2.20364i	0.356896	+	0.0956299i
$532$	−11.5476	−	6.36028i	−0.500651	−	0.275753i
$533$	−10.3881	−	4.74453i	−0.449957	−	0.205508i
$534$	−3.97455	+	6.88413i	−0.171996	+	0.297905i
$535$	−59.4032	+	15.9170i	−2.56822	+	0.688154i
$536$	−1.50496	+	2.60666i	−0.0650042	+	0.112591i
$537$	2.05697	+	3.56278i	0.0887648	+	0.153745i
$538$	20.8479	+	20.8479i	0.898815	+	0.898815i
$539$	−10.4521	−	2.35377i	−0.450204	−	0.101384i
$540$	−3.01304	+	0.807342i	−0.129661	+	0.0347425i
$541$	17.0819	−	4.57707i	0.734407	−	0.196784i	0.127816	−	0.991798i	$-0.459203\pi$
$541$	17.0819	−	4.57707i	0.734407	−	0.196784i	0.606591	+	0.795014i	$0.292537\pi$
$542$			2.69166i			0.115617i
$543$	3.94437	+	2.27728i	0.169269	+	0.0977276i
$544$	2.44970	−	2.44970i	0.105030	−	0.105030i
$545$	33.4788			1.43407
$546$	−1.39240	+	9.43722i	−0.0595894	+	0.403876i
$547$	2.57222			0.109980			0.0549900	−	0.998487i	$-0.482487\pi$
$547$	2.57222			0.109980			0.0549900	+	0.998487i	$0.482487\pi$
$548$	11.7225	−	11.7225i	0.500761	−	0.500761i
$549$	6.60836	+	3.81534i	0.282038	+	0.162835i
$550$		−	7.23985i		−	0.308708i
$551$	12.5231	−	3.35556i	0.533503	−	0.142952i
$552$	−7.17236	+	1.92183i	−0.305276	+	0.0817984i
$553$	26.8814	−	27.9871i	1.14311	−	1.19013i
$554$	−4.77611	−	4.77611i	−0.202918	−	0.202918i
$555$	−7.37918	−	12.7811i	−0.313229	−	0.542528i
$556$	−10.3907	+	17.9972i	−0.440664	+	0.763252i
$557$	−10.8621	+	2.91048i	−0.460240	+	0.123321i	−0.481487	−	0.876453i	$-0.659903\pi$
$557$	−10.8621	+	2.91048i	−0.460240	+	0.123321i	0.0212468	+	0.999774i	$0.493236\pi$
$558$	5.25469	−	9.10138i	0.222449	−	0.385292i
$559$	−17.2832	+	20.9307i	−0.731000	+	0.885276i
$560$	−8.25130	+	0.166280i	−0.348681	+	0.00702663i
$561$	5.12177	+	1.37237i	0.216241	+	0.0579416i
$562$	−0.0891524			−0.00376067
$563$	27.0870			1.14158			0.570791	−	0.821095i	$-0.306637\pi$
$563$	27.0870			1.14158			0.570791	+	0.821095i	$0.306637\pi$
$564$	9.42774	+	2.52616i	0.396980	+	0.106370i
$565$	−1.49629	+	5.58421i	−0.0629492	+	0.234930i
$566$	−7.42270	−	27.7019i	−0.311999	−	1.16440i
$567$	−1.83276	+	1.90814i	−0.0769685	+	0.0801344i
$568$	−1.33140	+	2.30605i	−0.0558643	+	0.0967599i
$569$		−	28.7941i		−	1.20711i	−0.797321	−	0.603555i	$-0.793750\pi$
$569$		−	28.7941i		−	1.20711i	0.797321	−	0.603555i	$-0.206250\pi$
$570$	−4.02284	−	15.0134i	−0.168498	−	0.628844i
$571$	18.8974	−	10.9104i	0.790830	−	0.456586i	−0.0494246	−	0.998778i	$-0.515739\pi$
$571$	18.8974	−	10.9104i	0.790830	−	0.456586i	0.840255	+	0.542192i	$0.182405\pi$
$572$	−5.49351	+	0.524364i	−0.229695	+	0.0219247i
$573$		−	12.1366i		−	0.507013i
$574$	−2.33160	−	8.04929i	−0.0973191	−	0.335971i
$575$	−17.5618	−	30.4180i	−0.732379	−	1.26852i
$576$	−0.866025	+	0.500000i	−0.0360844	+	0.0208333i
$577$	4.86870	−	18.1702i	0.202686	−	0.756436i	−0.787456	−	0.616371i	$-0.788602\pi$
$577$	4.86870	−	18.1702i	0.202686	−	0.756436i	0.990142	−	0.140065i	$-0.0447312\pi$
$578$	3.53406	−	3.53406i	0.146998	−	0.146998i
$579$	9.81910	+	2.63102i	0.408068	+	0.109341i
$580$	5.73905	−	5.73905i	0.238301	−	0.238301i
$581$	−10.4389	−	17.2676i	−0.433078	−	0.716381i
$582$	−3.83275	+	2.21284i	−0.158872	+	0.0917251i
$583$	7.23408	+	7.23408i	0.299605	+	0.299605i
$584$	−3.41168	−	5.90921i	−0.141177	−	0.244525i
$585$	−9.16170	+	6.52351i	−0.378790	+	0.269714i
$586$	10.6894	+	6.17151i	0.441574	+	0.254943i
$587$	3.39742	−	12.6793i	0.140226	−	0.523332i	−0.859695	−	0.510807i	$-0.829347\pi$
$587$	3.39742	−	12.6793i	0.140226	−	0.523332i	0.999922	−	0.0125246i	$-0.00398682\pi$
$588$	−5.91625	+	3.74139i	−0.243982	+	0.154292i
$589$	45.3506	+	26.1832i	1.86864	+	1.07886i
$590$	6.87389	+	25.6537i	0.282994	+	1.05615i
$591$	4.14910	+	4.14910i	0.170671	+	0.170671i
$592$	−3.34550	−	3.34550i	−0.137499	−	0.137499i
$593$	−1.78126	−	6.64776i	−0.0731477	−	0.272991i	0.919659	−	0.392717i	$-0.128465\pi$
$593$	−1.78126	−	6.64776i	−0.0731477	−	0.272991i	−0.992807	+	0.119727i	$0.961798\pi$
$594$	−1.32550	−	0.765275i	−0.0543857	−	0.0313996i
$595$	28.5858	−	0.576062i	1.17190	−	0.0236162i
$596$	2.52681	−	9.43017i	0.103502	−	0.386275i
$597$	10.3751	+	5.99004i	0.424623	+	0.245156i
$598$	−21.8088	+	15.5288i	−0.891830	+	0.635020i
$599$	11.7981	+	20.4349i	0.482057	+	0.834948i	0.999788	−	0.0205958i	$-0.00655630\pi$
$599$	11.7981	+	20.4349i	0.482057	+	0.834948i	−0.517730	+	0.855544i	$0.673223\pi$
$600$	−3.34477	−	3.34477i	−0.136550	−	0.136550i
$601$	−30.7423	+	17.7491i	−1.25401	+	0.724001i	−0.971903	−	0.235383i	$-0.924366\pi$
$601$	−30.7423	+	17.7491i	−1.25401	+	0.724001i	−0.282104	+	0.959384i	$0.591032\pi$
$602$	−19.9143	+	0.401314i	−0.811646	+	0.0163563i
$603$	−2.12833	+	2.12833i	−0.0866722	+	0.0866722i
$604$	8.30920	+	2.22644i	0.338096	+	0.0905927i
$605$	−19.0957	+	19.0957i	−0.776349	+	0.776349i
$606$	2.18640	−	8.15976i	0.0888165	−	0.331468i
$607$	−0.509281	+	0.294034i	−0.0206711	+	0.0119345i	−0.510300	−	0.859996i	$-0.670466\pi$
$607$	−0.509281	+	0.294034i	−0.0206711	+	0.0119345i	0.489629	+	0.871931i	$0.337132\pi$
$608$	−2.49141	−	4.31525i	−0.101040	−	0.175006i
$609$	1.64738	−	6.68401i	0.0667553	−	0.270850i
$610$			23.8026i			0.963739i
$611$	35.0321	−	3.34387i	1.41725	−	0.135278i
$612$	3.00026	−	1.73220i	0.121278	−	0.0700201i
$613$	−0.462410	−	1.72574i	−0.0186766	−	0.0697019i	0.955959	−	0.293501i	$-0.0948206\pi$
$613$	−0.462410	−	1.72574i	−0.0186766	−	0.0697019i	−0.974635	+	0.223800i	$0.928154\pi$
$614$			19.6224i			0.791896i
$615$	4.94010	−	8.55650i	0.199204	−	0.345031i
$616$	−2.92051	−	2.80513i	−0.117671	−	0.113022i
$617$	−3.25047	−	12.1309i	−0.130859	−	0.488373i	0.869122	−	0.494599i	$-0.164685\pi$
$617$	−3.25047	−	12.1309i	−0.130859	−	0.488373i	−0.999981	+	0.00622577i	$0.998018\pi$
$618$	−4.00520	+	14.9476i	−0.161113	+	0.601281i
$619$	22.8821	+	6.13124i	0.919709	+	0.246435i	0.687461	−	0.726221i	$-0.258725\pi$
$619$	22.8821	+	6.13124i	0.919709	+	0.246435i	0.232248	+	0.972657i	$0.425392\pi$
$620$	32.7822			1.31657
$621$	−7.42537			−0.297970
$622$	−25.3541	−	6.79362i	−1.01661	−	0.272399i
$623$	−17.9981	+	10.8805i	−0.721080	+	0.435919i
$624$	−2.29572	+	2.78023i	−0.0919024	+	0.111298i
$625$	−13.1380	+	22.7558i	−0.525522	+	0.910231i
$626$	−12.4285	+	3.33021i	−0.496743	+	0.133102i
$627$	3.81323	−	6.60471i	0.152286	−	0.263767i
$628$	5.72384	+	9.91398i	0.228406	+	0.395611i
$629$	11.5902	+	11.5902i	0.462130	+	0.462130i
$630$	−8.01318	−	1.97498i	−0.319253	−	0.0786850i
$631$	14.9722	−	4.01178i	0.596032	−	0.159706i	0.0518237	−	0.998656i	$-0.483497\pi$
$631$	14.9722	−	4.01178i	0.596032	−	0.159706i	0.544209	+	0.838950i	$0.316830\pi$
$632$	14.1674	−	3.79615i	0.563550	−	0.151003i
$633$		−	3.45658i		−	0.137387i
$634$	−1.87169	−	1.08062i	−0.0743342	−	0.0429169i
$635$	−22.9601	+	22.9601i	−0.911143	+	0.911143i
$636$	6.68422			0.265047
$637$	−15.2729	+	20.0932i	−0.605136	+	0.796122i
$638$	3.98237			0.157663
$639$	−1.88288	+	1.88288i	−0.0744858	+	0.0744858i
$640$	−2.70142	−	1.55967i	−0.106783	−	0.0616512i
$641$		−	46.4479i		−	1.83458i	−0.398219	−	0.917290i	$-0.630372\pi$
$641$		−	46.4479i		−	1.83458i	0.398219	−	0.917290i	$-0.369628\pi$
$642$	−19.0436	+	5.10271i	−0.751590	+	0.201388i
$643$	−25.6665	+	6.87732i	−1.01219	+	0.271215i	−0.726543	−	0.687121i	$-0.758874\pi$
$643$	−25.6665	+	6.87732i	−1.01219	+	0.271215i	−0.285644	+	0.958336i	$0.592208\pi$
$644$	−19.0749	−	4.70131i	−0.751655	−	0.185258i
$645$	−16.6054	−	16.6054i	−0.653839	−	0.653839i
$646$	8.63125	+	14.9498i	0.339592	+	0.588190i
$647$	−8.84345	+	15.3173i	−0.347672	+	0.602185i	−0.985835	−	0.167715i	$-0.946361\pi$
$647$	−8.84345	+	15.3173i	−0.347672	+	0.602185i	0.638164	+	0.769901i	$0.279694\pi$
$648$	−0.965926	+	0.258819i	−0.0379452	+	0.0101674i
$649$	−6.51572	+	11.2856i	−0.255764	+	0.442997i
$650$	−15.5136	−	7.08550i	−0.608493	−	0.277916i
$651$	23.7950	−	14.3849i	0.932600	−	0.563790i
$652$	−4.50994	−	1.20844i	−0.176623	−	0.0473260i
$653$	37.6867			1.47480			0.737398	−	0.675459i	$-0.236054\pi$
$653$	37.6867			1.47480			0.737398	+	0.675459i	$0.236054\pi$
$654$	10.7327			0.419681
$655$	1.02605	+	0.274928i	0.0400910	+	0.0107423i
$656$	0.819786	−	3.05948i	0.0320073	−	0.119453i
$657$	−1.76602	−	6.59087i	−0.0688989	−	0.257134i
$658$	18.6241	+	17.8883i	0.726042	+	0.697357i
$659$	−16.0832	+	27.8570i	−0.626514	+	1.08515i	0.361732	+	0.932282i	$0.382186\pi$
$659$	−16.0832	+	27.8570i	−0.626514	+	1.08515i	−0.988246	+	0.152872i	$0.951148\pi$
$660$		−	4.77429i		−	0.185839i
$661$	−0.175434	−	0.654727i	−0.00682358	−	0.0254659i	0.962430	−	0.271530i	$-0.0875295\pi$
$661$	−0.175434	−	0.654727i	−0.00682358	−	0.0254659i	−0.969254	+	0.246064i	$0.920863\pi$
$662$	−16.0332	+	9.25676i	−0.623147	+	0.359774i
$663$	7.95330	−	9.63182i	0.308881	−	0.374069i
$664$		−	7.62647i		−	0.295964i
$665$	9.84096	−	39.9282i	0.381616	−	1.54835i
$666$	−2.36563	−	4.09739i	−0.0916662	−	0.158771i
$667$	16.7318	−	9.66010i	0.647857	−	0.374041i
$668$	−3.64150	+	13.5903i	−0.140894	+	0.525824i
$669$	−7.24161	+	7.24161i	−0.279977	+	0.279977i
$670$	−9.06899	−	2.43003i	−0.350366	−	0.0938802i
$671$	−8.25839	+	8.25839i	−0.318812	+	0.318812i
$672$	−2.64521	+	0.0533064i	−0.102041	+	0.00205634i
$673$	7.66521	−	4.42551i	0.295472	−	0.170591i	−0.344935	−	0.938627i	$-0.612099\pi$
$673$	7.66521	−	4.42551i	0.295472	−	0.170591i	0.640407	+	0.768036i	$0.278766\pi$
$674$	5.24342	+	5.24342i	0.201969	+	0.201969i
$675$	−2.36511	−	4.09650i	−0.0910332	−	0.157674i
$676$	−4.25278	+	12.2847i	−0.163569	+	0.472488i
$677$	−40.6957	−	23.4957i	−1.56406	−	0.903013i	−0.996839	−	0.0794506i	$-0.974683\pi$
$677$	−40.6957	−	23.4957i	−1.56406	−	0.903013i	−0.567226	−	0.823562i	$-0.691983\pi$
$678$	−0.479681	+	1.79020i	−0.0184221	+	0.0687520i
$679$	−11.7069	+	0.235917i	−0.449268	+	0.00905366i
$680$	9.35880	+	5.40331i	0.358894	+	0.207207i
$681$	1.68137	+	6.27496i	0.0644303	+	0.240457i
$682$	11.3739	+	11.3739i	0.435529	+	0.435529i
$683$	16.8468	+	16.8468i	0.644626	+	0.644626i	0.951689	−	0.307063i	$-0.0993463\pi$
$683$	16.8468	+	16.8468i	0.644626	+	0.644626i	−0.307063	+	0.951689i	$0.599346\pi$
$684$	−1.28965	−	4.81303i	−0.0493110	−	0.184031i
$685$	44.7845	+	25.8564i	1.71113	+	0.987921i
$686$	−18.4864	+	1.11883i	−0.705815	+	0.0427171i
$687$	−6.19109	+	23.1055i	−0.236205	+	0.881529i
$688$	−6.51981	−	3.76421i	−0.248565	−	0.143509i
$689$	22.5811	−	8.42136i	0.860271	−	0.320828i
$690$	−11.5811	−	20.0590i	−0.440885	−	0.763635i
$691$	23.4523	+	23.4523i	0.892167	+	0.892167i	0.994727	−	0.102560i	$-0.0327033\pi$
$691$	23.4523	+	23.4523i	0.892167	+	0.892167i	−0.102560	+	0.994727i	$0.532703\pi$
$692$	−6.02223	+	3.47694i	−0.228931	+	0.132173i
$693$	−2.09497	−	3.46543i	−0.0795815	−	0.131641i
$694$	6.07363	−	6.07363i	0.230552	−	0.230552i
$695$	−62.6152	−	16.7777i	−2.37513	−	0.636414i
$696$	1.83983	−	1.83983i	0.0697387	−	0.0697387i
$697$	−2.84007	+	10.5993i	−0.107575	+	0.401476i
$698$	−21.6421	+	12.4951i	−0.819165	+	0.472945i
$699$	−12.7417	−	22.0693i	−0.481936	−	0.834737i
$700$	−3.48202	−	12.0208i	−0.131608	−	0.454345i
$701$		−	40.5277i		−	1.53071i	−0.643609	−	0.765354i	$-0.722564\pi$
$701$		−	40.5277i		−	1.53071i	0.643609	−	0.765354i	$-0.277436\pi$
$702$	−2.93707	+	2.09132i	−0.110853	+	0.0789317i
$703$	20.4166	−	11.7875i	0.770025	−	0.444574i
$704$	−0.396136	−	1.47840i	−0.0149299	−	0.0557192i
$705$			30.4457i			1.14665i
$706$	10.2697	−	17.7876i	0.386505	−	0.669447i
$707$	15.4824	−	16.1192i	0.582276	−	0.606226i
$708$	2.20364	+	8.22410i	0.0828179	+	0.309081i
$709$	2.73474	−	10.2062i	0.102705	−	0.383302i	−0.895369	−	0.445324i	$-0.853088\pi$
$709$	2.73474	−	10.2062i	0.102705	−	0.383302i	0.998075	+	0.0620226i	$0.0197551\pi$
$710$	−8.02313	−	2.14979i	−0.301103	−	0.0806803i
$711$	14.6672			0.550063
$712$	−7.94911			−0.297905
$713$	75.3770	+	20.1972i	2.82289	+	0.756391i
$714$	9.16408	−	0.184675i	0.342957	−	0.00691129i
$715$	−6.01507	−	16.1288i	−0.224951	−	0.603184i
$716$	−2.05697	+	3.56278i	−0.0768726	+	0.133147i
$717$	11.1845	−	2.99688i	0.417693	−	0.111921i
$718$	−0.494126	+	0.855851i	−0.0184406	+	0.0319401i
$719$	−23.4920	−	40.6893i	−0.876103	−	1.51745i	−0.855583	−	0.517665i	$-0.826801\pi$
$719$	−23.4920	−	40.6893i	−0.876103	−	1.51745i	−0.0205193	−	0.999789i	$-0.506532\pi$
$720$	−2.20570	−	2.20570i	−0.0822016	−	0.0822016i
$721$	−28.3617	+	29.5283i	−1.05625	+	1.09969i
$722$	5.62990	−	1.50853i	0.209523	−	0.0561415i
$723$	−6.40241	+	1.71552i	−0.238108	+	0.0638009i
$724$			4.55457i			0.169269i
$725$	10.6587	+	6.15383i	0.395856	+	0.228548i
$726$	−6.12172	+	6.12172i	−0.227198	+	0.227198i
$727$	45.4801			1.68677			0.843383	−	0.537313i	$-0.180561\pi$
$727$	45.4801			1.68677			0.843383	+	0.537313i	$0.180561\pi$
$728$	−8.86908	+	3.51276i	−0.328710	+	0.130191i
$729$	−1.00000			−0.0370370
$730$	15.0503	−	15.0503i	0.557037	−	0.557037i
$731$	22.5872	+	13.0407i	0.835419	+	0.482329i
$732$			7.63067i			0.282038i
$733$	−16.6436	+	4.45964i	−0.614745	+	0.164720i	−0.552738	−	0.833355i	$-0.686417\pi$
$733$	−16.6436	+	4.45964i	−0.614745	+	0.164720i	−0.0620072	+	0.998076i	$0.519750\pi$
$734$	30.9610	−	8.29596i	1.14279	−	0.306210i
$735$	−16.0494	−	14.8053i	−0.591991	−	0.546103i
$736$	−5.25053	−	5.25053i	−0.193537	−	0.193537i
$737$	−2.30341	−	3.98962i	−0.0848472	−	0.146960i
$738$	1.58370	−	2.74306i	0.0582970	−	0.100973i
$739$	29.0174	−	7.77520i	1.06742	−	0.286015i	0.317990	−	0.948094i	$-0.396992\pi$
$739$	29.0174	−	7.77520i	1.06742	−	0.286015i	0.749434	+	0.662079i	$0.230326\pi$
$740$	7.37918	−	12.7811i	0.271264	−	0.469843i
$741$	−10.4207	−	14.6349i	−0.382812	−	0.537627i
$742$	15.4905	+	8.53202i	0.568675	+	0.313220i
$743$	−14.6591	−	3.92789i	−0.537790	−	0.144100i	−0.0203066	−	0.999794i	$-0.506464\pi$
$743$	−14.6591	−	3.92789i	−0.537790	−	0.144100i	−0.517483	+	0.855694i	$0.673131\pi$
$744$	10.5094			0.385292
$745$	30.4535			1.11573
$746$	32.8939	+	8.81389i	1.20433	+	0.322700i
$747$	1.97387	−	7.36660i	0.0722203	−	0.269530i
$748$	1.37237	+	5.12177i	0.0501789	+	0.187270i
$749$	−50.6463	−	12.4826i	−1.85058	−	0.456105i
$750$	−0.420758	+	0.728774i	−0.0153639	+	0.0266111i
$751$		−	10.0535i		−	0.366856i	−0.983033	−	0.183428i	$-0.941281\pi$
$751$		−	10.0535i		−	0.366856i	0.983033	−	0.183428i	$-0.0587195\pi$
$752$	2.52616	+	9.42774i	0.0921194	+	0.343794i
$753$	19.5296	−	11.2754i	0.711697	−	0.410899i
$754$	3.89747	−	8.53344i	0.141937	−	0.310769i
$755$			26.8335i			0.976570i
$756$	−2.56888	−	0.633142i	−0.0934292	−	0.0230271i
$757$	−8.64250	−	14.9693i	−0.314117	−	0.544067i	0.665132	−	0.746726i	$-0.268375\pi$
$757$	−8.64250	−	14.9693i	−0.314117	−	0.544067i	−0.979249	+	0.202659i	$0.935042\pi$
$758$	−30.7869	+	17.7748i	−1.11823	+	0.645611i
$759$	2.94145	−	10.9777i	0.106768	−	0.398464i
$760$	10.9906	−	10.9906i	0.398671	−	0.398671i
$761$	−39.9834	−	10.7135i	−1.44940	−	0.388364i	−0.553582	−	0.832795i	$-0.686739\pi$
$761$	−39.9834	−	10.7135i	−1.44940	−	0.388364i	−0.895813	+	0.444430i	$0.853406\pi$
$762$	−7.36058	+	7.36058i	−0.266646	+	0.266646i
$763$	24.8727	+	13.6996i	0.900453	+	0.495960i
$764$	10.5106	−	6.06829i	0.380259	−	0.219543i
$765$	7.64143	+	7.64143i	0.276277	+	0.276277i
$766$	−18.9673	−	32.8522i	−0.685315	−	1.18700i
$767$	17.8059	+	25.0069i	0.642935	+	0.902946i
$768$	−0.866025	−	0.500000i	−0.0312500	−	0.0180422i
$769$	−0.00508629	+	0.0189823i	−0.000183416	+	0.000684518i	−0.966017	−	0.258477i	$-0.916779\pi$
$769$	−0.00508629	+	0.0189823i	−0.000183416	+	0.000684518i	0.965834	+	0.259161i	$0.0834461\pi$
$770$	6.09411	−	11.0643i	0.219617	−	0.398730i
$771$	17.2547	+	9.96202i	0.621414	+	0.358774i
$772$	2.63102	+	9.81910i	0.0946925	+	0.353397i
$773$	−0.302402	−	0.302402i	−0.0108766	−	0.0108766i	0.701648	−	0.712524i	$-0.252448\pi$
$773$	−0.302402	−	0.302402i	−0.0108766	−	0.0108766i	−0.712524	+	0.701648i	$0.752448\pi$
$774$	−5.32340	−	5.32340i	−0.191346	−	0.191346i
$775$	12.8663	+	48.0178i	0.462172	+	1.72485i
$776$	−3.83275	−	2.21284i	−0.137588	−	0.0794362i
$777$	−0.252207	−	12.5152i	−0.00904786	−	0.448980i
$778$	5.17169	−	19.3010i	0.185414	−	0.691975i
$779$	13.6682	+	7.89132i	0.489713	+	0.282736i
$780$	−10.2304	−	4.67251i	−0.366306	−	0.167303i
$781$	−2.03778	−	3.52953i	−0.0729174	−	0.126297i
$782$	18.1899	+	18.1899i	0.650471	+	0.650471i
$783$	2.25333	−	1.30096i	0.0805274	−	0.0464925i
$784$	−6.19826	−	3.25293i	−0.221367	−	0.116176i
$785$	−25.2501	+	25.2501i	−0.901216	+	0.901216i
$786$	0.328932	+	0.0881370i	0.0117326	+	0.00314374i
$787$	18.4048	−	18.4048i	0.656059	−	0.656059i	−0.298386	−	0.954445i	$-0.596448\pi$
$787$	18.4048	−	18.4048i	0.656059	−	0.656059i	0.954445	+	0.298386i	$0.0964483\pi$
$788$	−1.51868	+	5.66778i	−0.0541006	+	0.201906i
$789$	−8.81139	+	5.08726i	−0.313694	+	0.181111i
$790$	22.8759	+	39.6223i	0.813889	+	1.40970i
$791$	−3.39673	+	3.53645i	−0.120774	+	0.125742i
$792$		−	1.53055i		−	0.0543857i
$793$	9.61379	+	25.7784i	0.341396	+	0.915419i
$794$	11.0464	−	6.37764i	0.392022	−	0.226334i
$795$	5.39645	+	20.1398i	0.191392	+	0.714286i
$796$			11.9801i			0.424623i
$797$	3.56473	−	6.17429i	0.126269	−	0.218705i	−0.795959	−	0.605350i	$-0.793033\pi$
$797$	3.56473	−	6.17429i	0.126269	−	0.218705i	0.922228	+	0.386646i	$0.126366\pi$
$798$	3.15483	−	12.8003i	0.111680	−	0.453124i
$799$	−8.75162	−	32.6615i	−0.309610	−	1.15548i
$800$	1.22427	−	4.56905i	0.0432846	−	0.161540i
$801$	−7.67825	−	2.05738i	−0.271298	−	0.0726940i
$802$	−11.9183			−0.420850
$803$	10.4435			0.368544
$804$	−2.90735	−	0.779022i	−0.102534	−	0.0274740i
$805$	−1.23469	−	61.2689i	−0.0435172	−	2.15945i
$806$	35.5035	−	13.2406i	1.25056	−	0.466381i
$807$	−14.7417	+	25.5333i	−0.518931	+	0.898815i
$808$	8.15976	−	2.18640i	0.287059	−	0.0769174i
$809$	5.55161	−	9.61567i	0.195184	−	0.338069i	−0.751777	−	0.659418i	$-0.770803\pi$
$809$	5.55161	−	9.61567i	0.195184	−	0.338069i	0.946961	+	0.321349i	$0.104136\pi$
$810$	−1.55967	−	2.70142i	−0.0548011	−	0.0949182i
$811$	27.9664	+	27.9664i	0.982032	+	0.982032i	0.999841	−	0.0178090i	$-0.00566907\pi$
$811$	27.9664	+	27.9664i	0.982032	+	0.982032i	−0.0178090	+	0.999841i	$0.505669\pi$
$812$	6.61221	−	1.91533i	0.232043	−	0.0672149i
$813$	−2.59995	+	0.696653i	−0.0911841	+	0.0244327i
$814$	6.99468	−	1.87422i	0.245164	−	0.0656914i
$815$		−	14.5643i		−	0.510164i
$816$	3.00026	+	1.73220i	0.105030	+	0.0606392i
$817$	26.5255	−	26.5255i	0.928011	−	0.928011i
$818$	−31.0046			−1.08405
$819$	−9.47604	+	1.09757i	−0.331120	+	0.0383524i
$820$	9.88020			0.345031
$821$	28.2587	−	28.2587i	0.986236	−	0.986236i	−0.0136709	−	0.999907i	$-0.504352\pi$
$821$	28.2587	−	28.2587i	0.986236	−	0.986236i	0.999907	+	0.0136709i	$0.00435172\pi$
$822$	14.3571	+	8.28907i	0.500761	+	0.289115i
$823$			23.2718i			0.811206i	0.914049	+	0.405603i	$0.132938\pi$
$823$			23.2718i			0.811206i	−0.914049	+	0.405603i	$0.867062\pi$
$824$	−14.9476	+	4.00520i	−0.520725	+	0.139528i
$825$	6.99316	−	1.87381i	0.243470	−	0.0652377i
$826$	−5.39071	+	21.8720i	−0.187567	+	0.761024i
$827$	−21.2660	−	21.2660i	−0.739490	−	0.739490i	0.232989	−	0.972479i	$-0.425149\pi$
$827$	−21.2660	−	21.2660i	−0.739490	−	0.739490i	−0.972479	+	0.232989i	$0.925149\pi$
$828$	−3.71268	−	6.43056i	−0.129025	−	0.223477i
$829$	−5.73745	+	9.93756i	−0.199270	+	0.345146i	−0.948292	−	0.317400i	$-0.897190\pi$
$829$	−5.73745	+	9.93756i	−0.199270	+	0.345146i	0.749022	+	0.662545i	$0.230524\pi$
$830$	22.9789	−	6.15717i	0.797608	−	0.213718i
$831$	3.37722	−	5.84952i	0.117154	−	0.202918i
$832$	−3.55561	−	0.598039i	−0.123269	−	0.0207333i
$833$	21.4733	+	11.2694i	0.744005	+	0.390463i
$834$	−20.0733	−	5.37862i	−0.695081	−	0.186246i
$835$	−43.8880			−1.51881
$836$	7.62646			0.263767
$837$	10.1513	+	2.72003i	0.350879	+	0.0940179i
$838$	−2.07343	+	7.73813i	−0.0716253	+	0.267309i
$839$	8.38592	+	31.2967i	0.289514	+	1.08048i	0.945477	+	0.325688i	$0.105596\pi$
$839$	8.38592	+	31.2967i	0.289514	+	1.08048i	−0.655963	+	0.754793i	$0.727737\pi$
$840$	−2.29621	−	7.92711i	−0.0792267	−	0.273511i
$841$	11.1150	−	19.2518i	0.383276	−	0.663854i
$842$			9.68442i			0.333747i
$843$	−0.0230743	−	0.0861146i	−0.000794722	−	0.00296594i
$844$	2.99349	−	1.72829i	0.103040	−	0.0594903i
$845$	−40.4478	−	2.89586i	−1.39145	−	0.0996205i
$846$			9.76032i			0.335567i
$847$	−22.0009	+	6.37291i	−0.755962	+	0.218976i
$848$	3.34211	+	5.78870i	0.114769	+	0.198785i
$849$	24.8368	−	14.3396i	0.852398	−	0.492132i
$850$	−4.24137	+	15.8290i	−0.145478	+	0.542931i
$851$	24.8416	−	24.8416i	0.851559	−	0.851559i
$852$	−2.57207	−	0.689184i	−0.0881176	−	0.0236110i
$853$	9.96970	−	9.96970i	0.341356	−	0.341356i	−0.515521	−	0.856877i	$-0.672402\pi$
$853$	9.96970	−	9.96970i	0.341356	−	0.341356i	0.856877	+	0.515521i	$0.172402\pi$
$854$	−9.74011	+	17.6839i	−0.333300	+	0.605131i
$855$	13.4607	−	7.77153i	0.460346	−	0.265781i
$856$	−13.9409	−	13.9409i	−0.476489	−	0.476489i
$857$	−9.01136	−	15.6081i	−0.307822	−	0.533164i	0.670063	−	0.742304i	$-0.266267\pi$
$857$	−9.01136	−	15.6081i	−0.307822	−	0.533164i	−0.977886	+	0.209140i	$0.932934\pi$
$858$	−1.92832	−	5.17061i	−0.0658318	−	0.176522i
$859$	42.4181	+	24.4901i	1.44729	+	0.835592i	0.998319	−	0.0579547i	$-0.0184579\pi$
$859$	42.4181	+	24.4901i	1.44729	+	0.835592i	0.448969	+	0.893547i	$0.351791\pi$
$860$	6.07802	−	22.6835i	0.207259	−	0.773500i
$861$	7.17155	−	4.33546i	0.244406	−	0.147752i
$862$	−4.48768	−	2.59096i	−0.152851	−	0.0882486i
$863$	6.48171	+	24.1901i	0.220640	+	0.823440i	0.984105	+	0.177590i	$0.0568302\pi$
$863$	6.48171	+	24.1901i	0.220640	+	0.823440i	−0.763464	+	0.645850i	$0.776503\pi$
$864$	−0.707107	−	0.707107i	−0.0240563	−	0.0240563i
$865$	−15.3382	−	15.3382i	−0.521513	−	0.521513i
$866$	2.95761	+	11.0379i	0.100504	+	0.375084i
$867$	4.32833	+	2.49896i	0.146998	+	0.0848692i
$868$	24.3552	+	13.4146i	0.826670	+	0.455322i
$869$	−5.81020	+	21.6840i	−0.197098	+	0.735578i
$870$	7.02888	+	4.05812i	0.238301	+	0.137583i
$871$	−10.8033	+	1.03119i	−0.366055	+	0.0349405i
$872$	5.36634	+	9.29477i	0.181727	+	0.314761i
$873$	−3.12942	−	3.12942i	−0.105915	−	0.105915i
$874$	32.0423	−	18.4996i	1.08385	−	0.625760i
$875$	−1.90534	+	1.15184i	−0.0644121	+	0.0389394i
$876$	4.82485	−	4.82485i	0.163017	−	0.163017i
$877$	51.0192	+	13.6706i	1.72280	+	0.461622i	0.978503	−	0.206232i	$-0.0661202\pi$
$877$	51.0192	+	13.6706i	1.72280	+	0.461622i	0.744292	+	0.667854i	$0.232787\pi$
$878$	18.3360	−	18.3360i	0.618811	−	0.618811i
$879$	−3.19461	+	11.9224i	−0.107751	+	0.402134i
$880$	4.13466	−	2.38715i	0.139379	−	0.0804707i
$881$	7.72842	+	13.3860i	0.260377	+	0.450986i	0.966342	−	0.257260i	$-0.0828198\pi$
$881$	7.72842	+	13.3860i	0.260377	+	0.450986i	−0.705965	+	0.708247i	$0.749487\pi$
$882$	−5.14514	−	4.74631i	−0.173246	−	0.159817i
$883$			5.66309i			0.190578i	0.995450	+	0.0952890i	$0.0303775\pi$
$883$			5.66309i			0.190578i	−0.995450	+	0.0952890i	$0.969622\pi$
$884$	12.3181	+	2.07185i	0.414301	+	0.0696837i
$885$	−23.0005	+	13.2793i	−0.773153	+	0.446380i
$886$	9.77102	+	36.4659i	0.328264	+	1.22510i
$887$			7.83508i			0.263076i	0.991311	+	0.131538i	$0.0419916\pi$
$887$			7.83508i			0.263076i	−0.991311	+	0.131538i	$0.958008\pi$
$888$	2.36563	−	4.09739i	0.0793853	−	0.137499i
$889$	−26.4533	+	7.66261i	−0.887216	+	0.256996i
$890$	−6.41765	−	23.9510i	−0.215120	−	0.802839i
$891$	0.396136	−	1.47840i	0.0132710	−	0.0495282i
$892$	−9.89222	−	2.65061i	−0.331216	−	0.0887491i
$893$	−48.6339			−1.62747
$894$	9.76283			0.326518
$895$	−12.3955	−	3.32136i	−0.414335	−	0.111021i
$896$	−1.36877	−	2.26417i	−0.0457275	−	0.0756406i
$897$	−20.6442	−	17.0466i	−0.689290	−	0.569169i
$898$	−1.70644	+	2.95565i	−0.0569448	+	0.0986312i
$899$	−26.4128	+	7.07729i	−0.880916	+	0.236041i
$900$	2.36511	−	4.09650i	0.0788371	−	0.136550i
$901$	−11.5784	−	20.0544i	−0.385733	−	0.668109i
$902$	3.42797	+	3.42797i	0.114139	+	0.114139i
$903$	−5.54184	−	19.1319i	−0.184421	−	0.636669i
$904$	−1.79020	+	0.479681i	−0.0595410	+	0.0159540i
$905$	−13.7231	+	3.67709i	−0.456171	+	0.122231i
$906$			8.60232i			0.285793i
$907$	−22.9907	−	13.2737i	−0.763393	−	0.440745i	0.0671194	−	0.997745i	$-0.478619\pi$
$907$	−22.9907	−	13.2737i	−0.763393	−	0.440745i	−0.830513	+	0.557000i	$0.811953\pi$
$908$	−4.59359	+	4.59359i	−0.152444	+	0.152444i
$909$	8.44761			0.280190
$910$	−17.7445	−	23.8869i	−0.588223	−	0.791843i
$911$	−17.3251			−0.574007			−0.287004	−	0.957929i	$-0.592659\pi$
$911$	−17.3251			−0.574007			−0.287004	+	0.957929i	$0.592659\pi$
$912$	3.52339	−	3.52339i	0.116671	−	0.116671i
$913$	10.1088	+	5.83635i	0.334554	+	0.193155i
$914$		−	16.1070i		−	0.532772i
$915$	−22.9915	+	6.16056i	−0.760077	+	0.203662i
$916$	−23.1055	+	6.19109i	−0.763426	+	0.204559i
$917$	0.649789	+	0.624117i	0.0214579	+	0.0206102i
$918$	2.44970	+	2.44970i	0.0808522	+	0.0808522i
$919$	10.5811	+	18.3270i	0.349038	+	0.604552i	0.986079	−	0.166278i	$-0.0531750\pi$
$919$	10.5811	+	18.3270i	0.349038	+	0.604552i	−0.637041	+	0.770830i	$0.719842\pi$
$920$	11.5811	−	20.0590i	0.381817	−	0.661327i
$921$	−18.9538	+	5.07865i	−0.624549	+	0.167347i
$922$	10.3452	−	17.9184i	0.340702	−	0.590112i
$923$	−9.55743	+	0.912271i	−0.314587	+	0.0300278i
$924$	1.95366	−	3.54701i	0.0642707	−	0.116688i
$925$	21.6173	+	5.79235i	0.710774	+	0.190451i
$926$	16.9854			0.558176
$927$	−15.4749			−0.508263
$928$	2.51326	+	0.673426i	0.0825018	+	0.0221063i
$929$	−9.98889	+	37.2791i	−0.327725	+	1.22309i	0.583819	+	0.811884i	$0.301558\pi$
$929$	−9.98889	+	37.2791i	−0.327725	+	1.22309i	−0.911544	+	0.411203i	$0.865109\pi$
$930$	8.48466	+	31.6652i	0.278223	+	1.03834i
$931$	23.6500	−	25.6373i	0.775099	−	0.840229i
$932$	12.7417	−	22.0693i	0.417369	−	0.722904i
$933$		−	26.2485i		−	0.859338i
$934$	−1.01470	−	3.78690i	−0.0332019	−	0.123911i
$935$	−14.3241	+	8.27004i	−0.468449	+	0.270459i
$936$	−3.27967	−	1.49792i	−0.107199	−	0.0489611i
$937$		−	17.7016i		−	0.578287i	−0.957286	−	0.289144i	$-0.906630\pi$
$937$		−	17.7016i		−	0.578287i	0.957286	−	0.289144i	$-0.0933705\pi$
$938$	−5.74334	−	5.51643i	−0.187527	−	0.180118i
$939$	−6.43346	−	11.1431i	−0.209948	−	0.363641i
$940$	−26.3667	+	15.2228i	−0.859987	+	0.496514i
$941$	−9.44742	+	35.2582i	−0.307977	+	1.14939i	0.622375	+	0.782719i	$0.286168\pi$
$941$	−9.44742	+	35.2582i	−0.307977	+	1.14939i	−0.930352	+	0.366667i	$0.880499\pi$
$942$	−8.09473	+	8.09473i	−0.263741	+	0.263741i
$943$	22.7178	+	6.08721i	0.739793	+	0.198227i
$944$	−6.02046	+	6.02046i	−0.195949	+	0.195949i
$945$	−0.166280	−	8.25130i	−0.00540910	−	0.268415i
$946$	9.97889	−	5.76132i	0.324442	−	0.187317i
$947$	7.44467	+	7.44467i	0.241919	+	0.241919i	0.817644	−	0.575724i	$-0.195280\pi$
$947$	7.44467	+	7.44467i	0.241919	+	0.241919i	−0.575724	+	0.817644i	$0.695280\pi$
$948$	7.33360	+	12.7022i	0.238184	+	0.412547i
$949$	10.2209	−	22.3784i	0.331783	−	0.726434i
$950$	20.4121	+	11.7849i	0.662256	+	0.382354i
$951$	0.559370	−	2.08760i	0.0181388	−	0.0676949i
$952$	4.74198	+	7.84399i	0.153688	+	0.254225i
$953$	33.8927	+	19.5680i	1.09789	+	0.633869i	0.935667	−	0.352884i	$-0.114799\pi$
$953$	33.8927	+	19.5680i	1.09789	+	0.633869i	0.162227	+	0.986754i	$0.448132\pi$
$954$	1.73000	+	6.45646i	0.0560109	+	0.209036i
$955$	26.7696	+	26.7696i	0.866245	+	0.866245i
$956$	8.18763	+	8.18763i	0.264807	+	0.264807i
$957$	1.03071	+	3.84667i	0.0333182	+	0.124345i
$958$	6.69673	+	3.86636i	0.216362	+	0.124916i
$959$	22.6917	+	37.5357i	0.732753	+	1.21209i
$960$	0.807342	−	3.01304i	0.0260569	−	0.0972455i
$961$	−68.8031	−	39.7235i	−2.21945	−	1.28140i
$962$	2.82947	−	16.8225i	0.0912259	−	0.542379i
$963$	−9.85768	−	17.0740i	−0.317659	−	0.550202i
$964$	−4.68689	−	4.68689i	−0.150955	−	0.150955i
$965$	−27.4612	+	15.8547i	−0.884008	+	0.510382i
$966$	−0.395820	−	19.6417i	−0.0127353	−	0.631961i
$967$	−41.6802	+	41.6802i	−1.34035	+	1.34035i	−0.444634	+	0.895713i	$0.646666\pi$
$967$	−41.6802	+	41.6802i	−1.34035	+	1.34035i	−0.895713	+	0.444634i	$0.853334\pi$
$968$	−8.36242	−	2.24070i	−0.268778	−	0.0720189i
$969$	−12.2064	+	12.2064i	−0.392127	+	0.392127i
$970$	3.57303	−	13.3347i	0.114723	−	0.428153i
$971$	−17.6946	+	10.2160i	−0.567847	+	0.327847i	−0.756289	−	0.654238i	$-0.772990\pi$
$971$	−17.6946	+	10.2160i	−0.567847	+	0.327847i	0.188442	+	0.982084i	$0.439656\pi$
$972$	−0.500000	−	0.866025i	−0.0160375	−	0.0277778i
$973$	−39.6539	−	38.0872i	−1.27124	−	1.22102i
$974$			13.7987i			0.442139i
$975$	2.82886	−	16.8188i	0.0905960	−	0.538634i
$976$	−6.60836	+	3.81534i	−0.211528	+	0.122126i
$977$	−10.6745	−	39.8379i	−0.341508	−	1.27453i	−0.896639	−	0.442763i	$-0.853998\pi$
$977$	−10.6745	−	39.8379i	−0.341508	−	1.27453i	0.555131	−	0.831763i	$-0.312668\pi$
$978$		−	4.66903i		−	0.149299i
$979$	6.08325	−	10.5365i	0.194422	−	0.336748i
$980$	4.79709	−	21.3019i	0.153237	−	0.680463i
$981$	2.77782	+	10.3670i	0.0886890	+	0.330992i
$982$	2.77420	−	10.3534i	0.0885282	−	0.330392i
$983$	32.1555	+	8.61605i	1.02560	+	0.274809i	0.732135	−	0.681160i	$-0.238524\pi$
$983$	32.1555	+	8.61605i	1.02560	+	0.274809i	0.293468	+	0.955969i	$0.405191\pi$
$984$	3.16741			0.100973
$985$	−18.3034			−0.583193
$986$	−8.70694	−	2.33302i	−0.277286	−	0.0742984i
$987$	−12.4585	+	22.6193i	−0.396558	+	0.719980i
$988$	7.46387	−	16.3420i	0.237457	−	0.519908i
$989$	27.9507	−	48.4120i	0.888779	−	1.53941i
$990$	4.61161	−	1.23568i	0.146567	−	0.0392724i
$991$	−21.8504	+	37.8461i	−0.694102	+	1.20222i	0.276381	+	0.961048i	$0.410865\pi$
$991$	−21.8504	+	37.8461i	−0.694102	+	1.20222i	−0.970483	+	0.241171i	$0.922468\pi$
$992$	5.25469	+	9.10138i	0.166836	+	0.288969i
$993$	−13.0910	−	13.0910i	−0.415431	−	0.415431i
$994$	−5.08100	−	4.88026i	−0.161160	−	0.154793i
$995$	−36.0965	+	9.67203i	−1.14434	+	0.306624i
$996$	7.36660	−	1.97387i	0.233420	−	0.0625446i
$997$			45.0828i			1.42779i	0.700254	+	0.713894i	$0.253070\pi$
$997$			45.0828i			1.42779i	−0.700254	+	0.713894i	$0.746930\pi$
$998$	−1.27071	−	0.733644i	−0.0402236	−	0.0232231i
$999$	3.34550	−	3.34550i	0.105847	−	0.105847i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.cg.b.145.4	yes	40
7.3	odd	6		546.2.by.b.535.4	yes	40
13.7	odd	12		546.2.by.b.397.4	✓	40
91.59	even	12	inner	546.2.cg.b.241.4	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.by.b.397.4	✓	40	13.7	odd	12
546.2.by.b.535.4	yes	40	7.3	odd	6
546.2.cg.b.145.4	yes	40	1.1	even	1	trivial
546.2.cg.b.241.4	yes	40	91.59	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.866025 - 0.500000i) q^{3} -1.00000i q^{4} +(3.01304 - 0.807342i) q^{5} +(0.965926 - 0.258819i) q^{6} +(2.56888 + 0.633142i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.866025 - 0.500000i) q^{3} -1.00000i q^{4} +(3.01304 - 0.807342i) q^{5} +(0.965926 - 0.258819i) q^{6} +(2.56888 + 0.633142i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.55967 + 2.70142i) q^{10} +(-1.47840 + 0.396136i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(-0.598039 + 3.55561i) q^{13} +(-2.26417 + 1.36877i) q^{14} +(-3.01304 - 0.807342i) q^{15} -1.00000 q^{16} +3.46440 q^{17} +(-0.965926 - 0.258819i) q^{18} +(1.28965 - 4.81303i) q^{19} +(-0.807342 - 3.01304i) q^{20} +(-1.90814 - 1.83276i) q^{21} +(0.765275 - 1.32550i) q^{22} -7.42537i q^{23} +(-0.258819 - 0.965926i) q^{24} +(4.09650 - 2.36511i) q^{25} +(-2.09132 - 2.93707i) q^{26} -1.00000i q^{27} +(0.633142 - 2.56888i) q^{28} +(1.30096 + 2.25333i) q^{29} +(2.70142 - 1.55967i) q^{30} +(-2.72003 + 10.1513i) q^{31} +(0.707107 - 0.707107i) q^{32} +(1.47840 + 0.396136i) q^{33} +(-2.44970 + 2.44970i) q^{34} +(8.25130 - 0.166280i) q^{35} +(0.866025 - 0.500000i) q^{36} +(3.34550 + 3.34550i) q^{37} +(2.49141 + 4.31525i) q^{38} +(2.29572 - 2.78023i) q^{39} +(2.70142 + 1.55967i) q^{40} +(-0.819786 + 3.05948i) q^{41} +(2.64521 - 0.0533064i) q^{42} +(6.51981 + 3.76421i) q^{43} +(0.396136 + 1.47840i) q^{44} +(2.20570 + 2.20570i) q^{45} +(5.25053 + 5.25053i) q^{46} +(-2.52616 - 9.42774i) q^{47} +(0.866025 + 0.500000i) q^{48} +(6.19826 + 3.25293i) q^{49} +(-1.22427 + 4.56905i) q^{50} +(-3.00026 - 1.73220i) q^{51} +(3.55561 + 0.598039i) q^{52} +(-3.34211 - 5.78870i) q^{53} +(0.707107 + 0.707107i) q^{54} +(-4.13466 + 2.38715i) q^{55} +(1.36877 + 2.26417i) q^{56} +(-3.52339 + 3.52339i) q^{57} +(-2.51326 - 0.673426i) q^{58} +(6.02046 - 6.02046i) q^{59} +(-0.807342 + 3.01304i) q^{60} +(6.60836 - 3.81534i) q^{61} +(-5.25469 - 9.10138i) q^{62} +(0.736122 + 2.54128i) q^{63} +1.00000i q^{64} +(1.06868 + 11.1960i) q^{65} +(-1.32550 + 0.765275i) q^{66} +(0.779022 + 2.90735i) q^{67} -3.46440i q^{68} +(-3.71268 + 6.43056i) q^{69} +(-5.71697 + 5.95213i) q^{70} +(0.689184 + 2.57207i) q^{71} +(-0.258819 + 0.965926i) q^{72} +(-6.59087 - 1.76602i) q^{73} -4.73126 q^{74} -4.73023 q^{75} +(-4.81303 - 1.28965i) q^{76} +(-4.04863 + 0.0815882i) q^{77} +(0.342598 + 3.58924i) q^{78} +(7.33360 - 12.7022i) q^{79} +(-3.01304 + 0.807342i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-1.58370 - 2.74306i) q^{82} +(-5.39273 - 5.39273i) q^{83} +(-1.83276 + 1.90814i) q^{84} +(10.4384 - 2.79696i) q^{85} +(-7.27190 + 1.94850i) q^{86} -2.60192i q^{87} +(-1.32550 - 0.765275i) q^{88} +(-5.62087 + 5.62087i) q^{89} -3.11933 q^{90} +(-3.78749 + 8.75528i) q^{91} -7.42537 q^{92} +(7.43125 - 7.43125i) q^{93} +(8.45268 + 4.88016i) q^{94} -15.5431i q^{95} +(-0.965926 + 0.258819i) q^{96} +(-4.27487 + 1.14545i) q^{97} +(-6.68300 + 2.08267i) q^{98} +(-1.08226 - 1.08226i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 4 q^{7} + 20 q^{9}+O(q^{10}) \) 40 * q + 4 * q^7 + 20 * q^9	\( 40 q + 4 q^{7} + 20 q^{9} + 8 q^{11} - 20 q^{12} + 4 q^{14} - 40 q^{16} + 16 q^{17} + 4 q^{19} + 4 q^{21} - 4 q^{22} - 24 q^{25} + 8 q^{26} - 4 q^{28} - 12 q^{29} - 8 q^{33} - 8 q^{34} - 32 q^{35} + 40 q^{37} + 8 q^{38} + 20 q^{39} + 20 q^{41} + 12 q^{42} - 24 q^{43} - 4 q^{44} + 32 q^{46} + 4 q^{47} + 32 q^{49} - 16 q^{50} + 24 q^{51} + 16 q^{52} - 4 q^{53} + 24 q^{55} + 12 q^{56} + 8 q^{57} + 12 q^{58} + 24 q^{59} + 60 q^{61} + 32 q^{62} - 4 q^{63} + 44 q^{65} - 12 q^{67} - 8 q^{69} - 24 q^{70} - 28 q^{71} + 60 q^{73} - 40 q^{74} - 72 q^{75} + 4 q^{76} - 12 q^{77} + 4 q^{78} - 20 q^{81} - 24 q^{82} + 60 q^{83} - 8 q^{84} - 4 q^{85} - 20 q^{86} - 36 q^{89} - 16 q^{92} - 24 q^{93} - 48 q^{97} - 88 q^{98} + 4 q^{99}+O(q^{100}) \) 40 * q + 4 * q^7 + 20 * q^9 + 8 * q^11 - 20 * q^12 + 4 * q^14 - 40 * q^16 + 16 * q^17 + 4 * q^19 + 4 * q^21 - 4 * q^22 - 24 * q^25 + 8 * q^26 - 4 * q^28 - 12 * q^29 - 8 * q^33 - 8 * q^34 - 32 * q^35 + 40 * q^37 + 8 * q^38 + 20 * q^39 + 20 * q^41 + 12 * q^42 - 24 * q^43 - 4 * q^44 + 32 * q^46 + 4 * q^47 + 32 * q^49 - 16 * q^50 + 24 * q^51 + 16 * q^52 - 4 * q^53 + 24 * q^55 + 12 * q^56 + 8 * q^57 + 12 * q^58 + 24 * q^59 + 60 * q^61 + 32 * q^62 - 4 * q^63 + 44 * q^65 - 12 * q^67 - 8 * q^69 - 24 * q^70 - 28 * q^71 + 60 * q^73 - 40 * q^74 - 72 * q^75 + 4 * q^76 - 12 * q^77 + 4 * q^78 - 20 * q^81 - 24 * q^82 + 60 * q^83 - 8 * q^84 - 4 * q^85 - 20 * q^86 - 36 * q^89 - 16 * q^92 - 24 * q^93 - 48 * q^97 - 88 * q^98 + 4 * q^99

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