LMFDB - Embedded newform 546.2.by.b.397.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(19,546)]

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, 5]))

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

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

chi := DirichletCharacter("546.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.by (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			397.4
Character	$\chi$	$=$	546.397
Dual form			546.2.by.b.535.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 + 0.965926i) q^{2} +1.00000i q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.807342 + 3.01304i) q^{5} +(-0.965926 - 0.258819i) q^{6} +(1.90814 + 1.83276i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(-0.258819 + 0.965926i) q^{2} +1.00000i q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.807342 + 3.01304i) q^{5} +(-0.965926 - 0.258819i) q^{6} +(1.90814 + 1.83276i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000 q^{9} -3.11933 q^{10} +(1.08226 - 1.08226i) 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} +(0.500000 + 0.866025i) q^{16} +(1.73220 - 3.00026i) q^{17} +(0.258819 - 0.965926i) q^{18} +(-3.52339 + 3.52339i) q^{19} +(0.807342 - 3.01304i) q^{20} +(-1.83276 + 1.90814i) q^{21} +(0.765275 + 1.32550i) q^{22} +(6.43056 - 3.71268i) q^{23} +(0.707107 + 0.707107i) q^{24} +(-4.09650 + 2.36511i) q^{25} +(-3.58924 - 0.342598i) q^{26} -1.00000i q^{27} +(-0.736122 - 2.54128i) q^{28} +(1.30096 - 2.25333i) q^{29} -3.11933i q^{30} +(-10.1513 - 2.72003i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(1.08226 + 1.08226i) q^{33} +(2.44970 + 2.44970i) q^{34} +(-3.98165 + 7.22897i) q^{35} +(0.866025 + 0.500000i) q^{36} +(-4.57004 - 1.22454i) q^{37} +(-2.49141 - 4.31525i) q^{38} +(-3.55561 + 0.598039i) q^{39} +(2.70142 + 1.55967i) q^{40} +(0.819786 + 3.05948i) q^{41} +(-1.36877 - 2.26417i) q^{42} +(6.51981 - 3.76421i) q^{43} +(-1.47840 + 0.396136i) q^{44} +(-0.807342 - 3.01304i) q^{45} +(1.92183 + 7.17236i) q^{46} +(-9.42774 + 2.52616i) q^{47} +(-0.866025 + 0.500000i) q^{48} +(0.282014 + 6.99432i) q^{49} +(-1.22427 - 4.56905i) q^{50} +(3.00026 + 1.73220i) q^{51} +(1.25989 - 3.37827i) q^{52} +(-3.34211 - 5.78870i) q^{53} +(0.965926 + 0.258819i) q^{54} +(4.13466 + 2.38715i) q^{55} +(2.64521 - 0.0533064i) q^{56} +(-3.52339 - 3.52339i) q^{57} +(1.83983 + 1.83983i) q^{58} +(8.22410 - 2.20364i) q^{59} +(3.01304 + 0.807342i) q^{60} +7.63067i q^{61} +(5.25469 - 9.10138i) q^{62} +(-1.90814 - 1.83276i) q^{63} -1.00000i q^{64} +(-10.2304 + 4.67251i) q^{65} +(-1.32550 + 0.765275i) q^{66} +(2.12833 + 2.12833i) q^{67} +(-3.00026 + 1.73220i) q^{68} +(3.71268 + 6.43056i) q^{69} +(-5.95213 - 5.71697i) q^{70} +(0.689184 - 2.57207i) q^{71} +(-0.707107 + 0.707107i) q^{72} +(-1.76602 + 6.59087i) q^{73} +(2.36563 - 4.09739i) q^{74} +(-2.36511 - 4.09650i) 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} +(-2.20570 + 2.20570i) q^{80} +1.00000 q^{81} -3.16741 q^{82} +(5.39273 - 5.39273i) q^{83} +(2.54128 - 0.736122i) q^{84} +(10.4384 + 2.79696i) q^{85} +(1.94850 + 7.27190i) q^{86} +(2.25333 + 1.30096i) q^{87} -1.53055i q^{88} +(2.05738 - 7.67825i) q^{89} +3.11933 q^{90} +(-5.37542 + 7.88067i) q^{91} -7.42537 q^{92} +(2.72003 - 10.1513i) q^{93} -9.76032i q^{94} +(-13.4607 - 7.77153i) q^{95} +(-0.258819 - 0.965926i) q^{96} +(4.27487 + 1.14545i) q^{97} +(-6.82898 - 1.53786i) q^{98} +(-1.08226 + 1.08226i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{7} - 40 q^{9}+O(q^{10}) $ 40 * q - 4 * q^7 - 40 * q^9	$ 40 q - 4 q^{7} - 40 q^{9} - 4 q^{11} + 20 q^{12} + 4 q^{14} + 20 q^{16} + 8 q^{17} + 8 q^{19} - 8 q^{21} - 4 q^{22} + 24 q^{23} + 24 q^{25} - 8 q^{26} + 4 q^{28} - 12 q^{29} + 24 q^{31} - 4 q^{33} + 8 q^{34} + 28 q^{35} - 8 q^{37} - 8 q^{38} - 16 q^{39} - 20 q^{41} - 12 q^{42} - 24 q^{43} + 8 q^{44} - 4 q^{46} - 16 q^{47} + 4 q^{49} - 16 q^{50} - 24 q^{51} - 4 q^{52} - 4 q^{53} - 24 q^{55} + 12 q^{56} + 8 q^{57} + 24 q^{58} - 12 q^{59} - 32 q^{62} + 4 q^{63} - 4 q^{65} - 24 q^{67} + 24 q^{68} + 8 q^{69} + 52 q^{70} - 28 q^{71} + 108 q^{73} + 20 q^{74} - 36 q^{75} - 4 q^{76} + 12 q^{77} + 4 q^{78} + 40 q^{81} - 48 q^{82} - 60 q^{83} - 8 q^{84} - 4 q^{85} - 20 q^{86} - 36 q^{87} - 60 q^{89} - 40 q^{91} - 16 q^{92} - 48 q^{95} + 48 q^{97} - 8 q^{98} + 4 q^{99}+O(q^{100}) $ 40 * q - 4 * q^7 - 40 * q^9 - 4 * q^11 + 20 * q^12 + 4 * q^14 + 20 * q^16 + 8 * q^17 + 8 * q^19 - 8 * q^21 - 4 * q^22 + 24 * q^23 + 24 * q^25 - 8 * q^26 + 4 * q^28 - 12 * q^29 + 24 * q^31 - 4 * q^33 + 8 * q^34 + 28 * q^35 - 8 * q^37 - 8 * q^38 - 16 * q^39 - 20 * q^41 - 12 * q^42 - 24 * q^43 + 8 * q^44 - 4 * q^46 - 16 * q^47 + 4 * q^49 - 16 * q^50 - 24 * q^51 - 4 * q^52 - 4 * q^53 - 24 * q^55 + 12 * q^56 + 8 * q^57 + 24 * q^58 - 12 * q^59 - 32 * q^62 + 4 * q^63 - 4 * q^65 - 24 * q^67 + 24 * q^68 + 8 * q^69 + 52 * q^70 - 28 * q^71 + 108 * q^73 + 20 * q^74 - 36 * q^75 - 4 * q^76 + 12 * q^77 + 4 * q^78 + 40 * q^81 - 48 * q^82 - 60 * q^83 - 8 * q^84 - 4 * q^85 - 20 * q^86 - 36 * q^87 - 60 * q^89 - 40 * q^91 - 16 * q^92 - 48 * q^95 + 48 * q^97 - 8 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{11}{12}\right)$

Coefficient data

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

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

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

$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	0.807342	+	3.01304i	0.361054	+	1.34747i	0.872692	+	0.488272i	$0.162373\pi$
$5$	0.807342	+	3.01304i	0.361054	+	1.34747i	−0.511637	+	0.859202i	$0.670961\pi$
$6$	−0.965926	−	0.258819i	−0.394338	−	0.105662i
$7$	1.90814	+	1.83276i	0.721210	+	0.692716i
$7$	1.90814	+	1.83276i	0.721210	+	0.692716i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−1.00000			−0.333333
$10$	−3.11933			−0.986419
$11$	1.08226	−	1.08226i	0.326314	−	0.326314i	−0.524869	−	0.851183i	$-0.675886\pi$
$11$	1.08226	−	1.08226i	0.326314	−	0.326314i	0.851183	+	0.524869i	$0.175886\pi$
$12$	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
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	1.73220	−	3.00026i	0.420120	−	0.727670i	−0.575830	−	0.817569i	$-0.695321\pi$
$17$	1.73220	−	3.00026i	0.420120	−	0.727670i	0.995951	+	0.0898993i	$0.0286545\pi$
$18$	0.258819	−	0.965926i	0.0610042	−	0.227671i
$19$	−3.52339	+	3.52339i	−0.808320	+	0.808320i	−0.984380	−	0.176059i	$-0.943665\pi$
$19$	−3.52339	+	3.52339i	−0.808320	+	0.808320i	0.176059	+	0.984380i	$0.443665\pi$
$20$	0.807342	−	3.01304i	0.180527	−	0.673737i
$21$	−1.83276	+	1.90814i	−0.399940	+	0.416391i
$22$	0.765275	+	1.32550i	0.163157	+	0.282597i
$23$	6.43056	−	3.71268i	1.34086	−	0.774148i	0.353930	−	0.935272i	$-0.384845\pi$
$23$	6.43056	−	3.71268i	1.34086	−	0.774148i	0.986934	+	0.161124i	$0.0515118\pi$
$24$	0.707107	+	0.707107i	0.144338	+	0.144338i
$25$	−4.09650	+	2.36511i	−0.819299	+	0.473023i
$26$	−3.58924	−	0.342598i	−0.703907	−	0.0671890i
$27$		−	1.00000i		−	0.192450i
$28$	−0.736122	−	2.54128i	−0.139114	−	0.480258i
$29$	1.30096	−	2.25333i	0.241582	−	0.418432i	−0.719583	−	0.694406i	$-0.755667\pi$
$29$	1.30096	−	2.25333i	0.241582	−	0.418432i	0.961165	+	0.275974i	$0.0890004\pi$
$30$		−	3.11933i		−	0.569509i
$31$	−10.1513	−	2.72003i	−1.82322	−	0.488531i	−0.826045	−	0.563604i	$-0.809414\pi$
$31$	−10.1513	−	2.72003i	−1.82322	−	0.488531i	−0.997178	+	0.0750732i	$0.976081\pi$
$32$	−0.965926	+	0.258819i	−0.170753	+	0.0457532i
$33$	1.08226	+	1.08226i	0.188398	+	0.188398i
$34$	2.44970	+	2.44970i	0.420120	+	0.420120i
$35$	−3.98165	+	7.22897i	−0.673021	+	1.22192i
$36$	0.866025	+	0.500000i	0.144338	+	0.0833333i
$37$	−4.57004	−	1.22454i	−0.751311	−	0.201313i	−0.137211	−	0.990542i	$-0.543814\pi$
$37$	−4.57004	−	1.22454i	−0.751311	−	0.201313i	−0.614099	+	0.789229i	$0.710481\pi$
$38$	−2.49141	−	4.31525i	−0.404160	−	0.700026i
$39$	−3.55561	+	0.598039i	−0.569353	+	0.0957628i
$40$	2.70142	+	1.55967i	0.427132	+	0.246605i
$41$	0.819786	+	3.05948i	0.128029	+	0.477811i	0.999930	−	0.0118723i	$-0.00377914\pi$
$41$	0.819786	+	3.05948i	0.128029	+	0.477811i	−0.871900	+	0.489683i	$0.837112\pi$
$42$	−1.36877	−	2.26417i	−0.211206	−	0.349369i
$43$	6.51981	−	3.76421i	0.994261	−	0.574037i	0.0877159	−	0.996146i	$-0.472043\pi$
$43$	6.51981	−	3.76421i	0.994261	−	0.574037i	0.906545	+	0.422109i	$0.138710\pi$
$44$	−1.47840	+	0.396136i	−0.222877	+	0.0597197i
$45$	−0.807342	−	3.01304i	−0.120351	−	0.449158i
$46$	1.92183	+	7.17236i	0.283358	+	1.05751i
$47$	−9.42774	+	2.52616i	−1.37518	+	0.368478i	−0.869367	−	0.494167i	$-0.835473\pi$
$47$	−9.42774	+	2.52616i	−1.37518	+	0.368478i	−0.505810	+	0.862645i	$0.668806\pi$
$48$	−0.866025	+	0.500000i	−0.125000	+	0.0721688i
$49$	0.282014	+	6.99432i	0.0402877	+	0.999188i
$50$	−1.22427	−	4.56905i	−0.173138	−	0.646161i
$51$	3.00026	+	1.73220i	0.420120	+	0.242557i
$52$	1.25989	−	3.37827i	0.174715	−	0.468481i
$53$	−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	$0.985152\pi$
$54$	0.965926	+	0.258819i	0.131446	+	0.0352208i
$55$	4.13466	+	2.38715i	0.557517	+	0.321883i
$56$	2.64521	−	0.0533064i	0.353482	−	0.00712337i
$57$	−3.52339	−	3.52339i	−0.466684	−	0.466684i
$58$	1.83983	+	1.83983i	0.241582	+	0.241582i
$59$	8.22410	−	2.20364i	1.07069	−	0.286890i	0.319912	−	0.947447i	$-0.396347\pi$
$59$	8.22410	−	2.20364i	1.07069	−	0.286890i	0.750775	+	0.660558i	$0.229680\pi$
$60$	3.01304	+	0.807342i	0.388982	+	0.104227i
$61$			7.63067i			0.977008i	0.872562	+	0.488504i	$0.162457\pi$
$61$			7.63067i			0.977008i	−0.872562	+	0.488504i	$0.837543\pi$
$62$	5.25469	−	9.10138i	0.667346	−	1.15588i
$63$	−1.90814	−	1.83276i	−0.240403	−	0.230905i
$64$		−	1.00000i		−	0.125000i
$65$	−10.2304	+	4.67251i	−1.26892	+	0.579553i
$66$	−1.32550	+	0.765275i	−0.163157	+	0.0941989i
$67$	2.12833	+	2.12833i	0.260017	+	0.260017i	0.825061	−	0.565044i	$-0.191141\pi$
$67$	2.12833	+	2.12833i	0.260017	+	0.260017i	−0.565044	+	0.825061i	$0.691141\pi$
$68$	−3.00026	+	1.73220i	−0.363835	+	0.210060i
$69$	3.71268	+	6.43056i	0.446955	+	0.774148i
$70$	−5.95213	−	5.71697i	−0.711415	−	0.683309i
$71$	0.689184	−	2.57207i	0.0817911	−	0.305248i	−0.912896	−	0.408192i	$-0.866159\pi$
$71$	0.689184	−	2.57207i	0.0817911	−	0.305248i	0.994687	+	0.102944i	$0.0328261\pi$
$72$	−0.707107	+	0.707107i	−0.0833333	+	0.0833333i
$73$	−1.76602	+	6.59087i	−0.206697	+	0.771403i	0.782229	+	0.622991i	$0.214083\pi$
$73$	−1.76602	+	6.59087i	−0.206697	+	0.771403i	−0.988926	+	0.148412i	$0.952584\pi$
$74$	2.36563	−	4.09739i	0.274999	−	0.476312i
$75$	−2.36511	−	4.09650i	−0.273100	−	0.473023i
$76$	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	$-0.142212\pi$
$80$	−2.20570	+	2.20570i	−0.246605	+	0.246605i
$81$	1.00000			0.111111
$82$	−3.16741			−0.349782
$83$	5.39273	−	5.39273i	0.591929	−	0.591929i	−0.346223	−	0.938152i	$-0.612536\pi$
$83$	5.39273	−	5.39273i	0.591929	−	0.591929i	0.938152	+	0.346223i	$0.112536\pi$
$84$	2.54128	−	0.736122i	0.277277	−	0.0803175i
$85$	10.4384	+	2.79696i	1.13220	+	0.303373i
$86$	1.94850	+	7.27190i	0.210112	+	0.784149i
$87$	2.25333	+	1.30096i	0.241582	+	0.139477i
$88$		−	1.53055i		−	0.163157i
$89$	2.05738	−	7.67825i	0.218082	−	0.813893i	−0.766977	−	0.641675i	$-0.778240\pi$
$89$	2.05738	−	7.67825i	0.218082	−	0.813893i	0.985059	−	0.172218i	$-0.0550933\pi$
$90$	3.11933			0.328806
$91$	−5.37542	+	7.88067i	−0.563497	+	0.826118i
$92$	−7.42537			−0.774148
$93$	2.72003	−	10.1513i	0.282054	−	1.05264i
$94$		−	9.76032i		−	1.00670i
$95$	−13.4607	−	7.77153i	−1.38104	−	0.797342i
$96$	−0.258819	−	0.965926i	−0.0264156	−	0.0985844i
$97$	4.27487	+	1.14545i	0.434048	+	0.116303i	0.469226	−	0.883078i	$-0.344533\pi$
$97$	4.27487	+	1.14545i	0.434048	+	0.116303i	−0.0351779	+	0.999381i	$0.511200\pi$
$98$	−6.82898	−	1.53786i	−0.689831	−	0.155347i
$99$	−1.08226	+	1.08226i	−0.108771	+	0.108771i
$100$	4.73023			0.473023
$101$	8.44761			0.840569			0.420284	−	0.907392i	$-0.361930\pi$
$101$	8.44761			0.840569			0.420284	+	0.907392i	$0.361930\pi$
$102$	−2.44970	+	2.44970i	−0.242557	+	0.242557i
$103$	7.73745	−	13.4017i	0.762394	−	1.32051i	−0.179219	−	0.983809i	$-0.557357\pi$
$103$	7.73745	−	13.4017i	0.762394	−	1.32051i	0.941613	−	0.336696i	$-0.109310\pi$
$104$	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
$107$	9.85768	+	17.0740i	0.952978	+	1.65061i	0.738930	+	0.673782i	$0.235332\pi$
$107$	9.85768	+	17.0740i	0.952978	+	1.65061i	0.214048	+	0.976823i	$0.431335\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	−2.77782	+	10.3670i	−0.266067	+	0.992976i	0.695527	+	0.718500i	$0.255171\pi$
$109$	−2.77782	+	10.3670i	−0.266067	+	0.992976i	−0.961594	+	0.274476i	$0.911496\pi$
$110$	−3.37594	+	3.37594i	−0.321883	+	0.321883i
$111$	1.22454	−	4.57004i	0.116228	−	0.433769i
$112$	−0.633142	+	2.56888i	−0.0598263	+	0.242736i
$113$	−0.926673	−	1.60505i	−0.0871741	−	0.150990i	0.819141	−	0.573592i	$-0.194450\pi$
$113$	−0.926673	−	1.60505i	−0.0871741	−	0.150990i	−0.906316	+	0.422602i	$0.861117\pi$
$114$	4.31525	−	2.49141i	0.404160	−	0.233342i
$115$	16.3781	+	16.3781i	1.52727	+	1.52727i
$116$	−2.25333	+	1.30096i	−0.209216	+	0.120791i
$117$	−0.598039	−	3.55561i	−0.0552887	−	0.328716i
$118$			8.51422i			0.783797i
$119$	8.80403	−	2.55022i	0.807064	−	0.233778i
$120$	−1.55967	+	2.70142i	−0.142377	+	0.246605i
$121$			8.65741i			0.787038i
$122$	−7.37066	−	1.97496i	−0.667309	−	0.178805i
$123$	−3.05948	+	0.819786i	−0.275864	+	0.0739176i
$124$	7.43125	+	7.43125i	0.667346	+	0.667346i
$125$	0.595042	+	0.595042i	0.0532222	+	0.0532222i
$126$	2.26417	−	1.36877i	0.201708	−	0.121940i
$127$	−9.01483	−	5.20472i	−0.799937	−	0.461844i	0.0435122	−	0.999053i	$-0.486145\pi$
$127$	−9.01483	−	5.20472i	−0.799937	−	0.461844i	−0.843449	+	0.537209i	$0.819479\pi$
$128$	0.965926	+	0.258819i	0.0853766	+	0.0228766i
$129$	3.76421	+	6.51981i	0.331420	+	0.574037i
$130$	−1.86548	−	11.0911i	−0.163613	−	0.972755i
$131$	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
$133$	−13.1806	+	0.265616i	−1.14291	+	0.0230319i
$134$	−2.60666	+	1.50496i	−0.225181	+	0.130008i
$135$	3.01304	−	0.807342i	0.259321	−	0.0694850i
$136$	−0.896653	−	3.34635i	−0.0768874	−	0.286948i
$137$	4.29074	+	16.0133i	0.366583	+	1.36810i	0.865263	+	0.501319i	$0.167152\pi$
$137$	4.29074	+	16.0133i	0.366583	+	1.36810i	−0.498680	+	0.866786i	$0.666182\pi$
$138$	−7.17236	+	1.92183i	−0.610551	+	0.163597i
$139$	17.9972	−	10.3907i	1.52650	−	0.881327i	0.526999	−	0.849866i	$-0.323317\pi$
$139$	17.9972	−	10.3907i	1.52650	−	0.881327i	0.999505	−	0.0314614i	$-0.0100161\pi$
$140$	7.06269	−	4.26965i	0.596907	−	0.360851i
$141$	−2.52616	−	9.42774i	−0.212741	−	0.793959i
$142$	2.30605	+	1.33140i	0.193520	+	0.111729i
$143$	4.49534	+	3.20087i	0.375919	+	0.267670i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	7.83969	+	2.10064i	0.651051	+	0.174449i
$146$	−5.90921	−	3.41168i	−0.489050	−	0.282353i
$147$	−6.99432	+	0.282014i	−0.576882	+	0.0232601i
$148$	3.34550	+	3.34550i	0.274999	+	0.274999i
$149$	−6.90337	−	6.90337i	−0.565546	−	0.565546i	0.365332	−	0.930877i	$-0.380956\pi$
$149$	−6.90337	−	6.90337i	−0.565546	−	0.565546i	−0.930877	+	0.365332i	$0.880956\pi$
$150$	4.56905	−	1.22427i	0.373061	−	0.0999614i
$151$	8.30920	+	2.22644i	0.676193	+	0.181185i	0.580543	−	0.814230i	$-0.302840\pi$
$151$	8.30920	+	2.22644i	0.676193	+	0.181185i	0.0956501	+	0.995415i	$0.469507\pi$
$152$			4.98282i			0.404160i
$153$	−1.73220	+	3.00026i	−0.140040	+	0.242557i
$154$	−0.969056	+	3.93180i	−0.0780887	+	0.316833i
$155$		−	32.7822i		−	2.63313i
$156$	3.37827	+	1.25989i	0.270478	+	0.100872i
$157$	−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	$0.484342\pi$
$158$	10.3713	+	10.3713i	0.825095	+	0.825095i
$159$	5.78870	−	3.34211i	0.459074	−	0.265047i
$160$	−1.55967	−	2.70142i	−0.123302	−	0.213566i
$161$	19.0749	+	4.70131i	1.50331	+	0.370515i
$162$	−0.258819	+	0.965926i	−0.0203347	+	0.0758903i
$163$	3.30151	−	3.30151i	0.258594	−	0.258594i	−0.565888	−	0.824482i	$-0.691467\pi$
$163$	3.30151	−	3.30151i	0.258594	−	0.258594i	0.824482	+	0.565888i	$0.191467\pi$
$164$	0.819786	−	3.05948i	0.0640145	−	0.238905i
$165$	−2.38715	+	4.13466i	−0.185839	+	0.321883i
$166$	3.81323	+	6.60471i	0.295964	+	0.512625i
$167$	13.5903	−	3.64150i	1.05165	−	0.281788i	0.308715	−	0.951155i	$-0.400101\pi$
$167$	13.5903	−	3.64150i	1.05165	−	0.281788i	0.742932	+	0.669367i	$0.233434\pi$
$168$	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
$171$	3.52339	−	3.52339i	0.269440	−	0.269440i
$172$	−7.52842			−0.574037
$173$	−6.95387			−0.528693			−0.264347	−	0.964428i	$-0.585156\pi$
$173$	−6.95387			−0.528693			−0.264347	+	0.964428i	$0.585156\pi$
$174$	−1.83983	+	1.83983i	−0.139477	+	0.139477i
$175$	−12.1514	−	2.99490i	−0.918557	−	0.226393i
$176$	1.47840	+	0.396136i	0.111438	+	0.0298598i
$177$	2.20364	+	8.22410i	0.165636	+	0.618162i
$178$	6.88413	+	3.97455i	0.515987	+	0.297905i
$179$		−	4.11394i		−	0.307490i	−0.988111	−	0.153745i	$-0.950867\pi$
$179$		−	4.11394i		−	0.307490i	0.988111	−	0.153745i	$-0.0491335\pi$
$180$	−0.807342	+	3.01304i	−0.0601757	+	0.224579i
$181$	4.55457			0.338538			0.169269	−	0.985570i	$-0.445859\pi$
$181$	4.55457			0.338538			0.169269	+	0.985570i	$0.445859\pi$
$182$	−6.22088	−	7.23192i	−0.461122	−	0.536066i
$183$	−7.63067			−0.564076
$184$	1.92183	−	7.17236i	0.141679	−	0.528753i
$185$		−	14.7584i		−	1.08506i
$186$	9.10138	+	5.25469i	0.667346	+	0.385292i
$187$	−1.37237	−	5.12177i	−0.100358	−	0.374541i
$188$	9.42774	+	2.52616i	0.687589	+	0.184239i
$189$	1.83276	−	1.90814i	0.133313	−	0.138797i
$190$	10.9906	−	10.9906i	0.797342	−	0.797342i
$191$	−12.1366			−0.878172			−0.439086	−	0.898445i	$-0.644698\pi$
$191$	−12.1366			−0.878172			−0.439086	+	0.898445i	$0.644698\pi$
$192$	1.00000			0.0721688
$193$	7.18808	−	7.18808i	0.517409	−	0.517409i	−0.399377	−	0.916787i	$-0.630774\pi$
$193$	7.18808	−	7.18808i	0.517409	−	0.517409i	0.916787	+	0.399377i	$0.130774\pi$
$194$	−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	−0.455008	−	0.890487i	$-0.650364\pi$
$197$	−5.66778	+	1.51868i	−0.403813	+	0.108201i	0.0511952	+	0.998689i	$0.483697\pi$
$198$	−0.765275	−	1.32550i	−0.0543857	−	0.0941989i
$199$	−5.99004	+	10.3751i	−0.424623	+	0.735468i	−0.996385	−	0.0849512i	$-0.972927\pi$
$199$	−5.99004	+	10.3751i	−0.424623	+	0.735468i	0.571762	+	0.820419i	$0.306260\pi$
$200$	−1.22427	+	4.56905i	−0.0865691	+	0.323080i
$201$	−2.12833	+	2.12833i	−0.150121	+	0.150121i
$202$	−2.18640	+	8.15976i	−0.153835	+	0.574119i
$203$	6.61221	−	1.91533i	0.464087	−	0.134430i
$204$	−1.73220	−	3.00026i	−0.121278	−	0.210060i
$205$	−8.55650	+	4.94010i	−0.597612	+	0.345031i
$206$	10.9424	+	10.9424i	0.762394	+	0.762394i
$207$	−6.43056	+	3.71268i	−0.446955	+	0.258049i
$208$	−2.78023	+	2.29572i	−0.192774	+	0.159180i
$209$			7.62646i			0.527533i
$210$	5.71697	−	5.95213i	0.394508	−	0.410736i
$211$	1.72829	−	2.99349i	0.118981	−	0.206080i	−0.800383	−	0.599488i	$-0.795371\pi$
$211$	1.72829	−	2.99349i	0.118981	−	0.206080i	0.919364	+	0.393408i	$0.128704\pi$
$212$			6.68422i			0.459074i
$213$	2.57207	+	0.689184i	0.176235	+	0.0472221i
$214$	−19.0436	+	5.10271i	−1.30179	+	0.348814i
$215$	16.6054	+	16.6054i	1.13248	+	1.13248i
$216$	−0.707107	−	0.707107i	−0.0481125	−	0.0481125i
$217$	−14.3849	−	23.7950i	−0.976513	−	1.61531i
$218$	−9.29477	−	5.36634i	−0.629521	−	0.363454i
$219$	−6.59087	−	1.76602i	−0.445370	−	0.119336i
$220$	−2.38715	−	4.13466i	−0.160941	−	0.278759i
$221$	11.7037	+	4.36476i	0.787274	+	0.293605i
$222$	4.09739	+	2.36563i	0.274999	+	0.158771i
$223$	−2.65061	−	9.89222i	−0.177498	−	0.662432i	−0.996113	−	0.0880887i	$-0.971924\pi$
$223$	−2.65061	−	9.89222i	−0.177498	−	0.662432i	0.818614	−	0.574343i	$-0.194743\pi$
$224$	−2.31748	−	1.27644i	−0.154843	−	0.0852859i
$225$	4.09650	−	2.36511i	0.273100	−	0.157674i
$226$	1.79020	−	0.479681i	0.119082	−	0.0319079i
$227$	1.68137	+	6.27496i	0.111597	+	0.416484i	0.999010	−	0.0444908i	$-0.0141665\pi$
$227$	1.68137	+	6.27496i	0.111597	+	0.416484i	−0.887413	+	0.460975i	$0.847500\pi$
$228$	1.28965	+	4.81303i	0.0854091	+	0.318751i
$229$	−23.1055	+	6.19109i	−1.52685	+	0.409119i	−0.921991	−	0.387212i	$-0.873438\pi$
$229$	−23.1055	+	6.19109i	−1.52685	+	0.409119i	−0.604862	+	0.796331i	$0.706772\pi$
$230$	−20.0590	+	11.5811i	−1.32265	+	0.763635i
$231$	0.0815882	+	4.04863i	0.00536811	+	0.266381i
$232$	−0.673426	−	2.51326i	−0.0442126	−	0.165004i
$233$	−22.0693	−	12.7417i	−1.44581	−	0.834737i	−0.447579	−	0.894244i	$-0.647714\pi$
$233$	−22.0693	−	12.7417i	−1.44581	−	0.834737i	−0.998228	+	0.0595070i	$0.981047\pi$
$234$	3.58924	+	0.342598i	0.234636	+	0.0223963i
$235$	−15.2228	−	26.3667i	−0.993028	−	1.71997i
$236$	−8.22410	−	2.20364i	−0.535344	−	0.143445i
$237$	12.7022	+	7.33360i	0.825095	+	0.476369i
$238$	0.184675	+	9.16408i	0.0119707	+	0.594019i
$239$	−8.18763	−	8.18763i	−0.529614	−	0.529614i	0.390843	−	0.920457i	$-0.372183\pi$
$239$	−8.18763	−	8.18763i	−0.529614	−	0.529614i	−0.920457	+	0.390843i	$0.872183\pi$
$240$	−2.20570	−	2.20570i	−0.142377	−	0.142377i
$241$	6.40241	−	1.71552i	0.412415	−	0.110506i	−0.0466447	−	0.998912i	$-0.514853\pi$
$241$	6.40241	−	1.71552i	0.412415	−	0.110506i	0.459060	+	0.888405i	$0.348186\pi$
$242$	−8.36242	−	2.24070i	−0.537557	−	0.144038i
$243$			1.00000i			0.0641500i
$244$	3.81534	−	6.60836i	0.244252	−	0.423057i
$245$	−20.8465	+	6.49653i	−1.33183	+	0.415048i
$246$		−	3.16741i		−	0.201947i
$247$	−14.6349	−	10.4207i	−0.931196	−	0.663051i
$248$	−9.10138	+	5.25469i	−0.577939	+	0.333673i
$249$	5.39273	+	5.39273i	0.341750	+	0.341750i
$250$	−0.728774	+	0.420758i	−0.0460917	+	0.0266111i
$251$	11.2754	+	19.5296i	0.711697	+	1.23270i	0.964220	+	0.265105i	$0.0854065\pi$
$251$	11.2754	+	19.5296i	0.711697	+	1.23270i	−0.252523	+	0.967591i	$0.581260\pi$
$252$	0.736122	+	2.54128i	0.0463713	+	0.160086i
$253$	2.94145	−	10.9777i	0.184928	−	0.690159i
$254$	7.36058	−	7.36058i	0.461844	−	0.461844i
$255$	−2.79696	+	10.4384i	−0.175152	+	0.653677i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−9.96202	−	17.2547i	−0.621414	−	1.07632i	−0.989223	−	0.146419i	$-0.953225\pi$
$257$	−9.96202	−	17.2547i	−0.621414	−	1.07632i	0.367809	−	0.929901i	$-0.380108\pi$
$258$	−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
$262$	−0.240795	+	0.240795i	−0.0148763	+	0.0148763i
$263$	−10.1745			−0.627387			−0.313694	−	0.949524i	$-0.601566\pi$
$263$	−10.1745			−0.627387			−0.313694	+	0.949524i	$0.601566\pi$
$264$	1.53055			0.0941989
$265$	14.7434	−	14.7434i	0.905679	−	0.905679i
$266$	3.15483	−	12.8003i	0.193435	−	0.784834i
$267$	7.67825	+	2.05738i	0.469901	+	0.125910i
$268$	−0.779022	−	2.90735i	−0.0475864	−	0.177595i
$269$	25.5333	+	14.7417i	1.55679	+	0.898815i	0.997561	+	0.0698041i	$0.0222374\pi$
$269$	25.5333	+	14.7417i	1.55679	+	0.898815i	0.559233	+	0.829011i	$0.311096\pi$
$270$			3.11933i			0.189836i
$271$	−0.696653	+	2.59995i	−0.0423187	+	0.157935i	−0.983852	−	0.178985i	$-0.942719\pi$
$271$	−0.696653	+	2.59995i	−0.0423187	+	0.157935i	0.941533	+	0.336920i	$0.109385\pi$
$272$	3.46440			0.210060
$273$	−7.88067	−	5.37542i	−0.476960	−	0.325335i
$274$	−16.5781			−1.00152
$275$	−1.87381	+	6.99316i	−0.112995	+	0.421703i
$276$		−	7.42537i		−	0.446955i
$277$	5.84952	+	3.37722i	0.351463	+	0.202918i	0.665330	−	0.746550i	$-0.268291\pi$
$277$	5.84952	+	3.37722i	0.351463	+	0.202918i	−0.313866	+	0.949467i	$0.601624\pi$
$278$	5.37862	+	20.0733i	0.322588	+	1.20392i
$279$	10.1513	+	2.72003i	0.607741	+	0.162844i
$280$	2.29621	+	7.92711i	0.137225	+	0.473735i
$281$	0.0630402	−	0.0630402i	0.00376067	−	0.00376067i	−0.705224	−	0.708985i	$-0.749154\pi$
$281$	0.0630402	−	0.0630402i	0.00376067	−	0.00376067i	0.708985	+	0.705224i	$0.249154\pi$
$282$	9.76032			0.581218
$283$	−28.6791			−1.70480			−0.852398	−	0.522893i	$-0.824853\pi$
$283$	−28.6791			−1.70480			−0.852398	+	0.522893i	$0.824853\pi$
$284$	−1.88288	+	1.88288i	−0.111729	+	0.111729i
$285$	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
$289$	2.49896	+	4.32833i	0.146998	+	0.254608i
$290$	−4.05812	+	7.02888i	−0.238301	+	0.412750i
$291$	−1.14545	+	4.27487i	−0.0671474	+	0.250598i
$292$	4.82485	−	4.82485i	0.282353	−	0.282353i
$293$	3.19461	−	11.9224i	0.186631	−	0.696516i	−0.807645	−	0.589670i	$-0.799258\pi$
$293$	3.19461	−	11.9224i	0.186631	−	0.696516i	0.994276	−	0.106847i	$-0.0340754\pi$
$294$	1.53786	−	6.82898i	0.0896897	−	0.398274i
$295$	13.2793	+	23.0005i	0.773153	+	1.33914i
$296$	−4.09739	+	2.36563i	−0.238156	+	0.137499i
$297$	−1.08226	−	1.08226i	−0.0627993	−	0.0627993i
$298$	8.45486	−	4.88142i	0.489777	−	0.282773i
$299$	17.0466	+	20.6442i	0.985829	+	1.19389i
$300$			4.73023i			0.273100i
$301$	19.3396	+	4.76656i	1.11472	+	0.274740i
$302$	−4.30116	+	7.44982i	−0.247504	+	0.428689i
$303$			8.44761i			0.485302i
$304$	−4.81303	−	1.28965i	−0.276046	−	0.0739664i
$305$	−22.9915	+	6.16056i	−1.31649	+	0.352753i
$306$	−2.44970	−	2.44970i	−0.140040	−	0.140040i
$307$	−13.8751	−	13.8751i	−0.791896	−	0.791896i	0.189906	−	0.981802i	$-0.439182\pi$
$307$	−13.8751	−	13.8751i	−0.791896	−	0.791896i	−0.981802	+	0.189906i	$0.939182\pi$
$308$	−3.54701	−	1.95366i	−0.202110	−	0.111320i
$309$	13.4017	+	7.73745i	0.762394	+	0.440168i
$310$	31.6652	+	8.48466i	1.79846	+	0.481896i
$311$	−13.1243	−	22.7319i	−0.744209	−	1.28901i	−0.950564	−	0.310530i	$-0.899493\pi$
$311$	−13.1243	−	22.7319i	−0.744209	−	1.28901i	0.206355	−	0.978477i	$-0.433840\pi$
$312$	−2.09132	+	2.93707i	−0.118398	+	0.166279i
$313$	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
$315$	3.98165	−	7.22897i	0.224340	−	0.407307i
$316$	−12.7022	+	7.33360i	−0.714553	+	0.412547i
$317$	−2.08760	+	0.559370i	−0.117251	+	0.0314173i	−0.316967	−	0.948436i	$-0.602665\pi$
$317$	−2.08760	+	0.559370i	−0.117251	+	0.0314173i	0.199716	+	0.979854i	$0.435998\pi$
$318$	1.73000	+	6.45646i	0.0970138	+	0.362060i
$319$	−1.03071	−	3.84667i	−0.0577088	−	0.215372i
$320$	3.01304	−	0.807342i	0.168434	−	0.0451318i
$321$	−17.0740	+	9.85768i	−0.952978	+	0.550202i
$322$	−9.47806	+	17.2081i	−0.528191	+	0.958971i
$323$	4.46786	+	16.6743i	0.248598	+	0.927782i
$324$	−0.866025	−	0.500000i	−0.0481125	−	0.0277778i
$325$	−10.8593	−	13.1511i	−0.602364	−	0.729492i
$326$	2.33452	+	4.04350i	0.129297	+	0.223949i
$327$	−10.3670	−	2.77782i	−0.573295	−	0.153614i
$328$	2.74306	+	1.58370i	0.151460	+	0.0874455i
$329$	−22.6193	−	12.4585i	−1.24704	−	0.686858i
$330$	−3.37594	−	3.37594i	−0.185839	−	0.185839i
$331$	−13.0910	−	13.0910i	−0.719548	−	0.719548i	0.248964	−	0.968513i	$-0.419910\pi$
$331$	−13.0910	−	13.0910i	−0.719548	−	0.719548i	−0.968513	+	0.248964i	$0.919910\pi$
$332$	−7.36660	+	1.97387i	−0.404295	+	0.108330i
$333$	4.57004	+	1.22454i	0.250437	+	0.0671044i
$334$			14.0697i			0.769859i
$335$	−4.69445	+	8.13103i	−0.256485	+	0.444246i
$336$	−2.56888	−	0.633142i	−0.140144	−	0.0345407i
$337$			7.41532i			0.403938i	0.979392	+	0.201969i	$0.0647340\pi$
$337$			7.41532i			0.403938i	−0.979392	+	0.201969i	$0.935266\pi$
$338$	−0.928358	−	12.9668i	−0.0504960	−	0.705301i
$339$	1.60505	−	0.926673i	0.0871741	−	0.0503300i
$340$	−7.64143	−	7.64143i	−0.414415	−	0.414415i
$341$	−13.9301	+	8.04256i	−0.754359	+	0.435529i
$342$	2.49141	+	4.31525i	0.134720	+	0.233342i
$343$	−12.2808	+	13.8630i	−0.663098	+	0.748532i
$344$	1.94850	−	7.27190i	0.105056	−	0.392075i
$345$	−16.3781	+	16.3781i	−0.881769	+	0.881769i
$346$	1.79979	−	6.71693i	0.0967576	−	0.361104i
$347$	4.29470	−	7.43864i	0.230552	−	0.399327i	−0.727419	−	0.686194i	$-0.759280\pi$
$347$	4.29470	−	7.43864i	0.230552	−	0.399327i	0.957971	+	0.286866i	$0.0926136\pi$
$348$	−1.30096	−	2.25333i	−0.0697387	−	0.120791i
$349$	−24.1386	+	6.46792i	−1.29211	+	0.346220i	−0.838462	−	0.544961i	$-0.816545\pi$
$349$	−24.1386	+	6.46792i	−1.29211	+	0.346220i	−0.453649	+	0.891181i	$0.649878\pi$
$350$	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
$353$	−14.5235	+	14.5235i	−0.773011	+	0.773011i	−0.978632	−	0.205621i	$-0.934079\pi$
$353$	−14.5235	+	14.5235i	−0.773011	+	0.773011i	0.205621	+	0.978632i	$0.434079\pi$
$354$	−8.51422			−0.452526
$355$	8.30616			0.440845
$356$	−5.62087	+	5.62087i	−0.297905	+	0.297905i
$357$	2.55022	+	8.80403i	0.134972	+	0.465959i
$358$	3.97376	+	1.06477i	0.210020	+	0.0562746i
$359$	−0.255778	−	0.954577i	−0.0134995	−	0.0503807i	0.958848	−	0.283921i	$-0.0916355\pi$
$359$	−0.255778	−	0.954577i	−0.0134995	−	0.0503807i	−0.972347	+	0.233541i	$0.924969\pi$
$360$	−2.70142	−	1.55967i	−0.142377	−	0.0822016i
$361$		−	5.82850i		−	0.306763i
$362$	−1.17881	+	4.39937i	−0.0619568	+	0.231226i
$363$	−8.65741			−0.454396
$364$	8.59558	−	4.13715i	0.450531	−	0.216845i
$365$	−21.2843			−1.11407
$366$	1.97496	−	7.37066i	0.103233	−	0.385271i
$367$			32.0531i			1.67316i	0.547844	+	0.836580i	$0.315449\pi$
$367$			32.0531i			1.67316i	−0.547844	+	0.836580i	$0.684551\pi$
$368$	6.43056	+	3.71268i	0.335216	+	0.193537i
$369$	−0.819786	−	3.05948i	−0.0426763	−	0.159270i
$370$	14.2555	+	3.81974i	0.741107	+	0.198579i
$371$	4.23206	−	17.1709i	0.219718	−	0.891471i
$372$	−7.43125	+	7.43125i	−0.385292	+	0.385292i
$373$	34.0543			1.76326			0.881632	−	0.471938i	$-0.156445\pi$
$373$	34.0543			1.76326			0.881632	+	0.471938i	$0.156445\pi$
$374$	5.30244			0.274183
$375$	−0.595042	+	0.595042i	−0.0307278	+	0.0307278i
$376$	−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	0.776352	−	0.630300i	$-0.217068\pi$
$379$	34.3383	−	9.20093i	1.76384	−	0.472620i	0.987490	+	0.157679i	$0.0504013\pi$
$380$	7.77153	+	13.4607i	0.398671	+	0.690519i
$381$	5.20472	−	9.01483i	0.266646	−	0.461844i
$382$	3.14118	−	11.7230i	0.160717	−	0.599802i
$383$	26.8237	−	26.8237i	1.37063	−	1.37063i	0.511120	−	0.859509i	$-0.329231\pi$
$383$	26.8237	−	26.8237i	1.37063	−	1.37063i	0.859509	−	0.511120i	$-0.170769\pi$
$384$	−0.258819	+	0.965926i	−0.0132078	+	0.0492922i
$385$	3.51446	+	12.1328i	0.179114	+	0.618347i
$386$	5.08274	+	8.80356i	0.258705	+	0.448090i
$387$	−6.51981	+	3.76421i	−0.331420	+	0.191346i
$388$	−3.12942	−	3.12942i	−0.158872	−	0.158872i
$389$	17.3048	−	9.99095i	0.877390	−	0.506561i	0.00759279	−	0.999971i	$-0.497583\pi$
$389$	17.3048	−	9.99095i	0.877390	−	0.506561i	0.869797	+	0.493410i	$0.164250\pi$
$390$	11.0911	−	1.86548i	0.561621	−	0.0944623i
$391$		−	25.7245i		−	1.30094i
$392$	5.14514	+	4.74631i	0.259869	+	0.239725i
$393$	−0.170268	+	0.294912i	−0.00858886	+	0.0148763i
$394$		−	5.86772i		−	0.295611i
$395$	44.1929	+	11.8415i	2.22359	+	0.595808i
$396$	1.47840	−	0.396136i	0.0742923	−	0.0199066i
$397$	−9.01935	−	9.01935i	−0.452668	−	0.452668i	0.443571	−	0.896239i	$-0.353711\pi$
$397$	−9.01935	−	9.01935i	−0.452668	−	0.452668i	−0.896239	+	0.443571i	$0.853711\pi$
$398$	−8.47120	−	8.47120i	−0.424623	−	0.424623i
$399$	−0.265616	−	13.1806i	−0.0132975	−	0.659857i
$400$	−4.09650	−	2.36511i	−0.204825	−	0.118256i
$401$	−11.5122	−	3.08469i	−0.574892	−	0.154042i	−0.0403530	−	0.999185i	$-0.512848\pi$
$401$	−11.5122	−	3.08469i	−0.574892	−	0.154042i	−0.534539	+	0.845144i	$0.679515\pi$
$402$	−1.50496	−	2.60666i	−0.0750603	−	0.130008i
$403$	3.60049	−	37.7206i	0.179353	−	1.87900i
$404$	−7.31584	−	4.22380i	−0.363977	−	0.210142i
$405$	0.807342	+	3.01304i	0.0401172	+	0.149719i
$406$	0.138699	+	6.88263i	0.00688352	+	0.341579i
$407$	−6.27126	+	3.62071i	−0.310855	+	0.179472i
$408$	3.34635	−	0.896653i	0.165669	−	0.0443909i
$409$	−8.02458	−	29.9481i	−0.396790	−	1.48084i	−0.818710	−	0.574207i	$-0.805310\pi$
$409$	−8.02458	−	29.9481i	−0.396790	−	1.48084i	0.421920	−	0.906633i	$-0.361356\pi$
$410$	−2.55718	−	9.54354i	−0.126290	−	0.471322i
$411$	−16.0133	+	4.29074i	−0.789876	+	0.211647i
$412$	−13.4017	+	7.73745i	−0.660253	+	0.381197i
$413$	19.7315	+	10.8679i	0.970924	+	0.534775i
$414$	−1.92183	−	7.17236i	−0.0944526	−	0.352502i
$415$	20.6023	+	11.8947i	1.01133	+	0.583890i
$416$	−1.49792	−	3.27967i	−0.0734416	−	0.160799i
$417$	10.3907	+	17.9972i	0.508835	+	0.881327i
$418$	−7.36659	−	1.97387i	−0.360312	−	0.0965453i
$419$	−6.93782	−	4.00555i	−0.338935	−	0.195684i	0.320866	−	0.947125i	$-0.396026\pi$
$419$	−6.93782	−	4.00555i	−0.338935	−	0.195684i	−0.659801	+	0.751441i	$0.729359\pi$
$420$	4.26965	+	7.06269i	0.208338	+	0.344624i
$421$	6.84792	+	6.84792i	0.333747	+	0.333747i	0.854008	−	0.520261i	$-0.174165\pi$
$421$	6.84792	+	6.84792i	0.333747	+	0.333747i	−0.520261	+	0.854008i	$0.674165\pi$
$422$	2.44417	+	2.44417i	0.118981	+	0.118981i
$423$	9.42774	−	2.52616i	0.458392	−	0.122826i
$424$	−6.45646	−	1.73000i	−0.313553	−	0.0840164i
$425$			16.3874i			0.794906i
$426$	−1.33140	+	2.30605i	−0.0645066	+	0.111729i
$427$	−13.9852	+	14.5604i	−0.676789	+	0.704628i
$428$		−	19.7154i		−	0.952978i
$429$	−3.20087	+	4.49534i	−0.154539	+	0.217037i
$430$	−20.3374	+	11.7418i	−0.980758	+	0.566241i
$431$	3.66418	+	3.66418i	0.176497	+	0.176497i	0.789827	−	0.613330i	$-0.210170\pi$
$431$	3.66418	+	3.66418i	0.176497	+	0.176497i	−0.613330	+	0.789827i	$0.710170\pi$
$432$	0.866025	−	0.500000i	0.0416667	−	0.0240563i
$433$	−5.71366	−	9.89634i	−0.274581	−	0.475588i	0.695448	−	0.718576i	$-0.255206\pi$
$433$	−5.71366	−	9.89634i	−0.274581	−	0.475588i	−0.970029	+	0.242988i	$0.921872\pi$
$434$	26.7073	−	7.73618i	1.28199	−	0.371349i
$435$	−2.10064	+	7.83969i	−0.100718	+	0.375884i
$436$	7.58915	−	7.58915i	0.363454	−	0.363454i
$437$	−9.57612	+	35.7386i	−0.458088	+	1.70961i
$438$	3.41168	−	5.90921i	0.163017	−	0.282353i
$439$	−12.9655	−	22.4570i	−0.618811	−	1.07181i	−0.989703	−	0.143136i	$-0.954281\pi$
$439$	−12.9655	−	22.4570i	−0.618811	−	1.07181i	0.370892	−	0.928676i	$-0.379052\pi$
$440$	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	$-0.187472\pi$
$444$	−3.34550	+	3.34550i	−0.158771	+	0.158771i
$445$	24.7959			1.17544
$446$	10.2412			0.484934
$447$	6.90337	−	6.90337i	0.326518	−	0.326518i
$448$	1.83276	−	1.90814i	0.0865896	−	0.0901512i
$449$	3.29660	+	0.883320i	0.155576	+	0.0416865i	0.335766	−	0.941945i	$-0.391005\pi$
$449$	3.29660	+	0.883320i	0.155576	+	0.0416865i	−0.180190	+	0.983632i	$0.557671\pi$
$450$	1.22427	+	4.56905i	0.0577128	+	0.215387i
$451$	4.19839	+	2.42394i	0.197694	+	0.114139i
$452$			1.85335i			0.0871741i
$453$	−2.22644	+	8.30920i	−0.104607	+	0.390400i
$454$	−6.49632			−0.304887
$455$	−28.0846	−	9.83397i	−1.31663	−	0.461024i
$456$	−4.98282			−0.233342
$457$	−4.16880	+	15.5582i	−0.195008	+	0.727780i	0.797257	+	0.603640i	$0.206284\pi$
$457$	−4.16880	+	15.5582i	−0.195008	+	0.727780i	−0.992265	+	0.124140i	$0.960383\pi$
$458$		−	23.9205i		−	1.11773i
$459$	−3.00026	−	1.73220i	−0.140040	−	0.0808522i
$460$	−5.99481	−	22.3729i	−0.279510	−	1.04314i
$461$	19.9854	+	5.35508i	0.930814	+	0.249411i	0.692202	−	0.721704i	$-0.256641\pi$
$461$	19.9854	+	5.35508i	0.930814	+	0.249411i	0.238612	+	0.971115i	$0.423308\pi$
$462$	−3.93180	−	0.969056i	−0.182924	−	0.0450845i
$463$	−12.0105	+	12.0105i	−0.558176	+	0.558176i	−0.928788	−	0.370612i	$-0.879148\pi$
$463$	−12.0105	+	12.0105i	−0.558176	+	0.558176i	0.370612	+	0.928788i	$0.379148\pi$
$464$	2.60192			0.120791
$465$	32.7822			1.52024
$466$	18.0195	−	18.0195i	0.834737	−	0.834737i
$467$	1.96024	−	3.39524i	0.0907092	−	0.157113i	−0.817101	−	0.576495i	$-0.804420\pi$
$467$	1.96024	−	3.39524i	0.0907092	−	0.157113i	0.907810	+	0.419382i	$0.137753\pi$
$468$	−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
$471$	−5.72384	−	9.91398i	−0.263741	−	0.456812i
$472$	4.25711	−	7.37353i	0.195949	−	0.339394i
$473$	2.98228	−	11.1300i	0.137125	−	0.511758i
$474$	−10.3713	+	10.3713i	−0.476369	+	0.476369i
$475$	6.10033	−	22.7667i	0.279902	−	1.04461i
$476$	−8.89962	−	2.19346i	−0.407914	−	0.100537i
$477$	3.34211	+	5.78870i	0.153025	+	0.265047i
$478$	10.0278	−	5.78953i	0.458659	−	0.264807i
$479$	5.46786	+	5.46786i	0.249833	+	0.249833i	0.820902	−	0.571069i	$-0.193471\pi$
$479$	5.46786	+	5.46786i	0.249833	+	0.249833i	−0.571069	+	0.820902i	$0.693471\pi$
$480$	2.70142	−	1.55967i	0.123302	−	0.0711887i
$481$	1.62092	−	16.9816i	0.0739076	−	0.774295i
$482$			6.62826i			0.301909i
$483$	−4.70131	+	19.0749i	−0.213917	+	0.867936i
$484$	4.32871	−	7.49754i	0.196759	−	0.340797i
$485$			13.8051i			0.626859i
$486$	−0.965926	−	0.258819i	−0.0438153	−	0.0117403i
$487$	−13.3285	+	3.57137i	−0.603973	+	0.161834i	−0.547831	−	0.836589i	$-0.684546\pi$
$487$	−13.3285	+	3.57137i	−0.603973	+	0.161834i	−0.0561415	+	0.998423i	$0.517880\pi$
$488$	5.39570	+	5.39570i	0.244252	+	0.244252i
$489$	3.30151	+	3.30151i	0.149299	+	0.149299i
$490$	−0.879695	−	21.8176i	−0.0397406	−	0.985618i
$491$	−9.28265	−	5.35934i	−0.418920	−	0.241864i	0.275695	−	0.961245i	$-0.411092\pi$
$491$	−9.28265	−	5.35934i	−0.418920	−	0.241864i	−0.694615	+	0.719382i	$0.744425\pi$
$492$	3.05948	+	0.819786i	0.137932	+	0.0369588i
$493$	−4.50705	−	7.80643i	−0.202987	−	0.351584i
$494$	13.8534	−	11.4392i	0.623293	−	0.514672i
$495$	−4.13466	−	2.38715i	−0.185839	−	0.107294i
$496$	−2.72003	−	10.1513i	−0.122133	−	0.455806i
$497$	6.02903	−	3.64477i	0.270439	−	0.163490i
$498$	−6.60471	+	3.81323i	−0.295964	+	0.170875i
$499$	−1.41729	+	0.379762i	−0.0634467	+	0.0170005i	−0.290403	−	0.956905i	$-0.593789\pi$
$499$	−1.41729	+	0.379762i	−0.0634467	+	0.0170005i	0.226956	+	0.973905i	$0.427123\pi$
$500$	−0.217800	−	0.812842i	−0.00974033	−	0.0363514i
$501$	3.64150	+	13.5903i	0.162690	+	0.607169i
$502$	−21.7824	+	5.83658i	−0.972196	+	0.260499i
$503$	0.457260	−	0.263999i	0.0203882	−	0.0117711i	−0.489771	−	0.871851i	$-0.662920\pi$
$503$	0.457260	−	0.263999i	0.0203882	−	0.0117711i	0.510159	+	0.860080i	$0.329586\pi$
$504$	−2.64521	+	0.0533064i	−0.117827	+	0.00237446i
$505$	6.82011	+	25.4530i	0.303491	+	1.13264i
$506$	9.84229	+	5.68245i	0.437543	+	0.252616i
$507$	−4.25278	−	12.2847i	−0.188873	−	0.545583i
$508$	5.20472	+	9.01483i	0.230922	+	0.399968i
$509$	32.5334	+	8.71729i	1.44202	+	0.386387i	0.893239	−	0.449582i	$-0.148427\pi$
$509$	32.5334	+	8.71729i	1.44202	+	0.386387i	0.548777	+	0.835969i	$0.315094\pi$
$510$	−9.35880	−	5.40331i	−0.414415	−	0.239262i
$511$	−15.4493	+	9.33964i	−0.683435	+	0.413161i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	3.52339	+	3.52339i	0.155561	+	0.155561i
$514$	19.2452	−	5.15672i	0.848867	−	0.227453i
$515$	46.6266	+	12.4935i	2.05461	+	0.550532i
$516$		−	7.52842i		−	0.331420i
$517$	−7.46933	+	12.9373i	−0.328501	+	0.568980i
$518$	12.0235	−	3.48278i	0.528281	−	0.153025i
$519$		−	6.95387i		−	0.305241i
$520$	−3.93001	+	10.5379i	−0.172342	+	0.462119i
$521$	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	$0.310483\pi$
$522$	−1.83983	−	1.83983i	−0.0805274	−	0.0805274i
$523$	−31.7576	+	18.3353i	−1.38866	+	0.801746i	−0.993165	−	0.116720i	$-0.962762\pi$
$523$	−31.7576	+	18.3353i	−1.38866	+	0.801746i	−0.395500	+	0.918466i	$0.629429\pi$
$524$	−0.170268	−	0.294912i	−0.00743817	−	0.0128833i
$525$	2.99490	−	12.1514i	0.130708	−	0.530329i
$526$	2.63336	−	9.82782i	0.114820	−	0.428514i
$527$	−25.7448	+	25.7448i	−1.12146	+	1.12146i
$528$	−0.396136	+	1.47840i	−0.0172396	+	0.0643390i
$529$	16.0680	−	27.8307i	0.698611	−	1.21003i
$530$	10.4251	+	18.0569i	0.452839	+	0.784341i
$531$	−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
$535$	−43.4862	+	43.4862i	−1.88007	+	1.88007i
$536$	3.00991			0.130008
$537$	4.11394			0.177530
$538$	−20.8479	+	20.8479i	−0.898815	+	0.898815i
$539$	7.87490	+	7.26448i	0.339196	+	0.312903i
$540$	−3.01304	−	0.807342i	−0.129661	−	0.0347425i
$541$	−4.57707	−	17.0819i	−0.196784	−	0.734407i	−0.991798	−	0.127816i	$-0.959203\pi$
$541$	−4.57707	−	17.0819i	−0.196784	−	0.734407i	0.795014	−	0.606591i	$-0.207463\pi$
$542$	−2.33105	−	1.34583i	−0.100127	−	0.0578084i
$543$			4.55457i			0.195455i
$544$	−0.896653	+	3.34635i	−0.0384437	+	0.143474i
$545$	−33.4788			−1.43407
$546$	7.23192	−	6.22088i	0.309498	−	0.266229i
$547$	2.57222			0.109980			0.0549900	−	0.998487i	$-0.482487\pi$
$547$	2.57222			0.109980			0.0549900	+	0.998487i	$0.482487\pi$
$548$	4.29074	−	16.0133i	0.183291	−	0.684052i
$549$		−	7.63067i		−	0.325669i
$550$	−6.26989	−	3.61992i	−0.267349	−	0.154354i
$551$	3.35556	+	12.5231i	0.142952	+	0.533503i
$552$	7.17236	+	1.92183i	0.305276	+	0.0817984i
$553$	37.2735	−	10.7969i	1.58503	−	0.459129i
$554$	−4.77611	+	4.77611i	−0.202918	+	0.202918i
$555$	14.7584			0.626457
$556$	−20.7814			−0.881327
$557$	7.95158	−	7.95158i	0.336919	−	0.336919i	−0.518287	−	0.855207i	$-0.673430\pi$
$557$	7.95158	−	7.95158i	0.336919	−	0.336919i	0.855207	+	0.518287i	$0.173430\pi$
$558$	−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
$562$	0.0445762	+	0.0772082i	0.00188033	+	0.00325683i
$563$	13.5435	−	23.4581i	0.570791	−	0.988639i	−0.425694	−	0.904867i	$-0.639970\pi$
$563$	13.5435	−	23.4581i	0.570791	−	0.988639i	0.996485	−	0.0837718i	$-0.0266967\pi$
$564$	−2.52616	+	9.42774i	−0.106370	+	0.396980i
$565$	4.08793	−	4.08793i	0.171980	−	0.171980i
$566$	7.42270	−	27.7019i	0.311999	−	1.16440i
$567$	1.90814	+	1.83276i	0.0801344	+	0.0769685i
$568$	−1.33140	−	2.30605i	−0.0558643	−	0.0967599i
$569$	24.9364	−	14.3970i	1.04539	−	0.603555i	0.124034	−	0.992278i	$-0.460417\pi$
$569$	24.9364	−	14.3970i	1.04539	−	0.603555i	0.921355	+	0.388723i	$0.127084\pi$
$570$	10.9906	+	10.9906i	0.460346	+	0.460346i
$571$	−18.8974	+	10.9104i	−0.790830	+	0.456586i	−0.840255	−	0.542192i	$-0.817595\pi$
$571$	−18.8974	+	10.9104i	−0.790830	+	0.456586i	0.0494246	+	0.998778i	$0.484261\pi$
$572$	−2.29264	−	5.01970i	−0.0958602	−	0.209884i
$573$		−	12.1366i		−	0.507013i
$574$	−6.04387	−	5.80509i	−0.252266	−	0.242300i
$575$	−17.5618	+	30.4180i	−0.732379	+	1.26852i
$576$			1.00000i			0.0416667i
$577$	18.1702	+	4.86870i	0.756436	+	0.202686i	0.616371	−	0.787456i	$-0.288602\pi$
$577$	18.1702	+	4.86870i	0.756436	+	0.202686i	0.140065	+	0.990142i	$0.455269\pi$
$578$	−4.82762	+	1.29356i	−0.200803	+	0.0538049i
$579$	7.18808	+	7.18808i	0.298726	+	0.298726i
$580$	−5.73905	−	5.73905i	−0.238301	−	0.238301i
$581$	20.1736	−	0.406540i	0.836944	−	0.0168661i
$582$	−3.83275	−	2.21284i	−0.158872	−	0.0917251i
$583$	−9.88194	−	2.64786i	−0.409268	−	0.109663i
$584$	3.41168	+	5.90921i	0.141177	+	0.244525i
$585$	10.2304	−	4.67251i	0.422974	−	0.193184i
$586$	10.6894	+	6.17151i	0.441574	+	0.254943i
$587$	−3.39742	−	12.6793i	−0.140226	−	0.523332i	−0.999922	−	0.0125246i	$-0.996013\pi$
$587$	−3.39742	−	12.6793i	−0.140226	−	0.523332i	0.859695	−	0.510807i	$-0.170653\pi$
$588$	6.19826	+	3.25293i	0.255612	+	0.134148i
$589$	45.3506	−	26.1832i	1.86864	−	1.07886i
$590$	−25.6537	+	6.87389i	−1.05615	+	0.282994i
$591$	−1.51868	−	5.66778i	−0.0624700	−	0.233141i
$592$	−1.22454	−	4.57004i	−0.0503283	−	0.187828i
$593$	−6.64776	+	1.78126i	−0.272991	+	0.0731477i	−0.392717	−	0.919659i	$-0.628465\pi$
$593$	−6.64776	+	1.78126i	−0.272991	+	0.0731477i	0.119727	+	0.992807i	$0.461798\pi$
$594$	1.32550	−	0.765275i	0.0543857	−	0.0313996i
$595$	14.7918	+	24.4680i	0.606404	+	1.00309i
$596$	2.52681	+	9.43017i	0.103502	+	0.386275i
$597$	−10.3751	−	5.99004i	−0.424623	−	0.245156i
$598$	−24.3528	+	11.1226i	−0.995858	+	0.454837i
$599$	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	$0.673223\pi$
$600$	−4.56905	−	1.22427i	−0.186531	−	0.0499807i
$601$	30.7423	+	17.7491i	1.25401	+	0.724001i	0.971903	−	0.235383i	$-0.0756344\pi$
$601$	30.7423	+	17.7491i	1.25401	+	0.724001i	0.282104	+	0.959384i	$0.408968\pi$
$602$	−9.60960	+	17.4469i	−0.391658	+	0.711084i
$603$	−2.12833	−	2.12833i	−0.0866722	−	0.0866722i
$604$	−6.08276	−	6.08276i	−0.247504	−	0.247504i
$605$	−26.0852	+	6.98950i	−1.06051	+	0.284163i
$606$	−8.15976	−	2.18640i	−0.331468	−	0.0888165i
$607$		−	0.588067i		−	0.0238689i	−0.999929	−	0.0119345i	$-0.996201\pi$
$607$		−	0.588067i		−	0.0238689i	0.999929	−	0.0119345i	$-0.00379895\pi$
$608$	2.49141	−	4.31525i	0.101040	−	0.175006i
$609$	1.91533	+	6.61221i	0.0776131	+	0.267940i
$610$		−	23.8026i		−	0.963739i
$611$	−14.6202	−	32.0106i	−0.591469	−	1.29501i
$612$	3.00026	−	1.73220i	0.121278	−	0.0700201i
$613$	−1.26333	−	1.26333i	−0.0510254	−	0.0510254i	0.681134	−	0.732159i	$-0.261487\pi$
$613$	−1.26333	−	1.26333i	−0.0510254	−	0.0510254i	−0.732159	+	0.681134i	$0.761487\pi$
$614$	16.9935	−	9.81120i	0.685802	−	0.395948i
$615$	−4.94010	−	8.55650i	−0.199204	−	0.345031i
$616$	2.80513	−	2.92051i	0.113022	−	0.117671i
$617$	−3.25047	+	12.1309i	−0.130859	+	0.488373i	−0.999981	−	0.00622577i	$-0.998018\pi$
$617$	−3.25047	+	12.1309i	−0.130859	+	0.488373i	0.869122	+	0.494599i	$0.164685\pi$
$618$	−10.9424	+	10.9424i	−0.440168	+	0.440168i
$619$	6.13124	−	22.8821i	0.246435	−	0.919709i	−0.726221	−	0.687461i	$-0.758725\pi$
$619$	6.13124	−	22.8821i	0.246435	−	0.919709i	0.972657	−	0.232248i	$-0.0746081\pi$
$620$	−16.3911	+	28.3902i	−0.658283	+	1.14018i
$621$	−3.71268	−	6.43056i	−0.148985	−	0.258049i
$622$	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
$626$	−9.09829	+	9.09829i	−0.363641	+	0.363641i
$627$	−7.62646			−0.304571
$628$	11.4477			0.456812
$629$	−11.5902	+	11.5902i	−0.462130	+	0.462130i
$630$	5.95213	+	5.71697i	0.237138	+	0.227770i
$631$	14.9722	+	4.01178i	0.596032	+	0.159706i	0.544209	−	0.838950i	$-0.316830\pi$
$631$	14.9722	+	4.01178i	0.596032	+	0.159706i	0.0518237	+	0.998656i	$0.483497\pi$
$632$	−3.79615	−	14.1674i	−0.151003	−	0.563550i
$633$	2.99349	+	1.72829i	0.118981	+	0.0686935i
$634$		−	2.16124i		−	0.0858337i
$635$	8.40397	−	31.3641i	0.333502	−	1.24464i
$636$	−6.68422			−0.265047
$637$	−24.7004	+	5.18560i	−0.978665	+	0.205461i
$638$	3.98237			0.157663
$639$	−0.689184	+	2.57207i	−0.0272637	+	0.101749i
$640$			3.11933i			0.123302i
$641$	−40.2250	−	23.2239i	−1.58879	−	0.917290i	−0.993506	−	0.113777i	$-0.963705\pi$
$641$	−40.2250	−	23.2239i	−1.58879	−	0.917290i	−0.595287	−	0.803513i	$-0.702962\pi$
$642$	−5.10271	−	19.0436i	−0.201388	−	0.751590i
$643$	25.6665	+	6.87732i	1.01219	+	0.271215i	0.726543	−	0.687121i	$-0.241126\pi$
$643$	25.6665	+	6.87732i	1.01219	+	0.271215i	0.285644	+	0.958336i	$0.407792\pi$
$644$	−14.1687	−	13.6089i	−0.558323	−	0.536265i
$645$	−16.6054	+	16.6054i	−0.653839	+	0.653839i
$646$	−17.2625			−0.679184
$647$	−17.6869			−0.695344			−0.347672	−	0.937616i	$-0.613028\pi$
$647$	−17.6869			−0.695344			−0.347672	+	0.937616i	$0.613028\pi$
$648$	0.707107	−	0.707107i	0.0277778	−	0.0277778i
$649$	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
$653$	−18.8434	−	32.6377i	−0.737398	−	1.27721i	−0.953663	−	0.300876i	$-0.902721\pi$
$653$	−18.8434	−	32.6377i	−0.737398	−	1.27721i	0.216265	−	0.976335i	$-0.430612\pi$
$654$	5.36634	−	9.29477i	0.209840	−	0.363454i
$655$	−0.274928	+	1.02605i	−0.0107423	+	0.0400910i
$656$	−2.23970	+	2.23970i	−0.0874455	+	0.0874455i
$657$	1.76602	−	6.59087i	0.0688989	−	0.257134i
$658$	17.8883	−	18.6241i	0.697357	−	0.726042i
$659$	−16.0832	−	27.8570i	−0.626514	−	1.08515i	−0.988246	−	0.152872i	$-0.951148\pi$
$659$	−16.0832	−	27.8570i	−0.626514	−	1.08515i	0.361732	−	0.932282i	$-0.382186\pi$
$660$	4.13466	−	2.38715i	0.160941	−	0.0929196i
$661$	0.479294	+	0.479294i	0.0186424	+	0.0186424i	0.716367	−	0.697724i	$-0.245804\pi$
$661$	0.479294	+	0.479294i	0.0186424	+	0.0186424i	−0.697724	+	0.716367i	$0.745804\pi$
$662$	16.0332	−	9.25676i	0.623147	−	0.359774i
$663$	−4.36476	+	11.7037i	−0.169513	+	0.454533i
$664$		−	7.62647i		−	0.295964i
$665$	−11.4416	−	39.4993i	−0.443686	−	1.53172i
$666$	−2.36563	+	4.09739i	−0.0916662	+	0.158771i
$667$		−	19.3202i		−	0.748081i
$668$	−13.5903	−	3.64150i	−0.525824	−	0.140894i
$669$	9.89222	−	2.65061i	0.382455	−	0.102479i
$670$	−6.63896	−	6.63896i	−0.256485	−	0.256485i
$671$	8.25839	+	8.25839i	0.318812	+	0.318812i
$672$	1.27644	−	2.31748i	0.0492398	−	0.0893986i
$673$	7.66521	+	4.42551i	0.295472	+	0.170591i	0.640407	−	0.768036i	$-0.278766\pi$
$673$	7.66521	+	4.42551i	0.295472	+	0.170591i	−0.344935	+	0.938627i	$0.612099\pi$
$674$	−7.16264	−	1.91922i	−0.275895	−	0.0739258i
$675$	2.36511	+	4.09650i	0.0910332	+	0.157674i
$676$	12.7653	+	2.45933i	0.490971	+	0.0945897i
$677$	−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
$679$	6.05774	+	10.0205i	0.232475	+	0.384551i
$680$	9.35880	−	5.40331i	0.358894	−	0.207207i
$681$	−6.27496	+	1.68137i	−0.240457	+	0.0644303i
$682$	−4.16314	−	15.5370i	−0.159415	−	0.594944i
$683$	6.16637	+	23.0132i	0.235949	+	0.880575i	0.977719	+	0.209920i	$0.0673204\pi$
$683$	6.16637	+	23.0132i	0.235949	+	0.880575i	−0.741769	+	0.670655i	$0.766013\pi$
$684$	−4.81303	+	1.28965i	−0.184031	+	0.0493110i
$685$	−44.7845	+	25.8564i	−1.71113	+	0.987921i
$686$	−10.2122	−	15.4503i	−0.389902	−	0.589895i
$687$	−6.19109	−	23.1055i	−0.236205	−	0.881529i
$688$	6.51981	+	3.76421i	0.248565	+	0.143509i
$689$	18.5837	−	15.3451i	0.707981	−	0.584602i
$690$	−11.5811	−	20.0590i	−0.440885	−	0.763635i
$691$	32.0364	+	8.58413i	1.21872	+	0.326556i	0.810179	−	0.586183i	$-0.199370\pi$
$691$	32.0364	+	8.58413i	1.21872	+	0.326556i	0.408544	+	0.912739i	$0.366037\pi$
$692$	6.02223	+	3.47694i	0.228931	+	0.132173i
$693$	−4.04863	+	0.0815882i	−0.153795	+	0.00309928i
$694$	6.07363	+	6.07363i	0.230552	+	0.230552i
$695$	45.8375	+	45.8375i	1.73872	+	1.73872i
$696$	2.51326	−	0.673426i	0.0952649	−	0.0255262i
$697$	10.5993	+	2.84007i	0.401476	+	0.107575i
$698$		−	24.9901i		−	0.945890i
$699$	12.7417	−	22.0693i	0.481936	−	0.834737i
$700$	9.02594	+	8.66935i	0.341149	+	0.327671i
$701$			40.5277i			1.53071i	0.643609	+	0.765354i	$0.277436\pi$
$701$			40.5277i			1.53071i	−0.643609	+	0.765354i	$0.722564\pi$
$702$	−0.342598	+	3.58924i	−0.0129305	+	0.135467i
$703$	20.4166	−	11.7875i	0.770025	−	0.444574i
$704$	−1.08226	−	1.08226i	−0.0407893	−	0.0407893i
$705$	26.3667	−	15.2228i	0.993028	−	0.573325i
$706$	−10.2697	−	17.7876i	−0.386505	−	0.669447i
$707$	16.1192	+	15.4824i	0.606226	+	0.582276i
$708$	2.20364	−	8.22410i	0.0828179	−	0.309081i
$709$	7.47145	−	7.47145i	0.280596	−	0.280596i	−0.552751	−	0.833347i	$-0.686422\pi$
$709$	7.47145	−	7.47145i	0.280596	−	0.280596i	0.833347	+	0.552751i	$0.186422\pi$
$710$	−2.14979	+	8.02313i	−0.0806803	+	0.301103i
$711$	−7.33360	+	12.7022i	−0.275032	+	0.476369i
$712$	−3.97455	−	6.88413i	−0.148953	−	0.257994i
$713$	−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
$717$	8.18763	−	8.18763i	0.305773	−	0.305773i
$718$	0.988251			0.0368812
$719$	−46.9839			−1.75221			−0.876103	−	0.482125i	$-0.839865\pi$
$719$	−46.9839			−1.75221			−0.876103	+	0.482125i	$0.839865\pi$
$720$	2.20570	−	2.20570i	0.0822016	−	0.0822016i
$721$	39.3261	−	11.3914i	1.46458	−	0.424239i
$722$	5.62990	+	1.50853i	0.209523	+	0.0561415i
$723$	1.71552	+	6.40241i	0.0638009	+	0.238108i
$724$	−3.94437	−	2.27728i	−0.146591	−	0.0846346i
$725$			12.3077i			0.457095i
$726$	2.24070	−	8.36242i	0.0831603	−	0.310359i
$727$	−45.4801			−1.68677			−0.843383	−	0.537313i	$-0.819439\pi$
$727$	−45.4801			−1.68677			−0.843383	+	0.537313i	$0.819439\pi$
$728$	1.77148	+	9.37347i	0.0656553	+	0.347404i
$729$	−1.00000			−0.0370370
$730$	5.50879	−	20.5591i	0.203890	−	0.760927i
$731$		−	26.0815i		−	0.964659i
$732$	6.60836	+	3.81534i	0.244252	+	0.141019i
$733$	−4.45964	−	16.6436i	−0.164720	−	0.614745i	−0.998076	−	0.0620072i	$-0.980250\pi$
$733$	−4.45964	−	16.6436i	−0.164720	−	0.614745i	0.833355	−	0.552738i	$-0.186417\pi$
$734$	−30.9610	−	8.29596i	−1.14279	−	0.306210i
$735$	−6.49653	−	20.8465i	−0.239628	−	0.768934i
$736$	−5.25053	+	5.25053i	−0.193537	+	0.193537i
$737$	4.60682			0.169694
$738$	3.16741			0.116594
$739$	−21.2422	+	21.2422i	−0.781409	+	0.781409i	−0.980068	−	0.198660i	$-0.936341\pi$
$739$	−21.2422	+	21.2422i	−0.781409	+	0.781409i	0.198660	+	0.980068i	$0.436341\pi$
$740$	−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	−0.517483	−	0.855694i	$-0.673131\pi$
$743$	−14.6591	+	3.92789i	−0.537790	+	0.144100i	−0.0203066	+	0.999794i	$0.506464\pi$
$744$	−5.25469	−	9.10138i	−0.192646	−	0.333673i
$745$	15.2268	−	26.3735i	0.557865	−	0.966251i
$746$	−8.81389	+	32.8939i	−0.322700	+	1.20433i
$747$	−5.39273	+	5.39273i	−0.197310	+	0.197310i
$748$	−1.37237	+	5.12177i	−0.0501789	+	0.187270i
$749$	−12.4826	+	50.6463i	−0.456105	+	1.85058i
$750$	−0.420758	−	0.728774i	−0.0153639	−	0.0266111i
$751$	8.70656	−	5.02674i	0.317707	−	0.183428i	−0.332663	−	0.943046i	$-0.607947\pi$
$751$	8.70656	−	5.02674i	0.317707	−	0.183428i	0.650370	+	0.759618i	$0.274614\pi$
$752$	−6.90159	−	6.90159i	−0.251675	−	0.251675i
$753$	−19.5296	+	11.2754i	−0.711697	+	0.410899i
$754$	−5.44144	+	7.64202i	−0.198165	+	0.278306i
$755$			26.8335i			0.976570i
$756$	−2.54128	+	0.736122i	−0.0924256	+	0.0267725i
$757$	−8.64250	+	14.9693i	−0.314117	+	0.544067i	−0.979249	−	0.202659i	$-0.935042\pi$
$757$	−8.64250	+	14.9693i	−0.314117	+	0.544067i	0.665132	+	0.746726i	$0.268375\pi$
$758$			35.5497i			1.29122i
$759$	10.9777	+	2.94145i	0.398464	+	0.106768i
$760$	−15.0134	+	4.02284i	−0.544595	+	0.145924i
$761$	−29.2698	−	29.2698i	−1.06103	−	1.06103i	−0.998012	−	0.0630189i	$-0.979927\pi$
$761$	−29.2698	−	29.2698i	−1.06103	−	1.06103i	−0.0630189	−	0.998012i	$-0.520073\pi$
$762$	7.36058	+	7.36058i	0.266646	+	0.266646i
$763$	−24.3006	+	14.6906i	−0.879741	+	0.531835i
$764$	10.5106	+	6.06829i	0.380259	+	0.219543i
$765$	−10.4384	−	2.79696i	−0.377401	−	0.101124i
$766$	18.9673	+	32.8522i	0.685315	+	1.18700i
$767$	12.7536	+	27.9238i	0.460507	+	1.00827i
$768$	−0.866025	−	0.500000i	−0.0312500	−	0.0180422i
$769$	0.00508629	+	0.0189823i	0.000183416	+	0.000684518i	0.966017	−	0.258477i	$-0.0832205\pi$
$769$	0.00508629	+	0.0189823i	0.000183416	+	0.000684518i	−0.965834	+	0.259161i	$0.916554\pi$
$770$	−12.6290	+	0.254501i	−0.455119	+	0.00917157i
$771$	17.2547	−	9.96202i	0.621414	−	0.358774i
$772$	−9.81910	+	2.63102i	−0.353397	+	0.0946925i
$773$	0.110687	+	0.413088i	0.00398112	+	0.0148578i	0.967888	−	0.251383i	$-0.0808852\pi$
$773$	0.110687	+	0.413088i	0.00398112	+	0.0148578i	−0.963907	+	0.266240i	$0.914219\pi$
$774$	−1.94850	−	7.27190i	−0.0700374	−	0.261383i
$775$	48.0178	−	12.8663i	1.72485	−	0.462172i
$776$	3.83275	−	2.21284i	0.137588	−	0.0794362i
$777$	10.7124	−	6.47601i	0.384304	−	0.232326i
$778$	5.17169	+	19.3010i	0.185414	+	0.691975i
$779$	−13.6682	−	7.89132i	−0.489713	−	0.282736i
$780$	−1.06868	+	11.1960i	−0.0382648	+	0.400882i
$781$	−2.03778	−	3.52953i	−0.0729174	−	0.126297i
$782$	24.8479	+	6.65798i	0.888560	+	0.238089i
$783$	−2.25333	−	1.30096i	−0.0805274	−	0.0464925i
$784$	−5.91625	+	3.74139i	−0.211295	+	0.133621i
$785$	−25.2501	−	25.2501i	−0.901216	−	0.901216i
$786$	−0.240795	−	0.240795i	−0.00858886	−	0.00858886i
$787$	25.1414	−	6.73661i	0.896194	−	0.240134i	0.218813	−	0.975767i	$-0.429782\pi$
$787$	25.1414	−	6.73661i	0.896194	−	0.240134i	0.677381	+	0.735633i	$0.263115\pi$
$788$	5.66778	+	1.51868i	0.201906	+	0.0541006i
$789$		−	10.1745i		−	0.362222i
$790$	−22.8759	+	39.6223i	−0.813889	+	1.40970i
$791$	1.17343	−	4.76102i	0.0417224	−	0.169282i
$792$			1.53055i			0.0543857i
$793$	−27.1317	+	4.56344i	−0.963474	+	0.162052i
$794$	11.0464	−	6.37764i	0.392022	−	0.226334i
$795$	14.7434	+	14.7434i	0.522894	+	0.522894i
$796$	10.3751	−	5.99004i	0.367734	−	0.212311i
$797$	−3.56473	−	6.17429i	−0.126269	−	0.218705i	0.795959	−	0.605350i	$-0.206967\pi$
$797$	−3.56473	−	6.17429i	−0.126269	−	0.218705i	−0.922228	+	0.386646i	$0.873634\pi$
$798$	12.8003	+	3.15483i	0.453124	+	0.111680i
$799$	−8.75162	+	32.6615i	−0.309610	+	1.15548i
$800$	3.34477	−	3.34477i	0.118256	−	0.118256i
$801$	−2.05738	+	7.67825i	−0.0726940	+	0.271298i
$802$	5.95916	−	10.3216i	0.210425	−	0.364467i
$803$	5.22176	+	9.04435i	0.184272	+	0.319168i
$804$	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
$808$	5.97336	−	5.97336i	0.210142	−	0.210142i
$809$	−11.1032			−0.390369			−0.195184	−	0.980767i	$-0.562530\pi$
$809$	−11.1032			−0.390369			−0.195184	+	0.980767i	$0.562530\pi$
$810$	−3.11933			−0.109602
$811$	−27.9664	+	27.9664i	−0.982032	+	0.982032i	−0.999841	−	0.0178090i	$-0.994331\pi$
$811$	−27.9664	+	27.9664i	−0.982032	+	0.982032i	0.0178090	+	0.999841i	$0.494331\pi$
$812$	−6.68401	−	1.64738i	−0.234563	−	0.0578118i
$813$	−2.59995	−	0.696653i	−0.0911841	−	0.0244327i
$814$	−1.87422	−	6.99468i	−0.0656914	−	0.245164i
$815$	12.6130	+	7.28213i	0.441815	+	0.255082i
$816$			3.46440i			0.121278i
$817$	−9.70902	+	36.2346i	−0.339676	+	1.26769i
$818$	31.0046			1.08405
$819$	5.37542	−	7.88067i	0.187832	−	0.275373i
$820$	9.88020			0.345031
$821$	10.3434	−	38.6021i	0.360987	−	1.34722i	−0.511793	−	0.859109i	$-0.671018\pi$
$821$	10.3434	−	38.6021i	0.360987	−	1.34722i	0.872780	−	0.488114i	$-0.162315\pi$
$822$		−	16.5781i		−	0.578229i
$823$	20.1540	+	11.6359i	0.702525	+	0.405603i	0.808287	−	0.588789i	$-0.200395\pi$
$823$	20.1540	+	11.6359i	0.702525	+	0.405603i	−0.105762	+	0.994391i	$0.533728\pi$
$824$	−4.00520	−	14.9476i	−0.139528	−	0.520725i
$825$	−6.99316	−	1.87381i	−0.243470	−	0.0652377i
$826$	−15.6045	+	16.2463i	−0.542949	+	0.565283i
$827$	−21.2660	+	21.2660i	−0.739490	+	0.739490i	−0.972479	−	0.232989i	$-0.925149\pi$
$827$	−21.2660	+	21.2660i	−0.739490	+	0.739490i	0.232989	+	0.972479i	$0.425149\pi$
$828$	7.42537			0.258049
$829$	−11.4749			−0.398540			−0.199270	−	0.979945i	$-0.563857\pi$
$829$	−11.4749			−0.398540			−0.199270	+	0.979945i	$0.563857\pi$
$830$	−16.8217	+	16.8217i	−0.583890	+	0.583890i
$831$	−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
$835$	21.9440	+	38.0081i	0.759404	+	1.31533i
$836$	3.81323	−	6.60471i	0.131883	−	0.228429i
$837$	−2.72003	+	10.1513i	−0.0940179	+	0.350879i
$838$	5.66471	−	5.66471i	0.195684	−	0.195684i
$839$	−8.38592	+	31.2967i	−0.289514	+	1.08048i	0.655963	+	0.754793i	$0.272263\pi$
$839$	−8.38592	+	31.2967i	−0.289514	+	1.08048i	−0.945477	+	0.325688i	$0.894404\pi$
$840$	−7.92711	+	2.29621i	−0.273511	+	0.0792267i
$841$	11.1150	+	19.2518i	0.383276	+	0.663854i
$842$	−8.38695	+	4.84221i	−0.289033	+	0.166874i
$843$	0.0630402	+	0.0630402i	0.00217122	+	0.00217122i
$844$	−2.99349	+	1.72829i	−0.103040	+	0.0594903i
$845$	−22.7318	−	33.5809i	−0.781997	−	1.15522i
$846$			9.76032i			0.335567i
$847$	−15.8669	+	16.5196i	−0.545194	+	0.567619i
$848$	3.34211	−	5.78870i	0.114769	−	0.198785i
$849$		−	28.6791i		−	0.984265i
$850$	−15.8290	−	4.24137i	−0.542931	−	0.145478i
$851$	−33.9343	+	9.09266i	−1.16325	+	0.311692i
$852$	−1.88288	−	1.88288i	−0.0645066	−	0.0645066i
$853$	−9.96970	−	9.96970i	−0.341356	−	0.341356i	0.515521	−	0.856877i	$-0.327598\pi$
$853$	−9.96970	−	9.96970i	−0.341356	−	0.341356i	−0.856877	+	0.515521i	$0.827598\pi$
$854$	−10.4447	−	17.2771i	−0.357409	−	0.591211i
$855$	13.4607	+	7.77153i	0.460346	+	0.265781i
$856$	19.0436	+	5.10271i	0.650896	+	0.174407i
$857$	9.01136	+	15.6081i	0.307822	+	0.533164i	0.977886	−	0.209140i	$-0.0670664\pi$
$857$	9.01136	+	15.6081i	0.307822	+	0.533164i	−0.670063	+	0.742304i	$0.733733\pi$
$858$	−3.51372	−	4.25528i	−0.119956	−	0.145273i
$859$	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
$861$	−7.34039	−	4.04302i	−0.250160	−	0.137786i
$862$	−4.48768	+	2.59096i	−0.152851	+	0.0882486i
$863$	−24.1901	+	6.48171i	−0.823440	+	0.220640i	−0.645850	−	0.763464i	$-0.723497\pi$
$863$	−24.1901	+	6.48171i	−0.823440	+	0.220640i	−0.177590	+	0.984105i	$0.556830\pi$
$864$	0.258819	+	0.965926i	0.00880520	+	0.0328615i
$865$	−5.61416	−	20.9523i	−0.190887	−	0.712400i
$866$	11.0379	−	2.95761i	0.375084	−	0.100504i
$867$	−4.32833	+	2.49896i	−0.146998	+	0.0848692i
$868$	0.560217	+	27.7995i	0.0190150	+	0.943578i
$869$	−5.81020	−	21.6840i	−0.197098	−	0.735578i
$870$	−7.02888	−	4.05812i	−0.238301	−	0.137583i
$871$	−6.29468	+	8.84032i	−0.213287	+	0.299543i
$872$	5.36634	+	9.29477i	0.181727	+	0.314761i
$873$	−4.27487	−	1.14545i	−0.144683	−	0.0387676i
$874$	−32.0423	−	18.4996i	−1.08385	−	0.625760i
$875$	0.0448582	+	2.22599i	0.00151649	+	0.0752522i
$876$	4.82485	+	4.82485i	0.163017	+	0.163017i
$877$	−37.3486	−	37.3486i	−1.26117	−	1.26117i	−0.950525	−	0.310649i	$-0.899454\pi$
$877$	−37.3486	−	37.3486i	−1.26117	−	1.26117i	−0.310649	−	0.950525i	$-0.600546\pi$
$878$	25.0475	−	6.71145i	0.845312	−	0.226501i
$879$	11.9224	+	3.19461i	0.402134	+	0.107751i
$880$			4.77429i			0.160941i
$881$	−7.72842	+	13.3860i	−0.260377	+	0.450986i	−0.966342	−	0.257260i	$-0.917180\pi$
$881$	−7.72842	+	13.3860i	−0.260377	+	0.450986i	0.705965	+	0.708247i	$0.250513\pi$
$882$	6.82898	+	1.53786i	0.229944	+	0.0517824i
$883$		−	5.66309i		−	0.190578i	−0.995450	−	0.0952890i	$-0.969622\pi$
$883$		−	5.66309i		−	0.190578i	0.995450	−	0.0952890i	$-0.0303775\pi$
$884$	−7.95330	−	9.63182i	−0.267498	−	0.323953i
$885$	−23.0005	+	13.2793i	−0.773153	+	0.446380i
$886$	26.6949	+	26.6949i	0.896833	+	0.896833i
$887$	6.78538	−	3.91754i	0.227831	−	0.131538i	−0.381740	−	0.924270i	$-0.624675\pi$
$887$	6.78538	−	3.91754i	0.227831	−	0.131538i	0.609571	+	0.792731i	$0.291342\pi$
$888$	−2.36563	−	4.09739i	−0.0793853	−	0.137499i
$889$	−7.66261	−	26.4533i	−0.256996	−	0.887216i
$890$	−6.41765	+	23.9510i	−0.215120	+	0.802839i
$891$	1.08226	−	1.08226i	0.0362572	−	0.0362572i
$892$	−2.65061	+	9.89222i	−0.0887491	+	0.331216i
$893$	24.3169	−	42.1182i	0.813736	−	1.40943i
$894$	4.88142	+	8.45486i	0.163259	+	0.282773i
$895$	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
$899$	−19.3355	+	19.3355i	−0.644875	+	0.644875i
$900$	−4.73023			−0.157674
$901$	−23.1568			−0.771466
$902$	−3.42797	+	3.42797i	−0.114139	+	0.114139i
$903$	−4.76656	+	19.3396i	−0.158621	+	0.643582i
$904$	−1.79020	−	0.479681i	−0.0595410	−	0.0159540i
$905$	3.67709	+	13.7231i	0.122231	+	0.456171i
$906$	−7.44982	−	4.30116i	−0.247504	−	0.142896i
$907$		−	26.5474i		−	0.881491i	−0.897632	−	0.440745i	$-0.854714\pi$
$907$		−	26.5474i		−	0.881491i	0.897632	−	0.440745i	$-0.145286\pi$
$908$	1.68137	−	6.27496i	0.0557983	−	0.208242i
$909$	−8.44761			−0.280190
$910$	16.7677	−	24.5824i	0.555844	−	0.814899i
$911$	−17.3251			−0.574007			−0.287004	−	0.957929i	$-0.592659\pi$
$911$	−17.3251			−0.574007			−0.287004	+	0.957929i	$0.592659\pi$
$912$	1.28965	−	4.81303i	0.0427045	−	0.159376i
$913$		−	11.6727i		−	0.386310i
$914$	−13.9491	−	8.05350i	−0.461394	−	0.266386i
$915$	−6.16056	−	22.9915i	−0.203662	−	0.760077i
$916$	23.1055	+	6.19109i	0.763426	+	0.204559i
$917$	0.250675	+	0.865396i	0.00827803	+	0.0285779i
$918$	2.44970	−	2.44970i	0.0808522	−	0.0808522i
$919$	−21.1622			−0.698076			−0.349038	−	0.937108i	$-0.613492\pi$
$919$	−21.1622			−0.698076			−0.349038	+	0.937108i	$0.613492\pi$
$920$	23.1622			0.763635
$921$	13.8751	−	13.8751i	0.457201	−	0.457201i
$922$	−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
$926$	−8.49272	−	14.7098i	−0.279088	−	0.483395i
$927$	−7.73745	+	13.4017i	−0.254131	+	0.440168i
$928$	−0.673426	+	2.51326i	−0.0221063	+	0.0825018i
$929$	27.2902	−	27.2902i	0.895361	−	0.895361i	−0.0996602	−	0.995022i	$-0.531776\pi$
$929$	27.2902	−	27.2902i	0.895361	−	0.895361i	0.995022	+	0.0996602i	$0.0317756\pi$
$930$	−8.48466	+	31.6652i	−0.278223	+	1.03834i
$931$	−25.6373	−	23.6500i	−0.840229	−	0.775099i
$932$	12.7417	+	22.0693i	0.417369	+	0.722904i
$933$	22.7319	−	13.1243i	0.744209	−	0.429669i
$934$	2.77220	+	2.77220i	0.0907092	+	0.0907092i
$935$	14.3241	−	8.27004i	0.468449	−	0.270459i
$936$	−2.93707	−	2.09132i	−0.0960012	−	0.0683568i
$937$		−	17.7016i		−	0.578287i	−0.957286	−	0.289144i	$-0.906630\pi$
$937$		−	17.7016i		−	0.578287i	0.957286	−	0.289144i	$-0.0933705\pi$
$938$	−7.73209	−	1.90570i	−0.252462	−	0.0622233i
$939$	−6.43346	+	11.1431i	−0.209948	+	0.363641i
$940$			30.4457i			0.993028i
$941$	−35.2582	−	9.44742i	−1.14939	−	0.307977i	−0.366667	−	0.930352i	$-0.619501\pi$
$941$	−35.2582	−	9.44742i	−1.14939	−	0.307977i	−0.782719	+	0.622375i	$0.786168\pi$
$942$	11.0576	−	2.96288i	0.360276	−	0.0965358i
$943$	16.6306	+	16.6306i	0.541566	+	0.541566i
$944$	6.02046	+	6.02046i	0.195949	+	0.195949i
$945$	7.22897	+	3.98165i	0.235159	+	0.129523i
$946$	9.97889	+	5.76132i	0.324442	+	0.187317i
$947$	−10.1696	−	2.72494i	−0.330468	−	0.0885486i	0.0897702	−	0.995963i	$-0.471387\pi$
$947$	−10.1696	−	2.72494i	−0.330468	−	0.0885486i	−0.420238	+	0.907414i	$0.638053\pi$
$948$	−7.33360	−	12.7022i	−0.238184	−	0.412547i
$949$	−24.4907	−	2.33767i	−0.795002	−	0.0758841i
$950$	20.4121	+	11.7849i	0.662256	+	0.382354i
$951$	−0.559370	−	2.08760i	−0.0181388	−	0.0676949i
$952$	4.42211	−	8.02867i	0.143321	−	0.260211i
$953$	33.8927	−	19.5680i	1.09789	−	0.633869i	0.162227	−	0.986754i	$-0.448132\pi$
$953$	33.8927	−	19.5680i	1.09789	−	0.633869i	0.935667	+	0.352884i	$0.114799\pi$
$954$	−6.45646	+	1.73000i	−0.209036	+	0.0560109i
$955$	−9.79837	−	36.5680i	−0.317068	−	1.18331i
$956$	2.99688	+	11.1845i	0.0969261	+	0.361733i
$957$	3.84667	−	1.03071i	0.124345	−	0.0333182i
$958$	−6.69673	+	3.86636i	−0.216362	+	0.124916i
$959$	−21.1610	+	38.4195i	−0.683326	+	1.24063i
$960$	0.807342	+	3.01304i	0.0260569	+	0.0972455i
$961$	68.8031	+	39.7235i	2.21945	+	1.28140i
$962$	15.9834	+	5.96085i	0.515327	+	0.192186i
$963$	−9.85768	−	17.0740i	−0.317659	−	0.550202i
$964$	−6.40241	−	1.71552i	−0.206208	−	0.0552532i
$965$	27.4612	+	15.8547i	0.884008	+	0.510382i
$966$	−17.2081	−	9.47806i	−0.553662	−	0.304951i
$967$	−41.6802	−	41.6802i	−1.34035	−	1.34035i	−0.895713	−	0.444634i	$-0.853334\pi$
$967$	−41.6802	−	41.6802i	−1.34035	−	1.34035i	−0.444634	−	0.895713i	$-0.646666\pi$
$968$	6.12172	+	6.12172i	0.196759	+	0.196759i
$969$	−16.6743	+	4.46786i	−0.535655	+	0.143528i
$970$	−13.3347	−	3.57303i	−0.428153	−	0.114723i
$971$		−	20.4320i		−	0.655694i	−0.944731	−	0.327847i	$-0.893677\pi$
$971$		−	20.4320i		−	0.655694i	0.944731	−	0.327847i	$-0.106323\pi$
$972$	0.500000	−	0.866025i	0.0160375	−	0.0277778i
$973$	53.3849	+	13.1576i	1.71144	+	0.421812i
$974$		−	13.7987i		−	0.442139i
$975$	13.1511	−	10.8593i	0.421172	−	0.347775i
$976$	−6.60836	+	3.81534i	−0.211528	+	0.122126i
$977$	−29.1633	−	29.1633i	−0.933018	−	0.933018i	0.0648757	−	0.997893i	$-0.479335\pi$
$977$	−29.1633	−	29.1633i	−0.933018	−	0.933018i	−0.997893	+	0.0648757i	$0.979335\pi$
$978$	−4.04350	+	2.33452i	−0.129297	+	0.0746496i
$979$	−6.08325	−	10.5365i	−0.194422	−	0.336748i
$980$	21.3019	+	4.79709i	0.680463	+	0.153237i
$981$	2.77782	−	10.3670i	0.0886890	−	0.330992i
$982$	7.57925	−	7.57925i	0.241864	−	0.241864i
$983$	8.61605	−	32.1555i	0.274809	−	1.02560i	−0.681160	−	0.732135i	$-0.738524\pi$
$983$	8.61605	−	32.1555i	0.274809	−	1.02560i	0.955969	−	0.293468i	$-0.0948092\pi$
$984$	−1.58370	+	2.74306i	−0.0504867	+	0.0874455i
$985$	−9.15168	−	15.8512i	−0.291597	−	0.505060i
$986$	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
$990$	3.37594	−	3.37594i	0.107294	−	0.107294i
$991$	43.7009			1.38820			0.694102	−	0.719877i	$-0.255802\pi$
$991$	43.7009			1.38820			0.694102	+	0.719877i	$0.255802\pi$
$992$	10.5094			0.333673
$993$	13.0910	−	13.0910i	0.415431	−	0.415431i
$994$	1.96015	+	6.76693i	0.0621721	+	0.214634i
$995$	−36.0965	−	9.67203i	−1.14434	−	0.306624i
$996$	−1.97387	−	7.36660i	−0.0625446	−	0.233420i
$997$	−39.0429	−	22.5414i	−1.23650	−	0.713894i	−0.268123	−	0.963385i	$-0.586403\pi$
$997$	−39.0429	−	22.5414i	−1.23650	−	0.713894i	−0.968377	+	0.249491i	$0.919737\pi$
$998$		−	1.46729i		−	0.0464462i
$999$	−1.22454	+	4.57004i	−0.0387427	+	0.144590i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.by.b.397.4	✓	40	1.1	even	1	trivial
546.2.by.b.535.4	yes	40	91.80	even	12	inner
546.2.cg.b.145.4	yes	40	13.2	odd	12
546.2.cg.b.241.4	yes	40	7.3	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.258819 + 0.965926i) q^{2} +1.00000i q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.807342 + 3.01304i) q^{5} +(-0.965926 - 0.258819i) q^{6} +(1.90814 + 1.83276i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(-0.258819 + 0.965926i) q^{2} +1.00000i q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.807342 + 3.01304i) q^{5} +(-0.965926 - 0.258819i) q^{6} +(1.90814 + 1.83276i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000 q^{9} -3.11933 q^{10} +(1.08226 - 1.08226i) 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} +(0.500000 + 0.866025i) q^{16} +(1.73220 - 3.00026i) q^{17} +(0.258819 - 0.965926i) q^{18} +(-3.52339 + 3.52339i) q^{19} +(0.807342 - 3.01304i) q^{20} +(-1.83276 + 1.90814i) q^{21} +(0.765275 + 1.32550i) q^{22} +(6.43056 - 3.71268i) q^{23} +(0.707107 + 0.707107i) q^{24} +(-4.09650 + 2.36511i) q^{25} +(-3.58924 - 0.342598i) q^{26} -1.00000i q^{27} +(-0.736122 - 2.54128i) q^{28} +(1.30096 - 2.25333i) q^{29} -3.11933i q^{30} +(-10.1513 - 2.72003i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(1.08226 + 1.08226i) q^{33} +(2.44970 + 2.44970i) q^{34} +(-3.98165 + 7.22897i) q^{35} +(0.866025 + 0.500000i) q^{36} +(-4.57004 - 1.22454i) q^{37} +(-2.49141 - 4.31525i) q^{38} +(-3.55561 + 0.598039i) q^{39} +(2.70142 + 1.55967i) q^{40} +(0.819786 + 3.05948i) q^{41} +(-1.36877 - 2.26417i) q^{42} +(6.51981 - 3.76421i) q^{43} +(-1.47840 + 0.396136i) q^{44} +(-0.807342 - 3.01304i) q^{45} +(1.92183 + 7.17236i) q^{46} +(-9.42774 + 2.52616i) q^{47} +(-0.866025 + 0.500000i) q^{48} +(0.282014 + 6.99432i) q^{49} +(-1.22427 - 4.56905i) q^{50} +(3.00026 + 1.73220i) q^{51} +(1.25989 - 3.37827i) q^{52} +(-3.34211 - 5.78870i) q^{53} +(0.965926 + 0.258819i) q^{54} +(4.13466 + 2.38715i) q^{55} +(2.64521 - 0.0533064i) q^{56} +(-3.52339 - 3.52339i) q^{57} +(1.83983 + 1.83983i) q^{58} +(8.22410 - 2.20364i) q^{59} +(3.01304 + 0.807342i) q^{60} +7.63067i q^{61} +(5.25469 - 9.10138i) q^{62} +(-1.90814 - 1.83276i) q^{63} -1.00000i q^{64} +(-10.2304 + 4.67251i) q^{65} +(-1.32550 + 0.765275i) q^{66} +(2.12833 + 2.12833i) q^{67} +(-3.00026 + 1.73220i) q^{68} +(3.71268 + 6.43056i) q^{69} +(-5.95213 - 5.71697i) q^{70} +(0.689184 - 2.57207i) q^{71} +(-0.707107 + 0.707107i) q^{72} +(-1.76602 + 6.59087i) q^{73} +(2.36563 - 4.09739i) q^{74} +(-2.36511 - 4.09650i) 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} +(-2.20570 + 2.20570i) q^{80} +1.00000 q^{81} -3.16741 q^{82} +(5.39273 - 5.39273i) q^{83} +(2.54128 - 0.736122i) q^{84} +(10.4384 + 2.79696i) q^{85} +(1.94850 + 7.27190i) q^{86} +(2.25333 + 1.30096i) q^{87} -1.53055i q^{88} +(2.05738 - 7.67825i) q^{89} +3.11933 q^{90} +(-5.37542 + 7.88067i) q^{91} -7.42537 q^{92} +(2.72003 - 10.1513i) q^{93} -9.76032i q^{94} +(-13.4607 - 7.77153i) q^{95} +(-0.258819 - 0.965926i) q^{96} +(4.27487 + 1.14545i) q^{97} +(-6.82898 - 1.53786i) q^{98} +(-1.08226 + 1.08226i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{7} - 40 q^{9}+O(q^{10}) \) 40 * q - 4 * q^7 - 40 * q^9	\( 40 q - 4 q^{7} - 40 q^{9} - 4 q^{11} + 20 q^{12} + 4 q^{14} + 20 q^{16} + 8 q^{17} + 8 q^{19} - 8 q^{21} - 4 q^{22} + 24 q^{23} + 24 q^{25} - 8 q^{26} + 4 q^{28} - 12 q^{29} + 24 q^{31} - 4 q^{33} + 8 q^{34} + 28 q^{35} - 8 q^{37} - 8 q^{38} - 16 q^{39} - 20 q^{41} - 12 q^{42} - 24 q^{43} + 8 q^{44} - 4 q^{46} - 16 q^{47} + 4 q^{49} - 16 q^{50} - 24 q^{51} - 4 q^{52} - 4 q^{53} - 24 q^{55} + 12 q^{56} + 8 q^{57} + 24 q^{58} - 12 q^{59} - 32 q^{62} + 4 q^{63} - 4 q^{65} - 24 q^{67} + 24 q^{68} + 8 q^{69} + 52 q^{70} - 28 q^{71} + 108 q^{73} + 20 q^{74} - 36 q^{75} - 4 q^{76} + 12 q^{77} + 4 q^{78} + 40 q^{81} - 48 q^{82} - 60 q^{83} - 8 q^{84} - 4 q^{85} - 20 q^{86} - 36 q^{87} - 60 q^{89} - 40 q^{91} - 16 q^{92} - 48 q^{95} + 48 q^{97} - 8 q^{98} + 4 q^{99}+O(q^{100}) \) 40 * q - 4 * q^7 - 40 * q^9 - 4 * q^11 + 20 * q^12 + 4 * q^14 + 20 * q^16 + 8 * q^17 + 8 * q^19 - 8 * q^21 - 4 * q^22 + 24 * q^23 + 24 * q^25 - 8 * q^26 + 4 * q^28 - 12 * q^29 + 24 * q^31 - 4 * q^33 + 8 * q^34 + 28 * q^35 - 8 * q^37 - 8 * q^38 - 16 * q^39 - 20 * q^41 - 12 * q^42 - 24 * q^43 + 8 * q^44 - 4 * q^46 - 16 * q^47 + 4 * q^49 - 16 * q^50 - 24 * q^51 - 4 * q^52 - 4 * q^53 - 24 * q^55 + 12 * q^56 + 8 * q^57 + 24 * q^58 - 12 * q^59 - 32 * q^62 + 4 * q^63 - 4 * q^65 - 24 * q^67 + 24 * q^68 + 8 * q^69 + 52 * q^70 - 28 * q^71 + 108 * q^73 + 20 * q^74 - 36 * q^75 - 4 * q^76 + 12 * q^77 + 4 * q^78 + 40 * q^81 - 48 * q^82 - 60 * q^83 - 8 * q^84 - 4 * q^85 - 20 * q^86 - 36 * q^87 - 60 * q^89 - 40 * q^91 - 16 * q^92 - 48 * q^95 + 48 * q^97 - 8 * q^98 + 4 * q^99

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