LMFDB - Embedded newform 546.2.by.b.397.5

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			397.5
Character	$\chi$	$=$	546.397
Dual form			546.2.by.b.535.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 + 0.965926i) q^{2} +1.00000i q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.939253 + 3.50534i) q^{5} +(-0.965926 - 0.258819i) q^{6} +(-2.04406 - 1.67982i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(-0.258819 + 0.965926i) q^{2} +1.00000i q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.939253 + 3.50534i) q^{5} +(-0.965926 - 0.258819i) q^{6} +(-2.04406 - 1.67982i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000 q^{9} -3.62900 q^{10} +(-1.98466 + 1.98466i) q^{11} +(0.500000 - 0.866025i) q^{12} +(-3.16979 - 1.71826i) q^{13} +(2.15163 - 1.53965i) q^{14} +(-3.50534 + 0.939253i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-1.98611 + 3.44004i) q^{17} +(0.258819 - 0.965926i) q^{18} +(1.23808 - 1.23808i) q^{19} +(0.939253 - 3.50534i) q^{20} +(1.67982 - 2.04406i) q^{21} +(-1.40337 - 2.43070i) q^{22} +(2.41124 - 1.39213i) q^{23} +(0.707107 + 0.707107i) q^{24} +(-7.07509 + 4.08481i) q^{25} +(2.48012 - 2.61706i) q^{26} -1.00000i q^{27} +(0.930302 + 2.47680i) q^{28} +(-2.41978 + 4.19119i) q^{29} -3.62900i q^{30} +(9.26580 + 2.48276i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(-1.98466 - 1.98466i) q^{33} +(-2.80878 - 2.80878i) q^{34} +(3.96845 - 8.74292i) q^{35} +(0.866025 + 0.500000i) q^{36} +(-11.2309 - 3.00931i) q^{37} +(0.875453 + 1.51633i) q^{38} +(1.71826 - 3.16979i) q^{39} +(3.14280 + 1.81450i) q^{40} +(-2.09174 - 7.80648i) q^{41} +(1.53965 + 2.15163i) q^{42} +(-1.95431 + 1.12832i) q^{43} +(2.71110 - 0.726436i) q^{44} +(-0.939253 - 3.50534i) q^{45} +(0.720620 + 2.68939i) q^{46} +(2.00862 - 0.538208i) q^{47} +(-0.866025 + 0.500000i) q^{48} +(1.35640 + 6.86733i) q^{49} +(-2.11445 - 7.89124i) q^{50} +(-3.44004 - 1.98611i) q^{51} +(1.88599 + 3.07295i) q^{52} +(2.21480 + 3.83615i) q^{53} +(0.965926 + 0.258819i) q^{54} +(-8.82101 - 5.09281i) q^{55} +(-2.63318 + 0.257559i) q^{56} +(1.23808 + 1.23808i) q^{57} +(-3.42209 - 3.42209i) q^{58} +(-5.27526 + 1.41350i) q^{59} +(3.50534 + 0.939253i) q^{60} +13.6956i q^{61} +(-4.79633 + 8.30749i) q^{62} +(2.04406 + 1.67982i) q^{63} -1.00000i q^{64} +(3.04586 - 12.7251i) q^{65} +(2.43070 - 1.40337i) q^{66} +(2.58500 + 2.58500i) q^{67} +(3.44004 - 1.98611i) q^{68} +(1.39213 + 2.41124i) q^{69} +(7.41790 + 6.09606i) q^{70} +(-1.90908 + 7.12477i) q^{71} +(-0.707107 + 0.707107i) q^{72} +(1.41102 - 5.26598i) q^{73} +(5.81353 - 10.0693i) q^{74} +(-4.08481 - 7.07509i) q^{75} +(-1.69124 + 0.453168i) q^{76} +(7.39065 - 0.722900i) q^{77} +(2.61706 + 2.48012i) q^{78} +(-2.35907 + 4.08603i) q^{79} +(-2.56609 + 2.56609i) q^{80} +1.00000 q^{81} +8.08186 q^{82} +(4.55850 - 4.55850i) q^{83} +(-2.47680 + 0.930302i) q^{84} +(-13.9240 - 3.73092i) q^{85} +(-0.584061 - 2.17975i) q^{86} +(-4.19119 - 2.41978i) q^{87} +2.80673i q^{88} +(-0.842441 + 3.14403i) q^{89} +3.62900 q^{90} +(3.59289 + 8.83692i) q^{91} -2.78426 q^{92} +(-2.48276 + 9.26580i) q^{93} +2.07947i q^{94} +(5.50275 + 3.17701i) q^{95} +(-0.258819 - 0.965926i) q^{96} +(14.9544 + 4.00703i) q^{97} +(-6.98439 - 0.467210i) q^{98} +(1.98466 - 1.98466i) 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
$5$	0.939253	+	3.50534i	0.420047	+	1.56764i	0.774507	+	0.632565i	$0.217998\pi$
$5$	0.939253	+	3.50534i	0.420047	+	1.56764i	−0.354460	+	0.935071i	$0.615335\pi$
$6$	−0.965926	−	0.258819i	−0.394338	−	0.105662i
$7$	−2.04406	−	1.67982i	−0.772584	−	0.634913i
$7$	−2.04406	−	1.67982i	−0.772584	−	0.634913i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−1.00000			−0.333333
$10$	−3.62900			−1.14759
$11$	−1.98466	+	1.98466i	−0.598398	+	0.598398i	−0.939886	−	0.341488i	$-0.889069\pi$
$11$	−1.98466	+	1.98466i	−0.598398	+	0.598398i	0.341488	+	0.939886i	$0.389069\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	−3.16979	−	1.71826i	−0.879142	−	0.476560i
$13$	−3.16979	−	1.71826i	−0.879142	−	0.476560i
$14$	2.15163	−	1.53965i	0.575046	−	0.411488i
$15$	−3.50534	+	0.939253i	−0.905075	+	0.242514i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−1.98611	+	3.44004i	−0.481702	+	0.834332i	−0.999779	−	0.0210016i	$-0.993314\pi$
$17$	−1.98611	+	3.44004i	−0.481702	+	0.834332i	0.518078	+	0.855334i	$0.326648\pi$
$18$	0.258819	−	0.965926i	0.0610042	−	0.227671i
$19$	1.23808	−	1.23808i	0.284034	−	0.284034i	−0.550681	−	0.834716i	$-0.685632\pi$
$19$	1.23808	−	1.23808i	0.284034	−	0.284034i	0.834716	+	0.550681i	$0.185632\pi$
$20$	0.939253	−	3.50534i	0.210023	−	0.783818i
$21$	1.67982	−	2.04406i	0.366567	−	0.446052i
$22$	−1.40337	−	2.43070i	−0.299199	−	0.518227i
$23$	2.41124	−	1.39213i	0.502779	−	0.290280i	−0.227081	−	0.973876i	$-0.572918\pi$
$23$	2.41124	−	1.39213i	0.502779	−	0.290280i	0.729860	+	0.683596i	$0.239585\pi$
$24$	0.707107	+	0.707107i	0.144338	+	0.144338i
$25$	−7.07509	+	4.08481i	−1.41502	+	0.816961i
$26$	2.48012	−	2.61706i	0.486391	−	0.513249i
$27$		−	1.00000i		−	0.192450i
$28$	0.930302	+	2.47680i	0.175810	+	0.468071i
$29$	−2.41978	+	4.19119i	−0.449343	+	0.778284i	−0.998343	−	0.0575376i	$-0.981675\pi$
$29$	−2.41978	+	4.19119i	−0.449343	+	0.778284i	0.549001	+	0.835822i	$0.315008\pi$
$30$		−	3.62900i		−	0.662561i
$31$	9.26580	+	2.48276i	1.66419	+	0.445918i	0.963534	−	0.267584i	$-0.0862254\pi$
$31$	9.26580	+	2.48276i	1.66419	+	0.445918i	0.700653	+	0.713502i	$0.252892\pi$
$32$	−0.965926	+	0.258819i	−0.170753	+	0.0457532i
$33$	−1.98466	−	1.98466i	−0.345485	−	0.345485i
$34$	−2.80878	−	2.80878i	−0.481702	−	0.481702i
$35$	3.96845	−	8.74292i	0.670791	−	1.47782i
$36$	0.866025	+	0.500000i	0.144338	+	0.0833333i
$37$	−11.2309	−	3.00931i	−1.84635	−	0.494727i	−0.847024	−	0.531555i	$-0.821608\pi$
$37$	−11.2309	−	3.00931i	−1.84635	−	0.494727i	−0.999322	+	0.0368283i	$0.988275\pi$
$38$	0.875453	+	1.51633i	0.142017	+	0.245981i
$39$	1.71826	−	3.16979i	0.275142	−	0.507573i
$40$	3.14280	+	1.81450i	0.496921	+	0.286897i
$41$	−2.09174	−	7.80648i	−0.326675	−	1.21917i	−0.912618	−	0.408814i	$-0.865942\pi$
$41$	−2.09174	−	7.80648i	−0.326675	−	1.21917i	0.585943	−	0.810352i	$-0.300724\pi$
$42$	1.53965	+	2.15163i	0.237572	+	0.332003i
$43$	−1.95431	+	1.12832i	−0.298029	+	0.172067i	−0.641557	−	0.767075i	$-0.721711\pi$
$43$	−1.95431	+	1.12832i	−0.298029	+	0.172067i	0.343528	+	0.939142i	$0.388378\pi$
$44$	2.71110	−	0.726436i	0.408713	−	0.109514i
$45$	−0.939253	−	3.50534i	−0.140016	−	0.522545i
$46$	0.720620	+	2.68939i	0.106250	+	0.396529i
$47$	2.00862	−	0.538208i	0.292987	−	0.0785056i	−0.109332	−	0.994005i	$-0.534871\pi$
$47$	2.00862	−	0.538208i	0.292987	−	0.0785056i	0.402319	+	0.915500i	$0.368204\pi$
$48$	−0.866025	+	0.500000i	−0.125000	+	0.0721688i
$49$	1.35640	+	6.86733i	0.193772	+	0.981047i
$50$	−2.11445	−	7.89124i	−0.299029	−	1.11599i
$51$	−3.44004	−	1.98611i	−0.481702	−	0.278111i
$52$	1.88599	+	3.07295i	0.261540	+	0.426142i
$53$	2.21480	+	3.83615i	0.304227	+	0.526936i	0.977089	−	0.212832i	$-0.0682687\pi$
$53$	2.21480	+	3.83615i	0.304227	+	0.526936i	−0.672862	+	0.739768i	$0.734935\pi$
$54$	0.965926	+	0.258819i	0.131446	+	0.0352208i
$55$	−8.82101	−	5.09281i	−1.18942	−	0.686715i
$56$	−2.63318	+	0.257559i	−0.351874	+	0.0344178i
$57$	1.23808	+	1.23808i	0.163987	+	0.163987i
$58$	−3.42209	−	3.42209i	−0.449343	−	0.449343i
$59$	−5.27526	+	1.41350i	−0.686781	+	0.184022i	−0.585302	−	0.810815i	$-0.699024\pi$
$59$	−5.27526	+	1.41350i	−0.686781	+	0.184022i	−0.101479	+	0.994838i	$0.532357\pi$
$60$	3.50534	+	0.939253i	0.452538	+	0.121257i
$61$			13.6956i			1.75354i	0.480911	+	0.876769i	$0.340306\pi$
$61$			13.6956i			1.75354i	−0.480911	+	0.876769i	$0.659694\pi$
$62$	−4.79633	+	8.30749i	−0.609135	+	1.05505i
$63$	2.04406	+	1.67982i	0.257528	+	0.211638i
$64$		−	1.00000i		−	0.125000i
$65$	3.04586	−	12.7251i	0.377792	−	1.57835i
$66$	2.43070	−	1.40337i	0.299199	−	0.172742i
$67$	2.58500	+	2.58500i	0.315808	+	0.315808i	0.847154	−	0.531347i	$-0.178314\pi$
$67$	2.58500	+	2.58500i	0.315808	+	0.315808i	−0.531347	+	0.847154i	$0.678314\pi$
$68$	3.44004	−	1.98611i	0.417166	−	0.240851i
$69$	1.39213	+	2.41124i	0.167593	+	0.290280i
$70$	7.41790	+	6.09606i	0.886609	+	0.728619i
$71$	−1.90908	+	7.12477i	−0.226566	+	0.845554i	0.755206	+	0.655488i	$0.227537\pi$
$71$	−1.90908	+	7.12477i	−0.226566	+	0.845554i	−0.981771	+	0.190066i	$0.939130\pi$
$72$	−0.707107	+	0.707107i	−0.0833333	+	0.0833333i
$73$	1.41102	−	5.26598i	0.165147	−	0.616337i	−0.832874	−	0.553462i	$-0.813306\pi$
$73$	1.41102	−	5.26598i	0.165147	−	0.616337i	0.998021	−	0.0628749i	$-0.0200269\pi$
$74$	5.81353	−	10.0693i	0.675809	−	1.17054i
$75$	−4.08481	−	7.07509i	−0.471673	−	0.816961i
$76$	−1.69124	+	0.453168i	−0.193999	+	0.0519819i
$77$	7.39065	−	0.722900i	0.842243	−	0.0823821i
$78$	2.61706	+	2.48012i	0.296324	+	0.280818i
$79$	−2.35907	+	4.08603i	−0.265416	+	0.459714i	−0.967673	−	0.252210i	$-0.918843\pi$
$79$	−2.35907	+	4.08603i	−0.265416	+	0.459714i	0.702257	+	0.711924i	$0.252176\pi$
$80$	−2.56609	+	2.56609i	−0.286897	+	0.286897i
$81$	1.00000			0.111111
$82$	8.08186			0.892492
$83$	4.55850	−	4.55850i	0.500361	−	0.500361i	−0.411189	−	0.911550i	$-0.634886\pi$
$83$	4.55850	−	4.55850i	0.500361	−	0.500361i	0.911550	+	0.411189i	$0.134886\pi$
$84$	−2.47680	+	0.930302i	−0.270241	+	0.101504i
$85$	−13.9240	−	3.73092i	−1.51027	−	0.404675i
$86$	−0.584061	−	2.17975i	−0.0629810	−	0.235048i
$87$	−4.19119	−	2.41978i	−0.449343	−	0.259428i
$88$			2.80673i			0.299199i
$89$	−0.842441	+	3.14403i	−0.0892986	+	0.333267i	−0.996093	−	0.0883052i	$-0.971855\pi$
$89$	−0.842441	+	3.14403i	−0.0892986	+	0.333267i	0.906795	+	0.421572i	$0.138522\pi$
$90$	3.62900			0.382530
$91$	3.59289	+	8.83692i	0.376637	+	0.926361i
$92$	−2.78426			−0.290280
$93$	−2.48276	+	9.26580i	−0.257451	+	0.960819i
$94$			2.07947i			0.214481i
$95$	5.50275	+	3.17701i	0.564570	+	0.325955i
$96$	−0.258819	−	0.965926i	−0.0264156	−	0.0985844i
$97$	14.9544	+	4.00703i	1.51839	+	0.406852i	0.919213	−	0.393762i	$-0.128826\pi$
$97$	14.9544	+	4.00703i	1.51839	+	0.406852i	0.599181	+	0.800614i	$0.295493\pi$
$98$	−6.98439	−	0.467210i	−0.705530	−	0.0471954i
$99$	1.98466	−	1.98466i	0.199466	−	0.199466i
$100$	8.16961			0.816961
$101$	−10.3382			−1.02869			−0.514343	−	0.857585i	$-0.671964\pi$
$101$	−10.3382			−1.02869			−0.514343	+	0.857585i	$0.671964\pi$
$102$	2.80878	−	2.80878i	0.278111	−	0.278111i
$103$	2.54798	−	4.41323i	0.251060	−	0.434849i	−0.712758	−	0.701410i	$-0.752554\pi$
$103$	2.54798	−	4.41323i	0.251060	−	0.434849i	0.963818	+	0.266561i	$0.0858875\pi$
$104$	−3.45638	+	1.02639i	−0.338925	+	0.100645i
$105$	8.74292	+	3.96845i	0.853222	+	0.387281i
$106$	−4.27867	+	1.14647i	−0.415581	+	0.111355i
$107$	8.31594	+	14.4036i	0.803932	+	1.39245i	0.917010	+	0.398865i	$0.130596\pi$
$107$	8.31594	+	14.4036i	0.803932	+	1.39245i	−0.113078	+	0.993586i	$0.536071\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	−0.167574	+	0.625393i	−0.0160506	+	0.0599018i	−0.973487	−	0.228744i	$-0.926538\pi$
$109$	−0.167574	+	0.625393i	−0.0160506	+	0.0599018i	0.957436	+	0.288645i	$0.0932049\pi$
$110$	7.20232	−	7.20232i	0.686715	−	0.686715i
$111$	3.00931	−	11.2309i	0.285631	−	1.06599i
$112$	0.432735	−	2.61012i	0.0408896	−	0.246633i
$113$	1.11284	+	1.92750i	0.104687	+	0.181324i	0.913610	−	0.406591i	$-0.133283\pi$
$113$	1.11284	+	1.92750i	0.104687	+	0.181324i	−0.808923	+	0.587914i	$0.799949\pi$
$114$	−1.51633	+	0.875453i	−0.142017	+	0.0819937i
$115$	7.14466	+	7.14466i	0.666243	+	0.666243i
$116$	4.19119	−	2.41978i	0.389142	−	0.224671i
$117$	3.16979	+	1.71826i	0.293047	+	0.158853i
$118$		−	5.46135i		−	0.502758i
$119$	9.83838	−	3.69536i	0.901883	−	0.338753i
$120$	−1.81450	+	3.14280i	−0.165640	+	0.286897i
$121$			3.12225i			0.283841i
$122$	−13.2289	−	3.54468i	−1.19769	−	0.320920i
$123$	7.80648	−	2.09174i	0.703886	−	0.188606i
$124$	−6.78304	−	6.78304i	−0.609135	−	0.609135i
$125$	−8.13351	−	8.13351i	−0.727483	−	0.727483i
$126$	−2.15163	+	1.53965i	−0.191682	+	0.137163i
$127$	−4.06795	−	2.34863i	−0.360972	−	0.208408i	0.308535	−	0.951213i	$-0.400161\pi$
$127$	−4.06795	−	2.34863i	−0.360972	−	0.208408i	−0.669507	+	0.742805i	$0.733495\pi$
$128$	0.965926	+	0.258819i	0.0853766	+	0.0228766i
$129$	−1.12832	−	1.95431i	−0.0993430	−	0.172067i
$130$	11.5032	+	6.23556i	1.00889	+	0.546895i
$131$	12.6996	+	7.33214i	1.10957	+	0.640612i	0.938719	−	0.344684i	$-0.112014\pi$
$131$	12.6996	+	7.33214i	1.10957	+	0.640612i	0.170854	+	0.985296i	$0.445347\pi$
$132$	0.726436	+	2.71110i	0.0632281	+	0.235971i
$133$	−4.61046	+	0.450962i	−0.399777	+	0.0391034i
$134$	−3.16596	+	1.82787i	−0.273497	+	0.157904i
$135$	3.50534	−	0.939253i	0.301692	−	0.0808381i
$136$	1.02808	+	3.83686i	0.0881575	+	0.329008i
$137$	−0.427959	−	1.59717i	−0.0365630	−	0.136455i	0.945232	−	0.326400i	$-0.105836\pi$
$137$	−0.427959	−	1.59717i	−0.0365630	−	0.136455i	−0.981795	+	0.189945i	$0.939169\pi$
$138$	−2.68939	+	0.720620i	−0.228936	+	0.0613433i
$139$	−7.64204	+	4.41213i	−0.648189	+	0.374232i	−0.787762	−	0.615980i	$-0.788760\pi$
$139$	−7.64204	+	4.41213i	−0.648189	+	0.374232i	0.139573	+	0.990212i	$0.455427\pi$
$140$	−7.80824	+	5.58737i	−0.659917	+	0.472219i
$141$	0.538208	+	2.00862i	0.0453253	+	0.169156i
$142$	−6.38789	−	3.68805i	−0.536060	−	0.309494i
$143$	9.70112	−	2.88079i	0.811249	−	0.240904i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−16.9643	−	4.54558i	−1.40881	−	0.377490i
$146$	4.72135	+	2.72587i	0.390742	+	0.225595i
$147$	−6.86733	+	1.35640i	−0.566408	+	0.111874i
$148$	8.22157	+	8.22157i	0.675809	+	0.675809i
$149$	11.7326	+	11.7326i	0.961171	+	0.961171i	0.999274	−	0.0381031i	$-0.0121315\pi$
$149$	11.7326	+	11.7326i	0.961171	+	0.961171i	−0.0381031	+	0.999274i	$0.512132\pi$
$150$	7.89124	−	2.11445i	0.644317	−	0.172644i
$151$	10.6785	+	2.86129i	0.869002	+	0.232848i	0.665656	−	0.746258i	$-0.268152\pi$
$151$	10.6785	+	2.86129i	0.869002	+	0.232848i	0.203346	+	0.979107i	$0.434818\pi$
$152$		−	1.75091i		−	0.142017i
$153$	1.98611	−	3.44004i	0.160567	−	0.278111i
$154$	−1.21457	+	7.32592i	−0.0978730	+	0.590339i
$155$			34.8117i			2.79615i
$156$	−3.07295	+	1.88599i	−0.246033	+	0.151000i
$157$	−8.31074	+	4.79821i	−0.663270	+	0.382939i	−0.793522	−	0.608542i	$-0.791755\pi$
$157$	−8.31074	+	4.79821i	−0.663270	+	0.382939i	0.130252	+	0.991481i	$0.458421\pi$
$158$	−3.33623	−	3.33623i	−0.265416	−	0.265416i
$159$	−3.83615	+	2.21480i	−0.304227	+	0.175645i
$160$	−1.81450	−	3.14280i	−0.143449	−	0.248460i
$161$	−7.26727	−	1.20485i	−0.572741	−	0.0949554i
$162$	−0.258819	+	0.965926i	−0.0203347	+	0.0758903i
$163$	−13.9940	+	13.9940i	−1.09610	+	1.09610i	−0.101234	+	0.994863i	$0.532279\pi$
$163$	−13.9940	+	13.9940i	−1.09610	+	1.09610i	−0.994863	+	0.101234i	$0.967721\pi$
$164$	−2.09174	+	7.80648i	−0.163337	+	0.609583i
$165$	5.09281	−	8.82101i	0.396475	−	0.686715i
$166$	3.22335	+	5.58300i	0.250180	+	0.433325i
$167$	−9.79382	+	2.62425i	−0.757868	+	0.203070i	−0.617005	−	0.786959i	$-0.711654\pi$
$167$	−9.79382	+	2.62425i	−0.757868	+	0.203070i	−0.140863	+	0.990029i	$0.544988\pi$
$168$	−0.257559	−	2.63318i	−0.0198711	−	0.203155i
$169$	7.09515	+	10.8931i	0.545781	+	0.837928i
$170$	7.20758	−	12.4839i	0.552796	−	0.957470i
$171$	−1.23808	+	1.23808i	−0.0946781	+	0.0946781i
$172$	2.25664			0.172067
$173$	17.1586			1.30454			0.652272	−	0.757985i	$-0.273816\pi$
$173$	17.1586			1.30454			0.652272	+	0.757985i	$0.273816\pi$
$174$	3.42209	−	3.42209i	0.259428	−	0.259428i
$175$	21.3237	+	3.53528i	1.61192	+	0.267242i
$176$	−2.71110	−	0.726436i	−0.204357	−	0.0547572i
$177$	−1.41350	−	5.27526i	−0.106245	−	0.396513i
$178$	−2.81886	−	1.62747i	−0.211283	−	0.121984i
$179$			15.0588i			1.12555i	0.826610	+	0.562775i	$0.190266\pi$
$179$			15.0588i			1.12555i	−0.826610	+	0.562775i	$0.809734\pi$
$180$	−0.939253	+	3.50534i	−0.0700078	+	0.261273i
$181$	−24.4184			−1.81501			−0.907504	−	0.420043i	$-0.862015\pi$
$181$	−24.4184			−1.81501			−0.907504	+	0.420043i	$0.862015\pi$
$182$	−9.46572	+	1.18330i	−0.701646	+	0.0877120i
$183$	−13.6956			−1.01241
$184$	0.720620	−	2.68939i	0.0531248	−	0.198265i
$185$		−	42.1946i		−	3.10221i
$186$	−8.30749	−	4.79633i	−0.609135	−	0.351684i
$187$	−2.88556	−	10.7691i	−0.211013	−	0.787511i
$188$	−2.00862	−	0.538208i	−0.146494	−	0.0392528i
$189$	−1.67982	+	2.04406i	−0.122189	+	0.148684i
$190$	−4.49298	+	4.49298i	−0.325955	+	0.325955i
$191$	−3.90688			−0.282692			−0.141346	−	0.989960i	$-0.545143\pi$
$191$	−3.90688			−0.282692			−0.141346	+	0.989960i	$0.545143\pi$
$192$	1.00000			0.0721688
$193$	12.4516	−	12.4516i	0.896284	−	0.896284i	−0.0988210	−	0.995105i	$-0.531507\pi$
$193$	12.4516	−	12.4516i	0.896284	−	0.896284i	0.995105	+	0.0988210i	$0.0315071\pi$
$194$	−7.74099	+	13.4078i	−0.555771	+	0.962623i
$195$	12.7251	+	3.04586i	0.911262	+	0.218118i
$196$	2.25898	−	6.62548i	0.161356	−	0.473249i
$197$	−15.6894	+	4.20397i	−1.11783	+	0.299521i	−0.770004	−	0.638040i	$-0.779746\pi$
$197$	−15.6894	+	4.20397i	−1.11783	+	0.299521i	−0.347823	+	0.937560i	$0.613079\pi$
$198$	1.40337	+	2.43070i	0.0997329	+	0.172742i
$199$	12.4589	−	21.5795i	0.883191	−	1.52973i	0.0354186	−	0.999373i	$-0.488724\pi$
$199$	12.4589	−	21.5795i	0.883191	−	1.52973i	0.847773	−	0.530360i	$-0.177943\pi$
$200$	−2.11445	+	7.89124i	−0.149514	+	0.557995i
$201$	−2.58500	+	2.58500i	−0.182332	+	0.182332i
$202$	2.67571	−	9.98589i	0.188262	−	0.702605i
$203$	11.9866	−	4.50226i	0.841297	−	0.315997i
$204$	1.98611	+	3.44004i	0.139055	+	0.240851i
$205$	25.3997	−	14.6645i	1.77399	−	1.02421i
$206$	3.60339	+	3.60339i	0.251060	+	0.251060i
$207$	−2.41124	+	1.39213i	−0.167593	+	0.0967598i
$208$	−0.0968376	−	3.60425i	−0.00671448	−	0.249910i
$209$			4.91432i			0.339931i
$210$	−6.09606	+	7.41790i	−0.420668	+	0.511884i
$211$	12.5816	−	21.7919i	0.866150	−	1.50022i	0.000250090	−	1.00000i	$-0.499920\pi$
$211$	12.5816	−	21.7919i	0.866150	−	1.50022i	0.865900	−	0.500217i	$-0.166746\pi$
$212$		−	4.42961i		−	0.304227i
$213$	−7.12477	−	1.90908i	−0.488181	−	0.130808i
$214$	−16.0652	+	4.30465i	−1.09819	+	0.294260i
$215$	−5.79074	−	5.79074i	−0.394925	−	0.394925i
$216$	−0.707107	−	0.707107i	−0.0481125	−	0.0481125i
$217$	−14.7693	−	20.6398i	−1.00261	−	1.40112i
$218$	−0.560712	−	0.323727i	−0.0379762	−	0.0219256i
$219$	5.26598	+	1.41102i	0.355842	+	0.0953477i
$220$	5.09281	+	8.82101i	0.343357	+	0.594712i
$221$	12.2064	−	7.49155i	0.821094	−	0.503936i
$222$	10.0693	+	5.81353i	0.675809	+	0.390179i
$223$	−4.49900	−	16.7905i	−0.301275	−	1.12437i	−0.936104	−	0.351722i	$-0.885596\pi$
$223$	−4.49900	−	16.7905i	−0.301275	−	1.12437i	0.634829	−	0.772652i	$-0.281070\pi$
$224$	2.40918	+	1.09354i	0.160970	+	0.0730652i
$225$	7.07509	−	4.08481i	0.471673	−	0.272320i
$226$	−2.14984	+	0.576049i	−0.143005	+	0.0383182i
$227$	−5.46249	−	20.3863i	−0.362558	−	1.35308i	−0.870701	−	0.491812i	$-0.836335\pi$
$227$	−5.46249	−	20.3863i	−0.362558	−	1.35308i	0.508143	−	0.861273i	$-0.330332\pi$
$228$	−0.453168	−	1.69124i	−0.0300118	−	0.112005i
$229$	10.0670	−	2.69746i	0.665249	−	0.178253i	0.0896351	−	0.995975i	$-0.471430\pi$
$229$	10.0670	−	2.69746i	0.665249	−	0.178253i	0.575614	+	0.817722i	$0.304763\pi$
$230$	−8.75039	+	5.05204i	−0.576984	+	0.333122i
$231$	0.722900	+	7.39065i	0.0475634	+	0.486269i
$232$	1.25257	+	4.67466i	0.0822354	+	0.306907i
$233$	18.3850	+	10.6146i	1.20444	+	0.695386i	0.961540	−	0.274665i	$-0.0885669\pi$
$233$	18.3850	+	10.6146i	1.20444	+	0.695386i	0.242903	+	0.970051i	$0.421900\pi$
$234$	−2.48012	+	2.61706i	−0.162130	+	0.171083i
$235$	3.77320	+	6.53538i	0.246137	+	0.426321i
$236$	5.27526	+	1.41350i	0.343390	+	0.0920112i
$237$	−4.08603	−	2.35907i	−0.265416	−	0.153238i
$238$	1.02308	+	10.4596i	0.0663165	+	0.677994i
$239$	−13.2336	−	13.2336i	−0.856011	−	0.856011i	0.134855	−	0.990865i	$-0.456943\pi$
$239$	−13.2336	−	13.2336i	−0.856011	−	0.856011i	−0.990865	+	0.134855i	$0.956943\pi$
$240$	−2.56609	−	2.56609i	−0.165640	−	0.165640i
$241$	−17.3135	+	4.63914i	−1.11526	+	0.298833i	−0.768965	−	0.639291i	$-0.779228\pi$
$241$	−17.3135	+	4.63914i	−1.11526	+	0.298833i	−0.346297	+	0.938125i	$0.612561\pi$
$242$	−3.01586	−	0.808097i	−0.193867	−	0.0519465i
$243$			1.00000i			0.0641500i
$244$	6.84779	−	11.8607i	0.438385	−	0.759305i
$245$	−22.7983	+	11.2048i	−1.45653	+	0.715849i
$246$			8.08186i			0.515280i
$247$	−6.05179	+	1.79711i	−0.385066	+	0.114347i
$248$	8.30749	−	4.79633i	0.527526	−	0.304567i
$249$	4.55850	+	4.55850i	0.288883	+	0.288883i
$250$	9.96147	−	5.75126i	0.630019	−	0.363741i
$251$	−2.34493	−	4.06154i	−0.148011	−	0.256362i	0.782481	−	0.622674i	$-0.213954\pi$
$251$	−2.34493	−	4.06154i	−0.148011	−	0.256362i	−0.930492	+	0.366312i	$0.880620\pi$
$252$	−0.930302	−	2.47680i	−0.0586035	−	0.156024i
$253$	−2.02259	+	7.54841i	−0.127159	+	0.474564i
$254$	3.32147	−	3.32147i	0.208408	−	0.208408i
$255$	3.73092	−	13.9240i	0.233639	−	0.871953i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−5.25727	−	9.10586i	−0.327939	−	0.568008i	0.654163	−	0.756353i	$-0.273021\pi$
$257$	−5.25727	−	9.10586i	−0.327939	−	0.568008i	−0.982103	+	0.188346i	$0.939688\pi$
$258$	2.17975	−	0.584061i	0.135705	−	0.0363621i
$259$	17.9016	+	25.0171i	1.11235	+	1.55449i
$260$	−9.00033	+	9.49732i	−0.558177	+	0.588999i
$261$	2.41978	−	4.19119i	0.149781	−	0.259428i
$262$	−10.3692	+	10.3692i	−0.640612	+	0.640612i
$263$	5.01761			0.309399			0.154700	−	0.987962i	$-0.450559\pi$
$263$	5.01761			0.309399			0.154700	+	0.987962i	$0.450559\pi$
$264$	−2.80673			−0.172742
$265$	−11.3668	+	11.3668i	−0.698254	+	0.698254i
$266$	0.757678	−	4.57008i	0.0464562	−	0.280209i
$267$	−3.14403	−	0.842441i	−0.192412	−	0.0515566i
$268$	−0.946174	−	3.53117i	−0.0577968	−	0.215701i
$269$	6.95285	+	4.01423i	0.423923	+	0.244752i	0.696754	−	0.717310i	$-0.254627\pi$
$269$	6.95285	+	4.01423i	0.423923	+	0.244752i	−0.272832	+	0.962062i	$0.587960\pi$
$270$			3.62900i			0.220854i
$271$	5.00226	−	18.6687i	0.303866	−	1.13404i	−0.630052	−	0.776553i	$-0.716966\pi$
$271$	5.00226	−	18.6687i	0.303866	−	1.13404i	0.933917	−	0.357489i	$-0.116367\pi$
$272$	−3.97221			−0.240851
$273$	−8.83692	+	3.59289i	−0.534835	+	0.217451i
$274$	1.65351			0.0998921
$275$	5.93470	−	22.1486i	0.357876	−	1.33561i
$276$		−	2.78426i		−	0.167593i
$277$	−16.4813	−	9.51546i	−0.990263	−	0.571728i	−0.0849099	−	0.996389i	$-0.527060\pi$
$277$	−16.4813	−	9.51546i	−0.990263	−	0.571728i	−0.905353	+	0.424660i	$0.860394\pi$
$278$	−2.28389	−	8.52358i	−0.136978	−	0.511211i
$279$	−9.26580	−	2.48276i	−0.554729	−	0.148639i
$280$	−3.37606	−	8.98830i	−0.201758	−	0.537154i
$281$	6.31850	−	6.31850i	0.376930	−	0.376930i	−0.493063	−	0.869993i	$-0.664123\pi$
$281$	6.31850	−	6.31850i	0.376930	−	0.376930i	0.869993	+	0.493063i	$0.164123\pi$
$282$	−2.07947			−0.123831
$283$	28.7184			1.70713			0.853566	−	0.520985i	$-0.174435\pi$
$283$	28.7184			1.70713			0.853566	+	0.520985i	$0.174435\pi$
$284$	5.21569	−	5.21569i	0.309494	−	0.309494i
$285$	−3.17701	+	5.50275i	−0.188190	+	0.325955i
$286$	0.271797	+	10.1162i	0.0160717	+	0.598182i
$287$	−8.83783	+	19.4707i	−0.521681	+	1.14932i
$288$	0.965926	−	0.258819i	0.0569177	−	0.0152511i
$289$	0.610755	+	1.05786i	0.0359268	+	0.0622270i
$290$	8.78139	−	15.2098i	0.515661	−	0.893151i
$291$	−4.00703	+	14.9544i	−0.234896	+	0.876645i
$292$	−3.85497	+	3.85497i	−0.225595	+	0.225595i
$293$	5.51855	−	20.5955i	0.322397	−	1.20320i	−0.594505	−	0.804092i	$-0.702652\pi$
$293$	5.51855	−	20.5955i	0.322397	−	1.20320i	0.916903	−	0.399111i	$-0.130681\pi$
$294$	0.467210	−	6.98439i	0.0272483	−	0.407338i
$295$	−9.90962	−	17.1640i	−0.576960	−	0.999324i
$296$	−10.0693	+	5.81353i	−0.585268	+	0.337905i
$297$	1.98466	+	1.98466i	0.115162	+	0.115162i
$298$	−14.3694	+	8.29619i	−0.832398	+	0.480585i
$299$	−10.0352	+	0.269621i	−0.580350	+	0.0155926i
$300$			8.16961i			0.471673i
$301$	5.89011	+	0.976528i	0.339500	+	0.0562861i
$302$	−5.52759	+	9.57406i	−0.318077	+	0.550925i
$303$		−	10.3382i		−	0.593912i
$304$	1.69124	+	0.453168i	0.0969995	+	0.0259909i
$305$	−48.0077	+	12.8636i	−2.74891	+	0.736569i
$306$	2.80878	+	2.80878i	0.160567	+	0.160567i
$307$	−15.0865	−	15.0865i	−0.861034	−	0.861034i	0.130424	−	0.991458i	$-0.458366\pi$
$307$	−15.0865	−	15.0865i	−0.861034	−	0.861034i	−0.991458	+	0.130424i	$0.958366\pi$
$308$	−6.76194	−	3.06927i	−0.385297	−	0.174888i
$309$	4.41323	+	2.54798i	0.251060	+	0.144950i
$310$	−33.6256	−	9.00994i	−1.90980	−	0.511730i
$311$	14.6633	+	25.3976i	0.831482	+	1.44017i	0.896863	+	0.442308i	$0.145840\pi$
$311$	14.6633	+	25.3976i	0.831482	+	1.44017i	−0.0653816	+	0.997860i	$0.520826\pi$
$312$	−1.02639	−	3.45638i	−0.0581077	−	0.195679i
$313$	20.0771	+	11.5915i	1.13483	+	0.655192i	0.945144	−	0.326654i	$-0.105921\pi$
$313$	20.0771	+	11.5915i	1.13483	+	0.655192i	0.189682	+	0.981846i	$0.439254\pi$
$314$	−2.48374	−	9.26943i	−0.140165	−	0.523104i
$315$	−3.96845	+	8.74292i	−0.223597	+	0.492608i
$316$	4.08603	−	2.35907i	0.229857	−	0.132708i
$317$	−30.0906	+	8.06274i	−1.69005	+	0.452849i	−0.970404	−	0.241488i	$-0.922364\pi$
$317$	−30.0906	+	8.06274i	−1.69005	+	0.452849i	−0.719650	+	0.694337i	$0.755698\pi$
$318$	−1.14647	−	4.27867i	−0.0642906	−	0.239936i
$319$	−3.51564	−	13.1205i	−0.196838	−	0.734609i
$320$	3.50534	−	0.939253i	0.195955	−	0.0525059i
$321$	−14.4036	+	8.31594i	−0.803932	+	0.464150i
$322$	3.04470	−	6.70781i	0.169675	−	0.373811i
$323$	1.80008	+	6.71799i	0.100159	+	0.373799i
$324$	−0.866025	−	0.500000i	−0.0481125	−	0.0277778i
$325$	29.4453	−	0.791126i	1.63333	−	0.0438838i
$326$	−9.89527	−	17.1391i	−0.548048	−	0.949248i
$327$	−0.625393	−	0.167574i	−0.0345843	−	0.00926684i
$328$	−6.99909	−	4.04093i	−0.386460	−	0.223123i
$329$	−5.00984	−	2.27399i	−0.276201	−	0.125369i
$330$	7.20232	+	7.20232i	0.396475	+	0.396475i
$331$	0.593522	+	0.593522i	0.0326229	+	0.0326229i	0.723230	−	0.690607i	$-0.242657\pi$
$331$	0.593522	+	0.593522i	0.0326229	+	0.0326229i	−0.690607	+	0.723230i	$0.742657\pi$
$332$	−6.22703	+	1.66853i	−0.341753	+	0.0915724i
$333$	11.2309	+	3.00931i	0.615448	+	0.164909i
$334$		−	10.1393i		−	0.554798i
$335$	−6.63333	+	11.4893i	−0.362417	+	0.627725i
$336$	2.61012	+	0.432735i	0.142394	+	0.0236076i
$337$		−	21.7718i		−	1.18598i	−0.805208	−	0.592992i	$-0.797947\pi$
$337$		−	21.7718i		−	1.18598i	0.805208	−	0.592992i	$-0.202053\pi$
$338$	−12.3583	+	4.03406i	−0.672200	+	0.219424i
$339$	−1.92750	+	1.11284i	−0.104687	+	0.0604412i
$340$	10.1931	+	10.1931i	0.552796	+	0.552796i
$341$	−23.3169	+	13.4620i	−1.26268	+	0.729010i
$342$	−0.875453	−	1.51633i	−0.0473391	−	0.0819937i
$343$	8.76330	−	16.3158i	0.473174	−	0.880969i
$344$	−0.584061	+	2.17975i	−0.0314905	+	0.117524i
$345$	−7.14466	+	7.14466i	−0.384656	+	0.384656i
$346$	−4.44097	+	16.5739i	−0.238748	+	0.891021i
$347$	3.32459	−	5.75836i	0.178473	−	0.309125i	−0.762885	−	0.646535i	$-0.776218\pi$
$347$	3.32459	−	5.75836i	0.178473	−	0.309125i	0.941358	+	0.337410i	$0.109551\pi$
$348$	2.41978	+	4.19119i	0.129714	+	0.224671i
$349$	6.21010	−	1.66399i	0.332419	−	0.0890714i	−0.0887491	−	0.996054i	$-0.528287\pi$
$349$	6.21010	−	1.66399i	0.332419	−	0.0890714i	0.421168	+	0.906983i	$0.361620\pi$
$350$	−8.93380	+	19.6821i	−0.477531	+	1.05205i
$351$	−1.71826	+	3.16979i	−0.0917140	+	0.169191i
$352$	1.40337	−	2.43070i	0.0747997	−	0.129557i
$353$	−15.7099	+	15.7099i	−0.836152	+	0.836152i	−0.988350	−	0.152198i	$-0.951365\pi$
$353$	−15.7099	+	15.7099i	−0.836152	+	0.836152i	0.152198	+	0.988350i	$0.451365\pi$
$354$	5.46135			0.290268
$355$	−26.7678			−1.42069
$356$	2.30159	−	2.30159i	0.121984	−	0.121984i
$357$	3.69536	+	9.83838i	0.195579	+	0.520702i
$358$	−14.5457	−	3.89751i	−0.768765	−	0.205990i
$359$	0.506100	+	1.88879i	0.0267109	+	0.0996865i	0.977994	−	0.208631i	$-0.0669008\pi$
$359$	0.506100	+	1.88879i	0.0267109	+	0.0996865i	−0.951284	+	0.308317i	$0.900234\pi$
$360$	−3.14280	−	1.81450i	−0.165640	−	0.0956324i
$361$			15.9343i			0.838649i
$362$	6.31996	−	23.5864i	0.332170	−	1.23967i
$363$	−3.12225			−0.163875
$364$	1.30693	−	9.44944i	0.0685016	−	0.495285i
$365$	19.7844			1.03556
$366$	3.54468	−	13.2289i	0.185283	−	0.691486i
$367$		−	16.6770i		−	0.870533i	−0.900302	−	0.435267i	$-0.856654\pi$
$367$		−	16.6770i		−	0.870533i	0.900302	−	0.435267i	$-0.143346\pi$
$368$	2.41124	+	1.39213i	0.125695	+	0.0725699i
$369$	2.09174	+	7.80648i	0.108892	+	0.406389i
$370$	40.7568	+	10.9208i	2.11885	+	0.567743i
$371$	1.91685	−	11.5618i	0.0995177	−	0.600260i
$372$	6.78304	−	6.78304i	0.351684	−	0.351684i
$373$	−12.4274			−0.643465			−0.321733	−	0.946831i	$-0.604265\pi$
$373$	−12.4274			−0.643465			−0.321733	+	0.946831i	$0.604265\pi$
$374$	11.1489			0.576498
$375$	8.13351	−	8.13351i	0.420012	−	0.420012i
$376$	1.03974	−	1.80088i	0.0536203	−	0.0928732i
$377$	14.8718	−	9.12737i	0.765935	−	0.470084i
$378$	−1.53965	−	2.15163i	−0.0791908	−	0.110668i
$379$	7.07722	−	1.89633i	0.363532	−	0.0974082i	−0.0724291	−	0.997374i	$-0.523075\pi$
$379$	7.07722	−	1.89633i	0.363532	−	0.0974082i	0.435961	+	0.899965i	$0.356408\pi$
$380$	−3.17701	−	5.50275i	−0.162977	−	0.282285i
$381$	2.34863	−	4.06795i	0.120324	−	0.208408i
$382$	1.01118	−	3.77376i	0.0517362	−	0.193082i
$383$	9.62294	−	9.62294i	0.491709	−	0.491709i	−0.417135	−	0.908844i	$-0.636966\pi$
$383$	9.62294	−	9.62294i	0.491709	−	0.491709i	0.908844	+	0.417135i	$0.136966\pi$
$384$	−0.258819	+	0.965926i	−0.0132078	+	0.0492922i
$385$	9.47570	+	25.2278i	0.482927	+	1.28573i
$386$	8.80460	+	15.2500i	0.448142	+	0.776205i
$387$	1.95431	−	1.12832i	0.0993430	−	0.0573557i
$388$	−10.9474	−	10.9474i	−0.555771	−	0.555771i
$389$	−4.45547	+	2.57237i	−0.225901	+	0.130424i	−0.608680	−	0.793416i	$-0.708301\pi$
$389$	−4.45547	+	2.57237i	−0.225901	+	0.130424i	0.382778	+	0.923840i	$0.374967\pi$
$390$	−6.23556	+	11.5032i	−0.315750	+	0.582485i
$391$			11.0597i			0.559313i
$392$	5.81505	+	3.89681i	0.293705	+	0.196819i
$393$	−7.33214	+	12.6996i	−0.369858	+	0.640612i
$394$		−	16.2429i		−	0.818306i
$395$	−16.5387	−	4.43153i	−0.832151	−	0.222974i
$396$	−2.71110	+	0.726436i	−0.136238	+	0.0365048i
$397$	9.55380	+	9.55380i	0.479491	+	0.479491i	0.904969	−	0.425478i	$-0.139894\pi$
$397$	9.55380	+	9.55380i	0.479491	+	0.479491i	−0.425478	+	0.904969i	$0.639894\pi$
$398$	17.6196	+	17.6196i	0.883191	+	0.883191i
$399$	−0.450962	−	4.61046i	−0.0225763	−	0.230812i
$400$	−7.07509	−	4.08481i	−0.353755	−	0.204240i
$401$	13.8999	+	3.72447i	0.694128	+	0.185991i	0.588599	−	0.808425i	$-0.299680\pi$
$401$	13.8999	+	3.72447i	0.694128	+	0.185991i	0.105529	+	0.994416i	$0.466346\pi$
$402$	−1.82787	−	3.16596i	−0.0911658	−	0.157904i
$403$	−25.1046	−	23.7909i	−1.25055	−	1.18511i
$404$	8.95311	+	5.16908i	0.445434	+	0.257171i
$405$	0.939253	+	3.50534i	0.0466719	+	0.174182i
$406$	1.24648	+	12.7435i	0.0618616	+	0.632448i
$407$	28.2619	−	16.3170i	1.40089	−	0.808805i
$408$	−3.83686	+	1.02808i	−0.189953	+	0.0508978i
$409$	5.94776	+	22.1974i	0.294098	+	1.09759i	0.941931	+	0.335806i	$0.109009\pi$
$409$	5.94776	+	22.1974i	0.294098	+	1.09759i	−0.647833	+	0.761782i	$0.724325\pi$
$410$	7.59091	+	28.3297i	0.374888	+	1.39910i
$411$	1.59717	−	0.427959i	0.0787824	−	0.0211097i
$412$	−4.41323	+	2.54798i	−0.217424	+	0.125530i
$413$	13.1574	+	5.97221i	0.647434	+	0.293873i
$414$	−0.720620	−	2.68939i	−0.0354166	−	0.132176i
$415$	20.2607	+	11.6975i	0.994559	+	0.574209i
$416$	3.50650	+	0.839311i	0.171920	+	0.0411506i
$417$	−4.41213	−	7.64204i	−0.216063	−	0.374232i
$418$	−4.74687	−	1.27192i	−0.232177	−	0.0622117i
$419$	28.1122	+	16.2306i	1.37337	+	0.792917i	0.991351	−	0.131236i	$-0.0418946\pi$
$419$	28.1122	+	16.2306i	1.37337	+	0.792917i	0.382022	+	0.924153i	$0.375228\pi$
$420$	−5.58737	−	7.80824i	−0.272636	−	0.381003i
$421$	−17.5164	−	17.5164i	−0.853695	−	0.853695i	0.136891	−	0.990586i	$-0.456289\pi$
$421$	−17.5164	−	17.5164i	−0.853695	−	0.853695i	−0.990586	+	0.136891i	$0.956289\pi$
$422$	17.7930	+	17.7930i	0.866150	+	0.866150i
$423$	−2.00862	+	0.538208i	−0.0976623	+	0.0261685i
$424$	4.27867	+	1.14647i	0.207791	+	0.0556773i
$425$		−	32.4515i		−	1.57413i
$426$	3.68805	−	6.38789i	0.178687	−	0.309494i
$427$	23.0061	−	27.9946i	1.11334	−	1.35476i
$428$		−	16.6319i		−	0.803932i
$429$	2.88079	+	9.70112i	0.139086	+	0.468375i
$430$	7.09217	−	4.09467i	0.342015	−	0.197462i
$431$	−1.30293	−	1.30293i	−0.0627599	−	0.0627599i	0.675030	−	0.737790i	$-0.264131\pi$
$431$	−1.30293	−	1.30293i	−0.0627599	−	0.0627599i	−0.737790	+	0.675030i	$0.764131\pi$
$432$	0.866025	−	0.500000i	0.0416667	−	0.0240563i
$433$	9.67519	+	16.7579i	0.464960	+	0.805335i	0.999200	−	0.0399985i	$-0.0127353\pi$
$433$	9.67519	+	16.7579i	0.464960	+	0.805335i	−0.534240	+	0.845333i	$0.679402\pi$
$434$	23.7591	−	8.92407i	1.14047	−	0.428369i
$435$	4.54558	−	16.9643i	0.217944	−	0.813378i
$436$	0.457819	−	0.457819i	0.0219256	−	0.0219256i
$437$	1.26174	−	4.70887i	0.0603571	−	0.225256i
$438$	−2.72587	+	4.72135i	−0.130247	+	0.225595i
$439$	−12.2927	−	21.2916i	−0.586698	−	1.01619i	−0.994661	−	0.103192i	$-0.967094\pi$
$439$	−12.2927	−	21.2916i	−0.586698	−	1.01619i	0.407963	−	0.912998i	$-0.366239\pi$
$440$	−9.83856	+	2.63623i	−0.469035	+	0.125678i
$441$	−1.35640	−	6.86733i	−0.0645906	−	0.327016i
$442$	4.07703	+	13.7295i	0.193924	+	0.653044i
$443$	12.3604	−	21.4088i	0.587260	−	1.01716i	−0.407330	−	0.913281i	$-0.633540\pi$
$443$	12.3604	−	21.4088i	0.587260	−	1.01716i	0.994590	−	0.103883i	$-0.0331267\pi$
$444$	−8.22157	+	8.22157i	−0.390179	+	0.390179i
$445$	−11.8122			−0.559951
$446$	17.3828			0.823099
$447$	−11.7326	+	11.7326i	−0.554932	+	0.554932i
$448$	−1.67982	+	2.04406i	−0.0793641	+	0.0965730i
$449$	24.5873	+	6.58814i	1.16034	+	0.310913i	0.787104	−	0.616821i	$-0.211580\pi$
$449$	24.5873	+	6.58814i	1.16034	+	0.310913i	0.373241	+	0.927734i	$0.378246\pi$
$450$	2.11445	+	7.89124i	0.0996762	+	0.371997i
$451$	19.6446	+	11.3418i	0.925028	+	0.534065i
$452$		−	2.22568i		−	0.104687i
$453$	−2.86129	+	10.6785i	−0.134435	+	0.501719i
$454$	21.1054			0.990527
$455$	−27.6018	+	20.8944i	−1.29399	+	0.979545i
$456$	1.75091			0.0819937
$457$	1.36006	−	5.07581i	0.0636209	−	0.237436i	−0.926792	−	0.375575i	$-0.877445\pi$
$457$	1.36006	−	5.07581i	0.0636209	−	0.237436i	0.990413	+	0.138139i	$0.0441119\pi$
$458$			10.4222i			0.486996i
$459$	3.44004	+	1.98611i	0.160567	+	0.0927036i
$460$	−2.61513	−	9.75979i	−0.121931	−	0.455053i
$461$	−0.174143	−	0.0466615i	−0.00811065	−	0.00217324i	0.254761	−	0.967004i	$-0.418003\pi$
$461$	−0.174143	−	0.0466615i	−0.00811065	−	0.00217324i	−0.262872	+	0.964831i	$0.584670\pi$
$462$	−7.32592	−	1.21457i	−0.340833	−	0.0565070i
$463$	3.43433	−	3.43433i	0.159607	−	0.159607i	−0.622786	−	0.782393i	$-0.713999\pi$
$463$	3.43433	−	3.43433i	0.159607	−	0.159607i	0.782393	+	0.622786i	$0.213999\pi$
$464$	−4.83957			−0.224671
$465$	−34.8117			−1.61436
$466$	−15.0113	+	15.0113i	−0.695386	+	0.695386i
$467$	−14.7088	+	25.4765i	−0.680644	+	1.17891i	0.294141	+	0.955762i	$0.404967\pi$
$467$	−14.7088	+	25.4765i	−0.680644	+	1.17891i	−0.974785	+	0.223148i	$0.928367\pi$
$468$	−1.88599	−	3.07295i	−0.0871799	−	0.142047i
$469$	−0.941569	−	9.62623i	−0.0434776	−	0.444498i
$470$	−7.28927	+	1.95315i	−0.336229	+	0.0900922i
$471$	−4.79821	−	8.31074i	−0.221090	−	0.382939i
$472$	−2.73068	+	4.72967i	−0.125690	+	0.217701i
$473$	1.63930	−	6.11797i	0.0753753	−	0.281304i
$474$	3.33623	−	3.33623i	0.153238	−	0.153238i
$475$	−3.70220	+	13.8168i	−0.169869	+	0.633959i
$476$	−10.3680	−	1.71892i	−0.475215	−	0.0787864i
$477$	−2.21480	−	3.83615i	−0.101409	−	0.175645i
$478$	16.2078	−	9.35757i	0.741327	−	0.428005i
$479$	13.6690	+	13.6690i	0.624553	+	0.624553i	0.946692	−	0.322140i	$-0.104402\pi$
$479$	13.6690	+	13.6690i	0.624553	+	0.624553i	−0.322140	+	0.946692i	$0.604402\pi$
$480$	3.14280	−	1.81450i	0.143449	−	0.0828201i
$481$	30.4288	+	28.8365i	1.38743	+	1.31483i
$482$		−	17.9243i		−	0.816428i
$483$	1.20485	−	7.26727i	0.0548225	−	0.330672i
$484$	1.56112	−	2.70395i	0.0709602	−	0.122907i
$485$			56.1840i			2.55119i
$486$	−0.965926	−	0.258819i	−0.0438153	−	0.0117403i
$487$	−33.7465	+	9.04234i	−1.52920	+	0.409748i	−0.922758	−	0.385381i	$-0.874070\pi$
$487$	−33.7465	+	9.04234i	−1.52920	+	0.409748i	−0.606441	+	0.795128i	$0.707403\pi$
$488$	9.68424	+	9.68424i	0.438385	+	0.438385i
$489$	−13.9940	−	13.9940i	−0.632832	−	0.632832i
$490$	−4.92238	−	24.9215i	−0.222370	−	1.12584i
$491$	8.91669	+	5.14805i	0.402404	+	0.232328i	0.687521	−	0.726165i	$-0.258699\pi$
$491$	8.91669	+	5.14805i	0.402404	+	0.232328i	−0.285117	+	0.958493i	$0.592032\pi$
$492$	−7.80648	−	2.09174i	−0.351943	−	0.0943029i
$493$	−9.61190	−	16.6483i	−0.432898	−	0.749802i
$494$	−0.169553	−	6.31070i	−0.00762857	−	0.283932i
$495$	8.82101	+	5.09281i	0.396475	+	0.228905i
$496$	2.48276	+	9.26580i	0.111479	+	0.416047i
$497$	15.8706	−	11.3566i	0.711894	−	0.509412i
$498$	−5.58300	+	3.22335i	−0.250180	+	0.144442i
$499$	15.3926	−	4.12442i	0.689065	−	0.184634i	0.102738	−	0.994708i	$-0.467240\pi$
$499$	15.3926	−	4.12442i	0.689065	−	0.184634i	0.586328	+	0.810074i	$0.300573\pi$
$500$	2.97707	+	11.1106i	0.133139	+	0.496880i
$501$	−2.62425	−	9.79382i	−0.117243	−	0.437556i
$502$	4.53006	−	1.21383i	0.202186	−	0.0541757i
$503$	−13.8649	+	8.00489i	−0.618205	+	0.356921i	−0.776170	−	0.630524i	$-0.782840\pi$
$503$	−13.8649	+	8.00489i	−0.618205	+	0.356921i	0.157965	+	0.987445i	$0.449507\pi$
$504$	2.63318	−	0.257559i	0.117291	−	0.0114726i
$505$	−9.71015	−	36.2388i	−0.432096	−	1.61260i
$506$	−6.76772	−	3.90734i	−0.300862	−	0.173703i
$507$	−10.8931	+	7.09515i	−0.483778	+	0.315107i
$508$	2.34863	+	4.06795i	0.104204	+	0.180486i
$509$	12.8430	+	3.44126i	0.569254	+	0.152531i	0.531955	−	0.846773i	$-0.321458\pi$
$509$	12.8430	+	3.44126i	0.569254	+	0.152531i	0.0372997	+	0.999304i	$0.488124\pi$
$510$	12.4839	+	7.20758i	0.552796	+	0.319157i
$511$	−11.7301	+	8.39376i	−0.518910	+	0.371318i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−1.23808	−	1.23808i	−0.0546624	−	0.0546624i
$514$	10.1563	−	2.72136i	0.447974	−	0.120034i
$515$	17.8631	+	4.78640i	0.787141	+	0.210914i
$516$			2.25664i			0.0993430i
$517$	−2.91826	+	5.05458i	−0.128345	+	0.222300i
$518$	−28.7979	+	10.8167i	−1.26531	+	0.475257i
$519$			17.1586i			0.753179i
$520$	−6.84425	−	11.1517i	−0.300140	−	0.489036i
$521$	16.2369	−	9.37438i	0.711351	−	0.410699i	−0.100210	−	0.994966i	$-0.531951\pi$
$521$	16.2369	−	9.37438i	0.711351	−	0.410699i	0.811561	+	0.584267i	$0.198618\pi$
$522$	3.42209	+	3.42209i	0.149781	+	0.149781i
$523$	4.34272	−	2.50727i	0.189894	−	0.109635i	−0.402039	−	0.915622i	$-0.631698\pi$
$523$	4.34272	−	2.50727i	0.189894	−	0.109635i	0.591933	+	0.805987i	$0.298365\pi$
$524$	−7.33214	−	12.6996i	−0.320306	−	0.554787i
$525$	−3.53528	+	21.3237i	−0.154292	+	0.930642i
$526$	−1.29865	+	4.84664i	−0.0566240	+	0.211324i
$527$	−26.9437	+	26.9437i	−1.17369	+	1.17369i
$528$	0.726436	−	2.71110i	0.0316141	−	0.117985i
$529$	−7.62394	+	13.2050i	−0.331476	+	0.574133i
$530$	−8.03751	−	13.9214i	−0.349127	−	0.604706i
$531$	5.27526	−	1.41350i	0.228927	−	0.0613408i
$532$	4.21825	+	1.91468i	0.182885	+	0.0830121i
$533$	−6.78319	+	28.3391i	−0.293813	+	1.22750i
$534$	1.62747	−	2.81886i	0.0704276	−	0.121984i
$535$	−42.6789	+	42.6789i	−1.84517	+	1.84517i
$536$	3.65574			0.157904
$537$	−15.0588			−0.649837
$538$	−5.67698	+	5.67698i	−0.244752	+	0.244752i
$539$	−16.3213	−	10.9373i	−0.703009	−	0.471103i
$540$	−3.50534	−	0.939253i	−0.150846	−	0.0404190i
$541$	2.27108	+	8.47577i	0.0976412	+	0.364402i	0.997407	−	0.0719719i	$-0.0229292\pi$
$541$	2.27108	+	8.47577i	0.0976412	+	0.364402i	−0.899765	+	0.436374i	$0.856263\pi$
$542$	16.7379	+	9.66362i	0.718954	+	0.415088i
$543$		−	24.4184i		−	1.04790i
$544$	1.02808	−	3.83686i	0.0440788	−	0.164504i
$545$	−2.34961			−0.100646
$546$	−1.18330	−	9.46572i	−0.0506406	−	0.405095i
$547$	−27.2919			−1.16692			−0.583459	−	0.812143i	$-0.698301\pi$
$547$	−27.2919			−1.16692			−0.583459	+	0.812143i	$0.698301\pi$
$548$	−0.427959	+	1.59717i	−0.0182815	+	0.0682276i
$549$		−	13.6956i		−	0.584513i
$550$	19.8579	+	11.4650i	0.846744	+	0.488868i
$551$	2.19314	+	8.18489i	0.0934307	+	0.348688i
$552$	2.68939	+	0.720620i	0.114468	+	0.0306716i
$553$	11.6859	−	4.38929i	0.496934	−	0.186652i
$554$	13.4569	−	13.4569i	0.571728	−	0.571728i
$555$	42.1946			1.79106
$556$	8.82426			0.374232
$557$	30.4514	−	30.4514i	1.29027	−	1.29027i	0.355649	−	0.934619i	$-0.384260\pi$
$557$	30.4514	−	30.4514i	1.29027	−	1.29027i	0.934619	−	0.355649i	$-0.115740\pi$
$558$	4.79633	−	8.30749i	0.203045	−	0.351684i
$559$	8.13350	−	0.218528i	0.344010	−	0.00924273i
$560$	9.55582	−	0.934682i	0.403807	−	0.0394975i
$561$	10.7691	−	2.88556i	0.454670	−	0.121828i
$562$	4.46785	+	7.73855i	0.188465	+	0.326431i
$563$	19.2908	−	33.4126i	0.813009	−	1.40817i	−0.0977392	−	0.995212i	$-0.531161\pi$
$563$	19.2908	−	33.4126i	0.813009	−	1.40817i	0.910749	−	0.412961i	$-0.135506\pi$
$564$	0.538208	−	2.00862i	0.0226626	−	0.0845781i
$565$	−5.71130	+	5.71130i	−0.240276	+	0.240276i
$566$	−7.43287	+	27.7398i	−0.312427	+	1.16599i
$567$	−2.04406	−	1.67982i	−0.0858427	−	0.0705459i
$568$	3.68805	+	6.38789i	0.154747	+	0.268030i
$569$	−12.3303	+	7.11890i	−0.516913	+	0.298440i	−0.735671	−	0.677339i	$-0.763133\pi$
$569$	−12.3303	+	7.11890i	−0.516913	+	0.298440i	0.218758	+	0.975779i	$0.429800\pi$
$570$	−4.49298	−	4.49298i	−0.188190	−	0.188190i
$571$	−0.320357	+	0.184958i	−0.0134065	+	0.00774025i	−0.506688	−	0.862129i	$-0.669130\pi$
$571$	−0.320357	+	0.184958i	−0.0134065	+	0.00774025i	0.493282	+	0.869870i	$0.335797\pi$
$572$	−9.84182	−	2.35572i	−0.411507	−	0.0984977i
$573$		−	3.90688i		−	0.163212i
$574$	−16.5198	−	13.5761i	−0.689525	−	0.566654i
$575$	−11.3732	+	19.6989i	−0.474294	+	0.821502i
$576$			1.00000i			0.0416667i
$577$	14.6550	+	3.92680i	0.610097	+	0.163475i	0.550622	−	0.834755i	$-0.314391\pi$
$577$	14.6550	+	3.92680i	0.610097	+	0.163475i	0.0594750	+	0.998230i	$0.481057\pi$
$578$	−1.17989	+	0.316150i	−0.0490769	+	0.0131501i
$579$	12.4516	+	12.4516i	0.517470	+	0.517470i
$580$	12.4188	+	12.4188i	0.515661	+	0.515661i
$581$	−16.9753	+	1.66041i	−0.704256	+	0.0688853i
$582$	−13.4078	−	7.74099i	−0.555771	−	0.320874i
$583$	−12.0091	−	3.21783i	−0.497366	−	0.133269i
$584$	−2.72587	−	4.72135i	−0.112797	−	0.195371i
$585$	−3.04586	+	12.7251i	−0.125931	+	0.526117i
$586$	18.4654	+	10.6610i	0.762800	+	0.440403i
$587$	−0.548765	−	2.04802i	−0.0226499	−	0.0845307i	0.953676	−	0.300837i	$-0.0972659\pi$
$587$	−0.548765	−	2.04802i	−0.0226499	−	0.0845307i	−0.976326	+	0.216306i	$0.930599\pi$
$588$	6.62548	+	2.25898i	0.273230	+	0.0931589i
$589$	14.5456	−	8.39793i	0.599342	−	0.346030i
$590$	19.1439	−	5.12959i	0.788142	−	0.211182i
$591$	−4.20397	−	15.6894i	−0.172928	−	0.645377i
$592$	−3.00931	−	11.2309i	−0.123682	−	0.461586i
$593$	−24.5618	+	6.58130i	−1.00863	+	0.270262i	−0.725057	−	0.688689i	$-0.758187\pi$
$593$	−24.5618	+	6.58130i	−1.00863	+	0.270262i	−0.283573	+	0.958951i	$0.591520\pi$
$594$	−2.43070	+	1.40337i	−0.0997329	+	0.0575808i
$595$	22.1942	+	31.0160i	0.909874	+	1.27153i
$596$	−4.29442	−	16.0270i	−0.175906	−	0.656492i
$597$	21.5795	+	12.4589i	0.883191	+	0.509911i
$598$	2.33686	−	9.76303i	0.0955614	−	0.399240i
$599$	8.48442	+	14.6954i	0.346664	+	0.600440i	0.985655	−	0.168775i	$-0.0539811\pi$
$599$	8.48442	+	14.6954i	0.346664	+	0.600440i	−0.638991	+	0.769215i	$0.720648\pi$
$600$	−7.89124	−	2.11445i	−0.322159	−	0.0863221i
$601$	30.9667	+	17.8786i	1.26316	+	0.729284i	0.973684	−	0.227903i	$-0.0731868\pi$
$601$	30.9667	+	17.8786i	1.26316	+	0.729284i	0.289472	+	0.957186i	$0.406520\pi$
$602$	−2.46773	+	5.43666i	−0.100577	+	0.221582i
$603$	−2.58500	−	2.58500i	−0.105269	−	0.105269i
$604$	−7.81719	−	7.81719i	−0.318077	−	0.318077i
$605$	−10.9445	+	2.93258i	−0.444959	+	0.119226i
$606$	9.98589	+	2.67571i	0.405649	+	0.108693i
$607$			25.3609i			1.02937i	0.857380	+	0.514685i	$0.172091\pi$
$607$			25.3609i			1.02937i	−0.857380	+	0.514685i	$0.827909\pi$
$608$	−0.875453	+	1.51633i	−0.0355043	+	0.0614952i
$609$	4.50226	+	11.9866i	0.182441	+	0.485723i
$610$		−	49.7012i		−	2.01234i
$611$	−7.29168	−	1.74533i	−0.294990	−	0.0706083i
$612$	−3.44004	+	1.98611i	−0.139055	+	0.0802836i
$613$	−16.7659	−	16.7659i	−0.677168	−	0.677168i	0.282191	−	0.959358i	$-0.408939\pi$
$613$	−16.7659	−	16.7659i	−0.677168	−	0.677168i	−0.959358	+	0.282191i	$0.908939\pi$
$614$	18.4772	−	10.6678i	0.745677	−	0.430517i
$615$	14.6645	+	25.3997i	0.591330	+	1.02421i
$616$	4.71481	−	5.73715i	0.189965	−	0.231156i
$617$	−2.21727	+	8.27497i	−0.0892639	+	0.333138i	−0.996087	−	0.0883729i	$-0.971833\pi$
$617$	−2.21727	+	8.27497i	−0.0892639	+	0.333138i	0.906824	+	0.421511i	$0.138500\pi$
$618$	−3.60339	+	3.60339i	−0.144950	+	0.144950i
$619$	6.58689	−	24.5826i	0.264749	−	0.988058i	−0.697654	−	0.716435i	$-0.745773\pi$
$619$	6.58689	−	24.5826i	0.264749	−	0.988058i	0.962404	−	0.271624i	$-0.0875606\pi$
$620$	17.4059	−	30.1479i	0.699037	−	1.21077i
$621$	−1.39213	−	2.41124i	−0.0558643	−	0.0967598i
$622$	−28.3274	+	7.59030i	−1.13582	+	0.304343i
$623$	7.00342	−	5.01146i	0.280586	−	0.200780i
$624$	3.60425	−	0.0968376i	0.144285	−	0.00387661i
$625$	0.447257	−	0.774672i	0.0178903	−	0.0309869i
$626$	−16.3929	+	16.3929i	−0.655192	+	0.655192i
$627$	−4.91432			−0.196259
$628$	9.59642			0.382939
$629$	32.6579	−	32.6579i	1.30215	−	1.30215i
$630$	−7.41790	−	6.09606i	−0.295536	−	0.242873i
$631$	−16.9334	−	4.53729i	−0.674108	−	0.180627i	−0.0945035	−	0.995525i	$-0.530126\pi$
$631$	−16.9334	−	4.53729i	−0.674108	−	0.180627i	−0.579605	+	0.814898i	$0.696793\pi$
$632$	1.22114	+	4.55737i	0.0485745	+	0.181282i
$633$	21.7919	+	12.5816i	0.866150	+	0.500072i
$634$		−	31.1520i		−	1.23721i
$635$	4.41192	−	16.4655i	0.175082	−	0.653414i
$636$	4.42961			0.175645
$637$	7.50035	−	24.0986i	0.297175	−	0.954823i
$638$	13.5834			0.537771
$639$	1.90908	−	7.12477i	0.0755219	−	0.281851i
$640$			3.62900i			0.143449i
$641$	−34.4564	−	19.8934i	−1.36095	−	0.785743i	−0.371196	−	0.928554i	$-0.621052\pi$
$641$	−34.4564	−	19.8934i	−1.36095	−	0.785743i	−0.989750	+	0.142812i	$0.954386\pi$
$642$	−4.30465	−	16.0652i	−0.169891	−	0.634041i
$643$	19.5278	+	5.23247i	0.770103	+	0.206348i	0.622417	−	0.782686i	$-0.286151\pi$
$643$	19.5278	+	5.23247i	0.770103	+	0.206348i	0.147686	+	0.989034i	$0.452818\pi$
$644$	5.69122	+	4.67706i	0.224265	+	0.184302i
$645$	5.79074	−	5.79074i	0.228010	−	0.228010i
$646$	−6.95497			−0.273640
$647$	−45.1014			−1.77312			−0.886560	−	0.462614i	$-0.846912\pi$
$647$	−45.1014			−1.77312			−0.886560	+	0.462614i	$0.846912\pi$
$648$	0.707107	−	0.707107i	0.0277778	−	0.0277778i
$649$	7.66428	−	13.2749i	0.300849	−	0.521086i
$650$	−6.85684	+	28.6468i	−0.268948	+	1.12362i
$651$	20.6398	−	14.7693i	0.808938	−	0.578855i
$652$	19.1162	−	5.12217i	0.748648	−	0.200600i
$653$	−0.247860	−	0.429306i	−0.00969950	−	0.0168000i	0.861135	−	0.508376i	$-0.169754\pi$
$653$	−0.247860	−	0.429306i	−0.00969950	−	0.0168000i	−0.870834	+	0.491576i	$0.836421\pi$
$654$	0.323727	−	0.560712i	0.0126587	−	0.0219256i
$655$	−13.7735	+	51.4033i	−0.538175	+	2.00849i
$656$	5.71474	−	5.71474i	0.223123	−	0.223123i
$657$	−1.41102	+	5.26598i	−0.0550490	+	0.205446i
$658$	3.49314	−	4.25058i	0.136177	−	0.165705i
$659$	12.2364	+	21.1940i	0.476661	+	0.825600i	0.999642	−	0.0267435i	$-0.00851374\pi$
$659$	12.2364	+	21.1940i	0.476661	+	0.825600i	−0.522982	+	0.852344i	$0.675180\pi$
$660$	−8.82101	+	5.09281i	−0.343357	+	0.198237i
$661$	13.2866	+	13.2866i	0.516787	+	0.516787i	0.916598	−	0.399811i	$-0.130924\pi$
$661$	13.2866	+	13.2866i	0.516787	+	0.516787i	−0.399811	+	0.916598i	$0.630924\pi$
$662$	−0.726913	+	0.419684i	−0.0282523	+	0.0163115i
$663$	7.49155	+	12.2064i	0.290948	+	0.474059i
$664$		−	6.44670i		−	0.250180i
$665$	−5.91116	−	15.7377i	−0.229225	−	0.610280i
$666$	−5.81353	+	10.0693i	−0.225270	+	0.390179i
$667$			13.4746i			0.521740i
$668$	9.79382	+	2.62425i	0.378934	+	0.101535i
$669$	16.7905	−	4.49900i	0.649158	−	0.173941i
$670$	−9.38094	−	9.38094i	−0.362417	−	0.362417i
$671$	−27.1811	−	27.1811i	−1.04931	−	1.04931i
$672$	−1.09354	+	2.40918i	−0.0421842	+	0.0929363i
$673$	11.8135	+	6.82054i	0.455378	+	0.262912i	0.710099	−	0.704102i	$-0.248650\pi$
$673$	11.8135	+	6.82054i	0.455378	+	0.262912i	−0.254721	+	0.967015i	$0.581984\pi$
$674$	21.0299	+	5.63495i	0.810042	+	0.217050i
$675$	4.08481	+	7.07509i	0.157224	+	0.272320i
$676$	−0.698054	−	12.9812i	−0.0268482	−	0.499279i
$677$	−40.7614	−	23.5336i	−1.56659	−	0.904471i	−0.996562	−	0.0828450i	$-0.973599\pi$
$677$	−40.7614	−	23.5336i	−1.56659	−	0.904471i	−0.570027	−	0.821626i	$-0.693067\pi$
$678$	−0.576049	−	2.14984i	−0.0221230	−	0.0825643i
$679$	−23.8368	−	33.3114i	−0.914771	−	1.27837i
$680$	−12.4839	+	7.20758i	−0.478735	+	0.276398i
$681$	20.3863	−	5.46249i	0.781204	−	0.209323i
$682$	−6.96846	−	26.0066i	−0.266836	−	0.995846i
$683$	−2.38126	−	8.88698i	−0.0911164	−	0.340051i	0.905286	−	0.424803i	$-0.139657\pi$
$683$	−2.38126	−	8.88698i	−0.0911164	−	0.340051i	−0.996402	+	0.0847524i	$0.972990\pi$
$684$	1.69124	−	0.453168i	0.0646664	−	0.0173273i
$685$	5.19665	−	3.00029i	0.198554	−	0.114635i
$686$	13.4917	+	12.6875i	0.515116	+	0.484412i
$687$	2.69746	+	10.0670i	0.102914	+	0.384082i
$688$	−1.95431	−	1.12832i	−0.0745073	−	0.0430168i
$689$	−0.428952	−	15.9654i	−0.0163418	−	0.608234i
$690$	−5.05204	−	8.75039i	−0.192328	−	0.333122i
$691$	−2.56542	−	0.687401i	−0.0975930	−	0.0261500i	0.209692	−	0.977767i	$-0.432754\pi$
$691$	−2.56542	−	0.687401i	−0.0975930	−	0.0261500i	−0.307285	+	0.951618i	$0.599421\pi$
$692$	−14.8598	−	8.57930i	−0.564884	−	0.326136i
$693$	−7.39065	+	0.722900i	−0.280748	+	0.0274607i
$694$	4.70168	+	4.70168i	0.178473	+	0.178473i
$695$	−22.6438	−	22.6438i	−0.858930	−	0.858930i
$696$	−4.67466	+	1.25257i	−0.177193	+	0.0474786i
$697$	31.0090	+	8.30884i	1.17455	+	0.314720i
$698$			6.42917i			0.243348i
$699$	−10.6146	+	18.3850i	−0.401481	+	0.695386i
$700$	−16.6992	−	13.7235i	−0.631171	−	0.518699i
$701$		−	27.9693i		−	1.05638i	−0.849125	−	0.528192i	$-0.822870\pi$
$701$		−	27.9693i		−	1.05638i	0.849125	−	0.528192i	$-0.177130\pi$
$702$	−2.61706	−	2.48012i	−0.0987747	−	0.0936059i
$703$	−17.6304	+	10.1789i	−0.664945	+	0.383906i
$704$	1.98466	+	1.98466i	0.0747997	+	0.0747997i
$705$	−6.53538	+	3.77320i	−0.246137	+	0.142107i
$706$	−11.1086	−	19.2406i	−0.418076	−	0.724129i
$707$	21.1319	+	17.3663i	0.794745	+	0.653125i
$708$	−1.41350	+	5.27526i	−0.0531227	+	0.198257i
$709$	−14.3488	+	14.3488i	−0.538882	+	0.538882i	−0.923201	−	0.384318i	$-0.874437\pi$
$709$	−14.3488	+	14.3488i	−0.538882	+	0.538882i	0.384318	+	0.923201i	$0.374437\pi$
$710$	6.92803	−	25.8558i	0.260004	−	0.970349i
$711$	2.35907	−	4.08603i	0.0884720	−	0.153238i
$712$	1.62747	+	2.81886i	0.0609921	+	0.105641i
$713$	25.7984	−	6.91267i	0.966159	−	0.258882i
$714$	−10.4596	+	1.02308i	−0.391440	+	0.0382878i
$715$	19.2100	+	31.3000i	0.718412	+	1.17055i
$716$	7.52942	−	13.0413i	0.281388	−	0.487378i
$717$	13.2336	−	13.2336i	0.494218	−	0.494218i
$718$	−1.95542			−0.0729756
$719$	14.8966			0.555551			0.277775	−	0.960646i	$-0.410403\pi$
$719$	14.8966			0.555551			0.277775	+	0.960646i	$0.410403\pi$
$720$	2.56609	−	2.56609i	0.0956324	−	0.0956324i
$721$	−12.6217	+	4.74078i	−0.470056	+	0.176556i
$722$	−15.3914	−	4.12411i	−0.572808	−	0.153483i
$723$	−4.63914	−	17.3135i	−0.172532	−	0.643897i
$724$	21.1470	+	12.2092i	0.785922	+	0.453752i
$725$		−	39.5374i		−	1.46838i
$726$	0.808097	−	3.01586i	0.0299913	−	0.111929i
$727$	−19.1877			−0.711634			−0.355817	−	0.934556i	$-0.615797\pi$
$727$	−19.1877			−0.711634			−0.355817	+	0.934556i	$0.615797\pi$
$728$	8.78920	+	3.70809i	0.325749	+	0.137431i
$729$	−1.00000			−0.0370370
$730$	−5.12057	+	19.1102i	−0.189521	+	0.707302i
$731$		−	8.96386i		−	0.331540i
$732$	11.8607	+	6.84779i	0.438385	+	0.253102i
$733$	10.4539	+	39.0143i	0.386122	+	1.44103i	0.836390	+	0.548134i	$0.184662\pi$
$733$	10.4539	+	39.0143i	0.386122	+	1.44103i	−0.450268	+	0.892893i	$0.648672\pi$
$734$	16.1088	+	4.31633i	0.594585	+	0.159319i
$735$	−11.2048	−	22.7983i	−0.413296	−	0.840929i
$736$	−1.96877	+	1.96877i	−0.0725699	+	0.0725699i
$737$	−10.2607			−0.377957
$738$	−8.08186			−0.297497
$739$	−9.27480	+	9.27480i	−0.341179	+	0.341179i	−0.856811	−	0.515631i	$-0.827557\pi$
$739$	−9.27480	+	9.27480i	−0.341179	+	0.341179i	0.515631	+	0.856811i	$0.327557\pi$
$740$	−21.0973	+	36.5416i	−0.775552	+	1.34329i
$741$	−1.79711	−	6.05179i	−0.0660183	−	0.222318i
$742$	10.6717	+	4.84395i	0.391772	+	0.177827i
$743$	16.2452	−	4.35289i	0.595979	−	0.159692i	0.0517945	−	0.998658i	$-0.483506\pi$
$743$	16.2452	−	4.35289i	0.595979	−	0.159692i	0.544184	+	0.838966i	$0.316839\pi$
$744$	4.79633	+	8.30749i	0.175842	+	0.304567i
$745$	−30.1068	+	52.1466i	−1.10303	+	1.91050i
$746$	3.21644	−	12.0039i	0.117762	−	0.439495i
$747$	−4.55850	+	4.55850i	−0.166787	+	0.166787i
$748$	−2.88556	+	10.7691i	−0.105507	+	0.393756i
$749$	7.19720	−	43.4112i	0.262980	−	1.58621i
$750$	5.75126	+	9.96147i	0.210006	+	0.363741i
$751$	−6.65583	+	3.84274i	−0.242875	+	0.140224i	−0.616497	−	0.787357i	$-0.711449\pi$
$751$	−6.65583	+	3.84274i	−0.242875	+	0.140224i	0.373623	+	0.927581i	$0.378116\pi$
$752$	1.47041	+	1.47041i	0.0536203	+	0.0536203i
$753$	4.06154	−	2.34493i	0.148011	−	0.0854540i
$754$	4.96727	+	16.7274i	0.180897	+	0.609175i
$755$			40.1192i			1.46009i
$756$	2.47680	−	0.930302i	0.0900803	−	0.0338347i
$757$	−0.600662	+	1.04038i	−0.0218314	+	0.0378131i	−0.876735	−	0.480974i	$-0.840283\pi$
$757$	−0.600662	+	1.04038i	−0.0218314	+	0.0378131i	0.854903	+	0.518787i	$0.173616\pi$
$758$			7.32687i			0.266124i
$759$	−7.54841	−	2.02259i	−0.273990	−	0.0734153i
$760$	6.13752	−	1.64454i	0.222631	−	0.0596539i
$761$	−23.7947	−	23.7947i	−0.862558	−	0.862558i	0.129076	−	0.991635i	$-0.458799\pi$
$761$	−23.7947	−	23.7947i	−0.862558	−	0.862558i	−0.991635	+	0.129076i	$0.958799\pi$
$762$	3.32147	+	3.32147i	0.120324	+	0.120324i
$763$	1.39308	−	0.996850i	0.0504329	−	0.0360884i
$764$	3.38346	+	1.95344i	0.122409	+	0.0706730i
$765$	13.9240	+	3.73092i	0.503422	+	0.134892i
$766$	6.80444	+	11.7856i	0.245855	+	0.425833i
$767$	19.1502	+	4.58377i	0.691475	+	0.165510i
$768$	−0.866025	−	0.500000i	−0.0312500	−	0.0180422i
$769$	−9.90694	−	36.9732i	−0.357253	−	1.33329i	−0.877625	−	0.479348i	$-0.840873\pi$
$769$	−9.90694	−	36.9732i	−0.357253	−	1.33329i	0.520371	−	0.853940i	$-0.325793\pi$
$770$	−26.8206	+	2.62340i	−0.966549	+	0.0945409i
$771$	9.10586	−	5.25727i	0.327939	−	0.189336i
$772$	−17.0092	+	4.55759i	−0.612174	+	0.164031i
$773$	3.89829	+	14.5486i	0.140212	+	0.523277i	0.999922	+	0.0124952i	$0.00397744\pi$
$773$	3.89829	+	14.5486i	0.140212	+	0.523277i	−0.859710	+	0.510782i	$0.829356\pi$
$774$	0.584061	+	2.17975i	0.0209937	+	0.0783494i
$775$	−75.6980	+	20.2832i	−2.71915	+	0.728595i
$776$	13.4078	−	7.74099i	0.481311	−	0.277885i
$777$	−25.0171	+	17.9016i	−0.897483	+	0.642215i
$778$	−1.33156	−	4.96943i	−0.0477386	−	0.178163i
$779$	−12.2548	−	7.07528i	−0.439072	−	0.253498i
$780$	−9.49732	−	9.00033i	−0.340059	−	0.322264i
$781$	−10.3514	−	17.9291i	−0.370401	−	0.641554i
$782$	−10.6828	−	2.86246i	−0.382018	−	0.102361i
$783$	4.19119	+	2.41978i	0.149781	+	0.0864760i
$784$	−5.26908	+	4.60834i	−0.188181	+	0.164584i
$785$	−24.6253	−	24.6253i	−0.878913	−	0.878913i
$786$	−10.3692	−	10.3692i	−0.369858	−	0.369858i
$787$	20.5676	−	5.51107i	0.733156	−	0.196448i	0.127122	−	0.991887i	$-0.459426\pi$
$787$	20.5676	−	5.51107i	0.733156	−	0.196448i	0.606034	+	0.795439i	$0.292760\pi$
$788$	15.6894	+	4.20397i	0.558913	+	0.149760i
$789$			5.01761i			0.178632i
$790$	8.56105	−	14.8282i	0.304588	−	0.527563i
$791$	0.963131	−	5.80930i	0.0342450	−	0.206555i
$792$		−	2.80673i		−	0.0997329i
$793$	23.5326	−	43.4121i	0.835667	−	1.54161i
$794$	−11.7010	+	6.75555i	−0.415252	+	0.239746i
$795$	−11.3668	−	11.3668i	−0.403137	−	0.403137i
$796$	−21.5795	+	12.4589i	−0.764866	+	0.441596i
$797$	17.2380	+	29.8571i	0.610601	+	1.05759i	0.991139	+	0.132827i	$0.0424054\pi$
$797$	17.2380	+	29.8571i	0.610601	+	1.05759i	−0.380538	+	0.924765i	$0.624261\pi$
$798$	4.57008	+	0.757678i	0.161779	+	0.0268215i
$799$	−2.13788	+	7.97866i	−0.0756326	+	0.282265i
$800$	5.77679	−	5.77679i	0.204240	−	0.204240i
$801$	0.842441	−	3.14403i	0.0297662	−	0.111089i
$802$	−7.19512	+	12.4623i	−0.254068	+	0.440059i
$803$	7.65080	+	13.2516i	0.269991	+	0.467638i
$804$	3.53117	−	0.946174i	0.124535	−	0.0333690i
$805$	−2.60240	−	26.6059i	−0.0917226	−	0.937735i
$806$	29.4778	−	18.0917i	1.03831	−	0.637252i
$807$	−4.01423	+	6.95285i	−0.141308	+	0.244752i
$808$	−7.31018	+	7.31018i	−0.257171	+	0.257171i
$809$	−25.7164			−0.904141			−0.452070	−	0.891982i	$-0.649314\pi$
$809$	−25.7164			−0.904141			−0.452070	+	0.891982i	$0.649314\pi$
$810$	−3.62900			−0.127510
$811$	23.6082	−	23.6082i	0.828996	−	0.828996i	−0.158382	−	0.987378i	$-0.550628\pi$
$811$	23.6082	−	23.6082i	0.828996	−	0.828996i	0.987378	+	0.158382i	$0.0506277\pi$
$812$	−12.6319	−	2.09425i	−0.443292	−	0.0734938i
$813$	18.6687	+	5.00226i	0.654740	+	0.175437i
$814$	8.44632	+	31.5221i	0.296043	+	1.10485i
$815$	−62.1978	−	35.9099i	−2.17869	−	1.25787i
$816$		−	3.97221i		−	0.139055i
$817$	−1.02264	+	3.81653i	−0.0357775	+	0.133523i
$818$	−22.9804			−0.803491
$819$	−3.59289	−	8.83692i	−0.125546	−	0.308787i
$820$	−29.3290			−1.02421
$821$	−11.2734	+	42.0729i	−0.393444	+	1.46835i	0.430970	+	0.902366i	$0.358171\pi$
$821$	−11.2734	+	42.0729i	−0.393444	+	1.46835i	−0.824414	+	0.565987i	$0.808495\pi$
$822$			1.65351i			0.0576727i
$823$	12.9041	+	7.45019i	0.449809	+	0.259697i	0.707749	−	0.706463i	$-0.249711\pi$
$823$	12.9041	+	7.45019i	0.449809	+	0.259697i	−0.257941	+	0.966161i	$0.583044\pi$
$824$	−1.31893	−	4.92232i	−0.0459472	−	0.171477i
$825$	22.1486	+	5.93470i	0.771116	+	0.206620i
$826$	−9.17410	+	11.1634i	−0.319208	+	0.388423i
$827$	−8.29951	+	8.29951i	−0.288602	+	0.288602i	−0.836527	−	0.547925i	$-0.815418\pi$
$827$	−8.29951	+	8.29951i	−0.288602	+	0.288602i	0.547925	+	0.836527i	$0.315418\pi$
$828$	2.78426			0.0967598
$829$	3.53776			0.122871			0.0614357	−	0.998111i	$-0.480432\pi$
$829$	3.53776			0.122871			0.0614357	+	0.998111i	$0.480432\pi$
$830$	−16.5428	+	16.5428i	−0.574209	+	0.574209i
$831$	9.51546	−	16.4813i	0.330088	−	0.571728i
$832$	−1.71826	+	3.16979i	−0.0595700	+	0.109893i
$833$	−26.3178	−	8.97317i	−0.911859	−	0.310902i
$834$	8.52358	−	2.28389i	0.295148	−	0.0790846i
$835$	−18.3978	−	31.8658i	−0.636680	−	1.10276i
$836$	2.45716	−	4.25593i	0.0849827	−	0.147194i
$837$	2.48276	−	9.26580i	0.0858169	−	0.320273i
$838$	−22.9535	+	22.9535i	−0.792917	+	0.792917i
$839$	1.46266	−	5.45871i	0.0504966	−	0.188456i	−0.936071	−	0.351812i	$-0.885565\pi$
$839$	1.46266	−	5.45871i	0.0504966	−	0.188456i	0.986567	+	0.163357i	$0.0522321\pi$
$840$	8.98830	−	3.37606i	0.310126	−	0.116485i
$841$	2.78929	+	4.83119i	0.0961824	+	0.166593i
$842$	21.4531	−	12.3859i	0.739321	−	0.426847i
$843$	6.31850	+	6.31850i	0.217621	+	0.217621i
$844$	−21.7919	+	12.5816i	−0.750108	+	0.433075i
$845$	−31.5197	+	35.1023i	−1.08431	+	1.20756i
$846$		−	2.07947i		−	0.0714938i
$847$	5.24482	−	6.38208i	0.180214	−	0.219291i
$848$	−2.21480	+	3.83615i	−0.0760566	+	0.131734i
$849$			28.7184i			0.985613i
$850$	31.3457	+	8.39906i	1.07515	+	0.288085i
$851$	−31.2697	+	8.37870i	−1.07191	+	0.287218i
$852$	5.21569	+	5.21569i	0.178687	+	0.178687i
$853$	17.9250	+	17.9250i	0.613739	+	0.613739i	0.943918	−	0.330179i	$-0.107109\pi$
$853$	17.9250	+	17.9250i	0.613739	+	0.613739i	−0.330179	+	0.943918i	$0.607109\pi$
$854$	21.0863	+	29.4678i	0.721559	+	1.00837i
$855$	−5.50275	−	3.17701i	−0.188190	−	0.108652i
$856$	16.0652	+	4.30465i	0.549096	+	0.147130i
$857$	−16.2816	−	28.2006i	−0.556170	−	0.963315i	−0.997811	−	0.0661232i	$-0.978937\pi$
$857$	−16.2816	−	28.2006i	−0.556170	−	0.963315i	0.441641	−	0.897192i	$-0.354396\pi$
$858$	−10.1162	+	0.271797i	−0.345360	+	0.00927901i
$859$	−15.7330	−	9.08344i	−0.536802	−	0.309923i	0.206980	−	0.978345i	$-0.433637\pi$
$859$	−15.7330	−	9.08344i	−0.536802	−	0.309923i	−0.743782	+	0.668422i	$0.766970\pi$
$860$	2.11956	+	7.91029i	0.0722763	+	0.269739i
$861$	−19.4707	−	8.83783i	−0.663559	−	0.301192i
$862$	1.59575	−	0.921309i	0.0543516	−	0.0313799i
$863$	−42.2764	+	11.3279i	−1.43911	+	0.385607i	−0.892221	−	0.451600i	$-0.850853\pi$
$863$	−42.2764	+	11.3279i	−1.43911	+	0.385607i	−0.546886	+	0.837207i	$0.684187\pi$
$864$	0.258819	+	0.965926i	0.00880520	+	0.0328615i
$865$	16.1163	+	60.1468i	0.547970	+	2.04505i
$866$	−18.6910	+	5.00825i	−0.635147	+	0.170187i
$867$	−1.05786	+	0.610755i	−0.0359268	+	0.0207423i
$868$	2.47068	+	25.2593i	0.0838604	+	0.857355i
$869$	−3.42742	−	12.7913i	−0.116267	−	0.433916i
$870$	15.2098	+	8.78139i	0.515661	+	0.297717i
$871$	−3.75220	−	12.6356i	−0.127138	−	0.428141i
$872$	0.323727	+	0.560712i	0.0109628	+	0.0189881i
$873$	−14.9544	−	4.00703i	−0.506131	−	0.135617i
$874$	4.22186	+	2.43749i	0.142806	+	0.0824494i
$875$	2.96258	+	30.2882i	0.100153	+	1.02393i
$876$	−3.85497	−	3.85497i	−0.130247	−	0.130247i
$877$	−31.0584	−	31.0584i	−1.04877	−	1.04877i	−0.998748	−	0.0500203i	$-0.984071\pi$
$877$	−31.0584	−	31.0584i	−1.04877	−	1.04877i	−0.0500203	−	0.998748i	$-0.515929\pi$
$878$	23.7476	−	6.36316i	0.801444	−	0.214746i
$879$	20.5955	+	5.51855i	0.694669	+	0.186136i
$880$		−	10.1856i		−	0.343357i
$881$	17.6961	−	30.6506i	0.596198	−	1.03265i	−0.397179	−	0.917741i	$-0.630011\pi$
$881$	17.6961	−	30.6506i	0.596198	−	1.03265i	0.993377	−	0.114904i	$-0.0366560\pi$
$882$	6.98439	+	0.467210i	0.235177	+	0.0157318i
$883$			35.4907i			1.19436i	0.802108	+	0.597179i	$0.203712\pi$
$883$			35.4907i			1.19436i	−0.802108	+	0.597179i	$0.796288\pi$
$884$	−14.3169	+	0.384660i	−0.481528	+	0.0129375i
$885$	17.1640	−	9.90962i	0.576960	−	0.333108i
$886$	17.4802	+	17.4802i	0.587260	+	0.587260i
$887$	14.2265	−	8.21366i	0.477678	−	0.275788i	−0.241770	−	0.970334i	$-0.577728\pi$
$887$	14.2265	−	8.21366i	0.477678	−	0.275788i	0.719449	+	0.694546i	$0.244395\pi$
$888$	−5.81353	−	10.0693i	−0.195089	−	0.337905i
$889$	4.36988	+	11.6342i	0.146561	+	0.390198i
$890$	3.05722	−	11.4097i	0.102478	−	0.382454i
$891$	−1.98466	+	1.98466i	−0.0664886	+	0.0664886i
$892$	−4.49900	+	16.7905i	−0.150638	+	0.562187i
$893$	1.82048	−	3.15317i	0.0609201	−	0.105517i
$894$	−8.29619	−	14.3694i	−0.277466	−	0.480585i
$895$	−52.7864	+	14.1441i	−1.76445	+	0.472784i
$896$	−1.53965	−	2.15163i	−0.0514359	−	0.0718808i
$897$	−0.269621	−	10.0352i	−0.00900239	−	0.335065i
$898$	−12.7273	+	22.0443i	−0.424716	+	0.735629i
$899$	−32.8270	+	32.8270i	−1.09484	+	1.09484i
$900$	−8.16961			−0.272320
$901$	−17.5953			−0.586186
$902$	−16.0397	+	16.0397i	−0.534065	+	0.534065i
$903$	−0.976528	+	5.89011i	−0.0324968	+	0.196010i
$904$	2.14984	+	0.576049i	0.0715027	+	0.0191591i
$905$	−22.9351	−	85.5950i	−0.762388	−	2.84527i
$906$	−9.57406	−	5.52759i	−0.318077	−	0.183642i
$907$			5.77070i			0.191613i	0.995400	+	0.0958065i	$0.0305430\pi$
$907$			5.77070i			0.191613i	−0.995400	+	0.0958065i	$0.969457\pi$
$908$	−5.46249	+	20.3863i	−0.181279	+	0.676542i
$909$	10.3382			0.342895
$910$	−13.0386	−	32.0691i	−0.432225	−	1.06308i
$911$	3.08708			0.102280			0.0511398	−	0.998692i	$-0.483715\pi$
$911$	3.08708			0.102280			0.0511398	+	0.998692i	$0.483715\pi$
$912$	−0.453168	+	1.69124i	−0.0150059	+	0.0560027i
$913$			18.0942i			0.598829i
$914$	4.55085	+	2.62743i	0.150529	+	0.0869077i
$915$	−12.8636	−	48.0077i	−0.425258	−	1.58708i
$916$	−10.0670	−	2.69746i	−0.332624	−	0.0891264i
$917$	−13.6422	−	36.3205i	−0.450506	−	1.19941i
$918$	−2.80878	+	2.80878i	−0.0927036	+	0.0927036i
$919$	−26.2200			−0.864919			−0.432459	−	0.901653i	$-0.642354\pi$
$919$	−26.2200			−0.864919			−0.432459	+	0.901653i	$0.642354\pi$
$920$	10.1041			0.333122
$921$	15.0865	−	15.0865i	0.497118	−	0.497118i
$922$	0.0901431	−	0.156132i	0.00296870	−	0.00514195i
$923$	18.2936	−	19.3037i	0.602141	−	0.635390i
$924$	3.06927	−	6.76194i	0.100972	−	0.222451i
$925$	91.7519	−	24.5849i	3.01679	−	0.808345i
$926$	2.42844	+	4.20618i	0.0798035	+	0.138224i
$927$	−2.54798	+	4.41323i	−0.0836866	+	0.144950i
$928$	1.25257	−	4.67466i	0.0411177	−	0.153453i
$929$	−6.73083	+	6.73083i	−0.220831	+	0.220831i	−0.808849	−	0.588017i	$-0.799909\pi$
$929$	−6.73083	+	6.73083i	−0.220831	+	0.220831i	0.588017	+	0.808849i	$0.299909\pi$
$930$	9.00994	−	33.6256i	0.295448	−	1.10263i
$931$	10.1816	+	6.82295i	0.333689	+	0.223613i
$932$	−10.6146	−	18.3850i	−0.347693	−	0.602222i
$933$	−25.3976	+	14.6633i	−0.831482	+	0.480056i
$934$	−20.8014	−	20.8014i	−0.680644	−	0.680644i
$935$	35.0389	−	20.2297i	1.14590	−	0.661583i
$936$	3.45638	−	1.02639i	0.112975	−	0.0335485i
$937$		−	0.688061i		−	0.0224780i	−0.999937	−	0.0112390i	$-0.996422\pi$
$937$		−	0.688061i		−	0.0224780i	0.999937	−	0.0112390i	$-0.00357755\pi$
$938$	9.54192	+	1.58197i	0.311555	+	0.0516530i
$939$	−11.5915	+	20.0771i	−0.378275	+	0.655192i
$940$		−	7.54640i		−	0.246137i
$941$	28.6118	+	7.66651i	0.932718	+	0.249921i	0.693013	−	0.720925i	$-0.256283\pi$
$941$	28.6118	+	7.66651i	0.932718	+	0.249921i	0.239705	+	0.970846i	$0.422949\pi$
$942$	9.26943	−	2.48374i	0.302014	−	0.0809245i
$943$	−15.9113	−	15.9113i	−0.518144	−	0.518144i
$944$	−3.86176	−	3.86176i	−0.125690	−	0.125690i
$945$	−8.74292	−	3.96845i	−0.284407	−	0.129094i
$946$	5.48522	+	3.16689i	0.178340	+	0.102965i
$947$	41.8643	+	11.2175i	1.36041	+	0.364520i	0.863966	−	0.503550i	$-0.167973\pi$
$947$	41.8643	+	11.2175i	1.36041	+	0.364520i	0.496441	+	0.868070i	$0.334640\pi$
$948$	2.35907	+	4.08603i	0.0766190	+	0.132708i
$949$	−13.5210	+	14.2676i	−0.438909	+	0.463145i
$950$	−12.3878	−	7.15211i	−0.401914	−	0.232045i
$951$	−8.06274	−	30.0906i	−0.261452	−	0.975753i
$952$	4.34377	−	9.56980i	0.140783	−	0.310159i
$953$	41.6155	−	24.0267i	1.34806	−	0.778302i	0.360084	−	0.932920i	$-0.382748\pi$
$953$	41.6155	−	24.0267i	1.34806	−	0.778302i	0.987974	+	0.154618i	$0.0494146\pi$
$954$	4.27867	−	1.14647i	0.138527	−	0.0371182i
$955$	−3.66955	−	13.6950i	−0.118744	−	0.443158i
$956$	4.84384	+	18.0774i	0.156661	+	0.584666i
$957$	13.1205	−	3.51564i	0.424127	−	0.113644i
$958$	−16.7410	+	9.66544i	−0.540878	+	0.312276i
$959$	−1.80818	+	3.98361i	−0.0583891	+	0.128637i
$960$	0.939253	+	3.50534i	0.0303143	+	0.113134i
$961$	52.8442	+	30.5096i	1.70465	+	0.984181i
$962$	−35.7294	+	21.9285i	−1.15196	+	0.707004i
$963$	−8.31594	−	14.4036i	−0.267977	−	0.464150i
$964$	17.3135	+	4.63914i	0.557631	+	0.149417i
$965$	55.3422	+	31.9518i	1.78153	+	1.02857i
$966$	6.70781	+	3.04470i	0.215820	+	0.0979617i
$967$	−2.01565	−	2.01565i	−0.0648191	−	0.0648191i	0.673954	−	0.738773i	$-0.264595\pi$
$967$	−2.01565	−	2.01565i	−0.0648191	−	0.0648191i	−0.738773	+	0.673954i	$0.764595\pi$
$968$	2.20776	+	2.20776i	0.0709602	+	0.0709602i
$969$	−6.71799	+	1.80008i	−0.215813	+	0.0578269i
$970$	−54.2696	−	14.5415i	−1.74249	−	0.466899i
$971$			40.8617i			1.31132i	0.755058	+	0.655658i	$0.227609\pi$
$971$			40.8617i			1.31132i	−0.755058	+	0.655658i	$0.772391\pi$
$972$	0.500000	−	0.866025i	0.0160375	−	0.0277778i
$973$	23.0324	+	3.81857i	0.738385	+	0.122418i
$974$		−	34.9369i		−	1.11945i
$975$	0.791126	+	29.4453i	0.0253363	+	0.943005i
$976$	−11.8607	+	6.84779i	−0.379652	+	0.219192i
$977$	27.1614	+	27.1614i	0.868971	+	0.868971i	0.992359	−	0.123387i	$-0.0393758\pi$
$977$	27.1614	+	27.1614i	0.868971	+	0.868971i	−0.123387	+	0.992359i	$0.539376\pi$
$978$	17.1391	−	9.89527i	0.548048	−	0.316416i
$979$	−4.56788	−	7.91180i	−0.145990	−	0.252862i
$980$	25.3463	+	1.69550i	0.809659	+	0.0541609i
$981$	0.167574	−	0.625393i	0.00535021	−	0.0199673i
$982$	−7.28044	+	7.28044i	−0.232328	+	0.232328i
$983$	0.499665	−	1.86477i	0.0159368	−	0.0594770i	−0.957500	−	0.288435i	$-0.906865\pi$
$983$	0.499665	−	1.86477i	0.0159368	−	0.0594770i	0.973436	+	0.228958i	$0.0735318\pi$
$984$	4.04093	−	6.99909i	0.128820	−	0.223123i
$985$	−29.4727	−	51.0482i	−0.939079	−	1.62653i
$986$	18.5688	−	4.97549i	0.591350	−	0.158452i
$987$	2.27399	−	5.00984i	0.0723818	−	0.159465i
$988$	6.13955	+	1.46955i	0.195325	+	0.0467527i
$989$	−3.14154	+	5.44131i	−0.0998952	+	0.173024i
$990$	−7.20232	+	7.20232i	−0.228905	+	0.228905i
$991$	30.7769			0.977661			0.488831	−	0.872379i	$-0.337424\pi$
$991$	30.7769			0.977661			0.488831	+	0.872379i	$0.337424\pi$
$992$	−9.59267			−0.304567
$993$	−0.593522	+	0.593522i	−0.0188349	+	0.0188349i
$994$	6.86200	+	18.2691i	0.217649	+	0.579462i
$995$	87.3457	+	23.4042i	2.76905	+	0.741963i
$996$	−1.66853	−	6.22703i	−0.0528693	−	0.197311i
$997$	3.09141	+	1.78482i	0.0979058	+	0.0565259i	0.548153	−	0.836378i	$-0.315331\pi$
$997$	3.09141	+	1.78482i	0.0979058	+	0.0565259i	−0.450248	+	0.892904i	$0.648664\pi$
$998$			15.9355i			0.504431i
$999$	−3.00931	+	11.2309i	−0.0952102	+	0.355329i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.by.b.397.5	✓	40
7.3	odd	6		546.2.cg.b.241.5	yes	40
13.2	odd	12		546.2.cg.b.145.5	yes	40
91.80	even	12	inner	546.2.by.b.535.5	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.by.b.397.5	✓	40	1.1	even	1	trivial
546.2.by.b.535.5	yes	40	91.80	even	12	inner
546.2.cg.b.145.5	yes	40	13.2	odd	12
546.2.cg.b.241.5	yes	40	7.3	odd	6

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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)

\(f(q)\)	\(=\)	\(q+(-0.258819 + 0.965926i) q^{2} +1.00000i q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.939253 + 3.50534i) q^{5} +(-0.965926 - 0.258819i) q^{6} +(-2.04406 - 1.67982i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(-0.258819 + 0.965926i) q^{2} +1.00000i q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.939253 + 3.50534i) q^{5} +(-0.965926 - 0.258819i) q^{6} +(-2.04406 - 1.67982i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000 q^{9} -3.62900 q^{10} +(-1.98466 + 1.98466i) q^{11} +(0.500000 - 0.866025i) q^{12} +(-3.16979 - 1.71826i) q^{13} +(2.15163 - 1.53965i) q^{14} +(-3.50534 + 0.939253i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-1.98611 + 3.44004i) q^{17} +(0.258819 - 0.965926i) q^{18} +(1.23808 - 1.23808i) q^{19} +(0.939253 - 3.50534i) q^{20} +(1.67982 - 2.04406i) q^{21} +(-1.40337 - 2.43070i) q^{22} +(2.41124 - 1.39213i) q^{23} +(0.707107 + 0.707107i) q^{24} +(-7.07509 + 4.08481i) q^{25} +(2.48012 - 2.61706i) q^{26} -1.00000i q^{27} +(0.930302 + 2.47680i) q^{28} +(-2.41978 + 4.19119i) q^{29} -3.62900i q^{30} +(9.26580 + 2.48276i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(-1.98466 - 1.98466i) q^{33} +(-2.80878 - 2.80878i) q^{34} +(3.96845 - 8.74292i) q^{35} +(0.866025 + 0.500000i) q^{36} +(-11.2309 - 3.00931i) q^{37} +(0.875453 + 1.51633i) q^{38} +(1.71826 - 3.16979i) q^{39} +(3.14280 + 1.81450i) q^{40} +(-2.09174 - 7.80648i) q^{41} +(1.53965 + 2.15163i) q^{42} +(-1.95431 + 1.12832i) q^{43} +(2.71110 - 0.726436i) q^{44} +(-0.939253 - 3.50534i) q^{45} +(0.720620 + 2.68939i) q^{46} +(2.00862 - 0.538208i) q^{47} +(-0.866025 + 0.500000i) q^{48} +(1.35640 + 6.86733i) q^{49} +(-2.11445 - 7.89124i) q^{50} +(-3.44004 - 1.98611i) q^{51} +(1.88599 + 3.07295i) q^{52} +(2.21480 + 3.83615i) q^{53} +(0.965926 + 0.258819i) q^{54} +(-8.82101 - 5.09281i) q^{55} +(-2.63318 + 0.257559i) q^{56} +(1.23808 + 1.23808i) q^{57} +(-3.42209 - 3.42209i) q^{58} +(-5.27526 + 1.41350i) q^{59} +(3.50534 + 0.939253i) q^{60} +13.6956i q^{61} +(-4.79633 + 8.30749i) q^{62} +(2.04406 + 1.67982i) q^{63} -1.00000i q^{64} +(3.04586 - 12.7251i) q^{65} +(2.43070 - 1.40337i) q^{66} +(2.58500 + 2.58500i) q^{67} +(3.44004 - 1.98611i) q^{68} +(1.39213 + 2.41124i) q^{69} +(7.41790 + 6.09606i) q^{70} +(-1.90908 + 7.12477i) q^{71} +(-0.707107 + 0.707107i) q^{72} +(1.41102 - 5.26598i) q^{73} +(5.81353 - 10.0693i) q^{74} +(-4.08481 - 7.07509i) q^{75} +(-1.69124 + 0.453168i) q^{76} +(7.39065 - 0.722900i) q^{77} +(2.61706 + 2.48012i) q^{78} +(-2.35907 + 4.08603i) q^{79} +(-2.56609 + 2.56609i) q^{80} +1.00000 q^{81} +8.08186 q^{82} +(4.55850 - 4.55850i) q^{83} +(-2.47680 + 0.930302i) q^{84} +(-13.9240 - 3.73092i) q^{85} +(-0.584061 - 2.17975i) q^{86} +(-4.19119 - 2.41978i) q^{87} +2.80673i q^{88} +(-0.842441 + 3.14403i) q^{89} +3.62900 q^{90} +(3.59289 + 8.83692i) q^{91} -2.78426 q^{92} +(-2.48276 + 9.26580i) q^{93} +2.07947i q^{94} +(5.50275 + 3.17701i) q^{95} +(-0.258819 - 0.965926i) q^{96} +(14.9544 + 4.00703i) q^{97} +(-6.98439 - 0.467210i) q^{98} +(1.98466 - 1.98466i) 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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