LMFDB - Embedded newform 546.2.cg.b.241.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("546.145");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			241.5
Character	$\chi$	$=$	546.241
Dual form			546.2.cg.b.145.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(-0.866025 + 0.500000i) q^{3} +1.00000i q^{4} +(3.50534 + 0.939253i) q^{5} +(0.965926 + 0.258819i) q^{6} +(-2.61012 + 0.432735i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.866025 + 0.500000i) q^{3} +1.00000i q^{4} +(3.50534 + 0.939253i) q^{5} +(0.965926 + 0.258819i) q^{6} +(-2.61012 + 0.432735i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.500000 - 0.866025i) q^{9} +(-1.81450 - 3.14280i) q^{10} +(2.71110 + 0.726436i) 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} -1.00000 q^{16} -3.97221 q^{17} +(-0.965926 + 0.258819i) q^{18} +(-0.453168 - 1.69124i) q^{19} +(-0.939253 + 3.50534i) q^{20} +(2.04406 - 1.67982i) q^{21} +(-1.40337 - 2.43070i) q^{22} +2.78426i q^{23} +(-0.258819 + 0.965926i) q^{24} +(7.07509 + 4.08481i) q^{25} +(-1.02639 - 3.45638i) q^{26} +1.00000i q^{27} +(-0.432735 - 2.61012i) q^{28} +(-2.41978 + 4.19119i) q^{29} +(3.14280 + 1.81450i) q^{30} +(2.48276 + 9.26580i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-2.71110 + 0.726436i) q^{33} +(2.80878 + 2.80878i) q^{34} +(-9.55582 - 0.934682i) q^{35} +(0.866025 + 0.500000i) q^{36} +(8.22157 - 8.22157i) q^{37} +(-0.875453 + 1.51633i) q^{38} +(-3.60425 + 0.0968376i) q^{39} +(3.14280 - 1.81450i) q^{40} +(2.09174 + 7.80648i) q^{41} +(-2.63318 - 0.257559i) q^{42} +(-1.95431 + 1.12832i) q^{43} +(-0.726436 + 2.71110i) q^{44} +(2.56609 - 2.56609i) q^{45} +(1.96877 - 1.96877i) q^{46} +(0.538208 - 2.00862i) q^{47} +(0.866025 - 0.500000i) q^{48} +(6.62548 - 2.25898i) q^{49} +(-2.11445 - 7.89124i) q^{50} +(3.44004 - 1.98611i) q^{51} +(-1.71826 + 3.16979i) q^{52} +(2.21480 - 3.83615i) q^{53} +(0.707107 - 0.707107i) q^{54} +(8.82101 + 5.09281i) q^{55} +(-1.53965 + 2.15163i) q^{56} +(1.23808 + 1.23808i) q^{57} +(4.67466 - 1.25257i) q^{58} +(-3.86176 - 3.86176i) q^{59} +(-0.939253 - 3.50534i) q^{60} +(11.8607 + 6.84779i) q^{61} +(4.79633 - 8.30749i) q^{62} +(-0.930302 + 2.47680i) q^{63} -1.00000i q^{64} +(9.49732 + 9.00033i) q^{65} +(2.43070 + 1.40337i) q^{66} +(0.946174 - 3.53117i) q^{67} -3.97221i q^{68} +(-1.39213 - 2.41124i) q^{69} +(6.09606 + 7.41790i) q^{70} +(-1.90908 + 7.12477i) q^{71} +(-0.258819 - 0.965926i) q^{72} +(5.26598 - 1.41102i) q^{73} -11.6271 q^{74} -8.16961 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} +(-3.50534 - 0.939253i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(4.04093 - 6.99909i) q^{82} +(-4.55850 + 4.55850i) q^{83} +(1.67982 + 2.04406i) q^{84} +(-13.9240 - 3.73092i) q^{85} +(2.17975 + 0.584061i) q^{86} -4.83957i q^{87} +(2.43070 - 1.40337i) q^{88} +(2.30159 + 2.30159i) q^{89} -3.62900 q^{90} +(-9.01710 - 3.11319i) q^{91} -2.78426 q^{92} +(-6.78304 - 6.78304i) q^{93} +(-1.80088 + 1.03974i) q^{94} -6.35403i q^{95} +(-0.965926 - 0.258819i) q^{96} +(-14.9544 - 4.00703i) q^{97} +(-6.28227 - 3.08758i) q^{98} +(1.98466 - 1.98466i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 4 q^{7} + 20 q^{9}+O(q^{10}) $ 40 * q + 4 * q^7 + 20 * q^9	$ 40 q + 4 q^{7} + 20 q^{9} + 8 q^{11} - 20 q^{12} + 4 q^{14} - 40 q^{16} + 16 q^{17} + 4 q^{19} + 4 q^{21} - 4 q^{22} - 24 q^{25} + 8 q^{26} - 4 q^{28} - 12 q^{29} - 8 q^{33} - 8 q^{34} - 32 q^{35} + 40 q^{37} + 8 q^{38} + 20 q^{39} + 20 q^{41} + 12 q^{42} - 24 q^{43} - 4 q^{44} + 32 q^{46} + 4 q^{47} + 32 q^{49} - 16 q^{50} + 24 q^{51} + 16 q^{52} - 4 q^{53} + 24 q^{55} + 12 q^{56} + 8 q^{57} + 12 q^{58} + 24 q^{59} + 60 q^{61} + 32 q^{62} - 4 q^{63} + 44 q^{65} - 12 q^{67} - 8 q^{69} - 24 q^{70} - 28 q^{71} + 60 q^{73} - 40 q^{74} - 72 q^{75} + 4 q^{76} - 12 q^{77} + 4 q^{78} - 20 q^{81} - 24 q^{82} + 60 q^{83} - 8 q^{84} - 4 q^{85} - 20 q^{86} - 36 q^{89} - 16 q^{92} - 24 q^{93} - 48 q^{97} - 88 q^{98} + 4 q^{99}+O(q^{100}) $ 40 * q + 4 * q^7 + 20 * q^9 + 8 * q^11 - 20 * q^12 + 4 * q^14 - 40 * q^16 + 16 * q^17 + 4 * q^19 + 4 * q^21 - 4 * q^22 - 24 * q^25 + 8 * q^26 - 4 * q^28 - 12 * q^29 - 8 * q^33 - 8 * q^34 - 32 * q^35 + 40 * q^37 + 8 * q^38 + 20 * q^39 + 20 * q^41 + 12 * q^42 - 24 * q^43 - 4 * q^44 + 32 * q^46 + 4 * q^47 + 32 * q^49 - 16 * q^50 + 24 * q^51 + 16 * q^52 - 4 * q^53 + 24 * q^55 + 12 * q^56 + 8 * q^57 + 12 * q^58 + 24 * q^59 + 60 * q^61 + 32 * q^62 - 4 * q^63 + 44 * q^65 - 12 * q^67 - 8 * q^69 - 24 * q^70 - 28 * q^71 + 60 * q^73 - 40 * q^74 - 72 * q^75 + 4 * q^76 - 12 * q^77 + 4 * q^78 - 20 * q^81 - 24 * q^82 + 60 * q^83 - 8 * q^84 - 4 * q^85 - 20 * q^86 - 36 * q^89 - 16 * q^92 - 24 * q^93 - 48 * q^97 - 88 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$			1.00000i			0.500000i
$5$	3.50534	+	0.939253i	1.56764	+	0.420047i	0.935071	−	0.354460i	$-0.115335\pi$
$5$	3.50534	+	0.939253i	1.56764	+	0.420047i	0.632565	+	0.774507i	$0.282002\pi$
$6$	0.965926	+	0.258819i	0.394338	+	0.105662i
$7$	−2.61012	+	0.432735i	−0.986534	+	0.163559i
$7$	−2.61012	+	0.432735i	−0.986534	+	0.163559i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	−1.81450	−	3.14280i	−0.573795	−	0.993842i
$11$	2.71110	+	0.726436i	0.817426	+	0.219029i	0.643221	−	0.765681i	$-0.277598\pi$
$11$	2.71110	+	0.726436i	0.817426	+	0.219029i	0.174205	+	0.984709i	$0.444264\pi$
$12$	−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
$16$	−1.00000			−0.250000
$17$	−3.97221			−0.963404			−0.481702	−	0.876335i	$-0.659981\pi$
$17$	−3.97221			−0.963404			−0.481702	+	0.876335i	$0.659981\pi$
$18$	−0.965926	+	0.258819i	−0.227671	+	0.0610042i
$19$	−0.453168	−	1.69124i	−0.103964	−	0.387998i	0.894262	−	0.447544i	$-0.147701\pi$
$19$	−0.453168	−	1.69124i	−0.103964	−	0.387998i	−0.998226	+	0.0595461i	$0.981035\pi$
$20$	−0.939253	+	3.50534i	−0.210023	+	0.783818i
$21$	2.04406	−	1.67982i	0.446052	−	0.366567i
$22$	−1.40337	−	2.43070i	−0.299199	−	0.518227i
$23$			2.78426i			0.580559i	0.956942	+	0.290280i	$0.0937483\pi$
$23$			2.78426i			0.580559i	−0.956942	+	0.290280i	$0.906252\pi$
$24$	−0.258819	+	0.965926i	−0.0528312	+	0.197169i
$25$	7.07509	+	4.08481i	1.41502	+	0.816961i
$26$	−1.02639	−	3.45638i	−0.201291	−	0.677851i
$27$			1.00000i			0.192450i
$28$	−0.432735	−	2.61012i	−0.0817793	−	0.493267i
$29$	−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	$0.315008\pi$
$30$	3.14280	+	1.81450i	0.573795	+	0.331281i
$31$	2.48276	+	9.26580i	0.445918	+	1.66419i	0.713502	+	0.700653i	$0.247108\pi$
$31$	2.48276	+	9.26580i	0.445918	+	1.66419i	−0.267584	+	0.963534i	$0.586225\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	−2.71110	+	0.726436i	−0.471941	+	0.126456i
$34$	2.80878	+	2.80878i	0.481702	+	0.481702i
$35$	−9.55582	−	0.934682i	−1.61523	−	0.157990i
$36$	0.866025	+	0.500000i	0.144338	+	0.0833333i
$37$	8.22157	−	8.22157i	1.35162	−	1.35162i	0.467767	−	0.883852i	$-0.345059\pi$
$37$	8.22157	−	8.22157i	1.35162	−	1.35162i	0.883852	−	0.467767i	$-0.154941\pi$
$38$	−0.875453	+	1.51633i	−0.142017	+	0.245981i
$39$	−3.60425	+	0.0968376i	−0.577142	+	0.0155064i
$40$	3.14280	−	1.81450i	0.496921	−	0.286897i
$41$	2.09174	+	7.80648i	0.326675	+	1.21917i	0.912618	+	0.408814i	$0.134058\pi$
$41$	2.09174	+	7.80648i	0.326675	+	1.21917i	−0.585943	+	0.810352i	$0.699276\pi$
$42$	−2.63318	−	0.257559i	−0.406309	−	0.0397423i
$43$	−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	$0.388378\pi$
$44$	−0.726436	+	2.71110i	−0.109514	+	0.408713i
$45$	2.56609	−	2.56609i	0.382530	−	0.382530i
$46$	1.96877	−	1.96877i	0.290280	−	0.290280i
$47$	0.538208	−	2.00862i	0.0785056	−	0.292987i	−0.915500	−	0.402319i	$-0.868204\pi$
$47$	0.538208	−	2.00862i	0.0785056	−	0.292987i	0.994005	+	0.109332i	$0.0348711\pi$
$48$	0.866025	−	0.500000i	0.125000	−	0.0721688i
$49$	6.62548	−	2.25898i	0.946497	−	0.322712i
$50$	−2.11445	−	7.89124i	−0.299029	−	1.11599i
$51$	3.44004	−	1.98611i	0.481702	−	0.278111i
$52$	−1.71826	+	3.16979i	−0.238280	+	0.439571i
$53$	2.21480	−	3.83615i	0.304227	−	0.526936i	−0.672862	−	0.739768i	$-0.734935\pi$
$53$	2.21480	−	3.83615i	0.304227	−	0.526936i	0.977089	+	0.212832i	$0.0682687\pi$
$54$	0.707107	−	0.707107i	0.0962250	−	0.0962250i
$55$	8.82101	+	5.09281i	1.18942	+	0.686715i
$56$	−1.53965	+	2.15163i	−0.205744	+	0.287523i
$57$	1.23808	+	1.23808i	0.163987	+	0.163987i
$58$	4.67466	−	1.25257i	0.613813	−	0.164471i
$59$	−3.86176	−	3.86176i	−0.502758	−	0.502758i	0.409536	−	0.912294i	$-0.365691\pi$
$59$	−3.86176	−	3.86176i	−0.502758	−	0.502758i	−0.912294	+	0.409536i	$0.865691\pi$
$60$	−0.939253	−	3.50534i	−0.121257	−	0.452538i
$61$	11.8607	+	6.84779i	1.51861	+	0.876769i	0.999760	+	0.0219037i	$0.00697272\pi$
$61$	11.8607	+	6.84779i	1.51861	+	0.876769i	0.518849	+	0.854866i	$0.326361\pi$
$62$	4.79633	−	8.30749i	0.609135	−	1.05505i
$63$	−0.930302	+	2.47680i	−0.117207	+	0.312047i
$64$		−	1.00000i		−	0.125000i
$65$	9.49732	+	9.00033i	1.17800	+	1.11635i
$66$	2.43070	+	1.40337i	0.299199	+	0.172742i
$67$	0.946174	−	3.53117i	0.115594	−	0.431401i	−0.883737	−	0.467984i	$-0.844981\pi$
$67$	0.946174	−	3.53117i	0.115594	−	0.431401i	0.999331	+	0.0365826i	$0.0116472\pi$
$68$		−	3.97221i		−	0.481702i
$69$	−1.39213	−	2.41124i	−0.167593	−	0.290280i
$70$	6.09606	+	7.41790i	0.728619	+	0.886609i
$71$	−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	$0.939130\pi$
$72$	−0.258819	−	0.965926i	−0.0305021	−	0.113835i
$73$	5.26598	−	1.41102i	0.616337	−	0.165147i	0.0628749	−	0.998021i	$-0.479973\pi$
$73$	5.26598	−	1.41102i	0.616337	−	0.165147i	0.553462	+	0.832874i	$0.313306\pi$
$74$	−11.6271			−1.35162
$75$	−8.16961			−0.943346
$76$	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	0.702257	−	0.711924i	$-0.252176\pi$
$79$	−2.35907	−	4.08603i	−0.265416	−	0.459714i	−0.967673	+	0.252210i	$0.918843\pi$
$80$	−3.50534	−	0.939253i	−0.391909	−	0.105012i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	4.04093	−	6.99909i	0.446246	−	0.772921i
$83$	−4.55850	+	4.55850i	−0.500361	+	0.500361i	−0.911550	−	0.411189i	$-0.865114\pi$
$83$	−4.55850	+	4.55850i	−0.500361	+	0.500361i	0.411189	+	0.911550i	$0.365114\pi$
$84$	1.67982	+	2.04406i	0.183283	+	0.223026i
$85$	−13.9240	−	3.73092i	−1.51027	−	0.404675i
$86$	2.17975	+	0.584061i	0.235048	+	0.0629810i
$87$		−	4.83957i		−	0.518856i
$88$	2.43070	−	1.40337i	0.259114	−	0.149599i
$89$	2.30159	+	2.30159i	0.243968	+	0.243968i	0.818490	−	0.574521i	$-0.194812\pi$
$89$	2.30159	+	2.30159i	0.243968	+	0.243968i	−0.574521	+	0.818490i	$0.694812\pi$
$90$	−3.62900			−0.382530
$91$	−9.01710	−	3.11319i	−0.945249	−	0.326351i
$92$	−2.78426			−0.290280
$93$	−6.78304	−	6.78304i	−0.703368	−	0.703368i
$94$	−1.80088	+	1.03974i	−0.185746	+	0.107241i
$95$		−	6.35403i		−	0.651910i
$96$	−0.965926	−	0.258819i	−0.0985844	−	0.0264156i
$97$	−14.9544	−	4.00703i	−1.51839	−	0.406852i	−0.599181	−	0.800614i	$-0.704507\pi$
$97$	−14.9544	−	4.00703i	−1.51839	−	0.406852i	−0.919213	+	0.393762i	$0.871174\pi$
$98$	−6.28227	−	3.08758i	−0.634605	−	0.311893i
$99$	1.98466	−	1.98466i	0.199466	−	0.199466i
$100$	−4.08481	+	7.07509i	−0.408481	+	0.707509i
$101$	−5.16908	−	8.95311i	−0.514343	−	0.890867i	−0.999862	−	0.0166412i	$-0.994703\pi$
$101$	−5.16908	−	8.95311i	−0.514343	−	0.890867i	0.485519	−	0.874226i	$-0.338631\pi$
$102$	−3.83686	−	1.02808i	−0.379906	−	0.101796i
$103$	−2.54798	−	4.41323i	−0.251060	−	0.434849i	0.712758	−	0.701410i	$-0.247446\pi$
$103$	−2.54798	−	4.41323i	−0.251060	−	0.434849i	−0.963818	+	0.266561i	$0.914112\pi$
$104$	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
$107$	−16.6319			−1.60786			−0.803932	−	0.594721i	$-0.797262\pi$
$107$	−16.6319			−1.60786			−0.803932	+	0.594721i	$0.797262\pi$
$108$	−1.00000			−0.0962250
$109$	0.625393	−	0.167574i	0.0599018	−	0.0160506i	−0.228744	−	0.973487i	$-0.573462\pi$
$109$	0.625393	−	0.167574i	0.0599018	−	0.0160506i	0.288645	+	0.957436i	$0.406795\pi$
$110$	−2.63623	−	9.83856i	−0.251355	−	0.938070i
$111$	−3.00931	+	11.2309i	−0.285631	+	1.06599i
$112$	2.61012	−	0.432735i	0.246633	−	0.0408896i
$113$	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	$0.799949\pi$
$114$		−	1.75091i		−	0.163987i
$115$	−2.61513	+	9.75979i	−0.243862	+	0.910105i
$116$	−4.19119	−	2.41978i	−0.389142	−	0.224671i
$117$	3.07295	−	1.88599i	0.284095	−	0.174360i
$118$			5.46135i			0.502758i
$119$	10.3680	−	1.71892i	0.950430	−	0.157573i
$120$	−1.81450	+	3.14280i	−0.165640	+	0.286897i
$121$	−2.70395	−	1.56112i	−0.245813	−	0.141920i
$122$	−3.54468	−	13.2289i	−0.320920	−	1.19769i
$123$	−5.71474	−	5.71474i	−0.515280	−	0.515280i
$124$	−9.26580	+	2.48276i	−0.832094	+	0.222959i
$125$	8.13351	+	8.13351i	0.727483	+	0.727483i
$126$	2.40918	−	1.09354i	0.214627	−	0.0974202i
$127$	−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	$0.733495\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	1.12832	−	1.95431i	0.0993430	−	0.172067i
$130$	−0.351423	−	13.0798i	−0.0308219	−	1.14718i
$131$	12.6996	−	7.33214i	1.10957	−	0.640612i	0.170854	−	0.985296i	$-0.445347\pi$
$131$	12.6996	−	7.33214i	1.10957	−	0.640612i	0.938719	+	0.344684i	$0.112014\pi$
$132$	−0.726436	−	2.71110i	−0.0632281	−	0.235971i
$133$	1.91468	+	4.21825i	0.166024	+	0.365769i
$134$	−3.16596	+	1.82787i	−0.273497	+	0.157904i
$135$	−0.939253	+	3.50534i	−0.0808381	+	0.301692i
$136$	−2.80878	+	2.80878i	−0.240851	+	0.240851i
$137$	−1.16921	+	1.16921i	−0.0998921	+	0.0998921i	−0.755287	−	0.655395i	$-0.772502\pi$
$137$	−1.16921	+	1.16921i	−0.0998921	+	0.0998921i	0.655395	+	0.755287i	$0.272502\pi$
$138$	−0.720620	+	2.68939i	−0.0613433	+	0.228936i
$139$	7.64204	−	4.41213i	0.648189	−	0.374232i	−0.139573	−	0.990212i	$-0.544573\pi$
$139$	7.64204	−	4.41213i	0.648189	−	0.374232i	0.787762	+	0.615980i	$0.211240\pi$
$140$	0.934682	−	9.55582i	0.0789950	−	0.807614i
$141$	0.538208	+	2.00862i	0.0453253	+	0.169156i
$142$	6.38789	−	3.68805i	0.536060	−	0.309494i
$143$	7.34540	+	6.96102i	0.614253	+	0.582110i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−12.4188	+	12.4188i	−1.03132	+	1.03132i
$146$	−4.72135	−	2.72587i	−0.390742	−	0.225595i
$147$	−4.60834	+	5.26908i	−0.380090	+	0.434586i
$148$	8.22157	+	8.22157i	0.675809	+	0.675809i
$149$	−16.0270	+	4.29442i	−1.31298	+	0.351813i	−0.846345	−	0.532635i	$-0.821202\pi$
$149$	−16.0270	+	4.29442i	−1.31298	+	0.351813i	−0.466639	+	0.884448i	$0.654535\pi$
$150$	5.77679	+	5.77679i	0.471673	+	0.471673i
$151$	−2.86129	−	10.6785i	−0.232848	−	0.869002i	−0.979107	−	0.203346i	$-0.934818\pi$
$151$	−2.86129	−	10.6785i	−0.232848	−	0.869002i	0.746258	−	0.665656i	$-0.231848\pi$
$152$	−1.51633	−	0.875453i	−0.122990	−	0.0710086i
$153$	−1.98611	+	3.44004i	−0.160567	+	0.278111i
$154$	4.71481	+	5.73715i	0.379930	+	0.462312i
$155$			34.8117i			2.79615i
$156$	−0.0968376	−	3.60425i	−0.00775321	−	0.288571i
$157$	−8.31074	−	4.79821i	−0.663270	−	0.382939i	0.130252	−	0.991481i	$-0.458421\pi$
$157$	−8.31074	−	4.79821i	−0.663270	−	0.382939i	−0.793522	+	0.608542i	$0.791755\pi$
$158$	−1.22114	+	4.55737i	−0.0971490	+	0.362565i
$159$			4.42961i			0.351291i
$160$	1.81450	+	3.14280i	0.143449	+	0.248460i
$161$	−1.20485	−	7.26727i	−0.0949554	−	0.572741i
$162$	−0.258819	+	0.965926i	−0.0203347	+	0.0758903i
$163$	−5.12217	−	19.1162i	−0.401199	−	1.49730i	−0.810959	−	0.585103i	$-0.801054\pi$
$163$	−5.12217	−	19.1162i	−0.401199	−	1.49730i	0.409760	−	0.912193i	$-0.365612\pi$
$164$	−7.80648	+	2.09174i	−0.609583	+	0.163337i
$165$	−10.1856			−0.792950
$166$	6.44670			0.500361
$167$	9.79382	−	2.62425i	0.757868	−	0.203070i	0.140863	−	0.990029i	$-0.455012\pi$
$167$	9.79382	−	2.62425i	0.757868	−	0.203070i	0.617005	+	0.786959i	$0.288346\pi$
$168$	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
$171$	−1.69124	−	0.453168i	−0.129333	−	0.0346546i
$172$	−1.12832	−	1.95431i	−0.0860336	−	0.149015i
$173$	8.57930	−	14.8598i	0.652272	−	1.12977i	−0.330298	−	0.943877i	$-0.607149\pi$
$173$	8.57930	−	14.8598i	0.652272	−	1.12977i	0.982570	−	0.185892i	$-0.0595175\pi$
$174$	−3.42209	+	3.42209i	−0.259428	+	0.259428i
$175$	−20.2345	−	7.60020i	−1.52958	−	0.574521i
$176$	−2.71110	−	0.726436i	−0.204357	−	0.0547572i
$177$	5.27526	+	1.41350i	0.396513	+	0.106245i
$178$		−	3.25494i		−	0.243968i
$179$	13.0413	−	7.52942i	0.974755	−	0.562775i	0.0740725	−	0.997253i	$-0.476400\pi$
$179$	13.0413	−	7.52942i	0.974755	−	0.562775i	0.900683	+	0.434478i	$0.143067\pi$
$180$	2.56609	+	2.56609i	0.191265	+	0.191265i
$181$	24.4184			1.81501			0.907504	−	0.420043i	$-0.137985\pi$
$181$	24.4184			1.81501			0.907504	+	0.420043i	$0.137985\pi$
$182$	4.17469	+	8.57741i	0.309449	+	0.635800i
$183$	−13.6956			−1.01241
$184$	1.96877	+	1.96877i	0.145140	+	0.145140i
$185$	36.5416	−	21.0973i	2.68659	−	1.55110i
$186$			9.59267i			0.703368i
$187$	−10.7691	−	2.88556i	−0.787511	−	0.211013i
$188$	2.00862	+	0.538208i	0.146494	+	0.0392528i
$189$	−0.432735	−	2.61012i	−0.0314769	−	0.189858i
$190$	−4.49298	+	4.49298i	−0.325955	+	0.325955i
$191$	1.95344	−	3.38346i	0.141346	−	0.244819i	−0.786658	−	0.617389i	$-0.788190\pi$
$191$	1.95344	−	3.38346i	0.141346	−	0.244819i	0.928004	+	0.372571i	$0.121524\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	−17.0092	−	4.55759i	−1.22435	−	0.328063i	−0.411971	−	0.911197i	$-0.635160\pi$
$193$	−17.0092	−	4.55759i	−1.22435	−	0.328063i	−0.812376	+	0.583134i	$0.801826\pi$
$194$	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	$0.613079\pi$
$198$	−2.80673			−0.199466
$199$	24.9179			1.76638			0.883191	−	0.469013i	$-0.155390\pi$
$199$	24.9179			1.76638			0.883191	+	0.469013i	$0.155390\pi$
$200$	7.89124	−	2.11445i	0.557995	−	0.149514i
$201$	0.946174	+	3.53117i	0.0667380	+	0.249070i
$202$	−2.67571	+	9.98589i	−0.188262	+	0.702605i
$203$	4.50226	−	11.9866i	0.315997	−	0.841297i
$204$	1.98611	+	3.44004i	0.139055	+	0.240851i
$205$			29.3290i			2.04843i
$206$	−1.31893	+	4.92232i	−0.0918943	+	0.342954i
$207$	2.41124	+	1.39213i	0.167593	+	0.0967598i
$208$	−3.16979	−	1.71826i	−0.219785	−	0.119140i
$209$		−	4.91432i		−	0.339931i
$210$	−8.98830	−	3.37606i	−0.620251	−	0.232970i
$211$	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	$-0.166746\pi$
$212$	3.83615	+	2.21480i	0.263468	+	0.152113i
$213$	−1.90908	−	7.12477i	−0.130808	−	0.488181i
$214$	11.7605	+	11.7605i	0.803932	+	0.803932i
$215$	−7.91029	+	2.11956i	−0.539477	+	0.144553i
$216$	0.707107	+	0.707107i	0.0481125	+	0.0481125i
$217$	−10.4900	−	23.1105i	−0.712105	−	1.56884i
$218$	−0.560712	−	0.323727i	−0.0379762	−	0.0219256i
$219$	−3.85497	+	3.85497i	−0.260495	+	0.260495i
$220$	−5.09281	+	8.82101i	−0.343357	+	0.594712i
$221$	−12.5911	−	6.82530i	−0.846969	−	0.459120i
$222$	10.0693	−	5.81353i	0.675809	−	0.390179i
$223$	4.49900	+	16.7905i	0.301275	+	1.12437i	0.936104	+	0.351722i	$0.114404\pi$
$223$	4.49900	+	16.7905i	0.301275	+	1.12437i	−0.634829	+	0.772652i	$0.718930\pi$
$224$	−2.15163	−	1.53965i	−0.143762	−	0.102872i
$225$	7.07509	−	4.08481i	0.471673	−	0.272320i
$226$	0.576049	−	2.14984i	0.0383182	−	0.143005i
$227$	14.9238	−	14.9238i	0.990527	−	0.990527i	−0.00942861	−	0.999956i	$-0.503001\pi$
$227$	14.9238	−	14.9238i	0.990527	−	0.990527i	0.999956	+	0.00942861i	$0.00300127\pi$
$228$	−1.23808	+	1.23808i	−0.0819937	+	0.0819937i
$229$	2.69746	−	10.0670i	0.178253	−	0.665249i	−0.817722	−	0.575614i	$-0.804763\pi$
$229$	2.69746	−	10.0670i	0.178253	−	0.665249i	0.995975	−	0.0896351i	$-0.0285701\pi$
$230$	8.75039	−	5.05204i	0.576984	−	0.333122i
$231$	6.76194	−	3.06927i	0.444903	−	0.201943i
$232$	1.25257	+	4.67466i	0.0822354	+	0.306907i
$233$	−18.3850	+	10.6146i	−1.20444	+	0.695386i	−0.961540	−	0.274665i	$-0.911433\pi$
$233$	−18.3850	+	10.6146i	−1.20444	+	0.695386i	−0.242903	+	0.970051i	$0.578100\pi$
$234$	−3.50650	−	0.839311i	−0.229227	−	0.0548675i
$235$	3.77320	−	6.53538i	0.246137	−	0.426321i
$236$	3.86176	−	3.86176i	0.251379	−	0.251379i
$237$	4.08603	+	2.35907i	0.265416	+	0.153238i
$238$	−8.54672	−	6.11580i	−0.554001	−	0.396429i
$239$	−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	$0.956943\pi$
$240$	3.50534	−	0.939253i	0.226269	−	0.0606285i
$241$	−12.6744	−	12.6744i	−0.816428	−	0.816428i	0.169160	−	0.985589i	$-0.445894\pi$
$241$	−12.6744	−	12.6744i	−0.816428	−	0.816428i	−0.985589	+	0.169160i	$0.945894\pi$
$242$	0.808097	+	3.01586i	0.0519465	+	0.193867i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	−6.84779	+	11.8607i	−0.438385	+	0.759305i
$245$	25.3463	−	1.69550i	1.61932	−	0.108322i
$246$			8.08186i			0.515280i
$247$	1.46955	−	6.13955i	0.0935055	−	0.390650i
$248$	8.30749	+	4.79633i	0.527526	+	0.304567i
$249$	1.66853	−	6.22703i	0.105739	−	0.394622i
$250$		−	11.5025i		−	0.727483i
$251$	2.34493	+	4.06154i	0.148011	+	0.256362i	0.930492	−	0.366312i	$-0.119380\pi$
$251$	2.34493	+	4.06154i	0.148011	+	0.256362i	−0.782481	+	0.622674i	$0.786046\pi$
$252$	−2.47680	−	0.930302i	−0.156024	−	0.0586035i
$253$	−2.02259	+	7.54841i	−0.127159	+	0.474564i
$254$	1.21574	+	4.53721i	0.0762825	+	0.284690i
$255$	13.9240	−	3.73092i	0.871953	−	0.233639i
$256$	1.00000			0.0625000
$257$	−10.5145			−0.655879			−0.327939	−	0.944699i	$-0.606354\pi$
$257$	−10.5145			−0.655879			−0.327939	+	0.944699i	$0.606354\pi$
$258$	−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
$262$	−14.1646	−	3.79540i	−0.875093	−	0.234480i
$263$	−2.50881	−	4.34538i	−0.154700	−	0.267947i	0.778250	−	0.627955i	$-0.216108\pi$
$263$	−2.50881	−	4.34538i	−0.154700	−	0.267947i	−0.932950	+	0.360007i	$0.882774\pi$
$264$	−1.40337	+	2.43070i	−0.0863712	+	0.149599i
$265$	11.3668	−	11.3668i	0.698254	−	0.698254i
$266$	1.62887	−	4.33664i	0.0998724	−	0.265897i
$267$	−3.14403	−	0.842441i	−0.192412	−	0.0515566i
$268$	3.53117	+	0.946174i	0.215701	+	0.0577968i
$269$			8.02846i			0.489504i	0.969586	+	0.244752i	$0.0787065\pi$
$269$			8.02846i			0.489504i	−0.969586	+	0.244752i	$0.921294\pi$
$270$	3.14280	−	1.81450i	0.191265	−	0.110427i
$271$	−13.6664	−	13.6664i	−0.830176	−	0.830176i	0.157364	−	0.987541i	$-0.449700\pi$
$271$	−13.6664	−	13.6664i	−0.830176	−	0.830176i	−0.987541	+	0.157364i	$0.949700\pi$
$272$	3.97221			0.240851
$273$	9.36563	−	1.81244i	0.566834	−	0.109694i
$274$	1.65351			0.0998921
$275$	16.2139	+	16.2139i	0.977735	+	0.977735i
$276$	2.41124	−	1.39213i	0.145140	−	0.0837965i
$277$			19.0309i			1.14346i	0.820443	+	0.571728i	$0.193727\pi$
$277$			19.0309i			1.14346i	−0.820443	+	0.571728i	$0.806273\pi$
$278$	−8.52358	−	2.28389i	−0.511211	−	0.136978i
$279$	9.26580	+	2.48276i	0.554729	+	0.148639i
$280$	−7.41790	+	6.09606i	−0.443305	+	0.364310i
$281$	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	$0.164123\pi$
$282$	1.03974	−	1.80088i	0.0619154	−	0.107241i
$283$	14.3592	+	24.8709i	0.853566	+	1.47842i	0.877969	+	0.478717i	$0.158898\pi$
$283$	14.3592	+	24.8709i	0.853566	+	1.47842i	−0.0244037	+	0.999702i	$0.507769\pi$
$284$	−7.12477	−	1.90908i	−0.422777	−	0.113283i
$285$	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
$289$	−1.22151			−0.0718535
$290$	17.5628			1.03132
$291$	14.9544	−	4.00703i	0.876645	−	0.234896i
$292$	1.41102	+	5.26598i	0.0825735	+	0.308168i
$293$	−5.51855	+	20.5955i	−0.322397	+	1.20320i	0.594505	+	0.804092i	$0.297348\pi$
$293$	−5.51855	+	20.5955i	−0.322397	+	1.20320i	−0.916903	+	0.399111i	$0.869319\pi$
$294$	6.98439	−	0.467210i	0.407338	−	0.0272483i
$295$	−9.90962	−	17.1640i	−0.576960	−	0.999324i
$296$		−	11.6271i		−	0.675809i
$297$	−0.726436	+	2.71110i	−0.0421521	+	0.157314i
$298$	14.3694	+	8.29619i	0.832398	+	0.480585i
$299$	−4.78409	+	8.82553i	−0.276671	+	0.510394i
$300$		−	8.16961i		−	0.471673i
$301$	4.61272	−	3.79075i	0.265873	−	0.218495i
$302$	−5.52759	+	9.57406i	−0.318077	+	0.550925i
$303$	8.95311	+	5.16908i	0.514343	+	0.296956i
$304$	0.453168	+	1.69124i	0.0259909	+	0.0969995i
$305$	35.1441	+	35.1441i	2.01234	+	2.01234i
$306$	3.83686	−	1.02808i	0.219339	−	0.0587717i
$307$	15.0865	+	15.0865i	0.861034	+	0.861034i	0.991458	−	0.130424i	$-0.0416339\pi$
$307$	15.0865	+	15.0865i	0.861034	+	0.861034i	−0.130424	+	0.991458i	$0.541634\pi$
$308$	0.722900	−	7.39065i	0.0411911	−	0.421121i
$309$	4.41323	+	2.54798i	0.251060	+	0.144950i
$310$	24.6156	−	24.6156i	1.39807	−	1.39807i
$311$	−14.6633	+	25.3976i	−0.831482	+	1.44017i	0.0653816	+	0.997860i	$0.479174\pi$
$311$	−14.6633	+	25.3976i	−0.831482	+	1.44017i	−0.896863	+	0.442308i	$0.854160\pi$
$312$	−2.48012	+	2.61706i	−0.140409	+	0.148162i
$313$	20.0771	−	11.5915i	1.13483	−	0.655192i	0.189682	−	0.981846i	$-0.439254\pi$
$313$	20.0771	−	11.5915i	1.13483	−	0.655192i	0.945144	+	0.326654i	$0.105921\pi$
$314$	2.48374	+	9.26943i	0.140165	+	0.523104i
$315$	−5.58737	+	7.80824i	−0.314812	+	0.439945i
$316$	4.08603	−	2.35907i	0.229857	−	0.132708i
$317$	8.06274	−	30.0906i	0.452849	−	1.69005i	−0.241488	−	0.970404i	$-0.577636\pi$
$317$	8.06274	−	30.0906i	0.452849	−	1.69005i	0.694337	−	0.719650i	$-0.255698\pi$
$318$	3.13220	−	3.13220i	0.175645	−	0.175645i
$319$	−9.60490	+	9.60490i	−0.537771	+	0.537771i
$320$	0.939253	−	3.50534i	0.0525059	−	0.195955i
$321$	14.4036	−	8.31594i	0.803932	−	0.464150i
$322$	−4.28678	+	5.99069i	−0.238893	+	0.333848i
$323$	1.80008	+	6.71799i	0.100159	+	0.373799i
$324$	0.866025	−	0.500000i	0.0481125	−	0.0277778i
$325$	15.4078	+	25.1048i	0.854671	+	1.39257i
$326$	−9.89527	+	17.1391i	−0.548048	+	0.949248i
$327$	−0.457819	+	0.457819i	−0.0253175	+	0.0253175i
$328$	6.99909	+	4.04093i	0.386460	+	0.223123i
$329$	−0.535588	+	5.47564i	−0.0295279	+	0.301882i
$330$	7.20232	+	7.20232i	0.396475	+	0.396475i
$331$	−0.810766	+	0.217244i	−0.0445638	+	0.0119408i	−0.281032	−	0.959698i	$-0.590677\pi$
$331$	−0.810766	+	0.217244i	−0.0445638	+	0.0119408i	0.236468	+	0.971639i	$0.424010\pi$
$332$	−4.55850	−	4.55850i	−0.250180	−	0.250180i
$333$	−3.00931	−	11.2309i	−0.164909	−	0.615448i
$334$	−8.78090	−	5.06965i	−0.480469	−	0.277399i
$335$	6.63333	−	11.4893i	0.362417	−	0.627725i
$336$	−2.04406	+	1.67982i	−0.111513	+	0.0916417i
$337$		−	21.7718i		−	1.18598i	−0.805208	−	0.592992i	$-0.797947\pi$
$337$		−	21.7718i		−	1.18598i	0.805208	−	0.592992i	$-0.202053\pi$
$338$	2.68553	−	12.7196i	0.146073	−	0.691854i
$339$	−1.92750	−	1.11284i	−0.104687	−	0.0604412i
$340$	3.73092	−	13.9240i	0.202337	−	0.755133i
$341$			26.9241i			1.45802i
$342$	0.875453	+	1.51633i	0.0473391	+	0.0819937i
$343$	−16.3158	+	8.76330i	−0.880969	+	0.473174i
$344$	−0.584061	+	2.17975i	−0.0314905	+	0.117524i
$345$	−2.61513	−	9.75979i	−0.140794	−	0.525450i
$346$	−16.5739	+	4.44097i	−0.891021	+	0.238748i
$347$	−6.64918			−0.356947			−0.178473	−	0.983945i	$-0.557116\pi$
$347$	−6.64918			−0.356947			−0.178473	+	0.983945i	$0.557116\pi$
$348$	4.83957			0.259428
$349$	−6.21010	+	1.66399i	−0.332419	+	0.0890714i	−0.421168	−	0.906983i	$-0.638380\pi$
$349$	−6.21010	+	1.66399i	−0.332419	+	0.0890714i	0.0887491	+	0.996054i	$0.471713\pi$
$350$	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
$353$	−21.4601	−	5.75021i	−1.14220	−	0.306053i	−0.362368	−	0.932035i	$-0.618032\pi$
$353$	−21.4601	−	5.75021i	−1.14220	−	0.306053i	−0.779837	+	0.625982i	$0.784698\pi$
$354$	−2.73068	−	4.72967i	−0.145134	−	0.251379i
$355$	−13.3839	+	23.1816i	−0.710345	+	1.23035i
$356$	−2.30159	+	2.30159i	−0.121984	+	0.121984i
$357$	−8.11946	+	6.67261i	−0.429728	+	0.353152i
$358$	−14.5457	−	3.89751i	−0.768765	−	0.205990i
$359$	−1.88879	−	0.506100i	−0.0996865	−	0.0267109i	0.208631	−	0.977994i	$-0.433099\pi$
$359$	−1.88879	−	0.506100i	−0.0996865	−	0.0267109i	−0.308317	+	0.951284i	$0.599766\pi$
$360$		−	3.62900i		−	0.191265i
$361$	13.7995	−	7.96717i	0.726291	−	0.419324i
$362$	−17.2664	−	17.2664i	−0.907504	−	0.907504i
$363$	3.12225			0.163875
$364$	3.11319	−	9.01710i	0.163176	−	0.472624i
$365$	19.7844			1.03556
$366$	9.68424	+	9.68424i	0.506203	+	0.506203i
$367$	14.4427	−	8.33851i	0.753904	−	0.435267i	−0.0731989	−	0.997317i	$-0.523321\pi$
$367$	14.4427	−	8.33851i	0.753904	−	0.435267i	0.827103	+	0.562051i	$0.189987\pi$
$368$		−	2.78426i		−	0.145140i
$369$	7.80648	+	2.09174i	0.406389	+	0.108892i
$370$	−40.7568	−	10.9208i	−2.11885	−	0.567743i
$371$	−4.12087	+	10.9712i	−0.213945	+	0.569599i
$372$	6.78304	−	6.78304i	0.351684	−	0.351684i
$373$	6.21369	−	10.7624i	0.321733	−	0.557257i	−0.659113	−	0.752044i	$-0.729068\pi$
$373$	6.21369	−	10.7624i	0.321733	−	0.557257i	0.980846	+	0.194787i	$0.0624014\pi$
$374$	5.57447	+	9.65527i	0.288249	+	0.499262i
$375$	−11.1106	−	2.97707i	−0.573748	−	0.153735i
$376$	−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	$0.356408\pi$
$380$	6.35403			0.325955
$381$	4.69727			0.240648
$382$	−3.77376	+	1.01118i	−0.193082	+	0.0517362i
$383$	−3.52224	−	13.1452i	−0.179978	−	0.671687i	−0.995650	−	0.0931724i	$-0.970299\pi$
$383$	−3.52224	−	13.1452i	−0.179978	−	0.671687i	0.815672	−	0.578515i	$-0.196367\pi$
$384$	0.258819	−	0.965926i	0.0132078	−	0.0492922i
$385$	−25.2278	−	9.47570i	−1.28573	−	0.482927i
$386$	8.80460	+	15.2500i	0.448142	+	0.776205i
$387$			2.25664i			0.114711i
$388$	4.00703	−	14.9544i	0.203426	−	0.759197i
$389$	4.45547	+	2.57237i	0.225901	+	0.130424i	0.608680	−	0.793416i	$-0.291699\pi$
$389$	4.45547	+	2.57237i	0.225901	+	0.130424i	−0.382778	+	0.923840i	$0.625033\pi$
$390$	6.84425	+	11.1517i	0.346572	+	0.564690i
$391$		−	11.0597i		−	0.559313i
$392$	3.08758	−	6.28227i	0.155946	−	0.317302i
$393$	−7.33214	+	12.6996i	−0.369858	+	0.640612i
$394$	14.0668	+	8.12145i	0.708673	+	0.409153i
$395$	−4.43153	−	16.5387i	−0.222974	−	0.832151i
$396$	1.98466	+	1.98466i	0.0997329	+	0.0997329i
$397$	13.0507	−	3.49693i	0.654997	−	0.175506i	0.0840100	−	0.996465i	$-0.473227\pi$
$397$	13.0507	−	3.49693i	0.654997	−	0.175506i	0.570987	+	0.820959i	$0.306561\pi$
$398$	−17.6196	−	17.6196i	−0.883191	−	0.883191i
$399$	−3.76729	−	2.69577i	−0.188601	−	0.134957i
$400$	−7.07509	−	4.08481i	−0.353755	−	0.204240i
$401$	−10.1754	+	10.1754i	−0.508137	+	0.508137i	−0.913954	−	0.405817i	$-0.866987\pi$
$401$	−10.1754	+	10.1754i	−0.508137	+	0.508137i	0.405817	+	0.913954i	$0.366987\pi$
$402$	1.82787	−	3.16596i	0.0911658	−	0.157904i
$403$	−8.05123	+	33.6367i	−0.401060	+	1.67556i
$404$	8.95311	−	5.16908i	0.445434	−	0.257171i
$405$	−0.939253	−	3.50534i	−0.0466719	−	0.174182i
$406$	−11.6594	+	5.29226i	−0.578647	+	0.262650i
$407$	28.2619	−	16.3170i	1.40089	−	0.808805i
$408$	1.02808	−	3.83686i	0.0508978	−	0.189953i
$409$	−16.2496	+	16.2496i	−0.803491	+	0.803491i	−0.983639	−	0.180149i	$-0.942342\pi$
$409$	−16.2496	+	16.2496i	−0.803491	+	0.803491i	0.180149	+	0.983639i	$0.442342\pi$
$410$	20.7388	−	20.7388i	1.02421	−	1.02421i
$411$	0.427959	−	1.59717i	0.0211097	−	0.0787824i
$412$	4.41323	−	2.54798i	0.217424	−	0.125530i
$413$	11.7508	+	8.40855i	0.578218	+	0.413758i
$414$	−0.720620	−	2.68939i	−0.0354166	−	0.132176i
$415$	−20.2607	+	11.6975i	−0.994559	+	0.574209i
$416$	1.02639	+	3.45638i	0.0503227	+	0.169463i
$417$	−4.41213	+	7.64204i	−0.216063	+	0.374232i
$418$	−3.47495	+	3.47495i	−0.169965	+	0.169965i
$419$	−28.1122	−	16.2306i	−1.37337	−	0.792917i	−0.382022	−	0.924153i	$-0.624772\pi$
$419$	−28.1122	−	16.2306i	−1.37337	−	0.792917i	−0.991351	+	0.131236i	$0.958105\pi$
$420$	3.96845	+	8.74292i	0.193641	+	0.426611i
$421$	−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	$0.956289\pi$
$422$	−24.3057	+	6.51270i	−1.18318	+	0.317033i
$423$	−1.47041	−	1.47041i	−0.0714938	−	0.0714938i
$424$	−1.14647	−	4.27867i	−0.0556773	−	0.207791i
$425$	−28.1038	−	16.2257i	−1.36323	−	0.787063i
$426$	−3.68805	+	6.38789i	−0.178687	+	0.309494i
$427$	−33.9212	−	12.7410i	−1.64156	−	0.616581i
$428$		−	16.6319i		−	0.803932i
$429$	−9.84182	−	2.35572i	−0.475167	−	0.113735i
$430$	7.09217	+	4.09467i	0.342015	+	0.197462i
$431$	−0.476905	+	1.77983i	−0.0229717	+	0.0857316i	−0.976460	−	0.215698i	$-0.930797\pi$
$431$	−0.476905	+	1.77983i	−0.0229717	+	0.0857316i	0.953488	+	0.301430i	$0.0974639\pi$
$432$		−	1.00000i		−	0.0481125i
$433$	−9.67519	−	16.7579i	−0.464960	−	0.805335i	0.534240	−	0.845333i	$-0.320598\pi$
$433$	−9.67519	−	16.7579i	−0.464960	−	0.805335i	−0.999200	+	0.0399985i	$0.987265\pi$
$434$	−8.92407	+	23.7591i	−0.428369	+	1.14047i
$435$	4.54558	−	16.9643i	0.217944	−	0.813378i
$436$	0.167574	+	0.625393i	0.00802532	+	0.0299509i
$437$	4.70887	−	1.26174i	0.225256	−	0.0603571i
$438$	5.45175			0.260495
$439$	−24.5854			−1.17340			−0.586698	−	0.809806i	$-0.699572\pi$
$439$	−24.5854			−1.17340			−0.586698	+	0.809806i	$0.699572\pi$
$440$	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	0.994590	+	0.103883i	$0.0331267\pi$
$443$	12.3604	+	21.4088i	0.587260	+	1.01716i	−0.407330	+	0.913281i	$0.633540\pi$
$444$	−11.2309	−	3.00931i	−0.532994	−	0.142815i
$445$	5.90609	+	10.2296i	0.279975	+	0.484932i
$446$	8.69140	−	15.0539i	0.411550	−	0.712825i
$447$	11.7326	−	11.7326i	0.554932	−	0.554932i
$448$	0.432735	+	2.61012i	0.0204448	+	0.123317i
$449$	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	$0.378246\pi$
$450$	−7.89124	−	2.11445i	−0.371997	−	0.0996762i
$451$			22.6836i			1.06813i
$452$	−1.92750	+	1.11284i	−0.0906618	+	0.0523436i
$453$	7.81719	+	7.81719i	0.367284	+	0.367284i
$454$	−21.1054			−0.990527
$455$	−28.6839	−	19.3821i	−1.34472	−	0.908649i
$456$	1.75091			0.0819937
$457$	3.71575	+	3.71575i	0.173815	+	0.173815i	0.788653	−	0.614838i	$-0.210779\pi$
$457$	3.71575	+	3.71575i	0.173815	+	0.173815i	−0.614838	+	0.788653i	$0.710779\pi$
$458$	−9.02586	+	5.21108i	−0.421751	+	0.243498i
$459$		−	3.97221i		−	0.185407i
$460$	−9.75979	−	2.61513i	−0.455053	−	0.121931i
$461$	0.174143	+	0.0466615i	0.00811065	+	0.00217324i	0.262872	−	0.964831i	$-0.415330\pi$
$461$	0.174143	+	0.0466615i	0.00811065	+	0.00217324i	−0.254761	+	0.967004i	$0.581997\pi$
$462$	−6.95172	−	2.61111i	−0.323423	−	0.121480i
$463$	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	$0.213999\pi$
$464$	2.41978	−	4.19119i	0.112336	−	0.194571i
$465$	−17.4059	−	30.1479i	−0.807178	−	1.39807i
$466$	20.5058	+	5.49452i	0.949914	+	0.254529i
$467$	14.7088	+	25.4765i	0.680644	+	1.17891i	0.974785	+	0.223148i	$0.0716333\pi$
$467$	14.7088	+	25.4765i	0.680644	+	1.17891i	−0.294141	+	0.955762i	$0.595033\pi$
$468$	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
$471$	9.59642			0.442180
$472$	−5.46135			−0.251379
$473$	−6.11797	+	1.63930i	−0.281304	+	0.0753753i
$474$	−1.22114	−	4.55737i	−0.0560890	−	0.209327i
$475$	3.70220	−	13.8168i	0.169869	−	0.633959i
$476$	1.71892	+	10.3680i	0.0787864	+	0.475215i
$477$	−2.21480	−	3.83615i	−0.101409	−	0.175645i
$478$			18.7151i			0.856011i
$479$	−5.00320	+	18.6722i	−0.228602	+	0.853155i	0.752327	+	0.658790i	$0.228931\pi$
$479$	−5.00320	+	18.6722i	−0.228602	+	0.853155i	−0.980929	+	0.194365i	$0.937735\pi$
$480$	−3.14280	−	1.81450i	−0.143449	−	0.0828201i
$481$	40.1875	−	11.9339i	1.83239	−	0.544137i
$482$			17.9243i			0.816428i
$483$	4.67706	+	5.69122i	0.212814	+	0.258959i
$484$	1.56112	−	2.70395i	0.0709602	−	0.122907i
$485$	−48.6568	−	28.0920i	−2.20939	−	1.27559i
$486$	−0.258819	−	0.965926i	−0.0117403	−	0.0438153i
$487$	24.7041	+	24.7041i	1.11945	+	1.11945i	0.991822	+	0.127629i	$0.0407368\pi$
$487$	24.7041	+	24.7041i	1.11945	+	1.11945i	0.127629	+	0.991822i	$0.459263\pi$
$488$	13.2289	−	3.54468i	0.598845	−	0.160460i
$489$	13.9940	+	13.9940i	0.632832	+	0.632832i
$490$	−19.1215	−	16.7237i	−0.863820	−	0.755498i
$491$	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	$0.592032\pi$
$492$	5.71474	−	5.71474i	0.257640	−	0.257640i
$493$	9.61190	−	16.6483i	0.432898	−	0.749802i
$494$	−5.38045	+	3.30219i	−0.242078	+	0.148572i
$495$	8.82101	−	5.09281i	0.396475	−	0.228905i
$496$	−2.48276	−	9.26580i	−0.111479	−	0.416047i
$497$	1.89978	−	19.4226i	0.0852169	−	0.871224i
$498$	−5.58300	+	3.22335i	−0.250180	+	0.144442i
$499$	−4.12442	+	15.3926i	−0.184634	+	0.689065i	0.810074	+	0.586328i	$0.199427\pi$
$499$	−4.12442	+	15.3926i	−0.184634	+	0.689065i	−0.994708	+	0.102738i	$0.967240\pi$
$500$	−8.13351	+	8.13351i	−0.363741	+	0.363741i
$501$	−7.16957	+	7.16957i	−0.320313	+	0.320313i
$502$	1.21383	−	4.53006i	0.0541757	−	0.202186i
$503$	13.8649	−	8.00489i	0.618205	−	0.356921i	−0.157965	−	0.987445i	$-0.550493\pi$
$503$	13.8649	−	8.00489i	0.618205	−	0.356921i	0.776170	+	0.630524i	$0.217160\pi$
$504$	1.09354	+	2.40918i	0.0487101	+	0.107314i
$505$	−9.71015	−	36.2388i	−0.432096	−	1.61260i
$506$	6.76772	−	3.90734i	0.300862	−	0.173703i
$507$	−11.5911	−	5.88609i	−0.514779	−	0.261410i
$508$	2.34863	−	4.06795i	0.104204	−	0.180486i
$509$	9.40170	−	9.40170i	0.416723	−	0.416723i	−0.467350	−	0.884073i	$-0.654791\pi$
$509$	9.40170	−	9.40170i	0.416723	−	0.416723i	0.884073	+	0.467350i	$0.154791\pi$
$510$	−12.4839	−	7.20758i	−0.552796	−	0.319157i
$511$	−13.1343	+	5.96170i	−0.581026	+	0.263730i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	1.69124	−	0.453168i	0.0746703	−	0.0200078i
$514$	7.43490	+	7.43490i	0.327939	+	0.327939i
$515$	−4.78640	−	17.8631i	−0.210914	−	0.787141i
$516$	1.95431	+	1.12832i	0.0860336	+	0.0496715i
$517$	2.91826	−	5.05458i	0.128345	−	0.222300i
$518$	30.3481	−	5.03144i	1.33342	−	0.221069i
$519$			17.1586i			0.753179i
$520$	13.0798	−	0.351423i	0.573588	−	0.0154109i
$521$	16.2369	+	9.37438i	0.711351	+	0.410699i	0.811561	−	0.584267i	$-0.198618\pi$
$521$	16.2369	+	9.37438i	0.711351	+	0.410699i	−0.100210	+	0.994966i	$0.531951\pi$
$522$	1.25257	−	4.67466i	0.0548236	−	0.204604i
$523$		−	5.01454i		−	0.219270i	−0.993972	−	0.109635i	$-0.965032\pi$
$523$		−	5.01454i		−	0.219270i	0.993972	−	0.109635i	$-0.0349682\pi$
$524$	7.33214	+	12.6996i	0.320306	+	0.554787i
$525$	21.3237	−	3.53528i	0.930642	−	0.154292i
$526$	−1.29865	+	4.84664i	−0.0566240	+	0.211324i
$527$	−9.86207	−	36.8058i	−0.429599	−	1.60328i
$528$	2.71110	−	0.726436i	0.117985	−	0.0316141i
$529$	15.2479			0.662951
$530$	−16.0750			−0.698254
$531$	−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
$535$	−58.3004	−	15.6215i	−2.52055	−	0.675378i
$536$	−1.82787	−	3.16596i	−0.0789519	−	0.136749i
$537$	−7.52942	+	13.0413i	−0.324918	+	0.562775i
$538$	5.67698	−	5.67698i	0.244752	−	0.244752i
$539$	19.6033	−	1.31133i	0.844375	−	0.0564832i
$540$	−3.50534	−	0.939253i	−0.150846	−	0.0404190i
$541$	−8.47577	−	2.27108i	−0.364402	−	0.0976412i	0.0719719	−	0.997407i	$-0.477071\pi$
$541$	−8.47577	−	2.27108i	−0.364402	−	0.0976412i	−0.436374	+	0.899765i	$0.643737\pi$
$542$			19.3272i			0.830176i
$543$	−21.1470	+	12.2092i	−0.907504	+	0.523948i
$544$	−2.80878	−	2.80878i	−0.120425	−	0.120425i
$545$	2.34961			0.100646
$546$	−7.90409	−	5.34091i	−0.338264	−	0.228570i
$547$	−27.2919			−1.16692			−0.583459	−	0.812143i	$-0.698301\pi$
$547$	−27.2919			−1.16692			−0.583459	+	0.812143i	$0.698301\pi$
$548$	−1.16921	−	1.16921i	−0.0499460	−	0.0499460i
$549$	11.8607	−	6.84779i	0.506203	−	0.292256i
$550$		−	22.9299i		−	0.977735i
$551$	8.18489	+	2.19314i	0.348688	+	0.0934307i
$552$	−2.68939	−	0.720620i	−0.114468	−	0.0306716i
$553$	7.92563	+	9.64418i	0.337032	+	0.410112i
$554$	13.4569	−	13.4569i	0.571728	−	0.571728i
$555$	−21.0973	+	36.5416i	−0.895530	+	1.55110i
$556$	4.41213	+	7.64204i	0.187116	+	0.324095i
$557$	−41.5974	−	11.1460i	−1.76254	−	0.472271i	−0.775311	−	0.631579i	$-0.782407\pi$
$557$	−41.5974	−	11.1460i	−1.76254	−	0.472271i	−0.987229	+	0.159308i	$0.949074\pi$
$558$	−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
$562$	−8.93571			−0.376930
$563$	38.5816			1.62602			0.813009	−	0.582251i	$-0.197828\pi$
$563$	38.5816			1.62602			0.813009	+	0.582251i	$0.197828\pi$
$564$	−2.00862	+	0.538208i	−0.0845781	+	0.0226626i
$565$	2.09048	+	7.80177i	0.0879471	+	0.328223i
$566$	7.43287	−	27.7398i	0.312427	−	1.16599i
$567$	1.67982	+	2.04406i	0.0705459	+	0.0858427i
$568$	3.68805	+	6.38789i	0.154747	+	0.268030i
$569$		−	14.2378i		−	0.596879i	−0.954429	−	0.298440i	$-0.903534\pi$
$569$		−	14.2378i		−	0.596879i	0.954429	−	0.298440i	$-0.0964662\pi$
$570$	1.64454	−	6.13752i	0.0688824	−	0.257072i
$571$	0.320357	+	0.184958i	0.0134065	+	0.00774025i	0.506688	−	0.862129i	$-0.330870\pi$
$571$	0.320357	+	0.184958i	0.0134065	+	0.00774025i	−0.493282	+	0.869870i	$0.664203\pi$
$572$	−6.96102	+	7.34540i	−0.291055	+	0.307127i
$573$			3.90688i			0.163212i
$574$	−7.51857	+	20.0171i	−0.313819	+	0.835500i
$575$	−11.3732	+	19.6989i	−0.474294	+	0.821502i
$576$	−0.866025	−	0.500000i	−0.0360844	−	0.0208333i
$577$	3.92680	+	14.6550i	0.163475	+	0.610097i	0.998230	+	0.0594750i	$0.0189427\pi$
$577$	3.92680	+	14.6550i	0.163475	+	0.610097i	−0.834755	+	0.550622i	$0.814391\pi$
$578$	0.863738	+	0.863738i	0.0359268	+	0.0359268i
$579$	17.0092	−	4.55759i	0.706877	−	0.189407i
$580$	−12.4188	−	12.4188i	−0.515661	−	0.515661i
$581$	9.92563	−	13.8709i	0.411784	−	0.575461i
$582$	−13.4078	−	7.74099i	−0.555771	−	0.320874i
$583$	8.79126	−	8.79126i	0.364097	−	0.364097i
$584$	2.72587	−	4.72135i	0.112797	−	0.195371i
$585$	12.5432	−	3.72475i	0.518596	−	0.154000i
$586$	18.4654	−	10.6610i	0.762800	−	0.440403i
$587$	0.548765	+	2.04802i	0.0226499	+	0.0845307i	0.976326	−	0.216306i	$-0.0694008\pi$
$587$	0.548765	+	2.04802i	0.0226499	+	0.0845307i	−0.953676	+	0.300837i	$0.902734\pi$
$588$	−5.26908	−	4.60834i	−0.217293	−	0.190045i
$589$	14.5456	−	8.39793i	0.599342	−	0.346030i
$590$	−5.12959	+	19.1439i	−0.211182	+	0.788142i
$591$	11.4855	−	11.4855i	0.472449	−	0.472449i
$592$	−8.22157	+	8.22157i	−0.337905	+	0.337905i
$593$	−6.58130	+	24.5618i	−0.270262	+	1.00863i	0.688689	+	0.725057i	$0.258187\pi$
$593$	−6.58130	+	24.5618i	−0.270262	+	1.00863i	−0.958951	+	0.283573i	$0.908480\pi$
$594$	2.43070	−	1.40337i	0.0997329	−	0.0575808i
$595$	37.9578	+	3.71276i	1.55612	+	0.152208i
$596$	−4.29442	−	16.0270i	−0.175906	−	0.656492i
$597$	−21.5795	+	12.4589i	−0.883191	+	0.509911i
$598$	9.62346	−	2.85773i	0.393533	−	0.116861i
$599$	8.48442	−	14.6954i	0.346664	−	0.600440i	−0.638991	−	0.769215i	$-0.720648\pi$
$599$	8.48442	−	14.6954i	0.346664	−	0.600440i	0.985655	+	0.168775i	$0.0539811\pi$
$600$	−5.77679	+	5.77679i	−0.235836	+	0.235836i
$601$	−30.9667	−	17.8786i	−1.26316	−	0.729284i	−0.289472	−	0.957186i	$-0.593480\pi$
$601$	−30.9667	−	17.8786i	−1.26316	−	0.729284i	−0.973684	+	0.227903i	$0.926813\pi$
$602$	−5.94215	−	0.581219i	−0.242184	−	0.0236887i
$603$	−2.58500	−	2.58500i	−0.105269	−	0.105269i
$604$	10.6785	−	2.86129i	0.434501	−	0.116424i
$605$	−8.01196	−	8.01196i	−0.325733	−	0.325733i
$606$	−2.67571	−	9.98589i	−0.108693	−	0.405649i
$607$	21.9632	+	12.6805i	0.891460	+	0.514685i	0.874420	−	0.485170i	$-0.161242\pi$
$607$	21.9632	+	12.6805i	0.891460	+	0.514685i	0.0170401	+	0.999855i	$0.494576\pi$
$608$	0.875453	−	1.51633i	0.0355043	−	0.0614952i
$609$	2.09425	+	12.6319i	0.0848634	+	0.511869i
$610$		−	49.7012i		−	2.01234i
$611$	5.15734	−	5.44212i	0.208644	−	0.220165i
$612$	−3.44004	−	1.98611i	−0.139055	−	0.0802836i
$613$	−6.13674	+	22.9026i	−0.247861	+	0.925029i	0.724063	+	0.689733i	$0.242272\pi$
$613$	−6.13674	+	22.9026i	−0.247861	+	0.925029i	−0.971924	+	0.235295i	$0.924394\pi$
$614$		−	21.3356i		−	0.861034i
$615$	−14.6645	−	25.3997i	−0.591330	−	1.02421i
$616$	−5.73715	+	4.71481i	−0.231156	+	0.189965i
$617$	−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	$0.138500\pi$
$618$	−1.31893	−	4.92232i	−0.0530552	−	0.198005i
$619$	24.5826	−	6.58689i	0.988058	−	0.264749i	0.271624	−	0.962404i	$-0.412439\pi$
$619$	24.5826	−	6.58689i	0.988058	−	0.264749i	0.716435	+	0.697654i	$0.245773\pi$
$620$	−34.8117			−1.39807
$621$	−2.78426			−0.111729
$622$	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
$626$	−22.3931	−	6.00022i	−0.895009	−	0.239817i
$627$	2.45716	+	4.25593i	0.0981296	+	0.169965i
$628$	4.79821	−	8.31074i	0.191469	−	0.331635i
$629$	−32.6579	+	32.6579i	−1.30215	+	1.30215i
$630$	9.47213	−	1.57039i	0.377378	−	0.0625660i
$631$	−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	$0.696793\pi$
$632$	−4.55737	−	1.22114i	−0.181282	−	0.0485745i
$633$			25.1631i			1.00014i
$634$	−26.9785	+	15.5760i	−1.07145	+	0.618603i
$635$	−12.0536	−	12.0536i	−0.478333	−	0.478333i
$636$	−4.42961			−0.175645
$637$	24.8829	+	4.22380i	0.985897	+	0.167353i
$638$	13.5834			0.537771
$639$	5.21569	+	5.21569i	0.206330	+	0.206330i
$640$	−3.14280	+	1.81450i	−0.124230	+	0.0717243i
$641$			39.7868i			1.57149i	0.618554	+	0.785743i	$0.287719\pi$
$641$			39.7868i			1.57149i	−0.618554	+	0.785743i	$0.712281\pi$
$642$	−16.0652	−	4.30465i	−0.634041	−	0.169891i
$643$	−19.5278	−	5.23247i	−0.770103	−	0.206348i	−0.147686	−	0.989034i	$-0.547182\pi$
$643$	−19.5278	−	5.23247i	−0.770103	−	0.206348i	−0.622417	+	0.782686i	$0.713849\pi$
$644$	7.26727	−	1.20485i	0.286371	−	0.0474777i
$645$	5.79074	−	5.79074i	0.228010	−	0.228010i
$646$	3.47749	−	6.02318i	0.136820	−	0.236979i
$647$	−22.5507	−	39.0590i	−0.886560	−	1.53557i	−0.843915	−	0.536476i	$-0.819755\pi$
$647$	−22.5507	−	39.0590i	−0.886560	−	1.53557i	−0.0426444	−	0.999090i	$-0.513578\pi$
$648$	−0.965926	−	0.258819i	−0.0379452	−	0.0101674i
$649$	−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
$653$	0.495719			0.0193990			0.00969950	−	0.999953i	$-0.496913\pi$
$653$	0.495719			0.0193990			0.00969950	+	0.999953i	$0.496913\pi$
$654$	0.647454			0.0253175
$655$	51.4033	−	13.7735i	2.00849	−	0.538175i
$656$	−2.09174	−	7.80648i	−0.0816687	−	0.304792i
$657$	1.41102	−	5.26598i	0.0550490	−	0.205446i
$658$	4.25058	−	3.49314i	0.165705	−	0.136177i
$659$	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	$0.675180\pi$
$660$		−	10.1856i		−	0.396475i
$661$	−4.86322	+	18.1498i	−0.189157	+	0.705945i	0.804545	+	0.593892i	$0.202409\pi$
$661$	−4.86322	+	18.1498i	−0.189157	+	0.705945i	−0.993702	+	0.112053i	$0.964257\pi$
$662$	0.726913	+	0.419684i	0.0282523	+	0.0163115i
$663$	14.3169	−	0.384660i	0.556021	−	0.0149389i
$664$			6.44670i			0.250180i
$665$	2.74961	+	16.5848i	0.106625	+	0.643131i
$666$	−5.81353	+	10.0693i	−0.225270	+	0.390179i
$667$	−11.6694	−	6.73732i	−0.451840	−	0.260870i
$668$	2.62425	+	9.79382i	0.101535	+	0.378934i
$669$	−12.2915	−	12.2915i	−0.475217	−	0.475217i
$670$	−12.8146	+	3.43366i	−0.495071	+	0.132654i
$671$	27.1811	+	27.1811i	1.04931	+	1.04931i
$672$	2.63318	+	0.257559i	0.101577	+	0.00993557i
$673$	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	$0.581984\pi$
$674$	−15.3950	+	15.3950i	−0.592992	+	0.592992i
$675$	−4.08481	+	7.07509i	−0.157224	+	0.272320i
$676$	−10.8931	+	7.09515i	−0.418964	+	0.272891i
$677$	−40.7614	+	23.5336i	−1.56659	+	0.904471i	−0.570027	+	0.821626i	$0.693067\pi$
$677$	−40.7614	+	23.5336i	−1.56659	+	0.904471i	−0.996562	+	0.0828450i	$0.973599\pi$
$678$	0.576049	+	2.14984i	0.0221230	+	0.0825643i
$679$	40.7669	+	3.98753i	1.56449	+	0.153027i
$680$	−12.4839	+	7.20758i	−0.478735	+	0.276398i
$681$	−5.46249	+	20.3863i	−0.209323	+	0.781204i
$682$	19.0382	−	19.0382i	0.729010	−	0.729010i
$683$	−6.50572	+	6.50572i	−0.248935	+	0.248935i	−0.820533	−	0.571599i	$-0.806323\pi$
$683$	−6.50572	+	6.50572i	−0.248935	+	0.248935i	0.571599	+	0.820533i	$0.306323\pi$
$684$	0.453168	−	1.69124i	0.0173273	−	0.0646664i
$685$	−5.19665	+	3.00029i	−0.198554	+	0.114635i
$686$	17.7336	+	5.34040i	0.677071	+	0.203898i
$687$	2.69746	+	10.0670i	0.102914	+	0.384082i
$688$	1.95431	−	1.12832i	0.0745073	−	0.0430168i
$689$	13.6120	−	8.35419i	0.518575	−	0.318269i
$690$	−5.05204	+	8.75039i	−0.192328	+	0.333122i
$691$	−1.87801	+	1.87801i	−0.0714430	+	0.0714430i	−0.741925	−	0.670482i	$-0.766087\pi$
$691$	−1.87801	+	1.87801i	−0.0714430	+	0.0714430i	0.670482	+	0.741925i	$0.266087\pi$
$692$	14.8598	+	8.57930i	0.564884	+	0.326136i
$693$	−4.32137	+	6.03904i	−0.164155	+	0.229404i
$694$	4.70168	+	4.70168i	0.178473	+	0.178473i
$695$	30.9321	−	8.28822i	1.17332	−	0.314390i
$696$	−3.42209	−	3.42209i	−0.129714	−	0.129714i
$697$	−8.30884	−	31.0090i	−0.314720	−	1.17455i
$698$	5.56782	+	3.21458i	0.210745	+	0.121674i
$699$	10.6146	−	18.3850i	0.401481	−	0.695386i
$700$	7.60020	−	20.2345i	0.287261	−	0.764792i
$701$		−	27.9693i		−	1.05638i	−0.849125	−	0.528192i	$-0.822870\pi$
$701$		−	27.9693i		−	1.05638i	0.849125	−	0.528192i	$-0.177130\pi$
$702$	3.45638	−	1.02639i	0.130452	−	0.0387385i
$703$	−17.6304	−	10.1789i	−0.664945	−	0.383906i
$704$	0.726436	−	2.71110i	0.0273786	−	0.102178i
$705$			7.54640i			0.284214i
$706$	11.1086	+	19.2406i	0.418076	+	0.724129i
$707$	17.3663	+	21.1319i	0.653125	+	0.794745i
$708$	−1.41350	+	5.27526i	−0.0531227	+	0.198257i
$709$	−5.25204	−	19.6009i	−0.197245	−	0.736127i	−0.991674	−	0.128771i	$-0.958897\pi$
$709$	−5.25204	−	19.6009i	−0.197245	−	0.736127i	0.794430	−	0.607356i	$-0.207770\pi$
$710$	25.8558	−	6.92803i	0.970349	−	0.260004i
$711$	−4.71814			−0.176944
$712$	3.25494			0.121984
$713$	−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
$717$	18.0774	+	4.84384i	0.675114	+	0.180896i
$718$	0.977709	+	1.69344i	0.0364878	+	0.0631987i
$719$	7.44832	−	12.9009i	0.277775	−	0.481121i	−0.693056	−	0.720883i	$-0.743736\pi$
$719$	7.44832	−	12.9009i	0.277775	−	0.481121i	0.970832	+	0.239763i	$0.0770696\pi$
$720$	−2.56609	+	2.56609i	−0.0956324	+	0.0956324i
$721$	8.56030	+	10.4165i	0.318802	+	0.387930i
$722$	−15.3914	−	4.12411i	−0.572808	−	0.153483i
$723$	17.3135	+	4.63914i	0.643897	+	0.172532i
$724$			24.4184i			0.907504i
$725$	−34.2404	+	19.7687i	−1.27166	+	0.734191i
$726$	−2.20776	−	2.20776i	−0.0819377	−	0.0819377i
$727$	19.1877			0.711634			0.355817	−	0.934556i	$-0.384203\pi$
$727$	19.1877			0.711634			0.355817	+	0.934556i	$0.384203\pi$
$728$	−8.57741	+	4.17469i	−0.317900	+	0.154724i
$729$	−1.00000			−0.0370370
$730$	−13.9897	−	13.9897i	−0.517781	−	0.517781i
$731$	7.76293	−	4.48193i	0.287122	−	0.165770i
$732$		−	13.6956i		−	0.506203i
$733$	39.0143	+	10.4539i	1.44103	+	0.386122i	0.892893	−	0.450268i	$-0.148672\pi$
$733$	39.0143	+	10.4539i	1.44103	+	0.386122i	0.548134	+	0.836390i	$0.315338\pi$
$734$	−16.1088	−	4.31633i	−0.594585	−	0.159319i
$735$	−21.1028	+	14.1415i	−0.778389	+	0.521618i
$736$	−1.96877	+	1.96877i	−0.0725699	+	0.0725699i
$737$	5.13034	−	8.88601i	0.188979	−	0.327320i
$738$	−4.04093	−	6.99909i	−0.148749	−	0.257640i
$739$	12.6696	+	3.39481i	0.466059	+	0.124880i	0.484204	−	0.874955i	$-0.339109\pi$
$739$	12.6696	+	3.39481i	0.466059	+	0.124880i	−0.0181446	+	0.999835i	$0.505776\pi$
$740$	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	$0.316839\pi$
$744$	−9.59267			−0.351684
$745$	−60.2137			−2.20606
$746$	−12.0039	+	3.21644i	−0.439495	+	0.117762i
$747$	1.66853	+	6.22703i	0.0610483	+	0.227835i
$748$	2.88556	−	10.7691i	0.105507	−	0.393756i
$749$	43.4112	−	7.19720i	1.58621	−	0.262980i
$750$	5.75126	+	9.96147i	0.210006	+	0.363741i
$751$		−	7.68549i		−	0.280447i	−0.990120	−	0.140224i	$-0.955218\pi$
$751$		−	7.68549i		−	0.280447i	0.990120	−	0.140224i	$-0.0447822\pi$
$752$	−0.538208	+	2.00862i	−0.0196264	+	0.0732468i
$753$	−4.06154	−	2.34493i	−0.148011	−	0.0854540i
$754$	16.9700	+	4.06190i	0.618009	+	0.147926i
$755$		−	40.1192i		−	1.46009i
$756$	2.61012	−	0.432735i	0.0949292	−	0.0157384i
$757$	−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	$0.173616\pi$
$758$	−6.34526	−	3.66344i	−0.230470	−	0.133062i
$759$	−2.02259	−	7.54841i	−0.0734153	−	0.273990i
$760$	−4.49298	−	4.49298i	−0.162977	−	0.162977i
$761$	−32.5042	+	8.70948i	−1.17828	+	0.315718i	−0.794243	−	0.607601i	$-0.792132\pi$
$761$	−32.5042	+	8.70948i	−1.17828	+	0.315718i	−0.384034	+	0.923319i	$0.625465\pi$
$762$	−3.32147	−	3.32147i	−0.120324	−	0.120324i
$763$	−1.55984	+	0.708017i	−0.0564699	+	0.0256319i
$764$	3.38346	+	1.95344i	0.122409	+	0.0706730i
$765$	−10.1931	+	10.1931i	−0.368531	+	0.368531i
$766$	−6.80444	+	11.7856i	−0.245855	+	0.425833i
$767$	−5.60546	−	18.8765i	−0.202401	−	0.681591i
$768$	−0.866025	+	0.500000i	−0.0312500	+	0.0180422i
$769$	9.90694	+	36.9732i	0.357253	+	1.33329i	0.877625	+	0.479348i	$0.159127\pi$
$769$	9.90694	+	36.9732i	0.357253	+	1.33329i	−0.520371	+	0.853940i	$0.674207\pi$
$770$	11.1384	+	24.5391i	0.401399	+	0.884326i
$771$	9.10586	−	5.25727i	0.327939	−	0.189336i
$772$	4.55759	−	17.0092i	0.164031	−	0.612174i
$773$	−10.6503	+	10.6503i	−0.383066	+	0.383066i	−0.872205	−	0.489140i	$-0.837311\pi$
$773$	−10.6503	+	10.6503i	−0.383066	+	0.383066i	0.489140	+	0.872205i	$0.337311\pi$
$774$	1.59569	−	1.59569i	0.0573557	−	0.0573557i
$775$	−20.2832	+	75.6980i	−0.728595	+	2.71915i
$776$	−13.4078	+	7.74099i	−0.481311	+	0.277885i
$777$	2.99466	−	30.6162i	0.107433	−	1.09835i
$778$	−1.33156	−	4.96943i	−0.0477386	−	0.178163i
$779$	12.2548	−	7.07528i	0.439072	−	0.253498i
$780$	3.04586	−	12.7251i	0.109059	−	0.455631i
$781$	−10.3514	+	17.9291i	−0.370401	+	0.641554i
$782$	−7.82038	+	7.82038i	−0.279656	+	0.279656i
$783$	−4.19119	−	2.41978i	−0.149781	−	0.0864760i
$784$	−6.62548	+	2.25898i	−0.236624	+	0.0806780i
$785$	−24.6253	−	24.6253i	−0.878913	−	0.878913i
$786$	14.1646	−	3.79540i	0.505235	−	0.135377i
$787$	15.0565	+	15.0565i	0.536707	+	0.536707i	0.922560	−	0.385853i	$-0.126093\pi$
$787$	15.0565	+	15.0565i	0.536707	+	0.536707i	−0.385853	+	0.922560i	$0.626093\pi$
$788$	−4.20397	−	15.6894i	−0.149760	−	0.558913i
$789$	4.34538	+	2.50881i	0.154700	+	0.0893158i
$790$	−8.56105	+	14.8282i	−0.304588	+	0.527563i
$791$	−3.73875	−	4.54944i	−0.132935	−	0.161759i
$792$		−	2.80673i		−	0.0997329i
$793$	25.8297	+	42.0859i	0.917240	+	1.49451i
$794$	−11.7010	−	6.75555i	−0.415252	−	0.239746i
$795$	−4.16052	+	15.5273i	−0.147559	+	0.550696i
$796$			24.9179i			0.883191i
$797$	−17.2380	−	29.8571i	−0.610601	−	1.05759i	−0.991139	−	0.132827i	$-0.957595\pi$
$797$	−17.2380	−	29.8571i	−0.610601	−	1.05759i	0.380538	−	0.924765i	$-0.375739\pi$
$798$	0.757678	+	4.57008i	0.0268215	+	0.161779i
$799$	−2.13788	+	7.97866i	−0.0756326	+	0.282265i
$800$	2.11445	+	7.89124i	0.0747571	+	0.278997i
$801$	3.14403	−	0.842441i	0.111089	−	0.0297662i
$802$	14.3902			0.508137
$803$	15.3016			0.539982
$804$	−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
$808$	−9.98589	−	2.67571i	−0.351302	−	0.0941312i
$809$	12.8582	+	22.2711i	0.452070	+	0.783009i	0.998515	−	0.0544866i	$-0.0173522\pi$
$809$	12.8582	+	22.2711i	0.452070	+	0.783009i	−0.546444	+	0.837496i	$0.684019\pi$
$810$	−1.81450	+	3.14280i	−0.0637550	+	0.110427i
$811$	−23.6082	+	23.6082i	−0.828996	+	0.828996i	−0.987378	−	0.158382i	$-0.949372\pi$
$811$	−23.6082	+	23.6082i	−0.828996	+	0.828996i	0.158382	+	0.987378i	$0.449372\pi$
$812$	11.9866	+	4.50226i	0.420649	+	0.157998i
$813$	18.6687	+	5.00226i	0.654740	+	0.175437i
$814$	−31.5221	−	8.44632i	−1.10485	−	0.296043i
$815$		−	71.8198i		−	2.51574i
$816$	−3.44004	+	1.98611i	−0.120425	+	0.0695277i
$817$	2.79389	+	2.79389i	0.0977460	+	0.0977460i
$818$	22.9804			0.803491
$819$	−7.20465	+	6.25244i	−0.251751	+	0.218478i
$820$	−29.3290			−1.02421
$821$	−30.7995	−	30.7995i	−1.07491	−	1.07491i	−0.996957	−	0.0779521i	$-0.975162\pi$
$821$	−30.7995	−	30.7995i	−1.07491	−	1.07491i	−0.0779521	−	0.996957i	$-0.524838\pi$
$822$	−1.43198	+	0.826754i	−0.0499460	+	0.0288364i
$823$		−	14.9004i		−	0.519395i	−0.965690	−	0.259697i	$-0.916377\pi$
$823$		−	14.9004i		−	0.519395i	0.965690	−	0.259697i	$-0.0836228\pi$
$824$	−4.92232	−	1.31893i	−0.171477	−	0.0459472i
$825$	−22.1486	−	5.93470i	−0.771116	−	0.206620i
$826$	−2.36332	−	14.2548i	−0.0822304	−	0.495988i
$827$	−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	$0.315418\pi$
$828$	−1.39213	+	2.41124i	−0.0483799	+	0.0837965i
$829$	1.76888	+	3.06379i	0.0614357	+	0.106410i	0.895107	−	0.445851i	$-0.147099\pi$
$829$	1.76888	+	3.06379i	0.0614357	+	0.106410i	−0.833672	+	0.552260i	$0.813765\pi$
$830$	22.5979	+	6.05508i	0.784384	+	0.210175i
$831$	−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
$835$	36.7955			1.27336
$836$	4.91432			0.169965
$837$	−9.26580	+	2.48276i	−0.320273	+	0.0858169i
$838$	8.40158	+	31.3551i	0.290228	+	1.08315i
$839$	−1.46266	+	5.45871i	−0.0504966	+	0.188456i	−0.986567	−	0.163357i	$-0.947768\pi$
$839$	−1.46266	+	5.45871i	−0.0504966	+	0.188456i	0.936071	+	0.351812i	$0.114435\pi$
$840$	3.37606	−	8.98830i	0.116485	−	0.310126i
$841$	2.78929	+	4.83119i	0.0961824	+	0.166593i
$842$			24.7719i			0.853695i
$843$	−2.31273	+	8.63123i	−0.0796547	+	0.297275i
$844$	21.7919	+	12.5816i	0.750108	+	0.433075i
$845$	14.6396	+	44.8480i	0.503617	+	1.54282i
$846$			2.07947i			0.0714938i
$847$	7.73318	+	2.90463i	0.265715	+	0.0998043i
$848$	−2.21480	+	3.83615i	−0.0760566	+	0.131734i
$849$	−24.8709	−	14.3592i	−0.853566	−	0.492806i
$850$	8.39906	+	31.3457i	0.288085	+	1.07515i
$851$	22.8910	+	22.8910i	0.784694	+	0.784694i
$852$	7.12477	−	1.90908i	0.244090	−	0.0654038i
$853$	−17.9250	−	17.9250i	−0.613739	−	0.613739i	0.330179	−	0.943918i	$-0.392891\pi$
$853$	−17.9250	−	17.9250i	−0.613739	−	0.613739i	−0.943918	+	0.330179i	$0.892891\pi$
$854$	14.9767	+	32.9952i	0.512491	+	1.12907i
$855$	−5.50275	−	3.17701i	−0.188190	−	0.108652i
$856$	−11.7605	+	11.7605i	−0.401966	+	0.401966i
$857$	16.2816	−	28.2006i	0.556170	−	0.963315i	−0.441641	−	0.897192i	$-0.645604\pi$
$857$	16.2816	−	28.2006i	0.556170	−	0.963315i	0.997811	−	0.0661232i	$-0.0210630\pi$
$858$	5.29347	+	8.62496i	0.180716	+	0.294451i
$859$	−15.7330	+	9.08344i	−0.536802	+	0.309923i	−0.743782	−	0.668422i	$-0.766970\pi$
$859$	−15.7330	+	9.08344i	−0.536802	+	0.309923i	0.206980	+	0.978345i	$0.433637\pi$
$860$	−2.11956	−	7.91029i	−0.0722763	−	0.269739i
$861$	17.3891	+	12.4432i	0.592620	+	0.424063i
$862$	1.59575	−	0.921309i	0.0543516	−	0.0313799i
$863$	11.3279	−	42.2764i	0.385607	−	1.43911i	−0.451600	−	0.892221i	$-0.649147\pi$
$863$	11.3279	−	42.2764i	0.385607	−	1.43911i	0.837207	−	0.546886i	$-0.184187\pi$
$864$	−0.707107	+	0.707107i	−0.0240563	+	0.0240563i
$865$	44.0305	−	44.0305i	1.49708	−	1.49708i
$866$	−5.00825	+	18.6910i	−0.170187	+	0.635147i
$867$	1.05786	−	0.610755i	0.0359268	−	0.0207423i
$868$	23.1105	−	10.4900i	0.784422	−	0.356052i
$869$	−3.42742	−	12.7913i	−0.116267	−	0.433916i
$870$	−15.2098	+	8.78139i	−0.515661	+	0.297717i
$871$	9.06665	−	9.56730i	0.307212	−	0.324176i
$872$	0.323727	−	0.560712i	0.0109628	−	0.0189881i
$873$	−10.9474	+	10.9474i	−0.370514	+	0.370514i
$874$	−4.22186	−	2.43749i	−0.142806	−	0.0824494i
$875$	−24.7491	−	17.7098i	−0.836672	−	0.598700i
$876$	−3.85497	−	3.85497i	−0.130247	−	0.130247i
$877$	42.4266	−	11.3682i	1.43264	−	0.383876i	0.542693	−	0.839931i	$-0.317405\pi$
$877$	42.4266	−	11.3682i	1.43264	−	0.383876i	0.889951	+	0.456055i	$0.150738\pi$
$878$	17.3845	+	17.3845i	0.586698	+	0.586698i
$879$	−5.51855	−	20.5955i	−0.186136	−	0.694669i
$880$	−8.82101	−	5.09281i	−0.297356	−	0.171679i
$881$	−17.6961	+	30.6506i	−0.596198	+	1.03265i	0.397179	+	0.917741i	$0.369989\pi$
$881$	−17.6961	+	30.6506i	−0.596198	+	1.03265i	−0.993377	+	0.114904i	$0.963344\pi$
$882$	−5.81505	+	3.89681i	−0.195803	+	0.131212i
$883$			35.4907i			1.19436i	0.802108	+	0.597179i	$0.203712\pi$
$883$			35.4907i			1.19436i	−0.802108	+	0.597179i	$0.796288\pi$
$884$	6.82530	−	12.5911i	0.229560	−	0.423484i
$885$	17.1640	+	9.90962i	0.576960	+	0.333108i
$886$	6.39821	−	23.8784i	0.214952	−	0.802212i
$887$		−	16.4273i		−	0.551576i	−0.961219	−	0.275788i	$-0.911061\pi$
$887$		−	16.4273i		−	0.551576i	0.961219	−	0.275788i	$-0.0889387\pi$
$888$	5.81353	+	10.0693i	0.195089	+	0.337905i
$889$	11.6342	+	4.36988i	0.390198	+	0.146561i
$890$	3.05722	−	11.4097i	0.102478	−	0.382454i
$891$	−0.726436	−	2.71110i	−0.0243365	−	0.0908251i
$892$	−16.7905	+	4.49900i	−0.562187	+	0.150638i
$893$	−3.64096			−0.121840
$894$	−16.5924			−0.554932
$895$	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
$899$	−44.8425	−	12.0155i	−1.49558	−	0.400740i
$900$	4.08481	+	7.07509i	0.136160	+	0.235836i
$901$	−8.79767	+	15.2380i	−0.293093	+	0.507652i
$902$	16.0397	−	16.0397i	0.534065	−	0.534065i
$903$	−2.09936	+	5.58925i	−0.0698622	+	0.185998i
$904$	2.14984	+	0.576049i	0.0715027	+	0.0191591i
$905$	85.5950	+	22.9351i	2.84527	+	0.762388i
$906$		−	11.0552i		−	0.367284i
$907$	4.99758	−	2.88535i	0.165942	−	0.0958065i	−0.414729	−	0.909945i	$-0.636124\pi$
$907$	4.99758	−	2.88535i	0.165942	−	0.0958065i	0.580671	+	0.814138i	$0.302790\pi$
$908$	14.9238	+	14.9238i	0.495263	+	0.495263i
$909$	−10.3382			−0.342895
$910$	6.57735	+	33.9878i	0.218037	+	1.12669i
$911$	3.08708			0.102280			0.0511398	−	0.998692i	$-0.483715\pi$
$911$	3.08708			0.102280			0.0511398	+	0.998692i	$0.483715\pi$
$912$	−1.23808	−	1.23808i	−0.0409968	−	0.0409968i
$913$	−15.6700	+	9.04708i	−0.518601	+	0.299415i
$914$		−	5.25486i		−	0.173815i
$915$	−48.0077	−	12.8636i	−1.58708	−	0.425258i
$916$	10.0670	+	2.69746i	0.332624	+	0.0891264i
$917$	−29.9748	+	24.6334i	−0.989854	+	0.813466i
$918$	−2.80878	+	2.80878i	−0.0927036	+	0.0927036i
$919$	13.1100	−	22.7072i	0.432459	−	0.749042i	−0.564625	−	0.825347i	$-0.690979\pi$
$919$	13.1100	−	22.7072i	0.432459	−	0.749042i	0.997084	+	0.0763059i	$0.0243126\pi$
$920$	5.05204	+	8.75039i	0.166561	+	0.288492i
$921$	−20.6086	−	5.52206i	−0.679076	−	0.181958i
$922$	−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
$926$	−4.85688			−0.159607
$927$	−5.09596			−0.167373
$928$	−4.67466	+	1.25257i	−0.153453	+	0.0411177i
$929$	2.46366	+	9.19449i	0.0808299	+	0.301661i	0.994492	−	0.104813i	$-0.0334245\pi$
$929$	2.46366	+	9.19449i	0.0808299	+	0.301661i	−0.913662	+	0.406475i	$0.866758\pi$
$930$	−9.00994	+	33.6256i	−0.295448	+	1.10263i
$931$	−6.82295	−	10.1816i	−0.223613	−	0.333689i
$932$	−10.6146	−	18.3850i	−0.347693	−	0.602222i
$933$		−	29.3267i		−	0.960112i
$934$	7.61386	−	28.4153i	0.249133	−	0.929777i
$935$	−35.0389	−	20.2297i	−1.14590	−	0.661583i
$936$	0.839311	−	3.50650i	0.0274337	−	0.114614i
$937$			0.688061i			0.0224780i	0.999937	+	0.0112390i	$0.00357755\pi$
$937$			0.688061i			0.0224780i	−0.999937	+	0.0112390i	$0.996422\pi$
$938$	7.47256	−	6.14098i	0.243988	−	0.200510i
$939$	−11.5915	+	20.0771i	−0.378275	+	0.655192i
$940$	6.53538	+	3.77320i	0.213161	+	0.123068i
$941$	7.66651	+	28.6118i	0.249921	+	0.932718i	0.970846	+	0.239705i	$0.0770507\pi$
$941$	7.66651	+	28.6118i	0.249921	+	0.932718i	−0.720925	+	0.693013i	$0.756283\pi$
$942$	−6.78569	−	6.78569i	−0.221090	−	0.221090i
$943$	−21.7353	+	5.82395i	−0.707798	+	0.189654i
$944$	3.86176	+	3.86176i	0.125690	+	0.125690i
$945$	0.934682	−	9.55582i	0.0304052	−	0.310851i
$946$	5.48522	+	3.16689i	0.178340	+	0.102965i
$947$	−30.6468	+	30.6468i	−0.995887	+	0.995887i	−0.999992	−	0.00410427i	$-0.998694\pi$
$947$	−30.6468	+	30.6468i	−0.995887	+	0.995887i	0.00410427	+	0.999992i	$0.498694\pi$
$948$	−2.35907	+	4.08603i	−0.0766190	+	0.132708i
$949$	19.1166	+	4.57571i	0.620550	+	0.148534i
$950$	−12.3878	+	7.15211i	−0.401914	+	0.232045i
$951$	8.06274	+	30.0906i	0.261452	+	0.975753i
$952$	6.11580	−	8.54672i	0.198214	−	0.277001i
$953$	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	$0.0494146\pi$
$954$	−1.14647	+	4.27867i	−0.0371182	+	0.138527i
$955$	10.0254	−	10.0254i	0.324414	−	0.324414i
$956$	13.2336	−	13.2336i	0.428005	−	0.428005i
$957$	3.51564	−	13.1205i	0.113644	−	0.424127i
$958$	16.7410	−	9.66544i	0.540878	−	0.312276i
$959$	2.54582	−	3.55773i	0.0822087	−	0.114885i
$960$	0.939253	+	3.50534i	0.0303143	+	0.113134i
$961$	−52.8442	+	30.5096i	−1.70465	+	0.984181i
$962$	−36.8554	−	19.9783i	−1.18826	−	0.644127i
$963$	−8.31594	+	14.4036i	−0.267977	+	0.464150i
$964$	12.6744	−	12.6744i	0.408214	−	0.408214i
$965$	−55.3422	−	31.9518i	−1.78153	−	1.02857i
$966$	0.717113	−	7.33148i	0.0230727	−	0.235887i
$967$	−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	$0.764595\pi$
$968$	−3.01586	+	0.808097i	−0.0969334	+	0.0259732i
$969$	−4.91791	−	4.91791i	−0.157986	−	0.157986i
$970$	14.5415	+	54.2696i	0.466899	+	1.74249i
$971$	35.3873	+	20.4309i	1.13563	+	0.655658i	0.945345	−	0.326071i	$-0.105725\pi$
$971$	35.3873	+	20.4309i	1.13563	+	0.655658i	0.190287	+	0.981728i	$0.439058\pi$
$972$	−0.500000	+	0.866025i	−0.0160375	+	0.0277778i
$973$	−18.0374	+	14.8232i	−0.578251	+	0.475209i
$974$		−	34.9369i		−	1.11945i
$975$	−25.8960	−	14.0375i	−0.829335	−	0.449561i
$976$	−11.8607	−	6.84779i	−0.379652	−	0.219192i
$977$	9.94177	−	37.1032i	0.318066	−	1.18704i	−0.603036	−	0.797714i	$-0.706042\pi$
$977$	9.94177	−	37.1032i	0.318066	−	1.18704i	0.921101	−	0.389323i	$-0.127291\pi$
$978$		−	19.7905i		−	0.632832i
$979$	4.56788	+	7.91180i	0.145990	+	0.252862i
$980$	1.69550	+	25.3463i	0.0541609	+	0.809659i
$981$	0.167574	−	0.625393i	0.00535021	−	0.0199673i
$982$	−2.66483	−	9.94527i	−0.0850380	−	0.317366i
$983$	1.86477	−	0.499665i	0.0594770	−	0.0159368i	−0.228958	−	0.973436i	$-0.573532\pi$
$983$	1.86477	−	0.499665i	0.0594770	−	0.0159368i	0.288435	+	0.957500i	$0.406865\pi$
$984$	−8.08186			−0.257640
$985$	−58.9454			−1.87816
$986$	−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
$990$	−9.83856	−	2.63623i	−0.312690	−	0.0837850i
$991$	−15.3885	−	26.6536i	−0.488831	−	0.846680i	0.511087	−	0.859529i	$-0.329243\pi$
$991$	−15.3885	−	26.6536i	−0.488831	−	0.846680i	−0.999917	+	0.0128495i	$0.995910\pi$
$992$	−4.79633	+	8.30749i	−0.152284	+	0.263763i
$993$	0.593522	−	0.593522i	0.0188349	−	0.0188349i
$994$	−15.0772	+	12.3905i	−0.478221	+	0.393004i
$995$	87.3457	+	23.4042i	2.76905	+	0.741963i
$996$	6.22703	+	1.66853i	0.197311	+	0.0528693i
$997$			3.56965i			0.113052i	0.998401	+	0.0565259i	$0.0180024\pi$
$997$			3.56965i			0.113052i	−0.998401	+	0.0565259i	$0.981998\pi$
$998$	13.8006	−	7.96777i	0.436850	−	0.252215i
$999$	8.22157	+	8.22157i	0.260119	+	0.260119i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.by.b.397.5	✓	40	7.5	odd	6
546.2.by.b.535.5	yes	40	13.2	odd	12
546.2.cg.b.145.5	yes	40	91.54	even	12	inner
546.2.cg.b.241.5	yes	40	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.866025 + 0.500000i) q^{3} +1.00000i q^{4} +(3.50534 + 0.939253i) q^{5} +(0.965926 + 0.258819i) q^{6} +(-2.61012 + 0.432735i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.866025 + 0.500000i) q^{3} +1.00000i q^{4} +(3.50534 + 0.939253i) q^{5} +(0.965926 + 0.258819i) q^{6} +(-2.61012 + 0.432735i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.500000 - 0.866025i) q^{9} +(-1.81450 - 3.14280i) q^{10} +(2.71110 + 0.726436i) 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} -1.00000 q^{16} -3.97221 q^{17} +(-0.965926 + 0.258819i) q^{18} +(-0.453168 - 1.69124i) q^{19} +(-0.939253 + 3.50534i) q^{20} +(2.04406 - 1.67982i) q^{21} +(-1.40337 - 2.43070i) q^{22} +2.78426i q^{23} +(-0.258819 + 0.965926i) q^{24} +(7.07509 + 4.08481i) q^{25} +(-1.02639 - 3.45638i) q^{26} +1.00000i q^{27} +(-0.432735 - 2.61012i) q^{28} +(-2.41978 + 4.19119i) q^{29} +(3.14280 + 1.81450i) q^{30} +(2.48276 + 9.26580i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-2.71110 + 0.726436i) q^{33} +(2.80878 + 2.80878i) q^{34} +(-9.55582 - 0.934682i) q^{35} +(0.866025 + 0.500000i) q^{36} +(8.22157 - 8.22157i) q^{37} +(-0.875453 + 1.51633i) q^{38} +(-3.60425 + 0.0968376i) q^{39} +(3.14280 - 1.81450i) q^{40} +(2.09174 + 7.80648i) q^{41} +(-2.63318 - 0.257559i) q^{42} +(-1.95431 + 1.12832i) q^{43} +(-0.726436 + 2.71110i) q^{44} +(2.56609 - 2.56609i) q^{45} +(1.96877 - 1.96877i) q^{46} +(0.538208 - 2.00862i) q^{47} +(0.866025 - 0.500000i) q^{48} +(6.62548 - 2.25898i) q^{49} +(-2.11445 - 7.89124i) q^{50} +(3.44004 - 1.98611i) q^{51} +(-1.71826 + 3.16979i) q^{52} +(2.21480 - 3.83615i) q^{53} +(0.707107 - 0.707107i) q^{54} +(8.82101 + 5.09281i) q^{55} +(-1.53965 + 2.15163i) q^{56} +(1.23808 + 1.23808i) q^{57} +(4.67466 - 1.25257i) q^{58} +(-3.86176 - 3.86176i) q^{59} +(-0.939253 - 3.50534i) q^{60} +(11.8607 + 6.84779i) q^{61} +(4.79633 - 8.30749i) q^{62} +(-0.930302 + 2.47680i) q^{63} -1.00000i q^{64} +(9.49732 + 9.00033i) q^{65} +(2.43070 + 1.40337i) q^{66} +(0.946174 - 3.53117i) q^{67} -3.97221i q^{68} +(-1.39213 - 2.41124i) q^{69} +(6.09606 + 7.41790i) q^{70} +(-1.90908 + 7.12477i) q^{71} +(-0.258819 - 0.965926i) q^{72} +(5.26598 - 1.41102i) q^{73} -11.6271 q^{74} -8.16961 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} +(-3.50534 - 0.939253i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(4.04093 - 6.99909i) q^{82} +(-4.55850 + 4.55850i) q^{83} +(1.67982 + 2.04406i) q^{84} +(-13.9240 - 3.73092i) q^{85} +(2.17975 + 0.584061i) q^{86} -4.83957i q^{87} +(2.43070 - 1.40337i) q^{88} +(2.30159 + 2.30159i) q^{89} -3.62900 q^{90} +(-9.01710 - 3.11319i) q^{91} -2.78426 q^{92} +(-6.78304 - 6.78304i) q^{93} +(-1.80088 + 1.03974i) q^{94} -6.35403i q^{95} +(-0.965926 - 0.258819i) q^{96} +(-14.9544 - 4.00703i) q^{97} +(-6.28227 - 3.08758i) q^{98} +(1.98466 - 1.98466i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 4 q^{7} + 20 q^{9}+O(q^{10}) \) 40 * q + 4 * q^7 + 20 * q^9	\( 40 q + 4 q^{7} + 20 q^{9} + 8 q^{11} - 20 q^{12} + 4 q^{14} - 40 q^{16} + 16 q^{17} + 4 q^{19} + 4 q^{21} - 4 q^{22} - 24 q^{25} + 8 q^{26} - 4 q^{28} - 12 q^{29} - 8 q^{33} - 8 q^{34} - 32 q^{35} + 40 q^{37} + 8 q^{38} + 20 q^{39} + 20 q^{41} + 12 q^{42} - 24 q^{43} - 4 q^{44} + 32 q^{46} + 4 q^{47} + 32 q^{49} - 16 q^{50} + 24 q^{51} + 16 q^{52} - 4 q^{53} + 24 q^{55} + 12 q^{56} + 8 q^{57} + 12 q^{58} + 24 q^{59} + 60 q^{61} + 32 q^{62} - 4 q^{63} + 44 q^{65} - 12 q^{67} - 8 q^{69} - 24 q^{70} - 28 q^{71} + 60 q^{73} - 40 q^{74} - 72 q^{75} + 4 q^{76} - 12 q^{77} + 4 q^{78} - 20 q^{81} - 24 q^{82} + 60 q^{83} - 8 q^{84} - 4 q^{85} - 20 q^{86} - 36 q^{89} - 16 q^{92} - 24 q^{93} - 48 q^{97} - 88 q^{98} + 4 q^{99}+O(q^{100}) \) 40 * q + 4 * q^7 + 20 * q^9 + 8 * q^11 - 20 * q^12 + 4 * q^14 - 40 * q^16 + 16 * q^17 + 4 * q^19 + 4 * q^21 - 4 * q^22 - 24 * q^25 + 8 * q^26 - 4 * q^28 - 12 * q^29 - 8 * q^33 - 8 * q^34 - 32 * q^35 + 40 * q^37 + 8 * q^38 + 20 * q^39 + 20 * q^41 + 12 * q^42 - 24 * q^43 - 4 * q^44 + 32 * q^46 + 4 * q^47 + 32 * q^49 - 16 * q^50 + 24 * q^51 + 16 * q^52 - 4 * q^53 + 24 * q^55 + 12 * q^56 + 8 * q^57 + 12 * q^58 + 24 * q^59 + 60 * q^61 + 32 * q^62 - 4 * q^63 + 44 * q^65 - 12 * q^67 - 8 * q^69 - 24 * q^70 - 28 * q^71 + 60 * q^73 - 40 * q^74 - 72 * q^75 + 4 * q^76 - 12 * q^77 + 4 * q^78 - 20 * q^81 - 24 * q^82 + 60 * q^83 - 8 * q^84 - 4 * q^85 - 20 * q^86 - 36 * q^89 - 16 * q^92 - 24 * q^93 - 48 * q^97 - 88 * q^98 + 4 * q^99

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