LMFDB - Embedded newform 930.2.be.a.37.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(37,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 10]))

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

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

chi := DirichletCharacter("930.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.be (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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			37.1
Character	$\chi$	$=$	930.37
Dual form			930.2.be.a.553.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(-0.258819 + 0.965926i) q^{3} +1.00000i q^{4} +(-2.04325 - 0.908360i) q^{5} +(0.866025 - 0.500000i) q^{6} +(-0.239418 + 0.893522i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.258819 + 0.965926i) q^{3} +1.00000i q^{4} +(-2.04325 - 0.908360i) q^{5} +(0.866025 - 0.500000i) q^{6} +(-0.239418 + 0.893522i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(0.802490 + 2.08711i) q^{10} +(-1.53637 - 0.887024i) q^{11} +(-0.965926 - 0.258819i) q^{12} +(4.03293 - 1.08062i) q^{13} +(0.801110 - 0.462521i) q^{14} +(1.40624 - 1.73853i) q^{15} -1.00000 q^{16} +(-1.86103 - 0.498662i) q^{17} +(0.258819 + 0.965926i) q^{18} +(-2.14477 + 1.23828i) q^{19} +(0.908360 - 2.04325i) q^{20} +(-0.801110 - 0.462521i) q^{21} +(0.459157 + 1.71360i) q^{22} +(-0.419493 - 0.419493i) q^{23} +(0.500000 + 0.866025i) q^{24} +(3.34976 + 3.71202i) q^{25} +(-3.61583 - 2.08760i) q^{26} +(0.707107 - 0.707107i) q^{27} +(-0.893522 - 0.239418i) q^{28} +5.24887 q^{29} +(-2.22369 + 0.234963i) q^{30} +(5.56129 + 0.268497i) q^{31} +(0.707107 + 0.707107i) q^{32} +(1.25444 - 1.25444i) q^{33} +(0.963341 + 1.66855i) q^{34} +(1.30083 - 1.60821i) q^{35} +(0.500000 - 0.866025i) q^{36} +(3.62271 + 0.970702i) q^{37} +(2.39218 + 0.640982i) q^{38} +4.17520i q^{39} +(-2.08711 + 0.802490i) q^{40} +(-0.951451 + 1.64796i) q^{41} +(0.239418 + 0.893522i) q^{42} +(1.73306 - 6.46785i) q^{43} +(0.887024 - 1.53637i) q^{44} +(1.31533 + 1.80829i) q^{45} +0.593252i q^{46} +(-0.278394 - 0.278394i) q^{47} +(0.258819 - 0.965926i) q^{48} +(5.32112 + 3.07215i) q^{49} +(0.256153 - 4.99343i) q^{50} +(0.963341 - 1.66855i) q^{51} +(1.08062 + 4.03293i) q^{52} +(13.6890 - 3.66795i) q^{53} -1.00000 q^{54} +(2.33346 + 3.20799i) q^{55} +(0.462521 + 0.801110i) q^{56} +(-0.640982 - 2.39218i) q^{57} +(-3.71151 - 3.71151i) q^{58} +(0.0261163 - 0.0150782i) q^{59} +(1.73853 + 1.40624i) q^{60} +11.5563i q^{61} +(-3.74257 - 4.12228i) q^{62} +(0.654103 - 0.654103i) q^{63} -1.00000i q^{64} +(-9.22189 - 1.45537i) q^{65} -1.77405 q^{66} +(2.17757 - 0.583477i) q^{67} +(0.498662 - 1.86103i) q^{68} +(0.513772 - 0.296626i) q^{69} +(-2.05700 + 0.217351i) q^{70} +(-4.10900 + 7.11700i) q^{71} +(-0.965926 + 0.258819i) q^{72} +(8.95831 - 2.40037i) q^{73} +(-1.87525 - 3.24803i) q^{74} +(-4.45252 + 2.27488i) q^{75} +(-1.23828 - 2.14477i) q^{76} +(1.16041 - 1.16041i) q^{77} +(2.95231 - 2.95231i) q^{78} +(-0.789699 - 1.36780i) q^{79} +(2.04325 + 0.908360i) q^{80} +(0.500000 + 0.866025i) q^{81} +(1.83806 - 0.492507i) q^{82} +(13.5075 - 3.61931i) q^{83} +(0.462521 - 0.801110i) q^{84} +(3.34959 + 2.70938i) q^{85} +(-5.79892 + 3.34801i) q^{86} +(-1.35851 + 5.07002i) q^{87} +(-1.71360 + 0.459157i) q^{88} +9.37759 q^{89} +(0.348576 - 2.20873i) q^{90} +3.86223i q^{91} +(0.419493 - 0.419493i) q^{92} +(-1.69871 + 5.30230i) q^{93} +0.393708i q^{94} +(5.50711 - 0.581902i) q^{95} +(-0.866025 + 0.500000i) q^{96} +(2.68339 + 2.68339i) q^{97} +(-1.59026 - 5.93494i) q^{98} +(0.887024 + 1.53637i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 8 q^{7}+O(q^{10}) $ 64 * q - 8 * q^7	$ 64 q - 8 q^{7} - 4 q^{10} + 24 q^{14} + 8 q^{15} - 64 q^{16} + 4 q^{17} - 12 q^{20} - 24 q^{21} - 8 q^{22} + 32 q^{24} - 20 q^{25} - 4 q^{28} + 16 q^{29} + 8 q^{31} + 4 q^{33} + 24 q^{35} + 32 q^{36} + 56 q^{37} - 4 q^{38} - 8 q^{41} + 8 q^{42} - 56 q^{43} - 4 q^{44} + 12 q^{45} + 8 q^{47} - 60 q^{49} - 8 q^{50} + 24 q^{53} - 64 q^{54} + 16 q^{55} - 28 q^{57} + 52 q^{58} + 24 q^{59} - 4 q^{62} - 4 q^{63} + 100 q^{65} + 8 q^{66} + 76 q^{67} + 4 q^{68} - 12 q^{69} - 44 q^{70} + 8 q^{71} - 52 q^{73} + 12 q^{74} - 8 q^{75} - 8 q^{76} - 104 q^{77} + 56 q^{79} + 32 q^{81} + 32 q^{82} + 24 q^{83} + 32 q^{85} - 24 q^{86} - 20 q^{87} + 4 q^{88} - 176 q^{89} + 8 q^{93} + 64 q^{95} - 68 q^{97} - 64 q^{98} - 4 q^{99}+O(q^{100}) $ 64 * q - 8 * q^7 - 4 * q^10 + 24 * q^14 + 8 * q^15 - 64 * q^16 + 4 * q^17 - 12 * q^20 - 24 * q^21 - 8 * q^22 + 32 * q^24 - 20 * q^25 - 4 * q^28 + 16 * q^29 + 8 * q^31 + 4 * q^33 + 24 * q^35 + 32 * q^36 + 56 * q^37 - 4 * q^38 - 8 * q^41 + 8 * q^42 - 56 * q^43 - 4 * q^44 + 12 * q^45 + 8 * q^47 - 60 * q^49 - 8 * q^50 + 24 * q^53 - 64 * q^54 + 16 * q^55 - 28 * q^57 + 52 * q^58 + 24 * q^59 - 4 * q^62 - 4 * q^63 + 100 * q^65 + 8 * q^66 + 76 * q^67 + 4 * q^68 - 12 * q^69 - 44 * q^70 + 8 * q^71 - 52 * q^73 + 12 * q^74 - 8 * q^75 - 8 * q^76 - 104 * q^77 + 56 * q^79 + 32 * q^81 + 32 * q^82 + 24 * q^83 + 32 * q^85 - 24 * q^86 - 20 * q^87 + 4 * q^88 - 176 * q^89 + 8 * q^93 + 64 * q^95 - 68 * q^97 - 64 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{5}{6}\right)$

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
$3$	−0.258819	+	0.965926i	−0.149429	+	0.557678i
$3$	−0.258819	+	0.965926i	−0.149429	+	0.557678i
$4$			1.00000i			0.500000i
$5$	−2.04325	−	0.908360i	−0.913770	−	0.406231i
$5$	−2.04325	−	0.908360i	−0.913770	−	0.406231i
$6$	0.866025	−	0.500000i	0.353553	−	0.204124i
$7$	−0.239418	+	0.893522i	−0.0904916	+	0.337719i	−0.996297	−	0.0859738i	$-0.972600\pi$
$7$	−0.239418	+	0.893522i	−0.0904916	+	0.337719i	0.905806	+	0.423693i	$0.139267\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−0.866025	−	0.500000i	−0.288675	−	0.166667i
$10$	0.802490	+	2.08711i	0.253770	+	0.660001i
$11$	−1.53637	−	0.887024i	−0.463233	−	0.267448i	0.250170	−	0.968202i	$-0.419514\pi$
$11$	−1.53637	−	0.887024i	−0.463233	−	0.267448i	−0.713403	+	0.700754i	$0.752847\pi$
$12$	−0.965926	−	0.258819i	−0.278839	−	0.0747146i
$13$	4.03293	−	1.08062i	1.11853	−	0.299710i	0.348244	−	0.937404i	$-0.386778\pi$
$13$	4.03293	−	1.08062i	1.11853	−	0.299710i	0.770290	+	0.637694i	$0.220112\pi$
$14$	0.801110	−	0.462521i	0.214106	−	0.123614i
$15$	1.40624	−	1.73853i	0.363090	−	0.448886i
$16$	−1.00000			−0.250000
$17$	−1.86103	−	0.498662i	−0.451366	−	0.120943i	0.0259723	−	0.999663i	$-0.491732\pi$
$17$	−1.86103	−	0.498662i	−0.451366	−	0.120943i	−0.477339	+	0.878719i	$0.658398\pi$
$18$	0.258819	+	0.965926i	0.0610042	+	0.227671i
$19$	−2.14477	+	1.23828i	−0.492043	+	0.284081i	−0.725422	−	0.688305i	$-0.758355\pi$
$19$	−2.14477	+	1.23828i	−0.492043	+	0.284081i	0.233378	+	0.972386i	$0.425022\pi$
$20$	0.908360	−	2.04325i	0.203116	−	0.456885i
$21$	−0.801110	−	0.462521i	−0.174816	−	0.100930i
$22$	0.459157	+	1.71360i	0.0978927	+	0.365341i
$23$	−0.419493	−	0.419493i	−0.0874703	−	0.0874703i	0.662018	−	0.749488i	$-0.269700\pi$
$23$	−0.419493	−	0.419493i	−0.0874703	−	0.0874703i	−0.749488	+	0.662018i	$0.769700\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	3.34976	+	3.71202i	0.669953	+	0.742404i
$26$	−3.61583	−	2.08760i	−0.709122	−	0.409412i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	−0.893522	−	0.239418i	−0.168860	−	0.0452458i
$29$	5.24887			0.974692			0.487346	−	0.873209i	$-0.337965\pi$
$29$	5.24887			0.974692			0.487346	+	0.873209i	$0.337965\pi$
$30$	−2.22369	+	0.234963i	−0.405988	+	0.0428983i
$31$	5.56129	+	0.268497i	0.998837	+	0.0482235i
$31$	5.56129	+	0.268497i	0.998837	+	0.0482235i
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	1.25444	−	1.25444i	0.218370	−	0.218370i
$34$	0.963341	+	1.66855i	0.165212	+	0.286155i
$35$	1.30083	−	1.60821i	0.219881	−	0.271837i
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	3.62271	+	0.970702i	0.595569	+	0.159582i	0.543997	−	0.839087i	$-0.316910\pi$
$37$	3.62271	+	0.970702i	0.595569	+	0.159582i	0.0515721	+	0.998669i	$0.483577\pi$
$38$	2.39218	+	0.640982i	0.388062	+	0.103981i
$39$			4.17520i			0.668566i
$40$	−2.08711	+	0.802490i	−0.330000	+	0.126885i
$41$	−0.951451	+	1.64796i	−0.148592	+	0.257368i	−0.930707	−	0.365765i	$-0.880807\pi$
$41$	−0.951451	+	1.64796i	−0.148592	+	0.257368i	0.782116	+	0.623133i	$0.214141\pi$
$42$	0.239418	+	0.893522i	0.0369431	+	0.137873i
$43$	1.73306	−	6.46785i	0.264289	−	0.986338i	−0.698396	−	0.715712i	$-0.746102\pi$
$43$	1.73306	−	6.46785i	0.264289	−	0.986338i	0.962684	−	0.270627i	$-0.0872309\pi$
$44$	0.887024	−	1.53637i	0.133724	−	0.231617i
$45$	1.31533	+	1.80829i	0.196078	+	0.269564i
$46$			0.593252i			0.0874703i
$47$	−0.278394	−	0.278394i	−0.0406079	−	0.0406079i	0.686511	−	0.727119i	$-0.259141\pi$
$47$	−0.278394	−	0.278394i	−0.0406079	−	0.0406079i	−0.727119	+	0.686511i	$0.759141\pi$
$48$	0.258819	−	0.965926i	0.0373573	−	0.139419i
$49$	5.32112	+	3.07215i	0.760160	+	0.438878i
$50$	0.256153	−	4.99343i	0.0362255	−	0.706178i
$51$	0.963341	−	1.66855i	0.134895	−	0.233644i
$52$	1.08062	+	4.03293i	0.149855	+	0.559267i
$53$	13.6890	−	3.66795i	1.88033	−	0.503832i	0.880788	−	0.473512i	$-0.157014\pi$
$53$	13.6890	−	3.66795i	1.88033	−	0.503832i	0.999540	−	0.0303206i	$-0.00965284\pi$
$54$	−1.00000			−0.136083
$55$	2.33346	+	3.20799i	0.314643	+	0.432566i
$56$	0.462521	+	0.801110i	0.0618069	+	0.107053i
$57$	−0.640982	−	2.39218i	−0.0849001	−	0.316852i
$58$	−3.71151	−	3.71151i	−0.487346	−	0.487346i
$59$	0.0261163	−	0.0150782i	0.00340005	−	0.00196302i	−0.498299	−	0.867005i	$-0.666042\pi$
$59$	0.0261163	−	0.0150782i	0.00340005	−	0.00196302i	0.501699	+	0.865042i	$0.332708\pi$
$60$	1.73853	+	1.40624i	0.224443	+	0.181545i
$61$			11.5563i			1.47964i	0.672807	+	0.739818i	$0.265088\pi$
$61$			11.5563i			1.47964i	−0.672807	+	0.739818i	$0.734912\pi$
$62$	−3.74257	−	4.12228i	−0.475307	−	0.523530i
$63$	0.654103	−	0.654103i	0.0824093	−	0.0824093i
$64$		−	1.00000i		−	0.125000i
$65$	−9.22189	−	1.45537i	−1.14383	−	0.180517i
$66$	−1.77405			−0.218370
$67$	2.17757	−	0.583477i	0.266032	−	0.0712830i	−0.123337	−	0.992365i	$-0.539360\pi$
$67$	2.17757	−	0.583477i	0.266032	−	0.0712830i	0.389369	+	0.921082i	$0.372693\pi$
$68$	0.498662	−	1.86103i	0.0604716	−	0.225683i
$69$	0.513772	−	0.296626i	0.0618508	−	0.0357096i
$70$	−2.05700	+	0.217351i	−0.245859	+	0.0259784i
$71$	−4.10900	+	7.11700i	−0.487649	+	0.844632i	−0.999899	−	0.0142037i	$-0.995479\pi$
$71$	−4.10900	+	7.11700i	−0.487649	+	0.844632i	0.512250	+	0.858836i	$0.328812\pi$
$72$	−0.965926	+	0.258819i	−0.113835	+	0.0305021i
$73$	8.95831	−	2.40037i	1.04849	−	0.280942i	0.306863	−	0.951754i	$-0.400721\pi$
$73$	8.95831	−	2.40037i	1.04849	−	0.280942i	0.741628	+	0.670811i	$0.234054\pi$
$74$	−1.87525	−	3.24803i	−0.217994	−	0.377576i
$75$	−4.45252	+	2.27488i	−0.514132	+	0.262681i
$76$	−1.23828	−	2.14477i	−0.142041	−	0.246022i
$77$	1.16041	−	1.16041i	0.132241	−	0.132241i
$78$	2.95231	−	2.95231i	0.334283	−	0.334283i
$79$	−0.789699	−	1.36780i	−0.0888481	−	0.153889i	0.818176	−	0.574967i	$-0.194985\pi$
$79$	−0.789699	−	1.36780i	−0.0888481	−	0.153889i	−0.907024	+	0.421078i	$0.861652\pi$
$80$	2.04325	+	0.908360i	0.228443	+	0.101558i
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	1.83806	−	0.492507i	0.202980	−	0.0543883i
$83$	13.5075	−	3.61931i	1.48264	−	0.397271i	0.575393	−	0.817877i	$-0.304849\pi$
$83$	13.5075	−	3.61931i	1.48264	−	0.397271i	0.907243	+	0.420606i	$0.138183\pi$
$84$	0.462521	−	0.801110i	0.0504652	−	0.0874082i
$85$	3.34959	+	2.70938i	0.363314	+	0.293873i
$86$	−5.79892	+	3.34801i	−0.625313	+	0.361025i
$87$	−1.35851	+	5.07002i	−0.145647	+	0.543564i
$88$	−1.71360	+	0.459157i	−0.182670	+	0.0489464i
$89$	9.37759			0.994022			0.497011	−	0.867744i	$-0.334431\pi$
$89$	9.37759			0.994022			0.497011	+	0.867744i	$0.334431\pi$
$90$	0.348576	−	2.20873i	0.0367431	−	0.232821i
$91$			3.86223i			0.404872i
$92$	0.419493	−	0.419493i	0.0437352	−	0.0437352i
$93$	−1.69871	+	5.30230i	−0.176149	+	0.549823i
$94$			0.393708i			0.0406079i
$95$	5.50711	−	0.581902i	0.565017	−	0.0597019i
$96$	−0.866025	+	0.500000i	−0.0883883	+	0.0510310i
$97$	2.68339	+	2.68339i	0.272457	+	0.272457i	0.830088	−	0.557632i	$-0.188290\pi$
$97$	2.68339	+	2.68339i	0.272457	+	0.272457i	−0.557632	+	0.830088i	$0.688290\pi$
$98$	−1.59026	−	5.93494i	−0.160641	−	0.599519i
$99$	0.887024	+	1.53637i	0.0891493	+	0.154411i
$100$	−3.71202	+	3.34976i	−0.371202	+	0.334976i
$101$	0.295687			0.0294219			0.0147110	−	0.999892i	$-0.495317\pi$
$101$	0.295687			0.0294219			0.0147110	+	0.999892i	$0.495317\pi$
$102$	−1.86103	+	0.498662i	−0.184270	+	0.0493749i
$103$	−2.46813	−	9.21120i	−0.243192	−	0.907607i	−0.974283	−	0.225327i	$-0.927655\pi$
$103$	−2.46813	−	9.21120i	−0.243192	−	0.907607i	0.731091	−	0.682280i	$-0.239012\pi$
$104$	2.08760	−	3.61583i	0.204706	−	0.354561i
$105$	1.21673	+	1.67274i	0.118741	+	0.163243i
$106$	−12.2732	−	7.08594i	−1.19208	−	0.688248i
$107$	0.0647831	−	0.241774i	0.00626282	−	0.0233732i	−0.962724	−	0.270487i	$-0.912815\pi$
$107$	0.0647831	−	0.241774i	0.00626282	−	0.0233732i	0.968987	+	0.247114i	$0.0794821\pi$
$108$	0.707107	+	0.707107i	0.0680414	+	0.0680414i
$109$			10.4102i			0.997119i	0.866855	+	0.498560i	$0.166137\pi$
$109$			10.4102i			0.997119i	−0.866855	+	0.498560i	$0.833863\pi$
$110$	0.618390	−	3.91840i	0.0589612	−	0.373604i
$111$	−1.87525	+	3.24803i	−0.177991	+	0.308289i
$112$	0.239418	−	0.893522i	0.0226229	−	0.0844299i
$113$	−2.86277	−	10.6840i	−0.269307	−	1.00507i	−0.959561	−	0.281500i	$-0.909168\pi$
$113$	−2.86277	−	10.6840i	−0.269307	−	1.00507i	0.690254	−	0.723567i	$-0.257499\pi$
$114$	−1.23828	+	2.14477i	−0.115976	+	0.200876i
$115$	0.476079	+	1.23818i	0.0443946	+	0.115461i
$116$			5.24887i			0.487346i
$117$	−4.03293	−	1.08062i	−0.372844	−	0.0999034i
$118$	−0.0291289	−	0.00780507i	−0.00268153	−	0.000718514i
$119$	0.891130	−	1.54348i	0.0816898	−	0.141491i
$120$	−0.234963	−	2.22369i	−0.0214491	−	0.202994i
$121$	−3.92638	−	6.80068i	−0.356943	−	0.618244i
$122$	8.17155	−	8.17155i	0.739818	−	0.739818i
$123$	−1.34555	−	1.34555i	−0.121325	−	0.121325i
$124$	−0.268497	+	5.56129i	−0.0241117	+	0.499418i
$125$	−3.47256	−	10.6274i	−0.310596	−	0.950542i
$126$	−0.925042			−0.0824093
$127$	−10.6083	−	2.84250i	−0.941338	−	0.252231i	−0.244656	−	0.969610i	$-0.578675\pi$
$127$	−10.6083	−	2.84250i	−0.941338	−	0.252231i	−0.696683	+	0.717379i	$0.745342\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	5.79892	+	3.34801i	0.510566	+	0.294776i
$130$	5.49175	+	7.54996i	0.481659	+	0.662175i
$131$	−0.00445771	−	0.00772098i	−0.000389472	−	0.000674585i	0.865831	−	0.500337i	$-0.166791\pi$
$131$	−0.00445771	−	0.00772098i	−0.000389472	−	0.000674585i	−0.866220	+	0.499663i	$0.833457\pi$
$132$	1.25444	+	1.25444i	0.109185	+	0.109185i
$133$	−0.592935	−	2.21286i	−0.0514140	−	0.191880i
$134$	−1.95235	−	1.12719i	−0.168658	−	0.0973745i
$135$	−2.08711	+	0.802490i	−0.179629	+	0.0690674i
$136$	−1.66855	+	0.963341i	−0.143077	+	0.0826058i
$137$	−2.58797	−	9.65843i	−0.221105	−	0.825175i	−0.983928	−	0.178567i	$-0.942854\pi$
$137$	−2.58797	−	9.65843i	−0.221105	−	0.825175i	0.762823	−	0.646608i	$-0.223813\pi$
$138$	−0.573038	−	0.153545i	−0.0487802	−	0.0130706i
$139$	−1.59181			−0.135016			−0.0675079	−	0.997719i	$-0.521505\pi$
$139$	−1.59181			−0.135016			−0.0675079	+	0.997719i	$0.521505\pi$
$140$	1.60821	+	1.30083i	0.135919	+	0.109940i
$141$	0.340961	−	0.196854i	0.0287141	−	0.0165781i
$142$	7.93798	−	2.12698i	0.666141	−	0.178492i
$143$	−7.15461	−	1.91707i	−0.598299	−	0.160314i
$144$	0.866025	+	0.500000i	0.0721688	+	0.0416667i
$145$	−10.7248	−	4.76787i	−0.890644	−	0.395950i
$146$	−8.03180	−	4.63716i	−0.664717	−	0.383774i
$147$	−4.34467	+	4.34467i	−0.358343	+	0.358343i
$148$	−0.970702	+	3.62271i	−0.0797912	+	0.297785i
$149$	−7.49609	+	4.32787i	−0.614104	+	0.354553i	−0.774570	−	0.632488i	$-0.782034\pi$
$149$	−7.49609	+	4.32787i	−0.614104	+	0.354553i	0.160466	+	0.987041i	$0.448700\pi$
$150$	4.75699	+	1.53982i	0.388407	+	0.125726i
$151$		−	19.8012i		−	1.61140i	−0.592325	−	0.805699i	$-0.701790\pi$
$151$		−	19.8012i		−	1.61140i	0.592325	−	0.805699i	$-0.298210\pi$
$152$	−0.640982	+	2.39218i	−0.0519905	+	0.194031i
$153$	1.36237	+	1.36237i	0.110141	+	0.110141i
$154$	−1.64107			−0.132241
$155$	−11.1192	−	5.60026i	−0.893117	−	0.449824i
$156$	−4.17520			−0.334283
$157$	8.42879	+	8.42879i	0.672690	+	0.672690i	0.958335	−	0.285645i	$-0.0922079\pi$
$157$	8.42879	+	8.42879i	0.672690	+	0.672690i	−0.285645	+	0.958335i	$0.592208\pi$
$158$	−0.408778	+	1.52558i	−0.0325207	+	0.121369i
$159$			14.1719i			1.12390i
$160$	−0.802490	−	2.08711i	−0.0634424	−	0.165000i
$161$	0.475260	−	0.274392i	0.0374557	−	0.0216251i
$162$	0.258819	−	0.965926i	0.0203347	−	0.0758903i
$163$	−4.06550	+	4.06550i	−0.318435	+	0.318435i	−0.848166	−	0.529731i	$-0.822293\pi$
$163$	−4.06550	+	4.06550i	−0.318435	+	0.318435i	0.529731	+	0.848166i	$0.322293\pi$
$164$	−1.64796	−	0.951451i	−0.128684	−	0.0742958i
$165$	−3.70263	+	1.42366i	−0.288249	+	0.110832i
$166$	−12.1105	−	6.99197i	−0.939953	−	0.542682i
$167$	−6.70677	−	1.79707i	−0.518985	−	0.139062i	−0.0101880	−	0.999948i	$-0.503243\pi$
$167$	−6.70677	−	1.79707i	−0.518985	−	0.139062i	−0.508797	+	0.860886i	$0.669910\pi$
$168$	−0.893522	+	0.239418i	−0.0689367	+	0.0184715i
$169$	3.83845	−	2.21613i	0.295265	−	0.170472i
$170$	−0.452700	−	4.28434i	−0.0347205	−	0.328594i
$171$	2.47656			0.189388
$172$	6.46785	+	1.73306i	0.493169	+	0.132144i
$173$	−1.58638	−	5.92046i	−0.120610	−	0.450124i	0.879035	−	0.476758i	$-0.158188\pi$
$173$	−1.58638	−	5.92046i	−0.120610	−	0.450124i	−0.999645	+	0.0266333i	$0.991521\pi$
$174$	4.54566	−	2.62444i	0.344605	−	0.198958i
$175$	−4.11876	+	2.10436i	−0.311349	+	0.159075i
$176$	1.53637	+	0.887024i	0.115808	+	0.0668620i
$177$	0.00780507	+	0.0291289i	0.000586665	+	0.00218946i
$178$	−6.63096	−	6.63096i	−0.497011	−	0.497011i
$179$	12.3988	+	21.4753i	0.926728	+	1.60514i	0.788758	+	0.614704i	$0.210725\pi$
$179$	12.3988	+	21.4753i	0.926728	+	1.60514i	0.137971	+	0.990436i	$0.455942\pi$
$180$	−1.80829	+	1.31533i	−0.134782	+	0.0980388i
$181$	4.55357	+	2.62901i	0.338464	+	0.195413i	0.659593	−	0.751623i	$-0.270729\pi$
$181$	4.55357	+	2.62901i	0.338464	+	0.195413i	−0.321128	+	0.947036i	$0.604062\pi$
$182$	2.73101	−	2.73101i	0.202436	−	0.202436i
$183$	−11.1626	−	2.99100i	−0.825160	−	0.221101i
$184$	−0.593252			−0.0437352
$185$	−6.52036	−	5.27411i	−0.479386	−	0.387760i
$186$	4.95046	−	2.54812i	0.362986	−	0.186837i
$187$	2.41691	+	2.41691i	0.176742	+	0.176742i
$188$	0.278394	−	0.278394i	0.0203040	−	0.0203040i
$189$	0.462521	+	0.801110i	0.0336434	+	0.0582721i
$190$	−4.30558	−	3.48265i	−0.312360	−	0.252658i
$191$	5.00658	−	8.67166i	0.362264	−	0.627459i	−0.626069	−	0.779767i	$-0.715337\pi$
$191$	5.00658	−	8.67166i	0.362264	−	0.627459i	0.988333	+	0.152308i	$0.0486707\pi$
$192$	0.965926	+	0.258819i	0.0697097	+	0.0186787i
$193$	10.4215	+	2.79242i	0.750153	+	0.201003i	0.613586	−	0.789628i	$-0.289726\pi$
$193$	10.4215	+	2.79242i	0.750153	+	0.201003i	0.136567	+	0.990631i	$0.456393\pi$
$194$		−	3.79488i		−	0.272457i
$195$	3.79258	−	8.53098i	0.271592	−	0.610916i
$196$	−3.07215	+	5.32112i	−0.219439	+	0.380080i
$197$	1.04506	+	3.90021i	0.0744573	+	0.277878i	0.993110	−	0.117188i	$-0.0373881\pi$
$197$	1.04506	+	3.90021i	0.0744573	+	0.277878i	−0.918652	+	0.395067i	$0.870721\pi$
$198$	0.459157	−	1.71360i	0.0326309	−	0.121780i
$199$	−10.6527	+	18.4511i	−0.755153	+	1.30796i	0.190145	+	0.981756i	$0.439104\pi$
$199$	−10.6527	+	18.4511i	−0.755153	+	1.30796i	−0.945298	+	0.326208i	$0.894229\pi$
$200$	4.99343	+	0.256153i	0.353089	+	0.0181127i
$201$			2.25438i			0.159012i
$202$	−0.209082	−	0.209082i	−0.0147110	−	0.0147110i
$203$	−1.25668	+	4.68998i	−0.0882014	+	0.329172i
$204$	1.66855	+	0.963341i	0.116822	+	0.0674473i
$205$	3.44100	−	2.50294i	0.240330	−	0.174813i
$206$	−4.76807	+	8.25854i	−0.332207	+	0.575400i
$207$	0.153545	+	0.573038i	0.0106721	+	0.0398289i
$208$	−4.03293	+	1.08062i	−0.279633	+	0.0749275i
$209$	4.39354			0.303908
$210$	0.322447	−	2.04317i	0.0222510	−	0.140992i
$211$	4.08045	+	7.06754i	0.280910	+	0.486550i	0.971609	−	0.236592i	$-0.0760306\pi$
$211$	4.08045	+	7.06754i	0.280910	+	0.486550i	−0.690699	+	0.723142i	$0.742697\pi$
$212$	3.66795	+	13.6890i	0.251916	+	0.940164i
$213$	−5.81101	−	5.81101i	−0.398164	−	0.398164i
$214$	−0.216769	+	0.125151i	−0.0148180	+	0.00855517i
$215$	−9.41621	+	11.6412i	−0.642180	+	0.793925i
$216$		−	1.00000i		−	0.0680414i
$217$	−1.57138	+	4.90485i	−0.106672	+	0.332963i
$218$	7.36114	−	7.36114i	0.498560	−	0.498560i
$219$			9.27433i			0.626701i
$220$	−3.20799	+	2.33346i	−0.216283	+	0.157322i
$221$	−8.04427			−0.541116
$222$	3.62271	−	0.970702i	0.243140	−	0.0651492i
$223$	0.397060	−	1.48185i	0.0265891	−	0.0992320i	−0.951356	−	0.308093i	$-0.900309\pi$
$223$	0.397060	−	1.48185i	0.0265891	−	0.0992320i	0.977945	+	0.208861i	$0.0669758\pi$
$224$	−0.801110	+	0.462521i	−0.0535264	+	0.0309035i
$225$	−1.04497	−	4.88958i	−0.0696647	−	0.325972i
$226$	−5.53045	+	9.57902i	−0.367880	+	0.637187i
$227$	2.81591	−	0.754521i	0.186899	−	0.0500794i	−0.164156	−	0.986434i	$-0.552490\pi$
$227$	2.81591	−	0.754521i	0.186899	−	0.0500794i	0.351054	+	0.936355i	$0.385823\pi$
$228$	2.39218	−	0.640982i	0.158426	−	0.0424501i
$229$	−13.1588	−	22.7917i	−0.869558	−	1.50612i	−0.862449	−	0.506144i	$-0.831071\pi$
$229$	−13.1588	−	22.7917i	−0.869558	−	1.50612i	−0.00710867	−	0.999975i	$-0.502263\pi$
$230$	0.538887	−	1.21216i	0.0355331	−	0.0799278i
$231$	0.820534	+	1.42121i	0.0539872	+	0.0935085i
$232$	3.71151	−	3.71151i	0.243673	−	0.243673i
$233$	−15.8215	+	15.8215i	−1.03650	+	1.03650i	−0.0371942	+	0.999308i	$0.511842\pi$
$233$	−15.8215	+	15.8215i	−1.03650	+	1.03650i	−0.999308	+	0.0371942i	$0.988158\pi$
$234$	2.08760	+	3.61583i	0.136471	+	0.236374i
$235$	0.315947	+	0.821711i	0.0206101	+	0.0536025i
$236$	0.0150782	+	0.0261163i	0.000981509	+	0.00170002i
$237$	1.52558	−	0.408778i	0.0990972	−	0.0265530i
$238$	−1.72153	+	0.461283i	−0.111590	+	0.0299005i
$239$	−6.73844	+	11.6713i	−0.435874	+	0.754955i	−0.997366	−	0.0725263i	$-0.976894\pi$
$239$	−6.73844	+	11.6713i	−0.435874	+	0.754955i	0.561493	+	0.827482i	$0.310227\pi$
$240$	−1.40624	+	1.73853i	−0.0907725	+	0.112222i
$241$	18.4047	−	10.6259i	1.18555	−	0.684477i	0.228258	−	0.973601i	$-0.426697\pi$
$241$	18.4047	−	10.6259i	1.18555	−	0.684477i	0.957292	+	0.289123i	$0.0933638\pi$
$242$	−2.03244	+	7.58518i	−0.130650	+	0.487594i
$243$	−0.965926	+	0.258819i	−0.0619642	+	0.0166032i
$244$	−11.5563			−0.739818
$245$	−8.08177	−	11.1107i	−0.516325	−	0.709835i
$246$			1.90290i			0.121325i
$247$	−7.31158	+	7.31158i	−0.465225	+	0.465225i
$248$	4.12228	−	3.74257i	0.261765	−	0.237653i
$249$			13.9839i			0.886197i
$250$	−5.05922	+	9.97017i	−0.319973	+	0.630569i
$251$	−23.7889	+	13.7346i	−1.50154	+	0.866917i	−0.501547	+	0.865131i	$0.667235\pi$
$251$	−23.7889	+	13.7346i	−1.50154	+	0.866917i	−0.999998	+	0.00178670i	$0.999431\pi$
$252$	0.654103	+	0.654103i	0.0412046	+	0.0412046i
$253$	0.272396	+	1.01660i	0.0171254	+	0.0639129i
$254$	5.49128	+	9.51118i	0.344554	+	0.596785i
$255$	−3.48400	+	2.53422i	−0.218176	+	0.158699i
$256$	1.00000			0.0625000
$257$	15.7416	−	4.21796i	0.981935	−	0.263109i	0.268076	−	0.963398i	$-0.413612\pi$
$257$	15.7416	−	4.21796i	0.981935	−	0.263109i	0.713859	+	0.700289i	$0.246946\pi$
$258$	−1.73306	−	6.46785i	−0.107895	−	0.402671i
$259$	−1.73469	+	3.00456i	−0.107788	+	0.186695i
$260$	1.45537	−	9.22189i	0.0902583	−	0.571917i
$261$	−4.54566	−	2.62444i	−0.281369	−	0.162449i
$262$	−0.00230748	+	0.00861164i	−0.000142557	+	0.000532029i
$263$	−2.31412	−	2.31412i	−0.142695	−	0.142695i	0.632151	−	0.774846i	$-0.282172\pi$
$263$	−2.31412	−	2.31412i	−0.142695	−	0.142695i	−0.774846	+	0.632151i	$0.782172\pi$
$264$		−	1.77405i		−	0.109185i
$265$	−31.3019	−	4.93998i	−1.92286	−	0.303460i
$266$	−1.14546	+	1.98400i	−0.0702328	+	0.121647i
$267$	−2.42710	+	9.05805i	−0.148536	+	0.554344i
$268$	0.583477	+	2.17757i	0.0356415	+	0.133016i
$269$	−4.67046	+	8.08947i	−0.284763	+	0.493224i	−0.972552	−	0.232687i	$-0.925248\pi$
$269$	−4.67046	+	8.08947i	−0.284763	+	0.493224i	0.687789	+	0.725911i	$0.258582\pi$
$270$	2.04325	+	0.908360i	0.124348	+	0.0552810i
$271$		−	9.75987i		−	0.592870i	−0.955053	−	0.296435i	$-0.904202\pi$
$271$		−	9.75987i		−	0.592870i	0.955053	−	0.296435i	$-0.0957978\pi$
$272$	1.86103	+	0.498662i	0.112842	+	0.0302358i
$273$	−3.73063	−	0.999619i	−0.225788	−	0.0604997i
$274$	−4.99957	+	8.65951i	−0.302035	+	0.523140i
$275$	−1.85383	−	8.67436i	−0.111790	−	0.523083i
$276$	0.296626	+	0.513772i	0.0178548	+	0.0309254i
$277$	7.68428	−	7.68428i	0.461704	−	0.461704i	−0.437510	−	0.899214i	$-0.644140\pi$
$277$	7.68428	−	7.68428i	0.461704	−	0.461704i	0.899214	+	0.437510i	$0.144140\pi$
$278$	1.12558	+	1.12558i	0.0675079	+	0.0675079i
$279$	−4.68197	−	3.01317i	−0.280302	−	0.180394i
$280$	−0.217351	−	2.05700i	−0.0129892	−	0.122930i
$281$	1.15179			0.0687099			0.0343550	−	0.999410i	$-0.489062\pi$
$281$	1.15179			0.0687099			0.0343550	+	0.999410i	$0.489062\pi$
$282$	−0.380293	−	0.101899i	−0.0226461	−	0.00606801i
$283$	−17.3761	+	17.3761i	−1.03290	+	1.03290i	−0.0334639	+	0.999440i	$0.510654\pi$
$283$	−17.3761	+	17.3761i	−1.03290	+	1.03290i	−0.999440	+	0.0334639i	$0.989346\pi$
$284$	−7.11700	−	4.10900i	−0.422316	−	0.243824i
$285$	−0.863270	+	5.47007i	−0.0511357	+	0.324019i
$286$	3.70350	+	6.41465i	0.218993	+	0.379306i
$287$	−1.24469	−	1.24469i	−0.0734720	−	0.0734720i
$288$	−0.258819	−	0.965926i	−0.0152511	−	0.0569177i
$289$	−11.5077	−	6.64395i	−0.676921	−	0.390821i
$290$	4.21217	+	10.9550i	0.247347	+	0.643297i
$291$	−3.28646	+	1.89744i	−0.192656	+	0.111230i
$292$	2.40037	+	8.95831i	0.140471	+	0.524246i
$293$	3.43792	+	0.921188i	0.200845	+	0.0538164i	0.357839	−	0.933783i	$-0.383514\pi$
$293$	3.43792	+	0.921188i	0.200845	+	0.0538164i	−0.156994	+	0.987600i	$0.550180\pi$
$294$	6.14430			0.358343
$295$	−0.0670586	+	0.00708566i	−0.00390430	+	0.000412543i
$296$	3.24803	−	1.87525i	0.188788	−	0.108997i
$297$	−1.71360	+	0.459157i	−0.0994331	+	0.0266430i
$298$	8.36080	+	2.24027i	0.484328	+	0.129775i
$299$	−2.14510	−	1.23847i	−0.124054	−	0.0716227i
$300$	−2.27488	−	4.45252i	−0.131340	−	0.257066i
$301$	5.36424	+	3.09705i	0.309190	+	0.178511i
$302$	−14.0016	+	14.0016i	−0.805699	+	0.805699i
$303$	−0.0765294	+	0.285611i	−0.00439650	+	0.0164080i
$304$	2.14477	−	1.23828i	0.123011	−	0.0710203i
$305$	10.4973	−	23.6125i	0.601074	−	1.35205i
$306$		−	1.92668i		−	0.110141i
$307$	−1.75348	+	6.54408i	−0.100076	+	0.373490i	−0.997740	−	0.0671907i	$-0.978596\pi$
$307$	−1.75348	+	6.54408i	−0.100076	+	0.373490i	0.897664	+	0.440681i	$0.145263\pi$
$308$	1.16041	+	1.16041i	0.0661205	+	0.0661205i
$309$	9.53614			0.542492
$310$	3.90250	+	11.8225i	0.221647	+	0.671470i
$311$	20.0424			1.13650			0.568251	−	0.822855i	$-0.307620\pi$
$311$	20.0424			1.13650			0.568251	+	0.822855i	$0.307620\pi$
$312$	2.95231	+	2.95231i	0.167142	+	0.167142i
$313$	−1.72653	+	6.44351i	−0.0975894	+	0.364208i	−0.997399	−	0.0720736i	$-0.977038\pi$
$313$	−1.72653	+	6.44351i	−0.0975894	+	0.364208i	0.899810	+	0.436282i	$0.143705\pi$
$314$		−	11.9201i		−	0.672690i
$315$	−1.93066	+	0.742337i	−0.108780	+	0.0418259i
$316$	1.36780	−	0.789699i	0.0769447	−	0.0444241i
$317$	2.62773	−	9.80683i	0.147588	−	0.550806i	−0.852038	−	0.523479i	$-0.824634\pi$
$317$	2.62773	−	9.80683i	0.147588	−	0.550806i	0.999627	−	0.0273271i	$-0.00869957\pi$
$318$	10.0210	−	10.0210i	0.561952	−	0.561952i
$319$	−8.06422	−	4.65588i	−0.451510	−	0.260679i
$320$	−0.908360	+	2.04325i	−0.0507789	+	0.114221i
$321$	0.216769	+	0.125151i	0.0120988	+	0.00698527i
$322$	−0.530084	−	0.142036i	−0.0295404	−	0.00791533i
$323$	4.60896	−	1.23497i	0.256450	−	0.0687155i
$324$	−0.866025	+	0.500000i	−0.0481125	+	0.0277778i
$325$	17.5206	+	11.3505i	0.971870	+	0.629612i
$326$	5.74949			0.318435
$327$	−10.0555	−	2.69437i	−0.556071	−	0.148999i
$328$	0.492507	+	1.83806i	0.0271942	+	0.101490i
$329$	0.315403	−	0.182098i	0.0173888	−	0.0100394i
$330$	3.62483	+	1.61147i	0.199540	+	0.0887088i
$331$	−6.95262	−	4.01410i	−0.382150	−	0.220635i	0.296603	−	0.955001i	$-0.404146\pi$
$331$	−6.95262	−	4.01410i	−0.382150	−	0.220635i	−0.678753	+	0.734366i	$0.737480\pi$
$332$	3.61931	+	13.5075i	0.198636	+	0.741318i
$333$	−2.65201	−	2.65201i	−0.145329	−	0.145329i
$334$	3.47168	+	6.01312i	0.189962	+	0.329023i
$335$	−4.97932	−	0.785823i	−0.272050	−	0.0429341i
$336$	0.801110	+	0.462521i	0.0437041	+	0.0252326i
$337$	13.0029	−	13.0029i	0.708313	−	0.708313i	−0.257868	−	0.966180i	$-0.583020\pi$
$337$	13.0029	−	13.0029i	0.708313	−	0.708313i	0.966180	+	0.257868i	$0.0830198\pi$
$338$	−4.28123	−	1.14715i	−0.232868	−	0.0623969i
$339$	11.0609			0.600746
$340$	−2.70938	+	3.34959i	−0.146937	+	0.181657i
$341$	−8.30604	−	5.34551i	−0.449797	−	0.289475i
$342$	−1.75120	−	1.75120i	−0.0946938	−	0.0946938i
$343$	−8.59773	+	8.59773i	−0.464234	+	0.464234i
$344$	−3.34801	−	5.79892i	−0.180512	−	0.312657i
$345$	−1.31921	+	0.139393i	−0.0710238	+	0.00750465i
$346$	−3.06466	+	5.30814i	−0.164757	+	0.285367i
$347$	21.6172	+	5.79232i	1.16047	+	0.310948i	0.787155	−	0.616755i	$-0.211553\pi$
$347$	21.6172	+	5.79232i	1.16047	+	0.310948i	0.373319	+	0.927703i	$0.378220\pi$
$348$	−5.07002	−	1.35851i	−0.271782	−	0.0728237i
$349$		−	10.3084i		−	0.551798i	−0.961187	−	0.275899i	$-0.911024\pi$
$349$		−	10.3084i		−	0.551798i	0.961187	−	0.275899i	$-0.0889755\pi$
$350$	4.40041	+	1.42440i	0.235212	+	0.0761373i
$351$	2.08760	−	3.61583i	0.111428	−	0.192998i
$352$	−0.459157	−	1.71360i	−0.0244732	−	0.0913351i
$353$	3.47273	−	12.9604i	0.184835	−	0.689812i	−0.809831	−	0.586663i	$-0.800441\pi$
$353$	3.47273	−	12.9604i	0.184835	−	0.689812i	0.994666	−	0.103149i	$-0.0328919\pi$
$354$	0.0150782	−	0.0261163i	0.000801399	−	0.00138806i
$355$	14.8605	−	10.8094i	0.788715	−	0.573702i
$356$			9.37759i			0.497011i
$357$	1.26025	+	1.26025i	0.0666994	+	0.0666994i
$358$	6.41808	−	23.9526i	0.339206	−	1.26593i
$359$	9.05214	+	5.22626i	0.477754	+	0.275831i	0.719480	−	0.694513i	$-0.244380\pi$
$359$	9.05214	+	5.22626i	0.477754	+	0.275831i	−0.241726	+	0.970344i	$0.577714\pi$
$360$	2.20873	+	0.348576i	0.116410	+	0.0183716i
$361$	−6.43331	+	11.1428i	−0.338596	+	0.586465i
$362$	−1.36087	−	5.07885i	−0.0715260	−	0.266938i
$363$	7.58518	−	2.03244i	0.398119	−	0.106676i
$364$	−3.86223			−0.202436
$365$	−20.4845	−	3.23281i	−1.07221	−	0.169213i
$366$	5.77816	+	10.0081i	0.302029	+	0.523130i
$367$	0.379571	+	1.41658i	0.0198134	+	0.0739447i	0.975125	−	0.221657i	$-0.0711465\pi$
$367$	0.379571	+	1.41658i	0.0198134	+	0.0739447i	−0.955311	+	0.295602i	$0.904480\pi$
$368$	0.419493	+	0.419493i	0.0218676	+	0.0218676i
$369$	1.64796	−	0.951451i	0.0857894	−	0.0495305i
$370$	0.881231	+	8.33995i	0.0458130	+	0.433573i
$371$			13.1096i			0.680616i
$372$	−5.30230	−	1.69871i	−0.274911	−	0.0880743i
$373$	21.2301	−	21.2301i	1.09925	−	1.09925i	0.104756	−	0.994498i	$-0.466594\pi$
$373$	21.2301	−	21.2301i	1.09925	−	1.09925i	0.994498	−	0.104756i	$-0.0334062\pi$
$374$		−	3.41803i		−	0.176742i
$375$	11.1640	−	0.603670i	0.576508	−	0.0311734i
$376$	−0.393708			−0.0203040
$377$	21.1683	−	5.67204i	1.09023	−	0.292125i
$378$	0.239418	−	0.893522i	0.0123144	−	0.0459578i
$379$	21.7379	−	12.5504i	1.11660	−	0.644670i	0.176070	−	0.984378i	$-0.443661\pi$
$379$	21.7379	−	12.5504i	1.11660	−	0.644670i	0.940531	+	0.339708i	$0.110328\pi$
$380$	0.581902	+	5.50711i	0.0298509	+	0.282509i
$381$	5.49128	−	9.51118i	0.281327	−	0.487273i
$382$	−9.67198	+	2.59160i	−0.494861	+	0.132598i
$383$	−26.6976	+	7.15361i	−1.36419	+	0.365532i	−0.865352	−	0.501165i	$-0.832905\pi$
$383$	−26.6976	+	7.15361i	−1.36419	+	0.365532i	−0.498834	+	0.866698i	$0.666238\pi$
$384$	−0.500000	−	0.866025i	−0.0255155	−	0.0441942i
$385$	−3.42508	+	1.31694i	−0.174558	+	0.0671175i
$386$	−5.39455	−	9.34363i	−0.274575	−	0.475578i
$387$	−4.73480	+	4.73480i	−0.240683	+	0.240683i
$388$	−2.68339	+	2.68339i	−0.136228	+	0.136228i
$389$	−3.67726	−	6.36921i	−0.186445	−	0.322932i	0.757618	−	0.652699i	$-0.226363\pi$
$389$	−3.67726	−	6.36921i	−0.186445	−	0.322932i	−0.944062	+	0.329767i	$0.893030\pi$
$390$	−8.71407	+	3.35055i	−0.441254	+	0.169662i
$391$	0.571504	+	0.989874i	0.0289022	+	0.0500601i
$392$	5.93494	−	1.59026i	0.299760	−	0.0803203i
$393$	0.00861164	−	0.00230748i	0.000434400	−	0.000116397i
$394$	2.01890	−	3.49683i	0.101711	−	0.176168i
$395$	0.371101	+	3.51209i	0.0186721	+	0.176712i
$396$	−1.53637	+	0.887024i	−0.0772055	+	0.0445746i
$397$	4.34536	−	16.2171i	0.218087	−	0.813912i	−0.766970	−	0.641683i	$-0.778236\pi$
$397$	4.34536	−	16.2171i	0.218087	−	0.813912i	0.985057	−	0.172229i	$-0.0550970\pi$
$398$	20.5795	−	5.51427i	1.03156	−	0.276405i
$399$	2.29092			0.114690
$400$	−3.34976	−	3.71202i	−0.167488	−	0.185601i
$401$		−	9.97228i		−	0.497992i	−0.968505	−	0.248996i	$-0.919899\pi$
$401$		−	9.97228i		−	0.497992i	0.968505	−	0.248996i	$-0.0801006\pi$
$402$	1.59409	−	1.59409i	0.0795059	−	0.0795059i
$403$	22.7184	−	4.92681i	1.13169	−	0.245422i
$404$			0.295687i			0.0147110i
$405$	−0.234963	−	2.22369i	−0.0116754	−	0.110496i
$406$	4.20492	−	2.42771i	0.208687	−	0.120485i
$407$	−4.70479	−	4.70479i	−0.233208	−	0.233208i
$408$	−0.498662	−	1.86103i	−0.0246874	−	0.0921348i
$409$	−1.91448	−	3.31597i	−0.0946649	−	0.163964i	0.814804	−	0.579737i	$-0.196845\pi$
$409$	−1.91448	−	3.31597i	−0.0946649	−	0.163964i	−0.909469	+	0.415772i	$0.863511\pi$
$410$	−4.20300	−	0.663305i	−0.207571	−	0.0327583i
$411$	9.99914			0.493221
$412$	9.21120	−	2.46813i	0.453803	−	0.121596i
$413$	0.00722001	+	0.0269454i	0.000355273	+	0.00132590i
$414$	0.296626	−	0.513772i	0.0145784	−	0.0252505i
$415$	−30.8868	−	4.87447i	−1.51617	−	0.239278i
$416$	3.61583	+	2.08760i	0.177280	+	0.102353i
$417$	0.411992	−	1.53757i	0.0201753	−	0.0752953i
$418$	−3.10670	−	3.10670i	−0.151954	−	0.151954i
$419$			23.2144i			1.13410i	0.823685	+	0.567048i	$0.191915\pi$
$419$			23.2144i			1.13410i	−0.823685	+	0.567048i	$0.808085\pi$
$420$	−1.67274	+	1.21673i	−0.0816215	+	0.0593705i
$421$	19.1211	−	33.1188i	0.931907	−	1.61411i	0.151847	−	0.988404i	$-0.451478\pi$
$421$	19.1211	−	33.1188i	0.931907	−	1.61411i	0.780059	−	0.625705i	$-0.215189\pi$
$422$	2.11220	−	7.88282i	0.102820	−	0.383730i
$423$	0.101899	+	0.380293i	0.00495451	+	0.0184905i
$424$	7.08594	−	12.2732i	0.344124	−	0.596040i
$425$	−4.38297	−	8.57858i	−0.212605	−	0.416122i
$426$			8.21800i			0.398164i
$427$	−10.3258	−	2.76680i	−0.499702	−	0.133895i
$428$	0.241774	+	0.0647831i	0.0116866	+	0.00313141i
$429$	3.70350	−	6.41465i	0.178807	−	0.309702i
$430$	14.8899	−	1.57332i	0.718052	−	0.0758722i
$431$	−16.1581	−	27.9867i	−0.778308	−	1.34807i	−0.932916	−	0.360094i	$-0.882745\pi$
$431$	−16.1581	−	27.9867i	−0.778308	−	1.34807i	0.154608	−	0.987976i	$-0.450589\pi$
$432$	−0.707107	+	0.707107i	−0.0340207	+	0.0340207i
$433$	6.78867	+	6.78867i	0.326243	+	0.326243i	0.851156	−	0.524913i	$-0.175902\pi$
$433$	6.78867	+	6.78867i	0.326243	+	0.326243i	−0.524913	+	0.851156i	$0.675902\pi$
$434$	4.57938	−	2.35712i	0.219818	−	0.113145i
$435$	7.38118	−	9.12532i	0.353901	−	0.437526i
$436$	−10.4102			−0.498560
$437$	1.41917	+	0.380264i	0.0678879	+	0.0181905i
$438$	6.55794	−	6.55794i	0.313350	−	0.313350i
$439$	11.9007	+	6.87086i	0.567989	+	0.327928i	0.756346	−	0.654172i	$-0.226983\pi$
$439$	11.9007	+	6.87086i	0.567989	+	0.327928i	−0.188357	+	0.982101i	$0.560316\pi$
$440$	3.91840	+	0.618390i	0.186802	+	0.0294806i
$441$	−3.07215	−	5.32112i	−0.146293	−	0.253387i
$442$	5.68816	+	5.68816i	0.270558	+	0.270558i
$443$	1.01107	+	3.77335i	0.0480372	+	0.179277i	0.985776	−	0.168063i	$-0.0537513\pi$
$443$	1.01107	+	3.77335i	0.0480372	+	0.179277i	−0.937739	+	0.347341i	$0.887085\pi$
$444$	−3.24803	−	1.87525i	−0.154145	−	0.0889955i
$445$	−19.1608	−	8.51823i	−0.908308	−	0.403803i
$446$	−1.32859	+	0.767062i	−0.0629105	+	0.0363214i
$447$	−2.24027	−	8.36080i	−0.105961	−	0.395452i
$448$	0.893522	+	0.239418i	0.0422149	+	0.0113115i
$449$	24.8783			1.17408			0.587041	−	0.809557i	$-0.300293\pi$
$449$	24.8783			1.17408			0.587041	+	0.809557i	$0.300293\pi$
$450$	−2.71855	+	4.19636i	−0.128154	+	0.197819i
$451$	2.92356	−	1.68792i	0.137665	−	0.0794810i
$452$	10.6840	−	2.86277i	0.502534	−	0.134653i
$453$	19.1265	+	5.12492i	0.898640	+	0.240790i
$454$	−2.52468	−	1.45762i	−0.118489	−	0.0684097i
$455$	3.50830	−	7.89151i	0.164471	−	0.369960i
$456$	−2.14477	−	1.23828i	−0.100438	−	0.0579879i
$457$	13.0765	−	13.0765i	0.611694	−	0.611694i	−0.331693	−	0.943387i	$-0.607620\pi$
$457$	13.0765	−	13.0765i	0.611694	−	0.611694i	0.943387	+	0.331693i	$0.107620\pi$
$458$	−6.81150	+	25.4208i	−0.318280	+	1.18784i
$459$	−1.66855	+	0.963341i	−0.0778815	+	0.0449649i
$460$	−1.23818	+	0.476079i	−0.0577305	+	0.0221973i
$461$			35.2243i			1.64056i	0.571964	+	0.820278i	$0.306182\pi$
$461$			35.2243i			1.64056i	−0.571964	+	0.820278i	$0.693818\pi$
$462$	0.424740	−	1.58515i	0.0197607	−	0.0737479i
$463$	5.55552	+	5.55552i	0.258187	+	0.258187i	0.824316	−	0.566129i	$-0.191560\pi$
$463$	5.55552	+	5.55552i	0.258187	+	0.258187i	−0.566129	+	0.824316i	$0.691560\pi$
$464$	−5.24887			−0.243673
$465$	8.28730	−	9.29089i	0.384314	−	0.430855i
$466$	22.3750			1.03650
$467$	28.7323	+	28.7323i	1.32957	+	1.32957i	0.905743	+	0.423828i	$0.139314\pi$
$467$	28.7323	+	28.7323i	1.32957	+	1.32957i	0.423828	+	0.905743i	$0.360686\pi$
$468$	1.08062	−	4.03293i	0.0499517	−	0.186422i
$469$			2.08540i			0.0962947i
$470$	0.357629	−	0.804445i	0.0164962	−	0.0371063i
$471$	−10.3231	+	5.96005i	−0.475664	+	0.274625i
$472$	0.00780507	−	0.0291289i	0.000359257	−	0.00134077i
$473$	−8.39976	+	8.39976i	−0.386221	+	0.386221i
$474$	−1.36780	−	0.789699i	−0.0628251	−	0.0362721i
$475$	−11.7810	−	3.81346i	−0.540549	−	0.174974i
$476$	1.54348	+	0.891130i	0.0707454	+	0.0408449i
$477$	−13.6890	−	3.66795i	−0.626776	−	0.167944i
$478$	13.0177	−	3.48807i	0.595414	−	0.159541i
$479$	−14.8675	+	8.58377i	−0.679314	+	0.392202i	−0.799597	−	0.600537i	$-0.794953\pi$
$479$	−14.8675	+	8.58377i	−0.679314	+	0.392202i	0.120282	+	0.992740i	$0.461620\pi$
$480$	2.22369	−	0.234963i	0.101497	−	0.0107246i
$481$	15.6591			0.713993
$482$	−20.5278	−	5.50039i	−0.935014	−	0.250536i
$483$	0.142036	+	0.530084i	0.00646284	+	0.0241197i
$484$	6.80068	−	3.92638i	0.309122	−	0.178472i
$485$	−3.04536	−	7.92032i	−0.138282	−	0.359643i
$486$	0.866025	+	0.500000i	0.0392837	+	0.0226805i
$487$	−9.62829	−	35.9333i	−0.436300	−	1.62829i	−0.737937	−	0.674870i	$-0.764200\pi$
$487$	−9.62829	−	35.9333i	−0.436300	−	1.62829i	0.301637	−	0.953423i	$-0.402467\pi$
$488$	8.17155	+	8.17155i	0.369909	+	0.369909i
$489$	−2.87474	−	4.97920i	−0.130000	−	0.225167i
$490$	−2.14175	+	13.5711i	−0.0967546	+	0.613080i
$491$	35.6939	+	20.6079i	1.61085	+	0.930022i	0.989175	+	0.146743i	$0.0468790\pi$
$491$	35.6939	+	20.6079i	1.61085	+	0.930022i	0.621671	+	0.783279i	$0.286454\pi$
$492$	1.34555	−	1.34555i	0.0606623	−	0.0606623i
$493$	−9.76832	−	2.61741i	−0.439943	−	0.117882i
$494$	10.3401			0.465225
$495$	−0.416836	−	3.94493i	−0.0187354	−	0.177311i
$496$	−5.56129	−	0.268497i	−0.249709	−	0.0120559i
$497$	−5.37542	−	5.37542i	−0.241121	−	0.241121i
$498$	9.88814	−	9.88814i	0.443098	−	0.443098i
$499$	−9.63143	−	16.6821i	−0.431162	−	0.746795i	0.565812	−	0.824535i	$-0.308563\pi$
$499$	−9.63143	−	16.6821i	−0.431162	−	0.746795i	−0.996974	+	0.0777399i	$0.975230\pi$
$500$	10.6274	−	3.47256i	0.475271	−	0.155298i
$501$	3.47168	−	6.01312i	0.155103	−	0.268646i
$502$	26.5331	+	7.10953i	1.18423	+	0.317314i
$503$	23.1581	+	6.20520i	1.03257	+	0.276676i	0.735031	−	0.678033i	$-0.237168\pi$
$503$	23.1581	+	6.20520i	1.03257	+	0.276676i	0.297539	+	0.954710i	$0.403834\pi$
$504$		−	0.925042i		−	0.0412046i
$505$	−0.604163	−	0.268590i	−0.0268849	−	0.0119521i
$506$	0.526229	−	0.911456i	0.0233937	−	0.0405192i
$507$	1.14715	+	4.28123i	0.0509469	+	0.190136i
$508$	2.84250	−	10.6083i	0.126115	−	0.470669i
$509$	−1.37695	+	2.38494i	−0.0610321	+	0.105711i	−0.894927	−	0.446213i	$-0.852773\pi$
$509$	−1.37695	+	2.38494i	−0.0610321	+	0.105711i	0.833895	+	0.551923i	$0.186106\pi$
$510$	4.25552	+	0.671594i	0.188438	+	0.0297387i
$511$			8.57914i			0.379519i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−0.640982	+	2.39218i	−0.0283000	+	0.105617i
$514$	−14.1136	−	8.14846i	−0.622522	−	0.359413i
$515$	−3.32407	+	21.0628i	−0.146476	+	0.928136i
$516$	−3.34801	+	5.79892i	−0.147388	+	0.255283i
$517$	0.180774	+	0.674658i	0.00795043	+	0.0296714i
$518$	3.35116	−	0.897939i	0.147241	−	0.0394532i
$519$	6.12931			0.269047
$520$	−7.54996	+	5.49175i	−0.331088	+	0.240829i
$521$	−1.02801	−	1.78056i	−0.0450379	−	0.0780079i	0.842628	−	0.538497i	$-0.181008\pi$
$521$	−1.02801	−	1.78056i	−0.0450379	−	0.0780079i	−0.887666	+	0.460489i	$0.847674\pi$
$522$	1.35851	+	5.07002i	0.0594603	+	0.221909i
$523$	−6.43419	−	6.43419i	−0.281347	−	0.281347i	0.552299	−	0.833646i	$-0.313751\pi$
$523$	−6.43419	−	6.43419i	−0.281347	−	0.281347i	−0.833646	+	0.552299i	$0.813751\pi$
$524$	0.00772098	−	0.00445771i	0.000337293	−	0.000194736i
$525$	−0.966642	−	4.52307i	−0.0421877	−	0.197403i
$526$			3.27266i			0.142695i
$527$	−10.2158	−	3.27288i	−0.445009	−	0.142569i
$528$	−1.25444	+	1.25444i	−0.0545926	+	0.0545926i
$529$		−	22.6481i		−	0.984698i
$530$	18.6407	+	25.6269i	0.809700	+	1.11316i
$531$	−0.0301565			−0.00130868
$532$	2.21286	−	0.592935i	0.0959398	−	0.0257070i
$533$	−2.05631	+	7.67427i	−0.0890688	+	0.332409i
$534$	8.12123	−	4.68879i	0.351440	−	0.202904i
$535$	−0.351986	+	0.435159i	−0.0152177	+	0.0188136i
$536$	1.12719	−	1.95235i	0.0486872	−	0.0843288i
$537$	−23.9526	+	6.41808i	−1.03363	+	0.276961i
$538$	9.02263	−	2.41761i	0.388993	−	0.104230i
$539$	−5.45014	−	9.43992i	−0.234754	−	0.406606i
$540$	−0.802490	−	2.08711i	−0.0345337	−	0.0898147i
$541$	1.88472	+	3.26443i	0.0810305	+	0.140349i	0.903693	−	0.428181i	$-0.140846\pi$
$541$	1.88472	+	3.26443i	0.0810305	+	0.140349i	−0.822662	+	0.568530i	$0.807512\pi$
$542$	−6.90127	+	6.90127i	−0.296435	+	0.296435i
$543$	−3.71798	+	3.71798i	−0.159554	+	0.159554i
$544$	−0.963341	−	1.66855i	−0.0413029	−	0.0715387i
$545$	9.45624	−	21.2707i	0.405061	−	0.911138i
$546$	1.93111	+	3.34479i	0.0826441	+	0.143144i
$547$	11.0564	−	2.96255i	0.472737	−	0.126669i	−0.0145818	−	0.999894i	$-0.504642\pi$
$547$	11.0564	−	2.96255i	0.472737	−	0.126669i	0.487319	+	0.873224i	$0.337975\pi$
$548$	9.65843	−	2.58797i	0.412588	−	0.110553i
$549$	5.77816	−	10.0081i	0.246606	−	0.427134i
$550$	−4.82284	+	7.44455i	−0.205647	+	0.317437i
$551$	−11.2576	+	6.49959i	−0.479591	+	0.276892i
$552$	0.153545	−	0.573038i	0.00653531	−	0.0243901i
$553$	1.41123	−	0.378137i	0.0600115	−	0.0160800i
$554$	−10.8672			−0.461704
$555$	6.78199	−	4.93314i	0.287880	−	0.209400i
$556$		−	1.59181i		−	0.0675079i
$557$	−25.4370	+	25.4370i	−1.07780	+	1.07780i	−0.0810920	+	0.996707i	$0.525841\pi$
$557$	−25.4370	+	25.4370i	−1.07780	+	1.07780i	−0.996707	+	0.0810920i	$0.974159\pi$
$558$	1.18002	+	5.44128i	0.0499542	+	0.230348i
$559$		−	27.9572i		−	1.18246i
$560$	−1.30083	+	1.60821i	−0.0549702	+	0.0679594i
$561$	−2.96010	+	1.70901i	−0.124975	+	0.0721546i
$562$	−0.814437	−	0.814437i	−0.0343550	−	0.0343550i
$563$	−5.68658	−	21.2226i	−0.239661	−	0.894427i	−0.975992	−	0.217805i	$-0.930110\pi$
$563$	−5.68658	−	21.2226i	−0.239661	−	0.894427i	0.736331	−	0.676621i	$-0.236557\pi$
$564$	0.196854	+	0.340961i	0.00828905	+	0.0143571i
$565$	−3.85556	+	24.4306i	−0.162205	+	1.02780i
$566$	24.5736			1.03290
$567$	−0.893522	+	0.239418i	−0.0375244	+	0.0100546i
$568$	2.12698	+	7.93798i	0.0892459	+	0.333070i
$569$	−12.9250	+	22.3868i	−0.541845	+	0.938503i	0.456953	+	0.889491i	$0.348941\pi$
$569$	−12.9250	+	22.3868i	−0.541845	+	0.938503i	−0.998798	+	0.0490124i	$0.984393\pi$
$570$	4.47834	−	3.25750i	0.187577	−	0.136441i
$571$	39.1052	+	22.5774i	1.63650	+	0.944835i	0.982025	+	0.188753i	$0.0604445\pi$
$571$	39.1052	+	22.5774i	1.63650	+	0.944835i	0.654477	+	0.756082i	$0.272889\pi$
$572$	1.91707	−	7.15461i	0.0801568	−	0.299149i
$573$	7.08038	+	7.08038i	0.295787	+	0.295787i
$574$			1.76026i			0.0734720i
$575$	0.151963	−	2.96237i	0.00633731	−	0.123539i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−4.06018	+	15.1528i	−0.169027	+	0.630819i	0.828465	+	0.560041i	$0.189215\pi$
$577$	−4.06018	+	15.1528i	−0.169027	+	0.630819i	−0.997492	+	0.0707777i	$0.977452\pi$
$578$	3.43916	+	12.8351i	0.143050	+	0.533871i
$579$	−5.39455	+	9.34363i	−0.224190	+	0.388308i
$580$	4.76787	−	10.7248i	0.197975	−	0.445322i
$581$			12.9357i			0.536665i
$582$	3.66557	+	0.982188i	0.151943	+	0.0407130i
$583$	−24.2849	−	6.50713i	−1.00578	−	0.269498i
$584$	4.63716	−	8.03180i	0.191887	−	0.332358i
$585$	7.25870	+	5.87133i	0.300110	+	0.242750i
$586$	−1.77960	−	3.08235i	−0.0735145	−	0.127331i
$587$	1.82192	−	1.82192i	0.0751985	−	0.0751985i	−0.668507	−	0.743706i	$-0.733066\pi$
$587$	1.82192	−	1.82192i	0.0751985	−	0.0751985i	0.743706	+	0.668507i	$0.233066\pi$
$588$	−4.34467	−	4.34467i	−0.179171	−	0.179171i
$589$	−12.2601	+	6.31058i	−0.505170	+	0.260023i
$590$	0.0524279	+	0.0424073i	0.00215842	+	0.00174588i
$591$	−4.03779			−0.166093
$592$	−3.62271	−	0.970702i	−0.148892	−	0.0398956i
$593$	−18.6982	+	18.6982i	−0.767844	+	0.767844i	−0.977727	−	0.209882i	$-0.932692\pi$
$593$	−18.6982	+	18.6982i	−0.767844	+	0.767844i	0.209882	+	0.977727i	$0.432692\pi$
$594$	1.53637	+	0.887024i	0.0630381	+	0.0363950i
$595$	−3.22284	+	2.34426i	−0.132124	+	0.0961052i
$596$	−4.32787	−	7.49609i	−0.177276	−	0.307052i
$597$	−15.0653	−	15.0653i	−0.616580	−	0.616580i
$598$	0.641081	+	2.39255i	0.0262157	+	0.0978385i
$599$	−4.20820	−	2.42961i	−0.171943	−	0.0992711i	0.411559	−	0.911383i	$-0.364984\pi$
$599$	−4.20820	−	2.42961i	−0.171943	−	0.0992711i	−0.583501	+	0.812112i	$0.698318\pi$
$600$	−1.53982	+	4.75699i	−0.0628629	+	0.194203i
$601$	30.7543	−	17.7560i	1.25449	−	0.724282i	0.282495	−	0.959269i	$-0.408838\pi$
$601$	30.7543	−	17.7560i	1.25449	−	0.724282i	0.971999	+	0.234986i	$0.0755046\pi$
$602$	−1.60315	−	5.98303i	−0.0653395	−	0.243850i
$603$	−2.17757	−	0.583477i	−0.0886773	−	0.0237610i
$604$	19.8012			0.805699
$605$	1.84511	+	17.4621i	0.0750144	+	0.709934i
$606$	0.256072	−	0.147843i	0.0104022	−	0.00600573i
$607$	−10.0181	+	2.68434i	−0.406622	+	0.108954i	−0.456332	−	0.889810i	$-0.650837\pi$
$607$	−10.0181	+	2.68434i	−0.406622	+	0.108954i	0.0497100	+	0.998764i	$0.484170\pi$
$608$	−2.39218	−	0.640982i	−0.0970156	−	0.0259953i
$609$	−4.20492	−	2.42771i	−0.170392	−	0.0983759i
$610$	−24.1193	+	9.27384i	−0.976561	+	0.375487i
$611$	−1.42358	−	0.821904i	−0.0575919	−	0.0332507i
$612$	−1.36237	+	1.36237i	−0.0550705	+	0.0550705i
$613$	−10.3809	+	38.7419i	−0.419279	+	1.56477i	0.356829	+	0.934170i	$0.383858\pi$
$613$	−10.3809	+	38.7419i	−0.419279	+	1.56477i	−0.776108	+	0.630600i	$0.782809\pi$
$614$	5.86726	−	3.38747i	0.236783	−	0.136707i
$615$	1.52706	+	3.97156i	0.0615770	+	0.160149i
$616$		−	1.64107i		−	0.0661205i
$617$	−7.42196	+	27.6991i	−0.298797	+	1.11512i	0.639358	+	0.768909i	$0.279200\pi$
$617$	−7.42196	+	27.6991i	−0.298797	+	1.11512i	−0.938155	+	0.346216i	$0.887466\pi$
$618$	−6.74307	−	6.74307i	−0.271246	−	0.271246i
$619$	3.84607			0.154587			0.0772933	−	0.997008i	$-0.475372\pi$
$619$	3.84607			0.154587			0.0772933	+	0.997008i	$0.475372\pi$
$620$	5.60026	−	11.1192i	0.224912	−	0.446559i
$621$	−0.593252			−0.0238064
$622$	−14.1721	−	14.1721i	−0.568251	−	0.568251i
$623$	−2.24517	+	8.37908i	−0.0899507	+	0.335701i
$624$		−	4.17520i		−	0.167142i
$625$	−2.55817	+	24.8688i	−0.102327	+	0.994751i
$626$	5.77709	−	3.33540i	0.230899	−	0.133310i
$627$	−1.13713	+	4.24384i	−0.0454127	+	0.169483i
$628$	−8.42879	+	8.42879i	−0.336345	+	0.336345i
$629$	−6.25792	−	3.61301i	−0.249520	−	0.144060i
$630$	1.89009	+	0.840271i	0.0753031	+	0.0334772i
$631$	−38.7139	−	22.3515i	−1.54118	−	0.889798i	−0.998765	−	0.0496848i	$-0.984178\pi$
$631$	−38.7139	−	22.3515i	−1.54118	−	0.889798i	−0.542411	−	0.840113i	$-0.682488\pi$
$632$	−1.52558	−	0.408778i	−0.0606844	−	0.0162603i
$633$	−7.88282	+	2.11220i	−0.313314	+	0.0839522i
$634$	−8.79256	+	5.07639i	−0.349197	+	0.201609i
$635$	19.0935	+	15.4441i	0.757703	+	0.612882i
$636$	−14.1719			−0.561952
$637$	24.7795	+	6.63965i	0.981800	+	0.263073i
$638$	2.41006	+	8.99447i	0.0954152	+	0.356094i
$639$	7.11700	−	4.10900i	0.281544	−	0.162550i
$640$	2.08711	−	0.802490i	0.0825001	−	0.0317212i
$641$	−16.3360	−	9.43160i	−0.645234	−	0.372526i	0.141394	−	0.989953i	$-0.454842\pi$
$641$	−16.3360	−	9.43160i	−0.645234	−	0.372526i	−0.786628	+	0.617427i	$0.788175\pi$
$642$	−0.0647831	−	0.241774i	−0.00255679	−	0.00954205i
$643$	7.16702	+	7.16702i	0.282640	+	0.282640i	0.834161	−	0.551521i	$-0.185952\pi$
$643$	7.16702	+	7.16702i	0.282640	+	0.282640i	−0.551521	+	0.834161i	$0.685952\pi$
$644$	0.274392	+	0.475260i	0.0108125	+	0.0187279i
$645$	−8.80746	−	12.1083i	−0.346793	−	0.476765i
$646$	−4.13228	−	2.38577i	−0.162583	−	0.0938671i
$647$	−17.4077	+	17.4077i	−0.684368	+	0.684368i	−0.960981	−	0.276613i	$-0.910788\pi$
$647$	−17.4077	+	17.4077i	−0.684368	+	0.684368i	0.276613	+	0.960981i	$0.410788\pi$
$648$	0.965926	+	0.258819i	0.0379452	+	0.0101674i
$649$	−0.0534990			−0.00210002
$650$	−4.36296	−	20.4150i	−0.171129	−	0.800741i
$651$	−4.33101	−	2.78731i	−0.169746	−	0.109243i
$652$	−4.06550	−	4.06550i	−0.159217	−	0.159217i
$653$	8.86593	−	8.86593i	0.346951	−	0.346951i	−0.512022	−	0.858972i	$-0.671103\pi$
$653$	8.86593	−	8.86593i	0.346951	−	0.346951i	0.858972	+	0.512022i	$0.171103\pi$
$654$	5.20511	+	9.01552i	0.203536	+	0.352535i
$655$	0.00209480	+	0.0198251i	8.18506e−5	+	0.000774632i
$656$	0.951451	−	1.64796i	0.0371479	−	0.0643421i
$657$	−8.95831	−	2.40037i	−0.349497	−	0.0936475i
$658$	−0.351787	−	0.0942610i	−0.0137141	−	0.00367468i
$659$		−	1.43515i		−	0.0559055i	−0.999609	−	0.0279528i	$-0.991101\pi$
$659$		−	1.43515i		−	0.0559055i	0.999609	−	0.0279528i	$-0.00889880\pi$
$660$	−1.42366	−	3.70263i	−0.0554158	−	0.144125i
$661$	19.6213	−	33.9851i	0.763181	−	1.32187i	−0.178022	−	0.984026i	$-0.556970\pi$
$661$	19.6213	−	33.9851i	0.763181	−	1.32187i	0.941203	−	0.337841i	$-0.109697\pi$
$662$	2.07785	+	7.75464i	0.0807579	+	0.301393i
$663$	2.08201	−	7.77017i	0.0808586	−	0.301768i
$664$	6.99197	−	12.1105i	0.271341	−	0.469977i
$665$	−0.798561	+	5.06004i	−0.0309669	+	0.196220i
$666$			3.75050i			0.145329i
$667$	−2.20187	−	2.20187i	−0.0852566	−	0.0852566i
$668$	1.79707	−	6.70677i	0.0695308	−	0.259493i
$669$	1.32859	+	0.767062i	0.0513662	+	0.0296563i
$670$	2.96525	+	4.07657i	0.114558	+	0.157492i
$671$	10.2507	−	17.7548i	0.395725	−	0.685416i
$672$	−0.239418	−	0.893522i	−0.00923576	−	0.0344683i
$673$	19.3762	−	5.19185i	0.746899	−	0.200131i	0.134757	−	0.990879i	$-0.456975\pi$
$673$	19.3762	−	5.19185i	0.746899	−	0.200131i	0.612142	+	0.790748i	$0.290308\pi$
$674$	−18.3889			−0.708313
$675$	4.99343	+	0.256153i	0.192197	+	0.00985933i
$676$	2.21613	+	3.83845i	0.0852358	+	0.147633i
$677$	1.80622	+	6.74089i	0.0694185	+	0.259073i	0.991910	−	0.126944i	$-0.0405170\pi$
$677$	1.80622	+	6.74089i	0.0694185	+	0.259073i	−0.922491	+	0.386018i	$0.873850\pi$
$678$	−7.82124	−	7.82124i	−0.300373	−	0.300373i
$679$	−3.04012	+	1.75521i	−0.116669	+	0.0673588i
$680$	4.28434	−	0.452700i	0.164297	−	0.0173602i
$681$			2.91525i			0.111713i
$682$	2.09341	+	9.65310i	0.0801608	+	0.369636i
$683$	9.75298	−	9.75298i	0.373187	−	0.373187i	−0.495449	−	0.868637i	$-0.664997\pi$
$683$	9.75298	−	9.75298i	0.373187	−	0.373187i	0.868637	+	0.495449i	$0.164997\pi$
$684$			2.47656i			0.0946938i
$685$	−3.48546	+	22.0854i	−0.133173	+	0.843840i
$686$	12.1590			0.464234
$687$	25.4208	−	6.81150i	0.969866	−	0.259875i
$688$	−1.73306	+	6.46785i	−0.0660721	+	0.246585i
$689$	51.2431	−	29.5852i	1.95221	−	1.12711i
$690$	1.03139	+	0.834256i	0.0392642	+	0.0317596i
$691$	12.9099	−	22.3605i	0.491114	−	0.850635i	−0.508833	−	0.860865i	$-0.669923\pi$
$691$	12.9099	−	22.3605i	0.491114	−	0.850635i	0.999948	+	0.0102299i	$0.00325634\pi$
$692$	5.92046	−	1.58638i	0.225062	−	0.0603052i
$693$	−1.58515	+	0.424740i	−0.0602149	+	0.0161345i
$694$	−11.1899	−	19.3815i	−0.424763	−	0.735711i
$695$	3.25248	+	1.44594i	0.123373	+	0.0548476i
$696$	2.62444	+	4.54566i	0.0994790	+	0.172303i
$697$	2.59245	−	2.59245i	0.0981962	−	0.0981962i
$698$	−7.28917	+	7.28917i	−0.275899	+	0.275899i
$699$	−11.1875	−	19.3773i	−0.423150	−	0.732918i
$700$	−2.10436	−	4.11876i	−0.0795374	−	0.155675i
$701$	10.6969	+	18.5276i	0.404016	+	0.699776i	0.994206	−	0.107488i	$-0.0342807\pi$
$701$	10.6969	+	18.5276i	0.404016	+	0.699776i	−0.590191	+	0.807264i	$0.700947\pi$
$702$	−4.03293	+	1.08062i	−0.152213	+	0.0407854i
$703$	−8.97187	+	2.40400i	−0.338380	+	0.0906688i
$704$	−0.887024	+	1.53637i	−0.0334310	+	0.0579042i
$705$	−0.875485	+	0.0925070i	−0.0329727	+	0.00348402i
$706$	−11.6200	+	6.70879i	−0.437323	+	0.252489i
$707$	−0.0707928	+	0.264203i	−0.00266244	+	0.00993636i
$708$	−0.0291289	+	0.00780507i	−0.00109473	+	0.000293332i
$709$	−47.6241			−1.78856			−0.894280	−	0.447508i	$-0.852311\pi$
$709$	−47.6241			−1.78856			−0.894280	+	0.447508i	$0.852311\pi$
$710$	−18.1514	−	2.86460i	−0.681209	−	0.107506i
$711$			1.57940i			0.0592321i
$712$	6.63096	−	6.63096i	0.248506	−	0.248506i
$713$	−2.22029	−	2.44555i	−0.0831504	−	0.0915867i
$714$		−	1.78226i		−	0.0666994i
$715$	12.8773	+	10.4160i	0.481583	+	0.389537i
$716$	−21.4753	+	12.3988i	−0.802570	+	0.463364i
$717$	−9.52960	−	9.52960i	−0.355889	−	0.355889i
$718$	−2.70531	−	10.0963i	−0.100961	−	0.376792i
$719$	23.2407	+	40.2541i	0.866733	+	1.50123i	0.865316	+	0.501226i	$0.167117\pi$
$719$	23.2407	+	40.2541i	0.866733	+	1.50123i	0.00141631	+	0.999999i	$0.499549\pi$
$720$	−1.31533	−	1.80829i	−0.0490194	−	0.0673910i
$721$	8.82132			0.328523
$722$	12.4282	−	3.33013i	0.462530	−	0.123935i
$723$	5.50039	+	20.5278i	0.204562	+	0.763435i
$724$	−2.62901	+	4.55357i	−0.0977063	+	0.169232i
$725$	17.5825	+	19.4839i	0.652997	+	0.723615i
$726$	−6.80068	−	3.92638i	−0.252397	−	0.145721i
$727$	4.52810	−	16.8991i	0.167938	−	0.626753i	−0.829709	−	0.558196i	$-0.811494\pi$
$727$	4.52810	−	16.8991i	0.167938	−	0.626753i	0.997647	−	0.0685572i	$-0.0218396\pi$
$728$	2.73101	+	2.73101i	0.101218	+	0.101218i
$729$		−	1.00000i		−	0.0370370i
$730$	12.1988	+	16.7707i	0.451497	+	0.620710i
$731$	−6.45054	+	11.1727i	−0.238582	+	0.413236i
$732$	2.99100	−	11.1626i	0.110550	−	0.412580i
$733$	4.19466	+	15.6547i	0.154933	+	0.578219i	0.999111	+	0.0421558i	$0.0134226\pi$
$733$	4.19466	+	15.6547i	0.154933	+	0.578219i	−0.844178	+	0.536064i	$0.819911\pi$
$734$	0.733274	−	1.27007i	0.0270656	−	0.0468791i
$735$	12.8238	−	4.93074i	0.473013	−	0.181873i
$736$		−	0.593252i		−	0.0218676i
$737$	−3.86311	−	1.03512i	−0.142299	−	0.0381290i
$738$	−1.83806	−	0.492507i	−0.0676600	−	0.0181294i
$739$	−0.831871	+	1.44084i	−0.0306009	+	0.0530023i	−0.880920	−	0.473265i	$-0.843075\pi$
$739$	−0.831871	+	1.44084i	−0.0306009	+	0.0530023i	0.850319	+	0.526267i	$0.176409\pi$
$740$	5.27411	−	6.52036i	0.193880	−	0.239693i
$741$	−5.17007	−	8.95482i	−0.189927	−	0.328964i
$742$	9.26988	−	9.26988i	0.340308	−	0.340308i
$743$	−32.6565	−	32.6565i	−1.19805	−	1.19805i	−0.974749	−	0.223303i	$-0.928316\pi$
$743$	−32.6565	−	32.6565i	−1.19805	−	1.19805i	−0.223303	−	0.974749i	$-0.571684\pi$
$744$	2.54812	+	4.95046i	0.0934185	+	0.181493i
$745$	19.2477	−	2.03378i	0.705180	−	0.0745120i
$746$	−30.0239			−1.09925
$747$	−13.5075	−	3.61931i	−0.494212	−	0.132424i
$748$	−2.41691	+	2.41691i	−0.0883709	+	0.0883709i
$749$	0.200520	+	0.115770i	0.00732684	+	0.00423015i
$750$	−8.32102	−	7.46730i	−0.303841	−	0.272667i
$751$	−7.17507	−	12.4276i	−0.261822	−	0.453489i	0.704904	−	0.709303i	$-0.250990\pi$
$751$	−7.17507	−	12.4276i	−0.261822	−	0.453489i	−0.966726	+	0.255814i	$0.917657\pi$
$752$	0.278394	+	0.278394i	0.0101520	+	0.0101520i
$753$	−7.10953	−	26.5331i	−0.259086	−	0.966921i
$754$	−18.9790	−	10.9575i	−0.691175	−	0.399050i
$755$	−17.9866	+	40.4588i	−0.654600	+	1.47245i
$756$	−0.801110	+	0.462521i	−0.0291361	+	0.0168217i
$757$	11.4314	+	42.6625i	0.415481	+	1.55060i	0.783871	+	0.620924i	$0.213243\pi$
$757$	11.4314	+	42.6625i	0.415481	+	1.55060i	−0.368390	+	0.929671i	$0.620091\pi$
$758$	−24.2455	−	6.49656i	−0.880636	−	0.235966i
$759$	−1.05246			−0.0382018
$760$	3.48265	−	4.30558i	0.126329	−	0.156180i
$761$	−11.9296	+	6.88754i	−0.432446	+	0.249673i	−0.700388	−	0.713762i	$-0.746990\pi$
$761$	−11.9296	+	6.88754i	−0.432446	+	0.249673i	0.267942	+	0.963435i	$0.413656\pi$
$762$	−10.6083	+	2.84250i	−0.384300	+	0.102973i
$763$	−9.30176	−	2.49240i	−0.336746	−	0.0902309i
$764$	8.67166	+	5.00658i	0.313730	+	0.181132i
$765$	−1.54614	−	4.02119i	−0.0559009	−	0.145386i
$766$	23.9364	+	13.8197i	0.864859	+	0.499327i
$767$	0.0890312	−	0.0890312i	0.00321473	−	0.00321473i
$768$	−0.258819	+	0.965926i	−0.00933933	+	0.0348548i
$769$	−4.35930	+	2.51684i	−0.157200	+	0.0907597i	−0.576537	−	0.817071i	$-0.695596\pi$
$769$	−4.35930	+	2.51684i	−0.157200	+	0.0907597i	0.419336	+	0.907831i	$0.362263\pi$
$770$	3.35312	+	1.49068i	0.120838	+	0.0537204i
$771$			16.2969i			0.586920i
$772$	−2.79242	+	10.4215i	−0.100501	+	0.375077i
$773$	−13.1392	−	13.1392i	−0.472583	−	0.472583i	0.430166	−	0.902750i	$-0.358455\pi$
$773$	−13.1392	−	13.1392i	−0.472583	−	0.472583i	−0.902750	+	0.430166i	$0.858455\pi$
$774$	6.69601			0.240683
$775$	17.6323	+	21.5430i	0.633372	+	0.773847i
$776$	3.79488			0.136228
$777$	−2.45322	−	2.45322i	−0.0880086	−	0.0880086i
$778$	−1.90349	+	7.10393i	−0.0682435	+	0.254688i
$779$		−	4.71266i		−	0.168848i
$780$	8.53098	+	3.79258i	0.305458	+	0.135796i
$781$	12.6259	−	7.28957i	0.451790	−	0.260841i
$782$	0.295832	−	1.10406i	0.0105789	−	0.0394811i
$783$	3.71151	−	3.71151i	0.132639	−	0.132639i
$784$	−5.32112	−	3.07215i	−0.190040	−	0.109720i
$785$	−9.56577	−	24.8785i	−0.341417	−	0.887952i
$786$	−0.00772098	−	0.00445771i	−0.000275398	−	0.000159001i
$787$	1.13569	+	0.304308i	0.0404830	+	0.0108474i	0.279004	−	0.960290i	$-0.409996\pi$
$787$	1.13569	+	0.304308i	0.0404830	+	0.0108474i	−0.238521	+	0.971137i	$0.576662\pi$
$788$	−3.90021	+	1.04506i	−0.138939	+	0.0372286i
$789$	2.83421	−	1.63633i	0.100901	−	0.0582549i
$790$	2.22102	−	2.74583i	0.0790202	−	0.0976923i
$791$	10.2318			0.363801
$792$	1.71360	+	0.459157i	0.0608901	+	0.0163155i
$793$	12.4880	+	46.6058i	0.443462	+	1.65502i
$794$	−14.5398	+	8.39458i	−0.516000	+	0.297913i
$795$	12.8732	−	28.9567i	0.456565	−	1.02699i
$796$	−18.4511	−	10.6527i	−0.653982	−	0.377577i
$797$	−4.30663	−	16.0726i	−0.152549	−	0.569320i	−0.999303	−	0.0373352i	$-0.988113\pi$
$797$	−4.30663	−	16.0726i	−0.152549	−	0.569320i	0.846754	−	0.531985i	$-0.178554\pi$
$798$	−1.61993	−	1.61993i	−0.0573448	−	0.0573448i
$799$	0.379275	+	0.656924i	0.0134178	+	0.0232403i
$800$	−0.256153	+	4.99343i	−0.00905637	+	0.176545i
$801$	−8.12123	−	4.68879i	−0.286949	−	0.165670i
$802$	−7.05146	+	7.05146i	−0.248996	+	0.248996i
$803$	−15.8925	−	4.25838i	−0.560833	−	0.150275i
$804$	−2.25438			−0.0795059
$805$	−1.22032	+	0.128944i	−0.0430107	+	0.00454468i
$806$	−19.5481	−	12.5806i	−0.688553	−	0.443132i
$807$	−6.60503	−	6.60503i	−0.232508	−	0.232508i
$808$	0.209082	−	0.209082i	0.00735548	−	0.00735548i
$809$	−7.51022	−	13.0081i	−0.264045	−	0.457340i	0.703268	−	0.710925i	$-0.251723\pi$
$809$	−7.51022	−	13.0081i	−0.264045	−	0.457340i	−0.967313	+	0.253585i	$0.918390\pi$
$810$	−1.40624	+	1.73853i	−0.0494103	+	0.0610857i
$811$	−10.9162	+	18.9075i	−0.383321	+	0.663932i	−0.991535	−	0.129842i	$-0.958553\pi$
$811$	−10.9162	+	18.9075i	−0.383321	+	0.663932i	0.608214	+	0.793773i	$0.291886\pi$
$812$	−4.68998	−	1.25668i	−0.164586	−	0.0441007i
$813$	9.42731	+	2.52604i	0.330630	+	0.0885921i
$814$			6.65357i			0.233208i
$815$	11.9998	−	4.61391i	0.420334	−	0.161618i
$816$	−0.963341	+	1.66855i	−0.0337237	+	0.0584111i
$817$	4.29202	+	16.0181i	0.150159	+	0.560401i
$818$	−0.991007	+	3.69849i	−0.0346498	+	0.129315i
$819$	1.93111	−	3.34479i	0.0674786	−	0.116876i
$820$	2.50294	+	3.44100i	0.0874065	+	0.120165i
$821$			19.2417i			0.671541i	0.941944	+	0.335770i	$0.108997\pi$
$821$			19.2417i			0.671541i	−0.941944	+	0.335770i	$0.891003\pi$
$822$	−7.07046	−	7.07046i	−0.246611	−	0.246611i
$823$	−11.2256	+	41.8943i	−0.391298	+	1.46034i	0.436697	+	0.899609i	$0.356148\pi$
$823$	−11.2256	+	41.8943i	−0.391298	+	1.46034i	−0.827995	+	0.560736i	$0.810518\pi$
$824$	−8.25854	−	4.76807i	−0.287700	−	0.166104i
$825$	8.85859	+	0.454428i	0.308417	+	0.0158211i
$826$	0.0139480	−	0.0241586i	0.000485313	−	0.000840586i
$827$	−1.36699	−	5.10167i	−0.0475348	−	0.177402i	0.938077	−	0.346427i	$-0.112605\pi$
$827$	−1.36699	−	5.10167i	−0.0475348	−	0.177402i	−0.985612	+	0.169024i	$0.945938\pi$
$828$	−0.573038	+	0.153545i	−0.0199144	+	0.00533606i
$829$	1.16517			0.0404681			0.0202341	−	0.999795i	$-0.493559\pi$
$829$	1.16517			0.0404681			0.0202341	+	0.999795i	$0.493559\pi$
$830$	18.3935	+	25.2870i	0.638447	+	0.877725i
$831$	5.43361	+	9.41128i	0.188490	+	0.326474i
$832$	−1.08062	−	4.03293i	−0.0374638	−	0.139817i
$833$	−8.37080	−	8.37080i	−0.290031	−	0.290031i
$834$	−1.37855	+	0.795906i	−0.0477353	+	0.0275600i
$835$	12.0712	+	9.76403i	0.417742	+	0.337898i
$836$			4.39354i			0.151954i
$837$	4.12228	−	3.74257i	0.142487	−	0.129362i
$838$	16.4150	−	16.4150i	0.567048	−	0.567048i
$839$			42.8846i			1.48054i	0.672308	+	0.740271i	$0.265303\pi$
$839$			42.8846i			1.48054i	−0.672308	+	0.740271i	$0.734697\pi$
$840$	2.04317	+	0.322447i	0.0704960	+	0.0111255i
$841$	−1.44932			−0.0499764
$842$	−36.9392	+	9.89782i	−1.27301	+	0.341101i
$843$	−0.298105	+	1.11254i	−0.0102673	+	0.0383180i
$844$	−7.06754	+	4.08045i	−0.243275	+	0.140455i
$845$	−9.85597	+	1.04142i	−0.339056	+	0.0358259i
$846$	0.196854	−	0.340961i	0.00676798	−	0.0117225i
$847$	7.01660	−	1.88009i	0.241093	−	0.0646008i
$848$	−13.6890	+	3.66795i	−0.470082	+	0.125958i
$849$	−12.2868	−	21.2813i	−0.421681	−	0.730373i
$850$	−2.96674	+	9.16520i	−0.101758	+	0.314364i
$851$	−1.11250	−	1.92690i	−0.0381359	−	0.0660534i
$852$	5.81101	−	5.81101i	0.199082	−	0.199082i
$853$	−31.5604	+	31.5604i	−1.08061	+	1.08061i	−0.0841548	+	0.996453i	$0.526819\pi$
$853$	−31.5604	+	31.5604i	−1.08061	+	1.08061i	−0.996453	+	0.0841548i	$0.973181\pi$
$854$	5.34504	+	9.25788i	0.182903	+	0.316798i
$855$	−5.06025	−	2.24961i	−0.173057	−	0.0769351i
$856$	−0.125151	−	0.216769i	−0.00427759	−	0.00740900i
$857$	25.4975	−	6.83202i	0.870977	−	0.233377i	0.204467	−	0.978874i	$-0.434454\pi$
$857$	25.4975	−	6.83202i	0.870977	−	0.233377i	0.666510	+	0.745496i	$0.267787\pi$
$858$	−7.15461	+	1.91707i	−0.244254	+	0.0654478i
$859$	4.62014	−	8.00231i	0.157637	−	0.273035i	−0.776379	−	0.630266i	$-0.782946\pi$
$859$	4.62014	−	8.00231i	0.157637	−	0.273035i	0.934016	+	0.357231i	$0.116279\pi$
$860$	−11.6412	−	9.41621i	−0.396962	−	0.321090i
$861$	1.52443	−	0.880131i	0.0519525	−	0.0299948i
$862$	−8.36405	+	31.2151i	−0.284881	+	1.06319i
$863$	−22.1981	+	5.94797i	−0.755633	+	0.202471i	−0.616015	−	0.787734i	$-0.711254\pi$
$863$	−22.1981	+	5.94797i	−0.755633	+	0.202471i	−0.139618	+	0.990205i	$0.544587\pi$
$864$	1.00000			0.0340207
$865$	−2.13653	+	13.5380i	−0.0726442	+	0.460306i
$866$		−	9.60062i		−	0.326243i
$867$	9.39596	−	9.39596i	0.319104	−	0.319104i
$868$	−4.90485	−	1.57138i	−0.166481	−	0.0533362i
$869$			2.80193i			0.0950489i
$870$	−11.6719	+	1.23329i	−0.395713	+	0.0418126i
$871$	8.15145	−	4.70624i	0.276201	−	0.159465i
$872$	7.36114	+	7.36114i	0.249280	+	0.249280i
$873$	−0.982188	−	3.66557i	−0.0332420	−	0.124061i
$874$	−0.734614	−	1.27239i	−0.0248487	−	0.0430392i
$875$	10.3272	−	0.558420i	0.349123	−	0.0188780i
$876$	−9.27433			−0.313350
$877$	−46.6522	+	12.5004i	−1.57533	+	0.422109i	−0.937477	−	0.348046i	$-0.886845\pi$
$877$	−46.6522	+	12.5004i	−1.57533	+	0.422109i	−0.637856	+	0.770156i	$0.720179\pi$
$878$	−3.55662	−	13.2735i	−0.120030	−	0.447959i
$879$	−1.77960	+	3.08235i	−0.0600243	+	0.103965i
$880$	−2.33346	−	3.20799i	−0.0786608	−	0.108141i
$881$	−31.6077	−	18.2487i	−1.06489	−	0.614814i	−0.138108	−	0.990417i	$-0.544102\pi$
$881$	−31.6077	−	18.2487i	−1.06489	−	0.614814i	−0.926781	+	0.375603i	$0.877436\pi$
$882$	−1.59026	+	5.93494i	−0.0535469	+	0.199840i
$883$	17.5233	+	17.5233i	0.589707	+	0.589707i	0.937552	−	0.347845i	$-0.113087\pi$
$883$	17.5233	+	17.5233i	0.589707	+	0.589707i	−0.347845	+	0.937552i	$0.613087\pi$
$884$		−	8.04427i		−	0.270558i
$885$	0.0105118	−	0.0666075i	0.000353351	−	0.00223899i
$886$	1.95323	−	3.38310i	0.0656201	−	0.113657i
$887$	7.04260	−	26.2833i	0.236467	−	0.882508i	−0.741015	−	0.671489i	$-0.765655\pi$
$887$	7.04260	−	26.2833i	0.236467	−	0.882508i	0.977482	−	0.211019i	$-0.0676782\pi$
$888$	0.970702	+	3.62271i	0.0325746	+	0.121570i
$889$	5.07967	−	8.79824i	0.170367	−	0.295083i
$890$	7.52542	+	19.5720i	0.252253	+	0.656055i
$891$		−	1.77405i		−	0.0594329i
$892$	1.48185	+	0.397060i	0.0496160	+	0.0132946i
$893$	0.941820	+	0.252360i	0.0315168	+	0.00844490i
$894$	−4.32787	+	7.49609i	−0.144746	+	0.250707i
$895$	−5.82652	−	55.1421i	−0.194759	−	1.84320i
$896$	−0.462521	−	0.801110i	−0.0154517	−	0.0267632i
$897$	1.75146	−	1.75146i	0.0584797	−	0.0584797i
$898$	−17.5916	−	17.5916i	−0.587041	−	0.587041i
$899$	29.1905	+	1.40931i	0.973558	+	0.0470030i
$900$	4.88958	−	1.04497i	0.162986	−	0.0348324i
$901$	−27.3047			−0.909652
$902$	−3.26081	−	0.873731i	−0.108573	−	0.0290921i
$903$	−4.37988	+	4.37988i	−0.145753	+	0.145753i
$904$	−9.57902	−	5.53045i	−0.318594	−	0.183940i
$905$	−6.91602	−	9.50801i	−0.229896	−	0.316057i
$906$	−9.90059	−	17.1483i	−0.328925	−	0.569715i
$907$	−7.98883	−	7.98883i	−0.265265	−	0.265265i	0.561924	−	0.827189i	$-0.310061\pi$
$907$	−7.98883	−	7.98883i	−0.265265	−	0.265265i	−0.827189	+	0.561924i	$0.810061\pi$
$908$	0.754521	+	2.81591i	0.0250397	+	0.0934493i
$909$	−0.256072	−	0.147843i	−0.00849338	−	0.00490366i
$910$	−8.06088	+	3.09940i	−0.267216	+	0.102744i
$911$	27.0826	−	15.6362i	0.897287	−	0.518049i	0.0209682	−	0.999780i	$-0.493325\pi$
$911$	27.0826	−	15.6362i	0.897287	−	0.518049i	0.876319	+	0.481731i	$0.159992\pi$
$912$	0.640982	+	2.39218i	0.0212250	+	0.0792129i
$913$	−23.9629	−	6.42083i	−0.793055	−	0.212499i
$914$	−18.4930			−0.611694
$915$	20.0910	+	16.2510i	0.664188	+	0.537241i
$916$	22.7917	−	13.1588i	0.753059	−	0.434779i
$917$	0.00796612	−	0.00213452i	0.000263065	−	7.04879e-5i
$918$	1.86103	+	0.498662i	0.0614232	+	0.0164583i
$919$	−40.5224	−	23.3956i	−1.33671	−	0.771751i	−0.350394	−	0.936603i	$-0.613952\pi$
$919$	−40.5224	−	23.3956i	−1.33671	−	0.771751i	−0.986318	+	0.164852i	$0.947285\pi$
$920$	1.21216	+	0.538887i	0.0399639	+	0.0177666i
$921$	−5.86726	−	3.38747i	−0.193333	−	0.111621i
$922$	24.9073	−	24.9073i	0.820278	−	0.820278i
$923$	−8.88054	+	33.1426i	−0.292307	+	1.09090i
$924$	−1.42121	+	0.820534i	−0.0467543	+	0.0269936i
$925$	8.53195	+	16.6992i	0.280529	+	0.549066i
$926$		−	7.85670i		−	0.258187i
$927$	−2.46813	+	9.21120i	−0.0810642	+	0.302536i
$928$	3.71151	+	3.71151i	0.121836	+	0.121836i
$929$	−21.9107			−0.718866			−0.359433	−	0.933171i	$-0.617030\pi$
$929$	−21.9107			−0.718866			−0.359433	+	0.933171i	$0.617030\pi$
$930$	−12.4297	+	0.709646i	−0.407585	+	0.0232702i
$931$	−15.2167			−0.498709
$932$	−15.8215	−	15.8215i	−0.518251	−	0.518251i
$933$	−5.18736	+	19.3595i	−0.169827	+	0.633801i
$934$		−	40.6336i		−	1.32957i
$935$	−2.74293	−	7.13378i	−0.0897035	−	0.233300i
$936$	−3.61583	+	2.08760i	−0.118187	+	0.0682353i
$937$	−11.2136	+	41.8498i	−0.366333	+	1.36717i	0.499272	+	0.866445i	$0.333601\pi$
$937$	−11.2136	+	41.8498i	−0.366333	+	1.36717i	−0.865605	+	0.500727i	$0.833066\pi$
$938$	1.47460	−	1.47460i	0.0481473	−	0.0481473i
$939$	−5.77709	−	3.33540i	−0.188528	−	0.108847i
$940$	−0.821711	+	0.315947i	−0.0268012	+	0.0103051i
$941$	4.57809	+	2.64316i	0.149242	+	0.0861647i	0.572761	−	0.819722i	$-0.305872\pi$
$941$	4.57809	+	2.64316i	0.149242	+	0.0861647i	−0.423520	+	0.905887i	$0.639206\pi$
$942$	11.5139	+	3.08515i	0.375144	+	0.100520i
$943$	1.09043	−	0.292181i	0.0355094	−	0.00951472i
$944$	−0.0261163	+	0.0150782i	−0.000850012	+	0.000490755i
$945$	−0.217351	−	2.05700i	−0.00707043	−	0.0669144i
$946$	11.8791			0.386221
$947$	−26.4896	−	7.09786i	−0.860795	−	0.230649i	−0.198692	−	0.980062i	$-0.563669\pi$
$947$	−26.4896	−	7.09786i	−0.860795	−	0.230649i	−0.662103	+	0.749413i	$0.730336\pi$
$948$	0.408778	+	1.52558i	0.0132765	+	0.0495486i
$949$	33.5344	−	19.3611i	1.08857	−	0.628487i
$950$	5.63389	+	11.0269i	0.182788	+	0.357761i
$951$	8.79256	+	5.07639i	0.285118	+	0.164613i
$952$	−0.461283	−	1.72153i	−0.0149503	−	0.0557951i
$953$	16.3611	+	16.3611i	0.529986	+	0.529986i	0.920568	−	0.390582i	$-0.127726\pi$
$953$	16.3611	+	16.3611i	0.529986	+	0.529986i	−0.390582	+	0.920568i	$0.627726\pi$
$954$	7.08594	+	12.2732i	0.229416	+	0.397360i
$955$	−18.1067	+	13.1706i	−0.585919	+	0.426191i
$956$	−11.6713	−	6.73844i	−0.377478	−	0.217937i
$957$	6.58441	−	6.58441i	0.212844	−	0.212844i
$958$	16.5826	+	4.44329i	0.535758	+	0.143556i
$959$	9.24962			0.298686
$960$	−1.73853	−	1.40624i	−0.0561108	−	0.0453862i
$961$	30.8558	+	2.98638i	0.995349	+	0.0963347i
$962$	−11.0726	−	11.0726i	−0.356996	−	0.356996i
$963$	−0.176991	+	0.176991i	−0.00570345	+	0.00570345i
$964$	10.6259	+	18.4047i	0.342239	+	0.592775i
$965$	−18.7572	−	15.1721i	−0.603814	−	0.488406i
$966$	0.274392	−	0.475260i	0.00882840	−	0.0152912i
$967$	−9.65305	−	2.58653i	−0.310421	−	0.0831771i	0.100245	−	0.994963i	$-0.468037\pi$
$967$	−9.65305	−	2.58653i	−0.310421	−	0.0831771i	−0.410666	+	0.911786i	$0.634704\pi$
$968$	−7.58518	−	2.03244i	−0.243797	−	0.0653252i
$969$			4.77155i			0.153284i
$970$	−3.44712	+	7.75390i	−0.110680	+	0.248963i
$971$	22.2342	−	38.5107i	0.713528	−	1.23587i	−0.249996	−	0.968247i	$-0.580429\pi$
$971$	22.2342	−	38.5107i	0.713528	−	1.23587i	0.963525	−	0.267620i	$-0.0862372\pi$
$972$	−0.258819	−	0.965926i	−0.00830162	−	0.0309821i
$973$	0.381109	−	1.42232i	0.0122178	−	0.0455975i
$974$	−18.6004	+	32.2169i	−0.595996	+	1.03230i
$975$	−15.4984	+	13.9859i	−0.496346	+	0.447908i
$976$		−	11.5563i		−	0.369909i
$977$	−1.05906	−	1.05906i	−0.0338824	−	0.0338824i	0.689963	−	0.723845i	$-0.257627\pi$
$977$	−1.05906	−	1.05906i	−0.0338824	−	0.0338824i	−0.723845	+	0.689963i	$0.757627\pi$
$978$	−1.48808	+	5.55358i	−0.0475835	+	0.177584i
$979$	−14.4075	−	8.31815i	−0.460464	−	0.265849i
$980$	11.1107	−	8.08177i	0.354917	−	0.258163i
$981$	5.20511	−	9.01552i	0.166187	−	0.287843i
$982$	−10.6674	−	39.8114i	−0.340412	−	1.27043i
$983$	−13.8599	+	3.71374i	−0.442061	+	0.118450i	−0.472982	−	0.881072i	$-0.656823\pi$
$983$	−13.8599	+	3.71374i	−0.442061	+	0.118450i	0.0309212	+	0.999522i	$0.490156\pi$
$984$	−1.90290			−0.0606623
$985$	1.40748	−	8.91840i	0.0448459	−	0.284164i
$986$	5.05645	+	8.75803i	0.161030	+	0.278913i
$987$	0.0942610	+	0.351787i	0.00300036	+	0.0111975i
$988$	−7.31158	−	7.31158i	−0.232612	−	0.232612i
$989$	−3.44022	+	1.98621i	−0.109393	+	0.0631579i
$990$	−2.49474	+	3.08424i	−0.0792880	+	0.0980234i
$991$			23.8131i			0.756447i	0.925714	+	0.378223i	$0.123465\pi$
$991$			23.8131i			0.756447i	−0.925714	+	0.378223i	$0.876535\pi$
$992$	3.74257	+	4.12228i	0.118827	+	0.130883i
$993$	5.67679	−	5.67679i	0.180147	−	0.180147i
$994$			7.60199i			0.241121i
$995$	38.5265	−	28.0237i	1.22137	−	0.888412i
$996$	−13.9839			−0.443098
$997$	39.0093	−	10.4525i	1.23544	−	0.331034i	0.418742	−	0.908105i	$-0.362471\pi$
$997$	39.0093	−	10.4525i	1.23544	−	0.331034i	0.816694	+	0.577071i	$0.195804\pi$
$998$	−4.98560	+	18.6065i	−0.157816	+	0.588978i
$999$	3.24803	−	1.87525i	0.102763	−	0.0593303i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.be.a.37.1	✓	64
5.3	odd	4		930.2.be.b.223.7	yes	64
31.26	odd	6		930.2.be.b.367.7	yes	64
155.88	even	12	inner	930.2.be.a.553.1	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.be.a.37.1	✓	64	1.1	even	1	trivial
930.2.be.a.553.1	yes	64	155.88	even	12	inner
930.2.be.b.223.7	yes	64	5.3	odd	4
930.2.be.b.367.7	yes	64	31.26	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.be (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.258819 + 0.965926i) q^{3} +1.00000i q^{4} +(-2.04325 - 0.908360i) q^{5} +(0.866025 - 0.500000i) q^{6} +(-0.239418 + 0.893522i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.258819 + 0.965926i) q^{3} +1.00000i q^{4} +(-2.04325 - 0.908360i) q^{5} +(0.866025 - 0.500000i) q^{6} +(-0.239418 + 0.893522i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(0.802490 + 2.08711i) q^{10} +(-1.53637 - 0.887024i) q^{11} +(-0.965926 - 0.258819i) q^{12} +(4.03293 - 1.08062i) q^{13} +(0.801110 - 0.462521i) q^{14} +(1.40624 - 1.73853i) q^{15} -1.00000 q^{16} +(-1.86103 - 0.498662i) q^{17} +(0.258819 + 0.965926i) q^{18} +(-2.14477 + 1.23828i) q^{19} +(0.908360 - 2.04325i) q^{20} +(-0.801110 - 0.462521i) q^{21} +(0.459157 + 1.71360i) q^{22} +(-0.419493 - 0.419493i) q^{23} +(0.500000 + 0.866025i) q^{24} +(3.34976 + 3.71202i) q^{25} +(-3.61583 - 2.08760i) q^{26} +(0.707107 - 0.707107i) q^{27} +(-0.893522 - 0.239418i) q^{28} +5.24887 q^{29} +(-2.22369 + 0.234963i) q^{30} +(5.56129 + 0.268497i) q^{31} +(0.707107 + 0.707107i) q^{32} +(1.25444 - 1.25444i) q^{33} +(0.963341 + 1.66855i) q^{34} +(1.30083 - 1.60821i) q^{35} +(0.500000 - 0.866025i) q^{36} +(3.62271 + 0.970702i) q^{37} +(2.39218 + 0.640982i) q^{38} +4.17520i q^{39} +(-2.08711 + 0.802490i) q^{40} +(-0.951451 + 1.64796i) q^{41} +(0.239418 + 0.893522i) q^{42} +(1.73306 - 6.46785i) q^{43} +(0.887024 - 1.53637i) q^{44} +(1.31533 + 1.80829i) q^{45} +0.593252i q^{46} +(-0.278394 - 0.278394i) q^{47} +(0.258819 - 0.965926i) q^{48} +(5.32112 + 3.07215i) q^{49} +(0.256153 - 4.99343i) q^{50} +(0.963341 - 1.66855i) q^{51} +(1.08062 + 4.03293i) q^{52} +(13.6890 - 3.66795i) q^{53} -1.00000 q^{54} +(2.33346 + 3.20799i) q^{55} +(0.462521 + 0.801110i) q^{56} +(-0.640982 - 2.39218i) q^{57} +(-3.71151 - 3.71151i) q^{58} +(0.0261163 - 0.0150782i) q^{59} +(1.73853 + 1.40624i) q^{60} +11.5563i q^{61} +(-3.74257 - 4.12228i) q^{62} +(0.654103 - 0.654103i) q^{63} -1.00000i q^{64} +(-9.22189 - 1.45537i) q^{65} -1.77405 q^{66} +(2.17757 - 0.583477i) q^{67} +(0.498662 - 1.86103i) q^{68} +(0.513772 - 0.296626i) q^{69} +(-2.05700 + 0.217351i) q^{70} +(-4.10900 + 7.11700i) q^{71} +(-0.965926 + 0.258819i) q^{72} +(8.95831 - 2.40037i) q^{73} +(-1.87525 - 3.24803i) q^{74} +(-4.45252 + 2.27488i) q^{75} +(-1.23828 - 2.14477i) q^{76} +(1.16041 - 1.16041i) q^{77} +(2.95231 - 2.95231i) q^{78} +(-0.789699 - 1.36780i) q^{79} +(2.04325 + 0.908360i) q^{80} +(0.500000 + 0.866025i) q^{81} +(1.83806 - 0.492507i) q^{82} +(13.5075 - 3.61931i) q^{83} +(0.462521 - 0.801110i) q^{84} +(3.34959 + 2.70938i) q^{85} +(-5.79892 + 3.34801i) q^{86} +(-1.35851 + 5.07002i) q^{87} +(-1.71360 + 0.459157i) q^{88} +9.37759 q^{89} +(0.348576 - 2.20873i) q^{90} +3.86223i q^{91} +(0.419493 - 0.419493i) q^{92} +(-1.69871 + 5.30230i) q^{93} +0.393708i q^{94} +(5.50711 - 0.581902i) q^{95} +(-0.866025 + 0.500000i) q^{96} +(2.68339 + 2.68339i) q^{97} +(-1.59026 - 5.93494i) q^{98} +(0.887024 + 1.53637i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 8 q^{7}+O(q^{10}) \) 64 * q - 8 * q^7	\( 64 q - 8 q^{7} - 4 q^{10} + 24 q^{14} + 8 q^{15} - 64 q^{16} + 4 q^{17} - 12 q^{20} - 24 q^{21} - 8 q^{22} + 32 q^{24} - 20 q^{25} - 4 q^{28} + 16 q^{29} + 8 q^{31} + 4 q^{33} + 24 q^{35} + 32 q^{36} + 56 q^{37} - 4 q^{38} - 8 q^{41} + 8 q^{42} - 56 q^{43} - 4 q^{44} + 12 q^{45} + 8 q^{47} - 60 q^{49} - 8 q^{50} + 24 q^{53} - 64 q^{54} + 16 q^{55} - 28 q^{57} + 52 q^{58} + 24 q^{59} - 4 q^{62} - 4 q^{63} + 100 q^{65} + 8 q^{66} + 76 q^{67} + 4 q^{68} - 12 q^{69} - 44 q^{70} + 8 q^{71} - 52 q^{73} + 12 q^{74} - 8 q^{75} - 8 q^{76} - 104 q^{77} + 56 q^{79} + 32 q^{81} + 32 q^{82} + 24 q^{83} + 32 q^{85} - 24 q^{86} - 20 q^{87} + 4 q^{88} - 176 q^{89} + 8 q^{93} + 64 q^{95} - 68 q^{97} - 64 q^{98} - 4 q^{99}+O(q^{100}) \) 64 * q - 8 * q^7 - 4 * q^10 + 24 * q^14 + 8 * q^15 - 64 * q^16 + 4 * q^17 - 12 * q^20 - 24 * q^21 - 8 * q^22 + 32 * q^24 - 20 * q^25 - 4 * q^28 + 16 * q^29 + 8 * q^31 + 4 * q^33 + 24 * q^35 + 32 * q^36 + 56 * q^37 - 4 * q^38 - 8 * q^41 + 8 * q^42 - 56 * q^43 - 4 * q^44 + 12 * q^45 + 8 * q^47 - 60 * q^49 - 8 * q^50 + 24 * q^53 - 64 * q^54 + 16 * q^55 - 28 * q^57 + 52 * q^58 + 24 * q^59 - 4 * q^62 - 4 * q^63 + 100 * q^65 + 8 * q^66 + 76 * q^67 + 4 * q^68 - 12 * q^69 - 44 * q^70 + 8 * q^71 - 52 * q^73 + 12 * q^74 - 8 * q^75 - 8 * q^76 - 104 * q^77 + 56 * q^79 + 32 * q^81 + 32 * q^82 + 24 * q^83 + 32 * q^85 - 24 * q^86 - 20 * q^87 + 4 * q^88 - 176 * q^89 + 8 * q^93 + 64 * q^95 - 68 * q^97 - 64 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more