LMFDB - Embedded newform 546.2.by.b.397.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 10, 5]))

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

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

chi := DirichletCharacter("546.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			397.10
Character	$\chi$	$=$	546.397
Dual form			546.2.by.b.535.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 - 0.965926i) q^{2} +1.00000i q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.711118 + 2.65393i) q^{5} +(0.965926 + 0.258819i) q^{6} +(2.33866 - 1.23721i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(0.258819 - 0.965926i) q^{2} +1.00000i q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.711118 + 2.65393i) q^{5} +(0.965926 + 0.258819i) q^{6} +(2.33866 - 1.23721i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.00000 q^{9} +2.74755 q^{10} +(-1.56804 + 1.56804i) q^{11} +(0.500000 - 0.866025i) q^{12} +(0.354780 + 3.58805i) q^{13} +(-0.589766 - 2.57918i) q^{14} +(-2.65393 + 0.711118i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-0.838134 + 1.45169i) q^{17} +(-0.258819 + 0.965926i) q^{18} +(0.129680 - 0.129680i) q^{19} +(0.711118 - 2.65393i) q^{20} +(1.23721 + 2.33866i) q^{21} +(1.10877 + 1.92045i) q^{22} +(0.472973 - 0.273071i) q^{23} +(-0.707107 - 0.707107i) q^{24} +(-2.20753 + 1.27452i) q^{25} +(3.55762 + 0.585966i) q^{26} -1.00000i q^{27} +(-2.64394 - 0.0978714i) q^{28} +(-2.18139 + 3.77828i) q^{29} +2.74755i q^{30} +(7.55600 + 2.02462i) q^{31} +(0.965926 - 0.258819i) q^{32} +(-1.56804 - 1.56804i) q^{33} +(1.18530 + 1.18530i) q^{34} +(4.94653 + 5.32682i) q^{35} +(0.866025 + 0.500000i) q^{36} +(-1.24303 - 0.333069i) q^{37} +(-0.0916976 - 0.158825i) q^{38} +(-3.58805 + 0.354780i) q^{39} +(-2.37945 - 1.37378i) q^{40} +(1.32782 + 4.95550i) q^{41} +(2.57918 - 0.589766i) q^{42} +(-2.86766 + 1.65565i) q^{43} +(2.14199 - 0.573943i) q^{44} +(-0.711118 - 2.65393i) q^{45} +(-0.141352 - 0.527533i) q^{46} +(9.74801 - 2.61197i) q^{47} +(-0.866025 + 0.500000i) q^{48} +(3.93862 - 5.78682i) q^{49} +(0.659739 + 2.46218i) q^{50} +(-1.45169 - 0.838134i) q^{51} +(1.48678 - 3.28474i) q^{52} +(1.78093 + 3.08467i) q^{53} +(-0.965926 - 0.258819i) q^{54} +(-5.27654 - 3.04641i) q^{55} +(-0.778839 + 2.52852i) q^{56} +(0.129680 + 0.129680i) q^{57} +(3.08495 + 3.08495i) q^{58} +(-1.43669 + 0.384959i) q^{59} +(2.65393 + 0.711118i) q^{60} -13.6609i q^{61} +(3.91127 - 6.77452i) q^{62} +(-2.33866 + 1.23721i) q^{63} -1.00000i q^{64} +(-9.27015 + 3.49309i) q^{65} +(-1.92045 + 1.10877i) q^{66} +(-4.98405 - 4.98405i) q^{67} +(1.45169 - 0.838134i) q^{68} +(0.273071 + 0.472973i) q^{69} +(6.42557 - 3.39930i) q^{70} +(1.04867 - 3.91368i) q^{71} +(0.707107 - 0.707107i) q^{72} +(2.29736 - 8.57385i) q^{73} +(-0.643441 + 1.11447i) q^{74} +(-1.27452 - 2.20753i) q^{75} +(-0.177146 + 0.0474662i) q^{76} +(-1.72711 + 5.60711i) q^{77} +(-0.585966 + 3.55762i) q^{78} +(4.42139 - 7.65808i) q^{79} +(-1.94281 + 1.94281i) q^{80} +1.00000 q^{81} +5.13031 q^{82} +(-11.3594 + 11.3594i) q^{83} +(0.0978714 - 2.64394i) q^{84} +(-4.44870 - 1.19203i) q^{85} +(0.857026 + 3.19846i) q^{86} +(-3.77828 - 2.18139i) q^{87} -2.21755i q^{88} +(4.16412 - 15.5407i) q^{89} -2.74755 q^{90} +(5.26889 + 7.95228i) q^{91} -0.546143 q^{92} +(-2.02462 + 7.55600i) q^{93} -10.0919i q^{94} +(0.436380 + 0.251944i) q^{95} +(0.258819 + 0.965926i) q^{96} +(-15.6069 - 4.18186i) q^{97} +(-4.57025 - 5.30215i) q^{98} +(1.56804 - 1.56804i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{7} - 40 q^{9}+O(q^{10}) $ 40 * q - 4 * q^7 - 40 * q^9	$ 40 q - 4 q^{7} - 40 q^{9} - 4 q^{11} + 20 q^{12} + 4 q^{14} + 20 q^{16} + 8 q^{17} + 8 q^{19} - 8 q^{21} - 4 q^{22} + 24 q^{23} + 24 q^{25} - 8 q^{26} + 4 q^{28} - 12 q^{29} + 24 q^{31} - 4 q^{33} + 8 q^{34} + 28 q^{35} - 8 q^{37} - 8 q^{38} - 16 q^{39} - 20 q^{41} - 12 q^{42} - 24 q^{43} + 8 q^{44} - 4 q^{46} - 16 q^{47} + 4 q^{49} - 16 q^{50} - 24 q^{51} - 4 q^{52} - 4 q^{53} - 24 q^{55} + 12 q^{56} + 8 q^{57} + 24 q^{58} - 12 q^{59} - 32 q^{62} + 4 q^{63} - 4 q^{65} - 24 q^{67} + 24 q^{68} + 8 q^{69} + 52 q^{70} - 28 q^{71} + 108 q^{73} + 20 q^{74} - 36 q^{75} - 4 q^{76} + 12 q^{77} + 4 q^{78} + 40 q^{81} - 48 q^{82} - 60 q^{83} - 8 q^{84} - 4 q^{85} - 20 q^{86} - 36 q^{87} - 60 q^{89} - 40 q^{91} - 16 q^{92} - 48 q^{95} + 48 q^{97} - 8 q^{98} + 4 q^{99}+O(q^{100}) $ 40 * q - 4 * q^7 - 40 * q^9 - 4 * q^11 + 20 * q^12 + 4 * q^14 + 20 * q^16 + 8 * q^17 + 8 * q^19 - 8 * q^21 - 4 * q^22 + 24 * q^23 + 24 * q^25 - 8 * q^26 + 4 * q^28 - 12 * q^29 + 24 * q^31 - 4 * q^33 + 8 * q^34 + 28 * q^35 - 8 * q^37 - 8 * q^38 - 16 * q^39 - 20 * q^41 - 12 * q^42 - 24 * q^43 + 8 * q^44 - 4 * q^46 - 16 * q^47 + 4 * q^49 - 16 * q^50 - 24 * q^51 - 4 * q^52 - 4 * q^53 - 24 * q^55 + 12 * q^56 + 8 * q^57 + 24 * q^58 - 12 * q^59 - 32 * q^62 + 4 * q^63 - 4 * q^65 - 24 * q^67 + 24 * q^68 + 8 * q^69 + 52 * q^70 - 28 * q^71 + 108 * q^73 + 20 * q^74 - 36 * q^75 - 4 * q^76 + 12 * q^77 + 4 * q^78 + 40 * q^81 - 48 * q^82 - 60 * q^83 - 8 * q^84 - 4 * q^85 - 20 * q^86 - 36 * q^87 - 60 * q^89 - 40 * q^91 - 16 * q^92 - 48 * q^95 + 48 * q^97 - 8 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	0.711118	+	2.65393i	0.318022	+	1.18687i	0.921143	+	0.389224i	$0.127257\pi$
$5$	0.711118	+	2.65393i	0.318022	+	1.18687i	−0.603121	+	0.797650i	$0.706077\pi$
$6$	0.965926	+	0.258819i	0.394338	+	0.105662i
$7$	2.33866	−	1.23721i	0.883929	−	0.467622i
$7$	2.33866	−	1.23721i	0.883929	−	0.467622i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−1.00000			−0.333333
$10$	2.74755			0.868852
$11$	−1.56804	+	1.56804i	−0.472783	+	0.472783i	−0.902814	−	0.430031i	$-0.858502\pi$
$11$	−1.56804	+	1.56804i	−0.472783	+	0.472783i	0.430031	+	0.902814i	$0.358502\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	0.354780	+	3.58805i	0.0983982	+	0.995147i
$13$	0.354780	+	3.58805i	0.0983982	+	0.995147i
$14$	−0.589766	−	2.57918i	−0.157621	−	0.689315i
$15$	−2.65393	+	0.711118i	−0.685242	+	0.183610i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−0.838134	+	1.45169i	−0.203277	+	0.352087i	−0.949583	−	0.313517i	$-0.898493\pi$
$17$	−0.838134	+	1.45169i	−0.203277	+	0.352087i	0.746305	+	0.665604i	$0.231826\pi$
$18$	−0.258819	+	0.965926i	−0.0610042	+	0.227671i
$19$	0.129680	−	0.129680i	0.0297506	−	0.0297506i	−0.692075	−	0.721826i	$-0.743303\pi$
$19$	0.129680	−	0.129680i	0.0297506	−	0.0297506i	0.721826	+	0.692075i	$0.243303\pi$
$20$	0.711118	−	2.65393i	0.159011	−	0.593437i
$21$	1.23721	+	2.33866i	0.269982	+	0.510336i
$22$	1.10877	+	1.92045i	0.236391	+	0.409442i
$23$	0.472973	−	0.273071i	0.0986218	−	0.0569393i	−0.449878	−	0.893090i	$-0.648533\pi$
$23$	0.472973	−	0.273071i	0.0986218	−	0.0569393i	0.548500	+	0.836151i	$0.315199\pi$
$24$	−0.707107	−	0.707107i	−0.144338	−	0.144338i
$25$	−2.20753	+	1.27452i	−0.441506	+	0.254903i
$26$	3.55762	+	0.585966i	0.697706	+	0.114917i
$27$		−	1.00000i		−	0.192450i
$28$	−2.64394	−	0.0978714i	−0.499658	−	0.0184960i
$29$	−2.18139	+	3.77828i	−0.405074	+	0.701609i	−0.994330	−	0.106337i	$-0.966088\pi$
$29$	−2.18139	+	3.77828i	−0.405074	+	0.701609i	0.589256	+	0.807946i	$0.299421\pi$
$30$			2.74755i			0.501632i
$31$	7.55600	+	2.02462i	1.35710	+	0.363633i	0.862750	−	0.505631i	$-0.168740\pi$
$31$	7.55600	+	2.02462i	1.35710	+	0.363633i	0.494347	+	0.869264i	$0.335407\pi$
$32$	0.965926	−	0.258819i	0.170753	−	0.0457532i
$33$	−1.56804	−	1.56804i	−0.272961	−	0.272961i
$34$	1.18530	+	1.18530i	0.203277	+	0.203277i
$35$	4.94653	+	5.32682i	0.836117	+	0.900398i
$36$	0.866025	+	0.500000i	0.144338	+	0.0833333i
$37$	−1.24303	−	0.333069i	−0.204353	−	0.0547563i	0.155190	−	0.987885i	$-0.450401\pi$
$37$	−1.24303	−	0.333069i	−0.204353	−	0.0547563i	−0.359544	+	0.933128i	$0.617068\pi$
$38$	−0.0916976	−	0.158825i	−0.0148753	−	0.0257648i
$39$	−3.58805	+	0.354780i	−0.574548	+	0.0568102i
$40$	−2.37945	−	1.37378i	−0.376224	−	0.217213i
$41$	1.32782	+	4.95550i	0.207371	+	0.773919i	0.988714	+	0.149817i	$0.0478685\pi$
$41$	1.32782	+	4.95550i	0.207371	+	0.773919i	−0.781343	+	0.624102i	$0.785465\pi$
$42$	2.57918	−	0.589766i	0.397976	−	0.0910028i
$43$	−2.86766	+	1.65565i	−0.437315	+	0.252484i	−0.702458	−	0.711725i	$-0.747914\pi$
$43$	−2.86766	+	1.65565i	−0.437315	+	0.252484i	0.265143	+	0.964209i	$0.414581\pi$
$44$	2.14199	−	0.573943i	0.322917	−	0.0865252i
$45$	−0.711118	−	2.65393i	−0.106007	−	0.395625i
$46$	−0.141352	−	0.527533i	−0.0208412	−	0.0777806i
$47$	9.74801	−	2.61197i	1.42189	−	0.380995i	0.535738	−	0.844384i	$-0.320033\pi$
$47$	9.74801	−	2.61197i	1.42189	−	0.380995i	0.886155	+	0.463389i	$0.153367\pi$
$48$	−0.866025	+	0.500000i	−0.125000	+	0.0721688i
$49$	3.93862	−	5.78682i	0.562660	−	0.826689i
$50$	0.659739	+	2.46218i	0.0933011	+	0.348205i
$51$	−1.45169	−	0.838134i	−0.203277	−	0.117362i
$52$	1.48678	−	3.28474i	0.206179	−	0.455511i
$53$	1.78093	+	3.08467i	0.244630	+	0.423712i	0.962028	−	0.272952i	$-0.0880002\pi$
$53$	1.78093	+	3.08467i	0.244630	+	0.423712i	−0.717397	+	0.696664i	$0.754667\pi$
$54$	−0.965926	−	0.258819i	−0.131446	−	0.0352208i
$55$	−5.27654	−	3.04641i	−0.711488	−	0.410778i
$56$	−0.778839	+	2.52852i	−0.104077	+	0.337888i
$57$	0.129680	+	0.129680i	0.0171765	+	0.0171765i
$58$	3.08495	+	3.08495i	0.405074	+	0.405074i
$59$	−1.43669	+	0.384959i	−0.187041	+	0.0501174i	−0.351123	−	0.936329i	$-0.614200\pi$
$59$	−1.43669	+	0.384959i	−0.187041	+	0.0501174i	0.164083	+	0.986447i	$0.447534\pi$
$60$	2.65393	+	0.711118i	0.342621	+	0.0918050i
$61$		−	13.6609i		−	1.74910i	−0.484934	−	0.874551i	$-0.661156\pi$
$61$		−	13.6609i		−	1.74910i	0.484934	−	0.874551i	$-0.338844\pi$
$62$	3.91127	−	6.77452i	0.496732	−	0.860365i
$63$	−2.33866	+	1.23721i	−0.294643	+	0.155874i
$64$		−	1.00000i		−	0.125000i
$65$	−9.27015	+	3.49309i	−1.14982	+	0.433265i
$66$	−1.92045	+	1.10877i	−0.236391	+	0.136481i
$67$	−4.98405	−	4.98405i	−0.608898	−	0.608898i	0.333760	−	0.942658i	$-0.391683\pi$
$67$	−4.98405	−	4.98405i	−0.608898	−	0.608898i	−0.942658	+	0.333760i	$0.891683\pi$
$68$	1.45169	−	0.838134i	0.176043	−	0.101639i
$69$	0.273071	+	0.472973i	0.0328739	+	0.0569393i
$70$	6.42557	−	3.39930i	0.768003	−	0.406294i
$71$	1.04867	−	3.91368i	0.124454	−	0.464469i	−0.875366	−	0.483462i	$-0.839379\pi$
$71$	1.04867	−	3.91368i	0.124454	−	0.464469i	0.999820	+	0.0189927i	$0.00604594\pi$
$72$	0.707107	−	0.707107i	0.0833333	−	0.0833333i
$73$	2.29736	−	8.57385i	0.268885	−	1.00349i	−0.690944	−	0.722908i	$-0.742805\pi$
$73$	2.29736	−	8.57385i	0.268885	−	1.00349i	0.959829	−	0.280585i	$-0.0905285\pi$
$74$	−0.643441	+	1.11447i	−0.0747985	+	0.129555i
$75$	−1.27452	−	2.20753i	−0.147169	−	0.254903i
$76$	−0.177146	+	0.0474662i	−0.0203201	+	0.00544475i
$77$	−1.72711	+	5.60711i	−0.196823	+	0.638990i
$78$	−0.585966	+	3.55762i	−0.0663475	+	0.402821i
$79$	4.42139	−	7.65808i	0.497445	−	0.861601i	−0.502550	−	0.864548i	$-0.667605\pi$
$79$	4.42139	−	7.65808i	0.497445	−	0.861601i	0.999996	+	0.00294723i	$0.000938134\pi$
$80$	−1.94281	+	1.94281i	−0.217213	+	0.217213i
$81$	1.00000			0.111111
$82$	5.13031			0.566548
$83$	−11.3594	+	11.3594i	−1.24686	+	1.24686i	−0.289759	+	0.957100i	$0.593575\pi$
$83$	−11.3594	+	11.3594i	−1.24686	+	1.24686i	−0.957100	+	0.289759i	$0.906425\pi$
$84$	0.0978714	−	2.64394i	0.0106786	−	0.288478i
$85$	−4.44870	−	1.19203i	−0.482529	−	0.129293i
$86$	0.857026	+	3.19846i	0.0924154	+	0.344899i
$87$	−3.77828	−	2.18139i	−0.405074	−	0.233870i
$88$		−	2.21755i		−	0.236391i
$89$	4.16412	−	15.5407i	0.441396	−	1.64731i	−0.283884	−	0.958859i	$-0.591623\pi$
$89$	4.16412	−	15.5407i	0.441396	−	1.64731i	0.725280	−	0.688454i	$-0.241710\pi$
$90$	−2.74755			−0.289617
$91$	5.26889	+	7.95228i	0.552330	+	0.833626i
$92$	−0.546143			−0.0569393
$93$	−2.02462	+	7.55600i	−0.209944	+	0.783520i
$94$		−	10.0919i		−	1.04090i
$95$	0.436380	+	0.251944i	0.0447716	+	0.0258489i
$96$	0.258819	+	0.965926i	0.0264156	+	0.0985844i
$97$	−15.6069	−	4.18186i	−1.58464	−	0.424603i	−0.644282	−	0.764788i	$-0.722844\pi$
$97$	−15.6069	−	4.18186i	−1.58464	−	0.424603i	−0.940358	+	0.340185i	$0.889510\pi$
$98$	−4.57025	−	5.30215i	−0.461665	−	0.535598i
$99$	1.56804	−	1.56804i	0.157594	−	0.157594i
$100$	2.54903			0.254903
$101$	−15.8707			−1.57919			−0.789597	−	0.613626i	$-0.789710\pi$
$101$	−15.8707			−1.57919			−0.789597	+	0.613626i	$0.789710\pi$
$102$	−1.18530	+	1.18530i	−0.117362	+	0.117362i
$103$	4.73336	−	8.19841i	0.466391	−	0.807814i	−0.532872	−	0.846196i	$-0.678887\pi$
$103$	4.73336	−	8.19841i	0.466391	−	0.807814i	0.999263	+	0.0383824i	$0.0122205\pi$
$104$	−2.78800	−	2.28627i	−0.273386	−	0.224187i
$105$	−5.32682	+	4.94653i	−0.519845	+	0.482732i
$106$	3.44050	−	0.921879i	0.334171	−	0.0895408i
$107$	−1.60445	−	2.77899i	−0.155108	−	0.268655i	0.777990	−	0.628276i	$-0.216239\pi$
$107$	−1.60445	−	2.77899i	−0.155108	−	0.268655i	−0.933098	+	0.359621i	$0.882906\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	−2.43579	+	9.09049i	−0.233306	+	0.870711i	0.745599	+	0.666395i	$0.232164\pi$
$109$	−2.43579	+	9.09049i	−0.233306	+	0.870711i	−0.978905	+	0.204316i	$0.934503\pi$
$110$	−4.30828	+	4.30828i	−0.410778	+	0.410778i
$111$	0.333069	−	1.24303i	0.0316135	−	0.117983i
$112$	2.24078	+	1.40673i	0.211734	+	0.132923i
$113$	1.81014	+	3.13525i	0.170283	+	0.294940i	0.938519	−	0.345228i	$-0.112198\pi$
$113$	1.81014	+	3.13525i	0.170283	+	0.294940i	−0.768235	+	0.640167i	$0.778865\pi$
$114$	0.158825	−	0.0916976i	0.0148753	−	0.00858827i
$115$	1.06105	+	1.06105i	0.0989437	+	0.0989437i
$116$	3.77828	−	2.18139i	0.350805	−	0.202537i
$117$	−0.354780	−	3.58805i	−0.0327994	−	0.331716i
$118$			1.48737i			0.136923i
$119$	−0.164059	+	4.43195i	−0.0150392	+	0.406277i
$120$	1.37378	−	2.37945i	0.125408	−	0.217213i
$121$			6.08249i			0.552953i
$122$	−13.1954	−	3.53571i	−1.19466	−	0.320108i
$123$	−4.95550	+	1.32782i	−0.446822	+	0.119726i
$124$	−5.53137	−	5.53137i	−0.496732	−	0.496732i
$125$	4.76177	+	4.76177i	0.425905	+	0.425905i
$126$	0.589766	+	2.57918i	0.0525405	+	0.229772i
$127$	11.5855	+	6.68890i	1.02805	+	0.593544i	0.916425	−	0.400207i	$-0.131062\pi$
$127$	11.5855	+	6.68890i	1.02805	+	0.593544i	0.111623	+	0.993751i	$0.464395\pi$
$128$	−0.965926	−	0.258819i	−0.0853766	−	0.0228766i
$129$	−1.65565	−	2.86766i	−0.145772	−	0.252484i
$130$	0.974776	+	9.85836i	0.0854935	+	0.864635i
$131$	16.7924	+	9.69509i	1.46716	+	0.847064i	0.999324	−	0.0367535i	$-0.0117016\pi$
$131$	16.7924	+	9.69509i	1.46716	+	0.847064i	0.467833	+	0.883817i	$0.345035\pi$
$132$	0.573943	+	2.14199i	0.0499554	+	0.186436i
$133$	0.142835	−	0.463719i	0.0123854	−	0.0402095i
$134$	−6.10419	+	3.52425i	−0.527321	+	0.304449i
$135$	2.65393	−	0.711118i	0.228414	−	0.0612033i
$136$	−0.433850	−	1.61915i	−0.0372023	−	0.138841i
$137$	−3.58980	−	13.3973i	−0.306697	−	1.14461i	−0.931474	−	0.363807i	$-0.881477\pi$
$137$	−3.58980	−	13.3973i	−0.306697	−	1.14461i	0.624777	−	0.780803i	$-0.285190\pi$
$138$	0.527533	−	0.141352i	0.0449066	−	0.0120327i
$139$	13.7082	−	7.91444i	1.16272	−	0.671294i	0.210762	−	0.977537i	$-0.432405\pi$
$139$	13.7082	−	7.91444i	1.16272	−	0.671294i	0.951953	+	0.306243i	$0.0990720\pi$
$140$	−1.62041	−	7.08643i	−0.136950	−	0.598913i
$141$	2.61197	+	9.74801i	0.219968	+	0.820930i
$142$	−3.50891	−	2.02587i	−0.294461	−	0.170007i
$143$	−6.18253	−	5.06991i	−0.517009	−	0.423967i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−11.5785	−	3.10245i	−0.961544	−	0.257645i
$146$	−7.68711	−	4.43815i	−0.636189	−	0.367304i
$147$	5.78682	+	3.93862i	0.477289	+	0.324852i
$148$	0.909963	+	0.909963i	0.0747985	+	0.0747985i
$149$	−10.1736	−	10.1736i	−0.833456	−	0.833456i	0.154532	−	0.987988i	$-0.450613\pi$
$149$	−10.1736	−	10.1736i	−0.833456	−	0.833456i	−0.987988	+	0.154532i	$0.950613\pi$
$150$	−2.46218	+	0.659739i	−0.201036	+	0.0538674i
$151$	2.24796	+	0.602340i	0.182937	+	0.0490177i	0.349124	−	0.937076i	$-0.386479\pi$
$151$	2.24796	+	0.602340i	0.182937	+	0.0490177i	−0.166188	+	0.986094i	$0.553146\pi$
$152$			0.183395i			0.0148753i
$153$	0.838134	−	1.45169i	0.0677591	−	0.117362i
$154$	4.96904	+	3.11949i	0.400417	+	0.251376i
$155$			21.4928i			1.72635i
$156$	3.28474	+	1.48678i	0.262989	+	0.119038i
$157$	4.62239	−	2.66874i	0.368907	−	0.212988i	−0.304074	−	0.952648i	$-0.598347\pi$
$157$	4.62239	−	2.66874i	0.368907	−	0.212988i	0.672981	+	0.739660i	$0.265014\pi$
$158$	−6.25279	−	6.25279i	−0.497445	−	0.497445i
$159$	−3.08467	+	1.78093i	−0.244630	+	0.141237i
$160$	1.37378	+	2.37945i	0.108606	+	0.188112i
$161$	0.768275	−	1.22379i	0.0605486	−	0.0964480i
$162$	0.258819	−	0.965926i	0.0203347	−	0.0758903i
$163$	3.95898	−	3.95898i	0.310091	−	0.310091i	−0.534854	−	0.844945i	$-0.679633\pi$
$163$	3.95898	−	3.95898i	0.310091	−	0.310091i	0.844945	+	0.534854i	$0.179633\pi$
$164$	1.32782	−	4.95550i	0.103686	−	0.386960i
$165$	3.04641	−	5.27654i	0.237163	−	0.410778i
$166$	8.03232	+	13.9124i	0.623429	+	1.07981i
$167$	6.88324	−	1.84436i	0.532641	−	0.142721i	0.0175335	−	0.999846i	$-0.494419\pi$
$167$	6.88324	−	1.84436i	0.532641	−	0.142721i	0.515108	+	0.857126i	$0.327752\pi$
$168$	−2.52852	−	0.778839i	−0.195080	−	0.0600887i
$169$	−12.7483	+	2.54594i	−0.980636	+	0.195841i
$170$	−2.30282	+	3.98859i	−0.176618	+	0.305911i
$171$	−0.129680	+	0.129680i	−0.00991688	+	0.00991688i
$172$	3.31129			0.252484
$173$	2.84253			0.216114			0.108057	−	0.994145i	$-0.465537\pi$
$173$	2.84253			0.216114			0.108057	+	0.994145i	$0.465537\pi$
$174$	−3.08495	+	3.08495i	−0.233870	+	0.233870i
$175$	−3.58580	+	5.71183i	−0.271061	+	0.431774i
$176$	−2.14199	−	0.573943i	−0.161458	−	0.0432626i
$177$	−0.384959	−	1.43669i	−0.0289353	−	0.107988i
$178$	−13.9334	−	8.04447i	−1.04435	−	0.602958i
$179$		−	25.5380i		−	1.90880i	−0.298535	−	0.954399i	$-0.596498\pi$
$179$		−	25.5380i		−	1.90880i	0.298535	−	0.954399i	$-0.403502\pi$
$180$	−0.711118	+	2.65393i	−0.0530036	+	0.197812i
$181$	−16.1216			−1.19831			−0.599155	−	0.800633i	$-0.704497\pi$
$181$	−16.1216			−1.19831			−0.599155	+	0.800633i	$0.704497\pi$
$182$	9.04500	−	3.03115i	0.670460	−	0.224684i
$183$	13.6609			1.00984
$184$	−0.141352	+	0.527533i	−0.0104206	+	0.0388903i
$185$		−	3.53577i		−	0.259955i
$186$	6.77452	+	3.91127i	0.496732	+	0.286788i
$187$	−0.962083	−	3.59054i	−0.0703545	−	0.262567i
$188$	−9.74801	−	2.61197i	−0.710947	−	0.190498i
$189$	−1.23721	−	2.33866i	−0.0899939	−	0.170112i
$190$	0.356302	−	0.356302i	0.0258489	−	0.0258489i
$191$	1.63311			0.118168			0.0590839	−	0.998253i	$-0.481182\pi$
$191$	1.63311			0.118168			0.0590839	+	0.998253i	$0.481182\pi$
$192$	1.00000			0.0721688
$193$	6.69093	−	6.69093i	0.481623	−	0.481623i	−0.424026	−	0.905650i	$-0.639384\pi$
$193$	6.69093	−	6.69093i	0.481623	−	0.481623i	0.905650	+	0.424026i	$0.139384\pi$
$194$	−8.07872	+	13.9928i	−0.580019	+	1.00462i
$195$	−3.49309	−	9.27015i	−0.250146	−	0.663849i
$196$	−6.30435	+	3.04223i	−0.450311	+	0.217302i
$197$	10.9689	−	2.93910i	0.781500	−	0.209402i	0.154054	−	0.988062i	$-0.450767\pi$
$197$	10.9689	−	2.93910i	0.781500	−	0.209402i	0.627446	+	0.778660i	$0.284100\pi$
$198$	−1.10877	−	1.92045i	−0.0787971	−	0.136481i
$199$	−9.05233	+	15.6791i	−0.641702	+	1.11146i	0.343350	+	0.939207i	$0.388438\pi$
$199$	−9.05233	+	15.6791i	−0.641702	+	1.11146i	−0.985053	+	0.172254i	$0.944895\pi$
$200$	0.659739	−	2.46218i	0.0466506	−	0.174102i
$201$	4.98405	−	4.98405i	0.351548	−	0.351548i
$202$	−4.10764	+	15.3299i	−0.289012	+	1.07861i
$203$	−0.426992	+	11.5349i	−0.0299689	+	0.809594i
$204$	0.838134	+	1.45169i	0.0586811	+	0.101639i
$205$	−12.2073	+	7.04790i	−0.852596	+	0.492246i
$206$	−6.69398	−	6.69398i	−0.466391	−	0.466391i
$207$	−0.472973	+	0.273071i	−0.0328739	+	0.0189798i
$208$	−2.92996	+	2.10128i	−0.203156	+	0.145697i
$209$			0.406688i			0.0281312i
$210$	3.39930	+	6.42557i	0.234574	+	0.443407i
$211$	0.00906917	−	0.0157083i	0.000624347	−	0.00108140i	−0.865713	−	0.500541i	$-0.833135\pi$
$211$	0.00906917	−	0.0157083i	0.000624347	−	0.00108140i	0.866337	+	0.499459i	$0.166468\pi$
$212$		−	3.56187i		−	0.244630i
$213$	3.91368	+	1.04867i	0.268161	+	0.0718536i
$214$	−3.09956	+	0.830525i	−0.211882	+	0.0567735i
$215$	−6.43322	−	6.43322i	−0.438742	−	0.438742i
$216$	0.707107	+	0.707107i	0.0481125	+	0.0481125i
$217$	20.1758	−	4.61347i	1.36962	−	0.313183i
$218$	8.15031	+	4.70559i	0.552009	+	0.318702i
$219$	8.57385	+	2.29736i	0.579367	+	0.155241i
$220$	3.04641	+	5.27654i	0.205389	+	0.355744i
$221$	−5.50610	−	2.49224i	−0.370380	−	0.167646i
$222$	−1.11447	−	0.643441i	−0.0747985	−	0.0431849i
$223$	−3.72027	−	13.8843i	−0.249128	−	0.929758i	−0.971264	−	0.238007i	$-0.923506\pi$
$223$	−3.72027	−	13.8843i	−0.249128	−	0.929758i	0.722136	−	0.691752i	$-0.243161\pi$
$224$	1.93875	−	1.80034i	0.129538	−	0.120290i
$225$	2.20753	−	1.27452i	0.147169	−	0.0849678i
$226$	3.49692	−	0.936996i	0.232612	−	0.0623281i
$227$	1.07187	+	4.00027i	0.0711424	+	0.265507i	0.992331	−	0.123609i	$-0.0394470\pi$
$227$	1.07187	+	4.00027i	0.0711424	+	0.265507i	−0.921189	+	0.389117i	$0.872780\pi$
$228$	−0.0474662	−	0.177146i	−0.00314353	−	0.0117318i
$229$	−8.43158	+	2.25923i	−0.557174	+	0.149294i	−0.526408	−	0.850232i	$-0.676461\pi$
$229$	−8.43158	+	2.25923i	−0.557174	+	0.149294i	−0.0307665	+	0.999527i	$0.509795\pi$
$230$	1.29952	−	0.750277i	0.0856877	−	0.0494718i
$231$	−5.60711	−	1.72711i	−0.368921	−	0.113636i
$232$	−1.12917	−	4.21412i	−0.0741337	−	0.276671i
$233$	−5.73199	−	3.30937i	−0.375515	−	0.216804i	0.300350	−	0.953829i	$-0.402897\pi$
$233$	−5.73199	−	3.30937i	−0.375515	−	0.216804i	−0.675865	+	0.737025i	$0.736230\pi$
$234$	−3.55762	−	0.585966i	−0.232569	−	0.0383058i
$235$	13.8640	+	24.0131i	0.904386	+	1.56644i
$236$	1.43669	+	0.384959i	0.0935204	+	0.0250587i
$237$	7.65808	+	4.42139i	0.497445	+	0.287200i
$238$	4.23848	+	1.30554i	0.274740	+	0.0846258i
$239$	−4.05600	−	4.05600i	−0.262361	−	0.262361i	0.563652	−	0.826013i	$-0.309396\pi$
$239$	−4.05600	−	4.05600i	−0.262361	−	0.262361i	−0.826013	+	0.563652i	$0.809396\pi$
$240$	−1.94281	−	1.94281i	−0.125408	−	0.125408i
$241$	8.69348	−	2.32941i	0.559996	−	0.150051i	0.0322917	−	0.999478i	$-0.489719\pi$
$241$	8.69348	−	2.32941i	0.559996	−	0.150051i	0.527705	+	0.849428i	$0.323053\pi$
$242$	5.87523	+	1.57426i	0.377674	+	0.101197i
$243$			1.00000i			0.0641500i
$244$	−6.83046	+	11.8307i	−0.437275	+	0.757383i
$245$	18.1586	+	6.33770i	1.16011	+	0.404901i
$246$			5.13031i			0.327097i
$247$	0.511307	+	0.419291i	0.0325337	+	0.0266789i
$248$	−6.77452	+	3.91127i	−0.430183	+	0.248366i
$249$	−11.3594	−	11.3594i	−0.719874	−	0.719874i
$250$	5.83195	−	3.36708i	0.368845	−	0.212953i
$251$	7.77241	+	13.4622i	0.490590	+	0.849727i	0.999941	−	0.0108317i	$-0.00344792\pi$
$251$	7.77241	+	13.4622i	0.490590	+	0.849727i	−0.509351	+	0.860559i	$0.670115\pi$
$252$	2.64394	+	0.0978714i	0.166553	+	0.00616532i
$253$	−0.313455	+	1.16983i	−0.0197067	+	0.0735466i
$254$	9.45953	−	9.45953i	0.593544	−	0.593544i
$255$	1.19203	−	4.44870i	0.0746475	−	0.278588i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	3.58530	+	6.20992i	0.223645	+	0.387364i	0.955912	−	0.293653i	$-0.0948712\pi$
$257$	3.58530	+	6.20992i	0.223645	+	0.387364i	−0.732267	+	0.681017i	$0.761538\pi$
$258$	−3.19846	+	0.857026i	−0.199128	+	0.0533561i
$259$	−3.31910	+	0.758958i	−0.206239	+	0.0471594i
$260$	9.77473	+	1.60997i	0.606203	+	0.0998461i
$261$	2.18139	−	3.77828i	0.135025	−	0.233870i
$262$	13.7109	−	13.7109i	0.847064	−	0.847064i
$263$	7.22009			0.445210			0.222605	−	0.974909i	$-0.428544\pi$
$263$	7.22009			0.445210			0.222605	+	0.974909i	$0.428544\pi$
$264$	2.21755			0.136481
$265$	−6.92004	+	6.92004i	−0.425094	+	0.425094i
$266$	−0.410949	−	0.257988i	−0.0251969	−	0.0158182i
$267$	15.5407	+	4.16412i	0.951077	+	0.254840i
$268$	1.82429	+	6.80833i	0.111436	+	0.415885i
$269$	1.74426	+	1.00705i	0.106350	+	0.0614010i	0.552231	−	0.833691i	$-0.313776\pi$
$269$	1.74426	+	1.00705i	0.106350	+	0.0614010i	−0.445882	+	0.895092i	$0.647110\pi$
$270$		−	2.74755i		−	0.167211i
$271$	5.92863	−	22.1259i	0.360139	−	1.34406i	−0.513755	−	0.857937i	$-0.671746\pi$
$271$	5.92863	−	22.1259i	0.360139	−	1.34406i	0.873893	−	0.486118i	$-0.161588\pi$
$272$	−1.67627			−0.101639
$273$	−7.95228	+	5.26889i	−0.481294	+	0.318888i
$274$	−13.8699			−0.837913
$275$	1.46300	−	5.45999i	0.0882223	−	0.329250i
$276$		−	0.546143i		−	0.0328739i
$277$	22.1306	+	12.7771i	1.32970	+	0.767702i	0.985253	−	0.171105i	$-0.0547337\pi$
$277$	22.1306	+	12.7771i	1.32970	+	0.767702i	0.344445	+	0.938806i	$0.388067\pi$
$278$	−4.09682	−	15.2895i	−0.245711	−	0.917005i
$279$	−7.55600	−	2.02462i	−0.452366	−	0.121211i
$280$	−7.26436	−	0.268907i	−0.434129	−	0.0160702i
$281$	−10.1284	+	10.1284i	−0.604210	+	0.604210i	−0.941427	−	0.337217i	$-0.890514\pi$
$281$	−10.1284	+	10.1284i	−0.604210	+	0.604210i	0.337217	+	0.941427i	$0.390514\pi$
$282$	10.0919			0.600963
$283$	30.4081			1.80757			0.903786	−	0.427985i	$-0.140776\pi$
$283$	30.4081			1.80757			0.903786	+	0.427985i	$0.140776\pi$
$284$	−2.86502	+	2.86502i	−0.170007	+	0.170007i
$285$	−0.251944	+	0.436380i	−0.0149239	+	0.0258489i
$286$	−6.49731	+	4.65968i	−0.384194	+	0.275532i
$287$	9.23632	+	9.94641i	0.545203	+	0.587118i
$288$	−0.965926	+	0.258819i	−0.0569177	+	0.0152511i
$289$	7.09506	+	12.2890i	0.417357	+	0.722883i
$290$	−5.99348	+	10.3810i	−0.351949	+	0.609594i
$291$	4.18186	−	15.6069i	0.245145	−	0.914892i
$292$	−6.27650	+	6.27650i	−0.367304	+	0.367304i
$293$	1.88727	−	7.04340i	0.110256	−	0.411480i	−0.888633	−	0.458620i	$-0.848344\pi$
$293$	1.88727	−	7.04340i	0.110256	−	0.411480i	0.998888	+	0.0471399i	$0.0150107\pi$
$294$	5.30215	−	4.57025i	0.309228	−	0.266542i
$295$	−2.04331	−	3.53912i	−0.118966	−	0.206055i
$296$	1.11447	−	0.643441i	0.0647774	−	0.0373992i
$297$	1.56804	+	1.56804i	0.0909870	+	0.0909870i
$298$	−12.4601	+	7.19384i	−0.721794	+	0.416728i
$299$	1.14760	+	1.60017i	0.0663672	+	0.0925405i
$300$			2.54903i			0.147169i
$301$	−4.65809	+	7.41989i	−0.268488	+	0.427675i
$302$	1.16363	−	2.01547i	0.0669594	−	0.115977i
$303$		−	15.8707i		−	0.911748i
$304$	0.177146	+	0.0474662i	0.0101600	+	0.00272237i
$305$	36.2551	−	9.71453i	2.07596	−	0.556253i
$306$	−1.18530	−	1.18530i	−0.0677591	−	0.0677591i
$307$	−1.04129	−	1.04129i	−0.0594295	−	0.0594295i	0.676767	−	0.736197i	$-0.263380\pi$
$307$	−1.04129	−	1.04129i	−0.0594295	−	0.0594295i	−0.736197	+	0.676767i	$0.763380\pi$
$308$	4.29928	−	3.99234i	0.244974	−	0.227485i
$309$	8.19841	+	4.73336i	0.466391	+	0.269271i
$310$	20.7605	+	5.56275i	1.17912	+	0.315943i
$311$	10.3053	+	17.8493i	0.584360	+	1.01214i	0.994955	+	0.100324i	$0.0319879\pi$
$311$	10.3053	+	17.8493i	0.584360	+	1.01214i	−0.410594	+	0.911818i	$0.634679\pi$
$312$	2.28627	−	2.78800i	0.129435	−	0.157840i
$313$	−8.86536	−	5.11842i	−0.501100	−	0.289310i	0.228068	−	0.973645i	$-0.426759\pi$
$313$	−8.86536	−	5.11842i	−0.501100	−	0.289310i	−0.729168	+	0.684335i	$0.760093\pi$
$314$	−1.38144	−	5.15561i	−0.0779592	−	0.290948i
$315$	−4.94653	−	5.32682i	−0.278706	−	0.300133i
$316$	−7.65808	+	4.42139i	−0.430800	+	0.248723i
$317$	−0.359788	+	0.0964049i	−0.0202077	+	0.00541464i	−0.268909	−	0.963166i	$-0.586663\pi$
$317$	−0.359788	+	0.0964049i	−0.0202077	+	0.00541464i	0.248701	+	0.968580i	$0.419996\pi$
$318$	0.921879	+	3.44050i	0.0516964	+	0.192934i
$319$	−2.50399	−	9.34502i	−0.140197	−	0.523221i
$320$	2.65393	−	0.711118i	0.148359	−	0.0397527i
$321$	2.77899	−	1.60445i	0.155108	−	0.0895517i
$322$	−0.983244	−	1.05884i	−0.0547941	−	0.0590066i
$323$	0.0795661	+	0.296945i	0.00442718	+	0.0165224i
$324$	−0.866025	−	0.500000i	−0.0481125	−	0.0277778i
$325$	−5.35622	−	7.46856i	−0.297110	−	0.414281i
$326$	−2.79942	−	4.84873i	−0.155045	−	0.268547i
$327$	−9.09049	−	2.43579i	−0.502705	−	0.134700i
$328$	−4.44298	−	2.56516i	−0.245323	−	0.141637i
$329$	19.5657	−	18.1688i	1.07869	−	1.00168i
$330$	−4.30828	−	4.30828i	−0.237163	−	0.237163i
$331$	−9.41790	−	9.41790i	−0.517654	−	0.517654i	0.399207	−	0.916861i	$-0.369286\pi$
$331$	−9.41790	−	9.41790i	−0.517654	−	0.517654i	−0.916861	+	0.399207i	$0.869286\pi$
$332$	15.5173	−	4.15784i	0.851620	−	0.228191i
$333$	1.24303	+	0.333069i	0.0681177	+	0.0182521i
$334$		−	7.12605i		−	0.389920i
$335$	9.68306	−	16.7716i	0.529042	−	0.916328i
$336$	−1.40673	+	2.24078i	−0.0767434	+	0.122245i
$337$			22.8350i			1.24390i	0.783057	+	0.621950i	$0.213659\pi$
$337$			22.8350i			1.24390i	−0.783057	+	0.621950i	$0.786341\pi$
$338$	−0.840305	+	12.9728i	−0.0457066	+	0.705628i
$339$	−3.13525	+	1.81014i	−0.170283	+	0.0983132i
$340$	3.25667	+	3.25667i	0.176618	+	0.176618i
$341$	−15.0228	+	8.67343i	−0.813531	+	0.469692i
$342$	0.0916976	+	0.158825i	0.00495844	+	0.00858827i
$343$	2.05155	−	18.4063i	0.110773	−	0.993846i
$344$	0.857026	−	3.19846i	0.0462077	−	0.172450i
$345$	−1.06105	+	1.06105i	−0.0571251	+	0.0571251i
$346$	0.735701	−	2.74567i	0.0395515	−	0.147608i
$347$	−7.44118	+	12.8885i	−0.399463	+	0.691891i	−0.993660	−	0.112429i	$-0.964137\pi$
$347$	−7.44118	+	12.8885i	−0.399463	+	0.691891i	0.594196	+	0.804320i	$0.297470\pi$
$348$	2.18139	+	3.77828i	0.116935	+	0.202537i
$349$	9.60502	−	2.57366i	0.514145	−	0.137765i	0.00758807	−	0.999971i	$-0.497585\pi$
$349$	9.60502	−	2.57366i	0.514145	−	0.137765i	0.506557	+	0.862206i	$0.330918\pi$
$350$	4.58913	+	4.94195i	0.245300	+	0.264158i
$351$	3.58805	−	0.354780i	0.191516	−	0.0189367i
$352$	−1.10877	+	1.92045i	−0.0590978	+	0.102360i
$353$	15.3409	−	15.3409i	0.816511	−	0.816511i	−0.169089	−	0.985601i	$-0.554083\pi$
$353$	15.3409	−	15.3409i	0.816511	−	0.816511i	0.985601	+	0.169089i	$0.0540827\pi$
$354$	−1.48737			−0.0790527
$355$	11.1324			0.590845
$356$	−11.3766	+	11.3766i	−0.602958	+	0.602958i
$357$	−4.43195	−	0.164059i	−0.234564	−	0.00868291i
$358$	−24.6678	−	6.60971i	−1.30373	−	0.349334i
$359$	6.80517	+	25.3972i	0.359163	+	1.34042i	0.875164	+	0.483827i	$0.160754\pi$
$359$	6.80517	+	25.3972i	0.359163	+	1.34042i	−0.516000	+	0.856588i	$0.672580\pi$
$360$	2.37945	+	1.37378i	0.125408	+	0.0724043i
$361$			18.9664i			0.998230i
$362$	−4.17258	+	15.5723i	−0.219306	+	0.818462i
$363$	−6.08249			−0.319248
$364$	−0.586849	−	9.52132i	−0.0307592	−	0.499053i
$365$	24.3881			1.27653
$366$	3.53571	−	13.1954i	0.184814	−	0.689737i
$367$			9.00455i			0.470034i	0.971991	+	0.235017i	$0.0755145\pi$
$367$			9.00455i			0.470034i	−0.971991	+	0.235017i	$0.924485\pi$
$368$	0.472973	+	0.273071i	0.0246554	+	0.0142348i
$369$	−1.32782	−	4.95550i	−0.0691237	−	0.257973i
$370$	−3.41529	−	0.915125i	−0.177553	−	0.0475751i
$371$	7.98137	+	5.01058i	0.414372	+	0.260137i
$372$	5.53137	−	5.53137i	0.286788	−	0.286788i
$373$	−26.7314			−1.38410			−0.692049	−	0.721850i	$-0.743292\pi$
$373$	−26.7314			−1.38410			−0.692049	+	0.721850i	$0.743292\pi$
$374$	−3.71720			−0.192212
$375$	−4.76177	+	4.76177i	−0.245896	+	0.245896i
$376$	−5.04594	+	8.73983i	−0.260225	+	0.450722i
$377$	−14.3306	−	6.48649i	−0.738063	−	0.334071i
$378$	−2.57918	+	0.589766i	−0.132659	+	0.0303343i
$379$	−10.5843	+	2.83605i	−0.543678	+	0.145678i	−0.520197	−	0.854046i	$-0.674142\pi$
$379$	−10.5843	+	2.83605i	−0.543678	+	0.145678i	−0.0234808	+	0.999724i	$0.507475\pi$
$380$	−0.251944	−	0.436380i	−0.0129244	−	0.0223858i
$381$	−6.68890	+	11.5855i	−0.342683	+	0.593544i
$382$	0.422680	−	1.57746i	0.0216262	−	0.0807101i
$383$	−16.5002	+	16.5002i	−0.843123	+	0.843123i	−0.989264	−	0.146141i	$-0.953315\pi$
$383$	−16.5002	+	16.5002i	−0.843123	+	0.843123i	0.146141	+	0.989264i	$0.453315\pi$
$384$	0.258819	−	0.965926i	0.0132078	−	0.0492922i
$385$	−16.1091	−	0.596313i	−0.820994	−	0.0303909i
$386$	−4.73120	−	8.19468i	−0.240812	−	0.417098i
$387$	2.86766	−	1.65565i	0.145772	−	0.0841612i
$388$	11.4250	+	11.4250i	0.580019	+	0.580019i
$389$	−24.3558	+	14.0618i	−1.23489	+	0.712962i	−0.968044	−	0.250779i	$-0.919313\pi$
$389$	−24.3558	+	14.0618i	−1.23489	+	0.712962i	−0.266842	+	0.963740i	$0.585980\pi$
$390$	−9.85836	+	0.974776i	−0.499197	+	0.0493597i
$391$			0.915482i			0.0462979i
$392$	1.30688	+	6.87692i	0.0660073	+	0.347337i
$393$	−9.69509	+	16.7924i	−0.489052	+	0.847064i
$394$		−	11.3558i		−	0.572098i
$395$	23.4681	+	6.28827i	1.18081	+	0.316397i
$396$	−2.14199	+	0.573943i	−0.107639	+	0.0288417i
$397$	−15.4530	−	15.4530i	−0.775566	−	0.775566i	0.203508	−	0.979073i	$-0.434766\pi$
$397$	−15.4530	−	15.4530i	−0.775566	−	0.775566i	−0.979073	+	0.203508i	$0.934766\pi$
$398$	12.8019	+	12.8019i	0.641702	+	0.641702i
$399$	0.463719	+	0.142835i	0.0232150	+	0.00715071i
$400$	−2.20753	−	1.27452i	−0.110376	−	0.0637259i
$401$	−19.8564	−	5.32051i	−0.991582	−	0.265693i	−0.273667	−	0.961825i	$-0.588237\pi$
$401$	−19.8564	−	5.32051i	−0.991582	−	0.265693i	−0.717915	+	0.696131i	$0.754903\pi$
$402$	−3.52425	−	6.10419i	−0.175774	−	0.304449i
$403$	−4.58374	+	27.8296i	−0.228332	+	1.38629i
$404$	13.7444	+	7.93535i	0.683811	+	0.394798i
$405$	0.711118	+	2.65393i	0.0353358	+	0.131875i
$406$	11.0314	+	3.39790i	0.547478	+	0.168635i
$407$	2.47139	−	1.42686i	0.122502	−	0.0707268i
$408$	1.61915	−	0.433850i	0.0801599	−	0.0214788i
$409$	10.2338	+	38.1929i	0.506027	+	1.88852i	0.456452	+	0.889748i	$0.349120\pi$
$409$	10.2338	+	38.1929i	0.506027	+	1.88852i	0.0495754	+	0.998770i	$0.484213\pi$
$410$	3.64826	+	13.6155i	0.180175	+	0.672421i
$411$	13.3973	−	3.58980i	0.660841	−	0.177072i
$412$	−8.19841	+	4.73336i	−0.403907	+	0.233196i
$413$	−2.88364	+	2.67777i	−0.141895	+	0.131765i
$414$	0.141352	+	0.527533i	0.00694708	+	0.0259269i
$415$	−38.2250	−	22.0692i	−1.87639	−	1.08334i
$416$	1.27135	+	3.37397i	0.0623330	+	0.165422i
$417$	7.91444	+	13.7082i	0.387572	+	0.671294i
$418$	0.392830	+	0.105258i	0.0192139	+	0.00514836i
$419$	−19.3975	−	11.1991i	−0.947629	−	0.547114i	−0.0552851	−	0.998471i	$-0.517607\pi$
$419$	−19.3975	−	11.1991i	−0.947629	−	0.547114i	−0.892343	+	0.451357i	$0.850940\pi$
$420$	7.08643	−	1.62041i	0.345782	−	0.0790680i
$421$	−5.11816	−	5.11816i	−0.249444	−	0.249444i	0.571299	−	0.820742i	$-0.306440\pi$
$421$	−5.11816	−	5.11816i	−0.249444	−	0.249444i	−0.820742	+	0.571299i	$0.806440\pi$
$422$	−0.0128257	−	0.0128257i	−0.000624347	−	0.000624347i
$423$	−9.74801	+	2.61197i	−0.473964	+	0.126998i
$424$	−3.44050	−	0.921879i	−0.167085	−	0.0447704i
$425$		−	4.27287i		−	0.207264i
$426$	2.02587	−	3.50891i	0.0981538	−	0.170007i
$427$	−16.9014	−	31.9482i	−0.817918	−	1.54608i
$428$			3.20890i			0.155108i
$429$	5.06991	−	6.18253i	0.244778	−	0.298495i
$430$	−7.87905	+	4.54897i	−0.379962	+	0.219371i
$431$	−26.6773	−	26.6773i	−1.28500	−	1.28500i	−0.937786	−	0.347215i	$-0.887128\pi$
$431$	−26.6773	−	26.6773i	−1.28500	−	1.28500i	−0.347215	−	0.937786i	$-0.612872\pi$
$432$	0.866025	−	0.500000i	0.0416667	−	0.0240563i
$433$	18.4530	+	31.9616i	0.886795	+	1.53597i	0.843642	+	0.536906i	$0.180407\pi$
$433$	18.4530	+	31.9616i	0.886795	+	1.53597i	0.0431533	+	0.999068i	$0.486260\pi$
$434$	0.765603	−	20.6823i	0.0367501	−	0.992784i
$435$	3.10245	−	11.5785i	0.148751	−	0.555148i
$436$	6.65470	−	6.65470i	0.318702	−	0.318702i
$437$	0.0259233	−	0.0967471i	0.00124008	−	0.00462804i
$438$	4.43815	−	7.68711i	0.212063	−	0.367304i
$439$	5.08287	+	8.80379i	0.242592	+	0.420182i	0.961452	−	0.274973i	$-0.0886690\pi$
$439$	5.08287	+	8.80379i	0.242592	+	0.420182i	−0.718860	+	0.695155i	$0.755336\pi$
$440$	5.88521	−	1.57694i	0.280567	−	0.0751776i
$441$	−3.93862	+	5.78682i	−0.187553	+	0.275563i
$442$	−3.83240	+	4.67344i	−0.182289	+	0.222293i
$443$	−1.02220	+	1.77050i	−0.0485662	+	0.0841192i	−0.889287	−	0.457350i	$-0.848799\pi$
$443$	−1.02220	+	1.77050i	−0.0485662	+	0.0841192i	0.840720	+	0.541470i	$0.182132\pi$
$444$	−0.909963	+	0.909963i	−0.0431849	+	0.0431849i
$445$	44.2052			2.09553
$446$	−14.3740			−0.680630
$447$	10.1736	−	10.1736i	0.481196	−	0.481196i
$448$	−1.23721	−	2.33866i	−0.0584527	−	0.110491i
$449$	−19.3298	−	5.17939i	−0.912228	−	0.244431i	−0.227968	−	0.973669i	$-0.573208\pi$
$449$	−19.3298	−	5.17939i	−0.912228	−	0.244431i	−0.684260	+	0.729238i	$0.739875\pi$
$450$	−0.659739	−	2.46218i	−0.0311004	−	0.116068i
$451$	−9.85252	−	5.68835i	−0.463937	−	0.267854i
$452$		−	3.62028i		−	0.170283i
$453$	−0.602340	+	2.24796i	−0.0283004	+	0.105618i
$454$	4.14138			0.194365
$455$	−17.3580	+	19.6383i	−0.813756	+	0.920657i
$456$	−0.183395			−0.00858827
$457$	−8.54224	+	31.8801i	−0.399589	+	1.49129i	0.414232	+	0.910171i	$0.364050\pi$
$457$	−8.54224	+	31.8801i	−0.399589	+	1.49129i	−0.813821	+	0.581116i	$0.802616\pi$
$458$			8.72901i			0.407880i
$459$	1.45169	+	0.838134i	0.0677591	+	0.0391208i
$460$	−0.388372	−	1.44942i	−0.0181079	−	0.0675798i
$461$	−13.7371	−	3.68085i	−0.639801	−	0.171434i	−0.0756877	−	0.997132i	$-0.524115\pi$
$461$	−13.7371	−	3.68085i	−0.639801	−	0.171434i	−0.564113	+	0.825697i	$0.690782\pi$
$462$	−3.11949	+	4.96904i	−0.145132	+	0.231181i
$463$	−15.3894	+	15.3894i	−0.715207	+	0.715207i	−0.967620	−	0.252412i	$-0.918776\pi$
$463$	−15.3894	+	15.3894i	−0.715207	+	0.715207i	0.252412	+	0.967620i	$0.418776\pi$
$464$	−4.36278			−0.202537
$465$	−21.4928			−0.996706
$466$	−4.68015	+	4.68015i	−0.216804	+	0.216804i
$467$	20.4707	−	35.4563i	0.947272	−	1.64072i	0.196136	−	0.980577i	$-0.437160\pi$
$467$	20.4707	−	35.4563i	0.947272	−	1.64072i	0.751136	−	0.660147i	$-0.229506\pi$
$468$	−1.48678	+	3.28474i	−0.0687264	+	0.151837i
$469$	−17.8223	−	5.48965i	−0.822957	−	0.253488i
$470$	26.7831	−	7.17652i	1.23541	−	0.331028i
$471$	2.66874	+	4.62239i	0.122969	+	0.212988i
$472$	0.743684	−	1.28810i	0.0342308	−	0.0592896i
$473$	1.90049	−	7.09274i	0.0873848	−	0.326125i
$474$	6.25279	−	6.25279i	0.287200	−	0.287200i
$475$	−0.120993	+	0.451552i	−0.00555154	+	0.0207186i
$476$	2.35806	−	3.75616i	0.108081	−	0.172163i
$477$	−1.78093	−	3.08467i	−0.0815433	−	0.141237i
$478$	−4.96757	+	2.86803i	−0.227211	+	0.131180i
$479$	−8.21255	−	8.21255i	−0.375241	−	0.375241i	0.494141	−	0.869382i	$-0.335483\pi$
$479$	−8.21255	−	8.21255i	−0.375241	−	0.375241i	−0.869382	+	0.494141i	$0.835483\pi$
$480$	−2.37945	+	1.37378i	−0.108606	+	0.0627040i
$481$	0.754068	−	4.57823i	0.0343826	−	0.208749i
$482$		−	9.00015i		−	0.409946i
$483$	1.22379	+	0.768275i	0.0556843	+	0.0349577i
$484$	3.04124	−	5.26759i	0.138238	−	0.239436i
$485$		−	44.3934i		−	2.01580i
$486$	0.965926	+	0.258819i	0.0438153	+	0.0117403i
$487$	−10.1285	+	2.71392i	−0.458965	+	0.122979i	−0.480891	−	0.876780i	$-0.659687\pi$
$487$	−10.1285	+	2.71392i	−0.458965	+	0.122979i	0.0219263	+	0.999760i	$0.493020\pi$
$488$	9.65973	+	9.65973i	0.437275	+	0.437275i
$489$	3.95898	+	3.95898i	0.179031	+	0.179031i
$490$	10.8216	−	15.8996i	0.488868	−	0.718270i
$491$	−3.98650	−	2.30160i	−0.179908	−	0.103870i	0.407341	−	0.913276i	$-0.366456\pi$
$491$	−3.98650	−	2.30160i	−0.179908	−	0.103870i	−0.587249	+	0.809406i	$0.699789\pi$
$492$	4.95550	+	1.32782i	0.223411	+	0.0598629i
$493$	−3.65660	−	6.33341i	−0.164685	−	0.285243i
$494$	0.537340	−	0.385364i	0.0241761	−	0.0173383i
$495$	5.27654	+	3.04641i	0.237163	+	0.136926i
$496$	2.02462	+	7.55600i	0.0909083	+	0.339274i
$497$	−2.38958	−	10.4502i	−0.107187	−	0.468755i
$498$	−13.9124	+	8.03232i	−0.623429	+	0.359937i
$499$	−12.1721	+	3.26150i	−0.544897	+	0.146005i	−0.520759	−	0.853704i	$-0.674351\pi$
$499$	−12.1721	+	3.26150i	−0.544897	+	0.146005i	−0.0241385	+	0.999709i	$0.507684\pi$
$500$	−1.74293	−	6.50469i	−0.0779461	−	0.290899i
$501$	1.84436	+	6.88324i	0.0823999	+	0.307520i
$502$	15.0151	−	4.02329i	0.670159	−	0.179568i
$503$	25.3394	−	14.6297i	1.12983	−	0.652306i	0.185936	−	0.982562i	$-0.440468\pi$
$503$	25.3394	−	14.6297i	1.12983	−	0.652306i	0.943891	+	0.330256i	$0.107135\pi$
$504$	0.778839	−	2.52852i	0.0346922	−	0.112629i
$505$	−11.2859	−	42.1197i	−0.502218	−	1.87430i
$506$	1.04884	+	0.605549i	0.0466267	+	0.0269199i
$507$	−2.54594	−	12.7483i	−0.113069	−	0.566170i
$508$	−6.68890	−	11.5855i	−0.296772	−	0.514024i
$509$	−23.6536	−	6.33797i	−1.04843	−	0.280926i	−0.306827	−	0.951765i	$-0.599267\pi$
$509$	−23.6536	−	6.33797i	−1.04843	−	0.280926i	−0.741603	+	0.670840i	$0.765934\pi$
$510$	−3.98859	−	2.30282i	−0.176618	−	0.101970i
$511$	−5.23494	−	22.8936i	−0.231580	−	1.01275i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−0.129680	−	0.129680i	−0.00572551	−	0.00572551i
$514$	6.92626	−	1.85589i	0.305504	−	0.0818596i
$515$	25.1240	+	6.73195i	1.10710	+	0.296645i
$516$			3.31129i			0.145772i
$517$	−11.1896	+	19.3810i	−0.492118	+	0.852374i
$518$	−0.125949	+	3.40244i	−0.00553388	+	0.149495i
$519$			2.84253i			0.124773i
$520$	4.08500	−	9.02498i	0.179139	−	0.395771i
$521$	7.83904	−	4.52587i	0.343434	−	0.198282i	−0.318355	−	0.947971i	$-0.603131\pi$
$521$	7.83904	−	4.52587i	0.343434	−	0.198282i	0.661790	+	0.749690i	$0.269797\pi$
$522$	−3.08495	−	3.08495i	−0.135025	−	0.135025i
$523$	5.50352	−	3.17746i	0.240652	−	0.138941i	−0.374824	−	0.927096i	$-0.622297\pi$
$523$	5.50352	−	3.17746i	0.240652	−	0.138941i	0.615476	+	0.788155i	$0.288964\pi$
$524$	−9.69509	−	16.7924i	−0.423532	−	0.733579i
$525$	−5.71183	−	3.58580i	−0.249285	−	0.156497i
$526$	1.86870	−	6.97407i	0.0814790	−	0.304084i
$527$	−9.27207	+	9.27207i	−0.403898	+	0.403898i
$528$	0.573943	−	2.14199i	0.0249777	−	0.0932180i
$529$	−11.3509	+	19.6603i	−0.493516	+	0.854794i
$530$	4.89321	+	8.47528i	0.212547	+	0.368143i
$531$	1.43669	−	0.384959i	0.0623469	−	0.0167058i
$532$	−0.355558	+	0.330174i	−0.0154154	+	0.0143149i
$533$	−17.3095	+	6.52241i	−0.749759	+	0.282517i
$534$	8.04447	−	13.9334i	0.348118	−	0.602958i
$535$	6.23429	−	6.23429i	0.269532	−	0.269532i
$536$	7.04851			0.304449
$537$	25.5380			1.10204
$538$	1.42419	−	1.42419i	0.0614010	−	0.0614010i
$539$	2.89806	+	15.2499i	0.124828	+	0.656860i
$540$	−2.65393	−	0.711118i	−0.114207	−	0.0306017i
$541$	−0.426380	−	1.59127i	−0.0183315	−	0.0684142i	0.956154	−	0.292864i	$-0.0946082\pi$
$541$	−0.426380	−	1.59127i	−0.0183315	−	0.0684142i	−0.974486	+	0.224450i	$0.927942\pi$
$542$	−19.8376	−	11.4532i	−0.852097	−	0.491958i
$543$		−	16.1216i		−	0.691845i
$544$	−0.433850	+	1.61915i	−0.0186012	+	0.0694205i
$545$	−25.8577			−1.10762
$546$	3.03115	+	9.04500i	0.129721	+	0.387090i
$547$	30.4255			1.30090			0.650451	−	0.759548i	$-0.274580\pi$
$547$	30.4255			1.30090			0.650451	+	0.759548i	$0.274580\pi$
$548$	−3.58980	+	13.3973i	−0.153349	+	0.572305i
$549$			13.6609i			0.583034i
$550$	−4.89530	−	2.82630i	−0.208736	−	0.120514i
$551$	0.207085	+	0.772850i	0.00882210	+	0.0329245i
$552$	−0.527533	−	0.141352i	−0.0224533	−	0.00601635i
$553$	0.865456	−	23.3798i	0.0368029	−	0.994210i
$554$	18.0695	−	18.0695i	0.767702	−	0.767702i
$555$	3.53577			0.150085
$556$	−15.8289			−0.671294
$557$	23.7404	−	23.7404i	1.00591	−	1.00591i	0.00593079	−	0.999982i	$-0.498112\pi$
$557$	23.7404	−	23.7404i	1.00591	−	1.00591i	0.999982	−	0.00593079i	$-0.00188784\pi$
$558$	−3.91127	+	6.77452i	−0.165577	+	0.286788i
$559$	−6.95794	−	9.70194i	−0.294289	−	0.410348i
$560$	−2.13990	+	6.94723i	−0.0904272	+	0.293574i
$561$	3.59054	−	0.962083i	0.151593	−	0.0406192i
$562$	7.16186	+	12.4047i	0.302105	+	0.523261i
$563$	8.00463	−	13.8644i	0.337355	−	0.584316i	−0.646580	−	0.762847i	$-0.723801\pi$
$563$	8.00463	−	13.8644i	0.337355	−	0.584316i	0.983934	+	0.178531i	$0.0571345\pi$
$564$	2.61197	−	9.74801i	0.109984	−	0.410465i
$565$	−7.03351	+	7.03351i	−0.295902	+	0.295902i
$566$	7.87019	−	29.3719i	0.330809	−	1.23459i
$567$	2.33866	−	1.23721i	0.0982143	−	0.0519580i
$568$	2.02587	+	3.50891i	0.0850037	+	0.147231i
$569$	3.99122	−	2.30433i	0.167321	−	0.0966027i	−0.414001	−	0.910276i	$-0.635869\pi$
$569$	3.99122	−	2.30433i	0.167321	−	0.0966027i	0.581322	+	0.813674i	$0.302536\pi$
$570$	0.356302	+	0.356302i	0.0149239	+	0.0149239i
$571$	22.7993	−	13.1632i	0.954120	−	0.550861i	0.0597613	−	0.998213i	$-0.480966\pi$
$571$	22.7993	−	13.1632i	0.954120	−	0.550861i	0.894358	+	0.447352i	$0.147633\pi$
$572$	2.81927	+	7.48194i	0.117880	+	0.312835i
$573$			1.63311i			0.0682242i
$574$	11.9980	−	6.34728i	0.500788	−	0.264930i
$575$	−0.696068	+	1.20563i	−0.0290281	+	0.0502781i
$576$			1.00000i			0.0416667i
$577$	39.6530	+	10.6250i	1.65078	+	0.442324i	0.959830	−	0.280582i	$-0.0905276\pi$
$577$	39.6530	+	10.6250i	1.65078	+	0.442324i	0.690946	+	0.722907i	$0.257194\pi$
$578$	13.7066	−	3.67267i	0.570120	−	0.152763i
$579$	6.69093	+	6.69093i	0.278065	+	0.278065i
$580$	8.47606	+	8.47606i	0.351949	+	0.351949i
$581$	−12.5118	+	40.6198i	−0.519076	+	1.68519i
$582$	−13.9928	−	8.07872i	−0.580019	−	0.334874i
$583$	−7.62947	−	2.04431i	−0.315980	−	0.0846667i
$584$	4.43815	+	7.68711i	0.183652	+	0.318095i
$585$	9.27015	−	3.49309i	0.383274	−	0.144422i
$586$	−6.31494	−	3.64593i	−0.260868	−	0.150612i
$587$	6.32248	+	23.5958i	0.260957	+	0.973904i	0.964679	+	0.263429i	$0.0848534\pi$
$587$	6.32248	+	23.5958i	0.260957	+	0.973904i	−0.703722	+	0.710475i	$0.748480\pi$
$588$	−3.04223	−	6.30435i	−0.125459	−	0.259987i
$589$	1.24242	−	0.717309i	0.0511928	−	0.0295562i
$590$	−3.94737	+	1.05770i	−0.162511	+	0.0435446i
$591$	2.93910	+	10.9689i	0.120898	+	0.451199i
$592$	−0.333069	−	1.24303i	−0.0136891	−	0.0510883i
$593$	35.6497	−	9.55230i	1.46396	−	0.392266i	0.563103	−	0.826387i	$-0.309608\pi$
$593$	35.6497	−	9.55230i	1.46396	−	0.392266i	0.900855	+	0.434121i	$0.142941\pi$
$594$	1.92045	−	1.10877i	0.0787971	−	0.0454935i
$595$	−11.8788	+	2.71624i	−0.486982	+	0.111355i
$596$	3.72381	+	13.8974i	0.152533	+	0.569261i
$597$	−15.6791	−	9.05233i	−0.641702	−	0.370487i
$598$	1.84267	−	0.694337i	0.0753524	−	0.0283936i
$599$	−2.06623	−	3.57882i	−0.0844240	−	0.146227i	0.820722	−	0.571328i	$-0.193572\pi$
$599$	−2.06623	−	3.57882i	−0.0844240	−	0.146227i	−0.905146	+	0.425102i	$0.860238\pi$
$600$	2.46218	+	0.659739i	0.100518	+	0.0269337i
$601$	19.4142	+	11.2088i	0.791923	+	0.457217i	0.840639	−	0.541596i	$-0.182180\pi$
$601$	19.4142	+	11.2088i	0.791923	+	0.457217i	−0.0487163	+	0.998813i	$0.515513\pi$
$602$	5.96146	+	6.41978i	0.242971	+	0.261651i
$603$	4.98405	+	4.98405i	0.202966	+	0.202966i
$604$	−1.64562	−	1.64562i	−0.0669594	−	0.0669594i
$605$	−16.1425	+	4.32537i	−0.656286	+	0.175851i
$606$	−15.3299	−	4.10764i	−0.622735	−	0.166861i
$607$			17.3306i			0.703429i	0.936107	+	0.351715i	$0.114401\pi$
$607$			17.3306i			0.703429i	−0.936107	+	0.351715i	$0.885599\pi$
$608$	0.0916976	−	0.158825i	0.00371883	−	0.00644120i
$609$	−11.5349	−	0.426992i	−0.467419	−	0.0173026i
$610$		−	37.5341i		−	1.51971i
$611$	12.8303	+	34.0497i	0.519058	+	1.37750i
$612$	−1.45169	+	0.838134i	−0.0586811	+	0.0338796i
$613$	−27.2016	−	27.2016i	−1.09866	−	1.09866i	−0.994567	−	0.104097i	$-0.966805\pi$
$613$	−27.2016	−	27.2016i	−1.09866	−	1.09866i	−0.104097	−	0.994567i	$-0.533195\pi$
$614$	−1.27531	+	0.736302i	−0.0514674	+	0.0297147i
$615$	−7.04790	−	12.2073i	−0.284199	−	0.492246i
$616$	−2.74357	−	5.18608i	−0.110542	−	0.208953i
$617$	9.83501	−	36.7048i	0.395943	−	1.47768i	−0.424226	−	0.905556i	$-0.639454\pi$
$617$	9.83501	−	36.7048i	0.395943	−	1.47768i	0.820169	−	0.572121i	$-0.193879\pi$
$618$	6.69398	−	6.69398i	0.269271	−	0.269271i
$619$	−6.14818	+	22.9453i	−0.247116	+	0.922250i	0.725192	+	0.688547i	$0.241751\pi$
$619$	−6.14818	+	22.9453i	−0.247116	+	0.922250i	−0.972308	+	0.233703i	$0.924916\pi$
$620$	10.7464	−	18.6133i	0.431586	−	0.747530i
$621$	−0.273071	−	0.472973i	−0.0109580	−	0.0189798i
$622$	19.9083	−	5.33442i	0.798251	−	0.213891i
$623$	−9.48870	−	41.4963i	−0.380157	−	1.66251i
$624$	−2.10128	−	2.92996i	−0.0841183	−	0.117292i
$625$	−15.6238	+	27.0612i	−0.624952	+	1.08245i
$626$	−7.23854	+	7.23854i	−0.289310	+	0.289310i
$627$	−0.406688			−0.0162415
$628$	−5.33748			−0.212988
$629$	1.52534	−	1.52534i	0.0608193	−	0.0608193i
$630$	−6.42557	+	3.39930i	−0.256001	+	0.135431i
$631$	−38.9228	−	10.4293i	−1.54949	−	0.415185i	−0.620173	−	0.784465i	$-0.712937\pi$
$631$	−38.9228	−	10.4293i	−1.54949	−	0.415185i	−0.929318	+	0.369280i	$0.879604\pi$
$632$	2.28868	+	8.54147i	0.0910388	+	0.339762i
$633$	0.0157083	+	0.00906917i	0.000624347	+	0.000360467i
$634$			0.372480i			0.0147931i
$635$	−9.51320	+	35.5037i	−0.377520	+	1.40892i
$636$	3.56187			0.141237
$637$	22.1608	+	12.0789i	0.878042	+	0.478584i
$638$	−9.67467			−0.383024
$639$	−1.04867	+	3.91368i	−0.0414847	+	0.154823i
$640$		−	2.74755i		−	0.108606i
$641$	−38.0770	−	21.9838i	−1.50395	−	0.868307i	−0.999990	−	0.00458225i	$-0.998541\pi$
$641$	−38.0770	−	21.9838i	−1.50395	−	0.868307i	−0.503963	−	0.863725i	$-0.668125\pi$
$642$	−0.830525	−	3.09956i	−0.0327782	−	0.122330i
$643$	−25.5889	−	6.85652i	−1.00913	−	0.270395i	−0.283863	−	0.958865i	$-0.591616\pi$
$643$	−25.5889	−	6.85652i	−1.00913	−	0.270395i	−0.725265	+	0.688470i	$0.758283\pi$
$644$	−1.27724	+	0.675694i	−0.0503303	+	0.0266261i
$645$	6.43322	−	6.43322i	0.253308	−	0.253308i
$646$	0.307420			0.0120953
$647$	−31.6089			−1.24267			−0.621337	−	0.783544i	$-0.713410\pi$
$647$	−31.6089			−1.24267			−0.621337	+	0.783544i	$0.713410\pi$
$648$	−0.707107	+	0.707107i	−0.0277778	+	0.0277778i
$649$	1.64915	−	2.85642i	0.0647350	−	0.112124i
$650$	−8.60037	+	3.24071i	−0.337334	+	0.127111i
$651$	4.61347	+	20.1758i	0.180816	+	0.790750i
$652$	−5.40806	+	1.44909i	−0.211796	+	0.0567506i
$653$	0.477891	+	0.827732i	0.0187013	+	0.0323917i	0.875225	−	0.483717i	$-0.160713\pi$
$653$	0.477891	+	0.827732i	0.0187013	+	0.0323917i	−0.856523	+	0.516108i	$0.827380\pi$
$654$	−4.70559	+	8.15031i	−0.184003	+	0.318702i
$655$	−13.7887	+	51.4602i	−0.538769	+	2.01071i
$656$	−3.62768	+	3.62768i	−0.141637	+	0.141637i
$657$	−2.29736	+	8.57385i	−0.0896284	+	0.334498i
$658$	−12.4858	−	23.6014i	−0.486747	−	0.920080i
$659$	−12.1342	−	21.0171i	−0.472681	−	0.818708i	0.526830	−	0.849971i	$-0.323381\pi$
$659$	−12.1342	−	21.0171i	−0.472681	−	0.818708i	−0.999511	+	0.0312626i	$0.990047\pi$
$660$	−5.27654	+	3.04641i	−0.205389	+	0.118581i
$661$	−14.9896	−	14.9896i	−0.583026	−	0.583026i	0.352707	−	0.935734i	$-0.385261\pi$
$661$	−14.9896	−	14.9896i	−0.583026	−	0.583026i	−0.935734	+	0.352707i	$0.885261\pi$
$662$	−11.5345	+	6.65946i	−0.448302	+	0.258827i
$663$	2.49224	−	5.50610i	0.0967906	−	0.213839i
$664$		−	16.0646i		−	0.623429i
$665$	1.33225	+	0.0493162i	0.0516624	+	0.00191240i
$666$	0.643441	−	1.11447i	0.0249328	−	0.0431849i
$667$			2.38270i			0.0922586i
$668$	−6.88324	−	1.84436i	−0.266321	−	0.0713604i
$669$	13.8843	−	3.72027i	0.536796	−	0.143834i
$670$	−13.6939	−	13.6939i	−0.529042	−	0.529042i
$671$	21.4209	+	21.4209i	0.826945	+	0.826945i
$672$	1.80034	+	1.93875i	0.0694497	+	0.0747891i
$673$	35.5408	+	20.5195i	1.37000	+	0.790969i	0.990927	−	0.134399i	$-0.0429105\pi$
$673$	35.5408	+	20.5195i	1.37000	+	0.790969i	0.379070	+	0.925368i	$0.376244\pi$
$674$	22.0569	+	5.91012i	0.849599	+	0.227649i
$675$	1.27452	+	2.20753i	0.0490562	+	0.0849678i
$676$	12.3133	+	4.16928i	0.473588	+	0.160357i
$677$	−3.46230	−	1.99896i	−0.133067	−	0.0768264i	0.431989	−	0.901879i	$-0.357812\pi$
$677$	−3.46230	−	1.99896i	−0.133067	−	0.0768264i	−0.565056	+	0.825053i	$0.691145\pi$
$678$	0.936996	+	3.49692i	0.0359851	+	0.134298i
$679$	−41.6730	+	9.52911i	−1.59926	+	0.365694i
$680$	3.98859	−	2.30282i	0.152956	−	0.0883090i
$681$	−4.00027	+	1.07187i	−0.153291	+	0.0410741i
$682$	4.48970	+	16.7558i	0.171919	+	0.641612i
$683$	−3.04139	−	11.3506i	−0.116375	−	0.434319i	0.883011	−	0.469353i	$-0.155513\pi$
$683$	−3.04139	−	11.3506i	−0.116375	−	0.434319i	−0.999386	+	0.0350339i	$0.988846\pi$
$684$	0.177146	−	0.0474662i	0.00677336	−	0.00181492i
$685$	33.0028	−	19.0542i	1.26097	−	0.728022i
$686$	−17.2481	−	6.74554i	−0.658536	−	0.257546i
$687$	−2.25923	−	8.43158i	−0.0861952	−	0.321685i
$688$	−2.86766	−	1.65565i	−0.109329	−	0.0631209i
$689$	−10.4361	+	7.48446i	−0.397584	+	0.285135i
$690$	0.750277	+	1.29952i	0.0285626	+	0.0494718i
$691$	27.8755	+	7.46923i	1.06044	+	0.284143i	0.746558	−	0.665321i	$-0.231705\pi$
$691$	27.8755	+	7.46923i	1.06044	+	0.284143i	0.313877	+	0.949463i	$0.398372\pi$
$692$	−2.46170	−	1.42127i	−0.0935799	−	0.0540284i
$693$	1.72711	−	5.60711i	0.0656075	−	0.212997i
$694$	10.5234	+	10.5234i	0.399463	+	0.399463i
$695$	30.7525	+	30.7525i	1.16651	+	1.16651i
$696$	4.21412	−	1.12917i	0.159736	−	0.0428011i
$697$	−8.30675	−	2.22579i	−0.314641	−	0.0843077i
$698$		−	9.94385i		−	0.376380i
$699$	3.30937	−	5.73199i	0.125172	−	0.216804i
$700$	5.96131	−	3.15369i	0.225316	−	0.119198i
$701$			8.49261i			0.320761i	0.987055	+	0.160381i	$0.0512722\pi$
$701$			8.49261i			0.320761i	−0.987055	+	0.160381i	$0.948728\pi$
$702$	0.585966	−	3.55762i	0.0221158	−	0.134274i
$703$	−0.204389	+	0.118004i	−0.00770867	+	0.00445060i
$704$	1.56804	+	1.56804i	0.0590978	+	0.0590978i
$705$	−24.0131	+	13.8640i	−0.904386	+	0.522148i
$706$	−10.8476	−	18.7886i	−0.408256	−	0.707119i
$707$	−37.1161	+	19.6354i	−1.39589	+	0.738465i
$708$	−0.384959	+	1.43669i	−0.0144677	+	0.0539940i
$709$	26.8947	−	26.8947i	1.01005	−	1.01005i	0.0101025	−	0.999949i	$-0.496784\pi$
$709$	26.8947	−	26.8947i	1.01005	−	1.01005i	0.999949	−	0.0101025i	$-0.00321578\pi$
$710$	2.88127	−	10.7530i	0.108132	−	0.403555i
$711$	−4.42139	+	7.65808i	−0.165815	+	0.287200i
$712$	8.04447	+	13.9334i	0.301479	+	0.522177i
$713$	4.12665	−	1.10573i	0.154544	−	0.0414100i
$714$	−1.30554	+	4.23848i	−0.0488587	+	0.158621i
$715$	9.05868	−	20.0133i	0.338775	−	0.748455i
$716$	−12.7690	+	22.1165i	−0.477199	+	0.826534i
$717$	4.05600	−	4.05600i	0.151474	−	0.151474i
$718$	26.2932			0.981252
$719$	−47.9707			−1.78901			−0.894503	−	0.447062i	$-0.852470\pi$
$719$	−47.9707			−1.78901			−0.894503	+	0.447062i	$0.852470\pi$
$720$	1.94281	−	1.94281i	0.0724043	−	0.0724043i
$721$	0.926520	−	25.0294i	0.0345054	−	0.932144i
$722$	18.3201	+	4.90886i	0.681804	+	0.182689i
$723$	2.32941	+	8.69348i	0.0866317	+	0.323314i
$724$	13.9617	+	8.06081i	0.518884	+	0.299578i
$725$		−	11.1209i		−	0.413019i
$726$	−1.57426	+	5.87523i	−0.0584264	+	0.218050i
$727$	29.5720			1.09677			0.548383	−	0.836227i	$-0.315244\pi$
$727$	29.5720			1.09677			0.548383	+	0.836227i	$0.315244\pi$
$728$	−9.34878	−	1.89745i	−0.346489	−	0.0703241i
$729$	−1.00000			−0.0370370
$730$	6.31210	−	23.5571i	0.233621	−	0.871887i
$731$		−	5.55062i		−	0.205297i
$732$	−11.8307	−	6.83046i	−0.437275	−	0.252461i
$733$	8.81361	+	32.8929i	0.325538	+	1.21493i	0.913770	+	0.406233i	$0.133158\pi$
$733$	8.81361	+	32.8929i	0.325538	+	1.21493i	−0.588232	+	0.808693i	$0.700176\pi$
$734$	8.69773	+	2.33055i	0.321039	+	0.0860221i
$735$	−6.33770	+	18.1586i	−0.233770	+	0.669792i
$736$	0.386181	−	0.386181i	0.0142348	−	0.0142348i
$737$	15.6304			0.575753
$738$	−5.13031			−0.188849
$739$	−13.6291	+	13.6291i	−0.501356	+	0.501356i	−0.911859	−	0.410503i	$-0.865353\pi$
$739$	−13.6291	+	13.6291i	−0.501356	+	0.501356i	0.410503	+	0.911859i	$0.365353\pi$
$740$	−1.76789	+	3.06207i	−0.0649888	+	0.112564i
$741$	−0.419291	+	0.511307i	−0.0154030	+	0.0187833i
$742$	6.90558	−	6.41258i	0.253512	−	0.235413i
$743$	−40.9049	+	10.9604i	−1.50065	+	0.402099i	−0.913319	−	0.407245i	$-0.866490\pi$
$743$	−40.9049	+	10.9604i	−1.50065	+	0.402099i	−0.587335	+	0.809344i	$0.699823\pi$
$744$	−3.91127	−	6.77452i	−0.143394	−	0.248366i
$745$	19.7654	−	34.2347i	0.724150	−	1.25426i
$746$	−6.91859	+	25.8205i	−0.253308	+	0.945357i
$747$	11.3594	−	11.3594i	0.415620	−	0.415620i
$748$	−0.962083	+	3.59054i	−0.0351772	+	0.131283i
$749$	−7.19046	−	4.51406i	−0.262734	−	0.164940i
$750$	3.36708	+	5.83195i	0.122948	+	0.212953i
$751$	1.31453	−	0.758942i	0.0479678	−	0.0276942i	−0.475824	−	0.879540i	$-0.657850\pi$
$751$	1.31453	−	0.758942i	0.0479678	−	0.0276942i	0.523792	+	0.851846i	$0.324517\pi$
$752$	7.13604	+	7.13604i	0.260225	+	0.260225i
$753$	−13.4622	+	7.77241i	−0.490590	+	0.283242i
$754$	−9.97450	+	12.1635i	−0.363250	+	0.442967i
$755$			6.39427i			0.232711i
$756$	−0.0978714	+	2.64394i	−0.00355955	+	0.0961592i
$757$	10.3621	−	17.9476i	0.376616	−	0.652318i	−0.613951	−	0.789344i	$-0.710421\pi$
$757$	10.3621	−	17.9476i	0.376616	−	0.652318i	0.990568	+	0.137026i	$0.0437542\pi$
$758$			10.9577i			0.398000i
$759$	−1.16983	−	0.313455i	−0.0424621	−	0.0113777i
$760$	−0.486718	+	0.130416i	−0.0176551	+	0.00473068i
$761$	7.45318	+	7.45318i	0.270177	+	0.270177i	0.829172	−	0.558994i	$-0.188813\pi$
$761$	7.45318	+	7.45318i	0.270177	+	0.270177i	−0.558994	+	0.829172i	$0.688813\pi$
$762$	9.45953	+	9.45953i	0.342683	+	0.342683i
$763$	5.55038	+	24.2731i	0.200937	+	0.878746i
$764$	−1.41432	−	0.816556i	−0.0511682	−	0.0295419i
$765$	4.44870	+	1.19203i	0.160843	+	0.0430978i
$766$	11.6674	+	20.2086i	0.421562	+	0.730166i
$767$	−1.89096	−	5.01834i	−0.0682787	−	0.181202i
$768$	−0.866025	−	0.500000i	−0.0312500	−	0.0180422i
$769$	1.89366	+	7.06724i	0.0682871	+	0.254851i	0.991627	−	0.129132i	$-0.0412189\pi$
$769$	1.89366	+	7.06724i	0.0682871	+	0.254851i	−0.923340	+	0.383983i	$0.874552\pi$
$770$	−4.74533	+	15.4058i	−0.171010	+	0.555187i
$771$	−6.20992	+	3.58530i	−0.223645	+	0.129121i
$772$	−9.13997	+	2.44905i	−0.328955	+	0.0881432i
$773$	10.6183	+	39.6280i	0.381914	+	1.42532i	0.842975	+	0.537953i	$0.180802\pi$
$773$	10.6183	+	39.6280i	0.381914	+	1.42532i	−0.461061	+	0.887368i	$0.652531\pi$
$774$	−0.857026	−	3.19846i	−0.0308051	−	0.114966i
$775$	−19.2605	+	5.16083i	−0.691857	+	0.185383i
$776$	13.9928	−	8.07872i	0.502311	−	0.290009i
$777$	−0.758958	−	3.31910i	−0.0272275	−	0.119072i
$778$	7.27893	+	27.1653i	0.260962	+	0.973924i
$779$	0.814822	+	0.470438i	0.0291940	+	0.0168552i
$780$	−1.60997	+	9.77473i	−0.0576462	+	0.349992i
$781$	4.49247	+	7.78118i	0.160753	+	0.278433i
$782$	0.884288	+	0.236944i	0.0316221	+	0.00847311i
$783$	3.77828	+	2.18139i	0.135025	+	0.0779566i
$784$	6.98084	+	0.517532i	0.249316	+	0.0184833i
$785$	10.3697	+	10.3697i	0.370111	+	0.370111i
$786$	13.7109	+	13.7109i	0.489052	+	0.489052i
$787$	50.2838	−	13.4735i	1.79242	−	0.480278i	0.799668	−	0.600442i	$-0.205009\pi$
$787$	50.2838	−	13.4735i	1.79242	−	0.480278i	0.992754	+	0.120164i	$0.0383420\pi$
$788$	−10.9689	−	2.93910i	−0.390750	−	0.104701i
$789$			7.22009i			0.257042i
$790$	12.1480	−	21.0409i	0.432206	−	0.748603i
$791$	8.11226	+	5.09275i	0.288439	+	0.181077i
$792$			2.21755i			0.0787971i
$793$	49.0161	−	4.84662i	1.74061	−	0.172109i
$794$	−18.9260	+	10.9269i	−0.671659	+	0.387783i
$795$	−6.92004	−	6.92004i	−0.245428	−	0.245428i
$796$	15.6791	−	9.05233i	0.555731	−	0.320851i
$797$	9.81837	+	17.0059i	0.347784	+	0.602380i	0.985856	−	0.167597i	$-0.0536008\pi$
$797$	9.81837	+	17.0059i	0.347784	+	0.602380i	−0.638071	+	0.769977i	$0.720267\pi$
$798$	0.257988	−	0.410949i	0.00913266	−	0.0145474i
$799$	−4.37836	+	16.3403i	−0.154895	+	0.578078i
$800$	−1.80244	+	1.80244i	−0.0637259	+	0.0637259i
$801$	−4.16412	+	15.5407i	−0.147132	+	0.549104i
$802$	−10.2784	+	17.8028i	−0.362944	+	0.628637i
$803$	9.84181	+	17.0465i	0.347310	+	0.601559i
$804$	−6.80833	+	1.82429i	−0.240111	+	0.0643377i
$805$	3.79418	+	1.16869i	0.133727	+	0.0411909i
$806$	25.6950	+	11.6304i	0.905067	+	0.409663i
$807$	−1.00705	+	1.74426i	−0.0354499	+	0.0614010i
$808$	11.2223	−	11.2223i	0.394798	−	0.394798i
$809$	−15.0254			−0.528264			−0.264132	−	0.964487i	$-0.585085\pi$
$809$	−15.0254			−0.528264			−0.264132	+	0.964487i	$0.585085\pi$
$810$	2.74755			0.0965391
$811$	22.5797	−	22.5797i	0.792880	−	0.792880i	−0.189081	−	0.981961i	$-0.560551\pi$
$811$	22.5797	−	22.5797i	0.792880	−	0.792880i	0.981961	+	0.189081i	$0.0605509\pi$
$812$	6.13725	−	9.77605i	0.215375	−	0.343072i
$813$	22.1259	+	5.92863i	0.775991	+	0.207926i
$814$	−0.738597	−	2.75648i	−0.0258878	−	0.0966146i
$815$	13.3221	+	7.69154i	0.466654	+	0.269423i
$816$		−	1.67627i		−	0.0586811i
$817$	−0.157174	+	0.586583i	−0.00549884	+	0.0205219i
$818$	39.5402			1.38249
$819$	−5.26889	−	7.95228i	−0.184110	−	0.277875i
$820$	14.0958			0.492246
$821$	14.2056	−	53.0161i	0.495780	−	1.85028i	−0.0298368	−	0.999555i	$-0.509499\pi$
$821$	14.2056	−	53.0161i	0.495780	−	1.85028i	0.525617	−	0.850721i	$-0.323835\pi$
$822$		−	13.8699i		−	0.483769i
$823$	−42.6136	−	24.6030i	−1.48542	−	0.857606i	−0.485554	−	0.874207i	$-0.661382\pi$
$823$	−42.6136	−	24.6030i	−1.48542	−	0.857606i	−0.999862	+	0.0166011i	$0.994715\pi$
$824$	2.45017	+	9.14414i	0.0853555	+	0.318551i
$825$	5.45999	+	1.46300i	0.190093	+	0.0509352i
$826$	1.84019	+	3.47844i	0.0640284	+	0.121030i
$827$	7.82426	−	7.82426i	0.272076	−	0.272076i	−0.557859	−	0.829936i	$-0.688377\pi$
$827$	7.82426	−	7.82426i	0.272076	−	0.272076i	0.829936	+	0.557859i	$0.188377\pi$
$828$	0.546143			0.0189798
$829$	−11.0437			−0.383564			−0.191782	−	0.981438i	$-0.561427\pi$
$829$	−11.0437			−0.383564			−0.191782	+	0.981438i	$0.561427\pi$
$830$	−31.2106	+	31.2106i	−1.08334	+	1.08334i
$831$	−12.7771	+	22.1306i	−0.443233	+	0.767702i
$832$	3.58805	−	0.354780i	0.124393	−	0.0122998i
$833$	5.09959	+	10.5678i	0.176690	+	0.366152i
$834$	15.2895	−	4.09682i	0.529433	−	0.141861i
$835$	9.78960	+	16.9561i	0.338783	+	0.586789i
$836$	0.203344	−	0.352202i	0.00703279	−	0.0121812i
$837$	2.02462	−	7.55600i	0.0699812	−	0.261173i
$838$	−15.8380	+	15.8380i	−0.547114	+	0.547114i
$839$	0.556614	−	2.07731i	0.0192164	−	0.0717167i	−0.955652	−	0.294499i	$-0.904847\pi$
$839$	0.556614	−	2.07731i	0.0192164	−	0.0717167i	0.974868	+	0.222782i	$0.0715139\pi$
$840$	0.268907	−	7.26436i	0.00927816	−	0.250644i
$841$	4.98306	+	8.63092i	0.171830	+	0.297618i
$842$	−6.26844	+	3.61909i	−0.216025	+	0.124722i
$843$	−10.1284	−	10.1284i	−0.348841	−	0.348841i
$844$	−0.0157083	+	0.00906917i	−0.000540701	+	0.000312174i
$845$	−15.8223	−	32.0225i	−0.544303	−	1.10161i
$846$			10.0919i			0.346966i
$847$	7.52532	+	14.2248i	0.258573	+	0.488771i
$848$	−1.78093	+	3.08467i	−0.0611575	+	0.105928i
$849$			30.4081i			1.04360i
$850$	−4.12727	−	1.10590i	−0.141564	−	0.0379320i
$851$	−0.678873	+	0.181903i	−0.0232715	+	0.00623557i
$852$	−2.86502	−	2.86502i	−0.0981538	−	0.0981538i
$853$	−27.5693	−	27.5693i	−0.943954	−	0.943954i	0.0545571	−	0.998511i	$-0.482625\pi$
$853$	−27.5693	−	27.5693i	−0.943954	−	0.943954i	−0.998511	+	0.0545571i	$0.982625\pi$
$854$	−35.2340	+	8.05674i	−1.20568	+	0.275696i
$855$	−0.436380	−	0.251944i	−0.0149239	−	0.00861630i
$856$	3.09956	+	0.830525i	0.105941	+	0.0283868i
$857$	−10.0100	−	17.3379i	−0.341936	−	0.592251i	0.642856	−	0.765987i	$-0.277749\pi$
$857$	−10.0100	−	17.3379i	−0.341936	−	0.592251i	−0.984792	+	0.173736i	$0.944416\pi$
$858$	−4.65968	−	6.49731i	−0.159079	−	0.221815i
$859$	−22.5936	−	13.0444i	−0.770884	−	0.445070i	0.0623061	−	0.998057i	$-0.480155\pi$
$859$	−22.5936	−	13.0444i	−0.770884	−	0.445070i	−0.833190	+	0.552987i	$0.813488\pi$
$860$	2.35472	+	8.78794i	0.0802953	+	0.299666i
$861$	−9.94641	+	9.23632i	−0.338973	+	0.314773i
$862$	−32.6729	+	18.8637i	−1.11284	+	0.642500i
$863$	34.9355	−	9.36095i	1.18922	−	0.318651i	0.390642	−	0.920543i	$-0.372253\pi$
$863$	34.9355	−	9.36095i	1.18922	−	0.318651i	0.798578	+	0.601892i	$0.205586\pi$
$864$	−0.258819	−	0.965926i	−0.00880520	−	0.0328615i
$865$	2.02138	+	7.54388i	0.0687288	+	0.256499i
$866$	35.6485	−	9.55198i	1.21138	−	0.324590i
$867$	−12.2890	+	7.09506i	−0.417357	+	0.240961i
$868$	−19.7795	−	6.09250i	−0.671358	−	0.206793i
$869$	5.07526	+	18.9411i	0.172166	+	0.642533i
$870$	−10.3810	−	5.99348i	−0.351949	−	0.203198i
$871$	16.1148	−	19.6513i	0.546029	−	0.665858i
$872$	−4.70559	−	8.15031i	−0.159351	−	0.276004i
$873$	15.6069	+	4.18186i	0.528213	+	0.141534i
$874$	−0.0867411	−	0.0500800i	−0.00293406	−	0.00169398i
$875$	17.0274	+	5.24482i	0.575632	+	0.177307i
$876$	−6.27650	−	6.27650i	−0.212063	−	0.212063i
$877$	17.3153	+	17.3153i	0.584697	+	0.584697i	0.936190	−	0.351493i	$-0.114326\pi$
$877$	17.3153	+	17.3153i	0.584697	+	0.584697i	−0.351493	+	0.936190i	$0.614326\pi$
$878$	9.81936	−	2.63109i	0.331387	−	0.0887949i
$879$	7.04340	+	1.88727i	0.237568	+	0.0636562i
$880$		−	6.09282i		−	0.205389i
$881$	0.802614	−	1.39017i	0.0270407	−	0.0468359i	−0.852188	−	0.523235i	$-0.824725\pi$
$881$	0.802614	−	1.39017i	0.0270407	−	0.0468359i	0.879229	+	0.476399i	$0.158058\pi$
$882$	4.57025	+	5.30215i	0.153888	+	0.178533i
$883$		−	38.8748i		−	1.30824i	−0.756391	−	0.654120i	$-0.773039\pi$
$883$		−	38.8748i		−	1.30824i	0.756391	−	0.654120i	$-0.226961\pi$
$884$	3.52230	+	4.91139i	0.118468	+	0.165188i
$885$	3.53912	−	2.04331i	0.118966	−	0.0686851i
$886$	1.44561	+	1.44561i	0.0485662	+	0.0485662i
$887$	−47.5716	+	27.4655i	−1.59730	+	0.922201i	−0.605295	+	0.796001i	$0.706945\pi$
$887$	−47.5716	+	27.4655i	−1.59730	+	0.922201i	−0.992005	+	0.126200i	$0.959722\pi$
$888$	0.643441	+	1.11447i	0.0215925	+	0.0373992i
$889$	35.3701	+	1.30930i	1.18628	+	0.0439126i
$890$	11.4411	−	42.6989i	0.383508	−	1.43127i
$891$	−1.56804	+	1.56804i	−0.0525314	+	0.0525314i
$892$	−3.72027	+	13.8843i	−0.124564	+	0.464879i
$893$	0.925402	−	1.60284i	0.0309674	−	0.0536371i
$894$	−7.19384	−	12.4601i	−0.240598	−	0.416728i
$895$	67.7760	−	18.1605i	2.26550	−	0.607039i
$896$	−2.57918	+	0.589766i	−0.0861644	+	0.0197027i
$897$	−1.60017	+	1.14760i	−0.0534283	+	0.0383171i
$898$	−10.0058	+	17.3306i	−0.333899	+	0.578329i
$899$	−24.1322	+	24.1322i	−0.804853	+	0.804853i
$900$	−2.54903			−0.0849678
$901$	−5.97065			−0.198911
$902$	−8.04455	+	8.04455i	−0.267854	+	0.267854i
$903$	−7.41989	−	4.65809i	−0.246919	−	0.155012i
$904$	−3.49692	−	0.936996i	−0.116306	−	0.0311640i
$905$	−11.4644	−	42.7857i	−0.381089	−	1.42224i
$906$	2.01547	+	1.16363i	0.0669594	+	0.0386590i
$907$			10.8818i			0.361324i	0.983545	+	0.180662i	$0.0578240\pi$
$907$			10.8818i			0.361324i	−0.983545	+	0.180662i	$0.942176\pi$
$908$	1.07187	−	4.00027i	0.0355712	−	0.132754i
$909$	15.8707			0.526398
$910$	14.4765	+	21.8493i	0.479893	+	0.724297i
$911$	−42.6469			−1.41296			−0.706478	−	0.707735i	$-0.749717\pi$
$911$	−42.6469			−1.41296			−0.706478	+	0.707735i	$0.749717\pi$
$912$	−0.0474662	+	0.177146i	−0.00157176	+	0.00586590i
$913$		−	35.6241i		−	1.17899i
$914$	28.5829	+	16.5023i	0.945438	+	0.545849i
$915$	9.71453	+	36.2551i	0.321153	+	1.19856i
$916$	8.43158	+	2.25923i	0.278587	+	0.0746472i
$917$	51.2665	+	1.89774i	1.69297	+	0.0626690i
$918$	1.18530	−	1.18530i	0.0391208	−	0.0391208i
$919$	−15.2066			−0.501621			−0.250810	−	0.968036i	$-0.580697\pi$
$919$	−15.2066			−0.501621			−0.250810	+	0.968036i	$0.580697\pi$
$920$	−1.50055			−0.0494718
$921$	1.04129	−	1.04129i	0.0343116	−	0.0343116i
$922$	−7.11085	+	12.3164i	−0.234183	+	0.405618i
$923$	14.4146	+	2.37418i	0.474461	+	0.0781472i
$924$	3.99234	+	4.29928i	0.131338	+	0.141436i
$925$	3.16853	−	0.849005i	0.104181	−	0.0279151i
$926$	10.8820	+	18.8481i	0.357604	+	0.619388i
$927$	−4.73336	+	8.19841i	−0.155464	+	0.269271i
$928$	−1.12917	+	4.21412i	−0.0370669	+	0.138335i
$929$	−9.51058	+	9.51058i	−0.312032	+	0.312032i	−0.845696	−	0.533664i	$-0.820815\pi$
$929$	−9.51058	+	9.51058i	−0.312032	+	0.312032i	0.533664	+	0.845696i	$0.320815\pi$
$930$	−5.56275	+	20.7605i	−0.182410	+	0.680763i
$931$	−0.239675	−	1.26120i	−0.00785503	−	0.0413340i
$932$	3.30937	+	5.73199i	0.108402	+	0.187758i
$933$	−17.8493	+	10.3053i	−0.584360	+	0.337381i
$934$	−28.9500	−	28.9500i	−0.947272	−	0.947272i
$935$	8.84490	−	5.10660i	0.289259	−	0.167004i
$936$	2.78800	+	2.28627i	0.0911288	+	0.0747291i
$937$		−	24.6205i		−	0.804315i	−0.915570	−	0.402158i	$-0.868260\pi$
$937$		−	24.6205i		−	0.804315i	0.915570	−	0.402158i	$-0.131740\pi$
$938$	−9.91534	+	15.7942i	−0.323747	+	0.515698i
$939$	5.11842	−	8.86536i	0.167033	−	0.289310i
$940$		−	27.7280i		−	0.904386i
$941$	3.11094	+	0.833574i	0.101414	+	0.0271737i	0.309169	−	0.951007i	$-0.399949\pi$
$941$	3.11094	+	0.833574i	0.101414	+	0.0271737i	−0.207755	+	0.978181i	$0.566616\pi$
$942$	5.15561	−	1.38144i	0.167979	−	0.0450098i
$943$	1.98123	+	1.98123i	0.0645177	+	0.0645177i
$944$	−1.05173	−	1.05173i	−0.0342308	−	0.0342308i
$945$	5.32682	−	4.94653i	0.173282	−	0.160911i
$946$	−6.35918	−	3.67147i	−0.206755	−	0.119370i
$947$	−11.1074	−	2.97622i	−0.360942	−	0.0967141i	0.0737905	−	0.997274i	$-0.476490\pi$
$947$	−11.1074	−	2.97622i	−0.360942	−	0.0967141i	−0.434732	+	0.900560i	$0.643157\pi$
$948$	−4.42139	−	7.65808i	−0.143600	−	0.248723i
$949$	31.5785	+	5.20121i	1.02508	+	0.168838i
$950$	0.404850	+	0.233740i	0.0131351	+	0.00758354i
$951$	−0.0964049	−	0.359788i	−0.00312614	−	0.0116669i
$952$	−3.01786	−	3.24987i	−0.0978093	−	0.105329i
$953$	39.2103	−	22.6381i	1.27015	−	0.733319i	0.295130	−	0.955457i	$-0.404637\pi$
$953$	39.2103	−	22.6381i	1.27015	−	0.733319i	0.975015	+	0.222138i	$0.0713037\pi$
$954$	−3.44050	+	0.921879i	−0.111390	+	0.0298469i
$955$	1.16134	+	4.33416i	0.0375799	+	0.140250i
$956$	1.48460	+	5.54060i	0.0480154	+	0.179196i
$957$	9.34502	−	2.50399i	0.302082	−	0.0809425i
$958$	−10.0583	+	5.80715i	−0.324968	+	0.187620i
$959$	−24.9706	−	26.8904i	−0.806343	−	0.868335i
$960$	0.711118	+	2.65393i	0.0229512	+	0.0856552i
$961$	26.1472	+	15.0961i	0.843458	+	0.486971i
$962$	−4.22707	−	1.91331i	−0.136286	−	0.0616875i
$963$	1.60445	+	2.77899i	0.0517027	+	0.0895517i
$964$	−8.69348	−	2.32941i	−0.279998	−	0.0750253i
$965$	22.5153	+	12.9992i	0.724793	+	0.418459i
$966$	1.05884	−	0.983244i	0.0340675	−	0.0316354i
$967$	−31.2769	−	31.2769i	−1.00580	−	1.00580i	−0.999983	−	0.00581309i	$-0.998150\pi$
$967$	−31.2769	−	31.2769i	−1.00580	−	1.00580i	−0.00581309	−	0.999983i	$-0.501850\pi$
$968$	−4.30097	−	4.30097i	−0.138238	−	0.138238i
$969$	−0.296945	+	0.0795661i	−0.00953924	+	0.00255603i
$970$	−42.8807	−	11.4899i	−1.37682	−	0.368917i
$971$		−	18.0376i		−	0.578853i	−0.957200	−	0.289426i	$-0.906535\pi$
$971$		−	18.0376i		−	0.578853i	0.957200	−	0.289426i	$-0.0934645\pi$
$972$	0.500000	−	0.866025i	0.0160375	−	0.0277778i
$973$	22.2670	−	35.4691i	0.713846	−	1.13709i
$974$			10.4858i			0.335986i
$975$	7.46856	−	5.35622i	0.239185	−	0.171536i
$976$	11.8307	−	6.83046i	0.378692	−	0.218638i
$977$	−7.34343	−	7.34343i	−0.234937	−	0.234937i	0.579813	−	0.814750i	$-0.303126\pi$
$977$	−7.34343	−	7.34343i	−0.234937	−	0.234937i	−0.814750	+	0.579813i	$0.803126\pi$
$978$	4.84873	−	2.79942i	0.155045	−	0.0895155i
$979$	17.8390	+	30.8980i	0.570136	+	0.987505i
$980$	−12.5570	−	14.5679i	−0.401118	−	0.465355i
$981$	2.43579	−	9.09049i	0.0777688	−	0.290237i
$982$	−3.25496	+	3.25496i	−0.103870	+	0.103870i
$983$	5.89909	−	22.0157i	0.188152	−	0.702192i	−0.805782	−	0.592212i	$-0.798255\pi$
$983$	5.89909	−	22.0157i	0.188152	−	0.702192i	0.993934	−	0.109980i	$-0.0350786\pi$
$984$	2.56516	−	4.44298i	0.0817742	−	0.141637i
$985$	15.6003	+	27.0206i	0.497068	+	0.860947i
$986$	−7.06400	+	1.89279i	−0.224964	+	0.0602788i
$987$	18.1688	+	19.5657i	0.578321	+	0.622782i
$988$	−0.233159	−	0.618770i	−0.00741778	−	0.0196857i
$989$	−0.904219	+	1.56615i	−0.0287525	+	0.0498008i
$990$	4.30828	−	4.30828i	0.136926	−	0.136926i
$991$	15.5356			0.493504			0.246752	−	0.969079i	$-0.420637\pi$
$991$	15.5356			0.493504			0.246752	+	0.969079i	$0.420637\pi$
$992$	7.82254			0.248366
$993$	9.41790	−	9.41790i	0.298868	−	0.298868i
$994$	−10.7126	−	0.396550i	−0.339782	−	0.0125778i
$995$	−48.0485	−	12.8746i	−1.52324	−	0.408151i
$996$	4.15784	+	15.5173i	0.131746	+	0.491683i
$997$	6.81984	+	3.93744i	0.215987	+	0.124700i	0.604091	−	0.796916i	$-0.293537\pi$
$997$	6.81984	+	3.93744i	0.215987	+	0.124700i	−0.388104	+	0.921616i	$0.626870\pi$
$998$			12.6015i			0.398893i
$999$	−0.333069	+	1.24303i	−0.0105378	+	0.0393278i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.by.b.397.10	✓	40
7.3	odd	6		546.2.cg.b.241.10	yes	40
13.2	odd	12		546.2.cg.b.145.10	yes	40
91.80	even	12	inner	546.2.by.b.535.10	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.by.b.397.10	✓	40	1.1	even	1	trivial
546.2.by.b.535.10	yes	40	91.80	even	12	inner
546.2.cg.b.145.10	yes	40	13.2	odd	12
546.2.cg.b.241.10	yes	40	7.3	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.258819 - 0.965926i) q^{2} +1.00000i q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.711118 + 2.65393i) q^{5} +(0.965926 + 0.258819i) q^{6} +(2.33866 - 1.23721i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(0.258819 - 0.965926i) q^{2} +1.00000i q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.711118 + 2.65393i) q^{5} +(0.965926 + 0.258819i) q^{6} +(2.33866 - 1.23721i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.00000 q^{9} +2.74755 q^{10} +(-1.56804 + 1.56804i) q^{11} +(0.500000 - 0.866025i) q^{12} +(0.354780 + 3.58805i) q^{13} +(-0.589766 - 2.57918i) q^{14} +(-2.65393 + 0.711118i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-0.838134 + 1.45169i) q^{17} +(-0.258819 + 0.965926i) q^{18} +(0.129680 - 0.129680i) q^{19} +(0.711118 - 2.65393i) q^{20} +(1.23721 + 2.33866i) q^{21} +(1.10877 + 1.92045i) q^{22} +(0.472973 - 0.273071i) q^{23} +(-0.707107 - 0.707107i) q^{24} +(-2.20753 + 1.27452i) q^{25} +(3.55762 + 0.585966i) q^{26} -1.00000i q^{27} +(-2.64394 - 0.0978714i) q^{28} +(-2.18139 + 3.77828i) q^{29} +2.74755i q^{30} +(7.55600 + 2.02462i) q^{31} +(0.965926 - 0.258819i) q^{32} +(-1.56804 - 1.56804i) q^{33} +(1.18530 + 1.18530i) q^{34} +(4.94653 + 5.32682i) q^{35} +(0.866025 + 0.500000i) q^{36} +(-1.24303 - 0.333069i) q^{37} +(-0.0916976 - 0.158825i) q^{38} +(-3.58805 + 0.354780i) q^{39} +(-2.37945 - 1.37378i) q^{40} +(1.32782 + 4.95550i) q^{41} +(2.57918 - 0.589766i) q^{42} +(-2.86766 + 1.65565i) q^{43} +(2.14199 - 0.573943i) q^{44} +(-0.711118 - 2.65393i) q^{45} +(-0.141352 - 0.527533i) q^{46} +(9.74801 - 2.61197i) q^{47} +(-0.866025 + 0.500000i) q^{48} +(3.93862 - 5.78682i) q^{49} +(0.659739 + 2.46218i) q^{50} +(-1.45169 - 0.838134i) q^{51} +(1.48678 - 3.28474i) q^{52} +(1.78093 + 3.08467i) q^{53} +(-0.965926 - 0.258819i) q^{54} +(-5.27654 - 3.04641i) q^{55} +(-0.778839 + 2.52852i) q^{56} +(0.129680 + 0.129680i) q^{57} +(3.08495 + 3.08495i) q^{58} +(-1.43669 + 0.384959i) q^{59} +(2.65393 + 0.711118i) q^{60} -13.6609i q^{61} +(3.91127 - 6.77452i) q^{62} +(-2.33866 + 1.23721i) q^{63} -1.00000i q^{64} +(-9.27015 + 3.49309i) q^{65} +(-1.92045 + 1.10877i) q^{66} +(-4.98405 - 4.98405i) q^{67} +(1.45169 - 0.838134i) q^{68} +(0.273071 + 0.472973i) q^{69} +(6.42557 - 3.39930i) q^{70} +(1.04867 - 3.91368i) q^{71} +(0.707107 - 0.707107i) q^{72} +(2.29736 - 8.57385i) q^{73} +(-0.643441 + 1.11447i) q^{74} +(-1.27452 - 2.20753i) q^{75} +(-0.177146 + 0.0474662i) q^{76} +(-1.72711 + 5.60711i) q^{77} +(-0.585966 + 3.55762i) q^{78} +(4.42139 - 7.65808i) q^{79} +(-1.94281 + 1.94281i) q^{80} +1.00000 q^{81} +5.13031 q^{82} +(-11.3594 + 11.3594i) q^{83} +(0.0978714 - 2.64394i) q^{84} +(-4.44870 - 1.19203i) q^{85} +(0.857026 + 3.19846i) q^{86} +(-3.77828 - 2.18139i) q^{87} -2.21755i q^{88} +(4.16412 - 15.5407i) q^{89} -2.74755 q^{90} +(5.26889 + 7.95228i) q^{91} -0.546143 q^{92} +(-2.02462 + 7.55600i) q^{93} -10.0919i q^{94} +(0.436380 + 0.251944i) q^{95} +(0.258819 + 0.965926i) q^{96} +(-15.6069 - 4.18186i) q^{97} +(-4.57025 - 5.30215i) q^{98} +(1.56804 - 1.56804i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{7} - 40 q^{9}+O(q^{10}) \) 40 * q - 4 * q^7 - 40 * q^9	\( 40 q - 4 q^{7} - 40 q^{9} - 4 q^{11} + 20 q^{12} + 4 q^{14} + 20 q^{16} + 8 q^{17} + 8 q^{19} - 8 q^{21} - 4 q^{22} + 24 q^{23} + 24 q^{25} - 8 q^{26} + 4 q^{28} - 12 q^{29} + 24 q^{31} - 4 q^{33} + 8 q^{34} + 28 q^{35} - 8 q^{37} - 8 q^{38} - 16 q^{39} - 20 q^{41} - 12 q^{42} - 24 q^{43} + 8 q^{44} - 4 q^{46} - 16 q^{47} + 4 q^{49} - 16 q^{50} - 24 q^{51} - 4 q^{52} - 4 q^{53} - 24 q^{55} + 12 q^{56} + 8 q^{57} + 24 q^{58} - 12 q^{59} - 32 q^{62} + 4 q^{63} - 4 q^{65} - 24 q^{67} + 24 q^{68} + 8 q^{69} + 52 q^{70} - 28 q^{71} + 108 q^{73} + 20 q^{74} - 36 q^{75} - 4 q^{76} + 12 q^{77} + 4 q^{78} + 40 q^{81} - 48 q^{82} - 60 q^{83} - 8 q^{84} - 4 q^{85} - 20 q^{86} - 36 q^{87} - 60 q^{89} - 40 q^{91} - 16 q^{92} - 48 q^{95} + 48 q^{97} - 8 q^{98} + 4 q^{99}+O(q^{100}) \) 40 * q - 4 * q^7 - 40 * q^9 - 4 * q^11 + 20 * q^12 + 4 * q^14 + 20 * q^16 + 8 * q^17 + 8 * q^19 - 8 * q^21 - 4 * q^22 + 24 * q^23 + 24 * q^25 - 8 * q^26 + 4 * q^28 - 12 * q^29 + 24 * q^31 - 4 * q^33 + 8 * q^34 + 28 * q^35 - 8 * q^37 - 8 * q^38 - 16 * q^39 - 20 * q^41 - 12 * q^42 - 24 * q^43 + 8 * q^44 - 4 * q^46 - 16 * q^47 + 4 * q^49 - 16 * q^50 - 24 * q^51 - 4 * q^52 - 4 * q^53 - 24 * q^55 + 12 * q^56 + 8 * q^57 + 24 * q^58 - 12 * q^59 - 32 * q^62 + 4 * q^63 - 4 * q^65 - 24 * q^67 + 24 * q^68 + 8 * q^69 + 52 * q^70 - 28 * q^71 + 108 * q^73 + 20 * q^74 - 36 * q^75 - 4 * q^76 + 12 * q^77 + 4 * q^78 + 40 * q^81 - 48 * q^82 - 60 * q^83 - 8 * q^84 - 4 * q^85 - 20 * q^86 - 36 * q^87 - 60 * q^89 - 40 * q^91 - 16 * q^92 - 48 * q^95 + 48 * q^97 - 8 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more