LMFDB - Embedded newform 546.2.by.a.19.1

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:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			19.1
Character	$\chi$	$=$	546.19
Dual form			546.2.by.a.115.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 - 0.258819i) q^{2} +1.00000i q^{3} +(0.866025 + 0.500000i) q^{4} +(-2.19856 + 0.589103i) q^{5} +(0.258819 - 0.965926i) q^{6} +(1.83682 - 1.90423i) q^{7} +(-0.707107 - 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(-0.965926 - 0.258819i) q^{2} +1.00000i q^{3} +(0.866025 + 0.500000i) q^{4} +(-2.19856 + 0.589103i) q^{5} +(0.258819 - 0.965926i) q^{6} +(1.83682 - 1.90423i) q^{7} +(-0.707107 - 0.707107i) q^{8} -1.00000 q^{9} +2.27612 q^{10} +(1.40267 + 1.40267i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(-0.977625 + 3.47048i) q^{13} +(-2.26709 + 1.36394i) q^{14} +(-0.589103 - 2.19856i) q^{15} +(0.500000 + 0.866025i) q^{16} +(1.96650 - 3.40608i) q^{17} +(0.965926 + 0.258819i) q^{18} +(5.46709 + 5.46709i) q^{19} +(-2.19856 - 0.589103i) q^{20} +(1.90423 + 1.83682i) q^{21} +(-0.991836 - 1.71791i) q^{22} +(-5.55484 + 3.20709i) q^{23} +(0.707107 - 0.707107i) q^{24} +(0.156509 - 0.0903604i) q^{25} +(1.84254 - 3.09920i) q^{26} -1.00000i q^{27} +(2.54285 - 0.730696i) q^{28} +(-4.71295 + 8.16308i) q^{29} +2.27612i q^{30} +(1.22535 - 4.57305i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(-1.40267 + 1.40267i) q^{33} +(-2.78106 + 2.78106i) q^{34} +(-2.91659 + 5.26864i) q^{35} +(-0.866025 - 0.500000i) q^{36} +(-2.78324 + 10.3872i) q^{37} +(-3.86582 - 6.69579i) q^{38} +(-3.47048 - 0.977625i) q^{39} +(1.97118 + 1.13806i) q^{40} +(-2.94495 + 0.789098i) q^{41} +(-1.36394 - 2.26709i) q^{42} +(-1.75771 + 1.01482i) q^{43} +(0.513412 + 1.91608i) q^{44} +(2.19856 - 0.589103i) q^{45} +(6.19562 - 1.66011i) q^{46} +(-0.0610541 - 0.227857i) q^{47} +(-0.866025 + 0.500000i) q^{48} +(-0.252153 - 6.99546i) q^{49} +(-0.174563 + 0.0467740i) q^{50} +(3.40608 + 1.96650i) q^{51} +(-2.58189 + 2.51671i) q^{52} +(2.68231 + 4.64590i) q^{53} +(-0.258819 + 0.965926i) q^{54} +(-3.91017 - 2.25754i) q^{55} +(-2.64532 + 0.0476601i) q^{56} +(-5.46709 + 5.46709i) q^{57} +(6.66512 - 6.66512i) q^{58} +(3.41773 + 12.7551i) q^{59} +(0.589103 - 2.19856i) q^{60} -10.1669i q^{61} +(-2.36719 + 4.10009i) q^{62} +(-1.83682 + 1.90423i) q^{63} +1.00000i q^{64} +(0.104898 - 8.20600i) q^{65} +(1.71791 - 0.991836i) q^{66} +(4.29914 - 4.29914i) q^{67} +(3.40608 - 1.96650i) q^{68} +(-3.20709 - 5.55484i) q^{69} +(4.18083 - 4.33425i) q^{70} +(11.8718 + 3.18104i) q^{71} +(0.707107 + 0.707107i) q^{72} +(9.50232 + 2.54614i) q^{73} +(5.37681 - 9.31291i) q^{74} +(0.0903604 + 0.156509i) q^{75} +(2.00109 + 7.46819i) q^{76} +(5.24745 - 0.0945420i) q^{77} +(3.09920 + 1.84254i) q^{78} +(-8.63462 + 14.9556i) q^{79} +(-1.60946 - 1.60946i) q^{80} +1.00000 q^{81} +3.04884 q^{82} +(-7.22658 - 7.22658i) q^{83} +(0.730696 + 2.54285i) q^{84} +(-2.31695 + 8.64696i) q^{85} +(1.96048 - 0.525308i) q^{86} +(-8.16308 - 4.71295i) q^{87} -1.98367i q^{88} +(9.02389 + 2.41794i) q^{89} -2.27612 q^{90} +(4.81286 + 8.23629i) q^{91} -6.41418 q^{92} +(4.57305 + 1.22535i) q^{93} +0.235895i q^{94} +(-15.2404 - 8.79906i) q^{95} +(0.965926 - 0.258819i) q^{96} +(1.24725 - 4.65479i) q^{97} +(-1.56700 + 6.82235i) q^{98} +(-1.40267 - 1.40267i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 8 q^{7} - 32 q^{9}+O(q^{10}) $ 32 * q + 8 * q^7 - 32 * q^9	$ 32 q + 8 q^{7} - 32 q^{9} - 4 q^{11} - 16 q^{12} + 4 q^{14} + 16 q^{16} - 8 q^{17} - 12 q^{19} - 8 q^{21} - 4 q^{22} - 24 q^{23} - 24 q^{25} + 8 q^{26} - 4 q^{28} - 12 q^{29} - 28 q^{31} + 4 q^{33} - 8 q^{34} - 44 q^{35} - 36 q^{37} + 8 q^{38} - 20 q^{39} - 28 q^{41} + 12 q^{42} + 84 q^{43} + 8 q^{44} - 4 q^{46} + 16 q^{47} + 24 q^{49} - 16 q^{50} + 8 q^{52} - 4 q^{53} + 48 q^{55} + 12 q^{56} + 12 q^{57} + 24 q^{58} + 12 q^{59} - 40 q^{62} - 8 q^{63} - 4 q^{65} + 8 q^{67} - 8 q^{69} + 60 q^{70} + 20 q^{71} + 4 q^{73} + 20 q^{74} + 8 q^{75} + 36 q^{76} - 12 q^{77} - 20 q^{78} + 32 q^{81} - 48 q^{82} + 12 q^{83} - 16 q^{84} - 4 q^{85} + 52 q^{86} - 36 q^{87} - 36 q^{89} - 16 q^{92} + 4 q^{93} - 48 q^{95} + 76 q^{97} + 8 q^{98} + 4 q^{99}+O(q^{100}) $ 32 * q + 8 * q^7 - 32 * q^9 - 4 * q^11 - 16 * q^12 + 4 * q^14 + 16 * q^16 - 8 * q^17 - 12 * q^19 - 8 * q^21 - 4 * q^22 - 24 * q^23 - 24 * q^25 + 8 * q^26 - 4 * q^28 - 12 * q^29 - 28 * q^31 + 4 * q^33 - 8 * q^34 - 44 * q^35 - 36 * q^37 + 8 * q^38 - 20 * q^39 - 28 * q^41 + 12 * q^42 + 84 * q^43 + 8 * q^44 - 4 * q^46 + 16 * q^47 + 24 * q^49 - 16 * q^50 + 8 * q^52 - 4 * q^53 + 48 * q^55 + 12 * q^56 + 12 * q^57 + 24 * q^58 + 12 * q^59 - 40 * q^62 - 8 * q^63 - 4 * q^65 + 8 * q^67 - 8 * q^69 + 60 * q^70 + 20 * q^71 + 4 * q^73 + 20 * q^74 + 8 * q^75 + 36 * q^76 - 12 * q^77 - 20 * q^78 + 32 * q^81 - 48 * q^82 + 12 * q^83 - 16 * q^84 - 4 * q^85 + 52 * q^86 - 36 * q^87 - 36 * q^89 - 16 * q^92 + 4 * q^93 - 48 * q^95 + 76 * q^97 + 8 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	−2.19856	+	0.589103i	−0.983227	+	0.263455i	−0.714403	−	0.699734i	$-0.753302\pi$
$5$	−2.19856	+	0.589103i	−0.983227	+	0.263455i	−0.268824	+	0.963189i	$0.586635\pi$
$6$	0.258819	−	0.965926i	0.105662	−	0.394338i
$7$	1.83682	−	1.90423i	0.694254	−	0.719730i
$7$	1.83682	−	1.90423i	0.694254	−	0.719730i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	−1.00000			−0.333333
$10$	2.27612			0.719772
$11$	1.40267	+	1.40267i	0.422920	+	0.422920i	0.886208	−	0.463288i	$-0.153330\pi$
$11$	1.40267	+	1.40267i	0.422920	+	0.422920i	−0.463288	+	0.886208i	$0.653330\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	−0.977625	+	3.47048i	−0.271144	+	0.962539i
$13$	−0.977625	+	3.47048i	−0.271144	+	0.962539i
$14$	−2.26709	+	1.36394i	−0.605904	+	0.364527i
$15$	−0.589103	−	2.19856i	−0.152106	−	0.567666i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	1.96650	−	3.40608i	0.476947	−	0.826096i	−0.522704	−	0.852514i	$-0.675077\pi$
$17$	1.96650	−	3.40608i	0.476947	−	0.826096i	0.999651	+	0.0264178i	$0.00841002\pi$
$18$	0.965926	+	0.258819i	0.227671	+	0.0610042i
$19$	5.46709	+	5.46709i	1.25424	+	1.25424i	0.953802	+	0.300435i	$0.0971317\pi$
$19$	5.46709	+	5.46709i	1.25424	+	1.25424i	0.300435	+	0.953802i	$0.402868\pi$
$20$	−2.19856	−	0.589103i	−0.491614	−	0.131727i
$21$	1.90423	+	1.83682i	0.415536	+	0.400828i
$22$	−0.991836	−	1.71791i	−0.211460	−	0.366260i
$23$	−5.55484	+	3.20709i	−1.15826	+	0.668724i	−0.950887	−	0.309537i	$-0.899826\pi$
$23$	−5.55484	+	3.20709i	−1.15826	+	0.668724i	−0.207377	+	0.978261i	$0.566493\pi$
$24$	0.707107	−	0.707107i	0.144338	−	0.144338i
$25$	0.156509	−	0.0903604i	0.0313018	−	0.0180721i
$26$	1.84254	−	3.09920i	0.361352	−	0.607803i
$27$		−	1.00000i		−	0.192450i
$28$	2.54285	−	0.730696i	0.480553	−	0.138089i
$29$	−4.71295	+	8.16308i	−0.875174	+	1.51585i	−0.0185960	+	0.999827i	$0.505920\pi$
$29$	−4.71295	+	8.16308i	−0.875174	+	1.51585i	−0.856578	+	0.516018i	$0.827414\pi$
$30$			2.27612i			0.415561i
$31$	1.22535	−	4.57305i	0.220079	−	0.821345i	−0.764238	−	0.644934i	$-0.776885\pi$
$31$	1.22535	−	4.57305i	0.220079	−	0.821345i	0.984317	−	0.176410i	$-0.0564486\pi$
$32$	−0.258819	−	0.965926i	−0.0457532	−	0.170753i
$33$	−1.40267	+	1.40267i	−0.244173	+	0.244173i
$34$	−2.78106	+	2.78106i	−0.476947	+	0.476947i
$35$	−2.91659	+	5.26864i	−0.492993	+	0.890563i
$36$	−0.866025	−	0.500000i	−0.144338	−	0.0833333i
$37$	−2.78324	+	10.3872i	−0.457562	+	1.70765i	0.222882	+	0.974845i	$0.428454\pi$
$37$	−2.78324	+	10.3872i	−0.457562	+	1.70765i	−0.680444	+	0.732800i	$0.738213\pi$
$38$	−3.86582	−	6.69579i	−0.627118	−	1.08620i
$39$	−3.47048	−	0.977625i	−0.555722	−	0.156545i
$40$	1.97118	+	1.13806i	0.311671	+	0.179943i
$41$	−2.94495	+	0.789098i	−0.459925	+	0.123236i	−0.481339	−	0.876534i	$-0.659850\pi$
$41$	−2.94495	+	0.789098i	−0.459925	+	0.123236i	0.0214149	+	0.999771i	$0.493183\pi$
$42$	−1.36394	−	2.26709i	−0.210460	−	0.349819i
$43$	−1.75771	+	1.01482i	−0.268049	+	0.154758i	−0.628001	−	0.778213i	$-0.716127\pi$
$43$	−1.75771	+	1.01482i	−0.268049	+	0.154758i	0.359952	+	0.932971i	$0.382793\pi$
$44$	0.513412	+	1.91608i	0.0773998	+	0.288860i
$45$	2.19856	−	0.589103i	0.327742	−	0.0878183i
$46$	6.19562	−	1.66011i	0.913494	−	0.244770i
$47$	−0.0610541	−	0.227857i	−0.00890566	−	0.0332364i	0.961330	−	0.275399i	$-0.0888099\pi$
$47$	−0.0610541	−	0.227857i	−0.00890566	−	0.0332364i	−0.970236	+	0.242163i	$0.922143\pi$
$48$	−0.866025	+	0.500000i	−0.125000	+	0.0721688i
$49$	−0.252153	−	6.99546i	−0.0360218	−	0.999351i
$50$	−0.174563	+	0.0467740i	−0.0246869	+	0.00661484i
$51$	3.40608	+	1.96650i	0.476947	+	0.275365i
$52$	−2.58189	+	2.51671i	−0.358044	+	0.349005i
$53$	2.68231	+	4.64590i	0.368444	+	0.638164i	0.989322	−	0.145743i	$-0.0465573\pi$
$53$	2.68231	+	4.64590i	0.368444	+	0.638164i	−0.620879	+	0.783907i	$0.713224\pi$
$54$	−0.258819	+	0.965926i	−0.0352208	+	0.131446i
$55$	−3.91017	−	2.25754i	−0.527247	−	0.304406i
$56$	−2.64532	+	0.0476601i	−0.353496	+	0.00636885i
$57$	−5.46709	+	5.46709i	−0.724134	+	0.724134i
$58$	6.66512	−	6.66512i	0.875174	−	0.875174i
$59$	3.41773	+	12.7551i	0.444950	+	1.66058i	0.716067	+	0.698031i	$0.245940\pi$
$59$	3.41773	+	12.7551i	0.444950	+	1.66058i	−0.271117	+	0.962546i	$0.587393\pi$
$60$	0.589103	−	2.19856i	0.0760529	−	0.283833i
$61$		−	10.1669i		−	1.30174i	−0.759190	−	0.650869i	$-0.774405\pi$
$61$		−	10.1669i		−	1.30174i	0.759190	−	0.650869i	$-0.225595\pi$
$62$	−2.36719	+	4.10009i	−0.300633	+	0.520712i
$63$	−1.83682	+	1.90423i	−0.231418	+	0.239910i
$64$			1.00000i			0.125000i
$65$	0.104898	−	8.20600i	0.0130110	−	1.01783i
$66$	1.71791	−	0.991836i	0.211460	−	0.122087i
$67$	4.29914	−	4.29914i	0.525223	−	0.525223i	−0.393921	−	0.919144i	$-0.628882\pi$
$67$	4.29914	−	4.29914i	0.525223	−	0.525223i	0.919144	+	0.393921i	$0.128882\pi$
$68$	3.40608	−	1.96650i	0.413048	−	0.238474i
$69$	−3.20709	−	5.55484i	−0.386088	−	0.668724i
$70$	4.18083	−	4.33425i	0.499705	−	0.518041i
$71$	11.8718	+	3.18104i	1.40893	+	0.377520i	0.881541	−	0.472107i	$-0.156506\pi$
$71$	11.8718	+	3.18104i	1.40893	+	0.377520i	0.527384	+	0.849627i	$0.323173\pi$
$72$	0.707107	+	0.707107i	0.0833333	+	0.0833333i
$73$	9.50232	+	2.54614i	1.11216	+	0.298003i	0.767708	−	0.640800i	$-0.221397\pi$
$73$	9.50232	+	2.54614i	1.11216	+	0.298003i	0.344454	+	0.938803i	$0.388064\pi$
$74$	5.37681	−	9.31291i	0.625042	−	1.08260i
$75$	0.0903604	+	0.156509i	0.0104339	+	0.0180721i
$76$	2.00109	+	7.46819i	0.229541	+	0.856660i
$77$	5.24745	−	0.0945420i	0.598003	−	0.0107741i
$78$	3.09920	+	1.84254i	0.350915	+	0.208627i
$79$	−8.63462	+	14.9556i	−0.971470	+	1.68264i	−0.280348	+	0.959898i	$0.590450\pi$
$79$	−8.63462	+	14.9556i	−0.971470	+	1.68264i	−0.691123	+	0.722738i	$0.742884\pi$
$80$	−1.60946	−	1.60946i	−0.179943	−	0.179943i
$81$	1.00000			0.111111
$82$	3.04884			0.336688
$83$	−7.22658	−	7.22658i	−0.793220	−	0.793220i	0.188796	−	0.982016i	$-0.439541\pi$
$83$	−7.22658	−	7.22658i	−0.793220	−	0.793220i	−0.982016	+	0.188796i	$0.939541\pi$
$84$	0.730696	+	2.54285i	0.0797255	+	0.277448i
$85$	−2.31695	+	8.64696i	−0.251308	+	0.937895i
$86$	1.96048	−	0.525308i	0.211404	−	0.0566454i
$87$	−8.16308	−	4.71295i	−0.875174	−	0.505282i
$88$		−	1.98367i		−	0.211460i
$89$	9.02389	+	2.41794i	0.956530	+	0.256301i	0.703131	−	0.711060i	$-0.251785\pi$
$89$	9.02389	+	2.41794i	0.956530	+	0.256301i	0.253399	+	0.967362i	$0.418451\pi$
$90$	−2.27612			−0.239924
$91$	4.81286	+	8.23629i	0.504525	+	0.863397i
$92$	−6.41418			−0.668724
$93$	4.57305	+	1.22535i	0.474204	+	0.127062i
$94$			0.235895i			0.0243307i
$95$	−15.2404	−	8.79906i	−1.56363	−	0.902765i
$96$	0.965926	−	0.258819i	0.0985844	−	0.0264156i
$97$	1.24725	−	4.65479i	0.126639	−	0.472622i	−0.873254	−	0.487265i	$-0.837995\pi$
$97$	1.24725	−	4.65479i	0.126639	−	0.472622i	0.999893	+	0.0146430i	$0.00466117\pi$
$98$	−1.56700	+	6.82235i	−0.158291	+	0.689162i
$99$	−1.40267	−	1.40267i	−0.140973	−	0.140973i
$100$	0.180721			0.0180721
$101$	8.26274			0.822174			0.411087	−	0.911596i	$-0.365149\pi$
$101$	8.26274			0.822174			0.411087	+	0.911596i	$0.365149\pi$
$102$	−2.78106	−	2.78106i	−0.275365	−	0.275365i
$103$	−1.52472	+	2.64090i	−0.150235	+	0.260215i	−0.931314	−	0.364218i	$-0.881336\pi$
$103$	−1.52472	+	2.64090i	−0.150235	+	0.260215i	0.781079	+	0.624433i	$0.214670\pi$
$104$	3.14529	−	1.76272i	0.308421	−	0.172849i
$105$	−5.26864	−	2.91659i	−0.514167	−	0.284630i
$106$	−1.38847	−	5.18183i	−0.134860	−	0.503304i
$107$	−8.97443	−	15.5442i	−0.867590	−	1.50271i	−0.864452	−	0.502716i	$-0.832334\pi$
$107$	−8.97443	−	15.5442i	−0.867590	−	1.50271i	−0.00313869	−	0.999995i	$-0.500999\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	−6.94473	−	1.86084i	−0.665185	−	0.178236i	−0.0896000	−	0.995978i	$-0.528559\pi$
$109$	−6.94473	−	1.86084i	−0.665185	−	0.178236i	−0.575585	+	0.817742i	$0.695226\pi$
$110$	3.19264	+	3.19264i	0.304406	+	0.304406i
$111$	−10.3872	−	2.78324i	−0.985910	−	0.264174i
$112$	2.56752	+	0.638624i	0.242608	+	0.0603443i
$113$	−0.0716321	−	0.124070i	−0.00673858	−	0.0116716i	0.862636	−	0.505824i	$-0.168812\pi$
$113$	−0.0716321	−	0.124070i	−0.00673858	−	0.0116716i	−0.869375	+	0.494153i	$0.835478\pi$
$114$	6.69579	−	3.86582i	0.627118	−	0.362067i
$115$	10.3234	−	10.3234i	0.962658	−	0.962658i
$116$	−8.16308	+	4.71295i	−0.757923	+	0.437587i
$117$	0.977625	−	3.47048i	0.0903815	−	0.320846i
$118$		−	13.2051i		−	1.21563i
$119$	−2.87383	−	10.0010i	−0.263444	−	0.916794i
$120$	−1.13806	+	1.97118i	−0.103890	+	0.179943i
$121$		−	7.06505i		−	0.642277i
$122$	−2.63139	+	9.82047i	−0.238235	+	0.889103i
$123$	−0.789098	−	2.94495i	−0.0711506	−	0.265538i
$124$	3.34771	−	3.34771i	0.300633	−	0.300633i
$125$	7.75644	−	7.75644i	0.693757	−	0.693757i
$126$	2.26709	−	1.36394i	0.201968	−	0.121509i
$127$	4.41008	+	2.54616i	0.391331	+	0.225935i	0.682737	−	0.730664i	$-0.260790\pi$
$127$	4.41008	+	2.54616i	0.391331	+	0.225935i	−0.291405	+	0.956600i	$0.594123\pi$
$128$	0.258819	−	0.965926i	0.0228766	−	0.0853766i
$129$	−1.01482	−	1.75771i	−0.0893497	−	0.154758i
$130$	−2.22519	+	7.89923i	−0.195162	+	0.692809i
$131$	−8.23164	−	4.75254i	−0.719202	−	0.415231i	0.0952570	−	0.995453i	$-0.469633\pi$
$131$	−8.23164	−	4.75254i	−0.719202	−	0.415231i	−0.814459	+	0.580221i	$0.802966\pi$
$132$	−1.91608	+	0.513412i	−0.166773	+	0.0446868i
$133$	20.4527	−	0.368491i	1.77347	−	0.0319522i
$134$	−5.26534	+	3.03995i	−0.454856	+	0.262611i
$135$	0.589103	+	2.19856i	0.0507019	+	0.189222i
$136$	−3.79899	+	1.01794i	−0.325761	+	0.0872874i
$137$	19.2193	−	5.14980i	1.64202	−	0.439977i	0.684655	−	0.728867i	$-0.259953\pi$
$137$	19.2193	−	5.14980i	1.64202	−	0.439977i	0.957362	+	0.288890i	$0.0932863\pi$
$138$	1.66011	+	6.19562i	0.141318	+	0.527406i
$139$	−2.51054	+	1.44946i	−0.212941	+	0.122941i	−0.602677	−	0.797985i	$-0.705899\pi$
$139$	−2.51054	+	1.44946i	−0.212941	+	0.122941i	0.389737	+	0.920926i	$0.372566\pi$
$140$	−5.16016	+	3.10448i	−0.436113	+	0.262377i
$141$	0.227857	−	0.0610541i	0.0191890	−	0.00514169i
$142$	−10.6440	−	6.14530i	−0.893223	−	0.515702i
$143$	−6.23922	+	3.49665i	−0.521750	+	0.292405i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	5.55283	−	20.7235i	0.461138	−	1.72099i
$146$	−8.51955	−	4.91876i	−0.705083	−	0.407080i
$147$	6.99546	−	0.252153i	0.576976	−	0.0207972i
$148$	−7.60396	+	7.60396i	−0.625042	+	0.625042i
$149$	7.74899	−	7.74899i	0.634822	−	0.634822i	−0.314452	−	0.949273i	$-0.601821\pi$
$149$	7.74899	−	7.74899i	0.634822	−	0.634822i	0.949273	+	0.314452i	$0.101821\pi$
$150$	−0.0467740	−	0.174563i	−0.00381908	−	0.0142530i
$151$	−3.69059	+	13.7735i	−0.300336	+	1.12087i	0.636551	+	0.771235i	$0.280361\pi$
$151$	−3.69059	+	13.7735i	−0.300336	+	1.12087i	−0.936886	+	0.349634i	$0.886306\pi$
$152$		−	7.73164i		−	0.627118i
$153$	−1.96650	+	3.40608i	−0.158982	+	0.275365i
$154$	−5.09312	−	1.26682i	−0.410415	−	0.102083i
$155$			10.7760i			0.865549i
$156$	−2.51671	−	2.58189i	−0.201498	−	0.206717i
$157$	8.93922	−	5.16106i	0.713428	−	0.411898i	−0.0989012	−	0.995097i	$-0.531533\pi$
$157$	8.93922	−	5.16106i	0.713428	−	0.411898i	0.812329	+	0.583200i	$0.198199\pi$
$158$	12.2112	−	12.2112i	0.971470	−	0.971470i
$159$	−4.64590	+	2.68231i	−0.368444	+	0.212721i
$160$	1.13806	+	1.97118i	0.0899715	+	0.155835i
$161$	−4.09624	+	16.4685i	−0.322829	+	1.29790i
$162$	−0.965926	−	0.258819i	−0.0758903	−	0.0203347i
$163$	−10.6417	−	10.6417i	−0.833523	−	0.833523i	0.154474	−	0.987997i	$-0.450632\pi$
$163$	−10.6417	−	10.6417i	−0.833523	−	0.833523i	−0.987997	+	0.154474i	$0.950632\pi$
$164$	−2.94495	−	0.789098i	−0.229962	−	0.0616182i
$165$	2.25754	−	3.91017i	0.175749	−	0.304406i
$166$	5.10996	+	8.85071i	0.396610	+	0.686949i
$167$	−0.832246	−	3.10599i	−0.0644012	−	0.240348i	0.926220	−	0.376982i	$-0.123038\pi$
$167$	−0.832246	−	3.10599i	−0.0644012	−	0.240348i	−0.990622	+	0.136634i	$0.956372\pi$
$168$	−0.0476601	−	2.64532i	−0.00367706	−	0.204091i
$169$	−11.0885	−	6.78566i	−0.852961	−	0.521974i
$170$	4.47600	−	7.75265i	0.343293	−	0.594601i
$171$	−5.46709	−	5.46709i	−0.418079	−	0.418079i
$172$	−2.02963			−0.154758
$173$	−1.09962			−0.0836024			−0.0418012	−	0.999126i	$-0.513310\pi$
$173$	−1.09962			−0.0836024			−0.0418012	+	0.999126i	$0.513310\pi$
$174$	6.66512	+	6.66512i	0.505282	+	0.505282i
$175$	0.115413	−	0.464004i	0.00872437	−	0.0350754i
$176$	−0.513412	+	1.91608i	−0.0386999	+	0.144430i
$177$	−12.7551	+	3.41773i	−0.958735	+	0.256892i
$178$	−8.09059	−	4.67111i	−0.606416	−	0.350114i
$179$		−	10.1077i		−	0.755488i	−0.925910	−	0.377744i	$-0.876700\pi$
$179$		−	10.1077i		−	0.755488i	0.925910	−	0.377744i	$-0.123300\pi$
$180$	2.19856	+	0.589103i	0.163871	+	0.0439092i
$181$	3.31301			0.246254			0.123127	−	0.992391i	$-0.460708\pi$
$181$	3.31301			0.246254			0.123127	+	0.992391i	$0.460708\pi$
$182$	−2.51716	−	9.20130i	−0.186584	−	0.682046i
$183$	10.1669			0.751559
$184$	6.19562	+	1.66011i	0.456747	+	0.122385i
$185$		−	24.4765i		−	1.79955i
$186$	−4.10009	−	2.36719i	−0.300633	−	0.173571i
$187$	7.53595	−	2.01925i	0.551084	−	0.147662i
$188$	0.0610541	−	0.227857i	0.00445283	−	0.0166182i
$189$	−1.90423	−	1.83682i	−0.138512	−	0.133609i
$190$	12.4438	+	12.4438i	0.902765	+	0.902765i
$191$	6.63312			0.479956			0.239978	−	0.970778i	$-0.422860\pi$
$191$	6.63312			0.479956			0.239978	+	0.970778i	$0.422860\pi$
$192$	−1.00000			−0.0721688
$193$	−11.5247	−	11.5247i	−0.829564	−	0.829564i	0.157892	−	0.987456i	$-0.449530\pi$
$193$	−11.5247	−	11.5247i	−0.829564	−	0.829564i	−0.987456	+	0.157892i	$0.949530\pi$
$194$	−2.40950	+	4.17337i	−0.172992	+	0.299630i
$195$	8.20600	+	0.104898i	0.587644	+	0.00751190i
$196$	3.27936	−	6.18432i	0.234240	−	0.441737i
$197$	−0.609343	−	2.27410i	−0.0434139	−	0.162023i	0.940816	−	0.338919i	$-0.110061\pi$
$197$	−0.609343	−	2.27410i	−0.0434139	−	0.162023i	−0.984230	+	0.176896i	$0.943394\pi$
$198$	0.991836	+	1.71791i	0.0704867	+	0.122087i
$199$	−6.17285	+	10.6917i	−0.437582	+	0.757914i	−0.997502	−	0.0706322i	$-0.977498\pi$
$199$	−6.17285	+	10.6917i	−0.437582	+	0.757914i	0.559921	+	0.828546i	$0.310832\pi$
$200$	−0.174563	−	0.0467740i	−0.0123435	−	0.00330742i
$201$	4.29914	+	4.29914i	0.303238	+	0.303238i
$202$	−7.98120	−	2.13855i	−0.561555	−	0.150468i
$203$	6.88747	+	23.9687i	0.483406	+	1.68227i
$204$	1.96650	+	3.40608i	0.137683	+	0.238474i
$205$	6.00981	−	3.46976i	0.419743	−	0.242339i
$206$	2.15628	−	2.15628i	0.150235	−	0.150235i
$207$	5.55484	−	3.20709i	0.386088	−	0.222908i
$208$	−3.49434	+	0.888593i	−0.242289	+	0.0616128i
$209$			15.3370i			1.06088i
$210$	4.33425	+	4.18083i	0.299091	+	0.288505i
$211$	−1.51300	+	2.62060i	−0.104160	+	0.180410i	−0.913395	−	0.407076i	$-0.866549\pi$
$211$	−1.51300	+	2.62060i	−0.104160	+	0.180410i	0.809235	+	0.587485i	$0.199882\pi$
$212$			5.36462i			0.368444i
$213$	−3.18104	+	11.8718i	−0.217961	+	0.813443i
$214$	4.64550	+	17.3373i	0.317560	+	1.18515i
$215$	3.26661	−	3.26661i	0.222781	−	0.222781i
$216$	−0.707107	+	0.707107i	−0.0481125	+	0.0481125i
$217$	−6.45738	−	10.7332i	−0.438356	−	0.728619i
$218$	6.22648	+	3.59486i	0.421710	+	0.243475i
$219$	−2.54614	+	9.50232i	−0.172052	+	0.642107i
$220$	−2.25754	−	3.91017i	−0.152203	−	0.263624i
$221$	9.89825	+	10.1546i	0.665828	+	0.683071i
$222$	9.31291	+	5.37681i	0.625042	+	0.360868i
$223$	−20.3067	+	5.44116i	−1.35984	+	0.364367i	−0.863756	−	0.503910i	$-0.831894\pi$
$223$	−20.3067	+	5.44116i	−1.35984	+	0.364367i	−0.496079	+	0.868277i	$0.665227\pi$
$224$	−2.31475	−	1.28139i	−0.154660	−	0.0856162i
$225$	−0.156509	+	0.0903604i	−0.0104339	+	0.00602403i
$226$	0.0370795	+	0.138383i	0.00246649	+	0.00920507i
$227$	4.59018	−	1.22993i	0.304661	−	0.0816336i	−0.103250	−	0.994655i	$-0.532924\pi$
$227$	4.59018	−	1.22993i	0.304661	−	0.0816336i	0.407911	+	0.913022i	$0.366257\pi$
$228$	−7.46819	+	2.00109i	−0.494593	+	0.132526i
$229$	−0.0336500	−	0.125583i	−0.00222365	−	0.00829879i	0.964805	−	0.262966i	$-0.0847007\pi$
$229$	−0.0336500	−	0.125583i	−0.00222365	−	0.00829879i	−0.967029	+	0.254667i	$0.918034\pi$
$230$	−12.6435	+	7.29972i	−0.833686	+	0.481329i
$231$	0.0945420	+	5.24745i	0.00622041	+	0.345257i
$232$	9.10473	−	2.43960i	0.597755	−	0.160168i
$233$	8.03580	+	4.63947i	0.526443	+	0.303942i	0.739567	−	0.673083i	$-0.235030\pi$
$233$	8.03580	+	4.63947i	0.526443	+	0.303942i	−0.213124	+	0.977025i	$0.568364\pi$
$234$	−1.84254	+	3.09920i	−0.120451	+	0.202601i
$235$	0.268463	+	0.464991i	0.0175126	+	0.0303327i
$236$	−3.41773	+	12.7551i	−0.222475	+	0.830289i
$237$	−14.9556	−	8.63462i	−0.971470	−	0.560879i
$238$	0.187448	+	10.4041i	0.0121504	+	0.674395i
$239$	−8.02522	+	8.02522i	−0.519108	+	0.519108i	−0.917302	−	0.398193i	$-0.869637\pi$
$239$	−8.02522	+	8.02522i	−0.519108	+	0.519108i	0.398193	+	0.917302i	$0.369637\pi$
$240$	1.60946	−	1.60946i	0.103890	−	0.103890i
$241$	5.09278	+	19.0065i	0.328055	+	1.22432i	0.911205	+	0.411953i	$0.135153\pi$
$241$	5.09278	+	19.0065i	0.328055	+	1.22432i	−0.583151	+	0.812364i	$0.698180\pi$
$242$	−1.82857	+	6.82431i	−0.117545	+	0.438683i
$243$			1.00000i			0.0641500i
$244$	5.08345	−	8.80479i	0.325434	−	0.563669i
$245$	4.67542	+	15.2314i	0.298702	+	0.973099i
$246$			3.04884i			0.194387i
$247$	−24.3182	+	13.6287i	−1.54733	+	0.867172i
$248$	−4.10009	+	2.36719i	−0.260356	+	0.150317i
$249$	7.22658	−	7.22658i	0.457966	−	0.457966i
$250$	−9.49965	+	5.48463i	−0.600811	+	0.346878i
$251$	5.35285	+	9.27140i	0.337869	+	0.585206i	0.984032	−	0.177994i	$-0.0569607\pi$
$251$	5.35285	+	9.27140i	0.337869	+	0.585206i	−0.646163	+	0.763199i	$0.723627\pi$
$252$	−2.54285	+	0.730696i	−0.160184	+	0.0460295i
$253$	−12.2901	−	3.29312i	−0.772670	−	0.207036i
$254$	−3.60082	−	3.60082i	−0.225935	−	0.225935i
$255$	−8.64696	−	2.31695i	−0.541494	−	0.145093i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−7.48569	−	12.9656i	−0.466945	−	0.808772i	0.532342	−	0.846529i	$-0.321312\pi$
$257$	−7.48569	−	12.9656i	−0.466945	−	0.808772i	−0.999287	+	0.0377573i	$0.987979\pi$
$258$	0.525308	+	1.96048i	0.0327042	+	0.122054i
$259$	14.6673	+	24.3794i	0.911379	+	1.51486i
$260$	4.19384	−	7.05415i	0.260091	−	0.437480i
$261$	4.71295	−	8.16308i	0.291725	−	0.505282i
$262$	6.72111	+	6.72111i	0.415231	+	0.415231i
$263$	16.5831			1.02256			0.511278	−	0.859415i	$-0.329172\pi$
$263$	16.5831			1.02256			0.511278	+	0.859415i	$0.329172\pi$
$264$	1.98367			0.122087
$265$	−8.63415	−	8.63415i	−0.530391	−	0.530391i
$266$	−19.8511	−	4.93761i	−1.21715	−	0.302744i
$267$	−2.41794	+	9.02389i	−0.147976	+	0.552253i
$268$	5.87273	−	1.57359i	0.358734	−	0.0961225i
$269$	19.4954	+	11.2557i	1.18865	+	0.686269i	0.958000	−	0.286767i	$-0.0925805\pi$
$269$	19.4954	+	11.2557i	1.18865	+	0.686269i	0.230653	+	0.973036i	$0.425914\pi$
$270$		−	2.27612i		−	0.138520i
$271$	22.2784	+	5.96948i	1.35332	+	0.362620i	0.861358	−	0.507999i	$-0.169614\pi$
$271$	22.2784	+	5.96948i	1.35332	+	0.362620i	0.491959	+	0.870619i	$0.336281\pi$
$272$	3.93301			0.238474
$273$	−8.23629	+	4.81286i	−0.498483	+	0.291287i
$274$	−19.8973			−1.20204
$275$	0.346275	+	0.0927842i	0.0208812	+	0.00559510i
$276$		−	6.41418i		−	0.386088i
$277$	4.69021	+	2.70790i	0.281808	+	0.162702i	0.634241	−	0.773135i	$-0.281312\pi$
$277$	4.69021	+	2.70790i	0.281808	+	0.162702i	−0.352434	+	0.935837i	$0.614646\pi$
$278$	2.80014	−	0.750295i	0.167941	−	0.0449997i
$279$	−1.22535	+	4.57305i	−0.0733595	+	0.273782i
$280$	5.78783	−	1.66315i	0.345889	−	0.0993923i
$281$	13.1743	+	13.1743i	0.785914	+	0.785914i	0.980822	−	0.194907i	$-0.0624406\pi$
$281$	13.1743	+	13.1743i	0.785914	+	0.785914i	−0.194907	+	0.980822i	$0.562441\pi$
$282$	−0.235895			−0.0140473
$283$	−6.65461			−0.395576			−0.197788	−	0.980245i	$-0.563376\pi$
$283$	−6.65461			−0.395576			−0.197788	+	0.980245i	$0.563376\pi$
$284$	8.69077	+	8.69077i	0.515702	+	0.515702i
$285$	8.79906	−	15.2404i	0.521212	−	0.902765i
$286$	6.93162	−	1.76268i	0.409875	−	0.104229i
$287$	−3.90674	+	7.05729i	−0.230608	+	0.416579i
$288$	0.258819	+	0.965926i	0.0152511	+	0.0569177i
$289$	0.765733	+	1.32629i	0.0450431	+	0.0780169i
$290$	−10.7272	+	18.5801i	−0.629926	+	1.09106i
$291$	4.65479	+	1.24725i	0.272869	+	0.0731149i
$292$	6.95618	+	6.95618i	0.407080	+	0.407080i
$293$	2.44950	+	0.656343i	0.143102	+	0.0383439i	0.329659	−	0.944100i	$-0.393066\pi$
$293$	2.44950	+	0.656343i	0.143102	+	0.0383439i	−0.186557	+	0.982444i	$0.559733\pi$
$294$	−6.82235	−	1.56700i	−0.397888	−	0.0913891i
$295$	−15.0282	−	26.0296i	−0.874975	−	1.51550i
$296$	9.31291	−	5.37681i	0.541302	−	0.312521i
$297$	1.40267	−	1.40267i	0.0813910	−	0.0813910i
$298$	−9.49053	+	5.47936i	−0.549772	+	0.317411i
$299$	−5.69959	−	22.4133i	−0.329616	−	1.29619i
$300$			0.180721i			0.0104339i
$301$	−1.29617	+	5.21113i	−0.0747101	+	0.300364i
$302$	7.12967	−	12.3490i	0.410266	−	0.710602i
$303$			8.26274i			0.474682i
$304$	−2.00109	+	7.46819i	−0.114771	+	0.428330i
$305$	5.98935	+	22.3526i	0.342949	+	1.27990i
$306$	2.78106	−	2.78106i	0.158982	−	0.158982i
$307$	7.32158	−	7.32158i	0.417865	−	0.417865i	−0.466603	−	0.884467i	$-0.654522\pi$
$307$	7.32158	−	7.32158i	0.417865	−	0.417865i	0.884467	+	0.466603i	$0.154522\pi$
$308$	4.59170	+	2.54185i	0.261636	+	0.144835i
$309$	−2.64090	−	1.52472i	−0.150235	−	0.0867384i
$310$	2.78903	−	10.4088i	0.158406	−	0.591181i
$311$	−8.38300	−	14.5198i	−0.475356	−	0.823341i	0.524245	−	0.851567i	$-0.324348\pi$
$311$	−8.38300	−	14.5198i	−0.475356	−	0.823341i	−0.999602	+	0.0282259i	$0.991014\pi$
$312$	1.76272	+	3.14529i	0.0997942	+	0.178067i
$313$	−2.62774	−	1.51713i	−0.148529	−	0.0857532i	0.423894	−	0.905712i	$-0.360663\pi$
$313$	−2.62774	−	1.51713i	−0.148529	−	0.0857532i	−0.572423	+	0.819959i	$0.693996\pi$
$314$	−9.97041	+	2.67156i	−0.562663	+	0.150765i
$315$	2.91659	−	5.26864i	0.164331	−	0.296854i
$316$	−14.9556	+	8.63462i	−0.841318	+	0.485735i
$317$	−0.579728	−	2.16358i	−0.0325608	−	0.121519i	0.947733	−	0.319066i	$-0.103369\pi$
$317$	−0.579728	−	2.16358i	−0.0325608	−	0.121519i	−0.980293	+	0.197547i	$0.936702\pi$
$318$	5.18183	−	1.38847i	0.290583	−	0.0778614i
$319$	−18.0608	+	4.83938i	−1.01121	+	0.270953i
$320$	−0.589103	−	2.19856i	−0.0329319	−	0.122903i
$321$	15.5442	−	8.97443i	0.867590	−	0.500904i
$322$	8.21904	−	14.8472i	0.458029	−	0.827402i
$323$	29.3724	−	7.87032i	1.63433	−	0.437916i
$324$	0.866025	+	0.500000i	0.0481125	+	0.0277778i
$325$	0.160587	+	0.631500i	0.00890778	+	0.0350293i
$326$	7.52482	+	13.0334i	0.416761	+	0.721852i
$327$	1.86084	−	6.94473i	0.102904	−	0.384045i
$328$	2.64037	+	1.52442i	0.145790	+	0.0841720i
$329$	−0.546037	−	0.302273i	−0.0301040	−	0.0166648i
$330$	−3.19264	+	3.19264i	−0.175749	+	0.175749i
$331$	10.0911	−	10.0911i	0.554656	−	0.554656i	−0.373125	−	0.927781i	$-0.621714\pi$
$331$	10.0911	−	10.0911i	0.554656	−	0.554656i	0.927781	+	0.373125i	$0.121714\pi$
$332$	−2.64511	−	9.87169i	−0.145169	−	0.541779i
$333$	2.78324	−	10.3872i	0.152521	−	0.569215i
$334$			3.21555i			0.175947i
$335$	−6.91928	+	11.9846i	−0.378041	+	0.654786i
$336$	−0.638624	+	2.56752i	−0.0348398	+	0.140070i
$337$		−	15.4670i		−	0.842541i	−0.906935	−	0.421270i	$-0.861584\pi$
$337$		−	15.4670i		−	0.842541i	0.906935	−	0.421270i	$-0.138416\pi$
$338$	8.95441	+	9.42436i	0.487056	+	0.512618i
$339$	0.124070	−	0.0716321i	0.00673858	−	0.00389052i
$340$	−6.33001	+	6.33001i	−0.343293	+	0.343293i
$341$	8.13323	−	4.69572i	0.440439	−	0.254288i
$342$	3.86582	+	6.69579i	0.209039	+	0.362067i
$343$	−13.7841	−	12.3693i	−0.744271	−	0.667878i
$344$	1.96048	+	0.525308i	0.105702	+	0.0283227i
$345$	10.3234	+	10.3234i	0.555791	+	0.555791i
$346$	1.06215	+	0.284602i	0.0571015	+	0.0153003i
$347$	−0.754741	+	1.30725i	−0.0405166	+	0.0701768i	−0.885573	−	0.464501i	$-0.846234\pi$
$347$	−0.754741	+	1.30725i	−0.0405166	+	0.0701768i	0.845056	+	0.534678i	$0.179567\pi$
$348$	−4.71295	−	8.16308i	−0.252641	−	0.437587i
$349$	−8.01723	−	29.9207i	−0.429152	−	1.60162i	−0.754685	−	0.656088i	$-0.772210\pi$
$349$	−8.01723	−	29.9207i	−0.429152	−	1.60162i	0.325532	−	0.945531i	$-0.394457\pi$
$350$	−0.231573	+	0.418323i	−0.0123781	+	0.0223603i
$351$	3.47048	+	0.977625i	0.185241	+	0.0521818i
$352$	0.991836	−	1.71791i	0.0528650	−	0.0915649i
$353$	−14.5716	−	14.5716i	−0.775568	−	0.775568i	0.203506	−	0.979074i	$-0.434766\pi$
$353$	−14.5716	−	14.5716i	−0.775568	−	0.775568i	−0.979074	+	0.203506i	$0.934766\pi$
$354$	13.2051			0.701843
$355$	−27.9749			−1.48475
$356$	6.60594	+	6.60594i	0.350114	+	0.350114i
$357$	10.0010	−	2.87383i	0.529311	−	0.152099i
$358$	−2.61608	+	9.76333i	−0.138264	+	0.516008i
$359$	−2.88546	+	0.773156i	−0.152289	+	0.0408056i	−0.334158	−	0.942517i	$-0.608452\pi$
$359$	−2.88546	+	0.773156i	−0.152289	+	0.0408056i	0.181869	+	0.983323i	$0.441785\pi$
$360$	−1.97118	−	1.13806i	−0.103890	−	0.0599810i
$361$			40.7782i			2.14622i
$362$	−3.20012	−	0.857471i	−0.168195	−	0.0450677i
$363$	7.06505			0.370819
$364$	0.0499138	+	9.53926i	0.00261619	+	0.499993i
$365$	−22.3914			−1.17202
$366$	−9.82047	−	2.63139i	−0.513324	−	0.137545i
$367$		−	6.90349i		−	0.360359i	−0.983634	−	0.180180i	$-0.942332\pi$
$367$		−	6.90349i		−	0.360359i	0.983634	−	0.180180i	$-0.0576679\pi$
$368$	−5.55484	−	3.20709i	−0.289566	−	0.167181i
$369$	2.94495	−	0.789098i	0.153308	−	0.0410788i
$370$	−6.33499	+	23.6425i	−0.329341	+	1.22912i
$371$	13.7738	+	3.42598i	0.715099	+	0.177868i
$372$	3.34771	+	3.34771i	0.173571	+	0.173571i
$373$	−20.6159			−1.06745			−0.533725	−	0.845658i	$-0.679208\pi$
$373$	−20.6159			−1.06745			−0.533725	+	0.845658i	$0.679208\pi$
$374$	−7.80179			−0.403421
$375$	7.75644	+	7.75644i	0.400541	+	0.400541i
$376$	−0.117948	+	0.204291i	−0.00608268	+	0.0105355i
$377$	−23.7223	−	24.3367i	−1.22176	−	1.25340i
$378$	1.36394	+	2.26709i	0.0701533	+	0.116606i
$379$	1.29360	+	4.82778i	0.0664478	+	0.247986i	0.991158	−	0.132685i	$-0.0423597\pi$
$379$	1.29360	+	4.82778i	0.0664478	+	0.247986i	−0.924711	+	0.380671i	$0.875693\pi$
$380$	−8.79906	−	15.2404i	−0.451382	−	0.781817i
$381$	−2.54616	+	4.41008i	−0.130444	+	0.225935i
$382$	−6.40710	−	1.71678i	−0.327816	−	0.0878380i
$383$	−8.24270	−	8.24270i	−0.421182	−	0.421182i	0.464428	−	0.885611i	$-0.346260\pi$
$383$	−8.24270	−	8.24270i	−0.421182	−	0.421182i	−0.885611	+	0.464428i	$0.846260\pi$
$384$	0.965926	+	0.258819i	0.0492922	+	0.0132078i
$385$	−11.4812	+	3.29915i	−0.585134	+	0.168140i
$386$	8.14918	+	14.1148i	0.414782	+	0.718424i
$387$	1.75771	−	1.01482i	0.0893497	−	0.0515861i
$388$	3.40754	−	3.40754i	0.172992	−	0.172992i
$389$	−13.0265	+	7.52087i	−0.660472	+	0.381323i	−0.792457	−	0.609928i	$-0.791198\pi$
$389$	−13.0265	+	7.52087i	−0.660472	+	0.381323i	0.131985	+	0.991252i	$0.457865\pi$
$390$	−7.89923	−	2.22519i	−0.399993	−	0.112677i
$391$			25.2270i			1.27578i
$392$	−4.76824	+	5.12483i	−0.240832	+	0.258843i
$393$	4.75254	−	8.23164i	0.239734	−	0.415231i
$394$			2.35432i			0.118609i
$395$	10.1734	−	37.9675i	0.511877	−	1.91035i
$396$	−0.513412	−	1.91608i	−0.0257999	−	0.0962866i
$397$	−11.8425	+	11.8425i	−0.594356	+	0.594356i	−0.938805	−	0.344449i	$-0.888066\pi$
$397$	−11.8425	+	11.8425i	−0.594356	+	0.594356i	0.344449	+	0.938805i	$0.388066\pi$
$398$	8.72973	−	8.72973i	0.437582	−	0.437582i
$399$	0.368491	+	20.4527i	0.0184476	+	1.02391i
$400$	0.156509	+	0.0903604i	0.00782544	+	0.00451802i
$401$	−3.48242	+	12.9966i	−0.173904	+	0.649017i	0.822832	+	0.568284i	$0.192393\pi$
$401$	−3.48242	+	12.9966i	−0.173904	+	0.649017i	−0.996736	+	0.0807326i	$0.974274\pi$
$402$	−3.03995	−	5.26534i	−0.151619	−	0.262611i
$403$	14.6728	+	8.72327i	0.730903	+	0.434537i
$404$	7.15574	+	4.13137i	0.356012	+	0.205543i
$405$	−2.19856	+	0.589103i	−0.109247	+	0.0292728i
$406$	−0.449240	−	24.9346i	−0.0222954	−	1.23748i
$407$	−18.4738	+	10.6658i	−0.915710	+	0.528686i
$408$	−1.01794	−	3.79899i	−0.0503954	−	0.188078i
$409$	37.7327	−	10.1105i	1.86576	−	0.499930i	0.865763	−	0.500454i	$-0.166833\pi$
$409$	37.7327	−	10.1105i	1.86576	−	0.499930i	1.00000		0.000523754i	$0.000166716\pi$
$410$	−6.70307	+	1.79608i	−0.331041	+	0.0887021i
$411$	5.14980	+	19.2193i	0.254021	+	0.948019i
$412$	−2.64090	+	1.52472i	−0.130108	+	0.0751177i
$413$	30.5664	+	16.9208i	1.50408	+	0.832619i
$414$	−6.19562	+	1.66011i	−0.304498	+	0.0815900i
$415$	20.1453	+	11.6309i	0.988893	+	0.570938i
$416$	3.60526	+	0.0460863i	0.176762	+	0.00225957i
$417$	−1.44946	−	2.51054i	−0.0709803	−	0.122941i
$418$	3.96952	−	14.8144i	0.194155	−	0.724598i
$419$	17.7160	+	10.2283i	0.865484	+	0.499687i	0.865845	−	0.500313i	$-0.166782\pi$
$419$	17.7160	+	10.2283i	0.865484	+	0.499687i	−0.000360967		1.00000i	$0.500115\pi$
$420$	−3.10448	−	5.16016i	−0.151483	−	0.251790i
$421$	−0.718792	+	0.718792i	−0.0350318	+	0.0350318i	−0.724406	−	0.689374i	$-0.757886\pi$
$421$	−0.718792	+	0.718792i	−0.0350318	+	0.0350318i	0.689374	+	0.724406i	$0.257886\pi$
$422$	2.13971	−	2.13971i	0.104160	−	0.104160i
$423$	0.0610541	+	0.227857i	0.00296855	+	0.0110788i
$424$	1.38847	−	5.18183i	0.0674299	−	0.251652i
$425$		−	0.710776i		−	0.0344777i
$426$	6.14530	−	10.6440i	0.297741	−	0.515702i
$427$	−19.3601	−	18.6748i	−0.936899	−	0.903737i
$428$		−	17.9489i		−	0.867590i
$429$	−3.49665	−	6.23922i	−0.168820	−	0.301232i
$430$	−4.00077	+	2.30985i	−0.192934	+	0.111391i
$431$	7.65078	−	7.65078i	0.368525	−	0.368525i	−0.498414	−	0.866939i	$-0.666084\pi$
$431$	7.65078	−	7.65078i	0.368525	−	0.368525i	0.866939	+	0.498414i	$0.166084\pi$
$432$	0.866025	−	0.500000i	0.0416667	−	0.0240563i
$433$	−7.13199	−	12.3530i	−0.342742	−	0.593646i	0.642199	−	0.766538i	$-0.278022\pi$
$433$	−7.13199	−	12.3530i	−0.342742	−	0.593646i	−0.984941	+	0.172892i	$0.944689\pi$
$434$	3.45939	+	12.0388i	0.166056	+	0.577881i
$435$	20.7235	+	5.55283i	0.993613	+	0.266238i
$436$	−5.08390	−	5.08390i	−0.243475	−	0.243475i
$437$	−47.9023	−	12.8354i	−2.29148	−	0.613999i
$438$	4.91876	−	8.51955i	0.235028	−	0.407080i
$439$	−13.1006	−	22.6909i	−0.625257	−	1.08298i	−0.988491	−	0.151278i	$-0.951661\pi$
$439$	−13.1006	−	22.6909i	−0.625257	−	1.08298i	0.363235	−	0.931698i	$-0.381672\pi$
$440$	1.16859	+	4.36123i	0.0557102	+	0.207913i
$441$	0.252153	+	6.99546i	0.0120073	+	0.333117i
$442$	−6.93277	−	12.3704i	−0.329758	−	0.588401i
$443$	1.18805	−	2.05776i	0.0564458	−	0.0977671i	−0.836422	−	0.548086i	$-0.815357\pi$
$443$	1.18805	−	2.05776i	0.0564458	−	0.0977671i	0.892868	+	0.450319i	$0.148690\pi$
$444$	−7.60396	−	7.60396i	−0.360868	−	0.360868i
$445$	−21.2640			−1.00801
$446$	21.0230			0.995468
$447$	7.74899	+	7.74899i	0.366514	+	0.366514i
$448$	1.90423	+	1.83682i	0.0899662	+	0.0867818i
$449$	−4.14317	+	15.4625i	−0.195528	+	0.729721i	0.796601	+	0.604505i	$0.206629\pi$
$449$	−4.14317	+	15.4625i	−0.195528	+	0.729721i	−0.992130	+	0.125216i	$0.960038\pi$
$450$	0.174563	−	0.0467740i	0.00822897	−	0.00220495i
$451$	−5.23764	−	3.02395i	−0.246631	−	0.142392i
$452$		−	0.143264i		−	0.00673858i
$453$	−13.7735	−	3.69059i	−0.647134	−	0.173399i
$454$	−4.75210			−0.223027
$455$	−15.4334	−	15.2727i	−0.723529	−	0.715996i
$456$	7.73164			0.362067
$457$	15.5117	+	4.15636i	0.725608	+	0.194426i	0.602673	−	0.797989i	$-0.294103\pi$
$457$	15.5117	+	4.15636i	0.725608	+	0.194426i	0.122935	+	0.992415i	$0.460769\pi$
$458$			0.130014i			0.00607513i
$459$	−3.40608	−	1.96650i	−0.158982	−	0.0917885i
$460$	14.1020	−	3.77861i	0.657508	−	0.176179i
$461$	3.02908	−	11.3047i	0.141078	−	0.526511i	−0.858820	−	0.512277i	$-0.828802\pi$
$461$	3.02908	−	11.3047i	0.141078	−	0.526511i	0.999899	−	0.0142346i	$-0.00453115\pi$
$462$	1.26682	−	5.09312i	0.0589378	−	0.236953i
$463$	18.3713	+	18.3713i	0.853787	+	0.853787i	0.990597	−	0.136810i	$-0.0436851\pi$
$463$	18.3713	+	18.3713i	0.853787	+	0.853787i	−0.136810	+	0.990597i	$0.543685\pi$
$464$	−9.42591			−0.437587
$465$	−10.7760			−0.499725
$466$	−6.56120	−	6.56120i	−0.303942	−	0.303942i
$467$	−18.1319	+	31.4054i	−0.839044	+	1.45327i	0.0516500	+	0.998665i	$0.483552\pi$
$467$	−18.1319	+	31.4054i	−0.839044	+	1.45327i	−0.890694	+	0.454602i	$0.849781\pi$
$468$	2.58189	−	2.51671i	0.119348	−	0.116335i
$469$	−0.289768	−	16.0833i	−0.0133803	−	0.742657i
$470$	−0.138967	−	0.518630i	−0.00641005	−	0.0239226i
$471$	5.16106	+	8.93922i	0.237809	+	0.411898i
$472$	6.60255	−	11.4359i	0.303907	−	0.526382i
$473$	−3.88894	−	1.04204i	−0.178814	−	0.0479130i
$474$	12.2112	+	12.2112i	0.560879	+	0.560879i
$475$	1.34966	+	0.361639i	0.0619265	+	0.0165932i
$476$	2.51171	−	10.0981i	0.115124	−	0.462844i
$477$	−2.68231	−	4.64590i	−0.122815	−	0.212721i
$478$	9.82885	−	5.67469i	0.449561	−	0.259554i
$479$	−0.458819	+	0.458819i	−0.0209640	+	0.0209640i	−0.717511	−	0.696547i	$-0.754719\pi$
$479$	−0.458819	+	0.458819i	−0.0209640	+	0.0209640i	0.696547	+	0.717511i	$0.254719\pi$
$480$	−1.97118	+	1.13806i	−0.0899715	+	0.0519451i
$481$	−33.3276	−	19.8140i	−1.51961	−	0.903440i
$482$		−	19.6770i		−	0.896262i
$483$	−16.4685	−	4.09624i	−0.749344	−	0.186386i
$484$	3.53252	−	6.11851i	0.160569	−	0.278114i
$485$			10.9686i			0.498059i
$486$	0.258819	−	0.965926i	0.0117403	−	0.0438153i
$487$	−6.43996	−	24.0343i	−0.291822	−	1.08910i	−0.943708	−	0.330779i	$-0.892689\pi$
$487$	−6.43996	−	24.0343i	−0.291822	−	1.08910i	0.651886	−	0.758317i	$-0.273978\pi$
$488$	−7.18908	+	7.18908i	−0.325434	+	0.325434i
$489$	10.6417	−	10.6417i	0.481235	−	0.481235i
$490$	−0.573930	−	15.9225i	−0.0259275	−	0.719305i
$491$	−21.9510	−	12.6734i	−0.990633	−	0.571942i	−0.0851695	−	0.996366i	$-0.527143\pi$
$491$	−21.9510	−	12.6734i	−0.990633	−	0.571942i	−0.905463	+	0.424424i	$0.860477\pi$
$492$	0.789098	−	2.94495i	0.0355753	−	0.132769i
$493$	18.5361	+	32.1054i	0.834823	+	1.44596i
$494$	27.0170	−	6.87028i	1.21555	−	0.309108i
$495$	3.91017	+	2.25754i	0.175749	+	0.101469i
$496$	4.57305	−	1.22535i	0.205336	−	0.0550197i
$497$	27.8639	−	16.7636i	1.24987	−	0.751950i
$498$	−8.85071	+	5.10996i	−0.396610	+	0.228983i
$499$	4.09508	+	15.2830i	0.183321	+	0.684163i	0.994984	+	0.100037i	$0.0318961\pi$
$499$	4.09508	+	15.2830i	0.183321	+	0.684163i	−0.811663	+	0.584126i	$0.801437\pi$
$500$	10.5955	−	2.83905i	0.473845	−	0.126966i
$501$	3.10599	−	0.832246i	0.138765	−	0.0371820i
$502$	−2.77084	−	10.3409i	−0.123669	−	0.461537i
$503$	20.3646	−	11.7575i	0.908011	−	0.524240i	0.0282204	−	0.999602i	$-0.491016\pi$
$503$	20.3646	−	11.7575i	0.908011	−	0.524240i	0.879791	+	0.475361i	$0.157683\pi$
$504$	2.64532	−	0.0476601i	0.117832	−	0.00212295i
$505$	−18.1662	+	4.86761i	−0.808383	+	0.216606i
$506$	11.0190	+	6.36181i	0.489853	+	0.282817i
$507$	6.78566	−	11.0885i	0.301362	−	0.492458i
$508$	2.54616	+	4.41008i	0.112968	+	0.195666i
$509$	−2.46128	+	9.18564i	−0.109095	+	0.407146i	−0.998777	−	0.0494325i	$-0.984259\pi$
$509$	−2.46128	+	9.18564i	−0.109095	+	0.407146i	0.889683	+	0.456579i	$0.150925\pi$
$510$	7.75265	+	4.47600i	0.343293	+	0.198200i
$511$	22.3025	−	13.4178i	0.986605	−	0.593566i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	5.46709	−	5.46709i	0.241378	−	0.241378i
$514$	3.87488	+	14.4612i	0.170914	+	0.637858i
$515$	1.79644	−	6.70439i	0.0791605	−	0.295431i
$516$		−	2.02963i		−	0.0893497i
$517$	0.233969	−	0.405247i	0.0102900	−	0.0178227i
$518$	−7.85763	−	27.3448i	−0.345244	−	1.20146i
$519$		−	1.09962i		−	0.0482679i
$520$	−5.87669	+	5.72834i	−0.257710	+	0.251204i
$521$	22.3968	−	12.9308i	0.981224	−	0.566510i	0.0785844	−	0.996907i	$-0.474960\pi$
$521$	22.3968	−	12.9308i	0.981224	−	0.566510i	0.902639	+	0.430398i	$0.141627\pi$
$522$	−6.66512	+	6.66512i	−0.291725	+	0.291725i
$523$	25.3946	−	14.6616i	1.11043	−	0.641106i	0.171488	−	0.985186i	$-0.445143\pi$
$523$	25.3946	−	14.6616i	1.11043	−	0.641106i	0.938940	+	0.344080i	$0.111809\pi$
$524$	−4.75254	−	8.23164i	−0.207616	−	0.359601i
$525$	0.464004	+	0.115413i	0.0202508	+	0.00503702i
$526$	−16.0180	−	4.29202i	−0.698419	−	0.187141i
$527$	−13.1666	−	13.1666i	−0.573544	−	0.573544i
$528$	−1.91608	−	0.513412i	−0.0833867	−	0.0223434i
$529$	9.07083	−	15.7111i	0.394384	−	0.683093i
$530$	6.10526	+	10.5746i	0.265196	+	0.459332i
$531$	−3.41773	−	12.7551i	−0.148317	−	0.553526i
$532$	17.8968	+	9.90721i	0.775924	+	0.429532i
$533$	0.140510	−	10.9919i	0.00608616	−	0.476110i
$534$	4.67111	−	8.09059i	0.202139	−	0.350114i
$535$	28.8880	+	28.8880i	1.24894	+	1.24894i
$536$	−6.07990			−0.262611
$537$	10.1077			0.436181
$538$	−15.9179	−	15.9179i	−0.686269	−	0.686269i
$539$	9.45862	−	10.1660i	0.407411	−	0.437880i
$540$	−0.589103	+	2.19856i	−0.0253510	+	0.0946111i
$541$	−36.7275	+	9.84110i	−1.57904	+	0.423102i	−0.938628	−	0.344931i	$-0.887902\pi$
$541$	−36.7275	+	9.84110i	−1.57904	+	0.423102i	−0.640410	+	0.768033i	$0.721235\pi$
$542$	−19.9743	−	11.5321i	−0.857968	−	0.495348i
$543$			3.31301i			0.142175i
$544$	−3.79899	−	1.01794i	−0.162880	−	0.0436437i
$545$	16.3647			0.700985
$546$	9.20130	−	2.51716i	0.393779	−	0.107724i
$547$	11.0101			0.470757			0.235379	−	0.971904i	$-0.424367\pi$
$547$	11.0101			0.470757			0.235379	+	0.971904i	$0.424367\pi$
$548$	19.2193	+	5.14980i	0.821008	+	0.219989i
$549$			10.1669i			0.433913i
$550$	−0.310462	−	0.179245i	−0.0132381	−	0.00764305i
$551$	−70.3944	+	18.8621i	−2.99890	+	0.803554i
$552$	−1.66011	+	6.19562i	−0.0706590	+	0.263703i
$553$	12.6186	+	43.9131i	0.536596	+	1.86737i
$554$	−3.82954	−	3.82954i	−0.162702	−	0.162702i
$555$	24.4765			1.03897
$556$	−2.89892			−0.122941
$557$	−3.82860	−	3.82860i	−0.162223	−	0.162223i	0.621328	−	0.783551i	$-0.286594\pi$
$557$	−3.82860	−	3.82860i	−0.162223	−	0.162223i	−0.783551	+	0.621328i	$0.786594\pi$
$558$	2.36719	−	4.10009i	0.100211	−	0.173571i
$559$	−1.80352	−	7.09223i	−0.0762807	−	0.299969i
$560$	−6.02107	+	0.108480i	−0.254437	+	0.00458412i
$561$	2.01925	+	7.53595i	0.0852529	+	0.318168i
$562$	−9.31566	−	16.1352i	−0.392957	−	0.680622i
$563$	−20.8560	+	36.1237i	−0.878977	+	1.52243i	−0.0265124	+	0.999648i	$0.508440\pi$
$563$	−20.8560	+	36.1237i	−0.878977	+	1.52243i	−0.852465	+	0.522785i	$0.824893\pi$
$564$	0.227857	+	0.0610541i	0.00959452	+	0.00257084i
$565$	0.230578	+	0.230578i	0.00970049	+	0.00970049i
$566$	6.42786	+	1.72234i	0.270183	+	0.0723953i
$567$	1.83682	−	1.90423i	0.0771394	−	0.0799700i
$568$	−6.14530	−	10.6440i	−0.257851	−	0.446611i
$569$	11.4564	−	6.61436i	0.480278	−	0.277289i	−0.240254	−	0.970710i	$-0.577231\pi$
$569$	11.4564	−	6.61436i	0.480278	−	0.277289i	0.720532	+	0.693421i	$0.243898\pi$
$570$	−12.4438	+	12.4438i	−0.521212	+	0.521212i
$571$	−16.0469	+	9.26466i	−0.671540	+	0.387714i	−0.796660	−	0.604428i	$-0.793402\pi$
$571$	−16.0469	+	9.26466i	−0.671540	+	0.387714i	0.125120	+	0.992142i	$0.460068\pi$
$572$	−7.15165	−	0.0914201i	−0.299025	−	0.00382247i
$573$			6.63312i			0.277103i
$574$	5.60019	−	5.80568i	0.233747	−	0.242324i
$575$	−0.579587	+	1.00387i	−0.0241705	+	0.0418645i
$576$		−	1.00000i		−	0.0416667i
$577$	11.6779	−	43.5824i	0.486156	−	1.81436i	−0.0886429	−	0.996063i	$-0.528253\pi$
$577$	11.6779	−	43.5824i	0.486156	−	1.81436i	0.574799	−	0.818295i	$-0.305080\pi$
$578$	−0.396372	−	1.47928i	−0.0164869	−	0.0615300i
$579$	11.5247	−	11.5247i	0.478949	−	0.478949i
$580$	15.1706	−	15.1706i	0.629926	−	0.629926i
$581$	−27.0350	+	0.487083i	−1.12160	+	0.0202076i
$582$	−4.17337	−	2.40950i	−0.172992	−	0.0998768i
$583$	−2.75426	+	10.2790i	−0.114070	+	0.425715i
$584$	−4.91876	−	8.51955i	−0.203540	−	0.352541i
$585$	−0.104898	+	8.20600i	−0.00433700	+	0.339276i
$586$	−2.19616	−	1.26796i	−0.0907227	−	0.0523788i
$587$	−7.48626	+	2.00594i	−0.308991	+	0.0827939i	−0.409982	−	0.912093i	$-0.634465\pi$
$587$	−7.48626	+	2.00594i	−0.308991	+	0.0827939i	0.100991	+	0.994887i	$0.467799\pi$
$588$	6.18432	+	3.27936i	0.255037	+	0.135238i
$589$	31.7004	−	18.3022i	1.30619	−	0.754130i
$590$	7.77916	+	29.0322i	0.320263	+	1.19524i
$591$	2.27410	−	0.609343i	0.0935439	−	0.0250650i
$592$	−10.3872	+	2.78324i	−0.426911	+	0.114391i
$593$	2.13061	+	7.95154i	0.0874936	+	0.326531i	0.995775	−	0.0918298i	$-0.0292716\pi$
$593$	2.13061	+	7.95154i	0.0874936	+	0.326531i	−0.908281	+	0.418360i	$0.862605\pi$
$594$	−1.71791	+	0.991836i	−0.0704867	+	0.0406955i
$595$	12.2099	+	20.2949i	0.500559	+	0.832011i
$596$	10.5853	−	2.83633i	0.433591	−	0.116180i
$597$	−10.6917	−	6.17285i	−0.437582	−	0.252638i
$598$	−0.295606	+	23.1248i	−0.0120882	+	0.945641i
$599$	−18.9617	−	32.8427i	−0.774755	−	1.34191i	−0.934932	−	0.354826i	$-0.884540\pi$
$599$	−18.9617	−	32.8427i	−0.774755	−	1.34191i	0.160178	−	0.987088i	$-0.448793\pi$
$600$	0.0467740	−	0.174563i	0.00190954	−	0.00712650i
$601$	20.5717	+	11.8771i	0.839136	+	0.484475i	0.856970	−	0.515366i	$-0.172344\pi$
$601$	20.5717	+	11.8771i	0.839136	+	0.484475i	−0.0178346	+	0.999841i	$0.505677\pi$
$602$	2.60075	−	4.69809i	0.105998	−	0.191480i
$603$	−4.29914	+	4.29914i	−0.175074	+	0.175074i
$604$	−10.0829	+	10.0829i	−0.410266	+	0.410266i
$605$	4.16204	+	15.5329i	0.169211	+	0.631504i
$606$	2.13855	−	7.98120i	0.0868729	−	0.324214i
$607$		−	7.48624i		−	0.303857i	−0.988391	−	0.151929i	$-0.951452\pi$
$607$		−	7.48624i		−	0.303857i	0.988391	−	0.151929i	$-0.0485484\pi$
$608$	3.86582	−	6.69579i	0.156780	−	0.271550i
$609$	−23.9687	+	6.88747i	−0.971259	+	0.279094i
$610$		−	23.1411i		−	0.936955i
$611$	0.850462	+	0.0108715i	0.0344060	+	0.000439815i
$612$	−3.40608	+	1.96650i	−0.137683	+	0.0794912i
$613$	−7.86907	+	7.86907i	−0.317829	+	0.317829i	−0.847933	−	0.530104i	$-0.822153\pi$
$613$	−7.86907	+	7.86907i	−0.317829	+	0.317829i	0.530104	+	0.847933i	$0.322153\pi$
$614$	−8.96707	+	5.17714i	−0.361881	+	0.208932i
$615$	3.46976	+	6.00981i	0.139914	+	0.242339i
$616$	−3.77736	−	3.64366i	−0.152194	−	0.146807i
$617$	36.0694	+	9.66477i	1.45210	+	0.389089i	0.896754	−	0.442530i	$-0.145919\pi$
$617$	36.0694	+	9.66477i	1.45210	+	0.389089i	0.555346	+	0.831619i	$0.312586\pi$
$618$	2.15628	+	2.15628i	0.0867384	+	0.0867384i
$619$	33.1839	+	8.89159i	1.33377	+	0.357383i	0.854120	−	0.520075i	$-0.174096\pi$
$619$	33.1839	+	8.89159i	1.33377	+	0.357383i	0.479652	+	0.877459i	$0.340763\pi$
$620$	−5.38800	+	9.33229i	−0.216387	+	0.374794i
$621$	3.20709	+	5.55484i	0.128696	+	0.222908i
$622$	4.33936	+	16.1947i	0.173993	+	0.649349i
$623$	21.1796	−	12.7422i	0.848543	−	0.510505i
$624$	−0.888593	−	3.49434i	−0.0355722	−	0.139885i
$625$	−12.9355	+	22.4049i	−0.517419	+	0.896196i
$626$	2.14554	+	2.14554i	0.0857532	+	0.0857532i
$627$	−15.3370			−0.612502
$628$	10.3221			0.411898
$629$	29.9064	+	29.9064i	1.19245	+	1.19245i
$630$	−4.18083	+	4.33425i	−0.166568	+	0.172680i
$631$	10.6934	−	39.9084i	0.425699	−	1.58873i	−0.336694	−	0.941614i	$-0.609309\pi$
$631$	10.6934	−	39.9084i	0.425699	−	1.58873i	0.762393	−	0.647115i	$-0.224025\pi$
$632$	16.6808	−	4.46961i	0.663527	−	0.177791i
$633$	−2.62060	−	1.51300i	−0.104160	−	0.0601365i
$634$			2.23990i			0.0889577i
$635$	−11.1958	−	2.99990i	−0.444292	−	0.119048i
$636$	−5.36462			−0.212721
$637$	24.5241	+	5.96384i	0.971681	+	0.236296i
$638$	18.6979			0.740257
$639$	−11.8718	−	3.18104i	−0.469642	−	0.125840i
$640$			2.27612i			0.0899715i
$641$	−18.5778	−	10.7259i	−0.733781	−	0.423648i	0.0860230	−	0.996293i	$-0.472584\pi$
$641$	−18.5778	−	10.7259i	−0.733781	−	0.423648i	−0.819804	+	0.572645i	$0.805917\pi$
$642$	−17.3373	+	4.64550i	−0.684247	+	0.183343i
$643$	−0.0568055	+	0.212001i	−0.00224019	+	0.00836050i	−0.967037	−	0.254636i	$-0.918044\pi$
$643$	−0.0568055	+	0.212001i	−0.00224019	+	0.00836050i	0.964797	+	0.262997i	$0.0847109\pi$
$644$	−11.7817	+	12.2140i	−0.464265	+	0.481301i
$645$	3.26661	+	3.26661i	0.128623	+	0.128623i
$646$	−30.4086			−1.19641
$647$	−32.5771			−1.28074			−0.640369	−	0.768067i	$-0.721219\pi$
$647$	−32.5771			−1.28074			−0.640369	+	0.768067i	$0.721219\pi$
$648$	−0.707107	−	0.707107i	−0.0277778	−	0.0277778i
$649$	−13.0973	+	22.6852i	−0.514113	+	0.890471i
$650$	0.00832875	−	0.651545i	0.000326681	−	0.0255557i
$651$	10.7332	−	6.45738i	0.420669	−	0.253085i
$652$	−3.89514	−	14.5368i	−0.152545	−	0.569307i
$653$	8.95934	+	15.5180i	0.350606	+	0.607268i	0.986356	−	0.164628i	$-0.0526422\pi$
$653$	8.95934	+	15.5180i	0.350606	+	0.607268i	−0.635750	+	0.771895i	$0.719309\pi$
$654$	−3.59486	+	6.22648i	−0.140570	+	0.243475i
$655$	20.8975	+	5.59947i	0.816533	+	0.218789i
$656$	−2.15586	−	2.15586i	−0.0841720	−	0.0841720i
$657$	−9.50232	−	2.54614i	−0.370721	−	0.0993343i
$658$	0.449198	+	0.433298i	0.0175115	+	0.0168917i
$659$	7.34203	+	12.7168i	0.286005	+	0.495375i	0.972852	−	0.231427i	$-0.0743393\pi$
$659$	7.34203	+	12.7168i	0.286005	+	0.495375i	−0.686847	+	0.726802i	$0.741006\pi$
$660$	3.91017	−	2.25754i	0.152203	−	0.0878745i
$661$	14.3981	−	14.3981i	0.560021	−	0.560021i	−0.369293	−	0.929313i	$-0.620400\pi$
$661$	14.3981	−	14.3981i	0.560021	−	0.560021i	0.929313	+	0.369293i	$0.120400\pi$
$662$	−12.3590	+	7.13548i	−0.480347	+	0.277328i
$663$	−10.1546	+	9.89825i	−0.394371	+	0.384416i
$664$			10.2199i			0.396610i
$665$	−44.7494	+	12.8589i	−1.73531	+	0.498646i
$666$	−5.37681	+	9.31291i	−0.208347	+	0.360868i
$667$		−	60.4594i		−	2.34100i
$668$	0.832246	−	3.10599i	0.0322006	−	0.120174i
$669$	−5.44116	−	20.3067i	−0.210367	−	0.785101i
$670$	9.78535	−	9.78535i	0.378041	−	0.378041i
$671$	14.2608	−	14.2608i	0.550531	−	0.550531i
$672$	1.28139	−	2.31475i	0.0494305	−	0.0892933i
$673$	−0.178731	−	0.103190i	−0.00688958	−	0.00397770i	0.496551	−	0.868007i	$-0.334599\pi$
$673$	−0.178731	−	0.103190i	−0.00688958	−	0.00397770i	−0.503441	+	0.864030i	$0.667933\pi$
$674$	−4.00315	+	14.9400i	−0.154196	+	0.575466i
$675$	−0.0903604	−	0.156509i	−0.00347797	−	0.00602403i
$676$	−6.21009	−	11.4208i	−0.238850	−	0.439262i
$677$	29.7120	+	17.1543i	1.14193	+	0.659292i	0.946907	−	0.321508i	$-0.104190\pi$
$677$	29.7120	+	17.1543i	1.14193	+	0.659292i	0.195020	+	0.980799i	$0.437523\pi$
$678$	−0.138383	+	0.0370795i	−0.00531455	+	0.00142403i
$679$	−6.57280	−	10.9251i	−0.252241	−	0.419266i
$680$	7.75265	−	4.47600i	0.297301	−	0.171647i
$681$	1.22993	+	4.59018i	0.0471312	+	0.175896i
$682$	−9.07144	+	2.43068i	−0.347363	+	0.0930757i
$683$	7.73257	−	2.07194i	0.295879	−	0.0792804i	−0.107826	−	0.994170i	$-0.534389\pi$
$683$	7.73257	−	2.07194i	0.295879	−	0.0792804i	0.403705	+	0.914889i	$0.367722\pi$
$684$	−2.00109	−	7.46819i	−0.0765138	−	0.285553i
$685$	−39.2211	+	22.6443i	−1.49856	+	0.865195i
$686$	10.1130	+	15.5154i	0.386116	+	0.592380i
$687$	0.125583	−	0.0336500i	0.00479131	−	0.00128383i
$688$	−1.75771	−	1.01482i	−0.0670123	−	0.0386895i
$689$	−18.7458	+	4.76697i	−0.714159	+	0.181607i
$690$	−7.29972	−	12.6435i	−0.277895	−	0.481329i
$691$	−7.73464	+	28.8661i	−0.294240	+	1.09812i	0.647580	+	0.761998i	$0.275781\pi$
$691$	−7.73464	+	28.8661i	−0.294240	+	1.09812i	−0.941819	+	0.336119i	$0.890885\pi$
$692$	−0.952297	−	0.549809i	−0.0362009	−	0.0209006i
$693$	−5.24745	+	0.0945420i	−0.199334	+	0.00359135i
$694$	1.06736	−	1.06736i	0.0405166	−	0.0405166i
$695$	4.66569	−	4.66569i	0.176980	−	0.176980i
$696$	2.43960	+	9.10473i	0.0924730	+	0.345114i
$697$	−3.10353	+	11.5825i	−0.117554	+	0.438719i
$698$			30.9762i			1.17247i
$699$	−4.63947	+	8.03580i	−0.175481	+	0.303942i
$700$	0.331952	−	0.344133i	0.0125466	−	0.0130070i
$701$			8.92430i			0.337066i	0.985696	+	0.168533i	$0.0539030\pi$
$701$			8.92430i			0.337066i	−0.985696	+	0.168533i	$0.946097\pi$
$702$	−3.09920	−	1.84254i	−0.116972	−	0.0695422i
$703$	−72.0040	+	41.5716i	−2.71568	+	1.56790i
$704$	−1.40267	+	1.40267i	−0.0528650	+	0.0528650i
$705$	−0.464991	+	0.268463i	−0.0175126	+	0.0101109i
$706$	10.3037	+	17.8465i	0.387784	+	0.671661i
$707$	15.1772	−	15.7341i	0.570798	−	0.591743i
$708$	−12.7551	−	3.41773i	−0.479367	−	0.128446i
$709$	12.8555	+	12.8555i	0.482800	+	0.482800i	0.906025	−	0.423225i	$-0.139102\pi$
$709$	12.8555	+	12.8555i	0.482800	+	0.482800i	−0.423225	+	0.906025i	$0.639102\pi$
$710$	27.0217	+	7.24043i	1.01411	+	0.271729i
$711$	8.63462	−	14.9556i	0.323823	−	0.560879i
$712$	−4.67111	−	8.09059i	−0.175057	−	0.303208i
$713$	7.85959	+	29.3324i	0.294344	+	1.09851i
$714$	−10.4041	+	0.187448i	−0.389362	+	0.00701505i
$715$	11.6574	−	11.3631i	0.435963	−	0.424958i
$716$	5.05387	−	8.75356i	0.188872	−	0.327136i
$717$	−8.02522	−	8.02522i	−0.299707	−	0.299707i
$718$	2.98725			0.111483
$719$	9.16932			0.341958			0.170979	−	0.985275i	$-0.445307\pi$
$719$	9.16932			0.341958			0.170979	+	0.985275i	$0.445307\pi$
$720$	1.60946	+	1.60946i	0.0599810	+	0.0599810i
$721$	2.22822	+	7.75428i	0.0829831	+	0.288784i
$722$	10.5542	−	39.3887i	0.392786	−	1.46590i
$723$	−19.0065	+	5.09278i	−0.706860	+	0.189402i
$724$	2.86915	+	1.65651i	0.106631	+	0.0615636i
$725$			1.70346i			0.0632648i
$726$	−6.82431	−	1.82857i	−0.253274	−	0.0678645i
$727$	33.0605			1.22615			0.613073	−	0.790027i	$-0.289933\pi$
$727$	33.0605			1.22615			0.613073	+	0.790027i	$0.289933\pi$
$728$	2.42073	−	9.22714i	0.0897182	−	0.341980i
$729$	−1.00000			−0.0370370
$730$	21.6284	+	5.79532i	0.800504	+	0.214494i
$731$			7.98256i			0.295246i
$732$	8.80479	+	5.08345i	0.325434	+	0.187890i
$733$	33.3246	−	8.92931i	1.23087	−	0.329812i	0.415954	−	0.909386i	$-0.363448\pi$
$733$	33.3246	−	8.92931i	1.23087	−	0.329812i	0.814920	+	0.579574i	$0.196781\pi$
$734$	−1.78676	+	6.66826i	−0.0659504	+	0.246130i
$735$	−15.2314	+	4.67542i	−0.561819	+	0.172455i
$736$	4.53551	+	4.53551i	0.167181	+	0.167181i
$737$	12.0605			0.444255
$738$	−3.04884			−0.112229
$739$	2.54568	+	2.54568i	0.0936445	+	0.0936445i	0.752377	−	0.658733i	$-0.228907\pi$
$739$	2.54568	+	2.54568i	0.0936445	+	0.0936445i	−0.658733	+	0.752377i	$0.728907\pi$
$740$	12.2383	−	21.1973i	0.449888	−	0.779228i
$741$	−13.6287	−	24.3182i	−0.500662	−	0.893352i
$742$	−12.4177	−	6.87416i	−0.455870	−	0.252358i
$743$	−4.63329	−	17.2917i	−0.169979	−	0.634370i	−0.997353	−	0.0727180i	$-0.976833\pi$
$743$	−4.63329	−	17.2917i	−0.169979	−	0.634370i	0.827374	−	0.561652i	$-0.189834\pi$
$744$	−2.36719	−	4.10009i	−0.0867853	−	0.150317i
$745$	−12.4717	+	21.6016i	−0.456927	+	0.791421i
$746$	19.9134	+	5.33578i	0.729082	+	0.195357i
$747$	7.22658	+	7.22658i	0.264407	+	0.264407i
$748$	7.53595	+	2.01925i	0.275542	+	0.0738312i
$749$	−46.0840	−	11.4626i	−1.68387	−	0.418833i
$750$	−5.48463	−	9.49965i	−0.200270	−	0.346878i
$751$	−17.9172	+	10.3445i	−0.653809	+	0.377477i	−0.789914	−	0.613217i	$-0.789875\pi$
$751$	−17.9172	+	10.3445i	−0.653809	+	0.377477i	0.136105	+	0.990694i	$0.456542\pi$
$752$	0.166803	−	0.166803i	0.00608268	−	0.00608268i
$753$	−9.27140	+	5.35285i	−0.337869	+	0.195069i
$754$	16.6152	+	29.6472i	0.605090	+	1.07969i
$755$		−	32.4560i		−	1.18119i
$756$	−0.730696	−	2.54285i	−0.0265752	−	0.0924825i
$757$	−6.73653	+	11.6680i	−0.244844	+	0.424081i	−0.962088	−	0.272741i	$-0.912070\pi$
$757$	−6.73653	+	11.6680i	−0.244844	+	0.424081i	0.717244	+	0.696822i	$0.245403\pi$
$758$		−	4.99809i		−	0.181539i
$759$	3.29312	−	12.2901i	0.119533	−	0.446101i
$760$	4.55473	+	16.9985i	0.165217	+	0.616600i
$761$	−1.25407	+	1.25407i	−0.0454599	+	0.0454599i	−0.729471	−	0.684011i	$-0.760234\pi$
$761$	−1.25407	+	1.25407i	−0.0454599	+	0.0454599i	0.684011	+	0.729471i	$0.260234\pi$
$762$	3.60082	−	3.60082i	0.130444	−	0.130444i
$763$	−16.2997	+	9.80631i	−0.590089	+	0.355012i
$764$	5.74445	+	3.31656i	0.207827	+	0.119989i
$765$	2.31695	−	8.64696i	0.0837694	−	0.312632i
$766$	5.82847	+	10.0952i	0.210591	+	0.364755i
$767$	−47.6077	−	0.608574i	−1.71902	−	0.0219743i
$768$	−0.866025	−	0.500000i	−0.0312500	−	0.0180422i
$769$	−1.88357	+	0.504701i	−0.0679232	+	0.0182000i	−0.292621	−	0.956229i	$-0.594527\pi$
$769$	−1.88357	+	0.504701i	−0.0679232	+	0.0182000i	0.224697	+	0.974429i	$0.427861\pi$
$770$	11.9438	−	0.215189i	0.430426	−	0.00775487i
$771$	12.9656	−	7.48569i	0.466945	−	0.269591i
$772$	−4.21832	−	15.7430i	−0.151821	−	0.566603i
$773$	12.7023	−	3.40358i	0.456871	−	0.122418i	−0.0230414	−	0.999735i	$-0.507335\pi$
$773$	12.7023	−	3.40358i	0.456871	−	0.122418i	0.479913	+	0.877316i	$0.340668\pi$
$774$	−1.96048	+	0.525308i	−0.0704679	+	0.0188818i
$775$	−0.221445	−	0.826446i	−0.00795456	−	0.0296868i
$776$	−4.17337	+	2.40950i	−0.149815	+	0.0864959i
$777$	−24.3794	+	14.6673i	−0.874606	+	0.526185i
$778$	14.5292	−	3.89309i	0.520898	−	0.139574i
$779$	−20.4144	−	11.7863i	−0.731422	−	0.422287i
$780$	7.05415	+	4.19384i	0.252579	+	0.150164i
$781$	12.1903	+	21.1142i	0.436202	+	0.755524i
$782$	6.52923	−	24.3674i	0.233485	−	0.871377i
$783$	8.16308	+	4.71295i	0.291725	+	0.168427i
$784$	5.93217	−	3.71610i	0.211863	−	0.132718i
$785$	−16.6130	+	16.6130i	−0.592945	+	0.592945i
$786$	−6.72111	+	6.72111i	−0.239734	+	0.239734i
$787$	−0.502785	−	1.87642i	−0.0179223	−	0.0668871i	0.956386	−	0.292107i	$-0.0943565\pi$
$787$	−0.502785	−	1.87642i	−0.0179223	−	0.0668871i	−0.974308	+	0.225220i	$0.927690\pi$
$788$	0.609343	−	2.27410i	0.0217069	−	0.0810114i
$789$			16.5831i			0.590373i
$790$	−19.6534	+	34.0407i	−0.699237	+	1.21111i
$791$	−0.367834	−	0.0914919i	−0.0130787	−	0.00325308i
$792$			1.98367i			0.0704867i
$793$	35.2840	+	9.93941i	1.25297	+	0.352959i
$794$	14.5040	−	8.37388i	0.514727	−	0.297178i
$795$	8.63415	−	8.63415i	0.306222	−	0.306222i
$796$	−10.6917	+	6.17285i	−0.378957	+	0.218791i
$797$	4.30541	+	7.45718i	0.152505	+	0.264147i	0.932148	−	0.362078i	$-0.117933\pi$
$797$	4.30541	+	7.45718i	0.152505	+	0.264147i	−0.779643	+	0.626225i	$0.784599\pi$
$798$	4.93761	−	19.8511i	0.174789	−	0.702722i
$799$	−0.896164	−	0.240126i	−0.0317040	−	0.00849506i
$800$	−0.127789	−	0.127789i	−0.00451802	−	0.00451802i
$801$	−9.02389	−	2.41794i	−0.318843	−	0.0854338i
$802$	6.72751	−	11.6524i	0.237557	−	0.411460i
$803$	9.75721	+	16.9000i	0.344324	+	0.596388i
$804$	1.57359	+	5.87273i	0.0554963	+	0.207115i
$805$	−0.695811	−	38.6202i	−0.0245241	−	1.36118i
$806$	−11.9151	−	12.2236i	−0.419690	−	0.430559i
$807$	−11.2557	+	19.4954i	−0.396218	+	0.686269i
$808$	−5.84264	−	5.84264i	−0.205543	−	0.205543i
$809$	35.7418			1.25661			0.628307	−	0.777965i	$-0.283748\pi$
$809$	35.7418			1.25661			0.628307	+	0.777965i	$0.283748\pi$
$810$	2.27612			0.0799747
$811$	8.73082	+	8.73082i	0.306581	+	0.306581i	0.843582	−	0.537001i	$-0.180443\pi$
$811$	8.73082	+	8.73082i	0.306581	+	0.306581i	−0.537001	+	0.843582i	$0.680443\pi$
$812$	−6.01961	+	24.2012i	−0.211247	+	0.849296i
$813$	−5.96948	+	22.2784i	−0.209359	+	0.781338i
$814$	20.6048	−	5.52104i	0.722198	−	0.193512i
$815$	29.6655	+	17.1274i	1.03914	+	0.599947i
$816$			3.93301i			0.137683i
$817$	−15.1577	−	4.06149i	−0.530300	−	0.142094i
$818$	−39.0638			−1.36583
$819$	−4.81286	−	8.23629i	−0.168175	−	0.287799i
$820$	6.93953			0.242339
$821$	−19.7682	−	5.29688i	−0.689916	−	0.184862i	−0.103206	−	0.994660i	$-0.532910\pi$
$821$	−19.7682	−	5.29688i	−0.689916	−	0.184862i	−0.586709	+	0.809798i	$0.699577\pi$
$822$		−	19.8973i		−	0.693998i
$823$	10.2759	+	5.93280i	0.358196	+	0.206804i	0.668289	−	0.743902i	$-0.267027\pi$
$823$	10.2759	+	5.93280i	0.358196	+	0.206804i	−0.310093	+	0.950706i	$0.600360\pi$
$824$	2.94554	−	0.789254i	0.102613	−	0.0274950i
$825$	−0.0927842	+	0.346275i	−0.00323033	+	0.0120558i
$826$	−25.1455	−	24.2554i	−0.874923	−	0.843954i
$827$	10.8488	+	10.8488i	0.377250	+	0.377250i	0.870109	−	0.492859i	$-0.164048\pi$
$827$	10.8488	+	10.8488i	0.377250	+	0.377250i	−0.492859	+	0.870109i	$0.664048\pi$
$828$	6.41418			0.222908
$829$	1.27106			0.0441457			0.0220729	−	0.999756i	$-0.492973\pi$
$829$	1.27106			0.0441457			0.0220729	+	0.999756i	$0.492973\pi$
$830$	−16.4486	−	16.4486i	−0.570938	−	0.570938i
$831$	−2.70790	+	4.69021i	−0.0939359	+	0.162702i
$832$	−3.47048	−	0.977625i	−0.120317	−	0.0338931i
$833$	−24.3230	−	12.8977i	−0.842741	−	0.446880i
$834$	0.750295	+	2.80014i	0.0259806	+	0.0969609i
$835$	3.65949	+	6.33843i	0.126642	+	0.219350i
$836$	−7.66851	+	13.2823i	−0.265221	+	0.459376i
$837$	−4.57305	−	1.22535i	−0.158068	−	0.0423542i
$838$	−14.4651	−	14.4651i	−0.499687	−	0.499687i
$839$	24.4783	+	6.55894i	0.845084	+	0.226440i	0.655284	−	0.755383i	$-0.272549\pi$
$839$	24.4783	+	6.55894i	0.845084	+	0.226440i	0.189801	+	0.981823i	$0.439216\pi$
$840$	1.66315	+	5.78783i	0.0573842	+	0.199699i
$841$	−29.9239	−	51.8297i	−1.03186	−	1.78723i
$842$	0.880337	−	0.508263i	0.0303384	−	0.0175159i
$843$	−13.1743	+	13.1743i	−0.453748	+	0.453748i
$844$	−2.62060	+	1.51300i	−0.0902048	+	0.0520798i
$845$	28.3762	+	8.38643i	0.976171	+	0.288502i
$846$		−	0.235895i		−	0.00811024i
$847$	−13.4534	−	12.9772i	−0.462266	−	0.445904i
$848$	−2.68231	+	4.64590i	−0.0921110	+	0.159541i
$849$		−	6.65461i		−	0.228386i
$850$	−0.183962	+	0.686557i	−0.00630986	+	0.0235487i
$851$	−17.8522	−	66.6253i	−0.611966	−	2.28389i
$852$	−8.69077	+	8.69077i	−0.297741	+	0.297741i
$853$	34.3681	−	34.3681i	1.17674	−	1.17674i	0.196171	−	0.980570i	$-0.437149\pi$
$853$	34.3681	−	34.3681i	1.17674	−	1.17674i	0.980570	−	0.196171i	$-0.0628509\pi$
$854$	13.8670	+	23.0492i	0.474519	+	0.788728i
$855$	15.2404	+	8.79906i	0.521212	+	0.300922i
$856$	−4.64550	+	17.3373i	−0.158780	+	0.592575i
$857$	−17.3495	−	30.0503i	−0.592649	−	1.02650i	−0.993874	−	0.110518i	$-0.964749\pi$
$857$	−17.3495	−	30.0503i	−0.592649	−	1.02650i	0.401226	−	0.915979i	$-0.368584\pi$
$858$	1.76268	+	6.93162i	0.0601768	+	0.236642i
$859$	34.6518	+	20.0062i	1.18230	+	0.682604i	0.956546	−	0.291580i	$-0.0941810\pi$
$859$	34.6518	+	20.0062i	1.18230	+	0.682604i	0.225758	+	0.974184i	$0.427514\pi$
$860$	4.46228	−	1.19566i	0.152162	−	0.0407718i
$861$	−7.05729	−	3.90674i	−0.240512	−	0.133141i
$862$	−9.37026	+	5.40992i	−0.319152	+	0.184263i
$863$	−3.10822	−	11.6001i	−0.105805	−	0.394870i	0.892630	−	0.450790i	$-0.148858\pi$
$863$	−3.10822	−	11.6001i	−0.105805	−	0.394870i	−0.998435	+	0.0559195i	$0.982191\pi$
$864$	−0.965926	+	0.258819i	−0.0328615	+	0.00880520i
$865$	2.41758	−	0.647788i	0.0822001	−	0.0220255i
$866$	3.69179	+	13.7780i	0.125452	+	0.468194i
$867$	−1.32629	+	0.765733i	−0.0450431	+	0.0260056i
$868$	−0.225641	−	12.5239i	−0.00765875	−	0.425090i
$869$	−33.0892	+	8.86623i	−1.12248	+	0.300766i
$870$	−18.5801	−	10.7272i	−0.629926	−	0.363688i
$871$	10.7171	+	19.1230i	0.363136	+	0.647959i
$872$	3.59486	+	6.22648i	0.121737	+	0.210855i
$873$	−1.24725	+	4.65479i	−0.0422129	+	0.157541i
$874$	42.9480	+	24.7960i	1.45274	+	0.838738i
$875$	−0.522796	−	29.0172i	−0.0176737	−	0.980961i
$876$	−6.95618	+	6.95618i	−0.235028	+	0.235028i
$877$	−24.0542	+	24.0542i	−0.812252	+	0.812252i	−0.984971	−	0.172719i	$-0.944745\pi$
$877$	−24.0542	+	24.0542i	−0.812252	+	0.812252i	0.172719	+	0.984971i	$0.444745\pi$
$878$	6.78136	+	25.3084i	0.228860	+	0.854116i
$879$	−0.656343	+	2.44950i	−0.0221379	+	0.0826197i
$880$		−	4.51507i		−	0.152203i
$881$	3.83668	−	6.64532i	0.129261	−	0.223886i	−0.794130	−	0.607749i	$-0.792073\pi$
$881$	3.83668	−	6.64532i	0.129261	−	0.223886i	0.923390	+	0.383862i	$0.125406\pi$
$882$	1.56700	−	6.82235i	0.0527635	−	0.229721i
$883$		−	34.3688i		−	1.15660i	−0.815823	−	0.578301i	$-0.803716\pi$
$883$		−	34.3688i		−	1.15660i	0.815823	−	0.578301i	$-0.196284\pi$
$884$	3.49484	+	13.7433i	0.117544	+	0.462236i
$885$	26.0296	−	15.0282i	0.874975	−	0.505167i
$886$	−1.68015	+	1.68015i	−0.0564458	+	0.0564458i
$887$	−1.83670	+	1.06042i	−0.0616704	+	0.0356054i	−0.530518	−	0.847674i	$-0.678003\pi$
$887$	−1.83670	+	1.06042i	−0.0616704	+	0.0356054i	0.468848	+	0.883279i	$0.344669\pi$
$888$	5.37681	+	9.31291i	0.180434	+	0.312521i
$889$	12.9490	−	3.72094i	0.434296	−	0.124796i
$890$	20.5394	+	5.50353i	0.688484	+	0.184479i
$891$	1.40267	+	1.40267i	0.0469911	+	0.0469911i
$892$	−20.3067	−	5.44116i	−0.679918	−	0.182183i
$893$	0.911928	−	1.57950i	0.0305165	−	0.0528561i
$894$	−5.47936	−	9.49053i	−0.183257	−	0.317411i
$895$	5.95450	+	22.2225i	0.199037	+	0.742817i
$896$	−1.36394	−	2.26709i	−0.0455659	−	0.0757380i
$897$	22.4133	−	5.69959i	0.748358	−	0.190304i
$898$	8.00398	−	13.8633i	0.267096	−	0.462624i
$899$	31.5552	+	31.5552i	1.05242	+	1.05242i
$900$	−0.180721			−0.00602403
$901$	21.0991			0.702913
$902$	4.27651	+	4.27651i	0.142392	+	0.142392i
$903$	−5.21113	−	1.29617i	−0.173415	−	0.0431339i
$904$	−0.0370795	+	0.138383i	−0.00123325	+	0.00460254i
$905$	−7.28387	+	1.95171i	−0.242124	+	0.0648769i
$906$	12.3490	+	7.12967i	0.410266	+	0.236867i
$907$			26.6721i			0.885634i	0.896612	+	0.442817i	$0.146021\pi$
$907$			26.6721i			0.885634i	−0.896612	+	0.442817i	$0.853979\pi$
$908$	4.59018	+	1.22993i	0.152330	+	0.0408168i
$909$	−8.26274			−0.274058
$910$	10.9546	+	18.7468i	0.363143	+	0.621449i
$911$	12.1780			0.403474			0.201737	−	0.979440i	$-0.435341\pi$
$911$	12.1780			0.403474			0.201737	+	0.979440i	$0.435341\pi$
$912$	−7.46819	−	2.00109i	−0.247296	−	0.0662629i
$913$		−	20.2730i		−	0.670938i
$914$	−13.9074	−	8.02946i	−0.460017	−	0.265591i
$915$	−22.3526	+	5.98935i	−0.738953	+	0.198002i
$916$	0.0336500	−	0.125583i	0.00111183	−	0.00414939i
$917$	−24.1700	+	6.94532i	−0.798163	+	0.229355i
$918$	2.78106	+	2.78106i	0.0917885	+	0.0917885i
$919$	−23.2843			−0.768077			−0.384038	−	0.923317i	$-0.625467\pi$
$919$	−23.2843			−0.768077			−0.384038	+	0.923317i	$0.625467\pi$
$920$	−14.5994			−0.481329
$921$	7.32158	+	7.32158i	0.241254	+	0.241254i
$922$	−5.85173	+	10.1355i	−0.192717	+	0.333795i
$923$	−22.6459	+	38.0911i	−0.745400	+	1.25378i
$924$	−2.54185	+	4.59170i	−0.0836207	+	0.151056i
$925$	0.502990	+	1.87718i	0.0165382	+	0.0617214i
$926$	−12.9905	−	22.5002i	−0.426893	−	0.739401i
$927$	1.52472	−	2.64090i	0.0500784	−	0.0867384i
$928$	9.10473	+	2.43960i	0.298877	+	0.0800839i
$929$	−21.6123	−	21.6123i	−0.709078	−	0.709078i	0.257263	−	0.966341i	$-0.417179\pi$
$929$	−21.6123	−	21.6123i	−0.709078	−	0.709078i	−0.966341	+	0.257263i	$0.917179\pi$
$930$	10.4088	+	2.78903i	0.341319	+	0.0914560i
$931$	36.8663	−	39.6234i	1.20824	−	1.29860i
$932$	4.63947	+	8.03580i	0.151971	+	0.263221i
$933$	14.5198	−	8.38300i	0.475356	−	0.274447i
$934$	25.6424	−	25.6424i	0.839044	−	0.839044i
$935$	−15.3787	+	8.87891i	−0.502938	+	0.290371i
$936$	−3.14529	+	1.76272i	−0.102807	+	0.0576162i
$937$			10.3421i			0.337862i	0.985628	+	0.168931i	$0.0540315\pi$
$937$			10.3421i			0.337862i	−0.985628	+	0.168931i	$0.945969\pi$
$938$	−3.88276	+	15.6103i	−0.126777	+	0.509693i
$939$	1.51713	−	2.62774i	0.0495096	−	0.0857532i
$940$			0.536926i			0.0175126i
$941$	−6.65332	+	24.8305i	−0.216892	+	0.809452i	0.768600	+	0.639730i	$0.220954\pi$
$941$	−6.65332	+	24.8305i	−0.216892	+	0.809452i	−0.985492	+	0.169722i	$0.945713\pi$
$942$	−2.67156	−	9.97041i	−0.0870442	−	0.324853i
$943$	13.8280	−	13.8280i	0.450303	−	0.450303i
$944$	−9.33741	+	9.33741i	−0.303907	+	0.303907i
$945$	5.26864	+	2.91659i	0.171389	+	0.0948766i
$946$	3.48673	+	2.01306i	0.113363	+	0.0654504i
$947$	−13.4929	+	50.3563i	−0.438461	+	1.63636i	0.294184	+	0.955749i	$0.404952\pi$
$947$	−13.4929	+	50.3563i	−0.438461	+	1.63636i	−0.732645	+	0.680610i	$0.761715\pi$
$948$	−8.63462	−	14.9556i	−0.280439	−	0.485735i
$949$	−18.1260	+	30.4885i	−0.588396	+	0.989697i
$950$	−1.21007	−	0.698634i	−0.0392598	−	0.0226667i
$951$	2.16358	−	0.579728i	0.0701588	−	0.0187990i
$952$	−5.03970	+	9.10391i	−0.163338	+	0.295059i
$953$	33.0411	−	19.0763i	1.07031	−	0.617941i	0.142041	−	0.989861i	$-0.454634\pi$
$953$	33.0411	−	19.0763i	1.07031	−	0.617941i	0.928265	+	0.371920i	$0.121300\pi$
$954$	1.38847	+	5.18183i	0.0449533	+	0.167768i
$955$	−14.5833	+	3.90759i	−0.471906	+	0.126447i
$956$	−10.9627	+	2.93743i	−0.354558	+	0.0950034i
$957$	−4.83938	−	18.0608i	−0.156435	−	0.583823i
$958$	0.561936	−	0.324434i	0.0181553	−	0.0104820i
$959$	25.4961	−	46.0572i	0.823313	−	1.48726i
$960$	2.19856	−	0.589103i	0.0709583	−	0.0190132i
$961$	7.43544	+	4.29285i	0.239853	+	0.138479i
$962$	27.0638	+	27.7647i	0.872572	+	0.895169i
$963$	8.97443	+	15.5442i	0.289197	+	0.500904i
$964$	−5.09278	+	19.0065i	−0.164027	+	0.612158i
$965$	32.1269	+	18.5485i	1.03420	+	0.597097i
$966$	14.8472	+	8.21904i	0.477700	+	0.264443i
$967$	36.1740	−	36.1740i	1.16328	−	1.16328i	0.179523	−	0.983754i	$-0.442544\pi$
$967$	36.1740	−	36.1740i	1.16328	−	1.16328i	0.983754	−	0.179523i	$-0.0574555\pi$
$968$	−4.99574	+	4.99574i	−0.160569	+	0.160569i
$969$	7.87032	+	29.3724i	0.252831	+	0.943578i
$970$	2.83888	−	10.5949i	0.0911511	−	0.340180i
$971$		−	5.67259i		−	0.182042i	−0.995849	−	0.0910211i	$-0.970987\pi$
$971$		−	5.67259i		−	0.182042i	0.995849	−	0.0910211i	$-0.0290131\pi$
$972$	−0.500000	+	0.866025i	−0.0160375	+	0.0277778i
$973$	−1.85132	+	7.44303i	−0.0593505	+	0.238613i
$974$			24.8821i			0.797274i
$975$	−0.631500	+	0.160587i	−0.0202242	+	0.00514291i
$976$	8.80479	−	5.08345i	0.281834	−	0.162717i
$977$	−12.6562	+	12.6562i	−0.404908	+	0.404908i	−0.879959	−	0.475050i	$-0.842430\pi$
$977$	−12.6562	+	12.6562i	−0.404908	+	0.404908i	0.475050	+	0.879959i	$0.342430\pi$
$978$	−13.0334	+	7.52482i	−0.416761	+	0.240617i
$979$	9.26594	+	16.0491i	0.296141	+	0.512931i
$980$	−3.56667	+	15.5285i	−0.113933	+	0.496040i
$981$	6.94473	+	1.86084i	0.221728	+	0.0594119i
$982$	17.9229	+	17.9229i	0.571942	+	0.571942i
$983$	−38.2510	−	10.2493i	−1.22002	−	0.326902i	−0.409332	−	0.912386i	$-0.634238\pi$
$983$	−38.2510	−	10.2493i	−1.22002	−	0.326902i	−0.810684	+	0.585483i	$0.800905\pi$
$984$	−1.52442	+	2.64037i	−0.0485967	+	0.0841720i
$985$	2.67936	+	4.64078i	0.0853714	+	0.147868i
$986$	−9.59498	−	35.8090i	−0.305566	−	1.14039i
$987$	0.302273	−	0.546037i	0.00962145	−	0.0173806i
$988$	−27.8745	−	0.356323i	−0.886807	−	0.0113361i
$989$	6.50922	−	11.2743i	0.206981	−	0.358502i
$990$	−3.19264	−	3.19264i	−0.101469	−	0.101469i
$991$	−16.4248			−0.521753			−0.260876	−	0.965372i	$-0.584011\pi$
$991$	−16.4248			−0.521753			−0.260876	+	0.965372i	$0.584011\pi$
$992$	−4.73437			−0.150317
$993$	10.0911	+	10.0911i	0.320231	+	0.320231i
$994$	−31.2532	+	8.98070i	−0.991290	+	0.284850i
$995$	7.27289	−	27.1428i	0.230566	−	0.860485i
$996$	9.87169	−	2.64511i	0.312796	−	0.0838136i
$997$	6.65665	+	3.84322i	0.210818	+	0.121716i	0.601692	−	0.798728i	$-0.294494\pi$
$997$	6.65665	+	3.84322i	0.210818	+	0.121716i	−0.390873	+	0.920444i	$0.627827\pi$
$998$		−	15.8222i		−	0.500842i
$999$	10.3872	+	2.78324i	0.328637	+	0.0880579i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.by.a.19.1	✓	32
7.3	odd	6		546.2.cg.a.409.5	yes	32
13.11	odd	12		546.2.cg.a.271.5	yes	32
91.24	even	12	inner	546.2.by.a.115.1	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.by.a.19.1	✓	32	1.1	even	1	trivial
546.2.by.a.115.1	yes	32	91.24	even	12	inner
546.2.cg.a.271.5	yes	32	13.11	odd	12
546.2.cg.a.409.5	yes	32	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)

\(f(q)\)	\(=\)	\(q+(-0.965926 - 0.258819i) q^{2} +1.00000i q^{3} +(0.866025 + 0.500000i) q^{4} +(-2.19856 + 0.589103i) q^{5} +(0.258819 - 0.965926i) q^{6} +(1.83682 - 1.90423i) q^{7} +(-0.707107 - 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(-0.965926 - 0.258819i) q^{2} +1.00000i q^{3} +(0.866025 + 0.500000i) q^{4} +(-2.19856 + 0.589103i) q^{5} +(0.258819 - 0.965926i) q^{6} +(1.83682 - 1.90423i) q^{7} +(-0.707107 - 0.707107i) q^{8} -1.00000 q^{9} +2.27612 q^{10} +(1.40267 + 1.40267i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(-0.977625 + 3.47048i) q^{13} +(-2.26709 + 1.36394i) q^{14} +(-0.589103 - 2.19856i) q^{15} +(0.500000 + 0.866025i) q^{16} +(1.96650 - 3.40608i) q^{17} +(0.965926 + 0.258819i) q^{18} +(5.46709 + 5.46709i) q^{19} +(-2.19856 - 0.589103i) q^{20} +(1.90423 + 1.83682i) q^{21} +(-0.991836 - 1.71791i) q^{22} +(-5.55484 + 3.20709i) q^{23} +(0.707107 - 0.707107i) q^{24} +(0.156509 - 0.0903604i) q^{25} +(1.84254 - 3.09920i) q^{26} -1.00000i q^{27} +(2.54285 - 0.730696i) q^{28} +(-4.71295 + 8.16308i) q^{29} +2.27612i q^{30} +(1.22535 - 4.57305i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(-1.40267 + 1.40267i) q^{33} +(-2.78106 + 2.78106i) q^{34} +(-2.91659 + 5.26864i) q^{35} +(-0.866025 - 0.500000i) q^{36} +(-2.78324 + 10.3872i) q^{37} +(-3.86582 - 6.69579i) q^{38} +(-3.47048 - 0.977625i) q^{39} +(1.97118 + 1.13806i) q^{40} +(-2.94495 + 0.789098i) q^{41} +(-1.36394 - 2.26709i) q^{42} +(-1.75771 + 1.01482i) q^{43} +(0.513412 + 1.91608i) q^{44} +(2.19856 - 0.589103i) q^{45} +(6.19562 - 1.66011i) q^{46} +(-0.0610541 - 0.227857i) q^{47} +(-0.866025 + 0.500000i) q^{48} +(-0.252153 - 6.99546i) q^{49} +(-0.174563 + 0.0467740i) q^{50} +(3.40608 + 1.96650i) q^{51} +(-2.58189 + 2.51671i) q^{52} +(2.68231 + 4.64590i) q^{53} +(-0.258819 + 0.965926i) q^{54} +(-3.91017 - 2.25754i) q^{55} +(-2.64532 + 0.0476601i) q^{56} +(-5.46709 + 5.46709i) q^{57} +(6.66512 - 6.66512i) q^{58} +(3.41773 + 12.7551i) q^{59} +(0.589103 - 2.19856i) q^{60} -10.1669i q^{61} +(-2.36719 + 4.10009i) q^{62} +(-1.83682 + 1.90423i) q^{63} +1.00000i q^{64} +(0.104898 - 8.20600i) q^{65} +(1.71791 - 0.991836i) q^{66} +(4.29914 - 4.29914i) q^{67} +(3.40608 - 1.96650i) q^{68} +(-3.20709 - 5.55484i) q^{69} +(4.18083 - 4.33425i) q^{70} +(11.8718 + 3.18104i) q^{71} +(0.707107 + 0.707107i) q^{72} +(9.50232 + 2.54614i) q^{73} +(5.37681 - 9.31291i) q^{74} +(0.0903604 + 0.156509i) q^{75} +(2.00109 + 7.46819i) q^{76} +(5.24745 - 0.0945420i) q^{77} +(3.09920 + 1.84254i) q^{78} +(-8.63462 + 14.9556i) q^{79} +(-1.60946 - 1.60946i) q^{80} +1.00000 q^{81} +3.04884 q^{82} +(-7.22658 - 7.22658i) q^{83} +(0.730696 + 2.54285i) q^{84} +(-2.31695 + 8.64696i) q^{85} +(1.96048 - 0.525308i) q^{86} +(-8.16308 - 4.71295i) q^{87} -1.98367i q^{88} +(9.02389 + 2.41794i) q^{89} -2.27612 q^{90} +(4.81286 + 8.23629i) q^{91} -6.41418 q^{92} +(4.57305 + 1.22535i) q^{93} +0.235895i q^{94} +(-15.2404 - 8.79906i) q^{95} +(0.965926 - 0.258819i) q^{96} +(1.24725 - 4.65479i) q^{97} +(-1.56700 + 6.82235i) q^{98} +(-1.40267 - 1.40267i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{7} - 32 q^{9}+O(q^{10}) \) 32 * q + 8 * q^7 - 32 * q^9	\( 32 q + 8 q^{7} - 32 q^{9} - 4 q^{11} - 16 q^{12} + 4 q^{14} + 16 q^{16} - 8 q^{17} - 12 q^{19} - 8 q^{21} - 4 q^{22} - 24 q^{23} - 24 q^{25} + 8 q^{26} - 4 q^{28} - 12 q^{29} - 28 q^{31} + 4 q^{33} - 8 q^{34} - 44 q^{35} - 36 q^{37} + 8 q^{38} - 20 q^{39} - 28 q^{41} + 12 q^{42} + 84 q^{43} + 8 q^{44} - 4 q^{46} + 16 q^{47} + 24 q^{49} - 16 q^{50} + 8 q^{52} - 4 q^{53} + 48 q^{55} + 12 q^{56} + 12 q^{57} + 24 q^{58} + 12 q^{59} - 40 q^{62} - 8 q^{63} - 4 q^{65} + 8 q^{67} - 8 q^{69} + 60 q^{70} + 20 q^{71} + 4 q^{73} + 20 q^{74} + 8 q^{75} + 36 q^{76} - 12 q^{77} - 20 q^{78} + 32 q^{81} - 48 q^{82} + 12 q^{83} - 16 q^{84} - 4 q^{85} + 52 q^{86} - 36 q^{87} - 36 q^{89} - 16 q^{92} + 4 q^{93} - 48 q^{95} + 76 q^{97} + 8 q^{98} + 4 q^{99}+O(q^{100}) \) 32 * q + 8 * q^7 - 32 * q^9 - 4 * q^11 - 16 * q^12 + 4 * q^14 + 16 * q^16 - 8 * q^17 - 12 * q^19 - 8 * q^21 - 4 * q^22 - 24 * q^23 - 24 * q^25 + 8 * q^26 - 4 * q^28 - 12 * q^29 - 28 * q^31 + 4 * q^33 - 8 * q^34 - 44 * q^35 - 36 * q^37 + 8 * q^38 - 20 * q^39 - 28 * q^41 + 12 * q^42 + 84 * q^43 + 8 * q^44 - 4 * q^46 + 16 * q^47 + 24 * q^49 - 16 * q^50 + 8 * q^52 - 4 * q^53 + 48 * q^55 + 12 * q^56 + 12 * q^57 + 24 * q^58 + 12 * q^59 - 40 * q^62 - 8 * q^63 - 4 * q^65 + 8 * q^67 - 8 * q^69 + 60 * q^70 + 20 * q^71 + 4 * q^73 + 20 * q^74 + 8 * q^75 + 36 * q^76 - 12 * q^77 - 20 * q^78 + 32 * q^81 - 48 * q^82 + 12 * q^83 - 16 * q^84 - 4 * q^85 + 52 * q^86 - 36 * q^87 - 36 * q^89 - 16 * q^92 + 4 * q^93 - 48 * q^95 + 76 * q^97 + 8 * q^98 + 4 * q^99

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