LMFDB - Embedded newform 546.2.by.b.19.3

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			19.3
Character	$\chi$	$=$	546.19
Dual form			546.2.by.b.115.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 - 0.258819i) q^{2} -1.00000i q^{3} +(0.866025 + 0.500000i) q^{4} +(0.195603 - 0.0524115i) q^{5} +(-0.258819 + 0.965926i) q^{6} +(-2.35070 + 1.21417i) q^{7} +(-0.707107 - 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(-0.965926 - 0.258819i) q^{2} -1.00000i q^{3} +(0.866025 + 0.500000i) q^{4} +(0.195603 - 0.0524115i) q^{5} +(-0.258819 + 0.965926i) q^{6} +(-2.35070 + 1.21417i) q^{7} +(-0.707107 - 0.707107i) q^{8} -1.00000 q^{9} -0.202503 q^{10} +(1.97664 + 1.97664i) q^{11} +(0.500000 - 0.866025i) q^{12} +(-1.90556 + 3.06086i) q^{13} +(2.58485 - 0.564393i) q^{14} +(-0.0524115 - 0.195603i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-1.34500 + 2.32961i) q^{17} +(0.965926 + 0.258819i) q^{18} +(2.84265 + 2.84265i) q^{19} +(0.195603 + 0.0524115i) q^{20} +(1.21417 + 2.35070i) q^{21} +(-1.39770 - 2.42088i) q^{22} +(1.97359 - 1.13945i) q^{23} +(-0.707107 + 0.707107i) q^{24} +(-4.29461 + 2.47950i) q^{25} +(2.63283 - 2.46337i) q^{26} +1.00000i q^{27} +(-2.64285 - 0.123847i) q^{28} +(1.82561 - 3.16205i) q^{29} +0.202503i q^{30} +(-1.51982 + 5.67204i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(1.97664 - 1.97664i) q^{33} +(1.90212 - 1.90212i) q^{34} +(-0.396166 + 0.360699i) q^{35} +(-0.866025 - 0.500000i) q^{36} +(-0.427713 + 1.59625i) q^{37} +(-2.01005 - 3.48152i) q^{38} +(3.06086 + 1.90556i) q^{39} +(-0.175372 - 0.101251i) q^{40} +(10.6586 - 2.85597i) q^{41} +(-0.564393 - 2.58485i) q^{42} +(-5.73742 + 3.31250i) q^{43} +(0.723502 + 2.70015i) q^{44} +(-0.195603 + 0.0524115i) q^{45} +(-2.20125 + 0.589824i) q^{46} +(1.56321 + 5.83398i) q^{47} +(0.866025 - 0.500000i) q^{48} +(4.05158 - 5.70830i) q^{49} +(4.79002 - 1.28348i) q^{50} +(2.32961 + 1.34500i) q^{51} +(-3.18069 + 1.69800i) q^{52} +(0.577609 + 1.00045i) q^{53} +(0.258819 - 0.965926i) q^{54} +(0.490235 + 0.283038i) q^{55} +(2.52074 + 0.803647i) q^{56} +(2.84265 - 2.84265i) q^{57} +(-2.58180 + 2.58180i) q^{58} +(1.27738 + 4.76725i) q^{59} +(0.0524115 - 0.195603i) q^{60} +2.01287i q^{61} +(2.93607 - 5.08541i) q^{62} +(2.35070 - 1.21417i) q^{63} +1.00000i q^{64} +(-0.212307 + 0.698585i) q^{65} +(-2.42088 + 1.39770i) q^{66} +(-7.22594 + 7.22594i) q^{67} +(-2.32961 + 1.34500i) q^{68} +(-1.13945 - 1.97359i) q^{69} +(0.476023 - 0.245873i) q^{70} +(1.05839 + 0.283594i) q^{71} +(0.707107 + 0.707107i) q^{72} +(11.4851 + 3.07743i) q^{73} +(0.826278 - 1.43115i) q^{74} +(2.47950 + 4.29461i) q^{75} +(1.04048 + 3.88313i) q^{76} +(-7.04648 - 2.24651i) q^{77} +(-2.46337 - 2.63283i) q^{78} +(-0.0814611 + 0.141095i) q^{79} +(0.143191 + 0.143191i) q^{80} +1.00000 q^{81} -11.0346 q^{82} +(5.03290 + 5.03290i) q^{83} +(-0.123847 + 2.64285i) q^{84} +(-0.140987 + 0.526171i) q^{85} +(6.39926 - 1.71468i) q^{86} +(-3.16205 - 1.82561i) q^{87} -2.79540i q^{88} +(-14.6198 - 3.91737i) q^{89} +0.202503 q^{90} +(0.762985 - 9.50883i) q^{91} +2.27891 q^{92} +(5.67204 + 1.51982i) q^{93} -6.03978i q^{94} +(0.705016 + 0.407041i) q^{95} +(-0.965926 + 0.258819i) q^{96} +(2.70252 - 10.0859i) q^{97} +(-5.39094 + 4.46517i) q^{98} +(-1.97664 - 1.97664i) 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 $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

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

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
$5$	0.195603	−	0.0524115i	0.0874761	−	0.0234392i	−0.214816	−	0.976655i	$-0.568915\pi$
$5$	0.195603	−	0.0524115i	0.0874761	−	0.0234392i	0.302292	+	0.953215i	$0.402248\pi$
$6$	−0.258819	+	0.965926i	−0.105662	+	0.394338i
$7$	−2.35070	+	1.21417i	−0.888481	+	0.458913i
$7$	−2.35070	+	1.21417i	−0.888481	+	0.458913i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	−1.00000			−0.333333
$10$	−0.202503			−0.0640370
$11$	1.97664	+	1.97664i	0.595981	+	0.595981i	0.939240	−	0.343260i	$-0.111531\pi$
$11$	1.97664	+	1.97664i	0.595981	+	0.595981i	−0.343260	+	0.939240i	$0.611531\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	−1.90556	+	3.06086i	−0.528506	+	0.848929i
$13$	−1.90556	+	3.06086i	−0.528506	+	0.848929i
$14$	2.58485	−	0.564393i	0.690831	−	0.150840i
$15$	−0.0524115	−	0.195603i	−0.0135326	−	0.0505044i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−1.34500	+	2.32961i	−0.326211	+	0.565013i	−0.981757	−	0.190142i	$-0.939105\pi$
$17$	−1.34500	+	2.32961i	−0.326211	+	0.565013i	0.655546	+	0.755155i	$0.272439\pi$
$18$	0.965926	+	0.258819i	0.227671	+	0.0610042i
$19$	2.84265	+	2.84265i	0.652148	+	0.652148i	0.953510	−	0.301362i	$-0.0974413\pi$
$19$	2.84265	+	2.84265i	0.652148	+	0.652148i	−0.301362	+	0.953510i	$0.597441\pi$
$20$	0.195603	+	0.0524115i	0.0437381	+	0.0117196i
$21$	1.21417	+	2.35070i	0.264954	+	0.512965i
$22$	−1.39770	−	2.42088i	−0.297990	−	0.516134i
$23$	1.97359	−	1.13945i	0.411522	−	0.237592i	−0.279921	−	0.960023i	$-0.590308\pi$
$23$	1.97359	−	1.13945i	0.411522	−	0.237592i	0.691444	+	0.722430i	$0.256975\pi$
$24$	−0.707107	+	0.707107i	−0.144338	+	0.144338i
$25$	−4.29461	+	2.47950i	−0.858923	+	0.495899i
$26$	2.63283	−	2.46337i	0.516341	−	0.483106i
$27$			1.00000i			0.192450i
$28$	−2.64285	−	0.123847i	−0.499452	−	0.0234049i
$29$	1.82561	−	3.16205i	0.339008	−	0.587178i	−0.645239	−	0.763981i	$-0.723242\pi$
$29$	1.82561	−	3.16205i	0.339008	−	0.587178i	0.984246	+	0.176803i	$0.0565754\pi$
$30$			0.202503i			0.0369718i
$31$	−1.51982	+	5.67204i	−0.272968	+	1.01873i	0.684224	+	0.729272i	$0.260141\pi$
$31$	−1.51982	+	5.67204i	−0.272968	+	1.01873i	−0.957191	+	0.289457i	$0.906525\pi$
$32$	−0.258819	−	0.965926i	−0.0457532	−	0.170753i
$33$	1.97664	−	1.97664i	0.344090	−	0.344090i
$34$	1.90212	−	1.90212i	0.326211	−	0.326211i
$35$	−0.396166	+	0.360699i	−0.0669643	+	0.0609692i
$36$	−0.866025	−	0.500000i	−0.144338	−	0.0833333i
$37$	−0.427713	+	1.59625i	−0.0703155	+	0.262421i	−0.992130	−	0.125209i	$-0.960040\pi$
$37$	−0.427713	+	1.59625i	−0.0703155	+	0.262421i	0.921815	+	0.387631i	$0.126706\pi$
$38$	−2.01005	−	3.48152i	−0.326074	−	0.564777i
$39$	3.06086	+	1.90556i	0.490130	+	0.305133i
$40$	−0.175372	−	0.101251i	−0.0277288	−	0.0160092i
$41$	10.6586	−	2.85597i	1.66460	−	0.446027i	0.700950	−	0.713211i	$-0.252760\pi$
$41$	10.6586	−	2.85597i	1.66460	−	0.446027i	0.963646	+	0.267184i	$0.0860931\pi$
$42$	−0.564393	−	2.58485i	−0.0870878	−	0.398851i
$43$	−5.73742	+	3.31250i	−0.874948	+	0.505151i	−0.868989	−	0.494831i	$-0.835230\pi$
$43$	−5.73742	+	3.31250i	−0.874948	+	0.505151i	−0.00595841	+	0.999982i	$0.501897\pi$
$44$	0.723502	+	2.70015i	0.109072	+	0.407062i
$45$	−0.195603	+	0.0524115i	−0.0291587	+	0.00781305i
$46$	−2.20125	+	0.589824i	−0.324557	+	0.0869649i
$47$	1.56321	+	5.83398i	0.228018	+	0.850973i	0.981173	+	0.193130i	$0.0618641\pi$
$47$	1.56321	+	5.83398i	0.228018	+	0.850973i	−0.753156	+	0.657842i	$0.771469\pi$
$48$	0.866025	−	0.500000i	0.125000	−	0.0721688i
$49$	4.05158	−	5.70830i	0.578797	−	0.815472i
$50$	4.79002	−	1.28348i	0.677411	−	0.181512i
$51$	2.32961	+	1.34500i	0.326211	+	0.188338i
$52$	−3.18069	+	1.69800i	−0.441082	+	0.235471i
$53$	0.577609	+	1.00045i	0.0793407	+	0.137422i	0.902966	−	0.429713i	$-0.141385\pi$
$53$	0.577609	+	1.00045i	0.0793407	+	0.137422i	−0.823625	+	0.567135i	$0.808052\pi$
$54$	0.258819	−	0.965926i	0.0352208	−	0.131446i
$55$	0.490235	+	0.283038i	0.0661033	+	0.0381648i
$56$	2.52074	+	0.803647i	0.336849	+	0.107392i
$57$	2.84265	−	2.84265i	0.376518	−	0.376518i
$58$	−2.58180	+	2.58180i	−0.339008	+	0.339008i
$59$	1.27738	+	4.76725i	0.166301	+	0.620643i	0.997871	+	0.0652230i	$0.0207759\pi$
$59$	1.27738	+	4.76725i	0.166301	+	0.620643i	−0.831570	+	0.555420i	$0.812557\pi$
$60$	0.0524115	−	0.195603i	0.00676630	−	0.0252522i
$61$			2.01287i			0.257722i	0.991663	+	0.128861i	$0.0411321\pi$
$61$			2.01287i			0.257722i	−0.991663	+	0.128861i	$0.958868\pi$
$62$	2.93607	−	5.08541i	0.372881	−	0.645848i
$63$	2.35070	−	1.21417i	0.296160	−	0.152971i
$64$			1.00000i			0.125000i
$65$	−0.212307	+	0.698585i	−0.0263335	+	0.0866488i
$66$	−2.42088	+	1.39770i	−0.297990	+	0.172045i
$67$	−7.22594	+	7.22594i	−0.882789	+	0.882789i	−0.993817	−	0.111028i	$-0.964586\pi$
$67$	−7.22594	+	7.22594i	−0.882789	+	0.882789i	0.111028	+	0.993817i	$0.464586\pi$
$68$	−2.32961	+	1.34500i	−0.282507	+	0.163105i
$69$	−1.13945	−	1.97359i	−0.137174	−	0.237592i
$70$	0.476023	−	0.245873i	0.0568956	−	0.0293874i
$71$	1.05839	+	0.283594i	0.125607	+	0.0336564i	0.321075	−	0.947054i	$-0.395956\pi$
$71$	1.05839	+	0.283594i	0.125607	+	0.0336564i	−0.195468	+	0.980710i	$0.562622\pi$
$72$	0.707107	+	0.707107i	0.0833333	+	0.0833333i
$73$	11.4851	+	3.07743i	1.34423	+	0.360186i	0.858003	−	0.513644i	$-0.171705\pi$
$73$	11.4851	+	3.07743i	1.34423	+	0.360186i	0.486230	+	0.873831i	$0.338372\pi$
$74$	0.826278	−	1.43115i	0.0960528	−	0.166368i
$75$	2.47950	+	4.29461i	0.286308	+	0.495899i
$76$	1.04048	+	3.88313i	0.119351	+	0.445425i
$77$	−7.04648	−	2.24651i	−0.803021	−	0.256014i
$78$	−2.46337	−	2.63283i	−0.278921	−	0.298110i
$79$	−0.0814611	+	0.141095i	−0.00916509	+	0.0158744i	−0.870572	−	0.492042i	$-0.836251\pi$
$79$	−0.0814611	+	0.141095i	−0.00916509	+	0.0158744i	0.861406	+	0.507916i	$0.169584\pi$
$80$	0.143191	+	0.143191i	0.0160092	+	0.0160092i
$81$	1.00000			0.111111
$82$	−11.0346			−1.21857
$83$	5.03290	+	5.03290i	0.552432	+	0.552432i	0.927142	−	0.374710i	$-0.122258\pi$
$83$	5.03290	+	5.03290i	0.552432	+	0.552432i	−0.374710	+	0.927142i	$0.622258\pi$
$84$	−0.123847	+	2.64285i	−0.0135128	+	0.288359i
$85$	−0.140987	+	0.526171i	−0.0152922	+	0.0570713i
$86$	6.39926	−	1.71468i	0.690049	−	0.184898i
$87$	−3.16205	−	1.82561i	−0.339008	−	0.195726i
$88$		−	2.79540i		−	0.297990i
$89$	−14.6198	−	3.91737i	−1.54970	−	0.415241i	−0.620315	−	0.784353i	$-0.712995\pi$
$89$	−14.6198	−	3.91737i	−1.54970	−	0.415241i	−0.929385	+	0.369112i	$0.879662\pi$
$90$	0.202503			0.0213457
$91$	0.762985	−	9.50883i	0.0799826	−	0.996796i
$92$	2.27891			0.237592
$93$	5.67204	+	1.51982i	0.588163	+	0.157598i
$94$		−	6.03978i		−	0.622955i
$95$	0.705016	+	0.407041i	0.0723331	+	0.0417616i
$96$	−0.965926	+	0.258819i	−0.0985844	+	0.0264156i
$97$	2.70252	−	10.0859i	0.274399	−	1.02407i	−0.681844	−	0.731498i	$-0.738822\pi$
$97$	2.70252	−	10.0859i	0.274399	−	1.02407i	0.956243	−	0.292573i	$-0.0945116\pi$
$98$	−5.39094	+	4.46517i	−0.544567	+	0.451050i
$99$	−1.97664	−	1.97664i	−0.198660	−	0.198660i
$100$	−4.95899			−0.495899
$101$	−13.7985			−1.37300			−0.686501	−	0.727128i	$-0.740854\pi$
$101$	−13.7985			−1.37300			−0.686501	+	0.727128i	$0.740854\pi$
$102$	−1.90212	−	1.90212i	−0.188338	−	0.188338i
$103$	−2.45936	+	4.25973i	−0.242327	+	0.419723i	−0.961377	−	0.275236i	$-0.911244\pi$
$103$	−2.45936	+	4.25973i	−0.242327	+	0.419723i	0.719049	+	0.694959i	$0.244577\pi$
$104$	3.51179	−	0.816922i	0.344359	−	0.0801058i
$105$	0.360699	+	0.396166i	0.0352006	+	0.0386619i
$106$	−0.298992	−	1.11585i	−0.0290407	−	0.108381i
$107$	−3.68809	−	6.38796i	−0.356541	−	0.617547i	0.630839	−	0.775913i	$-0.282711\pi$
$107$	−3.68809	−	6.38796i	−0.356541	−	0.617547i	−0.987380	+	0.158366i	$0.949377\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	−9.72438	−	2.60564i	−0.931427	−	0.249575i	−0.238964	−	0.971028i	$-0.576808\pi$
$109$	−9.72438	−	2.60564i	−0.931427	−	0.249575i	−0.692463	+	0.721453i	$0.743474\pi$
$110$	−0.400276	−	0.400276i	−0.0381648	−	0.0381648i
$111$	1.59625	+	0.427713i	0.151509	+	0.0405967i
$112$	−2.22685	−	1.42868i	−0.210418	−	0.134998i
$113$	−8.01512	−	13.8826i	−0.753999	−	1.30596i	−0.945871	−	0.324544i	$-0.894789\pi$
$113$	−8.01512	−	13.8826i	−0.753999	−	1.30596i	0.191872	−	0.981420i	$-0.438544\pi$
$114$	−3.48152	+	2.01005i	−0.326074	+	0.188259i
$115$	0.326319	−	0.326319i	0.0304294	−	0.0304294i
$116$	3.16205	−	1.82561i	0.293589	−	0.169504i
$117$	1.90556	−	3.06086i	0.176169	−	0.282976i
$118$		−	4.93542i		−	0.454342i
$119$	0.333148	−	7.10927i	0.0305397	−	0.651706i
$120$	−0.101251	+	0.175372i	−0.00924294	+	0.0160092i
$121$		−	3.18576i		−	0.289614i
$122$	0.520969	−	1.94428i	0.0471664	−	0.176027i
$123$	−2.85597	−	10.6586i	−0.257514	−	0.961054i
$124$	−4.15222	+	4.15222i	−0.372881	+	0.372881i
$125$	−1.42604	+	1.42604i	−0.127549	+	0.127549i
$126$	−2.58485	+	0.564393i	−0.230277	+	0.0502802i
$127$	−7.41110	−	4.27880i	−0.657629	−	0.379682i	0.133744	−	0.991016i	$-0.457300\pi$
$127$	−7.41110	−	4.27880i	−0.657629	−	0.379682i	−0.791373	+	0.611334i	$0.790633\pi$
$128$	0.258819	−	0.965926i	0.0228766	−	0.0853766i
$129$	3.31250	+	5.73742i	0.291649	+	0.505151i
$130$	0.385880	−	0.619832i	0.0338439	−	0.0543629i
$131$	11.3107	+	6.53021i	0.988217	+	0.570547i	0.904741	−	0.425962i	$-0.140064\pi$
$131$	11.3107	+	6.53021i	0.988217	+	0.570547i	0.0834763	+	0.996510i	$0.473398\pi$
$132$	2.70015	−	0.723502i	0.235018	−	0.0629728i
$133$	−10.1337	−	3.23075i	−0.878700	−	0.280141i
$134$	8.84993	−	5.10951i	0.764518	−	0.441394i
$135$	0.0524115	+	0.195603i	0.00451087	+	0.0168348i
$136$	2.59834	−	0.696224i	0.222806	−	0.0597007i
$137$	−3.47555	+	0.931270i	−0.296936	+	0.0795637i	−0.404211	−	0.914666i	$-0.632454\pi$
$137$	−3.47555	+	0.931270i	−0.296936	+	0.0795637i	0.107275	+	0.994229i	$0.465787\pi$
$138$	0.589824	+	2.20125i	0.0502092	+	0.187383i
$139$	13.7433	−	7.93471i	1.16569	−	0.673013i	0.213031	−	0.977045i	$-0.431666\pi$
$139$	13.7433	−	7.93471i	1.16569	−	0.673013i	0.952662	+	0.304033i	$0.0983332\pi$
$140$	−0.523439	+	0.114291i	−0.0442387	+	0.00965936i
$141$	5.83398	−	1.56321i	0.491309	−	0.131646i
$142$	−0.948923	−	0.547861i	−0.0796319	−	0.0459755i
$143$	−9.81683	+	2.28362i	−0.820925	+	0.190966i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	0.191366	−	0.714188i	0.0158921	−	0.0593101i
$146$	−10.2973	−	5.94514i	−0.852210	−	0.492024i
$147$	−5.70830	−	4.05158i	−0.470813	−	0.334168i
$148$	−1.16853	+	1.16853i	−0.0960528	+	0.0960528i
$149$	12.7676	−	12.7676i	1.04596	−	1.04596i	0.0470721	−	0.998891i	$-0.485011\pi$
$149$	12.7676	−	12.7676i	1.04596	−	1.04596i	0.998891	−	0.0470721i	$-0.0149891\pi$
$150$	−1.28348	−	4.79002i	−0.104796	−	0.391103i
$151$	−4.43840	+	16.5643i	−0.361192	+	1.34799i	0.511319	+	0.859391i	$0.329157\pi$
$151$	−4.43840	+	16.5643i	−0.361192	+	1.34799i	−0.872511	+	0.488595i	$0.837510\pi$
$152$		−	4.02011i		−	0.326074i
$153$	1.34500	−	2.32961i	0.108737	−	0.188338i
$154$	6.22494	+	3.99373i	0.501620	+	0.321824i
$155$			1.18912i			0.0955126i
$156$	1.69800	+	3.18069i	0.135949	+	0.254659i
$157$	−2.58381	+	1.49176i	−0.206211	+	0.119056i	−0.599549	−	0.800338i	$-0.704653\pi$
$157$	−2.58381	+	1.49176i	−0.206211	+	0.119056i	0.393338	+	0.919394i	$0.371320\pi$
$158$	0.115203	−	0.115203i	0.00916509	−	0.00916509i
$159$	1.00045	−	0.577609i	0.0793407	−	0.0458073i
$160$	−0.101251	−	0.175372i	−0.00800462	−	0.0138644i
$161$	−3.25583	+	5.07479i	−0.256595	+	0.399949i
$162$	−0.965926	−	0.258819i	−0.0758903	−	0.0203347i
$163$	2.46737	+	2.46737i	0.193259	+	0.193259i	0.797103	−	0.603844i	$-0.206365\pi$
$163$	2.46737	+	2.46737i	0.193259	+	0.193259i	−0.603844	+	0.797103i	$0.706365\pi$
$164$	10.6586	+	2.85597i	0.832298	+	0.223013i
$165$	0.283038	−	0.490235i	0.0220344	−	0.0381648i
$166$	−3.55880	−	6.16401i	−0.276216	−	0.478420i
$167$	1.13433	+	4.23339i	0.0877773	+	0.327589i	0.995826	−	0.0912760i	$-0.0290946\pi$
$167$	1.13433	+	4.23339i	0.0877773	+	0.327589i	−0.908048	+	0.418865i	$0.862428\pi$
$168$	0.803647	−	2.52074i	0.0620027	−	0.194480i
$169$	−5.73771	−	11.6653i	−0.441362	−	0.897329i
$170$	0.272366	−	0.471752i	0.0208895	−	0.0361817i
$171$	−2.84265	−	2.84265i	−0.217383	−	0.217383i
$172$	−6.62500			−0.505151
$173$	−22.1494			−1.68398			−0.841992	−	0.539490i	$-0.818617\pi$
$173$	−22.1494			−1.68398			−0.841992	+	0.539490i	$0.818617\pi$
$174$	2.58180	+	2.58180i	0.195726	+	0.195726i
$175$	7.08481	−	11.0429i	0.535562	−	0.834768i
$176$	−0.723502	+	2.70015i	−0.0545360	+	0.203531i
$177$	4.76725	−	1.27738i	0.358329	−	0.0960138i
$178$	13.1078	+	7.56779i	0.982470	+	0.567230i
$179$			4.97827i			0.372093i	0.982541	+	0.186047i	$0.0595675\pi$
$179$			4.97827i			0.372093i	−0.982541	+	0.186047i	$0.940432\pi$
$180$	−0.195603	−	0.0524115i	−0.0145794	−	0.00390653i
$181$	16.9305			1.25843			0.629216	−	0.777230i	$-0.283376\pi$
$181$	16.9305			1.25843			0.629216	+	0.777230i	$0.283376\pi$
$182$	−3.19805	+	8.98735i	−0.237055	+	0.666187i
$183$	2.01287			0.148796
$184$	−2.20125	−	0.589824i	−0.162279	−	0.0434824i
$185$			0.334647i			0.0246037i
$186$	−5.08541	−	2.93607i	−0.372881	−	0.215283i
$187$	−7.26340	+	1.94622i	−0.531152	+	0.142322i
$188$	−1.56321	+	5.83398i	−0.114009	+	0.425486i
$189$	−1.21417	−	2.35070i	−0.0883179	−	0.170988i
$190$	−0.575643	−	0.575643i	−0.0417616	−	0.0417616i
$191$	−19.8491			−1.43623			−0.718115	−	0.695924i	$-0.754995\pi$
$191$	−19.8491			−1.43623			−0.718115	+	0.695924i	$0.754995\pi$
$192$	1.00000			0.0721688
$193$	9.36842	+	9.36842i	0.674353	+	0.674353i	0.958717	−	0.284363i	$-0.0917822\pi$
$193$	9.36842	+	9.36842i	0.674353	+	0.674353i	−0.284363	+	0.958717i	$0.591782\pi$
$194$	−5.22086	+	9.04280i	−0.374836	+	0.649235i
$195$	0.698585	+	0.212307i	0.0500267	+	0.0152036i
$196$	6.36292	−	2.91775i	0.454494	−	0.208410i
$197$	−3.80520	−	14.2012i	−0.271109	−	1.01179i	−0.958404	−	0.285415i	$-0.907869\pi$
$197$	−3.80520	−	14.2012i	−0.271109	−	1.01179i	0.687295	−	0.726379i	$-0.258798\pi$
$198$	1.39770	+	2.42088i	0.0993301	+	0.172045i
$199$	−5.25165	+	9.09613i	−0.372280	+	0.644807i	−0.989916	−	0.141657i	$-0.954757\pi$
$199$	−5.25165	+	9.09613i	−0.372280	+	0.644807i	0.617636	+	0.786464i	$0.288090\pi$
$200$	4.79002	+	1.28348i	0.338705	+	0.0907559i
$201$	7.22594	+	7.22594i	0.509678	+	0.509678i
$202$	13.3283	+	3.57132i	0.937778	+	0.251277i
$203$	−0.452193	+	9.64964i	−0.0317377	+	0.677272i
$204$	1.34500	+	2.32961i	0.0941689	+	0.163105i
$205$	1.93517	−	1.11727i	0.135158	−	0.0780334i
$206$	3.47805	−	3.47805i	0.242327	−	0.242327i
$207$	−1.97359	+	1.13945i	−0.137174	+	0.0791975i
$208$	−3.60356	−	0.119831i	−0.249862	−	0.00830879i
$209$			11.2378i			0.777335i
$210$	−0.245873	−	0.476023i	−0.0169668	−	0.0328487i
$211$	11.7054	−	20.2743i	0.805831	−	1.39574i	−0.109898	−	0.993943i	$-0.535052\pi$
$211$	11.7054	−	20.2743i	0.805831	−	1.39574i	0.915729	−	0.401797i	$-0.131614\pi$
$212$			1.15522i			0.0793407i
$213$	0.283594	−	1.05839i	0.0194315	−	0.0725195i
$214$	1.90909	+	7.12484i	0.130503	+	0.487044i
$215$	−0.948640	+	0.948640i	−0.0646967	+	0.0646967i
$216$	0.707107	−	0.707107i	0.0481125	−	0.0481125i
$217$	−3.31419	−	15.1786i	−0.224982	−	1.03039i
$218$	8.71864	+	5.03371i	0.590501	+	0.340926i
$219$	3.07743	−	11.4851i	0.207954	−	0.776094i
$220$	0.283038	+	0.490235i	0.0190824	+	0.0330517i
$221$	−4.56763	−	8.55606i	−0.307252	−	0.575543i
$222$	−1.43115	−	0.826278i	−0.0960528	−	0.0554561i
$223$	−12.9381	+	3.46676i	−0.866400	+	0.232151i	−0.664531	−	0.747261i	$-0.731368\pi$
$223$	−12.9381	+	3.46676i	−0.866400	+	0.232151i	−0.201870	+	0.979412i	$0.564702\pi$
$224$	1.78120	+	1.95635i	0.119012	+	0.130714i
$225$	4.29461	−	2.47950i	0.286308	−	0.165300i
$226$	4.14893	+	15.4840i	0.275983	+	1.02998i
$227$	9.54548	−	2.55770i	0.633556	−	0.169761i	0.0722732	−	0.997385i	$-0.476975\pi$
$227$	9.54548	−	2.55770i	0.633556	−	0.169761i	0.561283	+	0.827624i	$0.310308\pi$
$228$	3.88313	−	1.04048i	0.257166	−	0.0689075i
$229$	−3.24133	−	12.0968i	−0.214193	−	0.799379i	−0.986449	−	0.164068i	$-0.947539\pi$
$229$	−3.24133	−	12.0968i	−0.214193	−	0.799379i	0.772256	−	0.635311i	$-0.219128\pi$
$230$	−0.399657	+	0.230742i	−0.0263526	+	0.0152147i
$231$	−2.24651	+	7.04648i	−0.147810	+	0.463624i
$232$	−3.52681	+	0.945006i	−0.231546	+	0.0620427i
$233$	22.4609	+	12.9678i	1.47146	+	0.849549i	0.999486	−	0.0320619i	$-0.0102074\pi$
$233$	22.4609	+	12.9678i	1.47146	+	0.849549i	0.471976	+	0.881611i	$0.343541\pi$
$234$	−2.63283	+	2.46337i	−0.172114	+	0.161035i
$235$	0.611535	+	1.05921i	0.0398922	+	0.0690953i
$236$	−1.27738	+	4.76725i	−0.0831504	+	0.310322i
$237$	0.141095	+	0.0814611i	0.00916509	+	0.00529147i
$238$	−2.16181	+	6.78081i	−0.140129	+	0.439534i
$239$	3.56842	−	3.56842i	0.230822	−	0.230822i	−0.582214	−	0.813036i	$-0.697813\pi$
$239$	3.56842	−	3.56842i	0.230822	−	0.230822i	0.813036	+	0.582214i	$0.197813\pi$
$240$	0.143191	−	0.143191i	0.00924294	−	0.00924294i
$241$	4.43559	+	16.5538i	0.285721	+	1.06633i	0.948311	+	0.317344i	$0.102791\pi$
$241$	4.43559	+	16.5538i	0.285721	+	1.06633i	−0.662589	+	0.748983i	$0.730542\pi$
$242$	−0.824535	+	3.07721i	−0.0530031	+	0.197810i
$243$		−	1.00000i		−	0.0641500i
$244$	−1.00644	+	1.74320i	−0.0644304	+	0.111597i
$245$	0.493318	−	1.32891i	0.0315169	−	0.0849008i
$246$			11.0346i			0.703541i
$247$	−14.1178	+	3.28412i	−0.898292	+	0.208963i
$248$	5.08541	−	2.93607i	0.322924	−	0.186440i
$249$	5.03290	−	5.03290i	0.318947	−	0.318947i
$250$	1.74653	−	1.00836i	0.110460	−	0.0637744i
$251$	7.30883	+	12.6593i	0.461329	+	0.799045i	0.999027	−	0.0440920i	$-0.0140395\pi$
$251$	7.30883	+	12.6593i	0.461329	+	0.799045i	−0.537698	+	0.843137i	$0.680706\pi$
$252$	2.64285	+	0.123847i	0.166484	+	0.00780162i
$253$	6.15338	+	1.64879i	0.386860	+	0.103659i
$254$	6.05114	+	6.05114i	0.379682	+	0.379682i
$255$	0.526171	+	0.140987i	0.0329501	+	0.00882895i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	2.58405	+	4.47570i	0.161188	+	0.279186i	0.935295	−	0.353869i	$-0.115134\pi$
$257$	2.58405	+	4.47570i	0.161188	+	0.279186i	−0.774107	+	0.633055i	$0.781801\pi$
$258$	−1.71468	−	6.39926i	−0.106751	−	0.398400i
$259$	−0.932691	−	4.27161i	−0.0579546	−	0.265425i
$260$	−0.533156	+	0.498838i	−0.0330649	+	0.0309366i
$261$	−1.82561	+	3.16205i	−0.113003	+	0.195726i
$262$	−9.23512	−	9.23512i	−0.570547	−	0.570547i
$263$	11.9526			0.737031			0.368516	−	0.929622i	$-0.379866\pi$
$263$	11.9526			0.737031			0.368516	+	0.929622i	$0.379866\pi$
$264$	−2.79540			−0.172045
$265$	0.165417	+	0.165417i	0.0101615	+	0.0101615i
$266$	8.95219	+	5.74345i	0.548894	+	0.352153i
$267$	−3.91737	+	14.6198i	−0.239739	+	0.894720i
$268$	−9.87081	+	2.64488i	−0.602956	+	0.161562i
$269$	−18.1439	−	10.4754i	−1.10625	−	0.638696i	−0.168398	−	0.985719i	$-0.553859\pi$
$269$	−18.1439	−	10.4754i	−1.10625	−	0.638696i	−0.937857	+	0.347023i	$0.887193\pi$
$270$		−	0.202503i		−	0.0123239i
$271$	18.4852	+	4.95309i	1.12290	+	0.300879i	0.772055	−	0.635556i	$-0.219229\pi$
$271$	18.4852	+	4.95309i	1.12290	+	0.300879i	0.350841	+	0.936435i	$0.385896\pi$
$272$	−2.69000			−0.163105
$273$	−9.50883	−	0.762985i	−0.575501	−	0.0461780i
$274$	3.59815			0.217372
$275$	−13.3900	−	3.58784i	−0.807448	−	0.216355i
$276$		−	2.27891i		−	0.137174i
$277$	18.4523	+	10.6534i	1.10869	+	0.640103i	0.938490	−	0.345307i	$-0.112225\pi$
$277$	18.4523	+	10.6534i	1.10869	+	0.640103i	0.170201	+	0.985409i	$0.445558\pi$
$278$	−15.3287	+	4.10731i	−0.919353	+	0.246340i
$279$	1.51982	−	5.67204i	0.0909892	−	0.339576i
$280$	0.535184	+	0.0250793i	0.0319834	+	0.00149878i
$281$	10.6777	+	10.6777i	0.636978	+	0.636978i	0.949809	−	0.312831i	$-0.101277\pi$
$281$	10.6777	+	10.6777i	0.636978	+	0.636978i	−0.312831	+	0.949809i	$0.601277\pi$
$282$	−6.03978			−0.359663
$283$	11.1258			0.661361			0.330680	−	0.943743i	$-0.392722\pi$
$283$	11.1258			0.661361			0.330680	+	0.943743i	$0.392722\pi$
$284$	0.774793	+	0.774793i	0.0459755	+	0.0459755i
$285$	0.407041	−	0.705016i	0.0241110	−	0.0417616i
$286$	10.0734	+	0.334975i	0.595651	+	0.0198075i
$287$	−21.5876	+	19.6549i	−1.27427	+	1.16019i
$288$	0.258819	+	0.965926i	0.0152511	+	0.0569177i
$289$	4.88195	+	8.45578i	0.287173	+	0.497399i
$290$	−0.369691	+	0.640324i	−0.0217090	+	0.0376011i
$291$	−10.0859	−	2.70252i	−0.591248	−	0.158424i
$292$	8.40770	+	8.40770i	0.492024	+	0.492024i
$293$	20.7576	+	5.56198i	1.21267	+	0.324934i	0.807809	−	0.589444i	$-0.200653\pi$
$293$	20.7576	+	5.56198i	1.21267	+	0.324934i	0.404862	+	0.914378i	$0.367320\pi$
$294$	4.46517	+	5.39094i	0.260414	+	0.314406i
$295$	0.499718	+	0.865537i	0.0290947	+	0.0503935i
$296$	1.43115	−	0.826278i	0.0831842	−	0.0480264i
$297$	−1.97664	+	1.97664i	−0.114697	+	0.114697i
$298$	−15.6371	+	9.02807i	−0.905831	+	0.522982i
$299$	−0.273084	+	8.21218i	−0.0157928	+	0.474922i
$300$			4.95899i			0.286308i
$301$	9.46500	−	14.7529i	0.545554	−	0.850343i
$302$	8.57432	−	14.8512i	0.493397	−	0.854589i
$303$			13.7985i			0.792704i
$304$	−1.04048	+	3.88313i	−0.0596757	+	0.222713i
$305$	0.105498	+	0.393723i	0.00604078	+	0.0225445i
$306$	−1.90212	+	1.90212i	−0.108737	+	0.108737i
$307$	−15.0456	+	15.0456i	−0.858698	+	0.858698i	−0.991185	−	0.132487i	$-0.957704\pi$
$307$	−15.0456	+	15.0456i	−0.858698	+	0.858698i	0.132487	+	0.991185i	$0.457704\pi$
$308$	−4.97917	−	5.46878i	−0.283715	−	0.311612i
$309$	4.25973	+	2.45936i	0.242327	+	0.139908i
$310$	0.307767	−	1.14860i	0.0174800	−	0.0652363i
$311$	0.952113	+	1.64911i	0.0539894	+	0.0935124i	0.891757	−	0.452515i	$-0.149473\pi$
$311$	0.952113	+	1.64911i	0.0539894	+	0.0935124i	−0.837768	+	0.546027i	$0.816140\pi$
$312$	−0.816922	−	3.51179i	−0.0462491	−	0.198816i
$313$	10.7514	+	6.20732i	0.607705	+	0.350859i	0.772067	−	0.635542i	$-0.219223\pi$
$313$	10.7514	+	6.20732i	0.607705	+	0.350859i	−0.164362	+	0.986400i	$0.552556\pi$
$314$	2.88187	−	0.772194i	0.162633	−	0.0435774i
$315$	0.396166	−	0.360699i	0.0223214	−	0.0203231i
$316$	−0.141095	+	0.0814611i	−0.00793720	+	0.00458255i
$317$	−6.43782	−	24.0263i	−0.361584	−	1.34945i	−0.871993	−	0.489518i	$-0.837173\pi$
$317$	−6.43782	−	24.0263i	−0.361584	−	1.34945i	0.510410	−	0.859931i	$-0.329494\pi$
$318$	−1.11585	+	0.298992i	−0.0625740	+	0.0167667i
$319$	9.85883	−	2.64167i	0.551989	−	0.147905i
$320$	0.0524115	+	0.195603i	0.00292989	+	0.0109345i
$321$	−6.38796	+	3.68809i	−0.356541	+	0.205849i
$322$	4.45834	−	4.05920i	0.248454	−	0.226210i
$323$	−10.4456	+	2.79889i	−0.581210	+	0.155735i
$324$	0.866025	+	0.500000i	0.0481125	+	0.0277778i
$325$	0.594241	−	17.8700i	0.0329626	−	0.991251i
$326$	−1.74469	−	3.02189i	−0.0966295	−	0.167367i
$327$	−2.60564	+	9.72438i	−0.144092	+	0.537760i
$328$	−9.55625	−	5.51730i	−0.527656	−	0.304642i
$329$	−10.7581	−	11.8159i	−0.593112	−	0.651433i
$330$	−0.400276	+	0.400276i	−0.0220344	+	0.0220344i
$331$	17.1243	−	17.1243i	0.941236	−	0.941236i	−0.0571304	−	0.998367i	$-0.518195\pi$
$331$	17.1243	−	17.1243i	0.941236	−	0.941236i	0.998367	+	0.0571304i	$0.0181951\pi$
$332$	1.84217	+	6.87507i	0.101102	+	0.377318i
$333$	0.427713	−	1.59625i	0.0234385	−	0.0874737i
$334$		−	4.38273i		−	0.239812i
$335$	−1.03469	+	1.79213i	−0.0565311	+	0.0979147i
$336$	−1.42868	+	2.22685i	−0.0779409	+	0.121485i
$337$		−	24.8568i		−	1.35403i	−0.735967	−	0.677017i	$-0.763272\pi$
$337$		−	24.8568i		−	1.35403i	0.735967	−	0.677017i	$-0.236728\pi$
$338$	2.52301	+	12.7528i	0.137233	+	0.693662i
$339$	−13.8826	+	8.01512i	−0.753999	+	0.435321i
$340$	−0.385184	+	0.385184i	−0.0208895	+	0.0208895i
$341$	−14.2157	+	8.20747i	−0.769826	+	0.444459i
$342$	2.01005	+	3.48152i	0.108691	+	0.188259i
$343$	−2.59319	+	18.3378i	−0.140019	+	0.990149i
$344$	6.39926	+	1.71468i	0.345025	+	0.0924491i
$345$	−0.326319	−	0.326319i	−0.0175684	−	0.0175684i
$346$	21.3946	+	5.73267i	1.15018	+	0.308190i
$347$	2.40733	−	4.16962i	0.129232	−	0.223837i	−0.794147	−	0.607726i	$-0.792082\pi$
$347$	2.40733	−	4.16962i	0.129232	−	0.223837i	0.923379	+	0.383889i	$0.125415\pi$
$348$	−1.82561	−	3.16205i	−0.0978631	−	0.169504i
$349$	8.18170	+	30.5345i	0.437956	+	1.63448i	0.733891	+	0.679267i	$0.237702\pi$
$349$	8.18170	+	30.5345i	0.437956	+	1.63448i	−0.295935	+	0.955208i	$0.595631\pi$
$350$	−9.70153	+	8.83298i	−0.518569	+	0.472143i
$351$	−3.06086	−	1.90556i	−0.163377	−	0.101711i
$352$	1.39770	−	2.42088i	0.0744976	−	0.129034i
$353$	3.54343	+	3.54343i	0.188598	+	0.188598i	0.795090	−	0.606492i	$-0.207424\pi$
$353$	3.54343	+	3.54343i	0.188598	+	0.188598i	−0.606492	+	0.795090i	$0.707424\pi$
$354$	−4.93542			−0.262315
$355$	0.221887			0.0117765
$356$	−10.7025	−	10.7025i	−0.567230	−	0.567230i
$357$	−7.10927	−	0.333148i	−0.376263	−	0.0176321i
$358$	1.28847	−	4.80864i	0.0680978	−	0.254144i
$359$	10.5607	−	2.82972i	0.557371	−	0.149347i	0.0308727	−	0.999523i	$-0.490171\pi$
$359$	10.5607	−	2.82972i	0.557371	−	0.149347i	0.526498	+	0.850176i	$0.323505\pi$
$360$	0.175372	+	0.101251i	0.00924294	+	0.00533641i
$361$		−	2.83873i		−	0.149407i
$362$	−16.3536	−	4.38193i	−0.859525	−	0.230309i
$363$	−3.18576			−0.167209
$364$	5.41518	−	7.85340i	0.283833	−	0.411630i
$365$	2.40781			0.126031
$366$	−1.94428	−	0.520969i	−0.101629	−	0.0272315i
$367$		−	15.8760i		−	0.828721i	−0.910113	−	0.414361i	$-0.864005\pi$
$367$		−	15.8760i		−	0.828721i	0.910113	−	0.414361i	$-0.135995\pi$
$368$	1.97359	+	1.13945i	0.102881	+	0.0593981i
$369$	−10.6586	+	2.85597i	−0.554865	+	0.148676i
$370$	0.0866130	−	0.323244i	0.00450279	−	0.0168047i
$371$	−2.57250	−	1.65044i	−0.133557	−	0.0856864i
$372$	4.15222	+	4.15222i	0.215283	+	0.215283i
$373$	−0.161078			−0.00834030			−0.00417015	−	0.999991i	$-0.501327\pi$
$373$	−0.161078			−0.00834030			−0.00417015	+	0.999991i	$0.501327\pi$
$374$	7.51962			0.388830
$375$	1.42604	+	1.42604i	0.0736403	+	0.0736403i
$376$	3.01989	−	5.23060i	0.155739	−	0.269748i
$377$	6.19979	+	11.6134i	0.319305	+	0.598121i
$378$	0.564393	+	2.58485i	0.0290293	+	0.132950i
$379$	−1.62284	−	6.05652i	−0.0833597	−	0.311103i	0.911639	−	0.410992i	$-0.134818\pi$
$379$	−1.62284	−	6.05652i	−0.0833597	−	0.311103i	−0.994999	+	0.0998896i	$0.968151\pi$
$380$	0.407041	+	0.705016i	0.0208808	+	0.0361666i
$381$	−4.27880	+	7.41110i	−0.219210	+	0.379682i
$382$	19.1728	+	5.13732i	0.980963	+	0.262848i
$383$	14.5419	+	14.5419i	0.743058	+	0.743058i	0.973165	−	0.230107i	$-0.0739076\pi$
$383$	14.5419	+	14.5419i	0.743058	+	0.743058i	−0.230107	+	0.973165i	$0.573908\pi$
$384$	−0.965926	−	0.258819i	−0.0492922	−	0.0132078i
$385$	−1.49605	−	0.0701066i	−0.0762459	−	0.00357297i
$386$	−6.62447	−	11.4739i	−0.337177	−	0.584007i
$387$	5.73742	−	3.31250i	0.291649	−	0.168384i
$388$	7.38341	−	7.38341i	0.374836	−	0.374836i
$389$	15.7262	−	9.07952i	0.797349	−	0.460350i	−0.0451941	−	0.998978i	$-0.514391\pi$
$389$	15.7262	−	9.07952i	0.797349	−	0.460350i	0.842543	+	0.538628i	$0.181057\pi$
$390$	−0.619832	−	0.385880i	−0.0313864	−	0.0195398i
$391$			6.13026i			0.310021i
$392$	−6.90128	+	1.17148i	−0.348567	+	0.0591688i
$393$	6.53021	−	11.3107i	0.329406	−	0.570547i
$394$			14.7022i			0.740684i
$395$	−0.00853900	+	0.0318680i	−0.000429644	+	0.00160345i
$396$	−0.723502	−	2.70015i	−0.0363573	−	0.135687i
$397$	9.53585	−	9.53585i	0.478590	−	0.478590i	−0.426090	−	0.904681i	$-0.640109\pi$
$397$	9.53585	−	9.53585i	0.478590	−	0.478590i	0.904681	+	0.426090i	$0.140109\pi$
$398$	7.42696	−	7.42696i	0.372280	−	0.372280i
$399$	−3.23075	+	10.1337i	−0.161740	+	0.507318i
$400$	−4.29461	−	2.47950i	−0.214731	−	0.123975i
$401$	5.49978	−	20.5254i	0.274646	−	1.02499i	−0.681433	−	0.731881i	$-0.738643\pi$
$401$	5.49978	−	20.5254i	0.274646	−	1.02499i	0.956078	−	0.293111i	$-0.0946905\pi$
$402$	−5.10951	−	8.84993i	−0.254839	−	0.441394i
$403$	−14.4652	−	15.4603i	−0.720564	−	0.770135i
$404$	−11.9499	−	6.89925i	−0.594528	−	0.343251i
$405$	0.195603	−	0.0524115i	0.00971957	−	0.00260435i
$406$	2.93430	−	9.20380i	0.145627	−	0.456777i
$407$	−4.00064	+	2.30977i	−0.198305	+	0.114491i
$408$	−0.696224	−	2.59834i	−0.0344682	−	0.128637i
$409$	27.4612	−	7.35820i	1.35787	−	0.363839i	0.494834	−	0.868987i	$-0.335229\pi$
$409$	27.4612	−	7.35820i	1.35787	−	0.363839i	0.863033	+	0.505148i	$0.168562\pi$
$410$	−2.15840	+	0.578341i	−0.106596	+	0.0285622i
$411$	0.931270	+	3.47555i	0.0459361	+	0.171436i
$412$	−4.25973	+	2.45936i	−0.209862	+	0.121164i
$413$	−8.79100	−	9.65542i	−0.432577	−	0.475112i
$414$	2.20125	−	0.589824i	0.108186	−	0.0289883i
$415$	1.24823	+	0.720665i	0.0612732	+	0.0353761i
$416$	3.44976	+	1.04842i	0.169138	+	0.0514029i
$417$	−7.93471	−	13.7433i	−0.388564	−	0.673013i
$418$	2.90856	−	10.8549i	0.142262	−	0.530929i
$419$	−22.4063	−	12.9363i	−1.09462	−	0.631978i	−0.159816	−	0.987147i	$-0.551090\pi$
$419$	−22.4063	−	12.9363i	−1.09462	−	0.631978i	−0.934802	+	0.355168i	$0.884424\pi$
$420$	0.114291	+	0.523439i	0.00557684	+	0.0255412i
$421$	−0.259512	+	0.259512i	−0.0126478	+	0.0126478i	−0.713402	−	0.700755i	$-0.752847\pi$
$421$	−0.259512	+	0.259512i	−0.0126478	+	0.0126478i	0.700755	+	0.713402i	$0.252847\pi$
$422$	−16.5539	+	16.5539i	−0.805831	+	0.805831i
$423$	−1.56321	−	5.83398i	−0.0760058	−	0.283658i
$424$	0.298992	−	1.11585i	0.0145203	−	0.0541907i
$425$		−	13.3397i		−	0.647070i
$426$	−0.547861	+	0.948923i	−0.0265440	+	0.0459755i
$427$	−2.44397	−	4.73166i	−0.118272	−	0.228981i
$428$		−	7.37618i		−	0.356541i
$429$	2.28362	+	9.81683i	0.110254	+	0.473961i
$430$	1.16184	−	0.670790i	0.0560290	−	0.0323483i
$431$	0.542188	−	0.542188i	0.0261163	−	0.0261163i	−0.693928	−	0.720044i	$-0.744121\pi$
$431$	0.542188	−	0.542188i	0.0261163	−	0.0261163i	0.720044	+	0.693928i	$0.244121\pi$
$432$	−0.866025	+	0.500000i	−0.0416667	+	0.0240563i
$433$	1.45861	+	2.52639i	0.0700964	+	0.121411i	0.898943	−	0.438065i	$-0.144336\pi$
$433$	1.45861	+	2.52639i	0.0700964	+	0.121411i	−0.828847	+	0.559475i	$0.811003\pi$
$434$	−0.727245	+	15.5192i	−0.0349089	+	0.744944i
$435$	−0.714188	−	0.191366i	−0.0342427	−	0.00917531i
$436$	−7.11874	−	7.11874i	−0.340926	−	0.340926i
$437$	8.84928	+	2.37116i	0.423319	+	0.113428i
$438$	−5.94514	+	10.2973i	−0.284070	+	0.492024i
$439$	3.34704	+	5.79725i	0.159746	+	0.276688i	0.934777	−	0.355235i	$-0.115599\pi$
$439$	3.34704	+	5.79725i	0.159746	+	0.276688i	−0.775031	+	0.631923i	$0.782266\pi$
$440$	−0.146511	−	0.546787i	−0.00698464	−	0.0260670i
$441$	−4.05158	+	5.70830i	−0.192932	+	0.271824i
$442$	2.19752	+	9.44671i	0.104525	+	0.449334i
$443$	14.1212	−	24.4587i	0.670920	−	1.16207i	−0.306724	−	0.951799i	$-0.599233\pi$
$443$	14.1212	−	24.4587i	0.670920	−	1.16207i	0.977644	−	0.210269i	$-0.0674339\pi$
$444$	1.16853	+	1.16853i	0.0554561	+	0.0554561i
$445$	−3.06499			−0.145295
$446$	13.3945			0.634249
$447$	−12.7676	−	12.7676i	−0.603887	−	0.603887i
$448$	−1.21417	−	2.35070i	−0.0573642	−	0.111060i
$449$	−10.2498	+	38.2527i	−0.483716	+	1.80525i	0.102056	+	0.994779i	$0.467458\pi$
$449$	−10.2498	+	38.2527i	−0.483716	+	1.80525i	−0.585772	+	0.810476i	$0.699209\pi$
$450$	−4.79002	+	1.28348i	−0.225804	+	0.0605039i
$451$	26.7135	+	15.4230i	1.25789	+	0.726243i
$452$		−	16.0302i		−	0.753999i
$453$	16.5643	+	4.43840i	0.778260	+	0.208534i
$454$	−9.88221			−0.463795
$455$	−0.349131	−	1.89994i	−0.0163675	−	0.0890706i
$456$	−4.02011			−0.188259
$457$	−39.7751	−	10.6577i	−1.86060	−	0.498547i	−0.860658	−	0.509183i	$-0.829948\pi$
$457$	−39.7751	−	10.6577i	−1.86060	−	0.498547i	−0.999943	+	0.0106359i	$0.996614\pi$
$458$			12.5235i			0.585186i
$459$	−2.32961	−	1.34500i	−0.108737	−	0.0627793i
$460$	0.445760	−	0.119441i	0.0207837	−	0.00556897i
$461$	4.00295	−	14.9392i	0.186436	−	0.695788i	−0.807883	−	0.589343i	$-0.799387\pi$
$461$	4.00295	−	14.9392i	0.186436	−	0.695788i	0.994319	−	0.106445i	$-0.0339467\pi$
$462$	3.99373	−	6.22494i	0.185805	−	0.289610i
$463$	−27.1074	−	27.1074i	−1.25979	−	1.25979i	−0.951194	−	0.308594i	$-0.900142\pi$
$463$	−27.1074	−	27.1074i	−1.25979	−	1.25979i	−0.308594	−	0.951194i	$-0.599858\pi$
$464$	3.65122			0.169504
$465$	1.18912			0.0551442
$466$	−18.3392	−	18.3392i	−0.849549	−	0.849549i
$467$	7.15792	−	12.3979i	0.331229	−	0.573706i	−0.651524	−	0.758628i	$-0.725870\pi$
$467$	7.15792	−	12.3979i	0.331229	−	0.573706i	0.982753	+	0.184922i	$0.0592034\pi$
$468$	3.18069	−	1.69800i	0.147027	−	0.0784902i
$469$	8.21249	−	25.7595i	0.379217	−	1.18946i
$470$	−0.316554	−	1.18140i	−0.0146015	−	0.0544937i
$471$	1.49176	+	2.58381i	0.0687369	+	0.119056i
$472$	2.46771	−	4.27420i	0.113586	−	0.196736i
$473$	−17.8885	−	4.79320i	−0.822512	−	0.220391i
$474$	−0.115203	−	0.115203i	−0.00529147	−	0.00529147i
$475$	−19.2564	−	5.15974i	−0.883544	−	0.236745i
$476$	3.84315	−	5.99024i	0.176151	−	0.274562i
$477$	−0.577609	−	1.00045i	−0.0264469	−	0.0458073i
$478$	−4.37041	+	2.52326i	−0.199898	+	0.115411i
$479$	−3.07778	+	3.07778i	−0.140628	+	0.140628i	−0.773916	−	0.633288i	$-0.781705\pi$
$479$	−3.07778	+	3.07778i	−0.140628	+	0.140628i	0.633288	+	0.773916i	$0.281705\pi$
$480$	−0.175372	+	0.101251i	−0.00800462	+	0.00462147i
$481$	−4.07085	−	4.35090i	−0.185615	−	0.198384i
$482$		−	17.1378i		−	0.780606i
$483$	5.07479	+	3.25583i	0.230911	+	0.148145i
$484$	1.59288	−	2.75895i	0.0724036	−	0.125407i
$485$		−	2.11448i		−	0.0960134i
$486$	−0.258819	+	0.965926i	−0.0117403	+	0.0438153i
$487$	2.98980	+	11.1581i	0.135481	+	0.505621i	0.999995	+	0.00301340i	$0.000959198\pi$
$487$	2.98980	+	11.1581i	0.135481	+	0.505621i	−0.864515	+	0.502607i	$0.832374\pi$
$488$	1.42332	−	1.42332i	0.0644304	−	0.0644304i
$489$	2.46737	−	2.46737i	0.111578	−	0.111578i
$490$	−0.820455	+	1.15595i	−0.0370644	+	0.0522203i
$491$	30.9800	+	17.8863i	1.39811	+	0.807198i	0.994194	−	0.107599i	$-0.0343162\pi$
$491$	30.9800	+	17.8863i	1.39811	+	0.807198i	0.403914	+	0.914797i	$0.367650\pi$
$492$	2.85597	−	10.6586i	0.128757	−	0.480527i
$493$	4.91090	+	8.50592i	0.221176	+	0.383088i
$494$	14.4867	+	0.481734i	0.651787	+	0.0216742i
$495$	−0.490235	−	0.283038i	−0.0220344	−	0.0127216i
$496$	−5.67204	+	1.51982i	−0.254682	+	0.0682419i
$497$	−2.83228	+	0.618418i	−0.127045	+	0.0277399i
$498$	−6.16401	+	3.55880i	−0.276216	+	0.159473i
$499$	9.75294	+	36.3985i	0.436602	+	1.62942i	0.737204	+	0.675670i	$0.236145\pi$
$499$	9.75294	+	36.3985i	0.436602	+	1.62942i	−0.300603	+	0.953749i	$0.597188\pi$
$500$	−1.94800	+	0.521966i	−0.0871174	+	0.0233430i
$501$	4.23339	−	1.13433i	0.189134	−	0.0506783i
$502$	−3.78333	−	14.1196i	−0.168858	−	0.630187i
$503$	−1.14985	+	0.663864i	−0.0512691	+	0.0296003i	−0.525415	−	0.850846i	$-0.676090\pi$
$503$	−1.14985	+	0.663864i	−0.0512691	+	0.0296003i	0.474146	+	0.880446i	$0.342757\pi$
$504$	−2.52074	−	0.803647i	−0.112283	−	0.0357973i
$505$	−2.69902	+	0.723201i	−0.120105	+	0.0321820i
$506$	−5.51697	−	3.18522i	−0.245259	−	0.141600i
$507$	−11.6653	+	5.73771i	−0.518073	+	0.254821i
$508$	−4.27880	−	7.41110i	−0.189841	−	0.328815i
$509$	−2.90664	+	10.8477i	−0.128835	+	0.480817i	−0.999947	−	0.0102661i	$-0.996732\pi$
$509$	−2.90664	+	10.8477i	−0.128835	+	0.480817i	0.871113	+	0.491083i	$0.163399\pi$
$510$	−0.471752	−	0.272366i	−0.0208895	−	0.0120606i
$511$	−30.7346	+	6.71080i	−1.35962	+	0.296868i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−2.84265	+	2.84265i	−0.125506	+	0.125506i
$514$	−1.33760	−	4.99199i	−0.0589990	−	0.220187i
$515$	−0.257797	+	0.962112i	−0.0113599	+	0.0423957i
$516$			6.62500i			0.291649i
$517$	−8.44179	+	14.6216i	−0.371269	+	0.643057i
$518$	−0.204664	+	4.36746i	−0.00899241	+	0.191895i
$519$			22.1494i			0.972249i
$520$	0.644098	−	0.343850i	0.0282456	−	0.0150788i
$521$	−24.4358	+	14.1080i	−1.07055	+	0.618083i	−0.928332	−	0.371752i	$-0.878757\pi$
$521$	−24.4358	+	14.1080i	−1.07055	+	0.618083i	−0.142219	+	0.989835i	$0.545424\pi$
$522$	2.58180	−	2.58180i	0.113003	−	0.113003i
$523$	20.2352	−	11.6828i	0.884823	−	0.510853i	0.0125777	−	0.999921i	$-0.495996\pi$
$523$	20.2352	−	11.6828i	0.884823	−	0.510853i	0.872246	+	0.489068i	$0.162663\pi$
$524$	6.53021	+	11.3107i	0.285274	+	0.494109i
$525$	−11.0429	−	7.08481i	−0.481954	−	0.309207i
$526$	−11.5454	−	3.09357i	−0.503402	−	0.134886i
$527$	−11.1695	−	11.1695i	−0.486550	−	0.486550i
$528$	2.70015	+	0.723502i	0.117509	+	0.0314864i
$529$	−8.90329	+	15.4210i	−0.387100	+	0.670476i
$530$	−0.116967	−	0.202593i	−0.00508073	−	0.00880009i
$531$	−1.27738	−	4.76725i	−0.0554336	−	0.206881i
$532$	−7.16064	−	7.86474i	−0.310453	−	0.340980i
$533$	−11.5689	+	38.0667i	−0.501104	+	1.64885i
$534$	7.56779	−	13.1078i	0.327490	−	0.567230i
$535$	−1.05620	−	1.05620i	−0.0456636	−	0.0456636i
$536$	10.2190			0.441394
$537$	4.97827			0.214828
$538$	14.8144	+	14.8144i	0.638696	+	0.638696i
$539$	19.2918	−	3.27476i	0.830957	−	0.141054i
$540$	−0.0524115	+	0.195603i	−0.00225543	+	0.00841739i
$541$	7.88973	−	2.11405i	0.339206	−	0.0908899i	−0.0851952	−	0.996364i	$-0.527151\pi$
$541$	7.88973	−	2.11405i	0.339206	−	0.0908899i	0.424401	+	0.905474i	$0.360485\pi$
$542$	−16.5734	−	9.56864i	−0.711887	−	0.411008i
$543$		−	16.9305i		−	0.726556i
$544$	2.59834	+	0.696224i	0.111403	+	0.0298503i
$545$	−2.03868			−0.0873274
$546$	8.98735	+	3.19805i	0.384623	+	0.136864i
$547$	−26.1644			−1.11871			−0.559354	−	0.828929i	$-0.688951\pi$
$547$	−26.1644			−1.11871			−0.559354	+	0.828929i	$0.688951\pi$
$548$	−3.47555	−	0.931270i	−0.148468	−	0.0397819i
$549$		−	2.01287i		−	0.0859073i
$550$	12.0051	+	6.93118i	0.511901	+	0.295546i
$551$	14.1782	−	3.79903i	0.604010	−	0.161844i
$552$	−0.589824	+	2.20125i	−0.0251046	+	0.0936916i
$553$	0.0201774	−	0.430579i	0.000858031	−	0.0183101i
$554$	−15.0662	−	15.0662i	−0.640103	−	0.640103i
$555$	0.334647			0.0142050
$556$	15.8694			0.673013
$557$	−32.2306	−	32.2306i	−1.36565	−	1.36565i	−0.866530	−	0.499125i	$-0.833655\pi$
$557$	−32.2306	−	32.2306i	−1.36565	−	1.36565i	−0.499125	−	0.866530i	$-0.666345\pi$
$558$	−2.93607	+	5.08541i	−0.124294	+	0.215283i
$559$	0.793880	−	23.8736i	0.0335775	−	1.00974i
$560$	−0.510457	−	0.162741i	−0.0215708	−	0.00687705i
$561$	1.94622	+	7.26340i	0.0821695	+	0.306661i
$562$	−7.55027	−	13.0774i	−0.318489	−	0.551639i
$563$	16.2747	−	28.1887i	0.685898	−	1.18801i	−0.287255	−	0.957854i	$-0.592743\pi$
$563$	16.2747	−	28.1887i	0.685898	−	1.18801i	0.973154	−	0.230157i	$-0.0739239\pi$
$564$	5.83398	+	1.56321i	0.245655	+	0.0658230i
$565$	−2.29538	−	2.29538i	−0.0965675	−	0.0965675i
$566$	−10.7467	−	2.87957i	−0.451718	−	0.121037i
$567$	−2.35070	+	1.21417i	−0.0987201	+	0.0509904i
$568$	−0.547861	−	0.948923i	−0.0229877	−	0.0398159i
$569$	6.58799	−	3.80358i	0.276183	−	0.159454i	−0.355511	−	0.934672i	$-0.615693\pi$
$569$	6.58799	−	3.80358i	0.276183	−	0.159454i	0.631694	+	0.775218i	$0.282360\pi$
$570$	−0.575643	+	0.575643i	−0.0241110	+	0.0241110i
$571$	15.5269	−	8.96445i	0.649780	−	0.375150i	−0.138592	−	0.990350i	$-0.544258\pi$
$571$	15.5269	−	8.96445i	0.649780	−	0.375150i	0.788372	+	0.615199i	$0.210924\pi$
$572$	−9.64344	−	2.93074i	−0.403212	−	0.122541i
$573$			19.8491i			0.829208i
$574$	25.9390	−	13.3979i	1.08267	−	0.559217i
$575$	−5.65054	+	9.78702i	−0.235644	+	0.408147i
$576$		−	1.00000i		−	0.0416667i
$577$	−11.5319	+	43.0378i	−0.480081	+	1.79169i	0.121177	+	0.992631i	$0.461333\pi$
$577$	−11.5319	+	43.0378i	−0.480081	+	1.79169i	−0.601258	+	0.799055i	$0.705333\pi$
$578$	−2.52708	−	9.43120i	−0.105113	−	0.392286i
$579$	9.36842	−	9.36842i	0.389338	−	0.389338i
$580$	0.522822	−	0.522822i	0.0217090	−	0.0217090i
$581$	−17.9416	−	5.72003i	−0.744344	−	0.237307i
$582$	9.04280	+	5.22086i	0.374836	+	0.216412i
$583$	−0.835802	+	3.11925i	−0.0346154	+	0.129186i
$584$	−5.94514	−	10.2973i	−0.246012	−	0.426105i
$585$	0.212307	−	0.698585i	0.00877783	−	0.0288829i
$586$	−18.6107	−	10.7449i	−0.768803	−	0.443868i
$587$	31.6736	−	8.48692i	1.30731	−	0.350293i	0.463100	−	0.886306i	$-0.346737\pi$
$587$	31.6736	−	8.48692i	1.30731	−	0.350293i	0.844210	+	0.536013i	$0.180070\pi$
$588$	−2.91775	−	6.36292i	−0.120326	−	0.262402i
$589$	−20.4439	+	11.8033i	−0.842377	+	0.486347i
$590$	−0.258673	−	0.965381i	−0.0106494	−	0.0397441i
$591$	−14.2012	+	3.80520i	−0.584159	+	0.156525i
$592$	−1.59625	+	0.427713i	−0.0656053	+	0.0175789i
$593$	−0.0954348	−	0.356168i	−0.00391904	−	0.0146261i	0.963939	−	0.266125i	$-0.0857433\pi$
$593$	−0.0954348	−	0.356168i	−0.00391904	−	0.0146261i	−0.967858	+	0.251499i	$0.919077\pi$
$594$	2.42088	−	1.39770i	0.0993301	−	0.0573483i
$595$	−0.307443	−	1.40805i	−0.0126039	−	0.0577245i
$596$	17.4409	−	4.67327i	0.714406	−	0.191425i
$597$	9.09613	+	5.25165i	0.372280	+	0.214936i
$598$	2.38925	−	7.86167i	0.0977035	−	0.321488i
$599$	−2.12688	−	3.68386i	−0.0869019	−	0.150518i	0.819298	−	0.573368i	$-0.194363\pi$
$599$	−2.12688	−	3.68386i	−0.0869019	−	0.150518i	−0.906200	+	0.422849i	$0.861030\pi$
$600$	1.28348	−	4.79002i	0.0523979	−	0.195552i
$601$	−9.57883	−	5.53034i	−0.390729	−	0.225587i	0.291747	−	0.956496i	$-0.405763\pi$
$601$	−9.57883	−	5.53034i	−0.390729	−	0.225587i	−0.682476	+	0.730908i	$0.739097\pi$
$602$	−12.9608	+	11.8005i	−0.528244	+	0.480952i
$603$	7.22594	−	7.22594i	0.294263	−	0.294263i
$604$	−12.1259	+	12.1259i	−0.493397	+	0.493397i
$605$	−0.166971	−	0.623142i	−0.00678832	−	0.0253343i
$606$	3.57132	−	13.3283i	0.145075	−	0.541427i
$607$			9.57737i			0.388733i	0.980929	+	0.194367i	$0.0622652\pi$
$607$			9.57737i			0.388733i	−0.980929	+	0.194367i	$0.937735\pi$
$608$	2.01005	−	3.48152i	0.0815185	−	0.141194i
$609$	9.64964	+	0.452193i	0.391023	+	0.0183238i
$610$		−	0.407612i		−	0.0165037i
$611$	−20.8358	−	6.33221i	−0.842925	−	0.256174i
$612$	2.32961	−	1.34500i	0.0941689	−	0.0543684i
$613$	−2.38382	+	2.38382i	−0.0962815	+	0.0962815i	−0.753607	−	0.657325i	$-0.771688\pi$
$613$	−2.38382	+	2.38382i	−0.0962815	+	0.0962815i	0.657325	+	0.753607i	$0.271688\pi$
$614$	18.4270	−	10.6388i	0.743654	−	0.429349i
$615$	−1.11727	−	1.93517i	−0.0450526	−	0.0780334i
$616$	3.39409	+	6.57114i	0.136752	+	0.264759i
$617$	30.4996	+	8.17235i	1.22787	+	0.329006i	0.813749	−	0.581216i	$-0.197423\pi$
$617$	30.4996	+	8.17235i	1.22787	+	0.329006i	0.414119	+	0.910223i	$0.364090\pi$
$618$	−3.47805	−	3.47805i	−0.139908	−	0.139908i
$619$	4.90539	+	1.31440i	0.197164	+	0.0528300i	0.356050	−	0.934467i	$-0.384123\pi$
$619$	4.90539	+	1.31440i	0.197164	+	0.0528300i	−0.158885	+	0.987297i	$0.550790\pi$
$620$	−0.594561	+	1.02981i	−0.0238781	+	0.0413582i
$621$	1.13945	+	1.97359i	0.0457247	+	0.0791975i
$622$	−0.492850	−	1.83934i	−0.0197615	−	0.0737509i
$623$	39.1232	−	8.54242i	1.56744	−	0.342245i
$624$	−0.119831	+	3.60356i	−0.00479708	+	0.144258i
$625$	12.1933	−	21.1194i	0.487731	−	0.844776i
$626$	−8.77848	−	8.77848i	−0.350859	−	0.350859i
$627$	11.2378			0.448794
$628$	−2.98353			−0.119056
$629$	−3.14336	−	3.14336i	−0.125334	−	0.125334i
$630$	−0.476023	+	0.245873i	−0.0189652	+	0.00979581i
$631$	−8.63674	+	32.2328i	−0.343823	+	1.28317i	0.550158	+	0.835061i	$0.314568\pi$
$631$	−8.63674	+	32.2328i	−0.343823	+	1.28317i	−0.893981	+	0.448105i	$0.852099\pi$
$632$	0.157371	−	0.0421674i	0.00625987	−	0.00167733i
$633$	−20.2743	−	11.7054i	−0.805831	−	0.465247i
$634$			24.8738i			0.987865i
$635$	−1.67389	−	0.448517i	−0.0664263	−	0.0177989i
$636$	1.15522			0.0458073
$637$	9.75180	+	23.2788i	0.386380	+	0.922340i
$638$	−10.2066			−0.404084
$639$	−1.05839	−	0.283594i	−0.0418691	−	0.0112188i
$640$		−	0.202503i		−	0.00800462i
$641$	7.52017	+	4.34177i	0.297029	+	0.171490i	0.641107	−	0.767451i	$-0.278475\pi$
$641$	7.52017	+	4.34177i	0.297029	+	0.171490i	−0.344078	+	0.938941i	$0.611809\pi$
$642$	7.12484	−	1.90909i	0.281195	−	0.0753460i
$643$	5.45002	−	20.3398i	0.214928	−	0.802122i	−0.771264	−	0.636515i	$-0.780375\pi$
$643$	5.45002	−	20.3398i	0.214928	−	0.802122i	0.986192	−	0.165606i	$-0.0529581\pi$
$644$	−5.35703	+	2.76698i	−0.211096	+	0.109034i
$645$	0.948640	+	0.948640i	0.0373527	+	0.0373527i
$646$	10.8141			0.425475
$647$	−27.9234			−1.09778			−0.548890	−	0.835894i	$-0.684949\pi$
$647$	−27.9234			−1.09778			−0.548890	+	0.835894i	$0.684949\pi$
$648$	−0.707107	−	0.707107i	−0.0277778	−	0.0277778i
$649$	−6.89823	+	11.9481i	−0.270779	+	0.469003i
$650$	−5.19910	+	17.1073i	−0.203925	+	0.671004i
$651$	−15.1786	+	3.31419i	−0.594896	+	0.129893i
$652$	0.903119	+	3.37049i	0.0353689	+	0.131998i
$653$	11.1596	+	19.3289i	0.436708	+	0.756400i	0.997433	−	0.0716016i	$-0.0228110\pi$
$653$	11.1596	+	19.3289i	0.436708	+	0.756400i	−0.560725	+	0.828002i	$0.689478\pi$
$654$	5.03371	−	8.71864i	0.196834	−	0.340926i
$655$	2.55465	+	0.684517i	0.0998185	+	0.0267463i
$656$	7.80264	+	7.80264i	0.304642	+	0.304642i
$657$	−11.4851	−	3.07743i	−0.448078	−	0.120062i
$658$	7.33332	+	14.1977i	0.285883	+	0.553484i
$659$	16.2186	+	28.0915i	0.631788	+	1.09429i	0.987186	+	0.159574i	$0.0510121\pi$
$659$	16.2186	+	28.0915i	0.631788	+	1.09429i	−0.355398	+	0.934715i	$0.615655\pi$
$660$	0.490235	−	0.283038i	0.0190824	−	0.0110172i
$661$	9.56629	−	9.56629i	0.372086	−	0.372086i	−0.496151	−	0.868236i	$-0.665254\pi$
$661$	9.56629	−	9.56629i	0.372086	−	0.372086i	0.868236	+	0.496151i	$0.165254\pi$
$662$	−20.9729	+	12.1087i	−0.815135	+	0.470618i
$663$	−8.55606	+	4.56763i	−0.332290	+	0.177392i
$664$		−	7.11759i		−	0.276216i
$665$	−2.15150	−	0.100822i	−0.0834316	−	0.00390969i
$666$	−0.826278	+	1.43115i	−0.0320176	+	0.0554561i
$667$		−	8.32080i		−	0.322183i
$668$	−1.13433	+	4.23339i	−0.0438887	+	0.163795i
$669$	3.46676	+	12.9381i	0.134033	+	0.500216i
$670$	1.46327	−	1.46327i	0.0565311	−	0.0565311i
$671$	−3.97873	+	3.97873i	−0.153597	+	0.153597i
$672$	1.95635	−	1.78120i	0.0754679	−	0.0687115i
$673$	23.0933	+	13.3329i	0.890180	+	0.513946i	0.874001	−	0.485923i	$-0.161517\pi$
$673$	23.0933	+	13.3329i	0.890180	+	0.513946i	0.0161787	+	0.999869i	$0.494850\pi$
$674$	−6.43341	+	24.0098i	−0.247806	+	0.924823i
$675$	−2.47950	−	4.29461i	−0.0954359	−	0.165300i
$676$	0.863636	−	12.9713i	0.0332168	−	0.498895i
$677$	29.7732	+	17.1896i	1.14428	+	0.660648i	0.947486	−	0.319797i	$-0.103615\pi$
$677$	29.7732	+	17.1896i	1.14428	+	0.660648i	0.196790	+	0.980446i	$0.436948\pi$
$678$	15.4840	−	4.14893i	0.594660	−	0.159339i
$679$	5.89324	+	26.9903i	0.226162	+	1.03579i
$680$	0.471752	−	0.272366i	0.0180909	−	0.0104448i
$681$	−2.55770	−	9.54548i	−0.0980115	−	0.365784i
$682$	15.8556	−	4.24850i	0.607143	−	0.162683i
$683$	26.7897	−	7.17827i	1.02508	−	0.274669i	0.293162	−	0.956063i	$-0.405293\pi$
$683$	26.7897	−	7.17827i	1.02508	−	0.274669i	0.731917	+	0.681394i	$0.238626\pi$
$684$	−1.04048	−	3.88313i	−0.0397838	−	0.148475i
$685$	−0.631016	+	0.364317i	−0.0241099	+	0.0139199i
$686$	7.25100	−	17.0418i	0.276845	−	0.650659i
$687$	−12.0968	+	3.24133i	−0.461522	+	0.123664i
$688$	−5.73742	−	3.31250i	−0.218737	−	0.126288i
$689$	−4.16289	−	0.138431i	−0.158594	−	0.00527380i
$690$	0.230742	+	0.399657i	0.00878421	+	0.0152147i
$691$	0.375575	−	1.40166i	0.0142875	−	0.0533218i	−0.958414	−	0.285381i	$-0.907880\pi$
$691$	0.375575	−	1.40166i	0.0142875	−	0.0533218i	0.972702	+	0.232060i	$0.0745464\pi$
$692$	−19.1819	−	11.0747i	−0.729187	−	0.420996i
$693$	7.04648	+	2.24651i	0.267674	+	0.0853379i
$694$	−3.40448	+	3.40448i	−0.129232	+	0.129232i
$695$	2.27236	−	2.27236i	0.0861954	−	0.0861954i
$696$	0.945006	+	3.52681i	0.0358204	+	0.133683i
$697$	−7.68255	+	28.6717i	−0.290997	+	1.08602i
$698$		−	31.6117i		−	1.19652i
$699$	12.9678	−	22.4609i	0.490487	−	0.849549i
$700$	11.6571	−	6.02107i	0.440597	−	0.227575i
$701$			10.5142i			0.397116i	0.980089	+	0.198558i	$0.0636258\pi$
$701$			10.5142i			0.397116i	−0.980089	+	0.198558i	$0.936374\pi$
$702$	2.46337	+	2.63283i	0.0929738	+	0.0993699i
$703$	−5.75340	+	3.32173i	−0.216994	+	0.125281i
$704$	−1.97664	+	1.97664i	−0.0744976	+	0.0744976i
$705$	1.05921	−	0.611535i	0.0398922	−	0.0230318i
$706$	−2.50559	−	4.33980i	−0.0942990	−	0.163331i
$707$	32.4361	−	16.7537i	1.21989	−	0.630090i
$708$	4.76725	+	1.27738i	0.179164	+	0.0480069i
$709$	14.6418	+	14.6418i	0.549885	+	0.549885i	0.926407	−	0.376523i	$-0.122880\pi$
$709$	14.6418	+	14.6418i	0.549885	+	0.549885i	−0.376523	+	0.926407i	$0.622880\pi$
$710$	−0.214326	−	0.0574285i	−0.00804351	−	0.00215525i
$711$	0.0814611	−	0.141095i	0.00305503	−	0.00529147i
$712$	7.56779	+	13.1078i	0.283615	+	0.491235i
$713$	3.46353	+	12.9261i	0.129710	+	0.484085i
$714$	6.78081	+	2.16181i	0.253765	+	0.0809038i
$715$	−1.80051	+	0.961197i	−0.0673352	+	0.0359467i
$716$	−2.48913	+	4.31131i	−0.0930233	+	0.161121i
$717$	−3.56842	−	3.56842i	−0.133265	−	0.133265i
$718$	−10.9332			−0.408024
$719$	15.4767			0.577185			0.288593	−	0.957452i	$-0.406813\pi$
$719$	15.4767			0.577185			0.288593	+	0.957452i	$0.406813\pi$
$720$	−0.143191	−	0.143191i	−0.00533641	−	0.00533641i
$721$	0.609167	−	12.9994i	0.0226866	−	0.484124i
$722$	−0.734716	+	2.74200i	−0.0273433	+	0.102047i
$723$	16.5538	−	4.43559i	0.615644	−	0.164961i
$724$	14.6622	+	8.46524i	0.544917	+	0.314608i
$725$			18.1064i			0.672454i
$726$	3.07721	+	0.824535i	0.114206	+	0.0306014i
$727$	−34.5270			−1.28054			−0.640268	−	0.768152i	$-0.721177\pi$
$727$	−34.5270			−1.28054			−0.640268	+	0.768152i	$0.721177\pi$
$728$	−7.26327	+	6.18425i	−0.269195	+	0.229203i
$729$	−1.00000			−0.0370370
$730$	−2.32577	−	0.623188i	−0.0860806	−	0.0230652i
$731$		−	17.8213i		−	0.659143i
$732$	1.74320	+	1.00644i	0.0644304	+	0.0371989i
$733$	23.1376	−	6.19969i	0.854605	−	0.228991i	0.195186	−	0.980766i	$-0.437469\pi$
$733$	23.1376	−	6.19969i	0.854605	−	0.228991i	0.659419	+	0.751775i	$0.270802\pi$
$734$	−4.10901	+	15.3351i	−0.151666	+	0.566027i
$735$	−1.32891	−	0.493318i	−0.0490175	−	0.0181963i
$736$	−1.61143	−	1.61143i	−0.0593981	−	0.0593981i
$737$	−28.5662			−1.05225
$738$	11.0346			0.406189
$739$	−11.5248	−	11.5248i	−0.423946	−	0.423946i	0.462614	−	0.886560i	$-0.346912\pi$
$739$	−11.5248	−	11.5248i	−0.423946	−	0.423946i	−0.886560	+	0.462614i	$0.846912\pi$
$740$	−0.167323	+	0.289813i	−0.00615093	+	0.0106537i
$741$	3.28412	+	14.1178i	0.120645	+	0.518629i
$742$	2.05768	+	2.26001i	0.0755398	+	0.0829676i
$743$	3.59453	+	13.4150i	0.131870	+	0.492147i	0.999991	−	0.00420608i	$-0.00133884\pi$
$743$	3.59453	+	13.4150i	0.131870	+	0.492147i	−0.868121	+	0.496353i	$0.834672\pi$
$744$	−2.93607	−	5.08541i	−0.107641	−	0.186440i
$745$	1.82821	−	3.16655i	0.0669803	−	0.116013i
$746$	0.155589	+	0.0416900i	0.00569653	+	0.00152638i
$747$	−5.03290	−	5.03290i	−0.184144	−	0.184144i
$748$	−7.26340	−	1.94622i	−0.265576	−	0.0711609i
$749$	16.4257	+	10.5382i	0.600180	+	0.385057i
$750$	−1.00836	−	1.74653i	−0.0368201	−	0.0637744i
$751$	−35.6855	+	20.6030i	−1.30218	+	0.751815i	−0.980778	−	0.195127i	$-0.937488\pi$
$751$	−35.6855	+	20.6030i	−1.30218	+	0.751815i	−0.321405	+	0.946942i	$0.604155\pi$
$752$	−4.27077	+	4.27077i	−0.155739	+	0.155739i
$753$	12.6593	−	7.30883i	0.461329	−	0.266348i
$754$	−2.98276	−	12.8223i	−0.108626	−	0.466961i
$755$			3.47265i			0.126383i
$756$	0.123847	−	2.64285i	0.00450427	−	0.0961196i
$757$	21.4812	−	37.2065i	0.780747	−	1.35229i	−0.150760	−	0.988570i	$-0.548172\pi$
$757$	21.4812	−	37.2065i	0.780747	−	1.35229i	0.931507	−	0.363723i	$-0.118495\pi$
$758$			6.27017i			0.227743i
$759$	1.64879	−	6.15338i	0.0598474	−	0.223354i
$760$	−0.210700	−	0.786343i	−0.00764289	−	0.0285237i
$761$	−0.614251	+	0.614251i	−0.0222666	+	0.0222666i	−0.718152	−	0.695886i	$-0.755012\pi$
$761$	−0.614251	+	0.614251i	−0.0222666	+	0.0222666i	0.695886	+	0.718152i	$0.255012\pi$
$762$	6.05114	−	6.05114i	0.219210	−	0.219210i
$763$	26.0228	−	5.68199i	0.942089	−	0.205702i
$764$	−17.1898	−	9.92455i	−0.621906	−	0.359058i
$765$	0.140987	−	0.526171i	0.00509740	−	0.0190238i
$766$	−10.2827	−	17.8102i	−0.371529	−	0.643507i
$767$	−17.0260	−	5.17438i	−0.614773	−	0.186836i
$768$	0.866025	+	0.500000i	0.0312500	+	0.0180422i
$769$	−23.3053	+	6.24465i	−0.840412	+	0.225188i	−0.653251	−	0.757142i	$-0.726595\pi$
$769$	−23.3053	+	6.24465i	−0.840412	+	0.225188i	−0.187161	+	0.982329i	$0.559929\pi$
$770$	1.42693	+	0.454925i	0.0514230	+	0.0163943i
$771$	4.47570	−	2.58405i	0.161188	−	0.0930621i
$772$	3.42908	+	12.7975i	0.123415	+	0.460592i
$773$	−1.15399	+	0.309211i	−0.0415061	+	0.0111215i	−0.279512	−	0.960142i	$-0.590173\pi$
$773$	−1.15399	+	0.309211i	−0.0415061	+	0.0111215i	0.238006	+	0.971264i	$0.423506\pi$
$774$	−6.39926	+	1.71468i	−0.230016	+	0.0616327i
$775$	−7.53677	−	28.1276i	−0.270729	−	1.01037i
$776$	−9.04280	+	5.22086i	−0.324618	+	0.187418i
$777$	−4.27161	+	0.932691i	−0.153243	+	0.0334601i
$778$	−17.5403	+	4.69990i	−0.628850	+	0.168500i
$779$	38.4172	+	22.1802i	1.37644	+	0.794687i
$780$	0.498838	+	0.533156i	0.0178613	+	0.0190900i
$781$	1.53149	+	2.65262i	0.0548010	+	0.0949181i
$782$	1.58663	−	5.92138i	0.0567377	−	0.211748i
$783$	3.16205	+	1.82561i	0.113003	+	0.0652420i
$784$	6.96932	+	0.654618i	0.248904	+	0.0233792i
$785$	−0.427215	+	0.427215i	−0.0152479	+	0.0152479i
$786$	−9.23512	+	9.23512i	−0.329406	+	0.329406i
$787$	−2.24990	−	8.39674i	−0.0802003	−	0.299311i	0.914162	−	0.405349i	$-0.132850\pi$
$787$	−2.24990	−	8.39674i	−0.0802003	−	0.299311i	−0.994362	+	0.106038i	$0.966183\pi$
$788$	3.80520	−	14.2012i	0.135555	−	0.505897i
$789$		−	11.9526i		−	0.425525i
$790$	0.0164961	−	0.0285721i	0.000586905	−	0.00101655i
$791$	35.6970	+	22.9021i	1.26924	+	0.814304i
$792$			2.79540i			0.0993301i
$793$	−6.16111	−	3.83564i	−0.218788	−	0.136208i
$794$	−11.6790	+	6.74286i	−0.414471	+	0.239295i
$795$	0.165417	−	0.165417i	0.00586673	−	0.00586673i
$796$	−9.09613	+	5.25165i	−0.322404	+	0.186140i
$797$	−14.2978	−	24.7644i	−0.506453	−	0.877202i	−0.999972	−	0.00746693i	$-0.997623\pi$
$797$	−14.2978	−	24.7644i	−0.506453	−	0.877202i	0.493520	−	0.869735i	$-0.335710\pi$
$798$	5.74345	−	8.95219i	0.203316	−	0.316904i
$799$	−15.6934	−	4.20504i	−0.555193	−	0.148763i
$800$	3.50654	+	3.50654i	0.123975	+	0.123975i
$801$	14.6198	+	3.91737i	0.516567	+	0.138414i
$802$	−10.6248	+	18.4026i	−0.375173	+	0.649819i
$803$	16.6190	+	28.7850i	0.586473	+	1.01580i
$804$	2.64488	+	9.87081i	0.0932776	+	0.348117i
$805$	−0.370871	+	1.16328i	−0.0130715	+	0.0410004i
$806$	9.97090	+	18.6774i	0.351210	+	0.657884i
$807$	−10.4754	+	18.1439i	−0.368751	+	0.638696i
$808$	9.75702	+	9.75702i	0.343251	+	0.343251i
$809$	27.1833			0.955714			0.477857	−	0.878438i	$-0.341414\pi$
$809$	27.1833			0.955714			0.477857	+	0.878438i	$0.341414\pi$
$810$	−0.202503			−0.00711522
$811$	−22.9191	−	22.9191i	−0.804799	−	0.804799i	0.179043	−	0.983841i	$-0.442700\pi$
$811$	−22.9191	−	22.9191i	−0.804799	−	0.804799i	−0.983841	+	0.179043i	$0.942700\pi$
$812$	−5.21643	+	8.13074i	−0.183061	+	0.285333i
$813$	4.95309	−	18.4852i	0.173713	−	0.648304i
$814$	4.46214	−	1.19563i	0.156398	−	0.0419067i
$815$	0.611942	+	0.353305i	0.0214354	+	0.0123757i
$816$			2.69000i			0.0941689i
$817$	−25.7257	−	6.89318i	−0.900028	−	0.241162i
$818$	−28.4299			−0.994028
$819$	−0.762985	+	9.50883i	−0.0266609	+	0.332265i
$820$	2.23454			0.0780334
$821$	−36.5358	−	9.78973i	−1.27511	−	0.341664i	−0.443121	−	0.896462i	$-0.646129\pi$
$821$	−36.5358	−	9.78973i	−1.27511	−	0.341664i	−0.831985	+	0.554798i	$0.812796\pi$
$822$		−	3.59815i		−	0.125500i
$823$	25.2800	+	14.5954i	0.881204	+	0.508763i	0.871055	−	0.491185i	$-0.163436\pi$
$823$	25.2800	+	14.5954i	0.881204	+	0.508763i	0.0101489	+	0.999948i	$0.496769\pi$
$824$	4.75111	−	1.27306i	0.165513	−	0.0443490i
$825$	−3.58784	+	13.3900i	−0.124913	+	0.466180i
$826$	5.99245	+	11.6017i	0.208504	+	0.403675i
$827$	−33.4695	−	33.4695i	−1.16385	−	1.16385i	−0.983626	−	0.180223i	$-0.942318\pi$
$827$	−33.4695	−	33.4695i	−1.16385	−	1.16385i	−0.180223	−	0.983626i	$-0.557682\pi$
$828$	−2.27891			−0.0791975
$829$	−41.6537			−1.44669			−0.723347	−	0.690485i	$-0.757397\pi$
$829$	−41.6537			−1.44669			−0.723347	+	0.690485i	$0.757397\pi$
$830$	−1.01917	−	1.01917i	−0.0353761	−	0.0353761i
$831$	10.6534	−	18.4523i	0.369563	−	0.640103i
$832$	−3.06086	−	1.90556i	−0.106116	−	0.0660633i
$833$	7.84874	+	17.1163i	0.271943	+	0.593043i
$834$	4.10731	+	15.3287i	0.142224	+	0.530789i
$835$	0.443757	+	0.768609i	0.0153568	+	0.0265988i
$836$	−5.61890	+	9.73222i	−0.194334	+	0.336596i
$837$	−5.67204	−	1.51982i	−0.196054	−	0.0525326i
$838$	18.2947	+	18.2947i	0.631978	+	0.631978i
$839$	−3.23633	−	0.867171i	−0.111730	−	0.0299381i	0.202521	−	0.979278i	$-0.435087\pi$
$839$	−3.23633	−	0.867171i	−0.111730	−	0.0299381i	−0.314251	+	0.949340i	$0.601753\pi$
$840$	0.0250793	−	0.535184i	0.000865319	−	0.0184656i
$841$	7.83428	+	13.5694i	0.270148	+	0.467910i
$842$	0.317836	−	0.183503i	0.0109534	−	0.00632392i
$843$	10.6777	−	10.6777i	0.367759	−	0.367759i
$844$	20.2743	−	11.7054i	0.697870	−	0.402915i
$845$	−1.73371	−	1.98104i	−0.0596413	−	0.0681497i
$846$			6.03978i			0.207652i
$847$	3.86806	+	7.48876i	0.132908	+	0.257317i
$848$	−0.577609	+	1.00045i	−0.0198352	+	0.0343555i
$849$		−	11.1258i		−	0.381837i
$850$	−3.45257	+	12.8852i	−0.118422	+	0.441957i
$851$	0.974717	+	3.63769i	0.0334129	+	0.124699i
$852$	0.774793	−	0.774793i	0.0265440	−	0.0265440i
$853$	−38.1904	+	38.1904i	−1.30761	+	1.30761i	−0.384479	+	0.923134i	$0.625619\pi$
$853$	−38.1904	+	38.1904i	−1.30761	+	1.30761i	−0.923134	+	0.384479i	$0.874381\pi$
$854$	1.13605	+	5.20297i	0.0388749	+	0.178042i
$855$	−0.705016	−	0.407041i	−0.0241110	−	0.0139205i
$856$	−1.90909	+	7.12484i	−0.0652515	+	0.243522i
$857$	−23.7123	−	41.0709i	−0.809997	−	1.40296i	−0.912865	−	0.408261i	$-0.866135\pi$
$857$	−23.7123	−	41.0709i	−0.809997	−	1.40296i	0.102868	−	0.994695i	$-0.467198\pi$
$858$	0.334975	−	10.0734i	0.0114359	−	0.343899i
$859$	−18.7079	−	10.8010i	−0.638305	−	0.368526i	0.145656	−	0.989335i	$-0.453471\pi$
$859$	−18.7079	−	10.8010i	−0.638305	−	0.368526i	−0.783961	+	0.620809i	$0.786804\pi$
$860$	−1.29587	+	0.347226i	−0.0441887	+	0.0118403i
$861$	19.6549	+	21.5876i	0.669837	+	0.735702i
$862$	−0.664042	+	0.383385i	−0.0226174	+	0.0130581i
$863$	5.71445	+	21.3266i	0.194522	+	0.725966i	0.992390	+	0.123134i	$0.0392945\pi$
$863$	5.71445	+	21.3266i	0.194522	+	0.725966i	−0.797868	+	0.602832i	$0.794039\pi$
$864$	0.965926	−	0.258819i	0.0328615	−	0.00880520i
$865$	−4.33247	+	1.16088i	−0.147308	+	0.0394712i
$866$	−0.755033	−	2.81782i	−0.0256571	−	0.0957535i
$867$	8.45578	−	4.88195i	0.287173	−	0.165800i
$868$	4.71912	−	14.8021i	0.160177	−	0.502417i
$869$	−0.439914	+	0.117875i	−0.0149231	+	0.00399862i
$870$	0.640324	+	0.369691i	0.0217090	+	0.0125337i
$871$	−8.34814	−	35.8870i	−0.282866	−	1.21598i
$872$	5.03371	+	8.71864i	0.170463	+	0.295251i
$873$	−2.70252	+	10.0859i	−0.0914663	+	0.341357i
$874$	−7.93405	−	4.58073i	−0.268373	−	0.154945i
$875$	1.62073	−	5.08364i	0.0547908	−	0.171858i
$876$	8.40770	−	8.40770i	0.284070	−	0.284070i
$877$	5.15862	−	5.15862i	0.174194	−	0.174194i	−0.614625	−	0.788819i	$-0.710693\pi$
$877$	5.15862	−	5.15862i	0.174194	−	0.174194i	0.788819	+	0.614625i	$0.210693\pi$
$878$	−1.73256	−	6.46599i	−0.0584710	−	0.218217i
$879$	5.56198	−	20.7576i	0.187601	−	0.700136i
$880$			0.566075i			0.0190824i
$881$	−10.5727	+	18.3125i	−0.356204	+	0.616964i	−0.987323	−	0.158722i	$-0.949263\pi$
$881$	−10.5727	+	18.3125i	−0.356204	+	0.616964i	0.631119	+	0.775686i	$0.282596\pi$
$882$	5.39094	−	4.46517i	0.181522	−	0.150350i
$883$			35.0673i			1.18011i	0.807363	+	0.590055i	$0.200894\pi$
$883$			35.0673i			1.18011i	−0.807363	+	0.590055i	$0.799106\pi$
$884$	0.322346	−	9.69358i	0.0108417	−	0.326030i
$885$	0.865537	−	0.499718i	0.0290947	−	0.0167978i
$886$	−19.9704	+	19.9704i	−0.670920	+	0.670920i
$887$	45.1499	−	26.0673i	1.51598	−	0.875254i	0.516161	−	0.856492i	$-0.327361\pi$
$887$	45.1499	−	26.0673i	1.51598	−	0.875254i	0.999824	−	0.0187625i	$-0.00597263\pi$
$888$	−0.826278	−	1.43115i	−0.0277281	−	0.0480264i
$889$	22.6165	+	1.05983i	0.758532	+	0.0355457i
$890$	2.96056	+	0.793279i	0.0992381	+	0.0265908i
$891$	1.97664	+	1.97664i	0.0662201	+	0.0662201i
$892$	−12.9381	−	3.46676i	−0.433200	−	0.116076i
$893$	−12.1403	+	21.0276i	−0.406259	+	0.703661i
$894$	9.02807	+	15.6371i	0.301944	+	0.522982i
$895$	0.260919	+	0.973762i	0.00872155	+	0.0325493i
$896$	0.564393	+	2.58485i	0.0188551	+	0.0863538i
$897$	8.21218	+	0.273084i	0.274197	+	0.00911800i
$898$	19.8010	−	34.2964i	0.660769	−	1.14449i
$899$	15.1607	+	15.1607i	0.505637	+	0.505637i
$900$	4.95899			0.165300
$901$	−3.10754			−0.103527
$902$	−21.8115	−	21.8115i	−0.726243	−	0.726243i
$903$	−14.7529	−	9.46500i	−0.490946	−	0.314976i
$904$	−4.14893	+	15.4840i	−0.137991	+	0.514991i
$905$	3.31164	−	0.887352i	0.110083	−	0.0294966i
$906$	−14.8512	−	8.57432i	−0.493397	−	0.284863i
$907$			28.0120i			0.930124i	0.885278	+	0.465062i	$0.153968\pi$
$907$			28.0120i			0.930124i	−0.885278	+	0.465062i	$0.846032\pi$
$908$	9.54548	+	2.55770i	0.316778	+	0.0848804i
$909$	13.7985			0.457668
$910$	−0.154506	+	1.92556i	−0.00512184	+	0.0638318i
$911$	−18.6644			−0.618379			−0.309189	−	0.951000i	$-0.600058\pi$
$911$	−18.6644			−0.618379			−0.309189	+	0.951000i	$0.600058\pi$
$912$	3.88313	+	1.04048i	0.128583	+	0.0344538i
$913$			19.8965i			0.658478i
$914$	35.6614	+	20.5891i	1.17957	+	0.681028i
$915$	0.393723	−	0.105498i	0.0130161	−	0.00348765i
$916$	3.24133	−	12.0968i	0.107096	−	0.399689i
$917$	−34.5168	−	1.61749i	−1.13984	−	0.0534143i
$918$	1.90212	+	1.90212i	0.0627793	+	0.0627793i
$919$	40.3772			1.33192			0.665961	−	0.745987i	$-0.268022\pi$
$919$	40.3772			1.33192			0.665961	+	0.745987i	$0.268022\pi$
$920$	−0.461485			−0.0152147
$921$	15.0456	+	15.0456i	0.495769	+	0.495769i
$922$	−7.73310	+	13.3941i	−0.254676	+	0.441112i
$923$	−2.88486	+	2.69917i	−0.0949562	+	0.0888442i
$924$	−5.46878	+	4.97917i	−0.179910	+	0.163803i
$925$	−2.12102	−	7.91577i	−0.0697389	−	0.260269i
$926$	19.1678	+	33.1996i	0.629894	+	1.09101i
$927$	2.45936	−	4.25973i	0.0807758	−	0.139908i
$928$	−3.52681	−	0.945006i	−0.115773	−	0.0310213i
$929$	−38.9271	−	38.9271i	−1.27716	−	1.27716i	−0.942253	−	0.334903i	$-0.891297\pi$
$929$	−38.9271	−	38.9271i	−1.27716	−	1.27716i	−0.334903	−	0.942253i	$-0.608703\pi$
$930$	−1.14860	−	0.307767i	−0.0376642	−	0.0100921i
$931$	27.7439	−	4.70948i	0.909269	−	0.154347i
$932$	12.9678	+	22.4609i	0.424775	+	0.735731i
$933$	1.64911	−	0.952113i	0.0539894	−	0.0311708i
$934$	−10.1228	+	10.1228i	−0.331229	+	0.331229i
$935$	−1.31873	+	0.761371i	−0.0431272	+	0.0248995i
$936$	−3.51179	+	0.816922i	−0.114786	+	0.0267019i
$937$			17.0327i			0.556434i	0.960518	+	0.278217i	$0.0897435\pi$
$937$			17.0327i			0.556434i	−0.960518	+	0.278217i	$0.910256\pi$
$938$	−14.5997	+	22.7563i	−0.476697	+	0.743018i
$939$	6.20732	−	10.7514i	0.202568	−	0.350859i
$940$			1.22307i			0.0398922i
$941$	7.98694	−	29.8077i	0.260367	−	0.971702i	−0.704659	−	0.709546i	$-0.748900\pi$
$941$	7.98694	−	29.8077i	0.260367	−	0.971702i	0.965026	−	0.262155i	$-0.0844333\pi$
$942$	−0.772194	−	2.88187i	−0.0251595	−	0.0938964i
$943$	17.7815	−	17.7815i	0.579045	−	0.579045i
$944$	−3.48987	+	3.48987i	−0.113586	+	0.113586i
$945$	−0.360699	−	0.396166i	−0.0117335	−	0.0128873i
$946$	16.0384	+	9.25975i	0.521452	+	0.301060i
$947$	7.76748	−	28.9886i	0.252409	−	0.942004i	−0.717104	−	0.696966i	$-0.754533\pi$
$947$	7.76748	−	28.9886i	0.252409	−	0.942004i	0.969514	−	0.245038i	$-0.0788004\pi$
$948$	0.0814611	+	0.141095i	0.00264573	+	0.00458255i
$949$	−31.3052	+	29.2902i	−1.01621	+	0.950799i
$950$	17.2648	+	9.96785i	0.560145	+	0.323400i
$951$	−24.0263	+	6.43782i	−0.779105	+	0.208760i
$952$	−5.26259	+	4.79144i	−0.170561	+	0.155292i
$953$	32.6542	−	18.8529i	1.05777	−	0.610705i	0.132957	−	0.991122i	$-0.457553\pi$
$953$	32.6542	−	18.8529i	1.05777	−	0.610705i	0.924815	+	0.380416i	$0.124219\pi$
$954$	0.298992	+	1.11585i	0.00968023	+	0.0361271i
$955$	−3.88253	+	1.04032i	−0.125636	+	0.0336640i
$956$	4.87456	−	1.30613i	0.157654	−	0.0422434i
$957$	−2.64167	−	9.85883i	−0.0853930	−	0.318691i
$958$	3.76950	−	2.17632i	0.121787	−	0.0703138i
$959$	7.03924	−	6.40904i	0.227309	−	0.206959i
$960$	0.195603	−	0.0524115i	0.00631304	−	0.00169158i
$961$	−3.01543	−	1.74096i	−0.0972720	−	0.0561600i
$962$	2.80604	+	5.25626i	0.0904705	+	0.169469i
$963$	3.68809	+	6.38796i	0.118847	+	0.205849i
$964$	−4.43559	+	16.5538i	−0.142861	+	0.533164i
$965$	2.32350	+	1.34147i	0.0747961	+	0.0431835i
$966$	−4.05920	−	4.45834i	−0.130603	−	0.143445i
$967$	−33.3921	+	33.3921i	−1.07382	+	1.07382i	−0.0767673	+	0.997049i	$0.524460\pi$
$967$	−33.3921	+	33.3921i	−1.07382	+	1.07382i	−0.997049	+	0.0767673i	$0.975540\pi$
$968$	−2.25267	+	2.25267i	−0.0724036	+	0.0724036i
$969$	2.79889	+	10.4456i	0.0899134	+	0.335562i
$970$	−0.547267	+	2.04243i	−0.0175717	+	0.0655784i
$971$			9.74125i			0.312612i	0.987709	+	0.156306i	$0.0499585\pi$
$971$			9.74125i			0.312612i	−0.987709	+	0.156306i	$0.950041\pi$
$972$	0.500000	−	0.866025i	0.0160375	−	0.0277778i
$973$	−22.6723	+	35.3388i	−0.726841	+	1.13291i
$974$		−	11.5517i		−	0.370140i
$975$	−17.8700	−	0.594241i	−0.572299	−	0.0190309i
$976$	−1.74320	+	1.00644i	−0.0557984	+	0.0322152i
$977$	29.1893	−	29.1893i	0.933849	−	0.933849i	−0.0640950	−	0.997944i	$-0.520416\pi$
$977$	29.1893	−	29.1893i	0.933849	−	0.933849i	0.997944	+	0.0640950i	$0.0204161\pi$
$978$	−3.02189	+	1.74469i	−0.0966295	+	0.0557891i
$979$	−21.1550	−	36.6415i	−0.676116	−	1.17107i
$980$	1.09168	−	0.904209i	0.0348724	−	0.0288839i
$981$	9.72438	+	2.60564i	0.310476	+	0.0831917i
$982$	−25.2951	−	25.2951i	−0.807198	−	0.807198i
$983$	18.4889	+	4.95409i	0.589705	+	0.158011i	0.541318	−	0.840818i	$-0.317925\pi$
$983$	18.4889	+	4.95409i	0.589705	+	0.158011i	0.0483867	+	0.998829i	$0.484592\pi$
$984$	−5.51730	+	9.55625i	−0.175885	+	0.304642i
$985$	−1.48861	−	2.57835i	−0.0474312	−	0.0821532i
$986$	−2.54207	−	9.48713i	−0.0809559	−	0.302132i
$987$	−11.8159	+	10.7581i	−0.376105	+	0.342433i
$988$	−13.8684	−	4.21475i	−0.441212	−	0.134089i
$989$	−7.54887	+	13.0750i	−0.240040	+	0.415762i
$990$	0.400276	+	0.400276i	0.0127216	+	0.0127216i
$991$	17.6073			0.559315			0.279658	−	0.960100i	$-0.409779\pi$
$991$	17.6073			0.559315			0.279658	+	0.960100i	$0.409779\pi$
$992$	5.87213			0.186440
$993$	−17.1243	−	17.1243i	−0.543423	−	0.543423i
$994$	2.89583	+	0.135702i	0.0918502	+	0.00430420i
$995$	−0.550494	+	2.05447i	−0.0174518	+	0.0651311i
$996$	6.87507	−	1.84217i	0.217845	−	0.0583713i
$997$	28.7542	+	16.6013i	0.910655	+	0.525767i	0.880642	−	0.473783i	$-0.157112\pi$
$997$	28.7542	+	16.6013i	0.910655	+	0.525767i	0.0300132	+	0.999550i	$0.490445\pi$
$998$		−	37.6825i		−	1.19282i
$999$	−1.59625	−	0.427713i	−0.0505030	−	0.0135322i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.by.b.19.3	✓	40
7.3	odd	6		546.2.cg.b.409.8	yes	40
13.11	odd	12		546.2.cg.b.271.8	yes	40
91.24	even	12	inner	546.2.by.b.115.3	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.by.b.19.3	✓	40	1.1	even	1	trivial
546.2.by.b.115.3	yes	40	91.24	even	12	inner
546.2.cg.b.271.8	yes	40	13.11	odd	12
546.2.cg.b.409.8	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)

\(f(q)\)	\(=\)	\(q+(-0.965926 - 0.258819i) q^{2} -1.00000i q^{3} +(0.866025 + 0.500000i) q^{4} +(0.195603 - 0.0524115i) q^{5} +(-0.258819 + 0.965926i) q^{6} +(-2.35070 + 1.21417i) q^{7} +(-0.707107 - 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(-0.965926 - 0.258819i) q^{2} -1.00000i q^{3} +(0.866025 + 0.500000i) q^{4} +(0.195603 - 0.0524115i) q^{5} +(-0.258819 + 0.965926i) q^{6} +(-2.35070 + 1.21417i) q^{7} +(-0.707107 - 0.707107i) q^{8} -1.00000 q^{9} -0.202503 q^{10} +(1.97664 + 1.97664i) q^{11} +(0.500000 - 0.866025i) q^{12} +(-1.90556 + 3.06086i) q^{13} +(2.58485 - 0.564393i) q^{14} +(-0.0524115 - 0.195603i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-1.34500 + 2.32961i) q^{17} +(0.965926 + 0.258819i) q^{18} +(2.84265 + 2.84265i) q^{19} +(0.195603 + 0.0524115i) q^{20} +(1.21417 + 2.35070i) q^{21} +(-1.39770 - 2.42088i) q^{22} +(1.97359 - 1.13945i) q^{23} +(-0.707107 + 0.707107i) q^{24} +(-4.29461 + 2.47950i) q^{25} +(2.63283 - 2.46337i) q^{26} +1.00000i q^{27} +(-2.64285 - 0.123847i) q^{28} +(1.82561 - 3.16205i) q^{29} +0.202503i q^{30} +(-1.51982 + 5.67204i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(1.97664 - 1.97664i) q^{33} +(1.90212 - 1.90212i) q^{34} +(-0.396166 + 0.360699i) q^{35} +(-0.866025 - 0.500000i) q^{36} +(-0.427713 + 1.59625i) q^{37} +(-2.01005 - 3.48152i) q^{38} +(3.06086 + 1.90556i) q^{39} +(-0.175372 - 0.101251i) q^{40} +(10.6586 - 2.85597i) q^{41} +(-0.564393 - 2.58485i) q^{42} +(-5.73742 + 3.31250i) q^{43} +(0.723502 + 2.70015i) q^{44} +(-0.195603 + 0.0524115i) q^{45} +(-2.20125 + 0.589824i) q^{46} +(1.56321 + 5.83398i) q^{47} +(0.866025 - 0.500000i) q^{48} +(4.05158 - 5.70830i) q^{49} +(4.79002 - 1.28348i) q^{50} +(2.32961 + 1.34500i) q^{51} +(-3.18069 + 1.69800i) q^{52} +(0.577609 + 1.00045i) q^{53} +(0.258819 - 0.965926i) q^{54} +(0.490235 + 0.283038i) q^{55} +(2.52074 + 0.803647i) q^{56} +(2.84265 - 2.84265i) q^{57} +(-2.58180 + 2.58180i) q^{58} +(1.27738 + 4.76725i) q^{59} +(0.0524115 - 0.195603i) q^{60} +2.01287i q^{61} +(2.93607 - 5.08541i) q^{62} +(2.35070 - 1.21417i) q^{63} +1.00000i q^{64} +(-0.212307 + 0.698585i) q^{65} +(-2.42088 + 1.39770i) q^{66} +(-7.22594 + 7.22594i) q^{67} +(-2.32961 + 1.34500i) q^{68} +(-1.13945 - 1.97359i) q^{69} +(0.476023 - 0.245873i) q^{70} +(1.05839 + 0.283594i) q^{71} +(0.707107 + 0.707107i) q^{72} +(11.4851 + 3.07743i) q^{73} +(0.826278 - 1.43115i) q^{74} +(2.47950 + 4.29461i) q^{75} +(1.04048 + 3.88313i) q^{76} +(-7.04648 - 2.24651i) q^{77} +(-2.46337 - 2.63283i) q^{78} +(-0.0814611 + 0.141095i) q^{79} +(0.143191 + 0.143191i) q^{80} +1.00000 q^{81} -11.0346 q^{82} +(5.03290 + 5.03290i) q^{83} +(-0.123847 + 2.64285i) q^{84} +(-0.140987 + 0.526171i) q^{85} +(6.39926 - 1.71468i) q^{86} +(-3.16205 - 1.82561i) q^{87} -2.79540i q^{88} +(-14.6198 - 3.91737i) q^{89} +0.202503 q^{90} +(0.762985 - 9.50883i) q^{91} +2.27891 q^{92} +(5.67204 + 1.51982i) q^{93} -6.03978i q^{94} +(0.705016 + 0.407041i) q^{95} +(-0.965926 + 0.258819i) q^{96} +(2.70252 - 10.0859i) q^{97} +(-5.39094 + 4.46517i) q^{98} +(-1.97664 - 1.97664i) 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

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