LMFDB - Embedded newform 546.2.u.a.425.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(185,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1, 2]))

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

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

chi := DirichletCharacter("546.185");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.u (of order $6$, degree $2$, 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:	$76$
Relative dimension:	$38$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			425.5
Character	$\chi$	$=$	546.425
Dual form			546.2.u.a.185.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(-1.38893 - 1.03484i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.75377 + 3.03762i) q^{5} +(1.72026 + 0.201730i) q^{6} +(1.37341 + 2.26136i) q^{7} +1.00000i q^{8} +(0.858232 + 2.87462i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(-1.38893 - 1.03484i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.75377 + 3.03762i) q^{5} +(1.72026 + 0.201730i) q^{6} +(1.37341 + 2.26136i) q^{7} +1.00000i q^{8} +(0.858232 + 2.87462i) q^{9} -3.50754i q^{10} -3.53979i q^{11} +(-1.59066 + 0.685428i) q^{12} +(-3.59167 - 0.316032i) q^{13} +(-2.32009 - 1.27169i) q^{14} +(5.57930 - 2.40417i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.97842 - 3.42672i) q^{17} +(-2.18056 - 2.06038i) q^{18} +6.65733i q^{19} +(1.75377 + 3.03762i) q^{20} +(0.432561 - 4.56211i) q^{21} +(1.76989 + 3.06555i) q^{22} +(1.11366 - 0.642974i) q^{23} +(1.03484 - 1.38893i) q^{24} +(-3.65143 - 6.32446i) q^{25} +(3.26850 - 1.52215i) q^{26} +(1.78274 - 4.88076i) q^{27} +(2.64510 - 0.0587331i) q^{28} +(-5.71124 - 3.29739i) q^{29} +(-3.62973 + 4.87172i) q^{30} +(-8.14013 + 4.69971i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-3.66310 + 4.91650i) q^{33} +3.95683i q^{34} +(-9.27780 + 0.206009i) q^{35} +(2.91861 + 0.694059i) q^{36} +(-5.28837 - 9.15972i) q^{37} +(-3.32866 - 5.76542i) q^{38} +(4.66153 + 4.15574i) q^{39} +(-3.03762 - 1.75377i) q^{40} +(-2.84220 + 4.92284i) q^{41} +(1.90645 + 4.16719i) q^{42} +(-2.79284 - 4.83734i) q^{43} +(-3.06555 - 1.76989i) q^{44} +(-10.2372 - 2.43444i) q^{45} +(-0.642974 + 1.11366i) q^{46} +(-0.0582673 + 0.100922i) q^{47} +(-0.201730 + 1.72026i) q^{48} +(-3.22747 + 6.21156i) q^{49} +(6.32446 + 3.65143i) q^{50} +(-6.29397 + 2.71212i) q^{51} +(-2.06953 + 2.95247i) q^{52} +(-6.70912 + 3.87351i) q^{53} +(0.896487 + 5.11823i) q^{54} +(10.7525 + 6.20798i) q^{55} +(-2.26136 + 1.37341i) q^{56} +(6.88924 - 9.24654i) q^{57} +6.59478 q^{58} +(2.84121 - 4.92113i) q^{59} +(0.707578 - 6.03390i) q^{60} -10.9893i q^{61} +(4.69971 - 8.14013i) q^{62} +(-5.32183 + 5.88881i) q^{63} -1.00000 q^{64} +(7.25896 - 10.3559i) q^{65} +(0.714083 - 6.08936i) q^{66} +7.68334 q^{67} +(-1.97842 - 3.42672i) q^{68} +(-2.21217 - 0.259415i) q^{69} +(7.93181 - 4.81731i) q^{70} +(-8.18290 + 4.72440i) q^{71} +(-2.87462 + 0.858232i) q^{72} +(3.73438 - 2.15605i) q^{73} +(9.15972 + 5.28837i) q^{74} +(-1.47321 + 12.5628i) q^{75} +(5.76542 + 3.32866i) q^{76} +(8.00472 - 4.86159i) q^{77} +(-6.11487 - 1.26821i) q^{78} +(-2.63559 + 4.56498i) q^{79} +3.50754 q^{80} +(-7.52687 + 4.93418i) q^{81} -5.68441i q^{82} +2.03056 q^{83} +(-3.73463 - 2.65567i) q^{84} +(6.93939 + 12.0194i) q^{85} +(4.83734 + 2.79284i) q^{86} +(4.52024 + 10.4900i) q^{87} +3.53979 q^{88} +(-0.177296 - 0.307085i) q^{89} +(10.0829 - 3.01029i) q^{90} +(-4.21820 - 8.55610i) q^{91} -1.28595i q^{92} +(16.1695 + 1.89615i) q^{93} -0.116535i q^{94} +(-20.2224 - 11.6754i) q^{95} +(-0.685428 - 1.59066i) q^{96} +(-0.507481 + 0.292994i) q^{97} +(-0.310710 - 6.99310i) q^{98} +(10.1755 - 3.03796i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q + 38 q^{4} + 10 q^{7} - 8 q^{9}+O(q^{10}) $ 76 * q + 38 * q^4 + 10 * q^7 - 8 * q^9	$ 76 q + 38 q^{4} + 10 q^{7} - 8 q^{9} + 2 q^{13} + 12 q^{15} - 38 q^{16} - 8 q^{21} - 42 q^{25} + 20 q^{28} + 20 q^{30} + 12 q^{31} - 4 q^{36} - 6 q^{37} + 12 q^{39} + 8 q^{42} - 2 q^{43} - 4 q^{46} + 2 q^{49} + 10 q^{51} - 14 q^{52} + 18 q^{54} + 24 q^{55} + 8 q^{57} + 16 q^{58} - 12 q^{60} + 32 q^{63} - 76 q^{64} - 24 q^{66} + 96 q^{67} - 30 q^{69} - 54 q^{73} - 12 q^{75} + 18 q^{76} - 12 q^{78} - 60 q^{79} + 8 q^{81} + 8 q^{84} + 8 q^{85} - 24 q^{87} + 48 q^{91} + 16 q^{93} - 66 q^{97}+O(q^{100}) $ 76 * q + 38 * q^4 + 10 * q^7 - 8 * q^9 + 2 * q^13 + 12 * q^15 - 38 * q^16 - 8 * q^21 - 42 * q^25 + 20 * q^28 + 20 * q^30 + 12 * q^31 - 4 * q^36 - 6 * q^37 + 12 * q^39 + 8 * q^42 - 2 * q^43 - 4 * q^46 + 2 * q^49 + 10 * q^51 - 14 * q^52 + 18 * q^54 + 24 * q^55 + 8 * q^57 + 16 * q^58 - 12 * q^60 + 32 * q^63 - 76 * q^64 - 24 * q^66 + 96 * q^67 - 30 * q^69 - 54 * q^73 - 12 * q^75 + 18 * q^76 - 12 * q^78 - 60 * q^79 + 8 * q^81 + 8 * q^84 + 8 * q^85 - 24 * q^87 + 48 * q^91 + 16 * q^93 - 66 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	−1.38893	−	1.03484i	−0.801897	−	0.597462i
$3$	−1.38893	−	1.03484i	−0.801897	−	0.597462i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−1.75377	+	3.03762i	−0.784311	+	1.35847i	0.145099	+	0.989417i	$0.453650\pi$
$5$	−1.75377	+	3.03762i	−0.784311	+	1.35847i	−0.929410	+	0.369049i	$0.879684\pi$
$6$	1.72026	+	0.201730i	0.702294	+	0.0823561i
$7$	1.37341	+	2.26136i	0.519102	+	0.854712i
$7$	1.37341	+	2.26136i	0.519102	+	0.854712i
$8$			1.00000i			0.353553i
$9$	0.858232	+	2.87462i	0.286077	+	0.958207i
$10$		−	3.50754i		−	1.10918i
$11$		−	3.53979i		−	1.06729i	−0.845710	−	0.533643i	$-0.820823\pi$
$11$		−	3.53979i		−	1.06729i	0.845710	−	0.533643i	$-0.179177\pi$
$12$	−1.59066	+	0.685428i	−0.459183	+	0.197866i
$13$	−3.59167	−	0.316032i	−0.996151	−	0.0876514i
$13$	−3.59167	−	0.316032i	−0.996151	−	0.0876514i
$14$	−2.32009	−	1.27169i	−0.620070	−	0.339872i
$15$	5.57930	−	2.40417i	1.44057	−	0.620754i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.97842	−	3.42672i	0.479837	−	0.831102i	−0.519896	−	0.854230i	$-0.674029\pi$
$17$	1.97842	−	3.42672i	0.479837	−	0.831102i	0.999733	+	0.0231281i	$0.00736256\pi$
$18$	−2.18056	−	2.06038i	−0.513963	−	0.485636i
$19$			6.65733i			1.52730i	0.645633	+	0.763648i	$0.276594\pi$
$19$			6.65733i			1.52730i	−0.645633	+	0.763648i	$0.723406\pi$
$20$	1.75377	+	3.03762i	0.392155	+	0.679233i
$21$	0.432561	−	4.56211i	0.0943924	−	0.995535i
$22$	1.76989	+	3.06555i	0.377343	+	0.653576i
$23$	1.11366	−	0.642974i	0.232215	−	0.134069i	−0.379379	−	0.925242i	$-0.623862\pi$
$23$	1.11366	−	0.642974i	0.232215	−	0.134069i	0.611593	+	0.791172i	$0.290529\pi$
$24$	1.03484	−	1.38893i	0.211235	−	0.283513i
$25$	−3.65143	−	6.32446i	−0.730286	−	1.26489i
$26$	3.26850	−	1.52215i	0.641005	−	0.298517i
$27$	1.78274	−	4.88076i	0.343088	−	0.939303i
$28$	2.64510	−	0.0587331i	0.499877	−	0.0110995i
$29$	−5.71124	−	3.29739i	−1.06055	−	0.612310i	−0.134967	−	0.990850i	$-0.543093\pi$
$29$	−5.71124	−	3.29739i	−1.06055	−	0.612310i	−0.925585	+	0.378540i	$0.876426\pi$
$30$	−3.62973	+	4.87172i	−0.662695	+	0.889450i
$31$	−8.14013	+	4.69971i	−1.46201	+	0.844092i	−0.999104	−	0.0423149i	$-0.986527\pi$
$31$	−8.14013	+	4.69971i	−1.46201	+	0.844092i	−0.462906	+	0.886407i	$0.653193\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	−3.66310	+	4.91650i	−0.637663	+	0.855853i
$34$			3.95683i			0.678592i
$35$	−9.27780	+	0.206009i	−1.56823	+	0.0348219i
$36$	2.91861	+	0.694059i	0.486435	+	0.115676i
$37$	−5.28837	−	9.15972i	−0.869402	−	1.50585i	−0.862609	−	0.505871i	$-0.831171\pi$
$37$	−5.28837	−	9.15972i	−0.869402	−	1.50585i	−0.00679300	−	0.999977i	$-0.502162\pi$
$38$	−3.32866	−	5.76542i	−0.539981	−	0.935274i
$39$	4.66153	+	4.15574i	0.746442	+	0.665450i
$40$	−3.03762	−	1.75377i	−0.480290	−	0.277296i
$41$	−2.84220	+	4.92284i	−0.443877	+	0.768818i	−0.997973	−	0.0636346i	$-0.979731\pi$
$41$	−2.84220	+	4.92284i	−0.443877	+	0.768818i	0.554096	+	0.832453i	$0.313064\pi$
$42$	1.90645	+	4.16719i	0.294171	+	0.643011i
$43$	−2.79284	−	4.83734i	−0.425904	−	0.737688i	0.570600	−	0.821228i	$-0.306711\pi$
$43$	−2.79284	−	4.83734i	−0.425904	−	0.737688i	−0.996504	+	0.0835402i	$0.973377\pi$
$44$	−3.06555	−	1.76989i	−0.462148	−	0.266821i
$45$	−10.2372	−	2.43444i	−1.52606	−	0.362905i
$46$	−0.642974	+	1.11366i	−0.0948013	+	0.164201i
$47$	−0.0582673	+	0.100922i	−0.00849915	+	0.0147210i	−0.870244	−	0.492621i	$-0.836039\pi$
$47$	−0.0582673	+	0.100922i	−0.00849915	+	0.0147210i	0.861745	+	0.507342i	$0.169372\pi$
$48$	−0.201730	+	1.72026i	−0.0291173	+	0.248299i
$49$	−3.22747	+	6.21156i	−0.461067	+	0.887365i
$50$	6.32446	+	3.65143i	0.894414	+	0.516390i
$51$	−6.29397	+	2.71212i	−0.881332	+	0.379773i
$52$	−2.06953	+	2.95247i	−0.286992	+	0.409433i
$53$	−6.70912	+	3.87351i	−0.921568	+	0.532068i	−0.884135	−	0.467231i	$-0.845251\pi$
$53$	−6.70912	+	3.87351i	−0.921568	+	0.532068i	−0.0374333	+	0.999299i	$0.511918\pi$
$54$	0.896487	+	5.11823i	0.121996	+	0.696503i
$55$	10.7525	+	6.20798i	1.44987	+	0.837084i
$56$	−2.26136	+	1.37341i	−0.302186	+	0.183530i
$57$	6.88924	−	9.24654i	0.912502	−	1.22473i
$58$	6.59478			0.865937
$59$	2.84121	−	4.92113i	0.369894	−	0.640676i	−0.619654	−	0.784875i	$-0.712727\pi$
$59$	2.84121	−	4.92113i	0.369894	−	0.640676i	0.989549	+	0.144199i	$0.0460605\pi$
$60$	0.707578	−	6.03390i	0.0913480	−	0.778973i
$61$		−	10.9893i		−	1.40704i	−0.710677	−	0.703519i	$-0.751611\pi$
$61$		−	10.9893i		−	1.40704i	0.710677	−	0.703519i	$-0.248389\pi$
$62$	4.69971	−	8.14013i	0.596863	−	1.03380i
$63$	−5.32183	+	5.88881i	−0.670488	+	0.741921i
$64$	−1.00000			−0.125000
$65$	7.25896	−	10.3559i	0.900363	−	1.28449i
$66$	0.714083	−	6.08936i	0.0878975	−	0.749549i
$67$	7.68334			0.938670			0.469335	−	0.883020i	$-0.344494\pi$
$67$	7.68334			0.938670			0.469335	+	0.883020i	$0.344494\pi$
$68$	−1.97842	−	3.42672i	−0.239918	−	0.415551i
$69$	−2.21217	−	0.259415i	−0.266314	−	0.0312299i
$70$	7.93181	−	4.81731i	0.948032	−	0.575779i
$71$	−8.18290	+	4.72440i	−0.971132	+	0.560683i	−0.899581	−	0.436754i	$-0.856128\pi$
$71$	−8.18290	+	4.72440i	−0.971132	+	0.560683i	−0.0715506	+	0.997437i	$0.522795\pi$
$72$	−2.87462	+	0.858232i	−0.338777	+	0.101144i
$73$	3.73438	−	2.15605i	0.437076	−	0.252346i	−0.265280	−	0.964171i	$-0.585464\pi$
$73$	3.73438	−	2.15605i	0.437076	−	0.252346i	0.702357	+	0.711825i	$0.252131\pi$
$74$	9.15972	+	5.28837i	1.06480	+	0.614760i
$75$	−1.47321	+	12.5628i	−0.170112	+	1.45063i
$76$	5.76542	+	3.32866i	0.661338	+	0.381824i
$77$	8.00472	−	4.86159i	0.912222	−	0.554030i
$78$	−6.11487	−	1.26821i	−0.692373	−	0.143596i
$79$	−2.63559	+	4.56498i	−0.296527	+	0.513601i	−0.975339	−	0.220712i	$-0.929162\pi$
$79$	−2.63559	+	4.56498i	−0.296527	+	0.513601i	0.678812	+	0.734312i	$0.262495\pi$
$80$	3.50754			0.392155
$81$	−7.52687	+	4.93418i	−0.836319	+	0.548243i
$82$		−	5.68441i		−	0.627738i
$83$	2.03056			0.222882			0.111441	−	0.993771i	$-0.464453\pi$
$83$	2.03056			0.222882			0.111441	+	0.993771i	$0.464453\pi$
$84$	−3.73463	−	2.65567i	−0.407481	−	0.289757i
$85$	6.93939	+	12.0194i	0.752682	+	1.30368i
$86$	4.83734	+	2.79284i	0.521624	+	0.301160i
$87$	4.52024	+	10.4900i	0.484621	+	1.12465i
$88$	3.53979			0.377343
$89$	−0.177296	−	0.307085i	−0.0187933	−	0.0325509i	0.856476	−	0.516187i	$-0.172649\pi$
$89$	−0.177296	−	0.307085i	−0.0187933	−	0.0325509i	−0.875269	+	0.483636i	$0.839316\pi$
$90$	10.0829	−	3.01029i	1.06283	−	0.317312i
$91$	−4.21820	−	8.55610i	−0.442187	−	0.896923i
$92$		−	1.28595i		−	0.134069i
$93$	16.1695	+	1.89615i	1.67670	+	0.196621i
$94$		−	0.116535i		−	0.0120196i
$95$	−20.2224	−	11.6754i	−2.07478	−	1.19787i
$96$	−0.685428	−	1.59066i	−0.0699562	−	0.162346i
$97$	−0.507481	+	0.292994i	−0.0515269	+	0.0297491i	−0.525542	−	0.850768i	$-0.676137\pi$
$97$	−0.507481	+	0.292994i	−0.0515269	+	0.0297491i	0.474015	+	0.880517i	$0.342804\pi$
$98$	−0.310710	−	6.99310i	−0.0313865	−	0.706410i
$99$	10.1755	−	3.03796i	1.02268	−	0.305326i
$100$	−7.30286			−0.730286
$101$	3.92396			0.390449			0.195224	−	0.980759i	$-0.437457\pi$
$101$	3.92396			0.390449			0.195224	+	0.980759i	$0.437457\pi$
$102$	4.09467	−	5.49575i	0.405433	−	0.544161i
$103$	−10.0847	−	5.82239i	−0.993673	−	0.573698i	−0.0873031	−	0.996182i	$-0.527825\pi$
$103$	−10.0847	−	5.82239i	−0.993673	−	0.573698i	−0.906370	+	0.422484i	$0.861158\pi$
$104$	0.316032	−	3.59167i	0.0309895	−	0.352193i
$105$	13.0994	+	9.31486i	1.27837	+	0.909038i
$106$	3.87351	−	6.70912i	0.376229	−	0.651647i
$107$	−6.26058	+	3.61455i	−0.605233	+	0.349432i	−0.771098	−	0.636717i	$-0.780292\pi$
$107$	−6.26058	+	3.61455i	−0.605233	+	0.349432i	0.165864	+	0.986149i	$0.446959\pi$
$108$	−3.33550	−	3.98428i	−0.320958	−	0.383387i
$109$	2.42081	+	4.19296i	0.231871	+	0.401613i	0.958359	−	0.285567i	$-0.0921818\pi$
$109$	2.42081	+	4.19296i	0.231871	+	0.401613i	−0.726487	+	0.687180i	$0.758848\pi$
$110$	−12.4160			−1.18381
$111$	−2.13365	+	18.1948i	−0.202517	+	1.72697i
$112$	1.27169	−	2.32009i	0.120163	−	0.219228i
$113$	17.4151	−	10.0546i	1.63828	−	0.945859i	0.656848	−	0.754023i	$-0.271889\pi$
$113$	17.4151	−	10.0546i	1.63828	−	0.945859i	0.981427	−	0.191836i	$-0.0614442\pi$
$114$	−1.34299	+	11.4524i	−0.125782	+	1.07261i
$115$			4.51052i			0.420608i
$116$	−5.71124	+	3.29739i	−0.530276	+	0.306155i
$117$	−2.17402	−	10.5959i	−0.200988	−	0.979594i
$118$			5.68243i			0.523110i
$119$	10.4662	−	0.232397i	0.959437	−	0.0213038i
$120$	2.40417	+	5.57930i	0.219470	+	0.509318i
$121$	−1.53009			−0.139099
$122$	5.49466	+	9.51703i	0.497463	+	0.861631i
$123$	9.04194	−	3.89625i	0.815284	−	0.351313i
$124$			9.39941i			0.844092i
$125$	8.07739			0.722464
$126$	1.66444	−	7.76078i	0.148280	−	0.691385i
$127$	1.68665	−	2.92136i	0.149666	−	0.259228i	−0.781438	−	0.623983i	$-0.785514\pi$
$127$	1.68665	−	2.92136i	0.149666	−	0.259228i	0.931104	+	0.364754i	$0.118847\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−1.12680	+	9.60884i	−0.0992094	+	0.846011i
$130$	−1.10850	+	12.5980i	−0.0972215	+	1.10491i
$131$	−3.63596	+	6.29766i	−0.317675	+	0.550229i	−0.980002	−	0.198985i	$-0.936235\pi$
$131$	−3.63596	+	6.29766i	−0.317675	+	0.550229i	0.662328	+	0.749214i	$0.269569\pi$
$132$	2.42627	+	5.63059i	0.211180	+	0.490080i
$133$	−15.0546	+	9.14327i	−1.30540	+	0.792822i
$134$	−6.65397	+	3.84167i	−0.574815	+	0.331870i
$135$	11.6994	+	13.9750i	1.00692	+	1.20278i
$136$	3.42672	+	1.97842i	0.293839	+	0.169648i
$137$	−6.43264	−	3.71389i	−0.549578	−	0.317299i	0.199374	−	0.979923i	$-0.436109\pi$
$137$	−6.43264	−	3.71389i	−0.549578	−	0.317299i	−0.748952	+	0.662625i	$0.769443\pi$
$138$	2.04550	−	0.881424i	0.174125	−	0.0750318i
$139$	−3.55436	+	2.05211i	−0.301477	+	0.174058i	−0.643106	−	0.765777i	$-0.722355\pi$
$139$	−3.55436	+	2.05211i	−0.301477	+	0.174058i	0.341629	+	0.939835i	$0.389021\pi$
$140$	−4.46049	+	8.13782i	−0.376980	+	0.687771i
$141$	0.185366	−	0.0798760i	0.0156107	−	0.00672677i
$142$	4.72440	−	8.18290i	0.396463	−	0.686694i
$143$	−1.11868	+	12.7138i	−0.0935491	+	1.06318i
$144$	2.06038	−	2.18056i	0.171698	−	0.181713i
$145$	20.0324	−	11.5657i	1.66360	−	0.960482i
$146$	−2.15605	+	3.73438i	−0.178436	+	0.309060i
$147$	10.9107	−	5.28750i	0.899896	−	0.436106i
$148$	−10.5767			−0.869402
$149$		−	2.55296i		−	0.209147i	−0.994517	−	0.104573i	$-0.966652\pi$
$149$		−	2.55296i		−	0.209147i	0.994517	−	0.104573i	$-0.0333477\pi$
$150$	−5.00559	−	11.6163i	−0.408704	−	0.948471i
$151$	4.89737	+	8.48249i	0.398542	+	0.690296i	0.993546	−	0.113427i	$-0.0361829\pi$
$151$	4.89737	+	8.48249i	0.398542	+	0.690296i	−0.595004	+	0.803723i	$0.702850\pi$
$152$	−6.65733			−0.539981
$153$	11.5485	+	2.74628i	0.933637	+	0.222023i
$154$	−4.50149	+	8.21262i	−0.362741	+	0.661792i
$155$		−	32.9689i		−	2.64812i
$156$	5.92974	−	1.95914i	0.474759	−	0.156856i
$157$	−11.3514	+	6.55373i	−0.905940	+	0.523045i	−0.879123	−	0.476596i	$-0.841871\pi$
$157$	−11.3514	+	6.55373i	−0.905940	+	0.523045i	−0.0268175	+	0.999640i	$0.508537\pi$
$158$		−	5.27119i		−	0.419353i
$159$	13.3269	+	1.56281i	1.05689	+	0.123939i
$160$	−3.03762	+	1.75377i	−0.240145	+	0.138648i
$161$	2.98351	+	1.63532i	0.235134	+	0.128881i
$162$	4.05137	−	8.03656i	0.318306	−	0.631412i
$163$	14.4366			1.13076			0.565380	−	0.824831i	$-0.308730\pi$
$163$	14.4366			1.13076			0.565380	+	0.824831i	$0.308730\pi$
$164$	2.84220	+	4.92284i	0.221939	+	0.384409i
$165$	−8.51024	−	19.7495i	−0.662521	−	1.53750i
$166$	−1.75851	+	1.01528i	−0.136487	+	0.0788009i
$167$	−8.84596	+	15.3217i	−0.684521	+	1.18563i	0.289066	+	0.957309i	$0.406655\pi$
$167$	−8.84596	+	15.3217i	−0.684521	+	1.18563i	−0.973587	+	0.228316i	$0.926678\pi$
$168$	4.56211	+	0.432561i	0.351975	+	0.0333728i
$169$	12.8002	+	2.27017i	0.984634	+	0.174628i
$170$	−12.0194	−	6.93939i	−0.921844	−	0.532227i
$171$	−19.1373	+	5.71353i	−1.46346	+	0.436925i
$172$	−5.58568			−0.425904
$173$	−5.71063			−0.434171			−0.217086	−	0.976153i	$-0.569655\pi$
$173$	−5.71063			−0.434171			−0.217086	+	0.976153i	$0.569655\pi$
$174$	−9.15966	−	6.82451i	−0.694392	−	0.517365i
$175$	9.28694	−	16.9433i	0.702027	−	1.28079i
$176$	−3.06555	+	1.76989i	−0.231074	+	0.133411i
$177$	−9.03879	+	3.89489i	−0.679397	+	0.292758i
$178$	0.307085	+	0.177296i	0.0230170	+	0.0132889i
$179$			15.3079i			1.14417i	0.820196	+	0.572083i	$0.193864\pi$
$179$			15.3079i			1.14417i	−0.820196	+	0.572083i	$0.806136\pi$
$180$	−7.22686	+	7.64841i	−0.538659	+	0.570079i
$181$			16.4841i			1.22525i	0.790373	+	0.612627i	$0.209887\pi$
$181$			16.4841i			1.22525i	−0.790373	+	0.612627i	$0.790113\pi$
$182$	7.93111	+	5.30070i	0.587893	+	0.392914i
$183$	−11.3721	+	15.2633i	−0.840652	+	1.12830i
$184$	0.642974	+	1.11366i	0.0474007	+	0.0821003i
$185$	37.0983			2.72752
$186$	−14.9512	+	6.44262i	−1.09628	+	0.472396i
$187$	−12.1299	−	7.00318i	−0.887023	−	0.512123i
$188$	0.0582673	+	0.100922i	0.00424958	+	0.00736048i
$189$	13.4856	−	2.67191i	0.980932	−	0.194353i
$190$	23.3509			1.69405
$191$			7.99466i			0.578473i	0.957258	+	0.289237i	$0.0934015\pi$
$191$			7.99466i			0.578473i	−0.957258	+	0.289237i	$0.906599\pi$
$192$	1.38893	+	1.03484i	0.100237	+	0.0746828i
$193$	−15.9681			−1.14941			−0.574703	−	0.818362i	$-0.694882\pi$
$193$	−15.9681			−1.14941			−0.574703	+	0.818362i	$0.694882\pi$
$194$	0.292994	−	0.507481i	0.0210358	−	0.0364350i
$195$	−20.7988	+	6.87175i	−1.48943	+	0.492096i
$196$	3.76563	+	5.90085i	0.268974	+	0.421489i
$197$	−23.1575	−	13.3700i	−1.64990	−	0.952571i	−0.977109	−	0.212741i	$-0.931761\pi$
$197$	−23.1575	−	13.3700i	−1.64990	−	0.952571i	−0.672794	−	0.739830i	$-0.734906\pi$
$198$	−7.29330	+	7.71872i	−0.518312	+	0.548546i
$199$	−1.88267	−	1.08696i	−0.133459	−	0.0770526i	0.431784	−	0.901977i	$-0.357884\pi$
$199$	−1.88267	−	1.08696i	−0.133459	−	0.0770526i	−0.565243	+	0.824924i	$0.691218\pi$
$200$	6.32446	−	3.65143i	0.447207	−	0.258195i
$201$	−10.6716	−	7.95099i	−0.752716	−	0.560820i
$202$	−3.39825	+	1.96198i	−0.239100	+	0.138044i
$203$	−0.387332	−	17.4438i	−0.0271854	−	1.22432i
$204$	−0.798214	+	6.80680i	−0.0558862	+	0.476571i
$205$	−9.96915	−	17.2671i	−0.696276	−	1.20598i
$206$	11.6448			0.811331
$207$	2.80409	+	2.64954i	0.194898	+	0.184156i
$208$	1.52215	+	3.26850i	0.105542	+	0.226629i
$209$	23.5655			1.63006
$210$	−16.0018	−	1.51722i	−1.10423	−	0.104698i
$211$	−2.63990	+	4.57244i	−0.181738	+	0.314779i	−0.942472	−	0.334284i	$-0.891506\pi$
$211$	−2.63990	+	4.57244i	−0.181738	+	0.314779i	0.760734	+	0.649063i	$0.224839\pi$
$212$			7.74702i			0.532068i
$213$	16.2544	+	1.90611i	1.11373	+	0.130605i
$214$	3.61455	−	6.26058i	0.247085	−	0.427964i
$215$	19.5920			1.33616
$216$	4.88076	+	1.78274i	0.332094	+	0.121300i
$217$	−21.8075	−	11.9531i	−1.48039	−	0.811429i
$218$	−4.19296	−	2.42081i	−0.283983	−	0.163958i
$219$	−7.41793	−	0.869880i	−0.501258	−	0.0587811i
$220$	10.7525	−	6.20798i	0.724936	−	0.418542i
$221$	−8.18878	+	11.6824i	−0.550837	+	0.785844i
$222$	−7.24959	−	16.8239i	−0.486560	−	1.12915i
$223$	9.21057	+	5.31772i	0.616785	+	0.356101i	0.775616	−	0.631205i	$-0.217439\pi$
$223$	9.21057	+	5.31772i	0.616785	+	0.356101i	−0.158831	+	0.987306i	$0.550773\pi$
$224$	0.0587331	+	2.64510i	0.00392427	+	0.176733i
$225$	15.0467	−	15.9243i	1.00311	−	1.06162i
$226$	−10.0546	+	17.4151i	−0.668823	+	1.15844i
$227$	0.975509	−	1.68963i	0.0647468	−	0.112145i	−0.831835	−	0.555023i	$-0.812709\pi$
$227$	0.975509	−	1.68963i	0.0647468	−	0.112145i	0.896582	+	0.442878i	$0.146043\pi$
$228$	−4.56312	−	10.5895i	−0.302200	−	0.701308i
$229$	−10.1017	−	5.83221i	−0.667538	−	0.385403i	0.127605	−	0.991825i	$-0.459271\pi$
$229$	−10.1017	−	5.83221i	−0.667538	−	0.385403i	−0.795143	+	0.606422i	$0.792604\pi$
$230$	−2.25526	−	3.90622i	−0.148707	−	0.257569i
$231$	−16.1489	−	1.53117i	−1.06252	−	0.100744i
$232$	3.29739	−	5.71124i	0.216484	−	0.374962i
$233$	11.6531	+	6.72790i	0.763418	+	0.440759i	0.830521	−	0.556987i	$-0.188043\pi$
$233$	11.6531	+	6.72790i	0.763418	+	0.440759i	−0.0671038	+	0.997746i	$0.521376\pi$
$234$	7.18072	+	8.08933i	0.469418	+	0.528816i
$235$	−0.204375	−	0.353988i	−0.0133320	−	0.0230916i
$236$	−2.84121	−	4.92113i	−0.184947	−	0.320338i
$237$	8.38465	−	3.61302i	0.544641	−	0.234691i
$238$	−8.94782	+	5.43437i	−0.580001	+	0.352258i
$239$			4.27464i			0.276504i	0.990397	+	0.138252i	$0.0441483\pi$
$239$			4.27464i			0.276504i	−0.990397	+	0.138252i	$0.955852\pi$
$240$	−4.87172	−	3.62973i	−0.314468	−	0.234298i
$241$	−12.5372	−	7.23838i	−0.807595	−	0.466265i	0.0385251	−	0.999258i	$-0.487734\pi$
$241$	−12.5372	−	7.23838i	−0.807595	−	0.466265i	−0.846120	+	0.532993i	$0.821067\pi$
$242$	1.32510	−	0.765044i	0.0851804	−	0.0491789i
$243$	15.5603	+	0.935859i	0.998196	+	0.0600354i
$244$	−9.51703	−	5.49466i	−0.609265	−	0.351759i
$245$	−13.2081	−	20.6975i	−0.843836	−	1.32231i
$246$	−5.88242	+	7.89522i	−0.375050	+	0.503381i
$247$	2.10393	−	23.9110i	0.133870	−	1.52142i
$248$	−4.69971	−	8.14013i	−0.298432	−	0.516899i
$249$	−2.82029	−	2.10129i	−0.178729	−	0.133164i
$250$	−6.99523	+	4.03870i	−0.442417	+	0.255430i
$251$	−0.147269	−	0.255078i	−0.00929556	−	0.0161004i	0.861340	−	0.508029i	$-0.169626\pi$
$251$	−0.147269	−	0.255078i	−0.00929556	−	0.0161004i	−0.870636	+	0.491928i	$0.836292\pi$
$252$	2.43895	+	7.55325i	0.153639	+	0.475810i
$253$	−2.27599	−	3.94213i	−0.143090	−	0.247840i
$254$			3.37329i			0.211659i
$255$	2.79977	−	23.8751i	0.175328	−	1.49512i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	5.59938	+	9.69842i	0.349280	+	0.604971i	0.986122	−	0.166024i	$-0.0530929\pi$
$257$	5.59938	+	9.69842i	0.349280	+	0.604971i	−0.636842	+	0.770995i	$0.719760\pi$
$258$	−3.82858	−	8.88490i	−0.238357	−	0.553150i
$259$	13.4503	−	24.5390i	0.835759	−	1.52478i
$260$	−5.33899	−	11.4644i	−0.331110	−	0.710992i
$261$	4.57716	−	19.2476i	0.283319	−	1.19140i
$262$		−	7.27191i		−	0.449260i
$263$			4.16185i			0.256631i	0.991733	+	0.128315i	$0.0409570\pi$
$263$			4.16185i			0.256631i	−0.991733	+	0.128315i	$0.959043\pi$
$264$	−4.91650	−	3.66310i	−0.302590	−	0.225448i
$265$		−	27.1730i		−	1.66923i
$266$	8.46603	−	15.4456i	0.519085	−	0.947030i
$267$	−0.0715318	+	0.609990i	−0.00437768	+	0.0373308i
$268$	3.84167	−	6.65397i	0.234667	−	0.406456i
$269$	−12.1358	+	21.0198i	−0.739930	+	1.28160i	0.212596	+	0.977140i	$0.431808\pi$
$269$	−12.1358	+	21.0198i	−0.739930	+	1.28160i	−0.952526	+	0.304457i	$0.901525\pi$
$270$	−17.1195	−	6.25302i	−1.04186	−	0.380547i
$271$	10.7289	−	6.19435i	0.651736	−	0.376280i	−0.137385	−	0.990518i	$-0.543870\pi$
$271$	10.7289	−	6.19435i	0.651736	−	0.376280i	0.789121	+	0.614238i	$0.210536\pi$
$272$	−3.95683			−0.239918
$273$	−2.99539	+	16.2489i	−0.181289	+	0.983430i
$274$	7.42778			0.448728
$275$	−22.3873	+	12.9253i	−1.35000	+	0.779424i
$276$	−1.33074	+	1.78609i	−0.0801014	+	0.107510i
$277$	5.14794	−	8.91649i	0.309310	−	0.535740i	−0.668902	−	0.743351i	$-0.733235\pi$
$277$	5.14794	−	8.91649i	0.309310	−	0.535740i	0.978212	+	0.207611i	$0.0665688\pi$
$278$	2.05211	−	3.55436i	0.123077	−	0.213176i
$279$	−20.4960	−	19.3663i	−1.22706	−	1.15943i
$280$	−0.206009	−	9.27780i	−0.0123114	−	0.554455i
$281$		−	6.21604i		−	0.370818i	−0.982661	−	0.185409i	$-0.940639\pi$
$281$		−	6.21604i		−	0.370818i	0.982661	−	0.185409i	$-0.0593610\pi$
$282$	−0.120594	+	0.161858i	−0.00718127	+	0.00963850i
$283$			13.4407i			0.798967i	0.916740	+	0.399484i	$0.130811\pi$
$283$			13.4407i			0.798967i	−0.916740	+	0.399484i	$0.869189\pi$
$284$			9.44880i			0.560683i
$285$	16.0053	+	37.1432i	0.948074	+	2.20017i
$286$	−5.38807	−	11.5698i	−0.318603	−	0.684136i
$287$	−15.0358	+	0.333863i	−0.887536	+	0.0197073i
$288$	−0.694059	+	2.91861i	−0.0408978	+	0.171981i
$289$	0.671728	+	1.16347i	0.0395134	+	0.0684393i
$290$	−11.5657	+	20.0324i	−0.679163	+	1.17635i
$291$	1.00805	+	0.118212i	0.0590932	+	0.00692969i
$292$		−	4.31209i		−	0.252346i
$293$	6.36341	+	11.0218i	0.371755	+	0.643898i	0.989836	−	0.142217i	$-0.0454230\pi$
$293$	6.36341	+	11.0218i	0.371755	+	0.643898i	−0.618081	+	0.786114i	$0.712090\pi$
$294$	−6.80515	+	10.0344i	−0.396885	+	0.585220i
$295$	9.96568	+	17.2611i	0.580224	+	1.00498i
$296$	9.15972	−	5.28837i	0.532398	−	0.307380i
$297$	−17.2769	−	6.31050i	−1.00251	−	0.366173i
$298$	1.27648	+	2.21093i	0.0739445	+	0.128076i
$299$	−4.20312	+	1.95740i	−0.243072	+	0.113199i
$300$	10.1431	+	7.55726i	0.585614	+	0.436319i
$301$	7.10323	−	12.9593i	0.409423	−	0.746961i
$302$	−8.48249	−	4.89737i	−0.488113	−	0.281812i
$303$	−5.45009	−	4.06065i	−0.313100	−	0.233278i
$304$	5.76542	−	3.32866i	0.330669	−	0.190912i
$305$	33.3814	+	19.2728i	1.91141	+	1.10355i
$306$	−11.3744	+	3.39588i	−0.650231	+	0.194130i
$307$			25.8938i			1.47784i	0.673796	+	0.738918i	$0.264663\pi$
$307$			25.8938i			1.47784i	−0.673796	+	0.738918i	$0.735337\pi$
$308$	−0.207903	−	9.36309i	−0.0118464	−	0.533511i
$309$	7.98166	+	18.5229i	0.454061	+	1.05373i
$310$	16.4844	+	28.5519i	0.936253	+	1.62164i
$311$	−2.45036	−	4.24415i	−0.138947	−	0.240664i	0.788151	−	0.615482i	$-0.211038\pi$
$311$	−2.45036	−	4.24415i	−0.138947	−	0.240664i	−0.927098	+	0.374818i	$0.877705\pi$
$312$	−4.15574	+	4.66153i	−0.235272	+	0.263907i
$313$	−18.2027	−	10.5093i	−1.02888	−	0.594022i	−0.112213	−	0.993684i	$-0.535794\pi$
$313$	−18.2027	−	10.5093i	−1.02888	−	0.594022i	−0.916662	+	0.399663i	$0.869127\pi$
$314$	6.55373	−	11.3514i	0.369849	−	0.640596i
$315$	−8.55471	−	26.4933i	−0.482003	−	1.49273i
$316$	2.63559	+	4.56498i	0.148264	+	0.256800i
$317$	−12.9313	−	7.46591i	−0.726296	−	0.419327i	0.0907693	−	0.995872i	$-0.471067\pi$
$317$	−12.9313	−	7.46591i	−0.726296	−	0.419327i	−0.817066	+	0.576545i	$0.804401\pi$
$318$	−12.3229	+	5.31003i	−0.691031	+	0.297771i
$319$	−11.6721	+	20.2166i	−0.653509	+	1.13191i
$320$	1.75377	−	3.03762i	0.0980388	−	0.169808i
$321$	12.4359	+	1.45833i	0.694107	+	0.0813960i
$322$	−3.40146	+	0.0755278i	−0.189556	+	0.00420900i
$323$	22.8128	+	13.1710i	1.26934	+	0.732853i
$324$	0.509690	+	8.98556i	0.0283161	+	0.499198i
$325$	11.1160	+	23.8694i	0.616606	+	1.32404i
$326$	−12.5024	+	7.21828i	−0.692446	+	0.399784i
$327$	0.976701	−	8.32885i	0.0540117	−	0.460587i
$328$	−4.92284	−	2.84220i	−0.271818	−	0.156934i
$329$	−0.308245	+	0.00684444i	−0.0169941	+	0.000377346i
$330$	17.2448	+	12.8485i	0.949298	+	0.707285i
$331$	1.02485			0.0563309			0.0281655	−	0.999603i	$-0.491033\pi$
$331$	1.02485			0.0563309			0.0281655	+	0.999603i	$0.491033\pi$
$332$	1.01528	−	1.75851i	0.0557206	−	0.0965109i
$333$	21.7921	−	23.0632i	1.19420	−	1.26386i
$334$		−	17.6919i		−	0.968059i
$335$	−13.4748	+	23.3391i	−0.736208	+	1.27515i
$336$	−4.16719	+	1.90645i	−0.227339	+	0.104005i
$337$	20.0548			1.09245			0.546226	−	0.837638i	$-0.316064\pi$
$337$	20.0548			1.09245			0.546226	+	0.837638i	$0.316064\pi$
$338$	−12.2204	+	4.43410i	−0.664703	+	0.241183i
$339$	−34.5932	−	4.05664i	−1.87884	−	0.220327i
$340$	13.8788			0.752682
$341$	16.6360	+	28.8143i	0.900888	+	1.56038i
$342$	13.7166	−	14.5167i	0.741709	−	0.784974i
$343$	−18.4792	+	1.23259i	−0.997783	+	0.0665534i
$344$	4.83734	−	2.79284i	0.260812	−	0.150580i
$345$	4.66764	−	6.26478i	0.251297	−	0.337284i
$346$	4.94555	−	2.85532i	0.265875	−	0.153503i
$347$	21.6096	+	12.4763i	1.16006	+	0.669763i	0.951319	−	0.308208i	$-0.0997292\pi$
$347$	21.6096	+	12.4763i	1.16006	+	0.669763i	0.208744	+	0.977970i	$0.433063\pi$
$348$	11.3448	+	1.33037i	0.608143	+	0.0713152i
$349$	7.17962	+	4.14516i	0.384316	+	0.221885i	0.679695	−	0.733495i	$-0.262112\pi$
$349$	7.17962	+	4.14516i	0.384316	+	0.221885i	−0.295378	+	0.955380i	$0.595446\pi$
$350$	0.428920	+	19.3168i	0.0229267	+	1.03253i
$351$	−7.94548	+	16.9667i	−0.424099	+	0.905616i
$352$	1.76989	−	3.06555i	0.0943356	−	0.163394i
$353$	−34.6377			−1.84358			−0.921789	−	0.387691i	$-0.873273\pi$
$353$	−34.6377			−1.84358			−0.921789	+	0.387691i	$0.873273\pi$
$354$	5.88037	−	7.89247i	0.312538	−	0.419480i
$355$		−	33.1421i		−	1.75900i
$356$	−0.354591			−0.0187933
$357$	−14.7773	−	10.5080i	−0.782098	−	0.556144i
$358$	−7.65395	−	13.2570i	−0.404524	−	0.700656i
$359$	5.14944	+	2.97303i	0.271777	+	0.156910i	0.629695	−	0.776843i	$-0.283180\pi$
$359$	5.14944	+	2.97303i	0.271777	+	0.156910i	−0.357918	+	0.933753i	$0.616513\pi$
$360$	2.43444	−	10.2372i	0.128306	−	0.539545i
$361$	−25.3200			−1.33263
$362$	−8.24205	−	14.2756i	−0.433192	−	0.750311i
$363$	2.12518	+	1.58339i	0.111543	+	0.0831064i
$364$	−9.51890	−	0.624985i	−0.498926	−	0.0327581i
$365$			15.1249i			0.791671i
$366$	2.21688	−	18.9045i	0.115878	−	0.988155i
$367$		−	23.5380i		−	1.22867i	−0.789044	−	0.614336i	$-0.789424\pi$
$367$		−	23.5380i		−	1.22867i	0.789044	−	0.614336i	$-0.210576\pi$
$368$	−1.11366	−	0.642974i	−0.0580537	−	0.0335173i
$369$	−16.5906	−	3.94531i	−0.863670	−	0.205385i
$370$	−32.1281	+	18.5492i	−1.67026	+	0.964326i
$371$	−17.9738	−	9.85178i	−0.933153	−	0.511479i
$372$	9.72684	−	13.0551i	0.504313	−	0.676875i
$373$	1.51382			0.0783824			0.0391912	−	0.999232i	$-0.487522\pi$
$373$	1.51382			0.0783824			0.0391912	+	0.999232i	$0.487522\pi$
$374$	14.0064			0.724251
$375$	−11.2189	−	8.35877i	−0.579342	−	0.431645i
$376$	−0.100922	−	0.0582673i	−0.00520465	−	0.00300491i
$377$	19.4709	+	13.6481i	1.00280	+	0.702912i
$378$	−10.3429	+	9.05673i	−0.531982	+	0.465828i
$379$	−12.9429	+	22.4178i	−0.664832	+	1.15152i	0.314499	+	0.949258i	$0.398163\pi$
$379$	−12.9429	+	22.4178i	−0.664832	+	1.15152i	−0.979331	+	0.202265i	$0.935170\pi$
$380$	−20.2224	+	11.6754i	−1.03739	+	0.598937i
$381$	−5.36575	+	2.31215i	−0.274896	+	0.118455i
$382$	−3.99733	−	6.92358i	−0.204521	−	0.354241i
$383$	−9.62313			−0.491719			−0.245859	−	0.969306i	$-0.579070\pi$
$383$	−9.62313			−0.491719			−0.245859	+	0.969306i	$0.579070\pi$
$384$	−1.72026	−	0.201730i	−0.0877868	−	0.0102945i
$385$	0.729228	+	32.8414i	0.0371649	+	1.67375i
$386$	13.8287	−	7.98403i	0.703864	−	0.406376i
$387$	11.5086	−	12.1799i	0.585016	−	0.619140i
$388$			0.585988i			0.0297491i
$389$	−17.2937	+	9.98452i	−0.876825	+	0.506235i	−0.869610	−	0.493739i	$-0.835630\pi$
$389$	−17.2937	+	9.98452i	−0.876825	+	0.506235i	−0.00721490	+	0.999974i	$0.502297\pi$
$390$	14.5764	−	16.3505i	0.738106	−	0.827941i
$391$		−	5.08828i		−	0.257326i
$392$	−6.21156	−	3.22747i	−0.313731	−	0.163012i
$393$	11.5671	−	4.98437i	0.583484	−	0.251428i
$394$	26.7400			1.34714
$395$	−9.24446	−	16.0119i	−0.465139	−	0.805645i
$396$	2.45682	−	10.3313i	0.123460	−	0.519165i
$397$			15.0494i			0.755306i	0.925947	+	0.377653i	$0.123269\pi$
$397$			15.0494i			0.755306i	−0.925947	+	0.377653i	$0.876731\pi$
$398$	2.17392			0.108969
$399$	30.3715	+	2.87970i	1.52048	+	0.144165i
$400$	−3.65143	+	6.32446i	−0.182572	+	0.316223i
$401$	26.6844	−	15.4062i	1.33256	−	0.769351i	0.346865	−	0.937915i	$-0.387246\pi$
$401$	26.6844	−	15.4062i	1.33256	−	0.769351i	0.985691	+	0.168564i	$0.0539129\pi$
$402$	13.2174	+	1.54996i	0.659222	+	0.0773052i
$403$	30.7220	−	14.3073i	1.53037	−	0.712696i
$404$	1.96198	−	3.39825i	0.0976121	−	0.169069i
$405$	−1.78776	−	31.5172i	−0.0888346	−	1.56610i
$406$	9.05736	+	14.9131i	0.449509	+	0.740127i
$407$	−32.4234	+	18.7197i	−1.60717	+	0.927900i
$408$	−2.71212	−	6.29397i	−0.134270	−	0.311598i
$409$	2.86894	+	1.65638i	0.141860	+	0.0819028i	0.569250	−	0.822164i	$-0.307234\pi$
$409$	2.86894	+	1.65638i	0.141860	+	0.0819028i	−0.427390	+	0.904067i	$0.640567\pi$
$410$	17.2671	+	9.96915i	0.852760	+	0.492341i
$411$	5.09120	+	11.8150i	0.251131	+	0.582793i
$412$	−10.0847	+	5.82239i	−0.496837	+	0.286849i
$413$	15.0306	−	0.333747i	0.739607	−	0.0164226i
$414$	−3.75318	−	0.892523i	−0.184459	−	0.0438651i
$415$	−3.56113	+	6.16806i	−0.174809	+	0.302778i
$416$	−2.95247	−	2.06953i	−0.144757	−	0.101467i
$417$	7.06033	+	0.827946i	0.345746	+	0.0405447i
$418$	−20.4083	+	11.7828i	−0.998204	+	0.576314i
$419$	9.29999	−	16.1081i	0.454334	−	0.786930i	−0.544315	−	0.838881i	$-0.683210\pi$
$419$	9.29999	−	16.1081i	0.454334	−	0.786930i	0.998650	+	0.0519505i	$0.0165438\pi$
$420$	14.6166	−	6.68695i	0.713217	−	0.326290i
$421$	0.699811			0.0341067			0.0170534	−	0.999855i	$-0.494571\pi$
$421$	0.699811			0.0341067			0.0170534	+	0.999855i	$0.494571\pi$
$422$		−	5.27979i		−	0.257016i
$423$	−0.340119	−	0.0808818i	−0.0165371	−	0.00393261i
$424$	−3.87351	−	6.70912i	−0.188114	−	0.325824i
$425$	−28.8962			−1.40167
$426$	−15.0298	+	6.47647i	−0.728196	+	0.313786i
$427$	24.8508	−	15.0929i	1.20261	−	0.730396i
$428$			7.22910i			0.349432i
$429$	14.7104	−	16.5008i	0.710226	−	0.796667i
$430$	−16.9672	+	9.79601i	−0.818231	+	0.472406i
$431$			17.3613i			0.836264i	0.908386	+	0.418132i	$0.137315\pi$
$431$			17.3613i			0.836264i	−0.908386	+	0.418132i	$0.862685\pi$
$432$	−5.11823	+	0.896487i	−0.246251	+	0.0431323i
$433$	−23.7833	+	13.7313i	−1.14295	+	0.659884i	−0.947160	−	0.320761i	$-0.896061\pi$
$433$	−23.7833	+	13.7313i	−1.14295	+	0.659884i	−0.195793	+	0.980645i	$0.562728\pi$
$434$	24.8624	−	0.552057i	1.19343	−	0.0264996i
$435$	−39.7922	−	4.66632i	−1.90789	−	0.223733i
$436$	4.84162			0.231871
$437$	4.28049	+	7.41402i	0.204763	+	0.354661i
$438$	6.85906	−	2.95563i	0.327739	−	0.141225i
$439$	−10.4717	+	6.04586i	−0.499789	+	0.288553i	−0.728626	−	0.684911i	$-0.759841\pi$
$439$	−10.4717	+	6.04586i	−0.499789	+	0.288553i	0.228838	+	0.973465i	$0.426508\pi$
$440$	−6.20798	+	10.7525i	−0.295954	+	0.512607i
$441$	−20.6258	−	3.94678i	−0.982180	−	0.187942i
$442$	1.25049	−	14.2117i	0.0594795	−	0.675980i
$443$	8.19745	+	4.73280i	0.389473	+	0.224862i	0.681932	−	0.731416i	$-0.261140\pi$
$443$	8.19745	+	4.73280i	0.389473	+	0.224862i	−0.292459	+	0.956278i	$0.594473\pi$
$444$	14.6903	+	10.9452i	0.697171	+	0.519435i
$445$	1.24374			0.0589591
$446$	−10.6354			−0.503603
$447$	−2.64189	+	3.54587i	−0.124957	+	0.167714i
$448$	−1.37341	−	2.26136i	−0.0648877	−	0.106839i
$449$	−1.05989	+	0.611927i	−0.0500193	+	0.0288786i	−0.524801	−	0.851225i	$-0.675860\pi$
$449$	−1.05989	+	0.611927i	−0.0500193	+	0.0288786i	0.474782	+	0.880104i	$0.342527\pi$
$450$	−5.06862	+	21.3142i	−0.238937	+	1.00476i
$451$	17.4258	+	10.0608i	0.820549	+	0.473744i
$452$		−	20.1092i		−	0.945859i
$453$	1.97590	−	16.8495i	0.0928357	−	0.791660i
$454$			1.95102i			0.0915658i
$455$	33.3879	+	2.19216i	1.56525	+	0.102770i
$456$	9.24654	+	6.88924i	0.433009	+	0.322618i
$457$	−3.06846	−	5.31473i	−0.143536	−	0.248613i	0.785289	−	0.619129i	$-0.212514\pi$
$457$	−3.06846	−	5.31473i	−0.143536	−	0.248613i	−0.928826	+	0.370516i	$0.879181\pi$
$458$	11.6644			0.545042
$459$	−13.1980	−	15.7651i	−0.616030	−	0.735853i
$460$	3.90622	+	2.25526i	0.182129	+	0.105152i
$461$	−12.7435	−	22.0723i	−0.593523	−	1.02801i	−0.993754	−	0.111597i	$-0.964403\pi$
$461$	−12.7435	−	22.0723i	−0.593523	−	1.02801i	0.400231	−	0.916414i	$-0.368930\pi$
$462$	14.7510	−	6.74842i	0.686276	−	0.313965i
$463$	15.6848			0.728937			0.364468	−	0.931216i	$-0.381251\pi$
$463$	15.6848			0.728937			0.364468	+	0.931216i	$0.381251\pi$
$464$			6.59478i			0.306155i
$465$	−34.1173	+	45.7913i	−1.58215	+	2.12352i
$466$	−13.4558			−0.623328
$467$	13.1716	−	22.8139i	0.609508	−	1.05570i	−0.381813	−	0.924239i	$-0.624700\pi$
$467$	13.1716	−	22.8139i	0.609508	−	1.05570i	0.991322	−	0.131460i	$-0.0419664\pi$
$468$	−10.2634	−	3.41521i	−0.474424	−	0.157868i
$469$	10.5524	+	17.3748i	0.487265	+	0.802293i
$470$	0.353988	+	0.204375i	0.0163282	+	0.00942712i
$471$	22.5483	+	2.64417i	1.03897	+	0.121837i
$472$	4.92113	+	2.84121i	0.226513	+	0.130777i
$473$	−17.1232	+	9.88606i	−0.787324	+	0.454562i
$474$	−5.45481	+	7.32129i	−0.250548	+	0.336278i
$475$	42.1040	−	24.3088i	1.93187	−	1.11536i
$476$	5.03185	−	9.18021i	0.230634	−	0.420774i
$477$	−16.8929	−	15.9618i	−0.773471	−	0.730840i
$478$	−2.13732	−	3.70195i	−0.0977588	−	0.169323i
$479$	38.7622			1.77109			0.885545	−	0.464553i	$-0.153785\pi$
$479$	38.7622			1.77109			0.885545	+	0.464553i	$0.153785\pi$
$480$	6.03390	+	0.707578i	0.275408	+	0.0322964i
$481$	16.0993	+	34.5700i	0.734066	+	1.57626i
$482$	14.4768			0.659398
$483$	−2.45159	−	5.35879i	−0.111551	−	0.243833i
$484$	−0.765044	+	1.32510i	−0.0347747	+	0.0602316i
$485$		−	2.05538i		−	0.0933300i
$486$	−13.9436	+	6.96969i	−0.632494	+	0.316152i
$487$	9.97678	−	17.2803i	0.452091	−	0.783045i	−0.546425	−	0.837508i	$-0.684011\pi$
$487$	9.97678	−	17.2803i	0.452091	−	0.783045i	0.998516	+	0.0544634i	$0.0173448\pi$
$488$	10.9893			0.497463
$489$	−20.0513	−	14.9395i	−0.906752	−	0.675586i
$490$	21.7873	+	11.3205i	0.984250	+	0.511407i
$491$	−4.36750	−	2.52158i	−0.197103	−	0.113797i	0.398201	−	0.917298i	$-0.369635\pi$
$491$	−4.36750	−	2.52158i	−0.197103	−	0.113797i	−0.595303	+	0.803501i	$0.702968\pi$
$492$	1.14672	−	9.77867i	0.0516980	−	0.440857i
$493$	−22.5985	+	13.0472i	−1.01778	+	0.587617i
$494$	10.1334	+	21.7595i	0.455924	+	0.979004i
$495$	−8.61740	+	36.2373i	−0.387323	+	1.62875i
$496$	8.14013	+	4.69971i	0.365503	+	0.211023i
$497$	−21.9221	−	12.0159i	−0.983339	−	0.538987i
$498$	3.49309	+	0.409625i	0.156529	+	0.0183557i
$499$	−18.5321	+	32.0985i	−0.829609	+	1.43693i	0.0687359	+	0.997635i	$0.478103\pi$
$499$	−18.5321	+	32.0985i	−0.829609	+	1.43693i	−0.898345	+	0.439290i	$0.855230\pi$
$500$	4.03870	−	6.99523i	0.180616	−	0.312836i
$501$	28.1418	−	12.1265i	1.25728	−	0.541774i
$502$	0.255078	+	0.147269i	0.0113847	+	0.00657296i
$503$	−12.8063	−	22.1812i	−0.571005	−	0.989010i	−0.996463	−	0.0840317i	$-0.973220\pi$
$503$	−12.8063	−	22.1812i	−0.571005	−	0.989010i	0.425458	−	0.904978i	$-0.360113\pi$
$504$	−5.88881	−	5.32183i	−0.262309	−	0.237053i
$505$	−6.88173	+	11.9195i	−0.306233	+	0.530411i
$506$	3.94213	+	2.27599i	0.175249	+	0.101180i
$507$	−15.4294	−	16.3992i	−0.685242	−	0.728316i
$508$	−1.68665	−	2.92136i	−0.0748328	−	0.129614i
$509$	−4.97268	−	8.61293i	−0.220410	−	0.381762i	0.734522	−	0.678584i	$-0.237406\pi$
$509$	−4.97268	−	8.61293i	−0.220410	−	0.381762i	−0.954933	+	0.296823i	$0.904073\pi$
$510$	9.51290	+	22.0764i	0.421238	+	0.977558i
$511$	10.0044	+	5.48363i	0.442571	+	0.242581i
$512$		−	1.00000i		−	0.0441942i
$513$	32.4928	+	11.8683i	1.43459	+	0.523996i
$514$	−9.69842	−	5.59938i	−0.427779	−	0.246978i
$515$	35.3725	−	20.4223i	1.55870	−	0.899914i
$516$	7.75810	+	5.78026i	0.341531	+	0.254462i
$517$	0.357242	+	0.206254i	0.0157115	+	0.00907103i
$518$	0.621205	+	27.9765i	0.0272942	+	1.22922i
$519$	7.93165	+	5.90956i	0.348161	+	0.259401i
$520$	10.3559	+	7.25896i	0.454136	+	0.318327i
$521$	−7.83412	−	13.5691i	−0.343219	−	0.594473i	0.641810	−	0.766864i	$-0.278184\pi$
$521$	−7.83412	−	13.5691i	−0.343219	−	0.594473i	−0.985029	+	0.172391i	$0.944851\pi$
$522$	5.65985	+	18.9575i	0.247725	+	0.829746i
$523$	−32.1956	+	18.5881i	−1.40781	+	0.812802i	−0.995177	−	0.0980929i	$-0.968726\pi$
$523$	−32.1956	+	18.5881i	−1.40781	+	0.812802i	−0.412638	+	0.910895i	$0.635392\pi$
$524$	3.63596	+	6.29766i	0.158837	+	0.275115i
$525$	−30.4324	+	13.9225i	−1.32818	+	0.607629i
$526$	−2.08093	−	3.60427i	−0.0907327	−	0.157154i
$527$			37.1919i			1.62011i
$528$	6.08936	+	0.714083i	0.265006	+	0.0310765i
$529$	−10.6732	+	18.4865i	−0.464051	+	0.803760i
$530$	13.5865	+	23.5325i	0.590160	+	1.02219i
$531$	16.5848	+	3.94394i	0.719718	+	0.171152i
$532$	0.391006	+	17.6093i	0.0169523	+	0.763460i
$533$	11.7640	−	16.7830i	0.509557	−	0.726953i
$534$	−0.243047	−	0.564033i	−0.0105177	−	0.0244081i
$535$		−	25.3564i		−	1.09625i
$536$			7.68334i			0.331870i
$537$	15.8411	−	21.2615i	0.683596	−	0.917503i
$538$		−	24.2715i		−	1.04642i
$539$	21.9876	+	11.4245i	0.947073	+	0.492090i
$540$	17.9524	−	3.14447i	0.772549	−	0.135316i
$541$	2.98669	−	5.17310i	0.128408	−	0.222409i	−0.794652	−	0.607065i	$-0.792347\pi$
$541$	2.98669	−	5.17310i	0.128408	−	0.222409i	0.923060	+	0.384656i	$0.125680\pi$
$542$	−6.19435	+	10.7289i	−0.266070	+	0.460847i
$543$	17.0583	−	22.8952i	0.732043	−	0.982527i
$544$	3.42672	−	1.97842i	0.146919	−	0.0848240i
$545$	−16.9822			−0.727437
$546$	−5.53038	−	15.5697i	−0.236678	−	0.666321i
$547$	3.17249			0.135646			0.0678230	−	0.997697i	$-0.478395\pi$
$547$	3.17249			0.135646			0.0678230	+	0.997697i	$0.478395\pi$
$548$	−6.43264	+	3.71389i	−0.274789	+	0.158649i
$549$	31.5901	−	9.43139i	1.34823	−	0.402522i
$550$	12.9253	−	22.3873i	0.551136	−	0.954596i
$551$	21.9518	−	38.0216i	0.935178	−	1.61978i
$552$	0.259415	−	2.21217i	0.0110414	−	0.0941561i
$553$	−13.9428	+	0.309593i	−0.592909	+	0.0131652i
$554$			10.2959i			0.437430i
$555$	−51.5269	−	38.3907i	−2.18719	−	1.62959i
$556$			4.10422i			0.174058i
$557$		−	9.32521i		−	0.395122i	−0.980291	−	0.197561i	$-0.936698\pi$
$557$		−	9.32521i		−	0.395122i	0.980291	−	0.197561i	$-0.0633020\pi$
$558$	27.4332	+	6.52375i	1.16134	+	0.276172i
$559$	8.50222	+	18.2568i	0.359606	+	0.772180i
$560$	4.81731	+	7.93181i	0.203568	+	0.335180i
$561$	9.60034	+	22.2793i	0.405327	+	0.940633i
$562$	3.10802	+	5.38325i	0.131104	+	0.227079i
$563$	11.2254	−	19.4430i	0.473094	−	0.819423i	−0.526432	−	0.850217i	$-0.676470\pi$
$563$	11.2254	−	19.4430i	0.473094	−	0.819423i	0.999526	+	0.0307944i	$0.00980372\pi$
$564$	0.0235086	−	0.200470i	0.000989889	−	0.00844131i
$565$			70.5340i			2.96739i
$566$	−6.72035	−	11.6400i	−0.282478	−	0.489265i
$567$	−21.4955	−	10.2443i	−0.902725	−	0.430219i
$568$	−4.72440	−	8.18290i	−0.198231	−	0.343347i
$569$	20.5990	−	11.8928i	0.863554	−	0.498573i	−0.00164667	−	0.999999i	$-0.500524\pi$
$569$	20.5990	−	11.8928i	0.863554	−	0.498573i	0.865201	+	0.501425i	$0.167191\pi$
$570$	−32.4326	−	24.1643i	−1.35845	−	1.01213i
$571$	14.7275	+	25.5087i	0.616326	+	1.06751i	0.990150	+	0.140008i	$0.0447128\pi$
$571$	14.7275	+	25.5087i	0.616326	+	1.06751i	−0.373825	+	0.927499i	$0.621954\pi$
$572$	10.4511	+	7.32569i	0.436982	+	0.306302i
$573$	8.27316	−	11.1040i	0.345616	−	0.463876i
$574$	12.8545	−	7.80704i	0.536535	−	0.325860i
$575$	−8.13293	−	4.69555i	−0.339167	−	0.195818i
$576$	−0.858232	−	2.87462i	−0.0357597	−	0.119776i
$577$	26.6927	−	15.4110i	1.11123	−	0.641570i	0.172083	−	0.985082i	$-0.444950\pi$
$577$	26.6927	−	15.4110i	1.11123	−	0.641570i	0.939148	+	0.343513i	$0.111617\pi$
$578$	−1.16347	−	0.671728i	−0.0483939	−	0.0279402i
$579$	22.1784	+	16.5243i	0.921705	+	0.686727i
$580$		−	23.1315i		−	0.960482i
$581$	2.78879	+	4.59181i	0.115699	+	0.190500i
$582$	−0.932106	+	0.401653i	−0.0386371	+	0.0166490i
$583$	13.7114	+	23.7488i	0.567868	+	0.983577i
$584$	2.15605	+	3.73438i	0.0892178	+	0.154530i
$585$	35.9992	+	11.9790i	1.48838	+	0.495270i
$586$	−11.0218	−	6.36341i	−0.455304	−	0.262870i
$587$	8.17657	−	14.1622i	0.337483	−	0.584538i	−0.646476	−	0.762935i	$-0.723758\pi$
$587$	8.17657	−	14.1622i	0.337483	−	0.584538i	0.983959	+	0.178397i	$0.0570911\pi$
$588$	0.876218	−	12.0927i	0.0361346	−	0.498693i
$589$	−31.2875	−	54.1915i	−1.28918	−	2.23292i
$590$	−17.2611	−	9.96568i	−0.710627	−	0.410281i
$591$	18.3283	+	42.5341i	0.753926	+	1.74962i
$592$	−5.28837	+	9.15972i	−0.217350	+	0.376462i
$593$	−16.4539	+	28.4990i	−0.675681	+	1.17031i	0.300588	+	0.953754i	$0.402817\pi$
$593$	−16.4539	+	28.4990i	−0.675681	+	1.17031i	−0.976269	+	0.216560i	$0.930516\pi$
$594$	18.1175	−	3.17337i	0.743368	−	0.130205i
$595$	−17.6494	+	32.2000i	−0.723556	+	1.32007i
$596$	−2.21093	−	1.27648i	−0.0905631	−	0.0522866i
$597$	1.49007	+	3.45796i	0.0609844	+	0.141525i
$598$	2.66131	−	3.79672i	0.108829	−	0.155259i
$599$	6.08634	−	3.51395i	0.248681	−	0.143576i	−0.370479	−	0.928841i	$-0.620807\pi$
$599$	6.08634	−	3.51395i	0.248681	−	0.143576i	0.619160	+	0.785265i	$0.287473\pi$
$600$	−12.5628	−	1.47321i	−0.512876	−	0.0601435i
$601$	−5.83732	−	3.37018i	−0.238109	−	0.137473i	0.376198	−	0.926539i	$-0.377231\pi$
$601$	−5.83732	−	3.37018i	−0.238109	−	0.137473i	−0.614307	+	0.789067i	$0.710565\pi$
$602$	0.328065	+	14.7747i	0.0133709	+	0.602171i
$603$	6.59409	+	22.0867i	0.268532	+	0.899439i
$604$	9.79474			0.398542
$605$	2.68343	−	4.64783i	0.109097	−	0.188961i
$606$	6.75024	+	0.791582i	0.274210	+	0.0321558i
$607$		−	4.54393i		−	0.184432i	−0.995739	−	0.0922162i	$-0.970605\pi$
$607$		−	4.54393i		−	0.184432i	0.995739	−	0.0922162i	$-0.0293951\pi$
$608$	−3.32866	+	5.76542i	−0.134995	+	0.233818i
$609$	−17.5135	+	24.6290i	−0.709684	+	0.998019i
$610$	−38.5455			−1.56066
$611$	0.241172	−	0.344064i	0.00975676	−	0.0139193i
$612$	8.15257	−	8.62812i	0.329548	−	0.348771i
$613$	8.90889			0.359827			0.179913	−	0.983682i	$-0.442418\pi$
$613$	8.90889			0.359827			0.179913	+	0.983682i	$0.442418\pi$
$614$	−12.9469	−	22.4247i	−0.522494	−	0.904986i
$615$	−4.02216	+	34.2991i	−0.162189	+	1.38307i
$616$	4.86159	+	8.00472i	0.195879	+	0.322519i
$617$	−12.9991	+	7.50505i	−0.523325	+	0.302142i	−0.738294	−	0.674479i	$-0.764368\pi$
$617$	−12.9991	+	7.50505i	−0.523325	+	0.302142i	0.214969	+	0.976621i	$0.431035\pi$
$618$	−16.1738	−	12.0504i	−0.650604	−	0.484740i
$619$	−7.24862	+	4.18499i	−0.291347	+	0.168209i	−0.638549	−	0.769581i	$-0.720465\pi$
$619$	−7.24862	+	4.18499i	−0.291347	+	0.168209i	0.347202	+	0.937790i	$0.387132\pi$
$620$	−28.5519	−	16.4844i	−1.14667	−	0.662031i
$621$	−1.15284	−	6.58178i	−0.0462617	−	0.264118i
$622$	4.24415	+	2.45036i	0.170175	+	0.0982505i
$623$	0.450928	−	0.822683i	0.0180661	−	0.0329601i
$624$	1.26821	−	6.11487i	0.0507689	−	0.244791i
$625$	4.09126	−	7.08626i	0.163650	−	0.283450i
$626$	21.0186			0.840073
$627$	−32.7308	−	24.3864i	−1.30714	−	0.973900i
$628$			13.1075i			0.523045i
$629$	−41.8504			−1.66868
$630$	20.6553	+	18.6666i	0.822925	+	0.743693i
$631$	6.27126	+	10.8621i	0.249655	+	0.432415i	0.963430	−	0.267960i	$-0.0863494\pi$
$631$	6.27126	+	10.8621i	0.249655	+	0.432415i	−0.713775	+	0.700375i	$0.753016\pi$
$632$	−4.56498	−	2.63559i	−0.181585	−	0.104838i
$633$	8.39834	−	3.61892i	0.333804	−	0.143839i
$634$	14.9318			0.593019
$635$	5.91598	+	10.2468i	0.234769	+	0.406631i
$636$	8.01689	−	10.7600i	0.317890	−	0.426663i
$637$	13.5551	−	21.2899i	0.537071	−	0.843537i
$638$		−	23.3441i		−	0.924202i
$639$	−20.6037	−	19.4681i	−0.815069	−	0.770146i
$640$			3.50754i			0.138648i
$641$	−0.920157	−	0.531253i	−0.0363440	−	0.0209832i	0.481718	−	0.876326i	$-0.340013\pi$
$641$	−0.920157	−	0.531253i	−0.0363440	−	0.0209832i	−0.518062	+	0.855343i	$0.673346\pi$
$642$	−11.4990	+	4.95502i	−0.453830	+	0.195559i
$643$	−19.3910	+	11.1954i	−0.764708	+	0.441504i	−0.830983	−	0.556297i	$-0.812222\pi$
$643$	−19.3910	+	11.1954i	−0.764708	+	0.441504i	0.0662756	+	0.997801i	$0.478888\pi$
$644$	2.90799	−	1.76614i	0.114591	−	0.0695956i
$645$	−27.2119	−	20.2745i	−1.07147	−	0.798308i
$646$	−26.3419			−1.03641
$647$	8.38696			0.329725			0.164863	−	0.986317i	$-0.447282\pi$
$647$	8.38696			0.329725			0.164863	+	0.986317i	$0.447282\pi$
$648$	−4.93418	−	7.52687i	−0.193833	−	0.295684i
$649$	−17.4197	−	10.0573i	−0.683784	−	0.394783i
$650$	−21.5614	−	15.1135i	−0.845710	−	0.592800i
$651$	17.9195	+	39.1691i	0.702321	+	1.53516i
$652$	7.21828	−	12.5024i	0.282690	−	0.489633i
$653$	−4.17251	+	2.40900i	−0.163283	+	0.0942715i	−0.579415	−	0.815033i	$-0.696719\pi$
$653$	−4.17251	+	2.40900i	−0.163283	+	0.0942715i	0.416132	+	0.909304i	$0.363386\pi$
$654$	3.31858	+	7.70135i	0.129767	+	0.301147i
$655$	−12.7533	−	22.0893i	−0.498312	−	0.863101i
$656$	5.68441			0.221939
$657$	9.40278	+	8.88454i	0.366837	+	0.346619i
$658$	0.263526	−	0.160050i	0.0102733	−	0.00623941i
$659$	−35.0181	+	20.2177i	−1.36411	+	0.787570i	−0.990168	−	0.139881i	$-0.955328\pi$
$659$	−35.0181	+	20.2177i	−1.36411	+	0.787570i	−0.373943	+	0.927452i	$0.621995\pi$
$660$	−21.3587	−	2.50468i	−0.831387	−	0.0974944i
$661$		−	32.1486i		−	1.25044i	−0.780450	−	0.625219i	$-0.785010\pi$
$661$		−	32.1486i		−	1.25044i	0.780450	−	0.625219i	$-0.214990\pi$
$662$	−0.887547	+	0.512426i	−0.0344955	+	0.0199160i
$663$	23.4630	−	7.75198i	0.911227	−	0.301062i
$664$			2.03056i			0.0788009i
$665$	−1.37147	−	61.7654i	−0.0531833	−	2.39516i
$666$	−7.34087	+	30.8693i	−0.284453	+	1.19616i
$667$	−8.48054			−0.328368
$668$	8.84596	+	15.3217i	0.342261	+	0.592813i
$669$	−7.28983	−	16.9173i	−0.281841	−	0.654062i
$670$		−	26.9497i		−	1.04116i
$671$	−38.8998			−1.50171
$672$	2.65567	−	3.73463i	0.102445	−	0.144066i
$673$	−11.9937	+	20.7737i	−0.462323	+	0.800766i	−0.999076	−	0.0429727i	$-0.986317\pi$
$673$	−11.9937	+	20.7737i	−0.462323	+	0.800766i	0.536754	+	0.843739i	$0.319650\pi$
$674$	−17.3679	+	10.0274i	−0.668988	+	0.386240i
$675$	−37.3778	+	6.54692i	−1.43867	+	0.251991i
$676$	8.36615	−	9.95026i	0.321775	−	0.382702i
$677$	23.8364	−	41.2858i	0.916107	−	1.58674i	0.110835	−	0.993839i	$-0.464648\pi$
$677$	23.8364	−	41.2858i	0.916107	−	1.58674i	0.805272	−	0.592905i	$-0.202019\pi$
$678$	31.9869	−	13.7834i	1.22845	−	0.529349i
$679$	−1.35955	−	0.745193i	−0.0521746	−	0.0285979i
$680$	−12.0194	+	6.93939i	−0.460922	+	0.266113i
$681$	−3.10340	+	1.33728i	−0.118923	+	0.0512448i
$682$	−28.8143	−	16.6360i	−1.10336	−	0.637024i
$683$	−16.2285	−	9.36954i	−0.620967	−	0.358516i	0.156278	−	0.987713i	$-0.450050\pi$
$683$	−16.2285	−	9.36954i	−0.620967	−	0.358516i	−0.777246	+	0.629197i	$0.783384\pi$
$684$	−4.62058	+	19.4301i	−0.176672	+	0.742930i
$685$	22.5628	−	13.0266i	0.862079	−	0.497722i
$686$	15.3872	−	10.3070i	0.587485	−	0.393525i
$687$	7.99511	+	18.5541i	0.305033	+	0.707882i
$688$	−2.79284	+	4.83734i	−0.106476	+	0.184422i
$689$	25.3211	−	11.7921i	0.964658	−	0.449243i
$690$	−0.909909	+	7.75928i	−0.0346396	+	0.295391i
$691$	23.5469	−	13.5948i	0.895765	−	0.517170i	0.0199411	−	0.999801i	$-0.493652\pi$
$691$	23.5469	−	13.5948i	0.895765	−	0.517170i	0.875824	+	0.482631i	$0.160319\pi$
$692$	−2.85532	+	4.94555i	−0.108543	+	0.188002i
$693$	20.8451	+	18.8381i	0.791841	+	0.715602i
$694$	−24.9526			−0.947187
$695$		−	14.3957i		−	0.546061i
$696$	−10.4900	+	4.52024i	−0.397623	+	0.171339i
$697$	11.2461	+	19.4789i	0.425977	+	0.737815i
$698$	−8.29031			−0.313793
$699$	−9.22298	−	21.4036i	−0.348845	−	0.809557i
$700$	−10.0299	−	16.5144i	−0.379093	−	0.624185i
$701$		−	32.5254i		−	1.22847i	−0.789124	−	0.614233i	$-0.789465\pi$
$701$		−	32.5254i		−	1.22847i	0.789124	−	0.614233i	$-0.210535\pi$
$702$	−1.60237	−	18.6663i	−0.0604774	−	0.704516i
$703$	60.9792	−	35.2064i	2.29988	−	1.32783i
$704$			3.53979i			0.133411i
$705$	−0.0824573	+	0.703157i	−0.00310552	+	0.0264824i
$706$	29.9971	−	17.3189i	1.12896	−	0.651804i
$707$	5.38922	+	8.87347i	0.202683	+	0.333721i
$708$	−1.14632	+	9.77527i	−0.0430813	+	0.367377i
$709$	−22.9336			−0.861291			−0.430645	−	0.902521i	$-0.641714\pi$
$709$	−22.9336			−0.861291			−0.430645	+	0.902521i	$0.641714\pi$
$710$	16.5710	+	28.7019i	0.621900	+	1.07716i
$711$	−15.3845	−	3.65851i	−0.576965	−	0.137205i
$712$	0.307085	−	0.177296i	0.0115085	−	0.00664443i
$713$	−6.04358	+	10.4678i	−0.226334	+	0.392022i
$714$	18.0515	+	1.71157i	0.675562	+	0.0640539i
$715$	−36.6577	−	25.6952i	−1.37092	−	0.960945i
$716$	13.2570	+	7.65395i	0.495438	+	0.286041i
$717$	4.42355	−	5.93717i	0.165201	−	0.221727i
$718$	−5.94606			−0.221905
$719$	−0.733573			−0.0273577			−0.0136788	−	0.999906i	$-0.504354\pi$
$719$	−0.733573			−0.0273577			−0.0136788	+	0.999906i	$0.504354\pi$
$720$	3.01029	+	10.0829i	0.112187	+	0.375766i
$721$	−0.683935	−	30.8016i	−0.0254711	−	1.14711i
$722$	21.9278	−	12.6600i	0.816067	−	0.471157i
$723$	9.92278	+	23.0276i	0.369032	+	0.856404i
$724$	14.2756	+	8.24205i	0.530550	+	0.306313i
$725$			48.1608i			1.78865i
$726$	−2.63215	−	0.308665i	−0.0976884	−	0.0114556i
$727$		−	45.5164i		−	1.68811i	−0.536258	−	0.844054i	$-0.680163\pi$
$727$		−	45.5164i		−	1.68811i	0.536258	−	0.844054i	$-0.319837\pi$
$728$	8.55610	−	4.21820i	0.317110	−	0.156337i
$729$	−20.6437	−	17.4022i	−0.764582	−	0.644527i
$730$	−7.56243	−	13.0985i	−0.279898	−	0.484798i
$731$	−22.1016			−0.817458
$732$	7.53238	+	17.4802i	0.278405	+	0.646088i
$733$	22.4581	+	12.9662i	0.829508	+	0.478917i	0.853684	−	0.520791i	$-0.174363\pi$
$733$	22.4581	+	12.9662i	0.829508	+	0.478917i	−0.0241759	+	0.999708i	$0.507696\pi$
$734$	11.7690	+	20.3845i	0.434401	+	0.752405i
$735$	−3.07337	+	42.4155i	−0.113363	+	1.56452i
$736$	1.28595			0.0474007
$737$		−	27.1974i		−	1.00183i
$738$	16.3405	−	4.87854i	0.601502	−	0.179582i
$739$	−29.4441			−1.08312			−0.541559	−	0.840663i	$-0.682166\pi$
$739$	−29.4441			−1.08312			−0.541559	+	0.840663i	$0.682166\pi$
$740$	18.5492	−	32.1281i	0.681881	−	1.18105i
$741$	−27.6661	+	31.0333i	−1.01634	+	1.14004i
$742$	20.4916	−	0.455007i	0.752272	−	0.0167038i
$743$	23.1459	+	13.3633i	0.849140	+	0.490251i	0.860361	−	0.509686i	$-0.170238\pi$
$743$	23.1459	+	13.3633i	0.849140	+	0.490251i	−0.0112203	+	0.999937i	$0.503572\pi$
$744$	−1.89615	+	16.1695i	−0.0695161	+	0.592801i
$745$	7.75493	+	4.47731i	0.284118	+	0.164036i
$746$	−1.31100	+	0.756908i	−0.0479992	+	0.0277124i
$747$	1.74269	+	5.83708i	0.0637616	+	0.213567i
$748$	−12.1299	+	7.00318i	−0.443511	+	0.256061i
$749$	−16.7722	−	9.19313i	−0.612841	−	0.335910i
$750$	13.8952	+	1.62946i	0.507382	+	0.0594993i
$751$	−13.5765	−	23.5152i	−0.495413	−	0.858081i	0.504573	−	0.863369i	$-0.331650\pi$
$751$	−13.5765	−	23.5152i	−0.495413	−	0.858081i	−0.999986	+	0.00528812i	$0.998317\pi$
$752$	0.116535			0.00424958
$753$	−0.0594174	+	0.506684i	−0.00216529	+	0.0184646i
$754$	−23.6863	−	2.08416i	−0.862604	−	0.0759006i
$755$	−34.3555			−1.25032
$756$	4.42885	−	13.0148i	0.161076	−	0.473344i
$757$	9.16804	−	15.8795i	0.333218	−	0.577151i	−0.649923	−	0.760000i	$-0.725199\pi$
$757$	9.16804	−	15.8795i	0.333218	−	0.577151i	0.983141	+	0.182849i	$0.0585321\pi$
$758$		−	25.8858i		−	0.940214i
$759$	−0.918273	+	7.83060i	−0.0333312	+	0.284233i
$760$	11.6754	−	20.2224i	0.423513	−	0.733545i
$761$	−49.3861			−1.79024			−0.895122	−	0.445821i	$-0.852912\pi$
$761$	−49.3861			−1.79024			−0.895122	+	0.445821i	$0.852912\pi$
$762$	3.49080	−	4.68525i	0.126458	−	0.169729i
$763$	−6.15701	+	11.2330i	−0.222899	+	0.406661i
$764$	6.92358	+	3.99733i	0.250486	+	0.144618i
$765$	−28.5955	+	30.2635i	−1.03387	+	1.09418i
$766$	8.33387	−	4.81156i	0.301115	−	0.173849i
$767$	−11.7599	+	16.7772i	−0.424627	+	0.605788i
$768$	1.59066	−	0.685428i	0.0573979	−	0.0247332i
$769$	−0.485650	−	0.280390i	−0.0175130	−	0.0101111i	0.491218	−	0.871037i	$-0.336552\pi$
$769$	−0.485650	−	0.280390i	−0.0175130	−	0.0101111i	−0.508731	+	0.860926i	$0.669885\pi$
$770$	−17.0522	−	28.0769i	−0.614520	−	1.01182i
$771$	2.25913	−	19.2648i	0.0813607	−	0.693806i
$772$	−7.98403	+	13.8287i	−0.287351	+	0.497707i
$773$	−15.6030	+	27.0252i	−0.561202	+	0.972030i	0.436190	+	0.899855i	$0.356328\pi$
$773$	−15.6030	+	27.0252i	−0.561202	+	0.972030i	−0.997392	+	0.0721757i	$0.977006\pi$
$774$	−3.87679	+	16.3024i	−0.139348	+	0.585979i
$775$	59.4463	+	34.3213i	2.13537	+	1.23286i
$776$	−0.292994	−	0.507481i	−0.0105179	−	0.0182175i
$777$	−44.0752	+	20.1640i	−1.58119	+	0.723379i
$778$	9.98452	−	17.2937i	0.357962	−	0.620009i
$779$	−32.7730	−	18.9215i	−1.17421	−	0.677932i
$780$	−4.44829	+	21.4482i	−0.159274	+	0.767968i
$781$	16.7234	+	28.9657i	0.598409	+	1.03648i
$782$	2.54414	+	4.40658i	0.0909783	+	0.157579i
$783$	−26.2754	+	21.9969i	−0.939007	+	0.786104i
$784$	6.99310	−	0.310710i	0.249754	−	0.0110968i
$785$		−	45.9750i		−	1.64092i
$786$	−7.52523	+	10.1001i	−0.268416	+	0.360260i
$787$	5.10352	+	2.94652i	0.181921	+	0.105032i	0.588195	−	0.808719i	$-0.299839\pi$
$787$	5.10352	+	2.94652i	0.181921	+	0.105032i	−0.406274	+	0.913751i	$0.633172\pi$
$788$	−23.1575	+	13.3700i	−0.824951	+	0.476286i
$789$	4.30683	−	5.78051i	0.153327	−	0.205792i
$790$	16.0119	+	9.24446i	0.569677	+	0.328903i
$791$	46.6552	+	25.5726i	1.65887	+	0.909258i
$792$	3.03796	+	10.1755i	0.107949	+	0.361572i
$793$	−3.47297	+	39.4700i	−0.123329	+	1.40162i
$794$	−7.52468	−	13.0331i	−0.267041	−	0.462528i
$795$	−28.1196	+	37.7413i	−0.997299	+	1.33855i
$796$	−1.88267	+	1.08696i	−0.0667295	+	0.0385263i
$797$	24.1017	+	41.7453i	0.853724	+	1.47869i	0.877823	+	0.478984i	$0.158995\pi$
$797$	24.1017	+	41.7453i	0.853724	+	1.47869i	−0.0240989	+	0.999710i	$0.507672\pi$
$798$	−27.7423	+	12.6919i	−0.982068	+	0.449287i
$799$	0.230554	+	0.399331i	0.00815641	+	0.0141273i
$800$		−	7.30286i		−	0.258195i
$801$	0.730592	−	0.773208i	0.0258142	−	0.0273199i
$802$	−15.4062	+	26.6844i	−0.544014	+	0.942259i
$803$	−7.63194	−	13.2189i	−0.269325	−	0.466485i
$804$	−12.2216	+	5.26638i	−0.431021	+	0.185731i
$805$	−10.1999	+	6.19481i	−0.359499	+	0.218338i
$806$	−19.4524	+	27.7514i	−0.685180	+	0.977503i
$807$	38.6077	−	16.6364i	1.35905	−	0.585628i
$808$			3.92396i			0.138044i
$809$			1.43782i			0.0505510i	0.999681	+	0.0252755i	$0.00804630\pi$
$809$			1.43782i			0.0505510i	−0.999681	+	0.0252755i	$0.991954\pi$
$810$	17.3069	+	26.4008i	0.608101	+	0.927631i
$811$		−	25.7211i		−	0.903192i	−0.892223	−	0.451596i	$-0.850855\pi$
$811$		−	25.7211i		−	0.903192i	0.892223	−	0.451596i	$-0.149145\pi$
$812$	−15.3005	−	8.38648i	−0.536941	−	0.294308i
$813$	−21.3118	−	2.49918i	−0.747439	−	0.0876500i
$814$	18.7197	−	32.4234i	0.656125	−	1.13644i
$815$	−25.3184	+	43.8528i	−0.886867	+	1.53610i
$816$	5.49575	+	4.09467i	0.192390	+	0.143342i
$817$	32.2038	−	18.5929i	1.12667	−	0.650482i
$818$	−3.31277			−0.115828
$819$	20.9753	−	19.4688i	0.732938	−	0.680296i
$820$	−19.9383			−0.696276
$821$	−5.32395	+	3.07378i	−0.185807	+	0.107276i	−0.590018	−	0.807390i	$-0.700879\pi$
$821$	−5.32395	+	3.07378i	−0.185807	+	0.107276i	0.404211	+	0.914666i	$0.367546\pi$
$822$	−10.3166	−	7.68652i	−0.359834	−	0.268098i
$823$	−1.26766	+	2.19566i	−0.0441880	+	0.0765359i	−0.887274	−	0.461244i	$-0.847403\pi$
$823$	−1.26766	+	2.19566i	−0.0441880	+	0.0765359i	0.843085	+	0.537780i	$0.180737\pi$
$824$	5.82239	−	10.0847i	0.202833	−	0.351317i
$825$	44.4698	+	5.21485i	1.54824	+	0.181558i
$826$	−12.8500	+	7.80432i	−0.447108	+	0.271547i
$827$			19.0006i			0.660717i	0.943856	+	0.330359i	$0.107170\pi$
$827$			19.0006i			0.660717i	−0.943856	+	0.330359i	$0.892830\pi$
$828$	3.69661	−	1.10364i	0.128466	−	0.0383542i
$829$			16.9691i			0.589361i	0.955596	+	0.294681i	$0.0952132\pi$
$829$			16.9691i			0.589361i	−0.955596	+	0.294681i	$0.904787\pi$
$830$		−	7.12226i		−	0.247217i
$831$	−16.3772	+	7.05708i	−0.568119	+	0.244807i
$832$	3.59167	+	0.316032i	0.124519	+	0.0109564i
$833$	14.9000	+	23.3487i	0.516254	+	0.808984i
$834$	−6.52840	+	2.81314i	−0.226060	+	0.0974112i
$835$	−31.0276	−	53.7414i	−1.07375	−	1.85980i
$836$	11.7828	−	20.4083i	0.407515	−	0.705837i
$837$	8.42645	+	48.1084i	0.291261	+	1.66287i
$838$			18.6000i			0.642526i
$839$	−6.69259	−	11.5919i	−0.231054	−	0.400197i	0.727065	−	0.686569i	$-0.240884\pi$
$839$	−6.69259	−	11.5919i	−0.231054	−	0.400197i	−0.958119	+	0.286372i	$0.907551\pi$
$840$	−9.31486	+	13.0994i	−0.321393	+	0.451971i
$841$	7.24554	+	12.5496i	0.249846	+	0.432747i
$842$	−0.606054	+	0.349906i	−0.0208860	+	0.0120585i
$843$	−6.43258	+	8.63363i	−0.221550	+	0.297358i
$844$	2.63990	+	4.57244i	0.0908690	+	0.157390i
$845$	−29.3446	+	34.9010i	−1.00949	+	1.20063i
$846$	0.334992	−	0.100014i	0.0115173	−	0.00343854i
$847$	−2.10144	−	3.46008i	−0.0722065	−	0.118890i
$848$	6.70912	+	3.87351i	0.230392	+	0.133017i
$849$	13.9089	−	18.6682i	0.477353	−	0.640689i
$850$	25.0249	−	14.4481i	0.858346	−	0.495566i
$851$	−11.7789	−	6.80056i	−0.403776	−	0.233120i
$852$	9.77795	−	13.1237i	0.334987	−	0.449610i
$853$		−	9.31358i		−	0.318891i	−0.987207	−	0.159445i	$-0.949029\pi$
$853$		−	9.31358i		−	0.318891i	0.987207	−	0.159445i	$-0.0509706\pi$
$854$	−13.9750	+	25.4962i	−0.478213	+	0.872462i
$855$	16.2069	−	68.1521i	0.554263	−	2.33075i
$856$	−3.61455	−	6.26058i	−0.123543	−	0.213982i
$857$	−5.60469	−	9.70761i	−0.191453	−	0.331606i	0.754279	−	0.656554i	$-0.227986\pi$
$857$	−5.60469	−	9.70761i	−0.191453	−	0.331606i	−0.945732	+	0.324948i	$0.894653\pi$
$858$	−4.48918	+	21.6453i	−0.153258	+	0.738960i
$859$	−22.6022	−	13.0494i	−0.771177	−	0.445239i	0.0621172	−	0.998069i	$-0.480215\pi$
$859$	−22.6022	−	13.0494i	−0.771177	−	0.445239i	−0.833294	+	0.552830i	$0.813548\pi$
$860$	9.79601	−	16.9672i	0.334041	−	0.578576i
$861$	21.2291	+	15.0959i	0.723487	+	0.514466i
$862$	−8.68065	−	15.0353i	−0.295664	−	0.512105i
$863$	26.4923	+	15.2954i	0.901809	+	0.520660i	0.877787	−	0.479051i	$-0.159019\pi$
$863$	26.4923	+	15.2954i	0.901809	+	0.520660i	0.0240226	+	0.999711i	$0.492353\pi$
$864$	3.98428	−	3.33550i	0.135548	−	0.113476i
$865$	10.0151	−	17.3467i	0.340525	−	0.589807i
$866$	13.7313	−	23.7833i	0.466609	−	0.808190i
$867$	0.271016	−	2.31110i	0.00920419	−	0.0784890i
$868$	−21.2554	+	12.9093i	−0.721456	+	0.438170i
$869$	16.1591	+	9.32944i	0.548159	+	0.316479i
$870$	36.7942	−	15.8550i	1.24744	−	0.537533i
$871$	−27.5961	−	2.42818i	−0.935057	−	0.0822757i
$872$	−4.19296	+	2.42081i	−0.141992	+	0.0819789i
$873$	−1.27778	−	1.20736i	−0.0432464	−	0.0408628i
$874$	−7.41402	−	4.28049i	−0.250783	−	0.144790i
$875$	11.0936	+	18.2659i	0.375032	+	0.617499i
$876$	−4.46231	+	5.98918i	−0.150767	+	0.202356i
$877$	−6.91746			−0.233586			−0.116793	−	0.993156i	$-0.537261\pi$
$877$	−6.91746			−0.233586			−0.116793	+	0.993156i	$0.537261\pi$
$878$	6.04586	−	10.4717i	0.204038	−	0.353404i
$879$	2.56739	−	21.8935i	0.0865958	−	0.738449i
$880$		−	12.4160i		−	0.418542i
$881$	−4.74525	+	8.21901i	−0.159871	+	0.276905i	−0.934822	−	0.355116i	$-0.884441\pi$
$881$	−4.74525	+	8.21901i	−0.159871	+	0.276905i	0.774951	+	0.632022i	$0.217775\pi$
$882$	19.8358	−	6.89488i	0.667908	−	0.232163i
$883$	21.2743			0.715938			0.357969	−	0.933733i	$-0.383469\pi$
$883$	21.2743			0.715938			0.357969	+	0.933733i	$0.383469\pi$
$884$	6.02288	+	12.9329i	0.202571	+	0.434981i
$885$	4.02076	−	34.2872i	0.135156	−	1.15255i
$886$	−9.46560			−0.318003
$887$	−11.8749	−	20.5679i	−0.398719	−	0.690601i	0.594849	−	0.803837i	$-0.297212\pi$
$887$	−11.8749	−	20.5679i	−0.398719	−	0.690601i	−0.993568	+	0.113236i	$0.963878\pi$
$888$	−18.1948	−	2.13365i	−0.610576	−	0.0716006i
$889$	8.92269	−	0.198124i	0.299257	−	0.00664487i
$890$	−1.07711	+	0.621872i	−0.0361049	+	0.0208452i
$891$	17.4660	+	26.6435i	0.585131	+	0.892592i
$892$	9.21057	−	5.31772i	0.308393	−	0.178051i
$893$	−0.671870	−	0.387904i	−0.0224833	−	0.0129807i
$894$	0.515010	−	4.39176i	0.0172245	−	0.146882i
$895$	−46.4996	−	26.8466i	−1.55431	−	0.897381i
$896$	2.32009	+	1.27169i	0.0775088	+	0.0424840i
$897$	7.86340	+	1.63085i	0.262551	+	0.0544525i
$898$	0.611927	−	1.05989i	0.0204203	−	0.0353690i
$899$	61.9870			2.06738
$900$	−6.26755	−	20.9930i	−0.208918	−	0.699765i
$901$			30.6537i			1.02122i
$902$	−20.1216			−0.669975
$903$	−23.2766	+	10.6488i	−0.774596	+	0.354370i
$904$	10.0546	+	17.4151i	0.334412	+	0.579218i
$905$	−50.0724	−	28.9093i	−1.66446	−	0.960979i
$906$	6.71359	+	15.5801i	0.223044	+	0.517613i
$907$	32.7231			1.08655			0.543276	−	0.839554i	$-0.317184\pi$
$907$	32.7231			1.08655			0.543276	+	0.839554i	$0.317184\pi$
$908$	−0.975509	−	1.68963i	−0.0323734	−	0.0560724i
$909$	3.36767	+	11.2799i	0.111699	+	0.374130i
$910$	−30.0109	+	14.7955i	−0.994851	+	0.490466i
$911$			48.1424i			1.59503i	0.603299	+	0.797515i	$0.293852\pi$
$911$			48.1424i			1.59503i	−0.603299	+	0.797515i	$0.706148\pi$
$912$	−11.4524	−	1.34299i	−0.379225	−	0.0444707i
$913$		−	7.18773i		−	0.237879i
$914$	5.31473	+	3.06846i	0.175796	+	0.101496i
$915$	−26.4202	−	61.3127i	−0.873424	−	2.02693i
$916$	−10.1017	+	5.83221i	−0.333769	+	0.192702i
$917$	−19.2349	+	0.427102i	−0.635193	+	0.0141042i
$918$	19.3124	+	7.05399i	0.637403	+	0.232816i
$919$	42.6158			1.40576			0.702882	−	0.711306i	$-0.251896\pi$
$919$	42.6158			1.40576			0.702882	+	0.711306i	$0.251896\pi$
$920$	−4.51052			−0.148707
$921$	26.7958	−	35.9645i	0.882951	−	1.18507i
$922$	22.0723	+	12.7435i	0.726914	+	0.419684i
$923$	30.8834	−	14.3824i	1.01654	−	0.473404i
$924$	−9.40049	+	13.2198i	−0.309253	+	0.434899i
$925$	−38.6202	+	66.8922i	−1.26982	+	2.19940i
$926$	−13.5835	+	7.84242i	−0.446381	+	0.257718i
$927$	8.08217	−	33.9866i	0.265453	−	1.11627i
$928$	−3.29739	−	5.71124i	−0.108242	−	0.187481i
$929$	44.1016			1.44693			0.723463	−	0.690363i	$-0.242549\pi$
$929$	44.1016			1.44693			0.723463	+	0.690363i	$0.242549\pi$
$930$	6.65082	−	56.7151i	0.218089	−	1.85976i
$931$	−41.3524	−	21.4863i	−1.35527	−	0.704185i
$932$	11.6531	−	6.72790i	0.381709	−	0.220380i
$933$	−0.988624	+	8.43053i	−0.0323661	+	0.276003i
$934$			26.3432i			0.861975i
$935$	42.5460	−	24.5639i	1.39140	−	0.803327i
$936$	10.5959	−	2.17402i	0.346339	−	0.0710601i
$937$		−	30.8284i		−	1.00712i	−0.863960	−	0.503560i	$-0.832023\pi$
$937$		−	30.8284i		−	1.00712i	0.863960	−	0.503560i	$-0.167977\pi$
$938$	−17.8260	−	9.77079i	−0.582041	−	0.319028i
$939$	14.4068	+	33.4334i	0.470147	+	1.09106i
$940$	−0.408750			−0.0133320
$941$	−8.81522	−	15.2684i	−0.287368	−	0.497736i	0.685813	−	0.727778i	$-0.259447\pi$
$941$	−8.81522	−	15.2684i	−0.287368	−	0.497736i	−0.973181	+	0.230042i	$0.926114\pi$
$942$	−20.8495	+	8.98422i	−0.679313	+	0.292722i
$943$			7.30985i			0.238041i
$944$	−5.68243			−0.184947
$945$	−15.5344	+	45.6500i	−0.505334	+	1.48500i
$946$	9.88606	−	17.1232i	0.321424	−	0.556722i
$947$	3.10131	−	1.79054i	0.100779	−	0.0581847i	−0.448763	−	0.893651i	$-0.648135\pi$
$947$	3.10131	−	1.79054i	0.100779	−	0.0581847i	0.549542	+	0.835466i	$0.314802\pi$
$948$	1.06336	−	9.06783i	0.0345363	−	0.294509i
$949$	−14.0941	+	6.56363i	−0.457513	+	0.213065i
$950$	−24.3088	+	42.1040i	−0.788681	+	1.36604i
$951$	10.2347	+	23.7514i	0.331883	+	0.770192i
$952$	0.232397	+	10.4662i	0.00753204	+	0.339212i
$953$	−37.1462	+	21.4464i	−1.20328	+	0.694716i	−0.961284	−	0.275560i	$-0.911137\pi$
$953$	−37.1462	+	21.4464i	−1.20328	+	0.694716i	−0.242000	+	0.970276i	$0.577803\pi$
$954$	22.6105	+	5.37689i	0.732043	+	0.174083i
$955$	−24.2848	−	14.0208i	−0.785836	−	0.453703i
$956$	3.70195	+	2.13732i	0.119730	+	0.0691259i
$957$	37.1325	−	16.0007i	1.20032	−	0.517229i
$958$	−33.5691	+	19.3811i	−1.08457	+	0.626175i
$959$	−0.436257	−	19.6472i	−0.0140875	−	0.634441i
$960$	−5.57930	+	2.40417i	−0.180071	+	0.0775942i
$961$	28.6745	−	49.6657i	0.924984	−	1.60212i
$962$	−31.2274	−	21.8888i	−1.00681	−	0.705725i
$963$	−15.7635	−	14.8947i	−0.507971	−	0.479974i
$964$	−12.5372	+	7.23838i	−0.403797	+	0.233133i
$965$	28.0043	−	48.5049i	0.901491	−	1.56143i
$966$	4.80253	+	3.41505i	0.154519	+	0.109877i
$967$	49.7801			1.60082			0.800411	−	0.599452i	$-0.204615\pi$
$967$	49.7801			1.60082			0.800411	+	0.599452i	$0.204615\pi$
$968$		−	1.53009i		−	0.0491789i
$969$	−18.0555	−	41.9010i	−0.580026	−	1.34605i
$970$	1.02769	+	1.78001i	0.0329971	+	0.0571527i
$971$	42.6716			1.36940			0.684698	−	0.728827i	$-0.259934\pi$
$971$	42.6716			1.36940			0.684698	+	0.728827i	$0.259934\pi$
$972$	8.59065	−	13.0077i	0.275545	−	0.417223i
$973$	−9.52215	−	5.21927i	−0.305266	−	0.167322i
$974$			19.9536i			0.639354i
$975$	9.26155	−	44.6561i	0.296607	−	1.43014i
$976$	−9.51703	+	5.49466i	−0.304633	+	0.175880i
$977$			17.2634i			0.552305i	0.961114	+	0.276152i	$0.0890594\pi$
$977$			17.2634i			0.552305i	−0.961114	+	0.276152i	$0.910941\pi$
$978$	24.8347	+	2.91230i	0.794126	+	0.0931249i
$979$	−1.08702	+	0.627589i	−0.0347412	+	0.0200578i
$980$	−24.5286	+	1.08983i	−0.783538	+	0.0348133i
$981$	−9.97556	+	10.5574i	−0.318495	+	0.337073i
$982$	5.04316			0.160934
$983$	−15.2048	−	26.3355i	−0.484957	−	0.839971i	0.514893	−	0.857254i	$-0.327832\pi$
$983$	−15.2048	−	26.3355i	−0.484957	−	0.839971i	−0.999851	+	0.0172834i	$0.994498\pi$
$984$	3.89625	+	9.04194i	0.124208	+	0.288246i
$985$	81.2259	−	46.8958i	2.58807	−	1.49422i
$986$	13.0472	−	22.5985i	0.415508	−	0.719681i
$987$	0.435213	+	0.309477i	0.0138530	+	0.00985075i
$988$	−19.6555	−	13.7775i	−0.625326	−	0.438322i
$989$	−6.22057	−	3.59145i	−0.197803	−	0.114201i
$990$	−10.6558	−	35.6911i	−0.338663	−	1.13434i
$991$	−7.53150			−0.239246			−0.119623	−	0.992819i	$-0.538169\pi$
$991$	−7.53150			−0.239246			−0.119623	+	0.992819i	$0.538169\pi$
$992$	−9.39941			−0.298432
$993$	−1.42344	−	1.06055i	−0.0451716	−	0.0336556i
$994$	24.9930	−	0.554958i	0.792730	−	0.0176022i
$995$	6.60355	−	3.81256i	0.209347	−	0.120866i
$996$	−3.22992	+	1.39180i	−0.102344	+	0.0441009i
$997$	13.7533	+	7.94047i	0.435572	+	0.251477i	0.701717	−	0.712455i	$-0.252417\pi$
$997$	13.7533	+	7.94047i	0.435572	+	0.251477i	−0.266146	+	0.963933i	$0.585750\pi$
$998$		−	37.0641i		−	1.17324i
$999$	−54.1342	+	9.48190i	−1.71273	+	0.299994i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.u.a.425.5	yes	76
3.2	odd	2	inner	546.2.u.a.425.34	yes	76
7.3	odd	6		546.2.bb.a.269.11	yes	76
13.3	even	3		546.2.bb.a.341.17	yes	76
21.17	even	6		546.2.bb.a.269.36	yes	76
39.29	odd	6		546.2.bb.a.341.30	yes	76
91.3	odd	6	inner	546.2.u.a.185.34	yes	76
273.185	even	6	inner	546.2.u.a.185.5	✓	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.u.a.185.5	✓	76	273.185	even	6	inner
546.2.u.a.185.34	yes	76	91.3	odd	6	inner
546.2.u.a.425.5	yes	76	1.1	even	1	trivial
546.2.u.a.425.34	yes	76	3.2	odd	2	inner
546.2.bb.a.269.11	yes	76	7.3	odd	6
546.2.bb.a.269.36	yes	76	21.17	even	6
546.2.bb.a.341.17	yes	76	13.3	even	3
546.2.bb.a.341.30	yes	76	39.29	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.u (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-1.38893 - 1.03484i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.75377 + 3.03762i) q^{5} +(1.72026 + 0.201730i) q^{6} +(1.37341 + 2.26136i) q^{7} +1.00000i q^{8} +(0.858232 + 2.87462i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-1.38893 - 1.03484i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.75377 + 3.03762i) q^{5} +(1.72026 + 0.201730i) q^{6} +(1.37341 + 2.26136i) q^{7} +1.00000i q^{8} +(0.858232 + 2.87462i) q^{9} -3.50754i q^{10} -3.53979i q^{11} +(-1.59066 + 0.685428i) q^{12} +(-3.59167 - 0.316032i) q^{13} +(-2.32009 - 1.27169i) q^{14} +(5.57930 - 2.40417i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.97842 - 3.42672i) q^{17} +(-2.18056 - 2.06038i) q^{18} +6.65733i q^{19} +(1.75377 + 3.03762i) q^{20} +(0.432561 - 4.56211i) q^{21} +(1.76989 + 3.06555i) q^{22} +(1.11366 - 0.642974i) q^{23} +(1.03484 - 1.38893i) q^{24} +(-3.65143 - 6.32446i) q^{25} +(3.26850 - 1.52215i) q^{26} +(1.78274 - 4.88076i) q^{27} +(2.64510 - 0.0587331i) q^{28} +(-5.71124 - 3.29739i) q^{29} +(-3.62973 + 4.87172i) q^{30} +(-8.14013 + 4.69971i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-3.66310 + 4.91650i) q^{33} +3.95683i q^{34} +(-9.27780 + 0.206009i) q^{35} +(2.91861 + 0.694059i) q^{36} +(-5.28837 - 9.15972i) q^{37} +(-3.32866 - 5.76542i) q^{38} +(4.66153 + 4.15574i) q^{39} +(-3.03762 - 1.75377i) q^{40} +(-2.84220 + 4.92284i) q^{41} +(1.90645 + 4.16719i) q^{42} +(-2.79284 - 4.83734i) q^{43} +(-3.06555 - 1.76989i) q^{44} +(-10.2372 - 2.43444i) q^{45} +(-0.642974 + 1.11366i) q^{46} +(-0.0582673 + 0.100922i) q^{47} +(-0.201730 + 1.72026i) q^{48} +(-3.22747 + 6.21156i) q^{49} +(6.32446 + 3.65143i) q^{50} +(-6.29397 + 2.71212i) q^{51} +(-2.06953 + 2.95247i) q^{52} +(-6.70912 + 3.87351i) q^{53} +(0.896487 + 5.11823i) q^{54} +(10.7525 + 6.20798i) q^{55} +(-2.26136 + 1.37341i) q^{56} +(6.88924 - 9.24654i) q^{57} +6.59478 q^{58} +(2.84121 - 4.92113i) q^{59} +(0.707578 - 6.03390i) q^{60} -10.9893i q^{61} +(4.69971 - 8.14013i) q^{62} +(-5.32183 + 5.88881i) q^{63} -1.00000 q^{64} +(7.25896 - 10.3559i) q^{65} +(0.714083 - 6.08936i) q^{66} +7.68334 q^{67} +(-1.97842 - 3.42672i) q^{68} +(-2.21217 - 0.259415i) q^{69} +(7.93181 - 4.81731i) q^{70} +(-8.18290 + 4.72440i) q^{71} +(-2.87462 + 0.858232i) q^{72} +(3.73438 - 2.15605i) q^{73} +(9.15972 + 5.28837i) q^{74} +(-1.47321 + 12.5628i) q^{75} +(5.76542 + 3.32866i) q^{76} +(8.00472 - 4.86159i) q^{77} +(-6.11487 - 1.26821i) q^{78} +(-2.63559 + 4.56498i) q^{79} +3.50754 q^{80} +(-7.52687 + 4.93418i) q^{81} -5.68441i q^{82} +2.03056 q^{83} +(-3.73463 - 2.65567i) q^{84} +(6.93939 + 12.0194i) q^{85} +(4.83734 + 2.79284i) q^{86} +(4.52024 + 10.4900i) q^{87} +3.53979 q^{88} +(-0.177296 - 0.307085i) q^{89} +(10.0829 - 3.01029i) q^{90} +(-4.21820 - 8.55610i) q^{91} -1.28595i q^{92} +(16.1695 + 1.89615i) q^{93} -0.116535i q^{94} +(-20.2224 - 11.6754i) q^{95} +(-0.685428 - 1.59066i) q^{96} +(-0.507481 + 0.292994i) q^{97} +(-0.310710 - 6.99310i) q^{98} +(10.1755 - 3.03796i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q + 38 q^{4} + 10 q^{7} - 8 q^{9}+O(q^{10}) \) 76 * q + 38 * q^4 + 10 * q^7 - 8 * q^9	\( 76 q + 38 q^{4} + 10 q^{7} - 8 q^{9} + 2 q^{13} + 12 q^{15} - 38 q^{16} - 8 q^{21} - 42 q^{25} + 20 q^{28} + 20 q^{30} + 12 q^{31} - 4 q^{36} - 6 q^{37} + 12 q^{39} + 8 q^{42} - 2 q^{43} - 4 q^{46} + 2 q^{49} + 10 q^{51} - 14 q^{52} + 18 q^{54} + 24 q^{55} + 8 q^{57} + 16 q^{58} - 12 q^{60} + 32 q^{63} - 76 q^{64} - 24 q^{66} + 96 q^{67} - 30 q^{69} - 54 q^{73} - 12 q^{75} + 18 q^{76} - 12 q^{78} - 60 q^{79} + 8 q^{81} + 8 q^{84} + 8 q^{85} - 24 q^{87} + 48 q^{91} + 16 q^{93} - 66 q^{97}+O(q^{100}) \) 76 * q + 38 * q^4 + 10 * q^7 - 8 * q^9 + 2 * q^13 + 12 * q^15 - 38 * q^16 - 8 * q^21 - 42 * q^25 + 20 * q^28 + 20 * q^30 + 12 * q^31 - 4 * q^36 - 6 * q^37 + 12 * q^39 + 8 * q^42 - 2 * q^43 - 4 * q^46 + 2 * q^49 + 10 * q^51 - 14 * q^52 + 18 * q^54 + 24 * q^55 + 8 * q^57 + 16 * q^58 - 12 * q^60 + 32 * q^63 - 76 * q^64 - 24 * q^66 + 96 * q^67 - 30 * q^69 - 54 * q^73 - 12 * q^75 + 18 * q^76 - 12 * q^78 - 60 * q^79 + 8 * q^81 + 8 * q^84 + 8 * q^85 - 24 * q^87 + 48 * q^91 + 16 * q^93 - 66 * q^97

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