LMFDB - Embedded newform 546.2.u.a.425.6

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			425.6
Character	$\chi$	$=$	546.425
Dual form			546.2.u.a.185.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(-1.18075 + 1.26722i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.386492 - 0.669424i) q^{5} +(0.388948 - 1.68782i) q^{6} +(0.662023 + 2.56159i) q^{7} +1.00000i q^{8} +(-0.211678 - 2.99252i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(-1.18075 + 1.26722i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.386492 - 0.669424i) q^{5} +(0.388948 - 1.68782i) q^{6} +(0.662023 + 2.56159i) q^{7} +1.00000i q^{8} +(-0.211678 - 2.99252i) q^{9} +0.772984i q^{10} +2.70245i q^{11} +(0.507069 + 1.65616i) q^{12} +(3.14302 - 1.76675i) q^{13} +(-1.85412 - 1.88739i) q^{14} +(0.391956 + 1.28019i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.32378 - 2.29285i) q^{17} +(1.67958 + 2.48576i) q^{18} +4.67151i q^{19} +(-0.386492 - 0.669424i) q^{20} +(-4.02777 - 2.18566i) q^{21} +(-1.35122 - 2.34039i) q^{22} +(-4.66390 + 2.69271i) q^{23} +(-1.26722 - 1.18075i) q^{24} +(2.20125 + 3.81267i) q^{25} +(-1.83856 + 3.10156i) q^{26} +(4.04211 + 3.26517i) q^{27} +(2.54941 + 0.707464i) q^{28} +(4.22905 + 2.44165i) q^{29} +(-0.979539 - 0.912698i) q^{30} +(-3.24180 + 1.87166i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-3.42459 - 3.19090i) q^{33} +2.64755i q^{34} +(1.97065 + 0.546859i) q^{35} +(-2.69744 - 1.31294i) q^{36} +(-2.28416 - 3.95628i) q^{37} +(-2.33575 - 4.04565i) q^{38} +(-1.47225 + 6.06898i) q^{39} +(0.669424 + 0.386492i) q^{40} +(-4.90014 + 8.48729i) q^{41} +(4.58098 - 0.121050i) q^{42} +(-5.66191 - 9.80672i) q^{43} +(2.34039 + 1.35122i) q^{44} +(-2.08508 - 1.01488i) q^{45} +(2.69271 - 4.66390i) q^{46} +(-2.63336 + 4.56112i) q^{47} +(1.68782 + 0.388948i) q^{48} +(-6.12345 + 3.39166i) q^{49} +(-3.81267 - 2.20125i) q^{50} +(1.34249 + 4.38478i) q^{51} +(0.0414579 - 3.60531i) q^{52} +(-3.16257 + 1.82591i) q^{53} +(-5.13316 - 0.806662i) q^{54} +(1.80908 + 1.04447i) q^{55} +(-2.56159 + 0.662023i) q^{56} +(-5.91981 - 5.51587i) q^{57} -4.88329 q^{58} +(-5.61242 + 9.72100i) q^{59} +(1.30465 + 0.300650i) q^{60} +13.0175i q^{61} +(1.87166 - 3.24180i) q^{62} +(7.52547 - 2.52335i) q^{63} -1.00000 q^{64} +(0.0320463 - 2.78685i) q^{65} +(4.56123 + 1.05111i) q^{66} -6.94137 q^{67} +(-1.32378 - 2.29285i) q^{68} +(2.09464 - 9.08958i) q^{69} +(-1.98007 + 0.511734i) q^{70} +(9.71163 - 5.60701i) q^{71} +(2.99252 - 0.211678i) q^{72} +(8.99614 - 5.19392i) q^{73} +(3.95628 + 2.28416i) q^{74} +(-7.43060 - 1.71234i) q^{75} +(4.04565 + 2.33575i) q^{76} +(-6.92255 + 1.78908i) q^{77} +(-1.75948 - 5.99201i) q^{78} +(5.14638 - 8.91380i) q^{79} -0.772984 q^{80} +(-8.91039 + 1.26690i) q^{81} -9.80028i q^{82} +16.3639 q^{83} +(-3.90672 + 2.39532i) q^{84} +(-1.02326 - 1.77234i) q^{85} +(9.80672 + 5.66191i) q^{86} +(-8.08753 + 2.47617i) q^{87} -2.70245 q^{88} +(5.17484 + 8.96309i) q^{89} +(2.31317 - 0.163624i) q^{90} +(6.60644 + 6.88149i) q^{91} +5.38541i q^{92} +(1.45595 - 6.31802i) q^{93} -5.26673i q^{94} +(3.12722 + 1.80550i) q^{95} +(-1.65616 + 0.507069i) q^{96} +(6.86925 - 3.96597i) q^{97} +(3.60723 - 5.99899i) q^{98} +(8.08713 - 0.572048i) 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
$3$	−1.18075	+	1.26722i	−0.681704	+	0.731628i
$3$	−1.18075	+	1.26722i	−0.681704	+	0.731628i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	0.386492	−	0.669424i	0.172845	−	0.299376i	−0.766569	−	0.642162i	$-0.778038\pi$
$5$	0.386492	−	0.669424i	0.172845	−	0.299376i	0.939413	+	0.342787i	$0.111371\pi$
$6$	0.388948	−	1.68782i	0.158787	−	0.689048i
$7$	0.662023	+	2.56159i	0.250221	+	0.968189i
$7$	0.662023	+	2.56159i	0.250221	+	0.968189i
$8$			1.00000i			0.353553i
$9$	−0.211678	−	2.99252i	−0.0705592	−	0.997508i
$10$			0.772984i			0.244439i
$11$			2.70245i			0.814818i	0.913246	+	0.407409i	$0.133568\pi$
$11$			2.70245i			0.814818i	−0.913246	+	0.407409i	$0.866432\pi$
$12$	0.507069	+	1.65616i	0.146378	+	0.478094i
$13$	3.14302	−	1.76675i	0.871717	−	0.490009i
$13$	3.14302	−	1.76675i	0.871717	−	0.490009i
$14$	−1.85412	−	1.88739i	−0.495535	−	0.504425i
$15$	0.391956	+	1.28019i	0.101203	+	0.330543i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.32378	−	2.29285i	0.321063	−	0.556097i	−0.659645	−	0.751578i	$-0.729293\pi$
$17$	1.32378	−	2.29285i	0.321063	−	0.556097i	0.980708	+	0.195480i	$0.0626265\pi$
$18$	1.67958	+	2.48576i	0.395881	+	0.585900i
$19$			4.67151i			1.07172i	0.844308	+	0.535859i	$0.180012\pi$
$19$			4.67151i			1.07172i	−0.844308	+	0.535859i	$0.819988\pi$
$20$	−0.386492	−	0.669424i	−0.0864223	−	0.149688i
$21$	−4.02777	−	2.18566i	−0.878931	−	0.476949i
$22$	−1.35122	−	2.34039i	−0.288082	−	0.498972i
$23$	−4.66390	+	2.69271i	−0.972491	+	0.561468i	−0.899995	−	0.435901i	$-0.856430\pi$
$23$	−4.66390	+	2.69271i	−0.972491	+	0.561468i	−0.0724962	+	0.997369i	$0.523097\pi$
$24$	−1.26722	−	1.18075i	−0.258670	−	0.241019i
$25$	2.20125	+	3.81267i	0.440250	+	0.762535i
$26$	−1.83856	+	3.10156i	−0.360571	+	0.608267i
$27$	4.04211	+	3.26517i	0.777905	+	0.628382i
$28$	2.54941	+	0.707464i	0.481793	+	0.133698i
$29$	4.22905	+	2.44165i	0.785316	+	0.453402i	0.838311	−	0.545193i	$-0.183543\pi$
$29$	4.22905	+	2.44165i	0.785316	+	0.453402i	−0.0529953	+	0.998595i	$0.516877\pi$
$30$	−0.979539	−	0.912698i	−0.178839	−	0.166635i
$31$	−3.24180	+	1.87166i	−0.582245	+	0.336159i	−0.762025	−	0.647547i	$-0.775795\pi$
$31$	−3.24180	+	1.87166i	−0.582245	+	0.336159i	0.179780	+	0.983707i	$0.442461\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	−3.42459	−	3.19090i	−0.596144	−	0.555465i
$34$			2.64755i			0.454052i
$35$	1.97065	+	0.546859i	0.333101	+	0.0924360i
$36$	−2.69744	−	1.31294i	−0.449573	−	0.218824i
$37$	−2.28416	−	3.95628i	−0.375514	−	0.650409i	0.614890	−	0.788613i	$-0.289200\pi$
$37$	−2.28416	−	3.95628i	−0.375514	−	0.650409i	−0.990404	+	0.138204i	$0.955867\pi$
$38$	−2.33575	−	4.04565i	−0.378909	−	0.656290i
$39$	−1.47225	+	6.06898i	−0.235749	+	0.971814i
$40$	0.669424	+	0.386492i	0.105845	+	0.0611098i
$41$	−4.90014	+	8.48729i	−0.765273	+	1.32549i	0.174829	+	0.984599i	$0.444063\pi$
$41$	−4.90014	+	8.48729i	−0.765273	+	1.32549i	−0.940102	+	0.340894i	$0.889270\pi$
$42$	4.58098	−	0.121050i	0.706860	−	0.0186785i
$43$	−5.66191	−	9.80672i	−0.863434	−	1.49551i	−0.868594	−	0.495525i	$-0.834976\pi$
$43$	−5.66191	−	9.80672i	−0.863434	−	1.49551i	0.00516013	−	0.999987i	$-0.498357\pi$
$44$	2.34039	+	1.35122i	0.352827	+	0.203705i
$45$	−2.08508	−	1.01488i	−0.310825	−	0.151290i
$46$	2.69271	−	4.66390i	0.397018	−	0.687655i
$47$	−2.63336	+	4.56112i	−0.384116	+	0.665308i	−0.991646	−	0.128989i	$-0.958827\pi$
$47$	−2.63336	+	4.56112i	−0.384116	+	0.665308i	0.607530	+	0.794296i	$0.292160\pi$
$48$	1.68782	+	0.388948i	0.243615	+	0.0561397i
$49$	−6.12345	+	3.39166i	−0.874779	+	0.484523i
$50$	−3.81267	−	2.20125i	−0.539193	−	0.311303i
$51$	1.34249	+	4.38478i	0.187987	+	0.613993i
$52$	0.0414579	−	3.60531i	0.00574918	−	0.499967i
$53$	−3.16257	+	1.82591i	−0.434413	+	0.250808i	−0.701225	−	0.712940i	$-0.747363\pi$
$53$	−3.16257	+	1.82591i	−0.434413	+	0.250808i	0.266812	+	0.963749i	$0.414030\pi$
$54$	−5.13316	−	0.806662i	−0.698534	−	0.109773i
$55$	1.80908	+	1.04447i	0.243937	+	0.140837i
$56$	−2.56159	+	0.662023i	−0.342306	+	0.0884666i
$57$	−5.91981	−	5.51587i	−0.784099	−	0.730594i
$58$	−4.88329			−0.641207
$59$	−5.61242	+	9.72100i	−0.730675	+	1.26557i	0.225920	+	0.974146i	$0.427461\pi$
$59$	−5.61242	+	9.72100i	−0.730675	+	1.26557i	−0.956595	+	0.291420i	$0.905872\pi$
$60$	1.30465	+	0.300650i	0.168430	+	0.0388138i
$61$			13.0175i			1.66672i	0.552731	+	0.833359i	$0.313586\pi$
$61$			13.0175i			1.66672i	−0.552731	+	0.833359i	$0.686414\pi$
$62$	1.87166	−	3.24180i	0.237701	−	0.411710i
$63$	7.52547	−	2.52335i	0.948120	−	0.317912i
$64$	−1.00000			−0.125000
$65$	0.0320463	−	2.78685i	0.00397486	−	0.345666i
$66$	4.56123	+	1.05111i	0.561448	+	0.129383i
$67$	−6.94137			−0.848023			−0.424011	−	0.905657i	$-0.639378\pi$
$67$	−6.94137			−0.848023			−0.424011	+	0.905657i	$0.639378\pi$
$68$	−1.32378	−	2.29285i	−0.160532	−	0.278049i
$69$	2.09464	−	9.08958i	0.252165	−	1.09426i
$70$	−1.98007	+	0.511734i	−0.236663	+	0.0611639i
$71$	9.71163	−	5.60701i	1.15256	−	0.665430i	0.203049	−	0.979169i	$-0.434915\pi$
$71$	9.71163	−	5.60701i	1.15256	−	0.665430i	0.949509	+	0.313739i	$0.101582\pi$
$72$	2.99252	−	0.211678i	0.352672	−	0.0249465i
$73$	8.99614	−	5.19392i	1.05292	−	0.607903i	0.129453	−	0.991586i	$-0.458678\pi$
$73$	8.99614	−	5.19392i	1.05292	−	0.607903i	0.923465	+	0.383683i	$0.125344\pi$
$74$	3.95628	+	2.28416i	0.459909	+	0.265528i
$75$	−7.43060	−	1.71234i	−0.858012	−	0.197724i
$76$	4.04565	+	2.33575i	0.464067	+	0.267929i
$77$	−6.92255	+	1.78908i	−0.788898	+	0.203885i
$78$	−1.75948	−	5.99201i	−0.199222	−	0.678462i
$79$	5.14638	−	8.91380i	0.579013	−	1.00288i	−0.416580	−	0.909099i	$-0.636771\pi$
$79$	5.14638	−	8.91380i	0.579013	−	1.00288i	0.995593	−	0.0937812i	$-0.0298954\pi$
$80$	−0.772984			−0.0864223
$81$	−8.91039	+	1.26690i	−0.990043	+	0.140767i
$82$		−	9.80028i		−	1.08226i
$83$	16.3639			1.79617			0.898086	−	0.439820i	$-0.144958\pi$
$83$	16.3639			1.79617			0.898086	+	0.439820i	$0.144958\pi$
$84$	−3.90672	+	2.39532i	−0.426258	+	0.261351i
$85$	−1.02326	−	1.77234i	−0.110988	−	0.192237i
$86$	9.80672	+	5.66191i	1.05749	+	0.610540i
$87$	−8.08753	+	2.47617i	−0.867075	+	0.265473i
$88$	−2.70245			−0.288082
$89$	5.17484	+	8.96309i	0.548532	+	0.950085i	0.998375	+	0.0569778i	$0.0181464\pi$
$89$	5.17484	+	8.96309i	0.548532	+	0.950085i	−0.449844	+	0.893107i	$0.648520\pi$
$90$	2.31317	−	0.163624i	0.243830	−	0.0172474i
$91$	6.60644	+	6.88149i	0.692543	+	0.721376i
$92$			5.38541i			0.561468i
$93$	1.45595	−	6.31802i	0.150975	−	0.655148i
$94$		−	5.26673i		−	0.543221i
$95$	3.12722	+	1.80550i	0.320846	+	0.185241i
$96$	−1.65616	+	0.507069i	−0.169032	+	0.0517525i
$97$	6.86925	−	3.96597i	0.697467	−	0.402683i	−0.108936	−	0.994049i	$-0.534744\pi$
$97$	6.86925	−	3.96597i	0.697467	−	0.402683i	0.806403	+	0.591366i	$0.201411\pi$
$98$	3.60723	−	5.99899i	0.364386	−	0.605989i
$99$	8.08713	−	0.572048i	0.812787	−	0.0574929i
$100$	4.40250			0.440250
$101$	−10.1670			−1.01165			−0.505825	−	0.862636i	$-0.668812\pi$
$101$	−10.1670			−1.01165			−0.505825	+	0.862636i	$0.668812\pi$
$102$	−3.35502	−	3.12609i	−0.332197	−	0.309529i
$103$	8.01582	+	4.62793i	0.789822	+	0.456004i	0.839900	−	0.542741i	$-0.182614\pi$
$103$	8.01582	+	4.62793i	0.789822	+	0.456004i	−0.0500780	+	0.998745i	$0.515947\pi$
$104$	1.76675	+	3.14302i	0.173244	+	0.308199i
$105$	−3.01983	+	1.85155i	−0.294705	+	0.180692i
$106$	1.82591	−	3.16257i	0.177348	−	0.307176i
$107$	−1.04934	+	0.605838i	−0.101444	+	0.0585686i	−0.549864	−	0.835254i	$-0.685320\pi$
$107$	−1.04934	+	0.605838i	−0.101444	+	0.0585686i	0.448420	+	0.893823i	$0.351987\pi$
$108$	4.84877	−	1.86799i	0.466574	−	0.179747i
$109$	−3.83041	−	6.63447i	−0.366887	−	0.635467i	0.622190	−	0.782866i	$-0.286243\pi$
$109$	−3.83041	−	6.63447i	−0.366887	−	0.635467i	−0.989077	+	0.147400i	$0.952910\pi$
$110$	−2.08895			−0.199173
$111$	7.71048	+	1.77684i	0.731847	+	0.168650i
$112$	1.88739	−	1.85412i	0.178341	−	0.175198i
$113$	8.89202	−	5.13381i	0.836491	−	0.482948i	−0.0195790	−	0.999808i	$-0.506233\pi$
$113$	8.89202	−	5.13381i	0.836491	−	0.482948i	0.856070	+	0.516860i	$0.172899\pi$
$114$	7.88464	+	1.81697i	0.738464	+	0.170175i
$115$			4.16284i			0.388187i
$116$	4.22905	−	2.44165i	0.392658	−	0.226701i
$117$	−5.95236	−	9.03158i	−0.550295	−	0.834970i
$118$		−	11.2248i		−	1.03333i
$119$	6.74970	+	1.87305i	0.618744	+	0.171702i
$120$	−1.28019	+	0.391956i	−0.116865	+	0.0357806i
$121$	3.69679			0.336071
$122$	−6.50875	−	11.2735i	−0.589274	−	1.02065i
$123$	−4.96942	−	16.2309i	−0.448077	−	1.46349i
$124$			3.74331i			0.336159i
$125$	7.26798			0.650068
$126$	−5.25557	+	5.94802i	−0.468204	+	0.529892i
$127$	−3.63055	+	6.28830i	−0.322159	+	0.557996i	−0.980933	−	0.194345i	$-0.937742\pi$
$127$	−3.63055	+	6.28830i	−0.322159	+	0.557996i	0.658774	+	0.752341i	$0.271075\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	19.1125	+	4.40438i	1.68276	+	0.387784i
$130$	1.36567	+	2.42951i	0.119777	+	0.213082i
$131$	5.48186	−	9.49487i	0.478953	−	0.829570i	−0.520756	−	0.853706i	$-0.674350\pi$
$131$	5.48186	−	9.49487i	0.478953	−	0.829570i	0.999709	+	0.0241352i	$0.00768323\pi$
$132$	−4.47570	+	1.37033i	−0.389559	+	0.119272i
$133$	−11.9665	+	3.09265i	−1.03762	+	0.268167i
$134$	6.01140	−	3.47068i	0.519306	−	0.299821i
$135$	3.74803	−	1.44393i	0.322579	−	0.124273i
$136$	2.29285	+	1.32378i	0.196610	+	0.113513i
$137$	4.31921	+	2.49370i	0.369015	+	0.213051i	0.673028	−	0.739617i	$-0.264993\pi$
$137$	4.31921	+	2.49370i	0.369015	+	0.213051i	−0.304013	+	0.952668i	$0.598327\pi$
$138$	2.73078	+	8.91913i	0.232459	+	0.759246i
$139$	−0.244965	+	0.141431i	−0.0207777	+	0.0119960i	−0.510353	−	0.859965i	$-0.670485\pi$
$139$	−0.244965	+	0.141431i	−0.0207777	+	0.0119960i	0.489575	+	0.871961i	$0.337152\pi$
$140$	1.45892	−	1.43321i	0.123301	−	0.121128i
$141$	−2.67059	−	8.72257i	−0.224905	−	0.734573i
$142$	−5.60701	+	9.71163i	−0.470530	+	0.814982i
$143$	4.77455	+	8.49385i	0.399268	+	0.710291i
$144$	−2.48576	+	1.67958i	−0.207147	+	0.139965i
$145$	3.26899	−	1.88735i	0.271475	−	0.156736i
$146$	−5.19392	+	8.99614i	−0.429852	+	0.744525i
$147$	2.93227	−	11.7644i	0.241850	−	0.970314i
$148$	−4.56832			−0.375514
$149$			0.399655i			0.0327410i	0.999866	+	0.0163705i	$0.00521113\pi$
$149$			0.399655i			0.0327410i	−0.999866	+	0.0163705i	$0.994789\pi$
$150$	7.29126	−	2.23237i	0.595329	−	0.182272i
$151$	3.60132	+	6.23766i	0.293071	+	0.507614i	0.974534	−	0.224238i	$-0.0719894\pi$
$151$	3.60132	+	6.23766i	0.293071	+	0.507614i	−0.681463	+	0.731852i	$0.738656\pi$
$152$	−4.67151			−0.378909
$153$	−7.14162	−	3.47609i	−0.577365	−	0.281025i
$154$	5.10056	−	5.01067i	0.411015	−	0.403771i
$155$			2.89352i			0.232413i
$156$	4.51976	+	4.30950i	0.361871	+	0.345036i
$157$	−10.4752	+	6.04786i	−0.836012	+	0.482672i	−0.855907	−	0.517130i	$-0.827000\pi$
$157$	−10.4752	+	6.04786i	−0.836012	+	0.482672i	0.0198945	+	0.999802i	$0.493667\pi$
$158$			10.2928i			0.818848i
$159$	1.42037	−	6.16360i	0.112643	−	0.488806i
$160$	0.669424	−	0.386492i	0.0529226	−	0.0305549i
$161$	−9.98521	−	10.1644i	−0.786945	−	0.801063i
$162$	7.08317	−	5.55236i	0.556506	−	0.436235i
$163$	−9.44469			−0.739765			−0.369883	−	0.929079i	$-0.620602\pi$
$163$	−9.44469			−0.739765			−0.369883	+	0.929079i	$0.620602\pi$
$164$	4.90014	+	8.48729i	0.382637	+	0.662746i
$165$	−3.45964	+	1.05924i	−0.269333	+	0.0824618i
$166$	−14.1716	+	8.18195i	−1.09993	+	0.635043i
$167$	9.42868	−	16.3310i	0.729614	−	1.26373i	−0.227433	−	0.973794i	$-0.573033\pi$
$167$	9.42868	−	16.3310i	0.729614	−	1.26373i	0.957047	−	0.289934i	$-0.0936333\pi$
$168$	2.18566	−	4.02777i	0.168627	−	0.310749i
$169$	6.75717	−	11.1059i	0.519782	−	0.854299i
$170$	1.77234	+	1.02326i	0.135932	+	0.0784804i
$171$	13.9796	−	0.988854i	1.06905	−	0.0756196i
$172$	−11.3238			−0.863434
$173$	−12.0181			−0.913722			−0.456861	−	0.889538i	$-0.651026\pi$
$173$	−12.0181			−0.913722			−0.456861	+	0.889538i	$0.651026\pi$
$174$	5.76593	−	6.18819i	0.437114	−	0.469125i
$175$	−8.30921	+	8.16276i	−0.628117	+	0.617047i
$176$	2.34039	−	1.35122i	0.176413	−	0.101852i
$177$	−5.69177	−	18.5902i	−0.427820	−	1.39732i
$178$	−8.96309	−	5.17484i	−0.671812	−	0.387871i
$179$		−	13.6960i		−	1.02369i	−0.859078	−	0.511844i	$-0.828962\pi$
$179$		−	13.6960i		−	1.02369i	0.859078	−	0.511844i	$-0.171038\pi$
$180$	−1.92146	+	1.29829i	−0.143217	+	0.0967687i
$181$		−	13.0400i		−	0.969257i	−0.874720	−	0.484628i	$-0.838955\pi$
$181$		−	13.0400i		−	0.969257i	0.874720	−	0.484628i	$-0.161045\pi$
$182$	−9.16209	−	2.65632i	−0.679140	−	0.196900i
$183$	−16.4960	−	15.3704i	−1.21942	−	1.13621i
$184$	−2.69271	−	4.66390i	−0.198509	−	0.343827i
$185$	−3.53124			−0.259622
$186$	1.89812	+	6.19954i	0.139177	+	0.454572i
$187$	6.19630	+	3.57744i	0.453118	+	0.261608i
$188$	2.63336	+	4.56112i	0.192058	+	0.332654i
$189$	−5.68804	+	12.5158i	−0.413744	+	0.910393i
$190$	−3.61100			−0.261970
$191$		−	1.94038i		−	0.140401i	−0.997533	−	0.0702005i	$-0.977636\pi$
$191$		−	1.94038i		−	0.140401i	0.997533	−	0.0702005i	$-0.0223639\pi$
$192$	1.18075	−	1.26722i	0.0852130	−	0.0914535i
$193$	10.0456			0.723095			0.361548	−	0.932354i	$-0.382249\pi$
$193$	10.0456			0.723095			0.361548	+	0.932354i	$0.382249\pi$
$194$	−3.96597	+	6.86925i	−0.284740	+	0.493184i
$195$	3.49371	+	3.33117i	0.250189	+	0.238550i
$196$	−0.124461	+	6.99889i	−0.00889008	+	0.499921i
$197$	−2.55609	−	1.47576i	−0.182114	−	0.105143i	0.406172	−	0.913797i	$-0.366863\pi$
$197$	−2.55609	−	1.47576i	−0.182114	−	0.105143i	−0.588285	+	0.808653i	$0.700197\pi$
$198$	−6.71764	+	4.53897i	−0.477402	+	0.322571i
$199$	2.42516	+	1.40017i	0.171915	+	0.0992553i	0.583489	−	0.812121i	$-0.301687\pi$
$199$	2.42516	+	1.40017i	0.171915	+	0.0992553i	−0.411573	+	0.911377i	$0.635021\pi$
$200$	−3.81267	+	2.20125i	−0.269597	+	0.155652i
$201$	8.19599	−	8.79622i	0.578100	−	0.620437i
$202$	8.80484	−	5.08348i	0.619507	−	0.357672i
$203$	−3.45475	+	12.4495i	−0.242476	+	0.873784i
$204$	4.46858	+	1.02976i	0.312863	+	0.0720976i
$205$	3.78773	+	6.56054i	0.264547	+	0.458208i
$206$	−9.25587			−0.644887
$207$	9.04523	+	13.3868i	0.628687	+	0.930450i
$208$	−3.10156	−	1.83856i	−0.215055	−	0.127481i
$209$	−12.6245			−0.873255
$210$	1.68948	−	3.11340i	0.116585	−	0.214845i
$211$	−6.57341	+	11.3855i	−0.452532	+	0.783809i	−0.998543	−	0.0539696i	$-0.982813\pi$
$211$	−6.57341	+	11.3855i	−0.452532	+	0.783809i	0.546010	+	0.837778i	$0.316146\pi$
$212$			3.65182i			0.250808i
$213$	−4.36167	+	18.9272i	−0.298856	+	1.29687i
$214$	0.605838	−	1.04934i	0.0414142	−	0.0717315i
$215$	−8.75314			−0.596959
$216$	−3.26517	+	4.04211i	−0.222167	+	0.275031i
$217$	−6.94056	−	7.06508i	−0.471156	−	0.479609i
$218$	6.63447	+	3.83041i	0.449343	+	0.259428i
$219$	−4.04033	+	17.5328i	−0.273020	+	1.18475i
$220$	1.80908	−	1.04447i	0.121968	−	0.0704184i
$221$	0.109762	−	9.54526i	0.00738340	−	0.642084i
$222$	−7.56589	+	2.31646i	−0.507790	+	0.155470i
$223$	2.33020	+	1.34534i	0.156042	+	0.0900908i	0.575988	−	0.817458i	$-0.304618\pi$
$223$	2.33020	+	1.34534i	0.156042	+	0.0900908i	−0.419946	+	0.907549i	$0.637951\pi$
$224$	−0.707464	+	2.54941i	−0.0472694	+	0.170340i
$225$	10.9436	−	7.39434i	0.729570	−	0.492956i
$226$	−5.13381	+	8.89202i	−0.341496	+	0.591488i
$227$	−2.64013	+	4.57284i	−0.175232	+	0.303510i	−0.940241	−	0.340509i	$-0.889401\pi$
$227$	−2.64013	+	4.57284i	−0.175232	+	0.303510i	0.765010	+	0.644019i	$0.222734\pi$
$228$	−7.73679	+	2.36878i	−0.512381	+	0.156876i
$229$	22.9130	+	13.2288i	1.51414	+	0.874187i	0.999863	+	0.0165604i	$0.00527159\pi$
$229$	22.9130	+	13.2288i	1.51414	+	0.874187i	0.514273	+	0.857626i	$0.328062\pi$
$230$	−2.08142	−	3.60512i	−0.137245	−	0.237715i
$231$	5.90662	−	10.8848i	0.388627	−	0.716169i
$232$	−2.44165	+	4.22905i	−0.160302	+	0.277651i
$233$	3.01825	+	1.74259i	0.197732	+	0.114161i	0.595597	−	0.803283i	$-0.296915\pi$
$233$	3.01825	+	1.74259i	0.197732	+	0.114161i	−0.397865	+	0.917444i	$0.630249\pi$
$234$	9.67068	+	4.84540i	0.632192	+	0.316754i
$235$	2.03555	+	3.52567i	0.132785	+	0.229990i
$236$	5.61242	+	9.72100i	0.365337	+	0.632783i
$237$	5.21914	+	17.0465i	0.339020	+	1.10729i
$238$	−6.78194	+	1.75274i	−0.439608	+	0.113613i
$239$		−	11.0001i		−	0.711539i	−0.934574	−	0.355769i	$-0.884219\pi$
$239$		−	11.0001i		−	0.711539i	0.934574	−	0.355769i	$-0.115781\pi$
$240$	0.912698	−	0.979539i	0.0589144	−	0.0632290i
$241$	2.00211	+	1.15592i	0.128967	+	0.0744594i	0.563096	−	0.826392i	$-0.309610\pi$
$241$	2.00211	+	1.15592i	0.128967	+	0.0744594i	−0.434128	+	0.900851i	$0.642944\pi$
$242$	−3.20151	+	1.84839i	−0.205801	+	0.118819i
$243$	8.91546	−	12.7873i	0.571927	−	0.820304i
$244$	11.2735	+	6.50875i	0.721710	+	0.416680i
$245$	−0.0962065	+	5.41004i	−0.00614641	+	0.345634i
$246$	12.4191	+	11.5716i	0.791812	+	0.737781i
$247$	8.25340	+	14.6827i	0.525151	+	0.934235i
$248$	−1.87166	−	3.24180i	−0.118850	−	0.205855i
$249$	−19.3216	+	20.7366i	−1.22446	+	1.31413i
$250$	−6.29426	+	3.63399i	−0.398084	+	0.229834i
$251$	4.19795	+	7.27107i	0.264973	+	0.458946i	0.967556	−	0.252655i	$-0.0813038\pi$
$251$	4.19795	+	7.27107i	0.264973	+	0.458946i	−0.702584	+	0.711601i	$0.747970\pi$
$252$	1.57745	−	7.77892i	0.0993700	−	0.490026i
$253$	−7.27689	−	12.6039i	−0.457494	−	0.792403i
$254$		−	7.26110i		−	0.455602i
$255$	3.45414	+	0.795988i	0.216307	+	0.0498467i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−12.3210	−	21.3406i	−0.768564	−	1.33119i	−0.938342	−	0.345709i	$-0.887638\pi$
$257$	−12.3210	−	21.3406i	−0.768564	−	1.33119i	0.169778	−	0.985482i	$-0.445695\pi$
$258$	−18.7541	+	5.74196i	−1.16758	+	0.357479i
$259$	8.62219	−	8.47023i	0.535757	−	0.526314i
$260$	−2.39746	−	1.42118i	−0.148684	−	0.0881377i
$261$	6.41148	−	13.1724i	0.396861	−	0.815350i
$262$			10.9637i			0.677341i
$263$		−	22.8097i		−	1.40651i	−0.710939	−	0.703254i	$-0.751730\pi$
$263$		−	22.8097i		−	1.40651i	0.710939	−	0.703254i	$-0.248270\pi$
$264$	3.19090	−	3.42459i	0.196386	−	0.210769i
$265$			2.82280i			0.173403i
$266$	8.81695	−	8.66155i	0.540602	−	0.531074i
$267$	−17.4683	−	4.02548i	−1.06905	−	0.246356i
$268$	−3.47068	+	6.01140i	−0.212006	+	0.367205i
$269$	−0.914446	+	1.58387i	−0.0557548	+	0.0965701i	−0.892556	−	0.450937i	$-0.851090\pi$
$269$	−0.914446	+	1.58387i	−0.0557548	+	0.0965701i	0.836801	+	0.547507i	$0.184423\pi$
$270$	−2.52392	+	3.12449i	−0.153601	+	0.190150i
$271$	6.32104	−	3.64945i	0.383976	−	0.221689i	−0.295571	−	0.955321i	$-0.595510\pi$
$271$	6.32104	−	3.64945i	0.383976	−	0.221689i	0.679547	+	0.733632i	$0.262176\pi$
$272$	−2.64755			−0.160532
$273$	−16.5209	+	0.246506i	−0.999889	+	0.0149192i
$274$	−4.98739			−0.301299
$275$	−10.3035	+	5.94875i	−0.621327	+	0.358723i
$276$	−6.82448	−	6.35880i	−0.410786	−	0.382755i
$277$	8.45914	−	14.6517i	0.508260	−	0.880333i	−0.491694	−	0.870768i	$-0.663622\pi$
$277$	8.45914	−	14.6517i	0.508260	−	0.880333i	0.999954	−	0.00956470i	$-0.00304459\pi$
$278$	0.141431	−	0.244965i	0.00848244	−	0.0146920i
$279$	6.28719	+	9.30498i	0.376404	+	0.557075i
$280$	−0.546859	+	1.97065i	−0.0326811	+	0.117769i
$281$			31.6214i			1.88637i	0.332263	+	0.943187i	$0.392188\pi$
$281$			31.6214i			1.88637i	−0.332263	+	0.943187i	$0.607812\pi$
$282$	6.67409	+	6.21867i	0.397436	+	0.370316i
$283$		−	0.682132i		−	0.0405485i	−0.999794	−	0.0202743i	$-0.993546\pi$
$283$		−	0.682132i		−	0.0405485i	0.999794	−	0.0202743i	$-0.00645394\pi$
$284$		−	11.2140i		−	0.665430i
$285$	−5.98042	+	1.83103i	−0.354249	+	0.108461i
$286$	−8.38181	−	4.96861i	−0.495627	−	0.293800i
$287$	−24.9849	−	6.93335i	−1.47481	−	0.409263i
$288$	1.31294	−	2.69744i	0.0773659	−	0.158948i
$289$	4.99523	+	8.65199i	0.293837	+	0.508941i
$290$	−1.88735	+	3.26899i	−0.110829	+	0.191962i
$291$	−3.08511	+	13.3876i	−0.180852	+	0.784797i
$292$		−	10.3878i		−	0.607903i
$293$	3.90007	+	6.75511i	0.227844	+	0.394638i	0.957169	−	0.289530i	$-0.0934989\pi$
$293$	3.90007	+	6.75511i	0.227844	+	0.394638i	−0.729325	+	0.684168i	$0.760166\pi$
$294$	3.34279	+	11.6544i	0.194956	+	0.679700i
$295$	4.33831	+	7.51418i	0.252586	+	0.437492i
$296$	3.95628	−	2.28416i	0.229954	−	0.132764i
$297$	−8.82394	+	10.9236i	−0.512017	+	0.633851i
$298$	−0.199827	−	0.346111i	−0.0115757	−	0.0200497i
$299$	−9.90140	+	16.7032i	−0.572613	+	0.965971i
$300$	−5.19823	+	5.57892i	−0.300120	+	0.322099i
$301$	21.3724	−	20.9958i	1.23189	−	1.21018i
$302$	−6.23766	−	3.60132i	−0.358937	−	0.207233i
$303$	12.0046	−	12.8837i	0.689646	−	0.740152i
$304$	4.04565	−	2.33575i	0.232034	−	0.133965i
$305$	8.71422	+	5.03116i	0.498975	+	0.288083i
$306$	7.92286	−	0.560428i	0.452920	−	0.0320375i
$307$			1.62307i			0.0926335i	0.998927	+	0.0463167i	$0.0147484\pi$
$307$			1.62307i			0.0926335i	−0.998927	+	0.0463167i	$0.985252\pi$
$308$	−1.91188	+	6.88964i	−0.108940	+	0.392574i
$309$	−15.3292	+	4.69336i	−0.872050	+	0.266996i
$310$	−1.44676	−	2.50586i	−0.0821705	−	0.142324i
$311$	−15.1988	−	26.3252i	−0.861847	−	1.49276i	−0.870144	−	0.492798i	$-0.835974\pi$
$311$	−15.1988	−	26.3252i	−0.861847	−	1.49276i	0.00829636	−	0.999966i	$-0.497359\pi$
$312$	−6.06898	−	1.47225i	−0.343588	−	0.0833498i
$313$	4.29992	+	2.48256i	0.243046	+	0.140323i	0.616576	−	0.787296i	$-0.288519\pi$
$313$	4.29992	+	2.48256i	0.243046	+	0.140323i	−0.373530	+	0.927618i	$0.621853\pi$
$314$	6.04786	−	10.4752i	0.341301	−	0.591150i
$315$	1.21934	−	6.01299i	0.0687022	−	0.338793i
$316$	−5.14638	−	8.91380i	−0.289507	−	0.501440i
$317$	−11.5891	−	6.69094i	−0.650906	−	0.375801i	0.137897	−	0.990447i	$-0.455966\pi$
$317$	−11.5891	−	6.69094i	−0.650906	−	0.375801i	−0.788803	+	0.614646i	$0.789299\pi$
$318$	1.85173	+	6.04802i	0.103840	+	0.339156i
$319$	−6.59841	+	11.4288i	−0.369440	+	0.639889i
$320$	−0.386492	+	0.669424i	−0.0216056	+	0.0374219i
$321$	0.471278	−	2.04508i	0.0263042	−	0.114145i
$322$	13.7296	+	3.80998i	0.765122	+	0.212322i
$323$	10.7111	+	6.18403i	0.595979	+	0.344089i
$324$	−3.35802	+	8.35007i	−0.186557	+	0.463893i
$325$	13.6546	+	8.09425i	0.757422	+	0.448988i
$326$	8.17934	−	4.72234i	0.453012	−	0.261546i
$327$	12.9300	+	2.97966i	0.715033	+	0.164775i
$328$	−8.48729	−	4.90014i	−0.468632	−	0.270565i
$329$	−13.4271	−	3.72602i	−0.740257	−	0.205422i
$330$	2.46652	−	2.64715i	0.135777	−	0.145721i
$331$	−29.5150			−1.62229			−0.811145	−	0.584845i	$-0.801155\pi$
$331$	−29.5150			−1.62229			−0.811145	+	0.584845i	$0.801155\pi$
$332$	8.18195	−	14.1716i	0.449043	−	0.777765i
$333$	−11.3558	+	7.67286i	−0.622292	+	0.420470i
$334$			18.8574i			1.03183i
$335$	−2.68278	+	4.64672i	−0.146576	+	0.253877i
$336$	0.121050	+	4.58098i	0.00660383	+	0.249913i
$337$	−30.1118			−1.64030			−0.820148	−	0.572152i	$-0.806109\pi$
$337$	−30.1118			−1.64030			−0.820148	+	0.572152i	$0.806109\pi$
$338$	−0.298938	+	12.9966i	−0.0162601	+	0.706920i
$339$	−3.99357	+	17.3298i	−0.216901	+	0.941228i
$340$	−2.04652			−0.110988
$341$	−5.05805	−	8.76080i	−0.273909	−	0.474424i
$342$	−11.6123	+	7.84617i	−0.627919	+	0.424272i
$343$	−12.7419	−	13.4404i	−0.687998	−	0.725713i
$344$	9.80672	−	5.66191i	0.528743	−	0.305270i
$345$	−5.27522	−	4.91525i	−0.284008	−	0.264628i
$346$	10.4080	−	6.00907i	0.559538	−	0.323050i
$347$	−11.6548	−	6.72891i	−0.625663	−	0.361227i	0.153408	−	0.988163i	$-0.450975\pi$
$347$	−11.6548	−	6.72891i	−0.625663	−	0.361227i	−0.779070	+	0.626936i	$0.784309\pi$
$348$	−1.89934	+	8.24209i	−0.101816	+	0.441822i
$349$	−8.96543	−	5.17619i	−0.479908	−	0.277075i	0.240470	−	0.970657i	$-0.422698\pi$
$349$	−8.96543	−	5.17619i	−0.479908	−	0.277075i	−0.720378	+	0.693581i	$0.756032\pi$
$350$	3.11461	−	11.2238i	0.166483	−	0.599936i
$351$	18.4732	+	3.12108i	0.986026	+	0.166591i
$352$	−1.35122	+	2.34039i	−0.0720204	+	0.124743i
$353$	29.9025			1.59155			0.795775	−	0.605593i	$-0.207064\pi$
$353$	29.9025			1.59155			0.795775	+	0.605593i	$0.207064\pi$
$354$	14.2243	+	13.2537i	0.756013	+	0.704425i
$355$		−	8.66826i		−	0.460064i
$356$	10.3497			0.548532
$357$	−10.3432	+	6.34174i	−0.547422	+	0.335640i
$358$	6.84801	+	11.8611i	0.361929	+	0.626879i
$359$	5.15529	+	2.97641i	0.272086	+	0.157089i	0.629835	−	0.776729i	$-0.283122\pi$
$359$	5.15529	+	2.97641i	0.272086	+	0.157089i	−0.357749	+	0.933818i	$0.616456\pi$
$360$	1.01488	−	2.08508i	0.0534891	−	0.109893i
$361$	−2.82299			−0.148579
$362$	6.52001	+	11.2930i	0.342684	+	0.593546i
$363$	−4.36497	+	4.68463i	−0.229101	+	0.245879i
$364$	9.26277	−	2.28060i	0.485501	−	0.119536i
$365$		−	8.02964i		−	0.420291i
$366$	21.9711	+	5.06312i	1.14845	+	0.264654i
$367$			17.0616i			0.890607i	0.895380	+	0.445303i	$0.146904\pi$
$367$			17.0616i			0.890607i	−0.895380	+	0.445303i	$0.853096\pi$
$368$	4.66390	+	2.69271i	0.243123	+	0.140367i
$369$	26.4357	+	12.8672i	1.37619	+	0.669840i
$370$	3.05815	−	1.76562i	0.158985	−	0.0917903i
$371$	−6.77093	−	6.89241i	−0.351529	−	0.357836i
$372$	−4.74359	−	4.41990i	−0.245944	−	0.229161i
$373$	23.6660			1.22538			0.612690	−	0.790324i	$-0.290088\pi$
$373$	23.6660			1.22538			0.612690	+	0.790324i	$0.290088\pi$
$374$	−7.15487			−0.369970
$375$	−8.58164	+	9.21011i	−0.443154	+	0.475608i
$376$	−4.56112	−	2.63336i	−0.235222	−	0.135805i
$377$	17.6058	+	0.202451i	0.906744	+	0.0104268i
$378$	−1.33194	−	13.6831i	−0.0685074	−	0.703780i
$379$	13.2966	−	23.0303i	0.682998	−	1.18299i	−0.291063	−	0.956704i	$-0.594009\pi$
$379$	13.2966	−	23.0303i	0.682998	−	1.18299i	0.974061	−	0.226284i	$-0.0726576\pi$
$380$	3.12722	−	1.80550i	0.160423	−	0.0926203i
$381$	−3.68188	−	12.0256i	−0.188628	−	0.616089i
$382$	0.970190	+	1.68042i	0.0496392	+	0.0859777i
$383$	15.6354			0.798929			0.399465	−	0.916749i	$-0.369196\pi$
$383$	15.6354			0.798929			0.399465	+	0.916749i	$0.369196\pi$
$384$	−0.388948	+	1.68782i	−0.0198484	+	0.0861310i
$385$	−1.47786	+	5.32559i	−0.0753185	+	0.271417i
$386$	−8.69971	+	5.02278i	−0.442804	+	0.255653i
$387$	−28.1483	+	19.0193i	−1.43086	+	0.966804i
$388$		−	7.93193i		−	0.402683i
$389$	−4.64668	+	2.68276i	−0.235596	+	0.136021i	−0.613151	−	0.789966i	$-0.710098\pi$
$389$	−4.64668	+	2.68276i	−0.235596	+	0.136021i	0.377555	+	0.925987i	$0.376765\pi$
$390$	−4.69122	−	1.13803i	−0.237549	−	0.0576262i
$391$			14.2582i			0.721066i
$392$	−3.39166	−	6.12345i	−0.171305	−	0.309281i
$393$	5.55937	+	18.1577i	0.280433	+	0.915937i
$394$	2.95151			0.148695
$395$	−3.97807	−	6.89023i	−0.200159	−	0.346685i
$396$	3.54816	−	7.28968i	0.178302	−	0.366320i
$397$			5.81650i			0.291922i	0.989290	+	0.145961i	$0.0466273\pi$
$397$			5.81650i			0.291922i	−0.989290	+	0.145961i	$0.953373\pi$
$398$	−2.80034			−0.140368
$399$	10.2103	−	18.8157i	0.511155	−	0.941966i
$400$	2.20125	−	3.81267i	0.110062	−	0.190634i
$401$	7.52248	−	4.34311i	0.375655	−	0.216884i	−0.300271	−	0.953854i	$-0.597077\pi$
$401$	7.52248	−	4.34311i	0.375655	−	0.216884i	0.675926	+	0.736969i	$0.263744\pi$
$402$	−2.69983	+	11.7157i	−0.134655	+	0.584328i
$403$	−6.88231	+	11.6101i	−0.342832	+	0.578341i
$404$	−5.08348	+	8.80484i	−0.252913	+	0.438057i
$405$	−2.59570	+	6.45447i	−0.128981	+	0.320725i
$406$	−3.23285	−	12.5090i	−0.160444	−	0.620810i
$407$	10.6916	−	6.17282i	0.529965	−	0.305975i
$408$	−4.38478	+	1.34249i	−0.217079	+	0.0664633i
$409$	8.71787	+	5.03326i	0.431071	+	0.248879i	0.699803	−	0.714336i	$-0.253271\pi$
$409$	8.71787	+	5.03326i	0.431071	+	0.248879i	−0.268732	+	0.963215i	$0.586605\pi$
$410$	−6.56054	−	3.78773i	−0.324002	−	0.187063i
$411$	−8.25994	+	2.52895i	−0.407433	+	0.124744i
$412$	8.01582	−	4.62793i	0.394911	−	0.228002i
$413$	−28.6167	−	7.94117i	−1.40814	−	0.390759i
$414$	−14.5268	−	7.07074i	−0.713954	−	0.347508i
$415$	6.32452	−	10.9544i	0.310458	−	0.537730i
$416$	3.60531	+	0.0414579i	0.176765	+	0.00203264i
$417$	0.110018	−	0.477417i	0.00538761	−	0.0233792i
$418$	10.9331	−	6.31225i	0.534757	−	0.308742i
$419$	6.88362	−	11.9228i	0.336287	−	0.582466i	−0.647444	−	0.762113i	$-0.724162\pi$
$419$	6.88362	−	11.9228i	0.336287	−	0.582466i	0.983731	+	0.179647i	$0.0574955\pi$
$420$	0.0935700	+	3.54102i	0.00456575	+	0.172784i
$421$	5.26092			0.256402			0.128201	−	0.991748i	$-0.459080\pi$
$421$	5.26092			0.256402			0.128201	+	0.991748i	$0.459080\pi$
$422$		−	13.1468i		−	0.639977i
$423$	14.2067	+	6.91491i	0.690752	+	0.336215i
$424$	−1.82591	−	3.16257i	−0.0886741	−	0.153588i
$425$	11.6558			0.565391
$426$	−5.68628	−	18.5723i	−0.275501	−	0.899829i
$427$	−33.3454	+	8.61788i	−1.61370	+	0.417049i
$428$			1.21168i			0.0585686i
$429$	−16.4011	−	3.97868i	−0.791852	−	0.192092i
$430$	7.58044	−	4.37657i	0.365561	−	0.211057i
$431$		−	22.0983i		−	1.06444i	−0.846606	−	0.532220i	$-0.821358\pi$
$431$		−	22.0983i		−	1.06444i	0.846606	−	0.532220i	$-0.178642\pi$
$432$	0.806662	−	5.13316i	0.0388105	−	0.246969i
$433$	0.698470	−	0.403262i	0.0335663	−	0.0193795i	−0.483123	−	0.875553i	$-0.660498\pi$
$433$	0.698470	−	0.403262i	0.0335663	−	0.0193795i	0.516689	+	0.856173i	$0.327164\pi$
$434$	9.54324	+	2.64826i	0.458090	+	0.127121i
$435$	−1.46816	+	6.37101i	−0.0703930	+	0.305466i
$436$	−7.66082			−0.366887
$437$	−12.5790	−	21.7875i	−0.601735	−	1.04224i
$438$	−5.26735	−	17.2040i	−0.251684	−	0.822038i
$439$	−19.1502	+	11.0564i	−0.913987	+	0.527691i	−0.881712	−	0.471788i	$-0.843609\pi$
$439$	−19.1502	+	11.0564i	−0.913987	+	0.527691i	−0.0322754	+	0.999479i	$0.510275\pi$
$440$	−1.04447	+	1.80908i	−0.0497934	+	0.0862446i
$441$	11.4458	+	17.6066i	0.545039	+	0.838411i
$442$	4.67757	+	8.32132i	0.222489	+	0.395805i
$443$	22.9597	+	13.2558i	1.09085	+	0.629800i	0.933802	−	0.357791i	$-0.116470\pi$
$443$	22.9597	+	13.2558i	1.09085	+	0.629800i	0.157044	+	0.987592i	$0.449803\pi$
$444$	5.39403	−	5.78906i	0.255989	−	0.274736i
$445$	8.00014			0.379243
$446$	−2.69068			−0.127408
$447$	−0.506450	−	0.471891i	−0.0239542	−	0.0223197i
$448$	−0.662023	−	2.56159i	−0.0312777	−	0.121024i
$449$	−32.5645	+	18.8011i	−1.53681	+	0.887279i	−0.537789	+	0.843079i	$0.680740\pi$
$449$	−32.5645	+	18.8011i	−1.53681	+	0.887279i	−0.999023	+	0.0441993i	$0.985926\pi$
$450$	−5.78023	+	11.8755i	−0.272482	+	0.559815i
$451$	−22.9364	−	13.2424i	−1.08004	−	0.623559i
$452$		−	10.2676i		−	0.482948i
$453$	−12.1567	−	2.80145i	−0.571172	−	0.131623i
$454$		−	5.28026i		−	0.247815i
$455$	7.15997	−	1.76287i	0.335665	−	0.0826447i
$456$	5.51587	−	5.91981i	0.258304	−	0.277221i
$457$	−9.55304	−	16.5464i	−0.446873	−	0.774006i	0.551308	−	0.834302i	$-0.314129\pi$
$457$	−9.55304	−	16.5464i	−0.446873	−	0.774006i	−0.998181	+	0.0602958i	$0.980796\pi$
$458$	−26.4577			−1.23629
$459$	12.8374	−	4.94560i	0.599198	−	0.230841i
$460$	3.60512	+	2.08142i	0.168090	+	0.0970467i
$461$	−2.14345	−	3.71257i	−0.0998306	−	0.172912i	0.811784	−	0.583958i	$-0.198497\pi$
$461$	−2.14345	−	3.71257i	−0.0998306	−	0.172912i	−0.911614	+	0.411046i	$0.865163\pi$
$462$	0.327132	+	12.3798i	0.0152195	+	0.575962i
$463$	30.5605			1.42027			0.710134	−	0.704066i	$-0.248634\pi$
$463$	30.5605			1.42027			0.710134	+	0.704066i	$0.248634\pi$
$464$		−	4.88329i		−	0.226701i
$465$	−3.66672	−	3.41652i	−0.170040	−	0.158437i
$466$	−3.48518			−0.161448
$467$	9.65321	−	16.7199i	0.446697	−	0.773703i	−0.551471	−	0.834194i	$-0.685933\pi$
$467$	9.65321	−	16.7199i	0.446697	−	0.773703i	0.998169	+	0.0604912i	$0.0192667\pi$
$468$	−10.7978	+	0.639100i	−0.499126	+	0.0295424i
$469$	−4.59535	−	17.7809i	−0.212193	−	0.821046i
$470$	−3.52567	−	2.03555i	−0.162627	−	0.0938929i
$471$	4.70460	−	20.4153i	0.216777	−	0.940689i
$472$	−9.72100	−	5.61242i	−0.447445	−	0.258333i
$473$	26.5021	−	15.3010i	1.21857	−	0.703541i
$474$	−13.0432	−	12.1531i	−0.599093	−	0.558212i
$475$	−17.8109	+	10.2831i	−0.817222	+	0.471823i
$476$	4.99696	−	4.90889i	0.229035	−	0.224999i
$477$	6.13353	+	9.07756i	0.280835	+	0.415633i
$478$	5.50006	+	9.52638i	0.251567	+	0.435727i
$479$	37.6069			1.71830			0.859152	−	0.511720i	$-0.170991\pi$
$479$	37.6069			1.71830			0.859152	+	0.511720i	$0.170991\pi$
$480$	−0.300650	+	1.30465i	−0.0137228	+	0.0595491i
$481$	−14.1689	−	8.39914i	−0.646048	−	0.382968i
$482$	−2.31184			−0.105302
$483$	24.6704	−	0.651905i	1.12254	−	0.0296627i
$484$	1.84839	−	3.20151i	0.0840179	−	0.145523i
$485$		−	6.13126i		−	0.278406i
$486$	−1.32738	+	15.5318i	−0.0602111	+	0.704539i
$487$	17.5209	−	30.3471i	0.793948	−	1.37516i	−0.129558	−	0.991572i	$-0.541356\pi$
$487$	17.5209	−	30.3471i	0.793948	−	1.37516i	0.923505	−	0.383586i	$-0.125311\pi$
$488$	−13.0175			−0.589274
$489$	11.1518	−	11.9685i	0.504301	−	0.541233i
$490$	−2.62170	−	4.73333i	−0.118436	−	0.213830i
$491$	21.2054	+	12.2429i	0.956985	+	0.552516i	0.895244	−	0.445576i	$-0.147001\pi$
$491$	21.2054	+	12.2429i	0.956985	+	0.552516i	0.0617415	+	0.998092i	$0.480335\pi$
$492$	−16.5411	−	3.81180i	−0.745729	−	0.171849i
$493$	11.1966	−	6.46439i	0.504272	−	0.291141i
$494$	−14.4890	−	8.58885i	−0.651890	−	0.386431i
$495$	2.74267	−	5.63481i	0.123274	−	0.253266i
$496$	3.24180	+	1.87166i	0.145561	+	0.0840399i
$497$	20.7922	+	21.1652i	0.932656	+	0.949389i
$498$	6.36470	−	27.6192i	0.285209	−	1.23765i
$499$	9.94836	−	17.2311i	0.445350	−	0.771368i	−0.552727	−	0.833363i	$-0.686413\pi$
$499$	9.94836	−	17.2311i	0.445350	−	0.771368i	0.998077	+	0.0619941i	$0.0197460\pi$
$500$	3.63399	−	6.29426i	0.162517	−	0.281488i
$501$	9.56199	+	31.2309i	0.427198	+	1.39529i
$502$	−7.27107	−	4.19795i	−0.324524	−	0.187364i
$503$	5.22211	+	9.04495i	0.232842	+	0.403295i	0.958643	−	0.284610i	$-0.0918641\pi$
$503$	5.22211	+	9.04495i	0.232842	+	0.403295i	−0.725801	+	0.687905i	$0.758531\pi$
$504$	2.52335	+	7.52547i	0.112399	+	0.335211i
$505$	−3.92945	+	6.80601i	−0.174858	+	0.302863i
$506$	12.6039	+	7.27689i	0.560314	+	0.323497i
$507$	6.09506	+	21.6760i	0.270691	+	0.962666i
$508$	3.63055	+	6.28830i	0.161080	+	0.278998i
$509$	0.749658	+	1.29845i	0.0332280	+	0.0575526i	0.882161	−	0.470948i	$-0.156088\pi$
$509$	0.749658	+	1.29845i	0.0332280	+	0.0575526i	−0.848933	+	0.528500i	$0.822755\pi$
$510$	−3.38937	+	1.03773i	−0.150084	+	0.0459513i
$511$	19.2603	+	19.6059i	0.852027	+	0.867313i
$512$		−	1.00000i		−	0.0441942i
$513$	−15.2533	+	18.8828i	−0.673448	+	0.833695i
$514$	21.3406	+	12.3210i	0.941295	+	0.543457i
$515$	6.19610	−	3.57732i	0.273033	−	0.157636i
$516$	13.3706	−	14.3497i	0.588606	−	0.631712i
$517$	−12.3262	−	7.11652i	−0.542105	−	0.312984i
$518$	−3.23192	+	11.6465i	−0.142003	+	0.511719i
$519$	14.1904	−	15.2296i	0.622888	−	0.668505i
$520$	2.78685	+	0.0320463i	0.122211	+	0.00140533i
$521$	−9.88915	−	17.1285i	−0.433252	−	0.750414i	0.563900	−	0.825843i	$-0.309301\pi$
$521$	−9.88915	−	17.1285i	−0.433252	−	0.750414i	−0.997151	+	0.0754296i	$0.975967\pi$
$522$	1.03368	+	14.6134i	0.0452431	+	0.639609i
$523$	11.4165	−	6.59133i	0.499210	−	0.288219i	−0.229178	−	0.973385i	$-0.573604\pi$
$523$	11.4165	−	6.59133i	0.499210	−	0.288219i	0.728387	+	0.685166i	$0.240270\pi$
$524$	−5.48186	−	9.49487i	−0.239476	−	0.414785i
$525$	−0.532923	−	20.1677i	−0.0232587	−	0.880192i
$526$	11.4049	+	19.7538i	0.497275	+	0.861306i
$527$			9.91062i			0.431713i
$528$	−1.05111	+	4.56123i	−0.0457437	+	0.198502i
$529$	3.00132	−	5.19845i	0.130492	−	0.226019i
$530$	−1.41140	−	2.44462i	−0.0613074	−	0.106187i
$531$	30.2783	+	14.7376i	1.31397	+	0.639556i
$532$	−3.30492	+	11.9096i	−0.143287	+	0.516346i
$533$	−0.406300	+	35.3331i	−0.0175988	+	1.53045i
$534$	17.1408	−	5.24800i	0.741754	−	0.227103i
$535$			0.936606i			0.0404930i
$536$		−	6.94137i		−	0.299821i
$537$	17.3558	+	16.1715i	0.748960	+	0.697853i
$538$		−	1.82889i		−	0.0788492i
$539$	−9.16578	−	16.5483i	−0.394798	−	0.712785i
$540$	0.623537	−	3.96785i	0.0268328	−	0.170749i
$541$	10.6958	−	18.5257i	0.459848	−	0.796480i	−0.539104	−	0.842239i	$-0.681237\pi$
$541$	10.6958	−	18.5257i	0.459848	−	0.796480i	0.998953	+	0.0457586i	$0.0145705\pi$
$542$	−3.64945	+	6.32104i	−0.156757	+	0.271512i
$543$	16.5245	+	15.3969i	0.709135	+	0.660746i
$544$	2.29285	−	1.32378i	0.0983051	−	0.0567565i
$545$	−5.92170			−0.253658
$546$	14.1842	−	8.47392i	0.607030	−	0.362650i
$547$	−25.6199			−1.09543			−0.547713	−	0.836666i	$-0.684501\pi$
$547$	−25.6199			−1.09543			−0.547713	+	0.836666i	$0.684501\pi$
$548$	4.31921	−	2.49370i	0.184507	−	0.106525i
$549$	38.9551	−	2.75551i	1.66256	−	0.117602i
$550$	5.94875	−	10.3035i	0.253656	−	0.439344i
$551$	−11.4062	+	19.7561i	−0.485919	+	0.841636i
$552$	9.08958	+	2.09464i	0.386878	+	0.0891539i
$553$	26.2405	+	7.28176i	1.11586	+	0.309652i
$554$			16.9183i			0.718789i
$555$	4.16950	−	4.47485i	0.176985	−	0.189947i
$556$			0.282861i			0.0119960i
$557$		−	15.8251i		−	0.670532i	−0.942124	−	0.335266i	$-0.891174\pi$
$557$		−	15.8251i		−	0.670532i	0.942124	−	0.335266i	$-0.108826\pi$
$558$	−10.0974	−	4.91476i	−0.427455	−	0.208058i
$559$	−35.1216	−	20.8195i	−1.48548	−	0.880573i
$560$	−0.511734	−	1.98007i	−0.0216247	−	0.0836731i
$561$	−11.8496	+	3.62801i	−0.500292	+	0.153175i
$562$	−15.8107	−	27.3849i	−0.666934	−	1.15516i
$563$	−4.87300	+	8.44029i	−0.205373	+	0.355716i	−0.950251	−	0.311484i	$-0.899174\pi$
$563$	−4.87300	+	8.44029i	−0.205373	+	0.355716i	0.744879	+	0.667200i	$0.232507\pi$
$564$	−8.88926	−	2.04848i	−0.374305	−	0.0862566i
$565$		−	7.93671i		−	0.333900i
$566$	0.341066	+	0.590743i	0.0143361	+	0.0248308i
$567$	−9.14416	−	21.9860i	−0.384019	−	0.923325i
$568$	5.60701	+	9.71163i	0.235265	+	0.407491i
$569$	16.0935	−	9.29160i	0.674675	−	0.389524i	−0.123171	−	0.992386i	$-0.539306\pi$
$569$	16.0935	−	9.29160i	0.674675	−	0.389524i	0.797846	+	0.602862i	$0.205973\pi$
$570$	4.26368	−	4.57592i	0.178586	−	0.191664i
$571$	−16.5767	−	28.7116i	−0.693712	−	1.20154i	−0.970613	−	0.240646i	$-0.922641\pi$
$571$	−16.5767	−	28.7116i	−0.693712	−	1.20154i	0.276901	−	0.960899i	$-0.410693\pi$
$572$	9.74316	+	0.112038i	0.407382	+	0.00468454i
$573$	2.45888	+	2.29110i	0.102721	+	0.0957119i
$574$	25.1043	−	6.48802i	1.04783	−	0.270805i
$575$	−20.5328	−	11.8546i	−0.856277	−	0.494372i
$576$	0.211678	+	2.99252i	0.00881990	+	0.124688i
$577$	−31.6525	+	18.2746i	−1.31771	+	0.760780i	−0.983360	−	0.181668i	$-0.941850\pi$
$577$	−31.6525	+	18.2746i	−1.31771	+	0.760780i	−0.334350	+	0.942449i	$0.608517\pi$
$578$	−8.65199	−	4.99523i	−0.359875	−	0.207774i
$579$	−11.8613	+	12.7299i	−0.492937	+	0.529037i
$580$		−	3.77471i		−	0.156736i
$581$	10.8333	+	41.9175i	0.449440	+	1.73903i
$582$	−4.02204	−	13.1366i	−0.166719	−	0.544529i
$583$	−4.93443	−	8.54668i	−0.204363	−	0.353967i
$584$	5.19392	+	8.99614i	0.214926	+	0.372263i
$585$	−8.34650	+	0.494015i	−0.345085	+	0.0204250i
$586$	−6.75511	−	3.90007i	−0.279051	−	0.161110i
$587$	−17.2008	+	29.7927i	−0.709953	+	1.22967i	0.254921	+	0.966962i	$0.417951\pi$
$587$	−17.2008	+	29.7927i	−0.709953	+	1.22967i	−0.964874	+	0.262713i	$0.915383\pi$
$588$	−8.72216	−	8.42163i	−0.359696	−	0.347302i
$589$	−8.74346	−	15.1441i	−0.360268	−	0.624002i
$590$	−7.51418	−	4.33831i	−0.309354	−	0.178605i
$591$	4.88819	−	1.49662i	0.201073	−	0.0615628i
$592$	−2.28416	+	3.95628i	−0.0938785	+	0.162602i
$593$	1.21051	−	2.09667i	0.0497099	−	0.0861000i	−0.840100	−	0.542432i	$-0.817504\pi$
$593$	1.21051	−	2.09667i	0.0497099	−	0.0861000i	0.889810	+	0.456332i	$0.150837\pi$
$594$	2.17996	−	13.8721i	0.0894448	−	0.569178i
$595$	3.86257	−	3.79449i	0.158350	−	0.155559i
$596$	0.346111	+	0.199827i	0.0141773	+	0.00818525i
$597$	−4.63782	+	1.41996i	−0.189813	+	0.0581153i
$598$	0.223268	−	19.4161i	0.00913011	−	0.793983i
$599$	29.8409	−	17.2287i	1.21927	−	0.703944i	0.254506	−	0.967071i	$-0.418087\pi$
$599$	29.8409	−	17.2287i	1.21927	−	0.703944i	0.964761	+	0.263127i	$0.0847539\pi$
$600$	1.71234	−	7.43060i	0.0699060	−	0.303353i
$601$	14.8253	+	8.55938i	0.604736	+	0.349145i	0.770903	−	0.636953i	$-0.219806\pi$
$601$	14.8253	+	8.55938i	0.604736	+	0.349145i	−0.166166	+	0.986098i	$0.553139\pi$
$602$	−8.01120	+	28.8691i	−0.326512	+	1.17662i
$603$	1.46933	+	20.7722i	0.0598358	+	0.845909i
$604$	7.20263			0.293071
$605$	1.42878	−	2.47472i	0.0580881	−	0.100612i
$606$	−3.95441	+	17.1599i	−0.160637	+	0.697075i
$607$			14.6934i			0.596388i	0.954505	+	0.298194i	$0.0963843\pi$
$607$			14.6934i			0.596388i	−0.954505	+	0.298194i	$0.903616\pi$
$608$	−2.33575	+	4.04565i	−0.0947273	+	0.164073i
$609$	−11.6970	−	19.0776i	−0.473988	−	0.773065i
$610$	−10.0623			−0.407411
$611$	−0.218348	+	18.9882i	−0.00883340	+	0.768180i
$612$	−6.58119	+	4.44678i	−0.266029	+	0.179750i
$613$	29.6540			1.19771			0.598857	−	0.800856i	$-0.295622\pi$
$613$	29.6540			1.19771			0.598857	+	0.800856i	$0.295622\pi$
$614$	−0.811535	−	1.40562i	−0.0327509	−	0.0567262i
$615$	−12.7860	−	2.94646i	−0.515581	−	0.118813i
$616$	−1.78908	−	6.92255i	−0.0720842	−	0.278917i
$617$	15.2938	−	8.82986i	0.615704	−	0.355477i	−0.159491	−	0.987199i	$-0.550985\pi$
$617$	15.2938	−	8.82986i	0.615704	−	0.355477i	0.775195	+	0.631723i	$0.217652\pi$
$618$	10.9288	−	11.7292i	0.439622	−	0.471817i
$619$	−21.5803	+	12.4594i	−0.867387	+	0.500786i	−0.866479	−	0.499214i	$-0.833622\pi$
$619$	−21.5803	+	12.4594i	−0.867387	+	0.500786i	−0.000907672		1.00000i	$0.500289\pi$
$620$	2.50586	+	1.44676i	0.100638	+	0.0581033i
$621$	−27.6442	−	4.34420i	−1.10932	−	0.174327i
$622$	26.3252	+	15.1988i	1.05554	+	0.609418i
$623$	−19.5339	+	19.1896i	−0.782607	+	0.768814i
$624$	5.99201	−	1.75948i	0.239873	−	0.0704356i
$625$	−8.19722	+	14.1980i	−0.327889	+	0.567920i
$626$	−4.96512			−0.198446
$627$	14.9063	−	15.9980i	0.595301	−	0.638898i
$628$			12.0957i			0.482672i
$629$	−12.0949			−0.482254
$630$	1.95051	+	5.81707i	0.0777102	+	0.231758i
$631$	4.25946	+	7.37761i	0.169567	+	0.293698i	0.938268	−	0.345910i	$-0.112430\pi$
$631$	4.25946	+	7.37761i	0.169567	+	0.293698i	−0.768701	+	0.639608i	$0.779097\pi$
$632$	8.91380	+	5.14638i	0.354572	+	0.204712i
$633$	−6.66635	−	21.7733i	−0.264963	−	0.865411i
$634$	13.3819			0.531463
$635$	2.80636	+	4.86076i	0.111367	+	0.192893i
$636$	−4.62765	−	4.31188i	−0.183498	−	0.170977i
$637$	−13.2539	+	21.4787i	−0.525139	+	0.851016i
$638$		−	13.1968i		−	0.522467i
$639$	−18.8348	−	27.8754i	−0.745095	−	1.10273i
$640$		−	0.772984i		−	0.0305549i
$641$	17.6989	+	10.2185i	0.699065	+	0.403605i	0.806999	−	0.590553i	$-0.201090\pi$
$641$	17.6989	+	10.2185i	0.699065	+	0.403605i	−0.107934	+	0.994158i	$0.534424\pi$
$642$	0.614403	+	2.00673i	0.0242486	+	0.0791995i
$643$	−28.2804	+	16.3277i	−1.11527	+	0.643902i	−0.940190	−	0.340652i	$-0.889352\pi$
$643$	−28.2804	+	16.3277i	−1.11527	+	0.643902i	−0.175082	+	0.984554i	$0.556019\pi$
$644$	−13.7952	+	3.56527i	−0.543607	+	0.140491i
$645$	10.3352	−	11.0921i	0.406950	−	0.436752i
$646$	−12.3681			−0.486615
$647$	−3.26300			−0.128282			−0.0641410	−	0.997941i	$-0.520431\pi$
$647$	−3.26300			−0.128282			−0.0641410	+	0.997941i	$0.520431\pi$
$648$	−1.26690	−	8.91039i	−0.0497686	−	0.350033i
$649$	−26.2705	−	15.1673i	−1.03121	−	0.595367i
$650$	−15.8724	−	0.182518i	−0.622566	−	0.00715896i
$651$	17.1480	−	0.453129i	0.672084	−	0.0177595i
$652$	−4.72234	+	8.17934i	−0.184941	+	0.320328i
$653$	23.5817	−	13.6149i	0.922822	−	0.532792i	0.0382879	−	0.999267i	$-0.487810\pi$
$653$	23.5817	−	13.6149i	0.922822	−	0.532792i	0.884534	+	0.466475i	$0.154476\pi$
$654$	−12.6876	+	3.88457i	−0.496124	+	0.151899i
$655$	−4.23739	−	7.33938i	−0.165569	−	0.286773i
$656$	9.80028			0.382637
$657$	−17.4472	−	25.8217i	−0.680680	−	1.00740i
$658$	13.4912	−	3.48670i	0.525941	−	0.135926i
$659$	−40.7276	+	23.5141i	−1.58652	+	0.915980i	−0.592650	+	0.805460i	$0.701918\pi$
$659$	−40.7276	+	23.5141i	−1.58652	+	0.915980i	−0.993874	+	0.110520i	$0.964748\pi$
$660$	−0.812491	+	3.52576i	−0.0316262	+	0.137240i
$661$			4.05512i			0.157726i	0.996885	+	0.0788630i	$0.0251290\pi$
$661$			4.05512i			0.157726i	−0.996885	+	0.0788630i	$0.974871\pi$
$662$	25.5607	−	14.7575i	0.993445	−	0.573566i
$663$	11.9663	+	11.4096i	0.464733	+	0.443113i
$664$			16.3639i			0.635043i
$665$	−2.55466	+	9.20593i	−0.0990653	+	0.356991i
$666$	5.99795	−	12.3228i	0.232416	−	0.477498i
$667$	−26.2985			−1.01828
$668$	−9.42868	−	16.3310i	−0.364807	−	0.631864i
$669$	−4.45622	+	1.36436i	−0.172287	+	0.0527493i
$670$		−	5.36557i		−	0.207290i
$671$	−35.1791			−1.35807
$672$	−2.39532	−	3.90672i	−0.0924015	−	0.150705i
$673$	20.5401	−	35.5765i	0.791763	−	1.37137i	−0.133111	−	0.991101i	$-0.542497\pi$
$673$	20.5401	−	35.5765i	0.791763	−	1.37137i	0.924874	−	0.380273i	$-0.124170\pi$
$674$	26.0776	−	15.0559i	1.00447	−	0.579932i
$675$	−3.55132	+	22.5987i	−0.136691	+	0.869824i
$676$	−6.23939	−	11.4048i	−0.239977	−	0.438647i
$677$	−0.255669	+	0.442832i	−0.00982616	+	0.0170194i	−0.870897	−	0.491466i	$-0.836461\pi$
$677$	−0.255669	+	0.442832i	−0.00982616	+	0.0170194i	0.861071	+	0.508486i	$0.169794\pi$
$678$	−5.20639	−	17.0049i	−0.199950	−	0.653068i
$679$	14.7068	+	14.9706i	0.564394	+	0.574520i
$680$	1.77234	−	1.02326i	0.0679660	−	0.0392402i
$681$	−2.67746	−	8.74498i	−0.102600	−	0.335108i
$682$	8.76080	+	5.05805i	0.335468	+	0.193683i
$683$	15.1002	+	8.71812i	0.577794	+	0.333589i	0.760256	−	0.649623i	$-0.225073\pi$
$683$	15.1002	+	8.71812i	0.577794	+	0.333589i	−0.182462	+	0.983213i	$0.558407\pi$
$684$	6.13343	−	12.6011i	0.234517	−	0.481816i
$685$	3.33868	−	1.92759i	0.127564	−	0.0736493i
$686$	17.7550	+	5.26877i	0.677889	+	0.201163i
$687$	−43.8183	+	13.4159i	−1.67177	+	0.511848i
$688$	−5.66191	+	9.80672i	−0.215858	+	0.373878i
$689$	−6.71410	+	11.3264i	−0.255787	+	0.431500i
$690$	7.02610	+	1.61913i	0.267479	+	0.0616391i
$691$	−7.83883	+	4.52575i	−0.298203	+	0.172168i	−0.641635	−	0.767010i	$-0.721744\pi$
$691$	−7.83883	+	4.52575i	−0.298203	+	0.172168i	0.343432	+	0.939177i	$0.388410\pi$
$692$	−6.00907	+	10.4080i	−0.228431	+	0.395653i
$693$	6.81922	+	20.3372i	0.259041	+	0.772545i
$694$	13.4578			0.510852
$695$			0.218647i			0.00829377i
$696$	−2.47617	−	8.08753i	−0.0938588	−	0.306557i
$697$	12.9734	+	22.4706i	0.491402	+	0.851133i
$698$	10.3524			0.391844
$699$	−5.77203	+	1.76723i	−0.218318	+	0.0668427i
$700$	2.91455	+	11.2774i	0.110160	+	0.426245i
$701$			0.299896i			0.0113269i	0.999984	+	0.00566346i	$0.00180274\pi$
$701$			0.299896i			0.0113269i	−0.999984	+	0.00566346i	$0.998197\pi$
$702$	−17.5588	+	6.53366i	−0.662714	+	0.246597i
$703$	18.4818	−	10.6705i	0.697055	−	0.402445i
$704$		−	2.70245i		−	0.101852i
$705$	−6.87126	−	1.58344i	−0.258787	−	0.0596359i
$706$	−25.8963	+	14.9512i	−0.974621	+	0.562698i
$707$	−6.73076	−	26.0435i	−0.253136	−	0.979468i
$708$	−18.9455	−	4.36587i	−0.712014	−	0.164080i
$709$	−35.4700			−1.33210			−0.666052	−	0.745905i	$-0.732017\pi$
$709$	−35.4700			−1.33210			−0.666052	+	0.745905i	$0.732017\pi$
$710$	4.33413	+	7.50694i	0.162657	+	0.281730i
$711$	−27.7641	−	13.5138i	−1.04124	−	0.506808i
$712$	−8.96309	+	5.17484i	−0.335906	+	0.193935i
$713$	10.0796	−	17.4584i	0.377485	−	0.653824i
$714$	5.78664	−	10.6637i	0.216560	−	0.399080i
$715$	7.53131	+	0.0866035i	0.281655	+	0.00323879i
$716$	−11.8611	−	6.84801i	−0.443270	−	0.255922i
$717$	13.9395	+	12.9883i	0.520582	+	0.485059i
$718$	−5.95282			−0.222157
$719$	45.3957			1.69297			0.846487	−	0.532410i	$-0.178713\pi$
$719$	45.3957			1.69297			0.846487	+	0.532410i	$0.178713\pi$
$720$	0.163624	+	2.31317i	0.00609789	+	0.0862069i
$721$	−6.54819	+	23.5970i	−0.243868	+	0.878798i
$722$	2.44478	−	1.41150i	0.0909854	−	0.0525305i
$723$	−3.82879	+	1.17226i	−0.142394	+	0.0435970i
$724$	−11.2930	−	6.52001i	−0.419701	−	0.242314i
$725$			21.4987i			0.798440i
$726$	1.43786	−	6.23949i	0.0533638	−	0.231569i
$727$		−	11.4955i		−	0.426346i	−0.977014	−	0.213173i	$-0.931620\pi$
$727$		−	11.4955i		−	0.426346i	0.977014	−	0.213173i	$-0.0683798\pi$
$728$	−6.88149	+	6.60644i	−0.255045	+	0.244851i
$729$	5.67736	+	26.3964i	0.210273	+	0.977643i
$730$	4.01482	+	6.95387i	0.148595	+	0.257374i
$731$	−29.9804			−1.10887
$732$	−21.5591	+	6.60077i	−0.796847	+	0.243971i
$733$	3.91444	+	2.26000i	0.144583	+	0.0834751i	0.570546	−	0.821265i	$-0.306731\pi$
$733$	3.91444	+	2.26000i	0.144583	+	0.0834751i	−0.425963	+	0.904740i	$0.640065\pi$
$734$	−8.53079	−	14.7758i	−0.314877	−	0.545383i
$735$	−6.74209	−	6.50979i	−0.248686	−	0.240117i
$736$	−5.38541			−0.198509
$737$		−	18.7587i		−	0.690984i
$738$	−29.3276	+	2.07450i	−1.07956	+	0.0763634i
$739$	7.97258			0.293276			0.146638	−	0.989190i	$-0.453155\pi$
$739$	7.97258			0.293276			0.146638	+	0.989190i	$0.453155\pi$
$740$	−1.76562	+	3.05815i	−0.0649055	+	0.112420i
$741$	−28.3513	−	6.87763i	−1.04151	−	0.252656i
$742$	9.31000	+	2.58353i	0.341781	+	0.0948445i
$743$	−18.4735	−	10.6657i	−0.677726	−	0.391285i	0.121272	−	0.992619i	$-0.461303\pi$
$743$	−18.4735	−	10.6657i	−0.677726	−	0.391285i	−0.798998	+	0.601334i	$0.794636\pi$
$744$	6.31802	+	1.45595i	0.231630	+	0.0533778i
$745$	0.267539	+	0.154464i	0.00980186	+	0.00565911i
$746$	−20.4954	+	11.8330i	−0.750388	+	0.433237i
$747$	−3.46387	−	48.9693i	−0.126736	−	1.79169i
$748$	6.19630	−	3.57744i	0.226559	−	0.130804i
$749$	−2.24660	−	2.28690i	−0.0820888	−	0.0835616i
$750$	2.82686	−	12.2670i	0.103222	−	0.447928i
$751$	18.8325	+	32.6189i	0.687209	+	1.19028i	0.972737	+	0.231910i	$0.0744976\pi$
$751$	18.8325	+	32.6189i	0.687209	+	1.19028i	−0.285528	+	0.958370i	$0.592169\pi$
$752$	5.26673			0.192058
$753$	−14.1707	−	3.26557i	−0.516411	−	0.119004i
$754$	−15.3483	+	8.62757i	−0.558952	+	0.314197i
$755$	5.56752			0.202623
$756$	7.99502	+	11.1839i	0.290776	+	0.406755i
$757$	−16.7324	+	28.9814i	−0.608150	+	1.05335i	0.383395	+	0.923584i	$0.374755\pi$
$757$	−16.7324	+	28.9814i	−0.608150	+	1.05335i	−0.991545	+	0.129762i	$0.958579\pi$
$758$			26.5931i			0.965905i
$759$	24.5641	+	5.66066i	0.891620	+	0.205469i
$760$	−1.80550	+	3.12722i	−0.0654924	+	0.113436i
$761$	10.2577			0.371840			0.185920	−	0.982565i	$-0.440473\pi$
$761$	10.2577			0.371840			0.185920	+	0.982565i	$0.440473\pi$
$762$	9.20139	+	8.57352i	0.333331	+	0.310586i
$763$	14.4589	−	14.2041i	0.523449	−	0.514223i
$764$	−1.68042	−	0.970190i	−0.0607954	−	0.0351002i
$765$	−5.08716	+	3.43729i	−0.183926	+	0.124275i
$766$	−13.5406	+	7.81768i	−0.489242	+	0.282464i
$767$	−0.465359	+	40.4691i	−0.0168031	+	1.46125i
$768$	−0.507069	−	1.65616i	−0.0182973	−	0.0597617i
$769$	23.6054	+	13.6286i	0.851232	+	0.491459i	0.861066	−	0.508493i	$-0.169797\pi$
$769$	23.6054	+	13.6286i	0.851232	+	0.491459i	−0.00983428	+	0.999952i	$0.503130\pi$
$770$	−1.38293	−	5.35102i	−0.0498374	−	0.192837i
$771$	41.5912	+	9.58446i	1.49787	+	0.345176i
$772$	5.02278	−	8.69971i	0.180774	−	0.313109i
$773$	19.7527	−	34.2128i	0.710457	−	1.23055i	−0.254229	−	0.967144i	$-0.581822\pi$
$773$	19.7527	−	34.2128i	0.710457	−	1.23055i	0.964686	−	0.263403i	$-0.0848451\pi$
$774$	14.8675	−	30.5453i	0.534403	−	1.09793i
$775$	−14.2720	−	8.23996i	−0.512666	−	0.295988i
$776$	3.96597	+	6.86925i	0.142370	+	0.246592i
$777$	0.552997	+	20.9274i	0.0198386	+	0.750766i
$778$	2.68276	−	4.64668i	0.0961817	−	0.166592i
$779$	−39.6485	−	22.8910i	−1.42055	−	0.820157i
$780$	4.63173	−	1.36005i	0.165843	−	0.0486977i
$781$	15.1526	+	26.2451i	0.542204	+	0.939125i
$782$	−7.12908	−	12.3479i	−0.254935	−	0.441561i
$783$	9.12193	+	23.6780i	0.325991	+	0.846182i
$784$	5.99899	+	3.60723i	0.214250	+	0.128830i
$785$			9.34981i			0.333709i
$786$	−13.8934	−	12.9454i	−0.495562	−	0.461746i
$787$	−22.6916	−	13.1010i	−0.808869	−	0.467001i	0.0376937	−	0.999289i	$-0.487999\pi$
$787$	−22.6916	−	13.1010i	−0.808869	−	0.467001i	−0.846563	+	0.532288i	$0.821332\pi$
$788$	−2.55609	+	1.47576i	−0.0910568	+	0.0525717i
$789$	28.9049	+	26.9325i	1.02904	+	0.958822i
$790$	6.89023	+	3.97807i	0.245143	+	0.141534i
$791$	19.0374	+	19.3790i	0.676893	+	0.689037i
$792$	0.572048	+	8.08713i	0.0203268	+	0.287364i
$793$	22.9987	+	40.9143i	0.816707	+	1.45291i
$794$	−2.90825	−	5.03723i	−0.103210	−	0.178765i
$795$	−3.57710	−	3.33301i	−0.126867	−	0.118210i
$796$	2.42516	−	1.40017i	0.0859576	−	0.0496277i
$797$	−19.9610	−	34.5734i	−0.707054	−	1.22465i	−0.965945	−	0.258747i	$-0.916690\pi$
$797$	−19.9610	−	34.5734i	−0.707054	−	1.22465i	0.258891	−	0.965906i	$-0.416643\pi$
$798$	0.565487	+	21.4001i	0.0200180	+	0.757554i
$799$	6.97197	+	12.0758i	0.246651	+	0.427211i
$800$			4.40250i			0.155652i
$801$	25.7268	−	17.3831i	0.909013	−	0.614202i
$802$	−4.34311	+	7.52248i	−0.153360	+	0.265628i
$803$	14.0363	+	24.3116i	0.495330	+	0.857937i
$804$	−3.51975	−	11.4960i	−0.124132	−	0.405434i
$805$	−10.6635	+	2.75590i	−0.375838	+	0.0971326i
$806$	0.155190	−	13.4958i	0.00546634	−	0.475370i
$807$	−0.927375	−	3.02895i	−0.0326451	−	0.106624i
$808$		−	10.1670i		−	0.357672i
$809$			55.0898i			1.93685i	0.249297	+	0.968427i	$0.419801\pi$
$809$			55.0898i			1.93685i	−0.249297	+	0.968427i	$0.580199\pi$
$810$	−0.979294	−	6.88759i	−0.0344089	−	0.242005i
$811$			7.30412i			0.256482i	0.991743	+	0.128241i	$0.0409331\pi$
$811$			7.30412i			0.256482i	−0.991743	+	0.128241i	$0.959067\pi$
$812$	9.05422	+	9.21666i	0.317741	+	0.323441i
$813$	−2.83889	+	12.3192i	−0.0995643	+	0.432054i
$814$	−6.17282	+	10.6916i	−0.216357	+	0.374742i
$815$	−3.65030	+	6.32250i	−0.127864	+	0.221468i
$816$	3.12609	−	3.35502i	0.109435	−	0.117449i
$817$	45.8122	−	26.4497i	1.60277	−	0.925357i
$818$	−10.0665			−0.351968
$819$	19.1946	−	21.2266i	0.670713	−	0.741717i
$820$	7.57546			0.264547
$821$	−25.4411	+	14.6884i	−0.887901	+	0.512630i	−0.873255	−	0.487263i	$-0.837995\pi$
$821$	−25.4411	+	14.6884i	−0.887901	+	0.512630i	−0.0146455	+	0.999893i	$0.504662\pi$
$822$	5.88884	−	6.32011i	0.205397	−	0.220439i
$823$	6.11227	−	10.5868i	0.213060	−	0.369031i	−0.739611	−	0.673035i	$-0.764990\pi$
$823$	6.11227	−	10.5868i	0.213060	−	0.369031i	0.952671	+	0.304004i	$0.0983236\pi$
$824$	−4.62793	+	8.01582i	−0.161222	+	0.279244i
$825$	4.62751	−	20.0808i	0.161109	−	0.699123i
$826$	28.7534	−	7.43111i	1.00046	−	0.258561i
$827$			30.9380i			1.07582i	0.843003	+	0.537910i	$0.180786\pi$
$827$			30.9380i			1.07582i	−0.843003	+	0.537910i	$0.819214\pi$
$828$	16.1160	−	1.13997i	0.560068	−	0.0396167i
$829$		−	49.0993i		−	1.70529i	−0.522490	−	0.852645i	$-0.674997\pi$
$829$		−	49.0993i		−	1.70529i	0.522490	−	0.852645i	$-0.325003\pi$
$830$			12.6490i			0.439055i
$831$	8.57874	+	28.0195i	0.297593	+	0.971984i
$832$	−3.14302	+	1.76675i	−0.108965	+	0.0612511i
$833$	−0.329518	+	18.5299i	−0.0114171	+	0.642025i
$834$	0.143430	+	0.468465i	0.00496658	+	0.0162216i
$835$	−7.28823	−	12.6236i	−0.252219	−	0.436857i
$836$	−6.31225	+	10.9331i	−0.218314	+	0.378130i
$837$	−19.2150	−	3.01959i	−0.664168	−	0.104372i
$838$			13.7672i			0.475582i
$839$	8.62928	+	14.9464i	0.297916	+	0.516005i	0.975659	−	0.219293i	$-0.0703752\pi$
$839$	8.62928	+	14.9464i	0.297916	+	0.516005i	−0.677743	+	0.735299i	$0.737042\pi$
$840$	−1.85155	−	3.01983i	−0.0638844	−	0.104194i
$841$	−2.57674	−	4.46304i	−0.0888530	−	0.153898i
$842$	−4.55609	+	2.63046i	−0.157013	+	0.0906517i
$843$	−40.0711	−	37.3368i	−1.38012	−	1.28595i
$844$	6.57341	+	11.3855i	0.226266	+	0.391904i
$845$	−4.82295	−	8.81575i	−0.165915	−	0.303271i
$846$	−15.7608	+	1.11485i	−0.541868	+	0.0383293i
$847$	2.44736	+	9.46964i	0.0840922	+	0.325381i
$848$	3.16257	+	1.82591i	0.108603	+	0.0627021i
$849$	0.864409	+	0.805424i	0.0296664	+	0.0276421i
$850$	−10.0943	+	5.82792i	−0.346230	+	0.199896i
$851$	21.3062	+	12.3011i	0.730368	+	0.421678i
$852$	14.2106	+	13.2409i	0.486847	+	0.453626i
$853$			1.10853i			0.0379553i	0.999820	+	0.0189776i	$0.00604113\pi$
$853$			1.10853i			0.0379553i	−0.999820	+	0.0189776i	$0.993959\pi$
$854$	24.5690	−	24.1360i	0.840735	−	0.825918i
$855$	4.74104	−	9.74046i	0.162140	−	0.333117i
$856$	−0.605838	−	1.04934i	−0.0207071	−	0.0358658i
$857$	−17.4478	−	30.2204i	−0.596005	−	1.03231i	−0.993404	−	0.114665i	$-0.963421\pi$
$857$	−17.4478	−	30.2204i	−0.596005	−	1.03231i	0.397399	−	0.917646i	$-0.369913\pi$
$858$	16.1931	−	4.75490i	0.552823	−	0.162330i
$859$	−17.5635	−	10.1403i	−0.599259	−	0.345982i	0.169491	−	0.985532i	$-0.445788\pi$
$859$	−17.5635	−	10.1403i	−0.599259	−	0.345982i	−0.768750	+	0.639550i	$0.779121\pi$
$860$	−4.37657	+	7.58044i	−0.149240	+	0.258491i
$861$	38.2869	−	23.4748i	1.30481	−	0.800020i
$862$	11.0492	+	19.1377i	0.376336	+	0.651833i
$863$	−36.5693	−	21.1133i	−1.24484	−	0.718706i	−0.274760	−	0.961513i	$-0.588599\pi$
$863$	−36.5693	−	21.1133i	−1.24484	−	0.718706i	−0.970075	+	0.242807i	$0.921932\pi$
$864$	1.86799	+	4.84877i	0.0635503	+	0.164959i
$865$	−4.64492	+	8.04523i	−0.157932	+	0.273546i
$866$	−0.403262	+	0.698470i	−0.0137034	+	0.0237350i
$867$	−16.8621	−	3.88577i	−0.572665	−	0.131968i
$868$	−9.58882	+	2.47816i	−0.325466	+	0.0841143i
$869$	24.0891	+	13.9078i	0.817165	+	0.471791i
$870$	−1.91404	−	6.25154i	−0.0648919	−	0.211947i
$871$	−21.8169	+	12.2637i	−0.739236	+	0.415539i
$872$	6.63447	−	3.83041i	0.224671	−	0.129714i
$873$	−13.3223	−	19.7169i	−0.450892	−	0.667316i
$874$	21.7875	+	12.5790i	0.736972	+	0.425491i
$875$	4.81157	+	18.6176i	0.162661	+	0.629389i
$876$	13.1637	+	12.2654i	0.444759	+	0.414410i
$877$	19.6485			0.663484			0.331742	−	0.943370i	$-0.392364\pi$
$877$	19.6485			0.663484			0.331742	+	0.943370i	$0.392364\pi$
$878$	11.0564	−	19.1502i	0.373134	−	0.646287i
$879$	−13.1652	−	3.03384i	−0.444051	−	0.102329i
$880$		−	2.08895i		−	0.0704184i
$881$	3.68778	−	6.38743i	0.124245	−	0.215198i	−0.797193	−	0.603725i	$-0.793683\pi$
$881$	3.68778	−	6.38743i	0.124245	−	0.215198i	0.921437	+	0.388527i	$0.127016\pi$
$882$	−18.7157	−	9.52488i	−0.630190	−	0.320719i
$883$	40.9675			1.37867			0.689333	−	0.724445i	$-0.257904\pi$
$883$	40.9675			1.37867			0.689333	+	0.724445i	$0.257904\pi$
$884$	−8.21156	−	4.86769i	−0.276184	−	0.163718i
$885$	−14.6445	−	3.37475i	−0.492271	−	0.113441i
$886$	−26.5115			−0.890672
$887$	−11.1082	−	19.2399i	−0.372976	−	0.646014i	0.617045	−	0.786927i	$-0.288329\pi$
$887$	−11.1082	−	19.2399i	−0.372976	−	0.646014i	−0.990022	+	0.140913i	$0.954996\pi$
$888$	−1.77684	+	7.71048i	−0.0596268	+	0.258747i
$889$	−18.5115	−	5.13697i	−0.620857	−	0.172288i
$890$	−6.92833	+	4.00007i	−0.232238	+	0.134083i
$891$	−3.42373	−	24.0798i	−0.114699	−	0.806705i
$892$	2.33020	−	1.34534i	0.0780209	−	0.0450454i
$893$	−21.3073	−	12.3018i	−0.713022	−	0.411663i
$894$	0.674544	+	0.155445i	0.0225601	+	0.00519885i
$895$	−9.16845	−	5.29341i	−0.306467	−	0.176939i
$896$	1.85412	+	1.88739i	0.0619419	+	0.0630532i
$897$	−9.47553	−	32.2695i	−0.316379	−	1.07745i
$898$	18.8011	−	32.5645i	0.627401	−	1.08669i
$899$	−18.2797			−0.609662
$900$	−0.931910	−	13.1746i	−0.0310637	−	0.439152i
$901$			9.66840i			0.322101i
$902$	26.4847			0.881845
$903$	1.37075	+	51.8742i	0.0456158	+	1.72627i
$904$	5.13381	+	8.89202i	0.170748	+	0.295744i
$905$	−8.72930	−	5.03986i	−0.290172	−	0.167531i
$906$	11.9287	−	3.65223i	0.396306	−	0.121337i
$907$	−42.1902			−1.40090			−0.700452	−	0.713700i	$-0.747018\pi$
$907$	−42.1902			−1.40090			−0.700452	+	0.713700i	$0.747018\pi$
$908$	2.64013	+	4.57284i	0.0876158	+	0.151755i
$909$	2.15212	+	30.4249i	0.0713813	+	1.00913i
$910$	−5.31928	+	5.10668i	−0.176333	+	0.169285i
$911$			22.5763i			0.747985i	0.927432	+	0.373992i	$0.122011\pi$
$911$			22.5763i			0.747985i	−0.927432	+	0.373992i	$0.877989\pi$
$912$	−1.81697	+	7.88464i	−0.0601660	+	0.261087i
$913$			44.2226i			1.46355i
$914$	16.5464	+	9.55304i	0.547305	+	0.315987i
$915$	−16.6649	+	5.10229i	−0.550923	+	0.168677i
$916$	22.9130	−	13.2288i	0.757068	−	0.437093i
$917$	27.9510	+	7.75644i	0.923025	+	0.256140i
$918$	−8.64471	+	10.7017i	−0.285318	+	0.353209i
$919$	10.0764			0.332389			0.166195	−	0.986093i	$-0.446852\pi$
$919$	10.0764			0.332389			0.166195	+	0.986093i	$0.446852\pi$
$920$	−4.16284			−0.137245
$921$	−2.05678	−	1.91643i	−0.0677733	−	0.0631486i
$922$	3.71257	+	2.14345i	0.122267	+	0.0705909i
$923$	20.6176	−	34.7810i	0.678638	−	1.14483i
$924$	−6.47323	−	10.5577i	−0.212953	−	0.347323i
$925$	10.0560	−	17.4175i	0.330640	−	0.572685i
$926$	−26.4662	+	15.2803i	−0.869733	+	0.502141i
$927$	12.1524	−	24.9671i	0.399138	−	0.820029i
$928$	2.44165	+	4.22905i	0.0801509	+	0.138825i
$929$	7.56797			0.248297			0.124149	−	0.992264i	$-0.460380\pi$
$929$	7.56797			0.248297			0.124149	+	0.992264i	$0.460380\pi$
$930$	4.88373	+	1.12543i	0.160144	+	0.0369043i
$931$	−15.8442	−	28.6057i	−0.519272	−	0.937516i
$932$	3.01825	−	1.74259i	0.0988662	−	0.0570804i
$933$	51.3057	+	11.8231i	1.67967	+	0.387071i
$934$			19.3064i			0.631726i
$935$	4.78964	−	2.76530i	0.156638	−	0.0904350i
$936$	9.03158	−	5.95236i	0.295206	−	0.194559i
$937$			47.8920i			1.56456i	0.622925	+	0.782282i	$0.285944\pi$
$937$			47.8920i			1.56456i	−0.622925	+	0.782282i	$0.714056\pi$
$938$	12.8701	+	13.1010i	0.420225	+	0.427764i
$939$	−8.22306	+	2.51766i	−0.268349	+	0.0821607i
$940$	4.07110			0.132785
$941$	−7.73208	−	13.3924i	−0.252059	−	0.436578i	0.712034	−	0.702145i	$-0.247774\pi$
$941$	−7.73208	−	13.3924i	−0.252059	−	0.436578i	−0.964092	+	0.265567i	$0.914441\pi$
$942$	6.13337	+	20.0325i	0.199836	+	0.652694i
$943$		−	52.7785i		−	1.71871i
$944$	11.2248			0.365337
$945$	6.18002	+	8.64498i	0.201036	+	0.281221i
$946$	−15.3010	+	26.5021i	−0.497479	+	0.861659i
$947$	3.97730	−	2.29629i	0.129245	−	0.0746196i	−0.433984	−	0.900921i	$-0.642892\pi$
$947$	3.97730	−	2.29629i	0.129245	−	0.0746196i	0.563228	+	0.826301i	$0.309559\pi$
$948$	17.3723	+	4.00335i	0.564226	+	0.130023i
$949$	19.0987	−	32.2186i	0.619969	−	1.04586i
$950$	10.2831	−	17.8109i	0.333629	−	0.577863i
$951$	22.1626	−	6.78554i	0.718672	−	0.220036i
$952$	−1.87305	+	6.74970i	−0.0607059	+	0.218759i
$953$	−45.1678	+	26.0776i	−1.46313	+	0.844737i	−0.999155	−	0.0411118i	$-0.986910\pi$
$953$	−45.1678	+	26.0776i	−1.46313	+	0.844737i	−0.463973	+	0.885849i	$0.653577\pi$
$954$	−9.85057	−	4.79464i	−0.318924	−	0.155232i
$955$	−1.29894	−	0.749942i	−0.0420326	−	0.0242675i
$956$	−9.52638	−	5.50006i	−0.308105	−	0.177885i
$957$	−6.69170	−	21.8561i	−0.216312	−	0.706508i
$958$	−32.5686	+	18.8035i	−1.05224	+	0.607512i
$959$	−3.52840	+	12.7149i	−0.113938	+	0.410586i
$960$	−0.391956	−	1.28019i	−0.0126503	−	0.0413179i
$961$	−8.49380	+	14.7117i	−0.273994	+	0.474571i
$962$	16.4702	+	0.189393i	0.531022	+	0.00610628i
$963$	2.03511	+	3.01194i	0.0655804	+	0.0970583i
$964$	2.00211	−	1.15592i	0.0644837	−	0.0372297i
$965$	3.88253	−	6.72474i	0.124983	−	0.216477i
$966$	−21.0393	+	12.8998i	−0.676928	+	0.415044i
$967$	54.0463			1.73801			0.869006	−	0.494802i	$-0.164759\pi$
$967$	54.0463			1.73801			0.869006	+	0.494802i	$0.164759\pi$
$968$			3.69679i			0.118819i
$969$	−20.4836	+	6.27147i	−0.658027	+	0.201468i
$970$	3.06563	+	5.30983i	0.0984314	+	0.170488i
$971$	−38.2786			−1.22842			−0.614209	−	0.789143i	$-0.710525\pi$
$971$	−38.2786			−1.22842			−0.614209	+	0.789143i	$0.710525\pi$
$972$	−6.61638	−	14.1147i	−0.212220	−	0.452728i
$973$	−0.524459	−	0.533869i	−0.0168134	−	0.0171150i
$974$			35.0418i			1.12281i
$975$	−26.3798	+	7.74611i	−0.844830	+	0.248074i
$976$	11.2735	−	6.50875i	0.360855	−	0.208340i
$977$		−	48.6766i		−	1.55730i	−0.627458	−	0.778651i	$-0.715905\pi$
$977$		−	48.6766i		−	1.55730i	0.627458	−	0.778651i	$-0.284095\pi$
$978$	−3.67349	+	15.9409i	−0.117465	+	0.509733i
$979$	−24.2223	+	13.9847i	−0.774147	+	0.446954i
$980$	4.63712	+	2.78834i	0.148128	+	0.0890701i
$981$	−19.0430	+	12.8670i	−0.607995	+	0.410810i
$982$	−24.4859			−0.781375
$983$	−10.2329	−	17.7240i	−0.326380	−	0.565307i	0.655411	−	0.755273i	$-0.272496\pi$
$983$	−10.2329	−	17.7240i	−0.326380	−	0.565307i	−0.981791	+	0.189966i	$0.939162\pi$
$984$	16.2309	−	4.96942i	0.517422	−	0.158419i
$985$	−1.97582	+	1.14074i	−0.0629547	+	0.0363469i
$986$	−6.46439	+	11.1966i	−0.205868	+	0.356574i
$987$	20.5756	−	12.6155i	0.654929	−	0.401556i
$988$	16.8423	+	0.193671i	0.535823	+	0.00616150i
$989$	52.8132	+	30.4917i	1.67936	+	0.969581i
$990$	0.442184	+	6.25123i	0.0140535	+	0.198677i
$991$	−38.6798			−1.22870			−0.614352	−	0.789032i	$-0.710583\pi$
$991$	−38.6798			−1.22870			−0.614352	+	0.789032i	$0.710583\pi$
$992$	−3.74331			−0.118850
$993$	34.8497	−	37.4019i	1.10592	−	1.18691i
$994$	−28.5891	−	7.93352i	−0.906792	−	0.251636i
$995$	1.87461	−	1.08231i	0.0594292	−	0.0343115i
$996$	8.29763	+	27.1013i	0.262920	+	0.858738i
$997$	2.45283	+	1.41614i	0.0776819	+	0.0448497i	0.538338	−	0.842729i	$-0.319052\pi$
$997$	2.45283	+	1.41614i	0.0776819	+	0.0448497i	−0.460656	+	0.887579i	$0.652386\pi$
$998$			19.8967i			0.629820i
$999$	3.68509	−	23.4499i	0.116591	−	0.741923i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.u.a.425.6	yes	76
3.2	odd	2	inner	546.2.u.a.425.33	yes	76
7.3	odd	6		546.2.bb.a.269.1	yes	76
13.3	even	3		546.2.bb.a.341.8	yes	76
21.17	even	6		546.2.bb.a.269.27	yes	76
39.29	odd	6		546.2.bb.a.341.20	yes	76
91.3	odd	6	inner	546.2.u.a.185.33	yes	76
273.185	even	6	inner	546.2.u.a.185.6	✓	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.u.a.185.6	✓	76	273.185	even	6	inner
546.2.u.a.185.33	yes	76	91.3	odd	6	inner
546.2.u.a.425.6	yes	76	1.1	even	1	trivial
546.2.u.a.425.33	yes	76	3.2	odd	2	inner
546.2.bb.a.269.1	yes	76	7.3	odd	6
546.2.bb.a.269.27	yes	76	21.17	even	6
546.2.bb.a.341.8	yes	76	13.3	even	3
546.2.bb.a.341.20	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)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-1.18075 + 1.26722i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.386492 - 0.669424i) q^{5} +(0.388948 - 1.68782i) q^{6} +(0.662023 + 2.56159i) q^{7} +1.00000i q^{8} +(-0.211678 - 2.99252i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-1.18075 + 1.26722i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.386492 - 0.669424i) q^{5} +(0.388948 - 1.68782i) q^{6} +(0.662023 + 2.56159i) q^{7} +1.00000i q^{8} +(-0.211678 - 2.99252i) q^{9} +0.772984i q^{10} +2.70245i q^{11} +(0.507069 + 1.65616i) q^{12} +(3.14302 - 1.76675i) q^{13} +(-1.85412 - 1.88739i) q^{14} +(0.391956 + 1.28019i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.32378 - 2.29285i) q^{17} +(1.67958 + 2.48576i) q^{18} +4.67151i q^{19} +(-0.386492 - 0.669424i) q^{20} +(-4.02777 - 2.18566i) q^{21} +(-1.35122 - 2.34039i) q^{22} +(-4.66390 + 2.69271i) q^{23} +(-1.26722 - 1.18075i) q^{24} +(2.20125 + 3.81267i) q^{25} +(-1.83856 + 3.10156i) q^{26} +(4.04211 + 3.26517i) q^{27} +(2.54941 + 0.707464i) q^{28} +(4.22905 + 2.44165i) q^{29} +(-0.979539 - 0.912698i) q^{30} +(-3.24180 + 1.87166i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-3.42459 - 3.19090i) q^{33} +2.64755i q^{34} +(1.97065 + 0.546859i) q^{35} +(-2.69744 - 1.31294i) q^{36} +(-2.28416 - 3.95628i) q^{37} +(-2.33575 - 4.04565i) q^{38} +(-1.47225 + 6.06898i) q^{39} +(0.669424 + 0.386492i) q^{40} +(-4.90014 + 8.48729i) q^{41} +(4.58098 - 0.121050i) q^{42} +(-5.66191 - 9.80672i) q^{43} +(2.34039 + 1.35122i) q^{44} +(-2.08508 - 1.01488i) q^{45} +(2.69271 - 4.66390i) q^{46} +(-2.63336 + 4.56112i) q^{47} +(1.68782 + 0.388948i) q^{48} +(-6.12345 + 3.39166i) q^{49} +(-3.81267 - 2.20125i) q^{50} +(1.34249 + 4.38478i) q^{51} +(0.0414579 - 3.60531i) q^{52} +(-3.16257 + 1.82591i) q^{53} +(-5.13316 - 0.806662i) q^{54} +(1.80908 + 1.04447i) q^{55} +(-2.56159 + 0.662023i) q^{56} +(-5.91981 - 5.51587i) q^{57} -4.88329 q^{58} +(-5.61242 + 9.72100i) q^{59} +(1.30465 + 0.300650i) q^{60} +13.0175i q^{61} +(1.87166 - 3.24180i) q^{62} +(7.52547 - 2.52335i) q^{63} -1.00000 q^{64} +(0.0320463 - 2.78685i) q^{65} +(4.56123 + 1.05111i) q^{66} -6.94137 q^{67} +(-1.32378 - 2.29285i) q^{68} +(2.09464 - 9.08958i) q^{69} +(-1.98007 + 0.511734i) q^{70} +(9.71163 - 5.60701i) q^{71} +(2.99252 - 0.211678i) q^{72} +(8.99614 - 5.19392i) q^{73} +(3.95628 + 2.28416i) q^{74} +(-7.43060 - 1.71234i) q^{75} +(4.04565 + 2.33575i) q^{76} +(-6.92255 + 1.78908i) q^{77} +(-1.75948 - 5.99201i) q^{78} +(5.14638 - 8.91380i) q^{79} -0.772984 q^{80} +(-8.91039 + 1.26690i) q^{81} -9.80028i q^{82} +16.3639 q^{83} +(-3.90672 + 2.39532i) q^{84} +(-1.02326 - 1.77234i) q^{85} +(9.80672 + 5.66191i) q^{86} +(-8.08753 + 2.47617i) q^{87} -2.70245 q^{88} +(5.17484 + 8.96309i) q^{89} +(2.31317 - 0.163624i) q^{90} +(6.60644 + 6.88149i) q^{91} +5.38541i q^{92} +(1.45595 - 6.31802i) q^{93} -5.26673i q^{94} +(3.12722 + 1.80550i) q^{95} +(-1.65616 + 0.507069i) q^{96} +(6.86925 - 3.96597i) q^{97} +(3.60723 - 5.99899i) q^{98} +(8.08713 - 0.572048i) 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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