LMFDB - Embedded newform 546.2.u.a.185.12

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			185.12
Character	$\chi$	$=$	546.185
Dual form			546.2.u.a.425.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.696855 + 1.58568i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.42622 - 2.47029i) q^{5} +(0.189348 - 1.72167i) q^{6} +(2.54641 + 0.718201i) q^{7} -1.00000i q^{8} +(-2.02879 + 2.20998i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.696855 + 1.58568i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.42622 - 2.47029i) q^{5} +(0.189348 - 1.72167i) q^{6} +(2.54641 + 0.718201i) q^{7} -1.00000i q^{8} +(-2.02879 + 2.20998i) q^{9} +2.85245i q^{10} -2.06166i q^{11} +(-1.02481 + 1.39634i) q^{12} +(3.41477 - 1.15729i) q^{13} +(-1.84615 - 1.89518i) q^{14} +(2.92323 - 3.98298i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.04280 + 3.53824i) q^{17} +(2.86197 - 0.899509i) q^{18} -4.34067i q^{19} +(1.42622 - 2.47029i) q^{20} +(0.635636 + 4.53828i) q^{21} +(-1.03083 + 1.78545i) q^{22} +(1.19354 + 0.689091i) q^{23} +(1.58568 - 0.696855i) q^{24} +(-1.56823 + 2.71626i) q^{25} +(-3.53593 - 0.705144i) q^{26} +(-4.91811 - 1.67697i) q^{27} +(0.651223 + 2.56435i) q^{28} +(6.75519 - 3.90011i) q^{29} +(-4.52308 + 1.98774i) q^{30} +(2.44780 + 1.41324i) q^{31} +(0.866025 - 0.500000i) q^{32} +(3.26914 - 1.43668i) q^{33} -4.08561i q^{34} +(-1.85758 - 7.31469i) q^{35} +(-2.92829 - 0.651988i) q^{36} +(3.17853 - 5.50538i) q^{37} +(-2.17033 + 3.75913i) q^{38} +(4.21470 + 4.60829i) q^{39} +(-2.47029 + 1.42622i) q^{40} +(3.55429 + 6.15620i) q^{41} +(1.71866 - 4.24808i) q^{42} +(-5.02540 + 8.70425i) q^{43} +(1.78545 - 1.03083i) q^{44} +(8.35281 + 1.85976i) q^{45} +(-0.689091 - 1.19354i) q^{46} +(3.65196 + 6.32538i) q^{47} +(-1.72167 - 0.189348i) q^{48} +(5.96837 + 3.65767i) q^{49} +(2.71626 - 1.56823i) q^{50} +(-4.18699 + 5.70488i) q^{51} +(2.70963 + 2.37864i) q^{52} +(5.80600 + 3.35210i) q^{53} +(3.42072 + 3.91135i) q^{54} +(-5.09290 + 2.94039i) q^{55} +(0.718201 - 2.54641i) q^{56} +(6.88293 - 3.02482i) q^{57} -7.80022 q^{58} +(-5.42203 - 9.39123i) q^{59} +(4.91098 + 0.540104i) q^{60} -3.94023i q^{61} +(-1.41324 - 2.44780i) q^{62} +(-6.75333 + 4.17044i) q^{63} -1.00000 q^{64} +(-7.72908 - 6.78494i) q^{65} +(-3.54950 - 0.390370i) q^{66} +12.9299 q^{67} +(-2.04280 + 3.53824i) q^{68} +(-0.260955 + 2.37277i) q^{69} +(-2.04863 + 7.26350i) q^{70} +(-5.66543 - 3.27094i) q^{71} +(2.20998 + 2.02879i) q^{72} +(2.16906 + 1.25231i) q^{73} +(-5.50538 + 3.17853i) q^{74} +(-5.39996 - 0.593882i) q^{75} +(3.75913 - 2.17033i) q^{76} +(1.48069 - 5.24982i) q^{77} +(-1.34589 - 6.09824i) q^{78} +(-7.08737 - 12.2757i) q^{79} +2.85245 q^{80} +(-0.768056 - 8.96717i) q^{81} -7.10857i q^{82} -10.2916 q^{83} +(-3.61245 + 2.81962i) q^{84} +(5.82700 - 10.0927i) q^{85} +(8.70425 - 5.02540i) q^{86} +(10.8917 + 7.99379i) q^{87} -2.06166 q^{88} +(-3.01547 + 5.22295i) q^{89} +(-6.30387 - 5.78701i) q^{90} +(9.52657 - 0.494437i) q^{91} +1.37818i q^{92} +(-0.535186 + 4.86626i) q^{93} -7.30392i q^{94} +(-10.7227 + 6.19077i) q^{95} +(1.39634 + 1.02481i) q^{96} +(-15.8274 - 9.13794i) q^{97} +(-3.33993 - 6.15182i) q^{98} +(4.55623 + 4.18267i) 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 $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

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

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
$3$	0.696855	+	1.58568i	0.402329	+	0.915495i
$3$	0.696855	+	1.58568i	0.402329	+	0.915495i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−1.42622	−	2.47029i	−0.637827	−	1.10475i	−0.985909	−	0.167285i	$-0.946500\pi$
$5$	−1.42622	−	2.47029i	−0.637827	−	1.10475i	0.348082	−	0.937464i	$-0.386833\pi$
$6$	0.189348	−	1.72167i	0.0773009	−	0.702869i
$7$	2.54641	+	0.718201i	0.962451	+	0.271455i
$7$	2.54641	+	0.718201i	0.962451	+	0.271455i
$8$		−	1.00000i		−	0.353553i
$9$	−2.02879	+	2.20998i	−0.676262	+	0.736661i
$10$			2.85245i			0.902024i
$11$		−	2.06166i		−	0.621614i	−0.950473	−	0.310807i	$-0.899401\pi$
$11$		−	2.06166i		−	0.621614i	0.950473	−	0.310807i	$-0.100599\pi$
$12$	−1.02481	+	1.39634i	−0.295839	+	0.403088i
$13$	3.41477	−	1.15729i	0.947088	−	0.320975i
$13$	3.41477	−	1.15729i	0.947088	−	0.320975i
$14$	−1.84615	−	1.89518i	−0.493405	−	0.506509i
$15$	2.92323	−	3.98298i	0.754775	−	1.02840i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.04280	+	3.53824i	0.495453	+	0.858150i	0.999986	−	0.00524255i	$-0.00166876\pi$
$17$	2.04280	+	3.53824i	0.495453	+	0.858150i	−0.504533	+	0.863392i	$0.668335\pi$
$18$	2.86197	−	0.899509i	0.674573	−	0.212016i
$19$		−	4.34067i		−	0.995817i	−0.867229	−	0.497909i	$-0.834101\pi$
$19$		−	4.34067i		−	0.995817i	0.867229	−	0.497909i	$-0.165899\pi$
$20$	1.42622	−	2.47029i	0.318913	−	0.552374i
$21$	0.635636	+	4.53828i	0.138707	+	0.990333i
$22$	−1.03083	+	1.78545i	−0.219774	+	0.380659i
$23$	1.19354	+	0.689091i	0.248870	+	0.143685i	0.619247	−	0.785196i	$-0.287438\pi$
$23$	1.19354	+	0.689091i	0.248870	+	0.143685i	−0.370377	+	0.928882i	$0.620771\pi$
$24$	1.58568	−	0.696855i	0.323676	−	0.142245i
$25$	−1.56823	+	2.71626i	−0.313647	+	0.543252i
$26$	−3.53593	−	0.705144i	−0.693452	−	0.138290i
$27$	−4.91811	−	1.67697i	−0.946490	−	0.322734i
$28$	0.651223	+	2.56435i	0.123070	+	0.484617i
$29$	6.75519	−	3.90011i	1.25441	−	0.724233i	0.282426	−	0.959289i	$-0.408861\pi$
$29$	6.75519	−	3.90011i	1.25441	−	0.724233i	0.971982	+	0.235056i	$0.0755275\pi$
$30$	−4.52308	+	1.98774i	−0.825798	+	0.362911i
$31$	2.44780	+	1.41324i	0.439638	+	0.253825i	0.703444	−	0.710751i	$-0.251645\pi$
$31$	2.44780	+	1.41324i	0.439638	+	0.253825i	−0.263806	+	0.964576i	$0.584978\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	3.26914	−	1.43668i	0.569084	−	0.250094i
$34$		−	4.08561i		−	0.700676i
$35$	−1.85758	−	7.31469i	−0.313988	−	1.23641i
$36$	−2.92829	−	0.651988i	−0.488049	−	0.108665i
$37$	3.17853	−	5.50538i	0.522547	−	0.905078i	−0.477109	−	0.878844i	$-0.658315\pi$
$37$	3.17853	−	5.50538i	0.522547	−	0.905078i	0.999656	−	0.0262341i	$-0.00835152\pi$
$38$	−2.17033	+	3.75913i	−0.352075	+	0.609811i
$39$	4.21470	+	4.60829i	0.674892	+	0.737916i
$40$	−2.47029	+	1.42622i	−0.390588	+	0.225506i
$41$	3.55429	+	6.15620i	0.555086	+	0.961438i	0.997897	+	0.0648225i	$0.0206481\pi$
$41$	3.55429	+	6.15620i	0.555086	+	0.961438i	−0.442811	+	0.896615i	$0.646019\pi$
$42$	1.71866	−	4.24808i	0.265195	−	0.655493i
$43$	−5.02540	+	8.70425i	−0.766367	+	1.32739i	0.173155	+	0.984895i	$0.444604\pi$
$43$	−5.02540	+	8.70425i	−0.766367	+	1.32739i	−0.939521	+	0.342491i	$0.888729\pi$
$44$	1.78545	−	1.03083i	0.269167	−	0.155403i
$45$	8.35281	+	1.85976i	1.24516	+	0.277237i
$46$	−0.689091	−	1.19354i	−0.101601	−	0.175978i
$47$	3.65196	+	6.32538i	0.532693	+	0.922652i	0.999271	+	0.0381719i	$0.0121534\pi$
$47$	3.65196	+	6.32538i	0.532693	+	0.922652i	−0.466578	+	0.884480i	$0.654513\pi$
$48$	−1.72167	−	0.189348i	−0.248502	−	0.0273300i
$49$	5.96837	+	3.65767i	0.852625	+	0.522524i
$50$	2.71626	−	1.56823i	0.384137	−	0.221782i
$51$	−4.18699	+	5.70488i	−0.586296	+	0.798844i
$52$	2.70963	+	2.37864i	0.375758	+	0.329857i
$53$	5.80600	+	3.35210i	0.797516	+	0.460446i	0.842602	−	0.538537i	$-0.181023\pi$
$53$	5.80600	+	3.35210i	0.797516	+	0.460446i	−0.0450859	+	0.998983i	$0.514356\pi$
$54$	3.42072	+	3.91135i	0.465501	+	0.532268i
$55$	−5.09290	+	2.94039i	−0.686727	+	0.396482i
$56$	0.718201	−	2.54641i	0.0959737	−	0.340278i
$57$	6.88293	−	3.02482i	0.911666	−	0.400647i
$58$	−7.80022			−1.02422
$59$	−5.42203	−	9.39123i	−0.705888	−	1.22263i	−0.966370	−	0.257156i	$-0.917215\pi$
$59$	−5.42203	−	9.39123i	−0.705888	−	1.22263i	0.260482	−	0.965479i	$-0.416119\pi$
$60$	4.91098	+	0.540104i	0.634004	+	0.0697272i
$61$		−	3.94023i		−	0.504495i	−0.967663	−	0.252247i	$-0.918830\pi$
$61$		−	3.94023i		−	0.504495i	0.967663	−	0.252247i	$-0.0811697\pi$
$62$	−1.41324	−	2.44780i	−0.179481	−	0.310871i
$63$	−6.75333	+	4.17044i	−0.850839	+	0.525426i
$64$	−1.00000			−0.125000
$65$	−7.72908	−	6.78494i	−0.958675	−	0.841568i
$66$	−3.54950	−	0.390370i	−0.436913	−	0.0480513i
$67$	12.9299			1.57964			0.789820	−	0.613339i	$-0.210174\pi$
$67$	12.9299			1.57964			0.789820	+	0.613339i	$0.210174\pi$
$68$	−2.04280	+	3.53824i	−0.247726	+	0.429075i
$69$	−0.260955	+	2.37277i	−0.0314153	+	0.285648i
$70$	−2.04863	+	7.26350i	−0.244858	+	0.868154i
$71$	−5.66543	−	3.27094i	−0.672362	−	0.388189i	0.124609	−	0.992206i	$-0.460232\pi$
$71$	−5.66543	−	3.27094i	−0.672362	−	0.388189i	−0.796971	+	0.604017i	$0.793566\pi$
$72$	2.20998	+	2.02879i	0.260449	+	0.239095i
$73$	2.16906	+	1.25231i	0.253869	+	0.146571i	0.621535	−	0.783387i	$-0.286510\pi$
$73$	2.16906	+	1.25231i	0.253869	+	0.146571i	−0.367666	+	0.929958i	$0.619843\pi$
$74$	−5.50538	+	3.17853i	−0.639987	+	0.369497i
$75$	−5.39996	−	0.593882i	−0.623533	−	0.0685756i
$76$	3.75913	−	2.17033i	0.431202	−	0.248954i
$77$	1.48069	−	5.24982i	0.168740	−	0.598273i
$78$	−1.34589	−	6.09824i	−0.152392	−	0.690490i
$79$	−7.08737	−	12.2757i	−0.797391	−	1.38112i	−0.921310	−	0.388829i	$-0.872880\pi$
$79$	−7.08737	−	12.2757i	−0.797391	−	1.38112i	0.123919	−	0.992292i	$-0.460454\pi$
$80$	2.85245			0.318913
$81$	−0.768056	−	8.96717i	−0.0853395	−	0.996352i
$82$		−	7.10857i		−	0.785011i
$83$	−10.2916			−1.12965			−0.564825	−	0.825211i	$-0.691056\pi$
$83$	−10.2916			−1.12965			−0.564825	+	0.825211i	$0.691056\pi$
$84$	−3.61245	+	2.81962i	−0.394150	+	0.307645i
$85$	5.82700	−	10.0927i	0.632027	−	1.09470i
$86$	8.70425	−	5.02540i	0.938603	−	0.541903i
$87$	10.8917	+	7.99379i	1.16772	+	0.857024i
$88$	−2.06166			−0.219774
$89$	−3.01547	+	5.22295i	−0.319639	+	0.553632i	−0.980413	−	0.196954i	$-0.936895\pi$
$89$	−3.01547	+	5.22295i	−0.319639	+	0.553632i	0.660773	+	0.750586i	$0.270228\pi$
$90$	−6.30387	−	5.78701i	−0.664486	−	0.610004i
$91$	9.52657	−	0.494437i	0.998656	−	0.0518311i
$92$			1.37818i			0.143685i
$93$	−0.535186	+	4.86626i	−0.0554963	+	0.504607i
$94$		−	7.30392i		−	0.753342i
$95$	−10.7227	+	6.19077i	−1.10013	+	0.635159i
$96$	1.39634	+	1.02481i	0.142513	+	0.104595i
$97$	−15.8274	−	9.13794i	−1.60703	−	0.927817i	−0.990031	−	0.140850i	$-0.955016\pi$
$97$	−15.8274	−	9.13794i	−1.60703	−	0.927817i	−0.616995	−	0.786967i	$-0.711650\pi$
$98$	−3.33993	−	6.15182i	−0.337384	−	0.621427i
$99$	4.55623	+	4.18267i	0.457919	+	0.420374i
$100$	−3.13647			−0.313647
$101$	−10.9459			−1.08915			−0.544577	−	0.838711i	$-0.683310\pi$
$101$	−10.9459			−1.08915			−0.544577	+	0.838711i	$0.683310\pi$
$102$	6.47848	−	2.84708i	0.641466	−	0.281903i
$103$	−2.40226	+	1.38694i	−0.236701	+	0.136660i	−0.613660	−	0.789571i	$-0.710303\pi$
$103$	−2.40226	+	1.38694i	−0.236701	+	0.136660i	0.376958	+	0.926230i	$0.376970\pi$
$104$	−1.15729	−	3.41477i	−0.113482	−	0.334846i
$105$	10.3043	−	8.04281i	1.00560	−	0.784898i
$106$	−3.35210	−	5.80600i	−0.325585	−	0.563929i
$107$	−0.775767	−	0.447890i	−0.0749963	−	0.0432991i	0.462033	−	0.886863i	$-0.347120\pi$
$107$	−0.775767	−	0.447890i	−0.0749963	−	0.0432991i	−0.537029	+	0.843564i	$0.680454\pi$
$108$	−1.00675	−	5.09769i	−0.0968746	−	0.490526i
$109$	−5.76038	+	9.97726i	−0.551744	+	0.955648i	0.446405	+	0.894831i	$0.352704\pi$
$109$	−5.76038	+	9.97726i	−0.551744	+	0.955648i	−0.998149	+	0.0608174i	$0.980629\pi$
$110$	5.88078			0.560710
$111$	10.9448	+	1.20369i	1.03883	+	0.114250i
$112$	−1.89518	+	1.84615i	−0.179078	+	0.174445i
$113$	−2.96337	−	1.71090i	−0.278771	−	0.160948i	0.354096	−	0.935209i	$-0.384789\pi$
$113$	−2.96337	−	1.71090i	−0.278771	−	0.160948i	−0.632867	+	0.774261i	$0.718122\pi$
$114$	−7.47320	−	0.821895i	−0.699929	−	0.0769775i
$115$		−	3.93119i		−	0.366586i
$116$	6.75519	+	3.90011i	0.627204	+	0.362116i
$117$	−4.37025	+	9.89449i	−0.404030	+	0.914746i
$118$			10.8441i			0.998277i
$119$	2.66064	+	10.4769i	0.243901	+	0.960420i
$120$	−3.98298	−	2.92323i	−0.363594	−	0.266853i
$121$	6.74956			0.613596
$122$	−1.97012	+	3.41234i	−0.178366	+	0.308939i
$123$	−7.28497	+	9.92596i	−0.656864	+	0.894993i
$124$			2.82648i			0.253825i
$125$	−5.31564			−0.475445
$126$	7.93377	−	0.235043i	0.706797	−	0.0209393i
$127$	5.80763	+	10.0591i	0.515343	+	0.892601i	0.999841	+	0.0178086i	$0.00566895\pi$
$127$	5.80763	+	10.0591i	0.515343	+	0.892601i	−0.484498	+	0.874792i	$0.660998\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−17.3042	−	1.90310i	−1.52355	−	0.167558i
$130$	3.30111	+	9.74047i	0.289527	+	0.854296i
$131$	−0.606766	−	1.05095i	−0.0530134	−	0.0918218i	0.838301	−	0.545208i	$-0.183549\pi$
$131$	−0.606766	−	1.05095i	−0.0530134	−	0.0918218i	−0.891314	+	0.453386i	$0.850216\pi$
$132$	2.87877	+	2.11282i	0.250565	+	0.183897i
$133$	3.11747	−	11.0531i	0.270319	−	0.958426i
$134$	−11.1976	−	6.46495i	−0.967328	−	0.558487i
$135$	2.87170	+	14.5409i	0.247157	+	1.25148i
$136$	3.53824	−	2.04280i	0.303402	−	0.175169i
$137$	8.19933	−	4.73388i	0.700516	−	0.404443i	−0.107024	−	0.994256i	$-0.534132\pi$
$137$	8.19933	−	4.73388i	0.700516	−	0.404443i	0.807540	+	0.589813i	$0.200799\pi$
$138$	1.41238	−	1.92440i	0.120230	−	0.163816i
$139$	−5.66528	−	3.27085i	−0.480522	−	0.277430i	0.240112	−	0.970745i	$-0.422816\pi$
$139$	−5.66528	−	3.27085i	−0.480522	−	0.277430i	−0.720634	+	0.693316i	$0.756149\pi$
$140$	5.40592	−	5.26605i	0.456883	−	0.445063i
$141$	−7.48517	+	10.1987i	−0.630365	+	0.858888i
$142$	3.27094	+	5.66543i	0.274491	+	0.475432i
$143$	−2.38594	−	7.04010i	−0.199522	−	0.588723i
$144$	−0.899509	−	2.86197i	−0.0749591	−	0.238498i
$145$	−19.2688	−	11.1249i	−1.60019	−	0.923870i
$146$	−1.25231	−	2.16906i	−0.103642	−	0.179513i
$147$	−1.64081	+	12.0128i	−0.135332	+	0.990800i
$148$	6.35706			0.522547
$149$			19.7517i			1.61812i	0.587725	+	0.809061i	$0.300024\pi$
$149$			19.7517i			1.61812i	−0.587725	+	0.809061i	$0.699976\pi$
$150$	4.37956	+	3.21430i	0.357590	+	0.262446i
$151$	−11.0526	+	19.1436i	−0.899444	+	1.55788i	−0.0712375	+	0.997459i	$0.522695\pi$
$151$	−11.0526	+	19.1436i	−0.899444	+	1.55788i	−0.828206	+	0.560423i	$0.810639\pi$
$152$	−4.34067			−0.352075
$153$	−11.9639	−	2.66377i	−0.967222	−	0.215353i
$154$	−3.90722	+	3.80614i	−0.314853	+	0.306707i
$155$		−	8.06238i		−	0.647586i
$156$	−1.88354	+	5.95418i	−0.150804	+	0.476716i
$157$	−13.7392	−	7.93232i	−1.09651	−	0.633068i	−0.161205	−	0.986921i	$-0.551538\pi$
$157$	−13.7392	−	7.93232i	−1.09651	−	0.633068i	−0.935301	+	0.353853i	$0.884871\pi$
$158$			14.1747i			1.12768i
$159$	−1.26942	+	11.5424i	−0.100672	+	0.915373i
$160$	−2.47029	−	1.42622i	−0.195294	−	0.112753i
$161$	2.54433	+	2.61191i	0.200522	+	0.205847i
$162$	−3.81843	+	8.14982i	−0.300004	+	0.640311i
$163$	3.73475			0.292528			0.146264	−	0.989246i	$-0.453275\pi$
$163$	3.73475			0.292528			0.146264	+	0.989246i	$0.453275\pi$
$164$	−3.55429	+	6.15620i	−0.277543	+	0.480719i
$165$	−8.21154	−	6.02671i	−0.639268	−	0.469179i
$166$	8.91279	+	5.14580i	0.691766	+	0.399392i
$167$	−7.93312	−	13.7406i	−0.613883	−	1.06328i	−0.990579	−	0.136940i	$-0.956273\pi$
$167$	−7.93312	−	13.7406i	−0.613883	−	1.06328i	0.376696	−	0.926337i	$-0.377060\pi$
$168$	4.53828	−	0.635636i	0.350136	−	0.0490404i
$169$	10.3214	−	7.90377i	0.793951	−	0.607982i
$170$	−10.0927	+	5.82700i	−0.774071	+	0.446910i
$171$	9.59280	+	8.80629i	0.733580	+	0.673433i
$172$	−10.0508			−0.766367
$173$	−5.58526			−0.424640			−0.212320	−	0.977200i	$-0.568102\pi$
$173$	−5.58526			−0.424640			−0.212320	+	0.977200i	$0.568102\pi$
$174$	−5.43563	−	12.3687i	−0.412074	−	0.937668i
$175$	−5.94418	+	5.79039i	−0.449338	+	0.437713i
$176$	1.78545	+	1.03083i	0.134583	+	0.0777017i
$177$	11.1132	−	15.1420i	0.835316	−	1.13814i
$178$	5.22295	−	3.01547i	0.391477	−	0.226019i
$179$			0.264943i			0.0198028i	0.999951	+	0.00990139i	$0.00315176\pi$
$179$			0.264943i			0.0198028i	−0.999951	+	0.00990139i	$0.996848\pi$
$180$	2.56580	+	8.16363i	0.191244	+	0.608481i
$181$			2.90040i			0.215585i	0.994173	+	0.107792i	$0.0343782\pi$
$181$			2.90040i			0.215585i	−0.994173	+	0.107792i	$0.965622\pi$
$182$	−8.49747	−	4.33509i	−0.629874	−	0.321338i
$183$	6.24796	−	2.74577i	0.461863	−	0.202973i
$184$	0.689091	−	1.19354i	0.0508005	−	0.0879890i
$185$	−18.1332			−1.33318
$186$	2.89661	−	3.94671i	0.212390	−	0.289387i
$187$	7.29465	−	4.21157i	0.533438	−	0.307980i
$188$	−3.65196	+	6.32538i	−0.266347	+	0.461326i
$189$	−11.3191	−	7.80245i	−0.823343	−	0.567545i
$190$	12.3815			0.898251
$191$		−	0.588168i		−	0.0425584i	−0.999774	−	0.0212792i	$-0.993226\pi$
$191$		−	0.588168i		−	0.0425584i	0.999774	−	0.0212792i	$-0.00677388\pi$
$192$	−0.696855	−	1.58568i	−0.0502912	−	0.114437i
$193$	−18.6836			−1.34487			−0.672437	−	0.740154i	$-0.734753\pi$
$193$	−18.6836			−1.34487			−0.672437	+	0.740154i	$0.734753\pi$
$194$	9.13794	+	15.8274i	0.656066	+	1.13634i
$195$	5.37271	−	16.9840i	0.384748	−	1.21625i
$196$	−0.183445	+	6.99760i	−0.0131032	+	0.499828i
$197$	20.3079	−	11.7248i	1.44688	−	0.835357i	0.448586	−	0.893740i	$-0.351928\pi$
$197$	20.3079	−	11.7248i	1.44688	−	0.835357i	0.998294	+	0.0583826i	$0.0185943\pi$
$198$	−1.85448	−	5.90041i	−0.131792	−	0.419324i
$199$	−16.2378	+	9.37488i	−1.15106	+	0.664567i	−0.949146	−	0.314835i	$-0.898051\pi$
$199$	−16.2378	+	9.37488i	−1.15106	+	0.664567i	−0.201918	+	0.979402i	$0.564717\pi$
$200$	2.71626	+	1.56823i	0.192068	+	0.110891i
$201$	9.01027	+	20.5027i	0.635536	+	1.44615i
$202$	9.47939	+	5.47293i	0.666968	+	0.385074i
$203$	20.0025	−	5.07968i	1.40390	−	0.356524i
$204$	−7.03407	−	0.773601i	−0.492484	−	0.0541629i
$205$	10.1384	−	17.5603i	0.708098	−	1.22646i
$206$	2.77389			0.193266
$207$	−3.94432	+	1.23969i	−0.274149	+	0.0861642i
$208$	−0.705144	+	3.53593i	−0.0488929	+	0.245172i
$209$	−8.94898			−0.619014
$210$	−12.9452	+	1.81312i	−0.893304	+	0.125117i
$211$	2.78247	+	4.81937i	0.191553	+	0.331779i	0.945765	−	0.324852i	$-0.105314\pi$
$211$	2.78247	+	4.81937i	0.191553	+	0.331779i	−0.754212	+	0.656631i	$0.771981\pi$
$212$			6.70420i			0.460446i
$213$	1.23869	−	11.2629i	0.0848735	−	0.771724i
$214$	0.447890	+	0.775767i	0.0306171	+	0.0530304i
$215$	28.6694			1.95524
$216$	−1.67697	+	4.91811i	−0.114104	+	0.334635i
$217$	5.21810	+	5.35669i	0.354228	+	0.363636i
$218$	9.97726	−	5.76038i	0.675746	−	0.390142i
$219$	−0.474243	+	4.31212i	−0.0320463	+	0.291386i
$220$	−5.09290	−	2.94039i	−0.343364	−	0.198241i
$221$	11.0705	+	9.71818i	0.744682	+	0.653715i
$222$	−8.87660	−	6.51481i	−0.595758	−	0.437246i
$223$	1.62683	−	0.939253i	0.108941	−	0.0628971i	−0.444540	−	0.895759i	$-0.646633\pi$
$223$	1.62683	−	0.939253i	0.108941	−	0.0628971i	0.553480	+	0.832862i	$0.313299\pi$
$224$	2.56435	−	0.651223i	0.171338	−	0.0435116i
$225$	−2.82128	−	8.97648i	−0.188085	−	0.598432i
$226$	1.71090	+	2.96337i	0.113808	+	0.197121i
$227$	−5.38152	−	9.32107i	−0.357184	−	0.618661i	0.630305	−	0.776347i	$-0.282930\pi$
$227$	−5.38152	−	9.32107i	−0.357184	−	0.618661i	−0.987489	+	0.157687i	$0.949596\pi$
$228$	6.06103	+	4.44838i	0.401402	+	0.294601i
$229$	4.85743	−	2.80444i	0.320988	−	0.185323i	−0.330845	−	0.943685i	$-0.607334\pi$
$229$	4.85743	−	2.80444i	0.320988	−	0.185323i	0.651833	+	0.758363i	$0.274000\pi$
$230$	−1.96560	+	3.40451i	−0.129608	+	0.224487i
$231$	9.35638	−	1.31047i	0.615605	−	0.0862223i
$232$	−3.90011	−	6.75519i	−0.256055	−	0.443500i
$233$	12.8530	−	7.42068i	0.842027	−	0.486145i	−0.0159256	−	0.999873i	$-0.505069\pi$
$233$	12.8530	−	7.42068i	0.842027	−	0.486145i	0.857953	+	0.513729i	$0.171736\pi$
$234$	8.73199	−	6.38375i	0.570828	−	0.417319i
$235$	10.4170	−	18.0428i	0.679532	−	1.17698i
$236$	5.42203	−	9.39123i	0.352944	−	0.611317i
$237$	14.5265	−	19.7927i	0.943596	−	1.28567i
$238$	2.93429	−	10.4036i	0.190202	−	0.674367i
$239$			12.7315i			0.823530i	0.911290	+	0.411765i	$0.135088\pi$
$239$			12.7315i			0.823530i	−0.911290	+	0.411765i	$0.864912\pi$
$240$	1.98774	+	4.52308i	0.128308	+	0.291964i
$241$	−2.61871	+	1.51191i	−0.168686	+	0.0973908i	−0.581966	−	0.813213i	$-0.697716\pi$
$241$	−2.61871	+	1.51191i	−0.168686	+	0.0973908i	0.413280	+	0.910604i	$0.364383\pi$
$242$	−5.84529	−	3.37478i	−0.375749	−	0.216939i
$243$	13.6839	−	7.46671i	0.877821	−	0.478990i
$244$	3.41234	−	1.97012i	0.218453	−	0.126124i
$245$	0.523267	−	19.9603i	0.0334303	−	1.27522i
$246$	11.2719	−	4.95365i	0.718673	−	0.315833i
$247$	−5.02341	−	14.8224i	−0.319632	−	0.943127i
$248$	1.41324	−	2.44780i	0.0897407	−	0.155435i
$249$	−7.17175	−	16.3192i	−0.454491	−	1.03419i
$250$	4.60348	+	2.65782i	0.291149	+	0.168095i
$251$	−11.9432	+	20.6862i	−0.753849	+	1.30570i	0.192096	+	0.981376i	$0.438472\pi$
$251$	−11.9432	+	20.6862i	−0.753849	+	1.30570i	−0.945945	+	0.324328i	$0.894862\pi$
$252$	−6.98837	−	3.76333i	−0.440226	−	0.237068i
$253$	1.42067	−	2.46067i	0.0893168	−	0.154701i
$254$		−	11.6153i		−	0.728806i
$255$	20.0643	+	2.20666i	1.25648	+	0.138186i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	5.54072	−	9.59680i	0.345620	−	0.598632i	−0.639846	−	0.768503i	$-0.721002\pi$
$257$	5.54072	−	9.59680i	0.345620	−	0.598632i	0.985466	+	0.169871i	$0.0543352\pi$
$258$	14.0343	+	10.3002i	0.873737	+	0.641263i
$259$	12.0478	−	11.7361i	0.748614	−	0.729246i
$260$	2.01139	−	10.0860i	0.124741	−	0.625510i
$261$	−5.08565	+	22.8414i	−0.314794	+	1.41384i
$262$			1.21353i			0.0749722i
$263$			4.09428i			0.252464i	0.992001	+	0.126232i	$0.0402884\pi$
$263$			4.09428i			0.252464i	−0.992001	+	0.126232i	$0.959712\pi$
$264$	−1.43668	−	3.26914i	−0.0884214	−	0.201202i
$265$		−	19.1234i		−	1.17474i
$266$	−8.22636	+	8.01353i	−0.504391	+	0.491341i
$267$	−10.3833	−	1.14195i	−0.635448	−	0.0698859i
$268$	6.46495	+	11.1976i	0.394910	+	0.684004i
$269$	9.08811	+	15.7411i	0.554112	+	0.959749i	0.997972	+	0.0636535i	$0.0202752\pi$
$269$	9.08811	+	15.7411i	0.554112	+	0.959749i	−0.443860	+	0.896096i	$0.646391\pi$
$270$	4.78348	−	14.0286i	0.291114	−	0.853756i
$271$	12.4365	+	7.18024i	0.755466	+	0.436169i	0.827666	−	0.561222i	$-0.189668\pi$
$271$	12.4365	+	7.18024i	0.755466	+	0.436169i	−0.0721994	+	0.997390i	$0.523002\pi$
$272$	−4.08561			−0.247726
$273$	7.42266	+	14.7616i	0.449240	+	0.893411i
$274$	−9.46777			−0.571969
$275$	5.60000	+	3.23316i	0.337693	+	0.194967i
$276$	−2.18536	+	0.960393i	−0.131543	+	0.0578089i
$277$	−2.91981	−	5.05725i	−0.175434	−	0.303861i	0.764877	−	0.644176i	$-0.222800\pi$
$277$	−2.91981	−	5.05725i	−0.175434	−	0.303861i	−0.940311	+	0.340315i	$0.889466\pi$
$278$	3.27085	+	5.66528i	0.196172	+	0.339781i
$279$	−8.08929	+	2.54244i	−0.484293	+	0.152212i
$280$	−7.31469	+	1.85758i	−0.437136	+	0.111012i
$281$		−	14.5423i		−	0.867519i	−0.901029	−	0.433760i	$-0.857187\pi$
$281$		−	14.5423i		−	0.867519i	0.901029	−	0.433760i	$-0.142813\pi$
$282$	11.5817	−	5.08978i	0.689681	−	0.303092i
$283$			5.11830i			0.304251i	0.988361	+	0.152126i	$0.0486118\pi$
$283$			5.11830i			0.304251i	−0.988361	+	0.152126i	$0.951388\pi$
$284$		−	6.54187i		−	0.388189i
$285$	−17.2888	−	12.6888i	−1.02410	−	0.751618i
$286$	−1.45377	+	7.28988i	−0.0859630	+	0.431059i
$287$	4.62926	+	18.2289i	0.273257	+	1.07602i
$288$	−0.651988	+	2.92829i	−0.0384188	+	0.172551i
$289$	0.153897	−	0.266557i	0.00905275	−	0.0156798i
$290$	11.1249	+	19.2688i	0.653275	+	1.13151i
$291$	3.46049	−	31.4650i	0.202858	−	1.84451i
$292$			2.50461i			0.146571i
$293$	−15.1987	+	26.3249i	−0.887917	+	1.53792i	−0.0455833	+	0.998961i	$0.514515\pi$
$293$	−15.1987	+	26.3249i	−0.887917	+	1.53792i	−0.842334	+	0.538957i	$0.818819\pi$
$294$	7.42739	−	9.58300i	0.433174	−	0.558892i
$295$	−15.4661	+	26.7880i	−0.900469	+	1.55966i
$296$	−5.50538	−	3.17853i	−0.319994	−	0.184748i
$297$	−3.45735	+	10.1395i	−0.200616	+	0.588351i
$298$	9.87585	−	17.1055i	0.572093	−	0.990893i
$299$	4.87315	+	0.971816i	0.281821	+	0.0562016i
$300$	−2.18566	−	4.97344i	−0.126189	−	0.287142i
$301$	−19.0481	+	18.5553i	−1.09792	+	1.06951i
$302$	19.1436	−	11.0526i	1.10159	−	0.636003i
$303$	−7.62768	−	17.3567i	−0.438199	−	0.997115i
$304$	3.75913	+	2.17033i	0.215601	+	0.124477i
$305$	−9.73353	+	5.61966i	−0.557340	+	0.321781i
$306$	9.02913	+	8.28883i	0.516161	+	0.473841i
$307$			1.17043i			0.0667999i	0.999442	+	0.0333999i	$0.0106335\pi$
$307$			1.17043i			0.0667999i	−0.999442	+	0.0333999i	$0.989366\pi$
$308$	5.28682	−	1.34260i	0.301245	−	0.0765017i
$309$	−3.87328	−	2.84272i	−0.220343	−	0.161717i
$310$	−4.03119	+	6.98222i	−0.228956	+	0.396564i
$311$	1.48661	−	2.57489i	0.0842980	−	0.146008i	−0.820794	−	0.571225i	$-0.806469\pi$
$311$	1.48661	−	2.57489i	0.0842980	−	0.146008i	0.905092	+	0.425216i	$0.139802\pi$
$312$	4.60829	−	4.21470i	0.260893	−	0.238610i
$313$	−10.5964	+	6.11782i	−0.598942	+	0.345799i	−0.768625	−	0.639699i	$-0.779059\pi$
$313$	−10.5964	+	6.11782i	−0.598942	+	0.345799i	0.169683	+	0.985499i	$0.445726\pi$
$314$	7.93232	+	13.7392i	0.447647	+	0.775346i
$315$	19.9340	+	10.7347i	1.12315	+	0.604833i
$316$	7.08737	−	12.2757i	0.398696	−	0.690561i
$317$	9.60122	−	5.54327i	0.539258	−	0.311341i	−0.205520	−	0.978653i	$-0.565889\pi$
$317$	9.60122	−	5.54327i	0.539258	−	0.311341i	0.744778	+	0.667312i	$0.232555\pi$
$318$	6.87056	−	9.36131i	0.385282	−	0.524956i
$319$	−8.04070	−	13.9269i	−0.450193	−	0.779757i
$320$	1.42622	+	2.47029i	0.0797284	+	0.138094i
$321$	0.169614	−	1.54224i	0.00946691	−	0.0860792i
$322$	−0.897503	−	3.53415i	−0.0500159	−	0.196950i
$323$	15.3583	−	8.86714i	0.854560	−	0.493381i
$324$	7.38177	−	5.14874i	0.410098	−	0.286041i
$325$	−2.21166	+	11.0903i	−0.122681	+	0.615180i
$326$	−3.23439	−	1.86738i	−0.179136	−	0.103424i
$327$	−19.8349	−	2.18143i	−1.09687	−	0.120633i
$328$	6.15620	−	3.55429i	0.339920	−	0.196253i
$329$	4.75648	+	18.7298i	0.262233	+	1.03261i
$330$	4.09805	+	9.32506i	0.225590	+	0.513327i
$331$	−26.9933			−1.48369			−0.741844	−	0.670573i	$-0.766048\pi$
$331$	−26.9933			−1.48369			−0.741844	+	0.670573i	$0.766048\pi$
$332$	−5.14580	−	8.91279i	−0.282412	−	0.489153i
$333$	5.71823	+	18.1937i	0.313357	+	0.997010i
$334$			15.8662i			0.868162i
$335$	−18.4410	−	31.9407i	−1.00754	−	1.74511i
$336$	−4.24808	−	1.71866i	−0.231752	−	0.0937607i
$337$	4.24529			0.231256			0.115628	−	0.993293i	$-0.463112\pi$
$337$	4.24529			0.231256			0.115628	+	0.993293i	$0.463112\pi$
$338$	−12.8904	+	1.68419i	−0.701148	+	0.0916078i
$339$	0.647911	−	5.89122i	0.0351897	−	0.319967i
$340$	11.6540			0.632027
$341$	2.91362	−	5.04653i	0.157781	−	0.273285i
$342$	−3.90447	−	12.4229i	−0.211130	−	0.671752i
$343$	12.5710	+	13.6004i	0.678768	+	0.734353i
$344$	8.70425	+	5.02540i	0.469302	+	0.270951i
$345$	6.23363	−	2.73947i	0.335607	−	0.147488i
$346$	4.83698	+	2.79263i	0.260038	+	0.150133i
$347$	6.90261	−	3.98523i	0.370552	−	0.213938i	−0.303148	−	0.952944i	$-0.598038\pi$
$347$	6.90261	−	3.98523i	0.370552	−	0.213938i	0.673699	+	0.739005i	$0.264704\pi$
$348$	−1.47695	+	13.4294i	−0.0791730	+	0.719892i
$349$	5.06976	−	2.92703i	0.271378	−	0.156680i	−0.358136	−	0.933670i	$-0.616587\pi$
$349$	5.06976	−	2.92703i	0.271378	−	0.156680i	0.629514	+	0.776989i	$0.283254\pi$
$350$	8.04301	−	2.04254i	0.429917	−	0.109178i
$351$	−18.7350	−	0.0348107i	−0.999998	−	0.00185806i
$352$	−1.03083	−	1.78545i	−0.0549434	−	0.0951648i
$353$	−14.2591			−0.758936			−0.379468	−	0.925205i	$-0.623893\pi$
$353$	−14.2591			−0.758936			−0.379468	+	0.925205i	$0.623893\pi$
$354$	−17.1953	+	7.55674i	−0.913917	+	0.401636i
$355$			18.6604i			0.990389i
$356$	−6.03095			−0.319639
$357$	−14.7590	+	11.5199i	−0.781131	+	0.609695i
$358$	0.132472	−	0.229448i	0.00700134	−	0.0121267i
$359$	7.12892	−	4.11588i	0.376250	−	0.217228i	−0.299935	−	0.953959i	$-0.596965\pi$
$359$	7.12892	−	4.11588i	0.376250	−	0.217228i	0.676185	+	0.736731i	$0.263632\pi$
$360$	1.85976	−	8.35281i	0.0980181	−	0.440232i
$361$	0.158604			0.00834759
$362$	1.45020	−	2.51182i	0.0762208	−	0.132018i
$363$	4.70347	+	10.7027i	0.246868	+	0.561744i
$364$	5.19148	+	8.00303i	0.272107	+	0.419473i
$365$		−	7.14428i		−	0.373949i
$366$	−6.78378	−	0.746074i	−0.354594	−	0.0389979i
$367$			23.9368i			1.24949i	0.780829	+	0.624745i	$0.214797\pi$
$367$			23.9368i			1.24949i	−0.780829	+	0.624745i	$0.785203\pi$
$368$	−1.19354	+	0.689091i	−0.0622176	+	0.0359213i
$369$	−20.8160	−	4.63471i	−1.08364	−	0.241273i
$370$	15.7038	+	9.06660i	0.816402	+	0.471350i
$371$	12.3770	+	12.7057i	0.642580	+	0.659646i
$372$	−4.48190	+	1.96964i	−0.232375	+	0.102121i
$373$	21.3521			1.10557			0.552786	−	0.833324i	$-0.313565\pi$
$373$	21.3521			1.10557			0.552786	+	0.833324i	$0.313565\pi$
$374$	−8.42314			−0.435550
$375$	−3.70423	−	8.42892i	−0.191286	−	0.435268i
$376$	6.32538	−	3.65196i	0.326207	−	0.188336i
$377$	18.5539	−	21.1357i	0.955574	−	1.08855i
$378$	5.90139	+	12.4167i	0.303535	+	0.638644i
$379$	−7.80867	−	13.5250i	−0.401104	−	0.694733i	0.592755	−	0.805383i	$-0.298040\pi$
$379$	−7.80867	−	13.5250i	−0.401104	−	0.694733i	−0.993859	+	0.110650i	$0.964707\pi$
$380$	−10.7227	−	6.19077i	−0.550064	−	0.317580i
$381$	−11.9035	+	16.2188i	−0.609834	+	0.830914i
$382$	−0.294084	+	0.509369i	−0.0150466	+	0.0260616i
$383$	9.65249			0.493219			0.246610	−	0.969115i	$-0.420683\pi$
$383$	9.65249			0.493219			0.246610	+	0.969115i	$0.420683\pi$
$384$	−0.189348	+	1.72167i	−0.00966261	+	0.0878586i
$385$	−15.0804	+	3.82970i	−0.768568	+	0.195179i
$386$	16.1805	+	9.34180i	0.823564	+	0.475485i
$387$	−9.04079	−	28.7651i	−0.459569	−	1.46221i
$388$		−	18.2759i		−	0.927817i
$389$	7.14154	+	4.12317i	0.362090	+	0.209053i	0.669997	−	0.742364i	$-0.266295\pi$
$389$	7.14154	+	4.12317i	0.362090	+	0.209053i	−0.307907	+	0.951416i	$0.599629\pi$
$390$	−13.1449	+	12.0222i	−0.665618	+	0.608769i
$391$			5.63071i			0.284757i
$392$	3.65767	−	5.96837i	0.184740	−	0.301448i
$393$	1.24364	−	1.69450i	0.0627336	−	0.0854761i
$394$	−23.4496			−1.18137
$395$	−20.2164	+	35.0157i	−1.01720	+	1.76183i
$396$	−1.34418	+	6.03715i	−0.0675475	+	0.303378i
$397$			10.3395i			0.518924i	0.965753	+	0.259462i	$0.0835452\pi$
$397$			10.3395i			0.518924i	−0.965753	+	0.259462i	$0.916455\pi$
$398$	18.7498			0.939840
$399$	19.6992	−	2.75909i	0.986191	−	0.138127i
$400$	−1.56823	−	2.71626i	−0.0784116	−	0.135813i
$401$	22.2943	+	12.8716i	1.11332	+	0.642777i	0.939688	−	0.342033i	$-0.111116\pi$
$401$	22.2943	+	12.8716i	1.11332	+	0.642777i	0.173635	+	0.984810i	$0.444449\pi$
$402$	2.44825	−	22.2610i	0.122108	−	1.11028i
$403$	9.99421	+	1.99307i	0.497847	+	0.0992820i
$404$	−5.47293	−	9.47939i	−0.272288	−	0.471617i
$405$	−21.0561	+	14.6865i	−1.04629	+	0.729779i
$406$	−19.8625	−	5.60213i	−0.985761	−	0.278029i
$407$	−11.3502	−	6.55305i	−0.562609	−	0.324823i
$408$	5.70488	+	4.18699i	0.282434	+	0.207287i
$409$	30.0138	−	17.3285i	1.48409	−	0.856839i	0.484252	−	0.874929i	$-0.339092\pi$
$409$	30.0138	−	17.3285i	1.48409	−	0.856839i	0.999836	+	0.0180896i	$0.00575842\pi$
$410$	−17.5603	+	10.1384i	−0.867239	+	0.500701i
$411$	13.2202	+	9.70271i	0.652104	+	0.478599i
$412$	−2.40226	−	1.38694i	−0.118351	−	0.0683298i
$413$	−7.06190	−	27.8080i	−0.347493	−	1.36834i
$414$	4.03572	+	0.898558i	0.198345	+	0.0441617i
$415$	14.6781	+	25.4233i	0.720521	+	1.24798i
$416$	2.37864	−	2.70963i	0.116622	−	0.132851i
$417$	1.23865	−	11.2626i	0.0606572	−	0.551534i
$418$	7.75004	+	4.47449i	0.379067	+	0.218854i
$419$	18.0720	+	31.3016i	0.882873	+	1.52918i	0.848132	+	0.529785i	$0.177727\pi$
$419$	18.0720	+	31.3016i	0.882873	+	1.52918i	0.0347413	+	0.999396i	$0.488939\pi$
$420$	12.1174	+	4.90240i	0.591270	+	0.239212i
$421$	−19.0053			−0.926260			−0.463130	−	0.886290i	$-0.653274\pi$
$421$	−19.0053			−0.926260			−0.463130	+	0.886290i	$0.653274\pi$
$422$		−	5.56493i		−	0.270897i
$423$	−21.3880	−	4.76207i	−1.03992	−	0.231540i
$424$	3.35210	−	5.80600i	0.162792	−	0.281964i
$425$	−12.8144			−0.621588
$426$	−6.70421	+	9.13465i	−0.324820	+	0.442575i
$427$	2.82988	−	10.0334i	0.136948	−	0.485552i
$428$		−	0.895779i		−	0.0432991i
$429$	9.50072	−	8.68928i	0.458699	−	0.419522i
$430$	−24.8284	−	14.3347i	−1.19733	−	0.691281i
$431$			36.6823i			1.76692i	0.468504	+	0.883461i	$0.344793\pi$
$431$			36.6823i			1.76692i	−0.468504	+	0.883461i	$0.655207\pi$
$432$	3.91135	−	3.42072i	0.188185	−	0.164579i
$433$	4.92583	+	2.84393i	0.236720	+	0.136670i	0.613668	−	0.789564i	$-0.289693\pi$
$433$	4.92583	+	2.84393i	0.236720	+	0.136670i	−0.376948	+	0.926234i	$0.623027\pi$
$434$	−1.84066	−	7.24808i	−0.0883547	−	0.347919i
$435$	4.21294	−	38.3067i	0.201995	−	1.83667i
$436$	−11.5208			−0.551744
$437$	2.99111	−	5.18076i	0.143084	−	0.247829i
$438$	2.56676	−	3.49728i	0.122645	−	0.167107i
$439$	−17.1676	−	9.91174i	−0.819366	−	0.473061i	0.0308315	−	0.999525i	$-0.490184\pi$
$439$	−17.1676	−	9.91174i	−0.819366	−	0.473061i	−0.850198	+	0.526463i	$0.823518\pi$
$440$	2.94039	+	5.09290i	0.140178	+	0.242795i
$441$	−20.1919	+	5.76939i	−0.961521	+	0.274733i
$442$	−4.72824	−	13.9514i	−0.224899	−	0.663602i
$443$	0.526014	−	0.303694i	0.0249917	−	0.0144290i	−0.487452	−	0.873150i	$-0.662074\pi$
$443$	0.526014	−	0.303694i	0.0249917	−	0.0144290i	0.512444	+	0.858721i	$0.328740\pi$
$444$	4.42995	+	10.0803i	0.210236	+	0.478389i
$445$	17.2030			0.815499
$446$	−1.87851			−0.0889499
$447$	−31.3199	+	13.7641i	−1.48138	+	0.651018i
$448$	−2.54641	−	0.718201i	−0.120306	−	0.0339318i
$449$	−0.384292	−	0.221871i	−0.0181359	−	0.0104707i	0.490905	−	0.871213i	$-0.336666\pi$
$449$	−0.384292	−	0.221871i	−0.0181359	−	0.0104707i	−0.509041	+	0.860743i	$0.670000\pi$
$450$	−2.04494	+	9.18450i	−0.0963993	+	0.432961i
$451$	12.6920	−	7.32773i	0.597643	−	0.345049i
$452$		−	3.42181i		−	0.160948i
$453$	−38.0577	−	4.18555i	−1.78811	−	0.196654i
$454$			10.7630i			0.505135i
$455$	−14.8084	−	22.8282i	−0.694230	−	1.07020i
$456$	−3.02482	−	6.88293i	−0.141650	−	0.322323i
$457$	14.2899	−	24.7508i	0.668453	−	1.15779i	−0.309884	−	0.950774i	$-0.600290\pi$
$457$	14.2899	−	24.7508i	0.668453	−	1.15779i	0.978337	−	0.207020i	$-0.0663765\pi$
$458$	−5.60888			−0.262086
$459$	−4.11319	−	20.8272i	−0.191987	−	0.972129i
$460$	3.40451	−	1.96560i	0.158736	−	0.0916464i
$461$	18.2440	−	31.5996i	0.849709	−	1.47174i	−0.0317595	−	0.999496i	$-0.510111\pi$
$461$	18.2440	−	31.5996i	0.849709	−	1.47174i	0.881468	−	0.472243i	$-0.156556\pi$
$462$	−8.75810	−	3.54330i	−0.407464	−	0.164849i
$463$	−38.3097			−1.78040			−0.890201	−	0.455567i	$-0.849436\pi$
$463$	−38.3097			−1.78040			−0.890201	+	0.455567i	$0.849436\pi$
$464$			7.80022i			0.362116i
$465$	12.7844	−	5.61831i	0.592861	−	0.260543i
$466$	−14.8414			−0.687512
$467$	11.2682	+	19.5171i	0.521431	+	0.903145i	0.999689	+	0.0249257i	$0.00793491\pi$
$467$	11.2682	+	19.5171i	0.521431	+	0.903145i	−0.478258	+	0.878219i	$0.658732\pi$
$468$	−10.7540	+	1.16250i	−0.497104	+	0.0537364i
$469$	32.9248	+	9.28628i	1.52033	+	0.428801i
$470$	−18.0428	+	10.4170i	−0.832254	+	0.480502i
$471$	3.00393	−	27.3137i	0.138414	−	1.25855i
$472$	−9.39123	+	5.42203i	−0.432267	+	0.249569i
$473$	17.9452	+	10.3607i	0.825121	+	0.476384i
$474$	−22.4766	+	9.87774i	−1.03239	+	0.453699i
$475$	11.7904	+	6.80718i	0.540980	+	0.312335i
$476$	−7.74298	+	7.54266i	−0.354899	+	0.345717i
$477$	−19.1872	+	6.03048i	−0.878522	+	0.276117i
$478$	6.36573	−	11.0258i	0.291162	−	0.504307i
$479$	−18.6725			−0.853168			−0.426584	−	0.904448i	$-0.640283\pi$
$479$	−18.6725			−0.853168			−0.426584	+	0.904448i	$0.640283\pi$
$480$	0.540104	−	4.91098i	0.0246523	−	0.224154i
$481$	4.48264	−	22.4781i	0.204391	−	1.02491i
$482$	3.02382			0.137731
$483$	−2.36863	+	5.85463i	−0.107776	+	0.266395i
$484$	3.37478	+	5.84529i	0.153399	+	0.265695i
$485$			52.1310i			2.36715i
$486$	−15.5839	−	0.375574i	−0.706902	−	0.0170364i
$487$	0.780349	+	1.35160i	0.0353610	+	0.0612470i	0.883164	−	0.469064i	$-0.155409\pi$
$487$	0.780349	+	1.35160i	0.0353610	+	0.0612470i	−0.847803	+	0.530311i	$0.822075\pi$
$488$	−3.94023			−0.178366
$489$	2.60258	+	5.92214i	0.117693	+	0.267808i
$490$	−10.4333	+	17.0245i	−0.471329	+	0.769088i
$491$	−23.0262	+	13.2942i	−1.03916	+	0.599959i	−0.919595	−	0.392868i	$-0.871483\pi$
$491$	−23.0262	+	13.2942i	−1.03916	+	0.599959i	−0.119564	+	0.992826i	$0.538150\pi$
$492$	−12.2386	−	1.34599i	−0.551759	−	0.0606820i
$493$	27.5991	+	15.9343i	1.24300	+	0.717646i
$494$	−3.06079	+	15.3483i	−0.137712	+	0.690552i
$495$	3.83420	−	17.2207i	0.172334	−	0.774011i
$496$	−2.44780	+	1.41324i	−0.109909	+	0.0634562i
$497$	−12.0773	−	12.3981i	−0.541740	−	0.556129i
$498$	−1.94869	+	17.7187i	−0.0873229	+	0.793996i
$499$	−2.95848	−	5.12424i	−0.132440	−	0.229392i	0.792177	−	0.610292i	$-0.208948\pi$
$499$	−2.95848	−	5.12424i	−0.132440	−	0.229392i	−0.924617	+	0.380899i	$0.875614\pi$
$500$	−2.65782	−	4.60348i	−0.118861	−	0.205874i
$501$	16.2600	−	22.1546i	0.726441	−	0.989795i
$502$	20.6862	−	11.9432i	0.923272	−	0.533052i
$503$	−21.6022	+	37.4160i	−0.963193	+	1.66830i	−0.248798	+	0.968555i	$0.580036\pi$
$503$	−21.6022	+	37.4160i	−0.963193	+	1.66830i	−0.714395	+	0.699743i	$0.753298\pi$
$504$	4.17044	+	6.75333i	0.185766	+	0.300817i
$505$	15.6113	+	27.0395i	0.694692	+	1.20324i
$506$	−2.46067	+	1.42067i	−0.109390	+	0.0631565i
$507$	19.7254	+	10.8586i	0.876035	+	0.482248i
$508$	−5.80763	+	10.0591i	−0.257672	+	0.446300i
$509$	−16.6682	+	28.8701i	−0.738803	+	1.27965i	0.214231	+	0.976783i	$0.431275\pi$
$509$	−16.6682	+	28.8701i	−0.738803	+	1.27965i	−0.953034	+	0.302862i	$0.902058\pi$
$510$	−16.2729	−	11.9432i	−0.720576	−	0.528853i
$511$	4.62390	+	4.74670i	0.204549	+	0.209982i
$512$			1.00000i			0.0441942i
$513$	−7.27919	+	21.3479i	−0.321384	+	0.942531i
$514$	−9.59680	+	5.54072i	−0.423297	+	0.244390i
$515$	6.85232	+	3.95619i	0.301949	+	0.174330i
$516$	−7.00395	−	15.9374i	−0.308332	−	0.701605i
$517$	13.0408	−	7.52910i	0.573533	−	0.331130i
$518$	−16.3018	+	4.13986i	−0.716258	+	0.181895i
$519$	−3.89212	−	8.85646i	−0.170845	−	0.388755i
$520$	−6.78494	+	7.72908i	−0.297539	+	0.338943i
$521$	−3.50547	+	6.07166i	−0.153578	+	0.266004i	−0.932540	−	0.361066i	$-0.882413\pi$
$521$	−3.50547	+	6.07166i	−0.153578	+	0.266004i	0.778963	+	0.627070i	$0.215746\pi$
$522$	15.8250	−	17.2384i	0.692641	−	0.754503i
$523$	15.8120	+	9.12904i	0.691409	+	0.399185i	0.804140	−	0.594441i	$-0.202626\pi$
$523$	15.8120	+	9.12904i	0.691409	+	0.399185i	−0.112731	+	0.993626i	$0.535960\pi$
$524$	0.606766	−	1.05095i	0.0265067	−	0.0459109i
$525$	−13.3240	−	5.39052i	−0.581505	−	0.235262i
$526$	2.04714	−	3.54575i	0.0892596	−	0.154602i
$527$			11.5479i			0.503033i
$528$	−0.390370	+	3.54950i	−0.0169887	+	0.154472i
$529$	−10.5503	−	18.2737i	−0.458709	−	0.794507i
$530$	−9.56169	+	16.5613i	−0.415333	+	0.719378i
$531$	31.7546	+	7.07020i	1.37803	+	0.306821i
$532$	11.1310	−	2.82674i	0.482590	−	0.122555i
$533$	19.2616	+	16.9087i	0.834313	+	0.732397i
$534$	8.42123	+	6.18060i	0.364422	+	0.267461i
$535$			2.55516i			0.110469i
$536$		−	12.9299i		−	0.558487i
$537$	−0.420116	+	0.184627i	−0.0181293	+	0.00796724i
$538$		−	18.1762i		−	0.783632i
$539$	7.54086	−	12.3048i	0.324808	−	0.530003i
$540$	−11.1569	+	9.75742i	−0.480118	+	0.419892i
$541$	7.10217	+	12.3013i	0.305346	+	0.528875i	0.977338	−	0.211683i	$-0.0678944\pi$
$541$	7.10217	+	12.3013i	0.305346	+	0.528875i	−0.671992	+	0.740558i	$0.734561\pi$
$542$	−7.18024	−	12.4365i	−0.308418	−	0.534195i
$543$	−4.59911	+	2.02116i	−0.197367	+	0.0867361i
$544$	3.53824	+	2.04280i	0.151701	+	0.0875845i
$545$	32.8624			1.40767
$546$	0.952576	−	16.4952i	0.0407665	−	0.705931i
$547$	1.17690			0.0503208			0.0251604	−	0.999683i	$-0.491990\pi$
$547$	1.17690			0.0503208			0.0251604	+	0.999683i	$0.491990\pi$
$548$	8.19933	+	4.73388i	0.350258	+	0.202221i
$549$	8.70785	+	7.99389i	0.371642	+	0.341171i
$550$	−3.23316	−	5.60000i	−0.137862	−	0.238785i
$551$	−16.9291	−	29.3220i	−0.721204	−	1.24916i
$552$	2.37277	+	0.260955i	0.100992	+	0.0111070i
$553$	−9.23091	−	36.3490i	−0.392538	−	1.54572i
$554$			5.83961i			0.248101i
$555$	−12.6362	−	28.7535i	−0.536377	−	1.22052i
$556$		−	6.54170i		−	0.277430i
$557$		−	30.3478i		−	1.28588i	−0.765918	−	0.642938i	$-0.777715\pi$
$557$		−	30.3478i		−	1.28588i	0.765918	−	0.642938i	$-0.222285\pi$
$558$	8.27675	+	1.84283i	0.350383	+	0.0780132i
$559$	−7.08726	+	35.5389i	−0.299759	+	1.50314i
$560$	7.26350	+	2.04863i	0.306939	+	0.0865705i
$561$	11.7615	+	8.63216i	0.496572	+	0.364450i
$562$	−7.27114	+	12.5940i	−0.306714	+	0.531245i
$563$	−8.71129	−	15.0884i	−0.367137	−	0.635900i	0.621979	−	0.783034i	$-0.286329\pi$
$563$	−8.71129	−	15.0884i	−0.367137	−	0.635900i	−0.989117	+	0.147133i	$0.952995\pi$
$564$	−12.5749	−	1.38298i	−0.529501	−	0.0582340i
$565$			9.76053i			0.410629i
$566$	2.55915	−	4.43257i	0.107569	−	0.186315i
$567$	4.48445	−	23.3857i	0.188329	−	0.982106i
$568$	−3.27094	+	5.66543i	−0.137245	+	0.237716i
$569$	−36.4062	−	21.0191i	−1.52623	−	0.881167i	−0.999516	−	0.0311223i	$-0.990092\pi$
$569$	−36.4062	−	21.0191i	−1.52623	−	0.881167i	−0.526711	−	0.850045i	$-0.676575\pi$
$570$	8.62813	+	19.6332i	0.361393	+	0.822344i
$571$	−17.8452	+	30.9087i	−0.746797	+	1.29349i	0.202553	+	0.979271i	$0.435076\pi$
$571$	−17.8452	+	30.9087i	−0.746797	+	1.29349i	−0.949350	+	0.314219i	$0.898257\pi$
$572$	4.90394	−	5.58633i	0.205044	−	0.233576i
$573$	0.932649	−	0.409868i	0.0389620	−	0.0171225i
$574$	5.10539	−	18.1013i	0.213095	−	0.755534i
$575$	−3.74350	+	2.16131i	−0.156115	+	0.0901328i
$576$	2.02879	−	2.20998i	0.0845327	−	0.0920827i
$577$	−34.3730	−	19.8453i	−1.43097	−	0.826170i	−0.433773	−	0.901022i	$-0.642818\pi$
$577$	−34.3730	−	19.8453i	−1.43097	−	0.826170i	−0.997195	+	0.0748524i	$0.976151\pi$
$578$	−0.266557	+	0.153897i	−0.0110873	+	0.00640126i
$579$	−13.0198	−	29.6263i	−0.541083	−	1.23123i
$580$		−	22.2497i		−	0.923870i
$581$	−26.2066	−	7.39144i	−1.08723	−	0.306649i
$582$	−18.7294	+	25.5193i	−0.776358	+	1.05781i
$583$	6.91088	−	11.9700i	0.286220	−	0.495747i
$584$	1.25231	−	2.16906i	0.0518208	−	0.0897563i
$585$	30.6752	−	3.31596i	1.26827	−	0.137098i
$586$	26.3249	−	15.1987i	1.08747	−	0.627852i
$587$	−5.31225	−	9.20108i	−0.219260	−	0.379769i	0.735322	−	0.677718i	$-0.237031\pi$
$587$	−5.31225	−	9.20108i	−0.219260	−	0.379769i	−0.954582	+	0.297949i	$0.903698\pi$
$588$	−11.2238	+	4.58542i	−0.462862	+	0.189100i
$589$	6.13440	−	10.6251i	0.252763	−	0.437799i
$590$	26.7880	−	15.4661i	1.10285	−	0.636728i
$591$	32.7435	+	24.0315i	1.34689	+	0.988523i
$592$	3.17853	+	5.50538i	0.130637	+	0.226270i
$593$	−17.5065	−	30.3222i	−0.718907	−	1.24518i	−0.961433	−	0.275038i	$-0.911310\pi$
$593$	−17.5065	−	30.3222i	−0.718907	−	1.24518i	0.242527	−	0.970145i	$-0.422024\pi$
$594$	8.06388	−	7.05235i	0.330865	−	0.289362i
$595$	22.0865	−	21.5150i	0.905457	−	0.882031i
$596$	−17.1055	+	9.87585i	−0.700667	+	0.404531i
$597$	−26.1810	−	19.2150i	−1.07152	−	0.786419i
$598$	−3.73436	−	3.27819i	−0.152709	−	0.134055i
$599$	−8.65396	−	4.99637i	−0.353591	−	0.204146i	0.312675	−	0.949860i	$-0.398775\pi$
$599$	−8.65396	−	4.99637i	−0.353591	−	0.204146i	−0.666266	+	0.745714i	$0.732108\pi$
$600$	−0.593882	+	5.39996i	−0.0242451	+	0.220452i
$601$	6.92945	−	4.00072i	0.282658	−	0.163193i	−0.351968	−	0.936012i	$-0.614487\pi$
$601$	6.92945	−	4.00072i	0.282658	−	0.163193i	0.634626	+	0.772819i	$0.281154\pi$
$602$	25.7738	−	6.54531i	1.05046	−	0.266767i
$603$	−26.2320	+	28.5749i	−1.06825	+	1.16366i
$604$	−22.1051			−0.899444
$605$	−9.62639	−	16.6734i	−0.391368	−	0.677870i
$606$	−2.07257	+	18.8452i	−0.0841925	+	0.765532i
$607$		−	34.3379i		−	1.39373i	−0.717201	−	0.696866i	$-0.754577\pi$
$607$		−	34.3379i		−	1.39373i	0.717201	−	0.696866i	$-0.245423\pi$
$608$	−2.17033	−	3.75913i	−0.0880187	−	0.152453i
$609$	21.9936	+	28.1779i	0.891227	+	1.14183i
$610$	11.2393			0.455066
$611$	19.7909	+	17.3734i	0.800655	+	0.702851i
$612$	−3.67504	−	11.6929i	−0.148555	−	0.472657i
$613$	29.1643			1.17793			0.588967	−	0.808157i	$-0.299535\pi$
$613$	29.1643			1.17793			0.588967	+	0.808157i	$0.299535\pi$
$614$	0.585214	−	1.01362i	0.0236173	−	0.0409064i
$615$	34.9100	+	3.83937i	1.40771	+	0.154818i
$616$	−5.24982	−	1.48069i	−0.211521	−	0.0596586i
$617$	13.7657	+	7.94764i	0.554187	+	0.319960i	0.750809	−	0.660519i	$-0.229664\pi$
$617$	13.7657	+	7.94764i	0.554187	+	0.319960i	−0.196622	+	0.980479i	$0.562997\pi$
$618$	1.93300	+	4.39851i	0.0777566	+	0.176934i
$619$	−12.0626	−	6.96433i	−0.484835	−	0.279920i	0.237594	−	0.971365i	$-0.423641\pi$
$619$	−12.0626	−	6.96433i	−0.484835	−	0.279920i	−0.722429	+	0.691445i	$0.756975\pi$
$620$	6.98222	−	4.03119i	0.280413	−	0.161896i
$621$	−4.71437	−	5.39056i	−0.189181	−	0.216316i
$622$	−2.57489	+	1.48661i	−0.103244	+	0.0596077i
$623$	−11.4298	+	11.1340i	−0.457923	+	0.446076i
$624$	−6.09824	+	1.34589i	−0.244125	+	0.0538789i
$625$	15.4225	+	26.7125i	0.616898	+	1.06850i
$626$	12.2356			0.489034
$627$	−6.23614	−	14.1903i	−0.249048	−	0.566704i
$628$		−	15.8646i		−	0.633068i
$629$	25.9725			1.03559
$630$	−11.8960	−	19.2635i	−0.473947	−	0.767477i
$631$	9.83148	−	17.0286i	0.391385	−	0.677899i	−0.601247	−	0.799063i	$-0.705329\pi$
$631$	9.83148	−	17.0286i	0.391385	−	0.677899i	0.992633	+	0.121164i	$0.0386627\pi$
$632$	−12.2757	+	7.08737i	−0.488300	+	0.281920i
$633$	−5.70302	+	7.77052i	−0.226675	+	0.308850i
$634$	−11.0865			−0.440302
$635$	16.5660	−	28.6931i	0.657400	−	1.13865i
$636$	−10.6307	+	4.67185i	−0.421536	+	0.185251i
$637$	24.6136	+	5.58296i	0.975227	+	0.221205i
$638$			16.0814i			0.636669i
$639$	18.7227	−	5.88447i	0.740657	−	0.232786i
$640$		−	2.85245i		−	0.112753i
$641$	−42.9310	+	24.7862i	−1.69567	+	0.978998i	−0.745902	+	0.666056i	$0.767981\pi$
$641$	−42.9310	+	24.7862i	−1.69567	+	0.978998i	−0.949772	+	0.312942i	$0.898685\pi$
$642$	−0.918008	+	1.25081i	−0.0362309	+	0.0493655i
$643$	−30.8334	−	17.8017i	−1.21595	−	0.702030i	−0.251902	−	0.967753i	$-0.581056\pi$
$643$	−30.8334	−	17.8017i	−1.21595	−	0.702030i	−0.964049	+	0.265723i	$0.914389\pi$
$644$	−0.989812	+	3.50941i	−0.0390041	+	0.138290i
$645$	19.9784	+	45.4606i	0.786649	+	1.79001i
$646$	−17.7343			−0.697746
$647$	23.9676			0.942264			0.471132	−	0.882063i	$-0.343846\pi$
$647$	23.9676			0.942264			0.471132	+	0.882063i	$0.343846\pi$
$648$	−8.96717	+	0.768056i	−0.352264	+	0.0301721i
$649$	−19.3615	+	11.1784i	−0.760006	+	0.438790i
$650$	7.46051	−	8.49866i	0.292625	−	0.333345i
$651$	−4.85776	+	12.0071i	−0.190390	+	0.470595i
$652$	1.86738	+	3.23439i	0.0731321	+	0.126669i
$653$	−0.425013	−	0.245381i	−0.0166320	−	0.00960251i	0.491661	−	0.870787i	$-0.336390\pi$
$653$	−0.425013	−	0.245381i	−0.0166320	−	0.00960251i	−0.508293	+	0.861184i	$0.669723\pi$
$654$	16.0868	+	11.8066i	0.629045	+	0.461676i
$655$	−1.73077	+	2.99778i	−0.0676267	+	0.117133i
$656$	−7.10857			−0.277543
$657$	−7.16813	+	2.25292i	−0.279655	+	0.0878949i
$658$	5.24569	−	18.5988i	0.204498	−	0.725055i
$659$	18.7736	+	10.8389i	0.731314	+	0.422225i	0.818903	−	0.573932i	$-0.194583\pi$
$659$	18.7736	+	10.8389i	0.731314	+	0.422225i	−0.0875884	+	0.996157i	$0.527916\pi$
$660$	1.11351	−	10.1248i	0.0433434	−	0.394106i
$661$			27.7315i			1.07863i	0.842104	+	0.539315i	$0.181317\pi$
$661$			27.7315i			1.07863i	−0.842104	+	0.539315i	$0.818683\pi$
$662$	23.3769	+	13.4967i	0.908570	+	0.524563i
$663$	−7.69543	+	24.3265i	−0.298866	+	0.944761i
$664$			10.2916i			0.399392i
$665$	−31.7506	+	8.06313i	−1.23124	+	0.312675i
$666$	4.14473	−	18.6154i	0.160605	−	0.721330i
$667$	10.7501			0.416247
$668$	7.93312	−	13.7406i	0.306942	−	0.531638i
$669$	2.62303	+	1.92512i	0.101412	+	0.0744295i
$670$			36.8819i			1.42487i
$671$	−8.12342			−0.313601
$672$	2.81962	+	3.61245i	0.108769	+	0.139353i
$673$	0.414076	+	0.717200i	0.0159614	+	0.0276460i	0.873896	−	0.486113i	$-0.161586\pi$
$673$	0.414076	+	0.717200i	0.0159614	+	0.0276460i	−0.857934	+	0.513759i	$0.828252\pi$
$674$	−3.67653	−	2.12265i	−0.141615	−	0.0817613i
$675$	12.2678	−	10.7290i	0.472189	−	0.412958i
$676$	12.0055	+	4.98667i	0.461752	+	0.191795i
$677$	−10.5010	−	18.1882i	−0.403586	−	0.699031i	0.590570	−	0.806986i	$-0.298903\pi$
$677$	−10.5010	−	18.1882i	−0.403586	−	0.699031i	−0.994156	+	0.107955i	$0.965570\pi$
$678$	−3.50672	+	4.77799i	−0.134675	+	0.183498i
$679$	−33.7400	−	34.6361i	−1.29482	−	1.32921i
$680$	−10.0927	−	5.82700i	−0.387036	−	0.223455i
$681$	11.0301	−	15.0288i	0.422675	−	0.575906i
$682$	−5.04653	+	2.91362i	−0.193242	+	0.111568i
$683$	2.10299	−	1.21416i	0.0804689	−	0.0464587i	−0.459226	−	0.888320i	$-0.651873\pi$
$683$	2.10299	−	1.21416i	0.0804689	−	0.0464587i	0.539695	+	0.841861i	$0.318540\pi$
$684$	−2.83006	+	12.7108i	−0.108210	+	0.486008i
$685$	−23.3882	−	13.5032i	−0.893616	−	0.515929i
$686$	−4.08657	−	18.0638i	−0.156026	−	0.689678i
$687$	7.83188	+	5.74806i	0.298805	+	0.219302i
$688$	−5.02540	−	8.70425i	−0.191592	−	0.331846i
$689$	23.7055	+	4.72742i	0.903109	+	0.180100i
$690$	−6.76822	−	0.744362i	−0.257662	−	0.0283374i
$691$	−7.95152	−	4.59081i	−0.302490	−	0.174643i	0.341071	−	0.940038i	$-0.389210\pi$
$691$	−7.95152	−	4.59081i	−0.302490	−	0.174643i	−0.643561	+	0.765395i	$0.722544\pi$
$692$	−2.79263	−	4.83698i	−0.106160	−	0.183874i
$693$	8.59803	+	13.9231i	0.326612	+	0.528893i
$694$	−7.97045			−0.302554
$695$			18.6599i			0.707809i
$696$	7.99379	−	10.8917i	0.303004	−	0.412850i
$697$	−14.5214	+	25.1519i	−0.550038	+	0.952694i
$698$	−5.85406			−0.221579
$699$	20.7235	+	15.2096i	0.783835	+	0.575281i
$700$	−7.98672	−	2.25261i	−0.301870	−	0.0851408i
$701$			7.30740i			0.275997i	0.990432	+	0.137998i	$0.0440669\pi$
$701$			7.30740i			0.275997i	−0.990432	+	0.137998i	$0.955933\pi$
$702$	16.2075	+	9.39763i	0.611714	+	0.354691i
$703$	−23.8970	−	13.7969i	−0.901293	−	0.520362i
$704$			2.06166i			0.0777017i
$705$	35.8694	+	3.94488i	1.35092	+	0.148573i
$706$	12.3488	+	7.12956i	0.464751	+	0.268324i
$707$	−27.8726	−	7.86133i	−1.04826	−	0.295656i
$708$	18.6699	+	2.05330i	0.701658	+	0.0771676i
$709$	−7.09910			−0.266612			−0.133306	−	0.991075i	$-0.542559\pi$
$709$	−7.09910			−0.266612			−0.133306	+	0.991075i	$0.542559\pi$
$710$	9.33018	−	16.1603i	0.350155	−	0.606487i
$711$	41.5078	+	9.24176i	1.55666	+	0.346593i
$712$	5.22295	+	3.01547i	0.195738	+	0.113010i
$713$	1.94770	+	3.37351i	0.0729419	+	0.126339i
$714$	18.5416	−	2.59696i	0.693903	−	0.0971888i
$715$	−13.9882	+	15.9347i	−0.523130	+	0.595925i
$716$	−0.229448	+	0.132472i	−0.00857486	+	0.00495070i
$717$	−20.1881	+	8.87199i	−0.753938	+	0.331330i
$718$	−8.23177			−0.307207
$719$	−16.4441			−0.613260			−0.306630	−	0.951829i	$-0.599201\pi$
$719$	−16.4441			−0.613260			−0.306630	+	0.951829i	$0.599201\pi$
$720$	−5.78701	+	6.30387i	−0.215669	+	0.234931i
$721$	−7.11323	+	1.80642i	−0.264910	+	0.0672745i
$722$	−0.137355	−	0.0793021i	−0.00511183	−	0.00295132i
$723$	−4.22227	−	3.09886i	−0.157028	−	0.115248i
$724$	−2.51182	+	1.45020i	−0.0933510	+	0.0538962i
$725$			24.4651i			0.908612i
$726$	1.27801	−	11.6205i	0.0474315	−	0.431278i
$727$			37.5539i			1.39280i	0.717656	+	0.696398i	$0.245215\pi$
$727$			37.5539i			1.39280i	−0.717656	+	0.696398i	$0.754785\pi$
$728$	−0.494437	−	9.52657i	−0.0183251	−	0.353078i
$729$	21.3755	+	16.4951i	0.791686	+	0.610929i
$730$	−3.57214	+	6.18713i	−0.132211	+	0.228996i
$731$	−41.0637			−1.51879
$732$	5.50189	+	4.03801i	0.203356	+	0.149249i
$733$	3.68363	−	2.12674i	0.136058	−	0.0785531i	−0.430426	−	0.902626i	$-0.641637\pi$
$733$	3.68363	−	2.12674i	0.136058	−	0.0785531i	0.566484	+	0.824073i	$0.308303\pi$
$734$	11.9684	−	20.7299i	0.441761	−	0.765153i
$735$	32.0153	−	13.0797i	1.18090	−	0.482452i
$736$	1.37818			0.0508005
$737$		−	26.6571i		−	0.981926i
$738$	15.7098	+	14.4218i	0.578287	+	0.530873i
$739$	16.7414			0.615843			0.307921	−	0.951412i	$-0.400367\pi$
$739$	16.7414			0.615843			0.307921	+	0.951412i	$0.400367\pi$
$740$	−9.06660	−	15.7038i	−0.333295	−	0.577283i
$741$	20.0030	−	18.2946i	0.734830	−	0.672069i
$742$	−4.36592	−	17.1919i	−0.160278	−	0.631136i
$743$	37.8379	−	21.8457i	1.38814	−	0.801441i	0.395032	−	0.918667i	$-0.370734\pi$
$743$	37.8379	−	21.8457i	1.38814	−	0.801441i	0.993105	+	0.117226i	$0.0374002\pi$
$744$	4.86626	+	0.535186i	0.178406	+	0.0196209i
$745$	48.7925	−	28.1704i	1.78762	−	1.03208i
$746$	−18.4915	−	10.6761i	−0.677021	−	0.390878i
$747$	20.8795	−	22.7443i	0.763939	−	0.832169i
$748$	7.29465	+	4.21157i	0.266719	+	0.153990i
$749$	−1.65374	−	1.69767i	−0.0604265	−	0.0620314i
$750$	−1.00650	+	9.15177i	−0.0367523	+	0.334176i
$751$	−18.5204	+	32.0783i	−0.675820	+	1.17055i	0.300408	+	0.953811i	$0.402877\pi$
$751$	−18.5204	+	32.0783i	−0.675820	+	1.17055i	−0.976228	+	0.216744i	$0.930456\pi$
$752$	−7.30392			−0.266347
$753$	−41.1245	−	4.52284i	−1.49866	−	0.164821i
$754$	−26.6360	+	9.02713i	−0.970026	+	0.328749i
$755$	63.0537			2.29476
$756$	1.09757	−	13.7038i	0.0399184	−	0.498404i
$757$	11.1135	+	19.2491i	0.403926	+	0.699621i	0.994196	−	0.107585i	$-0.0343119\pi$
$757$	11.1135	+	19.2491i	0.403926	+	0.699621i	−0.590269	+	0.807206i	$0.700979\pi$
$758$			15.6173i			0.567247i
$759$	4.89185	+	0.538001i	0.177563	+	0.0195282i
$760$	6.19077	+	10.7227i	0.224563	+	0.388954i
$761$	0.638902			0.0231602			0.0115801	−	0.999933i	$-0.496314\pi$
$761$	0.638902			0.0231602			0.0115801	+	0.999933i	$0.496314\pi$
$762$	18.4181	−	8.09415i	0.667218	−	0.293220i
$763$	−21.8339	+	21.2691i	−0.790442	+	0.769992i
$764$	0.509369	−	0.294084i	0.0184283	−	0.0106396i
$765$	10.4829	+	33.3534i	0.379009	+	1.20589i
$766$	−8.35931	−	4.82625i	−0.302034	−	0.174379i
$767$	−29.3834	−	25.7941i	−1.06097	−	0.931370i
$768$	1.02481	−	1.39634i	0.0369798	−	0.0503859i
$769$	−32.7494	+	18.9079i	−1.18097	+	0.681835i	−0.956239	−	0.292586i	$-0.905484\pi$
$769$	−32.7494	+	18.9079i	−1.18097	+	0.681835i	−0.224733	+	0.974420i	$0.572151\pi$
$770$	14.9749	+	4.22358i	0.539656	+	0.152207i
$771$	19.0786	+	2.09824i	0.687098	+	0.0755664i
$772$	−9.34180	−	16.1805i	−0.336219	−	0.582348i
$773$	−5.11479	−	8.85908i	−0.183966	−	0.318639i	0.759261	−	0.650786i	$-0.225560\pi$
$773$	−5.11479	−	8.85908i	−0.183966	−	0.318639i	−0.943228	+	0.332147i	$0.892227\pi$
$774$	−6.55301	+	29.4317i	−0.235543	+	1.05790i
$775$	−7.67744	+	4.43257i	−0.275782	+	0.159223i
$776$	−9.13794	+	15.8274i	−0.328033	+	0.568170i
$777$	27.0053	+	10.9256i	0.968811	+	0.391955i
$778$	−4.12317	−	7.14154i	−0.147823	−	0.256036i
$779$	26.7220	−	15.4280i	0.957416	−	0.552765i
$780$	17.3949	−	3.83909i	0.622838	−	0.137462i
$781$	−6.74356	+	11.6802i	−0.241303	+	0.417950i
$782$	2.81536	−	4.87634i	0.100677	−	0.174378i
$783$	−39.7631	+	7.85288i	−1.42102	+	0.280639i
$784$	−6.15182	+	3.33993i	−0.219708	+	0.119283i
$785$			45.2531i			1.61515i
$786$	−1.92428	+	0.845655i	−0.0686367	+	0.0301635i
$787$	−15.5026	+	8.95045i	−0.552609	+	0.319049i	−0.750174	−	0.661241i	$-0.770030\pi$
$787$	−15.5026	+	8.95045i	−0.552609	+	0.319049i	0.197564	+	0.980290i	$0.436697\pi$
$788$	20.3079	+	11.7248i	0.723440	+	0.417678i
$789$	−6.49224	+	2.85312i	−0.231130	+	0.101574i
$790$	35.0157	−	20.2164i	1.24580	−	0.719266i
$791$	−6.31718	−	6.48495i	−0.224613	−	0.230578i
$792$	4.18267	−	4.55623i	0.148625	−	0.161899i
$793$	−4.55999	−	13.4550i	−0.161930	−	0.477801i
$794$	5.16974	−	8.95426i	0.183467	−	0.317775i
$795$	30.3236	−	13.3262i	1.07547	−	0.472632i
$796$	−16.2378	−	9.37488i	−0.575532	−	0.332284i
$797$	16.6924	−	28.9121i	0.591275	−	1.02412i	−0.402786	−	0.915294i	$-0.631958\pi$
$797$	16.6924	−	28.9121i	0.591275	−	1.02412i	0.994061	−	0.108824i	$-0.0347084\pi$
$798$	−18.4395	−	7.46014i	−0.652752	−	0.264086i
$799$	−14.9205	+	25.8430i	−0.527849	+	0.914261i
$800$			3.13647i			0.110891i
$801$	−5.42489	−	17.2604i	−0.191679	−	0.609866i
$802$	−12.8716	−	22.2943i	−0.454512	−	0.787238i
$803$	2.58183	−	4.47186i	0.0911108	−	0.157809i
$804$	−13.2508	+	18.0545i	−0.467318	+	0.636733i
$805$	2.82339	−	10.0104i	0.0995114	−	0.352821i
$806$	−7.65870	−	6.72315i	−0.269766	−	0.236813i
$807$	−18.6273	+	25.3801i	−0.655710	+	0.893422i
$808$			10.9459i			0.385074i
$809$			8.83310i			0.310555i	0.987871	+	0.155278i	$0.0496272\pi$
$809$			8.83310i			0.310555i	−0.987871	+	0.155278i	$0.950373\pi$
$810$	25.5784	−	2.19084i	0.898733	−	0.0769783i
$811$		−	0.491936i		−	0.0172742i	−0.999963	−	0.00863710i	$-0.997251\pi$
$811$		−	0.491936i		−	0.0172742i	0.999963	−	0.00863710i	$-0.00274931\pi$
$812$	14.4004	+	14.7829i	0.505355	+	0.518777i
$813$	−2.71912	+	24.7240i	−0.0953638	+	0.867109i
$814$	6.55305	+	11.3502i	0.229684	+	0.397825i
$815$	−5.32660	−	9.22594i	−0.186583	−	0.323170i
$816$	−2.84708	−	6.47848i	−0.0996677	−	0.226792i
$817$	37.7823	+	21.8136i	1.32183	+	0.763161i
$818$	−34.6570			−1.21175
$819$	−18.2347	+	22.0567i	−0.637171	+	0.770722i
$820$	20.2768			0.708098
$821$	−33.5047	−	19.3440i	−1.16932	−	0.675109i	−0.215803	−	0.976437i	$-0.569237\pi$
$821$	−33.5047	−	19.3440i	−1.16932	−	0.675109i	−0.953521	+	0.301328i	$0.902570\pi$
$822$	−6.59766	−	15.0129i	−0.230120	−	0.523635i
$823$	−9.38976	−	16.2635i	−0.327307	−	0.566912i	0.654670	−	0.755915i	$-0.272808\pi$
$823$	−9.38976	−	16.2635i	−0.327307	−	0.566912i	−0.981976	+	0.189003i	$0.939474\pi$
$824$	1.38694	+	2.40226i	0.0483165	+	0.0836866i
$825$	−1.22438	+	11.1329i	−0.0426276	+	0.387597i
$826$	−7.78822	+	27.6134i	−0.270987	+	0.960793i
$827$		−	24.1251i		−	0.838912i	−0.907776	−	0.419456i	$-0.862221\pi$
$827$		−	24.1251i		−	0.838912i	0.907776	−	0.419456i	$-0.137779\pi$
$828$	−3.04576	−	2.79604i	−0.105847	−	0.0971690i
$829$			2.77462i			0.0963666i	0.998839	+	0.0481833i	$0.0153432\pi$
$829$			2.77462i			0.0963666i	−0.998839	+	0.0481833i	$0.984657\pi$
$830$		−	29.3563i		−	1.01897i
$831$	5.98452	−	8.15406i	0.207601	−	0.282861i
$832$	−3.41477	+	1.15729i	−0.118386	+	0.0401218i
$833$	−0.749485	+	28.5894i	−0.0259681	+	0.990566i
$834$	−6.70403	+	9.13441i	−0.232142	+	0.316299i
$835$	−22.6288	+	39.1943i	−0.783103	+	1.35637i
$836$	−4.47449	−	7.75004i	−0.154753	−	0.268041i
$837$	−9.66857	−	11.0553i	−0.334195	−	0.382129i
$838$		−	36.1439i		−	1.24857i
$839$	15.5301	−	26.8988i	0.536157	−	0.928651i	−0.462949	−	0.886385i	$-0.653209\pi$
$839$	15.5301	−	26.8988i	0.536157	−	0.928651i	0.999106	−	0.0422665i	$-0.0134579\pi$
$840$	−8.04281	−	10.3043i	−0.277503	−	0.355533i
$841$	15.9217	−	27.5773i	0.549026	−	0.950941i
$842$	16.4590	+	9.50263i	0.567216	+	0.327482i
$843$	23.0594	−	10.1339i	0.794209	−	0.349029i
$844$	−2.78247	+	4.81937i	−0.0957764	+	0.165890i
$845$	−34.2452	−	14.2242i	−1.17807	−	0.489328i
$846$	16.1416	+	14.8181i	0.554958	+	0.509457i
$847$	17.1871	+	4.84754i	0.590557	+	0.166564i
$848$	−5.80600	+	3.35210i	−0.199379	+	0.115112i
$849$	−8.11600	+	3.56671i	−0.278540	+	0.122409i
$850$	11.0976	+	6.40719i	0.380644	+	0.219765i
$851$	7.58741	−	4.38059i	0.260093	−	0.150165i
$852$	10.3733	−	4.55874i	0.355385	−	0.156180i
$853$		−	5.16044i		−	0.176690i	−0.996090	−	0.0883451i	$-0.971842\pi$
$853$		−	5.16044i		−	0.176690i	0.996090	−	0.0883451i	$-0.0281578\pi$
$854$	−7.46746	+	7.27427i	−0.255531	+	0.248920i
$855$	8.07261	−	36.2568i	0.276078	−	1.23996i
$856$	−0.447890	+	0.775767i	−0.0153085	+	0.0265152i
$857$	0.856918	−	1.48422i	0.0292717	−	0.0507002i	−0.851018	−	0.525136i	$-0.824015\pi$
$857$	0.856918	−	1.48422i	0.0292717	−	0.0507002i	0.880290	+	0.474436i	$0.157348\pi$
$858$	−12.5725	+	2.77477i	−0.429218	+	0.0947292i
$859$	49.7659	−	28.7323i	1.69799	−	0.980335i	0.750324	−	0.661070i	$-0.229897\pi$
$859$	49.7659	−	28.7323i	1.69799	−	0.980335i	0.947665	−	0.319265i	$-0.103436\pi$
$860$	14.3347	+	24.8284i	0.488809	+	0.846642i
$861$	−25.6793	+	20.0434i	−0.875149	+	0.683079i
$862$	18.3411	−	31.7678i	0.624701	−	1.08201i
$863$	35.2165	−	20.3323i	1.19878	−	0.692118i	0.238500	−	0.971142i	$-0.423344\pi$
$863$	35.2165	−	20.3323i	1.19878	−	0.692118i	0.960284	+	0.279024i	$0.0900109\pi$
$864$	−5.09769	+	1.00675i	−0.173427	+	0.0342503i
$865$	7.96584	+	13.7972i	0.270847	+	0.469120i
$866$	−2.84393	−	4.92583i	−0.0966406	−	0.167386i
$867$	0.529919	+	0.0582800i	0.0179970	+	0.00197929i
$868$	−2.02998	+	7.19736i	−0.0689020	+	0.244294i
$869$	−25.3083	+	14.6117i	−0.858524	+	0.495669i
$870$	−22.8019	+	31.0681i	−0.773056	+	1.05331i
$871$	44.1527	−	14.9637i	1.49606	−	0.507024i
$872$	9.97726	+	5.76038i	0.337873	+	0.195071i
$873$	52.3050	−	16.4393i	1.77026	−	0.556387i
$874$	−5.18076	+	2.99111i	−0.175242	+	0.101176i
$875$	−13.5358	−	3.81770i	−0.457593	−	0.129062i
$876$	−3.97152	+	1.74535i	−0.134185	+	0.0589700i
$877$	11.9444			0.403335			0.201668	−	0.979454i	$-0.435364\pi$
$877$	11.9444			0.403335			0.201668	+	0.979454i	$0.435364\pi$
$878$	9.91174	+	17.1676i	0.334505	+	0.579380i
$879$	−52.3343	−	5.75567i	−1.76519	−	0.194134i
$880$		−	5.88078i		−	0.198241i
$881$	6.30204	+	10.9155i	0.212321	+	0.367751i	0.952441	−	0.304724i	$-0.0985644\pi$
$881$	6.30204	+	10.9155i	0.212321	+	0.367751i	−0.740119	+	0.672475i	$0.765231\pi$
$882$	20.3714	+	5.09953i	0.685941	+	0.171710i
$883$	−46.6817			−1.57097			−0.785483	−	0.618884i	$-0.787585\pi$
$883$	−46.6817			−1.57097			−0.785483	+	0.618884i	$0.787585\pi$
$884$	−2.88094	+	14.4464i	−0.0968966	+	0.485885i
$885$	−53.2549	−	5.85693i	−1.79014	−	0.196878i
$886$	−0.607389			−0.0204056
$887$	20.8848	−	36.1735i	0.701243	−	1.21459i	−0.266787	−	0.963756i	$-0.585962\pi$
$887$	20.8848	−	36.1735i	0.701243	−	1.21459i	0.968030	−	0.250833i	$-0.0807046\pi$
$888$	1.20369	−	10.9448i	0.0403933	−	0.367282i
$889$	7.56411	+	29.7856i	0.253692	+	0.998977i
$890$	−14.8982	−	8.60148i	−0.499389	−	0.288322i
$891$	−18.4872	+	1.58347i	−0.619346	+	0.0530482i
$892$	1.62683	+	0.939253i	0.0544704	+	0.0314485i
$893$	27.4564	−	15.8520i	0.918793	−	0.530465i
$894$	34.0059	+	3.73994i	1.13733	+	0.125082i
$895$	0.654487	−	0.377868i	0.0218771	−	0.0126307i
$896$	1.84615	+	1.89518i	0.0616756	+	0.0633137i
$897$	1.85489	+	8.40449i	0.0619328	+	0.280618i
$898$	0.221871	+	0.384292i	0.00740393	+	0.0128240i
$899$	22.0471			0.735313
$900$	6.36322	−	6.93154i	0.212107	−	0.231051i
$901$			27.3907i			0.912517i
$902$	−14.6555			−0.487973
$903$	−42.6966	−	17.2739i	−1.42085	−	0.574840i
$904$	−1.71090	+	2.96337i	−0.0569038	+	0.0985603i
$905$	7.16483	−	4.13662i	0.238167	−	0.137506i
$906$	30.8662	+	22.6536i	1.02546	+	0.752617i
$907$	−29.6579			−0.984775			−0.492388	−	0.870376i	$-0.663876\pi$
$907$	−29.6579			−0.984775			−0.492388	+	0.870376i	$0.663876\pi$
$908$	5.38152	−	9.32107i	0.178592	−	0.309330i
$909$	22.2068	−	24.1902i	0.736553	−	0.802337i
$910$	1.41036	+	27.1741i	0.0467529	+	0.900811i
$911$		−	37.9318i		−	1.25674i	−0.777916	−	0.628368i	$-0.783723\pi$
$911$		−	37.9318i		−	1.25674i	0.777916	−	0.628368i	$-0.216277\pi$
$912$	−0.821895	+	7.47320i	−0.0272157	+	0.247462i
$913$			21.2178i			0.702206i
$914$	−24.7508	+	14.2899i	−0.818684	+	0.472668i
$915$	−15.6939	−	11.5182i	−0.518823	−	0.380780i
$916$	4.85743	+	2.80444i	0.160494	+	0.0926613i
$917$	−0.790279	−	3.11192i	−0.0260973	−	0.102765i
$918$	−6.85146	+	20.0935i	−0.226132	+	0.663183i
$919$	16.3051			0.537857			0.268928	−	0.963160i	$-0.413330\pi$
$919$	16.3051			0.537857			0.268928	+	0.963160i	$0.413330\pi$
$920$	−3.93119			−0.129608
$921$	−1.85593	+	0.815619i	−0.0611550	+	0.0268756i
$922$	−31.5996	+	18.2440i	−1.04068	+	0.600835i
$923$	−23.1316	−	4.61296i	−0.761385	−	0.151837i
$924$	5.81309	+	7.44763i	0.191237	+	0.245009i
$925$	9.96935	+	17.2674i	0.327790	+	0.567749i
$926$	33.1772	+	19.1549i	1.09027	+	0.629467i
$927$	1.80854	−	8.12276i	0.0594003	−	0.266786i
$928$	3.90011	−	6.75519i	0.128027	−	0.221750i
$929$	45.1402			1.48100			0.740500	−	0.672056i	$-0.234589\pi$
$929$	45.1402			1.48100			0.740500	+	0.672056i	$0.234589\pi$
$930$	−13.8808	−	1.52659i	−0.455168	−	0.0500589i
$931$	15.8767	−	25.9067i	0.520338	−	0.849059i
$932$	12.8530	+	7.42068i	0.421014	+	0.243072i
$933$	5.11891	+	0.562973i	0.167586	+	0.0184309i
$934$		−	22.5364i		−	0.737415i
$935$	−20.8076	−	12.0133i	−0.680482	−	0.392876i
$936$	9.89449	+	4.37025i	0.323411	+	0.142846i
$937$			8.79906i			0.287453i	0.989617	+	0.143726i	$0.0459085\pi$
$937$			8.79906i			0.287453i	−0.989617	+	0.143726i	$0.954091\pi$
$938$	−23.8706	−	24.5046i	−0.779402	−	0.800102i
$939$	−17.0851	−	12.5393i	−0.557550	−	0.409203i
$940$	20.8341			0.679532
$941$	29.1636	−	50.5128i	0.950705	−	1.64667i	0.206801	−	0.978383i	$-0.433695\pi$
$941$	29.1636	−	50.5128i	0.950705	−	1.64667i	0.743904	−	0.668286i	$-0.232972\pi$
$942$	−16.2583	+	22.1524i	−0.529724	+	0.721763i
$943$			9.79691i			0.319031i
$944$	10.8441			0.352944
$945$	−3.13077	+	39.0895i	−0.101844	+	1.27158i
$946$	−10.3607	−	17.9452i	−0.336854	−	0.583449i
$947$	−14.6204	−	8.44108i	−0.475099	−	0.274298i	0.243273	−	0.969958i	$-0.421779\pi$
$947$	−14.6204	−	8.44108i	−0.475099	−	0.274298i	−0.718372	+	0.695659i	$0.755112\pi$
$948$	24.4042	+	2.68395i	0.792612	+	0.0871707i
$949$	8.85613	+	1.76611i	0.287482	+	0.0573304i
$950$	−6.80718	−	11.7904i	−0.220854	−	0.382530i
$951$	15.4805	+	11.3616i	0.501990	+	0.368427i
$952$	10.4769	−	2.66064i	0.339560	−	0.0862319i
$953$	−27.3038	−	15.7639i	−0.884457	−	0.510641i	−0.0123316	−	0.999924i	$-0.503925\pi$
$953$	−27.3038	−	15.7639i	−0.884457	−	0.510641i	−0.872125	+	0.489282i	$0.837259\pi$
$954$	19.6319	+	4.37106i	0.635605	+	0.141518i
$955$	−1.45295	+	0.838860i	−0.0470163	+	0.0271449i
$956$	−11.0258	+	6.36573i	−0.356599	+	0.205883i
$957$	16.4805	−	22.4550i	0.532738	−	0.725869i
$958$	16.1709	+	9.33625i	0.522457	+	0.301640i
$959$	24.2787	−	6.16562i	0.784000	−	0.199098i
$960$	−2.92323	+	3.98298i	−0.0943469	+	0.128550i
$961$	−11.5055	−	19.9281i	−0.371146	−	0.642843i
$962$	−15.1211	+	17.2253i	−0.487525	+	0.555366i
$963$	2.56369	−	0.805761i	0.0826139	−	0.0259653i
$964$	−2.61871	−	1.51191i	−0.0843429	−	0.0486954i
$965$	26.6470	+	46.1540i	0.857797	+	1.48575i
$966$	4.97861	−	3.88594i	0.160184	−	0.125028i
$967$	−24.7371			−0.795492			−0.397746	−	0.917496i	$-0.630207\pi$
$967$	−24.7371			−0.795492			−0.397746	+	0.917496i	$0.630207\pi$
$968$		−	6.74956i		−	0.216939i
$969$	24.7630	+	18.1743i	0.795502	+	0.583844i
$970$	26.0655	−	45.1468i	0.836913	−	1.44958i
$971$	−41.4711			−1.33087			−0.665436	−	0.746455i	$-0.731754\pi$
$971$	−41.4711			−1.33087			−0.665436	+	0.746455i	$0.731754\pi$
$972$	13.3083	+	8.11722i	0.426864	+	0.260360i
$973$	−12.0770	−	12.3977i	−0.387170	−	0.397453i
$974$		−	1.56070i		−	0.0500080i
$975$	−19.1269	+	4.22135i	−0.612552	+	0.135191i
$976$	3.41234	+	1.97012i	0.109226	+	0.0630619i
$977$			31.8240i			1.01814i	0.860725	+	0.509071i	$0.170011\pi$
$977$			31.8240i			1.01814i	−0.860725	+	0.509071i	$0.829989\pi$
$978$	0.707167	−	6.43001i	0.0226127	−	0.205609i
$979$	10.7679	+	6.21688i	0.344145	+	0.198692i
$980$	17.5477	−	9.52698i	0.560542	−	0.304328i
$981$	−10.3630	−	32.9721i	−0.330866	−	1.05272i
$982$	26.5884			0.848470
$983$	−11.3615	+	19.6787i	−0.362376	+	0.627653i	−0.988351	−	0.152189i	$-0.951368\pi$
$983$	−11.3615	+	19.6787i	−0.362376	+	0.627653i	0.625975	+	0.779843i	$0.284701\pi$
$984$	9.92596	+	7.28497i	0.316428	+	0.232236i
$985$	−57.9274	−	33.4444i	−1.84572	−	1.06563i
$986$	−15.9343	−	27.5991i	−0.507453	−	0.878934i
$987$	−26.3850	+	20.5943i	−0.839845	+	0.655523i
$988$	10.3249	−	11.7616i	0.328478	−	0.374186i
$989$	−11.9960	+	6.92592i	−0.381452	+	0.220231i
$990$	−11.9308	+	12.9964i	−0.379187	+	0.413054i
$991$	50.5915			1.60709			0.803546	−	0.595243i	$-0.202944\pi$
$991$	50.5915			1.60709			0.803546	+	0.595243i	$0.202944\pi$
$992$	2.82648			0.0897407
$993$	−18.8104	−	42.8029i	−0.596931	−	1.35831i
$994$	4.26021	+	16.7757i	0.135126	+	0.532092i
$995$	46.3174	+	26.7414i	1.46836	+	0.847758i
$996$	10.5470	−	14.3705i	0.334194	−	0.455348i
$997$	4.22239	−	2.43780i	0.133724	−	0.0772058i	−0.431645	−	0.902043i	$-0.642067\pi$
$997$	4.22239	−	2.43780i	0.133724	−	0.0772058i	0.565370	+	0.824838i	$0.308733\pi$
$998$			5.91696i			0.187298i
$999$	−24.8647	+	21.7457i	−0.786685	+	0.688004i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.u.a.185.12	✓	76
3.2	odd	2	inner	546.2.u.a.185.27	yes	76
7.5	odd	6		546.2.bb.a.341.38	yes	76
13.9	even	3		546.2.bb.a.269.32	yes	76
21.5	even	6		546.2.bb.a.341.13	yes	76
39.35	odd	6		546.2.bb.a.269.19	yes	76
91.61	odd	6	inner	546.2.u.a.425.27	yes	76
273.152	even	6	inner	546.2.u.a.425.12	yes	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.u.a.185.12	✓	76	1.1	even	1	trivial
546.2.u.a.185.27	yes	76	3.2	odd	2	inner
546.2.u.a.425.12	yes	76	273.152	even	6	inner
546.2.u.a.425.27	yes	76	91.61	odd	6	inner
546.2.bb.a.269.19	yes	76	39.35	odd	6
546.2.bb.a.269.32	yes	76	13.9	even	3
546.2.bb.a.341.13	yes	76	21.5	even	6
546.2.bb.a.341.38	yes	76	7.5	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)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.696855 + 1.58568i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.42622 - 2.47029i) q^{5} +(0.189348 - 1.72167i) q^{6} +(2.54641 + 0.718201i) q^{7} -1.00000i q^{8} +(-2.02879 + 2.20998i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.696855 + 1.58568i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.42622 - 2.47029i) q^{5} +(0.189348 - 1.72167i) q^{6} +(2.54641 + 0.718201i) q^{7} -1.00000i q^{8} +(-2.02879 + 2.20998i) q^{9} +2.85245i q^{10} -2.06166i q^{11} +(-1.02481 + 1.39634i) q^{12} +(3.41477 - 1.15729i) q^{13} +(-1.84615 - 1.89518i) q^{14} +(2.92323 - 3.98298i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.04280 + 3.53824i) q^{17} +(2.86197 - 0.899509i) q^{18} -4.34067i q^{19} +(1.42622 - 2.47029i) q^{20} +(0.635636 + 4.53828i) q^{21} +(-1.03083 + 1.78545i) q^{22} +(1.19354 + 0.689091i) q^{23} +(1.58568 - 0.696855i) q^{24} +(-1.56823 + 2.71626i) q^{25} +(-3.53593 - 0.705144i) q^{26} +(-4.91811 - 1.67697i) q^{27} +(0.651223 + 2.56435i) q^{28} +(6.75519 - 3.90011i) q^{29} +(-4.52308 + 1.98774i) q^{30} +(2.44780 + 1.41324i) q^{31} +(0.866025 - 0.500000i) q^{32} +(3.26914 - 1.43668i) q^{33} -4.08561i q^{34} +(-1.85758 - 7.31469i) q^{35} +(-2.92829 - 0.651988i) q^{36} +(3.17853 - 5.50538i) q^{37} +(-2.17033 + 3.75913i) q^{38} +(4.21470 + 4.60829i) q^{39} +(-2.47029 + 1.42622i) q^{40} +(3.55429 + 6.15620i) q^{41} +(1.71866 - 4.24808i) q^{42} +(-5.02540 + 8.70425i) q^{43} +(1.78545 - 1.03083i) q^{44} +(8.35281 + 1.85976i) q^{45} +(-0.689091 - 1.19354i) q^{46} +(3.65196 + 6.32538i) q^{47} +(-1.72167 - 0.189348i) q^{48} +(5.96837 + 3.65767i) q^{49} +(2.71626 - 1.56823i) q^{50} +(-4.18699 + 5.70488i) q^{51} +(2.70963 + 2.37864i) q^{52} +(5.80600 + 3.35210i) q^{53} +(3.42072 + 3.91135i) q^{54} +(-5.09290 + 2.94039i) q^{55} +(0.718201 - 2.54641i) q^{56} +(6.88293 - 3.02482i) q^{57} -7.80022 q^{58} +(-5.42203 - 9.39123i) q^{59} +(4.91098 + 0.540104i) q^{60} -3.94023i q^{61} +(-1.41324 - 2.44780i) q^{62} +(-6.75333 + 4.17044i) q^{63} -1.00000 q^{64} +(-7.72908 - 6.78494i) q^{65} +(-3.54950 - 0.390370i) q^{66} +12.9299 q^{67} +(-2.04280 + 3.53824i) q^{68} +(-0.260955 + 2.37277i) q^{69} +(-2.04863 + 7.26350i) q^{70} +(-5.66543 - 3.27094i) q^{71} +(2.20998 + 2.02879i) q^{72} +(2.16906 + 1.25231i) q^{73} +(-5.50538 + 3.17853i) q^{74} +(-5.39996 - 0.593882i) q^{75} +(3.75913 - 2.17033i) q^{76} +(1.48069 - 5.24982i) q^{77} +(-1.34589 - 6.09824i) q^{78} +(-7.08737 - 12.2757i) q^{79} +2.85245 q^{80} +(-0.768056 - 8.96717i) q^{81} -7.10857i q^{82} -10.2916 q^{83} +(-3.61245 + 2.81962i) q^{84} +(5.82700 - 10.0927i) q^{85} +(8.70425 - 5.02540i) q^{86} +(10.8917 + 7.99379i) q^{87} -2.06166 q^{88} +(-3.01547 + 5.22295i) q^{89} +(-6.30387 - 5.78701i) q^{90} +(9.52657 - 0.494437i) q^{91} +1.37818i q^{92} +(-0.535186 + 4.86626i) q^{93} -7.30392i q^{94} +(-10.7227 + 6.19077i) q^{95} +(1.39634 + 1.02481i) q^{96} +(-15.8274 - 9.13794i) q^{97} +(-3.33993 - 6.15182i) q^{98} +(4.55623 + 4.18267i) 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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