LMFDB - Embedded newform 504.2.cs.b.85.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(85,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2, 0]))

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

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

chi := DirichletCharacter("504.85");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.cs (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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			85.15
Character	$\chi$	$=$	504.85
Dual form			504.2.cs.b.421.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.462760 + 1.33636i) q^{2} +(-1.16981 + 1.27732i) q^{3} +(-1.57171 - 1.23683i) q^{4} +(-0.563250 - 0.325193i) q^{5} +(-1.16562 - 2.15438i) q^{6} +(-0.500000 - 0.866025i) q^{7} +(2.38016 - 1.52801i) q^{8} +(-0.263093 - 2.98844i) q^{9} +O(q^{10})$	\(q+(-0.462760 + 1.33636i) q^{2} +(-1.16981 + 1.27732i) q^{3} +(-1.57171 - 1.23683i) q^{4} +(-0.563250 - 0.325193i) q^{5} +(-1.16562 - 2.15438i) q^{6} +(-0.500000 - 0.866025i) q^{7} +(2.38016 - 1.52801i) q^{8} +(-0.263093 - 2.98844i) q^{9} +(0.695224 - 0.602218i) q^{10} +(2.20106 - 1.27078i) q^{11} +(3.41842 - 0.560724i) q^{12} +(0.330225 + 0.190655i) q^{13} +(1.38870 - 0.267418i) q^{14} +(1.07427 - 0.339038i) q^{15} +(0.940527 + 3.88785i) q^{16} +4.11399 q^{17} +(4.11538 + 1.03134i) q^{18} -0.275717i q^{19} +(0.483058 + 1.20775i) q^{20} +(1.69110 + 0.374424i) q^{21} +(0.679658 + 3.52947i) q^{22} +(-0.974828 + 1.68845i) q^{23} +(-0.832578 + 4.82771i) q^{24} +(-2.28850 - 3.96380i) q^{25} +(-0.407598 + 0.353071i) q^{26} +(4.12496 + 3.15985i) q^{27} +(-0.285268 + 1.97955i) q^{28} +(7.40561 - 4.27563i) q^{29} +(-0.0440534 + 1.59250i) q^{30} +(-3.59920 + 6.23399i) q^{31} +(-5.63080 - 0.542260i) q^{32} +(-0.951622 + 4.29802i) q^{33} +(-1.90379 + 5.49776i) q^{34} +0.650385i q^{35} +(-3.28267 + 5.02236i) q^{36} +2.84592i q^{37} +(0.368457 + 0.127591i) q^{38} +(-0.629828 + 0.198772i) q^{39} +(-1.83753 + 0.0866409i) q^{40} +(5.98003 - 10.3577i) q^{41} +(-1.28294 + 2.08664i) q^{42} +(5.05692 - 2.91961i) q^{43} +(-5.03115 - 0.725027i) q^{44} +(-0.823632 + 1.76880i) q^{45} +(-1.80526 - 2.08407i) q^{46} +(4.62536 + 8.01136i) q^{47} +(-6.06627 - 3.34669i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(6.35608 - 1.22397i) q^{50} +(-4.81258 + 5.25488i) q^{51} +(-0.283209 - 0.708084i) q^{52} -5.56863i q^{53} +(-6.13156 + 4.05018i) q^{54} -1.65299 q^{55} +(-2.51338 - 1.29728i) q^{56} +(0.352179 + 0.322536i) q^{57} +(2.28676 + 11.8751i) q^{58} +(0.981080 + 0.566427i) q^{59} +(-2.10777 - 0.795817i) q^{60} +(-1.17619 + 0.679073i) q^{61} +(-6.66529 - 7.69466i) q^{62} +(-2.45652 + 1.72207i) q^{63} +(3.33036 - 7.27384i) q^{64} +(-0.123999 - 0.214773i) q^{65} +(-5.30333 - 3.26066i) q^{66} +(8.47415 + 4.89255i) q^{67} +(-6.46598 - 5.08828i) q^{68} +(-1.01633 - 3.22033i) q^{69} +(-0.869148 - 0.300972i) q^{70} +3.65788 q^{71} +(-5.19258 - 6.71097i) q^{72} +4.35806 q^{73} +(-3.80317 - 1.31698i) q^{74} +(7.74015 + 1.71374i) q^{75} +(-0.341014 + 0.433346i) q^{76} +(-2.20106 - 1.27078i) q^{77} +(0.0258278 - 0.933659i) q^{78} +(-7.28376 - 12.6158i) q^{79} +(0.734550 - 2.49569i) q^{80} +(-8.86156 + 1.57248i) q^{81} +(11.0743 + 12.7846i) q^{82} +(4.69138 - 2.70857i) q^{83} +(-2.19481 - 2.68008i) q^{84} +(-2.31720 - 1.33784i) q^{85} +(1.56151 + 8.10894i) q^{86} +(-3.20180 + 14.4610i) q^{87} +(3.29711 - 6.38790i) q^{88} +5.64356 q^{89} +(-1.98260 - 1.91920i) q^{90} -0.381311i q^{91} +(3.62046 - 1.44806i) q^{92} +(-3.75243 - 11.8899i) q^{93} +(-12.8465 + 2.47381i) q^{94} +(-0.0896612 + 0.155298i) q^{95} +(7.27961 - 6.55800i) q^{96} +(1.96718 + 3.40725i) q^{97} +(-0.925940 - 1.06894i) q^{98} +(-4.37674 - 6.24339i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 2 q^{6} - 36 q^{7} + 6 q^{8}+O(q^{10}) $ 72 * q + 2 * q^6 - 36 * q^7 + 6 * q^8	$ 72 q + 2 q^{6} - 36 q^{7} + 6 q^{8} - 8 q^{12} - 40 q^{17} - 21 q^{18} + 12 q^{20} + 12 q^{22} + 12 q^{23} - 12 q^{24} + 36 q^{25} - 14 q^{26} - 60 q^{30} - 15 q^{32} + 8 q^{33} + 6 q^{34} + 18 q^{36} - 3 q^{38} - 20 q^{39} + 21 q^{40} - 32 q^{41} - 13 q^{42} - 64 q^{44} + 12 q^{46} + 29 q^{48} - 36 q^{49} + 5 q^{50} - 9 q^{52} + 30 q^{54} - 3 q^{56} + 4 q^{57} + 9 q^{58} + 34 q^{60} - 12 q^{62} - 54 q^{64} + 40 q^{65} + 120 q^{66} + 55 q^{68} - 56 q^{71} + 15 q^{72} - 22 q^{74} + 12 q^{76} + 62 q^{78} + 94 q^{80} - 4 q^{81} + 12 q^{82} + 4 q^{84} - 3 q^{86} - 28 q^{87} - 12 q^{88} + 88 q^{89} - 83 q^{90} + 55 q^{92} - 18 q^{94} - 40 q^{95} - 83 q^{96}+O(q^{100}) $ 72 * q + 2 * q^6 - 36 * q^7 + 6 * q^8 - 8 * q^12 - 40 * q^17 - 21 * q^18 + 12 * q^20 + 12 * q^22 + 12 * q^23 - 12 * q^24 + 36 * q^25 - 14 * q^26 - 60 * q^30 - 15 * q^32 + 8 * q^33 + 6 * q^34 + 18 * q^36 - 3 * q^38 - 20 * q^39 + 21 * q^40 - 32 * q^41 - 13 * q^42 - 64 * q^44 + 12 * q^46 + 29 * q^48 - 36 * q^49 + 5 * q^50 - 9 * q^52 + 30 * q^54 - 3 * q^56 + 4 * q^57 + 9 * q^58 + 34 * q^60 - 12 * q^62 - 54 * q^64 + 40 * q^65 + 120 * q^66 + 55 * q^68 - 56 * q^71 + 15 * q^72 - 22 * q^74 + 12 * q^76 + 62 * q^78 + 94 * q^80 - 4 * q^81 + 12 * q^82 + 4 * q^84 - 3 * q^86 - 28 * q^87 - 12 * q^88 + 88 * q^89 - 83 * q^90 + 55 * q^92 - 18 * q^94 - 40 * q^95 - 83 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$1$	$1$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.462760	+	1.33636i	−0.327220	+	0.944948i
$2$	−0.462760	+	1.33636i	−0.327220	+	0.944948i
$3$	−1.16981	+	1.27732i	−0.675390	+	0.737461i
$3$	−1.16981	+	1.27732i	−0.675390	+	0.737461i
$4$	−1.57171	−	1.23683i	−0.785854	−	0.618413i
$5$	−0.563250	−	0.325193i	−0.251893	−	0.145431i	0.368738	−	0.929534i	$-0.379790\pi$
$5$	−0.563250	−	0.325193i	−0.251893	−	0.145431i	−0.620631	+	0.784103i	$0.713123\pi$
$6$	−1.16562	−	2.15438i	−0.475861	−	0.879520i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$8$	2.38016	−	1.52801i	0.841515	−	0.540234i
$9$	−0.263093	−	2.98844i	−0.0876977	−	0.996147i
$10$	0.695224	−	0.602218i	0.219849	−	0.190438i
$11$	2.20106	−	1.27078i	0.663643	−	0.383155i	−0.130020	−	0.991511i	$-0.541504\pi$
$11$	2.20106	−	1.27078i	0.663643	−	0.383155i	0.793664	+	0.608357i	$0.208171\pi$
$12$	3.41842	−	0.560724i	0.986813	−	0.161867i
$13$	0.330225	+	0.190655i	0.0915878	+	0.0528783i	0.545094	−	0.838375i	$-0.316494\pi$
$13$	0.330225	+	0.190655i	0.0915878	+	0.0528783i	−0.453507	+	0.891253i	$0.649827\pi$
$14$	1.38870	−	0.267418i	0.371146	−	0.0714704i
$15$	1.07427	−	0.339038i	0.277375	−	0.0875391i
$16$	0.940527	+	3.88785i	0.235132	+	0.971963i
$17$	4.11399			0.997788			0.498894	−	0.866663i	$-0.333740\pi$
$17$	4.11399			0.997788			0.498894	+	0.866663i	$0.333740\pi$
$18$	4.11538	+	1.03134i	0.970004	+	0.243090i
$19$		−	0.275717i		−	0.0632538i	−0.999500	−	0.0316269i	$-0.989931\pi$
$19$		−	0.275717i		−	0.0632538i	0.999500	−	0.0316269i	$-0.0100688\pi$
$20$	0.483058	+	1.20775i	0.108015	+	0.270061i
$21$	1.69110	+	0.374424i	0.369027	+	0.0817061i
$22$	0.679658	+	3.52947i	0.144904	+	0.752485i
$23$	−0.974828	+	1.68845i	−0.203266	+	0.352066i	−0.949579	−	0.313529i	$-0.898489\pi$
$23$	−0.974828	+	1.68845i	−0.203266	+	0.352066i	0.746313	+	0.665595i	$0.231822\pi$
$24$	−0.832578	+	4.82771i	−0.169949	+	0.985453i
$25$	−2.28850	−	3.96380i	−0.457700	−	0.792759i
$26$	−0.407598	+	0.353071i	−0.0799366	+	0.0692429i
$27$	4.12496	+	3.15985i	0.793850	+	0.608114i
$28$	−0.285268	+	1.97955i	−0.0539107	+	0.374100i
$29$	7.40561	−	4.27563i	1.37519	−	0.793965i	0.383611	−	0.923495i	$-0.374680\pi$
$29$	7.40561	−	4.27563i	1.37519	−	0.793965i	0.991575	+	0.129530i	$0.0413469\pi$
$30$	−0.0440534	+	1.59250i	−0.00804301	+	0.290750i
$31$	−3.59920	+	6.23399i	−0.646435	+	1.11966i	0.337533	+	0.941314i	$0.390408\pi$
$31$	−3.59920	+	6.23399i	−0.646435	+	1.11966i	−0.983968	+	0.178345i	$0.942926\pi$
$32$	−5.63080	−	0.542260i	−0.995395	−	0.0958590i
$33$	−0.951622	+	4.29802i	−0.165656	+	0.748190i
$34$	−1.90379	+	5.49776i	−0.326497	+	0.942858i
$35$			0.650385i			0.109935i
$36$	−3.28267	+	5.02236i	−0.547112	+	0.837059i
$37$			2.84592i			0.467867i	0.972253	+	0.233933i	$0.0751598\pi$
$37$			2.84592i			0.467867i	−0.972253	+	0.233933i	$0.924840\pi$
$38$	0.368457	+	0.127591i	0.0597716	+	0.0206979i
$39$	−0.629828	+	0.198772i	−0.100853	+	0.0318290i
$40$	−1.83753	+	0.0866409i	−0.290538	+	0.0136991i
$41$	5.98003	−	10.3577i	0.933924	−	1.61760i	0.157382	−	0.987538i	$-0.449694\pi$
$41$	5.98003	−	10.3577i	0.933924	−	1.61760i	0.776542	−	0.630066i	$-0.216972\pi$
$42$	−1.28294	+	2.08664i	−0.197961	+	0.321976i
$43$	5.05692	−	2.91961i	0.771173	−	0.445237i	−0.0621198	−	0.998069i	$-0.519786\pi$
$43$	5.05692	−	2.91961i	0.771173	−	0.445237i	0.833293	+	0.552832i	$0.186453\pi$
$44$	−5.03115	−	0.725027i	−0.758474	−	0.109302i
$45$	−0.823632	+	1.76880i	−0.122780	+	0.263677i
$46$	−1.80526	−	2.08407i	−0.266172	−	0.307279i
$47$	4.62536	+	8.01136i	0.674678	+	1.16858i	0.976563	+	0.215233i	$0.0690509\pi$
$47$	4.62536	+	8.01136i	0.674678	+	1.16858i	−0.301885	+	0.953344i	$0.597616\pi$
$48$	−6.06627	−	3.34669i	−0.875591	−	0.483054i
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	6.35608	−	1.22397i	0.898885	−	0.173096i
$51$	−4.81258	+	5.25488i	−0.673896	+	0.735830i
$52$	−0.283209	−	0.708084i	−0.0392740	−	0.0981936i
$53$		−	5.56863i		−	0.764911i	−0.923974	−	0.382455i	$-0.875079\pi$
$53$		−	5.56863i		−	0.764911i	0.923974	−	0.382455i	$-0.124921\pi$
$54$	−6.13156	+	4.05018i	−0.834400	+	0.551160i
$55$	−1.65299			−0.222890
$56$	−2.51338	−	1.29728i	−0.335864	−	0.173356i
$57$	0.352179	+	0.322536i	0.0466472	+	0.0427210i
$58$	2.28676	+	11.8751i	0.300266	+	1.55928i
$59$	0.981080	+	0.566427i	0.127726	+	0.0737425i	0.562502	−	0.826796i	$-0.309839\pi$
$59$	0.981080	+	0.566427i	0.127726	+	0.0737425i	−0.434776	+	0.900539i	$0.643172\pi$
$60$	−2.10777	−	0.795817i	−0.272112	−	0.102740i
$61$	−1.17619	+	0.679073i	−0.150596	+	0.0869464i	−0.573404	−	0.819273i	$-0.694378\pi$
$61$	−1.17619	+	0.679073i	−0.150596	+	0.0869464i	0.422809	+	0.906219i	$0.361044\pi$
$62$	−6.66529	−	7.69466i	−0.846492	−	0.977223i
$63$	−2.45652	+	1.72207i	−0.309492	+	0.216960i
$64$	3.33036	−	7.27384i	0.416295	−	0.909229i
$65$	−0.123999	−	0.214773i	−0.0153802	−	0.0266393i
$66$	−5.30333	−	3.26066i	−0.652795	−	0.401360i
$67$	8.47415	+	4.89255i	1.03528	+	0.597720i	0.918493	−	0.395437i	$-0.129407\pi$
$67$	8.47415	+	4.89255i	1.03528	+	0.597720i	0.116789	+	0.993157i	$0.462740\pi$
$68$	−6.46598	−	5.08828i	−0.784115	−	0.617045i
$69$	−1.01633	−	3.22033i	−0.122352	−	0.387682i
$70$	−0.869148	−	0.300972i	−0.103883	−	0.0359730i
$71$	3.65788			0.434110			0.217055	−	0.976159i	$-0.430355\pi$
$71$	3.65788			0.434110			0.217055	+	0.976159i	$0.430355\pi$
$72$	−5.19258	−	6.71097i	−0.611951	−	0.790896i
$73$	4.35806			0.510073			0.255036	−	0.966931i	$-0.417913\pi$
$73$	4.35806			0.510073			0.255036	+	0.966931i	$0.417913\pi$
$74$	−3.80317	−	1.31698i	−0.442110	−	0.153096i
$75$	7.74015	+	1.71374i	0.893755	+	0.197886i
$76$	−0.341014	+	0.433346i	−0.0391170	+	0.0497082i
$77$	−2.20106	−	1.27078i	−0.250834	−	0.144819i
$78$	0.0258278	−	0.933659i	0.00292442	−	0.105716i
$79$	−7.28376	−	12.6158i	−0.819487	−	1.41939i	−0.906061	−	0.423147i	$-0.860925\pi$
$79$	−7.28376	−	12.6158i	−0.819487	−	1.41939i	0.0865743	−	0.996245i	$-0.472408\pi$
$80$	0.734550	−	2.49569i	0.0821252	−	0.279026i
$81$	−8.86156	+	1.57248i	−0.984618	+	0.174720i
$82$	11.0743	+	12.7846i	1.22295	+	1.41182i
$83$	4.69138	−	2.70857i	0.514946	−	0.297304i	−0.219919	−	0.975518i	$-0.570579\pi$
$83$	4.69138	−	2.70857i	0.514946	−	0.297304i	0.734864	+	0.678214i	$0.237246\pi$
$84$	−2.19481	−	2.68008i	−0.239473	−	0.292420i
$85$	−2.31720	−	1.33784i	−0.251336	−	0.145109i
$86$	1.56151	+	8.10894i	0.168382	+	0.874409i
$87$	−3.20180	+	14.4610i	−0.343269	+	1.55038i
$88$	3.29711	−	6.38790i	0.351473	−	0.680953i
$89$	5.64356			0.598216			0.299108	−	0.954219i	$-0.403311\pi$
$89$	5.64356			0.598216			0.299108	+	0.954219i	$0.403311\pi$
$90$	−1.98260	−	1.91920i	−0.208985	−	0.202301i
$91$		−	0.381311i		−	0.0399722i
$92$	3.62046	−	1.44806i	0.377459	−	0.150971i
$93$	−3.75243	−	11.8899i	−0.389109	−	1.23293i
$94$	−12.8465	+	2.47381i	−1.32501	+	0.255154i
$95$	−0.0896612	+	0.155298i	−0.00919904	+	0.0159332i
$96$	7.27961	−	6.55800i	0.742972	−	0.669323i
$97$	1.96718	+	3.40725i	0.199736	+	0.345954i	0.948443	−	0.316948i	$-0.102658\pi$
$97$	1.96718	+	3.40725i	0.199736	+	0.345954i	−0.748706	+	0.662902i	$0.769325\pi$
$98$	−0.925940	−	1.06894i	−0.0935341	−	0.107979i
$99$	−4.37674	−	6.24339i	−0.439878	−	0.627485i
$100$	−1.30567	+	9.06040i	−0.130567	+	0.906040i
$101$	3.76919	−	2.17615i	0.375049	−	0.216535i	−0.300613	−	0.953746i	$-0.597191\pi$
$101$	3.76919	−	2.17615i	0.375049	−	0.216535i	0.675662	+	0.737212i	$0.263858\pi$
$102$	−4.79533	−	8.86307i	−0.474808	−	0.877575i
$103$	3.49728	−	6.05747i	0.344597	−	0.596860i	−0.640683	−	0.767805i	$-0.721349\pi$
$103$	3.49728	−	6.05747i	0.344597	−	0.596860i	0.985281	+	0.170945i	$0.0546822\pi$
$104$	1.07731	−	0.0507961i	0.105639	−	0.00498097i
$105$	−0.830750	−	0.760827i	−0.0810729	−	0.0742491i
$106$	7.44169	+	2.57694i	0.722801	+	0.250294i
$107$		−	7.87245i		−	0.761059i	−0.924769	−	0.380529i	$-0.875742\pi$
$107$		−	7.87245i		−	0.761059i	0.924769	−	0.380529i	$-0.124258\pi$
$108$	−2.57505	−	10.0682i	−0.247785	−	0.968815i
$109$		−	7.52943i		−	0.721188i	−0.932723	−	0.360594i	$-0.882574\pi$
$109$		−	7.52943i		−	0.721188i	0.932723	−	0.360594i	$-0.117426\pi$
$110$	0.764939	−	2.20899i	0.0729341	−	0.210619i
$111$	−3.63515	−	3.32919i	−0.345033	−	0.315992i
$112$	2.89672	−	2.75845i	0.273714	−	0.260649i
$113$	6.82840	−	11.8271i	0.642362	−	1.11260i	−0.342542	−	0.939503i	$-0.611288\pi$
$113$	6.82840	−	11.8271i	0.642362	−	1.11260i	0.984904	−	0.173101i	$-0.0553788\pi$
$114$	−0.593998	+	0.321380i	−0.0556330	+	0.0301000i
$115$	1.09814	−	0.634014i	0.102402	−	0.0591221i
$116$	−16.9277	−	2.43940i	−1.57169	−	0.226493i
$117$	0.482882	−	1.03702i	0.0446425	−	0.0958723i
$118$	−1.21095	+	1.04896i	−0.111477	+	0.0965642i
$119$	−2.05699	−	3.56282i	−0.188564	−	0.326603i
$120$	2.03889	−	2.44846i	0.186124	−	0.223513i
$121$	−2.27023	+	3.93216i	−0.206385	+	0.357469i
$122$	−0.363192	−	1.88606i	−0.0328819	−	0.170756i
$123$	6.23463	+	19.7550i	0.562157	+	1.78125i
$124$	13.3672	−	5.34643i	1.20041	−	0.480124i
$125$			6.22874i			0.557116i
$126$	−1.16452	−	4.07969i	−0.103744	−	0.363448i
$127$	−7.61942			−0.676114			−0.338057	−	0.941126i	$-0.609770\pi$
$127$	−7.61942			−0.676114			−0.338057	+	0.941126i	$0.609770\pi$
$128$	8.17929	+	7.81659i	0.722954	+	0.690896i
$129$	−2.18635	+	9.87470i	−0.192497	+	0.869419i
$130$	0.344396	−	0.0663193i	0.0302055	−	0.00581658i
$131$	−15.2196	−	8.78704i	−1.32974	−	0.767727i	−0.344483	−	0.938792i	$-0.611946\pi$
$131$	−15.2196	−	8.78704i	−1.32974	−	0.767727i	−0.985260	+	0.171065i	$0.945279\pi$
$132$	6.81158	−	5.57824i	0.592872	−	0.485524i
$133$	−0.238778	+	0.137858i	−0.0207047	+	0.0119538i
$134$	−10.4597	+	9.06042i	−0.903580	+	0.782701i
$135$	−1.29583	−	3.12120i	−0.111527	−	0.268630i
$136$	9.79196	−	6.28622i	0.839654	−	0.539039i
$137$	4.80166	+	8.31673i	0.410234	+	0.710546i	0.994915	−	0.100717i	$-0.0321137\pi$
$137$	4.80166	+	8.31673i	0.410234	+	0.710546i	−0.584681	+	0.811263i	$0.698780\pi$
$138$	4.77383	+	0.132058i	0.406376	+	0.0112416i
$139$	13.0905	+	7.55779i	1.11032	+	0.641043i	0.938912	−	0.344157i	$-0.111835\pi$
$139$	13.0905	+	7.55779i	1.11032	+	0.641043i	0.171407	+	0.985200i	$0.445169\pi$
$140$	0.804413	−	1.02222i	0.0679853	−	0.0863930i
$141$	−15.6439	−	3.46370i	−1.31745	−	0.291696i
$142$	−1.69272	+	4.88823i	−0.142050	+	0.410212i
$143$	0.969124			0.0810422
$144$	11.3712	−	3.83358i	0.947598	−	0.319465i
$145$	−5.56162			−0.461867
$146$	−2.01674	+	5.82394i	−0.166906	+	0.481992i
$147$	−0.521287	−	1.65174i	−0.0429950	−	0.136234i
$148$	3.51991	−	4.47296i	0.289335	−	0.367675i
$149$	−11.3580	−	6.55754i	−0.930483	−	0.537215i	−0.0435188	−	0.999053i	$-0.513857\pi$
$149$	−11.3580	−	6.55754i	−0.930483	−	0.537215i	−0.886964	+	0.461838i	$0.847190\pi$
$150$	−5.87200	+	9.55056i	−0.479447	+	0.779800i
$151$	−8.95009	−	15.5020i	−0.728348	−	1.26154i	−0.957581	−	0.288164i	$-0.906955\pi$
$151$	−8.95009	−	15.5020i	−0.728348	−	1.26154i	0.229233	−	0.973372i	$-0.426378\pi$
$152$	−0.421299	−	0.656252i	−0.0341718	−	0.0532290i
$153$	−1.08236	−	12.2944i	−0.0875037	−	0.993944i
$154$	2.71678	−	2.35333i	0.218924	−	0.189637i
$155$	4.05450	−	2.34087i	0.325665	−	0.188023i
$156$	1.23575	+	0.466575i	0.0989393	+	0.0373559i
$157$	−4.60492	−	2.65865i	−0.367512	−	0.212183i	0.304859	−	0.952398i	$-0.401391\pi$
$157$	−4.60492	−	2.65865i	−0.367512	−	0.212183i	−0.672371	+	0.740214i	$0.734724\pi$
$158$	20.2299	−	3.89561i	1.60940	−	0.309918i
$159$	7.11293	+	6.51424i	0.564092	+	0.516613i
$160$	2.99521	+	2.13652i	0.236792	+	0.168907i
$161$	1.94966			0.153654
$162$	1.99938	−	12.5699i	0.157086	−	0.987585i
$163$			6.57875i			0.515288i	0.966240	+	0.257644i	$0.0829461\pi$
$163$			6.57875i			0.515288i	−0.966240	+	0.257644i	$0.917054\pi$
$164$	−22.2095	+	8.88305i	−1.73427	+	0.693649i
$165$	1.93369	−	2.11140i	0.150537	−	0.164372i
$166$	1.44864	+	7.52278i	0.112436	+	0.583881i
$167$	−2.30277	+	3.98852i	−0.178194	+	0.308641i	−0.941262	−	0.337677i	$-0.890359\pi$
$167$	−2.30277	+	3.98852i	−0.178194	+	0.308641i	0.763068	+	0.646318i	$0.223692\pi$
$168$	4.59721	−	1.69282i	0.354683	−	0.130604i
$169$	−6.42730	−	11.1324i	−0.494408	−	0.856339i
$170$	2.86014	−	2.47752i	0.219363	−	0.190017i
$171$	−0.823964	+	0.0725392i	−0.0630101	+	0.00554721i
$172$	−11.5591	−	1.66575i	−0.881369	−	0.127012i
$173$	−10.1139	+	5.83924i	−0.768943	+	0.443950i	−0.832497	−	0.554029i	$-0.813090\pi$
$173$	−10.1139	+	5.83924i	−0.768943	+	0.443950i	0.0635543	+	0.997978i	$0.479756\pi$
$174$	−17.8434	−	10.9707i	−1.35271	−	0.831688i
$175$	−2.28850	+	3.96380i	−0.172994	+	0.299635i
$176$	7.01076	+	7.36218i	0.528456	+	0.554945i
$177$	−1.87119	+	0.590542i	−0.140647	+	0.0443879i
$178$	−2.61161	+	7.54181i	−0.195748	+	0.565283i
$179$			21.7056i			1.62235i	0.584803	+	0.811176i	$0.301172\pi$
$179$			21.7056i			1.62235i	−0.584803	+	0.811176i	$0.698828\pi$
$180$	3.48220	−	1.76134i	0.259548	−	0.131283i
$181$			26.5849i			1.97604i	0.154315	+	0.988022i	$0.450683\pi$
$181$			26.5849i			1.97604i	−0.154315	+	0.988022i	$0.549317\pi$
$182$	0.509568	+	0.176455i	0.0377717	+	0.0130797i
$183$	0.508523	−	2.29676i	0.0375911	−	0.169781i
$184$	0.259723	+	5.50834i	0.0191470	+	0.406080i
$185$	0.925473	−	1.60297i	0.0680421	−	0.117852i
$186$	17.6257	+	0.487578i	1.29238	+	0.0357509i
$187$	9.05511	−	5.22797i	0.662175	−	0.382307i
$188$	2.63894	−	18.3123i	0.192464	−	1.33556i
$189$	0.674030	−	5.15225i	0.0490284	−	0.374771i
$190$	−0.166042	−	0.191685i	−0.0120459	−	0.0139063i
$191$	7.12851	+	12.3469i	0.515801	+	0.893394i	0.999832	+	0.0183428i	$0.00583902\pi$
$191$	7.12851	+	12.3469i	0.515801	+	0.893394i	−0.484031	+	0.875051i	$0.660828\pi$
$192$	5.39513	+	12.7629i	0.389360	+	0.921086i
$193$	5.40052	−	9.35398i	0.388738	−	0.673314i	−0.603542	−	0.797331i	$-0.706244\pi$
$193$	5.40052	−	9.35398i	0.388738	−	0.673314i	0.992280	+	0.124017i	$0.0395778\pi$
$194$	−5.46363	+	1.05212i	−0.392266	+	0.0755375i
$195$	0.419390	+	0.0928568i	0.0300331	+	0.00664961i
$196$	1.85698	−	0.742726i	0.132641	−	0.0530518i
$197$			10.8319i			0.771740i	0.922553	+	0.385870i	$0.126099\pi$
$197$			10.8319i			0.771740i	−0.922553	+	0.385870i	$0.873901\pi$
$198$	10.3688	−	2.95970i	0.736878	−	0.210336i
$199$	−7.90135			−0.560112			−0.280056	−	0.959984i	$-0.590353\pi$
$199$	−7.90135			−0.560112			−0.280056	+	0.959984i	$0.590353\pi$
$200$	−11.5037	−	5.93763i	−0.813437	−	0.419854i
$201$	−16.1625	+	5.10085i	−1.14001	+	0.359786i
$202$	1.16388	+	6.04403i	0.0818903	+	0.425256i
$203$	−7.40561	−	4.27563i	−0.519772	−	0.300090i
$204$	14.0633	−	2.30681i	0.984630	−	0.161509i
$205$	−6.73651	+	3.88933i	−0.470498	+	0.271642i
$206$	6.47655	+	7.47677i	0.451242	+	0.520931i
$207$	5.30231	+	2.46900i	0.368536	+	0.171607i
$208$	−0.430655	+	1.46318i	−0.0298605	+	0.101453i
$209$	−0.350376	−	0.606869i	−0.0242360	−	0.0419780i
$210$	1.40118	−	0.758100i	0.0966903	−	0.0523139i
$211$	−19.8758	−	11.4753i	−1.36831	−	0.789994i	−0.377597	−	0.925970i	$-0.623250\pi$
$211$	−19.8758	−	11.4753i	−1.36831	−	0.789994i	−0.990712	+	0.135976i	$0.956583\pi$
$212$	−6.88743	+	8.75226i	−0.473030	+	0.601108i
$213$	−4.27902	+	4.67228i	−0.293193	+	0.320139i
$214$	10.5204	+	3.64305i	0.719161	+	0.249034i
$215$	−3.79775			−0.259004
$216$	14.6464	+	1.21797i	0.996560	+	0.0828726i
$217$	7.19840			0.488659
$218$	10.0620	+	3.48431i	0.681485	+	0.235988i
$219$	−5.09810	+	5.56664i	−0.344498	+	0.376159i
$220$	2.59802	+	2.04446i	0.175159	+	0.137838i
$221$	1.35854	+	0.784353i	0.0913852	+	0.0527613i
$222$	6.13119	−	3.31726i	0.411498	−	0.222640i
$223$	−6.27529	−	10.8691i	−0.420225	−	0.727850i	0.575737	−	0.817635i	$-0.304715\pi$
$223$	−6.27529	−	10.8691i	−0.420225	−	0.727850i	−0.995961	+	0.0897849i	$0.971382\pi$
$224$	2.34579	+	5.14755i	0.156735	+	0.343935i
$225$	−11.2435	+	7.88189i	−0.749566	+	0.525460i
$226$	12.6454	+	14.5983i	0.841159	+	0.971065i
$227$	−16.1277	+	9.31131i	−1.07043	+	0.618013i	−0.928299	−	0.371835i	$-0.878729\pi$
$227$	−16.1277	+	9.31131i	−1.07043	+	0.618013i	−0.142131	+	0.989848i	$0.545395\pi$
$228$	−0.154601	−	0.942516i	−0.0102387	−	0.0624197i
$229$	−25.5878	−	14.7731i	−1.69089	−	0.976234i	−0.953802	−	0.300435i	$-0.902868\pi$
$229$	−25.5878	−	14.7731i	−1.69089	−	0.976234i	−0.737085	−	0.675800i	$-0.763798\pi$
$230$	0.339093	+	1.76091i	0.0223591	+	0.116111i
$231$	4.19801	−	1.32488i	0.276209	−	0.0871709i
$232$	11.0934	−	21.4926i	0.728314	−	1.41106i
$233$	23.2846			1.52543			0.762714	−	0.646736i	$-0.223866\pi$
$233$	23.2846			1.52543			0.762714	+	0.646736i	$0.223866\pi$
$234$	1.16237	+	1.12519i	0.0759864	+	0.0735562i
$235$		−	6.01654i		−	0.392475i
$236$	−0.841400	−	2.10368i	−0.0547705	−	0.136938i
$237$	24.6351	+	5.45443i	1.60022	+	0.354303i
$238$	5.71309	−	1.10015i	0.370325	−	0.0713123i
$239$	0.280507	−	0.485852i	0.0181445	−	0.0314272i	−0.856811	−	0.515631i	$-0.827557\pi$
$239$	0.280507	−	0.485852i	0.0181445	−	0.0314272i	0.874955	+	0.484204i	$0.160891\pi$
$240$	2.32851	+	3.85773i	0.150305	+	0.249016i
$241$	12.0450	+	20.8626i	0.775890	+	1.34388i	0.934293	+	0.356506i	$0.116032\pi$
$241$	12.0450	+	20.8626i	0.775890	+	1.34388i	−0.158404	+	0.987374i	$0.550635\pi$
$242$	−4.20420	−	4.85349i	−0.270256	−	0.311994i
$243$	8.35778	−	13.1586i	0.536152	−	0.844121i
$244$	2.68852	+	0.387436i	0.172115	+	0.0248031i
$245$	0.563250	−	0.325193i	0.0359847	−	0.0207758i
$246$	−29.2848	−	0.810105i	−1.86713	−	0.0516504i
$247$	0.0525669	−	0.0910485i	0.00334475	−	0.00579328i
$248$	0.958932	+	20.3375i	0.0608922	+	1.29144i
$249$	−2.02831	+	9.16090i	−0.128539	+	0.580549i
$250$	−8.32383	−	2.88241i	−0.526445	−	0.182300i
$251$		−	2.14312i		−	0.135272i	−0.997710	−	0.0676362i	$-0.978454\pi$
$251$		−	2.14312i		−	0.135272i	0.997710	−	0.0676362i	$-0.0215457\pi$
$252$	5.99082	+	0.331702i	0.377386	+	0.0208952i
$253$			4.95517i			0.311529i
$254$	3.52596	−	10.1823i	0.221238	−	0.638892i
$255$	4.41953	−	1.39480i	0.276762	−	0.0873455i
$256$	−14.2308	+	7.31326i	−0.889426	+	0.457079i
$257$	−5.28744	+	9.15811i	−0.329821	+	0.571267i	−0.982476	−	0.186388i	$-0.940322\pi$
$257$	−5.28744	+	9.15811i	−0.329821	+	0.571267i	0.652655	+	0.757655i	$0.273655\pi$
$258$	−12.1844	−	7.49136i	−0.758566	−	0.466391i
$259$	2.46464	−	1.42296i	0.153145	−	0.0884185i
$260$	−0.0707462	+	0.490926i	−0.00438749	+	0.0304460i
$261$	−14.7258	−	21.0063i	−0.911506	−	1.30026i
$262$	18.7857	−	16.2726i	1.16058	−	1.00532i
$263$	5.47502	+	9.48302i	0.337604	+	0.584748i	0.983982	−	0.178270i	$-0.0570501\pi$
$263$	5.47502	+	9.48302i	0.337604	+	0.584748i	−0.646377	+	0.763018i	$0.723717\pi$
$264$	4.30241	+	11.6841i	0.264795	+	0.719106i
$265$	−1.81088	+	3.13654i	−0.111241	+	0.192676i
$266$	−0.0737316	−	0.382888i	−0.00452077	−	0.0234764i
$267$	−6.60188	+	7.20863i	−0.404029	+	0.441161i
$268$	−7.26765	−	18.1707i	−0.443942	−	1.10995i
$269$			18.7007i			1.14020i	0.821575	+	0.570100i	$0.193096\pi$
$269$			18.7007i			1.14020i	−0.821575	+	0.570100i	$0.806904\pi$
$270$	4.77069	−	0.287326i	0.290335	−	0.0174861i
$271$	25.0803			1.52352			0.761759	−	0.647861i	$-0.224336\pi$
$271$	25.0803			1.52352			0.761759	+	0.647861i	$0.224336\pi$
$272$	3.86931	+	15.9946i	0.234612	+	0.969813i
$273$	0.487056	+	0.446061i	0.0294779	+	0.0269968i
$274$	−13.3361	+	2.56810i	−0.805666	+	0.155145i
$275$	−10.0742	−	5.81636i	−0.607499	−	0.350740i
$276$	−2.38561	+	6.31844i	−0.143597	+	0.380326i
$277$	−0.187030	+	0.107982i	−0.0112375	+	0.00648800i	−0.505608	−	0.862763i	$-0.668732\pi$
$277$	−0.187030	+	0.107982i	−0.0112375	+	0.00648800i	0.494371	+	0.869251i	$0.335399\pi$
$278$	−16.1577	+	13.9961i	−0.969072	+	0.839432i
$279$	19.5769	+	9.11587i	1.17204	+	0.545753i
$280$	0.993796	+	1.54802i	0.0593907	+	0.0925121i
$281$	−6.20406	−	10.7457i	−0.370103	−	0.641038i	0.619478	−	0.785014i	$-0.287344\pi$
$281$	−6.20406	−	10.7457i	−0.370103	−	0.641038i	−0.989581	+	0.143977i	$0.954011\pi$
$282$	11.8681	−	19.3029i	0.706734	−	1.14947i
$283$	−4.76875	−	2.75324i	−0.283473	−	0.163663i	0.351522	−	0.936180i	$-0.385664\pi$
$283$	−4.76875	−	2.75324i	−0.283473	−	0.163663i	−0.634995	+	0.772517i	$0.718998\pi$
$284$	−5.74911	−	4.52415i	−0.341147	−	0.268459i
$285$	−0.0934784	−	0.296195i	−0.00553718	−	0.0175451i
$286$	−0.448471	+	1.29510i	−0.0265187	+	0.0765807i
$287$	−11.9601			−0.705980
$288$	−0.139087	+	16.9700i	−0.00819580	+	0.999966i
$289$	−0.0751273			−0.00441925
$290$	2.57369	−	7.43231i	0.151132	−	0.436440i
$291$	−6.65337	−	1.47312i	−0.390027	−	0.0863557i
$292$	−6.84960	−	5.39016i	−0.400843	−	0.315436i
$293$	26.0114	+	15.0177i	1.51960	+	0.877344i	0.999733	+	0.0230994i	$0.00735341\pi$
$293$	26.0114	+	15.0177i	1.51960	+	0.877344i	0.519871	+	0.854245i	$0.325980\pi$
$294$	2.44855	+	0.0677342i	0.142803	+	0.00395034i
$295$	−0.368396	−	0.638080i	−0.0214488	−	0.0371505i
$296$	4.34860	+	6.77376i	0.252757	+	0.393717i
$297$	13.0948	+	1.71309i	0.759835	+	0.0994034i
$298$	14.0192	−	12.1438i	0.812113	−	0.703471i
$299$	−0.643824	+	0.371712i	−0.0372333	+	0.0214967i
$300$	−10.0456	−	12.2667i	−0.579986	−	0.708218i
$301$	−5.05692	−	2.91961i	−0.291476	−	0.168284i
$302$	24.8580	−	4.78682i	1.43042	−	0.275451i
$303$	−1.62960	+	7.36014i	−0.0936183	+	0.422829i
$304$	1.07195	−	0.259319i	0.0614804	−	0.0148730i
$305$	0.883318			0.0505787
$306$	16.9306	+	4.24293i	0.967858	+	0.242552i
$307$			5.85643i			0.334244i	0.985936	+	0.167122i	$0.0534474\pi$
$307$			5.85643i			0.334244i	−0.985936	+	0.167122i	$0.946553\pi$
$308$	1.88768	+	4.71962i	0.107561	+	0.268925i
$309$	3.64617	+	11.5532i	0.207424	+	0.657240i
$310$	1.25198	+	6.50152i	0.0711076	+	0.369262i
$311$	−4.70853	+	8.15541i	−0.266996	+	0.462451i	−0.968085	−	0.250623i	$-0.919364\pi$
$311$	−4.70853	+	8.15541i	−0.266996	+	0.462451i	0.701089	+	0.713074i	$0.252698\pi$
$312$	−1.19537	+	1.43549i	−0.0676743	+	0.0812689i
$313$	1.37620	+	2.38365i	0.0777875	+	0.134732i	0.902295	−	0.431119i	$-0.141881\pi$
$313$	1.37620	+	2.38365i	0.0777875	+	0.134732i	−0.824508	+	0.565851i	$0.808548\pi$
$314$	5.68388	−	4.92350i	0.320760	−	0.277849i
$315$	1.94364	−	0.171112i	0.109512	−	0.00964107i
$316$	−4.15565	+	28.8371i	−0.233774	+	1.62222i
$317$	25.3262	−	14.6221i	1.42246	−	0.821257i	0.425951	−	0.904746i	$-0.359940\pi$
$317$	25.3262	−	14.6221i	1.42246	−	0.821257i	0.996509	+	0.0834890i	$0.0266063\pi$
$318$	−11.9969	+	6.49089i	−0.672755	+	0.363991i
$319$	10.8668	−	18.8218i	0.608422	−	1.05382i
$320$	−4.24123	+	3.01398i	−0.237092	+	0.168487i
$321$	10.0556	+	9.20926i	0.561251	+	0.514011i
$322$	−0.902222	+	2.60544i	−0.0502788	+	0.145195i
$323$		−	1.13430i		−	0.0631139i
$324$	15.8727	+	8.48873i	0.881815	+	0.471596i
$325$		−	1.74526i		−	0.0968095i
$326$	−8.79157	−	3.04438i	−0.486920	−	0.168613i
$327$	9.61749	+	8.80799i	0.531848	+	0.487083i
$328$	−1.59326	−	33.7906i	−0.0879728	−	1.86578i
$329$	4.62536	−	8.01136i	0.255004	−	0.441681i
$330$	1.92676	+	3.56117i	0.106065	+	0.196036i
$331$	−18.5309	+	10.6988i	−1.01855	+	0.588059i	−0.913683	−	0.406427i	$-0.866775\pi$
$331$	−18.5309	+	10.6988i	−1.01855	+	0.588059i	−0.104865	+	0.994486i	$0.533441\pi$
$332$	−10.7235	−	1.54534i	−0.588529	−	0.0848115i
$333$	8.50487	−	0.748742i	0.466064	−	0.0410308i
$334$	−4.26446	−	4.92306i	−0.233341	−	0.269378i
$335$	−3.18204	−	5.51146i	−0.173854	−	0.301123i
$336$	0.134814	+	6.92689i	0.00735473	+	0.377893i
$337$	−5.78431	+	10.0187i	−0.315091	+	0.545754i	−0.979457	−	0.201654i	$-0.935369\pi$
$337$	−5.78431	+	10.0187i	−0.315091	+	0.545754i	0.664366	+	0.747408i	$0.268702\pi$
$338$	17.8512	−	3.43755i	0.970977	−	0.186978i
$339$	7.11912	+	22.5576i	0.386657	+	1.22516i
$340$	1.98729	+	4.96867i	0.107776	+	0.269464i
$341$			18.2952i			0.990739i
$342$	0.284359	−	1.13468i	0.0153764	−	0.0613564i
$343$	1.00000			0.0539949
$344$	7.57510	−	14.6762i	0.408422	−	0.791287i
$345$	−0.474780	+	2.14436i	−0.0255613	+	0.115448i
$346$	−3.12303	−	16.2179i	−0.167895	−	0.871881i
$347$	−4.96639	−	2.86735i	−0.266610	−	0.153927i	0.360736	−	0.932668i	$-0.382525\pi$
$347$	−4.96639	−	2.86735i	−0.266610	−	0.153927i	−0.627346	+	0.778741i	$0.715859\pi$
$348$	22.9180	−	18.7684i	1.22854	−	1.00609i
$349$	−1.81499	+	1.04789i	−0.0971543	+	0.0560920i	−0.547790	−	0.836616i	$-0.684531\pi$
$349$	−1.81499	+	1.04789i	−0.0971543	+	0.0560920i	0.450636	+	0.892708i	$0.351197\pi$
$350$	−4.23803	−	4.89254i	−0.226532	−	0.261517i
$351$	0.759722	+	1.82991i	0.0405510	+	0.0976732i
$352$	−13.0828	+	5.96197i	−0.697316	+	0.317774i
$353$	−13.4873	−	23.3606i	−0.717855	−	1.24336i	−0.961848	−	0.273585i	$-0.911791\pi$
$353$	−13.4873	−	23.3606i	−0.717855	−	1.24336i	0.243993	−	0.969777i	$-0.421543\pi$
$354$	0.0767330	−	2.77385i	0.00407831	−	0.147429i
$355$	−2.06030	−	1.18952i	−0.109349	−	0.0631329i
$356$	−8.87002	−	6.98009i	−0.470110	−	0.369944i
$357$	6.95714	+	1.54038i	0.368211	+	0.0815254i
$358$	−29.0064	−	10.0445i	−1.53304	−	0.530866i
$359$	0.0285211			0.00150528			0.000752642	−	1.00000i	$-0.499760\pi$
$359$	0.0285211			0.00150528			0.000752642		1.00000i	$0.499760\pi$
$360$	0.742362	+	5.46855i	0.0391259	+	0.288218i
$361$	18.9240			0.995999
$362$	−35.5270	−	12.3024i	−1.86726	−	0.646602i
$363$	−2.36689	−	7.49969i	−0.124229	−	0.393632i
$364$	−0.471614	+	0.599309i	−0.0247193	+	0.0314123i
$365$	−2.45468	−	1.41721i	−0.128484	−	0.0741802i
$366$	2.83396	+	1.74241i	0.148134	+	0.0910775i
$367$	−2.07713	−	3.59770i	−0.108425	−	0.187798i	0.806707	−	0.590951i	$-0.201248\pi$
$367$	−2.07713	−	3.59770i	−0.108425	−	0.187798i	−0.915133	+	0.403153i	$0.867914\pi$
$368$	−7.48130	−	2.20195i	−0.389990	−	0.114785i
$369$	−32.5267	−	15.1459i	−1.69327	−	0.788466i
$370$	1.71387	+	1.97855i	0.0890997	+	0.102860i
$371$	−4.82258	+	2.78432i	−0.250376	+	0.144555i
$372$	−8.80802	+	23.3286i	−0.456675	+	1.20953i
$373$	−7.80969	−	4.50893i	−0.404370	−	0.233463i	0.283998	−	0.958825i	$-0.408339\pi$
$373$	−7.80969	−	4.50893i	−0.404370	−	0.233463i	−0.688368	+	0.725362i	$0.741673\pi$
$374$	2.79610	+	14.5202i	0.144583	+	0.750820i
$375$	−7.95610	−	7.28644i	−0.410851	−	0.376270i
$376$	23.2506	+	12.0007i	1.19906	+	0.618891i
$377$	3.26069			0.167934
$378$	6.57334	+	3.28500i	0.338096	+	0.168962i
$379$		−	29.5716i		−	1.51899i	−0.650513	−	0.759495i	$-0.725446\pi$
$379$		−	29.5716i		−	1.51899i	0.650513	−	0.759495i	$-0.274554\pi$
$380$	0.332997	−	0.133187i	0.0170824	−	0.00683236i
$381$	8.91326	−	9.73243i	0.456640	−	0.498608i
$382$	−19.7987	+	3.81258i	−1.01299	+	0.195069i
$383$	0.000970819	−	0.00168151i	4.96065e−5	−	8.59210e-5i	−0.866001	−	0.500043i	$-0.833318\pi$
$383$	0.000970819	−	0.00168151i	4.96065e−5	−	8.59210e-5i	0.866050	+	0.499957i	$0.166651\pi$
$384$	−19.5525	+	1.30365i	−0.997785	+	0.0665268i
$385$	0.826497	+	1.43154i	0.0421222	+	0.0729578i
$386$	10.0011	+	11.5457i	0.509044	+	0.587659i
$387$	−10.0555	−	14.3442i	−0.511152	−	0.729156i
$388$	1.12235	−	7.78825i	0.0569785	−	0.395388i
$389$	26.4825	−	15.2897i	1.34272	−	0.775219i	0.355513	−	0.934671i	$-0.384306\pi$
$389$	26.4825	−	15.2897i	1.34272	−	0.775219i	0.987206	+	0.159453i	$0.0509729\pi$
$390$	−0.318167	+	0.517485i	−0.0161110	+	0.0262039i
$391$	−4.01043	+	6.94626i	−0.202816	+	0.351288i
$392$	0.133215	+	2.82529i	0.00672836	+	0.142699i
$393$	29.0279	−	9.16114i	1.46426	−	0.462118i
$394$	−14.4753	−	5.01256i	−0.729255	−	0.252529i
$395$			9.47450i			0.476714i
$396$	−0.843040	+	15.2260i	−0.0423644	+	0.765137i
$397$			30.5066i			1.53108i	0.643386	+	0.765542i	$0.277529\pi$
$397$			30.5066i			1.53108i	−0.643386	+	0.765542i	$0.722471\pi$
$398$	3.65643	−	10.5590i	0.183280	−	0.529277i
$399$	0.103235	−	0.466264i	0.00516822	−	0.0233424i
$400$	13.2583	−	12.6254i	0.662913	−	0.631271i
$401$	−12.2503	+	21.2182i	−0.611753	+	1.05959i	0.379192	+	0.925318i	$0.376202\pi$
$401$	−12.2503	+	21.2182i	−0.611753	+	1.05959i	−0.990945	+	0.134269i	$0.957131\pi$
$402$	0.662786	−	23.9593i	0.0330568	−	1.19498i
$403$	−2.37709	+	1.37241i	−0.118411	+	0.0683647i
$404$	−8.61558	−	1.24157i	−0.428641	−	0.0617705i
$405$	5.50264	+	1.99602i	0.273428	+	0.0991829i
$406$	9.14079	−	7.91796i	0.453650	−	0.392962i
$407$	3.61654	+	6.26403i	0.179265	+	0.310497i
$408$	−3.42521	+	19.8611i	−0.169573	+	0.983273i
$409$	7.03943	−	12.1926i	0.348077	−	0.602887i	−0.637831	−	0.770177i	$-0.720168\pi$
$409$	7.03943	−	12.1926i	0.348077	−	0.602887i	0.985908	+	0.167289i	$0.0535014\pi$
$410$	−2.08015	−	10.8022i	−0.102731	−	0.533483i
$411$	−16.2402	−	3.59572i	−0.801068	−	0.177364i
$412$	−12.9887	+	5.19504i	−0.639909	+	0.255941i
$413$		−	1.13285i		−	0.0557441i
$414$	−5.75316	+	5.94323i	−0.282752	+	0.292094i
$415$	−3.52323			−0.172948
$416$	−1.75605	−	1.25261i	−0.0860972	−	0.0614143i
$417$	−24.9671	+	7.87956i	−1.22264	+	0.385863i
$418$	0.973134	−	0.187393i	0.0475975	−	0.00916571i
$419$	−10.3174	−	5.95675i	−0.504038	−	0.291006i	0.226342	−	0.974048i	$-0.427323\pi$
$419$	−10.3174	−	5.95675i	−0.504038	−	0.291006i	−0.730379	+	0.683042i	$0.760657\pi$
$420$	0.364687	+	2.22329i	0.0177949	+	0.108485i
$421$	3.18434	−	1.83848i	0.155195	−	0.0896021i	−0.420391	−	0.907343i	$-0.638107\pi$
$421$	3.18434	−	1.83848i	0.155195	−	0.0896021i	0.575587	+	0.817741i	$0.304774\pi$
$422$	24.5329	−	21.2509i	1.19424	−	1.03448i
$423$	22.7246	−	15.9304i	1.10491	−	0.774560i
$424$	−8.50894	−	13.2543i	−0.413230	−	0.643684i
$425$	−9.41485	−	16.3070i	−0.456687	−	0.791006i
$426$	−4.26368	−	7.88044i	−0.206576	−	0.381809i
$427$	1.17619	+	0.679073i	0.0569198	+	0.0328626i
$428$	−9.73684	+	12.3732i	−0.470648	+	0.598081i
$429$	−1.13369	+	1.23788i	−0.0547351	+	0.0597655i
$430$	1.75744	−	5.07515i	0.0847515	−	0.244746i
$431$	12.3366			0.594235			0.297118	−	0.954841i	$-0.403975\pi$
$431$	12.3366			0.594235			0.297118	+	0.954841i	$0.403975\pi$
$432$	−8.40540	+	19.0092i	−0.404405	+	0.914580i
$433$	−27.7226			−1.33226			−0.666131	−	0.745835i	$-0.732051\pi$
$433$	−27.7226			−1.33226			−0.666131	+	0.745835i	$0.732051\pi$
$434$	−3.33113	+	9.61964i	−0.159899	+	0.461757i
$435$	6.50603	−	7.10396i	0.311940	−	0.340609i
$436$	−9.31258	+	11.8341i	−0.445992	+	0.566748i
$437$	0.465535	+	0.268777i	0.0222695	+	0.0128573i
$438$	−5.07983	−	9.38891i	−0.242724	−	0.448620i
$439$	−10.8249	−	18.7493i	−0.516644	−	0.894853i	−0.999813	−	0.0193264i	$-0.993848\pi$
$439$	−10.8249	−	18.7493i	−0.516644	−	0.894853i	0.483169	−	0.875527i	$-0.339486\pi$
$440$	−3.93440	+	2.52579i	−0.187565	+	0.120413i
$441$	2.71961	+	1.26638i	0.129505	+	0.0603036i
$442$	−1.67685	+	1.45253i	−0.0797598	+	0.0690897i
$443$	19.7049	−	11.3766i	0.936206	−	0.540519i	0.0474369	−	0.998874i	$-0.484895\pi$
$443$	19.7049	−	11.3766i	0.936206	−	0.540519i	0.888769	+	0.458356i	$0.151561\pi$
$444$	1.59578	+	9.72855i	0.0757322	+	0.461697i
$445$	−3.17874	−	1.83524i	−0.150687	−	0.0869989i
$446$	17.4290	−	3.35625i	0.825287	−	0.158923i
$447$	21.6628	−	6.83672i	1.02461	−	0.323366i
$448$	−7.96451	+	0.752740i	−0.376288	+	0.0355636i
$449$	−35.3042			−1.66611			−0.833055	−	0.553191i	$-0.813410\pi$
$449$	−35.3042			−1.66611			−0.833055	+	0.553191i	$0.813410\pi$
$450$	−5.33000	−	18.6727i	−0.251259	−	0.880242i
$451$		−	30.3972i		−	1.43135i
$452$	−25.3604	+	10.1433i	−1.19285	+	0.477099i
$453$	30.2709	+	6.70226i	1.42225	+	0.314900i
$454$	−4.98002	−	25.8612i	−0.233724	−	1.21373i
$455$	−0.123999	+	0.214773i	−0.00581318	+	0.0100687i
$456$	1.33108	+	0.229556i	0.0623336	+	0.0107499i
$457$	7.67088	+	13.2864i	0.358829	+	0.621509i	0.987765	−	0.155947i	$-0.0498429\pi$
$457$	7.67088	+	13.2864i	0.358829	+	0.621509i	−0.628937	+	0.777456i	$0.716510\pi$
$458$	31.5832	−	27.3580i	1.47578	−	1.27836i
$459$	16.9700	+	12.9996i	0.792094	+	0.606769i
$460$	−2.51013	−	0.361728i	−0.117035	−	0.0168657i
$461$	−2.84349	+	1.64169i	−0.132435	+	0.0764612i	−0.564754	−	0.825260i	$-0.691029\pi$
$461$	−2.84349	+	1.64169i	−0.132435	+	0.0764612i	0.432319	+	0.901721i	$0.357695\pi$
$462$	−0.172151	+	6.22315i	−0.00800917	+	0.289527i
$463$	−17.6350	+	30.5448i	−0.819569	+	1.41954i	0.0864309	+	0.996258i	$0.472454\pi$
$463$	−17.6350	+	30.5448i	−0.819569	+	1.41954i	−0.906000	+	0.423278i	$0.860880\pi$
$464$	23.5882	+	24.7706i	1.09505	+	1.14995i
$465$	−1.75295	+	7.91726i	−0.0812913	+	0.367154i
$466$	−10.7752	+	31.1166i	−0.499151	+	1.44145i
$467$		−	30.4858i		−	1.41071i	−0.708852	−	0.705357i	$-0.750787\pi$
$467$		−	30.4858i		−	1.41071i	0.708852	−	0.705357i	$-0.249213\pi$
$468$	−2.04156	+	1.03265i	−0.0943711	+	0.0477341i
$469$		−	9.78510i		−	0.451834i
$470$	8.04025	+	2.78421i	0.370869	+	0.128426i
$471$	8.78282	−	2.77184i	0.404691	−	0.127720i
$472$	3.20064	−	0.150913i	0.147321	−	0.00694632i
$473$	7.42038	−	12.8525i	0.341189	−	0.590957i
$474$	−18.6892	+	30.3972i	−0.858423	+	1.39619i
$475$	−1.09289	+	0.630978i	−0.0501451	+	0.0289513i
$476$	−1.17359	+	8.14384i	−0.0537914	+	0.373272i
$477$	−16.6415	+	1.46507i	−0.761964	+	0.0670809i
$478$	0.519465	+	0.599690i	0.0237598	+	0.0274292i
$479$	−20.7437	−	35.9292i	−0.947806	−	1.64165i	−0.750034	−	0.661399i	$-0.769963\pi$
$479$	−20.7437	−	35.9292i	−0.947806	−	1.64165i	−0.197771	−	0.980248i	$-0.563370\pi$
$480$	−6.23285	+	1.32652i	−0.284490	+	0.0605471i
$481$	−0.542590	+	0.939794i	−0.0247400	+	0.0428509i
$482$	−33.4539	+	6.44212i	−1.52378	+	0.293430i
$483$	−2.28072	+	2.49033i	−0.103777	+	0.113314i
$484$	8.43154	−	3.37232i	0.383252	−	0.153287i
$485$		−	2.55885i		−	0.116191i
$486$	13.7169	+	17.2582i	0.622211	+	0.782850i
$487$	24.4657			1.10865			0.554324	−	0.832301i	$-0.312977\pi$
$487$	24.4657			1.10865			0.554324	+	0.832301i	$0.312977\pi$
$488$	−1.76189	+	3.41353i	−0.0797571	+	0.154523i
$489$	−8.40317	−	7.69588i	−0.380005	−	0.348020i
$490$	0.173925	+	0.903190i	0.00785711	+	0.0408020i
$491$	9.36735	+	5.40824i	0.422743	+	0.244070i	0.696250	−	0.717799i	$-0.254851\pi$
$491$	9.36735	+	5.40824i	0.422743	+	0.244070i	−0.273507	+	0.961870i	$0.588184\pi$
$492$	14.6344	−	38.7602i	0.659771	−	1.74744i
$493$	30.4666	−	17.5899i	1.37214	−	0.792208i
$494$	0.0973476	+	0.112382i	0.00437988	+	0.00505630i
$495$	0.434891	+	4.93988i	0.0195469	+	0.222031i
$496$	−27.6220	−	8.12992i	−1.24026	−	0.365044i
$497$	−1.82894	−	3.16781i	−0.0820391	−	0.142096i
$498$	−11.3036	−	6.94984i	−0.506528	−	0.311430i
$499$	23.9022	+	13.8000i	1.07001	+	0.617771i	0.928184	−	0.372121i	$-0.121369\pi$
$499$	23.9022	+	13.8000i	1.07001	+	0.617771i	0.141826	+	0.989892i	$0.454703\pi$
$500$	7.70386	−	9.78976i	0.344527	−	0.437811i
$501$	−2.40081	−	7.60718i	−0.107260	−	0.339864i
$502$	2.86398	+	0.991749i	0.127825	+	0.0442639i
$503$	−24.9186			−1.11106			−0.555532	−	0.831495i	$-0.687485\pi$
$503$	−24.9186			−1.11106			−0.555532	+	0.831495i	$0.687485\pi$
$504$	−3.21558	+	7.85239i	−0.143233	+	0.349773i
$505$	−2.83067			−0.125963
$506$	−6.62188	−	2.29305i	−0.294378	−	0.101939i
$507$	21.7384	+	4.81308i	0.965435	+	0.213756i
$508$	11.9755	+	9.42389i	0.531326	+	0.418117i
$509$	7.06763	+	4.08050i	0.313267	+	0.180865i	0.648388	−	0.761310i	$-0.275444\pi$
$509$	7.06763	+	4.08050i	0.313267	+	0.180865i	−0.335120	+	0.942175i	$0.608777\pi$
$510$	−0.181235	+	6.55154i	−0.00802521	+	0.290107i
$511$	−2.17903	−	3.77419i	−0.0963947	−	0.166961i
$512$	−3.18770	−	22.4018i	−0.140878	−	0.990027i
$513$	0.871225	−	1.13732i	0.0384655	−	0.0502140i
$514$	−9.79170	−	11.3039i	−0.431893	−	0.498594i
$515$	−3.93969	+	2.27458i	−0.173603	+	0.100230i
$516$	15.6496	−	12.8160i	0.688934	−	0.564193i
$517$	20.3614	+	11.7556i	0.895492	+	0.517012i
$518$	0.761050	+	3.95213i	0.0334386	+	0.173647i
$519$	4.37271	−	19.7494i	0.191941	−	0.866905i
$520$	−0.623315	−	0.321723i	−0.0273342	−	0.0141085i
$521$	−6.49477			−0.284541			−0.142270	−	0.989828i	$-0.545440\pi$
$521$	−6.49477			−0.284541			−0.142270	+	0.989828i	$0.545440\pi$
$522$	34.8865	−	9.95811i	1.52694	−	0.435855i
$523$		−	32.9112i		−	1.43911i	−0.694437	−	0.719553i	$-0.744347\pi$
$523$		−	32.9112i		−	1.43911i	0.694437	−	0.719553i	$-0.255653\pi$
$524$	13.0527	+	32.6346i	0.570211	+	1.42565i
$525$	−2.38593	−	7.56003i	−0.104131	−	0.329947i
$526$	−15.2063	+	2.92823i	−0.663027	+	0.127677i
$527$	−14.8070	+	25.6466i	−0.645005	+	1.11718i
$528$	−17.6051	+	0.342639i	−0.766164	+	0.0149115i
$529$	9.59942	+	16.6267i	0.417366	+	0.722899i
$530$	−3.35353	−	3.87145i	−0.145668	−	0.168165i
$531$	1.43462	−	3.08092i	0.0622571	−	0.133701i
$532$	0.545796	+	0.0786533i	0.0236632	+	0.00341005i
$533$	3.94951	−	2.28025i	0.171072	−	0.0987685i
$534$	−6.57823	−	12.1583i	−0.284668	−	0.526143i
$535$	−2.56006	+	4.43416i	−0.110681	+	0.191705i
$536$	27.6457	−	1.30352i	1.19411	−	0.0563034i
$537$	−27.7250	−	25.3914i	−1.19642	−	1.09572i
$538$	−24.9908	−	8.65392i	−1.07743	−	0.373097i
$539$			2.54156i			0.109473i
$540$	−1.82371	+	6.50832i	−0.0784801	+	0.280073i
$541$			13.1641i			0.565967i	0.959125	+	0.282984i	$0.0913242\pi$
$541$			13.1641i			0.565967i	−0.959125	+	0.282984i	$0.908676\pi$
$542$	−11.6061	+	33.5162i	−0.498526	+	1.43965i
$543$	−33.9575	−	31.0993i	−1.45726	−	1.33460i
$544$	−23.1650	−	2.23085i	−0.993193	−	0.0956469i
$545$	−2.44852	+	4.24095i	−0.104883	+	0.181662i
$546$	−0.821486	+	0.444462i	−0.0351564	+	0.0190212i
$547$	10.4271	−	6.02009i	0.445830	−	0.257400i	−0.260237	−	0.965545i	$-0.583801\pi$
$547$	10.4271	−	6.02009i	0.445830	−	0.257400i	0.706068	+	0.708144i	$0.250467\pi$
$548$	2.73953	−	19.0103i	0.117027	−	0.812079i
$549$	2.33882	+	3.33631i	0.0998183	+	0.142390i
$550$	12.4347	−	10.7712i	0.530217	−	0.459286i
$551$	−1.17886	−	2.04185i	−0.0502213	−	0.0869858i
$552$	−7.33974	−	6.11196i	−0.312400	−	0.260142i
$553$	−7.28376	+	12.6158i	−0.309737	+	0.536480i
$554$	−0.0577525	−	0.299909i	−0.00245367	−	0.0127419i
$555$	0.964874	+	3.05729i	0.0409566	+	0.129775i
$556$	−11.2267	−	28.0693i	−0.476119	−	1.19040i
$557$			28.4395i			1.20502i	0.798111	+	0.602510i	$0.205833\pi$
$557$			28.4395i			1.20502i	−0.798111	+	0.602510i	$0.794167\pi$
$558$	−21.2414	+	21.9432i	−0.899222	+	0.928931i
$559$	2.22656			0.0941734
$560$	−2.52860	+	0.611705i	−0.106853	+	0.0258493i
$561$	−3.91496	+	17.6820i	−0.165290	+	0.746535i
$562$	17.2312	−	3.31815i	0.726852	−	0.139968i
$563$	−14.8259	−	8.55971i	−0.624835	−	0.360749i	0.153914	−	0.988084i	$-0.450812\pi$
$563$	−14.8259	−	8.55971i	−0.624835	−	0.360749i	−0.778749	+	0.627335i	$0.784145\pi$
$564$	20.3036	+	24.7926i	0.854935	+	1.04396i
$565$	−7.69220	+	4.44109i	−0.323613	+	0.186838i
$566$	5.88610	−	5.09867i	0.247411	−	0.214313i
$567$	5.79259	+	6.88810i	0.243266	+	0.289273i
$568$	8.70635	−	5.58928i	0.365310	−	0.234521i
$569$	4.24083	+	7.34533i	0.177785	+	0.307932i	0.941122	−	0.338068i	$-0.109774\pi$
$569$	4.24083	+	7.34533i	0.177785	+	0.307932i	−0.763337	+	0.646001i	$0.776440\pi$
$570$	0.439080	+	0.0121463i	0.0183910	+	0.000508751i
$571$	−2.82466	−	1.63082i	−0.118208	−	0.0682476i	0.439730	−	0.898130i	$-0.355074\pi$
$571$	−2.82466	−	1.63082i	−0.118208	−	0.0682476i	−0.557938	+	0.829882i	$0.688407\pi$
$572$	−1.52318	−	1.19864i	−0.0636873	−	0.0501175i
$573$	−24.1100	−	5.33818i	−1.00721	−	0.223006i
$574$	5.53463	−	15.9829i	0.231011	−	0.667115i
$575$	8.92357			0.372139
$576$	−22.6136	−	8.03890i	−0.942234	−	0.334954i
$577$	−13.7437			−0.572157			−0.286078	−	0.958206i	$-0.592352\pi$
$577$	−13.7437			−0.572157			−0.286078	+	0.958206i	$0.592352\pi$
$578$	0.0347659	−	0.100397i	0.00144607	−	0.00417596i
$579$	5.63044	+	17.8406i	0.233993	+	0.741428i
$580$	8.74123	+	6.87875i	0.362960	+	0.285624i
$581$	−4.69138	−	2.70857i	−0.194631	−	0.112370i
$582$	5.04752	−	8.20958i	0.209227	−	0.340298i
$583$	−7.07651	−	12.2569i	−0.293079	−	0.507628i
$584$	10.3729	−	6.65917i	0.429234	−	0.275559i
$585$	−0.609214	+	0.427070i	−0.0251879	+	0.0176572i
$586$	−32.1061	+	27.8110i	−1.32629	+	1.14886i
$587$	22.3911	−	12.9275i	0.924179	−	0.533575i	0.0392129	−	0.999231i	$-0.487515\pi$
$587$	22.3911	−	12.9275i	0.924179	−	0.533575i	0.884966	+	0.465656i	$0.154182\pi$
$588$	−1.22361	+	3.24080i	−0.0504608	+	0.133648i
$589$	1.71882	+	0.992360i	0.0708227	+	0.0408895i
$590$	1.02318	−	0.197031i	0.0421238	−	0.00811164i
$591$	−13.8358	−	12.6712i	−0.569129	−	0.521225i
$592$	−11.0645	+	2.67667i	−0.454749	+	0.110010i
$593$	−15.3377			−0.629842			−0.314921	−	0.949118i	$-0.601978\pi$
$593$	−15.3377			−0.629842			−0.314921	+	0.949118i	$0.601978\pi$
$594$	−8.34902	+	16.7065i	−0.342565	+	0.685478i
$595$			2.67568i			0.109692i
$596$	9.74091	+	24.3544i	0.399003	+	0.997595i
$597$	9.24307	−	10.0926i	0.378294	−	0.413061i
$598$	−0.198805	−	1.03239i	−0.00812973	−	0.0422177i
$599$	−9.73061	+	16.8539i	−0.397582	+	0.688632i	−0.993427	−	0.114467i	$-0.963484\pi$
$599$	−9.73061	+	16.8539i	−0.397582	+	0.688632i	0.595845	+	0.803099i	$0.296817\pi$
$600$	21.0414	−	7.74805i	0.859013	−	0.316313i
$601$	18.9584	+	32.8369i	0.773328	+	1.33944i	0.935729	+	0.352719i	$0.114743\pi$
$601$	18.9584	+	32.8369i	0.773328	+	1.33944i	−0.162401	+	0.986725i	$0.551924\pi$
$602$	6.24179	−	5.40678i	0.254396	−	0.220364i
$603$	12.3916	−	26.6117i	0.504625	−	1.08371i
$604$	−5.10635	+	35.4343i	−0.207775	+	1.44180i
$605$	2.55742	−	1.47653i	0.103974	−	0.0600294i
$606$	−9.08167	−	5.58371i	−0.368918	−	0.226823i
$607$	9.93800	−	17.2131i	0.403371	−	0.698659i	−0.590759	−	0.806848i	$-0.701172\pi$
$607$	9.93800	−	17.2131i	0.403371	−	0.698659i	0.994130	+	0.108189i	$0.0345051\pi$
$608$	−0.149510	+	1.55251i	−0.00606345	+	0.0629625i
$609$	14.1245	−	4.45766i	0.572353	−	0.180634i
$610$	−0.408764	+	1.18043i	−0.0165504	+	0.0477942i
$611$			3.52740i			0.142703i
$612$	−13.5049	+	20.6619i	−0.545902	+	0.835208i
$613$		−	14.8585i		−	0.600129i	−0.953919	−	0.300065i	$-0.902992\pi$
$613$		−	14.8585i		−	0.600129i	0.953919	−	0.300065i	$-0.0970083\pi$
$614$	−7.82629	−	2.71012i	−0.315843	−	0.109372i
$615$	2.91252	−	13.1544i	0.117444	−	0.530439i
$616$	−7.18064	+	0.338573i	−0.289316	+	0.0136415i
$617$	−17.3444	+	30.0414i	−0.698259	+	1.20942i	0.270811	+	0.962633i	$0.412708\pi$
$617$	−17.3444	+	30.0414i	−0.698259	+	1.20942i	−0.969070	+	0.246787i	$0.920625\pi$
$618$	−17.1266	−	0.473771i	−0.688931	−	0.0190579i
$619$	−23.7452	+	13.7093i	−0.954400	+	0.551023i	−0.894445	−	0.447178i	$-0.852429\pi$
$619$	−23.7452	+	13.7093i	−0.954400	+	0.551023i	−0.0599547	+	0.998201i	$0.519096\pi$
$620$	−9.26773	−	1.33555i	−0.372201	−	0.0536370i
$621$	−9.35639	+	3.88449i	−0.375459	+	0.155879i
$622$	−8.71963	−	10.0663i	−0.349625	−	0.403621i
$623$	−2.82178	−	4.88746i	−0.113052	−	0.195812i
$624$	−1.36517	−	2.26173i	−0.0546504	−	0.0905415i
$625$	−9.41696	+	16.3106i	−0.376678	+	0.652426i
$626$	−3.82226	+	0.736041i	−0.152768	+	0.0294181i
$627$	1.18504	+	0.262378i	0.0473259	+	0.0104784i
$628$	3.94929	+	9.87409i	0.157594	+	0.394019i
$629$			11.7081i			0.466832i
$630$	−0.670771	+	2.67658i	−0.0267241	+	0.106638i
$631$	3.12371			0.124353			0.0621765	−	0.998065i	$-0.480196\pi$
$631$	3.12371			0.124353			0.0621765	+	0.998065i	$0.480196\pi$
$632$	−36.6137	−	18.8981i	−1.45641	−	0.751726i
$633$	37.9086	−	11.9639i	1.50673	−	0.475521i
$634$	7.82040	+	40.6113i	0.310588	+	1.61288i
$635$	4.29164	+	2.47778i	0.170308	+	0.0983277i
$636$	−3.12247	−	19.0359i	−0.123814	−	0.754824i
$637$	−0.330225	+	0.190655i	−0.0130840	+	0.00755404i
$638$	20.1240	+	23.2319i	0.796716	+	0.919759i
$639$	−0.962362	−	10.9314i	−0.0380705	−	0.432438i
$640$	−2.06509	−	7.06255i	−0.0816299	−	0.279172i
$641$	21.4463	+	37.1460i	0.847077	+	1.46718i	0.883805	+	0.467855i	$0.154973\pi$
$641$	21.4463	+	37.1460i	0.847077	+	1.46718i	−0.0367285	+	0.999325i	$0.511694\pi$
$642$	−16.9602	+	9.17626i	−0.669367	+	0.362158i
$643$	35.2154	+	20.3316i	1.38876	+	0.801801i	0.993176	−	0.116628i	$-0.0372085\pi$
$643$	35.2154	+	20.3316i	1.38876	+	0.801801i	0.395585	+	0.918429i	$0.370542\pi$
$644$	−3.06429	−	2.41138i	−0.120750	−	0.0950218i
$645$	4.44264	−	4.85094i	0.174929	−	0.191006i
$646$	1.51583	+	0.524906i	0.0596393	+	0.0206522i
$647$	12.0632			0.474254			0.237127	−	0.971479i	$-0.423794\pi$
$647$	12.0632			0.474254			0.237127	+	0.971479i	$0.423794\pi$
$648$	−18.6892	+	17.2833i	−0.734182	+	0.678953i
$649$	2.87922			0.113019
$650$	2.33229	+	0.807635i	0.0914799	+	0.0316780i
$651$	−8.42075	+	9.19466i	−0.330035	+	0.360367i
$652$	8.13677	−	10.3399i	0.318660	−	0.404941i
$653$	14.9305	+	8.62010i	0.584274	+	0.337331i	0.762830	−	0.646599i	$-0.223809\pi$
$653$	14.9305	+	8.62010i	0.584274	+	0.337331i	−0.178556	+	0.983930i	$0.557143\pi$
$654$	−16.2212	+	8.77643i	−0.634300	+	0.343185i
$655$	5.71496	+	9.89861i	0.223302	+	0.386771i
$656$	45.8937	+	13.5078i	1.79185	+	0.527390i
$657$	−1.14658	−	13.0238i	−0.0447322	−	0.508108i
$658$	8.56562	+	9.88847i	0.333923	+	0.385493i
$659$	−22.6656	+	13.0860i	−0.882926	+	0.509757i	−0.871622	−	0.490179i	$-0.836932\pi$
$659$	−22.6656	+	13.0860i	−0.882926	+	0.509757i	−0.0113038	+	0.999936i	$0.503598\pi$
$660$	−5.65063	+	0.926873i	−0.219950	+	0.0360785i
$661$	4.47602	+	2.58423i	0.174097	+	0.100515i	0.584516	−	0.811382i	$-0.301284\pi$
$661$	4.47602	+	2.58423i	0.174097	+	0.100515i	−0.410419	+	0.911897i	$0.634618\pi$
$662$	−5.72210	−	29.7149i	−0.222396	−	1.15490i
$663$	−2.59110	+	0.817746i	−0.100630	+	0.0317586i
$664$	7.02753	−	13.6153i	0.272721	−	0.528377i
$665$	0.179322			0.00695382
$666$	−2.93512	+	11.7120i	−0.113734	+	0.453832i
$667$			16.6720i			0.645543i
$668$	8.55239	−	3.42066i	0.330902	−	0.132349i
$669$	21.2242	+	4.69924i	0.820577	+	0.181683i
$670$	8.83781	−	1.70187i	0.341434	−	0.0657490i
$671$	−1.72591	+	2.98936i	−0.0666278	+	0.115403i
$672$	−9.31920	−	3.02532i	−0.359496	−	0.116704i
$673$	8.77902	+	15.2057i	0.338406	+	0.586137i	0.984133	−	0.177432i	$-0.0567789\pi$
$673$	8.77902	+	15.2057i	0.338406	+	0.586137i	−0.645727	+	0.763568i	$0.723446\pi$
$674$	−10.7119	−	12.3662i	−0.412605	−	0.476327i
$675$	3.08503	−	23.5818i	0.118743	−	0.907666i
$676$	−3.66701	+	25.4463i	−0.141039	+	0.978705i
$677$	−32.4915	+	18.7590i	−1.24875	+	0.720967i	−0.970860	−	0.239645i	$-0.922969\pi$
$677$	−32.4915	+	18.7590i	−1.24875	+	0.720967i	−0.277891	+	0.960613i	$0.589635\pi$
$678$	−33.4394	−	0.925033i	−1.28423	−	0.0355257i
$679$	1.96718	−	3.40725i	0.0754933	−	0.130758i
$680$	−7.55956	+	0.356439i	−0.289896	+	0.0136688i
$681$	6.97276	−	31.4926i	0.267197	−	1.20680i
$682$	−24.4489	−	8.46626i	−0.936196	−	0.324190i
$683$			22.0581i			0.844031i	0.906589	+	0.422015i	$0.138677\pi$
$683$			22.0581i			0.844031i	−0.906589	+	0.422015i	$0.861323\pi$
$684$	1.38475	+	0.905089i	0.0529472	+	0.0346069i
$685$		−	6.24587i		−	0.238642i
$686$	−0.462760	+	1.33636i	−0.0176682	+	0.0510224i
$687$	48.8028	−	15.4021i	1.86194	−	0.587625i
$688$	16.1072	+	16.9146i	0.614081	+	0.644863i
$689$	1.06169	−	1.83890i	0.0404471	−	0.0700565i
$690$	−2.64592	−	1.62680i	−0.100728	−	0.0619312i
$691$	17.9747	−	10.3777i	0.683791	−	0.394787i	−0.117491	−	0.993074i	$-0.537485\pi$
$691$	17.9747	−	10.3777i	0.683791	−	0.394787i	0.801282	+	0.598287i	$0.204152\pi$
$692$	23.1182	+	3.33150i	0.878821	+	0.126645i
$693$	−3.21857	+	6.91206i	−0.122263	+	0.262567i
$694$	6.13005	−	5.30998i	0.232693	−	0.201564i
$695$	−4.91548	−	8.51385i	−0.186455	−	0.322949i
$696$	14.4758	+	39.3119i	0.548703	+	1.49012i
$697$	24.6018	−	42.6115i	0.931858	−	1.61403i
$698$	−0.560446	−	2.91040i	−0.0212132	−	0.110160i
$699$	−27.2386	+	29.7419i	−1.03026	+	1.12494i
$700$	8.49937	−	3.39946i	0.321246	−	0.128487i
$701$		−	39.1099i		−	1.47716i	−0.674165	−	0.738580i	$-0.735497\pi$
$701$		−	39.1099i		−	1.47716i	0.674165	−	0.738580i	$-0.264503\pi$
$702$	−2.79698	+	0.168454i	−0.105565	+	0.00635790i
$703$	0.784669			0.0295944
$704$	−1.91313	−	20.2423i	−0.0721039	−	0.762910i
$705$	7.68504	+	7.03820i	0.289435	+	0.265074i
$706$	37.4596	−	7.21347i	1.40981	−	0.271483i
$707$	−3.76919	−	2.17615i	−0.141755	−	0.0818424i
$708$	3.67135	+	1.38617i	0.137978	+	0.0520955i
$709$	25.9908	−	15.0058i	0.976105	−	0.563554i	0.0750129	−	0.997183i	$-0.476100\pi$
$709$	25.9908	−	15.0058i	0.976105	−	0.563554i	0.901092	+	0.433628i	$0.142767\pi$
$710$	2.54304	−	2.20284i	0.0954387	−	0.0826711i
$711$	−35.7854	+	25.0862i	−1.34206	+	0.940807i
$712$	13.4326	−	8.62342i	0.503408	−	0.323176i
$713$	−7.01720	−	12.1541i	−0.262796	−	0.455176i
$714$	−5.27798	+	8.58441i	−0.197523	+	0.321264i
$715$	−0.545859	−	0.315152i	−0.0204140	−	0.0117860i
$716$	26.8460	−	34.1148i	1.00328	−	1.27493i
$717$	0.292449	+	0.926651i	0.0109217	+	0.0346064i
$718$	−0.0131984	+	0.0381144i	−0.000492560	+	0.00142242i
$719$	29.5953			1.10372			0.551860	−	0.833937i	$-0.313918\pi$
$719$	29.5953			1.10372			0.551860	+	0.833937i	$0.313918\pi$
$720$	−7.65147	−	1.53856i	−0.285154	−	0.0573388i
$721$	−6.99456			−0.260491
$722$	−8.75725	+	25.2892i	−0.325911	+	0.941167i
$723$	−40.7387	−	9.01992i	−1.51509	−	0.335454i
$724$	32.8809	−	41.7838i	1.22201	−	1.55288i
$725$	−33.8955	−	19.5696i	−1.25885	−	0.726795i
$726$	11.1176	+	0.307545i	0.412612	+	0.0114141i
$727$	24.1526	+	41.8335i	0.895770	+	1.55152i	0.832849	+	0.553500i	$0.186708\pi$
$727$	24.1526	+	41.8335i	0.895770	+	1.55152i	0.0629205	+	0.998019i	$0.479959\pi$
$728$	−0.582647	−	0.907582i	−0.0215943	−	0.0336372i
$729$	7.03067	+	26.0686i	0.260395	+	0.965502i
$730$	3.02983	−	2.62451i	0.112139	−	0.0971373i
$731$	20.8041	−	12.0112i	0.769467	−	0.444252i
$732$	−3.63993	+	2.98087i	−0.134536	+	0.110176i
$733$	15.2976	+	8.83209i	0.565031	+	0.326221i	0.755162	−	0.655538i	$-0.227558\pi$
$733$	15.2976	+	8.83209i	0.565031	+	0.326221i	−0.190131	+	0.981759i	$0.560891\pi$
$734$	5.76903	−	1.11092i	0.212939	−	0.0410049i
$735$	−0.243520	+	1.09986i	−0.00898238	+	0.0405691i
$736$	6.40464	−	8.97873i	0.236078	−	0.330960i
$737$	24.8694			0.916077
$738$	35.2924	−	36.4585i	1.29913	−	1.34205i
$739$			7.14501i			0.262833i	0.991327	+	0.131417i	$0.0419526\pi$
$739$			7.14501i			0.262833i	−0.991327	+	0.131417i	$0.958047\pi$
$740$	−3.43716	+	1.37475i	−0.126353	+	0.0505367i
$741$	0.0548049	+	0.173654i	0.00201331	+	0.00637934i
$742$	−1.48915	−	7.73316i	−0.0546685	−	0.283893i
$743$	17.1692	−	29.7380i	0.629878	−	1.09098i	−0.357697	−	0.933838i	$-0.616438\pi$
$743$	17.1692	−	29.7380i	0.629878	−	1.09098i	0.987576	−	0.157144i	$-0.0502286\pi$
$744$	−27.0993	−	22.5662i	−0.993509	−	0.827316i
$745$	4.26493	+	7.38707i	0.156255	+	0.270641i
$746$	9.63955	−	8.34999i	0.352929	−	0.305715i
$747$	−9.32867	−	13.3073i	−0.341318	−	0.486889i
$748$	−20.6981	−	2.98275i	−0.756796	−	0.109060i
$749$	−6.81774	+	3.93623i	−0.249115	+	0.143827i
$750$	13.4191	−	7.26033i	0.489994	−	0.265110i
$751$	−12.5390	+	21.7181i	−0.457553	+	0.792505i	−0.998831	−	0.0483387i	$-0.984607\pi$
$751$	−12.5390	+	21.7181i	−0.457553	+	0.792505i	0.541278	+	0.840844i	$0.317941\pi$
$752$	−26.7967	+	25.5176i	−0.977176	+	0.930532i
$753$	2.73745	+	2.50704i	0.0997582	+	0.0913616i
$754$	−1.50891	+	4.35744i	−0.0549514	+	0.158689i
$755$			11.6420i			0.423696i
$756$	−7.43181	+	7.26417i	−0.270292	+	0.264195i
$757$			51.0824i			1.85662i	0.371808	+	0.928310i	$0.378738\pi$
$757$			51.0824i			1.85662i	−0.371808	+	0.928310i	$0.621262\pi$
$758$	39.5182	+	13.6845i	1.43537	+	0.497045i
$759$	−6.32934	−	5.79660i	−0.229740	−	0.210403i
$760$	0.0238884	+	0.506637i	0.000866522	+	0.0183777i
$761$	9.50244	−	16.4587i	0.344463	−	0.596628i	−0.640793	−	0.767714i	$-0.721394\pi$
$761$	9.50244	−	16.4587i	0.344463	−	0.596628i	0.985256	+	0.171086i	$0.0547276\pi$
$762$	8.88132	+	16.4151i	0.321736	+	0.594656i
$763$	−6.52068	+	3.76471i	−0.236064	+	0.136292i
$764$	4.06708	−	28.2225i	0.147142	−	1.02105i
$765$	−3.38841	+	7.27680i	−0.122508	+	0.263093i
$766$	0.00179784	+	0.00207550i	6.49586e−5	+	7.49907e-5i
$767$	0.215985	+	0.374096i	0.00779875	+	0.0135078i
$768$	7.30596	−	26.7324i	0.263631	−	0.964624i
$769$	−16.2156	+	28.0862i	−0.584749	+	1.01282i	0.410158	+	0.912015i	$0.365474\pi$
$769$	−16.2156	+	28.0862i	−0.584749	+	1.01282i	−0.994907	+	0.100800i	$0.967860\pi$
$770$	−2.29551	+	0.442040i	−0.0827246	+	0.0159300i
$771$	−5.51254	−	17.4670i	−0.198529	−	0.629058i
$772$	−20.0573	+	8.02221i	−0.721877	+	0.288726i
$773$		−	32.3434i		−	1.16331i	−0.813436	−	0.581655i	$-0.802405\pi$
$773$		−	32.3434i		−	1.16331i	0.813436	−	0.581655i	$-0.197595\pi$
$774$	23.8223	−	6.79989i	0.856273	−	0.244417i
$775$	32.9471			1.18349
$776$	9.88852	+	5.10394i	0.354977	+	0.183221i
$777$	−1.06558	+	4.81273i	−0.0382276	+	0.172656i
$778$	8.17747	+	42.4656i	0.293177	+	1.52247i
$779$	−2.85580	−	1.64880i	−0.102320	−	0.0590742i
$780$	−0.544310	−	0.664656i	−0.0194894	−	0.0237985i
$781$	8.05119	−	4.64836i	0.288094	−	0.166331i
$782$	−7.42683	−	8.57382i	−0.265583	−	0.306599i
$783$	44.0582	+	5.76380i	1.57451	+	0.205982i
$784$	−3.83724	−	1.12941i	−0.137044	−	0.0403360i
$785$	1.72915	+	2.99497i	0.0617159	+	0.106895i
$786$	−1.19037	+	43.0311i	−0.0424590	+	1.53487i
$787$	46.1972	+	26.6720i	1.64675	+	0.950753i	0.978351	+	0.206951i	$0.0663542\pi$
$787$	46.1972	+	26.6720i	1.64675	+	0.950753i	0.668401	+	0.743801i	$0.266979\pi$
$788$	13.3972	−	17.0246i	0.477254	−	0.606475i
$789$	−18.5176	−	4.09996i	−0.659243	−	0.145963i
$790$	−12.6613	−	4.38441i	−0.450470	−	0.155990i
$791$	−13.6568			−0.485580
$792$	−19.9573	−	8.17260i	−0.709153	−	0.290401i
$793$	−0.517875			−0.0183903
$794$	−40.7678	−	14.1172i	−1.44679	−	0.501002i
$795$	−1.88798	−	5.98222i	−0.0669596	−	0.212167i
$796$	12.4186	+	9.77259i	0.440166	+	0.346380i
$797$	−17.2656	−	9.96829i	−0.611578	−	0.353095i	0.162005	−	0.986790i	$-0.448204\pi$
$797$	−17.2656	−	9.96829i	−0.611578	−	0.353095i	−0.773583	+	0.633695i	$0.781537\pi$
$798$	0.575323	+	0.353727i	0.0203662	+	0.0125218i
$799$	19.0287	+	32.9586i	0.673186	+	1.16599i
$800$	10.7367	+	23.5603i	0.379599	+	0.832983i
$801$	−1.48478	−	16.8654i	−0.0524622	−	0.595911i
$802$	−22.6862	−	26.1898i	−0.801076	−	0.924793i
$803$	9.59235	−	5.53814i	0.338507	−	0.195437i
$804$	31.7116	+	11.9731i	1.11838	+	0.422260i
$805$	−1.09814	−	0.634014i	−0.0387045	−	0.0223460i
$806$	−0.734014	−	3.81174i	−0.0258546	−	0.134263i
$807$	−23.8868	−	21.8762i	−0.840854	−	0.770080i
$808$	5.64613	−	10.9390i	0.198630	−	0.384831i
$809$	18.4879			0.649999			0.325000	−	0.945714i	$-0.394636\pi$
$809$	18.4879			0.649999			0.325000	+	0.945714i	$0.394636\pi$
$810$	−5.21379	+	6.42982i	−0.183194	+	0.225921i
$811$		−	9.08842i		−	0.319138i	−0.987187	−	0.159569i	$-0.948990\pi$
$811$		−	9.08842i		−	0.319138i	0.987187	−	0.159569i	$-0.0510104\pi$
$812$	6.35124	+	15.8795i	0.222885	+	0.557261i
$813$	−29.3391	+	32.0355i	−1.02897	+	1.12354i
$814$	−10.0446	+	1.93425i	−0.352062	+	0.0677956i
$815$	2.13936	−	3.70548i	0.0749386	−	0.129797i
$816$	−24.9565	−	13.7682i	−0.873654	−	0.481985i
$817$	−0.804987	−	1.39428i	−0.0281629	−	0.0487796i
$818$	13.0362	+	15.0495i	0.455799	+	0.526192i
$819$	−1.13952	+	0.100320i	−0.0398182	+	0.00350547i
$820$	15.3982	+	2.21900i	0.537730	+	0.0774910i
$821$	20.5085	−	11.8406i	0.715753	−	0.413240i	−0.0974345	−	0.995242i	$-0.531064\pi$
$821$	20.5085	−	11.8406i	0.715753	−	0.413240i	0.813188	+	0.582002i	$0.197730\pi$
$822$	12.3205	−	20.0387i	0.429725	−	0.698930i
$823$	−1.67747	+	2.90546i	−0.0584729	+	0.101278i	−0.893780	−	0.448506i	$-0.851956\pi$
$823$	−1.67747	+	2.90546i	−0.0584729	+	0.101278i	0.835307	+	0.549783i	$0.185290\pi$
$824$	−0.931778	−	19.7616i	−0.0324600	−	0.688430i
$825$	19.2143	−	6.06399i	0.668955	−	0.211121i
$826$	1.51390	+	0.524239i	0.0526753	+	0.0182406i
$827$			0.683428i			0.0237651i	0.999929	+	0.0118826i	$0.00378243\pi$
$827$			0.683428i			0.0237651i	−0.999929	+	0.0118826i	$0.996218\pi$
$828$	−5.27996	−	10.4386i	−0.183491	−	0.362765i
$829$			0.172036i			0.00597507i	0.999996	+	0.00298754i	$0.000950964\pi$
$829$			0.172036i			0.00597507i	−0.999996	+	0.00298754i	$0.999049\pi$
$830$	1.63041	−	4.70830i	0.0565923	−	0.163427i
$831$	0.0808621	−	0.365215i	0.00280507	−	0.0126692i
$832$	2.48656	−	1.76705i	0.0862061	−	0.0612614i
$833$	−2.05699	+	3.56282i	−0.0712706	+	0.123444i
$834$	1.02384	−	37.0113i	0.0354527	−	1.28160i
$835$	2.59408	−	1.49769i	0.0897717	−	0.0518297i
$836$	−0.199902	+	1.38717i	−0.00691376	+	0.0479764i
$837$	−34.5451	+	14.3421i	−1.19405	+	0.495735i
$838$	12.7348	−	11.0312i	0.439917	−	0.381066i
$839$	−1.65731	−	2.87054i	−0.0572165	−	0.0991020i	0.835998	−	0.548732i	$-0.184889\pi$
$839$	−1.65731	−	2.87054i	−0.0572165	−	0.0991020i	−0.893215	+	0.449630i	$0.851556\pi$
$840$	−3.13987	−	0.541497i	−0.108336	−	0.0186834i
$841$	22.0620	−	38.2125i	0.760759	−	1.31767i
$842$	0.983285	+	5.10620i	0.0338862	+	0.175971i
$843$	20.9833	+	4.64590i	0.722704	+	0.160013i
$844$	17.0460	+	42.6188i	0.586749	+	1.46700i
$845$			8.36045i			0.287608i
$846$	10.7726	+	37.7401i	0.370371	+	1.29753i
$847$	4.54047			0.156012
$848$	21.6500	−	5.23745i	0.743465	−	0.179855i
$849$	9.09530	−	2.87046i	0.312150	−	0.0985139i
$850$	26.1488	−	5.03540i	0.896897	−	0.172713i
$851$	−4.80520	−	2.77428i	−0.164720	−	0.0951012i
$852$	12.5042	−	2.05106i	0.428385	−	0.0702681i
$853$	−31.9005	+	18.4178i	−1.09225	+	0.630612i	−0.934175	−	0.356814i	$-0.883863\pi$
$853$	−31.9005	+	18.4178i	−1.09225	+	0.630612i	−0.158077	+	0.987427i	$0.550530\pi$
$854$	−1.45178	+	1.25756i	−0.0496788	+	0.0430329i
$855$	0.487687	+	0.227089i	0.0166786	+	0.00776629i
$856$	−12.0292	−	18.7377i	−0.411149	−	0.640442i
$857$	−18.4566	−	31.9677i	−0.630465	−	1.09200i	−0.987457	−	0.157890i	$-0.949531\pi$
$857$	−18.4566	−	31.9677i	−0.630465	−	1.09200i	0.356992	−	0.934108i	$-0.383802\pi$
$858$	−1.12963	−	2.08786i	−0.0385648	−	0.0712783i
$859$	−12.9520	−	7.47782i	−0.441915	−	0.255140i	0.262495	−	0.964933i	$-0.415455\pi$
$859$	−12.9520	−	7.47782i	−0.441915	−	0.255140i	−0.704410	+	0.709794i	$0.748788\pi$
$860$	5.96895	+	4.69715i	0.203540	+	0.160172i
$861$	13.9910	−	15.2768i	0.476812	−	0.520633i
$862$	−5.70890	+	16.4862i	−0.194446	+	0.561521i
$863$	−39.2886			−1.33740			−0.668699	−	0.743533i	$-0.733149\pi$
$863$	−39.2886			−1.33740			−0.668699	+	0.743533i	$0.733149\pi$
$864$	−21.5134	−	20.0293i	−0.731901	−	0.681411i
$865$	7.59552			0.258255
$866$	12.8289	−	37.0473i	0.435943	−	1.25892i
$867$	0.0878846	−	0.0959616i	0.00298472	−	0.00325903i
$868$	−11.3138	−	8.90316i	−0.384014	−	0.302193i
$869$	−32.0639	−	18.5121i	−1.08769	−	0.627980i
$870$	6.48271	+	11.9818i	0.219785	+	0.406221i
$871$	1.86558	+	3.23128i	0.0632128	+	0.109488i
$872$	−11.5051	−	17.9213i	−0.389610	−	0.606891i
$873$	9.66481	−	6.77521i	0.327104	−	0.229306i
$874$	−0.574612	+	0.497742i	−0.0194366	+	0.0168364i
$875$	5.39425	−	3.11437i	0.182359	−	0.105285i
$876$	14.8977	−	2.44367i	0.503346	−	0.0825640i
$877$	−33.2002	−	19.1681i	−1.12109	−	0.647262i	−0.179412	−	0.983774i	$-0.557419\pi$
$877$	−33.2002	−	19.1681i	−1.12109	−	0.647262i	−0.941679	+	0.336512i	$0.890753\pi$
$878$	30.0650	−	5.78953i	1.01465	−	0.195387i
$879$	−49.6108	+	15.6571i	−1.67333	+	0.528100i
$880$	−1.55469	−	6.42660i	−0.0524085	−	0.216641i
$881$	−16.0465			−0.540619			−0.270310	−	0.962773i	$-0.587126\pi$
$881$	−16.0465			−0.540619			−0.270310	+	0.962773i	$0.587126\pi$
$882$	−2.95086	+	3.04835i	−0.0993606	+	0.102643i
$883$			33.7695i			1.13643i	0.822879	+	0.568216i	$0.192366\pi$
$883$			33.7695i			1.13643i	−0.822879	+	0.568216i	$0.807634\pi$
$884$	−1.16512	−	2.91305i	−0.0391872	−	0.0979764i
$885$	1.24599	+	0.275873i	0.0418834	+	0.00927336i
$886$	6.08461	+	31.5974i	0.204416	+	1.06153i
$887$	−14.3815	+	24.9094i	−0.482882	+	0.836376i	−0.999807	−	0.0196546i	$-0.993743\pi$
$887$	−14.3815	+	24.9094i	−0.482882	+	0.836376i	0.516925	+	0.856031i	$0.327077\pi$
$888$	−13.7393	−	2.36945i	−0.461061	−	0.0795136i
$889$	3.80971	+	6.59861i	0.127774	+	0.221310i
$890$	3.92353	−	3.39865i	0.131517	−	0.113923i
$891$	−17.5065	+	14.7222i	−0.586491	+	0.493213i
$892$	−3.58028	+	24.8445i	−0.119877	+	0.831856i
$893$	2.20887	−	1.27529i	0.0739169	−	0.0426760i
$894$	−0.888340	+	32.1130i	−0.0297105	+	1.07402i
$895$	7.05850	−	12.2257i	0.235940	−	0.408659i
$896$	2.67972	−	10.9918i	0.0895232	−	0.367209i
$897$	0.278356	−	1.25720i	0.00929404	−	0.0419767i
$898$	16.3374	−	47.1791i	0.545185	−	1.57439i
$899$			61.5554i			2.05299i
$900$	27.4200	+	1.51820i	0.914000	+	0.0506066i
$901$		−	22.9093i		−	0.763219i
$902$	40.6216	+	14.0666i	1.35255	+	0.468367i
$903$	9.64491	−	3.04391i	0.320963	−	0.101295i
$904$	−1.81929	−	38.5844i	−0.0605086	−	1.28330i
$905$	8.64523	−	14.9740i	0.287377	−	0.497752i
$906$	−22.9648	+	37.3513i	−0.762954	+	1.24091i
$907$	−40.0377	+	23.1157i	−1.32943	+	0.767546i	−0.985211	−	0.171344i	$-0.945189\pi$
$907$	−40.0377	+	23.1157i	−1.32943	+	0.767546i	−0.344217	+	0.938890i	$0.611856\pi$
$908$	36.8644	+	5.31244i	1.22339	+	0.176300i
$909$	−7.49493	−	10.6915i	−0.248591	−	0.354614i
$910$	−0.229632	−	0.265096i	−0.00761223	−	0.00878785i
$911$	17.4088	+	30.1529i	0.576778	+	0.999009i	0.995846	+	0.0910543i	$0.0290237\pi$
$911$	17.4088	+	30.1529i	0.576778	+	0.999009i	−0.419068	+	0.907955i	$0.637643\pi$
$912$	−0.922740	+	1.67257i	−0.0305550	+	0.0553845i
$913$	6.88399	−	11.9234i	0.227827	−	0.394608i
$914$	−21.3051	+	4.10266i	−0.704710	+	0.135704i
$915$	−1.03331	+	1.12828i	−0.0341603	+	0.0372998i
$916$	21.9447	+	54.8666i	0.725075	+	1.81284i
$917$			17.5741i			0.580347i
$918$	−25.2252	+	16.6624i	−0.832554	+	0.549940i
$919$	25.8037			0.851185			0.425593	−	0.904915i	$-0.360066\pi$
$919$	25.8037			0.851185			0.425593	+	0.904915i	$0.360066\pi$
$920$	1.64498	−	3.18703i	0.0542335	−	0.105073i
$921$	−7.48054	−	6.85091i	−0.246492	−	0.225745i
$922$	−0.878034	−	4.55963i	−0.0289165	−	0.150163i
$923$	1.20792	+	0.697393i	0.0397592	+	0.0229550i
$924$	−8.23669	−	3.10988i	−0.270967	−	0.102307i
$925$	11.2807	−	6.51289i	0.370906	−	0.214143i
$926$	−32.6580	−	37.7016i	−1.07321	−	1.23895i
$927$	−19.0225	−	8.85774i	−0.624781	−	0.290926i
$928$	−44.0180	+	20.0595i	−1.44496	+	0.658484i
$929$	15.8483	+	27.4501i	0.519966	+	0.900607i	0.999731	+	0.0232100i	$0.00738863\pi$
$929$	15.8483	+	27.4501i	0.519966	+	0.900607i	−0.479765	+	0.877397i	$0.659278\pi$
$930$	−9.76910	−	6.00636i	−0.320341	−	0.196956i
$931$	0.238778	+	0.137858i	0.00782563	+	0.00451813i
$932$	−36.5966	−	28.7990i	−1.19876	−	0.943344i
$933$	−4.90899	−	15.5546i	−0.160713	−	0.509234i
$934$	40.7399	+	14.1076i	1.33305	+	0.461615i
$935$	−6.80039			−0.222397
$936$	−0.435235	−	3.20612i	−0.0142261	−	0.104795i
$937$	−30.3580			−0.991751			−0.495876	−	0.868394i	$-0.665153\pi$
$937$	−30.3580			−0.991751			−0.495876	+	0.868394i	$0.665153\pi$
$938$	13.0764	+	4.52815i	0.426960	+	0.147849i
$939$	−4.65458	−	1.03057i	−0.151896	−	0.0336313i
$940$	−7.44140	+	9.45623i	−0.242712	+	0.308428i
$941$	−30.5115	−	17.6158i	−0.994646	−	0.574259i	−0.0879864	−	0.996122i	$-0.528043\pi$
$941$	−30.5115	−	17.6158i	−0.994646	−	0.574259i	−0.906660	+	0.421862i	$0.861377\pi$
$942$	−0.360163	+	13.0197i	−0.0117347	+	0.424204i
$943$	11.6590	+	20.1940i	0.379669	+	0.657606i
$944$	−1.27945	+	4.34704i	−0.0416426	+	0.141484i
$945$	−2.05512	+	2.68282i	−0.0668531	+	0.0872721i
$946$	13.7417	+	15.8639i	0.446780	+	0.515779i
$947$	−6.48495	+	3.74408i	−0.210732	+	0.121666i	−0.601652	−	0.798759i	$-0.705490\pi$
$947$	−6.48495	+	3.74408i	−0.210732	+	0.121666i	0.390919	+	0.920425i	$0.372157\pi$
$948$	−31.9729	−	39.0420i	−1.03843	−	1.26803i
$949$	1.43914	+	0.830888i	0.0467165	+	0.0269718i
$950$	−0.337469	−	1.75248i	−0.0109490	−	0.0568579i
$951$	−10.9497	+	49.4547i	−0.355069	+	1.60368i
$952$	−10.3400	−	5.33698i	−0.335121	−	0.172972i
$953$	−25.2439			−0.817729			−0.408864	−	0.912595i	$-0.634075\pi$
$953$	−25.2439			−0.817729			−0.408864	+	0.912595i	$0.634075\pi$
$954$	5.74317	−	22.9170i	0.185942	−	0.741966i
$955$		−	9.27256i		−	0.300053i
$956$	−1.04179	+	0.416679i	−0.0336939	+	0.0134764i
$957$	11.3294	+	35.8983i	0.366228	+	1.16043i
$958$	57.6137	−	11.0945i	1.86141	−	0.358446i
$959$	4.80166	−	8.31673i	0.155054	−	0.268561i
$960$	1.11161	−	8.94319i	0.0358770	−	0.288640i
$961$	−10.4085	−	18.0280i	−0.335757	−	0.581548i
$962$	−1.00481	−	1.15999i	−0.0323964	−	0.0373997i
$963$	−23.5264	+	2.07119i	−0.758126	+	0.0667431i
$964$	6.87214	−	47.6876i	0.221337	−	1.53591i
$965$	−6.08369	+	3.51242i	−0.195841	+	0.113069i
$966$	−2.27255	−	4.20029i	−0.0731181	−	0.135142i
$967$	−25.9085	+	44.8748i	−0.833160	+	1.44308i	0.0623602	+	0.998054i	$0.480137\pi$
$967$	−25.9085	+	44.8748i	−0.833160	+	1.44308i	−0.895520	+	0.445021i	$0.853196\pi$
$968$	0.604857	+	12.8281i	0.0194408	+	0.412312i
$969$	1.44886	+	1.32691i	0.0465440	+	0.0426265i
$970$	3.41953	+	1.18413i	0.109795	+	0.0380201i
$971$		−	56.9089i		−	1.82629i	−0.407633	−	0.913146i	$-0.633646\pi$
$971$		−	56.9089i		−	1.82629i	0.407633	−	0.913146i	$-0.366354\pi$
$972$	−29.4108	+	10.3443i	−0.943352	+	0.331793i
$973$		−	15.1156i		−	0.484583i
$974$	−11.3217	+	32.6950i	−0.362772	+	1.04761i
$975$	2.22925	+	2.04162i	0.0713932	+	0.0653841i
$976$	−3.74637	−	3.93416i	−0.119919	−	0.125930i
$977$	−9.84868	+	17.0584i	−0.315087	+	0.545747i	−0.979456	−	0.201658i	$-0.935367\pi$
$977$	−9.84868	+	17.0584i	−0.315087	+	0.545747i	0.664369	+	0.747405i	$0.268700\pi$
$978$	14.1731	−	7.66831i	0.453206	−	0.245205i
$979$	12.4218	−	7.17172i	0.397002	−	0.229209i
$980$	−1.28747	−	0.185534i	−0.0411268	−	0.00592668i
$981$	−22.5013	+	1.98094i	−0.718410	+	0.0632466i
$982$	−11.5622	+	10.0154i	−0.368964	+	0.319605i
$983$	−18.9416	−	32.8078i	−0.604143	−	1.04641i	−0.992186	−	0.124766i	$-0.960182\pi$
$983$	−18.9416	−	32.8078i	−0.604143	−	1.04641i	0.388043	−	0.921641i	$-0.373151\pi$
$984$	45.0252	+	37.4935i	1.43535	+	1.19525i
$985$	3.52245	−	6.10107i	0.112235	−	0.194396i
$986$	9.40769	+	48.8541i	0.299602	+	1.55583i
$987$	4.82228	+	15.2798i	0.153495	+	0.486362i
$988$	−0.195231	+	0.0780856i	−0.00621112	+	0.00248423i
$989$			11.3845i			0.362005i
$990$	−6.80270	−	1.70480i	−0.216204	−	0.0541822i
$991$	−50.1684			−1.59365			−0.796825	−	0.604210i	$-0.793489\pi$
$991$	−50.1684			−1.59365			−0.796825	+	0.604210i	$0.793489\pi$
$992$	23.6468	−	33.1507i	0.750788	−	1.05254i
$993$	8.01179	−	36.1854i	0.254246	−	1.14831i
$994$	5.07969	−	0.978181i	0.161118	−	0.0310260i
$995$	4.45044	+	2.56946i	0.141088	+	0.0814574i
$996$	14.5183	−	11.8896i	0.460031	−	0.376736i
$997$	17.5464	−	10.1304i	0.555699	−	0.320833i	−0.195718	−	0.980660i	$-0.562704\pi$
$997$	17.5464	−	10.1304i	0.555699	−	0.320833i	0.751417	+	0.659827i	$0.229370\pi$
$998$	−29.5027	+	25.5559i	−0.933891	+	0.808957i
$999$	−8.99269	+	11.7393i	−0.284516	+	0.371416i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.cs.b.85.15	✓	72
8.5	even	2	inner	504.2.cs.b.85.35	yes	72
9.7	even	3	inner	504.2.cs.b.421.35	yes	72
72.61	even	6	inner	504.2.cs.b.421.15	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.cs.b.85.15	✓	72	1.1	even	1	trivial
504.2.cs.b.85.35	yes	72	8.5	even	2	inner
504.2.cs.b.421.15	yes	72	72.61	even	6	inner
504.2.cs.b.421.35	yes	72	9.7	even	3	inner

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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.cs (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.462760 + 1.33636i) q^{2} +(-1.16981 + 1.27732i) q^{3} +(-1.57171 - 1.23683i) q^{4} +(-0.563250 - 0.325193i) q^{5} +(-1.16562 - 2.15438i) q^{6} +(-0.500000 - 0.866025i) q^{7} +(2.38016 - 1.52801i) q^{8} +(-0.263093 - 2.98844i) q^{9} +O(q^{10})\)	\(q+(-0.462760 + 1.33636i) q^{2} +(-1.16981 + 1.27732i) q^{3} +(-1.57171 - 1.23683i) q^{4} +(-0.563250 - 0.325193i) q^{5} +(-1.16562 - 2.15438i) q^{6} +(-0.500000 - 0.866025i) q^{7} +(2.38016 - 1.52801i) q^{8} +(-0.263093 - 2.98844i) q^{9} +(0.695224 - 0.602218i) q^{10} +(2.20106 - 1.27078i) q^{11} +(3.41842 - 0.560724i) q^{12} +(0.330225 + 0.190655i) q^{13} +(1.38870 - 0.267418i) q^{14} +(1.07427 - 0.339038i) q^{15} +(0.940527 + 3.88785i) q^{16} +4.11399 q^{17} +(4.11538 + 1.03134i) q^{18} -0.275717i q^{19} +(0.483058 + 1.20775i) q^{20} +(1.69110 + 0.374424i) q^{21} +(0.679658 + 3.52947i) q^{22} +(-0.974828 + 1.68845i) q^{23} +(-0.832578 + 4.82771i) q^{24} +(-2.28850 - 3.96380i) q^{25} +(-0.407598 + 0.353071i) q^{26} +(4.12496 + 3.15985i) q^{27} +(-0.285268 + 1.97955i) q^{28} +(7.40561 - 4.27563i) q^{29} +(-0.0440534 + 1.59250i) q^{30} +(-3.59920 + 6.23399i) q^{31} +(-5.63080 - 0.542260i) q^{32} +(-0.951622 + 4.29802i) q^{33} +(-1.90379 + 5.49776i) q^{34} +0.650385i q^{35} +(-3.28267 + 5.02236i) q^{36} +2.84592i q^{37} +(0.368457 + 0.127591i) q^{38} +(-0.629828 + 0.198772i) q^{39} +(-1.83753 + 0.0866409i) q^{40} +(5.98003 - 10.3577i) q^{41} +(-1.28294 + 2.08664i) q^{42} +(5.05692 - 2.91961i) q^{43} +(-5.03115 - 0.725027i) q^{44} +(-0.823632 + 1.76880i) q^{45} +(-1.80526 - 2.08407i) q^{46} +(4.62536 + 8.01136i) q^{47} +(-6.06627 - 3.34669i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(6.35608 - 1.22397i) q^{50} +(-4.81258 + 5.25488i) q^{51} +(-0.283209 - 0.708084i) q^{52} -5.56863i q^{53} +(-6.13156 + 4.05018i) q^{54} -1.65299 q^{55} +(-2.51338 - 1.29728i) q^{56} +(0.352179 + 0.322536i) q^{57} +(2.28676 + 11.8751i) q^{58} +(0.981080 + 0.566427i) q^{59} +(-2.10777 - 0.795817i) q^{60} +(-1.17619 + 0.679073i) q^{61} +(-6.66529 - 7.69466i) q^{62} +(-2.45652 + 1.72207i) q^{63} +(3.33036 - 7.27384i) q^{64} +(-0.123999 - 0.214773i) q^{65} +(-5.30333 - 3.26066i) q^{66} +(8.47415 + 4.89255i) q^{67} +(-6.46598 - 5.08828i) q^{68} +(-1.01633 - 3.22033i) q^{69} +(-0.869148 - 0.300972i) q^{70} +3.65788 q^{71} +(-5.19258 - 6.71097i) q^{72} +4.35806 q^{73} +(-3.80317 - 1.31698i) q^{74} +(7.74015 + 1.71374i) q^{75} +(-0.341014 + 0.433346i) q^{76} +(-2.20106 - 1.27078i) q^{77} +(0.0258278 - 0.933659i) q^{78} +(-7.28376 - 12.6158i) q^{79} +(0.734550 - 2.49569i) q^{80} +(-8.86156 + 1.57248i) q^{81} +(11.0743 + 12.7846i) q^{82} +(4.69138 - 2.70857i) q^{83} +(-2.19481 - 2.68008i) q^{84} +(-2.31720 - 1.33784i) q^{85} +(1.56151 + 8.10894i) q^{86} +(-3.20180 + 14.4610i) q^{87} +(3.29711 - 6.38790i) q^{88} +5.64356 q^{89} +(-1.98260 - 1.91920i) q^{90} -0.381311i q^{91} +(3.62046 - 1.44806i) q^{92} +(-3.75243 - 11.8899i) q^{93} +(-12.8465 + 2.47381i) q^{94} +(-0.0896612 + 0.155298i) q^{95} +(7.27961 - 6.55800i) q^{96} +(1.96718 + 3.40725i) q^{97} +(-0.925940 - 1.06894i) q^{98} +(-4.37674 - 6.24339i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 2 q^{6} - 36 q^{7} + 6 q^{8}+O(q^{10}) \) 72 * q + 2 * q^6 - 36 * q^7 + 6 * q^8	\( 72 q + 2 q^{6} - 36 q^{7} + 6 q^{8} - 8 q^{12} - 40 q^{17} - 21 q^{18} + 12 q^{20} + 12 q^{22} + 12 q^{23} - 12 q^{24} + 36 q^{25} - 14 q^{26} - 60 q^{30} - 15 q^{32} + 8 q^{33} + 6 q^{34} + 18 q^{36} - 3 q^{38} - 20 q^{39} + 21 q^{40} - 32 q^{41} - 13 q^{42} - 64 q^{44} + 12 q^{46} + 29 q^{48} - 36 q^{49} + 5 q^{50} - 9 q^{52} + 30 q^{54} - 3 q^{56} + 4 q^{57} + 9 q^{58} + 34 q^{60} - 12 q^{62} - 54 q^{64} + 40 q^{65} + 120 q^{66} + 55 q^{68} - 56 q^{71} + 15 q^{72} - 22 q^{74} + 12 q^{76} + 62 q^{78} + 94 q^{80} - 4 q^{81} + 12 q^{82} + 4 q^{84} - 3 q^{86} - 28 q^{87} - 12 q^{88} + 88 q^{89} - 83 q^{90} + 55 q^{92} - 18 q^{94} - 40 q^{95} - 83 q^{96}+O(q^{100}) \) 72 * q + 2 * q^6 - 36 * q^7 + 6 * q^8 - 8 * q^12 - 40 * q^17 - 21 * q^18 + 12 * q^20 + 12 * q^22 + 12 * q^23 - 12 * q^24 + 36 * q^25 - 14 * q^26 - 60 * q^30 - 15 * q^32 + 8 * q^33 + 6 * q^34 + 18 * q^36 - 3 * q^38 - 20 * q^39 + 21 * q^40 - 32 * q^41 - 13 * q^42 - 64 * q^44 + 12 * q^46 + 29 * q^48 - 36 * q^49 + 5 * q^50 - 9 * q^52 + 30 * q^54 - 3 * q^56 + 4 * q^57 + 9 * q^58 + 34 * q^60 - 12 * q^62 - 54 * q^64 + 40 * q^65 + 120 * q^66 + 55 * q^68 - 56 * q^71 + 15 * q^72 - 22 * q^74 + 12 * q^76 + 62 * q^78 + 94 * q^80 - 4 * q^81 + 12 * q^82 + 4 * q^84 - 3 * q^86 - 28 * q^87 - 12 * q^88 + 88 * q^89 - 83 * q^90 + 55 * q^92 - 18 * q^94 - 40 * q^95 - 83 * q^96

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