LMFDB - Embedded newform 572.2.j.a.463.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(463,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 1]))

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

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

chi := DirichletCharacter("572.463");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.j (of order $4$, 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:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$140$
Relative dimension:	$70$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			463.2
Character	$\chi$	$=$	572.463
Dual form			572.2.j.a.551.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40874 - 0.124340i) q^{2} -2.77989i q^{3} +(1.96908 + 0.350325i) q^{4} +(-0.0767607 - 0.0767607i) q^{5} +(-0.345652 + 3.91613i) q^{6} +(2.31083 + 2.31083i) q^{7} +(-2.73035 - 0.738352i) q^{8} -4.72779 q^{9} +O(q^{10})$	\(q+(-1.40874 - 0.124340i) q^{2} -2.77989i q^{3} +(1.96908 + 0.350325i) q^{4} +(-0.0767607 - 0.0767607i) q^{5} +(-0.345652 + 3.91613i) q^{6} +(2.31083 + 2.31083i) q^{7} +(-2.73035 - 0.738352i) q^{8} -4.72779 q^{9} +(0.0985912 + 0.117680i) q^{10} +(0.707107 + 0.707107i) q^{11} +(0.973866 - 5.47382i) q^{12} +(-1.33391 - 3.34973i) q^{13} +(-2.96802 - 3.54268i) q^{14} +(-0.213386 + 0.213386i) q^{15} +(3.75454 + 1.37964i) q^{16} -6.76443i q^{17} +(6.66021 + 0.587855i) q^{18} +(2.05169 - 2.05169i) q^{19} +(-0.124257 - 0.178039i) q^{20} +(6.42386 - 6.42386i) q^{21} +(-0.908206 - 1.08405i) q^{22} -8.37077 q^{23} +(-2.05254 + 7.59009i) q^{24} -4.98822i q^{25} +(1.46262 + 4.88475i) q^{26} +4.80307i q^{27} +(3.74067 + 5.35975i) q^{28} +7.08101 q^{29} +(0.327138 - 0.274073i) q^{30} +(0.869596 - 0.869596i) q^{31} +(-5.11762 - 2.41039i) q^{32} +(1.96568 - 1.96568i) q^{33} +(-0.841091 + 9.52930i) q^{34} -0.354762i q^{35} +(-9.30939 - 1.65627i) q^{36} +(-4.67934 + 4.67934i) q^{37} +(-3.14540 + 2.63519i) q^{38} +(-9.31188 + 3.70811i) q^{39} +(0.152907 + 0.266260i) q^{40} +(-6.70089 - 6.70089i) q^{41} +(-9.84827 + 8.25078i) q^{42} +6.50308 q^{43} +(1.14463 + 1.64007i) q^{44} +(0.362908 + 0.362908i) q^{45} +(11.7922 + 1.04082i) q^{46} +(4.43311 + 4.43311i) q^{47} +(3.83524 - 10.4372i) q^{48} +3.67989i q^{49} +(-0.620236 + 7.02708i) q^{50} -18.8044 q^{51} +(-1.45307 - 7.06318i) q^{52} -13.6440 q^{53} +(0.597215 - 6.76626i) q^{54} -0.108556i q^{55} +(-4.60318 - 8.01560i) q^{56} +(-5.70348 - 5.70348i) q^{57} +(-9.97528 - 0.880455i) q^{58} +(3.75573 + 3.75573i) q^{59} +(-0.494929 + 0.345420i) q^{60} +6.24023 q^{61} +(-1.33316 + 1.11691i) q^{62} +(-10.9251 - 10.9251i) q^{63} +(6.90967 + 4.03193i) q^{64} +(-0.154736 + 0.359519i) q^{65} +(-3.01354 + 2.52471i) q^{66} +(-4.10604 + 4.10604i) q^{67} +(2.36975 - 13.3197i) q^{68} +23.2698i q^{69} +(-0.0441112 + 0.499766i) q^{70} +(9.24559 - 9.24559i) q^{71} +(12.9085 + 3.49077i) q^{72} +(7.62885 - 7.62885i) q^{73} +(7.17379 - 6.01013i) q^{74} -13.8667 q^{75} +(4.75870 - 3.32118i) q^{76} +3.26801i q^{77} +(13.5791 - 4.06592i) q^{78} +10.2638i q^{79} +(-0.182299 - 0.394103i) q^{80} -0.831370 q^{81} +(8.60661 + 10.2730i) q^{82} +(7.34882 - 7.34882i) q^{83} +(14.8995 - 10.3986i) q^{84} +(-0.519242 + 0.519242i) q^{85} +(-9.16112 - 0.808594i) q^{86} -19.6844i q^{87} +(-1.40856 - 2.45275i) q^{88} +(-2.53329 + 2.53329i) q^{89} +(-0.466118 - 0.556367i) q^{90} +(4.65823 - 10.8231i) q^{91} +(-16.4827 - 2.93249i) q^{92} +(-2.41738 - 2.41738i) q^{93} +(-5.69387 - 6.79629i) q^{94} -0.314979 q^{95} +(-6.70061 + 14.2264i) q^{96} +(0.553742 + 0.553742i) q^{97} +(0.457558 - 5.18399i) q^{98} +(-3.34305 - 3.34305i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 140 q + 4 q^{5} - 12 q^{6} + 12 q^{8} - 140 q^{9}+O(q^{10}) $ 140 * q + 4 * q^5 - 12 * q^6 + 12 * q^8 - 140 * q^9	$ 140 q + 4 q^{5} - 12 q^{6} + 12 q^{8} - 140 q^{9} + 16 q^{14} - 12 q^{18} - 8 q^{20} - 16 q^{21} - 32 q^{26} - 20 q^{28} + 20 q^{32} - 8 q^{34} + 36 q^{37} - 80 q^{40} - 20 q^{41} - 20 q^{42} - 8 q^{44} - 20 q^{45} + 60 q^{46} + 20 q^{48} + 88 q^{50} - 8 q^{53} + 88 q^{54} - 80 q^{57} - 60 q^{58} + 12 q^{60} - 40 q^{61} - 20 q^{65} - 20 q^{66} - 80 q^{68} - 28 q^{70} + 20 q^{72} + 100 q^{73} - 136 q^{74} - 32 q^{76} - 88 q^{78} - 72 q^{80} + 140 q^{81} + 92 q^{84} + 24 q^{85} - 32 q^{86} - 60 q^{89} - 68 q^{92} - 80 q^{93} + 64 q^{94} + 100 q^{96} - 20 q^{97} + 92 q^{98}+O(q^{100}) $ 140 * q + 4 * q^5 - 12 * q^6 + 12 * q^8 - 140 * q^9 + 16 * q^14 - 12 * q^18 - 8 * q^20 - 16 * q^21 - 32 * q^26 - 20 * q^28 + 20 * q^32 - 8 * q^34 + 36 * q^37 - 80 * q^40 - 20 * q^41 - 20 * q^42 - 8 * q^44 - 20 * q^45 + 60 * q^46 + 20 * q^48 + 88 * q^50 - 8 * q^53 + 88 * q^54 - 80 * q^57 - 60 * q^58 + 12 * q^60 - 40 * q^61 - 20 * q^65 - 20 * q^66 - 80 * q^68 - 28 * q^70 + 20 * q^72 + 100 * q^73 - 136 * q^74 - 32 * q^76 - 88 * q^78 - 72 * q^80 + 140 * q^81 + 92 * q^84 + 24 * q^85 - 32 * q^86 - 60 * q^89 - 68 * q^92 - 80 * q^93 + 64 * q^94 + 100 * q^96 - 20 * q^97 + 92 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$

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 $

$2$	−1.40874	−	0.124340i	−0.996127	−	0.0879218i
$2$	−1.40874	−	0.124340i	−0.996127	−	0.0879218i
$3$		−	2.77989i		−	1.60497i	−0.596672	−	0.802485i	$-0.703511\pi$
$3$		−	2.77989i		−	1.60497i	0.596672	−	0.802485i	$-0.296489\pi$
$4$	1.96908	+	0.350325i	0.984539	+	0.175163i
$5$	−0.0767607	−	0.0767607i	−0.0343284	−	0.0343284i	0.689734	−	0.724063i	$-0.257727\pi$
$5$	−0.0767607	−	0.0767607i	−0.0343284	−	0.0343284i	−0.724063	+	0.689734i	$0.757727\pi$
$6$	−0.345652	+	3.91613i	−0.141112	+	1.59875i
$7$	2.31083	+	2.31083i	0.873412	+	0.873412i	0.992843	−	0.119430i	$-0.0381068\pi$
$7$	2.31083	+	2.31083i	0.873412	+	0.873412i	−0.119430	+	0.992843i	$0.538107\pi$
$8$	−2.73035	−	0.738352i	−0.965326	−	0.261047i
$9$	−4.72779			−1.57593
$10$	0.0985912	+	0.117680i	0.0311773	+	0.0372137i
$11$	0.707107	+	0.707107i	0.213201	+	0.213201i
$11$	0.707107	+	0.707107i	0.213201	+	0.213201i
$12$	0.973866	−	5.47382i	0.281131	−	1.58016i
$13$	−1.33391	−	3.34973i	−0.369959	−	0.929048i
$13$	−1.33391	−	3.34973i	−0.369959	−	0.929048i
$14$	−2.96802	−	3.54268i	−0.793238	−	0.946822i
$15$	−0.213386	+	0.213386i	−0.0550961	+	0.0550961i
$16$	3.75454	+	1.37964i	0.938636	+	0.344909i
$17$		−	6.76443i		−	1.64062i	−0.571923	−	0.820308i	$-0.693802\pi$
$17$		−	6.76443i		−	1.64062i	0.571923	−	0.820308i	$-0.306198\pi$
$18$	6.66021	+	0.587855i	1.56983	+	0.138559i
$19$	2.05169	−	2.05169i	0.470691	−	0.470691i	−0.431447	−	0.902138i	$-0.641997\pi$
$19$	2.05169	−	2.05169i	0.470691	−	0.470691i	0.902138	+	0.431447i	$0.141997\pi$
$20$	−0.124257	−	0.178039i	−0.0277846	−	0.0398107i
$21$	6.42386	−	6.42386i	1.40180	−	1.40180i
$22$	−0.908206	−	1.08405i	−0.193630	−	0.231120i
$23$	−8.37077			−1.74543			−0.872713	−	0.488234i	$-0.837641\pi$
$23$	−8.37077			−1.74543			−0.872713	+	0.488234i	$0.837641\pi$
$24$	−2.05254	+	7.59009i	−0.418973	+	1.54932i
$25$		−	4.98822i		−	0.997643i
$26$	1.46262	+	4.88475i	0.286843	+	0.957978i
$27$			4.80307i			0.924351i
$28$	3.74067	+	5.35975i	0.706920	+	1.01290i
$29$	7.08101			1.31491			0.657455	−	0.753493i	$-0.271633\pi$
$29$	7.08101			1.31491			0.657455	+	0.753493i	$0.271633\pi$
$30$	0.327138	−	0.274073i	0.0597269	−	0.0500386i
$31$	0.869596	−	0.869596i	0.156184	−	0.156184i	−0.624689	−	0.780873i	$-0.714774\pi$
$31$	0.869596	−	0.869596i	0.156184	−	0.156184i	0.780873	+	0.624689i	$0.214774\pi$
$32$	−5.11762	−	2.41039i	−0.904676	−	0.426100i
$33$	1.96568	−	1.96568i	0.342181	−	0.342181i
$34$	−0.841091	+	9.52930i	−0.144246	+	1.63426i
$35$		−	0.354762i		−	0.0599657i
$36$	−9.30939	−	1.65627i	−1.55157	−	0.276044i
$37$	−4.67934	+	4.67934i	−0.769279	+	0.769279i	−0.977980	−	0.208701i	$-0.933077\pi$
$37$	−4.67934	+	4.67934i	−0.769279	+	0.769279i	0.208701	+	0.977980i	$0.433077\pi$
$38$	−3.14540	+	2.63519i	−0.510252	+	0.427484i
$39$	−9.31188	+	3.70811i	−1.49109	+	0.593774i
$40$	0.152907	+	0.266260i	0.0241768	+	0.0420994i
$41$	−6.70089	−	6.70089i	−1.04650	−	1.04650i	−0.998865	−	0.0476392i	$-0.984830\pi$
$41$	−6.70089	−	6.70089i	−1.04650	−	1.04650i	−0.0476392	−	0.998865i	$-0.515170\pi$
$42$	−9.84827	+	8.25078i	−1.51962	+	1.27312i
$43$	6.50308			0.991710			0.495855	−	0.868405i	$-0.334855\pi$
$43$	6.50308			0.991710			0.495855	+	0.868405i	$0.334855\pi$
$44$	1.14463	+	1.64007i	0.172560	+	0.247249i
$45$	0.362908	+	0.362908i	0.0540992	+	0.0540992i
$46$	11.7922	+	1.04082i	1.73867	+	0.153461i
$47$	4.43311	+	4.43311i	0.646635	+	0.646635i	0.952178	−	0.305543i	$-0.0988381\pi$
$47$	4.43311	+	4.43311i	0.646635	+	0.646635i	−0.305543	+	0.952178i	$0.598838\pi$
$48$	3.83524	−	10.4372i	0.553569	−	1.50648i
$49$			3.67989i			0.525698i
$50$	−0.620236	+	7.02708i	−0.0877146	+	0.993780i
$51$	−18.8044			−2.63314
$52$	−1.45307	−	7.06318i	−0.201505	−	0.979488i
$53$	−13.6440			−1.87415			−0.937076	−	0.349126i	$-0.886478\pi$
$53$	−13.6440			−1.87415			−0.937076	+	0.349126i	$0.886478\pi$
$54$	0.597215	−	6.76626i	0.0812706	−	0.920771i
$55$		−	0.108556i		−	0.0146377i
$56$	−4.60318	−	8.01560i	−0.615126	−	1.07113i
$57$	−5.70348	−	5.70348i	−0.755444	−	0.755444i
$58$	−9.97528	−	0.880455i	−1.30982	−	0.115609i
$59$	3.75573	+	3.75573i	0.488954	+	0.488954i	0.907976	−	0.419022i	$-0.137627\pi$
$59$	3.75573	+	3.75573i	0.488954	+	0.488954i	−0.419022	+	0.907976i	$0.637627\pi$
$60$	−0.494929	+	0.345420i	−0.0638951	+	0.0445935i
$61$	6.24023			0.798979			0.399490	−	0.916738i	$-0.369187\pi$
$61$	6.24023			0.798979			0.399490	+	0.916738i	$0.369187\pi$
$62$	−1.33316	+	1.11691i	−0.169311	+	0.141847i
$63$	−10.9251	−	10.9251i	−1.37644	−	1.37644i
$64$	6.90967	+	4.03193i	0.863709	+	0.503991i
$65$	−0.154736	+	0.359519i	−0.0191926	+	0.0445929i
$66$	−3.01354	+	2.52471i	−0.370941	+	0.310771i
$67$	−4.10604	+	4.10604i	−0.501633	+	0.501633i	−0.911945	−	0.410312i	$-0.865420\pi$
$67$	−4.10604	+	4.10604i	−0.501633	+	0.501633i	0.410312	+	0.911945i	$0.365420\pi$
$68$	2.36975	−	13.3197i	0.287375	−	1.61525i
$69$			23.2698i			2.80136i
$70$	−0.0441112	+	0.499766i	−0.00527230	+	0.0597335i
$71$	9.24559	−	9.24559i	1.09725	−	1.09725i	0.102519	−	0.994731i	$-0.467310\pi$
$71$	9.24559	−	9.24559i	1.09725	−	1.09725i	0.994731	−	0.102519i	$-0.0326903\pi$
$72$	12.9085	+	3.49077i	1.52129	+	0.411392i
$73$	7.62885	−	7.62885i	0.892889	−	0.892889i	−0.101905	−	0.994794i	$-0.532494\pi$
$73$	7.62885	−	7.62885i	0.892889	−	0.892889i	0.994794	+	0.101905i	$0.0324938\pi$
$74$	7.17379	−	6.01013i	0.833936	−	0.698663i
$75$	−13.8667			−1.60119
$76$	4.75870	−	3.32118i	0.545861	−	0.380966i
$77$			3.26801i			0.372424i
$78$	13.5791	−	4.06592i	1.53753	−	0.460374i
$79$			10.2638i			1.15477i	0.816471	+	0.577386i	$0.195927\pi$
$79$			10.2638i			1.15477i	−0.816471	+	0.577386i	$0.804073\pi$
$80$	−0.182299	−	0.394103i	−0.0203817	−	0.0440621i
$81$	−0.831370			−0.0923745
$82$	8.60661	+	10.2730i	0.950441	+	1.13446i
$83$	7.34882	−	7.34882i	0.806638	−	0.806638i	−0.177485	−	0.984123i	$-0.556796\pi$
$83$	7.34882	−	7.34882i	0.806638	−	0.806638i	0.984123	+	0.177485i	$0.0567963\pi$
$84$	14.8995	−	10.3986i	1.62567	−	1.13459i
$85$	−0.519242	+	0.519242i	−0.0563197	+	0.0563197i
$86$	−9.16112	−	0.808594i	−0.987869	−	0.0871930i
$87$		−	19.6844i		−	2.11039i
$88$	−1.40856	−	2.45275i	−0.150153	−	0.261464i
$89$	−2.53329	+	2.53329i	−0.268528	+	0.268528i	−0.828507	−	0.559979i	$-0.810809\pi$
$89$	−2.53329	+	2.53329i	−0.268528	+	0.268528i	0.559979	+	0.828507i	$0.310809\pi$
$90$	−0.466118	−	0.556367i	−0.0491332	−	0.0586462i
$91$	4.65823	−	10.8231i	0.488315	−	1.13457i
$92$	−16.4827	−	2.93249i	−1.71844	−	0.305733i
$93$	−2.41738	−	2.41738i	−0.250671	−	0.250671i
$94$	−5.69387	−	6.79629i	−0.587277	−	0.700984i
$95$	−0.314979			−0.0323161
$96$	−6.70061	+	14.2264i	−0.683878	+	1.45198i
$97$	0.553742	+	0.553742i	0.0562240	+	0.0562240i	0.734660	−	0.678436i	$-0.237342\pi$
$97$	0.553742	+	0.553742i	0.0562240	+	0.0562240i	−0.678436	+	0.734660i	$0.737342\pi$
$98$	0.457558	−	5.18399i	0.0462204	−	0.523662i
$99$	−3.34305	−	3.34305i	−0.335989	−	0.335989i
$100$	1.74750	−	9.82219i	0.174750	−	0.982219i
$101$			8.92658i			0.888228i	0.895970	+	0.444114i	$0.146482\pi$
$101$			8.92658i			0.888228i	−0.895970	+	0.444114i	$0.853518\pi$
$102$	26.4904	+	2.33814i	2.62294	+	0.231510i
$103$	−11.5204			−1.13514			−0.567570	−	0.823325i	$-0.692117\pi$
$103$	−11.5204			−1.13514			−0.567570	+	0.823325i	$0.692117\pi$
$104$	1.16876	+	10.1308i	0.114606	+	0.993411i
$105$	−0.986200			−0.0962432
$106$	19.2208	+	1.69650i	1.86689	+	0.164779i
$107$			1.70601i			0.164927i	0.996594	+	0.0824633i	$0.0262787\pi$
$107$			1.70601i			0.164927i	−0.996594	+	0.0824633i	$0.973721\pi$
$108$	−1.68264	+	9.45762i	−0.161912	+	0.910060i
$109$	5.51157	+	5.51157i	0.527912	+	0.527912i	0.919949	−	0.392037i	$-0.128229\pi$
$109$	5.51157	+	5.51157i	0.527912	+	0.527912i	−0.392037	+	0.919949i	$0.628229\pi$
$110$	−0.0134979	+	0.152927i	−0.00128697	+	0.0145810i
$111$	13.0081	+	13.0081i	1.23467	+	1.23467i
$112$	5.48801	+	11.8642i	0.518568	+	1.12106i
$113$	3.52027			0.331159			0.165580	−	0.986196i	$-0.447050\pi$
$113$	3.52027			0.331159			0.165580	+	0.986196i	$0.447050\pi$
$114$	7.32553	+	8.74388i	0.686099	+	0.818939i
$115$	0.642546	+	0.642546i	0.0599177	+	0.0599177i
$116$	13.9431	+	2.48066i	1.29458	+	0.230323i
$117$	6.30643	+	15.8368i	0.583030	+	1.46411i
$118$	−4.82384	−	5.75782i	−0.444071	−	0.530050i
$119$	15.6315	−	15.6315i	1.43293	−	1.43293i
$120$	0.740174	−	0.425066i	0.0675684	−	0.0388030i
$121$			1.00000i			0.0909091i
$122$	−8.79084	−	0.775912i	−0.795885	−	0.0702477i
$123$	−18.6277	+	18.6277i	−1.67961	+	1.67961i
$124$	2.01695	−	1.40766i	0.181127	−	0.126412i
$125$	−0.766702	+	0.766702i	−0.0685759	+	0.0685759i
$126$	14.0322	+	16.7491i	1.25009	+	1.49213i
$127$	−3.79454			−0.336711			−0.168356	−	0.985726i	$-0.553846\pi$
$127$	−3.79454			−0.336711			−0.168356	+	0.985726i	$0.553846\pi$
$128$	−9.23258	−	6.53907i	−0.816052	−	0.577978i
$129$		−	18.0778i		−	1.59166i
$130$	0.262685	−	0.487228i	0.0230390	−	0.0427327i
$131$			8.80345i			0.769161i	0.923091	+	0.384580i	$0.125654\pi$
$131$			8.80345i			0.769161i	−0.923091	+	0.384580i	$0.874346\pi$
$132$	4.55921	−	3.18195i	0.396828	−	0.276953i
$133$	9.48223			0.822214
$134$	6.29487	−	5.27378i	0.543794	−	0.455585i
$135$	0.368687	−	0.368687i	0.0317315	−	0.0317315i
$136$	−4.99453	+	18.4693i	−0.428277	+	1.58373i
$137$	6.50454	−	6.50454i	0.555720	−	0.555720i	−0.372366	−	0.928086i	$-0.621453\pi$
$137$	6.50454	−	6.50454i	0.555720	−	0.555720i	0.928086	+	0.372366i	$0.121453\pi$
$138$	2.89337	−	32.7810i	0.246300	−	2.79051i
$139$			2.89699i			0.245719i	0.992424	+	0.122860i	$0.0392065\pi$
$139$			2.89699i			0.245719i	−0.992424	+	0.122860i	$0.960794\pi$
$140$	0.124282	−	0.698554i	0.0105038	−	0.0590386i
$141$	12.3235	−	12.3235i	1.03783	−	1.03783i
$142$	−14.1742	+	11.8750i	−1.18947	+	0.996529i
$143$	1.42540	−	3.31183i	0.119198	−	0.276949i
$144$	−17.7507	−	6.52263i	−1.47922	−	0.543553i
$145$	−0.543543	−	0.543543i	−0.0451388	−	0.0451388i
$146$	−11.6956	+	9.79846i	−0.967936	+	0.810927i
$147$	10.2297			0.843730
$148$	−10.8533	+	7.57470i	−0.892135	+	0.622637i
$149$	0.389201	+	0.389201i	0.0318846	+	0.0318846i	0.722869	−	0.690985i	$-0.242823\pi$
$149$	0.389201	+	0.389201i	0.0318846	+	0.0318846i	−0.690985	+	0.722869i	$0.742823\pi$
$150$	19.5345	+	1.72419i	1.59499	+	0.140779i
$151$	3.19339	+	3.19339i	0.259875	+	0.259875i	0.825003	−	0.565128i	$-0.191173\pi$
$151$	3.19339	+	3.19339i	0.259875	+	0.259875i	−0.565128	+	0.825003i	$0.691173\pi$
$152$	−7.11672	+	4.08698i	−0.577242	+	0.331498i
$153$			31.9808i			2.58549i
$154$	0.406345	−	4.60377i	0.0327442	−	0.370982i
$155$	−0.133502			−0.0107231
$156$	−19.6349	+	4.03938i	−1.57205	+	0.323409i
$157$	24.4293			1.94967			0.974834	−	0.222931i	$-0.0715624\pi$
$157$	24.4293			1.94967			0.974834	+	0.222931i	$0.0715624\pi$
$158$	1.27621	−	14.4591i	0.101530	−	1.15030i
$159$			37.9289i			3.00796i
$160$	0.207809	+	0.577855i	0.0164288	+	0.0456834i
$161$	−19.3434	−	19.3434i	−1.52448	−	1.52448i
$162$	1.17118	+	0.103373i	0.0920167	+	0.00812173i
$163$	0.977646	+	0.977646i	0.0765752	+	0.0765752i	0.744357	−	0.667782i	$-0.232756\pi$
$163$	0.977646	+	0.977646i	0.0765752	+	0.0765752i	−0.667782	+	0.744357i	$0.732756\pi$
$164$	−10.8471	−	15.5421i	−0.847016	−	1.21363i
$165$	−0.301774			−0.0234931
$166$	−11.2663	+	9.43880i	−0.874435	+	0.732593i
$167$	6.90762	+	6.90762i	0.534528	+	0.534528i	0.921916	−	0.387389i	$-0.126623\pi$
$167$	6.90762	+	6.90762i	0.534528	+	0.534528i	−0.387389	+	0.921916i	$0.626623\pi$
$168$	−22.2825	+	12.7963i	−1.71913	+	0.987259i
$169$	−9.44139	+	8.93646i	−0.726260	+	0.687420i
$170$	0.796038	−	0.666913i	0.0610533	−	0.0511499i
$171$	−9.69997	+	9.69997i	−0.741775	+	0.741775i
$172$	12.8051	+	2.27819i	0.976377	+	0.173711i
$173$		−	7.98779i		−	0.607300i	−0.952784	−	0.303650i	$-0.901795\pi$
$173$		−	7.98779i		−	0.607300i	0.952784	−	0.303650i	$-0.0982054\pi$
$174$	−2.44757	+	27.7302i	−0.185550	+	2.10222i
$175$	11.5269	−	11.5269i	0.871354	−	0.871354i
$176$	1.67931	+	3.63041i	0.126583	+	0.273653i
$177$	10.4405	−	10.4405i	0.784757	−	0.784757i
$178$	3.88373	−	3.25375i	0.291098	−	0.243879i
$179$	12.7283			0.951354			0.475677	−	0.879620i	$-0.342203\pi$
$179$	12.7283			0.951354			0.475677	+	0.879620i	$0.342203\pi$
$180$	0.587459	+	0.841731i	0.0437866	+	0.0627389i
$181$		−	3.96475i		−	0.294697i	−0.989085	−	0.147349i	$-0.952926\pi$
$181$		−	3.96475i		−	0.294697i	0.989085	−	0.147349i	$-0.0470740\pi$
$182$	−7.90797	+	14.6677i	−0.586177	+	1.08724i
$183$		−	17.3472i		−	1.28234i
$184$	22.8552	+	6.18057i	1.68490	+	0.455638i
$185$	0.718379			0.0528163
$186$	3.10488	+	3.70603i	0.227661	+	0.271740i
$187$	4.78317	−	4.78317i	0.349780	−	0.349780i
$188$	7.17611	+	10.2822i	0.523371	+	0.749904i
$189$	−11.0991	+	11.0991i	−0.807339	+	0.807339i
$190$	0.443722	+	0.0391645i	0.0321910	+	0.00284129i
$191$		−	7.37091i		−	0.533340i	−0.963788	−	0.266670i	$-0.914077\pi$
$191$		−	7.37091i		−	0.533340i	0.963788	−	0.266670i	$-0.0859235\pi$
$192$	11.2083	−	19.2081i	0.808890	−	1.38623i
$193$	−4.55482	+	4.55482i	−0.327863	+	0.327863i	−0.851773	−	0.523910i	$-0.824473\pi$
$193$	−4.55482	+	4.55482i	−0.327863	+	0.327863i	0.523910	+	0.851773i	$0.324473\pi$
$194$	−0.711225	−	0.848930i	−0.0510630	−	0.0609496i
$195$	0.999424	+	0.430149i	0.0715702	+	0.0308036i
$196$	−1.28916	+	7.24599i	−0.0920827	+	0.517571i
$197$	12.3305	+	12.3305i	0.878513	+	0.878513i	0.993381	−	0.114868i	$-0.0366445\pi$
$197$	12.3305	+	12.3305i	0.878513	+	0.878513i	−0.114868	+	0.993381i	$0.536644\pi$
$198$	4.29381	+	5.12516i	0.305147	+	0.364229i
$199$	−2.84662			−0.201791			−0.100896	−	0.994897i	$-0.532171\pi$
$199$	−2.84662			−0.201791			−0.100896	+	0.994897i	$0.532171\pi$
$200$	−3.68306	+	13.6196i	−0.260432	+	0.963051i
$201$	11.4143	+	11.4143i	0.805105	+	0.805105i
$202$	1.10993	−	12.5752i	0.0780947	−	0.884788i
$203$	16.3630	+	16.3630i	1.14846	+	1.14846i
$204$	−37.0273	−	6.58765i	−2.59243	−	0.461228i
$205$			1.02873i			0.0718496i
$206$	16.2292	+	1.43245i	1.13075	+	0.0998037i
$207$	39.5752			2.75067
$208$	−0.386800	−	14.4170i	−0.0268198	−	0.999640i
$209$	2.90153			0.200703
$210$	1.38930	+	0.122624i	0.0958705	+	0.00846188i
$211$		−	20.5877i		−	1.41732i	−0.705552	−	0.708658i	$-0.749301\pi$
$211$		−	20.5877i		−	1.41732i	0.705552	−	0.708658i	$-0.250699\pi$
$212$	−26.8662	−	4.77985i	−1.84518	−	0.328281i
$213$	−25.7017	−	25.7017i	−1.76105	−	1.76105i
$214$	0.212126	−	2.40332i	0.0145006	−	0.164288i
$215$	−0.499181	−	0.499181i	−0.0340438	−	0.0340438i
$216$	3.54636	−	13.1141i	0.241299	−	0.892300i
$217$	4.01898			0.272826
$218$	−7.07904	−	8.44966i	−0.479453	−	0.572283i
$219$	−21.2074	−	21.2074i	−1.43306	−	1.43306i
$220$	0.0380299	−	0.213755i	0.00256398	−	0.0144114i
$221$	−22.6590	+	9.02312i	−1.52421	+	0.606961i
$222$	−16.7075	−	19.9424i	−1.12133	−	1.33844i
$223$	4.18094	−	4.18094i	0.279976	−	0.279976i	−0.553123	−	0.833099i	$-0.686564\pi$
$223$	4.18094	−	4.18094i	0.279976	−	0.279976i	0.833099	+	0.553123i	$0.186564\pi$
$224$	−6.25596	−	17.3960i	−0.417994	−	1.16232i
$225$			23.5832i			1.57222i
$226$	−4.95914	−	0.437712i	−0.329877	−	0.0291161i
$227$	−12.1717	+	12.1717i	−0.807865	+	0.807865i	−0.984310	−	0.176445i	$-0.943540\pi$
$227$	−12.1717	+	12.1717i	−0.807865	+	0.807865i	0.176445	+	0.984310i	$0.443540\pi$
$228$	−9.23253	−	13.2287i	−0.611439	−	0.876091i
$229$	5.97461	−	5.97461i	0.394813	−	0.394813i	−0.481586	−	0.876399i	$-0.659939\pi$
$229$	5.97461	−	5.97461i	0.394813	−	0.394813i	0.876399	+	0.481586i	$0.159939\pi$
$230$	−0.825283	−	0.985072i	−0.0544176	−	0.0649537i
$231$	9.08471			0.597730
$232$	−19.3337	−	5.22828i	−1.26932	−	0.343253i
$233$			8.68105i			0.568714i	0.958718	+	0.284357i	$0.0917801\pi$
$233$			8.68105i			0.568714i	−0.958718	+	0.284357i	$0.908220\pi$
$234$	−6.91495	−	23.0941i	−0.452044	−	1.50971i
$235$		−	0.680576i		−	0.0443959i
$236$	6.07960	+	8.71105i	0.395748	+	0.567041i
$237$	28.5324			1.85338
$238$	−23.9642	+	20.0770i	−1.55337	+	1.30140i
$239$	1.78641	−	1.78641i	0.115553	−	0.115553i	−0.646966	−	0.762519i	$-0.723962\pi$
$239$	1.78641	−	1.78641i	0.115553	−	0.115553i	0.762519	+	0.646966i	$0.223962\pi$
$240$	−1.09556	+	0.506773i	−0.0707183	+	0.0327120i
$241$	−0.721838	+	0.721838i	−0.0464977	+	0.0464977i	−0.729973	−	0.683476i	$-0.760468\pi$
$241$	−0.721838	+	0.721838i	−0.0464977	+	0.0464977i	0.683476	+	0.729973i	$0.260468\pi$
$242$	0.124340	−	1.40874i	0.00799290	−	0.0905570i
$243$			16.7203i			1.07261i
$244$	12.2875	+	2.18611i	0.786627	+	0.139951i
$245$	0.282471	−	0.282471i	0.0180464	−	0.0180464i
$246$	28.5578	−	23.9254i	1.82078	−	1.52543i
$247$	−9.60938	−	4.13585i	−0.611430	−	0.263158i
$248$	−3.01637	+	1.73224i	−0.191540	+	0.109997i
$249$	−20.4289	−	20.4289i	−1.29463	−	1.29463i
$250$	1.17541	−	0.984750i	0.0743397	−	0.0622810i
$251$	7.66044			0.483522			0.241761	−	0.970336i	$-0.422275\pi$
$251$	7.66044			0.483522			0.241761	+	0.970336i	$0.422275\pi$
$252$	−17.6851	−	25.3398i	−1.11406	−	1.59626i
$253$	−5.91902	−	5.91902i	−0.372126	−	0.372126i
$254$	5.34551	+	0.471815i	0.335407	+	0.0296043i
$255$	1.44344	+	1.44344i	0.0903915	+	0.0903915i
$256$	12.1932	+	10.3598i	0.762075	+	0.647488i
$257$		−	24.4721i		−	1.52652i	−0.646089	−	0.763262i	$-0.723596\pi$
$257$		−	24.4721i		−	1.52652i	0.646089	−	0.763262i	$-0.276404\pi$
$258$	−2.24780	+	25.4669i	−0.139942	+	1.58550i
$259$	−21.6263			−1.34380
$260$	−0.430636	+	0.653714i	−0.0267069	+	0.0405416i
$261$	−33.4775			−2.07221
$262$	1.09462	−	12.4017i	0.0676260	−	0.766182i
$263$		−	17.4138i		−	1.07378i	−0.843652	−	0.536890i	$-0.819599\pi$
$263$		−	17.4138i		−	1.07378i	0.843652	−	0.536890i	$-0.180401\pi$
$264$	−6.81837	+	3.91564i	−0.419641	+	0.240991i
$265$	1.04732	+	1.04732i	0.0643367	+	0.0643367i
$266$	−13.3580	−	1.17902i	−0.819030	−	0.0722906i
$267$	7.04227	+	7.04227i	0.430980	+	0.430980i
$268$	−9.52357	+	6.64667i	−0.581744	+	0.406010i
$269$	7.19738			0.438832			0.219416	−	0.975631i	$-0.429585\pi$
$269$	7.19738			0.438832			0.219416	+	0.975631i	$0.429585\pi$
$270$	−0.565225	+	0.473540i	−0.0343985	+	0.0288187i
$271$	−2.94478	−	2.94478i	−0.178883	−	0.178883i	0.611986	−	0.790869i	$-0.290371\pi$
$271$	−2.94478	−	2.94478i	−0.178883	−	0.178883i	−0.790869	+	0.611986i	$0.790371\pi$
$272$	9.33246	−	25.3973i	0.565863	−	1.53994i
$273$	−30.0870	−	12.9494i	−1.82095	−	0.783731i
$274$	−9.97196	+	8.35441i	−0.602428	+	0.504708i
$275$	3.52720	−	3.52720i	0.212698	−	0.212698i
$276$	−8.15201	+	45.8201i	−0.490693	+	2.75805i
$277$		−	18.1163i		−	1.08850i	−0.838923	−	0.544251i	$-0.816814\pi$
$277$		−	18.1163i		−	1.08850i	0.838923	−	0.544251i	$-0.183186\pi$
$278$	0.360212	−	4.08109i	0.0216041	−	0.244768i
$279$	−4.11127	+	4.11127i	−0.246135	+	0.246135i
$280$	−0.261939	+	0.968626i	−0.0156539	+	0.0578865i
$281$	−10.5572	+	10.5572i	−0.629790	+	0.629790i	−0.948015	−	0.318225i	$-0.896913\pi$
$281$	−10.5572	+	10.5572i	−0.629790	+	0.629790i	0.318225	+	0.948015i	$0.396913\pi$
$282$	−18.8929	+	15.8283i	−1.12506	+	0.942563i
$283$	2.21726			0.131803			0.0659013	−	0.997826i	$-0.479008\pi$
$283$	2.21726			0.131803			0.0659013	+	0.997826i	$0.479008\pi$
$284$	21.4443	−	14.9663i	1.27248	−	0.888089i
$285$			0.875606i			0.0518664i
$286$	−2.41981	+	4.48826i	−0.143086	+	0.265397i
$287$		−	30.9693i		−	1.82806i
$288$	24.1950	+	11.3958i	1.42571	+	0.671504i
$289$	−28.7575			−1.69162
$290$	0.698125	+	0.833294i	0.0409953	+	0.0489327i
$291$	1.53934	−	1.53934i	0.0902379	−	0.0902379i
$292$	17.6944	−	12.3492i	1.03549	−	0.722684i
$293$	1.57090	−	1.57090i	0.0917729	−	0.0917729i	−0.659730	−	0.751503i	$-0.729329\pi$
$293$	1.57090	−	1.57090i	0.0917729	−	0.0917729i	0.751503	+	0.659730i	$0.229329\pi$
$294$	−14.4109	−	1.27196i	−0.840463	−	0.0741823i
$295$		−	0.576585i		−	0.0335700i
$296$	16.2313	−	9.32126i	0.943423	−	0.541787i
$297$	−3.39628	+	3.39628i	−0.197072	+	0.197072i
$298$	−0.499889	−	0.596676i	−0.0289578	−	0.0345645i
$299$	11.1658	+	28.0398i	0.645736	+	1.62158i
$300$	−27.3046	−	4.85786i	−1.57643	−	0.280468i
$301$	15.0275	+	15.0275i	0.866172	+	0.866172i
$302$	−4.10158	−	4.89572i	−0.236020	−	0.281717i
$303$	24.8149			1.42558
$304$	10.5338	−	4.87258i	0.604153	−	0.279462i
$305$	−0.479004	−	0.479004i	−0.0274277	−	0.0274277i
$306$	3.97650	−	45.0525i	0.227321	−	2.57548i
$307$	12.4509	+	12.4509i	0.710610	+	0.710610i	0.966663	−	0.256053i	$-0.0824222\pi$
$307$	12.4509	+	12.4509i	0.710610	+	0.710610i	−0.256053	+	0.966663i	$0.582422\pi$
$308$	−1.14487	+	6.43497i	−0.0652348	+	0.366666i
$309$			32.0255i			1.82187i
$310$	0.188069	+	0.0165996i	0.0106816	+	0.000942795i
$311$	−4.47048			−0.253497			−0.126749	−	0.991935i	$-0.540454\pi$
$311$	−4.47048			−0.253497			−0.126749	+	0.991935i	$0.540454\pi$
$312$	28.1626	−	3.24902i	1.59440	−	0.183939i
$313$	7.05722			0.398898			0.199449	−	0.979908i	$-0.436085\pi$
$313$	7.05722			0.398898			0.199449	+	0.979908i	$0.436085\pi$
$314$	−34.4144	−	3.03754i	−1.94212	−	0.171418i
$315$			1.67724i			0.0945018i
$316$	−3.59568	+	20.2103i	−0.202273	+	1.13692i
$317$	18.4249	+	18.4249i	1.03484	+	1.03484i	0.999371	+	0.0354732i	$0.0112938\pi$
$317$	18.4249	+	18.4249i	1.03484	+	1.03484i	0.0354732	+	0.999371i	$0.488706\pi$
$318$	4.71609	−	53.4318i	0.264465	−	2.99631i
$319$	5.00703	+	5.00703i	0.280340	+	0.280340i
$320$	−0.220898	−	0.839885i	−0.0123486	−	0.0469510i
$321$	4.74253			0.264702
$322$	24.8446	+	29.6550i	1.38454	+	1.65261i
$323$	−13.8785	−	13.8785i	−0.772222	−	0.772222i
$324$	−1.63703	−	0.291250i	−0.0909463	−	0.0161806i
$325$	−16.7092	+	6.65381i	−0.926858	+	0.369087i
$326$	−1.25569	−	1.49881i	−0.0695460	−	0.0830113i
$327$	15.3216	−	15.3216i	0.847284	−	0.847284i
$328$	13.3482	+	23.2434i	0.737031	+	1.28340i
$329$			20.4883i			1.12956i
$330$	0.425120	+	0.0375226i	0.0234021	+	0.00206555i
$331$	−13.7348	+	13.7348i	−0.754931	+	0.754931i	−0.975395	−	0.220464i	$-0.929243\pi$
$331$	−13.7348	+	13.7348i	−0.754931	+	0.754931i	0.220464	+	0.975395i	$0.429243\pi$
$332$	17.0449	−	11.8959i	0.935460	−	0.652874i
$333$	22.1229	−	22.1229i	1.21233	−	1.21233i
$334$	−8.87212	−	10.5899i	−0.485461	−	0.579454i
$335$	0.630365			0.0344405
$336$	32.9813	−	15.2561i	1.79928	−	0.832287i
$337$		−	14.8093i		−	0.806712i	−0.915043	−	0.403356i	$-0.867844\pi$
$337$		−	14.8093i		−	0.806712i	0.915043	−	0.403356i	$-0.132156\pi$
$338$	14.4116	−	11.4152i	0.783887	−	0.620903i
$339$		−	9.78597i		−	0.531501i
$340$	−1.20433	+	0.840525i	−0.0653141	+	0.0455839i
$341$	1.22979			0.0665971
$342$	14.8708	−	12.4586i	0.804121	−	0.673685i
$343$	7.67222	−	7.67222i	0.414261	−	0.414261i
$344$	−17.7557	−	4.80156i	−0.957323	−	0.258883i
$345$	1.78621	−	1.78621i	0.0961661	−	0.0961661i
$346$	−0.993204	+	11.2527i	−0.0533950	+	0.604948i
$347$			23.1498i			1.24275i	0.783514	+	0.621374i	$0.213425\pi$
$347$			23.1498i			1.24275i	−0.783514	+	0.621374i	$0.786575\pi$
$348$	6.89596	−	38.7602i	0.369662	−	2.07777i
$349$	1.71268	−	1.71268i	0.0916775	−	0.0916775i	−0.659781	−	0.751458i	$-0.729351\pi$
$349$	1.71268	−	1.71268i	0.0916775	−	0.0916775i	0.751458	+	0.659781i	$0.229351\pi$
$350$	−17.6717	+	14.8051i	−0.944590	+	0.791368i
$351$	16.0890	−	6.40684i	0.858766	−	0.341972i
$352$	−1.91430	−	5.32310i	−0.102033	−	0.283722i
$353$	18.5722	+	18.5722i	0.988500	+	0.988500i	0.999935	−	0.0114344i	$-0.00363976\pi$
$353$	18.5722	+	18.5722i	0.988500	+	0.988500i	−0.0114344	+	0.999935i	$0.503640\pi$
$354$	−16.0061	+	13.4098i	−0.850715	+	0.712721i
$355$	−1.41940			−0.0753337
$356$	−5.87572	+	4.10077i	−0.311413	+	0.217341i
$357$	−43.4537	−	43.4537i	−2.29982	−	2.29982i
$358$	−17.9308	−	1.58263i	−0.947670	−	0.0836448i
$359$	19.8935	+	19.8935i	1.04994	+	1.04994i	0.998686	+	0.0512526i	$0.0163214\pi$
$359$	19.8935	+	19.8935i	1.04994	+	1.04994i	0.0512526	+	0.998686i	$0.483679\pi$
$360$	−0.722914	−	1.25882i	−0.0381009	−	0.0663458i
$361$			10.5811i			0.556901i
$362$	−0.492978	+	5.58529i	−0.0259103	+	0.293556i
$363$	2.77989			0.145906
$364$	12.9640	−	19.6796i	0.679500	−	1.03149i
$365$	−1.17119			−0.0613029
$366$	−2.15695	+	24.4376i	−0.112746	+	1.27737i
$367$		−	4.37902i		−	0.228583i	−0.993447	−	0.114291i	$-0.963540\pi$
$367$		−	4.37902i		−	0.228583i	0.993447	−	0.114291i	$-0.0364598\pi$
$368$	−31.4284	−	11.5486i	−1.63832	−	0.602013i
$369$	31.6804	+	31.6804i	1.64922	+	1.64922i
$370$	−1.01201	−	0.0893234i	−0.0526117	−	0.00464370i
$371$	−31.5291	−	31.5291i	−1.63691	−	1.63691i
$372$	−3.91315	−	5.60689i	−0.202887	−	0.290704i
$373$	8.85889			0.458696			0.229348	−	0.973345i	$-0.426341\pi$
$373$	8.85889			0.458696			0.229348	+	0.973345i	$0.426341\pi$
$374$	−7.33297	+	6.14349i	−0.379179	+	0.317672i
$375$	2.13135	+	2.13135i	0.110062	+	0.110062i
$376$	−8.83076	−	15.3771i	−0.455412	−	0.793016i
$377$	−9.44541	−	23.7195i	−0.486463	−	1.22162i
$378$	17.0157	−	14.2556i	0.875196	−	0.733230i
$379$	−17.2438	+	17.2438i	−0.885756	+	0.885756i	−0.994112	−	0.108357i	$-0.965441\pi$
$379$	−17.2438	+	17.2438i	−0.885756	+	0.885756i	0.108357	+	0.994112i	$0.465441\pi$
$380$	−0.620218	−	0.110345i	−0.0318165	−	0.00566058i
$381$			10.5484i			0.540412i
$382$	−0.916501	+	10.3837i	−0.0468923	+	0.531275i
$383$	−18.6055	+	18.6055i	−0.950697	+	0.950697i	−0.998840	−	0.0481433i	$-0.984670\pi$
$383$	−18.6055	+	18.6055i	−0.950697	+	0.950697i	0.0481433	+	0.998840i	$0.484670\pi$
$384$	−18.1779	+	25.6656i	−0.927637	+	1.30974i
$385$	0.250855	−	0.250855i	0.0127847	−	0.0127847i
$386$	6.98289	−	5.85019i	0.355420	−	0.297767i
$387$	−30.7452			−1.56287
$388$	0.896372	+	1.28435i	0.0455064	+	0.0652031i
$389$			12.1917i			0.618143i	0.951039	+	0.309072i	$0.100018\pi$
$389$			12.1917i			0.618143i	−0.951039	+	0.309072i	$0.899982\pi$
$390$	−1.35444	−	0.730235i	−0.0685848	−	0.0369769i
$391$			56.6234i			2.86357i
$392$	2.71705	−	10.0474i	0.137232	−	0.507470i
$393$	24.4726			1.23448
$394$	−15.8373	−	18.9036i	−0.797870	−	0.952351i
$395$	0.787859	−	0.787859i	0.0396415	−	0.0396415i
$396$	−5.41158	−	7.75389i	−0.271942	−	0.389648i
$397$	6.41283	−	6.41283i	0.321851	−	0.321851i	−0.527626	−	0.849477i	$-0.676918\pi$
$397$	6.41283	−	6.41283i	0.321851	−	0.321851i	0.849477	+	0.527626i	$0.176918\pi$
$398$	4.01014	+	0.353949i	0.201010	+	0.0177419i
$399$		−	26.3596i		−	1.31963i
$400$	6.88193	−	18.7285i	0.344096	−	0.936424i
$401$	−1.23822	+	1.23822i	−0.0618339	+	0.0618339i	−0.737348	−	0.675514i	$-0.763922\pi$
$401$	−1.23822	+	1.23822i	−0.0618339	+	0.0618339i	0.675514	+	0.737348i	$0.263922\pi$
$402$	−14.6605	−	17.4991i	−0.731201	−	0.872774i
$403$	−4.07287	−	1.75295i	−0.202884	−	0.0873208i
$404$	−3.12721	+	17.5771i	−0.155584	+	0.874496i
$405$	0.0638165	+	0.0638165i	0.00317107	+	0.00317107i
$406$	−21.0166	−	25.0858i	−1.04304	−	1.24499i
$407$	−6.61759			−0.328022
$408$	51.3426	+	13.8842i	2.54184	+	0.687373i
$409$	27.9690	+	27.9690i	1.38298	+	1.38298i	0.839283	+	0.543694i	$0.182975\pi$
$409$	27.9690	+	27.9690i	1.38298	+	1.38298i	0.543694	+	0.839283i	$0.317025\pi$
$410$	0.127913	−	1.44921i	0.00631715	−	0.0715714i
$411$	−18.0819	−	18.0819i	−0.891914	−	0.891914i
$412$	−22.6846	−	4.03590i	−1.11759	−	0.198834i
$413$			17.3577i			0.854117i
$414$	−55.7511	−	4.92079i	−2.74002	−	0.241844i
$415$	−1.12820			−0.0553812
$416$	−1.24772	+	20.3579i	−0.0611743	+	0.998127i
$417$	8.05331			0.394372
$418$	−4.08749	−	0.360777i	−0.199926	−	0.0176462i
$419$			7.85898i			0.383936i	0.981401	+	0.191968i	$0.0614871\pi$
$419$			7.85898i			0.383936i	−0.981401	+	0.191968i	$0.938513\pi$
$420$	−1.94190	−	0.345491i	−0.0947553	−	0.0168582i
$421$	−9.51073	−	9.51073i	−0.463525	−	0.463525i	0.436284	−	0.899809i	$-0.356294\pi$
$421$	−9.51073	−	9.51073i	−0.463525	−	0.463525i	−0.899809	+	0.436284i	$0.856294\pi$
$422$	−2.55988	+	29.0027i	−0.124613	+	1.41183i
$423$	−20.9588	−	20.9588i	−1.01905	−	1.01905i
$424$	37.2530	+	10.0741i	1.80917	+	0.489241i
$425$	−33.7424			−1.63675
$426$	33.0112	+	39.4027i	1.59940	+	1.90907i
$427$	14.4201	+	14.4201i	0.697838	+	0.697838i
$428$	−0.597660	+	3.35928i	−0.0288890	+	0.162377i
$429$	−9.20653	−	3.96246i	−0.444495	−	0.191309i
$430$	0.641146	+	0.765282i	0.0309188	+	0.0369052i
$431$	−6.28228	+	6.28228i	−0.302607	+	0.302607i	−0.842033	−	0.539426i	$-0.818641\pi$
$431$	−6.28228	+	6.28228i	−0.302607	+	0.302607i	0.539426	+	0.842033i	$0.318641\pi$
$432$	−6.62649	+	18.0333i	−0.318817	+	0.867629i
$433$			9.73318i			0.467747i	0.972267	+	0.233874i	$0.0751402\pi$
$433$			9.73318i			0.467747i	−0.972267	+	0.233874i	$0.924860\pi$
$434$	−5.66169	−	0.499721i	−0.271770	−	0.0239874i
$435$	−1.51099	+	1.51099i	−0.0724465	+	0.0724465i
$436$	8.92187	+	12.7836i	0.427280	+	0.612221i
$437$	−17.1742	+	17.1742i	−0.821555	+	0.821555i
$438$	27.2387	+	32.5125i	1.30151	+	1.55351i
$439$	−28.1441			−1.34324			−0.671622	−	0.740894i	$-0.734402\pi$
$439$	−28.1441			−1.34324			−0.671622	+	0.740894i	$0.734402\pi$
$440$	−0.0801526	+	0.296396i	−0.00382112	+	0.0141301i
$441$		−	17.3977i		−	0.828464i
$442$	33.0425	−	9.89377i	1.57167	−	0.470599i
$443$			11.2274i			0.533428i	0.963776	+	0.266714i	$0.0859380\pi$
$443$			11.2274i			0.533428i	−0.963776	+	0.266714i	$0.914062\pi$
$444$	21.0568	+	30.1709i	0.999313	+	1.43185i
$445$	0.388914			0.0184363
$446$	−6.40970	+	5.36998i	−0.303508	+	0.254276i
$447$	1.08194	−	1.08194i	0.0511739	−	0.0511739i
$448$	6.64999	+	25.2842i	0.314182	+	1.19457i
$449$	−15.6426	+	15.6426i	−0.738221	+	0.738221i	−0.972234	−	0.234013i	$-0.924814\pi$
$449$	−15.6426	+	15.6426i	−0.738221	+	0.738221i	0.234013	+	0.972234i	$0.424814\pi$
$450$	2.93235	−	33.2226i	0.138232	−	1.56613i
$451$		−	9.47649i		−	0.446231i
$452$	6.93170	+	1.23324i	0.326040	+	0.0580068i
$453$	8.87728	−	8.87728i	0.417091	−	0.417091i
$454$	18.6602	−	15.6333i	0.875766	−	0.733708i
$455$	−1.18836	+	0.473219i	−0.0557110	+	0.0221849i
$456$	11.3613	+	19.7837i	0.532044	+	0.926457i
$457$	2.59987	+	2.59987i	0.121617	+	0.121617i	0.765296	−	0.643679i	$-0.222593\pi$
$457$	2.59987	+	2.59987i	0.121617	+	0.121617i	−0.643679	+	0.765296i	$0.722593\pi$
$458$	−9.15953	+	7.67376i	−0.427997	+	0.358571i
$459$	32.4900			1.51650
$460$	1.04012	+	1.49032i	0.0484960	+	0.0694867i
$461$	−13.9280	−	13.9280i	−0.648690	−	0.648690i	0.303987	−	0.952676i	$-0.401682\pi$
$461$	−13.9280	−	13.9280i	−0.648690	−	0.648690i	−0.952676	+	0.303987i	$0.901682\pi$
$462$	−12.7980	−	1.12960i	−0.595415	−	0.0525535i
$463$	−4.99151	−	4.99151i	−0.231975	−	0.231975i	0.581542	−	0.813517i	$-0.302450\pi$
$463$	−4.99151	−	4.99151i	−0.231975	−	0.231975i	−0.813517	+	0.581542i	$0.802450\pi$
$464$	26.5860	+	9.76923i	1.23422	+	0.453525i
$465$			0.371120i			0.0172103i
$466$	1.07940	−	12.2293i	0.0500024	−	0.566512i
$467$	−5.93449			−0.274615			−0.137308	−	0.990528i	$-0.543845\pi$
$467$	−5.93449			−0.274615			−0.137308	+	0.990528i	$0.543845\pi$
$468$	6.86982	+	33.3933i	0.317558	+	1.54360i
$469$	−18.9767			−0.876264
$470$	−0.0846231	+	0.958753i	−0.00390337	+	0.0442240i
$471$		−	67.9107i		−	3.12916i
$472$	−7.48142	−	13.0275i	−0.344360	−	0.599640i
$473$	4.59837	+	4.59837i	0.211433	+	0.211433i
$474$	−40.1946	−	3.54772i	−1.84620	−	0.162952i
$475$	−10.2343	−	10.2343i	−0.469581	−	0.469581i
$476$	36.2557	−	25.3035i	1.66178	−	1.15978i
$477$	64.5061			2.95353
$478$	−2.73870	+	2.29446i	−0.125265	+	0.104946i
$479$	2.47057	+	2.47057i	0.112883	+	0.112883i	0.761292	−	0.648409i	$-0.224565\pi$
$479$	2.47057	+	2.47057i	0.112883	+	0.112883i	−0.648409	+	0.761292i	$0.724565\pi$
$480$	1.60637	−	0.577687i	0.0733206	−	0.0263677i
$481$	21.9163	+	9.43273i	0.999299	+	0.430095i
$482$	1.10663	−	0.927126i	0.0504058	−	0.0422294i
$483$	−53.7726	+	53.7726i	−2.44674	+	2.44674i
$484$	−0.350325	+	1.96908i	−0.0159239	+	0.0895036i
$485$		−	0.0850113i		−	0.00386016i
$486$	2.07901	−	23.5545i	0.0943058	−	1.06846i
$487$	−8.34162	+	8.34162i	−0.377995	+	0.377995i	−0.870378	−	0.492384i	$-0.836126\pi$
$487$	−8.34162	+	8.34162i	−0.377995	+	0.377995i	0.492384	+	0.870378i	$0.336126\pi$
$488$	−17.0380	−	4.60749i	−0.771276	−	0.208571i
$489$	2.71775	−	2.71775i	0.122901	−	0.122901i
$490$	−0.433049	+	0.362804i	−0.0195632	+	0.0163898i
$491$	37.1944			1.67856			0.839280	−	0.543700i	$-0.182977\pi$
$491$	37.1944			1.67856			0.839280	+	0.543700i	$0.182977\pi$
$492$	−43.2053	+	30.1537i	−1.94784	+	1.35944i
$493$		−	47.8990i		−	2.15726i
$494$	13.0228	+	7.02116i	0.585925	+	0.315897i
$495$			0.513230i			0.0230680i
$496$	4.46466	−	2.06521i	0.200469	−	0.0927307i
$497$	42.7300			1.91670
$498$	26.2388	+	31.3191i	1.17579	+	1.40344i
$499$	16.4576	−	16.4576i	0.736742	−	0.736742i	−0.235204	−	0.971946i	$-0.575576\pi$
$499$	16.4576	−	16.4576i	0.736742	−	0.736742i	0.971946	+	0.235204i	$0.0755757\pi$
$500$	−1.77829	+	1.24110i	−0.0795277	+	0.0555038i
$501$	19.2024	−	19.2024i	0.857901	−	0.857901i
$502$	−10.7915	−	0.952501i	−0.481650	−	0.0425122i
$503$			34.4171i			1.53458i	0.641300	+	0.767291i	$0.278396\pi$
$503$			34.4171i			1.53458i	−0.641300	+	0.767291i	$0.721604\pi$
$504$	21.7629	+	37.8961i	0.969396	+	1.68802i
$505$	0.685211	−	0.685211i	0.0304915	−	0.0304915i
$506$	7.60238	+	9.07432i	0.337967	+	0.403403i
$507$	24.8424	+	26.2460i	1.10329	+	1.16563i
$508$	−7.47176	−	1.32933i	−0.331506	−	0.0589793i
$509$	−17.3675	−	17.3675i	−0.769799	−	0.769799i	0.208272	−	0.978071i	$-0.433216\pi$
$509$	−17.3675	−	17.3675i	−0.769799	−	0.769799i	−0.978071	+	0.208272i	$0.933216\pi$
$510$	−1.85394	−	2.21290i	−0.0820940	−	0.0979888i
$511$	35.2580			1.55972
$512$	−15.8889	−	16.1104i	−0.702196	−	0.711984i
$513$	9.85442	+	9.85442i	0.435083	+	0.435083i
$514$	−3.04286	+	34.4747i	−0.134215	+	1.52061i
$515$	0.884315	+	0.884315i	0.0389676	+	0.0389676i
$516$	6.33313	−	35.5967i	0.278800	−	1.56706i
$517$			6.26936i			0.275726i
$518$	30.4658	+	2.68903i	1.33859	+	0.118149i
$519$	−22.2052			−0.974699
$520$	0.687936	−	0.867365i	0.0301680	−	0.0380365i
$521$	−15.0004			−0.657178			−0.328589	−	0.944473i	$-0.606573\pi$
$521$	−15.0004			−0.657178			−0.328589	+	0.944473i	$0.606573\pi$
$522$	47.1610	+	4.16261i	2.06418	+	0.182192i
$523$		−	29.7329i		−	1.30013i	−0.759879	−	0.650064i	$-0.774742\pi$
$523$		−	29.7329i		−	1.30013i	0.759879	−	0.650064i	$-0.225258\pi$
$524$	−3.08407	+	17.3347i	−0.134728	+	0.757269i
$525$	−32.0436	−	32.0436i	−1.39850	−	1.39850i
$526$	−2.16524	+	24.5315i	−0.0944088	+	1.06962i
$527$	−5.88232	−	5.88232i	−0.256238	−	0.256238i
$528$	10.0922	−	4.66831i	0.439205	−	0.203162i
$529$	47.0697			2.04651
$530$	−1.34518	−	1.60563i	−0.0584309	−	0.0697441i
$531$	−17.7563	−	17.7563i	−0.770558	−	0.770558i
$532$	18.6713	+	3.32187i	0.809502	+	0.144021i
$533$	−13.5078	+	31.3846i	−0.585089	+	1.35942i
$534$	−9.04507	−	10.7963i	−0.391418	−	0.467203i
$535$	0.130955	−	0.130955i	0.00566167	−	0.00566167i
$536$	14.2426	−	8.17924i	0.615189	−	0.353289i
$537$		−	35.3831i		−	1.52690i
$538$	−10.1392	−	0.894924i	−0.437133	−	0.0385829i
$539$	−2.60207	+	2.60207i	−0.112079	+	0.112079i
$540$	0.855134	−	0.596813i	0.0367991	−	0.0256827i
$541$	−22.9954	+	22.9954i	−0.988651	+	0.988651i	−0.999936	−	0.0112856i	$-0.996408\pi$
$541$	−22.9954	+	22.9954i	−0.988651	+	0.988651i	0.0112856	+	0.999936i	$0.496408\pi$
$542$	3.78227	+	4.51458i	0.162462	+	0.193918i
$543$	−11.0216			−0.472981
$544$	−16.3049	+	34.6178i	−0.699066	+	1.48423i
$545$		−	0.846143i		−	0.0362448i
$546$	40.7746	+	21.9833i	1.74499	+	0.940797i
$547$			2.08996i			0.0893603i	0.999001	+	0.0446802i	$0.0142269\pi$
$547$			2.08996i			0.0893603i	−0.999001	+	0.0446802i	$0.985773\pi$
$548$	15.0867	−	10.5292i	0.644470	−	0.449787i
$549$	−29.5025			−1.25914
$550$	−5.40747	+	4.53032i	−0.230575	+	0.193174i
$551$	14.5281	−	14.5281i	0.618916	−	0.618916i
$552$	17.1813	−	63.5348i	0.731285	−	2.70422i
$553$	−23.7180	+	23.7180i	−1.00859	+	1.00859i
$554$	−2.25258	+	25.5211i	−0.0957030	+	1.08429i
$555$		−	1.99701i		−	0.0847685i
$556$	−1.01489	+	5.70440i	−0.0430408	+	0.241920i
$557$	2.11091	−	2.11091i	0.0894423	−	0.0894423i	−0.660970	−	0.750412i	$-0.729855\pi$
$557$	2.11091	−	2.11091i	0.0894423	−	0.0894423i	0.750412	+	0.660970i	$0.229855\pi$
$558$	6.30289	−	5.28050i	0.266823	−	0.223541i
$559$	−8.67450	−	21.7836i	−0.366892	−	0.921346i
$560$	0.489443	−	1.33197i	0.0206827	−	0.0562860i
$561$	−13.2967	−	13.2967i	−0.561387	−	0.561387i
$562$	16.1850	−	13.5596i	0.682723	−	0.571979i
$563$	26.9433			1.13552			0.567762	−	0.823193i	$-0.307809\pi$
$563$	26.9433			1.13552			0.567762	+	0.823193i	$0.307809\pi$
$564$	28.5833	−	19.9488i	1.20357	−	0.839995i
$565$	−0.270219	−	0.270219i	−0.0113682	−	0.0113682i
$566$	−3.12354	−	0.275695i	−0.131292	−	0.0115883i
$567$	−1.92116	−	1.92116i	−0.0806810	−	0.0806810i
$568$	−32.0703	+	18.4172i	−1.34564	+	0.772770i
$569$		−	23.9264i		−	1.00305i	−0.865145	−	0.501523i	$-0.832773\pi$
$569$		−	23.9264i		−	1.00305i	0.865145	−	0.501523i	$-0.167227\pi$
$570$	0.108873	−	1.23350i	0.00456019	−	0.0516656i
$571$	33.5749			1.40507			0.702533	−	0.711651i	$-0.252052\pi$
$571$	33.5749			1.40507			0.702533	+	0.711651i	$0.252052\pi$
$572$	3.96695	−	6.02190i	0.165866	−	0.251788i
$573$	−20.4903			−0.855996
$574$	−3.85073	+	43.6276i	−0.160726	+	1.82098i
$575$			41.7552i			1.74131i
$576$	−32.6675	−	19.0621i	−1.36115	−	0.794254i
$577$	−19.5370	−	19.5370i	−0.813334	−	0.813334i	0.171798	−	0.985132i	$-0.445042\pi$
$577$	−19.5370	−	19.5370i	−0.813334	−	0.813334i	−0.985132	+	0.171798i	$0.945042\pi$
$578$	40.5117	+	3.57572i	1.68507	+	0.148730i
$579$	12.6619	+	12.6619i	0.526210	+	0.526210i
$580$	−0.879863	−	1.26070i	−0.0365343	−	0.0523476i
$581$	33.9638			1.40906
$582$	−2.35993	+	1.97713i	−0.0978223	+	0.0819545i
$583$	−9.64778	−	9.64778i	−0.399570	−	0.399570i
$584$	−26.4622	+	15.1967i	−1.09501	+	0.628843i
$585$	0.731559	−	1.69973i	0.0302463	−	0.0702752i
$586$	−2.40831	+	2.01766i	−0.0994863	+	0.0833486i
$587$	−16.3672	+	16.3672i	−0.675547	+	0.675547i	−0.958989	−	0.283443i	$-0.908523\pi$
$587$	−16.3672	+	16.3672i	−0.675547	+	0.675547i	0.283443	+	0.958989i	$0.408523\pi$
$588$	20.1431	+	3.58372i	0.830686	+	0.147790i
$589$		−	3.56829i		−	0.147029i
$590$	−0.0716927	+	0.812256i	−0.00295154	+	0.0334400i
$591$	34.2775	−	34.2775i	1.40999	−	1.40999i
$592$	−24.0246	+	11.1130i	−0.987404	+	0.456742i
$593$	29.0256	−	29.0256i	1.19194	−	1.19194i	0.215416	−	0.976522i	$-0.430889\pi$
$593$	29.0256	−	29.0256i	1.19194	−	1.19194i	0.976522	−	0.215416i	$-0.0691106\pi$
$594$	5.20676	−	4.36217i	0.213636	−	0.178982i
$595$	−2.39976			−0.0983807
$596$	0.630021	+	0.902716i	0.0258067	+	0.0369767i
$597$			7.91329i			0.323869i
$598$	−12.2432	−	40.8891i	−0.500663	−	1.67208i
$599$		−	25.0691i		−	1.02429i	−0.858898	−	0.512147i	$-0.828850\pi$
$599$		−	25.0691i		−	1.02429i	0.858898	−	0.512147i	$-0.171150\pi$
$600$	37.8610	+	10.2385i	1.54567	+	0.417985i
$601$	21.3902			0.872526			0.436263	−	0.899819i	$-0.356302\pi$
$601$	21.3902			0.872526			0.436263	+	0.899819i	$0.356302\pi$
$602$	−19.3013	−	23.0383i	−0.786662	−	0.938973i
$603$	19.4125	−	19.4125i	0.790538	−	0.790538i
$604$	5.16932	+	7.40677i	0.210336	+	0.301377i
$605$	0.0767607	−	0.0767607i	0.00312077	−	0.00312077i
$606$	−34.9577	−	3.08549i	−1.42006	−	0.125340i
$607$		−	4.02251i		−	0.163269i	−0.996662	−	0.0816343i	$-0.973986\pi$
$607$		−	4.02251i		−	0.163269i	0.996662	−	0.0816343i	$-0.0260140\pi$
$608$	−15.4452	+	5.55441i	−0.626384	+	0.225261i
$609$	45.4874	−	45.4874i	1.84324	−	1.84324i
$610$	0.615231	+	0.734350i	0.0249100	+	0.0297330i
$611$	8.93636	−	20.7631i	0.361526	−	0.839983i
$612$	−11.2037	+	62.9727i	−0.452882	+	2.54552i
$613$	1.81584	+	1.81584i	0.0733413	+	0.0733413i	0.742826	−	0.669485i	$-0.233485\pi$
$613$	1.81584	+	1.81584i	0.0733413	+	0.0733413i	−0.669485	+	0.742826i	$0.733485\pi$
$614$	−15.9919	−	19.0882i	−0.645380	−	0.770336i
$615$	2.85976			0.115317
$616$	2.41294	−	8.92283i	0.0972202	−	0.359511i
$617$	13.4223	+	13.4223i	0.540363	+	0.540363i	0.923635	−	0.383273i	$-0.125203\pi$
$617$	13.4223	+	13.4223i	0.540363	+	0.540363i	−0.383273	+	0.923635i	$0.625203\pi$
$618$	3.98206	−	45.1155i	0.160182	−	1.81481i
$619$	−27.0493	−	27.0493i	−1.08720	−	1.08720i	−0.995815	−	0.0913890i	$-0.970869\pi$
$619$	−27.0493	−	27.0493i	−1.08720	−	1.08720i	−0.0913890	−	0.995815i	$-0.529131\pi$
$620$	−0.262875	−	0.0467690i	−0.0105573	−	0.00187829i
$621$		−	40.2053i		−	1.61339i
$622$	6.29772	+	0.555860i	0.252516	+	0.0222880i
$623$	−11.7080			−0.469072
$624$	−40.0777	+	1.07526i	−1.60439	+	0.0430450i
$625$	−24.8234			−0.992935
$626$	−9.94177	−	0.877497i	−0.397353	−	0.0350718i
$627$		−	8.06594i		−	0.322123i
$628$	48.1032	+	8.55820i	1.91953	+	0.341509i
$629$	31.6531	+	31.6531i	1.26209	+	1.26209i
$630$	0.208549	−	2.36279i	0.00830877	−	0.0941358i
$631$	7.14958	+	7.14958i	0.284620	+	0.284620i	0.834948	−	0.550328i	$-0.185497\pi$
$631$	7.14958	+	7.14958i	0.284620	+	0.284620i	−0.550328	+	0.834948i	$0.685497\pi$
$632$	7.57833	−	28.0239i	0.301450	−	1.11473i
$633$	−57.2316			−2.27475
$634$	−23.6648	−	28.2467i	−0.939851	−	1.12182i
$635$	0.291272	+	0.291272i	0.0115588	+	0.0115588i
$636$	−13.2875	+	74.6850i	−0.526882	+	2.96145i
$637$	12.3266	−	4.90863i	0.488399	−	0.194487i
$638$	−6.43101	−	7.67617i	−0.254606	−	0.303902i
$639$	−43.7112	+	43.7112i	−1.72919	+	1.72919i
$640$	0.206755	+	1.21064i	0.00817272	+	0.0478549i
$641$			9.75108i			0.385144i	0.981283	+	0.192572i	$0.0616830\pi$
$641$			9.75108i			0.385144i	−0.981283	+	0.192572i	$0.938317\pi$
$642$	−6.68098	−	0.589688i	−0.263677	−	0.0232731i
$643$	−0.614239	+	0.614239i	−0.0242232	+	0.0242232i	−0.719115	−	0.694891i	$-0.755452\pi$
$643$	−0.614239	+	0.614239i	−0.0242232	+	0.0242232i	0.694891	+	0.719115i	$0.255452\pi$
$644$	−31.3122	−	44.8652i	−1.23388	−	1.76794i
$645$	−1.38767	+	1.38767i	−0.0546393	+	0.0546393i
$646$	17.8255	+	21.2769i	0.701336	+	0.837127i
$647$	43.0589			1.69282			0.846411	−	0.532531i	$-0.178759\pi$
$647$	43.0589			1.69282			0.846411	+	0.532531i	$0.178759\pi$
$648$	2.26994	+	0.613844i	0.0891715	+	0.0241141i
$649$			5.31140i			0.208491i
$650$	24.3662	−	7.29585i	0.955720	−	0.286167i
$651$		−	11.1723i		−	0.437878i
$652$	1.58257	+	2.26756i	0.0619782	+	0.0888044i
$653$	12.2674			0.480060			0.240030	−	0.970765i	$-0.422843\pi$
$653$	12.2674			0.480060			0.240030	+	0.970765i	$0.422843\pi$
$654$	−23.4891	+	19.6790i	−0.918497	+	0.769508i
$655$	0.675759	−	0.675759i	0.0264041	−	0.0264041i
$656$	−15.9140	−	34.4036i	−0.621337	−	1.34324i
$657$	−36.0676	+	36.0676i	−1.40713	+	1.40713i
$658$	2.54752	−	28.8627i	0.0993128	−	1.12518i
$659$		−	15.3549i		−	0.598143i	−0.954231	−	0.299071i	$-0.903323\pi$
$659$		−	15.3549i		−	0.598143i	0.954231	−	0.299071i	$-0.0966769\pi$
$660$	−0.594216	−	0.105719i	−0.0231298	−	0.00411511i
$661$	12.0975	−	12.0975i	0.470538	−	0.470538i	−0.431551	−	0.902089i	$-0.642033\pi$
$661$	12.0975	−	12.0975i	0.470538	−	0.470538i	0.902089	+	0.431551i	$0.142033\pi$
$662$	21.0565	−	17.6409i	0.818382	−	0.685633i
$663$	25.0833	+	62.9896i	0.974154	+	2.44631i
$664$	−25.4909	+	14.6389i	−0.989239	+	0.568098i
$665$	−0.727863	−	0.727863i	−0.0282253	−	0.0282253i
$666$	−33.9162	+	28.4146i	−1.31423	+	1.10104i
$667$	−59.2735			−2.29508
$668$	11.1817	+	16.0216i	0.432634	+	0.619893i
$669$	−11.6225	−	11.6225i	−0.449353	−	0.449353i
$670$	−0.888018	−	0.0783797i	−0.0343071	−	0.00302807i
$671$	4.41251	+	4.41251i	0.170343	+	0.170343i
$672$	−48.3589	+	17.3909i	−1.86548	+	0.670868i
$673$		−	32.7636i		−	1.26294i	−0.775399	−	0.631471i	$-0.782451\pi$
$673$		−	32.7636i		−	1.26294i	0.775399	−	0.631471i	$-0.217549\pi$
$674$	−1.84139	+	20.8624i	−0.0709276	+	0.803588i
$675$	23.9587			0.922172
$676$	−21.7215	+	14.2890i	−0.835442	+	0.549578i
$677$	5.05756			0.194378			0.0971890	−	0.995266i	$-0.469015\pi$
$677$	5.05756			0.194378			0.0971890	+	0.995266i	$0.469015\pi$
$678$	−1.21679	+	13.7859i	−0.0467306	+	0.529443i
$679$			2.55921i			0.0982135i
$680$	1.80110	−	1.03433i	0.0690690	−	0.0396648i
$681$	33.8360	+	33.8360i	1.29660	+	1.29660i
$682$	−1.73246	−	0.152913i	−0.0663392	−	0.00585534i
$683$	14.9145	+	14.9145i	0.570688	+	0.570688i	0.932321	−	0.361633i	$-0.117781\pi$
$683$	14.9145	+	14.9145i	0.570688	+	0.570688i	−0.361633	+	0.932321i	$0.617781\pi$
$684$	−22.4982	+	15.7019i	−0.860239	+	0.600376i
$685$	−0.998586			−0.0381540
$686$	−11.7621	+	9.85418i	−0.449079	+	0.376234i
$687$	−16.6088	−	16.6088i	−0.633663	−	0.633663i
$688$	24.4161	+	8.97188i	0.930855	+	0.342050i
$689$	18.1999	+	45.7038i	0.693359	+	1.74118i
$690$	−2.73839	+	2.29420i	−0.104249	+	0.0873386i
$691$	−19.1362	+	19.1362i	−0.727977	+	0.727977i	−0.970217	−	0.242239i	$-0.922118\pi$
$691$	−19.1362	+	19.1362i	−0.727977	+	0.727977i	0.242239	+	0.970217i	$0.422118\pi$
$692$	2.79832	−	15.7286i	0.106376	−	0.597911i
$693$		−	15.4505i		−	0.586915i
$694$	2.87846	−	32.6120i	0.109265	−	1.23794i
$695$	0.222375	−	0.222375i	0.00843515	−	0.00843515i
$696$	−14.5340	+	53.7455i	−0.550912	+	2.03722i
$697$	−45.3277	+	45.3277i	−1.71691	+	1.71691i
$698$	−2.62566	+	2.19976i	−0.0993829	+	0.0832620i
$699$	24.1324			0.912770
$700$	26.7356	−	18.6593i	1.01051	−	0.705254i
$701$		−	34.1835i		−	1.29109i	−0.763721	−	0.645546i	$-0.776630\pi$
$701$		−	34.1835i		−	1.29109i	0.763721	−	0.645546i	$-0.223370\pi$
$702$	−23.4618	+	7.02505i	−0.885507	+	0.265143i
$703$			19.2011i			0.724185i
$704$	2.03487	+	7.73688i	0.0766922	+	0.291595i
$705$	−1.89193			−0.0712541
$706$	−23.8541	−	28.4727i	−0.897761	−	1.07158i
$707$	−20.6278	+	20.6278i	−0.775790	+	0.775790i
$708$	24.2158	−	16.9006i	0.910084	−	0.635164i
$709$	10.6109	−	10.6109i	0.398500	−	0.398500i	−0.479204	−	0.877704i	$-0.659075\pi$
$709$	10.6109	−	10.6109i	0.398500	−	0.398500i	0.877704	+	0.479204i	$0.159075\pi$
$710$	1.99956	+	0.176488i	0.0750420	+	0.00662348i
$711$		−	48.5253i		−	1.81984i
$712$	8.78724	−	5.04632i	0.329316	−	0.189119i
$713$	−7.27919	+	7.27919i	−0.272608	+	0.272608i
$714$	55.8118	+	66.6179i	2.08871	+	2.49311i
$715$	−0.363633	+	0.144804i	−0.0135991	+	0.00541535i
$716$	25.0629	+	4.45903i	0.936646	+	0.166642i
$717$	−4.96602	−	4.96602i	−0.185459	−	0.185459i
$718$	−25.5511	−	30.4983i	−0.953560	−	1.13818i
$719$	1.64715			0.0614283			0.0307141	−	0.999528i	$-0.490222\pi$
$719$	1.64715			0.0614283			0.0307141	+	0.999528i	$0.490222\pi$
$720$	0.861874	+	1.86324i	0.0321201	+	0.0694388i
$721$	−26.6218	−	26.6218i	−0.991446	−	0.991446i
$722$	1.31566	−	14.9060i	0.0489637	−	0.554744i
$723$	2.00663	+	2.00663i	0.0746274	+	0.0746274i
$724$	1.38895	−	7.80690i	0.0516200	−	0.290141i
$725$		−	35.3216i		−	1.31181i
$726$	−3.91613	−	0.345652i	−0.145341	−	0.0128284i
$727$	−41.7562			−1.54865			−0.774326	−	0.632787i	$-0.781911\pi$
$727$	−41.7562			−1.54865			−0.774326	+	0.632787i	$0.781911\pi$
$728$	−20.7099	+	26.1115i	−0.767559	+	0.967756i
$729$	43.9865			1.62913
$730$	1.64990	+	0.145626i	0.0610655	+	0.00538987i
$731$		−	43.9896i		−	1.62701i
$732$	6.07715	−	34.1579i	0.224618	−	1.26251i
$733$	−1.41867	−	1.41867i	−0.0523997	−	0.0523997i	0.680421	−	0.732821i	$-0.261797\pi$
$733$	−1.41867	−	1.41867i	−0.0523997	−	0.0523997i	−0.732821	+	0.680421i	$0.761797\pi$
$734$	−0.544488	+	6.16888i	−0.0200974	+	0.227698i
$735$	−0.785237	−	0.785237i	−0.0289639	−	0.0289639i
$736$	42.8384	+	20.1768i	1.57904	+	0.743726i
$737$	−5.80682			−0.213897
$738$	−40.6902	−	48.5685i	−1.49783	−	1.78783i
$739$	−17.1490	−	17.1490i	−0.630838	−	0.630838i	0.317441	−	0.948278i	$-0.397177\pi$
$739$	−17.1490	−	17.1490i	−0.630838	−	0.630838i	−0.948278	+	0.317441i	$0.897177\pi$
$740$	1.41454	+	0.251666i	0.0519997	+	0.00925144i
$741$	−11.4972	+	26.7130i	−0.422361	+	0.981328i
$742$	40.4958	+	48.3365i	1.48665	+	1.77449i
$743$	−11.6229	+	11.6229i	−0.426402	+	0.426402i	−0.887401	−	0.460999i	$-0.847491\pi$
$743$	−11.6229	+	11.6229i	−0.426402	+	0.426402i	0.460999	+	0.887401i	$0.347491\pi$
$744$	4.81543	+	8.38519i	0.176542	+	0.307416i
$745$		−	0.0597507i		−	0.00218910i
$746$	−12.4798	−	1.10152i	−0.456920	−	0.0403294i
$747$	−34.7437	+	34.7437i	−1.27121	+	1.27121i
$748$	11.0941	−	7.74278i	0.405641	−	0.283104i
$749$	−3.94231	+	3.94231i	−0.144049	+	0.144049i
$750$	−2.73750	−	3.26752i	−0.0999592	−	0.119313i
$751$	−19.2102			−0.700990			−0.350495	−	0.936565i	$-0.613987\pi$
$751$	−19.2102			−0.700990			−0.350495	+	0.936565i	$0.613987\pi$
$752$	10.5282	+	22.7604i	0.383925	+	0.829985i
$753$		−	21.2952i		−	0.776039i
$754$	10.3568	+	34.5889i	0.377173	+	1.25966i
$755$		−	0.490254i		−	0.0178422i
$756$	−25.7433	+	17.9667i	−0.936273	+	0.653442i
$757$	−44.6030			−1.62112			−0.810561	−	0.585654i	$-0.800838\pi$
$757$	−44.6030			−1.62112			−0.810561	+	0.585654i	$0.800838\pi$
$758$	26.4361	−	22.1479i	0.960203	−	0.804448i
$759$	−16.4542	+	16.4542i	−0.597251	+	0.597251i
$760$	0.860003	+	0.232565i	0.0311956	+	0.00843603i
$761$	14.9655	−	14.9655i	0.542498	−	0.542498i	−0.381762	−	0.924261i	$-0.624683\pi$
$761$	14.9655	−	14.9655i	0.542498	−	0.542498i	0.924261	+	0.381762i	$0.124683\pi$
$762$	1.31159	−	14.8599i	0.0475140	−	0.538319i
$763$			25.4726i			0.922171i
$764$	2.58222	−	14.5139i	0.0934214	−	0.525095i
$765$	2.45487	−	2.45487i	0.0887559	−	0.0887559i
$766$	28.5237	−	23.8969i	1.03060	−	0.863428i
$767$	7.57089	−	17.5905i	0.273369	−	0.635155i
$768$	28.7992	−	33.8958i	1.03920	−	1.22311i
$769$	−28.2415	−	28.2415i	−1.01842	−	1.01842i	−0.999827	−	0.0185881i	$-0.994083\pi$
$769$	−28.2415	−	28.2415i	−1.01842	−	1.01842i	−0.0185881	−	0.999827i	$-0.505917\pi$
$770$	−0.384580	+	0.322197i	−0.0138593	+	0.0116112i
$771$	−68.0296			−2.45003
$772$	−10.5645	+	7.37313i	−0.380223	+	0.265365i
$773$	15.9917	+	15.9917i	0.575180	+	0.575180i	0.933571	−	0.358391i	$-0.116675\pi$
$773$	15.9917	+	15.9917i	0.575180	+	0.575180i	−0.358391	+	0.933571i	$0.616675\pi$
$774$	43.3119	+	3.82286i	1.55681	+	0.137410i
$775$	−4.33773	−	4.33773i	−0.155816	−	0.155816i
$776$	−1.10306	−	1.92077i	−0.0395974	−	0.0689516i
$777$			60.1189i			2.15675i
$778$	1.51592	−	17.1749i	0.0543483	−	0.615749i
$779$	−27.4963			−0.985159
$780$	1.81725	+	1.19712i	0.0650681	+	0.0428638i
$781$	13.0752			0.467869
$782$	7.04057	−	79.7675i	0.251770	−	2.85248i
$783$			34.0106i			1.21544i
$784$	−5.07691	+	13.8163i	−0.181318	+	0.493439i
$785$	−1.87521	−	1.87521i	−0.0669290	−	0.0669290i
$786$	−34.4755	−	3.04293i	−1.22970	−	0.108538i
$787$	−7.15288	−	7.15288i	−0.254973	−	0.254973i	0.568033	−	0.823006i	$-0.307705\pi$
$787$	−7.15288	−	7.15288i	−0.254973	−	0.254973i	−0.823006	+	0.568033i	$0.807705\pi$
$788$	19.9601	+	28.5995i	0.711048	+	1.01881i
$789$	−48.4085			−1.72339
$790$	−1.20785	+	1.01192i	−0.0429733	+	0.0360026i
$791$	8.13476	+	8.13476i	0.289239	+	0.289239i
$792$	6.65937	+	11.5961i	0.236630	+	0.412048i
$793$	−8.32388	−	20.9031i	−0.295590	−	0.742290i
$794$	−9.83136	+	8.23662i	−0.348902	+	0.292307i
$795$	2.91145	−	2.91145i	0.103258	−	0.103258i
$796$	−5.60522	−	0.997243i	−0.198672	−	0.0353463i
$797$			42.2503i			1.49658i	0.663371	+	0.748291i	$0.269125\pi$
$797$			42.2503i			1.49658i	−0.663371	+	0.748291i	$0.730875\pi$
$798$	−3.27756	+	37.1337i	−0.116024	+	1.31452i
$799$	29.9874	−	29.9874i	1.06088	−	1.06088i
$800$	−12.0235	+	25.5278i	−0.425096	+	0.902544i
$801$	11.9769	−	11.9769i	0.423182	−	0.423182i
$802$	1.89829	−	1.59037i	0.0670310	−	0.0561579i
$803$	10.7888			0.380729
$804$	18.4770	+	26.4745i	0.651634	+	0.933682i
$805$			2.96963i			0.104666i
$806$	5.51964	+	2.97587i	0.194421	+	0.104821i
$807$		−	20.0079i		−	0.704312i
$808$	6.59096	−	24.3727i	0.231869	−	0.857430i
$809$	−19.7671			−0.694974			−0.347487	−	0.937685i	$-0.612965\pi$
$809$	−19.7671			−0.694974			−0.347487	+	0.937685i	$0.612965\pi$
$810$	−0.0819657	−	0.0978357i	−0.00287998	−	0.00343760i
$811$	−1.50183	+	1.50183i	−0.0527364	+	0.0527364i	−0.732983	−	0.680247i	$-0.761873\pi$
$811$	−1.50183	+	1.50183i	−0.0527364	+	0.0527364i	0.680247	+	0.732983i	$0.261873\pi$
$812$	26.4877	+	37.9525i	0.929536	+	1.33187i
$813$	−8.18617	+	8.18617i	−0.287102	+	0.287102i
$814$	9.32244	+	0.822833i	0.326751	+	0.0288403i
$815$		−	0.150090i		−	0.00525741i
$816$	−70.6018	−	25.9432i	−2.47156	−	0.908194i
$817$	13.3423	−	13.3423i	0.466788	−	0.466788i
$818$	−35.9233	−	42.8786i	−1.25603	−	1.49922i
$819$	−22.0231	+	51.1693i	−0.769550	+	1.78800i
$820$	−0.360390	+	2.02565i	−0.0125854	+	0.0707388i
$821$	26.1048	+	26.1048i	0.911063	+	0.911063i	0.996356	−	0.0852929i	$-0.0271826\pi$
$821$	26.1048	+	26.1048i	0.911063	+	0.911063i	−0.0852929	+	0.996356i	$0.527183\pi$
$822$	23.2243	+	27.7210i	0.810042	+	0.966879i
$823$	−1.05392			−0.0367373			−0.0183686	−	0.999831i	$-0.505847\pi$
$823$	−1.05392			−0.0367373			−0.0183686	+	0.999831i	$0.505847\pi$
$824$	31.4548	+	8.50613i	1.09578	+	0.296325i
$825$	−9.80523	−	9.80523i	−0.341374	−	0.341374i
$826$	2.15826	−	24.4525i	0.0750956	−	0.850810i
$827$	−34.8532	−	34.8532i	−1.21196	−	1.21196i	−0.970380	−	0.241584i	$-0.922333\pi$
$827$	−34.8532	−	34.8532i	−1.21196	−	1.21196i	−0.241584	−	0.970380i	$-0.577667\pi$
$828$	77.9267	+	13.8642i	2.70814	+	0.481814i
$829$		−	17.2569i		−	0.599358i	−0.954040	−	0.299679i	$-0.903120\pi$
$829$		−	17.2569i		−	0.599358i	0.954040	−	0.299679i	$-0.0968795\pi$
$830$	1.58934	+	0.140281i	0.0551667	+	0.00486922i
$831$	−50.3612			−1.74701
$832$	4.28901	−	28.5238i	0.148695	−	0.988883i
$833$	24.8923			0.862468
$834$	−11.3450	−	1.00135i	−0.392845	−	0.0346739i
$835$		−	1.06047i		−	0.0366990i
$836$	5.71334	+	1.01648i	0.197600	+	0.0351557i
$837$	4.17673	+	4.17673i	0.144369	+	0.144369i
$838$	0.977188	−	11.0712i	0.0337564	−	0.382450i
$839$	16.1452	+	16.1452i	0.557393	+	0.557393i	0.928564	−	0.371171i	$-0.121044\pi$
$839$	16.1452	+	16.1452i	0.557393	+	0.557393i	−0.371171	+	0.928564i	$0.621044\pi$
$840$	2.69267	+	0.728163i	0.0929061	+	0.0251240i
$841$	21.1407			0.728991
$842$	12.2156	+	14.5807i	0.420976	+	0.502484i
$843$	29.3479	+	29.3479i	1.01079	+	1.01079i
$844$	7.21240	−	40.5388i	0.248261	−	1.39540i
$845$	1.41070	+	0.0387587i	0.0485294	+	0.00133334i
$846$	26.9194	+	32.1314i	0.925508	+	1.10470i
$847$	−2.31083	+	2.31083i	−0.0794011	+	0.0794011i
$848$	−51.2271	−	18.8238i	−1.75915	−	0.646412i
$849$		−	6.16375i		−	0.211539i
$850$	47.5342	+	4.19554i	1.63041	+	0.143906i
$851$	39.1697	−	39.1697i	1.34272	−	1.34272i
$852$	−41.6048	−	59.6127i	−1.42536	−	2.04230i
$853$	2.02581	−	2.02581i	0.0693623	−	0.0693623i	−0.671575	−	0.740937i	$-0.734382\pi$
$853$	2.02581	−	2.02581i	0.0693623	−	0.0693623i	0.740937	+	0.671575i	$0.234382\pi$
$854$	−18.5212	−	22.1072i	−0.633781	−	0.756491i
$855$	1.48915			0.0509280
$856$	1.25964	−	4.65802i	0.0430536	−	0.159208i
$857$			25.5069i			0.871299i	0.900116	+	0.435649i	$0.143481\pi$
$857$			25.5069i			0.871299i	−0.900116	+	0.435649i	$0.856519\pi$
$858$	12.4769	+	6.72681i	0.425954	+	0.229649i
$859$		−	11.1373i		−	0.380001i	−0.981784	−	0.190001i	$-0.939151\pi$
$859$		−	11.1373i		−	0.380001i	0.981784	−	0.190001i	$-0.0608490\pi$
$860$	−0.808050	−	1.15780i	−0.0275543	−	0.0394807i
$861$	−86.0912			−2.93398
$862$	9.63122	−	8.06894i	0.328041	−	0.274829i
$863$	16.3609	−	16.3609i	0.556933	−	0.556933i	−0.371500	−	0.928433i	$-0.621156\pi$
$863$	16.3609	−	16.3609i	0.556933	−	0.556933i	0.928433	+	0.371500i	$0.121156\pi$
$864$	11.5772	−	24.5803i	0.393866	−	0.836238i
$865$	−0.613148	+	0.613148i	−0.0208477	+	0.0208477i
$866$	1.21023	−	13.7115i	0.0411252	−	0.465936i
$867$			79.9427i			2.71500i
$868$	7.91369	+	1.40795i	0.268608	+	0.0477890i
$869$	−7.25763	+	7.25763i	−0.246198	+	0.246198i
$870$	2.31647	−	1.94071i	0.0785355	−	0.0657963i
$871$	19.2312	+	8.27705i	0.651624	+	0.280457i
$872$	−10.9791	−	19.1180i	−0.371798	−	0.647418i
$873$	−2.61798	−	2.61798i	−0.0886051	−	0.0886051i
$874$	26.3294	−	22.0585i	0.890606	−	0.746141i
$875$	−3.54344			−0.119790
$876$	−34.3295	−	49.1884i	−1.15989	−	1.66192i
$877$	−0.392554	−	0.392554i	−0.0132556	−	0.0132556i	0.700448	−	0.713704i	$-0.252984\pi$
$877$	−0.392554	−	0.392554i	−0.0132556	−	0.0132556i	−0.713704	+	0.700448i	$0.752984\pi$
$878$	39.6476	+	3.49944i	1.33804	+	0.118100i
$879$	−4.36693	−	4.36693i	−0.147293	−	0.147293i
$880$	0.149768	−	0.407578i	0.00504867	−	0.0137395i
$881$			17.4091i			0.586529i	0.956031	+	0.293264i	$0.0947416\pi$
$881$			17.4091i			0.586529i	−0.956031	+	0.293264i	$0.905258\pi$
$882$	−2.16324	+	24.5088i	−0.0728401	+	0.825255i
$883$	−14.9831			−0.504223			−0.252111	−	0.967698i	$-0.581125\pi$
$883$	−14.9831			−0.504223			−0.252111	+	0.967698i	$0.581125\pi$
$884$	−47.7784	+	9.82920i	−1.60696	+	0.330592i
$885$	−1.60284			−0.0538789
$886$	1.39601	−	15.8164i	0.0469000	−	0.531363i
$887$		−	22.3439i		−	0.750236i	−0.926977	−	0.375118i	$-0.877602\pi$
$887$		−	22.3439i		−	0.750236i	0.926977	−	0.375118i	$-0.122398\pi$
$888$	−25.9121	−	45.1211i	−0.869552	−	1.51417i
$889$	−8.76855	−	8.76855i	−0.294088	−	0.294088i
$890$	−0.547878	−	0.0483577i	−0.0183649	−	0.00162095i
$891$	−0.587868	−	0.587868i	−0.0196943	−	0.0196943i
$892$	9.69728	−	6.76790i	0.324689	−	0.226606i
$893$	18.1907			0.608730
$894$	−1.65869	+	1.38964i	−0.0554750	+	0.0464764i
$895$	−0.977029	−	0.977029i	−0.0326585	−	0.0326585i
$896$	−6.22424	−	36.4456i	−0.207937	−	1.21756i
$897$	77.9476	−	31.0398i	2.60259	−	1.03639i
$898$	23.9813	−	20.0913i	0.800268	−	0.670456i
$899$	6.15762	−	6.15762i	0.205368	−	0.205368i
$900$	−8.26181	+	46.4373i	−0.275394	+	1.54791i
$901$			92.2941i			3.07476i
$902$	−1.17831	+	13.3499i	−0.0392334	+	0.444503i
$903$	41.7748	−	41.7748i	1.39018	−	1.39018i
$904$	−9.61159	−	2.59920i	−0.319677	−	0.0864481i
$905$	−0.304337	+	0.304337i	−0.0101165	+	0.0101165i
$906$	−13.6096	+	11.4019i	−0.452147	+	0.378804i
$907$	−5.54050			−0.183969			−0.0919846	−	0.995760i	$-0.529321\pi$
$907$	−5.54050			−0.183969			−0.0919846	+	0.995760i	$0.529321\pi$
$908$	−28.2311	+	19.7030i	−0.936883	+	0.653868i
$909$		−	42.2030i		−	1.39979i
$910$	1.73292	−	0.518881i	0.0574458	−	0.0172007i
$911$		−	18.7340i		−	0.620686i	−0.950625	−	0.310343i	$-0.899556\pi$
$911$		−	18.7340i		−	0.620686i	0.950625	−	0.310343i	$-0.100444\pi$
$912$	−13.5452	−	29.2827i	−0.448528	−	0.969647i
$913$	10.3928			0.343952
$914$	−3.33926	−	3.98580i	−0.110453	−	0.131838i
$915$	−1.33158	+	1.33158i	−0.0440206	+	0.0440206i
$916$	13.8575	−	9.67142i	0.457866	−	0.319553i
$917$	−20.3433	+	20.3433i	−0.671795	+	0.671795i
$918$	−45.7699	−	4.03982i	−1.51063	−	0.133334i
$919$		−	18.3104i		−	0.604006i	−0.953307	−	0.302003i	$-0.902345\pi$
$919$		−	18.3104i		−	0.604006i	0.953307	−	0.302003i	$-0.0976552\pi$
$920$	−1.27995	−	2.22880i	−0.0421988	−	0.0734814i
$921$	34.6121	−	34.6121i	1.14051	−	1.14051i
$922$	17.8890	+	21.3526i	0.589143	+	0.703211i
$923$	−43.3030	−	18.6375i	−1.42534	−	0.613460i
$924$	17.8885	+	3.18260i	0.588489	+	0.104700i
$925$	23.3416	+	23.3416i	0.767466	+	0.767466i
$926$	6.41108	+	7.65237i	0.210681	+	0.251473i
$927$	54.4661			1.78890
$928$	−36.2379	−	17.0680i	−1.18957	−	0.560284i
$929$	15.4967	+	15.4967i	0.508429	+	0.508429i	0.914044	−	0.405615i	$-0.132943\pi$
$929$	15.4967	+	15.4967i	0.508429	+	0.508429i	−0.405615	+	0.914044i	$0.632943\pi$
$930$	0.0461451	−	0.522810i	0.00151316	−	0.0171436i
$931$	7.55000	+	7.55000i	0.247441	+	0.247441i
$932$	−3.04119	+	17.0937i	−0.0996175	+	0.559922i
$933$			12.4274i			0.406856i
$934$	8.36014	+	0.737896i	0.273552	+	0.0241447i
$935$	−0.734319			−0.0240148
$936$	−5.52564	−	47.8965i	−0.180611	−	1.56555i
$937$	30.0527			0.981778			0.490889	−	0.871222i	$-0.336672\pi$
$937$	30.0527			0.981778			0.490889	+	0.871222i	$0.336672\pi$
$938$	26.7332	+	2.35957i	0.872871	+	0.0770428i
$939$		−	19.6183i		−	0.640219i
$940$	0.238423	−	1.34011i	0.00777651	−	0.0437095i
$941$	35.8388	+	35.8388i	1.16831	+	1.16831i	0.982605	+	0.185706i	$0.0594571\pi$
$941$	35.8388	+	35.8388i	1.16831	+	1.16831i	0.185706	+	0.982605i	$0.440543\pi$
$942$	−8.44404	+	95.6683i	−0.275122	+	3.11704i
$943$	56.0916	+	56.0916i	1.82659	+	1.82659i
$944$	8.91951	+	19.2826i	0.290305	+	0.627595i
$945$	1.70395			0.0554294
$946$	−5.90613	−	7.04965i	−0.192025	−	0.229204i
$947$	37.7414	+	37.7414i	1.22643	+	1.22643i	0.965304	+	0.261128i	$0.0840945\pi$
$947$	37.7414	+	37.7414i	1.22643	+	1.22643i	0.261128	+	0.965304i	$0.415905\pi$
$948$	56.1825	+	9.99561i	1.82472	+	0.324642i
$949$	−35.7307	−	15.3784i	−1.15987	−	0.499204i
$950$	13.1449	+	15.6899i	0.426476	+	0.509049i
$951$	51.2191	−	51.2191i	1.66089	−	1.66089i
$952$	−54.2209	+	31.1379i	−1.75731	+	1.00919i
$953$		−	28.6517i		−	0.928118i	−0.885804	−	0.464059i	$-0.846393\pi$
$953$		−	28.6517i		−	0.928118i	0.885804	−	0.464059i	$-0.153607\pi$
$954$	−90.8721	−	8.02071i	−2.94209	−	0.259680i
$955$	−0.565796	+	0.565796i	−0.0183087	+	0.0183087i
$956$	4.14341	−	2.89176i	0.134007	−	0.0935261i
$957$	13.9190	−	13.9190i	0.449937	−	0.449937i
$958$	−3.17319	−	3.78757i	−0.102521	−	0.122371i
$959$	30.0618			0.970746
$960$	−2.33479	+	0.614071i	−0.0753549	+	0.0198191i
$961$			29.4876i			0.951213i
$962$	−29.7015	−	16.0133i	−0.957614	−	0.516290i
$963$		−	8.06567i		−	0.259913i
$964$	−1.67423	+	1.16848i	−0.0539234	+	0.0376341i
$965$	0.699262			0.0225100
$966$	82.4376	−	69.0654i	2.65239	−	2.22214i
$967$	−26.5375	+	26.5375i	−0.853390	+	0.853390i	−0.990549	−	0.137159i	$-0.956203\pi$
$967$	−26.5375	+	26.5375i	−0.853390	+	0.853390i	0.137159	+	0.990549i	$0.456203\pi$
$968$	0.738352	−	2.73035i	0.0237315	−	0.0877569i
$969$	−38.5808	+	38.5808i	−1.23939	+	1.23939i
$970$	−0.0105703	+	0.119759i	−0.000339393	+	0.00384521i
$971$			23.9094i			0.767290i	0.923481	+	0.383645i	$0.125331\pi$
$971$			23.9094i			0.767290i	−0.923481	+	0.383645i	$0.874669\pi$
$972$	−5.85755	+	32.9236i	−0.187881	+	1.05603i
$973$	−6.69445	+	6.69445i	−0.214614	+	0.214614i
$974$	12.7883	−	10.7139i	0.409765	−	0.343297i
$975$	18.4969	+	46.4497i	0.592374	+	1.48758i
$976$	23.4292	+	8.60925i	0.749951	+	0.275575i
$977$	−34.8576	−	34.8576i	−1.11519	−	1.11519i	−0.992437	−	0.122755i	$-0.960827\pi$
$977$	−34.8576	−	34.8576i	−1.11519	−	1.11519i	−0.122755	−	0.992437i	$-0.539173\pi$
$978$	−4.16652	+	3.49067i	−0.133231	+	0.111619i
$979$	−3.58261			−0.114501
$980$	0.655164	−	0.457250i	0.0209284	−	0.0146063i
$981$	−26.0575	−	26.0575i	−0.831953	−	0.831953i
$982$	−52.3971	−	4.62476i	−1.67206	−	0.147582i
$983$	24.0392	+	24.0392i	0.766731	+	0.766731i	0.977529	−	0.210799i	$-0.0676065\pi$
$983$	24.0392	+	24.0392i	0.766731	+	0.766731i	−0.210799	+	0.977529i	$0.567606\pi$
$984$	64.6142	−	37.1065i	2.05983	−	1.18291i
$985$		−	1.89300i		−	0.0603159i
$986$	−5.95577	+	67.4771i	−0.189671	+	2.14891i
$987$	56.9553			1.81291
$988$	−17.4727	−	11.5102i	−0.555882	−	0.366189i
$989$	−54.4357			−1.73096
$990$	0.0638152	−	0.723006i	0.00202818	−	0.0229786i
$991$		−	43.6673i		−	1.38714i	−0.720391	−	0.693568i	$-0.756038\pi$
$991$		−	43.6673i		−	1.38714i	0.720391	−	0.693568i	$-0.243962\pi$
$992$	−6.54633	+	2.35420i	−0.207846	+	0.0747459i
$993$	38.1811	+	38.1811i	1.21164	+	1.21164i
$994$	−60.1954	−	5.31306i	−1.90928	−	0.168520i
$995$	0.218508	+	0.218508i	0.00692718	+	0.00692718i
$996$	−33.0694	−	47.3829i	−1.04784	−	1.50139i
$997$	−44.7962			−1.41871			−0.709355	−	0.704851i	$-0.751014\pi$
$997$	−44.7962			−1.41871			−0.709355	+	0.704851i	$0.751014\pi$
$998$	−25.2307	+	21.1381i	−0.798665	+	0.669113i
$999$	−22.4752	−	22.4752i	−0.711084	−	0.711084i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.j.a.463.2	✓	140
4.3	odd	2	inner	572.2.j.a.463.34	yes	140
13.5	odd	4	inner	572.2.j.a.551.34	yes	140
52.31	even	4	inner	572.2.j.a.551.2	yes	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.j.a.463.2	✓	140	1.1	even	1	trivial
572.2.j.a.463.34	yes	140	4.3	odd	2	inner
572.2.j.a.551.2	yes	140	52.31	even	4	inner
572.2.j.a.551.34	yes	140	13.5	odd	4	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:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40874 - 0.124340i) q^{2} -2.77989i q^{3} +(1.96908 + 0.350325i) q^{4} +(-0.0767607 - 0.0767607i) q^{5} +(-0.345652 + 3.91613i) q^{6} +(2.31083 + 2.31083i) q^{7} +(-2.73035 - 0.738352i) q^{8} -4.72779 q^{9} +O(q^{10})\)	\(q+(-1.40874 - 0.124340i) q^{2} -2.77989i q^{3} +(1.96908 + 0.350325i) q^{4} +(-0.0767607 - 0.0767607i) q^{5} +(-0.345652 + 3.91613i) q^{6} +(2.31083 + 2.31083i) q^{7} +(-2.73035 - 0.738352i) q^{8} -4.72779 q^{9} +(0.0985912 + 0.117680i) q^{10} +(0.707107 + 0.707107i) q^{11} +(0.973866 - 5.47382i) q^{12} +(-1.33391 - 3.34973i) q^{13} +(-2.96802 - 3.54268i) q^{14} +(-0.213386 + 0.213386i) q^{15} +(3.75454 + 1.37964i) q^{16} -6.76443i q^{17} +(6.66021 + 0.587855i) q^{18} +(2.05169 - 2.05169i) q^{19} +(-0.124257 - 0.178039i) q^{20} +(6.42386 - 6.42386i) q^{21} +(-0.908206 - 1.08405i) q^{22} -8.37077 q^{23} +(-2.05254 + 7.59009i) q^{24} -4.98822i q^{25} +(1.46262 + 4.88475i) q^{26} +4.80307i q^{27} +(3.74067 + 5.35975i) q^{28} +7.08101 q^{29} +(0.327138 - 0.274073i) q^{30} +(0.869596 - 0.869596i) q^{31} +(-5.11762 - 2.41039i) q^{32} +(1.96568 - 1.96568i) q^{33} +(-0.841091 + 9.52930i) q^{34} -0.354762i q^{35} +(-9.30939 - 1.65627i) q^{36} +(-4.67934 + 4.67934i) q^{37} +(-3.14540 + 2.63519i) q^{38} +(-9.31188 + 3.70811i) q^{39} +(0.152907 + 0.266260i) q^{40} +(-6.70089 - 6.70089i) q^{41} +(-9.84827 + 8.25078i) q^{42} +6.50308 q^{43} +(1.14463 + 1.64007i) q^{44} +(0.362908 + 0.362908i) q^{45} +(11.7922 + 1.04082i) q^{46} +(4.43311 + 4.43311i) q^{47} +(3.83524 - 10.4372i) q^{48} +3.67989i q^{49} +(-0.620236 + 7.02708i) q^{50} -18.8044 q^{51} +(-1.45307 - 7.06318i) q^{52} -13.6440 q^{53} +(0.597215 - 6.76626i) q^{54} -0.108556i q^{55} +(-4.60318 - 8.01560i) q^{56} +(-5.70348 - 5.70348i) q^{57} +(-9.97528 - 0.880455i) q^{58} +(3.75573 + 3.75573i) q^{59} +(-0.494929 + 0.345420i) q^{60} +6.24023 q^{61} +(-1.33316 + 1.11691i) q^{62} +(-10.9251 - 10.9251i) q^{63} +(6.90967 + 4.03193i) q^{64} +(-0.154736 + 0.359519i) q^{65} +(-3.01354 + 2.52471i) q^{66} +(-4.10604 + 4.10604i) q^{67} +(2.36975 - 13.3197i) q^{68} +23.2698i q^{69} +(-0.0441112 + 0.499766i) q^{70} +(9.24559 - 9.24559i) q^{71} +(12.9085 + 3.49077i) q^{72} +(7.62885 - 7.62885i) q^{73} +(7.17379 - 6.01013i) q^{74} -13.8667 q^{75} +(4.75870 - 3.32118i) q^{76} +3.26801i q^{77} +(13.5791 - 4.06592i) q^{78} +10.2638i q^{79} +(-0.182299 - 0.394103i) q^{80} -0.831370 q^{81} +(8.60661 + 10.2730i) q^{82} +(7.34882 - 7.34882i) q^{83} +(14.8995 - 10.3986i) q^{84} +(-0.519242 + 0.519242i) q^{85} +(-9.16112 - 0.808594i) q^{86} -19.6844i q^{87} +(-1.40856 - 2.45275i) q^{88} +(-2.53329 + 2.53329i) q^{89} +(-0.466118 - 0.556367i) q^{90} +(4.65823 - 10.8231i) q^{91} +(-16.4827 - 2.93249i) q^{92} +(-2.41738 - 2.41738i) q^{93} +(-5.69387 - 6.79629i) q^{94} -0.314979 q^{95} +(-6.70061 + 14.2264i) q^{96} +(0.553742 + 0.553742i) q^{97} +(0.457558 - 5.18399i) q^{98} +(-3.34305 - 3.34305i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 140 q + 4 q^{5} - 12 q^{6} + 12 q^{8} - 140 q^{9}+O(q^{10}) \) 140 * q + 4 * q^5 - 12 * q^6 + 12 * q^8 - 140 * q^9	\( 140 q + 4 q^{5} - 12 q^{6} + 12 q^{8} - 140 q^{9} + 16 q^{14} - 12 q^{18} - 8 q^{20} - 16 q^{21} - 32 q^{26} - 20 q^{28} + 20 q^{32} - 8 q^{34} + 36 q^{37} - 80 q^{40} - 20 q^{41} - 20 q^{42} - 8 q^{44} - 20 q^{45} + 60 q^{46} + 20 q^{48} + 88 q^{50} - 8 q^{53} + 88 q^{54} - 80 q^{57} - 60 q^{58} + 12 q^{60} - 40 q^{61} - 20 q^{65} - 20 q^{66} - 80 q^{68} - 28 q^{70} + 20 q^{72} + 100 q^{73} - 136 q^{74} - 32 q^{76} - 88 q^{78} - 72 q^{80} + 140 q^{81} + 92 q^{84} + 24 q^{85} - 32 q^{86} - 60 q^{89} - 68 q^{92} - 80 q^{93} + 64 q^{94} + 100 q^{96} - 20 q^{97} + 92 q^{98}+O(q^{100}) \) 140 * q + 4 * q^5 - 12 * q^6 + 12 * q^8 - 140 * q^9 + 16 * q^14 - 12 * q^18 - 8 * q^20 - 16 * q^21 - 32 * q^26 - 20 * q^28 + 20 * q^32 - 8 * q^34 + 36 * q^37 - 80 * q^40 - 20 * q^41 - 20 * q^42 - 8 * q^44 - 20 * q^45 + 60 * q^46 + 20 * q^48 + 88 * q^50 - 8 * q^53 + 88 * q^54 - 80 * q^57 - 60 * q^58 + 12 * q^60 - 40 * q^61 - 20 * q^65 - 20 * q^66 - 80 * q^68 - 28 * q^70 + 20 * q^72 + 100 * q^73 - 136 * q^74 - 32 * q^76 - 88 * q^78 - 72 * q^80 + 140 * q^81 + 92 * q^84 + 24 * q^85 - 32 * q^86 - 60 * q^89 - 68 * q^92 - 80 * q^93 + 64 * q^94 + 100 * q^96 - 20 * q^97 + 92 * q^98

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