LMFDB - Embedded newform 52.2.f.b.47.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [52,2,Mod(31,52)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(52, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("52.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 52 = 2^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	52.f (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:	$0.415222090511$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.18939904.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 14x^{6} - 28x^{5} + 43x^{4} - 44x^{3} + 30x^{2} - 12x + 2 $ x^8 - 4x^7 + 14x^6 - 28x^5 + 43x^4 - 44x^3 + 30x^2 - 12*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			47.3
Root			$0.500000 + 0.0297061i$ of defining polynomial
Character	$\chi$	$=$	52.47
Dual form			52.2.f.b.31.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.332548 - 1.37456i) q^{2} -1.47363i q^{3} +(-1.77882 + 0.914214i) q^{4} +(0.707107 + 0.707107i) q^{5} +(-2.02559 + 0.490051i) q^{6} +(-1.04201 - 1.04201i) q^{7} +(1.84818 + 2.14108i) q^{8} +0.828427 q^{9} +O(q^{10})$	\(q+(-0.332548 - 1.37456i) q^{2} -1.47363i q^{3} +(-1.77882 + 0.914214i) q^{4} +(0.707107 + 0.707107i) q^{5} +(-2.02559 + 0.490051i) q^{6} +(-1.04201 - 1.04201i) q^{7} +(1.84818 + 2.14108i) q^{8} +0.828427 q^{9} +(0.736813 - 1.20711i) q^{10} +(3.55765 + 3.55765i) q^{11} +(1.34721 + 2.62132i) q^{12} +(-3.53553 - 0.707107i) q^{13} +(-1.08579 + 1.77882i) q^{14} +(1.04201 - 1.04201i) q^{15} +(2.32843 - 3.25245i) q^{16} +0.171573i q^{17} +(-0.275492 - 1.13872i) q^{18} +(-5.03127 + 5.03127i) q^{19} +(-1.90426 - 0.611372i) q^{20} +(-1.53553 + 1.53553i) q^{21} +(3.70711 - 6.07328i) q^{22} -2.08402 q^{23} +(3.15515 - 2.72353i) q^{24} -4.00000i q^{25} +(0.203775 + 5.09495i) q^{26} -5.64167i q^{27} +(2.80617 + 0.900933i) q^{28} -3.41421 q^{29} +(-1.77882 - 1.08579i) q^{30} +(2.08402 - 2.08402i) q^{31} +(-5.24500 - 2.11896i) q^{32} +(5.24264 - 5.24264i) q^{33} +(0.235837 - 0.0570562i) q^{34} -1.47363i q^{35} +(-1.47363 + 0.757359i) q^{36} +(-6.12132 + 6.12132i) q^{37} +(8.58892 + 5.24264i) q^{38} +(-1.04201 + 5.21005i) q^{39} +(-0.207107 + 2.82083i) q^{40} +(4.24264 + 4.24264i) q^{41} +(2.62132 + 1.60004i) q^{42} +5.64167 q^{43} +(-9.58088 - 3.07598i) q^{44} +(0.585786 + 0.585786i) q^{45} +(0.693037 + 2.86461i) q^{46} +(1.04201 + 1.04201i) q^{47} +(-4.79289 - 3.43123i) q^{48} -4.82843i q^{49} +(-5.49824 + 1.33019i) q^{50} +0.252834 q^{51} +(6.93554 - 1.97441i) q^{52} +8.24264 q^{53} +(-7.75481 + 1.87613i) q^{54} +5.03127i q^{55} +(0.305198 - 4.15685i) q^{56} +(7.41421 + 7.41421i) q^{57} +(1.13539 + 4.69304i) q^{58} +(-7.11529 - 7.11529i) q^{59} +(-0.900933 + 2.80617i) q^{60} -4.82843 q^{61} +(-3.55765 - 2.17157i) q^{62} +(-0.863230 - 0.863230i) q^{63} +(-1.16843 + 7.91421i) q^{64} +(-2.00000 - 3.00000i) q^{65} +(-8.94975 - 5.46289i) q^{66} +(1.47363 - 1.47363i) q^{67} +(-0.156854 - 0.305198i) q^{68} +3.07107i q^{69} +(-2.02559 + 0.490051i) q^{70} +(9.02054 - 9.02054i) q^{71} +(1.53109 + 1.77373i) q^{72} +(1.65685 - 1.65685i) q^{73} +(10.4497 + 6.37848i) q^{74} -5.89450 q^{75} +(4.35009 - 13.5494i) q^{76} -7.41421i q^{77} +(7.50804 - 0.300288i) q^{78} +0.863230i q^{79} +(3.94628 - 0.653382i) q^{80} -5.82843 q^{81} +(4.42088 - 7.24264i) q^{82} +(0.610396 - 0.610396i) q^{83} +(1.32764 - 4.13525i) q^{84} +(-0.121320 + 0.121320i) q^{85} +(-1.87613 - 7.75481i) q^{86} +5.03127i q^{87} +(-1.04201 + 14.1924i) q^{88} +(-2.24264 + 2.24264i) q^{89} +(0.610396 - 1.00000i) q^{90} +(2.94725 + 4.42088i) q^{91} +(3.70711 - 1.90524i) q^{92} +(-3.07107 - 3.07107i) q^{93} +(1.08579 - 1.77882i) q^{94} -7.11529 q^{95} +(-3.12256 + 7.72916i) q^{96} +(-2.41421 - 2.41421i) q^{97} +(-6.63696 + 1.60568i) q^{98} +(2.94725 + 2.94725i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} + 8 q^{6} - 4 q^{8} - 16 q^{9}+O(q^{10}) $ 8 * q - 4 * q^2 + 8 * q^6 - 4 * q^8 - 16 * q^9	$ 8 q - 4 q^{2} + 8 q^{6} - 4 q^{8} - 16 q^{9} - 20 q^{14} - 4 q^{16} - 8 q^{20} + 16 q^{21} + 24 q^{22} + 32 q^{24} + 8 q^{26} + 12 q^{28} - 16 q^{29} - 4 q^{32} + 8 q^{33} + 4 q^{34} - 32 q^{37} + 4 q^{40} + 4 q^{42} - 28 q^{44} + 16 q^{45} - 20 q^{46} - 44 q^{48} - 16 q^{50} + 8 q^{52} + 32 q^{53} - 32 q^{54} + 48 q^{57} + 12 q^{58} - 12 q^{60} - 16 q^{61} - 16 q^{65} - 32 q^{66} + 44 q^{68} + 8 q^{70} + 16 q^{72} - 32 q^{73} + 44 q^{74} + 32 q^{76} + 40 q^{78} + 16 q^{80} - 24 q^{81} - 48 q^{84} + 16 q^{85} + 32 q^{86} + 16 q^{89} + 24 q^{92} + 32 q^{93} + 20 q^{94} - 24 q^{96} - 8 q^{97} - 16 q^{98}+O(q^{100}) $ 8 * q - 4 * q^2 + 8 * q^6 - 4 * q^8 - 16 * q^9 - 20 * q^14 - 4 * q^16 - 8 * q^20 + 16 * q^21 + 24 * q^22 + 32 * q^24 + 8 * q^26 + 12 * q^28 - 16 * q^29 - 4 * q^32 + 8 * q^33 + 4 * q^34 - 32 * q^37 + 4 * q^40 + 4 * q^42 - 28 * q^44 + 16 * q^45 - 20 * q^46 - 44 * q^48 - 16 * q^50 + 8 * q^52 + 32 * q^53 - 32 * q^54 + 48 * q^57 + 12 * q^58 - 12 * q^60 - 16 * q^61 - 16 * q^65 - 32 * q^66 + 44 * q^68 + 8 * q^70 + 16 * q^72 - 32 * q^73 + 44 * q^74 + 32 * q^76 + 40 * q^78 + 16 * q^80 - 24 * q^81 - 48 * q^84 + 16 * q^85 + 32 * q^86 + 16 * q^89 + 24 * q^92 + 32 * q^93 + 20 * q^94 - 24 * q^96 - 8 * q^97 - 16 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/52\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.332548	−	1.37456i	−0.235147	−	0.971960i
$2$	−0.332548	−	1.37456i	−0.235147	−	0.971960i
$3$		−	1.47363i		−	0.850798i	−0.905006	−	0.425399i	$-0.860134\pi$
$3$		−	1.47363i		−	0.850798i	0.905006	−	0.425399i	$-0.139866\pi$
$4$	−1.77882	+	0.914214i	−0.889412	+	0.457107i
$5$	0.707107	+	0.707107i	0.316228	+	0.316228i	0.847316	−	0.531089i	$-0.178217\pi$
$5$	0.707107	+	0.707107i	0.316228	+	0.316228i	−0.531089	+	0.847316i	$0.678217\pi$
$6$	−2.02559	+	0.490051i	−0.826942	+	0.200063i
$7$	−1.04201	−	1.04201i	−0.393843	−	0.393843i	0.482212	−	0.876055i	$-0.339834\pi$
$7$	−1.04201	−	1.04201i	−0.393843	−	0.393843i	−0.876055	+	0.482212i	$0.839834\pi$
$8$	1.84818	+	2.14108i	0.653432	+	0.756985i
$9$	0.828427			0.276142
$10$	0.736813	−	1.20711i	0.233001	−	0.381721i
$11$	3.55765	+	3.55765i	1.07267	+	1.07267i	0.997144	+	0.0755273i	$0.0240640\pi$
$11$	3.55765	+	3.55765i	1.07267	+	1.07267i	0.0755273	+	0.997144i	$0.475936\pi$
$12$	1.34721	+	2.62132i	0.388906	+	0.756710i
$13$	−3.53553	−	0.707107i	−0.980581	−	0.196116i
$13$	−3.53553	−	0.707107i	−0.980581	−	0.196116i
$14$	−1.08579	+	1.77882i	−0.290189	+	0.475411i
$15$	1.04201	−	1.04201i	0.269046	−	0.269046i
$16$	2.32843	−	3.25245i	0.582107	−	0.813112i
$17$			0.171573i			0.0416125i	0.999784	+	0.0208063i	$0.00662332\pi$
$17$			0.171573i			0.0416125i	−0.999784	+	0.0208063i	$0.993377\pi$
$18$	−0.275492	−	1.13872i	−0.0649340	−	0.268399i
$19$	−5.03127	+	5.03127i	−1.15425	+	1.15425i	−0.168562	+	0.985691i	$0.553912\pi$
$19$	−5.03127	+	5.03127i	−1.15425	+	1.15425i	−0.985691	+	0.168562i	$0.946088\pi$
$20$	−1.90426	−	0.611372i	−0.425807	−	0.136707i
$21$	−1.53553	+	1.53553i	−0.335081	+	0.335081i
$22$	3.70711	−	6.07328i	0.790358	−	1.29483i
$23$	−2.08402			−0.434549			−0.217274	−	0.976111i	$-0.569717\pi$
$23$	−2.08402			−0.434549			−0.217274	+	0.976111i	$0.569717\pi$
$24$	3.15515	−	2.72353i	0.644042	−	0.555939i
$25$		−	4.00000i		−	0.800000i
$26$	0.203775	+	5.09495i	0.0399636	+	0.999201i
$27$		−	5.64167i		−	1.08574i
$28$	2.80617	+	0.900933i	0.530317	+	0.170260i
$29$	−3.41421			−0.634004			−0.317002	−	0.948425i	$-0.602676\pi$
$29$	−3.41421			−0.634004			−0.317002	+	0.948425i	$0.602676\pi$
$30$	−1.77882	−	1.08579i	−0.324767	−	0.198237i
$31$	2.08402	−	2.08402i	0.374301	−	0.374301i	−0.494740	−	0.869041i	$-0.664737\pi$
$31$	2.08402	−	2.08402i	0.374301	−	0.374301i	0.869041	+	0.494740i	$0.164737\pi$
$32$	−5.24500	−	2.11896i	−0.927193	−	0.374584i
$33$	5.24264	−	5.24264i	0.912627	−	0.912627i
$34$	0.235837	−	0.0570562i	0.0404457	−	0.00978506i
$35$		−	1.47363i		−	0.249088i
$36$	−1.47363	+	0.757359i	−0.245604	+	0.126227i
$37$	−6.12132	+	6.12132i	−1.00634	+	1.00634i	−0.00635908	+	0.999980i	$0.502024\pi$
$37$	−6.12132	+	6.12132i	−1.00634	+	1.00634i	−0.999980	+	0.00635908i	$0.997976\pi$
$38$	8.58892	+	5.24264i	1.39331	+	0.850469i
$39$	−1.04201	+	5.21005i	−0.166855	+	0.834276i
$40$	−0.207107	+	2.82083i	−0.0327465	+	0.446013i
$41$	4.24264	+	4.24264i	0.662589	+	0.662589i	0.955990	−	0.293400i	$-0.0947869\pi$
$41$	4.24264	+	4.24264i	0.662589	+	0.662589i	−0.293400	+	0.955990i	$0.594787\pi$
$42$	2.62132	+	1.60004i	0.404479	+	0.246892i
$43$	5.64167			0.860346			0.430173	−	0.902746i	$-0.358452\pi$
$43$	5.64167			0.860346			0.430173	+	0.902746i	$0.358452\pi$
$44$	−9.58088	−	3.07598i	−1.44437	−	0.463721i
$45$	0.585786	+	0.585786i	0.0873239	+	0.0873239i
$46$	0.693037	+	2.86461i	0.102183	+	0.422364i
$47$	1.04201	+	1.04201i	0.151993	+	0.151993i	0.779007	−	0.627015i	$-0.215723\pi$
$47$	1.04201	+	1.04201i	0.151993	+	0.151993i	−0.627015	+	0.779007i	$0.715723\pi$
$48$	−4.79289	−	3.43123i	−0.691795	−	0.495255i
$49$		−	4.82843i		−	0.689775i
$50$	−5.49824	+	1.33019i	−0.777568	+	0.188118i
$51$	0.252834			0.0354039
$52$	6.93554	−	1.97441i	0.961786	−	0.273802i
$53$	8.24264			1.13221			0.566107	−	0.824332i	$-0.308449\pi$
$53$	8.24264			1.13221			0.566107	+	0.824332i	$0.308449\pi$
$54$	−7.75481	+	1.87613i	−1.05530	+	0.255308i
$55$			5.03127i			0.678417i
$56$	0.305198	−	4.15685i	0.0407838	−	0.555483i
$57$	7.41421	+	7.41421i	0.982037	+	0.982037i
$58$	1.13539	+	4.69304i	0.149084	+	0.616226i
$59$	−7.11529	−	7.11529i	−0.926332	−	0.926332i	0.0711343	−	0.997467i	$-0.477338\pi$
$59$	−7.11529	−	7.11529i	−0.926332	−	0.926332i	−0.997467	+	0.0711343i	$0.977338\pi$
$60$	−0.900933	+	2.80617i	−0.116310	+	0.362275i
$61$	−4.82843			−0.618217			−0.309108	−	0.951027i	$-0.600031\pi$
$61$	−4.82843			−0.618217			−0.309108	+	0.951027i	$0.600031\pi$
$62$	−3.55765	−	2.17157i	−0.451822	−	0.275790i
$63$	−0.863230	−	0.863230i	−0.108757	−	0.108757i
$64$	−1.16843	+	7.91421i	−0.146053	+	0.989277i
$65$	−2.00000	−	3.00000i	−0.248069	−	0.372104i
$66$	−8.94975	−	5.46289i	−1.10164	−	0.672435i
$67$	1.47363	−	1.47363i	0.180032	−	0.180032i	−0.611338	−	0.791370i	$-0.709368\pi$
$67$	1.47363	−	1.47363i	0.180032	−	0.180032i	0.791370	+	0.611338i	$0.209368\pi$
$68$	−0.156854	−	0.305198i	−0.0190214	−	0.0370107i
$69$			3.07107i			0.369713i
$70$	−2.02559	+	0.490051i	−0.242104	+	0.0585723i
$71$	9.02054	−	9.02054i	1.07054	−	1.07054i	0.0732252	−	0.997315i	$-0.476671\pi$
$71$	9.02054	−	9.02054i	1.07054	−	1.07054i	0.997315	−	0.0732252i	$-0.0233292\pi$
$72$	1.53109	+	1.77373i	0.180440	+	0.209036i
$73$	1.65685	−	1.65685i	0.193920	−	0.193920i	−0.603467	−	0.797388i	$-0.706215\pi$
$73$	1.65685	−	1.65685i	0.193920	−	0.193920i	0.797388	+	0.603467i	$0.206215\pi$
$74$	10.4497	+	6.37848i	1.21476	+	0.741483i
$75$	−5.89450			−0.680639
$76$	4.35009	−	13.5494i	0.498989	−	1.55422i
$77$		−	7.41421i		−	0.844928i
$78$	7.50804	−	0.300288i	0.850119	−	0.0340009i
$79$			0.863230i			0.0971210i	0.998820	+	0.0485605i	$0.0154634\pi$
$79$			0.863230i			0.0971210i	−0.998820	+	0.0485605i	$0.984537\pi$
$80$	3.94628	−	0.653382i	0.441207	−	0.0730504i
$81$	−5.82843			−0.647603
$82$	4.42088	−	7.24264i	0.488204	−	0.799816i
$83$	0.610396	−	0.610396i	0.0669996	−	0.0669996i	−0.672813	−	0.739813i	$-0.734914\pi$
$83$	0.610396	−	0.610396i	0.0669996	−	0.0669996i	0.739813	+	0.672813i	$0.234914\pi$
$84$	1.32764	−	4.13525i	0.144857	−	0.451193i
$85$	−0.121320	+	0.121320i	−0.0131590	+	0.0131590i
$86$	−1.87613	−	7.75481i	−0.202308	−	0.836222i
$87$			5.03127i			0.539409i
$88$	−1.04201	+	14.1924i	−0.111079	+	1.51291i
$89$	−2.24264	+	2.24264i	−0.237719	+	0.237719i	−0.815905	−	0.578186i	$-0.803761\pi$
$89$	−2.24264	+	2.24264i	−0.237719	+	0.237719i	0.578186	+	0.815905i	$0.303761\pi$
$90$	0.610396	−	1.00000i	0.0643414	−	0.105409i
$91$	2.94725	+	4.42088i	0.308956	+	0.463434i
$92$	3.70711	−	1.90524i	0.386493	−	0.198635i
$93$	−3.07107	−	3.07107i	−0.318455	−	0.318455i
$94$	1.08579	−	1.77882i	0.111990	−	0.183472i
$95$	−7.11529			−0.730014
$96$	−3.12256	+	7.72916i	−0.318695	+	0.788854i
$97$	−2.41421	−	2.41421i	−0.245126	−	0.245126i	0.573841	−	0.818967i	$-0.305453\pi$
$97$	−2.41421	−	2.41421i	−0.245126	−	0.245126i	−0.818967	+	0.573841i	$0.805453\pi$
$98$	−6.63696	+	1.60568i	−0.670434	+	0.162199i
$99$	2.94725	+	2.94725i	0.296210	+	0.296210i
$100$	3.65685	+	7.11529i	0.365685	+	0.711529i
$101$			5.17157i			0.514591i	0.966333	+	0.257295i	$0.0828313\pi$
$101$			5.17157i			0.514591i	−0.966333	+	0.257295i	$0.917169\pi$
$102$	−0.0840795	−	0.347535i	−0.00832511	−	0.0344111i
$103$	−15.0938			−1.48724			−0.743619	−	0.668603i	$-0.766892\pi$
$103$	−15.0938			−1.48724			−0.743619	+	0.668603i	$0.766892\pi$
$104$	−5.02035	−	8.87672i	−0.492286	−	0.870434i
$105$	−2.17157			−0.211924
$106$	−2.74107	−	11.3300i	−0.266237	−	1.10047i
$107$			11.2833i			1.09080i	0.838175	+	0.545401i	$0.183623\pi$
$107$			11.2833i			1.09080i	−0.838175	+	0.545401i	$0.816377\pi$
$108$	5.15769	+	10.0355i	0.496299	+	0.965670i
$109$	−3.29289	−	3.29289i	−0.315402	−	0.315402i	0.531596	−	0.846998i	$-0.321592\pi$
$109$	−3.29289	−	3.29289i	−0.315402	−	0.315402i	−0.846998	+	0.531596i	$0.821592\pi$
$110$	6.91578	−	1.67314i	0.659394	−	0.159528i
$111$	9.02054	+	9.02054i	0.856191	+	0.856191i
$112$	−5.81533	+	0.962841i	−0.549497	+	0.0909799i
$113$	−7.31371			−0.688016			−0.344008	−	0.938967i	$-0.611785\pi$
$113$	−7.31371			−0.688016			−0.344008	+	0.938967i	$0.611785\pi$
$114$	7.72569	−	12.6569i	0.723577	−	1.18542i
$115$	−1.47363	−	1.47363i	−0.137416	−	0.137416i
$116$	6.07328	−	3.12132i	0.563890	−	0.289807i
$117$	−2.92893	−	0.585786i	−0.270780	−	0.0541560i
$118$	−7.41421	+	12.1466i	−0.682534	+	1.11818i
$119$	0.178781	−	0.178781i	0.0163888	−	0.0163888i
$120$	4.15685	+	0.305198i	0.379467	+	0.0278606i
$121$			14.3137i			1.30125i
$122$	1.60568	+	6.63696i	0.145372	+	0.600882i
$123$	6.25206	−	6.25206i	0.563730	−	0.563730i
$124$	−1.80187	+	5.61235i	−0.161812	+	0.504004i
$125$	6.36396	−	6.36396i	0.569210	−	0.569210i
$126$	−0.899495	+	1.47363i	−0.0801334	+	0.131281i
$127$	13.8730			1.23103			0.615516	−	0.788124i	$-0.288948\pi$
$127$	13.8730			1.23103			0.615516	+	0.788124i	$0.288948\pi$
$128$	11.2671	−	1.02578i	0.995881	−	0.0906673i
$129$		−	8.31371i		−	0.731981i
$130$	−3.45858	+	3.74676i	−0.303338	+	0.328613i
$131$			2.69442i			0.235412i	0.993048	+	0.117706i	$0.0375541\pi$
$131$			2.69442i			0.235412i	−0.993048	+	0.117706i	$0.962446\pi$
$132$	−4.53284	+	14.1186i	−0.394533	+	1.22887i
$133$	10.4853			0.909189
$134$	−2.51564	−	1.53553i	−0.217318	−	0.132650i
$135$	3.98926	−	3.98926i	0.343341	−	0.343341i
$136$	−0.367351	+	0.317098i	−0.0315001	+	0.0271910i
$137$	−2.65685	+	2.65685i	−0.226990	+	0.226990i	−0.811434	−	0.584444i	$-0.801313\pi$
$137$	−2.65685	+	2.65685i	−0.226990	+	0.226990i	0.584444	+	0.811434i	$0.301313\pi$
$138$	4.22136	−	1.02128i	0.359346	−	0.0869369i
$139$		−	3.20009i		−	0.271428i	−0.990748	−	0.135714i	$-0.956667\pi$
$139$		−	3.20009i		−	0.271428i	0.990748	−	0.135714i	$-0.0433328\pi$
$140$	1.34721	+	2.62132i	0.113860	+	0.221542i
$141$	1.53553	−	1.53553i	0.129315	−	0.129315i
$142$	−15.3990	−	9.39949i	−1.29226	−	0.788788i
$143$	−10.0625	−	15.0938i	−0.841472	−	1.26221i
$144$	1.92893	−	2.69442i	0.160744	−	0.224535i
$145$	−2.41421	−	2.41421i	−0.200490	−	0.200490i
$146$	−2.82843	−	1.72646i	−0.234082	−	0.142883i
$147$	−7.11529			−0.586860
$148$	5.29256	−	16.4849i	0.435045	−	1.35505i
$149$	10.4853	+	10.4853i	0.858988	+	0.858988i	0.991219	−	0.132231i	$-0.0422141\pi$
$149$	10.4853	+	10.4853i	0.858988	+	0.858988i	−0.132231	+	0.991219i	$0.542214\pi$
$150$	1.96021	+	8.10234i	0.160050	+	0.661553i
$151$	−11.1046	−	11.1046i	−0.903676	−	0.903676i	0.0920760	−	0.995752i	$-0.470650\pi$
$151$	−11.1046	−	11.1046i	−0.903676	−	0.903676i	−0.995752	+	0.0920760i	$0.970650\pi$
$152$	−20.0711	−	1.47363i	−1.62798	−	0.119527i
$153$			0.142136i			0.0114910i
$154$	−10.1913	+	2.46558i	−0.821236	+	0.198682i
$155$	2.94725			0.236729
$156$	−2.90955	−	10.2204i	−0.232950	−	0.818286i
$157$	12.0000			0.957704			0.478852	−	0.877896i	$-0.341053\pi$
$157$	12.0000			0.957704			0.478852	+	0.877896i	$0.341053\pi$
$158$	1.18656	−	0.287065i	0.0943977	−	0.0228377i
$159$		−	12.1466i		−	0.963285i
$160$	−2.21044	−	5.20711i	−0.174751	−	0.411658i
$161$	2.17157	+	2.17157i	0.171144	+	0.171144i
$162$	1.93823	+	8.01152i	0.152282	+	0.629444i
$163$	2.69442	+	2.69442i	0.211043	+	0.211043i	0.804710	−	0.593667i	$-0.202321\pi$
$163$	2.69442	+	2.69442i	0.211043	+	0.211043i	−0.593667	+	0.804710i	$0.702321\pi$
$164$	−11.4256	−	3.66823i	−0.892189	−	0.286441i
$165$	7.41421			0.577196
$166$	−1.04201	−	0.636039i	−0.0808757	−	0.0493662i
$167$	0.863230	+	0.863230i	0.0667987	+	0.0667987i	0.739717	−	0.672918i	$-0.234959\pi$
$167$	0.863230	+	0.863230i	0.0667987	+	0.0667987i	−0.672918	+	0.739717i	$0.734959\pi$
$168$	−6.12565	−	0.449747i	−0.472604	−	0.0346988i
$169$	12.0000	+	5.00000i	0.923077	+	0.384615i
$170$	0.207107	+	0.126417i	0.0158844	+	0.00969575i
$171$	−4.16804	+	4.16804i	−0.318738	+	0.318738i
$172$	−10.0355	+	5.15769i	−0.765202	+	0.393270i
$173$		−	24.3848i		−	1.85394i	−0.375135	−	0.926970i	$-0.622404\pi$
$173$		−	24.3848i		−	1.85394i	0.375135	−	0.926970i	$-0.377596\pi$
$174$	6.91578	−	1.67314i	0.524284	−	0.126840i
$175$	−4.16804	+	4.16804i	−0.315074	+	0.315074i
$176$	19.8548	−	3.28735i	1.49661	−	0.247793i
$177$	−10.4853	+	10.4853i	−0.788122	+	0.788122i
$178$	3.82843	+	2.33686i	0.286953	+	0.175155i
$179$	12.7570			0.953500			0.476750	−	0.879039i	$-0.341815\pi$
$179$	12.7570			0.953500			0.476750	+	0.879039i	$0.341815\pi$
$180$	−1.57754	−	0.506477i	−0.117583	−	0.0377506i
$181$			8.58579i			0.638176i	0.947725	+	0.319088i	$0.103377\pi$
$181$			8.58579i			0.638176i	−0.947725	+	0.319088i	$0.896623\pi$
$182$	5.09665	−	5.52132i	0.377789	−	0.409268i
$183$			7.11529i			0.525978i
$184$	−3.85166	−	4.46205i	−0.283948	−	0.328947i
$185$	−8.65685			−0.636465
$186$	−3.20009	+	5.24264i	−0.234642	+	0.384409i
$187$	−0.610396	+	0.610396i	−0.0446366	+	0.0446366i
$188$	−2.80617	−	0.900933i	−0.204661	−	0.0657073i
$189$	−5.87868	+	5.87868i	−0.427611	+	0.427611i
$190$	2.36618	+	9.78039i	0.171661	+	0.709544i
$191$			16.8203i			1.21707i	0.793526	+	0.608536i	$0.208243\pi$
$191$			16.8203i			1.21707i	−0.793526	+	0.608536i	$0.791757\pi$
$192$	11.6626	+	1.72183i	0.841675	+	0.124262i
$193$	8.07107	−	8.07107i	0.580968	−	0.580968i	−0.354201	−	0.935169i	$-0.615247\pi$
$193$	8.07107	−	8.07107i	0.580968	−	0.580968i	0.935169	+	0.354201i	$0.115247\pi$
$194$	−2.51564	+	4.12132i	−0.180612	+	0.295894i
$195$	−4.42088	+	2.94725i	−0.316586	+	0.211057i
$196$	4.41421	+	8.58892i	0.315301	+	0.613494i
$197$	2.60660	+	2.60660i	0.185713	+	0.185713i	0.793840	−	0.608127i	$-0.208079\pi$
$197$	2.60660	+	2.60660i	0.185713	+	0.185713i	−0.608127	+	0.793840i	$0.708079\pi$
$198$	3.07107	−	5.03127i	0.218251	−	0.357557i
$199$	20.4827			1.45198			0.725988	−	0.687707i	$-0.241383\pi$
$199$	20.4827			1.45198			0.725988	+	0.687707i	$0.241383\pi$
$200$	8.56431	−	7.39274i	0.605588	−	0.522746i
$201$	−2.17157	−	2.17157i	−0.153171	−	0.153171i
$202$	7.10863	−	1.71980i	0.500162	−	0.121004i
$203$	3.55765	+	3.55765i	0.249698	+	0.249698i
$204$	−0.449747	+	0.231144i	−0.0314886	+	0.0161833i
$205$			6.00000i			0.419058i
$206$	5.01942	+	20.7473i	0.349720	+	1.44554i
$207$	−1.72646			−0.119997
$208$	−10.5321	+	9.85270i	−0.730267	+	0.683162i
$209$	−35.7990			−2.47627
$210$	0.722152	+	2.98495i	0.0498332	+	0.205981i
$211$		−	19.8723i		−	1.36806i	−0.729453	−	0.684031i	$-0.760225\pi$
$211$		−	19.8723i		−	1.36806i	0.729453	−	0.684031i	$-0.239775\pi$
$212$	−14.6622	+	7.53553i	−1.00700	+	0.517543i
$213$	−13.2929	−	13.2929i	−0.910814	−	0.910814i
$214$	15.5096	−	3.75225i	1.06022	−	0.256499i
$215$	3.98926	+	3.98926i	0.272065	+	0.272065i
$216$	12.0793	−	10.4268i	0.821889	−	0.709457i
$217$	−4.34315			−0.294832
$218$	−3.43123	+	5.62132i	−0.232392	+	0.380724i
$219$	−2.44158	−	2.44158i	−0.164987	−	0.164987i
$220$	−4.59966	−	8.94975i	−0.310109	−	0.603392i
$221$	0.121320	−	0.606602i	0.00816089	−	0.0408044i
$222$	9.39949	−	15.3990i	0.630853	−	1.03351i
$223$	−9.37810	+	9.37810i	−0.628004	+	0.628004i	−0.947565	−	0.319562i	$-0.896464\pi$
$223$	−9.37810	+	9.37810i	−0.628004	+	0.628004i	0.319562	+	0.947565i	$0.396464\pi$
$224$	3.25736	+	7.67333i	0.217641	+	0.512696i
$225$		−	3.31371i		−	0.220914i
$226$	2.43216	+	10.0531i	0.161785	+	0.668724i
$227$	−10.9258	+	10.9258i	−0.725169	+	0.725169i	−0.969653	−	0.244484i	$-0.921381\pi$
$227$	−10.9258	+	10.9258i	−0.725169	+	0.725169i	0.244484	+	0.969653i	$0.421381\pi$
$228$	−19.9668	−	6.41040i	−1.32233	−	0.424539i
$229$	13.2929	−	13.2929i	0.878419	−	0.878419i	−0.114952	−	0.993371i	$-0.536671\pi$
$229$	13.2929	−	13.2929i	0.878419	−	0.878419i	0.993371	+	0.114952i	$0.0366714\pi$
$230$	−1.53553	+	2.51564i	−0.101250	+	0.165876i
$231$	−10.9258			−0.718863
$232$	−6.31010	−	7.31010i	−0.414278	−	0.479931i
$233$			21.9706i			1.43934i	0.694317	+	0.719670i	$0.255707\pi$
$233$			21.9706i			1.43934i	−0.694317	+	0.719670i	$0.744293\pi$
$234$	0.168813	+	4.22079i	0.0110356	+	0.275922i
$235$			1.47363i			0.0961287i
$236$	19.1618	+	6.15196i	1.24732	+	0.400458i
$237$	1.27208			0.0826303
$238$	−0.305198	−	0.186292i	−0.0197830	−	0.0120755i
$239$	−10.2413	+	10.2413i	−0.662456	+	0.662456i	−0.955958	−	0.293502i	$-0.905179\pi$
$239$	−10.2413	+	10.2413i	−0.662456	+	0.662456i	0.293502	+	0.955958i	$0.405179\pi$
$240$	−0.962841	−	5.81533i	−0.0621511	−	0.375378i
$241$	−1.07107	+	1.07107i	−0.0689935	+	0.0689935i	−0.740762	−	0.671768i	$-0.765535\pi$
$241$	−1.07107	+	1.07107i	−0.0689935	+	0.0689935i	0.671768	+	0.740762i	$0.265535\pi$
$242$	19.6750	−	4.76000i	1.26476	−	0.305984i
$243$		−	8.33609i		−	0.534760i
$244$	8.58892	−	4.41421i	0.549849	−	0.282591i
$245$	3.41421	−	3.41421i	0.218126	−	0.218126i
$246$	−10.6729	−	6.51472i	−0.680482	−	0.415363i
$247$	21.3459	−	14.2306i	1.35821	−	0.905471i
$248$	8.31371	+	0.610396i	0.527921	+	0.0387602i
$249$	−0.899495	−	0.899495i	−0.0570032	−	0.0570032i
$250$	−10.8640	−	6.63132i	−0.687097	−	0.419401i
$251$	−15.4514			−0.975283			−0.487641	−	0.873044i	$-0.662143\pi$
$251$	−15.4514			−0.975283			−0.487641	+	0.873044i	$0.662143\pi$
$252$	2.32471	+	0.746357i	0.146443	+	0.0470161i
$253$	−7.41421	−	7.41421i	−0.466128	−	0.466128i
$254$	−4.61345	−	19.0693i	−0.289473	−	1.19651i
$255$	0.178781	+	0.178781i	0.0111957	+	0.0111957i
$256$	−5.15685	−	15.1462i	−0.322303	−	0.946636i
$257$		−	10.6569i		−	0.664756i	−0.943146	−	0.332378i	$-0.892149\pi$
$257$		−	10.6569i		−	0.664756i	0.943146	−	0.332378i	$-0.107851\pi$
$258$	−11.4277	+	2.76471i	−0.711456	+	0.172123i
$259$	12.7570			0.792679
$260$	6.30029	+	3.50804i	0.390727	+	0.217560i
$261$	−2.82843			−0.175075
$262$	3.70363	−	0.896023i	0.228811	−	0.0553565i
$263$			13.0098i			0.802218i	0.916030	+	0.401109i	$0.131375\pi$
$263$			13.0098i			0.802218i	−0.916030	+	0.401109i	$0.868625\pi$
$264$	20.9143	+	1.53553i	1.28718	+	0.0945056i
$265$	5.82843	+	5.82843i	0.358037	+	0.358037i
$266$	−3.48686	−	14.4126i	−0.213793	−	0.883695i
$267$	3.30481	+	3.30481i	0.202251	+	0.202251i
$268$	−1.27411	+	3.96853i	−0.0778288	+	0.242416i
$269$	20.1421			1.22809			0.614044	−	0.789272i	$-0.289542\pi$
$269$	20.1421			1.22809			0.614044	+	0.789272i	$0.289542\pi$
$270$	−6.81010	−	4.15685i	−0.414449	−	0.252978i
$271$	−4.85249	−	4.85249i	−0.294768	−	0.294768i	0.544192	−	0.838960i	$-0.316836\pi$
$271$	−4.85249	−	4.85249i	−0.294768	−	0.294768i	−0.838960	+	0.544192i	$0.816836\pi$
$272$	0.558032	+	0.399495i	0.0338357	+	0.0242229i
$273$	6.51472	−	4.34315i	0.394289	−	0.262859i
$274$	4.53553	+	2.76847i	0.274002	+	0.167249i
$275$	14.2306	−	14.2306i	0.858137	−	0.858137i
$276$	−2.80761	−	5.46289i	−0.168998	−	0.328827i
$277$			6.00000i			0.360505i	0.983620	+	0.180253i	$0.0576915\pi$
$277$			6.00000i			0.360505i	−0.983620	+	0.180253i	$0.942309\pi$
$278$	−4.39871	+	1.06418i	−0.263817	+	0.0638254i
$279$	1.72646	−	1.72646i	0.103360	−	0.103360i
$280$	3.15515	−	2.72353i	0.188556	−	0.162762i
$281$	−16.2426	+	16.2426i	−0.968955	+	0.968955i	−0.999532	−	0.0305777i	$-0.990265\pi$
$281$	−16.2426	+	16.2426i	−0.968955	+	0.968955i	0.0305777	+	0.999532i	$0.490265\pi$
$282$	−2.62132	−	1.60004i	−0.156097	−	0.0952812i
$283$	−24.2931			−1.44408			−0.722038	−	0.691853i	$-0.756795\pi$
$283$	−24.2931			−1.44408			−0.722038	+	0.691853i	$0.756795\pi$
$284$	−7.79925	+	24.2926i	−0.462800	+	1.44150i
$285$			10.4853i			0.621094i
$286$	−17.4011	+	18.8510i	−1.02895	+	1.11468i
$287$		−	8.84175i		−	0.521912i
$288$	−4.34510	−	1.75541i	−0.256037	−	0.103438i
$289$	16.9706			0.998268
$290$	−2.51564	+	4.12132i	−0.147723	+	0.242012i
$291$	−3.55765	+	3.55765i	−0.208553	+	0.208553i
$292$	−1.43253	+	4.46197i	−0.0838326	+	0.261117i
$293$	−0.807612	+	0.807612i	−0.0471812	+	0.0471812i	−0.730304	−	0.683123i	$-0.760621\pi$
$293$	−0.807612	+	0.807612i	−0.0471812	+	0.0471812i	0.683123	+	0.730304i	$0.260621\pi$
$294$	2.36618	+	9.78039i	0.137998	+	0.570404i
$295$		−	10.0625i		−	0.585864i
$296$	−24.4196	−	1.79289i	−1.41936	−	0.104210i
$297$	20.0711	−	20.0711i	1.16464	−	1.16464i
$298$	10.9258	−	17.8995i	0.632913	−	1.03689i
$299$	7.36813	+	1.47363i	0.426110	+	0.0852220i
$300$	10.4853	−	5.38883i	0.605368	−	0.311125i
$301$	−5.87868	−	5.87868i	−0.338841	−	0.338841i
$302$	−11.5711	+	18.9567i	−0.665840	+	1.09083i
$303$	7.62096			0.437813
$304$	4.64901	+	28.0789i	0.266639	+	1.61044i
$305$	−3.41421	−	3.41421i	−0.195497	−	0.195497i
$306$	0.195374	−	0.0472669i	0.0111688	−	0.00270207i
$307$	1.72646	+	1.72646i	0.0985343	+	0.0985343i	0.754656	−	0.656121i	$-0.227804\pi$
$307$	1.72646	+	1.72646i	0.0985343	+	0.0985343i	−0.656121	+	0.754656i	$0.727804\pi$
$308$	6.77817	+	13.1886i	0.386222	+	0.751489i
$309$			22.2426i			1.26534i
$310$	−0.980103	−	4.05117i	−0.0556661	−	0.230091i
$311$	29.6820			1.68311			0.841555	−	0.540171i	$-0.181641\pi$
$311$	29.6820			1.68311			0.841555	+	0.540171i	$0.181641\pi$
$312$	−13.0810	+	7.39811i	−0.740563	+	0.418836i
$313$	3.48528			0.197000			0.0984999	−	0.995137i	$-0.468596\pi$
$313$	3.48528			0.197000			0.0984999	+	0.995137i	$0.468596\pi$
$314$	−3.99058	−	16.4947i	−0.225201	−	0.930850i
$315$		−	1.22079i		−	0.0687838i
$316$	−0.789177	−	1.53553i	−0.0443946	−	0.0863805i
$317$	−15.6569	−	15.6569i	−0.879377	−	0.879377i	0.114093	−	0.993470i	$-0.463604\pi$
$317$	−15.6569	−	15.6569i	−0.879377	−	0.879377i	−0.993470	+	0.114093i	$0.963604\pi$
$318$	−16.6962	+	4.03932i	−0.936275	+	0.226514i
$319$	−12.1466	−	12.1466i	−0.680077	−	0.680077i
$320$	−6.42240	+	4.76999i	−0.359023	+	0.266651i
$321$	16.6274			0.928052
$322$	2.26280	−	3.70711i	0.126101	−	0.206589i
$323$	−0.863230	−	0.863230i	−0.0480314	−	0.0480314i
$324$	10.3677	−	5.32843i	0.575986	−	0.296024i
$325$	−2.82843	+	14.1421i	−0.156893	+	0.784465i
$326$	2.80761	−	4.59966i	0.155499	−	0.254751i
$327$	−4.85249	+	4.85249i	−0.268343	+	0.268343i
$328$	−1.24264	+	16.9250i	−0.0686134	+	0.934527i
$329$		−	2.17157i		−	0.119723i
$330$	−2.46558	−	10.1913i	−0.135726	−	0.561011i
$331$	−4.77844	+	4.77844i	−0.262647	+	0.262647i	−0.826129	−	0.563482i	$-0.809462\pi$
$331$	−4.77844	+	4.77844i	−0.262647	+	0.262647i	0.563482	+	0.826129i	$0.309462\pi$
$332$	−0.527754	+	1.64382i	−0.0289643	+	0.0902163i
$333$	−5.07107	+	5.07107i	−0.277893	+	0.277893i
$334$	0.899495	−	1.47363i	0.0492182	−	0.0806332i
$335$	2.08402			0.113862
$336$	1.41887	+	8.56963i	0.0774056	+	0.467511i
$337$			13.8284i			0.753282i	0.926359	+	0.376641i	$0.122921\pi$
$337$			13.8284i			0.753282i	−0.926359	+	0.376641i	$0.877079\pi$
$338$	2.88222	−	18.1574i	0.156772	−	0.987635i
$339$			10.7777i			0.585363i
$340$	0.104895	−	0.326720i	0.00568872	−	0.0177189i
$341$	14.8284			0.803004
$342$	7.11529	+	4.34315i	0.384751	+	0.234850i
$343$	−12.3253	+	12.3253i	−0.665506	+	0.665506i
$344$	10.4268	+	12.0793i	0.562178	+	0.651270i
$345$	−2.17157	+	2.17157i	−0.116914	+	0.116914i
$346$	−33.5183	+	8.10911i	−1.80196	+	0.435948i
$347$		−	21.5987i		−	1.15948i	−0.814802	−	0.579740i	$-0.803154\pi$
$347$		−	21.5987i		−	1.15948i	0.814802	−	0.579740i	$-0.196846\pi$
$348$	−4.59966	−	8.94975i	−0.246568	−	0.479757i
$349$	−7.53553	+	7.53553i	−0.403368	+	0.403368i	−0.879418	−	0.476050i	$-0.842068\pi$
$349$	−7.53553	+	7.53553i	−0.403368	+	0.403368i	0.476050	+	0.879418i	$0.342068\pi$
$350$	7.11529	+	4.34315i	0.380328	+	0.232151i
$351$	−3.98926	+	19.9463i	−0.212931	+	1.06466i
$352$	−11.1213	−	26.1984i	−0.592768	−	1.39638i
$353$	−1.58579	−	1.58579i	−0.0844029	−	0.0844029i	0.663645	−	0.748048i	$-0.269009\pi$
$353$	−1.58579	−	1.58579i	−0.0844029	−	0.0844029i	−0.748048	+	0.663645i	$0.769009\pi$
$354$	17.8995	+	10.9258i	0.951347	+	0.580698i
$355$	12.7570			0.677069
$356$	1.93901	−	6.03951i	0.102767	−	0.320094i
$357$	−0.263456	−	0.263456i	−0.0139436	−	0.0139436i
$358$	−4.24230	−	17.5352i	−0.224213	−	0.926764i
$359$	2.08402	+	2.08402i	0.109990	+	0.109990i	0.759960	−	0.649970i	$-0.225218\pi$
$359$	2.08402	+	2.08402i	0.109990	+	0.109990i	−0.649970	+	0.759960i	$0.725218\pi$
$360$	−0.171573	+	2.33686i	−0.00904268	+	0.123163i
$361$		−	31.6274i		−	1.66460i
$362$	11.8017	−	2.85519i	0.620282	−	0.150065i
$363$	21.0930			1.10710
$364$	−9.28427	−	5.16954i	−0.486628	−	0.270958i
$365$	2.34315			0.122646
$366$	9.78039	−	2.36618i	0.511229	−	0.123682i
$367$			3.81048i			0.198906i	0.995042	+	0.0994528i	$0.0317092\pi$
$367$			3.81048i			0.198906i	−0.995042	+	0.0994528i	$0.968291\pi$
$368$	−4.85249	+	6.77817i	−0.252954	+	0.353337i
$369$	3.51472	+	3.51472i	0.182969	+	0.182969i
$370$	2.87882	+	11.8994i	0.149663	+	0.618618i
$371$	−8.58892	−	8.58892i	−0.445915	−	0.445915i
$372$	8.27050	+	2.65528i	0.428805	+	0.137670i
$373$	−14.6274			−0.757379			−0.378689	−	0.925524i	$-0.623625\pi$
$373$	−14.6274			−0.757379			−0.378689	+	0.925524i	$0.623625\pi$
$374$	1.04201	+	0.636039i	0.0538811	+	0.0328888i
$375$	−9.37810	−	9.37810i	−0.484283	−	0.484283i
$376$	−0.305198	+	4.15685i	−0.0157394	+	0.214373i
$377$	12.0711	+	2.41421i	0.621692	+	0.124338i
$378$	10.0355	+	6.12565i	0.516172	+	0.315069i
$379$	−7.36813	+	7.36813i	−0.378475	+	0.378475i	−0.870552	−	0.492077i	$-0.836238\pi$
$379$	−7.36813	+	7.36813i	−0.378475	+	0.378475i	0.492077	+	0.870552i	$0.336238\pi$
$380$	12.6569	−	6.50490i	0.649283	−	0.333694i
$381$		−	20.4437i		−	1.04736i
$382$	23.1205	−	5.59355i	1.18295	−	0.286191i
$383$	0.178781	−	0.178781i	0.00913527	−	0.00913527i	−0.702524	−	0.711660i	$-0.747944\pi$
$383$	0.178781	−	0.178781i	0.00913527	−	0.00913527i	0.711660	+	0.702524i	$0.247944\pi$
$384$	−1.51162	−	16.6035i	−0.0771396	−	0.847294i
$385$	5.24264	−	5.24264i	0.267190	−	0.267190i
$386$	−13.7782	−	8.41014i	−0.701291	−	0.428065i
$387$	4.67371			0.237578
$388$	6.50157	+	2.08735i	0.330067	+	0.105969i
$389$			6.14214i			0.311419i	0.987803	+	0.155709i	$0.0497663\pi$
$389$			6.14214i			0.311419i	−0.987803	+	0.155709i	$0.950234\pi$
$390$	5.52132	+	5.09665i	0.279583	+	0.258079i
$391$		−	0.357562i		−	0.0180827i
$392$	10.3380	−	8.92382i	0.522150	−	0.450721i
$393$	3.97056			0.200288
$394$	2.71611	−	4.44975i	0.136835	−	0.224175i
$395$	−0.610396	+	0.610396i	−0.0307123	+	0.0307123i
$396$	−7.93706	−	2.54822i	−0.398852	−	0.128053i
$397$	−18.4853	+	18.4853i	−0.927750	+	0.927750i	−0.997560	−	0.0698106i	$-0.977761\pi$
$397$	−18.4853	+	18.4853i	−0.927750	+	0.927750i	0.0698106	+	0.997560i	$0.477761\pi$
$398$	−6.81147	−	28.1546i	−0.341428	−	1.41126i
$399$		−	15.4514i		−	0.773537i
$400$	−13.0098	−	9.31371i	−0.650490	−	0.465685i
$401$	2.51472	−	2.51472i	0.125579	−	0.125579i	−0.641524	−	0.767103i	$-0.721698\pi$
$401$	2.51472	−	2.51472i	0.125579	−	0.125579i	0.767103	+	0.641524i	$0.221698\pi$
$402$	−2.26280	+	3.70711i	−0.112858	+	0.184894i
$403$	−8.84175	+	5.89450i	−0.440439	+	0.293626i
$404$	−4.72792	−	9.19932i	−0.235223	−	0.457683i
$405$	−4.12132	−	4.12132i	−0.204790	−	0.204790i
$406$	3.70711	−	6.07328i	0.183981	−	0.301412i
$407$	−43.5550			−2.15894
$408$	0.467284	+	0.541338i	0.0231340	+	0.0268002i
$409$	−23.1421	−	23.1421i	−1.14430	−	1.14430i	−0.987654	−	0.156651i	$-0.949930\pi$
$409$	−23.1421	−	23.1421i	−1.14430	−	1.14430i	−0.156651	−	0.987654i	$-0.550070\pi$
$410$	8.24735	−	1.99529i	0.407308	−	0.0985403i
$411$	3.91521	+	3.91521i	0.193123	+	0.193123i
$412$	26.8492	−	13.7990i	1.32277	−	0.679827i
$413$			14.8284i			0.729659i
$414$	0.574131	+	2.37312i	0.0282170	+	0.116633i
$415$	0.863230			0.0423743
$416$	17.0455	+	11.2004i	0.835726	+	0.549147i
$417$	−4.71573			−0.230930
$418$	11.9049	+	49.2078i	0.582287	+	2.40683i
$419$			5.64167i			0.275614i	0.990459	+	0.137807i	$0.0440053\pi$
$419$			5.64167i			0.275614i	−0.990459	+	0.137807i	$0.955995\pi$
$420$	3.86285	−	1.98528i	0.188488	−	0.0968718i
$421$	−24.0208	−	24.0208i	−1.17070	−	1.17070i	−0.982042	−	0.188661i	$-0.939585\pi$
$421$	−24.0208	−	24.0208i	−1.17070	−	1.17070i	−0.188661	−	0.982042i	$-0.560415\pi$
$422$	−27.3156	+	6.60848i	−1.32970	+	0.321696i
$423$	0.863230	+	0.863230i	0.0419717	+	0.0419717i
$424$	15.2339	+	17.6481i	0.739825	+	0.857069i
$425$	0.686292			0.0332900
$426$	−13.8513	+	22.6924i	−0.671100	+	1.09945i
$427$	5.03127	+	5.03127i	0.243480	+	0.243480i
$428$	−10.3154	−	20.0711i	−0.498613	−	0.970172i
$429$	−22.2426	+	14.8284i	−1.07388	+	0.715923i
$430$	4.15685	−	6.81010i	0.200461	−	0.328412i
$431$	15.7783	−	15.7783i	0.760012	−	0.760012i	−0.216312	−	0.976324i	$-0.569403\pi$
$431$	15.7783	−	15.7783i	0.760012	−	0.760012i	0.976324	+	0.216312i	$0.0694028\pi$
$432$	−18.3492	−	13.1362i	−0.882828	−	0.632016i
$433$			32.3137i			1.55290i	0.630180	+	0.776449i	$0.282981\pi$
$433$			32.3137i			1.55290i	−0.630180	+	0.776449i	$0.717019\pi$
$434$	1.44430	+	5.96991i	0.0693288	+	0.286565i
$435$	−3.55765	+	3.55765i	−0.170576	+	0.170576i
$436$	8.86788	+	2.84707i	0.424695	+	0.136350i
$437$	10.4853	−	10.4853i	0.501579	−	0.501579i
$438$	−2.54416	+	4.16804i	−0.121564	+	0.199157i
$439$	12.5041			0.596790			0.298395	−	0.954443i	$-0.403549\pi$
$439$	12.5041			0.596790			0.298395	+	0.954443i	$0.403549\pi$
$440$	−10.7723	+	9.29872i	−0.513551	+	0.443299i
$441$		−	4.00000i		−	0.190476i
$442$	−0.874155	+	0.0349622i	−0.0415793	+	0.00166298i
$443$			6.14734i			0.292069i	0.989280	+	0.146034i	$0.0466510\pi$
$443$			6.14734i			0.292069i	−0.989280	+	0.146034i	$0.953349\pi$
$444$	−24.2926	−	7.79925i	−1.15288	−	0.370136i
$445$	−3.17157			−0.150347
$446$	16.0094	+	9.77208i	0.758068	+	0.462721i
$447$	15.4514	−	15.4514i	0.730825	−	0.730825i
$448$	9.46421	−	7.02918i	0.447142	−	0.332098i
$449$	25.7279	−	25.7279i	1.21418	−	1.21418i	0.244535	−	0.969640i	$-0.421365\pi$
$449$	25.7279	−	25.7279i	1.21418	−	1.21418i	0.969640	−	0.244535i	$-0.0786354\pi$
$450$	−4.55489	+	1.10197i	−0.214719	+	0.0519472i
$451$			30.1876i			1.42148i
$452$	13.0098	−	6.68629i	0.611929	−	0.314497i
$453$	−16.3640	+	16.3640i	−0.768846	+	0.768846i
$454$	18.6515	+	11.3848i	0.875357	+	0.534314i
$455$	−1.04201	+	5.21005i	−0.0488502	+	0.244251i
$456$	−2.17157	+	29.5772i	−0.101693	+	1.38508i
$457$	0.585786	+	0.585786i	0.0274019	+	0.0274019i	0.720675	−	0.693273i	$-0.243832\pi$
$457$	0.585786	+	0.585786i	0.0274019	+	0.0274019i	−0.693273	+	0.720675i	$0.743832\pi$
$458$	−22.6924	−	13.8513i	−1.06035	−	0.647231i
$459$	0.967957			0.0451804
$460$	3.96853	+	1.27411i	0.185034	+	0.0594058i
$461$	6.46447	+	6.46447i	0.301080	+	0.301080i	0.841436	−	0.540356i	$-0.181710\pi$
$461$	6.46447	+	6.46447i	0.301080	+	0.301080i	−0.540356	+	0.841436i	$0.681710\pi$
$462$	3.63335	+	15.0181i	0.169039	+	0.698706i
$463$	20.9883	+	20.9883i	0.975410	+	0.975410i	0.999705	−	0.0242948i	$-0.00773403\pi$
$463$	20.9883	+	20.9883i	0.975410	+	0.975410i	−0.0242948	+	0.999705i	$0.507734\pi$
$464$	−7.94975	+	11.1046i	−0.369058	+	0.515516i
$465$		−	4.34315i		−	0.201409i
$466$	30.1998	−	7.30627i	1.39898	−	0.338456i
$467$	−21.3459			−0.987770			−0.493885	−	0.869527i	$-0.664424\pi$
$467$	−21.3459			−0.987770			−0.493885	+	0.869527i	$0.664424\pi$
$468$	5.74559	−	1.63566i	0.265590	−	0.0756084i
$469$	−3.07107			−0.141809
$470$	2.02559	−	0.490051i	0.0934333	−	0.0226044i
$471$		−	17.6835i		−	0.814813i
$472$	2.08402	−	28.3848i	0.0959249	−	1.30652i
$473$	20.0711	+	20.0711i	0.922869	+	0.922869i
$474$	−0.423027	−	1.74855i	−0.0194303	−	0.0803134i
$475$	20.1251	+	20.1251i	0.923403	+	0.923403i
$476$	−0.154576	+	0.481463i	−0.00708496	+	0.0220678i
$477$	6.82843			0.312652
$478$	17.4830	+	10.6716i	0.799656	+	0.488106i
$479$	1.90524	+	1.90524i	0.0870527	+	0.0870527i	0.749292	−	0.662240i	$-0.230394\pi$
$479$	1.90524	+	1.90524i	0.0870527	+	0.0870527i	−0.662240	+	0.749292i	$0.730394\pi$
$480$	−7.67333	+	3.25736i	−0.350238	+	0.148677i
$481$	25.9706	−	17.3137i	1.18416	−	0.789437i
$482$	1.82843	+	1.11606i	0.0832826	+	0.0508353i
$483$	3.20009	−	3.20009i	0.145609	−	0.145609i
$484$	−13.0858	−	25.4616i	−0.594808	−	1.15734i
$485$		−	3.41421i		−	0.155031i
$486$	−11.4584	+	2.77215i	−0.519765	+	0.125747i
$487$	−9.19932	+	9.19932i	−0.416861	+	0.416861i	−0.884120	−	0.467259i	$-0.845241\pi$
$487$	−9.19932	+	9.19932i	−0.416861	+	0.416861i	0.467259	+	0.884120i	$0.345241\pi$
$488$	−8.92382	−	10.3380i	−0.403963	−	0.467981i
$489$	3.97056	−	3.97056i	0.179555	−	0.179555i
$490$	−5.82843	−	3.55765i	−0.263301	−	0.160718i
$491$	−1.47363			−0.0665038			−0.0332519	−	0.999447i	$-0.510586\pi$
$491$	−1.47363			−0.0665038			−0.0332519	+	0.999447i	$0.510586\pi$
$492$	−5.40560	+	16.8370i	−0.243703	+	0.759073i
$493$		−	0.585786i		−	0.0263825i
$494$	−26.6593	−	24.6088i	−1.19946	−	1.10720i
$495$			4.16804i			0.187340i
$496$	−1.92568	−	11.6307i	−0.0864657	−	0.522232i
$497$	−18.7990			−0.843250
$498$	−0.937283	+	1.53553i	−0.0420007	+	0.0688089i
$499$	−2.08402	+	2.08402i	−0.0932936	+	0.0932936i	−0.752213	−	0.658920i	$-0.771014\pi$
$499$	−2.08402	+	2.08402i	−0.0932936	+	0.0932936i	0.658920	+	0.752213i	$0.271014\pi$
$500$	−5.50234	+	17.1384i	−0.246072	+	0.766452i
$501$	1.27208	−	1.27208i	0.0568323	−	0.0568323i
$502$	5.13833	+	21.2388i	0.229335	+	0.947935i
$503$		−	28.9668i		−	1.29157i	−0.763520	−	0.645784i	$-0.776531\pi$
$503$		−	28.9668i		−	1.29157i	0.763520	−	0.645784i	$-0.223469\pi$
$504$	0.252834	−	3.44365i	0.0112621	−	0.153392i
$505$	−3.65685	+	3.65685i	−0.162728	+	0.162728i
$506$	−7.72569	+	12.6569i	−0.343449	+	0.562666i
$507$	7.36813	−	17.6835i	0.327230	−	0.785352i
$508$	−24.6777	+	12.6829i	−1.09489	+	0.562713i
$509$	19.6569	+	19.6569i	0.871275	+	0.871275i	0.992611	−	0.121337i	$-0.0387181\pi$
$509$	19.6569	+	19.6569i	0.871275	+	0.871275i	−0.121337	+	0.992611i	$0.538718\pi$
$510$	0.186292	−	0.305198i	0.00824913	−	0.0135144i
$511$	−3.45292			−0.152748
$512$	−19.1044	+	12.1252i	−0.844304	+	0.535865i
$513$	28.3848	+	28.3848i	1.25322	+	1.25322i
$514$	−14.6485	+	3.54392i	−0.646116	+	0.156315i
$515$	−10.6729	−	10.6729i	−0.470306	−	0.470306i
$516$	7.60051	+	14.7886i	0.334594	+	0.651033i
$517$			7.41421i			0.326077i
$518$	−4.24230	−	17.5352i	−0.186396	−	0.770452i
$519$	−35.9340			−1.57733
$520$	2.72686	−	9.82671i	0.119581	−	0.430930i
$521$	11.0000			0.481919			0.240959	−	0.970535i	$-0.422538\pi$
$521$	11.0000			0.481919			0.240959	+	0.970535i	$0.422538\pi$
$522$	0.940588	+	3.88784i	0.0411684	+	0.170166i
$523$		−	25.5139i		−	1.11565i	−0.829960	−	0.557823i	$-0.811637\pi$
$523$		−	25.5139i		−	1.11565i	0.829960	−	0.557823i	$-0.188363\pi$
$524$	−2.46327	−	4.79289i	−0.107609	−	0.209379i
$525$	6.14214	+	6.14214i	0.268065	+	0.268065i
$526$	17.8827	−	4.32638i	0.779724	−	0.188639i
$527$	0.357562	+	0.357562i	0.0155756	+	0.0155756i
$528$	−4.84432	−	29.2585i	−0.210822	−	1.27331i
$529$	−18.6569			−0.811168
$530$	6.07328	−	9.94975i	0.263807	−	0.432189i
$531$	−5.89450	−	5.89450i	−0.255800	−	0.255800i
$532$	−18.6515	+	9.58579i	−0.808644	+	0.415597i
$533$	−12.0000	−	18.0000i	−0.519778	−	0.779667i
$534$	3.44365	−	5.64167i	0.149021	−	0.244139i
$535$	−7.97852	+	7.97852i	−0.344942	+	0.344942i
$536$	5.87868	+	0.431615i	0.253920	+	0.0186429i
$537$		−	18.7990i		−	0.811236i
$538$	−6.69823	−	27.6865i	−0.288781	−	1.19365i
$539$	17.1778	−	17.1778i	0.739902	−	0.739902i
$540$	−3.44916	+	10.7432i	−0.148428	+	0.462315i
$541$	11.8787	−	11.8787i	0.510704	−	0.510704i	−0.404038	−	0.914742i	$-0.632394\pi$
$541$	11.8787	−	11.8787i	0.510704	−	0.510704i	0.914742	+	0.404038i	$0.132394\pi$
$542$	−5.05635	+	8.28372i	−0.217189	+	0.355816i
$543$	12.6522			0.542959
$544$	0.363557	−	0.899899i	0.0155874	−	0.0385829i
$545$		−	4.65685i		−	0.199478i
$546$	−8.13637	−	7.51056i	−0.348204	−	0.321422i
$547$		−	34.1028i		−	1.45813i	−0.684443	−	0.729066i	$-0.739955\pi$
$547$		−	34.1028i		−	1.45813i	0.684443	−	0.729066i	$-0.260045\pi$
$548$	2.29714	−	7.15501i	0.0981291	−	0.305647i
$549$	−4.00000			−0.170716
$550$	−24.2931	−	14.8284i	−1.03586	−	0.632286i
$551$	17.1778	−	17.1778i	0.731801	−	0.731801i
$552$	−6.57539	+	5.67590i	−0.279867	+	0.241582i
$553$	0.899495	−	0.899495i	0.0382504	−	0.0382504i
$554$	8.24735	−	1.99529i	0.350396	−	0.0847717i
$555$			12.7570i			0.541503i
$556$	2.92556	+	5.69239i	0.124071	+	0.241411i
$557$	4.36396	−	4.36396i	0.184907	−	0.184907i	−0.608583	−	0.793490i	$-0.708262\pi$
$557$	4.36396	−	4.36396i	0.184907	−	0.184907i	0.793490	+	0.608583i	$0.208262\pi$
$558$	−2.94725	−	1.79899i	−0.124767	−	0.0761573i
$559$	−19.9463	−	3.98926i	−0.843639	−	0.168728i
$560$	−4.79289	−	3.43123i	−0.202537	−	0.144996i
$561$	0.899495	+	0.899495i	0.0379767	+	0.0379767i
$562$	27.7279	+	16.9250i	1.16963	+	0.713938i
$563$	23.3252			0.983039			0.491520	−	0.870867i	$-0.336442\pi$
$563$	23.3252			0.983039			0.491520	+	0.870867i	$0.336442\pi$
$564$	−1.32764	+	4.13525i	−0.0559036	+	0.174125i
$565$	−5.17157	−	5.17157i	−0.217570	−	0.217570i
$566$	8.07863	+	33.3923i	0.339570	+	1.40358i
$567$	6.07328	+	6.07328i	0.255054	+	0.255054i
$568$	35.9853	+	2.64205i	1.50991	+	0.110858i
$569$		−	12.5147i		−	0.524644i	−0.964980	−	0.262322i	$-0.915512\pi$
$569$		−	12.5147i		−	0.524644i	0.964980	−	0.262322i	$-0.0844883\pi$
$570$	14.4126	−	3.48686i	0.603679	−	0.146048i
$571$	−14.4834			−0.606112			−0.303056	−	0.952973i	$-0.598007\pi$
$571$	−14.4834			−0.606112			−0.303056	+	0.952973i	$0.598007\pi$
$572$	31.6985	+	17.6499i	1.32538	+	0.737980i
$573$	24.7868			1.03548
$574$	−12.1535	+	2.94031i	−0.507278	+	0.122726i
$575$			8.33609i			0.347639i
$576$	−0.967957	+	6.55635i	−0.0403316	+	0.273181i
$577$	16.4853	+	16.4853i	0.686291	+	0.686291i	0.961410	−	0.275119i	$-0.0887172\pi$
$577$	16.4853	+	16.4853i	0.686291	+	0.686291i	−0.275119	+	0.961410i	$0.588717\pi$
$578$	−5.64353	−	23.3270i	−0.234740	−	0.970277i
$579$	−11.8937	−	11.8937i	−0.494287	−	0.494287i
$580$	6.50157	+	2.08735i	0.269963	+	0.0866726i
$581$	−1.27208			−0.0527747
$582$	6.07328	+	3.70711i	0.251746	+	0.153665i
$583$	29.3244	+	29.3244i	1.21449	+	1.21449i
$584$	6.60963	+	0.485281i	0.273508	+	0.0200811i
$585$	−1.65685	−	2.48528i	−0.0685025	−	0.102754i
$586$	1.37868	+	0.841540i	0.0569527	+	0.0347637i
$587$	−13.2626	+	13.2626i	−0.547407	+	0.547407i	−0.925690	−	0.378283i	$-0.876515\pi$
$587$	−13.2626	+	13.2626i	−0.547407	+	0.547407i	0.378283	+	0.925690i	$0.376515\pi$
$588$	12.6569	−	6.50490i	0.521960	−	0.268258i
$589$			20.9706i			0.864077i
$590$	−13.8316	+	3.34628i	−0.569436	+	0.137764i
$591$	3.84116	−	3.84116i	0.158004	−	0.158004i
$592$	5.65624	+	34.1623i	0.232470	+	1.40406i
$593$	−32.5563	+	32.5563i	−1.33693	+	1.33693i	−0.437910	+	0.899019i	$0.644281\pi$
$593$	−32.5563	+	32.5563i	−1.33693	+	1.33693i	−0.899019	+	0.437910i	$0.855719\pi$
$594$	−34.2635	−	20.9143i	−1.40585	−	0.858123i
$595$	0.252834			0.0103652
$596$	−28.2373	−	9.06568i	−1.15664	−	0.371345i
$597$		−	30.1838i		−	1.23534i
$598$	−0.424671	−	10.6180i	−0.0173661	−	0.434201i
$599$			42.6918i			1.74434i	0.489204	+	0.872169i	$0.337287\pi$
$599$			42.6918i			1.74434i	−0.489204	+	0.872169i	$0.662713\pi$
$600$	−10.8941	−	12.6206i	−0.444751	−	0.515233i
$601$	−17.9706			−0.733035			−0.366517	−	0.930411i	$-0.619450\pi$
$601$	−17.9706			−0.733035			−0.366517	+	0.930411i	$0.619450\pi$
$602$	−6.12565	+	10.0355i	−0.249663	+	0.409018i
$603$	1.22079	−	1.22079i	0.0497145	−	0.0497145i
$604$	29.9050	+	9.60111i	1.21682	+	0.390664i
$605$	−10.1213	+	10.1213i	−0.411490	+	0.411490i
$606$	−2.53434	−	10.4755i	−0.102950	−	0.425537i
$607$			36.7973i			1.49355i	0.665074	+	0.746777i	$0.268400\pi$
$607$			36.7973i			1.49355i	−0.665074	+	0.746777i	$0.731600\pi$
$608$	37.0501	−	15.7279i	1.50258	−	0.637851i
$609$	5.24264	−	5.24264i	0.212443	−	0.212443i
$610$	−3.55765	+	5.82843i	−0.144045	+	0.235986i
$611$	−2.94725	−	4.42088i	−0.119233	−	0.178850i
$612$	−0.129942	−	0.252834i	−0.00525261	−	0.0102202i
$613$	−22.8701	−	22.8701i	−0.923713	−	0.923713i	0.0735766	−	0.997290i	$-0.476559\pi$
$613$	−22.8701	−	22.8701i	−0.923713	−	0.923713i	−0.997290	+	0.0735766i	$0.976559\pi$
$614$	1.79899	−	2.94725i	0.0726013	−	0.118941i
$615$	8.84175			0.356534
$616$	15.8744	−	13.7028i	0.639598	−	0.552103i
$617$	−7.51472	−	7.51472i	−0.302531	−	0.302531i	0.539472	−	0.842003i	$-0.318624\pi$
$617$	−7.51472	−	7.51472i	−0.302531	−	0.302531i	−0.842003	+	0.539472i	$0.818624\pi$
$618$	30.5738	−	7.39675i	1.22986	−	0.297541i
$619$	−34.7132	−	34.7132i	−1.39524	−	1.39524i	−0.813052	−	0.582191i	$-0.802196\pi$
$619$	−34.7132	−	34.7132i	−1.39524	−	1.39524i	−0.582191	−	0.813052i	$-0.697804\pi$
$620$	−5.24264	+	2.69442i	−0.210550	+	0.108210i
$621$			11.7574i			0.471807i
$622$	−9.87068	−	40.7996i	−0.395778	−	1.63592i
$623$	4.67371			0.187248
$624$	14.5192	+	15.5203i	0.581233	+	0.621310i
$625$	−11.0000			−0.440000
$626$	−1.15902	−	4.79072i	−0.0463239	−	0.191476i
$627$			52.7543i			2.10680i
$628$	−21.3459	+	10.9706i	−0.851793	+	0.437773i
$629$	−1.05025	−	1.05025i	−0.0418763	−	0.0418763i
$630$	−1.67805	+	0.405972i	−0.0668551	+	0.0161743i
$631$	1.04201	+	1.04201i	0.0414818	+	0.0414818i	0.727543	−	0.686062i	$-0.240662\pi$
$631$	1.04201	+	1.04201i	0.0414818	+	0.0414818i	−0.686062	+	0.727543i	$0.740662\pi$
$632$	−1.84824	+	1.59541i	−0.0735191	+	0.0634619i
$633$	−29.2843			−1.16395
$634$	−16.3146	+	26.7279i	−0.647936	+	1.06150i
$635$	9.80971	+	9.80971i	0.389287	+	0.389287i
$636$	11.1046	+	21.6066i	0.440324	+	0.856757i
$637$	−3.41421	+	17.0711i	−0.135276	+	0.676380i
$638$	−12.6569	+	20.7355i	−0.501090	+	0.820926i
$639$	7.47286	−	7.47286i	0.295622	−	0.295622i
$640$	8.69239	+	7.24171i	0.343597	+	0.286254i
$641$			9.85786i			0.389362i	0.980867	+	0.194681i	$0.0623672\pi$
$641$			9.85786i			0.389362i	−0.980867	+	0.194681i	$0.937633\pi$
$642$	−5.52941	−	22.8554i	−0.218229	−	0.902029i
$643$	17.4307	−	17.4307i	0.687399	−	0.687399i	−0.274258	−	0.961656i	$-0.588432\pi$
$643$	17.4307	−	17.4307i	0.687399	−	0.687399i	0.961656	+	0.274258i	$0.0884321\pi$
$644$	−5.84813	−	1.87756i	−0.230448	−	0.0739864i
$645$	5.87868	−	5.87868i	0.231473	−	0.231473i
$646$	−0.899495	+	1.47363i	−0.0353902	+	0.0579790i
$647$	−17.6835			−0.695210			−0.347605	−	0.937641i	$-0.613005\pi$
$647$	−17.6835			−0.695210			−0.347605	+	0.937641i	$0.613005\pi$
$648$	−10.7720	−	12.4791i	−0.423164	−	0.490226i
$649$		−	50.6274i		−	1.98730i
$650$	20.3798	−	0.815100i	0.799361	−	0.0319708i
$651$			6.40017i			0.250842i
$652$	−7.25617	−	2.32962i	−0.284173	−	0.0912350i
$653$	−9.17157			−0.358911			−0.179456	−	0.983766i	$-0.557434\pi$
$653$	−9.17157			−0.358911			−0.179456	+	0.983766i	$0.557434\pi$
$654$	8.28372	+	5.05635i	0.323919	+	0.197719i
$655$	−1.90524	+	1.90524i	−0.0744439	+	0.0744439i
$656$	23.6777	−	3.92029i	0.924457	−	0.153062i
$657$	1.37258	−	1.37258i	0.0535496	−	0.0535496i
$658$	−2.98495	+	0.722152i	−0.116366	+	0.0281524i
$659$			34.8613i			1.35801i	0.734136	+	0.679003i	$0.237588\pi$
$659$			34.8613i			1.35801i	−0.734136	+	0.679003i	$0.762412\pi$
$660$	−13.1886	+	6.77817i	−0.513365	+	0.263840i
$661$	−16.9289	+	16.9289i	−0.658459	+	0.658459i	−0.955015	−	0.296556i	$-0.904162\pi$
$661$	−16.9289	+	16.9289i	−0.658459	+	0.658459i	0.296556	+	0.955015i	$0.404162\pi$
$662$	8.15731	+	4.97918i	0.317043	+	0.193522i
$663$	−0.893904	−	0.178781i	−0.0347164	−	0.00694327i
$664$	2.43503	+	0.178781i	0.0944974	+	0.00693804i
$665$	7.41421	+	7.41421i	0.287511	+	0.287511i
$666$	8.65685	+	5.28411i	0.335446	+	0.204755i
$667$	7.11529			0.275505
$668$	−2.32471	−	0.746357i	−0.0899457	−	0.0288774i
$669$	13.8198	+	13.8198i	0.534305	+	0.534305i
$670$	−0.693037	−	2.86461i	−0.0267744	−	0.110670i
$671$	−17.1778	−	17.1778i	−0.663143	−	0.663143i
$672$	11.3076	−	4.80013i	0.436201	−	0.185169i
$673$		−	3.20101i		−	0.123390i	−0.998095	−	0.0616949i	$-0.980349\pi$
$673$		−	3.20101i		−	0.123390i	0.998095	−	0.0616949i	$-0.0196506\pi$
$674$	19.0080	−	4.59862i	0.732160	−	0.177132i
$675$	−22.5667			−0.868592
$676$	−25.9170	+	2.07644i	−0.996806	+	0.0798633i
$677$	11.2132			0.430958			0.215479	−	0.976508i	$-0.430869\pi$
$677$	11.2132			0.430958			0.215479	+	0.976508i	$0.430869\pi$
$678$	14.8145	−	3.58409i	0.568949	−	0.137646i
$679$			5.03127i			0.193083i
$680$	−0.483979	−	0.0355339i	−0.0185597	−	0.00136266i
$681$	16.1005	+	16.1005i	0.616973	+	0.616973i
$682$	−4.93116	−	20.3825i	−0.188824	−	0.780488i
$683$	4.06332	+	4.06332i	0.155478	+	0.155478i	0.780560	−	0.625081i	$-0.214934\pi$
$683$	4.06332	+	4.06332i	0.155478	+	0.155478i	−0.625081	+	0.780560i	$0.714934\pi$
$684$	3.60373	−	11.2247i	0.137792	−	0.429187i
$685$	−3.75736			−0.143561
$686$	21.0407	+	12.8431i	0.803337	+	0.490354i
$687$	−19.5887	−	19.5887i	−0.747357	−	0.747357i
$688$	13.1362	−	18.3492i	0.500813	−	0.699558i
$689$	−29.1421	−	5.82843i	−1.11023	−	0.222045i
$690$	3.70711	+	2.26280i	0.141127	+	0.0861434i
$691$	−7.11529	+	7.11529i	−0.270679	+	0.270679i	−0.829373	−	0.558695i	$-0.811302\pi$
$691$	−7.11529	+	7.11529i	−0.270679	+	0.270679i	0.558695	+	0.829373i	$0.311302\pi$
$692$	22.2929	+	43.3762i	0.847449	+	1.64892i
$693$		−	6.14214i		−	0.233320i
$694$	−29.6887	+	7.18261i	−1.12697	+	0.272648i
$695$	2.26280	−	2.26280i	0.0858330	−	0.0858330i
$696$	−10.7723	+	9.29872i	−0.408325	+	0.352467i
$697$	−0.727922	+	0.727922i	−0.0275720	+	0.0275720i
$698$	12.8640	+	7.85211i	0.486908	+	0.297207i
$699$	32.3764			1.22459
$700$	3.60373	−	11.2247i	0.136208	−	0.424254i
$701$		−	39.3553i		−	1.48643i	−0.669052	−	0.743215i	$-0.733300\pi$
$701$		−	39.3553i		−	1.48643i	0.669052	−	0.743215i	$-0.266700\pi$
$702$	28.7440	−	1.14963i	1.08487	−	0.0433900i
$703$		−	61.5961i		−	2.32314i
$704$	−32.3128	+	23.9991i	−1.21784	+	0.904501i
$705$	2.17157			0.0817862
$706$	−1.65241	+	2.70711i	−0.0621891	+	0.101883i
$707$	5.38883	−	5.38883i	0.202668	−	0.202668i
$708$	9.06568	−	28.2373i	0.340709	−	1.06122i
$709$	30.9706	−	30.9706i	1.16312	−	1.16312i	0.179336	−	0.983788i	$-0.442605\pi$
$709$	30.9706	−	30.9706i	1.16312	−	1.16312i	0.983788	−	0.179336i	$-0.0573949\pi$
$710$	−4.24230	−	17.5352i	−0.159211	−	0.658084i
$711$			0.715123i			0.0268192i
$712$	−8.94648	−	0.656854i	−0.335284	−	0.0246167i
$713$	−4.34315	+	4.34315i	−0.162652	+	0.162652i
$714$	−0.274524	+	0.449747i	−0.0102738	+	0.0168314i
$715$	3.55765	−	17.7882i	0.133048	−	0.665242i
$716$	−22.6924	+	11.6626i	−0.848054	+	0.435851i
$717$	15.0919	+	15.0919i	0.563617	+	0.563617i
$718$	2.17157	−	3.55765i	0.0810424	−	0.132770i
$719$	38.1662			1.42336			0.711679	−	0.702505i	$-0.247935\pi$
$719$	38.1662			1.42336			0.711679	+	0.702505i	$0.247935\pi$
$720$	3.26920	−	0.541280i	0.121836	−	0.0201723i
$721$	15.7279	+	15.7279i	0.585738	+	0.585738i
$722$	−43.4737	+	10.5176i	−1.61793	+	0.391426i
$723$	1.57835	+	1.57835i	0.0586996	+	0.0586996i
$724$	−7.84924	−	15.2726i	−0.291715	−	0.567602i
$725$			13.6569i			0.507203i
$726$	−7.01445	−	28.9936i	−0.260331	−	1.07605i
$727$	18.5467			0.687860			0.343930	−	0.938995i	$-0.388242\pi$
$727$	18.5467			0.687860			0.343930	+	0.938995i	$0.388242\pi$
$728$	−4.01838	+	14.4809i	−0.148931	+	0.536698i
$729$	−29.7696			−1.10258
$730$	−0.779208	−	3.22079i	−0.0288398	−	0.119207i
$731$			0.967957i			0.0358012i
$732$	−6.50490	−	12.6569i	−0.240428	−	0.467811i
$733$	14.8492	+	14.8492i	0.548469	+	0.548469i	0.925998	−	0.377529i	$-0.123226\pi$
$733$	14.8492	+	14.8492i	0.548469	+	0.548469i	−0.377529	+	0.925998i	$0.623226\pi$
$734$	5.23773	−	1.26717i	0.193328	−	0.0467720i
$735$	−5.03127	−	5.03127i	−0.185581	−	0.185581i
$736$	10.9307	+	4.41597i	0.402910	+	0.162775i
$737$	10.4853			0.386230
$738$	3.66237	−	6.00000i	0.134814	−	0.220863i
$739$	−15.5995	−	15.5995i	−0.573836	−	0.573836i	0.359362	−	0.933198i	$-0.382994\pi$
$739$	−15.5995	−	15.5995i	−0.573836	−	0.573836i	−0.933198	+	0.359362i	$0.882994\pi$
$740$	15.3990	−	7.91421i	0.566079	−	0.290932i
$741$	−20.9706	−	31.4558i	−0.770373	−	1.15556i
$742$	−8.94975	+	14.6622i	−0.328556	+	0.538266i
$743$	6.93651	−	6.93651i	0.254476	−	0.254476i	−0.568327	−	0.822803i	$-0.692409\pi$
$743$	6.93651	−	6.93651i	0.254476	−	0.254476i	0.822803	+	0.568327i	$0.192409\pi$
$744$	0.899495	−	12.2513i	0.0329771	−	0.449154i
$745$			14.8284i			0.543272i
$746$	4.86432	+	20.1062i	0.178095	+	0.736142i
$747$	0.505668	−	0.505668i	0.0185014	−	0.0185014i
$748$	0.527754	−	1.64382i	0.0192966	−	0.0601040i
$749$	11.7574	−	11.7574i	0.429605	−	0.429605i
$750$	−9.77208	+	16.0094i	−0.356826	+	0.584581i
$751$	−45.6390			−1.66539			−0.832696	−	0.553731i	$-0.813204\pi$
$751$	−45.6390			−1.66539			−0.832696	+	0.553731i	$0.813204\pi$
$752$	5.81533	−	0.962841i	0.212063	−	0.0351112i
$753$			22.7696i			0.829769i
$754$	−0.695731	−	17.3952i	−0.0253370	−	0.633497i
$755$		−	15.7042i		−	0.571535i
$756$	5.08277	−	15.8315i	0.184858	−	0.575786i
$757$	19.2721			0.700456			0.350228	−	0.936665i	$-0.386104\pi$
$757$	19.2721			0.700456			0.350228	+	0.936665i	$0.386104\pi$
$758$	12.5782	+	7.67767i	0.456860	+	0.278866i
$759$	−10.9258	+	10.9258i	−0.396581	+	0.396581i
$760$	−13.1504	−	15.2344i	−0.477014	−	0.552610i
$761$	−11.6569	+	11.6569i	−0.422561	+	0.422561i	−0.886084	−	0.463524i	$-0.846585\pi$
$761$	−11.6569	+	11.6569i	−0.422561	+	0.422561i	0.463524	+	0.886084i	$0.346585\pi$
$762$	−28.1010	+	6.79850i	−1.01799	+	0.246284i
$763$			6.86246i			0.248438i
$764$	−15.3773	−	29.9203i	−0.556332	−	1.08248i
$765$	−0.100505	+	0.100505i	−0.00363377	+	0.00363377i
$766$	−0.305198	−	0.186292i	−0.0110272	−	0.00673099i
$767$	20.1251	+	30.1876i	0.726675	+	1.09001i
$768$	−22.3198	+	7.59927i	−0.805397	+	0.274215i
$769$	9.65685	+	9.65685i	0.348235	+	0.348235i	0.859452	−	0.511217i	$-0.170805\pi$
$769$	9.65685	+	9.65685i	0.348235	+	0.348235i	−0.511217	+	0.859452i	$0.670805\pi$
$770$	−8.94975	−	5.46289i	−0.322527	−	0.196869i
$771$	−15.7042			−0.565573
$772$	−6.97833	+	21.7357i	−0.251155	+	0.782284i
$773$	27.8787	+	27.8787i	1.00273	+	1.00273i	0.999996	+	0.00273014i	$0.000869031\pi$
$773$	27.8787	+	27.8787i	1.00273	+	1.00273i	0.00273014	+	0.999996i	$0.499131\pi$
$774$	−1.55423	−	6.42429i	−0.0558658	−	0.230916i
$775$	−8.33609	−	8.33609i	−0.299441	−	0.299441i
$776$	0.707107	−	9.63093i	0.0253837	−	0.345730i
$777$		−	18.7990i		−	0.674410i
$778$	8.44273	−	2.04255i	0.302686	−	0.0732291i
$779$	−42.6918			−1.52959
$780$	5.16954	−	9.28427i	0.185099	−	0.332430i
$781$	64.1838			2.29668
$782$	−0.491489	+	0.118906i	−0.0175756	+	0.00425208i
$783$			19.2619i			0.688363i
$784$	−15.7042	−	11.2426i	−0.560865	−	0.401523i
$785$	8.48528	+	8.48528i	0.302853	+	0.302853i
$786$	−1.32040	−	5.45777i	−0.0470972	−	0.194672i
$787$	13.8730	+	13.8730i	0.494520	+	0.494520i	0.909727	−	0.415207i	$-0.136291\pi$
$787$	13.8730	+	13.8730i	0.494520	+	0.494520i	−0.415207	+	0.909727i	$0.636291\pi$
$788$	−7.01968	−	2.25369i	−0.250066	−	0.0802845i
$789$	19.1716			0.682526
$790$	1.04201	+	0.636039i	0.0370731	+	0.0226293i
$791$	7.62096	+	7.62096i	0.270970	+	0.270970i
$792$	−0.863230	+	11.7574i	−0.0306735	+	0.417780i
$793$	17.0711	+	3.41421i	0.606211	+	0.121242i
$794$	31.5563	+	19.2619i	1.11989	+	0.683578i
$795$	8.58892	−	8.58892i	0.304618	−	0.304618i
$796$	−36.4350	+	18.7255i	−1.29141	+	0.663708i
$797$		−	36.8284i		−	1.30453i	−0.757991	−	0.652265i	$-0.773819\pi$
$797$		−	36.8284i		−	1.30453i	0.757991	−	0.652265i	$-0.226181\pi$
$798$	−21.2388	+	5.13833i	−0.751846	+	0.181895i
$799$	−0.178781	+	0.178781i	−0.00632481	+	0.00632481i
$800$	−8.47586	+	20.9800i	−0.299667	+	0.741755i
$801$	−1.85786	+	1.85786i	−0.0656444	+	0.0656444i
$802$	−4.29289	−	2.62036i	−0.151587	−	0.0925283i
$803$	11.7890			0.416025
$804$	5.84813	+	1.87756i	0.206248	+	0.0662166i
$805$			3.07107i			0.108241i
$806$	11.0426	+	10.1933i	0.388961	+	0.359044i
$807$		−	29.6820i		−	1.04485i
$808$	−11.0727	+	9.55802i	−0.389538	+	0.336250i
$809$	−35.1421			−1.23553			−0.617766	−	0.786362i	$-0.711962\pi$
$809$	−35.1421			−1.23553			−0.617766	+	0.786362i	$0.711962\pi$
$810$	−4.29446	+	7.03553i	−0.150892	+	0.247203i
$811$	20.1251	−	20.1251i	0.706688	−	0.706688i	−0.259150	−	0.965837i	$-0.583442\pi$
$811$	20.1251	−	20.1251i	0.706688	−	0.706688i	0.965837	+	0.259150i	$0.0834423\pi$
$812$	−9.58088	−	3.07598i	−0.336223	−	0.107946i
$813$	−7.15076	+	7.15076i	−0.250788	+	0.250788i
$814$	14.4841	+	59.8689i	0.507668	+	2.09840i
$815$			3.81048i			0.133475i
$816$	0.588706	−	0.822330i	0.0206088	−	0.0287873i
$817$	−28.3848	+	28.3848i	−0.993058	+	0.993058i
$818$	−24.1144	+	39.5061i	−0.843139	+	1.38130i
$819$	2.44158	+	3.66237i	0.0853158	+	0.127974i
$820$	−5.48528	−	10.6729i	−0.191554	−	0.372715i
$821$	−17.7782	−	17.7782i	−0.620463	−	0.620463i	0.325187	−	0.945650i	$-0.394573\pi$
$821$	−17.7782	−	17.7782i	−0.620463	−	0.620463i	−0.945650	+	0.325187i	$0.894573\pi$
$822$	4.07969	−	6.68368i	0.142296	−	0.233120i
$823$	4.88317			0.170216			0.0851082	−	0.996372i	$-0.472876\pi$
$823$	4.88317			0.170216			0.0851082	+	0.996372i	$0.472876\pi$
$824$	−27.8962	−	32.3170i	−0.971809	−	1.12582i
$825$	−20.9706	−	20.9706i	−0.730101	−	0.730101i
$826$	20.3825	−	4.93116i	0.709199	−	0.171577i
$827$	28.8187	+	28.8187i	1.00213	+	1.00213i	0.999998	+	0.00212804i	$0.000677377\pi$
$827$	28.8187	+	28.8187i	1.00213	+	1.00213i	0.00212804	+	0.999998i	$0.499323\pi$
$828$	3.07107	−	1.57835i	0.106727	−	0.0548516i
$829$			14.3848i			0.499604i	0.968297	+	0.249802i	$0.0803655\pi$
$829$			14.3848i			0.499604i	−0.968297	+	0.249802i	$0.919634\pi$
$830$	−0.287065	−	1.18656i	−0.00996419	−	0.0411861i
$831$	8.84175			0.306717
$832$	9.72721	−	27.1548i	0.337230	−	0.941422i
$833$	0.828427			0.0287033
$834$	1.56821	+	6.48205i	0.0543025	+	0.224455i
$835$			1.22079i			0.0422472i
$836$	63.6801	−	32.7279i	2.20242	−	1.13192i
$837$	−11.7574	−	11.7574i	−0.406394	−	0.406394i
$838$	7.75481	−	1.87613i	0.267885	−	0.0648097i
$839$	−16.8203	−	16.8203i	−0.580701	−	0.580701i	0.354395	−	0.935096i	$-0.384687\pi$
$839$	−16.8203	−	16.8203i	−0.580701	−	0.580701i	−0.935096	+	0.354395i	$0.884687\pi$
$840$	−4.01347	−	4.64951i	−0.138478	−	0.160423i
$841$	−17.3431			−0.598040
$842$	−25.0299	+	41.0061i	−0.862589	+	1.41316i
$843$	23.9356	+	23.9356i	0.824385	+	0.824385i
$844$	18.1675	+	35.3492i	0.625351	+	1.21677i
$845$	4.94975	+	12.0208i	0.170276	+	0.413529i
$846$	0.899495	−	1.47363i	0.0309253	−	0.0506643i
$847$	14.9150	−	14.9150i	0.512487	−	0.512487i
$848$	19.1924	−	26.8088i	0.659069	−	0.920617i
$849$			35.7990i			1.22862i
$850$	−0.228225	−	0.943348i	−0.00782805	−	0.0323566i
$851$	12.7570	−	12.7570i	0.437303	−	0.437303i
$852$	35.7983	+	11.4932i	1.22643	+	0.393749i
$853$	15.5772	−	15.5772i	0.533352	−	0.533352i	−0.388216	−	0.921568i	$-0.626909\pi$
$853$	15.5772	−	15.5772i	0.533352	−	0.533352i	0.921568	+	0.388216i	$0.126909\pi$
$854$	5.24264	−	8.58892i	0.179399	−	0.293907i
$855$	−5.89450			−0.201588
$856$	−24.1585	+	20.8537i	−0.825721	+	0.712764i
$857$			1.85786i			0.0634634i	0.999496	+	0.0317317i	$0.0101022\pi$
$857$			1.85786i			0.0634634i	−0.999496	+	0.0317317i	$0.989898\pi$
$858$	27.7793	+	25.6427i	0.948369	+	0.875426i
$859$			48.0806i			1.64049i	0.572013	+	0.820244i	$0.306163\pi$
$859$			48.0806i			1.64049i	−0.572013	+	0.820244i	$0.693837\pi$
$860$	−10.7432	−	3.44916i	−0.366341	−	0.117615i
$861$	−13.0294			−0.444042
$862$	−26.9352	−	16.4411i	−0.917416	−	0.559987i
$863$	−27.9248	+	27.9248i	−0.950572	+	0.950572i	−0.998835	−	0.0482622i	$-0.984632\pi$
$863$	−27.9248	+	27.9248i	−0.950572	+	0.950572i	0.0482622	+	0.998835i	$0.484632\pi$
$864$	−11.9545	+	29.5905i	−0.406700	+	1.00669i
$865$	17.2426	−	17.2426i	0.586267	−	0.586267i
$866$	44.4171	−	10.7459i	1.50935	−	0.365159i
$867$		−	25.0083i		−	0.849325i
$868$	7.72569	−	3.97056i	0.262227	−	0.134770i
$869$	−3.07107	+	3.07107i	−0.104179	+	0.104179i
$870$	6.07328	+	3.70711i	0.205904	+	0.125683i
$871$	−6.25206	+	4.16804i	−0.211843	+	0.141229i
$872$	0.964466	−	13.1362i	0.0326609	−	0.444848i
$873$	−2.00000	−	2.00000i	−0.0676897	−	0.0676897i
$874$	−17.8995	−	10.9258i	−0.605459	−	0.369570i
$875$	−13.2626			−0.448359
$876$	6.57527	+	2.11102i	0.222158	+	0.0713247i
$877$	−18.2635	−	18.2635i	−0.616713	−	0.616713i	0.327974	−	0.944687i	$-0.393634\pi$
$877$	−18.2635	−	18.2635i	−0.616713	−	0.616713i	−0.944687	+	0.327974i	$0.893634\pi$
$878$	−4.15822	−	17.1877i	−0.140333	−	0.580055i
$879$	1.19012	+	1.19012i	0.0401417	+	0.0401417i
$880$	16.3640	+	11.7150i	0.551629	+	0.394911i
$881$			10.3137i			0.347478i	0.984792	+	0.173739i	$0.0555849\pi$
$881$			10.3137i			0.347478i	−0.984792	+	0.173739i	$0.944415\pi$
$882$	−5.49824	+	1.33019i	−0.185135	+	0.0447899i
$883$	15.1985			0.511472			0.255736	−	0.966747i	$-0.417682\pi$
$883$	15.1985			0.511472			0.255736	+	0.966747i	$0.417682\pi$
$884$	0.338756	+	1.18995i	0.0113936	+	0.0400224i
$885$	−14.8284			−0.498452
$886$	8.44988	−	2.04428i	0.283879	−	0.0686791i
$887$		−	42.1861i		−	1.41647i	−0.705976	−	0.708235i	$-0.749492\pi$
$887$		−	42.1861i		−	1.41647i	0.705976	−	0.708235i	$-0.250508\pi$
$888$	−2.64205	+	35.9853i	−0.0886615	+	1.20759i
$889$	−14.4558	−	14.4558i	−0.484833	−	0.484833i
$890$	1.05470	+	4.35951i	0.0353536	+	0.146131i
$891$	−20.7355	−	20.7355i	−0.694665	−	0.694665i
$892$	8.10840	−	25.2556i	0.271489	−	0.845619i
$893$	−10.4853			−0.350877
$894$	−26.3772	−	16.1005i	−0.882184	−	0.538481i
$895$	9.02054	+	9.02054i	0.301523	+	0.301523i
$896$	−12.8093	−	10.6716i	−0.427930	−	0.356512i
$897$	2.17157	−	10.8579i	0.0725067	−	0.362534i
$898$	−43.9203	−	26.8088i	−1.46564	−	0.894620i
$899$	−7.11529	+	7.11529i	−0.237308	+	0.237308i
$900$	3.02944	+	5.89450i	0.100981	+	0.196483i
$901$			1.41421i			0.0471143i
$902$	41.4947	−	10.0388i	1.38162	−	0.334257i
$903$	−8.66297	+	8.66297i	−0.288286	+	0.288286i
$904$	−13.5171	−	15.6592i	−0.449571	−	0.520818i
$905$	−6.07107	+	6.07107i	−0.201809	+	0.201809i
$906$	27.9350	+	17.0514i	0.928079	+	0.566496i
$907$	0.252834			0.00839522			0.00419761	−	0.999991i	$-0.498664\pi$
$907$	0.252834			0.00839522			0.00419761	+	0.999991i	$0.498664\pi$
$908$	9.44654	−	29.4235i	0.313494	−	0.976454i
$909$			4.28427i			0.142100i
$910$	7.50804	−	0.300288i	0.248889	−	0.00995445i
$911$			15.0938i			0.500081i	0.968235	+	0.250040i	$0.0804439\pi$
$911$			15.0938i			0.500081i	−0.968235	+	0.250040i	$0.919556\pi$
$912$	41.3778	−	6.85090i	1.37016	−	0.226856i
$913$	4.34315			0.143737
$914$	0.610396	−	1.00000i	0.0201901	−	0.0330771i
$915$	−5.03127	+	5.03127i	−0.166329	+	0.166329i
$916$	−11.4932	+	35.7983i	−0.379745	+	1.18281i
$917$	2.80761	−	2.80761i	0.0927155	−	0.0927155i
$918$	−0.321892	−	1.33051i	−0.0106240	−	0.0439135i
$919$		−	21.8516i		−	0.720816i	−0.932795	−	0.360408i	$-0.882637\pi$
$919$		−	21.8516i		−	0.720816i	0.932795	−	0.360408i	$-0.117363\pi$
$920$	0.431615	−	5.87868i	0.0142299	−	0.193814i
$921$	2.54416	−	2.54416i	0.0838328	−	0.0838328i
$922$	6.73604	−	11.0355i	0.221840	−	0.363436i
$923$	−38.2709	+	25.5139i	−1.25970	+	0.839801i
$924$	19.4350	−	9.98849i	0.639366	−	0.328597i
$925$	24.4853	+	24.4853i	0.805071	+	0.805071i
$926$	21.8701	−	35.8293i	0.718695	−	1.17742i
$927$	−12.5041			−0.410689
$928$	17.9075	+	7.23460i	0.587844	+	0.237487i
$929$	−24.6274	−	24.6274i	−0.807999	−	0.807999i	0.176331	−	0.984331i	$-0.443577\pi$
$929$	−24.6274	−	24.6274i	−0.807999	−	0.807999i	−0.984331	+	0.176331i	$0.943577\pi$
$930$	−5.96991	+	1.44430i	−0.195761	+	0.0473606i
$931$	24.2931	+	24.2931i	0.796175	+	0.796175i
$932$	−20.0858	−	39.0818i	−0.657932	−	1.28017i
$933$		−	43.7401i		−	1.43199i
$934$	7.09853	+	29.3412i	0.232271	+	0.960072i
$935$	−0.863230			−0.0282306
$936$	−4.15899	−	7.35371i	−0.135941	−	0.240364i
$937$	24.9706			0.815753			0.407876	−	0.913037i	$-0.366269\pi$
$937$	24.9706			0.815753			0.407876	+	0.913037i	$0.366269\pi$
$938$	1.02128	+	4.22136i	0.0333459	+	0.137832i
$939$		−	5.13600i		−	0.167607i
$940$	−1.34721	−	2.62132i	−0.0439411	−	0.0854980i
$941$	1.73654	+	1.73654i	0.0566097	+	0.0566097i	0.734845	−	0.678235i	$-0.237255\pi$
$941$	1.73654	+	1.73654i	0.0566097	+	0.0566097i	−0.678235	+	0.734845i	$0.737255\pi$
$942$	−24.3070	+	5.88062i	−0.791966	+	0.191601i
$943$	−8.84175	−	8.84175i	−0.287927	−	0.287927i
$944$	−39.7096	+	6.57469i	−1.29244	+	0.213988i
$945$	−8.31371			−0.270445
$946$	20.9143	−	34.2635i	0.679982	−	1.11400i
$947$	−30.7980	−	30.7980i	−1.00080	−	1.00080i	−1.00000		0.000801955i	$-0.999745\pi$
$947$	−30.7980	−	30.7980i	−1.00080	−	1.00080i	−0.000801955	−	1.00000i	$-0.500255\pi$
$948$	−2.26280	+	1.16295i	−0.0734924	+	0.0377709i
$949$	−7.02944	+	4.68629i	−0.228185	+	0.152123i
$950$	20.9706	−	34.3557i	0.680375	−	1.11465i
$951$	−23.0723	+	23.0723i	−0.748172	+	0.748172i
$952$	0.713203	+	0.0523637i	0.0231151	+	0.00169712i
$953$		−	22.8579i		−	0.740439i	−0.928944	−	0.370219i	$-0.879282\pi$
$953$		−	22.8579i		−	0.740439i	0.928944	−	0.370219i	$-0.120718\pi$
$954$	−2.27078	−	9.38607i	−0.0735192	−	0.303885i
$955$	−11.8937	+	11.8937i	−0.384872	+	0.384872i
$956$	8.85475	−	27.5803i	0.286383	−	0.892010i
$957$	−17.8995	+	17.8995i	−0.578608	+	0.578608i
$958$	1.98528	−	3.25245i	0.0641415	−	0.105082i
$959$	5.53694			0.178797
$960$	7.02918	+	9.46421i	0.226866	+	0.305456i
$961$			22.3137i			0.719797i
$962$	−32.4352	−	29.9404i	−1.04575	−	0.965318i
$963$			9.34742i			0.301216i
$964$	0.926056	−	2.88443i	0.0298263	−	0.0929011i
$965$	11.4142			0.367437
$966$	−5.46289	−	3.33452i	−0.175766	−	0.107287i
$967$	31.2296	−	31.2296i	1.00428	−	1.00428i	0.00428700	−	0.999991i	$-0.498635\pi$
$967$	31.2296	−	31.2296i	1.00428	−	1.00428i	0.999991	−	0.00428700i	$-0.00136460\pi$
$968$	−30.6468	+	26.4544i	−0.985024	+	0.850276i
$969$	−1.27208	+	1.27208i	−0.0408650	+	0.0408650i
$970$	−4.69304	+	1.13539i	−0.150684	+	0.0364552i
$971$		−	32.8821i		−	1.05524i	−0.849482	−	0.527618i	$-0.823085\pi$
$971$		−	32.8821i		−	1.05524i	0.849482	−	0.527618i	$-0.176915\pi$
$972$	7.62096	+	14.8284i	0.244443	+	0.475622i
$973$	−3.33452	+	3.33452i	−0.106900	+	0.106900i
$974$	15.7042	+	9.58579i	0.503196	+	0.307148i
$975$	20.8402	+	4.16804i	0.667421	+	0.133484i
$976$	−11.2426	+	15.7042i	−0.359868	+	0.502680i
$977$	−9.62742	−	9.62742i	−0.308008	−	0.308008i	0.536128	−	0.844137i	$-0.319886\pi$
$977$	−9.62742	−	9.62742i	−0.308008	−	0.308008i	−0.844137	+	0.536128i	$0.819886\pi$
$978$	−6.77817	−	4.13737i	−0.216742	−	0.132298i
$979$	−15.9570			−0.509990
$980$	−2.95196	+	9.19460i	−0.0942970	+	0.293711i
$981$	−2.72792	−	2.72792i	−0.0870958	−	0.0870958i
$982$	0.490051	+	2.02559i	0.0156382	+	0.0646390i
$983$	10.5989	+	10.5989i	0.338052	+	0.338052i	0.855634	−	0.517582i	$-0.173168\pi$
$983$	10.5989	+	10.5989i	0.338052	+	0.338052i	−0.517582	+	0.855634i	$0.673168\pi$
$984$	24.9411	+	1.83119i	0.795094	+	0.0583761i
$985$			3.68629i			0.117455i
$986$	−0.805198	+	0.194802i	−0.0256427	+	0.00620376i
$987$	−3.20009			−0.101860
$988$	−24.9608	+	44.8284i	−0.794108	+	1.42618i
$989$	−11.7574			−0.373862
$990$	5.72922	−	1.38607i	0.182087	−	0.0440523i
$991$			5.38883i			0.171182i	0.996330	+	0.0855910i	$0.0272778\pi$
$991$			5.38883i			0.171182i	−0.996330	+	0.0855910i	$0.972722\pi$
$992$	−15.3467	+	6.51472i	−0.487257	+	0.206843i
$993$	7.04163	+	7.04163i	0.223459	+	0.223459i
$994$	6.25157	+	25.8403i	0.198288	+	0.819605i
$995$	14.4834	+	14.4834i	0.459155	+	0.459155i
$996$	2.42237	+	0.777712i	0.0767558	+	0.0246428i
$997$	−2.92893			−0.0927602			−0.0463801	−	0.998924i	$-0.514769\pi$
$997$	−2.92893			−0.0927602			−0.0463801	+	0.998924i	$0.514769\pi$
$998$	3.55765	+	2.17157i	0.112615	+	0.0687399i
$999$	34.5345	+	34.5345i	1.09262	+	1.09262i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	52.2.f.b.47.3	yes	8
3.2	odd	2		468.2.n.i.307.2		8
4.3	odd	2	inner	52.2.f.b.47.1	yes	8
8.3	odd	2		832.2.k.h.255.2		8
8.5	even	2		832.2.k.h.255.3		8
12.11	even	2		468.2.n.i.307.4		8
13.2	odd	12		676.2.l.l.19.3		16
13.3	even	3		676.2.l.l.319.4		16
13.4	even	6		676.2.l.h.427.3		16
13.5	odd	4	inner	52.2.f.b.31.1	✓	8
13.6	odd	12		676.2.l.l.587.3		16
13.7	odd	12		676.2.l.h.587.2		16
13.8	odd	4		676.2.f.g.239.4		8
13.9	even	3		676.2.l.l.427.2		16
13.10	even	6		676.2.l.h.319.1		16
13.11	odd	12		676.2.l.h.19.2		16
13.12	even	2		676.2.f.g.99.2		8
39.5	even	4		468.2.n.i.343.4		8
52.3	odd	6		676.2.l.l.319.3		16
52.7	even	12		676.2.l.h.587.1		16
52.11	even	12		676.2.l.h.19.3		16
52.15	even	12		676.2.l.l.19.2		16
52.19	even	12		676.2.l.l.587.4		16
52.23	odd	6		676.2.l.h.319.2		16
52.31	even	4	inner	52.2.f.b.31.3	yes	8
52.35	odd	6		676.2.l.l.427.3		16
52.43	odd	6		676.2.l.h.427.2		16
52.47	even	4		676.2.f.g.239.2		8
52.51	odd	2		676.2.f.g.99.4		8
104.5	odd	4		832.2.k.h.447.3		8
104.83	even	4		832.2.k.h.447.2		8
156.83	odd	4		468.2.n.i.343.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
52.2.f.b.31.1	✓	8	13.5	odd	4	inner
52.2.f.b.31.3	yes	8	52.31	even	4	inner
52.2.f.b.47.1	yes	8	4.3	odd	2	inner
52.2.f.b.47.3	yes	8	1.1	even	1	trivial
468.2.n.i.307.2		8	3.2	odd	2
468.2.n.i.307.4		8	12.11	even	2
468.2.n.i.343.2		8	156.83	odd	4
468.2.n.i.343.4		8	39.5	even	4
676.2.f.g.99.2		8	13.12	even	2
676.2.f.g.99.4		8	52.51	odd	2
676.2.f.g.239.2		8	52.47	even	4
676.2.f.g.239.4		8	13.8	odd	4
676.2.l.h.19.2		16	13.11	odd	12
676.2.l.h.19.3		16	52.11	even	12
676.2.l.h.319.1		16	13.10	even	6
676.2.l.h.319.2		16	52.23	odd	6
676.2.l.h.427.2		16	52.43	odd	6
676.2.l.h.427.3		16	13.4	even	6
676.2.l.h.587.1		16	52.7	even	12
676.2.l.h.587.2		16	13.7	odd	12
676.2.l.l.19.2		16	52.15	even	12
676.2.l.l.19.3		16	13.2	odd	12
676.2.l.l.319.3		16	52.3	odd	6
676.2.l.l.319.4		16	13.3	even	3
676.2.l.l.427.2		16	13.9	even	3
676.2.l.l.427.3		16	52.35	odd	6
676.2.l.l.587.3		16	13.6	odd	12
676.2.l.l.587.4		16	52.19	even	12
832.2.k.h.255.2		8	8.3	odd	2
832.2.k.h.255.3		8	8.5	even	2
832.2.k.h.447.2		8	104.83	even	4
832.2.k.h.447.3		8	104.5	odd	4

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:	\( N \)	\(=\)	\( 52 = 2^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	52.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.332548 - 1.37456i) q^{2} -1.47363i q^{3} +(-1.77882 + 0.914214i) q^{4} +(0.707107 + 0.707107i) q^{5} +(-2.02559 + 0.490051i) q^{6} +(-1.04201 - 1.04201i) q^{7} +(1.84818 + 2.14108i) q^{8} +0.828427 q^{9} +O(q^{10})\)	\(q+(-0.332548 - 1.37456i) q^{2} -1.47363i q^{3} +(-1.77882 + 0.914214i) q^{4} +(0.707107 + 0.707107i) q^{5} +(-2.02559 + 0.490051i) q^{6} +(-1.04201 - 1.04201i) q^{7} +(1.84818 + 2.14108i) q^{8} +0.828427 q^{9} +(0.736813 - 1.20711i) q^{10} +(3.55765 + 3.55765i) q^{11} +(1.34721 + 2.62132i) q^{12} +(-3.53553 - 0.707107i) q^{13} +(-1.08579 + 1.77882i) q^{14} +(1.04201 - 1.04201i) q^{15} +(2.32843 - 3.25245i) q^{16} +0.171573i q^{17} +(-0.275492 - 1.13872i) q^{18} +(-5.03127 + 5.03127i) q^{19} +(-1.90426 - 0.611372i) q^{20} +(-1.53553 + 1.53553i) q^{21} +(3.70711 - 6.07328i) q^{22} -2.08402 q^{23} +(3.15515 - 2.72353i) q^{24} -4.00000i q^{25} +(0.203775 + 5.09495i) q^{26} -5.64167i q^{27} +(2.80617 + 0.900933i) q^{28} -3.41421 q^{29} +(-1.77882 - 1.08579i) q^{30} +(2.08402 - 2.08402i) q^{31} +(-5.24500 - 2.11896i) q^{32} +(5.24264 - 5.24264i) q^{33} +(0.235837 - 0.0570562i) q^{34} -1.47363i q^{35} +(-1.47363 + 0.757359i) q^{36} +(-6.12132 + 6.12132i) q^{37} +(8.58892 + 5.24264i) q^{38} +(-1.04201 + 5.21005i) q^{39} +(-0.207107 + 2.82083i) q^{40} +(4.24264 + 4.24264i) q^{41} +(2.62132 + 1.60004i) q^{42} +5.64167 q^{43} +(-9.58088 - 3.07598i) q^{44} +(0.585786 + 0.585786i) q^{45} +(0.693037 + 2.86461i) q^{46} +(1.04201 + 1.04201i) q^{47} +(-4.79289 - 3.43123i) q^{48} -4.82843i q^{49} +(-5.49824 + 1.33019i) q^{50} +0.252834 q^{51} +(6.93554 - 1.97441i) q^{52} +8.24264 q^{53} +(-7.75481 + 1.87613i) q^{54} +5.03127i q^{55} +(0.305198 - 4.15685i) q^{56} +(7.41421 + 7.41421i) q^{57} +(1.13539 + 4.69304i) q^{58} +(-7.11529 - 7.11529i) q^{59} +(-0.900933 + 2.80617i) q^{60} -4.82843 q^{61} +(-3.55765 - 2.17157i) q^{62} +(-0.863230 - 0.863230i) q^{63} +(-1.16843 + 7.91421i) q^{64} +(-2.00000 - 3.00000i) q^{65} +(-8.94975 - 5.46289i) q^{66} +(1.47363 - 1.47363i) q^{67} +(-0.156854 - 0.305198i) q^{68} +3.07107i q^{69} +(-2.02559 + 0.490051i) q^{70} +(9.02054 - 9.02054i) q^{71} +(1.53109 + 1.77373i) q^{72} +(1.65685 - 1.65685i) q^{73} +(10.4497 + 6.37848i) q^{74} -5.89450 q^{75} +(4.35009 - 13.5494i) q^{76} -7.41421i q^{77} +(7.50804 - 0.300288i) q^{78} +0.863230i q^{79} +(3.94628 - 0.653382i) q^{80} -5.82843 q^{81} +(4.42088 - 7.24264i) q^{82} +(0.610396 - 0.610396i) q^{83} +(1.32764 - 4.13525i) q^{84} +(-0.121320 + 0.121320i) q^{85} +(-1.87613 - 7.75481i) q^{86} +5.03127i q^{87} +(-1.04201 + 14.1924i) q^{88} +(-2.24264 + 2.24264i) q^{89} +(0.610396 - 1.00000i) q^{90} +(2.94725 + 4.42088i) q^{91} +(3.70711 - 1.90524i) q^{92} +(-3.07107 - 3.07107i) q^{93} +(1.08579 - 1.77882i) q^{94} -7.11529 q^{95} +(-3.12256 + 7.72916i) q^{96} +(-2.41421 - 2.41421i) q^{97} +(-6.63696 + 1.60568i) q^{98} +(2.94725 + 2.94725i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} + 8 q^{6} - 4 q^{8} - 16 q^{9}+O(q^{10}) \) 8 * q - 4 * q^2 + 8 * q^6 - 4 * q^8 - 16 * q^9	\( 8 q - 4 q^{2} + 8 q^{6} - 4 q^{8} - 16 q^{9} - 20 q^{14} - 4 q^{16} - 8 q^{20} + 16 q^{21} + 24 q^{22} + 32 q^{24} + 8 q^{26} + 12 q^{28} - 16 q^{29} - 4 q^{32} + 8 q^{33} + 4 q^{34} - 32 q^{37} + 4 q^{40} + 4 q^{42} - 28 q^{44} + 16 q^{45} - 20 q^{46} - 44 q^{48} - 16 q^{50} + 8 q^{52} + 32 q^{53} - 32 q^{54} + 48 q^{57} + 12 q^{58} - 12 q^{60} - 16 q^{61} - 16 q^{65} - 32 q^{66} + 44 q^{68} + 8 q^{70} + 16 q^{72} - 32 q^{73} + 44 q^{74} + 32 q^{76} + 40 q^{78} + 16 q^{80} - 24 q^{81} - 48 q^{84} + 16 q^{85} + 32 q^{86} + 16 q^{89} + 24 q^{92} + 32 q^{93} + 20 q^{94} - 24 q^{96} - 8 q^{97} - 16 q^{98}+O(q^{100}) \) 8 * q - 4 * q^2 + 8 * q^6 - 4 * q^8 - 16 * q^9 - 20 * q^14 - 4 * q^16 - 8 * q^20 + 16 * q^21 + 24 * q^22 + 32 * q^24 + 8 * q^26 + 12 * q^28 - 16 * q^29 - 4 * q^32 + 8 * q^33 + 4 * q^34 - 32 * q^37 + 4 * q^40 + 4 * q^42 - 28 * q^44 + 16 * q^45 - 20 * q^46 - 44 * q^48 - 16 * q^50 + 8 * q^52 + 32 * q^53 - 32 * q^54 + 48 * q^57 + 12 * q^58 - 12 * q^60 - 16 * q^61 - 16 * q^65 - 32 * q^66 + 44 * q^68 + 8 * q^70 + 16 * q^72 - 32 * q^73 + 44 * q^74 + 32 * q^76 + 40 * q^78 + 16 * q^80 - 24 * q^81 - 48 * q^84 + 16 * q^85 + 32 * q^86 + 16 * q^89 + 24 * q^92 + 32 * q^93 + 20 * q^94 - 24 * q^96 - 8 * q^97 - 16 * q^98

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