LMFDB - Embedded newform 240.2.bc.e.43.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [240,2,Mod(43,240)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(240, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0, 3]))

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

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

chi := DirichletCharacter("240.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	240.bc (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:	$1.91640964851$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} + 14 x^{14} - 10 x^{13} - 26 x^{12} + 78 x^{11} - 66 x^{10} - 74 x^{9} + 233 x^{8} + \cdots + 256 $ x^16 - 6x^15 + 14x^14 - 10x^13 - 26x^12 + 78x^11 - 66x^10 - 74x^9 + 233x^8 - 148x^7 - 264x^6 + 624x^5 - 416x^4 - 320x^3 + 896x^2 - 768*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.3
Root			$0.424183 + 1.34910i$ of defining polynomial
Character	$\chi$	$=$	240.43
Dual form			240.2.bc.e.67.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.733173 - 1.20932i) q^{2} +1.00000i q^{3} +(-0.924916 + 1.77328i) q^{4} +(-0.609492 - 2.15140i) q^{5} +(1.20932 - 0.733173i) q^{6} +(0.566689 - 0.566689i) q^{7} +(2.82259 - 0.181602i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(-0.733173 - 1.20932i) q^{2} +1.00000i q^{3} +(-0.924916 + 1.77328i) q^{4} +(-0.609492 - 2.15140i) q^{5} +(1.20932 - 0.733173i) q^{6} +(0.566689 - 0.566689i) q^{7} +(2.82259 - 0.181602i) q^{8} -1.00000 q^{9} +(-2.15487 + 2.31442i) q^{10} +(3.64458 - 3.64458i) q^{11} +(-1.77328 - 0.924916i) q^{12} -2.74185 q^{13} +(-1.10079 - 0.269828i) q^{14} +(2.15140 - 0.609492i) q^{15} +(-2.28906 - 3.28027i) q^{16} +(2.08381 - 2.08381i) q^{17} +(0.733173 + 1.20932i) q^{18} +(5.79168 - 5.79168i) q^{19} +(4.37877 + 0.909061i) q^{20} +(0.566689 + 0.566689i) q^{21} +(-7.07957 - 1.73536i) q^{22} +(-4.28027 - 4.28027i) q^{23} +(0.181602 + 2.82259i) q^{24} +(-4.25704 + 2.62252i) q^{25} +(2.01025 + 3.31578i) q^{26} -1.00000i q^{27} +(0.480760 + 1.52904i) q^{28} +(2.63716 + 2.63716i) q^{29} +(-2.31442 - 2.15487i) q^{30} +8.10909i q^{31} +(-2.28863 + 5.17322i) q^{32} +(3.64458 + 3.64458i) q^{33} +(-4.04778 - 0.992201i) q^{34} +(-1.56457 - 0.873782i) q^{35} +(0.924916 - 1.77328i) q^{36} -2.28428 q^{37} +(-11.2503 - 2.75770i) q^{38} -2.74185i q^{39} +(-2.11105 - 5.96184i) q^{40} -2.27486i q^{41} +(0.269828 - 1.10079i) q^{42} +3.06480 q^{43} +(3.09194 + 9.83379i) q^{44} +(0.609492 + 2.15140i) q^{45} +(-2.03805 + 8.31441i) q^{46} +(-1.80573 - 1.80573i) q^{47} +(3.28027 - 2.28906i) q^{48} +6.35773i q^{49} +(6.29262 + 3.22536i) q^{50} +(2.08381 + 2.08381i) q^{51} +(2.53598 - 4.86207i) q^{52} +6.32215i q^{53} +(-1.20932 + 0.733173i) q^{54} +(-10.0623 - 5.61960i) q^{55} +(1.49662 - 1.70244i) q^{56} +(5.79168 + 5.79168i) q^{57} +(1.25568 - 5.12267i) q^{58} +(5.56839 + 5.56839i) q^{59} +(-0.909061 + 4.37877i) q^{60} +(4.82071 - 4.82071i) q^{61} +(9.80650 - 5.94536i) q^{62} +(-0.566689 + 0.566689i) q^{63} +(7.93404 - 1.02518i) q^{64} +(1.67114 + 5.89881i) q^{65} +(1.73536 - 7.07957i) q^{66} +3.34296 q^{67} +(1.76783 + 5.62252i) q^{68} +(4.28027 - 4.28027i) q^{69} +(0.0904149 + 2.53270i) q^{70} -2.81803 q^{71} +(-2.82259 + 0.181602i) q^{72} +(-10.7052 + 10.7052i) q^{73} +(1.67477 + 2.76243i) q^{74} +(-2.62252 - 4.25704i) q^{75} +(4.91347 + 15.6271i) q^{76} -4.13068i q^{77} +(-3.31578 + 2.01025i) q^{78} +12.1478 q^{79} +(-5.66201 + 6.92399i) q^{80} +1.00000 q^{81} +(-2.75103 + 1.66786i) q^{82} -1.97640i q^{83} +(-1.52904 + 0.480760i) q^{84} +(-5.75316 - 3.21304i) q^{85} +(-2.24703 - 3.70633i) q^{86} +(-2.63716 + 2.63716i) q^{87} +(9.62528 - 10.9490i) q^{88} -10.0322 q^{89} +(2.15487 - 2.31442i) q^{90} +(-1.55378 + 1.55378i) q^{91} +(11.5490 - 3.63124i) q^{92} -8.10909 q^{93} +(-0.859794 + 3.50761i) q^{94} +(-15.9902 - 8.93024i) q^{95} +(-5.17322 - 2.28863i) q^{96} +(-1.02135 + 1.02135i) q^{97} +(7.68853 - 4.66131i) q^{98} +(-3.64458 + 3.64458i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{2} + 8 q^{4} - 8 q^{5} + 2 q^{6} - 4 q^{7} + 8 q^{8} - 16 q^{9}+O(q^{10}) $ 16 * q + 2 * q^2 + 8 * q^4 - 8 * q^5 + 2 * q^6 - 4 * q^7 + 8 * q^8 - 16 * q^9	$ 16 q + 2 q^{2} + 8 q^{4} - 8 q^{5} + 2 q^{6} - 4 q^{7} + 8 q^{8} - 16 q^{9} - 2 q^{10} - 4 q^{12} - 8 q^{13} + 4 q^{14} + 4 q^{15} - 8 q^{16} - 8 q^{17} - 2 q^{18} - 8 q^{19} + 4 q^{20} - 4 q^{21} + 4 q^{24} - 32 q^{25} + 20 q^{26} + 12 q^{28} - 12 q^{29} + 2 q^{30} - 28 q^{32} + 12 q^{35} - 8 q^{36} - 24 q^{37} + 16 q^{38} + 16 q^{40} + 24 q^{42} + 24 q^{43} - 52 q^{44} + 8 q^{45} - 16 q^{46} + 32 q^{47} - 16 q^{48} + 6 q^{50} - 8 q^{51} + 24 q^{52} - 2 q^{54} - 4 q^{55} + 20 q^{56} - 8 q^{57} + 12 q^{58} + 24 q^{59} + 24 q^{60} + 40 q^{61} + 28 q^{62} + 4 q^{63} + 8 q^{64} - 4 q^{65} - 8 q^{66} + 16 q^{67} - 8 q^{68} + 12 q^{70} - 8 q^{72} - 8 q^{73} - 64 q^{74} + 24 q^{75} + 16 q^{76} + 12 q^{78} + 48 q^{79} + 16 q^{81} - 32 q^{82} - 12 q^{84} - 8 q^{85} - 8 q^{86} + 12 q^{87} + 24 q^{88} + 2 q^{90} - 40 q^{91} - 16 q^{92} - 32 q^{93} + 20 q^{94} - 8 q^{95} - 28 q^{96} + 48 q^{97} + 62 q^{98}+O(q^{100}) $ 16 * q + 2 * q^2 + 8 * q^4 - 8 * q^5 + 2 * q^6 - 4 * q^7 + 8 * q^8 - 16 * q^9 - 2 * q^10 - 4 * q^12 - 8 * q^13 + 4 * q^14 + 4 * q^15 - 8 * q^16 - 8 * q^17 - 2 * q^18 - 8 * q^19 + 4 * q^20 - 4 * q^21 + 4 * q^24 - 32 * q^25 + 20 * q^26 + 12 * q^28 - 12 * q^29 + 2 * q^30 - 28 * q^32 + 12 * q^35 - 8 * q^36 - 24 * q^37 + 16 * q^38 + 16 * q^40 + 24 * q^42 + 24 * q^43 - 52 * q^44 + 8 * q^45 - 16 * q^46 + 32 * q^47 - 16 * q^48 + 6 * q^50 - 8 * q^51 + 24 * q^52 - 2 * q^54 - 4 * q^55 + 20 * q^56 - 8 * q^57 + 12 * q^58 + 24 * q^59 + 24 * q^60 + 40 * q^61 + 28 * q^62 + 4 * q^63 + 8 * q^64 - 4 * q^65 - 8 * q^66 + 16 * q^67 - 8 * q^68 + 12 * q^70 - 8 * q^72 - 8 * q^73 - 64 * q^74 + 24 * q^75 + 16 * q^76 + 12 * q^78 + 48 * q^79 + 16 * q^81 - 32 * q^82 - 12 * q^84 - 8 * q^85 - 8 * q^86 + 12 * q^87 + 24 * q^88 + 2 * q^90 - 40 * q^91 - 16 * q^92 - 32 * q^93 + 20 * q^94 - 8 * q^95 - 28 * q^96 + 48 * q^97 + 62 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$181$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.733173	−	1.20932i	−0.518431	−	0.855119i
$2$	−0.733173	−	1.20932i	−0.518431	−	0.855119i
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	−0.924916	+	1.77328i	−0.462458	+	0.886641i
$5$	−0.609492	−	2.15140i	−0.272573	−	0.962135i
$5$	−0.609492	−	2.15140i	−0.272573	−	0.962135i
$6$	1.20932	−	0.733173i	0.493703	−	0.299316i
$7$	0.566689	−	0.566689i	0.214188	−	0.214188i	−0.591856	−	0.806044i	$-0.701604\pi$
$7$	0.566689	−	0.566689i	0.214188	−	0.214188i	0.806044	+	0.591856i	$0.201604\pi$
$8$	2.82259	−	0.181602i	0.997937	−	0.0642061i
$9$	−1.00000			−0.333333
$10$	−2.15487	+	2.31442i	−0.681430	+	0.731884i
$11$	3.64458	−	3.64458i	1.09888	−	1.09888i	0.104339	−	0.994542i	$-0.466727\pi$
$11$	3.64458	−	3.64458i	1.09888	−	1.09888i	0.994542	−	0.104339i	$-0.0332727\pi$
$12$	−1.77328	−	0.924916i	−0.511903	−	0.267000i
$13$	−2.74185			−0.760452			−0.380226	−	0.924894i	$-0.624154\pi$
$13$	−2.74185			−0.760452			−0.380226	+	0.924894i	$0.624154\pi$
$14$	−1.10079	−	0.269828i	−0.294198	−	0.0721146i
$15$	2.15140	−	0.609492i	0.555489	−	0.157370i
$16$	−2.28906	−	3.28027i	−0.572266	−	0.820068i
$17$	2.08381	−	2.08381i	0.505397	−	0.505397i	−0.407713	−	0.913110i	$-0.633674\pi$
$17$	2.08381	−	2.08381i	0.505397	−	0.505397i	0.913110	+	0.407713i	$0.133674\pi$
$18$	0.733173	+	1.20932i	0.172810	+	0.285040i
$19$	5.79168	−	5.79168i	1.32870	−	1.32870i	0.422201	−	0.906502i	$-0.361258\pi$
$19$	5.79168	−	5.79168i	1.32870	−	1.32870i	0.906502	−	0.422201i	$-0.138742\pi$
$20$	4.37877	+	0.909061i	0.979122	+	0.203272i
$21$	0.566689	+	0.566689i	0.123662	+	0.123662i
$22$	−7.07957	−	1.73536i	−1.50937	−	0.369980i
$23$	−4.28027	−	4.28027i	−0.892499	−	0.892499i	0.102259	−	0.994758i	$-0.467393\pi$
$23$	−4.28027	−	4.28027i	−0.892499	−	0.892499i	−0.994758	+	0.102259i	$0.967393\pi$
$24$	0.181602	+	2.82259i	0.0370694	+	0.576159i
$25$	−4.25704	+	2.62252i	−0.851408	+	0.524505i
$26$	2.01025	+	3.31578i	0.394242	+	0.650277i
$27$		−	1.00000i		−	0.192450i
$28$	0.480760	+	1.52904i	0.0908551	+	0.288961i
$29$	2.63716	+	2.63716i	0.489709	+	0.489709i	0.908214	−	0.418506i	$-0.137446\pi$
$29$	2.63716	+	2.63716i	0.489709	+	0.489709i	−0.418506	+	0.908214i	$0.637446\pi$
$30$	−2.31442	−	2.15487i	−0.422553	−	0.393424i
$31$			8.10909i			1.45644i	0.685346	+	0.728218i	$0.259651\pi$
$31$			8.10909i			1.45644i	−0.685346	+	0.728218i	$0.740349\pi$
$32$	−2.28863	+	5.17322i	−0.404576	+	0.914504i
$33$	3.64458	+	3.64458i	0.634439	+	0.634439i
$34$	−4.04778	−	0.992201i	−0.694189	−	0.170161i
$35$	−1.56457	−	0.873782i	−0.264460	−	0.147696i
$36$	0.924916	−	1.77328i	0.154153	−	0.295547i
$37$	−2.28428			−0.375534			−0.187767	−	0.982214i	$-0.560125\pi$
$37$	−2.28428			−0.375534			−0.187767	+	0.982214i	$0.560125\pi$
$38$	−11.2503	−	2.75770i	−1.82504	−	0.447358i
$39$		−	2.74185i		−	0.439047i
$40$	−2.11105	−	5.96184i	−0.333786	−	0.942649i
$41$		−	2.27486i		−	0.355273i	−0.984096	−	0.177637i	$-0.943155\pi$
$41$		−	2.27486i		−	0.355273i	0.984096	−	0.177637i	$-0.0568452\pi$
$42$	0.269828	−	1.10079i	0.0416354	−	0.169856i
$43$	3.06480			0.467378			0.233689	−	0.972311i	$-0.424920\pi$
$43$	3.06480			0.467378			0.233689	+	0.972311i	$0.424920\pi$
$44$	3.09194	+	9.83379i	0.466127	+	1.48250i
$45$	0.609492	+	2.15140i	0.0908578	+	0.320712i
$46$	−2.03805	+	8.31441i	−0.300493	+	1.22589i
$47$	−1.80573	−	1.80573i	−0.263392	−	0.263392i	0.563039	−	0.826431i	$-0.309632\pi$
$47$	−1.80573	−	1.80573i	−0.263392	−	0.263392i	−0.826431	+	0.563039i	$0.809632\pi$
$48$	3.28027	−	2.28906i	0.473467	−	0.330398i
$49$			6.35773i			0.908247i
$50$	6.29262	+	3.22536i	0.889910	+	0.456135i
$51$	2.08381	+	2.08381i	0.291791	+	0.291791i
$52$	2.53598	−	4.86207i	0.351677	−	0.674248i
$53$			6.32215i			0.868415i	0.900813	+	0.434207i	$0.142971\pi$
$53$			6.32215i			0.868415i	−0.900813	+	0.434207i	$0.857029\pi$
$54$	−1.20932	+	0.733173i	−0.164568	+	0.0997722i
$55$	−10.0623	−	5.61960i	−1.35680	−	0.757746i
$56$	1.49662	−	1.70244i	0.199994	−	0.227498i
$57$	5.79168	+	5.79168i	0.767127	+	0.767127i
$58$	1.25568	−	5.12267i	0.164879	−	0.672640i
$59$	5.56839	+	5.56839i	0.724942	+	0.724942i	0.969608	−	0.244665i	$-0.0786780\pi$
$59$	5.56839	+	5.56839i	0.724942	+	0.724942i	−0.244665	+	0.969608i	$0.578678\pi$
$60$	−0.909061	+	4.37877i	−0.117359	+	0.565297i
$61$	4.82071	−	4.82071i	0.617228	−	0.617228i	−0.327591	−	0.944820i	$-0.606237\pi$
$61$	4.82071	−	4.82071i	0.617228	−	0.617228i	0.944820	+	0.327591i	$0.106237\pi$
$62$	9.80650	−	5.94536i	1.24543	−	0.755062i
$63$	−0.566689	+	0.566689i	−0.0713961	+	0.0713961i
$64$	7.93404	−	1.02518i	0.991755	−	0.128147i
$65$	1.67114	+	5.89881i	0.207279	+	0.731658i
$66$	1.73536	−	7.07957i	0.213608	−	0.871434i
$67$	3.34296			0.408407			0.204204	−	0.978928i	$-0.434539\pi$
$67$	3.34296			0.408407			0.204204	+	0.978928i	$0.434539\pi$
$68$	1.76783	+	5.62252i	0.214381	+	0.681831i
$69$	4.28027	−	4.28027i	0.515284	−	0.515284i
$70$	0.0904149	+	2.53270i	0.0108066	+	0.302715i
$71$	−2.81803			−0.334439			−0.167219	−	0.985920i	$-0.553479\pi$
$71$	−2.81803			−0.334439			−0.167219	+	0.985920i	$0.553479\pi$
$72$	−2.82259	+	0.181602i	−0.332646	+	0.0214020i
$73$	−10.7052	+	10.7052i	−1.25295	+	1.25295i	−0.298559	+	0.954391i	$0.596506\pi$
$73$	−10.7052	+	10.7052i	−1.25295	+	1.25295i	−0.954391	+	0.298559i	$0.903494\pi$
$74$	1.67477	+	2.76243i	0.194688	+	0.321126i
$75$	−2.62252	−	4.25704i	−0.302823	−	0.491560i
$76$	4.91347	+	15.6271i	0.563614	+	1.79255i
$77$		−	4.13068i		−	0.470735i
$78$	−3.31578	+	2.01025i	−0.375438	+	0.227616i
$79$	12.1478			1.36673			0.683367	−	0.730075i	$-0.260515\pi$
$79$	12.1478			1.36673			0.683367	+	0.730075i	$0.260515\pi$
$80$	−5.66201	+	6.92399i	−0.633032	+	0.774125i
$81$	1.00000			0.111111
$82$	−2.75103	+	1.66786i	−0.303801	+	0.184185i
$83$		−	1.97640i		−	0.216938i	−0.994100	−	0.108469i	$-0.965405\pi$
$83$		−	1.97640i		−	0.216938i	0.994100	−	0.108469i	$-0.0345948\pi$
$84$	−1.52904	+	0.480760i	−0.166832	+	0.0524552i
$85$	−5.75316	−	3.21304i	−0.624018	−	0.348503i
$86$	−2.24703	−	3.70633i	−0.242303	−	0.399664i
$87$	−2.63716	+	2.63716i	−0.282733	+	0.282733i
$88$	9.62528	−	10.9490i	1.02606	−	1.16717i
$89$	−10.0322			−1.06341			−0.531706	−	0.846929i	$-0.678449\pi$
$89$	−10.0322			−1.06341			−0.531706	+	0.846929i	$0.678449\pi$
$90$	2.15487	−	2.31442i	0.227143	−	0.243961i
$91$	−1.55378	+	1.55378i	−0.162880	+	0.162880i
$92$	11.5490	−	3.63124i	1.20407	−	0.378583i
$93$	−8.10909			−0.840874
$94$	−0.859794	+	3.50761i	−0.0886809	+	0.361782i
$95$	−15.9902	−	8.93024i	−1.64056	−	0.916223i
$96$	−5.17322	−	2.28863i	−0.527989	−	0.233582i
$97$	−1.02135	+	1.02135i	−0.103702	+	0.103702i	−0.757054	−	0.653352i	$-0.773362\pi$
$97$	−1.02135	+	1.02135i	−0.103702	+	0.103702i	0.653352	+	0.757054i	$0.273362\pi$
$98$	7.68853	−	4.66131i	0.776659	−	0.470864i
$99$	−3.64458	+	3.64458i	−0.366294	+	0.366294i
$100$	−0.713073	−	9.97454i	−0.0713073	−	0.997454i
$101$	−13.1932	−	13.1932i	−1.31277	−	1.31277i	−0.919362	−	0.393412i	$-0.871295\pi$
$101$	−13.1932	−	13.1932i	−1.31277	−	1.31277i	−0.393412	−	0.919362i	$-0.628705\pi$
$102$	0.992201	−	4.04778i	0.0982426	−	0.400790i
$103$	4.51726	+	4.51726i	0.445099	+	0.445099i	0.893721	−	0.448623i	$-0.148085\pi$
$103$	4.51726	+	4.51726i	0.445099	+	0.445099i	−0.448623	+	0.893721i	$0.648085\pi$
$104$	−7.73912	+	0.497926i	−0.758883	+	0.0488257i
$105$	0.873782	−	1.56457i	0.0852723	−	0.152686i
$106$	7.64551	−	4.63523i	0.742598	−	0.450213i
$107$		−	3.88249i		−	0.375334i	−0.982233	−	0.187667i	$-0.939907\pi$
$107$		−	3.88249i		−	0.375334i	0.982233	−	0.187667i	$-0.0600926\pi$
$108$	1.77328	+	0.924916i	0.170634	+	0.0890000i
$109$	2.51614	+	2.51614i	0.241003	+	0.241003i	0.817265	−	0.576262i	$-0.195489\pi$
$109$	2.51614	+	2.51614i	0.241003	+	0.241003i	−0.576262	+	0.817265i	$0.695489\pi$
$110$	0.581490	+	16.2887i	0.0554429	+	1.55306i
$111$		−	2.28428i		−	0.216815i
$112$	−3.15608	−	0.561708i	−0.298222	−	0.0530765i
$113$	−3.89520	−	3.89520i	−0.366429	−	0.366429i	0.499744	−	0.866173i	$-0.333427\pi$
$113$	−3.89520	−	3.89520i	−0.366429	−	0.366429i	−0.866173	+	0.499744i	$0.833427\pi$
$114$	2.75770	−	11.2503i	0.258282	−	1.05369i
$115$	−6.59978	+	11.8174i	−0.615433	+	1.10198i
$116$	−7.11559	+	2.23728i	−0.660666	+	0.207726i
$117$	2.74185			0.253484
$118$	2.65138	−	10.8166i	0.244079	−	0.995745i
$119$		−	2.36174i		−	0.216500i
$120$	5.96184	−	2.11105i	0.544239	−	0.192711i
$121$		−	15.5659i		−	1.41508i
$122$	−9.36420	−	2.29537i	−0.847795	−	0.207813i
$123$	2.27486			0.205117
$124$	−14.3797	−	7.50023i	−1.29134	−	0.673540i
$125$	8.23673	+	7.56018i	0.736715	+	0.676203i
$126$	1.10079	+	0.269828i	0.0980661	+	0.0240382i
$127$	3.11993	+	3.11993i	0.276849	+	0.276849i	0.831850	−	0.555001i	$-0.187282\pi$
$127$	3.11993	+	3.11993i	0.276849	+	0.276849i	−0.555001	+	0.831850i	$0.687282\pi$
$128$	−7.05679	−	8.84317i	−0.623738	−	0.781633i
$129$			3.06480i			0.269841i
$130$	5.90833	−	6.34579i	0.518195	−	0.556563i
$131$	−8.69631	−	8.69631i	−0.759800	−	0.759800i	0.216486	−	0.976286i	$-0.430541\pi$
$131$	−8.69631	−	8.69631i	−0.759800	−	0.759800i	−0.976286	+	0.216486i	$0.930541\pi$
$132$	−9.83379	+	3.09194i	−0.855921	+	0.269119i
$133$		−	6.56416i		−	0.569185i
$134$	−2.45097	−	4.04271i	−0.211731	−	0.349237i
$135$	−2.15140	+	0.609492i	−0.185163	+	0.0524567i
$136$	5.50331	−	6.26016i	0.471905	−	0.536804i
$137$	16.1963	+	16.1963i	1.38375	+	1.38375i	0.837856	+	0.545891i	$0.183809\pi$
$137$	16.1963	+	16.1963i	1.38375	+	1.38375i	0.545891	+	0.837856i	$0.316191\pi$
$138$	−8.31441	−	2.03805i	−0.707769	−	0.173490i
$139$	10.8859	+	10.8859i	0.923329	+	0.923329i	0.997263	−	0.0739337i	$-0.0235553\pi$
$139$	10.8859	+	10.8859i	0.923329	+	0.923329i	−0.0739337	+	0.997263i	$0.523555\pi$
$140$	2.99655	−	1.96624i	0.253255	−	0.166178i
$141$	1.80573	−	1.80573i	0.152070	−	0.152070i
$142$	2.06610	+	3.40790i	0.173383	+	0.285985i
$143$	−9.99288	+	9.99288i	−0.835646	+	0.835646i
$144$	2.28906	+	3.28027i	0.190755	+	0.273356i
$145$	4.06626	−	7.28092i	0.337684	−	0.604647i
$146$	20.7948	+	5.09727i	1.72099	+	0.421853i
$147$	−6.35773			−0.524377
$148$	2.11277	−	4.05068i	0.173669	−	0.332964i
$149$	−8.06960	+	8.06960i	−0.661088	+	0.661088i	−0.955636	−	0.294549i	$-0.904831\pi$
$149$	−8.06960	+	8.06960i	−0.661088	+	0.661088i	0.294549	+	0.955636i	$0.404831\pi$
$150$	−3.22536	+	6.29262i	−0.263350	+	0.513790i
$151$	10.9071			0.887609			0.443804	−	0.896124i	$-0.353628\pi$
$151$	10.9071			0.887609			0.443804	+	0.896124i	$0.353628\pi$
$152$	15.2958	−	17.3993i	1.24065	−	1.41127i
$153$	−2.08381	+	2.08381i	−0.168466	+	0.168466i
$154$	−4.99532	+	3.02850i	−0.402534	+	0.244044i
$155$	17.4459	−	4.94243i	1.40129	−	0.396985i
$156$	4.86207	+	2.53598i	0.389277	+	0.203041i
$157$		−	14.0713i		−	1.12301i	−0.827472	−	0.561507i	$-0.810222\pi$
$157$		−	14.0713i		−	1.12301i	0.827472	−	0.561507i	$-0.189778\pi$
$158$	−8.90644	−	14.6906i	−0.708558	−	1.16872i
$159$	−6.32215			−0.501379
$160$	12.5246	+	1.77071i	0.990153	+	0.139987i
$161$	−4.85117			−0.382325
$162$	−0.733173	−	1.20932i	−0.0576035	−	0.0950132i
$163$			2.82750i			0.221467i	0.993850	+	0.110734i	$0.0353200\pi$
$163$			2.82750i			0.221467i	−0.993850	+	0.110734i	$0.964680\pi$
$164$	4.03397	+	2.10405i	0.315000	+	0.164299i
$165$	5.61960	−	10.0623i	0.437485	−	0.783347i
$166$	−2.39010	+	1.44904i	−0.185508	+	0.112468i
$167$	−5.12509	+	5.12509i	−0.396591	+	0.396591i	−0.877029	−	0.480438i	$-0.840478\pi$
$167$	−5.12509	+	5.12509i	−0.396591	+	0.396591i	0.480438	+	0.877029i	$0.340478\pi$
$168$	1.70244	+	1.49662i	0.131346	+	0.115467i
$169$	−5.48226			−0.421712
$170$	0.332470	+	9.31313i	0.0254993	+	0.714285i
$171$	−5.79168	+	5.79168i	−0.442901	+	0.442901i
$172$	−2.83468	+	5.43476i	−0.216143	+	0.414396i
$173$	4.60016			0.349743			0.174872	−	0.984591i	$-0.444049\pi$
$173$	4.60016			0.349743			0.174872	+	0.984591i	$0.444049\pi$
$174$	5.12267	+	1.25568i	0.388349	+	0.0951929i
$175$	−0.926262	+	3.89857i	−0.0700188	+	0.294704i
$176$	−20.2979	−	3.61254i	−1.53001	−	0.272306i
$177$	−5.56839	+	5.56839i	−0.418546	+	0.418546i
$178$	7.35534	+	12.1322i	0.551306	+	0.909343i
$179$	3.06396	−	3.06396i	0.229011	−	0.229011i	−0.583268	−	0.812280i	$-0.698226\pi$
$179$	3.06396	−	3.06396i	0.229011	−	0.229011i	0.812280	+	0.583268i	$0.198226\pi$
$180$	−4.37877	−	0.909061i	−0.326374	−	0.0677574i
$181$	−3.08559	−	3.08559i	−0.229350	−	0.229350i	0.583071	−	0.812421i	$-0.301851\pi$
$181$	−3.08559	−	3.08559i	−0.229350	−	0.229350i	−0.812421	+	0.583071i	$0.801851\pi$
$182$	3.01820	+	0.739828i	0.223724	+	0.0548397i
$183$	4.82071	+	4.82071i	0.356357	+	0.356357i
$184$	−12.8588	−	11.3042i	−0.947961	−	0.833353i
$185$	1.39225	+	4.91440i	0.102360	+	0.361314i
$186$	5.94536	+	9.80650i	0.435935	+	0.719047i
$187$		−	15.1892i		−	1.11074i
$188$	4.87221	−	1.53192i	0.355342	−	0.111727i
$189$	−0.566689	−	0.566689i	−0.0412205	−	0.0412205i
$190$	0.924060	+	25.8847i	0.0670383	+	1.87787i
$191$			21.0908i			1.52608i	0.646353	+	0.763038i	$0.276293\pi$
$191$			21.0908i			1.52608i	−0.646353	+	0.763038i	$0.723707\pi$
$192$	1.02518	+	7.93404i	0.0739858	+	0.572590i
$193$	15.2332	+	15.2332i	1.09651	+	1.09651i	0.994816	+	0.101692i	$0.0324255\pi$
$193$	15.2332	+	15.2332i	1.09651	+	1.09651i	0.101692	+	0.994816i	$0.467574\pi$
$194$	1.98396	+	0.486314i	0.142440	+	0.0349153i
$195$	−5.89881	+	1.67114i	−0.422423	+	0.119673i
$196$	−11.2740	−	5.88036i	−0.805289	−	0.420026i
$197$	14.0460			1.00073			0.500367	−	0.865814i	$-0.333199\pi$
$197$	14.0460			1.00073			0.500367	+	0.865814i	$0.333199\pi$
$198$	7.07957	+	1.73536i	0.503123	+	0.123327i
$199$		−	2.42066i		−	0.171596i	−0.996313	−	0.0857978i	$-0.972656\pi$
$199$		−	2.42066i		−	0.171596i	0.996313	−	0.0857978i	$-0.0273439\pi$
$200$	−11.5396	+	8.17540i	−0.815975	+	0.578088i
$201$			3.34296i			0.235794i
$202$	−6.28193	+	25.6277i	−0.441995	+	1.80316i
$203$	2.98890			0.209780
$204$	−5.62252	+	1.76783i	−0.393655	+	0.123773i
$205$	−4.89413	+	1.38651i	−0.341821	+	0.0968380i
$206$	2.15089	−	8.77474i	0.149859	−	0.611365i
$207$	4.28027	+	4.28027i	0.297500	+	0.297500i
$208$	6.27626	+	8.99402i	0.435181	+	0.623623i
$209$		−	42.2164i		−	2.92017i
$210$	−2.53270	+	0.0904149i	−0.174773	+	0.00623922i
$211$	5.18795	+	5.18795i	0.357153	+	0.357153i	0.862762	−	0.505609i	$-0.168732\pi$
$211$	5.18795	+	5.18795i	0.357153	+	0.357153i	−0.505609	+	0.862762i	$0.668732\pi$
$212$	−11.2110	−	5.84746i	−0.769972	−	0.401605i
$213$		−	2.81803i		−	0.193088i
$214$	−4.69518	+	2.84653i	−0.320956	+	0.194585i
$215$	−1.86797	−	6.59361i	−0.127395	−	0.449681i
$216$	−0.181602	−	2.82259i	−0.0123565	−	0.192053i
$217$	4.59533	+	4.59533i	0.311951	+	0.311951i
$218$	1.19806	−	4.88759i	0.0811427	−	0.331029i
$219$	−10.7052	−	10.7052i	−0.723391	−	0.723391i
$220$	19.2719	−	12.6456i	1.29931	−	0.852567i
$221$	−5.71348	+	5.71348i	−0.384331	+	0.384331i
$222$	−2.76243	+	1.67477i	−0.185402	+	0.112403i
$223$	11.3379	−	11.3379i	0.759240	−	0.759240i	−0.216944	−	0.976184i	$-0.569609\pi$
$223$	11.3379	−	11.3379i	0.759240	−	0.759240i	0.976184	+	0.216944i	$0.0696089\pi$
$224$	1.63467	+	4.22854i	0.109221	+	0.282532i
$225$	4.25704	−	2.62252i	0.283803	−	0.174835i
$226$	−1.85469	+	7.56640i	−0.123372	+	0.503309i
$227$	19.8951			1.32049			0.660243	−	0.751052i	$-0.270453\pi$
$227$	19.8951			1.32049			0.660243	+	0.751052i	$0.270453\pi$
$228$	−15.6271	+	4.91347i	−1.03493	+	0.325403i
$229$	14.1933	−	14.1933i	0.937918	−	0.937918i	−0.0602643	−	0.998182i	$-0.519194\pi$
$229$	14.1933	−	14.1933i	0.937918	−	0.937918i	0.998182	+	0.0602643i	$0.0191943\pi$
$230$	19.1298	−	0.682915i	1.26138	−	0.0450301i
$231$	4.13068			0.271779
$232$	7.92255	+	6.96472i	0.520141	+	0.457256i
$233$	13.9475	−	13.9475i	0.913734	−	0.913734i	−0.0828295	−	0.996564i	$-0.526396\pi$
$233$	13.9475	−	13.9475i	0.913734	−	0.913734i	0.996564	+	0.0828295i	$0.0263957\pi$
$234$	−2.01025	−	3.31578i	−0.131414	−	0.216759i
$235$	−2.78426	+	4.98541i	−0.181625	+	0.325212i
$236$	−15.0246	+	4.72404i	−0.978019	+	0.307509i
$237$			12.1478i			0.789085i
$238$	−2.85610	+	1.73156i	−0.185134	+	0.112241i
$239$	−16.4452			−1.06375			−0.531876	−	0.846822i	$-0.678513\pi$
$239$	−16.4452			−1.06375			−0.531876	+	0.846822i	$0.678513\pi$
$240$	−6.92399	−	5.66201i	−0.446942	−	0.365481i
$241$	−4.70995			−0.303394			−0.151697	−	0.988427i	$-0.548474\pi$
$241$	−4.70995			−0.303394			−0.151697	+	0.988427i	$0.548474\pi$
$242$	−18.8241	+	11.4125i	−1.21006	+	0.733621i
$243$			1.00000i			0.0641500i
$244$	4.08973	+	13.0072i	0.261818	+	0.832702i
$245$	13.6780	−	3.87499i	0.873856	−	0.247564i
$246$	−1.66786	−	2.75103i	−0.106339	−	0.175400i
$247$	−15.8799	+	15.8799i	−1.01042	+	1.01042i
$248$	1.47263	+	22.8887i	0.0935121	+	1.45343i
$249$	1.97640			0.125249
$250$	3.10375	−	15.5038i	0.196298	−	0.980544i
$251$	−14.6935	+	14.6935i	−0.927448	+	0.927448i	−0.997541	−	0.0700924i	$-0.977671\pi$
$251$	−14.6935	+	14.6935i	−0.927448	+	0.927448i	0.0700924	+	0.997541i	$0.477671\pi$
$252$	−0.480760	−	1.52904i	−0.0302850	−	0.0963204i
$253$	−31.1996			−1.96150
$254$	1.48555	−	6.06045i	0.0932117	−	0.380266i
$255$	3.21304	−	5.75316i	0.201208	−	0.360277i
$256$	−5.52039	+	15.0175i	−0.345024	+	0.938594i
$257$	5.02979	−	5.02979i	0.313750	−	0.313750i	−0.532611	−	0.846360i	$-0.678789\pi$
$257$	5.02979	−	5.02979i	0.313750	−	0.313750i	0.846360	+	0.532611i	$0.178789\pi$
$258$	3.70633	−	2.24703i	0.230746	−	0.139894i
$259$	−1.29448	+	1.29448i	−0.0804349	+	0.0804349i
$260$	−12.0059	−	2.49251i	−0.744576	−	0.154579i
$261$	−2.63716	−	2.63716i	−0.163236	−	0.163236i
$262$	−4.14073	+	16.8925i	−0.255815	+	1.04362i
$263$	8.84851	+	8.84851i	0.545622	+	0.545622i	0.925172	−	0.379549i	$-0.123921\pi$
$263$	8.84851	+	8.84851i	0.545622	+	0.545622i	−0.379549	+	0.925172i	$0.623921\pi$
$264$	10.9490	+	9.62528i	0.673865	+	0.592395i
$265$	13.6015	−	3.85330i	0.835532	−	0.236707i
$266$	−7.93818	+	4.81267i	−0.486721	+	0.295083i
$267$		−	10.0322i		−	0.613961i
$268$	−3.09196	+	5.92801i	−0.188871	+	0.362111i
$269$	4.66057	+	4.66057i	0.284160	+	0.284160i	0.834766	−	0.550605i	$-0.185603\pi$
$269$	4.66057	+	4.66057i	0.284160	+	0.284160i	−0.550605	+	0.834766i	$0.685603\pi$
$270$	2.31442	+	2.15487i	0.140851	+	0.131141i
$271$		−	3.87643i		−	0.235477i	−0.993045	−	0.117738i	$-0.962436\pi$
$271$		−	3.87643i		−	0.235477i	0.993045	−	0.117738i	$-0.0375644\pi$
$272$	−11.6054	−	2.06549i	−0.703682	−	0.125239i
$273$	−1.55378	−	1.55378i	−0.0940388	−	0.0940388i
$274$	7.71187	−	31.4613i	0.465891	−	1.90065i
$275$	−5.95712	+	25.0731i	−0.359228	+	1.51196i
$276$	3.63124	+	11.5490i	0.218575	+	0.695170i
$277$	−14.6951			−0.882941			−0.441471	−	0.897276i	$-0.645543\pi$
$277$	−14.6951			−0.882941			−0.441471	+	0.897276i	$0.645543\pi$
$278$	5.18330	−	21.1458i	0.310874	−	1.26824i
$279$		−	8.10909i		−	0.485479i
$280$	−4.57481	−	2.18220i	−0.273397	−	0.130411i
$281$		−	0.328587i		−	0.0196019i	−0.999952	−	0.00980093i	$-0.996880\pi$
$281$		−	0.328587i		−	0.0196019i	0.999952	−	0.00980093i	$-0.00311978\pi$
$282$	−3.50761	−	0.859794i	−0.208875	−	0.0512000i
$283$	−22.9890			−1.36656			−0.683278	−	0.730158i	$-0.739446\pi$
$283$	−22.9890			−1.36656			−0.683278	+	0.730158i	$0.739446\pi$
$284$	2.60644	−	4.99716i	0.154664	−	0.296527i
$285$	8.93024	−	15.9902i	0.528981	−	0.947178i
$286$	19.4111	+	4.75809i	1.14780	+	0.281352i
$287$	−1.28914	−	1.28914i	−0.0760953	−	0.0760953i
$288$	2.28863	−	5.17322i	0.134859	−	0.304835i
$289$			8.31550i			0.489147i
$290$	−11.7862	+	0.420758i	−0.692112	+	0.0247078i
$291$	−1.02135	−	1.02135i	−0.0598725	−	0.0598725i
$292$	−9.08195	−	28.8848i	−0.531481	−	1.69035i
$293$			22.0162i			1.28620i	0.765781	+	0.643101i	$0.222352\pi$
$293$			22.0162i			1.28620i	−0.765781	+	0.643101i	$0.777648\pi$
$294$	4.66131	+	7.68853i	0.271853	+	0.448404i
$295$	8.58594	−	15.3737i	0.499893	−	0.895092i
$296$	−6.44760	+	0.414831i	−0.374759	+	0.0241116i
$297$	−3.64458	−	3.64458i	−0.211480	−	0.211480i
$298$	15.6752	+	3.84233i	0.908037	+	0.222580i
$299$	11.7359	+	11.7359i	0.678703	+	0.678703i
$300$	9.97454	−	0.713073i	0.575881	−	0.0411693i
$301$	1.73679	−	1.73679i	0.100107	−	0.100107i
$302$	−7.99680	−	13.1902i	−0.460164	−	0.759011i
$303$	13.1932	−	13.1932i	0.757931	−	0.757931i
$304$	−32.2558	−	5.74078i	−1.85000	−	0.329256i
$305$	−13.3095	−	7.43308i	−0.762097	−	0.425617i
$306$	4.04778	+	0.992201i	0.231396	+	0.0567204i
$307$	−3.08698			−0.176183			−0.0880916	−	0.996112i	$-0.528077\pi$
$307$	−3.08698			−0.176183			−0.0880916	+	0.996112i	$0.528077\pi$
$308$	7.32486	+	3.82053i	0.417373	+	0.217695i
$309$	−4.51726	+	4.51726i	−0.256978	+	0.256978i
$310$	−18.7678	−	17.4740i	−1.06594	−	0.992459i
$311$	24.3682			1.38179			0.690897	−	0.722953i	$-0.257216\pi$
$311$	24.3682			1.38179			0.690897	+	0.722953i	$0.257216\pi$
$312$	−0.497926	−	7.73912i	−0.0281895	−	0.438141i
$313$	3.31911	−	3.31911i	0.187607	−	0.187607i	−0.607054	−	0.794661i	$-0.707649\pi$
$313$	3.31911	−	3.31911i	0.187607	−	0.187607i	0.794661	+	0.607054i	$0.207649\pi$
$314$	−17.0168	+	10.3167i	−0.960311	+	0.582206i
$315$	1.56457	+	0.873782i	0.0881533	+	0.0492320i
$316$	−11.2357	+	21.5415i	−0.632057	+	1.21180i
$317$		−	5.35749i		−	0.300907i	−0.988617	−	0.150453i	$-0.951927\pi$
$317$		−	5.35749i		−	0.300907i	0.988617	−	0.150453i	$-0.0480733\pi$
$318$	4.63523	+	7.64551i	0.259931	+	0.428739i
$319$	19.2227			1.07626
$320$	−7.04130	−	16.4445i	−0.393621	−	0.919273i
$321$	3.88249			0.216699
$322$	3.55674	+	5.86662i	0.198210	+	0.326934i
$323$		−	24.1375i		−	1.34305i
$324$	−0.924916	+	1.77328i	−0.0513842	+	0.0985157i
$325$	11.6722	−	7.19056i	0.647455	−	0.398861i
$326$	3.41936	−	2.07305i	0.189381	−	0.114816i
$327$	−2.51614	+	2.51614i	−0.139143	+	0.139143i
$328$	−0.413119	−	6.42099i	−0.0228107	−	0.354540i
$329$	−2.04657			−0.112831
$330$	−16.2887	+	0.581490i	−0.896661	+	0.0320100i
$331$	−2.76903	+	2.76903i	−0.152200	+	0.152200i	−0.779100	−	0.626900i	$-0.784323\pi$
$331$	−2.76903	+	2.76903i	−0.152200	+	0.152200i	0.626900	+	0.779100i	$0.284323\pi$
$332$	3.50472	+	1.82800i	0.192346	+	0.100325i
$333$	2.28428			0.125178
$334$	9.95545	+	2.44030i	0.544738	+	0.133527i
$335$	−2.03751	−	7.19204i	−0.111321	−	0.392943i
$336$	0.561708	−	3.15608i	0.0306437	−	0.172178i
$337$	−7.30028	+	7.30028i	−0.397672	+	0.397672i	−0.877411	−	0.479739i	$-0.840731\pi$
$337$	−7.30028	+	7.30028i	−0.397672	+	0.397672i	0.479739	+	0.877411i	$0.340731\pi$
$338$	4.01944	+	6.62981i	0.218629	+	0.360614i
$339$	3.89520	−	3.89520i	0.211558	−	0.211558i
$340$	11.0188	−	7.23020i	0.597579	−	0.392113i
$341$	29.5542	+	29.5542i	1.60045	+	1.60045i
$342$	11.2503	+	2.75770i	0.608347	+	0.149119i
$343$	7.56968	+	7.56968i	0.408724	+	0.408724i
$344$	8.65068	−	0.556575i	0.466413	−	0.0300085i
$345$	−11.8174	−	6.59978i	−0.636226	−	0.355320i
$346$	−3.37271	−	5.56307i	−0.181318	−	0.299072i
$347$			17.0824i			0.917032i	0.888686	+	0.458516i	$0.151619\pi$
$347$			17.0824i			0.917032i	−0.888686	+	0.458516i	$0.848381\pi$
$348$	−2.23728	−	7.11559i	−0.119931	−	0.381435i
$349$	−1.38113	−	1.38113i	−0.0739302	−	0.0739302i	0.669175	−	0.743105i	$-0.266648\pi$
$349$	−1.38113	−	1.38113i	−0.0739302	−	0.0739302i	−0.743105	+	0.669175i	$0.766648\pi$
$350$	5.39373	−	1.73818i	0.288307	−	0.0929095i
$351$			2.74185i			0.146349i
$352$	10.5131	+	27.1953i	0.560351	+	1.44951i
$353$	−6.69565	−	6.69565i	−0.356373	−	0.356373i	0.506101	−	0.862474i	$-0.331086\pi$
$353$	−6.69565	−	6.69565i	−0.356373	−	0.356373i	−0.862474	+	0.506101i	$0.831086\pi$
$354$	10.8166	+	2.65138i	0.574894	+	0.140919i
$355$	1.71757	+	6.06271i	0.0911590	+	0.321775i
$356$	9.27894	−	17.7899i	0.491783	−	0.942864i
$357$	2.36174			0.124997
$358$	−5.95173	−	1.45890i	−0.314559	−	0.0771054i
$359$			1.90946i			0.100777i	0.998730	+	0.0503886i	$0.0160460\pi$
$359$			1.90946i			0.100777i	−0.998730	+	0.0503886i	$0.983954\pi$
$360$	2.11105	+	5.96184i	0.111262	+	0.314216i
$361$		−	48.0872i		−	2.53090i
$362$	−1.46920	+	5.99374i	−0.0772194	+	0.315024i
$363$	15.5659			0.816996
$364$	−1.31817	−	4.19239i	−0.0690910	−	0.219741i
$365$	29.5559	+	16.5064i	1.54703	+	0.863986i
$366$	2.29537	−	9.36420i	0.119981	−	0.489474i
$367$	−20.2767	−	20.2767i	−1.05844	−	1.05844i	−0.998183	−	0.0602537i	$-0.980809\pi$
$367$	−20.2767	−	20.2767i	−1.05844	−	1.05844i	−0.0602537	−	0.998183i	$-0.519191\pi$
$368$	−4.24266	+	23.8383i	−0.221164	+	1.24266i
$369$			2.27486i			0.118424i
$370$	4.92233	−	5.28679i	0.255900	−	0.274847i
$371$	3.58269	+	3.58269i	0.186004	+	0.186004i
$372$	7.50023	−	14.3797i	0.388869	−	0.745553i
$373$			34.5736i			1.79015i	0.445914	+	0.895076i	$0.352879\pi$
$373$			34.5736i			1.79015i	−0.445914	+	0.895076i	$0.647121\pi$
$374$	−18.3686	+	11.1363i	−0.949818	+	0.575844i
$375$	−7.56018	+	8.23673i	−0.390406	+	0.425343i
$376$	−5.42475	−	4.76890i	−0.279760	−	0.245937i
$377$	−7.23070	−	7.23070i	−0.372400	−	0.372400i
$378$	−0.269828	+	1.10079i	−0.0138785	+	0.0566185i
$379$	−21.2172	−	21.2172i	−1.08986	−	1.08986i	−0.995543	−	0.0943133i	$-0.969934\pi$
$379$	−21.2172	−	21.2172i	−1.08986	−	1.08986i	−0.0943133	−	0.995543i	$-0.530066\pi$
$380$	30.6254	−	20.0954i	1.57105	−	1.03087i
$381$	−3.11993	+	3.11993i	−0.159839	+	0.159839i
$382$	25.5056	−	15.4632i	1.30498	−	0.791166i
$383$	−3.13204	+	3.13204i	−0.160040	+	0.160040i	−0.782584	−	0.622544i	$-0.786099\pi$
$383$	−3.13204	+	3.13204i	−0.160040	+	0.160040i	0.622544	+	0.782584i	$0.286099\pi$
$384$	8.84317	−	7.05679i	0.451276	−	0.360115i
$385$	−8.88674	+	2.51762i	−0.452910	+	0.128310i
$386$	7.25325	−	29.5903i	0.369181	−	1.50611i
$387$	−3.06480			−0.155793
$388$	−0.866478	−	2.75580i	−0.0439888	−	0.139905i
$389$	−15.2777	+	15.2777i	−0.774610	+	0.774610i	−0.978909	−	0.204299i	$-0.934509\pi$
$389$	−15.2777	+	15.2777i	−0.774610	+	0.774610i	0.204299	+	0.978909i	$0.434509\pi$
$390$	6.34579	+	5.90833i	0.321332	+	0.299180i
$391$	−17.8385			−0.902133
$392$	1.15458	+	17.9453i	0.0583150	+	0.906373i
$393$	8.69631	−	8.69631i	0.438671	−	0.438671i
$394$	−10.2981	−	16.9861i	−0.518811	−	0.855746i
$395$	−7.40399	−	26.1348i	−0.372535	−	1.31498i
$396$	−3.09194	−	9.83379i	−0.155376	−	0.494166i
$397$		−	9.39676i		−	0.471610i	−0.971800	−	0.235805i	$-0.924227\pi$
$397$		−	9.39676i		−	0.471610i	0.971800	−	0.235805i	$-0.0757726\pi$
$398$	−2.92735	+	1.77476i	−0.146735	+	0.0889606i
$399$	6.56416			0.328619
$400$	18.3472	+	7.96113i	0.917361	+	0.398057i
$401$	0.722171			0.0360635			0.0180317	−	0.999837i	$-0.494260\pi$
$401$	0.722171			0.0360635			0.0180317	+	0.999837i	$0.494260\pi$
$402$	4.04271	−	2.45097i	0.201632	−	0.122243i
$403$		−	22.2339i		−	1.10755i
$404$	35.5979	−	11.1927i	1.77106	−	0.556857i
$405$	−0.609492	−	2.15140i	−0.0302859	−	0.106904i
$406$	−2.19138	−	3.61454i	−0.108756	−	0.179387i
$407$	−8.32524	+	8.32524i	−0.412667	+	0.412667i
$408$	6.26016	+	5.50331i	0.309924	+	0.272454i
$409$	−20.7860			−1.02780			−0.513900	−	0.857850i	$-0.671800\pi$
$409$	−20.7860			−1.02780			−0.513900	+	0.857850i	$0.671800\pi$
$410$	5.26498	+	4.90202i	0.260019	+	0.242094i
$411$	−16.1963	+	16.1963i	−0.798907	+	0.798907i
$412$	−12.1885	+	3.83229i	−0.600482	+	0.188803i
$413$	6.31109			0.310548
$414$	2.03805	−	8.31441i	0.100164	−	0.408631i
$415$	−4.25203	+	1.20460i	−0.208724	+	0.0591315i
$416$	6.27507	−	14.1842i	0.307661	−	0.695437i
$417$	−10.8859	+	10.8859i	−0.533085	+	0.533085i
$418$	−51.0532	+	30.9519i	−2.49710	+	1.51391i
$419$	6.25484	−	6.25484i	0.305569	−	0.305569i	−0.537619	−	0.843188i	$-0.680676\pi$
$419$	6.25484	−	6.25484i	0.305569	−	0.305569i	0.843188	+	0.537619i	$0.180676\pi$
$420$	1.96624	+	2.99655i	0.0959429	+	0.146217i
$421$	16.2076	+	16.2076i	0.789909	+	0.789909i	0.981479	−	0.191570i	$-0.0613580\pi$
$421$	16.2076	+	16.2076i	0.789909	+	0.789909i	−0.191570	+	0.981479i	$0.561358\pi$
$422$	2.47023	−	10.0776i	0.120249	−	0.490568i
$423$	1.80573	+	1.80573i	0.0877974	+	0.0877974i
$424$	1.14812	+	17.8449i	0.0557575	+	0.866623i
$425$	−3.40601	+	14.3357i	−0.165216	+	0.695382i
$426$	−3.40790	+	2.06610i	−0.165113	+	0.100103i
$427$		−	5.46368i		−	0.264406i
$428$	6.88475	+	3.59097i	0.332787	+	0.173576i
$429$	−9.99288	−	9.99288i	−0.482461	−	0.482461i
$430$	−6.60425	+	7.09323i	−0.318485	+	0.342066i
$431$		−	16.1416i		−	0.777512i	−0.921341	−	0.388756i	$-0.872905\pi$
$431$		−	16.1416i		−	0.777512i	0.921341	−	0.388756i	$-0.127095\pi$
$432$	−3.28027	+	2.28906i	−0.157822	+	0.110133i
$433$	−23.9381	−	23.9381i	−1.15039	−	1.15039i	−0.986474	−	0.163919i	$-0.947586\pi$
$433$	−23.9381	−	23.9381i	−1.15039	−	1.15039i	−0.163919	−	0.986474i	$-0.552414\pi$
$434$	2.18806	−	8.92640i	0.105030	−	0.428481i
$435$	7.28092	+	4.06626i	0.349093	+	0.194962i
$436$	−6.78905	+	2.13461i	−0.325136	+	0.102229i
$437$	−49.5800			−2.37173
$438$	−5.09727	+	20.7948i	−0.243557	+	0.993614i
$439$			13.2194i			0.630927i	0.948938	+	0.315464i	$0.102160\pi$
$439$			13.2194i			0.630927i	−0.948938	+	0.315464i	$0.897840\pi$
$440$	−29.4222	−	14.0345i	−1.40265	−	0.669068i
$441$		−	6.35773i		−	0.302749i
$442$	11.0984	+	2.72047i	0.527897	+	0.129399i
$443$	−7.03868			−0.334418			−0.167209	−	0.985921i	$-0.553475\pi$
$443$	−7.03868			−0.334418			−0.167209	+	0.985921i	$0.553475\pi$
$444$	4.05068	+	2.11277i	0.192237	+	0.100268i
$445$	6.11455	+	21.5833i	0.289857	+	1.02315i
$446$	−22.0237	−	5.39851i	−1.04285	−	0.255627i
$447$	−8.06960	−	8.06960i	−0.381679	−	0.381679i
$448$	3.91518	−	5.07709i	0.184975	−	0.239870i
$449$			28.2211i			1.33184i	0.746025	+	0.665918i	$0.231960\pi$
$449$			28.2211i			1.33184i	−0.746025	+	0.665918i	$0.768040\pi$
$450$	−6.29262	−	3.22536i	−0.296637	−	0.152045i
$451$	−8.29089	−	8.29089i	−0.390403	−	0.390403i
$452$	10.5100	−	3.30456i	0.494350	−	0.155433i
$453$			10.9071i			0.512461i
$454$	−14.5866	−	24.0596i	−0.684581	−	1.12917i
$455$	4.28981	+	2.39578i	0.201109	+	0.112316i
$456$	17.3993	+	15.2958i	0.814798	+	0.716290i
$457$	27.6086	+	27.6086i	1.29148	+	1.29148i	0.933873	+	0.357605i	$0.116406\pi$
$457$	27.6086	+	27.6086i	1.29148	+	1.29148i	0.357605	+	0.933873i	$0.383594\pi$
$458$	−27.5704	−	6.75811i	−1.28828	−	0.315786i
$459$	−2.08381	−	2.08381i	−0.0972638	−	0.0972638i
$460$	−14.8513	−	22.6334i	−0.692445	−	1.05529i
$461$	−16.4823	+	16.4823i	−0.767657	+	0.767657i	−0.977694	−	0.210036i	$-0.932642\pi$
$461$	−16.4823	+	16.4823i	−0.767657	+	0.767657i	0.210036	+	0.977694i	$0.432642\pi$
$462$	−3.02850	−	4.99532i	−0.140899	−	0.232403i
$463$	18.5827	−	18.5827i	0.863610	−	0.863610i	−0.128145	−	0.991755i	$-0.540902\pi$
$463$	18.5827	−	18.5827i	0.863610	−	0.863610i	0.991755	+	0.128145i	$0.0409024\pi$
$464$	2.61399	−	14.6872i	0.121351	−	0.681838i
$465$	4.94243	+	17.4459i	0.229200	+	0.809034i
$466$	−27.0930	−	6.64110i	−1.25506	−	0.307643i
$467$	11.5112			0.532676			0.266338	−	0.963880i	$-0.414186\pi$
$467$	11.5112			0.532676			0.266338	+	0.963880i	$0.414186\pi$
$468$	−2.53598	+	4.86207i	−0.117226	+	0.224749i
$469$	1.89442	−	1.89442i	0.0874761	−	0.0874761i
$470$	8.07031	−	0.288103i	0.372256	−	0.0132892i
$471$	14.0713			0.648373
$472$	16.7285	+	14.7061i	0.769992	+	0.676901i
$473$	11.1699	−	11.1699i	0.513593	−	0.513593i
$474$	14.6906	−	8.90644i	0.674761	−	0.409086i
$475$	−9.46659	+	39.8442i	−0.434357	+	1.82818i
$476$	4.18803	+	2.18441i	0.191958	+	0.100122i
$477$		−	6.32215i		−	0.289472i
$478$	12.0572	+	19.8875i	0.551482	+	0.909634i
$479$	10.5991			0.484286			0.242143	−	0.970241i	$-0.422150\pi$
$479$	10.5991			0.484286			0.242143	+	0.970241i	$0.422150\pi$
$480$	−1.77071	+	12.5246i	−0.0808216	+	0.571665i
$481$	6.26316			0.285575
$482$	3.45321	+	5.69584i	0.157289	+	0.259438i
$483$		−	4.85117i		−	0.220736i
$484$	27.6027	+	14.3971i	1.25467	+	0.654414i
$485$	2.81983	+	1.57482i	0.128042	+	0.0715091i
$486$	1.20932	−	0.733173i	0.0548559	−	0.0332574i
$487$	23.1871	−	23.1871i	1.05071	−	1.05071i	0.0520644	−	0.998644i	$-0.483420\pi$
$487$	23.1871	−	23.1871i	1.05071	−	1.05071i	0.998644	−	0.0520644i	$-0.0165801\pi$
$488$	12.7314	−	14.4823i	0.576325	−	0.655585i
$489$	−2.82750			−0.127864
$490$	−14.7144	−	13.7001i	−0.664731	−	0.618906i
$491$	−17.0460	+	17.0460i	−0.769277	+	0.769277i	−0.977979	−	0.208702i	$-0.933076\pi$
$491$	−17.0460	+	17.0460i	−0.769277	+	0.769277i	0.208702	+	0.977979i	$0.433076\pi$
$492$	−2.10405	+	4.03397i	−0.0948580	+	0.181865i
$493$	10.9907			0.494995
$494$	30.8467	+	7.56120i	1.38786	+	0.340195i
$495$	10.0623	+	5.61960i	0.452266	+	0.252582i
$496$	26.6000	−	18.5622i	1.19438	−	0.833468i
$497$	−1.59695	+	1.59695i	−0.0716328	+	0.0716328i
$498$	−1.44904	−	2.39010i	−0.0649332	−	0.107103i
$499$	−23.5253	+	23.5253i	−1.05314	+	1.05314i	−0.0546291	+	0.998507i	$0.517398\pi$
$499$	−23.5253	+	23.5253i	−1.05314	+	1.05314i	−0.998507	+	0.0546291i	$0.982602\pi$
$500$	−21.0246	+	7.61351i	−0.940249	+	0.340487i
$501$	−5.12509	−	5.12509i	−0.228972	−	0.228972i
$502$	28.5421	+	6.99631i	1.27390	+	0.312261i
$503$	−16.1405	−	16.1405i	−0.719669	−	0.719669i	0.248868	−	0.968537i	$-0.419941\pi$
$503$	−16.1405	−	16.1405i	−0.719669	−	0.719669i	−0.968537	+	0.248868i	$0.919941\pi$
$504$	−1.49662	+	1.70244i	−0.0666647	+	0.0758328i
$505$	−20.3427	+	36.4250i	−0.905239	+	1.62089i
$506$	22.8747	+	37.7303i	1.01690	+	1.67732i
$507$		−	5.48226i		−	0.243476i
$508$	−8.41819	+	2.64685i	−0.373497	+	0.117435i
$509$	−29.4832	−	29.4832i	−1.30682	−	1.30682i	−0.923697	−	0.383124i	$-0.874848\pi$
$509$	−29.4832	−	29.4832i	−1.30682	−	1.30682i	−0.383124	−	0.923697i	$-0.625152\pi$
$510$	−9.31313	+	0.332470i	−0.412392	+	0.0147220i
$511$			12.1330i			0.536734i
$512$	22.2084	−	4.33450i	0.981481	−	0.191560i
$513$	−5.79168	−	5.79168i	−0.255709	−	0.255709i
$514$	−9.77034	−	2.39493i	−0.430951	−	0.105636i
$515$	6.96519	−	12.4717i	0.306923	−	0.549567i
$516$	−5.43476	−	2.83468i	−0.239252	−	0.124790i
$517$	−13.1622			−0.578873
$518$	2.51451	+	0.616364i	0.110481	+	0.0270815i
$519$			4.60016i			0.201924i
$520$	5.78817	+	16.3465i	0.253828	+	0.716840i
$521$		−	18.6350i		−	0.816416i	−0.912889	−	0.408208i	$-0.866154\pi$
$521$		−	18.6350i		−	0.816416i	0.912889	−	0.408208i	$-0.133846\pi$
$522$	−1.25568	+	5.12267i	−0.0549597	+	0.224213i
$523$	−16.2282			−0.709611			−0.354805	−	0.934940i	$-0.615453\pi$
$523$	−16.2282			−0.709611			−0.354805	+	0.934940i	$0.615453\pi$
$524$	23.4644	−	7.37766i	1.02505	−	0.322295i
$525$	−3.89857	−	0.926262i	−0.170148	−	0.0404254i
$526$	4.21320	−	17.1882i	0.183704	−	0.749440i
$527$	16.8978	+	16.8978i	0.736079	+	0.736079i
$528$	3.61254	−	20.2979i	0.157216	−	0.883351i
$529$			13.6415i			0.593108i
$530$	−14.6321	−	13.6234i	−0.635578	−	0.591763i
$531$	−5.56839	−	5.56839i	−0.241647	−	0.241647i
$532$	11.6401	+	6.07130i	0.504663	+	0.263224i
$533$			6.23732i			0.270168i
$534$	−12.1322	+	7.35534i	−0.525010	+	0.318297i
$535$	−8.35278	+	2.36635i	−0.361122	+	0.102306i
$536$	9.43581	−	0.607089i	0.407565	−	0.0262222i
$537$	3.06396	+	3.06396i	0.132220	+	0.132220i
$538$	2.21913	−	9.05314i	0.0956733	−	0.390308i
$539$	23.1712	+	23.1712i	0.998055	+	0.998055i
$540$	0.909061	−	4.37877i	0.0391197	−	0.188432i
$541$	−12.4579	+	12.4579i	−0.535609	+	0.535609i	−0.922236	−	0.386627i	$-0.873640\pi$
$541$	−12.4579	+	12.4579i	−0.535609	+	0.535609i	0.386627	+	0.922236i	$0.373640\pi$
$542$	−4.68785	+	2.84210i	−0.201361	+	0.122078i
$543$	3.08559	−	3.08559i	0.132415	−	0.132415i
$544$	6.01093	+	15.5490i	0.257717	+	0.666660i
$545$	3.87966	−	6.94679i	0.166186	−	0.297568i
$546$	−0.739828	+	3.01820i	−0.0316617	+	0.129167i
$547$	1.52574			0.0652358			0.0326179	−	0.999468i	$-0.489616\pi$
$547$	1.52574			0.0652358			0.0326179	+	0.999468i	$0.489616\pi$
$548$	−43.7010	+	13.7404i	−1.86681	+	0.586963i
$549$	−4.82071	+	4.82071i	−0.205743	+	0.205743i
$550$	34.6890	−	11.1788i	1.47914	−	0.476667i
$551$	30.5472			1.30135
$552$	11.3042	−	12.8588i	0.481137	−	0.547306i
$553$	6.88402	−	6.88402i	0.292738	−	0.292738i
$554$	10.7740	+	17.7711i	0.457744	+	0.755020i
$555$	−4.91440	+	1.39225i	−0.208605	+	0.0590978i
$556$	−29.3723	+	9.23523i	−1.24566	+	0.391661i
$557$		−	14.5277i		−	0.615560i	−0.951458	−	0.307780i	$-0.900414\pi$
$557$		−	14.5277i		−	0.615560i	0.951458	−	0.307780i	$-0.0995860\pi$
$558$	−9.80650	+	5.94536i	−0.415142	+	0.251687i
$559$	−8.40322			−0.355419
$560$	0.715148	+	7.13235i	0.0302205	+	0.301397i
$561$	15.1892			0.641288
$562$	−0.397367	+	0.240911i	−0.0167619	+	0.0101622i
$563$		−	37.1864i		−	1.56722i	−0.621253	−	0.783610i	$-0.713376\pi$
$563$		−	37.1864i		−	1.56722i	0.621253	−	0.783610i	$-0.286624\pi$
$564$	1.53192	+	4.87221i	0.0645054	+	0.205157i
$565$	−6.00603	+	10.7542i	−0.252676	+	0.452434i
$566$	16.8549	+	27.8011i	0.708466	+	1.16857i
$567$	0.566689	−	0.566689i	0.0237987	−	0.0237987i
$568$	−7.95414	+	0.511760i	−0.333748	+	0.0214730i
$569$	−22.2439			−0.932513			−0.466256	−	0.884650i	$-0.654398\pi$
$569$	−22.2439			−0.932513			−0.466256	+	0.884650i	$0.654398\pi$
$570$	−25.8847	+	0.924060i	−1.08419	+	0.0387046i
$571$	32.0005	−	32.0005i	1.33918	−	1.33918i	0.442327	−	0.896854i	$-0.354153\pi$
$571$	32.0005	−	32.0005i	1.33918	−	1.33918i	0.896854	−	0.442327i	$-0.145847\pi$
$572$	−8.47763	−	26.9628i	−0.354467	−	1.12737i
$573$	−21.0908			−0.881081
$574$	−0.613821	+	2.50414i	−0.0256204	+	0.104521i
$575$	29.4464	+	6.99617i	1.22800	+	0.291761i
$576$	−7.93404	+	1.02518i	−0.330585	+	0.0427157i
$577$	3.38284	−	3.38284i	0.140830	−	0.140830i	−0.633177	−	0.774007i	$-0.718250\pi$
$577$	3.38284	−	3.38284i	0.140830	−	0.140830i	0.774007	+	0.633177i	$0.218250\pi$
$578$	10.0561	−	6.09670i	0.418279	−	0.253589i
$579$	−15.2332	+	15.2332i	−0.633069	+	0.633069i
$580$	9.15018	+	13.9449i	0.379941	+	0.579029i
$581$	−1.12000	−	1.12000i	−0.0464656	−	0.0464656i
$582$	−0.486314	+	1.98396i	−0.0201583	+	0.0822379i
$583$	23.0416	+	23.0416i	0.954284	+	0.954284i
$584$	−28.2723	+	32.1605i	−1.16992	+	1.33081i
$585$	−1.67114	−	5.89881i	−0.0690930	−	0.243886i
$586$	26.6247	−	16.1417i	1.09986	−	0.666807i
$587$		−	5.27446i		−	0.217700i	−0.994058	−	0.108850i	$-0.965283\pi$
$587$		−	5.27446i		−	0.217700i	0.994058	−	0.108850i	$-0.0347168\pi$
$588$	5.88036	−	11.2740i	0.242502	−	0.464934i
$589$	46.9653	+	46.9653i	1.93517	+	1.93517i
$590$	−24.8867	+	0.888433i	−1.02457	+	0.0365762i
$591$			14.0460i			0.577774i
$592$	5.22886	+	7.49307i	0.214905	+	0.307963i
$593$	20.6039	+	20.6039i	0.846101	+	0.846101i	0.989644	−	0.143543i	$-0.0458495\pi$
$593$	20.6039	+	20.6039i	0.846101	+	0.846101i	−0.143543	+	0.989644i	$0.545850\pi$
$594$	−1.73536	+	7.07957i	−0.0712027	+	0.290478i
$595$	−5.08105	+	1.43946i	−0.208303	+	0.0590122i
$596$	−6.84598	−	21.7734i	−0.280422	−	0.891873i
$597$	2.42066			0.0990708
$598$	5.58802	−	22.7968i	0.228511	−	0.932233i
$599$		−	31.6423i		−	1.29287i	−0.762969	−	0.646435i	$-0.776259\pi$
$599$		−	31.6423i		−	1.29287i	0.762969	−	0.646435i	$-0.223741\pi$
$600$	−8.17540	−	11.5396i	−0.333759	−	0.471103i
$601$			12.1679i			0.496338i	0.968717	+	0.248169i	$0.0798289\pi$
$601$			12.1679i			0.496338i	−0.968717	+	0.248169i	$0.920171\pi$
$602$	−3.37370	−	0.826969i	−0.137502	−	0.0337048i
$603$	−3.34296			−0.136136
$604$	−10.0882	+	19.3414i	−0.410482	+	0.786991i
$605$	−33.4884	+	9.48727i	−1.36150	+	0.385712i
$606$	−25.6277	−	6.28193i	−1.04106	−	0.255186i
$607$	−19.4977	−	19.4977i	−0.791387	−	0.791387i	0.190332	−	0.981720i	$-0.439043\pi$
$607$	−19.4977	−	19.4977i	−0.791387	−	0.791387i	−0.981720	+	0.190332i	$0.939043\pi$
$608$	16.7066	+	43.2166i	0.677544	+	1.75267i
$609$			2.98890i			0.121116i
$610$	0.769142	+	21.5451i	0.0311416	+	0.872337i
$611$	4.95103	+	4.95103i	0.200297	+	0.200297i
$612$	−1.76783	−	5.62252i	−0.0714604	−	0.227277i
$613$		−	40.9232i		−	1.65287i	−0.563029	−	0.826437i	$-0.690364\pi$
$613$		−	40.9232i		−	1.65287i	0.563029	−	0.826437i	$-0.309636\pi$
$614$	2.26329	+	3.73315i	0.0913389	+	0.150658i
$615$	−1.38651	−	4.89413i	−0.0559094	−	0.197350i
$616$	−0.750141	−	11.6592i	−0.0302240	−	0.469763i
$617$	−12.9650	−	12.9650i	−0.521952	−	0.521952i	0.396209	−	0.918160i	$-0.370326\pi$
$617$	−12.9650	−	12.9650i	−0.521952	−	0.521952i	−0.918160	+	0.396209i	$0.870326\pi$
$618$	8.77474	+	2.15089i	0.352972	+	0.0865213i
$619$	−12.2565	−	12.2565i	−0.492632	−	0.492632i	0.416503	−	0.909135i	$-0.363256\pi$
$619$	−12.2565	−	12.2565i	−0.492632	−	0.492632i	−0.909135	+	0.416503i	$0.863256\pi$
$620$	−7.37166	+	35.5078i	−0.296053	+	1.42603i
$621$	−4.28027	+	4.28027i	−0.171761	+	0.171761i
$622$	−17.8661	−	29.4690i	−0.716366	−	1.18160i
$623$	−5.68514	+	5.68514i	−0.227770	+	0.227770i
$624$	−8.99402	+	6.27626i	−0.360049	+	0.251252i
$625$	11.2447	−	22.3284i	0.449790	−	0.893134i
$626$	−6.44735	−	1.58039i	−0.257688	−	0.0631650i
$627$	42.2164			1.68596
$628$	24.9524	+	13.0148i	0.995711	+	0.519347i
$629$	−4.76000	+	4.76000i	−0.189794	+	0.189794i
$630$	−0.0904149	−	2.53270i	−0.00360222	−	0.100905i
$631$	7.42406			0.295547			0.147774	−	0.989021i	$-0.452789\pi$
$631$	7.42406			0.295547			0.147774	+	0.989021i	$0.452789\pi$
$632$	34.2883	−	2.20607i	1.36391	−	0.0877527i
$633$	−5.18795	+	5.18795i	−0.206202	+	0.206202i
$634$	−6.47892	+	3.92796i	−0.257311	+	0.155999i
$635$	4.81064	−	8.61379i	0.190905	−	0.341828i
$636$	5.84746	−	11.2110i	0.231867	−	0.444544i
$637$		−	17.4319i		−	0.690678i
$638$	−14.0935	−	23.2464i	−0.557969	−	0.920333i
$639$	2.81803			0.111480
$640$	−14.7241	+	20.5718i	−0.582023	+	0.813173i
$641$	−28.7869			−1.13702			−0.568508	−	0.822678i	$-0.692479\pi$
$641$	−28.7869			−1.13702			−0.568508	+	0.822678i	$0.692479\pi$
$642$	−2.84653	−	4.69518i	−0.112344	−	0.185304i
$643$		−	5.25971i		−	0.207423i	−0.994607	−	0.103711i	$-0.966928\pi$
$643$		−	5.25971i		−	0.207423i	0.994607	−	0.103711i	$-0.0330718\pi$
$644$	4.48692	−	8.60249i	0.176809	−	0.338986i
$645$	6.59361	−	1.86797i	0.259623	−	0.0735514i
$646$	−29.1900	+	17.6969i	−1.14846	+	0.696277i
$647$	−32.0670	+	32.0670i	−1.26068	+	1.26068i	−0.309923	+	0.950762i	$0.600303\pi$
$647$	−32.0670	+	32.0670i	−1.26068	+	1.26068i	−0.950762	+	0.309923i	$0.899697\pi$
$648$	2.82259	−	0.181602i	0.110882	−	0.00713401i
$649$	40.5888			1.59325
$650$	−17.2534	−	8.84347i	−0.676734	−	0.346869i
$651$	−4.59533	+	4.59533i	−0.180105	+	0.180105i
$652$	−5.01396	−	2.61520i	−0.196362	−	0.102419i
$653$	31.6376			1.23807			0.619037	−	0.785362i	$-0.287523\pi$
$653$	31.6376			1.23807			0.619037	+	0.785362i	$0.287523\pi$
$654$	4.88759	+	1.19806i	0.191120	+	0.0468477i
$655$	−13.4089	+	24.0096i	−0.523929	+	0.938131i
$656$	−7.46216	+	5.20729i	−0.291348	+	0.203311i
$657$	10.7052	−	10.7052i	0.417650	−	0.417650i
$658$	1.50049	+	2.47496i	0.0584951	+	0.0964840i
$659$	−12.8616	+	12.8616i	−0.501015	+	0.501015i	−0.911753	−	0.410738i	$-0.865271\pi$
$659$	−12.8616	+	12.8616i	−0.501015	+	0.501015i	0.410738	+	0.911753i	$0.365271\pi$
$660$	12.6456	+	19.2719i	0.492230	+	0.750157i
$661$	28.8603	+	28.8603i	1.12254	+	1.12254i	0.991359	+	0.131178i	$0.0418761\pi$
$661$	28.8603	+	28.8603i	1.12254	+	1.12254i	0.131178	+	0.991359i	$0.458124\pi$
$662$	5.37883	+	1.31847i	0.209054	+	0.0512438i
$663$	−5.71348	−	5.71348i	−0.221893	−	0.221893i
$664$	−0.358919	−	5.57857i	−0.0139287	−	0.216491i
$665$	−14.1221	+	4.00081i	−0.547633	+	0.155145i
$666$	−1.67477	−	2.76243i	−0.0648962	−	0.107042i
$667$		−	22.5756i		−	0.874129i
$668$	−4.34795	−	13.8285i	−0.168227	−	0.535041i
$669$	11.3379	+	11.3379i	0.438347	+	0.438347i
$670$	−7.20364	+	7.73701i	−0.278301	+	0.298907i
$671$		−	35.1389i		−	1.35652i
$672$	−4.22854	+	1.63467i	−0.163120	+	0.0630586i
$673$	8.69401	+	8.69401i	0.335130	+	0.335130i	0.854531	−	0.519401i	$-0.173845\pi$
$673$	8.69401	+	8.69401i	0.335130	+	0.335130i	−0.519401	+	0.854531i	$0.673845\pi$
$674$	14.1808	+	3.47602i	0.546222	+	0.133891i
$675$	2.62252	+	4.25704i	0.100941	+	0.163853i
$676$	5.07063	−	9.72160i	0.195024	−	0.373908i
$677$	13.3965			0.514871			0.257435	−	0.966295i	$-0.417123\pi$
$677$	13.3965			0.514871			0.257435	+	0.966295i	$0.417123\pi$
$678$	−7.56640	−	1.85469i	−0.290586	−	0.0712291i
$679$			1.15757i			0.0444236i
$680$	−16.8223	−	8.02430i	−0.645107	−	0.307718i
$681$			19.8951i			0.762383i
$682$	14.0722	−	57.4089i	0.538852	−	2.19830i
$683$	−20.0009			−0.765312			−0.382656	−	0.923891i	$-0.624991\pi$
$683$	−20.0009			−0.765312			−0.382656	+	0.923891i	$0.624991\pi$
$684$	−4.91347	−	15.6271i	−0.187871	−	0.597517i
$685$	24.9733	−	44.7164i	0.954179	−	1.70852i
$686$	3.60429	−	14.7040i	0.137612	−	0.561403i
$687$	14.1933	+	14.1933i	0.541507	+	0.541507i
$688$	−7.01552	−	10.0534i	−0.267464	−	0.383282i
$689$		−	17.3344i		−	0.660388i
$690$	0.682915	+	19.1298i	0.0259981	+	0.728258i
$691$	−29.3786	−	29.3786i	−1.11761	−	1.11761i	−0.992091	−	0.125524i	$-0.959939\pi$
$691$	−29.3786	−	29.3786i	−1.11761	−	1.11761i	−0.125524	−	0.992091i	$-0.540061\pi$
$692$	−4.25476	+	8.15738i	−0.161742	+	0.310097i
$693$			4.13068i			0.156912i
$694$	20.6581	−	12.5244i	0.784172	−	0.475418i
$695$	16.7850	−	30.0548i	0.636693	−	1.14004i
$696$	−6.96472	+	7.92255i	−0.263997	+	0.300303i
$697$	−4.74036	−	4.74036i	−0.179554	−	0.179554i
$698$	−0.657623	+	2.68284i	−0.0248914	+	0.101547i
$699$	13.9475	+	13.9475i	0.527545	+	0.527545i
$700$	−6.05655	−	5.24837i	−0.228916	−	0.198370i
$701$	22.4862	−	22.4862i	0.849291	−	0.849291i	−0.140754	−	0.990045i	$-0.544953\pi$
$701$	22.4862	−	22.4862i	0.849291	−	0.849291i	0.990045	+	0.140754i	$0.0449525\pi$
$702$	3.31578	−	2.01025i	0.125146	−	0.0758720i
$703$	−13.2298	+	13.2298i	−0.498973	+	0.498973i
$704$	25.1799	−	32.6526i	0.949002	−	1.23064i
$705$	−4.98541	−	2.78426i	−0.187762	−	0.104861i
$706$	−3.18812	+	13.0063i	−0.119987	+	0.489497i
$707$	−14.9529			−0.562362
$708$	−4.72404	−	15.0246i	−0.177540	−	0.564660i
$709$	3.15802	−	3.15802i	0.118602	−	0.118602i	−0.645315	−	0.763917i	$-0.723274\pi$
$709$	3.15802	−	3.15802i	0.118602	−	0.118602i	0.763917	+	0.645315i	$0.223274\pi$
$710$	6.07249	−	6.52210i	0.227896	−	0.244770i
$711$	−12.1478			−0.455578
$712$	−28.3168	+	1.82187i	−1.06122	+	0.0682775i
$713$	34.7091	−	34.7091i	1.29987	−	1.29987i
$714$	−1.73156	−	2.85610i	−0.0648021	−	0.106887i
$715$	27.5893	+	15.4081i	1.03178	+	0.576230i
$716$	2.59937	+	8.26718i	0.0971429	+	0.308959i
$717$		−	16.4452i		−	0.614157i
$718$	2.30914	−	1.39996i	0.0861765	−	0.0522461i
$719$	1.88866			0.0704352			0.0352176	−	0.999380i	$-0.488788\pi$
$719$	1.88866			0.0704352			0.0352176	+	0.999380i	$0.488788\pi$
$720$	5.66201	−	6.92399i	0.211011	−	0.258042i
$721$	5.11976			0.190670
$722$	−58.1528	+	35.2562i	−2.16422	+	1.31210i
$723$		−	4.70995i		−	0.175165i
$724$	8.32554	−	2.61771i	0.309416	−	0.0972866i
$725$	−18.1425	−	4.31048i	−0.673796	−	0.160087i
$726$	−11.4125	−	18.8241i	−0.423556	−	0.698629i
$727$	−0.978984	+	0.978984i	−0.0363085	+	0.0363085i	−0.725028	−	0.688719i	$-0.758173\pi$
$727$	−0.978984	+	0.978984i	−0.0363085	+	0.0363085i	0.688719	+	0.725028i	$0.258173\pi$
$728$	−4.10350	+	4.66784i	−0.152086	+	0.173002i
$729$	−1.00000			−0.0370370
$730$	−1.70801	−	47.8447i	−0.0632163	−	1.77081i
$731$	6.38645	−	6.38645i	0.236211	−	0.236211i
$732$	−13.0072	+	4.08973i	−0.480761	+	0.151161i
$733$	−18.1447			−0.670189			−0.335094	−	0.942185i	$-0.608768\pi$
$733$	−18.1447			−0.670189			−0.335094	+	0.942185i	$0.608768\pi$
$734$	−9.65474	+	39.3874i	−0.356363	+	1.45382i
$735$	3.87499	+	13.6780i	0.142931	+	0.504521i
$736$	31.9387	−	12.3468i	1.17728	−	0.455111i
$737$	12.1837	−	12.1837i	0.448791	−	0.448791i
$738$	2.75103	−	1.66786i	0.101267	−	0.0613949i
$739$	18.8493	−	18.8493i	0.693383	−	0.693383i	−0.269592	−	0.962975i	$-0.586889\pi$
$739$	18.8493	−	18.8493i	0.693383	−	0.693383i	0.962975	+	0.269592i	$0.0868887\pi$
$740$	−10.0023	−	2.07655i	−0.367693	−	0.0763356i
$741$	−15.8799	−	15.8799i	−0.583364	−	0.583364i
$742$	1.70589	−	6.95936i	0.0626254	−	0.255486i
$743$	−6.80504	−	6.80504i	−0.249653	−	0.249653i	0.571175	−	0.820828i	$-0.306488\pi$
$743$	−6.80504	−	6.80504i	−0.249653	−	0.249653i	−0.820828	+	0.571175i	$0.806488\pi$
$744$	−22.8887	+	1.47263i	−0.839139	+	0.0539892i
$745$	22.2793	+	12.4426i	0.816250	+	0.455861i
$746$	41.8106	−	25.3484i	1.53079	−	0.928071i
$747$			1.97640i			0.0723127i
$748$	26.9347	+	14.0487i	0.984830	+	0.513672i
$749$	−2.20016	−	2.20016i	−0.0803922	−	0.0803922i
$750$	15.5038	+	3.10375i	0.566117	+	0.113333i
$751$			1.26232i			0.0460627i	0.999735	+	0.0230313i	$0.00733175\pi$
$751$			1.26232i			0.0460627i	−0.999735	+	0.0230313i	$0.992668\pi$
$752$	−1.78986	+	10.0567i	−0.0652693	+	0.366730i
$753$	−14.6935	−	14.6935i	−0.535462	−	0.535462i
$754$	−3.44289	+	14.0456i	−0.125383	+	0.511510i
$755$	−6.64781	−	23.4656i	−0.241938	−	0.854000i
$756$	1.52904	−	0.480760i	0.0556106	−	0.0174851i
$757$	29.2534			1.06323			0.531617	−	0.846985i	$-0.321585\pi$
$757$	29.2534			1.06323			0.531617	+	0.846985i	$0.321585\pi$
$758$	−10.1026	+	41.2143i	−0.366941	+	1.49697i
$759$		−	31.1996i		−	1.13247i
$760$	−46.7556	−	22.3025i	−1.69600	−	0.808998i
$761$			43.1952i			1.56583i	0.622131	+	0.782913i	$0.286267\pi$
$761$			43.1952i			1.56583i	−0.622131	+	0.782913i	$0.713733\pi$
$762$	6.06045	+	1.48555i	0.219547	+	0.0538158i
$763$	2.85174			0.103240
$764$	−37.3999	−	19.5072i	−1.35308	−	0.705746i
$765$	5.75316	+	3.21304i	0.208006	+	0.116168i
$766$	6.08397	+	1.49132i	0.219823	+	0.0538835i
$767$	−15.2677	−	15.2677i	−0.551284	−	0.551284i
$768$	−15.0175	−	5.52039i	−0.541897	−	0.199200i
$769$			22.3663i			0.806550i	0.915079	+	0.403275i	$0.132128\pi$
$769$			22.3663i			0.806550i	−0.915079	+	0.403275i	$0.867872\pi$
$770$	9.56013	+	8.90108i	0.344523	+	0.320773i
$771$	5.02979	+	5.02979i	0.181143	+	0.181143i
$772$	−41.1021	+	12.9233i	−1.47930	+	0.465120i
$773$		−	25.3081i		−	0.910270i	−0.890422	−	0.455135i	$-0.849591\pi$
$773$		−	25.3081i		−	0.910270i	0.890422	−	0.455135i	$-0.150409\pi$
$774$	2.24703	+	3.70633i	0.0807678	+	0.133221i
$775$	−21.2663	−	34.5207i	−0.763907	−	1.24002i
$776$	−2.69737	+	3.06833i	−0.0968299	+	0.110147i
$777$	−1.29448	−	1.29448i	−0.0464391	−	0.0464391i
$778$	29.6768	+	7.27445i	1.06397	+	0.260802i
$779$	−13.1753	−	13.1753i	−0.472053	−	0.472053i
$780$	2.49251	−	12.0059i	0.0892461	−	0.429881i
$781$	−10.2705	+	10.2705i	−0.367508	+	0.367508i
$782$	13.0787	+	21.5725i	0.467694	+	0.771431i
$783$	2.63716	−	2.63716i	0.0942445	−	0.0942445i
$784$	20.8551	−	14.5532i	0.744824	−	0.519758i
$785$	−30.2731	+	8.57637i	−1.08049	+	0.306104i
$786$	−16.8925	−	4.14073i	−0.602536	−	0.147695i
$787$	28.2019			1.00529			0.502645	−	0.864493i	$-0.332360\pi$
$787$	28.2019			1.00529			0.502645	+	0.864493i	$0.332360\pi$
$788$	−12.9913	+	24.9075i	−0.462797	+	0.887291i
$789$	−8.84851	+	8.84851i	−0.315015	+	0.315015i
$790$	−26.1769	+	28.1151i	−0.931333	+	1.00029i
$791$	−4.41473			−0.156970
$792$	−9.62528	+	10.9490i	−0.342020	+	0.389056i
$793$	−13.2177	+	13.2177i	−0.469373	+	0.469373i
$794$	−11.3637	+	6.88945i	−0.403283	+	0.244497i
$795$	3.85330	+	13.6015i	0.136663	+	0.482395i
$796$	4.29251	+	2.23890i	0.152144	+	0.0793558i
$797$		−	15.2969i		−	0.541846i	−0.962601	−	0.270923i	$-0.912671\pi$
$797$		−	15.2969i		−	0.541846i	0.962601	−	0.270923i	$-0.0873288\pi$
$798$	−4.81267	−	7.93818i	−0.170367	−	0.281009i
$799$	−7.52557			−0.266235
$800$	−3.82411	−	28.0246i	−0.135203	−	0.990818i
$801$	10.0322			0.354470
$802$	−0.529476	−	0.873336i	−0.0186964	−	0.0308386i
$803$			78.0319i			2.75369i
$804$	−5.92801	−	3.09196i	−0.209065	−	0.109045i
$805$	2.95675	+	10.4368i	0.104212	+	0.367849i
$806$	−26.8879	+	16.3013i	−0.947087	+	0.574189i
$807$	−4.66057	+	4.66057i	−0.164060	+	0.164060i
$808$	−39.6350	−	34.8431i	−1.39435	−	1.22578i
$809$	−6.74990			−0.237314			−0.118657	−	0.992935i	$-0.537859\pi$
$809$	−6.74990			−0.237314			−0.118657	+	0.992935i	$0.537859\pi$
$810$	−2.15487	+	2.31442i	−0.0757144	+	0.0813204i
$811$	−4.99242	+	4.99242i	−0.175307	+	0.175307i	−0.789307	−	0.613999i	$-0.789560\pi$
$811$	−4.99242	+	4.99242i	−0.175307	+	0.175307i	0.613999	+	0.789307i	$0.289560\pi$
$812$	−2.76448	+	5.30017i	−0.0970143	+	0.185999i
$813$	3.87643			0.135952
$814$	16.1717	+	3.96405i	0.566819	+	0.138940i
$815$	6.08309	−	1.72334i	0.213081	−	0.0603660i
$816$	2.06549	−	11.6054i	0.0723067	−	0.406271i
$817$	17.7504	−	17.7504i	0.621006	−	0.621006i
$818$	15.2397	+	25.1369i	0.532844	+	0.878892i
$819$	1.55378	−	1.55378i	0.0542933	−	0.0542933i
$820$	2.06798	−	9.96108i	0.0722171	−	0.347856i
$821$	−28.2761	−	28.2761i	−0.986842	−	0.986842i	0.0130724	−	0.999915i	$-0.495839\pi$
$821$	−28.2761	−	28.2761i	−0.986842	−	0.986842i	−0.999915	+	0.0130724i	$0.995839\pi$
$822$	31.4613	+	7.71187i	1.09734	+	0.268982i
$823$	20.7586	+	20.7586i	0.723599	+	0.723599i	0.969336	−	0.245738i	$-0.0790302\pi$
$823$	20.7586	+	20.7586i	0.723599	+	0.723599i	−0.245738	+	0.969336i	$0.579030\pi$
$824$	13.5707	+	11.9300i	0.472758	+	0.415602i
$825$	−25.0731	−	5.95712i	−0.872933	−	0.207400i
$826$	−4.62712	−	7.63213i	−0.160998	−	0.265556i
$827$		−	17.1914i		−	0.597804i	−0.954284	−	0.298902i	$-0.903380\pi$
$827$		−	17.1914i		−	0.597804i	0.954284	−	0.298902i	$-0.0966204\pi$
$828$	−11.5490	+	3.63124i	−0.401356	+	0.126194i
$829$	−21.3409	−	21.3409i	−0.741201	−	0.741201i	0.231608	−	0.972809i	$-0.425601\pi$
$829$	−21.3409	−	21.3409i	−0.741201	−	0.741201i	−0.972809	+	0.231608i	$0.925601\pi$
$830$	4.57422	+	4.25889i	0.158773	+	0.147828i
$831$		−	14.6951i		−	0.509766i
$832$	−21.7539	+	2.81088i	−0.754182	+	0.0974498i
$833$	13.2483	+	13.2483i	0.459025	+	0.459025i
$834$	21.1458	+	5.18330i	0.732219	+	0.179483i
$835$	14.1498	+	7.90241i	0.489674	+	0.273474i
$836$	74.8617	+	39.0467i	2.58915	+	1.35046i
$837$	8.10909			0.280291
$838$	−12.1500	−	2.97824i	−0.419715	−	0.102881i
$839$			24.3978i			0.842305i	0.906990	+	0.421153i	$0.138374\pi$
$839$			24.3978i			0.842305i	−0.906990	+	0.421153i	$0.861626\pi$
$840$	2.18220	−	4.57481i	0.0752930	−	0.157846i
$841$		−	15.0907i		−	0.520371i
$842$	7.71721	−	31.4831i	0.265953	−	1.08498i
$843$	0.328587			0.0113171
$844$	−13.9981	+	4.40128i	−0.481835	+	0.151498i
$845$	3.34140	+	11.7945i	0.114947	+	0.405744i
$846$	0.859794	−	3.50761i	0.0295603	−	0.120594i
$847$	−8.82100	−	8.82100i	−0.303093	−	0.303093i
$848$	20.7384	−	14.4718i	0.712159	−	0.496964i
$849$		−	22.9890i		−	0.788982i
$850$	19.8336	−	6.39156i	0.680288	−	0.219229i
$851$	9.77735	+	9.77735i	0.335163	+	0.335163i
$852$	4.99716	+	2.60644i	0.171200	+	0.0892951i
$853$		−	57.1946i		−	1.95831i	−0.203124	−	0.979153i	$-0.565109\pi$
$853$		−	57.1946i		−	1.95831i	0.203124	−	0.979153i	$-0.434891\pi$
$854$	−6.60735	+	4.00582i	−0.226099	+	0.137076i
$855$	15.9902	+	8.93024i	0.546854	+	0.305408i
$856$	−0.705069	−	10.9587i	−0.0240987	−	0.374560i
$857$	−13.4584	−	13.4584i	−0.459731	−	0.459731i	0.438836	−	0.898567i	$-0.355391\pi$
$857$	−13.4584	−	13.4584i	−0.459731	−	0.459731i	−0.898567	+	0.438836i	$0.855391\pi$
$858$	−4.75809	+	19.4111i	−0.162439	+	0.662684i
$859$	−2.91627	−	2.91627i	−0.0995019	−	0.0995019i	0.655603	−	0.755105i	$-0.272414\pi$
$859$	−2.91627	−	2.91627i	−0.0995019	−	0.0995019i	−0.755105	+	0.655603i	$0.772414\pi$
$860$	13.4201	+	2.78609i	0.457620	+	0.0950049i
$861$	1.28914	−	1.28914i	0.0439337	−	0.0439337i
$862$	−19.5203	+	11.8346i	−0.664865	+	0.403086i
$863$	−25.5234	+	25.5234i	−0.868825	+	0.868825i	−0.992342	−	0.123517i	$-0.960583\pi$
$863$	−25.5234	+	25.5234i	−0.868825	+	0.868825i	0.123517	+	0.992342i	$0.460583\pi$
$864$	5.17322	+	2.28863i	0.175996	+	0.0778607i
$865$	−2.80376	−	9.89677i	−0.0953307	−	0.336500i
$866$	−11.3981	+	46.4997i	−0.387323	+	1.58012i
$867$	−8.31550			−0.282409
$868$	−12.3991	+	3.89853i	−0.420853	+	0.132325i
$869$	44.2736	−	44.2736i	1.50188	−	1.50188i
$870$	−0.420758	−	11.7862i	−0.0142650	−	0.399591i
$871$	−9.16589			−0.310574
$872$	7.55898	+	6.64510i	0.255979	+	0.225032i
$873$	1.02135	−	1.02135i	0.0345674	−	0.0345674i
$874$	36.3507	+	59.9581i	1.22958	+	2.02811i
$875$	8.95193	−	0.383390i	0.302631	−	0.0129609i
$876$	28.8848	−	9.08195i	0.975926	−	0.306851i
$877$			52.9978i			1.78961i	0.446460	+	0.894804i	$0.352685\pi$
$877$			52.9978i			1.78961i	−0.446460	+	0.894804i	$0.647315\pi$
$878$	15.9865	−	9.69210i	0.539518	−	0.327093i
$879$	−22.0162			−0.742589
$880$	4.59937	+	45.8706i	0.155045	+	1.54630i
$881$	42.2460			1.42331			0.711653	−	0.702531i	$-0.247947\pi$
$881$	42.2460			1.42331			0.711653	+	0.702531i	$0.247947\pi$
$882$	−7.68853	+	4.66131i	−0.258886	+	0.156955i
$883$			23.6484i			0.795830i	0.917422	+	0.397915i	$0.130266\pi$
$883$			23.6484i			0.795830i	−0.917422	+	0.397915i	$0.869734\pi$
$884$	−4.84713	−	15.4161i	−0.163027	−	0.518500i
$885$	15.3737	+	8.58594i	0.516782	+	0.288613i
$886$	5.16057	+	8.51203i	0.173373	+	0.285967i
$887$	−30.6018	+	30.6018i	−1.02751	+	1.02751i	−0.0278982	+	0.999611i	$0.508881\pi$
$887$	−30.6018	+	30.6018i	−1.02751	+	1.02751i	−0.999611	+	0.0278982i	$0.991119\pi$
$888$	−0.414831	−	6.44760i	−0.0139208	−	0.216367i
$889$	3.53606			0.118596
$890$	21.6181	−	23.2187i	0.724640	−	0.778293i
$891$	3.64458	−	3.64458i	0.122098	−	0.122098i
$892$	9.61868	+	30.5918i	0.322057	+	1.02429i
$893$	−20.9164			−0.699940
$894$	−3.84233	+	15.6752i	−0.128507	+	0.524256i
$895$	−8.45927	−	4.72435i	−0.282762	−	0.157918i
$896$	−9.01033	−	1.01232i	−0.301014	−	0.0338193i
$897$	−11.7359	+	11.7359i	−0.391849	+	0.391849i
$898$	34.1284	−	20.6909i	1.13888	−	0.690465i
$899$	−21.3850	+	21.3850i	−0.713229	+	0.713229i
$900$	0.713073	+	9.97454i	0.0237691	+	0.332485i
$901$	13.1741	+	13.1741i	0.438894	+	0.438894i
$902$	−3.94770	+	16.1050i	−0.131444	+	0.536238i
$903$	1.73679	+	1.73679i	0.0577967	+	0.0577967i
$904$	−11.7019	−	10.2872i	−0.389200	−	0.342146i
$905$	−4.75770	+	8.51898i	−0.158151	+	0.283181i
$906$	13.1902	−	7.99680i	0.438215	−	0.265676i
$907$			34.6654i			1.15105i	0.817785	+	0.575523i	$0.195202\pi$
$907$			34.6654i			1.15105i	−0.817785	+	0.575523i	$0.804798\pi$
$908$	−18.4013	+	35.2797i	−0.610669	+	1.17080i
$909$	13.1932	+	13.1932i	0.437591	+	0.437591i
$910$	−0.247904	−	6.94427i	−0.00821794	−	0.230200i
$911$		−	19.8125i		−	0.656418i	−0.944605	−	0.328209i	$-0.893555\pi$
$911$		−	19.8125i		−	0.656418i	0.944605	−	0.328209i	$-0.106445\pi$
$912$	5.74078	−	32.2558i	0.190096	−	1.06810i
$913$	−7.20314	−	7.20314i	−0.238389	−	0.238389i
$914$	13.1458	−	53.6296i	0.434825	−	1.77391i
$915$	7.43308	−	13.3095i	0.245730	−	0.439997i
$916$	12.0411	+	38.2963i	0.397849	+	1.26534i
$917$	−9.85620			−0.325480
$918$	−0.992201	+	4.04778i	−0.0327475	+	0.133597i
$919$			16.7104i			0.551226i	0.961269	+	0.275613i	$0.0888808\pi$
$919$			16.7104i			0.551226i	−0.961269	+	0.275613i	$0.911119\pi$
$920$	−16.4824	+	34.5541i	−0.543410	+	1.13922i
$921$		−	3.08698i		−	0.101719i
$922$	32.0168	+	7.84802i	1.05442	+	0.258461i
$923$	7.72661			0.254325
$924$	−3.82053	+	7.32486i	−0.125686	+	0.240970i
$925$	9.72428	−	5.99058i	0.319732	−	0.196969i
$926$	−36.0967	−	8.84811i	−1.18621	−	0.290767i
$927$	−4.51726	−	4.51726i	−0.148366	−	0.148366i
$928$	−19.6781	+	7.60714i	−0.645965	+	0.249717i
$929$			9.62355i			0.315739i	0.987460	+	0.157869i	$0.0504625\pi$
$929$			9.62355i			0.315739i	−0.987460	+	0.157869i	$0.949538\pi$
$930$	17.4740	−	18.7678i	0.572996	−	0.615422i
$931$	36.8219	+	36.8219i	1.20679	+	1.20679i
$932$	11.8326	+	37.6332i	0.387591	+	1.23272i
$933$			24.3682i			0.797780i
$934$	−8.43971	−	13.9208i	−0.276156	−	0.455501i
$935$	−32.6780	+	9.25769i	−1.06868	+	0.302759i
$936$	7.73912	−	0.497926i	0.252961	−	0.0162752i
$937$	19.6920	+	19.6920i	0.643310	+	0.643310i	0.951368	−	0.308057i	$-0.0996789\pi$
$937$	19.6920	+	19.6920i	0.643310	+	0.643310i	−0.308057	+	0.951368i	$0.599679\pi$
$938$	−3.67990	−	0.902024i	−0.120153	−	0.0294521i
$939$	3.31911	+	3.31911i	0.108315	+	0.108315i
$940$	−6.26534	−	9.54837i	−0.204353	−	0.311433i
$941$	−19.3709	+	19.3709i	−0.631473	+	0.631473i	−0.948437	−	0.316965i	$-0.897336\pi$
$941$	−19.3709	+	19.3709i	−0.631473	+	0.631473i	0.316965	+	0.948437i	$0.397336\pi$
$942$	−10.3167	−	17.0168i	−0.336137	−	0.554436i
$943$	−9.73702	+	9.73702i	−0.317081	+	0.317081i
$944$	5.51945	−	31.0122i	0.179643	−	1.00936i
$945$	−0.873782	+	1.56457i	−0.0284241	+	0.0508954i
$946$	−21.6975	−	5.31853i	−0.705445	−	0.172920i
$947$	−3.74620			−0.121735			−0.0608676	−	0.998146i	$-0.519387\pi$
$947$	−3.74620			−0.121735			−0.0608676	+	0.998146i	$0.519387\pi$
$948$	−21.5415	−	11.2357i	−0.699635	−	0.364918i
$949$	29.3521	−	29.3521i	0.952809	−	0.952809i
$950$	55.1251	−	17.7645i	1.78850	−	0.576358i
$951$	5.35749			0.173728
$952$	−0.428897	−	6.66623i	−0.0139006	−	0.216054i
$953$	−11.3723	+	11.3723i	−0.368385	+	0.368385i	−0.866888	−	0.498503i	$-0.833883\pi$
$953$	−11.3723	+	11.3723i	−0.368385	+	0.368385i	0.498503	+	0.866888i	$0.333883\pi$
$954$	−7.64551	+	4.63523i	−0.247533	+	0.150071i
$955$	45.3747	−	12.8547i	1.46829	−	0.415968i
$956$	15.2104	−	29.1620i	0.491940	−	0.943166i
$957$			19.2227i			0.621381i
$958$	−7.77098	−	12.8177i	−0.251069	−	0.414122i
$959$	18.3566			0.592765
$960$	16.4445	−	7.04130i	0.530742	−	0.227257i
$961$	−34.7574			−1.12121
$962$	−4.59198	−	7.57417i	−0.148051	−	0.244201i
$963$			3.88249i			0.125111i
$964$	4.35631	−	8.35207i	0.140307	−	0.269002i
$965$	23.4881	−	42.0571i	0.756110	−	1.35387i
$966$	−5.86662	+	3.55674i	−0.188755	+	0.114436i
$967$	−7.94580	+	7.94580i	−0.255520	+	0.255520i	−0.823229	−	0.567709i	$-0.807830\pi$
$967$	−7.94580	+	7.94580i	−0.255520	+	0.255520i	0.567709	+	0.823229i	$0.307830\pi$
$968$	−2.82680	−	43.9361i	−0.0908566	−	1.41216i
$969$	24.1375			0.775408
$970$	−0.162956	−	4.56470i	−0.00523219	−	0.146564i
$971$	27.9413	−	27.9413i	0.896679	−	0.896679i	−0.0984615	−	0.995141i	$-0.531392\pi$
$971$	27.9413	−	27.9413i	0.896679	−	0.896679i	0.995141	+	0.0984615i	$0.0313921\pi$
$972$	−1.77328	−	0.924916i	−0.0568781	−	0.0296667i
$973$	12.3378			0.395533
$974$	−45.0408	−	11.0405i	−1.44320	−	0.353761i
$975$	7.19056	+	11.6722i	0.230282	+	0.373808i
$976$	−26.8481	−	4.77834i	−0.859388	−	0.152951i
$977$	−26.4111	+	26.4111i	−0.844968	+	0.844968i	−0.989500	−	0.144533i	$-0.953832\pi$
$977$	−26.4111	+	26.4111i	−0.844968	+	0.844968i	0.144533	+	0.989500i	$0.453832\pi$
$978$	2.07305	+	3.41936i	0.0662888	+	0.109339i
$979$	−36.5631	+	36.5631i	−1.16856	+	1.16856i
$980$	−5.77956	+	27.8390i	−0.184621	+	0.889285i
$981$	−2.51614	−	2.51614i	−0.0803342	−	0.0803342i
$982$	33.1118	+	8.11645i	1.05664	+	0.259006i
$983$	25.4583	+	25.4583i	0.811993	+	0.811993i	0.984932	−	0.172940i	$-0.0553265\pi$
$983$	25.4583	+	25.4583i	0.811993	+	0.811993i	−0.172940	+	0.984932i	$0.555327\pi$
$984$	6.42099	−	0.413119i	0.204694	−	0.0131698i
$985$	−8.56090	−	30.2185i	−0.272773	−	0.962840i
$986$	−8.05806	−	13.2913i	−0.256621	−	0.423280i
$987$		−	2.04657i		−	0.0651430i
$988$	−13.4720	−	42.8472i	−0.428601	−	1.36315i
$989$	−13.1182	−	13.1182i	−0.417134	−	0.417134i
$990$	−0.581490	−	16.2887i	−0.0184810	−	0.517688i
$991$			29.0499i			0.922801i	0.887192	+	0.461400i	$0.152653\pi$
$991$			29.0499i			0.922801i	−0.887192	+	0.461400i	$0.847347\pi$
$992$	−41.9501	−	18.5587i	−1.33192	−	0.589239i
$993$	−2.76903	−	2.76903i	−0.0878726	−	0.0878726i
$994$	3.10206	+	0.760383i	0.0983913	+	0.0241179i
$995$	−5.20780	+	1.47537i	−0.165098	+	0.0467724i
$996$	−1.82800	+	3.50472i	−0.0579225	+	0.111051i
$997$	−40.4803			−1.28202			−0.641011	−	0.767531i	$-0.721485\pi$
$997$	−40.4803			−1.28202			−0.641011	+	0.767531i	$0.721485\pi$
$998$	45.6977	+	11.2015i	1.44654	+	0.354578i
$999$			2.28428i			0.0722715i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.2.bc.e.43.3	yes	16
3.2	odd	2		720.2.bd.f.523.6		16
4.3	odd	2		960.2.bc.e.463.5		16
5.2	odd	4		240.2.y.e.187.8	yes	16
8.3	odd	2		1920.2.bc.j.1183.4		16
8.5	even	2		1920.2.bc.i.1183.4		16
15.2	even	4		720.2.z.f.667.1		16
16.3	odd	4		240.2.y.e.163.8	✓	16
16.5	even	4		1920.2.y.j.223.7		16
16.11	odd	4		1920.2.y.i.223.7		16
16.13	even	4		960.2.y.e.943.2		16
20.7	even	4		960.2.y.e.847.2		16
40.27	even	4		1920.2.y.j.1567.7		16
40.37	odd	4		1920.2.y.i.1567.7		16
48.35	even	4		720.2.z.f.163.1		16
80.27	even	4		1920.2.bc.i.607.4		16
80.37	odd	4		1920.2.bc.j.607.4		16
80.67	even	4	inner	240.2.bc.e.67.3	yes	16
80.77	odd	4		960.2.bc.e.367.5		16
240.227	odd	4		720.2.bd.f.307.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.y.e.163.8	✓	16	16.3	odd	4
240.2.y.e.187.8	yes	16	5.2	odd	4
240.2.bc.e.43.3	yes	16	1.1	even	1	trivial
240.2.bc.e.67.3	yes	16	80.67	even	4	inner
720.2.z.f.163.1		16	48.35	even	4
720.2.z.f.667.1		16	15.2	even	4
720.2.bd.f.307.6		16	240.227	odd	4
720.2.bd.f.523.6		16	3.2	odd	2
960.2.y.e.847.2		16	20.7	even	4
960.2.y.e.943.2		16	16.13	even	4
960.2.bc.e.367.5		16	80.77	odd	4
960.2.bc.e.463.5		16	4.3	odd	2
1920.2.y.i.223.7		16	16.11	odd	4
1920.2.y.i.1567.7		16	40.37	odd	4
1920.2.y.j.223.7		16	16.5	even	4
1920.2.y.j.1567.7		16	40.27	even	4
1920.2.bc.i.607.4		16	80.27	even	4
1920.2.bc.i.1183.4		16	8.5	even	2
1920.2.bc.j.607.4		16	80.37	odd	4
1920.2.bc.j.1183.4		16	8.3	odd	2

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:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	240.bc (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.733173 - 1.20932i) q^{2} +1.00000i q^{3} +(-0.924916 + 1.77328i) q^{4} +(-0.609492 - 2.15140i) q^{5} +(1.20932 - 0.733173i) q^{6} +(0.566689 - 0.566689i) q^{7} +(2.82259 - 0.181602i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(-0.733173 - 1.20932i) q^{2} +1.00000i q^{3} +(-0.924916 + 1.77328i) q^{4} +(-0.609492 - 2.15140i) q^{5} +(1.20932 - 0.733173i) q^{6} +(0.566689 - 0.566689i) q^{7} +(2.82259 - 0.181602i) q^{8} -1.00000 q^{9} +(-2.15487 + 2.31442i) q^{10} +(3.64458 - 3.64458i) q^{11} +(-1.77328 - 0.924916i) q^{12} -2.74185 q^{13} +(-1.10079 - 0.269828i) q^{14} +(2.15140 - 0.609492i) q^{15} +(-2.28906 - 3.28027i) q^{16} +(2.08381 - 2.08381i) q^{17} +(0.733173 + 1.20932i) q^{18} +(5.79168 - 5.79168i) q^{19} +(4.37877 + 0.909061i) q^{20} +(0.566689 + 0.566689i) q^{21} +(-7.07957 - 1.73536i) q^{22} +(-4.28027 - 4.28027i) q^{23} +(0.181602 + 2.82259i) q^{24} +(-4.25704 + 2.62252i) q^{25} +(2.01025 + 3.31578i) q^{26} -1.00000i q^{27} +(0.480760 + 1.52904i) q^{28} +(2.63716 + 2.63716i) q^{29} +(-2.31442 - 2.15487i) q^{30} +8.10909i q^{31} +(-2.28863 + 5.17322i) q^{32} +(3.64458 + 3.64458i) q^{33} +(-4.04778 - 0.992201i) q^{34} +(-1.56457 - 0.873782i) q^{35} +(0.924916 - 1.77328i) q^{36} -2.28428 q^{37} +(-11.2503 - 2.75770i) q^{38} -2.74185i q^{39} +(-2.11105 - 5.96184i) q^{40} -2.27486i q^{41} +(0.269828 - 1.10079i) q^{42} +3.06480 q^{43} +(3.09194 + 9.83379i) q^{44} +(0.609492 + 2.15140i) q^{45} +(-2.03805 + 8.31441i) q^{46} +(-1.80573 - 1.80573i) q^{47} +(3.28027 - 2.28906i) q^{48} +6.35773i q^{49} +(6.29262 + 3.22536i) q^{50} +(2.08381 + 2.08381i) q^{51} +(2.53598 - 4.86207i) q^{52} +6.32215i q^{53} +(-1.20932 + 0.733173i) q^{54} +(-10.0623 - 5.61960i) q^{55} +(1.49662 - 1.70244i) q^{56} +(5.79168 + 5.79168i) q^{57} +(1.25568 - 5.12267i) q^{58} +(5.56839 + 5.56839i) q^{59} +(-0.909061 + 4.37877i) q^{60} +(4.82071 - 4.82071i) q^{61} +(9.80650 - 5.94536i) q^{62} +(-0.566689 + 0.566689i) q^{63} +(7.93404 - 1.02518i) q^{64} +(1.67114 + 5.89881i) q^{65} +(1.73536 - 7.07957i) q^{66} +3.34296 q^{67} +(1.76783 + 5.62252i) q^{68} +(4.28027 - 4.28027i) q^{69} +(0.0904149 + 2.53270i) q^{70} -2.81803 q^{71} +(-2.82259 + 0.181602i) q^{72} +(-10.7052 + 10.7052i) q^{73} +(1.67477 + 2.76243i) q^{74} +(-2.62252 - 4.25704i) q^{75} +(4.91347 + 15.6271i) q^{76} -4.13068i q^{77} +(-3.31578 + 2.01025i) q^{78} +12.1478 q^{79} +(-5.66201 + 6.92399i) q^{80} +1.00000 q^{81} +(-2.75103 + 1.66786i) q^{82} -1.97640i q^{83} +(-1.52904 + 0.480760i) q^{84} +(-5.75316 - 3.21304i) q^{85} +(-2.24703 - 3.70633i) q^{86} +(-2.63716 + 2.63716i) q^{87} +(9.62528 - 10.9490i) q^{88} -10.0322 q^{89} +(2.15487 - 2.31442i) q^{90} +(-1.55378 + 1.55378i) q^{91} +(11.5490 - 3.63124i) q^{92} -8.10909 q^{93} +(-0.859794 + 3.50761i) q^{94} +(-15.9902 - 8.93024i) q^{95} +(-5.17322 - 2.28863i) q^{96} +(-1.02135 + 1.02135i) q^{97} +(7.68853 - 4.66131i) q^{98} +(-3.64458 + 3.64458i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{2} + 8 q^{4} - 8 q^{5} + 2 q^{6} - 4 q^{7} + 8 q^{8} - 16 q^{9}+O(q^{10}) \) 16 * q + 2 * q^2 + 8 * q^4 - 8 * q^5 + 2 * q^6 - 4 * q^7 + 8 * q^8 - 16 * q^9	\( 16 q + 2 q^{2} + 8 q^{4} - 8 q^{5} + 2 q^{6} - 4 q^{7} + 8 q^{8} - 16 q^{9} - 2 q^{10} - 4 q^{12} - 8 q^{13} + 4 q^{14} + 4 q^{15} - 8 q^{16} - 8 q^{17} - 2 q^{18} - 8 q^{19} + 4 q^{20} - 4 q^{21} + 4 q^{24} - 32 q^{25} + 20 q^{26} + 12 q^{28} - 12 q^{29} + 2 q^{30} - 28 q^{32} + 12 q^{35} - 8 q^{36} - 24 q^{37} + 16 q^{38} + 16 q^{40} + 24 q^{42} + 24 q^{43} - 52 q^{44} + 8 q^{45} - 16 q^{46} + 32 q^{47} - 16 q^{48} + 6 q^{50} - 8 q^{51} + 24 q^{52} - 2 q^{54} - 4 q^{55} + 20 q^{56} - 8 q^{57} + 12 q^{58} + 24 q^{59} + 24 q^{60} + 40 q^{61} + 28 q^{62} + 4 q^{63} + 8 q^{64} - 4 q^{65} - 8 q^{66} + 16 q^{67} - 8 q^{68} + 12 q^{70} - 8 q^{72} - 8 q^{73} - 64 q^{74} + 24 q^{75} + 16 q^{76} + 12 q^{78} + 48 q^{79} + 16 q^{81} - 32 q^{82} - 12 q^{84} - 8 q^{85} - 8 q^{86} + 12 q^{87} + 24 q^{88} + 2 q^{90} - 40 q^{91} - 16 q^{92} - 32 q^{93} + 20 q^{94} - 8 q^{95} - 28 q^{96} + 48 q^{97} + 62 q^{98}+O(q^{100}) \) 16 * q + 2 * q^2 + 8 * q^4 - 8 * q^5 + 2 * q^6 - 4 * q^7 + 8 * q^8 - 16 * q^9 - 2 * q^10 - 4 * q^12 - 8 * q^13 + 4 * q^14 + 4 * q^15 - 8 * q^16 - 8 * q^17 - 2 * q^18 - 8 * q^19 + 4 * q^20 - 4 * q^21 + 4 * q^24 - 32 * q^25 + 20 * q^26 + 12 * q^28 - 12 * q^29 + 2 * q^30 - 28 * q^32 + 12 * q^35 - 8 * q^36 - 24 * q^37 + 16 * q^38 + 16 * q^40 + 24 * q^42 + 24 * q^43 - 52 * q^44 + 8 * q^45 - 16 * q^46 + 32 * q^47 - 16 * q^48 + 6 * q^50 - 8 * q^51 + 24 * q^52 - 2 * q^54 - 4 * q^55 + 20 * q^56 - 8 * q^57 + 12 * q^58 + 24 * q^59 + 24 * q^60 + 40 * q^61 + 28 * q^62 + 4 * q^63 + 8 * q^64 - 4 * q^65 - 8 * q^66 + 16 * q^67 - 8 * q^68 + 12 * q^70 - 8 * q^72 - 8 * q^73 - 64 * q^74 + 24 * q^75 + 16 * q^76 + 12 * q^78 + 48 * q^79 + 16 * q^81 - 32 * q^82 - 12 * q^84 - 8 * q^85 - 8 * q^86 + 12 * q^87 + 24 * q^88 + 2 * q^90 - 40 * q^91 - 16 * q^92 - 32 * q^93 + 20 * q^94 - 8 * q^95 - 28 * q^96 + 48 * q^97 + 62 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more