LMFDB - Embedded newform 1320.2.z.b.571.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1320,2,Mod(571,1320)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1320, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1320.571");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1320 = 2^{3} \cdot 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1320.z (of order $2$, degree $1$, 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:	$10.5402530668$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 25 $ x^4 + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			571.3
Root			$-1.58114 + 1.58114i$ of defining polynomial
Character	$\chi$	$=$	1320.571
Dual form			1320.2.z.b.571.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.00000i) q^{2} -1.00000 q^{3} +2.00000i q^{4} -1.00000i q^{5} +(-1.00000 - 1.00000i) q^{6} -2.00000 q^{7} +(-2.00000 + 2.00000i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(1.00000 + 1.00000i) q^{2} -1.00000 q^{3} +2.00000i q^{4} -1.00000i q^{5} +(-1.00000 - 1.00000i) q^{6} -2.00000 q^{7} +(-2.00000 + 2.00000i) q^{8} +1.00000 q^{9} +(1.00000 - 1.00000i) q^{10} +(-3.16228 - 1.00000i) q^{11} -2.00000i q^{12} +2.00000 q^{13} +(-2.00000 - 2.00000i) q^{14} +1.00000i q^{15} -4.00000 q^{16} +(1.00000 + 1.00000i) q^{18} -4.32456i q^{19} +2.00000 q^{20} +2.00000 q^{21} +(-2.16228 - 4.16228i) q^{22} -4.32456i q^{23} +(2.00000 - 2.00000i) q^{24} -1.00000 q^{25} +(2.00000 + 2.00000i) q^{26} -1.00000 q^{27} -4.00000i q^{28} +2.32456 q^{29} +(-1.00000 + 1.00000i) q^{30} -4.00000i q^{31} +(-4.00000 - 4.00000i) q^{32} +(3.16228 + 1.00000i) q^{33} +2.00000i q^{35} +2.00000i q^{36} -4.32456i q^{37} +(4.32456 - 4.32456i) q^{38} -2.00000 q^{39} +(2.00000 + 2.00000i) q^{40} +8.32456i q^{41} +(2.00000 + 2.00000i) q^{42} -10.3246i q^{43} +(2.00000 - 6.32456i) q^{44} -1.00000i q^{45} +(4.32456 - 4.32456i) q^{46} -4.32456i q^{47} +4.00000 q^{48} -3.00000 q^{49} +(-1.00000 - 1.00000i) q^{50} +4.00000i q^{52} -6.00000i q^{53} +(-1.00000 - 1.00000i) q^{54} +(-1.00000 + 3.16228i) q^{55} +(4.00000 - 4.00000i) q^{56} +4.32456i q^{57} +(2.32456 + 2.32456i) q^{58} -10.3246 q^{59} -2.00000 q^{60} +2.32456 q^{61} +(4.00000 - 4.00000i) q^{62} -2.00000 q^{63} -8.00000i q^{64} -2.00000i q^{65} +(2.16228 + 4.16228i) q^{66} +4.32456i q^{69} +(-2.00000 + 2.00000i) q^{70} +2.32456i q^{71} +(-2.00000 + 2.00000i) q^{72} -2.32456i q^{73} +(4.32456 - 4.32456i) q^{74} +1.00000 q^{75} +8.64911 q^{76} +(6.32456 + 2.00000i) q^{77} +(-2.00000 - 2.00000i) q^{78} +10.0000 q^{79} +4.00000i q^{80} +1.00000 q^{81} +(-8.32456 + 8.32456i) q^{82} -10.6491i q^{83} +4.00000i q^{84} +(10.3246 - 10.3246i) q^{86} -2.32456 q^{87} +(8.32456 - 4.32456i) q^{88} -6.64911 q^{89} +(1.00000 - 1.00000i) q^{90} -4.00000 q^{91} +8.64911 q^{92} +4.00000i q^{93} +(4.32456 - 4.32456i) q^{94} -4.32456 q^{95} +(4.00000 + 4.00000i) q^{96} -14.6491 q^{97} +(-3.00000 - 3.00000i) q^{98} +(-3.16228 - 1.00000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 4 q^{3} - 4 q^{6} - 8 q^{7} - 8 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 - 4 * q^3 - 4 * q^6 - 8 * q^7 - 8 * q^8 + 4 * q^9	$ 4 q + 4 q^{2} - 4 q^{3} - 4 q^{6} - 8 q^{7} - 8 q^{8} + 4 q^{9} + 4 q^{10} + 8 q^{13} - 8 q^{14} - 16 q^{16} + 4 q^{18} + 8 q^{20} + 8 q^{21} + 4 q^{22} + 8 q^{24} - 4 q^{25} + 8 q^{26} - 4 q^{27} - 16 q^{29} - 4 q^{30} - 16 q^{32} - 8 q^{38} - 8 q^{39} + 8 q^{40} + 8 q^{42} + 8 q^{44} - 8 q^{46} + 16 q^{48} - 12 q^{49} - 4 q^{50} - 4 q^{54} - 4 q^{55} + 16 q^{56} - 16 q^{58} - 16 q^{59} - 8 q^{60} - 16 q^{61} + 16 q^{62} - 8 q^{63} - 4 q^{66} - 8 q^{70} - 8 q^{72} - 8 q^{74} + 4 q^{75} - 16 q^{76} - 8 q^{78} + 40 q^{79} + 4 q^{81} - 8 q^{82} + 16 q^{86} + 16 q^{87} + 8 q^{88} + 24 q^{89} + 4 q^{90} - 16 q^{91} - 16 q^{92} - 8 q^{94} + 8 q^{95} + 16 q^{96} - 8 q^{97} - 12 q^{98}+O(q^{100}) $ 4 * q + 4 * q^2 - 4 * q^3 - 4 * q^6 - 8 * q^7 - 8 * q^8 + 4 * q^9 + 4 * q^10 + 8 * q^13 - 8 * q^14 - 16 * q^16 + 4 * q^18 + 8 * q^20 + 8 * q^21 + 4 * q^22 + 8 * q^24 - 4 * q^25 + 8 * q^26 - 4 * q^27 - 16 * q^29 - 4 * q^30 - 16 * q^32 - 8 * q^38 - 8 * q^39 + 8 * q^40 + 8 * q^42 + 8 * q^44 - 8 * q^46 + 16 * q^48 - 12 * q^49 - 4 * q^50 - 4 * q^54 - 4 * q^55 + 16 * q^56 - 16 * q^58 - 16 * q^59 - 8 * q^60 - 16 * q^61 + 16 * q^62 - 8 * q^63 - 4 * q^66 - 8 * q^70 - 8 * q^72 - 8 * q^74 + 4 * q^75 - 16 * q^76 - 8 * q^78 + 40 * q^79 + 4 * q^81 - 8 * q^82 + 16 * q^86 + 16 * q^87 + 8 * q^88 + 24 * q^89 + 4 * q^90 - 16 * q^91 - 16 * q^92 - 8 * q^94 + 8 * q^95 + 16 * q^96 - 8 * q^97 - 12 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1320\mathbb{Z}\right)^\times$.

$n$	$661$	$881$	$991$	$1057$	$1201$
$\chi(n)$	$-1$	$1$	$-1$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.00000	+	1.00000i	0.707107	+	0.707107i
$2$	1.00000	+	1.00000i	0.707107	+	0.707107i
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$			2.00000i			1.00000i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	−1.00000	−	1.00000i	−0.408248	−	0.408248i
$7$	−2.00000			−0.755929			−0.377964	−	0.925820i	$-0.623376\pi$
$7$	−2.00000			−0.755929			−0.377964	+	0.925820i	$0.623376\pi$
$8$	−2.00000	+	2.00000i	−0.707107	+	0.707107i
$9$	1.00000			0.333333
$10$	1.00000	−	1.00000i	0.316228	−	0.316228i
$11$	−3.16228	−	1.00000i	−0.953463	−	0.301511i
$11$	−3.16228	−	1.00000i	−0.953463	−	0.301511i
$12$		−	2.00000i		−	0.577350i
$13$	2.00000			0.554700			0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000			0.554700			0.277350	+	0.960769i	$0.410544\pi$
$14$	−2.00000	−	2.00000i	−0.534522	−	0.534522i
$15$			1.00000i			0.258199i
$16$	−4.00000			−1.00000
$17$		0			0		1.00000			$0$
$17$		0			0		−1.00000			$\pi$
$18$	1.00000	+	1.00000i	0.235702	+	0.235702i
$19$		−	4.32456i		−	0.992121i	−0.868288	−	0.496061i	$-0.834779\pi$
$19$		−	4.32456i		−	0.992121i	0.868288	−	0.496061i	$-0.165221\pi$
$20$	2.00000			0.447214
$21$	2.00000			0.436436
$22$	−2.16228	−	4.16228i	−0.460999	−	0.887401i
$23$		−	4.32456i		−	0.901732i	−0.892592	−	0.450866i	$-0.851115\pi$
$23$		−	4.32456i		−	0.901732i	0.892592	−	0.450866i	$-0.148885\pi$
$24$	2.00000	−	2.00000i	0.408248	−	0.408248i
$25$	−1.00000			−0.200000
$26$	2.00000	+	2.00000i	0.392232	+	0.392232i
$27$	−1.00000			−0.192450
$28$		−	4.00000i		−	0.755929i
$29$	2.32456			0.431659			0.215830	−	0.976431i	$-0.430754\pi$
$29$	2.32456			0.431659			0.215830	+	0.976431i	$0.430754\pi$
$30$	−1.00000	+	1.00000i	−0.182574	+	0.182574i
$31$		−	4.00000i		−	0.718421i	−0.933257	−	0.359211i	$-0.883046\pi$
$31$		−	4.00000i		−	0.718421i	0.933257	−	0.359211i	$-0.116954\pi$
$32$	−4.00000	−	4.00000i	−0.707107	−	0.707107i
$33$	3.16228	+	1.00000i	0.550482	+	0.174078i
$34$		0			0
$35$			2.00000i			0.338062i
$36$			2.00000i			0.333333i
$37$		−	4.32456i		−	0.710953i	−0.934685	−	0.355476i	$-0.884319\pi$
$37$		−	4.32456i		−	0.710953i	0.934685	−	0.355476i	$-0.115681\pi$
$38$	4.32456	−	4.32456i	0.701536	−	0.701536i
$39$	−2.00000			−0.320256
$40$	2.00000	+	2.00000i	0.316228	+	0.316228i
$41$			8.32456i			1.30008i	0.759901	+	0.650039i	$0.225247\pi$
$41$			8.32456i			1.30008i	−0.759901	+	0.650039i	$0.774753\pi$
$42$	2.00000	+	2.00000i	0.308607	+	0.308607i
$43$		−	10.3246i		−	1.57448i	−0.616647	−	0.787240i	$-0.711509\pi$
$43$		−	10.3246i		−	1.57448i	0.616647	−	0.787240i	$-0.288491\pi$
$44$	2.00000	−	6.32456i	0.301511	−	0.953463i
$45$		−	1.00000i		−	0.149071i
$46$	4.32456	−	4.32456i	0.637621	−	0.637621i
$47$		−	4.32456i		−	0.630801i	−0.948959	−	0.315401i	$-0.897861\pi$
$47$		−	4.32456i		−	0.630801i	0.948959	−	0.315401i	$-0.102139\pi$
$48$	4.00000			0.577350
$49$	−3.00000			−0.428571
$50$	−1.00000	−	1.00000i	−0.141421	−	0.141421i
$51$		0			0
$52$			4.00000i			0.554700i
$53$		−	6.00000i		−	0.824163i	−0.911147	−	0.412082i	$-0.864802\pi$
$53$		−	6.00000i		−	0.824163i	0.911147	−	0.412082i	$-0.135198\pi$
$54$	−1.00000	−	1.00000i	−0.136083	−	0.136083i
$55$	−1.00000	+	3.16228i	−0.134840	+	0.426401i
$56$	4.00000	−	4.00000i	0.534522	−	0.534522i
$57$			4.32456i			0.572801i
$58$	2.32456	+	2.32456i	0.305229	+	0.305229i
$59$	−10.3246			−1.34414			−0.672071	−	0.740486i	$-0.734595\pi$
$59$	−10.3246			−1.34414			−0.672071	+	0.740486i	$0.734595\pi$
$60$	−2.00000			−0.258199
$61$	2.32456			0.297629			0.148814	−	0.988865i	$-0.452454\pi$
$61$	2.32456			0.297629			0.148814	+	0.988865i	$0.452454\pi$
$62$	4.00000	−	4.00000i	0.508001	−	0.508001i
$63$	−2.00000			−0.251976
$64$		−	8.00000i		−	1.00000i
$65$		−	2.00000i		−	0.248069i
$66$	2.16228	+	4.16228i	0.266158	+	0.512341i
$67$		0			0			−	1.00000i	$-0.5\pi$
$67$		0			0				1.00000i	$0.5\pi$
$68$		0			0
$69$			4.32456i			0.520615i
$70$	−2.00000	+	2.00000i	−0.239046	+	0.239046i
$71$			2.32456i			0.275874i	0.990441	+	0.137937i	$0.0440471\pi$
$71$			2.32456i			0.275874i	−0.990441	+	0.137937i	$0.955953\pi$
$72$	−2.00000	+	2.00000i	−0.235702	+	0.235702i
$73$		−	2.32456i		−	0.272069i	−0.990704	−	0.136034i	$-0.956564\pi$
$73$		−	2.32456i		−	0.272069i	0.990704	−	0.136034i	$-0.0434357\pi$
$74$	4.32456	−	4.32456i	0.502719	−	0.502719i
$75$	1.00000			0.115470
$76$	8.64911			0.992121
$77$	6.32456	+	2.00000i	0.720750	+	0.227921i
$78$	−2.00000	−	2.00000i	−0.226455	−	0.226455i
$79$	10.0000			1.12509			0.562544	−	0.826767i	$-0.309823\pi$
$79$	10.0000			1.12509			0.562544	+	0.826767i	$0.309823\pi$
$80$			4.00000i			0.447214i
$81$	1.00000			0.111111
$82$	−8.32456	+	8.32456i	−0.919293	+	0.919293i
$83$		−	10.6491i		−	1.16889i	−0.811433	−	0.584446i	$-0.801312\pi$
$83$		−	10.6491i		−	1.16889i	0.811433	−	0.584446i	$-0.198688\pi$
$84$			4.00000i			0.436436i
$85$		0			0
$86$	10.3246	−	10.3246i	1.11333	−	1.11333i
$87$	−2.32456			−0.249218
$88$	8.32456	−	4.32456i	0.887401	−	0.460999i
$89$	−6.64911			−0.704804			−0.352402	−	0.935849i	$-0.614635\pi$
$89$	−6.64911			−0.704804			−0.352402	+	0.935849i	$0.614635\pi$
$90$	1.00000	−	1.00000i	0.105409	−	0.105409i
$91$	−4.00000			−0.419314
$92$	8.64911			0.901732
$93$			4.00000i			0.414781i
$94$	4.32456	−	4.32456i	0.446044	−	0.446044i
$95$	−4.32456			−0.443690
$96$	4.00000	+	4.00000i	0.408248	+	0.408248i
$97$	−14.6491			−1.48739			−0.743696	−	0.668518i	$-0.766929\pi$
$97$	−14.6491			−1.48739			−0.743696	+	0.668518i	$0.766929\pi$
$98$	−3.00000	−	3.00000i	−0.303046	−	0.303046i
$99$	−3.16228	−	1.00000i	−0.317821	−	0.100504i
$100$		−	2.00000i		−	0.200000i
$101$	10.3246			1.02733			0.513666	−	0.857990i	$-0.328287\pi$
$101$	10.3246			1.02733			0.513666	+	0.857990i	$0.328287\pi$
$102$		0			0
$103$			14.3246i			1.41144i	0.708491	+	0.705720i	$0.249376\pi$
$103$			14.3246i			1.41144i	−0.708491	+	0.705720i	$0.750624\pi$
$104$	−4.00000	+	4.00000i	−0.392232	+	0.392232i
$105$		−	2.00000i		−	0.195180i
$106$	6.00000	−	6.00000i	0.582772	−	0.582772i
$107$			10.0000i			0.966736i	0.875417	+	0.483368i	$0.160587\pi$
$107$			10.0000i			0.966736i	−0.875417	+	0.483368i	$0.839413\pi$
$108$		−	2.00000i		−	0.192450i
$109$	6.32456			0.605783			0.302891	−	0.953025i	$-0.402048\pi$
$109$	6.32456			0.605783			0.302891	+	0.953025i	$0.402048\pi$
$110$	−4.16228	+	2.16228i	−0.396858	+	0.206165i
$111$			4.32456i			0.410469i
$112$	8.00000			0.755929
$113$	−14.3246			−1.34754			−0.673770	−	0.738941i	$-0.735326\pi$
$113$	−14.3246			−1.34754			−0.673770	+	0.738941i	$0.735326\pi$
$114$	−4.32456	+	4.32456i	−0.405032	+	0.405032i
$115$	−4.32456			−0.403267
$116$			4.64911i			0.431659i
$117$	2.00000			0.184900
$118$	−10.3246	−	10.3246i	−0.950452	−	0.950452i
$119$		0			0
$120$	−2.00000	−	2.00000i	−0.182574	−	0.182574i
$121$	9.00000	+	6.32456i	0.818182	+	0.574960i
$122$	2.32456	+	2.32456i	0.210455	+	0.210455i
$123$		−	8.32456i		−	0.750600i
$124$	8.00000			0.718421
$125$			1.00000i			0.0894427i
$126$	−2.00000	−	2.00000i	−0.178174	−	0.178174i
$127$	−14.0000			−1.24230			−0.621150	−	0.783692i	$-0.713334\pi$
$127$	−14.0000			−1.24230			−0.621150	+	0.783692i	$0.713334\pi$
$128$	8.00000	−	8.00000i	0.707107	−	0.707107i
$129$			10.3246i			0.909026i
$130$	2.00000	−	2.00000i	0.175412	−	0.175412i
$131$			6.00000i			0.524222i	0.965038	+	0.262111i	$0.0844187\pi$
$131$			6.00000i			0.524222i	−0.965038	+	0.262111i	$0.915581\pi$
$132$	−2.00000	+	6.32456i	−0.174078	+	0.550482i
$133$			8.64911i			0.749973i
$134$		0			0
$135$			1.00000i			0.0860663i
$136$		0			0
$137$	5.67544			0.484886			0.242443	−	0.970166i	$-0.422051\pi$
$137$	5.67544			0.484886			0.242443	+	0.970166i	$0.422051\pi$
$138$	−4.32456	+	4.32456i	−0.368131	+	0.368131i
$139$		−	4.32456i		−	0.366804i	−0.983038	−	0.183402i	$-0.941289\pi$
$139$		−	4.32456i		−	0.366804i	0.983038	−	0.183402i	$-0.0587110\pi$
$140$	−4.00000			−0.338062
$141$			4.32456i			0.364193i
$142$	−2.32456	+	2.32456i	−0.195072	+	0.195072i
$143$	−6.32456	−	2.00000i	−0.528886	−	0.167248i
$144$	−4.00000			−0.333333
$145$		−	2.32456i		−	0.193044i
$146$	2.32456	−	2.32456i	0.192382	−	0.192382i
$147$	3.00000			0.247436
$148$	8.64911			0.710953
$149$	−2.32456			−0.190435			−0.0952175	−	0.995456i	$-0.530355\pi$
$149$	−2.32456			−0.190435			−0.0952175	+	0.995456i	$0.530355\pi$
$150$	1.00000	+	1.00000i	0.0816497	+	0.0816497i
$151$	22.6491			1.84316			0.921579	−	0.388190i	$-0.126900\pi$
$151$	22.6491			1.84316			0.921579	+	0.388190i	$0.126900\pi$
$152$	8.64911	+	8.64911i	0.701536	+	0.701536i
$153$		0			0
$154$	4.32456	+	8.32456i	0.348483	+	0.670812i
$155$	−4.00000			−0.321288
$156$		−	4.00000i		−	0.320256i
$157$		−	16.3246i		−	1.30284i	−0.758717	−	0.651421i	$-0.774173\pi$
$157$		−	16.3246i		−	1.30284i	0.758717	−	0.651421i	$-0.225827\pi$
$158$	10.0000	+	10.0000i	0.795557	+	0.795557i
$159$			6.00000i			0.475831i
$160$	−4.00000	+	4.00000i	−0.316228	+	0.316228i
$161$			8.64911i			0.681645i
$162$	1.00000	+	1.00000i	0.0785674	+	0.0785674i
$163$	0.649111			0.0508423			0.0254211	−	0.999677i	$-0.491907\pi$
$163$	0.649111			0.0508423			0.0254211	+	0.999677i	$0.491907\pi$
$164$	−16.6491			−1.30008
$165$	1.00000	−	3.16228i	0.0778499	−	0.246183i
$166$	10.6491	−	10.6491i	0.826531	−	0.826531i
$167$	−14.6491			−1.13358			−0.566791	−	0.823862i	$-0.691815\pi$
$167$	−14.6491			−1.13358			−0.566791	+	0.823862i	$0.691815\pi$
$168$	−4.00000	+	4.00000i	−0.308607	+	0.308607i
$169$	−9.00000			−0.692308
$170$		0			0
$171$		−	4.32456i		−	0.330707i
$172$	20.6491			1.57448
$173$	−12.0000			−0.912343			−0.456172	−	0.889892i	$-0.650780\pi$
$173$	−12.0000			−0.912343			−0.456172	+	0.889892i	$0.650780\pi$
$174$	−2.32456	−	2.32456i	−0.176224	−	0.176224i
$175$	2.00000			0.151186
$176$	12.6491	+	4.00000i	0.953463	+	0.301511i
$177$	10.3246			0.776041
$178$	−6.64911	−	6.64911i	−0.498372	−	0.498372i
$179$	−18.9737			−1.41816			−0.709079	−	0.705129i	$-0.750889\pi$
$179$	−18.9737			−1.41816			−0.709079	+	0.705129i	$0.750889\pi$
$180$	2.00000			0.149071
$181$		−	8.00000i		−	0.594635i	−0.954779	−	0.297318i	$-0.903908\pi$
$181$		−	8.00000i		−	0.594635i	0.954779	−	0.297318i	$-0.0960920\pi$
$182$	−4.00000	−	4.00000i	−0.296500	−	0.296500i
$183$	−2.32456			−0.171836
$184$	8.64911	+	8.64911i	0.637621	+	0.637621i
$185$	−4.32456			−0.317948
$186$	−4.00000	+	4.00000i	−0.293294	+	0.293294i
$187$		0			0
$188$	8.64911			0.630801
$189$	2.00000			0.145479
$190$	−4.32456	−	4.32456i	−0.313736	−	0.313736i
$191$			26.3246i			1.90478i	0.304886	+	0.952389i	$0.401382\pi$
$191$			26.3246i			1.90478i	−0.304886	+	0.952389i	$0.598618\pi$
$192$			8.00000i			0.577350i
$193$		−	5.67544i		−	0.408527i	−0.978916	−	0.204264i	$-0.934520\pi$
$193$		−	5.67544i		−	0.408527i	0.978916	−	0.204264i	$-0.0654800\pi$
$194$	−14.6491	−	14.6491i	−1.05174	−	1.05174i
$195$			2.00000i			0.143223i
$196$		−	6.00000i		−	0.428571i
$197$	16.6491			1.18620			0.593100	−	0.805129i	$-0.297904\pi$
$197$	16.6491			1.18620			0.593100	+	0.805129i	$0.297904\pi$
$198$	−2.16228	−	4.16228i	−0.153666	−	0.295800i
$199$		−	4.00000i		−	0.283552i	−0.989899	−	0.141776i	$-0.954719\pi$
$199$		−	4.00000i		−	0.283552i	0.989899	−	0.141776i	$-0.0452813\pi$
$200$	2.00000	−	2.00000i	0.141421	−	0.141421i
$201$		0			0
$202$	10.3246	+	10.3246i	0.726433	+	0.726433i
$203$	−4.64911			−0.326304
$204$		0			0
$205$	8.32456			0.581412
$206$	−14.3246	+	14.3246i	−0.998039	+	0.998039i
$207$		−	4.32456i		−	0.300577i
$208$	−8.00000			−0.554700
$209$	−4.32456	+	13.6754i	−0.299136	+	0.945950i
$210$	2.00000	−	2.00000i	0.138013	−	0.138013i
$211$			0.324555i			0.0223433i	0.999938	+	0.0111717i	$0.00355612\pi$
$211$			0.324555i			0.0223433i	−0.999938	+	0.0111717i	$0.996444\pi$
$212$	12.0000			0.824163
$213$		−	2.32456i		−	0.159276i
$214$	−10.0000	+	10.0000i	−0.683586	+	0.683586i
$215$	−10.3246			−0.704129
$216$	2.00000	−	2.00000i	0.136083	−	0.136083i
$217$			8.00000i			0.543075i
$218$	6.32456	+	6.32456i	0.428353	+	0.428353i
$219$			2.32456i			0.157079i
$220$	−6.32456	−	2.00000i	−0.426401	−	0.134840i
$221$		0			0
$222$	−4.32456	+	4.32456i	−0.290245	+	0.290245i
$223$		−	5.67544i		−	0.380056i	−0.981779	−	0.190028i	$-0.939142\pi$
$223$		−	5.67544i		−	0.380056i	0.981779	−	0.190028i	$-0.0608579\pi$
$224$	8.00000	+	8.00000i	0.534522	+	0.534522i
$225$	−1.00000			−0.0666667
$226$	−14.3246	−	14.3246i	−0.952855	−	0.952855i
$227$		−	18.0000i		−	1.19470i	−0.801980	−	0.597351i	$-0.796220\pi$
$227$		−	18.0000i		−	1.19470i	0.801980	−	0.597351i	$-0.203780\pi$
$228$	−8.64911			−0.572801
$229$		−	4.00000i		−	0.264327i	−0.991228	−	0.132164i	$-0.957808\pi$
$229$		−	4.00000i		−	0.264327i	0.991228	−	0.132164i	$-0.0421925\pi$
$230$	−4.32456	−	4.32456i	−0.285153	−	0.285153i
$231$	−6.32456	−	2.00000i	−0.416125	−	0.131590i
$232$	−4.64911	+	4.64911i	−0.305229	+	0.305229i
$233$			16.6491i			1.09072i	0.838202	+	0.545360i	$0.183607\pi$
$233$			16.6491i			1.09072i	−0.838202	+	0.545360i	$0.816393\pi$
$234$	2.00000	+	2.00000i	0.130744	+	0.130744i
$235$	−4.32456			−0.282103
$236$		−	20.6491i		−	1.34414i
$237$	−10.0000			−0.649570
$238$		0			0
$239$	−25.2982			−1.63641			−0.818203	−	0.574930i	$-0.805029\pi$
$239$	−25.2982			−1.63641			−0.818203	+	0.574930i	$0.805029\pi$
$240$		−	4.00000i		−	0.258199i
$241$			4.00000i			0.257663i	0.991667	+	0.128831i	$0.0411226\pi$
$241$			4.00000i			0.257663i	−0.991667	+	0.128831i	$0.958877\pi$
$242$	2.67544	+	15.3246i	0.171984	+	0.985100i
$243$	−1.00000			−0.0641500
$244$			4.64911i			0.297629i
$245$			3.00000i			0.191663i
$246$	8.32456	−	8.32456i	0.530754	−	0.530754i
$247$		−	8.64911i		−	0.550330i
$248$	8.00000	+	8.00000i	0.508001	+	0.508001i
$249$			10.6491i			0.674860i
$250$	−1.00000	+	1.00000i	−0.0632456	+	0.0632456i
$251$	−14.9737			−0.945129			−0.472565	−	0.881296i	$-0.656672\pi$
$251$	−14.9737			−0.945129			−0.472565	+	0.881296i	$0.656672\pi$
$252$		−	4.00000i		−	0.251976i
$253$	−4.32456	+	13.6754i	−0.271882	+	0.859768i
$254$	−14.0000	−	14.0000i	−0.878438	−	0.878438i
$255$		0			0
$256$	16.0000			1.00000
$257$	−26.3246			−1.64208			−0.821040	−	0.570870i	$-0.806606\pi$
$257$	−26.3246			−1.64208			−0.821040	+	0.570870i	$0.806606\pi$
$258$	−10.3246	+	10.3246i	−0.642779	+	0.642779i
$259$			8.64911i			0.537430i
$260$	4.00000			0.248069
$261$	2.32456			0.143886
$262$	−6.00000	+	6.00000i	−0.370681	+	0.370681i
$263$	−14.6491			−0.903303			−0.451651	−	0.892194i	$-0.649165\pi$
$263$	−14.6491			−0.903303			−0.451651	+	0.892194i	$0.649165\pi$
$264$	−8.32456	+	4.32456i	−0.512341	+	0.266158i
$265$	−6.00000			−0.368577
$266$	−8.64911	+	8.64911i	−0.530311	+	0.530311i
$267$	6.64911			0.406919
$268$		0			0
$269$		−	2.64911i		−	0.161519i	−0.996734	−	0.0807596i	$-0.974265\pi$
$269$		−	2.64911i		−	0.161519i	0.996734	−	0.0807596i	$-0.0257346\pi$
$270$	−1.00000	+	1.00000i	−0.0608581	+	0.0608581i
$271$	−2.00000			−0.121491			−0.0607457	−	0.998153i	$-0.519348\pi$
$271$	−2.00000			−0.121491			−0.0607457	+	0.998153i	$0.519348\pi$
$272$		0			0
$273$	4.00000			0.242091
$274$	5.67544	+	5.67544i	0.342866	+	0.342866i
$275$	3.16228	+	1.00000i	0.190693	+	0.0603023i
$276$	−8.64911			−0.520615
$277$	18.6491			1.12052			0.560258	−	0.828318i	$-0.310702\pi$
$277$	18.6491			1.12052			0.560258	+	0.828318i	$0.310702\pi$
$278$	4.32456	−	4.32456i	0.259370	−	0.259370i
$279$		−	4.00000i		−	0.239474i
$280$	−4.00000	−	4.00000i	−0.239046	−	0.239046i
$281$			16.9737i			1.01256i	0.862368	+	0.506282i	$0.168981\pi$
$281$			16.9737i			1.01256i	−0.862368	+	0.506282i	$0.831019\pi$
$282$	−4.32456	+	4.32456i	−0.257524	+	0.257524i
$283$			5.67544i			0.337370i	0.985670	+	0.168685i	$0.0539521\pi$
$283$			5.67544i			0.337370i	−0.985670	+	0.168685i	$0.946048\pi$
$284$	−4.64911			−0.275874
$285$	4.32456			0.256165
$286$	−4.32456	−	8.32456i	−0.255716	−	0.492241i
$287$		−	16.6491i		−	0.982766i
$288$	−4.00000	−	4.00000i	−0.235702	−	0.235702i
$289$	17.0000			1.00000
$290$	2.32456	−	2.32456i	0.136503	−	0.136503i
$291$	14.6491			0.858746
$292$	4.64911			0.272069
$293$	3.35089			0.195761			0.0978805	−	0.995198i	$-0.468794\pi$
$293$	3.35089			0.195761			0.0978805	+	0.995198i	$0.468794\pi$
$294$	3.00000	+	3.00000i	0.174964	+	0.174964i
$295$			10.3246i			0.601119i
$296$	8.64911	+	8.64911i	0.502719	+	0.502719i
$297$	3.16228	+	1.00000i	0.183494	+	0.0580259i
$298$	−2.32456	−	2.32456i	−0.134658	−	0.134658i
$299$		−	8.64911i		−	0.500191i
$300$			2.00000i			0.115470i
$301$			20.6491i			1.19019i
$302$	22.6491	+	22.6491i	1.30331	+	1.30331i
$303$	−10.3246			−0.593130
$304$			17.2982i			0.992121i
$305$		−	2.32456i		−	0.133104i
$306$		0			0
$307$			14.3246i			0.817546i	0.912636	+	0.408773i	$0.134043\pi$
$307$			14.3246i			0.817546i	−0.912636	+	0.408773i	$0.865957\pi$
$308$	−4.00000	+	12.6491i	−0.227921	+	0.720750i
$309$		−	14.3246i		−	0.814895i
$310$	−4.00000	−	4.00000i	−0.227185	−	0.227185i
$311$			18.9737i			1.07590i	0.842977	+	0.537949i	$0.180801\pi$
$311$			18.9737i			1.07590i	−0.842977	+	0.537949i	$0.819199\pi$
$312$	4.00000	−	4.00000i	0.226455	−	0.226455i
$313$	30.6491			1.73239			0.866195	−	0.499706i	$-0.166559\pi$
$313$	30.6491			1.73239			0.866195	+	0.499706i	$0.166559\pi$
$314$	16.3246	−	16.3246i	0.921248	−	0.921248i
$315$			2.00000i			0.112687i
$316$			20.0000i			1.12509i
$317$		−	34.6491i		−	1.94609i	−0.230620	−	0.973044i	$-0.574075\pi$
$317$		−	34.6491i		−	1.94609i	0.230620	−	0.973044i	$-0.425925\pi$
$318$	−6.00000	+	6.00000i	−0.336463	+	0.336463i
$319$	−7.35089	−	2.32456i	−0.411571	−	0.130150i
$320$	−8.00000			−0.447214
$321$		−	10.0000i		−	0.558146i
$322$	−8.64911	+	8.64911i	−0.481996	+	0.481996i
$323$		0			0
$324$			2.00000i			0.111111i
$325$	−2.00000			−0.110940
$326$	0.649111	+	0.649111i	0.0359509	+	0.0359509i
$327$	−6.32456			−0.349749
$328$	−16.6491	−	16.6491i	−0.919293	−	0.919293i
$329$			8.64911i			0.476841i
$330$	4.16228	−	2.16228i	0.229126	−	0.119029i
$331$	10.0000			0.549650			0.274825	−	0.961494i	$-0.411380\pi$
$331$	10.0000			0.549650			0.274825	+	0.961494i	$0.411380\pi$
$332$	21.2982			1.16889
$333$		−	4.32456i		−	0.236984i
$334$	−14.6491	−	14.6491i	−0.801564	−	0.801564i
$335$		0			0
$336$	−8.00000			−0.436436
$337$		−	18.3246i		−	0.998202i	−0.866544	−	0.499101i	$-0.833664\pi$
$337$		−	18.3246i		−	0.998202i	0.866544	−	0.499101i	$-0.166336\pi$
$338$	−9.00000	−	9.00000i	−0.489535	−	0.489535i
$339$	14.3246			0.778003
$340$		0			0
$341$	−4.00000	+	12.6491i	−0.216612	+	0.684988i
$342$	4.32456	−	4.32456i	0.233845	−	0.233845i
$343$	20.0000			1.07990
$344$	20.6491	+	20.6491i	1.11333	+	1.11333i
$345$	4.32456			0.232826
$346$	−12.0000	−	12.0000i	−0.645124	−	0.645124i
$347$			14.6491i			0.786405i	0.919452	+	0.393203i	$0.128633\pi$
$347$			14.6491i			0.786405i	−0.919452	+	0.393203i	$0.871367\pi$
$348$		−	4.64911i		−	0.249218i
$349$	−10.3246			−0.552661			−0.276330	−	0.961063i	$-0.589118\pi$
$349$	−10.3246			−0.552661			−0.276330	+	0.961063i	$0.589118\pi$
$350$	2.00000	+	2.00000i	0.106904	+	0.106904i
$351$	−2.00000			−0.106752
$352$	8.64911	+	16.6491i	0.460999	+	0.887401i
$353$	13.6754			0.727870			0.363935	−	0.931424i	$-0.381433\pi$
$353$	13.6754			0.727870			0.363935	+	0.931424i	$0.381433\pi$
$354$	10.3246	+	10.3246i	0.548744	+	0.548744i
$355$	2.32456			0.123375
$356$		−	13.2982i		−	0.704804i
$357$		0			0
$358$	−18.9737	−	18.9737i	−1.00279	−	1.00279i
$359$	−12.0000			−0.633336			−0.316668	−	0.948536i	$-0.602564\pi$
$359$	−12.0000			−0.633336			−0.316668	+	0.948536i	$0.602564\pi$
$360$	2.00000	+	2.00000i	0.105409	+	0.105409i
$361$	0.298221			0.0156959
$362$	8.00000	−	8.00000i	0.420471	−	0.420471i
$363$	−9.00000	−	6.32456i	−0.472377	−	0.331953i
$364$		−	8.00000i		−	0.419314i
$365$	−2.32456			−0.121673
$366$	−2.32456	−	2.32456i	−0.121506	−	0.121506i
$367$		−	18.9737i		−	0.990417i	−0.868774	−	0.495209i	$-0.835092\pi$
$367$		−	18.9737i		−	0.990417i	0.868774	−	0.495209i	$-0.164908\pi$
$368$			17.2982i			0.901732i
$369$			8.32456i			0.433359i
$370$	−4.32456	−	4.32456i	−0.224823	−	0.224823i
$371$			12.0000i			0.623009i
$372$	−8.00000			−0.414781
$373$	−35.2982			−1.82767			−0.913836	−	0.406083i	$-0.866894\pi$
$373$	−35.2982			−1.82767			−0.913836	+	0.406083i	$0.866894\pi$
$374$		0			0
$375$		−	1.00000i		−	0.0516398i
$376$	8.64911	+	8.64911i	0.446044	+	0.446044i
$377$	4.64911			0.239441
$378$	2.00000	+	2.00000i	0.102869	+	0.102869i
$379$	30.6491			1.57434			0.787170	−	0.616737i	$-0.211546\pi$
$379$	30.6491			1.57434			0.787170	+	0.616737i	$0.211546\pi$
$380$		−	8.64911i		−	0.443690i
$381$	14.0000			0.717242
$382$	−26.3246	+	26.3246i	−1.34688	+	1.34688i
$383$		−	4.32456i		−	0.220974i	−0.993878	−	0.110487i	$-0.964759\pi$
$383$		−	4.32456i		−	0.220974i	0.993878	−	0.110487i	$-0.0352411\pi$
$384$	−8.00000	+	8.00000i	−0.408248	+	0.408248i
$385$	2.00000	−	6.32456i	0.101929	−	0.322329i
$386$	5.67544	−	5.67544i	0.288873	−	0.288873i
$387$		−	10.3246i		−	0.524827i
$388$		−	29.2982i		−	1.48739i
$389$			2.64911i			0.134315i	0.997742	+	0.0671576i	$0.0213930\pi$
$389$			2.64911i			0.134315i	−0.997742	+	0.0671576i	$0.978607\pi$
$390$	−2.00000	+	2.00000i	−0.101274	+	0.101274i
$391$		0			0
$392$	6.00000	−	6.00000i	0.303046	−	0.303046i
$393$		−	6.00000i		−	0.302660i
$394$	16.6491	+	16.6491i	0.838770	+	0.838770i
$395$		−	10.0000i		−	0.503155i
$396$	2.00000	−	6.32456i	0.100504	−	0.317821i
$397$		−	16.9737i		−	0.851884i	−0.904750	−	0.425942i	$-0.859943\pi$
$397$		−	16.9737i		−	0.851884i	0.904750	−	0.425942i	$-0.140057\pi$
$398$	4.00000	−	4.00000i	0.200502	−	0.200502i
$399$		−	8.64911i		−	0.432997i
$400$	4.00000			0.200000
$401$	30.0000			1.49813			0.749064	−	0.662497i	$-0.230503\pi$
$401$	30.0000			1.49813			0.749064	+	0.662497i	$0.230503\pi$
$402$		0			0
$403$		−	8.00000i		−	0.398508i
$404$			20.6491i			1.02733i
$405$		−	1.00000i		−	0.0496904i
$406$	−4.64911	−	4.64911i	−0.230731	−	0.230731i
$407$	−4.32456	+	13.6754i	−0.214360	+	0.677867i
$408$		0			0
$409$		−	28.0000i		−	1.38451i	−0.721653	−	0.692255i	$-0.756617\pi$
$409$		−	28.0000i		−	1.38451i	0.721653	−	0.692255i	$-0.243383\pi$
$410$	8.32456	+	8.32456i	0.411120	+	0.411120i
$411$	−5.67544			−0.279949
$412$	−28.6491			−1.41144
$413$	20.6491			1.01608
$414$	4.32456	−	4.32456i	0.212540	−	0.212540i
$415$	−10.6491			−0.522744
$416$	−8.00000	−	8.00000i	−0.392232	−	0.392232i
$417$			4.32456i			0.211774i
$418$	−18.0000	+	9.35089i	−0.880409	+	0.457367i
$419$	−13.6754			−0.668089			−0.334045	−	0.942557i	$-0.608414\pi$
$419$	−13.6754			−0.668089			−0.334045	+	0.942557i	$0.608414\pi$
$420$	4.00000			0.195180
$421$			8.64911i			0.421532i	0.977537	+	0.210766i	$0.0675958\pi$
$421$			8.64911i			0.421532i	−0.977537	+	0.210766i	$0.932404\pi$
$422$	−0.324555	+	0.324555i	−0.0157991	+	0.0157991i
$423$		−	4.32456i		−	0.210267i
$424$	12.0000	+	12.0000i	0.582772	+	0.582772i
$425$		0			0
$426$	2.32456	−	2.32456i	0.112625	−	0.112625i
$427$	−4.64911			−0.224986
$428$	−20.0000			−0.966736
$429$	6.32456	+	2.00000i	0.305352	+	0.0965609i
$430$	−10.3246	−	10.3246i	−0.497894	−	0.497894i
$431$	32.6491			1.57265			0.786326	−	0.617812i	$-0.211981\pi$
$431$	32.6491			1.57265			0.786326	+	0.617812i	$0.211981\pi$
$432$	4.00000			0.192450
$433$	2.64911			0.127308			0.0636541	−	0.997972i	$-0.479725\pi$
$433$	2.64911			0.127308			0.0636541	+	0.997972i	$0.479725\pi$
$434$	−8.00000	+	8.00000i	−0.384012	+	0.384012i
$435$			2.32456i			0.111454i
$436$			12.6491i			0.605783i
$437$	−18.7018			−0.894627
$438$	−2.32456	+	2.32456i	−0.111072	+	0.111072i
$439$	−1.35089			−0.0644744			−0.0322372	−	0.999480i	$-0.510263\pi$
$439$	−1.35089			−0.0644744			−0.0322372	+	0.999480i	$0.510263\pi$
$440$	−4.32456	−	8.32456i	−0.206165	−	0.396858i
$441$	−3.00000			−0.142857
$442$		0			0
$443$	−15.3509			−0.729343			−0.364671	−	0.931136i	$-0.618819\pi$
$443$	−15.3509			−0.729343			−0.364671	+	0.931136i	$0.618819\pi$
$444$	−8.64911			−0.410469
$445$			6.64911i			0.315198i
$446$	5.67544	−	5.67544i	0.268740	−	0.268740i
$447$	2.32456			0.109948
$448$			16.0000i			0.755929i
$449$	6.64911			0.313791			0.156895	−	0.987615i	$-0.449851\pi$
$449$	6.64911			0.313791			0.156895	+	0.987615i	$0.449851\pi$
$450$	−1.00000	−	1.00000i	−0.0471405	−	0.0471405i
$451$	8.32456	−	26.3246i	0.391988	−	1.23957i
$452$		−	28.6491i		−	1.34754i
$453$	−22.6491			−1.06415
$454$	18.0000	−	18.0000i	0.844782	−	0.844782i
$455$			4.00000i			0.187523i
$456$	−8.64911	−	8.64911i	−0.405032	−	0.405032i
$457$		−	14.9737i		−	0.700439i	−0.936668	−	0.350219i	$-0.886107\pi$
$457$		−	14.9737i		−	0.700439i	0.936668	−	0.350219i	$-0.113893\pi$
$458$	4.00000	−	4.00000i	0.186908	−	0.186908i
$459$		0			0
$460$		−	8.64911i		−	0.403267i
$461$	13.6754			0.636929			0.318464	−	0.947935i	$-0.396833\pi$
$461$	13.6754			0.636929			0.318464	+	0.947935i	$0.396833\pi$
$462$	−4.32456	−	8.32456i	−0.201197	−	0.387293i
$463$		−	6.32456i		−	0.293927i	−0.989142	−	0.146964i	$-0.953050\pi$
$463$		−	6.32456i		−	0.293927i	0.989142	−	0.146964i	$-0.0469500\pi$
$464$	−9.29822			−0.431659
$465$	4.00000			0.185496
$466$	−16.6491	+	16.6491i	−0.771255	+	0.771255i
$467$	20.0000			0.925490			0.462745	−	0.886492i	$-0.346865\pi$
$467$	20.0000			0.925490			0.462745	+	0.886492i	$0.346865\pi$
$468$			4.00000i			0.184900i
$469$		0			0
$470$	−4.32456	−	4.32456i	−0.199477	−	0.199477i
$471$			16.3246i			0.752196i
$472$	20.6491	−	20.6491i	0.950452	−	0.950452i
$473$	−10.3246	+	32.6491i	−0.474724	+	1.50121i
$474$	−10.0000	−	10.0000i	−0.459315	−	0.459315i
$475$			4.32456i			0.198424i
$476$		0			0
$477$		−	6.00000i		−	0.274721i
$478$	−25.2982	−	25.2982i	−1.15711	−	1.15711i
$479$	24.0000			1.09659			0.548294	−	0.836286i	$-0.315277\pi$
$479$	24.0000			1.09659			0.548294	+	0.836286i	$0.315277\pi$
$480$	4.00000	−	4.00000i	0.182574	−	0.182574i
$481$		−	8.64911i		−	0.394365i
$482$	−4.00000	+	4.00000i	−0.182195	+	0.182195i
$483$		−	8.64911i		−	0.393548i
$484$	−12.6491	+	18.0000i	−0.574960	+	0.818182i
$485$			14.6491i			0.665182i
$486$	−1.00000	−	1.00000i	−0.0453609	−	0.0453609i
$487$		−	30.3246i		−	1.37414i	−0.726593	−	0.687068i	$-0.758897\pi$
$487$		−	30.3246i		−	1.37414i	0.726593	−	0.687068i	$-0.241103\pi$
$488$	−4.64911	+	4.64911i	−0.210455	+	0.210455i
$489$	−0.649111			−0.0293538
$490$	−3.00000	+	3.00000i	−0.135526	+	0.135526i
$491$		−	18.6491i		−	0.841623i	−0.907148	−	0.420811i	$-0.861745\pi$
$491$		−	18.6491i		−	0.841623i	0.907148	−	0.420811i	$-0.138255\pi$
$492$	16.6491			0.750600
$493$		0			0
$494$	8.64911	−	8.64911i	0.389142	−	0.389142i
$495$	−1.00000	+	3.16228i	−0.0449467	+	0.142134i
$496$			16.0000i			0.718421i
$497$		−	4.64911i		−	0.208541i
$498$	−10.6491	+	10.6491i	−0.477198	+	0.477198i
$499$	15.2982			0.684842			0.342421	−	0.939547i	$-0.388753\pi$
$499$	15.2982			0.684842			0.342421	+	0.939547i	$0.388753\pi$
$500$	−2.00000			−0.0894427
$501$	14.6491			0.654474
$502$	−14.9737	−	14.9737i	−0.668307	−	0.668307i
$503$	11.2982			0.503763			0.251881	−	0.967758i	$-0.418951\pi$
$503$	11.2982			0.503763			0.251881	+	0.967758i	$0.418951\pi$
$504$	4.00000	−	4.00000i	0.178174	−	0.178174i
$505$		−	10.3246i		−	0.459437i
$506$	−18.0000	+	9.35089i	−0.800198	+	0.415698i
$507$	9.00000			0.399704
$508$		−	28.0000i		−	1.24230i
$509$			5.35089i			0.237174i	0.992944	+	0.118587i	$0.0378365\pi$
$509$			5.35089i			0.237174i	−0.992944	+	0.118587i	$0.962164\pi$
$510$		0			0
$511$			4.64911i			0.205665i
$512$	16.0000	+	16.0000i	0.707107	+	0.707107i
$513$			4.32456i			0.190934i
$514$	−26.3246	−	26.3246i	−1.16113	−	1.16113i
$515$	14.3246			0.631215
$516$	−20.6491			−0.909026
$517$	−4.32456	+	13.6754i	−0.190194	+	0.601445i
$518$	−8.64911	+	8.64911i	−0.380020	+	0.380020i
$519$	12.0000			0.526742
$520$	4.00000	+	4.00000i	0.175412	+	0.175412i
$521$	−22.6491			−0.992276			−0.496138	−	0.868244i	$-0.665249\pi$
$521$	−22.6491			−0.992276			−0.496138	+	0.868244i	$0.665249\pi$
$522$	2.32456	+	2.32456i	0.101743	+	0.101743i
$523$		−	6.32456i		−	0.276553i	−0.990394	−	0.138277i	$-0.955844\pi$
$523$		−	6.32456i		−	0.276553i	0.990394	−	0.138277i	$-0.0441563\pi$
$524$	−12.0000			−0.524222
$525$	−2.00000			−0.0872872
$526$	−14.6491	−	14.6491i	−0.638732	−	0.638732i
$527$		0			0
$528$	−12.6491	−	4.00000i	−0.550482	−	0.174078i
$529$	4.29822			0.186879
$530$	−6.00000	−	6.00000i	−0.260623	−	0.260623i
$531$	−10.3246			−0.448048
$532$	−17.2982			−0.749973
$533$			16.6491i			0.721153i
$534$	6.64911	+	6.64911i	0.287735	+	0.287735i
$535$	10.0000			0.432338
$536$		0			0
$537$	18.9737			0.818774
$538$	2.64911	−	2.64911i	0.114211	−	0.114211i
$539$	9.48683	+	3.00000i	0.408627	+	0.129219i
$540$	−2.00000			−0.0860663
$541$	−14.9737			−0.643768			−0.321884	−	0.946779i	$-0.604316\pi$
$541$	−14.9737			−0.643768			−0.321884	+	0.946779i	$0.604316\pi$
$542$	−2.00000	−	2.00000i	−0.0859074	−	0.0859074i
$543$			8.00000i			0.343313i
$544$		0			0
$545$		−	6.32456i		−	0.270914i
$546$	4.00000	+	4.00000i	0.171184	+	0.171184i
$547$			34.9737i			1.49537i	0.664056	+	0.747683i	$0.268834\pi$
$547$			34.9737i			1.49537i	−0.664056	+	0.747683i	$0.731166\pi$
$548$			11.3509i			0.484886i
$549$	2.32456			0.0992096
$550$	2.16228	+	4.16228i	0.0921998	+	0.177480i
$551$		−	10.0527i		−	0.428258i
$552$	−8.64911	−	8.64911i	−0.368131	−	0.368131i
$553$	−20.0000			−0.850487
$554$	18.6491	+	18.6491i	0.792325	+	0.792325i
$555$	4.32456			0.183567
$556$	8.64911			0.366804
$557$	24.6491			1.04442			0.522208	−	0.852818i	$-0.325108\pi$
$557$	24.6491			1.04442			0.522208	+	0.852818i	$0.325108\pi$
$558$	4.00000	−	4.00000i	0.169334	−	0.169334i
$559$		−	20.6491i		−	0.873364i
$560$		−	8.00000i		−	0.338062i
$561$		0			0
$562$	−16.9737	+	16.9737i	−0.715991	+	0.715991i
$563$		−	26.6491i		−	1.12313i	−0.827434	−	0.561563i	$-0.810200\pi$
$563$		−	26.6491i		−	1.12313i	0.827434	−	0.561563i	$-0.189800\pi$
$564$	−8.64911			−0.364193
$565$			14.3246i			0.602639i
$566$	−5.67544	+	5.67544i	−0.238557	+	0.238557i
$567$	−2.00000			−0.0839921
$568$	−4.64911	−	4.64911i	−0.195072	−	0.195072i
$569$		−	19.6754i		−	0.824838i	−0.910994	−	0.412419i	$-0.864684\pi$
$569$		−	19.6754i		−	0.824838i	0.910994	−	0.412419i	$-0.135316\pi$
$570$	4.32456	+	4.32456i	0.181136	+	0.181136i
$571$			24.3246i			1.01795i	0.860781	+	0.508975i	$0.169976\pi$
$571$			24.3246i			1.01795i	−0.860781	+	0.508975i	$0.830024\pi$
$572$	4.00000	−	12.6491i	0.167248	−	0.528886i
$573$		−	26.3246i		−	1.09972i
$574$	16.6491	−	16.6491i	0.694920	−	0.694920i
$575$			4.32456i			0.180346i
$576$		−	8.00000i		−	0.333333i
$577$	22.6491			0.942895			0.471447	−	0.881894i	$-0.343732\pi$
$577$	22.6491			0.942895			0.471447	+	0.881894i	$0.343732\pi$
$578$	17.0000	+	17.0000i	0.707107	+	0.707107i
$579$			5.67544i			0.235863i
$580$	4.64911			0.193044
$581$			21.2982i			0.883599i
$582$	14.6491	+	14.6491i	0.607225	+	0.607225i
$583$	−6.00000	+	18.9737i	−0.248495	+	0.785809i
$584$	4.64911	+	4.64911i	0.192382	+	0.192382i
$585$		−	2.00000i		−	0.0826898i
$586$	3.35089	+	3.35089i	0.138424	+	0.138424i
$587$	−12.0000			−0.495293			−0.247647	−	0.968850i	$-0.579657\pi$
$587$	−12.0000			−0.495293			−0.247647	+	0.968850i	$0.579657\pi$
$588$			6.00000i			0.247436i
$589$	−17.2982			−0.712761
$590$	−10.3246	+	10.3246i	−0.425055	+	0.425055i
$591$	−16.6491			−0.684853
$592$			17.2982i			0.710953i
$593$		−	7.35089i		−	0.301865i	−0.988544	−	0.150932i	$-0.951772\pi$
$593$		−	7.35089i		−	0.301865i	0.988544	−	0.150932i	$-0.0482276\pi$
$594$	2.16228	+	4.16228i	0.0887193	+	0.170780i
$595$		0			0
$596$		−	4.64911i		−	0.190435i
$597$			4.00000i			0.163709i
$598$	8.64911	−	8.64911i	0.353688	−	0.353688i
$599$			22.9737i			0.938679i	0.883018	+	0.469339i	$0.155508\pi$
$599$			22.9737i			0.938679i	−0.883018	+	0.469339i	$0.844492\pi$
$600$	−2.00000	+	2.00000i	−0.0816497	+	0.0816497i
$601$		−	0.649111i		−	0.0264778i	−0.999912	−	0.0132389i	$-0.995786\pi$
$601$		−	0.649111i		−	0.0264778i	0.999912	−	0.0132389i	$-0.00421419\pi$
$602$	−20.6491	+	20.6491i	−0.841595	+	0.841595i
$603$		0			0
$604$			45.2982i			1.84316i
$605$	6.32456	−	9.00000i	0.257130	−	0.365902i
$606$	−10.3246	−	10.3246i	−0.419406	−	0.419406i
$607$	22.0000			0.892952			0.446476	−	0.894795i	$-0.352679\pi$
$607$	22.0000			0.892952			0.446476	+	0.894795i	$0.352679\pi$
$608$	−17.2982	+	17.2982i	−0.701536	+	0.701536i
$609$	4.64911			0.188391
$610$	2.32456	−	2.32456i	0.0941185	−	0.0941185i
$611$		−	8.64911i		−	0.349906i
$612$		0			0
$613$	−10.6491			−0.430114			−0.215057	−	0.976602i	$-0.568994\pi$
$613$	−10.6491			−0.430114			−0.215057	+	0.976602i	$0.568994\pi$
$614$	−14.3246	+	14.3246i	−0.578092	+	0.578092i
$615$	−8.32456			−0.335678
$616$	−16.6491	+	8.64911i	−0.670812	+	0.348483i
$617$	18.3246			0.737719			0.368859	−	0.929485i	$-0.379748\pi$
$617$	18.3246			0.737719			0.368859	+	0.929485i	$0.379748\pi$
$618$	14.3246	−	14.3246i	0.576218	−	0.576218i
$619$	7.29822			0.293340			0.146670	−	0.989185i	$-0.453144\pi$
$619$	7.29822			0.293340			0.146670	+	0.989185i	$0.453144\pi$
$620$		−	8.00000i		−	0.321288i
$621$			4.32456i			0.173538i
$622$	−18.9737	+	18.9737i	−0.760775	+	0.760775i
$623$	13.2982			0.532782
$624$	8.00000			0.320256
$625$	1.00000			0.0400000
$626$	30.6491	+	30.6491i	1.22498	+	1.22498i
$627$	4.32456	−	13.6754i	0.172706	−	0.546145i
$628$	32.6491			1.30284
$629$		0			0
$630$	−2.00000	+	2.00000i	−0.0796819	+	0.0796819i
$631$			28.0000i			1.11466i	0.830290	+	0.557331i	$0.188175\pi$
$631$			28.0000i			1.11466i	−0.830290	+	0.557331i	$0.811825\pi$
$632$	−20.0000	+	20.0000i	−0.795557	+	0.795557i
$633$		−	0.324555i		−	0.0128999i
$634$	34.6491	−	34.6491i	1.37609	−	1.37609i
$635$			14.0000i			0.555573i
$636$	−12.0000			−0.475831
$637$	−6.00000			−0.237729
$638$	−5.02633	−	9.67544i	−0.198994	−	0.383055i
$639$			2.32456i			0.0919580i
$640$	−8.00000	−	8.00000i	−0.316228	−	0.316228i
$641$	−6.00000			−0.236986			−0.118493	−	0.992955i	$-0.537806\pi$
$641$	−6.00000			−0.236986			−0.118493	+	0.992955i	$0.537806\pi$
$642$	10.0000	−	10.0000i	0.394669	−	0.394669i
$643$	36.0000			1.41970			0.709851	−	0.704352i	$-0.248762\pi$
$643$	36.0000			1.41970			0.709851	+	0.704352i	$0.248762\pi$
$644$	−17.2982			−0.681645
$645$	10.3246			0.406529
$646$		0			0
$647$			4.32456i			0.170016i	0.996380	+	0.0850079i	$0.0270916\pi$
$647$			4.32456i			0.170016i	−0.996380	+	0.0850079i	$0.972908\pi$
$648$	−2.00000	+	2.00000i	−0.0785674	+	0.0785674i
$649$	32.6491	+	10.3246i	1.28159	+	0.405274i
$650$	−2.00000	−	2.00000i	−0.0784465	−	0.0784465i
$651$		−	8.00000i		−	0.313545i
$652$			1.29822i			0.0508423i
$653$		−	18.6491i		−	0.729796i	−0.931047	−	0.364898i	$-0.881104\pi$
$653$		−	18.6491i		−	0.729796i	0.931047	−	0.364898i	$-0.118896\pi$
$654$	−6.32456	−	6.32456i	−0.247310	−	0.247310i
$655$	6.00000			0.234439
$656$		−	33.2982i		−	1.30008i
$657$		−	2.32456i		−	0.0906895i
$658$	−8.64911	+	8.64911i	−0.337177	+	0.337177i
$659$		−	31.9473i		−	1.24449i	−0.782822	−	0.622246i	$-0.786220\pi$
$659$		−	31.9473i		−	1.24449i	0.782822	−	0.622246i	$-0.213780\pi$
$660$	6.32456	+	2.00000i	0.246183	+	0.0778499i
$661$			7.35089i			0.285916i	0.989729	+	0.142958i	$0.0456615\pi$
$661$			7.35089i			0.285916i	−0.989729	+	0.142958i	$0.954339\pi$
$662$	10.0000	+	10.0000i	0.388661	+	0.388661i
$663$		0			0
$664$	21.2982	+	21.2982i	0.826531	+	0.826531i
$665$	8.64911			0.335398
$666$	4.32456	−	4.32456i	0.167573	−	0.167573i
$667$		−	10.0527i		−	0.389241i
$668$		−	29.2982i		−	1.13358i
$669$			5.67544i			0.219425i
$670$		0			0
$671$	−7.35089	−	2.32456i	−0.283778	−	0.0897385i
$672$	−8.00000	−	8.00000i	−0.308607	−	0.308607i
$673$		−	18.3246i		−	0.706360i	−0.935555	−	0.353180i	$-0.885100\pi$
$673$		−	18.3246i		−	0.706360i	0.935555	−	0.353180i	$-0.114900\pi$
$674$	18.3246	−	18.3246i	0.705835	−	0.705835i
$675$	1.00000			0.0384900
$676$		−	18.0000i		−	0.692308i
$677$	45.2982			1.74095			0.870476	−	0.492211i	$-0.163811\pi$
$677$	45.2982			1.74095			0.870476	+	0.492211i	$0.163811\pi$
$678$	14.3246	+	14.3246i	0.550131	+	0.550131i
$679$	29.2982			1.12436
$680$		0			0
$681$			18.0000i			0.689761i
$682$	−16.6491	+	8.64911i	−0.637527	+	0.331192i
$683$	12.0000			0.459167			0.229584	−	0.973289i	$-0.426264\pi$
$683$	12.0000			0.459167			0.229584	+	0.973289i	$0.426264\pi$
$684$	8.64911			0.330707
$685$		−	5.67544i		−	0.216848i
$686$	20.0000	+	20.0000i	0.763604	+	0.763604i
$687$			4.00000i			0.152610i
$688$			41.2982i			1.57448i
$689$		−	12.0000i		−	0.457164i
$690$	4.32456	+	4.32456i	0.164633	+	0.164633i
$691$	6.64911			0.252944			0.126472	−	0.991970i	$-0.459635\pi$
$691$	6.64911			0.252944			0.126472	+	0.991970i	$0.459635\pi$
$692$		−	24.0000i		−	0.912343i
$693$	6.32456	+	2.00000i	0.240250	+	0.0759737i
$694$	−14.6491	+	14.6491i	−0.556073	+	0.556073i
$695$	−4.32456			−0.164040
$696$	4.64911	−	4.64911i	0.176224	−	0.176224i
$697$		0			0
$698$	−10.3246	−	10.3246i	−0.390790	−	0.390790i
$699$		−	16.6491i		−	0.629727i
$700$			4.00000i			0.151186i
$701$	−34.3246			−1.29642			−0.648210	−	0.761461i	$-0.724482\pi$
$701$	−34.3246			−1.29642			−0.648210	+	0.761461i	$0.724482\pi$
$702$	−2.00000	−	2.00000i	−0.0754851	−	0.0754851i
$703$	−18.7018			−0.705351
$704$	−8.00000	+	25.2982i	−0.301511	+	0.953463i
$705$	4.32456			0.162872
$706$	13.6754	+	13.6754i	0.514682	+	0.514682i
$707$	−20.6491			−0.776590
$708$			20.6491i			0.776041i
$709$			8.00000i			0.300446i	0.988652	+	0.150223i	$0.0479992\pi$
$709$			8.00000i			0.300446i	−0.988652	+	0.150223i	$0.952001\pi$
$710$	2.32456	+	2.32456i	0.0872390	+	0.0872390i
$711$	10.0000			0.375029
$712$	13.2982	−	13.2982i	0.498372	−	0.498372i
$713$	−17.2982			−0.647823
$714$		0			0
$715$	−2.00000	+	6.32456i	−0.0747958	+	0.236525i
$716$		−	37.9473i		−	1.41816i
$717$	25.2982			0.944779
$718$	−12.0000	−	12.0000i	−0.447836	−	0.447836i
$719$		−	43.6228i		−	1.62686i	−0.581666	−	0.813428i	$-0.697599\pi$
$719$		−	43.6228i		−	1.62686i	0.581666	−	0.813428i	$-0.302401\pi$
$720$			4.00000i			0.149071i
$721$		−	28.6491i		−	1.06695i
$722$	0.298221	+	0.298221i	0.0110986	+	0.0110986i
$723$		−	4.00000i		−	0.148762i
$724$	16.0000			0.594635
$725$	−2.32456			−0.0863318
$726$	−2.67544	−	15.3246i	−0.0992951	−	0.568748i
$727$			50.9737i			1.89051i	0.326335	+	0.945254i	$0.394186\pi$
$727$			50.9737i			1.89051i	−0.326335	+	0.945254i	$0.605814\pi$
$728$	8.00000	−	8.00000i	0.296500	−	0.296500i
$729$	1.00000			0.0370370
$730$	−2.32456	−	2.32456i	−0.0860357	−	0.0860357i
$731$		0			0
$732$		−	4.64911i		−	0.171836i
$733$	−7.29822			−0.269566			−0.134783	−	0.990875i	$-0.543034\pi$
$733$	−7.29822			−0.269566			−0.134783	+	0.990875i	$0.543034\pi$
$734$	18.9737	−	18.9737i	0.700331	−	0.700331i
$735$		−	3.00000i		−	0.110657i
$736$	−17.2982	+	17.2982i	−0.637621	+	0.637621i
$737$		0			0
$738$	−8.32456	+	8.32456i	−0.306431	+	0.306431i
$739$		−	7.02633i		−	0.258468i	−0.991614	−	0.129234i	$-0.958748\pi$
$739$		−	7.02633i		−	0.258468i	0.991614	−	0.129234i	$-0.0412518\pi$
$740$		−	8.64911i		−	0.317948i
$741$			8.64911i			0.317733i
$742$	−12.0000	+	12.0000i	−0.440534	+	0.440534i
$743$	38.6491			1.41790			0.708949	−	0.705260i	$-0.249170\pi$
$743$	38.6491			1.41790			0.708949	+	0.705260i	$0.249170\pi$
$744$	−8.00000	−	8.00000i	−0.293294	−	0.293294i
$745$			2.32456i			0.0851651i
$746$	−35.2982	−	35.2982i	−1.29236	−	1.29236i
$747$		−	10.6491i		−	0.389631i
$748$		0			0
$749$		−	20.0000i		−	0.730784i
$750$	1.00000	−	1.00000i	0.0365148	−	0.0365148i
$751$		−	53.2982i		−	1.94488i	−0.233154	−	0.972440i	$-0.574905\pi$
$751$		−	53.2982i		−	1.94488i	0.233154	−	0.972440i	$-0.425095\pi$
$752$			17.2982i			0.630801i
$753$	14.9737			0.545671
$754$	4.64911	+	4.64911i	0.169311	+	0.169311i
$755$		−	22.6491i		−	0.824286i
$756$			4.00000i			0.145479i
$757$		−	20.3246i		−	0.738709i	−0.929289	−	0.369354i	$-0.879579\pi$
$757$		−	20.3246i		−	0.738709i	0.929289	−	0.369354i	$-0.120421\pi$
$758$	30.6491	+	30.6491i	1.11323	+	1.11323i
$759$	4.32456	−	13.6754i	0.156971	−	0.496387i
$760$	8.64911	−	8.64911i	0.313736	−	0.313736i
$761$			8.97367i			0.325295i	0.986684	+	0.162648i	$0.0520034\pi$
$761$			8.97367i			0.325295i	−0.986684	+	0.162648i	$0.947997\pi$
$762$	14.0000	+	14.0000i	0.507166	+	0.507166i
$763$	−12.6491			−0.457929
$764$	−52.6491			−1.90478
$765$		0			0
$766$	4.32456	−	4.32456i	0.156253	−	0.156253i
$767$	−20.6491			−0.745596
$768$	−16.0000			−0.577350
$769$			40.0000i			1.44244i	0.692708	+	0.721218i	$0.256418\pi$
$769$			40.0000i			1.44244i	−0.692708	+	0.721218i	$0.743582\pi$
$770$	8.32456	−	4.32456i	0.299996	−	0.155846i
$771$	26.3246			0.948056
$772$	11.3509			0.408527
$773$			1.35089i			0.0485881i	0.999705	+	0.0242941i	$0.00773380\pi$
$773$			1.35089i			0.0485881i	−0.999705	+	0.0242941i	$0.992266\pi$
$774$	10.3246	−	10.3246i	0.371108	−	0.371108i
$775$			4.00000i			0.143684i
$776$	29.2982	−	29.2982i	1.05174	−	1.05174i
$777$		−	8.64911i		−	0.310285i
$778$	−2.64911	+	2.64911i	−0.0949752	+	0.0949752i
$779$	36.0000			1.28983
$780$	−4.00000			−0.143223
$781$	2.32456	−	7.35089i	0.0831791	−	0.263036i
$782$		0			0
$783$	−2.32456			−0.0830728
$784$	12.0000			0.428571
$785$	−16.3246			−0.582648
$786$	6.00000	−	6.00000i	0.214013	−	0.214013i
$787$			50.3246i			1.79388i	0.442156	+	0.896938i	$0.354214\pi$
$787$			50.3246i			1.79388i	−0.442156	+	0.896938i	$0.645786\pi$
$788$			33.2982i			1.18620i
$789$	14.6491			0.521522
$790$	10.0000	−	10.0000i	0.355784	−	0.355784i
$791$	28.6491			1.01865
$792$	8.32456	−	4.32456i	0.295800	−	0.153666i
$793$	4.64911			0.165095
$794$	16.9737	−	16.9737i	0.602373	−	0.602373i
$795$	6.00000			0.212798
$796$	8.00000			0.283552
$797$		−	23.2982i		−	0.825265i	−0.910898	−	0.412633i	$-0.864609\pi$
$797$		−	23.2982i		−	0.825265i	0.910898	−	0.412633i	$-0.135391\pi$
$798$	8.64911	−	8.64911i	0.306175	−	0.306175i
$799$		0			0
$800$	4.00000	+	4.00000i	0.141421	+	0.141421i
$801$	−6.64911			−0.234935
$802$	30.0000	+	30.0000i	1.05934	+	1.05934i
$803$	−2.32456	+	7.35089i	−0.0820318	+	0.259407i
$804$		0			0
$805$	8.64911			0.304841
$806$	8.00000	−	8.00000i	0.281788	−	0.281788i
$807$			2.64911i			0.0932531i
$808$	−20.6491	+	20.6491i	−0.726433	+	0.726433i
$809$		−	21.6228i		−	0.760216i	−0.924942	−	0.380108i	$-0.875887\pi$
$809$		−	21.6228i		−	0.760216i	0.924942	−	0.380108i	$-0.124113\pi$
$810$	1.00000	−	1.00000i	0.0351364	−	0.0351364i
$811$			4.97367i			0.174649i	0.996180	+	0.0873245i	$0.0278317\pi$
$811$			4.97367i			0.174649i	−0.996180	+	0.0873245i	$0.972168\pi$
$812$		−	9.29822i		−	0.326304i
$813$	2.00000			0.0701431
$814$	−18.0000	+	9.35089i	−0.630900	+	0.327749i
$815$		−	0.649111i		−	0.0227374i
$816$		0			0
$817$	−44.6491			−1.56207
$818$	28.0000	−	28.0000i	0.978997	−	0.978997i
$819$	−4.00000			−0.139771
$820$			16.6491i			0.581412i
$821$	34.3246			1.19794			0.598968	−	0.800773i	$-0.295578\pi$
$821$	34.3246			1.19794			0.598968	+	0.800773i	$0.295578\pi$
$822$	−5.67544	−	5.67544i	−0.197954	−	0.197954i
$823$			19.6228i			0.684007i	0.939699	+	0.342003i	$0.111105\pi$
$823$			19.6228i			0.684007i	−0.939699	+	0.342003i	$0.888895\pi$
$824$	−28.6491	−	28.6491i	−0.998039	−	0.998039i
$825$	−3.16228	−	1.00000i	−0.110096	−	0.0348155i
$826$	20.6491	+	20.6491i	0.718474	+	0.718474i
$827$			43.9473i			1.52820i	0.645099	+	0.764099i	$0.276816\pi$
$827$			43.9473i			1.52820i	−0.645099	+	0.764099i	$0.723184\pi$
$828$	8.64911			0.300577
$829$		−	33.9473i		−	1.17904i	−0.807754	−	0.589520i	$-0.799317\pi$
$829$		−	33.9473i		−	1.17904i	0.807754	−	0.589520i	$-0.200683\pi$
$830$	−10.6491	−	10.6491i	−0.369636	−	0.369636i
$831$	−18.6491			−0.646930
$832$		−	16.0000i		−	0.554700i
$833$		0			0
$834$	−4.32456	+	4.32456i	−0.149747	+	0.149747i
$835$			14.6491i			0.506953i
$836$	−27.3509	−	8.64911i	−0.945950	−	0.299136i
$837$			4.00000i			0.138260i
$838$	−13.6754	−	13.6754i	−0.472410	−	0.472410i
$839$			38.3246i			1.32311i	0.749896	+	0.661555i	$0.230103\pi$
$839$			38.3246i			1.32311i	−0.749896	+	0.661555i	$0.769897\pi$
$840$	4.00000	+	4.00000i	0.138013	+	0.138013i
$841$	−23.5964			−0.813670
$842$	−8.64911	+	8.64911i	−0.298068	+	0.298068i
$843$		−	16.9737i		−	0.584604i
$844$	−0.649111			−0.0223433
$845$			9.00000i			0.309609i
$846$	4.32456	−	4.32456i	0.148681	−	0.148681i
$847$	−18.0000	−	12.6491i	−0.618487	−	0.434629i
$848$			24.0000i			0.824163i
$849$		−	5.67544i		−	0.194781i
$850$		0			0
$851$	−18.7018			−0.641089
$852$	4.64911			0.159276
$853$	1.35089			0.0462536			0.0231268	−	0.999733i	$-0.492638\pi$
$853$	1.35089			0.0462536			0.0231268	+	0.999733i	$0.492638\pi$
$854$	−4.64911	−	4.64911i	−0.159089	−	0.159089i
$855$	−4.32456			−0.147897
$856$	−20.0000	−	20.0000i	−0.683586	−	0.683586i
$857$		−	25.9473i		−	0.886344i	−0.896437	−	0.443172i	$-0.853853\pi$
$857$		−	25.9473i		−	0.886344i	0.896437	−	0.443172i	$-0.146147\pi$
$858$	4.32456	+	8.32456i	0.147638	+	0.284196i
$859$	−38.6491			−1.31869			−0.659345	−	0.751840i	$-0.729166\pi$
$859$	−38.6491			−1.31869			−0.659345	+	0.751840i	$0.729166\pi$
$860$		−	20.6491i		−	0.704129i
$861$			16.6491i			0.567400i
$862$	32.6491	+	32.6491i	1.11203	+	1.11203i
$863$		−	42.2719i		−	1.43895i	−0.694517	−	0.719476i	$-0.744382\pi$
$863$		−	42.2719i		−	1.43895i	0.694517	−	0.719476i	$-0.255618\pi$
$864$	4.00000	+	4.00000i	0.136083	+	0.136083i
$865$			12.0000i			0.408012i
$866$	2.64911	+	2.64911i	0.0900204	+	0.0900204i
$867$	−17.0000			−0.577350
$868$	−16.0000			−0.543075
$869$	−31.6228	−	10.0000i	−1.07273	−	0.339227i
$870$	−2.32456	+	2.32456i	−0.0788098	+	0.0788098i
$871$		0			0
$872$	−12.6491	+	12.6491i	−0.428353	+	0.428353i
$873$	−14.6491			−0.495797
$874$	−18.7018	−	18.7018i	−0.632597	−	0.632597i
$875$		−	2.00000i		−	0.0676123i
$876$	−4.64911			−0.157079
$877$	−54.6491			−1.84537			−0.922685	−	0.385555i	$-0.874010\pi$
$877$	−54.6491			−1.84537			−0.922685	+	0.385555i	$0.874010\pi$
$878$	−1.35089	−	1.35089i	−0.0455903	−	0.0455903i
$879$	−3.35089			−0.113023
$880$	4.00000	−	12.6491i	0.134840	−	0.426401i
$881$	6.00000			0.202145			0.101073	−	0.994879i	$-0.467773\pi$
$881$	6.00000			0.202145			0.101073	+	0.994879i	$0.467773\pi$
$882$	−3.00000	−	3.00000i	−0.101015	−	0.101015i
$883$	−44.6491			−1.50256			−0.751281	−	0.659982i	$-0.770564\pi$
$883$	−44.6491			−1.50256			−0.751281	+	0.659982i	$0.770564\pi$
$884$		0			0
$885$		−	10.3246i		−	0.347056i
$886$	−15.3509	−	15.3509i	−0.515723	−	0.515723i
$887$	−52.5964			−1.76602			−0.883008	−	0.469358i	$-0.844485\pi$
$887$	−52.5964			−1.76602			−0.883008	+	0.469358i	$0.844485\pi$
$888$	−8.64911	−	8.64911i	−0.290245	−	0.290245i
$889$	28.0000			0.939090
$890$	−6.64911	+	6.64911i	−0.222879	+	0.222879i
$891$	−3.16228	−	1.00000i	−0.105940	−	0.0335013i
$892$	11.3509			0.380056
$893$	−18.7018			−0.625831
$894$	2.32456	+	2.32456i	0.0777448	+	0.0777448i
$895$			18.9737i			0.634220i
$896$	−16.0000	+	16.0000i	−0.534522	+	0.534522i
$897$			8.64911i			0.288785i
$898$	6.64911	+	6.64911i	0.221884	+	0.221884i
$899$		−	9.29822i		−	0.310113i
$900$		−	2.00000i		−	0.0666667i
$901$		0			0
$902$	34.6491	−	18.0000i	1.15369	−	0.599334i
$903$		−	20.6491i		−	0.687159i
$904$	28.6491	−	28.6491i	0.952855	−	0.952855i
$905$	−8.00000			−0.265929
$906$	−22.6491	−	22.6491i	−0.752466	−	0.752466i
$907$	24.6491			0.818460			0.409230	−	0.912431i	$-0.365797\pi$
$907$	24.6491			0.818460			0.409230	+	0.912431i	$0.365797\pi$
$908$	36.0000			1.19470
$909$	10.3246			0.342444
$910$	−4.00000	+	4.00000i	−0.132599	+	0.132599i
$911$			6.32456i			0.209542i	0.994496	+	0.104771i	$0.0334109\pi$
$911$			6.32456i			0.209542i	−0.994496	+	0.104771i	$0.966589\pi$
$912$		−	17.2982i		−	0.572801i
$913$	−10.6491	+	33.6754i	−0.352434	+	1.11449i
$914$	14.9737	−	14.9737i	0.495285	−	0.495285i
$915$			2.32456i			0.0768474i
$916$	8.00000			0.264327
$917$		−	12.0000i		−	0.396275i
$918$		0			0
$919$	47.9473			1.58164			0.790818	−	0.612051i	$-0.209655\pi$
$919$	47.9473			1.58164			0.790818	+	0.612051i	$0.209655\pi$
$920$	8.64911	−	8.64911i	0.285153	−	0.285153i
$921$		−	14.3246i		−	0.472010i
$922$	13.6754	+	13.6754i	0.450377	+	0.450377i
$923$			4.64911i			0.153027i
$924$	4.00000	−	12.6491i	0.131590	−	0.416125i
$925$			4.32456i			0.142191i
$926$	6.32456	−	6.32456i	0.207838	−	0.207838i
$927$			14.3246i			0.470480i
$928$	−9.29822	−	9.29822i	−0.305229	−	0.305229i
$929$	−18.0000			−0.590561			−0.295280	−	0.955411i	$-0.595413\pi$
$929$	−18.0000			−0.590561			−0.295280	+	0.955411i	$0.595413\pi$
$930$	4.00000	+	4.00000i	0.131165	+	0.131165i
$931$			12.9737i			0.425195i
$932$	−33.2982			−1.09072
$933$		−	18.9737i		−	0.621170i
$934$	20.0000	+	20.0000i	0.654420	+	0.654420i
$935$		0			0
$936$	−4.00000	+	4.00000i	−0.130744	+	0.130744i
$937$		−	46.9737i		−	1.53456i	−0.641311	−	0.767281i	$-0.721609\pi$
$937$		−	46.9737i		−	1.53456i	0.641311	−	0.767281i	$-0.278391\pi$
$938$		0			0
$939$	−30.6491			−1.00020
$940$		−	8.64911i		−	0.282103i
$941$	−14.9737			−0.488128			−0.244064	−	0.969759i	$-0.578481\pi$
$941$	−14.9737			−0.488128			−0.244064	+	0.969759i	$0.578481\pi$
$942$	−16.3246	+	16.3246i	−0.531883	+	0.531883i
$943$	36.0000			1.17232
$944$	41.2982			1.34414
$945$		−	2.00000i		−	0.0650600i
$946$	−42.9737	+	22.3246i	−1.39719	+	0.725834i
$947$	−16.6491			−0.541023			−0.270512	−	0.962717i	$-0.587193\pi$
$947$	−16.6491			−0.541023			−0.270512	+	0.962717i	$0.587193\pi$
$948$		−	20.0000i		−	0.649570i
$949$		−	4.64911i		−	0.150917i
$950$	−4.32456	+	4.32456i	−0.140307	+	0.140307i
$951$			34.6491i			1.12357i
$952$		0			0
$953$			36.0000i			1.16615i	0.812417	+	0.583077i	$0.198151\pi$
$953$			36.0000i			1.16615i	−0.812417	+	0.583077i	$0.801849\pi$
$954$	6.00000	−	6.00000i	0.194257	−	0.194257i
$955$	26.3246			0.851843
$956$		−	50.5964i		−	1.63641i
$957$	7.35089	+	2.32456i	0.237621	+	0.0751422i
$958$	24.0000	+	24.0000i	0.775405	+	0.775405i
$959$	−11.3509			−0.366539
$960$	8.00000			0.258199
$961$	15.0000			0.483871
$962$	8.64911	−	8.64911i	0.278859	−	0.278859i
$963$			10.0000i			0.322245i
$964$	−8.00000			−0.257663
$965$	−5.67544			−0.182699
$966$	8.64911	−	8.64911i	0.278281	−	0.278281i
$967$	−27.2982			−0.877852			−0.438926	−	0.898523i	$-0.644641\pi$
$967$	−27.2982			−0.877852			−0.438926	+	0.898523i	$0.644641\pi$
$968$	−30.6491	+	5.35089i	−0.985100	+	0.171984i
$969$		0			0
$970$	−14.6491	+	14.6491i	−0.470355	+	0.470355i
$971$	−10.3246			−0.331331			−0.165665	−	0.986182i	$-0.552977\pi$
$971$	−10.3246			−0.331331			−0.165665	+	0.986182i	$0.552977\pi$
$972$		−	2.00000i		−	0.0641500i
$973$			8.64911i			0.277278i
$974$	30.3246	−	30.3246i	0.971661	−	0.971661i
$975$	2.00000			0.0640513
$976$	−9.29822			−0.297629
$977$	18.9737			0.607021			0.303511	−	0.952828i	$-0.401841\pi$
$977$	18.9737			0.607021			0.303511	+	0.952828i	$0.401841\pi$
$978$	−0.649111	−	0.649111i	−0.0207563	−	0.0207563i
$979$	21.0263	+	6.64911i	0.672005	+	0.212506i
$980$	−6.00000			−0.191663
$981$	6.32456			0.201928
$982$	18.6491	−	18.6491i	0.595117	−	0.595117i
$983$		−	32.3246i		−	1.03099i	−0.856892	−	0.515497i	$-0.827607\pi$
$983$		−	32.3246i		−	1.03099i	0.856892	−	0.515497i	$-0.172393\pi$
$984$	16.6491	+	16.6491i	0.530754	+	0.530754i
$985$		−	16.6491i		−	0.530485i
$986$		0			0
$987$		−	8.64911i		−	0.275304i
$988$	17.2982			0.550330
$989$	−44.6491			−1.41976
$990$	−4.16228	+	2.16228i	−0.132286	+	0.0687217i
$991$		−	0.649111i		−	0.0206197i	−0.999947	−	0.0103098i	$-0.996718\pi$
$991$		−	0.649111i		−	0.0206197i	0.999947	−	0.0103098i	$-0.00328178\pi$
$992$	−16.0000	+	16.0000i	−0.508001	+	0.508001i
$993$	−10.0000			−0.317340
$994$	4.64911	−	4.64911i	0.147461	−	0.147461i
$995$	−4.00000			−0.126809
$996$	−21.2982			−0.674860
$997$	−6.00000			−0.190022			−0.0950110	−	0.995476i	$-0.530289\pi$
$997$	−6.00000			−0.190022			−0.0950110	+	0.995476i	$0.530289\pi$
$998$	15.2982	+	15.2982i	0.484257	+	0.484257i
$999$			4.32456i			0.136823i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1320.2.z.b.571.3	yes	4
4.3	odd	2		5280.2.z.b.1231.2		4
8.3	odd	2		1320.2.z.a.571.3	yes	4
8.5	even	2		5280.2.z.a.1231.4		4
11.10	odd	2		1320.2.z.a.571.1	✓	4
44.43	even	2		5280.2.z.a.1231.2		4
88.21	odd	2		5280.2.z.b.1231.4		4
88.43	even	2	inner	1320.2.z.b.571.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1320.2.z.a.571.1	✓	4	11.10	odd	2
1320.2.z.a.571.3	yes	4	8.3	odd	2
1320.2.z.b.571.1	yes	4	88.43	even	2	inner
1320.2.z.b.571.3	yes	4	1.1	even	1	trivial
5280.2.z.a.1231.2		4	44.43	even	2
5280.2.z.a.1231.4		4	8.5	even	2
5280.2.z.b.1231.2		4	4.3	odd	2
5280.2.z.b.1231.4		4	88.21	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:	\( N \)	\(=\)	\( 1320 = 2^{3} \cdot 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1320.z (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.00000i) q^{2} -1.00000 q^{3} +2.00000i q^{4} -1.00000i q^{5} +(-1.00000 - 1.00000i) q^{6} -2.00000 q^{7} +(-2.00000 + 2.00000i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(1.00000 + 1.00000i) q^{2} -1.00000 q^{3} +2.00000i q^{4} -1.00000i q^{5} +(-1.00000 - 1.00000i) q^{6} -2.00000 q^{7} +(-2.00000 + 2.00000i) q^{8} +1.00000 q^{9} +(1.00000 - 1.00000i) q^{10} +(-3.16228 - 1.00000i) q^{11} -2.00000i q^{12} +2.00000 q^{13} +(-2.00000 - 2.00000i) q^{14} +1.00000i q^{15} -4.00000 q^{16} +(1.00000 + 1.00000i) q^{18} -4.32456i q^{19} +2.00000 q^{20} +2.00000 q^{21} +(-2.16228 - 4.16228i) q^{22} -4.32456i q^{23} +(2.00000 - 2.00000i) q^{24} -1.00000 q^{25} +(2.00000 + 2.00000i) q^{26} -1.00000 q^{27} -4.00000i q^{28} +2.32456 q^{29} +(-1.00000 + 1.00000i) q^{30} -4.00000i q^{31} +(-4.00000 - 4.00000i) q^{32} +(3.16228 + 1.00000i) q^{33} +2.00000i q^{35} +2.00000i q^{36} -4.32456i q^{37} +(4.32456 - 4.32456i) q^{38} -2.00000 q^{39} +(2.00000 + 2.00000i) q^{40} +8.32456i q^{41} +(2.00000 + 2.00000i) q^{42} -10.3246i q^{43} +(2.00000 - 6.32456i) q^{44} -1.00000i q^{45} +(4.32456 - 4.32456i) q^{46} -4.32456i q^{47} +4.00000 q^{48} -3.00000 q^{49} +(-1.00000 - 1.00000i) q^{50} +4.00000i q^{52} -6.00000i q^{53} +(-1.00000 - 1.00000i) q^{54} +(-1.00000 + 3.16228i) q^{55} +(4.00000 - 4.00000i) q^{56} +4.32456i q^{57} +(2.32456 + 2.32456i) q^{58} -10.3246 q^{59} -2.00000 q^{60} +2.32456 q^{61} +(4.00000 - 4.00000i) q^{62} -2.00000 q^{63} -8.00000i q^{64} -2.00000i q^{65} +(2.16228 + 4.16228i) q^{66} +4.32456i q^{69} +(-2.00000 + 2.00000i) q^{70} +2.32456i q^{71} +(-2.00000 + 2.00000i) q^{72} -2.32456i q^{73} +(4.32456 - 4.32456i) q^{74} +1.00000 q^{75} +8.64911 q^{76} +(6.32456 + 2.00000i) q^{77} +(-2.00000 - 2.00000i) q^{78} +10.0000 q^{79} +4.00000i q^{80} +1.00000 q^{81} +(-8.32456 + 8.32456i) q^{82} -10.6491i q^{83} +4.00000i q^{84} +(10.3246 - 10.3246i) q^{86} -2.32456 q^{87} +(8.32456 - 4.32456i) q^{88} -6.64911 q^{89} +(1.00000 - 1.00000i) q^{90} -4.00000 q^{91} +8.64911 q^{92} +4.00000i q^{93} +(4.32456 - 4.32456i) q^{94} -4.32456 q^{95} +(4.00000 + 4.00000i) q^{96} -14.6491 q^{97} +(-3.00000 - 3.00000i) q^{98} +(-3.16228 - 1.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 4 q^{3} - 4 q^{6} - 8 q^{7} - 8 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 - 4 * q^3 - 4 * q^6 - 8 * q^7 - 8 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} - 4 q^{3} - 4 q^{6} - 8 q^{7} - 8 q^{8} + 4 q^{9} + 4 q^{10} + 8 q^{13} - 8 q^{14} - 16 q^{16} + 4 q^{18} + 8 q^{20} + 8 q^{21} + 4 q^{22} + 8 q^{24} - 4 q^{25} + 8 q^{26} - 4 q^{27} - 16 q^{29} - 4 q^{30} - 16 q^{32} - 8 q^{38} - 8 q^{39} + 8 q^{40} + 8 q^{42} + 8 q^{44} - 8 q^{46} + 16 q^{48} - 12 q^{49} - 4 q^{50} - 4 q^{54} - 4 q^{55} + 16 q^{56} - 16 q^{58} - 16 q^{59} - 8 q^{60} - 16 q^{61} + 16 q^{62} - 8 q^{63} - 4 q^{66} - 8 q^{70} - 8 q^{72} - 8 q^{74} + 4 q^{75} - 16 q^{76} - 8 q^{78} + 40 q^{79} + 4 q^{81} - 8 q^{82} + 16 q^{86} + 16 q^{87} + 8 q^{88} + 24 q^{89} + 4 q^{90} - 16 q^{91} - 16 q^{92} - 8 q^{94} + 8 q^{95} + 16 q^{96} - 8 q^{97} - 12 q^{98}+O(q^{100}) \) 4 * q + 4 * q^2 - 4 * q^3 - 4 * q^6 - 8 * q^7 - 8 * q^8 + 4 * q^9 + 4 * q^10 + 8 * q^13 - 8 * q^14 - 16 * q^16 + 4 * q^18 + 8 * q^20 + 8 * q^21 + 4 * q^22 + 8 * q^24 - 4 * q^25 + 8 * q^26 - 4 * q^27 - 16 * q^29 - 4 * q^30 - 16 * q^32 - 8 * q^38 - 8 * q^39 + 8 * q^40 + 8 * q^42 + 8 * q^44 - 8 * q^46 + 16 * q^48 - 12 * q^49 - 4 * q^50 - 4 * q^54 - 4 * q^55 + 16 * q^56 - 16 * q^58 - 16 * q^59 - 8 * q^60 - 16 * q^61 + 16 * q^62 - 8 * q^63 - 4 * q^66 - 8 * q^70 - 8 * q^72 - 8 * q^74 + 4 * q^75 - 16 * q^76 - 8 * q^78 + 40 * q^79 + 4 * q^81 - 8 * q^82 + 16 * q^86 + 16 * q^87 + 8 * q^88 + 24 * q^89 + 4 * q^90 - 16 * q^91 - 16 * q^92 - 8 * q^94 + 8 * q^95 + 16 * q^96 - 8 * q^97 - 12 * q^98

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