LMFDB - Embedded newform 840.2.z.b.811.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [840,2,Mod(811,840)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(840, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 0, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("840.811"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	840.z (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,-4,0,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.70743376979$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 9 $ x^4 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			811.1
Root			$-1.22474 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	840.811
Dual form			840.2.z.b.811.4

$q$-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} -1.00000i q^{3} +2.00000i q^{4} +1.00000 q^{5} +(-1.00000 + 1.00000i) q^{6} +(-1.00000 - 2.44949i) q^{7} +(2.00000 - 2.00000i) q^{8} -1.00000 q^{9} +(-1.00000 - 1.00000i) q^{10} +2.00000 q^{11} +2.00000 q^{12} +6.89898 q^{13} +(-1.44949 + 3.44949i) q^{14} -1.00000i q^{15} -4.00000 q^{16} -4.89898i q^{17} +(1.00000 + 1.00000i) q^{18} +6.89898i q^{19} +2.00000i q^{20} +(-2.44949 + 1.00000i) q^{21} +(-2.00000 - 2.00000i) q^{22} +6.00000i q^{23} +(-2.00000 - 2.00000i) q^{24} +1.00000 q^{25} +(-6.89898 - 6.89898i) q^{26} +1.00000i q^{27} +(4.89898 - 2.00000i) q^{28} -8.89898i q^{29} +(-1.00000 + 1.00000i) q^{30} +2.00000 q^{31} +(4.00000 + 4.00000i) q^{32} -2.00000i q^{33} +(-4.89898 + 4.89898i) q^{34} +(-1.00000 - 2.44949i) q^{35} -2.00000i q^{36} -7.79796i q^{37} +(6.89898 - 6.89898i) q^{38} -6.89898i q^{39} +(2.00000 - 2.00000i) q^{40} -2.89898i q^{41} +(3.44949 + 1.44949i) q^{42} -8.89898 q^{43} +4.00000i q^{44} -1.00000 q^{45} +(6.00000 - 6.00000i) q^{46} +10.8990 q^{47} +4.00000i q^{48} +(-5.00000 + 4.89898i) q^{49} +(-1.00000 - 1.00000i) q^{50} -4.89898 q^{51} +13.7980i q^{52} -9.79796i q^{53} +(1.00000 - 1.00000i) q^{54} +2.00000 q^{55} +(-6.89898 - 2.89898i) q^{56} +6.89898 q^{57} +(-8.89898 + 8.89898i) q^{58} -3.10102i q^{59} +2.00000 q^{60} -0.898979 q^{61} +(-2.00000 - 2.00000i) q^{62} +(1.00000 + 2.44949i) q^{63} -8.00000i q^{64} +6.89898 q^{65} +(-2.00000 + 2.00000i) q^{66} -4.89898 q^{67} +9.79796 q^{68} +6.00000 q^{69} +(-1.44949 + 3.44949i) q^{70} -12.8990i q^{71} +(-2.00000 + 2.00000i) q^{72} +8.89898i q^{73} +(-7.79796 + 7.79796i) q^{74} -1.00000i q^{75} -13.7980 q^{76} +(-2.00000 - 4.89898i) q^{77} +(-6.89898 + 6.89898i) q^{78} +4.00000i q^{79} -4.00000 q^{80} +1.00000 q^{81} +(-2.89898 + 2.89898i) q^{82} -4.00000i q^{83} +(-2.00000 - 4.89898i) q^{84} -4.89898i q^{85} +(8.89898 + 8.89898i) q^{86} -8.89898 q^{87} +(4.00000 - 4.00000i) q^{88} +1.10102i q^{89} +(1.00000 + 1.00000i) q^{90} +(-6.89898 - 16.8990i) q^{91} -12.0000 q^{92} -2.00000i q^{93} +(-10.8990 - 10.8990i) q^{94} +6.89898i q^{95} +(4.00000 - 4.00000i) q^{96} +0.898979i q^{97} +(9.89898 + 0.101021i) q^{98} -2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + 4 q^{5} - 4 q^{6} - 4 q^{7} + 8 q^{8} - 4 q^{9} - 4 q^{10} + 8 q^{11} + 8 q^{12} + 8 q^{13} + 4 q^{14} - 16 q^{16} + 4 q^{18} - 8 q^{22} - 8 q^{24} + 4 q^{25} - 8 q^{26} - 4 q^{30} + 8 q^{31}+ \cdots - 8 q^{99}+O(q^{100}) $ 4 * q - 4 * q^2 + 4 * q^5 - 4 * q^6 - 4 * q^7 + 8 * q^8 - 4 * q^9 - 4 * q^10 + 8 * q^11 + 8 * q^12 + 8 * q^13 + 4 * q^14 - 16 * q^16 + 4 * q^18 - 8 * q^22 - 8 * q^24 + 4 * q^25 - 8 * q^26 - 4 * q^30 + 8 * q^31 + 16 * q^32 - 4 * q^35 + 8 * q^38 + 8 * q^40 + 4 * q^42 - 16 * q^43 - 4 * q^45 + 24 * q^46 + 24 * q^47 - 20 * q^49 - 4 * q^50 + 4 * q^54 + 8 * q^55 - 8 * q^56 + 8 * q^57 - 16 * q^58 + 8 * q^60 + 16 * q^61 - 8 * q^62 + 4 * q^63 + 8 * q^65 - 8 * q^66 + 24 * q^69 + 4 * q^70 - 8 * q^72 + 8 * q^74 - 16 * q^76 - 8 * q^77 - 8 * q^78 - 16 * q^80 + 4 * q^81 + 8 * q^82 - 8 * q^84 + 16 * q^86 - 16 * q^87 + 16 * q^88 + 4 * q^90 - 8 * q^91 - 48 * q^92 - 24 * q^94 + 16 * q^96 + 20 * q^98 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$.

$n$	$241$	$281$	$337$	$421$	$631$
$\chi(n)$	$-1$	$1$	$1$	$-1$	$-1$

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
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$			2.00000i			1.00000i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	−1.00000	+	1.00000i	−0.408248	+	0.408248i
$7$	−1.00000	−	2.44949i	−0.377964	−	0.925820i
$7$	−1.00000	−	2.44949i	−0.377964	−	0.925820i
$8$	2.00000	−	2.00000i	0.707107	−	0.707107i
$9$	−1.00000			−0.333333
$10$	−1.00000	−	1.00000i	−0.316228	−	0.316228i
$11$	2.00000			0.603023			0.301511	−	0.953463i	$-0.402509\pi$
$11$	2.00000			0.603023			0.301511	+	0.953463i	$0.402509\pi$
$12$	2.00000			0.577350
$13$	6.89898			1.91343			0.956716	−	0.291022i	$-0.0939953\pi$
$13$	6.89898			1.91343			0.956716	+	0.291022i	$0.0939953\pi$
$14$	−1.44949	+	3.44949i	−0.387392	+	0.921915i
$15$		−	1.00000i		−	0.258199i
$16$	−4.00000			−1.00000
$17$		−	4.89898i		−	1.18818i	−0.804400	−	0.594089i	$-0.797513\pi$
$17$		−	4.89898i		−	1.18818i	0.804400	−	0.594089i	$-0.202487\pi$
$18$	1.00000	+	1.00000i	0.235702	+	0.235702i
$19$			6.89898i			1.58273i	0.611341	+	0.791367i	$0.290630\pi$
$19$			6.89898i			1.58273i	−0.611341	+	0.791367i	$0.709370\pi$
$20$			2.00000i			0.447214i
$21$	−2.44949	+	1.00000i	−0.534522	+	0.218218i
$22$	−2.00000	−	2.00000i	−0.426401	−	0.426401i
$23$			6.00000i			1.25109i	0.780189	+	0.625543i	$0.215123\pi$
$23$			6.00000i			1.25109i	−0.780189	+	0.625543i	$0.784877\pi$
$24$	−2.00000	−	2.00000i	−0.408248	−	0.408248i
$25$	1.00000			0.200000
$26$	−6.89898	−	6.89898i	−1.35300	−	1.35300i
$27$			1.00000i			0.192450i
$28$	4.89898	−	2.00000i	0.925820	−	0.377964i
$29$		−	8.89898i		−	1.65250i	−0.563304	−	0.826250i	$-0.690470\pi$
$29$		−	8.89898i		−	1.65250i	0.563304	−	0.826250i	$-0.309530\pi$
$30$	−1.00000	+	1.00000i	−0.182574	+	0.182574i
$31$	2.00000			0.359211			0.179605	−	0.983739i	$-0.442518\pi$
$31$	2.00000			0.359211			0.179605	+	0.983739i	$0.442518\pi$
$32$	4.00000	+	4.00000i	0.707107	+	0.707107i
$33$		−	2.00000i		−	0.348155i
$34$	−4.89898	+	4.89898i	−0.840168	+	0.840168i
$35$	−1.00000	−	2.44949i	−0.169031	−	0.414039i
$36$		−	2.00000i		−	0.333333i
$37$		−	7.79796i		−	1.28198i	−0.767551	−	0.640988i	$-0.778525\pi$
$37$		−	7.79796i		−	1.28198i	0.767551	−	0.640988i	$-0.221475\pi$
$38$	6.89898	−	6.89898i	1.11916	−	1.11916i
$39$		−	6.89898i		−	1.10472i
$40$	2.00000	−	2.00000i	0.316228	−	0.316228i
$41$		−	2.89898i		−	0.452745i	−0.974041	−	0.226372i	$-0.927313\pi$
$41$		−	2.89898i		−	0.452745i	0.974041	−	0.226372i	$-0.0726866\pi$
$42$	3.44949	+	1.44949i	0.532268	+	0.223661i
$43$	−8.89898			−1.35708			−0.678541	−	0.734563i	$-0.737387\pi$
$43$	−8.89898			−1.35708			−0.678541	+	0.734563i	$0.737387\pi$
$44$			4.00000i			0.603023i
$45$	−1.00000			−0.149071
$46$	6.00000	−	6.00000i	0.884652	−	0.884652i
$47$	10.8990			1.58978			0.794890	−	0.606754i	$-0.207529\pi$
$47$	10.8990			1.58978			0.794890	+	0.606754i	$0.207529\pi$
$48$			4.00000i			0.577350i
$49$	−5.00000	+	4.89898i	−0.714286	+	0.699854i
$50$	−1.00000	−	1.00000i	−0.141421	−	0.141421i
$51$	−4.89898			−0.685994
$52$			13.7980i			1.91343i
$53$		−	9.79796i		−	1.34585i	−0.739709	−	0.672927i	$-0.765037\pi$
$53$		−	9.79796i		−	1.34585i	0.739709	−	0.672927i	$-0.234963\pi$
$54$	1.00000	−	1.00000i	0.136083	−	0.136083i
$55$	2.00000			0.269680
$56$	−6.89898	−	2.89898i	−0.921915	−	0.387392i
$57$	6.89898			0.913792
$58$	−8.89898	+	8.89898i	−1.16849	+	1.16849i
$59$		−	3.10102i		−	0.403718i	−0.979415	−	0.201859i	$-0.935302\pi$
$59$		−	3.10102i		−	0.403718i	0.979415	−	0.201859i	$-0.0646984\pi$
$60$	2.00000			0.258199
$61$	−0.898979			−0.115103			−0.0575513	−	0.998343i	$-0.518329\pi$
$61$	−0.898979			−0.115103			−0.0575513	+	0.998343i	$0.518329\pi$
$62$	−2.00000	−	2.00000i	−0.254000	−	0.254000i
$63$	1.00000	+	2.44949i	0.125988	+	0.308607i
$64$		−	8.00000i		−	1.00000i
$65$	6.89898			0.855713
$66$	−2.00000	+	2.00000i	−0.246183	+	0.246183i
$67$	−4.89898			−0.598506			−0.299253	−	0.954174i	$-0.596737\pi$
$67$	−4.89898			−0.598506			−0.299253	+	0.954174i	$0.596737\pi$
$68$	9.79796			1.18818
$69$	6.00000			0.722315
$70$	−1.44949	+	3.44949i	−0.173247	+	0.412293i
$71$		−	12.8990i		−	1.53083i	−0.643539	−	0.765414i	$-0.722534\pi$
$71$		−	12.8990i		−	1.53083i	0.643539	−	0.765414i	$-0.277466\pi$
$72$	−2.00000	+	2.00000i	−0.235702	+	0.235702i
$73$			8.89898i			1.04155i	0.853695	+	0.520773i	$0.174356\pi$
$73$			8.89898i			1.04155i	−0.853695	+	0.520773i	$0.825644\pi$
$74$	−7.79796	+	7.79796i	−0.906494	+	0.906494i
$75$		−	1.00000i		−	0.115470i
$76$	−13.7980			−1.58273
$77$	−2.00000	−	4.89898i	−0.227921	−	0.558291i
$78$	−6.89898	+	6.89898i	−0.781156	+	0.781156i
$79$			4.00000i			0.450035i	0.974355	+	0.225018i	$0.0722440\pi$
$79$			4.00000i			0.450035i	−0.974355	+	0.225018i	$0.927756\pi$
$80$	−4.00000			−0.447214
$81$	1.00000			0.111111
$82$	−2.89898	+	2.89898i	−0.320139	+	0.320139i
$83$		−	4.00000i		−	0.439057i	−0.975606	−	0.219529i	$-0.929548\pi$
$83$		−	4.00000i		−	0.439057i	0.975606	−	0.219529i	$-0.0704519\pi$
$84$	−2.00000	−	4.89898i	−0.218218	−	0.534522i
$85$		−	4.89898i		−	0.531369i
$86$	8.89898	+	8.89898i	0.959602	+	0.959602i
$87$	−8.89898			−0.954071
$88$	4.00000	−	4.00000i	0.426401	−	0.426401i
$89$			1.10102i			0.116708i	0.998296	+	0.0583540i	$0.0185852\pi$
$89$			1.10102i			0.116708i	−0.998296	+	0.0583540i	$0.981415\pi$
$90$	1.00000	+	1.00000i	0.105409	+	0.105409i
$91$	−6.89898	−	16.8990i	−0.723210	−	1.77149i
$92$	−12.0000			−1.25109
$93$		−	2.00000i		−	0.207390i
$94$	−10.8990	−	10.8990i	−1.12414	−	1.12414i
$95$			6.89898i			0.707820i
$96$	4.00000	−	4.00000i	0.408248	−	0.408248i
$97$			0.898979i			0.0912775i	0.998958	+	0.0456388i	$0.0145323\pi$
$97$			0.898979i			0.0912775i	−0.998958	+	0.0456388i	$0.985468\pi$
$98$	9.89898	+	0.101021i	0.999948	+	0.0102046i
$99$	−2.00000			−0.201008
$100$			2.00000i			0.200000i
$101$	−3.79796			−0.377911			−0.188956	−	0.981986i	$-0.560510\pi$
$101$	−3.79796			−0.377911			−0.188956	+	0.981986i	$0.560510\pi$
$102$	4.89898	+	4.89898i	0.485071	+	0.485071i
$103$	−0.202041			−0.0199077			−0.00995385	−	0.999950i	$-0.503168\pi$
$103$	−0.202041			−0.0199077			−0.00995385	+	0.999950i	$0.503168\pi$
$104$	13.7980	−	13.7980i	1.35300	−	1.35300i
$105$	−2.44949	+	1.00000i	−0.239046	+	0.0975900i
$106$	−9.79796	+	9.79796i	−0.951662	+	0.951662i
$107$	−7.79796			−0.753857			−0.376929	−	0.926242i	$-0.623020\pi$
$107$	−7.79796			−0.753857			−0.376929	+	0.926242i	$0.623020\pi$
$108$	−2.00000			−0.192450
$109$			4.00000i			0.383131i	0.981480	+	0.191565i	$0.0613564\pi$
$109$			4.00000i			0.383131i	−0.981480	+	0.191565i	$0.938644\pi$
$110$	−2.00000	−	2.00000i	−0.190693	−	0.190693i
$111$	−7.79796			−0.740150
$112$	4.00000	+	9.79796i	0.377964	+	0.925820i
$113$	−1.79796			−0.169138			−0.0845689	−	0.996418i	$-0.526951\pi$
$113$	−1.79796			−0.169138			−0.0845689	+	0.996418i	$0.526951\pi$
$114$	−6.89898	−	6.89898i	−0.646149	−	0.646149i
$115$			6.00000i			0.559503i
$116$	17.7980			1.65250
$117$	−6.89898			−0.637811
$118$	−3.10102	+	3.10102i	−0.285472	+	0.285472i
$119$	−12.0000	+	4.89898i	−1.10004	+	0.449089i
$120$	−2.00000	−	2.00000i	−0.182574	−	0.182574i
$121$	−7.00000			−0.636364
$122$	0.898979	+	0.898979i	0.0813898	+	0.0813898i
$123$	−2.89898			−0.261392
$124$			4.00000i			0.359211i
$125$	1.00000			0.0894427
$126$	1.44949	−	3.44949i	0.129131	−	0.307305i
$127$			0.898979i			0.0797715i	0.999204	+	0.0398858i	$0.0126994\pi$
$127$			0.898979i			0.0797715i	−0.999204	+	0.0398858i	$0.987301\pi$
$128$	−8.00000	+	8.00000i	−0.707107	+	0.707107i
$129$			8.89898i			0.783511i
$130$	−6.89898	−	6.89898i	−0.605081	−	0.605081i
$131$			7.10102i			0.620419i	0.950668	+	0.310210i	$0.100399\pi$
$131$			7.10102i			0.620419i	−0.950668	+	0.310210i	$0.899601\pi$
$132$	4.00000			0.348155
$133$	16.8990	−	6.89898i	1.46533	−	0.598217i
$134$	4.89898	+	4.89898i	0.423207	+	0.423207i
$135$			1.00000i			0.0860663i
$136$	−9.79796	−	9.79796i	−0.840168	−	0.840168i
$137$	13.7980			1.17884			0.589420	−	0.807827i	$-0.299356\pi$
$137$	13.7980			1.17884			0.589420	+	0.807827i	$0.299356\pi$
$138$	−6.00000	−	6.00000i	−0.510754	−	0.510754i
$139$			6.89898i			0.585164i	0.956240	+	0.292582i	$0.0945144\pi$
$139$			6.89898i			0.585164i	−0.956240	+	0.292582i	$0.905486\pi$
$140$	4.89898	−	2.00000i	0.414039	−	0.169031i
$141$		−	10.8990i		−	0.917860i
$142$	−12.8990	+	12.8990i	−1.08246	+	1.08246i
$143$	13.7980			1.15384
$144$	4.00000			0.333333
$145$		−	8.89898i		−	0.739020i
$146$	8.89898	−	8.89898i	0.736485	−	0.736485i
$147$	4.89898	+	5.00000i	0.404061	+	0.412393i
$148$	15.5959			1.28198
$149$			16.8990i			1.38442i	0.721697	+	0.692209i	$0.243362\pi$
$149$			16.8990i			1.38442i	−0.721697	+	0.692209i	$0.756638\pi$
$150$	−1.00000	+	1.00000i	−0.0816497	+	0.0816497i
$151$			5.79796i			0.471831i	0.971774	+	0.235916i	$0.0758089\pi$
$151$			5.79796i			0.471831i	−0.971774	+	0.235916i	$0.924191\pi$
$152$	13.7980	+	13.7980i	1.11916	+	1.11916i
$153$			4.89898i			0.396059i
$154$	−2.89898	+	6.89898i	−0.233606	+	0.555936i
$155$	2.00000			0.160644
$156$	13.7980			1.10472
$157$	16.6969			1.33256			0.666280	−	0.745701i	$-0.267885\pi$
$157$	16.6969			1.33256			0.666280	+	0.745701i	$0.267885\pi$
$158$	4.00000	−	4.00000i	0.318223	−	0.318223i
$159$	−9.79796			−0.777029
$160$	4.00000	+	4.00000i	0.316228	+	0.316228i
$161$	14.6969	−	6.00000i	1.15828	−	0.472866i
$162$	−1.00000	−	1.00000i	−0.0785674	−	0.0785674i
$163$	22.6969			1.77776			0.888881	−	0.458139i	$-0.151484\pi$
$163$	22.6969			1.77776			0.888881	+	0.458139i	$0.151484\pi$
$164$	5.79796			0.452745
$165$		−	2.00000i		−	0.155700i
$166$	−4.00000	+	4.00000i	−0.310460	+	0.310460i
$167$	10.8990			0.843388			0.421694	−	0.906738i	$-0.361436\pi$
$167$	10.8990			0.843388			0.421694	+	0.906738i	$0.361436\pi$
$168$	−2.89898	+	6.89898i	−0.223661	+	0.532268i
$169$	34.5959			2.66122
$170$	−4.89898	+	4.89898i	−0.375735	+	0.375735i
$171$		−	6.89898i		−	0.527578i
$172$		−	17.7980i		−	1.35708i
$173$	−11.7980			−0.896982			−0.448491	−	0.893787i	$-0.648038\pi$
$173$	−11.7980			−0.896982			−0.448491	+	0.893787i	$0.648038\pi$
$174$	8.89898	+	8.89898i	0.674630	+	0.674630i
$175$	−1.00000	−	2.44949i	−0.0755929	−	0.185164i
$176$	−8.00000			−0.603023
$177$	−3.10102			−0.233087
$178$	1.10102	−	1.10102i	0.0825250	−	0.0825250i
$179$	−10.0000			−0.747435			−0.373718	−	0.927543i	$-0.621917\pi$
$179$	−10.0000			−0.747435			−0.373718	+	0.927543i	$0.621917\pi$
$180$		−	2.00000i		−	0.149071i
$181$	−20.8990			−1.55341			−0.776704	−	0.629865i	$-0.783110\pi$
$181$	−20.8990			−1.55341			−0.776704	+	0.629865i	$0.783110\pi$
$182$	−10.0000	+	23.7980i	−0.741249	+	1.76402i
$183$			0.898979i			0.0664545i
$184$	12.0000	+	12.0000i	0.884652	+	0.884652i
$185$		−	7.79796i		−	0.573317i
$186$	−2.00000	+	2.00000i	−0.146647	+	0.146647i
$187$		−	9.79796i		−	0.716498i
$188$			21.7980i			1.58978i
$189$	2.44949	−	1.00000i	0.178174	−	0.0727393i
$190$	6.89898	−	6.89898i	0.500505	−	0.500505i
$191$			7.10102i			0.513812i	0.966436	+	0.256906i	$0.0827030\pi$
$191$			7.10102i			0.513812i	−0.966436	+	0.256906i	$0.917297\pi$
$192$	−8.00000			−0.577350
$193$	−0.202041			−0.0145432			−0.00727162	−	0.999974i	$-0.502315\pi$
$193$	−0.202041			−0.0145432			−0.00727162	+	0.999974i	$0.502315\pi$
$194$	0.898979	−	0.898979i	0.0645430	−	0.0645430i
$195$		−	6.89898i		−	0.494046i
$196$	−9.79796	−	10.0000i	−0.699854	−	0.714286i
$197$			13.7980i			0.983064i	0.870860	+	0.491532i	$0.163563\pi$
$197$			13.7980i			0.983064i	−0.870860	+	0.491532i	$0.836437\pi$
$198$	2.00000	+	2.00000i	0.142134	+	0.142134i
$199$	10.0000			0.708881			0.354441	−	0.935079i	$-0.384671\pi$
$199$	10.0000			0.708881			0.354441	+	0.935079i	$0.384671\pi$
$200$	2.00000	−	2.00000i	0.141421	−	0.141421i
$201$			4.89898i			0.345547i
$202$	3.79796	+	3.79796i	0.267223	+	0.267223i
$203$	−21.7980	+	8.89898i	−1.52992	+	0.624586i
$204$		−	9.79796i		−	0.685994i
$205$		−	2.89898i		−	0.202474i
$206$	0.202041	+	0.202041i	0.0140769	+	0.0140769i
$207$		−	6.00000i		−	0.417029i
$208$	−27.5959			−1.91343
$209$			13.7980i			0.954425i
$210$	3.44949	+	1.44949i	0.238037	+	0.100024i
$211$	22.0000			1.51454			0.757271	−	0.653101i	$-0.226532\pi$
$211$	22.0000			1.51454			0.757271	+	0.653101i	$0.226532\pi$
$212$	19.5959			1.34585
$213$	−12.8990			−0.883824
$214$	7.79796	+	7.79796i	0.533058	+	0.533058i
$215$	−8.89898			−0.606905
$216$	2.00000	+	2.00000i	0.136083	+	0.136083i
$217$	−2.00000	−	4.89898i	−0.135769	−	0.332564i
$218$	4.00000	−	4.00000i	0.270914	−	0.270914i
$219$	8.89898			0.601337
$220$			4.00000i			0.269680i
$221$		−	33.7980i		−	2.27350i
$222$	7.79796	+	7.79796i	0.523365	+	0.523365i
$223$	−6.00000			−0.401790			−0.200895	−	0.979613i	$-0.564385\pi$
$223$	−6.00000			−0.401790			−0.200895	+	0.979613i	$0.564385\pi$
$224$	5.79796	−	13.7980i	0.387392	−	0.921915i
$225$	−1.00000			−0.0666667
$226$	1.79796	+	1.79796i	0.119598	+	0.119598i
$227$		−	12.0000i		−	0.796468i	−0.917284	−	0.398234i	$-0.869623\pi$
$227$		−	12.0000i		−	0.796468i	0.917284	−	0.398234i	$-0.130377\pi$
$228$			13.7980i			0.913792i
$229$	24.4949			1.61867			0.809334	−	0.587348i	$-0.199828\pi$
$229$	24.4949			1.61867			0.809334	+	0.587348i	$0.199828\pi$
$230$	6.00000	−	6.00000i	0.395628	−	0.395628i
$231$	−4.89898	+	2.00000i	−0.322329	+	0.131590i
$232$	−17.7980	−	17.7980i	−1.16849	−	1.16849i
$233$	−16.0000			−1.04819			−0.524097	−	0.851658i	$-0.675597\pi$
$233$	−16.0000			−1.04819			−0.524097	+	0.851658i	$0.675597\pi$
$234$	6.89898	+	6.89898i	0.451000	+	0.451000i
$235$	10.8990			0.710971
$236$	6.20204			0.403718
$237$	4.00000			0.259828
$238$	16.8990	+	7.10102i	1.09540	+	0.460291i
$239$			2.69694i			0.174450i	0.996189	+	0.0872252i	$0.0278000\pi$
$239$			2.69694i			0.174450i	−0.996189	+	0.0872252i	$0.972200\pi$
$240$			4.00000i			0.258199i
$241$			20.0000i			1.28831i	0.764894	+	0.644157i	$0.222792\pi$
$241$			20.0000i			1.28831i	−0.764894	+	0.644157i	$0.777208\pi$
$242$	7.00000	+	7.00000i	0.449977	+	0.449977i
$243$		−	1.00000i		−	0.0641500i
$244$		−	1.79796i		−	0.115103i
$245$	−5.00000	+	4.89898i	−0.319438	+	0.312984i
$246$	2.89898	+	2.89898i	0.184832	+	0.184832i
$247$			47.5959i			3.02846i
$248$	4.00000	−	4.00000i	0.254000	−	0.254000i
$249$	−4.00000			−0.253490
$250$	−1.00000	−	1.00000i	−0.0632456	−	0.0632456i
$251$		−	12.8990i		−	0.814176i	−0.913389	−	0.407088i	$-0.866544\pi$
$251$		−	12.8990i		−	0.814176i	0.913389	−	0.407088i	$-0.133456\pi$
$252$	−4.89898	+	2.00000i	−0.308607	+	0.125988i
$253$			12.0000i			0.754434i
$254$	0.898979	−	0.898979i	0.0564070	−	0.0564070i
$255$	−4.89898			−0.306786
$256$	16.0000			1.00000
$257$			15.1010i			0.941976i	0.882140	+	0.470988i	$0.156102\pi$
$257$			15.1010i			0.941976i	−0.882140	+	0.470988i	$0.843898\pi$
$258$	8.89898	−	8.89898i	0.554026	−	0.554026i
$259$	−19.1010	+	7.79796i	−1.18688	+	0.484542i
$260$			13.7980i			0.855713i
$261$			8.89898i			0.550833i
$262$	7.10102	−	7.10102i	0.438703	−	0.438703i
$263$			11.7980i			0.727493i	0.931498	+	0.363747i	$0.118503\pi$
$263$			11.7980i			0.727493i	−0.931498	+	0.363747i	$0.881497\pi$
$264$	−4.00000	−	4.00000i	−0.246183	−	0.246183i
$265$		−	9.79796i		−	0.601884i
$266$	−23.7980	−	10.0000i	−1.45915	−	0.613139i
$267$	1.10102			0.0673814
$268$		−	9.79796i		−	0.598506i
$269$	15.7980			0.963219			0.481609	−	0.876386i	$-0.340052\pi$
$269$	15.7980			0.963219			0.481609	+	0.876386i	$0.340052\pi$
$270$	1.00000	−	1.00000i	0.0608581	−	0.0608581i
$271$	−23.7980			−1.44562			−0.722812	−	0.691045i	$-0.757151\pi$
$271$	−23.7980			−1.44562			−0.722812	+	0.691045i	$0.757151\pi$
$272$			19.5959i			1.18818i
$273$	−16.8990	+	6.89898i	−1.02277	+	0.417545i
$274$	−13.7980	−	13.7980i	−0.833565	−	0.833565i
$275$	2.00000			0.120605
$276$			12.0000i			0.722315i
$277$			3.79796i			0.228197i	0.993469	+	0.114099i	$0.0363980\pi$
$277$			3.79796i			0.228197i	−0.993469	+	0.114099i	$0.963602\pi$
$278$	6.89898	−	6.89898i	0.413773	−	0.413773i
$279$	−2.00000			−0.119737
$280$	−6.89898	−	2.89898i	−0.412293	−	0.173247i
$281$	27.7980			1.65829			0.829144	−	0.559036i	$-0.188829\pi$
$281$	27.7980			1.65829			0.829144	+	0.559036i	$0.188829\pi$
$282$	−10.8990	+	10.8990i	−0.649025	+	0.649025i
$283$		−	9.79796i		−	0.582428i	−0.956658	−	0.291214i	$-0.905941\pi$
$283$		−	9.79796i		−	0.582428i	0.956658	−	0.291214i	$-0.0940592\pi$
$284$	25.7980			1.53083
$285$	6.89898			0.408660
$286$	−13.7980	−	13.7980i	−0.815890	−	0.815890i
$287$	−7.10102	+	2.89898i	−0.419160	+	0.171121i
$288$	−4.00000	−	4.00000i	−0.235702	−	0.235702i
$289$	−7.00000			−0.411765
$290$	−8.89898	+	8.89898i	−0.522566	+	0.522566i
$291$	0.898979			0.0526991
$292$	−17.7980			−1.04155
$293$	−17.5959			−1.02796			−0.513982	−	0.857801i	$-0.671830\pi$
$293$	−17.5959			−1.02796			−0.513982	+	0.857801i	$0.671830\pi$
$294$	0.101021	−	9.89898i	0.00589164	−	0.577320i
$295$		−	3.10102i		−	0.180548i
$296$	−15.5959	−	15.5959i	−0.906494	−	0.906494i
$297$			2.00000i			0.116052i
$298$	16.8990	−	16.8990i	0.978932	−	0.978932i
$299$			41.3939i			2.39387i
$300$	2.00000			0.115470
$301$	8.89898	+	21.7980i	0.512929	+	1.25641i
$302$	5.79796	−	5.79796i	0.333635	−	0.333635i
$303$			3.79796i			0.218187i
$304$		−	27.5959i		−	1.58273i
$305$	−0.898979			−0.0514754
$306$	4.89898	−	4.89898i	0.280056	−	0.280056i
$307$		−	23.5959i		−	1.34669i	−0.739328	−	0.673345i	$-0.764857\pi$
$307$		−	23.5959i		−	1.34669i	0.739328	−	0.673345i	$-0.235143\pi$
$308$	9.79796	−	4.00000i	0.558291	−	0.227921i
$309$			0.202041i			0.0114937i
$310$	−2.00000	−	2.00000i	−0.113592	−	0.113592i
$311$	−8.00000			−0.453638			−0.226819	−	0.973937i	$-0.572833\pi$
$311$	−8.00000			−0.453638			−0.226819	+	0.973937i	$0.572833\pi$
$312$	−13.7980	−	13.7980i	−0.781156	−	0.781156i
$313$			20.4949i			1.15844i	0.815171	+	0.579220i	$0.196643\pi$
$313$			20.4949i			1.15844i	−0.815171	+	0.579220i	$0.803357\pi$
$314$	−16.6969	−	16.6969i	−0.942263	−	0.942263i
$315$	1.00000	+	2.44949i	0.0563436	+	0.138013i
$316$	−8.00000			−0.450035
$317$		−	12.0000i		−	0.673987i	−0.941507	−	0.336994i	$-0.890590\pi$
$317$		−	12.0000i		−	0.673987i	0.941507	−	0.336994i	$-0.109410\pi$
$318$	9.79796	+	9.79796i	0.549442	+	0.549442i
$319$		−	17.7980i		−	0.996494i
$320$		−	8.00000i		−	0.447214i
$321$			7.79796i			0.435240i
$322$	−20.6969	−	8.69694i	−1.15340	−	0.484661i
$323$	33.7980			1.88057
$324$			2.00000i			0.111111i
$325$	6.89898			0.382687
$326$	−22.6969	−	22.6969i	−1.25707	−	1.25707i
$327$	4.00000			0.221201
$328$	−5.79796	−	5.79796i	−0.320139	−	0.320139i
$329$	−10.8990	−	26.6969i	−0.600880	−	1.47185i
$330$	−2.00000	+	2.00000i	−0.110096	+	0.110096i
$331$	−35.3939			−1.94542			−0.972712	−	0.232017i	$-0.925467\pi$
$331$	−35.3939			−1.94542			−0.972712	+	0.232017i	$0.925467\pi$
$332$	8.00000			0.439057
$333$			7.79796i			0.427326i
$334$	−10.8990	−	10.8990i	−0.596366	−	0.596366i
$335$	−4.89898			−0.267660
$336$	9.79796	−	4.00000i	0.534522	−	0.218218i
$337$	12.2020			0.664688			0.332344	−	0.943158i	$-0.392161\pi$
$337$	12.2020			0.664688			0.332344	+	0.943158i	$0.392161\pi$
$338$	−34.5959	−	34.5959i	−1.88177	−	1.88177i
$339$			1.79796i			0.0976517i
$340$	9.79796			0.531369
$341$	4.00000			0.216612
$342$	−6.89898	+	6.89898i	−0.373054	+	0.373054i
$343$	17.0000	+	7.34847i	0.917914	+	0.396780i
$344$	−17.7980	+	17.7980i	−0.959602	+	0.959602i
$345$	6.00000			0.323029
$346$	11.7980	+	11.7980i	0.634262	+	0.634262i
$347$	−13.5959			−0.729867			−0.364934	−	0.931034i	$-0.618908\pi$
$347$	−13.5959			−0.729867			−0.364934	+	0.931034i	$0.618908\pi$
$348$		−	17.7980i		−	0.954071i
$349$	−1.30306			−0.0697513			−0.0348756	−	0.999392i	$-0.511104\pi$
$349$	−1.30306			−0.0697513			−0.0348756	+	0.999392i	$0.511104\pi$
$350$	−1.44949	+	3.44949i	−0.0774785	+	0.184383i
$351$			6.89898i			0.368240i
$352$	8.00000	+	8.00000i	0.426401	+	0.426401i
$353$		−	5.30306i		−	0.282253i	−0.989992	−	0.141127i	$-0.954927\pi$
$353$		−	5.30306i		−	0.282253i	0.989992	−	0.141127i	$-0.0450725\pi$
$354$	3.10102	+	3.10102i	0.164817	+	0.164817i
$355$		−	12.8990i		−	0.684607i
$356$	−2.20204			−0.116708
$357$	4.89898	+	12.0000i	0.259281	+	0.635107i
$358$	10.0000	+	10.0000i	0.528516	+	0.528516i
$359$			16.8990i			0.891894i	0.895059	+	0.445947i	$0.147133\pi$
$359$			16.8990i			0.891894i	−0.895059	+	0.445947i	$0.852867\pi$
$360$	−2.00000	+	2.00000i	−0.105409	+	0.105409i
$361$	−28.5959			−1.50505
$362$	20.8990	+	20.8990i	1.09843	+	1.09843i
$363$			7.00000i			0.367405i
$364$	33.7980	−	13.7980i	1.77149	−	0.723210i
$365$			8.89898i			0.465794i
$366$	0.898979	−	0.898979i	0.0469904	−	0.0469904i
$367$	3.79796			0.198252			0.0991259	−	0.995075i	$-0.468395\pi$
$367$	3.79796			0.198252			0.0991259	+	0.995075i	$0.468395\pi$
$368$		−	24.0000i		−	1.25109i
$369$			2.89898i			0.150915i
$370$	−7.79796	+	7.79796i	−0.405397	+	0.405397i
$371$	−24.0000	+	9.79796i	−1.24602	+	0.508685i
$372$	4.00000			0.207390
$373$		−	14.0000i		−	0.724893i	−0.932005	−	0.362446i	$-0.881942\pi$
$373$		−	14.0000i		−	0.724893i	0.932005	−	0.362446i	$-0.118058\pi$
$374$	−9.79796	+	9.79796i	−0.506640	+	0.506640i
$375$		−	1.00000i		−	0.0516398i
$376$	21.7980	−	21.7980i	1.12414	−	1.12414i
$377$		−	61.3939i		−	3.16195i
$378$	−3.44949	−	1.44949i	−0.177423	−	0.0745537i
$379$	−27.3939			−1.40713			−0.703564	−	0.710631i	$-0.748409\pi$
$379$	−27.3939			−1.40713			−0.703564	+	0.710631i	$0.748409\pi$
$380$	−13.7980			−0.707820
$381$	0.898979			0.0460561
$382$	7.10102	−	7.10102i	0.363320	−	0.363320i
$383$	−18.8990			−0.965693			−0.482846	−	0.875705i	$-0.660397\pi$
$383$	−18.8990			−0.965693			−0.482846	+	0.875705i	$0.660397\pi$
$384$	8.00000	+	8.00000i	0.408248	+	0.408248i
$385$	−2.00000	−	4.89898i	−0.101929	−	0.249675i
$386$	0.202041	+	0.202041i	0.0102836	+	0.0102836i
$387$	8.89898			0.452361
$388$	−1.79796			−0.0912775
$389$			2.69694i			0.136740i	0.997660	+	0.0683701i	$0.0217799\pi$
$389$			2.69694i			0.136740i	−0.997660	+	0.0683701i	$0.978220\pi$
$390$	−6.89898	+	6.89898i	−0.349343	+	0.349343i
$391$	29.3939			1.48651
$392$	−0.202041	+	19.7980i	−0.0102046	+	0.999948i
$393$	7.10102			0.358199
$394$	13.7980	−	13.7980i	0.695131	−	0.695131i
$395$			4.00000i			0.201262i
$396$		−	4.00000i		−	0.201008i
$397$	16.6969			0.837995			0.418998	−	0.907987i	$-0.362382\pi$
$397$	16.6969			0.837995			0.418998	+	0.907987i	$0.362382\pi$
$398$	−10.0000	−	10.0000i	−0.501255	−	0.501255i
$399$	−6.89898	−	16.8990i	−0.345381	−	0.846007i
$400$	−4.00000			−0.200000
$401$	7.79796			0.389411			0.194706	−	0.980862i	$-0.437625\pi$
$401$	7.79796			0.389411			0.194706	+	0.980862i	$0.437625\pi$
$402$	4.89898	−	4.89898i	0.244339	−	0.244339i
$403$	13.7980			0.687325
$404$		−	7.59592i		−	0.377911i
$405$	1.00000			0.0496904
$406$	30.6969	+	12.8990i	1.52346	+	0.640166i
$407$		−	15.5959i		−	0.773061i
$408$	−9.79796	+	9.79796i	−0.485071	+	0.485071i
$409$			4.00000i			0.197787i	0.995098	+	0.0988936i	$0.0315304\pi$
$409$			4.00000i			0.197787i	−0.995098	+	0.0988936i	$0.968470\pi$
$410$	−2.89898	+	2.89898i	−0.143170	+	0.143170i
$411$		−	13.7980i		−	0.680603i
$412$		−	0.404082i		−	0.0199077i
$413$	−7.59592	+	3.10102i	−0.373771	+	0.152591i
$414$	−6.00000	+	6.00000i	−0.294884	+	0.294884i
$415$		−	4.00000i		−	0.196352i
$416$	27.5959	+	27.5959i	1.35300	+	1.35300i
$417$	6.89898			0.337844
$418$	13.7980	−	13.7980i	0.674880	−	0.674880i
$419$			34.2929i			1.67532i	0.546195	+	0.837658i	$0.316076\pi$
$419$			34.2929i			1.67532i	−0.546195	+	0.837658i	$0.683924\pi$
$420$	−2.00000	−	4.89898i	−0.0975900	−	0.239046i
$421$			25.7980i			1.25732i	0.777682	+	0.628658i	$0.216395\pi$
$421$			25.7980i			1.25732i	−0.777682	+	0.628658i	$0.783605\pi$
$422$	−22.0000	−	22.0000i	−1.07094	−	1.07094i
$423$	−10.8990			−0.529927
$424$	−19.5959	−	19.5959i	−0.951662	−	0.951662i
$425$		−	4.89898i		−	0.237635i
$426$	12.8990	+	12.8990i	0.624958	+	0.624958i
$427$	0.898979	+	2.20204i	0.0435047	+	0.106564i
$428$		−	15.5959i		−	0.753857i
$429$		−	13.7980i		−	0.666172i
$430$	8.89898	+	8.89898i	0.429147	+	0.429147i
$431$			12.8990i			0.621322i	0.950521	+	0.310661i	$0.100550\pi$
$431$			12.8990i			0.621322i	−0.950521	+	0.310661i	$0.899450\pi$
$432$		−	4.00000i		−	0.192450i
$433$			34.6969i			1.66743i	0.552196	+	0.833714i	$0.313790\pi$
$433$			34.6969i			1.66743i	−0.552196	+	0.833714i	$0.686210\pi$
$434$	−2.89898	+	6.89898i	−0.139155	+	0.331162i
$435$	−8.89898			−0.426673
$436$	−8.00000			−0.383131
$437$	−41.3939			−1.98014
$438$	−8.89898	−	8.89898i	−0.425210	−	0.425210i
$439$	4.20204			0.200552			0.100276	−	0.994960i	$-0.468027\pi$
$439$	4.20204			0.200552			0.100276	+	0.994960i	$0.468027\pi$
$440$	4.00000	−	4.00000i	0.190693	−	0.190693i
$441$	5.00000	−	4.89898i	0.238095	−	0.233285i
$442$	−33.7980	+	33.7980i	−1.60760	+	1.60760i
$443$	−6.00000			−0.285069			−0.142534	−	0.989790i	$-0.545525\pi$
$443$	−6.00000			−0.285069			−0.142534	+	0.989790i	$0.545525\pi$
$444$		−	15.5959i		−	0.740150i
$445$			1.10102i			0.0521934i
$446$	6.00000	+	6.00000i	0.284108	+	0.284108i
$447$	16.8990			0.799294
$448$	−19.5959	+	8.00000i	−0.925820	+	0.377964i
$449$	4.20204			0.198307			0.0991533	−	0.995072i	$-0.468387\pi$
$449$	4.20204			0.198307			0.0991533	+	0.995072i	$0.468387\pi$
$450$	1.00000	+	1.00000i	0.0471405	+	0.0471405i
$451$		−	5.79796i		−	0.273015i
$452$		−	3.59592i		−	0.169138i
$453$	5.79796			0.272412
$454$	−12.0000	+	12.0000i	−0.563188	+	0.563188i
$455$	−6.89898	−	16.8990i	−0.323429	−	0.792236i
$456$	13.7980	−	13.7980i	0.646149	−	0.646149i
$457$	−7.79796			−0.364773			−0.182387	−	0.983227i	$-0.558382\pi$
$457$	−7.79796			−0.364773			−0.182387	+	0.983227i	$0.558382\pi$
$458$	−24.4949	−	24.4949i	−1.14457	−	1.14457i
$459$	4.89898			0.228665
$460$	−12.0000			−0.559503
$461$	−23.7980			−1.10838			−0.554191	−	0.832390i	$-0.686972\pi$
$461$	−23.7980			−1.10838			−0.554191	+	0.832390i	$0.686972\pi$
$462$	6.89898	+	2.89898i	0.320970	+	0.134873i
$463$		−	2.69694i		−	0.125337i	−0.998034	−	0.0626687i	$-0.980039\pi$
$463$		−	2.69694i		−	0.125337i	0.998034	−	0.0626687i	$-0.0199611\pi$
$464$			35.5959i			1.65250i
$465$		−	2.00000i		−	0.0927478i
$466$	16.0000	+	16.0000i	0.741186	+	0.741186i
$467$			2.20204i			0.101898i	0.998701	+	0.0509492i	$0.0162246\pi$
$467$			2.20204i			0.101898i	−0.998701	+	0.0509492i	$0.983775\pi$
$468$		−	13.7980i		−	0.637811i
$469$	4.89898	+	12.0000i	0.226214	+	0.554109i
$470$	−10.8990	−	10.8990i	−0.502732	−	0.502732i
$471$		−	16.6969i		−	0.769354i
$472$	−6.20204	−	6.20204i	−0.285472	−	0.285472i
$473$	−17.7980			−0.818351
$474$	−4.00000	−	4.00000i	−0.183726	−	0.183726i
$475$			6.89898i			0.316547i
$476$	−9.79796	−	24.0000i	−0.449089	−	1.10004i
$477$			9.79796i			0.448618i
$478$	2.69694	−	2.69694i	0.123355	−	0.123355i
$479$	−11.5959			−0.529831			−0.264916	−	0.964272i	$-0.585344\pi$
$479$	−11.5959			−0.529831			−0.264916	+	0.964272i	$0.585344\pi$
$480$	4.00000	−	4.00000i	0.182574	−	0.182574i
$481$		−	53.7980i		−	2.45298i
$482$	20.0000	−	20.0000i	0.910975	−	0.910975i
$483$	−6.00000	−	14.6969i	−0.273009	−	0.668734i
$484$		−	14.0000i		−	0.636364i
$485$			0.898979i			0.0408206i
$486$	−1.00000	+	1.00000i	−0.0453609	+	0.0453609i
$487$		−	24.8990i		−	1.12828i	−0.825679	−	0.564140i	$-0.809208\pi$
$487$		−	24.8990i		−	1.12828i	0.825679	−	0.564140i	$-0.190792\pi$
$488$	−1.79796	+	1.79796i	−0.0813898	+	0.0813898i
$489$		−	22.6969i		−	1.02639i
$490$	9.89898	+	0.101021i	0.447190	+	0.00456364i
$491$	13.5959			0.613575			0.306788	−	0.951778i	$-0.400746\pi$
$491$	13.5959			0.613575			0.306788	+	0.951778i	$0.400746\pi$
$492$		−	5.79796i		−	0.261392i
$493$	−43.5959			−1.96346
$494$	47.5959	−	47.5959i	2.14144	−	2.14144i
$495$	−2.00000			−0.0898933
$496$	−8.00000			−0.359211
$497$	−31.5959	+	12.8990i	−1.41727	+	0.578598i
$498$	4.00000	+	4.00000i	0.179244	+	0.179244i
$499$	10.0000			0.447661			0.223831	−	0.974628i	$-0.428144\pi$
$499$	10.0000			0.447661			0.223831	+	0.974628i	$0.428144\pi$
$500$			2.00000i			0.0894427i
$501$		−	10.8990i		−	0.486930i
$502$	−12.8990	+	12.8990i	−0.575710	+	0.575710i
$503$	38.4949			1.71640			0.858201	−	0.513313i	$-0.171582\pi$
$503$	38.4949			1.71640			0.858201	+	0.513313i	$0.171582\pi$
$504$	6.89898	+	2.89898i	0.307305	+	0.129131i
$505$	−3.79796			−0.169007
$506$	12.0000	−	12.0000i	0.533465	−	0.533465i
$507$		−	34.5959i		−	1.53646i
$508$	−1.79796			−0.0797715
$509$	−1.59592			−0.0707378			−0.0353689	−	0.999374i	$-0.511261\pi$
$509$	−1.59592			−0.0707378			−0.0353689	+	0.999374i	$0.511261\pi$
$510$	4.89898	+	4.89898i	0.216930	+	0.216930i
$511$	21.7980	−	8.89898i	0.964285	−	0.393668i
$512$	−16.0000	−	16.0000i	−0.707107	−	0.707107i
$513$	−6.89898			−0.304597
$514$	15.1010	−	15.1010i	0.666077	−	0.666077i
$515$	−0.202041			−0.00890299
$516$	−17.7980			−0.783511
$517$	21.7980			0.958673
$518$	26.8990	+	11.3031i	1.18187	+	0.496628i
$519$			11.7980i			0.517873i
$520$	13.7980	−	13.7980i	0.605081	−	0.605081i
$521$			42.8990i			1.87944i	0.341947	+	0.939719i	$0.388914\pi$
$521$			42.8990i			1.87944i	−0.341947	+	0.939719i	$0.611086\pi$
$522$	8.89898	−	8.89898i	0.389498	−	0.389498i
$523$		−	35.5959i		−	1.55650i	−0.627954	−	0.778250i	$-0.716107\pi$
$523$		−	35.5959i		−	1.55650i	0.627954	−	0.778250i	$-0.283893\pi$
$524$	−14.2020			−0.620419
$525$	−2.44949	+	1.00000i	−0.106904	+	0.0436436i
$526$	11.7980	−	11.7980i	0.514415	−	0.514415i
$527$		−	9.79796i		−	0.426806i
$528$			8.00000i			0.348155i
$529$	−13.0000			−0.565217
$530$	−9.79796	+	9.79796i	−0.425596	+	0.425596i
$531$			3.10102i			0.134573i
$532$	13.7980	+	33.7980i	0.598217	+	1.46533i
$533$		−	20.0000i		−	0.866296i
$534$	−1.10102	−	1.10102i	−0.0476458	−	0.0476458i
$535$	−7.79796			−0.337135
$536$	−9.79796	+	9.79796i	−0.423207	+	0.423207i
$537$			10.0000i			0.431532i
$538$	−15.7980	−	15.7980i	−0.681098	−	0.681098i
$539$	−10.0000	+	9.79796i	−0.430730	+	0.422028i
$540$	−2.00000			−0.0860663
$541$			17.3939i			0.747821i	0.927465	+	0.373911i	$0.121983\pi$
$541$			17.3939i			0.747821i	−0.927465	+	0.373911i	$0.878017\pi$
$542$	23.7980	+	23.7980i	1.02221	+	1.02221i
$543$			20.8990i			0.896861i
$544$	19.5959	−	19.5959i	0.840168	−	0.840168i
$545$			4.00000i			0.171341i
$546$	23.7980	+	10.0000i	1.01846	+	0.427960i
$547$	38.2929			1.63728			0.818642	−	0.574304i	$-0.194727\pi$
$547$	38.2929			1.63728			0.818642	+	0.574304i	$0.194727\pi$
$548$			27.5959i			1.17884i
$549$	0.898979			0.0383675
$550$	−2.00000	−	2.00000i	−0.0852803	−	0.0852803i
$551$	61.3939			2.61547
$552$	12.0000	−	12.0000i	0.510754	−	0.510754i
$553$	9.79796	−	4.00000i	0.416652	−	0.170097i
$554$	3.79796	−	3.79796i	0.161360	−	0.161360i
$555$	−7.79796			−0.331005
$556$	−13.7980			−0.585164
$557$			13.7980i			0.584638i	0.956321	+	0.292319i	$0.0944269\pi$
$557$			13.7980i			0.584638i	−0.956321	+	0.292319i	$0.905573\pi$
$558$	2.00000	+	2.00000i	0.0846668	+	0.0846668i
$559$	−61.3939			−2.59668
$560$	4.00000	+	9.79796i	0.169031	+	0.414039i
$561$	−9.79796			−0.413670
$562$	−27.7980	−	27.7980i	−1.17259	−	1.17259i
$563$			21.7980i			0.918674i	0.888262	+	0.459337i	$0.151913\pi$
$563$			21.7980i			0.918674i	−0.888262	+	0.459337i	$0.848087\pi$
$564$	21.7980			0.917860
$565$	−1.79796			−0.0756407
$566$	−9.79796	+	9.79796i	−0.411839	+	0.411839i
$567$	−1.00000	−	2.44949i	−0.0419961	−	0.102869i
$568$	−25.7980	−	25.7980i	−1.08246	−	1.08246i
$569$	−21.5959			−0.905348			−0.452674	−	0.891676i	$-0.649530\pi$
$569$	−21.5959			−0.905348			−0.452674	+	0.891676i	$0.649530\pi$
$570$	−6.89898	−	6.89898i	−0.288966	−	0.288966i
$571$	−3.79796			−0.158940			−0.0794698	−	0.996837i	$-0.525323\pi$
$571$	−3.79796			−0.158940			−0.0794698	+	0.996837i	$0.525323\pi$
$572$			27.5959i			1.15384i
$573$	7.10102			0.296649
$574$	10.0000	+	4.20204i	0.417392	+	0.175390i
$575$			6.00000i			0.250217i
$576$			8.00000i			0.333333i
$577$			15.1010i			0.628664i	0.949313	+	0.314332i	$0.101780\pi$
$577$			15.1010i			0.628664i	−0.949313	+	0.314332i	$0.898220\pi$
$578$	7.00000	+	7.00000i	0.291162	+	0.291162i
$579$			0.202041i			0.00839654i
$580$	17.7980			0.739020
$581$	−9.79796	+	4.00000i	−0.406488	+	0.165948i
$582$	−0.898979	−	0.898979i	−0.0372639	−	0.0372639i
$583$		−	19.5959i		−	0.811580i
$584$	17.7980	+	17.7980i	0.736485	+	0.736485i
$585$	−6.89898			−0.285238
$586$	17.5959	+	17.5959i	0.726881	+	0.726881i
$587$		−	26.2020i		−	1.08147i	−0.841192	−	0.540737i	$-0.818145\pi$
$587$		−	26.2020i		−	1.08147i	0.841192	−	0.540737i	$-0.181855\pi$
$588$	−10.0000	+	9.79796i	−0.412393	+	0.404061i
$589$			13.7980i			0.568535i
$590$	−3.10102	+	3.10102i	−0.127667	+	0.127667i
$591$	13.7980			0.567572
$592$			31.1918i			1.28198i
$593$			3.10102i			0.127344i	0.997971	+	0.0636718i	$0.0202811\pi$
$593$			3.10102i			0.127344i	−0.997971	+	0.0636718i	$0.979719\pi$
$594$	2.00000	−	2.00000i	0.0820610	−	0.0820610i
$595$	−12.0000	+	4.89898i	−0.491952	+	0.200839i
$596$	−33.7980			−1.38442
$597$		−	10.0000i		−	0.409273i
$598$	41.3939	−	41.3939i	1.69272	−	1.69272i
$599$		−	8.89898i		−	0.363602i	−0.983335	−	0.181801i	$-0.941807\pi$
$599$		−	8.89898i		−	0.363602i	0.983335	−	0.181801i	$-0.0581927\pi$
$600$	−2.00000	−	2.00000i	−0.0816497	−	0.0816497i
$601$			5.79796i			0.236504i	0.992984	+	0.118252i	$0.0377290\pi$
$601$			5.79796i			0.236504i	−0.992984	+	0.118252i	$0.962271\pi$
$602$	12.8990	−	30.6969i	0.525723	−	1.25111i
$603$	4.89898			0.199502
$604$	−11.5959			−0.471831
$605$	−7.00000			−0.284590
$606$	3.79796	−	3.79796i	0.154282	−	0.154282i
$607$	−22.0000			−0.892952			−0.446476	−	0.894795i	$-0.647321\pi$
$607$	−22.0000			−0.892952			−0.446476	+	0.894795i	$0.647321\pi$
$608$	−27.5959	+	27.5959i	−1.11916	+	1.11916i
$609$	8.89898	+	21.7980i	0.360605	+	0.883298i
$610$	0.898979	+	0.898979i	0.0363986	+	0.0363986i
$611$	75.1918			3.04194
$612$	−9.79796			−0.396059
$613$		−	19.7980i		−	0.799632i	−0.916595	−	0.399816i	$-0.869074\pi$
$613$		−	19.7980i		−	0.799632i	0.916595	−	0.399816i	$-0.130926\pi$
$614$	−23.5959	+	23.5959i	−0.952254	+	0.952254i
$615$	−2.89898			−0.116898
$616$	−13.7980	−	5.79796i	−0.555936	−	0.233606i
$617$	22.2020			0.893821			0.446910	−	0.894579i	$-0.352524\pi$
$617$	22.2020			0.893821			0.446910	+	0.894579i	$0.352524\pi$
$618$	0.202041	−	0.202041i	0.00812728	−	0.00812728i
$619$			24.2929i			0.976412i	0.872728	+	0.488206i	$0.162349\pi$
$619$			24.2929i			0.976412i	−0.872728	+	0.488206i	$0.837651\pi$
$620$			4.00000i			0.160644i
$621$	−6.00000			−0.240772
$622$	8.00000	+	8.00000i	0.320771	+	0.320771i
$623$	2.69694	−	1.10102i	0.108051	−	0.0441115i
$624$			27.5959i			1.10472i
$625$	1.00000			0.0400000
$626$	20.4949	−	20.4949i	0.819141	−	0.819141i
$627$	13.7980			0.551037
$628$			33.3939i			1.33256i
$629$	−38.2020			−1.52322
$630$	1.44949	−	3.44949i	0.0577491	−	0.137431i
$631$			5.79796i			0.230813i	0.993318	+	0.115407i	$0.0368171\pi$
$631$			5.79796i			0.230813i	−0.993318	+	0.115407i	$0.963183\pi$
$632$	8.00000	+	8.00000i	0.318223	+	0.318223i
$633$		−	22.0000i		−	0.874421i
$634$	−12.0000	+	12.0000i	−0.476581	+	0.476581i
$635$			0.898979i			0.0356749i
$636$		−	19.5959i		−	0.777029i
$637$	−34.4949	+	33.7980i	−1.36674	+	1.33912i
$638$	−17.7980	+	17.7980i	−0.704628	+	0.704628i
$639$			12.8990i			0.510276i
$640$	−8.00000	+	8.00000i	−0.316228	+	0.316228i
$641$	−6.40408			−0.252946			−0.126473	−	0.991970i	$-0.540366\pi$
$641$	−6.40408			−0.252946			−0.126473	+	0.991970i	$0.540366\pi$
$642$	7.79796	−	7.79796i	0.307761	−	0.307761i
$643$			36.0000i			1.41970i	0.704352	+	0.709851i	$0.251238\pi$
$643$			36.0000i			1.41970i	−0.704352	+	0.709851i	$0.748762\pi$
$644$	12.0000	+	29.3939i	0.472866	+	1.15828i
$645$			8.89898i			0.350397i
$646$	−33.7980	−	33.7980i	−1.32976	−	1.32976i
$647$	−3.30306			−0.129857			−0.0649284	−	0.997890i	$-0.520682\pi$
$647$	−3.30306			−0.129857			−0.0649284	+	0.997890i	$0.520682\pi$
$648$	2.00000	−	2.00000i	0.0785674	−	0.0785674i
$649$		−	6.20204i		−	0.243451i
$650$	−6.89898	−	6.89898i	−0.270600	−	0.270600i
$651$	−4.89898	+	2.00000i	−0.192006	+	0.0783862i
$652$			45.3939i			1.77776i
$653$		−	44.0000i		−	1.72185i	−0.508729	−	0.860927i	$-0.669885\pi$
$653$		−	44.0000i		−	1.72185i	0.508729	−	0.860927i	$-0.330115\pi$
$654$	−4.00000	−	4.00000i	−0.156412	−	0.156412i
$655$			7.10102i			0.277460i
$656$			11.5959i			0.452745i
$657$		−	8.89898i		−	0.347182i
$658$	−15.7980	+	37.5959i	−0.615869	+	1.46564i
$659$	−30.0000			−1.16863			−0.584317	−	0.811525i	$-0.698638\pi$
$659$	−30.0000			−1.16863			−0.584317	+	0.811525i	$0.698638\pi$
$660$	4.00000			0.155700
$661$	30.6969			1.19397			0.596986	−	0.802251i	$-0.296365\pi$
$661$	30.6969			1.19397			0.596986	+	0.802251i	$0.296365\pi$
$662$	35.3939	+	35.3939i	1.37562	+	1.37562i
$663$	−33.7980			−1.31260
$664$	−8.00000	−	8.00000i	−0.310460	−	0.310460i
$665$	16.8990	−	6.89898i	0.655314	−	0.267531i
$666$	7.79796	−	7.79796i	0.302165	−	0.302165i
$667$	53.3939			2.06742
$668$			21.7980i			0.843388i
$669$			6.00000i			0.231973i
$670$	4.89898	+	4.89898i	0.189264	+	0.189264i
$671$	−1.79796			−0.0694094
$672$	−13.7980	−	5.79796i	−0.532268	−	0.223661i
$673$	25.5959			0.986650			0.493325	−	0.869845i	$-0.335781\pi$
$673$	25.5959			0.986650			0.493325	+	0.869845i	$0.335781\pi$
$674$	−12.2020	−	12.2020i	−0.470005	−	0.470005i
$675$			1.00000i			0.0384900i
$676$			69.1918i			2.66122i
$677$	12.2020			0.468963			0.234481	−	0.972121i	$-0.424661\pi$
$677$	12.2020			0.468963			0.234481	+	0.972121i	$0.424661\pi$
$678$	1.79796	−	1.79796i	0.0690502	−	0.0690502i
$679$	2.20204	−	0.898979i	0.0845066	−	0.0344997i
$680$	−9.79796	−	9.79796i	−0.375735	−	0.375735i
$681$	−12.0000			−0.459841
$682$	−4.00000	−	4.00000i	−0.153168	−	0.153168i
$683$	−31.7980			−1.21672			−0.608358	−	0.793663i	$-0.708171\pi$
$683$	−31.7980			−1.21672			−0.608358	+	0.793663i	$0.708171\pi$
$684$	13.7980			0.527578
$685$	13.7980			0.527193
$686$	−9.65153	−	24.3485i	−0.368497	−	0.929629i
$687$		−	24.4949i		−	0.934539i
$688$	35.5959			1.35708
$689$		−	67.5959i		−	2.57520i
$690$	−6.00000	−	6.00000i	−0.228416	−	0.228416i
$691$			14.4949i			0.551412i	0.961242	+	0.275706i	$0.0889116\pi$
$691$			14.4949i			0.551412i	−0.961242	+	0.275706i	$0.911088\pi$
$692$		−	23.5959i		−	0.896982i
$693$	2.00000	+	4.89898i	0.0759737	+	0.186097i
$694$	13.5959	+	13.5959i	0.516094	+	0.516094i
$695$			6.89898i			0.261693i
$696$	−17.7980	+	17.7980i	−0.674630	+	0.674630i
$697$	−14.2020			−0.537941
$698$	1.30306	+	1.30306i	0.0493216	+	0.0493216i
$699$			16.0000i			0.605176i
$700$	4.89898	−	2.00000i	0.185164	−	0.0755929i
$701$			32.8990i			1.24258i	0.783582	+	0.621289i	$0.213391\pi$
$701$			32.8990i			1.24258i	−0.783582	+	0.621289i	$0.786609\pi$
$702$	6.89898	−	6.89898i	0.260385	−	0.260385i
$703$	53.7980			2.02903
$704$		−	16.0000i		−	0.603023i
$705$		−	10.8990i		−	0.410479i
$706$	−5.30306	+	5.30306i	−0.199583	+	0.199583i
$707$	3.79796	+	9.30306i	0.142837	+	0.349878i
$708$		−	6.20204i		−	0.233087i
$709$		−	10.2020i		−	0.383146i	−0.981478	−	0.191573i	$-0.938641\pi$
$709$		−	10.2020i		−	0.383146i	0.981478	−	0.191573i	$-0.0613588\pi$
$710$	−12.8990	+	12.8990i	−0.484090	+	0.484090i
$711$		−	4.00000i		−	0.150012i
$712$	2.20204	+	2.20204i	0.0825250	+	0.0825250i
$713$			12.0000i			0.449404i
$714$	7.10102	−	16.8990i	0.265749	−	0.632428i
$715$	13.7980			0.516014
$716$		−	20.0000i		−	0.747435i
$717$	2.69694			0.100719
$718$	16.8990	−	16.8990i	0.630664	−	0.630664i
$719$	45.7980			1.70798			0.853988	−	0.520293i	$-0.174177\pi$
$719$	45.7980			1.70798			0.853988	+	0.520293i	$0.174177\pi$
$720$	4.00000			0.149071
$721$	0.202041	+	0.494897i	0.00752440	+	0.0184309i
$722$	28.5959	+	28.5959i	1.06423	+	1.06423i
$723$	20.0000			0.743808
$724$		−	41.7980i		−	1.55341i
$725$		−	8.89898i		−	0.330500i
$726$	7.00000	−	7.00000i	0.259794	−	0.259794i
$727$	−19.3939			−0.719279			−0.359640	−	0.933091i	$-0.617100\pi$
$727$	−19.3939			−0.719279			−0.359640	+	0.933091i	$0.617100\pi$
$728$	−47.5959	−	20.0000i	−1.76402	−	0.741249i
$729$	−1.00000			−0.0370370
$730$	8.89898	−	8.89898i	0.329366	−	0.329366i
$731$			43.5959i			1.61245i
$732$	−1.79796			−0.0664545
$733$	−50.4949			−1.86507			−0.932536	−	0.361078i	$-0.882409\pi$
$733$	−50.4949			−1.86507			−0.932536	+	0.361078i	$0.882409\pi$
$734$	−3.79796	−	3.79796i	−0.140185	−	0.140185i
$735$	4.89898	+	5.00000i	0.180702	+	0.184428i
$736$	−24.0000	+	24.0000i	−0.884652	+	0.884652i
$737$	−9.79796			−0.360912
$738$	2.89898	−	2.89898i	0.106713	−	0.106713i
$739$	−10.0000			−0.367856			−0.183928	−	0.982940i	$-0.558881\pi$
$739$	−10.0000			−0.367856			−0.183928	+	0.982940i	$0.558881\pi$
$740$	15.5959			0.573317
$741$	47.5959			1.74848
$742$	33.7980	+	14.2020i	1.24076	+	0.521373i
$743$			6.00000i			0.220119i	0.993925	+	0.110059i	$0.0351041\pi$
$743$			6.00000i			0.220119i	−0.993925	+	0.110059i	$0.964896\pi$
$744$	−4.00000	−	4.00000i	−0.146647	−	0.146647i
$745$			16.8990i			0.619131i
$746$	−14.0000	+	14.0000i	−0.512576	+	0.512576i
$747$			4.00000i			0.146352i
$748$	19.5959			0.716498
$749$	7.79796	+	19.1010i	0.284931	+	0.697936i
$750$	−1.00000	+	1.00000i	−0.0365148	+	0.0365148i
$751$		−	5.79796i		−	0.211571i	−0.994389	−	0.105785i	$-0.966264\pi$
$751$		−	5.79796i		−	0.211571i	0.994389	−	0.105785i	$-0.0337356\pi$
$752$	−43.5959			−1.58978
$753$	−12.8990			−0.470065
$754$	−61.3939	+	61.3939i	−2.23583	+	2.23583i
$755$			5.79796i			0.211009i
$756$	2.00000	+	4.89898i	0.0727393	+	0.178174i
$757$		−	33.5959i		−	1.22106i	−0.791991	−	0.610532i	$-0.790956\pi$
$757$		−	33.5959i		−	1.22106i	0.791991	−	0.610532i	$-0.209044\pi$
$758$	27.3939	+	27.3939i	0.994990	+	0.994990i
$759$	12.0000			0.435572
$760$	13.7980	+	13.7980i	0.500505	+	0.500505i
$761$			28.6969i			1.04026i	0.854086	+	0.520132i	$0.174117\pi$
$761$			28.6969i			1.04026i	−0.854086	+	0.520132i	$0.825883\pi$
$762$	−0.898979	−	0.898979i	−0.0325666	−	0.0325666i
$763$	9.79796	−	4.00000i	0.354710	−	0.144810i
$764$	−14.2020			−0.513812
$765$			4.89898i			0.177123i
$766$	18.8990	+	18.8990i	0.682848	+	0.682848i
$767$		−	21.3939i		−	0.772488i
$768$		−	16.0000i		−	0.577350i
$769$			12.4041i			0.447303i	0.974669	+	0.223651i	$0.0717977\pi$
$769$			12.4041i			0.447303i	−0.974669	+	0.223651i	$0.928202\pi$
$770$	−2.89898	+	6.89898i	−0.104472	+	0.248622i
$771$	15.1010			0.543850
$772$		−	0.404082i		−	0.0145432i
$773$	−0.202041			−0.00726691			−0.00363346	−	0.999993i	$-0.501157\pi$
$773$	−0.202041			−0.00726691			−0.00363346	+	0.999993i	$0.501157\pi$
$774$	−8.89898	−	8.89898i	−0.319867	−	0.319867i
$775$	2.00000			0.0718421
$776$	1.79796	+	1.79796i	0.0645430	+	0.0645430i
$777$	7.79796	+	19.1010i	0.279750	+	0.685245i
$778$	2.69694	−	2.69694i	0.0966899	−	0.0966899i
$779$	20.0000			0.716574
$780$	13.7980			0.494046
$781$		−	25.7980i		−	0.923124i
$782$	−29.3939	−	29.3939i	−1.05112	−	1.05112i
$783$	8.89898			0.318024
$784$	20.0000	−	19.5959i	0.714286	−	0.699854i
$785$	16.6969			0.595939
$786$	−7.10102	−	7.10102i	−0.253285	−	0.253285i
$787$		−	3.59592i		−	0.128181i	−0.997944	−	0.0640903i	$-0.979585\pi$
$787$		−	3.59592i		−	0.128181i	0.997944	−	0.0640903i	$-0.0204146\pi$
$788$	−27.5959			−0.983064
$789$	11.7980			0.420018
$790$	4.00000	−	4.00000i	0.142314	−	0.142314i
$791$	1.79796	+	4.40408i	0.0639281	+	0.156591i
$792$	−4.00000	+	4.00000i	−0.142134	+	0.142134i
$793$	−6.20204			−0.220241
$794$	−16.6969	−	16.6969i	−0.592552	−	0.592552i
$795$	−9.79796			−0.347498
$796$			20.0000i			0.708881i
$797$	−13.5959			−0.481592			−0.240796	−	0.970576i	$-0.577408\pi$
$797$	−13.5959			−0.481592			−0.240796	+	0.970576i	$0.577408\pi$
$798$	−10.0000	+	23.7980i	−0.353996	+	0.842439i
$799$		−	53.3939i		−	1.88894i
$800$	4.00000	+	4.00000i	0.141421	+	0.141421i
$801$		−	1.10102i		−	0.0389026i
$802$	−7.79796	−	7.79796i	−0.275356	−	0.275356i
$803$			17.7980i			0.628076i
$804$	−9.79796			−0.345547
$805$	14.6969	−	6.00000i	0.517999	−	0.211472i
$806$	−13.7980	−	13.7980i	−0.486012	−	0.486012i
$807$		−	15.7980i		−	0.556114i
$808$	−7.59592	+	7.59592i	−0.267223	+	0.267223i
$809$	4.20204			0.147736			0.0738679	−	0.997268i	$-0.476466\pi$
$809$	4.20204			0.147736			0.0738679	+	0.997268i	$0.476466\pi$
$810$	−1.00000	−	1.00000i	−0.0351364	−	0.0351364i
$811$			22.8990i			0.804092i	0.915619	+	0.402046i	$0.131701\pi$
$811$			22.8990i			0.804092i	−0.915619	+	0.402046i	$0.868299\pi$
$812$	−17.7980	−	43.5959i	−0.624586	−	1.52992i
$813$			23.7980i			0.834631i
$814$	−15.5959	+	15.5959i	−0.546637	+	0.546637i
$815$	22.6969			0.795039
$816$	19.5959			0.685994
$817$		−	61.3939i		−	2.14790i
$818$	4.00000	−	4.00000i	0.139857	−	0.139857i
$819$	6.89898	+	16.8990i	0.241070	+	0.590498i
$820$	5.79796			0.202474
$821$		−	18.6969i		−	0.652528i	−0.945279	−	0.326264i	$-0.894210\pi$
$821$		−	18.6969i		−	0.652528i	0.945279	−	0.326264i	$-0.105790\pi$
$822$	−13.7980	+	13.7980i	−0.481259	+	0.481259i
$823$		−	8.49490i		−	0.296114i	−0.988979	−	0.148057i	$-0.952698\pi$
$823$		−	8.49490i		−	0.296114i	0.988979	−	0.148057i	$-0.0473018\pi$
$824$	−0.404082	+	0.404082i	−0.0140769	+	0.0140769i
$825$		−	2.00000i		−	0.0696311i
$826$	10.6969	+	4.49490i	0.372194	+	0.156397i
$827$	−45.1918			−1.57147			−0.785737	−	0.618561i	$-0.787716\pi$
$827$	−45.1918			−1.57147			−0.785737	+	0.618561i	$0.787716\pi$
$828$	12.0000			0.417029
$829$	38.6969			1.34400			0.672000	−	0.740551i	$-0.265435\pi$
$829$	38.6969			1.34400			0.672000	+	0.740551i	$0.265435\pi$
$830$	−4.00000	+	4.00000i	−0.138842	+	0.138842i
$831$	3.79796			0.131750
$832$		−	55.1918i		−	1.91343i
$833$	24.0000	+	24.4949i	0.831551	+	0.848698i
$834$	−6.89898	−	6.89898i	−0.238892	−	0.238892i
$835$	10.8990			0.377175
$836$	−27.5959			−0.954425
$837$			2.00000i			0.0691301i
$838$	34.2929	−	34.2929i	1.18463	−	1.18463i
$839$	−45.7980			−1.58112			−0.790561	−	0.612384i	$-0.790211\pi$
$839$	−45.7980			−1.58112			−0.790561	+	0.612384i	$0.790211\pi$
$840$	−2.89898	+	6.89898i	−0.100024	+	0.238037i
$841$	−50.1918			−1.73075
$842$	25.7980	−	25.7980i	0.889056	−	0.889056i
$843$		−	27.7980i		−	0.957413i
$844$			44.0000i			1.51454i
$845$	34.5959			1.19014
$846$	10.8990	+	10.8990i	0.374715	+	0.374715i
$847$	7.00000	+	17.1464i	0.240523	+	0.589158i
$848$			39.1918i			1.34585i
$849$	−9.79796			−0.336265
$850$	−4.89898	+	4.89898i	−0.168034	+	0.168034i
$851$	46.7878			1.60386
$852$		−	25.7980i		−	0.883824i
$853$	15.3031			0.523967			0.261983	−	0.965072i	$-0.415623\pi$
$853$	15.3031			0.523967			0.261983	+	0.965072i	$0.415623\pi$
$854$	1.30306	−	3.10102i	0.0445898	−	0.106115i
$855$		−	6.89898i		−	0.235940i
$856$	−15.5959	+	15.5959i	−0.533058	+	0.533058i
$857$		−	36.4949i		−	1.24664i	−0.781966	−	0.623321i	$-0.785783\pi$
$857$		−	36.4949i		−	1.24664i	0.781966	−	0.623321i	$-0.214217\pi$
$858$	−13.7980	+	13.7980i	−0.471055	+	0.471055i
$859$		−	18.8990i		−	0.644825i	−0.946599	−	0.322412i	$-0.895506\pi$
$859$		−	18.8990i		−	0.644825i	0.946599	−	0.322412i	$-0.104494\pi$
$860$		−	17.7980i		−	0.606905i
$861$	2.89898	+	7.10102i	0.0987970	+	0.242002i
$862$	12.8990	−	12.8990i	0.439341	−	0.439341i
$863$			6.00000i			0.204242i	0.994772	+	0.102121i	$0.0325630\pi$
$863$			6.00000i			0.204242i	−0.994772	+	0.102121i	$0.967437\pi$
$864$	−4.00000	+	4.00000i	−0.136083	+	0.136083i
$865$	−11.7980			−0.401143
$866$	34.6969	−	34.6969i	1.17905	−	1.17905i
$867$			7.00000i			0.237732i
$868$	9.79796	−	4.00000i	0.332564	−	0.135769i
$869$			8.00000i			0.271381i
$870$	8.89898	+	8.89898i	0.301704	+	0.301704i
$871$	−33.7980			−1.14520
$872$	8.00000	+	8.00000i	0.270914	+	0.270914i
$873$		−	0.898979i		−	0.0304258i
$874$	41.3939	+	41.3939i	1.40017	+	1.40017i
$875$	−1.00000	−	2.44949i	−0.0338062	−	0.0828079i
$876$			17.7980i			0.601337i
$877$		−	22.0000i		−	0.742887i	−0.928456	−	0.371444i	$-0.878863\pi$
$877$		−	22.0000i		−	0.742887i	0.928456	−	0.371444i	$-0.121137\pi$
$878$	−4.20204	−	4.20204i	−0.141812	−	0.141812i
$879$			17.5959i			0.593496i
$880$	−8.00000			−0.269680
$881$			28.6969i			0.966824i	0.875393	+	0.483412i	$0.160603\pi$
$881$			28.6969i			0.966824i	−0.875393	+	0.483412i	$0.839397\pi$
$882$	−9.89898	−	0.101021i	−0.333316	−	0.00340154i
$883$	8.49490			0.285876			0.142938	−	0.989732i	$-0.454345\pi$
$883$	8.49490			0.285876			0.142938	+	0.989732i	$0.454345\pi$
$884$	67.5959			2.27350
$885$	−3.10102			−0.104240
$886$	6.00000	+	6.00000i	0.201574	+	0.201574i
$887$	−6.49490			−0.218077			−0.109039	−	0.994038i	$-0.534777\pi$
$887$	−6.49490			−0.218077			−0.109039	+	0.994038i	$0.534777\pi$
$888$	−15.5959	+	15.5959i	−0.523365	+	0.523365i
$889$	2.20204	−	0.898979i	0.0738541	−	0.0301508i
$890$	1.10102	−	1.10102i	0.0369063	−	0.0369063i
$891$	2.00000			0.0670025
$892$		−	12.0000i		−	0.401790i
$893$			75.1918i			2.51620i
$894$	−16.8990	−	16.8990i	−0.565186	−	0.565186i
$895$	−10.0000			−0.334263
$896$	27.5959	+	11.5959i	0.921915	+	0.387392i
$897$	41.3939			1.38210
$898$	−4.20204	−	4.20204i	−0.140224	−	0.140224i
$899$		−	17.7980i		−	0.593595i
$900$		−	2.00000i		−	0.0666667i
$901$	−48.0000			−1.59911
$902$	−5.79796	+	5.79796i	−0.193051	+	0.193051i
$903$	21.7980	−	8.89898i	0.725391	−	0.296139i
$904$	−3.59592	+	3.59592i	−0.119598	+	0.119598i
$905$	−20.8990			−0.694706
$906$	−5.79796	−	5.79796i	−0.192624	−	0.192624i
$907$	12.4949			0.414886			0.207443	−	0.978247i	$-0.433486\pi$
$907$	12.4949			0.414886			0.207443	+	0.978247i	$0.433486\pi$
$908$	24.0000			0.796468
$909$	3.79796			0.125970
$910$	−10.0000	+	23.7980i	−0.331497	+	0.788895i
$911$		−	32.8990i		−	1.08999i	−0.838439	−	0.544996i	$-0.816531\pi$
$911$		−	32.8990i		−	1.08999i	0.838439	−	0.544996i	$-0.183469\pi$
$912$	−27.5959			−0.913792
$913$		−	8.00000i		−	0.264761i
$914$	7.79796	+	7.79796i	0.257934	+	0.257934i
$915$			0.898979i			0.0297193i
$916$			48.9898i			1.61867i
$917$	17.3939	−	7.10102i	0.574396	−	0.234496i
$918$	−4.89898	−	4.89898i	−0.161690	−	0.161690i
$919$		−	33.3939i		−	1.10156i	−0.834650	−	0.550781i	$-0.814330\pi$
$919$		−	33.3939i		−	1.10156i	0.834650	−	0.550781i	$-0.185670\pi$
$920$	12.0000	+	12.0000i	0.395628	+	0.395628i
$921$	−23.5959			−0.777512
$922$	23.7980	+	23.7980i	0.783744	+	0.783744i
$923$		−	88.9898i		−	2.92913i
$924$	−4.00000	−	9.79796i	−0.131590	−	0.322329i
$925$		−	7.79796i		−	0.256395i
$926$	−2.69694	+	2.69694i	−0.0886269	+	0.0886269i
$927$	0.202041			0.00663590
$928$	35.5959	−	35.5959i	1.16849	−	1.16849i
$929$		−	10.4949i		−	0.344326i	−0.985068	−	0.172163i	$-0.944924\pi$
$929$		−	10.4949i		−	0.344326i	0.985068	−	0.172163i	$-0.0550756\pi$
$930$	−2.00000	+	2.00000i	−0.0655826	+	0.0655826i
$931$	−33.7980	−	34.4949i	−1.10768	−	1.13052i
$932$		−	32.0000i		−	1.04819i
$933$			8.00000i			0.261908i
$934$	2.20204	−	2.20204i	0.0720530	−	0.0720530i
$935$		−	9.79796i		−	0.320428i
$936$	−13.7980	+	13.7980i	−0.451000	+	0.451000i
$937$			12.4949i			0.408191i	0.978951	+	0.204095i	$0.0654252\pi$
$937$			12.4949i			0.408191i	−0.978951	+	0.204095i	$0.934575\pi$
$938$	7.10102	−	16.8990i	0.231857	−	0.551771i
$939$	20.4949			0.668826
$940$			21.7980i			0.710971i
$941$	−3.79796			−0.123810			−0.0619050	−	0.998082i	$-0.519718\pi$
$941$	−3.79796			−0.123810			−0.0619050	+	0.998082i	$0.519718\pi$
$942$	−16.6969	+	16.6969i	−0.544016	+	0.544016i
$943$	17.3939			0.566423
$944$			12.4041i			0.403718i
$945$	2.44949	−	1.00000i	0.0796819	−	0.0325300i
$946$	17.7980	+	17.7980i	0.578662	+	0.578662i
$947$	12.2020			0.396513			0.198257	−	0.980150i	$-0.436472\pi$
$947$	12.2020			0.396513			0.198257	+	0.980150i	$0.436472\pi$
$948$			8.00000i			0.259828i
$949$			61.3939i			1.99293i
$950$	6.89898	−	6.89898i	0.223832	−	0.223832i
$951$	−12.0000			−0.389127
$952$	−14.2020	+	33.7980i	−0.460291	+	1.09540i
$953$	24.0000			0.777436			0.388718	−	0.921357i	$-0.372918\pi$
$953$	24.0000			0.777436			0.388718	+	0.921357i	$0.372918\pi$
$954$	9.79796	−	9.79796i	0.317221	−	0.317221i
$955$			7.10102i			0.229784i
$956$	−5.39388			−0.174450
$957$	−17.7980			−0.575326
$958$	11.5959	+	11.5959i	0.374647	+	0.374647i
$959$	−13.7980	−	33.7980i	−0.445559	−	1.09139i
$960$	−8.00000			−0.258199
$961$	−27.0000			−0.870968
$962$	−53.7980	+	53.7980i	−1.73452	+	1.73452i
$963$	7.79796			0.251286
$964$	−40.0000			−1.28831
$965$	−0.202041			−0.00650393
$966$	−8.69694	+	20.6969i	−0.279819	+	0.665913i
$967$		−	7.50510i		−	0.241348i	−0.992692	−	0.120674i	$-0.961494\pi$
$967$		−	7.50510i		−	0.241348i	0.992692	−	0.120674i	$-0.0385055\pi$
$968$	−14.0000	+	14.0000i	−0.449977	+	0.449977i
$969$		−	33.7980i		−	1.08575i
$970$	0.898979	−	0.898979i	0.0288645	−	0.0288645i
$971$		−	12.8990i		−	0.413948i	−0.978346	−	0.206974i	$-0.933638\pi$
$971$		−	12.8990i		−	0.413948i	0.978346	−	0.206974i	$-0.0663615\pi$
$972$	2.00000			0.0641500
$973$	16.8990	−	6.89898i	0.541756	−	0.221171i
$974$	−24.8990	+	24.8990i	−0.797815	+	0.797815i
$975$		−	6.89898i		−	0.220944i
$976$	3.59592			0.115103
$977$	−55.1918			−1.76574			−0.882872	−	0.469614i	$-0.844393\pi$
$977$	−55.1918			−1.76574			−0.882872	+	0.469614i	$0.844393\pi$
$978$	−22.6969	+	22.6969i	−0.725768	+	0.725768i
$979$			2.20204i			0.0703775i
$980$	−9.79796	−	10.0000i	−0.312984	−	0.319438i
$981$		−	4.00000i		−	0.127710i
$982$	−13.5959	−	13.5959i	−0.433863	−	0.433863i
$983$	6.89898			0.220043			0.110022	−	0.993929i	$-0.464908\pi$
$983$	6.89898			0.220043			0.110022	+	0.993929i	$0.464908\pi$
$984$	−5.79796	+	5.79796i	−0.184832	+	0.184832i
$985$			13.7980i			0.439640i
$986$	43.5959	+	43.5959i	1.38838	+	1.38838i
$987$	−26.6969	+	10.8990i	−0.849773	+	0.346918i
$988$	−95.1918			−3.02846
$989$		−	53.3939i		−	1.69783i
$990$	2.00000	+	2.00000i	0.0635642	+	0.0635642i
$991$			20.0000i			0.635321i	0.948205	+	0.317660i	$0.102897\pi$
$991$			20.0000i			0.635321i	−0.948205	+	0.317660i	$0.897103\pi$
$992$	8.00000	+	8.00000i	0.254000	+	0.254000i
$993$			35.3939i			1.12319i
$994$	44.4949	+	18.6969i	1.41129	+	0.593031i
$995$	10.0000			0.317021
$996$		−	8.00000i		−	0.253490i
$997$	−52.2929			−1.65613			−0.828066	−	0.560631i	$-0.810559\pi$
$997$	−52.2929			−1.65613			−0.828066	+	0.560631i	$0.810559\pi$
$998$	−10.0000	−	10.0000i	−0.316544	−	0.316544i
$999$	7.79796			0.246717

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	840.2.z.b.811.1	yes	4
4.3	odd	2		3360.2.z.b.1231.4		4
7.6	odd	2		840.2.z.a.811.1	✓	4
8.3	odd	2		840.2.z.a.811.4	yes	4
8.5	even	2		3360.2.z.a.1231.3		4
28.27	even	2		3360.2.z.a.1231.2		4
56.13	odd	2		3360.2.z.b.1231.1		4
56.27	even	2	inner	840.2.z.b.811.4	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.z.a.811.1	✓	4	7.6	odd	2
840.2.z.a.811.4	yes	4	8.3	odd	2
840.2.z.b.811.1	yes	4	1.1	even	1	trivial
840.2.z.b.811.4	yes	4	56.27	even	2	inner
3360.2.z.a.1231.2		4	28.27	even	2
3360.2.z.a.1231.3		4	8.5	even	2
3360.2.z.b.1231.1		4	56.13	odd	2
3360.2.z.b.1231.4		4	4.3	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	840.z (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.00000i) q^{2} -1.00000i q^{3} +2.00000i q^{4} +1.00000 q^{5} +(-1.00000 + 1.00000i) q^{6} +(-1.00000 - 2.44949i) q^{7} +(2.00000 - 2.00000i) q^{8} -1.00000 q^{9} +(-1.00000 - 1.00000i) q^{10} +2.00000 q^{11} +2.00000 q^{12} +6.89898 q^{13} +(-1.44949 + 3.44949i) q^{14} -1.00000i q^{15} -4.00000 q^{16} -4.89898i q^{17} +(1.00000 + 1.00000i) q^{18} +6.89898i q^{19} +2.00000i q^{20} +(-2.44949 + 1.00000i) q^{21} +(-2.00000 - 2.00000i) q^{22} +6.00000i q^{23} +(-2.00000 - 2.00000i) q^{24} +1.00000 q^{25} +(-6.89898 - 6.89898i) q^{26} +1.00000i q^{27} +(4.89898 - 2.00000i) q^{28} -8.89898i q^{29} +(-1.00000 + 1.00000i) q^{30} +2.00000 q^{31} +(4.00000 + 4.00000i) q^{32} -2.00000i q^{33} +(-4.89898 + 4.89898i) q^{34} +(-1.00000 - 2.44949i) q^{35} -2.00000i q^{36} -7.79796i q^{37} +(6.89898 - 6.89898i) q^{38} -6.89898i q^{39} +(2.00000 - 2.00000i) q^{40} -2.89898i q^{41} +(3.44949 + 1.44949i) q^{42} -8.89898 q^{43} +4.00000i q^{44} -1.00000 q^{45} +(6.00000 - 6.00000i) q^{46} +10.8990 q^{47} +4.00000i q^{48} +(-5.00000 + 4.89898i) q^{49} +(-1.00000 - 1.00000i) q^{50} -4.89898 q^{51} +13.7980i q^{52} -9.79796i q^{53} +(1.00000 - 1.00000i) q^{54} +2.00000 q^{55} +(-6.89898 - 2.89898i) q^{56} +6.89898 q^{57} +(-8.89898 + 8.89898i) q^{58} -3.10102i q^{59} +2.00000 q^{60} -0.898979 q^{61} +(-2.00000 - 2.00000i) q^{62} +(1.00000 + 2.44949i) q^{63} -8.00000i q^{64} +6.89898 q^{65} +(-2.00000 + 2.00000i) q^{66} -4.89898 q^{67} +9.79796 q^{68} +6.00000 q^{69} +(-1.44949 + 3.44949i) q^{70} -12.8990i q^{71} +(-2.00000 + 2.00000i) q^{72} +8.89898i q^{73} +(-7.79796 + 7.79796i) q^{74} -1.00000i q^{75} -13.7980 q^{76} +(-2.00000 - 4.89898i) q^{77} +(-6.89898 + 6.89898i) q^{78} +4.00000i q^{79} -4.00000 q^{80} +1.00000 q^{81} +(-2.89898 + 2.89898i) q^{82} -4.00000i q^{83} +(-2.00000 - 4.89898i) q^{84} -4.89898i q^{85} +(8.89898 + 8.89898i) q^{86} -8.89898 q^{87} +(4.00000 - 4.00000i) q^{88} +1.10102i q^{89} +(1.00000 + 1.00000i) q^{90} +(-6.89898 - 16.8990i) q^{91} -12.0000 q^{92} -2.00000i q^{93} +(-10.8990 - 10.8990i) q^{94} +6.89898i q^{95} +(4.00000 - 4.00000i) q^{96} +0.898979i q^{97} +(9.89898 + 0.101021i) q^{98} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 4 q^{5} - 4 q^{6} - 4 q^{7} + 8 q^{8} - 4 q^{9} - 4 q^{10} + 8 q^{11} + 8 q^{12} + 8 q^{13} + 4 q^{14} - 16 q^{16} + 4 q^{18} - 8 q^{22} - 8 q^{24} + 4 q^{25} - 8 q^{26} - 4 q^{30} + 8 q^{31}+ \cdots - 8 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 + 4 * q^5 - 4 * q^6 - 4 * q^7 + 8 * q^8 - 4 * q^9 - 4 * q^10 + 8 * q^11 + 8 * q^12 + 8 * q^13 + 4 * q^14 - 16 * q^16 + 4 * q^18 - 8 * q^22 - 8 * q^24 + 4 * q^25 - 8 * q^26 - 4 * q^30 + 8 * q^31 + 16 * q^32 - 4 * q^35 + 8 * q^38 + 8 * q^40 + 4 * q^42 - 16 * q^43 - 4 * q^45 + 24 * q^46 + 24 * q^47 - 20 * q^49 - 4 * q^50 + 4 * q^54 + 8 * q^55 - 8 * q^56 + 8 * q^57 - 16 * q^58 + 8 * q^60 + 16 * q^61 - 8 * q^62 + 4 * q^63 + 8 * q^65 - 8 * q^66 + 24 * q^69 + 4 * q^70 - 8 * q^72 + 8 * q^74 - 16 * q^76 - 8 * q^77 - 8 * q^78 - 16 * q^80 + 4 * q^81 + 8 * q^82 - 8 * q^84 + 16 * q^86 - 16 * q^87 + 16 * q^88 + 4 * q^90 - 8 * q^91 - 48 * q^92 - 24 * q^94 + 16 * q^96 + 20 * q^98 - 8 * q^99

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