LMFDB - Embedded newform 840.2.z.b.811.2

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			811.2
Root			$1.22474 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	840.811
Dual form			840.2.z.b.811.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-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} -2.89898 q^{13} +(3.44949 - 1.44949i) q^{14} -1.00000i q^{15} -4.00000 q^{16} +4.89898i q^{17} +(1.00000 + 1.00000i) q^{18} -2.89898i 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} +(2.89898 + 2.89898i) q^{26} +1.00000i q^{27} +(-4.89898 - 2.00000i) q^{28} +0.898979i 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} +11.7980i q^{37} +(-2.89898 + 2.89898i) q^{38} +2.89898i q^{39} +(2.00000 - 2.00000i) q^{40} +6.89898i q^{41} +(-1.44949 - 3.44949i) q^{42} +0.898979 q^{43} +4.00000i q^{44} -1.00000 q^{45} +(6.00000 - 6.00000i) q^{46} +1.10102 q^{47} +4.00000i q^{48} +(-5.00000 - 4.89898i) q^{49} +(-1.00000 - 1.00000i) q^{50} +4.89898 q^{51} -5.79796i q^{52} +9.79796i q^{53} +(1.00000 - 1.00000i) q^{54} +2.00000 q^{55} +(2.89898 + 6.89898i) q^{56} -2.89898 q^{57} +(0.898979 - 0.898979i) q^{58} -12.8990i q^{59} +2.00000 q^{60} +8.89898 q^{61} +(-2.00000 - 2.00000i) q^{62} +(1.00000 - 2.44949i) q^{63} -8.00000i q^{64} -2.89898 q^{65} +(-2.00000 + 2.00000i) q^{66} +4.89898 q^{67} -9.79796 q^{68} +6.00000 q^{69} +(3.44949 - 1.44949i) q^{70} -3.10102i q^{71} +(-2.00000 + 2.00000i) q^{72} -0.898979i q^{73} +(11.7980 - 11.7980i) q^{74} -1.00000i q^{75} +5.79796 q^{76} +(-2.00000 + 4.89898i) q^{77} +(2.89898 - 2.89898i) q^{78} +4.00000i q^{79} -4.00000 q^{80} +1.00000 q^{81} +(6.89898 - 6.89898i) q^{82} -4.00000i q^{83} +(-2.00000 + 4.89898i) q^{84} +4.89898i q^{85} +(-0.898979 - 0.898979i) q^{86} +0.898979 q^{87} +(4.00000 - 4.00000i) q^{88} +10.8990i q^{89} +(1.00000 + 1.00000i) q^{90} +(2.89898 - 7.10102i) q^{91} -12.0000 q^{92} -2.00000i q^{93} +(-1.10102 - 1.10102i) q^{94} -2.89898i q^{95} +(4.00000 - 4.00000i) q^{96} -8.89898i q^{97} +(0.101021 + 9.89898i) 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
$13$	−2.89898			−0.804032			−0.402016	−	0.915633i	$-0.631690\pi$
$13$	−2.89898			−0.804032			−0.402016	+	0.915633i	$0.631690\pi$
$14$	3.44949	−	1.44949i	0.921915	−	0.387392i
$15$		−	1.00000i		−	0.258199i
$16$	−4.00000			−1.00000
$17$			4.89898i			1.18818i	0.804400	+	0.594089i	$0.202487\pi$
$17$			4.89898i			1.18818i	−0.804400	+	0.594089i	$0.797513\pi$
$18$	1.00000	+	1.00000i	0.235702	+	0.235702i
$19$		−	2.89898i		−	0.665072i	−0.943091	−	0.332536i	$-0.892096\pi$
$19$		−	2.89898i		−	0.665072i	0.943091	−	0.332536i	$-0.107904\pi$
$20$			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
$26$	2.89898	+	2.89898i	0.568537	+	0.568537i
$27$			1.00000i			0.192450i
$28$	−4.89898	−	2.00000i	−0.925820	−	0.377964i
$29$			0.898979i			0.166936i	0.996510	+	0.0834681i	$0.0265997\pi$
$29$			0.898979i			0.166936i	−0.996510	+	0.0834681i	$0.973400\pi$
$30$	−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
$37$			11.7980i			1.93957i	0.243956	+	0.969786i	$0.421555\pi$
$37$			11.7980i			1.93957i	−0.243956	+	0.969786i	$0.578445\pi$
$38$	−2.89898	+	2.89898i	−0.470277	+	0.470277i
$39$			2.89898i			0.464208i
$40$	2.00000	−	2.00000i	0.316228	−	0.316228i
$41$			6.89898i			1.07744i	0.842485	+	0.538720i	$0.181092\pi$
$41$			6.89898i			1.07744i	−0.842485	+	0.538720i	$0.818908\pi$
$42$	−1.44949	−	3.44949i	−0.223661	−	0.532268i
$43$	0.898979			0.137093			0.0685465	−	0.997648i	$-0.478164\pi$
$43$	0.898979			0.137093			0.0685465	+	0.997648i	$0.478164\pi$
$44$			4.00000i			0.603023i
$45$	−1.00000			−0.149071
$46$	6.00000	−	6.00000i	0.884652	−	0.884652i
$47$	1.10102			0.160600			0.0803002	−	0.996771i	$-0.474412\pi$
$47$	1.10102			0.160600			0.0803002	+	0.996771i	$0.474412\pi$
$48$			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
$52$		−	5.79796i		−	0.804032i
$53$			9.79796i			1.34585i	0.739709	+	0.672927i	$0.234963\pi$
$53$			9.79796i			1.34585i	−0.739709	+	0.672927i	$0.765037\pi$
$54$	1.00000	−	1.00000i	0.136083	−	0.136083i
$55$	2.00000			0.269680
$56$	2.89898	+	6.89898i	0.387392	+	0.921915i
$57$	−2.89898			−0.383979
$58$	0.898979	−	0.898979i	0.118042	−	0.118042i
$59$		−	12.8990i		−	1.67930i	−0.543125	−	0.839652i	$-0.682759\pi$
$59$		−	12.8990i		−	1.67930i	0.543125	−	0.839652i	$-0.317241\pi$
$60$	2.00000			0.258199
$61$	8.89898			1.13940			0.569699	−	0.821854i	$-0.307060\pi$
$61$	8.89898			1.13940			0.569699	+	0.821854i	$0.307060\pi$
$62$	−2.00000	−	2.00000i	−0.254000	−	0.254000i
$63$	1.00000	−	2.44949i	0.125988	−	0.308607i
$64$		−	8.00000i		−	1.00000i
$65$	−2.89898			−0.359574
$66$	−2.00000	+	2.00000i	−0.246183	+	0.246183i
$67$	4.89898			0.598506			0.299253	−	0.954174i	$-0.403263\pi$
$67$	4.89898			0.598506			0.299253	+	0.954174i	$0.403263\pi$
$68$	−9.79796			−1.18818
$69$	6.00000			0.722315
$70$	3.44949	−	1.44949i	0.412293	−	0.173247i
$71$		−	3.10102i		−	0.368023i	−0.982924	−	0.184012i	$-0.941092\pi$
$71$		−	3.10102i		−	0.368023i	0.982924	−	0.184012i	$-0.0589084\pi$
$72$	−2.00000	+	2.00000i	−0.235702	+	0.235702i
$73$		−	0.898979i		−	0.105218i	−0.998615	−	0.0526088i	$-0.983246\pi$
$73$		−	0.898979i		−	0.105218i	0.998615	−	0.0526088i	$-0.0167536\pi$
$74$	11.7980	−	11.7980i	1.37148	−	1.37148i
$75$		−	1.00000i		−	0.115470i
$76$	5.79796			0.665072
$77$	−2.00000	+	4.89898i	−0.227921	+	0.558291i
$78$	2.89898	−	2.89898i	0.328245	−	0.328245i
$79$			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
$82$	6.89898	−	6.89898i	0.761865	−	0.761865i
$83$		−	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
$86$	−0.898979	−	0.898979i	−0.0969395	−	0.0969395i
$87$	0.898979			0.0963807
$88$	4.00000	−	4.00000i	0.426401	−	0.426401i
$89$			10.8990i			1.15529i	0.816288	+	0.577645i	$0.196028\pi$
$89$			10.8990i			1.15529i	−0.816288	+	0.577645i	$0.803972\pi$
$90$	1.00000	+	1.00000i	0.105409	+	0.105409i
$91$	2.89898	−	7.10102i	0.303896	−	0.744389i
$92$	−12.0000			−1.25109
$93$		−	2.00000i		−	0.207390i
$94$	−1.10102	−	1.10102i	−0.113562	−	0.113562i
$95$		−	2.89898i		−	0.297429i
$96$	4.00000	−	4.00000i	0.408248	−	0.408248i
$97$		−	8.89898i		−	0.903554i	−0.892131	−	0.451777i	$-0.850790\pi$
$97$		−	8.89898i		−	0.903554i	0.892131	−	0.451777i	$-0.149210\pi$
$98$	0.101021	+	9.89898i	0.0102046	+	0.999948i
$99$	−2.00000			−0.201008
$100$			2.00000i			0.200000i
$101$	15.7980			1.57196			0.785978	−	0.618255i	$-0.212160\pi$
$101$	15.7980			1.57196			0.785978	+	0.618255i	$0.212160\pi$
$102$	−4.89898	−	4.89898i	−0.485071	−	0.485071i
$103$	−19.7980			−1.95075			−0.975375	−	0.220551i	$-0.929214\pi$
$103$	−19.7980			−1.95075			−0.975375	+	0.220551i	$0.929214\pi$
$104$	−5.79796	+	5.79796i	−0.568537	+	0.568537i
$105$	2.44949	+	1.00000i	0.239046	+	0.0975900i
$106$	9.79796	−	9.79796i	0.951662	−	0.951662i
$107$	11.7980			1.14055			0.570276	−	0.821453i	$-0.306836\pi$
$107$	11.7980			1.14055			0.570276	+	0.821453i	$0.306836\pi$
$108$	−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
$111$	11.7980			1.11981
$112$	4.00000	−	9.79796i	0.377964	−	0.925820i
$113$	17.7980			1.67429			0.837146	−	0.546980i	$-0.184223\pi$
$113$	17.7980			1.67429			0.837146	+	0.546980i	$0.184223\pi$
$114$	2.89898	+	2.89898i	0.271514	+	0.271514i
$115$			6.00000i			0.559503i
$116$	−1.79796			−0.166936
$117$	2.89898			0.268011
$118$	−12.8990	+	12.8990i	−1.18745	+	1.18745i
$119$	−12.0000	−	4.89898i	−1.10004	−	0.449089i
$120$	−2.00000	−	2.00000i	−0.182574	−	0.182574i
$121$	−7.00000			−0.636364
$122$	−8.89898	−	8.89898i	−0.805676	−	0.805676i
$123$	6.89898			0.622060
$124$			4.00000i			0.359211i
$125$	1.00000			0.0894427
$126$	−3.44949	+	1.44949i	−0.307305	+	0.129131i
$127$		−	8.89898i		−	0.789657i	−0.918755	−	0.394828i	$-0.870804\pi$
$127$		−	8.89898i		−	0.789657i	0.918755	−	0.394828i	$-0.129196\pi$
$128$	−8.00000	+	8.00000i	−0.707107	+	0.707107i
$129$		−	0.898979i		−	0.0791507i
$130$	2.89898	+	2.89898i	0.254257	+	0.254257i
$131$			16.8990i			1.47647i	0.674543	+	0.738235i	$0.264341\pi$
$131$			16.8990i			1.47647i	−0.674543	+	0.738235i	$0.735659\pi$
$132$	4.00000			0.348155
$133$	7.10102	+	2.89898i	0.615737	+	0.251373i
$134$	−4.89898	−	4.89898i	−0.423207	−	0.423207i
$135$			1.00000i			0.0860663i
$136$	9.79796	+	9.79796i	0.840168	+	0.840168i
$137$	−5.79796			−0.495353			−0.247677	−	0.968843i	$-0.579667\pi$
$137$	−5.79796			−0.495353			−0.247677	+	0.968843i	$0.579667\pi$
$138$	−6.00000	−	6.00000i	−0.510754	−	0.510754i
$139$		−	2.89898i		−	0.245888i	−0.992414	−	0.122944i	$-0.960766\pi$
$139$		−	2.89898i		−	0.245888i	0.992414	−	0.122944i	$-0.0392336\pi$
$140$	−4.89898	−	2.00000i	−0.414039	−	0.169031i
$141$		−	1.10102i		−	0.0927227i
$142$	−3.10102	+	3.10102i	−0.260232	+	0.260232i
$143$	−5.79796			−0.484850
$144$	4.00000			0.333333
$145$			0.898979i			0.0746562i
$146$	−0.898979	+	0.898979i	−0.0744001	+	0.0744001i
$147$	−4.89898	+	5.00000i	−0.404061	+	0.412393i
$148$	−23.5959			−1.93957
$149$			7.10102i			0.581738i	0.956763	+	0.290869i	$0.0939444\pi$
$149$			7.10102i			0.581738i	−0.956763	+	0.290869i	$0.906056\pi$
$150$	−1.00000	+	1.00000i	−0.0816497	+	0.0816497i
$151$		−	13.7980i		−	1.12286i	−0.827524	−	0.561431i	$-0.810251\pi$
$151$		−	13.7980i		−	1.12286i	0.827524	−	0.561431i	$-0.189749\pi$
$152$	−5.79796	−	5.79796i	−0.470277	−	0.470277i
$153$		−	4.89898i		−	0.396059i
$154$	6.89898	−	2.89898i	0.555936	−	0.233606i
$155$	2.00000			0.160644
$156$	−5.79796			−0.464208
$157$	−12.6969			−1.01333			−0.506663	−	0.862144i	$-0.669121\pi$
$157$	−12.6969			−1.01333			−0.506663	+	0.862144i	$0.669121\pi$
$158$	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
$163$	−6.69694			−0.524545			−0.262272	−	0.964994i	$-0.584472\pi$
$163$	−6.69694			−0.524545			−0.262272	+	0.964994i	$0.584472\pi$
$164$	−13.7980			−1.07744
$165$		−	2.00000i		−	0.155700i
$166$	−4.00000	+	4.00000i	−0.310460	+	0.310460i
$167$	1.10102			0.0851995			0.0425998	−	0.999092i	$-0.486436\pi$
$167$	1.10102			0.0851995			0.0425998	+	0.999092i	$0.486436\pi$
$168$	6.89898	−	2.89898i	0.532268	−	0.223661i
$169$	−4.59592			−0.353532
$170$	4.89898	−	4.89898i	0.375735	−	0.375735i
$171$			2.89898i			0.221691i
$172$			1.79796i			0.137093i
$173$	7.79796			0.592868			0.296434	−	0.955053i	$-0.404203\pi$
$173$	7.79796			0.592868			0.296434	+	0.955053i	$0.404203\pi$
$174$	−0.898979	−	0.898979i	−0.0681515	−	0.0681515i
$175$	−1.00000	+	2.44949i	−0.0755929	+	0.185164i
$176$	−8.00000			−0.603023
$177$	−12.8990			−0.969547
$178$	10.8990	−	10.8990i	0.816913	−	0.816913i
$179$	−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
$181$	−11.1010			−0.825132			−0.412566	−	0.910928i	$-0.635367\pi$
$181$	−11.1010			−0.825132			−0.412566	+	0.910928i	$0.635367\pi$
$182$	−10.0000	+	4.20204i	−0.741249	+	0.311476i
$183$		−	8.89898i		−	0.657831i
$184$	12.0000	+	12.0000i	0.884652	+	0.884652i
$185$			11.7980i			0.867403i
$186$	−2.00000	+	2.00000i	−0.146647	+	0.146647i
$187$			9.79796i			0.716498i
$188$			2.20204i			0.160600i
$189$	−2.44949	−	1.00000i	−0.178174	−	0.0727393i
$190$	−2.89898	+	2.89898i	−0.210314	+	0.210314i
$191$			16.8990i			1.22277i	0.791334	+	0.611384i	$0.209387\pi$
$191$			16.8990i			1.22277i	−0.791334	+	0.611384i	$0.790613\pi$
$192$	−8.00000			−0.577350
$193$	−19.7980			−1.42509			−0.712544	−	0.701627i	$-0.752457\pi$
$193$	−19.7980			−1.42509			−0.712544	+	0.701627i	$0.752457\pi$
$194$	−8.89898	+	8.89898i	−0.638909	+	0.638909i
$195$			2.89898i			0.207600i
$196$	9.79796	−	10.0000i	0.699854	−	0.714286i
$197$		−	5.79796i		−	0.413087i	−0.978437	−	0.206544i	$-0.933778\pi$
$197$		−	5.79796i		−	0.413087i	0.978437	−	0.206544i	$-0.0662216\pi$
$198$	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
$202$	−15.7980	−	15.7980i	−1.11154	−	1.11154i
$203$	−2.20204	−	0.898979i	−0.154553	−	0.0630960i
$204$			9.79796i			0.685994i
$205$			6.89898i			0.481846i
$206$	19.7980	+	19.7980i	1.37939	+	1.37939i
$207$		−	6.00000i		−	0.417029i
$208$	11.5959			0.804032
$209$		−	5.79796i		−	0.401053i
$210$	−1.44949	−	3.44949i	−0.100024	−	0.238037i
$211$	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
$213$	−3.10102			−0.212478
$214$	−11.7980	−	11.7980i	−0.806492	−	0.806492i
$215$	0.898979			0.0613099
$216$	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
$219$	−0.898979			−0.0607474
$220$			4.00000i			0.269680i
$221$		−	14.2020i		−	0.955333i
$222$	−11.7980	−	11.7980i	−0.791827	−	0.791827i
$223$	−6.00000			−0.401790			−0.200895	−	0.979613i	$-0.564385\pi$
$223$	−6.00000			−0.401790			−0.200895	+	0.979613i	$0.564385\pi$
$224$	−13.7980	+	5.79796i	−0.921915	+	0.387392i
$225$	−1.00000			−0.0666667
$226$	−17.7980	−	17.7980i	−1.18390	−	1.18390i
$227$		−	12.0000i		−	0.796468i	−0.917284	−	0.398234i	$-0.869623\pi$
$227$		−	12.0000i		−	0.796468i	0.917284	−	0.398234i	$-0.130377\pi$
$228$		−	5.79796i		−	0.383979i
$229$	−24.4949			−1.61867			−0.809334	−	0.587348i	$-0.800172\pi$
$229$	−24.4949			−1.61867			−0.809334	+	0.587348i	$0.800172\pi$
$230$	6.00000	−	6.00000i	0.395628	−	0.395628i
$231$	4.89898	+	2.00000i	0.322329	+	0.131590i
$232$	1.79796	+	1.79796i	0.118042	+	0.118042i
$233$	−16.0000			−1.04819			−0.524097	−	0.851658i	$-0.675597\pi$
$233$	−16.0000			−1.04819			−0.524097	+	0.851658i	$0.675597\pi$
$234$	−2.89898	−	2.89898i	−0.189512	−	0.189512i
$235$	1.10102			0.0718227
$236$	25.7980			1.67930
$237$	4.00000			0.259828
$238$	7.10102	+	16.8990i	0.460291	+	1.09540i
$239$		−	26.6969i		−	1.72688i	−0.504450	−	0.863441i	$-0.668305\pi$
$239$		−	26.6969i		−	1.72688i	0.504450	−	0.863441i	$-0.331695\pi$
$240$			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
$244$			17.7980i			1.13940i
$245$	−5.00000	−	4.89898i	−0.319438	−	0.312984i
$246$	−6.89898	−	6.89898i	−0.439863	−	0.439863i
$247$			8.40408i			0.534739i
$248$	4.00000	−	4.00000i	0.254000	−	0.254000i
$249$	−4.00000			−0.253490
$250$	−1.00000	−	1.00000i	−0.0632456	−	0.0632456i
$251$		−	3.10102i		−	0.195735i	−0.995199	−	0.0978673i	$-0.968798\pi$
$251$		−	3.10102i		−	0.195735i	0.995199	−	0.0978673i	$-0.0312021\pi$
$252$	4.89898	+	2.00000i	0.308607	+	0.125988i
$253$			12.0000i			0.754434i
$254$	−8.89898	+	8.89898i	−0.558372	+	0.558372i
$255$	4.89898			0.306786
$256$	16.0000			1.00000
$257$			24.8990i			1.55316i	0.630021	+	0.776578i	$0.283046\pi$
$257$			24.8990i			1.55316i	−0.630021	+	0.776578i	$0.716954\pi$
$258$	−0.898979	+	0.898979i	−0.0559680	+	0.0559680i
$259$	−28.8990	−	11.7980i	−1.79570	−	0.733090i
$260$		−	5.79796i		−	0.359574i
$261$		−	0.898979i		−	0.0556454i
$262$	16.8990	−	16.8990i	1.04402	−	1.04402i
$263$		−	7.79796i		−	0.480843i	−0.970669	−	0.240421i	$-0.922714\pi$
$263$		−	7.79796i		−	0.480843i	0.970669	−	0.240421i	$-0.0772856\pi$
$264$	−4.00000	−	4.00000i	−0.246183	−	0.246183i
$265$			9.79796i			0.601884i
$266$	−4.20204	−	10.0000i	−0.257644	−	0.613139i
$267$	10.8990			0.667007
$268$			9.79796i			0.598506i
$269$	−3.79796			−0.231566			−0.115783	−	0.993275i	$-0.536938\pi$
$269$	−3.79796			−0.231566			−0.115783	+	0.993275i	$0.536938\pi$
$270$	1.00000	−	1.00000i	0.0608581	−	0.0608581i
$271$	−4.20204			−0.255256			−0.127628	−	0.991822i	$-0.540736\pi$
$271$	−4.20204			−0.255256			−0.127628	+	0.991822i	$0.540736\pi$
$272$		−	19.5959i		−	1.18818i
$273$	−7.10102	−	2.89898i	−0.429773	−	0.175454i
$274$	5.79796	+	5.79796i	0.350268	+	0.350268i
$275$	2.00000			0.120605
$276$			12.0000i			0.722315i
$277$		−	15.7980i		−	0.949207i	−0.880200	−	0.474604i	$-0.842591\pi$
$277$		−	15.7980i		−	0.949207i	0.880200	−	0.474604i	$-0.157409\pi$
$278$	−2.89898	+	2.89898i	−0.173869	+	0.173869i
$279$	−2.00000			−0.119737
$280$	2.89898	+	6.89898i	0.173247	+	0.412293i
$281$	8.20204			0.489293			0.244646	−	0.969612i	$-0.421328\pi$
$281$	8.20204			0.489293			0.244646	+	0.969612i	$0.421328\pi$
$282$	−1.10102	+	1.10102i	−0.0655648	+	0.0655648i
$283$			9.79796i			0.582428i	0.956658	+	0.291214i	$0.0940592\pi$
$283$			9.79796i			0.582428i	−0.956658	+	0.291214i	$0.905941\pi$
$284$	6.20204			0.368023
$285$	−2.89898			−0.171721
$286$	5.79796	+	5.79796i	0.342841	+	0.342841i
$287$	−16.8990	−	6.89898i	−0.997515	−	0.407234i
$288$	−4.00000	−	4.00000i	−0.235702	−	0.235702i
$289$	−7.00000			−0.411765
$290$	0.898979	−	0.898979i	0.0527899	−	0.0527899i
$291$	−8.89898			−0.521667
$292$	1.79796			0.105218
$293$	21.5959			1.26165			0.630823	−	0.775926i	$-0.282717\pi$
$293$	21.5959			1.26165			0.630823	+	0.775926i	$0.282717\pi$
$294$	9.89898	−	0.101021i	0.577320	−	0.00589164i
$295$		−	12.8990i		−	0.751008i
$296$	23.5959	+	23.5959i	1.37148	+	1.37148i
$297$			2.00000i			0.116052i
$298$	7.10102	−	7.10102i	0.411351	−	0.411351i
$299$		−	17.3939i		−	1.00591i
$300$	2.00000			0.115470
$301$	−0.898979	+	2.20204i	−0.0518163	+	0.126924i
$302$	−13.7980	+	13.7980i	−0.793983	+	0.793983i
$303$		−	15.7980i		−	0.907569i
$304$			11.5959i			0.665072i
$305$	8.89898			0.509554
$306$	−4.89898	+	4.89898i	−0.280056	+	0.280056i
$307$			15.5959i			0.890106i	0.895504	+	0.445053i	$0.146815\pi$
$307$			15.5959i			0.890106i	−0.895504	+	0.445053i	$0.853185\pi$
$308$	−9.79796	−	4.00000i	−0.558291	−	0.227921i
$309$			19.7980i			1.12627i
$310$	−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	$0.572833\pi$
$312$	5.79796	+	5.79796i	0.328245	+	0.328245i
$313$		−	28.4949i		−	1.61063i	−0.592849	−	0.805313i	$-0.701997\pi$
$313$		−	28.4949i		−	1.61063i	0.592849	−	0.805313i	$-0.298003\pi$
$314$	12.6969	+	12.6969i	0.716530	+	0.716530i
$315$	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
$319$			1.79796i			0.100666i
$320$		−	8.00000i		−	0.447214i
$321$		−	11.7980i		−	0.658498i
$322$	8.69694	+	20.6969i	0.484661	+	1.15340i
$323$	14.2020			0.790223
$324$			2.00000i			0.111111i
$325$	−2.89898			−0.160806
$326$	6.69694	+	6.69694i	0.370909	+	0.370909i
$327$	4.00000			0.221201
$328$	13.7980	+	13.7980i	0.761865	+	0.761865i
$329$	−1.10102	+	2.69694i	−0.0607012	+	0.148687i
$330$	−2.00000	+	2.00000i	−0.110096	+	0.110096i
$331$	23.3939			1.28584			0.642922	−	0.765932i	$-0.277722\pi$
$331$	23.3939			1.28584			0.642922	+	0.765932i	$0.277722\pi$
$332$	8.00000			0.439057
$333$		−	11.7980i		−	0.646524i
$334$	−1.10102	−	1.10102i	−0.0602452	−	0.0602452i
$335$	4.89898			0.267660
$336$	−9.79796	−	4.00000i	−0.534522	−	0.218218i
$337$	31.7980			1.73215			0.866073	−	0.499918i	$-0.166637\pi$
$337$	31.7980			1.73215			0.866073	+	0.499918i	$0.166637\pi$
$338$	4.59592	+	4.59592i	0.249985	+	0.249985i
$339$		−	17.7980i		−	0.966652i
$340$	−9.79796			−0.531369
$341$	4.00000			0.216612
$342$	2.89898	−	2.89898i	0.156759	−	0.156759i
$343$	17.0000	−	7.34847i	0.917914	−	0.396780i
$344$	1.79796	−	1.79796i	0.0969395	−	0.0969395i
$345$	6.00000			0.323029
$346$	−7.79796	−	7.79796i	−0.419221	−	0.419221i
$347$	25.5959			1.37406			0.687030	−	0.726629i	$-0.258914\pi$
$347$	25.5959			1.37406			0.687030	+	0.726629i	$0.258914\pi$
$348$			1.79796i			0.0963807i
$349$	−30.6969			−1.64317			−0.821585	−	0.570086i	$-0.806910\pi$
$349$	−30.6969			−1.64317			−0.821585	+	0.570086i	$0.806910\pi$
$350$	3.44949	−	1.44949i	0.184383	−	0.0774785i
$351$		−	2.89898i		−	0.154736i
$352$	8.00000	+	8.00000i	0.426401	+	0.426401i
$353$		−	34.6969i		−	1.84673i	−0.383921	−	0.923366i	$-0.625427\pi$
$353$		−	34.6969i		−	1.84673i	0.383921	−	0.923366i	$-0.374573\pi$
$354$	12.8990	+	12.8990i	0.685573	+	0.685573i
$355$		−	3.10102i		−	0.164585i
$356$	−21.7980			−1.15529
$357$	−4.89898	+	12.0000i	−0.259281	+	0.635107i
$358$	10.0000	+	10.0000i	0.528516	+	0.528516i
$359$			7.10102i			0.374778i	0.982286	+	0.187389i	$0.0600024\pi$
$359$			7.10102i			0.374778i	−0.982286	+	0.187389i	$0.939998\pi$
$360$	−2.00000	+	2.00000i	−0.105409	+	0.105409i
$361$	10.5959			0.557680
$362$	11.1010	+	11.1010i	0.583457	+	0.583457i
$363$			7.00000i			0.367405i
$364$	14.2020	+	5.79796i	0.744389	+	0.303896i
$365$		−	0.898979i		−	0.0470547i
$366$	−8.89898	+	8.89898i	−0.465157	+	0.465157i
$367$	−15.7980			−0.824647			−0.412323	−	0.911038i	$-0.635283\pi$
$367$	−15.7980			−0.824647			−0.412323	+	0.911038i	$0.635283\pi$
$368$		−	24.0000i		−	1.25109i
$369$		−	6.89898i		−	0.359147i
$370$	11.7980	−	11.7980i	0.613347	−	0.613347i
$371$	−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
$376$	2.20204	−	2.20204i	0.113562	−	0.113562i
$377$		−	2.60612i		−	0.134222i
$378$	1.44949	+	3.44949i	0.0745537	+	0.177423i
$379$	31.3939			1.61260			0.806298	−	0.591510i	$-0.201468\pi$
$379$	31.3939			1.61260			0.806298	+	0.591510i	$0.201468\pi$
$380$	5.79796			0.297429
$381$	−8.89898			−0.455909
$382$	16.8990	−	16.8990i	0.864627	−	0.864627i
$383$	−9.10102			−0.465040			−0.232520	−	0.972592i	$-0.574697\pi$
$383$	−9.10102			−0.465040			−0.232520	+	0.972592i	$0.574697\pi$
$384$	8.00000	+	8.00000i	0.408248	+	0.408248i
$385$	−2.00000	+	4.89898i	−0.101929	+	0.249675i
$386$	19.7980	+	19.7980i	1.00769	+	1.00769i
$387$	−0.898979			−0.0456977
$388$	17.7980			0.903554
$389$		−	26.6969i		−	1.35359i	−0.736172	−	0.676794i	$-0.763369\pi$
$389$		−	26.6969i		−	1.35359i	0.736172	−	0.676794i	$-0.236631\pi$
$390$	2.89898	−	2.89898i	0.146796	−	0.146796i
$391$	−29.3939			−1.48651
$392$	−19.7980	+	0.202041i	−0.999948	+	0.0102046i
$393$	16.8990			0.852441
$394$	−5.79796	+	5.79796i	−0.292097	+	0.292097i
$395$			4.00000i			0.201262i
$396$		−	4.00000i		−	0.201008i
$397$	−12.6969			−0.637241			−0.318621	−	0.947882i	$-0.603220\pi$
$397$	−12.6969			−0.637241			−0.318621	+	0.947882i	$0.603220\pi$
$398$	−10.0000	−	10.0000i	−0.501255	−	0.501255i
$399$	2.89898	−	7.10102i	0.145131	−	0.355496i
$400$	−4.00000			−0.200000
$401$	−11.7980			−0.589162			−0.294581	−	0.955627i	$-0.595180\pi$
$401$	−11.7980			−0.589162			−0.294581	+	0.955627i	$0.595180\pi$
$402$	−4.89898	+	4.89898i	−0.244339	+	0.244339i
$403$	−5.79796			−0.288817
$404$			31.5959i			1.57196i
$405$	1.00000			0.0496904
$406$	1.30306	+	3.10102i	0.0646699	+	0.153901i
$407$			23.5959i			1.16961i
$408$	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	$0.968470\pi$
$410$	6.89898	−	6.89898i	0.340716	−	0.340716i
$411$			5.79796i			0.285992i
$412$		−	39.5959i		−	1.95075i
$413$	31.5959	+	12.8990i	1.55473	+	0.634717i
$414$	−6.00000	+	6.00000i	−0.294884	+	0.294884i
$415$		−	4.00000i		−	0.196352i
$416$	−11.5959	−	11.5959i	−0.568537	−	0.568537i
$417$	−2.89898			−0.141964
$418$	−5.79796	+	5.79796i	−0.283587	+	0.283587i
$419$		−	34.2929i		−	1.67532i	−0.546195	−	0.837658i	$-0.683924\pi$
$419$		−	34.2929i		−	1.67532i	0.546195	−	0.837658i	$-0.316076\pi$
$420$	−2.00000	+	4.89898i	−0.0975900	+	0.239046i
$421$			6.20204i			0.302269i	0.988513	+	0.151134i	$0.0482927\pi$
$421$			6.20204i			0.302269i	−0.988513	+	0.151134i	$0.951707\pi$
$422$	−22.0000	−	22.0000i	−1.07094	−	1.07094i
$423$	−1.10102			−0.0535334
$424$	19.5959	+	19.5959i	0.951662	+	0.951662i
$425$			4.89898i			0.237635i
$426$	3.10102	+	3.10102i	0.150245	+	0.150245i
$427$	−8.89898	+	21.7980i	−0.430652	+	1.05488i
$428$			23.5959i			1.14055i
$429$			5.79796i			0.279928i
$430$	−0.898979	−	0.898979i	−0.0433526	−	0.0433526i
$431$			3.10102i			0.149371i	0.997207	+	0.0746855i	$0.0237953\pi$
$431$			3.10102i			0.149371i	−0.997207	+	0.0746855i	$0.976205\pi$
$432$		−	4.00000i		−	0.192450i
$433$			5.30306i			0.254849i	0.991848	+	0.127424i	$0.0406710\pi$
$433$			5.30306i			0.254849i	−0.991848	+	0.127424i	$0.959329\pi$
$434$	6.89898	−	2.89898i	0.331162	−	0.139155i
$435$	0.898979			0.0431028
$436$	−8.00000			−0.383131
$437$	17.3939			0.832062
$438$	0.898979	+	0.898979i	0.0429549	+	0.0429549i
$439$	23.7980			1.13581			0.567907	−	0.823093i	$-0.307753\pi$
$439$	23.7980			1.13581			0.567907	+	0.823093i	$0.307753\pi$
$440$	4.00000	−	4.00000i	0.190693	−	0.190693i
$441$	5.00000	+	4.89898i	0.238095	+	0.233285i
$442$	−14.2020	+	14.2020i	−0.675522	+	0.675522i
$443$	−6.00000			−0.285069			−0.142534	−	0.989790i	$-0.545525\pi$
$443$	−6.00000			−0.285069			−0.142534	+	0.989790i	$0.545525\pi$
$444$			23.5959i			1.11981i
$445$			10.8990i			0.516661i
$446$	6.00000	+	6.00000i	0.284108	+	0.284108i
$447$	7.10102			0.335867
$448$	19.5959	+	8.00000i	0.925820	+	0.377964i
$449$	23.7980			1.12310			0.561548	−	0.827444i	$-0.310206\pi$
$449$	23.7980			1.12310			0.561548	+	0.827444i	$0.310206\pi$
$450$	1.00000	+	1.00000i	0.0471405	+	0.0471405i
$451$			13.7980i			0.649721i
$452$			35.5959i			1.67429i
$453$	−13.7980			−0.648285
$454$	−12.0000	+	12.0000i	−0.563188	+	0.563188i
$455$	2.89898	−	7.10102i	0.135906	−	0.332901i
$456$	−5.79796	+	5.79796i	−0.271514	+	0.271514i
$457$	11.7980			0.551885			0.275943	−	0.961174i	$-0.411010\pi$
$457$	11.7980			0.551885			0.275943	+	0.961174i	$0.411010\pi$
$458$	24.4949	+	24.4949i	1.14457	+	1.14457i
$459$	−4.89898			−0.228665
$460$	−12.0000			−0.559503
$461$	−4.20204			−0.195709			−0.0978543	−	0.995201i	$-0.531198\pi$
$461$	−4.20204			−0.195709			−0.0978543	+	0.995201i	$0.531198\pi$
$462$	−2.89898	−	6.89898i	−0.134873	−	0.320970i
$463$			26.6969i			1.24071i	0.784320	+	0.620356i	$0.213012\pi$
$463$			26.6969i			1.24071i	−0.784320	+	0.620356i	$0.786988\pi$
$464$		−	3.59592i		−	0.166936i
$465$		−	2.00000i		−	0.0927478i
$466$	16.0000	+	16.0000i	0.741186	+	0.741186i
$467$			21.7980i			1.00869i	0.863502	+	0.504345i	$0.168266\pi$
$467$			21.7980i			1.00869i	−0.863502	+	0.504345i	$0.831734\pi$
$468$			5.79796i			0.268011i
$469$	−4.89898	+	12.0000i	−0.226214	+	0.554109i
$470$	−1.10102	−	1.10102i	−0.0507863	−	0.0507863i
$471$			12.6969i			0.585044i
$472$	−25.7980	−	25.7980i	−1.18745	−	1.18745i
$473$	1.79796			0.0826702
$474$	−4.00000	−	4.00000i	−0.183726	−	0.183726i
$475$		−	2.89898i		−	0.133014i
$476$	9.79796	−	24.0000i	0.449089	−	1.10004i
$477$		−	9.79796i		−	0.448618i
$478$	−26.6969	+	26.6969i	−1.22109	+	1.22109i
$479$	27.5959			1.26089			0.630445	−	0.776234i	$-0.282873\pi$
$479$	27.5959			1.26089			0.630445	+	0.776234i	$0.282873\pi$
$480$	4.00000	−	4.00000i	0.182574	−	0.182574i
$481$		−	34.2020i		−	1.55948i
$482$	20.0000	−	20.0000i	0.910975	−	0.910975i
$483$	−6.00000	+	14.6969i	−0.273009	+	0.668734i
$484$		−	14.0000i		−	0.636364i
$485$		−	8.89898i		−	0.404082i
$486$	−1.00000	+	1.00000i	−0.0453609	+	0.0453609i
$487$		−	15.1010i		−	0.684293i	−0.939647	−	0.342146i	$-0.888846\pi$
$487$		−	15.1010i		−	0.684293i	0.939647	−	0.342146i	$-0.111154\pi$
$488$	17.7980	−	17.7980i	0.805676	−	0.805676i
$489$			6.69694i			0.302846i
$490$	0.101021	+	9.89898i	0.00456364	+	0.447190i
$491$	−25.5959			−1.15513			−0.577564	−	0.816346i	$-0.695997\pi$
$491$	−25.5959			−1.15513			−0.577564	+	0.816346i	$0.695997\pi$
$492$			13.7980i			0.622060i
$493$	−4.40408			−0.198350
$494$	8.40408	−	8.40408i	0.378118	−	0.378118i
$495$	−2.00000			−0.0898933
$496$	−8.00000			−0.359211
$497$	7.59592	+	3.10102i	0.340723	+	0.139100i
$498$	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
$501$		−	1.10102i		−	0.0491900i
$502$	−3.10102	+	3.10102i	−0.138405	+	0.138405i
$503$	−10.4949			−0.467944			−0.233972	−	0.972243i	$-0.575172\pi$
$503$	−10.4949			−0.467944			−0.233972	+	0.972243i	$0.575172\pi$
$504$	−2.89898	−	6.89898i	−0.129131	−	0.307305i
$505$	15.7980			0.703000
$506$	12.0000	−	12.0000i	0.533465	−	0.533465i
$507$			4.59592i			0.204112i
$508$	17.7980			0.789657
$509$	37.5959			1.66641			0.833205	−	0.552964i	$-0.186503\pi$
$509$	37.5959			1.66641			0.833205	+	0.552964i	$0.186503\pi$
$510$	−4.89898	−	4.89898i	−0.216930	−	0.216930i
$511$	2.20204	+	0.898979i	0.0974126	+	0.0397685i
$512$	−16.0000	−	16.0000i	−0.707107	−	0.707107i
$513$	2.89898			0.127993
$514$	24.8990	−	24.8990i	1.09825	−	1.09825i
$515$	−19.7980			−0.872402
$516$	1.79796			0.0791507
$517$	2.20204			0.0968457
$518$	17.1010	+	40.6969i	0.751376	+	1.78812i
$519$		−	7.79796i		−	0.342292i
$520$	−5.79796	+	5.79796i	−0.254257	+	0.254257i
$521$			33.1010i			1.45018i	0.688653	+	0.725091i	$0.258202\pi$
$521$			33.1010i			1.45018i	−0.688653	+	0.725091i	$0.741798\pi$
$522$	−0.898979	+	0.898979i	−0.0393473	+	0.0393473i
$523$			3.59592i			0.157239i	0.996905	+	0.0786193i	$0.0250511\pi$
$523$			3.59592i			0.157239i	−0.996905	+	0.0786193i	$0.974949\pi$
$524$	−33.7980			−1.47647
$525$	2.44949	+	1.00000i	0.106904	+	0.0436436i
$526$	−7.79796	+	7.79796i	−0.340007	+	0.340007i
$527$			9.79796i			0.426806i
$528$			8.00000i			0.348155i
$529$	−13.0000			−0.565217
$530$	9.79796	−	9.79796i	0.425596	−	0.425596i
$531$			12.8990i			0.559768i
$532$	−5.79796	+	14.2020i	−0.251373	+	0.615737i
$533$		−	20.0000i		−	0.866296i
$534$	−10.8990	−	10.8990i	−0.471645	−	0.471645i
$535$	11.7980			0.510070
$536$	9.79796	−	9.79796i	0.423207	−	0.423207i
$537$			10.0000i			0.431532i
$538$	3.79796	+	3.79796i	0.163742	+	0.163742i
$539$	−10.0000	−	9.79796i	−0.430730	−	0.422028i
$540$	−2.00000			−0.0860663
$541$		−	41.3939i		−	1.77966i	−0.456290	−	0.889831i	$-0.650822\pi$
$541$		−	41.3939i		−	1.77966i	0.456290	−	0.889831i	$-0.349178\pi$
$542$	4.20204	+	4.20204i	0.180493	+	0.180493i
$543$			11.1010i			0.476390i
$544$	−19.5959	+	19.5959i	−0.840168	+	0.840168i
$545$			4.00000i			0.171341i
$546$	4.20204	+	10.0000i	0.179831	+	0.427960i
$547$	−30.2929			−1.29523			−0.647615	−	0.761968i	$-0.724233\pi$
$547$	−30.2929			−1.29523			−0.647615	+	0.761968i	$0.724233\pi$
$548$		−	11.5959i		−	0.495353i
$549$	−8.89898			−0.379799
$550$	−2.00000	−	2.00000i	−0.0852803	−	0.0852803i
$551$	2.60612			0.111025
$552$	12.0000	−	12.0000i	0.510754	−	0.510754i
$553$	−9.79796	−	4.00000i	−0.416652	−	0.170097i
$554$	−15.7980	+	15.7980i	−0.671191	+	0.671191i
$555$	11.7980			0.500795
$556$	5.79796			0.245888
$557$		−	5.79796i		−	0.245667i	−0.992427	−	0.122834i	$-0.960802\pi$
$557$		−	5.79796i		−	0.245667i	0.992427	−	0.122834i	$-0.0391982\pi$
$558$	2.00000	+	2.00000i	0.0846668	+	0.0846668i
$559$	−2.60612			−0.110227
$560$	4.00000	−	9.79796i	0.169031	−	0.414039i
$561$	9.79796			0.413670
$562$	−8.20204	−	8.20204i	−0.345982	−	0.345982i
$563$			2.20204i			0.0928050i	0.998923	+	0.0464025i	$0.0147757\pi$
$563$			2.20204i			0.0928050i	−0.998923	+	0.0464025i	$0.985224\pi$
$564$	2.20204			0.0927227
$565$	17.7980			0.748766
$566$	9.79796	−	9.79796i	0.411839	−	0.411839i
$567$	−1.00000	+	2.44949i	−0.0419961	+	0.102869i
$568$	−6.20204	−	6.20204i	−0.260232	−	0.260232i
$569$	17.5959			0.737659			0.368830	−	0.929497i	$-0.379759\pi$
$569$	17.5959			0.737659			0.368830	+	0.929497i	$0.379759\pi$
$570$	2.89898	+	2.89898i	0.121425	+	0.121425i
$571$	15.7980			0.661124			0.330562	−	0.943784i	$-0.392762\pi$
$571$	15.7980			0.661124			0.330562	+	0.943784i	$0.392762\pi$
$572$		−	11.5959i		−	0.484850i
$573$	16.8990			0.705965
$574$	10.0000	+	23.7980i	0.417392	+	0.993308i
$575$			6.00000i			0.250217i
$576$			8.00000i			0.333333i
$577$			24.8990i			1.03656i	0.855212	+	0.518279i	$0.173427\pi$
$577$			24.8990i			1.03656i	−0.855212	+	0.518279i	$0.826573\pi$
$578$	7.00000	+	7.00000i	0.291162	+	0.291162i
$579$			19.7980i			0.822775i
$580$	−1.79796			−0.0746562
$581$	9.79796	+	4.00000i	0.406488	+	0.165948i
$582$	8.89898	+	8.89898i	0.368875	+	0.368875i
$583$			19.5959i			0.811580i
$584$	−1.79796	−	1.79796i	−0.0744001	−	0.0744001i
$585$	2.89898			0.119858
$586$	−21.5959	−	21.5959i	−0.892119	−	0.892119i
$587$		−	45.7980i		−	1.89028i	−0.326660	−	0.945142i	$-0.605923\pi$
$587$		−	45.7980i		−	1.89028i	0.326660	−	0.945142i	$-0.394077\pi$
$588$	−10.0000	−	9.79796i	−0.412393	−	0.404061i
$589$		−	5.79796i		−	0.238901i
$590$	−12.8990	+	12.8990i	−0.531043	+	0.531043i
$591$	−5.79796			−0.238496
$592$		−	47.1918i		−	1.93957i
$593$			12.8990i			0.529698i	0.964290	+	0.264849i	$0.0853220\pi$
$593$			12.8990i			0.529698i	−0.964290	+	0.264849i	$0.914678\pi$
$594$	2.00000	−	2.00000i	0.0820610	−	0.0820610i
$595$	−12.0000	−	4.89898i	−0.491952	−	0.200839i
$596$	−14.2020			−0.581738
$597$		−	10.0000i		−	0.409273i
$598$	−17.3939	+	17.3939i	−0.711289	+	0.711289i
$599$			0.898979i			0.0367313i	0.999831	+	0.0183657i	$0.00584630\pi$
$599$			0.898979i			0.0367313i	−0.999831	+	0.0183657i	$0.994154\pi$
$600$	−2.00000	−	2.00000i	−0.0816497	−	0.0816497i
$601$		−	13.7980i		−	0.562830i	−0.959586	−	0.281415i	$-0.909196\pi$
$601$		−	13.7980i		−	0.562830i	0.959586	−	0.281415i	$-0.0908038\pi$
$602$	3.10102	−	1.30306i	0.126388	−	0.0531088i
$603$	−4.89898			−0.199502
$604$	27.5959			1.12286
$605$	−7.00000			−0.284590
$606$	−15.7980	+	15.7980i	−0.641748	+	0.641748i
$607$	−22.0000			−0.892952			−0.446476	−	0.894795i	$-0.647321\pi$
$607$	−22.0000			−0.892952			−0.446476	+	0.894795i	$0.647321\pi$
$608$	11.5959	−	11.5959i	0.470277	−	0.470277i
$609$	−0.898979	+	2.20204i	−0.0364285	+	0.0892312i
$610$	−8.89898	−	8.89898i	−0.360309	−	0.360309i
$611$	−3.19184			−0.129128
$612$	9.79796			0.396059
$613$		−	0.202041i		−	0.00816036i	−0.999992	−	0.00408018i	$-0.998701\pi$
$613$		−	0.202041i		−	0.00816036i	0.999992	−	0.00408018i	$-0.00129877\pi$
$614$	15.5959	−	15.5959i	0.629400	−	0.629400i
$615$	6.89898			0.278194
$616$	5.79796	+	13.7980i	0.233606	+	0.555936i
$617$	41.7980			1.68272			0.841361	−	0.540473i	$-0.181755\pi$
$617$	41.7980			1.68272			0.841361	+	0.540473i	$0.181755\pi$
$618$	19.7980	−	19.7980i	0.796391	−	0.796391i
$619$		−	44.2929i		−	1.78028i	−0.455687	−	0.890140i	$-0.650606\pi$
$619$		−	44.2929i		−	1.78028i	0.455687	−	0.890140i	$-0.349394\pi$
$620$			4.00000i			0.160644i
$621$	−6.00000			−0.240772
$622$	8.00000	+	8.00000i	0.320771	+	0.320771i
$623$	−26.6969	−	10.8990i	−1.06959	−	0.436658i
$624$		−	11.5959i		−	0.464208i
$625$	1.00000			0.0400000
$626$	−28.4949	+	28.4949i	−1.13889	+	1.13889i
$627$	−5.79796			−0.231548
$628$		−	25.3939i		−	1.01333i
$629$	−57.7980			−2.30456
$630$	−3.44949	+	1.44949i	−0.137431	+	0.0577491i
$631$		−	13.7980i		−	0.549288i	−0.961546	−	0.274644i	$-0.911440\pi$
$631$		−	13.7980i		−	0.549288i	0.961546	−	0.274644i	$-0.0885600\pi$
$632$	8.00000	+	8.00000i	0.318223	+	0.318223i
$633$		−	22.0000i		−	0.874421i
$634$	−12.0000	+	12.0000i	−0.476581	+	0.476581i
$635$		−	8.89898i		−	0.353145i
$636$			19.5959i			0.777029i
$637$	14.4949	+	14.2020i	0.574309	+	0.562705i
$638$	1.79796	−	1.79796i	0.0711819	−	0.0711819i
$639$			3.10102i			0.122674i
$640$	−8.00000	+	8.00000i	−0.316228	+	0.316228i
$641$	−45.5959			−1.80093			−0.900465	−	0.434928i	$-0.856774\pi$
$641$	−45.5959			−1.80093			−0.900465	+	0.434928i	$0.856774\pi$
$642$	−11.7980	+	11.7980i	−0.465628	+	0.465628i
$643$			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
$645$		−	0.898979i		−	0.0353973i
$646$	−14.2020	−	14.2020i	−0.558772	−	0.558772i
$647$	−32.6969			−1.28545			−0.642725	−	0.766097i	$-0.722196\pi$
$647$	−32.6969			−1.28545			−0.642725	+	0.766097i	$0.722196\pi$
$648$	2.00000	−	2.00000i	0.0785674	−	0.0785674i
$649$		−	25.7980i		−	1.01266i
$650$	2.89898	+	2.89898i	0.113707	+	0.113707i
$651$	4.89898	+	2.00000i	0.192006	+	0.0783862i
$652$		−	13.3939i		−	0.524545i
$653$		−	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
$655$			16.8990i			0.660298i
$656$		−	27.5959i		−	1.07744i
$657$			0.898979i			0.0350725i
$658$	3.79796	−	1.59592i	0.148060	−	0.0622154i
$659$	−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
$661$	1.30306			0.0506832			0.0253416	−	0.999679i	$-0.491933\pi$
$661$	1.30306			0.0506832			0.0253416	+	0.999679i	$0.491933\pi$
$662$	−23.3939	−	23.3939i	−0.909229	−	0.909229i
$663$	−14.2020			−0.551562
$664$	−8.00000	−	8.00000i	−0.310460	−	0.310460i
$665$	7.10102	+	2.89898i	0.275366	+	0.112418i
$666$	−11.7980	+	11.7980i	−0.457162	+	0.457162i
$667$	−5.39388			−0.208852
$668$			2.20204i			0.0851995i
$669$			6.00000i			0.231973i
$670$	−4.89898	−	4.89898i	−0.189264	−	0.189264i
$671$	17.7980			0.687083
$672$	5.79796	+	13.7980i	0.223661	+	0.532268i
$673$	−13.5959			−0.524084			−0.262042	−	0.965056i	$-0.584396\pi$
$673$	−13.5959			−0.524084			−0.262042	+	0.965056i	$0.584396\pi$
$674$	−31.7980	−	31.7980i	−1.22481	−	1.22481i
$675$			1.00000i			0.0384900i
$676$		−	9.19184i		−	0.353532i
$677$	31.7980			1.22209			0.611047	−	0.791594i	$-0.290748\pi$
$677$	31.7980			1.22209			0.611047	+	0.791594i	$0.290748\pi$
$678$	−17.7980	+	17.7980i	−0.683526	+	0.683526i
$679$	21.7980	+	8.89898i	0.836529	+	0.341511i
$680$	9.79796	+	9.79796i	0.375735	+	0.375735i
$681$	−12.0000			−0.459841
$682$	−4.00000	−	4.00000i	−0.153168	−	0.153168i
$683$	−12.2020			−0.466898			−0.233449	−	0.972369i	$-0.575001\pi$
$683$	−12.2020			−0.466898			−0.233449	+	0.972369i	$0.575001\pi$
$684$	−5.79796			−0.221691
$685$	−5.79796			−0.221529
$686$	−24.3485	−	9.65153i	−0.929629	−	0.368497i
$687$			24.4949i			0.934539i
$688$	−3.59592			−0.137093
$689$		−	28.4041i		−	1.08211i
$690$	−6.00000	−	6.00000i	−0.228416	−	0.228416i
$691$		−	34.4949i		−	1.31225i	−0.754653	−	0.656124i	$-0.772195\pi$
$691$		−	34.4949i		−	1.31225i	0.754653	−	0.656124i	$-0.227805\pi$
$692$			15.5959i			0.592868i
$693$	2.00000	−	4.89898i	0.0759737	−	0.186097i
$694$	−25.5959	−	25.5959i	−0.971608	−	0.971608i
$695$		−	2.89898i		−	0.109965i
$696$	1.79796	−	1.79796i	0.0681515	−	0.0681515i
$697$	−33.7980			−1.28019
$698$	30.6969	+	30.6969i	1.16190	+	1.16190i
$699$			16.0000i			0.605176i
$700$	−4.89898	−	2.00000i	−0.185164	−	0.0755929i
$701$			23.1010i			0.872514i	0.899822	+	0.436257i	$0.143696\pi$
$701$			23.1010i			0.872514i	−0.899822	+	0.436257i	$0.856304\pi$
$702$	−2.89898	+	2.89898i	−0.109415	+	0.109415i
$703$	34.2020			1.28995
$704$		−	16.0000i		−	0.603023i
$705$		−	1.10102i		−	0.0414668i
$706$	−34.6969	+	34.6969i	−1.30584	+	1.30584i
$707$	−15.7980	+	38.6969i	−0.594143	+	1.45535i
$708$		−	25.7980i		−	0.969547i
$709$		−	29.7980i		−	1.11909i	−0.828801	−	0.559543i	$-0.810977\pi$
$709$		−	29.7980i		−	1.11909i	0.828801	−	0.559543i	$-0.189023\pi$
$710$	−3.10102	+	3.10102i	−0.116379	+	0.116379i
$711$		−	4.00000i		−	0.150012i
$712$	21.7980	+	21.7980i	0.816913	+	0.816913i
$713$			12.0000i			0.449404i
$714$	16.8990	−	7.10102i	0.632428	−	0.265749i
$715$	−5.79796			−0.216831
$716$		−	20.0000i		−	0.747435i
$717$	−26.6969			−0.997015
$718$	7.10102	−	7.10102i	0.265008	−	0.265008i
$719$	26.2020			0.977171			0.488586	−	0.872516i	$-0.337513\pi$
$719$	26.2020			0.977171			0.488586	+	0.872516i	$0.337513\pi$
$720$	4.00000			0.149071
$721$	19.7980	−	48.4949i	0.737315	−	1.80604i
$722$	−10.5959	−	10.5959i	−0.394339	−	0.394339i
$723$	20.0000			0.743808
$724$		−	22.2020i		−	0.825132i
$725$			0.898979i			0.0333873i
$726$	7.00000	−	7.00000i	0.259794	−	0.259794i
$727$	39.3939			1.46104			0.730519	−	0.682892i	$-0.239278\pi$
$727$	39.3939			1.46104			0.730519	+	0.682892i	$0.239278\pi$
$728$	−8.40408	−	20.0000i	−0.311476	−	0.741249i
$729$	−1.00000			−0.0370370
$730$	−0.898979	+	0.898979i	−0.0332727	+	0.0332727i
$731$			4.40408i			0.162891i
$732$	17.7980			0.657831
$733$	−1.50510			−0.0555922			−0.0277961	−	0.999614i	$-0.508849\pi$
$733$	−1.50510			−0.0555922			−0.0277961	+	0.999614i	$0.508849\pi$
$734$	15.7980	+	15.7980i	0.583113	+	0.583113i
$735$	−4.89898	+	5.00000i	−0.180702	+	0.184428i
$736$	−24.0000	+	24.0000i	−0.884652	+	0.884652i
$737$	9.79796			0.360912
$738$	−6.89898	+	6.89898i	−0.253955	+	0.253955i
$739$	−10.0000			−0.367856			−0.183928	−	0.982940i	$-0.558881\pi$
$739$	−10.0000			−0.367856			−0.183928	+	0.982940i	$0.558881\pi$
$740$	−23.5959			−0.867403
$741$	8.40408			0.308732
$742$	14.2020	+	33.7980i	0.521373	+	1.24076i
$743$			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
$745$			7.10102i			0.260161i
$746$	−14.0000	+	14.0000i	−0.512576	+	0.512576i
$747$			4.00000i			0.146352i
$748$	−19.5959			−0.716498
$749$	−11.7980	+	28.8990i	−0.431088	+	1.05595i
$750$	−1.00000	+	1.00000i	−0.0365148	+	0.0365148i
$751$			13.7980i			0.503495i	0.967793	+	0.251747i	$0.0810052\pi$
$751$			13.7980i			0.503495i	−0.967793	+	0.251747i	$0.918995\pi$
$752$	−4.40408			−0.160600
$753$	−3.10102			−0.113007
$754$	−2.60612	+	2.60612i	−0.0949094	+	0.0949094i
$755$		−	13.7980i		−	0.502159i
$756$	2.00000	−	4.89898i	0.0727393	−	0.178174i
$757$			5.59592i			0.203387i	0.994816	+	0.101694i	$0.0324261\pi$
$757$			5.59592i			0.203387i	−0.994816	+	0.101694i	$0.967574\pi$
$758$	−31.3939	−	31.3939i	−1.14028	−	1.14028i
$759$	12.0000			0.435572
$760$	−5.79796	−	5.79796i	−0.210314	−	0.210314i
$761$		−	0.696938i		−	0.0252640i	−0.999920	−	0.0126320i	$-0.995979\pi$
$761$		−	0.696938i		−	0.0252640i	0.999920	−	0.0126320i	$-0.00402100\pi$
$762$	8.89898	+	8.89898i	0.322376	+	0.322376i
$763$	−9.79796	−	4.00000i	−0.354710	−	0.144810i
$764$	−33.7980			−1.22277
$765$		−	4.89898i		−	0.177123i
$766$	9.10102	+	9.10102i	0.328833	+	0.328833i
$767$			37.3939i			1.35021i
$768$		−	16.0000i		−	0.577350i
$769$			51.5959i			1.86060i	0.366804	+	0.930298i	$0.380452\pi$
$769$			51.5959i			1.86060i	−0.366804	+	0.930298i	$0.619548\pi$
$770$	6.89898	−	2.89898i	0.248622	−	0.104472i
$771$	24.8990			0.896715
$772$		−	39.5959i		−	1.42509i
$773$	−19.7980			−0.712083			−0.356042	−	0.934470i	$-0.615874\pi$
$773$	−19.7980			−0.712083			−0.356042	+	0.934470i	$0.615874\pi$
$774$	0.898979	+	0.898979i	0.0323132	+	0.0323132i
$775$	2.00000			0.0718421
$776$	−17.7980	−	17.7980i	−0.638909	−	0.638909i
$777$	−11.7980	+	28.8990i	−0.423249	+	1.03675i
$778$	−26.6969	+	26.6969i	−0.957132	+	0.957132i
$779$	20.0000			0.716574
$780$	−5.79796			−0.207600
$781$		−	6.20204i		−	0.221926i
$782$	29.3939	+	29.3939i	1.05112	+	1.05112i
$783$	−0.898979			−0.0321269
$784$	20.0000	+	19.5959i	0.714286	+	0.699854i
$785$	−12.6969			−0.453173
$786$	−16.8990	−	16.8990i	−0.602767	−	0.602767i
$787$			35.5959i			1.26886i	0.772981	+	0.634429i	$0.218765\pi$
$787$			35.5959i			1.26886i	−0.772981	+	0.634429i	$0.781235\pi$
$788$	11.5959			0.413087
$789$	−7.79796			−0.277615
$790$	4.00000	−	4.00000i	0.142314	−	0.142314i
$791$	−17.7980	+	43.5959i	−0.632823	+	1.55009i
$792$	−4.00000	+	4.00000i	−0.142134	+	0.142134i
$793$	−25.7980			−0.916112
$794$	12.6969	+	12.6969i	0.450597	+	0.450597i
$795$	9.79796			0.347498
$796$			20.0000i			0.708881i
$797$	25.5959			0.906654			0.453327	−	0.891344i	$-0.350237\pi$
$797$	25.5959			0.906654			0.453327	+	0.891344i	$0.350237\pi$
$798$	−10.0000	+	4.20204i	−0.353996	+	0.148751i
$799$			5.39388i			0.190822i
$800$	4.00000	+	4.00000i	0.141421	+	0.141421i
$801$		−	10.8990i		−	0.385097i
$802$	11.7980	+	11.7980i	0.416600	+	0.416600i
$803$		−	1.79796i		−	0.0634486i
$804$	9.79796			0.345547
$805$	−14.6969	−	6.00000i	−0.517999	−	0.211472i
$806$	5.79796	+	5.79796i	0.204224	+	0.204224i
$807$			3.79796i			0.133694i
$808$	31.5959	−	31.5959i	1.11154	−	1.11154i
$809$	23.7980			0.836692			0.418346	−	0.908288i	$-0.362610\pi$
$809$	23.7980			0.836692			0.418346	+	0.908288i	$0.362610\pi$
$810$	−1.00000	−	1.00000i	−0.0351364	−	0.0351364i
$811$			13.1010i			0.460039i	0.973186	+	0.230020i	$0.0738790\pi$
$811$			13.1010i			0.460039i	−0.973186	+	0.230020i	$0.926121\pi$
$812$	1.79796	−	4.40408i	0.0630960	−	0.154553i
$813$			4.20204i			0.147372i
$814$	23.5959	−	23.5959i	0.827036	−	0.827036i
$815$	−6.69694			−0.234584
$816$	−19.5959			−0.685994
$817$		−	2.60612i		−	0.0911767i
$818$	4.00000	−	4.00000i	0.139857	−	0.139857i
$819$	−2.89898	+	7.10102i	−0.101299	+	0.248130i
$820$	−13.7980			−0.481846
$821$			10.6969i			0.373326i	0.982424	+	0.186663i	$0.0597672\pi$
$821$			10.6969i			0.373326i	−0.982424	+	0.186663i	$0.940233\pi$
$822$	5.79796	−	5.79796i	0.202227	−	0.202227i
$823$			40.4949i			1.41156i	0.708429	+	0.705782i	$0.249404\pi$
$823$			40.4949i			1.41156i	−0.708429	+	0.705782i	$0.750596\pi$
$824$	−39.5959	+	39.5959i	−1.37939	+	1.37939i
$825$		−	2.00000i		−	0.0696311i
$826$	−18.6969	−	44.4949i	−0.650550	−	1.54818i
$827$	33.1918			1.15419			0.577097	−	0.816676i	$-0.304186\pi$
$827$	33.1918			1.15419			0.577097	+	0.816676i	$0.304186\pi$
$828$	12.0000			0.417029
$829$	9.30306			0.323109			0.161554	−	0.986864i	$-0.448349\pi$
$829$	9.30306			0.323109			0.161554	+	0.986864i	$0.448349\pi$
$830$	−4.00000	+	4.00000i	−0.138842	+	0.138842i
$831$	−15.7980			−0.548025
$832$			23.1918i			0.804032i
$833$	24.0000	−	24.4949i	0.831551	−	0.848698i
$834$	2.89898	+	2.89898i	0.100383	+	0.100383i
$835$	1.10102			0.0381024
$836$	11.5959			0.401053
$837$			2.00000i			0.0691301i
$838$	−34.2929	+	34.2929i	−1.18463	+	1.18463i
$839$	−26.2020			−0.904595			−0.452297	−	0.891867i	$-0.649395\pi$
$839$	−26.2020			−0.904595			−0.452297	+	0.891867i	$0.649395\pi$
$840$	6.89898	−	2.89898i	0.238037	−	0.100024i
$841$	28.1918			0.972132
$842$	6.20204	−	6.20204i	0.213736	−	0.213736i
$843$		−	8.20204i		−	0.282493i
$844$			44.0000i			1.51454i
$845$	−4.59592			−0.158104
$846$	1.10102	+	1.10102i	0.0378539	+	0.0378539i
$847$	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
$851$	−70.7878			−2.42657
$852$		−	6.20204i		−	0.212478i
$853$	44.6969			1.53039			0.765197	−	0.643796i	$-0.222642\pi$
$853$	44.6969			1.53039			0.765197	+	0.643796i	$0.222642\pi$
$854$	30.6969	−	12.8990i	1.05043	−	0.441394i
$855$			2.89898i			0.0991430i
$856$	23.5959	−	23.5959i	0.806492	−	0.806492i
$857$			12.4949i			0.426818i	0.976963	+	0.213409i	$0.0684566\pi$
$857$			12.4949i			0.426818i	−0.976963	+	0.213409i	$0.931543\pi$
$858$	5.79796	−	5.79796i	0.197939	−	0.197939i
$859$		−	9.10102i		−	0.310523i	−0.987873	−	0.155261i	$-0.950378\pi$
$859$		−	9.10102i		−	0.310523i	0.987873	−	0.155261i	$-0.0496220\pi$
$860$			1.79796i			0.0613099i
$861$	−6.89898	+	16.8990i	−0.235117	+	0.575916i
$862$	3.10102	−	3.10102i	0.105621	−	0.105621i
$863$			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
$865$	7.79796			0.265139
$866$	5.30306	−	5.30306i	0.180205	−	0.180205i
$867$			7.00000i			0.237732i
$868$	−9.79796	−	4.00000i	−0.332564	−	0.135769i
$869$			8.00000i			0.271381i
$870$	−0.898979	−	0.898979i	−0.0304783	−	0.0304783i
$871$	−14.2020			−0.481218
$872$	8.00000	+	8.00000i	0.270914	+	0.270914i
$873$			8.89898i			0.301185i
$874$	−17.3939	−	17.3939i	−0.588357	−	0.588357i
$875$	−1.00000	+	2.44949i	−0.0338062	+	0.0828079i
$876$		−	1.79796i		−	0.0607474i
$877$		−	22.0000i		−	0.742887i	−0.928456	−	0.371444i	$-0.878863\pi$
$877$		−	22.0000i		−	0.742887i	0.928456	−	0.371444i	$-0.121137\pi$
$878$	−23.7980	−	23.7980i	−0.803142	−	0.803142i
$879$		−	21.5959i		−	0.728412i
$880$	−8.00000			−0.269680
$881$		−	0.696938i		−	0.0234805i	−0.999931	−	0.0117402i	$-0.996263\pi$
$881$		−	0.696938i		−	0.0234805i	0.999931	−	0.0117402i	$-0.00373712\pi$
$882$	−0.101021	−	9.89898i	−0.00340154	−	0.333316i
$883$	−40.4949			−1.36276			−0.681381	−	0.731929i	$-0.738620\pi$
$883$	−40.4949			−1.36276			−0.681381	+	0.731929i	$0.738620\pi$
$884$	28.4041			0.955333
$885$	−12.8990			−0.433594
$886$	6.00000	+	6.00000i	0.201574	+	0.201574i
$887$	42.4949			1.42684			0.713420	−	0.700737i	$-0.247145\pi$
$887$	42.4949			1.42684			0.713420	+	0.700737i	$0.247145\pi$
$888$	23.5959	−	23.5959i	0.791827	−	0.791827i
$889$	21.7980	+	8.89898i	0.731080	+	0.298462i
$890$	10.8990	−	10.8990i	0.365335	−	0.365335i
$891$	2.00000			0.0670025
$892$		−	12.0000i		−	0.401790i
$893$		−	3.19184i		−	0.106811i
$894$	−7.10102	−	7.10102i	−0.237494	−	0.237494i
$895$	−10.0000			−0.334263
$896$	−11.5959	−	27.5959i	−0.387392	−	0.921915i
$897$	−17.3939			−0.580765
$898$	−23.7980	−	23.7980i	−0.794148	−	0.794148i
$899$			1.79796i			0.0599653i
$900$		−	2.00000i		−	0.0666667i
$901$	−48.0000			−1.59911
$902$	13.7980	−	13.7980i	0.459422	−	0.459422i
$903$	2.20204	+	0.898979i	0.0732793	+	0.0299162i
$904$	35.5959	−	35.5959i	1.18390	−	1.18390i
$905$	−11.1010			−0.369010
$906$	13.7980	+	13.7980i	0.458406	+	0.458406i
$907$	−36.4949			−1.21179			−0.605897	−	0.795543i	$-0.707185\pi$
$907$	−36.4949			−1.21179			−0.605897	+	0.795543i	$0.707185\pi$
$908$	24.0000			0.796468
$909$	−15.7980			−0.523985
$910$	−10.0000	+	4.20204i	−0.331497	+	0.139296i
$911$		−	23.1010i		−	0.765371i	−0.923879	−	0.382685i	$-0.874999\pi$
$911$		−	23.1010i		−	0.765371i	0.923879	−	0.382685i	$-0.125001\pi$
$912$	11.5959			0.383979
$913$		−	8.00000i		−	0.264761i
$914$	−11.7980	−	11.7980i	−0.390242	−	0.390242i
$915$		−	8.89898i		−	0.294191i
$916$		−	48.9898i		−	1.61867i
$917$	−41.3939	−	16.8990i	−1.36695	−	0.558053i
$918$	4.89898	+	4.89898i	0.161690	+	0.161690i
$919$			25.3939i			0.837667i	0.908063	+	0.418833i	$0.137561\pi$
$919$			25.3939i			0.837667i	−0.908063	+	0.418833i	$0.862439\pi$
$920$	12.0000	+	12.0000i	0.395628	+	0.395628i
$921$	15.5959			0.513903
$922$	4.20204	+	4.20204i	0.138387	+	0.138387i
$923$			8.98979i			0.295903i
$924$	−4.00000	+	9.79796i	−0.131590	+	0.322329i
$925$			11.7980i			0.387915i
$926$	26.6969	−	26.6969i	0.877316	−	0.877316i
$927$	19.7980			0.650250
$928$	−3.59592	+	3.59592i	−0.118042	+	0.118042i
$929$			38.4949i			1.26298i	0.775385	+	0.631488i	$0.217556\pi$
$929$			38.4949i			1.26298i	−0.775385	+	0.631488i	$0.782444\pi$
$930$	−2.00000	+	2.00000i	−0.0655826	+	0.0655826i
$931$	−14.2020	+	14.4949i	−0.465453	+	0.475051i
$932$		−	32.0000i		−	1.04819i
$933$			8.00000i			0.261908i
$934$	21.7980	−	21.7980i	0.713251	−	0.713251i
$935$			9.79796i			0.320428i
$936$	5.79796	−	5.79796i	0.189512	−	0.189512i
$937$		−	36.4949i		−	1.19224i	−0.802897	−	0.596118i	$-0.796709\pi$
$937$		−	36.4949i		−	1.19224i	0.802897	−	0.596118i	$-0.203291\pi$
$938$	16.8990	−	7.10102i	0.551771	−	0.231857i
$939$	−28.4949			−0.929896
$940$			2.20204i			0.0718227i
$941$	15.7980			0.514999			0.257499	−	0.966278i	$-0.417101\pi$
$941$	15.7980			0.514999			0.257499	+	0.966278i	$0.417101\pi$
$942$	12.6969	−	12.6969i	0.413689	−	0.413689i
$943$	−41.3939			−1.34797
$944$			51.5959i			1.67930i
$945$	−2.44949	−	1.00000i	−0.0796819	−	0.0325300i
$946$	−1.79796	−	1.79796i	−0.0584567	−	0.0584567i
$947$	31.7980			1.03329			0.516647	−	0.856198i	$-0.327180\pi$
$947$	31.7980			1.03329			0.516647	+	0.856198i	$0.327180\pi$
$948$			8.00000i			0.259828i
$949$			2.60612i			0.0845983i
$950$	−2.89898	+	2.89898i	−0.0940553	+	0.0940553i
$951$	−12.0000			−0.389127
$952$	−33.7980	+	14.2020i	−1.09540	+	0.460291i
$953$	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
$955$			16.8990i			0.546838i
$956$	53.3939			1.72688
$957$	1.79796			0.0581198
$958$	−27.5959	−	27.5959i	−0.891584	−	0.891584i
$959$	5.79796	−	14.2020i	0.187226	−	0.458608i
$960$	−8.00000			−0.258199
$961$	−27.0000			−0.870968
$962$	−34.2020	+	34.2020i	−1.10272	+	1.10272i
$963$	−11.7980			−0.380184
$964$	−40.0000			−1.28831
$965$	−19.7980			−0.637319
$966$	20.6969	−	8.69694i	0.665913	−	0.279819i
$967$		−	56.4949i		−	1.81675i	−0.418153	−	0.908377i	$-0.637322\pi$
$967$		−	56.4949i		−	1.81675i	0.418153	−	0.908377i	$-0.362678\pi$
$968$	−14.0000	+	14.0000i	−0.449977	+	0.449977i
$969$		−	14.2020i		−	0.456235i
$970$	−8.89898	+	8.89898i	−0.285729	+	0.285729i
$971$		−	3.10102i		−	0.0995165i	−0.998761	−	0.0497582i	$-0.984155\pi$
$971$		−	3.10102i		−	0.0995165i	0.998761	−	0.0497582i	$-0.0158451\pi$
$972$	2.00000			0.0641500
$973$	7.10102	+	2.89898i	0.227648	+	0.0929370i
$974$	−15.1010	+	15.1010i	−0.483868	+	0.483868i
$975$			2.89898i			0.0928416i
$976$	−35.5959			−1.13940
$977$	23.1918			0.741973			0.370986	−	0.928638i	$-0.379020\pi$
$977$	23.1918			0.741973			0.370986	+	0.928638i	$0.379020\pi$
$978$	6.69694	−	6.69694i	0.214144	−	0.214144i
$979$			21.7980i			0.696666i
$980$	9.79796	−	10.0000i	0.312984	−	0.319438i
$981$		−	4.00000i		−	0.127710i
$982$	25.5959	+	25.5959i	0.816799	+	0.816799i
$983$	−2.89898			−0.0924631			−0.0462315	−	0.998931i	$-0.514721\pi$
$983$	−2.89898			−0.0924631			−0.0462315	+	0.998931i	$0.514721\pi$
$984$	13.7980	−	13.7980i	0.439863	−	0.439863i
$985$		−	5.79796i		−	0.184738i
$986$	4.40408	+	4.40408i	0.140255	+	0.140255i
$987$	2.69694	+	1.10102i	0.0858445	+	0.0350459i
$988$	−16.8082			−0.534739
$989$			5.39388i			0.171515i
$990$	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
$993$		−	23.3939i		−	0.742382i
$994$	−4.49490	−	10.6969i	−0.142569	−	0.339286i
$995$	10.0000			0.317021
$996$		−	8.00000i		−	0.253490i
$997$	16.2929			0.516000			0.258000	−	0.966145i	$-0.416937\pi$
$997$	16.2929			0.516000			0.258000	+	0.966145i	$0.416937\pi$
$998$	−10.0000	−	10.0000i	−0.316544	−	0.316544i
$999$	−11.7980			−0.373271

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	840.2.z.b.811.2	yes	4
4.3	odd	2		3360.2.z.b.1231.3		4
7.6	odd	2		840.2.z.a.811.2	✓	4
8.3	odd	2		840.2.z.a.811.3	yes	4
8.5	even	2		3360.2.z.a.1231.4		4
28.27	even	2		3360.2.z.a.1231.1		4
56.13	odd	2		3360.2.z.b.1231.2		4
56.27	even	2	inner	840.2.z.b.811.3	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.z.a.811.2	✓	4	7.6	odd	2
840.2.z.a.811.3	yes	4	8.3	odd	2
840.2.z.b.811.2	yes	4	1.1	even	1	trivial
840.2.z.b.811.3	yes	4	56.27	even	2	inner
3360.2.z.a.1231.1		4	28.27	even	2
3360.2.z.a.1231.4		4	8.5	even	2
3360.2.z.b.1231.2		4	56.13	odd	2
3360.2.z.b.1231.3		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} -2.89898 q^{13} +(3.44949 - 1.44949i) q^{14} -1.00000i q^{15} -4.00000 q^{16} +4.89898i q^{17} +(1.00000 + 1.00000i) q^{18} -2.89898i 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} +(2.89898 + 2.89898i) q^{26} +1.00000i q^{27} +(-4.89898 - 2.00000i) q^{28} +0.898979i 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} +11.7980i q^{37} +(-2.89898 + 2.89898i) q^{38} +2.89898i q^{39} +(2.00000 - 2.00000i) q^{40} +6.89898i q^{41} +(-1.44949 - 3.44949i) q^{42} +0.898979 q^{43} +4.00000i q^{44} -1.00000 q^{45} +(6.00000 - 6.00000i) q^{46} +1.10102 q^{47} +4.00000i q^{48} +(-5.00000 - 4.89898i) q^{49} +(-1.00000 - 1.00000i) q^{50} +4.89898 q^{51} -5.79796i q^{52} +9.79796i q^{53} +(1.00000 - 1.00000i) q^{54} +2.00000 q^{55} +(2.89898 + 6.89898i) q^{56} -2.89898 q^{57} +(0.898979 - 0.898979i) q^{58} -12.8990i q^{59} +2.00000 q^{60} +8.89898 q^{61} +(-2.00000 - 2.00000i) q^{62} +(1.00000 - 2.44949i) q^{63} -8.00000i q^{64} -2.89898 q^{65} +(-2.00000 + 2.00000i) q^{66} +4.89898 q^{67} -9.79796 q^{68} +6.00000 q^{69} +(3.44949 - 1.44949i) q^{70} -3.10102i q^{71} +(-2.00000 + 2.00000i) q^{72} -0.898979i q^{73} +(11.7980 - 11.7980i) q^{74} -1.00000i q^{75} +5.79796 q^{76} +(-2.00000 + 4.89898i) q^{77} +(2.89898 - 2.89898i) q^{78} +4.00000i q^{79} -4.00000 q^{80} +1.00000 q^{81} +(6.89898 - 6.89898i) q^{82} -4.00000i q^{83} +(-2.00000 + 4.89898i) q^{84} +4.89898i q^{85} +(-0.898979 - 0.898979i) q^{86} +0.898979 q^{87} +(4.00000 - 4.00000i) q^{88} +10.8990i q^{89} +(1.00000 + 1.00000i) q^{90} +(2.89898 - 7.10102i) q^{91} -12.0000 q^{92} -2.00000i q^{93} +(-1.10102 - 1.10102i) q^{94} -2.89898i q^{95} +(4.00000 - 4.00000i) q^{96} -8.89898i q^{97} +(0.101021 + 9.89898i) 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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