LMFDB - Embedded newform 40.2.d.a.21.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [40,2,Mod(21,40)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(40, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("40.21"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$N$	$=$	$40 = 2^{3} \cdot 5$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	40.d (of order $2$ , degree $1$ , minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$0.319401608085$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{4} - x^{2} + 1$ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$2$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			21.4
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	40.21
Dual form			40.2.d.a.21.3

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.366025 + 1.36603i) q^{2} -0.732051i q^{3} +(-1.73205 + 1.00000i) q^{4} -1.00000i q^{5} +(1.00000 - 0.267949i) q^{6} -2.73205 q^{7} +(-2.00000 - 2.00000i) q^{8} +2.46410 q^{9} +(1.36603 - 0.366025i) q^{10} -2.00000i q^{11} +(0.732051 + 1.26795i) q^{12} +3.46410i q^{13} +(-1.00000 - 3.73205i) q^{14} -0.732051 q^{15} +(2.00000 - 3.46410i) q^{16} -3.46410 q^{17} +(0.901924 + 3.36603i) q^{18} +7.46410i q^{19} +(1.00000 + 1.73205i) q^{20} +2.00000i q^{21} +(2.73205 - 0.732051i) q^{22} +4.19615 q^{23} +(-1.46410 + 1.46410i) q^{24} -1.00000 q^{25} +(-4.73205 + 1.26795i) q^{26} -4.00000i q^{27} +(4.73205 - 2.73205i) q^{28} -6.92820i q^{29} +(-0.267949 - 1.00000i) q^{30} +1.46410 q^{31} +(5.46410 + 1.46410i) q^{32} -1.46410 q^{33} +(-1.26795 - 4.73205i) q^{34} +2.73205i q^{35} +(-4.26795 + 2.46410i) q^{36} -2.00000i q^{37} +(-10.1962 + 2.73205i) q^{38} +2.53590 q^{39} +(-2.00000 + 2.00000i) q^{40} -5.46410 q^{41} +(-2.73205 + 0.732051i) q^{42} -8.73205i q^{43} +(2.00000 + 3.46410i) q^{44} -2.46410i q^{45} +(1.53590 + 5.73205i) q^{46} +6.73205 q^{47} +(-2.53590 - 1.46410i) q^{48} +0.464102 q^{49} +(-0.366025 - 1.36603i) q^{50} +2.53590i q^{51} +(-3.46410 - 6.00000i) q^{52} +4.53590i q^{53} +(5.46410 - 1.46410i) q^{54} -2.00000 q^{55} +(5.46410 + 5.46410i) q^{56} +5.46410 q^{57} +(9.46410 - 2.53590i) q^{58} -0.535898i q^{59} +(1.26795 - 0.732051i) q^{60} +4.92820i q^{61} +(0.535898 + 2.00000i) q^{62} -6.73205 q^{63} +8.00000i q^{64} +3.46410 q^{65} +(-0.535898 - 2.00000i) q^{66} +7.26795i q^{67} +(6.00000 - 3.46410i) q^{68} -3.07180i q^{69} +(-3.73205 + 1.00000i) q^{70} -1.46410 q^{71} +(-4.92820 - 4.92820i) q^{72} +0.535898 q^{73} +(2.73205 - 0.732051i) q^{74} +0.732051i q^{75} +(-7.46410 - 12.9282i) q^{76} +5.46410i q^{77} +(0.928203 + 3.46410i) q^{78} -14.9282 q^{79} +(-3.46410 - 2.00000i) q^{80} +4.46410 q^{81} +(-2.00000 - 7.46410i) q^{82} +4.73205i q^{83} +(-2.00000 - 3.46410i) q^{84} +3.46410i q^{85} +(11.9282 - 3.19615i) q^{86} -5.07180 q^{87} +(-4.00000 + 4.00000i) q^{88} -4.92820 q^{89} +(3.36603 - 0.901924i) q^{90} -9.46410i q^{91} +(-7.26795 + 4.19615i) q^{92} -1.07180i q^{93} +(2.46410 + 9.19615i) q^{94} +7.46410 q^{95} +(1.07180 - 4.00000i) q^{96} +6.39230 q^{97} +(0.169873 + 0.633975i) q^{98} -4.92820i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$4 q - 2 q^{2} + 4 q^{6} - 4 q^{7} - 8 q^{8} - 4 q^{9} + 2 q^{10} - 4 q^{12} - 4 q^{14} + 4 q^{15} + 8 q^{16} + 14 q^{18} + 4 q^{20} + 4 q^{22} - 4 q^{23} + 8 q^{24} - 4 q^{25} - 12 q^{26} + 12 q^{28} - 8 q^{30}+ \cdots + 18 q^{98}+O(q^{100})$ 4 * q - 2 * q^2 + 4 * q^6 - 4 * q^7 - 8 * q^8 - 4 * q^9 + 2 * q^10 - 4 * q^12 - 4 * q^14 + 4 * q^15 + 8 * q^16 + 14 * q^18 + 4 * q^20 + 4 * q^22 - 4 * q^23 + 8 * q^24 - 4 * q^25 - 12 * q^26 + 12 * q^28 - 8 * q^30 - 8 * q^31 + 8 * q^32 + 8 * q^33 - 12 * q^34 - 24 * q^36 - 20 * q^38 + 24 * q^39 - 8 * q^40 - 8 * q^41 - 4 * q^42 + 8 * q^44 + 20 * q^46 + 20 * q^47 - 24 * q^48 - 12 * q^49 + 2 * q^50 + 8 * q^54 - 8 * q^55 + 8 * q^56 + 8 * q^57 + 24 * q^58 + 12 * q^60 + 16 * q^62 - 20 * q^63 - 16 * q^66 + 24 * q^68 - 8 * q^70 + 8 * q^71 + 8 * q^72 + 16 * q^73 + 4 * q^74 - 16 * q^76 - 24 * q^78 - 32 * q^79 + 4 * q^81 - 8 * q^82 - 8 * q^84 + 20 * q^86 - 48 * q^87 - 16 * q^88 + 8 * q^89 + 10 * q^90 - 36 * q^92 - 4 * q^94 + 16 * q^95 + 32 * q^96 - 16 * q^97 + 18 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/40\mathbb{Z}\right)^\times$ .

$n$	$17$	$21$	$31$
$\chi(n)$	$1$	$-1$	$1$

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

)

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

$2$	0.366025	+	1.36603i	0.258819	+	0.965926i
$2$	0.366025	+	1.36603i	0.258819	+	0.965926i
$3$		−	0.732051i		−	0.422650i	−0.977416	−	0.211325i	$-0.932222\pi$
$3$		−	0.732051i		−	0.422650i	0.977416	−	0.211325i	$-0.0677778\pi$
$4$	−1.73205	+	1.00000i	−0.866025	+	0.500000i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	1.00000	−	0.267949i	0.408248	−	0.109390i
$7$	−2.73205			−1.03262			−0.516309	−	0.856402i	$-0.672694\pi$
$7$	−2.73205			−1.03262			−0.516309	+	0.856402i	$0.672694\pi$
$8$	−2.00000	−	2.00000i	−0.707107	−	0.707107i
$9$	2.46410			0.821367
$10$	1.36603	−	0.366025i	0.431975	−	0.115747i
$11$		−	2.00000i		−	0.603023i	−0.953463	−	0.301511i	$-0.902509\pi$
$11$		−	2.00000i		−	0.603023i	0.953463	−	0.301511i	$-0.0974911\pi$
$12$	0.732051	+	1.26795i	0.211325	+	0.366025i
$13$			3.46410i			0.960769i	0.877058	+	0.480384i	$0.159503\pi$
$13$			3.46410i			0.960769i	−0.877058	+	0.480384i	$0.840497\pi$
$14$	−1.00000	−	3.73205i	−0.267261	−	0.997433i
$15$	−0.732051			−0.189015
$16$	2.00000	−	3.46410i	0.500000	−	0.866025i
$17$	−3.46410			−0.840168			−0.420084	−	0.907485i	$-0.637999\pi$
$17$	−3.46410			−0.840168			−0.420084	+	0.907485i	$0.637999\pi$
$18$	0.901924	+	3.36603i	0.212585	+	0.793380i
$19$			7.46410i			1.71238i	0.516659	+	0.856191i	$0.327175\pi$
$19$			7.46410i			1.71238i	−0.516659	+	0.856191i	$0.672825\pi$
$20$	1.00000	+	1.73205i	0.223607	+	0.387298i
$21$			2.00000i			0.436436i
$22$	2.73205	−	0.732051i	0.582475	−	0.156074i
$23$	4.19615			0.874958			0.437479	−	0.899229i	$-0.355871\pi$
$23$	4.19615			0.874958			0.437479	+	0.899229i	$0.355871\pi$
$24$	−1.46410	+	1.46410i	−0.298858	+	0.298858i
$25$	−1.00000			−0.200000
$26$	−4.73205	+	1.26795i	−0.928032	+	0.248665i
$27$		−	4.00000i		−	0.769800i
$28$	4.73205	−	2.73205i	0.894274	−	0.516309i
$29$		−	6.92820i		−	1.28654i	−0.765641	−	0.643268i	$-0.777578\pi$
$29$		−	6.92820i		−	1.28654i	0.765641	−	0.643268i	$-0.222422\pi$
$30$	−0.267949	−	1.00000i	−0.0489206	−	0.182574i
$31$	1.46410			0.262960			0.131480	−	0.991319i	$-0.458027\pi$
$31$	1.46410			0.262960			0.131480	+	0.991319i	$0.458027\pi$
$32$	5.46410	+	1.46410i	0.965926	+	0.258819i
$33$	−1.46410			−0.254867
$34$	−1.26795	−	4.73205i	−0.217451	−	0.811540i
$35$			2.73205i			0.461801i
$36$	−4.26795	+	2.46410i	−0.711325	+	0.410684i
$37$		−	2.00000i		−	0.328798i	−0.986394	−	0.164399i	$-0.947432\pi$
$37$		−	2.00000i		−	0.328798i	0.986394	−	0.164399i	$-0.0525685\pi$
$38$	−10.1962	+	2.73205i	−1.65403	+	0.443197i
$39$	2.53590			0.406069
$40$	−2.00000	+	2.00000i	−0.316228	+	0.316228i
$41$	−5.46410			−0.853349			−0.426675	−	0.904405i	$-0.640315\pi$
$41$	−5.46410			−0.853349			−0.426675	+	0.904405i	$0.640315\pi$
$42$	−2.73205	+	0.732051i	−0.421565	+	0.112958i
$43$		−	8.73205i		−	1.33163i	−0.746119	−	0.665813i	$-0.768085\pi$
$43$		−	8.73205i		−	1.33163i	0.746119	−	0.665813i	$-0.231915\pi$
$44$	2.00000	+	3.46410i	0.301511	+	0.522233i
$45$		−	2.46410i		−	0.367327i
$46$	1.53590	+	5.73205i	0.226456	+	0.845145i
$47$	6.73205			0.981971			0.490985	−	0.871168i	$-0.336637\pi$
$47$	6.73205			0.981971			0.490985	+	0.871168i	$0.336637\pi$
$48$	−2.53590	−	1.46410i	−0.366025	−	0.211325i
$49$	0.464102			0.0663002
$50$	−0.366025	−	1.36603i	−0.0517638	−	0.193185i
$51$			2.53590i			0.355097i
$52$	−3.46410	−	6.00000i	−0.480384	−	0.832050i
$53$			4.53590i			0.623054i	0.950237	+	0.311527i	$0.100840\pi$
$53$			4.53590i			0.623054i	−0.950237	+	0.311527i	$0.899160\pi$
$54$	5.46410	−	1.46410i	0.743570	−	0.199239i
$55$	−2.00000			−0.269680
$56$	5.46410	+	5.46410i	0.730171	+	0.730171i
$57$	5.46410			0.723738
$58$	9.46410	−	2.53590i	1.24270	−	0.332980i
$59$		−	0.535898i		−	0.0697680i	−0.999391	−	0.0348840i	$-0.988894\pi$
$59$		−	0.535898i		−	0.0697680i	0.999391	−	0.0348840i	$-0.0111062\pi$
$60$	1.26795	−	0.732051i	0.163692	−	0.0945074i
$61$			4.92820i			0.630992i	0.948927	+	0.315496i	$0.102171\pi$
$61$			4.92820i			0.630992i	−0.948927	+	0.315496i	$0.897829\pi$
$62$	0.535898	+	2.00000i	0.0680592	+	0.254000i
$63$	−6.73205			−0.848159
$64$			8.00000i			1.00000i
$65$	3.46410			0.429669
$66$	−0.535898	−	2.00000i	−0.0659645	−	0.246183i
$67$			7.26795i			0.887921i	0.896046	+	0.443961i	$0.146427\pi$
$67$			7.26795i			0.887921i	−0.896046	+	0.443961i	$0.853573\pi$
$68$	6.00000	−	3.46410i	0.727607	−	0.420084i
$69$		−	3.07180i		−	0.369801i
$70$	−3.73205	+	1.00000i	−0.446065	+	0.119523i
$71$	−1.46410			−0.173757			−0.0868784	−	0.996219i	$-0.527689\pi$
$71$	−1.46410			−0.173757			−0.0868784	+	0.996219i	$0.527689\pi$
$72$	−4.92820	−	4.92820i	−0.580794	−	0.580794i
$73$	0.535898			0.0627222			0.0313611	−	0.999508i	$-0.490016\pi$
$73$	0.535898			0.0627222			0.0313611	+	0.999508i	$0.490016\pi$
$74$	2.73205	−	0.732051i	0.317594	−	0.0850992i
$75$			0.732051i			0.0845299i
$76$	−7.46410	−	12.9282i	−0.856191	−	1.48297i
$77$			5.46410i			0.622692i
$78$	0.928203	+	3.46410i	0.105098	+	0.392232i
$79$	−14.9282			−1.67955			−0.839777	−	0.542931i	$-0.817314\pi$
$79$	−14.9282			−1.67955			−0.839777	+	0.542931i	$0.817314\pi$
$80$	−3.46410	−	2.00000i	−0.387298	−	0.223607i
$81$	4.46410			0.496011
$82$	−2.00000	−	7.46410i	−0.220863	−	0.824272i
$83$			4.73205i			0.519410i	0.965688	+	0.259705i	$0.0836253\pi$
$83$			4.73205i			0.519410i	−0.965688	+	0.259705i	$0.916375\pi$
$84$	−2.00000	−	3.46410i	−0.218218	−	0.377964i
$85$			3.46410i			0.375735i
$86$	11.9282	−	3.19615i	1.28625	−	0.344650i
$87$	−5.07180			−0.543754
$88$	−4.00000	+	4.00000i	−0.426401	+	0.426401i
$89$	−4.92820			−0.522388			−0.261194	−	0.965286i	$-0.584116\pi$
$89$	−4.92820			−0.522388			−0.261194	+	0.965286i	$0.584116\pi$
$90$	3.36603	−	0.901924i	0.354810	−	0.0950711i
$91$		−	9.46410i		−	0.992107i
$92$	−7.26795	+	4.19615i	−0.757736	+	0.437479i
$93$		−	1.07180i		−	0.111140i
$94$	2.46410	+	9.19615i	0.254153	+	0.948511i
$95$	7.46410			0.765801
$96$	1.07180	−	4.00000i	0.109390	−	0.408248i
$97$	6.39230			0.649040			0.324520	−	0.945879i	$-0.394797\pi$
$97$	6.39230			0.649040			0.324520	+	0.945879i	$0.394797\pi$
$98$	0.169873	+	0.633975i	0.0171598	+	0.0640411i
$99$		−	4.92820i		−	0.495303i
$100$	1.73205	−	1.00000i	0.173205	−	0.100000i
$101$		−	10.9282i		−	1.08740i	−0.839281	−	0.543698i	$-0.817024\pi$
$101$		−	10.9282i		−	1.08740i	0.839281	−	0.543698i	$-0.182976\pi$
$102$	−3.46410	+	0.928203i	−0.342997	+	0.0919058i
$103$	−1.66025			−0.163590			−0.0817948	−	0.996649i	$-0.526065\pi$
$103$	−1.66025			−0.163590			−0.0817948	+	0.996649i	$0.526065\pi$
$104$	6.92820	−	6.92820i	0.679366	−	0.679366i
$105$	2.00000			0.195180
$106$	−6.19615	+	1.66025i	−0.601824	+	0.161258i
$107$		−	0.732051i		−	0.0707700i	−0.999374	−	0.0353850i	$-0.988734\pi$
$107$		−	0.732051i		−	0.0707700i	0.999374	−	0.0353850i	$-0.0112658\pi$
$108$	4.00000	+	6.92820i	0.384900	+	0.666667i
$109$			3.07180i			0.294225i	0.989120	+	0.147112i	$0.0469979\pi$
$109$			3.07180i			0.294225i	−0.989120	+	0.147112i	$0.953002\pi$
$110$	−0.732051	−	2.73205i	−0.0697983	−	0.260491i
$111$	−1.46410			−0.138966
$112$	−5.46410	+	9.46410i	−0.516309	+	0.894274i
$113$	0.928203			0.0873180			0.0436590	−	0.999046i	$-0.486098\pi$
$113$	0.928203			0.0873180			0.0436590	+	0.999046i	$0.486098\pi$
$114$	2.00000	+	7.46410i	0.187317	+	0.699077i
$115$		−	4.19615i		−	0.391293i
$116$	6.92820	+	12.0000i	0.643268	+	1.11417i
$117$			8.53590i			0.789144i
$118$	0.732051	−	0.196152i	0.0673907	−	0.0180573i
$119$	9.46410			0.867573
$120$	1.46410	+	1.46410i	0.133654	+	0.133654i
$121$	7.00000			0.636364
$122$	−6.73205	+	1.80385i	−0.609491	+	0.163313i
$123$			4.00000i			0.360668i
$124$	−2.53590	+	1.46410i	−0.227730	+	0.131480i
$125$			1.00000i			0.0894427i
$126$	−2.46410	−	9.19615i	−0.219520	−	0.819258i
$127$	13.2679			1.17734			0.588670	−	0.808373i	$-0.299652\pi$
$127$	13.2679			1.17734			0.588670	+	0.808373i	$0.299652\pi$
$128$	−10.9282	+	2.92820i	−0.965926	+	0.258819i
$129$	−6.39230			−0.562811
$130$	1.26795	+	4.73205i	0.111207	+	0.415028i
$131$			7.85641i			0.686417i	0.939259	+	0.343209i	$0.111514\pi$
$131$			7.85641i			0.686417i	−0.939259	+	0.343209i	$0.888486\pi$
$132$	2.53590	−	1.46410i	0.220722	−	0.127434i
$133$		−	20.3923i		−	1.76824i
$134$	−9.92820	+	2.66025i	−0.857666	+	0.229811i
$135$	−4.00000			−0.344265
$136$	6.92820	+	6.92820i	0.594089	+	0.594089i
$137$	−8.92820			−0.762788			−0.381394	−	0.924413i	$-0.624556\pi$
$137$	−8.92820			−0.762788			−0.381394	+	0.924413i	$0.624556\pi$
$138$	4.19615	−	1.12436i	0.357200	−	0.0957115i
$139$		−	7.46410i		−	0.633097i	−0.948576	−	0.316548i	$-0.897476\pi$
$139$		−	7.46410i		−	0.633097i	0.948576	−	0.316548i	$-0.102524\pi$
$140$	−2.73205	−	4.73205i	−0.230900	−	0.399931i
$141$		−	4.92820i		−	0.415030i
$142$	−0.535898	−	2.00000i	−0.0449716	−	0.167836i
$143$	6.92820			0.579365
$144$	4.92820	−	8.53590i	0.410684	−	0.711325i
$145$	−6.92820			−0.575356
$146$	0.196152	+	0.732051i	0.0162337	+	0.0605850i
$147$		−	0.339746i		−	0.0280218i
$148$	2.00000	+	3.46410i	0.164399	+	0.284747i
$149$			19.8564i			1.62670i	0.581775	+	0.813350i	$0.302359\pi$
$149$			19.8564i			1.62670i	−0.581775	+	0.813350i	$0.697641\pi$
$150$	−1.00000	+	0.267949i	−0.0816497	+	0.0218780i
$151$	8.39230			0.682956			0.341478	−	0.939890i	$-0.389073\pi$
$151$	8.39230			0.682956			0.341478	+	0.939890i	$0.389073\pi$
$152$	14.9282	−	14.9282i	1.21084	−	1.21084i
$153$	−8.53590			−0.690086
$154$	−7.46410	+	2.00000i	−0.601474	+	0.161165i
$155$		−	1.46410i		−	0.117599i
$156$	−4.39230	+	2.53590i	−0.351666	+	0.203034i
$157$		−	16.9282i		−	1.35102i	−0.737352	−	0.675509i	$-0.763924\pi$
$157$		−	16.9282i		−	1.35102i	0.737352	−	0.675509i	$-0.236076\pi$
$158$	−5.46410	−	20.3923i	−0.434701	−	1.62232i
$159$	3.32051			0.263333
$160$	1.46410	−	5.46410i	0.115747	−	0.431975i
$161$	−11.4641			−0.903498
$162$	1.63397	+	6.09808i	0.128377	+	0.479110i
$163$			10.1962i			0.798624i	0.916815	+	0.399312i	$0.130751\pi$
$163$			10.1962i			0.798624i	−0.916815	+	0.399312i	$0.869249\pi$
$164$	9.46410	−	5.46410i	0.739022	−	0.426675i
$165$			1.46410i			0.113980i
$166$	−6.46410	+	1.73205i	−0.501712	+	0.134433i
$167$	−20.1962			−1.56283			−0.781413	−	0.624015i	$-0.785501\pi$
$167$	−20.1962			−1.56283			−0.781413	+	0.624015i	$0.785501\pi$
$168$	4.00000	−	4.00000i	0.308607	−	0.308607i
$169$	1.00000			0.0769231
$170$	−4.73205	+	1.26795i	−0.362932	+	0.0972473i
$171$			18.3923i			1.40649i
$172$	8.73205	+	15.1244i	0.665813	+	1.15322i
$173$			2.00000i			0.152057i	0.997106	+	0.0760286i	$0.0242240\pi$
$173$			2.00000i			0.152057i	−0.997106	+	0.0760286i	$0.975776\pi$
$174$	−1.85641	−	6.92820i	−0.140734	−	0.525226i
$175$	2.73205			0.206524
$176$	−6.92820	−	4.00000i	−0.522233	−	0.301511i
$177$	−0.392305			−0.0294874
$178$	−1.80385	−	6.73205i	−0.135204	−	0.504589i
$179$		−	15.4641i		−	1.15584i	−0.816093	−	0.577921i	$-0.803864\pi$
$179$		−	15.4641i		−	1.15584i	0.816093	−	0.577921i	$-0.196136\pi$
$180$	2.46410	+	4.26795i	0.183663	+	0.318114i
$181$			16.0000i			1.18927i	0.803996	+	0.594635i	$0.202704\pi$
$181$			16.0000i			1.18927i	−0.803996	+	0.594635i	$0.797296\pi$
$182$	12.9282	−	3.46410i	0.958302	−	0.256776i
$183$	3.60770			0.266688
$184$	−8.39230	−	8.39230i	−0.618689	−	0.618689i
$185$	−2.00000			−0.147043
$186$	1.46410	−	0.392305i	0.107353	−	0.0287652i
$187$			6.92820i			0.506640i
$188$	−11.6603	+	6.73205i	−0.850411	+	0.490985i
$189$			10.9282i			0.794910i
$190$	2.73205	+	10.1962i	0.198204	+	0.739707i
$191$	−19.3205			−1.39798			−0.698991	−	0.715130i	$-0.746367\pi$
$191$	−19.3205			−1.39798			−0.698991	+	0.715130i	$0.746367\pi$
$192$	5.85641			0.422650
$193$	7.46410			0.537278			0.268639	−	0.963241i	$-0.413426\pi$
$193$	7.46410			0.537278			0.268639	+	0.963241i	$0.413426\pi$
$194$	2.33975	+	8.73205i	0.167984	+	0.626925i
$195$		−	2.53590i		−	0.181599i
$196$	−0.803848	+	0.464102i	−0.0574177	+	0.0331501i
$197$		−	12.5359i		−	0.893146i	−0.894747	−	0.446573i	$-0.852644\pi$
$197$		−	12.5359i		−	0.893146i	0.894747	−	0.446573i	$-0.147356\pi$
$198$	6.73205	−	1.80385i	0.478426	−	0.128194i
$199$	25.8564			1.83291			0.916456	−	0.400135i	$-0.131037\pi$
$199$	25.8564			1.83291			0.916456	+	0.400135i	$0.131037\pi$
$200$	2.00000	+	2.00000i	0.141421	+	0.141421i
$201$	5.32051			0.375280
$202$	14.9282	−	4.00000i	1.05034	−	0.281439i
$203$			18.9282i			1.32850i
$204$	−2.53590	−	4.39230i	−0.177548	−	0.307523i
$205$			5.46410i			0.381629i
$206$	−0.607695	−	2.26795i	−0.0423401	−	0.158016i
$207$	10.3397			0.718662
$208$	12.0000	+	6.92820i	0.832050	+	0.480384i
$209$	14.9282			1.03261
$210$	0.732051	+	2.73205i	0.0505163	+	0.188529i
$211$		−	14.7846i		−	1.01781i	−0.860821	−	0.508907i	$-0.830050\pi$
$211$		−	14.7846i		−	1.01781i	0.860821	−	0.508907i	$-0.169950\pi$
$212$	−4.53590	−	7.85641i	−0.311527	−	0.539580i
$213$			1.07180i			0.0734383i
$214$	1.00000	−	0.267949i	0.0683586	−	0.0183166i
$215$	−8.73205			−0.595521
$216$	−8.00000	+	8.00000i	−0.544331	+	0.544331i
$217$	−4.00000			−0.271538
$218$	−4.19615	+	1.12436i	−0.284199	+	0.0761510i
$219$		−	0.392305i		−	0.0265095i
$220$	3.46410	−	2.00000i	0.233550	−	0.134840i
$221$		−	12.0000i		−	0.807207i
$222$	−0.535898	−	2.00000i	−0.0359671	−	0.134231i
$223$	−16.1962			−1.08457			−0.542287	−	0.840193i	$-0.682442\pi$
$223$	−16.1962			−1.08457			−0.542287	+	0.840193i	$0.682442\pi$
$224$	−14.9282	−	4.00000i	−0.997433	−	0.267261i
$225$	−2.46410			−0.164273
$226$	0.339746	+	1.26795i	0.0225996	+	0.0843427i
$227$		−	28.0526i		−	1.86191i	−0.365129	−	0.930957i	$-0.618975\pi$
$227$		−	28.0526i		−	1.86191i	0.365129	−	0.930957i	$-0.381025\pi$
$228$	−9.46410	+	5.46410i	−0.626775	+	0.361869i
$229$		−	4.00000i		−	0.264327i	−0.991228	−	0.132164i	$-0.957808\pi$
$229$		−	4.00000i		−	0.264327i	0.991228	−	0.132164i	$-0.0421925\pi$
$230$	5.73205	−	1.53590i	0.377960	−	0.101274i
$231$	4.00000			0.263181
$232$	−13.8564	+	13.8564i	−0.909718	+	0.909718i
$233$	29.3205			1.92085			0.960425	−	0.278538i	$-0.0898499\pi$
$233$	29.3205			1.92085			0.960425	+	0.278538i	$0.0898499\pi$
$234$	−11.6603	+	3.12436i	−0.762255	+	0.204246i
$235$		−	6.73205i		−	0.439151i
$236$	0.535898	+	0.928203i	0.0348840	+	0.0604209i
$237$			10.9282i			0.709863i
$238$	3.46410	+	12.9282i	0.224544	+	0.838011i
$239$	−20.0000			−1.29369			−0.646846	−	0.762620i	$-0.723912\pi$
$239$	−20.0000			−1.29369			−0.646846	+	0.762620i	$0.723912\pi$
$240$	−1.46410	+	2.53590i	−0.0945074	+	0.163692i
$241$	−4.39230			−0.282933			−0.141467	−	0.989943i	$-0.545182\pi$
$241$	−4.39230			−0.282933			−0.141467	+	0.989943i	$0.545182\pi$
$242$	2.56218	+	9.56218i	0.164703	+	0.614680i
$243$		−	15.2679i		−	0.979439i
$244$	−4.92820	−	8.53590i	−0.315496	−	0.546455i
$245$		−	0.464102i		−	0.0296504i
$246$	−5.46410	+	1.46410i	−0.348378	+	0.0933477i
$247$	−25.8564			−1.64520
$248$	−2.92820	−	2.92820i	−0.185941	−	0.185941i
$249$	3.46410			0.219529
$250$	−1.36603	+	0.366025i	−0.0863950	+	0.0231495i
$251$			11.0718i			0.698846i	0.936965	+	0.349423i	$0.113622\pi$
$251$			11.0718i			0.698846i	−0.936965	+	0.349423i	$0.886378\pi$
$252$	11.6603	−	6.73205i	0.734527	−	0.424079i
$253$		−	8.39230i		−	0.527620i
$254$	4.85641	+	18.1244i	0.304718	+	1.13722i
$255$	2.53590			0.158804
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$	−2.00000			−0.124757			−0.0623783	−	0.998053i	$-0.519869\pi$
$257$	−2.00000			−0.124757			−0.0623783	+	0.998053i	$0.519869\pi$
$258$	−2.33975	−	8.73205i	−0.145666	−	0.543634i
$259$			5.46410i			0.339523i
$260$	−6.00000	+	3.46410i	−0.372104	+	0.214834i
$261$		−	17.0718i		−	1.05672i
$262$	−10.7321	+	2.87564i	−0.663028	+	0.177658i
$263$	5.66025			0.349026			0.174513	−	0.984655i	$-0.444165\pi$
$263$	5.66025			0.349026			0.174513	+	0.984655i	$0.444165\pi$
$264$	2.92820	+	2.92820i	0.180218	+	0.180218i
$265$	4.53590			0.278638
$266$	27.8564	−	7.46410i	1.70799	−	0.457653i
$267$			3.60770i			0.220787i
$268$	−7.26795	−	12.5885i	−0.443961	−	0.768962i
$269$			4.92820i			0.300478i	0.988650	+	0.150239i	$0.0480043\pi$
$269$			4.92820i			0.300478i	−0.988650	+	0.150239i	$0.951996\pi$
$270$	−1.46410	−	5.46410i	−0.0891024	−	0.332535i
$271$	15.3205			0.930655			0.465327	−	0.885139i	$-0.345937\pi$
$271$	15.3205			0.930655			0.465327	+	0.885139i	$0.345937\pi$
$272$	−6.92820	+	12.0000i	−0.420084	+	0.727607i
$273$	−6.92820			−0.419314
$274$	−3.26795	−	12.1962i	−0.197424	−	0.736797i
$275$			2.00000i			0.120605i
$276$	3.07180	+	5.32051i	0.184900	+	0.320257i
$277$			2.00000i			0.120168i	0.998193	+	0.0600842i	$0.0191369\pi$
$277$			2.00000i			0.120168i	−0.998193	+	0.0600842i	$0.980863\pi$
$278$	10.1962	−	2.73205i	0.611525	−	0.163858i
$279$	3.60770			0.215987
$280$	5.46410	−	5.46410i	0.326543	−	0.326543i
$281$	17.4641			1.04182			0.520910	−	0.853611i	$-0.325593\pi$
$281$	17.4641			1.04182			0.520910	+	0.853611i	$0.325593\pi$
$282$	6.73205	−	1.80385i	0.400888	−	0.107418i
$283$			7.66025i			0.455355i	0.973737	+	0.227677i	$0.0731132\pi$
$283$			7.66025i			0.455355i	−0.973737	+	0.227677i	$0.926887\pi$
$284$	2.53590	−	1.46410i	0.150478	−	0.0868784i
$285$		−	5.46410i		−	0.323665i
$286$	2.53590	+	9.46410i	0.149951	+	0.559624i
$287$	14.9282			0.881184
$288$	13.4641	+	3.60770i	0.793380	+	0.212585i
$289$	−5.00000			−0.294118
$290$	−2.53590	−	9.46410i	−0.148913	−	0.555751i
$291$		−	4.67949i		−	0.274317i
$292$	−0.928203	+	0.535898i	−0.0543190	+	0.0313611i
$293$			11.8564i			0.692659i	0.938113	+	0.346329i	$0.112572\pi$
$293$			11.8564i			0.692659i	−0.938113	+	0.346329i	$0.887428\pi$
$294$	0.464102	−	0.124356i	0.0270670	−	0.00725257i
$295$	−0.535898			−0.0312012
$296$	−4.00000	+	4.00000i	−0.232495	+	0.232495i
$297$	−8.00000			−0.464207
$298$	−27.1244	+	7.26795i	−1.57127	+	0.421021i
$299$			14.5359i			0.840633i
$300$	−0.732051	−	1.26795i	−0.0422650	−	0.0732051i
$301$			23.8564i			1.37506i
$302$	3.07180	+	11.4641i	0.176762	+	0.659685i
$303$	−8.00000			−0.459588
$304$	25.8564	+	14.9282i	1.48297	+	0.856191i
$305$	4.92820			0.282188
$306$	−3.12436	−	11.6603i	−0.178608	−	0.666572i
$307$			26.9808i			1.53987i	0.638120	+	0.769937i	$0.279712\pi$
$307$			26.9808i			1.53987i	−0.638120	+	0.769937i	$0.720288\pi$
$308$	−5.46410	−	9.46410i	−0.311346	−	0.539267i
$309$			1.21539i			0.0691411i
$310$	2.00000	−	0.535898i	0.113592	−	0.0304370i
$311$	−3.32051			−0.188289			−0.0941444	−	0.995559i	$-0.530012\pi$
$311$	−3.32051			−0.188289			−0.0941444	+	0.995559i	$0.530012\pi$
$312$	−5.07180	−	5.07180i	−0.287134	−	0.287134i
$313$	−31.8564			−1.80063			−0.900315	−	0.435238i	$-0.856664\pi$
$313$	−31.8564			−1.80063			−0.900315	+	0.435238i	$0.856664\pi$
$314$	23.1244	−	6.19615i	1.30498	−	0.349669i
$315$			6.73205i			0.379308i
$316$	25.8564	−	14.9282i	1.45454	−	0.839777i
$317$			15.4641i			0.868550i	0.900780	+	0.434275i	$0.142995\pi$
$317$			15.4641i			0.868550i	−0.900780	+	0.434275i	$0.857005\pi$
$318$	1.21539	+	4.53590i	0.0681557	+	0.254361i
$319$	−13.8564			−0.775810
$320$	8.00000			0.447214
$321$	−0.535898			−0.0299109
$322$	−4.19615	−	15.6603i	−0.233842	−	0.872712i
$323$		−	25.8564i		−	1.43869i
$324$	−7.73205	+	4.46410i	−0.429558	+	0.248006i
$325$		−	3.46410i		−	0.192154i
$326$	−13.9282	+	3.73205i	−0.771412	+	0.206699i
$327$	2.24871			0.124354
$328$	10.9282	+	10.9282i	0.603409	+	0.603409i
$329$	−18.3923			−1.01400
$330$	−2.00000	+	0.535898i	−0.110096	+	0.0295002i
$331$		−	14.0000i		−	0.769510i	−0.923019	−	0.384755i	$-0.874286\pi$
$331$		−	14.0000i		−	0.769510i	0.923019	−	0.384755i	$-0.125714\pi$
$332$	−4.73205	−	8.19615i	−0.259705	−	0.449822i
$333$		−	4.92820i		−	0.270064i
$334$	−7.39230	−	27.5885i	−0.404489	−	1.50957i
$335$	7.26795			0.397090
$336$	6.92820	+	4.00000i	0.377964	+	0.218218i
$337$	7.85641			0.427966			0.213983	−	0.976837i	$-0.431356\pi$
$337$	7.85641			0.427966			0.213983	+	0.976837i	$0.431356\pi$
$338$	0.366025	+	1.36603i	0.0199092	+	0.0743020i
$339$		−	0.679492i		−	0.0369049i
$340$	−3.46410	−	6.00000i	−0.187867	−	0.325396i
$341$		−	2.92820i		−	0.158571i
$342$	−25.1244	+	6.73205i	−1.35857	+	0.364028i
$343$	17.8564			0.964155
$344$	−17.4641	+	17.4641i	−0.941601	+	0.941601i
$345$	−3.07180			−0.165380
$346$	−2.73205	+	0.732051i	−0.146876	+	0.0393553i
$347$			15.6603i			0.840686i	0.907365	+	0.420343i	$0.138090\pi$
$347$			15.6603i			0.840686i	−0.907365	+	0.420343i	$0.861910\pi$
$348$	8.78461	−	5.07180i	0.470905	−	0.271877i
$349$		−	28.0000i		−	1.49881i	−0.662114	−	0.749403i	$-0.730341\pi$
$349$		−	28.0000i		−	1.49881i	0.662114	−	0.749403i	$-0.269659\pi$
$350$	1.00000	+	3.73205i	0.0534522	+	0.199487i
$351$	13.8564			0.739600
$352$	2.92820	−	10.9282i	0.156074	−	0.582475i
$353$	−0.928203			−0.0494033			−0.0247016	−	0.999695i	$-0.507864\pi$
$353$	−0.928203			−0.0494033			−0.0247016	+	0.999695i	$0.507864\pi$
$354$	−0.143594	−	0.535898i	−0.00763191	−	0.0284827i
$355$			1.46410i			0.0777064i
$356$	8.53590	−	4.92820i	0.452402	−	0.261194i
$357$		−	6.92820i		−	0.366679i
$358$	21.1244	−	5.66025i	1.11646	−	0.299154i
$359$	5.07180			0.267679			0.133840	−	0.991003i	$-0.457269\pi$
$359$	5.07180			0.267679			0.133840	+	0.991003i	$0.457269\pi$
$360$	−4.92820	+	4.92820i	−0.259739	+	0.259739i
$361$	−36.7128			−1.93225
$362$	−21.8564	+	5.85641i	−1.14875	+	0.307806i
$363$		−	5.12436i		−	0.268959i
$364$	9.46410	+	16.3923i	0.496054	+	0.859190i
$365$		−	0.535898i		−	0.0280502i
$366$	1.32051	+	4.92820i	0.0690241	+	0.257601i
$367$	27.1244			1.41588			0.707940	−	0.706273i	$-0.249625\pi$
$367$	27.1244			1.41588			0.707940	+	0.706273i	$0.249625\pi$
$368$	8.39230	−	14.5359i	0.437479	−	0.757736i
$369$	−13.4641			−0.700913
$370$	−0.732051	−	2.73205i	−0.0380575	−	0.142033i
$371$		−	12.3923i		−	0.643376i
$372$	1.07180	+	1.85641i	0.0555701	+	0.0962502i
$373$			29.7128i			1.53847i	0.638965	+	0.769236i	$0.279363\pi$
$373$			29.7128i			1.53847i	−0.638965	+	0.769236i	$0.720637\pi$
$374$	−9.46410	+	2.53590i	−0.489377	+	0.131128i
$375$	0.732051			0.0378029
$376$	−13.4641	−	13.4641i	−0.694358	−	0.694358i
$377$	24.0000			1.23606
$378$	−14.9282	+	4.00000i	−0.767824	+	0.205738i
$379$			12.2487i			0.629174i	0.949229	+	0.314587i	$0.101866\pi$
$379$			12.2487i			0.629174i	−0.949229	+	0.314587i	$0.898134\pi$
$380$	−12.9282	+	7.46410i	−0.663203	+	0.382900i
$381$		−	9.71281i		−	0.497602i
$382$	−7.07180	−	26.3923i	−0.361825	−	1.35035i
$383$	−3.12436			−0.159647			−0.0798236	−	0.996809i	$-0.525436\pi$
$383$	−3.12436			−0.159647			−0.0798236	+	0.996809i	$0.525436\pi$
$384$	2.14359	+	8.00000i	0.109390	+	0.408248i
$385$	5.46410			0.278476
$386$	2.73205	+	10.1962i	0.139058	+	0.518970i
$387$		−	21.5167i		−	1.09375i
$388$	−11.0718	+	6.39230i	−0.562085	+	0.324520i
$389$		−	34.7846i		−	1.76365i	−0.471577	−	0.881825i	$-0.656315\pi$
$389$		−	34.7846i		−	1.76365i	0.471577	−	0.881825i	$-0.343685\pi$
$390$	3.46410	−	0.928203i	0.175412	−	0.0470014i
$391$	−14.5359			−0.735112
$392$	−0.928203	−	0.928203i	−0.0468813	−	0.0468813i
$393$	5.75129			0.290114
$394$	17.1244	−	4.58846i	0.862713	−	0.231163i
$395$			14.9282i			0.751119i
$396$	4.92820	+	8.53590i	0.247652	+	0.428945i
$397$		−	16.2487i		−	0.815499i	−0.913094	−	0.407750i	$-0.866314\pi$
$397$		−	16.2487i		−	0.815499i	0.913094	−	0.407750i	$-0.133686\pi$
$398$	9.46410	+	35.3205i	0.474393	+	1.77046i
$399$	−14.9282			−0.747345
$400$	−2.00000	+	3.46410i	−0.100000	+	0.173205i
$401$	19.8564			0.991582			0.495791	−	0.868442i	$-0.334878\pi$
$401$	19.8564			0.991582			0.495791	+	0.868442i	$0.334878\pi$
$402$	1.94744	+	7.26795i	0.0971295	+	0.362492i
$403$			5.07180i			0.252644i
$404$	10.9282	+	18.9282i	0.543698	+	0.941713i
$405$		−	4.46410i		−	0.221823i
$406$	−25.8564	+	6.92820i	−1.28323	+	0.343841i
$407$	−4.00000			−0.198273
$408$	5.07180	−	5.07180i	0.251091	−	0.251091i
$409$	23.3205			1.15312			0.576562	−	0.817053i	$-0.304394\pi$
$409$	23.3205			1.15312			0.576562	+	0.817053i	$0.304394\pi$
$410$	−7.46410	+	2.00000i	−0.368626	+	0.0987730i
$411$			6.53590i			0.322392i
$412$	2.87564	−	1.66025i	0.141673	−	0.0817948i
$413$			1.46410i			0.0720437i
$414$	3.78461	+	14.1244i	0.186003	+	0.694174i
$415$	4.73205			0.232287
$416$	−5.07180	+	18.9282i	−0.248665	+	0.928032i
$417$	−5.46410			−0.267578
$418$	5.46410	+	20.3923i	0.267258	+	0.997420i
$419$		−	2.39230i		−	0.116872i	−0.998291	−	0.0584359i	$-0.981389\pi$
$419$		−	2.39230i		−	0.116872i	0.998291	−	0.0584359i	$-0.0186113\pi$
$420$	−3.46410	+	2.00000i	−0.169031	+	0.0975900i
$421$			27.8564i			1.35764i	0.734306	+	0.678819i	$0.237508\pi$
$421$			27.8564i			1.35764i	−0.734306	+	0.678819i	$0.762492\pi$
$422$	20.1962	−	5.41154i	0.983133	−	0.263430i
$423$	16.5885			0.806558
$424$	9.07180	−	9.07180i	0.440565	−	0.440565i
$425$	3.46410			0.168034
$426$	−1.46410	+	0.392305i	−0.0709360	+	0.0190072i
$427$		−	13.4641i		−	0.651574i
$428$	0.732051	+	1.26795i	0.0353850	+	0.0612886i
$429$		−	5.07180i		−	0.244869i
$430$	−3.19615	−	11.9282i	−0.154132	−	0.575229i
$431$	−14.5359			−0.700170			−0.350085	−	0.936718i	$-0.613847\pi$
$431$	−14.5359			−0.700170			−0.350085	+	0.936718i	$0.613847\pi$
$432$	−13.8564	−	8.00000i	−0.666667	−	0.384900i
$433$	−12.5359			−0.602437			−0.301218	−	0.953555i	$-0.597393\pi$
$433$	−12.5359			−0.602437			−0.301218	+	0.953555i	$0.597393\pi$
$434$	−1.46410	−	5.46410i	−0.0702791	−	0.262285i
$435$			5.07180i			0.243174i
$436$	−3.07180	−	5.32051i	−0.147112	−	0.254806i
$437$			31.3205i			1.49826i
$438$	0.535898	−	0.143594i	0.0256062	−	0.00686116i
$439$	−0.784610			−0.0374474			−0.0187237	−	0.999825i	$-0.505960\pi$
$439$	−0.784610			−0.0374474			−0.0187237	+	0.999825i	$0.505960\pi$
$440$	4.00000	+	4.00000i	0.190693	+	0.190693i
$441$	1.14359			0.0544568
$442$	16.3923	−	4.39230i	0.779702	−	0.208921i
$443$		−	30.9808i		−	1.47194i	−0.677014	−	0.735970i	$-0.736726\pi$
$443$		−	30.9808i		−	1.47194i	0.677014	−	0.735970i	$-0.263274\pi$
$444$	2.53590	−	1.46410i	0.120348	−	0.0694832i
$445$			4.92820i			0.233619i
$446$	−5.92820	−	22.1244i	−0.280709	−	1.04762i
$447$	14.5359			0.687524
$448$		−	21.8564i		−	1.03262i
$449$	11.3205			0.534248			0.267124	−	0.963662i	$-0.413927\pi$
$449$	11.3205			0.534248			0.267124	+	0.963662i	$0.413927\pi$
$450$	−0.901924	−	3.36603i	−0.0425171	−	0.158676i
$451$			10.9282i			0.514589i
$452$	−1.60770	+	0.928203i	−0.0756196	+	0.0436590i
$453$		−	6.14359i		−	0.288651i
$454$	38.3205	−	10.2679i	1.79847	−	0.481899i
$455$	−9.46410			−0.443684
$456$	−10.9282	−	10.9282i	−0.511760	−	0.511760i
$457$	14.7846			0.691595			0.345797	−	0.938309i	$-0.387608\pi$
$457$	14.7846			0.691595			0.345797	+	0.938309i	$0.387608\pi$
$458$	5.46410	−	1.46410i	0.255321	−	0.0684130i
$459$			13.8564i			0.646762i
$460$	4.19615	+	7.26795i	0.195647	+	0.338870i
$461$			2.92820i			0.136380i	0.997672	+	0.0681900i	$0.0217224\pi$
$461$			2.92820i			0.136380i	−0.997672	+	0.0681900i	$0.978278\pi$
$462$	1.46410	+	5.46410i	0.0681162	+	0.254213i
$463$	−14.7321			−0.684656			−0.342328	−	0.939580i	$-0.611215\pi$
$463$	−14.7321			−0.684656			−0.342328	+	0.939580i	$0.611215\pi$
$464$	−24.0000	−	13.8564i	−1.11417	−	0.643268i
$465$	−1.07180			−0.0497034
$466$	10.7321	+	40.0526i	0.497153	+	1.85540i
$467$		−	8.33975i		−	0.385917i	−0.981207	−	0.192959i	$-0.938192\pi$
$467$		−	8.33975i		−	0.385917i	0.981207	−	0.192959i	$-0.0618083\pi$
$468$	−8.53590	−	14.7846i	−0.394572	−	0.683419i
$469$		−	19.8564i		−	0.916884i
$470$	9.19615	−	2.46410i	0.424187	−	0.113661i
$471$	−12.3923			−0.571007
$472$	−1.07180	+	1.07180i	−0.0493334	+	0.0493334i
$473$	−17.4641			−0.803000
$474$	−14.9282	+	4.00000i	−0.685675	+	0.183726i
$475$		−	7.46410i		−	0.342476i
$476$	−16.3923	+	9.46410i	−0.751340	+	0.433786i
$477$			11.1769i			0.511756i
$478$	−7.32051	−	27.3205i	−0.334832	−	1.24961i
$479$	−21.8564			−0.998645			−0.499322	−	0.866416i	$-0.666418\pi$
$479$	−21.8564			−0.998645			−0.499322	+	0.866416i	$0.666418\pi$
$480$	−4.00000	−	1.07180i	−0.182574	−	0.0489206i
$481$	6.92820			0.315899
$482$	−1.60770	−	6.00000i	−0.0732285	−	0.273293i
$483$			8.39230i			0.381863i
$484$	−12.1244	+	7.00000i	−0.551107	+	0.318182i
$485$		−	6.39230i		−	0.290260i
$486$	20.8564	−	5.58846i	0.946066	−	0.253498i
$487$	−24.5885			−1.11421			−0.557105	−	0.830442i	$-0.688088\pi$
$487$	−24.5885			−1.11421			−0.557105	+	0.830442i	$0.688088\pi$
$488$	9.85641	−	9.85641i	0.446179	−	0.446179i
$489$	7.46410			0.337538
$490$	0.633975	−	0.169873i	0.0286401	−	0.00767408i
$491$		−	3.07180i		−	0.138628i	−0.997595	−	0.0693141i	$-0.977919\pi$
$491$		−	3.07180i		−	0.138628i	0.997595	−	0.0693141i	$-0.0220811\pi$
$492$	−4.00000	−	6.92820i	−0.180334	−	0.312348i
$493$			24.0000i			1.08091i
$494$	−9.46410	−	35.3205i	−0.425810	−	1.58914i
$495$	−4.92820			−0.221506
$496$	2.92820	−	5.07180i	0.131480	−	0.227730i
$497$	4.00000			0.179425
$498$	1.26795	+	4.73205i	0.0568182	+	0.212048i
$499$			24.5359i			1.09838i	0.835698	+	0.549189i	$0.185063\pi$
$499$			24.5359i			1.09838i	−0.835698	+	0.549189i	$0.814937\pi$
$500$	−1.00000	−	1.73205i	−0.0447214	−	0.0774597i
$501$			14.7846i			0.660528i
$502$	−15.1244	+	4.05256i	−0.675033	+	0.180875i
$503$	−17.6603			−0.787432			−0.393716	−	0.919232i	$-0.628811\pi$
$503$	−17.6603			−0.787432			−0.393716	+	0.919232i	$0.628811\pi$
$504$	13.4641	+	13.4641i	0.599739	+	0.599739i
$505$	−10.9282			−0.486299
$506$	11.4641	−	3.07180i	0.509641	−	0.136558i
$507$		−	0.732051i		−	0.0325115i
$508$	−22.9808	+	13.2679i	−1.01961	+	0.588670i
$509$			25.8564i			1.14607i	0.819533	+	0.573033i	$0.194233\pi$
$509$			25.8564i			1.14607i	−0.819533	+	0.573033i	$0.805767\pi$
$510$	0.928203	+	3.46410i	0.0411015	+	0.153393i
$511$	−1.46410			−0.0647680
$512$	16.0000	−	16.0000i	0.707107	−	0.707107i
$513$	29.8564			1.31819
$514$	−0.732051	−	2.73205i	−0.0322894	−	0.120506i
$515$			1.66025i			0.0731595i
$516$	11.0718	−	6.39230i	0.487409	−	0.281406i
$517$		−	13.4641i		−	0.592151i
$518$	−7.46410	+	2.00000i	−0.327954	+	0.0878750i
$519$	1.46410			0.0642669
$520$	−6.92820	−	6.92820i	−0.303822	−	0.303822i
$521$	−16.1436			−0.707264			−0.353632	−	0.935385i	$-0.615053\pi$
$521$	−16.1436			−0.707264			−0.353632	+	0.935385i	$0.615053\pi$
$522$	23.3205	−	6.24871i	1.02071	−	0.273499i
$523$		−	22.1962i		−	0.970570i	−0.874356	−	0.485285i	$-0.838716\pi$
$523$		−	22.1962i		−	0.970570i	0.874356	−	0.485285i	$-0.161284\pi$
$524$	−7.85641	−	13.6077i	−0.343209	−	0.594455i
$525$		−	2.00000i		−	0.0872872i
$526$	2.07180	+	7.73205i	0.0903346	+	0.337133i
$527$	−5.07180			−0.220931
$528$	−2.92820	+	5.07180i	−0.127434	+	0.220722i
$529$	−5.39230			−0.234448
$530$	1.66025	+	6.19615i	0.0721168	+	0.269144i
$531$		−	1.32051i		−	0.0573052i
$532$	20.3923	+	35.3205i	0.884119	+	1.53134i
$533$		−	18.9282i		−	0.819871i
$534$	−4.92820	+	1.32051i	−0.213264	+	0.0571440i
$535$	−0.732051			−0.0316493
$536$	14.5359	−	14.5359i	0.627855	−	0.627855i
$537$	−11.3205			−0.488516
$538$	−6.73205	+	1.80385i	−0.290239	+	0.0777694i
$539$		−	0.928203i		−	0.0399805i
$540$	6.92820	−	4.00000i	0.298142	−	0.172133i
$541$		−	13.0718i		−	0.562000i	−0.959708	−	0.281000i	$-0.909334\pi$
$541$		−	13.0718i		−	0.562000i	0.959708	−	0.281000i	$-0.0906662\pi$
$542$	5.60770	+	20.9282i	0.240871	+	0.898943i
$543$	11.7128			0.502645
$544$	−18.9282	−	5.07180i	−0.811540	−	0.217451i
$545$	3.07180			0.131581
$546$	−2.53590	−	9.46410i	−0.108526	−	0.405026i
$547$			36.7321i			1.57055i	0.619148	+	0.785275i	$0.287478\pi$
$547$			36.7321i			1.57055i	−0.619148	+	0.785275i	$0.712522\pi$
$548$	15.4641	−	8.92820i	0.660594	−	0.381394i
$549$			12.1436i			0.518276i
$550$	−2.73205	+	0.732051i	−0.116495	+	0.0312148i
$551$	51.7128			2.20304
$552$	−6.14359	+	6.14359i	−0.261489	+	0.261489i
$553$	40.7846			1.73434
$554$	−2.73205	+	0.732051i	−0.116074	+	0.0311019i
$555$			1.46410i			0.0621477i
$556$	7.46410	+	12.9282i	0.316548	+	0.548278i
$557$		−	26.7846i		−	1.13490i	−0.823408	−	0.567450i	$-0.807930\pi$
$557$		−	26.7846i		−	1.13490i	0.823408	−	0.567450i	$-0.192070\pi$
$558$	1.32051	+	4.92820i	0.0559016	+	0.208627i
$559$	30.2487			1.27938
$560$	9.46410	+	5.46410i	0.399931	+	0.230900i
$561$	5.07180			0.214131
$562$	6.39230	+	23.8564i	0.269643	+	1.00632i
$563$			16.0526i			0.676535i	0.941050	+	0.338267i	$0.109841\pi$
$563$			16.0526i			0.676535i	−0.941050	+	0.338267i	$0.890159\pi$
$564$	4.92820	+	8.53590i	0.207515	+	0.359426i
$565$		−	0.928203i		−	0.0390498i
$566$	−10.4641	+	2.80385i	−0.439839	+	0.117855i
$567$	−12.1962			−0.512190
$568$	2.92820	+	2.92820i	0.122865	+	0.122865i
$569$	−6.53590			−0.273999			−0.137000	−	0.990571i	$-0.543746\pi$
$569$	−6.53590			−0.273999			−0.137000	+	0.990571i	$0.543746\pi$
$570$	7.46410	−	2.00000i	0.312637	−	0.0837708i
$571$		−	34.7846i		−	1.45569i	−0.685741	−	0.727845i	$-0.740522\pi$
$571$		−	34.7846i		−	1.45569i	0.685741	−	0.727845i	$-0.259478\pi$
$572$	−12.0000	+	6.92820i	−0.501745	+	0.289683i
$573$			14.1436i			0.590857i
$574$	5.46410	+	20.3923i	0.228067	+	0.851158i
$575$	−4.19615			−0.174992
$576$			19.7128i			0.821367i
$577$	−43.5692			−1.81381			−0.906905	−	0.421335i	$-0.861562\pi$
$577$	−43.5692			−1.81381			−0.906905	+	0.421335i	$0.861562\pi$
$578$	−1.83013	−	6.83013i	−0.0761232	−	0.284096i
$579$		−	5.46410i		−	0.227080i
$580$	12.0000	−	6.92820i	0.498273	−	0.287678i
$581$		−	12.9282i		−	0.536352i
$582$	6.39230	−	1.71281i	0.264970	−	0.0709984i
$583$	9.07180			0.375715
$584$	−1.07180	−	1.07180i	−0.0443513	−	0.0443513i
$585$	8.53590			0.352916
$586$	−16.1962	+	4.33975i	−0.669057	+	0.179273i
$587$		−	14.1962i		−	0.585938i	−0.956122	−	0.292969i	$-0.905357\pi$
$587$		−	14.1962i		−	0.585938i	0.956122	−	0.292969i	$-0.0946433\pi$
$588$	0.339746	+	0.588457i	0.0140109	+	0.0242676i
$589$			10.9282i			0.450289i
$590$	−0.196152	−	0.732051i	−0.00807547	−	0.0301381i
$591$	−9.17691			−0.377488
$592$	−6.92820	−	4.00000i	−0.284747	−	0.164399i
$593$	−36.6410			−1.50467			−0.752333	−	0.658783i	$-0.771072\pi$
$593$	−36.6410			−1.50467			−0.752333	+	0.658783i	$0.771072\pi$
$594$	−2.92820	−	10.9282i	−0.120146	−	0.448390i
$595$		−	9.46410i		−	0.387990i
$596$	−19.8564	−	34.3923i	−0.813350	−	1.40876i
$597$		−	18.9282i		−	0.774680i
$598$	−19.8564	+	5.32051i	−0.811989	+	0.217572i
$599$	34.6410			1.41539			0.707697	−	0.706516i	$-0.249734\pi$
$599$	34.6410			1.41539			0.707697	+	0.706516i	$0.249734\pi$
$600$	1.46410	−	1.46410i	0.0597717	−	0.0597717i
$601$	25.4641			1.03870			0.519351	−	0.854561i	$-0.326174\pi$
$601$	25.4641			1.03870			0.519351	+	0.854561i	$0.326174\pi$
$602$	−32.5885	+	8.73205i	−1.32821	+	0.355892i
$603$			17.9090i			0.729309i
$604$	−14.5359	+	8.39230i	−0.591457	+	0.341478i
$605$		−	7.00000i		−	0.284590i
$606$	−2.92820	−	10.9282i	−0.118950	−	0.443928i
$607$	−20.9808			−0.851583			−0.425791	−	0.904821i	$-0.640004\pi$
$607$	−20.9808			−0.851583			−0.425791	+	0.904821i	$0.640004\pi$
$608$	−10.9282	+	40.7846i	−0.443197	+	1.65403i
$609$	13.8564			0.561490
$610$	1.80385	+	6.73205i	0.0730357	+	0.272573i
$611$			23.3205i			0.943447i
$612$	14.7846	−	8.53590i	0.597632	−	0.345043i
$613$			5.60770i			0.226493i	0.993567	+	0.113246i	$0.0361249\pi$
$613$			5.60770i			0.226493i	−0.993567	+	0.113246i	$0.963875\pi$
$614$	−36.8564	+	9.87564i	−1.48740	+	0.398549i
$615$	4.00000			0.161296
$616$	10.9282	−	10.9282i	0.440310	−	0.440310i
$617$	−27.4641			−1.10566			−0.552832	−	0.833293i	$-0.686453\pi$
$617$	−27.4641			−1.10566			−0.552832	+	0.833293i	$0.686453\pi$
$618$	−1.66025	+	0.444864i	−0.0667852	+	0.0178950i
$619$		−	33.3205i		−	1.33926i	−0.742693	−	0.669632i	$-0.766452\pi$
$619$		−	33.3205i		−	1.33926i	0.742693	−	0.669632i	$-0.233548\pi$
$620$	1.46410	+	2.53590i	0.0587997	+	0.101844i
$621$		−	16.7846i		−	0.673543i
$622$	−1.21539	−	4.53590i	−0.0487327	−	0.181873i
$623$	13.4641			0.539428
$624$	5.07180	−	8.78461i	0.203034	−	0.351666i
$625$	1.00000			0.0400000
$626$	−11.6603	−	43.5167i	−0.466037	−	1.73928i
$627$		−	10.9282i		−	0.436430i
$628$	16.9282	+	29.3205i	0.675509	+	1.17002i
$629$			6.92820i			0.276246i
$630$	−9.19615	+	2.46410i	−0.366383	+	0.0981722i
$631$	11.3205			0.450662			0.225331	−	0.974282i	$-0.427654\pi$
$631$	11.3205			0.450662			0.225331	+	0.974282i	$0.427654\pi$
$632$	29.8564	+	29.8564i	1.18762	+	1.18762i
$633$	−10.8231			−0.430179
$634$	−21.1244	+	5.66025i	−0.838955	+	0.224797i
$635$		−	13.2679i		−	0.526523i
$636$	−5.75129	+	3.32051i	−0.228053	+	0.131667i
$637$			1.60770i			0.0636992i
$638$	−5.07180	−	18.9282i	−0.200794	−	0.749375i
$639$	−3.60770			−0.142718
$640$	2.92820	+	10.9282i	0.115747	+	0.431975i
$641$	−20.3923			−0.805448			−0.402724	−	0.915322i	$-0.631936\pi$
$641$	−20.3923			−0.805448			−0.402724	+	0.915322i	$0.631936\pi$
$642$	−0.196152	−	0.732051i	−0.00774152	−	0.0288917i
$643$			14.8756i			0.586638i	0.956015	+	0.293319i	$0.0947598\pi$
$643$			14.8756i			0.586638i	−0.956015	+	0.293319i	$0.905240\pi$
$644$	19.8564	−	11.4641i	0.782452	−	0.451749i
$645$			6.39230i			0.251697i
$646$	35.3205	−	9.46410i	1.38967	−	0.372360i
$647$	13.2679			0.521617			0.260808	−	0.965391i	$-0.416011\pi$
$647$	13.2679			0.521617			0.260808	+	0.965391i	$0.416011\pi$
$648$	−8.92820	−	8.92820i	−0.350733	−	0.350733i
$649$	−1.07180			−0.0420717
$650$	4.73205	−	1.26795i	0.185606	−	0.0497331i
$651$			2.92820i			0.114765i
$652$	−10.1962	−	17.6603i	−0.399312	−	0.691629i
$653$		−	36.2487i		−	1.41852i	−0.704946	−	0.709261i	$-0.749029\pi$
$653$		−	36.2487i		−	1.41852i	0.704946	−	0.709261i	$-0.250971\pi$
$654$	0.823085	+	3.07180i	0.0321852	+	0.120117i
$655$	7.85641			0.306975
$656$	−10.9282	+	18.9282i	−0.426675	+	0.739022i
$657$	1.32051			0.0515179
$658$	−6.73205	−	25.1244i	−0.262443	−	0.979449i
$659$			17.3205i			0.674711i	0.941377	+	0.337356i	$0.109532\pi$
$659$			17.3205i			0.674711i	−0.941377	+	0.337356i	$0.890468\pi$
$660$	−1.46410	−	2.53590i	−0.0569901	−	0.0987097i
$661$		−	35.8564i		−	1.39465i	−0.716754	−	0.697326i	$-0.754373\pi$
$661$		−	35.8564i		−	1.39465i	0.716754	−	0.697326i	$-0.245627\pi$
$662$	19.1244	−	5.12436i	0.743289	−	0.199164i
$663$	−8.78461			−0.341166
$664$	9.46410	−	9.46410i	0.367278	−	0.367278i
$665$	−20.3923			−0.790780
$666$	6.73205	−	1.80385i	0.260862	−	0.0698977i
$667$		−	29.0718i		−	1.12566i
$668$	34.9808	−	20.1962i	1.35345	−	0.781413i
$669$			11.8564i			0.458395i
$670$	2.66025	+	9.92820i	0.102775	+	0.383560i
$671$	9.85641			0.380502
$672$	−2.92820	+	10.9282i	−0.112958	+	0.421565i
$673$	19.4641			0.750286			0.375143	−	0.926967i	$-0.377594\pi$
$673$	19.4641			0.750286			0.375143	+	0.926967i	$0.377594\pi$
$674$	2.87564	+	10.7321i	0.110766	+	0.413383i
$675$			4.00000i			0.153960i
$676$	−1.73205	+	1.00000i	−0.0666173	+	0.0384615i
$677$			38.3923i			1.47554i	0.675054	+	0.737768i	$0.264120\pi$
$677$			38.3923i			1.47554i	−0.675054	+	0.737768i	$0.735880\pi$
$678$	0.928203	−	0.248711i	0.0356474	−	0.00955170i
$679$	−17.4641			−0.670211
$680$	6.92820	−	6.92820i	0.265684	−	0.265684i
$681$	−20.5359			−0.786937
$682$	4.00000	−	1.07180i	0.153168	−	0.0410412i
$683$			34.9808i			1.33850i	0.743037	+	0.669251i	$0.233385\pi$
$683$			34.9808i			1.33850i	−0.743037	+	0.669251i	$0.766615\pi$
$684$	−18.3923	−	31.8564i	−0.703247	−	1.21806i
$685$			8.92820i			0.341129i
$686$	6.53590	+	24.3923i	0.249542	+	0.931303i
$687$	−2.92820			−0.111718
$688$	−30.2487	−	17.4641i	−1.15322	−	0.665813i
$689$	−15.7128			−0.598610
$690$	−1.12436	−	4.19615i	−0.0428035	−	0.159745i
$691$			18.0000i			0.684752i	0.939563	+	0.342376i	$0.111232\pi$
$691$			18.0000i			0.684752i	−0.939563	+	0.342376i	$0.888768\pi$
$692$	−2.00000	−	3.46410i	−0.0760286	−	0.131685i
$693$			13.4641i			0.511459i
$694$	−21.3923	+	5.73205i	−0.812041	+	0.217586i
$695$	−7.46410			−0.283130
$696$	10.1436	+	10.1436i	0.384492	+	0.384492i
$697$	18.9282			0.716957
$698$	38.2487	−	10.2487i	1.44774	−	0.387919i
$699$		−	21.4641i		−	0.811847i
$700$	−4.73205	+	2.73205i	−0.178855	+	0.103262i
$701$			32.9282i			1.24368i	0.783144	+	0.621841i	$0.213615\pi$
$701$			32.9282i			1.24368i	−0.783144	+	0.621841i	$0.786385\pi$
$702$	5.07180	+	18.9282i	0.191423	+	0.714399i
$703$	14.9282			0.563028
$704$	16.0000			0.603023
$705$	−4.92820			−0.185607
$706$	−0.339746	−	1.26795i	−0.0127865	−	0.0477199i
$707$			29.8564i			1.12287i
$708$	0.679492	−	0.392305i	0.0255369	−	0.0147437i
$709$			28.7846i			1.08103i	0.841335	+	0.540514i	$0.181770\pi$
$709$			28.7846i			1.08103i	−0.841335	+	0.540514i	$0.818230\pi$
$710$	−2.00000	+	0.535898i	−0.0750587	+	0.0201119i
$711$	−36.7846			−1.37953
$712$	9.85641	+	9.85641i	0.369384	+	0.369384i
$713$	6.14359			0.230079
$714$	9.46410	−	2.53590i	0.354185	−	0.0949036i
$715$		−	6.92820i		−	0.259100i
$716$	15.4641	+	26.7846i	0.577921	+	1.00099i
$717$			14.6410i			0.546779i
$718$	1.85641	+	6.92820i	0.0692805	+	0.258558i
$719$	25.8564			0.964281			0.482141	−	0.876094i	$-0.339859\pi$
$719$	25.8564			0.964281			0.482141	+	0.876094i	$0.339859\pi$
$720$	−8.53590	−	4.92820i	−0.318114	−	0.183663i
$721$	4.53590			0.168926
$722$	−13.4378	−	50.1506i	−0.500104	−	1.86641i
$723$			3.21539i			0.119582i
$724$	−16.0000	−	27.7128i	−0.594635	−	1.02994i
$725$			6.92820i			0.257307i
$726$	7.00000	−	1.87564i	0.259794	−	0.0696117i
$727$	14.0526			0.521181			0.260590	−	0.965449i	$-0.416083\pi$
$727$	14.0526			0.521181			0.260590	+	0.965449i	$0.416083\pi$
$728$	−18.9282	+	18.9282i	−0.701526	+	0.701526i
$729$	2.21539			0.0820515
$730$	0.732051	−	0.196152i	0.0270944	−	0.00725993i
$731$			30.2487i			1.11879i
$732$	−6.24871	+	3.60770i	−0.230959	+	0.133344i
$733$		−	48.9282i		−	1.80720i	−0.428373	−	0.903602i	$-0.640913\pi$
$733$		−	48.9282i		−	1.80720i	0.428373	−	0.903602i	$-0.359087\pi$
$734$	9.92820	+	37.0526i	0.366457	+	1.36763i
$735$	−0.339746			−0.0125317
$736$	22.9282	+	6.14359i	0.845145	+	0.226456i
$737$	14.5359			0.535437
$738$	−4.92820	−	18.3923i	−0.181410	−	0.677030i
$739$		−	5.32051i		−	0.195718i	−0.995200	−	0.0978590i	$-0.968801\pi$
$739$		−	5.32051i		−	0.195718i	0.995200	−	0.0978590i	$-0.0311994\pi$
$740$	3.46410	−	2.00000i	0.127343	−	0.0735215i
$741$			18.9282i			0.695345i
$742$	16.9282	−	4.53590i	0.621454	−	0.166518i
$743$	−40.9808			−1.50344			−0.751719	−	0.659483i	$-0.770775\pi$
$743$	−40.9808			−1.50344			−0.751719	+	0.659483i	$0.770775\pi$
$744$	−2.14359	+	2.14359i	−0.0785880	+	0.0785880i
$745$	19.8564			0.727482
$746$	−40.5885	+	10.8756i	−1.48605	+	0.398186i
$747$			11.6603i			0.426626i
$748$	−6.92820	−	12.0000i	−0.253320	−	0.438763i
$749$			2.00000i			0.0730784i
$750$	0.267949	+	1.00000i	0.00978412	+	0.0365148i
$751$	−22.2487			−0.811867			−0.405934	−	0.913903i	$-0.633054\pi$
$751$	−22.2487			−0.811867			−0.405934	+	0.913903i	$0.633054\pi$
$752$	13.4641	−	23.3205i	0.490985	−	0.850411i
$753$	8.10512			0.295367
$754$	8.78461	+	32.7846i	0.319917	+	1.19395i
$755$		−	8.39230i		−	0.305427i
$756$	−10.9282	−	18.9282i	−0.397455	−	0.688412i
$757$		−	32.9282i		−	1.19680i	−0.801199	−	0.598398i	$-0.795804\pi$
$757$		−	32.9282i		−	1.19680i	0.801199	−	0.598398i	$-0.204196\pi$
$758$	−16.7321	+	4.48334i	−0.607735	+	0.162842i
$759$	−6.14359			−0.222998
$760$	−14.9282	−	14.9282i	−0.541503	−	0.541503i
$761$	49.7128			1.80209			0.901044	−	0.433728i	$-0.142802\pi$
$761$	49.7128			1.80209			0.901044	+	0.433728i	$0.142802\pi$
$762$	13.2679	−	3.55514i	0.480647	−	0.128789i
$763$		−	8.39230i		−	0.303822i
$764$	33.4641	−	19.3205i	1.21069	−	0.698991i
$765$			8.53590i			0.308616i
$766$	−1.14359	−	4.26795i	−0.0413197	−	0.154207i
$767$	1.85641			0.0670310
$768$	−10.1436	+	5.85641i	−0.366025	+	0.211325i
$769$	−0.928203			−0.0334719			−0.0167359	−	0.999860i	$-0.505327\pi$
$769$	−0.928203			−0.0334719			−0.0167359	+	0.999860i	$0.505327\pi$
$770$	2.00000	+	7.46410i	0.0720750	+	0.268988i
$771$			1.46410i			0.0527283i
$772$	−12.9282	+	7.46410i	−0.465296	+	0.268639i
$773$		−	1.60770i		−	0.0578248i	−0.999582	−	0.0289124i	$-0.990796\pi$
$773$		−	1.60770i		−	0.0578248i	0.999582	−	0.0289124i	$-0.00920438\pi$
$774$	29.3923	−	7.87564i	1.05648	−	0.283084i
$775$	−1.46410			−0.0525921
$776$	−12.7846	−	12.7846i	−0.458941	−	0.458941i
$777$	4.00000			0.143499
$778$	47.5167	−	12.7321i	1.70355	−	0.456466i
$779$		−	40.7846i		−	1.46126i
$780$	2.53590	+	4.39230i	0.0907997	+	0.157270i
$781$			2.92820i			0.104779i
$782$	−5.32051	−	19.8564i	−0.190261	−	0.710064i
$783$	−27.7128			−0.990375
$784$	0.928203	−	1.60770i	0.0331501	−	0.0574177i
$785$	−16.9282			−0.604193
$786$	2.10512	+	7.85641i	0.0750871	+	0.280229i
$787$		−	14.5885i		−	0.520022i	−0.965606	−	0.260011i	$-0.916274\pi$
$787$		−	14.5885i		−	0.520022i	0.965606	−	0.260011i	$-0.0837262\pi$
$788$	12.5359	+	21.7128i	0.446573	+	0.773487i
$789$		−	4.14359i		−	0.147516i
$790$	−20.3923	+	5.46410i	−0.725526	+	0.194404i
$791$	−2.53590			−0.0901662
$792$	−9.85641	+	9.85641i	−0.350232	+	0.350232i
$793$	−17.0718			−0.606237
$794$	22.1962	−	5.94744i	0.787712	−	0.211067i
$795$		−	3.32051i		−	0.117766i
$796$	−44.7846	+	25.8564i	−1.58735	+	0.916456i
$797$		−	26.1051i		−	0.924691i	−0.886700	−	0.462345i	$-0.847008\pi$
$797$		−	26.1051i		−	0.924691i	0.886700	−	0.462345i	$-0.152992\pi$
$798$	−5.46410	−	20.3923i	−0.193427	−	0.721880i
$799$	−23.3205			−0.825020
$800$	−5.46410	−	1.46410i	−0.193185	−	0.0517638i
$801$	−12.1436			−0.429073
$802$	7.26795	+	27.1244i	0.256640	+	0.957794i
$803$		−	1.07180i		−	0.0378229i
$804$	−9.21539	+	5.32051i	−0.325002	+	0.187640i
$805$			11.4641i			0.404056i
$806$	−6.92820	+	1.85641i	−0.244036	+	0.0653891i
$807$	3.60770			0.126997
$808$	−21.8564	+	21.8564i	−0.768906	+	0.768906i
$809$	−3.85641			−0.135584			−0.0677920	−	0.997699i	$-0.521595\pi$
$809$	−3.85641			−0.135584			−0.0677920	+	0.997699i	$0.521595\pi$
$810$	6.09808	−	1.63397i	0.214265	−	0.0574120i
$811$		−	15.0718i		−	0.529242i	−0.964352	−	0.264621i	$-0.914753\pi$
$811$		−	15.0718i		−	0.529242i	0.964352	−	0.264621i	$-0.0852469\pi$
$812$	−18.9282	−	32.7846i	−0.664250	−	1.15051i
$813$		−	11.2154i		−	0.393341i
$814$	−1.46410	−	5.46410i	−0.0513167	−	0.191517i
$815$	10.1962			0.357156
$816$	8.78461	+	5.07180i	0.307523	+	0.177548i
$817$	65.1769			2.28025
$818$	8.53590	+	31.8564i	0.298451	+	1.11383i
$819$		−	23.3205i		−	0.814885i
$820$	−5.46410	−	9.46410i	−0.190815	−	0.330501i
$821$		−	6.78461i		−	0.236785i	−0.992967	−	0.118392i	$-0.962226\pi$
$821$		−	6.78461i		−	0.236785i	0.992967	−	0.118392i	$-0.0377740\pi$
$822$	−8.92820	+	2.39230i	−0.311407	+	0.0834412i
$823$	15.1244			0.527202			0.263601	−	0.964632i	$-0.415090\pi$
$823$	15.1244			0.527202			0.263601	+	0.964632i	$0.415090\pi$
$824$	3.32051	+	3.32051i	0.115675	+	0.115675i
$825$	1.46410			0.0509735
$826$	−2.00000	+	0.535898i	−0.0695889	+	0.0186463i
$827$		−	1.12436i		−	0.0390977i	−0.999809	−	0.0195488i	$-0.993777\pi$
$827$		−	1.12436i		−	0.0390977i	0.999809	−	0.0195488i	$-0.00622298\pi$
$828$	−17.9090	+	10.3397i	−0.622380	+	0.359331i
$829$			15.0718i			0.523465i	0.965140	+	0.261733i	$0.0842938\pi$
$829$			15.0718i			0.523465i	−0.965140	+	0.261733i	$0.915706\pi$
$830$	1.73205	+	6.46410i	0.0601204	+	0.224372i
$831$	1.46410			0.0507891
$832$	−27.7128			−0.960769
$833$	−1.60770			−0.0557033
$834$	−2.00000	−	7.46410i	−0.0692543	−	0.258461i
$835$			20.1962i			0.698917i
$836$	−25.8564	+	14.9282i	−0.894263	+	0.516303i
$837$		−	5.85641i		−	0.202427i
$838$	3.26795	−	0.875644i	0.112889	−	0.0302486i
$839$	−16.7846			−0.579469			−0.289735	−	0.957107i	$-0.593567\pi$
$839$	−16.7846			−0.579469			−0.289735	+	0.957107i	$0.593567\pi$
$840$	−4.00000	−	4.00000i	−0.138013	−	0.138013i
$841$	−19.0000			−0.655172
$842$	−38.0526	+	10.1962i	−1.31138	+	0.351383i
$843$		−	12.7846i		−	0.440325i
$844$	14.7846	+	25.6077i	0.508907	+	0.881453i
$845$		−	1.00000i		−	0.0344010i
$846$	6.07180	+	22.6603i	0.208753	+	0.779076i
$847$	−19.1244			−0.657121
$848$	15.7128	+	9.07180i	0.539580	+	0.311527i
$849$	5.60770			0.192456
$850$	1.26795	+	4.73205i	0.0434903	+	0.162308i
$851$		−	8.39230i		−	0.287685i
$852$	−1.07180	−	1.85641i	−0.0367192	−	0.0635994i
$853$		−	42.3923i		−	1.45148i	−0.687967	−	0.725742i	$-0.741496\pi$
$853$		−	42.3923i		−	1.45148i	0.687967	−	0.725742i	$-0.258504\pi$
$854$	18.3923	−	4.92820i	0.629372	−	0.168640i
$855$	18.3923			0.629004
$856$	−1.46410	+	1.46410i	−0.0500420	+	0.0500420i
$857$	7.85641			0.268370			0.134185	−	0.990956i	$-0.457158\pi$
$857$	7.85641			0.268370			0.134185	+	0.990956i	$0.457158\pi$
$858$	6.92820	−	1.85641i	0.236525	−	0.0633767i
$859$		−	20.2487i		−	0.690877i	−0.938441	−	0.345439i	$-0.887730\pi$
$859$		−	20.2487i		−	0.690877i	0.938441	−	0.345439i	$-0.112270\pi$
$860$	15.1244	−	8.73205i	0.515736	−	0.297760i
$861$		−	10.9282i		−	0.372432i
$862$	−5.32051	−	19.8564i	−0.181217	−	0.676312i
$863$	30.3397			1.03278			0.516388	−	0.856354i	$-0.327276\pi$
$863$	30.3397			1.03278			0.516388	+	0.856354i	$0.327276\pi$
$864$	5.85641	−	21.8564i	0.199239	−	0.743570i
$865$	2.00000			0.0680020
$866$	−4.58846	−	17.1244i	−0.155922	−	0.581909i
$867$			3.66025i			0.124309i
$868$	6.92820	−	4.00000i	0.235159	−	0.135769i
$869$			29.8564i			1.01281i
$870$	−6.92820	+	1.85641i	−0.234888	+	0.0629381i
$871$	−25.1769			−0.853087
$872$	6.14359	−	6.14359i	0.208048	−	0.208048i
$873$	15.7513			0.533100
$874$	−42.7846	+	11.4641i	−1.44721	+	0.387779i
$875$		−	2.73205i		−	0.0923602i
$876$	0.392305	+	0.679492i	0.0132548	+	0.0229579i
$877$			53.7128i			1.81375i	0.421397	+	0.906876i	$0.361540\pi$
$877$			53.7128i			1.81375i	−0.421397	+	0.906876i	$0.638460\pi$
$878$	−0.287187	−	1.07180i	−0.00969209	−	0.0361714i
$879$	8.67949			0.292752
$880$	−4.00000	+	6.92820i	−0.134840	+	0.233550i
$881$	2.53590			0.0854366			0.0427183	−	0.999087i	$-0.486398\pi$
$881$	2.53590			0.0854366			0.0427183	+	0.999087i	$0.486398\pi$
$882$	0.418584	+	1.56218i	0.0140945	+	0.0526013i
$883$			37.9090i			1.27574i	0.770145	+	0.637869i	$0.220184\pi$
$883$			37.9090i			1.27574i	−0.770145	+	0.637869i	$0.779816\pi$
$884$	12.0000	+	20.7846i	0.403604	+	0.699062i
$885$			0.392305i			0.0131872i
$886$	42.3205	−	11.3397i	1.42179	−	0.380966i
$887$	51.9090			1.74293			0.871466	−	0.490455i	$-0.163170\pi$
$887$	51.9090			1.74293			0.871466	+	0.490455i	$0.163170\pi$
$888$	2.92820	+	2.92820i	0.0982641	+	0.0982641i
$889$	−36.2487			−1.21574
$890$	−6.73205	+	1.80385i	−0.225659	+	0.0604651i
$891$		−	8.92820i		−	0.299106i
$892$	28.0526	−	16.1962i	0.939269	−	0.542287i
$893$			50.2487i			1.68151i
$894$	5.32051	+	19.8564i	0.177944	+	0.664098i
$895$	−15.4641			−0.516908
$896$	29.8564	−	8.00000i	0.997433	−	0.267261i
$897$	10.6410			0.355293
$898$	4.14359	+	15.4641i	0.138274	+	0.516044i
$899$		−	10.1436i		−	0.338308i
$900$	4.26795	−	2.46410i	0.142265	−	0.0821367i
$901$		−	15.7128i		−	0.523470i
$902$	−14.9282	+	4.00000i	−0.497055	+	0.133185i
$903$	17.4641			0.581169
$904$	−1.85641	−	1.85641i	−0.0617432	−	0.0617432i
$905$	16.0000			0.531858
$906$	8.39230	−	2.24871i	0.278816	−	0.0747084i
$907$			29.1244i			0.967058i	0.875328	+	0.483529i	$0.160645\pi$
$907$			29.1244i			0.967058i	−0.875328	+	0.483529i	$0.839355\pi$
$908$	28.0526	+	48.5885i	0.930957	+	1.61246i
$909$		−	26.9282i		−	0.893152i
$910$	−3.46410	−	12.9282i	−0.114834	−	0.428566i
$911$	13.1769			0.436571			0.218285	−	0.975885i	$-0.429954\pi$
$911$	13.1769			0.436571			0.218285	+	0.975885i	$0.429954\pi$
$912$	10.9282	−	18.9282i	0.361869	−	0.626775i
$913$	9.46410			0.313216
$914$	5.41154	+	20.1962i	0.178998	+	0.668029i
$915$		−	3.60770i		−	0.119267i
$916$	4.00000	+	6.92820i	0.132164	+	0.228914i
$917$		−	21.4641i		−	0.708807i
$918$	−18.9282	+	5.07180i	−0.624724	+	0.167394i
$919$	−25.0718			−0.827042			−0.413521	−	0.910495i	$-0.635701\pi$
$919$	−25.0718			−0.827042			−0.413521	+	0.910495i	$0.635701\pi$
$920$	−8.39230	+	8.39230i	−0.276686	+	0.276686i
$921$	19.7513			0.650827
$922$	−4.00000	+	1.07180i	−0.131733	+	0.0352977i
$923$		−	5.07180i		−	0.166940i
$924$	−6.92820	+	4.00000i	−0.227921	+	0.131590i
$925$			2.00000i			0.0657596i
$926$	−5.39230	−	20.1244i	−0.177202	−	0.661327i
$927$	−4.09103			−0.134367
$928$	10.1436	−	37.8564i	0.332980	−	1.24270i
$929$	−10.5359			−0.345672			−0.172836	−	0.984951i	$-0.555293\pi$
$929$	−10.5359			−0.345672			−0.172836	+	0.984951i	$0.555293\pi$
$930$	−0.392305	−	1.46410i	−0.0128642	−	0.0480098i
$931$			3.46410i			0.113531i
$932$	−50.7846	+	29.3205i	−1.66351	+	0.960425i
$933$			2.43078i			0.0795802i
$934$	11.3923	−	3.05256i	0.372768	−	0.0998828i
$935$	6.92820			0.226576
$936$	17.0718	−	17.0718i	0.558009	−	0.558009i
$937$	−44.2487			−1.44554			−0.722771	−	0.691087i	$-0.757132\pi$
$937$	−44.2487			−1.44554			−0.722771	+	0.691087i	$0.757132\pi$
$938$	27.1244	−	7.26795i	0.885642	−	0.237307i
$939$			23.3205i			0.761036i
$940$	6.73205	+	11.6603i	0.219575	+	0.380316i
$941$		−	32.0000i		−	1.04317i	−0.853199	−	0.521585i	$-0.825341\pi$
$941$		−	32.0000i		−	1.04317i	0.853199	−	0.521585i	$-0.174659\pi$
$942$	−4.53590	−	16.9282i	−0.147788	−	0.551551i
$943$	−22.9282			−0.746645
$944$	−1.85641	−	1.07180i	−0.0604209	−	0.0348840i
$945$	10.9282			0.355494
$946$	−6.39230	−	23.8564i	−0.207832	−	0.775639i
$947$			21.1244i			0.686449i	0.939253	+	0.343225i	$0.111519\pi$
$947$			21.1244i			0.686449i	−0.939253	+	0.343225i	$0.888481\pi$
$948$	−10.9282	−	18.9282i	−0.354932	−	0.614759i
$949$			1.85641i			0.0602615i
$950$	10.1962	−	2.73205i	0.330807	−	0.0886394i
$951$	11.3205			0.367093
$952$	−18.9282	−	18.9282i	−0.613467	−	0.613467i
$953$	−58.7846			−1.90422			−0.952110	−	0.305755i	$-0.901091\pi$
$953$	−58.7846			−1.90422			−0.952110	+	0.305755i	$0.901091\pi$
$954$	−15.2679	+	4.09103i	−0.494318	+	0.132452i
$955$			19.3205i			0.625197i
$956$	34.6410	−	20.0000i	1.12037	−	0.646846i
$957$			10.1436i			0.327896i
$958$	−8.00000	−	29.8564i	−0.258468	−	0.964617i
$959$	24.3923			0.787669
$960$		−	5.85641i		−	0.189015i
$961$	−28.8564			−0.930852
$962$	2.53590	+	9.46410i	0.0817606	+	0.305135i
$963$		−	1.80385i		−	0.0581282i
$964$	7.60770	−	4.39230i	0.245027	−	0.141467i
$965$		−	7.46410i		−	0.240278i
$966$	−11.4641	+	3.07180i	−0.368851	+	0.0988334i
$967$	33.6603			1.08244			0.541220	−	0.840881i	$-0.317962\pi$
$967$	33.6603			1.08244			0.541220	+	0.840881i	$0.317962\pi$
$968$	−14.0000	−	14.0000i	−0.449977	−	0.449977i
$969$	−18.9282			−0.608061
$970$	8.73205	−	2.33975i	0.280369	−	0.0751247i
$971$			23.0718i			0.740409i	0.928950	+	0.370205i	$0.120712\pi$
$971$			23.0718i			0.740409i	−0.928950	+	0.370205i	$0.879288\pi$
$972$	15.2679	+	26.4449i	0.489720	+	0.848219i
$973$			20.3923i			0.653747i
$974$	−9.00000	−	33.5885i	−0.288379	−	1.07624i
$975$	−2.53590			−0.0812137
$976$	17.0718	+	9.85641i	0.546455	+	0.315496i
$977$	−31.4641			−1.00663			−0.503313	−	0.864104i	$-0.667886\pi$
$977$	−31.4641			−1.00663			−0.503313	+	0.864104i	$0.667886\pi$
$978$	2.73205	+	10.1962i	0.0873614	+	0.326037i
$979$			9.85641i			0.315012i
$980$	0.464102	+	0.803848i	0.0148252	+	0.0256780i
$981$			7.56922i			0.241667i
$982$	4.19615	−	1.12436i	0.133905	−	0.0358796i
$983$	−45.2679			−1.44382			−0.721912	−	0.691985i	$-0.756736\pi$
$983$	−45.2679			−1.44382			−0.721912	+	0.691985i	$0.756736\pi$
$984$	8.00000	−	8.00000i	0.255031	−	0.255031i
$985$	−12.5359			−0.399427
$986$	−32.7846	+	8.78461i	−1.04407	+	0.279759i
$987$			13.4641i			0.428567i
$988$	44.7846	−	25.8564i	1.42479	−	0.822602i
$989$		−	36.6410i		−	1.16512i
$990$	−1.80385	−	6.73205i	−0.0573300	−	0.213959i
$991$	34.5359			1.09707			0.548534	−	0.836128i	$-0.315186\pi$
$991$	34.5359			1.09707			0.548534	+	0.836128i	$0.315186\pi$
$992$	8.00000	+	2.14359i	0.254000	+	0.0680592i
$993$	−10.2487			−0.325233
$994$	1.46410	+	5.46410i	0.0464385	+	0.173311i
$995$		−	25.8564i		−	0.819703i
$996$	−6.00000	+	3.46410i	−0.190117	+	0.109764i
$997$			51.1769i			1.62079i	0.585884	+	0.810395i	$0.300747\pi$
$997$			51.1769i			1.62079i	−0.585884	+	0.810395i	$0.699253\pi$
$998$	−33.5167	+	8.98076i	−1.06095	+	0.284281i
$999$	−8.00000			−0.253109

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	40.2.d.a.21.4	yes	4
3.2	odd	2		360.2.k.e.181.1		4
4.3	odd	2		160.2.d.a.81.3		4
5.2	odd	4		200.2.f.c.149.2		4
5.3	odd	4		200.2.f.e.149.3		4
5.4	even	2		200.2.d.f.101.1		4
8.3	odd	2		160.2.d.a.81.2		4
8.5	even	2	inner	40.2.d.a.21.3	✓	4
12.11	even	2		1440.2.k.e.721.4		4
15.2	even	4		1800.2.d.p.1549.3		4
15.8	even	4		1800.2.d.l.1549.2		4
15.14	odd	2		1800.2.k.j.901.4		4
16.3	odd	4		1280.2.a.n.1.1		2
16.5	even	4		1280.2.a.o.1.1		2
16.11	odd	4		1280.2.a.d.1.2		2
16.13	even	4		1280.2.a.a.1.2		2
20.3	even	4		800.2.f.e.49.1		4
20.7	even	4		800.2.f.c.49.4		4
20.19	odd	2		800.2.d.e.401.2		4
24.5	odd	2		360.2.k.e.181.2		4
24.11	even	2		1440.2.k.e.721.2		4
40.3	even	4		800.2.f.c.49.3		4
40.13	odd	4		200.2.f.c.149.1		4
40.19	odd	2		800.2.d.e.401.3		4
40.27	even	4		800.2.f.e.49.2		4
40.29	even	2		200.2.d.f.101.2		4
40.37	odd	4		200.2.f.e.149.4		4
60.23	odd	4		7200.2.d.n.2449.1		4
60.47	odd	4		7200.2.d.o.2449.4		4
60.59	even	2		7200.2.k.j.3601.1		4
80.19	odd	4		6400.2.a.be.1.2		2
80.29	even	4		6400.2.a.ce.1.1		2
80.59	odd	4		6400.2.a.cj.1.1		2
80.69	even	4		6400.2.a.z.1.2		2
120.29	odd	2		1800.2.k.j.901.3		4
120.53	even	4		1800.2.d.p.1549.4		4
120.59	even	2		7200.2.k.j.3601.2		4
120.77	even	4		1800.2.d.l.1549.1		4
120.83	odd	4		7200.2.d.o.2449.1		4
120.107	odd	4		7200.2.d.n.2449.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.2.d.a.21.3	✓	4	8.5	even	2	inner
40.2.d.a.21.4	yes	4	1.1	even	1	trivial
160.2.d.a.81.2		4	8.3	odd	2
160.2.d.a.81.3		4	4.3	odd	2
200.2.d.f.101.1		4	5.4	even	2
200.2.d.f.101.2		4	40.29	even	2
200.2.f.c.149.1		4	40.13	odd	4
200.2.f.c.149.2		4	5.2	odd	4
200.2.f.e.149.3		4	5.3	odd	4
200.2.f.e.149.4		4	40.37	odd	4
360.2.k.e.181.1		4	3.2	odd	2
360.2.k.e.181.2		4	24.5	odd	2
800.2.d.e.401.2		4	20.19	odd	2
800.2.d.e.401.3		4	40.19	odd	2
800.2.f.c.49.3		4	40.3	even	4
800.2.f.c.49.4		4	20.7	even	4
800.2.f.e.49.1		4	20.3	even	4
800.2.f.e.49.2		4	40.27	even	4
1280.2.a.a.1.2		2	16.13	even	4
1280.2.a.d.1.2		2	16.11	odd	4
1280.2.a.n.1.1		2	16.3	odd	4
1280.2.a.o.1.1		2	16.5	even	4
1440.2.k.e.721.2		4	24.11	even	2
1440.2.k.e.721.4		4	12.11	even	2
1800.2.d.l.1549.1		4	120.77	even	4
1800.2.d.l.1549.2		4	15.8	even	4
1800.2.d.p.1549.3		4	15.2	even	4
1800.2.d.p.1549.4		4	120.53	even	4
1800.2.k.j.901.3		4	120.29	odd	2
1800.2.k.j.901.4		4	15.14	odd	2
6400.2.a.z.1.2		2	80.69	even	4
6400.2.a.be.1.2		2	80.19	odd	4
6400.2.a.ce.1.1		2	80.29	even	4
6400.2.a.cj.1.1		2	80.59	odd	4
7200.2.d.n.2449.1		4	60.23	odd	4
7200.2.d.n.2449.4		4	120.107	odd	4
7200.2.d.o.2449.1		4	120.83	odd	4
7200.2.d.o.2449.4		4	60.47	odd	4
7200.2.k.j.3601.1		4	60.59	even	2
7200.2.k.j.3601.2		4	120.59	even	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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	40.2.d.a.21.4

Level	$40$
Weight	$2$
Character	40.21
Analytic conductor	$0.319$
Analytic rank	$0$
Dimension	$4$
Inner twists	$2$