LMFDB - Embedded newform 840.2.cp.b.521.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [840,2,Mod(521,840)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(840, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 3, 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("840.521"); 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.cp (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,0,0,16] 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:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			521.13
Character	$\chi$	$=$	840.521
Dual form			840.2.cp.b.761.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.51560 - 0.838429i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-1.32384 + 2.29073i) q^{7} +(1.59407 - 2.54144i) q^{9} +(3.96585 + 2.28969i) q^{11} -3.34155i q^{13} +(1.48390 + 0.893332i) q^{15} +(-1.18957 + 2.06040i) q^{17} +(1.42211 - 0.821057i) q^{19} +(-0.0858002 + 4.58177i) q^{21} +(5.45465 - 3.14924i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(0.285156 - 5.18832i) q^{27} +10.4727i q^{29} +(0.580062 + 0.334899i) q^{31} +(7.93038 + 0.145158i) q^{33} +(-2.64575 - 0.00111720i) q^{35} +(2.44443 + 4.23388i) q^{37} +(-2.80165 - 5.06444i) q^{39} +7.20642 q^{41} +0.255178 q^{43} +(2.99799 + 0.109787i) q^{45} +(0.506642 + 0.877529i) q^{47} +(-3.49488 - 6.06513i) q^{49} +(-0.0754144 + 4.12010i) q^{51} +(-6.27078 - 3.62044i) q^{53} +4.57937i q^{55} +(1.46695 - 2.43673i) q^{57} +(4.29866 - 7.44549i) q^{59} +(-11.7955 + 6.81012i) q^{61} +(3.71145 + 7.01606i) q^{63} +(2.89387 - 1.67077i) q^{65} +(5.64814 - 9.78286i) q^{67} +(5.62664 - 9.34632i) q^{69} -3.10631i q^{71} +(-11.9359 - 6.89118i) q^{73} +(-0.0316982 + 1.73176i) q^{75} +(-10.4952 + 6.05351i) q^{77} +(-6.43012 - 11.1373i) q^{79} +(-3.91786 - 8.10249i) q^{81} -5.90484 q^{83} -2.37914 q^{85} +(8.78061 + 15.8724i) q^{87} +(3.29074 + 5.69973i) q^{89} +(7.65458 + 4.42369i) q^{91} +(1.15993 + 0.0212314i) q^{93} +(1.42211 + 0.821057i) q^{95} -4.71324i q^{97} +(12.1410 - 6.42906i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{5} - 2 q^{7} + 8 q^{9} + 6 q^{19} - 14 q^{21} + 24 q^{23} - 16 q^{25} + 24 q^{27} + 42 q^{31} + 18 q^{33} + 2 q^{35} + 6 q^{37} + 12 q^{39} + 44 q^{41} - 20 q^{43} + 10 q^{45} + 4 q^{47} + 16 q^{49}+ \cdots - 8 q^{99}+O(q^{100}) $ 32 * q + 16 * q^5 - 2 * q^7 + 8 * q^9 + 6 * q^19 - 14 * q^21 + 24 * q^23 - 16 * q^25 + 24 * q^27 + 42 * q^31 + 18 * q^33 + 2 * q^35 + 6 * q^37 + 12 * q^39 + 44 * q^41 - 20 * q^43 + 10 * q^45 + 4 * q^47 + 16 * q^49 - 36 * q^51 + 12 * q^59 - 18 * q^61 + 34 * q^63 - 6 * q^65 - 6 * q^67 - 34 * q^69 - 6 * q^73 + 40 * q^77 - 2 * q^79 - 12 * q^81 - 88 * q^83 - 72 * q^87 - 6 * q^89 - 26 * q^91 + 50 * q^93 + 6 * q^95 - 8 * q^99

Character values

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

$n$	$241$	$281$	$337$	$421$	$631$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$1$	$1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	1.51560	−	0.838429i	0.875031	−	0.484067i
$3$	1.51560	−	0.838429i	0.875031	−	0.484067i
$4$		0			0
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$		0			0
$7$	−1.32384	+	2.29073i	−0.500366	+	0.865814i
$7$	−1.32384	+	2.29073i	−0.500366	+	0.865814i
$8$		0			0
$9$	1.59407	−	2.54144i	0.531358	−	0.847147i
$10$		0			0
$11$	3.96585	+	2.28969i	1.19575	+	0.690366i	0.959605	−	0.281352i	$-0.0907827\pi$
$11$	3.96585	+	2.28969i	1.19575	+	0.690366i	0.236145	+	0.971718i	$0.424116\pi$
$12$		0			0
$13$		−	3.34155i		−	0.926779i	−0.886155	−	0.463389i	$-0.846633\pi$
$13$		−	3.34155i		−	0.926779i	0.886155	−	0.463389i	$-0.153367\pi$
$14$		0			0
$15$	1.48390	+	0.893332i	0.383141	+	0.230657i
$16$		0			0
$17$	−1.18957	+	2.06040i	−0.288513	+	0.499719i	−0.973455	−	0.228878i	$-0.926494\pi$
$17$	−1.18957	+	2.06040i	−0.288513	+	0.499719i	0.684942	+	0.728598i	$0.259828\pi$
$18$		0			0
$19$	1.42211	−	0.821057i	0.326255	−	0.188363i	−0.327922	−	0.944705i	$-0.606348\pi$
$19$	1.42211	−	0.821057i	0.326255	−	0.188363i	0.654177	+	0.756341i	$0.273015\pi$
$20$		0			0
$21$	−0.0858002	+	4.58177i	−0.0187231	+	0.999825i
$22$		0			0
$23$	5.45465	−	3.14924i	1.13737	−	0.656663i	0.191594	−	0.981474i	$-0.438634\pi$
$23$	5.45465	−	3.14924i	1.13737	−	0.656663i	0.945779	+	0.324811i	$0.105301\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$	0.285156	−	5.18832i	0.0548783	−	0.998493i
$28$		0			0
$29$			10.4727i			1.94473i	0.233465	+	0.972365i	$0.424994\pi$
$29$			10.4727i			1.94473i	−0.233465	+	0.972365i	$0.575006\pi$
$30$		0			0
$31$	0.580062	+	0.334899i	0.104182	+	0.0601496i	0.551186	−	0.834383i	$-0.314176\pi$
$31$	0.580062	+	0.334899i	0.104182	+	0.0601496i	−0.447004	+	0.894532i	$0.647509\pi$
$32$		0			0
$33$	7.93038	+	0.145158i	1.38050	+	0.0252687i
$34$		0			0
$35$	−2.64575	−	0.00111720i	−0.447214	−	0.000188841i
$36$		0			0
$37$	2.44443	+	4.23388i	0.401862	+	0.696045i	0.993951	−	0.109827i	$-0.0350298\pi$
$37$	2.44443	+	4.23388i	0.401862	+	0.696045i	−0.592089	+	0.805873i	$0.701696\pi$
$38$		0			0
$39$	−2.80165	−	5.06444i	−0.448623	−	0.810960i
$40$		0			0
$41$	7.20642			1.12545			0.562727	−	0.826643i	$-0.309752\pi$
$41$	7.20642			1.12545			0.562727	+	0.826643i	$0.309752\pi$
$42$		0			0
$43$	0.255178			0.0389143			0.0194571	−	0.999811i	$-0.493806\pi$
$43$	0.255178			0.0389143			0.0194571	+	0.999811i	$0.493806\pi$
$44$		0			0
$45$	2.99799	+	0.109787i	0.446914	+	0.0163661i
$46$		0			0
$47$	0.506642	+	0.877529i	0.0739013	+	0.128001i	0.900608	−	0.434632i	$-0.143122\pi$
$47$	0.506642	+	0.877529i	0.0739013	+	0.128001i	−0.826707	+	0.562633i	$0.809788\pi$
$48$		0			0
$49$	−3.49488	−	6.06513i	−0.499268	−	0.866447i
$50$		0			0
$51$	−0.0754144	+	4.12010i	−0.0105601	+	0.576930i
$52$		0			0
$53$	−6.27078	−	3.62044i	−0.861358	−	0.497305i	0.00310897	−	0.999995i	$-0.499010\pi$
$53$	−6.27078	−	3.62044i	−0.861358	−	0.497305i	−0.864467	+	0.502690i	$0.832344\pi$
$54$		0			0
$55$			4.57937i			0.617482i
$56$		0			0
$57$	1.46695	−	2.43673i	0.194303	−	0.322753i
$58$		0			0
$59$	4.29866	−	7.44549i	0.559637	−	0.969320i	−0.437889	−	0.899029i	$-0.644274\pi$
$59$	4.29866	−	7.44549i	0.559637	−	0.969320i	0.997526	−	0.0702915i	$-0.0223929\pi$
$60$		0			0
$61$	−11.7955	+	6.81012i	−1.51026	+	0.871947i	−0.510328	+	0.859980i	$0.670476\pi$
$61$	−11.7955	+	6.81012i	−1.51026	+	0.871947i	−0.999928	+	0.0119671i	$0.996191\pi$
$62$		0			0
$63$	3.71145	+	7.01606i	0.467599	+	0.883941i
$64$		0			0
$65$	2.89387	−	1.67077i	0.358940	−	0.207234i
$66$		0			0
$67$	5.64814	−	9.78286i	0.690030	−	1.19517i	−0.281798	−	0.959474i	$-0.590931\pi$
$67$	5.64814	−	9.78286i	0.690030	−	1.19517i	0.971828	−	0.235693i	$-0.0757358\pi$
$68$		0			0
$69$	5.62664	−	9.34632i	0.677368	−	1.12517i
$70$		0			0
$71$		−	3.10631i		−	0.368652i	−0.982865	−	0.184326i	$-0.940990\pi$
$71$		−	3.10631i		−	0.368652i	0.982865	−	0.184326i	$-0.0590101\pi$
$72$		0			0
$73$	−11.9359	−	6.89118i	−1.39699	−	0.806551i	−0.402912	−	0.915239i	$-0.632002\pi$
$73$	−11.9359	−	6.89118i	−1.39699	−	0.806551i	−0.994076	+	0.108688i	$0.965335\pi$
$74$		0			0
$75$	−0.0316982	+	1.73176i	−0.00366019	+	0.199967i
$76$		0			0
$77$	−10.4952	+	6.05351i	−1.19604	+	0.689861i
$78$		0			0
$79$	−6.43012	−	11.1373i	−0.723445	−	1.25304i	−0.959611	−	0.281331i	$-0.909224\pi$
$79$	−6.43012	−	11.1373i	−0.723445	−	1.25304i	0.236165	−	0.971713i	$-0.424109\pi$
$80$		0			0
$81$	−3.91786	−	8.10249i	−0.435317	−	0.900277i
$82$		0			0
$83$	−5.90484			−0.648140			−0.324070	−	0.946033i	$-0.605051\pi$
$83$	−5.90484			−0.648140			−0.324070	+	0.946033i	$0.605051\pi$
$84$		0			0
$85$	−2.37914			−0.258054
$86$		0			0
$87$	8.78061	+	15.8724i	0.941380	+	1.70170i
$88$		0			0
$89$	3.29074	+	5.69973i	0.348818	+	0.604170i	0.986040	−	0.166510i	$-0.0532499\pi$
$89$	3.29074	+	5.69973i	0.348818	+	0.604170i	−0.637222	+	0.770680i	$0.719917\pi$
$90$		0			0
$91$	7.65458	+	4.42369i	0.802418	+	0.463728i
$92$		0			0
$93$	1.15993	+	0.0212314i	0.120279	+	0.00220159i
$94$		0			0
$95$	1.42211	+	0.821057i	0.145906	+	0.0842386i
$96$		0			0
$97$		−	4.71324i		−	0.478557i	−0.970951	−	0.239279i	$-0.923089\pi$
$97$		−	4.71324i		−	0.478557i	0.970951	−	0.239279i	$-0.0769109\pi$
$98$		0			0
$99$	12.1410	−	6.42906i	1.22021	−	0.646144i
$100$		0			0
$101$	4.61658	−	7.99614i	0.459366	−	0.795646i	−0.539561	−	0.841946i	$-0.681410\pi$
$101$	4.61658	−	7.99614i	0.459366	−	0.795646i	0.998928	+	0.0463004i	$0.0147432\pi$
$102$		0			0
$103$	−10.2264	+	5.90419i	−1.00763	+	0.581758i	−0.910498	−	0.413514i	$-0.864301\pi$
$103$	−10.2264	+	5.90419i	−1.00763	+	0.581758i	−0.0971357	+	0.995271i	$0.530968\pi$
$104$		0			0
$105$	−4.01083	+	2.21658i	−0.391417	+	0.216316i
$106$		0			0
$107$	1.22015	−	0.704454i	0.117956	−	0.0681022i	−0.439861	−	0.898066i	$-0.644972\pi$
$107$	1.22015	−	0.704454i	0.117956	−	0.0681022i	0.557817	+	0.829964i	$0.311639\pi$
$108$		0			0
$109$	−7.09515	+	12.2892i	−0.679592	+	1.17709i	0.295512	+	0.955339i	$0.404510\pi$
$109$	−7.09515	+	12.2892i	−0.679592	+	1.17709i	−0.975104	+	0.221749i	$0.928823\pi$
$110$		0			0
$111$	7.25458	+	4.36738i	0.688574	+	0.414533i
$112$		0			0
$113$			11.4105i			1.07341i	0.843770	+	0.536705i	$0.180331\pi$
$113$			11.4105i			1.07341i	−0.843770	+	0.536705i	$0.819669\pi$
$114$		0			0
$115$	5.45465	+	3.14924i	0.508649	+	0.293668i
$116$		0			0
$117$	−8.49235	−	5.32668i	−0.785118	−	0.492451i
$118$		0			0
$119$	−3.14500	−	5.45262i	−0.288302	−	0.499841i
$120$		0			0
$121$	4.98532	+	8.63483i	0.453211	+	0.784985i
$122$		0			0
$123$	10.9220	−	6.04207i	0.984807	−	0.544795i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	4.47781			0.397342			0.198671	−	0.980066i	$-0.436338\pi$
$127$	4.47781			0.397342			0.198671	+	0.980066i	$0.436338\pi$
$128$		0			0
$129$	0.386747	−	0.213949i	0.0340512	−	0.0188371i
$130$		0			0
$131$	2.84104	+	4.92083i	0.248223	+	0.429934i	0.963033	−	0.269384i	$-0.0868202\pi$
$131$	2.84104	+	4.92083i	0.248223	+	0.429934i	−0.714810	+	0.699319i	$0.753487\pi$
$132$		0			0
$133$	−0.00183456	+	4.34462i	−0.000159077	+	0.376727i
$134$		0			0
$135$	4.63580	−	2.34721i	0.398986	−	0.202016i
$136$		0			0
$137$	−11.4176	−	6.59193i	−0.975467	−	0.563186i	−0.0745687	−	0.997216i	$-0.523758\pi$
$137$	−11.4176	−	6.59193i	−0.975467	−	0.563186i	−0.900899	+	0.434030i	$0.857091\pi$
$138$		0			0
$139$		−	4.22728i		−	0.358553i	−0.983799	−	0.179277i	$-0.942624\pi$
$139$		−	4.22728i		−	0.358553i	0.983799	−	0.179277i	$-0.0573757\pi$
$140$		0			0
$141$	1.50361	+	0.905198i	0.126627	+	0.0762314i
$142$		0			0
$143$	7.65110	−	13.2521i	0.639817	−	1.10820i
$144$		0			0
$145$	−9.06962	+	5.23635i	−0.753191	+	0.434855i
$146$		0			0
$147$	−10.3820	−	6.26209i	−0.856294	−	0.516489i
$148$		0			0
$149$	−3.91208	+	2.25864i	−0.320490	+	0.185035i	−0.651611	−	0.758553i	$-0.725907\pi$
$149$	−3.91208	+	2.25864i	−0.320490	+	0.185035i	0.331121	+	0.943588i	$0.392573\pi$
$150$		0			0
$151$	−12.0815	+	20.9257i	−0.983176	+	1.70291i	−0.333397	+	0.942786i	$0.608195\pi$
$151$	−12.0815	+	20.9257i	−0.983176	+	1.70291i	−0.649778	+	0.760124i	$0.725138\pi$
$152$		0			0
$153$	3.34011	+	6.30765i	0.270032	+	0.509943i
$154$		0			0
$155$			0.669798i			0.0537995i
$156$		0			0
$157$	−19.9609	−	11.5244i	−1.59306	−	0.919751i	−0.992779	−	0.119958i	$-0.961724\pi$
$157$	−19.9609	−	11.5244i	−1.59306	−	0.919751i	−0.600276	−	0.799793i	$-0.704943\pi$
$158$		0			0
$159$	−12.5395	−	0.229522i	−0.994444	−	0.0182023i
$160$		0			0
$161$	−0.00703665	+	16.6642i	−0.000554565	+	1.31333i
$162$		0			0
$163$	4.48563	+	7.76934i	0.351342	+	0.608541i	0.986485	−	0.163853i	$-0.0523923\pi$
$163$	4.48563	+	7.76934i	0.351342	+	0.608541i	−0.635143	+	0.772394i	$0.719059\pi$
$164$		0			0
$165$	3.83948	+	6.94049i	0.298903	+	0.540316i
$166$		0			0
$167$	12.0287			0.930807			0.465404	−	0.885099i	$-0.345909\pi$
$167$	12.0287			0.930807			0.465404	+	0.885099i	$0.345909\pi$
$168$		0			0
$169$	1.83405			0.141081
$170$		0			0
$171$	0.180283	−	4.92304i	0.0137866	−	0.376474i
$172$		0			0
$173$	−9.48818	−	16.4340i	−0.721373	−	1.24946i	−0.960449	−	0.278454i	$-0.910178\pi$
$173$	−9.48818	−	16.4340i	−0.721373	−	1.24946i	0.239076	−	0.971001i	$-0.423155\pi$
$174$		0			0
$175$	−1.32191	−	2.29185i	−0.0999269	−	0.173247i
$176$		0			0
$177$	0.272519	−	14.8885i	0.0204838	−	1.11909i
$178$		0			0
$179$	−21.1228	−	12.1952i	−1.57879	−	0.911515i	−0.995028	−	0.0995908i	$-0.968247\pi$
$179$	−21.1228	−	12.1952i	−1.57879	−	0.911515i	−0.583762	−	0.811925i	$-0.698420\pi$
$180$		0			0
$181$			14.9046i			1.10785i	0.832567	+	0.553925i	$0.186871\pi$
$181$			14.9046i			1.10785i	−0.832567	+	0.553925i	$0.813129\pi$
$182$		0			0
$183$	−12.1674	+	20.2111i	−0.899440	+	1.49405i
$184$		0			0
$185$	−2.44443	+	4.23388i	−0.179718	+	0.311281i
$186$		0			0
$187$	−9.43532	+	5.44748i	−0.689979	+	0.398359i
$188$		0			0
$189$	11.5075	+	7.52174i	0.837050	+	0.547126i
$190$		0			0
$191$	9.86445	−	5.69524i	0.713766	−	0.412093i	−0.0986876	−	0.995118i	$-0.531464\pi$
$191$	9.86445	−	5.69524i	0.713766	−	0.412093i	0.812454	+	0.583025i	$0.198131\pi$
$192$		0			0
$193$	−1.40547	+	2.43435i	−0.101168	+	0.175228i	−0.912166	−	0.409821i	$-0.865591\pi$
$193$	−1.40547	+	2.43435i	−0.101168	+	0.175228i	0.810998	+	0.585049i	$0.198925\pi$
$194$		0			0
$195$	2.98511	−	4.95852i	0.213768	−	0.355087i
$196$		0			0
$197$		−	12.0926i		−	0.861563i	−0.902456	−	0.430782i	$-0.858238\pi$
$197$		−	12.0926i		−	0.861563i	0.902456	−	0.430782i	$-0.141762\pi$
$198$		0			0
$199$	1.98467	+	1.14585i	0.140690	+	0.0812272i	0.568693	−	0.822550i	$-0.307449\pi$
$199$	1.98467	+	1.14585i	0.140690	+	0.0812272i	−0.428003	+	0.903777i	$0.640783\pi$
$200$		0			0
$201$	0.358071	−	19.5624i	0.0252564	−	1.37983i
$202$		0			0
$203$	−23.9901	−	13.8642i	−1.68378	−	0.973076i
$204$		0			0
$205$	3.60321	+	6.24095i	0.251659	+	0.435887i
$206$		0			0
$207$	0.691494	−	18.8828i	0.0480622	−	1.31245i
$208$		0			0
$209$	7.51985			0.520159
$210$		0			0
$211$	1.42829			0.0983274			0.0491637	−	0.998791i	$-0.484344\pi$
$211$	1.42829			0.0983274			0.0491637	+	0.998791i	$0.484344\pi$
$212$		0			0
$213$	−2.60442	−	4.70792i	−0.178452	−	0.322581i
$214$		0			0
$215$	0.127589	+	0.220991i	0.00870149	+	0.0150714i
$216$		0			0
$217$	−1.53507	+	0.885412i	−0.104208	+	0.0601057i
$218$		0			0
$219$	−23.8677	−	0.436875i	−1.61283	−	0.0295213i
$220$		0			0
$221$	6.88491	+	3.97501i	0.463129	+	0.267388i
$222$		0			0
$223$			1.01844i			0.0682000i	0.999418	+	0.0341000i	$0.0108565\pi$
$223$			1.01844i			0.0682000i	−0.999418	+	0.0341000i	$0.989144\pi$
$224$		0			0
$225$	1.40392	+	2.65123i	0.0935944	+	0.176749i
$226$		0			0
$227$	−0.582916	+	1.00964i	−0.0386895	+	0.0670122i	−0.884722	−	0.466120i	$-0.845652\pi$
$227$	−0.582916	+	1.00964i	−0.0386895	+	0.0670122i	0.846032	+	0.533132i	$0.178985\pi$
$228$		0			0
$229$	21.6754	−	12.5143i	1.43235	−	0.826969i	0.435052	−	0.900405i	$-0.356730\pi$
$229$	21.6754	−	12.5143i	1.43235	−	0.826969i	0.997300	+	0.0734361i	$0.0233965\pi$
$230$		0			0
$231$	−10.8311	+	17.9742i	−0.712633	+	1.18261i
$232$		0			0
$233$	−6.40367	+	3.69716i	−0.419518	+	0.242209i	−0.694871	−	0.719134i	$-0.744539\pi$
$233$	−6.40367	+	3.69716i	−0.419518	+	0.242209i	0.275353	+	0.961343i	$0.411205\pi$
$234$		0			0
$235$	−0.506642	+	0.877529i	−0.0330497	+	0.0572437i
$236$		0			0
$237$	−19.0833	−	11.4885i	−1.23959	−	0.746256i
$238$		0			0
$239$			7.48792i			0.484353i	0.970232	+	0.242176i	$0.0778613\pi$
$239$			7.48792i			0.484353i	−0.970232	+	0.242176i	$0.922139\pi$
$240$		0			0
$241$	−14.4880	−	8.36465i	−0.933254	−	0.538814i	−0.0454145	−	0.998968i	$-0.514461\pi$
$241$	−14.4880	−	8.36465i	−0.933254	−	0.538814i	−0.887839	+	0.460154i	$0.847794\pi$
$242$		0			0
$243$	−12.7313	−	8.99528i	−0.816711	−	0.577047i
$244$		0			0
$245$	3.50512	−	6.05922i	0.223934	−	0.387109i
$246$		0			0
$247$	−2.74360	−	4.75206i	−0.174571	−	0.302366i
$248$		0			0
$249$	−8.94936	+	4.95079i	−0.567143	+	0.313743i
$250$		0			0
$251$	15.5876			0.983879			0.491939	−	0.870629i	$-0.336288\pi$
$251$	15.5876			0.983879			0.491939	+	0.870629i	$0.336288\pi$
$252$		0			0
$253$	28.8431			1.81335
$254$		0			0
$255$	−3.60582	+	1.99474i	−0.225805	+	0.124915i
$256$		0			0
$257$	−8.25966	−	14.3061i	−0.515223	−	0.892393i	−0.999844	−	0.0176685i	$-0.994376\pi$
$257$	−8.25966	−	14.3061i	−0.515223	−	0.892393i	0.484621	−	0.874724i	$-0.338958\pi$
$258$		0			0
$259$	−12.9347	−	0.00546182i	−0.803724	−	0.000339381i
$260$		0			0
$261$	26.6157	+	16.6942i	1.64747	+	1.03335i
$262$		0			0
$263$	8.72306	+	5.03626i	0.537887	+	0.310549i	0.744222	−	0.667932i	$-0.232820\pi$
$263$	8.72306	+	5.03626i	0.537887	+	0.310549i	−0.206335	+	0.978481i	$0.566154\pi$
$264$		0			0
$265$		−	7.24087i		−	0.444803i
$266$		0			0
$267$	9.76626	+	5.87945i	0.597685	+	0.359816i
$268$		0			0
$269$	−7.54206	+	13.0632i	−0.459847	+	0.796479i	−0.998952	−	0.0457596i	$-0.985429\pi$
$269$	−7.54206	+	13.0632i	−0.459847	+	0.796479i	0.539105	+	0.842238i	$0.318763\pi$
$270$		0			0
$271$	−9.55078	+	5.51414i	−0.580168	+	0.334960i	−0.761200	−	0.648517i	$-0.775390\pi$
$271$	−9.55078	+	5.51414i	−0.580168	+	0.334960i	0.181032	+	0.983477i	$0.442056\pi$
$272$		0			0
$273$	15.3102	+	0.286706i	0.926616	+	0.0173522i
$274$		0			0
$275$	−3.96585	+	2.28969i	−0.239150	+	0.138073i
$276$		0			0
$277$	5.75687	−	9.97119i	0.345897	−	0.599111i	−0.639619	−	0.768692i	$-0.720908\pi$
$277$	5.75687	−	9.97119i	0.345897	−	0.599111i	0.985516	+	0.169581i	$0.0542414\pi$
$278$		0			0
$279$	1.77579	−	0.940341i	0.106314	−	0.0562967i
$280$		0			0
$281$			21.8401i			1.30287i	0.758704	+	0.651436i	$0.225833\pi$
$281$			21.8401i			1.30287i	−0.758704	+	0.651436i	$0.774167\pi$
$282$		0			0
$283$	−8.93010	−	5.15579i	−0.530839	−	0.306480i	0.210519	−	0.977590i	$-0.432485\pi$
$283$	−8.93010	−	5.15579i	−0.530839	−	0.306480i	−0.741358	+	0.671110i	$0.765818\pi$
$284$		0			0
$285$	2.84375	+	0.0520520i	0.168449	+	0.00308329i
$286$		0			0
$287$	−9.54017	+	16.5080i	−0.563139	+	0.974434i
$288$		0			0
$289$	5.66985	+	9.82046i	0.333520	+	0.577674i
$290$		0			0
$291$	−3.95172	−	7.14338i	−0.231654	−	0.418752i
$292$		0			0
$293$	−18.2766			−1.06773			−0.533865	−	0.845570i	$-0.679261\pi$
$293$	−18.2766			−1.06773			−0.533865	+	0.845570i	$0.679261\pi$
$294$		0			0
$295$	8.59731			0.500555
$296$		0			0
$297$	13.0105	−	19.9232i	0.754947	−	1.15606i
$298$		0			0
$299$	−10.5234	−	18.2270i	−0.608581	−	1.05409i
$300$		0			0
$301$	−0.337815	+	0.584543i	−0.0194714	+	0.0336925i
$302$		0			0
$303$	0.292674	−	15.9896i	0.0168137	−	0.918579i
$304$		0			0
$305$	−11.7955	−	6.81012i	−0.675407	−	0.389947i
$306$		0			0
$307$		−	28.7426i		−	1.64042i	−0.572059	−	0.820212i	$-0.693855\pi$
$307$		−	28.7426i		−	1.64042i	0.572059	−	0.820212i	$-0.306145\pi$
$308$		0			0
$309$	−10.5488	+	17.5225i	−0.600101	+	0.996818i
$310$		0			0
$311$	−4.33624	+	7.51059i	−0.245886	+	0.425887i	−0.962380	−	0.271706i	$-0.912412\pi$
$311$	−4.33624	+	7.51059i	−0.245886	+	0.425887i	0.716494	+	0.697593i	$0.245745\pi$
$312$		0			0
$313$	13.8193	−	7.97859i	0.781115	−	0.450977i	−0.0557104	−	0.998447i	$-0.517742\pi$
$313$	13.8193	−	7.97859i	0.781115	−	0.450977i	0.836825	+	0.547470i	$0.184409\pi$
$314$		0			0
$315$	−4.22036	+	6.72224i	−0.237790	+	0.378755i
$316$		0			0
$317$	−2.07065	+	1.19549i	−0.116300	+	0.0671456i	−0.557021	−	0.830498i	$-0.688056\pi$
$317$	−2.07065	+	1.19549i	−0.116300	+	0.0671456i	0.440722	+	0.897644i	$0.354723\pi$
$318$		0			0
$319$	−23.9792	+	41.5332i	−1.34258	+	2.32541i
$320$		0			0
$321$	1.25862	−	2.09068i	0.0702495	−	0.116690i
$322$		0			0
$323$			3.90682i			0.217381i
$324$		0			0
$325$	2.89387	+	1.67077i	0.160523	+	0.0926779i
$326$		0			0
$327$	−0.449807	+	24.5742i	−0.0248744	+	1.35896i
$328$		0			0
$329$	−2.68090	−	0.00113204i	−0.147803	−	6.24112e-5i
$330$		0			0
$331$	−12.8685	−	22.2888i	−0.707315	−	1.22511i	−0.965850	−	0.259104i	$-0.916573\pi$
$331$	−12.8685	−	22.2888i	−0.707315	−	1.22511i	0.258535	−	0.966002i	$-0.416760\pi$
$332$		0			0
$333$	14.6568	+	0.536735i	0.803186	+	0.0294129i
$334$		0			0
$335$	11.2963			0.617181
$336$		0			0
$337$	5.27090			0.287124			0.143562	−	0.989641i	$-0.454144\pi$
$337$	5.27090			0.287124			0.143562	+	0.989641i	$0.454144\pi$
$338$		0			0
$339$	9.56690	+	17.2937i	0.519603	+	0.939267i
$340$		0			0
$341$	1.53363	+	2.65632i	0.0830506	+	0.143848i
$342$		0			0
$343$	18.5202	+	0.0234611i	0.999999	+	0.00126678i
$344$		0			0
$345$	10.9075	+	0.199651i	0.587239	+	0.0107488i
$346$		0			0
$347$	21.0562	+	12.1568i	1.13035	+	0.652611i	0.944024	−	0.329876i	$-0.107007\pi$
$347$	21.0562	+	12.1568i	1.13035	+	0.652611i	0.186331	+	0.982487i	$0.440340\pi$
$348$		0			0
$349$		−	33.1786i		−	1.77601i	−0.459832	−	0.888006i	$-0.652090\pi$
$349$		−	33.1786i		−	1.77601i	0.459832	−	0.888006i	$-0.347910\pi$
$350$		0			0
$351$	−17.3370	−	0.952863i	−0.925382	−	0.0508601i
$352$		0			0
$353$	−1.30341	+	2.25758i	−0.0693736	+	0.120159i	−0.898626	−	0.438716i	$-0.855433\pi$
$353$	−1.30341	+	2.25758i	−0.0693736	+	0.120159i	0.829252	+	0.558875i	$0.188767\pi$
$354$		0			0
$355$	2.69015	−	1.55316i	0.142778	−	0.0824330i
$356$		0			0
$357$	−9.33820	−	5.62712i	−0.494230	−	0.297819i
$358$		0			0
$359$	−1.52866	+	0.882573i	−0.0806796	+	0.0465804i	−0.539797	−	0.841795i	$-0.681499\pi$
$359$	−1.52866	+	0.882573i	−0.0806796	+	0.0465804i	0.459117	+	0.888376i	$0.348166\pi$
$360$		0			0
$361$	−8.15173	+	14.1192i	−0.429039	+	0.743117i
$362$		0			0
$363$	14.7954	+	8.90709i	0.776559	+	0.467501i
$364$		0			0
$365$		−	13.7824i		−	0.721401i
$366$		0			0
$367$	−12.4341	−	7.17881i	−0.649053	−	0.374731i	0.139040	−	0.990287i	$-0.455598\pi$
$367$	−12.4341	−	7.17881i	−0.649053	−	0.374731i	−0.788093	+	0.615556i	$0.788932\pi$
$368$		0			0
$369$	11.4876	−	18.3147i	0.598019	−	0.953426i
$370$		0			0
$371$	16.5950	−	9.57177i	0.861568	−	0.496941i
$372$		0			0
$373$	−2.14148	−	3.70915i	−0.110882	−	0.192053i	0.805244	−	0.592943i	$-0.202034\pi$
$373$	−2.14148	−	3.70915i	−0.110882	−	0.192053i	−0.916126	+	0.400890i	$0.868701\pi$
$374$		0			0
$375$	−1.51560	+	0.838429i	−0.0782651	+	0.0432963i
$376$		0			0
$377$	34.9950			1.80233
$378$		0			0
$379$	13.1755			0.676780			0.338390	−	0.941006i	$-0.390118\pi$
$379$	13.1755			0.676780			0.338390	+	0.941006i	$0.390118\pi$
$380$		0			0
$381$	6.78656	−	3.75433i	0.347686	−	0.192340i
$382$		0			0
$383$	−11.2109	−	19.4179i	−0.572852	−	0.992209i	−0.996271	−	0.0862753i	$-0.972504\pi$
$383$	−11.2109	−	19.4179i	−0.572852	−	0.992209i	0.423419	−	0.905934i	$-0.360830\pi$
$384$		0			0
$385$	−10.4901	−	6.06237i	−0.534625	−	0.308967i
$386$		0			0
$387$	0.406772	−	0.648520i	0.0206774	−	0.0329661i
$388$		0			0
$389$	23.4684	+	13.5495i	1.18989	+	0.686986i	0.958283	−	0.285823i	$-0.0922668\pi$
$389$	23.4684	+	13.5495i	1.18989	+	0.686986i	0.231612	+	0.972808i	$0.425600\pi$
$390$		0			0
$391$			14.9850i			0.757823i
$392$		0			0
$393$	8.43164	+	5.07598i	0.425320	+	0.256049i
$394$		0			0
$395$	6.43012	−	11.1373i	0.323535	−	0.560378i
$396$		0			0
$397$	17.4836	−	10.0942i	0.877478	−	0.506612i	0.00765220	−	0.999971i	$-0.497564\pi$
$397$	17.4836	−	10.0942i	0.877478	−	0.506612i	0.869826	+	0.493358i	$0.164231\pi$
$398$		0			0
$399$	3.63988	+	6.58624i	0.182222	+	0.329724i
$400$		0			0
$401$	−11.9366	+	6.89159i	−0.596085	+	0.344150i	−0.767500	−	0.641049i	$-0.778499\pi$
$401$	−11.9366	+	6.89159i	−0.596085	+	0.344150i	0.171415	+	0.985199i	$0.445166\pi$
$402$		0			0
$403$	1.11908	−	1.93831i	0.0557454	−	0.0965539i
$404$		0			0
$405$	5.05804	−	7.44421i	0.251336	−	0.369906i
$406$		0			0
$407$			22.3879i			1.10973i
$408$		0			0
$409$	12.2565	+	7.07628i	0.606044	+	0.349899i	0.771415	−	0.636332i	$-0.219549\pi$
$409$	12.2565	+	7.07628i	0.606044	+	0.349899i	−0.165372	+	0.986231i	$0.552882\pi$
$410$		0			0
$411$	−22.8313	−	0.417904i	−1.12618	−	0.0206137i
$412$		0			0
$413$	11.3649	+	19.7037i	0.559228	+	0.969557i
$414$		0			0
$415$	−2.95242	−	5.11374i	−0.144929	−	0.251024i
$416$		0			0
$417$	−3.54427	−	6.40685i	−0.173564	−	0.313745i
$418$		0			0
$419$	36.2097			1.76896			0.884479	−	0.466579i	$-0.154514\pi$
$419$	36.2097			1.76896			0.884479	+	0.466579i	$0.154514\pi$
$420$		0			0
$421$	21.6548			1.05539			0.527694	−	0.849435i	$-0.323057\pi$
$421$	21.6548			1.05539			0.527694	+	0.849435i	$0.323057\pi$
$422$		0			0
$423$	3.03781	+	0.111246i	0.147704	+	0.00540895i
$424$		0			0
$425$	−1.18957	−	2.06040i	−0.0577026	−	0.0999439i
$426$		0			0
$427$	0.0152165	−	36.0358i	0.000736378	−	1.74389i
$428$		0			0
$429$	0.485052	−	26.4997i	0.0234185	−	1.27942i
$430$		0			0
$431$	23.1646	+	13.3741i	1.11580	+	0.644206i	0.940325	−	0.340278i	$-0.110521\pi$
$431$	23.1646	+	13.3741i	1.11580	+	0.644206i	0.175473	+	0.984484i	$0.443855\pi$
$432$		0			0
$433$			8.57658i			0.412164i	0.978535	+	0.206082i	$0.0660714\pi$
$433$			8.57658i			0.412164i	−0.978535	+	0.206082i	$0.933929\pi$
$434$		0			0
$435$	−9.35559	+	15.5404i	−0.448566	+	0.745106i
$436$		0			0
$437$	5.17141	−	8.95715i	0.247382	−	0.428479i
$438$		0			0
$439$	19.0918	−	11.0226i	0.911201	−	0.526082i	0.0303838	−	0.999538i	$-0.490327\pi$
$439$	19.0918	−	11.0226i	0.911201	−	0.526082i	0.880817	+	0.473456i	$0.156994\pi$
$440$		0			0
$441$	−20.9853	−	0.786234i	−0.999299	−	0.0374397i
$442$		0			0
$443$	−28.3326	+	16.3578i	−1.34612	+	0.777183i	−0.987698	−	0.156377i	$-0.950019\pi$
$443$	−28.3326	+	16.3578i	−1.34612	+	0.777183i	−0.358423	+	0.933559i	$0.616685\pi$
$444$		0			0
$445$	−3.29074	+	5.69973i	−0.155996	+	0.270193i
$446$		0			0
$447$	−4.03543	+	6.70319i	−0.190869	+	0.317050i
$448$		0			0
$449$			12.2185i			0.576629i	0.957536	+	0.288314i	$0.0930948\pi$
$449$			12.2185i			0.576629i	−0.957536	+	0.288314i	$0.906905\pi$
$450$		0			0
$451$	28.5796	+	16.5004i	1.34576	+	0.776976i
$452$		0			0
$453$	−0.765921	+	41.8444i	−0.0359861	+	1.96602i
$454$		0			0
$455$	−0.00373317	+	8.84091i	−0.000175013	+	0.414468i
$456$		0			0
$457$	20.4850	+	35.4811i	0.958250	+	1.65974i	0.726750	+	0.686902i	$0.241030\pi$
$457$	20.4850	+	35.4811i	0.958250	+	1.65974i	0.231500	+	0.972835i	$0.425637\pi$
$458$		0			0
$459$	10.3508	+	6.75941i	0.483133	+	0.315502i
$460$		0			0
$461$	29.9492			1.39487			0.697437	−	0.716646i	$-0.254324\pi$
$461$	29.9492			1.39487			0.697437	+	0.716646i	$0.254324\pi$
$462$		0			0
$463$	−13.4377			−0.624502			−0.312251	−	0.950000i	$-0.601083\pi$
$463$	−13.4377			−0.624502			−0.312251	+	0.950000i	$0.601083\pi$
$464$		0			0
$465$	0.561578	+	1.01514i	0.0260426	+	0.0470762i
$466$		0			0
$467$	8.83482	+	15.3024i	0.408827	+	0.708109i	0.994759	−	0.102252i	$-0.0326047\pi$
$467$	8.83482	+	15.3024i	0.408827	+	0.708109i	−0.585932	+	0.810360i	$0.699271\pi$
$468$		0			0
$469$	14.9326	+	25.8893i	0.689525	+	1.19546i
$470$		0			0
$471$	−39.9152	−	0.730608i	−1.83919	−	0.0336646i
$472$		0			0
$473$	1.01200	+	0.584277i	0.0465317	+	0.0268651i
$474$		0			0
$475$			1.64211i			0.0753453i
$476$		0			0
$477$	−19.1972	+	10.1656i	−0.878980	+	0.465450i
$478$		0			0
$479$	1.17226	−	2.03041i	0.0535618	−	0.0927717i	−0.838001	−	0.545668i	$-0.816276\pi$
$479$	1.17226	−	2.03041i	0.0535618	−	0.0927717i	0.891563	+	0.452896i	$0.149609\pi$
$480$		0			0
$481$	14.1477	−	8.16819i	0.645080	−	0.372437i
$482$		0			0
$483$	13.9611	+	25.2622i	0.635252	+	1.14947i
$484$		0			0
$485$	4.08179	−	2.35662i	0.185344	−	0.107009i
$486$		0			0
$487$	1.55112	−	2.68661i	0.0702878	−	0.121742i	−0.828740	−	0.559634i	$-0.810942\pi$
$487$	1.55112	−	2.68661i	0.0702878	−	0.121742i	0.899027	+	0.437892i	$0.144275\pi$
$488$		0			0
$489$	13.3124	+	8.01431i	0.602010	+	0.362420i
$490$		0			0
$491$			1.65953i			0.0748937i	0.999299	+	0.0374468i	$0.0119225\pi$
$491$			1.65953i			0.0748937i	−0.999299	+	0.0374468i	$0.988078\pi$
$492$		0			0
$493$	−21.5779	−	12.4580i	−0.971819	−	0.561080i
$494$		0			0
$495$	11.6382	+	7.29986i	0.523099	+	0.328104i
$496$		0			0
$497$	7.11572	+	4.11227i	0.319184	+	0.184461i
$498$		0			0
$499$	−8.79584	−	15.2348i	−0.393756	−	0.682005i	0.599185	−	0.800610i	$-0.295491\pi$
$499$	−8.79584	−	15.2348i	−0.393756	−	0.682005i	−0.992942	+	0.118605i	$0.962158\pi$
$500$		0			0
$501$	18.2306	−	10.0852i	0.814485	−	0.450573i
$502$		0			0
$503$	11.8921			0.530244			0.265122	−	0.964215i	$-0.414588\pi$
$503$	11.8921			0.530244			0.265122	+	0.964215i	$0.414588\pi$
$504$		0			0
$505$	9.23315			0.410870
$506$		0			0
$507$	2.77969	−	1.53772i	0.123450	−	0.0682927i
$508$		0			0
$509$	−20.3441	−	35.2370i	−0.901735	−	1.56185i	−0.825241	−	0.564781i	$-0.808961\pi$
$509$	−20.3441	−	35.2370i	−0.901735	−	1.56185i	−0.0764941	−	0.997070i	$-0.524373\pi$
$510$		0			0
$511$	31.5870	−	18.2190i	1.39733	−	0.805961i
$512$		0			0
$513$	−3.85438	−	7.61250i	−0.170175	−	0.336100i
$514$		0			0
$515$	−10.2264	−	5.90419i	−0.450627	−	0.260170i
$516$		0			0
$517$			4.64020i			0.204076i
$518$		0			0
$519$	−28.1590	−	16.9522i	−1.23604	−	0.744119i
$520$		0			0
$521$	−1.21998	+	2.11307i	−0.0534483	+	0.0925752i	−0.891512	−	0.452998i	$-0.850355\pi$
$521$	−1.21998	+	2.11307i	−0.0534483	+	0.0925752i	0.838063	+	0.545573i	$0.183688\pi$
$522$		0			0
$523$	−1.67444	+	0.966739i	−0.0732182	+	0.0422726i	−0.536162	−	0.844115i	$-0.680126\pi$
$523$	−1.67444	+	0.966739i	−0.0732182	+	0.0422726i	0.462944	+	0.886388i	$0.346793\pi$
$524$		0			0
$525$	−3.92503	−	2.36519i	−0.171302	−	0.103225i
$526$		0			0
$527$	−1.38005	+	0.796772i	−0.0601159	+	0.0347079i
$528$		0			0
$529$	8.33547	−	14.4375i	0.362412	−	0.627716i
$530$		0			0
$531$	−12.0699	−	22.7935i	−0.523790	−	0.989152i
$532$		0			0
$533$		−	24.0806i		−	1.04305i
$534$		0			0
$535$	1.22015	+	0.704454i	0.0527517	+	0.0304562i
$536$		0			0
$537$	−42.2385	−	0.773134i	−1.82273	−	0.0333632i
$538$		0			0
$539$	0.0270716	−	32.0556i	0.00116606	−	1.38073i
$540$		0			0
$541$	−9.53749	−	16.5194i	−0.410049	−	0.710225i	0.584846	−	0.811144i	$-0.301155\pi$
$541$	−9.53749	−	16.5194i	−0.410049	−	0.710225i	−0.994895	+	0.100919i	$0.967822\pi$
$542$		0			0
$543$	12.4964	+	22.5894i	0.536274	+	0.969403i
$544$		0			0
$545$	−14.1903			−0.607846
$546$		0			0
$547$	36.9219			1.57867			0.789334	−	0.613964i	$-0.210426\pi$
$547$	36.9219			1.57867			0.789334	+	0.613964i	$0.210426\pi$
$548$		0			0
$549$	−1.49533	+	40.8334i	−0.0638191	+	1.74273i
$550$		0			0
$551$	8.59867	+	14.8933i	0.366316	+	0.634478i
$552$		0			0
$553$	34.0250	+	0.0143674i	1.44689	+	0.000610965i
$554$		0			0
$555$	−0.154968	+	8.46634i	−0.00657803	+	0.359376i
$556$		0			0
$557$	−39.3573	−	22.7229i	−1.66762	−	0.962802i	−0.968915	−	0.247394i	$-0.920426\pi$
$557$	−39.3573	−	22.7229i	−1.66762	−	0.962802i	−0.698707	−	0.715408i	$-0.746241\pi$
$558$		0			0
$559$		−	0.852689i		−	0.0360649i
$560$		0			0
$561$	−9.73282	+	16.1670i	−0.410920	+	0.682573i
$562$		0			0
$563$	3.36343	−	5.82564i	0.141752	−	0.245521i	−0.786405	−	0.617712i	$-0.788060\pi$
$563$	3.36343	−	5.82564i	0.141752	−	0.245521i	0.928156	+	0.372190i	$0.121393\pi$
$564$		0			0
$565$	−9.88179	+	5.70526i	−0.415730	+	0.240022i
$566$		0			0
$567$	23.7472	+	1.75168i	0.997291	+	0.0735636i
$568$		0			0
$569$	7.80887	−	4.50846i	0.327365	−	0.189004i	−0.327306	−	0.944919i	$-0.606141\pi$
$569$	7.80887	−	4.50846i	0.327365	−	0.189004i	0.654671	+	0.755914i	$0.272807\pi$
$570$		0			0
$571$	20.4021	−	35.3374i	0.853799	−	1.47882i	−0.0239548	−	0.999713i	$-0.507626\pi$
$571$	20.4021	−	35.3374i	0.853799	−	1.47882i	0.877754	−	0.479111i	$-0.159041\pi$
$572$		0			0
$573$	10.1755	−	16.9023i	0.425087	−	0.706105i
$574$		0			0
$575$			6.29849i			0.262665i
$576$		0			0
$577$	1.66415	+	0.960799i	0.0692796	+	0.0399986i	0.534240	−	0.845333i	$-0.320598\pi$
$577$	1.66415	+	0.960799i	0.0692796	+	0.0399986i	−0.464960	+	0.885332i	$0.653931\pi$
$578$		0			0
$579$	−0.0891018	+	4.86788i	−0.00370294	+	0.202302i
$580$		0			0
$581$	7.81708	−	13.5264i	0.324307	−	0.561169i
$582$		0			0
$583$	−16.5793	−	28.7162i	−0.686645	−	1.18930i
$584$		0			0
$585$	0.366860	−	10.0179i	0.0151678	−	0.414190i
$586$		0			0
$587$	−23.2576			−0.959944			−0.479972	−	0.877284i	$-0.659353\pi$
$587$	−23.2576			−0.959944			−0.479972	+	0.877284i	$0.659353\pi$
$588$		0			0
$589$	1.09988			0.0453199
$590$		0			0
$591$	−10.1388	−	18.3275i	−0.417054	−	0.753894i
$592$		0			0
$593$	−2.11803	−	3.66853i	−0.0869770	−	0.150649i	0.819255	−	0.573429i	$-0.194387\pi$
$593$	−2.11803	−	3.66853i	−0.0869770	−	0.150649i	−0.906232	+	0.422781i	$0.861054\pi$
$594$		0			0
$595$	3.14961	−	5.44996i	0.129121	−	0.223427i
$596$		0			0
$597$	3.96868	+	0.0726427i	0.162427	+	0.00297307i
$598$		0			0
$599$	3.49694	+	2.01896i	0.142881	+	0.0824925i	0.569736	−	0.821827i	$-0.307045\pi$
$599$	3.49694	+	2.01896i	0.142881	+	0.0824925i	−0.426855	+	0.904320i	$0.640379\pi$
$600$		0			0
$601$			0.420595i			0.0171564i	0.999963	+	0.00857821i	$0.00273056\pi$
$601$			0.420595i			0.0171564i	−0.999963	+	0.00857821i	$0.997269\pi$
$602$		0			0
$603$	−15.8590	−	29.9490i	−0.645829	−	1.21962i
$604$		0			0
$605$	−4.98532	+	8.63483i	−0.202682	+	0.351056i
$606$		0			0
$607$	−33.6082	+	19.4037i	−1.36411	+	0.787572i	−0.990169	−	0.139878i	$-0.955329\pi$
$607$	−33.6082	+	19.4037i	−1.36411	+	0.787572i	−0.373946	+	0.927450i	$0.621996\pi$
$608$		0			0
$609$	−47.9835	−	0.898559i	−1.94439	−	0.0364115i
$610$		0			0
$611$	2.93231	−	1.69297i	0.118628	−	0.0684901i
$612$		0			0
$613$	−1.20336	+	2.08429i	−0.0486034	+	0.0841836i	−0.889304	−	0.457317i	$-0.848810\pi$
$613$	−1.20336	+	2.08429i	−0.0486034	+	0.0841836i	0.840700	+	0.541501i	$0.182144\pi$
$614$		0			0
$615$	10.6936	+	6.43773i	0.431208	+	0.259594i
$616$		0			0
$617$			37.0222i			1.49046i	0.666809	+	0.745229i	$0.267660\pi$
$617$			37.0222i			1.49046i	−0.666809	+	0.745229i	$0.732340\pi$
$618$		0			0
$619$	−38.4406	−	22.1937i	−1.54506	−	0.892040i	−0.998508	−	0.0546145i	$-0.982607\pi$
$619$	−38.4406	−	22.1937i	−1.54506	−	0.892040i	−0.546551	−	0.837426i	$-0.684060\pi$
$620$		0			0
$621$	−14.7839	−	29.1985i	−0.593256	−	1.17170i
$622$		0			0
$623$	−17.4130	−	0.00735281i	−0.697636	−	0.000294584i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	11.3971	−	6.30486i	0.455155	−	0.251792i
$628$		0			0
$629$	−11.6313			−0.463770
$630$		0			0
$631$	43.2826			1.72305			0.861526	−	0.507713i	$-0.169509\pi$
$631$	43.2826			1.72305			0.861526	+	0.507713i	$0.169509\pi$
$632$		0			0
$633$	2.16471	−	1.19752i	0.0860395	−	0.0475971i
$634$		0			0
$635$	2.23891	+	3.87790i	0.0888483	+	0.153890i
$636$		0			0
$637$	−20.2669	+	11.6783i	−0.803005	+	0.462711i
$638$		0			0
$639$	−7.89452	−	4.95169i	−0.312302	−	0.195886i
$640$		0			0
$641$	3.29528	+	1.90253i	0.130156	+	0.0751453i	0.563664	−	0.826004i	$-0.309391\pi$
$641$	3.29528	+	1.90253i	0.130156	+	0.0751453i	−0.433509	+	0.901149i	$0.642725\pi$
$642$		0			0
$643$			32.4867i			1.28115i	0.767896	+	0.640574i	$0.221304\pi$
$643$			32.4867i			1.28115i	−0.767896	+	0.640574i	$0.778696\pi$
$644$		0			0
$645$	0.378658	+	0.227959i	0.0149097	+	0.00897586i
$646$		0			0
$647$	17.9573	−	31.1030i	0.705975	−	1.22278i	−0.260363	−	0.965511i	$-0.583842\pi$
$647$	17.9573	−	31.1030i	0.705975	−	1.22278i	0.966338	−	0.257274i	$-0.0828243\pi$
$648$		0			0
$649$	34.0957	−	19.6851i	1.33837	−	0.772710i
$650$		0			0
$651$	−1.58420	+	2.62898i	−0.0620897	+	0.103038i
$652$		0			0
$653$	−5.22686	+	3.01773i	−0.204543	+	0.118093i	−0.598773	−	0.800919i	$-0.704345\pi$
$653$	−5.22686	+	3.01773i	−0.204543	+	0.118093i	0.394230	+	0.919012i	$0.371011\pi$
$654$		0			0
$655$	−2.84104	+	4.92083i	−0.111009	+	0.192273i
$656$		0			0
$657$	−36.5402	+	19.3493i	−1.42557	+	0.754887i
$658$		0			0
$659$			44.2426i			1.72345i	0.507378	+	0.861724i	$0.330615\pi$
$659$			44.2426i			1.72345i	−0.507378	+	0.861724i	$0.669385\pi$
$660$		0			0
$661$	−32.5001	−	18.7639i	−1.26411	−	0.729832i	−0.290240	−	0.956954i	$-0.593735\pi$
$661$	−32.5001	−	18.7639i	−1.26411	−	0.729832i	−0.973866	+	0.227122i	$0.927068\pi$
$662$		0			0
$663$	13.7675	+	0.252001i	0.534686	+	0.00978690i
$664$		0			0
$665$	−3.76347	+	2.17072i	−0.145941	+	0.0841770i
$666$		0			0
$667$	32.9811	+	57.1249i	1.27703	+	2.21188i
$668$		0			0
$669$	0.853893	+	1.54355i	0.0330134	+	0.0596771i
$670$		0			0
$671$	−62.3722			−2.40785
$672$		0			0
$673$	−42.0580			−1.62122			−0.810608	−	0.585589i	$-0.800863\pi$
$673$	−42.0580			−1.62122			−0.810608	+	0.585589i	$0.800863\pi$
$674$		0			0
$675$	4.35064	+	2.84111i	0.167456	+	0.109355i
$676$		0			0
$677$	8.48672	+	14.6994i	0.326171	+	0.564945i	0.981749	−	0.190183i	$-0.0609081\pi$
$677$	8.48672	+	14.6994i	0.326171	+	0.564945i	−0.655577	+	0.755128i	$0.727575\pi$
$678$		0			0
$679$	10.7968	+	6.23959i	0.414342	+	0.239454i
$680$		0			0
$681$	−0.0369548	+	2.01894i	−0.00141611	+	0.0773661i
$682$		0			0
$683$	−28.4430	−	16.4216i	−1.08834	−	0.628354i	−0.155206	−	0.987882i	$-0.549604\pi$
$683$	−28.4430	−	16.4216i	−1.08834	−	0.628354i	−0.933134	+	0.359528i	$0.882938\pi$
$684$		0			0
$685$		−	13.1839i		−	0.503729i
$686$		0			0
$687$	22.3589	−	37.1400i	0.853044	−	1.41698i
$688$		0			0
$689$	−12.0979	+	20.9541i	−0.460892	+	0.798288i
$690$		0			0
$691$	−4.90189	+	2.83011i	−0.186477	+	0.107662i	−0.590332	−	0.807161i	$-0.701003\pi$
$691$	−4.90189	+	2.83011i	−0.186477	+	0.107662i	0.403855	+	0.914823i	$0.367670\pi$
$692$		0			0
$693$	−1.34551	+	36.3227i	−0.0511116	+	1.37979i
$694$		0			0
$695$	3.66093	−	2.11364i	0.138867	−	0.0801749i
$696$		0			0
$697$	−8.57254	+	14.8481i	−0.324708	+	0.562411i
$698$		0			0
$699$	−6.60558	+	10.9724i	−0.249846	+	0.415015i
$700$		0			0
$701$			4.15192i			0.156816i	0.996921	+	0.0784078i	$0.0249836\pi$
$701$			4.15192i			0.156816i	−0.996921	+	0.0784078i	$0.975016\pi$
$702$		0			0
$703$	6.95251	+	4.01403i	0.262219	+	0.151392i
$704$		0			0
$705$	−0.0321192	+	1.75476i	−0.00120968	+	0.0660883i
$706$		0			0
$707$	12.2054	+	21.1610i	0.459030	+	0.795840i
$708$		0			0
$709$	−11.4637	−	19.8557i	−0.430528	−	0.745697i	0.566390	−	0.824137i	$-0.308339\pi$
$709$	−11.4637	−	19.8557i	−0.430528	−	0.745697i	−0.996919	+	0.0784399i	$0.975006\pi$
$710$		0			0
$711$	−38.5549	−	1.41189i	−1.44592	−	0.0529501i
$712$		0			0
$713$	4.21872			0.157992
$714$		0			0
$715$	15.3022			0.572270
$716$		0			0
$717$	6.27809	+	11.3487i	0.234459	+	0.423824i
$718$		0			0
$719$	11.8053	+	20.4474i	0.440263	+	0.762558i	0.997709	−	0.0676554i	$-0.0215519\pi$
$719$	11.8053	+	20.4474i	0.440263	+	0.762558i	−0.557446	+	0.830213i	$0.688219\pi$
$720$		0			0
$721$	0.0131923	−	31.2421i	0.000491306	−	1.16352i
$722$		0			0
$723$	−28.9711	−	0.530288i	−1.07745	−	0.0197216i
$724$		0			0
$725$	−9.06962	−	5.23635i	−0.336837	−	0.194473i
$726$		0			0
$727$			23.9107i			0.886800i	0.896324	+	0.443400i	$0.146228\pi$
$727$			23.9107i			0.886800i	−0.896324	+	0.443400i	$0.853772\pi$
$728$		0			0
$729$	−26.8374	−	2.95896i	−0.993977	−	0.109591i
$730$		0			0
$731$	−0.303552	+	0.525767i	−0.0112273	+	0.0194462i
$732$		0			0
$733$	5.64644	−	3.25997i	0.208556	−	0.120410i	−0.392084	−	0.919929i	$-0.628246\pi$
$733$	5.64644	−	3.25997i	0.208556	−	0.120410i	0.600640	+	0.799519i	$0.294912\pi$
$734$		0			0
$735$	0.232125	−	12.1221i	0.00856205	−	0.447132i
$736$		0			0
$737$	44.7993	−	25.8649i	1.65020	−	0.952746i
$738$		0			0
$739$	−19.2254	+	33.2993i	−0.707217	+	1.22494i	0.258669	+	0.965966i	$0.416716\pi$
$739$	−19.2254	+	33.2993i	−0.707217	+	1.22494i	−0.965885	+	0.258970i	$0.916617\pi$
$740$		0			0
$741$	−8.14246	−	4.90189i	−0.299121	−	0.180075i
$742$		0			0
$743$		−	22.9796i		−	0.843039i	−0.906819	−	0.421519i	$-0.861497\pi$
$743$		−	22.9796i		−	0.843039i	0.906819	−	0.421519i	$-0.138503\pi$
$744$		0			0
$745$	−3.91208	−	2.25864i	−0.143328	−	0.0827502i
$746$		0			0
$747$	−9.41275	+	15.0068i	−0.344394	+	0.549070i
$748$		0			0
$749$	−0.00157403	+	3.72762i	−5.75137e−5	+	0.136204i
$750$		0			0
$751$	16.7413	+	28.9968i	0.610898	+	1.05811i	0.991089	+	0.133199i	$0.0425249\pi$
$751$	16.7413	+	28.9968i	0.610898	+	1.05811i	−0.380191	+	0.924908i	$0.624142\pi$
$752$		0			0
$753$	23.6245	−	13.0691i	0.860924	−	0.476263i
$754$		0			0
$755$	−24.1629			−0.879379
$756$		0			0
$757$	23.7732			0.864050			0.432025	−	0.901862i	$-0.357799\pi$
$757$	23.7732			0.864050			0.432025	+	0.901862i	$0.357799\pi$
$758$		0			0
$759$	43.7146	−	24.1829i	1.58674	−	0.877784i
$760$		0			0
$761$	0.339493	+	0.588019i	0.0123066	+	0.0213157i	0.872113	−	0.489304i	$-0.162749\pi$
$761$	0.339493	+	0.588019i	0.0123066	+	0.0213157i	−0.859807	+	0.510620i	$0.829416\pi$
$762$		0			0
$763$	−18.7583	−	32.5220i	−0.679095	−	1.17738i
$764$		0			0
$765$	−3.79252	+	6.04645i	−0.137119	+	0.218610i
$766$		0			0
$767$	−24.8795	−	14.3642i	−0.898346	−	0.518660i
$768$		0			0
$769$			6.05929i			0.218503i	0.994014	+	0.109252i	$0.0348455\pi$
$769$			6.05929i			0.218503i	−0.994014	+	0.109252i	$0.965155\pi$
$770$		0			0
$771$	−24.5130	−	14.7572i	−0.882814	−	0.531469i
$772$		0			0
$773$	−0.553516	+	0.958718i	−0.0199086	+	0.0344827i	−0.875808	−	0.482660i	$-0.839671\pi$
$773$	−0.553516	+	0.958718i	−0.0199086	+	0.0344827i	0.855899	+	0.517142i	$0.173004\pi$
$774$		0			0
$775$	−0.580062	+	0.334899i	−0.0208364	+	0.0120299i
$776$		0			0
$777$	−19.6084	+	10.8366i	−0.703448	+	0.388759i
$778$		0			0
$779$	10.2483	−	5.91688i	0.367185	−	0.211994i
$780$		0			0
$781$	7.11248	−	12.3192i	0.254505	−	0.440815i
$782$		0			0
$783$	54.3357	+	2.98635i	1.94180	+	0.106724i
$784$		0			0
$785$		−	23.0489i		−	0.822650i
$786$		0			0
$787$	18.2006	+	10.5081i	0.648781	+	0.374574i	0.787989	−	0.615689i	$-0.211122\pi$
$787$	18.2006	+	10.5081i	0.648781	+	0.374574i	−0.139208	+	0.990263i	$0.544456\pi$
$788$		0			0
$789$	17.4432	+	0.319281i	0.620994	+	0.0113667i
$790$		0			0
$791$	−26.1384	−	15.1057i	−0.929374	−	0.537098i
$792$		0			0
$793$	22.7564	+	39.4152i	0.808102	+	1.39967i
$794$		0			0
$795$	−6.07096	−	10.9743i	−0.215315	−	0.389217i
$796$		0			0
$797$	0.858844			0.0304218			0.0152109	−	0.999884i	$-0.495158\pi$
$797$	0.858844			0.0304218			0.0152109	+	0.999884i	$0.495158\pi$
$798$		0			0
$799$	−2.41074			−0.0852860
$800$		0			0
$801$	19.7312	+	0.722563i	0.697168	+	0.0255305i
$802$		0			0
$803$	−31.5573	−	54.6588i	−1.11363	−	1.92887i
$804$		0			0
$805$	−14.4352	+	8.32602i	−0.508773	+	0.293454i
$806$		0			0
$807$	−0.478139	+	26.1221i	−0.0168313	+	0.919541i
$808$		0			0
$809$	36.3644	+	20.9950i	1.27850	+	0.738144i	0.976573	−	0.215186i	$-0.0690359\pi$
$809$	36.3644	+	20.9950i	1.27850	+	0.738144i	0.301930	+	0.953330i	$0.402369\pi$
$810$		0			0
$811$		−	14.5311i		−	0.510257i	−0.966907	−	0.255128i	$-0.917882\pi$
$811$		−	14.5311i		−	0.510257i	0.966907	−	0.255128i	$-0.0821177\pi$
$812$		0			0
$813$	−9.85192	+	16.3649i	−0.345522	+	0.573941i
$814$		0			0
$815$	−4.48563	+	7.76934i	−0.157125	+	0.272148i
$816$		0			0
$817$	0.362891	−	0.209515i	0.0126960	−	0.00733002i
$818$		0			0
$819$	23.4445	−	12.4020i	0.819218	−	0.433361i
$820$		0			0
$821$	12.8950	−	7.44495i	0.450039	−	0.259830i	−0.257807	−	0.966196i	$-0.583000\pi$
$821$	12.8950	−	7.44495i	0.450039	−	0.259830i	0.707847	+	0.706366i	$0.249667\pi$
$822$		0			0
$823$	13.9686	−	24.1944i	0.486916	−	0.843363i	−0.512971	−	0.858406i	$-0.671455\pi$
$823$	13.9686	−	24.1944i	0.486916	−	0.843363i	0.999887	+	0.0150429i	$0.00478850\pi$
$824$		0			0
$825$	−4.09090	+	6.79533i	−0.142427	+	0.236583i
$826$		0			0
$827$		−	2.99272i		−	0.104067i	−0.998645	−	0.0520335i	$-0.983430\pi$
$827$		−	2.99272i		−	0.104067i	0.998645	−	0.0520335i	$-0.0165703\pi$
$828$		0			0
$829$	−2.27416	−	1.31299i	−0.0789850	−	0.0456020i	0.459987	−	0.887925i	$-0.347854\pi$
$829$	−2.27416	−	1.31299i	−0.0789850	−	0.0456020i	−0.538972	+	0.842323i	$0.681187\pi$
$830$		0			0
$831$	0.364965	−	19.9390i	0.0126605	−	0.691678i
$832$		0			0
$833$	16.6540	+	0.0140646i	0.577026	+	0.000487311i
$834$		0			0
$835$	6.01434	+	10.4171i	0.208135	+	0.360500i
$836$		0			0
$837$	1.90297	−	2.91405i	0.0657764	−	0.100724i
$838$		0			0
$839$	−29.6528			−1.02373			−0.511864	−	0.859067i	$-0.671045\pi$
$839$	−29.6528			−1.02373			−0.511864	+	0.859067i	$0.671045\pi$
$840$		0			0
$841$	−80.6773			−2.78198
$842$		0			0
$843$	18.3114	+	33.1008i	0.630677	+	1.14005i
$844$		0			0
$845$	0.917027	+	1.58834i	0.0315467	+	0.0546405i
$846$		0			0
$847$	−26.3798	−	0.0111392i	−0.906422	−	0.000382746i
$848$		0			0
$849$	−17.8572	−	0.326859i	−0.612858	−	0.0112178i
$850$		0			0
$851$	26.6670	+	15.3962i	0.914134	+	0.527776i
$852$		0			0
$853$			17.9134i			0.613341i	0.951816	+	0.306671i	$0.0992150\pi$
$853$			17.9134i			0.613341i	−0.951816	+	0.306671i	$0.900785\pi$
$854$		0			0
$855$	4.35362	−	2.30539i	0.148891	−	0.0788427i
$856$		0			0
$857$	−7.63917	+	13.2314i	−0.260949	+	0.451977i	−0.966494	−	0.256688i	$-0.917369\pi$
$857$	−7.63917	+	13.2314i	−0.260949	+	0.451977i	0.705545	+	0.708665i	$0.250702\pi$
$858$		0			0
$859$	−0.803639	+	0.463981i	−0.0274198	+	0.0158308i	−0.513647	−	0.858001i	$-0.671706\pi$
$859$	−0.803639	+	0.463981i	−0.0274198	+	0.0158308i	0.486227	+	0.873832i	$0.338373\pi$
$860$		0			0
$861$	−0.618313	+	33.0182i	−0.0210720	+	1.12526i
$862$		0			0
$863$	20.8695	−	12.0490i	0.710405	−	0.410153i	−0.100806	−	0.994906i	$-0.532142\pi$
$863$	20.8695	−	12.0490i	0.710405	−	0.410153i	0.811211	+	0.584754i	$0.198809\pi$
$864$		0			0
$865$	9.48818	−	16.4340i	0.322608	−	0.558773i
$866$		0			0
$867$	16.8270	+	10.1301i	0.571474	+	0.344037i
$868$		0			0
$869$		−	58.8918i		−	1.99777i
$870$		0			0
$871$	−32.6899	−	18.8735i	−1.10765	−	0.639505i
$872$		0			0
$873$	−11.9784	−	7.51325i	−0.405408	−	0.254285i
$874$		0			0
$875$	1.32384	−	2.29073i	0.0447541	−	0.0774408i
$876$		0			0
$877$	21.1571	+	36.6451i	0.714423	+	1.23742i	0.963182	+	0.268852i	$0.0866442\pi$
$877$	21.1571	+	36.6451i	0.714423	+	1.23742i	−0.248758	+	0.968566i	$0.580022\pi$
$878$		0			0
$879$	−27.7000	+	15.3236i	−0.934297	+	0.516853i
$880$		0			0
$881$	−44.6817			−1.50537			−0.752683	−	0.658384i	$-0.771240\pi$
$881$	−44.6817			−1.50537			−0.752683	+	0.658384i	$0.771240\pi$
$882$		0			0
$883$	1.03834			0.0349430			0.0174715	−	0.999847i	$-0.494438\pi$
$883$	1.03834			0.0349430			0.0174715	+	0.999847i	$0.494438\pi$
$884$		0			0
$885$	13.0301	−	7.20824i	0.438001	−	0.242302i
$886$		0			0
$887$	28.0197	+	48.5316i	0.940811	+	1.62953i	0.763929	+	0.645300i	$0.223268\pi$
$887$	28.0197	+	48.5316i	0.940811	+	1.62953i	0.176882	+	0.984232i	$0.443399\pi$
$888$		0			0
$889$	−5.92792	+	10.2575i	−0.198816	+	0.344024i
$890$		0			0
$891$	3.01452	−	41.1040i	0.100990	−	1.37703i
$892$		0			0
$893$	1.44100	+	0.831963i	0.0482213	+	0.0278406i
$894$		0			0
$895$		−	24.3905i		−	0.815284i
$896$		0			0
$897$	−31.2312	−	18.8017i	−1.04278	−	0.627770i
$898$		0			0
$899$	−3.50730	+	6.07481i	−0.116975	+	0.202606i
$900$		0			0
$901$	14.9191	−	8.61352i	0.497026	−	0.286958i
$902$		0			0
$903$	−0.0218943	+	1.16917i	−0.000728597	+	0.0389074i
$904$		0			0
$905$	−12.9078	+	7.45230i	−0.429068	+	0.247723i
$906$		0			0
$907$	−18.8838	+	32.7077i	−0.627027	+	1.08604i	0.361118	+	0.932520i	$0.382395\pi$
$907$	−18.8838	+	32.7077i	−0.627027	+	1.08604i	−0.988145	+	0.153523i	$0.950938\pi$
$908$		0			0
$909$	−12.9626	−	24.4792i	−0.429941	−	0.811924i
$910$		0			0
$911$		−	48.5155i		−	1.60739i	−0.595041	−	0.803696i	$-0.702864\pi$
$911$		−	48.5155i		−	1.60739i	0.595041	−	0.803696i	$-0.297136\pi$
$912$		0			0
$913$	−23.4177	−	13.5202i	−0.775013	−	0.447454i
$914$		0			0
$915$	−23.5870	−	0.431737i	−0.779762	−	0.0142728i
$916$		0			0
$917$	−15.0334	−	0.00634800i	−0.496446	−	0.000209629i
$918$		0			0
$919$	−5.38077	−	9.31976i	−0.177495	−	0.307431i	0.763527	−	0.645776i	$-0.223466\pi$
$919$	−5.38077	−	9.31976i	−0.177495	−	0.307431i	−0.941022	+	0.338346i	$0.890133\pi$
$920$		0			0
$921$	−24.0986	−	43.5622i	−0.794076	−	1.43542i
$922$		0			0
$923$	−10.3799			−0.341658
$924$		0			0
$925$	−4.88886			−0.160745
$926$		0			0
$927$	−1.29641	+	35.4014i	−0.0425797	+	1.16274i
$928$		0			0
$929$	2.28184	+	3.95227i	0.0748648	+	0.129670i	0.901027	−	0.433762i	$-0.142814\pi$
$929$	2.28184	+	3.95227i	0.0748648	+	0.129670i	−0.826163	+	0.563432i	$0.809481\pi$
$930$		0			0
$931$	−9.94992	−	5.75580i	−0.326096	−	0.188639i
$932$		0			0
$933$	−0.274902	+	15.0187i	−0.00899989	+	0.491689i
$934$		0			0
$935$	−9.43532	−	5.44748i	−0.308568	−	0.178152i
$936$		0			0
$937$			13.1080i			0.428220i	0.976810	+	0.214110i	$0.0686851\pi$
$937$			13.1080i			0.428220i	−0.976810	+	0.214110i	$0.931315\pi$
$938$		0			0
$939$	14.2551	−	23.6789i	0.465196	−	0.772731i
$940$		0			0
$941$	−5.26970	+	9.12739i	−0.171787	+	0.297545i	−0.939045	−	0.343795i	$-0.888288\pi$
$941$	−5.26970	+	9.12739i	−0.171787	+	0.297545i	0.767257	+	0.641339i	$0.221621\pi$
$942$		0			0
$943$	39.3085	−	22.6948i	1.28006	−	0.739044i
$944$		0			0
$945$	−0.760249	+	13.7267i	−0.0247309	+	0.446529i
$946$		0			0
$947$	29.2418	−	16.8828i	0.950231	−	0.548616i	0.0570785	−	0.998370i	$-0.481821\pi$
$947$	29.2418	−	16.8828i	0.950231	−	0.548616i	0.893153	+	0.449753i	$0.148488\pi$
$948$		0			0
$949$	−23.0272	+	39.8843i	−0.747495	+	1.29470i
$950$		0			0
$951$	−2.13594	+	3.54798i	−0.0692627	+	0.115051i
$952$		0			0
$953$		−	33.0923i		−	1.07197i	−0.844229	−	0.535983i	$-0.819941\pi$
$953$		−	33.0923i		−	1.07197i	0.844229	−	0.535983i	$-0.180059\pi$
$954$		0			0
$955$	9.86445	+	5.69524i	0.319206	+	0.184294i
$956$		0			0
$957$	−1.52019	+	83.0524i	−0.0491408	+	2.68470i
$958$		0			0
$959$	30.2154	−	17.4278i	0.975705	−	0.562774i
$960$		0			0
$961$	−15.2757	−	26.4583i	−0.492764	−	0.853492i
$962$		0			0
$963$	0.154680	−	4.22389i	0.00498450	−	0.136113i
$964$		0			0
$965$	−2.81094			−0.0904874
$966$		0			0
$967$	−12.5703			−0.404232			−0.202116	−	0.979362i	$-0.564782\pi$
$967$	−12.5703			−0.404232			−0.202116	+	0.979362i	$0.564782\pi$
$968$		0			0
$969$	3.27559	+	5.92116i	0.105227	+	0.190215i
$970$		0			0
$971$	22.9191	+	39.6971i	0.735510	+	1.27394i	0.954499	+	0.298213i	$0.0963907\pi$
$971$	22.9191	+	39.6971i	0.735510	+	1.27394i	−0.218989	+	0.975727i	$0.570276\pi$
$972$		0			0
$973$	9.68355	+	5.59625i	0.310440	+	0.179408i
$974$		0			0
$975$	5.78676	+	0.105921i	0.185325	+	0.00339219i
$976$		0			0
$977$	15.1701	+	8.75845i	0.485334	+	0.280208i	0.722637	−	0.691228i	$-0.242930\pi$
$977$	15.1701	+	8.75845i	0.485334	+	0.280208i	−0.237303	+	0.971436i	$0.576263\pi$
$978$		0			0
$979$			30.1390i			0.963248i
$980$		0			0
$981$	19.9220	+	37.6217i	0.636060	+	1.20117i
$982$		0			0
$983$	−9.58460	+	16.6010i	−0.305701	+	0.529490i	−0.977417	−	0.211319i	$-0.932224\pi$
$983$	−9.58460	+	16.6010i	−0.305701	+	0.529490i	0.671716	+	0.740809i	$0.265558\pi$
$984$		0			0
$985$	10.4725	−	6.04631i	0.333682	−	0.192651i
$986$		0			0
$987$	−4.06411	+	2.24602i	−0.129362	+	0.0714918i
$988$		0			0
$989$	1.39191	−	0.803617i	0.0442600	−	0.0255535i
$990$		0			0
$991$	−6.91260	+	11.9730i	−0.219586	+	0.380334i	−0.954681	−	0.297629i	$-0.903804\pi$
$991$	−6.91260	+	11.9730i	−0.219586	+	0.380334i	0.735095	+	0.677964i	$0.237137\pi$
$992$		0			0
$993$	−38.1910	−	22.9916i	−1.21196	−	0.729617i
$994$		0			0
$995$			2.29170i			0.0726518i
$996$		0			0
$997$	5.27252	+	3.04409i	0.166983	+	0.0964074i	0.581162	−	0.813788i	$-0.302598\pi$
$997$	5.27252	+	3.04409i	0.166983	+	0.0964074i	−0.414180	+	0.910195i	$0.635932\pi$
$998$		0			0
$999$	22.6638	−	11.4752i	0.717050	−	0.363059i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	840.2.cp.b.521.13	yes	32
3.2	odd	2		840.2.cp.a.521.9	✓	32
7.5	odd	6		840.2.cp.a.761.9	yes	32
21.5	even	6	inner	840.2.cp.b.761.13	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.cp.a.521.9	✓	32	3.2	odd	2
840.2.cp.a.761.9	yes	32	7.5	odd	6
840.2.cp.b.521.13	yes	32	1.1	even	1	trivial
840.2.cp.b.761.13	yes	32	21.5	even	6	inner

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.cp (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.51560 - 0.838429i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-1.32384 + 2.29073i) q^{7} +(1.59407 - 2.54144i) q^{9} +(3.96585 + 2.28969i) q^{11} -3.34155i q^{13} +(1.48390 + 0.893332i) q^{15} +(-1.18957 + 2.06040i) q^{17} +(1.42211 - 0.821057i) q^{19} +(-0.0858002 + 4.58177i) q^{21} +(5.45465 - 3.14924i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(0.285156 - 5.18832i) q^{27} +10.4727i q^{29} +(0.580062 + 0.334899i) q^{31} +(7.93038 + 0.145158i) q^{33} +(-2.64575 - 0.00111720i) q^{35} +(2.44443 + 4.23388i) q^{37} +(-2.80165 - 5.06444i) q^{39} +7.20642 q^{41} +0.255178 q^{43} +(2.99799 + 0.109787i) q^{45} +(0.506642 + 0.877529i) q^{47} +(-3.49488 - 6.06513i) q^{49} +(-0.0754144 + 4.12010i) q^{51} +(-6.27078 - 3.62044i) q^{53} +4.57937i q^{55} +(1.46695 - 2.43673i) q^{57} +(4.29866 - 7.44549i) q^{59} +(-11.7955 + 6.81012i) q^{61} +(3.71145 + 7.01606i) q^{63} +(2.89387 - 1.67077i) q^{65} +(5.64814 - 9.78286i) q^{67} +(5.62664 - 9.34632i) q^{69} -3.10631i q^{71} +(-11.9359 - 6.89118i) q^{73} +(-0.0316982 + 1.73176i) q^{75} +(-10.4952 + 6.05351i) q^{77} +(-6.43012 - 11.1373i) q^{79} +(-3.91786 - 8.10249i) q^{81} -5.90484 q^{83} -2.37914 q^{85} +(8.78061 + 15.8724i) q^{87} +(3.29074 + 5.69973i) q^{89} +(7.65458 + 4.42369i) q^{91} +(1.15993 + 0.0212314i) q^{93} +(1.42211 + 0.821057i) q^{95} -4.71324i q^{97} +(12.1410 - 6.42906i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{5} - 2 q^{7} + 8 q^{9} + 6 q^{19} - 14 q^{21} + 24 q^{23} - 16 q^{25} + 24 q^{27} + 42 q^{31} + 18 q^{33} + 2 q^{35} + 6 q^{37} + 12 q^{39} + 44 q^{41} - 20 q^{43} + 10 q^{45} + 4 q^{47} + 16 q^{49}+ \cdots - 8 q^{99}+O(q^{100}) \) 32 * q + 16 * q^5 - 2 * q^7 + 8 * q^9 + 6 * q^19 - 14 * q^21 + 24 * q^23 - 16 * q^25 + 24 * q^27 + 42 * q^31 + 18 * q^33 + 2 * q^35 + 6 * q^37 + 12 * q^39 + 44 * q^41 - 20 * q^43 + 10 * q^45 + 4 * q^47 + 16 * q^49 - 36 * q^51 + 12 * q^59 - 18 * q^61 + 34 * q^63 - 6 * q^65 - 6 * q^67 - 34 * q^69 - 6 * q^73 + 40 * q^77 - 2 * q^79 - 12 * q^81 - 88 * q^83 - 72 * q^87 - 6 * q^89 - 26 * q^91 + 50 * q^93 + 6 * q^95 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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