LMFDB - Embedded newform 1680.2.dx.d.31.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1680,2,Mod(31,1680)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1680, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 0, 0, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1680.31"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1680.dx (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,2,0,0,0,0,0,-2,0,6,0,0,0,0,0,18] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(17)] == traces)

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

Self dual:	no
Analytic conductor:	$13.4148675396$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.1
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1680.31
Dual form			1680.2.dx.d.271.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 - 0.866025i) q^{3} +(-0.866025 + 0.500000i) q^{5} +(-2.59808 - 0.500000i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(4.09808 + 2.36603i) q^{11} -1.00000i q^{13} +1.00000i q^{15} +(5.36603 + 3.09808i) q^{17} +(-2.23205 - 3.86603i) q^{19} +(-1.73205 + 2.00000i) q^{21} +(0.633975 - 0.366025i) q^{23} +(0.500000 - 0.866025i) q^{25} -1.00000 q^{27} -0.732051 q^{29} +(-0.232051 + 0.401924i) q^{31} +(4.09808 - 2.36603i) q^{33} +(2.50000 - 0.866025i) q^{35} +(5.86603 + 10.1603i) q^{37} +(-0.866025 - 0.500000i) q^{39} -6.19615i q^{41} -8.46410i q^{43} +(0.866025 + 0.500000i) q^{45} +(0.464102 + 0.803848i) q^{47} +(6.50000 + 2.59808i) q^{49} +(5.36603 - 3.09808i) q^{51} +(0.732051 - 1.26795i) q^{53} -4.73205 q^{55} -4.46410 q^{57} +(7.09808 - 12.2942i) q^{59} +(9.92820 - 5.73205i) q^{61} +(0.866025 + 2.50000i) q^{63} +(0.500000 + 0.866025i) q^{65} +(10.7942 + 6.23205i) q^{67} -0.732051i q^{69} -15.6603i q^{71} +(5.13397 + 2.96410i) q^{73} +(-0.500000 - 0.866025i) q^{75} +(-9.46410 - 8.19615i) q^{77} +(6.69615 - 3.86603i) q^{79} +(-0.500000 + 0.866025i) q^{81} +8.73205 q^{83} -6.19615 q^{85} +(-0.366025 + 0.633975i) q^{87} +(1.09808 - 0.633975i) q^{89} +(-0.500000 + 2.59808i) q^{91} +(0.232051 + 0.401924i) q^{93} +(3.86603 + 2.23205i) q^{95} +8.92820i q^{97} -4.73205i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} - 2 q^{9} + 6 q^{11} + 18 q^{17} - 2 q^{19} + 6 q^{23} + 2 q^{25} - 4 q^{27} + 4 q^{29} + 6 q^{31} + 6 q^{33} + 10 q^{35} + 20 q^{37} - 12 q^{47} + 26 q^{49} + 18 q^{51} - 4 q^{53} - 12 q^{55}+ \cdots + 12 q^{95}+O(q^{100}) $ 4 * q + 2 * q^3 - 2 * q^9 + 6 * q^11 + 18 * q^17 - 2 * q^19 + 6 * q^23 + 2 * q^25 - 4 * q^27 + 4 * q^29 + 6 * q^31 + 6 * q^33 + 10 * q^35 + 20 * q^37 - 12 * q^47 + 26 * q^49 + 18 * q^51 - 4 * q^53 - 12 * q^55 - 4 * q^57 + 18 * q^59 + 12 * q^61 + 2 * q^65 + 12 * q^67 + 24 * q^73 - 2 * q^75 - 24 * q^77 + 6 * q^79 - 2 * q^81 + 28 * q^83 - 4 * q^85 + 2 * q^87 - 6 * q^89 - 2 * q^91 - 6 * q^93 + 12 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1680\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$421$	$1121$	$1471$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$1$	$1$	$-1$

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
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$		0			0
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$6$		0			0
$7$	−2.59808	−	0.500000i	−0.981981	−	0.188982i
$7$	−2.59808	−	0.500000i	−0.981981	−	0.188982i
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	4.09808	+	2.36603i	1.23562	+	0.713384i	0.968195	−	0.250196i	$-0.0804951\pi$
$11$	4.09808	+	2.36603i	1.23562	+	0.713384i	0.267421	+	0.963580i	$0.413828\pi$
$12$		0			0
$13$		−	1.00000i		−	0.277350i	−0.990338	−	0.138675i	$-0.955716\pi$
$13$		−	1.00000i		−	0.277350i	0.990338	−	0.138675i	$-0.0442844\pi$
$14$		0			0
$15$			1.00000i			0.258199i
$16$		0			0
$17$	5.36603	+	3.09808i	1.30145	+	0.751394i	0.980653	−	0.195753i	$-0.0627152\pi$
$17$	5.36603	+	3.09808i	1.30145	+	0.751394i	0.320799	+	0.947147i	$0.396049\pi$
$18$		0			0
$19$	−2.23205	−	3.86603i	−0.512068	−	0.886927i	−0.999902	−	0.0139909i	$-0.995546\pi$
$19$	−2.23205	−	3.86603i	−0.512068	−	0.886927i	0.487835	−	0.872936i	$-0.337787\pi$
$20$		0			0
$21$	−1.73205	+	2.00000i	−0.377964	+	0.436436i
$22$		0			0
$23$	0.633975	−	0.366025i	0.132193	−	0.0763216i	−0.432445	−	0.901660i	$-0.642349\pi$
$23$	0.633975	−	0.366025i	0.132193	−	0.0763216i	0.564638	+	0.825339i	$0.309016\pi$
$24$		0			0
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	−0.732051			−0.135938			−0.0679692	−	0.997687i	$-0.521652\pi$
$29$	−0.732051			−0.135938			−0.0679692	+	0.997687i	$0.521652\pi$
$30$		0			0
$31$	−0.232051	+	0.401924i	−0.0416776	+	0.0721876i	−0.886112	−	0.463472i	$-0.846604\pi$
$31$	−0.232051	+	0.401924i	−0.0416776	+	0.0721876i	0.844434	+	0.535659i	$0.179937\pi$
$32$		0			0
$33$	4.09808	−	2.36603i	0.713384	−	0.411872i
$34$		0			0
$35$	2.50000	−	0.866025i	0.422577	−	0.146385i
$36$		0			0
$37$	5.86603	+	10.1603i	0.964369	+	1.67034i	0.711302	+	0.702887i	$0.248106\pi$
$37$	5.86603	+	10.1603i	0.964369	+	1.67034i	0.253067	+	0.967449i	$0.418561\pi$
$38$		0			0
$39$	−0.866025	−	0.500000i	−0.138675	−	0.0800641i
$40$		0			0
$41$		−	6.19615i		−	0.967676i	−0.875157	−	0.483838i	$-0.839242\pi$
$41$		−	6.19615i		−	0.967676i	0.875157	−	0.483838i	$-0.160758\pi$
$42$		0			0
$43$		−	8.46410i		−	1.29076i	−0.763860	−	0.645382i	$-0.776698\pi$
$43$		−	8.46410i		−	1.29076i	0.763860	−	0.645382i	$-0.223302\pi$
$44$		0			0
$45$	0.866025	+	0.500000i	0.129099	+	0.0745356i
$46$		0			0
$47$	0.464102	+	0.803848i	0.0676962	+	0.117253i	0.897887	−	0.440226i	$-0.145102\pi$
$47$	0.464102	+	0.803848i	0.0676962	+	0.117253i	−0.830191	+	0.557480i	$0.811768\pi$
$48$		0			0
$49$	6.50000	+	2.59808i	0.928571	+	0.371154i
$50$		0			0
$51$	5.36603	−	3.09808i	0.751394	−	0.433817i
$52$		0			0
$53$	0.732051	−	1.26795i	0.100555	−	0.174166i	−0.811359	−	0.584549i	$-0.801272\pi$
$53$	0.732051	−	1.26795i	0.100555	−	0.174166i	0.911913	+	0.410383i	$0.134605\pi$
$54$		0			0
$55$	−4.73205			−0.638070
$56$		0			0
$57$	−4.46410			−0.591285
$58$		0			0
$59$	7.09808	−	12.2942i	0.924091	−	1.60057i	0.131074	−	0.991373i	$-0.458157\pi$
$59$	7.09808	−	12.2942i	0.924091	−	1.60057i	0.793017	−	0.609200i	$-0.208509\pi$
$60$		0			0
$61$	9.92820	−	5.73205i	1.27118	−	0.733914i	0.295967	−	0.955198i	$-0.404358\pi$
$61$	9.92820	−	5.73205i	1.27118	−	0.733914i	0.975209	+	0.221284i	$0.0710249\pi$
$62$		0			0
$63$	0.866025	+	2.50000i	0.109109	+	0.314970i
$64$		0			0
$65$	0.500000	+	0.866025i	0.0620174	+	0.107417i
$66$		0			0
$67$	10.7942	+	6.23205i	1.31872	+	0.761366i	0.983524	−	0.180780i	$-0.0578623\pi$
$67$	10.7942	+	6.23205i	1.31872	+	0.761366i	0.335201	+	0.942146i	$0.391196\pi$
$68$		0			0
$69$		−	0.732051i		−	0.0881286i
$70$		0			0
$71$		−	15.6603i		−	1.85853i	−0.369414	−	0.929265i	$-0.620441\pi$
$71$		−	15.6603i		−	1.85853i	0.369414	−	0.929265i	$-0.379559\pi$
$72$		0			0
$73$	5.13397	+	2.96410i	0.600886	+	0.346922i	0.769390	−	0.638779i	$-0.220560\pi$
$73$	5.13397	+	2.96410i	0.600886	+	0.346922i	−0.168504	+	0.985701i	$0.553894\pi$
$74$		0			0
$75$	−0.500000	−	0.866025i	−0.0577350	−	0.100000i
$76$		0			0
$77$	−9.46410	−	8.19615i	−1.07853	−	0.934038i
$78$		0			0
$79$	6.69615	−	3.86603i	0.753376	−	0.434962i	−0.0735364	−	0.997293i	$-0.523429\pi$
$79$	6.69615	−	3.86603i	0.753376	−	0.434962i	0.826912	+	0.562331i	$0.190095\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	8.73205			0.958467			0.479234	−	0.877687i	$-0.340915\pi$
$83$	8.73205			0.958467			0.479234	+	0.877687i	$0.340915\pi$
$84$		0			0
$85$	−6.19615			−0.672067
$86$		0			0
$87$	−0.366025	+	0.633975i	−0.0392420	+	0.0679692i
$88$		0			0
$89$	1.09808	−	0.633975i	0.116396	−	0.0672012i	−0.440672	−	0.897668i	$-0.645260\pi$
$89$	1.09808	−	0.633975i	0.116396	−	0.0672012i	0.557068	+	0.830467i	$0.311926\pi$
$90$		0			0
$91$	−0.500000	+	2.59808i	−0.0524142	+	0.272352i
$92$		0			0
$93$	0.232051	+	0.401924i	0.0240625	+	0.0416776i
$94$		0			0
$95$	3.86603	+	2.23205i	0.396646	+	0.229004i
$96$		0			0
$97$			8.92820i			0.906522i	0.891378	+	0.453261i	$0.149739\pi$
$97$			8.92820i			0.906522i	−0.891378	+	0.453261i	$0.850261\pi$
$98$		0			0
$99$		−	4.73205i		−	0.475589i
$100$		0			0
$101$	−7.56218	−	4.36603i	−0.752465	−	0.434436i	0.0741190	−	0.997249i	$-0.476386\pi$
$101$	−7.56218	−	4.36603i	−0.752465	−	0.434436i	−0.826584	+	0.562814i	$0.809719\pi$
$102$		0			0
$103$	−1.13397	−	1.96410i	−0.111734	−	0.193529i	0.804736	−	0.593633i	$-0.202307\pi$
$103$	−1.13397	−	1.96410i	−0.111734	−	0.193529i	−0.916469	+	0.400105i	$0.868974\pi$
$104$		0			0
$105$	0.500000	−	2.59808i	0.0487950	−	0.253546i
$106$		0			0
$107$	−14.4904	+	8.36603i	−1.40084	+	0.808774i	−0.994479	−	0.104939i	$-0.966535\pi$
$107$	−14.4904	+	8.36603i	−1.40084	+	0.808774i	−0.406359	+	0.913713i	$0.633202\pi$
$108$		0			0
$109$	−8.96410	+	15.5263i	−0.858605	+	1.48715i	0.0146544	+	0.999893i	$0.495335\pi$
$109$	−8.96410	+	15.5263i	−0.858605	+	1.48715i	−0.873260	+	0.487255i	$0.837998\pi$
$110$		0			0
$111$	11.7321			1.11356
$112$		0			0
$113$	14.3923			1.35391			0.676957	−	0.736022i	$-0.263298\pi$
$113$	14.3923			1.35391			0.676957	+	0.736022i	$0.263298\pi$
$114$		0			0
$115$	−0.366025	+	0.633975i	−0.0341320	+	0.0591184i
$116$		0			0
$117$	−0.866025	+	0.500000i	−0.0800641	+	0.0462250i
$118$		0			0
$119$	−12.3923	−	10.7321i	−1.13600	−	0.983805i
$120$		0			0
$121$	5.69615	+	9.86603i	0.517832	+	0.896911i
$122$		0			0
$123$	−5.36603	−	3.09808i	−0.483838	−	0.279344i
$124$		0			0
$125$			1.00000i			0.0894427i
$126$		0			0
$127$		−	3.39230i		−	0.301018i	−0.988609	−	0.150509i	$-0.951909\pi$
$127$		−	3.39230i		−	0.301018i	0.988609	−	0.150509i	$-0.0480913\pi$
$128$		0			0
$129$	−7.33013	−	4.23205i	−0.645382	−	0.372611i
$130$		0			0
$131$	−3.73205	−	6.46410i	−0.326071	−	0.564771i	0.655658	−	0.755058i	$-0.272391\pi$
$131$	−3.73205	−	6.46410i	−0.326071	−	0.564771i	−0.981728	+	0.190287i	$0.939058\pi$
$132$		0			0
$133$	3.86603	+	11.1603i	0.335227	+	0.967717i
$134$		0			0
$135$	0.866025	−	0.500000i	0.0745356	−	0.0430331i
$136$		0			0
$137$	1.16987	−	2.02628i	0.0999490	−	0.173117i	−0.811714	−	0.584055i	$-0.801465\pi$
$137$	1.16987	−	2.02628i	0.0999490	−	0.173117i	0.911663	+	0.410938i	$0.134799\pi$
$138$		0			0
$139$	−5.92820			−0.502824			−0.251412	−	0.967880i	$-0.580895\pi$
$139$	−5.92820			−0.502824			−0.251412	+	0.967880i	$0.580895\pi$
$140$		0			0
$141$	0.928203			0.0781688
$142$		0			0
$143$	2.36603	−	4.09808i	0.197857	−	0.342698i
$144$		0			0
$145$	0.633975	−	0.366025i	0.0526487	−	0.0303968i
$146$		0			0
$147$	5.50000	−	4.33013i	0.453632	−	0.357143i
$148$		0			0
$149$	11.6603	+	20.1962i	0.955245	+	1.65453i	0.733806	+	0.679359i	$0.237742\pi$
$149$	11.6603	+	20.1962i	0.955245	+	1.65453i	0.221439	+	0.975174i	$0.428925\pi$
$150$		0			0
$151$	−15.4641	−	8.92820i	−1.25845	−	0.726567i	−0.285677	−	0.958326i	$-0.592219\pi$
$151$	−15.4641	−	8.92820i	−1.25845	−	0.726567i	−0.972773	+	0.231759i	$0.925552\pi$
$152$		0			0
$153$		−	6.19615i		−	0.500929i
$154$		0			0
$155$		−	0.464102i		−	0.0372775i
$156$		0			0
$157$	−17.3205	−	10.0000i	−1.38233	−	0.798087i	−0.389892	−	0.920860i	$-0.627488\pi$
$157$	−17.3205	−	10.0000i	−1.38233	−	0.798087i	−0.992435	+	0.122774i	$0.960821\pi$
$158$		0			0
$159$	−0.732051	−	1.26795i	−0.0580554	−	0.100555i
$160$		0			0
$161$	−1.83013	+	0.633975i	−0.144234	+	0.0499642i
$162$		0			0
$163$	−7.73205	+	4.46410i	−0.605621	+	0.349655i	−0.771250	−	0.636533i	$-0.780368\pi$
$163$	−7.73205	+	4.46410i	−0.605621	+	0.349655i	0.165629	+	0.986188i	$0.447035\pi$
$164$		0			0
$165$	−2.36603	+	4.09808i	−0.184195	+	0.319035i
$166$		0			0
$167$	17.1244			1.32512			0.662561	−	0.749008i	$-0.269469\pi$
$167$	17.1244			1.32512			0.662561	+	0.749008i	$0.269469\pi$
$168$		0			0
$169$	12.0000			0.923077
$170$		0			0
$171$	−2.23205	+	3.86603i	−0.170689	+	0.295642i
$172$		0			0
$173$	−3.80385	+	2.19615i	−0.289201	+	0.166970i	−0.637582	−	0.770383i	$-0.720065\pi$
$173$	−3.80385	+	2.19615i	−0.289201	+	0.166970i	0.348380	+	0.937353i	$0.386732\pi$
$174$		0			0
$175$	−1.73205	+	2.00000i	−0.130931	+	0.151186i
$176$		0			0
$177$	−7.09808	−	12.2942i	−0.533524	−	0.924091i
$178$		0			0
$179$	−3.00000	−	1.73205i	−0.224231	−	0.129460i	0.383677	−	0.923467i	$-0.374658\pi$
$179$	−3.00000	−	1.73205i	−0.224231	−	0.129460i	−0.607908	+	0.794008i	$0.707991\pi$
$180$		0			0
$181$			5.58846i			0.415387i	0.978194	+	0.207693i	$0.0665956\pi$
$181$			5.58846i			0.415387i	−0.978194	+	0.207693i	$0.933404\pi$
$182$		0			0
$183$		−	11.4641i		−	0.847451i
$184$		0			0
$185$	−10.1603	−	5.86603i	−0.746997	−	0.431279i
$186$		0			0
$187$	14.6603	+	25.3923i	1.07206	+	1.85687i
$188$		0			0
$189$	2.59808	+	0.500000i	0.188982	+	0.0363696i
$190$		0			0
$191$	−1.73205	+	1.00000i	−0.125327	+	0.0723575i	−0.561353	−	0.827577i	$-0.689719\pi$
$191$	−1.73205	+	1.00000i	−0.125327	+	0.0723575i	0.436026	+	0.899934i	$0.356386\pi$
$192$		0			0
$193$	4.59808	−	7.96410i	0.330977	−	0.573269i	−0.651727	−	0.758454i	$-0.725955\pi$
$193$	4.59808	−	7.96410i	0.330977	−	0.573269i	0.982704	+	0.185185i	$0.0592885\pi$
$194$		0			0
$195$	1.00000			0.0716115
$196$		0			0
$197$	−13.2679			−0.945302			−0.472651	−	0.881250i	$-0.656703\pi$
$197$	−13.2679			−0.945302			−0.472651	+	0.881250i	$0.656703\pi$
$198$		0			0
$199$	1.92820	−	3.33975i	0.136687	−	0.236748i	−0.789554	−	0.613681i	$-0.789688\pi$
$199$	1.92820	−	3.33975i	0.136687	−	0.236748i	0.926241	+	0.376933i	$0.123021\pi$
$200$		0			0
$201$	10.7942	−	6.23205i	0.761366	−	0.439575i
$202$		0			0
$203$	1.90192	+	0.366025i	0.133489	+	0.0256899i
$204$		0			0
$205$	3.09808	+	5.36603i	0.216379	+	0.374779i
$206$		0			0
$207$	−0.633975	−	0.366025i	−0.0440643	−	0.0254405i
$208$		0			0
$209$		−	21.1244i		−	1.46120i
$210$		0			0
$211$			24.7846i			1.70624i	0.521712	+	0.853121i	$0.325293\pi$
$211$			24.7846i			1.70624i	−0.521712	+	0.853121i	$0.674707\pi$
$212$		0			0
$213$	−13.5622	−	7.83013i	−0.929265	−	0.536511i
$214$		0			0
$215$	4.23205	+	7.33013i	0.288623	+	0.499911i
$216$		0			0
$217$	0.803848	−	0.928203i	0.0545687	−	0.0630105i
$218$		0			0
$219$	5.13397	−	2.96410i	0.346922	−	0.200295i
$220$		0			0
$221$	3.09808	−	5.36603i	0.208399	−	0.360958i
$222$		0			0
$223$	4.39230			0.294130			0.147065	−	0.989127i	$-0.453017\pi$
$223$	4.39230			0.294130			0.147065	+	0.989127i	$0.453017\pi$
$224$		0			0
$225$	−1.00000			−0.0666667
$226$		0			0
$227$	−8.02628	+	13.9019i	−0.532723	+	0.922703i	0.466547	+	0.884496i	$0.345498\pi$
$227$	−8.02628	+	13.9019i	−0.532723	+	0.922703i	−0.999270	+	0.0382067i	$0.987835\pi$
$228$		0			0
$229$	5.89230	−	3.40192i	0.389374	−	0.224805i	−0.292515	−	0.956261i	$-0.594492\pi$
$229$	5.89230	−	3.40192i	0.389374	−	0.224805i	0.681889	+	0.731456i	$0.261159\pi$
$230$		0			0
$231$	−11.8301	+	4.09808i	−0.778365	+	0.269634i
$232$		0			0
$233$	−3.00000	−	5.19615i	−0.196537	−	0.340411i	0.750867	−	0.660454i	$-0.229636\pi$
$233$	−3.00000	−	5.19615i	−0.196537	−	0.340411i	−0.947403	+	0.320043i	$0.896303\pi$
$234$		0			0
$235$	−0.803848	−	0.464102i	−0.0524372	−	0.0302747i
$236$		0			0
$237$		−	7.73205i		−	0.502251i
$238$		0			0
$239$			5.32051i			0.344155i	0.985083	+	0.172078i	$0.0550480\pi$
$239$			5.32051i			0.344155i	−0.985083	+	0.172078i	$0.944952\pi$
$240$		0			0
$241$	10.2679	+	5.92820i	0.661417	+	0.381869i	0.792817	−	0.609460i	$-0.208614\pi$
$241$	10.2679	+	5.92820i	0.661417	+	0.381869i	−0.131400	+	0.991329i	$0.541947\pi$
$242$		0			0
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$		0			0
$245$	−6.92820	+	1.00000i	−0.442627	+	0.0638877i
$246$		0			0
$247$	−3.86603	+	2.23205i	−0.245989	+	0.142022i
$248$		0			0
$249$	4.36603	−	7.56218i	0.276686	−	0.479234i
$250$		0			0
$251$	5.12436			0.323446			0.161723	−	0.986836i	$-0.448295\pi$
$251$	5.12436			0.323446			0.161723	+	0.986836i	$0.448295\pi$
$252$		0			0
$253$	3.46410			0.217786
$254$		0			0
$255$	−3.09808	+	5.36603i	−0.194009	+	0.336034i
$256$		0			0
$257$	15.2942	−	8.83013i	0.954028	−	0.550808i	0.0596980	−	0.998216i	$-0.480986\pi$
$257$	15.2942	−	8.83013i	0.954028	−	0.550808i	0.894330	+	0.447408i	$0.147653\pi$
$258$		0			0
$259$	−10.1603	−	29.3301i	−0.631327	−	1.82249i
$260$		0			0
$261$	0.366025	+	0.633975i	0.0226564	+	0.0392420i
$262$		0			0
$263$	20.1962	+	11.6603i	1.24535	+	0.719002i	0.970178	−	0.242393i	$-0.0779325\pi$
$263$	20.1962	+	11.6603i	1.24535	+	0.719002i	0.275170	+	0.961396i	$0.411266\pi$
$264$		0			0
$265$			1.46410i			0.0899390i
$266$		0			0
$267$		−	1.26795i		−	0.0775972i
$268$		0			0
$269$	−10.2679	−	5.92820i	−0.626048	−	0.361449i	0.153172	−	0.988200i	$-0.451051\pi$
$269$	−10.2679	−	5.92820i	−0.626048	−	0.361449i	−0.779220	+	0.626751i	$0.784384\pi$
$270$		0			0
$271$	1.00000	+	1.73205i	0.0607457	+	0.105215i	0.894799	−	0.446469i	$-0.147319\pi$
$271$	1.00000	+	1.73205i	0.0607457	+	0.105215i	−0.834053	+	0.551684i	$0.813985\pi$
$272$		0			0
$273$	2.00000	+	1.73205i	0.121046	+	0.104828i
$274$		0			0
$275$	4.09808	−	2.36603i	0.247123	−	0.142677i
$276$		0			0
$277$	−0.401924	+	0.696152i	−0.0241493	+	0.0418277i	−0.877847	−	0.478940i	$-0.841021\pi$
$277$	−0.401924	+	0.696152i	−0.0241493	+	0.0418277i	0.853698	+	0.520768i	$0.174354\pi$
$278$		0			0
$279$	0.464102			0.0277850
$280$		0			0
$281$	−13.8564			−0.826604			−0.413302	−	0.910594i	$-0.635625\pi$
$281$	−13.8564			−0.826604			−0.413302	+	0.910594i	$0.635625\pi$
$282$		0			0
$283$	−11.4019	+	19.7487i	−0.677774	+	1.17394i	0.297876	+	0.954605i	$0.403722\pi$
$283$	−11.4019	+	19.7487i	−0.677774	+	1.17394i	−0.975650	+	0.219334i	$0.929611\pi$
$284$		0			0
$285$	3.86603	−	2.23205i	0.229004	−	0.132215i
$286$		0			0
$287$	−3.09808	+	16.0981i	−0.182874	+	0.950239i
$288$		0			0
$289$	10.6962	+	18.5263i	0.629185	+	1.08978i
$290$		0			0
$291$	7.73205	+	4.46410i	0.453261	+	0.261690i
$292$		0			0
$293$			10.5359i			0.615514i	0.951465	+	0.307757i	$0.0995783\pi$
$293$			10.5359i			0.615514i	−0.951465	+	0.307757i	$0.900422\pi$
$294$		0			0
$295$			14.1962i			0.826532i
$296$		0			0
$297$	−4.09808	−	2.36603i	−0.237795	−	0.137291i
$298$		0			0
$299$	−0.366025	−	0.633975i	−0.0211678	−	0.0366637i
$300$		0			0
$301$	−4.23205	+	21.9904i	−0.243931	+	1.26750i
$302$		0			0
$303$	−7.56218	+	4.36603i	−0.434436	+	0.250822i
$304$		0			0
$305$	−5.73205	+	9.92820i	−0.328216	+	0.568487i
$306$		0			0
$307$	−20.1244			−1.14856			−0.574279	−	0.818660i	$-0.694717\pi$
$307$	−20.1244			−1.14856			−0.574279	+	0.818660i	$0.694717\pi$
$308$		0			0
$309$	−2.26795			−0.129019
$310$		0			0
$311$	−3.90192	+	6.75833i	−0.221258	+	0.383230i	−0.955190	−	0.295993i	$-0.904350\pi$
$311$	−3.90192	+	6.75833i	−0.221258	+	0.383230i	0.733932	+	0.679223i	$0.237683\pi$
$312$		0			0
$313$	16.4545	−	9.50000i	0.930062	−	0.536972i	0.0432311	−	0.999065i	$-0.486235\pi$
$313$	16.4545	−	9.50000i	0.930062	−	0.536972i	0.886831	+	0.462093i	$0.152902\pi$
$314$		0			0
$315$	−2.00000	−	1.73205i	−0.112687	−	0.0975900i
$316$		0			0
$317$	5.02628	+	8.70577i	0.282304	+	0.488965i	0.971952	−	0.235180i	$-0.0755680\pi$
$317$	5.02628	+	8.70577i	0.282304	+	0.488965i	−0.689648	+	0.724145i	$0.742235\pi$
$318$		0			0
$319$	−3.00000	−	1.73205i	−0.167968	−	0.0969762i
$320$		0			0
$321$			16.7321i			0.933892i
$322$		0			0
$323$		−	27.6603i		−	1.53906i
$324$		0			0
$325$	−0.866025	−	0.500000i	−0.0480384	−	0.0277350i
$326$		0			0
$327$	8.96410	+	15.5263i	0.495716	+	0.858605i
$328$		0			0
$329$	−0.803848	−	2.32051i	−0.0443176	−	0.127934i
$330$		0			0
$331$	−7.50000	+	4.33013i	−0.412237	+	0.238005i	−0.691751	−	0.722137i	$-0.743160\pi$
$331$	−7.50000	+	4.33013i	−0.412237	+	0.238005i	0.279513	+	0.960142i	$0.409827\pi$
$332$		0			0
$333$	5.86603	−	10.1603i	0.321456	−	0.556778i
$334$		0			0
$335$	−12.4641			−0.680987
$336$		0			0
$337$	−25.4449			−1.38607			−0.693035	−	0.720904i	$-0.743727\pi$
$337$	−25.4449			−1.38607			−0.693035	+	0.720904i	$0.743727\pi$
$338$		0			0
$339$	7.19615	−	12.4641i	0.390841	−	0.676957i
$340$		0			0
$341$	−1.90192	+	1.09808i	−0.102995	+	0.0594642i
$342$		0			0
$343$	−15.5885	−	10.0000i	−0.841698	−	0.539949i
$344$		0			0
$345$	0.366025	+	0.633975i	0.0197061	+	0.0341320i
$346$		0			0
$347$	2.19615	+	1.26795i	0.117896	+	0.0680671i	0.557788	−	0.829983i	$-0.311650\pi$
$347$	2.19615	+	1.26795i	0.117896	+	0.0680671i	−0.439893	+	0.898050i	$0.644983\pi$
$348$		0			0
$349$		−	26.9282i		−	1.44143i	−0.693230	−	0.720717i	$-0.743813\pi$
$349$		−	26.9282i		−	1.44143i	0.693230	−	0.720717i	$-0.256187\pi$
$350$		0			0
$351$			1.00000i			0.0533761i
$352$		0			0
$353$	−12.7583	−	7.36603i	−0.679057	−	0.392054i	0.120442	−	0.992720i	$-0.461569\pi$
$353$	−12.7583	−	7.36603i	−0.679057	−	0.392054i	−0.799500	+	0.600666i	$0.794902\pi$
$354$		0			0
$355$	7.83013	+	13.5622i	0.415580	+	0.719806i
$356$		0			0
$357$	−15.4904	+	5.36603i	−0.819838	+	0.284000i
$358$		0			0
$359$	−4.90192	+	2.83013i	−0.258714	+	0.149368i	−0.623748	−	0.781626i	$-0.714391\pi$
$359$	−4.90192	+	2.83013i	−0.258714	+	0.149368i	0.365034	+	0.930994i	$0.381057\pi$
$360$		0			0
$361$	−0.464102	+	0.803848i	−0.0244264	+	0.0423078i
$362$		0			0
$363$	11.3923			0.597941
$364$		0			0
$365$	−5.92820			−0.310296
$366$		0			0
$367$	−11.5981	+	20.0885i	−0.605415	+	1.04861i	0.386571	+	0.922260i	$0.373659\pi$
$367$	−11.5981	+	20.0885i	−0.605415	+	1.04861i	−0.991986	+	0.126349i	$0.959674\pi$
$368$		0			0
$369$	−5.36603	+	3.09808i	−0.279344	+	0.161279i
$370$		0			0
$371$	−2.53590	+	2.92820i	−0.131657	+	0.152025i
$372$		0			0
$373$	14.9904	+	25.9641i	0.776173	+	1.34437i	0.934133	+	0.356925i	$0.116175\pi$
$373$	14.9904	+	25.9641i	0.776173	+	1.34437i	−0.157961	+	0.987445i	$0.550492\pi$
$374$		0			0
$375$	0.866025	+	0.500000i	0.0447214	+	0.0258199i
$376$		0			0
$377$			0.732051i			0.0377025i
$378$		0			0
$379$			12.5167i			0.642938i	0.946920	+	0.321469i	$0.104177\pi$
$379$			12.5167i			0.642938i	−0.946920	+	0.321469i	$0.895823\pi$
$380$		0			0
$381$	−2.93782	−	1.69615i	−0.150509	−	0.0868965i
$382$		0			0
$383$	−2.92820	−	5.07180i	−0.149624	−	0.259157i	0.781464	−	0.623950i	$-0.214473\pi$
$383$	−2.92820	−	5.07180i	−0.149624	−	0.259157i	−0.931089	+	0.364793i	$0.881140\pi$
$384$		0			0
$385$	12.2942	+	2.36603i	0.626572	+	0.120584i
$386$		0			0
$387$	−7.33013	+	4.23205i	−0.372611	+	0.215127i
$388$		0			0
$389$	7.75833	−	13.4378i	0.393363	−	0.681325i	−0.599528	−	0.800354i	$-0.704645\pi$
$389$	7.75833	−	13.4378i	0.393363	−	0.681325i	0.992891	+	0.119029i	$0.0379782\pi$
$390$		0			0
$391$	4.53590			0.229390
$392$		0			0
$393$	−7.46410			−0.376514
$394$		0			0
$395$	−3.86603	+	6.69615i	−0.194521	+	0.336920i
$396$		0			0
$397$	−10.7942	+	6.23205i	−0.541747	+	0.312778i	−0.745787	−	0.666185i	$-0.767926\pi$
$397$	−10.7942	+	6.23205i	−0.541747	+	0.312778i	0.204040	+	0.978963i	$0.434593\pi$
$398$		0			0
$399$	11.5981	+	2.23205i	0.580630	+	0.111742i
$400$		0			0
$401$	−6.00000	−	10.3923i	−0.299626	−	0.518967i	0.676425	−	0.736512i	$-0.263528\pi$
$401$	−6.00000	−	10.3923i	−0.299626	−	0.518967i	−0.976050	+	0.217545i	$0.930195\pi$
$402$		0			0
$403$	0.401924	+	0.232051i	0.0200212	+	0.0115593i
$404$		0			0
$405$		−	1.00000i		−	0.0496904i
$406$		0			0
$407$			55.5167i			2.75186i
$408$		0			0
$409$	5.42820	+	3.13397i	0.268407	+	0.154965i	0.628164	−	0.778081i	$-0.283807\pi$
$409$	5.42820	+	3.13397i	0.268407	+	0.154965i	−0.359756	+	0.933046i	$0.617140\pi$
$410$		0			0
$411$	−1.16987	−	2.02628i	−0.0577056	−	0.0999490i
$412$		0			0
$413$	−24.5885	+	28.3923i	−1.20992	+	1.39709i
$414$		0			0
$415$	−7.56218	+	4.36603i	−0.371213	+	0.214320i
$416$		0			0
$417$	−2.96410	+	5.13397i	−0.145153	+	0.251412i
$418$		0			0
$419$	−8.92820			−0.436171			−0.218086	−	0.975930i	$-0.569981\pi$
$419$	−8.92820			−0.436171			−0.218086	+	0.975930i	$0.569981\pi$
$420$		0			0
$421$	−12.0718			−0.588343			−0.294172	−	0.955753i	$-0.595044\pi$
$421$	−12.0718			−0.588343			−0.294172	+	0.955753i	$0.595044\pi$
$422$		0			0
$423$	0.464102	−	0.803848i	0.0225654	−	0.0390844i
$424$		0			0
$425$	5.36603	−	3.09808i	0.260290	−	0.150279i
$426$		0			0
$427$	−28.6603	+	9.92820i	−1.38697	+	0.480459i
$428$		0			0
$429$	−2.36603	−	4.09808i	−0.114233	−	0.197857i
$430$		0			0
$431$	−2.66025	−	1.53590i	−0.128140	−	0.0739816i	0.434560	−	0.900643i	$-0.356904\pi$
$431$	−2.66025	−	1.53590i	−0.128140	−	0.0739816i	−0.562700	+	0.826661i	$0.690237\pi$
$432$		0			0
$433$		−	26.4641i		−	1.27178i	−0.771778	−	0.635892i	$-0.780632\pi$
$433$		−	26.4641i		−	1.27178i	0.771778	−	0.635892i	$-0.219368\pi$
$434$		0			0
$435$		−	0.732051i		−	0.0350991i
$436$		0			0
$437$	−2.83013	−	1.63397i	−0.135383	−	0.0781636i
$438$		0			0
$439$	−2.26795	−	3.92820i	−0.108243	−	0.187483i	0.806815	−	0.590804i	$-0.201189\pi$
$439$	−2.26795	−	3.92820i	−0.108243	−	0.187483i	−0.915059	+	0.403321i	$0.867856\pi$
$440$		0			0
$441$	−1.00000	−	6.92820i	−0.0476190	−	0.329914i
$442$		0			0
$443$	−16.3923	+	9.46410i	−0.778822	+	0.449653i	−0.836013	−	0.548710i	$-0.815119\pi$
$443$	−16.3923	+	9.46410i	−0.778822	+	0.449653i	0.0571907	+	0.998363i	$0.481786\pi$
$444$		0			0
$445$	−0.633975	+	1.09808i	−0.0300533	+	0.0520538i
$446$		0			0
$447$	23.3205			1.10302
$448$		0			0
$449$	21.3205			1.00618			0.503088	−	0.864235i	$-0.332197\pi$
$449$	21.3205			1.00618			0.503088	+	0.864235i	$0.332197\pi$
$450$		0			0
$451$	14.6603	−	25.3923i	0.690324	−	1.19568i
$452$		0			0
$453$	−15.4641	+	8.92820i	−0.726567	+	0.419484i
$454$		0			0
$455$	−0.866025	−	2.50000i	−0.0405999	−	0.117202i
$456$		0			0
$457$	−1.13397	−	1.96410i	−0.0530451	−	0.0918768i	0.838284	−	0.545234i	$-0.183559\pi$
$457$	−1.13397	−	1.96410i	−0.0530451	−	0.0918768i	−0.891329	+	0.453358i	$0.850226\pi$
$458$		0			0
$459$	−5.36603	−	3.09808i	−0.250465	−	0.144606i
$460$		0			0
$461$		−	32.1962i		−	1.49952i	−0.661707	−	0.749762i	$-0.730168\pi$
$461$		−	32.1962i		−	1.49952i	0.661707	−	0.749762i	$-0.269832\pi$
$462$		0			0
$463$		−	23.7846i		−	1.10536i	−0.833392	−	0.552682i	$-0.813604\pi$
$463$		−	23.7846i		−	1.10536i	0.833392	−	0.552682i	$-0.186396\pi$
$464$		0			0
$465$	−0.401924	−	0.232051i	−0.0186388	−	0.0107611i
$466$		0			0
$467$	6.85641	+	11.8756i	0.317277	+	0.549539i	0.979919	−	0.199397i	$-0.0638983\pi$
$467$	6.85641	+	11.8756i	0.317277	+	0.549539i	−0.662642	+	0.748936i	$0.730565\pi$
$468$		0			0
$469$	−24.9282	−	21.5885i	−1.15108	−	0.996862i
$470$		0			0
$471$	−17.3205	+	10.0000i	−0.798087	+	0.460776i
$472$		0			0
$473$	20.0263	−	34.6865i	0.920809	−	1.59489i
$474$		0			0
$475$	−4.46410			−0.204827
$476$		0			0
$477$	−1.46410			−0.0670366
$478$		0			0
$479$	16.9282	−	29.3205i	0.773469	−	1.33969i	−0.162181	−	0.986761i	$-0.551853\pi$
$479$	16.9282	−	29.3205i	0.773469	−	1.33969i	0.935651	−	0.352927i	$-0.114814\pi$
$480$		0			0
$481$	10.1603	−	5.86603i	0.463268	−	0.267468i
$482$		0			0
$483$	−0.366025	+	1.90192i	−0.0166547	+	0.0865405i
$484$		0			0
$485$	−4.46410	−	7.73205i	−0.202704	−	0.351094i
$486$		0			0
$487$	27.6506	+	15.9641i	1.25297	+	0.723402i	0.971698	−	0.236226i	$-0.0759105\pi$
$487$	27.6506	+	15.9641i	1.25297	+	0.723402i	0.281272	+	0.959628i	$0.409244\pi$
$488$		0			0
$489$			8.92820i			0.403747i
$490$		0			0
$491$		−	37.4641i		−	1.69073i	−0.534188	−	0.845366i	$-0.679383\pi$
$491$		−	37.4641i		−	1.69073i	0.534188	−	0.845366i	$-0.320617\pi$
$492$		0			0
$493$	−3.92820	−	2.26795i	−0.176917	−	0.102143i
$494$		0			0
$495$	2.36603	+	4.09808i	0.106345	+	0.184195i
$496$		0			0
$497$	−7.83013	+	40.6865i	−0.351229	+	1.82504i
$498$		0			0
$499$	−1.83975	+	1.06218i	−0.0823583	+	0.0475496i	−0.540614	−	0.841271i	$-0.681808\pi$
$499$	−1.83975	+	1.06218i	−0.0823583	+	0.0475496i	0.458255	+	0.888821i	$0.348475\pi$
$500$		0			0
$501$	8.56218	−	14.8301i	0.382530	−	0.662561i
$502$		0			0
$503$	−23.0718			−1.02872			−0.514360	−	0.857574i	$-0.671971\pi$
$503$	−23.0718			−1.02872			−0.514360	+	0.857574i	$0.671971\pi$
$504$		0			0
$505$	8.73205			0.388571
$506$		0			0
$507$	6.00000	−	10.3923i	0.266469	−	0.461538i
$508$		0			0
$509$	31.9808	−	18.4641i	1.41752	−	0.818407i	0.421442	−	0.906856i	$-0.361524\pi$
$509$	31.9808	−	18.4641i	1.41752	−	0.818407i	0.996081	+	0.0884486i	$0.0281909\pi$
$510$		0			0
$511$	−11.8564	−	10.2679i	−0.524497	−	0.454227i
$512$		0			0
$513$	2.23205	+	3.86603i	0.0985475	+	0.170689i
$514$		0			0
$515$	1.96410	+	1.13397i	0.0865487	+	0.0499689i
$516$		0			0
$517$			4.39230i			0.193173i
$518$		0			0
$519$			4.39230i			0.192801i
$520$		0			0
$521$	−35.9090	−	20.7321i	−1.57320	−	0.908288i	−0.995773	−	0.0918454i	$-0.970723\pi$
$521$	−35.9090	−	20.7321i	−1.57320	−	0.908288i	−0.577427	−	0.816442i	$-0.695943\pi$
$522$		0			0
$523$	13.5981	+	23.5526i	0.594602	+	1.02988i	0.993603	+	0.112931i	$0.0360238\pi$
$523$	13.5981	+	23.5526i	0.594602	+	1.02988i	−0.399001	+	0.916951i	$0.630643\pi$
$524$		0			0
$525$	0.866025	+	2.50000i	0.0377964	+	0.109109i
$526$		0			0
$527$	−2.49038	+	1.43782i	−0.108483	+	0.0626325i
$528$		0			0
$529$	−11.2321	+	19.4545i	−0.488350	+	0.845847i
$530$		0			0
$531$	−14.1962			−0.616061
$532$		0			0
$533$	−6.19615			−0.268385
$534$		0			0
$535$	8.36603	−	14.4904i	0.361695	−	0.626474i
$536$		0			0
$537$	−3.00000	+	1.73205i	−0.129460	+	0.0747435i
$538$		0			0
$539$	20.4904	+	26.0263i	0.882583	+	1.12103i
$540$		0			0
$541$	2.89230	+	5.00962i	0.124350	+	0.215380i	0.921479	−	0.388429i	$-0.126982\pi$
$541$	2.89230	+	5.00962i	0.124350	+	0.215380i	−0.797129	+	0.603809i	$0.793649\pi$
$542$		0			0
$543$	4.83975	+	2.79423i	0.207693	+	0.119912i
$544$		0			0
$545$		−	17.9282i		−	0.767960i
$546$		0			0
$547$			26.3923i			1.12845i	0.825620	+	0.564227i	$0.190826\pi$
$547$			26.3923i			1.12845i	−0.825620	+	0.564227i	$0.809174\pi$
$548$		0			0
$549$	−9.92820	−	5.73205i	−0.423725	−	0.244638i
$550$		0			0
$551$	1.63397	+	2.83013i	0.0696097	+	0.120567i
$552$		0			0
$553$	−19.3301	+	6.69615i	−0.822001	+	0.284749i
$554$		0			0
$555$	−10.1603	+	5.86603i	−0.431279	+	0.248999i
$556$		0			0
$557$	−9.73205	+	16.8564i	−0.412360	+	0.714229i	−0.995147	−	0.0983960i	$-0.968629\pi$
$557$	−9.73205	+	16.8564i	−0.412360	+	0.714229i	0.582787	+	0.812625i	$0.301962\pi$
$558$		0			0
$559$	−8.46410			−0.357993
$560$		0			0
$561$	29.3205			1.23791
$562$		0			0
$563$	3.19615	−	5.53590i	0.134702	−	0.233310i	−0.790782	−	0.612098i	$-0.790326\pi$
$563$	3.19615	−	5.53590i	0.134702	−	0.233310i	0.925483	+	0.378788i	$0.123659\pi$
$564$		0			0
$565$	−12.4641	+	7.19615i	−0.524369	+	0.302744i
$566$		0			0
$567$	1.73205	−	2.00000i	0.0727393	−	0.0839921i
$568$		0			0
$569$	4.29423	+	7.43782i	0.180023	+	0.311810i	0.941888	−	0.335926i	$-0.109049\pi$
$569$	4.29423	+	7.43782i	0.180023	+	0.311810i	−0.761865	+	0.647736i	$0.775716\pi$
$570$		0			0
$571$	16.6244	+	9.59808i	0.695708	+	0.401667i	0.805747	−	0.592260i	$-0.201764\pi$
$571$	16.6244	+	9.59808i	0.695708	+	0.401667i	−0.110039	+	0.993927i	$0.535098\pi$
$572$		0			0
$573$			2.00000i			0.0835512i
$574$		0			0
$575$		−	0.732051i		−	0.0305286i
$576$		0			0
$577$	−33.6506	−	19.4282i	−1.40089	−	0.808807i	−0.406410	−	0.913691i	$-0.633219\pi$
$577$	−33.6506	−	19.4282i	−1.40089	−	0.808807i	−0.994484	+	0.104884i	$0.966553\pi$
$578$		0			0
$579$	−4.59808	−	7.96410i	−0.191090	−	0.330977i
$580$		0			0
$581$	−22.6865	−	4.36603i	−0.941196	−	0.181133i
$582$		0			0
$583$	6.00000	−	3.46410i	0.248495	−	0.143468i
$584$		0			0
$585$	0.500000	−	0.866025i	0.0206725	−	0.0358057i
$586$		0			0
$587$	−9.66025			−0.398721			−0.199361	−	0.979926i	$-0.563887\pi$
$587$	−9.66025			−0.398721			−0.199361	+	0.979926i	$0.563887\pi$
$588$		0			0
$589$	2.07180			0.0853669
$590$		0			0
$591$	−6.63397	+	11.4904i	−0.272885	+	0.472651i
$592$		0			0
$593$	32.2750	−	18.6340i	1.32538	−	0.765206i	0.340795	−	0.940138i	$-0.389304\pi$
$593$	32.2750	−	18.6340i	1.32538	−	0.765206i	0.984580	+	0.174932i	$0.0559706\pi$
$594$		0			0
$595$	16.0981	+	3.09808i	0.659957	+	0.127009i
$596$		0			0
$597$	−1.92820	−	3.33975i	−0.0789161	−	0.136687i
$598$		0			0
$599$	−4.39230	−	2.53590i	−0.179465	−	0.103614i	0.407576	−	0.913171i	$-0.366374\pi$
$599$	−4.39230	−	2.53590i	−0.179465	−	0.103614i	−0.587041	+	0.809557i	$0.699707\pi$
$600$		0			0
$601$			11.3397i			0.462558i	0.972887	+	0.231279i	$0.0742910\pi$
$601$			11.3397i			0.462558i	−0.972887	+	0.231279i	$0.925709\pi$
$602$		0			0
$603$		−	12.4641i		−	0.507577i
$604$		0			0
$605$	−9.86603	−	5.69615i	−0.401111	−	0.231582i
$606$		0			0
$607$	−21.5981	−	37.4090i	−0.876639	−	1.51838i	−0.855007	−	0.518617i	$-0.826447\pi$
$607$	−21.5981	−	37.4090i	−0.876639	−	1.51838i	−0.0216322	−	0.999766i	$-0.506886\pi$
$608$		0			0
$609$	1.26795	−	1.46410i	0.0513799	−	0.0593284i
$610$		0			0
$611$	0.803848	−	0.464102i	0.0325202	−	0.0187755i
$612$		0			0
$613$	−19.3205	+	33.4641i	−0.780348	+	1.35160i	0.151391	+	0.988474i	$0.451625\pi$
$613$	−19.3205	+	33.4641i	−0.780348	+	1.35160i	−0.931739	+	0.363128i	$0.881709\pi$
$614$		0			0
$615$	6.19615			0.249853
$616$		0			0
$617$	6.00000			0.241551			0.120775	−	0.992680i	$-0.461462\pi$
$617$	6.00000			0.241551			0.120775	+	0.992680i	$0.461462\pi$
$618$		0			0
$619$	3.50000	−	6.06218i	0.140677	−	0.243659i	−0.787075	−	0.616858i	$-0.788405\pi$
$619$	3.50000	−	6.06218i	0.140677	−	0.243659i	0.927752	+	0.373198i	$0.121739\pi$
$620$		0			0
$621$	−0.633975	+	0.366025i	−0.0254405	+	0.0146881i
$622$		0			0
$623$	−3.16987	+	1.09808i	−0.126998	+	0.0439935i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	−18.2942	−	10.5622i	−0.730601	−	0.421813i
$628$		0			0
$629$			72.6936i			2.89848i
$630$		0			0
$631$			24.5359i			0.976759i	0.872631	+	0.488379i	$0.162412\pi$
$631$			24.5359i			0.976759i	−0.872631	+	0.488379i	$0.837588\pi$
$632$		0			0
$633$	21.4641	+	12.3923i	0.853121	+	0.492550i
$634$		0			0
$635$	1.69615	+	2.93782i	0.0673098	+	0.116584i
$636$		0			0
$637$	2.59808	−	6.50000i	0.102940	−	0.257539i
$638$		0			0
$639$	−13.5622	+	7.83013i	−0.536511	+	0.309755i
$640$		0			0
$641$	−18.2224	+	31.5622i	−0.719743	+	1.24663i	0.241359	+	0.970436i	$0.422407\pi$
$641$	−18.2224	+	31.5622i	−0.719743	+	1.24663i	−0.961102	+	0.276195i	$0.910926\pi$
$642$		0			0
$643$	−31.9808			−1.26120			−0.630599	−	0.776109i	$-0.717191\pi$
$643$	−31.9808			−1.26120			−0.630599	+	0.776109i	$0.717191\pi$
$644$		0			0
$645$	8.46410			0.333274
$646$		0			0
$647$	−3.09808	+	5.36603i	−0.121798	+	0.210960i	−0.920477	−	0.390797i	$-0.872199\pi$
$647$	−3.09808	+	5.36603i	−0.121798	+	0.210960i	0.798679	+	0.601758i	$0.205533\pi$
$648$		0			0
$649$	58.1769	−	33.5885i	2.28364	−	1.31846i
$650$		0			0
$651$	−0.401924	−	1.16025i	−0.0157526	−	0.0454739i
$652$		0			0
$653$	−4.70577	−	8.15064i	−0.184151	−	0.318959i	0.759139	−	0.650928i	$-0.225620\pi$
$653$	−4.70577	−	8.15064i	−0.184151	−	0.318959i	−0.943290	+	0.331969i	$0.892287\pi$
$654$		0			0
$655$	6.46410	+	3.73205i	0.252573	+	0.145823i
$656$		0			0
$657$		−	5.92820i		−	0.231281i
$658$		0			0
$659$		−	32.7846i		−	1.27711i	−0.769577	−	0.638554i	$-0.779533\pi$
$659$		−	32.7846i		−	1.27711i	0.769577	−	0.638554i	$-0.220467\pi$
$660$		0			0
$661$	41.5526	+	23.9904i	1.61621	+	0.933118i	0.987889	+	0.155161i	$0.0495897\pi$
$661$	41.5526	+	23.9904i	1.61621	+	0.933118i	0.628318	+	0.777957i	$0.283744\pi$
$662$		0			0
$663$	−3.09808	−	5.36603i	−0.120319	−	0.208399i
$664$		0			0
$665$	−8.92820	−	7.73205i	−0.346221	−	0.299836i
$666$		0			0
$667$	−0.464102	+	0.267949i	−0.0179701	+	0.0103750i
$668$		0			0
$669$	2.19615	−	3.80385i	0.0849082	−	0.147065i
$670$		0			0
$671$	54.2487			2.09425
$672$		0			0
$673$	−29.4449			−1.13502			−0.567508	−	0.823368i	$-0.692092\pi$
$673$	−29.4449			−1.13502			−0.567508	+	0.823368i	$0.692092\pi$
$674$		0			0
$675$	−0.500000	+	0.866025i	−0.0192450	+	0.0333333i
$676$		0			0
$677$	18.8827	−	10.9019i	0.725721	−	0.418995i	−0.0911340	−	0.995839i	$-0.529049\pi$
$677$	18.8827	−	10.9019i	0.725721	−	0.418995i	0.816855	+	0.576844i	$0.195716\pi$
$678$		0			0
$679$	4.46410	−	23.1962i	0.171316	−	0.890187i
$680$		0			0
$681$	8.02628	+	13.9019i	0.307568	+	0.532723i
$682$		0			0
$683$	−29.9545	−	17.2942i	−1.14618	−	0.661745i	−0.198224	−	0.980157i	$-0.563517\pi$
$683$	−29.9545	−	17.2942i	−1.14618	−	0.661745i	−0.947953	+	0.318412i	$0.896851\pi$
$684$		0			0
$685$			2.33975i			0.0893971i
$686$		0			0
$687$		−	6.80385i		−	0.259583i
$688$		0			0
$689$	−1.26795	−	0.732051i	−0.0483050	−	0.0278889i
$690$		0			0
$691$	18.2846	+	31.6699i	0.695579	+	1.20478i	0.969985	+	0.243165i	$0.0781856\pi$
$691$	18.2846	+	31.6699i	0.695579	+	1.20478i	−0.274406	+	0.961614i	$0.588481\pi$
$692$		0			0
$693$	−2.36603	+	12.2942i	−0.0898779	+	0.467019i
$694$		0			0
$695$	5.13397	−	2.96410i	0.194743	−	0.112435i
$696$		0			0
$697$	19.1962	−	33.2487i	0.727106	−	1.25938i
$698$		0			0
$699$	−6.00000			−0.226941
$700$		0			0
$701$	−45.9090			−1.73396			−0.866979	−	0.498345i	$-0.833941\pi$
$701$	−45.9090			−1.73396			−0.866979	+	0.498345i	$0.833941\pi$
$702$		0			0
$703$	26.1865	−	45.3564i	0.987644	−	1.71065i
$704$		0			0
$705$	−0.803848	+	0.464102i	−0.0302747	+	0.0174791i
$706$		0			0
$707$	17.4641	+	15.1244i	0.656805	+	0.568810i
$708$		0			0
$709$	21.8564	+	37.8564i	0.820835	+	1.42173i	0.905062	+	0.425281i	$0.139825\pi$
$709$	21.8564	+	37.8564i	0.820835	+	1.42173i	−0.0842270	+	0.996447i	$0.526842\pi$
$710$		0			0
$711$	−6.69615	−	3.86603i	−0.251125	−	0.144987i
$712$		0			0
$713$			0.339746i			0.0127236i
$714$		0			0
$715$			4.73205i			0.176969i
$716$		0			0
$717$	4.60770	+	2.66025i	0.172078	+	0.0993490i
$718$		0			0
$719$	5.53590	+	9.58846i	0.206454	+	0.357589i	0.950595	−	0.310434i	$-0.100474\pi$
$719$	5.53590	+	9.58846i	0.206454	+	0.357589i	−0.744141	+	0.668023i	$0.767141\pi$
$720$		0			0
$721$	1.96410	+	5.66987i	0.0731470	+	0.211157i
$722$		0			0
$723$	10.2679	−	5.92820i	0.381869	−	0.220472i
$724$		0			0
$725$	−0.366025	+	0.633975i	−0.0135938	+	0.0235452i
$726$		0			0
$727$	24.2679			0.900048			0.450024	−	0.893016i	$-0.351415\pi$
$727$	24.2679			0.900048			0.450024	+	0.893016i	$0.351415\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	26.2224	−	45.4186i	0.969872	−	1.67987i
$732$		0			0
$733$	−19.4545	+	11.2321i	−0.718568	+	0.414865i	−0.814225	−	0.580549i	$-0.802838\pi$
$733$	−19.4545	+	11.2321i	−0.718568	+	0.414865i	0.0956576	+	0.995414i	$0.469505\pi$
$734$		0			0
$735$	−2.59808	+	6.50000i	−0.0958315	+	0.239756i
$736$		0			0
$737$	29.4904	+	51.0788i	1.08629	+	1.88151i
$738$		0			0
$739$	−13.9641	−	8.06218i	−0.513678	−	0.296572i	0.220666	−	0.975349i	$-0.429177\pi$
$739$	−13.9641	−	8.06218i	−0.513678	−	0.296572i	−0.734344	+	0.678777i	$0.762510\pi$
$740$		0			0
$741$			4.46410i			0.163993i
$742$		0			0
$743$		−	10.4449i		−	0.383185i	−0.981475	−	0.191592i	$-0.938635\pi$
$743$		−	10.4449i		−	0.383185i	0.981475	−	0.191592i	$-0.0613652\pi$
$744$		0			0
$745$	−20.1962	−	11.6603i	−0.739930	−	0.427199i
$746$		0			0
$747$	−4.36603	−	7.56218i	−0.159745	−	0.276686i
$748$		0			0
$749$	41.8301	−	14.4904i	1.52844	−	0.529467i
$750$		0			0
$751$	13.0359	−	7.52628i	0.475687	−	0.274638i	−0.242931	−	0.970044i	$-0.578109\pi$
$751$	13.0359	−	7.52628i	0.475687	−	0.274638i	0.718617	+	0.695406i	$0.244775\pi$
$752$		0			0
$753$	2.56218	−	4.43782i	0.0933710	−	0.161723i
$754$		0			0
$755$	17.8564			0.649861
$756$		0			0
$757$	8.14359			0.295984			0.147992	−	0.988989i	$-0.452719\pi$
$757$	8.14359			0.295984			0.147992	+	0.988989i	$0.452719\pi$
$758$		0			0
$759$	1.73205	−	3.00000i	0.0628695	−	0.108893i
$760$		0			0
$761$	20.7058	−	11.9545i	0.750584	−	0.433350i	−0.0753211	−	0.997159i	$-0.523998\pi$
$761$	20.7058	−	11.9545i	0.750584	−	0.433350i	0.825905	+	0.563810i	$0.190665\pi$
$762$		0			0
$763$	31.0526	−	35.8564i	1.12418	−	1.29809i
$764$		0			0
$765$	3.09808	+	5.36603i	0.112011	+	0.194009i
$766$		0			0
$767$	−12.2942	−	7.09808i	−0.443919	−	0.256297i
$768$		0			0
$769$		−	21.8756i		−	0.788856i	−0.918927	−	0.394428i	$-0.870943\pi$
$769$		−	21.8756i		−	0.788856i	0.918927	−	0.394428i	$-0.129057\pi$
$770$		0			0
$771$		−	17.6603i		−	0.636019i
$772$		0			0
$773$	38.3660	+	22.1506i	1.37993	+	0.796703i	0.992151	−	0.125049i	$-0.0399089\pi$
$773$	38.3660	+	22.1506i	1.37993	+	0.796703i	0.387779	+	0.921752i	$0.373242\pi$
$774$		0			0
$775$	0.232051	+	0.401924i	0.00833551	+	0.0144375i
$776$		0			0
$777$	−30.4808	−	5.86603i	−1.09349	−	0.210442i
$778$		0			0
$779$	−23.9545	+	13.8301i	−0.858258	+	0.495516i
$780$		0			0
$781$	37.0526	−	64.1769i	1.32584	−	2.29643i
$782$		0			0
$783$	0.732051			0.0261614
$784$		0			0
$785$	20.0000			0.713831
$786$		0			0
$787$	19.1244	−	33.1244i	0.681710	−	1.18076i	−0.292749	−	0.956189i	$-0.594570\pi$
$787$	19.1244	−	33.1244i	0.681710	−	1.18076i	0.974459	−	0.224566i	$-0.0720966\pi$
$788$		0			0
$789$	20.1962	−	11.6603i	0.719002	−	0.415116i
$790$		0			0
$791$	−37.3923	−	7.19615i	−1.32952	−	0.255866i
$792$		0			0
$793$	−5.73205	−	9.92820i	−0.203551	−	0.352561i
$794$		0			0
$795$	1.26795	+	0.732051i	0.0449695	+	0.0259632i
$796$		0			0
$797$		−	39.3731i		−	1.39467i	−0.716747	−	0.697333i	$-0.754370\pi$
$797$		−	39.3731i		−	1.39467i	0.716747	−	0.697333i	$-0.245630\pi$
$798$		0			0
$799$			5.75129i			0.203466i
$800$		0			0
$801$	−1.09808	−	0.633975i	−0.0387986	−	0.0224004i
$802$		0			0
$803$	14.0263	+	24.2942i	0.494977	+	0.857325i
$804$		0			0
$805$	1.26795	−	1.46410i	0.0446893	−	0.0516028i
$806$		0			0
$807$	−10.2679	+	5.92820i	−0.361449	+	0.208683i
$808$		0			0
$809$	−12.8038	+	22.1769i	−0.450159	+	0.779699i	−0.998396	−	0.0566247i	$-0.981966\pi$
$809$	−12.8038	+	22.1769i	−0.450159	+	0.779699i	0.548236	+	0.836324i	$0.315299\pi$
$810$		0			0
$811$	−26.1051			−0.916675			−0.458337	−	0.888778i	$-0.651555\pi$
$811$	−26.1051			−0.916675			−0.458337	+	0.888778i	$0.651555\pi$
$812$		0			0
$813$	2.00000			0.0701431
$814$		0			0
$815$	4.46410	−	7.73205i	0.156371	−	0.270842i
$816$		0			0
$817$	−32.7224	+	18.8923i	−1.14481	+	0.660958i
$818$		0			0
$819$	2.50000	−	0.866025i	0.0873571	−	0.0302614i
$820$		0			0
$821$	−11.9545	−	20.7058i	−0.417214	−	0.722636i	0.578444	−	0.815722i	$-0.303660\pi$
$821$	−11.9545	−	20.7058i	−0.417214	−	0.722636i	−0.995658	+	0.0930859i	$0.970327\pi$
$822$		0			0
$823$	5.07180	+	2.92820i	0.176792	+	0.102071i	0.585784	−	0.810467i	$-0.300787\pi$
$823$	5.07180	+	2.92820i	0.176792	+	0.102071i	−0.408993	+	0.912538i	$0.634120\pi$
$824$		0			0
$825$		−	4.73205i		−	0.164749i
$826$		0			0
$827$		−	27.8564i		−	0.968662i	−0.874885	−	0.484331i	$-0.839063\pi$
$827$		−	27.8564i		−	0.968662i	0.874885	−	0.484331i	$-0.160937\pi$
$828$		0			0
$829$	−42.6962	−	24.6506i	−1.48290	−	0.856152i	−0.483087	−	0.875572i	$-0.660485\pi$
$829$	−42.6962	−	24.6506i	−1.48290	−	0.856152i	−0.999811	+	0.0194203i	$0.993818\pi$
$830$		0			0
$831$	0.401924	+	0.696152i	0.0139426	+	0.0241493i
$832$		0			0
$833$	26.8301	+	34.0788i	0.929609	+	1.18076i
$834$		0			0
$835$	−14.8301	+	8.56218i	−0.513218	+	0.296306i
$836$		0			0
$837$	0.232051	−	0.401924i	0.00802085	−	0.0138925i
$838$		0			0
$839$	18.9808			0.655289			0.327644	−	0.944801i	$-0.393745\pi$
$839$	18.9808			0.655289			0.327644	+	0.944801i	$0.393745\pi$
$840$		0			0
$841$	−28.4641			−0.981521
$842$		0			0
$843$	−6.92820	+	12.0000i	−0.238620	+	0.413302i
$844$		0			0
$845$	−10.3923	+	6.00000i	−0.357506	+	0.206406i
$846$		0			0
$847$	−9.86603	−	28.4808i	−0.339001	−	0.978611i
$848$		0			0
$849$	11.4019	+	19.7487i	0.391313	+	0.677774i
$850$		0			0
$851$	7.43782	+	4.29423i	0.254965	+	0.147204i
$852$		0			0
$853$		−	29.3923i		−	1.00637i	−0.864178	−	0.503187i	$-0.832161\pi$
$853$		−	29.3923i		−	1.00637i	0.864178	−	0.503187i	$-0.167839\pi$
$854$		0			0
$855$		−	4.46410i		−	0.152669i
$856$		0			0
$857$	24.8827	+	14.3660i	0.849976	+	0.490734i	0.860643	−	0.509209i	$-0.170062\pi$
$857$	24.8827	+	14.3660i	0.849976	+	0.490734i	−0.0106665	+	0.999943i	$0.503395\pi$
$858$		0			0
$859$	11.7321	+	20.3205i	0.400292	+	0.693327i	0.993761	−	0.111530i	$-0.0355752\pi$
$859$	11.7321	+	20.3205i	0.400292	+	0.693327i	−0.593469	+	0.804857i	$0.702242\pi$
$860$		0			0
$861$	12.3923	+	10.7321i	0.422329	+	0.365747i
$862$		0			0
$863$	−9.92820	+	5.73205i	−0.337960	+	0.195121i	−0.659370	−	0.751819i	$-0.729177\pi$
$863$	−9.92820	+	5.73205i	−0.337960	+	0.195121i	0.321410	+	0.946940i	$0.395843\pi$
$864$		0			0
$865$	2.19615	−	3.80385i	0.0746714	−	0.129335i
$866$		0			0
$867$	21.3923			0.726521
$868$		0			0
$869$	36.5885			1.24118
$870$		0			0
$871$	6.23205	−	10.7942i	0.211165	−	0.365748i
$872$		0			0
$873$	7.73205	−	4.46410i	0.261690	−	0.151087i
$874$		0			0
$875$	0.500000	−	2.59808i	0.0169031	−	0.0878310i
$876$		0			0
$877$	1.39230	+	2.41154i	0.0470148	+	0.0814320i	0.888575	−	0.458731i	$-0.151696\pi$
$877$	1.39230	+	2.41154i	0.0470148	+	0.0814320i	−0.841560	+	0.540163i	$0.818363\pi$
$878$		0			0
$879$	9.12436	+	5.26795i	0.307757	+	0.177684i
$880$		0			0
$881$			48.4974i			1.63392i	0.576695	+	0.816960i	$0.304342\pi$
$881$			48.4974i			1.63392i	−0.576695	+	0.816960i	$0.695658\pi$
$882$		0			0
$883$			27.5359i			0.926657i	0.886187	+	0.463328i	$0.153345\pi$
$883$			27.5359i			0.926657i	−0.886187	+	0.463328i	$0.846655\pi$
$884$		0			0
$885$	12.2942	+	7.09808i	0.413266	+	0.238599i
$886$		0			0
$887$	8.56218	+	14.8301i	0.287490	+	0.497947i	0.973210	−	0.229918i	$-0.0738459\pi$
$887$	8.56218	+	14.8301i	0.287490	+	0.497947i	−0.685720	+	0.727865i	$0.740513\pi$
$888$		0			0
$889$	−1.69615	+	8.81347i	−0.0568871	+	0.295594i
$890$		0			0
$891$	−4.09808	+	2.36603i	−0.137291	+	0.0792648i
$892$		0			0
$893$	2.07180	−	3.58846i	0.0693300	−	0.120083i
$894$		0			0
$895$	3.46410			0.115792
$896$		0			0
$897$	−0.732051			−0.0244425
$898$		0			0
$899$	0.169873	−	0.294229i	0.00566558	−	0.00981307i
$900$		0			0
$901$	7.85641	−	4.53590i	0.261735	−	0.151113i
$902$		0			0
$903$	16.9282	+	14.6603i	0.563335	+	0.487863i
$904$		0			0
$905$	−2.79423	−	4.83975i	−0.0928833	−	0.160879i
$906$		0			0
$907$	24.4019	+	14.0885i	0.810253	+	0.467800i	0.847044	−	0.531523i	$-0.178380\pi$
$907$	24.4019	+	14.0885i	0.810253	+	0.467800i	−0.0367910	+	0.999323i	$0.511714\pi$
$908$		0			0
$909$			8.73205i			0.289624i
$910$		0			0
$911$			29.3731i			0.973173i	0.873632	+	0.486587i	$0.161758\pi$
$911$			29.3731i			0.973173i	−0.873632	+	0.486587i	$0.838242\pi$
$912$		0			0
$913$	35.7846	+	20.6603i	1.18430	+	0.683755i
$914$		0			0
$915$	5.73205	+	9.92820i	0.189496	+	0.328216i
$916$		0			0
$917$	6.46410	+	18.6603i	0.213463	+	0.616216i
$918$		0			0
$919$	41.4282	−	23.9186i	1.36659	−	0.789001i	0.376099	−	0.926579i	$-0.377265\pi$
$919$	41.4282	−	23.9186i	1.36659	−	0.789001i	0.990491	+	0.137578i	$0.0439318\pi$
$920$		0			0
$921$	−10.0622	+	17.4282i	−0.331560	+	0.574279i
$922$		0			0
$923$	−15.6603			−0.515464
$924$		0			0
$925$	11.7321			0.385747
$926$		0			0
$927$	−1.13397	+	1.96410i	−0.0372446	+	0.0645096i
$928$		0			0
$929$	10.0981	−	5.83013i	0.331307	−	0.191280i	−0.325114	−	0.945675i	$-0.605403\pi$
$929$	10.0981	−	5.83013i	0.331307	−	0.191280i	0.656421	+	0.754395i	$0.272069\pi$
$930$		0			0
$931$	−4.46410	−	30.9282i	−0.146305	−	1.01363i
$932$		0			0
$933$	3.90192	+	6.75833i	0.127743	+	0.221258i
$934$		0			0
$935$	−25.3923	−	14.6603i	−0.830417	−	0.479442i
$936$		0			0
$937$		−	30.4641i		−	0.995219i	−0.867401	−	0.497609i	$-0.834211\pi$
$937$		−	30.4641i		−	0.995219i	0.867401	−	0.497609i	$-0.165789\pi$
$938$		0			0
$939$		−	19.0000i		−	0.620042i
$940$		0			0
$941$	16.3135	+	9.41858i	0.531804	+	0.307037i	0.741751	−	0.670676i	$-0.233996\pi$
$941$	16.3135	+	9.41858i	0.531804	+	0.307037i	−0.209947	+	0.977713i	$0.567329\pi$
$942$		0			0
$943$	−2.26795	−	3.92820i	−0.0738546	−	0.127920i
$944$		0			0
$945$	−2.50000	+	0.866025i	−0.0813250	+	0.0281718i
$946$		0			0
$947$	6.84936	−	3.95448i	0.222574	−	0.128503i	−0.384567	−	0.923097i	$-0.625649\pi$
$947$	6.84936	−	3.95448i	0.222574	−	0.128503i	0.607142	+	0.794594i	$0.292316\pi$
$948$		0			0
$949$	2.96410	−	5.13397i	0.0962188	−	0.166656i
$950$		0			0
$951$	10.0526			0.325977
$952$		0			0
$953$	−19.6077			−0.635156			−0.317578	−	0.948232i	$-0.602869\pi$
$953$	−19.6077			−0.635156			−0.317578	+	0.948232i	$0.602869\pi$
$954$		0			0
$955$	1.00000	−	1.73205i	0.0323592	−	0.0560478i
$956$		0			0
$957$	−3.00000	+	1.73205i	−0.0969762	+	0.0559893i
$958$		0			0
$959$	−4.05256	+	4.67949i	−0.130864	+	0.151109i
$960$		0			0
$961$	15.3923	+	26.6603i	0.496526	+	0.860008i
$962$		0			0
$963$	14.4904	+	8.36603i	0.466946	+	0.269591i
$964$		0			0
$965$			9.19615i			0.296035i
$966$		0			0
$967$			9.53590i			0.306654i	0.988176	+	0.153327i	$0.0489988\pi$
$967$			9.53590i			0.306654i	−0.988176	+	0.153327i	$0.951001\pi$
$968$		0			0
$969$	−23.9545	−	13.8301i	−0.769529	−	0.444288i
$970$		0			0
$971$	−21.4641	−	37.1769i	−0.688816	−	1.19306i	−0.972221	−	0.234064i	$-0.924798\pi$
$971$	−21.4641	−	37.1769i	−0.688816	−	1.19306i	0.283405	−	0.959000i	$-0.408536\pi$
$972$		0			0
$973$	15.4019	+	2.96410i	0.493763	+	0.0950247i
$974$		0			0
$975$	−0.866025	+	0.500000i	−0.0277350	+	0.0160128i
$976$		0			0
$977$	5.83013	−	10.0981i	0.186522	−	0.323066i	−0.757566	−	0.652758i	$-0.773612\pi$
$977$	5.83013	−	10.0981i	0.186522	−	0.323066i	0.944088	+	0.329692i	$0.106945\pi$
$978$		0			0
$979$	6.00000			0.191761
$980$		0			0
$981$	17.9282			0.572403
$982$		0			0
$983$	−20.0981	+	34.8109i	−0.641029	+	1.11029i	0.344174	+	0.938906i	$0.388159\pi$
$983$	−20.0981	+	34.8109i	−0.641029	+	1.11029i	−0.985203	+	0.171389i	$0.945174\pi$
$984$		0			0
$985$	11.4904	−	6.63397i	0.366114	−	0.211376i
$986$		0			0
$987$	−2.41154	−	0.464102i	−0.0767603	−	0.0147725i
$988$		0			0
$989$	−3.09808	−	5.36603i	−0.0985131	−	0.170630i
$990$		0			0
$991$	−20.7679	−	11.9904i	−0.659716	−	0.380887i	0.132453	−	0.991189i	$-0.457715\pi$
$991$	−20.7679	−	11.9904i	−0.659716	−	0.380887i	−0.792169	+	0.610302i	$0.791048\pi$
$992$		0			0
$993$			8.66025i			0.274825i
$994$		0			0
$995$			3.85641i			0.122256i
$996$		0			0
$997$	−39.3109	−	22.6962i	−1.24499	−	0.718794i	−0.274883	−	0.961478i	$-0.588639\pi$
$997$	−39.3109	−	22.6962i	−1.24499	−	0.718794i	−0.970106	+	0.242683i	$0.921972\pi$
$998$		0			0
$999$	−5.86603	−	10.1603i	−0.185593	−	0.321456i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1680.2.dx.d.31.1	yes	4
4.3	odd	2		1680.2.dx.a.31.1	✓	4
7.5	odd	6		1680.2.dx.a.271.1	yes	4
28.19	even	6	inner	1680.2.dx.d.271.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1680.2.dx.a.31.1	✓	4	4.3	odd	2
1680.2.dx.a.271.1	yes	4	7.5	odd	6
1680.2.dx.d.31.1	yes	4	1.1	even	1	trivial
1680.2.dx.d.271.1	yes	4	28.19	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:	\( N \)	\(=\)	\( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1680.dx (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{3} +(-0.866025 + 0.500000i) q^{5} +(-2.59808 - 0.500000i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(4.09808 + 2.36603i) q^{11} -1.00000i q^{13} +1.00000i q^{15} +(5.36603 + 3.09808i) q^{17} +(-2.23205 - 3.86603i) q^{19} +(-1.73205 + 2.00000i) q^{21} +(0.633975 - 0.366025i) q^{23} +(0.500000 - 0.866025i) q^{25} -1.00000 q^{27} -0.732051 q^{29} +(-0.232051 + 0.401924i) q^{31} +(4.09808 - 2.36603i) q^{33} +(2.50000 - 0.866025i) q^{35} +(5.86603 + 10.1603i) q^{37} +(-0.866025 - 0.500000i) q^{39} -6.19615i q^{41} -8.46410i q^{43} +(0.866025 + 0.500000i) q^{45} +(0.464102 + 0.803848i) q^{47} +(6.50000 + 2.59808i) q^{49} +(5.36603 - 3.09808i) q^{51} +(0.732051 - 1.26795i) q^{53} -4.73205 q^{55} -4.46410 q^{57} +(7.09808 - 12.2942i) q^{59} +(9.92820 - 5.73205i) q^{61} +(0.866025 + 2.50000i) q^{63} +(0.500000 + 0.866025i) q^{65} +(10.7942 + 6.23205i) q^{67} -0.732051i q^{69} -15.6603i q^{71} +(5.13397 + 2.96410i) q^{73} +(-0.500000 - 0.866025i) q^{75} +(-9.46410 - 8.19615i) q^{77} +(6.69615 - 3.86603i) q^{79} +(-0.500000 + 0.866025i) q^{81} +8.73205 q^{83} -6.19615 q^{85} +(-0.366025 + 0.633975i) q^{87} +(1.09808 - 0.633975i) q^{89} +(-0.500000 + 2.59808i) q^{91} +(0.232051 + 0.401924i) q^{93} +(3.86603 + 2.23205i) q^{95} +8.92820i q^{97} -4.73205i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} - 2 q^{9} + 6 q^{11} + 18 q^{17} - 2 q^{19} + 6 q^{23} + 2 q^{25} - 4 q^{27} + 4 q^{29} + 6 q^{31} + 6 q^{33} + 10 q^{35} + 20 q^{37} - 12 q^{47} + 26 q^{49} + 18 q^{51} - 4 q^{53} - 12 q^{55}+ \cdots + 12 q^{95}+O(q^{100}) \) 4 * q + 2 * q^3 - 2 * q^9 + 6 * q^11 + 18 * q^17 - 2 * q^19 + 6 * q^23 + 2 * q^25 - 4 * q^27 + 4 * q^29 + 6 * q^31 + 6 * q^33 + 10 * q^35 + 20 * q^37 - 12 * q^47 + 26 * q^49 + 18 * q^51 - 4 * q^53 - 12 * q^55 - 4 * q^57 + 18 * q^59 + 12 * q^61 + 2 * q^65 + 12 * q^67 + 24 * q^73 - 2 * q^75 - 24 * q^77 + 6 * q^79 - 2 * q^81 + 28 * q^83 - 4 * q^85 + 2 * q^87 - 6 * q^89 - 2 * q^91 - 6 * q^93 + 12 * q^95

Introduction

L-functions

Modular forms

Varieties

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Database

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