LMFDB - Embedded newform 560.2.ci.a.33.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(17,560)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 0, 3, 2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("560.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.ci (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			33.1
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	560.33
Dual form			560.2.ci.a.17.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.133975i) q^{3} +(-1.86603 + 1.23205i) q^{5} +(0.866025 - 2.50000i) q^{7} +(-2.36603 - 1.36603i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.133975i) q^{3} +(-1.86603 + 1.23205i) q^{5} +(0.866025 - 2.50000i) q^{7} +(-2.36603 - 1.36603i) q^{9} +(-1.36603 - 2.36603i) q^{11} +(2.00000 - 2.00000i) q^{13} +(-1.09808 + 0.366025i) q^{15} +(1.00000 - 3.73205i) q^{17} +(0.366025 - 0.633975i) q^{19} +(0.767949 - 1.13397i) q^{21} +(0.133975 - 0.0358984i) q^{23} +(1.96410 - 4.59808i) q^{25} +(-2.09808 - 2.09808i) q^{27} +3.00000i q^{29} +(6.46410 - 3.73205i) q^{31} +(-0.366025 - 1.36603i) q^{33} +(1.46410 + 5.73205i) q^{35} +(1.26795 + 4.73205i) q^{37} +(1.26795 - 0.732051i) q^{39} -6.46410i q^{41} +(-2.83013 - 2.83013i) q^{43} +(6.09808 - 0.366025i) q^{45} +(-8.83013 + 2.36603i) q^{47} +(-5.50000 - 4.33013i) q^{49} +(1.00000 - 1.73205i) q^{51} +(-1.83013 + 6.83013i) q^{53} +(5.46410 + 2.73205i) q^{55} +(0.267949 - 0.267949i) q^{57} +(-4.09808 - 7.09808i) q^{59} +(1.33013 + 0.767949i) q^{61} +(-5.46410 + 4.73205i) q^{63} +(-1.26795 + 6.19615i) q^{65} +(10.6962 + 2.86603i) q^{67} +0.0717968 q^{69} -1.26795 q^{71} +(-12.9282 - 3.46410i) q^{73} +(1.59808 - 2.03590i) q^{75} +(-7.09808 + 1.36603i) q^{77} +(2.83013 + 1.63397i) q^{79} +(3.33013 + 5.76795i) q^{81} +(-2.09808 + 2.09808i) q^{83} +(2.73205 + 8.19615i) q^{85} +(-0.401924 + 1.50000i) q^{87} +(0.330127 - 0.571797i) q^{89} +(-3.26795 - 6.73205i) q^{91} +(3.73205 - 1.00000i) q^{93} +(0.0980762 + 1.63397i) q^{95} +(5.92820 + 5.92820i) q^{97} +7.46410i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} - 4 q^{5} - 6 q^{9}+O(q^{10}) $ 4 * q + 2 * q^3 - 4 * q^5 - 6 * q^9	$ 4 q + 2 q^{3} - 4 q^{5} - 6 q^{9} - 2 q^{11} + 8 q^{13} + 6 q^{15} + 4 q^{17} - 2 q^{19} + 10 q^{21} + 4 q^{23} - 6 q^{25} + 2 q^{27} + 12 q^{31} + 2 q^{33} - 8 q^{35} + 12 q^{37} + 12 q^{39} + 6 q^{43} + 14 q^{45} - 18 q^{47} - 22 q^{49} + 4 q^{51} + 10 q^{53} + 8 q^{55} + 8 q^{57} - 6 q^{59} - 12 q^{61} - 8 q^{63} - 12 q^{65} + 22 q^{67} + 28 q^{69} - 12 q^{71} - 24 q^{73} - 4 q^{75} - 18 q^{77} - 6 q^{79} - 4 q^{81} + 2 q^{83} + 4 q^{85} - 12 q^{87} - 16 q^{89} - 20 q^{91} + 8 q^{93} - 10 q^{95} - 4 q^{97}+O(q^{100}) $ 4 * q + 2 * q^3 - 4 * q^5 - 6 * q^9 - 2 * q^11 + 8 * q^13 + 6 * q^15 + 4 * q^17 - 2 * q^19 + 10 * q^21 + 4 * q^23 - 6 * q^25 + 2 * q^27 + 12 * q^31 + 2 * q^33 - 8 * q^35 + 12 * q^37 + 12 * q^39 + 6 * q^43 + 14 * q^45 - 18 * q^47 - 22 * q^49 + 4 * q^51 + 10 * q^53 + 8 * q^55 + 8 * q^57 - 6 * q^59 - 12 * q^61 - 8 * q^63 - 12 * q^65 + 22 * q^67 + 28 * q^69 - 12 * q^71 - 24 * q^73 - 4 * q^75 - 18 * q^77 - 6 * q^79 - 4 * q^81 + 2 * q^83 + 4 * q^85 - 12 * q^87 - 16 * q^89 - 20 * q^91 + 8 * q^93 - 10 * q^95 - 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{4}\right)$	$1$	$1$

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	+	0.133975i	0.288675	+	0.0773503i	0.400251	−	0.916406i	$-0.368923\pi$
$3$	0.500000	+	0.133975i	0.288675	+	0.0773503i	−0.111576	+	0.993756i	$0.535590\pi$
$4$		0			0
$5$	−1.86603	+	1.23205i	−0.834512	+	0.550990i
$5$	−1.86603	+	1.23205i	−0.834512	+	0.550990i
$6$		0			0
$7$	0.866025	−	2.50000i	0.327327	−	0.944911i
$7$	0.866025	−	2.50000i	0.327327	−	0.944911i
$8$		0			0
$9$	−2.36603	−	1.36603i	−0.788675	−	0.455342i
$10$		0			0
$11$	−1.36603	−	2.36603i	−0.411872	−	0.713384i	0.583222	−	0.812313i	$-0.301792\pi$
$11$	−1.36603	−	2.36603i	−0.411872	−	0.713384i	−0.995094	+	0.0989291i	$0.968458\pi$
$12$		0			0
$13$	2.00000	−	2.00000i	0.554700	−	0.554700i	−0.373094	−	0.927794i	$-0.621703\pi$
$13$	2.00000	−	2.00000i	0.554700	−	0.554700i	0.927794	+	0.373094i	$0.121703\pi$
$14$		0			0
$15$	−1.09808	+	0.366025i	−0.283522	+	0.0945074i
$16$		0			0
$17$	1.00000	−	3.73205i	0.242536	−	0.905155i	−0.732070	−	0.681229i	$-0.761446\pi$
$17$	1.00000	−	3.73205i	0.242536	−	0.905155i	0.974606	−	0.223926i	$-0.0718875\pi$
$18$		0			0
$19$	0.366025	−	0.633975i	0.0839720	−	0.145444i	−0.820981	−	0.570956i	$-0.806573\pi$
$19$	0.366025	−	0.633975i	0.0839720	−	0.145444i	0.904953	+	0.425512i	$0.139906\pi$
$20$		0			0
$21$	0.767949	−	1.13397i	0.167580	−	0.247454i
$22$		0			0
$23$	0.133975	−	0.0358984i	0.0279356	−	0.00748533i	−0.244824	−	0.969567i	$-0.578730\pi$
$23$	0.133975	−	0.0358984i	0.0279356	−	0.00748533i	0.272760	+	0.962082i	$0.412064\pi$
$24$		0			0
$25$	1.96410	−	4.59808i	0.392820	−	0.919615i
$26$		0			0
$27$	−2.09808	−	2.09808i	−0.403775	−	0.403775i
$28$		0			0
$29$			3.00000i			0.557086i	0.960424	+	0.278543i	$0.0898515\pi$
$29$			3.00000i			0.557086i	−0.960424	+	0.278543i	$0.910149\pi$
$30$		0			0
$31$	6.46410	−	3.73205i	1.16099	−	0.670296i	0.209447	−	0.977820i	$-0.432834\pi$
$31$	6.46410	−	3.73205i	1.16099	−	0.670296i	0.951540	+	0.307524i	$0.0995004\pi$
$32$		0			0
$33$	−0.366025	−	1.36603i	−0.0637168	−	0.237795i
$34$		0			0
$35$	1.46410	+	5.73205i	0.247478	+	0.968893i
$36$		0			0
$37$	1.26795	+	4.73205i	0.208450	+	0.777944i	0.988370	+	0.152066i	$0.0485927\pi$
$37$	1.26795	+	4.73205i	0.208450	+	0.777944i	−0.779921	+	0.625878i	$0.784741\pi$
$38$		0			0
$39$	1.26795	−	0.732051i	0.203034	−	0.117222i
$40$		0			0
$41$		−	6.46410i		−	1.00952i	−0.863259	−	0.504762i	$-0.831580\pi$
$41$		−	6.46410i		−	1.00952i	0.863259	−	0.504762i	$-0.168420\pi$
$42$		0			0
$43$	−2.83013	−	2.83013i	−0.431590	−	0.431590i	0.457579	−	0.889169i	$-0.348717\pi$
$43$	−2.83013	−	2.83013i	−0.431590	−	0.431590i	−0.889169	+	0.457579i	$0.848717\pi$
$44$		0			0
$45$	6.09808	−	0.366025i	0.909048	−	0.0545638i
$46$		0			0
$47$	−8.83013	+	2.36603i	−1.28801	+	0.345120i	−0.836903	−	0.547351i	$-0.815636\pi$
$47$	−8.83013	+	2.36603i	−1.28801	+	0.345120i	−0.451103	+	0.892472i	$0.648969\pi$
$48$		0			0
$49$	−5.50000	−	4.33013i	−0.785714	−	0.618590i
$50$		0			0
$51$	1.00000	−	1.73205i	0.140028	−	0.242536i
$52$		0			0
$53$	−1.83013	+	6.83013i	−0.251387	+	0.938190i	0.718677	+	0.695344i	$0.244748\pi$
$53$	−1.83013	+	6.83013i	−0.251387	+	0.938190i	−0.970065	+	0.242846i	$0.921919\pi$
$54$		0			0
$55$	5.46410	+	2.73205i	0.736779	+	0.368390i
$56$		0			0
$57$	0.267949	−	0.267949i	0.0354907	−	0.0354907i
$58$		0			0
$59$	−4.09808	−	7.09808i	−0.533524	−	0.924091i	−0.999233	−	0.0391530i	$-0.987534\pi$
$59$	−4.09808	−	7.09808i	−0.533524	−	0.924091i	0.465709	−	0.884938i	$-0.345799\pi$
$60$		0			0
$61$	1.33013	+	0.767949i	0.170305	+	0.0983258i	0.582730	−	0.812666i	$-0.301985\pi$
$61$	1.33013	+	0.767949i	0.170305	+	0.0983258i	−0.412424	+	0.910992i	$0.635318\pi$
$62$		0			0
$63$	−5.46410	+	4.73205i	−0.688412	+	0.596182i
$64$		0			0
$65$	−1.26795	+	6.19615i	−0.157270	+	0.768538i
$66$		0			0
$67$	10.6962	+	2.86603i	1.30674	+	0.350141i	0.843996	−	0.536350i	$-0.180197\pi$
$67$	10.6962	+	2.86603i	1.30674	+	0.350141i	0.462747	+	0.886490i	$0.346864\pi$
$68$		0			0
$69$	0.0717968			0.00864332
$70$		0			0
$71$	−1.26795			−0.150478			−0.0752389	−	0.997166i	$-0.523972\pi$
$71$	−1.26795			−0.150478			−0.0752389	+	0.997166i	$0.523972\pi$
$72$		0			0
$73$	−12.9282	−	3.46410i	−1.51313	−	0.405442i	−0.595658	−	0.803238i	$-0.703109\pi$
$73$	−12.9282	−	3.46410i	−1.51313	−	0.405442i	−0.917474	+	0.397796i	$0.869775\pi$
$74$		0			0
$75$	1.59808	−	2.03590i	0.184530	−	0.235085i
$76$		0			0
$77$	−7.09808	+	1.36603i	−0.808901	+	0.155673i
$78$		0			0
$79$	2.83013	+	1.63397i	0.318414	+	0.183837i	0.650686	−	0.759347i	$-0.274482\pi$
$79$	2.83013	+	1.63397i	0.318414	+	0.183837i	−0.332271	+	0.943184i	$0.607815\pi$
$80$		0			0
$81$	3.33013	+	5.76795i	0.370014	+	0.640883i
$82$		0			0
$83$	−2.09808	+	2.09808i	−0.230294	+	0.230294i	−0.812815	−	0.582522i	$-0.802066\pi$
$83$	−2.09808	+	2.09808i	−0.230294	+	0.230294i	0.582522	+	0.812815i	$0.302066\pi$
$84$		0			0
$85$	2.73205	+	8.19615i	0.296333	+	0.888998i
$86$		0			0
$87$	−0.401924	+	1.50000i	−0.0430908	+	0.160817i
$88$		0			0
$89$	0.330127	−	0.571797i	0.0349934	−	0.0606103i	−0.847998	−	0.529999i	$-0.822192\pi$
$89$	0.330127	−	0.571797i	0.0349934	−	0.0606103i	0.882992	+	0.469389i	$0.155526\pi$
$90$		0			0
$91$	−3.26795	−	6.73205i	−0.342574	−	0.705711i
$92$		0			0
$93$	3.73205	−	1.00000i	0.386996	−	0.103695i
$94$		0			0
$95$	0.0980762	+	1.63397i	0.0100624	+	0.167642i
$96$		0			0
$97$	5.92820	+	5.92820i	0.601918	+	0.601918i	0.940821	−	0.338903i	$-0.110056\pi$
$97$	5.92820	+	5.92820i	0.601918	+	0.601918i	−0.338903	+	0.940821i	$0.610056\pi$
$98$		0			0
$99$			7.46410i			0.750170i
$100$		0			0
$101$	7.16025	−	4.13397i	0.712472	−	0.411346i	−0.0995037	−	0.995037i	$-0.531726\pi$
$101$	7.16025	−	4.13397i	0.712472	−	0.411346i	0.811976	+	0.583691i	$0.198392\pi$
$102$		0			0
$103$	−1.23205	−	4.59808i	−0.121398	−	0.453062i	0.878288	−	0.478132i	$-0.158686\pi$
$103$	−1.23205	−	4.59808i	−0.121398	−	0.453062i	−0.999686	+	0.0250698i	$0.992019\pi$
$104$		0			0
$105$	−0.0358984	+	3.06218i	−0.00350332	+	0.298838i
$106$		0			0
$107$	3.40192	+	12.6962i	0.328876	+	1.22738i	0.910357	+	0.413823i	$0.135807\pi$
$107$	3.40192	+	12.6962i	0.328876	+	1.22738i	−0.581481	+	0.813560i	$0.697526\pi$
$108$		0			0
$109$	8.76795	−	5.06218i	0.839817	−	0.484869i	−0.0173849	−	0.999849i	$-0.505534\pi$
$109$	8.76795	−	5.06218i	0.839817	−	0.484869i	0.857202	+	0.514980i	$0.172201\pi$
$110$		0			0
$111$			2.53590i			0.240697i
$112$		0			0
$113$	−7.73205	−	7.73205i	−0.727370	−	0.727370i	0.242725	−	0.970095i	$-0.421959\pi$
$113$	−7.73205	−	7.73205i	−0.727370	−	0.727370i	−0.970095	+	0.242725i	$0.921959\pi$
$114$		0			0
$115$	−0.205771	+	0.232051i	−0.0191883	+	0.0216388i
$116$		0			0
$117$	−7.46410	+	2.00000i	−0.690056	+	0.184900i
$118$		0			0
$119$	−8.46410	−	5.73205i	−0.775903	−	0.525456i
$120$		0			0
$121$	1.76795	−	3.06218i	0.160723	−	0.278380i
$122$		0			0
$123$	0.866025	−	3.23205i	0.0780869	−	0.291424i
$124$		0			0
$125$	2.00000	+	11.0000i	0.178885	+	0.983870i
$126$		0			0
$127$	−0.464102	+	0.464102i	−0.0411824	+	0.0411824i	−0.727398	−	0.686216i	$-0.759271\pi$
$127$	−0.464102	+	0.464102i	−0.0411824	+	0.0411824i	0.686216	+	0.727398i	$0.259271\pi$
$128$		0			0
$129$	−1.03590	−	1.79423i	−0.0912058	−	0.157973i
$130$		0			0
$131$	13.3923	+	7.73205i	1.17009	+	0.675552i	0.953702	−	0.300755i	$-0.0972385\pi$
$131$	13.3923	+	7.73205i	1.17009	+	0.675552i	0.216390	+	0.976307i	$0.430572\pi$
$132$		0			0
$133$	−1.26795	−	1.46410i	−0.109945	−	0.126954i
$134$		0			0
$135$	6.50000	+	1.33013i	0.559431	+	0.114479i
$136$		0			0
$137$	13.1962	+	3.53590i	1.12742	+	0.302092i	0.773884	−	0.633327i	$-0.218311\pi$
$137$	13.1962	+	3.53590i	1.12742	+	0.302092i	0.353539	+	0.935420i	$0.384978\pi$
$138$		0			0
$139$	−5.66025			−0.480096			−0.240048	−	0.970761i	$-0.577163\pi$
$139$	−5.66025			−0.480096			−0.240048	+	0.970761i	$0.577163\pi$
$140$		0			0
$141$	−4.73205			−0.398511
$142$		0			0
$143$	−7.46410	−	2.00000i	−0.624180	−	0.167248i
$144$		0			0
$145$	−3.69615	−	5.59808i	−0.306949	−	0.464895i
$146$		0			0
$147$	−2.16987	−	2.90192i	−0.178968	−	0.239347i
$148$		0			0
$149$	−0.696152	−	0.401924i	−0.0570310	−	0.0329269i	0.471213	−	0.882019i	$-0.343816\pi$
$149$	−0.696152	−	0.401924i	−0.0570310	−	0.0329269i	−0.528244	+	0.849092i	$0.677150\pi$
$150$		0			0
$151$	6.92820	+	12.0000i	0.563809	+	0.976546i	0.997159	+	0.0753205i	$0.0239980\pi$
$151$	6.92820	+	12.0000i	0.563809	+	0.976546i	−0.433350	+	0.901226i	$0.642669\pi$
$152$		0			0
$153$	−7.46410	+	7.46410i	−0.603437	+	0.603437i
$154$		0			0
$155$	−7.46410	+	14.9282i	−0.599531	+	1.19906i
$156$		0			0
$157$	−1.24167	+	4.63397i	−0.0990960	+	0.369831i	−0.997609	−	0.0691164i	$-0.977982\pi$
$157$	−1.24167	+	4.63397i	−0.0990960	+	0.369831i	0.898513	+	0.438948i	$0.144649\pi$
$158$		0			0
$159$	−1.83013	+	3.16987i	−0.145139	+	0.251387i
$160$		0			0
$161$	0.0262794	−	0.366025i	0.00207111	−	0.0288468i
$162$		0			0
$163$	−13.5622	+	3.63397i	−1.06227	+	0.284635i	−0.747314	−	0.664471i	$-0.768657\pi$
$163$	−13.5622	+	3.63397i	−1.06227	+	0.284635i	−0.314958	+	0.949106i	$0.601990\pi$
$164$		0			0
$165$	2.36603	+	2.09808i	0.184195	+	0.163335i
$166$		0			0
$167$	11.7583	+	11.7583i	0.909887	+	0.909887i	0.996263	−	0.0863757i	$-0.0275285\pi$
$167$	11.7583	+	11.7583i	0.909887	+	0.909887i	−0.0863757	+	0.996263i	$0.527529\pi$
$168$		0			0
$169$			5.00000i			0.384615i
$170$		0			0
$171$	−1.73205	+	1.00000i	−0.132453	+	0.0764719i
$172$		0			0
$173$	5.33975	+	19.9282i	0.405973	+	1.51511i	0.802253	+	0.596984i	$0.203634\pi$
$173$	5.33975	+	19.9282i	0.405973	+	1.51511i	−0.396280	+	0.918130i	$0.629699\pi$
$174$		0			0
$175$	−9.79423	−	8.89230i	−0.740374	−	0.672195i
$176$		0			0
$177$	−1.09808	−	4.09808i	−0.0825365	−	0.308030i
$178$		0			0
$179$	6.80385	−	3.92820i	0.508543	−	0.293608i	−0.223691	−	0.974660i	$-0.571811\pi$
$179$	6.80385	−	3.92820i	0.508543	−	0.293608i	0.732235	+	0.681052i	$0.238477\pi$
$180$		0			0
$181$		−	1.19615i		−	0.0889093i	−0.999011	−	0.0444547i	$-0.985845\pi$
$181$		−	1.19615i		−	0.0889093i	0.999011	−	0.0444547i	$-0.0141550\pi$
$182$		0			0
$183$	0.562178	+	0.562178i	0.0415574	+	0.0415574i
$184$		0			0
$185$	−8.19615	−	7.26795i	−0.602593	−	0.534350i
$186$		0			0
$187$	−10.1962	+	2.73205i	−0.745617	+	0.199787i
$188$		0			0
$189$	−7.06218	+	3.42820i	−0.513698	+	0.249365i
$190$		0			0
$191$	6.63397	−	11.4904i	0.480018	−	0.831415i	−0.519720	−	0.854337i	$-0.673964\pi$
$191$	6.63397	−	11.4904i	0.480018	−	0.831415i	0.999737	+	0.0229220i	$0.00729695\pi$
$192$		0			0
$193$	2.09808	−	7.83013i	0.151023	−	0.563625i	−0.848390	−	0.529371i	$-0.822428\pi$
$193$	2.09808	−	7.83013i	0.151023	−	0.563625i	0.999413	−	0.0342537i	$-0.0109054\pi$
$194$		0			0
$195$	−1.46410	+	2.92820i	−0.104846	+	0.209693i
$196$		0			0
$197$	−10.1244	+	10.1244i	−0.721330	+	0.721330i	−0.968876	−	0.247546i	$-0.920376\pi$
$197$	−10.1244	+	10.1244i	−0.721330	+	0.721330i	0.247546	+	0.968876i	$0.420376\pi$
$198$		0			0
$199$	−5.53590	−	9.58846i	−0.392429	−	0.679708i	0.600340	−	0.799745i	$-0.295032\pi$
$199$	−5.53590	−	9.58846i	−0.392429	−	0.679708i	−0.992769	+	0.120037i	$0.961699\pi$
$200$		0			0
$201$	4.96410	+	2.86603i	0.350141	+	0.202154i
$202$		0			0
$203$	7.50000	+	2.59808i	0.526397	+	0.182349i
$204$		0			0
$205$	7.96410	+	12.0622i	0.556237	+	0.842459i
$206$		0			0
$207$	−0.366025	−	0.0980762i	−0.0254405	−	0.00681677i
$208$		0			0
$209$	−2.00000			−0.138343
$210$		0			0
$211$	0.196152			0.0135037			0.00675184	−	0.999977i	$-0.497851\pi$
$211$	0.196152			0.0135037			0.00675184	+	0.999977i	$0.497851\pi$
$212$		0			0
$213$	−0.633975	−	0.169873i	−0.0434392	−	0.0116395i
$214$		0			0
$215$	8.76795	+	1.79423i	0.597969	+	0.122365i
$216$		0			0
$217$	−3.73205	−	19.3923i	−0.253348	−	1.31644i
$218$		0			0
$219$	−6.00000	−	3.46410i	−0.405442	−	0.234082i
$220$		0			0
$221$	−5.46410	−	9.46410i	−0.367555	−	0.636624i
$222$		0			0
$223$	18.1244	−	18.1244i	1.21370	−	1.21370i	0.243895	−	0.969802i	$-0.421575\pi$
$223$	18.1244	−	18.1244i	1.21370	−	1.21370i	0.969802	−	0.243895i	$-0.0784252\pi$
$224$		0			0
$225$	−10.9282	+	8.19615i	−0.728547	+	0.546410i
$226$		0			0
$227$	5.09808	−	19.0263i	0.338371	−	1.26282i	−0.561797	−	0.827275i	$-0.689890\pi$
$227$	5.09808	−	19.0263i	0.338371	−	1.26282i	0.900168	−	0.435543i	$-0.143444\pi$
$228$		0			0
$229$	9.19615	−	15.9282i	0.607699	−	1.05257i	−0.383920	−	0.923366i	$-0.625426\pi$
$229$	9.19615	−	15.9282i	0.607699	−	1.05257i	0.991619	−	0.129199i	$-0.0412406\pi$
$230$		0			0
$231$	−3.73205	−	0.267949i	−0.245551	−	0.0176298i
$232$		0			0
$233$	6.46410	−	1.73205i	0.423477	−	0.113470i	−0.0407854	−	0.999168i	$-0.512986\pi$
$233$	6.46410	−	1.73205i	0.423477	−	0.113470i	0.464263	+	0.885698i	$0.346319\pi$
$234$		0			0
$235$	13.5622	−	15.2942i	0.884699	−	0.997685i
$236$		0			0
$237$	1.19615	+	1.19615i	0.0776984	+	0.0776984i
$238$		0			0
$239$			2.39230i			0.154745i	0.997002	+	0.0773727i	$0.0246531\pi$
$239$			2.39230i			0.154745i	−0.997002	+	0.0773727i	$0.975347\pi$
$240$		0			0
$241$	21.4641	−	12.3923i	1.38262	−	0.798259i	0.390155	−	0.920749i	$-0.372422\pi$
$241$	21.4641	−	12.3923i	1.38262	−	0.798259i	0.992470	+	0.122491i	$0.0390882\pi$
$242$		0			0
$243$	3.19615	+	11.9282i	0.205033	+	0.765195i
$244$		0			0
$245$	15.5981	+	1.30385i	0.996525	+	0.0832998i
$246$		0			0
$247$	−0.535898	−	2.00000i	−0.0340984	−	0.127257i
$248$		0			0
$249$	−1.33013	+	0.767949i	−0.0842934	+	0.0486668i
$250$		0			0
$251$		−	21.8564i		−	1.37956i	−0.724017	−	0.689782i	$-0.757706\pi$
$251$		−	21.8564i		−	1.37956i	0.724017	−	0.689782i	$-0.242294\pi$
$252$		0			0
$253$	−0.267949	−	0.267949i	−0.0168458	−	0.0168458i
$254$		0			0
$255$	0.267949	+	4.46410i	0.0167796	+	0.279553i
$256$		0			0
$257$	−2.73205	+	0.732051i	−0.170421	+	0.0456641i	−0.343020	−	0.939328i	$-0.611450\pi$
$257$	−2.73205	+	0.732051i	−0.170421	+	0.0456641i	0.172600	+	0.984992i	$0.444783\pi$
$258$		0			0
$259$	12.9282	+	0.928203i	0.803319	+	0.0576757i
$260$		0			0
$261$	4.09808	−	7.09808i	0.253665	−	0.439360i
$262$		0			0
$263$	−4.06218	+	15.1603i	−0.250485	+	0.934821i	0.720062	+	0.693909i	$0.244113\pi$
$263$	−4.06218	+	15.1603i	−0.250485	+	0.934821i	−0.970547	+	0.240912i	$0.922553\pi$
$264$		0			0
$265$	−5.00000	−	15.0000i	−0.307148	−	0.921443i
$266$		0			0
$267$	0.241670	−	0.241670i	0.0147899	−	0.0147899i
$268$		0			0
$269$	−11.4282	−	19.7942i	−0.696790	−	1.20688i	−0.969574	−	0.244800i	$-0.921278\pi$
$269$	−11.4282	−	19.7942i	−0.696790	−	1.20688i	0.272784	−	0.962075i	$-0.412056\pi$
$270$		0			0
$271$	−18.4186	−	10.6340i	−1.11885	−	0.645968i	−0.177742	−	0.984077i	$-0.556879\pi$
$271$	−18.4186	−	10.6340i	−1.11885	−	0.645968i	−0.941107	+	0.338109i	$0.890213\pi$
$272$		0			0
$273$	−0.732051	−	3.80385i	−0.0443057	−	0.230219i
$274$		0			0
$275$	−13.5622	+	1.63397i	−0.817830	+	0.0985324i
$276$		0			0
$277$	5.19615	+	1.39230i	0.312207	+	0.0836555i	0.411520	−	0.911401i	$-0.364998\pi$
$277$	5.19615	+	1.39230i	0.312207	+	0.0836555i	−0.0993135	+	0.995056i	$0.531665\pi$
$278$		0			0
$279$	−20.3923			−1.22086
$280$		0			0
$281$	−0.928203			−0.0553720			−0.0276860	−	0.999617i	$-0.508814\pi$
$281$	−0.928203			−0.0553720			−0.0276860	+	0.999617i	$0.508814\pi$
$282$		0			0
$283$	1.90192	+	0.509619i	0.113058	+	0.0302937i	0.314904	−	0.949123i	$-0.398028\pi$
$283$	1.90192	+	0.509619i	0.113058	+	0.0302937i	−0.201847	+	0.979417i	$0.564694\pi$
$284$		0			0
$285$	−0.169873	+	0.830127i	−0.0100624	+	0.0491725i
$286$		0			0
$287$	−16.1603	−	5.59808i	−0.953910	−	0.330444i
$288$		0			0
$289$	1.79423	+	1.03590i	0.105543	+	0.0609352i
$290$		0			0
$291$	2.16987	+	3.75833i	0.127200	+	0.220317i
$292$		0			0
$293$	2.39230	−	2.39230i	0.139760	−	0.139760i	−0.633765	−	0.773525i	$-0.718492\pi$
$293$	2.39230	−	2.39230i	0.139760	−	0.139760i	0.773525	+	0.633765i	$0.218492\pi$
$294$		0			0
$295$	16.3923	+	8.19615i	0.954397	+	0.477198i
$296$		0			0
$297$	−2.09808	+	7.83013i	−0.121743	+	0.454350i
$298$		0			0
$299$	0.196152	−	0.339746i	0.0113438	−	0.0196480i
$300$		0			0
$301$	−9.52628	+	4.62436i	−0.549086	+	0.266543i
$302$		0			0
$303$	4.13397	−	1.10770i	0.237491	−	0.0636354i
$304$		0			0
$305$	−3.42820	+	0.205771i	−0.196298	+	0.0117824i
$306$		0			0
$307$	6.29423	+	6.29423i	0.359231	+	0.359231i	0.863529	−	0.504299i	$-0.168249\pi$
$307$	6.29423	+	6.29423i	0.359231	+	0.359231i	−0.504299	+	0.863529i	$0.668249\pi$
$308$		0			0
$309$		−	2.46410i		−	0.140178i
$310$		0			0
$311$	13.2224	−	7.63397i	0.749775	−	0.432883i	−0.0758374	−	0.997120i	$-0.524163\pi$
$311$	13.2224	−	7.63397i	0.749775	−	0.432883i	0.825613	+	0.564237i	$0.190830\pi$
$312$		0			0
$313$	−1.39230	−	5.19615i	−0.0786977	−	0.293704i	0.915349	−	0.402662i	$-0.131915\pi$
$313$	−1.39230	−	5.19615i	−0.0786977	−	0.293704i	−0.994046	+	0.108958i	$0.965248\pi$
$314$		0			0
$315$	4.36603	−	15.5622i	0.245998	−	0.876829i
$316$		0			0
$317$	−2.46410	−	9.19615i	−0.138398	−	0.516507i	−0.999961	−	0.00885679i	$-0.997181\pi$
$317$	−2.46410	−	9.19615i	−0.138398	−	0.516507i	0.861563	−	0.507651i	$-0.169486\pi$
$318$		0			0
$319$	7.09808	−	4.09808i	0.397416	−	0.229448i
$320$		0			0
$321$			6.80385i			0.379754i
$322$		0			0
$323$	−2.00000	−	2.00000i	−0.111283	−	0.111283i
$324$		0			0
$325$	−5.26795	−	13.1244i	−0.292213	−	0.728008i
$326$		0			0
$327$	5.06218	−	1.35641i	0.279939	−	0.0750094i
$328$		0			0
$329$	−1.73205	+	24.1244i	−0.0954911	+	1.33002i
$330$		0			0
$331$	−0.928203	+	1.60770i	−0.0510187	+	0.0883669i	−0.890407	−	0.455165i	$-0.849580\pi$
$331$	−0.928203	+	1.60770i	−0.0510187	+	0.0883669i	0.839388	+	0.543532i	$0.182913\pi$
$332$		0			0
$333$	3.46410	−	12.9282i	0.189832	−	0.708461i
$334$		0			0
$335$	−23.4904	+	7.83013i	−1.28342	+	0.427806i
$336$		0			0
$337$	9.53590	−	9.53590i	0.519453	−	0.519453i	−0.397953	−	0.917406i	$-0.630279\pi$
$337$	9.53590	−	9.53590i	0.519453	−	0.519453i	0.917406	+	0.397953i	$0.130279\pi$
$338$		0			0
$339$	−2.83013	−	4.90192i	−0.153711	−	0.266236i
$340$		0			0
$341$	−17.6603	−	10.1962i	−0.956356	−	0.552153i
$342$		0			0
$343$	−15.5885	+	10.0000i	−0.841698	+	0.539949i
$344$		0			0
$345$	−0.133975	+	0.0884573i	−0.00721295	+	0.00476238i
$346$		0			0
$347$	−29.0885	−	7.79423i	−1.56155	−	0.418416i	−0.628396	−	0.777893i	$-0.716288\pi$
$347$	−29.0885	−	7.79423i	−1.56155	−	0.418416i	−0.933154	+	0.359477i	$0.882955\pi$
$348$		0			0
$349$	−6.26795			−0.335516			−0.167758	−	0.985828i	$-0.553653\pi$
$349$	−6.26795			−0.335516			−0.167758	+	0.985828i	$0.553653\pi$
$350$		0			0
$351$	−8.39230			−0.447948
$352$		0			0
$353$	13.5622	+	3.63397i	0.721842	+	0.193417i	0.600993	−	0.799254i	$-0.294772\pi$
$353$	13.5622	+	3.63397i	0.721842	+	0.193417i	0.120849	+	0.992671i	$0.461438\pi$
$354$		0			0
$355$	2.36603	−	1.56218i	0.125576	−	0.0829118i
$356$		0			0
$357$	−3.46410	−	4.00000i	−0.183340	−	0.211702i
$358$		0			0
$359$	29.6603	+	17.1244i	1.56541	+	0.903789i	0.996693	+	0.0812542i	$0.0258926\pi$
$359$	29.6603	+	17.1244i	1.56541	+	0.903789i	0.568715	+	0.822535i	$0.307441\pi$
$360$		0			0
$361$	9.23205	+	15.9904i	0.485897	+	0.841599i
$362$		0			0
$363$	1.29423	−	1.29423i	0.0679294	−	0.0679294i
$364$		0			0
$365$	28.3923	−	9.46410i	1.48612	−	0.495374i
$366$		0			0
$367$	−0.133975	+	0.500000i	−0.00699342	+	0.0260998i	−0.969334	−	0.245746i	$-0.920967\pi$
$367$	−0.133975	+	0.500000i	−0.00699342	+	0.0260998i	0.962341	+	0.271845i	$0.0876339\pi$
$368$		0			0
$369$	−8.83013	+	15.2942i	−0.459678	+	0.796186i
$370$		0			0
$371$	15.4904	+	10.4904i	0.804221	+	0.544633i
$372$		0			0
$373$	−7.73205	+	2.07180i	−0.400350	+	0.107274i	−0.453376	−	0.891320i	$-0.649780\pi$
$373$	−7.73205	+	2.07180i	−0.400350	+	0.107274i	0.0530251	+	0.998593i	$0.483114\pi$
$374$		0			0
$375$	−0.473721	+	5.76795i	−0.0244628	+	0.297856i
$376$		0			0
$377$	6.00000	+	6.00000i	0.309016	+	0.309016i
$378$		0			0
$379$			2.33975i			0.120185i	0.998193	+	0.0600923i	$0.0191395\pi$
$379$			2.33975i			0.120185i	−0.998193	+	0.0600923i	$0.980860\pi$
$380$		0			0
$381$	−0.294229	+	0.169873i	−0.0150738	+	0.00870286i
$382$		0			0
$383$	−8.18653	−	30.5526i	−0.418312	−	1.56116i	−0.778107	−	0.628131i	$-0.783820\pi$
$383$	−8.18653	−	30.5526i	−0.418312	−	1.56116i	0.359795	−	0.933031i	$-0.382847\pi$
$384$		0			0
$385$	11.5622	−	11.2942i	0.589263	−	0.575607i
$386$		0			0
$387$	2.83013	+	10.5622i	0.143863	+	0.536906i
$388$		0			0
$389$	4.26795	−	2.46410i	0.216394	−	0.124935i	−0.387886	−	0.921707i	$-0.626794\pi$
$389$	4.26795	−	2.46410i	0.216394	−	0.124935i	0.604279	+	0.796773i	$0.293461\pi$
$390$		0			0
$391$		−	0.535898i		−	0.0271015i
$392$		0			0
$393$	5.66025	+	5.66025i	0.285522	+	0.285522i
$394$		0			0
$395$	−7.29423	+	0.437822i	−0.367012	+	0.0220292i
$396$		0			0
$397$	−3.63397	+	0.973721i	−0.182384	+	0.0488696i	−0.348855	−	0.937177i	$-0.613429\pi$
$397$	−3.63397	+	0.973721i	−0.182384	+	0.0488696i	0.166471	+	0.986046i	$0.446763\pi$
$398$		0			0
$399$	−0.437822	−	0.901924i	−0.0219185	−	0.0451527i
$400$		0			0
$401$	−5.50000	+	9.52628i	−0.274657	+	0.475720i	−0.970049	−	0.242911i	$-0.921898\pi$
$401$	−5.50000	+	9.52628i	−0.274657	+	0.475720i	0.695392	+	0.718631i	$0.255231\pi$
$402$		0			0
$403$	5.46410	−	20.3923i	0.272186	−	1.01581i
$404$		0			0
$405$	−13.3205	−	6.66025i	−0.661901	−	0.330951i
$406$		0			0
$407$	9.46410	−	9.46410i	0.469118	−	0.469118i
$408$		0			0
$409$	10.4282	+	18.0622i	0.515641	+	0.893117i	0.999835	+	0.0181564i	$0.00577967\pi$
$409$	10.4282	+	18.0622i	0.515641	+	0.893117i	−0.484194	+	0.874961i	$0.660887\pi$
$410$		0			0
$411$	6.12436	+	3.53590i	0.302092	+	0.174413i
$412$		0			0
$413$	−21.2942	+	4.09808i	−1.04782	+	0.201653i
$414$		0			0
$415$	1.33013	−	6.50000i	0.0652934	−	0.319072i
$416$		0			0
$417$	−2.83013	−	0.758330i	−0.138592	−	0.0371356i
$418$		0			0
$419$	23.8564			1.16546			0.582731	−	0.812665i	$-0.301984\pi$
$419$	23.8564			1.16546			0.582731	+	0.812665i	$0.301984\pi$
$420$		0			0
$421$	−17.3397			−0.845088			−0.422544	−	0.906343i	$-0.638863\pi$
$421$	−17.3397			−0.845088			−0.422544	+	0.906343i	$0.638863\pi$
$422$		0			0
$423$	24.1244	+	6.46410i	1.17297	+	0.314295i
$424$		0			0
$425$	−15.1962	−	11.9282i	−0.737122	−	0.578603i
$426$		0			0
$427$	3.07180	−	2.66025i	0.148655	−	0.128739i
$428$		0			0
$429$	−3.46410	−	2.00000i	−0.167248	−	0.0965609i
$430$		0			0
$431$	3.09808	+	5.36603i	0.149229	+	0.258472i	0.930943	−	0.365165i	$-0.118987\pi$
$431$	3.09808	+	5.36603i	0.149229	+	0.258472i	−0.781714	+	0.623637i	$0.785654\pi$
$432$		0			0
$433$	17.5359	−	17.5359i	0.842721	−	0.842721i	−0.146491	−	0.989212i	$-0.546798\pi$
$433$	17.5359	−	17.5359i	0.842721	−	0.842721i	0.989212	+	0.146491i	$0.0467978\pi$
$434$		0			0
$435$	−1.09808	−	3.29423i	−0.0526487	−	0.157946i
$436$		0			0
$437$	0.0262794	−	0.0980762i	0.00125712	−	0.00469162i
$438$		0			0
$439$	1.66025	−	2.87564i	0.0792396	−	0.137247i	−0.823682	−	0.567051i	$-0.808084\pi$
$439$	1.66025	−	2.87564i	0.0792396	−	0.137247i	0.902922	+	0.429804i	$0.141417\pi$
$440$		0			0
$441$	7.09808	+	17.7583i	0.338004	+	0.845635i
$442$		0			0
$443$	−13.0622	+	3.50000i	−0.620603	+	0.166290i	−0.555402	−	0.831582i	$-0.687436\pi$
$443$	−13.0622	+	3.50000i	−0.620603	+	0.166290i	−0.0652010	+	0.997872i	$0.520769\pi$
$444$		0			0
$445$	0.0884573	+	1.47372i	0.00419328	+	0.0698611i
$446$		0			0
$447$	−0.294229	−	0.294229i	−0.0139165	−	0.0139165i
$448$		0			0
$449$			33.0526i			1.55985i	0.625875	+	0.779923i	$0.284742\pi$
$449$			33.0526i			1.55985i	−0.625875	+	0.779923i	$0.715258\pi$
$450$		0			0
$451$	−15.2942	+	8.83013i	−0.720177	+	0.415794i
$452$		0			0
$453$	1.85641	+	6.92820i	0.0872216	+	0.325515i
$454$		0			0
$455$	14.3923	+	8.53590i	0.674722	+	0.400169i
$456$		0			0
$457$	3.14359	+	11.7321i	0.147051	+	0.548802i	0.999656	+	0.0262453i	$0.00835510\pi$
$457$	3.14359	+	11.7321i	0.147051	+	0.548802i	−0.852604	+	0.522557i	$0.824978\pi$
$458$		0			0
$459$	−9.92820	+	5.73205i	−0.463409	+	0.267549i
$460$		0			0
$461$		−	5.60770i		−	0.261176i	−0.991437	−	0.130588i	$-0.958313\pi$
$461$		−	5.60770i		−	0.261176i	0.991437	−	0.130588i	$-0.0416866\pi$
$462$		0			0
$463$	4.75833	+	4.75833i	0.221138	+	0.221138i	0.808978	−	0.587839i	$-0.200021\pi$
$463$	4.75833	+	4.75833i	0.221138	+	0.221138i	−0.587839	+	0.808978i	$0.700021\pi$
$464$		0			0
$465$	−5.73205	+	6.46410i	−0.265817	+	0.299766i
$466$		0			0
$467$	−13.5981	+	3.64359i	−0.629244	+	0.168605i	−0.559327	−	0.828947i	$-0.688940\pi$
$467$	−13.5981	+	3.64359i	−0.629244	+	0.168605i	−0.0699173	+	0.997553i	$0.522274\pi$
$468$		0			0
$469$	16.4282	−	24.2583i	0.758584	−	1.12015i
$470$		0			0
$471$	−1.24167	+	2.15064i	−0.0572131	+	0.0990960i
$472$		0			0
$473$	−2.83013	+	10.5622i	−0.130129	+	0.485649i
$474$		0			0
$475$	−2.19615	−	2.92820i	−0.100766	−	0.134355i
$476$		0			0
$477$	13.6603	−	13.6603i	0.625460	−	0.625460i
$478$		0			0
$479$	6.53590	+	11.3205i	0.298633	+	0.517247i	0.975823	−	0.218560i	$-0.0701361\pi$
$479$	6.53590	+	11.3205i	0.298633	+	0.517247i	−0.677191	+	0.735808i	$0.736803\pi$
$480$		0			0
$481$	12.0000	+	6.92820i	0.547153	+	0.315899i
$482$		0			0
$483$	0.0621778	−	0.179492i	0.00282919	−	0.00816717i
$484$		0			0
$485$	−18.3660	−	3.75833i	−0.833958	−	0.170657i
$486$		0			0
$487$	27.2224	+	7.29423i	1.23357	+	0.330533i	0.815967	−	0.578098i	$-0.196205\pi$
$487$	27.2224	+	7.29423i	1.23357	+	0.330533i	0.417599	+	0.908631i	$0.362872\pi$
$488$		0			0
$489$	−7.26795			−0.328668
$490$		0			0
$491$	−37.7128			−1.70196			−0.850978	−	0.525202i	$-0.823990\pi$
$491$	−37.7128			−1.70196			−0.850978	+	0.525202i	$0.823990\pi$
$492$		0			0
$493$	11.1962	+	3.00000i	0.504249	+	0.135113i
$494$		0			0
$495$	−9.19615	−	13.9282i	−0.413336	−	0.626026i
$496$		0			0
$497$	−1.09808	+	3.16987i	−0.0492554	+	0.142188i
$498$		0			0
$499$	−9.97372	−	5.75833i	−0.446485	−	0.257778i	0.259860	−	0.965646i	$-0.416324\pi$
$499$	−9.97372	−	5.75833i	−0.446485	−	0.257778i	−0.706345	+	0.707868i	$0.749657\pi$
$500$		0			0
$501$	4.30385	+	7.45448i	0.192282	+	0.333042i
$502$		0			0
$503$	−17.6340	+	17.6340i	−0.786260	+	0.786260i	−0.980879	−	0.194619i	$-0.937653\pi$
$503$	−17.6340	+	17.6340i	−0.786260	+	0.786260i	0.194619	+	0.980879i	$0.437653\pi$
$504$		0			0
$505$	−8.26795	+	16.5359i	−0.367919	+	0.735838i
$506$		0			0
$507$	−0.669873	+	2.50000i	−0.0297501	+	0.111029i
$508$		0			0
$509$	19.4545	−	33.6962i	0.862305	−	1.49356i	−0.00739389	−	0.999973i	$-0.502354\pi$
$509$	19.4545	−	33.6962i	0.862305	−	1.49356i	0.869699	−	0.493583i	$-0.164313\pi$
$510$		0			0
$511$	−19.8564	+	29.3205i	−0.878396	+	1.29706i
$512$		0			0
$513$	−2.09808	+	0.562178i	−0.0926323	+	0.0248208i
$514$		0			0
$515$	7.96410	+	7.06218i	0.350940	+	0.311197i
$516$		0			0
$517$	17.6603	+	17.6603i	0.776697	+	0.776697i
$518$		0			0
$519$			10.6795i			0.468778i
$520$		0			0
$521$	−20.6603	+	11.9282i	−0.905142	+	0.522584i	−0.878865	−	0.477071i	$-0.841699\pi$
$521$	−20.6603	+	11.9282i	−0.905142	+	0.522584i	−0.0262772	+	0.999655i	$0.508365\pi$
$522$		0			0
$523$	11.4904	+	42.8827i	0.502439	+	1.87513i	0.483568	+	0.875307i	$0.339341\pi$
$523$	11.4904	+	42.8827i	0.502439	+	1.87513i	0.0188717	+	0.999822i	$0.493993\pi$
$524$		0			0
$525$	−3.70577	−	5.75833i	−0.161733	−	0.251314i
$526$		0			0
$527$	−7.46410	−	27.8564i	−0.325141	−	1.21344i
$528$		0			0
$529$	−19.9019	+	11.4904i	−0.865301	+	0.499582i
$530$		0			0
$531$			22.3923i			0.971743i
$532$		0			0
$533$	−12.9282	−	12.9282i	−0.559983	−	0.559983i
$534$		0			0
$535$	−21.9904	−	19.5000i	−0.950727	−	0.843059i
$536$		0			0
$537$	3.92820	−	1.05256i	0.169514	−	0.0454213i
$538$		0			0
$539$	−2.73205	+	18.9282i	−0.117678	+	0.815295i
$540$		0			0
$541$	−18.3564	+	31.7942i	−0.789204	+	1.36694i	0.137252	+	0.990536i	$0.456173\pi$
$541$	−18.3564	+	31.7942i	−0.789204	+	1.36694i	−0.926455	+	0.376404i	$0.877160\pi$
$542$		0			0
$543$	0.160254	−	0.598076i	0.00687716	−	0.0256659i
$544$		0			0
$545$	−10.1244	+	20.2487i	−0.433680	+	0.867359i
$546$		0			0
$547$	16.7583	−	16.7583i	0.716534	−	0.716534i	−0.251359	−	0.967894i	$-0.580878\pi$
$547$	16.7583	−	16.7583i	0.716534	−	0.716534i	0.967894	+	0.251359i	$0.0808776\pi$
$548$		0			0
$549$	−2.09808	−	3.63397i	−0.0895437	−	0.155094i
$550$		0			0
$551$	1.90192	+	1.09808i	0.0810247	+	0.0467796i
$552$		0			0
$553$	6.53590	−	5.66025i	0.277935	−	0.240698i
$554$		0			0
$555$	−3.12436	−	4.73205i	−0.132622	−	0.200864i
$556$		0			0
$557$	−31.2224	−	8.36603i	−1.32294	−	0.354480i	−0.472860	−	0.881138i	$-0.656778\pi$
$557$	−31.2224	−	8.36603i	−1.32294	−	0.354480i	−0.850077	+	0.526658i	$0.823445\pi$
$558$		0			0
$559$	−11.3205			−0.478806
$560$		0			0
$561$	−5.46410			−0.230695
$562$		0			0
$563$	23.7224	+	6.35641i	0.999781	+	0.267891i	0.721354	−	0.692567i	$-0.243520\pi$
$563$	23.7224	+	6.35641i	0.999781	+	0.267891i	0.278427	+	0.960457i	$0.410187\pi$
$564$		0			0
$565$	23.9545	+	4.90192i	1.00777	+	0.206225i
$566$		0			0
$567$	17.3038	−	3.33013i	0.726693	−	0.139852i
$568$		0			0
$569$	25.0526	+	14.4641i	1.05026	+	0.606367i	0.922722	−	0.385467i	$-0.125960\pi$
$569$	25.0526	+	14.4641i	1.05026	+	0.606367i	0.127536	+	0.991834i	$0.459293\pi$
$570$		0			0
$571$	−9.02628	−	15.6340i	−0.377738	−	0.654261i	0.612995	−	0.790087i	$-0.289965\pi$
$571$	−9.02628	−	15.6340i	−0.377738	−	0.654261i	−0.990733	+	0.135826i	$0.956631\pi$
$572$		0			0
$573$	4.85641	−	4.85641i	0.202879	−	0.202879i
$574$		0			0
$575$	0.0980762	−	0.686533i	0.00409006	−	0.0286304i
$576$		0			0
$577$	1.50962	−	5.63397i	0.0628463	−	0.234545i	−0.927357	−	0.374177i	$-0.877925\pi$
$577$	1.50962	−	5.63397i	0.0628463	−	0.234545i	0.990204	+	0.139632i	$0.0445919\pi$
$578$		0			0
$579$	2.09808	−	3.63397i	0.0871931	−	0.151023i
$580$		0			0
$581$	3.42820	+	7.06218i	0.142226	+	0.292989i
$582$		0			0
$583$	18.6603	−	5.00000i	0.772829	−	0.207079i
$584$		0			0
$585$	11.4641	−	12.9282i	0.473982	−	0.534515i
$586$		0			0
$587$	15.7846	+	15.7846i	0.651501	+	0.651501i	0.953354	−	0.301854i	$-0.0976054\pi$
$587$	15.7846	+	15.7846i	0.651501	+	0.651501i	−0.301854	+	0.953354i	$0.597605\pi$
$588$		0			0
$589$		−	5.46410i		−	0.225144i
$590$		0			0
$591$	−6.41858	+	3.70577i	−0.264025	+	0.152435i
$592$		0			0
$593$	5.56218	+	20.7583i	0.228411	+	0.852442i	0.981009	+	0.193962i	$0.0621338\pi$
$593$	5.56218	+	20.7583i	0.228411	+	0.852442i	−0.752598	+	0.658481i	$0.771199\pi$
$594$		0			0
$595$	22.8564	+	0.267949i	0.937021	+	0.0109848i
$596$		0			0
$597$	−1.48334	−	5.53590i	−0.0607090	−	0.226569i
$598$		0			0
$599$	−15.3397	+	8.85641i	−0.626765	+	0.361863i	−0.779498	−	0.626405i	$-0.784526\pi$
$599$	−15.3397	+	8.85641i	−0.626765	+	0.361863i	0.152733	+	0.988267i	$0.451193\pi$
$600$		0			0
$601$		−	41.1769i		−	1.67964i	−0.542864	−	0.839821i	$-0.682660\pi$
$601$		−	41.1769i		−	1.67964i	0.542864	−	0.839821i	$-0.317340\pi$
$602$		0			0
$603$	−21.3923	−	21.3923i	−0.871162	−	0.871162i
$604$		0			0
$605$	0.473721	+	7.89230i	0.0192595	+	0.320868i
$606$		0			0
$607$	−12.6962	+	3.40192i	−0.515321	+	0.138080i	−0.507101	−	0.861886i	$-0.669283\pi$
$607$	−12.6962	+	3.40192i	−0.515321	+	0.138080i	−0.00821951	+	0.999966i	$0.502616\pi$
$608$		0			0
$609$	3.40192	+	2.30385i	0.137853	+	0.0933566i
$610$		0			0
$611$	−12.9282	+	22.3923i	−0.523019	+	0.905896i
$612$		0			0
$613$	−6.53590	+	24.3923i	−0.263982	+	0.985196i	0.698888	+	0.715231i	$0.253679\pi$
$613$	−6.53590	+	24.3923i	−0.263982	+	0.985196i	−0.962870	+	0.269965i	$0.912988\pi$
$614$		0			0
$615$	2.36603	+	7.09808i	0.0954074	+	0.286222i
$616$		0			0
$617$	33.9090	−	33.9090i	1.36512	−	1.36512i	0.497874	−	0.867249i	$-0.334114\pi$
$617$	33.9090	−	33.9090i	1.36512	−	1.36512i	0.867249	−	0.497874i	$-0.165886\pi$
$618$		0			0
$619$	5.09808	+	8.83013i	0.204909	+	0.354913i	0.950104	−	0.311934i	$-0.100977\pi$
$619$	5.09808	+	8.83013i	0.204909	+	0.354913i	−0.745195	+	0.666847i	$0.767643\pi$
$620$		0			0
$621$	−0.356406	−	0.205771i	−0.0143021	−	0.00825732i
$622$		0			0
$623$	−1.14359	−	1.32051i	−0.0458171	−	0.0529050i
$624$		0			0
$625$	−17.2846	−	18.0622i	−0.691384	−	0.722487i
$626$		0			0
$627$	−1.00000	−	0.267949i	−0.0399362	−	0.0107009i
$628$		0			0
$629$	18.9282			0.754717
$630$		0			0
$631$	4.58846			0.182664			0.0913318	−	0.995821i	$-0.470888\pi$
$631$	4.58846			0.182664			0.0913318	+	0.995821i	$0.470888\pi$
$632$		0			0
$633$	0.0980762	+	0.0262794i	0.00389818	+	0.00104451i
$634$		0			0
$635$	0.294229	−	1.43782i	0.0116761	−	0.0570582i
$636$		0			0
$637$	−19.6603	+	2.33975i	−0.778968	+	0.0927041i
$638$		0			0
$639$	3.00000	+	1.73205i	0.118678	+	0.0685189i
$640$		0			0
$641$	−5.33013	−	9.23205i	−0.210527	−	0.364644i	0.741352	−	0.671116i	$-0.234185\pi$
$641$	−5.33013	−	9.23205i	−0.210527	−	0.364644i	−0.951880	+	0.306472i	$0.900851\pi$
$642$		0			0
$643$	17.5359	−	17.5359i	0.691548	−	0.691548i	−0.271024	−	0.962573i	$-0.587362\pi$
$643$	17.5359	−	17.5359i	0.691548	−	0.691548i	0.962573	+	0.271024i	$0.0873623\pi$
$644$		0			0
$645$	4.14359	+	2.07180i	0.163154	+	0.0815769i
$646$		0			0
$647$	−10.5981	+	39.5526i	−0.416653	+	1.55497i	0.364847	+	0.931067i	$0.381121\pi$
$647$	−10.5981	+	39.5526i	−0.416653	+	1.55497i	−0.781501	+	0.623904i	$0.785546\pi$
$648$		0			0
$649$	−11.1962	+	19.3923i	−0.439487	+	0.761215i
$650$		0			0
$651$	0.732051	−	10.1962i	0.0286913	−	0.399619i
$652$		0			0
$653$	19.6603	−	5.26795i	0.769365	−	0.206151i	0.147274	−	0.989096i	$-0.452950\pi$
$653$	19.6603	−	5.26795i	0.769365	−	0.206151i	0.622091	+	0.782945i	$0.286283\pi$
$654$		0			0
$655$	−34.5167	+	2.07180i	−1.34868	+	0.0809518i
$656$		0			0
$657$	25.8564	+	25.8564i	1.00875	+	1.00875i
$658$		0			0
$659$		−	27.6603i		−	1.07749i	−0.842469	−	0.538745i	$-0.818899\pi$
$659$		−	27.6603i		−	1.07749i	0.842469	−	0.538745i	$-0.181101\pi$
$660$		0			0
$661$	−41.7224	+	24.0885i	−1.62281	+	0.936932i	−0.636652	+	0.771151i	$0.719681\pi$
$661$	−41.7224	+	24.0885i	−1.62281	+	0.936932i	−0.986163	+	0.165781i	$0.946985\pi$
$662$		0			0
$663$	−1.46410	−	5.46410i	−0.0568610	−	0.212208i
$664$		0			0
$665$	4.16987	+	1.16987i	0.161701	+	0.0453657i
$666$		0			0
$667$	0.107695	+	0.401924i	0.00416997	+	0.0155626i
$668$		0			0
$669$	11.4904	−	6.63397i	0.444244	−	0.256484i
$670$		0			0
$671$		−	4.19615i		−	0.161991i
$672$		0			0
$673$	4.39230	+	4.39230i	0.169311	+	0.169311i	0.786676	−	0.617366i	$-0.211800\pi$
$673$	4.39230	+	4.39230i	0.169311	+	0.169311i	−0.617366	+	0.786676i	$0.711800\pi$
$674$		0			0
$675$	−13.7679	+	5.52628i	−0.529929	+	0.212707i
$676$		0			0
$677$	−25.8564	+	6.92820i	−0.993742	+	0.266272i	−0.718822	−	0.695194i	$-0.755318\pi$
$677$	−25.8564	+	6.92820i	−0.993742	+	0.266272i	−0.274921	+	0.961467i	$0.588652\pi$
$678$		0			0
$679$	19.9545	−	9.68653i	0.765783	−	0.371735i
$680$		0			0
$681$	5.09808	−	8.83013i	0.195359	−	0.338371i
$682$		0			0
$683$	4.57180	−	17.0622i	0.174935	−	0.652866i	−0.821628	−	0.570024i	$-0.806934\pi$
$683$	4.57180	−	17.0622i	0.174935	−	0.652866i	0.996563	−	0.0828417i	$-0.0263996\pi$
$684$		0			0
$685$	−28.9808	+	9.66025i	−1.10730	+	0.369099i
$686$		0			0
$687$	6.73205	−	6.73205i	0.256844	−	0.256844i
$688$		0			0
$689$	10.0000	+	17.3205i	0.380970	+	0.659859i
$690$		0			0
$691$	44.0263	+	25.4186i	1.67484	+	0.966969i	0.964867	+	0.262738i	$0.0846255\pi$
$691$	44.0263	+	25.4186i	1.67484	+	0.966969i	0.709971	+	0.704231i	$0.248708\pi$
$692$		0			0
$693$	18.6603	+	6.46410i	0.708844	+	0.245551i
$694$		0			0
$695$	10.5622	−	6.97372i	0.400646	−	0.264528i
$696$		0			0
$697$	−24.1244	−	6.46410i	−0.913775	−	0.244845i
$698$		0			0
$699$	3.46410			0.131024
$700$		0			0
$701$	−20.2679			−0.765510			−0.382755	−	0.923850i	$-0.625025\pi$
$701$	−20.2679			−0.765510			−0.382755	+	0.923850i	$0.625025\pi$
$702$		0			0
$703$	3.46410	+	0.928203i	0.130651	+	0.0350078i
$704$		0			0
$705$	8.83013	−	5.83013i	0.332562	−	0.219575i
$706$		0			0
$707$	−4.13397	−	21.4808i	−0.155474	−	0.807867i
$708$		0			0
$709$	−18.9904	−	10.9641i	−0.713199	−	0.411765i	0.0990456	−	0.995083i	$-0.468421\pi$
$709$	−18.9904	−	10.9641i	−0.713199	−	0.411765i	−0.812244	+	0.583317i	$0.801754\pi$
$710$		0			0
$711$	−4.46410	−	7.73205i	−0.167417	−	0.289975i
$712$		0			0
$713$	0.732051	−	0.732051i	0.0274155	−	0.0274155i
$714$		0			0
$715$	16.3923	−	5.46410i	0.613037	−	0.204346i
$716$		0			0
$717$	−0.320508	+	1.19615i	−0.0119696	+	0.0446711i
$718$		0			0
$719$	19.2942	−	33.4186i	0.719553	−	1.24630i	−0.241624	−	0.970370i	$-0.577680\pi$
$719$	19.2942	−	33.4186i	0.719553	−	1.24630i	0.961177	−	0.275933i	$-0.0889867\pi$
$720$		0			0
$721$	−12.5622	−	0.901924i	−0.467840	−	0.0335894i
$722$		0			0
$723$	12.3923	−	3.32051i	0.460875	−	0.123491i
$724$		0			0
$725$	13.7942	+	5.89230i	0.512305	+	0.218835i
$726$		0			0
$727$	−10.0981	−	10.0981i	−0.374517	−	0.374517i	0.494602	−	0.869119i	$-0.335314\pi$
$727$	−10.0981	−	10.0981i	−0.374517	−	0.374517i	−0.869119	+	0.494602i	$0.835314\pi$
$728$		0			0
$729$		−	13.5885i		−	0.503276i
$730$		0			0
$731$	−13.3923	+	7.73205i	−0.495332	+	0.285980i
$732$		0			0
$733$	−1.16987	−	4.36603i	−0.0432102	−	0.161263i	0.940949	−	0.338547i	$-0.109935\pi$
$733$	−1.16987	−	4.36603i	−0.0432102	−	0.161263i	−0.984160	+	0.177284i	$0.943269\pi$
$734$		0			0
$735$	7.62436	+	2.74167i	0.281229	+	0.101128i
$736$		0			0
$737$	−7.83013	−	29.2224i	−0.288426	−	1.07642i
$738$		0			0
$739$	−19.5622	+	11.2942i	−0.719606	+	0.415465i	−0.814608	−	0.580012i	$-0.803048\pi$
$739$	−19.5622	+	11.2942i	−0.719606	+	0.415465i	0.0950014	+	0.995477i	$0.469714\pi$
$740$		0			0
$741$		−	1.07180i		−	0.0393734i
$742$		0			0
$743$	6.16987	+	6.16987i	0.226351	+	0.226351i	0.811166	−	0.584816i	$-0.198833\pi$
$743$	6.16987	+	6.16987i	0.226351	+	0.226351i	−0.584816	+	0.811166i	$0.698833\pi$
$744$		0			0
$745$	1.79423	−	0.107695i	0.0657355	−	0.00394565i
$746$		0			0
$747$	7.83013	−	2.09808i	0.286489	−	0.0767646i
$748$		0			0
$749$	34.6865	+	2.49038i	1.26742	+	0.0909965i
$750$		0			0
$751$	−3.19615	+	5.53590i	−0.116629	+	0.202008i	−0.918430	−	0.395584i	$-0.870542\pi$
$751$	−3.19615	+	5.53590i	−0.116629	+	0.202008i	0.801801	+	0.597592i	$0.203876\pi$
$752$		0			0
$753$	2.92820	−	10.9282i	0.106710	−	0.398246i
$754$		0			0
$755$	−27.7128	−	13.8564i	−1.00857	−	0.504286i
$756$		0			0
$757$	12.7321	−	12.7321i	0.462754	−	0.462754i	−0.436803	−	0.899557i	$-0.643889\pi$
$757$	12.7321	−	12.7321i	0.462754	−	0.462754i	0.899557	+	0.436803i	$0.143889\pi$
$758$		0			0
$759$	−0.0980762	−	0.169873i	−0.00355994	−	0.00616600i
$760$		0			0
$761$	24.9282	+	14.3923i	0.903647	+	0.521721i	0.878382	−	0.477960i	$-0.158624\pi$
$761$	24.9282	+	14.3923i	0.903647	+	0.521721i	0.0252651	+	0.999681i	$0.491957\pi$
$762$		0			0
$763$	−5.06218	−	26.3038i	−0.183263	−	0.952263i
$764$		0			0
$765$	4.73205	−	23.1244i	0.171088	−	0.836063i
$766$		0			0
$767$	−22.3923	−	6.00000i	−0.808539	−	0.216647i
$768$		0			0
$769$	−15.1769			−0.547294			−0.273647	−	0.961830i	$-0.588230\pi$
$769$	−15.1769			−0.547294			−0.273647	+	0.961830i	$0.588230\pi$
$770$		0			0
$771$	−1.46410			−0.0527283
$772$		0			0
$773$	15.1962	+	4.07180i	0.546568	+	0.146452i	0.521528	−	0.853234i	$-0.325362\pi$
$773$	15.1962	+	4.07180i	0.546568	+	0.146452i	0.0250395	+	0.999686i	$0.492029\pi$
$774$		0			0
$775$	−4.46410	−	37.0526i	−0.160355	−	1.33097i
$776$		0			0
$777$	6.33975	+	2.19615i	0.227437	+	0.0787865i
$778$		0			0
$779$	−4.09808	−	2.36603i	−0.146829	−	0.0847717i
$780$		0			0
$781$	1.73205	+	3.00000i	0.0619777	+	0.107348i
$782$		0			0
$783$	6.29423	−	6.29423i	0.224937	−	0.224937i
$784$		0			0
$785$	−3.39230	−	10.1769i	−0.121077	−	0.363230i
$786$		0			0
$787$	−8.35641	+	31.1865i	−0.297874	+	1.11168i	0.641034	+	0.767512i	$0.278506\pi$
$787$	−8.35641	+	31.1865i	−0.297874	+	1.11168i	−0.938908	+	0.344168i	$0.888161\pi$
$788$		0			0
$789$	−4.06218	+	7.03590i	−0.144617	+	0.250485i
$790$		0			0
$791$	−26.0263	+	12.6340i	−0.925388	+	0.449212i
$792$		0			0
$793$	4.19615	−	1.12436i	0.149010	−	0.0399270i
$794$		0			0
$795$	−0.490381	−	8.16987i	−0.0173920	−	0.289756i
$796$		0			0
$797$	−22.5359	−	22.5359i	−0.798262	−	0.798262i	0.184559	−	0.982821i	$-0.440914\pi$
$797$	−22.5359	−	22.5359i	−0.798262	−	0.798262i	−0.982821	+	0.184559i	$0.940914\pi$
$798$		0			0
$799$			35.3205i			1.24955i
$800$		0			0
$801$	−1.56218	+	0.901924i	−0.0551968	+	0.0318679i
$802$		0			0
$803$	9.46410	+	35.3205i	0.333981	+	1.24643i
$804$		0			0
$805$	0.401924	+	0.715390i	0.0141660	+	0.0252142i
$806$		0			0
$807$	−3.06218	−	11.4282i	−0.107794	−	0.402292i
$808$		0			0
$809$	3.99038	−	2.30385i	0.140294	−	0.0809990i	−0.428210	−	0.903679i	$-0.640856\pi$
$809$	3.99038	−	2.30385i	0.140294	−	0.0809990i	0.568504	+	0.822680i	$0.307522\pi$
$810$		0			0
$811$		−	42.9282i		−	1.50741i	−0.657211	−	0.753707i	$-0.728264\pi$
$811$		−	42.9282i		−	1.50741i	0.657211	−	0.753707i	$-0.271736\pi$
$812$		0			0
$813$	−7.78461	−	7.78461i	−0.273018	−	0.273018i
$814$		0			0
$815$	20.8301	−	23.4904i	0.729648	−	0.822832i
$816$		0			0
$817$	−2.83013	+	0.758330i	−0.0990136	+	0.0265306i
$818$		0			0
$819$	−1.46410	+	20.3923i	−0.0511599	+	0.712565i
$820$		0			0
$821$	24.6603	−	42.7128i	0.860649	−	1.49069i	−0.0106549	−	0.999943i	$-0.503392\pi$
$821$	24.6603	−	42.7128i	0.860649	−	1.49069i	0.871304	−	0.490744i	$-0.163275\pi$
$822$		0			0
$823$	−14.3038	+	53.3827i	−0.498601	+	1.86080i	0.0102479	+	0.999947i	$0.496738\pi$
$823$	−14.3038	+	53.3827i	−0.498601	+	1.86080i	−0.508849	+	0.860856i	$0.669929\pi$
$824$		0			0
$825$	−7.00000	−	1.00000i	−0.243709	−	0.0348155i
$826$		0			0
$827$	33.2224	−	33.2224i	1.15526	−	1.15526i	0.169774	−	0.985483i	$-0.445696\pi$
$827$	33.2224	−	33.2224i	1.15526	−	1.15526i	0.985483	−	0.169774i	$-0.0543038\pi$
$828$		0			0
$829$	7.26795	+	12.5885i	0.252426	+	0.437215i	0.964193	−	0.265200i	$-0.0854381\pi$
$829$	7.26795	+	12.5885i	0.252426	+	0.437215i	−0.711767	+	0.702416i	$0.752105\pi$
$830$		0			0
$831$	2.41154	+	1.39230i	0.0836555	+	0.0482985i
$832$		0			0
$833$	−21.6603	+	16.1962i	−0.750483	+	0.561163i
$834$		0			0
$835$	−36.4282	−	7.45448i	−1.26065	−	0.257973i
$836$		0			0
$837$	−21.3923	−	5.73205i	−0.739426	−	0.198129i
$838$		0			0
$839$	6.87564			0.237374			0.118687	−	0.992932i	$-0.462132\pi$
$839$	6.87564			0.237374			0.118687	+	0.992932i	$0.462132\pi$
$840$		0			0
$841$	20.0000			0.689655
$842$		0			0
$843$	−0.464102	−	0.124356i	−0.0159845	−	0.00428304i
$844$		0			0
$845$	−6.16025	−	9.33013i	−0.211919	−	0.320966i
$846$		0			0
$847$	−6.12436	−	7.07180i	−0.210435	−	0.242990i
$848$		0			0
$849$	0.882686	+	0.509619i	0.0302937	+	0.0174901i
$850$		0			0
$851$	0.339746	+	0.588457i	0.0116463	+	0.0201721i
$852$		0			0
$853$	18.1244	−	18.1244i	0.620566	−	0.620566i	−0.325110	−	0.945676i	$-0.605401\pi$
$853$	18.1244	−	18.1244i	0.620566	−	0.620566i	0.945676	+	0.325110i	$0.105401\pi$
$854$		0			0
$855$	2.00000	−	4.00000i	0.0683986	−	0.136797i
$856$		0			0
$857$	−2.97372	+	11.0981i	−0.101580	+	0.379103i	−0.997935	−	0.0642351i	$-0.979539\pi$
$857$	−2.97372	+	11.0981i	−0.101580	+	0.379103i	0.896354	+	0.443338i	$0.146206\pi$
$858$		0			0
$859$	−17.4641	+	30.2487i	−0.595867	+	1.03207i	0.397556	+	0.917578i	$0.369858\pi$
$859$	−17.4641	+	30.2487i	−0.595867	+	1.03207i	−0.993424	+	0.114495i	$0.963475\pi$
$860$		0			0
$861$	−7.33013	−	4.96410i	−0.249810	−	0.169176i
$862$		0			0
$863$	49.9449	−	13.3827i	1.70014	−	0.455552i	0.727167	−	0.686460i	$-0.240836\pi$
$863$	49.9449	−	13.3827i	1.70014	−	0.455552i	0.972976	+	0.230908i	$0.0741697\pi$
$864$		0			0
$865$	−34.5167	−	30.6077i	−1.17360	−	1.04069i
$866$		0			0
$867$	0.758330	+	0.758330i	0.0257542	+	0.0257542i
$868$		0			0
$869$		−	8.92820i		−	0.302869i
$870$		0			0
$871$	27.1244	−	15.6603i	0.919074	−	0.530627i
$872$		0			0
$873$	−5.92820	−	22.1244i	−0.200639	−	0.748796i
$874$		0			0
$875$	29.2321	+	4.52628i	0.988224	+	0.153016i
$876$		0			0
$877$	10.4904	+	39.1506i	0.354235	+	1.32202i	0.881444	+	0.472288i	$0.156572\pi$
$877$	10.4904	+	39.1506i	0.354235	+	1.32202i	−0.527209	+	0.849735i	$0.676762\pi$
$878$		0			0
$879$	1.51666	−	0.875644i	0.0511557	−	0.0295348i
$880$		0			0
$881$			25.1436i			0.847109i	0.905871	+	0.423555i	$0.139218\pi$
$881$			25.1436i			0.847109i	−0.905871	+	0.423555i	$0.860782\pi$
$882$		0			0
$883$	−8.07180	−	8.07180i	−0.271638	−	0.271638i	0.558122	−	0.829759i	$-0.311522\pi$
$883$	−8.07180	−	8.07180i	−0.271638	−	0.271638i	−0.829759	+	0.558122i	$0.811522\pi$
$884$		0			0
$885$	7.09808	+	6.29423i	0.238599	+	0.211578i
$886$		0			0
$887$	−10.8923	+	2.91858i	−0.365728	+	0.0979965i	−0.437003	−	0.899460i	$-0.643960\pi$
$887$	−10.8923	+	2.91858i	−0.365728	+	0.0979965i	0.0712748	+	0.997457i	$0.477293\pi$
$888$		0			0
$889$	0.758330	+	1.56218i	0.0254336	+	0.0523938i
$890$		0			0
$891$	9.09808	−	15.7583i	0.304797	−	0.527924i
$892$		0			0
$893$	−1.73205	+	6.46410i	−0.0579609	+	0.216313i
$894$		0			0
$895$	−7.85641	+	15.7128i	−0.262611	+	0.525221i
$896$		0			0
$897$	0.143594	−	0.143594i	0.00479445	−	0.00479445i
$898$		0			0
$899$	11.1962	+	19.3923i	0.373413	+	0.646770i
$900$		0			0
$901$	23.6603	+	13.6603i	0.788237	+	0.455089i
$902$		0			0
$903$	−5.38269	+	1.03590i	−0.179125	+	0.0344725i
$904$		0			0
$905$	1.47372	+	2.23205i	0.0489881	+	0.0741959i
$906$		0			0
$907$	−32.4545	−	8.69615i	−1.07763	−	0.288751i	−0.324007	−	0.946055i	$-0.605030\pi$
$907$	−32.4545	−	8.69615i	−1.07763	−	0.288751i	−0.753626	+	0.657304i	$0.771697\pi$
$908$		0			0
$909$	−22.5885			−0.749212
$910$		0			0
$911$	7.51666			0.249038			0.124519	−	0.992217i	$-0.460261\pi$
$911$	7.51666			0.249038			0.124519	+	0.992217i	$0.460261\pi$
$912$		0			0
$913$	7.83013	+	2.09808i	0.259139	+	0.0694362i
$914$		0			0
$915$	−1.74167	−	0.356406i	−0.0575778	−	0.0117824i
$916$		0			0
$917$	30.9282	−	26.7846i	1.02134	−	0.884506i
$918$		0			0
$919$	−48.6673	−	28.0981i	−1.60539	−	0.926870i	−0.990384	−	0.138344i	$-0.955822\pi$
$919$	−48.6673	−	28.0981i	−1.60539	−	0.926870i	−0.615002	−	0.788526i	$-0.710845\pi$
$920$		0			0
$921$	2.30385	+	3.99038i	0.0759144	+	0.131488i
$922$		0			0
$923$	−2.53590	+	2.53590i	−0.0834701	+	0.0834701i
$924$		0			0
$925$	24.2487	+	3.46410i	0.797293	+	0.113899i
$926$		0			0
$927$	−3.36603	+	12.5622i	−0.110555	+	0.412596i
$928$		0			0
$929$	18.1603	−	31.4545i	0.595819	−	1.03199i	−0.397612	−	0.917554i	$-0.630161\pi$
$929$	18.1603	−	31.4545i	0.595819	−	1.03199i	0.993431	−	0.114435i	$-0.0365056\pi$
$930$		0			0
$931$	−4.75833	+	1.90192i	−0.155948	+	0.0623330i
$932$		0			0
$933$	7.63397	−	2.04552i	0.249925	−	0.0669672i
$934$		0			0
$935$	15.6603	−	17.6603i	0.512145	−	0.577552i
$936$		0			0
$937$	−17.0718	−	17.0718i	−0.557711	−	0.557711i	0.370944	−	0.928655i	$-0.379034\pi$
$937$	−17.0718	−	17.0718i	−0.557711	−	0.557711i	−0.928655	+	0.370944i	$0.879034\pi$
$938$		0			0
$939$		−	2.78461i		−	0.0908723i
$940$		0			0
$941$	35.1962	−	20.3205i	1.14736	−	0.662430i	0.199119	−	0.979975i	$-0.436192\pi$
$941$	35.1962	−	20.3205i	1.14736	−	0.662430i	0.948243	+	0.317546i	$0.102859\pi$
$942$		0			0
$943$	−0.232051	−	0.866025i	−0.00755661	−	0.0282017i
$944$		0			0
$945$	8.95448	−	15.0981i	0.291289	−	0.491140i
$946$		0			0
$947$	−0.349365	−	1.30385i	−0.0113528	−	0.0423694i	0.960017	−	0.279941i	$-0.0903151\pi$
$947$	−0.349365	−	1.30385i	−0.0113528	−	0.0423694i	−0.971370	+	0.237572i	$0.923648\pi$
$948$		0			0
$949$	−32.7846	+	18.9282i	−1.06423	+	0.614435i
$950$		0			0
$951$		−	4.92820i		−	0.159808i
$952$		0			0
$953$	−37.8564	−	37.8564i	−1.22629	−	1.22629i	−0.965357	−	0.260932i	$-0.915970\pi$
$953$	−37.8564	−	37.8564i	−1.22629	−	1.22629i	−0.260932	−	0.965357i	$-0.584030\pi$
$954$		0			0
$955$	1.77757	+	29.6147i	0.0575208	+	0.958310i
$956$		0			0
$957$	4.09808	−	1.09808i	0.132472	−	0.0354958i
$958$		0			0
$959$	20.2679	−	29.9282i	0.654486	−	0.966432i
$960$		0			0
$961$	12.3564	−	21.4019i	0.398594	−	0.690385i
$962$		0			0
$963$	9.29423	−	34.6865i	0.299502	−	1.11776i
$964$		0			0
$965$	5.73205	+	17.1962i	0.184521	+	0.553564i
$966$		0			0
$967$	13.5622	−	13.5622i	0.436130	−	0.436130i	−0.454577	−	0.890707i	$-0.650210\pi$
$967$	13.5622	−	13.5622i	0.436130	−	0.436130i	0.890707	+	0.454577i	$0.150210\pi$
$968$		0			0
$969$	−0.732051	−	1.26795i	−0.0235169	−	0.0407324i
$970$		0			0
$971$	−29.0718	−	16.7846i	−0.932958	−	0.538644i	−0.0452124	−	0.998977i	$-0.514396\pi$
$971$	−29.0718	−	16.7846i	−0.932958	−	0.538644i	−0.887746	+	0.460334i	$0.847730\pi$
$972$		0			0
$973$	−4.90192	+	14.1506i	−0.157148	+	0.453649i
$974$		0			0
$975$	−0.875644	−	7.26795i	−0.0280431	−	0.232761i
$976$		0			0
$977$	0.562178	+	0.150635i	0.0179857	+	0.00481924i	0.267801	−	0.963474i	$-0.413703\pi$
$977$	0.562178	+	0.150635i	0.0179857	+	0.00481924i	−0.249815	+	0.968294i	$0.580370\pi$
$978$		0			0
$979$	−1.80385			−0.0576512
$980$		0			0
$981$	−27.6603			−0.883124
$982$		0			0
$983$	−54.1147	−	14.5000i	−1.72599	−	0.462478i	−0.746739	−	0.665118i	$-0.768381\pi$
$983$	−54.1147	−	14.5000i	−1.72599	−	0.462478i	−0.979253	+	0.202639i	$0.935048\pi$
$984$		0			0
$985$	6.41858	−	31.3660i	0.204513	−	0.999405i
$986$		0			0
$987$	−4.09808	+	11.8301i	−0.130443	+	0.376557i
$988$		0			0
$989$	−0.480762	−	0.277568i	−0.0152873	−	0.00882615i
$990$		0			0
$991$	15.8564	+	27.4641i	0.503695	+	0.872426i	0.999991	+	0.00427229i	$0.00135992\pi$
$991$	15.8564	+	27.4641i	0.503695	+	0.872426i	−0.496296	+	0.868154i	$0.665307\pi$
$992$		0			0
$993$	−0.679492	+	0.679492i	−0.0215630	+	0.0215630i
$994$		0			0
$995$	22.1436	+	11.0718i	0.701999	+	0.351000i
$996$		0			0
$997$	−10.6865	+	39.8827i	−0.338446	+	1.26310i	0.561639	+	0.827382i	$0.310171\pi$
$997$	−10.6865	+	39.8827i	−0.338446	+	1.26310i	−0.900085	+	0.435715i	$0.856496\pi$
$998$		0			0
$999$	7.26795	−	12.5885i	0.229948	−	0.398281i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.ci.a.33.1		4
4.3	odd	2		35.2.k.a.33.1	yes	4
5.2	odd	4		560.2.ci.b.257.1		4
7.3	odd	6		560.2.ci.b.353.1		4
12.11	even	2		315.2.bz.b.208.1		4
20.3	even	4		175.2.o.a.82.1		4
20.7	even	4		35.2.k.b.12.1	yes	4
20.19	odd	2		175.2.o.b.68.1		4
28.3	even	6		35.2.k.b.3.1	yes	4
28.11	odd	6		245.2.l.b.178.1		4
28.19	even	6		245.2.f.b.48.1		4
28.23	odd	6		245.2.f.a.48.1		4
28.27	even	2		245.2.l.a.68.1		4
35.17	even	12	inner	560.2.ci.a.17.1		4
60.47	odd	4		315.2.bz.a.82.1		4
84.59	odd	6		315.2.bz.a.73.1		4
140.3	odd	12		175.2.o.b.157.1		4
140.27	odd	4		245.2.l.b.117.1		4
140.47	odd	12		245.2.f.a.97.1		4
140.59	even	6		175.2.o.a.143.1		4
140.67	even	12		245.2.l.a.227.1		4
140.87	odd	12		35.2.k.a.17.1	✓	4
140.107	even	12		245.2.f.b.97.1		4
420.227	even	12		315.2.bz.b.262.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.2.k.a.17.1	✓	4	140.87	odd	12
35.2.k.a.33.1	yes	4	4.3	odd	2
35.2.k.b.3.1	yes	4	28.3	even	6
35.2.k.b.12.1	yes	4	20.7	even	4
175.2.o.a.82.1		4	20.3	even	4
175.2.o.a.143.1		4	140.59	even	6
175.2.o.b.68.1		4	20.19	odd	2
175.2.o.b.157.1		4	140.3	odd	12
245.2.f.a.48.1		4	28.23	odd	6
245.2.f.a.97.1		4	140.47	odd	12
245.2.f.b.48.1		4	28.19	even	6
245.2.f.b.97.1		4	140.107	even	12
245.2.l.a.68.1		4	28.27	even	2
245.2.l.a.227.1		4	140.67	even	12
245.2.l.b.117.1		4	140.27	odd	4
245.2.l.b.178.1		4	28.11	odd	6
315.2.bz.a.73.1		4	84.59	odd	6
315.2.bz.a.82.1		4	60.47	odd	4
315.2.bz.b.208.1		4	12.11	even	2
315.2.bz.b.262.1		4	420.227	even	12
560.2.ci.a.17.1		4	35.17	even	12	inner
560.2.ci.a.33.1		4	1.1	even	1	trivial
560.2.ci.b.257.1		4	5.2	odd	4
560.2.ci.b.353.1		4	7.3	odd	6

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.ci (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.133975i) q^{3} +(-1.86603 + 1.23205i) q^{5} +(0.866025 - 2.50000i) q^{7} +(-2.36603 - 1.36603i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.133975i) q^{3} +(-1.86603 + 1.23205i) q^{5} +(0.866025 - 2.50000i) q^{7} +(-2.36603 - 1.36603i) q^{9} +(-1.36603 - 2.36603i) q^{11} +(2.00000 - 2.00000i) q^{13} +(-1.09808 + 0.366025i) q^{15} +(1.00000 - 3.73205i) q^{17} +(0.366025 - 0.633975i) q^{19} +(0.767949 - 1.13397i) q^{21} +(0.133975 - 0.0358984i) q^{23} +(1.96410 - 4.59808i) q^{25} +(-2.09808 - 2.09808i) q^{27} +3.00000i q^{29} +(6.46410 - 3.73205i) q^{31} +(-0.366025 - 1.36603i) q^{33} +(1.46410 + 5.73205i) q^{35} +(1.26795 + 4.73205i) q^{37} +(1.26795 - 0.732051i) q^{39} -6.46410i q^{41} +(-2.83013 - 2.83013i) q^{43} +(6.09808 - 0.366025i) q^{45} +(-8.83013 + 2.36603i) q^{47} +(-5.50000 - 4.33013i) q^{49} +(1.00000 - 1.73205i) q^{51} +(-1.83013 + 6.83013i) q^{53} +(5.46410 + 2.73205i) q^{55} +(0.267949 - 0.267949i) q^{57} +(-4.09808 - 7.09808i) q^{59} +(1.33013 + 0.767949i) q^{61} +(-5.46410 + 4.73205i) q^{63} +(-1.26795 + 6.19615i) q^{65} +(10.6962 + 2.86603i) q^{67} +0.0717968 q^{69} -1.26795 q^{71} +(-12.9282 - 3.46410i) q^{73} +(1.59808 - 2.03590i) q^{75} +(-7.09808 + 1.36603i) q^{77} +(2.83013 + 1.63397i) q^{79} +(3.33013 + 5.76795i) q^{81} +(-2.09808 + 2.09808i) q^{83} +(2.73205 + 8.19615i) q^{85} +(-0.401924 + 1.50000i) q^{87} +(0.330127 - 0.571797i) q^{89} +(-3.26795 - 6.73205i) q^{91} +(3.73205 - 1.00000i) q^{93} +(0.0980762 + 1.63397i) q^{95} +(5.92820 + 5.92820i) q^{97} +7.46410i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} - 4 q^{5} - 6 q^{9}+O(q^{10}) \) 4 * q + 2 * q^3 - 4 * q^5 - 6 * q^9	\( 4 q + 2 q^{3} - 4 q^{5} - 6 q^{9} - 2 q^{11} + 8 q^{13} + 6 q^{15} + 4 q^{17} - 2 q^{19} + 10 q^{21} + 4 q^{23} - 6 q^{25} + 2 q^{27} + 12 q^{31} + 2 q^{33} - 8 q^{35} + 12 q^{37} + 12 q^{39} + 6 q^{43} + 14 q^{45} - 18 q^{47} - 22 q^{49} + 4 q^{51} + 10 q^{53} + 8 q^{55} + 8 q^{57} - 6 q^{59} - 12 q^{61} - 8 q^{63} - 12 q^{65} + 22 q^{67} + 28 q^{69} - 12 q^{71} - 24 q^{73} - 4 q^{75} - 18 q^{77} - 6 q^{79} - 4 q^{81} + 2 q^{83} + 4 q^{85} - 12 q^{87} - 16 q^{89} - 20 q^{91} + 8 q^{93} - 10 q^{95} - 4 q^{97}+O(q^{100}) \) 4 * q + 2 * q^3 - 4 * q^5 - 6 * q^9 - 2 * q^11 + 8 * q^13 + 6 * q^15 + 4 * q^17 - 2 * q^19 + 10 * q^21 + 4 * q^23 - 6 * q^25 + 2 * q^27 + 12 * q^31 + 2 * q^33 - 8 * q^35 + 12 * q^37 + 12 * q^39 + 6 * q^43 + 14 * q^45 - 18 * q^47 - 22 * q^49 + 4 * q^51 + 10 * q^53 + 8 * q^55 + 8 * q^57 - 6 * q^59 - 12 * q^61 - 8 * q^63 - 12 * q^65 + 22 * q^67 + 28 * q^69 - 12 * q^71 - 24 * q^73 - 4 * q^75 - 18 * q^77 - 6 * q^79 - 4 * q^81 + 2 * q^83 + 4 * q^85 - 12 * q^87 - 16 * q^89 - 20 * q^91 + 8 * q^93 - 10 * q^95 - 4 * q^97

Introduction

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