LMFDB - Embedded newform 272.2.v.b.161.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [272,2,Mod(49,272)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(272, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([0, 0, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("272.49"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 272 = 2^{4} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	272.v (of order $8$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,0,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$2.17193093498$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{8})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 34)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			161.1
Root			$-0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	272.161
Dual form			272.2.v.b.49.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 - 1.70711i) q^{3} +(-3.41421 - 1.41421i) q^{5} +(-1.41421 + 0.585786i) q^{7} +(-0.292893 - 0.292893i) q^{9} +(-1.70711 - 4.12132i) q^{11} -0.828427i q^{13} +(-4.82843 + 4.82843i) q^{15} +(-2.12132 - 3.53553i) q^{17} +(-0.585786 + 0.585786i) q^{19} +2.82843i q^{21} +(1.17157 + 2.82843i) q^{23} +(6.12132 + 6.12132i) q^{25} +(4.41421 - 1.82843i) q^{27} +(-1.41421 - 0.585786i) q^{29} +(1.41421 - 3.41421i) q^{31} -8.24264 q^{33} +5.65685 q^{35} +(0.828427 - 2.00000i) q^{37} +(-1.41421 - 0.585786i) q^{39} +(10.3640 - 4.29289i) q^{41} +(1.24264 + 1.24264i) q^{43} +(0.585786 + 1.41421i) q^{45} -9.65685i q^{47} +(-3.29289 + 3.29289i) q^{49} +(-7.53553 + 1.12132i) q^{51} +(0.585786 - 0.585786i) q^{53} +16.4853i q^{55} +(0.585786 + 1.41421i) q^{57} +(-0.414214 - 0.414214i) q^{59} +(6.82843 - 2.82843i) q^{61} +(0.585786 + 0.242641i) q^{63} +(-1.17157 + 2.82843i) q^{65} +7.41421 q^{67} +5.65685 q^{69} +(-0.828427 + 2.00000i) q^{71} +(-4.94975 - 2.05025i) q^{73} +(14.7782 - 6.12132i) q^{75} +(4.82843 + 4.82843i) q^{77} +(2.00000 + 4.82843i) q^{79} -10.0711i q^{81} +(-4.41421 + 4.41421i) q^{83} +(2.24264 + 15.0711i) q^{85} +(-2.00000 + 2.00000i) q^{87} +15.0711i q^{89} +(0.485281 + 1.17157i) q^{91} +(-4.82843 - 4.82843i) q^{93} +(2.82843 - 1.17157i) q^{95} +(-5.12132 - 2.12132i) q^{97} +(-0.707107 + 1.70711i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 8 q^{5} - 4 q^{9} - 4 q^{11} - 8 q^{15} - 8 q^{19} + 16 q^{23} + 16 q^{25} + 12 q^{27} - 16 q^{33} - 8 q^{37} + 16 q^{41} - 12 q^{43} + 8 q^{45} - 16 q^{49} - 16 q^{51} + 8 q^{53} + 8 q^{57} + 4 q^{59}+ \cdots - 12 q^{97}+O(q^{100}) $ 4 * q - 8 * q^5 - 4 * q^9 - 4 * q^11 - 8 * q^15 - 8 * q^19 + 16 * q^23 + 16 * q^25 + 12 * q^27 - 16 * q^33 - 8 * q^37 + 16 * q^41 - 12 * q^43 + 8 * q^45 - 16 * q^49 - 16 * q^51 + 8 * q^53 + 8 * q^57 + 4 * q^59 + 16 * q^61 + 8 * q^63 - 16 * q^65 + 24 * q^67 + 8 * q^71 + 28 * q^75 + 8 * q^77 + 8 * q^79 - 12 * q^83 - 8 * q^85 - 8 * q^87 - 32 * q^91 - 8 * q^93 - 12 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/272\mathbb{Z}\right)^\times$.

$n$	$69$	$239$	$241$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{8}\right)$

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
$3$	0.707107	−	1.70711i	0.408248	−	0.985599i	−0.577350	−	0.816497i	$-0.695913\pi$
$3$	0.707107	−	1.70711i	0.408248	−	0.985599i	0.985599	−	0.169102i	$-0.0540867\pi$
$4$		0			0
$5$	−3.41421	−	1.41421i	−1.52688	−	0.632456i	−0.547927	−	0.836526i	$-0.684583\pi$
$5$	−3.41421	−	1.41421i	−1.52688	−	0.632456i	−0.978956	+	0.204071i	$0.934583\pi$
$6$		0			0
$7$	−1.41421	+	0.585786i	−0.534522	+	0.221406i	−0.633583	−	0.773675i	$-0.718416\pi$
$7$	−1.41421	+	0.585786i	−0.534522	+	0.221406i	0.0990602	+	0.995081i	$0.468416\pi$
$8$		0			0
$9$	−0.292893	−	0.292893i	−0.0976311	−	0.0976311i
$10$		0			0
$11$	−1.70711	−	4.12132i	−0.514712	−	1.24262i	−0.941113	−	0.338091i	$-0.890219\pi$
$11$	−1.70711	−	4.12132i	−0.514712	−	1.24262i	0.426401	−	0.904534i	$-0.359781\pi$
$12$		0			0
$13$		−	0.828427i		−	0.229764i	−0.993379	−	0.114882i	$-0.963351\pi$
$13$		−	0.828427i		−	0.229764i	0.993379	−	0.114882i	$-0.0366490\pi$
$14$		0			0
$15$	−4.82843	+	4.82843i	−1.24669	+	1.24669i
$16$		0			0
$17$	−2.12132	−	3.53553i	−0.514496	−	0.857493i
$17$	−2.12132	−	3.53553i	−0.514496	−	0.857493i
$18$		0			0
$19$	−0.585786	+	0.585786i	−0.134389	+	0.134389i	−0.771101	−	0.636713i	$-0.780294\pi$
$19$	−0.585786	+	0.585786i	−0.134389	+	0.134389i	0.636713	+	0.771101i	$0.280294\pi$
$20$		0			0
$21$			2.82843i			0.617213i
$22$		0			0
$23$	1.17157	+	2.82843i	0.244290	+	0.589768i	0.997700	−	0.0677829i	$-0.0215925\pi$
$23$	1.17157	+	2.82843i	0.244290	+	0.589768i	−0.753410	+	0.657551i	$0.771593\pi$
$24$		0			0
$25$	6.12132	+	6.12132i	1.22426	+	1.22426i
$26$		0			0
$27$	4.41421	−	1.82843i	0.849516	−	0.351881i
$28$		0			0
$29$	−1.41421	−	0.585786i	−0.262613	−	0.108778i	0.247492	−	0.968890i	$-0.420394\pi$
$29$	−1.41421	−	0.585786i	−0.262613	−	0.108778i	−0.510105	+	0.860112i	$0.670394\pi$
$30$		0			0
$31$	1.41421	−	3.41421i	0.254000	−	0.613211i	−0.744520	−	0.667601i	$-0.767321\pi$
$31$	1.41421	−	3.41421i	0.254000	−	0.613211i	0.998520	+	0.0543898i	$0.0173214\pi$
$32$		0			0
$33$	−8.24264			−1.43486
$34$		0			0
$35$	5.65685			0.956183
$36$		0			0
$37$	0.828427	−	2.00000i	0.136193	−	0.328798i	−0.841039	−	0.540975i	$-0.818055\pi$
$37$	0.828427	−	2.00000i	0.136193	−	0.328798i	0.977231	+	0.212177i	$0.0680553\pi$
$38$		0			0
$39$	−1.41421	−	0.585786i	−0.226455	−	0.0938009i
$40$		0			0
$41$	10.3640	−	4.29289i	1.61858	−	0.670437i	0.624695	−	0.780869i	$-0.285223\pi$
$41$	10.3640	−	4.29289i	1.61858	−	0.670437i	0.993884	+	0.110432i	$0.0352233\pi$
$42$		0			0
$43$	1.24264	+	1.24264i	0.189501	+	0.189501i	0.795480	−	0.605979i	$-0.207219\pi$
$43$	1.24264	+	1.24264i	0.189501	+	0.189501i	−0.605979	+	0.795480i	$0.707219\pi$
$44$		0			0
$45$	0.585786	+	1.41421i	0.0873239	+	0.210819i
$46$		0			0
$47$		−	9.65685i		−	1.40860i	−0.709904	−	0.704298i	$-0.751262\pi$
$47$		−	9.65685i		−	1.40860i	0.709904	−	0.704298i	$-0.248738\pi$
$48$		0			0
$49$	−3.29289	+	3.29289i	−0.470413	+	0.470413i
$50$		0			0
$51$	−7.53553	+	1.12132i	−1.05519	+	0.157016i
$52$		0			0
$53$	0.585786	−	0.585786i	0.0804640	−	0.0804640i	−0.665729	−	0.746193i	$-0.731879\pi$
$53$	0.585786	−	0.585786i	0.0804640	−	0.0804640i	0.746193	+	0.665729i	$0.231879\pi$
$54$		0			0
$55$			16.4853i			2.22287i
$56$		0			0
$57$	0.585786	+	1.41421i	0.0775893	+	0.187317i
$58$		0			0
$59$	−0.414214	−	0.414214i	−0.0539260	−	0.0539260i	0.679630	−	0.733556i	$-0.262141\pi$
$59$	−0.414214	−	0.414214i	−0.0539260	−	0.0539260i	−0.733556	+	0.679630i	$0.762141\pi$
$60$		0			0
$61$	6.82843	−	2.82843i	0.874291	−	0.362143i	0.100011	−	0.994986i	$-0.468112\pi$
$61$	6.82843	−	2.82843i	0.874291	−	0.362143i	0.774280	+	0.632843i	$0.218112\pi$
$62$		0			0
$63$	0.585786	+	0.242641i	0.0738022	+	0.0305699i
$64$		0			0
$65$	−1.17157	+	2.82843i	−0.145316	+	0.350823i
$66$		0			0
$67$	7.41421			0.905790			0.452895	−	0.891564i	$-0.350391\pi$
$67$	7.41421			0.905790			0.452895	+	0.891564i	$0.350391\pi$
$68$		0			0
$69$	5.65685			0.681005
$70$		0			0
$71$	−0.828427	+	2.00000i	−0.0983162	+	0.237356i	−0.965383	−	0.260835i	$-0.916002\pi$
$71$	−0.828427	+	2.00000i	−0.0983162	+	0.237356i	0.867067	+	0.498191i	$0.166002\pi$
$72$		0			0
$73$	−4.94975	−	2.05025i	−0.579324	−	0.239964i	0.0737261	−	0.997279i	$-0.476511\pi$
$73$	−4.94975	−	2.05025i	−0.579324	−	0.239964i	−0.653050	+	0.757315i	$0.726511\pi$
$74$		0			0
$75$	14.7782	−	6.12132i	1.70644	−	0.706829i
$76$		0			0
$77$	4.82843	+	4.82843i	0.550250	+	0.550250i
$78$		0			0
$79$	2.00000	+	4.82843i	0.225018	+	0.543240i	0.995558	−	0.0941507i	$-0.0300136\pi$
$79$	2.00000	+	4.82843i	0.225018	+	0.543240i	−0.770540	+	0.637391i	$0.780014\pi$
$80$		0			0
$81$		−	10.0711i		−	1.11901i
$82$		0			0
$83$	−4.41421	+	4.41421i	−0.484523	+	0.484523i	−0.906573	−	0.422050i	$-0.861311\pi$
$83$	−4.41421	+	4.41421i	−0.484523	+	0.484523i	0.422050	+	0.906573i	$0.361311\pi$
$84$		0			0
$85$	2.24264	+	15.0711i	0.243249	+	1.63469i
$86$		0			0
$87$	−2.00000	+	2.00000i	−0.214423	+	0.214423i
$88$		0			0
$89$			15.0711i			1.59753i	0.601643	+	0.798765i	$0.294513\pi$
$89$			15.0711i			1.59753i	−0.601643	+	0.798765i	$0.705487\pi$
$90$		0			0
$91$	0.485281	+	1.17157i	0.0508713	+	0.122814i
$92$		0			0
$93$	−4.82843	−	4.82843i	−0.500685	−	0.500685i
$94$		0			0
$95$	2.82843	−	1.17157i	0.290191	−	0.120201i
$96$		0			0
$97$	−5.12132	−	2.12132i	−0.519991	−	0.215387i	0.107222	−	0.994235i	$-0.465804\pi$
$97$	−5.12132	−	2.12132i	−0.519991	−	0.215387i	−0.627213	+	0.778848i	$0.715804\pi$
$98$		0			0
$99$	−0.707107	+	1.70711i	−0.0710669	+	0.171571i
$100$		0			0
$101$	4.34315			0.432159			0.216080	−	0.976376i	$-0.430673\pi$
$101$	4.34315			0.432159			0.216080	+	0.976376i	$0.430673\pi$
$102$		0			0
$103$	−12.4853			−1.23021			−0.615106	−	0.788445i	$-0.710887\pi$
$103$	−12.4853			−1.23021			−0.615106	+	0.788445i	$0.710887\pi$
$104$		0			0
$105$	4.00000	−	9.65685i	0.390360	−	0.942412i
$106$		0			0
$107$	−10.7782	−	4.46447i	−1.04197	−	0.431596i	−0.204948	−	0.978773i	$-0.565703\pi$
$107$	−10.7782	−	4.46447i	−1.04197	−	0.431596i	−0.837017	+	0.547177i	$0.815703\pi$
$108$		0			0
$109$	−9.07107	+	3.75736i	−0.868851	+	0.359890i	−0.772163	−	0.635425i	$-0.780825\pi$
$109$	−9.07107	+	3.75736i	−0.868851	+	0.359890i	−0.0966881	+	0.995315i	$0.530825\pi$
$110$		0			0
$111$	−2.82843	−	2.82843i	−0.268462	−	0.268462i
$112$		0			0
$113$	−3.53553	−	8.53553i	−0.332595	−	0.802955i	−0.998385	−	0.0568160i	$-0.981905\pi$
$113$	−3.53553	−	8.53553i	−0.332595	−	0.802955i	0.665790	−	0.746140i	$-0.268095\pi$
$114$		0			0
$115$		−	11.3137i		−	1.05501i
$116$		0			0
$117$	−0.242641	+	0.242641i	−0.0224321	+	0.0224321i
$118$		0			0
$119$	5.07107	+	3.75736i	0.464864	+	0.344437i
$120$		0			0
$121$	−6.29289	+	6.29289i	−0.572081	+	0.572081i
$122$		0			0
$123$		−	20.7279i		−	1.86897i
$124$		0			0
$125$	−5.17157	−	12.4853i	−0.462560	−	1.11672i
$126$		0			0
$127$	9.17157	+	9.17157i	0.813845	+	0.813845i	0.985208	−	0.171363i	$-0.0548169\pi$
$127$	9.17157	+	9.17157i	0.813845	+	0.813845i	−0.171363	+	0.985208i	$0.554817\pi$
$128$		0			0
$129$	3.00000	−	1.24264i	0.264135	−	0.109408i
$130$		0			0
$131$	−0.121320	−	0.0502525i	−0.0105998	−	0.00439058i	0.377377	−	0.926060i	$-0.376826\pi$
$131$	−0.121320	−	0.0502525i	−0.0105998	−	0.00439058i	−0.387977	+	0.921669i	$0.626826\pi$
$132$		0			0
$133$	0.485281	−	1.17157i	0.0420792	−	0.101588i
$134$		0			0
$135$	−17.6569			−1.51966
$136$		0			0
$137$	−2.34315			−0.200188			−0.100094	−	0.994978i	$-0.531914\pi$
$137$	−2.34315			−0.200188			−0.100094	+	0.994978i	$0.531914\pi$
$138$		0			0
$139$	0.707107	−	1.70711i	0.0599760	−	0.144795i	−0.891051	−	0.453904i	$-0.850031\pi$
$139$	0.707107	−	1.70711i	0.0599760	−	0.144795i	0.951027	+	0.309109i	$0.100031\pi$
$140$		0			0
$141$	−16.4853	−	6.82843i	−1.38831	−	0.575057i
$142$		0			0
$143$	−3.41421	+	1.41421i	−0.285511	+	0.118262i
$144$		0			0
$145$	4.00000	+	4.00000i	0.332182	+	0.332182i
$146$		0			0
$147$	3.29289	+	7.94975i	0.271593	+	0.655684i
$148$		0			0
$149$		−	15.6569i		−	1.28266i	−0.767265	−	0.641330i	$-0.778383\pi$
$149$		−	15.6569i		−	1.28266i	0.767265	−	0.641330i	$-0.221617\pi$
$150$		0			0
$151$	15.6569	−	15.6569i	1.27414	−	1.27414i	0.330240	−	0.943897i	$-0.392870\pi$
$151$	15.6569	−	15.6569i	1.27414	−	1.27414i	0.943897	−	0.330240i	$-0.107130\pi$
$152$		0			0
$153$	−0.414214	+	1.65685i	−0.0334872	+	0.133949i
$154$		0			0
$155$	−9.65685	+	9.65685i	−0.775657	+	0.775657i
$156$		0			0
$157$		−	13.3137i		−	1.06255i	−0.847200	−	0.531275i	$-0.821713\pi$
$157$		−	13.3137i		−	1.06255i	0.847200	−	0.531275i	$-0.178287\pi$
$158$		0			0
$159$	−0.585786	−	1.41421i	−0.0464559	−	0.112154i
$160$		0			0
$161$	−3.31371	−	3.31371i	−0.261157	−	0.261157i
$162$		0			0
$163$	−21.0208	+	8.70711i	−1.64648	+	0.681993i	−0.996928	−	0.0783260i	$-0.975042\pi$
$163$	−21.0208	+	8.70711i	−1.64648	+	0.681993i	−0.649550	+	0.760319i	$0.725042\pi$
$164$		0			0
$165$	28.1421	+	11.6569i	2.19086	+	0.907485i
$166$		0			0
$167$	7.55635	−	18.2426i	0.584728	−	1.41166i	−0.303756	−	0.952750i	$-0.598241\pi$
$167$	7.55635	−	18.2426i	0.584728	−	1.41166i	0.888484	−	0.458908i	$-0.151759\pi$
$168$		0			0
$169$	12.3137			0.947208
$170$		0			0
$171$	0.343146			0.0262410
$172$		0			0
$173$	−2.24264	+	5.41421i	−0.170505	+	0.411635i	−0.985915	−	0.167249i	$-0.946512\pi$
$173$	−2.24264	+	5.41421i	−0.170505	+	0.411635i	0.815410	+	0.578884i	$0.196512\pi$
$174$		0			0
$175$	−12.2426	−	5.07107i	−0.925457	−	0.383337i
$176$		0			0
$177$	−1.00000	+	0.414214i	−0.0751646	+	0.0311342i
$178$		0			0
$179$	18.2426	+	18.2426i	1.36352	+	1.36352i	0.869387	+	0.494132i	$0.164514\pi$
$179$	18.2426	+	18.2426i	1.36352	+	1.36352i	0.494132	+	0.869387i	$0.335486\pi$
$180$		0			0
$181$	2.34315	+	5.65685i	0.174165	+	0.420471i	0.986724	−	0.162408i	$-0.0519262\pi$
$181$	2.34315	+	5.65685i	0.174165	+	0.420471i	−0.812559	+	0.582879i	$0.801926\pi$
$182$		0			0
$183$		−	13.6569i		−	1.00954i
$184$		0			0
$185$	−5.65685	+	5.65685i	−0.415900	+	0.415900i
$186$		0			0
$187$	−10.9497	+	14.7782i	−0.800725	+	1.08069i
$188$		0			0
$189$	−5.17157	+	5.17157i	−0.376177	+	0.376177i
$190$		0			0
$191$			2.82843i			0.204658i	0.994751	+	0.102329i	$0.0326294\pi$
$191$			2.82843i			0.204658i	−0.994751	+	0.102329i	$0.967371\pi$
$192$		0			0
$193$	4.70711	+	11.3640i	0.338825	+	0.817996i	0.997829	+	0.0658565i	$0.0209780\pi$
$193$	4.70711	+	11.3640i	0.338825	+	0.817996i	−0.659004	+	0.752139i	$0.729022\pi$
$194$		0			0
$195$	4.00000	+	4.00000i	0.286446	+	0.286446i
$196$		0			0
$197$	−18.4853	+	7.65685i	−1.31702	+	0.545528i	−0.926925	−	0.375246i	$-0.877558\pi$
$197$	−18.4853	+	7.65685i	−1.31702	+	0.545528i	−0.390096	+	0.920774i	$0.627558\pi$
$198$		0			0
$199$	19.3137	+	8.00000i	1.36911	+	0.567105i	0.941548	−	0.336880i	$-0.109372\pi$
$199$	19.3137	+	8.00000i	1.36911	+	0.567105i	0.427565	+	0.903985i	$0.359372\pi$
$200$		0			0
$201$	5.24264	−	12.6569i	0.369787	−	0.892746i
$202$		0			0
$203$	2.34315			0.164457
$204$		0			0
$205$	−41.4558			−2.89540
$206$		0			0
$207$	0.485281	−	1.17157i	0.0337294	−	0.0814299i
$208$		0			0
$209$	3.41421	+	1.41421i	0.236166	+	0.0978232i
$210$		0			0
$211$	0.121320	−	0.0502525i	0.00835204	−	0.00345953i	−0.378504	−	0.925600i	$-0.623561\pi$
$211$	0.121320	−	0.0502525i	0.00835204	−	0.00345953i	0.386856	+	0.922140i	$0.373561\pi$
$212$		0			0
$213$	2.82843	+	2.82843i	0.193801	+	0.193801i
$214$		0			0
$215$	−2.48528	−	6.00000i	−0.169495	−	0.409197i
$216$		0			0
$217$			5.65685i			0.384012i
$218$		0			0
$219$	−7.00000	+	7.00000i	−0.473016	+	0.473016i
$220$		0			0
$221$	−2.92893	+	1.75736i	−0.197021	+	0.118213i
$222$		0			0
$223$	17.3137	−	17.3137i	1.15941	−	1.15941i	0.174809	−	0.984602i	$-0.444069\pi$
$223$	17.3137	−	17.3137i	1.15941	−	1.15941i	0.984602	−	0.174809i	$-0.0559309\pi$
$224$		0			0
$225$		−	3.58579i		−	0.239052i
$226$		0			0
$227$	−7.77817	−	18.7782i	−0.516256	−	1.24635i	−0.940188	−	0.340657i	$-0.889350\pi$
$227$	−7.77817	−	18.7782i	−0.516256	−	1.24635i	0.423932	−	0.905694i	$-0.360650\pi$
$228$		0			0
$229$	13.0711	+	13.0711i	0.863760	+	0.863760i	0.991773	−	0.128012i	$-0.0408596\pi$
$229$	13.0711	+	13.0711i	0.863760	+	0.863760i	−0.128012	+	0.991773i	$0.540860\pi$
$230$		0			0
$231$	11.6569	−	4.82843i	0.766965	−	0.317687i
$232$		0			0
$233$	9.70711	+	4.02082i	0.635934	+	0.263412i	0.677272	−	0.735733i	$-0.263162\pi$
$233$	9.70711	+	4.02082i	0.635934	+	0.263412i	−0.0413382	+	0.999145i	$0.513162\pi$
$234$		0			0
$235$	−13.6569	+	32.9706i	−0.890875	+	2.15076i
$236$		0			0
$237$	9.65685			0.627280
$238$		0			0
$239$	−21.1716			−1.36948			−0.684738	−	0.728790i	$-0.740083\pi$
$239$	−21.1716			−1.36948			−0.684738	+	0.728790i	$0.740083\pi$
$240$		0			0
$241$	7.60660	−	18.3640i	0.489984	−	1.18293i	−0.464743	−	0.885445i	$-0.653853\pi$
$241$	7.60660	−	18.3640i	0.489984	−	1.18293i	0.954728	−	0.297481i	$-0.0961466\pi$
$242$		0			0
$243$	−3.94975	−	1.63604i	−0.253376	−	0.104952i
$244$		0			0
$245$	15.8995	−	6.58579i	1.01578	−	0.420750i
$246$		0			0
$247$	0.485281	+	0.485281i	0.0308777	+	0.0308777i
$248$		0			0
$249$	4.41421	+	10.6569i	0.279739	+	0.675351i
$250$		0			0
$251$			18.7279i			1.18210i	0.806636	+	0.591048i	$0.201286\pi$
$251$			18.7279i			1.18210i	−0.806636	+	0.591048i	$0.798714\pi$
$252$		0			0
$253$	9.65685	−	9.65685i	0.607121	−	0.607121i
$254$		0			0
$255$	27.3137	+	6.82843i	1.71045	+	0.427613i
$256$		0			0
$257$	5.82843	−	5.82843i	0.363567	−	0.363567i	−0.501557	−	0.865124i	$-0.667239\pi$
$257$	5.82843	−	5.82843i	0.363567	−	0.363567i	0.865124	+	0.501557i	$0.167239\pi$
$258$		0			0
$259$			3.31371i			0.205904i
$260$		0			0
$261$	0.242641	+	0.585786i	0.0150191	+	0.0362593i
$262$		0			0
$263$	−5.65685	−	5.65685i	−0.348817	−	0.348817i	0.510852	−	0.859669i	$-0.329330\pi$
$263$	−5.65685	−	5.65685i	−0.348817	−	0.348817i	−0.859669	+	0.510852i	$0.829330\pi$
$264$		0			0
$265$	−2.82843	+	1.17157i	−0.173749	+	0.0719691i
$266$		0			0
$267$	25.7279	+	10.6569i	1.57452	+	0.652189i
$268$		0			0
$269$	2.92893	−	7.07107i	0.178580	−	0.431131i	−0.809089	−	0.587686i	$-0.800039\pi$
$269$	2.92893	−	7.07107i	0.178580	−	0.431131i	0.987669	+	0.156555i	$0.0500390\pi$
$270$		0			0
$271$	14.8284			0.900763			0.450381	−	0.892836i	$-0.351288\pi$
$271$	14.8284			0.900763			0.450381	+	0.892836i	$0.351288\pi$
$272$		0			0
$273$	2.34315			0.141814
$274$		0			0
$275$	14.7782	−	35.6777i	0.891157	−	2.15144i
$276$		0			0
$277$	21.8995	+	9.07107i	1.31581	+	0.545028i	0.926575	−	0.376110i	$-0.122738\pi$
$277$	21.8995	+	9.07107i	1.31581	+	0.545028i	0.389238	+	0.921137i	$0.372738\pi$
$278$		0			0
$279$	−1.41421	+	0.585786i	−0.0846668	+	0.0350701i
$280$		0			0
$281$	10.1421	+	10.1421i	0.605029	+	0.605029i	0.941643	−	0.336614i	$-0.109282\pi$
$281$	10.1421	+	10.1421i	0.605029	+	0.605029i	−0.336614	+	0.941643i	$0.609282\pi$
$282$		0			0
$283$	−0.435029	−	1.05025i	−0.0258598	−	0.0624310i	0.910422	−	0.413680i	$-0.135757\pi$
$283$	−0.435029	−	1.05025i	−0.0258598	−	0.0624310i	−0.936282	+	0.351249i	$0.885757\pi$
$284$		0			0
$285$		−	5.65685i		−	0.335083i
$286$		0			0
$287$	−12.1421	+	12.1421i	−0.716728	+	0.716728i
$288$		0			0
$289$	−8.00000	+	15.0000i	−0.470588	+	0.882353i
$290$		0			0
$291$	−7.24264	+	7.24264i	−0.424571	+	0.424571i
$292$		0			0
$293$		−	22.0000i		−	1.28525i	−0.766179	−	0.642627i	$-0.777845\pi$
$293$		−	22.0000i		−	1.28525i	0.766179	−	0.642627i	$-0.222155\pi$
$294$		0			0
$295$	0.828427	+	2.00000i	0.0482329	+	0.116445i
$296$		0			0
$297$	−15.0711	−	15.0711i	−0.874512	−	0.874512i
$298$		0			0
$299$	2.34315	−	0.970563i	0.135508	−	0.0561291i
$300$		0			0
$301$	−2.48528	−	1.02944i	−0.143249	−	0.0593358i
$302$		0			0
$303$	3.07107	−	7.41421i	0.176428	−	0.425935i
$304$		0			0
$305$	−27.3137			−1.56398
$306$		0			0
$307$	−6.34315			−0.362022			−0.181011	−	0.983481i	$-0.557937\pi$
$307$	−6.34315			−0.362022			−0.181011	+	0.983481i	$0.557937\pi$
$308$		0			0
$309$	−8.82843	+	21.3137i	−0.502232	+	1.21249i
$310$		0			0
$311$	13.8995	+	5.75736i	0.788168	+	0.326470i	0.740207	−	0.672379i	$-0.234728\pi$
$311$	13.8995	+	5.75736i	0.788168	+	0.326470i	0.0479613	+	0.998849i	$0.484728\pi$
$312$		0			0
$313$	12.5355	−	5.19239i	0.708550	−	0.293491i	0.000845724	−	1.00000i	$-0.499731\pi$
$313$	12.5355	−	5.19239i	0.708550	−	0.293491i	0.707705	+	0.706509i	$0.249731\pi$
$314$		0			0
$315$	−1.65685	−	1.65685i	−0.0933532	−	0.0933532i
$316$		0			0
$317$	8.48528	+	20.4853i	0.476581	+	1.15057i	0.961202	+	0.275844i	$0.0889573\pi$
$317$	8.48528	+	20.4853i	0.476581	+	1.15057i	−0.484622	+	0.874724i	$0.661043\pi$
$318$		0			0
$319$			6.82843i			0.382319i
$320$		0			0
$321$	−15.2426	+	15.2426i	−0.850761	+	0.850761i
$322$		0			0
$323$	3.31371	+	0.828427i	0.184380	+	0.0460949i
$324$		0			0
$325$	5.07107	−	5.07107i	0.281292	−	0.281292i
$326$		0			0
$327$			18.1421i			1.00326i
$328$		0			0
$329$	5.65685	+	13.6569i	0.311872	+	0.752927i
$330$		0			0
$331$	−19.5858	−	19.5858i	−1.07653	−	1.07653i	−0.996818	−	0.0797144i	$-0.974599\pi$
$331$	−19.5858	−	19.5858i	−1.07653	−	1.07653i	−0.0797144	−	0.996818i	$-0.525401\pi$
$332$		0			0
$333$	−0.828427	+	0.343146i	−0.0453975	+	0.0188043i
$334$		0			0
$335$	−25.3137	−	10.4853i	−1.38304	−	0.572872i
$336$		0			0
$337$	4.46447	−	10.7782i	0.243195	−	0.587125i	−0.754402	−	0.656413i	$-0.772073\pi$
$337$	4.46447	−	10.7782i	0.243195	−	0.587125i	0.997597	+	0.0692885i	$0.0220729\pi$
$338$		0			0
$339$	−17.0711			−0.927173
$340$		0			0
$341$	−16.4853			−0.892728
$342$		0			0
$343$	6.82843	−	16.4853i	0.368700	−	0.890122i
$344$		0			0
$345$	−19.3137	−	8.00000i	−1.03982	−	0.430706i
$346$		0			0
$347$	14.9497	−	6.19239i	0.802544	−	0.332425i	0.0565694	−	0.998399i	$-0.481984\pi$
$347$	14.9497	−	6.19239i	0.802544	−	0.332425i	0.745975	+	0.665974i	$0.231984\pi$
$348$		0			0
$349$	−13.8995	−	13.8995i	−0.744023	−	0.744023i	0.229327	−	0.973350i	$-0.426348\pi$
$349$	−13.8995	−	13.8995i	−0.744023	−	0.744023i	−0.973350	+	0.229327i	$0.926348\pi$
$350$		0			0
$351$	−1.51472	−	3.65685i	−0.0808497	−	0.195188i
$352$		0			0
$353$		−	14.3848i		−	0.765624i	−0.923826	−	0.382812i	$-0.874956\pi$
$353$		−	14.3848i		−	0.765624i	0.923826	−	0.382812i	$-0.125044\pi$
$354$		0			0
$355$	5.65685	−	5.65685i	0.300235	−	0.300235i
$356$		0			0
$357$	10.0000	−	6.00000i	0.529256	−	0.317554i
$358$		0			0
$359$	−8.00000	+	8.00000i	−0.422224	+	0.422224i	−0.885969	−	0.463745i	$-0.846505\pi$
$359$	−8.00000	+	8.00000i	−0.422224	+	0.422224i	0.463745	+	0.885969i	$0.346505\pi$
$360$		0			0
$361$			18.3137i			0.963879i
$362$		0			0
$363$	6.29289	+	15.1924i	0.330291	+	0.797394i
$364$		0			0
$365$	14.0000	+	14.0000i	0.732793	+	0.732793i
$366$		0			0
$367$	−17.3137	+	7.17157i	−0.903768	+	0.374353i	−0.785668	−	0.618649i	$-0.787680\pi$
$367$	−17.3137	+	7.17157i	−0.903768	+	0.374353i	−0.118100	+	0.993002i	$0.537680\pi$
$368$		0			0
$369$	−4.29289	−	1.77817i	−0.223479	−	0.0925681i
$370$		0			0
$371$	−0.485281	+	1.17157i	−0.0251946	+	0.0608250i
$372$		0			0
$373$	−10.4853			−0.542907			−0.271454	−	0.962452i	$-0.587504\pi$
$373$	−10.4853			−0.542907			−0.271454	+	0.962452i	$0.587504\pi$
$374$		0			0
$375$	−24.9706			−1.28947
$376$		0			0
$377$	−0.485281	+	1.17157i	−0.0249933	+	0.0603391i
$378$		0			0
$379$	−8.60660	−	3.56497i	−0.442091	−	0.183120i	0.150523	−	0.988606i	$-0.451904\pi$
$379$	−8.60660	−	3.56497i	−0.442091	−	0.183120i	−0.592614	+	0.805486i	$0.701904\pi$
$380$		0			0
$381$	22.1421	−	9.17157i	1.13438	−	0.469874i
$382$		0			0
$383$	21.3137	+	21.3137i	1.08908	+	1.08908i	0.995623	+	0.0934562i	$0.0297915\pi$
$383$	21.3137	+	21.3137i	1.08908	+	1.08908i	0.0934562	+	0.995623i	$0.470208\pi$
$384$		0			0
$385$	−9.65685	−	23.3137i	−0.492159	−	1.18818i
$386$		0			0
$387$		−	0.727922i		−	0.0370024i
$388$		0			0
$389$	2.24264	−	2.24264i	0.113706	−	0.113706i	−0.647964	−	0.761671i	$-0.724379\pi$
$389$	2.24264	−	2.24264i	0.113706	−	0.113706i	0.761671	+	0.647964i	$0.224379\pi$
$390$		0			0
$391$	7.51472	−	10.1421i	0.380036	−	0.512910i
$392$		0			0
$393$	−0.171573	+	0.171573i	−0.00865471	+	0.00865471i
$394$		0			0
$395$		−	19.3137i		−	0.971778i
$396$		0			0
$397$	3.17157	+	7.65685i	0.159177	+	0.384286i	0.983267	−	0.182173i	$-0.0583129\pi$
$397$	3.17157	+	7.65685i	0.159177	+	0.384286i	−0.824090	+	0.566459i	$0.808313\pi$
$398$		0			0
$399$	−1.65685	−	1.65685i	−0.0829465	−	0.0829465i
$400$		0			0
$401$	−22.1924	+	9.19239i	−1.10823	+	0.459046i	−0.860330	−	0.509738i	$-0.829742\pi$
$401$	−22.1924	+	9.19239i	−1.10823	+	0.459046i	−0.247905	+	0.968784i	$0.579742\pi$
$402$		0			0
$403$	−2.82843	−	1.17157i	−0.140894	−	0.0583602i
$404$		0			0
$405$	−14.2426	+	34.3848i	−0.707723	+	1.70859i
$406$		0			0
$407$	−9.65685			−0.478672
$408$		0			0
$409$	15.5563			0.769212			0.384606	−	0.923081i	$-0.374337\pi$
$409$	15.5563			0.769212			0.384606	+	0.923081i	$0.374337\pi$
$410$		0			0
$411$	−1.65685	+	4.00000i	−0.0817266	+	0.197305i
$412$		0			0
$413$	0.828427	+	0.343146i	0.0407642	+	0.0168851i
$414$		0			0
$415$	21.3137	−	8.82843i	1.04625	−	0.433370i
$416$		0			0
$417$	−2.41421	−	2.41421i	−0.118225	−	0.118225i
$418$		0			0
$419$	6.60660	+	15.9497i	0.322754	+	0.779196i	0.999092	+	0.0426051i	$0.0135657\pi$
$419$	6.60660	+	15.9497i	0.322754	+	0.779196i	−0.676338	+	0.736591i	$0.736434\pi$
$420$		0			0
$421$		−	15.6569i		−	0.763068i	−0.924355	−	0.381534i	$-0.875396\pi$
$421$		−	15.6569i		−	0.763068i	0.924355	−	0.381534i	$-0.124604\pi$
$422$		0			0
$423$	−2.82843	+	2.82843i	−0.137523	+	0.137523i
$424$		0			0
$425$	8.65685	−	34.6274i	0.419919	−	1.67968i
$426$		0			0
$427$	−8.00000	+	8.00000i	−0.387147	+	0.387147i
$428$		0			0
$429$			6.82843i			0.329680i
$430$		0			0
$431$	5.51472	+	13.3137i	0.265635	+	0.641299i	0.999268	−	0.0382464i	$-0.0121772\pi$
$431$	5.51472	+	13.3137i	0.265635	+	0.641299i	−0.733634	+	0.679545i	$0.762177\pi$
$432$		0			0
$433$	−9.17157	−	9.17157i	−0.440758	−	0.440758i	0.451509	−	0.892267i	$-0.350886\pi$
$433$	−9.17157	−	9.17157i	−0.440758	−	0.440758i	−0.892267	+	0.451509i	$0.850886\pi$
$434$		0			0
$435$	9.65685	−	4.00000i	0.463011	−	0.191785i
$436$		0			0
$437$	−2.34315	−	0.970563i	−0.112088	−	0.0464283i
$438$		0			0
$439$	8.82843	−	21.3137i	0.421358	−	1.01725i	−0.560590	−	0.828094i	$-0.689425\pi$
$439$	8.82843	−	21.3137i	0.421358	−	1.01725i	0.981947	−	0.189154i	$-0.0605745\pi$
$440$		0			0
$441$	1.92893			0.0918539
$442$		0			0
$443$	36.8701			1.75175			0.875875	−	0.482539i	$-0.160285\pi$
$443$	36.8701			1.75175			0.875875	+	0.482539i	$0.160285\pi$
$444$		0			0
$445$	21.3137	−	51.4558i	1.01037	−	2.43924i
$446$		0			0
$447$	−26.7279	−	11.0711i	−1.26419	−	0.523644i
$448$		0			0
$449$	5.12132	−	2.12132i	0.241690	−	0.100111i	−0.258551	−	0.965998i	$-0.583245\pi$
$449$	5.12132	−	2.12132i	0.241690	−	0.100111i	0.500241	+	0.865886i	$0.333245\pi$
$450$		0			0
$451$	−35.3848	−	35.3848i	−1.66620	−	1.66620i
$452$		0			0
$453$	−15.6569	−	37.7990i	−0.735623	−	1.77595i
$454$		0			0
$455$		−	4.68629i		−	0.219697i
$456$		0			0
$457$	3.51472	−	3.51472i	0.164412	−	0.164412i	−0.620106	−	0.784518i	$-0.712911\pi$
$457$	3.51472	−	3.51472i	0.164412	−	0.164412i	0.784518	+	0.620106i	$0.212911\pi$
$458$		0			0
$459$	−15.8284	−	11.7279i	−0.738808	−	0.547413i
$460$		0			0
$461$	−24.7279	+	24.7279i	−1.15169	+	1.15169i	−0.165481	+	0.986213i	$0.552918\pi$
$461$	−24.7279	+	24.7279i	−1.15169	+	1.15169i	−0.986213	+	0.165481i	$0.947082\pi$
$462$		0			0
$463$		−	3.31371i		−	0.154001i	−0.997031	−	0.0770005i	$-0.975466\pi$
$463$		−	3.31371i		−	0.154001i	0.997031	−	0.0770005i	$-0.0245343\pi$
$464$		0			0
$465$	9.65685	+	23.3137i	0.447826	+	1.08115i
$466$		0			0
$467$	1.75736	+	1.75736i	0.0813209	+	0.0813209i	0.746597	−	0.665276i	$-0.231686\pi$
$467$	1.75736	+	1.75736i	0.0813209	+	0.0813209i	−0.665276	+	0.746597i	$0.731686\pi$
$468$		0			0
$469$	−10.4853	+	4.34315i	−0.484165	+	0.200548i
$470$		0			0
$471$	−22.7279	−	9.41421i	−1.04725	−	0.433784i
$472$		0			0
$473$	3.00000	−	7.24264i	0.137940	−	0.333017i
$474$		0			0
$475$	−7.17157			−0.329054
$476$		0			0
$477$	−0.343146			−0.0157116
$478$		0			0
$479$	−9.51472	+	22.9706i	−0.434739	+	1.04955i	0.543001	+	0.839732i	$0.317288\pi$
$479$	−9.51472	+	22.9706i	−0.434739	+	1.04955i	−0.977740	+	0.209820i	$0.932712\pi$
$480$		0			0
$481$	−1.65685	−	0.686292i	−0.0755461	−	0.0312922i
$482$		0			0
$483$	−8.00000	+	3.31371i	−0.364013	+	0.150779i
$484$		0			0
$485$	14.4853	+	14.4853i	0.657743	+	0.657743i
$486$		0			0
$487$	−8.48528	−	20.4853i	−0.384505	−	0.928277i	−0.991082	−	0.133252i	$-0.957458\pi$
$487$	−8.48528	−	20.4853i	−0.384505	−	0.928277i	0.606577	−	0.795024i	$-0.292542\pi$
$488$		0			0
$489$			42.0416i			1.90119i
$490$		0			0
$491$	−10.9289	+	10.9289i	−0.493216	+	0.493216i	−0.909318	−	0.416102i	$-0.863396\pi$
$491$	−10.9289	+	10.9289i	−0.493216	+	0.493216i	0.416102	+	0.909318i	$0.363396\pi$
$492$		0			0
$493$	0.928932	+	6.24264i	0.0418370	+	0.281154i
$494$		0			0
$495$	4.82843	−	4.82843i	0.217022	−	0.217022i
$496$		0			0
$497$		−	3.31371i		−	0.148640i
$498$		0			0
$499$	14.0919	+	34.0208i	0.630839	+	1.52298i	0.838569	+	0.544795i	$0.183392\pi$
$499$	14.0919	+	34.0208i	0.630839	+	1.52298i	−0.207730	+	0.978186i	$0.566608\pi$
$500$		0			0
$501$	−25.7990	−	25.7990i	−1.15261	−	1.15261i
$502$		0			0
$503$	−11.1716	+	4.62742i	−0.498116	+	0.206326i	−0.617574	−	0.786513i	$-0.711884\pi$
$503$	−11.1716	+	4.62742i	−0.498116	+	0.206326i	0.119458	+	0.992839i	$0.461884\pi$
$504$		0			0
$505$	−14.8284	−	6.14214i	−0.659856	−	0.273321i
$506$		0			0
$507$	8.70711	−	21.0208i	0.386696	−	0.933567i
$508$		0			0
$509$	16.6274			0.736997			0.368499	−	0.929628i	$-0.379872\pi$
$509$	16.6274			0.736997			0.368499	+	0.929628i	$0.379872\pi$
$510$		0			0
$511$	8.20101			0.362791
$512$		0			0
$513$	−1.51472	+	3.65685i	−0.0668765	+	0.161454i
$514$		0			0
$515$	42.6274	+	17.6569i	1.87839	+	0.778054i
$516$		0			0
$517$	−39.7990	+	16.4853i	−1.75036	+	0.725022i
$518$		0			0
$519$	7.65685	+	7.65685i	0.336099	+	0.336099i
$520$		0			0
$521$	13.4645	+	32.5061i	0.589889	+	1.42412i	0.883609	+	0.468226i	$0.155107\pi$
$521$	13.4645	+	32.5061i	0.589889	+	1.42412i	−0.293720	+	0.955892i	$0.594893\pi$
$522$		0			0
$523$		−	23.2132i		−	1.01504i	−0.861639	−	0.507521i	$-0.830562\pi$
$523$		−	23.2132i		−	1.01504i	0.861639	−	0.507521i	$-0.169438\pi$
$524$		0			0
$525$	−17.3137	+	17.3137i	−0.755632	+	0.755632i
$526$		0			0
$527$	−15.0711	+	2.24264i	−0.656506	+	0.0976910i
$528$		0			0
$529$	9.63604	−	9.63604i	0.418958	−	0.418958i
$530$		0			0
$531$			0.242641i			0.0105297i
$532$		0			0
$533$	−3.55635	−	8.58579i	−0.154043	−	0.371892i
$534$		0			0
$535$	30.4853	+	30.4853i	1.31799	+	1.31799i
$536$		0			0
$537$	44.0416	−	18.2426i	1.90054	−	0.787228i
$538$		0			0
$539$	19.1924	+	7.94975i	0.826675	+	0.342420i
$540$		0			0
$541$	7.79899	−	18.8284i	0.335305	−	0.809497i	−0.662849	−	0.748753i	$-0.730653\pi$
$541$	7.79899	−	18.8284i	0.335305	−	0.809497i	0.998153	−	0.0607439i	$-0.0193473\pi$
$542$		0			0
$543$	11.3137			0.485518
$544$		0			0
$545$	36.2843			1.55425
$546$		0			0
$547$	9.39340	−	22.6777i	0.401633	−	0.969627i	−0.585637	−	0.810573i	$-0.699156\pi$
$547$	9.39340	−	22.6777i	0.401633	−	0.969627i	0.987270	−	0.159054i	$-0.0508443\pi$
$548$		0			0
$549$	−2.82843	−	1.17157i	−0.120714	−	0.0500015i
$550$		0			0
$551$	1.17157	−	0.485281i	0.0499107	−	0.0206737i
$552$		0			0
$553$	−5.65685	−	5.65685i	−0.240554	−	0.240554i
$554$		0			0
$555$	5.65685	+	13.6569i	0.240120	+	0.579701i
$556$		0			0
$557$			41.1127i			1.74200i	0.491282	+	0.871000i	$0.336528\pi$
$557$			41.1127i			1.74200i	−0.491282	+	0.871000i	$0.663472\pi$
$558$		0			0
$559$	1.02944	−	1.02944i	0.0435406	−	0.0435406i
$560$		0			0
$561$	17.4853	+	29.1421i	0.738229	+	1.23038i
$562$		0			0
$563$	5.92893	−	5.92893i	0.249875	−	0.249875i	−0.571044	−	0.820919i	$-0.693462\pi$
$563$	5.92893	−	5.92893i	0.249875	−	0.249875i	0.820919	+	0.571044i	$0.193462\pi$
$564$		0			0
$565$			34.1421i			1.43637i
$566$		0			0
$567$	5.89949	+	14.2426i	0.247755	+	0.598135i
$568$		0			0
$569$	3.48528	+	3.48528i	0.146111	+	0.146111i	0.776378	−	0.630267i	$-0.217055\pi$
$569$	3.48528	+	3.48528i	0.146111	+	0.146111i	−0.630267	+	0.776378i	$0.717055\pi$
$570$		0			0
$571$	−2.22183	+	0.920310i	−0.0929805	+	0.0385138i	−0.428689	−	0.903452i	$-0.641024\pi$
$571$	−2.22183	+	0.920310i	−0.0929805	+	0.0385138i	0.335708	+	0.941966i	$0.391024\pi$
$572$		0			0
$573$	4.82843	+	2.00000i	0.201710	+	0.0835512i
$574$		0			0
$575$	−10.1421	+	24.4853i	−0.422956	+	1.02111i
$576$		0			0
$577$	−16.6274			−0.692208			−0.346104	−	0.938196i	$-0.612496\pi$
$577$	−16.6274			−0.692208			−0.346104	+	0.938196i	$0.612496\pi$
$578$		0			0
$579$	22.7279			0.944540
$580$		0			0
$581$	3.65685	−	8.82843i	0.151712	−	0.366265i
$582$		0			0
$583$	−3.41421	−	1.41421i	−0.141402	−	0.0585707i
$584$		0			0
$585$	1.17157	−	0.485281i	0.0484386	−	0.0200639i
$586$		0			0
$587$	2.14214	+	2.14214i	0.0884154	+	0.0884154i	0.749931	−	0.661516i	$-0.230087\pi$
$587$	2.14214	+	2.14214i	0.0884154	+	0.0884154i	−0.661516	+	0.749931i	$0.730087\pi$
$588$		0			0
$589$	1.17157	+	2.82843i	0.0482738	+	0.116543i
$590$		0			0
$591$			36.9706i			1.52077i
$592$		0			0
$593$	−3.00000	+	3.00000i	−0.123195	+	0.123195i	−0.766016	−	0.642821i	$-0.777764\pi$
$593$	−3.00000	+	3.00000i	−0.123195	+	0.123195i	0.642821	+	0.766016i	$0.277764\pi$
$594$		0			0
$595$	−12.0000	−	20.0000i	−0.491952	−	0.819920i
$596$		0			0
$597$	27.3137	−	27.3137i	1.11788	−	1.11788i
$598$		0			0
$599$			26.3431i			1.07635i	0.842833	+	0.538176i	$0.180886\pi$
$599$			26.3431i			1.07635i	−0.842833	+	0.538176i	$0.819114\pi$
$600$		0			0
$601$	−7.05025	−	17.0208i	−0.287586	−	0.694294i	0.712386	−	0.701788i	$-0.247615\pi$
$601$	−7.05025	−	17.0208i	−0.287586	−	0.694294i	−0.999972	+	0.00749419i	$0.997615\pi$
$602$		0			0
$603$	−2.17157	−	2.17157i	−0.0884333	−	0.0884333i
$604$		0			0
$605$	30.3848	−	12.5858i	1.23532	−	0.511685i
$606$		0			0
$607$	−9.07107	−	3.75736i	−0.368183	−	0.152507i	0.190918	−	0.981606i	$-0.438854\pi$
$607$	−9.07107	−	3.75736i	−0.368183	−	0.152507i	−0.559101	+	0.829100i	$0.688854\pi$
$608$		0			0
$609$	1.65685	−	4.00000i	0.0671391	−	0.162088i
$610$		0			0
$611$	−8.00000			−0.323645
$612$		0			0
$613$	37.7990			1.52669			0.763343	−	0.645993i	$-0.223556\pi$
$613$	37.7990			1.52669			0.763343	+	0.645993i	$0.223556\pi$
$614$		0			0
$615$	−29.3137	+	70.7696i	−1.18204	+	2.85370i
$616$		0			0
$617$	−16.7071	−	6.92031i	−0.672603	−	0.278601i	0.0201281	−	0.999797i	$-0.493593\pi$
$617$	−16.7071	−	6.92031i	−0.672603	−	0.278601i	−0.692731	+	0.721196i	$0.743593\pi$
$618$		0			0
$619$	−5.12132	+	2.12132i	−0.205843	+	0.0852631i	−0.483223	−	0.875497i	$-0.660534\pi$
$619$	−5.12132	+	2.12132i	−0.205843	+	0.0852631i	0.277380	+	0.960760i	$0.410534\pi$
$620$		0			0
$621$	10.3431	+	10.3431i	0.415056	+	0.415056i
$622$		0			0
$623$	−8.82843	−	21.3137i	−0.353703	−	0.853916i
$624$		0			0
$625$			6.65685i			0.266274i
$626$		0			0
$627$	4.82843	−	4.82843i	0.192829	−	0.192829i
$628$		0			0
$629$	−8.82843	+	1.31371i	−0.352012	+	0.0523810i
$630$		0			0
$631$	21.6569	−	21.6569i	0.862146	−	0.862146i	−0.129441	−	0.991587i	$-0.541318\pi$
$631$	21.6569	−	21.6569i	0.862146	−	0.862146i	0.991587	+	0.129441i	$0.0413184\pi$
$632$		0			0
$633$		−	0.242641i		−	0.00964410i
$634$		0			0
$635$	−18.3431	−	44.2843i	−0.727926	−	1.75737i
$636$		0			0
$637$	2.72792	+	2.72792i	0.108084	+	0.108084i
$638$		0			0
$639$	0.828427	−	0.343146i	0.0327721	−	0.0135746i
$640$		0			0
$641$	−13.4350	−	5.56497i	−0.530652	−	0.219803i	0.101237	−	0.994862i	$-0.467720\pi$
$641$	−13.4350	−	5.56497i	−0.530652	−	0.219803i	−0.631889	+	0.775059i	$0.717720\pi$
$642$		0			0
$643$	5.12132	−	12.3640i	0.201965	−	0.487587i	−0.790150	−	0.612913i	$-0.789998\pi$
$643$	5.12132	−	12.3640i	0.201965	−	0.487587i	0.992116	+	0.125326i	$0.0399976\pi$
$644$		0			0
$645$	−12.0000			−0.472500
$646$		0			0
$647$	−12.4853			−0.490847			−0.245424	−	0.969416i	$-0.578927\pi$
$647$	−12.4853			−0.490847			−0.245424	+	0.969416i	$0.578927\pi$
$648$		0			0
$649$	−1.00000	+	2.41421i	−0.0392534	+	0.0947662i
$650$		0			0
$651$	9.65685	+	4.00000i	0.378482	+	0.156772i
$652$		0			0
$653$	−23.8995	+	9.89949i	−0.935260	+	0.387397i	−0.797671	−	0.603092i	$-0.793935\pi$
$653$	−23.8995	+	9.89949i	−0.935260	+	0.387397i	−0.137588	+	0.990490i	$0.543935\pi$
$654$		0			0
$655$	0.343146	+	0.343146i	0.0134078	+	0.0134078i
$656$		0			0
$657$	0.849242	+	2.05025i	0.0331321	+	0.0799880i
$658$		0			0
$659$		−	39.3137i		−	1.53144i	−0.643171	−	0.765722i	$-0.722382\pi$
$659$		−	39.3137i		−	1.53144i	0.643171	−	0.765722i	$-0.277618\pi$
$660$		0			0
$661$	12.7279	−	12.7279i	0.495059	−	0.495059i	−0.414837	−	0.909896i	$-0.636161\pi$
$661$	12.7279	−	12.7279i	0.495059	−	0.495059i	0.909896	+	0.414837i	$0.136161\pi$
$662$		0			0
$663$	0.928932	+	6.24264i	0.0360767	+	0.242444i
$664$		0			0
$665$	−3.31371	+	3.31371i	−0.128500	+	0.128500i
$666$		0			0
$667$		−	4.68629i		−	0.181454i
$668$		0			0
$669$	−17.3137	−	41.7990i	−0.669387	−	1.61604i
$670$		0			0
$671$	−23.3137	−	23.3137i	−0.900016	−	0.900016i
$672$		0			0
$673$	0.949747	−	0.393398i	0.0366101	−	0.0151644i	−0.364303	−	0.931280i	$-0.618693\pi$
$673$	0.949747	−	0.393398i	0.0366101	−	0.0151644i	0.400913	+	0.916116i	$0.368693\pi$
$674$		0			0
$675$	38.2132	+	15.8284i	1.47083	+	0.609236i
$676$		0			0
$677$	−4.48528	+	10.8284i	−0.172383	+	0.416170i	−0.986333	−	0.164766i	$-0.947313\pi$
$677$	−4.48528	+	10.8284i	−0.172383	+	0.416170i	0.813949	+	0.580936i	$0.197313\pi$
$678$		0			0
$679$	8.48528			0.325635
$680$		0			0
$681$	−37.5563			−1.43916
$682$		0			0
$683$	4.15076	−	10.0208i	0.158824	−	0.383436i	−0.824356	−	0.566071i	$-0.808463\pi$
$683$	4.15076	−	10.0208i	0.158824	−	0.383436i	0.983181	+	0.182635i	$0.0584628\pi$
$684$		0			0
$685$	8.00000	+	3.31371i	0.305664	+	0.126610i
$686$		0			0
$687$	31.5563	−	13.0711i	1.20395	−	0.498692i
$688$		0			0
$689$	−0.485281	−	0.485281i	−0.0184877	−	0.0184877i
$690$		0			0
$691$	17.9914	+	43.4350i	0.684424	+	1.65235i	0.755723	+	0.654891i	$0.227286\pi$
$691$	17.9914	+	43.4350i	0.684424	+	1.65235i	−0.0712988	+	0.997455i	$0.522714\pi$
$692$		0			0
$693$		−	2.82843i		−	0.107443i
$694$		0			0
$695$	−4.82843	+	4.82843i	−0.183153	+	0.183153i
$696$		0			0
$697$	−37.1630	−	27.5355i	−1.40765	−	1.04298i
$698$		0			0
$699$	13.7279	−	13.7279i	0.519238	−	0.519238i
$700$		0			0
$701$			1.51472i			0.0572101i	0.999591	+	0.0286051i	$0.00910652\pi$
$701$			1.51472i			0.0572101i	−0.999591	+	0.0286051i	$0.990893\pi$
$702$		0			0
$703$	0.686292	+	1.65685i	0.0258840	+	0.0624894i
$704$		0			0
$705$	46.6274	+	46.6274i	1.75609	+	1.75609i
$706$		0			0
$707$	−6.14214	+	2.54416i	−0.230999	+	0.0956828i
$708$		0			0
$709$	−5.75736	−	2.38478i	−0.216222	−	0.0895622i	0.271943	−	0.962313i	$-0.412334\pi$
$709$	−5.75736	−	2.38478i	−0.216222	−	0.0895622i	−0.488165	+	0.872751i	$0.662334\pi$
$710$		0			0
$711$	0.828427	−	2.00000i	0.0310684	−	0.0750059i
$712$		0			0
$713$	11.3137			0.423702
$714$		0			0
$715$	13.6569			0.510737
$716$		0			0
$717$	−14.9706	+	36.1421i	−0.559086	+	1.34975i
$718$		0			0
$719$	−4.00000	−	1.65685i	−0.149175	−	0.0617902i	0.306847	−	0.951759i	$-0.400726\pi$
$719$	−4.00000	−	1.65685i	−0.149175	−	0.0617902i	−0.456022	+	0.889969i	$0.650726\pi$
$720$		0			0
$721$	17.6569	−	7.31371i	0.657576	−	0.272377i
$722$		0			0
$723$	−25.9706	−	25.9706i	−0.965856	−	0.965856i
$724$		0			0
$725$	−5.07107	−	12.2426i	−0.188335	−	0.454680i
$726$		0			0
$727$			32.2843i			1.19736i	0.800989	+	0.598679i	$0.204307\pi$
$727$			32.2843i			1.19736i	−0.800989	+	0.598679i	$0.795693\pi$
$728$		0			0
$729$	15.7782	−	15.7782i	0.584377	−	0.584377i
$730$		0			0
$731$	1.75736	−	7.02944i	0.0649983	−	0.259993i
$732$		0			0
$733$	−9.89949	+	9.89949i	−0.365646	+	0.365646i	−0.865887	−	0.500240i	$-0.833245\pi$
$733$	−9.89949	+	9.89949i	−0.365646	+	0.365646i	0.500240	+	0.865887i	$0.333245\pi$
$734$		0			0
$735$		−	31.7990i		−	1.17292i
$736$		0			0
$737$	−12.6569	−	30.5563i	−0.466221	−	1.12556i
$738$		0			0
$739$	0.485281	+	0.485281i	0.0178514	+	0.0178514i	0.715976	−	0.698125i	$-0.245982\pi$
$739$	0.485281	+	0.485281i	0.0178514	+	0.0178514i	−0.698125	+	0.715976i	$0.745982\pi$
$740$		0			0
$741$	1.17157	−	0.485281i	0.0430388	−	0.0178273i
$742$		0			0
$743$	−23.8995	−	9.89949i	−0.876787	−	0.363177i	−0.101537	−	0.994832i	$-0.532376\pi$
$743$	−23.8995	−	9.89949i	−0.876787	−	0.363177i	−0.775250	+	0.631654i	$0.782376\pi$
$744$		0			0
$745$	−22.1421	+	53.4558i	−0.811225	+	1.95847i
$746$		0			0
$747$	2.58579			0.0946090
$748$		0			0
$749$	17.8579			0.652512
$750$		0			0
$751$	−9.51472	+	22.9706i	−0.347197	+	0.838208i	0.649752	+	0.760147i	$0.274873\pi$
$751$	−9.51472	+	22.9706i	−0.347197	+	0.838208i	−0.996949	+	0.0780611i	$0.975127\pi$
$752$		0			0
$753$	31.9706	+	13.2426i	1.16507	+	0.482589i
$754$		0			0
$755$	−75.5980	+	31.3137i	−2.75129	+	1.13962i
$756$		0			0
$757$	−7.75736	−	7.75736i	−0.281946	−	0.281946i	0.551939	−	0.833885i	$-0.313888\pi$
$757$	−7.75736	−	7.75736i	−0.281946	−	0.281946i	−0.833885	+	0.551939i	$0.813888\pi$
$758$		0			0
$759$	−9.65685	−	23.3137i	−0.350522	−	0.846234i
$760$		0			0
$761$		−	53.2548i		−	1.93049i	−0.261354	−	0.965243i	$-0.584169\pi$
$761$		−	53.2548i		−	1.93049i	0.261354	−	0.965243i	$-0.415831\pi$
$762$		0			0
$763$	10.6274	−	10.6274i	0.384738	−	0.384738i
$764$		0			0
$765$	3.75736	−	5.07107i	0.135848	−	0.183345i
$766$		0			0
$767$	−0.343146	+	0.343146i	−0.0123903	+	0.0123903i
$768$		0			0
$769$		−	26.3431i		−	0.949958i	−0.879997	−	0.474979i	$-0.842456\pi$
$769$		−	26.3431i		−	0.949958i	0.879997	−	0.474979i	$-0.157544\pi$
$770$		0			0
$771$	−5.82843	−	14.0711i	−0.209906	−	0.506757i
$772$		0			0
$773$	2.58579	+	2.58579i	0.0930043	+	0.0930043i	0.752078	−	0.659074i	$-0.229052\pi$
$773$	2.58579	+	2.58579i	0.0930043	+	0.0930043i	−0.659074	+	0.752078i	$0.729052\pi$
$774$		0			0
$775$	29.5563	−	12.2426i	1.06170	−	0.439769i
$776$		0			0
$777$	5.65685	+	2.34315i	0.202939	+	0.0840599i
$778$		0			0
$779$	−3.55635	+	8.58579i	−0.127419	+	0.307618i
$780$		0			0
$781$	9.65685			0.345549
$782$		0			0
$783$	−7.31371			−0.261371
$784$		0			0
$785$	−18.8284	+	45.4558i	−0.672015	+	1.62239i
$786$		0			0
$787$	17.6066	+	7.29289i	0.627608	+	0.259964i	0.673736	−	0.738972i	$-0.264688\pi$
$787$	17.6066	+	7.29289i	0.627608	+	0.259964i	−0.0461286	+	0.998936i	$0.514688\pi$
$788$		0			0
$789$	−13.6569	+	5.65685i	−0.486197	+	0.201389i
$790$		0			0
$791$	10.0000	+	10.0000i	0.355559	+	0.355559i
$792$		0			0
$793$	−2.34315	−	5.65685i	−0.0832075	−	0.200881i
$794$		0			0
$795$			5.65685i			0.200628i
$796$		0			0
$797$	18.8701	−	18.8701i	0.668412	−	0.668412i	−0.288937	−	0.957348i	$-0.593302\pi$
$797$	18.8701	−	18.8701i	0.668412	−	0.668412i	0.957348	+	0.288937i	$0.0933017\pi$
$798$		0			0
$799$	−34.1421	+	20.4853i	−1.20786	+	0.724717i
$800$		0			0
$801$	4.41421	−	4.41421i	0.155969	−	0.155969i
$802$		0			0
$803$			23.8995i			0.843395i
$804$		0			0
$805$	6.62742	+	16.0000i	0.233586	+	0.563926i
$806$		0			0
$807$	−10.0000	−	10.0000i	−0.352017	−	0.352017i
$808$		0			0
$809$	−43.1630	+	17.8787i	−1.51753	+	0.628581i	−0.977095	−	0.212806i	$-0.931740\pi$
$809$	−43.1630	+	17.8787i	−1.51753	+	0.628581i	−0.540434	+	0.841386i	$0.681740\pi$
$810$		0			0
$811$	−45.5061	−	18.8492i	−1.59794	−	0.661886i	−0.606813	−	0.794844i	$-0.707553\pi$
$811$	−45.5061	−	18.8492i	−1.59794	−	0.661886i	−0.991122	+	0.132958i	$0.957553\pi$
$812$		0			0
$813$	10.4853	−	25.3137i	0.367735	−	0.887791i
$814$		0			0
$815$	84.0833			2.94531
$816$		0			0
$817$	−1.45584			−0.0509335
$818$		0			0
$819$	0.201010	−	0.485281i	0.00702386	−	0.0169571i
$820$		0			0
$821$	−0.343146	−	0.142136i	−0.0119759	−	0.00496057i	0.376687	−	0.926340i	$-0.377063\pi$
$821$	−0.343146	−	0.142136i	−0.0119759	−	0.00496057i	−0.388663	+	0.921380i	$0.627063\pi$
$822$		0			0
$823$	−40.2843	+	16.6863i	−1.40422	+	0.581648i	−0.950844	−	0.309671i	$-0.899781\pi$
$823$	−40.2843	+	16.6863i	−1.40422	+	0.581648i	−0.453378	+	0.891319i	$0.649781\pi$
$824$		0			0
$825$	−50.4558	−	50.4558i	−1.75665	−	1.75665i
$826$		0			0
$827$	9.15076	+	22.0919i	0.318203	+	0.768210i	0.999350	+	0.0360629i	$0.0114817\pi$
$827$	9.15076	+	22.0919i	0.318203	+	0.768210i	−0.681147	+	0.732147i	$0.738518\pi$
$828$		0			0
$829$			20.1421i			0.699565i	0.936831	+	0.349783i	$0.113745\pi$
$829$			20.1421i			0.699565i	−0.936831	+	0.349783i	$0.886255\pi$
$830$		0			0
$831$	30.9706	−	30.9706i	1.07436	−	1.07436i
$832$		0			0
$833$	18.6274	+	4.65685i	0.645402	+	0.161350i
$834$		0			0
$835$	−51.5980	+	51.5980i	−1.78562	+	1.78562i
$836$		0			0
$837$		−	17.6569i		−	0.610310i
$838$		0			0
$839$	−18.5269	−	44.7279i	−0.639620	−	1.54418i	−0.827187	−	0.561927i	$-0.810060\pi$
$839$	−18.5269	−	44.7279i	−0.639620	−	1.54418i	0.187566	−	0.982252i	$-0.439940\pi$
$840$		0			0
$841$	−18.8492	−	18.8492i	−0.649974	−	0.649974i
$842$		0			0
$843$	24.4853	−	10.1421i	0.843318	−	0.349314i
$844$		0			0
$845$	−42.0416	−	17.4142i	−1.44628	−	0.599067i
$846$		0			0
$847$	5.21320	−	12.5858i	0.179128	−	0.432453i
$848$		0			0
$849$	−2.10051			−0.0720891
$850$		0			0
$851$	6.62742			0.227185
$852$		0			0
$853$	−14.5269	+	35.0711i	−0.497392	+	1.20081i	0.453491	+	0.891261i	$0.350178\pi$
$853$	−14.5269	+	35.0711i	−0.497392	+	1.20081i	−0.950883	+	0.309550i	$0.899822\pi$
$854$		0			0
$855$	−1.17157	−	0.485281i	−0.0400669	−	0.0165963i
$856$		0			0
$857$	−37.1924	+	15.4056i	−1.27047	+	0.526245i	−0.913106	−	0.407721i	$-0.866324\pi$
$857$	−37.1924	+	15.4056i	−1.27047	+	0.526245i	−0.357361	+	0.933966i	$0.616324\pi$
$858$		0			0
$859$	−0.556349	−	0.556349i	−0.0189824	−	0.0189824i	0.697552	−	0.716534i	$-0.254273\pi$
$859$	−0.556349	−	0.556349i	−0.0189824	−	0.0189824i	−0.716534	+	0.697552i	$0.754273\pi$
$860$		0			0
$861$	12.1421	+	29.3137i	0.413803	+	0.999009i
$862$		0			0
$863$		−	0.970563i		−	0.0330383i	−0.999864	−	0.0165192i	$-0.994742\pi$
$863$		−	0.970563i		−	0.0330383i	0.999864	−	0.0165192i	$-0.00525845\pi$
$864$		0			0
$865$	15.3137	−	15.3137i	0.520682	−	0.520682i
$866$		0			0
$867$	19.9497	+	24.2635i	0.677529	+	0.824030i
$868$		0			0
$869$	16.4853	−	16.4853i	0.559225	−	0.559225i
$870$		0			0
$871$		−	6.14214i		−	0.208118i
$872$		0			0
$873$	0.878680	+	2.12132i	0.0297388	+	0.0717958i
$874$		0			0
$875$	14.6274	+	14.6274i	0.494497	+	0.494497i
$876$		0			0
$877$	9.89949	−	4.10051i	0.334282	−	0.138464i	−0.209228	−	0.977867i	$-0.567095\pi$
$877$	9.89949	−	4.10051i	0.334282	−	0.138464i	0.543510	+	0.839403i	$0.317095\pi$
$878$		0			0
$879$	−37.5563	−	15.5563i	−1.26674	−	0.524703i
$880$		0			0
$881$	−6.92031	+	16.7071i	−0.233151	+	0.562877i	−0.996545	−	0.0830568i	$-0.973532\pi$
$881$	−6.92031	+	16.7071i	−0.233151	+	0.562877i	0.763394	+	0.645934i	$0.223532\pi$
$882$		0			0
$883$	−34.5269			−1.16192			−0.580962	−	0.813931i	$-0.697323\pi$
$883$	−34.5269			−1.16192			−0.580962	+	0.813931i	$0.697323\pi$
$884$		0			0
$885$	4.00000			0.134459
$886$		0			0
$887$	0.970563	−	2.34315i	0.0325883	−	0.0786751i	−0.906748	−	0.421674i	$-0.861443\pi$
$887$	0.970563	−	2.34315i	0.0325883	−	0.0786751i	0.939336	+	0.342999i	$0.111443\pi$
$888$		0			0
$889$	−18.3431	−	7.59798i	−0.615209	−	0.254828i
$890$		0			0
$891$	−41.5061	+	17.1924i	−1.39051	+	0.575967i
$892$		0			0
$893$	5.65685	+	5.65685i	0.189299	+	0.189299i
$894$		0			0
$895$	−36.4853	−	88.0833i	−1.21957	−	2.94430i
$896$		0			0
$897$		−	4.68629i		−	0.156471i
$898$		0			0
$899$	−4.00000	+	4.00000i	−0.133407	+	0.133407i
$900$		0			0
$901$	−3.31371	−	0.828427i	−0.110396	−	0.0275989i
$902$		0			0
$903$	−3.51472	+	3.51472i	−0.116963	+	0.116963i
$904$		0			0
$905$		−	22.6274i		−	0.752161i
$906$		0			0
$907$	−5.60660	−	13.5355i	−0.186164	−	0.449440i	0.803051	−	0.595910i	$-0.203209\pi$
$907$	−5.60660	−	13.5355i	−0.186164	−	0.449440i	−0.989215	+	0.146470i	$0.953209\pi$
$908$		0			0
$909$	−1.27208	−	1.27208i	−0.0421922	−	0.0421922i
$910$		0			0
$911$	21.5563	−	8.92893i	0.714194	−	0.295829i	0.00415500	−	0.999991i	$-0.498677\pi$
$911$	21.5563	−	8.92893i	0.714194	−	0.295829i	0.710039	+	0.704163i	$0.248677\pi$
$912$		0			0
$913$	25.7279	+	10.6569i	0.851470	+	0.352690i
$914$		0			0
$915$	−19.3137	+	46.6274i	−0.638492	+	1.54145i
$916$		0			0
$917$	0.201010			0.00663794
$918$		0			0
$919$	2.34315			0.0772932			0.0386466	−	0.999253i	$-0.487695\pi$
$919$	2.34315			0.0772932			0.0386466	+	0.999253i	$0.487695\pi$
$920$		0			0
$921$	−4.48528	+	10.8284i	−0.147795	+	0.356809i
$922$		0			0
$923$	1.65685	+	0.686292i	0.0545360	+	0.0225896i
$924$		0			0
$925$	17.3137	−	7.17157i	0.569271	−	0.235800i
$926$		0			0
$927$	3.65685	+	3.65685i	0.120107	+	0.120107i
$928$		0			0
$929$	−3.53553	−	8.53553i	−0.115997	−	0.280042i	0.855209	−	0.518284i	$-0.173429\pi$
$929$	−3.53553	−	8.53553i	−0.115997	−	0.280042i	−0.971206	+	0.238242i	$0.923429\pi$
$930$		0			0
$931$		−	3.85786i		−	0.126436i
$932$		0			0
$933$	19.6569	−	19.6569i	0.643537	−	0.643537i
$934$		0			0
$935$	58.2843	−	34.9706i	1.90610	−	1.14366i
$936$		0			0
$937$	−3.75736	+	3.75736i	−0.122748	+	0.122748i	−0.765812	−	0.643064i	$-0.777663\pi$
$937$	−3.75736	+	3.75736i	−0.122748	+	0.122748i	0.643064	+	0.765812i	$0.277663\pi$
$938$		0			0
$939$		−	25.0711i		−	0.818163i
$940$		0			0
$941$	7.51472	+	18.1421i	0.244973	+	0.591417i	0.997763	−	0.0668433i	$-0.0212928\pi$
$941$	7.51472	+	18.1421i	0.244973	+	0.591417i	−0.752791	+	0.658260i	$0.771293\pi$
$942$		0			0
$943$	24.2843	+	24.2843i	0.790805	+	0.790805i
$944$		0			0
$945$	24.9706	−	10.3431i	0.812292	−	0.336463i
$946$		0			0
$947$	48.3345	+	20.0208i	1.57066	+	0.650589i	0.986900	−	0.161336i	$-0.0515803\pi$
$947$	48.3345	+	20.0208i	1.57066	+	0.650589i	0.583761	+	0.811925i	$0.301580\pi$
$948$		0			0
$949$	−1.69848	+	4.10051i	−0.0551352	+	0.133108i
$950$		0			0
$951$	40.9706			1.32856
$952$		0			0
$953$	−11.5563			−0.374347			−0.187173	−	0.982327i	$-0.559933\pi$
$953$	−11.5563			−0.374347			−0.187173	+	0.982327i	$0.559933\pi$
$954$		0			0
$955$	4.00000	−	9.65685i	0.129437	−	0.312488i
$956$		0			0
$957$	11.6569	+	4.82843i	0.376813	+	0.156081i
$958$		0			0
$959$	3.31371	−	1.37258i	0.107005	−	0.0443230i
$960$		0			0
$961$	12.2635	+	12.2635i	0.395595	+	0.395595i
$962$		0			0
$963$	1.84924	+	4.46447i	0.0595910	+	0.143865i
$964$		0			0
$965$		−	45.4558i		−	1.46328i
$966$		0			0
$967$	−9.65685	+	9.65685i	−0.310543	+	0.310543i	−0.845120	−	0.534577i	$-0.820471\pi$
$967$	−9.65685	+	9.65685i	−0.310543	+	0.310543i	0.534577	+	0.845120i	$0.320471\pi$
$968$		0			0
$969$	3.75736	−	5.07107i	0.120704	−	0.162906i
$970$		0			0
$971$	−15.0416	+	15.0416i	−0.482709	+	0.482709i	−0.905996	−	0.423287i	$-0.860876\pi$
$971$	−15.0416	+	15.0416i	−0.482709	+	0.482709i	0.423287	+	0.905996i	$0.360876\pi$
$972$		0			0
$973$			2.82843i			0.0906752i
$974$		0			0
$975$	−5.07107	−	12.2426i	−0.162404	−	0.392078i
$976$		0			0
$977$	20.1127	+	20.1127i	0.643462	+	0.643462i	0.951405	−	0.307943i	$-0.0996405\pi$
$977$	20.1127	+	20.1127i	0.643462	+	0.643462i	−0.307943	+	0.951405i	$0.599641\pi$
$978$		0			0
$979$	62.1127	−	25.7279i	1.98513	−	0.822268i
$980$		0			0
$981$	3.75736	+	1.55635i	0.119963	+	0.0496904i
$982$		0			0
$983$	−10.3431	+	24.9706i	−0.329895	+	0.796437i	0.668704	+	0.743529i	$0.266849\pi$
$983$	−10.3431	+	24.9706i	−0.329895	+	0.796437i	−0.998599	+	0.0529088i	$0.983151\pi$
$984$		0			0
$985$	73.9411			2.35596
$986$		0			0
$987$	27.3137			0.869405
$988$		0			0
$989$	−2.05887	+	4.97056i	−0.0654684	+	0.158055i
$990$		0			0
$991$	42.2843	+	17.5147i	1.34320	+	0.556373i	0.934392	−	0.356245i	$-0.115943\pi$
$991$	42.2843	+	17.5147i	1.34320	+	0.556373i	0.408812	+	0.912619i	$0.365943\pi$
$992$		0			0
$993$	−47.2843	+	19.5858i	−1.50052	+	0.621536i
$994$		0			0
$995$	−54.6274	−	54.6274i	−1.73181	−	1.73181i
$996$		0			0
$997$	−4.54416	−	10.9706i	−0.143915	−	0.347441i	0.835442	−	0.549578i	$-0.185211\pi$
$997$	−4.54416	−	10.9706i	−0.143915	−	0.347441i	−0.979357	+	0.202137i	$0.935211\pi$
$998$		0			0
$999$		−	10.3431i		−	0.327243i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	272.2.v.b.161.1		4
4.3	odd	2		34.2.d.a.25.1	yes	4
12.11	even	2		306.2.l.c.127.1		4
17.7	odd	16		4624.2.a.bn.1.1		4
17.10	odd	16		4624.2.a.bn.1.4		4
17.15	even	8	inner	272.2.v.b.49.1		4
20.3	even	4		850.2.o.a.399.1		4
20.7	even	4		850.2.o.b.399.1		4
20.19	odd	2		850.2.l.a.501.1		4
68.3	even	16		578.2.c.f.327.1		8
68.7	even	16		578.2.a.i.1.4		4
68.11	even	16		578.2.b.d.577.1		4
68.15	odd	8		34.2.d.a.15.1	✓	4
68.19	odd	8		578.2.d.b.423.1		4
68.23	even	16		578.2.b.d.577.4		4
68.27	even	16		578.2.a.i.1.1		4
68.31	even	16		578.2.c.f.327.4		8
68.39	even	16		578.2.c.f.251.1		8
68.43	odd	8		578.2.d.a.155.1		4
68.47	odd	4		578.2.d.a.179.1		4
68.55	odd	4		578.2.d.c.179.1		4
68.59	odd	8		578.2.d.c.155.1		4
68.63	even	16		578.2.c.f.251.4		8
68.67	odd	2		578.2.d.b.399.1		4
204.83	even	8		306.2.l.c.253.1		4
204.95	odd	16		5202.2.a.bw.1.4		4
204.143	odd	16		5202.2.a.bw.1.1		4
340.83	even	8		850.2.o.b.49.1		4
340.219	odd	8		850.2.l.a.151.1		4
340.287	even	8		850.2.o.a.49.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
34.2.d.a.15.1	✓	4	68.15	odd	8
34.2.d.a.25.1	yes	4	4.3	odd	2
272.2.v.b.49.1		4	17.15	even	8	inner
272.2.v.b.161.1		4	1.1	even	1	trivial
306.2.l.c.127.1		4	12.11	even	2
306.2.l.c.253.1		4	204.83	even	8
578.2.a.i.1.1		4	68.27	even	16
578.2.a.i.1.4		4	68.7	even	16
578.2.b.d.577.1		4	68.11	even	16
578.2.b.d.577.4		4	68.23	even	16
578.2.c.f.251.1		8	68.39	even	16
578.2.c.f.251.4		8	68.63	even	16
578.2.c.f.327.1		8	68.3	even	16
578.2.c.f.327.4		8	68.31	even	16
578.2.d.a.155.1		4	68.43	odd	8
578.2.d.a.179.1		4	68.47	odd	4
578.2.d.b.399.1		4	68.67	odd	2
578.2.d.b.423.1		4	68.19	odd	8
578.2.d.c.155.1		4	68.59	odd	8
578.2.d.c.179.1		4	68.55	odd	4
850.2.l.a.151.1		4	340.219	odd	8
850.2.l.a.501.1		4	20.19	odd	2
850.2.o.a.49.1		4	340.287	even	8
850.2.o.a.399.1		4	20.3	even	4
850.2.o.b.49.1		4	340.83	even	8
850.2.o.b.399.1		4	20.7	even	4
4624.2.a.bn.1.1		4	17.7	odd	16
4624.2.a.bn.1.4		4	17.10	odd	16
5202.2.a.bw.1.1		4	204.143	odd	16
5202.2.a.bw.1.4		4	204.95	odd	16

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:	\( N \)	\(=\)	\( 272 = 2^{4} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	272.v (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 1.70711i) q^{3} +(-3.41421 - 1.41421i) q^{5} +(-1.41421 + 0.585786i) q^{7} +(-0.292893 - 0.292893i) q^{9} +(-1.70711 - 4.12132i) q^{11} -0.828427i q^{13} +(-4.82843 + 4.82843i) q^{15} +(-2.12132 - 3.53553i) q^{17} +(-0.585786 + 0.585786i) q^{19} +2.82843i q^{21} +(1.17157 + 2.82843i) q^{23} +(6.12132 + 6.12132i) q^{25} +(4.41421 - 1.82843i) q^{27} +(-1.41421 - 0.585786i) q^{29} +(1.41421 - 3.41421i) q^{31} -8.24264 q^{33} +5.65685 q^{35} +(0.828427 - 2.00000i) q^{37} +(-1.41421 - 0.585786i) q^{39} +(10.3640 - 4.29289i) q^{41} +(1.24264 + 1.24264i) q^{43} +(0.585786 + 1.41421i) q^{45} -9.65685i q^{47} +(-3.29289 + 3.29289i) q^{49} +(-7.53553 + 1.12132i) q^{51} +(0.585786 - 0.585786i) q^{53} +16.4853i q^{55} +(0.585786 + 1.41421i) q^{57} +(-0.414214 - 0.414214i) q^{59} +(6.82843 - 2.82843i) q^{61} +(0.585786 + 0.242641i) q^{63} +(-1.17157 + 2.82843i) q^{65} +7.41421 q^{67} +5.65685 q^{69} +(-0.828427 + 2.00000i) q^{71} +(-4.94975 - 2.05025i) q^{73} +(14.7782 - 6.12132i) q^{75} +(4.82843 + 4.82843i) q^{77} +(2.00000 + 4.82843i) q^{79} -10.0711i q^{81} +(-4.41421 + 4.41421i) q^{83} +(2.24264 + 15.0711i) q^{85} +(-2.00000 + 2.00000i) q^{87} +15.0711i q^{89} +(0.485281 + 1.17157i) q^{91} +(-4.82843 - 4.82843i) q^{93} +(2.82843 - 1.17157i) q^{95} +(-5.12132 - 2.12132i) q^{97} +(-0.707107 + 1.70711i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 8 q^{5} - 4 q^{9} - 4 q^{11} - 8 q^{15} - 8 q^{19} + 16 q^{23} + 16 q^{25} + 12 q^{27} - 16 q^{33} - 8 q^{37} + 16 q^{41} - 12 q^{43} + 8 q^{45} - 16 q^{49} - 16 q^{51} + 8 q^{53} + 8 q^{57} + 4 q^{59}+ \cdots - 12 q^{97}+O(q^{100}) \) 4 * q - 8 * q^5 - 4 * q^9 - 4 * q^11 - 8 * q^15 - 8 * q^19 + 16 * q^23 + 16 * q^25 + 12 * q^27 - 16 * q^33 - 8 * q^37 + 16 * q^41 - 12 * q^43 + 8 * q^45 - 16 * q^49 - 16 * q^51 + 8 * q^53 + 8 * q^57 + 4 * q^59 + 16 * q^61 + 8 * q^63 - 16 * q^65 + 24 * q^67 + 8 * q^71 + 28 * q^75 + 8 * q^77 + 8 * q^79 - 12 * q^83 - 8 * q^85 - 8 * q^87 - 32 * q^91 - 8 * q^93 - 12 * q^97

Introduction

L-functions

Modular forms

Varieties

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Database

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