LMFDB - Embedded newform 640.2.s.c.223.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [640,2,Mod(223,640)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(640, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("640.223");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 640 = 2^{7} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	640.s (of order $4$, degree $2$, 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:	$5.11042572936$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 2 x^{16} - 4 x^{15} - 5 x^{14} - 14 x^{13} - 10 x^{12} + 6 x^{11} + 37 x^{10} + 70 x^{9} + \cdots + 512 $ x^18 + 2x^16 - 4x^15 - 5x^14 - 14x^13 - 10x^12 + 6x^11 + 37x^10 + 70x^9 + 74x^8 + 24x^7 - 80x^6 - 224x^5 - 160x^4 - 256x^3 + 256*x^2 + 512
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{13} $
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			223.8
Root			$1.41303 + 0.0578659i$ of defining polynomial
Character	$\chi$	$=$	640.223
Dual form			640.2.s.c.287.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.96251 q^{3} +(1.42182 - 1.72581i) q^{5} +(1.60205 - 1.60205i) q^{7} +0.851447 q^{9} +O(q^{10})$	\(q+1.96251 q^{3} +(1.42182 - 1.72581i) q^{5} +(1.60205 - 1.60205i) q^{7} +0.851447 q^{9} +(0.754587 + 0.754587i) q^{11} +5.94580i q^{13} +(2.79034 - 3.38692i) q^{15} +(1.95574 - 1.95574i) q^{17} +(0.780680 + 0.780680i) q^{19} +(3.14404 - 3.14404i) q^{21} +(-4.93121 - 4.93121i) q^{23} +(-0.956833 - 4.90759i) q^{25} -4.21656 q^{27} +(1.44802 - 1.44802i) q^{29} -3.60859i q^{31} +(1.48089 + 1.48089i) q^{33} +(-0.486998 - 5.04266i) q^{35} +10.2364i q^{37} +11.6687i q^{39} +6.93334i q^{41} -9.91344i q^{43} +(1.21061 - 1.46944i) q^{45} +(-0.104270 - 0.104270i) q^{47} +1.86688i q^{49} +(3.83816 - 3.83816i) q^{51} +4.03213 q^{53} +(2.37516 - 0.229383i) q^{55} +(1.53209 + 1.53209i) q^{57} +(-3.46736 + 3.46736i) q^{59} +(-0.680578 - 0.680578i) q^{61} +(1.36406 - 1.36406i) q^{63} +(10.2613 + 8.45388i) q^{65} +9.04721i q^{67} +(-9.67754 - 9.67754i) q^{69} +3.64007 q^{71} +(-2.94030 + 2.94030i) q^{73} +(-1.87779 - 9.63120i) q^{75} +2.41777 q^{77} -10.7140 q^{79} -10.8294 q^{81} -4.23845 q^{83} +(-0.594515 - 6.15595i) q^{85} +(2.84176 - 2.84176i) q^{87} +0.0426256 q^{89} +(9.52546 + 9.52546i) q^{91} -7.08189i q^{93} +(2.45730 - 0.237315i) q^{95} +(-1.91173 + 1.91173i) q^{97} +(0.642491 + 0.642491i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 2 q^{5} - 2 q^{7} + 10 q^{9}+O(q^{10}) $ 18 * q - 2 * q^5 - 2 * q^7 + 10 * q^9	$ 18 q - 2 q^{5} - 2 q^{7} + 10 q^{9} - 2 q^{11} + 20 q^{15} - 6 q^{17} - 2 q^{19} + 16 q^{21} + 2 q^{23} - 6 q^{25} - 24 q^{27} - 14 q^{29} - 8 q^{33} + 2 q^{35} + 14 q^{45} - 38 q^{47} + 8 q^{51} - 12 q^{53} + 6 q^{55} - 24 q^{57} + 10 q^{59} - 14 q^{61} + 6 q^{63} + 32 q^{69} - 24 q^{71} - 14 q^{73} + 16 q^{75} + 44 q^{77} + 16 q^{79} + 2 q^{81} + 40 q^{83} - 14 q^{85} - 24 q^{87} + 12 q^{89} - 34 q^{95} + 18 q^{97} + 22 q^{99}+O(q^{100}) $ 18 * q - 2 * q^5 - 2 * q^7 + 10 * q^9 - 2 * q^11 + 20 * q^15 - 6 * q^17 - 2 * q^19 + 16 * q^21 + 2 * q^23 - 6 * q^25 - 24 * q^27 - 14 * q^29 - 8 * q^33 + 2 * q^35 + 14 * q^45 - 38 * q^47 + 8 * q^51 - 12 * q^53 + 6 * q^55 - 24 * q^57 + 10 * q^59 - 14 * q^61 + 6 * q^63 + 32 * q^69 - 24 * q^71 - 14 * q^73 + 16 * q^75 + 44 * q^77 + 16 * q^79 + 2 * q^81 + 40 * q^83 - 14 * q^85 - 24 * q^87 + 12 * q^89 - 34 * q^95 + 18 * q^97 + 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/640\mathbb{Z}\right)^\times$.

$n$	$257$	$261$	$511$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$		0			0
$2$		0			0
$3$	1.96251			1.13306			0.566528	−	0.824043i	$-0.308286\pi$
$3$	1.96251			1.13306			0.566528	+	0.824043i	$0.308286\pi$
$4$		0			0
$5$	1.42182	−	1.72581i	0.635859	−	0.771805i
$5$	1.42182	−	1.72581i	0.635859	−	0.771805i
$6$		0			0
$7$	1.60205	−	1.60205i	0.605517	−	0.605517i	−0.336254	−	0.941771i	$-0.609160\pi$
$7$	1.60205	−	1.60205i	0.605517	−	0.605517i	0.941771	+	0.336254i	$0.109160\pi$
$8$		0			0
$9$	0.851447			0.283816
$10$		0			0
$11$	0.754587	+	0.754587i	0.227517	+	0.227517i	0.811654	−	0.584138i	$-0.198567\pi$
$11$	0.754587	+	0.754587i	0.227517	+	0.227517i	−0.584138	+	0.811654i	$0.698567\pi$
$12$		0			0
$13$			5.94580i			1.64907i	0.565812	+	0.824534i	$0.308563\pi$
$13$			5.94580i			1.64907i	−0.565812	+	0.824534i	$0.691437\pi$
$14$		0			0
$15$	2.79034	−	3.38692i	0.720464	−	0.874498i
$16$		0			0
$17$	1.95574	−	1.95574i	0.474336	−	0.474336i	−0.428978	−	0.903315i	$-0.641126\pi$
$17$	1.95574	−	1.95574i	0.474336	−	0.474336i	0.903315	+	0.428978i	$0.141126\pi$
$18$		0			0
$19$	0.780680	+	0.780680i	0.179100	+	0.179100i	0.790964	−	0.611863i	$-0.209580\pi$
$19$	0.780680	+	0.780680i	0.179100	+	0.179100i	−0.611863	+	0.790964i	$0.709580\pi$
$20$		0			0
$21$	3.14404	−	3.14404i	0.686085	−	0.686085i
$22$		0			0
$23$	−4.93121	−	4.93121i	−1.02823	−	1.02823i	−0.999590	−	0.0286378i	$-0.990883\pi$
$23$	−4.93121	−	4.93121i	−1.02823	−	1.02823i	−0.0286378	−	0.999590i	$-0.509117\pi$
$24$		0			0
$25$	−0.956833	−	4.90759i	−0.191367	−	0.981519i
$26$		0			0
$27$	−4.21656			−0.811477
$28$		0			0
$29$	1.44802	−	1.44802i	0.268891	−	0.268891i	−0.559762	−	0.828653i	$-0.689108\pi$
$29$	1.44802	−	1.44802i	0.268891	−	0.268891i	0.828653	+	0.559762i	$0.189108\pi$
$30$		0			0
$31$		−	3.60859i		−	0.648121i	−0.946036	−	0.324061i	$-0.894952\pi$
$31$		−	3.60859i		−	0.648121i	0.946036	−	0.324061i	$-0.105048\pi$
$32$		0			0
$33$	1.48089	+	1.48089i	0.257789	+	0.257789i
$34$		0			0
$35$	−0.486998	−	5.04266i	−0.0823177	−	0.852365i
$36$		0			0
$37$			10.2364i			1.68285i	0.540371	+	0.841427i	$0.318284\pi$
$37$			10.2364i			1.68285i	−0.540371	+	0.841427i	$0.681716\pi$
$38$		0			0
$39$			11.6687i			1.86849i
$40$		0			0
$41$			6.93334i			1.08281i	0.840763	+	0.541403i	$0.182107\pi$
$41$			6.93334i			1.08281i	−0.840763	+	0.541403i	$0.817893\pi$
$42$		0			0
$43$		−	9.91344i		−	1.51179i	−0.654695	−	0.755893i	$-0.727203\pi$
$43$		−	9.91344i		−	1.51179i	0.654695	−	0.755893i	$-0.272797\pi$
$44$		0			0
$45$	1.21061	−	1.46944i	0.180467	−	0.219050i
$46$		0			0
$47$	−0.104270	−	0.104270i	−0.0152093	−	0.0152093i	0.699461	−	0.714671i	$-0.253423\pi$
$47$	−0.104270	−	0.104270i	−0.0152093	−	0.0152093i	−0.714671	+	0.699461i	$0.753423\pi$
$48$		0			0
$49$			1.86688i			0.266698i
$50$		0			0
$51$	3.83816	−	3.83816i	0.537450	−	0.537450i
$52$		0			0
$53$	4.03213			0.553856			0.276928	−	0.960891i	$-0.410684\pi$
$53$	4.03213			0.553856			0.276928	+	0.960891i	$0.410684\pi$
$54$		0			0
$55$	2.37516	−	0.229383i	0.320267	−	0.0309300i
$56$		0			0
$57$	1.53209	+	1.53209i	0.202931	+	0.202931i
$58$		0			0
$59$	−3.46736	+	3.46736i	−0.451412	+	0.451412i	−0.895823	−	0.444411i	$-0.853413\pi$
$59$	−3.46736	+	3.46736i	−0.451412	+	0.451412i	0.444411	+	0.895823i	$0.353413\pi$
$60$		0			0
$61$	−0.680578	−	0.680578i	−0.0871391	−	0.0871391i	0.662194	−	0.749333i	$-0.269626\pi$
$61$	−0.680578	−	0.680578i	−0.0871391	−	0.0871391i	−0.749333	+	0.662194i	$0.769626\pi$
$62$		0			0
$63$	1.36406	−	1.36406i	0.171855	−	0.171855i
$64$		0			0
$65$	10.2613	+	8.45388i	1.27276	+	1.04857i
$66$		0			0
$67$			9.04721i			1.10529i	0.833416	+	0.552646i	$0.186382\pi$
$67$			9.04721i			1.10529i	−0.833416	+	0.552646i	$0.813618\pi$
$68$		0			0
$69$	−9.67754	−	9.67754i	−1.16504	−	1.16504i
$70$		0			0
$71$	3.64007			0.431997			0.215998	−	0.976394i	$-0.430699\pi$
$71$	3.64007			0.431997			0.215998	+	0.976394i	$0.430699\pi$
$72$		0			0
$73$	−2.94030	+	2.94030i	−0.344136	+	0.344136i	−0.857920	−	0.513784i	$-0.828243\pi$
$73$	−2.94030	+	2.94030i	−0.344136	+	0.344136i	0.513784	+	0.857920i	$0.328243\pi$
$74$		0			0
$75$	−1.87779	−	9.63120i	−0.216829	−	1.11212i
$76$		0			0
$77$	2.41777			0.275530
$78$		0			0
$79$	−10.7140			−1.20542			−0.602711	−	0.797960i	$-0.705913\pi$
$79$	−10.7140			−1.20542			−0.602711	+	0.797960i	$0.705913\pi$
$80$		0			0
$81$	−10.8294			−1.20326
$82$		0			0
$83$	−4.23845			−0.465230			−0.232615	−	0.972569i	$-0.574728\pi$
$83$	−4.23845			−0.465230			−0.232615	+	0.972569i	$0.574728\pi$
$84$		0			0
$85$	−0.594515	−	6.15595i	−0.0644842	−	0.667707i
$86$		0			0
$87$	2.84176	−	2.84176i	0.304668	−	0.304668i
$88$		0			0
$89$	0.0426256			0.00451831			0.00225915	−	0.999997i	$-0.499281\pi$
$89$	0.0426256			0.00451831			0.00225915	+	0.999997i	$0.499281\pi$
$90$		0			0
$91$	9.52546	+	9.52546i	0.998539	+	0.998539i
$92$		0			0
$93$		−	7.08189i		−	0.734358i
$94$		0			0
$95$	2.45730	−	0.237315i	0.252113	−	0.0243480i
$96$		0			0
$97$	−1.91173	+	1.91173i	−0.194106	+	0.194106i	−0.797468	−	0.603362i	$-0.793828\pi$
$97$	−1.91173	+	1.91173i	−0.194106	+	0.194106i	0.603362	+	0.797468i	$0.293828\pi$
$98$		0			0
$99$	0.642491	+	0.642491i	0.0645728	+	0.0645728i
$100$		0			0
$101$	−4.96537	+	4.96537i	−0.494073	+	0.494073i	−0.909587	−	0.415514i	$-0.863602\pi$
$101$	−4.96537	+	4.96537i	−0.494073	+	0.494073i	0.415514	+	0.909587i	$0.363602\pi$
$102$		0			0
$103$	−0.442220	−	0.442220i	−0.0435733	−	0.0435733i	0.684984	−	0.728558i	$-0.259809\pi$
$103$	−0.442220	−	0.442220i	−0.0435733	−	0.0435733i	−0.728558	+	0.684984i	$0.759809\pi$
$104$		0			0
$105$	−0.955739	−	9.89627i	−0.0932706	−	0.965777i
$106$		0			0
$107$	17.5924			1.70072			0.850359	−	0.526204i	$-0.176385\pi$
$107$	17.5924			1.70072			0.850359	+	0.526204i	$0.176385\pi$
$108$		0			0
$109$	−0.345161	+	0.345161i	−0.0330605	+	0.0330605i	−0.723444	−	0.690383i	$-0.757442\pi$
$109$	−0.345161	+	0.345161i	−0.0330605	+	0.0330605i	0.690383	+	0.723444i	$0.257442\pi$
$110$		0			0
$111$			20.0890i			1.90677i
$112$		0			0
$113$	−5.43662	−	5.43662i	−0.511435	−	0.511435i	0.403531	−	0.914966i	$-0.367783\pi$
$113$	−5.43662	−	5.43662i	−0.511435	−	0.511435i	−0.914966	+	0.403531i	$0.867783\pi$
$114$		0			0
$115$	−15.5216	+	1.49901i	−1.44740	+	0.139784i
$116$		0			0
$117$			5.06253i			0.468031i
$118$		0			0
$119$		−	6.26638i		−	0.574438i
$120$		0			0
$121$		−	9.86120i		−	0.896472i
$122$		0			0
$123$			13.6067i			1.22688i
$124$		0			0
$125$	−9.83002	−	5.32642i	−0.879223	−	0.476410i
$126$		0			0
$127$	6.27150	+	6.27150i	0.556505	+	0.556505i	0.928311	−	0.371805i	$-0.121261\pi$
$127$	6.27150	+	6.27150i	0.556505	+	0.556505i	−0.371805	+	0.928311i	$0.621261\pi$
$128$		0			0
$129$		−	19.4552i		−	1.71294i
$130$		0			0
$131$	1.61521	−	1.61521i	0.141122	−	0.141122i	−0.633017	−	0.774138i	$-0.718184\pi$
$131$	1.61521	−	1.61521i	0.141122	−	0.141122i	0.774138	+	0.633017i	$0.218184\pi$
$132$		0			0
$133$	2.50138			0.216897
$134$		0			0
$135$	−5.99520	+	7.27697i	−0.515985	+	0.626302i
$136$		0			0
$137$	6.83585	+	6.83585i	0.584026	+	0.584026i	0.936007	−	0.351981i	$-0.114492\pi$
$137$	6.83585	+	6.83585i	0.584026	+	0.584026i	−0.351981	+	0.936007i	$0.614492\pi$
$138$		0			0
$139$	−13.7427	+	13.7427i	−1.16564	+	1.16564i	−0.182423	+	0.983220i	$0.558394\pi$
$139$	−13.7427	+	13.7427i	−1.16564	+	1.16564i	−0.983220	+	0.182423i	$0.941606\pi$
$140$		0			0
$141$	−0.204631	−	0.204631i	−0.0172330	−	0.0172330i
$142$		0			0
$143$	−4.48662	+	4.48662i	−0.375190	+	0.375190i
$144$		0			0
$145$	−0.440176	−	4.55784i	−0.0365547	−	0.378508i
$146$		0			0
$147$			3.66378i			0.302184i
$148$		0			0
$149$	1.73811	+	1.73811i	0.142391	+	0.142391i	0.774709	−	0.632318i	$-0.217896\pi$
$149$	1.73811	+	1.73811i	0.142391	+	0.142391i	−0.632318	+	0.774709i	$0.717896\pi$
$150$		0			0
$151$	−5.83522			−0.474864			−0.237432	−	0.971404i	$-0.576306\pi$
$151$	−5.83522			−0.474864			−0.237432	+	0.971404i	$0.576306\pi$
$152$		0			0
$153$	1.66521	−	1.66521i	0.134624	−	0.134624i
$154$		0			0
$155$	−6.22773	−	5.13078i	−0.500223	−	0.412114i
$156$		0			0
$157$	−3.14732			−0.251183			−0.125592	−	0.992082i	$-0.540083\pi$
$157$	−3.14732			−0.251183			−0.125592	+	0.992082i	$0.540083\pi$
$158$		0			0
$159$	7.91310			0.627550
$160$		0			0
$161$	−15.8001			−1.24522
$162$		0			0
$163$	7.82117			0.612601			0.306301	−	0.951935i	$-0.400909\pi$
$163$	7.82117			0.612601			0.306301	+	0.951935i	$0.400909\pi$
$164$		0			0
$165$	4.66128	−	0.450167i	0.362880	−	0.0350454i
$166$		0			0
$167$	9.88460	−	9.88460i	0.764893	−	0.764893i	−0.212309	−	0.977203i	$-0.568098\pi$
$167$	9.88460	−	9.88460i	0.764893	−	0.764893i	0.977203	+	0.212309i	$0.0680985\pi$
$168$		0			0
$169$	−22.3525			−1.71942
$170$		0			0
$171$	0.664708	+	0.664708i	0.0508315	+	0.0508315i
$172$		0			0
$173$		−	3.49245i		−	0.265526i	−0.991148	−	0.132763i	$-0.957615\pi$
$173$		−	3.49245i		−	0.265526i	0.991148	−	0.132763i	$-0.0423849\pi$
$174$		0			0
$175$	−9.39509	−	6.32931i	−0.710202	−	0.478451i
$176$		0			0
$177$	−6.80473	+	6.80473i	−0.511475	+	0.511475i
$178$		0			0
$179$	−13.0809	−	13.0809i	−0.977713	−	0.977713i	0.0220444	−	0.999757i	$-0.492982\pi$
$179$	−13.0809	−	13.0809i	−0.977713	−	0.977713i	−0.999757	+	0.0220444i	$0.992982\pi$
$180$		0			0
$181$	−13.6393	+	13.6393i	−1.01380	+	1.01380i	−0.0138952	+	0.999903i	$0.504423\pi$
$181$	−13.6393	+	13.6393i	−1.01380	+	1.01380i	−0.999903	+	0.0138952i	$0.995577\pi$
$182$		0			0
$183$	−1.33564	−	1.33564i	−0.0987335	−	0.0987335i
$184$		0			0
$185$	17.6661	+	14.5544i	1.29884	+	1.07006i
$186$		0			0
$187$	2.95155			0.215839
$188$		0			0
$189$	−6.75513	+	6.75513i	−0.491363	+	0.491363i
$190$		0			0
$191$			2.92523i			0.211662i	0.994384	+	0.105831i	$0.0337503\pi$
$191$			2.92523i			0.211662i	−0.994384	+	0.105831i	$0.966250\pi$
$192$		0			0
$193$	0.0830702	+	0.0830702i	0.00597953	+	0.00597953i	0.710090	−	0.704111i	$-0.248654\pi$
$193$	0.0830702	+	0.0830702i	0.00597953	+	0.00597953i	−0.704111	+	0.710090i	$0.748654\pi$
$194$		0			0
$195$	20.1379	+	16.5908i	1.44211	+	1.18809i
$196$		0			0
$197$			7.80487i			0.556074i	0.960570	+	0.278037i	$0.0896838\pi$
$197$			7.80487i			0.556074i	−0.960570	+	0.278037i	$0.910316\pi$
$198$		0			0
$199$			10.9740i			0.777924i	0.921254	+	0.388962i	$0.127166\pi$
$199$			10.9740i			0.777924i	−0.921254	+	0.388962i	$0.872834\pi$
$200$		0			0
$201$			17.7552i			1.25236i
$202$		0			0
$203$		−	4.63960i		−	0.325636i
$204$		0			0
$205$	11.9656	+	9.85799i	0.835715	+	0.688512i
$206$		0			0
$207$	−4.19866	−	4.19866i	−0.291827	−	0.291827i
$208$		0			0
$209$			1.17818i			0.0814966i
$210$		0			0
$211$	−8.92204	+	8.92204i	−0.614218	+	0.614218i	−0.944042	−	0.329824i	$-0.893011\pi$
$211$	−8.92204	+	8.92204i	−0.614218	+	0.614218i	0.329824	+	0.944042i	$0.393011\pi$
$212$		0			0
$213$	7.14367			0.489477
$214$		0			0
$215$	−17.1087	−	14.0952i	−1.16680	−	0.961283i
$216$		0			0
$217$	−5.78113	−	5.78113i	−0.392449	−	0.392449i
$218$		0			0
$219$	−5.77037	+	5.77037i	−0.389926	+	0.389926i
$220$		0			0
$221$	11.6284	+	11.6284i	0.782213	+	0.782213i
$222$		0			0
$223$	13.1678	−	13.1678i	0.881784	−	0.881784i	−0.111931	−	0.993716i	$-0.535704\pi$
$223$	13.1678	−	13.1678i	0.881784	−	0.881784i	0.993716	+	0.111931i	$0.0357037\pi$
$224$		0			0
$225$	−0.814693	−	4.17856i	−0.0543129	−	0.278570i
$226$		0			0
$227$		−	19.3432i		−	1.28385i	−0.766766	−	0.641927i	$-0.778135\pi$
$227$		−	19.3432i		−	1.28385i	0.766766	−	0.641927i	$-0.221865\pi$
$228$		0			0
$229$	−13.2143	−	13.2143i	−0.873223	−	0.873223i	0.119599	−	0.992822i	$-0.461839\pi$
$229$	−13.2143	−	13.2143i	−0.873223	−	0.873223i	−0.992822	+	0.119599i	$0.961839\pi$
$230$		0			0
$231$	4.74490			0.312191
$232$		0			0
$233$	20.6884	−	20.6884i	1.35534	−	1.35534i	0.475769	−	0.879570i	$-0.342170\pi$
$233$	20.6884	−	20.6884i	1.35534	−	1.35534i	0.879570	−	0.475769i	$-0.157830\pi$
$234$		0			0
$235$	−0.328204	+	0.0316965i	−0.0214096	+	0.00206765i
$236$		0			0
$237$	−21.0264			−1.36581
$238$		0			0
$239$	−14.1053			−0.912395			−0.456198	−	0.889878i	$-0.650789\pi$
$239$	−14.1053			−0.912395			−0.456198	+	0.889878i	$0.650789\pi$
$240$		0			0
$241$	12.8011			0.824592			0.412296	−	0.911050i	$-0.364727\pi$
$241$	12.8011			0.824592			0.412296	+	0.911050i	$0.364727\pi$
$242$		0			0
$243$	−8.60310			−0.551889
$244$		0			0
$245$	3.22189	+	2.65438i	0.205839	+	0.169582i
$246$		0			0
$247$	−4.64177	+	4.64177i	−0.295349	+	0.295349i
$248$		0			0
$249$	−8.31800			−0.527132
$250$		0			0
$251$	−6.84118	−	6.84118i	−0.431812	−	0.431812i	0.457433	−	0.889244i	$-0.348769\pi$
$251$	−6.84118	−	6.84118i	−0.431812	−	0.431812i	−0.889244	+	0.457433i	$0.848769\pi$
$252$		0			0
$253$		−	7.44205i		−	0.467878i
$254$		0			0
$255$	−1.16674	−	12.0811i	−0.0730642	−	0.756549i
$256$		0			0
$257$	−6.66524	+	6.66524i	−0.415766	+	0.415766i	−0.883742	−	0.467975i	$-0.844984\pi$
$257$	−6.66524	+	6.66524i	−0.415766	+	0.415766i	0.467975	+	0.883742i	$0.344984\pi$
$258$		0			0
$259$	16.3992	+	16.3992i	1.01900	+	1.01900i
$260$		0			0
$261$	1.23291	−	1.23291i	0.0763154	−	0.0763154i
$262$		0			0
$263$	7.32015	+	7.32015i	0.451380	+	0.451380i	0.895812	−	0.444432i	$-0.146595\pi$
$263$	7.32015	+	7.32015i	0.451380	+	0.451380i	−0.444432	+	0.895812i	$0.646595\pi$
$264$		0			0
$265$	5.73298	−	6.95869i	0.352174	−	0.427469i
$266$		0			0
$267$	0.0836533			0.00511950
$268$		0			0
$269$	15.9801	−	15.9801i	0.974321	−	0.974321i	−0.0253576	−	0.999678i	$-0.508072\pi$
$269$	15.9801	−	15.9801i	0.974321	−	0.974321i	0.999678	+	0.0253576i	$0.00807242\pi$
$270$		0			0
$271$		−	3.59684i		−	0.218492i	−0.994015	−	0.109246i	$-0.965156\pi$
$271$		−	3.59684i		−	0.218492i	0.994015	−	0.109246i	$-0.0348437\pi$
$272$		0			0
$273$	18.6938	+	18.6938i	1.13140	+	1.13140i
$274$		0			0
$275$	2.98119	−	4.42522i	0.179773	−	0.266851i
$276$		0			0
$277$		−	20.9416i		−	1.25826i	−0.777300	−	0.629131i	$-0.783411\pi$
$277$		−	20.9416i		−	1.25826i	0.777300	−	0.629131i	$-0.216589\pi$
$278$		0			0
$279$		−	3.07252i		−	0.183947i
$280$		0			0
$281$			3.26699i			0.194892i	0.995241	+	0.0974462i	$0.0310674\pi$
$281$			3.26699i			0.194892i	−0.995241	+	0.0974462i	$0.968933\pi$
$282$		0			0
$283$		0	0.000151619i		0	9.01279e-6i	1.00000		4.50640e-6i	$1.43443e-6\pi$
$283$		0	0.000151619i		0	9.01279e-6i	−1.00000		4.50640e-6i	$0.999999\pi$
$284$		0			0
$285$	4.82247	−	0.465733i	0.285658	−	0.0275877i
$286$		0			0
$287$	11.1075	+	11.1075i	0.655657	+	0.655657i
$288$		0			0
$289$			9.35017i			0.550010i
$290$		0			0
$291$	−3.75178	+	3.75178i	−0.219933	+	0.219933i
$292$		0			0
$293$	11.0593			0.646091			0.323045	−	0.946384i	$-0.395293\pi$
$293$	11.0593			0.646091			0.323045	+	0.946384i	$0.395293\pi$
$294$		0			0
$295$	1.05402	+	10.9140i	0.0613677	+	0.635436i
$296$		0			0
$297$	−3.18176	−	3.18176i	−0.184624	−	0.184624i
$298$		0			0
$299$	29.3200	−	29.3200i	1.69562	−	1.69562i
$300$		0			0
$301$	−15.8818	−	15.8818i	−0.915413	−	0.915413i
$302$		0			0
$303$	−9.74459	+	9.74459i	−0.559812	+	0.559812i
$304$		0			0
$305$	−2.14221	+	0.206885i	−0.122663	+	0.0118462i
$306$		0			0
$307$		−	15.1317i		−	0.863613i	−0.901966	−	0.431806i	$-0.857876\pi$
$307$		−	15.1317i		−	0.863613i	0.901966	−	0.431806i	$-0.142124\pi$
$308$		0			0
$309$	−0.867862	−	0.867862i	−0.0493709	−	0.0493709i
$310$		0			0
$311$	27.1556			1.53985			0.769925	−	0.638134i	$-0.220293\pi$
$311$	27.1556			1.53985			0.769925	+	0.638134i	$0.220293\pi$
$312$		0			0
$313$	−13.6695	+	13.6695i	−0.772646	+	0.772646i	−0.978568	−	0.205922i	$-0.933981\pi$
$313$	−13.6695	+	13.6695i	−0.772646	+	0.772646i	0.205922	+	0.978568i	$0.433981\pi$
$314$		0			0
$315$	−0.414653	−	4.29356i	−0.0233631	−	0.241915i
$316$		0			0
$317$	25.8314			1.45084			0.725419	−	0.688307i	$-0.241646\pi$
$317$	25.8314			1.45084			0.725419	+	0.688307i	$0.241646\pi$
$318$		0			0
$319$	2.18532			0.122354
$320$		0			0
$321$	34.5252			1.92701
$322$		0			0
$323$	3.05361			0.169908
$324$		0			0
$325$	29.1796	−	5.68914i	1.61859	−	0.315576i
$326$		0			0
$327$	−0.677383	+	0.677383i	−0.0374594	+	0.0374594i
$328$		0			0
$329$	−0.334091			−0.0184190
$330$		0			0
$331$	−13.6207	−	13.6207i	−0.748659	−	0.748659i	0.225568	−	0.974227i	$-0.427576\pi$
$331$	−13.6207	−	13.6207i	−0.748659	−	0.748659i	−0.974227	+	0.225568i	$0.927576\pi$
$332$		0			0
$333$			8.71576i			0.477621i
$334$		0			0
$335$	15.6138	+	12.8635i	0.853071	+	0.702810i
$336$		0			0
$337$	16.0911	−	16.0911i	0.876536	−	0.876536i	−0.116638	−	0.993174i	$-0.537212\pi$
$337$	16.0911	−	16.0911i	0.876536	−	0.876536i	0.993174	+	0.116638i	$0.0372119\pi$
$338$		0			0
$339$	−10.6694	−	10.6694i	−0.579484	−	0.579484i
$340$		0			0
$341$	2.72299	−	2.72299i	0.147458	−	0.147458i
$342$		0			0
$343$	14.2052	+	14.2052i	0.767007	+	0.767007i
$344$		0			0
$345$	−30.4614	+	2.94183i	−1.63998	+	0.158383i
$346$		0			0
$347$	5.57562			0.299315			0.149658	−	0.988738i	$-0.452183\pi$
$347$	5.57562			0.299315			0.149658	+	0.988738i	$0.452183\pi$
$348$		0			0
$349$	−15.0811	+	15.0811i	−0.807273	+	0.807273i	−0.984220	−	0.176947i	$-0.943378\pi$
$349$	−15.0811	+	15.0811i	−0.807273	+	0.807273i	0.176947	+	0.984220i	$0.443378\pi$
$350$		0			0
$351$		−	25.0708i		−	1.33818i
$352$		0			0
$353$	2.57880	+	2.57880i	0.137256	+	0.137256i	0.772397	−	0.635141i	$-0.219058\pi$
$353$	2.57880	+	2.57880i	0.137256	+	0.137256i	−0.635141	+	0.772397i	$0.719058\pi$
$354$		0			0
$355$	5.17554	−	6.28206i	0.274689	−	0.333417i
$356$		0			0
$357$		−	12.2978i		−	0.650870i
$358$		0			0
$359$		−	5.77227i		−	0.304649i	−0.988331	−	0.152324i	$-0.951324\pi$
$359$		−	5.77227i		−	0.304649i	0.988331	−	0.152324i	$-0.0486758\pi$
$360$		0			0
$361$		−	17.7811i		−	0.935846i
$362$		0			0
$363$		−	19.3527i		−	1.01575i
$364$		0			0
$365$	0.893807	+	9.25499i	0.0467840	+	0.484428i
$366$		0			0
$367$	−8.30496	−	8.30496i	−0.433516	−	0.433516i	0.456307	−	0.889822i	$-0.349172\pi$
$367$	−8.30496	−	8.30496i	−0.433516	−	0.433516i	−0.889822	+	0.456307i	$0.849172\pi$
$368$		0			0
$369$			5.90337i			0.307317i
$370$		0			0
$371$	6.45967	−	6.45967i	0.335369	−	0.335369i
$372$		0			0
$373$	−16.0484			−0.830953			−0.415477	−	0.909604i	$-0.636385\pi$
$373$	−16.0484			−0.830953			−0.415477	+	0.909604i	$0.636385\pi$
$374$		0			0
$375$	−19.2915	−	10.4532i	−0.996209	−	0.539799i
$376$		0			0
$377$	8.60964	+	8.60964i	0.443419	+	0.443419i
$378$		0			0
$379$	−8.91367	+	8.91367i	−0.457865	+	0.457865i	−0.897954	−	0.440089i	$-0.854947\pi$
$379$	−8.91367	+	8.91367i	−0.457865	+	0.457865i	0.440089	+	0.897954i	$0.354947\pi$
$380$		0			0
$381$	12.3079	+	12.3079i	0.630552	+	0.630552i
$382$		0			0
$383$	24.8928	−	24.8928i	1.27196	−	1.27196i	0.326904	−	0.945057i	$-0.393995\pi$
$383$	24.8928	−	24.8928i	1.27196	−	1.27196i	0.945057	−	0.326904i	$-0.106005\pi$
$384$		0			0
$385$	3.43764	−	4.17261i	0.175199	−	0.212656i
$386$		0			0
$387$		−	8.44078i		−	0.429069i
$388$		0			0
$389$	16.5819	+	16.5819i	0.840738	+	0.840738i	0.988955	−	0.148217i	$-0.0473534\pi$
$389$	16.5819	+	16.5819i	0.840738	+	0.840738i	−0.148217	+	0.988955i	$0.547353\pi$
$390$		0			0
$391$	−19.2883			−0.975452
$392$		0			0
$393$	3.16987	−	3.16987i	0.159899	−	0.159899i
$394$		0			0
$395$	−15.2335	+	18.4904i	−0.766478	+	0.930351i
$396$		0			0
$397$	8.62531			0.432892			0.216446	−	0.976295i	$-0.430553\pi$
$397$	8.62531			0.432892			0.216446	+	0.976295i	$0.430553\pi$
$398$		0			0
$399$	4.90897			0.245756
$400$		0			0
$401$	19.7107			0.984307			0.492153	−	0.870508i	$-0.336210\pi$
$401$	19.7107			0.984307			0.492153	+	0.870508i	$0.336210\pi$
$402$		0			0
$403$	21.4559			1.06880
$404$		0			0
$405$	−15.3975	+	18.6894i	−0.765107	+	0.928686i
$406$		0			0
$407$	−7.72426	+	7.72426i	−0.382877	+	0.382877i
$408$		0			0
$409$	26.7930			1.32483			0.662414	−	0.749138i	$-0.269532\pi$
$409$	26.7930			1.32483			0.662414	+	0.749138i	$0.269532\pi$
$410$		0			0
$411$	13.4154	+	13.4154i	0.661734	+	0.661734i
$412$		0			0
$413$			11.1098i			0.546675i
$414$		0			0
$415$	−6.02633	+	7.31475i	−0.295821	+	0.359067i
$416$		0			0
$417$	−26.9702	+	26.9702i	−1.32074	+	1.32074i
$418$		0			0
$419$	11.0752	+	11.0752i	0.541061	+	0.541061i	0.923840	−	0.382779i	$-0.125033\pi$
$419$	11.0752	+	11.0752i	0.541061	+	0.541061i	−0.382779	+	0.923840i	$0.625033\pi$
$420$		0			0
$421$	0.243092	−	0.243092i	0.0118476	−	0.0118476i	−0.701158	−	0.713006i	$-0.747333\pi$
$421$	0.243092	−	0.243092i	0.0118476	−	0.0118476i	0.713006	+	0.701158i	$0.247333\pi$
$422$		0			0
$423$	−0.0887804	−	0.0887804i	−0.00431665	−	0.00431665i
$424$		0			0
$425$	−11.4693	−	7.72666i	−0.556342	−	0.374798i
$426$		0			0
$427$	−2.18064			−0.105528
$428$		0			0
$429$	−8.80505	+	8.80505i	−0.425112	+	0.425112i
$430$		0			0
$431$		−	20.7024i		−	0.997200i	−0.866832	−	0.498600i	$-0.833848\pi$
$431$		−	20.7024i		−	0.997200i	0.866832	−	0.498600i	$-0.166152\pi$
$432$		0			0
$433$	−5.68221	−	5.68221i	−0.273069	−	0.273069i	0.557265	−	0.830335i	$-0.311851\pi$
$433$	−5.68221	−	5.68221i	−0.273069	−	0.273069i	−0.830335	+	0.557265i	$0.811851\pi$
$434$		0			0
$435$	−0.863851	−	8.94480i	−0.0414185	−	0.428871i
$436$		0			0
$437$		−	7.69939i		−	0.368312i
$438$		0			0
$439$		−	18.7902i		−	0.896808i	−0.893831	−	0.448404i	$-0.851993\pi$
$439$		−	18.7902i		−	0.896808i	0.893831	−	0.448404i	$-0.148007\pi$
$440$		0			0
$441$			1.58955i			0.0756930i
$442$		0			0
$443$			12.1641i			0.577934i	0.957339	+	0.288967i	$0.0933119\pi$
$443$			12.1641i			0.577934i	−0.957339	+	0.288967i	$0.906688\pi$
$444$		0			0
$445$	0.0606062	−	0.0735637i	0.00287301	−	0.00348725i
$446$		0			0
$447$	3.41105	+	3.41105i	0.161337	+	0.161337i
$448$		0			0
$449$		−	27.2708i		−	1.28699i	−0.765452	−	0.643493i	$-0.777484\pi$
$449$		−	27.2708i		−	1.28699i	0.765452	−	0.643493i	$-0.222516\pi$
$450$		0			0
$451$	−5.23181	+	5.23181i	−0.246356	+	0.246356i
$452$		0			0
$453$	−11.4517			−0.538047
$454$		0			0
$455$	29.9826	−	2.89559i	1.40561	−	0.135748i
$456$		0			0
$457$	19.7514	+	19.7514i	0.923933	+	0.923933i	0.997305	−	0.0733714i	$-0.0233758\pi$
$457$	19.7514	+	19.7514i	0.923933	+	0.923933i	−0.0733714	+	0.997305i	$0.523376\pi$
$458$		0			0
$459$	−8.24649	+	8.24649i	−0.384913	+	0.384913i
$460$		0			0
$461$	−12.9262	−	12.9262i	−0.602035	−	0.602035i	0.338818	−	0.940852i	$-0.389973\pi$
$461$	−12.9262	−	12.9262i	−0.602035	−	0.602035i	−0.940852	+	0.338818i	$0.889973\pi$
$462$		0			0
$463$	−14.5647	+	14.5647i	−0.676879	+	0.676879i	−0.959293	−	0.282414i	$-0.908865\pi$
$463$	−14.5647	+	14.5647i	−0.676879	+	0.676879i	0.282414	+	0.959293i	$0.408865\pi$
$464$		0			0
$465$	−12.2220	−	10.0692i	−0.566781	−	0.466948i
$466$		0			0
$467$			42.3556i			1.95998i	0.199040	+	0.979991i	$0.436218\pi$
$467$			42.3556i			1.95998i	−0.199040	+	0.979991i	$0.563782\pi$
$468$		0			0
$469$	14.4941	+	14.4941i	0.669274	+	0.669274i
$470$		0			0
$471$	−6.17665			−0.284605
$472$		0			0
$473$	7.48056	−	7.48056i	0.343956	−	0.343956i
$474$		0			0
$475$	3.08428	−	4.57824i	0.141517	−	0.210064i
$476$		0			0
$477$	3.43315			0.157193
$478$		0			0
$479$	−27.0905			−1.23780			−0.618899	−	0.785470i	$-0.712421\pi$
$479$	−27.0905			−1.23780			−0.618899	+	0.785470i	$0.712421\pi$
$480$		0			0
$481$	−60.8636			−2.77514
$482$		0			0
$483$	−31.0078			−1.41090
$484$		0			0
$485$	0.581136	+	6.01741i	0.0263880	+	0.273236i
$486$		0			0
$487$	−21.9674	+	21.9674i	−0.995436	+	0.995436i	−0.999990	−	0.00455390i	$-0.998550\pi$
$487$	−21.9674	+	21.9674i	−0.995436	+	0.995436i	0.00455390	+	0.999990i	$0.498550\pi$
$488$		0			0
$489$	15.3491			0.694111
$490$		0			0
$491$	−6.11955	−	6.11955i	−0.276171	−	0.276171i	0.555407	−	0.831579i	$-0.312562\pi$
$491$	−6.11955	−	6.11955i	−0.276171	−	0.276171i	−0.831579	+	0.555407i	$0.812562\pi$
$492$		0			0
$493$		−	5.66390i		−	0.255089i
$494$		0			0
$495$	2.02233	−	0.195308i	0.0908968	−	0.00877842i
$496$		0			0
$497$	5.83157	−	5.83157i	0.261581	−	0.261581i
$498$		0			0
$499$	15.4115	+	15.4115i	0.689914	+	0.689914i	0.962213	−	0.272298i	$-0.0877838\pi$
$499$	15.4115	+	15.4115i	0.689914	+	0.689914i	−0.272298	+	0.962213i	$0.587784\pi$
$500$		0			0
$501$	19.3986	−	19.3986i	0.866667	−	0.866667i
$502$		0			0
$503$	−26.4312	−	26.4312i	−1.17851	−	1.17851i	−0.980124	−	0.198387i	$-0.936430\pi$
$503$	−26.4312	−	26.4312i	−1.17851	−	1.17851i	−0.198387	−	0.980124i	$-0.563570\pi$
$504$		0			0
$505$	1.50940	+	15.6292i	0.0671673	+	0.695488i
$506$		0			0
$507$	−43.8671			−1.94820
$508$		0			0
$509$	0.233714	−	0.233714i	0.0103592	−	0.0103592i	−0.701908	−	0.712267i	$-0.747668\pi$
$509$	0.233714	−	0.233714i	0.0103592	−	0.0103592i	0.712267	+	0.701908i	$0.247668\pi$
$510$		0			0
$511$			9.42101i			0.416761i
$512$		0			0
$513$	−3.29178	−	3.29178i	−0.145336	−	0.145336i
$514$		0			0
$515$	−1.39195	+	0.134428i	−0.0613365	+	0.00592362i
$516$		0			0
$517$		−	0.157362i		−	0.00692075i
$518$		0			0
$519$		−	6.85397i		−	0.300856i
$520$		0			0
$521$			4.50147i			0.197213i	0.995127	+	0.0986064i	$0.0314385\pi$
$521$			4.50147i			0.197213i	−0.995127	+	0.0986064i	$0.968562\pi$
$522$		0			0
$523$		−	12.6042i		−	0.551141i	−0.961281	−	0.275571i	$-0.911133\pi$
$523$		−	12.6042i		−	0.551141i	0.961281	−	0.275571i	$-0.0888668\pi$
$524$		0			0
$525$	−18.4380	−	12.4213i	−0.804699	−	0.542111i
$526$		0			0
$527$	−7.05746	−	7.05746i	−0.307428	−	0.307428i
$528$		0			0
$529$			25.6336i			1.11450i
$530$		0			0
$531$	−2.95227	+	2.95227i	−0.128118	+	0.128118i
$532$		0			0
$533$	−41.2242			−1.78562
$534$		0			0
$535$	25.0132	−	30.3610i	1.08142	−	1.31262i
$536$		0			0
$537$	−25.6714	−	25.6714i	−1.10780	−	1.10780i
$538$		0			0
$539$	−1.40873	+	1.40873i	−0.0606782	+	0.0606782i
$540$		0			0
$541$	−14.5013	−	14.5013i	−0.623459	−	0.623459i	0.322955	−	0.946414i	$-0.395324\pi$
$541$	−14.5013	−	14.5013i	−0.623459	−	0.623459i	−0.946414	+	0.322955i	$0.895324\pi$
$542$		0			0
$543$	−26.7672	+	26.7672i	−1.14869	+	1.14869i
$544$		0			0
$545$	0.104924	+	1.08644i	0.00449444	+	0.0465380i
$546$		0			0
$547$		−	30.2936i		−	1.29526i	−0.761955	−	0.647630i	$-0.775760\pi$
$547$		−	30.2936i		−	1.29526i	0.761955	−	0.647630i	$-0.224240\pi$
$548$		0			0
$549$	−0.579476	−	0.579476i	−0.0247314	−	0.0247314i
$550$		0			0
$551$	2.26088			0.0963169
$552$		0			0
$553$	−17.1644	+	17.1644i	−0.729904	+	0.729904i
$554$		0			0
$555$	34.6699	+	28.5631i	1.47165	+	1.21244i
$556$		0			0
$557$	9.72758			0.412171			0.206085	−	0.978534i	$-0.433928\pi$
$557$	9.72758			0.412171			0.206085	+	0.978534i	$0.433928\pi$
$558$		0			0
$559$	58.9433			2.49304
$560$		0			0
$561$	5.79245			0.244557
$562$		0			0
$563$	−17.7853			−0.749562			−0.374781	−	0.927113i	$-0.622282\pi$
$563$	−17.7853			−0.749562			−0.374781	+	0.927113i	$0.622282\pi$
$564$		0			0
$565$	−17.1125	+	1.65265i	−0.719928	+	0.0695276i
$566$		0			0
$567$	−17.3492	+	17.3492i	−0.728597	+	0.728597i
$568$		0			0
$569$	15.7897			0.661938			0.330969	−	0.943642i	$-0.392624\pi$
$569$	15.7897			0.661938			0.330969	+	0.943642i	$0.392624\pi$
$570$		0			0
$571$	23.3108	+	23.3108i	0.975528	+	0.975528i	0.999708	−	0.0241793i	$-0.00769727\pi$
$571$	23.3108	+	23.3108i	0.975528	+	0.975528i	−0.0241793	+	0.999708i	$0.507697\pi$
$572$		0			0
$573$			5.74079i			0.239825i
$574$		0			0
$575$	−19.4820	+	28.9187i	−0.812456	+	1.20599i
$576$		0			0
$577$	25.7383	−	25.7383i	1.07150	−	1.07150i	0.0742597	−	0.997239i	$-0.476341\pi$
$577$	25.7383	−	25.7383i	1.07150	−	1.07150i	0.997239	−	0.0742597i	$-0.0236594\pi$
$578$		0			0
$579$	0.163026	+	0.163026i	0.00677514	+	0.00677514i
$580$		0			0
$581$	−6.79020	+	6.79020i	−0.281705	+	0.281705i
$582$		0			0
$583$	3.04260	+	3.04260i	0.126011	+	0.126011i
$584$		0			0
$585$	8.73697	+	7.19803i	0.361229	+	0.297602i
$586$		0			0
$587$	23.1327			0.954790			0.477395	−	0.878689i	$-0.341581\pi$
$587$	23.1327			0.954790			0.477395	+	0.878689i	$0.341581\pi$
$588$		0			0
$589$	2.81715	−	2.81715i	0.116079	−	0.116079i
$590$		0			0
$591$			15.3171i			0.630063i
$592$		0			0
$593$	−25.5047	−	25.5047i	−1.04735	−	1.04735i	−0.998822	−	0.0485322i	$-0.984546\pi$
$593$	−25.5047	−	25.5047i	−1.04735	−	1.04735i	−0.0485322	−	0.998822i	$-0.515454\pi$
$594$		0			0
$595$	−10.8146	−	8.90969i	−0.443354	−	0.365261i
$596$		0			0
$597$			21.5365i			0.881432i
$598$		0			0
$599$			11.0699i			0.452304i	0.974092	+	0.226152i	$0.0726146\pi$
$599$			11.0699i			0.452304i	−0.974092	+	0.226152i	$0.927385\pi$
$600$		0			0
$601$		−	13.7579i		−	0.561197i	−0.959825	−	0.280599i	$-0.909467\pi$
$601$		−	13.7579i		−	0.561197i	0.959825	−	0.280599i	$-0.0905330\pi$
$602$		0			0
$603$			7.70322i			0.313700i
$604$		0			0
$605$	−17.0185	−	14.0209i	−0.691902	−	0.570030i
$606$		0			0
$607$	18.4675	+	18.4675i	0.749573	+	0.749573i	0.974399	−	0.224826i	$-0.0721813\pi$
$607$	18.4675	+	18.4675i	0.749573	+	0.749573i	−0.224826	+	0.974399i	$0.572181\pi$
$608$		0			0
$609$		−	9.10526i		−	0.368964i
$610$		0			0
$611$	0.619968	−	0.619968i	0.0250812	−	0.0250812i
$612$		0			0
$613$	11.6810			0.471790			0.235895	−	0.971779i	$-0.424198\pi$
$613$	11.6810			0.471790			0.235895	+	0.971779i	$0.424198\pi$
$614$		0			0
$615$	23.4826	+	19.3464i	0.946912	+	0.780122i
$616$		0			0
$617$	−29.1000	−	29.1000i	−1.17152	−	1.17152i	−0.981847	−	0.189677i	$-0.939256\pi$
$617$	−29.1000	−	29.1000i	−1.17152	−	1.17152i	−0.189677	−	0.981847i	$-0.560744\pi$
$618$		0			0
$619$	4.23279	−	4.23279i	0.170130	−	0.170130i	−0.616906	−	0.787036i	$-0.711614\pi$
$619$	4.23279	−	4.23279i	0.170130	−	0.170130i	0.787036	+	0.616906i	$0.211614\pi$
$620$		0			0
$621$	20.7927	+	20.7927i	0.834383	+	0.834383i
$622$		0			0
$623$	0.0682883	−	0.0682883i	0.00273591	−	0.00273591i
$624$		0			0
$625$	−23.1689	+	9.39149i	−0.926758	+	0.375660i
$626$		0			0
$627$			2.31220i			0.0923402i
$628$		0			0
$629$	20.0197	+	20.0197i	0.798239	+	0.798239i
$630$		0			0
$631$	1.33886			0.0532991			0.0266496	−	0.999645i	$-0.491516\pi$
$631$	1.33886			0.0532991			0.0266496	+	0.999645i	$0.491516\pi$
$632$		0			0
$633$	−17.5096	+	17.5096i	−0.695944	+	0.695944i
$634$		0			0
$635$	19.7404	−	1.90644i	0.783373	−	0.0756548i
$636$		0			0
$637$	−11.1001			−0.439803
$638$		0			0
$639$	3.09933			0.122608
$640$		0			0
$641$	24.5069			0.967965			0.483982	−	0.875078i	$-0.339190\pi$
$641$	24.5069			0.967965			0.483982	+	0.875078i	$0.339190\pi$
$642$		0			0
$643$	−10.8979			−0.429771			−0.214885	−	0.976639i	$-0.568938\pi$
$643$	−10.8979			−0.429771			−0.214885	+	0.976639i	$0.568938\pi$
$644$		0			0
$645$	−33.5760	−	27.6619i	−1.32205	−	1.08919i
$646$		0			0
$647$	11.6612	−	11.6612i	0.458448	−	0.458448i	−0.439698	−	0.898146i	$-0.644915\pi$
$647$	11.6612	−	11.6612i	0.458448	−	0.458448i	0.898146	+	0.439698i	$0.144915\pi$
$648$		0			0
$649$	−5.23285			−0.205407
$650$		0			0
$651$	−11.3455	−	11.3455i	−0.444666	−	0.444666i
$652$		0			0
$653$		−	5.28393i		−	0.206776i	−0.994641	−	0.103388i	$-0.967032\pi$
$653$		−	5.28393i		−	0.206776i	0.994641	−	0.103388i	$-0.0329684\pi$
$654$		0			0
$655$	−0.491000	−	5.08409i	−0.0191849	−	0.198652i
$656$		0			0
$657$	−2.50351	+	2.50351i	−0.0976713	+	0.0976713i
$658$		0			0
$659$	−16.2902	−	16.2902i	−0.634578	−	0.634578i	0.314635	−	0.949213i	$-0.398118\pi$
$659$	−16.2902	−	16.2902i	−0.634578	−	0.634578i	−0.949213	+	0.314635i	$0.898118\pi$
$660$		0			0
$661$	12.7924	−	12.7924i	0.497566	−	0.497566i	−0.413114	−	0.910679i	$-0.635559\pi$
$661$	12.7924	−	12.7924i	0.497566	−	0.497566i	0.910679	+	0.413114i	$0.135559\pi$
$662$		0			0
$663$	22.8209	+	22.8209i	0.886291	+	0.886291i
$664$		0			0
$665$	3.55652	−	4.31690i	0.137916	−	0.167402i
$666$		0			0
$667$	−14.2810			−0.552962
$668$		0			0
$669$	25.8420	−	25.8420i	0.999111	−	0.999111i
$670$		0			0
$671$		−	1.02711i		−	0.0396512i
$672$		0			0
$673$	11.9553	+	11.9553i	0.460841	+	0.460841i	0.898931	−	0.438090i	$-0.144345\pi$
$673$	11.9553	+	11.9553i	0.460841	+	0.460841i	−0.438090	+	0.898931i	$0.644345\pi$
$674$		0			0
$675$	4.03454	+	20.6931i	0.155290	+	0.796480i
$676$		0			0
$677$		−	3.18699i		−	0.122486i	−0.998123	−	0.0612430i	$-0.980494\pi$
$677$		−	3.18699i		−	0.122486i	0.998123	−	0.0612430i	$-0.0195065\pi$
$678$		0			0
$679$			6.12535i			0.235069i
$680$		0			0
$681$		−	37.9613i		−	1.45468i
$682$		0			0
$683$			35.1661i			1.34559i	0.739827	+	0.672797i	$0.234907\pi$
$683$			35.1661i			1.34559i	−0.739827	+	0.672797i	$0.765093\pi$
$684$		0			0
$685$	21.5167	−	2.07799i	0.822112	−	0.0793961i
$686$		0			0
$687$	−25.9331	−	25.9331i	−0.989410	−	0.989410i
$688$		0			0
$689$			23.9743i			0.913346i
$690$		0			0
$691$	2.90121	−	2.90121i	0.110367	−	0.110367i	−0.649767	−	0.760134i	$-0.725133\pi$
$691$	2.90121	−	2.90121i	0.110367	−	0.110367i	0.760134	+	0.649767i	$0.225133\pi$
$692$		0			0
$693$	2.05860			0.0781999
$694$		0			0
$695$	4.17758	+	43.2571i	0.158465	+	1.64083i
$696$		0			0
$697$	13.5598	+	13.5598i	0.513614	+	0.513614i
$698$		0			0
$699$	40.6011	−	40.6011i	1.53568	−	1.53568i
$700$		0			0
$701$	−15.7397	−	15.7397i	−0.594481	−	0.594481i	0.344358	−	0.938839i	$-0.388097\pi$
$701$	−15.7397	−	15.7397i	−0.594481	−	0.594481i	−0.938839	+	0.344358i	$0.888097\pi$
$702$		0			0
$703$	−7.99136	+	7.99136i	−0.301400	+	0.301400i
$704$		0			0
$705$	−0.644103	+	0.0622047i	−0.0242583	+	0.00234276i
$706$		0			0
$707$			15.9095i			0.598339i
$708$		0			0
$709$	−1.95755	−	1.95755i	−0.0735172	−	0.0735172i	0.669392	−	0.742909i	$-0.266555\pi$
$709$	−1.95755	−	1.95755i	−0.0735172	−	0.0735172i	−0.742909	+	0.669392i	$0.766555\pi$
$710$		0			0
$711$	−9.12243			−0.342118
$712$		0			0
$713$	−17.7947	+	17.7947i	−0.666416	+	0.666416i
$714$		0			0
$715$	1.36387	+	14.1222i	0.0510057	+	0.528142i
$716$		0			0
$717$	−27.6818			−1.03379
$718$		0			0
$719$	−0.0658604			−0.00245618			−0.00122809	−	0.999999i	$-0.500391\pi$
$719$	−0.0658604			−0.00245618			−0.00122809	+	0.999999i	$0.500391\pi$
$720$		0			0
$721$	−1.41692			−0.0527687
$722$		0			0
$723$	25.1223			0.934309
$724$		0			0
$725$	−8.49181	−	5.72078i	−0.315378	−	0.212465i
$726$		0			0
$727$	16.2286	−	16.2286i	0.601885	−	0.601885i	−0.338927	−	0.940813i	$-0.610064\pi$
$727$	16.2286	−	16.2286i	0.601885	−	0.601885i	0.940813	+	0.338927i	$0.110064\pi$
$728$		0			0
$729$	15.6045			0.577943
$730$		0			0
$731$	−19.3881	−	19.3881i	−0.717095	−	0.717095i
$732$		0			0
$733$			0.669106i			0.0247140i	0.999924	+	0.0123570i	$0.00393345\pi$
$733$			0.669106i			0.0247140i	−0.999924	+	0.0123570i	$0.996067\pi$
$734$		0			0
$735$	6.32298	+	5.20925i	0.233227	+	0.192146i
$736$		0			0
$737$	−6.82691	+	6.82691i	−0.251472	+	0.251472i
$738$		0			0
$739$	−23.4183	−	23.4183i	−0.861454	−	0.861454i	0.130053	−	0.991507i	$-0.458485\pi$
$739$	−23.4183	−	23.4183i	−0.861454	−	0.861454i	−0.991507	+	0.130053i	$0.958485\pi$
$740$		0			0
$741$	−9.10952	+	9.10952i	−0.334647	+	0.334647i
$742$		0			0
$743$	−30.0968	−	30.0968i	−1.10414	−	1.10414i	−0.993905	−	0.110238i	$-0.964839\pi$
$743$	−30.0968	−	30.0968i	−1.10414	−	1.10414i	−0.110238	−	0.993905i	$-0.535161\pi$
$744$		0			0
$745$	5.47092	−	0.528358i	0.200439	−	0.0193575i
$746$		0			0
$747$	−3.60882			−0.132040
$748$		0			0
$749$	28.1838	−	28.1838i	1.02981	−	1.02981i
$750$		0			0
$751$			53.2724i			1.94394i	0.235107	+	0.971970i	$0.424456\pi$
$751$			53.2724i			1.94394i	−0.235107	+	0.971970i	$0.575544\pi$
$752$		0			0
$753$	−13.4259	−	13.4259i	−0.489267	−	0.489267i
$754$		0			0
$755$	−8.29666	+	10.0705i	−0.301946	+	0.366502i
$756$		0			0
$757$		−	27.1717i		−	0.987574i	−0.869583	−	0.493787i	$-0.835612\pi$
$757$		−	27.1717i		−	0.987574i	0.869583	−	0.493787i	$-0.164388\pi$
$758$		0			0
$759$		−	14.6051i		−	0.530132i
$760$		0			0
$761$			12.9068i			0.467870i	0.972252	+	0.233935i	$0.0751604\pi$
$761$			12.9068i			0.467870i	−0.972252	+	0.233935i	$0.924840\pi$
$762$		0			0
$763$			1.10593i			0.0400374i
$764$		0			0
$765$	−0.506198	−	5.24147i	−0.0183016	−	0.189506i
$766$		0			0
$767$	−20.6162	−	20.6162i	−0.744409	−	0.744409i
$768$		0			0
$769$			34.4858i			1.24359i	0.783180	+	0.621795i	$0.213596\pi$
$769$			34.4858i			1.24359i	−0.783180	+	0.621795i	$0.786404\pi$
$770$		0			0
$771$	−13.0806	+	13.0806i	−0.471087	+	0.471087i
$772$		0			0
$773$	−26.6789			−0.959574			−0.479787	−	0.877385i	$-0.659286\pi$
$773$	−26.6789			−0.959574			−0.479787	+	0.877385i	$0.659286\pi$
$774$		0			0
$775$	−17.7095	+	3.45281i	−0.636143	+	0.124029i
$776$		0			0
$777$	32.1836	+	32.1836i	1.15458	+	1.15458i
$778$		0			0
$779$	−5.41272	+	5.41272i	−0.193931	+	0.193931i
$780$		0			0
$781$	2.74675	+	2.74675i	0.0982864	+	0.0982864i
$782$		0			0
$783$	−6.10566	+	6.10566i	−0.218199	+	0.218199i
$784$		0			0
$785$	−4.47493	+	5.43167i	−0.159717	+	0.193865i
$786$		0			0
$787$			33.2611i			1.18563i	0.805338	+	0.592815i	$0.201984\pi$
$787$			33.2611i			1.18563i	−0.805338	+	0.592815i	$0.798016\pi$
$788$		0			0
$789$	14.3659	+	14.3659i	0.511439	+	0.511439i
$790$		0			0
$791$	−17.4195			−0.619365
$792$		0			0
$793$	4.04658	−	4.04658i	0.143698	−	0.143698i
$794$		0			0
$795$	11.2510	−	13.6565i	0.399033	−	0.484346i
$796$		0			0
$797$	−15.9072			−0.563461			−0.281730	−	0.959494i	$-0.590908\pi$
$797$	−15.9072			−0.563461			−0.281730	+	0.959494i	$0.590908\pi$
$798$		0			0
$799$	−0.407850			−0.0144287
$800$		0			0
$801$	0.0362935			0.00128237
$802$		0			0
$803$	−4.43743			−0.156593
$804$		0			0
$805$	−22.4649	+	27.2679i	−0.791784	+	0.961067i
$806$		0			0
$807$	31.3610	−	31.3610i	1.10396	−	1.10396i
$808$		0			0
$809$	−12.4922			−0.439204			−0.219602	−	0.975590i	$-0.570476\pi$
$809$	−12.4922			−0.439204			−0.219602	+	0.975590i	$0.570476\pi$
$810$		0			0
$811$	−35.4886	−	35.4886i	−1.24617	−	1.24617i	−0.957396	−	0.288777i	$-0.906751\pi$
$811$	−35.4886	−	35.4886i	−1.24617	−	1.24617i	−0.288777	−	0.957396i	$-0.593249\pi$
$812$		0			0
$813$		−	7.05884i		−	0.247564i
$814$		0			0
$815$	11.1203	−	13.4978i	0.389528	−	0.472809i
$816$		0			0
$817$	7.73923	−	7.73923i	0.270761	−	0.270761i
$818$		0			0
$819$	8.11042	+	8.11042i	0.283401	+	0.283401i
$820$		0			0
$821$	15.9683	−	15.9683i	0.557299	−	0.557299i	−0.371239	−	0.928537i	$-0.621067\pi$
$821$	15.9683	−	15.9683i	0.557299	−	0.557299i	0.928537	+	0.371239i	$0.121067\pi$
$822$		0			0
$823$	21.7278	+	21.7278i	0.757384	+	0.757384i	0.975846	−	0.218462i	$-0.0701039\pi$
$823$	21.7278	+	21.7278i	0.757384	+	0.757384i	−0.218462	+	0.975846i	$0.570104\pi$
$824$		0			0
$825$	5.85062	−	8.68454i	0.203693	−	0.302357i
$826$		0			0
$827$	−39.2381			−1.36444			−0.682221	−	0.731146i	$-0.738986\pi$
$827$	−39.2381			−1.36444			−0.682221	+	0.731146i	$0.738986\pi$
$828$		0			0
$829$	−18.6072	+	18.6072i	−0.646254	+	0.646254i	−0.952086	−	0.305831i	$-0.901066\pi$
$829$	−18.6072	+	18.6072i	−0.646254	+	0.646254i	0.305831	+	0.952086i	$0.401066\pi$
$830$		0			0
$831$		−	41.0982i		−	1.42568i
$832$		0			0
$833$	3.65114	+	3.65114i	0.126504	+	0.126504i
$834$		0			0
$835$	−3.00477	−	31.1131i	−0.103984	−	1.07671i
$836$		0			0
$837$			15.2158i			0.525935i
$838$		0			0
$839$			12.5955i			0.434845i	0.976078	+	0.217422i	$0.0697649\pi$
$839$			12.5955i			0.434845i	−0.976078	+	0.217422i	$0.930235\pi$
$840$		0			0
$841$			24.8065i			0.855396i
$842$		0			0
$843$			6.41151i			0.220824i
$844$		0			0
$845$	−31.7814	+	38.5762i	−1.09331	+	1.32706i
$846$		0			0
$847$	−15.7981	−	15.7981i	−0.542829	−	0.542829i
$848$		0			0
$849$		0	0.000297553i		0	1.02120e-5i
$850$		0			0
$851$	50.4778	−	50.4778i	1.73036	−	1.73036i
$852$		0			0
$853$	43.6914			1.49597			0.747983	−	0.663718i	$-0.231022\pi$
$853$	43.6914			1.49597			0.747983	+	0.663718i	$0.231022\pi$
$854$		0			0
$855$	2.09226	−	0.202061i	0.0715537	−	0.00691035i
$856$		0			0
$857$	−28.9373	−	28.9373i	−0.988478	−	0.988478i	0.0114561	−	0.999934i	$-0.496353\pi$
$857$	−28.9373	−	28.9373i	−0.988478	−	0.988478i	−0.999934	+	0.0114561i	$0.996353\pi$
$858$		0			0
$859$	28.1247	−	28.1247i	0.959602	−	0.959602i	−0.0396134	−	0.999215i	$-0.512613\pi$
$859$	28.1247	−	28.1247i	0.959602	−	0.959602i	0.999215	+	0.0396134i	$0.0126126\pi$
$860$		0			0
$861$	21.7987	+	21.7987i	0.742896	+	0.742896i
$862$		0			0
$863$	22.2144	−	22.2144i	0.756186	−	0.756186i	−0.219440	−	0.975626i	$-0.570423\pi$
$863$	22.2144	−	22.2144i	0.756186	−	0.756186i	0.975626	+	0.219440i	$0.0704229\pi$
$864$		0			0
$865$	−6.02730	−	4.96565i	−0.204934	−	0.168837i
$866$		0			0
$867$			18.3498i			0.623192i
$868$		0			0
$869$	−8.08466	−	8.08466i	−0.274253	−	0.274253i
$870$		0			0
$871$	−53.7929			−1.82270
$872$		0			0
$873$	−1.62773	+	1.62773i	−0.0550904	+	0.0550904i
$874$		0			0
$875$	−24.2813	+	7.21497i	−0.820859	+	0.243911i
$876$		0			0
$877$	5.13889			0.173528			0.0867640	−	0.996229i	$-0.472347\pi$
$877$	5.13889			0.173528			0.0867640	+	0.996229i	$0.472347\pi$
$878$		0			0
$879$	21.7040			0.732057
$880$		0			0
$881$	−4.34528			−0.146396			−0.0731982	−	0.997317i	$-0.523321\pi$
$881$	−4.34528			−0.146396			−0.0731982	+	0.997317i	$0.523321\pi$
$882$		0			0
$883$	35.4317			1.19237			0.596186	−	0.802846i	$-0.296682\pi$
$883$	35.4317			1.19237			0.596186	+	0.802846i	$0.296682\pi$
$884$		0			0
$885$	2.06853	+	21.4188i	0.0695330	+	0.719985i
$886$		0			0
$887$	−37.4644	+	37.4644i	−1.25793	+	1.25793i	−0.305855	+	0.952078i	$0.598942\pi$
$887$	−37.4644	+	37.4644i	−1.25793	+	1.25793i	−0.952078	+	0.305855i	$0.901058\pi$
$888$		0			0
$889$	20.0945			0.673947
$890$		0			0
$891$	−8.17171	−	8.17171i	−0.273763	−	0.273763i
$892$		0			0
$893$		−	0.162803i		−	0.00544799i
$894$		0			0
$895$	−41.1739	+	3.97640i	−1.37629	+	0.132916i
$896$		0			0
$897$	57.5407	−	57.5407i	1.92123	−	1.92123i
$898$		0			0
$899$	−5.22531	−	5.22531i	−0.174274	−	0.174274i
$900$		0			0
$901$	7.88580	−	7.88580i	0.262714	−	0.262714i
$902$		0			0
$903$	−31.1682	−	31.1682i	−1.03721	−	1.03721i
$904$		0			0
$905$	4.14613	+	42.9314i	0.137822	+	1.42709i
$906$		0			0
$907$	0.181405			0.00602345			0.00301173	−	0.999995i	$-0.499041\pi$
$907$	0.181405			0.00602345			0.00301173	+	0.999995i	$0.499041\pi$
$908$		0			0
$909$	−4.22775	+	4.22775i	−0.140226	+	0.140226i
$910$		0			0
$911$		−	23.4249i		−	0.776101i	−0.921638	−	0.388050i	$-0.873149\pi$
$911$		−	23.4249i		−	0.776101i	0.921638	−	0.388050i	$-0.126851\pi$
$912$		0			0
$913$	−3.19828	−	3.19828i	−0.105848	−	0.105848i
$914$		0			0
$915$	−4.20411	+	0.406015i	−0.138984	+	0.0134224i
$916$		0			0
$917$		−	5.17529i		−	0.170903i
$918$		0			0
$919$		−	3.05885i		−	0.100902i	−0.998727	−	0.0504511i	$-0.983934\pi$
$919$		−	3.05885i		−	0.100902i	0.998727	−	0.0504511i	$-0.0160659\pi$
$920$		0			0
$921$		−	29.6962i		−	0.978522i
$922$		0			0
$923$			21.6431i			0.712392i
$924$		0			0
$925$	50.2361	−	9.79453i	1.65175	−	0.322042i
$926$		0			0
$927$	−0.376527	−	0.376527i	−0.0123668	−	0.0123668i
$928$		0			0
$929$			59.9772i			1.96779i	0.178752	+	0.983894i	$0.442794\pi$
$929$			59.9772i			1.96779i	−0.178752	+	0.983894i	$0.557206\pi$
$930$		0			0
$931$	−1.45744	+	1.45744i	−0.0477657	+	0.0477657i
$932$		0			0
$933$	53.2931			1.74474
$934$		0			0
$935$	4.19659	−	5.09381i	0.137243	−	0.166586i
$936$		0			0
$937$	−23.7463	−	23.7463i	−0.775759	−	0.775759i	0.203347	−	0.979107i	$-0.434818\pi$
$937$	−23.7463	−	23.7463i	−0.775759	−	0.775759i	−0.979107	+	0.203347i	$0.934818\pi$
$938$		0			0
$939$	−26.8266	+	26.8266i	−0.875451	+	0.875451i
$940$		0			0
$941$	35.2727	+	35.2727i	1.14986	+	1.14986i	0.986580	+	0.163278i	$0.0522068\pi$
$941$	35.2727	+	35.2727i	1.14986	+	1.14986i	0.163278	+	0.986580i	$0.447793\pi$
$942$		0			0
$943$	34.1897	−	34.1897i	1.11337	−	1.11337i
$944$		0			0
$945$	2.05346	+	21.2627i	0.0667989	+	0.691674i
$946$		0			0
$947$			19.9140i			0.647118i	0.946208	+	0.323559i	$0.104879\pi$
$947$			19.9140i			0.647118i	−0.946208	+	0.323559i	$0.895121\pi$
$948$		0			0
$949$	−17.4824	−	17.4824i	−0.567504	−	0.567504i
$950$		0			0
$951$	50.6945			1.64388
$952$		0			0
$953$	23.1060	−	23.1060i	0.748477	−	0.748477i	−0.225716	−	0.974193i	$-0.572472\pi$
$953$	23.1060	−	23.1060i	0.748477	−	0.748477i	0.974193	+	0.225716i	$0.0724722\pi$
$954$		0			0
$955$	5.04838	+	4.15916i	0.163362	+	0.134587i
$956$		0			0
$957$	4.28871			0.138634
$958$		0			0
$959$	21.9027			0.707276
$960$		0			0
$961$	17.9781			0.579939
$962$		0			0
$963$	14.9790			0.482690
$964$		0			0
$965$	0.261475	−	0.0252521i	0.00841717	−	0.000812894i
$966$		0			0
$967$	41.7332	−	41.7332i	1.34205	−	1.34205i	0.448030	−	0.894018i	$-0.352126\pi$
$967$	41.7332	−	41.7332i	1.34205	−	1.34205i	0.894018	−	0.448030i	$-0.147874\pi$
$968$		0			0
$969$	5.99275			0.192515
$970$		0			0
$971$	33.5030	+	33.5030i	1.07516	+	1.07516i	0.996936	+	0.0782268i	$0.0249258\pi$
$971$	33.5030	+	33.5030i	1.07516	+	1.07516i	0.0782268	+	0.996936i	$0.475074\pi$
$972$		0			0
$973$			44.0330i			1.41163i
$974$		0			0
$975$	57.2652	−	11.1650i	1.83395	−	0.357566i
$976$		0			0
$977$	9.16848	−	9.16848i	0.293326	−	0.293326i	−0.545067	−	0.838393i	$-0.683496\pi$
$977$	9.16848	−	9.16848i	0.293326	−	0.293326i	0.838393	+	0.545067i	$0.183496\pi$
$978$		0			0
$979$	0.0321648	+	0.0321648i	0.00102799	+	0.00102799i
$980$		0			0
$981$	−0.293887	+	0.293887i	−0.00938308	+	0.00938308i
$982$		0			0
$983$	39.1183	+	39.1183i	1.24768	+	1.24768i	0.956742	+	0.290936i	$0.0939668\pi$
$983$	39.1183	+	39.1183i	1.24768	+	1.24768i	0.290936	+	0.956742i	$0.406033\pi$
$984$		0			0
$985$	13.4697	+	11.0972i	0.429181	+	0.353585i
$986$		0			0
$987$	−0.655657			−0.0208698
$988$		0			0
$989$	−48.8852	+	48.8852i	−1.55446	+	1.55446i
$990$		0			0
$991$		−	12.9925i		−	0.412722i	−0.978476	−	0.206361i	$-0.933838\pi$
$991$		−	12.9925i		−	0.412722i	0.978476	−	0.206361i	$-0.0661621\pi$
$992$		0			0
$993$	−26.7307	−	26.7307i	−0.848273	−	0.848273i
$994$		0			0
$995$	18.9390	+	15.6031i	0.600406	+	0.494650i
$996$		0			0
$997$		−	8.89509i		−	0.281710i	−0.990030	−	0.140855i	$-0.955015\pi$
$997$		−	8.89509i		−	0.281710i	0.990030	−	0.140855i	$-0.0449852\pi$
$998$		0			0
$999$		−	43.1624i		−	1.36560i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	640.2.s.c.223.8		18
4.3	odd	2		640.2.s.d.223.2		18
5.2	odd	4		640.2.j.c.607.2		18
8.3	odd	2		80.2.s.b.3.6	yes	18
8.5	even	2		320.2.s.b.303.2		18
16.3	odd	4		320.2.j.b.143.2		18
16.5	even	4		640.2.j.d.543.2		18
16.11	odd	4		640.2.j.c.543.8		18
16.13	even	4		80.2.j.b.43.9	✓	18
20.7	even	4		640.2.j.d.607.8		18
24.11	even	2		720.2.z.g.163.4		18
40.3	even	4		400.2.j.d.307.1		18
40.13	odd	4		1600.2.j.d.1007.2		18
40.19	odd	2		400.2.s.d.243.4		18
40.27	even	4		80.2.j.b.67.9	yes	18
40.29	even	2		1600.2.s.d.943.8		18
40.37	odd	4		320.2.j.b.47.8		18
48.29	odd	4		720.2.bd.g.523.1		18
80.3	even	4		1600.2.s.d.207.8		18
80.13	odd	4		400.2.s.d.107.4		18
80.19	odd	4		1600.2.j.d.143.8		18
80.27	even	4	inner	640.2.s.c.287.8		18
80.29	even	4		400.2.j.d.43.1		18
80.37	odd	4		640.2.s.d.287.2		18
80.67	even	4		320.2.s.b.207.2		18
80.77	odd	4		80.2.s.b.27.6	yes	18
120.107	odd	4		720.2.bd.g.307.1		18
240.77	even	4		720.2.z.g.667.4		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.j.b.43.9	✓	18	16.13	even	4
80.2.j.b.67.9	yes	18	40.27	even	4
80.2.s.b.3.6	yes	18	8.3	odd	2
80.2.s.b.27.6	yes	18	80.77	odd	4
320.2.j.b.47.8		18	40.37	odd	4
320.2.j.b.143.2		18	16.3	odd	4
320.2.s.b.207.2		18	80.67	even	4
320.2.s.b.303.2		18	8.5	even	2
400.2.j.d.43.1		18	80.29	even	4
400.2.j.d.307.1		18	40.3	even	4
400.2.s.d.107.4		18	80.13	odd	4
400.2.s.d.243.4		18	40.19	odd	2
640.2.j.c.543.8		18	16.11	odd	4
640.2.j.c.607.2		18	5.2	odd	4
640.2.j.d.543.2		18	16.5	even	4
640.2.j.d.607.8		18	20.7	even	4
640.2.s.c.223.8		18	1.1	even	1	trivial
640.2.s.c.287.8		18	80.27	even	4	inner
640.2.s.d.223.2		18	4.3	odd	2
640.2.s.d.287.2		18	80.37	odd	4
720.2.z.g.163.4		18	24.11	even	2
720.2.z.g.667.4		18	240.77	even	4
720.2.bd.g.307.1		18	120.107	odd	4
720.2.bd.g.523.1		18	48.29	odd	4
1600.2.j.d.143.8		18	80.19	odd	4
1600.2.j.d.1007.2		18	40.13	odd	4
1600.2.s.d.207.8		18	80.3	even	4
1600.2.s.d.943.8		18	40.29	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 640 = 2^{7} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	640.s (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.96251 q^{3} +(1.42182 - 1.72581i) q^{5} +(1.60205 - 1.60205i) q^{7} +0.851447 q^{9} +O(q^{10})\)	\(q+1.96251 q^{3} +(1.42182 - 1.72581i) q^{5} +(1.60205 - 1.60205i) q^{7} +0.851447 q^{9} +(0.754587 + 0.754587i) q^{11} +5.94580i q^{13} +(2.79034 - 3.38692i) q^{15} +(1.95574 - 1.95574i) q^{17} +(0.780680 + 0.780680i) q^{19} +(3.14404 - 3.14404i) q^{21} +(-4.93121 - 4.93121i) q^{23} +(-0.956833 - 4.90759i) q^{25} -4.21656 q^{27} +(1.44802 - 1.44802i) q^{29} -3.60859i q^{31} +(1.48089 + 1.48089i) q^{33} +(-0.486998 - 5.04266i) q^{35} +10.2364i q^{37} +11.6687i q^{39} +6.93334i q^{41} -9.91344i q^{43} +(1.21061 - 1.46944i) q^{45} +(-0.104270 - 0.104270i) q^{47} +1.86688i q^{49} +(3.83816 - 3.83816i) q^{51} +4.03213 q^{53} +(2.37516 - 0.229383i) q^{55} +(1.53209 + 1.53209i) q^{57} +(-3.46736 + 3.46736i) q^{59} +(-0.680578 - 0.680578i) q^{61} +(1.36406 - 1.36406i) q^{63} +(10.2613 + 8.45388i) q^{65} +9.04721i q^{67} +(-9.67754 - 9.67754i) q^{69} +3.64007 q^{71} +(-2.94030 + 2.94030i) q^{73} +(-1.87779 - 9.63120i) q^{75} +2.41777 q^{77} -10.7140 q^{79} -10.8294 q^{81} -4.23845 q^{83} +(-0.594515 - 6.15595i) q^{85} +(2.84176 - 2.84176i) q^{87} +0.0426256 q^{89} +(9.52546 + 9.52546i) q^{91} -7.08189i q^{93} +(2.45730 - 0.237315i) q^{95} +(-1.91173 + 1.91173i) q^{97} +(0.642491 + 0.642491i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 2 q^{5} - 2 q^{7} + 10 q^{9}+O(q^{10}) \) 18 * q - 2 * q^5 - 2 * q^7 + 10 * q^9	\( 18 q - 2 q^{5} - 2 q^{7} + 10 q^{9} - 2 q^{11} + 20 q^{15} - 6 q^{17} - 2 q^{19} + 16 q^{21} + 2 q^{23} - 6 q^{25} - 24 q^{27} - 14 q^{29} - 8 q^{33} + 2 q^{35} + 14 q^{45} - 38 q^{47} + 8 q^{51} - 12 q^{53} + 6 q^{55} - 24 q^{57} + 10 q^{59} - 14 q^{61} + 6 q^{63} + 32 q^{69} - 24 q^{71} - 14 q^{73} + 16 q^{75} + 44 q^{77} + 16 q^{79} + 2 q^{81} + 40 q^{83} - 14 q^{85} - 24 q^{87} + 12 q^{89} - 34 q^{95} + 18 q^{97} + 22 q^{99}+O(q^{100}) \) 18 * q - 2 * q^5 - 2 * q^7 + 10 * q^9 - 2 * q^11 + 20 * q^15 - 6 * q^17 - 2 * q^19 + 16 * q^21 + 2 * q^23 - 6 * q^25 - 24 * q^27 - 14 * q^29 - 8 * q^33 + 2 * q^35 + 14 * q^45 - 38 * q^47 + 8 * q^51 - 12 * q^53 + 6 * q^55 - 24 * q^57 + 10 * q^59 - 14 * q^61 + 6 * q^63 + 32 * q^69 - 24 * q^71 - 14 * q^73 + 16 * q^75 + 44 * q^77 + 16 * q^79 + 2 * q^81 + 40 * q^83 - 14 * q^85 - 24 * q^87 + 12 * q^89 - 34 * q^95 + 18 * q^97 + 22 * q^99

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