LMFDB - Embedded newform 1445.2.b.e.579.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1445,2,Mod(579,1445)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1445.579"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1445, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1445 = 5 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1445.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,-8,2,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$11.5383830921$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.619810816.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{5} + 14x^{4} - 8x^{3} + 2x^{2} + 2x + 1 $ x^8 - 2x^5 + 14x^4 - 8x^3 + 2x^2 + 2*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 85)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			579.4
Root			$-1.49094 - 1.49094i$ of defining polynomial
Character	$\chi$	$=$	1445.579
Dual form			1445.2.b.e.579.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.134632i q^{2} +1.44579i q^{3} +1.98187 q^{4} +(1.29021 - 1.82630i) q^{5} +0.194649 q^{6} +2.86537i q^{7} -0.536087i q^{8} +0.909700 q^{9} +(-0.245878 - 0.173703i) q^{10} +3.84724 q^{11} +2.86537i q^{12} +6.22085i q^{13} +0.385770 q^{14} +(2.64044 + 1.86537i) q^{15} +3.89157 q^{16} -0.122475i q^{18} -6.62231 q^{19} +(2.55703 - 3.61949i) q^{20} -4.14271 q^{21} -0.517961i q^{22} -4.51796i q^{23} +0.775068 q^{24} +(-1.67072 - 4.71261i) q^{25} +0.837525 q^{26} +5.65259i q^{27} +5.67880i q^{28} -0.658562 q^{29} +(0.251138 - 0.355487i) q^{30} -3.49984 q^{31} -1.59610i q^{32} +5.56229i q^{33} +(5.23301 + 3.69693i) q^{35} +1.80291 q^{36} +3.34144i q^{37} +0.891574i q^{38} -8.99403 q^{39} +(-0.979054 - 0.691665i) q^{40} -2.04189 q^{41} +0.557741i q^{42} -1.29303i q^{43} +7.62475 q^{44} +(1.17370 - 1.66138i) q^{45} -0.608262 q^{46} -6.22085i q^{47} +5.62639i q^{48} -1.21033 q^{49} +(-0.634468 + 0.224932i) q^{50} +12.3290i q^{52} -9.92750i q^{53} +0.761019 q^{54} +(4.96375 - 7.02621i) q^{55} +1.53609 q^{56} -9.57445i q^{57} +0.0886634i q^{58} +2.00000 q^{59} +(5.23301 + 3.69693i) q^{60} +7.61634 q^{61} +0.471189i q^{62} +2.60662i q^{63} +7.56826 q^{64} +(11.3611 + 8.02621i) q^{65} +0.748862 q^{66} -0.257106i q^{67} +6.53201 q^{69} +(0.497724 - 0.704530i) q^{70} -1.18868 q^{71} -0.487678i q^{72} -3.26330i q^{73} +0.449864 q^{74} +(6.81343 - 2.41550i) q^{75} -13.1246 q^{76} +11.0238i q^{77} +1.21088i q^{78} -4.99756 q^{79} +(5.02095 - 7.10717i) q^{80} -5.44335 q^{81} +0.274904i q^{82} +7.91534i q^{83} -8.21033 q^{84} -0.174083 q^{86} -0.952140i q^{87} -2.06246i q^{88} -12.8013 q^{89} +(-0.223675 - 0.158018i) q^{90} -17.8250 q^{91} -8.95403i q^{92} -5.06002i q^{93} -0.837525 q^{94} +(-8.54417 + 12.0943i) q^{95} +2.30763 q^{96} -4.08866i q^{97} +0.162950i q^{98} +3.49984 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4} + 2 q^{5} - 8 q^{9} - 6 q^{10} + 4 q^{11} - 12 q^{14} - 8 q^{16} - 8 q^{19} + 2 q^{20} + 24 q^{21} - 12 q^{24} - 12 q^{25} - 8 q^{29} - 16 q^{30} + 24 q^{31} - 44 q^{39} - 22 q^{40} + 12 q^{41}+ \cdots - 24 q^{99}+O(q^{100}) $ 8 * q - 8 * q^4 + 2 * q^5 - 8 * q^9 - 6 * q^10 + 4 * q^11 - 12 * q^14 - 8 * q^16 - 8 * q^19 + 2 * q^20 + 24 * q^21 - 12 * q^24 - 12 * q^25 - 8 * q^29 - 16 * q^30 + 24 * q^31 - 44 * q^39 - 22 * q^40 + 12 * q^41 + 32 * q^44 + 22 * q^45 + 8 * q^46 - 16 * q^49 + 44 * q^50 + 20 * q^54 - 8 * q^55 + 8 * q^56 + 16 * q^59 - 12 * q^61 + 48 * q^64 - 20 * q^65 + 24 * q^66 - 8 * q^69 + 40 * q^70 + 20 * q^71 + 40 * q^74 - 4 * q^75 - 24 * q^76 - 24 * q^79 + 26 * q^80 - 8 * q^81 - 72 * q^84 + 40 * q^86 - 48 * q^89 + 74 * q^90 - 36 * q^91 - 4 * q^95 - 16 * q^96 - 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1445\mathbb{Z}\right)^\times$.

$n$	$581$	$1157$
$\chi(n)$	$1$	$-1$

Coefficient data

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

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

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

$2$		−	0.134632i		−	0.0951991i	−0.998866	−	0.0475996i	$-0.984843\pi$
$2$		−	0.134632i		−	0.0951991i	0.998866	−	0.0475996i	$-0.0151571\pi$
$3$			1.44579i			0.834726i	0.908740	+	0.417363i	$0.137046\pi$
$3$			1.44579i			0.834726i	−0.908740	+	0.417363i	$0.862954\pi$
$4$	1.98187			0.990937
$5$	1.29021	−	1.82630i	0.576999	−	0.816745i
$5$	1.29021	−	1.82630i	0.576999	−	0.816745i
$6$	0.194649			0.0794651
$7$			2.86537i			1.08301i	0.840698	+	0.541504i	$0.182145\pi$
$7$			2.86537i			1.08301i	−0.840698	+	0.541504i	$0.817855\pi$
$8$		−	0.536087i		−	0.189535i
$9$	0.909700			0.303233
$10$	−0.245878	−	0.173703i	−0.0777534	−	0.0549298i
$11$	3.84724			1.15999			0.579994	−	0.814621i	$-0.303055\pi$
$11$	3.84724			1.15999			0.579994	+	0.814621i	$0.303055\pi$
$12$			2.86537i			0.827161i
$13$			6.22085i			1.72535i	0.505755	+	0.862677i	$0.331214\pi$
$13$			6.22085i			1.72535i	−0.505755	+	0.862677i	$0.668786\pi$
$14$	0.385770			0.103101
$15$	2.64044	+	1.86537i	0.681758	+	0.481636i
$16$	3.89157			0.972894
$17$		0			0
$17$		0			0
$18$		−	0.122475i		−	0.0288675i
$19$	−6.62231			−1.51926			−0.759631	−	0.650354i	$-0.774620\pi$
$19$	−6.62231			−1.51926			−0.759631	+	0.650354i	$0.774620\pi$
$20$	2.55703	−	3.61949i	0.571770	−	0.809343i
$21$	−4.14271			−0.904014
$22$		−	0.517961i		−	0.110430i
$23$		−	4.51796i		−	0.942060i	−0.882117	−	0.471030i	$-0.843882\pi$
$23$		−	4.51796i		−	0.942060i	0.882117	−	0.471030i	$-0.156118\pi$
$24$	0.775068			0.158210
$25$	−1.67072	−	4.71261i	−0.334144	−	0.942522i
$26$	0.837525			0.164252
$27$			5.65259i			1.08784i
$28$			5.67880i			1.07319i
$29$	−0.658562			−0.122292			−0.0611459	−	0.998129i	$-0.519476\pi$
$29$	−0.658562			−0.122292			−0.0611459	+	0.998129i	$0.519476\pi$
$30$	0.251138	−	0.355487i	0.0458513	−	0.0649027i
$31$	−3.49984			−0.628589			−0.314295	−	0.949326i	$-0.601768\pi$
$31$	−3.49984			−0.628589			−0.314295	+	0.949326i	$0.601768\pi$
$32$		−	1.59610i		−	0.282154i
$33$			5.56229i			0.968271i
$34$		0			0
$35$	5.23301	+	3.69693i	0.884541	+	0.624894i
$36$	1.80291			0.300485
$37$			3.34144i			0.549329i	0.961540	+	0.274665i	$0.0885668\pi$
$37$			3.34144i			0.549329i	−0.961540	+	0.274665i	$0.911433\pi$
$38$			0.891574i			0.144632i
$39$	−8.99403			−1.44020
$40$	−0.979054	−	0.691665i	−0.154802	−	0.109362i
$41$	−2.04189			−0.318890			−0.159445	−	0.987207i	$-0.550970\pi$
$41$	−2.04189			−0.318890			−0.159445	+	0.987207i	$0.550970\pi$
$42$			0.557741i			0.0860613i
$43$		−	1.29303i		−	0.197185i	−0.995128	−	0.0985926i	$-0.968566\pi$
$43$		−	1.29303i		−	0.197185i	0.995128	−	0.0985926i	$-0.0314341\pi$
$44$	7.62475			1.14947
$45$	1.17370	−	1.66138i	0.174965	−	0.247664i
$46$	−0.608262			−0.0896833
$47$		−	6.22085i		−	0.907405i	−0.891153	−	0.453702i	$-0.850103\pi$
$47$		−	6.22085i		−	0.907405i	0.891153	−	0.453702i	$-0.149897\pi$
$48$			5.62639i			0.812099i
$49$	−1.21033			−0.172905
$50$	−0.634468	+	0.224932i	−0.0897273	+	0.0318102i
$51$		0			0
$52$			12.3290i			1.70972i
$53$		−	9.92750i		−	1.36365i	−0.731517	−	0.681823i	$-0.761187\pi$
$53$		−	9.92750i		−	1.36365i	0.731517	−	0.681823i	$-0.238813\pi$
$54$	0.761019			0.103562
$55$	4.96375	−	7.02621i	0.669312	−	0.947413i
$56$	1.53609			0.205268
$57$		−	9.57445i		−	1.26817i
$58$			0.0886634i			0.0116421i
$59$	2.00000			0.260378			0.130189	−	0.991489i	$-0.458442\pi$
$59$	2.00000			0.260378			0.130189	+	0.991489i	$0.458442\pi$
$60$	5.23301	+	3.69693i	0.675579	+	0.477271i
$61$	7.61634			0.975173			0.487586	−	0.873075i	$-0.337877\pi$
$61$	7.61634			0.975173			0.487586	+	0.873075i	$0.337877\pi$
$62$			0.471189i			0.0598411i
$63$			2.60662i			0.328404i
$64$	7.56826			0.946033
$65$	11.3611	+	8.02621i	1.40917	+	0.995528i
$66$	0.748862			0.0921785
$67$		−	0.257106i		−	0.0314106i	−0.999877	−	0.0157053i	$-0.995001\pi$
$67$		−	0.257106i		−	0.0314106i	0.999877	−	0.0157053i	$-0.00499935\pi$
$68$		0			0
$69$	6.53201			0.786362
$70$	0.497724	−	0.704530i	0.0594894	−	0.0842075i
$71$	−1.18868			−0.141070			−0.0705352	−	0.997509i	$-0.522471\pi$
$71$	−1.18868			−0.141070			−0.0705352	+	0.997509i	$0.522471\pi$
$72$		−	0.487678i		−	0.0574735i
$73$		−	3.26330i		−	0.381940i	−0.981596	−	0.190970i	$-0.938837\pi$
$73$		−	3.26330i		−	0.381940i	0.981596	−	0.190970i	$-0.0611633\pi$
$74$	0.449864			0.0522956
$75$	6.81343	−	2.41550i	0.786747	−	0.278918i
$76$	−13.1246			−1.50549
$77$			11.0238i			1.25627i
$78$			1.21088i			0.137106i
$79$	−4.99756			−0.562269			−0.281135	−	0.959668i	$-0.590711\pi$
$79$	−4.99756			−0.562269			−0.281135	+	0.959668i	$0.590711\pi$
$80$	5.02095	−	7.10717i	0.561359	−	0.794606i
$81$	−5.44335			−0.604816
$82$			0.274904i			0.0303580i
$83$			7.91534i			0.868821i	0.900715	+	0.434411i	$0.143043\pi$
$83$			7.91534i			0.868821i	−0.900715	+	0.434411i	$0.856957\pi$
$84$	−8.21033			−0.895821
$85$		0			0
$86$	−0.174083			−0.0187719
$87$		−	0.952140i		−	0.102080i
$88$		−	2.06246i		−	0.219859i
$89$	−12.8013			−1.35693			−0.678466	−	0.734632i	$-0.737355\pi$
$89$	−12.8013			−1.35693			−0.678466	+	0.734632i	$0.737355\pi$
$90$	−0.223675	−	0.158018i	−0.0235774	−	0.0166565i
$91$	−17.8250			−1.86857
$92$		−	8.95403i		−	0.933522i
$93$		−	5.06002i		−	0.524699i
$94$	−0.837525			−0.0863841
$95$	−8.54417	+	12.0943i	−0.876613	+	1.24085i
$96$	2.30763			0.235521
$97$		−	4.08866i		−	0.415141i	−0.978220	−	0.207570i	$-0.933444\pi$
$97$		−	4.08866i		−	0.415141i	0.978220	−	0.207570i	$-0.0665556\pi$
$98$			0.162950i			0.0164604i
$99$	3.49984			0.351747
$100$	−3.31116	−	9.33980i	−0.331116	−	0.933980i
$101$	12.2871			1.22261			0.611304	−	0.791396i	$-0.290645\pi$
$101$	12.2871			1.22261			0.611304	+	0.791396i	$0.290645\pi$
$102$		0			0
$103$			13.5623i			1.33633i	0.744012	+	0.668166i	$0.232921\pi$
$103$			13.5623i			1.33633i	−0.744012	+	0.668166i	$0.767079\pi$
$104$	3.33492			0.327016
$105$	−5.34497	+	7.56582i	−0.521615	+	0.738349i
$106$	−1.33656			−0.129818
$107$		−	6.63800i		−	0.641719i	−0.947127	−	0.320860i	$-0.896028\pi$
$107$		−	6.63800i		−	0.641719i	0.947127	−	0.320860i	$-0.103972\pi$
$108$			11.2027i			1.07798i
$109$	−2.58042			−0.247159			−0.123580	−	0.992335i	$-0.539437\pi$
$109$	−2.58042			−0.247159			−0.123580	+	0.992335i	$0.539437\pi$
$110$	−0.945951	−	0.668279i	−0.0901929	−	0.0637179i
$111$	−4.83101			−0.458539
$112$			11.1508i			1.05365i
$113$			8.63283i			0.812108i	0.913849	+	0.406054i	$0.133096\pi$
$113$			8.63283i			0.812108i	−0.913849	+	0.406054i	$0.866904\pi$
$114$	−1.28903			−0.120728
$115$	−8.25114	−	5.82912i	−0.769423	−	0.543568i
$116$	−1.30519			−0.121184
$117$			5.65911i			0.523185i
$118$		−	0.269264i		−	0.0247877i
$119$		0			0
$120$	1.00000	−	1.41550i	0.0912871	−	0.129217i
$121$	3.80127			0.345570
$122$		−	1.02540i		−	0.0928356i
$123$		−	2.95214i		−	0.266186i
$124$	−6.93623			−0.622892
$125$	−10.7622	−	3.02903i	−0.962601	−	0.270924i
$126$	0.350935			0.0312638
$127$		−	3.24550i		−	0.287991i	−0.989578	−	0.143996i	$-0.954005\pi$
$127$		−	3.24550i		−	0.287991i	0.989578	−	0.143996i	$-0.0459951\pi$
$128$		−	4.21114i		−	0.372216i
$129$	1.86945			0.164595
$130$	1.08058	−	1.52957i	0.0947734	−	0.134152i
$131$	3.44742			0.301203			0.150601	−	0.988595i	$-0.451879\pi$
$131$	3.44742			0.301203			0.150601	+	0.988595i	$0.451879\pi$
$132$			11.0238i			0.959496i
$133$		−	18.9754i		−	1.64537i
$134$	−0.0346147			−0.00299026
$135$	10.3233	+	7.29303i	0.888489	+	0.627684i
$136$		0			0
$137$		−	14.6869i		−	1.25478i	−0.778703	−	0.627392i	$-0.784122\pi$
$137$		−	14.6869i		−	1.25478i	0.778703	−	0.627392i	$-0.215878\pi$
$138$		−	0.879417i		−	0.0748609i
$139$	13.9883			1.18647			0.593237	−	0.805028i	$-0.297850\pi$
$139$	13.9883			1.18647			0.593237	+	0.805028i	$0.297850\pi$
$140$	10.3712	+	7.32684i	0.876524	+	0.619231i
$141$	8.99403			0.757434
$142$			0.160034i			0.0134298i
$143$			23.9331i			2.00139i
$144$	3.54016			0.295014
$145$	−0.849683	+	1.20273i	−0.0705623	+	0.0998812i
$146$	−0.439344			−0.0363603
$147$		−	1.74989i		−	0.144328i
$148$			6.62231i			0.544351i
$149$	17.8388			1.46141			0.730707	−	0.682691i	$-0.239191\pi$
$149$	17.8388			1.46141			0.730707	+	0.682691i	$0.239191\pi$
$150$	−0.325204	−	0.917305i	−0.0265528	−	0.0748976i
$151$	−2.80291			−0.228098			−0.114049	−	0.993475i	$-0.536382\pi$
$151$	−2.80291			−0.228098			−0.114049	+	0.993475i	$0.536382\pi$
$152$			3.55014i			0.287954i
$153$		0			0
$154$	1.48415			0.119596
$155$	−4.51552	+	6.39174i	−0.362695	+	0.513397i
$156$	−17.8250			−1.42715
$157$		−	3.60582i		−	0.287776i	−0.989594	−	0.143888i	$-0.954040\pi$
$157$		−	3.60582i		−	0.287776i	0.989594	−	0.143888i	$-0.0459605\pi$
$158$			0.672831i			0.0535275i
$159$	14.3530			1.13827
$160$	−2.91496	−	2.05931i	−0.230448	−	0.162803i
$161$	12.9456			1.02026
$162$			0.732848i			0.0575780i
$163$		−	13.7256i		−	1.07507i	−0.843242	−	0.537535i	$-0.819356\pi$
$163$		−	13.7256i		−	1.07507i	0.843242	−	0.537535i	$-0.180644\pi$
$164$	−4.04677			−0.316000
$165$	10.1584	+	7.17652i	0.790830	+	0.558692i
$166$	1.06566			0.0827110
$167$			6.32684i			0.489586i	0.969575	+	0.244793i	$0.0787199\pi$
$167$			6.32684i			0.489586i	−0.969575	+	0.244793i	$0.921280\pi$
$168$			2.22085i			0.171343i
$169$	−25.6990			−1.97685
$170$		0			0
$171$	−6.02431			−0.460691
$172$		−	2.56262i		−	0.195398i
$173$			1.76699i			0.134342i	0.997741	+	0.0671708i	$0.0213972\pi$
$173$			1.76699i			0.134342i	−0.997741	+	0.0671708i	$0.978603\pi$
$174$	−0.128188			−0.00971794
$175$	13.5034	−	4.78723i	1.02076	−	0.361880i
$176$	14.9718			1.12854
$177$			2.89157i			0.217344i
$178$			1.72346i			0.129179i
$179$	−1.10843			−0.0828476			−0.0414238	−	0.999142i	$-0.513189\pi$
$179$	−1.10843			−0.0828476			−0.0414238	+	0.999142i	$0.513189\pi$
$180$	2.32613	−	3.29265i	0.173380	−	0.245420i
$181$	10.8310			0.805062			0.402531	−	0.915406i	$-0.368130\pi$
$181$	10.8310			0.805062			0.402531	+	0.915406i	$0.368130\pi$
$182$			2.39982i			0.177886i
$183$			11.0116i			0.814002i
$184$	−2.42202			−0.178554
$185$	6.10246	+	4.31116i	0.448662	+	0.316962i
$186$	−0.681240			−0.0499509
$187$		0			0
$188$		−	12.3290i		−	0.899181i
$189$	−16.1968			−1.17814
$190$	1.62828	+	1.15032i	0.118128	+	0.0834528i
$191$	3.19221			0.230980			0.115490	−	0.993309i	$-0.463156\pi$
$191$	3.19221			0.230980			0.115490	+	0.993309i	$0.463156\pi$
$192$			10.9421i			0.789678i
$193$		−	7.11407i		−	0.512082i	−0.966666	−	0.256041i	$-0.917582\pi$
$193$		−	7.11407i		−	0.512082i	0.966666	−	0.256041i	$-0.0824182\pi$
$194$	−0.550464			−0.0395210
$195$	−11.6042	+	16.4258i	−0.830993	+	1.17627i
$196$	−2.39873			−0.171338
$197$		−	23.1721i		−	1.65095i	−0.564442	−	0.825473i	$-0.690909\pi$
$197$		−	23.1721i		−	1.65095i	0.564442	−	0.825473i	$-0.309091\pi$
$198$		−	0.471189i		−	0.0334860i
$199$	−24.7131			−1.75186			−0.875932	−	0.482434i	$-0.839753\pi$
$199$	−24.7131			−1.75186			−0.875932	+	0.482434i	$0.839753\pi$
$200$	−2.52637	+	0.895651i	−0.178641	+	0.0633321i
$201$	0.371721			0.0262192
$202$		−	1.65423i		−	0.116391i
$203$		−	1.88702i		−	0.132443i
$204$		0			0
$205$	−2.63447	+	3.72910i	−0.183999	+	0.260452i
$206$	1.82592			0.127218
$207$		−	4.10999i		−	0.285664i
$208$			24.2089i			1.67859i
$209$	−25.4776			−1.76232
$210$	1.01860	+	0.719603i	0.0702901	+	0.0496573i
$211$	4.27138			0.294054			0.147027	−	0.989133i	$-0.453030\pi$
$211$	4.27138			0.294054			0.147027	+	0.989133i	$0.453030\pi$
$212$		−	19.6751i		−	1.35129i
$213$		−	1.71858i		−	0.117755i
$214$	−0.893686			−0.0610911
$215$	−2.36146	−	1.66828i	−0.161050	−	0.113776i
$216$	3.03028			0.206185
$217$		−	10.0283i		−	0.680767i
$218$			0.347407i			0.0235293i
$219$	4.71803			0.318815
$220$	9.83753	−	13.9251i	0.663246	−	0.938827i
$221$		0			0
$222$			0.650408i			0.0436525i
$223$			3.65423i			0.244705i	0.992487	+	0.122353i	$0.0390439\pi$
$223$			3.65423i			0.244705i	−0.992487	+	0.122353i	$0.960956\pi$
$224$	4.57343			0.305575
$225$	−1.51985	−	4.28706i	−0.101324	−	0.285804i
$226$	1.16225			0.0773120
$227$			19.0016i			1.26118i	0.776117	+	0.630589i	$0.217187\pi$
$227$			19.0016i			1.26118i	−0.776117	+	0.630589i	$0.782813\pi$
$228$		−	18.9754i		−	1.25667i
$229$	20.8851			1.38012			0.690062	−	0.723751i	$-0.257583\pi$
$229$	20.8851			1.38012			0.690062	+	0.723751i	$0.257583\pi$
$230$	−0.784785	+	1.11087i	−0.0517472	+	0.0732483i
$231$	−15.9380			−1.04864
$232$			0.353047i			0.0231786i
$233$			0.682876i			0.0447367i	0.999750	+	0.0223684i	$0.00712066\pi$
$233$			0.682876i			0.0447367i	−0.999750	+	0.0223684i	$0.992879\pi$
$234$	0.761897			0.0498067
$235$	−11.3611	−	8.02621i	−0.741118	−	0.523572i
$236$	3.96375			0.258018
$237$		−	7.22541i		−	0.469341i
$238$		0			0
$239$	−28.9915			−1.87531			−0.937653	−	0.347574i	$-0.887006\pi$
$239$	−28.9915			−1.87531			−0.937653	+	0.347574i	$0.887006\pi$
$240$	10.2755	+	7.25922i	0.663278	+	0.468581i
$241$	18.0943			1.16556			0.582778	−	0.812631i	$-0.301966\pi$
$241$	18.0943			1.16556			0.582778	+	0.812631i	$0.301966\pi$
$242$		−	0.511773i		−	0.0328980i
$243$			9.08786i			0.582986i
$244$	15.0946			0.966335
$245$	−1.56158	+	2.21043i	−0.0997660	+	0.141219i
$246$	−0.397452			−0.0253406
$247$		−	41.1964i		−	2.62127i
$248$			1.87622i			0.119140i
$249$	−11.4439			−0.725227
$250$	−0.407803	+	1.44894i	−0.0257918	+	0.0916387i
$251$	−7.21325			−0.455296			−0.227648	−	0.973743i	$-0.573104\pi$
$251$	−7.21325			−0.455296			−0.227648	+	0.973743i	$0.573104\pi$
$252$			5.16600i			0.325428i
$253$		−	17.3817i		−	1.09278i
$254$	−0.436948			−0.0274165
$255$		0			0
$256$	14.5696			0.910598
$257$			4.87942i			0.304370i	0.988352	+	0.152185i	$0.0486309\pi$
$257$			4.87942i			0.304370i	−0.988352	+	0.152185i	$0.951369\pi$
$258$		−	0.251687i		−	0.0156693i
$259$	−9.57445			−0.594927
$260$	22.5163	+	15.9069i	1.39640	+	0.986506i
$261$	−0.599094			−0.0370830
$262$		−	0.464133i		−	0.0286742i
$263$			30.0234i			1.85132i	0.378351	+	0.925662i	$0.376491\pi$
$263$			30.0234i			1.85132i	−0.378351	+	0.925662i	$0.623509\pi$
$264$	2.98187			0.183522
$265$	−18.1306	−	12.8086i	−1.11375	−	0.786823i
$266$	−2.55469			−0.156638
$267$		−	18.5079i		−	1.13267i
$268$		−	0.509553i		−	0.0311259i
$269$	−29.6568			−1.80821			−0.904104	−	0.427312i	$-0.859460\pi$
$269$	−29.6568			−1.80821			−0.904104	+	0.427312i	$0.859460\pi$
$270$	0.981874	−	1.38985i	0.0597550	−	0.0845834i
$271$	3.91622			0.237893			0.118947	−	0.992901i	$-0.462048\pi$
$271$	3.91622			0.237893			0.118947	+	0.992901i	$0.462048\pi$
$272$		0			0
$273$		−	25.7712i		−	1.55974i
$274$	−1.97732			−0.119454
$275$	−6.42766	−	18.1306i	−0.387603	−	1.09331i
$276$	12.9456			0.779235
$277$		−	0.455504i		−	0.0273686i	−0.999906	−	0.0136843i	$-0.995644\pi$
$277$		−	0.455504i		−	0.0273686i	0.999906	−	0.0136843i	$-0.00435598\pi$
$278$		−	1.88327i		−	0.112951i
$279$	−3.18380			−0.190609
$280$	1.98187	−	2.80535i	0.118440	−	0.167652i
$281$	16.4941			0.983957			0.491978	−	0.870607i	$-0.336274\pi$
$281$	16.4941			0.983957			0.491978	+	0.870607i	$0.336274\pi$
$282$		−	1.21088i		−	0.0721071i
$283$		−	8.79775i		−	0.522972i	−0.965207	−	0.261486i	$-0.915788\pi$
$283$		−	8.79775i		−	0.522972i	0.965207	−	0.261486i	$-0.0842125\pi$
$284$	−2.35582			−0.139792
$285$	−17.4858	−	12.3530i	−1.03577	−	0.731731i
$286$	3.22216			0.190531
$287$		−	5.85077i		−	0.345360i
$288$		−	1.45198i		−	0.0855585i
$289$		0			0
$290$	0.161926	+	0.114394i	0.00950860	+	0.00671747i
$291$	5.91134			0.346529
$292$		−	6.46744i		−	0.378478i
$293$		−	22.5023i		−	1.31460i	−0.753630	−	0.657299i	$-0.771699\pi$
$293$		−	22.5023i		−	1.31460i	0.753630	−	0.657299i	$-0.228301\pi$
$294$	−0.235590			−0.0137399
$295$	2.58042	−	3.65259i	0.150238	−	0.212662i
$296$	1.79130			0.104117
$297$			21.7469i			1.26188i
$298$		−	2.40168i		−	0.139125i
$299$	28.1056			1.62539
$300$	13.5034	−	4.78723i	0.779617	−	0.276391i
$301$	3.70501			0.213553
$302$			0.377361i			0.0217147i
$303$			17.7645i			1.02054i
$304$	−25.7712			−1.47808
$305$	9.82668	−	13.9097i	0.562674	−	0.796467i
$306$		0			0
$307$		−	11.7034i		−	0.667947i	−0.942583	−	0.333973i	$-0.891610\pi$
$307$		−	11.7034i		−	0.667947i	0.942583	−	0.333973i	$-0.108390\pi$
$308$			21.8477i			1.24489i
$309$	−19.6082			−1.11547
$310$	0.860532	+	0.607933i	0.0488749	+	0.0345283i
$311$	21.0605			1.19423			0.597115	−	0.802155i	$-0.296313\pi$
$311$	21.0605			1.19423			0.597115	+	0.802155i	$0.296313\pi$
$312$			4.82159i			0.272969i
$313$		−	22.2911i		−	1.25997i	−0.776609	−	0.629983i	$-0.783062\pi$
$313$		−	22.2911i		−	1.25997i	0.776609	−	0.629983i	$-0.216938\pi$
$314$	−0.485459			−0.0273960
$315$	4.76047	+	3.36309i	0.268222	+	0.189489i
$316$	−9.90453			−0.557174
$317$		−	27.8613i		−	1.56485i	−0.622747	−	0.782423i	$-0.713984\pi$
$317$		−	27.8613i		−	1.56485i	0.622747	−	0.782423i	$-0.286016\pi$
$318$		−	1.93238i		−	0.108362i
$319$	−2.53365			−0.141857
$320$	9.76464	−	13.8219i	0.545860	−	0.772667i
$321$	9.59713			0.535659
$322$		−	1.74289i		−	0.0971277i
$323$		0			0
$324$	−10.7880			−0.599335
$325$	29.3165	−	10.3933i	1.62618	−	0.576517i
$326$	−1.84790			−0.102346
$327$		−	3.73074i		−	0.206310i
$328$			1.09463i			0.0604409i
$329$	17.8250			0.982726
$330$	0.966189	−	1.36764i	0.0531869	−	0.0752863i
$331$	−13.0067			−0.714914			−0.357457	−	0.933930i	$-0.616356\pi$
$331$	−13.0067			−0.714914			−0.357457	+	0.933930i	$0.616356\pi$
$332$			15.6872i			0.860947i
$333$			3.03971i			0.166575i
$334$	0.851794			0.0466081
$335$	−0.469553	−	0.331721i	−0.0256544	−	0.0181239i
$336$	−16.1217			−0.879509
$337$		−	15.1126i		−	0.823238i	−0.911356	−	0.411619i	$-0.864963\pi$
$337$		−	15.1126i		−	0.823238i	0.911356	−	0.411619i	$-0.135037\pi$
$338$			3.45991i			0.188194i
$339$	−12.4812			−0.677888
$340$		0			0
$341$	−13.4647			−0.729155
$342$			0.811065i			0.0438574i
$343$			16.5895i			0.895750i
$344$	−0.693177			−0.0373736
$345$	8.42766	−	11.9294i	0.453730	−	0.642257i
$346$	0.237893			0.0127892
$347$		−	3.58828i		−	0.192629i	−0.995351	−	0.0963144i	$-0.969295\pi$
$347$		−	3.58828i		−	0.192629i	0.995351	−	0.0963144i	$-0.0307054\pi$
$348$		−	1.88702i		−	0.101155i
$349$	−31.2851			−1.67465			−0.837326	−	0.546703i	$-0.815883\pi$
$349$	−31.2851			−1.67465			−0.837326	+	0.546703i	$0.815883\pi$
$350$	−0.644513	−	1.81798i	−0.0344507	−	0.0971753i
$351$	−35.1640			−1.87691
$352$		−	6.14060i		−	0.327295i
$353$		−	24.4417i		−	1.30090i	−0.759549	−	0.650450i	$-0.774580\pi$
$353$		−	24.4417i		−	1.30090i	0.759549	−	0.650450i	$-0.225420\pi$
$354$	0.389298			0.0206910
$355$	−1.53365	+	2.17088i	−0.0813975	+	0.115219i
$356$	−25.3705			−1.34463
$357$		0			0
$358$			0.149229i			0.00788702i
$359$	0.136195			0.00718808			0.00359404	−	0.999994i	$-0.498856\pi$
$359$	0.136195			0.00718808			0.00359404	+	0.999994i	$0.498856\pi$
$360$	−0.890646	−	0.629207i	−0.0469411	−	0.0331621i
$361$	24.8550			1.30816
$362$		−	1.45820i		−	0.0766412i
$363$			5.49583i			0.288456i
$364$	−35.3270			−1.85164
$365$	−5.95975	−	4.21033i	−0.311947	−	0.220379i
$366$	1.48251			0.0774922
$367$		−	16.9896i		−	0.886851i	−0.896311	−	0.443426i	$-0.853763\pi$
$367$		−	16.9896i		−	0.886851i	0.896311	−	0.443426i	$-0.146237\pi$
$368$		−	17.5820i		−	0.916524i
$369$	−1.85751			−0.0966980
$370$	0.580419	−	0.821585i	0.0301745	−	0.0427122i
$371$	28.4459			1.47684
$372$		−	10.0283i		−	0.519944i
$373$		−	18.3533i		−	0.950296i	−0.879906	−	0.475148i	$-0.842394\pi$
$373$		−	18.3533i		−	0.950296i	0.879906	−	0.475148i	$-0.157606\pi$
$374$		0			0
$375$	4.37933	−	15.5599i	0.226147	−	0.803507i
$376$	−3.33492			−0.171985
$377$		−	4.09682i		−	0.210997i
$378$			2.18060i			0.112158i
$379$	−35.1943			−1.80781			−0.903905	−	0.427732i	$-0.859313\pi$
$379$	−35.1943			−1.80781			−0.903905	+	0.427732i	$0.859313\pi$
$380$	−16.9335	+	23.9694i	−0.868668	+	1.22960i
$381$	4.69230			0.240394
$382$		−	0.429773i		−	0.0219891i
$383$			10.8237i			0.553067i	0.961004	+	0.276533i	$0.0891856\pi$
$383$			10.8237i			0.553067i	−0.961004	+	0.276533i	$0.910814\pi$
$384$	6.08841			0.310698
$385$	20.1327	+	14.2230i	1.02606	+	0.724870i
$386$	−0.957780			−0.0487497
$387$		−	1.17627i		−	0.0597931i
$388$		−	8.10322i		−	0.411379i
$389$	−0.174083			−0.00882636			−0.00441318	−	0.999990i	$-0.501405\pi$
$389$	−0.174083			−0.00882636			−0.00441318	+	0.999990i	$0.501405\pi$
$390$	2.21143	+	1.56229i	0.111980	+	0.0791098i
$391$		0			0
$392$			0.648845i			0.0327716i
$393$			4.98424i			0.251422i
$394$	−3.11971			−0.157169
$395$	−6.44790	+	9.12703i	−0.324429	+	0.459231i
$396$	6.93623			0.348559
$397$			2.75287i			0.138162i	0.997611	+	0.0690812i	$0.0220067\pi$
$397$			2.75287i			0.138162i	−0.997611	+	0.0690812i	$0.977993\pi$
$398$			3.32717i			0.166776i
$399$	27.4343			1.37343
$400$	−6.50173	−	18.3395i	−0.325086	−	0.916974i
$401$	−33.9912			−1.69744			−0.848719	−	0.528843i	$-0.822626\pi$
$401$	−33.9912			−1.69744			−0.848719	+	0.528843i	$0.822626\pi$
$402$		−	0.0500455i		−	0.00249604i
$403$		−	21.7720i		−	1.08454i
$404$	24.3514			1.21153
$405$	−7.02306	+	9.94117i	−0.348979	+	0.493981i
$406$	−0.254053			−0.0126085
$407$			12.8553i			0.637215i
$408$		0			0
$409$	4.68288			0.231553			0.115777	−	0.993275i	$-0.463064\pi$
$409$	4.68288			0.231553			0.115777	+	0.993275i	$0.463064\pi$
$410$	0.502056	+	0.354683i	0.0247948	+	0.0175166i
$411$	21.2341			1.04740
$412$			26.8788i			1.32422i
$413$			5.73074i			0.281991i
$414$	−0.553336			−0.0271950
$415$	14.4558	+	10.2124i	0.709605	+	0.501309i
$416$	9.92913			0.486816
$417$			20.2241i			0.990380i
$418$			3.43010i			0.167772i
$419$	−29.0991			−1.42158			−0.710792	−	0.703402i	$-0.751663\pi$
$419$	−29.0991			−1.42158			−0.710792	+	0.703402i	$0.751663\pi$
$420$	−10.5931	+	14.9945i	−0.516888	+	0.731657i
$421$	7.19057			0.350447			0.175224	−	0.984529i	$-0.443935\pi$
$421$	7.19057			0.350447			0.175224	+	0.984529i	$0.443935\pi$
$422$		−	0.575063i		−	0.0279936i
$423$		−	5.65911i		−	0.275155i
$424$	−5.32200			−0.258459
$425$		0			0
$426$	−0.231376			−0.0112102
$427$			21.8236i			1.05612i
$428$		−	13.1557i		−	0.635903i
$429$	−34.6022			−1.67061
$430$	−0.224604	+	0.317927i	−0.0108313	+	0.0153318i
$431$	−7.63181			−0.367611			−0.183806	−	0.982963i	$-0.558842\pi$
$431$	−7.63181			−0.367611			−0.183806	+	0.982963i	$0.558842\pi$
$432$			21.9975i			1.05835i
$433$		−	32.2894i		−	1.55173i	−0.630898	−	0.775865i	$-0.717314\pi$
$433$		−	32.2894i		−	1.55173i	0.630898	−	0.775865i	$-0.282686\pi$
$434$	−1.35013			−0.0648084
$435$	−1.73889	−	1.22846i	−0.0833734	−	0.0589002i
$436$	−5.11407			−0.244919
$437$			29.9193i			1.43124i
$438$		−	0.635197i		−	0.0303509i
$439$	−13.3974			−0.639422			−0.319711	−	0.947515i	$-0.603586\pi$
$439$	−13.3974			−0.639422			−0.319711	+	0.947515i	$0.603586\pi$
$440$	−3.76666	−	2.66100i	−0.179568	−	0.126858i
$441$	−1.10104			−0.0524305
$442$		0			0
$443$			6.89070i			0.327387i	0.986511	+	0.163693i	$0.0523408\pi$
$443$			6.89070i			0.327387i	−0.986511	+	0.163693i	$0.947659\pi$
$444$	−9.57445			−0.454383
$445$	−16.5163	+	23.3789i	−0.782949	+	1.10827i
$446$	0.491976			0.0232957
$447$			25.7912i			1.21988i
$448$			21.6859i			1.02456i
$449$	21.1778			0.999440			0.499720	−	0.866187i	$-0.333436\pi$
$449$	21.1778			0.999440			0.499720	+	0.866187i	$0.333436\pi$
$450$	−0.577175	+	0.204621i	−0.0272083	+	0.00964591i
$451$	−7.85565			−0.369908
$452$			17.1092i			0.804748i
$453$		−	4.05241i		−	0.190399i
$454$	2.55822			0.120063
$455$	−22.9980	+	32.5538i	−1.07816	+	1.52615i
$456$	−5.13274			−0.240363
$457$			30.2321i			1.41420i	0.707114	+	0.707100i	$0.249997\pi$
$457$			30.2321i			1.41420i	−0.707114	+	0.707100i	$0.750003\pi$
$458$		−	2.81179i		−	0.131387i
$459$		0			0
$460$	−16.3527	−	11.5526i	−0.762449	−	0.538642i
$461$	3.74267			0.174314			0.0871568	−	0.996195i	$-0.472222\pi$
$461$	3.74267			0.174314			0.0871568	+	0.996195i	$0.472222\pi$
$462$			2.14577i			0.0998300i
$463$			2.53452i			0.117789i	0.998264	+	0.0588947i	$0.0187576\pi$
$463$			2.53452i			0.117789i	−0.998264	+	0.0588947i	$0.981242\pi$
$464$	−2.56284			−0.118977
$465$	−9.24109	−	6.52848i	−0.428545	−	0.302751i
$466$	0.0919369			0.00425890
$467$			30.1170i			1.39365i	0.717242	+	0.696824i	$0.245404\pi$
$467$			30.1170i			1.39365i	−0.717242	+	0.696824i	$0.754596\pi$
$468$			11.2156i			0.518443i
$469$	0.736705			0.0340179
$470$	−1.08058	+	1.52957i	−0.0498436	+	0.0705538i
$471$	5.21325			0.240214
$472$		−	1.07217i		−	0.0493508i
$473$		−	4.97460i		−	0.228732i
$474$	−0.972770			−0.0446808
$475$	11.0640	+	31.2084i	0.507652	+	1.43194i
$476$		0			0
$477$		−	9.03104i		−	0.413503i
$478$			3.90318i			0.178527i
$479$	14.4995			0.662499			0.331250	−	0.943543i	$-0.392530\pi$
$479$	14.4995			0.662499			0.331250	+	0.943543i	$0.392530\pi$
$480$	2.97732	−	4.21441i	0.135896	−	0.192361i
$481$	−20.7866			−0.947787
$482$		−	2.43607i		−	0.110960i
$483$			18.7166i			0.851635i
$484$	7.53365			0.342438
$485$	−7.46711	−	5.27523i	−0.339064	−	0.239536i
$486$	1.22352			0.0554998
$487$			23.9424i			1.08493i	0.840077	+	0.542467i	$0.182510\pi$
$487$			23.9424i			1.08493i	−0.840077	+	0.542467i	$0.817490\pi$
$488$		−	4.08302i		−	0.184830i
$489$	19.8443			0.897388
$490$	0.297594	+	0.210239i	0.0134439	+	0.00949764i
$491$	−21.1295			−0.953559			−0.476780	−	0.879023i	$-0.658196\pi$
$491$	−21.1295			−0.953559			−0.476780	+	0.879023i	$0.658196\pi$
$492$		−	5.85077i		−	0.263773i
$493$		0			0
$494$	−5.54635			−0.249542
$495$	4.51552	−	6.39174i	0.202958	−	0.287287i
$496$	−13.6199			−0.611550
$497$		−	3.40601i		−	0.152780i
$498$			1.54071i			0.0690410i
$499$	4.01027			0.179524			0.0897621	−	0.995963i	$-0.471389\pi$
$499$	4.01027			0.179524			0.0897621	+	0.995963i	$0.471389\pi$
$500$	−21.3293	−	6.00315i	−0.953877	−	0.268469i
$501$	−9.14726			−0.408670
$502$			0.971133i			0.0433438i
$503$		−	1.44015i		−	0.0642130i	−0.999484	−	0.0321065i	$-0.989778\pi$
$503$		−	1.44015i		−	0.0642130i	0.999484	−	0.0321065i	$-0.0102216\pi$
$504$	1.39738			0.0622442
$505$	15.8529	−	22.4398i	0.705444	−	0.998559i
$506$	−2.34013			−0.104031
$507$		−	37.1553i		−	1.65013i
$508$		−	6.43217i		−	0.285381i
$509$	−31.1478			−1.38060			−0.690301	−	0.723522i	$-0.742522\pi$
$509$	−31.1478			−1.38060			−0.690301	+	0.723522i	$0.742522\pi$
$510$		0			0
$511$	9.35054			0.413644
$512$		−	10.3838i		−	0.458904i
$513$		−	37.4332i		−	1.65272i
$514$	0.656925			0.0289757
$515$	24.7688	+	17.4982i	1.09144	+	0.771063i
$516$	3.70501			0.163104
$517$		−	23.9331i		−	1.05258i
$518$			1.28903i			0.0566366i
$519$	−2.55469			−0.112138
$520$	4.30275	−	6.09055i	0.188688	−	0.267088i
$521$	39.1197			1.71387			0.856933	−	0.515428i	$-0.172367\pi$
$521$	39.1197			1.71387			0.856933	+	0.515428i	$0.172367\pi$
$522$			0.0806571i			0.00353027i
$523$		−	40.4813i		−	1.77012i	−0.465473	−	0.885062i	$-0.654116\pi$
$523$		−	40.4813i		−	1.77012i	0.465473	−	0.885062i	$-0.345884\pi$
$524$	6.83236			0.298473
$525$	6.92131	+	19.5230i	0.302071	+	0.852053i
$526$	4.04211			0.176244
$527$		0			0
$528$			21.6461i			0.942025i
$529$	2.58802			0.112523
$530$	−1.72444	+	2.44095i	−0.0749049	+	0.106028i
$531$	1.81940			0.0789552
$532$		−	37.6068i		−	1.63046i
$533$		−	12.7023i		−	0.550198i
$534$	−2.49176			−0.107829
$535$	−12.1229	−	8.56440i	−0.524121	−	0.370272i
$536$	−0.137831			−0.00595341
$537$		−	1.60255i		−	0.0691550i
$538$			3.99275i			0.172140i
$539$	−4.65645			−0.200568
$540$	20.4595	+	14.4539i	0.880437	+	0.621995i
$541$	18.5288			0.796614			0.398307	−	0.917252i	$-0.369598\pi$
$541$	18.5288			0.796614			0.398307	+	0.917252i	$0.369598\pi$
$542$		−	0.527248i		−	0.0226472i
$543$			15.6593i			0.672006i
$544$		0			0
$545$	−3.32928	+	4.71261i	−0.142611	+	0.201866i
$546$	−3.46963			−0.148486
$547$			43.2959i			1.85120i	0.378504	+	0.925600i	$0.376439\pi$
$547$			43.2959i			1.85120i	−0.378504	+	0.925600i	$0.623561\pi$
$548$		−	29.1075i		−	1.24341i
$549$	6.92858			0.295705
$550$	−2.44095	+	0.865368i	−0.104082	+	0.0368994i
$551$	4.36120			0.185793
$552$		−	3.50173i		−	0.149043i
$553$		−	14.3198i		−	0.608942i
$554$	−0.0613254			−0.00260546
$555$	−6.23301	+	8.82285i	−0.264577	+	0.374509i
$556$	27.7231			1.17572
$557$			25.3698i			1.07495i	0.843279	+	0.537476i	$0.180622\pi$
$557$			25.3698i			1.07495i	−0.843279	+	0.537476i	$0.819378\pi$
$558$			0.428641i			0.0181458i
$559$	8.04375			0.340214
$560$	20.3647	+	14.3869i	0.860564	+	0.607956i
$561$		0			0
$562$		−	2.22063i		−	0.0936718i
$563$		−	35.6622i		−	1.50298i	−0.659742	−	0.751492i	$-0.729335\pi$
$563$		−	35.6622i		−	1.50298i	0.659742	−	0.751492i	$-0.270665\pi$
$564$	17.8250			0.750570
$565$	15.7661	+	11.1382i	0.663285	+	0.468586i
$566$	−1.18446			−0.0497864
$567$		−	15.5972i		−	0.655021i
$568$			0.637236i			0.0267378i
$569$	−27.7944			−1.16520			−0.582602	−	0.812758i	$-0.697965\pi$
$569$	−27.7944			−1.16520			−0.582602	+	0.812758i	$0.697965\pi$
$570$	−1.66311	+	2.35414i	−0.0696602	+	0.0986043i
$571$	15.8578			0.663627			0.331813	−	0.943345i	$-0.392340\pi$
$571$	15.8578			0.663627			0.331813	+	0.943345i	$0.392340\pi$
$572$			47.4325i			1.98325i
$573$			4.61525i			0.192805i
$574$	−0.787700			−0.0328780
$575$	−21.2914	+	7.54824i	−0.887912	+	0.314784i
$576$	6.88485			0.286869
$577$		−	25.2762i		−	1.05226i	−0.850403	−	0.526131i	$-0.823642\pi$
$577$		−	25.2762i		−	1.05226i	0.850403	−	0.526131i	$-0.176358\pi$
$578$		0			0
$579$	10.2854			0.427448
$580$	−1.68396	+	2.38366i	−0.0699228	+	0.0989760i
$581$	−22.6804			−0.940940
$582$		−	0.795854i		−	0.0329892i
$583$		−	38.1935i		−	1.58181i
$584$	−1.74941			−0.0723911
$585$	10.3352	+	7.30144i	0.427309	+	0.301877i
$586$	−3.02952			−0.125148
$587$		−	15.7829i		−	0.651431i	−0.945468	−	0.325716i	$-0.894395\pi$
$587$		−	15.7829i		−	0.651431i	0.945468	−	0.325716i	$-0.105605\pi$
$588$		−	3.46805i		−	0.143020i
$589$	23.1770			0.954992
$590$	−0.491756	−	0.347407i	−0.0202453	−	0.0143025i
$591$	33.5019			1.37809
$592$			13.0035i			0.534439i
$593$			19.3560i			0.794855i	0.917634	+	0.397428i	$0.130097\pi$
$593$			19.3560i			0.794855i	−0.917634	+	0.397428i	$0.869903\pi$
$594$	2.92783			0.120130
$595$		0			0
$596$	35.3543			1.44817
$597$		−	35.7299i		−	1.46233i
$598$		−	3.78391i		−	0.154735i
$599$	15.8356			0.647023			0.323512	−	0.946224i	$-0.395136\pi$
$599$	15.8356			0.647023			0.323512	+	0.946224i	$0.395136\pi$
$600$	−1.29492	−	3.65259i	−0.0528649	−	0.149116i
$601$	−9.30443			−0.379536			−0.189768	−	0.981829i	$-0.560774\pi$
$601$	−9.30443			−0.379536			−0.189768	+	0.981829i	$0.560774\pi$
$602$		−	0.498812i		−	0.0203301i
$603$		−	0.233890i		−	0.00952473i
$604$	−5.55502			−0.226030
$605$	4.90444	−	6.94225i	0.199394	−	0.282243i
$606$	2.39166			0.0971547
$607$			26.6661i			1.08234i	0.840912	+	0.541172i	$0.182019\pi$
$607$			26.6661i			1.08234i	−0.840912	+	0.541172i	$0.817981\pi$
$608$			10.5699i			0.428666i
$609$	2.72823			0.110554
$610$	−1.87269	−	1.32298i	−0.0758230	−	0.0535661i
$611$	38.6990			1.56560
$612$		0			0
$613$			26.0929i			1.05388i	0.849902	+	0.526941i	$0.176661\pi$
$613$			26.0929i			1.05388i	−0.849902	+	0.526941i	$0.823339\pi$
$614$	−1.57565			−0.0635879
$615$	−5.39148	−	3.80888i	−0.217406	−	0.153589i
$616$	5.90970			0.238109
$617$			23.4622i			0.944554i	0.881450	+	0.472277i	$0.156568\pi$
$617$			23.4622i			0.944554i	−0.881450	+	0.472277i	$0.843432\pi$
$618$			2.63989i			0.106192i
$619$	3.50613			0.140923			0.0704617	−	0.997514i	$-0.477553\pi$
$619$	3.50613			0.140923			0.0704617	+	0.997514i	$0.477553\pi$
$620$	−8.94920	+	12.6676i	−0.359408	+	0.508744i
$621$	25.5382			1.02481
$622$		−	2.83541i		−	0.113690i
$623$		−	36.6804i		−	1.46957i
$624$	−35.0009			−1.40116
$625$	−19.4174	+	15.7469i	−0.776696	+	0.629876i
$626$	−3.00109			−0.119948
$627$		−	36.8352i		−	1.47106i
$628$		−	7.14628i		−	0.285168i
$629$		0			0
$630$	0.452779	−	0.640911i	0.0180392	−	0.0255345i
$631$	−7.57823			−0.301685			−0.150842	−	0.988558i	$-0.548199\pi$
$631$	−7.57823			−0.301685			−0.150842	+	0.988558i	$0.548199\pi$
$632$			2.67913i			0.106570i
$633$			6.17550i			0.245454i
$634$	−3.75102			−0.148972
$635$	−5.92724	−	4.18737i	−0.235215	−	0.166171i
$636$	28.4459			1.12795
$637$		−	7.52932i		−	0.298322i
$638$			0.341110i			0.0135047i
$639$	−1.08134			−0.0427772
$640$	−7.69079	−	5.43325i	−0.304005	−	0.214768i
$641$	−4.21055			−0.166307			−0.0831535	−	0.996537i	$-0.526499\pi$
$641$	−4.21055			−0.166307			−0.0831535	+	0.996537i	$0.526499\pi$
$642$		−	1.29208i		−	0.0509943i
$643$			39.0726i			1.54087i	0.637516	+	0.770437i	$0.279962\pi$
$643$			39.0726i			1.54087i	−0.637516	+	0.770437i	$0.720038\pi$
$644$	25.6566			1.01101
$645$	2.41198	−	3.41416i	0.0949715	−	0.134432i
$646$		0			0
$647$			27.0481i			1.06337i	0.846942	+	0.531685i	$0.178441\pi$
$647$			27.0481i			1.06337i	−0.846942	+	0.531685i	$0.821559\pi$
$648$			2.91811i			0.114634i
$649$	7.69448			0.302035
$650$	−1.39927	−	3.94693i	−0.0548839	−	0.154811i
$651$	14.4988			0.568253
$652$		−	27.2024i		−	1.06533i
$653$		−	35.6550i		−	1.39529i	−0.716445	−	0.697643i	$-0.754232\pi$
$653$		−	35.6550i		−	1.39529i	0.716445	−	0.697643i	$-0.245768\pi$
$654$	−0.502276			−0.0196405
$655$	4.44790	−	6.29602i	0.173794	−	0.246006i
$656$	−7.94617			−0.310246
$657$		−	2.96862i		−	0.115817i
$658$		−	2.39982i		−	0.0935547i
$659$	−0.586716			−0.0228552			−0.0114276	−	0.999935i	$-0.503638\pi$
$659$	−0.586716			−0.0228552			−0.0114276	+	0.999935i	$0.503638\pi$
$660$	20.1327	+	14.2230i	0.783663	+	0.553628i
$661$	18.8785			0.734290			0.367145	−	0.930164i	$-0.380335\pi$
$661$	18.8785			0.734290			0.367145	+	0.930164i	$0.380335\pi$
$662$			1.75112i			0.0680592i
$663$		0			0
$664$	4.24331			0.164672
$665$	−34.6546	−	24.4822i	−1.34385	−	0.949378i
$666$	0.409241			0.0158578
$667$			2.97536i			0.115206i
$668$			12.5390i			0.485149i
$669$	−5.28324			−0.204262
$670$	−0.0446602	+	0.0632168i	−0.00172538	+	0.00244228i
$671$	29.3019			1.13119
$672$			6.61220i			0.255071i
$673$			44.9680i			1.73339i	0.498841	+	0.866694i	$0.333759\pi$
$673$			44.9680i			1.73339i	−0.498841	+	0.866694i	$0.666241\pi$
$674$	−2.03464			−0.0783716
$675$	26.6385	−	9.44390i	1.02532	−	0.363496i
$676$	−50.9323			−1.95893
$677$			33.3876i			1.28319i	0.767044	+	0.641594i	$0.221727\pi$
$677$			33.3876i			1.28319i	−0.767044	+	0.641594i	$0.778273\pi$
$678$			1.68037i			0.0645343i
$679$	11.7155			0.449601
$680$		0			0
$681$	−27.4722			−1.05274
$682$			1.81278i			0.0694149i
$683$			22.0237i			0.842713i	0.906895	+	0.421357i	$0.138446\pi$
$683$			22.0237i			0.842713i	−0.906895	+	0.421357i	$0.861554\pi$
$684$	−11.9394			−0.456516
$685$	−26.8226	−	18.9492i	−1.02484	−	0.724010i
$686$	2.23348			0.0852746
$687$			30.1953i			1.15202i
$688$		−	5.03192i		−	0.191840i
$689$	61.7575			2.35277
$690$	−1.60608	−	1.13463i	−0.0611423	−	0.0431947i
$691$	−4.51396			−0.171719			−0.0858595	−	0.996307i	$-0.527364\pi$
$691$	−4.51396			−0.171719			−0.0858595	+	0.996307i	$0.527364\pi$
$692$			3.50195i			0.133124i
$693$			10.0283i			0.380944i
$694$	−0.483097			−0.0183381
$695$	18.0479	−	25.5468i	0.684594	−	0.969046i
$696$	−0.510430			−0.0193478
$697$		0			0
$698$			4.21197i			0.159425i
$699$	−0.987294			−0.0373429
$700$	26.7620	−	9.48768i	1.01151	−	0.358601i
$701$	−29.3948			−1.11023			−0.555114	−	0.831774i	$-0.687325\pi$
$701$	−29.3948			−1.11023			−0.555114	+	0.831774i	$0.687325\pi$
$702$			4.73419i			0.178681i
$703$		−	22.1280i		−	0.834575i
$704$	29.1169			1.09739
$705$	11.6042	−	16.4258i	0.437039	−	0.618630i
$706$	−3.29063			−0.123845
$707$			35.2070i			1.32409i
$708$			5.73074i			0.215374i
$709$	−1.86205			−0.0699308			−0.0349654	−	0.999389i	$-0.511132\pi$
$709$	−1.86205			−0.0699308			−0.0349654	+	0.999389i	$0.511132\pi$
$710$	0.292270	+	0.206478i	0.0109687	+	0.00774897i
$711$	−4.54628			−0.170499
$712$			6.86260i			0.257187i
$713$			15.8121i			0.592169i
$714$		0			0
$715$	43.7090	+	30.8788i	1.63462	+	1.15480i
$716$	−2.19676			−0.0820968
$717$		−	41.9156i		−	1.56537i
$718$		−	0.0183362i		−	0.000684299i
$719$	−15.8028			−0.589346			−0.294673	−	0.955598i	$-0.595211\pi$
$719$	−15.8028			−0.589346			−0.294673	+	0.955598i	$0.595211\pi$
$720$	4.56755	−	6.46539i	0.170223	−	0.240951i
$721$	−38.8610			−1.44726
$722$		−	3.34627i		−	0.124535i
$723$			26.1605i			0.972920i
$724$	21.4657			0.797766
$725$	1.10027	+	3.10355i	0.0408631	+	0.115263i
$726$	0.739914			0.0274608
$727$		−	21.0930i		−	0.782296i	−0.920328	−	0.391148i	$-0.872078\pi$
$727$		−	21.0930i		−	0.782296i	0.920328	−	0.391148i	$-0.127922\pi$
$728$			9.55578i			0.354161i
$729$	−29.4692			−1.09145
$730$	−0.566845	+	0.802372i	−0.0209799	+	0.0296971i
$731$		0			0
$732$			21.8236i			0.806624i
$733$			40.8012i			1.50703i	0.657434	+	0.753513i	$0.271642\pi$
$733$			40.8012i			1.50703i	−0.657434	+	0.753513i	$0.728358\pi$
$734$	−2.28735			−0.0844275
$735$	−3.19581	−	2.25772i	−0.117879	−	0.0832772i
$736$	−7.21114			−0.265806
$737$		−	0.989151i		−	0.0364358i
$738$			0.250080i			0.00920557i
$739$	−13.8161			−0.508234			−0.254117	−	0.967173i	$-0.581785\pi$
$739$	−13.8161			−0.508234			−0.254117	+	0.967173i	$0.581785\pi$
$740$	12.0943	+	8.54417i	0.444595	+	0.314090i
$741$	59.5613			2.18804
$742$		−	3.82973i		−	0.140594i
$743$		−	3.01696i		−	0.110682i	−0.998468	−	0.0553408i	$-0.982375\pi$
$743$		−	3.01696i		−	0.110682i	0.998468	−	0.0553408i	$-0.0176245\pi$
$744$	−2.71261			−0.0994491
$745$	23.0158	−	32.5790i	0.843235	−	1.19360i
$746$	−2.47093			−0.0904674
$747$			7.20058i			0.263456i
$748$		0			0
$749$	19.0203			0.694987
$750$	−2.09485	−	0.589597i	−0.0764932	−	0.0215290i
$751$	44.6641			1.62982			0.814909	−	0.579589i	$-0.196787\pi$
$751$	44.6641			1.62982			0.814909	+	0.579589i	$0.196787\pi$
$752$		−	24.2089i		−	0.882808i
$753$		−	10.4288i		−	0.380047i
$754$	−0.551562			−0.0200867
$755$	−3.61634	+	5.11895i	−0.131612	+	0.186298i
$756$	−32.0999			−1.16746
$757$			12.3652i			0.449421i	0.974426	+	0.224710i	$0.0721436\pi$
$757$			12.3652i			0.449421i	−0.974426	+	0.224710i	$0.927856\pi$
$758$			4.73828i			0.172102i
$759$	25.1302			0.912169
$760$	6.48360	+	4.58042i	0.235185	+	0.166149i
$761$	16.7175			0.606009			0.303004	−	0.952989i	$-0.402010\pi$
$761$	16.7175			0.606009			0.303004	+	0.952989i	$0.402010\pi$
$762$		−	0.631733i		−	0.0228853i
$763$		−	7.39385i		−	0.267675i
$764$	6.32656			0.228887
$765$		0			0
$766$	1.45722			0.0526515
$767$			12.4417i			0.449244i
$768$			21.0645i			0.760100i
$769$	−13.4025			−0.483308			−0.241654	−	0.970362i	$-0.577690\pi$
$769$	−13.4025			−0.483308			−0.241654	+	0.970362i	$0.577690\pi$
$770$	1.91486	−	2.71050i	0.0690069	−	0.0976796i
$771$	−7.05460			−0.254065
$772$		−	14.0992i		−	0.507441i
$773$		−	25.8358i		−	0.929248i	−0.885508	−	0.464624i	$-0.846189\pi$
$773$		−	25.8358i		−	0.929248i	0.885508	−	0.464624i	$-0.153811\pi$
$774$	−0.158363			−0.00569225
$775$	5.84724	+	16.4934i	0.210039	+	0.592459i
$776$	−2.19188			−0.0786839
$777$		−	13.8426i		−	0.496601i
$778$			0.0234371i			0.000840261i
$779$	13.5220			0.484477
$780$	−22.9980	+	32.5538i	−0.823462	+	1.16561i
$781$	−4.57314			−0.163640
$782$		0			0
$783$		−	3.72258i		−	0.133034i
$784$	−4.71011			−0.168218
$785$	−6.58530	−	4.65226i	−0.235039	−	0.166046i
$786$	0.671038			0.0239351
$787$		−	45.2989i		−	1.61473i	−0.590051	−	0.807366i	$-0.700892\pi$
$787$		−	45.2989i		−	1.61473i	0.590051	−	0.807366i	$-0.299108\pi$
$788$		−	45.9242i		−	1.63598i
$789$	−43.4075			−1.54535
$790$	1.22879	+	0.868093i	0.0437183	+	0.0308854i
$791$	−24.7362			−0.879519
$792$		−	1.87622i		−	0.0666685i
$793$			47.3802i			1.68252i
$794$	0.370623			0.0131529
$795$	18.5184	−	26.2129i	0.656781	−	0.929677i
$796$	−48.9782			−1.73599
$797$			29.3607i			1.04001i	0.854163	+	0.520005i	$0.174070\pi$
$797$			29.3607i			1.04001i	−0.854163	+	0.520005i	$0.825930\pi$
$798$		−	3.69353i		−	0.130750i
$799$		0			0
$800$	−7.52182	+	2.66664i	−0.265936	+	0.0942800i
$801$	−11.6453			−0.411467
$802$			4.57630i			0.161595i
$803$		−	12.5547i		−	0.443045i
$804$	0.736705			0.0259816
$805$	16.7026	−	23.6425i	0.588688	−	0.833290i
$806$	−2.93120			−0.103247
$807$		−	42.8774i		−	1.50936i
$808$		−	6.58694i		−	0.231728i
$809$	5.04830			0.177489			0.0887444	−	0.996054i	$-0.471715\pi$
$809$	5.04830			0.177489			0.0887444	+	0.996054i	$0.471715\pi$
$810$	1.33840	+	0.945527i	0.0470265	+	0.0332224i
$811$	−54.3374			−1.90805			−0.954023	−	0.299734i	$-0.903102\pi$
$811$	−54.3374			−1.90805			−0.954023	+	0.299734i	$0.903102\pi$
$812$		−	3.73984i		−	0.131243i
$813$			5.66202i			0.198576i
$814$	1.73074			0.0606623
$815$	−25.0670	−	17.7089i	−0.878057	−	0.620314i
$816$		0			0
$817$			8.56284i			0.299576i
$818$		−	0.630464i		−	0.0220437i
$819$	−16.2154			−0.566613
$820$	−5.22118	+	7.39061i	−0.182332	+	0.258091i
$821$	−3.05948			−0.106777			−0.0533883	−	0.998574i	$-0.517002\pi$
$821$	−3.05948			−0.106777			−0.0533883	+	0.998574i	$0.517002\pi$
$822$		−	2.85879i		−	0.0997116i
$823$			6.87523i			0.239656i	0.992795	+	0.119828i	$0.0382342\pi$
$823$			6.87523i			0.239656i	−0.992795	+	0.119828i	$0.961766\pi$
$824$	7.27057			0.253282
$825$	26.2129	−	9.29303i	0.912617	−	0.323542i
$826$	0.771540			0.0268453
$827$		−	24.2438i		−	0.843040i	−0.906819	−	0.421520i	$-0.861497\pi$
$827$		−	24.2438i		−	0.843040i	0.906819	−	0.421520i	$-0.138503\pi$
$828$		−	8.14548i		−	0.283075i
$829$	−15.7734			−0.547832			−0.273916	−	0.961754i	$-0.588319\pi$
$829$	−15.7734			−0.547832			−0.273916	+	0.961754i	$0.588319\pi$
$830$	1.37492	−	1.94621i	0.0477242	−	0.0675538i
$831$	0.658562			0.0228453
$832$			47.0811i			1.63224i
$833$		0			0
$834$	2.72281			0.0942833
$835$	11.5547	+	8.16295i	0.399866	+	0.282491i
$836$	−50.4935			−1.74635
$837$		−	19.7831i		−	0.683806i
$838$			3.91767i			0.135334i
$839$	9.98832			0.344835			0.172418	−	0.985024i	$-0.444842\pi$
$839$	9.98832			0.344835			0.172418	+	0.985024i	$0.444842\pi$
$840$	4.05594	+	2.86537i	0.139943	+	0.0988646i
$841$	−28.5663			−0.985045
$842$		−	0.968080i		−	0.0333622i
$843$			23.8470i			0.821334i
$844$	8.46533			0.291389
$845$	−33.1571	+	46.9341i	−1.14064	+	1.61458i
$846$	−0.761897			−0.0261945
$847$			10.8920i			0.374255i
$848$		−	38.6336i		−	1.32668i
$849$	12.7197			0.436538
$850$		0			0
$851$	15.0965			0.517501
$852$		−	3.40601i		−	0.116688i
$853$			31.1852i			1.06776i	0.845560	+	0.533880i	$0.179266\pi$
$853$			31.1852i			1.06776i	−0.845560	+	0.533880i	$0.820734\pi$
$854$	2.93816			0.100542
$855$	−7.77263	+	11.0022i	−0.265818	+	0.376267i
$856$	−3.55854			−0.121629
$857$			26.4712i			0.904240i	0.891957	+	0.452120i	$0.149332\pi$
$857$			26.4712i			0.904240i	−0.891957	+	0.452120i	$0.850668\pi$
$858$			4.65856i			0.159041i
$859$	−22.7223			−0.775273			−0.387637	−	0.921812i	$-0.626708\pi$
$859$	−22.7223			−0.775273			−0.387637	+	0.921812i	$0.626708\pi$
$860$	−4.68011	−	3.30632i	−0.159590	−	0.112745i
$861$	8.45897			0.288281
$862$			1.02748i			0.0349963i
$863$			35.3962i			1.20490i	0.798156	+	0.602451i	$0.205809\pi$
$863$			35.3962i			1.20490i	−0.798156	+	0.602451i	$0.794191\pi$
$864$	9.02213			0.306939
$865$	3.22704	+	2.27978i	0.109723	+	0.0775150i
$866$	−4.34719			−0.147723
$867$		0			0
$868$		−	19.8749i		−	0.674597i
$869$	−19.2268			−0.652225
$870$	−0.165390	+	0.234110i	−0.00560724	+	0.00793707i
$871$	1.59942			0.0541944
$872$			1.38333i			0.0468455i
$873$		−	3.71946i		−	0.125885i
$874$	4.02810			0.136252
$875$	8.67927	−	30.8377i	0.293413	−	1.04250i
$876$	9.35054			0.315926
$877$			1.09791i			0.0370736i	0.999828	+	0.0185368i	$0.00590079\pi$
$877$			1.09791i			0.0370736i	−0.999828	+	0.0185368i	$0.994099\pi$
$878$			1.80371i			0.0608724i
$879$	32.5335			1.09733
$880$	19.3168	−	27.3430i	0.651169	−	0.921732i
$881$	16.5399			0.557245			0.278622	−	0.960401i	$-0.410122\pi$
$881$	16.5399			0.557245			0.278622	+	0.960401i	$0.410122\pi$
$882$			0.148235i			0.00499134i
$883$			22.1505i			0.745425i	0.927947	+	0.372712i	$0.121572\pi$
$883$			22.1505i			0.745425i	−0.927947	+	0.372712i	$0.878428\pi$
$884$		0			0
$885$	5.28087	+	3.73074i	0.177515	+	0.125407i
$886$	0.927707			0.0311669
$887$		−	19.5836i		−	0.657553i	−0.944408	−	0.328776i	$-0.893364\pi$
$887$		−	19.5836i		−	0.657553i	0.944408	−	0.328776i	$-0.106636\pi$
$888$			2.58984i			0.0869094i
$889$	9.29955			0.311897
$890$	3.14755	+	2.22362i	0.105506	+	0.0745360i
$891$	−20.9419			−0.701579
$892$			7.24222i			0.242488i
$893$			41.1964i			1.37859i
$894$	3.47231			0.116131
$895$	−1.43010	+	2.02431i	−0.0478030	+	0.0676654i
$896$	12.0665			0.403112
$897$			40.6347i			1.35675i
$898$		−	2.85120i		−	0.0951458i
$899$	2.30486			0.0768713
$900$	−3.01216	−	8.49642i	−0.100405	−	0.283214i
$901$		0			0
$902$			1.05762i			0.0352149i
$903$			5.35665i			0.178258i
$904$	4.62795			0.153923
$905$	13.9743	−	19.7806i	0.464520	−	0.657531i
$906$	−0.545584			−0.0181258
$907$			38.3180i			1.27233i	0.771553	+	0.636165i	$0.219480\pi$
$907$			38.3180i			1.27233i	−0.771553	+	0.636165i	$0.780520\pi$
$908$			37.6587i			1.24975i
$909$	11.1775			0.370736
$910$	4.38278	+	3.09627i	0.145288	+	0.102640i
$911$	37.8395			1.25368			0.626840	−	0.779148i	$-0.284348\pi$
$911$	37.8395			1.25368			0.626840	+	0.779148i	$0.284348\pi$
$912$		−	37.2597i		−	1.23379i
$913$			30.4522i			1.00782i
$914$	4.07021			0.134631
$915$	20.1105	+	14.2073i	0.664831	+	0.469678i
$916$	41.3916			1.36762
$917$			9.87814i			0.326205i
$918$		0			0
$919$	28.8996			0.953309			0.476655	−	0.879091i	$-0.341849\pi$
$919$	28.8996			0.953309			0.476655	+	0.879091i	$0.341849\pi$
$920$	−3.12491	+	4.42333i	−0.103025	+	0.145833i
$921$	16.9206			0.557552
$922$		−	0.503883i		−	0.0165945i
$923$		−	7.39461i		−	0.243397i
$924$	−31.5871			−1.03914
$925$	15.7469	−	5.58260i	0.517755	−	0.183555i
$926$	0.341228			0.0112134
$927$			12.3376i			0.405220i
$928$			1.05113i			0.0345051i
$929$	−47.2978			−1.55179			−0.775895	−	0.630862i	$-0.782701\pi$
$929$	−47.2978			−1.55179			−0.775895	+	0.630862i	$0.782701\pi$
$930$	−0.878942	+	1.24415i	−0.0288216	+	0.0407971i
$931$	8.01521			0.262688
$932$			1.35338i			0.0443313i
$933$			30.4490i			0.996855i
$934$	4.05471			0.132674
$935$		0			0
$936$	3.03378			0.0991621
$937$			1.24572i			0.0406958i	0.999793	+	0.0203479i	$0.00647739\pi$
$937$			1.24572i			0.0406958i	−0.999793	+	0.0203479i	$0.993523\pi$
$938$		−	0.0991839i		−	0.00323847i
$939$	32.2281			1.05173
$940$	−22.5163	−	15.9069i	−0.734402	−	0.518827i
$941$	−37.9458			−1.23700			−0.618499	−	0.785785i	$-0.712259\pi$
$941$	−37.9458			−1.23700			−0.618499	+	0.785785i	$0.712259\pi$
$942$		−	0.701870i		−	0.0228681i
$943$			9.22519i			0.300413i
$944$	7.78315			0.253320
$945$	−20.8972	+	29.5801i	−0.679786	+	0.962240i
$946$	−0.669739			−0.0217751
$947$		−	52.2986i		−	1.69948i	−0.527205	−	0.849738i	$-0.676760\pi$
$947$		−	52.2986i		−	1.69948i	0.527205	−	0.849738i	$-0.323240\pi$
$948$		−	14.3198i		−	0.465087i
$949$	20.3005			0.658982
$950$	4.20164	−	1.48957i	0.136319	−	0.0483280i
$951$	40.2815			1.30622
$952$		0			0
$953$			0.806914i			0.0261385i	0.999915	+	0.0130693i	$0.00416019\pi$
$953$			0.806914i			0.0261385i	−0.999915	+	0.0130693i	$0.995840\pi$
$954$	−1.21587			−0.0393651
$955$	4.11862	−	5.82992i	0.133275	−	0.188652i
$956$	−57.4575			−1.85831
$957$		−	3.66311i		−	0.118412i
$958$		−	1.95210i		−	0.0630694i
$959$	42.0833			1.35894
$960$	19.9835	+	14.1176i	0.644965	+	0.455643i
$961$	−18.7511			−0.604876
$962$			2.79854i			0.0902285i
$963$		−	6.03858i		−	0.194591i
$964$	35.8606			1.15499
$965$	−12.9924	−	9.17864i	−0.418240	−	0.295471i
$966$	2.51985			0.0810749
$967$		−	27.3892i		−	0.880777i	−0.897807	−	0.440388i	$-0.854841\pi$
$967$		−	27.3892i		−	0.880777i	0.897807	−	0.440388i	$-0.145159\pi$
$968$		−	2.03781i		−	0.0654978i
$969$		0			0
$970$	−0.710214	+	1.00531i	−0.0228036	+	0.0322786i
$971$	26.7596			0.858757			0.429378	−	0.903125i	$-0.358733\pi$
$971$	26.7596			0.858757			0.429378	+	0.903125i	$0.358733\pi$
$972$			18.0110i			0.577703i
$973$			40.0817i			1.28496i
$974$	3.22341			0.103285
$975$	15.0265	+	42.3854i	0.481233	+	1.35742i
$976$	29.6396			0.948739
$977$		−	2.64662i		−	0.0846730i	−0.999103	−	0.0423365i	$-0.986520\pi$
$977$		−	2.64662i		−	0.0846730i	0.999103	−	0.0423365i	$-0.0134802\pi$
$978$		−	2.67167i		−	0.0854306i
$979$	−49.2496			−1.57402
$980$	−3.09487	+	4.38079i	−0.0988618	+	0.139939i
$981$	−2.34741			−0.0749469
$982$			2.84470i			0.0907780i
$983$		−	33.0275i		−	1.05341i	−0.850047	−	0.526707i	$-0.823427\pi$
$983$		−	33.0275i		−	1.05341i	0.850047	−	0.526707i	$-0.176573\pi$
$984$	−1.58260			−0.0504516
$985$	−42.3192	−	29.8969i	−1.34840	−	0.952594i
$986$		0			0
$987$			25.7712i			0.820307i
$988$		−	81.6461i		−	2.59751i
$989$	−5.84186			−0.185760
$990$	−0.860532	−	0.607933i	−0.0273495	−	0.0193214i
$991$	32.2132			1.02329			0.511643	−	0.859198i	$-0.329037\pi$
$991$	32.2132			1.02329			0.511643	+	0.859198i	$0.329037\pi$
$992$			5.58610i			0.177359i
$993$		−	18.8050i		−	0.596757i
$994$	−0.458557			−0.0145446
$995$	−31.8851	+	45.1334i	−1.01082	+	1.43083i
$996$	−22.6804			−0.718655
$997$			52.7919i			1.67194i	0.548777	+	0.835969i	$0.315093\pi$
$997$			52.7919i			1.67194i	−0.548777	+	0.835969i	$0.684907\pi$
$998$		−	0.539910i		−	0.0170905i
$999$	−18.8878			−0.597583

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1445.2.b.e.579.4		8
5.2	odd	4		7225.2.a.w.1.2		4
5.3	odd	4		7225.2.a.v.1.3		4
5.4	even	2	inner	1445.2.b.e.579.5		8
17.16	even	2		85.2.b.a.69.4	✓	8
51.50	odd	2		765.2.b.c.154.5		8
68.67	odd	2		1360.2.e.d.1089.6		8
85.33	odd	4		425.2.a.g.1.3		4
85.67	odd	4		425.2.a.h.1.2		4
85.84	even	2		85.2.b.a.69.5	yes	8
255.152	even	4		3825.2.a.bh.1.3		4
255.203	even	4		3825.2.a.bj.1.2		4
255.254	odd	2		765.2.b.c.154.4		8
340.67	even	4		6800.2.a.bt.1.4		4
340.203	even	4		6800.2.a.bw.1.1		4
340.339	odd	2		1360.2.e.d.1089.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.b.a.69.4	✓	8	17.16	even	2
85.2.b.a.69.5	yes	8	85.84	even	2
425.2.a.g.1.3		4	85.33	odd	4
425.2.a.h.1.2		4	85.67	odd	4
765.2.b.c.154.4		8	255.254	odd	2
765.2.b.c.154.5		8	51.50	odd	2
1360.2.e.d.1089.3		8	340.339	odd	2
1360.2.e.d.1089.6		8	68.67	odd	2
1445.2.b.e.579.4		8	1.1	even	1	trivial
1445.2.b.e.579.5		8	5.4	even	2	inner
3825.2.a.bh.1.3		4	255.152	even	4
3825.2.a.bj.1.2		4	255.203	even	4
6800.2.a.bt.1.4		4	340.67	even	4
6800.2.a.bw.1.1		4	340.203	even	4
7225.2.a.v.1.3		4	5.3	odd	4
7225.2.a.w.1.2		4	5.2	odd	4

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:	\( N \)	\(=\)	\( 1445 = 5 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1445.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.134632i q^{2} +1.44579i q^{3} +1.98187 q^{4} +(1.29021 - 1.82630i) q^{5} +0.194649 q^{6} +2.86537i q^{7} -0.536087i q^{8} +0.909700 q^{9} +(-0.245878 - 0.173703i) q^{10} +3.84724 q^{11} +2.86537i q^{12} +6.22085i q^{13} +0.385770 q^{14} +(2.64044 + 1.86537i) q^{15} +3.89157 q^{16} -0.122475i q^{18} -6.62231 q^{19} +(2.55703 - 3.61949i) q^{20} -4.14271 q^{21} -0.517961i q^{22} -4.51796i q^{23} +0.775068 q^{24} +(-1.67072 - 4.71261i) q^{25} +0.837525 q^{26} +5.65259i q^{27} +5.67880i q^{28} -0.658562 q^{29} +(0.251138 - 0.355487i) q^{30} -3.49984 q^{31} -1.59610i q^{32} +5.56229i q^{33} +(5.23301 + 3.69693i) q^{35} +1.80291 q^{36} +3.34144i q^{37} +0.891574i q^{38} -8.99403 q^{39} +(-0.979054 - 0.691665i) q^{40} -2.04189 q^{41} +0.557741i q^{42} -1.29303i q^{43} +7.62475 q^{44} +(1.17370 - 1.66138i) q^{45} -0.608262 q^{46} -6.22085i q^{47} +5.62639i q^{48} -1.21033 q^{49} +(-0.634468 + 0.224932i) q^{50} +12.3290i q^{52} -9.92750i q^{53} +0.761019 q^{54} +(4.96375 - 7.02621i) q^{55} +1.53609 q^{56} -9.57445i q^{57} +0.0886634i q^{58} +2.00000 q^{59} +(5.23301 + 3.69693i) q^{60} +7.61634 q^{61} +0.471189i q^{62} +2.60662i q^{63} +7.56826 q^{64} +(11.3611 + 8.02621i) q^{65} +0.748862 q^{66} -0.257106i q^{67} +6.53201 q^{69} +(0.497724 - 0.704530i) q^{70} -1.18868 q^{71} -0.487678i q^{72} -3.26330i q^{73} +0.449864 q^{74} +(6.81343 - 2.41550i) q^{75} -13.1246 q^{76} +11.0238i q^{77} +1.21088i q^{78} -4.99756 q^{79} +(5.02095 - 7.10717i) q^{80} -5.44335 q^{81} +0.274904i q^{82} +7.91534i q^{83} -8.21033 q^{84} -0.174083 q^{86} -0.952140i q^{87} -2.06246i q^{88} -12.8013 q^{89} +(-0.223675 - 0.158018i) q^{90} -17.8250 q^{91} -8.95403i q^{92} -5.06002i q^{93} -0.837525 q^{94} +(-8.54417 + 12.0943i) q^{95} +2.30763 q^{96} -4.08866i q^{97} +0.162950i q^{98} +3.49984 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} + 2 q^{5} - 8 q^{9} - 6 q^{10} + 4 q^{11} - 12 q^{14} - 8 q^{16} - 8 q^{19} + 2 q^{20} + 24 q^{21} - 12 q^{24} - 12 q^{25} - 8 q^{29} - 16 q^{30} + 24 q^{31} - 44 q^{39} - 22 q^{40} + 12 q^{41}+ \cdots - 24 q^{99}+O(q^{100}) \) 8 * q - 8 * q^4 + 2 * q^5 - 8 * q^9 - 6 * q^10 + 4 * q^11 - 12 * q^14 - 8 * q^16 - 8 * q^19 + 2 * q^20 + 24 * q^21 - 12 * q^24 - 12 * q^25 - 8 * q^29 - 16 * q^30 + 24 * q^31 - 44 * q^39 - 22 * q^40 + 12 * q^41 + 32 * q^44 + 22 * q^45 + 8 * q^46 - 16 * q^49 + 44 * q^50 + 20 * q^54 - 8 * q^55 + 8 * q^56 + 16 * q^59 - 12 * q^61 + 48 * q^64 - 20 * q^65 + 24 * q^66 - 8 * q^69 + 40 * q^70 + 20 * q^71 + 40 * q^74 - 4 * q^75 - 24 * q^76 - 24 * q^79 + 26 * q^80 - 8 * q^81 - 72 * q^84 + 40 * q^86 - 48 * q^89 + 74 * q^90 - 36 * q^91 - 4 * q^95 - 16 * q^96 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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