LMFDB - Embedded newform 460.2.i.b.137.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(137,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 2]))

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

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

chi := DirichletCharacter("460.137");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.i (of order $4$, degree $2$, 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:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 18x^{14} + 146x^{12} - 798x^{10} + 3934x^{8} - 19950x^{6} + 91250x^{4} - 281250x^{2} + 390625 $ x^16 - 18x^14 + 146x^12 - 798x^10 + 3934x^8 - 19950x^6 + 91250x^4 - 281250*x^2 + 390625
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			137.5
Root			$-1.88618 - 1.20098i$ of defining polynomial
Character	$\chi$	$=$	460.137
Dual form			460.2.i.b.413.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.09396 - 1.09396i) q^{3} +(-1.88618 + 1.20098i) q^{5} +(-2.67082 + 2.67082i) q^{7} +0.606488i q^{9} +O(q^{10})$	\(q+(1.09396 - 1.09396i) q^{3} +(-1.88618 + 1.20098i) q^{5} +(-2.67082 + 2.67082i) q^{7} +0.606488i q^{9} +2.02880i q^{11} +(-3.32122 + 3.32122i) q^{13} +(-0.749584 + 3.37723i) q^{15} +(2.17625 - 2.17625i) q^{17} +0.910896 q^{19} +5.84356i q^{21} +(-4.00642 + 2.63602i) q^{23} +(2.11532 - 4.53050i) q^{25} +(3.94537 + 3.94537i) q^{27} -3.41856i q^{29} +1.18793 q^{31} +(2.21943 + 2.21943i) q^{33} +(1.83005 - 8.24523i) q^{35} +(0.268872 - 0.268872i) q^{37} +7.26659i q^{39} +3.45451 q^{41} +(-2.89652 - 2.89652i) q^{43} +(-0.728377 - 1.14394i) q^{45} +(-0.714732 - 0.714732i) q^{47} -7.26659i q^{49} -4.76149i q^{51} +(7.75171 + 7.75171i) q^{53} +(-2.43654 - 3.82667i) q^{55} +(0.996487 - 0.996487i) q^{57} +8.22388i q^{59} -5.34976i q^{61} +(-1.61982 - 1.61982i) q^{63} +(2.27570 - 10.2531i) q^{65} +(-7.39648 + 7.39648i) q^{67} +(-1.49917 + 7.26659i) q^{69} +0.769366 q^{71} +(-10.5485 + 10.5485i) q^{73} +(-2.64212 - 7.27028i) q^{75} +(-5.41856 - 5.41856i) q^{77} -10.2238 q^{79} +6.81271 q^{81} +(6.32176 + 6.32176i) q^{83} +(-1.49117 + 6.71843i) q^{85} +(-3.73978 - 3.73978i) q^{87} +3.14670 q^{89} -17.7408i q^{91} +(1.29955 - 1.29955i) q^{93} +(-1.71811 + 1.09396i) q^{95} +(2.21132 - 2.21132i) q^{97} -1.23044 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{3}+O(q^{10}) $ 16 * q + 4 * q^3	$ 16 q + 4 q^{3} + 12 q^{13} + 12 q^{23} + 36 q^{25} + 52 q^{27} - 8 q^{31} + 16 q^{35} - 48 q^{41} + 4 q^{47} + 24 q^{55} + 8 q^{71} - 52 q^{73} - 56 q^{75} - 64 q^{77} - 152 q^{81} + 28 q^{85} + 28 q^{87} + 84 q^{93} - 68 q^{95}+O(q^{100}) $ 16 * q + 4 * q^3 + 12 * q^13 + 12 * q^23 + 36 * q^25 + 52 * q^27 - 8 * q^31 + 16 * q^35 - 48 * q^41 + 4 * q^47 + 24 * q^55 + 8 * q^71 - 52 * q^73 - 56 * q^75 - 64 * q^77 - 152 * q^81 + 28 * q^85 + 28 * q^87 + 84 * q^93 - 68 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$-1$

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
$3$	1.09396	−	1.09396i	0.631600	−	0.631600i	−0.316869	−	0.948469i	$-0.602632\pi$
$3$	1.09396	−	1.09396i	0.631600	−	0.631600i	0.948469	+	0.316869i	$0.102632\pi$
$4$		0			0
$5$	−1.88618	+	1.20098i	−0.843523	+	0.537092i
$5$	−1.88618	+	1.20098i	−0.843523	+	0.537092i
$6$		0			0
$7$	−2.67082	+	2.67082i	−1.00948	+	1.00948i	−0.00952135	+	0.999955i	$0.503031\pi$
$7$	−2.67082	+	2.67082i	−1.00948	+	1.00948i	−0.999955	+	0.00952135i	$0.996969\pi$
$8$		0			0
$9$			0.606488i			0.202163i
$10$		0			0
$11$			2.02880i			0.611706i	0.952079	+	0.305853i	$0.0989416\pi$
$11$			2.02880i			0.611706i	−0.952079	+	0.305853i	$0.901058\pi$
$12$		0			0
$13$	−3.32122	+	3.32122i	−0.921141	+	0.921141i	−0.997110	−	0.0759695i	$-0.975795\pi$
$13$	−3.32122	+	3.32122i	−0.921141	+	0.921141i	0.0759695	+	0.997110i	$0.475795\pi$
$14$		0			0
$15$	−0.749584	+	3.37723i	−0.193542	+	0.871997i
$16$		0			0
$17$	2.17625	−	2.17625i	0.527819	−	0.527819i	−0.392102	−	0.919922i	$-0.628252\pi$
$17$	2.17625	−	2.17625i	0.527819	−	0.527819i	0.919922	+	0.392102i	$0.128252\pi$
$18$		0			0
$19$	0.910896			0.208974			0.104487	−	0.994526i	$-0.466680\pi$
$19$	0.910896			0.208974			0.104487	+	0.994526i	$0.466680\pi$
$20$		0			0
$21$			5.84356i			1.27517i
$22$		0			0
$23$	−4.00642	+	2.63602i	−0.835396	+	0.549648i
$23$	−4.00642	+	2.63602i	−0.835396	+	0.549648i
$24$		0			0
$25$	2.11532	−	4.53050i	0.423063	−	0.906100i
$26$		0			0
$27$	3.94537	+	3.94537i	0.759286	+	0.759286i
$28$		0			0
$29$		−	3.41856i		−	0.634811i	−0.948290	−	0.317405i	$-0.897188\pi$
$29$		−	3.41856i		−	0.634811i	0.948290	−	0.317405i	$-0.102812\pi$
$30$		0			0
$31$	1.18793			0.213358			0.106679	−	0.994294i	$-0.465978\pi$
$31$	1.18793			0.213358			0.106679	+	0.994294i	$0.465978\pi$
$32$		0			0
$33$	2.21943	+	2.21943i	0.386353	+	0.386353i
$34$		0			0
$35$	1.83005	−	8.24523i	0.309335	−	1.39370i
$36$		0			0
$37$	0.268872	−	0.268872i	0.0442023	−	0.0442023i	−0.684660	−	0.728862i	$-0.740049\pi$
$37$	0.268872	−	0.268872i	0.0442023	−	0.0442023i	0.728862	+	0.684660i	$0.240049\pi$
$38$		0			0
$39$			7.26659i			1.16358i
$40$		0			0
$41$	3.45451			0.539504			0.269752	−	0.962930i	$-0.413058\pi$
$41$	3.45451			0.539504			0.269752	+	0.962930i	$0.413058\pi$
$42$		0			0
$43$	−2.89652	−	2.89652i	−0.441715	−	0.441715i	0.450873	−	0.892588i	$-0.351113\pi$
$43$	−2.89652	−	2.89652i	−0.441715	−	0.441715i	−0.892588	+	0.450873i	$0.851113\pi$
$44$		0			0
$45$	−0.728377	−	1.14394i	−0.108580	−	0.170529i
$46$		0			0
$47$	−0.714732	−	0.714732i	−0.104254	−	0.104254i	0.653056	−	0.757310i	$-0.273487\pi$
$47$	−0.714732	−	0.714732i	−0.104254	−	0.104254i	−0.757310	+	0.653056i	$0.773487\pi$
$48$		0			0
$49$		−	7.26659i		−	1.03808i
$50$		0			0
$51$		−	4.76149i		−	0.666741i
$52$		0			0
$53$	7.75171	+	7.75171i	1.06478	+	1.06478i	0.997751	+	0.0670281i	$0.0213517\pi$
$53$	7.75171	+	7.75171i	1.06478	+	1.06478i	0.0670281	+	0.997751i	$0.478648\pi$
$54$		0			0
$55$	−2.43654	−	3.82667i	−0.328543	−	0.515988i
$56$		0			0
$57$	0.996487	−	0.996487i	0.131988	−	0.131988i
$58$		0			0
$59$			8.22388i			1.07066i	0.844644	+	0.535329i	$0.179812\pi$
$59$			8.22388i			1.07066i	−0.844644	+	0.535329i	$0.820188\pi$
$60$		0			0
$61$		−	5.34976i		−	0.684966i	−0.939524	−	0.342483i	$-0.888732\pi$
$61$		−	5.34976i		−	0.684966i	0.939524	−	0.342483i	$-0.111268\pi$
$62$		0			0
$63$	−1.61982	−	1.61982i	−0.204078	−	0.204078i
$64$		0			0
$65$	2.27570	−	10.2531i	0.282266	−	1.27174i
$66$		0			0
$67$	−7.39648	+	7.39648i	−0.903624	+	0.903624i	−0.995748	−	0.0921233i	$-0.970635\pi$
$67$	−7.39648	+	7.39648i	−0.903624	+	0.903624i	0.0921233	+	0.995748i	$0.470635\pi$
$68$		0			0
$69$	−1.49917	+	7.26659i	−0.180479	+	0.874794i
$70$		0			0
$71$	0.769366			0.0913069			0.0456534	−	0.998957i	$-0.485463\pi$
$71$	0.769366			0.0913069			0.0456534	+	0.998957i	$0.485463\pi$
$72$		0			0
$73$	−10.5485	+	10.5485i	−1.23461	+	1.23461i	−0.272430	+	0.962176i	$0.587827\pi$
$73$	−10.5485	+	10.5485i	−1.23461	+	1.23461i	−0.962176	+	0.272430i	$0.912173\pi$
$74$		0			0
$75$	−2.64212	−	7.27028i	−0.305086	−	0.839500i
$76$		0			0
$77$	−5.41856	−	5.41856i	−0.617502	−	0.617502i
$78$		0			0
$79$	−10.2238			−1.15027			−0.575133	−	0.818060i	$-0.695050\pi$
$79$	−10.2238			−1.15027			−0.575133	+	0.818060i	$0.695050\pi$
$80$		0			0
$81$	6.81271			0.756968
$82$		0			0
$83$	6.32176	+	6.32176i	0.693903	+	0.693903i	0.963088	−	0.269185i	$-0.0867544\pi$
$83$	6.32176	+	6.32176i	0.693903	+	0.693903i	−0.269185	+	0.963088i	$0.586754\pi$
$84$		0			0
$85$	−1.49117	+	6.71843i	−0.161740	+	0.728716i
$86$		0			0
$87$	−3.73978	−	3.73978i	−0.400947	−	0.400947i
$88$		0			0
$89$	3.14670			0.333550			0.166775	−	0.985995i	$-0.446665\pi$
$89$	3.14670			0.333550			0.166775	+	0.985995i	$0.446665\pi$
$90$		0			0
$91$		−	17.7408i		−	1.85974i
$92$		0			0
$93$	1.29955	−	1.29955i	0.134757	−	0.134757i
$94$		0			0
$95$	−1.71811	+	1.09396i	−0.176274	+	0.112238i
$96$		0			0
$97$	2.21132	−	2.21132i	0.224525	−	0.224525i	−0.585876	−	0.810401i	$-0.699249\pi$
$97$	2.21132	−	2.21132i	0.224525	−	0.224525i	0.810401	+	0.585876i	$0.199249\pi$
$98$		0			0
$99$	−1.23044			−0.123664
$100$		0			0
$101$	18.1220			1.80321			0.901603	−	0.432564i	$-0.142391\pi$
$101$	18.1220			1.80321			0.901603	+	0.432564i	$0.142391\pi$
$102$		0			0
$103$	−11.8704	−	11.8704i	−1.16963	−	1.16963i	−0.982297	−	0.187329i	$-0.940017\pi$
$103$	−11.8704	−	11.8704i	−1.16963	−	1.16963i	−0.187329	−	0.982297i	$-0.559983\pi$
$104$		0			0
$105$	−7.01798	−	11.0220i	−0.684884	−	1.07564i
$106$		0			0
$107$	8.74008	−	8.74008i	0.844936	−	0.844936i	−0.144560	−	0.989496i	$-0.546177\pi$
$107$	8.74008	−	8.74008i	0.844936	−	0.844936i	0.989496	+	0.144560i	$0.0461768\pi$
$108$		0			0
$109$	16.2416			1.55566			0.777832	−	0.628472i	$-0.216319\pi$
$109$	16.2416			1.55566			0.777832	+	0.628472i	$0.216319\pi$
$110$		0			0
$111$		−	0.588273i		−	0.0558364i
$112$		0			0
$113$	2.97385	+	2.97385i	0.279756	+	0.279756i	0.833012	−	0.553255i	$-0.186615\pi$
$113$	2.97385	+	2.97385i	0.279756	+	0.279756i	−0.553255	+	0.833012i	$0.686615\pi$
$114$		0			0
$115$	4.39102	−	9.78361i	0.409465	−	0.912326i
$116$		0			0
$117$	−2.01428	−	2.01428i	−0.186220	−	0.186220i
$118$		0			0
$119$			11.6248i			1.06564i
$120$		0			0
$121$	6.88398			0.625816
$122$		0			0
$123$	3.77911	−	3.77911i	0.340751	−	0.340751i
$124$		0			0
$125$	1.45116	+	11.0858i	0.129796	+	0.991541i
$126$		0			0
$127$	−8.57353	−	8.57353i	−0.760777	−	0.760777i	0.215686	−	0.976463i	$-0.430801\pi$
$127$	−8.57353	−	8.57353i	−0.760777	−	0.760777i	−0.976463	+	0.215686i	$0.930801\pi$
$128$		0			0
$129$	−6.33737			−0.557974
$130$		0			0
$131$	−13.5997			−1.18821			−0.594107	−	0.804386i	$-0.702494\pi$
$131$	−13.5997			−1.18821			−0.594107	+	0.804386i	$0.702494\pi$
$132$		0			0
$133$	−2.43284	+	2.43284i	−0.210954	+	0.210954i
$134$		0			0
$135$	−12.1799	−	2.70337i	−1.04828	−	0.232669i
$136$		0			0
$137$	11.7148	−	11.7148i	1.00087	−	1.00087i	0.000866657	−	1.00000i	$-0.499724\pi$
$137$	11.7148	−	11.7148i	1.00087	−	1.00087i	1.00000		0.000866657i	$-0.000275865\pi$
$138$		0			0
$139$			5.23063i			0.443657i	0.975086	+	0.221828i	$0.0712025\pi$
$139$			5.23063i			0.443657i	−0.975086	+	0.221828i	$0.928798\pi$
$140$		0			0
$141$	−1.56378			−0.131694
$142$		0			0
$143$	−6.73809	−	6.73809i	−0.563467	−	0.563467i
$144$		0			0
$145$	4.10561	+	6.44801i	0.340952	+	0.535478i
$146$		0			0
$147$	−7.94938	−	7.94938i	−0.655654	−	0.655654i
$148$		0			0
$149$	19.0070			1.55712			0.778559	−	0.627572i	$-0.215951\pi$
$149$	19.0070			1.55712			0.778559	+	0.627572i	$0.215951\pi$
$150$		0			0
$151$	23.9023			1.94514			0.972570	−	0.232612i	$-0.0747273\pi$
$151$	23.9023			1.94514			0.972570	+	0.232612i	$0.0747273\pi$
$152$		0			0
$153$	1.31987	+	1.31987i	0.106705	+	0.106705i
$154$		0			0
$155$	−2.24064	+	1.42667i	−0.179972	+	0.114593i
$156$		0			0
$157$	−9.94434	+	9.94434i	−0.793645	+	0.793645i	−0.982085	−	0.188440i	$-0.939657\pi$
$157$	−9.94434	+	9.94434i	−0.793645	+	0.793645i	0.188440	+	0.982085i	$0.439657\pi$
$158$		0			0
$159$	16.9602			1.34503
$160$		0			0
$161$	3.66010	−	17.7408i	0.288456	−	1.39817i
$162$		0			0
$163$	−6.30694	+	6.30694i	−0.493998	+	0.493998i	−0.909563	−	0.415566i	$-0.863584\pi$
$163$	−6.30694	+	6.30694i	−0.493998	+	0.493998i	0.415566	+	0.909563i	$0.363584\pi$
$164$		0			0
$165$	−6.85172	−	1.52076i	−0.533406	−	0.118391i
$166$		0			0
$167$	−2.01428	−	2.01428i	−0.155870	−	0.155870i	0.624864	−	0.780734i	$-0.285154\pi$
$167$	−2.01428	−	2.01428i	−0.155870	−	0.155870i	−0.780734	+	0.624864i	$0.785154\pi$
$168$		0			0
$169$		−	9.06100i		−	0.697000i
$170$		0			0
$171$			0.552448i			0.0422467i
$172$		0			0
$173$	1.42194	−	1.42194i	0.108108	−	0.108108i	−0.650984	−	0.759092i	$-0.725643\pi$
$173$	1.42194	−	1.42194i	0.108108	−	0.108108i	0.759092	+	0.650984i	$0.225643\pi$
$174$		0			0
$175$	6.45053	+	17.7498i	0.487614	+	1.34176i
$176$		0			0
$177$	8.99662	+	8.99662i	0.676228	+	0.676228i
$178$		0			0
$179$		−	4.54549i		−	0.339746i	−0.985466	−	0.169873i	$-0.945664\pi$
$179$		−	4.54549i		−	0.339746i	0.985466	−	0.169873i	$-0.0543357\pi$
$180$		0			0
$181$			7.69810i			0.572196i	0.958200	+	0.286098i	$0.0923582\pi$
$181$			7.69810i			0.572196i	−0.958200	+	0.286098i	$0.907642\pi$
$182$		0			0
$183$	−5.85244	−	5.85244i	−0.432625	−	0.432625i
$184$		0			0
$185$	−0.184231	+	0.830049i	−0.0135450	+	0.0610264i
$186$		0			0
$187$	4.41518	+	4.41518i	0.322870	+	0.322870i
$188$		0			0
$189$	−21.0747			−1.53296
$190$		0			0
$191$			18.0276i			1.30443i	0.758034	+	0.652215i	$0.226160\pi$
$191$			18.0276i			1.30443i	−0.758034	+	0.652215i	$0.773840\pi$
$192$		0			0
$193$	−11.9779	+	11.9779i	−0.862191	+	0.862191i	−0.991592	−	0.129401i	$-0.958694\pi$
$193$	−11.9779	+	11.9779i	−0.862191	+	0.862191i	0.129401	+	0.991592i	$0.458694\pi$
$194$		0			0
$195$	−8.72699	−	13.7061i	−0.624953	−	0.981511i
$196$		0			0
$197$	−7.10487	−	7.10487i	−0.506201	−	0.506201i	0.407157	−	0.913358i	$-0.366520\pi$
$197$	−7.10487	−	7.10487i	−0.506201	−	0.506201i	−0.913358	+	0.407157i	$0.866520\pi$
$198$		0			0
$199$	−4.26460			−0.302310			−0.151155	−	0.988510i	$-0.548299\pi$
$199$	−4.26460			−0.302310			−0.151155	+	0.988510i	$0.548299\pi$
$200$		0			0
$201$			16.1830i			1.14146i
$202$		0			0
$203$	9.13037	+	9.13037i	0.640826	+	0.640826i
$204$		0			0
$205$	−6.51582	+	4.14878i	−0.455084	+	0.289764i
$206$		0			0
$207$	−1.59871	−	2.42985i	−0.111118	−	0.168886i
$208$		0			0
$209$			1.84802i			0.127831i
$210$		0			0
$211$	15.7768			1.08612			0.543058	−	0.839695i	$-0.317266\pi$
$211$	15.7768			1.08612			0.543058	+	0.839695i	$0.317266\pi$
$212$		0			0
$213$	0.841658	−	0.841658i	0.0576694	−	0.0576694i
$214$		0			0
$215$	8.94199	+	1.98470i	0.609839	+	0.135355i
$216$		0			0
$217$	−3.17274	+	3.17274i	−0.215380	+	0.215380i
$218$		0			0
$219$			23.0793i			1.55955i
$220$		0			0
$221$			14.4556i			0.972392i
$222$		0			0
$223$	14.1703	−	14.1703i	0.948911	−	0.948911i	−0.0498456	−	0.998757i	$-0.515873\pi$
$223$	14.1703	−	14.1703i	0.948911	−	0.948911i	0.998757	+	0.0498456i	$0.0158729\pi$
$224$		0			0
$225$	2.74769	+	1.28291i	0.183180	+	0.0855276i
$226$		0			0
$227$	−12.2443	+	12.2443i	−0.812684	+	0.812684i	−0.985036	−	0.172351i	$-0.944864\pi$
$227$	−12.2443	+	12.2443i	−0.812684	+	0.812684i	0.172351	+	0.985036i	$0.444864\pi$
$228$		0			0
$229$	−29.1442			−1.92590			−0.962951	−	0.269677i	$-0.913083\pi$
$229$	−29.1442			−1.92590			−0.962951	+	0.269677i	$0.913083\pi$
$230$		0			0
$231$	−11.8554			−0.780029
$232$		0			0
$233$	7.73640	−	7.73640i	0.506829	−	0.506829i	−0.406723	−	0.913552i	$-0.633329\pi$
$233$	7.73640	−	7.73640i	0.506829	−	0.506829i	0.913552	+	0.406723i	$0.133329\pi$
$234$		0			0
$235$	2.20648	+	0.489734i	0.143935	+	0.0319468i
$236$		0			0
$237$	−11.1844	+	11.1844i	−0.726508	+	0.726508i
$238$		0			0
$239$			16.9273i			1.09494i	0.836826	+	0.547469i	$0.184408\pi$
$239$			16.9273i			1.09494i	−0.836826	+	0.547469i	$0.815592\pi$
$240$		0			0
$241$		−	11.4034i		−	0.734558i	−0.930111	−	0.367279i	$-0.880289\pi$
$241$		−	11.4034i		−	0.734558i	0.930111	−	0.367279i	$-0.119711\pi$
$242$		0			0
$243$	−4.38324	+	4.38324i	−0.281185	+	0.281185i
$244$		0			0
$245$	8.72699	+	13.7061i	0.557547	+	0.875648i
$246$		0			0
$247$	−3.02529	+	3.02529i	−0.192494	+	0.192494i
$248$		0			0
$249$	13.8315			0.876538
$250$		0			0
$251$			30.4105i			1.91949i	0.280872	+	0.959745i	$0.409376\pi$
$251$			30.4105i			1.91949i	−0.280872	+	0.959745i	$0.590624\pi$
$252$		0			0
$253$	−5.34795	−	8.12822i	−0.336223	−	0.511017i
$254$		0			0
$255$	5.71843	+	8.98100i	0.358102	+	0.562412i
$256$		0			0
$257$	−15.8008	−	15.8008i	−0.985626	−	0.985626i	0.0142725	−	0.999898i	$-0.495457\pi$
$257$	−15.8008	−	15.8008i	−0.985626	−	0.985626i	−0.999898	+	0.0142725i	$0.995457\pi$
$258$		0			0
$259$			1.43622i			0.0892423i
$260$		0			0
$261$	2.07332			0.128335
$262$		0			0
$263$	9.48483	+	9.48483i	0.584860	+	0.584860i	0.936235	−	0.351375i	$-0.114286\pi$
$263$	9.48483	+	9.48483i	0.584860	+	0.584860i	−0.351375	+	0.936235i	$0.614286\pi$
$264$		0			0
$265$	−23.9307	−	5.31147i	−1.47005	−	0.326281i
$266$		0			0
$267$	3.44238	−	3.44238i	0.210670	−	0.210670i
$268$		0			0
$269$		−	26.5447i		−	1.61846i	−0.587492	−	0.809230i	$-0.699885\pi$
$269$		−	26.5447i		−	1.61846i	0.587492	−	0.809230i	$-0.300115\pi$
$270$		0			0
$271$	−13.2348			−0.803956			−0.401978	−	0.915649i	$-0.631677\pi$
$271$	−13.2348			−0.803956			−0.401978	+	0.915649i	$0.631677\pi$
$272$		0			0
$273$	−19.4078	−	19.4078i	−1.17461	−	1.17461i
$274$		0			0
$275$	9.19147	+	4.29155i	0.554267	+	0.258790i
$276$		0			0
$277$	17.2302	+	17.2302i	1.03527	+	1.03527i	0.999355	+	0.0359101i	$0.0114330\pi$
$277$	17.2302	+	17.2302i	1.03527	+	1.03527i	0.0359101	+	0.999355i	$0.488567\pi$
$278$		0			0
$279$			0.720463i			0.0431330i
$280$		0			0
$281$		−	24.4366i		−	1.45777i	−0.684639	−	0.728883i	$-0.740040\pi$
$281$		−	24.4366i		−	1.45777i	0.684639	−	0.728883i	$-0.259960\pi$
$282$		0			0
$283$	19.3369	+	19.3369i	1.14946	+	1.14946i	0.986659	+	0.162798i	$0.0520520\pi$
$283$	19.3369	+	19.3369i	1.14946	+	1.14946i	0.162798	+	0.986659i	$0.447948\pi$
$284$		0			0
$285$	−0.682793	+	3.07631i	−0.0404452	+	0.182225i
$286$		0			0
$287$	−9.22639	+	9.22639i	−0.544617	+	0.544617i
$288$		0			0
$289$			7.52783i			0.442813i
$290$		0			0
$291$		−	4.83820i		−	0.283620i
$292$		0			0
$293$	13.1813	+	13.1813i	0.770057	+	0.770057i	0.978116	−	0.208059i	$-0.0667146\pi$
$293$	13.1813	+	13.1813i	0.770057	+	0.770057i	−0.208059	+	0.978116i	$0.566715\pi$
$294$		0			0
$295$	−9.87667	−	15.5117i	−0.575042	−	0.903125i
$296$		0			0
$297$	−8.00435	+	8.00435i	−0.464460	+	0.464460i
$298$		0			0
$299$	4.55140	−	22.0610i	0.263214	−	1.27582i
$300$		0			0
$301$	15.4722			0.891801
$302$		0			0
$303$	19.8248	−	19.8248i	1.13891	−	1.13891i
$304$		0			0
$305$	6.42493	+	10.0906i	0.367890	+	0.577785i
$306$		0			0
$307$	5.87645	+	5.87645i	0.335387	+	0.335387i	0.854628	−	0.519241i	$-0.173785\pi$
$307$	5.87645	+	5.87645i	0.335387	+	0.335387i	−0.519241	+	0.854628i	$0.673785\pi$
$308$		0			0
$309$	−25.9716			−1.47747
$310$		0			0
$311$	14.4796			0.821061			0.410530	−	0.911847i	$-0.365344\pi$
$311$	14.4796			0.821061			0.410530	+	0.911847i	$0.365344\pi$
$312$		0			0
$313$	9.74776	+	9.74776i	0.550976	+	0.550976i	0.926722	−	0.375747i	$-0.122614\pi$
$313$	9.74776	+	9.74776i	0.550976	+	0.550976i	−0.375747	+	0.926722i	$0.622614\pi$
$314$		0			0
$315$	5.00063	+	1.10990i	0.281754	+	0.0625359i
$316$		0			0
$317$	8.65672	+	8.65672i	0.486210	+	0.486210i	0.907108	−	0.420898i	$-0.138285\pi$
$317$	8.65672	+	8.65672i	0.486210	+	0.486210i	−0.420898	+	0.907108i	$0.638285\pi$
$318$		0			0
$319$	6.93557			0.388318
$320$		0			0
$321$		−	19.1227i		−	1.06732i
$322$		0			0
$323$	1.98234	−	1.98234i	0.110300	−	0.110300i
$324$		0			0
$325$	8.02135	+	22.0722i	0.444945	+	1.22435i
$326$		0			0
$327$	17.7677	−	17.7677i	0.982557	−	0.982557i
$328$		0			0
$329$	3.81784			0.210484
$330$		0			0
$331$	−25.1146			−1.38042			−0.690212	−	0.723607i	$-0.742483\pi$
$331$	−25.1146			−1.38042			−0.690212	+	0.723607i	$0.742483\pi$
$332$		0			0
$333$	0.163068	+	0.163068i	0.00893606	+	0.00893606i
$334$		0			0
$335$	5.06807	−	22.8341i	0.276898	−	1.24756i
$336$		0			0
$337$	3.28590	−	3.28590i	0.178994	−	0.178994i	−0.611923	−	0.790917i	$-0.709604\pi$
$337$	3.28590	−	3.28590i	0.178994	−	0.178994i	0.790917	+	0.611923i	$0.209604\pi$
$338$		0			0
$339$	6.50656			0.353388
$340$		0			0
$341$			2.41006i			0.130512i
$342$		0			0
$343$	0.712003	+	0.712003i	0.0384446	+	0.0384446i
$344$		0			0
$345$	−5.89929	−	15.5065i	−0.317607	−	0.834843i
$346$		0			0
$347$	−7.52783	−	7.52783i	−0.404115	−	0.404115i	0.475565	−	0.879680i	$-0.342244\pi$
$347$	−7.52783	−	7.52783i	−0.404115	−	0.404115i	−0.879680	+	0.475565i	$0.842244\pi$
$348$		0			0
$349$		−	25.1939i		−	1.34860i	−0.738458	−	0.674299i	$-0.764446\pi$
$349$		−	25.1939i		−	1.34860i	0.738458	−	0.674299i	$-0.235554\pi$
$350$		0			0
$351$	−26.2069			−1.39882
$352$		0			0
$353$	−23.9921	+	23.9921i	−1.27697	+	1.27697i	−0.334615	+	0.942355i	$0.608606\pi$
$353$	−23.9921	+	23.9921i	−1.27697	+	1.27697i	−0.942355	+	0.334615i	$0.891394\pi$
$354$		0			0
$355$	−1.45116	+	0.923989i	−0.0770195	+	0.0490402i
$356$		0			0
$357$	12.7171	+	12.7171i	0.673060	+	0.673060i
$358$		0			0
$359$	21.4430			1.13172			0.565859	−	0.824502i	$-0.308545\pi$
$359$	21.4430			1.13172			0.565859	+	0.824502i	$0.308545\pi$
$360$		0			0
$361$	−18.1703			−0.956330
$362$		0			0
$363$	7.53082	−	7.53082i	0.395265	−	0.395265i
$364$		0			0
$365$	7.22782	−	32.5647i	0.378321	−	1.70452i
$366$		0			0
$367$	16.8389	−	16.8389i	0.878984	−	0.878984i	−0.114446	−	0.993429i	$-0.536509\pi$
$367$	16.8389	−	16.8389i	0.878984	−	0.878984i	0.993429	+	0.114446i	$0.0365093\pi$
$368$		0			0
$369$			2.09512i			0.109068i
$370$		0			0
$371$	−41.4069			−2.14974
$372$		0			0
$373$	−5.08320	−	5.08320i	−0.263198	−	0.263198i	0.563154	−	0.826352i	$-0.309588\pi$
$373$	−5.08320	−	5.08320i	−0.263198	−	0.263198i	−0.826352	+	0.563154i	$0.809588\pi$
$374$		0			0
$375$	13.7149	+	10.5399i	0.708236	+	0.544278i
$376$		0			0
$377$	11.3538	+	11.3538i	0.584750	+	0.584750i
$378$		0			0
$379$	−12.6597			−0.650287			−0.325144	−	0.945665i	$-0.605413\pi$
$379$	−12.6597			−0.650287			−0.325144	+	0.945665i	$0.605413\pi$
$380$		0			0
$381$	−18.7582			−0.961014
$382$		0			0
$383$	12.1817	+	12.1817i	0.622456	+	0.622456i	0.946159	−	0.323703i	$-0.104928\pi$
$383$	12.1817	+	12.1817i	0.622456	+	0.622456i	−0.323703	+	0.946159i	$0.604928\pi$
$384$		0			0
$385$	16.7279	+	3.71280i	0.852534	+	0.189222i
$386$		0			0
$387$	1.75670	−	1.75670i	0.0892983	−	0.0892983i
$388$		0			0
$389$	12.9565			0.656919			0.328460	−	0.944518i	$-0.393471\pi$
$389$	12.9565			0.656919			0.328460	+	0.944518i	$0.393471\pi$
$390$		0			0
$391$	−2.98234	+	14.4556i	−0.150824	+	0.731053i
$392$		0			0
$393$	−14.8776	+	14.8776i	−0.750476	+	0.750476i
$394$		0			0
$395$	19.2839	−	12.2785i	0.970276	−	0.617799i
$396$		0			0
$397$	17.4915	+	17.4915i	0.877873	+	0.877873i	0.993314	−	0.115442i	$-0.0368283\pi$
$397$	17.4915	+	17.4915i	0.877873	+	0.877873i	−0.115442	+	0.993314i	$0.536828\pi$
$398$		0			0
$399$			5.32288i			0.266477i
$400$		0			0
$401$		−	26.5568i		−	1.32618i	−0.748539	−	0.663091i	$-0.769244\pi$
$401$		−	26.5568i		−	1.32618i	0.748539	−	0.663091i	$-0.230756\pi$
$402$		0			0
$403$	−3.94537	+	3.94537i	−0.196533	+	0.196533i
$404$		0			0
$405$	−12.8500	+	8.18189i	−0.638520	+	0.406562i
$406$		0			0
$407$	0.545487	+	0.545487i	0.0270388	+	0.0270388i
$408$		0			0
$409$		−	23.4410i		−	1.15908i	−0.814943	−	0.579541i	$-0.803232\pi$
$409$		−	23.4410i		−	1.15908i	0.814943	−	0.579541i	$-0.196768\pi$
$410$		0			0
$411$		−	25.6312i		−	1.26429i
$412$		0			0
$413$	−21.9645	−	21.9645i	−1.08080	−	1.08080i
$414$		0			0
$415$	−19.5162	−	4.33167i	−0.958014	−	0.212633i
$416$		0			0
$417$	5.72212	+	5.72212i	0.280214	+	0.280214i
$418$		0			0
$419$	−35.1948			−1.71938			−0.859688	−	0.510819i	$-0.829342\pi$
$419$	−35.1948			−1.71938			−0.859688	+	0.510819i	$0.829342\pi$
$420$		0			0
$421$			27.6450i			1.34734i	0.739034	+	0.673668i	$0.235282\pi$
$421$			27.6450i			1.34734i	−0.739034	+	0.673668i	$0.764718\pi$
$422$		0			0
$423$	0.433476	−	0.433476i	0.0210763	−	0.0210763i
$424$		0			0
$425$	−5.25605	−	14.4630i	−0.254956	−	0.701558i
$426$		0			0
$427$	14.2883	+	14.2883i	0.691457	+	0.691457i
$428$		0			0
$429$	−14.7424			−0.711772
$430$		0			0
$431$			10.1371i			0.488289i	0.969739	+	0.244144i	$0.0785071\pi$
$431$			10.1371i			0.488289i	−0.969739	+	0.244144i	$0.921493\pi$
$432$		0			0
$433$	−27.4864	−	27.4864i	−1.32091	−	1.32091i	−0.913040	−	0.407871i	$-0.866271\pi$
$433$	−27.4864	−	27.4864i	−1.32091	−	1.32091i	−0.407871	−	0.913040i	$-0.633729\pi$
$434$		0			0
$435$	11.5453	+	2.56250i	0.553553	+	0.122862i
$436$		0			0
$437$	−3.64943	+	2.40114i	−0.174576	+	0.114862i
$438$		0			0
$439$		−	14.7889i		−	0.705834i	−0.935655	−	0.352917i	$-0.885190\pi$
$439$		−	14.7889i		−	0.705834i	0.935655	−	0.352917i	$-0.114810\pi$
$440$		0			0
$441$	4.40710			0.209862
$442$		0			0
$443$	10.8490	−	10.8490i	0.515454	−	0.515454i	−0.400739	−	0.916192i	$-0.631246\pi$
$443$	10.8490	−	10.8490i	0.515454	−	0.515454i	0.916192	+	0.400739i	$0.131246\pi$
$444$		0			0
$445$	−5.93523	+	3.77911i	−0.281357	+	0.179147i
$446$		0			0
$447$	20.7930	−	20.7930i	0.983476	−	0.983476i
$448$		0			0
$449$			3.01971i			0.142509i	0.997458	+	0.0712544i	$0.0227002\pi$
$449$			3.01971i			0.142509i	−0.997458	+	0.0712544i	$0.977300\pi$
$450$		0			0
$451$			7.00851i			0.330018i
$452$		0			0
$453$	26.1482	−	26.1482i	1.22855	−	1.22855i
$454$		0			0
$455$	21.3062	+	33.4622i	0.998852	+	1.56873i
$456$		0			0
$457$	21.9458	−	21.9458i	1.02658	−	1.02658i	0.0269457	−	0.999637i	$-0.491422\pi$
$457$	21.9458	−	21.9458i	1.02658	−	1.02658i	0.999637	−	0.0269457i	$-0.00857813\pi$
$458$		0			0
$459$	17.1722			0.801532
$460$		0			0
$461$	−14.8480			−0.691541			−0.345771	−	0.938319i	$-0.612383\pi$
$461$	−14.8480			−0.691541			−0.345771	+	0.938319i	$0.612383\pi$
$462$		0			0
$463$	−0.212976	+	0.212976i	−0.00989784	+	0.00989784i	−0.712038	−	0.702141i	$-0.752228\pi$
$463$	−0.212976	+	0.212976i	−0.00989784	+	0.00989784i	0.702141	+	0.712038i	$0.252228\pi$
$464$		0			0
$465$	−0.890451	+	4.01190i	−0.0412937	+	0.186048i
$466$		0			0
$467$	3.74464	−	3.74464i	0.173281	−	0.173281i	−0.615138	−	0.788419i	$-0.710900\pi$
$467$	3.74464	−	3.74464i	0.173281	−	0.173281i	0.788419	+	0.615138i	$0.210900\pi$
$468$		0			0
$469$		−	39.5094i		−	1.82437i
$470$		0			0
$471$			21.7575i			1.00253i
$472$		0			0
$473$	5.87645	−	5.87645i	0.270200	−	0.270200i
$474$		0			0
$475$	1.92683	−	4.12681i	0.0884092	−	0.189351i
$476$		0			0
$477$	−4.70132	+	4.70132i	−0.215259	+	0.215259i
$478$		0			0
$479$	14.4556			0.660495			0.330248	−	0.943894i	$-0.392868\pi$
$479$	14.4556			0.660495			0.330248	+	0.943894i	$0.392868\pi$
$480$		0			0
$481$			1.78597i			0.0814331i
$482$		0			0
$483$	−15.4037	−	23.4118i	−0.700895	−	1.06527i
$484$		0			0
$485$	−1.51520	+	6.82667i	−0.0688015	+	0.309983i
$486$		0			0
$487$	−12.0973	−	12.0973i	−0.548183	−	0.548183i	0.377732	−	0.925915i	$-0.376704\pi$
$487$	−12.0973	−	12.0973i	−0.548183	−	0.548183i	−0.925915	+	0.377732i	$0.876704\pi$
$488$		0			0
$489$			13.7991i			0.624018i
$490$		0			0
$491$	5.47773			0.247207			0.123603	−	0.992332i	$-0.460555\pi$
$491$	5.47773			0.247207			0.123603	+	0.992332i	$0.460555\pi$
$492$		0			0
$493$	−7.43966	−	7.43966i	−0.335065	−	0.335065i
$494$		0			0
$495$	2.32083	−	1.47773i	0.104314	−	0.0664190i
$496$		0			0
$497$	−2.05484	+	2.05484i	−0.0921721	+	0.0921721i
$498$		0			0
$499$		−	3.83712i		−	0.171773i	−0.996305	−	0.0858866i	$-0.972628\pi$
$499$		−	3.83712i		−	0.171773i	0.996305	−	0.0858866i	$-0.0273723\pi$
$500$		0			0
$501$	−4.40710			−0.196895
$502$		0			0
$503$	−25.2431	−	25.2431i	−1.12553	−	1.12553i	−0.990895	−	0.134638i	$-0.957013\pi$
$503$	−25.2431	−	25.2431i	−1.12553	−	1.12553i	−0.134638	−	0.990895i	$-0.542987\pi$
$504$		0			0
$505$	−34.1813	+	21.7641i	−1.52105	+	0.968489i
$506$		0			0
$507$	−9.91240	−	9.91240i	−0.440225	−	0.440225i
$508$		0			0
$509$			18.1397i			0.804026i	0.915634	+	0.402013i	$0.131689\pi$
$509$			18.1397i			0.804026i	−0.915634	+	0.402013i	$0.868311\pi$
$510$		0			0
$511$		−	56.3462i		−	2.49261i
$512$		0			0
$513$	3.59382	+	3.59382i	0.158671	+	0.158671i
$514$		0			0
$515$	36.6457	+	8.13361i	1.61480	+	0.358410i
$516$		0			0
$517$	1.45005	−	1.45005i	0.0637730	−	0.0637730i
$518$		0			0
$519$		−	3.11110i		−	0.136562i
$520$		0			0
$521$			19.1127i			0.837344i	0.908138	+	0.418672i	$0.137504\pi$
$521$			19.1127i			0.837344i	−0.908138	+	0.418672i	$0.862496\pi$
$522$		0			0
$523$	22.8217	+	22.8217i	0.997922	+	0.997922i	0.999998	−	0.00207617i	$-0.000660866\pi$
$523$	22.8217	+	22.8217i	0.997922	+	0.997922i	−0.00207617	+	0.999998i	$0.500661\pi$
$524$		0			0
$525$	26.4743	+	12.3610i	1.15543	+	0.539478i
$526$		0			0
$527$	2.58523	−	2.58523i	0.112614	−	0.112614i
$528$		0			0
$529$	9.10281	−	21.1220i	0.395774	−	0.918348i
$530$		0			0
$531$	−4.98768			−0.216447
$532$		0			0
$533$	−11.4732	+	11.4732i	−0.496959	+	0.496959i
$534$		0			0
$535$	−5.98871	+	26.9820i	−0.258914	+	1.16653i
$536$		0			0
$537$	−4.97260	−	4.97260i	−0.214583	−	0.214583i
$538$		0			0
$539$	14.7424			0.635002
$540$		0			0
$541$	−18.9626			−0.815267			−0.407634	−	0.913146i	$-0.633646\pi$
$541$	−18.9626			−0.815267			−0.407634	+	0.913146i	$0.633646\pi$
$542$		0			0
$543$	8.42144	+	8.42144i	0.361399	+	0.361399i
$544$		0			0
$545$	−30.6345	+	19.5058i	−1.31224	+	0.835535i
$546$		0			0
$547$	−11.2120	−	11.2120i	−0.479388	−	0.479388i	0.425548	−	0.904936i	$-0.360082\pi$
$547$	−11.2120	−	11.2120i	−0.479388	−	0.479388i	−0.904936	+	0.425548i	$0.860082\pi$
$548$		0			0
$549$	3.24457			0.138475
$550$		0			0
$551$		−	3.11395i		−	0.132659i
$552$		0			0
$553$	27.3059	−	27.3059i	1.16117	−	1.16117i
$554$		0			0
$555$	0.706501	+	1.10959i	0.0299893	+	0.0470993i
$556$		0			0
$557$	3.84016	−	3.84016i	0.162713	−	0.162713i	−0.621055	−	0.783767i	$-0.713295\pi$
$557$	3.84016	−	3.84016i	0.162713	−	0.162713i	0.783767	+	0.621055i	$0.213295\pi$
$558$		0			0
$559$	19.2399			0.813763
$560$		0			0
$561$	9.66010			0.407850
$562$		0			0
$563$	−20.9167	−	20.9167i	−0.881536	−	0.881536i	0.112155	−	0.993691i	$-0.464225\pi$
$563$	−20.9167	−	20.9167i	−0.881536	−	0.881536i	−0.993691	+	0.112155i	$0.964225\pi$
$564$		0			0
$565$	−9.18072	−	2.03768i	−0.386236	−	0.0857260i
$566$		0			0
$567$	−18.1955	+	18.1955i	−0.764141	+	0.764141i
$568$		0			0
$569$	−9.04416			−0.379151			−0.189576	−	0.981866i	$-0.560711\pi$
$569$	−9.04416			−0.379151			−0.189576	+	0.981866i	$0.560711\pi$
$570$		0			0
$571$			32.7847i			1.37200i	0.727603	+	0.685998i	$0.240634\pi$
$571$			32.7847i			1.37200i	−0.727603	+	0.685998i	$0.759366\pi$
$572$		0			0
$573$	19.7215	+	19.7215i	0.823878	+	0.823878i
$574$		0			0
$575$	3.46764	+	23.7271i	0.144610	+	0.989489i
$576$		0			0
$577$	4.96366	+	4.96366i	0.206640	+	0.206640i	0.802838	−	0.596198i	$-0.203323\pi$
$577$	4.96366	+	4.96366i	0.206640	+	0.206640i	−0.596198	+	0.802838i	$0.703323\pi$
$578$		0			0
$579$			26.2069i			1.08912i
$580$		0			0
$581$	−33.7686			−1.40096
$582$		0			0
$583$	−15.7267	+	15.7267i	−0.651332	+	0.651332i
$584$		0			0
$585$	6.21839	+	1.38019i	0.257099	+	0.0570637i
$586$		0			0
$587$	21.8042	+	21.8042i	0.899954	+	0.899954i	0.995432	−	0.0954776i	$-0.0304378\pi$
$587$	21.8042	+	21.8042i	0.899954	+	0.899954i	−0.0954776	+	0.995432i	$0.530438\pi$
$588$		0			0
$589$	1.08208			0.0445862
$590$		0			0
$591$	−15.5449			−0.639433
$592$		0			0
$593$	−1.66685	+	1.66685i	−0.0684495	+	0.0684495i	−0.740503	−	0.672053i	$-0.765413\pi$
$593$	−1.66685	+	1.66685i	−0.0684495	+	0.0684495i	0.672053	+	0.740503i	$0.265413\pi$
$594$		0			0
$595$	−13.9611	−	21.9264i	−0.572348	−	0.898894i
$596$		0			0
$597$	−4.66532	+	4.66532i	−0.190939	+	0.190939i
$598$		0			0
$599$		−	9.05424i		−	0.369946i	−0.982744	−	0.184973i	$-0.940780\pi$
$599$		−	9.05424i		−	0.369946i	0.982744	−	0.184973i	$-0.0592198\pi$
$600$		0			0
$601$	18.4062			0.750806			0.375403	−	0.926862i	$-0.377504\pi$
$601$	18.4062			0.750806			0.375403	+	0.926862i	$0.377504\pi$
$602$		0			0
$603$	−4.48588	−	4.48588i	−0.182679	−	0.182679i
$604$		0			0
$605$	−12.9844	+	8.26748i	−0.527890	+	0.336121i
$606$		0			0
$607$	−18.8697	−	18.8697i	−0.765897	−	0.765897i	0.211484	−	0.977381i	$-0.432170\pi$
$607$	−18.8697	−	18.8697i	−0.765897	−	0.765897i	−0.977381	+	0.211484i	$0.932170\pi$
$608$		0			0
$609$	19.9766			0.809492
$610$		0			0
$611$	4.74756			0.192066
$612$		0			0
$613$	26.1337	+	26.1337i	1.05553	+	1.05553i	0.998365	+	0.0571675i	$0.0182069\pi$
$613$	26.1337	+	26.1337i	1.05553	+	1.05553i	0.0571675	+	0.998365i	$0.481793\pi$
$614$		0			0
$615$	−2.58945	+	11.6667i	−0.104417	+	0.470446i
$616$		0			0
$617$	4.51130	−	4.51130i	0.181618	−	0.181618i	−0.610442	−	0.792061i	$-0.709008\pi$
$617$	4.51130	−	4.51130i	0.181618	−	0.181618i	0.792061	+	0.610442i	$0.209008\pi$
$618$		0			0
$619$	−23.0107			−0.924880			−0.462440	−	0.886651i	$-0.653026\pi$
$619$	−23.0107			−0.924880			−0.462440	+	0.886651i	$0.653026\pi$
$620$		0			0
$621$	−26.2069	−	5.40673i	−1.05164	−	0.216965i
$622$		0			0
$623$	−8.40428	+	8.40428i	−0.336710	+	0.336710i
$624$		0			0
$625$	−16.0509	−	19.1669i	−0.642035	−	0.766676i
$626$		0			0
$627$	2.02167	+	2.02167i	0.0807378	+	0.0807378i
$628$		0			0
$629$		−	1.17027i		−	0.0466617i
$630$		0			0
$631$		−	16.7613i		−	0.667257i	−0.942705	−	0.333629i	$-0.891727\pi$
$631$		−	16.7613i		−	0.667257i	0.942705	−	0.333629i	$-0.108273\pi$
$632$		0			0
$633$	17.2592	−	17.2592i	0.685991	−	0.685991i
$634$		0			0
$635$	26.4678	+	5.87458i	1.05034	+	0.233126i
$636$		0			0
$637$	24.1339	+	24.1339i	0.956221	+	0.956221i
$638$		0			0
$639$			0.466611i			0.0184588i
$640$		0			0
$641$			5.43640i			0.214725i	0.994220	+	0.107363i	$0.0342405\pi$
$641$			5.43640i			0.214725i	−0.994220	+	0.107363i	$0.965759\pi$
$642$		0			0
$643$	9.38867	+	9.38867i	0.370253	+	0.370253i	0.867569	−	0.497316i	$-0.165681\pi$
$643$	9.38867	+	9.38867i	0.370253	+	0.370253i	−0.497316	+	0.867569i	$0.665681\pi$
$644$		0			0
$645$	11.9534	−	7.61102i	0.470664	−	0.299684i
$646$		0			0
$647$	−7.06399	−	7.06399i	−0.277714	−	0.277714i	0.554482	−	0.832196i	$-0.312917\pi$
$647$	−7.06399	−	7.06399i	−0.277714	−	0.277714i	−0.832196	+	0.554482i	$0.812917\pi$
$648$		0			0
$649$	−16.6846			−0.654928
$650$		0			0
$651$			6.94173i			0.272068i
$652$		0			0
$653$	31.7634	−	31.7634i	1.24300	−	1.24300i	0.284248	−	0.958751i	$-0.408256\pi$
$653$	31.7634	−	31.7634i	1.24300	−	1.24300i	0.958751	−	0.284248i	$-0.0917438\pi$
$654$		0			0
$655$	25.6515	−	16.3329i	1.00229	−	0.638181i
$656$		0			0
$657$	−6.39752	−	6.39752i	−0.249591	−	0.249591i
$658$		0			0
$659$	−7.60364			−0.296196			−0.148098	−	0.988973i	$-0.547315\pi$
$659$	−7.60364			−0.296196			−0.148098	+	0.988973i	$0.547315\pi$
$660$		0			0
$661$			36.5736i			1.42255i	0.702916	+	0.711273i	$0.251881\pi$
$661$			36.5736i			1.42255i	−0.702916	+	0.711273i	$0.748119\pi$
$662$		0			0
$663$	15.8139	+	15.8139i	0.614163	+	0.614163i
$664$		0			0
$665$	1.66698	−	7.51055i	0.0646429	−	0.291247i
$666$		0			0
$667$	9.01139	+	13.6962i	0.348923	+	0.530319i
$668$		0			0
$669$		−	31.0035i		−	1.19866i
$670$		0			0
$671$	10.8536			0.418998
$672$		0			0
$673$	12.6021	−	12.6021i	0.485775	−	0.485775i	−0.421195	−	0.906970i	$-0.638389\pi$
$673$	12.6021	−	12.6021i	0.485775	−	0.485775i	0.906970	+	0.421195i	$0.138389\pi$
$674$		0			0
$675$	26.2202	−	9.52878i	1.00922	−	0.366763i
$676$		0			0
$677$	−7.82995	+	7.82995i	−0.300929	+	0.300929i	−0.841377	−	0.540448i	$-0.818255\pi$
$677$	−7.82995	+	7.82995i	−0.300929	+	0.300929i	0.540448	+	0.841377i	$0.318255\pi$
$678$		0			0
$679$			11.8121i			0.453306i
$680$		0			0
$681$			26.7897i			1.02658i
$682$		0			0
$683$	19.8457	−	19.8457i	0.759373	−	0.759373i	−0.216835	−	0.976208i	$-0.569573\pi$
$683$	19.8457	−	19.8457i	0.759373	−	0.759373i	0.976208	+	0.216835i	$0.0695733\pi$
$684$		0			0
$685$	−8.02701	+	36.1655i	−0.306696	+	1.38181i
$686$		0			0
$687$	−31.8827	+	31.8827i	−1.21640	+	1.21640i
$688$		0			0
$689$	−51.4903			−1.96162
$690$		0			0
$691$	23.2781			0.885542			0.442771	−	0.896635i	$-0.353996\pi$
$691$	23.2781			0.885542			0.442771	+	0.896635i	$0.353996\pi$
$692$		0			0
$693$	3.28629	−	3.28629i	0.124836	−	0.124836i
$694$		0			0
$695$	−6.28186	−	9.86590i	−0.238285	−	0.374235i
$696$		0			0
$697$	7.51790	−	7.51790i	0.284761	−	0.284761i
$698$		0			0
$699$		−	16.9267i		−	0.640226i
$700$		0			0
$701$		−	23.7913i		−	0.898587i	−0.893384	−	0.449293i	$-0.851676\pi$
$701$		−	23.7913i		−	0.898587i	0.893384	−	0.449293i	$-0.148324\pi$
$702$		0			0
$703$	0.244915	−	0.244915i	0.00923713	−	0.00923713i
$704$		0			0
$705$	2.94956	−	1.87806i	0.111087	−	0.0707319i
$706$		0			0
$707$	−48.4006	+	48.4006i	−1.82029	+	1.82029i
$708$		0			0
$709$	−28.2186			−1.05977			−0.529886	−	0.848069i	$-0.677765\pi$
$709$	−28.2186			−1.05977			−0.529886	+	0.848069i	$0.677765\pi$
$710$		0			0
$711$		−	6.20060i		−	0.232541i
$712$		0			0
$713$	−4.75933	+	3.13140i	−0.178238	+	0.117272i
$714$		0			0
$715$	20.8015	+	4.61694i	0.777932	+	0.172664i
$716$		0			0
$717$	18.5179	+	18.5179i	0.691562	+	0.691562i
$718$		0			0
$719$			2.42595i			0.0904728i	0.998976	+	0.0452364i	$0.0144041\pi$
$719$			2.42595i			0.0904728i	−0.998976	+	0.0452364i	$0.985596\pi$
$720$		0			0
$721$	63.4075			2.36142
$722$		0			0
$723$	−12.4749	−	12.4749i	−0.463947	−	0.463947i
$724$		0			0
$725$	−15.4878	−	7.23134i	−0.575202	−	0.268565i
$726$		0			0
$727$	−18.4783	+	18.4783i	−0.685323	+	0.685323i	−0.961195	−	0.275871i	$-0.911034\pi$
$727$	−18.4783	+	18.4783i	−0.685323	+	0.685323i	0.275871	+	0.961195i	$0.411034\pi$
$728$		0			0
$729$			30.0283i			1.11216i
$730$		0			0
$731$	−12.6071			−0.466291
$732$		0			0
$733$	0.242215	+	0.242215i	0.00894643	+	0.00894643i	0.711566	−	0.702619i	$-0.247986\pi$
$733$	0.242215	+	0.242215i	0.00894643	+	0.00894643i	−0.702619	+	0.711566i	$0.747986\pi$
$734$		0			0
$735$	24.5409	+	5.44692i	0.905206	+	0.200913i
$736$		0			0
$737$	−15.0060	−	15.0060i	−0.552752	−	0.552752i
$738$		0			0
$739$		−	37.8004i		−	1.39051i	−0.718763	−	0.695255i	$-0.755291\pi$
$739$		−	37.8004i		−	1.39051i	0.718763	−	0.695255i	$-0.244709\pi$
$740$		0			0
$741$			6.61910i			0.243159i
$742$		0			0
$743$	12.5334	+	12.5334i	0.459807	+	0.459807i	0.898592	−	0.438785i	$-0.144591\pi$
$743$	12.5334	+	12.5334i	0.459807	+	0.459807i	−0.438785	+	0.898592i	$0.644591\pi$
$744$		0			0
$745$	−35.8506	+	22.8270i	−1.31347	+	0.836316i
$746$		0			0
$747$	−3.83407	+	3.83407i	−0.140281	+	0.140281i
$748$		0			0
$749$			46.6864i			1.70588i
$750$		0			0
$751$			15.4402i			0.563420i	0.959500	+	0.281710i	$0.0909016\pi$
$751$			15.4402i			0.563420i	−0.959500	+	0.281710i	$0.909098\pi$
$752$		0			0
$753$	33.2679	+	33.2679i	1.21235	+	1.21235i
$754$		0			0
$755$	−45.0839	+	28.7060i	−1.64077	+	1.04472i
$756$		0			0
$757$	25.0867	−	25.0867i	0.911793	−	0.911793i	−0.0846205	−	0.996413i	$-0.526968\pi$
$757$	25.0867	−	25.0867i	0.911793	−	0.911793i	0.996413	+	0.0846205i	$0.0269678\pi$
$758$		0			0
$759$	−14.7424	−	3.04151i	−0.535117	−	0.110400i
$760$		0			0
$761$	14.3155			0.518936			0.259468	−	0.965752i	$-0.416453\pi$
$761$	14.3155			0.518936			0.259468	+	0.965752i	$0.416453\pi$
$762$		0			0
$763$	−43.3785	+	43.3785i	−1.57041	+	1.57041i
$764$		0			0
$765$	−4.07465	−	0.904377i	−0.147319	−	0.0326978i
$766$		0			0
$767$	−27.3133	−	27.3133i	−0.986226	−	0.986226i
$768$		0			0
$769$	3.71722			0.134046			0.0670232	−	0.997751i	$-0.478650\pi$
$769$	3.71722			0.134046			0.0670232	+	0.997751i	$0.478650\pi$
$770$		0			0
$771$	−34.5710			−1.24504
$772$		0			0
$773$	−4.39569	−	4.39569i	−0.158102	−	0.158102i	0.623623	−	0.781725i	$-0.285660\pi$
$773$	−4.39569	−	4.39569i	−0.158102	−	0.158102i	−0.781725	+	0.623623i	$0.785660\pi$
$774$		0			0
$775$	2.51284	−	5.38190i	0.0902640	−	0.193324i
$776$		0			0
$777$	1.57117	+	1.57117i	0.0563655	+	0.0563655i
$778$		0			0
$779$	3.14670			0.112742
$780$		0			0
$781$			1.56089i			0.0558530i
$782$		0			0
$783$	13.4875	−	13.4875i	0.482003	−	0.482003i
$784$		0			0
$785$	6.81387	−	30.6997i	0.243197	−	1.09572i
$786$		0			0
$787$	13.6700	−	13.6700i	0.487284	−	0.487284i	−0.420164	−	0.907448i	$-0.638028\pi$
$787$	13.6700	−	13.6700i	0.487284	−	0.487284i	0.907448	+	0.420164i	$0.138028\pi$
$788$		0			0
$789$	20.7521			0.738795
$790$		0			0
$791$	−15.8852			−0.564814
$792$		0			0
$793$	17.7677	+	17.7677i	0.630950	+	0.630950i
$794$		0			0
$795$	−31.9899	+	20.3687i	−1.13456	+	0.722405i
$796$		0			0
$797$	−20.4580	+	20.4580i	−0.724659	+	0.724659i	−0.969551	−	0.244891i	$-0.921248\pi$
$797$	−20.4580	+	20.4580i	−0.724659	+	0.724659i	0.244891	+	0.969551i	$0.421248\pi$
$798$		0			0
$799$	−3.11088			−0.110055
$800$		0			0
$801$			1.90844i			0.0674313i
$802$		0			0
$803$	−21.4007	−	21.4007i	−0.755216	−	0.755216i
$804$		0			0
$805$	14.4026	+	37.8579i	0.507627	+	1.33432i
$806$		0			0
$807$	−29.0389	−	29.0389i	−1.02222	−	1.02222i
$808$		0			0
$809$			32.5197i			1.14333i	0.820487	+	0.571665i	$0.193702\pi$
$809$			32.5197i			1.14333i	−0.820487	+	0.571665i	$0.806298\pi$
$810$		0			0
$811$	8.65868			0.304048			0.152024	−	0.988377i	$-0.451421\pi$
$811$	8.65868			0.304048			0.152024	+	0.988377i	$0.451421\pi$
$812$		0			0
$813$	−14.4784	+	14.4784i	−0.507778	+	0.507778i
$814$		0			0
$815$	4.32152	−	19.4705i	0.151376	−	0.682021i
$816$		0			0
$817$	−2.63843	−	2.63843i	−0.0923069	−	0.0923069i
$818$		0			0
$819$	10.7596			0.375970
$820$		0			0
$821$	−26.2380			−0.915713			−0.457857	−	0.889026i	$-0.651383\pi$
$821$	−26.2380			−0.915713			−0.457857	+	0.889026i	$0.651383\pi$
$822$		0			0
$823$	−8.15496	+	8.15496i	−0.284264	+	0.284264i	−0.834807	−	0.550543i	$-0.814421\pi$
$823$	−8.15496	+	8.15496i	−0.284264	+	0.284264i	0.550543	+	0.834807i	$0.314421\pi$
$824$		0			0
$825$	14.7499	−	5.36033i	0.513527	−	0.186623i
$826$		0			0
$827$	10.1209	−	10.1209i	0.351939	−	0.351939i	−0.508892	−	0.860830i	$-0.669945\pi$
$827$	10.1209	−	10.1209i	0.351939	−	0.351939i	0.860830	+	0.508892i	$0.169945\pi$
$828$		0			0
$829$			17.9714i			0.624174i	0.950054	+	0.312087i	$0.101028\pi$
$829$			17.9714i			0.624174i	−0.950054	+	0.312087i	$0.898972\pi$
$830$		0			0
$831$	37.6985			1.30775
$832$		0			0
$833$	−15.8139	−	15.8139i	−0.547921	−	0.547921i
$834$		0			0
$835$	6.21839	+	1.38019i	0.215196	+	0.0477633i
$836$		0			0
$837$	4.68681	+	4.68681i	0.162000	+	0.162000i
$838$		0			0
$839$	−55.7549			−1.92487			−0.962436	−	0.271509i	$-0.912477\pi$
$839$	−55.7549			−1.92487			−0.962436	+	0.271509i	$0.912477\pi$
$840$		0			0
$841$	17.3134			0.597015
$842$		0			0
$843$	−26.7327	−	26.7327i	−0.920724	−	0.920724i
$844$		0			0
$845$	10.8820	+	17.0906i	0.374353	+	0.587936i
$846$		0			0
$847$	−18.3859	+	18.3859i	−0.631746	+	0.631746i
$848$		0			0
$849$	42.3077			1.45200
$850$		0			0
$851$	−0.368463	+	1.78597i	−0.0126307	+	0.0612222i
$852$		0			0
$853$	−6.67579	+	6.67579i	−0.228575	+	0.228575i	−0.812097	−	0.583522i	$-0.801674\pi$
$853$	−6.67579	+	6.67579i	−0.228575	+	0.228575i	0.583522	+	0.812097i	$0.301674\pi$
$854$		0			0
$855$	−0.663476	−	1.04201i	−0.0226904	−	0.0356361i
$856$		0			0
$857$	−0.555867	−	0.555867i	−0.0189881	−	0.0189881i	0.697549	−	0.716537i	$-0.254274\pi$
$857$	−0.555867	−	0.555867i	−0.0189881	−	0.0189881i	−0.716537	+	0.697549i	$0.754274\pi$
$858$		0			0
$859$			13.5698i			0.462994i	0.972836	+	0.231497i	$0.0743624\pi$
$859$			13.5698i			0.462994i	−0.972836	+	0.231497i	$0.925638\pi$
$860$		0			0
$861$			20.1867i			0.687960i
$862$		0			0
$863$	31.8828	−	31.8828i	1.08530	−	1.08530i	0.0892989	−	0.996005i	$-0.471537\pi$
$863$	31.8828	−	31.8828i	1.08530	−	1.08530i	0.996005	−	0.0892989i	$-0.0284626\pi$
$864$		0			0
$865$	−0.974314	+	4.38974i	−0.0331277	+	0.149256i
$866$		0			0
$867$	8.23517	+	8.23517i	0.279681	+	0.279681i
$868$		0			0
$869$		−	20.7420i		−	0.703624i
$870$		0			0
$871$		−	49.1307i		−	1.66473i
$872$		0			0
$873$	1.34114	+	1.34114i	0.0453906	+	0.0453906i
$874$		0			0
$875$	−33.4839	−	25.7323i	−1.13196	−	0.869911i
$876$		0			0
$877$	3.52979	+	3.52979i	0.119193	+	0.119193i	0.764187	−	0.644995i	$-0.223140\pi$
$877$	3.52979	+	3.52979i	0.119193	+	0.119193i	−0.644995	+	0.764187i	$0.723140\pi$
$878$		0			0
$879$	28.8396			0.972737
$880$		0			0
$881$		−	32.2322i		−	1.08593i	−0.839755	−	0.542966i	$-0.817301\pi$
$881$		−	32.2322i		−	1.08593i	0.839755	−	0.542966i	$-0.182699\pi$
$882$		0			0
$883$	−6.50060	+	6.50060i	−0.218763	+	0.218763i	−0.807977	−	0.589214i	$-0.799437\pi$
$883$	−6.50060	+	6.50060i	−0.218763	+	0.218763i	0.589214	+	0.807977i	$0.299437\pi$
$884$		0			0
$885$	−27.7739	−	6.16449i	−0.933610	−	0.207217i
$886$		0			0
$887$	0.707341	+	0.707341i	0.0237502	+	0.0237502i	0.718882	−	0.695132i	$-0.244654\pi$
$887$	0.707341	+	0.707341i	0.0237502	+	0.0237502i	−0.695132	+	0.718882i	$0.744654\pi$
$888$		0			0
$889$	45.7967			1.53597
$890$		0			0
$891$			13.8216i			0.463041i
$892$		0			0
$893$	−0.651046	−	0.651046i	−0.0217864	−	0.0217864i
$894$		0			0
$895$	5.45902	+	8.57359i	0.182475	+	0.286583i
$896$		0			0
$897$	−19.1549	−	29.1130i	−0.639562	−	0.972055i
$898$		0			0
$899$		−	4.06100i		−	0.135442i
$900$		0			0
$901$	33.7394			1.12402
$902$		0			0
$903$	16.9260	−	16.9260i	0.563262	−	0.563262i
$904$		0			0
$905$	−9.24523	−	14.5200i	−0.307322	−	0.482660i
$906$		0			0
$907$	32.3163	−	32.3163i	1.07304	−	1.07304i	0.0759315	−	0.997113i	$-0.475807\pi$
$907$	32.3163	−	32.3163i	1.07304	−	1.07304i	0.997113	−	0.0759315i	$-0.0241930\pi$
$908$		0			0
$909$			10.9908i			0.364541i
$910$		0			0
$911$			15.7219i			0.520890i	0.965489	+	0.260445i	$0.0838693\pi$
$911$			15.7219i			0.520890i	−0.965489	+	0.260445i	$0.916131\pi$
$912$		0			0
$913$	−12.8256	+	12.8256i	−0.424465	+	0.424465i
$914$		0			0
$915$	18.0674	+	4.01010i	0.597289	+	0.132570i
$916$		0			0
$917$	36.3225	−	36.3225i	1.19947	−	1.19947i
$918$		0			0
$919$	1.78597			0.0589136			0.0294568	−	0.999566i	$-0.490622\pi$
$919$	1.78597			0.0589136			0.0294568	+	0.999566i	$0.490622\pi$
$920$		0			0
$921$	12.8572			0.423661
$922$		0			0
$923$	−2.55523	+	2.55523i	−0.0841065	+	0.0841065i
$924$		0			0
$925$	−0.649375	−	1.78688i	−0.0213513	−	0.0587521i
$926$		0			0
$927$	7.19926	−	7.19926i	0.236455	−	0.236455i
$928$		0			0
$929$		−	9.38261i		−	0.307833i	−0.988084	−	0.153917i	$-0.950811\pi$
$929$		−	9.38261i		−	0.307833i	0.988084	−	0.153917i	$-0.0491888\pi$
$930$		0			0
$931$		−	6.61910i		−	0.216932i
$932$		0			0
$933$	15.8401	−	15.8401i	0.518582	−	0.518582i
$934$		0			0
$935$	−13.6303	−	3.02529i	−0.445760	−	0.0989374i
$936$		0			0
$937$	27.7836	−	27.7836i	0.907650	−	0.907650i	−0.0884326	−	0.996082i	$-0.528186\pi$
$937$	27.7836	−	27.7836i	0.907650	−	0.907650i	0.996082	+	0.0884326i	$0.0281858\pi$
$938$		0			0
$939$	21.3274			0.695993
$940$		0			0
$941$		−	44.0906i		−	1.43731i	−0.695366	−	0.718655i	$-0.744758\pi$
$941$		−	44.0906i		−	1.43731i	0.695366	−	0.718655i	$-0.255242\pi$
$942$		0			0
$943$	−13.8402	+	9.10616i	−0.450700	+	0.296537i
$944$		0			0
$945$	39.7507	−	25.3102i	1.29309	−	0.823342i
$946$		0			0
$947$	−18.0987	−	18.0987i	−0.588130	−	0.588130i	0.348995	−	0.937125i	$-0.386523\pi$
$947$	−18.0987	−	18.0987i	−0.588130	−	0.588130i	−0.937125	+	0.348995i	$0.886523\pi$
$948$		0			0
$949$		−	70.0676i		−	2.27449i
$950$		0			0
$951$	18.9403			0.614180
$952$		0			0
$953$	−27.6404	−	27.6404i	−0.895360	−	0.895360i	0.0996615	−	0.995021i	$-0.468224\pi$
$953$	−27.6404	−	27.6404i	−0.895360	−	0.895360i	−0.995021	+	0.0996615i	$0.968224\pi$
$954$		0			0
$955$	−21.6507	−	34.0032i	−0.700599	−	1.10032i
$956$		0			0
$957$	7.58726	−	7.58726i	0.245261	−	0.245261i
$958$		0			0
$959$			62.5765i			2.02070i
$960$		0			0
$961$	−29.5888			−0.954478
$962$		0			0
$963$	5.30076	+	5.30076i	0.170814	+	0.170814i
$964$		0			0
$965$	8.20729	−	36.9777i	0.264202	−	1.19035i
$966$		0			0
$967$	39.8835	+	39.8835i	1.28257	+	1.28257i	0.939203	+	0.343362i	$0.111566\pi$
$967$	39.8835	+	39.8835i	1.28257	+	1.28257i	0.343362	+	0.939203i	$0.388434\pi$
$968$		0			0
$969$		−	4.33722i		−	0.139332i
$970$		0			0
$971$		−	0.783681i		−	0.0251495i	−0.999921	−	0.0125748i	$-0.995997\pi$
$971$		−	0.783681i		−	0.0251495i	0.999921	−	0.0125748i	$-0.00400277\pi$
$972$		0			0
$973$	−13.9701	−	13.9701i	−0.447861	−	0.447861i
$974$		0			0
$975$	32.9213	+	15.3711i	1.05432	+	0.492270i
$976$		0			0
$977$	7.44042	−	7.44042i	0.238040	−	0.238040i	−0.577998	−	0.816038i	$-0.696166\pi$
$977$	7.44042	−	7.44042i	0.238040	−	0.238040i	0.816038	+	0.577998i	$0.196166\pi$
$978$		0			0
$979$			6.38402i			0.204034i
$980$		0			0
$981$			9.85034i			0.314497i
$982$		0			0
$983$	−23.8534	−	23.8534i	−0.760804	−	0.760804i	0.215664	−	0.976468i	$-0.430809\pi$
$983$	−23.8534	−	23.8534i	−0.760804	−	0.760804i	−0.976468	+	0.215664i	$0.930809\pi$
$984$		0			0
$985$	21.9338	+	4.86826i	0.698869	+	0.155116i
$986$		0			0
$987$	4.17658	−	4.17658i	0.132942	−	0.132942i
$988$		0			0
$989$	19.2399	+	3.96939i	0.611795	+	0.126219i
$990$		0			0
$991$	43.2623			1.37427			0.687136	−	0.726529i	$-0.258868\pi$
$991$	43.2623			1.37427			0.687136	+	0.726529i	$0.258868\pi$
$992$		0			0
$993$	−27.4745	+	27.4745i	−0.871876	+	0.871876i
$994$		0			0
$995$	8.04379	−	5.12168i	0.255005	−	0.162368i
$996$		0			0
$997$	−35.8282	−	35.8282i	−1.13469	−	1.13469i	−0.989387	−	0.145303i	$-0.953584\pi$
$997$	−35.8282	−	35.8282i	−1.13469	−	1.13469i	−0.145303	−	0.989387i	$-0.546416\pi$
$998$		0			0
$999$	2.12160			0.0671244

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.i.b.137.5	✓	16
5.2	odd	4		2300.2.i.d.1793.3		16
5.3	odd	4	inner	460.2.i.b.413.6	yes	16
5.4	even	2		2300.2.i.d.1057.4		16
23.22	odd	2	inner	460.2.i.b.137.6	yes	16
115.22	even	4		2300.2.i.d.1793.4		16
115.68	even	4	inner	460.2.i.b.413.5	yes	16
115.114	odd	2		2300.2.i.d.1057.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.i.b.137.5	✓	16	1.1	even	1	trivial
460.2.i.b.137.6	yes	16	23.22	odd	2	inner
460.2.i.b.413.5	yes	16	115.68	even	4	inner
460.2.i.b.413.6	yes	16	5.3	odd	4	inner
2300.2.i.d.1057.3		16	115.114	odd	2
2300.2.i.d.1057.4		16	5.4	even	2
2300.2.i.d.1793.3		16	5.2	odd	4
2300.2.i.d.1793.4		16	115.22	even	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.09396 - 1.09396i) q^{3} +(-1.88618 + 1.20098i) q^{5} +(-2.67082 + 2.67082i) q^{7} +0.606488i q^{9} +O(q^{10})\)	\(q+(1.09396 - 1.09396i) q^{3} +(-1.88618 + 1.20098i) q^{5} +(-2.67082 + 2.67082i) q^{7} +0.606488i q^{9} +2.02880i q^{11} +(-3.32122 + 3.32122i) q^{13} +(-0.749584 + 3.37723i) q^{15} +(2.17625 - 2.17625i) q^{17} +0.910896 q^{19} +5.84356i q^{21} +(-4.00642 + 2.63602i) q^{23} +(2.11532 - 4.53050i) q^{25} +(3.94537 + 3.94537i) q^{27} -3.41856i q^{29} +1.18793 q^{31} +(2.21943 + 2.21943i) q^{33} +(1.83005 - 8.24523i) q^{35} +(0.268872 - 0.268872i) q^{37} +7.26659i q^{39} +3.45451 q^{41} +(-2.89652 - 2.89652i) q^{43} +(-0.728377 - 1.14394i) q^{45} +(-0.714732 - 0.714732i) q^{47} -7.26659i q^{49} -4.76149i q^{51} +(7.75171 + 7.75171i) q^{53} +(-2.43654 - 3.82667i) q^{55} +(0.996487 - 0.996487i) q^{57} +8.22388i q^{59} -5.34976i q^{61} +(-1.61982 - 1.61982i) q^{63} +(2.27570 - 10.2531i) q^{65} +(-7.39648 + 7.39648i) q^{67} +(-1.49917 + 7.26659i) q^{69} +0.769366 q^{71} +(-10.5485 + 10.5485i) q^{73} +(-2.64212 - 7.27028i) q^{75} +(-5.41856 - 5.41856i) q^{77} -10.2238 q^{79} +6.81271 q^{81} +(6.32176 + 6.32176i) q^{83} +(-1.49117 + 6.71843i) q^{85} +(-3.73978 - 3.73978i) q^{87} +3.14670 q^{89} -17.7408i q^{91} +(1.29955 - 1.29955i) q^{93} +(-1.71811 + 1.09396i) q^{95} +(2.21132 - 2.21132i) q^{97} -1.23044 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{3}+O(q^{10}) \) 16 * q + 4 * q^3	\( 16 q + 4 q^{3} + 12 q^{13} + 12 q^{23} + 36 q^{25} + 52 q^{27} - 8 q^{31} + 16 q^{35} - 48 q^{41} + 4 q^{47} + 24 q^{55} + 8 q^{71} - 52 q^{73} - 56 q^{75} - 64 q^{77} - 152 q^{81} + 28 q^{85} + 28 q^{87} + 84 q^{93} - 68 q^{95}+O(q^{100}) \) 16 * q + 4 * q^3 + 12 * q^13 + 12 * q^23 + 36 * q^25 + 52 * q^27 - 8 * q^31 + 16 * q^35 - 48 * q^41 + 4 * q^47 + 24 * q^55 + 8 * q^71 - 52 * q^73 - 56 * q^75 - 64 * q^77 - 152 * q^81 + 28 * q^85 + 28 * q^87 + 84 * q^93 - 68 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more