LMFDB - Embedded newform 1080.2.b.d.971.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1080,2,Mod(971,1080)] 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("1080.971"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1080, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1080 = 2^{3} \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1080.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$8.62384341830$
Analytic rank:	$0$
Dimension:	$16$
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} - 2 x^{15} + x^{14} + 2 x^{13} - 6 x^{12} + 8 x^{11} - 6 x^{10} - 8 x^{9} + 32 x^{8} - 16 x^{7} + \cdots + 256 $ x^16 - 2x^15 + x^14 + 2x^13 - 6x^12 + 8x^11 - 6x^10 - 8x^9 + 32x^8 - 16x^7 - 24x^6 + 64x^5 - 96x^4 + 64x^3 + 64x^2 - 256x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			971.7
Root			$-0.119860 + 1.40913i$ of defining polynomial
Character	$\chi$	$=$	1080.971
Dual form			1080.2.b.d.971.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.119860 - 1.40913i) q^{2} +(-1.97127 + 0.337796i) q^{4} -1.00000 q^{5} -1.81970i q^{7} +(0.712273 + 2.73727i) q^{8} +(0.119860 + 1.40913i) q^{10} -1.81755i q^{11} +1.62865i q^{13} +(-2.56418 + 0.218109i) q^{14} +(3.77179 - 1.33177i) q^{16} -3.36115i q^{17} -2.50290 q^{19} +(1.97127 - 0.337796i) q^{20} +(-2.56116 + 0.217852i) q^{22} -7.77601 q^{23} +1.00000 q^{25} +(2.29498 - 0.195211i) q^{26} +(0.614687 + 3.58711i) q^{28} -6.90702 q^{29} +4.41794i q^{31} +(-2.32872 - 5.15529i) q^{32} +(-4.73628 + 0.402867i) q^{34} +1.81970i q^{35} +12.0300i q^{37} +(0.299998 + 3.52690i) q^{38} +(-0.712273 - 2.73727i) q^{40} -2.07086i q^{41} +1.84704 q^{43} +(0.613961 + 3.58288i) q^{44} +(0.932034 + 10.9574i) q^{46} -5.65012 q^{47} +3.68869 q^{49} +(-0.119860 - 1.40913i) q^{50} +(-0.550153 - 3.21051i) q^{52} -0.710648 q^{53} +1.81755i q^{55} +(4.98102 - 1.29612i) q^{56} +(0.827877 + 9.73286i) q^{58} +2.31644i q^{59} +4.93340i q^{61} +(6.22542 - 0.529534i) q^{62} +(-6.98533 + 3.89937i) q^{64} -1.62865i q^{65} -7.15709 q^{67} +(1.13538 + 6.62572i) q^{68} +(2.56418 - 0.218109i) q^{70} -0.231207 q^{71} -12.0660 q^{73} +(16.9518 - 1.44192i) q^{74} +(4.93388 - 0.845469i) q^{76} -3.30740 q^{77} -8.07178i q^{79} +(-3.77179 + 1.33177i) q^{80} +(-2.91811 + 0.248214i) q^{82} +10.7382i q^{83} +3.36115i q^{85} +(-0.221386 - 2.60271i) q^{86} +(4.97514 - 1.29459i) q^{88} +9.05322i q^{89} +2.96366 q^{91} +(15.3286 - 2.62671i) q^{92} +(0.677224 + 7.96172i) q^{94} +2.50290 q^{95} -12.6810 q^{97} +(-0.442127 - 5.19783i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{2} + 2 q^{4} - 16 q^{5} - 4 q^{8} - 2 q^{10} + 6 q^{14} + 10 q^{16} - 8 q^{19} - 2 q^{20} + 4 q^{22} - 8 q^{23} + 16 q^{25} - 16 q^{26} + 20 q^{28} - 8 q^{32} + 18 q^{34} - 14 q^{38} + 4 q^{40}+ \cdots - 32 q^{98}+O(q^{100}) $ 16 * q + 2 * q^2 + 2 * q^4 - 16 * q^5 - 4 * q^8 - 2 * q^10 + 6 * q^14 + 10 * q^16 - 8 * q^19 - 2 * q^20 + 4 * q^22 - 8 * q^23 + 16 * q^25 - 16 * q^26 + 20 * q^28 - 8 * q^32 + 18 * q^34 - 14 * q^38 + 4 * q^40 + 6 * q^44 + 2 * q^46 - 16 * q^47 - 8 * q^49 + 2 * q^50 - 20 * q^52 + 32 * q^53 + 12 * q^56 - 16 * q^58 + 16 * q^62 + 14 * q^64 + 32 * q^67 - 8 * q^68 - 6 * q^70 + 24 * q^71 + 8 * q^73 + 34 * q^74 + 36 * q^76 - 10 * q^80 - 8 * q^82 - 34 * q^86 + 16 * q^88 + 48 * q^91 - 32 * q^92 + 10 * q^94 + 8 * q^95 - 8 * q^97 - 32 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1080\mathbb{Z}\right)^\times$.

$n$	$217$	$271$	$541$	$1001$
$\chi(n)$	$1$	$-1$	$-1$	$-1$

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 $

$2$	−0.119860	−	1.40913i	−0.0847539	−	0.996402i
$2$	−0.119860	−	1.40913i	−0.0847539	−	0.996402i
$3$		0			0
$3$		0			0
$4$	−1.97127	+	0.337796i	−0.985634	+	0.168898i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$		0			0
$7$		−	1.81970i		−	0.687782i	−0.939010	−	0.343891i	$-0.888255\pi$
$7$		−	1.81970i		−	0.687782i	0.939010	−	0.343891i	$-0.111745\pi$
$8$	0.712273	+	2.73727i	0.251827	+	0.967772i
$9$		0			0
$10$	0.119860	+	1.40913i	0.0379031	+	0.445604i
$11$		−	1.81755i		−	0.548012i	−0.961728	−	0.274006i	$-0.911651\pi$
$11$		−	1.81755i		−	0.548012i	0.961728	−	0.274006i	$-0.0883489\pi$
$12$		0			0
$13$			1.62865i			0.451708i	0.974161	+	0.225854i	$0.0725172\pi$
$13$			1.62865i			0.451708i	−0.974161	+	0.225854i	$0.927483\pi$
$14$	−2.56418	+	0.218109i	−0.685307	+	0.0582922i
$15$		0			0
$16$	3.77179	−	1.33177i	0.942947	−	0.332943i
$17$		−	3.36115i		−	0.815198i	−0.913161	−	0.407599i	$-0.866366\pi$
$17$		−	3.36115i		−	0.815198i	0.913161	−	0.407599i	$-0.133634\pi$
$18$		0			0
$19$	−2.50290			−0.574204			−0.287102	−	0.957900i	$-0.592692\pi$
$19$	−2.50290			−0.574204			−0.287102	+	0.957900i	$0.592692\pi$
$20$	1.97127	−	0.337796i	0.440789	−	0.0755335i
$21$		0			0
$22$	−2.56116	+	0.217852i	−0.546041	+	0.0464462i
$23$	−7.77601			−1.62141			−0.810705	−	0.585454i	$-0.800916\pi$
$23$	−7.77601			−1.62141			−0.810705	+	0.585454i	$0.800916\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$	2.29498	−	0.195211i	0.450082	−	0.0382840i
$27$		0			0
$28$	0.614687	+	3.58711i	0.116165	+	0.677901i
$29$	−6.90702			−1.28260			−0.641301	−	0.767290i	$-0.721605\pi$
$29$	−6.90702			−1.28260			−0.641301	+	0.767290i	$0.721605\pi$
$30$		0			0
$31$			4.41794i			0.793485i	0.917930	+	0.396742i	$0.129859\pi$
$31$			4.41794i			0.793485i	−0.917930	+	0.396742i	$0.870141\pi$
$32$	−2.32872	−	5.15529i	−0.411663	−	0.911336i
$33$		0			0
$34$	−4.73628	+	0.402867i	−0.812265	+	0.0690912i
$35$			1.81970i			0.307585i
$36$		0			0
$37$			12.0300i			1.97773i	0.148826	+	0.988863i	$0.452451\pi$
$37$			12.0300i			1.97773i	−0.148826	+	0.988863i	$0.547549\pi$
$38$	0.299998	+	3.52690i	0.0486661	+	0.572138i
$39$		0			0
$40$	−0.712273	−	2.73727i	−0.112620	−	0.432801i
$41$		−	2.07086i		−	0.323415i	−0.986839	−	0.161707i	$-0.948300\pi$
$41$		−	2.07086i		−	0.323415i	0.986839	−	0.161707i	$-0.0517000\pi$
$42$		0			0
$43$	1.84704			0.281671			0.140835	−	0.990033i	$-0.455021\pi$
$43$	1.84704			0.281671			0.140835	+	0.990033i	$0.455021\pi$
$44$	0.613961	+	3.58288i	0.0925582	+	0.540139i
$45$		0			0
$46$	0.932034	+	10.9574i	0.137421	+	1.61558i
$47$	−5.65012			−0.824155			−0.412077	−	0.911149i	$-0.635197\pi$
$47$	−5.65012			−0.824155			−0.412077	+	0.911149i	$0.635197\pi$
$48$		0			0
$49$	3.68869			0.526956
$50$	−0.119860	−	1.40913i	−0.0169508	−	0.199280i
$51$		0			0
$52$	−0.550153	−	3.21051i	−0.0762925	−	0.445218i
$53$	−0.710648			−0.0976150			−0.0488075	−	0.998808i	$-0.515542\pi$
$53$	−0.710648			−0.0976150			−0.0488075	+	0.998808i	$0.515542\pi$
$54$		0			0
$55$			1.81755i			0.245079i
$56$	4.98102	−	1.29612i	0.665616	−	0.173202i
$57$		0			0
$58$	0.827877	+	9.73286i	0.108706	+	1.27799i
$59$			2.31644i			0.301574i	0.988566	+	0.150787i	$0.0481808\pi$
$59$			2.31644i			0.301574i	−0.988566	+	0.150787i	$0.951819\pi$
$60$		0			0
$61$			4.93340i			0.631657i	0.948816	+	0.315829i	$0.102282\pi$
$61$			4.93340i			0.631657i	−0.948816	+	0.315829i	$0.897718\pi$
$62$	6.22542	−	0.529534i	0.790630	−	0.0672509i
$63$		0			0
$64$	−6.98533	+	3.89937i	−0.873167	+	0.487422i
$65$		−	1.62865i		−	0.202010i
$66$		0			0
$67$	−7.15709			−0.874378			−0.437189	−	0.899370i	$-0.644026\pi$
$67$	−7.15709			−0.874378			−0.437189	+	0.899370i	$0.644026\pi$
$68$	1.13538	+	6.62572i	0.137685	+	0.803486i
$69$		0			0
$70$	2.56418	−	0.218109i	0.306479	−	0.0260691i
$71$	−0.231207			−0.0274393			−0.0137196	−	0.999906i	$-0.504367\pi$
$71$	−0.231207			−0.0274393			−0.0137196	+	0.999906i	$0.504367\pi$
$72$		0			0
$73$	−12.0660			−1.41221			−0.706107	−	0.708105i	$-0.749550\pi$
$73$	−12.0660			−1.41221			−0.706107	+	0.708105i	$0.749550\pi$
$74$	16.9518	−	1.44192i	1.97061	−	0.167620i
$75$		0			0
$76$	4.93388	−	0.845469i	0.565955	−	0.0969819i
$77$	−3.30740			−0.376913
$78$		0			0
$79$		−	8.07178i		−	0.908146i	−0.890964	−	0.454073i	$-0.849970\pi$
$79$		−	8.07178i		−	0.908146i	0.890964	−	0.454073i	$-0.150030\pi$
$80$	−3.77179	+	1.33177i	−0.421699	+	0.148897i
$81$		0			0
$82$	−2.91811	+	0.248214i	−0.322251	+	0.0274107i
$83$			10.7382i			1.17867i	0.807890	+	0.589333i	$0.200609\pi$
$83$			10.7382i			1.17867i	−0.807890	+	0.589333i	$0.799391\pi$
$84$		0			0
$85$			3.36115i			0.364568i
$86$	−0.221386	−	2.60271i	−0.0238727	−	0.280657i
$87$		0			0
$88$	4.97514	−	1.29459i	0.530351	−	0.138004i
$89$			9.05322i			0.959640i	0.877367	+	0.479820i	$0.159298\pi$
$89$			9.05322i			0.959640i	−0.877367	+	0.479820i	$0.840702\pi$
$90$		0			0
$91$	2.96366			0.310676
$92$	15.3286	−	2.62671i	1.59812	−	0.273853i
$93$		0			0
$94$	0.677224	+	7.96172i	0.0698503	+	0.821189i
$95$	2.50290			0.256792
$96$		0			0
$97$	−12.6810			−1.28756			−0.643779	−	0.765211i	$-0.722634\pi$
$97$	−12.6810			−1.28756			−0.643779	+	0.765211i	$0.722634\pi$
$98$	−0.442127	−	5.19783i	−0.0446616	−	0.525060i
$99$		0			0
$100$	−1.97127	+	0.337796i	−0.197127	+	0.0337796i
$101$	−8.46064			−0.841865			−0.420932	−	0.907092i	$-0.638297\pi$
$101$	−8.46064			−0.841865			−0.420932	+	0.907092i	$0.638297\pi$
$102$		0			0
$103$		−	10.8866i		−	1.07269i	−0.843999	−	0.536345i	$-0.819805\pi$
$103$		−	10.8866i		−	1.07269i	0.843999	−	0.536345i	$-0.180195\pi$
$104$	−4.45807	+	1.16005i	−0.437150	+	0.113752i
$105$		0			0
$106$	0.0851784	+	1.00139i	0.00827325	+	0.0972638i
$107$		−	16.8706i		−	1.63095i	−0.578796	−	0.815473i	$-0.696477\pi$
$107$		−	16.8706i		−	1.63095i	0.578796	−	0.815473i	$-0.303523\pi$
$108$		0			0
$109$			14.1044i			1.35096i	0.737379	+	0.675479i	$0.236063\pi$
$109$			14.1044i			1.35096i	−0.737379	+	0.675479i	$0.763937\pi$
$110$	2.56116	−	0.217852i	0.244197	−	0.0207714i
$111$		0			0
$112$	−2.42342	−	6.86352i	−0.228992	−	0.648542i
$113$			0.973596i			0.0915882i	0.998951	+	0.0457941i	$0.0145818\pi$
$113$			0.973596i			0.0915882i	−0.998951	+	0.0457941i	$0.985418\pi$
$114$		0			0
$115$	7.77601			0.725117
$116$	13.6156	−	2.33316i	1.26418	−	0.216629i
$117$		0			0
$118$	3.26415	−	0.277648i	0.300489	−	0.0255596i
$119$	−6.11628			−0.560678
$120$		0			0
$121$	7.69651			0.699682
$122$	6.95178	−	0.591318i	0.629385	−	0.0535354i
$123$		0			0
$124$	−1.49236	−	8.70893i	−0.134018	−	0.782085i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$		−	6.73403i		−	0.597549i	−0.954324	−	0.298774i	$-0.903422\pi$
$127$		−	6.73403i		−	0.597549i	0.954324	−	0.298774i	$-0.0965778\pi$
$128$	6.33197	+	9.37583i	0.559672	+	0.828714i
$129$		0			0
$130$	−2.29498	+	0.195211i	−0.201283	+	0.0171211i
$131$		−	9.61835i		−	0.840359i	−0.907441	−	0.420180i	$-0.861967\pi$
$131$		−	9.61835i		−	0.840359i	0.907441	−	0.420180i	$-0.138033\pi$
$132$		0			0
$133$			4.55452i			0.394927i
$134$	0.857850	+	10.0852i	0.0741069	+	0.871231i
$135$		0			0
$136$	9.20038	−	2.39405i	0.788926	−	0.205288i
$137$		−	12.6763i		−	1.08301i	−0.840698	−	0.541504i	$-0.817855\pi$
$137$		−	12.6763i		−	1.08301i	0.840698	−	0.541504i	$-0.182145\pi$
$138$		0			0
$139$	14.5112			1.23082			0.615412	−	0.788205i	$-0.288989\pi$
$139$	14.5112			1.23082			0.615412	+	0.788205i	$0.288989\pi$
$140$	−0.614687	−	3.58711i	−0.0519505	−	0.303166i
$141$		0			0
$142$	0.0277125	+	0.325800i	0.00232558	+	0.0273405i
$143$	2.96016			0.247541
$144$		0			0
$145$	6.90702			0.573597
$146$	1.44623	+	17.0025i	0.119691	+	1.40713i
$147$		0			0
$148$	−4.06370	−	23.7144i	−0.334034	−	1.94931i
$149$	−1.62527			−0.133147			−0.0665737	−	0.997782i	$-0.521207\pi$
$149$	−1.62527			−0.133147			−0.0665737	+	0.997782i	$0.521207\pi$
$150$		0			0
$151$		−	21.7458i		−	1.76965i	−0.465926	−	0.884824i	$-0.654279\pi$
$151$		−	21.7458i		−	1.76965i	0.465926	−	0.884824i	$-0.345721\pi$
$152$	−1.78275	−	6.85112i	−0.144600	−	0.555699i
$153$		0			0
$154$	0.396425	+	4.66054i	0.0319448	+	0.375557i
$155$		−	4.41794i		−	0.354857i
$156$		0			0
$157$		−	15.7680i		−	1.25842i	−0.777235	−	0.629211i	$-0.783378\pi$
$157$		−	15.7680i		−	1.25842i	0.777235	−	0.629211i	$-0.216622\pi$
$158$	−11.3742	+	0.967485i	−0.904879	+	0.0769690i
$159$		0			0
$160$	2.32872	+	5.15529i	0.184101	+	0.407562i
$161$			14.1500i			1.11518i
$162$		0			0
$163$	−10.1506			−0.795053			−0.397527	−	0.917591i	$-0.630131\pi$
$163$	−10.1506			−0.795053			−0.397527	+	0.917591i	$0.630131\pi$
$164$	0.699529	+	4.08223i	0.0546241	+	0.318768i
$165$		0			0
$166$	15.1314	−	1.28708i	1.17442	−	0.0998965i
$167$	7.58284			0.586778			0.293389	−	0.955993i	$-0.405217\pi$
$167$	7.58284			0.586778			0.293389	+	0.955993i	$0.405217\pi$
$168$		0			0
$169$	10.3475			0.795960
$170$	4.73628	−	0.402867i	0.363256	−	0.0308985i
$171$		0			0
$172$	−3.64100	+	0.623922i	−0.277624	+	0.0475736i
$173$	−8.03931			−0.611218			−0.305609	−	0.952157i	$-0.598860\pi$
$173$	−8.03931			−0.611218			−0.305609	+	0.952157i	$0.598860\pi$
$174$		0			0
$175$		−	1.81970i		−	0.137556i
$176$	−2.42056	−	6.85542i	−0.182457	−	0.516747i
$177$		0			0
$178$	12.7571	−	1.08512i	0.956187	−	0.0813332i
$179$			14.5342i			1.08633i	0.839625	+	0.543167i	$0.182775\pi$
$179$			14.5342i			1.08633i	−0.839625	+	0.543167i	$0.817225\pi$
$180$		0			0
$181$			17.6839i			1.31443i	0.753701	+	0.657217i	$0.228267\pi$
$181$			17.6839i			1.31443i	−0.753701	+	0.657217i	$0.771733\pi$
$182$	−0.355225	−	4.17617i	−0.0263310	−	0.309558i
$183$		0			0
$184$	−5.53864	−	21.2851i	−0.408314	−	1.56916i
$185$		−	12.0300i		−	0.884466i
$186$		0			0
$187$	−6.10906			−0.446738
$188$	11.1379	−	1.90859i	0.812314	−	0.139198i
$189$		0			0
$190$	−0.299998	−	3.52690i	−0.0217641	−	0.255868i
$191$	−19.5451			−1.41423			−0.707115	−	0.707098i	$-0.750004\pi$
$191$	−19.5451			−1.41423			−0.707115	+	0.707098i	$0.750004\pi$
$192$		0			0
$193$	−15.0295			−1.08185			−0.540923	−	0.841072i	$-0.681925\pi$
$193$	−15.0295			−1.08185			−0.540923	+	0.841072i	$0.681925\pi$
$194$	1.51994	+	17.8691i	0.109126	+	1.28293i
$195$		0			0
$196$	−7.27140	+	1.24603i	−0.519386	+	0.0890018i
$197$	16.9578			1.20820			0.604098	−	0.796910i	$-0.293534\pi$
$197$	16.9578			1.20820			0.604098	+	0.796910i	$0.293534\pi$
$198$		0			0
$199$		−	10.7884i		−	0.764769i	−0.924003	−	0.382385i	$-0.875103\pi$
$199$		−	10.7884i		−	0.764769i	0.924003	−	0.382385i	$-0.124897\pi$
$200$	0.712273	+	2.73727i	0.0503653	+	0.193554i
$201$		0			0
$202$	1.01409	+	11.9221i	0.0713513	+	0.838836i
$203$			12.5687i			0.882150i
$204$		0			0
$205$			2.07086i			0.144635i
$206$	−15.3406	+	1.30487i	−1.06883	+	0.0909146i
$207$		0			0
$208$	2.16900	+	6.14294i	0.150393	+	0.425936i
$209$			4.54915i			0.314671i
$210$		0			0
$211$	4.74610			0.326735			0.163368	−	0.986565i	$-0.447764\pi$
$211$	4.74610			0.326735			0.163368	+	0.986565i	$0.447764\pi$
$212$	1.40088	−	0.240054i	0.0962126	−	0.0164870i
$213$		0			0
$214$	−23.7728	+	2.02212i	−1.62508	+	0.138229i
$215$	−1.84704			−0.125967
$216$		0			0
$217$	8.03931			0.545744
$218$	19.8749	−	1.69056i	1.34610	−	0.114499i
$219$		0			0
$220$	−0.613961	−	3.58288i	−0.0413933	−	0.241558i
$221$	5.47415			0.368231
$222$		0			0
$223$		−	8.77733i		−	0.587774i	−0.955840	−	0.293887i	$-0.905051\pi$
$223$		−	8.77733i		−	0.587774i	0.955840	−	0.293887i	$-0.0949489\pi$
$224$	−9.38109	+	4.23757i	−0.626800	+	0.283135i
$225$		0			0
$226$	1.37192	−	0.116695i	0.0912587	−	0.00776246i
$227$		−	17.1165i		−	1.13606i	−0.823007	−	0.568031i	$-0.807705\pi$
$227$		−	17.1165i		−	1.13606i	0.823007	−	0.568031i	$-0.192295\pi$
$228$		0			0
$229$		−	7.89367i		−	0.521628i	−0.965389	−	0.260814i	$-0.916009\pi$
$229$		−	7.89367i		−	0.521628i	0.965389	−	0.260814i	$-0.0839910\pi$
$230$	−0.932034	−	10.9574i	−0.0614565	−	0.722508i
$231$		0			0
$232$	−4.91969	−	18.9064i	−0.322993	−	1.24127i
$233$		−	12.7180i		−	0.833187i	−0.909093	−	0.416593i	$-0.863224\pi$
$233$		−	12.7180i		−	0.833187i	0.909093	−	0.416593i	$-0.136776\pi$
$234$		0			0
$235$	5.65012			0.368573
$236$	−0.782483	−	4.56631i	−0.0509353	−	0.297242i
$237$		0			0
$238$	0.733098	+	8.61860i	0.0475197	+	0.558661i
$239$	7.68918			0.497372			0.248686	−	0.968584i	$-0.420001\pi$
$239$	7.68918			0.497372			0.248686	+	0.968584i	$0.420001\pi$
$240$		0			0
$241$	−9.08135			−0.584981			−0.292491	−	0.956268i	$-0.594484\pi$
$241$	−9.08135			−0.584981			−0.292491	+	0.956268i	$0.594484\pi$
$242$	−0.922505	−	10.8453i	−0.0593008	−	0.697165i
$243$		0			0
$244$	−1.66648	−	9.72505i	−0.106686	−	0.622583i
$245$	−3.68869			−0.235662
$246$		0			0
$247$		−	4.07636i		−	0.259372i
$248$	−12.0931	+	3.14678i	−0.767912	+	0.199820i
$249$		0			0
$250$	0.119860	+	1.40913i	0.00758062	+	0.0891209i
$251$		−	2.26783i		−	0.143144i	−0.997435	−	0.0715722i	$-0.977198\pi$
$251$		−	2.26783i		−	0.143144i	0.997435	−	0.0715722i	$-0.0228016\pi$
$252$		0			0
$253$			14.1333i			0.888553i
$254$	−9.48909	+	0.807142i	−0.595398	+	0.0506446i
$255$		0			0
$256$	12.4528	−	10.0463i	0.778298	−	0.627895i
$257$			16.6994i			1.04168i	0.853655	+	0.520839i	$0.174381\pi$
$257$			16.6994i			1.04168i	−0.853655	+	0.520839i	$0.825619\pi$
$258$		0			0
$259$	21.8911			1.36024
$260$	0.550153	+	3.21051i	0.0341190	+	0.199108i
$261$		0			0
$262$	−13.5535	+	1.15286i	−0.837335	+	0.0712237i
$263$	−26.8597			−1.65624			−0.828121	−	0.560549i	$-0.810590\pi$
$263$	−26.8597			−1.65624			−0.828121	+	0.560549i	$0.810590\pi$
$264$		0			0
$265$	0.710648			0.0436548
$266$	6.41789	−	0.545906i	0.393506	−	0.0334716i
$267$		0			0
$268$	14.1085	−	2.41764i	0.861816	−	0.147681i
$269$	−22.0431			−1.34399			−0.671996	−	0.740555i	$-0.734563\pi$
$269$	−22.0431			−1.34399			−0.671996	+	0.740555i	$0.734563\pi$
$270$		0			0
$271$		−	20.8366i		−	1.26574i	−0.774260	−	0.632868i	$-0.781878\pi$
$271$		−	20.8366i		−	1.26574i	0.774260	−	0.632868i	$-0.218122\pi$
$272$	−4.47628	−	12.6775i	−0.271414	−	0.768688i
$273$		0			0
$274$	−17.8625	+	1.51938i	−1.07911	+	0.0917892i
$275$		−	1.81755i		−	0.109602i
$276$		0			0
$277$			6.94364i			0.417203i	0.978001	+	0.208601i	$0.0668912\pi$
$277$			6.94364i			0.417203i	−0.978001	+	0.208601i	$0.933109\pi$
$278$	−1.73932	−	20.4481i	−0.104317	−	1.22640i
$279$		0			0
$280$	−4.98102	+	1.29612i	−0.297673	+	0.0774582i
$281$			23.6671i			1.41186i	0.708280	+	0.705932i	$0.249471\pi$
$281$			23.6671i			1.41186i	−0.708280	+	0.705932i	$0.750529\pi$
$282$		0			0
$283$	−25.8883			−1.53890			−0.769450	−	0.638707i	$-0.779469\pi$
$283$	−25.8883			−1.53890			−0.769450	+	0.638707i	$0.779469\pi$
$284$	0.455771	−	0.0781009i	0.0270451	−	0.00463443i
$285$		0			0
$286$	−0.354806	−	4.17124i	−0.0209801	−	0.246651i
$287$	−3.76835			−0.222439
$288$		0			0
$289$	5.70270			0.335453
$290$	−0.827877	−	9.73286i	−0.0486146	−	0.571533i
$291$		0			0
$292$	23.7852	−	4.07584i	1.39193	−	0.238520i
$293$	25.7105			1.50202			0.751011	−	0.660290i	$-0.229567\pi$
$293$	25.7105			1.50202			0.751011	+	0.660290i	$0.229567\pi$
$294$		0			0
$295$		−	2.31644i		−	0.134868i
$296$	−32.9295	+	8.56867i	−1.91399	+	0.498044i
$297$		0			0
$298$	0.194805	+	2.29021i	0.0112848	+	0.132668i
$299$		−	12.6644i		−	0.732404i
$300$		0			0
$301$		−	3.36105i		−	0.193728i
$302$	−30.6425	+	2.60645i	−1.76328	+	0.149985i
$303$		0			0
$304$	−9.44040	+	3.33329i	−0.541444	+	0.191177i
$305$		−	4.93340i		−	0.282486i
$306$		0			0
$307$	11.7270			0.669293			0.334647	−	0.942344i	$-0.391383\pi$
$307$	11.7270			0.669293			0.334647	+	0.942344i	$0.391383\pi$
$308$	6.51976	−	1.11723i	0.371498	−	0.0636598i
$309$		0			0
$310$	−6.22542	+	0.529534i	−0.353580	+	0.0300755i
$311$	21.3624			1.21135			0.605675	−	0.795712i	$-0.292903\pi$
$311$	21.3624			1.21135			0.605675	+	0.795712i	$0.292903\pi$
$312$		0			0
$313$	22.1199			1.25029			0.625146	−	0.780508i	$-0.285039\pi$
$313$	22.1199			1.25029			0.625146	+	0.780508i	$0.285039\pi$
$314$	−22.2191	+	1.88995i	−1.25389	+	0.106656i
$315$		0			0
$316$	2.72661	+	15.9116i	0.153384	+	0.895100i
$317$	−27.5433			−1.54699			−0.773494	−	0.633804i	$-0.781493\pi$
$317$	−27.5433			−1.54699			−0.773494	+	0.633804i	$0.781493\pi$
$318$		0			0
$319$			12.5539i			0.702882i
$320$	6.98533	−	3.89937i	0.390492	−	0.217982i
$321$		0			0
$322$	19.9391	−	1.69602i	1.11116	−	0.0945156i
$323$			8.41261i			0.468090i
$324$		0			0
$325$			1.62865i			0.0903415i
$326$	1.21665	+	14.3034i	0.0673839	+	0.792192i
$327$		0			0
$328$	5.66852	−	1.47502i	0.312992	−	0.0814444i
$329$			10.2815i			0.566838i
$330$		0			0
$331$	−23.5166			−1.29259			−0.646294	−	0.763089i	$-0.723682\pi$
$331$	−23.5166			−1.29259			−0.646294	+	0.763089i	$0.723682\pi$
$332$	−3.62730	−	21.1678i	−0.199074	−	1.16173i
$333$		0			0
$334$	−0.908880	−	10.6852i	−0.0497317	−	0.584666i
$335$	7.15709			0.391034
$336$		0			0
$337$	1.93972			0.105663			0.0528315	−	0.998603i	$-0.483175\pi$
$337$	1.93972			0.105663			0.0528315	+	0.998603i	$0.483175\pi$
$338$	−1.24025	−	14.5809i	−0.0674608	−	0.793096i
$339$		0			0
$340$	−1.13538	−	6.62572i	−0.0615747	−	0.359330i
$341$	8.02982			0.434839
$342$		0			0
$343$		−	19.4502i		−	1.05021i
$344$	1.31559	+	5.05585i	0.0709321	+	0.272593i
$345$		0			0
$346$	0.963593	+	11.3284i	0.0518031	+	0.609019i
$347$		−	2.36962i		−	0.127208i	−0.997975	−	0.0636041i	$-0.979741\pi$
$347$		−	2.36962i		−	0.127208i	0.997975	−	0.0636041i	$-0.0202595\pi$
$348$		0			0
$349$			19.5697i			1.04754i	0.851859	+	0.523771i	$0.175475\pi$
$349$			19.5697i			1.04754i	−0.851859	+	0.523771i	$0.824525\pi$
$350$	−2.56418	+	0.218109i	−0.137061	+	0.0116584i
$351$		0			0
$352$	−9.37001	+	4.23257i	−0.499423	+	0.225597i
$353$		−	34.3742i		−	1.82955i	−0.403961	−	0.914776i	$-0.632367\pi$
$353$		−	34.3742i		−	1.82955i	0.403961	−	0.914776i	$-0.367633\pi$
$354$		0			0
$355$	0.231207			0.0122712
$356$	−3.05814	−	17.8463i	−0.162081	−	0.945853i
$357$		0			0
$358$	20.4804	−	1.74207i	1.08242	−	0.0920710i
$359$	18.0416			0.952197			0.476098	−	0.879392i	$-0.342051\pi$
$359$	18.0416			0.952197			0.476098	+	0.879392i	$0.342051\pi$
$360$		0			0
$361$	−12.7355			−0.670289
$362$	24.9188	−	2.11960i	1.30970	−	0.111403i
$363$		0			0
$364$	−5.84217	+	1.00111i	−0.306213	+	0.0524726i
$365$	12.0660			0.631562
$366$		0			0
$367$		−	31.7530i		−	1.65749i	−0.559624	−	0.828747i	$-0.689054\pi$
$367$		−	31.7530i		−	1.65749i	0.559624	−	0.828747i	$-0.310946\pi$
$368$	−29.3295	+	10.3559i	−1.52890	+	0.539837i
$369$		0			0
$370$	−16.9518	+	1.44192i	−0.881284	+	0.0749620i
$371$			1.29317i			0.0671378i
$372$		0			0
$373$		−	25.1719i		−	1.30335i	−0.758498	−	0.651675i	$-0.774067\pi$
$373$		−	25.1719i		−	1.30335i	0.758498	−	0.651675i	$-0.225933\pi$
$374$	0.732232	+	8.60842i	0.0378628	+	0.445131i
$375$		0			0
$376$	−4.02443	−	15.4659i	−0.207544	−	0.797594i
$377$		−	11.2492i		−	0.579361i
$378$		0			0
$379$	6.65638			0.341915			0.170958	−	0.985278i	$-0.445314\pi$
$379$	6.65638			0.341915			0.170958	+	0.985278i	$0.445314\pi$
$380$	−4.93388	+	0.845469i	−0.253103	+	0.0433716i
$381$		0			0
$382$	2.34267	+	27.5414i	0.119862	+	1.40914i
$383$	27.3801			1.39906			0.699529	−	0.714604i	$-0.253393\pi$
$383$	27.3801			1.39906			0.699529	+	0.714604i	$0.253393\pi$
$384$		0			0
$385$	3.30740			0.168561
$386$	1.80144	+	21.1784i	0.0916908	+	1.07795i
$387$		0			0
$388$	24.9976	−	4.28358i	1.26906	−	0.217466i
$389$	16.6119			0.842255			0.421128	−	0.907001i	$-0.361634\pi$
$389$	16.6119			0.842255			0.421128	+	0.907001i	$0.361634\pi$
$390$		0			0
$391$			26.1363i			1.32177i
$392$	2.62736	+	10.0970i	0.132702	+	0.509974i
$393$		0			0
$394$	−2.03257	−	23.8957i	−0.102399	−	1.20385i
$395$			8.07178i			0.406135i
$396$		0			0
$397$			14.6342i			0.734471i	0.930128	+	0.367235i	$0.119696\pi$
$397$			14.6342i			0.734471i	−0.930128	+	0.367235i	$0.880304\pi$
$398$	−15.2022	+	1.29310i	−0.762018	+	0.0648172i
$399$		0			0
$400$	3.77179	−	1.33177i	0.188589	−	0.0665886i
$401$			5.99427i			0.299339i	0.988736	+	0.149670i	$0.0478210\pi$
$401$			5.99427i			0.299339i	−0.988736	+	0.149670i	$0.952179\pi$
$402$		0			0
$403$	−7.19529			−0.358423
$404$	16.6782	−	2.85797i	0.829770	−	0.142189i
$405$		0			0
$406$	17.7109	−	1.50649i	0.878976	−	0.0747657i
$407$	21.8652			1.08382
$408$		0			0
$409$	15.7240			0.777501			0.388751	−	0.921343i	$-0.372907\pi$
$409$	15.7240			0.777501			0.388751	+	0.921343i	$0.372907\pi$
$410$	2.91811	−	0.248214i	0.144115	−	0.0122584i
$411$		0			0
$412$	3.67745	+	21.4604i	0.181175	+	1.05728i
$413$	4.21522			0.207417
$414$		0			0
$415$		−	10.7382i		−	0.527115i
$416$	8.39620	−	3.79268i	0.411657	−	0.185952i
$417$		0			0
$418$	6.41032	−	0.545261i	0.313539	−	0.0266696i
$419$			34.2549i			1.67346i	0.547615	+	0.836730i	$0.315536\pi$
$419$			34.2549i			1.67346i	−0.547615	+	0.836730i	$0.684464\pi$
$420$		0			0
$421$		−	9.72697i		−	0.474064i	−0.971502	−	0.237032i	$-0.923825\pi$
$421$		−	9.72697i		−	0.474064i	0.971502	−	0.237032i	$-0.0761746\pi$
$422$	−0.568868	−	6.68785i	−0.0276921	−	0.325559i
$423$		0			0
$424$	−0.506175	−	1.94524i	−0.0245820	−	0.0944691i
$425$		−	3.36115i		−	0.163040i
$426$		0			0
$427$	8.97731			0.434442
$428$	5.69883	+	33.2565i	0.275463	+	1.60751i
$429$		0			0
$430$	0.221386	+	2.60271i	0.0106762	+	0.125514i
$431$	2.31013			0.111275			0.0556375	−	0.998451i	$-0.482281\pi$
$431$	2.31013			0.111275			0.0556375	+	0.998451i	$0.482281\pi$
$432$		0			0
$433$	−30.5094			−1.46619			−0.733093	−	0.680128i	$-0.761924\pi$
$433$	−30.5094			−1.46619			−0.733093	+	0.680128i	$0.761924\pi$
$434$	−0.963593	−	11.3284i	−0.0462540	−	0.543781i
$435$		0			0
$436$	−4.76442	−	27.8036i	−0.228174	−	1.33155i
$437$	19.4626			0.931021
$438$		0			0
$439$			6.33025i			0.302126i	0.988524	+	0.151063i	$0.0482697\pi$
$439$			6.33025i			0.302126i	−0.988524	+	0.151063i	$0.951730\pi$
$440$	−4.97514	+	1.29459i	−0.237180	+	0.0617173i
$441$		0			0
$442$	−0.656132	−	7.71376i	−0.0312090	−	0.366906i
$443$			36.4003i			1.72943i	0.502261	+	0.864716i	$0.332502\pi$
$443$			36.4003i			1.72943i	−0.502261	+	0.864716i	$0.667498\pi$
$444$		0			0
$445$		−	9.05322i		−	0.429164i
$446$	−12.3684	+	1.05205i	−0.585659	+	0.0498161i
$447$		0			0
$448$	7.09569	+	12.7112i	0.335240	+	0.600548i
$449$		−	7.90597i		−	0.373106i	−0.982445	−	0.186553i	$-0.940268\pi$
$449$		−	7.90597i		−	0.373106i	0.982445	−	0.186553i	$-0.0597316\pi$
$450$		0			0
$451$	−3.76390			−0.177235
$452$	−0.328877	−	1.91922i	−0.0154691	−	0.0902724i
$453$		0			0
$454$	−24.1193	+	2.05159i	−1.13197	+	0.0962857i
$455$	−2.96366			−0.138939
$456$		0			0
$457$	−15.1551			−0.708927			−0.354463	−	0.935070i	$-0.615336\pi$
$457$	−15.1551			−0.708927			−0.354463	+	0.935070i	$0.615336\pi$
$458$	−11.1232	+	0.946136i	−0.519751	+	0.0442100i
$459$		0			0
$460$	−15.3286	+	2.62671i	−0.714700	+	0.122471i
$461$	−1.15336			−0.0537174			−0.0268587	−	0.999639i	$-0.508550\pi$
$461$	−1.15336			−0.0537174			−0.0268587	+	0.999639i	$0.508550\pi$
$462$		0			0
$463$			35.2580i			1.63858i	0.573381	+	0.819289i	$0.305632\pi$
$463$			35.2580i			1.63858i	−0.573381	+	0.819289i	$0.694368\pi$
$464$	−26.0518	+	9.19858i	−1.20943	+	0.427033i
$465$		0			0
$466$	−17.9213	+	1.52439i	−0.830189	+	0.0706158i
$467$		−	13.3689i		−	0.618637i	−0.950958	−	0.309319i	$-0.899899\pi$
$467$		−	13.3689i		−	0.618637i	0.950958	−	0.309319i	$-0.100101\pi$
$468$		0			0
$469$			13.0237i			0.601381i
$470$	−0.677224	−	7.96172i	−0.0312380	−	0.367247i
$471$		0			0
$472$	−6.34072	+	1.64993i	−0.291855	+	0.0759444i
$473$		−	3.35708i		−	0.154359i
$474$		0			0
$475$	−2.50290			−0.114841
$476$	12.0568	−	2.06605i	0.552623	−	0.0946974i
$477$		0			0
$478$	−0.921627	−	10.8350i	−0.0421542	−	0.495582i
$479$	−19.6701			−0.898750			−0.449375	−	0.893343i	$-0.648353\pi$
$479$	−19.6701			−0.898750			−0.449375	+	0.893343i	$0.648353\pi$
$480$		0			0
$481$	−19.5928			−0.893354
$482$	1.08849	+	12.7968i	0.0495795	+	0.582877i
$483$		0			0
$484$	−15.1719	+	2.59985i	−0.689631	+	0.118175i
$485$	12.6810			0.575814
$486$		0			0
$487$			4.76228i			0.215800i	0.994162	+	0.107900i	$0.0344126\pi$
$487$			4.76228i			0.215800i	−0.994162	+	0.107900i	$0.965587\pi$
$488$	−13.5041	+	3.51393i	−0.611301	+	0.159068i
$489$		0			0
$490$	0.442127	+	5.19783i	0.0199733	+	0.234814i
$491$		−	41.3658i		−	1.86681i	−0.358821	−	0.933407i	$-0.616821\pi$
$491$		−	41.3658i		−	1.86681i	0.358821	−	0.933407i	$-0.383179\pi$
$492$		0			0
$493$			23.2155i			1.04557i
$494$	−5.74410	+	0.488593i	−0.258439	+	0.0219828i
$495$		0			0
$496$	5.88368	+	16.6635i	0.264185	+	0.748214i
$497$			0.420728i			0.0188722i
$498$		0			0
$499$	22.7756			1.01957			0.509787	−	0.860301i	$-0.329724\pi$
$499$	22.7756			1.01957			0.509787	+	0.860301i	$0.329724\pi$
$500$	1.97127	−	0.337796i	0.0881577	−	0.0151067i
$501$		0			0
$502$	−3.19566	+	0.271823i	−0.142629	+	0.0121320i
$503$	27.4986			1.22610			0.613052	−	0.790043i	$-0.289942\pi$
$503$	27.4986			1.22610			0.613052	+	0.790043i	$0.289942\pi$
$504$		0			0
$505$	8.46064			0.376493
$506$	19.9156	−	1.69402i	0.885356	−	0.0753084i
$507$		0			0
$508$	2.27473	+	13.2746i	0.100925	+	0.588964i
$509$	27.5160			1.21963			0.609813	−	0.792545i	$-0.291244\pi$
$509$	27.5160			1.21963			0.609813	+	0.792545i	$0.291244\pi$
$510$		0			0
$511$			21.9564i			0.971296i
$512$	−15.6491	−	16.3434i	−0.691600	−	0.722281i
$513$		0			0
$514$	23.5315	−	2.00159i	1.03793	−	0.0882862i
$515$			10.8866i			0.479721i
$516$		0			0
$517$			10.2694i			0.451647i
$518$	−2.62387	−	30.8472i	−0.115286	−	1.35535i
$519$		0			0
$520$	4.45807	−	1.16005i	0.195499	−	0.0508714i
$521$			27.2736i			1.19488i	0.801914	+	0.597439i	$0.203815\pi$
$521$			27.2736i			1.19488i	−0.801914	+	0.597439i	$0.796185\pi$
$522$		0			0
$523$	−18.6666			−0.816231			−0.408116	−	0.912930i	$-0.633814\pi$
$523$	−18.6666			−0.816231			−0.408116	+	0.912930i	$0.633814\pi$
$524$	3.24904	+	18.9603i	0.141935	+	0.828286i
$525$		0			0
$526$	3.21941	+	37.8487i	0.140373	+	1.65028i
$527$	14.8493			0.646847
$528$		0			0
$529$	37.4664			1.62897
$530$	−0.0851784	−	1.00139i	−0.00369991	−	0.0434977i
$531$		0			0
$532$	−1.53850	−	8.97818i	−0.0667024	−	0.389253i
$533$	3.37272			0.146089
$534$		0			0
$535$			16.8706i			0.729381i
$536$	−5.09780	−	19.5909i	−0.220191	−	0.846198i
$537$		0			0
$538$	2.64209	+	31.0615i	0.113909	+	1.33916i
$539$		−	6.70439i		−	0.288779i
$540$		0			0
$541$		−	12.4926i		−	0.537099i	−0.963266	−	0.268550i	$-0.913456\pi$
$541$		−	12.4926i		−	0.537099i	0.963266	−	0.268550i	$-0.0865443\pi$
$542$	−29.3614	+	2.49748i	−1.26118	+	0.107276i
$543$		0			0
$544$	−17.3277	+	7.82717i	−0.742919	+	0.335587i
$545$		−	14.1044i		−	0.604167i
$546$		0			0
$547$	−26.4085			−1.12915			−0.564574	−	0.825383i	$-0.690959\pi$
$547$	−26.4085			−1.12915			−0.564574	+	0.825383i	$0.690959\pi$
$548$	4.28200	+	24.9883i	0.182918	+	1.06745i
$549$		0			0
$550$	−2.56116	+	0.217852i	−0.109208	+	0.00928924i
$551$	17.2876			0.736475
$552$		0			0
$553$	−14.6882			−0.624606
$554$	9.78446	−	0.832266i	0.415702	−	0.0353596i
$555$		0			0
$556$	−28.6055	+	4.90183i	−1.21314	+	0.207884i
$557$	18.2096			0.771568			0.385784	−	0.922589i	$-0.373931\pi$
$557$	18.2096			0.771568			0.385784	+	0.922589i	$0.373931\pi$
$558$		0			0
$559$			3.00819i			0.127233i
$560$	2.42342	+	6.86352i	0.102408	+	0.290037i
$561$		0			0
$562$	33.3500	−	2.83675i	1.40678	−	0.119661i
$563$			16.5404i			0.697096i	0.937291	+	0.348548i	$0.113325\pi$
$563$			16.5404i			0.697096i	−0.937291	+	0.348548i	$0.886675\pi$
$564$		0			0
$565$		−	0.973596i		−	0.0409595i
$566$	3.10297	+	36.4798i	0.130428	+	1.53336i
$567$		0			0
$568$	−0.164683	−	0.632878i	−0.00690993	−	0.0265550i
$569$			45.6110i			1.91211i	0.293186	+	0.956056i	$0.405285\pi$
$569$			45.6110i			1.91211i	−0.293186	+	0.956056i	$0.594715\pi$
$570$		0			0
$571$	−11.5936			−0.485177			−0.242589	−	0.970129i	$-0.577997\pi$
$571$	−11.5936			−0.485177			−0.242589	+	0.970129i	$0.577997\pi$
$572$	−5.83527	+	0.999931i	−0.243985	+	0.0418092i
$573$		0			0
$574$	0.451675	+	5.31008i	0.0188525	+	0.221638i
$575$	−7.77601			−0.324282
$576$		0			0
$577$	23.5612			0.980867			0.490434	−	0.871479i	$-0.336838\pi$
$577$	23.5612			0.980867			0.490434	+	0.871479i	$0.336838\pi$
$578$	−0.683526	−	8.03581i	−0.0284309	−	0.334246i
$579$		0			0
$580$	−13.6156	+	2.33316i	−0.565356	+	0.0968793i
$581$	19.5402			0.810665
$582$		0			0
$583$			1.29164i			0.0534942i
$584$	−8.59427	−	33.0279i	−0.355633	−	1.36670i
$585$		0			0
$586$	−3.08166	−	36.2293i	−0.127302	−	1.49662i
$587$		−	9.54307i		−	0.393885i	−0.980415	−	0.196942i	$-0.936899\pi$
$587$		−	9.54307i		−	0.393885i	0.980415	−	0.196942i	$-0.0631012\pi$
$588$		0			0
$589$		−	11.0576i		−	0.455622i
$590$	−3.26415	+	0.277648i	−0.134383	+	0.0114306i
$591$		0			0
$592$	16.0213	+	45.3748i	0.658470	+	1.86489i
$593$		−	13.3233i		−	0.547121i	−0.961855	−	0.273560i	$-0.911799\pi$
$593$		−	13.3233i		−	0.547121i	0.961855	−	0.273560i	$-0.0882014\pi$
$594$		0			0
$595$	6.11628			0.250743
$596$	3.20384	−	0.549010i	0.131235	−	0.0224883i
$597$		0			0
$598$	−17.8458	+	1.51796i	−0.729768	+	0.0620741i
$599$	−16.0049			−0.653942			−0.326971	−	0.945034i	$-0.606028\pi$
$599$	−16.0049			−0.653942			−0.326971	+	0.945034i	$0.606028\pi$
$600$		0			0
$601$	−28.7471			−1.17262			−0.586309	−	0.810087i	$-0.699420\pi$
$601$	−28.7471			−1.17262			−0.586309	+	0.810087i	$0.699420\pi$
$602$	−4.73614	+	0.402856i	−0.193031	+	0.0164192i
$603$		0			0
$604$	7.34564	+	42.8668i	0.298890	+	1.74422i
$605$	−7.69651			−0.312908
$606$		0			0
$607$			41.1332i			1.66955i	0.550593	+	0.834774i	$0.314401\pi$
$607$			41.1332i			1.66955i	−0.550593	+	0.834774i	$0.685599\pi$
$608$	5.82855	+	12.9032i	0.236379	+	0.523293i
$609$		0			0
$610$	−6.95178	+	0.591318i	−0.281469	+	0.0239418i
$611$		−	9.20209i		−	0.372277i
$612$		0			0
$613$		−	1.14958i		−	0.0464310i	−0.999730	−	0.0232155i	$-0.992610\pi$
$613$		−	1.14958i		−	0.0464310i	0.999730	−	0.0232155i	$-0.00739038\pi$
$614$	−1.40560	−	16.5248i	−0.0567252	−	0.666885i
$615$		0			0
$616$	−2.35577	−	9.05325i	−0.0949167	−	0.364766i
$617$			10.2790i			0.413817i	0.978360	+	0.206909i	$0.0663403\pi$
$617$			10.2790i			0.413817i	−0.978360	+	0.206909i	$0.933660\pi$
$618$		0			0
$619$	33.9667			1.36524			0.682618	−	0.730775i	$-0.260841\pi$
$619$	33.9667			1.36524			0.682618	+	0.730775i	$0.260841\pi$
$620$	1.49236	+	8.70893i	0.0599346	+	0.349759i
$621$		0			0
$622$	−2.56050	−	30.1023i	−0.102667	−	1.20699i
$623$	16.4741			0.660023
$624$		0			0
$625$	1.00000			0.0400000
$626$	−2.65130	−	31.1697i	−0.105967	−	1.24579i
$627$		0			0
$628$	5.32636	+	31.0829i	0.212545	+	1.24034i
$629$	40.4347			1.61224
$630$		0			0
$631$		−	5.34016i		−	0.212589i	−0.994335	−	0.106294i	$-0.966101\pi$
$631$		−	5.34016i		−	0.212589i	0.994335	−	0.106294i	$-0.0338986\pi$
$632$	22.0947	−	5.74931i	0.878879	−	0.228695i
$633$		0			0
$634$	3.30135	+	38.8120i	0.131113	+	1.54142i
$635$			6.73403i			0.267232i
$636$		0			0
$637$			6.00761i			0.238030i
$638$	17.6900	−	1.50471i	0.700353	−	0.0595720i
$639$		0			0
$640$	−6.33197	−	9.37583i	−0.250293	−	0.370612i
$641$		−	1.16117i		−	0.0458635i	−0.999737	−	0.0229317i	$-0.992700\pi$
$641$		−	1.16117i		−	0.0458635i	0.999737	−	0.0229317i	$-0.00730004\pi$
$642$		0			0
$643$	−11.0169			−0.434463			−0.217231	−	0.976120i	$-0.569703\pi$
$643$	−11.0169			−0.434463			−0.217231	+	0.976120i	$0.569703\pi$
$644$	−4.77981	−	27.8934i	−0.188351	−	1.09916i
$645$		0			0
$646$	11.8544	−	1.00834i	0.466406	−	0.0396725i
$647$	−3.84441			−0.151139			−0.0755697	−	0.997141i	$-0.524078\pi$
$647$	−3.84441			−0.151139			−0.0755697	+	0.997141i	$0.524078\pi$
$648$		0			0
$649$	4.21024			0.165266
$650$	2.29498	−	0.195211i	0.0900165	−	0.00765680i
$651$		0			0
$652$	20.0095	−	3.42882i	0.783631	−	0.134283i
$653$	−41.4866			−1.62349			−0.811747	−	0.584009i	$-0.801483\pi$
$653$	−41.4866			−1.62349			−0.811747	+	0.584009i	$0.801483\pi$
$654$		0			0
$655$			9.61835i			0.375820i
$656$	−2.75792	−	7.81086i	−0.107679	−	0.304963i
$657$		0			0
$658$	14.4879	−	1.23234i	0.564799	−	0.0480418i
$659$		−	42.3819i		−	1.65096i	−0.564429	−	0.825481i	$-0.690904\pi$
$659$		−	42.3819i		−	1.65096i	0.564429	−	0.825481i	$-0.309096\pi$
$660$		0			0
$661$		−	18.2025i		−	0.707994i	−0.935247	−	0.353997i	$-0.884822\pi$
$661$		−	18.2025i		−	0.707994i	0.935247	−	0.353997i	$-0.115178\pi$
$662$	2.81870	+	33.1378i	0.109552	+	1.28794i
$663$		0			0
$664$	−29.3933	+	7.64850i	−1.14068	+	0.296819i
$665$		−	4.55452i		−	0.176617i
$666$		0			0
$667$	53.7091			2.07962
$668$	−14.9478	+	2.56145i	−0.578348	+	0.0991055i
$669$		0			0
$670$	−0.857850	−	10.0852i	−0.0331416	−	0.389627i
$671$	8.96671			0.346156
$672$		0			0
$673$	−26.6523			−1.02737			−0.513686	−	0.857978i	$-0.671720\pi$
$673$	−26.6523			−1.02737			−0.513686	+	0.857978i	$0.671720\pi$
$674$	−0.232495	−	2.73330i	−0.00895536	−	0.105283i
$675$		0			0
$676$	−20.3977	+	3.49534i	−0.784525	+	0.134436i
$677$	21.2158			0.815388			0.407694	−	0.913119i	$-0.366333\pi$
$677$	21.2158			0.815388			0.407694	+	0.913119i	$0.366333\pi$
$678$		0			0
$679$			23.0756i			0.885559i
$680$	−9.20038	+	2.39405i	−0.352818	+	0.0918078i
$681$		0			0
$682$	−0.962456	−	11.3150i	−0.0368543	−	0.433275i
$683$			39.4448i			1.50931i	0.656119	+	0.754657i	$0.272197\pi$
$683$			39.4448i			1.50931i	−0.656119	+	0.754657i	$0.727803\pi$
$684$		0			0
$685$			12.6763i			0.484336i
$686$	−27.4078	+	2.33131i	−1.04643	+	0.0890096i
$687$		0			0
$688$	6.96663	−	2.45983i	0.265600	−	0.0937802i
$689$		−	1.15740i		−	0.0440934i
$690$		0			0
$691$	−11.5459			−0.439227			−0.219613	−	0.975587i	$-0.570480\pi$
$691$	−11.5459			−0.439227			−0.219613	+	0.975587i	$0.570480\pi$
$692$	15.8476	−	2.71565i	0.602437	−	0.103233i
$693$		0			0
$694$	−3.33910	+	0.284024i	−0.126750	+	0.0107814i
$695$	−14.5112			−0.550442
$696$		0			0
$697$	−6.96048			−0.263647
$698$	27.5762	−	2.34563i	1.04377	−	0.0887833i
$699$		0			0
$700$	0.614687	+	3.58711i	0.0232330	+	0.135580i
$701$	−27.9340			−1.05505			−0.527526	−	0.849539i	$-0.676880\pi$
$701$	−27.9340			−1.05505			−0.527526	+	0.849539i	$0.676880\pi$
$702$		0			0
$703$		−	30.1100i		−	1.13562i
$704$	7.08731	+	12.6962i	0.267113	+	0.478506i
$705$		0			0
$706$	−48.4375	+	4.12009i	−1.82297	+	0.155062i
$707$			15.3958i			0.579019i
$708$		0			0
$709$			17.6221i			0.661811i	0.943664	+	0.330905i	$0.107354\pi$
$709$			17.6221i			0.661811i	−0.943664	+	0.330905i	$0.892646\pi$
$710$	−0.0277125	−	0.325800i	−0.00104003	−	0.0122271i
$711$		0			0
$712$	−24.7811	+	6.44837i	−0.928713	+	0.241663i
$713$		−	34.3539i		−	1.28656i
$714$		0			0
$715$	−2.96016			−0.110704
$716$	−4.90958	−	28.6507i	−0.183480	−	1.07073i
$717$		0			0
$718$	−2.16246	−	25.4228i	−0.0807024	−	0.948771i
$719$	6.36450			0.237356			0.118678	−	0.992933i	$-0.462134\pi$
$719$	6.36450			0.237356			0.118678	+	0.992933i	$0.462134\pi$
$720$		0			0
$721$	−19.8104			−0.737776
$722$	1.52648	+	17.9459i	0.0568097	+	0.667878i
$723$		0			0
$724$	−5.97355	−	34.8597i	−0.222005	−	1.29555i
$725$	−6.90702			−0.256520
$726$		0			0
$727$			52.3131i			1.94019i	0.242735	+	0.970093i	$0.421956\pi$
$727$			52.3131i			1.94019i	−0.242735	+	0.970093i	$0.578044\pi$
$728$	2.11094	+	8.11236i	0.0782365	+	0.300664i
$729$		0			0
$730$	−1.44623	−	17.0025i	−0.0535273	−	0.629289i
$731$		−	6.20816i		−	0.229617i
$732$		0			0
$733$		−	37.4356i		−	1.38272i	−0.722512	−	0.691358i	$-0.757013\pi$
$733$		−	37.4356i		−	1.38272i	0.722512	−	0.691358i	$-0.242987\pi$
$734$	−44.7440	+	3.80592i	−1.65153	+	0.140479i
$735$		0			0
$736$	18.1082	+	40.0876i	0.667476	+	1.47765i
$737$			13.0084i			0.479170i
$738$		0			0
$739$	−16.8541			−0.619987			−0.309993	−	0.950739i	$-0.600327\pi$
$739$	−16.8541			−0.619987			−0.309993	+	0.950739i	$0.600327\pi$
$740$	4.06370	+	23.7144i	0.149385	+	0.871760i
$741$		0			0
$742$	1.82223	−	0.154999i	0.0668962	−	0.00569019i
$743$	−28.1294			−1.03197			−0.515983	−	0.856599i	$-0.672573\pi$
$743$	−28.1294			−1.03197			−0.515983	+	0.856599i	$0.672573\pi$
$744$		0			0
$745$	1.62527			0.0595453
$746$	−35.4703	+	3.01710i	−1.29866	+	0.110464i
$747$		0			0
$748$	12.0426	−	2.06361i	0.440320	−	0.0754532i
$749$	−30.6995			−1.12173
$750$		0			0
$751$		−	14.3476i		−	0.523553i	−0.965129	−	0.261776i	$-0.915692\pi$
$751$		−	14.3476i		−	0.523553i	0.965129	−	0.261776i	$-0.0843083\pi$
$752$	−21.3111	+	7.52467i	−0.777134	+	0.274396i
$753$		0			0
$754$	−15.8515	+	1.34833i	−0.577276	+	0.0491031i
$755$			21.7458i			0.791411i
$756$		0			0
$757$		−	37.6662i		−	1.36900i	−0.729013	−	0.684500i	$-0.760021\pi$
$757$		−	37.6662i		−	1.36900i	0.729013	−	0.684500i	$-0.239979\pi$
$758$	−0.797835	−	9.37967i	−0.0289787	−	0.340685i
$759$		0			0
$760$	1.78275	+	6.85112i	0.0646670	+	0.248516i
$761$			4.33123i			0.157007i	0.996914	+	0.0785035i	$0.0250142\pi$
$761$			4.33123i			0.157007i	−0.996914	+	0.0785035i	$0.974986\pi$
$762$		0			0
$763$	25.6658			0.929165
$764$	38.5285	−	6.60224i	1.39391	−	0.238861i
$765$		0			0
$766$	−3.28178	−	38.5820i	−0.118576	−	1.39402i
$767$	−3.77268			−0.136223
$768$		0			0
$769$	54.6426			1.97046			0.985231	−	0.171233i	$-0.0547751\pi$
$769$	54.6426			1.97046			0.985231	+	0.171233i	$0.0547751\pi$
$770$	−0.396425	−	4.66054i	−0.0142862	−	0.167954i
$771$		0			0
$772$	29.6271	−	5.07690i	1.06630	−	0.182722i
$773$	−5.82472			−0.209500			−0.104750	−	0.994499i	$-0.533404\pi$
$773$	−5.82472			−0.209500			−0.104750	+	0.994499i	$0.533404\pi$
$774$		0			0
$775$			4.41794i			0.158697i
$776$	−9.03232	−	34.7113i	−0.324241	−	1.24606i
$777$		0			0
$778$	−1.99110	−	23.4082i	−0.0713844	−	0.839225i
$779$			5.18316i			0.185706i
$780$		0			0
$781$			0.420231i			0.0150371i
$782$	36.8293	−	3.13270i	1.31701	−	0.112025i
$783$		0			0
$784$	13.9130	−	4.91250i	0.496892	−	0.175446i
$785$			15.7680i			0.562783i
$786$		0			0
$787$	−6.33406			−0.225785			−0.112892	−	0.993607i	$-0.536012\pi$
$787$	−6.33406			−0.225785			−0.112892	+	0.993607i	$0.536012\pi$
$788$	−33.4284	+	5.72829i	−1.19084	+	0.204062i
$789$		0			0
$790$	11.3742	−	0.967485i	0.404674	−	0.0344216i
$791$	1.77165			0.0629927
$792$		0			0
$793$	−8.03481			−0.285324
$794$	20.6215	−	1.75406i	0.731828	−	0.0622493i
$795$		0			0
$796$	3.64428	+	21.2668i	0.129168	+	0.753782i
$797$	−48.9281			−1.73312			−0.866562	−	0.499070i	$-0.833675\pi$
$797$	−48.9281			−1.73312			−0.866562	+	0.499070i	$0.833675\pi$
$798$		0			0
$799$			18.9909i			0.671849i
$800$	−2.32872	−	5.15529i	−0.0823327	−	0.182267i
$801$		0			0
$802$	8.44667	−	0.718474i	0.298262	−	0.0253702i
$803$			21.9305i			0.773911i
$804$		0			0
$805$		−	14.1500i		−	0.498722i
$806$	0.862429	+	10.1391i	0.0303778	+	0.357133i
$807$		0			0
$808$	−6.02628	−	23.1591i	−0.212004	−	0.814733i
$809$		−	54.9565i		−	1.93217i	−0.258228	−	0.966084i	$-0.583139\pi$
$809$		−	54.9565i		−	1.93217i	0.258228	−	0.966084i	$-0.416861\pi$
$810$		0			0
$811$	−22.3321			−0.784184			−0.392092	−	0.919926i	$-0.628249\pi$
$811$	−22.3321			−0.784184			−0.392092	+	0.919926i	$0.628249\pi$
$812$	−4.24566	−	24.7763i	−0.148993	−	0.869477i
$813$		0			0
$814$	−2.62077	−	30.8108i	−0.0918579	−	1.07992i
$815$	10.1506			0.355559
$816$		0			0
$817$	−4.62295			−0.161736
$818$	−1.88468	−	22.1571i	−0.0658963	−	0.774704i
$819$		0			0
$820$	−0.699529	−	4.08223i	−0.0244286	−	0.142558i
$821$	11.4773			0.400561			0.200281	−	0.979739i	$-0.435815\pi$
$821$	11.4773			0.400561			0.200281	+	0.979739i	$0.435815\pi$
$822$		0			0
$823$			42.1288i			1.46852i	0.678869	+	0.734259i	$0.262470\pi$
$823$			42.1288i			1.46852i	−0.678869	+	0.734259i	$0.737530\pi$
$824$	29.7996	−	7.75424i	1.03812	−	0.270132i
$825$		0			0
$826$	−0.505237	−	5.93977i	−0.0175794	−	0.206671i
$827$		−	6.31319i		−	0.219531i	−0.993958	−	0.109766i	$-0.964990\pi$
$827$		−	6.31319i		−	0.219531i	0.993958	−	0.109766i	$-0.0350100\pi$
$828$		0			0
$829$		−	52.3405i		−	1.81786i	−0.416948	−	0.908930i	$-0.636900\pi$
$829$		−	52.3405i		−	1.81786i	0.416948	−	0.908930i	$-0.363100\pi$
$830$	−15.1314	+	1.28708i	−0.525219	+	0.0446751i
$831$		0			0
$832$	−6.35073	−	11.3767i	−0.220172	−	0.394416i
$833$		−	12.3982i		−	0.429574i
$834$		0			0
$835$	−7.58284			−0.262415
$836$	−1.53668	−	8.96758i	−0.0531473	−	0.310150i
$837$		0			0
$838$	48.2694	−	4.10580i	1.66744	−	0.141832i
$839$	15.6390			0.539917			0.269959	−	0.962872i	$-0.412990\pi$
$839$	15.6390			0.539917			0.269959	+	0.962872i	$0.412990\pi$
$840$		0			0
$841$	18.7070			0.645067
$842$	−13.7065	+	1.16588i	−0.472358	+	0.0401788i
$843$		0			0
$844$	−9.35583	+	1.60321i	−0.322041	+	0.0551849i
$845$	−10.3475			−0.355964
$846$		0			0
$847$		−	14.0053i		−	0.481229i
$848$	−2.68041	+	0.946421i	−0.0920458	+	0.0325002i
$849$		0			0
$850$	−4.73628	+	0.402867i	−0.162453	+	0.0138182i
$851$		−	93.5458i		−	3.20671i
$852$		0			0
$853$		−	10.9782i		−	0.375888i	−0.982180	−	0.187944i	$-0.939818\pi$
$853$		−	10.9782i		−	0.375888i	0.982180	−	0.187944i	$-0.0601823\pi$
$854$	−1.07602	−	12.6501i	−0.0368207	−	0.432879i
$855$		0			0
$856$	46.1795	−	12.0165i	1.57838	−	0.410715i
$857$			30.4038i			1.03857i	0.854600	+	0.519286i	$0.173802\pi$
$857$			30.4038i			1.03857i	−0.854600	+	0.519286i	$0.826198\pi$
$858$		0			0
$859$	0.724677			0.0247256			0.0123628	−	0.999924i	$-0.496065\pi$
$859$	0.724677			0.0247256			0.0123628	+	0.999924i	$0.496065\pi$
$860$	3.64100	−	0.623922i	0.124157	−	0.0212755i
$861$		0			0
$862$	−0.276892	−	3.25526i	−0.00943100	−	0.110875i
$863$	−46.9042			−1.59664			−0.798320	−	0.602234i	$-0.794277\pi$
$863$	−46.9042			−1.59664			−0.798320	+	0.602234i	$0.794277\pi$
$864$		0			0
$865$	8.03931			0.273345
$866$	3.65686	+	42.9915i	0.124265	+	1.46091i
$867$		0			0
$868$	−15.8476	+	2.71565i	−0.537904	+	0.0921751i
$869$	−14.6709			−0.497675
$870$		0			0
$871$		−	11.6564i		−	0.394963i
$872$	−38.6077	+	10.0462i	−1.30742	+	0.340207i
$873$		0			0
$874$	−2.33279	−	27.4252i	−0.0789077	−	0.927671i
$875$			1.81970i			0.0615171i
$876$		0			0
$877$		−	36.9968i		−	1.24929i	−0.780907	−	0.624647i	$-0.785243\pi$
$877$		−	36.9968i		−	1.24929i	0.780907	−	0.624647i	$-0.214757\pi$
$878$	8.92011	−	0.758745i	0.301039	−	0.0256064i
$879$		0			0
$880$	2.42056	+	6.85542i	0.0815972	+	0.231096i
$881$			57.3681i			1.93278i	0.257077	+	0.966391i	$0.417241\pi$
$881$			57.3681i			1.93278i	−0.257077	+	0.966391i	$0.582759\pi$
$882$		0			0
$883$	−31.0907			−1.04629			−0.523143	−	0.852245i	$-0.675241\pi$
$883$	−31.0907			−1.04629			−0.523143	+	0.852245i	$0.675241\pi$
$884$	−10.7910	+	1.84914i	−0.362941	+	0.0621935i
$885$		0			0
$886$	51.2926	−	4.36295i	1.72321	−	0.146576i
$887$	−36.9352			−1.24016			−0.620082	−	0.784537i	$-0.712901\pi$
$887$	−36.9352			−1.24016			−0.620082	+	0.784537i	$0.712901\pi$
$888$		0			0
$889$	−12.2539			−0.410983
$890$	−12.7571	+	1.08512i	−0.427620	+	0.0363733i
$891$		0			0
$892$	2.96495	+	17.3025i	0.0992738	+	0.579330i
$893$	14.1417			0.473233
$894$		0			0
$895$		−	14.5342i		−	0.485823i
$896$	17.0612	−	11.5223i	0.569974	−	0.384932i
$897$		0			0
$898$	−11.1405	+	0.947610i	−0.371763	+	0.0316222i
$899$		−	30.5148i		−	1.01772i
$900$		0			0
$901$			2.38859i			0.0795755i
$902$	0.451142	+	5.30381i	0.0150214	+	0.176597i
$903$		0			0
$904$	−2.66500	+	0.693466i	−0.0886366	+	0.0230644i
$905$		−	17.6839i		−	0.587833i
$906$		0			0
$907$	−44.8204			−1.48824			−0.744118	−	0.668048i	$-0.767130\pi$
$907$	−44.8204			−1.48824			−0.744118	+	0.668048i	$0.767130\pi$
$908$	5.78188	+	33.7412i	0.191879	+	1.11974i
$909$		0			0
$910$	0.355225	+	4.17617i	0.0117756	+	0.138439i
$911$	5.21667			0.172836			0.0864180	−	0.996259i	$-0.472458\pi$
$911$	5.21667			0.172836			0.0864180	+	0.996259i	$0.472458\pi$
$912$		0			0
$913$	19.5171			0.645923
$914$	1.81650	+	21.3555i	0.0600843	+	0.706376i
$915$		0			0
$916$	2.66645	+	15.5605i	0.0881019	+	0.514134i
$917$	−17.5025			−0.577984
$918$		0			0
$919$		−	42.8019i		−	1.41191i	−0.708259	−	0.705953i	$-0.750519\pi$
$919$		−	42.8019i		−	1.41191i	0.708259	−	0.705953i	$-0.249481\pi$
$920$	5.53864	+	21.2851i	0.182604	+	0.701748i
$921$		0			0
$922$	0.138242	+	1.62523i	0.00455276	+	0.0535241i
$923$		−	0.376557i		−	0.0123945i
$924$		0			0
$925$			12.0300i			0.395545i
$926$	49.6829	−	4.22603i	1.63268	−	0.138876i
$927$		0			0
$928$	16.0845	+	35.6077i	0.528000	+	1.16888i
$929$		−	0.344767i		−	0.0113114i	−0.999984	−	0.00565572i	$-0.998200\pi$
$929$		−	0.344767i		−	0.0113114i	0.999984	−	0.00565572i	$-0.00180028\pi$
$930$		0			0
$931$	−9.23243			−0.302581
$932$	4.29610	+	25.0707i	0.140724	+	0.821217i
$933$		0			0
$934$	−18.8384	+	1.60239i	−0.616411	+	0.0524319i
$935$	6.10906			0.199787
$936$		0			0
$937$	56.2729			1.83835			0.919177	−	0.393844i	$-0.128855\pi$
$937$	56.2729			1.83835			0.919177	+	0.393844i	$0.128855\pi$
$938$	18.3521	−	1.56103i	0.599217	−	0.0509694i
$939$		0			0
$940$	−11.1379	+	1.90859i	−0.363278	+	0.0622512i
$941$	−50.2577			−1.63835			−0.819177	−	0.573541i	$-0.805570\pi$
$941$	−50.2577			−1.63835			−0.819177	+	0.573541i	$0.805570\pi$
$942$		0			0
$943$			16.1031i			0.524388i
$944$	3.08496	+	8.73711i	0.100407	+	0.284369i
$945$		0			0
$946$	−4.73055	+	0.402381i	−0.153804	+	0.0130825i
$947$		−	12.0214i		−	0.390642i	−0.980739	−	0.195321i	$-0.937425\pi$
$947$		−	12.0214i		−	0.390642i	0.980739	−	0.195321i	$-0.0625749\pi$
$948$		0			0
$949$		−	19.6513i		−	0.637908i
$950$	0.299998	+	3.52690i	0.00973321	+	0.114428i
$951$		0			0
$952$	−4.35646	−	16.7419i	−0.141194	−	0.542609i
$953$		−	11.3661i		−	0.368185i	−0.982909	−	0.184093i	$-0.941065\pi$
$953$		−	11.3661i		−	0.368185i	0.982909	−	0.184093i	$-0.0589346\pi$
$954$		0			0
$955$	19.5451			0.632463
$956$	−15.1574	+	2.59737i	−0.490226	+	0.0840051i
$957$		0			0
$958$	2.35766	+	27.7176i	0.0761726	+	0.895516i
$959$	−23.0670			−0.744873
$960$		0			0
$961$	11.4818			0.370382
$962$	2.34839	+	27.6087i	0.0757153	+	0.890140i
$963$		0			0
$964$	17.9018	−	3.06764i	0.576577	−	0.0988022i
$965$	15.0295			0.483817
$966$		0			0
$967$			30.6345i			0.985140i	0.870273	+	0.492570i	$0.163942\pi$
$967$			30.6345i			0.985140i	−0.870273	+	0.492570i	$0.836058\pi$
$968$	5.48201	+	21.0674i	0.176199	+	0.677133i
$969$		0			0
$970$	−1.51994	−	17.8691i	−0.0488025	−	0.573742i
$971$			7.61183i			0.244275i	0.992513	+	0.122138i	$0.0389749\pi$
$971$			7.61183i			0.244275i	−0.992513	+	0.122138i	$0.961025\pi$
$972$		0			0
$973$		−	26.4060i		−	0.846539i
$974$	6.71065	−	0.570808i	0.215023	−	0.0182899i
$975$		0			0
$976$	6.57017	+	18.6077i	0.210306	+	0.595619i
$977$			54.8810i			1.75580i	0.478845	+	0.877899i	$0.341055\pi$
$977$			54.8810i			1.75580i	−0.478845	+	0.877899i	$0.658945\pi$
$978$		0			0
$979$	16.4547			0.525894
$980$	7.27140	−	1.24603i	0.232276	−	0.0398028i
$981$		0			0
$982$	−58.2896	+	4.95811i	−1.86010	+	0.158220i
$983$	24.5795			0.783964			0.391982	−	0.919973i	$-0.371789\pi$
$983$	24.5795			0.783964			0.391982	+	0.919973i	$0.371789\pi$
$984$		0			0
$985$	−16.9578			−0.540322
$986$	32.7136	−	2.78261i	1.04181	−	0.0886165i
$987$		0			0
$988$	1.37698	+	8.03559i	0.0438075	+	0.255646i
$989$	−14.3626			−0.456704
$990$		0			0
$991$			16.9104i			0.537176i	0.963255	+	0.268588i	$0.0865570\pi$
$991$			16.9104i			0.537176i	−0.963255	+	0.268588i	$0.913443\pi$
$992$	22.7758	−	10.2881i	0.723131	−	0.326649i
$993$		0			0
$994$	0.592858	−	0.0504285i	0.0188043	−	0.00159949i
$995$			10.7884i			0.342015i
$996$		0			0
$997$		−	27.1453i		−	0.859700i	−0.902900	−	0.429850i	$-0.858566\pi$
$997$		−	27.1453i		−	0.859700i	0.902900	−	0.429850i	$-0.141434\pi$
$998$	−2.72988	−	32.0936i	−0.0864129	−	1.01591i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1080.2.b.d.971.7	yes	16
3.2	odd	2		1080.2.b.a.971.10	yes	16
4.3	odd	2		4320.2.b.b.431.12		16
8.3	odd	2		1080.2.b.a.971.9	✓	16
8.5	even	2		4320.2.b.d.431.5		16
12.11	even	2		4320.2.b.d.431.12		16
24.5	odd	2		4320.2.b.b.431.5		16
24.11	even	2	inner	1080.2.b.d.971.8	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1080.2.b.a.971.9	✓	16	8.3	odd	2
1080.2.b.a.971.10	yes	16	3.2	odd	2
1080.2.b.d.971.7	yes	16	1.1	even	1	trivial
1080.2.b.d.971.8	yes	16	24.11	even	2	inner
4320.2.b.b.431.5		16	24.5	odd	2
4320.2.b.b.431.12		16	4.3	odd	2
4320.2.b.d.431.5		16	8.5	even	2
4320.2.b.d.431.12		16	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1080.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.119860 - 1.40913i) q^{2} +(-1.97127 + 0.337796i) q^{4} -1.00000 q^{5} -1.81970i q^{7} +(0.712273 + 2.73727i) q^{8} +(0.119860 + 1.40913i) q^{10} -1.81755i q^{11} +1.62865i q^{13} +(-2.56418 + 0.218109i) q^{14} +(3.77179 - 1.33177i) q^{16} -3.36115i q^{17} -2.50290 q^{19} +(1.97127 - 0.337796i) q^{20} +(-2.56116 + 0.217852i) q^{22} -7.77601 q^{23} +1.00000 q^{25} +(2.29498 - 0.195211i) q^{26} +(0.614687 + 3.58711i) q^{28} -6.90702 q^{29} +4.41794i q^{31} +(-2.32872 - 5.15529i) q^{32} +(-4.73628 + 0.402867i) q^{34} +1.81970i q^{35} +12.0300i q^{37} +(0.299998 + 3.52690i) q^{38} +(-0.712273 - 2.73727i) q^{40} -2.07086i q^{41} +1.84704 q^{43} +(0.613961 + 3.58288i) q^{44} +(0.932034 + 10.9574i) q^{46} -5.65012 q^{47} +3.68869 q^{49} +(-0.119860 - 1.40913i) q^{50} +(-0.550153 - 3.21051i) q^{52} -0.710648 q^{53} +1.81755i q^{55} +(4.98102 - 1.29612i) q^{56} +(0.827877 + 9.73286i) q^{58} +2.31644i q^{59} +4.93340i q^{61} +(6.22542 - 0.529534i) q^{62} +(-6.98533 + 3.89937i) q^{64} -1.62865i q^{65} -7.15709 q^{67} +(1.13538 + 6.62572i) q^{68} +(2.56418 - 0.218109i) q^{70} -0.231207 q^{71} -12.0660 q^{73} +(16.9518 - 1.44192i) q^{74} +(4.93388 - 0.845469i) q^{76} -3.30740 q^{77} -8.07178i q^{79} +(-3.77179 + 1.33177i) q^{80} +(-2.91811 + 0.248214i) q^{82} +10.7382i q^{83} +3.36115i q^{85} +(-0.221386 - 2.60271i) q^{86} +(4.97514 - 1.29459i) q^{88} +9.05322i q^{89} +2.96366 q^{91} +(15.3286 - 2.62671i) q^{92} +(0.677224 + 7.96172i) q^{94} +2.50290 q^{95} -12.6810 q^{97} +(-0.442127 - 5.19783i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{2} + 2 q^{4} - 16 q^{5} - 4 q^{8} - 2 q^{10} + 6 q^{14} + 10 q^{16} - 8 q^{19} - 2 q^{20} + 4 q^{22} - 8 q^{23} + 16 q^{25} - 16 q^{26} + 20 q^{28} - 8 q^{32} + 18 q^{34} - 14 q^{38} + 4 q^{40}+ \cdots - 32 q^{98}+O(q^{100}) \) 16 * q + 2 * q^2 + 2 * q^4 - 16 * q^5 - 4 * q^8 - 2 * q^10 + 6 * q^14 + 10 * q^16 - 8 * q^19 - 2 * q^20 + 4 * q^22 - 8 * q^23 + 16 * q^25 - 16 * q^26 + 20 * q^28 - 8 * q^32 + 18 * q^34 - 14 * q^38 + 4 * q^40 + 6 * q^44 + 2 * q^46 - 16 * q^47 - 8 * q^49 + 2 * q^50 - 20 * q^52 + 32 * q^53 + 12 * q^56 - 16 * q^58 + 16 * q^62 + 14 * q^64 + 32 * q^67 - 8 * q^68 - 6 * q^70 + 24 * q^71 + 8 * q^73 + 34 * q^74 + 36 * q^76 - 10 * q^80 - 8 * q^82 - 34 * q^86 + 16 * q^88 + 48 * q^91 - 32 * q^92 + 10 * q^94 + 8 * q^95 - 8 * q^97 - 32 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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