LMFDB - Embedded newform 512.2.k.a.49.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [512,2,Mod(17,512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(512, base_ring=CyclotomicField(32))

chi = DirichletCharacter(H, H._module([0, 7]))

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

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

chi := DirichletCharacter("512.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 512 = 2^{9} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	512.k (of order $32$, degree $16$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.08834058349$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$15$ over $\Q(\zeta_{32})$
Twist minimal:	no (minimal twist has level 128)
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			49.1
Character	$\chi$	$=$	512.49
Dual form			512.2.k.a.209.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.317663 - 3.22529i) q^{3} +(1.50066 + 0.802122i) q^{5} +(-0.303583 + 1.52621i) q^{7} +(-7.35922 + 1.46384i) q^{9} +O(q^{10})$	\(q+(-0.317663 - 3.22529i) q^{3} +(1.50066 + 0.802122i) q^{5} +(-0.303583 + 1.52621i) q^{7} +(-7.35922 + 1.46384i) q^{9} +(-3.19359 - 3.89140i) q^{11} +(-2.40755 - 4.50420i) q^{13} +(2.11037 - 5.09488i) q^{15} +(-0.368847 - 0.890474i) q^{17} +(0.131803 - 0.434495i) q^{19} +(5.01891 + 0.494320i) q^{21} +(-0.236053 - 0.157726i) q^{23} +(-1.16926 - 1.74992i) q^{25} +(4.23671 + 13.9666i) q^{27} +(1.73837 + 1.42664i) q^{29} +(-2.94700 - 2.94700i) q^{31} +(-11.5364 + 11.5364i) q^{33} +(-1.67978 + 2.04682i) q^{35} +(8.70317 - 2.64008i) q^{37} +(-13.7626 + 9.19585i) q^{39} +(3.20695 - 4.79954i) q^{41} +(-0.328880 + 3.33918i) q^{43} +(-12.2179 - 3.70626i) q^{45} +(-2.66420 + 1.10355i) q^{47} +(4.22999 + 1.75212i) q^{49} +(-2.75487 + 1.47251i) q^{51} +(-4.50611 + 3.69807i) q^{53} +(-1.67113 - 8.40133i) q^{55} +(-1.44324 - 0.287078i) q^{57} +(2.31339 - 4.32806i) q^{59} +(3.85529 - 0.379713i) q^{61} -11.6761i q^{63} -8.69044i q^{65} +(6.80932 - 0.670660i) q^{67} +(-0.433726 + 0.811444i) q^{69} +(12.5407 + 2.49450i) q^{71} +(1.61764 + 8.13245i) q^{73} +(-5.27255 + 4.32707i) q^{75} +(6.90862 - 3.69274i) q^{77} +(8.12045 + 3.36360i) q^{79} +(22.9037 - 9.48701i) q^{81} +(0.849890 + 0.257811i) q^{83} +(0.160754 - 1.63216i) q^{85} +(4.04912 - 6.05994i) q^{87} +(-2.90325 + 1.93989i) q^{89} +(7.60526 - 2.30703i) q^{91} +(-8.56877 + 10.4411i) q^{93} +(0.546309 - 0.546309i) q^{95} +(-9.58537 - 9.58537i) q^{97} +(29.1987 + 23.9628i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 16 q^{3} - 16 q^{5} + 16 q^{7} - 16 q^{9}+O(q^{10}) $ 240 * q + 16 * q^3 - 16 * q^5 + 16 * q^7 - 16 * q^9	$ 240 q + 16 q^{3} - 16 q^{5} + 16 q^{7} - 16 q^{9} + 16 q^{11} - 16 q^{13} + 16 q^{15} - 16 q^{17} + 16 q^{19} - 16 q^{21} + 16 q^{23} - 16 q^{25} + 16 q^{27} - 16 q^{29} + 16 q^{31} - 16 q^{33} + 16 q^{35} - 16 q^{37} + 16 q^{39} - 16 q^{41} + 16 q^{43} - 16 q^{45} + 16 q^{47} - 16 q^{49} + 16 q^{51} - 16 q^{53} + 16 q^{55} - 16 q^{57} + 16 q^{59} - 16 q^{61} + 16 q^{67} - 16 q^{69} + 16 q^{71} - 16 q^{73} + 16 q^{75} - 16 q^{77} + 16 q^{79} - 16 q^{81} + 16 q^{83} - 16 q^{85} + 16 q^{87} - 16 q^{89} + 16 q^{91} - 16 q^{93} + 16 q^{95} - 16 q^{97} + 16 q^{99}+O(q^{100}) $ 240 * q + 16 * q^3 - 16 * q^5 + 16 * q^7 - 16 * q^9 + 16 * q^11 - 16 * q^13 + 16 * q^15 - 16 * q^17 + 16 * q^19 - 16 * q^21 + 16 * q^23 - 16 * q^25 + 16 * q^27 - 16 * q^29 + 16 * q^31 - 16 * q^33 + 16 * q^35 - 16 * q^37 + 16 * q^39 - 16 * q^41 + 16 * q^43 - 16 * q^45 + 16 * q^47 - 16 * q^49 + 16 * q^51 - 16 * q^53 + 16 * q^55 - 16 * q^57 + 16 * q^59 - 16 * q^61 + 16 * q^67 - 16 * q^69 + 16 * q^71 - 16 * q^73 + 16 * q^75 - 16 * q^77 + 16 * q^79 - 16 * q^81 + 16 * q^83 - 16 * q^85 + 16 * q^87 - 16 * q^89 + 16 * q^91 - 16 * q^93 + 16 * q^95 - 16 * q^97 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/512\mathbb{Z}\right)^\times$.

$n$	$5$	$511$
$\chi(n)$	$e\left(\frac{5}{32}\right)$	$1$

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
$3$	−0.317663	−	3.22529i	−0.183403	−	1.86212i	−0.443154	−	0.896446i	$-0.646140\pi$
$3$	−0.317663	−	3.22529i	−0.183403	−	1.86212i	0.259751	−	0.965676i	$-0.416360\pi$
$4$		0			0
$5$	1.50066	+	0.802122i	0.671118	+	0.358720i	0.771500	−	0.636229i	$-0.219507\pi$
$5$	1.50066	+	0.802122i	0.671118	+	0.358720i	−0.100383	+	0.994949i	$0.532007\pi$
$6$		0			0
$7$	−0.303583	+	1.52621i	−0.114743	+	0.576854i	0.880045	+	0.474891i	$0.157512\pi$
$7$	−0.303583	+	1.52621i	−0.114743	+	0.576854i	−0.994788	+	0.101963i	$0.967488\pi$
$8$		0			0
$9$	−7.35922	+	1.46384i	−2.45307	+	0.487947i
$10$		0			0
$11$	−3.19359	−	3.89140i	−0.962903	−	1.17330i	−0.984827	−	0.173541i	$-0.944479\pi$
$11$	−3.19359	−	3.89140i	−0.962903	−	1.17330i	0.0219235	−	0.999760i	$-0.493021\pi$
$12$		0			0
$13$	−2.40755	−	4.50420i	−0.667733	−	1.24924i	−0.956470	−	0.291832i	$-0.905735\pi$
$13$	−2.40755	−	4.50420i	−0.667733	−	1.24924i	0.288736	−	0.957409i	$-0.406765\pi$
$14$		0			0
$15$	2.11037	−	5.09488i	0.544895	−	1.31549i
$16$		0			0
$17$	−0.368847	−	0.890474i	−0.0894584	−	0.215972i	0.872818	−	0.488046i	$-0.162290\pi$
$17$	−0.368847	−	0.890474i	−0.0894584	−	0.215972i	−0.962276	+	0.272075i	$0.912290\pi$
$18$		0			0
$19$	0.131803	−	0.434495i	0.0302376	−	0.0996799i	−0.940523	−	0.339731i	$-0.889664\pi$
$19$	0.131803	−	0.434495i	0.0302376	−	0.0996799i	0.970760	+	0.240051i	$0.0771641\pi$
$20$		0			0
$21$	5.01891	+	0.494320i	1.09522	+	0.107869i
$22$		0			0
$23$	−0.236053	−	0.157726i	−0.0492205	−	0.0328881i	0.530717	−	0.847549i	$-0.321923\pi$
$23$	−0.236053	−	0.157726i	−0.0492205	−	0.0328881i	−0.579937	+	0.814661i	$0.696923\pi$
$24$		0			0
$25$	−1.16926	−	1.74992i	−0.233851	−	0.349983i
$26$		0			0
$27$	4.23671	+	13.9666i	0.815356	+	2.68787i
$28$		0			0
$29$	1.73837	+	1.42664i	0.322807	+	0.264921i	0.781814	−	0.623512i	$-0.214295\pi$
$29$	1.73837	+	1.42664i	0.322807	+	0.264921i	−0.459007	+	0.888433i	$0.651795\pi$
$30$		0			0
$31$	−2.94700	−	2.94700i	−0.529297	−	0.529297i	0.391066	−	0.920363i	$-0.372106\pi$
$31$	−2.94700	−	2.94700i	−0.529297	−	0.529297i	−0.920363	+	0.391066i	$0.872106\pi$
$32$		0			0
$33$	−11.5364	+	11.5364i	−2.00823	+	2.00823i
$34$		0			0
$35$	−1.67978	+	2.04682i	−0.283935	+	0.345976i
$36$		0			0
$37$	8.70317	−	2.64008i	1.43079	−	0.434026i	0.522599	−	0.852579i	$-0.324962\pi$
$37$	8.70317	−	2.64008i	1.43079	−	0.434026i	0.908193	+	0.418553i	$0.137462\pi$
$38$		0			0
$39$	−13.7626	+	9.19585i	−2.20377	+	1.47251i
$40$		0			0
$41$	3.20695	−	4.79954i	0.500842	−	0.749563i	−0.491793	−	0.870712i	$-0.663658\pi$
$41$	3.20695	−	4.79954i	0.500842	−	0.749563i	0.992634	+	0.121150i	$0.0386581\pi$
$42$		0			0
$43$	−0.328880	+	3.33918i	−0.0501538	+	0.509220i	0.936987	+	0.349365i	$0.113603\pi$
$43$	−0.328880	+	3.33918i	−0.0501538	+	0.509220i	−0.987141	+	0.159855i	$0.948897\pi$
$44$		0			0
$45$	−12.2179	−	3.70626i	−1.82134	−	0.552497i
$46$		0			0
$47$	−2.66420	+	1.10355i	−0.388614	+	0.160969i	−0.568431	−	0.822731i	$-0.692449\pi$
$47$	−2.66420	+	1.10355i	−0.388614	+	0.160969i	0.179817	+	0.983700i	$0.442449\pi$
$48$		0			0
$49$	4.22999	+	1.75212i	0.604285	+	0.250303i
$50$		0			0
$51$	−2.75487	+	1.47251i	−0.385759	+	0.206192i
$52$		0			0
$53$	−4.50611	+	3.69807i	−0.618961	+	0.507968i	−0.890813	−	0.454371i	$-0.849864\pi$
$53$	−4.50611	+	3.69807i	−0.618961	+	0.507968i	0.271851	+	0.962339i	$0.412364\pi$
$54$		0			0
$55$	−1.67113	−	8.40133i	−0.225335	−	1.13284i
$56$		0			0
$57$	−1.44324	−	0.287078i	−0.191162	−	0.0380244i
$58$		0			0
$59$	2.31339	−	4.32806i	0.301178	−	0.563465i	−0.685121	−	0.728429i	$-0.740251\pi$
$59$	2.31339	−	4.32806i	0.301178	−	0.563465i	0.986300	+	0.164964i	$0.0527508\pi$
$60$		0			0
$61$	3.85529	−	0.379713i	0.493619	−	0.0486172i	0.151855	−	0.988403i	$-0.451475\pi$
$61$	3.85529	−	0.379713i	0.493619	−	0.0486172i	0.341765	+	0.939786i	$0.388975\pi$
$62$		0			0
$63$		−	11.6761i		−	1.47105i
$64$		0			0
$65$		−	8.69044i		−	1.07792i
$66$		0			0
$67$	6.80932	−	0.670660i	0.831891	−	0.0819341i	0.326900	−	0.945059i	$-0.393996\pi$
$67$	6.80932	−	0.670660i	0.831891	−	0.0819341i	0.504991	+	0.863125i	$0.331496\pi$
$68$		0			0
$69$	−0.433726	+	0.811444i	−0.0522144	+	0.0976864i
$70$		0			0
$71$	12.5407	+	2.49450i	1.48831	+	0.296043i	0.871236	−	0.490865i	$-0.163319\pi$
$71$	12.5407	+	2.49450i	1.48831	+	0.296043i	0.617071	+	0.786908i	$0.288319\pi$
$72$		0			0
$73$	1.61764	+	8.13245i	0.189331	+	0.951831i	0.952246	+	0.305332i	$0.0987675\pi$
$73$	1.61764	+	8.13245i	0.189331	+	0.951831i	−0.762915	+	0.646499i	$0.776232\pi$
$74$		0			0
$75$	−5.27255	+	4.32707i	−0.608822	+	0.499647i
$76$		0			0
$77$	6.90862	−	3.69274i	0.787311	−	0.420826i
$78$		0			0
$79$	8.12045	+	3.36360i	0.913621	+	0.378434i	0.789442	−	0.613825i	$-0.210370\pi$
$79$	8.12045	+	3.36360i	0.913621	+	0.378434i	0.124180	+	0.992260i	$0.460370\pi$
$80$		0			0
$81$	22.9037	−	9.48701i	2.54485	−	1.05411i
$82$		0			0
$83$	0.849890	+	0.257811i	0.0932875	+	0.0282985i	0.336583	−	0.941654i	$-0.390729\pi$
$83$	0.849890	+	0.257811i	0.0932875	+	0.0282985i	−0.243296	+	0.969952i	$0.578229\pi$
$84$		0			0
$85$	0.160754	−	1.63216i	0.0174362	−	0.177033i
$86$		0			0
$87$	4.04912	−	6.05994i	0.434111	−	0.649694i
$88$		0			0
$89$	−2.90325	+	1.93989i	−0.307744	+	0.205628i	−0.699846	−	0.714294i	$-0.746748\pi$
$89$	−2.90325	+	1.93989i	−0.307744	+	0.205628i	0.392102	+	0.919922i	$0.371748\pi$
$90$		0			0
$91$	7.60526	−	2.30703i	0.797248	−	0.241843i
$92$		0			0
$93$	−8.56877	+	10.4411i	−0.888540	+	1.08269i
$94$		0			0
$95$	0.546309	−	0.546309i	0.0560501	−	0.0560501i
$96$		0			0
$97$	−9.58537	−	9.58537i	−0.973247	−	0.973247i	0.0264041	−	0.999651i	$-0.491594\pi$
$97$	−9.58537	−	9.58537i	−0.973247	−	0.973247i	−0.999651	+	0.0264041i	$0.991594\pi$
$98$		0			0
$99$	29.1987	+	23.9628i	2.93458	+	2.40835i
$100$		0			0
$101$	−3.79753	−	12.5188i	−0.377869	−	1.24567i	−0.915442	−	0.402450i	$-0.868159\pi$
$101$	−3.79753	−	12.5188i	−0.377869	−	1.24567i	0.537573	−	0.843217i	$-0.319341\pi$
$102$		0			0
$103$	0.0305437	+	0.0457118i	0.00300956	+	0.00450412i	0.832971	−	0.553316i	$-0.186638\pi$
$103$	0.0305437	+	0.0457118i	0.00300956	+	0.00450412i	−0.829962	+	0.557820i	$0.811638\pi$
$104$		0			0
$105$	7.13520	+	4.76759i	0.696325	+	0.465269i
$106$		0			0
$107$	−8.83330	−	0.870004i	−0.853947	−	0.0841064i	−0.338436	−	0.940989i	$-0.609898\pi$
$107$	−8.83330	−	0.870004i	−0.853947	−	0.0841064i	−0.515511	+	0.856883i	$0.672398\pi$
$108$		0			0
$109$	3.30779	−	10.9043i	0.316829	−	1.04445i	−0.643470	−	0.765471i	$-0.722506\pi$
$109$	3.30779	−	10.9043i	0.316829	−	1.04445i	0.960299	−	0.278974i	$-0.0899942\pi$
$110$		0			0
$111$	−11.2797	−	27.2316i	−1.07062	−	2.58471i
$112$		0			0
$113$	2.45674	−	5.93109i	0.231111	−	0.557950i	−0.765198	−	0.643795i	$-0.777359\pi$
$113$	2.45674	−	5.93109i	0.231111	−	0.557950i	0.996309	+	0.0858448i	$0.0273589\pi$
$114$		0			0
$115$	−0.227722	−	0.426037i	−0.0212351	−	0.0397282i
$116$		0			0
$117$	24.3111	+	29.6231i	2.24756	+	2.73866i
$118$		0			0
$119$	1.47103	−	0.292606i	0.134849	−	0.0268231i
$120$		0			0
$121$	−2.79798	+	14.0664i	−0.254362	+	1.27876i
$122$		0			0
$123$	−16.4986	−	8.81871i	−1.48763	−	0.795156i
$124$		0			0
$125$	−1.18494	−	12.0309i	−0.105984	−	1.07607i
$126$		0			0
$127$	3.73221			0.331180			0.165590	−	0.986195i	$-0.447047\pi$
$127$	3.73221			0.331180			0.165590	+	0.986195i	$0.447047\pi$
$128$		0			0
$129$	10.8743			0.957427
$130$		0			0
$131$	−0.291332	−	2.95794i	−0.0254538	−	0.258437i	−0.999487	−	0.0320310i	$-0.989802\pi$
$131$	−0.291332	−	2.95794i	−0.0254538	−	0.258437i	0.974033	−	0.226406i	$-0.0726975\pi$
$132$		0			0
$133$	0.623119	+	0.333064i	0.0540312	+	0.0288803i
$134$		0			0
$135$	−4.84501	+	24.3575i	−0.416992	+	2.09636i
$136$		0			0
$137$	−14.3917	+	2.86269i	−1.22957	+	0.244576i	−0.766789	−	0.641899i	$-0.778147\pi$
$137$	−14.3917	+	2.86269i	−1.22957	+	0.244576i	−0.462776	+	0.886475i	$0.653147\pi$
$138$		0			0
$139$	−10.9300	−	13.3183i	−0.927074	−	1.12964i	−0.991289	−	0.131707i	$-0.957954\pi$
$139$	−10.9300	−	13.3183i	−0.927074	−	1.12964i	0.0642150	−	0.997936i	$-0.479546\pi$
$140$		0			0
$141$	4.40558	+	8.24226i	0.371017	+	0.694123i
$142$		0			0
$143$	−9.83893	+	23.7533i	−0.822773	+	1.98635i
$144$		0			0
$145$	1.46437	+	3.53530i	0.121609	+	0.293591i
$146$		0			0
$147$	4.30738	−	14.1995i	0.355267	−	1.17116i
$148$		0			0
$149$	−15.7961	−	1.55578i	−1.29407	−	0.127454i	−0.572561	−	0.819862i	$-0.694050\pi$
$149$	−15.7961	−	1.55578i	−1.29407	−	0.127454i	−0.721506	+	0.692408i	$0.756550\pi$
$150$		0			0
$151$	16.4959	+	11.0222i	1.34242	+	0.896975i	0.999107	−	0.0422475i	$-0.0134518\pi$
$151$	16.4959	+	11.0222i	1.34242	+	0.896975i	0.343310	+	0.939222i	$0.388452\pi$
$152$		0			0
$153$	4.01794	+	6.01327i	0.324831	+	0.486144i
$154$		0			0
$155$	−2.05860	−	6.78631i	−0.165351	−	0.545089i
$156$		0			0
$157$	18.6720	+	15.3237i	1.49019	+	1.22297i	0.914042	+	0.405620i	$0.132944\pi$
$157$	18.6720	+	15.3237i	1.49019	+	1.22297i	0.576147	+	0.817346i	$0.304556\pi$
$158$		0			0
$159$	13.3588	+	13.3588i	1.05942	+	1.05942i
$160$		0			0
$161$	0.312385	−	0.312385i	0.0246194	−	0.0246194i
$162$		0			0
$163$	9.16668	−	11.1696i	0.717990	−	0.874873i	−0.278339	−	0.960483i	$-0.589784\pi$
$163$	9.16668	−	11.1696i	0.717990	−	0.874873i	0.996329	+	0.0856098i	$0.0272838\pi$
$164$		0			0
$165$	−26.5659	+	8.05867i	−2.06815	+	0.627366i
$166$		0			0
$167$	7.60459	−	5.08123i	0.588461	−	0.393197i	−0.225392	−	0.974268i	$-0.572366\pi$
$167$	7.60459	−	5.08123i	0.588461	−	0.393197i	0.813853	+	0.581071i	$0.197366\pi$
$168$		0			0
$169$	−7.26914	+	10.8790i	−0.559165	+	0.836849i
$170$		0			0
$171$	−0.333933	+	3.39048i	−0.0255365	+	0.259277i
$172$		0			0
$173$	−0.312440	−	0.0947775i	−0.0237543	−	0.00720580i	0.278385	−	0.960470i	$-0.410201\pi$
$173$	−0.312440	−	0.0947775i	−0.0237543	−	0.00720580i	−0.302139	+	0.953264i	$0.597701\pi$
$174$		0			0
$175$	3.02571	−	1.25329i	0.228722	−	0.0947398i
$176$		0			0
$177$	−14.6941	−	6.08650i	−1.10448	−	0.457489i
$178$		0			0
$179$	−3.98777	+	2.13151i	−0.298060	+	0.159316i	−0.613647	−	0.789580i	$-0.710298\pi$
$179$	−3.98777	+	2.13151i	−0.298060	+	0.159316i	0.315588	+	0.948896i	$0.397798\pi$
$180$		0			0
$181$	7.80016	−	6.40142i	0.579781	−	0.475814i	−0.298204	−	0.954502i	$-0.596388\pi$
$181$	7.80016	−	6.40142i	0.579781	−	0.475814i	0.877985	+	0.478688i	$0.158888\pi$
$182$		0			0
$183$	−2.44937	−	12.3138i	−0.181062	−	0.910262i
$184$		0			0
$185$	15.1782	+	3.01913i	1.11592	+	0.221971i
$186$		0			0
$187$	−2.28725	+	4.27914i	−0.167260	+	0.312922i
$188$		0			0
$189$	−22.6022	+	2.22612i	−1.64407	+	0.161926i
$190$		0			0
$191$			27.1343i			1.96337i	0.190505	+	0.981686i	$0.438987\pi$
$191$			27.1343i			1.96337i	−0.190505	+	0.981686i	$0.561013\pi$
$192$		0			0
$193$			1.59261i			0.114638i	0.998356	+	0.0573191i	$0.0182553\pi$
$193$			1.59261i			0.114638i	−0.998356	+	0.0573191i	$0.981745\pi$
$194$		0			0
$195$	−28.0292	+	2.76063i	−2.00721	+	0.197693i
$196$		0			0
$197$	−4.94604	+	9.25339i	−0.352391	+	0.659276i	−0.994195	−	0.107592i	$-0.965686\pi$
$197$	−4.94604	+	9.25339i	−0.352391	+	0.659276i	0.641805	+	0.766868i	$0.278186\pi$
$198$		0			0
$199$	2.99794	+	0.596327i	0.212518	+	0.0422725i	0.300201	−	0.953876i	$-0.402946\pi$
$199$	2.99794	+	0.596327i	0.212518	+	0.0422725i	−0.0876828	+	0.996148i	$0.527946\pi$
$200$		0			0
$201$	−4.32614	−	21.7490i	−0.305143	−	1.53406i
$202$		0			0
$203$	−2.70510	+	2.22002i	−0.189861	+	0.155815i
$204$		0			0
$205$	8.66238	−	4.63014i	0.605007	−	0.323383i
$206$		0			0
$207$	1.96805	+	0.815195i	0.136789	+	0.0566599i
$208$		0			0
$209$	−2.11172	+	0.874701i	−0.146070	+	0.0605043i
$210$		0			0
$211$	17.2416	+	5.23017i	1.18696	+	0.360060i	0.821195	−	0.570648i	$-0.193308\pi$
$211$	17.2416	+	5.23017i	1.18696	+	0.360060i	0.365764	+	0.930708i	$0.380808\pi$
$212$		0			0
$213$	4.06176	−	41.2398i	0.278307	−	2.82570i
$214$		0			0
$215$	−3.17197	+	4.74718i	−0.216326	+	0.323755i
$216$		0			0
$217$	5.39241	−	3.60309i	0.366060	−	0.244594i
$218$		0			0
$219$	25.7156	−	7.80075i	1.73770	−	0.527126i
$220$		0			0
$221$	−3.12286	+	3.80522i	−0.210066	+	0.255967i
$222$		0			0
$223$	−10.6068	+	10.6068i	−0.710285	+	0.710285i	−0.966595	−	0.256310i	$-0.917493\pi$
$223$	−10.6068	+	10.6068i	−0.710285	+	0.710285i	0.256310	+	0.966595i	$0.417493\pi$
$224$		0			0
$225$	11.1664	+	11.1664i	0.744428	+	0.744428i
$226$		0			0
$227$	−20.3904	−	16.7339i	−1.35336	−	1.11067i	−0.983366	−	0.181635i	$-0.941861\pi$
$227$	−20.3904	−	16.7339i	−1.35336	−	1.11067i	−0.369990	−	0.929036i	$-0.620639\pi$
$228$		0			0
$229$	4.35928	+	14.3706i	0.288069	+	0.949638i	0.974867	+	0.222789i	$0.0715160\pi$
$229$	4.35928	+	14.3706i	0.288069	+	0.949638i	−0.686797	+	0.726849i	$0.740984\pi$
$230$		0			0
$231$	−14.1048	−	21.1093i	−0.928025	−	1.38889i
$232$		0			0
$233$	−10.9074	−	7.28809i	−0.714567	−	0.477459i	0.144380	−	0.989522i	$-0.453881\pi$
$233$	−10.9074	−	7.28809i	−0.714567	−	0.477459i	−0.858948	+	0.512064i	$0.828881\pi$
$234$		0			0
$235$	−4.88325	−	0.480958i	−0.318548	−	0.0313743i
$236$		0			0
$237$	8.26901	−	27.2593i	0.537130	−	1.77068i
$238$		0			0
$239$	−5.92099	−	14.2945i	−0.382997	−	0.924636i	−0.991383	−	0.130995i	$-0.958183\pi$
$239$	−5.92099	−	14.2945i	−0.382997	−	0.924636i	0.608386	−	0.793641i	$-0.291817\pi$
$240$		0			0
$241$	1.01639	−	2.45379i	0.0654717	−	0.158063i	−0.887757	−	0.460312i	$-0.847738\pi$
$241$	1.01639	−	2.45379i	0.0654717	−	0.158063i	0.953229	+	0.302249i	$0.0977375\pi$
$242$		0			0
$243$	−17.2339	−	32.2423i	−1.10555	−	2.06834i
$244$		0			0
$245$	4.94239	+	6.02232i	0.315757	+	0.384752i
$246$		0			0
$247$	−2.27437	+	0.452401i	−0.144715	+	0.0287856i
$248$		0			0
$249$	0.561537	−	2.82304i	0.0355860	−	0.178903i
$250$		0			0
$251$	−2.38979	−	1.27737i	−0.150842	−	0.0806269i	0.394249	−	0.919004i	$-0.371005\pi$
$251$	−2.38979	−	1.27737i	−0.150842	−	0.0806269i	−0.545091	+	0.838377i	$0.683505\pi$
$252$		0			0
$253$	0.140083	+	1.42229i	0.00880696	+	0.0894185i
$254$		0			0
$255$	−5.31526			−0.332855
$256$		0			0
$257$	−3.22235			−0.201005			−0.100502	−	0.994937i	$-0.532045\pi$
$257$	−3.22235			−0.201005			−0.100502	+	0.994937i	$0.532045\pi$
$258$		0			0
$259$	1.38719	+	14.0844i	0.0861957	+	0.875160i
$260$		0			0
$261$	−14.8814	−	7.95429i	−0.921137	−	0.492358i
$262$		0			0
$263$	0.626902	−	3.15165i	0.0386564	−	0.194339i	−0.956632	−	0.291300i	$-0.905912\pi$
$263$	0.626902	−	3.15165i	0.0386564	−	0.194339i	0.995288	+	0.0969610i	$0.0309122\pi$
$264$		0			0
$265$	−9.72845	+	1.93511i	−0.597614	+	0.118873i
$266$		0			0
$267$	7.17897	+	8.74760i	0.439346	+	0.535344i
$268$		0			0
$269$	3.30637	+	6.18578i	0.201593	+	0.377154i	0.962321	−	0.271917i	$-0.0876578\pi$
$269$	3.30637	+	6.18578i	0.201593	+	0.377154i	−0.760728	+	0.649071i	$0.775158\pi$
$270$		0			0
$271$	6.51338	−	15.7247i	0.395660	−	0.955207i	−0.593023	−	0.805185i	$-0.702066\pi$
$271$	6.51338	−	15.7247i	0.395660	−	0.955207i	0.988683	−	0.150021i	$-0.0479342\pi$
$272$		0			0
$273$	−9.85675	−	23.7963i	−0.596558	−	1.44022i
$274$		0			0
$275$	−3.07550	+	10.1386i	−0.185459	+	0.611378i
$276$		0			0
$277$	2.17255	+	0.213978i	0.130536	+	0.0128567i	0.163074	−	0.986614i	$-0.447859\pi$
$277$	2.17255	+	0.213978i	0.130536	+	0.0128567i	−0.0325381	+	0.999470i	$0.510359\pi$
$278$		0			0
$279$	26.0015	+	17.3737i	1.55667	+	1.04013i
$280$		0			0
$281$	8.44049	+	12.6321i	0.503517	+	0.753567i	0.992958	−	0.118470i	$-0.0377989\pi$
$281$	8.44049	+	12.6321i	0.503517	+	0.753567i	−0.489440	+	0.872037i	$0.662799\pi$
$282$		0			0
$283$	−1.79122	−	5.90485i	−0.106477	−	0.351007i	0.887471	−	0.460864i	$-0.152461\pi$
$283$	−1.79122	−	5.90485i	−0.106477	−	0.351007i	−0.993947	+	0.109858i	$0.964961\pi$
$284$		0			0
$285$	−1.93555	−	1.58846i	−0.114652	−	0.0940924i
$286$		0			0
$287$	6.35155	+	6.35155i	0.374920	+	0.374920i
$288$		0			0
$289$	11.3639	−	11.3639i	0.668466	−	0.668466i
$290$		0			0
$291$	−27.8707	+	33.9605i	−1.63381	+	1.99080i
$292$		0			0
$293$	−17.0941	+	5.18545i	−0.998650	+	0.302937i	−0.746959	−	0.664870i	$-0.768487\pi$
$293$	−17.0941	+	5.18545i	−0.998650	+	0.302937i	−0.251691	+	0.967808i	$0.580987\pi$
$294$		0			0
$295$	6.94326	−	4.63934i	0.404252	−	0.270113i
$296$		0			0
$297$	40.8192	−	61.0902i	2.36857	−	3.54481i
$298$		0			0
$299$	−0.142120	+	1.44296i	−0.00821899	+	0.0834488i
$300$		0			0
$301$	−4.99645	−	1.51566i	−0.287991	−	0.0873610i
$302$		0			0
$303$	−39.1704	+	16.2249i	−2.25028	+	0.932096i
$304$		0			0
$305$	6.09007	+	2.52259i	0.348716	+	0.144443i
$306$		0			0
$307$	29.1953	−	15.6052i	1.66627	−	0.890638i	0.678518	−	0.734584i	$-0.262623\pi$
$307$	29.1953	−	15.6052i	1.66627	−	0.890638i	0.987749	−	0.156054i	$-0.0498774\pi$
$308$		0			0
$309$	0.137731	−	0.113033i	0.00783525	−	0.00643023i
$310$		0			0
$311$	1.45080	+	7.29367i	0.0822674	+	0.413586i	0.999871	+	0.0160885i	$0.00512136\pi$
$311$	1.45080	+	7.29367i	0.0822674	+	0.413586i	−0.917603	+	0.397498i	$0.869879\pi$
$312$		0			0
$313$	−6.64758	−	1.32229i	−0.375743	−	0.0747400i	0.00360599	−	0.999993i	$-0.498852\pi$
$313$	−6.64758	−	1.32229i	−0.375743	−	0.0747400i	−0.379349	+	0.925253i	$0.623852\pi$
$314$		0			0
$315$	9.36568	−	17.5220i	0.527697	−	0.987251i
$316$		0			0
$317$	−20.6716	+	2.03597i	−1.16103	+	0.114351i	−0.660128	−	0.751153i	$-0.729498\pi$
$317$	−20.6716	+	2.03597i	−1.16103	+	0.114351i	−0.500902	+	0.865504i	$0.666998\pi$
$318$		0			0
$319$		−	11.3208i		−	0.633843i
$320$		0			0
$321$			28.7663i			1.60558i
$322$		0			0
$323$	−0.435521	+	0.0428951i	−0.0242331	+	0.00238675i
$324$		0			0
$325$	−5.06694	+	9.47957i	−0.281063	+	0.525832i
$326$		0			0
$327$	−36.2204	−	7.20468i	−2.00299	−	0.398420i
$328$		0			0
$329$	−0.875444	−	4.40116i	−0.0482648	−	0.242644i
$330$		0			0
$331$	−20.5553	+	16.8693i	−1.12982	+	0.927220i	−0.997947	−	0.0640459i	$-0.979600\pi$
$331$	−20.5553	+	16.8693i	−1.12982	+	0.927220i	−0.131874	+	0.991266i	$0.542100\pi$
$332$		0			0
$333$	−60.1839	+	32.1689i	−3.29806	+	1.76285i
$334$		0			0
$335$	10.7565	+	4.45547i	0.587688	+	0.243428i
$336$		0			0
$337$	2.43935	−	1.01041i	0.132880	−	0.0550406i	−0.315253	−	0.949008i	$-0.602089\pi$
$337$	2.43935	−	1.01041i	0.132880	−	0.0550406i	0.448133	+	0.893967i	$0.352089\pi$
$338$		0			0
$339$	−19.9099	−	6.03960i	−1.08136	−	0.328026i
$340$		0			0
$341$	−2.05645	+	20.8794i	−0.111363	+	1.13069i
$342$		0			0
$343$	−10.0100	+	14.9810i	−0.540488	+	0.808897i
$344$		0			0
$345$	−1.30175	+	0.869804i	−0.0700841	+	0.0468287i
$346$		0			0
$347$	−18.4658	+	5.60153i	−0.991295	+	0.300706i	−0.743960	−	0.668224i	$-0.767055\pi$
$347$	−18.4658	+	5.60153i	−0.991295	+	0.300706i	−0.247335	+	0.968930i	$0.579555\pi$
$348$		0			0
$349$	−3.73575	+	4.55203i	−0.199970	+	0.243664i	−0.863334	−	0.504632i	$-0.831628\pi$
$349$	−3.73575	+	4.55203i	−0.199970	+	0.243664i	0.663364	+	0.748297i	$0.269128\pi$
$350$		0			0
$351$	52.7082	−	52.7082i	2.81335	−	2.81335i
$352$		0			0
$353$	−2.71466	−	2.71466i	−0.144487	−	0.144487i	0.631163	−	0.775650i	$-0.282578\pi$
$353$	−2.71466	−	2.71466i	−0.144487	−	0.144487i	−0.775650	+	0.631163i	$0.782578\pi$
$354$		0			0
$355$	16.8185	+	13.8026i	0.892632	+	0.732565i
$356$		0			0
$357$	−1.41103	−	4.65154i	−0.0746796	−	0.246186i
$358$		0			0
$359$	4.65855	+	6.97201i	0.245869	+	0.367969i	0.933793	−	0.357814i	$-0.116478\pi$
$359$	4.65855	+	6.97201i	0.245869	+	0.367969i	−0.687924	+	0.725783i	$0.741478\pi$
$360$		0			0
$361$	15.6265	+	10.4413i	0.822448	+	0.549542i
$362$		0			0
$363$	46.2571	+	4.55592i	2.42787	+	0.239124i
$364$		0			0
$365$	−4.09567	+	13.5016i	−0.214377	+	0.706708i
$366$		0			0
$367$	−1.34286	−	3.24194i	−0.0700966	−	0.169228i	0.884948	−	0.465689i	$-0.154194\pi$
$367$	−1.34286	−	3.24194i	−0.0700966	−	0.169228i	−0.955045	+	0.296461i	$0.904194\pi$
$368$		0			0
$369$	−16.5749	+	40.0154i	−0.862855	+	2.08312i
$370$		0			0
$371$	−4.27606	−	7.99995i	−0.222002	−	0.415336i
$372$		0			0
$373$	−17.3678	−	21.1627i	−0.899270	−	1.09576i	−0.994952	−	0.100352i	$-0.968003\pi$
$373$	−17.3678	−	21.1627i	−0.899270	−	1.09576i	0.0956819	−	0.995412i	$-0.469497\pi$
$374$		0			0
$375$	−38.4267	+	7.64354i	−1.98434	+	0.394711i
$376$		0			0
$377$	2.24068	−	11.2647i	0.115401	−	0.580161i
$378$		0			0
$379$	−1.51536	−	0.809979i	−0.0778390	−	0.0416058i	0.432018	−	0.901865i	$-0.357802\pi$
$379$	−1.51536	−	0.809979i	−0.0778390	−	0.0416058i	−0.509857	+	0.860259i	$0.670302\pi$
$380$		0			0
$381$	−1.18559	−	12.0375i	−0.0607394	−	0.616698i
$382$		0			0
$383$	28.6199			1.46241			0.731204	−	0.682159i	$-0.238959\pi$
$383$	28.6199			1.46241			0.731204	+	0.682159i	$0.238959\pi$
$384$		0			0
$385$	13.3295			0.679337
$386$		0			0
$387$	−2.46772	−	25.0552i	−0.125441	−	1.27363i
$388$		0			0
$389$	16.0060	+	8.55539i	0.811537	+	0.433775i	0.824307	−	0.566143i	$-0.191565\pi$
$389$	16.0060	+	8.55539i	0.811537	+	0.433775i	−0.0127704	+	0.999918i	$0.504065\pi$
$390$		0			0
$391$	−0.0533833	+	0.268376i	−0.00269971	+	0.0135724i
$392$		0			0
$393$	−9.44767	+	1.87926i	−0.476572	+	0.0947961i
$394$		0			0
$395$	9.48805	+	11.5612i	0.477396	+	0.581708i
$396$		0			0
$397$	2.64522	+	4.94887i	0.132760	+	0.248376i	0.939514	−	0.342511i	$-0.111278\pi$
$397$	2.64522	+	4.94887i	0.132760	+	0.248376i	−0.806754	+	0.590888i	$0.798778\pi$
$398$		0			0
$399$	0.876285	−	2.11554i	0.0438691	−	0.105909i
$400$		0			0
$401$	7.37348	+	17.8012i	0.368214	+	0.888947i	0.994043	+	0.108987i	$0.0347607\pi$
$401$	7.37348	+	17.8012i	0.368214	+	0.888947i	−0.625829	+	0.779960i	$0.715239\pi$
$402$		0			0
$403$	−6.17884	+	20.3689i	−0.307790	+	1.01465i
$404$		0			0
$405$	41.9805	+	4.13472i	2.08603	+	0.205456i
$406$		0			0
$407$	−38.0679	−	25.4362i	−1.88696	−	1.26082i
$408$		0			0
$409$	20.5780	+	30.7971i	1.01752	+	1.52282i	0.842820	+	0.538196i	$0.180894\pi$
$409$	20.5780	+	30.7971i	1.01752	+	1.52282i	0.174695	+	0.984623i	$0.444106\pi$
$410$		0			0
$411$	13.8047	+	45.5080i	0.680936	+	2.24474i
$412$		0			0
$413$	5.90323	+	4.84466i	0.290479	+	0.238390i
$414$		0			0
$415$	1.06860	+	1.06860i	0.0524557	+	0.0524557i
$416$		0			0
$417$	−39.4833	+	39.4833i	−1.93350	+	1.93350i
$418$		0			0
$419$	13.8228	−	16.8432i	0.675290	−	0.822843i	−0.316784	−	0.948498i	$-0.602603\pi$
$419$	13.8228	−	16.8432i	0.675290	−	0.822843i	0.992074	+	0.125655i	$0.0401032\pi$
$420$		0			0
$421$	12.9052	−	3.91476i	0.628963	−	0.190794i	0.0403199	−	0.999187i	$-0.487162\pi$
$421$	12.9052	−	3.91476i	0.628963	−	0.190794i	0.588643	+	0.808393i	$0.299662\pi$
$422$		0			0
$423$	17.9910	−	12.0212i	0.874753	−	0.584492i
$424$		0			0
$425$	−1.12698	+	1.68664i	−0.0546665	+	0.0818142i
$426$		0			0
$427$	−0.590876	+	5.99927i	−0.0285945	+	0.290325i
$428$		0			0
$429$	79.7367	+	24.1879i	3.84972	+	1.16780i
$430$		0			0
$431$	0.826940	−	0.342530i	0.0398323	−	0.0164991i	−0.362678	−	0.931914i	$-0.618138\pi$
$431$	0.826940	−	0.342530i	0.0398323	−	0.0164991i	0.402511	+	0.915415i	$0.368138\pi$
$432$		0			0
$433$	7.72303	+	3.19898i	0.371145	+	0.153733i	0.560457	−	0.828184i	$-0.310626\pi$
$433$	7.72303	+	3.19898i	0.371145	+	0.153733i	−0.189312	+	0.981917i	$0.560626\pi$
$434$		0			0
$435$	10.9372	−	5.84605i	0.524398	−	0.280296i
$436$		0			0
$437$	−0.0996435	+	0.0817753i	−0.00476659	+	0.00391184i
$438$		0			0
$439$	−1.33554	−	6.71421i	−0.0637418	−	0.320452i	0.935738	−	0.352695i	$-0.114735\pi$
$439$	−1.33554	−	6.71421i	−0.0637418	−	0.320452i	−0.999480	+	0.0322435i	$0.989735\pi$
$440$		0			0
$441$	−33.6943	−	6.70221i	−1.60449	−	0.319153i
$442$		0			0
$443$	16.7447	−	31.3272i	0.795567	−	1.48840i	−0.0754516	−	0.997149i	$-0.524040\pi$
$443$	16.7447	−	31.3272i	0.795567	−	1.48840i	0.871018	−	0.491251i	$-0.163460\pi$
$444$		0			0
$445$	−5.91284	+	0.582364i	−0.280295	+	0.0276067i
$446$		0			0
$447$			51.4412i			2.43309i
$448$		0			0
$449$		−	12.5022i		−	0.590014i	−0.955495	−	0.295007i	$-0.904678\pi$
$449$		−	12.5022i		−	0.590014i	0.955495	−	0.295007i	$-0.0953220\pi$
$450$		0			0
$451$	−28.9186	+	2.84824i	−1.36172	+	0.134118i
$452$		0			0
$453$	30.3097	−	56.7054i	1.42407	−	2.66425i
$454$		0			0
$455$	13.2635	+	2.63827i	0.621801	+	0.123684i
$456$		0			0
$457$	0.0109008	+	0.0548023i	0.000509920	+	0.00256354i	0.981039	−	0.193808i	$-0.0620840\pi$
$457$	0.0109008	+	0.0548023i	0.000509920	+	0.00256354i	−0.980529	+	0.196372i	$0.937084\pi$
$458$		0			0
$459$	10.8742	−	8.92421i	0.507563	−	0.416546i
$460$		0			0
$461$	35.0759	−	18.7485i	1.63365	−	0.873203i	0.639076	−	0.769144i	$-0.279317\pi$
$461$	35.0759	−	18.7485i	1.63365	−	0.873203i	0.994571	−	0.104059i	$-0.0331830\pi$
$462$		0			0
$463$	−31.7740	−	13.1612i	−1.47666	−	0.611653i	−0.508295	−	0.861183i	$-0.669724\pi$
$463$	−31.7740	−	13.1612i	−1.47666	−	0.611653i	−0.968367	+	0.249530i	$0.919724\pi$
$464$		0			0
$465$	−21.2339	+	8.79535i	−0.984697	+	0.407875i
$466$		0			0
$467$	−29.7366	−	9.02051i	−1.37605	−	0.417419i	−0.486268	−	0.873810i	$-0.661642\pi$
$467$	−29.7366	−	9.02051i	−1.37605	−	0.417419i	−0.889780	+	0.456390i	$0.849142\pi$
$468$		0			0
$469$	−1.04362	+	10.5961i	−0.0481900	+	0.489282i
$470$		0			0
$471$	43.4920	−	65.0904i	2.00401	−	2.99921i
$472$		0			0
$473$	14.0444	−	9.38415i	0.645761	−	0.431484i
$474$		0			0
$475$	−0.914440	+	0.277392i	−0.0419574	+	0.0127276i
$476$		0			0
$477$	27.7480	−	33.8111i	1.27050	−	1.54810i
$478$		0			0
$479$	−10.8301	+	10.8301i	−0.494840	+	0.494840i	−0.909827	−	0.414988i	$-0.863786\pi$
$479$	−10.8301	+	10.8301i	−0.494840	+	0.494840i	0.414988	+	0.909827i	$0.363786\pi$
$480$		0			0
$481$	−32.8447	−	32.8447i	−1.49759	−	1.49759i
$482$		0			0
$483$	−1.10676	−	0.908298i	−0.0503595	−	0.0413290i
$484$		0			0
$485$	−6.69579	−	22.0731i	−0.304040	−	1.00229i
$486$		0			0
$487$	7.32864	+	10.9681i	0.332092	+	0.497012i	0.959511	−	0.281671i	$-0.0908885\pi$
$487$	7.32864	+	10.9681i	0.332092	+	0.497012i	−0.627419	+	0.778682i	$0.715889\pi$
$488$		0			0
$489$	−38.9372	−	26.0170i	−1.76080	−	1.17653i
$490$		0			0
$491$	11.2709	+	1.11008i	0.508647	+	0.0500974i	0.349086	−	0.937091i	$-0.386492\pi$
$491$	11.2709	+	1.11008i	0.508647	+	0.0500974i	0.159561	+	0.987188i	$0.448992\pi$
$492$		0			0
$493$	0.629198	−	2.07419i	0.0283376	−	0.0934167i
$494$		0			0
$495$	24.5964	+	59.3810i	1.10553	+	2.66898i
$496$		0			0
$497$	−7.61427	+	18.3825i	−0.341547	+	0.824567i
$498$		0			0
$499$	10.2332	+	19.1450i	0.458102	+	0.857048i	0.999864	+	0.0165160i	$0.00525744\pi$
$499$	10.2332	+	19.1450i	0.458102	+	0.857048i	−0.541762	+	0.840532i	$0.682243\pi$
$500$		0			0
$501$	−18.8041	−	22.9129i	−0.840106	−	1.02367i
$502$		0			0
$503$	7.24137	−	1.44040i	0.322877	−	0.0642242i	−0.0309910	−	0.999520i	$-0.509866\pi$
$503$	7.24137	−	1.44040i	0.322877	−	0.0642242i	0.353868	+	0.935295i	$0.384866\pi$
$504$		0			0
$505$	4.34277	−	21.8326i	0.193251	−	0.971538i
$506$		0			0
$507$	37.3972	+	19.9892i	1.66087	+	0.887752i
$508$		0			0
$509$	3.84741	+	39.0634i	0.170534	+	1.73146i	0.576090	+	0.817386i	$0.304578\pi$
$509$	3.84741	+	39.0634i	0.170534	+	1.73146i	−0.405556	+	0.914070i	$0.632922\pi$
$510$		0			0
$511$	−12.9029			−0.570792
$512$		0			0
$513$	6.62681			0.292581
$514$		0			0
$515$	0.00916934	+	0.0930978i	0.000404049	+	0.00410238i
$516$		0			0
$517$	12.8027	+	6.84319i	0.563062	+	0.300963i
$518$		0			0
$519$	−0.206434	+	1.03782i	−0.00906146	+	0.0455550i
$520$		0			0
$521$	40.4270	−	8.04143i	1.77114	−	0.352301i	0.801717	−	0.597704i	$-0.203920\pi$
$521$	40.4270	−	8.04143i	1.77114	−	0.352301i	0.969421	+	0.245403i	$0.0789203\pi$
$522$		0			0
$523$	4.77315	+	5.81611i	0.208715	+	0.254321i	0.866838	−	0.498591i	$-0.166149\pi$
$523$	4.77315	+	5.81611i	0.208715	+	0.254321i	−0.658122	+	0.752911i	$0.728649\pi$
$524$		0			0
$525$	−5.00338	−	9.36067i	−0.218365	−	0.408533i
$526$		0			0
$527$	−1.53724	+	3.71122i	−0.0669631	+	0.161663i
$528$		0			0
$529$	−8.77088	−	21.1748i	−0.381342	−	0.920642i
$530$		0			0
$531$	−10.6892	+	35.2376i	−0.463872	+	1.52918i
$532$		0			0
$533$	−29.3390	−	2.88964i	−1.27081	−	0.125164i
$534$		0			0
$535$	−12.5580	−	8.39097i	−0.542928	−	0.362773i
$536$		0			0
$537$	8.14149	+	12.1846i	0.351331	+	0.525804i
$538$		0			0
$539$	−6.69066	−	22.0561i	−0.288187	−	0.950025i
$540$		0			0
$541$	−19.1837	−	15.7437i	−0.824771	−	0.676872i	0.124192	−	0.992258i	$-0.460366\pi$
$541$	−19.1837	−	15.7437i	−0.824771	−	0.676872i	−0.948964	+	0.315386i	$0.897866\pi$
$542$		0			0
$543$	−23.1243	−	23.1243i	−0.992357	−	0.992357i
$544$		0			0
$545$	13.7105	−	13.7105i	0.587293	−	0.587293i
$546$		0			0
$547$	4.13199	−	5.03485i	0.176671	−	0.215274i	−0.677144	−	0.735850i	$-0.736783\pi$
$547$	4.13199	−	5.03485i	0.176671	−	0.215274i	0.853815	+	0.520576i	$0.174283\pi$
$548$		0			0
$549$	−27.8161	+	8.43791i	−1.18716	+	0.360121i
$550$		0			0
$551$	0.848991	−	0.567278i	0.0361682	−	0.0241668i
$552$		0			0
$553$	−7.59879	+	11.3724i	−0.323134	+	0.483604i
$554$		0			0
$555$	4.91601	−	49.9131i	0.208673	−	2.11869i
$556$		0			0
$557$	−4.02846	−	1.22202i	−0.170691	−	0.0517787i	0.203782	−	0.979016i	$-0.434677\pi$
$557$	−4.02846	−	1.22202i	−0.170691	−	0.0517787i	−0.374474	+	0.927238i	$0.622177\pi$
$558$		0			0
$559$	15.8321	−	6.55788i	0.669627	−	0.277369i
$560$		0			0
$561$	14.5280	+	6.01771i	0.613374	+	0.254068i
$562$		0			0
$563$	11.8922	−	6.35649i	0.501194	−	0.267894i	−0.201369	−	0.979516i	$-0.564539\pi$
$563$	11.8922	−	6.35649i	0.501194	−	0.267894i	0.702563	+	0.711622i	$0.252039\pi$
$564$		0			0
$565$	8.44420	−	6.92998i	0.355250	−	0.291546i
$566$		0			0
$567$	7.52605	+	37.8360i	0.316064	+	1.58896i
$568$		0			0
$569$	−22.0718	−	4.39036i	−0.925299	−	0.184053i	−0.290628	−	0.956836i	$-0.593864\pi$
$569$	−22.0718	−	4.39036i	−0.925299	−	0.184053i	−0.634671	+	0.772783i	$0.718864\pi$
$570$		0			0
$571$	−2.20350	+	4.12245i	−0.0922135	+	0.172519i	−0.923799	−	0.382877i	$-0.874933\pi$
$571$	−2.20350	+	4.12245i	−0.0922135	+	0.172519i	0.831586	+	0.555396i	$0.187433\pi$
$572$		0			0
$573$	87.5161	−	8.61958i	3.65604	−	0.360088i
$574$		0			0
$575$			0.597495i			0.0249173i
$576$		0			0
$577$			24.9065i			1.03687i	0.855117	+	0.518436i	$0.173486\pi$
$577$			24.9065i			1.03687i	−0.855117	+	0.518436i	$0.826514\pi$
$578$		0			0
$579$	5.13661	−	0.505912i	0.213470	−	0.0210250i
$580$		0			0
$581$	−0.651487	+	1.21885i	−0.0270282	+	0.0505662i
$582$		0			0
$583$	28.7813	+	5.72495i	1.19200	+	0.237103i
$584$		0			0
$585$	12.7214	+	63.9549i	0.525966	+	2.64421i
$586$		0			0
$587$	−7.87127	+	6.45979i	−0.324882	+	0.266624i	−0.782669	−	0.622438i	$-0.786142\pi$
$587$	−7.87127	+	6.45979i	−0.324882	+	0.266624i	0.457787	+	0.889062i	$0.348642\pi$
$588$		0			0
$589$	−1.66888	+	0.892033i	−0.0687649	+	0.0367556i
$590$		0			0
$591$	31.4160	+	13.0129i	1.29228	+	0.535281i
$592$		0			0
$593$	4.64451	−	1.92382i	0.190727	−	0.0790018i	−0.285276	−	0.958446i	$-0.592085\pi$
$593$	4.64451	−	1.92382i	0.190727	−	0.0790018i	0.476003	+	0.879444i	$0.342085\pi$
$594$		0			0
$595$	2.44223	+	0.740841i	0.100122	+	0.0303715i
$596$		0			0
$597$	0.970993	−	9.85865i	0.0397401	−	0.403488i
$598$		0			0
$599$	9.29735	−	13.9145i	0.379879	−	0.568530i	−0.591428	−	0.806358i	$-0.701436\pi$
$599$	9.29735	−	13.9145i	0.379879	−	0.568530i	0.971307	+	0.237828i	$0.0764355\pi$
$600$		0			0
$601$	−5.77189	+	3.85666i	−0.235441	+	0.157316i	−0.667694	−	0.744436i	$-0.732719\pi$
$601$	−5.77189	+	3.85666i	−0.235441	+	0.157316i	0.432254	+	0.901752i	$0.357719\pi$
$602$		0			0
$603$	−49.1296	+	14.9033i	−2.00071	+	0.606909i
$604$		0			0
$605$	−15.4818	+	18.8646i	−0.629425	+	0.766957i
$606$		0			0
$607$	−21.1708	+	21.1708i	−0.859297	+	0.859297i	−0.991255	−	0.131958i	$-0.957874\pi$
$607$	−21.1708	+	21.1708i	−0.859297	+	0.859297i	0.131958	+	0.991255i	$0.457874\pi$
$608$		0			0
$609$	8.01952	+	8.01952i	0.324967	+	0.324967i
$610$		0			0
$611$	11.3848	+	9.34325i	0.460579	+	0.377988i
$612$		0			0
$613$	9.88141	+	32.5747i	0.399107	+	1.31568i	0.894523	+	0.447022i	$0.147516\pi$
$613$	9.88141	+	32.5747i	0.399107	+	1.31568i	−0.495416	+	0.868656i	$0.664984\pi$
$614$		0			0
$615$	−17.6852	−	26.4678i	−0.713138	−	1.06729i
$616$		0			0
$617$	29.3377	+	19.6028i	1.18109	+	0.789180i	0.981643	−	0.190729i	$-0.0610851\pi$
$617$	29.3377	+	19.6028i	1.18109	+	0.789180i	0.199448	+	0.979908i	$0.436085\pi$
$618$		0			0
$619$	−3.10600	−	0.305914i	−0.124841	−	0.0122957i	0.0354039	−	0.999373i	$-0.488728\pi$
$619$	−3.10600	−	0.305914i	−0.124841	−	0.0122957i	−0.160244	+	0.987077i	$0.551228\pi$
$620$		0			0
$621$	1.20280	−	3.96510i	0.0482666	−	0.159114i
$622$		0			0
$623$	−2.07931	−	5.01990i	−0.0833058	−	0.201118i
$624$		0			0
$625$	3.84505	−	9.28278i	0.153802	−	0.371311i
$626$		0			0
$627$	3.49198	+	6.53303i	0.139456	+	0.260904i
$628$		0			0
$629$	−5.56105	−	6.77616i	−0.221734	−	0.270183i
$630$		0			0
$631$	9.23405	−	1.83677i	0.367602	−	0.0731205i	−0.00783313	−	0.999969i	$-0.502493\pi$
$631$	9.23405	−	1.83677i	0.367602	−	0.0731205i	0.375435	+	0.926849i	$0.377493\pi$
$632$		0			0
$633$	11.3918	−	57.2705i	0.452784	−	2.27630i
$634$		0			0
$635$	5.60080	+	2.99369i	0.222261	+	0.118801i
$636$		0			0
$637$	−2.29200	−	23.2710i	−0.0908123	−	0.922033i
$638$		0			0
$639$	−95.9413			−3.79538
$640$		0			0
$641$	−27.4239			−1.08318			−0.541589	−	0.840644i	$-0.682177\pi$
$641$	−27.4239			−1.08318			−0.541589	+	0.840644i	$0.682177\pi$
$642$		0			0
$643$	2.96417	+	30.0958i	0.116896	+	1.18686i	0.857343	+	0.514746i	$0.172114\pi$
$643$	2.96417	+	30.0958i	0.116896	+	1.18686i	−0.740447	+	0.672115i	$0.765386\pi$
$644$		0			0
$645$	16.3186	+	8.72250i	0.642546	+	0.343448i
$646$		0			0
$647$	−0.229068	+	1.15160i	−0.00900561	+	0.0452742i	−0.985027	−	0.172401i	$-0.944847\pi$
$647$	−0.229068	+	1.15160i	−0.00900561	+	0.0452742i	0.976021	+	0.217675i	$0.0698474\pi$
$648$		0			0
$649$	−24.2302	+	4.81969i	−0.951119	+	0.189189i
$650$		0			0
$651$	−13.3340	−	16.2475i	−0.522600	−	0.636789i
$652$		0			0
$653$	2.84846	+	5.32910i	0.111469	+	0.208544i	0.931470	−	0.363818i	$-0.118527\pi$
$653$	2.84846	+	5.32910i	0.111469	+	0.208544i	−0.820001	+	0.572362i	$0.806027\pi$
$654$		0			0
$655$	1.93544	−	4.67256i	0.0756239	−	0.182572i
$656$		0			0
$657$	−23.8092	−	57.4805i	−0.928886	−	2.24253i
$658$		0			0
$659$	−13.3882	+	44.1349i	−0.521530	+	1.71925i	0.159684	+	0.987168i	$0.448953\pi$
$659$	−13.3882	+	44.1349i	−0.521530	+	1.71925i	−0.681213	+	0.732085i	$0.738547\pi$
$660$		0			0
$661$	−17.6719	−	1.74053i	−0.687358	−	0.0676988i	−0.251692	−	0.967807i	$-0.580987\pi$
$661$	−17.6719	−	1.74053i	−0.687358	−	0.0676988i	−0.435666	+	0.900109i	$0.643487\pi$
$662$		0			0
$663$	13.2649	+	8.86335i	0.515168	+	0.344224i
$664$		0			0
$665$	0.667934	+	0.999634i	0.0259014	+	0.0387642i
$666$		0			0
$667$	−0.185330	−	0.610950i	−0.00717599	−	0.0236561i
$668$		0			0
$669$	37.5794	+	30.8406i	1.45290	+	1.19237i
$670$		0			0
$671$	−13.7898	−	13.7898i	−0.532350	−	0.532350i
$672$		0			0
$673$	23.9537	−	23.9537i	0.923348	−	0.923348i	−0.0739160	−	0.997264i	$-0.523550\pi$
$673$	23.9537	−	23.9537i	0.923348	−	0.923348i	0.997264	+	0.0739160i	$0.0235497\pi$
$674$		0			0
$675$	19.4865	−	23.7444i	0.750037	−	0.913922i
$676$		0			0
$677$	−15.7200	+	4.76862i	−0.604170	+	0.183273i	−0.577526	−	0.816372i	$-0.695982\pi$
$677$	−15.7200	+	4.76862i	−0.604170	+	0.183273i	−0.0266435	+	0.999645i	$0.508482\pi$
$678$		0			0
$679$	17.5393	−	11.7194i	0.673096	−	0.449748i
$680$		0			0
$681$	−47.4945	+	71.0806i	−1.81999	+	2.72381i
$682$		0			0
$683$	1.86554	−	18.9411i	0.0713827	−	0.724761i	−0.891171	−	0.453668i	$-0.850115\pi$
$683$	1.86554	−	18.9411i	0.0713827	−	0.724761i	0.962553	−	0.271093i	$-0.0873850\pi$
$684$		0			0
$685$	−23.8933	−	7.24796i	−0.912917	−	0.276930i
$686$		0			0
$687$	44.9646	−	18.6250i	1.71551	−	0.710587i
$688$		0			0
$689$	27.5055	+	11.3931i	1.04788	+	0.434044i
$690$		0			0
$691$	20.9845	−	11.2165i	0.798290	−	0.426695i	−0.0212095	−	0.999775i	$-0.506752\pi$
$691$	20.9845	−	11.2165i	0.798290	−	0.426695i	0.819499	+	0.573080i	$0.194252\pi$
$692$		0			0
$693$	−45.4365	+	37.2888i	−1.72599	+	1.41648i
$694$		0			0
$695$	−5.71943	−	28.7535i	−0.216950	−	1.09068i
$696$		0			0
$697$	−5.45674	−	1.08541i	−0.206689	−	0.0411130i
$698$		0			0
$699$	−20.0413	+	37.4947i	−0.758032	+	1.41818i
$700$		0			0
$701$	−37.3433	+	3.67799i	−1.41044	+	0.138916i	−0.774377	−	0.632725i	$-0.781937\pi$
$701$	−37.3433	+	3.67799i	−1.41044	+	0.138916i	−0.636059	+	0.771640i	$0.719437\pi$
$702$		0			0
$703$		−	4.12945i		−	0.155745i
$704$		0			0
$705$			15.9027i			0.598930i
$706$		0			0
$707$	20.2592	−	1.99536i	0.761926	−	0.0750432i
$708$		0			0
$709$	−0.487908	+	0.912812i	−0.0183238	+	0.0342814i	−0.890917	−	0.454167i	$-0.849937\pi$
$709$	−0.487908	+	0.912812i	−0.0183238	+	0.0342814i	0.872593	+	0.488448i	$0.162437\pi$
$710$		0			0
$711$	−64.6839	−	12.8664i	−2.42584	−	0.482529i
$712$		0			0
$713$	0.230831	+	1.16047i	0.00864469	+	0.0434598i
$714$		0			0
$715$	−33.8180	+	27.7537i	−1.26472	+	1.03793i
$716$		0			0
$717$	−44.2231	+	23.6377i	−1.65154	+	0.882768i
$718$		0			0
$719$	5.59288	+	2.31665i	0.208579	+	0.0863963i	0.484527	−	0.874776i	$-0.338992\pi$
$719$	5.59288	+	2.31665i	0.208579	+	0.0863963i	−0.275948	+	0.961173i	$0.588992\pi$
$720$		0			0
$721$	−0.0790385	+	0.0327388i	−0.00294355	+	0.00121926i
$722$		0			0
$723$	−8.23706	−	2.49868i	−0.306339	−	0.0929270i
$724$		0			0
$725$	0.463906	−	4.71012i	0.0172290	−	0.174929i
$726$		0			0
$727$	−19.0684	+	28.5378i	−0.707206	+	1.05841i	0.287712	+	0.957717i	$0.407106\pi$
$727$	−19.0684	+	28.5378i	−0.707206	+	1.05841i	−0.994918	+	0.100692i	$0.967894\pi$
$728$		0			0
$729$	−36.6778	+	24.5073i	−1.35844	+	0.907680i
$730$		0			0
$731$	3.09476	−	0.938784i	0.114464	−	0.0347222i
$732$		0			0
$733$	28.7676	−	35.0534i	1.06256	−	1.29473i	0.108826	−	0.994061i	$-0.465291\pi$
$733$	28.7676	−	35.0534i	1.06256	−	1.29473i	0.953729	−	0.300667i	$-0.0972092\pi$
$734$		0			0
$735$	17.8537	−	17.8537i	0.658543	−	0.658543i
$736$		0			0
$737$	−24.3560	−	24.3560i	−0.897164	−	0.897164i
$738$		0			0
$739$	−25.9216	−	21.2733i	−0.953541	−	0.782551i	0.0225873	−	0.999745i	$-0.492810\pi$
$739$	−25.9216	−	21.2733i	−0.953541	−	0.782551i	−0.976129	+	0.217194i	$0.930310\pi$
$740$		0			0
$741$	2.18161	+	7.19180i	0.0801434	+	0.264197i
$742$		0			0
$743$	−5.69033	−	8.51618i	−0.208758	−	0.312428i	0.712284	−	0.701891i	$-0.247661\pi$
$743$	−5.69033	−	8.51618i	−0.208758	−	0.312428i	−0.921042	+	0.389463i	$0.872661\pi$
$744$		0			0
$745$	−22.4567	−	15.0051i	−0.822751	−	0.549745i
$746$		0			0
$747$	−6.63192	−	0.653187i	−0.242649	−	0.0238989i
$748$		0			0
$749$	4.00945	−	13.2174i	0.146502	−	0.482952i
$750$		0			0
$751$	−14.5426	−	35.1089i	−0.530667	−	1.28114i	−0.931082	−	0.364809i	$-0.881134\pi$
$751$	−14.5426	−	35.1089i	−0.530667	−	1.28114i	0.400416	−	0.916334i	$-0.368866\pi$
$752$		0			0
$753$	−3.36074	+	8.11355i	−0.122472	+	0.295674i
$754$		0			0
$755$	15.9137	+	29.7724i	0.579157	+	1.08353i
$756$		0			0
$757$	24.3204	+	29.6345i	0.883940	+	1.07708i	0.996513	+	0.0834409i	$0.0265910\pi$
$757$	24.3204	+	29.6345i	0.883940	+	1.07708i	−0.112572	+	0.993644i	$0.535909\pi$
$758$		0			0
$759$	4.54279	−	0.903618i	0.164893	−	0.0327992i
$760$		0			0
$761$	3.24170	−	16.2971i	0.117512	−	0.590770i	−0.876491	−	0.481417i	$-0.840122\pi$
$761$	3.24170	−	16.2971i	0.117512	−	0.590770i	0.994003	−	0.109353i	$-0.0348779\pi$
$762$		0			0
$763$	15.6381	+	8.35876i	0.566139	+	0.302607i
$764$		0			0
$765$	1.20620	+	12.2468i	0.0436103	+	0.442783i
$766$		0			0
$767$	−25.0640			−0.905010
$768$		0			0
$769$	16.4374			0.592747			0.296374	−	0.955072i	$-0.404223\pi$
$769$	16.4374			0.592747			0.296374	+	0.955072i	$0.404223\pi$
$770$		0			0
$771$	1.02362	+	10.3930i	0.0368649	+	0.374295i
$772$		0			0
$773$	−1.01004	−	0.539876i	−0.0363285	−	0.0194180i	0.453132	−	0.891443i	$-0.350306\pi$
$773$	−1.01004	−	0.539876i	−0.0363285	−	0.0194180i	−0.489461	+	0.872025i	$0.662806\pi$
$774$		0			0
$775$	−1.71120	+	8.60280i	−0.0614682	+	0.309022i
$776$		0			0
$777$	44.9855	−	8.94817i	1.61385	−	0.321014i
$778$		0			0
$779$	−1.66269	−	2.02600i	−0.0595721	−	0.0725888i
$780$		0			0
$781$	−30.3427	−	56.7672i	−1.08575	−	2.03129i
$782$		0			0
$783$	−12.5603	+	30.3234i	−0.448870	+	1.08367i
$784$		0			0
$785$	15.7289	+	37.9730i	0.561390	+	1.35531i
$786$		0			0
$787$	7.49741	−	24.7156i	0.267254	−	0.881017i	−0.715895	−	0.698208i	$-0.753981\pi$
$787$	7.49741	−	24.7156i	0.267254	−	0.881017i	0.983148	−	0.182809i	$-0.0585191\pi$
$788$		0			0
$789$	−10.3641	−	1.02078i	−0.368973	−	0.0363406i
$790$		0			0
$791$	8.30629	+	5.55008i	0.295338	+	0.197338i
$792$		0			0
$793$	−10.9921	−	16.4508i	−0.390340	−	0.584186i
$794$		0			0
$795$	9.33166	+	30.7624i	0.330960	+	1.09103i
$796$		0			0
$797$	18.8667	+	15.4835i	0.668293	+	0.548454i	0.906208	−	0.422832i	$-0.138964\pi$
$797$	18.8667	+	15.4835i	0.668293	+	0.548454i	−0.237915	+	0.971286i	$0.576464\pi$
$798$		0			0
$799$	1.96536	+	1.96536i	0.0695295	+	0.0695295i
$800$		0			0
$801$	18.5260	−	18.5260i	0.654583	−	0.654583i
$802$		0			0
$803$	26.4805	−	32.2666i	0.934477	−	1.13866i
$804$		0			0
$805$	0.719356	−	0.218214i	0.0253540	−	0.00769104i
$806$		0			0
$807$	18.9006	−	12.6290i	0.665333	−	0.444561i
$808$		0			0
$809$	8.01149	−	11.9900i	0.281669	−	0.421547i	−0.663476	−	0.748197i	$-0.730920\pi$
$809$	8.01149	−	11.9900i	0.281669	−	0.421547i	0.945145	+	0.326650i	$0.105920\pi$
$810$		0			0
$811$	4.33909	−	44.0555i	0.152366	−	1.54700i	−0.549989	−	0.835172i	$-0.685368\pi$
$811$	4.33909	−	44.0555i	0.152366	−	1.54700i	0.702355	−	0.711827i	$-0.252132\pi$
$812$		0			0
$813$	−52.7857	−	16.0124i	−1.85128	−	0.561578i
$814$		0			0
$815$	22.7155	−	9.40908i	0.795690	−	0.329586i
$816$		0			0
$817$	1.40751	+	0.583009i	0.0492425	+	0.0203969i
$818$		0			0
$819$	−52.5917	+	28.1108i	−1.83770	+	0.982272i
$820$		0			0
$821$	−38.2650	+	31.4033i	−1.33546	+	1.09598i	−0.348102	+	0.937457i	$0.613174\pi$
$821$	−38.2650	+	31.4033i	−1.33546	+	1.09598i	−0.987355	+	0.158524i	$0.949326\pi$
$822$		0			0
$823$	0.346033	+	1.73963i	0.0120620	+	0.0606396i	0.986348	−	0.164677i	$-0.0526583\pi$
$823$	0.346033	+	1.73963i	0.0120620	+	0.0606396i	−0.974286	+	0.225317i	$0.927658\pi$
$824$		0			0
$825$	33.6767	+	6.69872i	1.17247	+	0.233219i
$826$		0			0
$827$	−2.72781	+	5.10338i	−0.0948554	+	0.177462i	−0.924874	−	0.380274i	$-0.875830\pi$
$827$	−2.72781	+	5.10338i	−0.0948554	+	0.177462i	0.830019	+	0.557736i	$0.188330\pi$
$828$		0			0
$829$	−48.1702	+	4.74435i	−1.67302	+	0.164778i	−0.889608	−	0.456725i	$-0.849022\pi$
$829$	−48.1702	+	4.74435i	−1.67302	+	0.164778i	−0.783412	+	0.621503i	$0.786522\pi$
$830$		0			0
$831$		−	7.07509i		−	0.245432i
$832$		0			0
$833$		−	4.41296i		−	0.152900i
$834$		0			0
$835$	15.4877	−	1.52541i	0.535974	−	0.0527889i
$836$		0			0
$837$	28.6739	−	53.6451i	0.991114	−	1.85424i
$838$		0			0
$839$	33.8442	+	6.73204i	1.16843	+	0.232416i	0.740920	−	0.671594i	$-0.234390\pi$
$839$	33.8442	+	6.73204i	1.16843	+	0.232416i	0.427513	+	0.904009i	$0.359390\pi$
$840$		0			0
$841$	−4.67100	−	23.4827i	−0.161069	−	0.809748i
$842$		0			0
$843$	38.0609	−	31.2358i	1.31089	−	1.07582i
$844$		0			0
$845$	−19.6349	+	10.4951i	−0.675460	+	0.361041i
$846$		0			0
$847$	−20.6189	−	8.54064i	−0.708475	−	0.293460i
$848$		0			0
$849$	−18.4758	+	7.65294i	−0.634089	+	0.262648i
$850$		0			0
$851$	−2.47082	−	0.749515i	−0.0846986	−	0.0256930i
$852$		0			0
$853$	1.16885	−	11.8675i	0.0400206	−	0.406336i	−0.954215	−	0.299121i	$-0.903307\pi$
$853$	1.16885	−	11.8675i	0.0400206	−	0.406336i	0.994236	−	0.107215i	$-0.0341933\pi$
$854$		0			0
$855$	−3.22070	+	4.82012i	−0.110146	+	0.164845i
$856$		0			0
$857$	31.0562	−	20.7511i	1.06086	−	0.708843i	0.102594	−	0.994723i	$-0.467286\pi$
$857$	31.0562	−	20.7511i	1.06086	−	0.708843i	0.958265	+	0.285880i	$0.0922859\pi$
$858$		0			0
$859$	32.6742	−	9.91162i	1.11483	−	0.338180i	0.321462	−	0.946922i	$-0.395826\pi$
$859$	32.6742	−	9.91162i	1.11483	−	0.338180i	0.793368	+	0.608742i	$0.208326\pi$
$860$		0			0
$861$	18.4679	−	22.5032i	0.629385	−	0.766908i
$862$		0			0
$863$	25.9455	−	25.9455i	0.883196	−	0.883196i	−0.110662	−	0.993858i	$-0.535297\pi$
$863$	25.9455	−	25.9455i	0.883196	−	0.883196i	0.993858	+	0.110662i	$0.0352971\pi$
$864$		0			0
$865$	−0.392844	−	0.392844i	−0.0133571	−	0.0133571i
$866$		0			0
$867$	−40.2618	−	33.0420i	−1.36736	−	1.12217i
$868$		0			0
$869$	−12.8443	−	42.3418i	−0.435712	−	1.43635i
$870$		0			0
$871$	−19.4145	−	29.0559i	−0.657837	−	0.984522i
$872$		0			0
$873$	84.5723	+	56.5094i	2.86234	+	1.91255i
$874$		0			0
$875$	18.7214	+	1.84390i	0.632900	+	0.0623352i
$876$		0			0
$877$	−12.9341	+	42.6379i	−0.436752	+	1.43978i	0.412095	+	0.911141i	$0.364797\pi$
$877$	−12.9341	+	42.6379i	−0.436752	+	1.43978i	−0.848847	+	0.528638i	$0.822703\pi$
$878$		0			0
$879$	22.1547	+	53.4863i	0.747261	+	1.80405i
$880$		0			0
$881$	17.8344	−	43.0560i	0.600856	−	1.45059i	−0.271846	−	0.962341i	$-0.587634\pi$
$881$	17.8344	−	43.0560i	0.600856	−	1.45059i	0.872702	−	0.488254i	$-0.162366\pi$
$882$		0			0
$883$	−5.94142	−	11.1156i	−0.199945	−	0.374070i	0.761888	−	0.647709i	$-0.224273\pi$
$883$	−5.94142	−	11.1156i	−0.199945	−	0.374070i	−0.961833	+	0.273639i	$0.911773\pi$
$884$		0			0
$885$	−17.1688	−	20.9203i	−0.577123	−	0.703227i
$886$		0			0
$887$	−21.5169	+	4.27998i	−0.722467	+	0.143708i	−0.542610	−	0.839985i	$-0.682564\pi$
$887$	−21.5169	+	4.27998i	−0.722467	+	0.143708i	−0.179858	+	0.983693i	$0.557564\pi$
$888$		0			0
$889$	−1.13303	+	5.69615i	−0.0380008	+	0.191043i
$890$		0			0
$891$	−110.063	−	58.8297i	−3.68724	−	1.97087i
$892$		0			0
$893$	0.128337	+	1.30303i	0.00429465	+	0.0436043i
$894$		0			0
$895$	−7.69403			−0.257183
$896$		0			0
$897$	4.69912			0.156899
$898$		0			0
$899$	−0.918658	−	9.32729i	−0.0306390	−	0.311083i
$900$		0			0
$901$	4.95509	+	2.64855i	0.165078	+	0.0882361i
$902$		0			0
$903$	−3.30124	+	16.5965i	−0.109858	+	0.552296i
$904$		0			0
$905$	16.8401	−	3.34971i	0.559785	−	0.111348i
$906$		0			0
$907$	12.2027	+	14.8690i	0.405183	+	0.493717i	0.935125	−	0.354317i	$-0.115287\pi$
$907$	12.2027	+	14.8690i	0.405183	+	0.493717i	−0.529943	+	0.848033i	$0.677787\pi$
$908$		0			0
$909$	46.2724	+	86.5696i	1.53476	+	2.87133i
$910$		0			0
$911$	−2.85891	+	6.90203i	−0.0947201	+	0.228674i	−0.964137	−	0.265404i	$-0.914495\pi$
$911$	−2.85891	+	6.90203i	−0.0947201	+	0.228674i	0.869417	+	0.494079i	$0.164495\pi$
$912$		0			0
$913$	−1.71095	−	4.13060i	−0.0566242	−	0.136703i
$914$		0			0
$915$	6.20149	−	20.4436i	0.205015	−	0.675844i
$916$		0			0
$917$	4.60289	+	0.453346i	0.152001	+	0.0149708i
$918$		0			0
$919$	−5.42912	−	3.62762i	−0.179090	−	0.119664i	0.462794	−	0.886466i	$-0.346847\pi$
$919$	−5.42912	−	3.62762i	−0.179090	−	0.119664i	−0.641884	+	0.766802i	$0.721847\pi$
$920$		0			0
$921$	−59.6057	−	89.2062i	−1.96407	−	2.93944i
$922$		0			0
$923$	−18.9566	−	62.4914i	−0.623963	−	2.05693i
$924$		0			0
$925$	−14.7961	−	12.1429i	−0.486494	−	0.399256i
$926$		0			0
$927$	−0.291692	−	0.291692i	−0.00958043	−	0.00958043i
$928$		0			0
$929$	21.4804	−	21.4804i	0.704749	−	0.704749i	−0.260677	−	0.965426i	$-0.583946\pi$
$929$	21.4804	−	21.4804i	0.704749	−	0.704749i	0.965426	+	0.260677i	$0.0839457\pi$
$930$		0			0
$931$	1.31881	−	1.60698i	0.0432223	−	0.0526665i
$932$		0			0
$933$	23.0633	−	6.99619i	0.755060	−	0.229045i
$934$		0			0
$935$	−6.86478	+	4.58690i	−0.224502	+	0.150008i
$936$		0			0
$937$	−24.0018	+	35.9212i	−0.784105	+	1.17350i	0.197073	+	0.980389i	$0.436856\pi$
$937$	−24.0018	+	35.9212i	−0.784105	+	1.17350i	−0.981178	+	0.193107i	$0.938144\pi$
$938$		0			0
$939$	−2.15306	+	21.8604i	−0.0702625	+	0.713387i
$940$		0			0
$941$	41.6972	+	12.6487i	1.35929	+	0.412336i	0.883998	−	0.467491i	$-0.154842\pi$
$941$	41.6972	+	12.6487i	1.35929	+	0.412336i	0.475293	+	0.879827i	$0.342342\pi$
$942$		0			0
$943$	−1.51402	+	0.627129i	−0.0493034	+	0.0204221i
$944$		0			0
$945$	−35.7039	−	14.7890i	−1.16145	−	0.481087i
$946$		0			0
$947$	−40.3215	+	21.5523i	−1.31027	+	0.700355i	−0.970716	−	0.240230i	$-0.922777\pi$
$947$	−40.3215	+	21.5523i	−1.31027	+	0.700355i	−0.339557	+	0.940586i	$0.610277\pi$
$948$		0			0
$949$	32.7356	−	26.8654i	1.06264	−	0.872089i
$950$		0			0
$951$	13.1332	+	66.0250i	0.425873	+	2.14101i
$952$		0			0
$953$	−23.1834	−	4.61146i	−0.750983	−	0.149380i	−0.195265	−	0.980751i	$-0.562557\pi$
$953$	−23.1834	−	4.61146i	−0.750983	−	0.149380i	−0.555718	+	0.831371i	$0.687557\pi$
$954$		0			0
$955$	−21.7651	+	40.7196i	−0.704301	+	1.31765i
$956$		0			0
$957$	−36.5129	+	3.59620i	−1.18029	+	0.116249i
$958$		0			0
$959$		−	22.8339i		−	0.737344i
$960$		0			0
$961$		−	13.6304i		−	0.439690i
$962$		0			0
$963$	66.2797	−	6.52798i	2.13583	−	0.210361i
$964$		0			0
$965$	−1.27746	+	2.38997i	−0.0411230	+	0.0769358i
$966$		0			0
$967$	−26.9786	−	5.36638i	−0.867574	−	0.172571i	−0.258815	−	0.965927i	$-0.583332\pi$
$967$	−26.9786	−	5.36638i	−0.867574	−	0.172571i	−0.608758	+	0.793356i	$0.708332\pi$
$968$		0			0
$969$	0.276698	+	1.39106i	0.00888883	+	0.0446872i
$970$		0			0
$971$	−7.60083	+	6.23784i	−0.243922	+	0.200182i	−0.748409	−	0.663238i	$-0.769182\pi$
$971$	−7.60083	+	6.23784i	−0.243922	+	0.200182i	0.504487	+	0.863420i	$0.331682\pi$
$972$		0			0
$973$	23.6447	−	12.6384i	0.758015	−	0.405167i
$974$		0			0
$975$	32.1839	+	13.3310i	1.03071	+	0.426934i
$976$		0			0
$977$	−20.2214	+	8.37600i	−0.646941	+	0.267972i	−0.681932	−	0.731416i	$-0.738860\pi$
$977$	−20.2214	+	8.37600i	−0.646941	+	0.267972i	0.0349904	+	0.999388i	$0.488860\pi$
$978$		0			0
$979$	16.8207	+	5.10250i	0.537591	+	0.163077i
$980$		0			0
$981$	−8.38058	+	85.0894i	−0.267571	+	2.71670i
$982$		0			0
$983$	−20.6198	+	30.8596i	−0.657668	+	0.984270i	0.341349	+	0.939937i	$0.389116\pi$
$983$	−20.6198	+	30.8596i	−0.657668	+	0.984270i	−0.999017	+	0.0443331i	$0.985884\pi$
$984$		0			0
$985$	−14.8447	+	9.91890i	−0.472991	+	0.316043i
$986$		0			0
$987$	−13.9169	+	4.22165i	−0.442980	+	0.134376i
$988$		0			0
$989$	0.604308	−	0.736351i	0.0192159	−	0.0234146i
$990$		0			0
$991$	19.9838	−	19.9838i	0.634807	−	0.634807i	−0.314463	−	0.949270i	$-0.601824\pi$
$991$	19.9838	−	19.9838i	0.634807	−	0.634807i	0.949270	+	0.314463i	$0.101824\pi$
$992$		0			0
$993$	60.9380	+	60.9380i	1.93381	+	1.93381i
$994$		0			0
$995$	4.02058	+	3.29960i	0.127461	+	0.104604i
$996$		0			0
$997$	3.73559	+	12.3146i	0.118307	+	0.390007i	0.996015	−	0.0891902i	$-0.0284279\pi$
$997$	3.73559	+	12.3146i	0.118307	+	0.390007i	−0.877707	+	0.479197i	$0.840928\pi$
$998$		0			0
$999$	73.7456	+	110.368i	2.33321	+	3.49189i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	512.2.k.a.49.1		240
4.3	odd	2		128.2.k.a.53.1	yes	240
128.29	even	32	inner	512.2.k.a.209.1		240
128.99	odd	32		128.2.k.a.29.1	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
128.2.k.a.29.1	✓	240	128.99	odd	32
128.2.k.a.53.1	yes	240	4.3	odd	2
512.2.k.a.49.1		240	1.1	even	1	trivial
512.2.k.a.209.1		240	128.29	even	32	inner

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:	\( N \)	\(=\)	\( 512 = 2^{9} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	512.k (of order \(32\), degree \(16\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.317663 - 3.22529i) q^{3} +(1.50066 + 0.802122i) q^{5} +(-0.303583 + 1.52621i) q^{7} +(-7.35922 + 1.46384i) q^{9} +O(q^{10})\)	\(q+(-0.317663 - 3.22529i) q^{3} +(1.50066 + 0.802122i) q^{5} +(-0.303583 + 1.52621i) q^{7} +(-7.35922 + 1.46384i) q^{9} +(-3.19359 - 3.89140i) q^{11} +(-2.40755 - 4.50420i) q^{13} +(2.11037 - 5.09488i) q^{15} +(-0.368847 - 0.890474i) q^{17} +(0.131803 - 0.434495i) q^{19} +(5.01891 + 0.494320i) q^{21} +(-0.236053 - 0.157726i) q^{23} +(-1.16926 - 1.74992i) q^{25} +(4.23671 + 13.9666i) q^{27} +(1.73837 + 1.42664i) q^{29} +(-2.94700 - 2.94700i) q^{31} +(-11.5364 + 11.5364i) q^{33} +(-1.67978 + 2.04682i) q^{35} +(8.70317 - 2.64008i) q^{37} +(-13.7626 + 9.19585i) q^{39} +(3.20695 - 4.79954i) q^{41} +(-0.328880 + 3.33918i) q^{43} +(-12.2179 - 3.70626i) q^{45} +(-2.66420 + 1.10355i) q^{47} +(4.22999 + 1.75212i) q^{49} +(-2.75487 + 1.47251i) q^{51} +(-4.50611 + 3.69807i) q^{53} +(-1.67113 - 8.40133i) q^{55} +(-1.44324 - 0.287078i) q^{57} +(2.31339 - 4.32806i) q^{59} +(3.85529 - 0.379713i) q^{61} -11.6761i q^{63} -8.69044i q^{65} +(6.80932 - 0.670660i) q^{67} +(-0.433726 + 0.811444i) q^{69} +(12.5407 + 2.49450i) q^{71} +(1.61764 + 8.13245i) q^{73} +(-5.27255 + 4.32707i) q^{75} +(6.90862 - 3.69274i) q^{77} +(8.12045 + 3.36360i) q^{79} +(22.9037 - 9.48701i) q^{81} +(0.849890 + 0.257811i) q^{83} +(0.160754 - 1.63216i) q^{85} +(4.04912 - 6.05994i) q^{87} +(-2.90325 + 1.93989i) q^{89} +(7.60526 - 2.30703i) q^{91} +(-8.56877 + 10.4411i) q^{93} +(0.546309 - 0.546309i) q^{95} +(-9.58537 - 9.58537i) q^{97} +(29.1987 + 23.9628i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 16 q^{3} - 16 q^{5} + 16 q^{7} - 16 q^{9}+O(q^{10}) \) 240 * q + 16 * q^3 - 16 * q^5 + 16 * q^7 - 16 * q^9	\( 240 q + 16 q^{3} - 16 q^{5} + 16 q^{7} - 16 q^{9} + 16 q^{11} - 16 q^{13} + 16 q^{15} - 16 q^{17} + 16 q^{19} - 16 q^{21} + 16 q^{23} - 16 q^{25} + 16 q^{27} - 16 q^{29} + 16 q^{31} - 16 q^{33} + 16 q^{35} - 16 q^{37} + 16 q^{39} - 16 q^{41} + 16 q^{43} - 16 q^{45} + 16 q^{47} - 16 q^{49} + 16 q^{51} - 16 q^{53} + 16 q^{55} - 16 q^{57} + 16 q^{59} - 16 q^{61} + 16 q^{67} - 16 q^{69} + 16 q^{71} - 16 q^{73} + 16 q^{75} - 16 q^{77} + 16 q^{79} - 16 q^{81} + 16 q^{83} - 16 q^{85} + 16 q^{87} - 16 q^{89} + 16 q^{91} - 16 q^{93} + 16 q^{95} - 16 q^{97} + 16 q^{99}+O(q^{100}) \) 240 * q + 16 * q^3 - 16 * q^5 + 16 * q^7 - 16 * q^9 + 16 * q^11 - 16 * q^13 + 16 * q^15 - 16 * q^17 + 16 * q^19 - 16 * q^21 + 16 * q^23 - 16 * q^25 + 16 * q^27 - 16 * q^29 + 16 * q^31 - 16 * q^33 + 16 * q^35 - 16 * q^37 + 16 * q^39 - 16 * q^41 + 16 * q^43 - 16 * q^45 + 16 * q^47 - 16 * q^49 + 16 * q^51 - 16 * q^53 + 16 * q^55 - 16 * q^57 + 16 * q^59 - 16 * q^61 + 16 * q^67 - 16 * q^69 + 16 * q^71 - 16 * q^73 + 16 * q^75 - 16 * q^77 + 16 * q^79 - 16 * q^81 + 16 * q^83 - 16 * q^85 + 16 * q^87 - 16 * q^89 + 16 * q^91 - 16 * q^93 + 16 * q^95 - 16 * q^97 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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