LMFDB - Embedded newform 512.2.k.a.497.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [512,2,Mod(17,512)] 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("512.17"); S:= CuspForms(chi, 2); N := Newforms(S);

sage: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")

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:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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			497.4
Character	$\chi$	$=$	512.497
Dual form			512.2.k.a.273.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.68175 + 0.898916i) q^{3} +(-1.56899 - 1.91182i) q^{5} +(-3.63941 + 2.43178i) q^{7} +(0.353534 - 0.529101i) q^{9} +(4.39407 - 1.33293i) q^{11} +(1.74149 + 1.42920i) q^{13} +(4.35722 + 1.80482i) q^{15} +(3.75158 - 1.55396i) q^{17} +(-0.804629 - 8.16953i) q^{19} +(3.93463 - 7.36118i) q^{21} +(1.74729 - 0.347558i) q^{23} +(-0.217872 + 1.09532i) q^{25} +(0.441793 - 4.48560i) q^{27} +(0.598530 - 1.97309i) q^{29} +(3.81742 + 3.81742i) q^{31} +(-6.19155 + 6.19155i) q^{33} +(10.3593 + 3.14247i) q^{35} +(-1.04034 - 0.102465i) q^{37} +(-4.21349 - 0.838114i) q^{39} +(0.711436 + 3.57663i) q^{41} +(0.793119 + 0.423931i) q^{43} +(-1.56624 + 0.154261i) q^{45} +(-1.43424 - 3.46257i) q^{47} +(4.65300 - 11.2333i) q^{49} +(-4.91236 + 5.98573i) q^{51} +(1.79456 + 5.91588i) q^{53} +(-9.44255 - 6.30931i) q^{55} +(8.69691 + 13.0158i) q^{57} +(4.26007 - 3.49615i) q^{59} +(-2.89271 - 5.41187i) q^{61} +2.78534i q^{63} -5.57181i q^{65} +(2.61401 + 4.89047i) q^{67} +(-2.62609 + 2.15518i) q^{69} +(-0.916693 - 1.37193i) q^{71} +(6.52734 + 4.36143i) q^{73} +(-0.618190 - 2.03790i) q^{75} +(-12.7504 + 15.5365i) q^{77} +(4.05951 - 9.80052i) q^{79} +(4.01974 + 9.70452i) q^{81} +(0.630660 - 0.0621146i) q^{83} +(-8.85708 - 4.73421i) q^{85} +(0.767061 + 3.85628i) q^{87} +(3.26555 + 0.649558i) q^{89} +(-9.81350 - 0.966545i) q^{91} +(-9.85149 - 2.98842i) q^{93} +(-14.3562 + 14.3562i) q^{95} +(-12.6095 - 12.6095i) q^{97} +(0.848200 - 2.79614i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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}+ \cdots + 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

Character values

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

$n$	$5$	$511$
$\chi(n)$	$e\left(\frac{9}{32}\right)$	$1$

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
$3$	−1.68175	+	0.898916i	−0.970961	+	0.518989i	−0.879025	−	0.476776i	$-0.841805\pi$
$3$	−1.68175	+	0.898916i	−0.970961	+	0.518989i	−0.0919358	+	0.995765i	$0.529305\pi$
$4$		0			0
$5$	−1.56899	−	1.91182i	−0.701673	−	0.854991i	0.293207	−	0.956049i	$-0.405277\pi$
$5$	−1.56899	−	1.91182i	−0.701673	−	0.854991i	−0.994881	+	0.101058i	$0.967777\pi$
$6$		0			0
$7$	−3.63941	+	2.43178i	−1.37557	+	0.919126i	−0.999971	−	0.00765647i	$-0.997563\pi$
$7$	−3.63941	+	2.43178i	−1.37557	+	0.919126i	−0.375599	+	0.926782i	$0.622563\pi$
$8$		0			0
$9$	0.353534	−	0.529101i	0.117845	−	0.176367i
$10$		0			0
$11$	4.39407	−	1.33293i	1.32486	−	0.401892i	0.452941	−	0.891541i	$-0.350375\pi$
$11$	4.39407	−	1.33293i	1.32486	−	0.401892i	0.871920	+	0.489648i	$0.162875\pi$
$12$		0			0
$13$	1.74149	+	1.42920i	0.483002	+	0.396389i	0.844140	−	0.536123i	$-0.180112\pi$
$13$	1.74149	+	1.42920i	0.483002	+	0.396389i	−0.361138	+	0.932512i	$0.617612\pi$
$14$		0			0
$15$	4.35722	+	1.80482i	1.12503	+	0.466002i
$16$		0			0
$17$	3.75158	−	1.55396i	0.909893	−	0.376890i	0.121877	−	0.992545i	$-0.461109\pi$
$17$	3.75158	−	1.55396i	0.909893	−	0.376890i	0.788016	+	0.615655i	$0.211109\pi$
$18$		0			0
$19$	−0.804629	−	8.16953i	−0.184594	−	1.87422i	−0.427288	−	0.904116i	$-0.640531\pi$
$19$	−0.804629	−	8.16953i	−0.184594	−	1.87422i	0.242693	−	0.970103i	$-0.421969\pi$
$20$		0			0
$21$	3.93463	−	7.36118i	0.858607	−	1.60634i
$22$		0			0
$23$	1.74729	−	0.347558i	0.364336	−	0.0724709i	−0.00952772	−	0.999955i	$-0.503033\pi$
$23$	1.74729	−	0.347558i	0.364336	−	0.0724709i	0.373864	+	0.927484i	$0.378033\pi$
$24$		0			0
$25$	−0.217872	+	1.09532i	−0.0435744	+	0.219063i
$26$		0			0
$27$	0.441793	−	4.48560i	0.0850231	−	0.863254i
$28$		0			0
$29$	0.598530	−	1.97309i	0.111144	−	0.366393i	−0.883669	−	0.468112i	$-0.844934\pi$
$29$	0.598530	−	1.97309i	0.111144	−	0.366393i	0.994813	+	0.101719i	$0.0324343\pi$
$30$		0			0
$31$	3.81742	+	3.81742i	0.685628	+	0.685628i	0.961263	−	0.275634i	$-0.0888879\pi$
$31$	3.81742	+	3.81742i	0.685628	+	0.685628i	−0.275634	+	0.961263i	$0.588888\pi$
$32$		0			0
$33$	−6.19155	+	6.19155i	−1.07781	+	1.07781i
$34$		0			0
$35$	10.3593	+	3.14247i	1.75104	+	0.531174i
$36$		0			0
$37$	−1.04034	−	0.102465i	−0.171031	−	0.0168451i	0.0121392	−	0.999926i	$-0.496136\pi$
$37$	−1.04034	−	0.102465i	−0.171031	−	0.0168451i	−0.183170	+	0.983081i	$0.558636\pi$
$38$		0			0
$39$	−4.21349	−	0.838114i	−0.674698	−	0.134206i
$40$		0			0
$41$	0.711436	+	3.57663i	0.111108	+	0.558576i	0.995734	+	0.0922746i	$0.0294138\pi$
$41$	0.711436	+	3.57663i	0.111108	+	0.558576i	−0.884626	+	0.466301i	$0.845586\pi$
$42$		0			0
$43$	0.793119	+	0.423931i	0.120950	+	0.0646489i	0.530762	−	0.847521i	$-0.321906\pi$
$43$	0.793119	+	0.423931i	0.120950	+	0.0646489i	−0.409812	+	0.912170i	$0.634406\pi$
$44$		0			0
$45$	−1.56624	+	0.154261i	−0.233481	+	0.0229958i
$46$		0			0
$47$	−1.43424	−	3.46257i	−0.209206	−	0.505067i	0.784093	−	0.620644i	$-0.213129\pi$
$47$	−1.43424	−	3.46257i	−0.209206	−	0.505067i	−0.993299	+	0.115576i	$0.963129\pi$
$48$		0			0
$49$	4.65300	−	11.2333i	0.664715	−	1.60476i
$50$		0			0
$51$	−4.91236	+	5.98573i	−0.687869	+	0.838170i
$52$		0			0
$53$	1.79456	+	5.91588i	0.246502	+	0.812608i	0.989653	+	0.143484i	$0.0458306\pi$
$53$	1.79456	+	5.91588i	0.246502	+	0.812608i	−0.743151	+	0.669124i	$0.766669\pi$
$54$		0			0
$55$	−9.44255	−	6.30931i	−1.27323	−	0.850747i
$56$		0			0
$57$	8.69691	+	13.0158i	1.15193	+	1.72399i
$58$		0			0
$59$	4.26007	−	3.49615i	0.554614	−	0.455160i	−0.314861	−	0.949138i	$-0.601958\pi$
$59$	4.26007	−	3.49615i	0.554614	−	0.455160i	0.869474	+	0.493978i	$0.164458\pi$
$60$		0			0
$61$	−2.89271	−	5.41187i	−0.370373	−	0.692920i	0.625832	−	0.779958i	$-0.284760\pi$
$61$	−2.89271	−	5.41187i	−0.370373	−	0.692920i	−0.996205	+	0.0870386i	$0.972260\pi$
$62$		0			0
$63$			2.78534i			0.350919i
$64$		0			0
$65$		−	5.57181i		−	0.691098i
$66$		0			0
$67$	2.61401	+	4.89047i	0.319352	+	0.597466i	0.989461	−	0.144796i	$-0.0462527\pi$
$67$	2.61401	+	4.89047i	0.319352	+	0.597466i	−0.670109	+	0.742263i	$0.733753\pi$
$68$		0			0
$69$	−2.62609	+	2.15518i	−0.316144	+	0.259453i
$70$		0			0
$71$	−0.916693	−	1.37193i	−0.108791	−	0.162818i	0.773079	−	0.634310i	$-0.218716\pi$
$71$	−0.916693	−	1.37193i	−0.108791	−	0.162818i	−0.881870	+	0.471492i	$0.843716\pi$
$72$		0			0
$73$	6.52734	+	4.36143i	0.763967	+	0.510467i	0.875455	−	0.483299i	$-0.160562\pi$
$73$	6.52734	+	4.36143i	0.763967	+	0.510467i	−0.111488	+	0.993766i	$0.535562\pi$
$74$		0			0
$75$	−0.618190	−	2.03790i	−0.0713825	−	0.235316i
$76$		0			0
$77$	−12.7504	+	15.5365i	−1.45305	+	1.77054i
$78$		0			0
$79$	4.05951	−	9.80052i	0.456730	−	1.10264i	−0.512983	−	0.858399i	$-0.671460\pi$
$79$	4.05951	−	9.80052i	0.456730	−	1.10264i	0.969713	−	0.244246i	$-0.0785403\pi$
$80$		0			0
$81$	4.01974	+	9.70452i	0.446638	+	1.07828i
$82$		0			0
$83$	0.630660	−	0.0621146i	0.0692240	−	0.00681796i	−0.0633459	−	0.997992i	$-0.520177\pi$
$83$	0.630660	−	0.0621146i	0.0692240	−	0.00681796i	0.132570	+	0.991174i	$0.457677\pi$
$84$		0			0
$85$	−8.85708	−	4.73421i	−0.960685	−	0.513497i
$86$		0			0
$87$	0.767061	+	3.85628i	0.0822376	+	0.413436i
$88$		0			0
$89$	3.26555	+	0.649558i	0.346148	+	0.0688531i	0.365103	−	0.930967i	$-0.381034\pi$
$89$	3.26555	+	0.649558i	0.346148	+	0.0688531i	−0.0189549	+	0.999820i	$0.506034\pi$
$90$		0			0
$91$	−9.81350	−	0.966545i	−1.02873	−	0.101321i
$92$		0			0
$93$	−9.85149	−	2.98842i	−1.02155	−	0.309884i
$94$		0			0
$95$	−14.3562	+	14.3562i	−1.47292	+	1.47292i
$96$		0			0
$97$	−12.6095	−	12.6095i	−1.28030	−	1.28030i	−0.940498	−	0.339800i	$-0.889641\pi$
$97$	−12.6095	−	12.6095i	−1.28030	−	1.28030i	−0.339800	−	0.940498i	$-0.610359\pi$
$98$		0			0
$99$	0.848200	−	2.79614i	0.0852473	−	0.281023i
$100$		0			0
$101$	1.65754	−	16.8293i	0.164931	−	1.67458i	−0.455439	−	0.890267i	$-0.650518\pi$
$101$	1.65754	−	16.8293i	0.164931	−	1.67458i	0.620371	−	0.784309i	$-0.286982\pi$
$102$		0			0
$103$	0.751419	−	3.77764i	0.0740395	−	0.372222i	−0.925946	−	0.377657i	$-0.876730\pi$
$103$	0.751419	−	3.77764i	0.0740395	−	0.372222i	0.999985	+	0.00543482i	$0.00172997\pi$
$104$		0			0
$105$	−20.2466	+	4.02731i	−1.97587	+	0.393025i
$106$		0			0
$107$	−4.88476	+	9.13875i	−0.472228	+	0.883476i	0.527203	+	0.849739i	$0.323241\pi$
$107$	−4.88476	+	9.13875i	−0.472228	+	0.883476i	−0.999431	+	0.0337368i	$0.989259\pi$
$108$		0			0
$109$	−0.371358	−	3.77046i	−0.0355697	−	0.361145i	−0.996450	−	0.0841823i	$-0.973172\pi$
$109$	−0.371358	−	3.77046i	−0.0355697	−	0.361145i	0.960881	−	0.276963i	$-0.0893278\pi$
$110$		0			0
$111$	1.84170	−	0.762858i	0.174807	−	0.0724073i
$112$		0			0
$113$	0.504551	+	0.208992i	0.0474642	+	0.0196603i	0.406289	−	0.913745i	$-0.366823\pi$
$113$	0.504551	+	0.208992i	0.0474642	+	0.0196603i	−0.358825	+	0.933405i	$0.616823\pi$
$114$		0			0
$115$	−3.40595	−	2.79519i	−0.317607	−	0.260653i
$116$		0			0
$117$	1.37187	−	0.416152i	0.126829	−	0.0384732i
$118$		0			0
$119$	−9.87469	+	14.7785i	−0.905211	+	1.35474i
$120$		0			0
$121$	8.38497	−	5.60265i	0.762270	−	0.509332i
$122$		0			0
$123$	−4.41155	−	5.37549i	−0.397776	−	0.484692i
$124$		0			0
$125$	−8.47000	+	4.52731i	−0.757580	+	0.404935i
$126$		0			0
$127$	7.63294			0.677314			0.338657	−	0.940910i	$-0.390027\pi$
$127$	7.63294			0.677314			0.338657	+	0.940910i	$0.390027\pi$
$128$		0			0
$129$	−1.71491			−0.150989
$130$		0			0
$131$	−9.61705	+	5.14042i	−0.840246	+	0.449121i	−0.834595	−	0.550863i	$-0.814299\pi$
$131$	−9.61705	+	5.14042i	−0.840246	+	0.449121i	−0.00565023	+	0.999984i	$0.501799\pi$
$132$		0			0
$133$	22.7949	+	27.7756i	1.97657	+	2.40845i
$134$		0			0
$135$	−9.26882	+	6.19323i	−0.797733	+	0.533028i
$136$		0			0
$137$	4.58963	−	6.86886i	0.392118	−	0.586846i	−0.581916	−	0.813249i	$-0.697697\pi$
$137$	4.58963	−	6.86886i	0.392118	−	0.586846i	0.974034	+	0.226403i	$0.0726966\pi$
$138$		0			0
$139$	12.1714	−	3.69214i	1.03236	−	0.313164i	0.271748	−	0.962368i	$-0.412398\pi$
$139$	12.1714	−	3.69214i	1.03236	−	0.313164i	0.760614	+	0.649205i	$0.224898\pi$
$140$		0			0
$141$	5.52460	+	4.53392i	0.465255	+	0.381825i
$142$		0			0
$143$	9.55723	+	3.95874i	0.799216	+	0.331046i
$144$		0			0
$145$	−4.71127	+	1.95147i	−0.391250	+	0.162061i
$146$		0			0
$147$	2.27263	+	23.0744i	0.187443	+	1.90314i
$148$		0			0
$149$	0.204895	−	0.383332i	0.0167857	−	0.0314037i	−0.873389	−	0.487024i	$-0.838082\pi$
$149$	0.204895	−	0.383332i	0.0167857	−	0.0314037i	0.890174	+	0.455620i	$0.150582\pi$
$150$		0			0
$151$	15.1901	−	3.02150i	1.23615	−	0.245886i	0.466599	−	0.884469i	$-0.345479\pi$
$151$	15.1901	−	3.02150i	1.23615	−	0.245886i	0.769553	+	0.638583i	$0.220479\pi$
$152$		0			0
$153$	0.504113	−	2.53435i	0.0407551	−	0.204890i
$154$		0			0
$155$	1.30872	−	13.2877i	0.105119	−	1.06729i
$156$		0			0
$157$	4.98516	−	16.4339i	0.397859	−	1.31157i	−0.497980	−	0.867188i	$-0.665925\pi$
$157$	4.98516	−	16.4339i	0.397859	−	1.31157i	0.895839	−	0.444378i	$-0.146575\pi$
$158$		0			0
$159$	−8.33589	−	8.33589i	−0.661079	−	0.661079i
$160$		0			0
$161$	−5.51394	+	5.51394i	−0.434559	+	0.434559i
$162$		0			0
$163$	−5.85090	−	1.77485i	−0.458278	−	0.139017i	0.0527011	−	0.998610i	$-0.483217\pi$
$163$	−5.85090	−	1.77485i	−0.458278	−	0.139017i	−0.510979	+	0.859593i	$0.670717\pi$
$164$		0			0
$165$	21.5516	+	2.12265i	1.67779	+	0.165248i
$166$		0			0
$167$	15.8524	+	3.15325i	1.22670	+	0.244006i	0.765585	−	0.643335i	$-0.222450\pi$
$167$	15.8524	+	3.15325i	1.22670	+	0.244006i	0.461114	+	0.887341i	$0.347450\pi$
$168$		0			0
$169$	−1.54601	−	7.77233i	−0.118924	−	0.597872i
$170$		0			0
$171$	−4.60697	−	2.46248i	−0.352304	−	0.188310i
$172$		0			0
$173$	−6.40529	+	0.630866i	−0.486985	+	0.0479639i	−0.338531	−	0.940955i	$-0.609930\pi$
$173$	−6.40529	+	0.630866i	−0.486985	+	0.0479639i	−0.148455	+	0.988919i	$0.547430\pi$
$174$		0			0
$175$	−1.87064	−	4.51613i	−0.141407	−	0.341387i
$176$		0			0
$177$	−4.02164	+	9.70910i	−0.302285	+	0.729781i
$178$		0			0
$179$	−8.71765	+	10.6225i	−0.651588	+	0.793962i	−0.989082	−	0.147365i	$-0.952921\pi$
$179$	−8.71765	+	10.6225i	−0.651588	+	0.793962i	0.337494	+	0.941328i	$0.390421\pi$
$180$		0			0
$181$	−4.06412	−	13.3976i	−0.302083	−	0.995836i	−0.968240	−	0.250024i	$-0.919562\pi$
$181$	−4.06412	−	13.3976i	−0.302083	−	0.995836i	0.666156	−	0.745812i	$-0.267938\pi$
$182$		0			0
$183$	9.72964	+	6.50114i	0.719236	+	0.480578i
$184$		0			0
$185$	1.43639	+	2.14971i	0.105605	+	0.158050i
$186$		0			0
$187$	14.4134	−	11.8288i	1.05401	−	0.865006i
$188$		0			0
$189$	9.30012	+	17.3993i	0.676484	+	1.26561i
$190$		0			0
$191$			3.80481i			0.275307i	0.990480	+	0.137653i	$0.0439560\pi$
$191$			3.80481i			0.275307i	−0.990480	+	0.137653i	$0.956044\pi$
$192$		0			0
$193$			18.7673i			1.35090i	0.737405	+	0.675451i	$0.236051\pi$
$193$			18.7673i			1.35090i	−0.737405	+	0.675451i	$0.763949\pi$
$194$		0			0
$195$	5.00859	+	9.37041i	0.358673	+	0.671029i
$196$		0			0
$197$	9.57883	−	7.86115i	0.682464	−	0.560083i	−0.228006	−	0.973660i	$-0.573221\pi$
$197$	9.57883	−	7.86115i	0.682464	−	0.560083i	0.910469	+	0.413576i	$0.135721\pi$
$198$		0			0
$199$	−11.5313	−	17.2578i	−0.817434	−	1.22338i	−0.971904	−	0.235379i	$-0.924367\pi$
$199$	−11.5313	−	17.2578i	−0.817434	−	1.22338i	0.154470	−	0.987997i	$-0.450633\pi$
$200$		0			0
$201$	−8.79224	−	5.87479i	−0.620157	−	0.414376i
$202$		0			0
$203$	2.61982	+	8.63638i	0.183875	+	0.606155i
$204$		0			0
$205$	5.72163	−	6.97183i	0.399616	−	0.486934i
$206$		0			0
$207$	0.433834	−	1.04737i	0.0301536	−	0.0727972i
$208$		0			0
$209$	−14.4250	−	34.8250i	−0.997796	−	2.40889i
$210$		0			0
$211$	−14.5267	+	1.43075i	−1.00006	+	0.0984970i	−0.584775	−	0.811196i	$-0.698817\pi$
$211$	−14.5267	+	1.43075i	−1.00006	+	0.0984970i	−0.415282	+	0.909693i	$0.636317\pi$
$212$		0			0
$213$	2.77490	+	1.48322i	0.190133	+	0.101628i
$214$		0			0
$215$	−0.433916	−	2.18144i	−0.0295928	−	0.148773i
$216$		0			0
$217$	−23.1763	−	4.61005i	−1.57331	−	0.312950i
$218$		0			0
$219$	−14.8979	−	1.46732i	−1.00671	−	0.0991522i
$220$		0			0
$221$	8.75426	+	2.65558i	0.588875	+	0.178633i
$222$		0			0
$223$	−2.53055	+	2.53055i	−0.169458	+	0.169458i	−0.786741	−	0.617283i	$-0.788233\pi$
$223$	−2.53055	+	2.53055i	−0.169458	+	0.169458i	0.617283	+	0.786741i	$0.288233\pi$
$224$		0			0
$225$	0.502508	+	0.502508i	0.0335005	+	0.0335005i
$226$		0			0
$227$	6.88643	−	22.7015i	0.457068	−	1.50675i	−0.361516	−	0.932366i	$-0.617741\pi$
$227$	6.88643	−	22.7015i	0.457068	−	1.50675i	0.818584	−	0.574386i	$-0.194759\pi$
$228$		0			0
$229$	−0.692242	+	7.02845i	−0.0457446	+	0.464453i	0.944838	+	0.327538i	$0.106219\pi$
$229$	−0.692242	+	7.02845i	−0.0457446	+	0.464453i	−0.990583	+	0.136915i	$0.956281\pi$
$230$		0			0
$231$	7.47713	−	37.5901i	0.491959	−	2.47325i
$232$		0			0
$233$	20.0714	−	3.99244i	1.31492	−	0.261554i	0.512692	−	0.858573i	$-0.328648\pi$
$233$	20.0714	−	3.99244i	1.31492	−	0.261554i	0.802227	+	0.597019i	$0.203648\pi$
$234$		0			0
$235$	−4.36949	+	8.17474i	−0.285034	+	0.533261i
$236$		0			0
$237$	1.98275	+	20.1312i	0.128794	+	1.30766i
$238$		0			0
$239$	20.6777	−	8.56497i	1.33753	−	0.554022i	0.404734	−	0.914435i	$-0.367364\pi$
$239$	20.6777	−	8.56497i	1.33753	−	0.554022i	0.932793	+	0.360413i	$0.117364\pi$
$240$		0			0
$241$	7.83955	+	3.24725i	0.504990	+	0.209174i	0.620609	−	0.784120i	$-0.286885\pi$
$241$	7.83955	+	3.24725i	0.504990	+	0.209174i	−0.115620	+	0.993294i	$0.536885\pi$
$242$		0			0
$243$	−5.03120	−	4.12900i	−0.322751	−	0.264875i
$244$		0			0
$245$	−28.7766	+	8.72929i	−1.83847	+	0.557694i
$246$		0			0
$247$	10.2747	−	15.3771i	0.653761	−	0.978422i
$248$		0			0
$249$	−1.00478	+	0.671372i	−0.0636753	+	0.0425465i
$250$		0			0
$251$	2.54202	+	3.09747i	0.160451	+	0.195510i	0.847030	−	0.531545i	$-0.178388\pi$
$251$	2.54202	+	3.09747i	0.160451	+	0.195510i	−0.686579	+	0.727055i	$0.740888\pi$
$252$		0			0
$253$	7.21445	−	3.85621i	0.453569	−	0.242438i
$254$		0			0
$255$	19.1511			1.19929
$256$		0			0
$257$	4.96245			0.309549			0.154775	−	0.987950i	$-0.450535\pi$
$257$	4.96245			0.309549			0.154775	+	0.987950i	$0.450535\pi$
$258$		0			0
$259$	4.03540	−	2.15697i	0.250747	−	0.134027i
$260$		0			0
$261$	−0.832363	−	1.01424i	−0.0515220	−	0.0627797i
$262$		0			0
$263$	−17.6862	+	11.8176i	−1.09058	+	0.728702i	−0.964702	−	0.263344i	$-0.915175\pi$
$263$	−17.6862	+	11.8176i	−1.09058	+	0.728702i	−0.125877	+	0.992046i	$0.540175\pi$
$264$		0			0
$265$	8.49444	−	12.7128i	0.521809	−	0.780943i
$266$		0			0
$267$	−6.07575	+	1.84306i	−0.371830	+	0.112793i
$268$		0			0
$269$	7.90664	+	6.48881i	0.482076	+	0.395630i	0.843802	−	0.536655i	$-0.180312\pi$
$269$	7.90664	+	6.48881i	0.482076	+	0.395630i	−0.361726	+	0.932285i	$0.617812\pi$
$270$		0			0
$271$	−9.12131	−	3.77817i	−0.554080	−	0.229507i	0.0880329	−	0.996118i	$-0.471942\pi$
$271$	−9.12131	−	3.77817i	−0.554080	−	0.229507i	−0.642113	+	0.766610i	$0.721942\pi$
$272$		0			0
$273$	17.3727	−	7.19602i	1.05145	−	0.435523i
$274$		0			0
$275$	0.502631	+	5.10330i	0.0303098	+	0.307741i
$276$		0			0
$277$	−9.37186	+	17.5335i	−0.563101	+	1.05349i	0.425787	+	0.904823i	$0.359997\pi$
$277$	−9.37186	+	17.5335i	−0.563101	+	1.05349i	−0.988888	+	0.148664i	$0.952503\pi$
$278$		0			0
$279$	3.36939	−	0.670213i	0.201720	−	0.0401246i
$280$		0			0
$281$	−4.88244	+	24.5457i	−0.291262	+	1.46427i	0.506991	+	0.861952i	$0.330758\pi$
$281$	−4.88244	+	24.5457i	−0.291262	+	1.46427i	−0.798253	+	0.602323i	$0.794242\pi$
$282$		0			0
$283$	−2.40058	+	24.3735i	−0.142699	+	1.44885i	0.610999	+	0.791631i	$0.290768\pi$
$283$	−2.40058	+	24.3735i	−0.142699	+	1.44885i	−0.753699	+	0.657220i	$0.771732\pi$
$284$		0			0
$285$	11.2386	−	37.0486i	0.665716	−	2.19457i
$286$		0			0
$287$	−11.2868	−	11.2868i	−0.666238	−	0.666238i
$288$		0			0
$289$	−0.361209	+	0.361209i	−0.0212476	+	0.0212476i
$290$		0			0
$291$	32.5409	+	9.87117i	1.90758	+	0.578658i
$292$		0			0
$293$	−29.6021	−	2.91556i	−1.72938	−	0.170329i	−0.816166	−	0.577818i	$-0.803904\pi$
$293$	−29.6021	−	2.91556i	−1.72938	−	0.170329i	−0.913210	+	0.407490i	$0.866404\pi$
$294$		0			0
$295$	−13.3680	−	2.65906i	−0.778315	−	0.154816i
$296$		0			0
$297$	−4.03770	−	20.2989i	−0.234291	−	1.17786i
$298$		0			0
$299$	3.53962	+	1.89197i	0.204702	+	0.109415i
$300$		0			0
$301$	−3.91740	+	0.385830i	−0.225795	+	0.0222389i
$302$		0			0
$303$	12.3405	+	29.7927i	0.708945	+	1.71154i
$304$		0			0
$305$	−5.80790	+	14.0215i	−0.332559	+	0.802869i
$306$		0			0
$307$	18.4314	−	22.4588i	1.05194	−	1.28179i	0.0937673	−	0.995594i	$-0.470109\pi$
$307$	18.4314	−	22.4588i	1.05194	−	1.28179i	0.958171	−	0.286196i	$-0.0923910\pi$
$308$		0			0
$309$	2.13208	+	7.02852i	0.121290	+	0.399839i
$310$		0			0
$311$	21.6465	+	14.4637i	1.22746	+	0.820162i	0.988552	−	0.150881i	$-0.0482110\pi$
$311$	21.6465	+	14.4637i	1.22746	+	0.820162i	0.238907	+	0.971043i	$0.423211\pi$
$312$		0			0
$313$	6.08156	+	9.10170i	0.343750	+	0.514458i	0.962555	−	0.271086i	$-0.0873829\pi$
$313$	6.08156	+	9.10170i	0.343750	+	0.514458i	−0.618805	+	0.785545i	$0.712383\pi$
$314$		0			0
$315$	5.32506	−	4.37016i	0.300033	−	0.246231i
$316$		0			0
$317$	5.23478	+	9.79359i	0.294015	+	0.550063i	0.984947	−	0.172857i	$-0.0552997\pi$
$317$	5.23478	+	9.79359i	0.294015	+	0.550063i	−0.690932	+	0.722920i	$0.742800\pi$
$318$		0			0
$319$		−	9.46768i		−	0.530088i
$320$		0			0
$321$		−	19.7601i		−	1.10290i
$322$		0			0
$323$	−15.7137	−	29.3983i	−0.874336	−	1.63577i
$324$		0			0
$325$	−1.94485	+	1.59610i	−0.107881	+	0.0885355i
$326$		0			0
$327$	4.01386	+	6.00717i	0.221967	+	0.332197i
$328$		0			0
$329$	13.6400	+	9.11396i	0.751998	+	0.502469i
$330$		0			0
$331$	−0.117619	−	0.387737i	−0.00646490	−	0.0213119i	0.953649	−	0.300923i	$-0.0972946\pi$
$331$	−0.117619	−	0.387737i	−0.00646490	−	0.0213119i	−0.960113	+	0.279611i	$0.909795\pi$
$332$		0			0
$333$	−0.422010	+	0.514220i	−0.0231260	+	0.0281791i
$334$		0			0
$335$	5.24834	−	12.6706i	0.286747	−	0.692269i
$336$		0			0
$337$	−6.29112	−	15.1881i	−0.342699	−	0.827349i	−0.997441	−	0.0714966i	$-0.977222\pi$
$337$	−6.29112	−	15.1881i	−0.342699	−	0.827349i	0.654741	−	0.755853i	$-0.272778\pi$
$338$		0			0
$339$	−1.03640	+	0.102076i	−0.0562894	+	0.00554402i
$340$		0			0
$341$	21.8623	+	11.6856i	1.18391	+	0.632813i
$342$		0			0
$343$	4.40531	+	22.1470i	0.237864	+	1.19583i
$344$		0			0
$345$	8.24062	+	1.63916i	0.443660	+	0.0882494i
$346$		0			0
$347$	−6.76880	−	0.666668i	−0.363368	−	0.0357886i	−0.0853142	−	0.996354i	$-0.527189\pi$
$347$	−6.76880	−	0.666668i	−0.363368	−	0.0357886i	−0.278054	+	0.960565i	$0.589689\pi$
$348$		0			0
$349$	14.9383	+	4.53149i	0.799629	+	0.242565i	0.663549	−	0.748133i	$-0.269049\pi$
$349$	14.9383	+	4.53149i	0.799629	+	0.242565i	0.136080	+	0.990698i	$0.456549\pi$
$350$		0			0
$351$	7.18020	−	7.18020i	0.383251	−	0.383251i
$352$		0			0
$353$	2.73668	+	2.73668i	0.145659	+	0.145659i	0.776176	−	0.630517i	$-0.217157\pi$
$353$	2.73668	+	2.73668i	0.145659	+	0.145659i	−0.630517	+	0.776176i	$0.717157\pi$
$354$		0			0
$355$	−1.18460	+	3.90509i	−0.0628719	+	0.207261i
$356$		0			0
$357$	3.32215	−	33.7303i	0.175827	−	1.78520i
$358$		0			0
$359$	−2.95707	+	14.8662i	−0.156068	+	0.784608i	0.820875	+	0.571108i	$0.193486\pi$
$359$	−2.95707	+	14.8662i	−0.156068	+	0.784608i	−0.976943	+	0.213500i	$0.931514\pi$
$360$		0			0
$361$	−47.4589	+	9.44016i	−2.49784	+	0.496850i
$362$		0			0
$363$	−9.06513	+	16.9597i	−0.475796	+	0.890152i
$364$		0			0
$365$	−1.90306	−	19.3221i	−0.0996109	−	1.01137i
$366$		0			0
$367$	−26.6181	+	11.0256i	−1.38945	+	0.575530i	−0.946992	−	0.321258i	$-0.895894\pi$
$367$	−26.6181	+	11.0256i	−1.38945	+	0.575530i	−0.442460	+	0.896788i	$0.645894\pi$
$368$		0			0
$369$	2.14392	+	0.888040i	0.111608	+	0.0462295i
$370$		0			0
$371$	−20.9173	−	17.1664i	−1.08597	−	0.891233i
$372$		0			0
$373$	−5.14539	+	1.56084i	−0.266418	+	0.0808171i	−0.420668	−	0.907215i	$-0.638204\pi$
$373$	−5.14539	+	1.56084i	−0.266418	+	0.0808171i	0.154249	+	0.988032i	$0.450704\pi$
$374$		0			0
$375$	10.1748	−	15.2276i	0.525424	−	0.786352i
$376$		0			0
$377$	3.86227	−	2.58069i	0.198917	−	0.132912i
$378$		0			0
$379$	14.4264	+	17.5786i	0.741033	+	0.902951i	0.997984	−	0.0634733i	$-0.0202178\pi$
$379$	14.4264	+	17.5786i	0.741033	+	0.902951i	−0.256951	+	0.966425i	$0.582718\pi$
$380$		0			0
$381$	−12.8367	+	6.86137i	−0.657645	+	0.351519i
$382$		0			0
$383$	9.89152			0.505433			0.252716	−	0.967540i	$-0.418676\pi$
$383$	9.89152			0.505433			0.252716	+	0.967540i	$0.418676\pi$
$384$		0			0
$385$	49.7082			2.53336
$386$		0			0
$387$	0.504697	−	0.269766i	0.0256552	−	0.0137130i
$388$		0			0
$389$	−1.50951	−	1.83934i	−0.0765350	−	0.0932582i	0.733335	−	0.679867i	$-0.237963\pi$
$389$	−1.50951	−	1.83934i	−0.0765350	−	0.0932582i	−0.809870	+	0.586609i	$0.800463\pi$
$390$		0			0
$391$	6.01503	−	4.01911i	0.304193	−	0.203255i
$392$		0			0
$393$	11.5527	−	17.2898i	0.582757	−	0.872157i
$394$		0			0
$395$	−25.1061	+	7.61586i	−1.26323	+	0.383196i
$396$		0			0
$397$	−0.0704200	−	0.0577922i	−0.00353428	−	0.00290051i	0.632624	−	0.774459i	$-0.281978\pi$
$397$	−0.0704200	−	0.0577922i	−0.00353428	−	0.00290051i	−0.636159	+	0.771558i	$0.719478\pi$
$398$		0			0
$399$	−63.3033	−	26.2211i	−3.16913	−	1.31270i
$400$		0			0
$401$	25.0378	−	10.3710i	1.25033	−	0.517904i	0.343402	−	0.939189i	$-0.388421\pi$
$401$	25.0378	−	10.3710i	1.25033	−	0.517904i	0.906928	+	0.421285i	$0.138421\pi$
$402$		0			0
$403$	1.19212	+	12.1038i	0.0593839	+	0.602935i
$404$		0			0
$405$	12.2463	−	22.9113i	0.608526	−	1.13847i
$406$		0			0
$407$	−4.70790	+	0.936459i	−0.233362	+	0.0464186i
$408$		0			0
$409$	1.68226	−	8.45728i	0.0831823	−	0.418186i	−0.916647	−	0.399698i	$-0.869115\pi$
$409$	1.68226	−	8.45728i	0.0831823	−	0.418186i	0.999829	−	0.0184875i	$-0.00588508\pi$
$410$		0			0
$411$	−1.54409	+	15.6774i	−0.0761644	+	0.773310i
$412$		0			0
$413$	−7.00229	+	23.0835i	−0.344560	+	1.13586i
$414$		0			0
$415$	−1.10825	−	1.10825i	−0.0544019	−	0.0544019i
$416$		0			0
$417$	−17.1503	+	17.1503i	−0.839854	+	0.839854i
$418$		0			0
$419$	6.43563	+	1.95223i	0.314401	+	0.0953725i	0.443542	−	0.896254i	$-0.353722\pi$
$419$	6.43563	+	1.95223i	0.314401	+	0.0953725i	−0.129141	+	0.991626i	$0.541222\pi$
$420$		0			0
$421$	14.8015	+	1.45782i	0.721382	+	0.0710500i	0.452044	−	0.891996i	$-0.350695\pi$
$421$	14.8015	+	1.45782i	0.721382	+	0.0710500i	0.269338	+	0.963046i	$0.413195\pi$
$422$		0			0
$423$	−2.33910	−	0.465276i	−0.113731	−	0.0226225i
$424$		0			0
$425$	0.884710	+	4.44774i	0.0429147	+	0.215747i
$426$		0			0
$427$	23.6882	+	12.6616i	1.14635	+	0.612739i
$428$		0			0
$429$	−19.6315	+	1.93353i	−0.947817	+	0.0933518i
$430$		0			0
$431$	6.12187	+	14.7795i	0.294880	+	0.711903i	0.999996	+	0.00281137i	$0.000894887\pi$
$431$	6.12187	+	14.7795i	0.294880	+	0.711903i	−0.705116	+	0.709092i	$0.749105\pi$
$432$		0			0
$433$	−3.31705	+	8.00807i	−0.159407	+	0.384843i	−0.983323	−	0.181870i	$-0.941785\pi$
$433$	−3.31705	+	8.00807i	−0.159407	+	0.384843i	0.823915	+	0.566713i	$0.191785\pi$
$434$		0			0
$435$	6.16899	−	7.51693i	0.295780	−	0.360409i
$436$		0			0
$437$	−4.24531	−	13.9949i	−0.203081	−	0.669467i
$438$		0			0
$439$	−22.4423	−	14.9955i	−1.07111	−	0.715695i	−0.110582	−	0.993867i	$-0.535271\pi$
$439$	−22.4423	−	14.9955i	−1.07111	−	0.715695i	−0.960531	+	0.278172i	$0.910271\pi$
$440$		0			0
$441$	−4.29858	−	6.43328i	−0.204694	−	0.306347i
$442$		0			0
$443$	−0.107334	+	0.0880866i	−0.00509959	+	0.00418512i	−0.636940	−	0.770914i	$-0.719800\pi$
$443$	−0.107334	+	0.0880866i	−0.00509959	+	0.00418512i	0.631840	+	0.775099i	$0.282300\pi$
$444$		0			0
$445$	−3.88177	−	7.26229i	−0.184014	−	0.344266i
$446$		0			0
$447$			0.828852i			0.0392034i
$448$		0			0
$449$			36.3585i			1.71586i	0.513763	+	0.857932i	$0.328251\pi$
$449$			36.3585i			1.71586i	−0.513763	+	0.857932i	$0.671749\pi$
$450$		0			0
$451$	7.89348	+	14.7677i	0.371690	+	0.695382i
$452$		0			0
$453$	−22.8299	+	18.7360i	−1.07264	+	0.880296i
$454$		0			0
$455$	13.5494	+	20.2781i	0.635206	+	0.950653i
$456$		0			0
$457$	−35.3286	−	23.6058i	−1.65260	−	1.10423i	−0.888147	−	0.459559i	$-0.848008\pi$
$457$	−35.3286	−	23.6058i	−1.65260	−	1.10423i	−0.764456	−	0.644676i	$-0.776992\pi$
$458$		0			0
$459$	−5.31300	−	17.5146i	−0.247990	−	0.817513i
$460$		0			0
$461$	24.2882	−	29.5953i	1.13121	−	1.37839i	0.215526	−	0.976498i	$-0.430853\pi$
$461$	24.2882	−	29.5953i	1.13121	−	1.37839i	0.915688	−	0.401890i	$-0.131647\pi$
$462$		0			0
$463$	10.5092	−	25.3714i	0.488404	−	1.17911i	−0.467119	−	0.884194i	$-0.654708\pi$
$463$	10.5092	−	25.3714i	0.488404	−	1.17911i	0.955523	−	0.294917i	$-0.0952918\pi$
$464$		0			0
$465$	9.74356	+	23.5230i	0.451847	+	1.09086i
$466$		0			0
$467$	17.2916	−	1.70308i	0.800161	−	0.0788090i	0.310333	−	0.950628i	$-0.399560\pi$
$467$	17.2916	−	1.70308i	0.800161	−	0.0788090i	0.489828	+	0.871819i	$0.337060\pi$
$468$		0			0
$469$	−21.4060	−	11.4418i	−0.988438	−	0.528331i
$470$		0			0
$471$	6.38886	+	32.1190i	0.294383	+	1.47996i
$472$		0			0
$473$	4.05009	+	0.805613i	0.186223	+	0.0370421i
$474$		0			0
$475$	9.12353	+	0.898589i	0.418616	+	0.0412301i
$476$		0			0
$477$	3.76454	+	1.14196i	0.172366	+	0.0522868i
$478$		0			0
$479$	−18.9721	+	18.9721i	−0.866858	+	0.866858i	−0.992123	−	0.125266i	$-0.960022\pi$
$479$	−18.9721	+	18.9721i	−0.866858	+	0.866858i	0.125266	+	0.992123i	$0.460022\pi$
$480$		0			0
$481$	−1.66530	−	1.66530i	−0.0759310	−	0.0759310i
$482$		0			0
$483$	4.31652	−	14.2297i	0.196408	−	0.647472i
$484$		0			0
$485$	−4.32290	+	43.8911i	−0.196293	+	1.99299i
$486$		0			0
$487$	−2.41207	+	12.1263i	−0.109301	+	0.549494i	0.886866	+	0.462026i	$0.152877\pi$
$487$	−2.41207	+	12.1263i	−0.109301	+	0.549494i	−0.996167	+	0.0874678i	$0.972123\pi$
$488$		0			0
$489$	11.4352	−	2.27461i	0.517118	−	0.102861i
$490$		0			0
$491$	−2.75621	+	5.15651i	−0.124386	+	0.232710i	−0.936405	−	0.350921i	$-0.885869\pi$
$491$	−2.75621	+	5.15651i	−0.124386	+	0.232710i	0.812019	+	0.583631i	$0.198369\pi$
$492$		0			0
$493$	−0.820660	−	8.33230i	−0.0369607	−	0.375268i
$494$		0			0
$495$	−6.67653	+	2.76551i	−0.300088	+	0.124300i
$496$		0			0
$497$	6.67245	+	2.76382i	0.299300	+	0.123974i
$498$		0			0
$499$	−30.9124	−	25.3691i	−1.38383	−	1.13568i	−0.974781	−	0.223164i	$-0.928361\pi$
$499$	−30.9124	−	25.3691i	−1.38383	−	1.13568i	−0.409046	−	0.912514i	$-0.634139\pi$
$500$		0			0
$501$	−29.4944	+	8.94703i	−1.31771	+	0.399724i
$502$		0			0
$503$	−14.1947	+	21.2439i	−0.632911	+	0.947218i	0.366945	+	0.930243i	$0.380404\pi$
$503$	−14.1947	+	21.2439i	−0.632911	+	0.947218i	−0.999856	+	0.0169751i	$0.994596\pi$
$504$		0			0
$505$	−34.7752	+	23.2360i	−1.54747	+	1.03399i
$506$		0			0
$507$	9.58669	+	11.6814i	0.425760	+	0.518790i
$508$		0			0
$509$	−8.16150	+	4.36241i	−0.361752	+	0.193361i	−0.642252	−	0.766493i	$-0.722000\pi$
$509$	−8.16150	+	4.36241i	−0.361752	+	0.193361i	0.280500	+	0.959854i	$0.409500\pi$
$510$		0			0
$511$	−34.3617			−1.52007
$512$		0			0
$513$	−37.0007			−1.63362
$514$		0			0
$515$	−8.40113	+	4.49050i	−0.370198	+	0.197875i
$516$		0			0
$517$	−10.9175	−	13.3030i	−0.480151	−	0.585066i
$518$		0			0
$519$	10.2050	−	6.81878i	0.447951	−	0.299311i
$520$		0			0
$521$	−13.4624	+	20.1479i	−0.589799	+	0.882697i	−0.999565	−	0.0294940i	$-0.990610\pi$
$521$	−13.4624	+	20.1479i	−0.589799	+	0.882697i	0.409766	+	0.912191i	$0.365610\pi$
$522$		0			0
$523$	−5.10776	+	1.54942i	−0.223347	+	0.0677514i	−0.399975	−	0.916526i	$-0.630981\pi$
$523$	−5.10776	+	1.54942i	−0.223347	+	0.0677514i	0.176628	+	0.984278i	$0.443481\pi$
$524$		0			0
$525$	7.20557	+	5.91346i	0.314477	+	0.258085i
$526$		0			0
$527$	20.2535	+	8.38926i	0.882255	+	0.365442i
$528$		0			0
$529$	−18.3170	+	7.58715i	−0.796391	+	0.329876i
$530$		0			0
$531$	−0.343736	−	3.49001i	−0.0149169	−	0.151454i
$532$		0			0
$533$	−3.87277	+	7.24545i	−0.167748	+	0.313835i
$534$		0			0
$535$	25.1358	−	4.99981i	1.08671	−	0.216161i
$536$		0			0
$537$	5.11222	−	25.7009i	0.220608	−	1.10907i
$538$		0			0
$539$	5.47240	−	55.5622i	0.235713	−	2.39323i
$540$		0			0
$541$	−2.00876	+	6.62199i	−0.0863633	+	0.284702i	−0.989475	−	0.144704i	$-0.953777\pi$
$541$	−2.00876	+	6.62199i	−0.0863633	+	0.284702i	0.903112	+	0.429406i	$0.141277\pi$
$542$		0			0
$543$	18.8782	+	18.8782i	0.810139	+	0.810139i
$544$		0			0
$545$	−6.62578	+	6.62578i	−0.283817	+	0.283817i
$546$		0			0
$547$	−36.2016	−	10.9816i	−1.54787	−	0.469541i	−0.603207	−	0.797585i	$-0.706111\pi$
$547$	−36.2016	−	10.9816i	−1.54787	−	0.469541i	−0.944663	+	0.328043i	$0.893611\pi$
$548$		0			0
$549$	−3.88610	−	0.382748i	−0.165855	−	0.0163353i
$550$		0			0
$551$	−16.6008	−	3.30210i	−0.707218	−	0.140674i
$552$		0			0
$553$	9.05846	+	45.5400i	0.385205	+	1.93656i
$554$		0			0
$555$	−4.34806	−	2.32408i	−0.184565	−	0.0986519i
$556$		0			0
$557$	−10.0415	+	0.989001i	−0.425472	+	0.0419053i	−0.308487	−	0.951228i	$-0.599823\pi$
$557$	−10.0415	+	0.989001i	−0.425472	+	0.0419053i	−0.116984	+	0.993134i	$0.537323\pi$
$558$		0			0
$559$	0.775324	+	1.87180i	0.0327927	+	0.0791687i
$560$		0			0
$561$	−13.6067	+	32.8495i	−0.574476	+	1.38691i
$562$		0			0
$563$	12.8449	−	15.6515i	0.541346	−	0.659632i	−0.428445	−	0.903568i	$-0.640939\pi$
$563$	12.8449	−	15.6515i	0.541346	−	0.659632i	0.969791	+	0.243936i	$0.0784385\pi$
$564$		0			0
$565$	−0.392081	−	1.29252i	−0.0164950	−	0.0543766i
$566$		0			0
$567$	−38.2288	−	25.5436i	−1.60546	−	1.07273i
$568$		0			0
$569$	7.20899	+	10.7890i	0.302217	+	0.452299i	0.951232	−	0.308476i	$-0.0998190\pi$
$569$	7.20899	+	10.7890i	0.302217	+	0.452299i	−0.649016	+	0.760775i	$0.724819\pi$
$570$		0			0
$571$	−7.67267	+	6.29680i	−0.321091	+	0.263513i	−0.781106	−	0.624399i	$-0.785344\pi$
$571$	−7.67267	+	6.29680i	−0.321091	+	0.263513i	0.460015	+	0.887911i	$0.347844\pi$
$572$		0			0
$573$	−3.42021	−	6.39876i	−0.142881	−	0.267312i
$574$		0			0
$575$			1.98956i			0.0829705i
$576$		0			0
$577$		−	0.282562i		−	0.0117632i	−0.999983	−	0.00588161i	$-0.998128\pi$
$577$		−	0.282562i		−	0.0117632i	0.999983	−	0.00588161i	$-0.00187218\pi$
$578$		0			0
$579$	−16.8702	−	31.5620i	−0.701103	−	1.31167i
$580$		0			0
$581$	−2.14418	+	1.75969i	−0.0889558	+	0.0730041i
$582$		0			0
$583$	15.7709	+	23.6027i	0.653162	+	0.977526i
$584$		0			0
$585$	−2.94805	−	1.96983i	−0.121887	−	0.0814423i
$586$		0			0
$587$	−5.47518	−	18.0493i	−0.225985	−	0.744973i	−0.994462	−	0.105096i	$-0.966485\pi$
$587$	−5.47518	−	18.0493i	−0.225985	−	0.744973i	0.768477	−	0.639877i	$-0.221015\pi$
$588$		0			0
$589$	28.1149	−	34.2581i	1.15845	−	1.41158i
$590$		0			0
$591$	−9.04273	+	21.8311i	−0.371968	+	0.898010i
$592$		0			0
$593$	−1.91549	−	4.62440i	−0.0786598	−	0.189901i	0.879657	−	0.475608i	$-0.157772\pi$
$593$	−1.91549	−	4.62440i	−0.0786598	−	0.189901i	−0.958317	+	0.285706i	$0.907772\pi$
$594$		0			0
$595$	43.7471	−	4.30872i	1.79346	−	0.176640i
$596$		0			0
$597$	34.9062	+	18.6577i	1.42862	+	0.763611i
$598$		0			0
$599$	−2.96272	−	14.8946i	−0.121053	−	0.608577i	−0.992915	−	0.118825i	$-0.962087\pi$
$599$	−2.96272	−	14.8946i	−0.121053	−	0.608577i	0.871862	−	0.489752i	$-0.162913\pi$
$600$		0			0
$601$	−3.45188	−	0.686622i	−0.140805	−	0.0280079i	0.124184	−	0.992259i	$-0.460369\pi$
$601$	−3.45188	−	0.686622i	−0.140805	−	0.0280079i	−0.264990	+	0.964251i	$0.585369\pi$
$602$		0			0
$603$	3.51170	+	0.345872i	0.143007	+	0.0140850i
$604$		0			0
$605$	−23.8672	−	7.24003i	−0.970339	−	0.294349i
$606$		0			0
$607$	−28.4960	+	28.4960i	−1.15662	+	1.15662i	−0.171419	+	0.985198i	$0.554835\pi$
$607$	−28.4960	+	28.4960i	−1.15662	+	1.15662i	−0.985198	+	0.171419i	$0.945165\pi$
$608$		0			0
$609$	−12.1693	−	12.1693i	−0.493123	−	0.493123i
$610$		0			0
$611$	2.45099	−	8.07984i	0.0991566	−	0.326875i
$612$		0			0
$613$	2.65643	−	26.9711i	0.107292	−	1.08935i	−0.779252	−	0.626710i	$-0.784401\pi$
$613$	2.65643	−	26.9711i	0.107292	−	1.08935i	0.886544	−	0.462644i	$-0.153099\pi$
$614$		0			0
$615$	−3.35529	+	16.8682i	−0.135298	+	0.680190i
$616$		0			0
$617$	40.9008	−	8.13568i	1.64660	−	0.327530i	0.717278	−	0.696787i	$-0.245388\pi$
$617$	40.9008	−	8.13568i	1.64660	−	0.327530i	0.929327	+	0.369257i	$0.120388\pi$
$618$		0			0
$619$	−1.38510	+	2.59134i	−0.0556719	+	0.104155i	−0.908218	−	0.418497i	$-0.862557\pi$
$619$	−1.38510	+	2.59134i	−0.0556719	+	0.104155i	0.852546	+	0.522652i	$0.175057\pi$
$620$		0			0
$621$	−0.787065	−	7.99121i	−0.0315838	−	0.320676i
$622$		0			0
$623$	−13.4643	+	5.57708i	−0.539435	+	0.223441i
$624$		0			0
$625$	27.1036	+	11.2267i	1.08414	+	0.449067i
$626$		0			0
$627$	55.5639	+	45.6002i	2.21901	+	1.82109i
$628$		0			0
$629$	−4.06215	+	1.23224i	−0.161968	+	0.0491326i
$630$		0			0
$631$	19.7340	−	29.5340i	0.785599	−	1.17573i	−0.195210	−	0.980761i	$-0.562539\pi$
$631$	19.7340	−	29.5340i	0.785599	−	1.17573i	0.980809	−	0.194970i	$-0.0624610\pi$
$632$		0			0
$633$	23.1441	−	15.4644i	0.919897	−	0.614656i
$634$		0			0
$635$	−11.9760	−	14.5928i	−0.475253	−	0.579097i
$636$		0			0
$637$	24.1579	−	12.9126i	0.957170	−	0.511618i
$638$		0			0
$639$	−1.04997			−0.0415362
$640$		0			0
$641$	30.3265			1.19783			0.598913	−	0.800814i	$-0.295599\pi$
$641$	30.3265			1.19783			0.598913	+	0.800814i	$0.295599\pi$
$642$		0			0
$643$	−10.4899	+	5.60695i	−0.413680	+	0.221117i	−0.665089	−	0.746764i	$-0.731606\pi$
$643$	−10.4899	+	5.60695i	−0.413680	+	0.221117i	0.251409	+	0.967881i	$0.419106\pi$
$644$		0			0
$645$	2.69067	+	3.27860i	0.105945	+	0.129095i
$646$		0			0
$647$	16.2821	−	10.8794i	0.640115	−	0.427711i	−0.192703	−	0.981257i	$-0.561726\pi$
$647$	16.2821	−	10.8794i	0.640115	−	0.427711i	0.832819	+	0.553546i	$0.186726\pi$
$648$		0			0
$649$	14.0589	−	21.0407i	0.551861	−	0.825918i
$650$		0			0
$651$	43.1208	−	13.0806i	1.69004	−	0.512667i
$652$		0			0
$653$	32.0096	+	26.2696i	1.25263	+	1.02801i	0.998142	+	0.0609355i	$0.0194084\pi$
$653$	32.0096	+	26.2696i	1.25263	+	1.02801i	0.254492	+	0.967075i	$0.418092\pi$
$654$		0			0
$655$	24.9166	+	10.3208i	0.973572	+	0.403267i
$656$		0			0
$657$	4.61528	−	1.91171i	0.180059	−	0.0745829i
$658$		0			0
$659$	−0.532739	−	5.40899i	−0.0207525	−	0.210704i	−0.999969	−	0.00788572i	$-0.997490\pi$
$659$	−0.532739	−	5.40899i	−0.0207525	−	0.210704i	0.979216	−	0.202818i	$-0.0650101\pi$
$660$		0			0
$661$	5.91353	−	11.0634i	0.230010	−	0.430318i	−0.740268	−	0.672312i	$-0.765301\pi$
$661$	5.91353	−	11.0634i	0.230010	−	0.430318i	0.970278	+	0.241994i	$0.0778015\pi$
$662$		0			0
$663$	−17.1096	+	3.40332i	−0.664484	+	0.132174i
$664$		0			0
$665$	17.3371	−	87.1593i	0.672302	−	3.37989i
$666$		0			0
$667$	0.360044	−	3.65559i	0.0139410	−	0.141545i
$668$		0			0
$669$	1.98101	−	6.53051i	0.0765903	−	0.252484i
$670$		0			0
$671$	−19.9244	−	19.9244i	−0.769172	−	0.769172i
$672$		0			0
$673$	31.3341	−	31.3341i	1.20784	−	1.20784i	0.236116	−	0.971725i	$-0.424125\pi$
$673$	31.3341	−	31.3341i	1.20784	−	1.20784i	0.971725	−	0.236116i	$-0.0758747\pi$
$674$		0			0
$675$	4.81689	+	1.46119i	0.185402	+	0.0562412i
$676$		0			0
$677$	−46.7971	−	4.60911i	−1.79856	−	0.177143i	−0.857298	−	0.514821i	$-0.827858\pi$
$677$	−46.7971	−	4.60911i	−1.79856	−	0.177143i	−0.941262	+	0.337678i	$0.890358\pi$
$678$		0			0
$679$	76.5545	+	15.2276i	2.93789	+	0.584383i
$680$		0			0
$681$	8.82548	+	44.3687i	0.338193	+	1.70021i
$682$		0			0
$683$	1.29189	+	0.690532i	0.0494329	+	0.0264225i	0.495928	−	0.868364i	$-0.334828\pi$
$683$	1.29189	+	0.690532i	0.0494329	+	0.0264225i	−0.446495	+	0.894786i	$0.647328\pi$
$684$		0			0
$685$	−20.3331	+	2.00263i	−0.776887	+	0.0765167i
$686$		0			0
$687$	−5.15381	−	12.4424i	−0.196630	−	0.474707i
$688$		0			0
$689$	−5.32978	+	12.8672i	−0.203048	+	0.490202i
$690$		0			0
$691$	−6.68309	+	8.14337i	−0.254237	+	0.309788i	−0.884451	−	0.466633i	$-0.845467\pi$
$691$	−6.68309	+	8.14337i	−0.254237	+	0.309788i	0.630214	+	0.776421i	$0.282967\pi$
$692$		0			0
$693$	3.71264	+	12.2390i	0.141032	+	0.464919i
$694$		0			0
$695$	−26.1554	−	17.4765i	−0.992133	−	0.662922i
$696$		0			0
$697$	8.22695	+	12.3125i	0.311618	+	0.466369i
$698$		0			0
$699$	−30.1662	+	24.7568i	−1.14099	+	0.936388i
$700$		0			0
$701$	−8.96665	−	16.7754i	−0.338666	−	0.633599i	0.653724	−	0.756733i	$-0.273206\pi$
$701$	−8.96665	−	16.7754i	−0.338666	−	0.633599i	−0.992390	+	0.123134i	$0.960706\pi$
$702$		0			0
$703$			8.58153i			0.323659i
$704$		0			0
$705$		−	17.6757i		−	0.665705i
$706$		0			0
$707$	34.8926	+	65.2795i	1.31227	+	2.45509i
$708$		0			0
$709$	−4.50002	+	3.69307i	−0.169002	+	0.138696i	−0.715092	−	0.699030i	$-0.753615\pi$
$709$	−4.50002	+	3.69307i	−0.169002	+	0.138696i	0.546091	+	0.837726i	$0.316115\pi$
$710$		0			0
$711$	−3.75029	−	5.61271i	−0.140647	−	0.210493i
$712$		0			0
$713$	7.99692	+	5.34337i	0.299487	+	0.200111i
$714$		0			0
$715$	−7.42681	−	24.4829i	−0.277747	−	0.915609i
$716$		0			0
$717$	−27.0755	+	32.9916i	−1.01115	+	1.23210i
$718$		0			0
$719$	10.2579	−	24.7648i	0.382556	−	0.923571i	−0.608914	−	0.793236i	$-0.708395\pi$
$719$	10.2579	−	24.7648i	0.382556	−	0.923571i	0.991470	−	0.130335i	$-0.0416053\pi$
$720$		0			0
$721$	6.45166	+	15.5757i	0.240272	+	0.580069i
$722$		0			0
$723$	−16.1032	+	1.58603i	−0.598884	+	0.0589849i
$724$		0			0
$725$	2.03075	+	1.08546i	0.0754203	+	0.0403130i
$726$		0			0
$727$	−2.63556	−	13.2498i	−0.0977474	−	0.491410i	−0.998384	−	0.0568355i	$-0.981899\pi$
$727$	−2.63556	−	13.2498i	−0.0977474	−	0.491410i	0.900636	−	0.434574i	$-0.143101\pi$
$728$		0			0
$729$	−18.7339	−	3.72641i	−0.693850	−	0.138015i
$730$		0			0
$731$	3.63423	+	0.357940i	0.134417	+	0.0132389i
$732$		0			0
$733$	−2.50984	−	0.761353i	−0.0927032	−	0.0281212i	0.243592	−	0.969878i	$-0.421674\pi$
$733$	−2.50984	−	0.761353i	−0.0927032	−	0.0281212i	−0.336296	+	0.941756i	$0.609174\pi$
$734$		0			0
$735$	40.5483	−	40.5483i	1.49565	−	1.49565i
$736$		0			0
$737$	18.0048	+	18.0048i	0.663214	+	0.663214i
$738$		0			0
$739$	−10.8123	+	35.6433i	−0.397736	+	1.31116i	0.498233	+	0.867043i	$0.333983\pi$
$739$	−10.8123	+	35.6433i	−0.397736	+	1.31116i	−0.895969	+	0.444117i	$0.853517\pi$
$740$		0			0
$741$	−3.45671	+	35.0966i	−0.126985	+	1.28930i
$742$		0			0
$743$	8.18895	−	41.1686i	0.300423	−	1.51033i	−0.475620	−	0.879651i	$-0.657776\pi$
$743$	8.18895	−	41.1686i	0.300423	−	1.51033i	0.776043	−	0.630679i	$-0.217224\pi$
$744$		0			0
$745$	−1.05434	+	0.209721i	−0.0386280	+	0.00768358i
$746$		0			0
$747$	0.190095	−	0.355643i	0.00695521	−	0.0130123i
$748$		0			0
$749$	−4.44574	−	45.1384i	−0.162444	−	1.64932i
$750$		0			0
$751$	−27.6372	+	11.4477i	−1.00850	+	0.417733i	−0.824906	−	0.565270i	$-0.808772\pi$
$751$	−27.6372	+	11.4477i	−1.00850	+	0.417733i	−0.183591	+	0.983003i	$0.558772\pi$
$752$		0			0
$753$	−7.05942	−	2.92411i	−0.257260	−	0.106560i
$754$		0			0
$755$	−29.6096	−	24.3000i	−1.07761	−	0.884368i
$756$		0			0
$757$	25.4141	−	7.70930i	0.923693	−	0.280199i	0.207608	−	0.978212i	$-0.433432\pi$
$757$	25.4141	−	7.70930i	0.923693	−	0.280199i	0.716085	+	0.698013i	$0.245932\pi$
$758$		0			0
$759$	−8.66653	+	12.9704i	−0.314575	+	0.470795i
$760$		0			0
$761$	8.69419	−	5.80928i	0.315164	−	0.210586i	−0.387919	−	0.921693i	$-0.626806\pi$
$761$	8.69419	−	5.80928i	0.315164	−	0.210586i	0.703083	+	0.711107i	$0.251806\pi$
$762$		0			0
$763$	10.5205	+	12.8192i	0.380866	+	0.464087i
$764$		0			0
$765$	−5.63615	+	3.01259i	−0.203776	+	0.108920i
$766$		0			0
$767$	12.4156			0.448300
$768$		0			0
$769$	−25.4401			−0.917395			−0.458697	−	0.888593i	$-0.651684\pi$
$769$	−25.4401			−0.917395			−0.458697	+	0.888593i	$0.651684\pi$
$770$		0			0
$771$	−8.34563	+	4.46083i	−0.300560	+	0.160653i
$772$		0			0
$773$	−2.04624	−	2.49335i	−0.0735983	−	0.0896797i	0.734910	−	0.678165i	$-0.237225\pi$
$773$	−2.04624	−	2.49335i	−0.0735983	−	0.0896797i	−0.808508	+	0.588485i	$0.799725\pi$
$774$		0			0
$775$	−5.01299	+	3.34957i	−0.180072	+	0.120320i
$776$		0			0
$777$	−4.84761	+	7.25497i	−0.173907	+	0.260271i
$778$		0			0
$779$	28.6470	−	8.68996i	1.02638	−	0.311350i
$780$		0			0
$781$	−5.85669	−	4.80646i	−0.209569	−	0.171989i
$782$		0			0
$783$	−8.58605	−	3.55646i	−0.306841	−	0.127098i
$784$		0			0
$785$	−39.2403	+	16.2538i	−1.40054	+	0.580125i
$786$		0			0
$787$	2.33442	+	23.7017i	0.0832129	+	0.844875i	0.942683	+	0.333689i	$0.108294\pi$
$787$	2.33442	+	23.7017i	0.0832129	+	0.844875i	−0.859470	+	0.511186i	$0.829206\pi$
$788$		0			0
$789$	19.1209	−	35.7727i	0.680721	−	1.27354i
$790$		0			0
$791$	−2.34449	+	0.466349i	−0.0833606	+	0.0165815i
$792$		0			0
$793$	2.69705	−	13.5590i	0.0957750	−	0.481493i
$794$		0			0
$795$	−2.85779	+	29.0156i	−0.101355	+	1.02908i
$796$		0			0
$797$	−6.93545	+	22.8631i	−0.245666	+	0.809853i	0.744213	+	0.667942i	$0.232825\pi$
$797$	−6.93545	+	22.8631i	−0.245666	+	0.809853i	−0.989879	+	0.141911i	$0.954675\pi$
$798$		0			0
$799$	−10.7614	−	10.7614i	−0.380710	−	0.380710i
$800$		0			0
$801$	1.49817	−	1.49817i	0.0529351	−	0.0529351i
$802$		0			0
$803$	34.4950	+	10.4640i	1.21730	+	0.369265i
$804$		0			0
$805$	19.1930	+	1.89034i	0.676463	+	0.0666258i
$806$		0			0
$807$	−19.1299	−	3.80518i	−0.673405	−	0.133949i
$808$		0			0
$809$	−4.59684	−	23.1099i	−0.161616	−	0.812499i	−0.973501	−	0.228682i	$-0.926558\pi$
$809$	−4.59684	−	23.1099i	−0.161616	−	0.812499i	0.811885	−	0.583817i	$-0.198442\pi$
$810$		0			0
$811$	40.9674	+	21.8975i	1.43856	+	0.768926i	0.992049	−	0.125853i	$-0.0401667\pi$
$811$	40.9674	+	21.8975i	1.43856	+	0.768926i	0.446510	+	0.894779i	$0.352667\pi$
$812$		0			0
$813$	18.7360	−	1.84534i	0.657102	−	0.0647189i
$814$		0			0
$815$	5.78680	+	13.9706i	0.202703	+	0.489368i
$816$		0			0
$817$	2.82515	−	6.82052i	0.0988395	−	0.238620i
$818$		0			0
$819$	−3.98081	+	4.85063i	−0.139101	+	0.169495i
$820$		0			0
$821$	8.40973	+	27.7232i	0.293502	+	0.967545i	0.972401	+	0.233314i	$0.0749570\pi$
$821$	8.40973	+	27.7232i	0.293502	+	0.967545i	−0.678900	+	0.734231i	$0.737543\pi$
$822$		0			0
$823$	17.5336	+	11.7156i	0.611184	+	0.408380i	0.822278	−	0.569086i	$-0.192703\pi$
$823$	17.5336	+	11.7156i	0.611184	+	0.408380i	−0.211094	+	0.977466i	$0.567703\pi$
$824$		0			0
$825$	−5.43274	−	8.13067i	−0.189144	−	0.283074i
$826$		0			0
$827$	−41.1018	+	33.7314i	−1.42925	+	1.17296i	−0.472761	+	0.881191i	$0.656743\pi$
$827$	−41.1018	+	33.7314i	−1.42925	+	1.17296i	−0.956490	+	0.291765i	$0.905757\pi$
$828$		0			0
$829$	−7.07142	−	13.2297i	−0.245601	−	0.459486i	0.728671	−	0.684864i	$-0.240138\pi$
$829$	−7.07142	−	13.2297i	−0.245601	−	0.459486i	−0.974271	+	0.225378i	$0.927638\pi$
$830$		0			0
$831$		−	37.9116i		−	1.31514i
$832$		0			0
$833$		−	49.3734i		−	1.71069i
$834$		0			0
$835$	−18.8439	−	35.2544i	−0.652119	−	1.22003i
$836$		0			0
$837$	18.8099	−	15.4369i	0.650165	−	0.533577i
$838$		0			0
$839$	5.61363	+	8.40139i	0.193804	+	0.290048i	0.915626	−	0.402030i	$-0.131695\pi$
$839$	5.61363	+	8.40139i	0.193804	+	0.290048i	−0.721822	+	0.692078i	$0.756695\pi$
$840$		0			0
$841$	20.5778	+	13.7496i	0.709579	+	0.474125i
$842$		0			0
$843$	−13.8535	−	45.6687i	−0.477138	−	1.57291i
$844$		0			0
$845$	−12.4336	+	15.1504i	−0.427729	+	0.521189i
$846$		0			0
$847$	−16.8919	+	40.7808i	−0.580414	+	1.40124i
$848$		0			0
$849$	−17.8725	−	43.1481i	−0.613383	−	1.48084i
$850$		0			0
$851$	−1.85339	+	0.182543i	−0.0635334	+	0.00625750i
$852$		0			0
$853$	31.8164	+	17.0062i	1.08937	+	0.582282i	0.915432	−	0.402474i	$-0.131850\pi$
$853$	31.8164	+	17.0062i	1.08937	+	0.582282i	0.173942	+	0.984756i	$0.444350\pi$
$854$		0			0
$855$	2.52048	+	12.6713i	0.0861985	+	0.433349i
$856$		0			0
$857$	−17.3236	−	3.44588i	−0.591763	−	0.117709i	−0.109880	−	0.993945i	$-0.535047\pi$
$857$	−17.3236	−	3.44588i	−0.591763	−	0.117709i	−0.481882	+	0.876236i	$0.660047\pi$
$858$		0			0
$859$	−9.63287	−	0.948755i	−0.328669	−	0.0323711i	−0.0676631	−	0.997708i	$-0.521554\pi$
$859$	−9.63287	−	0.948755i	−0.328669	−	0.0323711i	−0.261006	+	0.965337i	$0.584054\pi$
$860$		0			0
$861$	29.1275	+	8.83572i	0.992661	+	0.301121i
$862$		0			0
$863$	31.4513	−	31.4513i	1.07061	−	1.07061i	0.0733040	−	0.997310i	$-0.476646\pi$
$863$	31.4513	−	31.4513i	1.07061	−	1.07061i	0.997310	−	0.0733040i	$-0.0233543\pi$
$864$		0			0
$865$	11.2559	+	11.2559i	0.382713	+	0.382713i
$866$		0			0
$867$	0.282768	−	0.932161i	0.00960330	−	0.0316578i
$868$		0			0
$869$	4.77438	−	48.4751i	0.161960	−	1.64441i
$870$		0			0
$871$	−2.43720	+	12.2526i	−0.0825815	+	0.415165i
$872$		0			0
$873$	−11.1296	+	2.21381i	−0.376679	+	0.0749260i
$874$		0			0
$875$	19.8164	−	37.0739i	0.669918	−	1.25333i
$876$		0			0
$877$	4.21090	+	42.7540i	0.142192	+	1.44370i	0.756169	+	0.654377i	$0.227069\pi$
$877$	4.21090	+	42.7540i	0.142192	+	1.44370i	−0.613976	+	0.789324i	$0.710431\pi$
$878$		0			0
$879$	52.4043	−	21.7066i	1.76755	−	0.732145i
$880$		0			0
$881$	−39.4734	−	16.3504i	−1.32989	−	0.550860i	−0.399269	−	0.916834i	$-0.630736\pi$
$881$	−39.4734	−	16.3504i	−1.32989	−	0.550860i	−0.930625	+	0.365974i	$0.880736\pi$
$882$		0			0
$883$	−9.58320	−	7.86473i	−0.322500	−	0.264669i	0.459187	−	0.888340i	$-0.348141\pi$
$883$	−9.58320	−	7.86473i	−0.322500	−	0.264669i	−0.781687	+	0.623670i	$0.785641\pi$
$884$		0			0
$885$	24.8719	−	7.54482i	0.836061	−	0.253616i
$886$		0			0
$887$	−9.79752	+	14.6630i	−0.328968	+	0.492336i	−0.958678	−	0.284495i	$-0.908174\pi$
$887$	−9.79752	+	14.6630i	−0.328968	+	0.492336i	0.629709	+	0.776831i	$0.283174\pi$
$888$		0			0
$889$	−27.7794	+	18.5616i	−0.931692	+	0.622537i
$890$		0			0
$891$	30.5984	+	37.2843i	1.02509	+	1.24907i
$892$		0			0
$893$	−27.1335	+	14.5032i	−0.907989	+	0.485330i
$894$		0			0
$895$	33.9862			1.13603
$896$		0			0
$897$	−7.65349			−0.255543
$898$		0			0
$899$	9.81693	−	5.24726i	0.327413	−	0.175006i
$900$		0			0
$901$	15.9255	+	19.4052i	0.530555	+	0.646483i
$902$		0			0
$903$	6.24127	−	4.17028i	0.207696	−	0.138778i
$904$		0			0
$905$	−19.2372	+	28.7905i	−0.639467	+	0.957030i
$906$		0			0
$907$	−36.9208	+	11.1998i	−1.22594	+	0.371884i	−0.835882	−	0.548909i	$-0.815043\pi$
$907$	−36.9208	+	11.1998i	−1.22594	+	0.371884i	−0.390053	+	0.920792i	$0.627543\pi$
$908$		0			0
$909$	−8.31839	−	6.82673i	−0.275904	−	0.226428i
$910$		0			0
$911$	−3.58163	−	1.48356i	−0.118665	−	0.0491525i	0.322561	−	0.946549i	$-0.395456\pi$
$911$	−3.58163	−	1.48356i	−0.118665	−	0.0491525i	−0.441226	+	0.897396i	$0.645456\pi$
$912$		0			0
$913$	2.68837	−	1.11356i	0.0889720	−	0.0368534i
$914$		0			0
$915$	−2.83670	−	28.8015i	−0.0937785	−	0.952149i
$916$		0			0
$917$	22.5001	−	42.0947i	0.743018	−	1.39009i
$918$		0			0
$919$	−6.93575	+	1.37961i	−0.228789	+	0.0455090i	−0.308153	−	0.951337i	$-0.599711\pi$
$919$	−6.93575	+	1.37961i	−0.228789	+	0.0455090i	0.0793641	+	0.996846i	$0.474711\pi$
$920$		0			0
$921$	−10.8086	+	54.3385i	−0.356155	+	1.79051i
$922$		0			0
$923$	0.364353	−	3.69934i	0.0119928	−	0.121765i
$924$		0			0
$925$	0.338892	−	1.11718i	0.0111427	−	0.0367325i
$926$		0			0
$927$	−1.73310	−	1.73310i	−0.0569225	−	0.0569225i
$928$		0			0
$929$	42.7880	−	42.7880i	1.40383	−	1.40383i	0.616373	−	0.787454i	$-0.288601\pi$
$929$	42.7880	−	42.7880i	1.40383	−	1.40383i	0.787454	−	0.616373i	$-0.211399\pi$
$930$		0			0
$931$	−95.5151	−	28.9742i	−3.13038	−	0.949591i
$932$		0			0
$933$	−49.4057	−	4.86603i	−1.61747	−	0.159307i
$934$		0			0
$935$	−45.2289	−	8.99660i	−1.47914	−	0.294220i
$936$		0			0
$937$	2.91321	+	14.6457i	0.0951704	+	0.478454i	0.998748	+	0.0500288i	$0.0159313\pi$
$937$	2.91321	+	14.6457i	0.0951704	+	0.478454i	−0.903577	+	0.428425i	$0.859069\pi$
$938$		0			0
$939$	−18.4093	−	9.84000i	−0.600766	−	0.321116i
$940$		0			0
$941$	37.8957	−	3.73240i	1.23536	−	0.121673i	0.540830	−	0.841132i	$-0.318110\pi$
$941$	37.8957	−	3.73240i	1.23536	−	0.121673i	0.694535	+	0.719459i	$0.255610\pi$
$942$		0			0
$943$	2.48618	+	6.00216i	0.0809610	+	0.195457i
$944$		0			0
$945$	18.6725	−	45.0794i	0.607417	−	1.46643i
$946$		0			0
$947$	7.01342	−	8.54588i	0.227906	−	0.277704i	−0.646485	−	0.762927i	$-0.723762\pi$
$947$	7.01342	−	8.54588i	0.227906	−	0.277704i	0.874390	+	0.485223i	$0.161262\pi$
$948$		0			0
$949$	5.13392	+	16.9243i	0.166654	+	0.549385i
$950$		0			0
$951$	−17.6072	−	11.7648i	−0.570954	−	0.381499i
$952$		0			0
$953$	−21.0958	−	31.5722i	−0.683361	−	1.02272i	−0.997311	−	0.0732831i	$-0.976652\pi$
$953$	−21.0958	−	31.5722i	−0.683361	−	1.02272i	0.313950	−	0.949440i	$-0.398348\pi$
$954$		0			0
$955$	7.27411	−	5.96971i	0.235385	−	0.193175i
$956$		0			0
$957$	8.51065	+	15.9223i	0.275110	+	0.514695i
$958$		0			0
$959$			36.1596i			1.16765i
$960$		0			0
$961$		−	1.85468i		−	0.0598283i
$962$		0			0
$963$	3.10839	+	5.81539i	0.100167	+	0.187398i
$964$		0			0
$965$	35.8797	−	29.4457i	1.15501	−	0.947891i
$966$		0			0
$967$	1.38573	+	2.07389i	0.0445620	+	0.0666918i	0.853082	−	0.521777i	$-0.174731\pi$
$967$	1.38573	+	2.07389i	0.0445620	+	0.0666918i	−0.808520	+	0.588469i	$0.799731\pi$
$968$		0			0
$969$	52.8533	+	35.3154i	1.69789	+	1.13449i
$970$		0			0
$971$	4.18674	+	13.8018i	0.134359	+	0.442922i	0.998141	−	0.0609432i	$-0.0194108\pi$
$971$	4.18674	+	13.8018i	0.134359	+	0.442922i	−0.863782	+	0.503865i	$0.831911\pi$
$972$		0			0
$973$	−35.3182	+	43.0353i	−1.13225	+	1.37965i
$974$		0			0
$975$	1.83600	−	4.43250i	0.0587991	−	0.141954i
$976$		0			0
$977$	10.8482	+	26.1899i	0.347065	+	0.837890i	0.996964	+	0.0778686i	$0.0248115\pi$
$977$	10.8482	+	26.1899i	0.347065	+	0.837890i	−0.649898	+	0.760021i	$0.725189\pi$
$978$		0			0
$979$	15.2149	−	1.49853i	0.486269	−	0.0478933i
$980$		0			0
$981$	−2.12624	−	1.13650i	−0.0678858	−	0.0362857i
$982$		0			0
$983$	0.706860	+	3.55362i	0.0225453	+	0.113343i	0.990419	−	0.138093i	$-0.0440972\pi$
$983$	0.706860	+	3.55362i	0.0225453	+	0.113343i	−0.967874	+	0.251436i	$0.919097\pi$
$984$		0			0
$985$	−30.0582	−	5.97894i	−0.957733	−	0.190505i
$986$		0			0
$987$	−31.1318	−	3.06621i	−0.990936	−	0.0975987i
$988$		0			0
$989$	1.53315	+	0.465077i	0.0487514	+	0.0147886i
$990$		0			0
$991$	28.2557	−	28.2557i	0.897571	−	0.897571i	−0.0976497	−	0.995221i	$-0.531132\pi$
$991$	28.2557	−	28.2557i	0.897571	−	0.897571i	0.995221	+	0.0976497i	$0.0311325\pi$
$992$		0			0
$993$	0.546348	+	0.546348i	0.0173378	+	0.0173378i
$994$		0			0
$995$	−14.9013	+	49.1232i	−0.472404	+	1.55731i
$996$		0			0
$997$	−3.63614	+	36.9183i	−0.115158	+	1.16921i	0.747795	+	0.663930i	$0.231113\pi$
$997$	−3.63614	+	36.9183i	−0.115158	+	1.16921i	−0.862953	+	0.505285i	$0.831387\pi$
$998$		0			0
$999$	−0.919229	+	4.62128i	−0.0290831	+	0.146211i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	512.2.k.a.497.4		240
4.3	odd	2		128.2.k.a.101.6	✓	240
128.19	odd	32		128.2.k.a.109.6	yes	240
128.109	even	32	inner	512.2.k.a.273.4		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
128.2.k.a.101.6	✓	240	4.3	odd	2
128.2.k.a.109.6	yes	240	128.19	odd	32
512.2.k.a.273.4		240	128.109	even	32	inner
512.2.k.a.497.4		240	1.1	even	1	trivial

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

\(f(q)\)	\(=\)	\(q+(-1.68175 + 0.898916i) q^{3} +(-1.56899 - 1.91182i) q^{5} +(-3.63941 + 2.43178i) q^{7} +(0.353534 - 0.529101i) q^{9} +(4.39407 - 1.33293i) q^{11} +(1.74149 + 1.42920i) q^{13} +(4.35722 + 1.80482i) q^{15} +(3.75158 - 1.55396i) q^{17} +(-0.804629 - 8.16953i) q^{19} +(3.93463 - 7.36118i) q^{21} +(1.74729 - 0.347558i) q^{23} +(-0.217872 + 1.09532i) q^{25} +(0.441793 - 4.48560i) q^{27} +(0.598530 - 1.97309i) q^{29} +(3.81742 + 3.81742i) q^{31} +(-6.19155 + 6.19155i) q^{33} +(10.3593 + 3.14247i) q^{35} +(-1.04034 - 0.102465i) q^{37} +(-4.21349 - 0.838114i) q^{39} +(0.711436 + 3.57663i) q^{41} +(0.793119 + 0.423931i) q^{43} +(-1.56624 + 0.154261i) q^{45} +(-1.43424 - 3.46257i) q^{47} +(4.65300 - 11.2333i) q^{49} +(-4.91236 + 5.98573i) q^{51} +(1.79456 + 5.91588i) q^{53} +(-9.44255 - 6.30931i) q^{55} +(8.69691 + 13.0158i) q^{57} +(4.26007 - 3.49615i) q^{59} +(-2.89271 - 5.41187i) q^{61} +2.78534i q^{63} -5.57181i q^{65} +(2.61401 + 4.89047i) q^{67} +(-2.62609 + 2.15518i) q^{69} +(-0.916693 - 1.37193i) q^{71} +(6.52734 + 4.36143i) q^{73} +(-0.618190 - 2.03790i) q^{75} +(-12.7504 + 15.5365i) q^{77} +(4.05951 - 9.80052i) q^{79} +(4.01974 + 9.70452i) q^{81} +(0.630660 - 0.0621146i) q^{83} +(-8.85708 - 4.73421i) q^{85} +(0.767061 + 3.85628i) q^{87} +(3.26555 + 0.649558i) q^{89} +(-9.81350 - 0.966545i) q^{91} +(-9.85149 - 2.98842i) q^{93} +(-14.3562 + 14.3562i) q^{95} +(-12.6095 - 12.6095i) q^{97} +(0.848200 - 2.79614i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 16 q^{3} - 16 q^{5} + 16 q^{7} - 16 q^{9} + 16 q^{11} - 16 q^{13} + 16 q^{15} - 16 q^{17} + 16 q^{19} - 16 q^{21} + 16 q^{23} - 16 q^{25} + 16 q^{27} - 16 q^{29} + 16 q^{31} - 16 q^{33} + 16 q^{35}+ \cdots + 16 q^{99}+O(q^{100}) \) 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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