LMFDB - Embedded newform 512.2.k.a.497.14

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			497.14
Character	$\chi$	$=$	512.497
Dual form			512.2.k.a.273.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.04524 - 1.09320i) q^{3} +(1.40777 + 1.71538i) q^{5} +(3.76720 - 2.51716i) q^{7} +(1.32120 - 1.97732i) q^{9} +(-2.34650 + 0.711804i) q^{11} +(0.439069 + 0.360335i) q^{13} +(4.75449 + 1.96937i) q^{15} +(-7.29065 + 3.01989i) q^{17} +(-0.155936 - 1.58325i) q^{19} +(4.95306 - 9.26652i) q^{21} +(-1.54399 + 0.307120i) q^{23} +(0.0147614 - 0.0742104i) q^{25} +(-0.141364 + 1.43529i) q^{27} +(-1.22667 + 4.04380i) q^{29} +(0.936536 + 0.936536i) q^{31} +(-4.02101 + 4.02101i) q^{33} +(9.62124 + 2.91857i) q^{35} +(7.54247 + 0.742868i) q^{37} +(1.29192 + 0.256979i) q^{39} +(-0.504297 - 2.53527i) q^{41} +(-8.44569 - 4.51431i) q^{43} +(5.25179 - 0.517256i) q^{45} +(-4.89792 - 11.8246i) q^{47} +(5.17691 - 12.4982i) q^{49} +(-11.6098 + 14.1466i) q^{51} +(-0.556917 - 1.83591i) q^{53} +(-4.52435 - 3.02307i) q^{55} +(-2.04974 - 3.06765i) q^{57} +(0.239847 - 0.196837i) q^{59} +(4.32711 + 8.09545i) q^{61} -10.7746i q^{63} +1.26044i q^{65} +(3.98633 + 7.45789i) q^{67} +(-2.82209 + 2.31603i) q^{69} +(-3.92813 - 5.87886i) q^{71} +(2.97590 + 1.98843i) q^{73} +(-0.0509365 - 0.167915i) q^{75} +(-7.04802 + 8.58804i) q^{77} +(-4.13418 + 9.98079i) q^{79} +(4.01012 + 9.68128i) q^{81} +(12.8936 - 1.26990i) q^{83} +(-15.4438 - 8.25489i) q^{85} +(1.91185 + 9.61154i) q^{87} +(-8.22013 - 1.63509i) q^{89} +(2.56108 + 0.252245i) q^{91} +(2.93927 + 0.891616i) q^{93} +(2.49634 - 2.49634i) q^{95} +(-6.77721 - 6.77721i) q^{97} +(-1.69274 + 5.58021i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	2.04524	−	1.09320i	1.18082	−	0.631161i	0.240233	−	0.970715i	$-0.422776\pi$
$3$	2.04524	−	1.09320i	1.18082	−	0.631161i	0.940587	+	0.339554i	$0.110276\pi$
$4$		0			0
$5$	1.40777	+	1.71538i	0.629575	+	0.767139i	0.985920	−	0.167215i	$-0.0534774\pi$
$5$	1.40777	+	1.71538i	0.629575	+	0.767139i	−0.356346	+	0.934354i	$0.615977\pi$
$6$		0			0
$7$	3.76720	−	2.51716i	1.42387	−	0.951399i	0.424935	−	0.905224i	$-0.360297\pi$
$7$	3.76720	−	2.51716i	1.42387	−	0.951399i	0.998933	−	0.0461749i	$-0.0147032\pi$
$8$		0			0
$9$	1.32120	−	1.97732i	0.440400	−	0.659105i
$10$		0			0
$11$	−2.34650	+	0.711804i	−0.707497	+	0.214617i	−0.623471	−	0.781847i	$-0.714278\pi$
$11$	−2.34650	+	0.711804i	−0.707497	+	0.214617i	−0.0840262	+	0.996464i	$0.526778\pi$
$12$		0			0
$13$	0.439069	+	0.360335i	0.121776	+	0.0999389i	0.693310	−	0.720639i	$-0.256152\pi$
$13$	0.439069	+	0.360335i	0.121776	+	0.0999389i	−0.571534	+	0.820578i	$0.693652\pi$
$14$		0			0
$15$	4.75449	+	1.96937i	1.22760	+	0.508490i
$16$		0			0
$17$	−7.29065	+	3.01989i	−1.76824	+	0.732430i	−0.773067	+	0.634324i	$0.781278\pi$
$17$	−7.29065	+	3.01989i	−1.76824	+	0.732430i	−0.995176	+	0.0981061i	$0.968722\pi$
$18$		0			0
$19$	−0.155936	−	1.58325i	−0.0357743	−	0.363222i	−0.996360	−	0.0852400i	$-0.972834\pi$
$19$	−0.155936	−	1.58325i	−0.0357743	−	0.363222i	0.960586	−	0.277982i	$-0.0896657\pi$
$20$		0			0
$21$	4.95306	−	9.26652i	1.08085	−	2.02212i
$22$		0			0
$23$	−1.54399	+	0.307120i	−0.321945	+	0.0640388i	−0.353417	−	0.935466i	$-0.614980\pi$
$23$	−1.54399	+	0.307120i	−0.321945	+	0.0640388i	0.0314723	+	0.999505i	$0.489980\pi$
$24$		0			0
$25$	0.0147614	−	0.0742104i	0.00295227	−	0.0148421i
$26$		0			0
$27$	−0.141364	+	1.43529i	−0.0272055	+	0.276222i
$28$		0			0
$29$	−1.22667	+	4.04380i	−0.227787	+	0.750915i	0.766315	+	0.642466i	$0.222088\pi$
$29$	−1.22667	+	4.04380i	−0.227787	+	0.750915i	−0.994102	+	0.108449i	$0.965412\pi$
$30$		0			0
$31$	0.936536	+	0.936536i	0.168207	+	0.168207i	0.786191	−	0.617984i	$-0.212050\pi$
$31$	0.936536	+	0.936536i	0.168207	+	0.168207i	−0.617984	+	0.786191i	$0.712050\pi$
$32$		0			0
$33$	−4.02101	+	4.02101i	−0.699968	+	0.699968i
$34$		0			0
$35$	9.62124	+	2.91857i	1.62629	+	0.493329i
$36$		0			0
$37$	7.54247	+	0.742868i	1.23997	+	0.122127i	0.696659	−	0.717402i	$-0.254669\pi$
$37$	7.54247	+	0.742868i	1.23997	+	0.122127i	0.543315	+	0.839529i	$0.317169\pi$
$38$		0			0
$39$	1.29192	+	0.256979i	0.206873	+	0.0411496i
$40$		0			0
$41$	−0.504297	−	2.53527i	−0.0787579	−	0.395943i	−0.999976	−	0.00689674i	$-0.997805\pi$
$41$	−0.504297	−	2.53527i	−0.0787579	−	0.395943i	0.921218	−	0.389046i	$-0.127195\pi$
$42$		0			0
$43$	−8.44569	−	4.51431i	−1.28796	−	0.688427i	−0.321903	−	0.946773i	$-0.604323\pi$
$43$	−8.44569	−	4.51431i	−1.28796	−	0.688427i	−0.966052	+	0.258346i	$0.916823\pi$
$44$		0			0
$45$	5.25179	−	0.517256i	0.782890	−	0.0771079i
$46$		0			0
$47$	−4.89792	−	11.8246i	−0.714435	−	1.72480i	−0.688611	−	0.725131i	$-0.741779\pi$
$47$	−4.89792	−	11.8246i	−0.714435	−	1.72480i	−0.0258237	−	0.999667i	$-0.508221\pi$
$48$		0			0
$49$	5.17691	−	12.4982i	0.739559	−	1.78545i
$50$		0			0
$51$	−11.6098	+	14.1466i	−1.62569	+	1.98091i
$52$		0			0
$53$	−0.556917	−	1.83591i	−0.0764984	−	0.252181i	0.910348	−	0.413844i	$-0.135814\pi$
$53$	−0.556917	−	1.83591i	−0.0764984	−	0.252181i	−0.986846	+	0.161663i	$0.948314\pi$
$54$		0			0
$55$	−4.52435	−	3.02307i	−0.610063	−	0.407631i
$56$		0			0
$57$	−2.04974	−	3.06765i	−0.271495	−	0.406321i
$58$		0			0
$59$	0.239847	−	0.196837i	0.0312254	−	0.0256261i	−0.618651	−	0.785666i	$-0.712321\pi$
$59$	0.239847	−	0.196837i	0.0312254	−	0.0256261i	0.649877	+	0.760040i	$0.274821\pi$
$60$		0			0
$61$	4.32711	+	8.09545i	0.554029	+	1.03652i	0.990593	+	0.136842i	$0.0436954\pi$
$61$	4.32711	+	8.09545i	0.554029	+	1.03652i	−0.436564	+	0.899673i	$0.643805\pi$
$62$		0			0
$63$		−	10.7746i		−	1.35747i
$64$		0			0
$65$			1.26044i			0.156338i
$66$		0			0
$67$	3.98633	+	7.45789i	0.487007	+	0.911126i	0.998651	+	0.0519286i	$0.0165368\pi$
$67$	3.98633	+	7.45789i	0.487007	+	0.911126i	−0.511644	+	0.859198i	$0.670963\pi$
$68$		0			0
$69$	−2.82209	+	2.31603i	−0.339740	+	0.278818i
$70$		0			0
$71$	−3.92813	−	5.87886i	−0.466183	−	0.697693i	0.521659	−	0.853154i	$-0.325313\pi$
$71$	−3.92813	−	5.87886i	−0.466183	−	0.697693i	−0.987842	+	0.155462i	$0.950313\pi$
$72$		0			0
$73$	2.97590	+	1.98843i	0.348303	+	0.232729i	0.717399	−	0.696663i	$-0.245333\pi$
$73$	2.97590	+	1.98843i	0.348303	+	0.232729i	−0.369096	+	0.929391i	$0.620333\pi$
$74$		0			0
$75$	−0.0509365	−	0.167915i	−0.00588164	−	0.0193892i
$76$		0			0
$77$	−7.04802	+	8.58804i	−0.803197	+	0.978698i
$78$		0			0
$79$	−4.13418	+	9.98079i	−0.465132	+	1.12293i	0.501132	+	0.865371i	$0.332917\pi$
$79$	−4.13418	+	9.98079i	−0.465132	+	1.12293i	−0.966263	+	0.257556i	$0.917083\pi$
$80$		0			0
$81$	4.01012	+	9.68128i	0.445569	+	1.07570i
$82$		0			0
$83$	12.8936	−	1.26990i	1.41525	−	0.139390i	0.638706	−	0.769451i	$-0.279470\pi$
$83$	12.8936	−	1.26990i	1.41525	−	0.139390i	0.776546	+	0.630061i	$0.216970\pi$
$84$		0			0
$85$	−15.4438	−	8.25489i	−1.67512	−	0.895369i
$86$		0			0
$87$	1.91185	+	9.61154i	0.204972	+	1.03047i
$88$		0			0
$89$	−8.22013	−	1.63509i	−0.871332	−	0.173319i	−0.260879	−	0.965371i	$-0.584012\pi$
$89$	−8.22013	−	1.63509i	−0.871332	−	0.173319i	−0.610453	+	0.792053i	$0.709012\pi$
$90$		0			0
$91$	2.56108	+	0.252245i	0.268475	+	0.0264424i
$92$		0			0
$93$	2.93927	+	0.891616i	0.304788	+	0.0924563i
$94$		0			0
$95$	2.49634	−	2.49634i	0.256120	−	0.256120i
$96$		0			0
$97$	−6.77721	−	6.77721i	−0.688121	−	0.688121i	0.273695	−	0.961816i	$-0.411754\pi$
$97$	−6.77721	−	6.77721i	−0.688121	−	0.688121i	−0.961816	+	0.273695i	$0.911754\pi$
$98$		0			0
$99$	−1.69274	+	5.58021i	−0.170127	+	0.560832i
$100$		0			0
$101$	−1.14299	+	11.6049i	−0.113731	+	1.15473i	0.753715	+	0.657202i	$0.228260\pi$
$101$	−1.14299	+	11.6049i	−0.113731	+	1.15473i	−0.867446	+	0.497532i	$0.834240\pi$
$102$		0			0
$103$	0.959856	−	4.82552i	0.0945774	−	0.475473i	−0.904247	−	0.427009i	$-0.859567\pi$
$103$	0.959856	−	4.82552i	0.0945774	−	0.475473i	0.998825	−	0.0484641i	$-0.0154327\pi$
$104$		0			0
$105$	22.8683	−	4.54880i	2.23172	−	0.443917i
$106$		0			0
$107$	0.542427	−	1.01481i	0.0524384	−	0.0981053i	−0.854337	−	0.519720i	$-0.826036\pi$
$107$	0.542427	−	1.01481i	0.0524384	−	0.0981053i	0.906775	+	0.421614i	$0.138536\pi$
$108$		0			0
$109$	0.598791	+	6.07963i	0.0573538	+	0.582323i	0.980316	+	0.197433i	$0.0632606\pi$
$109$	0.598791	+	6.07963i	0.0573538	+	0.582323i	−0.922963	+	0.384890i	$0.874239\pi$
$110$		0			0
$111$	16.2383	−	6.72610i	1.54127	−	0.638414i
$112$		0			0
$113$	2.76410	+	1.14493i	0.260024	+	0.107706i	0.508887	−	0.860833i	$-0.330057\pi$
$113$	2.76410	+	1.14493i	0.260024	+	0.107706i	−0.248863	+	0.968539i	$0.580057\pi$
$114$		0			0
$115$	−2.70042	−	2.21618i	−0.251815	−	0.206659i
$116$		0			0
$117$	1.29259	−	0.392104i	0.119500	−	0.0362500i
$118$		0			0
$119$	−19.8638	+	29.7283i	−1.82091	+	2.72519i
$120$		0			0
$121$	−4.14676	+	2.77078i	−0.376978	+	0.251889i
$122$		0			0
$123$	−3.80297	−	4.63394i	−0.342903	−	0.417828i
$124$		0			0
$125$	9.93337	−	5.30950i	0.888467	−	0.474896i
$126$		0			0
$127$	5.67946			0.503971			0.251985	−	0.967731i	$-0.418917\pi$
$127$	5.67946			0.503971			0.251985	+	0.967731i	$0.418917\pi$
$128$		0			0
$129$	−22.2085			−1.95535
$130$		0			0
$131$	−7.71227	+	4.12230i	−0.673824	+	0.360167i	−0.772555	−	0.634948i	$-0.781022\pi$
$131$	−7.71227	+	4.12230i	−0.673824	+	0.360167i	0.0987309	+	0.995114i	$0.468522\pi$
$132$		0			0
$133$	−4.57274	−	5.57190i	−0.396507	−	0.483145i
$134$		0			0
$135$	−2.66108	+	1.77807i	−0.229029	+	0.153032i
$136$		0			0
$137$	−2.44148	+	3.65394i	−0.208590	+	0.312177i	−0.920982	−	0.389604i	$-0.872612\pi$
$137$	−2.44148	+	3.65394i	−0.208590	+	0.312177i	0.712392	+	0.701782i	$0.247612\pi$
$138$		0			0
$139$	−10.3218	+	3.13110i	−0.875487	+	0.265576i	−0.695876	−	0.718161i	$-0.744984\pi$
$139$	−10.3218	+	3.13110i	−0.875487	+	0.265576i	−0.179611	+	0.983738i	$0.557484\pi$
$140$		0			0
$141$	−22.9441	−	18.8298i	−1.93224	−	1.58575i
$142$		0			0
$143$	−1.28676	−	0.532995i	−0.107605	−	0.0445713i
$144$		0			0
$145$	−8.66351	+	3.58854i	−0.719465	+	0.298012i
$146$		0			0
$147$	−3.07502	−	31.2212i	−0.253623	−	2.57508i
$148$		0			0
$149$	0.673039	−	1.25917i	0.0551375	−	0.103155i	−0.852843	−	0.522167i	$-0.825124\pi$
$149$	0.673039	−	1.25917i	0.0551375	−	0.103155i	0.907981	+	0.419012i	$0.137624\pi$
$150$		0			0
$151$	2.76618	−	0.550228i	0.225109	−	0.0447769i	−0.0812470	−	0.996694i	$-0.525890\pi$
$151$	2.76618	−	0.550228i	0.225109	−	0.0447769i	0.306356	+	0.951917i	$0.400890\pi$
$152$		0			0
$153$	−3.66114	+	18.4058i	−0.295986	+	1.48802i
$154$		0			0
$155$	−0.288082	+	2.92494i	−0.0231393	+	0.234937i
$156$		0			0
$157$	0.894050	−	2.94729i	0.0713530	−	0.235219i	−0.914009	−	0.405694i	$-0.867030\pi$
$157$	0.894050	−	2.94729i	0.0713530	−	0.235219i	0.985362	+	0.170474i	$0.0545300\pi$
$158$		0			0
$159$	−3.14605	−	3.14605i	−0.249498	−	0.249498i
$160$		0			0
$161$	−5.04347	+	5.04347i	−0.397481	+	0.397481i
$162$		0			0
$163$	−6.09144	−	1.84782i	−0.477119	−	0.144732i	0.0425605	−	0.999094i	$-0.486448\pi$
$163$	−6.09144	−	1.84782i	−0.477119	−	0.144732i	−0.519679	+	0.854362i	$0.673948\pi$
$164$		0			0
$165$	−12.5582	−	1.23688i	−0.977656	−	0.0962907i
$166$		0			0
$167$	−4.38348	−	0.871929i	−0.339204	−	0.0674719i	0.0225493	−	0.999746i	$-0.492822\pi$
$167$	−4.38348	−	0.871929i	−0.339204	−	0.0674719i	−0.361753	+	0.932274i	$0.617822\pi$
$168$		0			0
$169$	−2.47323	−	12.4338i	−0.190249	−	0.956445i
$170$		0			0
$171$	−3.33661	−	1.78345i	−0.255157	−	0.136384i
$172$		0			0
$173$	11.8857	−	1.17064i	0.903656	−	0.0890024i	0.364495	−	0.931205i	$-0.381242\pi$
$173$	11.8857	−	1.17064i	0.903656	−	0.0890024i	0.539161	+	0.842203i	$0.318742\pi$
$174$		0			0
$175$	−0.131191	−	0.316722i	−0.00991708	−	0.0239420i
$176$		0			0
$177$	0.275361	−	0.664781i	0.0206974	−	0.0499680i
$178$		0			0
$179$	10.6135	−	12.9326i	0.793288	−	0.966625i	−0.206642	−	0.978417i	$-0.566254\pi$
$179$	10.6135	−	12.9326i	0.793288	−	0.966625i	0.999930	+	0.0117920i	$0.00375361\pi$
$180$		0			0
$181$	3.78024	+	12.4618i	0.280983	+	0.926278i	0.977891	+	0.209117i	$0.0670589\pi$
$181$	3.78024	+	12.4618i	0.280983	+	0.926278i	−0.696907	+	0.717161i	$0.745441\pi$
$182$		0			0
$183$	17.6999	+	11.8267i	1.30842	+	0.874256i
$184$		0			0
$185$	9.34378	+	13.9839i	0.686968	+	1.02812i
$186$		0			0
$187$	14.9580	−	12.2757i	1.09383	−	0.897687i
$188$		0			0
$189$	3.08032	+	5.76288i	0.224061	+	0.419188i
$190$		0			0
$191$			8.12345i			0.587792i	0.955837	+	0.293896i	$0.0949520\pi$
$191$			8.12345i			0.587792i	−0.955837	+	0.293896i	$0.905048\pi$
$192$		0			0
$193$		−	19.2854i		−	1.38820i	−0.719880	−	0.694098i	$-0.755803\pi$
$193$		−	19.2854i		−	1.38820i	0.719880	−	0.694098i	$-0.244197\pi$
$194$		0			0
$195$	1.37791	+	2.57790i	0.0986745	+	0.184607i
$196$		0			0
$197$	2.95248	−	2.42304i	0.210355	−	0.172634i	−0.523316	−	0.852139i	$-0.675305\pi$
$197$	2.95248	−	2.42304i	0.210355	−	0.172634i	0.733671	+	0.679505i	$0.237805\pi$
$198$		0			0
$199$	−2.96170	−	4.43250i	−0.209950	−	0.314212i	0.711517	−	0.702669i	$-0.248008\pi$
$199$	−2.96170	−	4.43250i	−0.209950	−	0.314212i	−0.921467	+	0.388457i	$0.873008\pi$
$200$		0			0
$201$	16.3060	+	10.8953i	1.15014	+	0.768496i
$202$		0			0
$203$	5.55778	+	18.3215i	0.390080	+	1.28592i
$204$		0			0
$205$	3.63901	−	4.43414i	0.254159	−	0.309694i
$206$		0			0
$207$	−1.43265	+	3.45873i	−0.0995762	+	0.240398i
$208$		0			0
$209$	1.49287	+	3.60410i	0.103264	+	0.249301i
$210$		0			0
$211$	−19.3488	+	1.90569i	−1.33203	+	0.131193i	−0.738845	−	0.673876i	$-0.764628\pi$
$211$	−19.3488	+	1.90569i	−1.33203	+	0.131193i	−0.593181	+	0.805069i	$0.702128\pi$
$212$		0			0
$213$	−14.4608	−	7.72943i	−0.990835	−	0.529612i
$214$		0			0
$215$	−4.14586	−	20.8427i	−0.282745	−	1.42146i
$216$		0			0
$217$	5.88554	+	1.17071i	0.399536	+	0.0794727i
$218$		0			0
$219$	8.26019	+	0.813558i	0.558172	+	0.0549751i
$220$		0			0
$221$	−4.28927	−	1.30114i	−0.288528	−	0.0875239i
$222$		0			0
$223$	−10.0381	+	10.0381i	−0.672201	+	0.672201i	−0.958223	−	0.286022i	$-0.907667\pi$
$223$	−10.0381	+	10.0381i	−0.672201	+	0.672201i	0.286022	+	0.958223i	$0.407667\pi$
$224$		0			0
$225$	−0.127235	−	0.127235i	−0.00848231	−	0.00848231i
$226$		0			0
$227$	−3.82972	+	12.6249i	−0.254187	+	0.837944i	0.733254	+	0.679955i	$0.238001\pi$
$227$	−3.82972	+	12.6249i	−0.254187	+	0.837944i	−0.987441	+	0.157988i	$0.949499\pi$
$228$		0			0
$229$	2.42090	−	24.5798i	0.159978	−	1.62428i	−0.495181	−	0.868790i	$-0.664898\pi$
$229$	2.42090	−	24.5798i	0.159978	−	1.62428i	0.655159	−	0.755491i	$-0.272602\pi$
$230$		0			0
$231$	−5.02642	+	25.2695i	−0.330714	+	1.66261i
$232$		0			0
$233$	−5.07579	+	1.00964i	−0.332526	+	0.0661436i	−0.358530	−	0.933518i	$-0.616722\pi$
$233$	−5.07579	+	1.00964i	−0.332526	+	0.0661436i	0.0260035	+	0.999662i	$0.491722\pi$
$234$		0			0
$235$	13.3885	−	25.0481i	0.873370	−	1.63396i
$236$		0			0
$237$	2.45565	+	24.9326i	0.159511	+	1.61955i
$238$		0			0
$239$	18.2854	−	7.57405i	1.18278	−	0.489925i	0.297384	−	0.954758i	$-0.403886\pi$
$239$	18.2854	−	7.57405i	1.18278	−	0.489925i	0.885398	+	0.464833i	$0.153886\pi$
$240$		0			0
$241$	27.0340	+	11.1978i	1.74141	+	0.721316i	0.998660	+	0.0517493i	$0.0164797\pi$
$241$	27.0340	+	11.1978i	1.74141	+	0.721316i	0.742752	+	0.669567i	$0.233520\pi$
$242$		0			0
$243$	15.4407	+	12.6718i	0.990519	+	0.812898i
$244$		0			0
$245$	28.7270	−	8.71423i	1.83530	−	0.556732i
$246$		0			0
$247$	0.502033	−	0.751345i	0.0319436	−	0.0478070i
$248$		0			0
$249$	24.9821	−	16.6925i	1.58318	−	1.05785i
$250$		0			0
$251$	−2.71869	−	3.31274i	−0.171602	−	0.209098i	0.680107	−	0.733113i	$-0.261934\pi$
$251$	−2.71869	−	3.31274i	−0.171602	−	0.209098i	−0.851709	+	0.524015i	$0.824434\pi$
$252$		0			0
$253$	3.40438	−	1.81968i	0.214031	−	0.114402i
$254$		0			0
$255$	−40.6106			−2.54313
$256$		0			0
$257$	18.8503			1.17585			0.587923	−	0.808917i	$-0.299946\pi$
$257$	18.8503			1.17585			0.587923	+	0.808917i	$0.299946\pi$
$258$		0			0
$259$	30.2839	−	16.1871i	1.88175	−	1.00582i
$260$		0			0
$261$	6.37519	+	7.76819i	0.394614	+	0.480839i
$262$		0			0
$263$	16.1047	−	10.7608i	0.993060	−	0.663541i	0.0508993	−	0.998704i	$-0.483791\pi$
$263$	16.1047	−	10.7608i	0.993060	−	0.663541i	0.942160	+	0.335163i	$0.108791\pi$
$264$		0			0
$265$	2.36526	−	3.53986i	0.145297	−	0.217452i
$266$		0			0
$267$	−18.5996	+	5.64213i	−1.13828	+	0.345293i
$268$		0			0
$269$	−2.56839	−	2.10782i	−0.156597	−	0.128516i	0.552832	−	0.833293i	$-0.313547\pi$
$269$	−2.56839	−	2.10782i	−0.156597	−	0.128516i	−0.709429	+	0.704777i	$0.751047\pi$
$270$		0			0
$271$	17.9702	+	7.44348i	1.09161	+	0.452159i	0.854567	−	0.519340i	$-0.173822\pi$
$271$	17.9702	+	7.44348i	1.09161	+	0.452159i	0.237041	+	0.971500i	$0.423822\pi$
$272$		0			0
$273$	5.51378	−	2.28388i	0.333709	−	0.138227i
$274$		0			0
$275$	0.0181857	+	0.184642i	0.00109664	+	0.0111343i
$276$		0			0
$277$	−2.48038	+	4.64046i	−0.149032	+	0.278818i	−0.945349	−	0.326061i	$-0.894279\pi$
$277$	−2.48038	+	4.64046i	−0.149032	+	0.278818i	0.796317	+	0.604879i	$0.206779\pi$
$278$		0			0
$279$	3.08918	−	0.614476i	0.184944	−	0.0367877i
$280$		0			0
$281$	−3.07883	+	15.4783i	−0.183668	+	0.923360i	0.773493	+	0.633804i	$0.218508\pi$
$281$	−3.07883	+	15.4783i	−0.183668	+	0.923360i	−0.957161	+	0.289556i	$0.906492\pi$
$282$		0			0
$283$	0.221102	−	2.24489i	0.0131432	−	0.133445i	−0.986374	−	0.164519i	$-0.947393\pi$
$283$	0.221102	−	2.24489i	0.0131432	−	0.133445i	0.999517	+	0.0310743i	$0.00989284\pi$
$284$		0			0
$285$	2.37661	−	7.83463i	0.140778	−	0.464084i
$286$		0			0
$287$	−8.28148	−	8.28148i	−0.488840	−	0.488840i
$288$		0			0
$289$	32.0131	−	32.0131i	1.88312	−	1.88312i
$290$		0			0
$291$	−21.2699	−	6.45214i	−1.24686	−	0.378231i
$292$		0			0
$293$	−3.42937	−	0.337764i	−0.200346	−	0.0197324i	−0.00265369	−	0.999996i	$-0.500845\pi$
$293$	−3.42937	−	0.337764i	−0.200346	−	0.0197324i	−0.197692	+	0.980264i	$0.563345\pi$
$294$		0			0
$295$	0.675300	+	0.134326i	0.0393175	+	0.00782074i
$296$		0			0
$297$	−0.689936	−	3.46854i	−0.0400342	−	0.201265i
$298$		0			0
$299$	−0.788586	−	0.421508i	−0.0456051	−	0.0243764i
$300$		0			0
$301$	−43.1799	+	4.25285i	−2.48885	+	0.245130i
$302$		0			0
$303$	10.3489	+	24.9844i	0.594527	+	1.43531i
$304$		0			0
$305$	−7.79515	+	18.8192i	−0.446349	+	1.07758i
$306$		0			0
$307$	4.50050	−	5.48387i	0.256857	−	0.312981i	−0.628576	−	0.777748i	$-0.716362\pi$
$307$	4.50050	−	5.48387i	0.256857	−	0.312981i	0.885433	+	0.464767i	$0.153862\pi$
$308$		0			0
$309$	−3.31214	−	10.9187i	−0.188421	−	0.621141i
$310$		0			0
$311$	12.0130	+	8.02684i	0.681195	+	0.455160i	0.847417	−	0.530928i	$-0.178157\pi$
$311$	12.0130	+	8.02684i	0.681195	+	0.455160i	−0.166221	+	0.986088i	$0.553157\pi$
$312$		0			0
$313$	−14.6122	−	21.8687i	−0.825929	−	1.23609i	−0.969168	−	0.246401i	$-0.920752\pi$
$313$	−14.6122	−	21.8687i	−0.825929	−	1.23609i	0.143239	−	0.989688i	$-0.454248\pi$
$314$		0			0
$315$	18.4825	−	15.1682i	1.04137	−	0.854632i
$316$		0			0
$317$	−5.00462	−	9.36298i	−0.281087	−	0.525878i	0.701269	−	0.712897i	$-0.252617\pi$
$317$	−5.00462	−	9.36298i	−0.281087	−	0.525878i	−0.982356	+	0.187019i	$0.940117\pi$
$318$		0			0
$319$		−	10.3619i		−	0.580157i
$320$		0			0
$321$		−	2.66851i		−	0.148942i
$322$		0			0
$323$	5.91812	+	11.0720i	0.329293	+	0.616063i
$324$		0			0
$325$	0.0332218	−	0.0272645i	0.00184282	−	0.00151236i
$326$		0			0
$327$	7.87094	+	11.7797i	0.435264	+	0.651419i
$328$		0			0
$329$	−48.2159	−	32.2169i	−2.65823	−	1.77617i
$330$		0			0
$331$	3.59687	+	11.8573i	0.197702	+	0.651736i	0.998598	+	0.0529328i	$0.0168569\pi$
$331$	3.59687	+	11.8573i	0.197702	+	0.651736i	−0.800896	+	0.598803i	$0.795643\pi$
$332$		0			0
$333$	11.4340	−	13.9324i	0.626579	−	0.763488i
$334$		0			0
$335$	−7.18124	+	17.3371i	−0.392353	+	0.947225i
$336$		0			0
$337$	7.66218	+	18.4981i	0.417386	+	1.00766i	0.983102	+	0.183058i	$0.0585997\pi$
$337$	7.66218	+	18.4981i	0.417386	+	1.00766i	−0.565716	+	0.824600i	$0.691400\pi$
$338$		0			0
$339$	6.90488	−	0.680071i	0.375021	−	0.0369364i
$340$		0			0
$341$	−2.86421	−	1.53095i	−0.155106	−	0.0829058i
$342$		0			0
$343$	−5.77011	−	29.0083i	−0.311556	−	1.56630i
$344$		0			0
$345$	−7.94573	−	1.58050i	−0.427784	−	0.0850915i
$346$		0			0
$347$	8.03154	+	0.791037i	0.431156	+	0.0424651i	0.311268	−	0.950322i	$-0.399246\pi$
$347$	8.03154	+	0.791037i	0.431156	+	0.0424651i	0.119888	+	0.992787i	$0.461746\pi$
$348$		0			0
$349$	−1.42677	−	0.432807i	−0.0763734	−	0.0231676i	0.251867	−	0.967762i	$-0.418956\pi$
$349$	−1.42677	−	0.432807i	−0.0763734	−	0.0231676i	−0.328240	+	0.944594i	$0.606456\pi$
$350$		0			0
$351$	−0.579255	+	0.579255i	−0.0309183	+	0.0309183i
$352$		0			0
$353$	19.0177	+	19.0177i	1.01221	+	1.01221i	0.999925	+	0.0122829i	$0.00390988\pi$
$353$	19.0177	+	19.0177i	1.01221	+	1.01221i	0.0122829	+	0.999925i	$0.496090\pi$
$354$		0			0
$355$	4.55454	−	15.0143i	0.241730	−	0.796877i
$356$		0			0
$357$	−8.12718	+	82.5167i	−0.430136	+	4.36725i
$358$		0			0
$359$	5.62785	−	28.2931i	0.297026	−	1.49325i	−0.487482	−	0.873133i	$-0.662084\pi$
$359$	5.62785	−	28.2931i	0.297026	−	1.49325i	0.784508	−	0.620119i	$-0.212916\pi$
$360$		0			0
$361$	16.1526	−	3.21294i	0.850135	−	0.169102i
$362$		0			0
$363$	−5.45209	+	10.2001i	−0.286161	+	0.535369i
$364$		0			0
$365$	0.778481	+	7.90405i	0.0407476	+	0.413717i
$366$		0			0
$367$	−7.85587	+	3.25401i	−0.410073	+	0.169858i	−0.578177	−	0.815912i	$-0.696236\pi$
$367$	−7.85587	+	3.25401i	−0.410073	+	0.169858i	0.168104	+	0.985769i	$0.446236\pi$
$368$		0			0
$369$	−5.67931	−	2.35245i	−0.295653	−	0.122463i
$370$		0			0
$371$	−6.71930	−	5.51439i	−0.348849	−	0.286293i
$372$		0			0
$373$	15.0524	−	4.56610i	0.779385	−	0.236424i	0.124568	−	0.992211i	$-0.460246\pi$
$373$	15.0524	−	4.56610i	0.779385	−	0.236424i	0.654817	+	0.755787i	$0.272746\pi$
$374$		0			0
$375$	14.5118	−	21.7184i	0.749384	−	1.12153i
$376$		0			0
$377$	−1.99572	+	1.33349i	−0.102785	+	0.0686784i
$378$		0			0
$379$	−6.47267	−	7.88697i	−0.332478	−	0.405126i	0.579759	−	0.814788i	$-0.303147\pi$
$379$	−6.47267	−	7.88697i	−0.332478	−	0.405126i	−0.912237	+	0.409662i	$0.865647\pi$
$380$		0			0
$381$	11.6159	−	6.20880i	0.595098	−	0.318087i
$382$		0			0
$383$	−12.0338			−0.614899			−0.307449	−	0.951564i	$-0.599475\pi$
$383$	−12.0338			−0.614899			−0.307449	+	0.951564i	$0.599475\pi$
$384$		0			0
$385$	−24.6537			−1.25647
$386$		0			0
$387$	−20.0847	+	10.7355i	−1.02096	+	0.545715i
$388$		0			0
$389$	−17.6878	−	21.5527i	−0.896809	−	1.09277i	−0.995224	−	0.0976197i	$-0.968877\pi$
$389$	−17.6878	−	21.5527i	−0.896809	−	1.09277i	0.0984146	−	0.995146i	$-0.468623\pi$
$390$		0			0
$391$	10.3293	−	6.90179i	0.522373	−	0.349039i
$392$		0			0
$393$	−11.2669	+	16.8622i	−0.568342	+	0.850583i
$394$		0			0
$395$	−22.9408	+	6.95901i	−1.15428	+	0.350146i
$396$		0			0
$397$	−6.19082	−	5.08067i	−0.310708	−	0.254992i	0.466096	−	0.884734i	$-0.345660\pi$
$397$	−6.19082	−	5.08067i	−0.310708	−	0.254992i	−0.776804	+	0.629743i	$0.783160\pi$
$398$		0			0
$399$	−15.4436	−	6.39694i	−0.773146	−	0.320248i
$400$		0			0
$401$	8.58991	−	3.55806i	0.428960	−	0.177681i	−0.157749	−	0.987479i	$-0.550424\pi$
$401$	8.58991	−	3.55806i	0.428960	−	0.177681i	0.586708	+	0.809798i	$0.300424\pi$
$402$		0			0
$403$	0.0737376	+	0.748671i	0.00367313	+	0.0372939i
$404$		0			0
$405$	−10.9617	+	20.5079i	−0.544691	+	1.01905i
$406$		0			0
$407$	−18.2272	+	3.62561i	−0.903488	+	0.179715i
$408$		0			0
$409$	−6.33242	+	31.8352i	−0.313118	+	1.57415i	0.428635	+	0.903478i	$0.358994\pi$
$409$	−6.33242	+	31.8352i	−0.313118	+	1.57415i	−0.741753	+	0.670673i	$0.766006\pi$
$410$		0			0
$411$	−0.998921	+	10.1422i	−0.0492732	+	0.500279i
$412$		0			0
$413$	0.408081	−	1.34526i	0.0200803	−	0.0661960i
$414$		0			0
$415$	20.3295	+	20.3295i	0.997938	+	0.997938i
$416$		0			0
$417$	−17.6877	+	17.6877i	−0.866171	+	0.866171i
$418$		0			0
$419$	2.80314	+	0.850324i	0.136943	+	0.0415411i	0.358012	−	0.933717i	$-0.383455\pi$
$419$	2.80314	+	0.850324i	0.136943	+	0.0415411i	−0.221069	+	0.975258i	$0.570955\pi$
$420$		0			0
$421$	6.97688	+	0.687163i	0.340032	+	0.0334903i	0.266592	−	0.963809i	$-0.414102\pi$
$421$	6.97688	+	0.687163i	0.340032	+	0.0334903i	0.0734400	+	0.997300i	$0.476602\pi$
$422$		0			0
$423$	−29.8521	−	5.93796i	−1.45146	−	0.288713i
$424$		0			0
$425$	0.116487	+	0.585620i	0.00565045	+	0.0284067i
$426$		0			0
$427$	36.6787	+	19.6051i	1.77500	+	0.948760i
$428$		0			0
$429$	−3.21441	+	0.316592i	−0.155193	+	0.0152852i
$430$		0			0
$431$	0.417504	+	1.00794i	0.0201104	+	0.0485509i	0.933616	−	0.358276i	$-0.116635\pi$
$431$	0.417504	+	1.00794i	0.0201104	+	0.0485509i	−0.913505	+	0.406827i	$0.866635\pi$
$432$		0			0
$433$	4.65736	−	11.2439i	0.223818	−	0.540345i	−0.771584	−	0.636128i	$-0.780535\pi$
$433$	4.65736	−	11.2439i	0.223818	−	0.540345i	0.995402	+	0.0957822i	$0.0305352\pi$
$434$		0			0
$435$	−13.7959	+	16.8104i	−0.661465	+	0.805997i
$436$		0			0
$437$	0.727012	+	2.39664i	0.0347777	+	0.114647i
$438$		0			0
$439$	−16.2374	−	10.8495i	−0.774970	−	0.517818i	0.104068	−	0.994570i	$-0.466814\pi$
$439$	−16.2374	−	10.8495i	−0.774970	−	0.517818i	−0.879038	+	0.476752i	$0.841814\pi$
$440$		0			0
$441$	−17.8731	−	26.7490i	−0.851100	−	1.27376i
$442$		0			0
$443$	−20.0951	+	16.4916i	−0.954749	+	0.783542i	−0.976344	−	0.216225i	$-0.930626\pi$
$443$	−20.0951	+	16.4916i	−0.954749	+	0.783542i	0.0215950	+	0.999767i	$0.493126\pi$
$444$		0			0
$445$	−8.76728	−	16.4024i	−0.415609	−	0.777550i
$446$		0			0
$447$		−	3.31107i		−	0.156608i
$448$		0			0
$449$		−	10.2767i		−	0.484990i	−0.970153	−	0.242495i	$-0.922034\pi$
$449$		−	10.2767i		−	0.484990i	0.970153	−	0.242495i	$-0.0779658\pi$
$450$		0			0
$451$	2.98795	+	5.59006i	0.140697	+	0.263226i
$452$		0			0
$453$	5.05600	−	4.14935i	0.237551	−	0.194953i
$454$		0			0
$455$	3.17273	+	4.74832i	0.148740	+	0.222605i
$456$		0			0
$457$	−16.9203	−	11.3058i	−0.791501	−	0.528864i	0.0928539	−	0.995680i	$-0.470401\pi$
$457$	−16.9203	−	11.3058i	−0.791501	−	0.528864i	−0.884354	+	0.466816i	$0.845401\pi$
$458$		0			0
$459$	−3.30379	−	10.8911i	−0.154208	−	0.508355i
$460$		0			0
$461$	−5.81633	+	7.08722i	−0.270894	+	0.330085i	−0.890633	−	0.454723i	$-0.849738\pi$
$461$	−5.81633	+	7.08722i	−0.270894	+	0.330085i	0.619739	+	0.784808i	$0.287238\pi$
$462$		0			0
$463$	0.00843317	−	0.0203595i	0.000391923	−	0.000946185i	−0.923683	−	0.383156i	$-0.874837\pi$
$463$	0.00843317	−	0.0203595i	0.000391923	−	0.000946185i	0.924075	+	0.382210i	$0.124837\pi$
$464$		0			0
$465$	2.60836	+	6.29714i	0.120960	+	0.292023i
$466$		0			0
$467$	22.6309	−	2.22895i	1.04723	−	0.103144i	0.440264	−	0.897868i	$-0.354885\pi$
$467$	22.6309	−	2.22895i	1.04723	−	0.103144i	0.606970	+	0.794725i	$0.292385\pi$
$468$		0			0
$469$	33.7900	+	18.0611i	1.56028	+	0.833986i
$470$		0			0
$471$	−1.39344	−	7.00529i	−0.0642063	−	0.322787i
$472$		0			0
$473$	23.0311	+	4.58118i	1.05897	+	0.210643i
$474$		0			0
$475$	−0.119795	−	0.0117988i	−0.00549659	−	0.000541367i
$476$		0			0
$477$	−4.36597	−	1.32440i	−0.199904	−	0.0606402i
$478$		0			0
$479$	17.1872	−	17.1872i	0.785305	−	0.785305i	−0.195415	−	0.980721i	$-0.562605\pi$
$479$	17.1872	−	17.1872i	0.785305	−	0.785305i	0.980721	+	0.195415i	$0.0626055\pi$
$480$		0			0
$481$	3.04398	+	3.04398i	0.138794	+	0.138794i
$482$		0			0
$483$	−4.80156	+	15.8286i	−0.218479	+	0.720228i
$484$		0			0
$485$	2.08469	−	21.1662i	0.0946609	−	0.961108i
$486$		0			0
$487$	−2.47773	+	12.4564i	−0.112277	+	0.564453i	0.883164	+	0.469065i	$0.155409\pi$
$487$	−2.47773	+	12.4564i	−0.112277	+	0.564453i	−0.995440	+	0.0953877i	$0.969591\pi$
$488$		0			0
$489$	−14.4785	+	2.87995i	−0.654740	+	0.130236i
$490$		0			0
$491$	−8.97714	+	16.7950i	−0.405133	+	0.757950i	−0.998910	−	0.0466796i	$-0.985136\pi$
$491$	−8.97714	+	16.7950i	−0.405133	+	0.757950i	0.593777	+	0.804629i	$0.297636\pi$
$492$		0			0
$493$	−3.26857	−	33.1863i	−0.147209	−	1.49464i
$494$		0			0
$495$	−11.9551	+	4.95198i	−0.537344	+	0.222575i
$496$		0			0
$497$	−29.5961	−	12.2591i	−1.32757	−	0.549896i
$498$		0			0
$499$	−14.3455	−	11.7731i	−0.642194	−	0.527035i	0.255976	−	0.966683i	$-0.417603\pi$
$499$	−14.3455	−	11.7731i	−0.642194	−	0.527035i	−0.898170	+	0.439648i	$0.855103\pi$
$500$		0			0
$501$	−9.91846	+	3.00873i	−0.443124	+	0.134420i
$502$		0			0
$503$	−4.00119	+	5.98820i	−0.178404	+	0.267001i	−0.909884	−	0.414862i	$-0.863830\pi$
$503$	−4.00119	+	5.98820i	−0.178404	+	0.267001i	0.731480	+	0.681863i	$0.238830\pi$
$504$		0			0
$505$	−21.5159	+	14.3764i	−0.957444	+	0.639744i
$506$		0			0
$507$	−18.6510	−	22.7263i	−0.828320	−	1.00931i
$508$		0			0
$509$	36.3912	−	19.4515i	1.61301	−	0.862172i	0.615771	−	0.787925i	$-0.288845\pi$
$509$	36.3912	−	19.4515i	1.61301	−	0.862172i	0.997240	−	0.0742475i	$-0.0236555\pi$
$510$		0			0
$511$	16.2160			0.717355
$512$		0			0
$513$	2.29447			0.101303
$514$		0			0
$515$	9.62884	−	5.14672i	0.424298	−	0.226792i
$516$		0			0
$517$	19.9098	+	24.2601i	0.875631	+	1.06696i
$518$		0			0
$519$	23.0294	−	15.3878i	1.01088	−	0.675448i
$520$		0			0
$521$	−10.3772	+	15.5306i	−0.454634	+	0.680408i	−0.986002	−	0.166733i	$-0.946678\pi$
$521$	−10.3772	+	15.5306i	−0.454634	+	0.680408i	0.531368	+	0.847141i	$0.321678\pi$
$522$		0			0
$523$	24.0171	−	7.28549i	1.05019	−	0.318572i	0.282417	−	0.959292i	$-0.408864\pi$
$523$	24.0171	−	7.28549i	1.05019	−	0.318572i	0.767775	+	0.640719i	$0.221364\pi$
$524$		0			0
$525$	−0.614558	−	0.504355i	−0.0268215	−	0.0220119i
$526$		0			0
$527$	−9.65620	−	3.99973i	−0.420630	−	0.174231i
$528$		0			0
$529$	−18.9596	+	7.85334i	−0.824332	+	0.341449i
$530$		0			0
$531$	−0.0723237	−	0.734315i	−0.00313858	−	0.0318666i
$532$		0			0
$533$	0.692125	−	1.29487i	0.0299793	−	0.0560873i
$534$		0			0
$535$	2.50439	−	0.498155i	0.108274	−	0.0215371i
$536$		0			0
$537$	7.56918	−	38.0529i	0.326634	−	1.64210i
$538$		0			0
$539$	−3.25139	+	33.0119i	−0.140047	+	1.42193i
$540$		0			0
$541$	−8.54018	+	28.1532i	−0.367171	+	1.21040i	0.557675	+	0.830059i	$0.311693\pi$
$541$	−8.54018	+	28.1532i	−0.367171	+	1.21040i	−0.924846	+	0.380341i	$0.875807\pi$
$542$		0			0
$543$	21.3548	+	21.3548i	0.916421	+	0.916421i
$544$		0			0
$545$	−9.58589	+	9.58589i	−0.410614	+	0.410614i
$546$		0			0
$547$	−38.4203	−	11.6547i	−1.64273	−	0.498317i	−0.672419	−	0.740170i	$-0.734745\pi$
$547$	−38.4203	−	11.6547i	−1.64273	−	0.498317i	−0.970313	+	0.241853i	$0.922245\pi$
$548$		0			0
$549$	21.7242	+	2.13965i	0.927167	+	0.0913180i
$550$		0			0
$551$	6.59363	+	1.31155i	0.280898	+	0.0558741i
$552$		0			0
$553$	9.54900	+	48.0061i	0.406065	+	2.04143i
$554$		0			0
$555$	34.3976	+	18.3859i	1.46009	+	0.780437i
$556$		0			0
$557$	39.1636	−	3.85728i	1.65942	−	0.163438i	0.775585	−	0.631243i	$-0.217455\pi$
$557$	39.1636	−	3.85728i	1.65942	−	0.163438i	0.883832	+	0.467805i	$0.154955\pi$
$558$		0			0
$559$	−2.08158	−	5.02537i	−0.0880413	−	0.212551i
$560$		0			0
$561$	17.1728	−	41.4588i	0.725036	−	1.75039i
$562$		0			0
$563$	−10.9057	+	13.2886i	−0.459619	+	0.560048i	−0.950318	−	0.311282i	$-0.899242\pi$
$563$	−10.9057	+	13.2886i	−0.459619	+	0.560048i	0.490698	+	0.871330i	$0.336742\pi$
$564$		0			0
$565$	1.92724	+	6.35326i	0.0810796	+	0.267284i
$566$		0			0
$567$	39.4763	+	26.3772i	1.65785	+	1.10774i
$568$		0			0
$569$	−9.30148	−	13.9206i	−0.389938	−	0.583584i	0.583619	−	0.812028i	$-0.301636\pi$
$569$	−9.30148	−	13.9206i	−0.389938	−	0.583584i	−0.973557	+	0.228444i	$0.926636\pi$
$570$		0			0
$571$	−29.2947	+	24.0416i	−1.22595	+	1.00611i	−0.226461	+	0.974020i	$0.572716\pi$
$571$	−29.2947	+	24.0416i	−1.22595	+	1.00611i	−0.999485	+	0.0320878i	$0.989784\pi$
$572$		0			0
$573$	8.88058	+	16.6144i	0.370992	+	0.694076i
$574$		0			0
$575$			0.119114i			0.00496739i
$576$		0			0
$577$			15.8610i			0.660303i	0.943928	+	0.330151i	$0.107100\pi$
$577$			15.8610i			0.660303i	−0.943928	+	0.330151i	$0.892900\pi$
$578$		0			0
$579$	−21.0829	−	39.4434i	−0.876176	−	1.63921i
$580$		0			0
$581$	45.3761	−	37.2392i	1.88252	−	1.54494i
$582$		0			0
$583$	2.61361	+	3.91155i	0.108245	+	0.162000i
$584$		0			0
$585$	2.49228	+	1.66529i	0.103043	+	0.0688513i
$586$		0			0
$587$	−11.8843	−	39.1774i	−0.490519	−	1.61703i	−0.757160	−	0.653230i	$-0.773414\pi$
$587$	−11.8843	−	39.1774i	−0.490519	−	1.61703i	0.266640	−	0.963796i	$-0.414086\pi$
$588$		0			0
$589$	1.33673	−	1.62881i	0.0550790	−	0.0671140i
$590$		0			0
$591$	3.38966	−	8.18335i	0.139432	−	0.336618i
$592$		0			0
$593$	−15.7646	−	38.0592i	−0.647376	−	1.56290i	−0.816523	−	0.577313i	$-0.804101\pi$
$593$	−15.7646	−	38.0592i	−0.647376	−	1.56290i	0.169147	−	0.985591i	$-0.445899\pi$
$594$		0			0
$595$	−78.9589	+	7.77677i	−3.23700	+	0.318817i
$596$		0			0
$597$	−10.9030	−	5.82779i	−0.446231	−	0.238515i
$598$		0			0
$599$	3.60565	+	18.1268i	0.147323	+	0.740641i	0.981848	+	0.189671i	$0.0607422\pi$
$599$	3.60565	+	18.1268i	0.147323	+	0.740641i	−0.834525	+	0.550970i	$0.814258\pi$
$600$		0			0
$601$	−8.83434	−	1.75726i	−0.360360	−	0.0716801i	0.0115898	−	0.999933i	$-0.496311\pi$
$601$	−8.83434	−	1.75726i	−0.360360	−	0.0716801i	−0.371950	+	0.928253i	$0.621311\pi$
$602$		0			0
$603$	20.0133	+	1.97114i	0.815006	+	0.0802711i
$604$		0			0
$605$	−10.5906	−	3.21263i	−0.430570	−	0.130612i
$606$		0			0
$607$	−17.5604	+	17.5604i	−0.712754	+	0.712754i	−0.967110	−	0.254357i	$-0.918136\pi$
$607$	−17.5604	+	17.5604i	−0.712754	+	0.712754i	0.254357	+	0.967110i	$0.418136\pi$
$608$		0			0
$609$	31.3962	+	31.3962i	1.27224	+	1.27224i
$610$		0			0
$611$	2.11030	−	6.95671i	0.0853734	−	0.281438i
$612$		0			0
$613$	−1.36054	+	13.8138i	−0.0549517	+	0.557934i	0.927809	+	0.373054i	$0.121690\pi$
$613$	−1.36054	+	13.8138i	−0.0549517	+	0.557934i	−0.982761	+	0.184880i	$0.940810\pi$
$614$		0			0
$615$	2.59522	−	13.0471i	0.104649	−	0.526108i
$616$		0			0
$617$	20.8912	−	4.15551i	0.841046	−	0.167295i	0.244275	−	0.969706i	$-0.421450\pi$
$617$	20.8912	−	4.15551i	0.841046	−	0.167295i	0.596771	+	0.802411i	$0.296450\pi$
$618$		0			0
$619$	−4.73682	+	8.86196i	−0.190389	+	0.356192i	−0.958946	−	0.283589i	$-0.908475\pi$
$619$	−4.73682	+	8.86196i	−0.190389	+	0.356192i	0.768557	+	0.639781i	$0.220975\pi$
$620$		0			0
$621$	−0.222541	−	2.25950i	−0.00893028	−	0.0906706i
$622$		0			0
$623$	−35.0827	+	14.5317i	−1.40556	+	0.582201i
$624$		0			0
$625$	22.7422	+	9.42012i	0.909687	+	0.376805i
$626$		0			0
$627$	6.99329	+	5.73924i	0.279285	+	0.229203i
$628$		0			0
$629$	−57.2329	+	17.3614i	−2.28202	+	0.692244i
$630$		0			0
$631$	13.5766	−	20.3188i	0.540475	−	0.808878i	−0.456241	−	0.889856i	$-0.650804\pi$
$631$	13.5766	−	20.3188i	0.540475	−	0.808878i	0.996716	+	0.0809781i	$0.0258044\pi$
$632$		0			0
$633$	−37.4896	+	25.0497i	−1.49008	+	0.995638i
$634$		0			0
$635$	7.99539	+	9.74241i	0.317287	+	0.386616i
$636$		0			0
$637$	6.77655	−	3.62214i	0.268497	−	0.143514i
$638$		0			0
$639$	−16.8142			−0.665160
$640$		0			0
$641$	−24.4206			−0.964557			−0.482278	−	0.876018i	$-0.660191\pi$
$641$	−24.4206			−0.964557			−0.482278	+	0.876018i	$0.660191\pi$
$642$		0			0
$643$	9.38100	−	5.01425i	0.369951	−	0.197743i	−0.275936	−	0.961176i	$-0.588988\pi$
$643$	9.38100	−	5.01425i	0.369951	−	0.197743i	0.645887	+	0.763433i	$0.276488\pi$
$644$		0			0
$645$	−31.2645	−	38.0959i	−1.23104	−	1.50003i
$646$		0			0
$647$	18.2129	−	12.1694i	0.716022	−	0.478430i	−0.143421	−	0.989662i	$-0.545810\pi$
$647$	18.2129	−	12.1694i	0.716022	−	0.478430i	0.859443	+	0.511231i	$0.170810\pi$
$648$		0			0
$649$	−0.422692	+	0.632604i	−0.0165921	+	0.0248319i
$650$		0			0
$651$	13.3172	−	4.03971i	0.521940	−	0.158329i
$652$		0			0
$653$	30.8023	+	25.2788i	1.20539	+	0.989237i	0.999944	+	0.0105680i	$0.00336396\pi$
$653$	30.8023	+	25.2788i	1.20539	+	0.989237i	0.205444	+	0.978669i	$0.434136\pi$
$654$		0			0
$655$	−17.9284	−	7.42619i	−0.700521	−	0.290165i
$656$		0			0
$657$	7.86352	−	3.25718i	0.306785	−	0.127075i
$658$		0			0
$659$	−1.21719	−	12.3584i	−0.0474151	−	0.481413i	−0.989344	−	0.145600i	$-0.953489\pi$
$659$	−1.21719	−	12.3584i	−0.0474151	−	0.481413i	0.941929	−	0.335813i	$-0.109011\pi$
$660$		0			0
$661$	−7.51000	+	14.0502i	−0.292105	+	0.546490i	−0.984576	−	0.174955i	$-0.944022\pi$
$661$	−7.51000	+	14.0502i	−0.292105	+	0.546490i	0.692471	+	0.721446i	$0.256522\pi$
$662$		0			0
$663$	−10.1950	+	2.02791i	−0.395941	+	0.0787575i
$664$		0			0
$665$	3.12053	−	15.6879i	0.121009	−	0.608352i
$666$		0			0
$667$	0.652046	−	6.62034i	0.0252473	−	0.256340i
$668$		0			0
$669$	−9.55664	+	31.5040i	−0.369481	+	1.21802i
$670$		0			0
$671$	−15.9159	−	15.9159i	−0.614428	−	0.614428i
$672$		0			0
$673$	10.4977	−	10.4977i	0.404656	−	0.404656i	−0.475214	−	0.879870i	$-0.657629\pi$
$673$	10.4977	−	10.4977i	0.404656	−	0.404656i	0.879870	+	0.475214i	$0.157629\pi$
$674$		0			0
$675$	0.104427	+	0.0316776i	0.00401940	+	0.00121927i
$676$		0			0
$677$	−42.6603	−	4.20167i	−1.63957	−	0.161483i	−0.764213	−	0.644964i	$-0.776872\pi$
$677$	−42.6603	−	4.20167i	−1.63957	−	0.161483i	−0.875355	+	0.483481i	$0.839372\pi$
$678$		0			0
$679$	−42.5904	−	8.47177i	−1.63447	−	0.325117i
$680$		0			0
$681$	5.96888	+	30.0076i	0.228728	+	1.14989i
$682$		0			0
$683$	4.04663	+	2.16297i	0.154840	+	0.0827638i	0.546997	−	0.837135i	$-0.315771\pi$
$683$	4.04663	+	2.16297i	0.154840	+	0.0827638i	−0.392157	+	0.919898i	$0.628271\pi$
$684$		0			0
$685$	−9.70493	+	0.955852i	−0.370806	+	0.0365212i
$686$		0			0
$687$	−21.9194	−	52.9182i	−0.836278	−	2.01895i
$688$		0			0
$689$	0.417017	−	1.00677i	0.0158871	−	0.0383548i
$690$		0			0
$691$	1.75941	−	2.14385i	0.0669311	−	0.0815558i	−0.738469	−	0.674288i	$-0.764451\pi$
$691$	1.75941	−	2.14385i	0.0669311	−	0.0815558i	0.805400	+	0.592732i	$0.201951\pi$
$692$		0			0
$693$	7.66942	+	25.2827i	0.291337	+	0.960409i
$694$		0			0
$695$	−19.9018	−	13.2980i	−0.754919	−	0.504421i
$696$		0			0
$697$	11.3329	+	16.9609i	0.429264	+	0.642439i
$698$		0			0
$699$	−9.27747	+	7.61383i	−0.350906	+	0.287981i
$700$		0			0
$701$	0.358992	+	0.671626i	0.0135589	+	0.0253670i	0.888610	−	0.458664i	$-0.151672\pi$
$701$	0.358992	+	0.671626i	0.0135589	+	0.0253670i	−0.875051	+	0.484031i	$0.839172\pi$
$702$		0			0
$703$		−	12.0574i		−	0.454755i
$704$		0			0
$705$		−	65.8658i		−	2.48065i
$706$		0			0
$707$	24.9057	+	46.5952i	0.936673	+	1.75239i
$708$		0			0
$709$	−18.3108	+	15.0273i	−0.687676	+	0.564361i	−0.912019	−	0.410149i	$-0.865477\pi$
$709$	−18.3108	+	15.0273i	−0.687676	+	0.564361i	0.224342	+	0.974510i	$0.427977\pi$
$710$		0			0
$711$	14.2731	+	21.3612i	0.535283	+	0.801108i
$712$		0			0
$713$	−1.73364	−	1.15838i	−0.0649251	−	0.0433816i
$714$		0			0
$715$	−0.897184	−	2.95762i	−0.0335528	−	0.110609i
$716$		0			0
$717$	29.1180	−	35.4804i	1.08743	−	1.32504i
$718$		0			0
$719$	7.37349	−	17.8012i	0.274985	−	0.663872i	−0.724698	−	0.689067i	$-0.758021\pi$
$719$	7.37349	−	17.8012i	0.274985	−	0.663872i	0.999683	+	0.0251950i	$0.00802068\pi$
$720$		0			0
$721$	−8.53066	−	20.5948i	−0.317698	−	0.766992i
$722$		0			0
$723$	67.5325	−	6.65137i	2.51156	−	0.247367i
$724$		0			0
$725$	0.281985	+	0.150724i	0.0104726	+	0.00559774i
$726$		0			0
$727$	7.30974	+	36.7485i	0.271103	+	1.36293i	0.840921	+	0.541157i	$0.182014\pi$
$727$	7.30974	+	36.7485i	0.271103	+	1.36293i	−0.569818	+	0.821771i	$0.692986\pi$
$728$		0			0
$729$	14.6000	+	2.90411i	0.540739	+	0.107560i
$730$		0			0
$731$	75.2073	+	7.40727i	2.78164	+	0.273968i
$732$		0			0
$733$	−36.3396	−	11.0235i	−1.34223	−	0.407162i	−0.464187	−	0.885737i	$-0.653653\pi$
$733$	−36.3396	−	11.0235i	−1.34223	−	0.407162i	−0.878047	+	0.478575i	$0.841153\pi$
$734$		0			0
$735$	49.2271	−	49.2271i	1.81577	−	1.81577i
$736$		0			0
$737$	−14.6625	−	14.6625i	−0.540099	−	0.540099i
$738$		0			0
$739$	−8.09970	+	26.7011i	−0.297952	+	0.982217i	0.672332	+	0.740250i	$0.265293\pi$
$739$	−8.09970	+	26.7011i	−0.297952	+	0.982217i	−0.970284	+	0.241967i	$0.922207\pi$
$740$		0			0
$741$	0.205404	−	2.08551i	0.00754572	−	0.0766129i
$742$		0			0
$743$	−2.65866	+	13.3660i	−0.0975366	+	0.490350i	0.900878	+	0.434071i	$0.142923\pi$
$743$	−2.65866	+	13.3660i	−0.0975366	+	0.490350i	−0.998415	+	0.0562784i	$0.982077\pi$
$744$		0			0
$745$	3.10743	−	0.618107i	0.113848	−	0.0226457i
$746$		0			0
$747$	14.5240	−	27.1724i	0.531404	−	0.994187i
$748$		0			0
$749$	−0.511010	−	5.18837i	−0.0186719	−	0.189579i
$750$		0			0
$751$	42.3969	−	17.5614i	1.54708	−	0.640823i	0.564298	−	0.825571i	$-0.309147\pi$
$751$	42.3969	−	17.5614i	1.54708	−	0.640823i	0.982786	+	0.184748i	$0.0591468\pi$
$752$		0			0
$753$	−9.18187	−	3.80326i	−0.334606	−	0.138598i
$754$		0			0
$755$	4.83801	+	3.97045i	0.176073	+	0.144499i
$756$		0			0
$757$	37.0905	−	11.2513i	1.34808	−	0.408934i	0.467983	−	0.883737i	$-0.344981\pi$
$757$	37.0905	−	11.2513i	1.34808	−	0.408934i	0.880092	+	0.474803i	$0.157481\pi$
$758$		0			0
$759$	4.97349	−	7.44335i	0.180526	−	0.270176i
$760$		0			0
$761$	23.0354	−	15.3917i	0.835031	−	0.557950i	−0.0629336	−	0.998018i	$-0.520046\pi$
$761$	23.0354	−	15.3917i	0.835031	−	0.557950i	0.897964	+	0.440068i	$0.145046\pi$
$762$		0			0
$763$	17.5592	+	21.3959i	0.635686	+	0.774585i
$764$		0			0
$765$	−36.7269	+	19.6309i	−1.32786	+	0.709758i
$766$		0			0
$767$	0.176237			0.00636354
$768$		0			0
$769$	33.7124			1.21570			0.607851	−	0.794051i	$-0.292032\pi$
$769$	33.7124			1.21570			0.607851	+	0.794051i	$0.292032\pi$
$770$		0			0
$771$	38.5533	−	20.6072i	1.38846	−	0.742149i
$772$		0			0
$773$	24.7625	+	30.1732i	0.890645	+	1.08525i	0.995869	+	0.0908060i	$0.0289443\pi$
$773$	24.7625	+	30.1732i	0.890645	+	1.08525i	−0.105223	+	0.994449i	$0.533556\pi$
$774$		0			0
$775$	0.0833253	−	0.0556762i	0.00299313	−	0.00199995i
$776$		0			0
$777$	44.2421	−	66.2129i	1.58718	−	2.37538i
$778$		0			0
$779$	−3.93533	+	1.19377i	−0.140998	+	0.0427712i
$780$		0			0
$781$	13.4020	+	10.9987i	0.479560	+	0.393565i
$782$		0			0
$783$	−5.63063	−	2.33228i	−0.201222	−	0.0833490i
$784$		0			0
$785$	6.31433	−	2.61548i	0.225368	−	0.0933505i
$786$		0			0
$787$	2.96521	+	30.1063i	0.105698	+	1.07317i	0.890982	+	0.454038i	$0.150017\pi$
$787$	2.96521	+	30.1063i	0.105698	+	1.07317i	−0.785284	+	0.619136i	$0.787483\pi$
$788$		0			0
$789$	21.1742	−	39.6142i	0.753823	−	1.41030i
$790$		0			0
$791$	13.2949	−	2.64452i	0.472712	−	0.0940282i
$792$		0			0
$793$	−1.01717	+	5.11367i	−0.0361208	+	0.181592i
$794$		0			0
$795$	0.967735	−	9.82558i	0.0343220	−	0.348477i
$796$		0			0
$797$	−4.38486	+	14.4549i	−0.155320	+	0.512020i	−0.999719	−	0.0236934i	$-0.992457\pi$
$797$	−4.38486	+	14.4549i	−0.155320	+	0.512020i	0.844400	+	0.535714i	$0.179957\pi$
$798$		0			0
$799$	71.4180	+	71.4180i	2.52659	+	2.52659i
$800$		0			0
$801$	−14.0935	+	14.0935i	−0.497970	+	0.497970i
$802$		0			0
$803$	−8.39833	−	2.54761i	−0.296371	−	0.0899031i
$804$		0			0
$805$	−15.7515	−	1.55139i	−0.555167	−	0.0546792i
$806$		0			0
$807$	−7.55724	−	1.50323i	−0.266027	−	0.0529161i
$808$		0			0
$809$	0.111057	+	0.558323i	0.00390457	+	0.0196296i	0.982688	−	0.185266i	$-0.0593146\pi$
$809$	0.111057	+	0.558323i	0.00390457	+	0.0196296i	−0.978784	+	0.204895i	$0.934315\pi$
$810$		0			0
$811$	−48.4316	−	25.8872i	−1.70066	−	0.909024i	−0.975367	−	0.220588i	$-0.929202\pi$
$811$	−48.4316	−	25.8872i	−1.70066	−	0.909024i	−0.725297	−	0.688436i	$-0.758298\pi$
$812$		0			0
$813$	44.8905	−	4.42133i	1.57438	−	0.155063i
$814$		0			0
$815$	−5.40566	−	13.0504i	−0.189352	−	0.457136i
$816$		0			0
$817$	−5.83030	+	14.0756i	−0.203976	+	0.492442i
$818$		0			0
$819$	3.88247	−	4.73080i	0.135664	−	0.165308i
$820$		0			0
$821$	−2.26708	−	7.47357i	−0.0791218	−	0.260830i	0.908451	−	0.417991i	$-0.137266\pi$
$821$	−2.26708	−	7.47357i	−0.0791218	−	0.260830i	−0.987573	+	0.157162i	$0.949766\pi$
$822$		0			0
$823$	−22.9768	−	15.3526i	−0.800921	−	0.535158i	0.0864272	−	0.996258i	$-0.472455\pi$
$823$	−22.9768	−	15.3526i	−0.800921	−	0.535158i	−0.887348	+	0.461100i	$0.847455\pi$
$824$		0			0
$825$	0.239045	+	0.357757i	0.00832249	+	0.0124555i
$826$		0			0
$827$	−22.4110	+	18.3922i	−0.779308	+	0.639561i	−0.937555	−	0.347838i	$-0.886916\pi$
$827$	−22.4110	+	18.3922i	−0.779308	+	0.639561i	0.158247	+	0.987400i	$0.449416\pi$
$828$		0			0
$829$	−21.5366	−	40.2921i	−0.747996	−	1.39940i	−0.910844	−	0.412751i	$-0.864568\pi$
$829$	−21.5366	−	40.2921i	−0.747996	−	1.39940i	0.162847	−	0.986651i	$-0.447932\pi$
$830$		0			0
$831$			12.2024i			0.423297i
$832$		0			0
$833$			106.754i			3.69879i
$834$		0			0
$835$	−4.67526	−	8.74679i	−0.161794	−	0.302695i
$836$		0			0
$837$	−1.47660	+	1.21181i	−0.0510387	+	0.0418864i
$838$		0			0
$839$	−10.8684	−	16.2657i	−0.375218	−	0.561553i	0.595019	−	0.803712i	$-0.297145\pi$
$839$	−10.8684	−	16.2657i	−0.375218	−	0.561553i	−0.970237	+	0.242159i	$0.922145\pi$
$840$		0			0
$841$	9.26504	+	6.19070i	0.319484	+	0.213472i
$842$		0			0
$843$	10.6240	+	35.0227i	0.365910	+	1.20625i
$844$		0			0
$845$	17.8469	−	21.7465i	0.613951	−	0.748101i
$846$		0			0
$847$	−8.64718	+	20.8761i	−0.297121	+	0.717313i
$848$		0			0
$849$	−2.00191	−	4.83304i	−0.0687054	−	0.165870i
$850$		0			0
$851$	−11.8737	+	1.16945i	−0.407024	+	0.0400884i
$852$		0			0
$853$	−22.4766	−	12.0140i	−0.769584	−	0.411351i	0.0393689	−	0.999225i	$-0.487465\pi$
$853$	−22.4766	−	12.0140i	−0.769584	−	0.411351i	−0.808953	+	0.587874i	$0.799965\pi$
$854$		0			0
$855$	−1.63789	−	8.23423i	−0.0560147	−	0.281605i
$856$		0			0
$857$	27.8579	+	5.54127i	0.951607	+	0.189286i	0.646399	−	0.763000i	$-0.276274\pi$
$857$	27.8579	+	5.54127i	0.951607	+	0.189286i	0.305208	+	0.952286i	$0.401274\pi$
$858$		0			0
$859$	−16.2811	−	1.60355i	−0.555503	−	0.0547123i	−0.183629	−	0.982996i	$-0.558785\pi$
$859$	−16.2811	−	1.60355i	−0.555503	−	0.0547123i	−0.371874	+	0.928283i	$0.621285\pi$
$860$		0			0
$861$	−25.9910	−	7.88427i	−0.885769	−	0.268695i
$862$		0			0
$863$	−22.7782	+	22.7782i	−0.775379	+	0.775379i	−0.979041	−	0.203662i	$-0.934716\pi$
$863$	−22.7782	+	22.7782i	−0.775379	+	0.775379i	0.203662	+	0.979041i	$0.434716\pi$
$864$		0			0
$865$	18.7405	+	18.7405i	0.637196	+	0.637196i
$866$		0			0
$867$	30.4776	−	100.471i	1.03507	−	3.41218i
$868$		0			0
$869$	2.59650	−	26.3627i	0.0880801	−	0.894293i
$870$		0			0
$871$	−0.937064	+	4.71094i	−0.0317512	+	0.159624i
$872$		0			0
$873$	−22.3547	+	4.44663i	−0.756592	+	0.150496i
$874$		0			0
$875$	24.0561	−	45.0059i	0.813246	−	1.52148i
$876$		0			0
$877$	0.809517	+	8.21916i	0.0273354	+	0.277541i	0.999130	+	0.0417112i	$0.0132809\pi$
$877$	0.809517	+	8.21916i	0.0273354	+	0.277541i	−0.971794	+	0.235830i	$0.924219\pi$
$878$		0			0
$879$	−7.38313	+	3.05819i	−0.249027	+	0.103150i
$880$		0			0
$881$	−16.2171	−	6.71734i	−0.546368	−	0.226313i	0.0923873	−	0.995723i	$-0.470550\pi$
$881$	−16.2171	−	6.71734i	−0.546368	−	0.226313i	−0.638755	+	0.769410i	$0.720550\pi$
$882$		0			0
$883$	18.1147	+	14.8664i	0.609609	+	0.500294i	0.887798	−	0.460233i	$-0.152234\pi$
$883$	18.1147	+	14.8664i	0.609609	+	0.500294i	−0.278189	+	0.960526i	$0.589734\pi$
$884$		0			0
$885$	1.52800	−	0.463512i	0.0513630	−	0.0155808i
$886$		0			0
$887$	4.57914	−	6.85317i	0.153753	−	0.230107i	−0.746595	−	0.665279i	$-0.768313\pi$
$887$	4.57914	−	6.85317i	0.153753	−	0.230107i	0.900347	+	0.435172i	$0.143313\pi$
$888$		0			0
$889$	21.3957	−	14.2961i	0.717588	−	0.479477i
$890$		0			0
$891$	−16.3009	−	19.8627i	−0.546102	−	0.665427i
$892$		0			0
$893$	−17.9576	+	9.59851i	−0.600927	+	0.321202i
$894$		0			0
$895$	37.1255			1.24097
$896$		0			0
$897$	−2.07364			−0.0692368
$898$		0			0
$899$	−4.93599	+	2.63834i	−0.164624	+	0.0879936i
$900$		0			0
$901$	9.60453	+	11.7031i	0.319973	+	0.389888i
$902$		0			0
$903$	−83.6640	+	55.9025i	−2.78416	+	1.86032i
$904$		0			0
$905$	−16.0549	+	24.0279i	−0.533684	+	0.798715i
$906$		0			0
$907$	38.3564	−	11.6353i	1.27360	−	0.386344i	0.420123	−	0.907467i	$-0.361987\pi$
$907$	38.3564	−	11.6353i	1.27360	−	0.386344i	0.853481	+	0.521124i	$0.174487\pi$
$908$		0			0
$909$	21.4365	+	17.5925i	0.711004	+	0.583506i
$910$		0			0
$911$	32.8120	+	13.5912i	1.08711	+	0.450296i	0.852998	−	0.521913i	$-0.174782\pi$
$911$	32.8120	+	13.5912i	1.08711	+	0.450296i	0.234112	+	0.972210i	$0.424782\pi$
$912$		0			0
$913$	−29.3508	+	12.1575i	−0.971370	+	0.402355i
$914$		0			0
$915$	4.63021	+	47.0114i	0.153070	+	1.55415i
$916$		0			0
$917$	−18.6772	+	34.9426i	−0.616775	+	1.15391i
$918$		0			0
$919$	17.3233	−	3.44583i	0.571444	−	0.113667i	0.0990937	−	0.995078i	$-0.468406\pi$
$919$	17.3233	−	3.44583i	0.571444	−	0.113667i	0.472351	+	0.881411i	$0.343406\pi$
$920$		0			0
$921$	3.20961	−	16.1358i	0.105760	−	0.531692i
$922$		0			0
$923$	0.393637	−	3.99667i	0.0129567	−	0.131552i
$924$		0			0
$925$	0.166466	−	0.548764i	0.00547336	−	0.0180432i
$926$		0			0
$927$	−8.27342	−	8.27342i	−0.271735	−	0.271735i
$928$		0			0
$929$	15.9105	−	15.9105i	0.522007	−	0.522007i	−0.396170	−	0.918177i	$-0.629661\pi$
$929$	15.9105	−	15.9105i	0.522007	−	0.522007i	0.918177	+	0.396170i	$0.129661\pi$
$930$		0			0
$931$	−20.5950	−	6.24743i	−0.674974	−	0.204751i
$932$		0			0
$933$	33.3444	+	3.28414i	1.09165	+	0.107518i
$934$		0			0
$935$	42.1148	+	8.37716i	1.37730	+	0.273962i
$936$		0			0
$937$	−7.54939	−	37.9533i	−0.246628	−	1.23988i	−0.883323	−	0.468766i	$-0.844699\pi$
$937$	−7.54939	−	37.9533i	−0.246628	−	1.23988i	0.636695	−	0.771116i	$-0.280301\pi$
$938$		0			0
$939$	−53.7923	−	28.7526i	−1.75544	−	0.938304i
$940$		0			0
$941$	5.40997	−	0.532836i	0.176360	−	0.0173700i	−0.00945154	−	0.999955i	$-0.503009\pi$
$941$	5.40997	−	0.532836i	0.176360	−	0.0173700i	0.185812	+	0.982585i	$0.440509\pi$
$942$		0			0
$943$	1.55726	+	3.75956i	0.0507114	+	0.122428i
$944$		0			0
$945$	−5.54911	+	13.3967i	−0.180512	+	0.435796i
$946$		0			0
$947$	−6.38399	+	7.77891i	−0.207452	+	0.252781i	−0.866334	−	0.499466i	$-0.833530\pi$
$947$	−6.38399	+	7.77891i	−0.207452	+	0.252781i	0.658882	+	0.752246i	$0.271030\pi$
$948$		0			0
$949$	0.590125	+	1.94538i	0.0191563	+	0.0631497i
$950$		0			0
$951$	−20.4713	−	13.6785i	−0.663827	−	0.443555i
$952$		0			0
$953$	8.60748	+	12.8820i	0.278823	+	0.417289i	0.944278	−	0.329150i	$-0.106762\pi$
$953$	8.60748	+	12.8820i	0.278823	+	0.417289i	−0.665454	+	0.746439i	$0.731762\pi$
$954$		0			0
$955$	−13.9348	+	11.4360i	−0.450918	+	0.370059i
$956$		0			0
$957$	−11.3277	−	21.1926i	−0.366172	−	0.685060i
$958$		0			0
$959$			19.9107i			0.642952i
$960$		0			0
$961$		−	29.2458i		−	0.943413i
$962$		0			0
$963$	−1.28994	−	2.41331i	−0.0415678	−	0.0777680i
$964$		0			0
$965$	33.0818	−	27.1495i	1.06494	−	0.873974i
$966$		0			0
$967$	18.8949	+	28.2783i	0.607620	+	0.909368i	0.999945	−	0.0104589i	$-0.00332923\pi$
$967$	18.8949	+	28.2783i	0.607620	+	0.909368i	−0.392325	+	0.919827i	$0.628329\pi$
$968$		0			0
$969$	24.2079	+	16.1752i	0.777671	+	0.519623i
$970$		0			0
$971$	−14.8912	−	49.0896i	−0.477880	−	1.57536i	−0.782350	−	0.622838i	$-0.785979\pi$
$971$	−14.8912	−	49.0896i	−0.477880	−	1.57536i	0.304470	−	0.952522i	$-0.401521\pi$
$972$		0			0
$973$	−31.0030	+	37.7773i	−0.993910	+	1.21108i
$974$		0			0
$975$	0.0381410	−	0.0920806i	0.00122149	−	0.00294894i
$976$		0			0
$977$	9.88264	+	23.8588i	0.316174	+	0.763311i	0.999450	+	0.0331513i	$0.0105543\pi$
$977$	9.88264	+	23.8588i	0.316174	+	0.763311i	−0.683277	+	0.730160i	$0.739446\pi$
$978$		0			0
$979$	20.4524	−	2.01439i	0.653662	−	0.0643801i
$980$		0			0
$981$	12.8125	+	6.84841i	0.409071	+	0.218653i
$982$		0			0
$983$	−4.33096	−	21.7732i	−0.138136	−	0.694458i	−0.986331	−	0.164774i	$-0.947311\pi$
$983$	−4.33096	−	21.7732i	−0.138136	−	0.694458i	0.848195	−	0.529684i	$-0.177689\pi$
$984$		0			0
$985$	8.31284	+	1.65353i	0.264869	+	0.0526857i
$986$		0			0
$987$	−133.833	−	13.1814i	−4.25994	−	0.419568i
$988$		0			0
$989$	14.4265	+	4.37624i	0.458737	+	0.139156i
$990$		0			0
$991$	−20.4092	+	20.4092i	−0.648319	+	0.648319i	−0.952587	−	0.304268i	$-0.901588\pi$
$991$	−20.4092	+	20.4092i	−0.648319	+	0.648319i	0.304268	+	0.952587i	$0.401588\pi$
$992$		0			0
$993$	20.3189	+	20.3189i	0.644801	+	0.644801i
$994$		0			0
$995$	3.43400	−	11.3204i	0.108865	−	0.358880i
$996$		0			0
$997$	2.79544	−	28.3826i	0.0885324	−	0.898885i	−0.843649	−	0.536894i	$-0.819597\pi$
$997$	2.79544	−	28.3826i	0.0885324	−	0.898885i	0.932182	−	0.361990i	$-0.117903\pi$
$998$		0			0
$999$	−2.13247	+	10.7206i	−0.0674683	+	0.339186i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	512.2.k.a.497.14		240
4.3	odd	2		128.2.k.a.101.9	✓	240
128.19	odd	32		128.2.k.a.109.9	yes	240
128.109	even	32	inner	512.2.k.a.273.14		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
128.2.k.a.101.9	✓	240	4.3	odd	2
128.2.k.a.109.9	yes	240	128.19	odd	32
512.2.k.a.273.14		240	128.109	even	32	inner
512.2.k.a.497.14		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)

\(f(q)\)	\(=\)	\(q+(2.04524 - 1.09320i) q^{3} +(1.40777 + 1.71538i) q^{5} +(3.76720 - 2.51716i) q^{7} +(1.32120 - 1.97732i) q^{9} +(-2.34650 + 0.711804i) q^{11} +(0.439069 + 0.360335i) q^{13} +(4.75449 + 1.96937i) q^{15} +(-7.29065 + 3.01989i) q^{17} +(-0.155936 - 1.58325i) q^{19} +(4.95306 - 9.26652i) q^{21} +(-1.54399 + 0.307120i) q^{23} +(0.0147614 - 0.0742104i) q^{25} +(-0.141364 + 1.43529i) q^{27} +(-1.22667 + 4.04380i) q^{29} +(0.936536 + 0.936536i) q^{31} +(-4.02101 + 4.02101i) q^{33} +(9.62124 + 2.91857i) q^{35} +(7.54247 + 0.742868i) q^{37} +(1.29192 + 0.256979i) q^{39} +(-0.504297 - 2.53527i) q^{41} +(-8.44569 - 4.51431i) q^{43} +(5.25179 - 0.517256i) q^{45} +(-4.89792 - 11.8246i) q^{47} +(5.17691 - 12.4982i) q^{49} +(-11.6098 + 14.1466i) q^{51} +(-0.556917 - 1.83591i) q^{53} +(-4.52435 - 3.02307i) q^{55} +(-2.04974 - 3.06765i) q^{57} +(0.239847 - 0.196837i) q^{59} +(4.32711 + 8.09545i) q^{61} -10.7746i q^{63} +1.26044i q^{65} +(3.98633 + 7.45789i) q^{67} +(-2.82209 + 2.31603i) q^{69} +(-3.92813 - 5.87886i) q^{71} +(2.97590 + 1.98843i) q^{73} +(-0.0509365 - 0.167915i) q^{75} +(-7.04802 + 8.58804i) q^{77} +(-4.13418 + 9.98079i) q^{79} +(4.01012 + 9.68128i) q^{81} +(12.8936 - 1.26990i) q^{83} +(-15.4438 - 8.25489i) q^{85} +(1.91185 + 9.61154i) q^{87} +(-8.22013 - 1.63509i) q^{89} +(2.56108 + 0.252245i) q^{91} +(2.93927 + 0.891616i) q^{93} +(2.49634 - 2.49634i) q^{95} +(-6.77721 - 6.77721i) q^{97} +(-1.69274 + 5.58021i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 16 q^{3} - 16 q^{5} + 16 q^{7} - 16 q^{9} + 16 q^{11} - 16 q^{13} + 16 q^{15} - 16 q^{17} + 16 q^{19} - 16 q^{21} + 16 q^{23} - 16 q^{25} + 16 q^{27} - 16 q^{29} + 16 q^{31} - 16 q^{33} + 16 q^{35}+ \cdots + 16 q^{99}+O(q^{100}) \) 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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