LMFDB - Embedded newform 512.2.k.a.497.15

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			497.15
Character	$\chi$	$=$	512.497
Dual form			512.2.k.a.273.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.86311 - 1.53036i) q^{3} +(-0.865631 - 1.05477i) q^{5} +(-0.162245 + 0.108408i) q^{7} +(4.18867 - 6.26879i) q^{9} +(0.144127 - 0.0437204i) q^{11} +(-3.75158 - 3.07884i) q^{13} +(-4.09258 - 1.69520i) q^{15} +(-0.223463 + 0.0925613i) q^{17} +(0.742006 + 7.53372i) q^{19} +(-0.298620 + 0.558679i) q^{21} +(6.74055 - 1.34078i) q^{23} +(0.612220 - 3.07784i) q^{25} +(1.44447 - 14.6660i) q^{27} +(-1.92135 + 6.33383i) q^{29} +(2.37838 + 2.37838i) q^{31} +(0.345743 - 0.345743i) q^{33} +(0.254791 + 0.0772899i) q^{35} +(3.51713 + 0.346407i) q^{37} +(-15.4529 - 3.07378i) q^{39} +(0.456936 + 2.29717i) q^{41} +(-4.58870 - 2.45271i) q^{43} +(-10.2380 + 1.00836i) q^{45} +(3.90401 + 9.42513i) q^{47} +(-2.66421 + 6.43198i) q^{49} +(-0.498146 + 0.606993i) q^{51} +(-0.703882 - 2.32039i) q^{53} +(-0.170876 - 0.114176i) q^{55} +(13.6538 + 20.4343i) q^{57} +(1.33800 - 1.09807i) q^{59} +(-3.57815 - 6.69426i) q^{61} +1.47117i q^{63} +6.62221i q^{65} +(-1.30359 - 2.43884i) q^{67} +(17.2471 - 14.1543i) q^{69} +(3.30056 + 4.93964i) q^{71} +(-8.33969 - 5.57240i) q^{73} +(-2.95736 - 9.74910i) q^{75} +(-0.0186442 + 0.0227180i) q^{77} +(0.333360 - 0.804803i) q^{79} +(-9.65299 - 23.3044i) q^{81} +(1.71796 - 0.169204i) q^{83} +(0.291068 + 0.155579i) q^{85} +(4.19204 + 21.0748i) q^{87} +(8.77606 + 1.74567i) q^{89} +(0.942446 + 0.0928229i) q^{91} +(10.4494 + 3.16978i) q^{93} +(7.30407 - 7.30407i) q^{95} +(5.19447 + 5.19447i) q^{97} +(0.329626 - 1.08663i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	2.86311	−	1.53036i	1.65302	−	0.883556i	0.662049	−	0.749461i	$-0.269687\pi$
$3$	2.86311	−	1.53036i	1.65302	−	0.883556i	0.990968	−	0.134095i	$-0.0428128\pi$
$4$		0			0
$5$	−0.865631	−	1.05477i	−0.387122	−	0.471709i	0.542590	−	0.839998i	$-0.317444\pi$
$5$	−0.865631	−	1.05477i	−0.387122	−	0.471709i	−0.929712	+	0.368288i	$0.879944\pi$
$6$		0			0
$7$	−0.162245	+	0.108408i	−0.0613228	+	0.0409746i	−0.585854	−	0.810417i	$-0.699241\pi$
$7$	−0.162245	+	0.108408i	−0.0613228	+	0.0409746i	0.524531	+	0.851391i	$0.324241\pi$
$8$		0			0
$9$	4.18867	−	6.26879i	1.39622	−	2.08960i
$10$		0			0
$11$	0.144127	−	0.0437204i	0.0434559	−	0.0131822i	−0.268482	−	0.963285i	$-0.586522\pi$
$11$	0.144127	−	0.0437204i	0.0434559	−	0.0131822i	0.311938	+	0.950103i	$0.399022\pi$
$12$		0			0
$13$	−3.75158	−	3.07884i	−1.04050	−	0.853917i	−0.0510365	−	0.998697i	$-0.516252\pi$
$13$	−3.75158	−	3.07884i	−1.04050	−	0.853917i	−0.989464	+	0.144780i	$0.953752\pi$
$14$		0			0
$15$	−4.09258	−	1.69520i	−1.05670	−	0.437700i
$16$		0			0
$17$	−0.223463	+	0.0925613i	−0.0541977	+	0.0224494i	−0.409618	−	0.912257i	$-0.634338\pi$
$17$	−0.223463	+	0.0925613i	−0.0541977	+	0.0224494i	0.355420	+	0.934707i	$0.384338\pi$
$18$		0			0
$19$	0.742006	+	7.53372i	0.170228	+	1.72835i	0.578664	+	0.815566i	$0.303574\pi$
$19$	0.742006	+	7.53372i	0.170228	+	1.72835i	−0.408436	+	0.912787i	$0.633926\pi$
$20$		0			0
$21$	−0.298620	+	0.558679i	−0.0651643	+	0.121914i
$22$		0			0
$23$	6.74055	−	1.34078i	1.40550	−	0.279572i	0.566662	−	0.823950i	$-0.308234\pi$
$23$	6.74055	−	1.34078i	1.40550	−	0.279572i	0.838840	+	0.544378i	$0.183234\pi$
$24$		0			0
$25$	0.612220	−	3.07784i	0.122444	−	0.615567i
$26$		0			0
$27$	1.44447	−	14.6660i	0.277989	−	2.82247i
$28$		0			0
$29$	−1.92135	+	6.33383i	−0.356785	+	1.17616i	0.576522	+	0.817082i	$0.304410\pi$
$29$	−1.92135	+	6.33383i	−0.356785	+	1.17616i	−0.933307	+	0.359081i	$0.883090\pi$
$30$		0			0
$31$	2.37838	+	2.37838i	0.427170	+	0.427170i	0.887663	−	0.460493i	$-0.152327\pi$
$31$	2.37838	+	2.37838i	0.427170	+	0.427170i	−0.460493	+	0.887663i	$0.652327\pi$
$32$		0			0
$33$	0.345743	−	0.345743i	0.0601861	−	0.0601861i
$34$		0			0
$35$	0.254791	+	0.0772899i	0.0430675	+	0.0130644i
$36$		0			0
$37$	3.51713	+	0.346407i	0.578213	+	0.0569490i	0.382897	−	0.923791i	$-0.374927\pi$
$37$	3.51713	+	0.346407i	0.578213	+	0.0569490i	0.195317	+	0.980740i	$0.437427\pi$
$38$		0			0
$39$	−15.4529	−	3.07378i	−2.47445	−	0.492198i
$40$		0			0
$41$	0.456936	+	2.29717i	0.0713615	+	0.358758i	0.999923	−	0.0124205i	$-0.00395366\pi$
$41$	0.456936	+	2.29717i	0.0713615	+	0.358758i	−0.928561	+	0.371179i	$0.878954\pi$
$42$		0			0
$43$	−4.58870	−	2.45271i	−0.699771	−	0.374035i	0.0828263	−	0.996564i	$-0.473605\pi$
$43$	−4.58870	−	2.45271i	−0.699771	−	0.374035i	−0.782597	+	0.622529i	$0.786105\pi$
$44$		0			0
$45$	−10.2380	+	1.00836i	−1.52619	+	0.150317i
$46$		0			0
$47$	3.90401	+	9.42513i	0.569459	+	1.37480i	0.902012	+	0.431711i	$0.142090\pi$
$47$	3.90401	+	9.42513i	0.569459	+	1.37480i	−0.332553	+	0.943085i	$0.607910\pi$
$48$		0			0
$49$	−2.66421	+	6.43198i	−0.380602	+	0.918854i
$50$		0			0
$51$	−0.498146	+	0.606993i	−0.0697544	+	0.0849960i
$52$		0			0
$53$	−0.703882	−	2.32039i	−0.0966856	−	0.318730i	0.895234	−	0.445596i	$-0.147008\pi$
$53$	−0.703882	−	2.32039i	−0.0966856	−	0.318730i	−0.991920	+	0.126866i	$0.959508\pi$
$54$		0			0
$55$	−0.170876	−	0.114176i	−0.0230409	−	0.0153954i
$56$		0			0
$57$	13.6538	+	20.4343i	1.80849	+	2.70659i
$58$		0			0
$59$	1.33800	−	1.09807i	0.174193	−	0.142956i	−0.543257	−	0.839566i	$-0.682809\pi$
$59$	1.33800	−	1.09807i	0.174193	−	0.142956i	0.717450	+	0.696610i	$0.245309\pi$
$60$		0			0
$61$	−3.57815	−	6.69426i	−0.458136	−	0.857112i	−0.999863	−	0.0165573i	$-0.994729\pi$
$61$	−3.57815	−	6.69426i	−0.458136	−	0.857112i	0.541727	−	0.840554i	$-0.317771\pi$
$62$		0			0
$63$			1.47117i			0.185350i
$64$		0			0
$65$			6.62221i			0.821384i
$66$		0			0
$67$	−1.30359	−	2.43884i	−0.159259	−	0.297952i	0.789618	−	0.613599i	$-0.210279\pi$
$67$	−1.30359	−	2.43884i	−0.159259	−	0.297952i	−0.948877	+	0.315646i	$0.897779\pi$
$68$		0			0
$69$	17.2471	−	14.1543i	2.07630	−	1.70398i
$70$		0			0
$71$	3.30056	+	4.93964i	0.391704	+	0.586227i	0.973944	−	0.226790i	$-0.0728232\pi$
$71$	3.30056	+	4.93964i	0.391704	+	0.586227i	−0.582239	+	0.813018i	$0.697823\pi$
$72$		0			0
$73$	−8.33969	−	5.57240i	−0.976086	−	0.652200i	−0.0382465	−	0.999268i	$-0.512177\pi$
$73$	−8.33969	−	5.57240i	−0.976086	−	0.652200i	−0.937840	+	0.347068i	$0.887177\pi$
$74$		0			0
$75$	−2.95736	−	9.74910i	−0.341486	−	1.12573i
$76$		0			0
$77$	−0.0186442	+	0.0227180i	−0.00212470	+	0.00258896i
$78$		0			0
$79$	0.333360	−	0.804803i	0.0375060	−	0.0905474i	−0.904017	−	0.427497i	$-0.859395\pi$
$79$	0.333360	−	0.804803i	0.0375060	−	0.0905474i	0.941523	+	0.336950i	$0.109395\pi$
$80$		0			0
$81$	−9.65299	−	23.3044i	−1.07255	−	2.58938i
$82$		0			0
$83$	1.71796	−	0.169204i	0.188571	−	0.0185726i	−0.00329100	−	0.999995i	$-0.501048\pi$
$83$	1.71796	−	0.169204i	0.188571	−	0.0185726i	0.191862	+	0.981422i	$0.438548\pi$
$84$		0			0
$85$	0.291068	+	0.155579i	0.0315707	+	0.0168749i
$86$		0			0
$87$	4.19204	+	21.0748i	0.449434	+	2.25946i
$88$		0			0
$89$	8.77606	+	1.74567i	0.930260	+	0.185040i	0.636886	−	0.770958i	$-0.280222\pi$
$89$	8.77606	+	1.74567i	0.930260	+	0.185040i	0.293374	+	0.955998i	$0.405222\pi$
$90$		0			0
$91$	0.942446	+	0.0928229i	0.0987952	+	0.00973048i
$92$		0			0
$93$	10.4494	+	3.16978i	1.08355	+	0.328691i
$94$		0			0
$95$	7.30407	−	7.30407i	0.749381	−	0.749381i
$96$		0			0
$97$	5.19447	+	5.19447i	0.527418	+	0.527418i	0.919802	−	0.392383i	$-0.128349\pi$
$97$	5.19447	+	5.19447i	0.527418	+	0.527418i	−0.392383	+	0.919802i	$0.628349\pi$
$98$		0			0
$99$	0.329626	−	1.08663i	0.0331287	−	0.109211i
$100$		0			0
$101$	−0.0387557	+	0.393493i	−0.00385634	+	0.0391540i	−0.996920	−	0.0784211i	$-0.975012\pi$
$101$	−0.0387557	+	0.393493i	−0.00385634	+	0.0391540i	0.993064	+	0.117575i	$0.0375121\pi$
$102$		0			0
$103$	1.46072	−	7.34354i	0.143929	−	0.723580i	−0.839654	−	0.543122i	$-0.817242\pi$
$103$	1.46072	−	7.34354i	0.143929	−	0.723580i	0.983583	−	0.180458i	$-0.0577580\pi$
$104$		0			0
$105$	0.847775	−	0.168633i	0.0827344	−	0.0164569i
$106$		0			0
$107$	−7.44829	+	13.9348i	−0.720053	+	1.34712i	0.209270	+	0.977858i	$0.432891\pi$
$107$	−7.44829	+	13.9348i	−0.720053	+	1.34712i	−0.929323	+	0.369267i	$0.879609\pi$
$108$		0			0
$109$	1.12348	+	11.4069i	0.107610	+	1.09258i	0.885645	+	0.464362i	$0.153716\pi$
$109$	1.12348	+	11.4069i	0.107610	+	1.09258i	−0.778036	+	0.628220i	$0.783784\pi$
$110$		0			0
$111$	10.6001	−	4.39069i	1.00611	−	0.416746i
$112$		0			0
$113$	2.62802	+	1.08856i	0.247224	+	0.102403i	0.502854	−	0.864371i	$-0.332283\pi$
$113$	2.62802	+	1.08856i	0.247224	+	0.102403i	−0.255631	+	0.966774i	$0.582283\pi$
$114$		0			0
$115$	−7.24905	−	5.94914i	−0.675977	−	0.554760i
$116$		0			0
$117$	−35.0147	+	10.6216i	−3.23711	+	0.981968i
$118$		0			0
$119$	0.0262212	−	0.0392429i	0.00240370	−	0.00359739i
$120$		0			0
$121$	−9.12730	+	6.09867i	−0.829755	+	0.554425i
$122$		0			0
$123$	4.82377	+	5.87778i	0.434945	+	0.529982i
$124$		0			0
$125$	−9.79329	+	5.23463i	−0.875939	+	0.468199i
$126$		0			0
$127$	1.79922			0.159655			0.0798275	−	0.996809i	$-0.474563\pi$
$127$	1.79922			0.159655			0.0798275	+	0.996809i	$0.474563\pi$
$128$		0			0
$129$	−16.8915			−1.48721
$130$		0			0
$131$	7.98472	−	4.26792i	0.697628	−	0.372890i	−0.0841445	−	0.996454i	$-0.526816\pi$
$131$	7.98472	−	4.26792i	0.697628	−	0.372890i	0.781773	+	0.623564i	$0.214316\pi$
$132$		0			0
$133$	−0.937106	−	1.14187i	−0.0812574	−	0.0990124i
$134$		0			0
$135$	−16.7197	+	11.1717i	−1.43900	+	0.961510i
$136$		0			0
$137$	−0.528159	+	0.790446i	−0.0451237	+	0.0675323i	−0.853346	−	0.521346i	$-0.825430\pi$
$137$	−0.528159	+	0.790446i	−0.0451237	+	0.0675323i	0.808222	+	0.588878i	$0.200430\pi$
$138$		0			0
$139$	−15.2367	+	4.62199i	−1.29236	+	0.392032i	−0.860288	−	0.509809i	$-0.829716\pi$
$139$	−15.2367	+	4.62199i	−1.29236	+	0.392032i	−0.432068	+	0.901841i	$0.642216\pi$
$140$		0			0
$141$	25.6015	+	21.0106i	2.15603	+	1.76941i
$142$		0			0
$143$	−0.675311	−	0.279723i	−0.0564724	−	0.0233916i
$144$		0			0
$145$	8.34394	−	3.45617i	0.692926	−	0.287019i
$146$		0			0
$147$	2.21534	+	22.4927i	0.182718	+	1.85516i
$148$		0			0
$149$	6.11873	−	11.4473i	0.501266	−	0.937803i	−0.496305	−	0.868148i	$-0.665310\pi$
$149$	6.11873	−	11.4473i	0.501266	−	0.937803i	0.997571	−	0.0696548i	$-0.0221898\pi$
$150$		0			0
$151$	−6.96948	+	1.38632i	−0.567169	+	0.112817i	−0.470342	−	0.882484i	$-0.655869\pi$
$151$	−6.96948	+	1.38632i	−0.567169	+	0.112817i	−0.0968269	+	0.995301i	$0.530869\pi$
$152$		0			0
$153$	−0.355765	+	1.78855i	−0.0287619	+	0.144596i
$154$		0			0
$155$	0.449855	−	4.56746i	0.0361332	−	0.366867i
$156$		0			0
$157$	4.80591	−	15.8430i	0.383553	−	1.26441i	−0.526593	−	0.850118i	$-0.676531\pi$
$157$	4.80591	−	15.8430i	0.383553	−	1.26441i	0.910146	−	0.414288i	$-0.135969\pi$
$158$		0			0
$159$	−5.56633	−	5.56633i	−0.441439	−	0.441439i
$160$		0			0
$161$	−0.948267	+	0.948267i	−0.0747339	+	0.0747339i
$162$		0			0
$163$	−6.28708	−	1.90716i	−0.492442	−	0.149381i	0.0342903	−	0.999412i	$-0.489083\pi$
$163$	−6.28708	−	1.90716i	−0.492442	−	0.149381i	−0.526732	+	0.850031i	$0.676583\pi$
$164$		0			0
$165$	−0.663967	−	0.0653950i	−0.0516897	−	0.00509099i
$166$		0			0
$167$	−3.04803	−	0.606292i	−0.235864	−	0.0469163i	0.0757428	−	0.997127i	$-0.475867\pi$
$167$	−3.04803	−	0.606292i	−0.235864	−	0.0469163i	−0.311607	+	0.950211i	$0.600867\pi$
$168$		0			0
$169$	2.05890	+	10.3508i	0.158377	+	0.796216i
$170$		0			0
$171$	50.3353	+	26.9048i	3.84924	+	2.05746i
$172$		0			0
$173$	−15.4705	+	1.52371i	−1.17620	+	0.115845i	−0.667170	−	0.744905i	$-0.732495\pi$
$173$	−15.4705	+	1.52371i	−1.17620	+	0.115845i	−0.509027	+	0.860751i	$0.669995\pi$
$174$		0			0
$175$	0.234334	+	0.565733i	0.0177140	+	0.0427654i
$176$		0			0
$177$	2.15039	−	5.19151i	0.161634	−	0.390218i
$178$		0			0
$179$	−7.82280	+	9.53211i	−0.584703	+	0.712463i	−0.978387	−	0.206783i	$-0.933701\pi$
$179$	−7.82280	+	9.53211i	−0.584703	+	0.712463i	0.393683	+	0.919246i	$0.371201\pi$
$180$		0			0
$181$	−0.181651	−	0.598824i	−0.0135020	−	0.0445102i	0.949930	−	0.312461i	$-0.101153\pi$
$181$	−0.181651	−	0.598824i	−0.0135020	−	0.0445102i	−0.963433	+	0.267951i	$0.913653\pi$
$182$		0			0
$183$	−20.4893	−	13.6905i	−1.51461	−	1.01203i
$184$		0			0
$185$	−2.67916	−	4.00964i	−0.196976	−	0.294795i
$186$		0			0
$187$	−0.0281602	+	0.0231105i	−0.00205928	+	0.00169000i
$188$		0			0
$189$	1.35556	+	2.53607i	0.0986025	+	0.184472i
$190$		0			0
$191$			23.7786i			1.72056i	0.509822	+	0.860280i	$0.329711\pi$
$191$			23.7786i			1.72056i	−0.509822	+	0.860280i	$0.670289\pi$
$192$		0			0
$193$		−	19.6161i		−	1.41200i	−0.708214	−	0.705998i	$-0.750499\pi$
$193$		−	19.6161i		−	1.41200i	0.708214	−	0.705998i	$-0.249501\pi$
$194$		0			0
$195$	10.1344	+	18.9601i	0.725738	+	1.35776i
$196$		0			0
$197$	−6.21590	+	5.10126i	−0.442865	+	0.363450i	−0.829241	−	0.558892i	$-0.811227\pi$
$197$	−6.21590	+	5.10126i	−0.442865	+	0.363450i	0.386376	+	0.922341i	$0.373727\pi$
$198$		0			0
$199$	−12.4091	−	18.5716i	−0.879659	−	1.31650i	−0.947812	−	0.318828i	$-0.896711\pi$
$199$	−12.4091	−	18.5716i	−0.879659	−	1.31650i	0.0681530	−	0.997675i	$-0.478289\pi$
$200$		0			0
$201$	−7.46464	−	4.98771i	−0.526515	−	0.351806i
$202$		0			0
$203$	−0.374913	−	1.23592i	−0.0263137	−	0.0867446i
$204$		0			0
$205$	2.02746	−	2.47047i	0.141604	−	0.172545i
$206$		0			0
$207$	19.8289	−	47.8712i	1.37820	−	3.32728i
$208$		0			0
$209$	0.436320	+	1.05337i	0.0301809	+	0.0728632i
$210$		0			0
$211$	1.26380	−	0.124474i	0.0870038	−	0.00856913i	−0.0544215	−	0.998518i	$-0.517331\pi$
$211$	1.26380	−	0.124474i	0.0870038	−	0.00856913i	0.141425	+	0.989949i	$0.454831\pi$
$212$		0			0
$213$	17.0093	+	9.09167i	1.16546	+	0.622951i
$214$		0			0
$215$	1.38506	+	6.96319i	0.0944606	+	0.474886i
$216$		0			0
$217$	−0.643717	−	0.128043i	−0.0436983	−	0.00869214i
$218$		0			0
$219$	−32.4052	−	3.19164i	−2.18974	−	0.215671i
$220$		0			0
$221$	1.12332	+	0.340755i	0.0755627	+	0.0229217i
$222$		0			0
$223$	−3.40850	+	3.40850i	−0.228250	+	0.228250i	−0.811961	−	0.583711i	$-0.801600\pi$
$223$	−3.40850	+	3.40850i	−0.228250	+	0.228250i	0.583711	+	0.811961i	$0.301600\pi$
$224$		0			0
$225$	−16.7299	−	16.7299i	−1.11533	−	1.11533i
$226$		0			0
$227$	3.52798	−	11.6302i	0.234160	−	0.771923i	−0.758573	−	0.651588i	$-0.774103\pi$
$227$	3.52798	−	11.6302i	0.234160	−	0.771923i	0.992733	−	0.120335i	$-0.0383968\pi$
$228$		0			0
$229$	1.04627	−	10.6230i	0.0691394	−	0.701984i	−0.896664	−	0.442711i	$-0.854017\pi$
$229$	1.04627	−	10.6230i	0.0691394	−	0.701984i	0.965804	−	0.259274i	$-0.0834832\pi$
$230$		0			0
$231$	−0.0186135	+	0.0935765i	−0.00122468	+	0.00615688i
$232$		0			0
$233$	0.564171	−	0.112221i	0.0369600	−	0.00735181i	−0.176576	−	0.984287i	$-0.556502\pi$
$233$	0.564171	−	0.112221i	0.0369600	−	0.00735181i	0.213536	+	0.976935i	$0.431502\pi$
$234$		0			0
$235$	6.56194	−	12.2765i	0.428054	−	0.800833i
$236$		0			0
$237$	−0.277194	−	2.81440i	−0.0180057	−	0.182815i
$238$		0			0
$239$	8.23481	−	3.41097i	0.532665	−	0.220637i	−0.100105	−	0.994977i	$-0.531918\pi$
$239$	8.23481	−	3.41097i	0.532665	−	0.220637i	0.632770	+	0.774340i	$0.281918\pi$
$240$		0			0
$241$	13.1850	+	5.46139i	0.849319	+	0.351799i	0.764521	−	0.644599i	$-0.222976\pi$
$241$	13.1850	+	5.46139i	0.849319	+	0.351799i	0.0847977	+	0.996398i	$0.472976\pi$
$242$		0			0
$243$	−29.1263	−	23.9034i	−1.86845	−	1.53340i
$244$		0			0
$245$	9.09051	−	2.75758i	0.580771	−	0.176175i
$246$		0			0
$247$	20.4114	−	30.5478i	1.29875	−	1.94371i
$248$		0			0
$249$	4.65976	−	3.11355i	0.295300	−	0.197313i
$250$		0			0
$251$	−10.0256	−	12.2162i	−0.632811	−	0.771082i	0.353597	−	0.935398i	$-0.384958\pi$
$251$	−10.0256	−	12.2162i	−0.632811	−	0.771082i	−0.986408	+	0.164316i	$0.947458\pi$
$252$		0			0
$253$	0.912875	−	0.487942i	0.0573920	−	0.0306767i
$254$		0			0
$255$	1.07145			0.0670969
$256$		0			0
$257$	3.04880			0.190179			0.0950894	−	0.995469i	$-0.469686\pi$
$257$	3.04880			0.190179			0.0950894	+	0.995469i	$0.469686\pi$
$258$		0			0
$259$	−0.608190	+	0.325084i	−0.0377911	+	0.0201998i
$260$		0			0
$261$	31.6576	+	38.5749i	1.95955	+	2.38772i
$262$		0			0
$263$	18.0928	−	12.0892i	1.11565	−	0.745454i	0.145839	−	0.989308i	$-0.453412\pi$
$263$	18.0928	−	12.0892i	1.11565	−	0.745454i	0.969812	+	0.243854i	$0.0784118\pi$
$264$		0			0
$265$	−1.83818	+	2.75104i	−0.112919	+	0.168995i
$266$		0			0
$267$	27.7983	−	8.43253i	1.70123	−	0.516062i
$268$		0			0
$269$	14.0961	+	11.5684i	0.859456	+	0.705338i	0.957061	−	0.289888i	$-0.0936179\pi$
$269$	14.0961	+	11.5684i	0.859456	+	0.705338i	−0.0976042	+	0.995225i	$0.531118\pi$
$270$		0			0
$271$	−18.5319	−	7.67617i	−1.12573	−	0.466294i	−0.259405	−	0.965769i	$-0.583527\pi$
$271$	−18.5319	−	7.67617i	−1.12573	−	0.466294i	−0.866329	+	0.499474i	$0.833527\pi$
$272$		0			0
$273$	2.84038	−	1.17652i	0.171908	−	0.0712065i
$274$		0			0
$275$	−0.0463270	−	0.470366i	−0.00279362	−	0.0283641i
$276$		0			0
$277$	10.3694	−	19.3997i	0.623035	−	1.16562i	−0.350388	−	0.936605i	$-0.613950\pi$
$277$	10.3694	−	19.3997i	0.623035	−	1.16562i	0.973423	−	0.229012i	$-0.0735497\pi$
$278$		0			0
$279$	24.8718	−	4.94732i	1.48904	−	0.296188i
$280$		0			0
$281$	3.85751	−	19.3930i	0.230120	−	1.15689i	−0.676988	−	0.735994i	$-0.736715\pi$
$281$	3.85751	−	19.3930i	0.230120	−	1.15689i	0.907108	−	0.420897i	$-0.138285\pi$
$282$		0			0
$283$	−1.31008	+	13.3014i	−0.0778760	+	0.790688i	0.874350	+	0.485295i	$0.161288\pi$
$283$	−1.31008	+	13.3014i	−0.0778760	+	0.790688i	−0.952226	+	0.305393i	$0.901212\pi$
$284$		0			0
$285$	9.73446	−	32.0902i	0.576620	−	1.90086i
$286$		0			0
$287$	−0.323169	−	0.323169i	−0.0190761	−	0.0190761i
$288$		0			0
$289$	−11.9794	+	11.9794i	−0.704673	+	0.704673i
$290$		0			0
$291$	22.8218	+	6.92290i	1.33784	+	0.405828i
$292$		0			0
$293$	−16.6050	−	1.63545i	−0.970072	−	0.0955437i	−0.399448	−	0.916756i	$-0.630798\pi$
$293$	−16.6050	−	1.63545i	−0.970072	−	0.0955437i	−0.570623	+	0.821212i	$0.693298\pi$
$294$		0			0
$295$	−2.31643	−	0.460766i	−0.134867	−	0.0268268i
$296$		0			0
$297$	−0.433016	−	2.17692i	−0.0251261	−	0.126318i
$298$		0			0
$299$	−29.4157	−	15.7230i	−1.70116	−	0.909287i
$300$		0			0
$301$	1.01039	−	0.0995145i	0.0582378	−	0.00573592i
$302$		0			0
$303$	0.491226	+	1.18592i	0.0282202	+	0.0681296i
$304$		0			0
$305$	−3.96357	+	9.56890i	−0.226953	+	0.547914i
$306$		0			0
$307$	3.74974	−	4.56907i	0.214009	−	0.260771i	−0.654930	−	0.755689i	$-0.727302\pi$
$307$	3.74974	−	4.56907i	0.214009	−	0.260771i	0.868939	+	0.494918i	$0.164802\pi$
$308$		0			0
$309$	−7.05608	−	23.2608i	−0.401407	−	1.32326i
$310$		0			0
$311$	16.3214	+	10.9056i	0.925499	+	0.618399i	0.924327	−	0.381601i	$-0.124627\pi$
$311$	16.3214	+	10.9056i	0.925499	+	0.618399i	0.00117166	+	0.999999i	$0.499627\pi$
$312$		0			0
$313$	−8.80698	−	13.1806i	−0.497800	−	0.745011i	0.494458	−	0.869201i	$-0.335367\pi$
$313$	−8.80698	−	13.1806i	−0.497800	−	0.745011i	−0.992258	+	0.124191i	$0.960367\pi$
$314$		0			0
$315$	1.55175	−	1.27349i	0.0874311	−	0.0717529i
$316$		0			0
$317$	−2.36221	−	4.41939i	−0.132675	−	0.248218i	0.806807	−	0.590815i	$-0.201194\pi$
$317$	−2.36221	−	4.41939i	−0.132675	−	0.248218i	−0.939483	+	0.342597i	$0.888694\pi$
$318$		0			0
$319$			0.996877i			0.0558144i
$320$		0			0
$321$			51.2954i			2.86303i
$322$		0			0
$323$	−0.863142	−	1.61482i	−0.0480265	−	0.0898512i
$324$		0			0
$325$	−11.7730	+	9.66181i	−0.653046	+	0.535941i
$326$		0			0
$327$	20.6733	+	30.9399i	1.14324	+	1.71098i
$328$		0			0
$329$	−1.65517	−	1.10595i	−0.0912525	−	0.0609729i
$330$		0			0
$331$	0.0486908	+	0.160512i	0.00267629	+	0.00882254i	0.958268	−	0.285870i	$-0.0922827\pi$
$331$	0.0486908	+	0.160512i	0.00267629	+	0.00882254i	−0.955592	+	0.294693i	$0.904783\pi$
$332$		0			0
$333$	16.9037	−	20.5972i	0.926316	−	1.12872i
$334$		0			0
$335$	−1.44400	+	3.48613i	−0.0788943	+	0.190468i
$336$		0			0
$337$	−0.0500988	−	0.120949i	−0.00272906	−	0.00658852i	0.922509	−	0.385975i	$-0.126135\pi$
$337$	−0.0500988	−	0.120949i	−0.00272906	−	0.00658852i	−0.925238	+	0.379387i	$0.876135\pi$
$338$		0			0
$339$	9.19021	−	0.905157i	0.499144	−	0.0491614i
$340$		0			0
$341$	0.446773	+	0.238805i	0.0241941	+	0.0129320i
$342$		0			0
$343$	−0.531503	−	2.67204i	−0.0286984	−	0.144277i
$344$		0			0
$345$	−29.8592	−	5.93936i	−1.60756	−	0.319764i
$346$		0			0
$347$	−11.1775	−	1.10089i	−0.600041	−	0.0590989i	−0.206564	−	0.978433i	$-0.566228\pi$
$347$	−11.1775	−	1.10089i	−0.600041	−	0.0590989i	−0.393477	+	0.919334i	$0.628728\pi$
$348$		0			0
$349$	−30.0494	−	9.11537i	−1.60851	−	0.487935i	−0.646947	−	0.762535i	$-0.723954\pi$
$349$	−30.0494	−	9.11537i	−1.60851	−	0.487935i	−0.961558	+	0.274601i	$0.911454\pi$
$350$		0			0
$351$	−50.5733	+	50.5733i	−2.69940	+	2.69940i
$352$		0			0
$353$	4.28714	+	4.28714i	0.228182	+	0.228182i	0.811933	−	0.583751i	$-0.198416\pi$
$353$	4.28714	+	4.28714i	0.228182	+	0.228182i	−0.583751	+	0.811933i	$0.698416\pi$
$354$		0			0
$355$	2.35314	−	7.75725i	0.124891	−	0.411712i
$356$		0			0
$357$	0.0150184	−	0.152485i	0.000794860	−	0.00807034i
$358$		0			0
$359$	3.28081	−	16.4938i	0.173155	−	0.870507i	−0.792339	−	0.610081i	$-0.791137\pi$
$359$	3.28081	−	16.4938i	0.173155	−	0.870507i	0.965494	−	0.260426i	$-0.0838631\pi$
$360$		0			0
$361$	−37.5714	+	7.47342i	−1.97744	+	0.393338i
$362$		0			0
$363$	−16.7993	+	31.4293i	−0.881734	+	1.64961i
$364$		0			0
$365$	1.34147	+	13.6201i	0.0702155	+	0.712910i
$366$		0			0
$367$	−20.2741	+	8.39780i	−1.05830	+	0.438362i	−0.842847	−	0.538153i	$-0.819122\pi$
$367$	−20.2741	+	8.39780i	−1.05830	+	0.438362i	−0.215452	+	0.976515i	$0.569122\pi$
$368$		0			0
$369$	16.3145	+	6.75767i	0.849297	+	0.351790i
$370$		0			0
$371$	0.365751	+	0.300164i	0.0189888	+	0.0155837i
$372$		0			0
$373$	2.60073	−	0.788923i	0.134661	−	0.0408489i	−0.222235	−	0.974993i	$-0.571335\pi$
$373$	2.60073	−	0.788923i	0.134661	−	0.0408489i	0.356896	+	0.934144i	$0.383835\pi$
$374$		0			0
$375$	−20.0284	+	29.9746i	−1.03426	+	1.54788i
$376$		0			0
$377$	26.7089	−	17.8463i	1.37558	−	0.919133i
$378$		0			0
$379$	4.18516	+	5.09963i	0.214977	+	0.261950i	0.869322	−	0.494246i	$-0.164556\pi$
$379$	4.18516	+	5.09963i	0.214977	+	0.261950i	−0.654345	+	0.756196i	$0.727056\pi$
$380$		0			0
$381$	5.15137	−	2.75346i	0.263913	−	0.141064i
$382$		0			0
$383$	13.8834			0.709410			0.354705	−	0.934978i	$-0.384581\pi$
$383$	13.8834			0.709410			0.354705	+	0.934978i	$0.384581\pi$
$384$		0			0
$385$	0.0401013			0.00204375
$386$		0			0
$387$	−34.5961	+	18.4920i	−1.75862	+	0.940002i
$388$		0			0
$389$	−15.9507	−	19.4360i	−0.808733	−	0.985445i	−0.999992	−	0.00390496i	$-0.998757\pi$
$389$	−15.9507	−	19.4360i	−0.808733	−	0.985445i	0.191259	−	0.981540i	$-0.438743\pi$
$390$		0			0
$391$	−1.38216	+	0.923529i	−0.0698988	+	0.0467049i
$392$		0			0
$393$	16.3297	−	24.4391i	0.823722	−	1.23279i
$394$		0			0
$395$	−1.13745	+	0.345042i	−0.0572315	+	0.0173610i
$396$		0			0
$397$	−17.5168	−	14.3757i	−0.879145	−	0.721496i	0.0822661	−	0.996610i	$-0.473784\pi$
$397$	−17.5168	−	14.3757i	−0.879145	−	0.721496i	−0.961411	+	0.275114i	$0.911284\pi$
$398$		0			0
$399$	−4.43051	−	1.83518i	−0.221803	−	0.0918737i
$400$		0			0
$401$	24.4143	−	10.1127i	1.21919	−	0.505005i	0.322038	−	0.946727i	$-0.395632\pi$
$401$	24.4143	−	10.1127i	1.21919	−	0.505005i	0.897152	+	0.441721i	$0.145632\pi$
$402$		0			0
$403$	−1.60003	−	16.2453i	−0.0797030	−	0.809238i
$404$		0			0
$405$	−16.2249	+	30.3547i	−0.806224	+	1.50834i
$406$		0			0
$407$	0.522059	−	0.103844i	0.0258775	−	0.00514735i
$408$		0			0
$409$	2.28299	−	11.4774i	0.112886	−	0.567519i	−0.882397	−	0.470506i	$-0.844071\pi$
$409$	2.28299	−	11.4774i	0.112886	−	0.567519i	0.995283	−	0.0970124i	$-0.0309287\pi$
$410$		0			0
$411$	−0.302507	+	3.07141i	−0.0149216	+	0.151501i
$412$		0			0
$413$	−0.0980435	+	0.323206i	−0.00482440	+	0.0159039i
$414$		0			0
$415$	−1.66559	−	1.66559i	−0.0817606	−	0.0817606i
$416$		0			0
$417$	−36.5509	+	36.5509i	−1.78990	+	1.78990i
$418$		0			0
$419$	26.2140	+	7.95192i	1.28064	+	0.388477i	0.856041	−	0.516907i	$-0.172917\pi$
$419$	26.2140	+	7.95192i	1.28064	+	0.388477i	0.424594	+	0.905384i	$0.360417\pi$
$420$		0			0
$421$	39.8566	+	3.92553i	1.94249	+	0.191319i	0.992615	−	0.121309i	$-0.0387093\pi$
$421$	39.8566	+	3.92553i	1.94249	+	0.191319i	0.949876	+	0.312628i	$0.101209\pi$
$422$		0			0
$423$	75.4368	+	15.0053i	3.66786	+	0.729583i
$424$		0			0
$425$	0.148080	+	0.744450i	0.00718295	+	0.0361111i
$426$		0			0
$427$	1.30625	+	0.698206i	0.0632139	+	0.0337885i
$428$		0			0
$429$	−2.36157	+	0.232594i	−0.114018	+	0.0112298i
$430$		0			0
$431$	1.00757	+	2.43249i	0.0485330	+	0.117169i	0.946287	−	0.323329i	$-0.104802\pi$
$431$	1.00757	+	2.43249i	0.0485330	+	0.117169i	−0.897754	+	0.440498i	$0.854802\pi$
$432$		0			0
$433$	−4.69123	+	11.3256i	−0.225446	+	0.544275i	−0.995613	−	0.0935676i	$-0.970173\pi$
$433$	−4.69123	+	11.3256i	−0.225446	+	0.544275i	0.770167	+	0.637842i	$0.220173\pi$
$434$		0			0
$435$	18.6004	−	22.6647i	0.891821	−	1.08669i
$436$		0			0
$437$	15.1026	+	49.7865i	0.722454	+	2.38161i
$438$		0			0
$439$	−13.1415	−	8.78085i	−0.627208	−	0.419087i	0.200934	−	0.979605i	$-0.435602\pi$
$439$	−13.1415	−	8.78085i	−0.627208	−	0.419087i	−0.828143	+	0.560518i	$0.810602\pi$
$440$		0			0
$441$	29.1612	+	43.6429i	1.38863	+	2.07823i
$442$		0			0
$443$	1.62908	−	1.33695i	0.0774001	−	0.0635206i	−0.594898	−	0.803801i	$-0.702807\pi$
$443$	1.62908	−	1.33695i	0.0774001	−	0.0635206i	0.672298	+	0.740281i	$0.265307\pi$
$444$		0			0
$445$	−5.75554	−	10.7679i	−0.272839	−	0.510446i
$446$		0			0
$447$		−	42.1389i		−	1.99310i
$448$		0			0
$449$		−	36.1725i		−	1.70709i	−0.521023	−	0.853543i	$-0.674449\pi$
$449$		−	36.1725i		−	1.70709i	0.521023	−	0.853543i	$-0.325551\pi$
$450$		0			0
$451$	0.166290	+	0.311107i	0.00783030	+	0.0146495i
$452$		0			0
$453$	−17.8328	+	14.6350i	−0.837859	+	0.687613i
$454$		0			0
$455$	−0.717903	−	1.07442i	−0.0336558	−	0.0503695i
$456$		0			0
$457$	1.06878	+	0.714133i	0.0499952	+	0.0334057i	0.580317	−	0.814391i	$-0.302929\pi$
$457$	1.06878	+	0.714133i	0.0499952	+	0.0334057i	−0.530321	+	0.847797i	$0.677929\pi$
$458$		0			0
$459$	1.03472	+	3.41101i	0.0482965	+	0.159212i
$460$		0			0
$461$	−18.2743	+	22.2673i	−0.851117	+	1.03709i	0.147727	+	0.989028i	$0.452804\pi$
$461$	−18.2743	+	22.2673i	−0.851117	+	1.03709i	−0.998844	+	0.0480615i	$0.984696\pi$
$462$		0			0
$463$	−13.5855	+	32.7983i	−0.631371	+	1.52426i	0.206529	+	0.978440i	$0.433783\pi$
$463$	−13.5855	+	32.7983i	−0.631371	+	1.52426i	−0.837900	+	0.545824i	$0.816217\pi$
$464$		0			0
$465$	−5.70188	−	13.7656i	−0.264419	−	0.638363i
$466$		0			0
$467$	−27.8915	+	2.74707i	−1.29066	+	0.127119i	−0.719948	−	0.694028i	$-0.755834\pi$
$467$	−27.8915	+	2.74707i	−1.29066	+	0.127119i	−0.570716	+	0.821148i	$0.693334\pi$
$468$		0			0
$469$	0.475892	+	0.254370i	0.0219746	+	0.0117457i
$470$		0			0
$471$	−10.4856	−	52.7149i	−0.483153	−	2.42897i
$472$		0			0
$473$	−0.768589	−	0.152882i	−0.0353398	−	0.00702952i
$474$		0			0
$475$	23.6418	+	2.32852i	1.08476	+	0.106840i
$476$		0			0
$477$	−17.4944	−	5.30685i	−0.801011	−	0.242984i
$478$		0			0
$479$	−12.6269	+	12.6269i	−0.576937	+	0.576937i	−0.934058	−	0.357121i	$-0.883758\pi$
$479$	−12.6269	+	12.6269i	−0.576937	+	0.576937i	0.357121	+	0.934058i	$0.383758\pi$
$480$		0			0
$481$	−12.1283	−	12.1283i	−0.553001	−	0.553001i
$482$		0			0
$483$	−1.26380	+	4.16619i	−0.0575049	+	0.189568i
$484$		0			0
$485$	0.982499	−	9.97548i	0.0446130	−	0.452963i
$486$		0			0
$487$	2.66111	−	13.3783i	0.120586	−	0.606229i	−0.872478	−	0.488654i	$-0.837488\pi$
$487$	2.66111	−	13.3783i	0.120586	−	0.606229i	0.993064	−	0.117575i	$-0.0375120\pi$
$488$		0			0
$489$	−20.9192	+	4.16110i	−0.946001	+	0.188171i
$490$		0			0
$491$	4.76807	−	8.92043i	0.215180	−	0.402573i	−0.751054	−	0.660241i	$-0.770454\pi$
$491$	4.76807	−	8.92043i	0.215180	−	0.402573i	0.966234	+	0.257668i	$0.0829541\pi$
$492$		0			0
$493$	−0.156918	−	1.59322i	−0.00706724	−	0.0717549i
$494$		0			0
$495$	−1.43149	+	0.592941i	−0.0643405	+	0.0266507i
$496$		0			0
$497$	−1.07100	−	0.443622i	−0.0480408	−	0.0198992i
$498$		0			0
$499$	17.4315	+	14.3057i	0.780342	+	0.640410i	0.937824	−	0.347112i	$-0.112838\pi$
$499$	17.4315	+	14.3057i	0.780342	+	0.640410i	−0.157482	+	0.987522i	$0.550338\pi$
$500$		0			0
$501$	−9.65471	+	2.92872i	−0.431340	+	0.130846i
$502$		0			0
$503$	−16.4770	+	24.6595i	−0.734672	+	1.09951i	0.256450	+	0.966558i	$0.417447\pi$
$503$	−16.4770	+	24.6595i	−0.734672	+	1.09951i	−0.991122	+	0.132957i	$0.957553\pi$
$504$		0			0
$505$	0.448595	−	0.299741i	0.0199622	−	0.0133383i
$506$		0			0
$507$	21.7354	+	26.4846i	0.965301	+	1.17622i
$508$		0			0
$509$	−18.5335	+	9.90636i	−0.821483	+	0.439092i	−0.827892	−	0.560888i	$-0.810460\pi$
$509$	−18.5335	+	9.90636i	−0.821483	+	0.439092i	0.00640920	+	0.999979i	$0.497960\pi$
$510$		0			0
$511$	1.95717			0.0865799
$512$		0			0
$513$	111.561			4.92555
$514$		0			0
$515$	−9.01022	+	4.81606i	−0.397038	+	0.212221i
$516$		0			0
$517$	0.974744	+	1.18773i	0.0428692	+	0.0522363i
$518$		0			0
$519$	−41.9618	+	28.0380i	−1.84192	+	1.23073i
$520$		0			0
$521$	4.11838	−	6.16359i	0.180429	−	0.270032i	−0.730220	−	0.683213i	$-0.760582\pi$
$521$	4.11838	−	6.16359i	0.180429	−	0.270032i	0.910649	+	0.413181i	$0.135582\pi$
$522$		0			0
$523$	22.7413	−	6.89849i	0.994407	−	0.301650i	0.249177	−	0.968458i	$-0.419840\pi$
$523$	22.7413	−	6.89849i	0.994407	−	0.301650i	0.745230	+	0.666808i	$0.232340\pi$
$524$		0			0
$525$	1.53670	+	1.26114i	0.0670671	+	0.0550406i
$526$		0			0
$527$	−0.751626	−	0.311334i	−0.0327413	−	0.0135619i
$528$		0			0
$529$	22.3881	−	9.27346i	0.973396	−	0.403194i
$530$		0			0
$531$	−1.27912	−	12.9871i	−0.0555089	−	0.563591i
$532$		0			0
$533$	5.35840	−	10.0249i	0.232098	−	0.434225i
$534$		0			0
$535$	21.1455	−	4.20610i	0.914200	−	0.181846i
$536$		0			0
$537$	−7.80994	+	39.2632i	−0.337024	+	1.69433i
$538$		0			0
$539$	−0.102776	+	1.04350i	−0.00442687	+	0.0449468i
$540$		0			0
$541$	2.53495	−	8.35660i	0.108986	−	0.359278i	−0.885435	−	0.464763i	$-0.846139\pi$
$541$	2.53495	−	8.35660i	0.108986	−	0.359278i	0.994421	+	0.105485i	$0.0336395\pi$
$542$		0			0
$543$	−1.43651	−	1.43651i	−0.0616464	−	0.0616464i
$544$		0			0
$545$	11.0592	−	11.0592i	0.473723	−	0.473723i
$546$		0			0
$547$	16.0061	+	4.85540i	0.684372	+	0.207602i	0.613277	−	0.789868i	$-0.289851\pi$
$547$	16.0061	+	4.85540i	0.684372	+	0.207602i	0.0710944	+	0.997470i	$0.477351\pi$
$548$		0			0
$549$	−56.9526	−	5.60934i	−2.43068	−	0.239401i
$550$		0			0
$551$	−49.1429	−	9.77514i	−2.09356	−	0.416435i
$552$		0			0
$553$	0.0331615	+	0.166714i	0.00141017	+	0.00708941i
$554$		0			0
$555$	−13.8069	−	7.37996i	−0.586072	−	0.313262i
$556$		0			0
$557$	38.4640	−	3.78837i	1.62977	−	0.160518i	0.758620	−	0.651534i	$-0.225874\pi$
$557$	38.4640	−	3.78837i	1.62977	−	0.160518i	0.871151	+	0.491015i	$0.163374\pi$
$558$		0			0
$559$	9.66336	+	23.3294i	0.408717	+	0.986729i
$560$		0			0
$561$	−0.0452583	+	0.109263i	−0.00191081	+	0.00461309i
$562$		0			0
$563$	7.38497	−	8.99862i	0.311240	−	0.379246i	−0.593772	−	0.804633i	$-0.702362\pi$
$563$	7.38497	−	8.99862i	0.311240	−	0.379246i	0.905012	+	0.425387i	$0.139862\pi$
$564$		0			0
$565$	−1.12671	−	3.71426i	−0.0474010	−	0.156260i
$566$		0			0
$567$	4.09254	+	2.73455i	0.171871	+	0.114840i
$568$		0			0
$569$	−18.0568	−	27.0239i	−0.756979	−	1.13290i	−0.987157	−	0.159750i	$-0.948931\pi$
$569$	−18.0568	−	27.0239i	−0.756979	−	1.13290i	0.230179	−	0.973148i	$-0.426069\pi$
$570$		0			0
$571$	34.6976	−	28.4755i	1.45205	−	1.19166i	0.508219	−	0.861228i	$-0.330304\pi$
$571$	34.6976	−	28.4755i	1.45205	−	1.19166i	0.943828	−	0.330437i	$-0.107196\pi$
$572$		0			0
$573$	36.3899	+	68.0808i	1.52021	+	2.84412i
$574$		0			0
$575$		−	21.5672i		−	0.899413i
$576$		0			0
$577$			9.94863i			0.414167i	0.978323	+	0.207083i	$0.0663971\pi$
$577$			9.94863i			0.414167i	−0.978323	+	0.207083i	$0.933603\pi$
$578$		0			0
$579$	−30.0197	−	56.1630i	−1.24758	−	2.33405i
$580$		0			0
$581$	−0.260387	+	0.213694i	−0.0108027	+	0.00886552i
$582$		0			0
$583$	−0.202897	−	0.303656i	−0.00840312	−	0.0125762i
$584$		0			0
$585$	41.5132	+	27.7383i	1.71636	+	1.14684i
$586$		0			0
$587$	2.75765	+	9.09076i	0.113820	+	0.375216i	0.995280	−	0.0970434i	$-0.0309386\pi$
$587$	2.75765	+	9.09076i	0.113820	+	0.375216i	−0.881460	+	0.472259i	$0.843439\pi$
$588$		0			0
$589$	−16.1533	+	19.6828i	−0.665584	+	0.811017i
$590$		0			0
$591$	−9.99003	+	24.1181i	−0.410935	+	0.992084i
$592$		0			0
$593$	10.9497	+	26.4350i	0.449652	+	1.08556i	0.972452	+	0.233101i	$0.0748874\pi$
$593$	10.9497	+	26.4350i	0.449652	+	1.08556i	−0.522800	+	0.852455i	$0.675113\pi$
$594$		0			0
$595$	−0.0640903	+	0.00631234i	−0.00262745	+	0.000258781i
$596$		0			0
$597$	−63.9499	−	34.1820i	−2.61730	−	1.39897i
$598$		0			0
$599$	8.41706	+	42.3154i	0.343912	+	1.72896i	0.635219	+	0.772332i	$0.280910\pi$
$599$	8.41706	+	42.3154i	0.343912	+	1.72896i	−0.291307	+	0.956630i	$0.594090\pi$
$600$		0			0
$601$	−18.4819	−	3.67629i	−0.753894	−	0.149959i	−0.196841	−	0.980435i	$-0.563068\pi$
$601$	−18.4819	−	3.67629i	−0.753894	−	0.149959i	−0.557054	+	0.830477i	$0.688068\pi$
$602$		0			0
$603$	−20.7489	−	2.04359i	−0.844961	−	0.0832214i
$604$		0			0
$605$	14.3336	+	4.34805i	0.582744	+	0.176773i
$606$		0			0
$607$	15.4956	−	15.4956i	0.628947	−	0.628947i	−0.318856	−	0.947803i	$-0.603299\pi$
$607$	15.4956	−	15.4956i	0.628947	−	0.628947i	0.947803	+	0.318856i	$0.103299\pi$
$608$		0			0
$609$	−2.96482	−	2.96482i	−0.120141	−	0.120141i
$610$		0			0
$611$	14.3722	−	47.3789i	0.581439	−	1.91675i
$612$		0			0
$613$	−2.56143	+	26.0066i	−0.103455	+	1.05040i	0.793589	+	0.608455i	$0.208210\pi$
$613$	−2.56143	+	26.0066i	−0.103455	+	1.05040i	−0.897044	+	0.441942i	$0.854290\pi$
$614$		0			0
$615$	2.02413	−	10.1760i	0.0816207	−	0.410335i
$616$		0			0
$617$	15.1008	−	3.00375i	0.607937	−	0.120926i	0.118484	−	0.992956i	$-0.462196\pi$
$617$	15.1008	−	3.00375i	0.607937	−	0.120926i	0.489453	+	0.872030i	$0.337196\pi$
$618$		0			0
$619$	−13.8857	+	25.9783i	−0.558112	+	1.04416i	0.431732	+	0.902002i	$0.357903\pi$
$619$	−13.8857	+	25.9783i	−0.558112	+	1.04416i	−0.989845	+	0.142153i	$0.954597\pi$
$620$		0			0
$621$	−9.92730	−	100.794i	−0.398369	−	4.04471i
$622$		0			0
$623$	−1.61311	+	0.668174i	−0.0646281	+	0.0267698i
$624$		0			0
$625$	−0.497564	−	0.206098i	−0.0199026	−	0.00824392i
$626$		0			0
$627$	2.86127	+	2.34819i	0.114268	+	0.0937775i
$628$		0			0
$629$	−0.818013	+	0.248141i	−0.0326163	+	0.00989405i
$630$		0			0
$631$	0.870439	−	1.30270i	0.0346516	−	0.0518598i	−0.813739	−	0.581230i	$-0.802572\pi$
$631$	0.870439	−	1.30270i	0.0346516	−	0.0518598i	0.848391	+	0.529370i	$0.177572\pi$
$632$		0			0
$633$	3.42792	−	2.29046i	0.136247	−	0.0910377i
$634$		0			0
$635$	−1.55746	−	1.89777i	−0.0618060	−	0.0753108i
$636$		0			0
$637$	29.7980	−	15.9274i	1.18064	−	0.631066i
$638$		0			0
$639$	44.7905			1.77189
$640$		0			0
$641$	−0.546606			−0.0215897			−0.0107948	−	0.999942i	$-0.503436\pi$
$641$	−0.546606			−0.0215897			−0.0107948	+	0.999942i	$0.503436\pi$
$642$		0			0
$643$	−24.9021	+	13.3105i	−0.982043	+	0.524913i	−0.882597	−	0.470130i	$-0.844207\pi$
$643$	−24.9021	+	13.3105i	−0.982043	+	0.524913i	−0.0994462	+	0.995043i	$0.531707\pi$
$644$		0			0
$645$	14.6218	+	17.8167i	0.575733	+	0.701533i
$646$		0			0
$647$	−16.1546	+	10.7942i	−0.635104	+	0.424363i	−0.831008	−	0.556260i	$-0.812236\pi$
$647$	−16.1546	+	10.7942i	−0.635104	+	0.424363i	0.195904	+	0.980623i	$0.437236\pi$
$648$		0			0
$649$	0.144834	−	0.216759i	0.00568522	−	0.00850853i
$650$		0			0
$651$	−2.03898	+	0.618519i	−0.0799141	+	0.0242417i
$652$		0			0
$653$	−15.9635	−	13.1009i	−0.624701	−	0.512679i	0.267947	−	0.963434i	$-0.413655\pi$
$653$	−15.9635	−	13.1009i	−0.624701	−	0.512679i	−0.892648	+	0.450755i	$0.851155\pi$
$654$		0			0
$655$	−11.4135	−	4.72763i	−0.445963	−	0.184724i
$656$		0			0
$657$	−69.8644	+	28.9388i	−2.72567	+	1.12901i
$658$		0			0
$659$	0.237451	+	2.41088i	0.00924979	+	0.0939147i	0.998701	−	0.0509506i	$-0.0162251\pi$
$659$	0.237451	+	2.41088i	0.00924979	+	0.0939147i	−0.989451	+	0.144865i	$0.953725\pi$
$660$		0			0
$661$	−19.0704	+	35.6782i	−0.741752	+	1.38772i	0.173498	+	0.984834i	$0.444493\pi$
$661$	−19.0704	+	35.6782i	−0.741752	+	1.38772i	−0.915250	+	0.402886i	$0.868007\pi$
$662$		0			0
$663$	3.73767	−	0.743468i	0.145159	−	0.0288739i
$664$		0			0
$665$	−0.393224	+	1.97687i	−0.0152486	+	0.0766597i
$666$		0			0
$667$	−4.45867	+	45.2696i	−0.172640	+	1.75285i
$668$		0			0
$669$	−4.54266	+	14.9751i	−0.175629	+	0.578972i
$670$		0			0
$671$	−0.808384	−	0.808384i	−0.0312073	−	0.0312073i
$672$		0			0
$673$	2.88867	−	2.88867i	0.111350	−	0.111350i	−0.649237	−	0.760587i	$-0.724911\pi$
$673$	2.88867	−	2.88867i	0.111350	−	0.111350i	0.760587	+	0.649237i	$0.224911\pi$
$674$		0			0
$675$	−44.2552	−	13.4247i	−1.70338	−	0.516716i
$676$		0			0
$677$	−19.5225	−	1.92280i	−0.750310	−	0.0738991i	−0.284369	−	0.958715i	$-0.591784\pi$
$677$	−19.5225	−	1.92280i	−0.750310	−	0.0738991i	−0.465941	+	0.884816i	$0.654284\pi$
$678$		0			0
$679$	−1.40590	−	0.279651i	−0.0539535	−	0.0107320i
$680$		0			0
$681$	−7.69743	−	38.6976i	−0.294966	−	1.48289i
$682$		0			0
$683$	−23.2162	−	12.4093i	−0.888345	−	0.474830i	−0.0369267	−	0.999318i	$-0.511757\pi$
$683$	−23.2162	−	12.4093i	−0.888345	−	0.474830i	−0.851418	+	0.524488i	$0.824257\pi$
$684$		0			0
$685$	1.29093	−	0.127146i	0.0493240	−	0.00485799i
$686$		0			0
$687$	−13.2614	−	32.0159i	−0.505954	−	1.22148i
$688$		0			0
$689$	−4.50343	+	10.8723i	−0.171567	+	0.414200i
$690$		0			0
$691$	−30.1714	+	36.7639i	−1.14777	+	1.39856i	−0.244418	+	0.969670i	$0.578597\pi$
$691$	−30.1714	+	36.7639i	−1.14777	+	1.39856i	−0.903354	+	0.428895i	$0.858903\pi$
$692$		0			0
$693$	0.0643200	+	0.212035i	0.00244332	+	0.00805453i
$694$		0			0
$695$	18.0645	+	12.0703i	0.685224	+	0.457852i
$696$		0			0
$697$	−0.314738	−	0.471038i	−0.0119215	−	0.0178419i
$698$		0			0
$699$	1.44354	−	1.18469i	0.0545999	−	0.0448089i
$700$		0			0
$701$	20.3759	+	38.1206i	0.769587	+	1.43980i	0.894236	+	0.447595i	$0.147719\pi$
$701$	20.3759	+	38.1206i	0.769587	+	1.43980i	−0.124649	+	0.992201i	$0.539781\pi$
$702$		0			0
$703$			26.7541i			1.00905i
$704$		0			0
$705$		−	45.1912i		−	1.70200i
$706$		0			0
$707$	−0.0363701	−	0.0680437i	−0.00136784	−	0.00255905i
$708$		0			0
$709$	−24.6436	+	20.2245i	−0.925510	+	0.759546i	−0.970916	−	0.239422i	$-0.923042\pi$
$709$	−24.6436	+	20.2245i	−0.925510	+	0.759546i	0.0454055	+	0.998969i	$0.485542\pi$
$710$		0			0
$711$	−3.64881	−	5.46082i	−0.136841	−	0.204797i
$712$		0			0
$713$	19.2205	+	12.8427i	0.719813	+	0.480964i
$714$		0			0
$715$	0.289526	+	0.954438i	0.0108276	+	0.0356940i
$716$		0			0
$717$	18.3571	−	22.3682i	0.685560	−	0.835357i
$718$		0			0
$719$	7.12269	−	17.1957i	0.265632	−	0.641291i	−0.733637	−	0.679542i	$-0.762179\pi$
$719$	7.12269	−	17.1957i	0.265632	−	0.641291i	0.999268	+	0.0382507i	$0.0121786\pi$
$720$		0			0
$721$	0.559108	+	1.34981i	0.0208223	+	0.0502694i
$722$		0			0
$723$	46.1079	−	4.54124i	1.71477	−	0.168890i
$724$		0			0
$725$	18.3182	+	9.79128i	0.680321	+	0.363639i
$726$		0			0
$727$	6.68420	+	33.6037i	0.247903	+	1.24629i	0.881334	+	0.472494i	$0.156646\pi$
$727$	6.68420	+	33.6037i	0.247903	+	1.24629i	−0.633431	+	0.773799i	$0.718354\pi$
$728$		0			0
$729$	−45.7533	−	9.10089i	−1.69457	−	0.337070i
$730$		0			0
$731$	1.25243	+	0.123354i	0.0463228	+	0.00456240i
$732$		0			0
$733$	45.8766	+	13.9165i	1.69449	+	0.514018i	0.982195	−	0.187862i	$-0.0601558\pi$
$733$	45.8766	+	13.9165i	1.69449	+	0.514018i	0.712295	+	0.701880i	$0.247656\pi$
$734$		0			0
$735$	21.8070	−	21.8070i	0.804365	−	0.804365i
$736$		0			0
$737$	−0.294510	−	0.294510i	−0.0108484	−	0.0108484i
$738$		0			0
$739$	11.5396	−	38.0411i	0.424492	−	1.39936i	−0.440579	−	0.897714i	$-0.645227\pi$
$739$	11.5396	−	38.0411i	0.424492	−	1.39936i	0.865071	−	0.501649i	$-0.167273\pi$
$740$		0			0
$741$	11.6908	−	118.699i	0.429472	−	4.36051i
$742$		0			0
$743$	−2.46999	+	12.4175i	−0.0906151	+	0.455553i	0.908662	+	0.417533i	$0.137105\pi$
$743$	−2.46999	+	12.4175i	−0.0906151	+	0.455553i	−0.999277	+	0.0380201i	$0.987895\pi$
$744$		0			0
$745$	−17.3709	+	3.45529i	−0.636422	+	0.126592i
$746$		0			0
$747$	6.13526	−	11.4783i	0.224478	−	0.419968i
$748$		0			0
$749$	−0.302201	−	3.06830i	−0.0110422	−	0.112113i
$750$		0			0
$751$	−17.7882	+	7.36812i	−0.649101	+	0.268867i	−0.682844	−	0.730564i	$-0.739257\pi$
$751$	−17.7882	+	7.36812i	−0.649101	+	0.268867i	0.0337429	+	0.999431i	$0.489257\pi$
$752$		0			0
$753$	−47.3997	−	19.6336i	−1.72734	−	0.715488i
$754$		0			0
$755$	7.49525	+	6.15119i	0.272780	+	0.223865i
$756$		0			0
$757$	33.7719	−	10.2446i	1.22746	−	0.372346i	0.391009	−	0.920387i	$-0.372126\pi$
$757$	33.7719	−	10.2446i	1.22746	−	0.372346i	0.836452	+	0.548041i	$0.184626\pi$
$758$		0			0
$759$	1.86693	−	2.79406i	0.0677654	−	0.101418i
$760$		0			0
$761$	−18.9623	+	12.6702i	−0.687384	+	0.459295i	−0.849578	−	0.527464i	$-0.823143\pi$
$761$	−18.9623	+	12.6702i	−0.687384	+	0.459295i	0.162194	+	0.986759i	$0.448143\pi$
$762$		0			0
$763$	−1.41888	−	1.72891i	−0.0513670	−	0.0625909i
$764$		0			0
$765$	2.19448	−	1.17297i	0.0793415	−	0.0424089i
$766$		0			0
$767$	−8.40038			−0.303320
$768$		0			0
$769$	34.0603			1.22825			0.614123	−	0.789210i	$-0.289510\pi$
$769$	34.0603			1.22825			0.614123	+	0.789210i	$0.289510\pi$
$770$		0			0
$771$	8.72904	−	4.66577i	0.314369	−	0.168034i
$772$		0			0
$773$	8.79030	+	10.7110i	0.316165	+	0.385249i	0.906709	−	0.421757i	$-0.138587\pi$
$773$	8.79030	+	10.7110i	0.316165	+	0.385249i	−0.590543	+	0.807006i	$0.701087\pi$
$774$		0			0
$775$	8.77636	−	5.86418i	0.315256	−	0.210647i
$776$		0			0
$777$	−1.24382	+	1.86150i	−0.0446217	+	0.0667811i
$778$		0			0
$779$	−16.9672	+	5.14695i	−0.607913	+	0.184409i
$780$		0			0
$781$	0.691663	+	0.567633i	0.0247496	+	0.0203115i
$782$		0			0
$783$	90.1166	+	37.3275i	3.22050	+	1.33398i
$784$		0			0
$785$	−20.8709	+	8.64500i	−0.744914	+	0.308553i
$786$		0			0
$787$	−1.71371	−	17.3996i	−0.0610872	−	0.620229i	−0.976177	−	0.216978i	$-0.930380\pi$
$787$	−1.71371	−	17.3996i	−0.0610872	−	0.620229i	0.915089	−	0.403251i	$-0.132120\pi$
$788$		0			0
$789$	33.3008	−	62.3014i	1.18554	−	2.21799i
$790$		0			0
$791$	−0.544392	+	0.108286i	−0.0193564	+	0.00385022i
$792$		0			0
$793$	−7.18682	+	36.1306i	−0.255211	+	1.28303i
$794$		0			0
$795$	−1.05283	+	10.6896i	−0.0373402	+	0.379121i
$796$		0			0
$797$	7.77476	−	25.6299i	0.275396	−	0.907859i	−0.704729	−	0.709477i	$-0.748931\pi$
$797$	7.77476	−	25.6299i	0.275396	−	0.907859i	0.980125	−	0.198382i	$-0.0635687\pi$
$798$		0			0
$799$	−1.74480	−	1.74480i	−0.0617267	−	0.0617267i
$800$		0			0
$801$	47.7032	−	47.7032i	1.68551	−	1.68551i
$802$		0			0
$803$	−1.44560	−	0.438518i	−0.0510141	−	0.0154750i
$804$		0			0
$805$	1.82106	+	0.179359i	0.0641838	+	0.00632156i
$806$		0			0
$807$	58.0626	+	11.5494i	2.04390	+	0.406557i
$808$		0			0
$809$	5.04354	+	25.3556i	0.177322	+	0.891456i	0.962312	+	0.271948i	$0.0876678\pi$
$809$	5.04354	+	25.3556i	0.177322	+	0.891456i	−0.784990	+	0.619508i	$0.787332\pi$
$810$		0			0
$811$	12.6496	+	6.76135i	0.444187	+	0.237423i	0.678298	−	0.734787i	$-0.262718\pi$
$811$	12.6496	+	6.76135i	0.444187	+	0.237423i	−0.234111	+	0.972210i	$0.575218\pi$
$812$		0			0
$813$	−64.8063	+	6.38286i	−2.27286	+	0.223857i
$814$		0			0
$815$	3.43066	+	8.28235i	0.120171	+	0.290118i
$816$		0			0
$817$	15.0732	−	36.3899i	0.527344	−	1.27312i
$818$		0			0
$819$	4.52949	−	5.51919i	0.158273	−	0.192856i
$820$		0			0
$821$	0.620931	+	2.04693i	0.0216706	+	0.0714385i	0.967109	−	0.254363i	$-0.0818658\pi$
$821$	0.620931	+	2.04693i	0.0216706	+	0.0714385i	−0.945438	+	0.325802i	$0.894366\pi$
$822$		0			0
$823$	−25.0522	−	16.7393i	−0.873265	−	0.583497i	0.0361688	−	0.999346i	$-0.488485\pi$
$823$	−25.0522	−	16.7393i	−0.873265	−	0.583497i	−0.909434	+	0.415849i	$0.863485\pi$
$824$		0			0
$825$	−0.852470	−	1.27581i	−0.0296792	−	0.0444180i
$826$		0			0
$827$	17.2781	−	14.1797i	0.600817	−	0.493078i	−0.284120	−	0.958789i	$-0.591701\pi$
$827$	17.2781	−	14.1797i	0.600817	−	0.493078i	0.884937	+	0.465711i	$0.154201\pi$
$828$		0			0
$829$	−13.3858	−	25.0432i	−0.464910	−	0.869785i	−0.999693	−	0.0247952i	$-0.992107\pi$
$829$	−13.3858	−	25.0432i	−0.464910	−	0.869785i	0.534783	−	0.844989i	$-0.320393\pi$
$830$		0			0
$831$		−	71.4125i		−	2.47727i
$832$		0			0
$833$		−	1.68391i		−	0.0583441i
$834$		0			0
$835$	1.99897	+	3.73981i	0.0691773	+	0.129422i
$836$		0			0
$837$	38.3168	−	31.4458i	1.32442	−	1.08693i
$838$		0			0
$839$	−26.5008	−	39.6613i	−0.914910	−	1.36926i	−0.929285	−	0.369362i	$-0.879576\pi$
$839$	−26.5008	−	39.6613i	−0.914910	−	1.36926i	0.0143760	−	0.999897i	$-0.495424\pi$
$840$		0			0
$841$	−12.3132	−	8.22742i	−0.424593	−	0.283704i
$842$		0			0
$843$	−18.6339	−	61.4278i	−0.641786	−	2.11569i
$844$		0			0
$845$	9.13551	−	11.1317i	0.314271	−	0.382941i
$846$		0			0
$847$	0.819710	−	1.97895i	0.0281656	−	0.0679977i
$848$		0			0
$849$	16.6051	+	40.0883i	0.569887	+	1.37583i
$850$		0			0
$851$	24.1719	−	2.38072i	0.828601	−	0.0816101i
$852$		0			0
$853$	18.9420	+	10.1247i	0.648562	+	0.346664i	0.762654	−	0.646807i	$-0.223896\pi$
$853$	18.9420	+	10.1247i	0.648562	+	0.346664i	−0.114092	+	0.993470i	$0.536396\pi$
$854$		0			0
$855$	−15.1933	−	76.3820i	−0.519601	−	2.61221i
$856$		0			0
$857$	44.3065	+	8.81310i	1.51348	+	0.301050i	0.880847	−	0.473401i	$-0.156974\pi$
$857$	44.3065	+	8.81310i	1.51348	+	0.301050i	0.632633	+	0.774451i	$0.281974\pi$
$858$		0			0
$859$	25.1481	+	2.47687i	0.858041	+	0.0845097i	0.517462	−	0.855706i	$-0.326877\pi$
$859$	25.1481	+	2.47687i	0.858041	+	0.0845097i	0.340579	+	0.940216i	$0.389377\pi$
$860$		0			0
$861$	−1.41983	−	0.430702i	−0.0483878	−	0.0146783i
$862$		0			0
$863$	4.10853	−	4.10853i	0.139856	−	0.139856i	−0.633713	−	0.773569i	$-0.718470\pi$
$863$	4.10853	−	4.10853i	0.139856	−	0.139856i	0.773569	+	0.633713i	$0.218470\pi$
$864$		0			0
$865$	14.9989	+	14.9989i	0.509977	+	0.509977i
$866$		0			0
$867$	−15.9656	+	52.6314i	−0.542219	+	1.78746i
$868$		0			0
$869$	0.0128599	−	0.130568i	0.000436241	−	0.00442923i
$870$		0			0
$871$	−2.61829	+	13.1631i	−0.0887175	+	0.446013i
$872$		0			0
$873$	54.3210	−	10.8051i	1.83849	−	0.365698i
$874$		0			0
$875$	1.02143	−	1.91097i	0.0345307	−	0.0646025i
$876$		0			0
$877$	4.15053	+	42.1410i	0.140153	+	1.42300i	0.765893	+	0.642968i	$0.222297\pi$
$877$	4.15053	+	42.1410i	0.140153	+	1.42300i	−0.625739	+	0.780032i	$0.715203\pi$
$878$		0			0
$879$	−50.0446	+	20.7292i	−1.68796	+	0.699177i
$880$		0			0
$881$	−47.0203	−	19.4765i	−1.58415	−	0.656178i	−0.595090	−	0.803659i	$-0.702884\pi$
$881$	−47.0203	−	19.4765i	−1.58415	−	0.656178i	−0.989065	+	0.147481i	$0.952884\pi$
$882$		0			0
$883$	28.1130	+	23.0718i	0.946079	+	0.776427i	0.974782	−	0.223161i	$-0.0716375\pi$
$883$	28.1130	+	23.0718i	0.946079	+	0.776427i	−0.0287023	+	0.999588i	$0.509137\pi$
$884$		0			0
$885$	−7.33732	+	2.22575i	−0.246641	+	0.0748178i
$886$		0			0
$887$	1.48282	−	2.21919i	0.0497881	−	0.0745131i	−0.805740	−	0.592269i	$-0.798232\pi$
$887$	1.48282	−	2.21919i	0.0497881	−	0.0745131i	0.855529	+	0.517756i	$0.173232\pi$
$888$		0			0
$889$	−0.291914	+	0.195051i	−0.00979049	+	0.00654180i
$890$		0			0
$891$	−2.41013	−	2.93676i	−0.0807425	−	0.0983851i
$892$		0			0
$893$	−68.1094	+	36.4052i	−2.27919	+	1.21825i
$894$		0			0
$895$	16.8259			0.562427
$896$		0			0
$897$	−108.282			−3.61545
$898$		0			0
$899$	−19.6340	+	10.4946i	−0.654829	+	0.350013i
$900$		0			0
$901$	0.372070	+	0.453368i	0.0123954	+	0.0151039i
$902$		0			0
$903$	2.74056	−	1.83118i	0.0912001	−	0.0609379i
$904$		0			0
$905$	−0.474381	+	0.709961i	−0.0157690	+	0.0235999i
$906$		0			0
$907$	22.0926	−	6.70171i	0.733572	−	0.222527i	0.0986712	−	0.995120i	$-0.468541\pi$
$907$	22.0926	−	6.70171i	0.733572	−	0.222527i	0.634901	+	0.772593i	$0.281041\pi$
$908$		0			0
$909$	2.30439	+	1.89117i	0.0764319	+	0.0627260i
$910$		0			0
$911$	−4.55436	−	1.88648i	−0.150893	−	0.0625019i	0.305959	−	0.952045i	$-0.401023\pi$
$911$	−4.55436	−	1.88648i	−0.150893	−	0.0625019i	−0.456852	+	0.889543i	$0.651023\pi$
$912$		0			0
$913$	0.240206	−	0.0994968i	0.00794967	−	0.00329286i
$914$		0			0
$915$	3.29577	+	33.4625i	0.108955	+	1.10624i
$916$		0			0
$917$	−0.832800	+	1.55806i	−0.0275015	+	0.0514517i
$918$		0			0
$919$	−12.1036	+	2.40756i	−0.399262	+	0.0794181i	−0.390637	−	0.920545i	$-0.627745\pi$
$919$	−12.1036	+	2.40756i	−0.399262	+	0.0794181i	−0.00862457	+	0.999963i	$0.502745\pi$
$920$		0			0
$921$	3.74358	−	18.8202i	0.123355	−	0.620148i
$922$		0			0
$923$	2.82605	−	28.6933i	0.0930205	−	0.944453i
$924$		0			0
$925$	3.21944	−	10.6131i	0.105855	−	0.348956i
$926$		0			0
$927$	−39.9166	−	39.9166i	−1.31103	−	1.31103i
$928$		0			0
$929$	−10.7155	+	10.7155i	−0.351566	+	0.351566i	−0.860692	−	0.509126i	$-0.829969\pi$
$929$	−10.7155	+	10.7155i	−0.351566	+	0.351566i	0.509126	+	0.860692i	$0.329969\pi$
$930$		0			0
$931$	−50.4336	−	15.2989i	−1.65289	−	0.501400i
$932$		0			0
$933$	63.4193	+	6.24626i	2.07626	+	0.204493i
$934$		0			0
$935$	0.0487527	+	0.00969751i	0.00159438	+	0.000317142i
$936$		0			0
$937$	6.65123	+	33.4380i	0.217286	+	1.09237i	0.923272	+	0.384146i	$0.125504\pi$
$937$	6.65123	+	33.4380i	0.217286	+	1.09237i	−0.705986	+	0.708226i	$0.749496\pi$
$938$		0			0
$939$	−45.3865	−	24.2596i	−1.48113	−	0.791681i
$940$		0			0
$941$	24.6978	−	2.43252i	0.805124	−	0.0792978i	0.312922	−	0.949779i	$-0.398692\pi$
$941$	24.6978	−	2.43252i	0.805124	−	0.0792978i	0.492202	+	0.870481i	$0.336192\pi$
$942$		0			0
$943$	6.16001	+	14.8716i	0.200597	+	0.484285i
$944$		0			0
$945$	1.50157	−	3.62511i	0.0488461	−	0.117925i
$946$		0			0
$947$	−13.6876	+	16.6784i	−0.444787	+	0.541975i	−0.946349	−	0.323147i	$-0.895259\pi$
$947$	−13.6876	+	16.6784i	−0.444787	+	0.541975i	0.501562	+	0.865122i	$0.332759\pi$
$948$		0			0
$949$	14.1304	+	46.5818i	0.458694	+	1.51211i
$950$		0			0
$951$	−13.5266	−	9.03815i	−0.438629	−	0.293082i
$952$		0			0
$953$	−33.0015	−	49.3903i	−1.06902	−	1.59991i	−0.761261	−	0.648446i	$-0.775419\pi$
$953$	−33.0015	−	49.3903i	−1.06902	−	1.59991i	−0.307764	−	0.951463i	$-0.599581\pi$
$954$		0			0
$955$	25.0811	−	20.5835i	0.811604	−	0.666066i
$956$		0			0
$957$	1.52559	+	2.85417i	0.0493152	+	0.0922622i
$958$		0			0
$959$		−	0.185503i		−	0.00599019i
$960$		0			0
$961$		−	19.6866i		−	0.635052i
$962$		0			0
$963$	56.1557	+	105.060i	1.80959	+	3.38551i
$964$		0			0
$965$	−20.6905	+	16.9803i	−0.666052	+	0.546615i
$966$		0			0
$967$	2.51428	+	3.76288i	0.0808537	+	0.121006i	0.869692	−	0.493594i	$-0.164317\pi$
$967$	2.51428	+	3.76288i	0.0808537	+	0.121006i	−0.788839	+	0.614600i	$0.789317\pi$
$968$		0			0
$969$	−4.94254	−	3.30250i	−0.158777	−	0.106092i
$970$		0			0
$971$	4.47380	+	14.7482i	0.143571	+	0.473291i	0.999004	−	0.0446232i	$-0.0142087\pi$
$971$	4.47380	+	14.7482i	0.143571	+	0.473291i	−0.855433	+	0.517914i	$0.826709\pi$
$972$		0			0
$973$	1.97100	−	2.40168i	0.0631875	−	0.0769942i
$974$		0			0
$975$	−18.9212	+	45.6797i	−0.605962	+	1.46292i
$976$		0			0
$977$	−10.0872	−	24.3526i	−0.322717	−	0.779108i	−0.999094	−	0.0425525i	$-0.986451\pi$
$977$	−10.0872	−	24.3526i	−0.322717	−	0.779108i	0.676377	−	0.736555i	$-0.263549\pi$
$978$		0			0
$979$	1.34119	−	0.132095i	0.0428645	−	0.00422179i
$980$		0			0
$981$	76.2133	+	40.7369i	2.43330	+	1.30063i
$982$		0			0
$983$	1.83343	+	9.21726i	0.0584772	+	0.293985i	0.998946	−	0.0458944i	$-0.0146138\pi$
$983$	1.83343	+	9.21726i	0.0584772	+	0.293985i	−0.940469	+	0.339879i	$0.889614\pi$
$984$		0			0
$985$	10.7614	+	2.14057i	0.342885	+	0.0682041i
$986$		0			0
$987$	−6.43144	−	0.633441i	−0.204715	−	0.0201627i
$988$		0			0
$989$	−34.2189	−	10.3802i	−1.08810	−	0.330071i
$990$		0			0
$991$	29.5439	−	29.5439i	0.938492	−	0.938492i	−0.0597231	−	0.998215i	$-0.519022\pi$
$991$	29.5439	−	29.5439i	0.938492	−	0.938492i	0.998215	+	0.0597231i	$0.0190218\pi$
$992$		0			0
$993$	0.385049	+	0.385049i	0.0122192	+	0.0122192i
$994$		0			0
$995$	−8.84709	+	29.1649i	−0.280472	+	0.924591i
$996$		0			0
$997$	−3.80500	+	38.6328i	−0.120506	+	1.22351i	0.724697	+	0.689067i	$0.241980\pi$
$997$	−3.80500	+	38.6328i	−0.120506	+	1.22351i	−0.845203	+	0.534446i	$0.820520\pi$
$998$		0			0
$999$	10.1608	−	51.0819i	0.321474	−	1.61616i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	512.2.k.a.497.15		240
4.3	odd	2		128.2.k.a.101.4	✓	240
128.19	odd	32		128.2.k.a.109.4	yes	240
128.109	even	32	inner	512.2.k.a.273.15		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
128.2.k.a.101.4	✓	240	4.3	odd	2
128.2.k.a.109.4	yes	240	128.19	odd	32
512.2.k.a.273.15		240	128.109	even	32	inner
512.2.k.a.497.15		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)

\(f(q)\)	\(=\)	\(q+(2.86311 - 1.53036i) q^{3} +(-0.865631 - 1.05477i) q^{5} +(-0.162245 + 0.108408i) q^{7} +(4.18867 - 6.26879i) q^{9} +(0.144127 - 0.0437204i) q^{11} +(-3.75158 - 3.07884i) q^{13} +(-4.09258 - 1.69520i) q^{15} +(-0.223463 + 0.0925613i) q^{17} +(0.742006 + 7.53372i) q^{19} +(-0.298620 + 0.558679i) q^{21} +(6.74055 - 1.34078i) q^{23} +(0.612220 - 3.07784i) q^{25} +(1.44447 - 14.6660i) q^{27} +(-1.92135 + 6.33383i) q^{29} +(2.37838 + 2.37838i) q^{31} +(0.345743 - 0.345743i) q^{33} +(0.254791 + 0.0772899i) q^{35} +(3.51713 + 0.346407i) q^{37} +(-15.4529 - 3.07378i) q^{39} +(0.456936 + 2.29717i) q^{41} +(-4.58870 - 2.45271i) q^{43} +(-10.2380 + 1.00836i) q^{45} +(3.90401 + 9.42513i) q^{47} +(-2.66421 + 6.43198i) q^{49} +(-0.498146 + 0.606993i) q^{51} +(-0.703882 - 2.32039i) q^{53} +(-0.170876 - 0.114176i) q^{55} +(13.6538 + 20.4343i) q^{57} +(1.33800 - 1.09807i) q^{59} +(-3.57815 - 6.69426i) q^{61} +1.47117i q^{63} +6.62221i q^{65} +(-1.30359 - 2.43884i) q^{67} +(17.2471 - 14.1543i) q^{69} +(3.30056 + 4.93964i) q^{71} +(-8.33969 - 5.57240i) q^{73} +(-2.95736 - 9.74910i) q^{75} +(-0.0186442 + 0.0227180i) q^{77} +(0.333360 - 0.804803i) q^{79} +(-9.65299 - 23.3044i) q^{81} +(1.71796 - 0.169204i) q^{83} +(0.291068 + 0.155579i) q^{85} +(4.19204 + 21.0748i) q^{87} +(8.77606 + 1.74567i) q^{89} +(0.942446 + 0.0928229i) q^{91} +(10.4494 + 3.16978i) q^{93} +(7.30407 - 7.30407i) q^{95} +(5.19447 + 5.19447i) q^{97} +(0.329626 - 1.08663i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 16 q^{3} - 16 q^{5} + 16 q^{7} - 16 q^{9} + 16 q^{11} - 16 q^{13} + 16 q^{15} - 16 q^{17} + 16 q^{19} - 16 q^{21} + 16 q^{23} - 16 q^{25} + 16 q^{27} - 16 q^{29} + 16 q^{31} - 16 q^{33} + 16 q^{35}+ \cdots + 16 q^{99}+O(q^{100}) \) 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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