LMFDB - Embedded newform 484.3.f.e.481.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [484,3,Mod(161,484)] 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("484.161"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(484, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 7])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 484 = 2^{2} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	484.f (of order $10$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,5,0,-6,0,20] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$13.1880447950$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 19x^{6} - 37x^{5} + 229x^{4} + 196x^{3} + 1496x^{2} + 2952x + 26896 $ x^8 - x^7 + 19x^6 - 37x^5 + 229x^4 + 196x^3 + 1496x^2 + 2952x + 26896
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 44)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			481.2
Root			$1.06155 - 3.26710i$ of defining polynomial
Character	$\chi$	$=$	484.481
Dual form			484.3.f.e.161.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.56155 + 4.80594i) q^{3} +(-3.83565 - 2.78676i) q^{5} +(6.34071 + 2.06022i) q^{7} +(-13.3775 + 9.71933i) q^{9} +(8.85202 + 12.1838i) q^{13} +(7.40348 - 22.7856i) q^{15} +(-10.5051 + 14.4591i) q^{17} +(-30.7829 + 10.0020i) q^{19} +33.6902i q^{21} -3.58879 q^{23} +(-0.779257 - 2.39831i) q^{25} +(-30.8066 - 22.3823i) q^{27} +(12.1438 + 3.94576i) q^{29} +(-17.7103 + 12.8673i) q^{31} +(-18.5794 - 25.5723i) q^{35} +(-8.56561 + 26.3622i) q^{37} +(-44.7316 + 61.5678i) q^{39} +(47.1286 - 15.3130i) q^{41} +16.8760i q^{43} +78.3970 q^{45} +(-24.0957 - 74.1591i) q^{47} +(-3.68176 - 2.67495i) q^{49} +(-85.8936 - 27.9085i) q^{51} +(-8.01232 + 5.82129i) q^{53} +(-96.1378 - 132.322i) q^{57} +(11.3299 - 34.8698i) q^{59} +(-16.6357 + 22.8971i) q^{61} +(-104.847 + 34.0668i) q^{63} -71.4011i q^{65} -30.7234 q^{67} +(-5.60406 - 17.2475i) q^{69} +(33.2060 + 24.1255i) q^{71} +(58.7348 + 19.0841i) q^{73} +(10.3093 - 7.49013i) q^{75} +(73.0540 + 100.550i) q^{79} +(13.4743 - 41.4696i) q^{81} +(-1.81914 + 2.50384i) q^{83} +(80.5879 - 26.1846i) q^{85} +64.5240i q^{87} +60.4914 q^{89} +(31.0268 + 95.4908i) q^{91} +(-89.4948 - 65.0218i) q^{93} +(145.946 + 47.4206i) q^{95} +(-38.8061 + 28.1943i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 5 q^{3} - 6 q^{5} + 20 q^{7} - 21 q^{9} + 10 q^{13} + 77 q^{15} - 55 q^{17} - 110 q^{19} + 100 q^{23} - 34 q^{25} - 130 q^{27} + 90 q^{29} - 122 q^{31} + 115 q^{35} + 180 q^{37} - 245 q^{39} - 105 q^{41}+ \cdots + 200 q^{97}+O(q^{100}) $ 8 * q + 5 * q^3 - 6 * q^5 + 20 * q^7 - 21 * q^9 + 10 * q^13 + 77 * q^15 - 55 * q^17 - 110 * q^19 + 100 * q^23 - 34 * q^25 - 130 * q^27 + 90 * q^29 - 122 * q^31 + 115 * q^35 + 180 * q^37 - 245 * q^39 - 105 * q^41 + 332 * q^45 + 10 * q^47 - 98 * q^49 + 30 * q^51 - 40 * q^53 - 165 * q^57 + 122 * q^59 - 160 * q^61 - 365 * q^63 + 10 * q^67 - 36 * q^69 - 108 * q^71 + 35 * q^73 - 153 * q^75 + 310 * q^79 + 128 * q^81 - 130 * q^83 + 280 * q^85 + 18 * q^89 - 25 * q^91 + 155 * q^93 + 245 * q^95 + 200 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/484\mathbb{Z}\right)^\times$.

$n$	$243$	$365$
$\chi(n)$	$1$	$e\left(\frac{3}{10}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	1.56155	+	4.80594i	0.520515	+	1.60198i	0.773017	+	0.634385i	$0.218747\pi$
$3$	1.56155	+	4.80594i	0.520515	+	1.60198i	−0.252502	+	0.967596i	$0.581253\pi$
$4$		0			0
$5$	−3.83565	−	2.78676i	−0.767130	−	0.557353i	0.133959	−	0.990987i	$-0.457231\pi$
$5$	−3.83565	−	2.78676i	−0.767130	−	0.557353i	−0.901089	+	0.433634i	$0.857231\pi$
$6$		0			0
$7$	6.34071	+	2.06022i	0.905816	+	0.294317i	0.724635	−	0.689133i	$-0.242008\pi$
$7$	6.34071	+	2.06022i	0.905816	+	0.294317i	0.181180	+	0.983450i	$0.442008\pi$
$8$		0			0
$9$	−13.3775	+	9.71933i	−1.48639	+	1.07993i
$10$		0			0
$11$		0			0
$11$		0			0
$12$		0			0
$13$	8.85202	+	12.1838i	0.680924	+	0.937212i	0.999944	−	0.0105359i	$-0.00335374\pi$
$13$	8.85202	+	12.1838i	0.680924	+	0.937212i	−0.319020	+	0.947748i	$0.603354\pi$
$14$		0			0
$15$	7.40348	−	22.7856i	0.493566	−	1.51904i
$16$		0			0
$17$	−10.5051	+	14.4591i	−0.617948	+	0.850532i	−0.997202	−	0.0747604i	$-0.976181\pi$
$17$	−10.5051	+	14.4591i	−0.617948	+	0.850532i	0.379254	+	0.925293i	$0.376181\pi$
$18$		0			0
$19$	−30.7829	+	10.0020i	−1.62015	+	0.526419i	−0.971978	−	0.235072i	$-0.924467\pi$
$19$	−30.7829	+	10.0020i	−1.62015	+	0.526419i	−0.648175	+	0.761492i	$0.724467\pi$
$20$		0			0
$21$			33.6902i			1.60430i
$22$		0			0
$23$	−3.58879			−0.156034			−0.0780171	−	0.996952i	$-0.524859\pi$
$23$	−3.58879			−0.156034			−0.0780171	+	0.996952i	$0.524859\pi$
$24$		0			0
$25$	−0.779257	−	2.39831i	−0.0311703	−	0.0959323i
$26$		0			0
$27$	−30.8066	−	22.3823i	−1.14098	−	0.828973i
$28$		0			0
$29$	12.1438	+	3.94576i	0.418752	+	0.136061i	0.510812	−	0.859693i	$-0.329345\pi$
$29$	12.1438	+	3.94576i	0.418752	+	0.136061i	−0.0920594	+	0.995754i	$0.529345\pi$
$30$		0			0
$31$	−17.7103	+	12.8673i	−0.571300	+	0.415073i	−0.835577	−	0.549373i	$-0.814867\pi$
$31$	−17.7103	+	12.8673i	−0.571300	+	0.415073i	0.264277	+	0.964447i	$0.414867\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−18.5794	−	25.5723i	−0.530840	−	0.730638i
$36$		0			0
$37$	−8.56561	+	26.3622i	−0.231503	+	0.712492i	0.766063	+	0.642765i	$0.222213\pi$
$37$	−8.56561	+	26.3622i	−0.231503	+	0.712492i	−0.997566	+	0.0697273i	$0.977787\pi$
$38$		0			0
$39$	−44.7316	+	61.5678i	−1.14696	+	1.57866i
$40$		0			0
$41$	47.1286	−	15.3130i	1.14948	−	0.373488i	0.328531	−	0.944493i	$-0.393447\pi$
$41$	47.1286	−	15.3130i	1.14948	−	0.373488i	0.820946	+	0.571006i	$0.193447\pi$
$42$		0			0
$43$			16.8760i			0.392466i	0.980557	+	0.196233i	$0.0628708\pi$
$43$			16.8760i			0.392466i	−0.980557	+	0.196233i	$0.937129\pi$
$44$		0			0
$45$	78.3970			1.74215
$46$		0			0
$47$	−24.0957	−	74.1591i	−0.512675	−	1.57785i	−0.787472	−	0.616350i	$-0.788611\pi$
$47$	−24.0957	−	74.1591i	−0.512675	−	1.57785i	0.274797	−	0.961502i	$-0.411389\pi$
$48$		0			0
$49$	−3.68176	−	2.67495i	−0.0751379	−	0.0545909i
$50$		0			0
$51$	−85.8936	−	27.9085i	−1.68419	−	0.547226i
$52$		0			0
$53$	−8.01232	+	5.82129i	−0.151176	+	0.109836i	−0.660802	−	0.750560i	$-0.729784\pi$
$53$	−8.01232	+	5.82129i	−0.151176	+	0.109836i	0.509626	+	0.860396i	$0.329784\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−96.1378	−	132.322i	−1.68663	−	2.32144i
$58$		0			0
$59$	11.3299	−	34.8698i	0.192032	−	0.591014i	−0.807966	−	0.589229i	$-0.799432\pi$
$59$	11.3299	−	34.8698i	0.192032	−	0.591014i	0.999998	−	0.00178528i	$-0.000568273\pi$
$60$		0			0
$61$	−16.6357	+	22.8971i	−0.272716	+	0.375362i	−0.923304	−	0.384069i	$-0.874522\pi$
$61$	−16.6357	+	22.8971i	−0.272716	+	0.375362i	0.650588	+	0.759431i	$0.274522\pi$
$62$		0			0
$63$	−104.847	+	34.0668i	−1.66424	+	0.540743i
$64$		0			0
$65$		−	71.4011i		−	1.09848i
$66$		0			0
$67$	−30.7234			−0.458558			−0.229279	−	0.973361i	$-0.573637\pi$
$67$	−30.7234			−0.458558			−0.229279	+	0.973361i	$0.573637\pi$
$68$		0			0
$69$	−5.60406	−	17.2475i	−0.0812182	−	0.249964i
$70$		0			0
$71$	33.2060	+	24.1255i	0.467689	+	0.339796i	0.796540	−	0.604586i	$-0.206661\pi$
$71$	33.2060	+	24.1255i	0.467689	+	0.339796i	−0.328851	+	0.944382i	$0.606661\pi$
$72$		0			0
$73$	58.7348	+	19.0841i	0.804586	+	0.261426i	0.682303	−	0.731070i	$-0.260979\pi$
$73$	58.7348	+	19.0841i	0.804586	+	0.261426i	0.122283	+	0.992495i	$0.460979\pi$
$74$		0			0
$75$	10.3093	−	7.49013i	0.137457	−	0.0998684i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	73.0540	+	100.550i	0.924734	+	1.27279i	0.961878	+	0.273477i	$0.0881739\pi$
$79$	73.0540	+	100.550i	0.924734	+	1.27279i	−0.0371444	+	0.999310i	$0.511826\pi$
$80$		0			0
$81$	13.4743	−	41.4696i	0.166349	−	0.511970i
$82$		0			0
$83$	−1.81914	+	2.50384i	−0.0219174	+	0.0301667i	−0.819835	−	0.572600i	$-0.805935\pi$
$83$	−1.81914	+	2.50384i	−0.0219174	+	0.0301667i	0.797918	+	0.602766i	$0.205935\pi$
$84$		0			0
$85$	80.5879	−	26.1846i	0.948093	−	0.308054i
$86$		0			0
$87$			64.5240i			0.741655i
$88$		0			0
$89$	60.4914			0.679678			0.339839	−	0.940484i	$-0.389627\pi$
$89$	60.4914			0.679678			0.339839	+	0.940484i	$0.389627\pi$
$90$		0			0
$91$	31.0268	+	95.4908i	0.340954	+	1.04935i
$92$		0			0
$93$	−89.4948	−	65.0218i	−0.962310	−	0.699159i
$94$		0			0
$95$	145.946	+	47.4206i	1.53627	+	0.499164i
$96$		0			0
$97$	−38.8061	+	28.1943i	−0.400063	+	0.290663i	−0.769567	−	0.638566i	$-0.779528\pi$
$97$	−38.8061	+	28.1943i	−0.400063	+	0.290663i	0.369504	+	0.929229i	$0.379528\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	51.7134	+	71.1774i	0.512014	+	0.704727i	0.984257	−	0.176741i	$-0.0565556\pi$
$101$	51.7134	+	71.1774i	0.512014	+	0.704727i	−0.472243	+	0.881468i	$0.656556\pi$
$102$		0			0
$103$	−3.84144	+	11.8227i	−0.0372955	+	0.114784i	−0.967971	−	0.251062i	$-0.919220\pi$
$103$	−3.84144	+	11.8227i	−0.0372955	+	0.114784i	0.930676	+	0.365846i	$0.119220\pi$
$104$		0			0
$105$	93.8867	−	129.224i	0.894159	−	1.23070i
$106$		0			0
$107$	−1.13078	+	0.367413i	−0.0105681	+	0.00343377i	−0.314296	−	0.949325i	$-0.601769\pi$
$107$	−1.13078	+	0.367413i	−0.0105681	+	0.00343377i	0.303728	+	0.952759i	$0.401769\pi$
$108$		0			0
$109$			145.212i			1.33222i	0.745855	+	0.666108i	$0.232041\pi$
$109$			145.212i			1.33222i	−0.745855	+	0.666108i	$0.767959\pi$
$110$		0			0
$111$	−140.071			−1.26190
$112$		0			0
$113$	17.9878	+	55.3607i	0.159184	+	0.489918i	0.998561	−	0.0536323i	$-0.0170799\pi$
$113$	17.9878	+	55.3607i	0.159184	+	0.489918i	−0.839377	+	0.543550i	$0.817080\pi$
$114$		0			0
$115$	13.7653	+	10.0011i	0.119699	+	0.0869661i
$116$		0			0
$117$	−236.836	−	76.9527i	−2.02424	−	0.657715i
$118$		0			0
$119$	−96.3987	+	70.0378i	−0.810073	+	0.588553i
$120$		0			0
$121$		0			0
$122$		0			0
$123$	147.187	+	202.585i	1.19664	+	1.64703i
$124$		0			0
$125$	−40.3218	+	124.098i	−0.322574	+	0.992781i
$126$		0			0
$127$	−23.2499	+	32.0007i	−0.183070	+	0.251974i	−0.890682	−	0.454627i	$-0.849772\pi$
$127$	−23.2499	+	32.0007i	−0.183070	+	0.251974i	0.707612	+	0.706601i	$0.249772\pi$
$128$		0			0
$129$	−81.1052	+	26.3527i	−0.628723	+	0.204284i
$130$		0			0
$131$		−	130.281i		−	0.994510i	−0.867605	−	0.497255i	$-0.834341\pi$
$131$		−	130.281i		−	0.994510i	0.867605	−	0.497255i	$-0.165659\pi$
$132$		0			0
$133$	−215.792			−1.62249
$134$		0			0
$135$	55.7891	+	171.701i	0.413253	+	1.27186i
$136$		0			0
$137$	166.701	+	121.115i	1.21679	+	0.884053i	0.995830	−	0.0912289i	$-0.0290795\pi$
$137$	166.701	+	121.115i	1.21679	+	0.884053i	0.220965	+	0.975282i	$0.429079\pi$
$138$		0			0
$139$	203.713	+	66.1903i	1.46556	+	0.476189i	0.929763	−	0.368159i	$-0.120012\pi$
$139$	203.713	+	66.1903i	1.46556	+	0.476189i	0.535796	+	0.844347i	$0.320012\pi$
$140$		0			0
$141$	318.778	−	231.606i	2.26083	−	1.64259i
$142$		0			0
$143$		0			0
$144$		0			0
$145$	−35.5835	−	48.9765i	−0.245404	−	0.337769i
$146$		0			0
$147$	7.10644	−	21.8714i	0.0483432	−	0.148785i
$148$		0			0
$149$	35.3034	−	48.5909i	0.236935	−	0.326114i	−0.673947	−	0.738780i	$-0.735402\pi$
$149$	35.3034	−	48.5909i	0.236935	−	0.326114i	0.910882	+	0.412666i	$0.135402\pi$
$150$		0			0
$151$	122.735	−	39.8790i	0.812815	−	0.264100i	0.127025	−	0.991899i	$-0.459457\pi$
$151$	122.735	−	39.8790i	0.812815	−	0.264100i	0.685789	+	0.727800i	$0.259457\pi$
$152$		0			0
$153$		−	295.529i		−	1.93156i
$154$		0			0
$155$	103.789			0.669604
$156$		0			0
$157$	−84.3134	−	259.490i	−0.537028	−	1.65280i	−0.739226	−	0.673457i	$-0.764809\pi$
$157$	−84.3134	−	259.490i	−0.537028	−	1.65280i	0.202199	−	0.979345i	$-0.435191\pi$
$158$		0			0
$159$	−40.4884	−	29.4165i	−0.254644	−	0.185010i
$160$		0			0
$161$	−22.7555	−	7.39370i	−0.141338	−	0.0459236i
$162$		0			0
$163$	11.6539	−	8.46708i	0.0714966	−	0.0519453i	−0.551463	−	0.834199i	$-0.685930\pi$
$163$	11.6539	−	8.46708i	0.0714966	−	0.0519453i	0.622959	+	0.782254i	$0.285930\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−95.5676	−	131.538i	−0.572261	−	0.787650i	0.420559	−	0.907265i	$-0.361834\pi$
$167$	−95.5676	−	131.538i	−0.572261	−	0.787650i	−0.992820	+	0.119615i	$0.961834\pi$
$168$		0			0
$169$	−17.8618	+	54.9731i	−0.105691	+	0.325285i
$170$		0			0
$171$	314.586	−	432.991i	1.83969	−	2.53211i
$172$		0			0
$173$	106.539	−	34.6167i	0.615833	−	0.200096i	0.0155436	−	0.999879i	$-0.495052\pi$
$173$	106.539	−	34.6167i	0.615833	−	0.200096i	0.600289	+	0.799783i	$0.295052\pi$
$174$		0			0
$175$		−	16.8124i		−	0.0960709i
$176$		0			0
$177$	185.275			1.04675
$178$		0			0
$179$	48.5633	+	149.462i	0.271303	+	0.834986i	0.990174	+	0.139842i	$0.0446594\pi$
$179$	48.5633	+	149.462i	0.271303	+	0.834986i	−0.718871	+	0.695144i	$0.755341\pi$
$180$		0			0
$181$	275.606	+	200.240i	1.52269	+	1.10630i	0.960136	+	0.279532i	$0.0901794\pi$
$181$	275.606	+	200.240i	1.52269	+	1.10630i	0.562549	+	0.826764i	$0.309821\pi$
$182$		0			0
$183$	−136.019	−	44.1954i	−0.743275	−	0.241505i
$184$		0			0
$185$	106.320	−	77.2460i	0.574702	−	0.417546i
$186$		0			0
$187$		0			0
$188$		0			0
$189$	−149.223	−	205.388i	−0.789540	−	1.08671i
$190$		0			0
$191$	9.61642	−	29.5963i	0.0503477	−	0.154954i	−0.922722	−	0.385467i	$-0.874040\pi$
$191$	9.61642	−	29.5963i	0.0503477	−	0.154954i	0.973069	+	0.230513i	$0.0740403\pi$
$192$		0			0
$193$	−29.4802	+	40.5760i	−0.152747	+	0.210238i	−0.878532	−	0.477683i	$-0.841477\pi$
$193$	−29.4802	+	40.5760i	−0.152747	+	0.210238i	0.725785	+	0.687921i	$0.241477\pi$
$194$		0			0
$195$	343.150	−	111.496i	1.75974	−	0.571775i
$196$		0			0
$197$		−	225.831i		−	1.14635i	−0.819432	−	0.573176i	$-0.805711\pi$
$197$		−	225.831i		−	1.14635i	0.819432	−	0.573176i	$-0.194289\pi$
$198$		0			0
$199$	46.4242			0.233287			0.116644	−	0.993174i	$-0.462786\pi$
$199$	46.4242			0.233287			0.116644	+	0.993174i	$0.462786\pi$
$200$		0			0
$201$	−47.9760	−	147.655i	−0.238687	−	0.734602i
$202$		0			0
$203$	68.8712	+	50.0379i	0.339267	+	0.246492i
$204$		0			0
$205$	−223.442	−	72.6008i	−1.08996	−	0.354150i
$206$		0			0
$207$	48.0091	−	34.8806i	0.231928	−	0.168505i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	62.7649	+	86.3885i	0.297464	+	0.409424i	0.931421	−	0.363944i	$-0.118570\pi$
$211$	62.7649	+	86.3885i	0.297464	+	0.409424i	−0.633957	+	0.773369i	$0.718570\pi$
$212$		0			0
$213$	−64.0934	+	197.259i	−0.300908	+	0.926099i
$214$		0			0
$215$	47.0295	−	64.7305i	0.218742	−	0.301072i
$216$		0			0
$217$	−138.805	+	45.1005i	−0.639655	+	0.207837i
$218$		0			0
$219$			312.077i			1.42501i
$220$		0			0
$221$	−269.157			−1.21791
$222$		0			0
$223$	−41.2976	−	127.101i	−0.185191	−	0.569959i	0.814761	−	0.579797i	$-0.196868\pi$
$223$	−41.2976	−	127.101i	−0.185191	−	0.569959i	−0.999952	+	0.00983830i	$0.996868\pi$
$224$		0			0
$225$	33.7345	+	24.5095i	0.149931	+	0.108931i
$226$		0			0
$227$	172.678	+	56.1066i	0.760697	+	0.247165i	0.663578	−	0.748107i	$-0.269037\pi$
$227$	172.678	+	56.1066i	0.760697	+	0.247165i	0.0971193	+	0.995273i	$0.469037\pi$
$228$		0			0
$229$	212.790	−	154.601i	0.929214	−	0.675113i	−0.0165863	−	0.999862i	$-0.505280\pi$
$229$	212.790	−	154.601i	0.929214	−	0.675113i	0.945800	+	0.324749i	$0.105280\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−97.0017	−	133.511i	−0.416316	−	0.573010i	0.548428	−	0.836198i	$-0.315226\pi$
$233$	−97.0017	−	133.511i	−0.416316	−	0.573010i	−0.964745	+	0.263187i	$0.915226\pi$
$234$		0			0
$235$	−114.241	+	351.597i	−0.486132	+	1.49616i
$236$		0			0
$237$	−369.161	+	508.107i	−1.55764	+	2.14391i
$238$		0			0
$239$	−288.179	+	93.6350i	−1.20577	+	0.391778i	−0.841880	−	0.539664i	$-0.818551\pi$
$239$	−288.179	+	93.6350i	−1.20577	+	0.391778i	−0.363889	+	0.931442i	$0.618551\pi$
$240$		0			0
$241$		−	289.642i		−	1.20183i	−0.799311	−	0.600917i	$-0.794802\pi$
$241$		−	289.642i		−	1.20183i	0.799311	−	0.600917i	$-0.205198\pi$
$242$		0			0
$243$	−122.370			−0.503579
$244$		0			0
$245$	6.66748	+	20.5204i	0.0272142	+	0.0837567i
$246$		0			0
$247$	−394.352	−	286.514i	−1.59657	−	1.15997i
$248$		0			0
$249$	−14.8740	−	4.83285i	−0.0597349	−	0.0194090i
$250$		0			0
$251$	−217.867	+	158.290i	−0.867997	+	0.630637i	−0.930049	−	0.367436i	$-0.880236\pi$
$251$	−217.867	+	158.290i	−0.867997	+	0.630637i	0.0620517	+	0.998073i	$0.480236\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$	251.683	+	346.413i	0.986994	+	1.35848i
$256$		0			0
$257$	155.437	−	478.387i	0.604815	−	1.86143i	0.106758	−	0.994285i	$-0.465953\pi$
$257$	155.437	−	478.387i	0.604815	−	1.86143i	0.498057	−	0.867144i	$-0.334047\pi$
$258$		0			0
$259$	−108.624	+	149.508i	−0.419398	+	0.577251i
$260$		0			0
$261$	−200.804	+	65.2453i	−0.769365	+	0.249982i
$262$		0			0
$263$			178.603i			0.679099i	0.940588	+	0.339550i	$0.110275\pi$
$263$			178.603i			0.679099i	−0.940588	+	0.339550i	$0.889725\pi$
$264$		0			0
$265$	46.9550			0.177189
$266$		0			0
$267$	94.4600	+	290.718i	0.353783	+	1.08883i
$268$		0			0
$269$	−85.3325	−	61.9977i	−0.317221	−	0.230475i	0.417768	−	0.908554i	$-0.362813\pi$
$269$	−85.3325	−	61.9977i	−0.317221	−	0.230475i	−0.734989	+	0.678079i	$0.762813\pi$
$270$		0			0
$271$	−139.685	−	45.3862i	−0.515441	−	0.167477i	0.0397343	−	0.999210i	$-0.487349\pi$
$271$	−139.685	−	45.3862i	−0.515441	−	0.167477i	−0.555175	+	0.831733i	$0.687349\pi$
$272$		0			0
$273$	−410.473	+	298.226i	−1.50357	+	1.09240i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	152.951	+	210.519i	0.552171	+	0.759998i	0.990305	−	0.138912i	$-0.0443605\pi$
$277$	152.951	+	210.519i	0.552171	+	0.759998i	−0.438134	+	0.898910i	$0.644360\pi$
$278$		0			0
$279$	111.858	−	344.264i	0.400926	−	1.23392i
$280$		0			0
$281$	301.056	−	414.369i	1.07137	−	1.47462i	0.202699	−	0.979241i	$-0.435029\pi$
$281$	301.056	−	414.369i	1.07137	−	1.47462i	0.868676	−	0.495380i	$-0.164971\pi$
$282$		0			0
$283$	170.144	−	55.2832i	0.601216	−	0.195347i	0.00743336	−	0.999972i	$-0.497634\pi$
$283$	170.144	−	55.2832i	0.601216	−	0.195347i	0.593783	+	0.804625i	$0.297634\pi$
$284$		0			0
$285$			775.456i			2.72090i
$286$		0			0
$287$	330.377			1.15114
$288$		0			0
$289$	−9.40080	−	28.9327i	−0.0325287	−	0.100113i
$290$		0			0
$291$	−196.098	−	142.473i	−0.673875	−	0.489599i
$292$		0			0
$293$	494.623	+	160.713i	1.68813	+	0.548508i	0.986462	−	0.163992i	$-0.0524372\pi$
$293$	494.623	+	160.713i	1.68813	+	0.548508i	0.701672	+	0.712500i	$0.252437\pi$
$294$		0			0
$295$	−140.631	+	102.175i	−0.476717	+	0.346355i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−31.7680	−	43.7249i	−0.106248	−	0.146237i
$300$		0			0
$301$	−34.7683	+	107.006i	−0.115509	+	0.355501i
$302$		0			0
$303$	−261.322	+	359.679i	−0.862448	+	1.18706i
$304$		0			0
$305$	127.617	−	41.4654i	0.418418	−	0.135952i
$306$		0			0
$307$			453.784i			1.47812i	0.673638	+	0.739061i	$0.264731\pi$
$307$			453.784i			1.47812i	−0.673638	+	0.739061i	$0.735269\pi$
$308$		0			0
$309$	−62.8180			−0.203294
$310$		0			0
$311$	125.374	+	385.862i	0.403132	+	1.24071i	0.922445	+	0.386129i	$0.126188\pi$
$311$	125.374	+	385.862i	0.403132	+	1.24071i	−0.519313	+	0.854584i	$0.673812\pi$
$312$		0			0
$313$	−13.5100	−	9.81556i	−0.0431628	−	0.0313596i	0.565995	−	0.824409i	$-0.308492\pi$
$313$	−13.5100	−	9.81556i	−0.0431628	−	0.0313596i	−0.609157	+	0.793049i	$0.708492\pi$
$314$		0			0
$315$	497.092	+	161.515i	1.57807	+	0.512746i
$316$		0			0
$317$	−455.110	+	330.656i	−1.43568	+	1.04308i	−0.446753	+	0.894657i	$0.647420\pi$
$317$	−455.110	+	330.656i	−1.43568	+	1.04308i	−0.988924	+	0.148423i	$0.952580\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	−3.53153	−	4.86074i	−0.0110017	−	0.0151425i
$322$		0			0
$323$	178.759	−	550.163i	0.553433	−	1.70329i
$324$		0			0
$325$	22.3224	−	30.7241i	0.0686843	−	0.0945358i
$326$		0			0
$327$	−697.879	+	226.755i	−2.13419	+	0.693439i
$328$		0			0
$329$		−	519.864i		−	1.58013i
$330$		0			0
$331$	167.684			0.506597			0.253298	−	0.967388i	$-0.418485\pi$
$331$	167.684			0.506597			0.253298	+	0.967388i	$0.418485\pi$
$332$		0			0
$333$	−141.637	−	435.913i	−0.425336	−	1.30905i
$334$		0			0
$335$	117.844	+	85.6188i	0.351774	+	0.255579i
$336$		0			0
$337$	−167.110	−	54.2973i	−0.495875	−	0.161119i	0.0503940	−	0.998729i	$-0.483952\pi$
$337$	−167.110	−	54.2973i	−0.495875	−	0.161119i	−0.546269	+	0.837610i	$0.683952\pi$
$338$		0			0
$339$	−237.972	+	172.896i	−0.701981	+	0.510019i
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−209.854	−	288.839i	−0.611819	−	0.842096i
$344$		0			0
$345$	−26.5695	+	81.7726i	−0.0770131	+	0.237022i
$346$		0			0
$347$	−284.107	+	391.040i	−0.818752	+	1.12692i	0.171162	+	0.985243i	$0.445248\pi$
$347$	−284.107	+	391.040i	−0.818752	+	1.12692i	−0.989914	+	0.141673i	$0.954752\pi$
$348$		0			0
$349$	−153.162	+	49.7653i	−0.438859	+	0.142594i	−0.520109	−	0.854100i	$-0.674109\pi$
$349$	−153.162	+	49.7653i	−0.438859	+	0.142594i	0.0812500	+	0.996694i	$0.474109\pi$
$350$		0			0
$351$		−	573.468i		−	1.63381i
$352$		0			0
$353$	522.647			1.48059			0.740294	−	0.672284i	$-0.234687\pi$
$353$	522.647			1.48059			0.740294	+	0.672284i	$0.234687\pi$
$354$		0			0
$355$	−60.1343	−	185.074i	−0.169392	−	0.521336i
$356$		0			0
$357$	−487.129	−	353.920i	−1.36451	−	0.991372i
$358$		0			0
$359$	−544.263	−	176.842i	−1.51605	−	0.492595i	−0.571401	−	0.820671i	$-0.693600\pi$
$359$	−544.263	−	176.842i	−1.51605	−	0.492595i	−0.944651	+	0.328076i	$0.893600\pi$
$360$		0			0
$361$	555.492	−	403.589i	1.53876	−	1.11797i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−172.103	−	236.880i	−0.471516	−	0.648986i
$366$		0			0
$367$	52.0404	−	160.164i	0.141799	−	0.436414i	−0.854786	−	0.518980i	$-0.826312\pi$
$367$	52.0404	−	160.164i	0.141799	−	0.436414i	0.996586	+	0.0825667i	$0.0263117\pi$
$368$		0			0
$369$	−481.631	+	662.908i	−1.30523	+	1.79650i
$370$		0			0
$371$	−62.7969	+	20.4040i	−0.169264	+	0.0549972i
$372$		0			0
$373$			500.543i			1.34194i	0.741486	+	0.670969i	$0.234122\pi$
$373$			500.543i			1.34194i	−0.741486	+	0.670969i	$0.765878\pi$
$374$		0			0
$375$	−659.370			−1.75832
$376$		0			0
$377$	59.4230	+	182.885i	0.157621	+	0.485107i
$378$		0			0
$379$	−42.1894	−	30.6524i	−0.111318	−	0.0808769i	0.530734	−	0.847539i	$-0.321916\pi$
$379$	−42.1894	−	30.6524i	−0.111318	−	0.0808769i	−0.642051	+	0.766662i	$0.721916\pi$
$380$		0			0
$381$	−190.099	−	61.7670i	−0.498948	−	0.162118i
$382$		0			0
$383$	199.922	−	145.251i	0.521988	−	0.379247i	−0.295364	−	0.955385i	$-0.595441\pi$
$383$	199.922	−	145.251i	0.521988	−	0.379247i	0.817352	+	0.576138i	$0.195441\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−164.024	−	225.759i	−0.423834	−	0.583357i
$388$		0			0
$389$	−76.1520	+	234.372i	−0.195763	+	0.602498i	0.804203	+	0.594354i	$0.202592\pi$
$389$	−76.1520	+	234.372i	−0.195763	+	0.602498i	−0.999967	+	0.00814375i	$0.997408\pi$
$390$		0			0
$391$	37.7006	−	51.8905i	0.0964210	−	0.132712i
$392$		0			0
$393$	626.122	−	203.439i	1.59319	−	0.517658i
$394$		0			0
$395$		−	589.260i		−	1.49180i
$396$		0			0
$397$	50.7517			0.127838			0.0639191	−	0.997955i	$-0.479640\pi$
$397$	50.7517			0.127838			0.0639191	+	0.997955i	$0.479640\pi$
$398$		0			0
$399$	−336.969	−	1037.08i	−0.844533	−	2.59920i
$400$		0			0
$401$	−38.8963	−	28.2598i	−0.0969983	−	0.0704734i	0.538229	−	0.842799i	$-0.319094\pi$
$401$	−38.8963	−	28.2598i	−0.0969983	−	0.0704734i	−0.635227	+	0.772325i	$0.719094\pi$
$402$		0			0
$403$	−313.544	−	101.876i	−0.778024	−	0.252795i
$404$		0			0
$405$	−167.249	+	121.513i	−0.412960	+	0.300033i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−300.638	−	413.792i	−0.735055	−	1.01172i	−0.998888	−	0.0471485i	$-0.984987\pi$
$409$	−300.638	−	413.792i	−0.735055	−	1.01172i	0.263832	−	0.964569i	$-0.415013\pi$
$410$		0			0
$411$	−321.762	+	990.282i	−0.782876	+	2.40944i
$412$		0			0
$413$	143.679	−	197.757i	0.347891	−	0.478831i
$414$		0			0
$415$	13.9552	−	4.53432i	0.0336270	−	0.0109261i
$416$		0			0
$417$			1082.39i			2.59566i
$418$		0			0
$419$	790.955			1.88772			0.943860	−	0.330345i	$-0.107165\pi$
$419$	790.955			1.88772			0.943860	+	0.330345i	$0.107165\pi$
$420$		0			0
$421$	127.247	+	391.625i	0.302249	+	0.930225i	0.980690	+	0.195571i	$0.0626559\pi$
$421$	127.247	+	391.625i	0.302249	+	0.930225i	−0.678441	+	0.734655i	$0.737344\pi$
$422$		0			0
$423$	1043.12	+	757.870i	2.46600	+	1.79165i
$424$		0			0
$425$	42.8634	+	13.9272i	0.100855	+	0.0327698i
$426$		0			0
$427$	−152.655	+	110.910i	−0.357506	+	0.259743i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−165.842	−	228.262i	−0.384785	−	0.529611i	0.572059	−	0.820212i	$-0.306145\pi$
$431$	−165.842	−	228.262i	−0.384785	−	0.529611i	−0.956844	+	0.290601i	$0.906145\pi$
$432$		0			0
$433$	−17.1508	+	52.7846i	−0.0396091	+	0.121904i	−0.968906	−	0.247430i	$-0.920414\pi$
$433$	−17.1508	+	52.7846i	−0.0396091	+	0.121904i	0.929297	+	0.369334i	$0.120414\pi$
$434$		0			0
$435$	179.813	−	247.491i	0.413363	−	0.568946i
$436$		0			0
$437$	110.473	−	35.8949i	0.252799	−	0.0821394i
$438$		0			0
$439$			232.914i			0.530556i	0.964172	+	0.265278i	$0.0854638\pi$
$439$			232.914i			0.530556i	−0.964172	+	0.265278i	$0.914536\pi$
$440$		0			0
$441$	75.2516			0.170638
$442$		0			0
$443$	−131.473	−	404.633i	−0.296780	−	0.913394i	−0.982618	−	0.185640i	$-0.940564\pi$
$443$	−131.473	−	404.633i	−0.296780	−	0.913394i	0.685838	−	0.727754i	$-0.259436\pi$
$444$		0			0
$445$	−232.024	−	168.575i	−0.521402	−	0.378820i
$446$		0			0
$447$	288.653	+	93.7890i	0.645756	+	0.209819i
$448$		0			0
$449$	−37.3765	+	27.1556i	−0.0832440	+	0.0604803i	−0.628629	−	0.777705i	$-0.716384\pi$
$449$	−37.3765	+	27.1556i	−0.0832440	+	0.0604803i	0.545385	+	0.838186i	$0.316384\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$	383.313	+	527.585i	0.846165	+	1.16465i
$454$		0			0
$455$	147.102	−	452.734i	0.323301	−	0.995019i
$456$		0			0
$457$	90.9191	−	125.139i	0.198948	−	0.273828i	−0.697874	−	0.716221i	$-0.745870\pi$
$457$	90.9191	−	125.139i	0.198948	−	0.273828i	0.896821	+	0.442393i	$0.145870\pi$
$458$		0			0
$459$	647.253	−	210.305i	1.41014	−	0.458181i
$460$		0			0
$461$		−	775.943i		−	1.68317i	−0.540123	−	0.841586i	$-0.681622\pi$
$461$		−	775.943i		−	1.68317i	0.540123	−	0.841586i	$-0.318378\pi$
$462$		0			0
$463$	−829.285			−1.79111			−0.895557	−	0.444948i	$-0.853222\pi$
$463$	−829.285			−1.79111			−0.895557	+	0.444948i	$0.853222\pi$
$464$		0			0
$465$	162.071	+	498.802i	0.348539	+	1.07269i
$466$		0			0
$467$	−632.973	−	459.882i	−1.35540	−	0.984757i	−0.998723	−	0.0505306i	$-0.983909\pi$
$467$	−632.973	−	459.882i	−1.35540	−	0.984757i	−0.356680	−	0.934227i	$-0.616091\pi$
$468$		0			0
$469$	−194.808	−	63.2970i	−0.415369	−	0.134962i
$470$		0			0
$471$	1115.43	−	810.410i	2.36823	−	1.72062i
$472$		0			0
$473$		0			0
$474$		0			0
$475$	47.9756	+	66.0327i	0.101001	+	0.139016i
$476$		0			0
$477$	50.6058	−	155.749i	0.106092	−	0.326517i
$478$		0			0
$479$	47.7186	−	65.6790i	0.0996213	−	0.137117i	−0.756296	−	0.654229i	$-0.772993\pi$
$479$	47.7186	−	65.6790i	0.0996213	−	0.137117i	0.855917	+	0.517112i	$0.172993\pi$
$480$		0			0
$481$	−397.014	+	128.998i	−0.825393	+	0.268186i
$482$		0			0
$483$		−	120.907i		−	0.250325i
$484$		0			0
$485$	227.418			0.468902
$486$		0			0
$487$	−90.0200	−	277.053i	−0.184846	−	0.568897i	0.815100	−	0.579321i	$-0.196682\pi$
$487$	−90.0200	−	277.053i	−0.184846	−	0.568897i	−0.999946	+	0.0104234i	$0.996682\pi$
$488$		0			0
$489$	58.8905	+	42.7864i	0.120430	+	0.0874978i
$490$		0			0
$491$	−285.590	−	92.7938i	−0.581649	−	0.188989i	0.00339000	−	0.999994i	$-0.498921\pi$
$491$	−285.590	−	92.7938i	−0.581649	−	0.188989i	−0.585039	+	0.811005i	$0.698921\pi$
$492$		0			0
$493$	−184.624	+	134.137i	−0.374491	+	0.272084i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	160.845	+	221.385i	0.323632	+	0.445442i
$498$		0			0
$499$	95.0706	−	292.597i	0.190522	−	0.586367i	−0.809478	−	0.587151i	$-0.800250\pi$
$499$	95.0706	−	292.597i	0.190522	−	0.586367i	1.00000		0.000783928i	$0.000249532\pi$
$500$		0			0
$501$	482.929	−	664.694i	0.963930	−	1.32674i
$502$		0			0
$503$	−762.072	+	247.612i	−1.51505	+	0.492271i	−0.944366	−	0.328897i	$-0.893323\pi$
$503$	−762.072	+	247.612i	−1.51505	+	0.492271i	−0.570687	+	0.821167i	$0.693323\pi$
$504$		0			0
$505$		−	417.125i		−	0.825990i
$506$		0			0
$507$	−292.090			−0.576114
$508$		0			0
$509$	167.385	+	515.157i	0.328850	+	1.01210i	0.969673	+	0.244408i	$0.0785935\pi$
$509$	167.385	+	515.157i	0.328850	+	1.01210i	−0.640822	+	0.767689i	$0.721407\pi$
$510$		0			0
$511$	333.103	+	242.013i	0.651864	+	0.473607i
$512$		0			0
$513$	1172.18	+	380.865i	2.28495	+	0.742427i
$514$		0			0
$515$	47.6816	−	34.6427i	0.0925856	−	0.0672674i
$516$		0			0
$517$		0			0
$518$		0			0
$519$	332.731	+	457.965i	0.641101	+	0.882400i
$520$		0			0
$521$	220.495	−	678.613i	0.423215	−	1.30252i	−0.481479	−	0.876458i	$-0.659900\pi$
$521$	220.495	−	678.613i	0.423215	−	1.30252i	0.904693	−	0.426063i	$-0.140100\pi$
$522$		0			0
$523$	−267.311	+	367.922i	−0.511110	+	0.703483i	−0.984106	−	0.177582i	$-0.943173\pi$
$523$	−267.311	+	367.922i	−0.511110	+	0.703483i	0.472996	+	0.881065i	$0.343173\pi$
$524$		0			0
$525$	80.7995	−	26.2533i	0.153904	−	0.0500064i
$526$		0			0
$527$		−	391.246i		−	0.742403i
$528$		0			0
$529$	−516.121			−0.975653
$530$		0			0
$531$	187.346	+	576.591i	0.352817	+	1.08586i
$532$		0			0
$533$	603.753	+	438.652i	1.13274	+	0.822987i
$534$		0			0
$535$	5.36118	+	1.74195i	0.0100209	+	0.00325599i
$536$		0			0
$537$	−642.474	+	466.785i	−1.19641	+	0.869246i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	474.904	+	653.649i	0.877826	+	1.20822i	0.977018	+	0.213156i	$0.0683741\pi$
$541$	474.904	+	653.649i	0.877826	+	1.20822i	−0.0991922	+	0.995068i	$0.531626\pi$
$542$		0			0
$543$	−531.969	+	1637.23i	−0.979684	+	3.01516i
$544$		0			0
$545$	404.670	−	556.981i	0.742515	−	1.02198i
$546$		0			0
$547$	−162.421	+	52.7739i	−0.296931	+	0.0964788i	−0.453694	−	0.891157i	$-0.649894\pi$
$547$	−162.421	+	52.7739i	−0.296931	+	0.0964788i	0.156763	+	0.987636i	$0.449894\pi$
$548$		0			0
$549$		−	467.994i		−	0.852447i
$550$		0			0
$551$	−413.287			−0.750067
$552$		0			0
$553$	256.058	+	788.067i	0.463035	+	1.42508i
$554$		0			0
$555$	537.263	+	390.345i	0.968042	+	0.703324i
$556$		0			0
$557$	22.5907	+	7.34016i	0.0405578	+	0.0131780i	0.329226	−	0.944251i	$-0.393212\pi$
$557$	22.5907	+	7.34016i	0.0405578	+	0.0131780i	−0.288668	+	0.957429i	$0.593212\pi$
$558$		0			0
$559$	−205.613	+	149.387i	−0.367824	+	0.267239i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−351.344	−	483.584i	−0.624057	−	0.858941i	0.373583	−	0.927597i	$-0.378129\pi$
$563$	−351.344	−	483.584i	−0.624057	−	0.858941i	−0.997640	+	0.0686553i	$0.978129\pi$
$564$		0			0
$565$	85.2823	−	262.472i	0.150942	−	0.464552i
$566$		0			0
$567$	170.873	−	235.187i	0.301363	−	0.414791i
$568$		0			0
$569$	387.480	−	125.900i	0.680984	−	0.221265i	0.0519577	−	0.998649i	$-0.483454\pi$
$569$	387.480	−	125.900i	0.680984	−	0.221265i	0.629026	+	0.777384i	$0.283454\pi$
$570$		0			0
$571$			1036.11i			1.81456i	0.420530	+	0.907279i	$0.361844\pi$
$571$			1036.11i			1.81456i	−0.420530	+	0.907279i	$0.638156\pi$
$572$		0			0
$573$	157.255			0.274441
$574$		0			0
$575$	2.79659	+	8.60701i	0.00486363	+	0.0149687i
$576$		0			0
$577$	−556.716	−	404.478i	−0.964845	−	0.701001i	−0.0105741	−	0.999944i	$-0.503366\pi$
$577$	−556.716	−	404.478i	−0.964845	−	0.701001i	−0.954271	+	0.298943i	$0.903366\pi$
$578$		0			0
$579$	−241.040	−	78.3188i	−0.416305	−	0.135266i
$580$		0			0
$581$	−16.6931	+	12.1283i	−0.0287317	+	0.0208748i
$582$		0			0
$583$		0			0
$584$		0			0
$585$	693.971	+	955.170i	1.18628	+	1.63277i
$586$		0			0
$587$	185.459	−	570.785i	0.315944	−	0.972376i	−0.659420	−	0.751775i	$-0.729198\pi$
$587$	185.459	−	570.785i	0.315944	−	0.972376i	0.975364	−	0.220601i	$-0.0708019\pi$
$588$		0			0
$589$	416.476	−	573.230i	0.707090	−	0.973226i
$590$		0			0
$591$	1085.33	−	352.646i	1.83643	−	0.596694i
$592$		0			0
$593$			468.857i			0.790652i	0.918541	+	0.395326i	$0.129368\pi$
$593$			468.857i			0.790652i	−0.918541	+	0.395326i	$0.870632\pi$
$594$		0			0
$595$	564.931			0.949463
$596$		0			0
$597$	72.4935	+	223.112i	0.121430	+	0.373722i
$598$		0			0
$599$	−414.897	−	301.440i	−0.692650	−	0.503239i	0.184880	−	0.982761i	$-0.440810\pi$
$599$	−414.897	−	301.440i	−0.692650	−	0.503239i	−0.877530	+	0.479522i	$0.840810\pi$
$600$		0			0
$601$	−482.357	−	156.727i	−0.802591	−	0.260778i	−0.121134	−	0.992636i	$-0.538653\pi$
$601$	−482.357	−	156.727i	−0.802591	−	0.260778i	−0.681457	+	0.731859i	$0.738653\pi$
$602$		0			0
$603$	411.003	−	298.611i	0.681597	−	0.495209i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	198.249	+	272.867i	0.326605	+	0.449534i	0.940470	−	0.339878i	$-0.110386\pi$
$607$	198.249	+	272.867i	0.326605	+	0.449534i	−0.613864	+	0.789412i	$0.710386\pi$
$608$		0			0
$609$	−132.934	+	409.128i	−0.218282	+	0.671802i
$610$		0			0
$611$	690.240	−	950.034i	1.12969	−	1.55488i
$612$		0			0
$613$	320.720	−	104.208i	0.523197	−	0.169997i	−0.0354989	−	0.999370i	$-0.511302\pi$
$613$	320.720	−	104.208i	0.523197	−	0.169997i	0.558696	+	0.829373i	$0.311302\pi$
$614$		0			0
$615$		−	1187.22i		−	1.93044i
$616$		0			0
$617$	−269.856			−0.437369			−0.218684	−	0.975796i	$-0.570177\pi$
$617$	−269.856			−0.437369			−0.218684	+	0.975796i	$0.570177\pi$
$618$		0			0
$619$	168.029	+	517.140i	0.271452	+	0.835444i	0.990136	+	0.140107i	$0.0447447\pi$
$619$	168.029	+	517.140i	0.271452	+	0.835444i	−0.718684	+	0.695337i	$0.755255\pi$
$620$		0			0
$621$	110.558	+	80.3252i	0.178032	+	0.129348i
$622$		0			0
$623$	383.558	+	124.626i	0.615663	+	0.200041i
$624$		0			0
$625$	449.488	−	326.572i	0.719181	−	0.522515i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−291.190	−	400.789i	−0.462941	−	0.637184i
$630$		0			0
$631$	34.9768	−	107.647i	0.0554307	−	0.170598i	−0.919508	−	0.393071i	$-0.871413\pi$
$631$	34.9768	−	107.647i	0.0554307	−	0.170598i	0.974939	+	0.222473i	$0.0714128\pi$
$632$		0			0
$633$	−317.168	+	436.544i	−0.501055	+	0.689643i
$634$		0			0
$635$	178.357	−	57.9516i	0.280877	−	0.0912624i
$636$		0			0
$637$		−	68.5364i		−	0.107592i
$638$		0			0
$639$	−678.697			−1.06212
$640$		0			0
$641$	−163.020	−	501.723i	−0.254321	−	0.782719i	−0.993963	−	0.109718i	$-0.965005\pi$
$641$	−163.020	−	501.723i	−0.254321	−	0.782719i	0.739642	−	0.673001i	$-0.234995\pi$
$642$		0			0
$643$	−237.173	−	172.317i	−0.368854	−	0.267988i	0.387881	−	0.921709i	$-0.373207\pi$
$643$	−237.173	−	172.317i	−0.368854	−	0.267988i	−0.756736	+	0.653721i	$0.773207\pi$
$644$		0			0
$645$	384.530	+	124.941i	0.596170	+	0.193708i
$646$		0			0
$647$	537.037	−	390.180i	0.830042	−	0.603061i	−0.0895290	−	0.995984i	$-0.528536\pi$
$647$	537.037	−	390.180i	0.830042	−	0.603061i	0.919571	+	0.392923i	$0.128536\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$	−433.501	−	596.663i	−0.665901	−	0.916534i
$652$		0			0
$653$	−245.388	+	755.228i	−0.375786	+	1.15655i	0.567160	+	0.823607i	$0.308042\pi$
$653$	−245.388	+	755.228i	−0.375786	+	1.15655i	−0.942947	+	0.332944i	$0.891958\pi$
$654$		0			0
$655$	−363.062	+	499.712i	−0.554293	+	0.762918i
$656$		0			0
$657$	−971.210	+	315.565i	−1.47825	+	0.480312i
$658$		0			0
$659$		−	187.489i		−	0.284505i	−0.989830	−	0.142253i	$-0.954565\pi$
$659$		−	187.489i		−	0.284505i	0.989830	−	0.142253i	$-0.0454346\pi$
$660$		0			0
$661$	74.1929			0.112243			0.0561217	−	0.998424i	$-0.482127\pi$
$661$	74.1929			0.112243			0.0561217	+	0.998424i	$0.482127\pi$
$662$		0			0
$663$	−420.301	−	1293.55i	−0.633938	−	1.95106i
$664$		0			0
$665$	827.701	+	601.360i	1.24466	+	0.904301i
$666$		0			0
$667$	−43.5816	−	14.1605i	−0.0653397	−	0.0212301i
$668$		0			0
$669$	546.352	−	396.948i	0.816669	−	0.593345i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	555.249	+	764.235i	0.825036	+	1.13556i	0.988827	+	0.149069i	$0.0476278\pi$
$673$	555.249	+	764.235i	0.825036	+	1.13556i	−0.163791	+	0.986495i	$0.552372\pi$
$674$		0			0
$675$	−29.6733	+	91.3251i	−0.0439605	+	0.135296i
$676$		0			0
$677$	−425.480	+	585.623i	−0.628479	+	0.865027i	−0.997936	−	0.0642211i	$-0.979544\pi$
$677$	−425.480	+	585.623i	−0.628479	+	0.865027i	0.369457	+	0.929248i	$0.379544\pi$
$678$		0			0
$679$	−304.145	+	98.8226i	−0.447930	+	0.145541i
$680$		0			0
$681$			917.495i			1.34728i
$682$		0			0
$683$	660.998			0.967787			0.483893	−	0.875127i	$-0.339222\pi$
$683$	660.998			0.967787			0.483893	+	0.875127i	$0.339222\pi$
$684$		0			0
$685$	−301.887	−	929.112i	−0.440711	−	1.35637i
$686$		0			0
$687$	1075.28	+	781.240i	1.56519	+	1.13718i
$688$		0			0
$689$	−141.850	−	46.0900i	−0.205879	−	0.0668940i
$690$		0			0
$691$	326.986	−	237.569i	0.473207	−	0.343805i	−0.325483	−	0.945548i	$-0.605527\pi$
$691$	326.986	−	237.569i	0.473207	−	0.343805i	0.798690	+	0.601743i	$0.205527\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−596.914	−	821.582i	−0.858869	−	1.18213i
$696$		0			0
$697$	−273.680	+	842.299i	−0.392654	+	1.20846i
$698$		0			0
$699$	490.176	−	674.669i	0.701253	−	0.965192i
$700$		0			0
$701$	−377.389	+	122.621i	−0.538359	+	0.174923i	−0.565561	−	0.824707i	$-0.691340\pi$
$701$	−377.389	+	122.621i	−0.538359	+	0.174923i	0.0272022	+	0.999630i	$0.491340\pi$
$702$		0			0
$703$		−	897.178i		−	1.27621i
$704$		0			0
$705$	−1868.15			−2.64986
$706$		0			0
$707$	181.259	+	557.857i	0.256377	+	0.789047i
$708$		0			0
$709$	11.1279	+	8.08489i	0.0156952	+	0.0114032i	0.595605	−	0.803277i	$-0.296912\pi$
$709$	11.1279	+	8.08489i	0.0156952	+	0.0114032i	−0.579910	+	0.814681i	$0.696912\pi$
$710$		0			0
$711$	−1954.56	−	635.076i	−2.74903	−	0.893215i
$712$		0			0
$713$	63.5585	−	46.1779i	0.0891423	−	0.0647657i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−900.009	−	1238.76i	−1.25524	−	1.72769i
$718$		0			0
$719$	32.0897	−	98.7618i	0.0446310	−	0.137360i	−0.926258	−	0.376890i	$-0.876993\pi$
$719$	32.0897	−	98.7618i	0.0446310	−	0.137360i	0.970889	+	0.239530i	$0.0769934\pi$
$720$		0			0
$721$	−48.7149	+	67.0503i	−0.0675657	+	0.0929962i
$722$		0			0
$723$	1392.00	−	452.289i	1.92532	−	0.625573i
$724$		0			0
$725$		−	32.1994i		−	0.0444129i
$726$		0			0
$727$	1381.61			1.90043			0.950214	−	0.311599i	$-0.100864\pi$
$727$	1381.61			1.90043			0.950214	+	0.311599i	$0.100864\pi$
$728$		0			0
$729$	−312.354	−	961.328i	−0.428470	−	1.31869i
$730$		0			0
$731$	−244.011	−	177.285i	−0.333805	−	0.242523i
$732$		0			0
$733$	676.750	+	219.889i	0.923260	+	0.299985i	0.731804	−	0.681516i	$-0.238679\pi$
$733$	676.750	+	219.889i	0.923260	+	0.299985i	0.191457	+	0.981501i	$0.438679\pi$
$734$		0			0
$735$	−88.2082	+	64.0870i	−0.120011	+	0.0871932i
$736$		0			0
$737$		0			0
$738$		0			0
$739$	−209.516	−	288.374i	−0.283513	−	0.390223i	0.643380	−	0.765547i	$-0.277531\pi$
$739$	−209.516	−	288.374i	−0.283513	−	0.390223i	−0.926894	+	0.375324i	$0.877531\pi$
$740$		0			0
$741$	761.170	−	2342.64i	1.02722	−	3.16146i
$742$		0			0
$743$	−126.543	+	174.171i	−0.170313	+	0.234416i	−0.885638	−	0.464376i	$-0.846279\pi$
$743$	−126.543	+	174.171i	−0.170313	+	0.234416i	0.715325	+	0.698792i	$0.246279\pi$
$744$		0			0
$745$	−270.823	+	87.9957i	−0.363521	+	0.118115i
$746$		0			0
$747$		−	51.1760i		−	0.0685087i
$748$		0			0
$749$	−7.92691			−0.0105833
$750$		0			0
$751$	5.74512	+	17.6817i	0.00764997	+	0.0235442i	0.954809	−	0.297221i	$-0.0960599\pi$
$751$	5.74512	+	17.6817i	0.00764997	+	0.0235442i	−0.947159	+	0.320765i	$0.896060\pi$
$752$		0			0
$753$	−1100.94	−	799.881i	−1.46207	−	1.06226i
$754$		0			0
$755$	−581.902	−	189.071i	−0.770731	−	0.250426i
$756$		0			0
$757$	−259.291	+	188.386i	−0.342524	+	0.248858i	−0.745726	−	0.666253i	$-0.767897\pi$
$757$	−259.291	+	188.386i	−0.342524	+	0.248858i	0.403202	+	0.915111i	$0.367897\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−4.83191	−	6.65055i	−0.00634942	−	0.00873923i	0.805830	−	0.592146i	$-0.201719\pi$
$761$	−4.83191	−	6.65055i	−0.00634942	−	0.00873923i	−0.812180	+	0.583407i	$0.801719\pi$
$762$		0			0
$763$	−299.168	+	920.745i	−0.392094	+	1.20674i
$764$		0			0
$765$	−823.569	+	1133.55i	−1.07656	+	1.48176i
$766$		0			0
$767$	525.138	−	170.628i	0.684665	−	0.222461i
$768$		0			0
$769$		−	32.0029i		−	0.0416162i	−0.999783	−	0.0208081i	$-0.993376\pi$
$769$		−	32.0029i		−	0.0416162i	0.999783	−	0.0208081i	$-0.00662391\pi$
$770$		0			0
$771$	2541.83			3.29679
$772$		0			0
$773$	278.940	+	858.489i	0.360854	+	1.11059i	0.952537	+	0.304423i	$0.0984637\pi$
$773$	278.940	+	858.489i	0.360854	+	1.11059i	−0.591683	+	0.806171i	$0.701536\pi$
$774$		0			0
$775$	44.6606	+	32.4478i	0.0576265	+	0.0418681i
$776$		0			0
$777$	−888.149	−	288.577i	−1.14305	−	0.371399i
$778$		0			0
$779$	−1297.59	+	942.757i	−1.66572	+	1.21021i
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−285.794	−	393.362i	−0.364999	−	0.502377i
$784$		0			0
$785$	−399.740	+	1230.27i	−0.509223	+	1.56723i
$786$		0			0
$787$	496.500	−	683.374i	0.630877	−	0.868327i	−0.367211	−	0.930138i	$-0.619687\pi$
$787$	496.500	−	683.374i	0.630877	−	0.868327i	0.998088	+	0.0618102i	$0.0196873\pi$
$788$		0			0
$789$	−858.356	+	278.897i	−1.08790	+	0.353481i
$790$		0			0
$791$			388.085i			0.490626i
$792$		0			0
$793$	−426.232			−0.537493
$794$		0			0
$795$	73.3224	+	225.663i	0.0922294	+	0.283853i
$796$		0			0
$797$	346.108	+	251.462i	0.434264	+	0.315511i	0.783352	−	0.621579i	$-0.213508\pi$
$797$	346.108	+	251.462i	0.434264	+	0.315511i	−0.349088	+	0.937090i	$0.613508\pi$
$798$		0			0
$799$	1325.40	+	430.648i	1.65882	+	0.538984i
$800$		0			0
$801$	−809.224	+	587.936i	−1.01027	+	0.734002i
$802$		0			0
$803$		0			0
$804$		0			0
$805$	66.6775	+	91.7737i	0.0828292	+	0.114005i
$806$		0			0
$807$	164.707	−	506.915i	0.204098	−	0.628148i
$808$		0			0
$809$	−391.323	+	538.609i	−0.483712	+	0.665772i	−0.979213	−	0.202835i	$-0.934984\pi$
$809$	−391.323	+	538.609i	−0.483712	+	0.665772i	0.495501	+	0.868607i	$0.334984\pi$
$810$		0			0
$811$	618.897	−	201.092i	0.763129	−	0.247956i	0.0985078	−	0.995136i	$-0.468593\pi$
$811$	618.897	−	201.092i	0.763129	−	0.247956i	0.664621	+	0.747181i	$0.268593\pi$
$812$		0			0
$813$		−	742.189i		−	0.912901i
$814$		0			0
$815$	−68.2962			−0.0837990
$816$		0			0
$817$	−168.793	−	519.493i	−0.206602	−	0.635854i
$818$		0			0
$819$	−1343.17	−	975.869i	−1.64001	−	1.19154i
$820$		0			0
$821$	1174.46	+	381.605i	1.43052	+	0.464805i	0.918929	−	0.394422i	$-0.129055\pi$
$821$	1174.46	+	381.605i	1.43052	+	0.464805i	0.511594	+	0.859227i	$0.329055\pi$
$822$		0			0
$823$	−551.803	+	400.908i	−0.670477	+	0.487130i	−0.870185	−	0.492725i	$-0.836001\pi$
$823$	−551.803	+	400.908i	−0.670477	+	0.487130i	0.199708	+	0.979856i	$0.436001\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	128.263	+	176.539i	0.155094	+	0.213469i	0.879492	−	0.475913i	$-0.157882\pi$
$827$	128.263	+	176.539i	0.155094	+	0.213469i	−0.724398	+	0.689382i	$0.757882\pi$
$828$		0			0
$829$	392.047	−	1206.60i	0.472916	−	1.45549i	−0.375832	−	0.926688i	$-0.622643\pi$
$829$	392.047	−	1206.60i	0.472916	−	1.45549i	0.848748	−	0.528798i	$-0.177357\pi$
$830$		0			0
$831$	−772.904	+	1063.81i	−0.930089	+	1.28016i
$832$		0			0
$833$	77.3546	−	25.1340i	0.0928627	−	0.0301729i
$834$		0			0
$835$			770.856i			0.923181i
$836$		0			0
$837$	833.592			0.995928
$838$		0			0
$839$	280.558	+	863.468i	0.334395	+	1.02916i	0.967019	+	0.254704i	$0.0819779\pi$
$839$	280.558	+	863.468i	0.334395	+	1.02916i	−0.632624	+	0.774459i	$0.718022\pi$
$840$		0			0
$841$	−548.480	−	398.494i	−0.652176	−	0.473834i
$842$		0			0
$843$	2461.55	+	799.804i	2.91998	+	0.948760i
$844$		0			0
$845$	221.709	−	161.081i	0.262377	−	0.190628i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	531.376	+	731.376i	0.625884	+	0.861456i
$850$		0			0
$851$	30.7401	−	94.6084i	0.0361224	−	0.111173i
$852$		0			0
$853$	11.2278	−	15.4537i	0.0131627	−	0.0181169i	−0.802385	−	0.596807i	$-0.796436\pi$
$853$	11.2278	−	15.4537i	0.0131627	−	0.0181169i	0.815548	+	0.578690i	$0.196436\pi$
$854$		0			0
$855$	−2413.29	+	784.124i	−2.82256	+	0.917104i
$856$		0			0
$857$			488.737i			0.570289i	0.958485	+	0.285144i	$0.0920415\pi$
$857$			488.737i			0.570289i	−0.958485	+	0.285144i	$0.907958\pi$
$858$		0			0
$859$	−1449.51			−1.68744			−0.843721	−	0.536782i	$-0.819640\pi$
$859$	−1449.51			−1.68744			−0.843721	+	0.536782i	$0.819640\pi$
$860$		0			0
$861$	515.898	+	1587.77i	0.599185	+	1.84410i
$862$		0			0
$863$	−26.2857	−	19.0977i	−0.0304586	−	0.0221294i	0.572452	−	0.819938i	$-0.305992\pi$
$863$	−26.2857	−	19.0977i	−0.0304586	−	0.0221294i	−0.602910	+	0.797809i	$0.705992\pi$
$864$		0			0
$865$	−505.115	−	164.122i	−0.583948	−	0.189736i
$866$		0			0
$867$	124.369	−	90.3594i	0.143448	−	0.104221i
$868$		0			0
$869$		0			0
$870$		0			0
$871$	−271.964	−	374.326i	−0.312243	−	0.429766i
$872$		0			0
$873$	245.100	−	754.339i	0.280756	−	0.864077i
$874$		0			0
$875$	−511.337	+	703.795i	−0.584385	+	0.804337i
$876$		0			0
$877$	116.087	−	37.7191i	0.132369	−	0.0430092i	−0.242083	−	0.970255i	$-0.577831\pi$
$877$	116.087	−	37.7191i	0.132369	−	0.0430092i	0.374452	+	0.927246i	$0.377831\pi$
$878$		0			0
$879$			2628.09i			2.98986i
$880$		0			0
$881$	−545.388			−0.619055			−0.309528	−	0.950890i	$-0.600171\pi$
$881$	−545.388			−0.619055			−0.309528	+	0.950890i	$0.600171\pi$
$882$		0			0
$883$	−314.489	−	967.897i	−0.356159	−	1.09615i	−0.955334	−	0.295528i	$-0.904505\pi$
$883$	−314.489	−	967.897i	−0.356159	−	1.09615i	0.599175	−	0.800618i	$-0.295495\pi$
$884$		0			0
$885$	−710.648	−	516.316i	−0.802993	−	0.583408i
$886$		0			0
$887$	−1447.77	−	470.407i	−1.63220	−	0.530335i	−0.657427	−	0.753518i	$-0.728355\pi$
$887$	−1447.77	−	470.407i	−1.63220	−	0.530335i	−0.974777	+	0.223183i	$0.928355\pi$
$888$		0			0
$889$	−213.349	+	155.007i	−0.239988	+	0.174361i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	1483.47	+	2041.83i	1.66122	+	2.28648i
$894$		0			0
$895$	230.245	−	708.620i	0.257257	−	0.791754i
$896$		0			0
$897$	160.532	−	220.954i	0.178966	−	0.246325i
$898$		0			0
$899$	−265.842	+	86.3772i	−0.295708	+	0.0960814i
$900$		0			0
$901$		−	177.004i		−	0.196453i
$902$		0			0
$903$	−568.557			−0.629631
$904$		0			0
$905$	−499.109	−	1536.10i	−0.551501	−	1.69735i
$906$		0			0
$907$	507.814	+	368.948i	0.559883	+	0.406779i	0.831416	−	0.555650i	$-0.187531\pi$
$907$	507.814	+	368.948i	0.559883	+	0.406779i	−0.271533	+	0.962429i	$0.587531\pi$
$908$		0			0
$909$	−1383.59	−	449.557i	−1.52211	−	0.494562i
$910$		0			0
$911$	−580.440	+	421.715i	−0.637146	+	0.462914i	−0.858869	−	0.512196i	$-0.828832\pi$
$911$	−580.440	+	421.715i	−0.637146	+	0.462914i	0.221722	+	0.975110i	$0.428832\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	398.561	+	548.572i	0.435586	+	0.599532i
$916$		0			0
$917$	268.407	−	826.072i	0.292701	−	0.900842i
$918$		0			0
$919$	−523.551	+	720.606i	−0.569697	+	0.784120i	−0.992519	−	0.122093i	$-0.961040\pi$
$919$	−523.551	+	720.606i	−0.569697	+	0.784120i	0.422822	+	0.906213i	$0.361040\pi$
$920$		0			0
$921$	−2180.86	+	708.604i	−2.36792	+	0.769385i
$922$		0			0
$923$			618.133i			0.669700i
$924$		0			0
$925$	69.8995			0.0755670
$926$		0			0
$927$	−63.5202	−	195.495i	−0.0685223	−	0.210890i
$928$		0			0
$929$	656.164	+	476.731i	0.706312	+	0.513166i	0.881982	−	0.471283i	$-0.156209\pi$
$929$	656.164	+	476.731i	0.706312	+	0.513166i	−0.175670	+	0.984449i	$0.556209\pi$
$930$		0			0
$931$	140.090	+	45.5180i	0.150473	+	0.0488915i
$932$		0			0
$933$	−1658.65	+	1205.08i	−1.77776	+	1.29162i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−864.878	−	1190.40i	−0.923029	−	1.27044i	−0.962517	−	0.271221i	$-0.912573\pi$
$937$	−864.878	−	1190.40i	−0.923029	−	1.27044i	0.0394880	−	0.999220i	$-0.487427\pi$
$938$		0			0
$939$	26.0766	−	80.2556i	0.0277706	−	0.0854692i
$940$		0			0
$941$	−80.5218	+	110.829i	−0.0855705	+	0.117778i	−0.849656	−	0.527337i	$-0.823190\pi$
$941$	−80.5218	+	110.829i	−0.0855705	+	0.117778i	0.764086	+	0.645115i	$0.223190\pi$
$942$		0			0
$943$	−169.134	+	54.9551i	−0.179358	+	0.0582769i
$944$		0			0
$945$			1203.65i			1.27370i
$946$		0			0
$947$	−862.357			−0.910620			−0.455310	−	0.890333i	$-0.650472\pi$
$947$	−862.357			−0.910620			−0.455310	+	0.890333i	$0.650472\pi$
$948$		0			0
$949$	287.405	+	884.543i	0.302851	+	0.932079i
$950$		0			0
$951$	−2299.79	−	1670.90i	−2.41829	−	1.75699i
$952$		0			0
$953$	1416.96	+	460.397i	1.48684	+	0.483103i	0.936147	−	0.351608i	$-0.114365\pi$
$953$	1416.96	+	460.397i	1.48684	+	0.483103i	0.550689	+	0.834710i	$0.314365\pi$
$954$		0			0
$955$	−119.363	+	86.7224i	−0.124988	+	0.0908088i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	807.477	+	1111.40i	0.841999	+	1.15891i
$960$		0			0
$961$	−148.878	+	458.199i	−0.154920	+	0.476794i
$962$		0			0
$963$	11.5560	−	15.9055i	0.0120000	−	0.0165166i
$964$		0			0
$965$	226.151	−	73.4810i	0.234354	−	0.0761461i
$966$		0			0
$967$		−	961.962i		−	0.994790i	−0.867524	−	0.497395i	$-0.834290\pi$
$967$		−	961.962i		−	0.994790i	0.867524	−	0.497395i	$-0.165710\pi$
$968$		0			0
$969$	2923.19			3.01671
$970$		0			0
$971$	−316.015	−	972.593i	−0.325453	−	1.00164i	−0.971236	−	0.238119i	$-0.923469\pi$
$971$	−316.015	−	972.593i	−0.325453	−	1.00164i	0.645783	−	0.763521i	$-0.276531\pi$
$972$		0			0
$973$	1155.32	+	839.386i	1.18738	+	0.862679i
$974$		0			0
$975$	182.516	+	59.3030i	0.187196	+	0.0608236i
$976$		0			0
$977$	952.451	−	691.996i	0.974873	−	0.708286i	0.0183158	−	0.999832i	$-0.494170\pi$
$977$	952.451	−	691.996i	0.974873	−	0.708286i	0.956557	+	0.291546i	$0.0941696\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	−1411.36	−	1942.57i	−1.43870	−	1.98019i
$982$		0			0
$983$	−109.991	+	338.519i	−0.111894	+	0.344373i	−0.991286	−	0.131724i	$-0.957949\pi$
$983$	−109.991	+	338.519i	−0.111894	+	0.344373i	0.879393	+	0.476097i	$0.157949\pi$
$984$		0			0
$985$	−629.339	+	866.211i	−0.638923	+	0.879402i
$986$		0			0
$987$	2498.43	−	811.791i	2.53134	−	0.822483i
$988$		0			0
$989$		−	60.5645i		−	0.0612381i
$990$		0			0
$991$	−370.283			−0.373646			−0.186823	−	0.982394i	$-0.559819\pi$
$991$	−370.283			−0.373646			−0.186823	+	0.982394i	$0.559819\pi$
$992$		0			0
$993$	261.846	+	805.878i	0.263691	+	0.811559i
$994$		0			0
$995$	−178.067	−	129.373i	−0.178962	−	0.130023i
$996$		0			0
$997$	−26.5969	−	8.64186i	−0.0266769	−	0.00866786i	0.295648	−	0.955297i	$-0.404464\pi$
$997$	−26.5969	−	8.64186i	−0.0266769	−	0.00866786i	−0.322325	+	0.946629i	$0.604464\pi$
$998$		0			0
$999$	853.923	−	620.412i	0.854778	−	0.621033i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	484.3.f.e.481.2		8
11.2	odd	10		484.3.d.c.241.7		8
11.3	even	5		44.3.f.a.17.1	yes	8
11.4	even	5		484.3.f.d.161.2		8
11.5	even	5		484.3.f.a.233.1		8
11.6	odd	10		44.3.f.a.13.1	✓	8
11.7	odd	10	inner	484.3.f.e.161.2		8
11.8	odd	10		484.3.f.a.457.1		8
11.9	even	5		484.3.d.c.241.8		8
11.10	odd	2		484.3.f.d.481.2		8
33.2	even	10		4356.3.f.g.1693.3		8
33.14	odd	10		396.3.t.a.325.1		8
33.17	even	10		396.3.t.a.145.1		8
33.20	odd	10		4356.3.f.g.1693.4		8
44.3	odd	10		176.3.n.c.17.2		8
44.39	even	10		176.3.n.c.145.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
44.3.f.a.13.1	✓	8	11.6	odd	10
44.3.f.a.17.1	yes	8	11.3	even	5
176.3.n.c.17.2		8	44.3	odd	10
176.3.n.c.145.2		8	44.39	even	10
396.3.t.a.145.1		8	33.17	even	10
396.3.t.a.325.1		8	33.14	odd	10
484.3.d.c.241.7		8	11.2	odd	10
484.3.d.c.241.8		8	11.9	even	5
484.3.f.a.233.1		8	11.5	even	5
484.3.f.a.457.1		8	11.8	odd	10
484.3.f.d.161.2		8	11.4	even	5
484.3.f.d.481.2		8	11.10	odd	2
484.3.f.e.161.2		8	11.7	odd	10	inner
484.3.f.e.481.2		8	1.1	even	1	trivial
4356.3.f.g.1693.3		8	33.2	even	10
4356.3.f.g.1693.4		8	33.20	odd	10

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:	\( N \)	\(=\)	\( 484 = 2^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	484.f (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.56155 + 4.80594i) q^{3} +(-3.83565 - 2.78676i) q^{5} +(6.34071 + 2.06022i) q^{7} +(-13.3775 + 9.71933i) q^{9} +(8.85202 + 12.1838i) q^{13} +(7.40348 - 22.7856i) q^{15} +(-10.5051 + 14.4591i) q^{17} +(-30.7829 + 10.0020i) q^{19} +33.6902i q^{21} -3.58879 q^{23} +(-0.779257 - 2.39831i) q^{25} +(-30.8066 - 22.3823i) q^{27} +(12.1438 + 3.94576i) q^{29} +(-17.7103 + 12.8673i) q^{31} +(-18.5794 - 25.5723i) q^{35} +(-8.56561 + 26.3622i) q^{37} +(-44.7316 + 61.5678i) q^{39} +(47.1286 - 15.3130i) q^{41} +16.8760i q^{43} +78.3970 q^{45} +(-24.0957 - 74.1591i) q^{47} +(-3.68176 - 2.67495i) q^{49} +(-85.8936 - 27.9085i) q^{51} +(-8.01232 + 5.82129i) q^{53} +(-96.1378 - 132.322i) q^{57} +(11.3299 - 34.8698i) q^{59} +(-16.6357 + 22.8971i) q^{61} +(-104.847 + 34.0668i) q^{63} -71.4011i q^{65} -30.7234 q^{67} +(-5.60406 - 17.2475i) q^{69} +(33.2060 + 24.1255i) q^{71} +(58.7348 + 19.0841i) q^{73} +(10.3093 - 7.49013i) q^{75} +(73.0540 + 100.550i) q^{79} +(13.4743 - 41.4696i) q^{81} +(-1.81914 + 2.50384i) q^{83} +(80.5879 - 26.1846i) q^{85} +64.5240i q^{87} +60.4914 q^{89} +(31.0268 + 95.4908i) q^{91} +(-89.4948 - 65.0218i) q^{93} +(145.946 + 47.4206i) q^{95} +(-38.8061 + 28.1943i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 5 q^{3} - 6 q^{5} + 20 q^{7} - 21 q^{9} + 10 q^{13} + 77 q^{15} - 55 q^{17} - 110 q^{19} + 100 q^{23} - 34 q^{25} - 130 q^{27} + 90 q^{29} - 122 q^{31} + 115 q^{35} + 180 q^{37} - 245 q^{39} - 105 q^{41}+ \cdots + 200 q^{97}+O(q^{100}) \) 8 * q + 5 * q^3 - 6 * q^5 + 20 * q^7 - 21 * q^9 + 10 * q^13 + 77 * q^15 - 55 * q^17 - 110 * q^19 + 100 * q^23 - 34 * q^25 - 130 * q^27 + 90 * q^29 - 122 * q^31 + 115 * q^35 + 180 * q^37 - 245 * q^39 - 105 * q^41 + 332 * q^45 + 10 * q^47 - 98 * q^49 + 30 * q^51 - 40 * q^53 - 165 * q^57 + 122 * q^59 - 160 * q^61 - 365 * q^63 + 10 * q^67 - 36 * q^69 - 108 * q^71 + 35 * q^73 - 153 * q^75 + 310 * q^79 + 128 * q^81 - 130 * q^83 + 280 * q^85 + 18 * q^89 - 25 * q^91 + 155 * q^93 + 245 * q^95 + 200 * q^97

Introduction

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