LMFDB - Embedded newform 576.2.y.a.47.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [576,2,Mod(47,576)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(576, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 2]))

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

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

chi := DirichletCharacter("576.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 576 = 2^{6} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	576.y (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.59938315643$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 144)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			47.7
Character	$\chi$	$=$	576.47
Dual form			576.2.y.a.527.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.05993 - 1.36987i) q^{3} +(-0.746784 + 2.78704i) q^{5} +(-1.16672 + 2.02082i) q^{7} +(-0.753089 + 2.90394i) q^{9} +O(q^{10})$	\(q+(-1.05993 - 1.36987i) q^{3} +(-0.746784 + 2.78704i) q^{5} +(-1.16672 + 2.02082i) q^{7} +(-0.753089 + 2.90394i) q^{9} +(-1.48439 - 5.53982i) q^{11} +(1.04654 - 3.90572i) q^{13} +(4.60942 - 1.93107i) q^{15} -6.45489i q^{17} +(1.50499 - 1.50499i) q^{19} +(4.00491 - 0.543676i) q^{21} +(0.0418190 - 0.0241442i) q^{23} +(-2.87976 - 1.66263i) q^{25} +(4.77624 - 2.04634i) q^{27} +(-1.36254 - 5.08507i) q^{29} +(-1.65029 + 0.952797i) q^{31} +(-6.01548 + 7.90525i) q^{33} +(-4.76082 - 4.76082i) q^{35} +(0.489763 - 0.489763i) q^{37} +(-6.45959 + 2.70618i) q^{39} +(-0.0155357 - 0.0269087i) q^{41} +(-3.80267 + 1.01892i) q^{43} +(-7.53099 - 4.26750i) q^{45} +(0.0913288 - 0.158186i) q^{47} +(0.777520 + 1.34670i) q^{49} +(-8.84237 + 6.84175i) q^{51} +(-6.62061 - 6.62061i) q^{53} +16.5482 q^{55} +(-3.65682 - 0.466453i) q^{57} +(-4.15614 - 1.11363i) q^{59} +(6.39775 - 1.71427i) q^{61} +(-4.98970 - 4.90995i) q^{63} +(10.1039 + 5.83347i) q^{65} +(0.808279 + 0.216578i) q^{67} +(-0.0773998 - 0.0316954i) q^{69} +1.04372i q^{71} -4.74654i q^{73} +(0.774762 + 5.70717i) q^{75} +(12.9269 + 3.46374i) q^{77} +(7.29908 + 4.21413i) q^{79} +(-7.86571 - 4.37385i) q^{81} +(-11.9789 + 3.20973i) q^{83} +(17.9900 + 4.82041i) q^{85} +(-5.52169 + 7.25633i) q^{87} -2.85193 q^{89} +(6.67175 + 6.67175i) q^{91} +(3.05441 + 1.25079i) q^{93} +(3.07055 + 5.31835i) q^{95} +(3.29818 - 5.71262i) q^{97} +(17.2052 - 0.138600i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 4 q^{3} - 6 q^{5} + 4 q^{7}+O(q^{10}) $ 88 * q + 4 * q^3 - 6 * q^5 + 4 * q^7	$ 88 q + 4 q^{3} - 6 q^{5} + 4 q^{7} + 6 q^{11} - 2 q^{13} + 8 q^{19} + 2 q^{21} + 12 q^{23} + 16 q^{27} - 6 q^{29} - 8 q^{33} - 8 q^{37} + 32 q^{39} + 2 q^{43} + 6 q^{45} - 24 q^{49} + 12 q^{51} + 16 q^{55} + 42 q^{59} - 2 q^{61} - 12 q^{65} + 2 q^{67} - 10 q^{69} + 56 q^{75} - 6 q^{77} - 8 q^{81} - 54 q^{83} + 8 q^{85} - 48 q^{87} - 20 q^{91} - 34 q^{93} - 4 q^{97} - 46 q^{99}+O(q^{100}) $ 88 * q + 4 * q^3 - 6 * q^5 + 4 * q^7 + 6 * q^11 - 2 * q^13 + 8 * q^19 + 2 * q^21 + 12 * q^23 + 16 * q^27 - 6 * q^29 - 8 * q^33 - 8 * q^37 + 32 * q^39 + 2 * q^43 + 6 * q^45 - 24 * q^49 + 12 * q^51 + 16 * q^55 + 42 * q^59 - 2 * q^61 - 12 * q^65 + 2 * q^67 - 10 * q^69 + 56 * q^75 - 6 * q^77 - 8 * q^81 - 54 * q^83 + 8 * q^85 - 48 * q^87 - 20 * q^91 - 34 * q^93 - 4 * q^97 - 46 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/576\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$325$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

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
$3$	−1.05993	−	1.36987i	−0.611952	−	0.790895i
$3$	−1.05993	−	1.36987i	−0.611952	−	0.790895i
$4$		0			0
$5$	−0.746784	+	2.78704i	−0.333972	+	1.24640i	0.571007	+	0.820945i	$0.306553\pi$
$5$	−0.746784	+	2.78704i	−0.333972	+	1.24640i	−0.904979	+	0.425456i	$0.860114\pi$
$6$		0			0
$7$	−1.16672	+	2.02082i	−0.440979	+	0.763799i	−0.997762	−	0.0668592i	$-0.978702\pi$
$7$	−1.16672	+	2.02082i	−0.440979	+	0.763799i	0.556783	+	0.830658i	$0.312036\pi$
$8$		0			0
$9$	−0.753089	+	2.90394i	−0.251030	+	0.967979i
$10$		0			0
$11$	−1.48439	−	5.53982i	−0.447560	−	1.67032i	−0.709087	−	0.705121i	$-0.750893\pi$
$11$	−1.48439	−	5.53982i	−0.447560	−	1.67032i	0.261527	−	0.965196i	$-0.415774\pi$
$12$		0			0
$13$	1.04654	−	3.90572i	0.290257	−	1.08325i	−0.654655	−	0.755928i	$-0.727186\pi$
$13$	1.04654	−	3.90572i	0.290257	−	1.08325i	0.944912	−	0.327325i	$-0.106147\pi$
$14$		0			0
$15$	4.60942	−	1.93107i	1.19015	−	0.498601i
$16$		0			0
$17$		−	6.45489i		−	1.56554i	−0.622310	−	0.782771i	$-0.713806\pi$
$17$		−	6.45489i		−	1.56554i	0.622310	−	0.782771i	$-0.286194\pi$
$18$		0			0
$19$	1.50499	−	1.50499i	0.345267	−	0.345267i	−0.513076	−	0.858343i	$-0.671494\pi$
$19$	1.50499	−	1.50499i	0.345267	−	0.345267i	0.858343	+	0.513076i	$0.171494\pi$
$20$		0			0
$21$	4.00491	−	0.543676i	0.873943	−	0.118640i
$22$		0			0
$23$	0.0418190	−	0.0241442i	0.00871987	−	0.00503442i	−0.495634	−	0.868532i	$-0.665064\pi$
$23$	0.0418190	−	0.0241442i	0.00871987	−	0.00503442i	0.504354	+	0.863497i	$0.331731\pi$
$24$		0			0
$25$	−2.87976	−	1.66263i	−0.575952	−	0.332526i
$26$		0			0
$27$	4.77624	−	2.04634i	0.919188	−	0.393819i
$28$		0			0
$29$	−1.36254	−	5.08507i	−0.253018	−	0.944274i	−0.969183	−	0.246343i	$-0.920771\pi$
$29$	−1.36254	−	5.08507i	−0.253018	−	0.944274i	0.716165	−	0.697931i	$-0.245896\pi$
$30$		0			0
$31$	−1.65029	+	0.952797i	−0.296401	+	0.171127i	−0.640825	−	0.767687i	$-0.721408\pi$
$31$	−1.65029	+	0.952797i	−0.296401	+	0.171127i	0.344424	+	0.938814i	$0.388074\pi$
$32$		0			0
$33$	−6.01548	+	7.90525i	−1.04716	+	1.37613i
$34$		0			0
$35$	−4.76082	−	4.76082i	−0.804725	−	0.804725i
$36$		0			0
$37$	0.489763	−	0.489763i	0.0805165	−	0.0805165i	−0.665702	−	0.746218i	$-0.731868\pi$
$37$	0.489763	−	0.489763i	0.0805165	−	0.0805165i	0.746218	+	0.665702i	$0.231868\pi$
$38$		0			0
$39$	−6.45959	+	2.70618i	−1.03436	+	0.433336i
$40$		0			0
$41$	−0.0155357	−	0.0269087i	−0.00242628	−	0.00420243i	0.864810	−	0.502100i	$-0.167439\pi$
$41$	−0.0155357	−	0.0269087i	−0.00242628	−	0.00420243i	−0.867236	+	0.497897i	$0.834106\pi$
$42$		0			0
$43$	−3.80267	+	1.01892i	−0.579901	+	0.155384i	−0.536834	−	0.843688i	$-0.680380\pi$
$43$	−3.80267	+	1.01892i	−0.579901	+	0.155384i	−0.0430675	+	0.999072i	$0.513713\pi$
$44$		0			0
$45$	−7.53099	−	4.26750i	−1.12265	−	0.636162i
$46$		0			0
$47$	0.0913288	−	0.158186i	0.0133217	−	0.0230738i	−0.859288	−	0.511493i	$-0.829093\pi$
$47$	0.0913288	−	0.158186i	0.0133217	−	0.0230738i	0.872609	+	0.488419i	$0.162426\pi$
$48$		0			0
$49$	0.777520	+	1.34670i	0.111074	+	0.192386i
$50$		0			0
$51$	−8.84237	+	6.84175i	−1.23818	+	0.958036i
$52$		0			0
$53$	−6.62061	−	6.62061i	−0.909411	−	0.909411i	0.0868136	−	0.996225i	$-0.472332\pi$
$53$	−6.62061	−	6.62061i	−0.909411	−	0.909411i	−0.996225	+	0.0868136i	$0.972332\pi$
$54$		0			0
$55$	16.5482			2.23136
$56$		0			0
$57$	−3.65682	−	0.466453i	−0.484357	−	0.0617832i
$58$		0			0
$59$	−4.15614	−	1.11363i	−0.541083	−	0.144983i	−0.0220815	−	0.999756i	$-0.507029\pi$
$59$	−4.15614	−	1.11363i	−0.541083	−	0.144983i	−0.519001	+	0.854773i	$0.673696\pi$
$60$		0			0
$61$	6.39775	−	1.71427i	0.819148	−	0.219490i	0.175174	−	0.984537i	$-0.443951\pi$
$61$	6.39775	−	1.71427i	0.819148	−	0.219490i	0.643974	+	0.765047i	$0.277284\pi$
$62$		0			0
$63$	−4.98970	−	4.90995i	−0.628643	−	0.618595i
$64$		0			0
$65$	10.1039	+	5.83347i	1.25323	+	0.723552i
$66$		0			0
$67$	0.808279	+	0.216578i	0.0987470	+	0.0264592i	0.307854	−	0.951434i	$-0.400389\pi$
$67$	0.808279	+	0.216578i	0.0987470	+	0.0264592i	−0.209107	+	0.977893i	$0.567056\pi$
$68$		0			0
$69$	−0.0773998	−	0.0316954i	−0.00931784	−	0.00381568i
$70$		0			0
$71$			1.04372i			0.123867i	0.998080	+	0.0619333i	$0.0197266\pi$
$71$			1.04372i			0.123867i	−0.998080	+	0.0619333i	$0.980273\pi$
$72$		0			0
$73$		−	4.74654i		−	0.555540i	−0.960648	−	0.277770i	$-0.910405\pi$
$73$		−	4.74654i		−	0.555540i	0.960648	−	0.277770i	$-0.0895953\pi$
$74$		0			0
$75$	0.774762	+	5.70717i	0.0894618	+	0.659008i
$76$		0			0
$77$	12.9269	+	3.46374i	1.47315	+	0.394730i
$78$		0			0
$79$	7.29908	+	4.21413i	0.821211	+	0.474126i	0.850834	−	0.525435i	$-0.176097\pi$
$79$	7.29908	+	4.21413i	0.821211	+	0.474126i	−0.0296228	+	0.999561i	$0.509431\pi$
$80$		0			0
$81$	−7.86571	−	4.37385i	−0.873968	−	0.485983i
$82$		0			0
$83$	−11.9789	+	3.20973i	−1.31485	+	0.352313i	−0.847047	−	0.531519i	$-0.821622\pi$
$83$	−11.9789	+	3.20973i	−1.31485	+	0.352313i	−0.467805	+	0.883832i	$0.654955\pi$
$84$		0			0
$85$	17.9900	+	4.82041i	1.95129	+	0.522847i
$86$		0			0
$87$	−5.52169	+	7.25633i	−0.591987	+	0.777961i
$88$		0			0
$89$	−2.85193			−0.302304			−0.151152	−	0.988511i	$-0.548298\pi$
$89$	−2.85193			−0.302304			−0.151152	+	0.988511i	$0.548298\pi$
$90$		0			0
$91$	6.67175	+	6.67175i	0.699390	+	0.699390i
$92$		0			0
$93$	3.05441	+	1.25079i	0.316727	+	0.129701i
$94$		0			0
$95$	3.07055	+	5.31835i	0.315032	+	0.545651i
$96$		0			0
$97$	3.29818	−	5.71262i	0.334880	−	0.580028i	−0.648582	−	0.761145i	$-0.724638\pi$
$97$	3.29818	−	5.71262i	0.334880	−	0.580028i	0.983462	+	0.181116i	$0.0579710\pi$
$98$		0			0
$99$	17.2052	−	0.138600i	1.72918	−	0.0139299i
$100$		0			0
$101$	−8.02745	+	2.15095i	−0.798761	+	0.214027i	−0.635040	−	0.772479i	$-0.719016\pi$
$101$	−8.02745	+	2.15095i	−0.798761	+	0.214027i	−0.163721	+	0.986507i	$0.552350\pi$
$102$		0			0
$103$	−3.39607	−	5.88217i	−0.334625	−	0.579588i	0.648788	−	0.760970i	$-0.275276\pi$
$103$	−3.39607	−	5.88217i	−0.334625	−	0.579588i	−0.983413	+	0.181382i	$0.941943\pi$
$104$		0			0
$105$	−1.47556	+	11.5678i	−0.144000	+	1.12891i
$106$		0			0
$107$	11.9162	−	11.9162i	1.15198	−	1.15198i	0.165828	−	0.986155i	$-0.446970\pi$
$107$	11.9162	−	11.9162i	1.15198	−	1.15198i	0.986155	−	0.165828i	$-0.0530295\pi$
$108$		0			0
$109$	−0.518803	−	0.518803i	−0.0496923	−	0.0496923i	0.681824	−	0.731516i	$-0.261187\pi$
$109$	−0.518803	−	0.518803i	−0.0496923	−	0.0496923i	−0.731516	+	0.681824i	$0.761187\pi$
$110$		0			0
$111$	−1.19003	−	0.151796i	−0.112952	−	0.0144079i
$112$		0			0
$113$	−9.60012	+	5.54263i	−0.903103	+	0.521407i	−0.878206	−	0.478283i	$-0.841259\pi$
$113$	−9.60012	+	5.54263i	−0.903103	+	0.521407i	−0.0248974	+	0.999690i	$0.507926\pi$
$114$		0			0
$115$	0.0360611	+	0.134582i	0.00336271	+	0.0125498i
$116$		0			0
$117$	10.5538	+	5.98043i	0.975703	+	0.552891i
$118$		0			0
$119$	13.0442	+	7.53107i	1.19576	+	0.690372i
$120$		0			0
$121$	−18.9599	+	10.9465i	−1.72362	+	0.995135i
$122$		0			0
$123$	−0.0203946	+	0.0498033i	−0.00183892	+	0.00449062i
$124$		0			0
$125$	−3.41689	+	3.41689i	−0.305616	+	0.305616i
$126$		0			0
$127$		−	12.0823i		−	1.07213i	−0.844176	−	0.536067i	$-0.819910\pi$
$127$		−	12.0823i		−	1.07213i	0.844176	−	0.536067i	$-0.180090\pi$
$128$		0			0
$129$	5.42636	+	4.12917i	0.477764	+	0.363553i
$130$		0			0
$131$	0.702002	−	2.61991i	0.0613342	−	0.228902i	−0.928454	−	0.371447i	$-0.878862\pi$
$131$	0.702002	−	2.61991i	0.0613342	−	0.228902i	0.989788	+	0.142545i	$0.0455284\pi$
$132$		0			0
$133$	1.28541	+	4.79721i	0.111459	+	0.415971i
$134$		0			0
$135$	2.13641	+	14.8397i	0.183873	+	1.27720i
$136$		0			0
$137$	7.51859	−	13.0226i	0.642356	−	1.11259i	−0.342549	−	0.939500i	$-0.611290\pi$
$137$	7.51859	−	13.0226i	0.642356	−	1.11259i	0.984905	−	0.173094i	$-0.0553765\pi$
$138$		0			0
$139$	−2.22117	+	8.28951i	−0.188397	+	0.703107i	0.805481	+	0.592622i	$0.201907\pi$
$139$	−2.22117	+	8.28951i	−0.188397	+	0.703107i	−0.993878	+	0.110485i	$0.964760\pi$
$140$		0			0
$141$	−0.313497	+	0.0425579i	−0.0264012	+	0.00358402i
$142$		0			0
$143$	−23.1905			−1.93928
$144$		0			0
$145$	15.1898			1.26144
$146$		0			0
$147$	1.02069	−	2.49251i	0.0841852	−	0.205579i
$148$		0			0
$149$	−0.261866	+	0.977298i	−0.0214529	+	0.0800634i	−0.975822	−	0.218565i	$-0.929862\pi$
$149$	−0.261866	+	0.977298i	−0.0214529	+	0.0800634i	0.954369	+	0.298628i	$0.0965291\pi$
$150$		0			0
$151$	8.29411	−	14.3658i	0.674965	−	1.16907i	−0.301514	−	0.953462i	$-0.597492\pi$
$151$	8.29411	−	14.3658i	0.674965	−	1.16907i	0.976479	−	0.215612i	$-0.0691747\pi$
$152$		0			0
$153$	18.7446	+	4.86111i	1.51541	+	0.392997i
$154$		0			0
$155$	−1.42307	−	5.31096i	−0.114304	−	0.426587i
$156$		0			0
$157$	−5.68871	+	21.2306i	−0.454009	+	1.69438i	0.236977	+	0.971515i	$0.423843\pi$
$157$	−5.68871	+	21.2306i	−0.454009	+	1.69438i	−0.690986	+	0.722868i	$0.742823\pi$
$158$		0			0
$159$	−2.05198	+	16.0868i	−0.162733	+	1.27576i
$160$		0			0
$161$			0.112678i			0.00888030i
$162$		0			0
$163$	−0.153221	+	0.153221i	−0.0120012	+	0.0120012i	−0.713082	−	0.701081i	$-0.752701\pi$
$163$	−0.153221	+	0.153221i	−0.0120012	+	0.0120012i	0.701081	+	0.713082i	$0.252701\pi$
$164$		0			0
$165$	−17.5400	−	22.6689i	−1.36548	−	1.76477i
$166$		0			0
$167$	−1.83025	+	1.05669i	−0.141629	+	0.0817694i	−0.569140	−	0.822241i	$-0.692724\pi$
$167$	−1.83025	+	1.05669i	−0.141629	+	0.0817694i	0.427511	+	0.904010i	$0.359390\pi$
$168$		0			0
$169$	−2.90111	−	1.67495i	−0.223162	−	0.128843i
$170$		0			0
$171$	3.23700	+	5.50377i	0.247539	+	0.420884i
$172$		0			0
$173$	0.582108	+	2.17246i	0.0442568	+	0.165169i	0.984517	−	0.175287i	$-0.0560853\pi$
$173$	0.582108	+	2.17246i	0.0442568	+	0.165169i	−0.940261	+	0.340456i	$0.889419\pi$
$174$		0			0
$175$	6.71976	−	3.87966i	0.507966	−	0.293274i
$176$		0			0
$177$	2.87969	+	6.87374i	0.216451	+	0.516662i
$178$		0			0
$179$	4.33235	+	4.33235i	0.323815	+	0.323815i	0.850229	−	0.526413i	$-0.176464\pi$
$179$	4.33235	+	4.33235i	0.323815	+	0.323815i	−0.526413	+	0.850229i	$0.676464\pi$
$180$		0			0
$181$	−13.9507	+	13.9507i	−1.03695	+	1.03695i	−0.0376558	+	0.999291i	$0.511989\pi$
$181$	−13.9507	+	13.9507i	−1.03695	+	1.03695i	−0.999291	+	0.0376558i	$0.988011\pi$
$182$		0			0
$183$	−9.12951	−	6.94708i	−0.674873	−	0.513543i
$184$		0			0
$185$	0.999240	+	1.73073i	0.0734656	+	0.127246i
$186$		0			0
$187$	−35.7589	+	9.58157i	−2.61495	+	0.700674i
$188$		0			0
$189$	−1.43725	+	12.0394i	−0.104545	+	0.875741i
$190$		0			0
$191$	3.83161	−	6.63654i	0.277246	−	0.480203i	−0.693454	−	0.720501i	$-0.743912\pi$
$191$	3.83161	−	6.63654i	0.277246	−	0.480203i	0.970699	+	0.240298i	$0.0772451\pi$
$192$		0			0
$193$	−3.79037	−	6.56511i	−0.272836	−	0.472567i	0.696751	−	0.717314i	$-0.254628\pi$
$193$	−3.79037	−	6.56511i	−0.272836	−	0.472567i	−0.969587	+	0.244747i	$0.921295\pi$
$194$		0			0
$195$	−2.71831	−	20.0240i	−0.194662	−	1.43395i
$196$		0			0
$197$	−12.6000	−	12.6000i	−0.897715	−	0.897715i	0.0975188	−	0.995234i	$-0.468909\pi$
$197$	−12.6000	−	12.6000i	−0.897715	−	0.897715i	−0.995234	+	0.0975188i	$0.968909\pi$
$198$		0			0
$199$	−23.1095			−1.63819			−0.819096	−	0.573656i	$-0.805524\pi$
$199$	−23.1095			−1.63819			−0.819096	+	0.573656i	$0.805524\pi$
$200$		0			0
$201$	−0.560037	−	1.33679i	−0.0395020	−	0.0942902i
$202$		0			0
$203$	11.8657	+	3.17941i	0.832811	+	0.223151i
$204$		0			0
$205$	0.0865974	−	0.0232037i	0.00604822	−	0.00162062i
$206$		0			0
$207$	0.0386199	+	0.139623i	0.00268427	+	0.00970444i
$208$		0			0
$209$	−10.5713	−	6.10336i	−0.731234	−	0.422178i
$210$		0			0
$211$	12.7862	+	3.42605i	0.880238	+	0.235859i	0.670510	−	0.741901i	$-0.266075\pi$
$211$	12.7862	+	3.42605i	0.880238	+	0.235859i	0.209728	+	0.977760i	$0.432742\pi$
$212$		0			0
$213$	1.42976	−	1.10627i	0.0979654	−	0.0758004i
$214$		0			0
$215$		−	11.3591i		−	0.774683i
$216$		0			0
$217$		−	4.44660i		−	0.301855i
$218$		0			0
$219$	−6.50214	+	5.03100i	−0.439374	+	0.339964i
$220$		0			0
$221$	−25.2110	−	6.75527i	−1.69588	−	0.454409i
$222$		0			0
$223$	14.1219	+	8.15328i	0.945672	+	0.545984i	0.891734	−	0.452561i	$-0.149489\pi$
$223$	14.1219	+	8.15328i	0.945672	+	0.545984i	0.0539380	+	0.998544i	$0.482823\pi$
$224$		0			0
$225$	6.99689	−	7.11054i	0.466460	−	0.474036i
$226$		0			0
$227$	22.2456	−	5.96068i	1.47649	−	0.395624i	0.571339	−	0.820714i	$-0.306424\pi$
$227$	22.2456	−	5.96068i	1.47649	−	0.395624i	0.905151	+	0.425090i	$0.139758\pi$
$228$		0			0
$229$	18.8781	+	5.05838i	1.24750	+	0.334267i	0.821371	−	0.570394i	$-0.193209\pi$
$229$	18.8781	+	5.05838i	1.24750	+	0.334267i	0.426131	+	0.904661i	$0.359876\pi$
$230$		0			0
$231$	−8.95671	−	21.3794i	−0.589308	−	1.40666i
$232$		0			0
$233$	18.4018			1.20554			0.602771	−	0.797914i	$-0.294063\pi$
$233$	18.4018			1.20554			0.602771	+	0.797914i	$0.294063\pi$
$234$		0			0
$235$	0.372668	+	0.372668i	0.0243102	+	0.0243102i
$236$		0			0
$237$	−1.96372	−	14.4655i	−0.127558	−	0.939634i
$238$		0			0
$239$	12.4328	+	21.5343i	0.804212	+	1.39294i	0.916821	+	0.399298i	$0.130746\pi$
$239$	12.4328	+	21.5343i	0.804212	+	1.39294i	−0.112609	+	0.993639i	$0.535921\pi$
$240$		0			0
$241$	0.256221	−	0.443788i	0.0165047	−	0.0285869i	−0.857655	−	0.514225i	$-0.828079\pi$
$241$	0.256221	−	0.443788i	0.0165047	−	0.0285869i	0.874160	+	0.485638i	$0.161413\pi$
$242$		0			0
$243$	2.34552	+	15.4110i	0.150465	+	0.988615i
$244$		0			0
$245$	−4.33395	+	1.16128i	−0.276886	+	0.0741914i
$246$		0			0
$247$	−4.30304	−	7.45308i	−0.273796	−	0.474228i
$248$		0			0
$249$	17.0937	+	13.0074i	1.08327	+	0.824310i
$250$		0			0
$251$	−7.88443	+	7.88443i	−0.497661	+	0.497661i	−0.910709	−	0.413048i	$-0.864464\pi$
$251$	−7.88443	+	7.88443i	−0.497661	+	0.497661i	0.413048	+	0.910709i	$0.364464\pi$
$252$		0			0
$253$	−0.195830	−	0.195830i	−0.0123117	−	0.0123117i
$254$		0			0
$255$	−12.4649	−	29.7533i	−0.780580	−	1.86322i
$256$		0			0
$257$	10.6490	−	6.14820i	0.664266	−	0.383514i	−0.129635	−	0.991562i	$-0.541380\pi$
$257$	10.6490	−	6.14820i	0.664266	−	0.383514i	0.793900	+	0.608048i	$0.208047\pi$
$258$		0			0
$259$	0.418306	+	1.56114i	0.0259923	+	0.0970046i
$260$		0			0
$261$	15.7928	−	0.127223i	0.977553	−	0.00787492i
$262$		0			0
$263$	8.46535	+	4.88747i	0.521996	+	0.301375i	0.737751	−	0.675073i	$-0.235888\pi$
$263$	8.46535	+	4.88747i	0.521996	+	0.301375i	−0.215755	+	0.976448i	$0.569221\pi$
$264$		0			0
$265$	23.3961	−	13.5077i	1.43721	−	0.829773i
$266$		0			0
$267$	3.02285	+	3.90677i	0.184995	+	0.239091i
$268$		0			0
$269$	−5.64229	+	5.64229i	−0.344016	+	0.344016i	−0.857875	−	0.513859i	$-0.828216\pi$
$269$	−5.64229	+	5.64229i	−0.344016	+	0.344016i	0.513859	+	0.857875i	$0.328216\pi$
$270$		0			0
$271$			11.0524i			0.671386i	0.941971	+	0.335693i	$0.108971\pi$
$271$			11.0524i			0.671386i	−0.941971	+	0.335693i	$0.891029\pi$
$272$		0			0
$273$	2.06783	−	16.2110i	0.125151	−	0.981137i
$274$		0			0
$275$	−4.93598	+	18.4213i	−0.297651	+	1.11085i
$276$		0			0
$277$	−6.77180	−	25.2727i	−0.406878	−	1.51849i	−0.800565	−	0.599246i	$-0.795467\pi$
$277$	−6.77180	−	25.2727i	−0.406878	−	1.51849i	0.393687	−	0.919245i	$-0.371199\pi$
$278$		0			0
$279$	−1.52405	−	5.50989i	−0.0912423	−	0.329869i
$280$		0			0
$281$	12.8442	−	22.2468i	0.766219	−	1.32713i	−0.173381	−	0.984855i	$-0.555469\pi$
$281$	12.8442	−	22.2468i	0.766219	−	1.32713i	0.939600	−	0.342275i	$-0.111198\pi$
$282$		0			0
$283$	8.40360	−	31.3627i	0.499542	−	1.86432i	−0.00339463	−	0.999994i	$-0.501081\pi$
$283$	8.40360	−	31.3627i	0.499542	−	1.86432i	0.502937	−	0.864323i	$-0.332253\pi$
$284$		0			0
$285$	4.03088	−	9.84335i	0.238768	−	0.583070i
$286$		0			0
$287$	0.0725036			0.00427975
$288$		0			0
$289$	−24.6657			−1.45092
$290$		0			0
$291$	−11.3214	+	1.53690i	−0.663672	+	0.0900950i
$292$		0			0
$293$	−5.91051	+	22.0583i	−0.345296	+	1.28866i	0.546971	+	0.837152i	$0.315781\pi$
$293$	−5.91051	+	22.0583i	−0.345296	+	1.28866i	−0.892266	+	0.451510i	$0.850886\pi$
$294$		0			0
$295$	6.20747	−	10.7517i	0.361413	−	0.625986i
$296$		0			0
$297$	−18.4262	−	23.4219i	−1.06919	−	1.35908i
$298$		0			0
$299$	−0.0505356	−	0.188601i	−0.00292255	−	0.0109071i
$300$		0			0
$301$	2.37760	−	8.87331i	0.137042	−	0.511449i
$302$		0			0
$303$	11.4551	+	8.71670i	0.658076	+	0.500761i
$304$		0			0
$305$			19.1110i			1.09429i
$306$		0			0
$307$	−10.3124	+	10.3124i	−0.588560	+	0.588560i	−0.937241	−	0.348681i	$-0.886630\pi$
$307$	−10.3124	+	10.3124i	−0.588560	+	0.588560i	0.348681	+	0.937241i	$0.386630\pi$
$308$		0			0
$309$	−4.45821	+	10.8869i	−0.253619	+	0.619333i
$310$		0			0
$311$	0.887812	−	0.512578i	0.0503432	−	0.0290656i	−0.474617	−	0.880192i	$-0.657413\pi$
$311$	0.887812	−	0.512578i	0.0503432	−	0.0290656i	0.524960	+	0.851127i	$0.324080\pi$
$312$		0			0
$313$	−9.53399	−	5.50445i	−0.538893	−	0.311130i	0.205737	−	0.978607i	$-0.434041\pi$
$313$	−9.53399	−	5.50445i	−0.538893	−	0.311130i	−0.744630	+	0.667477i	$0.767374\pi$
$314$		0			0
$315$	17.4104	−	10.2398i	0.980967	−	0.576947i
$316$		0			0
$317$	4.91593	+	18.3465i	0.276106	+	1.03044i	0.955096	+	0.296295i	$0.0957512\pi$
$317$	4.91593	+	18.3465i	0.276106	+	1.03044i	−0.678990	+	0.734147i	$0.737582\pi$
$318$		0			0
$319$	−26.1478	+	15.0965i	−1.46400	+	0.845239i
$320$		0			0
$321$	−28.9540	−	3.69329i	−1.61605	−	0.206139i
$322$		0			0
$323$	−9.71452	−	9.71452i	−0.540531	−	0.540531i
$324$		0			0
$325$	−9.50755	+	9.50755i	−0.527384	+	0.527384i
$326$		0			0
$327$	−0.160797	+	1.26059i	−0.00889210	+	0.0697107i
$328$		0			0
$329$	0.213111	+	0.369119i	0.0117492	+	0.0203502i
$330$		0			0
$331$	18.4486	−	4.94329i	1.01403	−	0.271708i	0.286716	−	0.958015i	$-0.407436\pi$
$331$	18.4486	−	4.94329i	1.01403	−	0.271708i	0.727312	+	0.686307i	$0.240770\pi$
$332$		0			0
$333$	1.05341	+	1.79108i	0.0577263	+	0.0981504i
$334$		0			0
$335$	−1.20722	+	2.09097i	−0.0659575	+	0.114242i
$336$		0			0
$337$	−14.6805	−	25.4274i	−0.799699	−	1.38512i	−0.919812	−	0.392359i	$-0.871659\pi$
$337$	−14.6805	−	25.4274i	−0.799699	−	1.38512i	0.120113	−	0.992760i	$-0.461674\pi$
$338$		0			0
$339$	17.7682	+	7.27610i	0.965034	+	0.395184i
$340$		0			0
$341$	7.72800	+	7.72800i	0.418495	+	0.418495i
$342$		0			0
$343$	−19.9627			−1.07788
$344$		0			0
$345$	0.146137	−	0.192046i	0.00786776	−	0.0103394i
$346$		0			0
$347$	−20.5081	−	5.49514i	−1.10093	−	0.294995i	−0.337789	−	0.941222i	$-0.609679\pi$
$347$	−20.5081	−	5.49514i	−1.10093	−	0.294995i	−0.763145	+	0.646227i	$0.776346\pi$
$348$		0			0
$349$	24.7859	−	6.64137i	1.32676	−	0.355504i	0.475254	−	0.879849i	$-0.342356\pi$
$349$	24.7859	−	6.64137i	1.32676	−	0.355504i	0.851506	+	0.524345i	$0.175690\pi$
$350$		0			0
$351$	−2.99394	−	20.7962i	−0.159805	−	1.11002i
$352$		0			0
$353$	19.1119	+	11.0343i	1.01723	+	0.587296i	0.913299	−	0.407289i	$-0.133526\pi$
$353$	19.1119	+	11.0343i	1.01723	+	0.587296i	0.103927	+	0.994585i	$0.466859\pi$
$354$		0			0
$355$	−2.90888	−	0.779432i	−0.154387	−	0.0413680i
$356$		0			0
$357$	−3.50937	−	25.8513i	−0.185735	−	1.36819i
$358$		0			0
$359$			13.1522i			0.694145i	0.937838	+	0.347073i	$0.112824\pi$
$359$			13.1522i			0.694145i	−0.937838	+	0.347073i	$0.887176\pi$
$360$		0			0
$361$			14.4700i			0.761581i
$362$		0			0
$363$	35.0914	+	14.3700i	1.84182	+	0.754231i
$364$		0			0
$365$	13.2288	+	3.54464i	0.692425	+	0.185535i
$366$		0			0
$367$	−5.13483	−	2.96459i	−0.268036	−	0.154751i	0.359959	−	0.932968i	$-0.382791\pi$
$367$	−5.13483	−	2.96459i	−0.268036	−	0.154751i	−0.627995	+	0.778218i	$0.716124\pi$
$368$		0			0
$369$	0.0898410	−	0.0248502i	0.00467694	−	0.00129365i
$370$		0			0
$371$	21.1035	−	5.65466i	1.09564	−	0.293575i
$372$		0			0
$373$	−34.7509	−	9.31148i	−1.79933	−	0.482130i	−0.805460	−	0.592650i	$-0.798082\pi$
$373$	−34.7509	−	9.31148i	−1.79933	−	0.482130i	−0.993874	+	0.110520i	$0.964748\pi$
$374$		0			0
$375$	8.30237	+	1.05903i	0.428732	+	0.0546878i
$376$		0			0
$377$	−21.2868			−1.09633
$378$		0			0
$379$	−4.54655	−	4.54655i	−0.233540	−	0.233540i	0.580628	−	0.814169i	$-0.302807\pi$
$379$	−4.54655	−	4.54655i	−0.233540	−	0.233540i	−0.814169	+	0.580628i	$0.802807\pi$
$380$		0			0
$381$	−16.5512	+	12.8064i	−0.847945	+	0.656094i
$382$		0			0
$383$	−16.4216	−	28.4430i	−0.839104	−	1.45337i	−0.890645	−	0.454700i	$-0.849747\pi$
$383$	−16.4216	−	28.4430i	−0.839104	−	1.45337i	0.0515410	−	0.998671i	$-0.483587\pi$
$384$		0			0
$385$	−19.3071	+	33.4409i	−0.983983	+	1.70431i
$386$		0			0
$387$	−0.0951387	−	11.8100i	−0.00483617	−	0.600338i
$388$		0			0
$389$	31.5961	−	8.46615i	1.60199	−	0.429251i	0.656344	−	0.754462i	$-0.272102\pi$
$389$	31.5961	−	8.46615i	1.60199	−	0.429251i	0.945641	+	0.325211i	$0.105435\pi$
$390$		0			0
$391$	−0.155848	−	0.269937i	−0.00788159	−	0.0136513i
$392$		0			0
$393$	−4.33301	+	1.81527i	−0.218571	+	0.0915683i
$394$		0			0
$395$	−17.1958	+	17.1958i	−0.865213	+	0.865213i
$396$		0			0
$397$	−26.7370	−	26.7370i	−1.34189	−	1.34189i	−0.894174	−	0.447720i	$-0.852236\pi$
$397$	−26.7370	−	26.7370i	−1.34189	−	1.34189i	−0.447720	−	0.894174i	$-0.647764\pi$
$398$		0			0
$399$	5.20911	−	6.84556i	0.260782	−	0.342706i
$400$		0			0
$401$	2.15088	−	1.24181i	0.107410	−	0.0620130i	−0.445333	−	0.895365i	$-0.646915\pi$
$401$	2.15088	−	1.24181i	0.107410	−	0.0620130i	0.552743	+	0.833352i	$0.313581\pi$
$402$		0			0
$403$	1.99427	+	7.44272i	0.0993418	+	0.370748i
$404$		0			0
$405$	18.0641	−	18.6557i	0.897611	−	0.927010i
$406$		0			0
$407$	−3.44020	−	1.98620i	−0.170524	−	0.0984522i
$408$		0			0
$409$	−6.04923	+	3.49252i	−0.299115	+	0.172694i	−0.642045	−	0.766667i	$-0.721914\pi$
$409$	−6.04923	+	3.49252i	−0.299115	+	0.172694i	0.342930	+	0.939361i	$0.388581\pi$
$410$		0			0
$411$	−25.8084	+	3.50355i	−1.27304	+	0.172818i
$412$		0			0
$413$	7.09951	−	7.09951i	0.349344	−	0.349344i
$414$		0			0
$415$		−	35.7825i		−	1.75649i
$416$		0			0
$417$	13.7098	−	5.74361i	0.671374	−	0.281266i
$418$		0			0
$419$	−7.82032	+	29.1858i	−0.382048	+	1.42582i	0.460721	+	0.887545i	$0.347591\pi$
$419$	−7.82032	+	29.1858i	−0.382048	+	1.42582i	−0.842768	+	0.538276i	$0.819076\pi$
$420$		0			0
$421$	8.37195	+	31.2445i	0.408024	+	1.52277i	0.798410	+	0.602114i	$0.205675\pi$
$421$	8.37195	+	31.2445i	0.408024	+	1.52277i	−0.390386	+	0.920651i	$0.627659\pi$
$422$		0			0
$423$	0.390584	+	0.384342i	0.0189909	+	0.0186873i
$424$		0			0
$425$	−10.7321	+	18.5885i	−0.520584	+	0.901677i
$426$		0			0
$427$	−4.00016	+	14.9288i	−0.193581	+	0.722455i
$428$		0			0
$429$	24.5803	+	31.7679i	1.18675	+	1.53377i
$430$		0			0
$431$	30.2342			1.45633			0.728164	−	0.685403i	$-0.240374\pi$
$431$	30.2342			1.45633			0.728164	+	0.685403i	$0.240374\pi$
$432$		0			0
$433$	34.5522			1.66047			0.830237	−	0.557410i	$-0.188205\pi$
$433$	34.5522			1.66047			0.830237	+	0.557410i	$0.188205\pi$
$434$		0			0
$435$	−16.1002	−	20.8081i	−0.771944	−	0.997670i
$436$		0			0
$437$	0.0266003	−	0.0992738i	0.00127247	−	0.00474891i
$438$		0			0
$439$	−1.65747	+	2.87082i	−0.0791066	+	0.137017i	−0.902865	−	0.429925i	$-0.858540\pi$
$439$	−1.65747	+	2.87082i	−0.0791066	+	0.137017i	0.823758	+	0.566941i	$0.191873\pi$
$440$		0			0
$441$	−4.49629	+	1.24368i	−0.214109	+	0.0592229i
$442$		0			0
$443$	−4.14656	−	15.4752i	−0.197009	−	0.735248i	−0.991738	−	0.128283i	$-0.959053\pi$
$443$	−4.14656	−	15.4752i	−0.197009	−	0.735248i	0.794729	−	0.606965i	$-0.207613\pi$
$444$		0			0
$445$	2.12977	−	7.94843i	0.100961	−	0.376792i
$446$		0			0
$447$	1.61633	−	0.677147i	0.0764499	−	0.0320279i
$448$		0			0
$449$		−	11.1511i		−	0.526253i	−0.964761	−	0.263126i	$-0.915246\pi$
$449$		−	11.1511i		−	0.526253i	0.964761	−	0.263126i	$-0.0847536\pi$
$450$		0			0
$451$	−0.126008	+	0.126008i	−0.00593349	+	0.00593349i
$452$		0			0
$453$	−28.4705	+	3.86494i	−1.33766	+	0.181591i
$454$		0			0
$455$	−23.5768	+	13.6121i	−1.10530	+	0.638143i
$456$		0			0
$457$	20.6193	+	11.9046i	0.964530	+	0.556872i	0.897564	−	0.440884i	$-0.145335\pi$
$457$	20.6193	+	11.9046i	0.964530	+	0.556872i	0.0669658	+	0.997755i	$0.478668\pi$
$458$		0			0
$459$	−13.2089	−	30.8301i	−0.616540	−	1.43903i
$460$		0			0
$461$	3.10783	+	11.5986i	0.144746	+	0.540199i	0.999767	+	0.0216051i	$0.00687764\pi$
$461$	3.10783	+	11.5986i	0.144746	+	0.540199i	−0.855021	+	0.518594i	$0.826456\pi$
$462$		0			0
$463$	−11.7247	+	6.76924i	−0.544892	+	0.314593i	−0.747059	−	0.664758i	$-0.768535\pi$
$463$	−11.7247	+	6.76924i	−0.544892	+	0.314593i	0.202168	+	0.979351i	$0.435201\pi$
$464$		0			0
$465$	−5.76697	+	7.57868i	−0.267437	+	0.351453i
$466$		0			0
$467$	−11.6000	−	11.6000i	−0.536784	−	0.536784i	0.385799	−	0.922583i	$-0.373926\pi$
$467$	−11.6000	−	11.6000i	−0.536784	−	0.536784i	−0.922583	+	0.385799i	$0.873926\pi$
$468$		0			0
$469$	−1.38070	+	1.38070i	−0.0637549	+	0.0637549i
$470$		0			0
$471$	35.1128	−	14.7102i	1.61791	−	0.677808i
$472$		0			0
$473$	11.2893	+	19.5536i	0.519081	+	0.899075i
$474$		0			0
$475$	−6.83624	+	1.83176i	−0.313668	+	0.0840471i
$476$		0			0
$477$	24.2118	−	14.2399i	1.10858	−	0.652002i
$478$		0			0
$479$	−2.09571	+	3.62988i	−0.0957555	+	0.165853i	−0.909924	−	0.414776i	$-0.863860\pi$
$479$	−2.09571	+	3.62988i	−0.0957555	+	0.165853i	0.814168	+	0.580629i	$0.197193\pi$
$480$		0			0
$481$	−1.40032	−	2.42543i	−0.0638493	−	0.110590i
$482$		0			0
$483$	0.154355	−	0.119431i	0.00702338	−	0.00543432i
$484$		0			0
$485$	13.4582	+	13.4582i	0.611107	+	0.611107i
$486$		0			0
$487$	26.7152			1.21058			0.605291	−	0.796004i	$-0.293057\pi$
$487$	26.7152			1.21058			0.605291	+	0.796004i	$0.293057\pi$
$488$		0			0
$489$	0.372296	+	0.0474890i	0.0168358	+	0.00214753i
$490$		0			0
$491$	2.54253	+	0.681269i	0.114743	+	0.0307452i	0.315733	−	0.948848i	$-0.397749\pi$
$491$	2.54253	+	0.681269i	0.114743	+	0.0307452i	−0.200991	+	0.979593i	$0.564416\pi$
$492$		0			0
$493$	−32.8236	+	8.79506i	−1.47830	+	0.396109i
$494$		0			0
$495$	−12.4623	+	48.0549i	−0.560137	+	2.15991i
$496$		0			0
$497$	−2.10917	−	1.21773i	−0.0946091	−	0.0546226i
$498$		0			0
$499$	−9.20074	−	2.46533i	−0.411882	−	0.110363i	0.0469272	−	0.998898i	$-0.485057\pi$
$499$	−9.20074	−	2.46533i	−0.411882	−	0.110363i	−0.458809	+	0.888535i	$0.651724\pi$
$500$		0			0
$501$	3.38747	+	1.38718i	0.151341	+	0.0619745i
$502$		0			0
$503$			11.5953i			0.517010i	0.966010	+	0.258505i	$0.0832299\pi$
$503$			11.5953i			0.517010i	−0.966010	+	0.258505i	$0.916770\pi$
$504$		0			0
$505$		−	23.9791i		−	1.06706i
$506$		0			0
$507$	0.780505	+	5.74948i	0.0346634	+	0.255343i
$508$		0			0
$509$	11.1171	+	2.97882i	0.492757	+	0.132034i	0.496637	−	0.867959i	$-0.334568\pi$
$509$	11.1171	+	2.97882i	0.492757	+	0.132034i	−0.00387934	+	0.999992i	$0.501235\pi$
$510$		0			0
$511$	9.59190	+	5.53789i	0.424321	+	0.244982i
$512$		0			0
$513$	4.10846	−	10.2679i	0.181393	−	0.453339i
$514$		0			0
$515$	18.9300	−	5.07227i	0.834154	−	0.223511i
$516$		0			0
$517$	−1.01189	−	0.271135i	−0.0445029	−	0.0119245i
$518$		0			0
$519$	2.35899	−	3.10007i	0.103548	−	0.136078i
$520$		0			0
$521$	−12.7808			−0.559939			−0.279969	−	0.960009i	$-0.590324\pi$
$521$	−12.7808			−0.559939			−0.279969	+	0.960009i	$0.590324\pi$
$522$		0			0
$523$	22.1010	+	22.1010i	0.966409	+	0.966409i	0.999454	−	0.0330445i	$-0.0105203\pi$
$523$	22.1010	+	22.1010i	0.966409	+	0.966409i	−0.0330445	+	0.999454i	$0.510520\pi$
$524$		0			0
$525$	−12.4371	−	5.09303i	−0.542800	−	0.222278i
$526$		0			0
$527$	6.15020	+	10.6525i	0.267907	+	0.464029i
$528$		0			0
$529$	−11.4988	+	19.9166i	−0.499949	+	0.865938i
$530$		0			0
$531$	6.36386	−	11.2305i	0.276168	−	0.487362i
$532$		0			0
$533$	−0.121357	+	0.0325174i	−0.00525654	+	0.00140849i
$534$		0			0
$535$	24.3121	+	42.1097i	1.05110	+	1.82056i
$536$		0			0
$537$	1.34276	−	10.5268i	0.0579445	−	0.454263i
$538$		0			0
$539$	6.30635	−	6.30635i	0.271634	−	0.271634i
$540$		0			0
$541$	4.90029	+	4.90029i	0.210680	+	0.210680i	0.804556	−	0.593876i	$-0.202403\pi$
$541$	4.90029	+	4.90029i	0.210680	+	0.210680i	−0.593876	+	0.804556i	$0.702403\pi$
$542$		0			0
$543$	33.8974	+	4.32385i	1.45468	+	0.185554i
$544$		0			0
$545$	1.83336	−	1.05849i	0.0785324	−	0.0453407i
$546$		0			0
$547$	−7.82071	−	29.1873i	−0.334390	−	1.24796i	−0.904529	−	0.426411i	$-0.859778\pi$
$547$	−7.82071	−	29.1873i	−0.334390	−	1.24796i	0.570140	−	0.821548i	$-0.306889\pi$
$548$		0			0
$549$	0.160065	+	19.8697i	0.00683141	+	0.848017i
$550$		0			0
$551$	−9.70357	−	5.60236i	−0.413386	−	0.238668i
$552$		0			0
$553$	−17.0320	+	9.83343i	−0.724275	+	0.418160i
$554$		0			0
$555$	1.31176	−	3.20329i	0.0556809	−	0.135972i
$556$		0			0
$557$	−5.23259	+	5.23259i	−0.221712	+	0.221712i	−0.809219	−	0.587507i	$-0.800109\pi$
$557$	−5.23259	+	5.23259i	−0.221712	+	0.221712i	0.587507	+	0.809219i	$0.300109\pi$
$558$		0			0
$559$			15.9185i			0.673281i
$560$		0			0
$561$	51.0275	+	38.8293i	2.15438	+	1.63937i
$562$		0			0
$563$	6.70709	−	25.0312i	0.282670	−	1.05494i	−0.667855	−	0.744291i	$-0.732787\pi$
$563$	6.70709	−	25.0312i	0.282670	−	1.05494i	0.950525	−	0.310648i	$-0.100546\pi$
$564$		0			0
$565$	−8.27830	−	30.8950i	−0.348271	−	1.29976i
$566$		0			0
$567$	18.0159	−	10.7921i	0.756595	−	0.453227i
$568$		0			0
$569$	−12.2193	+	21.1644i	−0.512259	+	0.887259i	0.487640	+	0.873045i	$0.337858\pi$
$569$	−12.2193	+	21.1644i	−0.512259	+	0.887259i	−0.999899	+	0.0142138i	$0.995475\pi$
$570$		0			0
$571$	1.41760	−	5.29056i	0.0593248	−	0.221403i	−0.929899	−	0.367815i	$-0.880106\pi$
$571$	1.41760	−	5.29056i	0.0593248	−	0.221403i	0.989224	+	0.146412i	$0.0467726\pi$
$572$		0			0
$573$	−13.1525	+	1.78548i	−0.549452	+	0.0745893i
$574$		0			0
$575$	−0.160572			−0.00669630
$576$		0			0
$577$	18.8956			0.786634			0.393317	−	0.919403i	$-0.371327\pi$
$577$	18.8956			0.786634			0.393317	+	0.919403i	$0.371327\pi$
$578$		0			0
$579$	−4.97581	+	12.1509i	−0.206788	+	0.504973i
$580$		0			0
$581$	7.48972	−	27.9520i	0.310726	−	1.15964i
$582$		0			0
$583$	−26.8494	+	46.5045i	−1.11199	+	1.92602i
$584$		0			0
$585$	−24.5491	+	24.9479i	−1.01498	+	1.03147i
$586$		0			0
$587$	10.8169	+	40.3694i	0.446463	+	1.66622i	0.712045	+	0.702133i	$0.247769\pi$
$587$	10.8169	+	40.3694i	0.446463	+	1.66622i	−0.265583	+	0.964088i	$0.585564\pi$
$588$		0			0
$589$	−1.04972	+	3.91761i	−0.0432530	+	0.161422i
$590$		0			0
$591$	−3.90523	+	30.6156i	−0.160640	+	1.25936i
$592$		0			0
$593$			8.51816i			0.349799i	0.984586	+	0.174899i	$0.0559600\pi$
$593$			8.51816i			0.349799i	−0.984586	+	0.174899i	$0.944040\pi$
$594$		0			0
$595$	−30.7306	+	30.7306i	−1.25983	+	1.25983i
$596$		0			0
$597$	24.4945	+	31.6571i	1.00249	+	1.29564i
$598$		0			0
$599$	30.1886	−	17.4294i	1.23347	−	0.712145i	0.265719	−	0.964051i	$-0.414391\pi$
$599$	30.1886	−	17.4294i	1.23347	−	0.712145i	0.967752	+	0.251906i	$0.0810573\pi$
$600$		0			0
$601$	17.4933	+	10.0997i	0.713565	+	0.411977i	0.812380	−	0.583129i	$-0.198172\pi$
$601$	17.4933	+	10.0997i	0.713565	+	0.411977i	−0.0988146	+	0.995106i	$0.531505\pi$
$602$		0			0
$603$	−1.23763	+	2.18409i	−0.0504004	+	0.0889430i
$604$		0			0
$605$	−16.3493	−	61.0165i	−0.664695	−	2.48067i
$606$		0			0
$607$	0.0948018	−	0.0547339i	0.00384789	−	0.00222158i	−0.498075	−	0.867134i	$-0.665960\pi$
$607$	0.0948018	−	0.0547339i	0.00384789	−	0.00222158i	0.501923	+	0.864912i	$0.332626\pi$
$608$		0			0
$609$	−8.22148	−	19.6245i	−0.333151	−	0.795224i
$610$		0			0
$611$	−0.522253	−	0.522253i	−0.0211281	−	0.0211281i
$612$		0			0
$613$	13.4094	−	13.4094i	0.541603	−	0.541603i	−0.382396	−	0.923999i	$-0.624901\pi$
$613$	13.4094	−	13.4094i	0.541603	−	0.541603i	0.923999	+	0.382396i	$0.124901\pi$
$614$		0			0
$615$	−0.123573	−	0.0940328i	−0.00498296	−	0.00379177i
$616$		0			0
$617$	−1.92944	−	3.34190i	−0.0776765	−	0.134540i	0.824571	−	0.565759i	$-0.191417\pi$
$617$	−1.92944	−	3.34190i	−0.0776765	−	0.134540i	−0.902247	+	0.431219i	$0.858083\pi$
$618$		0			0
$619$	4.87142	−	1.30529i	0.195799	−	0.0524642i	−0.159587	−	0.987184i	$-0.551016\pi$
$619$	4.87142	−	1.30529i	0.195799	−	0.0524642i	0.355386	+	0.934720i	$0.384350\pi$
$620$		0			0
$621$	0.150330	−	0.200895i	0.00603255	−	0.00806163i
$622$		0			0
$623$	3.32741	−	5.76324i	0.133310	−	0.230899i
$624$		0			0
$625$	−15.2845	−	26.4735i	−0.611379	−	1.05894i
$626$		0			0
$627$	2.84408	+	20.9505i	0.113582	+	0.836682i
$628$		0			0
$629$	−3.16137	−	3.16137i	−0.126052	−	0.126052i
$630$		0			0
$631$	−33.0513			−1.31575			−0.657876	−	0.753127i	$-0.728545\pi$
$631$	−33.0513			−1.31575			−0.657876	+	0.753127i	$0.728545\pi$
$632$		0			0
$633$	−8.85925	−	21.1468i	−0.352123	−	0.840510i
$634$		0			0
$635$	33.6739	+	9.02289i	1.33631	+	0.358063i
$636$		0			0
$637$	6.07355	−	1.62740i	0.240643	−	0.0644801i
$638$		0			0
$639$	−3.03089	−	0.786012i	−0.119900	−	0.0310942i
$640$		0			0
$641$	3.03668	+	1.75323i	0.119942	+	0.0692483i	0.558770	−	0.829322i	$-0.311273\pi$
$641$	3.03668	+	1.75323i	0.119942	+	0.0692483i	−0.438829	+	0.898571i	$0.644607\pi$
$642$		0			0
$643$	1.39293	+	0.373234i	0.0549318	+	0.0147189i	0.286180	−	0.958176i	$-0.407614\pi$
$643$	1.39293	+	0.373234i	0.0549318	+	0.0147189i	−0.231248	+	0.972895i	$0.574281\pi$
$644$		0			0
$645$	−15.5605	+	12.0399i	−0.612693	+	0.474069i
$646$		0			0
$647$			17.3282i			0.681241i	0.940201	+	0.340621i	$0.110637\pi$
$647$			17.3282i			0.681241i	−0.940201	+	0.340621i	$0.889363\pi$
$648$		0			0
$649$			24.6773i			0.968668i
$650$		0			0
$651$	−6.09126	+	4.71309i	−0.238735	+	0.184721i
$652$		0			0
$653$	−4.06026	−	1.08794i	−0.158890	−	0.0425745i	0.178497	−	0.983940i	$-0.442877\pi$
$653$	−4.06026	−	1.08794i	−0.158890	−	0.0425745i	−0.337387	+	0.941366i	$0.609543\pi$
$654$		0			0
$655$	6.77753	+	3.91301i	0.264820	+	0.152894i
$656$		0			0
$657$	13.7836	+	3.57456i	0.537751	+	0.139457i
$658$		0			0
$659$	−45.3085	+	12.1404i	−1.76497	+	0.472922i	−0.987715	−	0.156265i	$-0.950055\pi$
$659$	−45.3085	+	12.1404i	−1.76497	+	0.472922i	−0.777254	+	0.629187i	$0.783388\pi$
$660$		0			0
$661$	31.6766	+	8.48771i	1.23208	+	0.330134i	0.815388	−	0.578915i	$-0.196524\pi$
$661$	31.6766	+	8.48771i	1.23208	+	0.330134i	0.416689	+	0.909049i	$0.363191\pi$
$662$		0			0
$663$	17.4681	+	41.6960i	0.678406	+	1.61934i
$664$		0			0
$665$	−14.3299			−0.555690
$666$		0			0
$667$	−0.179755	−	0.179755i	−0.00696015	−	0.00696015i
$668$		0			0
$669$	−3.79931	−	27.9871i	−0.146890	−	1.08204i
$670$		0			0
$671$	−18.9935	−	32.8977i	−0.733236	−	1.27000i
$672$		0			0
$673$	−1.37128	+	2.37512i	−0.0528588	+	0.0915541i	−0.891244	−	0.453524i	$-0.850167\pi$
$673$	−1.37128	+	2.37512i	−0.0528588	+	0.0915541i	0.838385	+	0.545078i	$0.183500\pi$
$674$		0			0
$675$	−17.1567	−	2.04815i	−0.660363	−	0.0788333i
$676$		0			0
$677$	34.2273	−	9.17117i	1.31546	−	0.352477i	0.468185	−	0.883630i	$-0.344908\pi$
$677$	34.2273	−	9.17117i	1.31546	−	0.352477i	0.847276	+	0.531154i	$0.178241\pi$
$678$		0			0
$679$	7.69612	+	13.3301i	0.295350	+	0.511561i
$680$		0			0
$681$	−31.7441	−	24.1556i	−1.21644	−	0.925645i
$682$		0			0
$683$	−0.646566	+	0.646566i	−0.0247402	+	0.0247402i	−0.719369	−	0.694628i	$-0.755569\pi$
$683$	−0.646566	+	0.646566i	−0.0247402	+	0.0247402i	0.694628	+	0.719369i	$0.255569\pi$
$684$		0			0
$685$	30.6796	+	30.6796i	1.17221	+	1.17221i
$686$		0			0
$687$	−13.0802	−	31.2221i	−0.499041	−	1.19120i
$688$		0			0
$689$	−32.7870	+	18.9296i	−1.24908	+	0.721159i
$690$		0			0
$691$	−9.25241	−	34.5305i	−0.351978	−	1.31360i	−0.884245	−	0.467024i	$-0.845326\pi$
$691$	−9.25241	−	34.5305i	−0.351978	−	1.31360i	0.532266	−	0.846577i	$-0.321341\pi$
$692$		0			0
$693$	−19.7936	+	34.9303i	−0.751895	+	1.32689i
$694$		0			0
$695$	−21.4444	−	12.3810i	−0.813434	−	0.469636i
$696$		0			0
$697$	−0.173693	+	0.100282i	−0.00657908	+	0.00379844i
$698$		0			0
$699$	−19.5047	−	25.2081i	−0.737734	−	0.953458i
$700$		0			0
$701$	25.7079	−	25.7079i	0.970975	−	0.970975i	−0.0286153	−	0.999590i	$-0.509110\pi$
$701$	25.7079	−	25.7079i	0.970975	−	0.970975i	0.999590	+	0.0286153i	$0.00910977\pi$
$702$		0			0
$703$		−	1.47417i		−	0.0555995i
$704$		0			0
$705$	0.115504	−	0.905509i	0.00435013	−	0.0341034i
$706$		0			0
$707$	5.01912	−	18.7316i	0.188763	−	0.704474i
$708$		0			0
$709$	−6.43610	−	24.0199i	−0.241713	−	0.902085i	−0.975007	−	0.222173i	$-0.928685\pi$
$709$	−6.43610	−	24.0199i	−0.241713	−	0.902085i	0.733294	−	0.679911i	$-0.237982\pi$
$710$		0			0
$711$	−17.7344	+	18.0225i	−0.665093	+	0.675896i
$712$		0			0
$713$	−0.0460091	+	0.0796901i	−0.00172305	+	0.00298442i
$714$		0			0
$715$	17.3183	−	64.6326i	0.647666	−	2.41712i
$716$		0			0
$717$	16.3212	−	39.8562i	0.609527	−	1.48846i
$718$		0			0
$719$	3.00765			0.112167			0.0560833	−	0.998426i	$-0.482139\pi$
$719$	3.00765			0.112167			0.0560833	+	0.998426i	$0.482139\pi$
$720$		0			0
$721$	15.8491			0.590251
$722$		0			0
$723$	−0.879510	+	0.119395i	−0.0327093	+	0.00444036i
$724$		0			0
$725$	−4.53080	+	16.9092i	−0.168270	+	0.627992i
$726$		0			0
$727$	19.1265	−	33.1281i	0.709363	−	1.22865i	−0.255730	−	0.966748i	$-0.582316\pi$
$727$	19.1265	−	33.1281i	0.709363	−	1.22865i	0.965094	−	0.261905i	$-0.0843507\pi$
$728$		0			0
$729$	18.6250	−	19.5477i	0.689814	−	0.723987i
$730$		0			0
$731$	6.57703	+	24.5458i	0.243260	+	0.907859i
$732$		0			0
$733$	3.07838	−	11.4887i	0.113702	−	0.424343i	−0.885484	−	0.464670i	$-0.846173\pi$
$733$	3.07838	−	11.4887i	0.113702	−	0.424343i	0.999187	+	0.0403263i	$0.0128397\pi$
$734$		0			0
$735$	6.18449	+	4.70608i	0.228119	+	0.173586i
$736$		0			0
$737$		−	4.79920i		−	0.176781i
$738$		0			0
$739$	30.0692	−	30.0692i	1.10611	−	1.10611i	0.112457	−	0.993657i	$-0.464128\pi$
$739$	30.0692	−	30.0692i	1.10611	−	1.10611i	0.993657	−	0.112457i	$-0.0358720\pi$
$740$		0			0
$741$	−5.64883	+	13.7944i	−0.207515	+	0.506748i
$742$		0			0
$743$	4.00273	−	2.31098i	0.146846	−	0.0847815i	−0.424777	−	0.905298i	$-0.639647\pi$
$743$	4.00273	−	2.31098i	0.146846	−	0.0847815i	0.571623	+	0.820517i	$0.306314\pi$
$744$		0			0
$745$	−2.52821	−	1.45966i	−0.0926264	−	0.0534779i
$746$		0			0
$747$	−0.299699	−	37.2031i	−0.0109654	−	1.36119i
$748$		0			0
$749$	10.1776	+	37.9834i	0.371882	+	1.38788i
$750$		0			0
$751$	10.7097	−	6.18323i	0.390801	−	0.225629i	−0.291706	−	0.956508i	$-0.594223\pi$
$751$	10.7097	−	6.18323i	0.390801	−	0.225629i	0.682507	+	0.730879i	$0.260890\pi$
$752$		0			0
$753$	19.1576	+	2.44369i	0.698142	+	0.0890529i
$754$		0			0
$755$	33.8442	+	33.8442i	1.23172	+	1.23172i
$756$		0			0
$757$	15.8033	−	15.8033i	0.574380	−	0.574380i	−0.358969	−	0.933349i	$-0.616872\pi$
$757$	15.8033	−	15.8033i	0.574380	−	0.574380i	0.933349	+	0.358969i	$0.116872\pi$
$758$		0			0
$759$	−0.0606953	+	0.475829i	−0.00220310	+	0.0172715i
$760$		0			0
$761$	3.67823	+	6.37089i	0.133336	+	0.230944i	0.924961	−	0.380063i	$-0.124098\pi$
$761$	3.67823	+	6.37089i	0.133336	+	0.230944i	−0.791625	+	0.611008i	$0.790764\pi$
$762$		0			0
$763$	1.65371	−	0.443110i	0.0598682	−	0.0160416i
$764$		0			0
$765$	−27.5463	+	48.6117i	−0.995938	+	1.75756i
$766$		0			0
$767$	−8.69908	+	15.0673i	−0.314106	+	0.544047i
$768$		0			0
$769$	0.792301	+	1.37231i	0.0285711	+	0.0494866i	0.879957	−	0.475053i	$-0.157571\pi$
$769$	0.792301	+	1.37231i	0.0285711	+	0.0494866i	−0.851386	+	0.524539i	$0.824238\pi$
$770$		0			0
$771$	−19.7094	−	8.07107i	−0.709818	−	0.290672i
$772$		0			0
$773$	6.11545	+	6.11545i	0.219958	+	0.219958i	0.808481	−	0.588523i	$-0.200290\pi$
$773$	6.11545	+	6.11545i	0.219958	+	0.219958i	−0.588523	+	0.808481i	$0.700290\pi$
$774$		0			0
$775$	6.33660			0.227617
$776$		0			0
$777$	1.69518	−	2.22773i	0.0608144	−	0.0799193i
$778$		0			0
$779$	−0.0638783	−	0.0171161i	−0.00228868	−	0.000613249i
$780$		0			0
$781$	5.78201	−	1.54928i	0.206896	−	0.0554377i
$782$		0			0
$783$	−16.9136	−	21.4993i	−0.604444	−	0.768323i
$784$		0			0
$785$	−54.9221	−	31.7093i	−1.96025	−	1.13175i
$786$		0			0
$787$	27.9901	+	7.49992i	0.997739	+	0.267343i	0.720498	−	0.693457i	$-0.243913\pi$
$787$	27.9901	+	7.49992i	0.997739	+	0.267343i	0.277241	+	0.960800i	$0.410580\pi$
$788$		0			0
$789$	−2.27749	−	16.7768i	−0.0810809	−	0.597271i
$790$		0			0
$791$		−	25.8668i		−	0.919719i
$792$		0			0
$793$		−	26.7819i		−	0.951053i
$794$		0			0
$795$	−43.3021	−	17.7323i	−1.53577	−	0.628900i
$796$		0			0
$797$	−43.3197	−	11.6075i	−1.53446	−	0.411158i	−0.609991	−	0.792408i	$-0.708827\pi$
$797$	−43.3197	−	11.6075i	−1.53446	−	0.411158i	−0.924472	+	0.381250i	$0.875494\pi$
$798$		0			0
$799$	−1.02107	−	0.589518i	−0.0361230	−	0.0208556i
$800$		0			0
$801$	2.14776	−	8.28182i	0.0758872	−	0.292624i
$802$		0			0
$803$	−26.2949	+	7.04571i	−0.927928	+	0.248638i
$804$		0			0
$805$	−0.314039	−	0.0841464i	−0.0110684	−	0.00296577i
$806$		0			0
$807$	13.7096	+	1.74876i	0.482602	+	0.0615593i
$808$		0			0
$809$	−17.6588			−0.620851			−0.310426	−	0.950598i	$-0.600472\pi$
$809$	−17.6588			−0.620851			−0.310426	+	0.950598i	$0.600472\pi$
$810$		0			0
$811$	0.326636	+	0.326636i	0.0114697	+	0.0114697i	0.712818	−	0.701349i	$-0.247418\pi$
$811$	0.326636	+	0.326636i	0.0114697	+	0.0114697i	−0.701349	+	0.712818i	$0.747418\pi$
$812$		0			0
$813$	15.1404	−	11.7148i	0.530996	−	0.410856i
$814$		0			0
$815$	−0.312609	−	0.541455i	−0.0109502	−	0.0189663i
$816$		0			0
$817$	−4.18950	+	7.25642i	−0.146572	+	0.253870i
$818$		0			0
$819$	−24.3988	+	14.3499i	−0.852563	+	0.501427i
$820$		0			0
$821$	−39.4337	+	10.5662i	−1.37625	+	0.368764i	−0.869756	−	0.493482i	$-0.835724\pi$
$821$	−39.4337	+	10.5662i	−1.37625	+	0.368764i	−0.506490	+	0.862246i	$0.669057\pi$
$822$		0			0
$823$	−3.27150	−	5.66640i	−0.114037	−	0.197518i	0.803357	−	0.595497i	$-0.203045\pi$
$823$	−3.27150	−	5.66640i	−0.114037	−	0.197518i	−0.917394	+	0.397979i	$0.869712\pi$
$824$		0			0
$825$	30.4666	−	12.7637i	1.06071	−	0.444375i
$826$		0			0
$827$	−0.510932	+	0.510932i	−0.0177668	+	0.0177668i	−0.715934	−	0.698168i	$-0.753999\pi$
$827$	−0.510932	+	0.510932i	−0.0177668	+	0.0177668i	0.698168	+	0.715934i	$0.253999\pi$
$828$		0			0
$829$	0.210205	+	0.210205i	0.00730073	+	0.00730073i	0.710748	−	0.703447i	$-0.248357\pi$
$829$	0.210205	+	0.210205i	0.00730073	+	0.00730073i	−0.703447	+	0.710748i	$0.748357\pi$
$830$		0			0
$831$	−27.4427	+	36.0639i	−0.951976	+	1.25104i
$832$		0			0
$833$	8.69283	−	5.01881i	0.301189	−	0.173891i
$834$		0			0
$835$	−1.57824	−	5.89009i	−0.0546174	−	0.203835i
$836$		0			0
$837$	−5.93245	+	7.92785i	−0.205055	+	0.274027i
$838$		0			0
$839$	−25.1098	−	14.4971i	−0.866885	−	0.500496i	−0.000573152	−	1.00000i	$-0.500182\pi$
$839$	−25.1098	−	14.4971i	−0.866885	−	0.500496i	−0.866312	+	0.499504i	$0.833516\pi$
$840$		0			0
$841$	1.11330	−	0.642762i	0.0383895	−	0.0221642i
$842$		0			0
$843$	−44.0891	+	5.98520i	−1.51851	+	0.206141i
$844$		0			0
$845$	6.83466	−	6.83466i	0.235119	−	0.235119i
$846$		0			0
$847$		−	51.0860i		−	1.75534i
$848$		0			0
$849$	−51.8700	+	21.7304i	−1.78018	+	0.745787i
$850$		0			0
$851$	0.00865646	−	0.0323063i	0.000296740	−	0.00110745i
$852$		0			0
$853$	−7.28025	−	27.1702i	−0.249271	−	0.930292i	−0.971189	−	0.238313i	$-0.923406\pi$
$853$	−7.28025	−	27.1702i	−0.249271	−	0.930292i	0.721918	−	0.691979i	$-0.243261\pi$
$854$		0			0
$855$	−17.7566	+	4.91150i	−0.607262	+	0.167970i
$856$		0			0
$857$	−28.3745	+	49.1461i	−0.969256	+	1.67880i	−0.271537	+	0.962428i	$0.587532\pi$
$857$	−28.3745	+	49.1461i	−0.969256	+	1.67880i	−0.697719	+	0.716372i	$0.745802\pi$
$858$		0			0
$859$	−1.68263	+	6.27967i	−0.0574106	+	0.214259i	−0.988672	−	0.150093i	$-0.952043\pi$
$859$	−1.68263	+	6.27967i	−0.0574106	+	0.214259i	0.931261	+	0.364352i	$0.118709\pi$
$860$		0			0
$861$	−0.0768489	−	0.0993205i	−0.00261900	−	0.00338483i
$862$		0			0
$863$	12.7093			0.432629			0.216314	−	0.976324i	$-0.430596\pi$
$863$	12.7093			0.432629			0.216314	+	0.976324i	$0.430596\pi$
$864$		0			0
$865$	−6.48942			−0.220647
$866$		0			0
$867$	26.1439	+	33.7887i	0.887894	+	1.14753i
$868$		0			0
$869$	12.5108	−	46.6910i	0.424400	−	1.58388i
$870$		0			0
$871$	1.69178	−	2.93026i	0.0573239	−	0.0992880i
$872$		0			0
$873$	14.1053	+	13.8798i	0.477391	+	0.469761i
$874$		0			0
$875$	−2.91836	−	10.8915i	−0.0986587	−	0.368199i
$876$		0			0
$877$	−9.47357	+	35.3558i	−0.319900	+	1.19388i	0.599441	+	0.800419i	$0.295390\pi$
$877$	−9.47357	+	35.3558i	−0.319900	+	1.19388i	−0.919341	+	0.393463i	$0.871277\pi$
$878$		0			0
$879$	36.4818	−	15.2837i	1.23050	−	0.515506i
$880$		0			0
$881$		−	39.6546i		−	1.33600i	−0.744163	−	0.667998i	$-0.767151\pi$
$881$		−	39.6546i		−	1.33600i	0.744163	−	0.667998i	$-0.232849\pi$
$882$		0			0
$883$	−16.6423	+	16.6423i	−0.560060	+	0.560060i	−0.929324	−	0.369265i	$-0.879610\pi$
$883$	−16.6423	+	16.6423i	−0.560060	+	0.560060i	0.369265	+	0.929324i	$0.379610\pi$
$884$		0			0
$885$	−21.3079	+	2.89259i	−0.716256	+	0.0972334i
$886$		0			0
$887$	−0.0199051	+	0.0114922i	−0.000668349	+	0.000385871i	−0.500334	−	0.865832i	$-0.666789\pi$
$887$	−0.0199051	+	0.0114922i	−0.000668349	+	0.000385871i	0.499666	+	0.866218i	$0.333456\pi$
$888$		0			0
$889$	24.4162	+	14.0967i	0.818894	+	0.472789i
$890$		0			0
$891$	−12.5545	+	50.0671i	−0.420593	+	1.67731i
$892$		0			0
$893$	−0.100619	−	0.375517i	−0.00336710	−	0.0125662i
$894$		0			0
$895$	−15.3098	+	8.83910i	−0.511749	+	0.295458i
$896$		0			0
$897$	−0.204795	+	0.269132i	−0.00683791	+	0.00898605i
$898$		0			0
$899$	7.09363	+	7.09363i	0.236586	+	0.236586i
$900$		0			0
$901$	−42.7353	+	42.7353i	−1.42372	+	1.42372i
$902$		0			0
$903$	−14.6754	+	6.14810i	−0.488366	+	0.204596i
$904$		0			0
$905$	−28.4629	−	49.2992i	−0.946140	−	1.63876i
$906$		0			0
$907$	38.1323	−	10.2175i	1.26616	−	0.339267i	0.437602	−	0.899169i	$-0.355828\pi$
$907$	38.1323	−	10.2175i	1.26616	−	0.339267i	0.828559	+	0.559902i	$0.189161\pi$
$908$		0			0
$909$	−0.200838	−	24.9311i	−0.00666139	−	0.826911i
$910$		0			0
$911$	22.7704	−	39.4395i	0.754417	−	1.30669i	−0.191246	−	0.981542i	$-0.561253\pi$
$911$	22.7704	−	39.4395i	0.754417	−	1.30669i	0.945664	−	0.325147i	$-0.105414\pi$
$912$		0			0
$913$	35.5626	+	61.5962i	1.17695	+	2.03854i
$914$		0			0
$915$	26.1795	−	20.2563i	0.865469	−	0.669653i
$916$		0			0
$917$	4.47532	+	4.47532i	0.147788	+	0.147788i
$918$		0			0
$919$	11.2611			0.371468			0.185734	−	0.982600i	$-0.440534\pi$
$919$	11.2611			0.371468			0.185734	+	0.982600i	$0.440534\pi$
$920$		0			0
$921$	25.0571	+	3.19621i	0.825659	+	0.105319i
$922$		0			0
$923$	4.07647	+	1.09229i	0.134179	+	0.0359531i
$924$		0			0
$925$	−2.22469	+	0.596105i	−0.0731475	+	0.0195998i
$926$		0			0
$927$	19.6390	−	5.43219i	0.645030	−	0.178417i
$928$		0			0
$929$	−16.8724	−	9.74127i	−0.553564	−	0.319601i	0.196994	−	0.980405i	$-0.436882\pi$
$929$	−16.8724	−	9.74127i	−0.553564	−	0.319601i	−0.750558	+	0.660804i	$0.770215\pi$
$930$		0			0
$931$	3.19693	+	0.856614i	0.104775	+	0.0280744i
$932$		0			0
$933$	−1.64319	−	0.672889i	−0.0537955	−	0.0220294i
$934$		0			0
$935$		−	106.817i		−	3.49328i
$936$		0			0
$937$			5.47240i			0.178775i	0.995997	+	0.0893877i	$0.0284910\pi$
$937$			5.47240i			0.178775i	−0.995997	+	0.0893877i	$0.971509\pi$
$938$		0			0
$939$	2.56499	+	18.8947i	0.0837054	+	0.616604i
$940$		0			0
$941$	11.9941	+	3.21380i	0.390995	+	0.104767i	0.448960	−	0.893552i	$-0.351795\pi$
$941$	11.9941	+	3.21380i	0.390995	+	0.104767i	−0.0579650	+	0.998319i	$0.518461\pi$
$942$		0			0
$943$	−0.00129938		0.000750197i	−4.23136e−5		2.44298e-5i
$944$		0			0
$945$	−32.4811	−	12.9965i	−1.05661	−	0.422778i
$946$		0			0
$947$	−0.0238937	+	0.00640230i	−0.000776441	+	0.000208047i	−0.259207	−	0.965822i	$-0.583461\pi$
$947$	−0.0238937	+	0.00640230i	−0.000776441	+	0.000208047i	0.258431	+	0.966030i	$0.416795\pi$
$948$		0			0
$949$	−18.5387	−	4.96742i	−0.601790	−	0.161249i
$950$		0			0
$951$	19.9218	−	26.1802i	0.646008	−	0.848952i
$952$		0			0
$953$	47.9215			1.55233			0.776164	−	0.630531i	$-0.217163\pi$
$953$	47.9215			1.55233			0.776164	+	0.630531i	$0.217163\pi$
$954$		0			0
$955$	15.6349	+	15.6349i	0.505934	+	0.505934i
$956$		0			0
$957$	48.3951	+	19.8179i	1.56439	+	0.640622i
$958$		0			0
$959$	17.5442	+	30.3875i	0.566532	+	0.981262i
$960$		0			0
$961$	−13.6844	+	23.7020i	−0.441431	+	0.764581i
$962$		0			0
$963$	25.6299	+	43.5779i	0.825913	+	1.40428i
$964$		0			0
$965$	21.1278	−	5.66117i	0.680127	−	0.182240i
$966$		0			0
$967$	−6.27580	−	10.8700i	−0.201816	−	0.349556i	0.747297	−	0.664490i	$-0.231351\pi$
$967$	−6.27580	−	10.8700i	−0.201816	−	0.349556i	−0.949114	+	0.314934i	$0.898018\pi$
$968$		0			0
$969$	−3.01090	+	23.6044i	−0.0967242	+	0.758282i
$970$		0			0
$971$	16.0701	−	16.0701i	0.515715	−	0.515715i	−0.400557	−	0.916272i	$-0.631183\pi$
$971$	16.0701	−	16.0701i	0.515715	−	0.515715i	0.916272	+	0.400557i	$0.131183\pi$
$972$		0			0
$973$	−14.1601	−	14.1601i	−0.453953	−	0.453953i
$974$		0			0
$975$	23.1015	+	2.94675i	0.739839	+	0.0943716i
$976$		0			0
$977$	47.1397	−	27.2161i	1.50813	−	0.870721i	0.508178	−	0.861252i	$-0.330319\pi$
$977$	47.1397	−	27.2161i	1.50813	−	0.870721i	0.999955	−	0.00946892i	$-0.00301410\pi$
$978$		0			0
$979$	4.23337	+	15.7992i	0.135299	+	0.504943i
$980$		0			0
$981$	1.89728	−	1.11587i	0.0605754	−	0.0356269i
$982$		0			0
$983$	−16.9623	−	9.79319i	−0.541014	−	0.312354i	0.204476	−	0.978872i	$-0.434451\pi$
$983$	−16.9623	−	9.79319i	−0.541014	−	0.312354i	−0.745490	+	0.666517i	$0.767784\pi$
$984$		0			0
$985$	44.5262	−	25.7072i	1.41872	−	0.819101i
$986$		0			0
$987$	0.279762	−	0.683175i	0.00890491	−	0.0217457i
$988$		0			0
$989$	−0.134423	+	0.134423i	−0.00427439	+	0.00427439i
$990$		0			0
$991$		−	29.8539i		−	0.948341i	−0.880433	−	0.474171i	$-0.842748\pi$
$991$		−	29.8539i		−	0.948341i	0.880433	−	0.474171i	$-0.157252\pi$
$992$		0			0
$993$	−26.3260	−	20.0327i	−0.835429	−	0.635717i
$994$		0			0
$995$	17.2578	−	64.4071i	0.547110	−	2.04184i
$996$		0			0
$997$	−7.41898	−	27.6880i	−0.234961	−	0.876888i	−0.978166	−	0.207824i	$-0.933362\pi$
$997$	−7.41898	−	27.6880i	−0.234961	−	0.876888i	0.743205	−	0.669064i	$-0.233305\pi$
$998$		0			0
$999$	1.33700	−	3.34145i	0.0423009	−	0.105719i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	576.2.y.a.47.7		88
3.2	odd	2		1728.2.z.a.1007.19		88
4.3	odd	2		144.2.u.a.83.10	yes	88
9.4	even	3		1728.2.z.a.1583.19		88
9.5	odd	6	inner	576.2.y.a.239.18		88
12.11	even	2		432.2.v.a.35.13		88
16.5	even	4		144.2.u.a.11.2	✓	88
16.11	odd	4	inner	576.2.y.a.335.18		88
36.23	even	6		144.2.u.a.131.2	yes	88
36.31	odd	6		432.2.v.a.179.21		88
48.5	odd	4		432.2.v.a.251.21		88
48.11	even	4		1728.2.z.a.143.19		88
144.5	odd	12		144.2.u.a.59.10	yes	88
144.59	even	12	inner	576.2.y.a.527.7		88
144.85	even	12		432.2.v.a.395.13		88
144.139	odd	12		1728.2.z.a.719.19		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.u.a.11.2	✓	88	16.5	even	4
144.2.u.a.59.10	yes	88	144.5	odd	12
144.2.u.a.83.10	yes	88	4.3	odd	2
144.2.u.a.131.2	yes	88	36.23	even	6
432.2.v.a.35.13		88	12.11	even	2
432.2.v.a.179.21		88	36.31	odd	6
432.2.v.a.251.21		88	48.5	odd	4
432.2.v.a.395.13		88	144.85	even	12
576.2.y.a.47.7		88	1.1	even	1	trivial
576.2.y.a.239.18		88	9.5	odd	6	inner
576.2.y.a.335.18		88	16.11	odd	4	inner
576.2.y.a.527.7		88	144.59	even	12	inner
1728.2.z.a.143.19		88	48.11	even	4
1728.2.z.a.719.19		88	144.139	odd	12
1728.2.z.a.1007.19		88	3.2	odd	2
1728.2.z.a.1583.19		88	9.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	576.y (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.05993 - 1.36987i) q^{3} +(-0.746784 + 2.78704i) q^{5} +(-1.16672 + 2.02082i) q^{7} +(-0.753089 + 2.90394i) q^{9} +O(q^{10})\)	\(q+(-1.05993 - 1.36987i) q^{3} +(-0.746784 + 2.78704i) q^{5} +(-1.16672 + 2.02082i) q^{7} +(-0.753089 + 2.90394i) q^{9} +(-1.48439 - 5.53982i) q^{11} +(1.04654 - 3.90572i) q^{13} +(4.60942 - 1.93107i) q^{15} -6.45489i q^{17} +(1.50499 - 1.50499i) q^{19} +(4.00491 - 0.543676i) q^{21} +(0.0418190 - 0.0241442i) q^{23} +(-2.87976 - 1.66263i) q^{25} +(4.77624 - 2.04634i) q^{27} +(-1.36254 - 5.08507i) q^{29} +(-1.65029 + 0.952797i) q^{31} +(-6.01548 + 7.90525i) q^{33} +(-4.76082 - 4.76082i) q^{35} +(0.489763 - 0.489763i) q^{37} +(-6.45959 + 2.70618i) q^{39} +(-0.0155357 - 0.0269087i) q^{41} +(-3.80267 + 1.01892i) q^{43} +(-7.53099 - 4.26750i) q^{45} +(0.0913288 - 0.158186i) q^{47} +(0.777520 + 1.34670i) q^{49} +(-8.84237 + 6.84175i) q^{51} +(-6.62061 - 6.62061i) q^{53} +16.5482 q^{55} +(-3.65682 - 0.466453i) q^{57} +(-4.15614 - 1.11363i) q^{59} +(6.39775 - 1.71427i) q^{61} +(-4.98970 - 4.90995i) q^{63} +(10.1039 + 5.83347i) q^{65} +(0.808279 + 0.216578i) q^{67} +(-0.0773998 - 0.0316954i) q^{69} +1.04372i q^{71} -4.74654i q^{73} +(0.774762 + 5.70717i) q^{75} +(12.9269 + 3.46374i) q^{77} +(7.29908 + 4.21413i) q^{79} +(-7.86571 - 4.37385i) q^{81} +(-11.9789 + 3.20973i) q^{83} +(17.9900 + 4.82041i) q^{85} +(-5.52169 + 7.25633i) q^{87} -2.85193 q^{89} +(6.67175 + 6.67175i) q^{91} +(3.05441 + 1.25079i) q^{93} +(3.07055 + 5.31835i) q^{95} +(3.29818 - 5.71262i) q^{97} +(17.2052 - 0.138600i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 4 q^{3} - 6 q^{5} + 4 q^{7}+O(q^{10}) \) 88 * q + 4 * q^3 - 6 * q^5 + 4 * q^7	\( 88 q + 4 q^{3} - 6 q^{5} + 4 q^{7} + 6 q^{11} - 2 q^{13} + 8 q^{19} + 2 q^{21} + 12 q^{23} + 16 q^{27} - 6 q^{29} - 8 q^{33} - 8 q^{37} + 32 q^{39} + 2 q^{43} + 6 q^{45} - 24 q^{49} + 12 q^{51} + 16 q^{55} + 42 q^{59} - 2 q^{61} - 12 q^{65} + 2 q^{67} - 10 q^{69} + 56 q^{75} - 6 q^{77} - 8 q^{81} - 54 q^{83} + 8 q^{85} - 48 q^{87} - 20 q^{91} - 34 q^{93} - 4 q^{97} - 46 q^{99}+O(q^{100}) \) 88 * q + 4 * q^3 - 6 * q^5 + 4 * q^7 + 6 * q^11 - 2 * q^13 + 8 * q^19 + 2 * q^21 + 12 * q^23 + 16 * q^27 - 6 * q^29 - 8 * q^33 - 8 * q^37 + 32 * q^39 + 2 * q^43 + 6 * q^45 - 24 * q^49 + 12 * q^51 + 16 * q^55 + 42 * q^59 - 2 * q^61 - 12 * q^65 + 2 * q^67 - 10 * q^69 + 56 * q^75 - 6 * q^77 - 8 * q^81 - 54 * q^83 + 8 * q^85 - 48 * q^87 - 20 * q^91 - 34 * q^93 - 4 * q^97 - 46 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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