LMFDB - Embedded newform 900.2.r.g.551.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [900,2,Mod(551,900)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(900, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 1, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("900.551"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	900.r (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0,2,0,0,0,0,12,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(12)] == traces)

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

Self dual:	no
Analytic conductor:	$7.18653618192$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 180)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			551.14
Character	$\chi$	$=$	900.551
Dual form			900.2.r.g.851.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.282343 - 1.38574i) q^{2} +(1.44177 + 0.959839i) q^{3} +(-1.84056 - 0.782509i) q^{4} +(1.73716 - 1.72692i) q^{6} +(0.953419 + 0.550457i) q^{7} +(-1.60403 + 2.32961i) q^{8} +(1.15742 + 2.76774i) q^{9} +(-2.84126 + 4.92120i) q^{11} +(-1.90259 - 2.89485i) q^{12} +(1.19828 + 2.07548i) q^{13} +(1.03198 - 1.16578i) q^{14} +(2.77536 + 2.88052i) q^{16} +1.29175i q^{17} +(4.16216 - 0.822430i) q^{18} -2.78362i q^{19} +(0.846263 + 1.70876i) q^{21} +(6.01731 + 5.32672i) q^{22} +(1.05393 + 1.82546i) q^{23} +(-4.54870 + 1.81916i) q^{24} +(3.21441 - 1.07451i) q^{26} +(-0.987853 + 5.10139i) q^{27} +(-1.32409 - 1.75921i) q^{28} +(5.51723 + 3.18537i) q^{29} +(2.78385 - 1.60725i) q^{31} +(4.77526 - 3.03264i) q^{32} +(-8.82001 + 4.36810i) q^{33} +(1.79003 + 0.364715i) q^{34} +(0.0354812 - 5.99990i) q^{36} -6.51687 q^{37} +(-3.85739 - 0.785937i) q^{38} +(-0.264482 + 4.14253i) q^{39} +(6.35642 - 3.66988i) q^{41} +(2.60684 - 0.690246i) q^{42} +(-3.90530 - 2.25473i) q^{43} +(9.08040 - 6.83448i) q^{44} +(2.82719 - 0.945071i) q^{46} +(-4.67439 + 8.09628i) q^{47} +(1.23660 + 6.81695i) q^{48} +(-2.89400 - 5.01255i) q^{49} +(-1.23987 + 1.86240i) q^{51} +(-0.581429 - 4.75773i) q^{52} -11.5954i q^{53} +(6.79030 + 2.80925i) q^{54} +(-2.81166 + 1.33815i) q^{56} +(2.67183 - 4.01335i) q^{57} +(5.97186 - 6.74609i) q^{58} +(3.66237 + 6.34341i) q^{59} +(2.48990 - 4.31263i) q^{61} +(-1.44124 - 4.31149i) q^{62} +(-0.420017 + 3.27592i) q^{63} +(-2.85419 - 7.47353i) q^{64} +(3.56280 + 13.4556i) q^{66} +(-3.20457 + 1.85016i) q^{67} +(1.01080 - 2.37754i) q^{68} +(-0.232621 + 3.64351i) q^{69} +12.6950 q^{71} +(-8.30429 - 1.74320i) q^{72} +9.86891 q^{73} +(-1.83999 + 9.03070i) q^{74} +(-2.17821 + 5.12344i) q^{76} +(-5.41781 + 3.12798i) q^{77} +(5.66581 + 1.53612i) q^{78} +(0.975531 + 0.563223i) q^{79} +(-6.32077 + 6.40686i) q^{81} +(-3.29082 - 9.84453i) q^{82} +(-5.76275 + 9.98138i) q^{83} +(-0.220480 - 3.80730i) q^{84} +(-4.22710 + 4.77514i) q^{86} +(4.89714 + 9.88823i) q^{87} +(-6.90704 - 14.5128i) q^{88} -9.16815i q^{89} +2.63841i q^{91} +(-0.511387 - 4.18460i) q^{92} +(5.55638 + 0.354749i) q^{93} +(9.89957 + 8.76343i) q^{94} +(9.79568 + 0.211108i) q^{96} +(6.42344 - 11.1257i) q^{97} +(-7.76320 + 2.59507i) q^{98} +(-16.9091 - 2.16798i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 2 q^{4} + 12 q^{9} + 42 q^{14} + 30 q^{16} - 12 q^{21} + 6 q^{24} + 4 q^{34} + 96 q^{36} + 96 q^{41} + 4 q^{46} - 32 q^{49} + 30 q^{54} + 6 q^{56} + 8 q^{61} + 20 q^{64} + 36 q^{66} + 96 q^{69} - 72 q^{74}+ \cdots + 54 q^{96}+O(q^{100}) $ 48 * q + 2 * q^4 + 12 * q^9 + 42 * q^14 + 30 * q^16 - 12 * q^21 + 6 * q^24 + 4 * q^34 + 96 * q^36 + 96 * q^41 + 4 * q^46 - 32 * q^49 + 30 * q^54 + 6 * q^56 + 8 * q^61 + 20 * q^64 + 36 * q^66 + 96 * q^69 - 72 * q^74 + 36 * q^81 + 6 * q^84 + 108 * q^86 + 62 * q^94 + 54 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	0.282343	−	1.38574i	0.199647	−	0.979868i
$2$	0.282343	−	1.38574i	0.199647	−	0.979868i
$3$	1.44177	+	0.959839i	0.832408	+	0.554163i
$3$	1.44177	+	0.959839i	0.832408	+	0.554163i
$4$	−1.84056	−	0.782509i	−0.920282	−	0.391255i
$5$		0			0
$5$		0			0
$6$	1.73716	−	1.72692i	0.709194	−	0.705013i
$7$	0.953419	+	0.550457i	0.360358	+	0.208053i	0.669238	−	0.743048i	$-0.266621\pi$
$7$	0.953419	+	0.550457i	0.360358	+	0.208053i	−0.308880	+	0.951101i	$0.599954\pi$
$8$	−1.60403	+	2.32961i	−0.567109	+	0.823643i
$9$	1.15742	+	2.76774i	0.385806	+	0.922580i
$10$		0			0
$11$	−2.84126	+	4.92120i	−0.856671	+	1.48380i	0.0184153	+	0.999830i	$0.494138\pi$
$11$	−2.84126	+	4.92120i	−0.856671	+	1.48380i	−0.875086	+	0.483967i	$0.839195\pi$
$12$	−1.90259	−	2.89485i	−0.549231	−	0.835670i
$13$	1.19828	+	2.07548i	0.332343	+	0.575636i	0.982971	−	0.183761i	$-0.0588274\pi$
$13$	1.19828	+	2.07548i	0.332343	+	0.575636i	−0.650627	+	0.759397i	$0.725494\pi$
$14$	1.03198	−	1.16578i	0.275809	−	0.311567i
$15$		0			0
$16$	2.77536	+	2.88052i	0.693839	+	0.720130i
$17$			1.29175i			0.313294i	0.987655	+	0.156647i	$0.0500685\pi$
$17$			1.29175i			0.313294i	−0.987655	+	0.156647i	$0.949931\pi$
$18$	4.16216	−	0.822430i	0.981031	−	0.193849i
$19$		−	2.78362i		−	0.638607i	−0.947652	−	0.319304i	$-0.896551\pi$
$19$		−	2.78362i		−	0.638607i	0.947652	−	0.319304i	$-0.103449\pi$
$20$		0			0
$21$	0.846263	+	1.70876i	0.184670	+	0.372882i
$22$	6.01731	+	5.32672i	1.28289	+	1.13566i
$23$	1.05393	+	1.82546i	0.219760	+	0.380635i	0.954735	−	0.297459i	$-0.0961392\pi$
$23$	1.05393	+	1.82546i	0.219760	+	0.380635i	−0.734975	+	0.678095i	$0.762806\pi$
$24$	−4.54870	+	1.81916i	−0.928499	+	0.371335i
$25$		0			0
$26$	3.21441	−	1.07451i	0.630398	−	0.210729i
$27$	−0.987853	+	5.10139i	−0.190112	+	0.981762i
$28$	−1.32409	−	1.75921i	−0.250230	−	0.332459i
$29$	5.51723	+	3.18537i	1.02452	+	0.591509i	0.915411	−	0.402521i	$-0.131866\pi$
$29$	5.51723	+	3.18537i	1.02452	+	0.591509i	0.109112	+	0.994029i	$0.465199\pi$
$30$		0			0
$31$	2.78385	−	1.60725i	0.499994	−	0.288671i	−0.228717	−	0.973493i	$-0.573453\pi$
$31$	2.78385	−	1.60725i	0.499994	−	0.288671i	0.728711	+	0.684821i	$0.240120\pi$
$32$	4.77526	−	3.03264i	0.844155	−	0.536100i
$33$	−8.82001	+	4.36810i	−1.53537	+	0.760389i
$34$	1.79003	+	0.364715i	0.306987	+	0.0625481i
$35$		0			0
$36$	0.0354812	−	5.99990i	0.00591353	−	0.999983i
$37$	−6.51687			−1.07137			−0.535683	−	0.844419i	$-0.679946\pi$
$37$	−6.51687			−1.07137			−0.535683	+	0.844419i	$0.679946\pi$
$38$	−3.85739	−	0.785937i	−0.625751	−	0.127496i
$39$	−0.264482	+	4.14253i	−0.0423510	+	0.663336i
$40$		0			0
$41$	6.35642	−	3.66988i	0.992706	−	0.573139i	0.0866240	−	0.996241i	$-0.472392\pi$
$41$	6.35642	−	3.66988i	0.992706	−	0.573139i	0.906082	+	0.423102i	$0.139059\pi$
$42$	2.60684	−	0.690246i	0.402244	−	0.106507i
$43$	−3.90530	−	2.25473i	−0.595553	−	0.343843i	0.171737	−	0.985143i	$-0.445062\pi$
$43$	−3.90530	−	2.25473i	−0.595553	−	0.343843i	−0.767290	+	0.641300i	$0.778395\pi$
$44$	9.08040	−	6.83448i	1.36892	−	1.03034i
$45$		0			0
$46$	2.82719	−	0.945071i	0.416847	−	0.139343i
$47$	−4.67439	+	8.09628i	−0.681830	+	1.18096i	0.292592	+	0.956237i	$0.405482\pi$
$47$	−4.67439	+	8.09628i	−0.681830	+	1.18096i	−0.974422	+	0.224726i	$0.927851\pi$
$48$	1.23660	+	6.81695i	0.178488	+	0.983942i
$49$	−2.89400	−	5.01255i	−0.413428	−	0.716078i
$50$		0			0
$51$	−1.23987	+	1.86240i	−0.173616	+	0.260789i
$52$	−0.581429	−	4.75773i	−0.0806296	−	0.659778i
$53$		−	11.5954i		−	1.59275i	−0.604800	−	0.796377i	$-0.706747\pi$
$53$		−	11.5954i		−	1.59275i	0.604800	−	0.796377i	$-0.293253\pi$
$54$	6.79030	+	2.80925i	0.924042	+	0.382291i
$55$		0			0
$56$	−2.81166	+	1.33815i	−0.375724	+	0.178818i
$57$	2.67183	−	4.01335i	0.353893	−	0.531582i
$58$	5.97186	−	6.74609i	0.784143	−	0.885805i
$59$	3.66237	+	6.34341i	0.476800	+	0.825842i	0.999647	−	0.0265849i	$-0.00846323\pi$
$59$	3.66237	+	6.34341i	0.476800	+	0.825842i	−0.522846	+	0.852427i	$0.675130\pi$
$60$		0			0
$61$	2.48990	−	4.31263i	0.318799	−	0.552175i	−0.661439	−	0.749999i	$-0.730054\pi$
$61$	2.48990	−	4.31263i	0.318799	−	0.552175i	0.980238	+	0.197823i	$0.0633873\pi$
$62$	−1.44124	−	4.31149i	−0.183038	−	0.547560i
$63$	−0.420017	+	3.27592i	−0.0529172	+	0.412728i
$64$	−2.85419	−	7.47353i	−0.356774	−	0.934191i
$65$		0			0
$66$	3.56280	+	13.4556i	0.438550	+	1.65627i
$67$	−3.20457	+	1.85016i	−0.391500	+	0.226033i	−0.682810	−	0.730596i	$-0.739242\pi$
$67$	−3.20457	+	1.85016i	−0.391500	+	0.226033i	0.291310	+	0.956629i	$0.405909\pi$
$68$	1.01080	−	2.37754i	0.122578	−	0.288319i
$69$	−0.232621	+	3.64351i	−0.0280043	+	0.438627i
$70$		0			0
$71$	12.6950			1.50662			0.753311	−	0.657664i	$-0.228455\pi$
$71$	12.6950			1.50662			0.753311	+	0.657664i	$0.228455\pi$
$72$	−8.30429	−	1.74320i	−0.978670	−	0.205438i
$73$	9.86891			1.15507			0.577534	−	0.816366i	$-0.304015\pi$
$73$	9.86891			1.15507			0.577534	+	0.816366i	$0.304015\pi$
$74$	−1.83999	+	9.03070i	−0.213895	+	1.04980i
$75$		0			0
$76$	−2.17821	+	5.12344i	−0.249858	+	0.587699i
$77$	−5.41781	+	3.12798i	−0.617417	+	0.356466i
$78$	5.66581	+	1.53612i	0.641527	+	0.173931i
$79$	0.975531	+	0.563223i	0.109756	+	0.0633676i	0.553873	−	0.832601i	$-0.313149\pi$
$79$	0.975531	+	0.563223i	0.109756	+	0.0633676i	−0.444117	+	0.895969i	$0.646483\pi$
$80$		0			0
$81$	−6.32077	+	6.40686i	−0.702308	+	0.711873i
$82$	−3.29082	−	9.84453i	−0.363410	−	1.08715i
$83$	−5.76275	+	9.98138i	−0.632544	+	1.09560i	0.354485	+	0.935062i	$0.384656\pi$
$83$	−5.76275	+	9.98138i	−0.632544	+	1.09560i	−0.987030	+	0.160537i	$0.948677\pi$
$84$	−0.220480	−	3.80730i	−0.0240564	−	0.415410i
$85$		0			0
$86$	−4.22710	+	4.77514i	−0.455820	+	0.514916i
$87$	4.89714	+	9.88823i	0.525029	+	1.06013i
$88$	−6.90704	−	14.5128i	−0.736293	−	1.54707i
$89$		−	9.16815i		−	0.971822i	−0.874008	−	0.485911i	$-0.838488\pi$
$89$		−	9.16815i		−	0.971822i	0.874008	−	0.485911i	$-0.161512\pi$
$90$		0			0
$91$			2.63841i			0.276580i
$92$	−0.511387	−	4.18460i	−0.0533158	−	0.436274i
$93$	5.55638	+	0.354749i	0.576170	+	0.0367858i
$94$	9.89957	+	8.76343i	1.02106	+	0.903878i
$95$		0			0
$96$	9.79568	+	0.211108i	0.999768	+	0.0215462i
$97$	6.42344	−	11.1257i	0.652202	−	1.12965i	−0.330386	−	0.943846i	$-0.607179\pi$
$97$	6.42344	−	11.1257i	0.652202	−	1.12965i	0.982587	−	0.185801i	$-0.0594879\pi$
$98$	−7.76320	+	2.59507i	−0.784201	+	0.262142i
$99$	−16.9091	−	2.16798i	−1.69943	−	0.217890i
$100$		0			0
$101$	14.4999	+	8.37150i	1.44279	+	0.832995i	0.998035	−	0.0626572i	$-0.0199575\pi$
$101$	14.4999	+	8.37150i	1.44279	+	0.832995i	0.444755	+	0.895652i	$0.353291\pi$
$102$	2.23074	+	2.24397i	0.220876	+	0.222187i
$103$	−1.17657	+	0.679292i	−0.115931	+	0.0669327i	−0.556844	−	0.830617i	$-0.687988\pi$
$103$	−1.17657	+	0.679292i	−0.115931	+	0.0669327i	0.440913	+	0.897550i	$0.354655\pi$
$104$	−6.75715	−	0.537601i	−0.662593	−	0.0527162i
$105$		0			0
$106$	−16.0683	−	3.27389i	−1.56069	−	0.317988i
$107$	−2.97211			−0.287324			−0.143662	−	0.989627i	$-0.545888\pi$
$107$	−2.97211			−0.287324			−0.143662	+	0.989627i	$0.545888\pi$
$108$	5.81009	−	8.61643i	0.559076	−	0.829116i
$109$	−5.12076			−0.490480			−0.245240	−	0.969462i	$-0.578867\pi$
$109$	−5.12076			−0.490480			−0.245240	+	0.969462i	$0.578867\pi$
$110$		0			0
$111$	−9.39584	−	6.25515i	−0.891814	−	0.593712i
$112$	1.06048	+	4.27405i	0.100206	+	0.403860i
$113$	−7.24900	+	4.18521i	−0.681928	+	0.393711i	−0.800581	−	0.599224i	$-0.795476\pi$
$113$	−7.24900	+	4.18521i	−0.681928	+	0.393711i	0.118653	+	0.992936i	$0.462142\pi$
$114$	−4.80710	−	4.83561i	−0.450226	−	0.452897i
$115$		0			0
$116$	−7.66223	−	10.1802i	−0.711420	−	0.945205i
$117$	−4.35749	+	5.71873i	−0.402850	+	0.528697i
$118$	9.82438	−	3.28409i	0.904408	−	0.302325i
$119$	−0.711050	+	1.23157i	−0.0651818	+	0.112898i
$120$		0			0
$121$	−10.6455	−	18.4385i	−0.967770	−	1.67623i
$122$	−5.27319	−	4.66800i	−0.477412	−	0.422621i
$123$	12.6870	+	0.810007i	1.14395	+	0.0730359i
$124$	−6.38154	+	0.779870i	−0.573079	+	0.0700344i
$125$		0			0
$126$	4.42100	+	1.50697i	0.393854	+	0.134252i
$127$			5.14729i			0.456748i	0.973573	+	0.228374i	$0.0733410\pi$
$127$			5.14729i			0.456748i	−0.973573	+	0.228374i	$0.926659\pi$
$128$	−11.1622	+	1.84508i	−0.986612	+	0.163084i
$129$	−3.46638	−	6.99926i	−0.305198	−	0.616251i
$130$		0			0
$131$	−7.10028	−	12.2980i	−0.620354	−	1.07449i	−0.989420	−	0.145082i	$-0.953656\pi$
$131$	−7.10028	−	12.2980i	−0.620354	−	1.07449i	0.369065	−	0.929403i	$-0.379678\pi$
$132$	19.6519	−	1.13804i	1.71048	−	0.0990535i
$133$	1.53226	−	2.65396i	0.132864	−	0.230127i
$134$	1.65906	+	4.96309i	0.143321	+	0.428746i
$135$		0			0
$136$	−3.00927	−	2.07199i	−0.258042	−	0.177672i
$137$	−6.01263	−	3.47139i	−0.513693	−	0.296581i	0.220657	−	0.975351i	$-0.429180\pi$
$137$	−6.01263	−	3.47139i	−0.513693	−	0.296581i	−0.734351	+	0.678770i	$0.762513\pi$
$138$	4.98329	+	1.35107i	0.424205	+	0.115011i
$139$	10.3321	−	5.96523i	0.876356	−	0.505964i	0.00690070	−	0.999976i	$-0.497803\pi$
$139$	10.3321	−	5.96523i	0.876356	−	0.505964i	0.869455	+	0.494012i	$0.164470\pi$
$140$		0			0
$141$	−14.5105	+	7.18633i	−1.22201	+	0.605198i
$142$	3.58435	−	17.5920i	0.300792	−	1.47629i
$143$	−13.6185			−1.13884
$144$	−4.76028	+	11.0154i	−0.396690	+	0.917953i
$145$		0			0
$146$	2.78642	−	13.6758i	0.230606	−	1.13182i
$147$	0.638756	−	10.0047i	0.0526837	−	0.825176i
$148$	11.9947	+	5.09951i	0.985960	+	0.419177i
$149$	−4.98019	+	2.87531i	−0.407993	+	0.235555i	−0.689927	−	0.723879i	$-0.742357\pi$
$149$	−4.98019	+	2.87531i	−0.407993	+	0.235555i	0.281934	+	0.959434i	$0.409024\pi$
$150$		0			0
$151$	1.85084	+	1.06858i	0.150619	+	0.0869599i	0.573415	−	0.819265i	$-0.305618\pi$
$151$	1.85084	+	1.06858i	0.150619	+	0.0869599i	−0.422796	+	0.906225i	$0.638951\pi$
$152$	6.48477	+	4.46501i	0.525984	+	0.362160i
$153$	−3.57521	+	1.49509i	−0.289039	+	0.120871i
$154$	2.80489	+	8.39086i	0.226024	+	0.676155i
$155$		0			0
$156$	3.72837	−	7.41764i	0.298508	−	0.593887i
$157$	5.02788	+	8.70855i	0.401269	+	0.695018i	0.993879	−	0.110471i	$-0.0352360\pi$
$157$	5.02788	+	8.70855i	0.401269	+	0.695018i	−0.592611	+	0.805489i	$0.701903\pi$
$158$	1.05592	−	1.19281i	0.0840042	−	0.0948951i
$159$	11.1297	−	16.7180i	0.882646	−	1.32582i
$160$		0			0
$161$			2.32057i			0.182887i
$162$	7.09363	+	10.5679i	0.557329	+	0.830292i
$163$		−	18.2146i		−	1.42668i	−0.700819	−	0.713339i	$-0.747182\pi$
$163$		−	18.2146i		−	1.42668i	0.700819	−	0.713339i	$-0.252818\pi$
$164$	−14.5711	+	1.78069i	−1.13781	+	0.139049i
$165$		0			0
$166$	12.2046	+	10.8039i	0.947257	+	0.838543i
$167$	3.72227	+	6.44716i	0.288038	+	0.498896i	0.973341	−	0.229362i	$-0.0736638\pi$
$167$	3.72227	+	6.44716i	0.288038	+	0.498896i	−0.685304	+	0.728258i	$0.740330\pi$
$168$	−5.33818	−	0.769435i	−0.411850	−	0.0593632i
$169$	3.62824	−	6.28430i	0.279096	−	0.483408i
$170$		0			0
$171$	7.70435	−	3.22181i	0.589166	−	0.246378i
$172$	5.42361	+	7.20591i	0.413547	+	0.549445i
$173$	−7.50742	−	4.33441i	−0.570778	−	0.329539i	0.186682	−	0.982420i	$-0.440227\pi$
$173$	−7.50742	−	4.33441i	−0.570778	−	0.329539i	−0.757460	+	0.652881i	$0.773560\pi$
$174$	15.0852	−	3.99430i	1.14361	−	0.302807i
$175$		0			0
$176$	−22.0611	+	5.47380i	−1.66292	+	0.412603i
$177$	−0.808350	+	12.6610i	−0.0607593	+	0.951663i
$178$	−12.7047	−	2.58856i	−0.952257	−	0.194021i
$179$	1.10988			0.0829560			0.0414780	−	0.999139i	$-0.486793\pi$
$179$	1.10988			0.0829560			0.0414780	+	0.999139i	$0.486793\pi$
$180$		0			0
$181$	−12.6629			−0.941229			−0.470615	−	0.882339i	$-0.655968\pi$
$181$	−12.6629			−0.941229			−0.470615	+	0.882339i	$0.655968\pi$
$182$	3.65615	+	0.744936i	0.271012	+	0.0552183i
$183$	7.72930	−	3.82793i	0.571366	−	0.282969i
$184$	−5.94316	−	0.472840i	−0.438135	−	0.0348582i
$185$		0			0
$186$	2.06040	−	7.59955i	0.151076	−	0.557226i
$187$	−6.35694	−	3.67018i	−0.464865	−	0.268390i
$188$	14.9389	−	11.2440i	1.08953	−	0.820051i
$189$	−3.74993	+	4.31999i	−0.272767	+	0.314233i
$190$		0			0
$191$	−11.3827	+	19.7154i	−0.823625	+	1.42656i	0.0793411	+	0.996848i	$0.474718\pi$
$191$	−11.3827	+	19.7154i	−0.823625	+	1.42656i	−0.902966	+	0.429712i	$0.858615\pi$
$192$	3.05829	−	13.5147i	0.220713	−	0.975339i
$193$	−5.81319	−	10.0687i	−0.418443	−	0.724764i	0.577340	−	0.816504i	$-0.304091\pi$
$193$	−5.81319	−	10.0687i	−0.418443	−	0.724764i	−0.995783	+	0.0917396i	$0.970757\pi$
$194$	−13.6038	−	12.0425i	−0.976695	−	0.864602i
$195$		0			0
$196$	1.40422	+	11.4905i	0.100301	+	0.820750i
$197$		−	12.2003i		−	0.869238i	−0.900614	−	0.434619i	$-0.856883\pi$
$197$		−	12.2003i		−	0.869238i	0.900614	−	0.434619i	$-0.143117\pi$
$198$	−7.77843	+	22.8196i	−0.552789	+	1.62172i
$199$			7.07921i			0.501832i	0.968009	+	0.250916i	$0.0807318\pi$
$199$			7.07921i			0.501832i	−0.968009	+	0.250916i	$0.919268\pi$
$200$		0			0
$201$	−6.39612	−	0.408363i	−0.451147	−	0.0288037i
$202$	15.6947	−	17.7294i	1.10427	−	1.24744i
$203$	3.50682	+	6.07399i	0.246130	+	0.426310i
$204$	3.73940	−	2.45767i	0.261811	−	0.172071i
$205$		0			0
$206$	0.609128	+	1.82222i	0.0424400	+	0.126960i
$207$	−3.83257	+	5.02983i	−0.266382	+	0.349597i
$208$	−2.65281	+	9.21188i	−0.183939	+	0.638729i
$209$	13.6988	+	7.90899i	0.947564	+	0.547076i
$210$		0			0
$211$	5.61368	−	3.24106i	0.386462	−	0.223124i	−0.294164	−	0.955755i	$-0.595041\pi$
$211$	5.61368	−	3.24106i	0.386462	−	0.223124i	0.680626	+	0.732631i	$0.261708\pi$
$212$	−9.07353	+	21.3421i	−0.623173	+	1.46578i
$213$	18.3033	+	12.1852i	1.25412	+	0.834915i
$214$	−0.839153	+	4.11857i	−0.0573633	+	0.281540i
$215$		0			0
$216$	−10.2997	−	10.4841i	−0.700807	−	0.713351i
$217$	3.53890			0.240236
$218$	−1.44581	+	7.09606i	−0.0979227	+	0.480606i
$219$	14.2287	+	9.47257i	0.961488	+	0.640097i
$220$		0			0
$221$	−2.68100	+	1.54787i	−0.180343	+	0.104121i
$222$	−11.3209	+	11.2541i	−0.759807	+	0.755327i
$223$	13.5931	+	7.84799i	0.910263	+	0.525540i	0.880516	−	0.474017i	$-0.157197\pi$
$223$	13.5931	+	7.84799i	0.910263	+	0.525540i	0.0297470	+	0.999557i	$0.490530\pi$
$224$	6.22216	−	0.262800i	0.415735	−	0.0175590i
$225$		0			0
$226$	3.75292	+	11.2269i	0.249640	+	0.746803i
$227$	−0.0980022	+	0.169745i	−0.00650463	+	0.0112664i	−0.869259	−	0.494356i	$-0.835404\pi$
$227$	−0.0980022	+	0.169745i	−0.00650463	+	0.0112664i	0.862755	+	0.505623i	$0.168737\pi$
$228$	−8.05817	+	5.29610i	−0.533665	+	0.350743i
$229$	−0.825139	−	1.42918i	−0.0545267	−	0.0944431i	0.837474	−	0.546478i	$-0.184032\pi$
$229$	−0.825139	−	1.42918i	−0.0545267	−	0.0944431i	−0.892000	+	0.452035i	$0.850698\pi$
$230$		0			0
$231$	−10.8136	−	0.690399i	−0.711483	−	0.0454249i
$232$	−16.2705	+	7.74358i	−1.06821	+	0.508391i
$233$			20.2270i			1.32512i	0.749010	+	0.662559i	$0.230530\pi$
$233$			20.2270i			1.32512i	−0.749010	+	0.662559i	$0.769470\pi$
$234$	6.69438	+	7.65300i	0.437626	+	0.500292i
$235$		0			0
$236$	−1.77705	−	14.5413i	−0.115676	−	0.946558i
$237$	0.865891	+	1.74839i	0.0562456	+	0.113570i
$238$	1.50588	+	1.33306i	0.0976120	+	0.0864093i
$239$	−10.1646	−	17.6056i	−0.657494	−	1.13881i	−0.981262	−	0.192676i	$-0.938283\pi$
$239$	−10.1646	−	17.6056i	−0.657494	−	1.13881i	0.323769	−	0.946136i	$-0.395050\pi$
$240$		0			0
$241$	8.62268	−	14.9349i	0.555436	−	0.962043i	−0.442434	−	0.896801i	$-0.645885\pi$
$241$	8.62268	−	14.9349i	0.555436	−	0.962043i	0.997869	−	0.0652417i	$-0.0207818\pi$
$242$	−28.5567	+	9.54590i	−1.83569	+	0.613634i
$243$	−15.2627	+	3.17031i	−0.979101	+	0.203376i
$244$	−7.95749	+	5.98930i	−0.509426	+	0.383426i
$245$		0			0
$246$	4.70455	−	17.3522i	0.299951	−	1.10634i
$247$	5.77737	−	3.33556i	0.367605	−	0.212237i
$248$	−0.721085	+	9.06336i	−0.0457889	+	0.575524i
$249$	−17.8891	+	8.85957i	−1.13368	+	0.561452i
$250$		0			0
$251$	−9.92020			−0.626157			−0.313079	−	0.949727i	$-0.601360\pi$
$251$	−9.92020			−0.626157			−0.313079	+	0.949727i	$0.601360\pi$
$252$	3.33651	−	5.70088i	0.210180	−	0.359122i
$253$	−11.9780			−0.753048
$254$	7.13282	+	1.45330i	0.447553	+	0.0911883i
$255$		0			0
$256$	−0.594777	+	15.9889i	−0.0371735	+	0.999309i
$257$	15.0253	−	8.67485i	0.937252	−	0.541122i	0.0481539	−	0.998840i	$-0.484666\pi$
$257$	15.0253	−	8.67485i	0.937252	−	0.541122i	0.889098	+	0.457717i	$0.151333\pi$
$258$	−10.6779	+	2.82732i	−0.664776	+	0.176021i
$259$	−6.21330	−	3.58725i	−0.386076	−	0.222901i
$260$		0			0
$261$	−2.43055	+	18.9571i	−0.150447	+	1.17341i
$262$	−19.0466	+	6.36689i	−1.17671	+	0.393348i
$263$	4.80637	−	8.32487i	0.296373	−	0.513334i	−0.678930	−	0.734203i	$-0.737556\pi$
$263$	4.80637	−	8.32487i	0.296373	−	0.513334i	0.975303	+	0.220869i	$0.0708894\pi$
$264$	3.97154	−	27.5538i	0.244431	−	1.69582i
$265$		0			0
$266$	−3.24508	−	2.87265i	−0.198969	−	0.176134i
$267$	8.79995	−	13.2184i	0.538548	−	0.808952i
$268$	7.34599	−	0.897732i	0.448727	−	0.0548377i
$269$			1.34482i			0.0819953i	0.999159	+	0.0409977i	$0.0130536\pi$
$269$			1.34482i			0.0819953i	−0.999159	+	0.0409977i	$0.986946\pi$
$270$		0			0
$271$		−	21.7288i		−	1.31993i	−0.751297	−	0.659964i	$-0.770571\pi$
$271$		−	21.7288i		−	1.31993i	0.751297	−	0.659964i	$-0.229429\pi$
$272$	−3.72090	+	3.58506i	−0.225612	+	0.217376i
$273$	−2.53245	+	3.80398i	−0.153271	+	0.230228i
$274$	−6.50808	+	7.35183i	−0.393167	+	0.444140i
$275$		0			0
$276$	3.27923	−	6.52409i	0.197387	−	0.392704i
$277$	−6.95713	+	12.0501i	−0.418014	+	0.724021i	−0.995740	−	0.0922100i	$-0.970607\pi$
$277$	−6.95713	+	12.0501i	−0.418014	+	0.724021i	0.577726	+	0.816231i	$0.303940\pi$
$278$	−5.34908	−	16.0018i	−0.320817	−	0.959727i
$279$	7.67053	+	5.84470i	0.459223	+	0.349913i
$280$		0			0
$281$	10.0948	+	5.82824i	0.602206	+	0.347684i	0.769909	−	0.638154i	$-0.220302\pi$
$281$	10.0948	+	5.82824i	0.602206	+	0.347684i	−0.167703	+	0.985838i	$0.553635\pi$
$282$	5.86146	+	22.1369i	0.349045	+	1.31823i
$283$	−10.7624	+	6.21367i	−0.639758	+	0.369365i	−0.784521	−	0.620102i	$-0.787091\pi$
$283$	−10.7624	+	6.21367i	−0.639758	+	0.369365i	0.144763	+	0.989466i	$0.453758\pi$
$284$	−23.3660	−	9.93398i	−1.38652	−	0.589473i
$285$		0			0
$286$	−3.84509	+	18.8717i	−0.227365	+	1.11591i
$287$	8.08044			0.476973
$288$	13.9205	+	9.70665i	0.820275	+	0.571970i
$289$	15.3314			0.901847
$290$		0			0
$291$	19.9401	−	9.87530i	1.16891	−	0.578900i
$292$	−18.1644	−	7.72252i	−1.06299	−	0.451926i
$293$	8.27006	−	4.77472i	0.483142	−	0.278942i	−0.238583	−	0.971122i	$-0.576683\pi$
$293$	8.27006	−	4.77472i	0.483142	−	0.278942i	0.721725	+	0.692180i	$0.243350\pi$
$294$	−13.6836	−	3.70991i	−0.798045	−	0.216367i
$295$		0			0
$296$	10.4532	−	15.1818i	0.607582	−	0.882423i
$297$	−22.2982	−	19.3558i	−1.29387	−	1.12314i
$298$	2.57832	+	7.71308i	0.149358	+	0.446807i
$299$	−2.52581	+	4.37484i	−0.146072	+	0.253003i
$300$		0			0
$301$	−2.48226	−	4.29940i	−0.143075	−	0.247813i
$302$	2.00335	−	2.26308i	0.115280	−	0.130225i
$303$	12.8702	+	25.9873i	0.739374	+	1.49293i
$304$	8.01828	−	7.72555i	0.459880	−	0.443091i
$305$		0			0
$306$	1.06237	+	5.37646i	0.0607317	+	0.307351i
$307$		−	13.4685i		−	0.768689i	−0.923190	−	0.384345i	$-0.874427\pi$
$307$		−	13.4685i		−	0.768689i	0.923190	−	0.384345i	$-0.125573\pi$
$308$	12.4195	−	1.51775i	0.707667	−	0.0864820i
$309$	−2.34836	−	0.149932i	−0.133593	−	0.00852932i
$310$		0			0
$311$	5.13110	+	8.88732i	0.290958	+	0.503954i	0.974037	−	0.226391i	$-0.0726927\pi$
$311$	5.13110	+	8.88732i	0.290958	+	0.503954i	−0.683079	+	0.730345i	$0.739359\pi$
$312$	−9.22626	−	7.26088i	−0.522334	−	0.411066i
$313$	0.802903	−	1.39067i	0.0453827	−	0.0786052i	−0.842442	−	0.538787i	$-0.818883\pi$
$313$	0.802903	−	1.39067i	0.0453827	−	0.0786052i	0.887824	+	0.460182i	$0.152216\pi$
$314$	13.4874	−	4.50855i	0.761138	−	0.254432i
$315$		0			0
$316$	−1.35480	−	1.80001i	−0.0762135	−	0.101259i
$317$	3.86467	+	2.23127i	0.217061	+	0.125320i	0.604589	−	0.796538i	$-0.293337\pi$
$317$	3.86467	+	2.23127i	0.217061	+	0.125320i	−0.387528	+	0.921858i	$0.626671\pi$
$318$	−20.0244	−	20.1432i	−1.12291	−	1.12957i
$319$	−31.3517	+	18.1009i	−1.75536	+	1.01346i
$320$		0			0
$321$	−4.28510	−	2.85274i	−0.239171	−	0.159225i
$322$	3.21572	+	0.655198i	0.179205	+	0.0365128i
$323$	3.59573			0.200072
$324$	16.6472	−	6.84618i	0.924845	−	0.380343i
$325$		0			0
$326$	−25.2408	−	5.14277i	−1.39796	−	0.284832i
$327$	−7.38297	−	4.91511i	−0.408279	−	0.271806i
$328$	−1.64647	+	20.6946i	−0.0909110	+	1.14267i
$329$	−8.91330	+	5.14610i	−0.491406	+	0.283713i
$330$		0			0
$331$	10.2107	+	5.89512i	0.561228	+	0.324025i	0.753638	−	0.657289i	$-0.228297\pi$
$331$	10.2107	+	5.89512i	0.561228	+	0.324025i	−0.192410	+	0.981315i	$0.561630\pi$
$332$	18.4172	−	13.8620i	1.01078	−	0.760775i
$333$	−7.54274	−	18.0370i	−0.413339	−	0.988421i
$334$	9.98506	−	3.33780i	0.546358	−	0.182636i
$335$		0			0
$336$	−2.57344	+	7.18010i	−0.140393	+	0.391707i
$337$	5.28111	+	9.14715i	0.287680	+	0.498277i	0.973256	−	0.229725i	$-0.0737826\pi$
$337$	5.28111	+	9.14715i	0.287680	+	0.498277i	−0.685575	+	0.728002i	$0.740449\pi$
$338$	−7.68402	−	6.80214i	−0.417955	−	0.369988i
$339$	−14.4685	−	0.923749i	−0.785823	−	0.0501712i
$340$		0			0
$341$			18.2665i			0.989186i
$342$	−2.28934	−	11.5859i	−0.123793	−	0.626494i
$343$		−	14.0785i		−	0.760166i
$344$	11.5168	−	5.48120i	0.620947	−	0.295526i
$345$		0			0
$346$	−8.12604	+	9.17956i	−0.436859	+	0.493496i
$347$	−11.6546	−	20.1864i	−0.625652	−	1.08366i	−0.988414	−	0.151779i	$-0.951500\pi$
$347$	−11.6546	−	20.1864i	−0.625652	−	1.08366i	0.362763	−	0.931882i	$-0.381834\pi$
$348$	−1.27587	−	22.0320i	−0.0683939	−	1.18104i
$349$	−2.84689	+	4.93095i	−0.152390	+	0.263948i	−0.932106	−	0.362186i	$-0.882030\pi$
$349$	−2.84689	+	4.93095i	−0.152390	+	0.263948i	0.779715	+	0.626134i	$0.215364\pi$
$350$		0			0
$351$	−11.7716	+	4.06262i	−0.628320	+	0.216847i
$352$	1.35648	+	32.1165i	0.0723004	+	1.71182i
$353$	1.31873	+	0.761369i	0.0701889	+	0.0405236i	0.534684	−	0.845052i	$-0.320431\pi$
$353$	1.31873	+	0.761369i	0.0701889	+	0.0405236i	−0.464495	+	0.885576i	$0.653764\pi$
$354$	17.3167	+	4.69492i	0.920373	+	0.249532i
$355$		0			0
$356$	−7.17416	+	16.8746i	−0.380230	+	0.894351i
$357$	−2.20729	+	1.09316i	−0.116822	+	0.0578560i
$358$	0.313366	−	1.53800i	0.0165619	−	0.0812860i
$359$	−9.46115			−0.499341			−0.249670	−	0.968331i	$-0.580322\pi$
$359$	−9.46115			−0.499341			−0.249670	+	0.968331i	$0.580322\pi$
$360$		0			0
$361$	11.2514			0.592181
$362$	−3.57529	+	17.5476i	−0.187913	+	0.922280i
$363$	2.34964	−	36.8021i	0.123324	−	1.93161i
$364$	2.06458	−	4.85616i	0.108213	−	0.254532i
$365$		0			0
$366$	−3.12221	−	11.7916i	−0.163201	−	0.616357i
$367$	7.04288	+	4.06621i	0.367635	+	0.212254i	0.672425	−	0.740165i	$-0.265253\pi$
$367$	7.04288	+	4.06621i	0.367635	+	0.212254i	−0.304790	+	0.952420i	$0.598586\pi$
$368$	−2.33324	+	8.10218i	−0.121629	+	0.422356i
$369$	17.5143	+	13.3453i	0.911758	+	0.694730i
$370$		0			0
$371$	6.38278	−	11.0553i	0.331377	−	0.573963i
$372$	−9.94928	−	5.00086i	−0.515846	−	0.259282i
$373$	5.80775	+	10.0593i	0.300714	+	0.520851i	0.976298	−	0.216432i	$-0.0694418\pi$
$373$	5.80775	+	10.0593i	0.300714	+	0.520851i	−0.675584	+	0.737283i	$0.736108\pi$
$374$	−6.88076	+	7.77283i	−0.355796	+	0.401923i
$375$		0			0
$376$	−11.3633	−	23.8762i	−0.586020	−	1.23132i
$377$			15.2679i			0.786336i
$378$	4.92762	+	6.41616i	0.253450	+	0.330011i
$379$			0.194316i			0.00998136i	0.999988	+	0.00499068i	$0.00158859\pi$
$379$			0.194316i			0.00998136i	−0.999988	+	0.00499068i	$0.998411\pi$
$380$		0			0
$381$	−4.94057	+	7.42123i	−0.253113	+	0.380201i
$382$	24.1067	+	21.3400i	1.23341	+	1.09185i
$383$	−9.25031	−	16.0220i	−0.472669	−	0.818686i	0.526842	−	0.849963i	$-0.323376\pi$
$383$	−9.25031	−	16.0220i	−0.472669	−	0.818686i	−0.999511	+	0.0312769i	$0.990043\pi$
$384$	−17.8644	−	8.05377i	−0.911639	−	0.410992i
$385$		0			0
$386$	−15.5940	+	5.21275i	−0.793714	+	0.265322i
$387$	1.72043	−	13.4185i	0.0874546	−	0.682102i
$388$	−20.5288	+	15.4512i	−1.04219	+	0.784417i
$389$	20.3869	+	11.7704i	1.03366	+	0.596783i	0.918031	−	0.396509i	$-0.129779\pi$
$389$	20.3869	+	11.7704i	1.03366	+	0.596783i	0.115628	+	0.993293i	$0.463112\pi$
$390$		0			0
$391$	−2.35803	+	1.36141i	−0.119251	+	0.0688495i
$392$	16.3193	+	1.29837i	0.824251	+	0.0655777i
$393$	1.56716	−	24.5461i	0.0790526	−	1.23819i
$394$	−16.9065	−	3.44468i	−0.851739	−	0.173541i
$395$		0			0
$396$	29.4259	+	17.2218i	1.47871	+	0.865430i
$397$	23.4091			1.17487			0.587435	−	0.809272i	$-0.300138\pi$
$397$	23.4091			1.17487			0.587435	+	0.809272i	$0.300138\pi$
$398$	9.80996	+	1.99877i	0.491729	+	0.100189i
$399$	4.75655	−	2.35568i	0.238125	−	0.117931i
$400$		0			0
$401$	25.9256	−	14.9681i	1.29466	−	0.747474i	0.315185	−	0.949030i	$-0.397933\pi$
$401$	25.9256	−	14.9681i	1.29466	−	0.747474i	0.979477	+	0.201557i	$0.0646000\pi$
$402$	−2.37178	+	8.74807i	−0.118294	+	0.436314i
$403$	6.67166	+	3.85189i	0.332339	+	0.191876i
$404$	−20.1372	−	26.7546i	−1.00186	−	1.33109i
$405$		0			0
$406$	9.40711	−	3.14460i	0.466867	−	0.156064i
$407$	18.5161	−	32.0708i	0.917809	−	1.58969i
$408$	−2.34990	−	5.87576i	−0.116337	−	0.290893i
$409$	−1.04012	−	1.80153i	−0.0514304	−	0.0890800i	0.839164	−	0.543878i	$-0.183045\pi$
$409$	−1.04012	−	1.80153i	−0.0514304	−	0.0890800i	−0.890594	+	0.454798i	$0.849711\pi$
$410$		0			0
$411$	−5.33686	−	10.7761i	−0.263248	−	0.531547i
$412$	2.69710	−	0.329605i	0.132877	−	0.0162385i
$413$			8.06390i			0.396799i
$414$	5.88795	+	6.73109i	0.289377	+	0.330815i
$415$		0			0
$416$	12.0163	+	6.27702i	0.589147	+	0.307756i
$417$	20.6222	+	1.31663i	1.00987	+	0.0644757i
$418$	14.8276	−	16.7499i	0.725240	−	0.819265i
$419$	4.89021	+	8.47010i	0.238903	+	0.413791i	0.960400	−	0.278626i	$-0.0898790\pi$
$419$	4.89021	+	8.47010i	0.238903	+	0.413791i	−0.721497	+	0.692417i	$0.756546\pi$
$420$		0			0
$421$	1.05097	−	1.82034i	0.0512212	−	0.0887177i	−0.839278	−	0.543703i	$-0.817022\pi$
$421$	1.05097	−	1.82034i	0.0512212	−	0.0887177i	0.890499	+	0.454985i	$0.150355\pi$
$422$	−2.90629	−	8.69420i	−0.141476	−	0.423227i
$423$	−27.8186	−	3.56672i	−1.35259	−	0.173420i
$424$	27.0129	+	18.5994i	1.31186	+	0.903266i
$425$		0			0
$426$	22.0534	−	21.9233i	1.06849	−	1.06219i
$427$	4.74783	−	2.74116i	0.229764	−	0.132654i
$428$	5.47035	+	2.32570i	0.264419	+	0.112417i
$429$	−19.6348	−	13.0716i	−0.947976	−	0.631101i
$430$		0			0
$431$	3.84204			0.185064			0.0925322	−	0.995710i	$-0.470504\pi$
$431$	3.84204			0.185064			0.0925322	+	0.995710i	$0.470504\pi$
$432$	−17.4363	+	11.3126i	−0.838904	+	0.544280i
$433$	6.66853			0.320469			0.160235	−	0.987079i	$-0.448775\pi$
$433$	6.66853			0.320469			0.160235	+	0.987079i	$0.448775\pi$
$434$	0.999182	−	4.90400i	0.0479623	−	0.235399i
$435$		0			0
$436$	9.42509	+	4.00704i	0.451380	+	0.191903i
$437$	5.08140	−	2.93375i	0.243077	−	0.140340i
$438$	17.1439	−	17.0428i	0.819168	−	0.814339i
$439$	33.5536	+	19.3722i	1.60143	+	0.924585i	0.991202	+	0.132357i	$0.0422544\pi$
$439$	33.5536	+	19.3722i	1.60143	+	0.924585i	0.610225	+	0.792228i	$0.291079\pi$
$440$		0			0
$441$	10.5239	−	13.8114i	0.501136	−	0.657687i
$442$	1.38799	+	4.15220i	0.0660202	+	0.197500i
$443$	11.7099	−	20.2821i	0.556354	−	0.963633i	−0.441443	−	0.897289i	$-0.645533\pi$
$443$	11.7099	−	20.2821i	0.556354	−	0.963633i	0.997797	−	0.0663436i	$-0.0211333\pi$
$444$	12.3989	+	18.8653i	0.588428	+	0.895309i
$445$		0			0
$446$	14.7132	−	16.6207i	0.696691	−	0.787015i
$447$	−9.94014	−	0.634632i	−0.470152	−	0.0300171i
$448$	1.39261	−	8.69651i	0.0657946	−	0.410871i
$449$		−	15.7865i		−	0.745011i	−0.928030	−	0.372506i	$-0.878499\pi$
$449$		−	15.7865i		−	0.745011i	0.928030	−	0.372506i	$-0.121501\pi$
$450$		0			0
$451$			41.7083i			1.96397i
$452$	16.6172	−	2.03074i	0.781608	−	0.0955181i
$453$	1.64282	+	3.31716i	0.0771864	+	0.155854i
$454$	0.207552	+	0.183732i	0.00974091	+	0.00862297i
$455$		0			0
$456$	5.06387	+	12.6619i	0.237137	+	0.592946i
$457$	−4.20812	+	7.28867i	−0.196847	+	0.340950i	−0.947505	−	0.319742i	$-0.896404\pi$
$457$	−4.20812	+	7.28867i	−0.196847	+	0.340950i	0.750657	+	0.660692i	$0.229737\pi$
$458$	−2.21345	+	0.739911i	−0.103428	+	0.0345738i
$459$	−6.58969	−	1.27605i	−0.307580	−	0.0595611i
$460$		0			0
$461$	21.4798	+	12.4014i	1.00042	+	0.577590i	0.908371	−	0.418165i	$-0.137326\pi$
$461$	21.4798	+	12.4014i	1.00042	+	0.577590i	0.0920445	+	0.995755i	$0.470660\pi$
$462$	−4.00986	+	14.7900i	−0.186556	+	0.688091i
$463$	−17.9437	+	10.3598i	−0.833913	+	0.481460i	−0.855191	−	0.518314i	$-0.826560\pi$
$463$	−17.9437	+	10.3598i	−0.833913	+	0.481460i	0.0212774	+	0.999774i	$0.493227\pi$
$464$	6.13675	+	24.7330i	0.284892	+	1.14820i
$465$		0			0
$466$	28.0295	+	5.71097i	1.29844	+	0.264555i
$467$	1.59588			0.0738487			0.0369243	−	0.999318i	$-0.488244\pi$
$467$	1.59588			0.0738487			0.0369243	+	0.999318i	$0.488244\pi$
$468$	12.4952	−	7.11592i	0.577591	−	0.328934i
$469$	−4.07373			−0.188107
$470$		0			0
$471$	−1.10974	+	17.3817i	−0.0511342	+	0.800907i
$472$	−20.6522	−	1.64310i	−0.950596	−	0.0756298i
$473$	22.1919	−	12.8125i	1.02039	−	0.589120i
$474$	2.66730	−	0.706255i	0.122513	−	0.0324394i
$475$		0			0
$476$	2.27245	−	1.71039i	0.104158	−	0.0783955i
$477$	32.0931	−	13.4207i	1.46944	−	0.614494i
$478$	−27.2668	+	9.11471i	−1.24715	+	0.416897i
$479$	−2.98947	+	5.17791i	−0.136592	+	0.236585i	−0.926205	−	0.377021i	$-0.876948\pi$
$479$	−2.98947	+	5.17791i	−0.136592	+	0.236585i	0.789612	+	0.613606i	$0.210282\pi$
$480$		0			0
$481$	−7.80904	−	13.5257i	−0.356062	−	0.616717i
$482$	−18.2614	−	16.1656i	−0.831784	−	0.736322i
$483$	−2.22738	+	3.34574i	−0.101349	+	0.152237i
$484$	5.16538	+	42.2674i	0.234790	+	1.92125i
$485$		0			0
$486$	0.0839300	+	22.0452i	0.00380714	+	0.999993i
$487$		−	16.5971i		−	0.752086i	−0.926602	−	0.376043i	$-0.877284\pi$
$487$		−	16.5971i		−	0.752086i	0.926602	−	0.376043i	$-0.122716\pi$
$488$	6.05289	+	12.7181i	0.274002	+	0.575720i
$489$	17.4831	−	26.2613i	0.790613	−	1.18758i
$490$		0			0
$491$	6.66941	+	11.5518i	0.300986	+	0.521323i	0.976360	−	0.216153i	$-0.0693509\pi$
$491$	6.66941	+	11.5518i	0.300986	+	0.521323i	−0.675373	+	0.737476i	$0.736018\pi$
$492$	−22.7174	−	11.4186i	−1.02418	−	0.514789i
$493$	−4.11469	+	7.12685i	−0.185316	+	0.320977i
$494$	−2.99103	−	8.94772i	−0.134573	−	0.402577i
$495$		0			0
$496$	12.3559	+	3.55822i	0.554796	+	0.159769i
$497$	12.1037	+	6.98806i	0.542924	+	0.313457i
$498$	7.22622	+	27.2911i	0.323815	+	1.22294i
$499$	35.7135	−	20.6192i	1.59875	−	0.923041i	0.607026	−	0.794682i	$-0.292362\pi$
$499$	35.7135	−	20.6192i	1.59875	−	0.923041i	0.991728	−	0.128359i	$-0.0409711\pi$
$500$		0			0
$501$	−0.821570	+	12.8681i	−0.0367050	+	0.574905i
$502$	−2.80090	+	13.7468i	−0.125010	+	0.613551i
$503$	24.1634			1.07739			0.538696	−	0.842500i	$-0.318917\pi$
$503$	24.1634			1.07739			0.538696	+	0.842500i	$0.318917\pi$
$504$	−6.95791	−	6.23315i	−0.309930	−	0.277646i
$505$		0			0
$506$	−3.38189	+	16.5984i	−0.150343	+	0.737887i
$507$	11.2630	−	5.57801i	0.500208	−	0.247728i
$508$	4.02781	−	9.47393i	0.178705	−	0.420338i
$509$	−10.2084	+	5.89380i	−0.452478	+	0.261238i	−0.708876	−	0.705333i	$-0.750797\pi$
$509$	−10.2084	+	5.89380i	−0.452478	+	0.261238i	0.256398	+	0.966571i	$0.417464\pi$
$510$		0			0
$511$	9.40921	+	5.43241i	0.416239	+	0.240316i
$512$	21.9886	+	5.33857i	0.971769	+	0.235934i
$513$	14.2003	+	2.74981i	0.626960	+	0.121407i
$514$	−7.77883	−	23.2705i	−0.343109	−	1.02642i
$515$		0			0
$516$	0.903109	+	15.5951i	0.0397572	+	0.686535i
$517$	−26.5623	−	46.0072i	−1.16821	−	2.02339i
$518$	−6.72529	+	7.59721i	−0.295492	+	0.333802i
$519$	−6.66365	−	13.4551i	−0.292502	−	0.590615i
$520$		0			0
$521$		−	32.5010i		−	1.42389i	−0.702234	−	0.711947i	$-0.747814\pi$
$521$		−	32.5010i		−	1.42389i	0.702234	−	0.711947i	$-0.252186\pi$
$522$	25.5834	+	8.72051i	1.11975	+	0.381686i
$523$		−	11.2435i		−	0.491645i	−0.969315	−	0.245822i	$-0.920942\pi$
$523$		−	11.2435i		−	0.491645i	0.969315	−	0.245822i	$-0.0790580\pi$
$524$	3.44519	+	28.1914i	0.150504	+	1.23155i
$525$		0			0
$526$	−10.1791	−	9.01086i	−0.443829	−	0.392892i
$527$	2.07616	+	3.59602i	0.0904391	+	0.156645i
$528$	−37.0611	−	13.2831i	−1.61288	−	0.578075i
$529$	9.27846	−	16.0708i	0.403411	−	0.698729i
$530$		0			0
$531$	−13.3180	+	17.4785i	−0.577953	+	0.758501i
$532$	−4.89698	+	3.68577i	−0.212311	+	0.159799i
$533$	15.2336	+	8.79510i	0.659839	+	0.380958i
$534$	−15.8327	−	15.9266i	−0.685147	−	0.689211i
$535$		0			0
$536$	0.830062	−	10.4331i	0.0358532	−	0.450642i
$537$	1.60019	+	1.06530i	0.0690533	+	0.0459712i
$538$	1.86358	+	0.379701i	0.0803446	+	0.0163701i
$539$	32.8903			1.41669
$540$		0			0
$541$	−8.40855			−0.361512			−0.180756	−	0.983528i	$-0.557854\pi$
$541$	−8.40855			−0.361512			−0.180756	+	0.983528i	$0.557854\pi$
$542$	−30.1105	−	6.13496i	−1.29336	−	0.263519i
$543$	−18.2571	−	12.1544i	−0.783487	−	0.521595i
$544$	3.91739	+	6.16842i	0.167957	+	0.264469i
$545$		0			0
$546$	4.55632	+	4.58335i	0.194993	+	0.196149i
$547$	−3.67716	−	2.12301i	−0.157224	−	0.0907734i	0.419324	−	0.907837i	$-0.362267\pi$
$547$	−3.67716	−	2.12301i	−0.157224	−	0.0907734i	−0.576548	+	0.817063i	$0.695601\pi$
$548$	8.35023	+	11.0943i	0.356704	+	0.473923i
$549$	14.8181	+	1.89988i	0.632420	+	0.0810848i
$550$		0			0
$551$	8.86688	−	15.3579i	0.377742	−	0.654268i
$552$	−8.11483	−	6.38620i	−0.345390	−	0.271815i
$553$	0.620060	+	1.07398i	0.0263676	+	0.0456701i
$554$	14.7340	+	13.0431i	0.625990	+	0.554146i
$555$		0			0
$556$	−23.6847	+	2.89444i	−1.00446	+	0.122752i
$557$			21.0221i			0.890734i	0.895348	+	0.445367i	$0.146927\pi$
$557$			21.0221i			0.890734i	−0.895348	+	0.445367i	$0.853073\pi$
$558$	10.2650	−	8.97918i	0.434551	−	0.380119i
$559$		−	10.8072i		−	0.457095i
$560$		0			0
$561$	−5.64248	−	11.3932i	−0.238225	−	0.481021i
$562$	10.9266	−	12.3433i	0.460913	−	0.520669i
$563$	10.9277	+	18.9272i	0.460546	+	0.797688i	0.998988	−	0.0449739i	$-0.0143205\pi$
$563$	10.9277	+	18.9272i	0.460546	+	0.797688i	−0.538443	+	0.842662i	$0.680987\pi$
$564$	32.3309	−	1.87228i	1.36138	−	0.0788373i
$565$		0			0
$566$	5.57187	+	16.6683i	0.234203	+	0.700621i
$567$	−9.55304	+	2.62911i	−0.401190	+	0.110412i
$568$	−20.3632	+	29.5745i	−0.854420	+	1.24092i
$569$	−12.7253	−	7.34697i	−0.533473	−	0.308001i	0.208956	−	0.977925i	$-0.432993\pi$
$569$	−12.7253	−	7.34697i	−0.533473	−	0.308001i	−0.742430	+	0.669924i	$0.766327\pi$
$570$		0			0
$571$	−15.5333	+	8.96816i	−0.650049	+	0.375306i	−0.788475	−	0.615067i	$-0.789129\pi$
$571$	−15.5333	+	8.96816i	−0.650049	+	0.375306i	0.138426	+	0.990373i	$0.455796\pi$
$572$	25.0657	+	10.6566i	1.04805	+	0.445575i
$573$	−35.3350	+	17.4996i	−1.47614	+	0.731057i
$574$	2.28146	−	11.1974i	0.0952261	−	0.467371i
$575$		0			0
$576$	17.3813	−	16.5497i	0.724220	−	0.689569i
$577$	−38.2696			−1.59318			−0.796592	−	0.604517i	$-0.793366\pi$
$577$	−38.2696			−1.59318			−0.796592	+	0.604517i	$0.793366\pi$
$578$	4.32871	−	21.2454i	0.180051	−	0.883691i
$579$	1.28307	−	20.0966i	0.0533227	−	0.835185i
$580$		0			0
$581$	−10.9886	+	6.34429i	−0.455885	+	0.263206i
$582$	−8.05469	−	30.4200i	−0.333878	−	1.26095i
$583$	57.0634	+	32.9456i	2.36333	+	1.36447i
$584$	−15.8300	+	22.9907i	−0.655050	+	0.951364i
$585$		0			0
$586$	−4.28154	−	12.8083i	−0.176869	−	0.529105i
$587$	−4.20276	+	7.27939i	−0.173466	+	0.300453i	−0.939629	−	0.342194i	$-0.888830\pi$
$587$	−4.20276	+	7.27939i	−0.173466	+	0.300453i	0.766163	+	0.642646i	$0.222163\pi$
$588$	−9.00446	+	17.9145i	−0.371338	+	0.738782i
$589$	−4.47399	−	7.74918i	−0.184348	−	0.319299i
$590$		0			0
$591$	11.7104	−	17.5901i	0.481700	−	0.723561i
$592$	−18.0866	−	18.7720i	−0.743356	−	0.771523i
$593$		−	35.1831i		−	1.44480i	−0.691477	−	0.722398i	$-0.743040\pi$
$593$		−	35.1831i		−	1.44480i	0.691477	−	0.722398i	$-0.256960\pi$
$594$	−33.1179	+	25.4346i	−1.35884	+	1.04359i
$595$		0			0
$596$	11.4163	−	1.39516i	0.467631	−	0.0571478i
$597$	−6.79490	+	10.2066i	−0.278097	+	0.417729i
$598$	5.34925	+	4.73533i	0.218747	+	0.193642i
$599$	−7.34116	−	12.7153i	−0.299952	−	0.519532i	0.676173	−	0.736743i	$-0.263637\pi$
$599$	−7.34116	−	12.7153i	−0.299952	−	0.519532i	−0.976125	+	0.217211i	$0.930304\pi$
$600$		0			0
$601$	13.6252	−	23.5995i	0.555783	−	0.962644i	−0.442059	−	0.896986i	$-0.645752\pi$
$601$	13.6252	−	23.5995i	0.555783	−	0.962644i	0.997842	−	0.0656584i	$-0.0209148\pi$
$602$	−6.65871	+	2.22587i	−0.271389	+	0.0907195i
$603$	−8.82978	−	6.72801i	−0.359577	−	0.273986i
$604$	−2.57041	−	3.41509i	−0.104589	−	0.138958i
$605$		0			0
$606$	39.6456	−	10.4975i	1.61049	−	0.426430i
$607$	−6.78317	+	3.91627i	−0.275320	+	0.158956i	−0.631303	−	0.775536i	$-0.717480\pi$
$607$	−6.78317	+	3.91627i	−0.275320	+	0.158956i	0.355983	+	0.934493i	$0.384146\pi$
$608$	−8.44172	−	13.2925i	−0.342357	−	0.539083i
$609$	−0.774017	+	12.1233i	−0.0313647	+	0.491261i
$610$		0			0
$611$	−22.4049			−0.906406
$612$	7.75034	+	0.0458326i	0.313289	+	0.00185267i
$613$	−1.17677			−0.0475293			−0.0237646	−	0.999718i	$-0.507565\pi$
$613$	−1.17677			−0.0475293			−0.0237646	+	0.999718i	$0.507565\pi$
$614$	−18.6639	−	3.80274i	−0.753214	−	0.153466i
$615$		0			0
$616$	1.40335	−	17.6388i	0.0565425	−	0.710686i
$617$	−35.3790	+	20.4261i	−1.42430	+	0.822322i	−0.996663	−	0.0816263i	$-0.973989\pi$
$617$	−35.3790	+	20.4261i	−1.42430	+	0.822322i	−0.427641	+	0.903949i	$0.640655\pi$
$618$	−0.870809	+	3.21189i	−0.0350291	+	0.129201i
$619$	−42.7230	−	24.6661i	−1.71718	−	0.991416i	−0.923965	−	0.382478i	$-0.875071\pi$
$619$	−42.7230	−	24.6661i	−1.71718	−	0.991416i	−0.793218	−	0.608938i	$-0.791596\pi$
$620$		0			0
$621$	−10.3535	+	3.57322i	−0.415473	+	0.143389i
$622$	13.7643	−	4.60111i	0.551897	−	0.184488i
$623$	5.04667	−	8.74109i	0.202190	−	0.350204i
$624$	−12.6667	+	10.7352i	−0.507073	+	0.429751i
$625$		0			0
$626$	−1.70041	−	1.50526i	−0.0679622	−	0.0601624i
$627$	12.1592	+	24.5516i	0.485590	+	0.980496i
$628$	−2.43962	−	19.9630i	−0.0973515	−	0.796611i
$629$		−	8.41813i		−	0.335653i
$630$		0			0
$631$		−	27.6752i		−	1.10173i	−0.834594	−	0.550866i	$-0.814297\pi$
$631$		−	27.6752i		−	1.10173i	0.834594	−	0.550866i	$-0.185703\pi$
$632$	−2.87687	+	1.36919i	−0.114436	+	0.0544633i
$633$	11.2045	+	0.715359i	0.445341	+	0.0284329i
$634$	4.18312	−	4.72545i	0.166133	−	0.187672i
$635$		0			0
$636$	−33.5670	+	22.0614i	−1.33102	+	0.874791i
$637$	6.93564	−	12.0129i	0.274800	−	0.475968i
$638$	16.2313	+	48.5561i	0.642602	+	1.92235i
$639$	14.6934	+	35.1365i	0.581264	+	1.38998i
$640$		0			0
$641$	−13.0424	−	7.53005i	−0.515145	−	0.297419i	0.219801	−	0.975545i	$-0.429459\pi$
$641$	−13.0424	−	7.53005i	−0.515145	−	0.297419i	−0.734946	+	0.678126i	$0.762793\pi$
$642$	−5.16304	+	5.13259i	−0.203769	+	0.202567i
$643$	−41.0665	+	23.7098i	−1.61951	+	0.935022i	−0.632458	+	0.774595i	$0.717954\pi$
$643$	−41.0665	+	23.7098i	−1.61951	+	0.935022i	−0.987048	+	0.160427i	$0.948713\pi$
$644$	1.81587	−	4.27117i	0.0715554	−	0.168308i
$645$		0			0
$646$	1.01523	−	4.98276i	0.0399437	−	0.196044i
$647$	−19.7634			−0.776977			−0.388489	−	0.921453i	$-0.627003\pi$
$647$	−19.7634			−0.776977			−0.388489	+	0.921453i	$0.627003\pi$
$648$	−4.78682	−	25.0017i	−0.188044	−	0.982161i
$649$	−41.6229			−1.63384
$650$		0			0
$651$	5.10228	+	3.39677i	0.199974	+	0.133130i
$652$	−14.2531	+	33.5252i	−0.558195	+	1.31295i
$653$	−30.2658	+	17.4740i	−1.18439	+	0.683809i	−0.957027	−	0.290000i	$-0.906345\pi$
$653$	−30.2658	+	17.4740i	−1.18439	+	0.683809i	−0.227366	+	0.973809i	$0.573011\pi$
$654$	−8.89560	+	8.84315i	−0.347846	+	0.345795i
$655$		0			0
$656$	28.2125	+	8.12455i	1.10151	+	0.317211i
$657$	11.4225	+	27.3146i	0.445632	+	1.06564i
$658$	4.61456	+	13.8045i	0.179894	+	0.538155i
$659$	−17.4893	+	30.2924i	−0.681288	+	1.18003i	0.293300	+	0.956021i	$0.405247\pi$
$659$	−17.4893	+	30.2924i	−0.681288	+	1.18003i	−0.974588	+	0.224005i	$0.928087\pi$
$660$		0			0
$661$	17.7487	+	30.7417i	0.690346	+	1.19571i	0.971725	+	0.236117i	$0.0758749\pi$
$661$	17.7487	+	30.7417i	0.690346	+	1.19571i	−0.281379	+	0.959597i	$0.590792\pi$
$662$	11.0520	−	12.4849i	0.429549	−	0.485239i
$663$	−5.35110	−	0.341643i	−0.207819	−	0.0132683i
$664$	−14.0091	−	29.4354i	−0.543660	−	1.14231i
$665$		0			0
$666$	−27.1243	+	5.35967i	−1.05104	+	0.207683i
$667$			13.4287i			0.519960i
$668$	−1.80611	−	14.7791i	−0.0698807	−	0.571821i
$669$	12.0654	+	24.3622i	0.466475	+	0.941898i
$670$		0			0
$671$	14.1489	+	24.5066i	0.546211	+	0.946065i
$672$	9.22318	+	5.59337i	0.355792	+	0.215769i
$673$	−23.9454	+	41.4746i	−0.923027	+	1.59873i	−0.128322	+	0.991733i	$0.540959\pi$
$673$	−23.9454	+	41.4746i	−0.923027	+	1.59873i	−0.794704	+	0.606997i	$0.792374\pi$
$674$	14.1667	−	4.73563i	0.545680	−	0.182409i
$675$		0			0
$676$	−11.5955	+	8.72753i	−0.445982	+	0.335674i
$677$	0.0747996	+	0.0431856i	0.00287478	+	0.00165976i	0.501437	−	0.865194i	$-0.332805\pi$
$677$	0.0747996	+	0.0431856i	0.00287478	+	0.00165976i	−0.498562	+	0.866854i	$0.666138\pi$
$678$	−5.36517	+	19.7888i	−0.206048	+	0.759986i
$679$	12.2485	−	7.07165i	0.470053	−	0.271385i
$680$		0			0
$681$	−0.304224	+	0.150667i	−0.0116579	+	0.00577357i
$682$	25.3126	+	5.15741i	0.969271	+	0.197488i
$683$	24.0380			0.919788			0.459894	−	0.887974i	$-0.347887\pi$
$683$	24.0380			0.919788			0.459894	+	0.887974i	$0.347887\pi$
$684$	−16.7015	−	0.0987662i	−0.638596	−	0.00377642i
$685$		0			0
$686$	−19.5091	−	3.97496i	−0.744862	−	0.151765i
$687$	0.182123	−	2.85256i	0.00694841	−	0.108832i
$688$	−4.34383	−	17.5070i	−0.165607	−	0.667447i
$689$	24.0661	−	13.8946i	0.916846	−	0.529342i
$690$		0			0
$691$	−36.1685	−	20.8819i	−1.37591	−	0.794384i	−0.384249	−	0.923229i	$-0.625540\pi$
$691$	−36.1685	−	20.8819i	−1.37591	−	0.794384i	−0.991665	+	0.128845i	$0.958873\pi$
$692$	10.4262	+	13.8524i	0.396344	+	0.526589i
$693$	−14.9281	−	11.3747i	−0.567071	−	0.432090i
$694$	−31.2637	+	10.4508i	−1.18675	+	0.396707i
$695$		0			0
$696$	−30.8909	−	4.45255i	−1.17092	−	0.168774i
$697$	4.74055	+	8.21087i	0.179561	+	0.311009i
$698$	6.02923	+	5.33727i	0.228210	+	0.202019i
$699$	−19.4147	+	29.1628i	−0.734332	+	1.10304i
$700$		0			0
$701$		−	2.12514i		−	0.0802654i	−0.999194	−	0.0401327i	$-0.987222\pi$
$701$		−	2.12514i		−	0.0802654i	0.999194	−	0.0401327i	$-0.0127781\pi$
$702$	2.30613	+	17.4594i	0.0870392	+	0.658963i
$703$			18.1405i			0.684182i
$704$	44.8882	+	7.18814i	1.69179	+	0.270913i
$705$		0			0
$706$	1.42739	−	1.61245i	0.0537207	−	0.0606854i
$707$	9.21629	+	15.9631i	0.346614	+	0.600354i
$708$	11.3952	−	22.6709i	0.428258	−	0.852026i
$709$	−2.08824	+	3.61694i	−0.0784256	+	0.135837i	−0.902571	−	0.430541i	$-0.858323\pi$
$709$	−2.08824	+	3.61694i	−0.0784256	+	0.135837i	0.824145	+	0.566379i	$0.191656\pi$
$710$		0			0
$711$	−0.429759	+	3.35190i	−0.0161172	+	0.125706i
$712$	21.3582	+	14.7060i	0.800434	+	0.551129i
$713$	5.86797	+	3.38787i	0.219757	+	0.126877i
$714$	0.891622	+	3.36737i	0.0333681	+	0.126021i
$715$		0			0
$716$	−2.04280	−	0.868489i	−0.0763430	−	0.0324569i
$717$	2.24351	−	35.1397i	0.0837853	−	1.31232i
$718$	−2.67129	+	13.1107i	−0.0996917	+	0.489288i
$719$	24.0884			0.898346			0.449173	−	0.893445i	$-0.351719\pi$
$719$	24.0884			0.898346			0.449173	+	0.893445i	$0.351719\pi$
$720$		0			0
$721$	−1.49568			−0.0557022
$722$	3.17676	−	15.5916i	0.118227	−	0.580259i
$723$	26.7671	−	13.2564i	0.995478	−	0.493010i
$724$	23.3070	+	9.90887i	0.866197	+	0.368260i
$725$		0			0
$726$	−50.3348	−	13.6468i	−1.86810	−	0.506480i
$727$	40.6108	+	23.4466i	1.50617	+	0.869587i	0.999974	+	0.00716831i	$0.00228176\pi$
$727$	40.6108	+	23.4466i	1.50617	+	0.869587i	0.506195	+	0.862419i	$0.331052\pi$
$728$	−6.14647	−	4.23208i	−0.227803	−	0.156851i
$729$	−25.0483	−	10.0788i	−0.927715	−	0.373290i
$730$		0			0
$731$	2.91253	−	5.04465i	0.107724	−	0.186583i
$732$	−17.2217	+	0.997305i	−0.636531	+	0.0368614i
$733$	−8.87721	−	15.3758i	−0.327887	−	0.567917i	0.654205	−	0.756317i	$-0.273003\pi$
$733$	−8.87721	−	15.3758i	−0.327887	−	0.567917i	−0.982092	+	0.188400i	$0.939670\pi$
$734$	7.62322	−	8.61155i	0.281378	−	0.317858i
$735$		0			0
$736$	10.5688	+	5.52087i	0.389570	+	0.203502i
$737$		−	21.0271i		−	0.774543i
$738$	23.4382	−	20.5024i	0.862774	−	0.754702i
$739$			8.50437i			0.312838i	0.987691	+	0.156419i	$0.0499951\pi$
$739$			8.50437i			0.312838i	−0.987691	+	0.156419i	$0.950005\pi$
$740$		0			0
$741$	11.5313	+	0.736218i	0.423611	+	0.0270456i
$742$	−13.5177	−	11.9663i	−0.496249	−	0.439296i
$743$	−25.1755	−	43.6052i	−0.923598	−	1.59972i	−0.793800	−	0.608179i	$-0.791900\pi$
$743$	−25.1755	−	43.6052i	−0.923598	−	1.59972i	−0.129798	−	0.991540i	$-0.541433\pi$
$744$	−9.73901	+	12.3752i	−0.357050	+	0.453696i
$745$		0			0
$746$	15.5794	−	5.20786i	0.570402	−	0.190673i
$747$	−34.2958	−	4.39718i	−1.25482	−	0.160884i
$748$	8.82840	+	11.7296i	0.322798	+	0.428875i
$749$	−2.83366	−	1.63601i	−0.103540	−	0.0597787i
$750$		0			0
$751$	44.8169	−	25.8750i	1.63539	−	0.944193i	0.652999	−	0.757359i	$-0.273511\pi$
$751$	44.8169	−	25.8750i	1.63539	−	0.944193i	0.982391	−	0.186834i	$-0.0598228\pi$
$752$	−36.2946	+	9.00541i	−1.32353	+	0.328393i
$753$	−14.3027	−	9.52179i	−0.521218	−	0.346993i
$754$	21.1574	+	4.31078i	0.770506	+	0.156989i
$755$		0			0
$756$	10.2824	−	5.01686i	0.373968	−	0.182462i
$757$	16.5374			0.601064			0.300532	−	0.953772i	$-0.402836\pi$
$757$	16.5374			0.601064			0.300532	+	0.953772i	$0.402836\pi$
$758$	0.269272	+	0.0548639i	0.00978042	+	0.00199275i
$759$	−17.2695	−	11.4969i	−0.626843	−	0.417312i
$760$		0			0
$761$	−30.1188	+	17.3891i	−1.09180	+	0.630354i	−0.934056	−	0.357126i	$-0.883757\pi$
$761$	−30.1188	+	17.3891i	−1.09180	+	0.630354i	−0.157748	+	0.987479i	$0.550423\pi$
$762$	8.88897	+	8.94169i	0.322014	+	0.323923i
$763$	−4.88223	−	2.81876i	−0.176749	−	0.102046i
$764$	36.3782	−	27.3805i	1.31612	−	0.990591i
$765$		0			0
$766$	−24.8141	+	8.29485i	−0.896571	+	0.299705i
$767$	−8.77710	+	15.2024i	−0.316923	+	0.548926i
$768$	−16.2043	+	22.4815i	−0.584724	+	0.811232i
$769$	7.71708	+	13.3664i	0.278285	+	0.482003i	0.970959	−	0.239248i	$-0.0769007\pi$
$769$	7.71708	+	13.3664i	0.278285	+	0.482003i	−0.692674	+	0.721251i	$0.743567\pi$
$770$		0			0
$771$	29.9895	+	1.91469i	1.08005	+	0.0689560i
$772$	2.82067	+	23.0811i	0.101518	+	0.830705i
$773$			29.3290i			1.05489i	0.849589	+	0.527446i	$0.176850\pi$
$773$			29.3290i			1.05489i	−0.849589	+	0.527446i	$0.823150\pi$
$774$	−18.1089	−	6.17270i	−0.650909	−	0.221873i
$775$		0			0
$776$	15.6153	+	32.8101i	0.560555	+	1.17781i
$777$	−5.51499	−	11.1358i	−0.197849	−	0.399494i
$778$	22.0669	−	24.9278i	0.791135	−	0.893703i
$779$	−10.2156	−	17.6939i	−0.366011	−	0.633949i
$780$		0			0
$781$	−36.0698	+	62.4748i	−1.29068	+	2.23552i
$782$	1.22079	+	3.65201i	0.0436554	+	0.130596i
$783$	−21.7000	+	24.9988i	−0.775496	+	0.893385i
$784$	6.40686	−	22.2478i	0.228817	−	0.794565i
$785$		0			0
$786$	−33.5721	−	9.10210i	−1.19748	−	0.324661i
$787$	−45.5713	+	26.3106i	−1.62444	+	0.937872i	−0.638730	+	0.769431i	$0.720540\pi$
$787$	−45.5713	+	26.3106i	−1.62444	+	0.937872i	−0.985712	+	0.168442i	$0.946127\pi$
$788$	−9.54688	+	22.4555i	−0.340094	+	0.799945i
$789$	14.9202	−	7.38923i	0.531174	−	0.263064i
$790$		0			0
$791$	−9.21510			−0.327651
$792$	32.1732	−	35.9142i	1.14323	−	1.27616i
$793$	11.9344			0.423803
$794$	6.60940	−	32.4390i	0.234559	−	1.15122i
$795$		0			0
$796$	5.53955	−	13.0297i	0.196344	−	0.461827i
$797$	2.15117	−	1.24198i	0.0761983	−	0.0439931i	−0.461417	−	0.887183i	$-0.652659\pi$
$797$	2.15117	−	1.24198i	0.0761983	−	0.0439931i	0.537615	+	0.843190i	$0.319325\pi$
$798$	−1.92139	−	7.25647i	−0.0680163	−	0.256876i
$799$	−10.4583	−	6.03812i	−0.369989	−	0.213613i
$800$		0			0
$801$	25.3751	−	10.6114i	0.896583	−	0.374934i
$802$	−13.4221	−	40.1523i	−0.473950	−	1.41783i
$803$	−28.0401	+	48.5669i	−0.989514	+	1.71389i
$804$	11.4529	+	5.75664i	0.403913	+	0.203021i
$805$		0			0
$806$	7.22142	−	8.15765i	0.254364	−	0.287341i
$807$	−1.29081	+	1.93893i	−0.0454388	+	0.0682535i
$808$	−42.7605	+	20.3510i	−1.50431	+	0.715944i
$809$			25.6629i			0.902261i	0.892458	+	0.451131i	$0.148979\pi$
$809$			25.6629i			0.902261i	−0.892458	+	0.451131i	$0.851021\pi$
$810$		0			0
$811$		−	26.5970i		−	0.933948i	−0.884271	−	0.466974i	$-0.845344\pi$
$811$		−	26.5970i		−	0.933948i	0.884271	−	0.466974i	$-0.154656\pi$
$812$	−1.70157	−	13.9237i	−0.0597135	−	0.488626i
$813$	20.8561	−	31.3279i	0.731456	−	1.09872i
$814$	−39.2140	−	34.7135i	−1.37445	−	1.21671i
$815$		0			0
$816$	−8.80576	+	1.59737i	−0.308263	+	0.0559192i
$817$	−6.27631	+	10.8709i	−0.219580	+	0.380324i
$818$	−2.79013	+	0.932682i	−0.0975546	+	0.0326105i
$819$	−7.30243	+	3.05374i	−0.255167	+	0.106706i
$820$		0			0
$821$	−26.3429	−	15.2091i	−0.919373	−	0.530800i	−0.0359383	−	0.999354i	$-0.511442\pi$
$821$	−26.3429	−	15.2091i	−0.919373	−	0.530800i	−0.883435	+	0.468554i	$0.844775\pi$
$822$	−16.4397	+	4.35296i	−0.573402	+	0.151827i
$823$	7.33737	−	4.23623i	0.255764	−	0.147666i	−0.366636	−	0.930364i	$-0.619491\pi$
$823$	7.33737	−	4.23623i	0.255764	−	0.147666i	0.622401	+	0.782699i	$0.286157\pi$
$824$	0.304760	−	3.83055i	0.0106168	−	0.133444i
$825$		0			0
$826$	11.1745	+	2.27679i	0.388810	+	0.0792196i
$827$	37.2624			1.29574			0.647871	−	0.761750i	$-0.275660\pi$
$827$	37.2624			1.29574			0.647871	+	0.761750i	$0.275660\pi$
$828$	10.9900	−	6.25871i	0.381928	−	0.217505i
$829$	18.4167			0.639639			0.319820	−	0.947478i	$-0.396378\pi$
$829$	18.4167			0.639639			0.319820	+	0.947478i	$0.396378\pi$
$830$		0			0
$831$	−21.5968	+	10.6958i	−0.749184	+	0.371033i
$832$	12.0911	−	14.8792i	0.419182	−	0.515844i
$833$	6.47493	−	3.73830i	0.224343	−	0.129525i
$834$	7.64704	−	28.2053i	0.264795	−	0.976669i
$835$		0			0
$836$	−19.0246	−	25.2764i	−0.657980	−	0.874203i
$837$	5.44920	+	15.7892i	0.188352	+	0.545755i
$838$	13.1181	−	4.38510i	0.453157	−	0.151481i
$839$	−7.35228	+	12.7345i	−0.253829	+	0.439645i	−0.964577	−	0.263802i	$-0.915023\pi$
$839$	−7.35228	+	12.7345i	−0.253829	+	0.439645i	0.710748	+	0.703447i	$0.248357\pi$
$840$		0			0
$841$	5.79320	+	10.0341i	0.199765	+	0.346004i
$842$	−2.22578	−	1.97033i	−0.0767055	−	0.0679022i
$843$	8.96025	+	18.0924i	0.308607	+	0.623135i
$844$	−12.8685	+	1.57262i	−0.442952	+	0.0541319i
$845$		0			0
$846$	−12.7969	+	37.5424i	−0.439968	+	1.29073i
$847$		−	23.4395i		−	0.805390i
$848$	33.4008	−	32.1815i	1.14699	−	1.10512i
$849$	−21.4811	−	1.37147i	−0.737228	−	0.0470686i
$850$		0			0
$851$	−6.86833	−	11.8963i	−0.235443	−	0.407800i
$852$	−24.1535	−	36.7502i	−0.827484	−	1.25904i
$853$	6.48519	−	11.2327i	0.222049	−	0.384600i	−0.733381	−	0.679818i	$-0.762059\pi$
$853$	6.48519	−	11.2327i	0.222049	−	0.384600i	0.955430	+	0.295218i	$0.0953922\pi$
$854$	−2.45803	−	7.35322i	−0.0841119	−	0.251622i
$855$		0			0
$856$	4.76734	−	6.92385i	0.162944	−	0.236652i
$857$	−5.82871	−	3.36521i	−0.199105	−	0.114953i	0.397133	−	0.917761i	$-0.370005\pi$
$857$	−5.82871	−	3.36521i	−0.199105	−	0.114953i	−0.596238	+	0.802808i	$0.703339\pi$
$858$	−23.6576	+	23.5181i	−0.807656	+	0.802894i
$859$	−33.3860	+	19.2754i	−1.13912	+	0.657669i	−0.946212	−	0.323549i	$-0.895124\pi$
$859$	−33.3860	+	19.2754i	−1.13912	+	0.657669i	−0.192904	+	0.981218i	$0.561791\pi$
$860$		0			0
$861$	11.6502	+	7.75592i	0.397036	+	0.264321i
$862$	1.08477	−	5.32407i	0.0369475	−	0.181339i
$863$	−13.4795			−0.458847			−0.229424	−	0.973327i	$-0.573684\pi$
$863$	−13.4795			−0.458847			−0.229424	+	0.973327i	$0.573684\pi$
$864$	10.7534	+	27.3562i	0.365838	+	0.930678i
$865$		0			0
$866$	1.88281	−	9.24087i	0.0639806	−	0.314018i
$867$	22.1044	+	14.7157i	0.750704	+	0.499770i
$868$	−6.51357	−	2.76922i	−0.221085	−	0.0939934i
$869$	−5.54347	+	3.20052i	−0.188049	+	0.108570i
$870$		0			0
$871$	−7.67995	−	4.43402i	−0.260225	−	0.150241i
$872$	8.21384	−	11.9294i	0.278156	−	0.403980i
$873$	38.2277	+	4.90131i	1.29381	+	0.165884i
$874$	−2.63072	−	7.86984i	−0.0889855	−	0.266201i
$875$		0			0
$876$	−18.7765	−	28.5690i	−0.634400	−	0.965257i
$877$	7.80171	+	13.5129i	0.263445	+	0.456300i	0.967155	−	0.254187i	$-0.0818080\pi$
$877$	7.80171	+	13.5129i	0.263445	+	0.456300i	−0.703710	+	0.710487i	$0.748475\pi$
$878$	36.3185	−	41.0271i	1.22569	−	1.38460i
$879$	16.5065	+	1.05387i	0.556751	+	0.0355460i
$880$		0			0
$881$		−	25.0226i		−	0.843032i	−0.906821	−	0.421516i	$-0.861498\pi$
$881$		−	25.0226i		−	0.843032i	0.906821	−	0.421516i	$-0.138502\pi$
$882$	−16.1678	−	18.4829i	−0.544397	−	0.622353i
$883$		−	13.8202i		−	0.465085i	−0.972586	−	0.232543i	$-0.925295\pi$
$883$		−	13.8202i		−	0.465085i	0.972586	−	0.232543i	$-0.0747046\pi$
$884$	6.14577	−	0.751058i	0.206705	−	0.0252608i
$885$		0			0
$886$	−24.7996	−	21.9534i	−0.833159	−	0.737539i
$887$	−9.33323	−	16.1656i	−0.313379	−	0.542789i	0.665712	−	0.746208i	$-0.268128\pi$
$887$	−9.33323	−	16.1656i	−0.313379	−	0.542789i	−0.979092	+	0.203420i	$0.934794\pi$
$888$	29.6433	−	11.8553i	0.994763	−	0.397836i
$889$	−2.83336	+	4.90753i	−0.0950279	+	0.164593i
$890$		0			0
$891$	−13.5705	−	49.3093i	−0.454629	−	1.65192i
$892$	−18.8779	−	25.0815i	−0.632079	−	0.839790i
$893$	22.5370	+	13.0117i	0.754172	+	0.435421i
$894$	−3.68596	+	13.5953i	−0.123277	+	0.454694i
$895$		0			0
$896$	−11.6579	−	4.38520i	−0.389464	−	0.146499i
$897$	−7.84079	+	3.88315i	−0.261796	+	0.129654i
$898$	−21.8760	−	4.45721i	−0.730013	−	0.148739i
$899$	20.4788			0.683007
$900$		0			0
$901$	14.9783			0.499001
$902$	57.7969	+	11.7760i	1.92443	+	0.392099i
$903$	0.547878	−	8.58132i	0.0182322	−	0.285569i
$904$	1.87767	−	23.6005i	0.0624503	−	0.784942i
$905$		0			0
$906$	5.06056	−	1.33995i	0.168126	−	0.0445168i
$907$	35.9025	+	20.7283i	1.19212	+	0.688273i	0.958788	−	0.284123i	$-0.0917025\pi$
$907$	35.9025	+	20.7283i	1.19212	+	0.688273i	0.233336	+	0.972396i	$0.425036\pi$
$908$	0.313206	−	0.235739i	0.0103941	−	0.00782326i
$909$	−6.38774	+	49.8212i	−0.211868	+	1.65246i
$910$		0			0
$911$	2.80277	−	4.85454i	0.0928600	−	0.160838i	−0.815853	−	0.578259i	$-0.803732\pi$
$911$	2.80277	−	4.85454i	0.0928600	−	0.160838i	0.908713	+	0.417420i	$0.137066\pi$
$912$	18.9758	−	3.44223i	0.628352	−	0.113984i
$913$	−32.7469	−	56.7193i	−1.08376	−	1.87714i
$914$	8.91209	+	7.88927i	0.294786	+	0.260954i
$915$		0			0
$916$	0.400373	+	3.27618i	0.0132287	+	0.108248i
$917$		−	15.6336i		−	0.516266i
$918$	−3.62884	+	8.77133i	−0.119769	+	0.289497i
$919$		−	30.8044i		−	1.01614i	−0.861315	−	0.508072i	$-0.830358\pi$
$919$		−	30.8044i		−	1.01614i	0.861315	−	0.508072i	$-0.169642\pi$
$920$		0			0
$921$	12.9276	−	19.4186i	0.425980	−	0.639863i
$922$	23.2498	−	26.2641i	0.765692	−	0.864961i
$923$	15.2122	+	26.3483i	0.500716	+	0.867266i
$924$	19.3629	+	9.73248i	0.636993	+	0.320175i
$925$		0			0
$926$	9.28972	+	27.7903i	0.305279	+	0.913247i
$927$	−3.24189	−	2.47021i	−0.106478	−	0.0811324i
$928$	36.0063	−	1.52077i	1.18196	−	0.0499216i
$929$	−23.8104	−	13.7469i	−0.781194	−	0.451023i	0.0556590	−	0.998450i	$-0.482274\pi$
$929$	−23.8104	−	13.7469i	−0.781194	−	0.451023i	−0.836853	+	0.547427i	$0.815607\pi$
$930$		0			0
$931$	−13.9530	+	8.05579i	−0.457293	+	0.264018i
$932$	15.8279	−	37.2292i	0.518459	−	1.21948i
$933$	−1.13252	+	17.7385i	−0.0370772	+	0.580733i
$934$	0.450587	−	2.21148i	0.0147436	−	0.0723620i
$935$		0			0
$936$	−6.33290	−	19.3243i	−0.206997	−	0.631633i
$937$	13.6341			0.445407			0.222704	−	0.974886i	$-0.428512\pi$
$937$	13.6341			0.445407			0.222704	+	0.974886i	$0.428512\pi$
$938$	−1.15019	+	5.64514i	−0.0375550	+	0.184320i
$939$	2.49242	−	1.23437i	0.0813371	−	0.0402822i
$940$		0			0
$941$	−49.7730	+	28.7364i	−1.62255	+	0.936781i	−0.636319	+	0.771426i	$0.719544\pi$
$941$	−49.7730	+	28.7364i	−1.62255	+	0.936781i	−0.986234	+	0.165355i	$0.947123\pi$
$942$	23.7732	+	6.44542i	0.774574	+	0.210003i
$943$	13.3985	+	7.73561i	0.436314	+	0.251906i
$944$	−8.10793	+	28.1548i	−0.263891	+	0.916360i
$945$		0			0
$946$	−11.4891	−	34.3698i	−0.373543	−	1.11746i
$947$	−9.68402	+	16.7732i	−0.314688	+	0.545056i	−0.979371	−	0.202069i	$-0.935233\pi$
$947$	−9.68402	+	16.7732i	−0.314688	+	0.545056i	0.664683	+	0.747126i	$0.268567\pi$
$948$	−0.225594	−	3.89560i	−0.00732695	−	0.126523i
$949$	11.8257	+	20.4828i	0.383880	+	0.664899i
$950$		0			0
$951$	3.43031	+	6.92644i	0.111236	+	0.224605i
$952$	−1.72855	−	3.63195i	−0.0560226	−	0.117712i
$953$		−	4.34158i		−	0.140638i	−0.997525	−	0.0703188i	$-0.977598\pi$
$953$		−	4.34158i		−	0.140638i	0.997525	−	0.0703188i	$-0.0224017\pi$
$954$	−9.53643	−	48.2621i	−0.308753	−	1.56254i
$955$		0			0
$956$	4.93206	+	40.3582i	0.159514	+	1.30528i
$957$	−62.5760	−	3.99519i	−2.02280	−	0.129146i
$958$	6.33119	+	5.60458i	0.204552	+	0.181076i
$959$	−3.82170	−	6.61938i	−0.123409	−	0.213751i
$960$		0			0
$961$	−10.3335	+	17.8981i	−0.333338	+	0.577358i
$962$	−20.9479	+	7.00245i	−0.675388	+	0.225768i
$963$	−3.43997	−	8.22601i	−0.110851	−	0.265080i
$964$	−27.5573	+	20.7414i	−0.887561	+	0.668034i
$965$		0			0
$966$	4.00745	+	4.03122i	0.128938	+	0.129702i
$967$	−28.6939	+	16.5665i	−0.922735	+	0.532741i	−0.884507	−	0.466528i	$-0.845505\pi$
$967$	−28.6939	+	16.5665i	−0.922735	+	0.532741i	−0.0382285	+	0.999269i	$0.512171\pi$
$968$	60.0302	+	4.77602i	1.92944	+	0.153507i
$969$	5.18423	+	3.45133i	0.166541	+	0.110873i
$970$		0			0
$971$	22.0082			0.706277			0.353138	−	0.935571i	$-0.385114\pi$
$971$	22.0082			0.706277			0.353138	+	0.935571i	$0.385114\pi$
$972$	30.5727	+	6.10802i	0.980621	+	0.195915i
$973$	13.1344			0.421070
$974$	−22.9993	−	4.68607i	−0.736945	−	0.150151i
$975$		0			0
$976$	19.3330	−	4.79689i	0.618833	−	0.153545i
$977$	25.5578	−	14.7558i	0.817667	−	0.472080i	−0.0319442	−	0.999490i	$-0.510170\pi$
$977$	25.5578	−	14.7558i	0.817667	−	0.472080i	0.849611	+	0.527409i	$0.176837\pi$
$978$	−31.4552	−	31.6418i	−1.00583	−	1.01179i
$979$	45.1183	+	26.0491i	1.44199	+	0.832532i
$980$		0			0
$981$	−5.92686	−	14.1729i	−0.189230	−	0.452507i
$982$	17.8908	−	5.98052i	0.570919	−	0.190846i
$983$	22.9895	−	39.8190i	0.733251	−	1.27003i	−0.222235	−	0.974993i	$-0.571335\pi$
$983$	22.9895	−	39.8190i	0.733251	−	1.27003i	0.955486	−	0.295035i	$-0.0953313\pi$
$984$	−22.2373	+	28.2565i	−0.708900	+	0.900786i
$985$		0			0
$986$	8.71423	+	7.71412i	0.277518	+	0.245668i
$987$	−17.7904	−	1.13583i	−0.566274	−	0.0361540i
$988$	−13.2437	+	1.61848i	−0.421339	+	0.0514907i
$989$		−	9.50531i		−	0.302251i
$990$		0			0
$991$			52.8232i			1.67798i	0.544144	+	0.838992i	$0.316854\pi$
$991$			52.8232i			1.67798i	−0.544144	+	0.838992i	$0.683146\pi$
$992$	8.41937	−	16.1175i	0.267315	−	0.511730i
$993$	9.06307	+	18.3000i	0.287608	+	0.580733i
$994$	13.1010	−	14.7996i	0.415540	−	0.469413i
$995$		0			0
$996$	39.8587	−	2.30822i	1.26297	−	0.0731386i
$997$	−25.0831	+	43.4452i	−0.794389	+	1.37592i	0.128837	+	0.991666i	$0.458876\pi$
$997$	−25.0831	+	43.4452i	−0.794389	+	1.37592i	−0.923226	+	0.384257i	$0.874458\pi$
$998$	−18.4894	−	55.3113i	−0.585272	−	1.75085i
$999$	6.43771	−	33.2451i	0.203680	−	1.05183i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.2.r.g.551.14		48
4.3	odd	2	inner	900.2.r.g.551.6		48
5.2	odd	4		180.2.n.d.119.23	yes	48
5.3	odd	4		180.2.n.d.119.2	yes	48
5.4	even	2	inner	900.2.r.g.551.11		48
9.5	odd	6	inner	900.2.r.g.851.6		48
15.2	even	4		540.2.n.d.359.2		48
15.8	even	4		540.2.n.d.359.23		48
20.3	even	4		180.2.n.d.119.18	yes	48
20.7	even	4		180.2.n.d.119.7	yes	48
20.19	odd	2	inner	900.2.r.g.551.19		48
36.23	even	6	inner	900.2.r.g.851.14		48
45.13	odd	12		540.2.n.d.179.18		48
45.14	odd	6	inner	900.2.r.g.851.19		48
45.22	odd	12		540.2.n.d.179.7		48
45.23	even	12		180.2.n.d.59.7	yes	48
45.32	even	12		180.2.n.d.59.18	yes	48
60.23	odd	4		540.2.n.d.359.7		48
60.47	odd	4		540.2.n.d.359.18		48
180.23	odd	12		180.2.n.d.59.23	yes	48
180.59	even	6	inner	900.2.r.g.851.11		48
180.67	even	12		540.2.n.d.179.23		48
180.103	even	12		540.2.n.d.179.2		48
180.167	odd	12		180.2.n.d.59.2	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.2.n.d.59.2	✓	48	180.167	odd	12
180.2.n.d.59.7	yes	48	45.23	even	12
180.2.n.d.59.18	yes	48	45.32	even	12
180.2.n.d.59.23	yes	48	180.23	odd	12
180.2.n.d.119.2	yes	48	5.3	odd	4
180.2.n.d.119.7	yes	48	20.7	even	4
180.2.n.d.119.18	yes	48	20.3	even	4
180.2.n.d.119.23	yes	48	5.2	odd	4
540.2.n.d.179.2		48	180.103	even	12
540.2.n.d.179.7		48	45.22	odd	12
540.2.n.d.179.18		48	45.13	odd	12
540.2.n.d.179.23		48	180.67	even	12
540.2.n.d.359.2		48	15.2	even	4
540.2.n.d.359.7		48	60.23	odd	4
540.2.n.d.359.18		48	60.47	odd	4
540.2.n.d.359.23		48	15.8	even	4
900.2.r.g.551.6		48	4.3	odd	2	inner
900.2.r.g.551.11		48	5.4	even	2	inner
900.2.r.g.551.14		48	1.1	even	1	trivial
900.2.r.g.551.19		48	20.19	odd	2	inner
900.2.r.g.851.6		48	9.5	odd	6	inner
900.2.r.g.851.11		48	180.59	even	6	inner
900.2.r.g.851.14		48	36.23	even	6	inner
900.2.r.g.851.19		48	45.14	odd	6	inner

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:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	900.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.282343 - 1.38574i) q^{2} +(1.44177 + 0.959839i) q^{3} +(-1.84056 - 0.782509i) q^{4} +(1.73716 - 1.72692i) q^{6} +(0.953419 + 0.550457i) q^{7} +(-1.60403 + 2.32961i) q^{8} +(1.15742 + 2.76774i) q^{9} +(-2.84126 + 4.92120i) q^{11} +(-1.90259 - 2.89485i) q^{12} +(1.19828 + 2.07548i) q^{13} +(1.03198 - 1.16578i) q^{14} +(2.77536 + 2.88052i) q^{16} +1.29175i q^{17} +(4.16216 - 0.822430i) q^{18} -2.78362i q^{19} +(0.846263 + 1.70876i) q^{21} +(6.01731 + 5.32672i) q^{22} +(1.05393 + 1.82546i) q^{23} +(-4.54870 + 1.81916i) q^{24} +(3.21441 - 1.07451i) q^{26} +(-0.987853 + 5.10139i) q^{27} +(-1.32409 - 1.75921i) q^{28} +(5.51723 + 3.18537i) q^{29} +(2.78385 - 1.60725i) q^{31} +(4.77526 - 3.03264i) q^{32} +(-8.82001 + 4.36810i) q^{33} +(1.79003 + 0.364715i) q^{34} +(0.0354812 - 5.99990i) q^{36} -6.51687 q^{37} +(-3.85739 - 0.785937i) q^{38} +(-0.264482 + 4.14253i) q^{39} +(6.35642 - 3.66988i) q^{41} +(2.60684 - 0.690246i) q^{42} +(-3.90530 - 2.25473i) q^{43} +(9.08040 - 6.83448i) q^{44} +(2.82719 - 0.945071i) q^{46} +(-4.67439 + 8.09628i) q^{47} +(1.23660 + 6.81695i) q^{48} +(-2.89400 - 5.01255i) q^{49} +(-1.23987 + 1.86240i) q^{51} +(-0.581429 - 4.75773i) q^{52} -11.5954i q^{53} +(6.79030 + 2.80925i) q^{54} +(-2.81166 + 1.33815i) q^{56} +(2.67183 - 4.01335i) q^{57} +(5.97186 - 6.74609i) q^{58} +(3.66237 + 6.34341i) q^{59} +(2.48990 - 4.31263i) q^{61} +(-1.44124 - 4.31149i) q^{62} +(-0.420017 + 3.27592i) q^{63} +(-2.85419 - 7.47353i) q^{64} +(3.56280 + 13.4556i) q^{66} +(-3.20457 + 1.85016i) q^{67} +(1.01080 - 2.37754i) q^{68} +(-0.232621 + 3.64351i) q^{69} +12.6950 q^{71} +(-8.30429 - 1.74320i) q^{72} +9.86891 q^{73} +(-1.83999 + 9.03070i) q^{74} +(-2.17821 + 5.12344i) q^{76} +(-5.41781 + 3.12798i) q^{77} +(5.66581 + 1.53612i) q^{78} +(0.975531 + 0.563223i) q^{79} +(-6.32077 + 6.40686i) q^{81} +(-3.29082 - 9.84453i) q^{82} +(-5.76275 + 9.98138i) q^{83} +(-0.220480 - 3.80730i) q^{84} +(-4.22710 + 4.77514i) q^{86} +(4.89714 + 9.88823i) q^{87} +(-6.90704 - 14.5128i) q^{88} -9.16815i q^{89} +2.63841i q^{91} +(-0.511387 - 4.18460i) q^{92} +(5.55638 + 0.354749i) q^{93} +(9.89957 + 8.76343i) q^{94} +(9.79568 + 0.211108i) q^{96} +(6.42344 - 11.1257i) q^{97} +(-7.76320 + 2.59507i) q^{98} +(-16.9091 - 2.16798i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 2 q^{4} + 12 q^{9} + 42 q^{14} + 30 q^{16} - 12 q^{21} + 6 q^{24} + 4 q^{34} + 96 q^{36} + 96 q^{41} + 4 q^{46} - 32 q^{49} + 30 q^{54} + 6 q^{56} + 8 q^{61} + 20 q^{64} + 36 q^{66} + 96 q^{69} - 72 q^{74}+ \cdots + 54 q^{96}+O(q^{100}) \) 48 * q + 2 * q^4 + 12 * q^9 + 42 * q^14 + 30 * q^16 - 12 * q^21 + 6 * q^24 + 4 * q^34 + 96 * q^36 + 96 * q^41 + 4 * q^46 - 32 * q^49 + 30 * q^54 + 6 * q^56 + 8 * q^61 + 20 * q^64 + 36 * q^66 + 96 * q^69 - 72 * q^74 + 36 * q^81 + 6 * q^84 + 108 * q^86 + 62 * q^94 + 54 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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