LMFDB - Embedded newform 900.2.r.g.851.11

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			851.11
Character	$\chi$	$=$	900.851
Dual form			900.2.r.g.551.11

$q$-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 $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$

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	$-0.733379\pi$
$7$	−0.953419	+	0.550457i	−0.360358	+	0.208053i	0.308880	+	0.951101i	$0.400046\pi$
$8$	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	−0.875086	−	0.483967i	$-0.839195\pi$
$11$	−2.84126	−	4.92120i	−0.856671	−	1.48380i	0.0184153	−	0.999830i	$-0.494138\pi$
$12$	1.90259	−	2.89485i	0.549231	−	0.835670i
$13$	−1.19828	+	2.07548i	−0.332343	+	0.575636i	−0.982971	−	0.183761i	$-0.941173\pi$
$13$	−1.19828	+	2.07548i	−0.332343	+	0.575636i	0.650627	+	0.759397i	$0.274506\pi$
$14$	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	$0.103449\pi$
$19$			2.78362i			0.638607i	−0.947652	+	0.319304i	$0.896551\pi$
$20$		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	$-0.903861\pi$
$23$	−1.05393	+	1.82546i	−0.219760	+	0.380635i	0.734975	+	0.678095i	$0.237194\pi$
$24$	−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	0.109112	−	0.994029i	$-0.465199\pi$
$29$	5.51723	−	3.18537i	1.02452	−	0.591509i	0.915411	+	0.402521i	$0.131866\pi$
$30$		0			0
$31$	2.78385	+	1.60725i	0.499994	+	0.288671i	0.728711	−	0.684821i	$-0.240120\pi$
$31$	2.78385	+	1.60725i	0.499994	+	0.288671i	−0.228717	+	0.973493i	$0.573453\pi$
$32$	−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	$-0.320054\pi$
$37$	6.51687			1.07137			0.535683	+	0.844419i	$0.320054\pi$
$38$	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	0.906082	−	0.423102i	$-0.139059\pi$
$41$	6.35642	+	3.66988i	0.992706	+	0.573139i	0.0866240	+	0.996241i	$0.472392\pi$
$42$	−2.60684	−	0.690246i	−0.402244	−	0.106507i
$43$	3.90530	−	2.25473i	0.595553	−	0.343843i	−0.171737	−	0.985143i	$-0.554938\pi$
$43$	3.90530	−	2.25473i	0.595553	−	0.343843i	0.767290	+	0.641300i	$0.221605\pi$
$44$	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	0.974422	+	0.224726i	$0.0721487\pi$
$47$	4.67439	+	8.09628i	0.681830	+	1.18096i	−0.292592	+	0.956237i	$0.594518\pi$
$48$	−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	−0.522846	−	0.852427i	$-0.675130\pi$
$59$	3.66237	−	6.34341i	0.476800	−	0.825842i	0.999647	+	0.0265849i	$0.00846323\pi$
$60$		0			0
$61$	2.48990	+	4.31263i	0.318799	+	0.552175i	0.980238	−	0.197823i	$-0.0633873\pi$
$61$	2.48990	+	4.31263i	0.318799	+	0.552175i	−0.661439	+	0.749999i	$0.730054\pi$
$62$	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	$-0.260758\pi$
$67$	3.20457	+	1.85016i	0.391500	+	0.226033i	−0.291310	+	0.956629i	$0.594091\pi$
$68$	−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	$-0.695985\pi$
$73$	−9.86891			−1.15507			−0.577534	+	0.816366i	$0.695985\pi$
$74$	−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	−0.444117	−	0.895969i	$-0.646483\pi$
$79$	0.975531	−	0.563223i	0.109756	−	0.0633676i	0.553873	+	0.832601i	$0.313149\pi$
$80$		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	0.987030	+	0.160537i	$0.0513227\pi$
$83$	5.76275	+	9.98138i	0.632544	+	1.09560i	−0.354485	+	0.935062i	$0.615344\pi$
$84$	−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	$0.161512\pi$
$89$			9.16815i			0.971822i	−0.874008	+	0.485911i	$0.838488\pi$
$90$		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	−0.982587	−	0.185801i	$-0.940512\pi$
$97$	−6.42344	−	11.1257i	−0.652202	−	1.12965i	0.330386	−	0.943846i	$-0.392821\pi$
$98$	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	0.444755	−	0.895652i	$-0.353291\pi$
$101$	14.4999	−	8.37150i	1.44279	−	0.832995i	0.998035	+	0.0626572i	$0.0199575\pi$
$102$	−2.23074	+	2.24397i	−0.220876	+	0.222187i
$103$	1.17657	+	0.679292i	0.115931	+	0.0669327i	0.556844	−	0.830617i	$-0.312012\pi$
$103$	1.17657	+	0.679292i	0.115931	+	0.0669327i	−0.440913	+	0.897550i	$0.645345\pi$
$104$	−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	$-0.454112\pi$
$107$	2.97211			0.287324			0.143662	+	0.989627i	$0.454112\pi$
$108$	−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	$-0.204524\pi$
$113$	7.24900	+	4.18521i	0.681928	+	0.393711i	−0.118653	+	0.992936i	$0.537858\pi$
$114$	−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	0.369065	+	0.929403i	$0.379678\pi$
$131$	−7.10028	+	12.2980i	−0.620354	+	1.07449i	−0.989420	+	0.145082i	$0.953656\pi$
$132$	−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	$-0.570820\pi$
$137$	6.01263	−	3.47139i	0.513693	−	0.296581i	0.734351	+	0.678770i	$0.237487\pi$
$138$	−4.98329	+	1.35107i	−0.424205	+	0.115011i
$139$	10.3321	+	5.96523i	0.876356	+	0.505964i	0.869455	−	0.494012i	$-0.164470\pi$
$139$	10.3321	+	5.96523i	0.876356	+	0.505964i	0.00690070	+	0.999976i	$0.497803\pi$
$140$		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	0.281934	−	0.959434i	$-0.409024\pi$
$149$	−4.98019	−	2.87531i	−0.407993	−	0.235555i	−0.689927	+	0.723879i	$0.742357\pi$
$150$		0			0
$151$	1.85084	−	1.06858i	0.150619	−	0.0869599i	−0.422796	−	0.906225i	$-0.638951\pi$
$151$	1.85084	−	1.06858i	0.150619	−	0.0869599i	0.573415	+	0.819265i	$0.305618\pi$
$152$	−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	$-0.964764\pi$
$157$	−5.02788	+	8.70855i	−0.401269	+	0.695018i	0.592611	+	0.805489i	$0.298097\pi$
$158$	−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	$-0.926336\pi$
$167$	−3.72227	+	6.44716i	−0.288038	+	0.498896i	0.685304	+	0.728258i	$0.259670\pi$
$168$	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	$-0.559773\pi$
$173$	7.50742	−	4.33441i	0.570778	−	0.329539i	0.757460	+	0.652881i	$0.226440\pi$
$174$	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	−0.902966	−	0.429712i	$-0.858615\pi$
$191$	−11.3827	−	19.7154i	−0.823625	−	1.42656i	0.0793411	−	0.996848i	$-0.474718\pi$
$192$	−3.05829	−	13.5147i	−0.220713	−	0.975339i
$193$	5.81319	−	10.0687i	0.418443	−	0.724764i	−0.577340	−	0.816504i	$-0.695909\pi$
$193$	5.81319	−	10.0687i	0.418443	−	0.724764i	0.995783	+	0.0917396i	$0.0292427\pi$
$194$	−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	$-0.919268\pi$
$199$		−	7.07921i		−	0.501832i	0.968009	−	0.250916i	$-0.0807318\pi$
$200$		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	0.680626	−	0.732631i	$-0.261708\pi$
$211$	5.61368	+	3.24106i	0.386462	+	0.223124i	−0.294164	+	0.955755i	$0.595041\pi$
$212$	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	$-0.842803\pi$
$223$	−13.5931	+	7.84799i	−0.910263	+	0.525540i	−0.0297470	+	0.999557i	$0.509470\pi$
$224$	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	$-0.164596\pi$
$227$	0.0980022	+	0.169745i	0.00650463	+	0.0112664i	−0.862755	+	0.505623i	$0.831263\pi$
$228$	8.05817	+	5.29610i	0.533665	+	0.350743i
$229$	−0.825139	+	1.42918i	−0.0545267	+	0.0944431i	−0.892000	−	0.452035i	$-0.850698\pi$
$229$	−0.825139	+	1.42918i	−0.0545267	+	0.0944431i	0.837474	+	0.546478i	$0.184032\pi$
$230$		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	0.323769	+	0.946136i	$0.395050\pi$
$239$	−10.1646	+	17.6056i	−0.657494	+	1.13881i	−0.981262	+	0.192676i	$0.938283\pi$
$240$		0			0
$241$	8.62268	+	14.9349i	0.555436	+	0.962043i	0.997869	+	0.0652417i	$0.0207818\pi$
$241$	8.62268	+	14.9349i	0.555436	+	0.962043i	−0.442434	+	0.896801i	$0.645885\pi$
$242$	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	$-0.515334\pi$
$257$	−15.0253	−	8.67485i	−0.937252	−	0.541122i	−0.889098	+	0.457717i	$0.848667\pi$
$258$	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	$-0.262444\pi$
$263$	−4.80637	−	8.32487i	−0.296373	−	0.513334i	−0.975303	+	0.220869i	$0.929111\pi$
$264$	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	$-0.986946\pi$
$269$		−	1.34482i		−	0.0819953i	0.999159	−	0.0409977i	$-0.0130536\pi$
$270$		0			0
$271$			21.7288i			1.31993i	0.751297	+	0.659964i	$0.229429\pi$
$271$			21.7288i			1.31993i	−0.751297	+	0.659964i	$0.770571\pi$
$272$	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	$-0.0293931\pi$
$277$	6.95713	+	12.0501i	0.418014	+	0.724021i	−0.577726	+	0.816231i	$0.696060\pi$
$278$	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	−0.167703	−	0.985838i	$-0.553635\pi$
$281$	10.0948	−	5.82824i	0.602206	−	0.347684i	0.769909	+	0.638154i	$0.220302\pi$
$282$	−5.86146	+	22.1369i	−0.349045	+	1.31823i
$283$	10.7624	+	6.21367i	0.639758	+	0.369365i	0.784521	−	0.620102i	$-0.212909\pi$
$283$	10.7624	+	6.21367i	0.639758	+	0.369365i	−0.144763	+	0.989466i	$0.546242\pi$
$284$	−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	$-0.423317\pi$
$293$	−8.27006	−	4.77472i	−0.483142	−	0.278942i	−0.721725	+	0.692180i	$0.756650\pi$
$294$	−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	−0.683079	−	0.730345i	$-0.739359\pi$
$311$	5.13110	−	8.88732i	0.290958	−	0.503954i	0.974037	+	0.226391i	$0.0726927\pi$
$312$	9.22626	−	7.26088i	0.522334	−	0.411066i
$313$	−0.802903	−	1.39067i	−0.0453827	−	0.0786052i	0.842442	−	0.538787i	$-0.181117\pi$
$313$	−0.802903	−	1.39067i	−0.0453827	−	0.0786052i	−0.887824	+	0.460182i	$0.847784\pi$
$314$	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	$-0.706663\pi$
$317$	−3.86467	+	2.23127i	−0.217061	+	0.125320i	0.387528	+	0.921858i	$0.373329\pi$
$318$	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	−0.192410	−	0.981315i	$-0.561630\pi$
$331$	10.2107	−	5.89512i	0.561228	−	0.324025i	0.753638	+	0.657289i	$0.228297\pi$
$332$	−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	$-0.926217\pi$
$337$	−5.28111	+	9.14715i	−0.287680	+	0.498277i	0.685575	+	0.728002i	$0.259551\pi$
$338$	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	−0.362763	−	0.931882i	$-0.618166\pi$
$347$	11.6546	−	20.1864i	0.625652	−	1.08366i	0.988414	−	0.151779i	$-0.0485002\pi$
$348$	1.27587	−	22.0320i	0.0683939	−	1.18104i
$349$	−2.84689	−	4.93095i	−0.152390	−	0.263948i	0.779715	−	0.626134i	$-0.215364\pi$
$349$	−2.84689	−	4.93095i	−0.152390	−	0.263948i	−0.932106	+	0.362186i	$0.882030\pi$
$350$		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	$-0.679569\pi$
$353$	−1.31873	+	0.761369i	−0.0701889	+	0.0405236i	0.464495	+	0.885576i	$0.346236\pi$
$354$	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	$-0.734747\pi$
$367$	−7.04288	+	4.06621i	−0.367635	+	0.212254i	0.304790	+	0.952420i	$0.401414\pi$
$368$	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	$-0.930558\pi$
$373$	−5.80775	+	10.0593i	−0.300714	+	0.520851i	0.675584	+	0.737283i	$0.263892\pi$
$374$	−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	$-0.998411\pi$
$379$		−	0.194316i		−	0.00998136i	0.999988	−	0.00499068i	$-0.00158859\pi$
$380$		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	$-0.676624\pi$
$383$	9.25031	−	16.0220i	0.472669	−	0.818686i	0.999511	+	0.0312769i	$0.00995738\pi$
$384$	−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	0.115628	−	0.993293i	$-0.463112\pi$
$389$	20.3869	−	11.7704i	1.03366	−	0.596783i	0.918031	+	0.396509i	$0.129779\pi$
$390$		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	$-0.699862\pi$
$397$	−23.4091			−1.17487			−0.587435	+	0.809272i	$0.699862\pi$
$398$	−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	0.979477	−	0.201557i	$-0.0646000\pi$
$401$	25.9256	+	14.9681i	1.29466	+	0.747474i	0.315185	+	0.949030i	$0.397933\pi$
$402$	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	−0.890594	−	0.454798i	$-0.849711\pi$
$409$	−1.04012	+	1.80153i	−0.0514304	+	0.0890800i	0.839164	+	0.543878i	$0.183045\pi$
$410$		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	−0.721497	−	0.692417i	$-0.756546\pi$
$419$	4.89021	−	8.47010i	0.238903	−	0.413791i	0.960400	+	0.278626i	$0.0898790\pi$
$420$		0			0
$421$	1.05097	+	1.82034i	0.0512212	+	0.0887177i	0.890499	−	0.454985i	$-0.150355\pi$
$421$	1.05097	+	1.82034i	0.0512212	+	0.0887177i	−0.839278	+	0.543703i	$0.817022\pi$
$422$	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	$-0.551225\pi$
$433$	−6.66853			−0.320469			−0.160235	+	0.987079i	$0.551225\pi$
$434$	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	0.610225	−	0.792228i	$-0.291079\pi$
$439$	33.5536	−	19.3722i	1.60143	−	0.924585i	0.991202	−	0.132357i	$-0.0422544\pi$
$440$		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	−0.997797	−	0.0663436i	$-0.978867\pi$
$443$	−11.7099	−	20.2821i	−0.556354	−	0.963633i	0.441443	−	0.897289i	$-0.354467\pi$
$444$	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	$0.121501\pi$
$449$			15.7865i			0.745011i	−0.928030	+	0.372506i	$0.878499\pi$
$450$		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	$-0.103596\pi$
$457$	4.20812	+	7.28867i	0.196847	+	0.340950i	−0.750657	+	0.660692i	$0.770263\pi$
$458$	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	0.0920445	−	0.995755i	$-0.470660\pi$
$461$	21.4798	−	12.4014i	1.00042	−	0.577590i	0.908371	+	0.418165i	$0.137326\pi$
$462$	4.00986	+	14.7900i	0.186556	+	0.688091i
$463$	17.9437	+	10.3598i	0.833913	+	0.481460i	0.855191	−	0.518314i	$-0.173440\pi$
$463$	17.9437	+	10.3598i	0.833913	+	0.481460i	−0.0212774	+	0.999774i	$0.506773\pi$
$464$	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	$-0.511756\pi$
$467$	−1.59588			−0.0738487			−0.0369243	+	0.999318i	$0.511756\pi$
$468$	−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	0.789612	−	0.613606i	$-0.210282\pi$
$479$	−2.98947	−	5.17791i	−0.136592	−	0.236585i	−0.926205	+	0.377021i	$0.876948\pi$
$480$		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	−0.675373	−	0.737476i	$-0.736018\pi$
$491$	6.66941	−	11.5518i	0.300986	−	0.521323i	0.976360	+	0.216153i	$0.0693509\pi$
$492$	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	0.991728	+	0.128359i	$0.0409711\pi$
$499$	35.7135	+	20.6192i	1.59875	+	0.923041i	0.607026	+	0.794682i	$0.292362\pi$
$500$		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	$-0.681083\pi$
$503$	−24.1634			−1.07739			−0.538696	+	0.842500i	$0.681083\pi$
$504$	−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	0.256398	−	0.966571i	$-0.417464\pi$
$509$	−10.2084	−	5.89380i	−0.452478	−	0.261238i	−0.708876	+	0.705333i	$0.750797\pi$
$510$		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	$0.252186\pi$
$521$			32.5010i			1.42389i	−0.702234	+	0.711947i	$0.747814\pi$
$522$	−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	$-0.637733\pi$
$547$	3.67716	−	2.12301i	0.157224	−	0.0907734i	0.576548	+	0.817063i	$0.304399\pi$
$548$	−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	$-0.985680\pi$
$563$	−10.9277	+	18.9272i	−0.460546	+	0.797688i	0.538443	+	0.842662i	$0.319013\pi$
$564$	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	−0.742430	−	0.669924i	$-0.766327\pi$
$569$	−12.7253	+	7.34697i	−0.533473	+	0.308001i	0.208956	+	0.977925i	$0.432993\pi$
$570$		0			0
$571$	−15.5333	−	8.96816i	−0.650049	−	0.375306i	0.138426	−	0.990373i	$-0.455796\pi$
$571$	−15.5333	−	8.96816i	−0.650049	−	0.375306i	−0.788475	+	0.615067i	$0.789129\pi$
$572$	−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	$-0.206634\pi$
$577$	38.2696			1.59318			0.796592	+	0.604517i	$0.206634\pi$
$578$	−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	$-0.111170\pi$
$587$	4.20276	+	7.27939i	0.173466	+	0.300453i	−0.766163	+	0.642646i	$0.777837\pi$
$588$	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	−0.976125	−	0.217211i	$-0.930304\pi$
$599$	−7.34116	+	12.7153i	−0.299952	+	0.519532i	0.676173	+	0.736743i	$0.263637\pi$
$600$		0			0
$601$	13.6252	+	23.5995i	0.555783	+	0.962644i	0.997842	+	0.0656584i	$0.0209148\pi$
$601$	13.6252	+	23.5995i	0.555783	+	0.962644i	−0.442059	+	0.896986i	$0.645752\pi$
$602$	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	$-0.282520\pi$
$607$	6.78317	+	3.91627i	0.275320	+	0.158956i	−0.355983	+	0.934493i	$0.615854\pi$
$608$	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	$-0.492435\pi$
$613$	1.17677			0.0475293			0.0237646	+	0.999718i	$0.492435\pi$
$614$	−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	$-0.0260114\pi$
$617$	35.3790	+	20.4261i	1.42430	+	0.822322i	0.427641	+	0.903949i	$0.359345\pi$
$618$	0.870809	+	3.21189i	0.0350291	+	0.129201i
$619$	−42.7230	+	24.6661i	−1.71718	+	0.991416i	−0.793218	+	0.608938i	$0.791596\pi$
$619$	−42.7230	+	24.6661i	−1.71718	+	0.991416i	−0.923965	+	0.382478i	$0.875071\pi$
$620$		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	$0.185703\pi$
$631$			27.6752i			1.10173i	−0.834594	+	0.550866i	$0.814297\pi$
$632$	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	−0.734946	−	0.678126i	$-0.762793\pi$
$641$	−13.0424	+	7.53005i	−0.515145	+	0.297419i	0.219801	+	0.975545i	$0.429459\pi$
$642$	5.16304	+	5.13259i	0.203769	+	0.202567i
$643$	41.0665	+	23.7098i	1.61951	+	0.935022i	0.987048	+	0.160427i	$0.0512872\pi$
$643$	41.0665	+	23.7098i	1.61951	+	0.935022i	0.632458	+	0.774595i	$0.282046\pi$
$644$	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	$-0.372997\pi$
$647$	19.7634			0.776977			0.388489	+	0.921453i	$0.372997\pi$
$648$	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	$-0.0936554\pi$
$653$	30.2658	+	17.4740i	1.18439	+	0.683809i	0.227366	+	0.973809i	$0.426989\pi$
$654$	−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	−0.974588	−	0.224005i	$-0.928087\pi$
$659$	−17.4893	−	30.2924i	−0.681288	−	1.18003i	0.293300	−	0.956021i	$-0.405247\pi$
$660$		0			0
$661$	17.7487	−	30.7417i	0.690346	−	1.19571i	−0.281379	−	0.959597i	$-0.590792\pi$
$661$	17.7487	−	30.7417i	0.690346	−	1.19571i	0.971725	−	0.236117i	$-0.0758749\pi$
$662$	−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	0.794704	+	0.606997i	$0.207626\pi$
$673$	23.9454	+	41.4746i	0.923027	+	1.59873i	0.128322	+	0.991733i	$0.459041\pi$
$674$	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	$-0.667195\pi$
$677$	−0.0747996	+	0.0431856i	−0.00287478	+	0.00165976i	0.498562	+	0.866854i	$0.333862\pi$
$678$	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	$-0.652113\pi$
$683$	−24.0380			−0.919788			−0.459894	+	0.887974i	$0.652113\pi$
$684$	−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	−0.991665	−	0.128845i	$-0.958873\pi$
$691$	−36.1685	+	20.8819i	−1.37591	+	0.794384i	−0.384249	+	0.923229i	$0.625540\pi$
$692$	−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	$0.0127781\pi$
$701$			2.12514i			0.0802654i	−0.999194	+	0.0401327i	$0.987222\pi$
$702$	−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	0.824145	−	0.566379i	$-0.191656\pi$
$709$	−2.08824	−	3.61694i	−0.0784256	−	0.135837i	−0.902571	+	0.430541i	$0.858323\pi$
$710$		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	−0.506195	+	0.862419i	$0.668948\pi$
$727$	−40.6108	+	23.4466i	−1.50617	+	0.869587i	−0.999974	+	0.00716831i	$0.997718\pi$
$728$	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	$-0.726997\pi$
$733$	8.87721	−	15.3758i	0.327887	−	0.567917i	0.982092	+	0.188400i	$0.0603301\pi$
$734$	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	$-0.950005\pi$
$739$		−	8.50437i		−	0.312838i	0.987691	−	0.156419i	$-0.0499951\pi$
$740$		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	0.129798	−	0.991540i	$-0.458567\pi$
$743$	25.1755	−	43.6052i	0.923598	−	1.59972i	0.793800	−	0.608179i	$-0.208100\pi$
$744$	−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	0.982391	+	0.186834i	$0.0598228\pi$
$751$	44.8169	+	25.8750i	1.63539	+	0.944193i	0.652999	+	0.757359i	$0.273511\pi$
$752$	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	$-0.597164\pi$
$757$	−16.5374			−0.601064			−0.300532	+	0.953772i	$0.597164\pi$
$758$	−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	−0.157748	−	0.987479i	$-0.550423\pi$
$761$	−30.1188	−	17.3891i	−1.09180	−	0.630354i	−0.934056	+	0.357126i	$0.883757\pi$
$762$	−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	−0.692674	−	0.721251i	$-0.743567\pi$
$769$	7.71708	−	13.3664i	0.278285	−	0.482003i	0.970959	+	0.239248i	$0.0769007\pi$
$770$		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	0.985712	+	0.168442i	$0.0538734\pi$
$787$	45.5713	+	26.3106i	1.62444	+	0.937872i	0.638730	+	0.769431i	$0.279460\pi$
$788$	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	$-0.347341\pi$
$797$	−2.15117	−	1.24198i	−0.0761983	−	0.0439931i	−0.537615	+	0.843190i	$0.680675\pi$
$798$	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	$-0.851021\pi$
$809$		−	25.6629i		−	0.902261i	0.892458	−	0.451131i	$-0.148979\pi$
$810$		0			0
$811$			26.5970i			0.933948i	0.884271	+	0.466974i	$0.154656\pi$
$811$			26.5970i			0.933948i	−0.884271	+	0.466974i	$0.845344\pi$
$812$	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	−0.883435	−	0.468554i	$-0.844775\pi$
$821$	−26.3429	+	15.2091i	−0.919373	+	0.530800i	−0.0359383	+	0.999354i	$0.511442\pi$
$822$	16.4397	+	4.35296i	0.573402	+	0.151827i
$823$	−7.33737	−	4.23623i	−0.255764	−	0.147666i	0.366636	−	0.930364i	$-0.380509\pi$
$823$	−7.33737	−	4.23623i	−0.255764	−	0.147666i	−0.622401	+	0.782699i	$0.713843\pi$
$824$	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	$-0.724340\pi$
$827$	−37.2624			−1.29574			−0.647871	+	0.761750i	$0.724340\pi$
$828$	−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	0.710748	−	0.703447i	$-0.248357\pi$
$839$	−7.35228	−	12.7345i	−0.253829	−	0.439645i	−0.964577	+	0.263802i	$0.915023\pi$
$840$		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	$-0.237941\pi$
$853$	−6.48519	−	11.2327i	−0.222049	−	0.384600i	−0.955430	+	0.295218i	$0.904608\pi$
$854$	−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	$-0.629995\pi$
$857$	5.82871	−	3.36521i	0.199105	−	0.114953i	0.596238	+	0.802808i	$0.296661\pi$
$858$	23.6576	+	23.5181i	0.807656	+	0.802894i
$859$	−33.3860	−	19.2754i	−1.13912	−	0.657669i	−0.192904	−	0.981218i	$-0.561791\pi$
$859$	−33.3860	−	19.2754i	−1.13912	−	0.657669i	−0.946212	+	0.323549i	$0.895124\pi$
$860$		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	$-0.426316\pi$
$863$	13.4795			0.458847			0.229424	+	0.973327i	$0.426316\pi$
$864$	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	$-0.918192\pi$
$877$	−7.80171	+	13.5129i	−0.263445	+	0.456300i	0.703710	+	0.710487i	$0.251525\pi$
$878$	−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	$0.138502\pi$
$881$			25.0226i			0.843032i	−0.906821	+	0.421516i	$0.861498\pi$
$882$	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	$-0.731872\pi$
$887$	9.33323	−	16.1656i	0.313379	−	0.542789i	0.979092	+	0.203420i	$0.0652056\pi$
$888$	−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	$-0.908297\pi$
$907$	−35.9025	+	20.7283i	−1.19212	+	0.688273i	−0.233336	+	0.972396i	$0.574964\pi$
$908$	−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	0.908713	−	0.417420i	$-0.137066\pi$
$911$	2.80277	+	4.85454i	0.0928600	+	0.160838i	−0.815853	+	0.578259i	$0.803732\pi$
$912$	−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	$0.169642\pi$
$919$			30.8044i			1.01614i	−0.861315	+	0.508072i	$0.830358\pi$
$920$		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	−0.836853	−	0.547427i	$-0.815607\pi$
$929$	−23.8104	+	13.7469i	−0.781194	+	0.451023i	0.0556590	+	0.998450i	$0.482274\pi$
$930$		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	$-0.571488\pi$
$937$	−13.6341			−0.445407			−0.222704	+	0.974886i	$0.571488\pi$
$938$	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	−0.986234	−	0.165355i	$-0.947123\pi$
$941$	−49.7730	−	28.7364i	−1.62255	−	0.936781i	−0.636319	−	0.771426i	$-0.719544\pi$
$942$	−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	$-0.0647666\pi$
$947$	9.68402	+	16.7732i	0.314688	+	0.545056i	−0.664683	+	0.747126i	$0.731433\pi$
$948$	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	$-0.154495\pi$
$967$	28.6939	+	16.5665i	0.922735	+	0.532741i	0.0382285	+	0.999269i	$0.487829\pi$
$968$	−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	$-0.489830\pi$
$977$	−25.5578	−	14.7558i	−0.817667	−	0.472080i	−0.849611	+	0.527409i	$0.823163\pi$
$978$	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	−0.955486	−	0.295035i	$-0.904669\pi$
$983$	−22.9895	−	39.8190i	−0.733251	−	1.27003i	0.222235	−	0.974993i	$-0.428665\pi$
$984$	−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	$-0.683146\pi$
$991$		−	52.8232i		−	1.67798i	0.544144	−	0.838992i	$-0.316854\pi$
$992$	−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	0.923226	+	0.384257i	$0.125542\pi$
$997$	25.0831	+	43.4452i	0.794389	+	1.37592i	−0.128837	+	0.991666i	$0.541124\pi$
$998$	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.851.11		48
4.3	odd	2	inner	900.2.r.g.851.19		48
5.2	odd	4		180.2.n.d.59.23	yes	48
5.3	odd	4		180.2.n.d.59.2	✓	48
5.4	even	2	inner	900.2.r.g.851.14		48
9.2	odd	6	inner	900.2.r.g.551.19		48
15.2	even	4		540.2.n.d.179.2		48
15.8	even	4		540.2.n.d.179.23		48
20.3	even	4		180.2.n.d.59.18	yes	48
20.7	even	4		180.2.n.d.59.7	yes	48
20.19	odd	2	inner	900.2.r.g.851.6		48
36.11	even	6	inner	900.2.r.g.551.11		48
45.2	even	12		180.2.n.d.119.18	yes	48
45.7	odd	12		540.2.n.d.359.7		48
45.29	odd	6	inner	900.2.r.g.551.6		48
45.38	even	12		180.2.n.d.119.7	yes	48
45.43	odd	12		540.2.n.d.359.18		48
60.23	odd	4		540.2.n.d.179.7		48
60.47	odd	4		540.2.n.d.179.18		48
180.7	even	12		540.2.n.d.359.23		48
180.43	even	12		540.2.n.d.359.2		48
180.47	odd	12		180.2.n.d.119.2	yes	48
180.83	odd	12		180.2.n.d.119.23	yes	48
180.119	even	6	inner	900.2.r.g.551.14		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.2.n.d.59.2	✓	48	5.3	odd	4
180.2.n.d.59.7	yes	48	20.7	even	4
180.2.n.d.59.18	yes	48	20.3	even	4
180.2.n.d.59.23	yes	48	5.2	odd	4
180.2.n.d.119.2	yes	48	180.47	odd	12
180.2.n.d.119.7	yes	48	45.38	even	12
180.2.n.d.119.18	yes	48	45.2	even	12
180.2.n.d.119.23	yes	48	180.83	odd	12
540.2.n.d.179.2		48	15.2	even	4
540.2.n.d.179.7		48	60.23	odd	4
540.2.n.d.179.18		48	60.47	odd	4
540.2.n.d.179.23		48	15.8	even	4
540.2.n.d.359.2		48	180.43	even	12
540.2.n.d.359.7		48	45.7	odd	12
540.2.n.d.359.18		48	45.43	odd	12
540.2.n.d.359.23		48	180.7	even	12
900.2.r.g.551.6		48	45.29	odd	6	inner
900.2.r.g.551.11		48	36.11	even	6	inner
900.2.r.g.551.14		48	180.119	even	6	inner
900.2.r.g.551.19		48	9.2	odd	6	inner
900.2.r.g.851.6		48	20.19	odd	2	inner
900.2.r.g.851.11		48	1.1	even	1	trivial
900.2.r.g.851.14		48	5.4	even	2	inner
900.2.r.g.851.19		48	4.3	odd	2	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

Related objects

Downloads

Learn more