LMFDB - Embedded newform 405.3.l.e.298.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [405,3,Mod(28,405)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("405.28"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(405, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([4, 9])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	405.l (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,-6,0,0,-6,0,26] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$11.0354507066$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	8.0.49787136.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 3x^{6} + 5x^{4} + 12x^{2} + 16 $ x^8 + 3x^6 + 5x^4 + 12*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			298.2
Root			$-1.09445 + 0.895644i$ of defining polynomial
Character	$\chi$	$=$	405.298
Dual form			405.3.l.e.352.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.167219 + 0.624069i) q^{2} +(3.10260 - 1.79129i) q^{4} +(0.726456 - 4.94694i) q^{5} +(-1.54050 - 5.74921i) q^{7} +(3.46410 + 3.46410i) q^{8} +(3.20871 - 0.373864i) q^{10} +(0.0476751 - 0.0825757i) q^{11} +(0.884839 - 3.30226i) q^{13} +(3.33030 - 1.92275i) q^{14} +(5.58258 - 9.66930i) q^{16} +(-14.4086 + 14.4086i) q^{17} -25.7477i q^{19} +(-6.60750 - 16.6497i) q^{20} +(0.0595051 + 0.0159443i) q^{22} +(-1.23305 + 4.60180i) q^{23} +(-23.9445 - 7.18747i) q^{25} +2.20880 q^{26} +(-15.0780 - 15.0780i) q^{28} +(-35.6216 - 20.5661i) q^{29} +(18.5000 + 32.0429i) q^{31} +(25.8960 + 6.93882i) q^{32} +(-11.4014 - 6.58258i) q^{34} +(-29.5601 + 3.44420i) q^{35} +(50.6170 - 50.6170i) q^{37} +(16.0684 - 4.30550i) q^{38} +(19.6532 - 14.6202i) q^{40} +(1.13218 + 1.96099i) q^{41} +(-33.7465 + 9.04235i) q^{43} -0.341599i q^{44} -3.07803 q^{46} +(5.97769 + 22.3091i) q^{47} +(11.7550 - 6.78674i) q^{49} +(0.481505 - 16.1449i) q^{50} +(-3.17000 - 11.8306i) q^{52} +(49.0894 + 49.0894i) q^{53} +(-0.373864 - 0.295834i) q^{55} +(14.5794 - 25.2523i) q^{56} +(6.87809 - 25.6694i) q^{58} +(86.6216 - 50.0110i) q^{59} +(27.7477 - 48.0605i) q^{61} +(-16.9035 + 16.9035i) q^{62} -27.3394i q^{64} +(-15.6933 - 6.77620i) q^{65} +(-50.9941 - 13.6638i) q^{67} +(-18.8942 + 70.5141i) q^{68} +(-7.09243 - 17.8716i) q^{70} +39.8770 q^{71} +(39.3739 + 39.3739i) q^{73} +(40.0527 + 23.1244i) q^{74} +(-46.1216 - 79.8849i) q^{76} +(-0.548188 - 0.146887i) q^{77} +(52.0212 + 30.0345i) q^{79} +(-43.7780 - 34.6410i) q^{80} +(-1.03447 + 1.03447i) q^{82} +(-105.717 + 28.3267i) q^{83} +(60.8114 + 81.7458i) q^{85} +(-11.2861 - 19.5481i) q^{86} +(0.451202 - 0.120899i) q^{88} -51.6755i q^{89} -20.3485 q^{91} +(4.41749 + 16.4863i) q^{92} +(-12.9228 + 7.46099i) q^{94} +(-127.373 - 18.7046i) q^{95} +(25.9114 + 96.7027i) q^{97} +(6.20105 + 6.20105i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 6 q^{2} - 6 q^{5} + 26 q^{7} + 44 q^{10} - 28 q^{13} - 120 q^{14} + 8 q^{16} - 24 q^{20} + 46 q^{22} - 60 q^{23} + 32 q^{25} + 136 q^{28} - 120 q^{29} + 148 q^{31} + 168 q^{32} + 20 q^{37} + 54 q^{38}+ \cdots - 274 q^{97}+O(q^{100}) $ 8 * q - 6 * q^2 - 6 * q^5 + 26 * q^7 + 44 * q^10 - 28 * q^13 - 120 * q^14 + 8 * q^16 - 24 * q^20 + 46 * q^22 - 60 * q^23 + 32 * q^25 + 136 * q^28 - 120 * q^29 + 148 * q^31 + 168 * q^32 + 20 * q^37 + 54 * q^38 - 48 * q^40 + 2 * q^43 + 232 * q^46 - 6 * q^47 - 42 * q^50 - 112 * q^52 + 52 * q^55 - 66 * q^58 + 528 * q^59 + 112 * q^61 + 84 * q^65 - 76 * q^67 - 156 * q^68 + 396 * q^70 + 260 * q^73 + 852 * q^74 - 204 * q^76 + 318 * q^77 + 340 * q^82 - 582 * q^83 + 194 * q^85 - 72 * q^88 - 896 * q^91 - 228 * q^92 - 342 * q^95 - 274 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	0.167219	+	0.624069i	0.0836094	+	0.312035i	0.995047	−	0.0994033i	$-0.0316934\pi$
$2$	0.167219	+	0.624069i	0.0836094	+	0.312035i	−0.911438	+	0.411438i	$0.865027\pi$
$3$		0			0
$3$		0			0
$4$	3.10260	−	1.79129i	0.775650	−	0.447822i
$5$	0.726456	−	4.94694i	0.145291	−	0.989389i
$5$	0.726456	−	4.94694i	0.145291	−	0.989389i
$6$		0			0
$7$	−1.54050	−	5.74921i	−0.220071	−	0.821315i	−0.984320	−	0.176394i	$-0.943557\pi$
$7$	−1.54050	−	5.74921i	−0.220071	−	0.821315i	0.764249	−	0.644921i	$-0.223110\pi$
$8$	3.46410	+	3.46410i	0.433013	+	0.433013i
$9$		0			0
$10$	3.20871	−	0.373864i	0.320871	−	0.0373864i
$11$	0.0476751	−	0.0825757i	0.00433410	−	0.00750688i	−0.863850	−	0.503749i	$-0.831954\pi$
$11$	0.0476751	−	0.0825757i	0.00433410	−	0.00750688i	0.868184	+	0.496242i	$0.165287\pi$
$12$		0			0
$13$	0.884839	−	3.30226i	0.0680645	−	0.254020i	−0.923507	−	0.383582i	$-0.874690\pi$
$13$	0.884839	−	3.30226i	0.0680645	−	0.254020i	0.991571	+	0.129562i	$0.0413570\pi$
$14$	3.33030	−	1.92275i	0.237879	−	0.137339i
$15$		0			0
$16$	5.58258	−	9.66930i	0.348911	−	0.604332i
$17$	−14.4086	+	14.4086i	−0.847565	+	0.847565i	−0.989829	−	0.142264i	$-0.954562\pi$
$17$	−14.4086	+	14.4086i	−0.847565	+	0.847565i	0.142264	+	0.989829i	$0.454562\pi$
$18$		0			0
$19$		−	25.7477i		−	1.35514i	−0.735457	−	0.677572i	$-0.763032\pi$
$19$		−	25.7477i		−	1.35514i	0.735457	−	0.677572i	$-0.236968\pi$
$20$	−6.60750	−	16.6497i	−0.330375	−	0.832484i
$21$		0			0
$22$	0.0595051	+	0.0159443i	0.00270478	+	0.000724743i
$23$	−1.23305	+	4.60180i	−0.0536108	+	0.200078i	−0.987537	−	0.157388i	$-0.949693\pi$
$23$	−1.23305	+	4.60180i	−0.0536108	+	0.200078i	0.933926	+	0.357466i	$0.116359\pi$
$24$		0			0
$25$	−23.9445	−	7.18747i	−0.957781	−	0.287499i
$26$	2.20880			0.0849539
$27$		0			0
$28$	−15.0780	−	15.0780i	−0.538501	−	0.538501i
$29$	−35.6216	−	20.5661i	−1.22833	−	0.709177i	−0.261650	−	0.965163i	$-0.584267\pi$
$29$	−35.6216	−	20.5661i	−1.22833	−	0.709177i	−0.966681	+	0.255986i	$0.917600\pi$
$30$		0			0
$31$	18.5000	+	32.0429i	0.596774	+	1.03364i	0.993294	+	0.115617i	$0.0368845\pi$
$31$	18.5000	+	32.0429i	0.596774	+	1.03364i	−0.396520	+	0.918026i	$0.629782\pi$
$32$	25.8960	+	6.93882i	0.809251	+	0.216838i
$33$		0			0
$34$	−11.4014	−	6.58258i	−0.335334	−	0.193605i
$35$	−29.5601	+	3.44420i	−0.844575	+	0.0984057i
$36$		0			0
$37$	50.6170	−	50.6170i	1.36803	−	1.36803i	0.504781	−	0.863248i	$-0.331573\pi$
$37$	50.6170	−	50.6170i	1.36803	−	1.36803i	0.863248	−	0.504781i	$-0.168427\pi$
$38$	16.0684	−	4.30550i	0.422852	−	0.113303i
$39$		0			0
$40$	19.6532	−	14.6202i	0.491331	−	0.365505i
$41$	1.13218	+	1.96099i	0.0276140	+	0.0478289i	0.879502	−	0.475895i	$-0.157876\pi$
$41$	1.13218	+	1.96099i	0.0276140	+	0.0478289i	−0.851888	+	0.523724i	$0.824542\pi$
$42$		0			0
$43$	−33.7465	+	9.04235i	−0.784803	+	0.210287i	−0.628901	−	0.777485i	$-0.716495\pi$
$43$	−33.7465	+	9.04235i	−0.784803	+	0.210287i	−0.155902	+	0.987773i	$0.549828\pi$
$44$		−	0.341599i		−	0.00776362i
$45$		0			0
$46$	−3.07803			−0.0669137
$47$	5.97769	+	22.3091i	0.127185	+	0.474661i	0.999908	−	0.0135547i	$-0.00431473\pi$
$47$	5.97769	+	22.3091i	0.127185	+	0.474661i	−0.872723	+	0.488215i	$0.837648\pi$
$48$		0			0
$49$	11.7550	−	6.78674i	0.239898	−	0.138505i
$50$	0.481505	−	16.1449i	0.00963011	−	0.322898i
$51$		0			0
$52$	−3.17000	−	11.8306i	−0.0609616	−	0.227512i
$53$	49.0894	+	49.0894i	0.926216	+	0.926216i	0.997459	−	0.0712434i	$-0.0226967\pi$
$53$	49.0894	+	49.0894i	0.926216	+	0.926216i	−0.0712434	+	0.997459i	$0.522697\pi$
$54$		0			0
$55$	−0.373864	−	0.295834i	−0.00679752	−	0.00537879i
$56$	14.5794	−	25.2523i	0.260347	−	0.450933i
$57$		0			0
$58$	6.87809	−	25.6694i	0.118588	−	0.442575i
$59$	86.6216	−	50.0110i	1.46816	−	0.847644i	0.468799	−	0.883305i	$-0.344687\pi$
$59$	86.6216	−	50.0110i	1.46816	−	0.847644i	0.999364	+	0.0356610i	$0.0113537\pi$
$60$		0			0
$61$	27.7477	−	48.0605i	0.454881	−	0.787877i	−0.543801	−	0.839214i	$-0.683015\pi$
$61$	27.7477	−	48.0605i	0.454881	−	0.787877i	0.998681	+	0.0513379i	$0.0163485\pi$
$62$	−16.9035	+	16.9035i	−0.272636	+	0.272636i
$63$		0			0
$64$		−	27.3394i		−	0.427178i
$65$	−15.6933	−	6.77620i	−0.241436	−	0.104249i
$66$		0			0
$67$	−50.9941	−	13.6638i	−0.761107	−	0.203938i	−0.142668	−	0.989771i	$-0.545568\pi$
$67$	−50.9941	−	13.6638i	−0.761107	−	0.203938i	−0.618439	+	0.785833i	$0.712235\pi$
$68$	−18.8942	+	70.5141i	−0.277856	+	1.03697i
$69$		0			0
$70$	−7.09243	−	17.8716i	−0.101320	−	0.255309i
$71$	39.8770			0.561647			0.280824	−	0.959759i	$-0.409392\pi$
$71$	39.8770			0.561647			0.280824	+	0.959759i	$0.409392\pi$
$72$		0			0
$73$	39.3739	+	39.3739i	0.539368	+	0.539368i	0.923343	−	0.383975i	$-0.125445\pi$
$73$	39.3739	+	39.3739i	0.539368	+	0.539368i	−0.383975	+	0.923343i	$0.625445\pi$
$74$	40.0527	+	23.1244i	0.541252	+	0.312492i
$75$		0			0
$76$	−46.1216	−	79.8849i	−0.606863	−	1.05112i
$77$	−0.548188	−	0.146887i	−0.00711933	−	0.00190762i
$78$		0			0
$79$	52.0212	+	30.0345i	0.658497	+	0.380183i	0.791704	−	0.610905i	$-0.209194\pi$
$79$	52.0212	+	30.0345i	0.658497	+	0.380183i	−0.133207	+	0.991088i	$0.542528\pi$
$80$	−43.7780	−	34.6410i	−0.547225	−	0.433013i
$81$		0			0
$82$	−1.03447	+	1.03447i	−0.0126155	+	0.0126155i
$83$	−105.717	+	28.3267i	−1.27370	+	0.341286i	−0.831446	−	0.555606i	$-0.812486\pi$
$83$	−105.717	+	28.3267i	−1.27370	+	0.341286i	−0.442251	+	0.896892i	$0.645820\pi$
$84$		0			0
$85$	60.8114	+	81.7458i	0.715428	+	0.961715i
$86$	−11.2861	−	19.5481i	−0.131234	−	0.227304i
$87$		0			0
$88$	0.451202	−	0.120899i	0.00512730	−	0.00137385i
$89$		−	51.6755i		−	0.580623i	−0.956932	−	0.290312i	$-0.906241\pi$
$89$		−	51.6755i		−	0.580623i	0.956932	−	0.290312i	$-0.0937590\pi$
$90$		0			0
$91$	−20.3485			−0.223610
$92$	4.41749	+	16.4863i	0.0480162	+	0.179199i
$93$		0			0
$94$	−12.9228	+	7.46099i	−0.137477	+	0.0793722i
$95$	−127.373	−	18.7046i	−1.34076	−	0.196890i
$96$		0			0
$97$	25.9114	+	96.7027i	0.267128	+	0.996935i	0.960935	+	0.276774i	$0.0892654\pi$
$97$	25.9114	+	96.7027i	0.267128	+	0.996935i	−0.693807	+	0.720161i	$0.744068\pi$
$98$	6.20105	+	6.20105i	0.0632760	+	0.0632760i
$99$		0			0
$100$	−87.1652	+	20.5917i	−0.871652	+	0.205917i
$101$	9.06943	−	15.7087i	0.0897963	−	0.155532i	−0.817629	−	0.575746i	$-0.804712\pi$
$101$	9.06943	−	15.7087i	0.0897963	−	0.155532i	0.907425	+	0.420214i	$0.138045\pi$
$102$		0			0
$103$	−16.4074	+	61.2331i	−0.159295	+	0.594496i	0.839404	+	0.543507i	$0.182904\pi$
$103$	−16.4074	+	61.2331i	−0.159295	+	0.594496i	−0.998699	+	0.0509890i	$0.983763\pi$
$104$	14.5045	−	8.37420i	0.139467	−	0.0805212i
$105$		0			0
$106$	−22.4265	+	38.8439i	−0.211571	+	0.366452i
$107$	150.617	−	150.617i	1.40764	−	1.40764i	0.635703	−	0.771934i	$-0.280710\pi$
$107$	150.617	−	150.617i	1.40764	−	1.40764i	0.771934	−	0.635703i	$-0.219290\pi$
$108$		0			0
$109$			126.495i			1.16051i	0.814435	+	0.580254i	$0.197047\pi$
$109$			126.495i			1.16051i	−0.814435	+	0.580254i	$0.802953\pi$
$110$	0.122104	−	0.282786i	0.00111003	−	0.00257078i
$111$		0			0
$112$	−64.1908	−	17.1999i	−0.573132	−	0.153570i
$113$	−48.5936	+	181.354i	−0.430032	+	1.60490i	0.322652	+	0.946518i	$0.395426\pi$
$113$	−48.5936	+	181.354i	−0.430032	+	1.60490i	−0.752683	+	0.658383i	$0.771241\pi$
$114$		0			0
$115$	21.8691	+	9.44283i	0.190166	+	0.0821115i
$116$	−147.359			−1.27034
$117$		0			0
$118$	45.6951	+	45.6951i	0.387246	+	0.387246i
$119$	105.034	+	60.6417i	0.882643	+	0.509594i
$120$		0			0
$121$	60.4955	+	104.781i	0.499962	+	0.865960i
$122$	34.6330	+	9.27988i	0.283877	+	0.0760646i
$123$		0			0
$124$	114.796	+	66.2777i	0.925776	+	0.534497i
$125$	−52.9507	+	113.231i	−0.423605	+	0.905847i
$126$		0			0
$127$	−58.8693	+	58.8693i	−0.463538	+	0.463538i	−0.899813	−	0.436275i	$-0.856297\pi$
$127$	−58.8693	+	58.8693i	−0.463538	+	0.463538i	0.436275	+	0.899813i	$0.356297\pi$
$128$	120.646	−	32.3269i	0.942545	−	0.252554i
$129$		0			0
$130$	1.60460	−	10.9268i	0.0123431	−	0.0840525i
$131$	−118.153	−	204.647i	−0.901931	−	1.56219i	−0.824984	−	0.565155i	$-0.808816\pi$
$131$	−118.153	−	204.647i	−0.901931	−	1.56219i	−0.0769467	−	0.997035i	$-0.524517\pi$
$132$		0			0
$133$	−148.029	+	39.6643i	−1.11300	+	0.298228i
$134$		−	34.1087i		−	0.254543i
$135$		0			0
$136$	−99.8258			−0.734013
$137$	18.8942	+	70.5141i	0.137914	+	0.514702i	0.999969	+	0.00788694i	$0.00251052\pi$
$137$	18.8942	+	70.5141i	0.137914	+	0.514702i	−0.862055	+	0.506815i	$0.830823\pi$
$138$		0			0
$139$	−138.044	+	79.6996i	−0.993121	+	0.573379i	−0.906206	−	0.422837i	$-0.861034\pi$
$139$	−138.044	+	79.6996i	−0.993121	+	0.573379i	−0.0869151	+	0.996216i	$0.527701\pi$
$140$	−85.5437	+	63.6367i	−0.611026	+	0.454548i
$141$		0			0
$142$	6.66818	+	24.8860i	0.0469590	+	0.175253i
$143$	−0.230502	−	0.230502i	−0.00161190	−	0.00161190i
$144$		0			0
$145$	−127.617	+	161.278i	−0.880118	+	1.11226i
$146$	−17.9880	+	31.1561i	−0.123205	+	0.213398i
$147$		0			0
$148$	66.3748	−	247.714i	0.448479	−	1.67374i
$149$	72.2341	−	41.7044i	0.484793	−	0.279895i	−0.237619	−	0.971358i	$-0.576367\pi$
$149$	72.2341	−	41.7044i	0.484793	−	0.279895i	0.722412	+	0.691463i	$0.243034\pi$
$150$		0			0
$151$	17.3784	−	30.1003i	0.115089	−	0.199340i	−0.802726	−	0.596347i	$-0.796618\pi$
$151$	17.3784	−	30.1003i	0.115089	−	0.199340i	0.917815	+	0.397008i	$0.129951\pi$
$152$	89.1927	−	89.1927i	0.586794	−	0.586794i
$153$		0			0
$154$		−	0.366669i		−	0.00238097i
$155$	171.954	−	68.2407i	1.10938	−	0.440263i
$156$		0			0
$157$	−6.45085	−	1.72850i	−0.0410882	−	0.0110096i	0.238216	−	0.971212i	$-0.423437\pi$
$157$	−6.45085	−	1.72850i	−0.0410882	−	0.0110096i	−0.279305	+	0.960203i	$0.590104\pi$
$158$	−10.0447	+	37.4872i	−0.0635738	+	0.237261i
$159$		0			0
$160$	53.1383	−	123.065i	0.332114	−	0.769159i
$161$	28.3562			0.176126
$162$		0			0
$163$	171.374	+	171.374i	1.05137	+	1.05137i	0.998607	+	0.0527665i	$0.0168039\pi$
$163$	171.374	+	171.374i	1.05137	+	1.05137i	0.0527665	+	0.998607i	$0.483196\pi$
$164$	7.02538	+	4.05610i	0.0428377	+	0.0247323i
$165$		0			0
$166$	−35.3557	−	61.2378i	−0.212986	−	0.368903i
$167$	73.2981	+	19.6402i	0.438911	+	0.117606i	0.471506	−	0.881863i	$-0.343711\pi$
$167$	73.2981	+	19.6402i	0.438911	+	0.117606i	−0.0325953	+	0.999469i	$0.510377\pi$
$168$		0			0
$169$	136.236	+	78.6561i	0.806132	+	0.465420i
$170$	−40.8462	+	51.6199i	−0.240272	+	0.303647i
$171$		0			0
$172$	−88.5045	+	88.5045i	−0.514561	+	0.514561i
$173$	−202.209	+	54.1816i	−1.16884	+	0.313189i	−0.790489	−	0.612476i	$-0.790174\pi$
$173$	−202.209	+	54.1816i	−1.16884	+	0.313189i	−0.378346	+	0.925664i	$0.623507\pi$
$174$		0			0
$175$	−4.43585	+	148.734i	−0.0253477	+	0.849910i
$176$	−0.532300	−	0.921970i	−0.00302443	−	0.00523847i
$177$		0			0
$178$	32.2491	−	8.64111i	0.181175	−	0.0485456i
$179$		−	140.296i		−	0.783777i	−0.920013	−	0.391889i	$-0.871822\pi$
$179$		−	140.296i		−	0.783777i	0.920013	−	0.391889i	$-0.128178\pi$
$180$		0			0
$181$	114.720			0.633815			0.316907	−	0.948457i	$-0.397356\pi$
$181$	114.720			0.633815			0.316907	+	0.948457i	$0.397356\pi$
$182$	−3.40265	−	12.6989i	−0.0186959	−	0.0697740i
$183$		0			0
$184$	−20.2125	+	11.6697i	−0.109851	+	0.0634223i
$185$	−213.629	−	287.171i	−1.15475	−	1.55227i
$186$		0			0
$187$	0.502869	+	1.87673i	0.00268914	+	0.0100360i
$188$	58.5083	+	58.5083i	0.311215	+	0.311215i
$189$		0			0
$190$	−9.62614	−	82.6170i	−0.0506639	−	0.434827i
$191$	−128.545	+	222.647i	−0.673012	+	1.16569i	0.304034	+	0.952661i	$0.401666\pi$
$191$	−128.545	+	222.647i	−0.673012	+	1.16569i	−0.977046	+	0.213030i	$0.931667\pi$
$192$		0			0
$193$	32.3085	−	120.577i	0.167402	−	0.624752i	−0.830320	−	0.557287i	$-0.811842\pi$
$193$	32.3085	−	120.577i	0.167402	−	0.624752i	0.997722	−	0.0674648i	$-0.0214910\pi$
$194$	−56.0163	+	32.3410i	−0.288744	+	0.166706i
$195$		0			0
$196$	24.3140	−	42.1131i	0.124051	−	0.214863i
$197$	44.6917	−	44.6917i	0.226862	−	0.226862i	−0.584519	−	0.811380i	$-0.698717\pi$
$197$	44.6917	−	44.6917i	0.226862	−	0.226862i	0.811380	+	0.584519i	$0.198717\pi$
$198$		0			0
$199$		−	297.964i		−	1.49730i	−0.662963	−	0.748652i	$-0.730701\pi$
$199$		−	297.964i		−	1.49730i	0.662963	−	0.748652i	$-0.269299\pi$
$200$	−58.0481	−	107.844i	−0.290241	−	0.539222i
$201$		0			0
$202$	11.3199	+	3.03316i	0.0560391	+	0.0150156i
$203$	−63.3641	+	236.478i	−0.312138	+	1.16492i
$204$		0			0
$205$	10.5234	−	4.17624i	0.0513335	−	0.0203719i
$206$	−40.9573			−0.198822
$207$		0			0
$208$	−26.9909	−	26.9909i	−0.129764	−	0.129764i
$209$	−2.12614	−	1.22753i	−0.0101729	−	0.00587333i
$210$		0			0
$211$	67.9864	+	117.756i	0.322210	+	0.558085i	0.980944	−	0.194292i	$-0.0622409\pi$
$211$	67.9864	+	117.756i	0.322210	+	0.558085i	−0.658734	+	0.752376i	$0.728908\pi$
$212$	240.238	+	64.3716i	1.13320	+	0.303640i
$213$		0			0
$214$	119.182	+	68.8095i	0.556923	+	0.321540i
$215$	20.2167	+	173.511i	0.0940310	+	0.807028i
$216$		0			0
$217$	155.722	−	155.722i	0.717615	−	0.717615i
$218$	−78.9419	+	21.1524i	−0.362119	+	0.0970294i
$219$		0			0
$220$	−1.68987	−	0.248157i	−0.00768124	−	0.00112799i
$221$	34.8317	+	60.3303i	0.157610	+	0.272988i
$222$		0			0
$223$	−218.658	+	58.5893i	−0.980530	+	0.262732i	−0.713268	−	0.700892i	$-0.752786\pi$
$223$	−218.658	+	58.5893i	−0.980530	+	0.262732i	−0.267262	+	0.963624i	$0.586119\pi$
$224$		−	159.571i		−	0.712370i
$225$		0			0
$226$	−121.303			−0.536739
$227$	−18.5379	−	69.1844i	−0.0816648	−	0.304777i	0.912997	−	0.407966i	$-0.133762\pi$
$227$	−18.5379	−	69.1844i	−0.0816648	−	0.304777i	−0.994662	+	0.103189i	$0.967095\pi$
$228$		0			0
$229$	−30.8909	+	17.8348i	−0.134895	+	0.0778814i	−0.565929	−	0.824454i	$-0.691482\pi$
$229$	−30.8909	+	17.8348i	−0.134895	+	0.0778814i	0.431034	+	0.902336i	$0.358149\pi$
$230$	−2.23605	+	15.2268i	−0.00972197	+	0.0662037i
$231$		0			0
$232$	−52.1536	−	194.640i	−0.224800	−	0.838965i
$233$	191.102	+	191.102i	0.820180	+	0.820180i	0.986134	−	0.165954i	$-0.0530703\pi$
$233$	191.102	+	191.102i	0.820180	+	0.820180i	−0.165954	+	0.986134i	$0.553070\pi$
$234$		0			0
$235$	114.704	−	13.3648i	0.488103	−	0.0568714i
$236$	179.168	−	310.328i	0.759187	−	1.31495i
$237$		0			0
$238$	−20.2809	+	75.6892i	−0.0852137	+	0.318022i
$239$	300.495	−	173.491i	1.25730	−	0.725904i	0.284754	−	0.958601i	$-0.408088\pi$
$239$	300.495	−	173.491i	1.25730	−	0.725904i	0.972549	+	0.232696i	$0.0747548\pi$
$240$		0			0
$241$	−7.14432	+	12.3743i	−0.0296445	+	0.0513457i	−0.880467	−	0.474107i	$-0.842771\pi$
$241$	−7.14432	+	12.3743i	−0.0296445	+	0.0513457i	0.850823	+	0.525453i	$0.176104\pi$
$242$	−55.2747	+	55.2747i	−0.228408	+	0.228408i
$243$		0			0
$244$		−	198.817i		−	0.814822i
$245$	−25.0342	−	63.0815i	−0.102180	−	0.257476i
$246$		0			0
$247$	−85.0258	−	22.7826i	−0.344234	−	0.0922372i
$248$	−46.9141	+	175.086i	−0.189170	+	0.705991i
$249$		0			0
$250$	−79.5182	−	14.1105i	−0.318073	−	0.0564422i
$251$	−399.294			−1.59081			−0.795406	−	0.606077i	$-0.792742\pi$
$251$	−399.294			−1.59081			−0.795406	+	0.606077i	$0.792742\pi$
$252$		0			0
$253$	0.321211	+	0.321211i	0.00126961	+	0.00126961i
$254$	−46.5826	−	26.8945i	−0.183396	−	0.105884i
$255$		0			0
$256$	−14.3303	−	24.8208i	−0.0559777	−	0.0969563i
$257$	337.408	+	90.4083i	1.31287	+	0.351783i	0.846303	−	0.532701i	$-0.178823\pi$
$257$	337.408	+	90.4083i	1.31287	+	0.351783i	0.466570	+	0.884484i	$0.345490\pi$
$258$		0			0
$259$	−368.983	−	213.033i	−1.42465	−	0.822520i
$260$	−60.8282	+	7.08741i	−0.233955	+	0.0272593i
$261$		0			0
$262$	107.956	−	107.956i	0.412047	−	0.412047i
$263$	21.1855	−	5.67663i	0.0805532	−	0.0215842i	−0.218317	−	0.975878i	$-0.570057\pi$
$263$	21.1855	−	5.67663i	0.0805532	−	0.0215842i	0.298871	+	0.954294i	$0.403390\pi$
$264$		0			0
$265$	278.504	−	207.181i	1.05096	−	0.781816i
$266$	−49.5065	−	85.7477i	−0.186115	−	0.322360i
$267$		0			0
$268$	−182.690	+	48.9517i	−0.681680	+	0.182656i
$269$			298.922i			1.11123i	0.831439	+	0.555617i	$0.187518\pi$
$269$			298.922i			1.11123i	−0.831439	+	0.555617i	$0.812482\pi$
$270$		0			0
$271$	−21.0091			−0.0775243			−0.0387622	−	0.999248i	$-0.512341\pi$
$271$	−21.0091			−0.0775243			−0.0387622	+	0.999248i	$0.512341\pi$
$272$	58.8841	+	219.758i	0.216486	+	0.807935i
$273$		0			0
$274$	−40.8462	+	23.5826i	−0.149074	+	0.0860678i
$275$	−1.73507	+	1.63457i	−0.00630934	+	0.00594390i
$276$		0			0
$277$	100.752	+	376.011i	0.363725	+	1.35744i	0.869140	+	0.494565i	$0.164673\pi$
$277$	100.752	+	376.011i	0.363725	+	1.35744i	−0.505415	+	0.862876i	$0.668661\pi$
$278$	−72.8216	−	72.8216i	−0.261948	−	0.261948i
$279$		0			0
$280$	−114.330	−	90.4682i	−0.408323	−	0.323101i
$281$	81.1601	−	140.573i	0.288826	−	0.500262i	−0.684704	−	0.728822i	$-0.740068\pi$
$281$	81.1601	−	140.573i	0.288826	−	0.500262i	0.973530	+	0.228560i	$0.0734017\pi$
$282$		0			0
$283$	46.6314	−	174.031i	0.164775	−	0.614949i	−0.833294	−	0.552831i	$-0.813548\pi$
$283$	46.6314	−	174.031i	0.164775	−	0.614949i	0.998069	−	0.0621185i	$-0.0197857\pi$
$284$	123.722	−	71.4311i	0.435642	−	0.251518i
$285$		0			0
$286$	0.105305	−	0.182393i	0.000368199	−	0.000637739i
$287$	9.53000	−	9.53000i	0.0332056	−	0.0332056i
$288$		0			0
$289$		−	126.216i		−	0.436733i
$290$	−121.988	−	52.6732i	−0.420650	−	0.181632i
$291$		0			0
$292$	192.691	+	51.6315i	0.659902	+	0.176820i
$293$	70.8962	−	264.588i	0.241967	−	0.903032i	−0.732917	−	0.680318i	$-0.761842\pi$
$293$	70.8962	−	264.588i	0.241967	−	0.903032i	0.974884	−	0.222714i	$-0.0714916\pi$
$294$		0			0
$295$	−184.475	−	464.843i	−0.625339	−	1.57574i
$296$	350.685			1.18475
$297$		0			0
$298$	38.1053	+	38.1053i	0.127870	+	0.127870i
$299$	14.1053	+	8.14370i	0.0471749	+	0.0272365i
$300$		0			0
$301$	103.973	+	180.086i	0.345424	+	0.598292i
$302$	21.6907	+	5.81199i	0.0718234	+	0.0192450i
$303$		0			0
$304$	−248.963	−	143.739i	−0.818956	−	0.472824i
$305$	−217.595	−	172.180i	−0.713426	−	0.564526i
$306$		0			0
$307$	405.347	−	405.347i	1.32035	−	1.32035i	0.406854	−	0.913493i	$-0.366626\pi$
$307$	405.347	−	405.347i	1.32035	−	1.32035i	0.913493	−	0.406854i	$-0.133374\pi$
$308$	−1.96393	+	0.526232i	−0.00637638	+	0.00170855i
$309$		0			0
$310$	71.3409	+	95.9001i	0.230132	+	0.309355i
$311$	87.9893	+	152.402i	0.282924	+	0.490038i	0.972104	−	0.234552i	$-0.0753623\pi$
$311$	87.9893	+	152.402i	0.282924	+	0.490038i	−0.689180	+	0.724590i	$0.742029\pi$
$312$		0			0
$313$	262.133	−	70.2383i	0.837486	−	0.224404i	0.185509	−	0.982643i	$-0.440607\pi$
$313$	262.133	−	70.2383i	0.837486	−	0.224404i	0.651977	+	0.758239i	$0.273940\pi$
$314$		−	4.31481i		−	0.0137414i
$315$		0			0
$316$	215.202			0.681017
$317$	−101.533	−	378.928i	−0.320294	−	1.19536i	−0.918958	−	0.394355i	$-0.870968\pi$
$317$	−101.533	−	378.928i	−0.320294	−	1.19536i	0.598664	−	0.801000i	$-0.295699\pi$
$318$		0			0
$319$	−3.39653	+	1.96099i	−0.0106474	+	0.00614729i
$320$	−135.246	−	19.8609i	−0.422645	−	0.0620652i
$321$		0			0
$322$	4.74169	+	17.6962i	0.0147257	+	0.0549572i
$323$	370.989	+	370.989i	1.14857	+	1.14857i
$324$		0			0
$325$	−44.9220	+	72.7114i	−0.138221	+	0.223727i
$326$	−78.2922	+	135.606i	−0.240160	+	0.415969i
$327$		0			0
$328$	−2.87108	+	10.7150i	−0.00875330	+	0.0326677i
$329$	119.051	−	68.7340i	0.361856	−	0.208918i
$330$		0			0
$331$	151.622	−	262.616i	0.458071	−	0.793403i	−0.540788	−	0.841159i	$-0.681874\pi$
$331$	151.622	−	262.616i	0.458071	−	0.793403i	0.998859	+	0.0477564i	$0.0152071\pi$
$332$	−277.256	+	277.256i	−0.835108	+	0.835108i
$333$		0			0
$334$			49.0273i			0.146788i
$335$	−104.639	+	242.339i	−0.312356	+	0.723400i
$336$		0			0
$337$	−58.5135	−	15.6786i	−0.173631	−	0.0465242i	0.170956	−	0.985279i	$-0.445314\pi$
$337$	−58.5135	−	15.6786i	−0.173631	−	0.0465242i	−0.344587	+	0.938754i	$0.611981\pi$
$338$	−26.3055	+	98.1736i	−0.0778271	+	0.290455i
$339$		0			0
$340$	335.104	+	144.694i	0.985599	+	0.425571i
$341$	3.52796			0.0103459
$342$		0			0
$343$	−263.354	−	263.354i	−0.767795	−	0.767795i
$344$	−148.225	−	85.5777i	−0.430887	−	0.248773i
$345$		0			0
$346$	−67.6261	−	117.132i	−0.195451	−	0.338532i
$347$	−618.732	−	165.789i	−1.78309	−	0.477777i	−0.791948	−	0.610588i	$-0.790933\pi$
$347$	−618.732	−	165.789i	−1.78309	−	0.477777i	−0.991141	+	0.132811i	$0.957600\pi$
$348$		0			0
$349$	123.659	+	71.3947i	0.354324	+	0.204569i	0.666588	−	0.745426i	$-0.267754\pi$
$349$	123.659	+	71.3947i	0.354324	+	0.204569i	−0.312264	+	0.949995i	$0.601087\pi$
$350$	−93.5622	+	22.1029i	−0.267321	+	0.0631511i
$351$		0			0
$352$	1.80757	−	1.80757i	0.00513515	−	0.00513515i
$353$	−264.219	+	70.7973i	−0.748496	+	0.200559i	−0.612851	−	0.790199i	$-0.709977\pi$
$353$	−264.219	+	70.7973i	−0.748496	+	0.200559i	−0.135645	+	0.990758i	$0.543311\pi$
$354$		0			0
$355$	28.9689	−	197.269i	0.0816024	−	0.555688i
$356$	−92.5656	−	160.328i	−0.260016	−	0.450361i
$357$		0			0
$358$	87.5545	−	23.4601i	0.244566	−	0.0655311i
$359$		−	354.888i		−	0.988546i	−0.869307	−	0.494273i	$-0.835434\pi$
$359$		−	354.888i		−	0.988546i	0.869307	−	0.494273i	$-0.164566\pi$
$360$		0			0
$361$	−301.945			−0.836414
$362$	19.1834	+	71.5935i	0.0529929	+	0.197772i
$363$		0			0
$364$	−63.1332	+	36.4500i	−0.173443	+	0.100137i
$365$	223.384	−	166.177i	0.612010	−	0.455279i
$366$		0			0
$367$	−61.2471	−	228.577i	−0.166886	−	0.622827i	−0.997792	−	0.0664143i	$-0.978844\pi$
$367$	−61.2471	−	228.577i	−0.166886	−	0.622827i	0.830906	−	0.556413i	$-0.187823\pi$
$368$	37.6126	+	37.6126i	0.102208	+	0.102208i
$369$		0			0
$370$	143.492	−	181.339i	0.387815	−	0.490106i
$371$	206.603	−	357.847i	0.556882	−	0.964548i
$372$		0			0
$373$	−61.0080	+	227.685i	−0.163560	+	0.610415i	0.834659	+	0.550767i	$0.185665\pi$
$373$	−61.0080	+	227.685i	−0.163560	+	0.610415i	−0.998219	+	0.0596484i	$0.981002\pi$
$374$	−1.08712	+	0.627650i	−0.00290674	+	0.00167821i
$375$		0			0
$376$	−56.5735	+	97.9881i	−0.150461	+	0.260607i
$377$	−99.4341	+	99.4341i	−0.263751	+	0.263751i
$378$		0			0
$379$			115.252i			0.304096i	0.988373	+	0.152048i	$0.0485868\pi$
$379$			115.252i			0.304096i	−0.988373	+	0.152048i	$0.951413\pi$
$380$	−428.692	+	170.128i	−1.12814	+	0.447705i
$381$		0			0
$382$	−160.442	−	42.9904i	−0.420006	−	0.112540i
$383$	−125.277	+	467.540i	−0.327094	+	1.22073i	0.585097	+	0.810964i	$0.301057\pi$
$383$	−125.277	+	467.540i	−0.327094	+	1.22073i	−0.912190	+	0.409767i	$0.865610\pi$
$384$		0			0
$385$	−1.12487	+	2.60515i	−0.00292175	+	0.00676662i
$386$	80.6510			0.208940
$387$		0			0
$388$	253.615	+	253.615i	0.653647	+	0.653647i
$389$	289.720	+	167.270i	0.744783	+	0.430000i	0.823806	−	0.566872i	$-0.191847\pi$
$389$	289.720	+	167.270i	0.744783	+	0.430000i	−0.0790230	+	0.996873i	$0.525180\pi$
$390$		0			0
$391$	−48.5390	−	84.0720i	−0.124141	−	0.215018i
$392$	64.2304	+	17.2105i	0.163853	+	0.0439043i
$393$		0			0
$394$	35.3640	+	20.4174i	0.0897564	+	0.0518209i
$395$	186.370	−	235.527i	0.471823	−	0.596272i
$396$		0			0
$397$	−469.973	+	469.973i	−1.18381	+	1.18381i	−0.205061	+	0.978749i	$0.565739\pi$
$397$	−469.973	+	469.973i	−1.18381	+	1.18381i	−0.978749	+	0.205061i	$0.934261\pi$
$398$	185.950	−	49.8251i	0.467211	−	0.125189i
$399$		0			0
$400$	−203.170	+	191.402i	−0.507925	+	0.478506i
$401$	94.6393	+	163.920i	0.236008	+	0.408778i	0.959565	−	0.281486i	$-0.0908274\pi$
$401$	94.6393	+	163.920i	0.236008	+	0.408778i	−0.723557	+	0.690265i	$0.757494\pi$
$402$		0			0
$403$	122.184	−	32.7390i	0.303185	−	0.0812383i
$404$		−	64.9838i		−	0.160851i
$405$		0			0
$406$	−158.174			−0.389592
$407$	−1.76656	−	6.59291i	−0.00434045	−	0.0161988i
$408$		0			0
$409$	370.071	−	213.661i	0.904819	−	0.522398i	0.0260585	−	0.999660i	$-0.491704\pi$
$409$	370.071	−	213.661i	0.904819	−	0.522398i	0.878761	+	0.477263i	$0.158371\pi$
$410$	4.36597	+	5.86896i	0.0106487	+	0.0143145i
$411$		0			0
$412$	58.7806	+	219.372i	0.142671	+	0.532457i
$413$	−420.964	−	420.964i	−1.01928	−	1.01928i
$414$		0			0
$415$	63.3322	+	543.553i	0.152608	+	1.30977i
$416$	45.8276	−	79.3758i	0.110163	−	0.190807i
$417$		0			0
$418$	0.410531	−	1.53212i	0.000982131	−	0.00366536i
$419$	−466.301	+	269.219i	−1.11289	+	0.642528i	−0.939577	−	0.342339i	$-0.888781\pi$
$419$	−466.301	+	269.219i	−1.11289	+	0.642528i	−0.173314	+	0.984867i	$0.555448\pi$
$420$		0			0
$421$	−197.500	+	342.080i	−0.469121	+	0.812542i	−0.999377	−	0.0352961i	$-0.988763\pi$
$421$	−197.500	+	342.080i	−0.469121	+	0.812542i	0.530256	+	0.847838i	$0.322096\pi$
$422$	−62.1192	+	62.1192i	−0.147202	+	0.147202i
$423$		0			0
$424$			340.102i			0.802126i
$425$	448.569	−	241.446i	1.05546	−	0.568108i
$426$		0			0
$427$	−319.055	−	85.4905i	−0.747201	−	0.200212i
$428$	197.506	−	737.104i	0.461463	−	1.72220i
$429$		0			0
$430$	−104.902	+	41.6309i	−0.243959	+	0.0968160i
$431$	60.0895			0.139419			0.0697094	−	0.997567i	$-0.477793\pi$
$431$	60.0895			0.139419			0.0697094	+	0.997567i	$0.477793\pi$
$432$		0			0
$433$	−192.514	−	192.514i	−0.444604	−	0.444604i	0.448952	−	0.893556i	$-0.351798\pi$
$433$	−192.514	−	192.514i	−0.444604	−	0.444604i	−0.893556	+	0.448952i	$0.851798\pi$
$434$	123.221	+	71.1418i	0.283920	+	0.163921i
$435$		0			0
$436$	226.590	+	392.465i	0.519701	+	0.900149i
$437$	118.486	+	31.7482i	0.271135	+	0.0726503i
$438$		0			0
$439$	−253.170	−	146.168i	−0.576697	−	0.332956i	0.183123	−	0.983090i	$-0.441379\pi$
$439$	−253.170	−	146.168i	−0.576697	−	0.332956i	−0.759820	+	0.650134i	$0.774713\pi$
$440$	−0.270303	−	2.31990i	−0.000614326	−	0.00527250i
$441$		0			0
$442$	−31.8258	+	31.8258i	−0.0720040	+	0.0720040i
$443$	365.264	−	97.8721i	0.824523	−	0.220930i	0.178200	−	0.983994i	$-0.442973\pi$
$443$	365.264	−	97.8721i	0.824523	−	0.220930i	0.646323	+	0.763064i	$0.276306\pi$
$444$		0			0
$445$	−255.636	−	37.5399i	−0.574462	−	0.0843594i
$446$	−73.1275	−	126.661i	−0.163963	−	0.283992i
$447$		0			0
$448$	−157.180	+	42.1162i	−0.350848	+	0.0940094i
$449$			101.349i			0.225721i	0.993611	+	0.112860i	$0.0360013\pi$
$449$			101.349i			0.225721i	−0.993611	+	0.112860i	$0.963999\pi$
$450$		0			0
$451$	0.215906			0.000478728
$452$	174.090	+	649.714i	0.385155	+	1.43742i
$453$		0			0
$454$	40.0760	−	23.1379i	0.0882731	−	0.0509645i
$455$	−14.7823	+	100.663i	−0.0324885	+	0.221237i
$456$		0			0
$457$	161.232	+	601.725i	0.352805	+	1.31669i	0.883224	+	0.468950i	$0.155368\pi$
$457$	161.232	+	601.725i	0.352805	+	1.31669i	−0.530420	+	0.847735i	$0.677966\pi$
$458$	−16.2957	−	16.2957i	−0.0355802	−	0.0355802i
$459$		0			0
$460$	84.7659	−	9.87651i	0.184274	−	0.0214707i
$461$	−291.735	+	505.300i	−0.632831	+	1.09610i	0.354139	+	0.935193i	$0.384774\pi$
$461$	−291.735	+	505.300i	−0.632831	+	1.09610i	−0.986970	+	0.160903i	$0.948559\pi$
$462$		0			0
$463$	−29.9470	+	111.764i	−0.0646803	+	0.241390i	−0.990696	−	0.136096i	$-0.956545\pi$
$463$	−29.9470	+	111.764i	−0.0646803	+	0.241390i	0.926015	+	0.377486i	$0.123211\pi$
$464$	−397.720	+	229.624i	−0.857156	+	0.494879i
$465$		0			0
$466$	−87.3049	+	151.217i	−0.187350	+	0.324499i
$467$	145.933	−	145.933i	0.312491	−	0.312491i	−0.533383	−	0.845874i	$-0.679079\pi$
$467$	145.933	−	145.933i	0.312491	−	0.312491i	0.845874	+	0.533383i	$0.179079\pi$
$468$		0			0
$469$			314.225i			0.669989i
$470$	27.5212	+	69.3485i	0.0585558	+	0.147550i
$471$		0			0
$472$	473.309	+	126.823i	1.00277	+	0.268692i
$473$	−0.862190	+	3.21774i	−0.00182281	+	0.00680283i
$474$		0			0
$475$	−185.061	+	616.517i	−0.389602	+	1.29793i
$476$	434.507			0.912829
$477$		0			0
$478$	158.519	+	158.519i	0.331630	+	0.331630i
$479$	325.761	+	188.078i	0.680086	+	0.392648i	0.799888	−	0.600150i	$-0.204892\pi$
$479$	325.761	+	188.078i	0.680086	+	0.392648i	−0.119801	+	0.992798i	$0.538226\pi$
$480$		0			0
$481$	−122.363	−	211.939i	−0.254393	−	0.440621i
$482$	−8.91710	−	2.38933i	−0.0185002	−	0.00495711i
$483$		0			0
$484$	375.387	+	216.730i	0.775592	+	0.447788i
$485$	497.206	−	57.9321i	1.02517	−	0.119448i
$486$		0			0
$487$	−402.693	+	402.693i	−0.826885	+	0.826885i	−0.987085	−	0.160199i	$-0.948786\pi$
$487$	−402.693	+	402.693i	−0.826885	+	0.826885i	0.160199	+	0.987085i	$0.448786\pi$
$488$	262.607	−	70.3654i	0.538130	−	0.144191i
$489$		0			0
$490$	35.1810	−	26.1715i	0.0717980	−	0.0534111i
$491$	174.608	+	302.429i	0.355616	+	0.615945i	0.987223	−	0.159343i	$-0.0509377\pi$
$491$	174.608	+	302.429i	0.355616	+	0.615945i	−0.631607	+	0.775289i	$0.717604\pi$
$492$		0			0
$493$	809.587	−	216.928i	1.64216	−	0.440017i
$494$		−	56.8716i		−	0.115125i
$495$		0			0
$496$	413.111			0.832884
$497$	−61.4303	−	229.261i	−0.123602	−	0.461290i
$498$		0			0
$499$	−462.780	+	267.186i	−0.927414	+	0.535443i	−0.885993	−	0.463699i	$-0.846522\pi$
$499$	−462.780	+	267.186i	−0.927414	+	0.535443i	−0.0414214	+	0.999142i	$0.513189\pi$
$500$	38.5442	+	446.160i	0.0770884	+	0.892320i
$501$		0			0
$502$	−66.7694	−	249.187i	−0.133007	−	0.496388i
$503$	−441.936	−	441.936i	−0.878600	−	0.878600i	0.114790	−	0.993390i	$-0.463381\pi$
$503$	−441.936	−	441.936i	−0.878600	−	0.878600i	−0.993390	+	0.114790i	$0.963381\pi$
$504$		0			0
$505$	−71.1216	−	56.2777i	−0.140835	−	0.111441i
$506$	−0.146745	+	0.254170i	−0.000290011	+	0.000502313i
$507$		0			0
$508$	−77.1961	+	288.100i	−0.151961	+	0.567126i
$509$	−217.149	+	125.371i	−0.426619	+	0.246308i	−0.697905	−	0.716190i	$-0.745884\pi$
$509$	−217.149	+	125.371i	−0.426619	+	0.246308i	0.271286	+	0.962499i	$0.412551\pi$
$510$		0			0
$511$	165.713	−	287.024i	0.324292	−	0.561690i
$512$	366.369	−	366.369i	0.715564	−	0.715564i
$513$		0			0
$514$			225.684i			0.439074i
$515$	290.998	+	125.649i	0.565044	+	0.243980i
$516$		0			0
$517$	2.12717	+	0.569974i	0.00411445	+	0.00110246i
$518$	71.2461	−	265.894i	0.137541	−	0.513309i
$519$		0			0
$520$	−30.8898	−	77.8367i	−0.0594035	−	0.149686i
$521$	−450.350			−0.864395			−0.432198	−	0.901779i	$-0.642262\pi$
$521$	−450.350			−0.864395			−0.432198	+	0.901779i	$0.642262\pi$
$522$		0			0
$523$	−233.027	−	233.027i	−0.445559	−	0.445559i	0.448316	−	0.893875i	$-0.352024\pi$
$523$	−233.027	−	233.027i	−0.445559	−	0.445559i	−0.893875	+	0.448316i	$0.852024\pi$
$524$	−733.163	−	423.292i	−1.39917	−	0.807809i
$525$		0			0
$526$	7.08522	+	12.2720i	0.0134700	+	0.0233307i
$527$	−728.253	−	195.135i	−1.38188	−	0.370275i
$528$		0			0
$529$	438.471	+	253.152i	0.828868	+	0.478547i
$530$	175.867	+	139.161i	0.331824	+	0.262568i
$531$		0			0
$532$	−388.225	+	388.225i	−0.729746	+	0.729746i
$533$	7.47748	−	2.00358i	0.0140290	−	0.00375907i
$534$		0			0
$535$	−635.678	−	854.511i	−1.18818	−	1.59722i
$536$	−129.316	−	223.982i	−0.241261	−	0.417877i
$537$		0			0
$538$	−186.548	+	49.9853i	−0.346743	+	0.0929096i
$539$		−	1.29423i		−	0.00240118i
$540$		0			0
$541$	−36.3250			−0.0671442			−0.0335721	−	0.999436i	$-0.510688\pi$
$541$	−36.3250			−0.0671442			−0.0335721	+	0.999436i	$0.510688\pi$
$542$	−3.51312	−	13.1111i	−0.00648176	−	0.0241903i
$543$		0			0
$544$	−473.104	+	273.147i	−0.869677	+	0.502108i
$545$	625.766	+	91.8934i	1.14819	+	0.168612i
$546$		0			0
$547$	−128.305	−	478.843i	−0.234562	−	0.875398i	−0.978346	−	0.206977i	$-0.933637\pi$
$547$	−128.305	−	478.843i	−0.234562	−	0.875398i	0.743784	−	0.668420i	$-0.233029\pi$
$548$	184.932	+	184.932i	0.337468	+	0.337468i
$549$		0			0
$550$	−1.31022	−	0.809471i	−0.00238222	−	0.00147177i
$551$	−529.531	+	917.175i	−0.961037	+	1.66456i
$552$		0			0
$553$	92.5359	−	345.349i	0.167334	−	0.624501i
$554$	−217.809	+	125.752i	−0.393158	+	0.226990i
$555$		0			0
$556$	−285.530	+	494.552i	−0.513543	+	0.889483i
$557$	22.1908	−	22.1908i	0.0398399	−	0.0398399i	−0.686906	−	0.726746i	$-0.741032\pi$
$557$	22.1908	−	22.1908i	0.0398399	−	0.0398399i	0.726746	+	0.686906i	$0.241032\pi$
$558$		0			0
$559$			119.441i			0.213669i
$560$	−131.719	+	305.053i	−0.235212	+	0.544738i
$561$		0			0
$562$	101.299	+	27.1430i	0.180247	+	0.0482972i
$563$	61.7007	−	230.270i	0.109593	−	0.409006i	−0.889233	−	0.457455i	$-0.848761\pi$
$563$	61.7007	−	230.270i	0.109593	−	0.409006i	0.998826	+	0.0484491i	$0.0154279\pi$
$564$		0			0
$565$	861.846	+	372.135i	1.52539	+	0.658647i
$566$	116.405			0.205662
$567$		0			0
$568$	138.138	+	138.138i	0.243200	+	0.243200i
$569$	−500.670	−	289.062i	−0.879913	−	0.508018i	−0.00928322	−	0.999957i	$-0.502955\pi$
$569$	−500.670	−	289.062i	−0.879913	−	0.508018i	−0.870630	+	0.491939i	$0.836288\pi$
$570$		0			0
$571$	−382.716	−	662.883i	−0.670256	−	1.16092i	−0.977832	−	0.209393i	$-0.932851\pi$
$571$	−382.716	−	662.883i	−0.670256	−	1.16092i	0.307576	−	0.951524i	$-0.400482\pi$
$572$	−1.12805	−	0.302260i	−0.00197212	−	0.000528427i
$573$		0			0
$574$	7.54097	+	4.35378i	0.0131376	+	0.00758499i
$575$	62.6001	−	101.325i	0.108870	−	0.176218i
$576$		0			0
$577$	176.644	−	176.644i	0.306143	−	0.306143i	−0.537269	−	0.843411i	$-0.680544\pi$
$577$	176.644	−	176.644i	0.306143	−	0.306143i	0.843411	+	0.537269i	$0.180544\pi$
$578$	78.7674	−	21.1057i	0.136276	−	0.0365150i
$579$		0			0
$580$	−107.050	+	728.979i	−0.184569	+	1.25686i
$581$	325.713	+	564.151i	0.560607	+	0.971000i
$582$		0			0
$583$	6.39394	−	1.71325i	0.0109673	−	0.00293868i
$584$			272.790i			0.467106i
$585$		0			0
$586$	176.977			0.302008
$587$	−141.291	−	527.304i	−0.240700	−	0.898304i	−0.975496	−	0.220016i	$-0.929389\pi$
$587$	−141.291	−	527.304i	−0.240700	−	0.898304i	0.734796	−	0.678288i	$-0.237278\pi$
$588$		0			0
$589$	825.033	−	476.333i	1.40073	−	0.808715i
$590$	259.246	−	192.856i	0.439401	−	0.326874i
$591$		0			0
$592$	−206.858	−	772.005i	−0.349423	−	1.30406i
$593$	−595.579	−	595.579i	−1.00435	−	1.00435i	−0.999990	−	0.00435896i	$-0.998612\pi$
$593$	−595.579	−	595.579i	−1.00435	−	1.00435i	−0.00435896	−	0.999990i	$-0.501388\pi$
$594$		0			0
$595$	376.294	−	475.546i	0.632427	−	0.799237i
$596$	149.409	−	258.784i	0.250686	−	0.434201i
$597$		0			0
$598$	−2.72356	+	10.1645i	−0.00455445	+	0.0169974i
$599$	−384.062	+	221.739i	−0.641173	+	0.370181i	−0.785066	−	0.619412i	$-0.787371\pi$
$599$	−384.062	+	221.739i	−0.641173	+	0.370181i	0.143893	+	0.989593i	$0.454038\pi$
$600$		0			0
$601$	163.594	−	283.354i	0.272204	−	0.471470i	−0.697222	−	0.716855i	$-0.745581\pi$
$601$	163.594	−	283.354i	0.272204	−	0.471470i	0.969426	+	0.245385i	$0.0789143\pi$
$602$	−94.9999	+	94.9999i	−0.157807	+	0.157807i
$603$		0			0
$604$		−	124.519i		−	0.206157i
$605$	562.294	−	223.149i	0.929412	−	0.368841i
$606$		0			0
$607$	160.611	+	43.0356i	0.264598	+	0.0708988i	0.388679	−	0.921373i	$-0.372932\pi$
$607$	160.611	+	43.0356i	0.264598	+	0.0708988i	−0.124081	+	0.992272i	$0.539598\pi$
$608$	178.659	−	666.764i	0.293847	−	1.09665i
$609$		0			0
$610$	71.0664	−	164.586i	0.116502	−	0.269813i
$611$	78.9596			0.129230
$612$		0			0
$613$	−60.4318	−	60.4318i	−0.0985837	−	0.0985837i	0.656095	−	0.754678i	$-0.272207\pi$
$613$	−60.4318	−	60.4318i	−0.0985837	−	0.0985837i	−0.754678	+	0.656095i	$0.772207\pi$
$614$	320.746	+	185.183i	0.522387	+	0.301600i
$615$		0			0
$616$	−1.39015	−	2.40781i	−0.00225674	−	0.00390878i
$617$	−392.130	−	105.071i	−0.635544	−	0.170293i	−0.0733596	−	0.997306i	$-0.523372\pi$
$617$	−392.130	−	105.071i	−0.635544	−	0.170293i	−0.562184	+	0.827012i	$0.690039\pi$
$618$		0			0
$619$	−391.642	−	226.114i	−0.632701	−	0.365290i	0.149097	−	0.988823i	$-0.452363\pi$
$619$	−391.642	−	226.114i	−0.632701	−	0.365290i	−0.781797	+	0.623533i	$0.785697\pi$
$620$	411.266	−	519.743i	0.663333	−	0.838295i
$621$		0			0
$622$	−80.3958	+	80.3958i	−0.129254	+	0.129254i
$623$	−297.093	+	79.6058i	−0.476875	+	0.127778i
$624$		0			0
$625$	521.680	+	344.201i	0.834689	+	0.550722i
$626$	87.6671	+	151.844i	0.140043	+	0.242562i
$627$		0			0
$628$	−23.1107	+	6.19248i	−0.0368004	+	0.00986064i
$629$			1458.64i			2.31899i
$630$		0			0
$631$	−195.973			−0.310575			−0.155287	−	0.987869i	$-0.549630\pi$
$631$	−195.973			−0.310575			−0.155287	+	0.987869i	$0.549630\pi$
$632$	76.1644	+	284.249i	0.120513	+	0.449761i
$633$		0			0
$634$	219.499	−	126.728i	0.346212	−	0.199886i
$635$	248.457	+	333.989i	0.391271	+	0.525967i
$636$		0			0
$637$	−12.0103	−	44.8232i	−0.0188545	−	0.0703661i
$638$	−1.79175	−	1.79175i	−0.00280839	−	0.00280839i
$639$		0			0
$640$	−72.2758	−	620.312i	−0.112931	−	0.969238i
$641$	130.750	−	226.466i	0.203978	−	0.353300i	−0.745829	−	0.666138i	$-0.767946\pi$
$641$	130.750	−	226.466i	0.203978	−	0.353300i	0.949807	+	0.312838i	$0.101280\pi$
$642$		0			0
$643$	−258.385	+	964.305i	−0.401842	+	1.49970i	0.407963	+	0.912998i	$0.366239\pi$
$643$	−258.385	+	964.305i	−0.401842	+	1.49970i	−0.809806	+	0.586698i	$0.800428\pi$
$644$	87.9780	−	50.7941i	0.136612	−	0.0788729i
$645$		0			0
$646$	−169.486	+	293.559i	−0.262363	+	0.454426i
$647$	−172.569	+	172.569i	−0.266722	+	0.266722i	−0.827778	−	0.561056i	$-0.810395\pi$
$647$	−172.569	+	172.569i	−0.266722	+	0.266722i	0.561056	+	0.827778i	$0.310395\pi$
$648$		0			0
$649$		−	9.53712i		−	0.0146951i
$650$	−52.8887	−	15.8757i	−0.0813672	−	0.0244242i
$651$		0			0
$652$	838.685	+	224.725i	1.28633	+	0.344670i
$653$	286.420	−	1068.93i	0.438622	−	1.63696i	−0.293626	−	0.955920i	$-0.594862\pi$
$653$	286.420	−	1068.93i	0.438622	−	1.63696i	0.732248	−	0.681038i	$-0.238471\pi$
$654$		0			0
$655$	−1098.21	+	435.829i	−1.67666	+	0.665388i
$656$	25.2818			0.0385394
$657$		0			0
$658$	62.8023	+	62.8023i	0.0954442	+	0.0954442i
$659$	373.508	+	215.645i	0.566780	+	0.327231i	0.755862	−	0.654731i	$-0.227218\pi$
$659$	373.508	+	215.645i	0.566780	+	0.327231i	−0.189082	+	0.981961i	$0.560551\pi$
$660$		0			0
$661$	−252.072	−	436.601i	−0.381349	−	0.660516i	0.609906	−	0.792473i	$-0.291207\pi$
$661$	−252.072	−	436.601i	−0.381349	−	0.660516i	−0.991255	+	0.131958i	$0.957874\pi$
$662$	189.245	+	50.7080i	0.285868	+	0.0765981i
$663$		0			0
$664$	−464.341	−	268.087i	−0.699308	−	0.403746i
$665$	88.6803	+	761.106i	0.133354	+	1.14452i
$666$		0			0
$667$	138.564	−	138.564i	0.207743	−	0.207743i
$668$	262.596	−	70.3624i	0.393108	−	0.105333i
$669$		0			0
$670$	−168.734	−	24.7785i	−0.251842	−	0.0369828i
$671$	−2.64575	−	4.58258i	−0.00394300	−	0.00682947i
$672$		0			0
$673$	−360.737	+	96.6593i	−0.536014	+	0.143624i	−0.516664	−	0.856188i	$-0.672826\pi$
$673$	−360.737	+	96.6593i	−0.536014	+	0.143624i	−0.0193499	+	0.999813i	$0.506160\pi$
$674$		−	39.1382i		−	0.0580686i
$675$		0			0
$676$	563.583			0.833702
$677$	−299.983	−	1119.55i	−0.443107	−	1.65370i	−0.720886	−	0.693053i	$-0.756265\pi$
$677$	−299.983	−	1119.55i	−0.443107	−	1.65370i	0.277779	−	0.960645i	$-0.410402\pi$
$678$		0			0
$679$	516.047	−	297.940i	0.760011	−	0.438793i
$680$	−72.5190	+	493.832i	−0.106646	+	0.726224i
$681$		0			0
$682$	0.589941	+	2.20169i	0.000865016	+	0.00322828i
$683$	−390.999	−	390.999i	−0.572473	−	0.572473i	0.360346	−	0.932819i	$-0.382659\pi$
$683$	−390.999	−	390.999i	−0.572473	−	0.572473i	−0.932819	+	0.360346i	$0.882659\pi$
$684$		0			0
$685$	362.555	−	42.2432i	0.529278	−	0.0616689i
$686$	120.313	−	208.389i	0.175384	−	0.303774i
$687$		0			0
$688$	−100.959	+	376.785i	−0.146743	+	0.547653i
$689$	205.542	−	118.670i	0.298320	−	0.172235i
$690$		0			0
$691$	206.234	−	357.208i	0.298457	−	0.516943i	−0.677326	−	0.735683i	$-0.736861\pi$
$691$	206.234	−	357.208i	0.298457	−	0.516943i	0.975783	+	0.218740i	$0.0701946\pi$
$692$	−530.318	+	530.318i	−0.766355	+	0.766355i
$693$		0			0
$694$		−	413.855i		−	0.596332i
$695$	293.987	+	740.793i	0.423003	+	1.06589i
$696$		0			0
$697$	−44.5681	−	11.9420i	−0.0639428	−	0.0171334i
$698$	−23.8771	+	89.1104i	−0.0342078	+	0.127665i
$699$		0			0
$700$	252.663	+	469.409i	0.360948	+	0.670585i
$701$	−458.287			−0.653762			−0.326881	−	0.945066i	$-0.605998\pi$
$701$	−458.287			−0.653762			−0.326881	+	0.945066i	$0.605998\pi$
$702$		0			0
$703$	−1303.27	−	1303.27i	−1.85387	−	1.85387i
$704$	−2.25757	−	1.30341i	−0.00320677	−	0.00185143i
$705$		0			0
$706$	−88.3648	−	153.052i	−0.125163	−	0.216788i
$707$	−104.284	−	27.9428i	−0.147502	−	0.0395231i
$708$		0			0
$709$	−560.267	−	323.470i	−0.790221	−	0.456234i	0.0498194	−	0.998758i	$-0.484135\pi$
$709$	−560.267	−	323.470i	−0.790221	−	0.456234i	−0.840040	+	0.542524i	$0.817469\pi$
$710$	127.954	−	14.9085i	0.180217	−	0.0209980i
$711$		0			0
$712$	179.009	−	179.009i	0.251417	−	0.251417i
$713$	−170.267	+	45.6228i	−0.238803	+	0.0639871i
$714$		0			0
$715$	−1.30773	+	0.972831i	−0.00182899	+	0.00136060i
$716$	−251.311	−	435.283i	−0.350993	−	0.607937i
$717$		0			0
$718$	221.475	−	59.3439i	0.308460	−	0.0826517i
$719$		−	98.3936i		−	0.136848i	−0.997656	−	0.0684239i	$-0.978203\pi$
$719$		−	98.3936i		−	0.136848i	0.997656	−	0.0684239i	$-0.0217970\pi$
$720$		0			0
$721$	377.317			0.523325
$722$	−50.4910	−	188.435i	−0.0699321	−	0.260990i
$723$		0			0
$724$	355.932	−	205.497i	0.491619	−	0.283836i
$725$	705.123	+	748.476i	0.972584	+	1.03238i
$726$		0			0
$727$	−273.252	−	1019.79i	−0.375862	−	1.40274i	−0.852082	−	0.523409i	$-0.824660\pi$
$727$	−273.252	−	1019.79i	−0.375862	−	1.40274i	0.476220	−	0.879326i	$-0.342007\pi$
$728$	−70.4892	−	70.4892i	−0.0968259	−	0.0968259i
$729$		0			0
$730$	141.060	+	111.619i	0.193233	+	0.152903i
$731$	355.953	−	616.528i	0.486939	−	0.843404i
$732$		0			0
$733$	29.8832	−	111.526i	0.0407684	−	0.152150i	−0.942541	−	0.334090i	$-0.891571\pi$
$733$	29.8832	−	111.526i	0.0407684	−	0.152150i	0.983310	+	0.181940i	$0.0582378\pi$
$734$	132.406	−	76.4449i	0.180390	−	0.104148i
$735$		0			0
$736$	−63.8621	+	110.612i	−0.0867692	+	0.150289i
$737$	−3.55945	+	3.55945i	−0.00482965	+	0.00482965i
$738$		0			0
$739$			427.280i			0.578186i	0.957301	+	0.289093i	$0.0933537\pi$
$739$			427.280i			0.578186i	−0.957301	+	0.289093i	$0.906646\pi$
$740$	−1177.21	−	508.306i	−1.59082	−	0.686900i
$741$		0			0
$742$	257.869	+	69.0959i	0.347533	+	0.0931212i
$743$	88.4669	−	330.163i	0.119067	−	0.444365i	−0.880492	−	0.474061i	$-0.842787\pi$
$743$	88.4669	−	330.163i	0.119067	−	0.444365i	0.999559	+	0.0296967i	$0.00945413\pi$
$744$		0			0
$745$	−153.834	−	387.634i	−0.206489	−	0.520315i
$746$	−152.293			−0.204146
$747$		0			0
$748$	4.92197	+	4.92197i	0.00658017	+	0.00658017i
$749$	−1097.95	−	633.904i	−1.46589	−	0.846334i
$750$		0			0
$751$	521.702	+	903.615i	0.694677	+	1.20322i	0.970290	+	0.241947i	$0.0777859\pi$
$751$	521.702	+	903.615i	0.694677	+	1.20322i	−0.275613	+	0.961269i	$0.588881\pi$
$752$	249.084	+	66.7418i	0.331229	+	0.0887524i
$753$		0			0
$754$	−78.6810	−	45.4265i	−0.104352	−	0.0602474i
$755$	−136.280	−	107.837i	−0.180503	−	0.142830i
$756$		0			0
$757$	641.252	−	641.252i	0.847097	−	0.847097i	−0.142673	−	0.989770i	$-0.545570\pi$
$757$	641.252	−	641.252i	0.847097	−	0.847097i	0.989770	+	0.142673i	$0.0455698\pi$
$758$	−71.9254	+	19.2723i	−0.0948884	+	0.0254253i
$759$		0			0
$760$	−376.437	−	506.026i	−0.495312	−	0.665824i
$761$	307.586	+	532.754i	0.404186	+	0.700071i	0.994226	−	0.107303i	$-0.0342214\pi$
$761$	307.586	+	532.754i	0.404186	+	0.700071i	−0.590040	+	0.807374i	$0.700888\pi$
$762$		0			0
$763$	727.249	−	194.866i	0.953144	−	0.255394i
$764$			921.046i			1.20556i
$765$		0			0
$766$	−312.726			−0.408258
$767$	−88.5033	−	330.299i	−0.115389	−	0.430637i
$768$		0			0
$769$	217.822	−	125.759i	0.283253	−	0.163536i	−0.351642	−	0.936135i	$-0.614377\pi$
$769$	217.822	−	125.759i	0.283253	−	0.163536i	0.634895	+	0.772598i	$0.281043\pi$
$770$	−1.81389	−	0.266369i	−0.00235571	−	0.000345934i
$771$		0			0
$772$	−115.748	−	431.977i	−0.149932	−	0.559555i
$773$	−364.839	−	364.839i	−0.471978	−	0.471978i	0.430576	−	0.902554i	$-0.358310\pi$
$773$	−364.839	−	364.839i	−0.471978	−	0.471978i	−0.902554	+	0.430576i	$0.858310\pi$
$774$		0			0
$775$	−212.666	−	900.221i	−0.274408	−	1.16158i
$776$	−245.228	+	424.748i	−0.316016	+	0.547355i
$777$		0			0
$778$	−55.9414	+	208.776i	−0.0719042	+	0.268350i
$779$	50.4909	−	29.1509i	0.0648150	−	0.0374210i
$780$		0			0
$781$	1.90114	−	3.29287i	0.00243424	−	0.00421622i
$782$	44.3501	−	44.3501i	0.0567137	−	0.0567137i
$783$		0			0
$784$		−	151.550i		−	0.193304i
$785$	−13.2371	+	30.6563i	−0.0168625	+	0.0390526i
$786$		0			0
$787$	−908.273	−	243.371i	−1.15410	−	0.309239i	−0.369490	−	0.929235i	$-0.620468\pi$
$787$	−908.273	−	243.371i	−1.15410	−	0.309239i	−0.784605	+	0.619996i	$0.787134\pi$
$788$	58.6049	−	218.716i	0.0743717	−	0.277559i
$789$		0			0
$790$	178.150	+	76.9231i	0.225506	+	0.0973710i
$791$	1117.50			1.41277
$792$		0			0
$793$	−134.156	−	134.156i	−0.169175	−	0.169175i
$794$	−371.884	−	214.707i	−0.468367	−	0.270412i
$795$		0			0
$796$	−533.739	−	924.462i	−0.670526	−	1.16138i
$797$	−1123.49	−	301.039i	−1.40965	−	0.377716i	−0.527852	−	0.849336i	$-0.677003\pi$
$797$	−1123.49	−	301.039i	−1.40965	−	0.377716i	−0.881802	+	0.471621i	$0.843669\pi$
$798$		0			0
$799$	−407.573	−	235.312i	−0.510103	−	0.294508i
$800$	−570.195	−	352.274i	−0.712744	−	0.440342i
$801$		0			0
$802$	−86.4720	+	86.4720i	−0.107820	+	0.107820i
$803$	5.12848	−	1.37417i	0.00638665	−	0.00171130i
$804$		0			0
$805$	20.5995	−	140.277i	0.0255895	−	0.174257i
$806$	40.8628	+	70.7765i	0.0506983	+	0.0878120i
$807$		0			0
$808$	85.8340	−	22.9992i	0.106230	−	0.0284643i
$809$			753.586i			0.931504i	0.884915	+	0.465752i	$0.154216\pi$
$809$			753.586i			0.931504i	−0.884915	+	0.465752i	$0.845784\pi$
$810$		0			0
$811$	568.270			0.700703			0.350352	−	0.936618i	$-0.386062\pi$
$811$	568.270			0.700703			0.350352	+	0.936618i	$0.386062\pi$
$812$	227.007	+	847.200i	0.279565	+	1.04335i
$813$		0			0
$814$	3.81903	−	2.20492i	0.00469168	−	0.00270874i
$815$	972.273	−	723.281i	1.19297	−	0.887462i
$816$		0			0
$817$	232.820	+	868.896i	0.284969	+	1.06352i
$818$	195.222	+	195.222i	0.238657	+	0.238657i
$819$		0			0
$820$	25.1689	−	31.8076i	0.0306938	−	0.0387897i
$821$	−298.755	+	517.458i	−0.363891	+	0.630278i	−0.988598	−	0.150582i	$-0.951885\pi$
$821$	−298.755	+	517.458i	−0.363891	+	0.630278i	0.624706	+	0.780860i	$0.285219\pi$
$822$		0			0
$823$	−24.1596	+	90.1649i	−0.0293555	+	0.109556i	−0.979049	−	0.203624i	$-0.934728\pi$
$823$	−24.1596	+	90.1649i	−0.0293555	+	0.109556i	0.949694	+	0.313181i	$0.101395\pi$
$824$	−268.955	+	155.281i	−0.326401	+	0.188448i
$825$		0			0
$826$	192.317	−	333.104i	0.232830	−	0.403273i
$827$	−7.50861	+	7.50861i	−0.00907934	+	0.00907934i	−0.711632	−	0.702553i	$-0.752044\pi$
$827$	−7.50861	+	7.50861i	−0.00907934	+	0.00907934i	0.702553	+	0.711632i	$0.252044\pi$
$828$		0			0
$829$		−	161.036i		−	0.194254i	−0.995272	−	0.0971269i	$-0.969035\pi$
$829$		−	161.036i		−	0.194254i	0.995272	−	0.0971269i	$-0.0309653\pi$
$830$	−328.625	+	130.416i	−0.395933	+	0.157128i
$831$		0			0
$832$	−90.2819	−	24.1910i	−0.108512	−	0.0290757i
$833$	−71.5854	+	267.160i	−0.0859369	+	0.320721i
$834$		0			0
$835$	150.407	−	348.334i	0.180128	−	0.417166i
$836$	−8.79541			−0.0105208
$837$		0			0
$838$	−245.986	−	245.986i	−0.293539	−	0.293539i
$839$	80.9864	+	46.7575i	0.0965272	+	0.0557300i	0.547487	−	0.836814i	$-0.315585\pi$
$839$	80.9864	+	46.7575i	0.0965272	+	0.0557300i	−0.450959	+	0.892545i	$0.648918\pi$
$840$		0			0
$841$	425.432	+	736.870i	0.505864	+	0.876183i
$842$	−246.507	−	66.0514i	−0.292764	−	0.0784459i
$843$		0			0
$844$	421.869	+	243.566i	0.499845	+	0.288586i
$845$	488.077	−	616.813i	0.577606	−	0.729957i
$846$		0			0
$847$	509.216	−	509.216i	0.601199	−	0.601199i
$848$	748.706	−	200.615i	0.882908	−	0.236575i
$849$		0			0
$850$	225.688	+	239.564i	0.265515	+	0.281840i
$851$	170.516	+	295.343i	0.200372	+	0.347054i
$852$		0			0
$853$	151.946	−	40.7138i	0.178131	−	0.0477301i	−0.168651	−	0.985676i	$-0.553941\pi$
$853$	151.946	−	40.7138i	0.178131	−	0.0477301i	0.346782	+	0.937946i	$0.387274\pi$
$854$		−	213.408i		−	0.249892i
$855$		0			0
$856$	1043.51			1.21905
$857$	26.8424	+	100.177i	0.0313214	+	0.116893i	0.979817	−	0.199898i	$-0.0640612\pi$
$857$	26.8424	+	100.177i	0.0313214	+	0.116893i	−0.948495	+	0.316791i	$0.897395\pi$
$858$		0			0
$859$	431.090	−	248.890i	0.501851	−	0.289744i	−0.227626	−	0.973749i	$-0.573096\pi$
$859$	431.090	−	248.890i	0.501851	−	0.289744i	0.729478	+	0.684004i	$0.239763\pi$
$860$	373.532	+	502.122i	0.434340	+	0.583862i
$861$		0			0
$862$	10.0481	+	37.5000i	0.0116567	+	0.0435035i
$863$	597.165	+	597.165i	0.691965	+	0.691965i	0.962664	−	0.270699i	$-0.0872549\pi$
$863$	597.165	+	597.165i	0.691965	+	0.691965i	−0.270699	+	0.962664i	$0.587255\pi$
$864$		0			0
$865$	121.138	+	1039.67i	0.140044	+	1.20194i
$866$	87.9499	−	152.334i	0.101559	−	0.175905i
$867$		0			0
$868$	204.201	−	762.088i	0.235254	−	0.877982i
$869$	4.96023	−	2.86379i	0.00570798	−	0.00329550i
$870$		0			0
$871$	−90.2432	+	156.306i	−0.103609	+	0.179456i
$872$	−438.193	+	438.193i	−0.502515	+	0.502515i
$873$		0			0
$874$			79.2523i			0.0906777i
$875$	732.558	+	129.993i	0.837209	+	0.148563i
$876$		0			0
$877$	860.660	+	230.613i	0.981368	+	0.262957i	0.713621	−	0.700532i	$-0.247054\pi$
$877$	860.660	+	230.613i	0.981368	+	0.262957i	0.267748	+	0.963489i	$0.413721\pi$
$878$	48.8840	−	182.438i	0.0556765	−	0.207788i
$879$		0			0
$880$	−4.94763	+	1.96349i	−0.00562230	+	0.00223123i
$881$	1619.10			1.83780			0.918902	−	0.394487i	$-0.129078\pi$
$881$	1619.10			1.83780			0.918902	+	0.394487i	$0.129078\pi$
$882$		0			0
$883$	881.301	+	881.301i	0.998076	+	0.998076i	0.999998	−	0.00192213i	$-0.000611833\pi$
$883$	881.301	+	881.301i	0.998076	+	0.998076i	−0.00192213	+	0.999998i	$0.500612\pi$
$884$	216.138	+	124.787i	0.244500	+	0.141162i
$885$		0			0
$886$	122.158	+	211.584i	0.137876	+	0.238808i
$887$	−353.303	−	94.6674i	−0.398313	−	0.106728i	0.0541016	−	0.998535i	$-0.482771\pi$
$887$	−353.303	−	94.6674i	−0.398313	−	0.106728i	−0.452414	+	0.891808i	$0.649437\pi$
$888$		0			0
$889$	429.140	+	247.764i	0.482722	+	0.278700i
$890$	−19.3196	−	165.812i	−0.0217074	−	0.186305i
$891$		0			0
$892$	−573.459	+	573.459i	−0.642891	+	0.642891i
$893$	574.407	−	153.912i	0.643233	−	0.172354i
$894$		0			0
$895$	−694.037	−	101.919i	−0.775460	−	0.113876i
$896$	−371.709	−	643.818i	−0.414853	−	0.718547i
$897$		0			0
$898$	−63.2485	+	16.9474i	−0.0704327	+	0.0188724i
$899$		−	1521.89i		−	1.69287i
$900$		0			0
$901$	−1414.62			−1.57006
$902$	0.0361036	+	0.134740i	4.00262e−5	+	0.000149380i
$903$		0			0
$904$	−796.561	+	459.895i	−0.881152	+	0.508733i
$905$	83.3393	−	567.516i	0.0920877	−	0.627089i
$906$		0			0
$907$	−27.7508	−	103.567i	−0.0305963	−	0.114187i	0.948939	−	0.315460i	$-0.102159\pi$
$907$	−27.7508	−	103.567i	−0.0305963	−	0.114187i	−0.979535	+	0.201273i	$0.935492\pi$
$908$	−181.445	−	181.445i	−0.199829	−	0.199829i
$909$		0			0
$910$	−65.2924	+	7.60756i	−0.0717499	+	0.00835995i
$911$	−422.343	+	731.520i	−0.463604	+	0.802985i	−0.999137	−	0.0415286i	$-0.986777\pi$
$911$	−422.343	+	731.520i	−0.463604	+	0.802985i	0.535533	+	0.844514i	$0.320111\pi$
$912$		0			0
$913$	−2.70096	+	10.0801i	−0.00295834	+	0.0110407i
$914$	−348.557	+	201.240i	−0.381354	+	0.220175i
$915$		0			0
$916$	−63.8947	+	110.669i	−0.0697540	+	0.120818i
$917$	−994.544	+	994.544i	−1.08456	+	1.08456i
$918$		0			0
$919$			298.720i			0.325049i	0.986704	+	0.162525i	$0.0519637\pi$
$919$			298.720i			0.325049i	−0.986704	+	0.162525i	$0.948036\pi$
$920$	43.0459	+	108.468i	0.0467890	+	0.117900i
$921$		0			0
$922$	−364.126	−	97.5673i	−0.394931	−	0.105821i
$923$	35.2847	−	131.684i	0.0382283	−	0.142670i
$924$		0			0
$925$	−1575.81	+	848.192i	−1.70358	+	0.916965i
$926$	−74.7559			−0.0807299
$927$		0			0
$928$	−779.753	−	779.753i	−0.840251	−	0.840251i
$929$	959.561	+	554.003i	1.03290	+	0.596343i	0.917813	−	0.397012i	$-0.129953\pi$
$929$	959.561	+	554.003i	1.03290	+	0.596343i	0.115084	+	0.993356i	$0.463286\pi$
$930$		0			0
$931$	−174.743	−	302.664i	−0.187694	−	0.325096i
$932$	935.231	+	250.594i	1.00347	+	0.268878i
$933$		0			0
$934$	115.475	+	66.6697i	0.123635	+	0.0713808i
$935$	9.64940	−	1.12430i	0.0103202	−	0.00120246i
$936$		0			0
$937$	−895.973	+	895.973i	−0.956214	+	0.956214i	−0.999081	−	0.0428666i	$-0.986351\pi$
$937$	−895.973	+	895.973i	−0.956214	+	0.956214i	0.0428666	+	0.999081i	$0.486351\pi$
$938$	−196.098	+	52.5443i	−0.209060	+	0.0560174i
$939$		0			0
$940$	331.941	−	246.934i	0.353129	−	0.262695i
$941$	647.160	+	1120.91i	0.687737	+	1.19119i	0.972568	+	0.232617i	$0.0747290\pi$
$941$	647.160	+	1120.91i	0.687737	+	1.19119i	−0.284832	+	0.958578i	$0.591938\pi$
$942$		0			0
$943$	−10.4201	+	2.79205i	−0.0110499	+	0.00296082i
$944$		−	1116.76i		−	1.18301i
$945$		0			0
$946$	−2.15226			−0.00227512
$947$	57.4999	+	214.593i	0.0607179	+	0.226602i	0.989617	−	0.143731i	$-0.0459100\pi$
$947$	57.4999	+	214.593i	0.0607179	+	0.226602i	−0.928899	+	0.370334i	$0.879243\pi$
$948$		0			0
$949$	164.862	−	95.1833i	0.173722	−	0.100299i
$950$	−415.695	−	12.3977i	−0.437574	−	0.0130502i
$951$		0			0
$952$	153.781	+	573.919i	0.161535	+	0.602856i
$953$	342.541	+	342.541i	0.359435	+	0.359435i	0.863605	−	0.504170i	$-0.168201\pi$
$953$	342.541	+	342.541i	0.359435	+	0.359435i	−0.504170	+	0.863605i	$0.668201\pi$
$954$		0			0
$955$	1008.04	+	797.650i	1.05554	+	0.835235i
$956$	621.545	−	1076.55i	0.650152	−	1.12610i
$957$		0			0
$958$	−62.9005	+	234.748i	−0.0656581	+	0.245039i
$959$	376.294	−	217.253i	0.392382	−	0.226542i
$960$		0			0
$961$	−204.000	+	353.338i	−0.212279	+	0.367678i
$962$	111.803	−	111.803i	0.116219	−	0.116219i
$963$		0			0
$964$			51.1901i			0.0531018i
$965$	−573.017	−	247.422i	−0.593801	−	0.256396i
$966$		0			0
$967$	−1133.35	−	303.679i	−1.17202	−	0.314043i	−0.380266	−	0.924877i	$-0.624167\pi$
$967$	−1133.35	−	303.679i	−1.17202	−	0.314043i	−0.791758	+	0.610834i	$0.790834\pi$
$968$	−153.410	+	572.535i	−0.158482	+	0.591462i
$969$		0			0
$970$	119.296	+	300.604i	0.122985	+	0.309901i
$971$	−1454.35			−1.49779			−0.748894	−	0.662690i	$-0.769415\pi$
$971$	−1454.35			−1.49779			−0.748894	+	0.662690i	$0.769415\pi$
$972$		0			0
$973$	670.866	+	670.866i	0.689482	+	0.689482i
$974$	−318.646	−	183.970i	−0.327152	−	0.188881i
$975$		0			0
$976$	−309.808	−	536.602i	−0.317426	−	0.549798i
$977$	23.1393	+	6.20014i	0.0236840	+	0.00634610i	0.270642	−	0.962680i	$-0.412764\pi$
$977$	23.1393	+	6.20014i	0.0236840	+	0.00634610i	−0.246958	+	0.969026i	$0.579431\pi$
$978$		0			0
$979$	−4.26714	−	2.46363i	−0.00435867	−	0.00251648i
$980$	−190.668	−	150.873i	−0.194559	−	0.153952i
$981$		0			0
$982$	−159.539	+	159.539i	−0.162463	+	0.162463i
$983$	405.117	−	108.551i	0.412123	−	0.110428i	−0.0467995	−	0.998904i	$-0.514902\pi$
$983$	405.117	−	108.551i	0.412123	−	0.110428i	0.458923	+	0.888476i	$0.348236\pi$
$984$		0			0
$985$	−188.621	−	253.554i	−0.191493	−	0.257415i
$986$	270.756	+	468.964i	0.274601	+	0.475622i
$987$		0			0
$988$	−304.611	+	81.6203i	−0.308311	+	0.0826117i
$989$		−	166.444i		−	0.168296i
$990$		0			0
$991$	−632.405			−0.638148			−0.319074	−	0.947730i	$-0.603372\pi$
$991$	−632.405			−0.638148			−0.319074	+	0.947730i	$0.603372\pi$
$992$	256.736	+	958.153i	0.258807	+	0.965880i
$993$		0			0
$994$	132.802	−	76.6735i	0.133604	−	0.0771363i
$995$	−1474.01	−	216.457i	−1.48142	−	0.217545i
$996$		0			0
$997$	225.847	+	842.872i	0.226527	+	0.845409i	0.981787	+	0.189984i	$0.0608436\pi$
$997$	225.847	+	842.872i	0.226527	+	0.845409i	−0.755261	+	0.655425i	$0.772490\pi$
$998$	−244.128	−	244.128i	−0.244617	−	0.244617i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.3.l.e.298.2		8
3.2	odd	2		405.3.l.i.298.1		8
5.2	odd	4		405.3.l.i.217.1		8
9.2	odd	6		405.3.g.d.163.2	yes	8
9.4	even	3		405.3.l.i.28.1		8
9.5	odd	6	inner	405.3.l.e.28.2		8
9.7	even	3		405.3.g.d.163.3	yes	8
15.2	even	4	inner	405.3.l.e.217.2		8
45.2	even	12		405.3.g.d.82.2	✓	8
45.7	odd	12		405.3.g.d.82.3	yes	8
45.22	odd	12	inner	405.3.l.e.352.2		8
45.32	even	12		405.3.l.i.352.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
405.3.g.d.82.2	✓	8	45.2	even	12
405.3.g.d.82.3	yes	8	45.7	odd	12
405.3.g.d.163.2	yes	8	9.2	odd	6
405.3.g.d.163.3	yes	8	9.7	even	3
405.3.l.e.28.2		8	9.5	odd	6	inner
405.3.l.e.217.2		8	15.2	even	4	inner
405.3.l.e.298.2		8	1.1	even	1	trivial
405.3.l.e.352.2		8	45.22	odd	12	inner
405.3.l.i.28.1		8	9.4	even	3
405.3.l.i.217.1		8	5.2	odd	4
405.3.l.i.298.1		8	3.2	odd	2
405.3.l.i.352.1		8	45.32	even	12

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:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	405.l (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.167219 + 0.624069i) q^{2} +(3.10260 - 1.79129i) q^{4} +(0.726456 - 4.94694i) q^{5} +(-1.54050 - 5.74921i) q^{7} +(3.46410 + 3.46410i) q^{8} +(3.20871 - 0.373864i) q^{10} +(0.0476751 - 0.0825757i) q^{11} +(0.884839 - 3.30226i) q^{13} +(3.33030 - 1.92275i) q^{14} +(5.58258 - 9.66930i) q^{16} +(-14.4086 + 14.4086i) q^{17} -25.7477i q^{19} +(-6.60750 - 16.6497i) q^{20} +(0.0595051 + 0.0159443i) q^{22} +(-1.23305 + 4.60180i) q^{23} +(-23.9445 - 7.18747i) q^{25} +2.20880 q^{26} +(-15.0780 - 15.0780i) q^{28} +(-35.6216 - 20.5661i) q^{29} +(18.5000 + 32.0429i) q^{31} +(25.8960 + 6.93882i) q^{32} +(-11.4014 - 6.58258i) q^{34} +(-29.5601 + 3.44420i) q^{35} +(50.6170 - 50.6170i) q^{37} +(16.0684 - 4.30550i) q^{38} +(19.6532 - 14.6202i) q^{40} +(1.13218 + 1.96099i) q^{41} +(-33.7465 + 9.04235i) q^{43} -0.341599i q^{44} -3.07803 q^{46} +(5.97769 + 22.3091i) q^{47} +(11.7550 - 6.78674i) q^{49} +(0.481505 - 16.1449i) q^{50} +(-3.17000 - 11.8306i) q^{52} +(49.0894 + 49.0894i) q^{53} +(-0.373864 - 0.295834i) q^{55} +(14.5794 - 25.2523i) q^{56} +(6.87809 - 25.6694i) q^{58} +(86.6216 - 50.0110i) q^{59} +(27.7477 - 48.0605i) q^{61} +(-16.9035 + 16.9035i) q^{62} -27.3394i q^{64} +(-15.6933 - 6.77620i) q^{65} +(-50.9941 - 13.6638i) q^{67} +(-18.8942 + 70.5141i) q^{68} +(-7.09243 - 17.8716i) q^{70} +39.8770 q^{71} +(39.3739 + 39.3739i) q^{73} +(40.0527 + 23.1244i) q^{74} +(-46.1216 - 79.8849i) q^{76} +(-0.548188 - 0.146887i) q^{77} +(52.0212 + 30.0345i) q^{79} +(-43.7780 - 34.6410i) q^{80} +(-1.03447 + 1.03447i) q^{82} +(-105.717 + 28.3267i) q^{83} +(60.8114 + 81.7458i) q^{85} +(-11.2861 - 19.5481i) q^{86} +(0.451202 - 0.120899i) q^{88} -51.6755i q^{89} -20.3485 q^{91} +(4.41749 + 16.4863i) q^{92} +(-12.9228 + 7.46099i) q^{94} +(-127.373 - 18.7046i) q^{95} +(25.9114 + 96.7027i) q^{97} +(6.20105 + 6.20105i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 6 q^{2} - 6 q^{5} + 26 q^{7} + 44 q^{10} - 28 q^{13} - 120 q^{14} + 8 q^{16} - 24 q^{20} + 46 q^{22} - 60 q^{23} + 32 q^{25} + 136 q^{28} - 120 q^{29} + 148 q^{31} + 168 q^{32} + 20 q^{37} + 54 q^{38}+ \cdots - 274 q^{97}+O(q^{100}) \) 8 * q - 6 * q^2 - 6 * q^5 + 26 * q^7 + 44 * q^10 - 28 * q^13 - 120 * q^14 + 8 * q^16 - 24 * q^20 + 46 * q^22 - 60 * q^23 + 32 * q^25 + 136 * q^28 - 120 * q^29 + 148 * q^31 + 168 * q^32 + 20 * q^37 + 54 * q^38 - 48 * q^40 + 2 * q^43 + 232 * q^46 - 6 * q^47 - 42 * q^50 - 112 * q^52 + 52 * q^55 - 66 * q^58 + 528 * q^59 + 112 * q^61 + 84 * q^65 - 76 * q^67 - 156 * q^68 + 396 * q^70 + 260 * q^73 + 852 * q^74 - 204 * q^76 + 318 * q^77 + 340 * q^82 - 582 * q^83 + 194 * q^85 - 72 * q^88 - 896 * q^91 - 228 * q^92 - 342 * q^95 - 274 * q^97

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