LMFDB - Embedded newform 864.2.bh.b.47.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(47,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 9, 7]))

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

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

chi := DirichletCharacter("864.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.bh (of order $18$, degree $6$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$32$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 216)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			47.5
Character	$\chi$	$=$	864.47
Dual form			864.2.bh.b.239.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.49214 - 0.879503i) q^{3} +(-0.189066 - 1.07225i) q^{5} +(-2.50853 + 2.98955i) q^{7} +(1.45295 + 2.62468i) q^{9} +O(q^{10})$	\(q+(-1.49214 - 0.879503i) q^{3} +(-0.189066 - 1.07225i) q^{5} +(-2.50853 + 2.98955i) q^{7} +(1.45295 + 2.62468i) q^{9} +(1.30329 + 0.229805i) q^{11} +(0.772112 - 2.12136i) q^{13} +(-0.660931 + 1.76622i) q^{15} +(1.18381 - 0.683475i) q^{17} +(0.288253 - 0.499269i) q^{19} +(6.37238 - 2.25456i) q^{21} +(6.27608 - 5.26625i) q^{23} +(3.58450 - 1.30465i) q^{25} +(0.140408 - 5.19426i) q^{27} +(-4.46923 + 1.62667i) q^{29} +(-2.27978 - 2.71694i) q^{31} +(-1.74257 - 1.48915i) q^{33} +(3.67981 + 2.12454i) q^{35} +(-8.63247 + 4.98396i) q^{37} +(-3.01784 + 2.48629i) q^{39} +(1.38072 - 3.79351i) q^{41} +(2.06746 - 11.7251i) q^{43} +(2.53960 - 2.05416i) q^{45} +(-5.45070 - 4.57368i) q^{47} +(-1.42914 - 8.10505i) q^{49} +(-2.36753 - 0.0213279i) q^{51} +4.81104 q^{53} -1.44090i q^{55} +(-0.869221 + 0.491459i) q^{57} +(13.2529 - 2.33685i) q^{59} +(3.52183 - 4.19715i) q^{61} +(-11.4914 - 2.24041i) q^{63} +(-2.42060 - 0.426818i) q^{65} +(-5.45749 - 1.98636i) q^{67} +(-13.9965 + 2.33815i) q^{69} +(2.97201 + 5.14767i) q^{71} +(6.04852 - 10.4764i) q^{73} +(-6.49600 - 1.20586i) q^{75} +(-3.95635 + 3.31977i) q^{77} +(-0.128051 - 0.351818i) q^{79} +(-4.77787 + 7.62706i) q^{81} +(2.33666 + 6.41991i) q^{83} +(-0.956672 - 1.14012i) q^{85} +(8.09936 + 1.50349i) q^{87} +(10.8058 + 6.23875i) q^{89} +(4.40504 + 7.62975i) q^{91} +(1.01219 + 6.05911i) q^{93} +(-0.589838 - 0.214684i) q^{95} +(1.51248 - 8.57770i) q^{97} +(1.29045 + 3.75461i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 12 q^{3} - 12 q^{9}+O(q^{10}) $ 192 * q + 12 * q^3 - 12 * q^9	$ 192 q + 12 q^{3} - 12 q^{9} + 30 q^{11} - 18 q^{17} + 6 q^{19} - 12 q^{25} - 18 q^{27} - 30 q^{33} + 18 q^{35} + 18 q^{41} + 42 q^{43} - 12 q^{49} + 18 q^{51} - 36 q^{57} + 84 q^{59} - 12 q^{65} - 30 q^{67} - 6 q^{73} + 96 q^{75} - 12 q^{81} + 72 q^{83} + 144 q^{89} + 6 q^{91} - 42 q^{97} + 12 q^{99}+O(q^{100}) $ 192 * q + 12 * q^3 - 12 * q^9 + 30 * q^11 - 18 * q^17 + 6 * q^19 - 12 * q^25 - 18 * q^27 - 30 * q^33 + 18 * q^35 + 18 * q^41 + 42 * q^43 - 12 * q^49 + 18 * q^51 - 36 * q^57 + 84 * q^59 - 12 * q^65 - 30 * q^67 - 6 * q^73 + 96 * q^75 - 12 * q^81 + 72 * q^83 + 144 * q^89 + 6 * q^91 - 42 * q^97 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$-1$	$e\left(\frac{7}{18}\right)$	$-1$

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			0
$2$		0			0
$3$	−1.49214	−	0.879503i	−0.861486	−	0.507781i
$3$	−1.49214	−	0.879503i	−0.861486	−	0.507781i
$4$		0			0
$5$	−0.189066	−	1.07225i	−0.0845529	−	0.479523i	−0.997452	−	0.0713384i	$-0.977273\pi$
$5$	−0.189066	−	1.07225i	−0.0845529	−	0.479523i	0.912899	−	0.408185i	$-0.133838\pi$
$6$		0			0
$7$	−2.50853	+	2.98955i	−0.948134	+	1.12994i	0.0432647	+	0.999064i	$0.486224\pi$
$7$	−2.50853	+	2.98955i	−0.948134	+	1.12994i	−0.991398	+	0.130878i	$0.958220\pi$
$8$		0			0
$9$	1.45295	+	2.62468i	0.484317	+	0.874893i
$10$		0			0
$11$	1.30329	+	0.229805i	0.392956	+	0.0692888i	0.366635	−	0.930365i	$-0.380510\pi$
$11$	1.30329	+	0.229805i	0.392956	+	0.0692888i	0.0263210	+	0.999654i	$0.491621\pi$
$12$		0			0
$13$	0.772112	−	2.12136i	0.214145	−	0.588360i	−0.785385	−	0.619008i	$-0.787535\pi$
$13$	0.772112	−	2.12136i	0.214145	−	0.588360i	0.999530	+	0.0306481i	$0.00975713\pi$
$14$		0			0
$15$	−0.660931	+	1.76622i	−0.170652	+	0.456037i
$16$		0			0
$17$	1.18381	−	0.683475i	0.287117	−	0.165767i	−0.349524	−	0.936927i	$-0.613657\pi$
$17$	1.18381	−	0.683475i	0.287117	−	0.165767i	0.636641	+	0.771160i	$0.280323\pi$
$18$		0			0
$19$	0.288253	−	0.499269i	0.0661298	−	0.114540i	−0.831065	−	0.556176i	$-0.812268\pi$
$19$	0.288253	−	0.499269i	0.0661298	−	0.114540i	0.897195	+	0.441635i	$0.145602\pi$
$20$		0			0
$21$	6.37238	−	2.25456i	1.39057	−	0.491985i
$22$		0			0
$23$	6.27608	−	5.26625i	1.30865	−	1.09809i	0.320073	−	0.947393i	$-0.396293\pi$
$23$	6.27608	−	5.26625i	1.30865	−	1.09809i	0.988580	−	0.150697i	$-0.0481518\pi$
$24$		0			0
$25$	3.58450	−	1.30465i	0.716899	−	0.260930i
$26$		0			0
$27$	0.140408	−	5.19426i	0.0270216	−	0.999635i
$28$		0			0
$29$	−4.46923	+	1.62667i	−0.829915	+	0.302064i	−0.721824	−	0.692077i	$-0.756696\pi$
$29$	−4.46923	+	1.62667i	−0.829915	+	0.302064i	−0.108091	+	0.994141i	$0.534474\pi$
$30$		0			0
$31$	−2.27978	−	2.71694i	−0.409460	−	0.487976i	0.521420	−	0.853300i	$-0.325403\pi$
$31$	−2.27978	−	2.71694i	−0.409460	−	0.487976i	−0.930880	+	0.365324i	$0.880958\pi$
$32$		0			0
$33$	−1.74257	−	1.48915i	−0.303343	−	0.259227i
$34$		0			0
$35$	3.67981	+	2.12454i	0.622001	+	0.359112i
$36$		0			0
$37$	−8.63247	+	4.98396i	−1.41917	+	0.819358i	−0.996226	−	0.0867980i	$-0.972337\pi$
$37$	−8.63247	+	4.98396i	−1.41917	+	0.819358i	−0.422944	+	0.906156i	$0.639003\pi$
$38$		0			0
$39$	−3.01784	+	2.48629i	−0.483241	+	0.398125i
$40$		0			0
$41$	1.38072	−	3.79351i	0.215633	−	0.592446i	−0.783965	−	0.620805i	$-0.786806\pi$
$41$	1.38072	−	3.79351i	0.215633	−	0.592446i	0.999598	+	0.0283588i	$0.00902811\pi$
$42$		0			0
$43$	2.06746	−	11.7251i	0.315284	−	1.78806i	−0.255338	−	0.966852i	$-0.582187\pi$
$43$	2.06746	−	11.7251i	0.315284	−	1.78806i	0.570622	−	0.821213i	$-0.306702\pi$
$44$		0			0
$45$	2.53960	−	2.05416i	0.378581	−	0.306216i
$46$		0			0
$47$	−5.45070	−	4.57368i	−0.795066	−	0.667139i	0.151928	−	0.988392i	$-0.451452\pi$
$47$	−5.45070	−	4.57368i	−0.795066	−	0.667139i	−0.946994	+	0.321252i	$0.895896\pi$
$48$		0			0
$49$	−1.42914	−	8.10505i	−0.204163	−	1.15786i
$50$		0			0
$51$	−2.36753	−	0.0213279i	−0.331520	−	0.00298651i
$52$		0			0
$53$	4.81104			0.660847			0.330424	−	0.943833i	$-0.392808\pi$
$53$	4.81104			0.660847			0.330424	+	0.943833i	$0.392808\pi$
$54$		0			0
$55$		−	1.44090i		−	0.194290i
$56$		0			0
$57$	−0.869221	+	0.491459i	−0.115131	+	0.0650953i
$58$		0			0
$59$	13.2529	−	2.33685i	1.72538	−	0.304232i	0.778939	−	0.627099i	$-0.215758\pi$
$59$	13.2529	−	2.33685i	1.72538	−	0.304232i	0.946444	+	0.322867i	$0.104647\pi$
$60$		0			0
$61$	3.52183	−	4.19715i	0.450924	−	0.537390i	−0.491913	−	0.870644i	$-0.663702\pi$
$61$	3.52183	−	4.19715i	0.450924	−	0.537390i	0.942837	+	0.333254i	$0.108147\pi$
$62$		0			0
$63$	−11.4914	−	2.24041i	−1.44778	−	0.282265i
$64$		0			0
$65$	−2.42060	−	0.426818i	−0.300239	−	0.0529402i
$66$		0			0
$67$	−5.45749	−	1.98636i	−0.666738	−	0.242673i	−0.0135952	−	0.999908i	$-0.504328\pi$
$67$	−5.45749	−	1.98636i	−0.666738	−	0.242673i	−0.653143	+	0.757235i	$0.726550\pi$
$68$		0			0
$69$	−13.9965	+	2.33815i	−1.68498	+	0.281480i
$70$		0			0
$71$	2.97201	+	5.14767i	0.352713	+	0.610917i	0.986724	−	0.162408i	$-0.0519259\pi$
$71$	2.97201	+	5.14767i	0.352713	+	0.610917i	−0.634011	+	0.773324i	$0.718593\pi$
$72$		0			0
$73$	6.04852	−	10.4764i	0.707926	−	1.22616i	−0.257699	−	0.966225i	$-0.582964\pi$
$73$	6.04852	−	10.4764i	0.707926	−	1.22616i	0.965625	−	0.259939i	$-0.0837024\pi$
$74$		0			0
$75$	−6.49600	−	1.20586i	−0.750094	−	0.139240i
$76$		0			0
$77$	−3.95635	+	3.31977i	−0.450867	+	0.378323i
$78$		0			0
$79$	−0.128051	−	0.351818i	−0.0144069	−	0.0395826i	0.932281	−	0.361736i	$-0.117816\pi$
$79$	−0.128051	−	0.351818i	−0.0144069	−	0.0395826i	−0.946688	+	0.322153i	$0.895593\pi$
$80$		0			0
$81$	−4.77787	+	7.62706i	−0.530874	+	0.847451i
$82$		0			0
$83$	2.33666	+	6.41991i	0.256482	+	0.704677i	0.999378	+	0.0352706i	$0.0112293\pi$
$83$	2.33666	+	6.41991i	0.256482	+	0.704677i	−0.742896	+	0.669407i	$0.766548\pi$
$84$		0			0
$85$	−0.956672	−	1.14012i	−0.103766	−	0.123663i
$86$		0			0
$87$	8.09936	+	1.50349i	0.868343	+	0.161191i
$88$		0			0
$89$	10.8058	+	6.23875i	1.14542	+	0.661306i	0.947766	−	0.318967i	$-0.103336\pi$
$89$	10.8058	+	6.23875i	1.14542	+	0.661306i	0.197650	+	0.980273i	$0.436669\pi$
$90$		0			0
$91$	4.40504	+	7.62975i	0.461774	+	0.799816i
$92$		0			0
$93$	1.01219	+	6.05911i	0.104960	+	0.628301i
$94$		0			0
$95$	−0.589838	−	0.214684i	−0.0605161	−	0.0220261i
$96$		0			0
$97$	1.51248	−	8.57770i	0.153569	−	0.870933i	−0.806513	−	0.591216i	$-0.798648\pi$
$97$	1.51248	−	8.57770i	0.153569	−	0.870933i	0.960082	−	0.279717i	$-0.0902407\pi$
$98$		0			0
$99$	1.29045	+	3.75461i	0.129695	+	0.377352i
$100$		0			0
$101$	4.05415	+	3.40184i	0.403403	+	0.338496i	0.821807	−	0.569765i	$-0.192966\pi$
$101$	4.05415	+	3.40184i	0.403403	+	0.338496i	−0.418404	+	0.908261i	$0.637410\pi$
$102$		0			0
$103$	12.3657	−	2.18041i	1.21843	−	0.214843i	0.472782	−	0.881180i	$-0.343250\pi$
$103$	12.3657	−	2.18041i	1.21843	−	0.214843i	0.745651	+	0.666337i	$0.232139\pi$
$104$		0			0
$105$	−3.62224	−	6.40650i	−0.353495	−	0.625211i
$106$		0			0
$107$			1.54312i			0.149179i	0.997214	+	0.0745894i	$0.0237646\pi$
$107$			1.54312i			0.149179i	−0.997214	+	0.0745894i	$0.976235\pi$
$108$		0			0
$109$		−	12.6373i		−	1.21044i	−0.796060	−	0.605218i	$-0.793086\pi$
$109$		−	12.6373i		−	1.21044i	0.796060	−	0.605218i	$-0.206914\pi$
$110$		0			0
$111$	17.2642	+	0.155525i	1.63865	+	0.0147618i
$112$		0			0
$113$	−1.50818	+	0.265932i	−0.141877	+	0.0250168i	−0.244136	−	0.969741i	$-0.578504\pi$
$113$	−1.50818	+	0.265932i	−0.141877	+	0.0250168i	0.102258	+	0.994758i	$0.467393\pi$
$114$		0			0
$115$	−6.83332	−	5.73383i	−0.637210	−	0.534683i
$116$		0			0
$117$	6.68973	−	1.05569i	0.618466	−	0.0975983i
$118$		0			0
$119$	−0.926347	+	5.25357i	−0.0849181	+	0.481594i
$120$		0			0
$121$	−8.69087	−	3.16322i	−0.790079	−	0.287565i
$122$		0			0
$123$	−5.39663	+	4.44608i	−0.486598	+	0.400890i
$124$		0			0
$125$	−4.79858	−	8.31139i	−0.429198	−	0.743393i
$126$		0			0
$127$	12.6812	+	7.32149i	1.12527	+	0.649678i	0.942742	−	0.333522i	$-0.108237\pi$
$127$	12.6812	+	7.32149i	1.12527	+	0.649678i	0.182532	+	0.983200i	$0.441571\pi$
$128$		0			0
$129$	−13.3972	+	15.6772i	−1.17956	+	1.38030i
$130$		0			0
$131$	7.84571	+	9.35015i	0.685483	+	0.816926i	0.990801	−	0.135324i	$-0.0432075\pi$
$131$	7.84571	+	9.35015i	0.685483	+	0.816926i	−0.305319	+	0.952250i	$0.598763\pi$
$132$		0			0
$133$	0.769497	+	2.11417i	0.0667238	+	0.183322i
$134$		0			0
$135$	−5.59607	+	0.831505i	−0.481633	+	0.0715646i
$136$		0			0
$137$	−2.20073	−	6.04645i	−0.188021	−	0.516583i	0.809487	−	0.587138i	$-0.199745\pi$
$137$	−2.20073	−	6.04645i	−0.188021	−	0.516583i	−0.997508	+	0.0705549i	$0.977523\pi$
$138$		0			0
$139$	−0.636525	+	0.534108i	−0.0539894	+	0.0453025i	−0.669383	−	0.742917i	$-0.733441\pi$
$139$	−0.636525	+	0.534108i	−0.0539894	+	0.0453025i	0.615394	+	0.788220i	$0.288997\pi$
$140$		0			0
$141$	4.11063	+	11.6185i	0.346178	+	0.978451i
$142$		0			0
$143$	1.49378	−	2.58731i	0.124917	−	0.216362i
$144$		0			0
$145$	2.58917	+	4.48457i	0.215019	+	0.372423i
$146$		0			0
$147$	−4.99594	+	13.3508i	−0.412058	+	1.10115i
$148$		0			0
$149$	9.65990	+	3.51592i	0.791370	+	0.288035i	0.705906	−	0.708306i	$-0.250540\pi$
$149$	9.65990	+	3.51592i	0.791370	+	0.288035i	0.0854647	+	0.996341i	$0.472763\pi$
$150$		0			0
$151$	−20.8179	−	3.67076i	−1.69414	−	0.298722i	−0.758497	−	0.651677i	$-0.774066\pi$
$151$	−20.8179	−	3.67076i	−1.69414	−	0.298722i	−0.935641	+	0.352954i	$0.885177\pi$
$152$		0			0
$153$	3.51392	+	2.11407i	0.284084	+	0.170913i
$154$		0			0
$155$	−2.48220	+	2.95817i	−0.199375	+	0.237606i
$156$		0			0
$157$	−15.9685	+	2.81567i	−1.27442	+	0.224715i	−0.769610	−	0.638515i	$-0.779549\pi$
$157$	−15.9685	+	2.81567i	−1.27442	+	0.224715i	−0.504812	+	0.863229i	$0.668438\pi$
$158$		0			0
$159$	−7.17873	−	4.23132i	−0.569311	−	0.335566i
$160$		0			0
$161$			31.9732i			2.51984i
$162$		0			0
$163$	0.195494			0.0153123			0.00765613	−	0.999971i	$-0.497563\pi$
$163$	0.195494			0.0153123			0.00765613	+	0.999971i	$0.497563\pi$
$164$		0			0
$165$	−1.26727	+	2.15001i	−0.0986569	+	0.167378i
$166$		0			0
$167$	−3.18742	−	18.0768i	−0.246650	−	1.39882i	−0.816629	−	0.577164i	$-0.804160\pi$
$167$	−3.18742	−	18.0768i	−0.246650	−	1.39882i	0.569978	−	0.821660i	$-0.306952\pi$
$168$		0			0
$169$	6.05456	+	5.08038i	0.465736	+	0.390799i
$170$		0			0
$171$	1.72924	+	0.0311583i	0.132238	+	0.00238273i
$172$		0			0
$173$	0.465894	−	2.64221i	0.0354212	−	0.200884i	−0.961962	−	0.273185i	$-0.911923\pi$
$173$	0.465894	−	2.64221i	0.0354212	−	0.200884i	0.997383	+	0.0723007i	$0.0230341\pi$
$174$		0			0
$175$	−5.09149	+	13.9888i	−0.384881	+	1.05745i
$176$		0			0
$177$	−21.8305	−	8.16908i	−1.64088	−	0.614026i
$178$		0			0
$179$	−21.0140	+	12.1324i	−1.57066	+	0.906820i	−0.574570	+	0.818456i	$0.694831\pi$
$179$	−21.0140	+	12.1324i	−1.57066	+	0.906820i	−0.996088	+	0.0883640i	$0.971836\pi$
$180$		0			0
$181$	8.40111	+	4.85038i	0.624449	+	0.360526i	0.778599	−	0.627521i	$-0.215931\pi$
$181$	8.40111	+	4.85038i	0.624449	+	0.360526i	−0.154150	+	0.988047i	$0.549264\pi$
$182$		0			0
$183$	−8.94645	+	3.16527i	−0.661341	+	0.233983i
$184$		0			0
$185$	6.97614	+	8.31384i	0.512896	+	0.611246i
$186$		0			0
$187$	1.69992	−	0.618719i	0.124310	−	0.0452452i
$188$		0			0
$189$	15.1762	+	13.4497i	1.10391	+	0.978320i
$190$		0			0
$191$	14.7034	−	5.35160i	1.06390	−	0.387228i	0.250008	−	0.968244i	$-0.419567\pi$
$191$	14.7034	−	5.35160i	1.06390	−	0.387228i	0.813892	+	0.581016i	$0.197345\pi$
$192$		0			0
$193$	−15.1168	+	12.6845i	−1.08813	+	0.913048i	−0.996570	−	0.0827519i	$-0.973629\pi$
$193$	−15.1168	+	12.6845i	−1.08813	+	0.913048i	−0.0915578	+	0.995800i	$0.529185\pi$
$194$		0			0
$195$	3.23649	+	2.76580i	0.231770	+	0.198063i
$196$		0			0
$197$	9.82877	−	17.0239i	0.700271	−	1.21291i	−0.268100	−	0.963391i	$-0.586396\pi$
$197$	9.82877	−	17.0239i	0.700271	−	1.21291i	0.968371	−	0.249514i	$-0.0802709\pi$
$198$		0			0
$199$	−5.37946	+	3.10583i	−0.381340	+	0.220167i	−0.678401	−	0.734692i	$-0.737327\pi$
$199$	−5.37946	+	3.10583i	−0.381340	+	0.220167i	0.297061	+	0.954858i	$0.403993\pi$
$200$		0			0
$201$	6.39631	+	7.76380i	0.451161	+	0.547616i
$202$		0			0
$203$	6.34819	−	17.4415i	0.445555	−	1.22415i
$204$		0			0
$205$	−4.32862	−	0.763253i	−0.302324	−	0.0533079i
$206$		0			0
$207$	22.9411	+	8.82107i	1.59451	+	0.613107i
$208$		0			0
$209$	0.490411	−	0.584449i	0.0339225	−	0.0404272i
$210$		0			0
$211$	0.767843	+	4.35465i	0.0528605	+	0.299787i	0.999764	−	0.0217317i	$-0.00691795\pi$
$211$	0.767843	+	4.35465i	0.0528605	+	0.299787i	−0.946903	+	0.321518i	$0.895807\pi$
$212$		0			0
$213$	0.0927421	−	10.2949i	0.00635459	−	0.705397i
$214$		0			0
$215$	−12.9631			−0.884077
$216$		0			0
$217$	13.8413			0.939608
$218$		0			0
$219$	−18.2392	+	10.3125i	−1.23249	+	0.696852i
$220$		0			0
$221$	−0.535860	−	3.03901i	−0.0360458	−	0.204426i
$222$		0			0
$223$	−2.69526	+	3.21209i	−0.180488	+	0.215097i	−0.848701	−	0.528873i	$-0.822615\pi$
$223$	−2.69526	+	3.21209i	−0.180488	+	0.215097i	0.668213	+	0.743970i	$0.267059\pi$
$224$		0			0
$225$	8.63238	+	7.51256i	0.575492	+	0.500837i
$226$		0			0
$227$	−15.4861	−	2.73062i	−1.02785	−	0.181238i	−0.365797	−	0.930695i	$-0.619204\pi$
$227$	−15.4861	−	2.73062i	−1.02785	−	0.181238i	−0.662053	+	0.749457i	$0.730315\pi$
$228$		0			0
$229$	−4.08483	+	11.2230i	−0.269933	+	0.741635i	0.728467	+	0.685081i	$0.240233\pi$
$229$	−4.08483	+	11.2230i	−0.269933	+	0.741635i	−0.998400	+	0.0565533i	$0.981989\pi$
$230$		0			0
$231$	8.82316	−	1.47394i	0.580521	−	0.0969779i
$232$		0			0
$233$	9.79148	−	5.65311i	0.641461	−	0.370348i	−0.143716	−	0.989619i	$-0.545905\pi$
$233$	9.79148	−	5.65311i	0.641461	−	0.370348i	0.785177	+	0.619271i	$0.212572\pi$
$234$		0			0
$235$	−3.87357	+	6.70922i	−0.252684	+	0.437661i
$236$		0			0
$237$	−0.118354	+	0.637581i	−0.00768795	+	0.0414154i
$238$		0			0
$239$	−20.0803	+	16.8494i	−1.29889	+	1.08990i	−0.308554	+	0.951207i	$0.599845\pi$
$239$	−20.0803	+	16.8494i	−1.29889	+	1.08990i	−0.990336	+	0.138691i	$0.955711\pi$
$240$		0			0
$241$	−14.8929	+	5.42058i	−0.959337	+	0.349170i	−0.773773	−	0.633462i	$-0.781633\pi$
$241$	−14.8929	+	5.42058i	−0.959337	+	0.349170i	−0.185563	+	0.982632i	$0.559411\pi$
$242$		0			0
$243$	13.8373	−	7.17847i	0.887660	−	0.460499i
$244$		0			0
$245$	−8.42041	+	3.06478i	−0.537960	+	0.195802i
$246$		0			0
$247$	−0.836566	−	0.996980i	−0.0532294	−	0.0634363i
$248$		0			0
$249$	2.15972	−	11.6345i	0.136866	−	0.737306i
$250$		0			0
$251$	9.88629	+	5.70785i	0.624017	+	0.360277i	0.778431	−	0.627730i	$-0.216016\pi$
$251$	9.88629	+	5.70785i	0.624017	+	0.360277i	−0.154414	+	0.988006i	$0.549349\pi$
$252$		0			0
$253$	9.38975	−	5.42118i	0.590329	−	0.340826i
$254$		0			0
$255$	0.424751	+	2.54261i	0.0265989	+	0.159224i
$256$		0			0
$257$	−0.219314	+	0.602559i	−0.0136804	+	0.0375866i	−0.946345	−	0.323158i	$-0.895255\pi$
$257$	−0.219314	+	0.602559i	−0.0136804	+	0.0375866i	0.932664	+	0.360745i	$0.117478\pi$
$258$		0			0
$259$	6.75501	−	38.3096i	0.419736	−	2.38044i
$260$		0			0
$261$	−10.7630	−	9.36682i	−0.666216	−	0.579792i
$262$		0			0
$263$	20.5545	+	17.2473i	1.26745	+	1.06351i	0.994847	+	0.101386i	$0.0323276\pi$
$263$	20.5545	+	17.2473i	1.26745	+	1.06351i	0.272599	+	0.962128i	$0.412117\pi$
$264$		0			0
$265$	−0.909604	−	5.15862i	−0.0558765	−	0.316892i
$266$		0			0
$267$	−10.6368	−	18.8128i	−0.650961	−	1.15133i
$268$		0			0
$269$	24.6044			1.50016			0.750078	−	0.661349i	$-0.230016\pi$
$269$	24.6044			1.50016			0.750078	+	0.661349i	$0.230016\pi$
$270$		0			0
$271$		−	26.2030i		−	1.59172i	−0.605483	−	0.795858i	$-0.707020\pi$
$271$		−	26.2030i		−	1.59172i	0.605483	−	0.795858i	$-0.292980\pi$
$272$		0			0
$273$	0.137460	−	15.2589i	0.00831946	−	0.923510i
$274$		0			0
$275$	4.97145	−	0.876600i	0.299790	−	0.0528610i
$276$		0			0
$277$	0.566742	−	0.675417i	0.0340522	−	0.0405819i	−0.748750	−	0.662853i	$-0.769345\pi$
$277$	0.566742	−	0.675417i	0.0340522	−	0.0405819i	0.782802	+	0.622271i	$0.213790\pi$
$278$		0			0
$279$	3.81867	−	9.93126i	0.228618	−	0.594569i
$280$		0			0
$281$	−7.66502	−	1.35155i	−0.457257	−	0.0806267i	−0.0597245	−	0.998215i	$-0.519022\pi$
$281$	−7.66502	−	1.35155i	−0.457257	−	0.0806267i	−0.397532	+	0.917588i	$0.630133\pi$
$282$		0			0
$283$	−1.84859	−	0.672831i	−0.109887	−	0.0399957i	0.286491	−	0.958083i	$-0.407511\pi$
$283$	−1.84859	−	0.672831i	−0.109887	−	0.0399957i	−0.396379	+	0.918087i	$0.629733\pi$
$284$		0			0
$285$	0.691305	+	0.839102i	0.0409494	+	0.0497041i
$286$		0			0
$287$	7.87728	+	13.6438i	0.464981	+	0.805371i
$288$		0			0
$289$	−7.56573	+	13.1042i	−0.445043	+	0.770836i
$290$		0			0
$291$	−9.80093	+	11.4689i	−0.574541	+	0.672317i
$292$		0			0
$293$	−6.37444	+	5.34879i	−0.372398	+	0.312479i	−0.809710	−	0.586831i	$-0.800375\pi$
$293$	−6.37444	+	5.34879i	−0.372398	+	0.312479i	0.437311	+	0.899310i	$0.355931\pi$
$294$		0			0
$295$	−5.01136	−	13.7686i	−0.291772	−	0.801638i
$296$		0			0
$297$	1.37666	−	6.73735i	0.0798818	−	0.390941i
$298$		0			0
$299$	−6.32579	−	17.3800i	−0.365830	−	1.00511i
$300$		0			0
$301$	29.8665	+	35.5935i	1.72148	+	2.05158i
$302$		0			0
$303$	−3.05743	−	8.64165i	−0.175645	−	0.496450i
$304$		0			0
$305$	−5.16624	−	2.98273i	−0.295818	−	0.170791i
$306$		0			0
$307$	2.95259	+	5.11404i	0.168513	+	0.291874i	0.937897	−	0.346913i	$-0.112770\pi$
$307$	2.95259	+	5.11404i	0.168513	+	0.291874i	−0.769384	+	0.638787i	$0.779437\pi$
$308$		0			0
$309$	−20.3691	−	7.62222i	−1.15876	−	0.433613i
$310$		0			0
$311$	−4.39513	−	1.59969i	−0.249225	−	0.0907104i	0.214387	−	0.976749i	$-0.431225\pi$
$311$	−4.39513	−	1.59969i	−0.249225	−	0.0907104i	−0.463612	+	0.886038i	$0.653447\pi$
$312$		0			0
$313$	3.61344	−	20.4928i	0.204243	−	1.15832i	−0.694382	−	0.719606i	$-0.744322\pi$
$313$	3.61344	−	20.4928i	0.204243	−	1.15832i	0.898626	−	0.438716i	$-0.144567\pi$
$314$		0			0
$315$	−0.229649	+	12.7452i	−0.0129392	+	0.718108i
$316$		0			0
$317$	−6.10426	−	5.12208i	−0.342849	−	0.287685i	0.455062	−	0.890460i	$-0.349617\pi$
$317$	−6.10426	−	5.12208i	−0.342849	−	0.287685i	−0.797911	+	0.602775i	$0.794062\pi$
$318$		0			0
$319$	−6.19851	+	1.09296i	−0.347050	+	0.0611943i
$320$		0			0
$321$	1.35718	−	2.30254i	0.0757502	−	0.128516i
$322$		0			0
$323$		−	0.788054i		−	0.0438485i
$324$		0			0
$325$		−	8.61135i		−	0.477672i
$326$		0			0
$327$	−11.1146	+	18.8566i	−0.614636	+	1.04277i
$328$		0			0
$329$	27.3464	−	4.82191i	1.50766	−	0.265841i
$330$		0			0
$331$	16.9638	+	14.2343i	0.932412	+	0.782387i	0.976249	−	0.216652i	$-0.0695137\pi$
$331$	16.9638	+	14.2343i	0.932412	+	0.782387i	−0.0438367	+	0.999039i	$0.513958\pi$
$332$		0			0
$333$	−25.6238	−	15.4160i	−1.40418	−	0.844792i
$334$		0			0
$335$	−1.09805	+	6.22733i	−0.0599926	+	0.340235i
$336$		0			0
$337$	−12.2497	−	4.45852i	−0.667282	−	0.242871i	−0.0139051	−	0.999903i	$-0.504426\pi$
$337$	−12.2497	−	4.45852i	−0.667282	−	0.242871i	−0.653377	+	0.757032i	$0.726648\pi$
$338$		0			0
$339$	2.48430	+	0.929639i	0.134929	+	0.0504910i
$340$		0			0
$341$	−2.34685	−	4.06486i	−0.127089	−	0.220124i
$342$		0			0
$343$	4.15735	+	2.40025i	0.224476	+	0.129601i
$344$		0			0
$345$	5.15333	+	14.5656i	0.277446	+	0.784185i
$346$		0			0
$347$	−3.35373	−	3.99682i	−0.180038	−	0.214560i	0.668476	−	0.743733i	$-0.266947\pi$
$347$	−3.35373	−	3.99682i	−0.180038	−	0.214560i	−0.848514	+	0.529173i	$0.822502\pi$
$348$		0			0
$349$	0.226359	+	0.621917i	0.0121167	+	0.0332905i	0.945604	−	0.325321i	$-0.105472\pi$
$349$	0.226359	+	0.621917i	0.0121167	+	0.0332905i	−0.933487	+	0.358612i	$0.883250\pi$
$350$		0			0
$351$	−10.9105	−	4.30840i	−0.582358	−	0.229966i
$352$		0			0
$353$	−9.48755	−	26.0668i	−0.504971	−	1.38740i	−0.886366	−	0.462985i	$-0.846778\pi$
$353$	−9.48755	−	26.0668i	−0.504971	−	1.38740i	0.381395	−	0.924412i	$-0.375444\pi$
$354$		0			0
$355$	4.95767	−	4.15998i	0.263126	−	0.220789i
$356$		0			0
$357$	6.00277	−	7.02433i	0.317700	−	0.371767i
$358$		0			0
$359$	3.32105	−	5.75223i	0.175278	−	0.303591i	−0.764979	−	0.644055i	$-0.777251\pi$
$359$	3.32105	−	5.75223i	0.175278	−	0.303591i	0.940258	+	0.340464i	$0.110584\pi$
$360$		0			0
$361$	9.33382	+	16.1667i	0.491254	+	0.850876i
$362$		0			0
$363$	10.1859	+	12.3636i	0.534622	+	0.648921i
$364$		0			0
$365$	−12.3768	−	4.50479i	−0.647832	−	0.235791i
$366$		0			0
$367$	6.67817	+	1.17754i	0.348598	+	0.0614671i	0.345206	−	0.938527i	$-0.387809\pi$
$367$	6.67817	+	1.17754i	0.348598	+	0.0614671i	0.00339194	+	0.999994i	$0.498920\pi$
$368$		0			0
$369$	11.9629	−	1.88782i	0.622761	−	0.0982762i
$370$		0			0
$371$	−12.0686	+	14.3828i	−0.626571	+	0.746719i
$372$		0			0
$373$	1.88673	−	0.332682i	0.0976914	−	0.0172256i	−0.124589	−	0.992208i	$-0.539761\pi$
$373$	1.88673	−	0.332682i	0.0976914	−	0.0172256i	0.222280	+	0.974983i	$0.428650\pi$
$374$		0			0
$375$	−0.149741	+	16.6221i	−0.00773257	+	0.858362i
$376$		0			0
$377$			10.7368i			0.552974i
$378$		0			0
$379$	8.95404			0.459938			0.229969	−	0.973198i	$-0.426137\pi$
$379$	8.95404			0.459938			0.229969	+	0.973198i	$0.426137\pi$
$380$		0			0
$381$	−12.4828	−	22.0778i	−0.639514	−	1.13108i
$382$		0			0
$383$	−1.45255	−	8.23785i	−0.0742221	−	0.420934i	−0.999166	−	0.0408309i	$-0.987000\pi$
$383$	−1.45255	−	8.23785i	−0.0742221	−	0.420934i	0.924944	−	0.380103i	$-0.124112\pi$
$384$		0			0
$385$	4.30762	+	3.61452i	0.219537	+	0.184213i
$386$		0			0
$387$	33.7786	−	11.6096i	1.71706	−	0.590150i
$388$		0			0
$389$	−1.07723	+	6.10927i	−0.0546177	+	0.309752i	−0.999862	−	0.0166113i	$-0.994712\pi$
$389$	−1.07723	+	6.10927i	−0.0546177	+	0.309752i	0.945244	+	0.326363i	$0.105823\pi$
$390$		0			0
$391$	3.83035	−	10.5238i	0.193709	−	0.532211i
$392$		0			0
$393$	−3.48340	−	20.8520i	−0.175714	−	1.05185i
$394$		0			0
$395$	−0.353025	+	0.203819i	−0.0177626	+	0.0102553i
$396$		0			0
$397$	−12.5258	−	7.23180i	−0.628654	−	0.362953i	0.151577	−	0.988445i	$-0.451565\pi$
$397$	−12.5258	−	7.23180i	−0.628654	−	0.362953i	−0.780231	+	0.625492i	$0.784898\pi$
$398$		0			0
$399$	0.711227	−	3.83141i	0.0356059	−	0.191811i
$400$		0			0
$401$	−8.00754	−	9.54302i	−0.399878	−	0.476555i	0.528105	−	0.849179i	$-0.322903\pi$
$401$	−8.00754	−	9.54302i	−0.399878	−	0.476555i	−0.927983	+	0.372624i	$0.878458\pi$
$402$		0			0
$403$	−7.52385	+	2.73846i	−0.374789	+	0.136412i
$404$		0			0
$405$	9.08142	+	3.68104i	0.451259	+	0.182912i
$406$		0			0
$407$	−12.3959	+	4.51175i	−0.614444	+	0.223639i
$408$		0			0
$409$	−18.9863	+	15.9314i	−0.938810	+	0.787755i	−0.977378	−	0.211501i	$-0.932165\pi$
$409$	−18.9863	+	15.9314i	−0.938810	+	0.787755i	0.0385679	+	0.999256i	$0.487720\pi$
$410$		0			0
$411$	−2.03408	+	10.9577i	−0.100334	+	0.540502i
$412$		0			0
$413$	−26.2592	+	45.4823i	−1.29213	+	2.23804i
$414$		0			0
$415$	6.44195	−	3.71926i	0.316223	−	0.182571i
$416$		0			0
$417$	1.41953	−	0.237137i	0.0695148	−	0.0116127i
$418$		0			0
$419$	5.14055	−	14.1235i	0.251132	−	0.689980i	−0.748507	−	0.663127i	$-0.769229\pi$
$419$	5.14055	−	14.1235i	0.251132	−	0.689980i	0.999639	−	0.0268532i	$-0.00854865\pi$
$420$		0			0
$421$	−10.0807	−	1.77749i	−0.491302	−	0.0866298i	−0.0774918	−	0.996993i	$-0.524691\pi$
$421$	−10.0807	−	1.77749i	−0.491302	−	0.0866298i	−0.413810	+	0.910363i	$0.635802\pi$
$422$		0			0
$423$	4.08484	−	20.9517i	0.198612	−	1.01870i
$424$		0			0
$425$	3.35168	−	3.99437i	0.162580	−	0.193756i
$426$		0			0
$427$	3.71297	+	21.0573i	0.179683	+	1.01903i
$428$		0			0
$429$	−4.50448	+	2.54684i	−0.217478	+	0.122962i
$430$		0			0
$431$	13.0887			0.630459			0.315229	−	0.949015i	$-0.397919\pi$
$431$	13.0887			0.630459			0.315229	+	0.949015i	$0.397919\pi$
$432$		0			0
$433$	0.793849			0.0381499			0.0190750	−	0.999818i	$-0.493928\pi$
$433$	0.793849			0.0381499			0.0190750	+	0.999818i	$0.493928\pi$
$434$		0			0
$435$	0.0807954	−	8.96878i	0.00387384	−	0.430020i
$436$		0			0
$437$	−0.820179	−	4.65146i	−0.0392345	−	0.222510i
$438$		0			0
$439$	15.8285	−	18.8637i	0.755455	−	0.900316i	−0.242096	−	0.970252i	$-0.577835\pi$
$439$	15.8285	−	18.8637i	0.755455	−	0.900316i	0.997551	+	0.0699359i	$0.0222795\pi$
$440$		0			0
$441$	19.1967	−	15.5273i	0.914127	−	0.739394i
$442$		0			0
$443$	−15.7110	−	2.77027i	−0.746452	−	0.131620i	−0.212531	−	0.977154i	$-0.568171\pi$
$443$	−15.7110	−	2.77027i	−0.746452	−	0.131620i	−0.533921	+	0.845535i	$0.679282\pi$
$444$		0			0
$445$	4.64646	−	12.7661i	0.220263	−	0.605169i
$446$		0			0
$447$	−11.3217	−	13.7421i	−0.535496	−	0.649981i
$448$		0			0
$449$	−1.28879	+	0.744086i	−0.0608219	+	0.0351156i	−0.530103	−	0.847934i	$-0.677847\pi$
$449$	−1.28879	+	0.744086i	−0.0608219	+	0.0351156i	0.469281	+	0.883049i	$0.344513\pi$
$450$		0			0
$451$	2.67125	−	4.62674i	0.125784	−	0.217864i
$452$		0			0
$453$	27.8347	+	23.7867i	1.30779	+	1.11760i
$454$		0			0
$455$	7.34814	−	6.16582i	0.344486	−	0.289058i
$456$		0			0
$457$	6.42664	−	2.33911i	0.300626	−	0.109419i	−0.187303	−	0.982302i	$-0.559975\pi$
$457$	6.42664	−	2.33911i	0.300626	−	0.109419i	0.487929	+	0.872883i	$0.337753\pi$
$458$		0			0
$459$	−3.38392	−	6.24499i	−0.157948	−	0.291491i
$460$		0			0
$461$	3.18627	−	1.15971i	0.148399	−	0.0540129i	−0.266753	−	0.963765i	$-0.585951\pi$
$461$	3.18627	−	1.15971i	0.148399	−	0.0540129i	0.415152	+	0.909752i	$0.363728\pi$
$462$		0			0
$463$	−14.1625	−	16.8782i	−0.658188	−	0.784398i	0.328936	−	0.944352i	$-0.393310\pi$
$463$	−14.1625	−	16.8782i	−0.658188	−	0.784398i	−0.987124	+	0.159954i	$0.948865\pi$
$464$		0			0
$465$	6.30549	−	2.23089i	0.292410	−	0.103455i
$466$		0			0
$467$	15.6602	+	9.04142i	0.724667	+	0.418387i	0.816468	−	0.577391i	$-0.195929\pi$
$467$	15.6602	+	9.04142i	0.724667	+	0.418387i	−0.0918008	+	0.995777i	$0.529262\pi$
$468$		0			0
$469$	19.6286	−	11.3326i	0.906363	−	0.523289i
$470$		0			0
$471$	26.3035	+	9.84293i	1.21200	+	0.453538i
$472$		0			0
$473$	5.38898	−	14.8061i	0.247786	−	0.680786i
$474$		0			0
$475$	0.381871	−	2.16570i	0.0175214	−	0.0993690i
$476$		0			0
$477$	6.99020	+	12.6274i	0.320059	+	0.578170i
$478$		0			0
$479$	−14.9230	−	12.5219i	−0.681850	−	0.572140i	0.234697	−	0.972069i	$-0.424590\pi$
$479$	−14.9230	−	12.5219i	−0.681850	−	0.572140i	−0.916546	+	0.399929i	$0.869035\pi$
$480$		0			0
$481$	3.90754	+	22.1608i	0.178169	+	1.01044i
$482$		0			0
$483$	28.1205	−	47.7084i	1.27953	−	2.17081i
$484$		0			0
$485$	−9.48337			−0.430617
$486$		0			0
$487$			42.8535i			1.94188i	0.239333	+	0.970938i	$0.423071\pi$
$487$			42.8535i			1.94188i	−0.239333	+	0.970938i	$0.576929\pi$
$488$		0			0
$489$	−0.291704	−	0.171937i	−0.0131913	−	0.00777527i
$490$		0			0
$491$	4.37930	−	0.772189i	0.197635	−	0.0348484i	−0.0739542	−	0.997262i	$-0.523562\pi$
$491$	4.37930	−	0.772189i	0.197635	−	0.0348484i	0.271589	+	0.962413i	$0.412451\pi$
$492$		0			0
$493$	−4.17895	+	4.98027i	−0.188210	+	0.224300i
$494$		0			0
$495$	3.78189	−	2.09355i	0.169983	−	0.0940981i
$496$		0			0
$497$	−22.8446	−	4.02811i	−1.02472	−	0.180686i
$498$		0			0
$499$	−24.8099	−	9.03007i	−1.11064	−	0.404242i	−0.279415	−	0.960171i	$-0.590140\pi$
$499$	−24.8099	−	9.03007i	−1.11064	−	0.404242i	−0.831230	+	0.555929i	$0.812363\pi$
$500$		0			0
$501$	−11.1425	+	29.7764i	−0.497810	+	1.33031i
$502$		0			0
$503$	−6.11688	−	10.5947i	−0.272738	−	0.472396i	0.696824	−	0.717242i	$-0.254596\pi$
$503$	−6.11688	−	10.5947i	−0.272738	−	0.472396i	−0.969562	+	0.244846i	$0.921263\pi$
$504$		0			0
$505$	2.88111	−	4.99023i	0.128208	−	0.222062i
$506$		0			0
$507$	−4.56603	−	12.9056i	−0.202785	−	0.573159i
$508$		0			0
$509$	32.7292	−	27.4631i	1.45070	−	1.21728i	0.518629	−	0.854999i	$-0.326442\pi$
$509$	32.7292	−	27.4631i	1.45070	−	1.21728i	0.932069	−	0.362281i	$-0.118002\pi$
$510$		0			0
$511$	16.1466	+	44.3625i	0.714285	+	1.96248i
$512$		0			0
$513$	−2.55286	−	1.56736i	−0.112711	−	0.0692007i
$514$		0			0
$515$	−4.67588	−	12.8469i	−0.206044	−	0.566101i
$516$		0			0
$517$	−6.05278	−	7.21342i	−0.266201	−	0.317246i
$518$		0			0
$519$	−3.01901	+	3.53279i	−0.132520	+	0.155072i
$520$		0			0
$521$	−31.9892	−	18.4690i	−1.40147	−	0.809141i	−0.406930	−	0.913459i	$-0.633401\pi$
$521$	−31.9892	−	18.4690i	−1.40147	−	0.809141i	−0.994544	+	0.104318i	$0.966734\pi$
$522$		0			0
$523$	18.4500	+	31.9563i	0.806761	+	1.39735i	0.915096	+	0.403236i	$0.132115\pi$
$523$	18.4500	+	31.9563i	0.806761	+	1.39735i	−0.108335	+	0.994114i	$0.534552\pi$
$524$		0			0
$525$	19.9004	−	16.3952i	0.868523	−	0.715544i
$526$		0			0
$527$	−4.55579	−	1.65817i	−0.198453	−	0.0722311i
$528$		0			0
$529$	7.66181	−	43.4523i	0.333122	−	1.88923i
$530$		0			0
$531$	25.3893	+	31.3893i	1.10180	+	1.36218i
$532$		0			0
$533$	−6.98132	−	5.85803i	−0.302395	−	0.253739i
$534$		0			0
$535$	1.65460	−	0.291751i	0.0715347	−	0.0126135i
$536$		0			0
$537$	42.0262	+	0.378594i	1.81357	+	0.0163376i
$538$		0			0
$539$		−	10.8916i		−	0.469136i
$540$		0			0
$541$			14.4407i			0.620855i	0.950597	+	0.310427i	$0.100472\pi$
$541$			14.4407i			0.620855i	−0.950597	+	0.310427i	$0.899528\pi$
$542$		0			0
$543$	−8.26969	−	14.6262i	−0.354886	−	0.627672i
$544$		0			0
$545$	−13.5503	+	2.38929i	−0.580432	+	0.102346i
$546$		0			0
$547$	5.54811	+	4.65542i	0.237220	+	0.199051i	0.753646	−	0.657281i	$-0.228293\pi$
$547$	5.54811	+	4.65542i	0.237220	+	0.199051i	−0.516426	+	0.856332i	$0.672738\pi$
$548$		0			0
$549$	16.1332	+	3.14541i	0.688548	+	0.134243i
$550$		0			0
$551$	−0.476125	+	2.70024i	−0.0202836	+	0.115034i
$552$		0			0
$553$	1.37299	+	0.499729i	0.0583856	+	0.0212506i
$554$		0			0
$555$	−3.09732	−	18.5409i	−0.131474	−	0.787019i
$556$		0			0
$557$	1.67088	+	2.89404i	0.0707973	+	0.122625i	0.899251	−	0.437433i	$-0.144112\pi$
$557$	1.67088	+	2.89404i	0.0707973	+	0.122625i	−0.828454	+	0.560058i	$0.810779\pi$
$558$		0			0
$559$	−23.2769	−	13.4389i	−0.984509	−	0.568406i
$560$		0			0
$561$	−3.08067	−	0.571866i	−0.130066	−	0.0241442i
$562$		0			0
$563$	−13.1252	−	15.6421i	−0.553163	−	0.659234i	0.414922	−	0.909857i	$-0.363809\pi$
$563$	−13.1252	−	15.6421i	−0.553163	−	0.659234i	−0.968085	+	0.250623i	$0.919365\pi$
$564$		0			0
$565$	0.570291	+	1.56686i	0.0239923	+	0.0659183i
$566$		0			0
$567$	−10.8160	−	33.4163i	−0.454230	−	1.40335i
$568$		0			0
$569$	2.43319	+	6.68514i	0.102005	+	0.280256i	0.980188	−	0.198068i	$-0.0634667\pi$
$569$	2.43319	+	6.68514i	0.102005	+	0.280256i	−0.878184	+	0.478324i	$0.841245\pi$
$570$		0			0
$571$	−23.1842	+	19.4539i	−0.970229	+	0.814119i	−0.982587	−	0.185804i	$-0.940511\pi$
$571$	−23.1842	+	19.4539i	−0.970229	+	0.814119i	0.0123573	+	0.999924i	$0.496066\pi$
$572$		0			0
$573$	−26.6462	−	4.94635i	−1.11316	−	0.206637i
$574$		0			0
$575$	15.6260	−	27.0650i	0.651647	−	1.12869i
$576$		0			0
$577$	12.4445	+	21.5546i	0.518073	+	0.897328i	0.999780	+	0.0209957i	$0.00668363\pi$
$577$	12.4445	+	21.5546i	0.518073	+	0.897328i	−0.481707	+	0.876332i	$0.659983\pi$
$578$		0			0
$579$	33.7123	−	5.63175i	1.40104	−	0.234047i
$580$		0			0
$581$	−25.0542	−	9.11898i	−1.03942	−	0.378319i
$582$		0			0
$583$	6.27017	+	1.10560i	0.259684	+	0.0457893i
$584$		0			0
$585$	−2.39676	−	6.97345i	−0.0990937	−	0.288317i
$586$		0			0
$587$	9.77734	−	11.6522i	0.403554	−	0.480937i	−0.525546	−	0.850765i	$-0.676139\pi$
$587$	9.77734	−	11.6522i	0.403554	−	0.480937i	0.929100	+	0.369828i	$0.120583\pi$
$588$		0			0
$589$	−2.01363	+	0.355058i	−0.0829704	+	0.0146299i
$590$		0			0
$591$	−29.6385	+	16.7576i	−1.21916	+	0.689317i
$592$		0			0
$593$			14.7671i			0.606414i	0.952925	+	0.303207i	$0.0980573\pi$
$593$			14.7671i			0.606414i	−0.952925	+	0.303207i	$0.901943\pi$
$594$		0			0
$595$	5.80827			0.238116
$596$		0			0
$597$	10.7585	+	0.0969181i	0.440315	+	0.00396659i
$598$		0			0
$599$	5.76811	+	32.7126i	0.235679	+	1.33660i	0.841180	+	0.540756i	$0.181862\pi$
$599$	5.76811	+	32.7126i	0.235679	+	1.33660i	−0.605501	+	0.795845i	$0.707027\pi$
$600$		0			0
$601$	24.6643	+	20.6958i	1.00608	+	0.844201i	0.987815	−	0.155633i	$-0.0497416\pi$
$601$	24.6643	+	20.6958i	1.00608	+	0.844201i	0.0182640	+	0.999833i	$0.494186\pi$
$602$		0			0
$603$	−2.71590	−	17.2102i	−0.110600	−	0.700855i
$604$		0			0
$605$	−1.74860	+	9.91681i	−0.0710908	+	0.403176i
$606$		0			0
$607$	−5.09832	+	14.0075i	−0.206935	+	0.568548i	−0.999129	−	0.0417204i	$-0.986716\pi$
$607$	−5.09832	+	14.0075i	−0.206935	+	0.568548i	0.792195	+	0.610268i	$0.208938\pi$
$608$		0			0
$609$	−24.8122	+	20.4419i	−1.00544	+	0.828347i
$610$		0			0
$611$	−13.9110	+	8.03150i	−0.562778	+	0.324920i
$612$		0			0
$613$	−15.4587	−	8.92510i	−0.624372	−	0.360482i	0.154197	−	0.988040i	$-0.450721\pi$
$613$	−15.4587	−	8.92510i	−0.624372	−	0.360482i	−0.778569	+	0.627559i	$0.784054\pi$
$614$		0			0
$615$	5.78762	+	4.94591i	0.233379	+	0.199438i
$616$		0			0
$617$	−7.17341	−	8.54893i	−0.288790	−	0.344167i	0.602071	−	0.798443i	$-0.294343\pi$
$617$	−7.17341	−	8.54893i	−0.288790	−	0.344167i	−0.890861	+	0.454276i	$0.849898\pi$
$618$		0			0
$619$	−30.1106	+	10.9594i	−1.21025	+	0.440494i	−0.866790	−	0.498673i	$-0.833821\pi$
$619$	−30.1106	+	10.9594i	−1.21025	+	0.440494i	−0.343459	+	0.939168i	$0.611598\pi$
$620$		0			0
$621$	−26.4731	−	33.3390i	−1.06233	−	1.33785i
$622$		0			0
$623$	−45.7577	+	16.6544i	−1.83324	+	0.667246i
$624$		0			0
$625$	6.60593	−	5.54303i	0.264237	−	0.221721i
$626$		0			0
$627$	−1.24579	+	0.440761i	−0.0497519	+	0.0176023i
$628$		0			0
$629$	−6.81282	+	11.8001i	−0.271645	+	0.470503i
$630$		0			0
$631$	13.2272	−	7.63670i	0.526565	−	0.304012i	−0.213052	−	0.977041i	$-0.568340\pi$
$631$	13.2272	−	7.63670i	0.526565	−	0.304012i	0.739616	+	0.673029i	$0.235007\pi$
$632$		0			0
$633$	2.68420	−	7.17306i	0.106687	−	0.285104i
$634$		0			0
$635$	5.45286	−	14.9816i	0.216390	−	0.594528i
$636$		0			0
$637$	−18.2972	−	3.22629i	−0.724961	−	0.127830i
$638$		0			0
$639$	−9.19280	+	15.2799i	−0.363662	+	0.604463i
$640$		0			0
$641$	−2.72071	+	3.24241i	−0.107462	+	0.128068i	−0.817094	−	0.576504i	$-0.804416\pi$
$641$	−2.72071	+	3.24241i	−0.107462	+	0.128068i	0.709633	+	0.704572i	$0.248861\pi$
$642$		0			0
$643$	−4.05606	−	23.0031i	−0.159956	−	0.907153i	−0.954114	−	0.299443i	$-0.903199\pi$
$643$	−4.05606	−	23.0031i	−0.159956	−	0.907153i	0.794159	−	0.607710i	$-0.207912\pi$
$644$		0			0
$645$	19.3428	+	11.4011i	0.761620	+	0.448918i
$646$		0			0
$647$	−25.2856			−0.994078			−0.497039	−	0.867728i	$-0.665579\pi$
$647$	−25.2856			−0.994078			−0.497039	+	0.867728i	$0.665579\pi$
$648$		0			0
$649$	17.8094			0.699080
$650$		0			0
$651$	−20.6531	−	12.1734i	−0.809459	−	0.477115i
$652$		0			0
$653$	0.0680562	+	0.385966i	0.00266324	+	0.0151040i	0.986110	−	0.166091i	$-0.0531146\pi$
$653$	0.0680562	+	0.385966i	0.00266324	+	0.0151040i	−0.983447	+	0.181195i	$0.942003\pi$
$654$		0			0
$655$	8.54231	−	10.1803i	0.333776	−	0.397778i
$656$		0			0
$657$	36.2853	+	0.653806i	1.41562	+	0.0255074i
$658$		0			0
$659$	−17.8895	−	3.15440i	−0.696875	−	0.122878i	−0.186021	−	0.982546i	$-0.559559\pi$
$659$	−17.8895	−	3.15440i	−0.696875	−	0.122878i	−0.510853	+	0.859668i	$0.670670\pi$
$660$		0			0
$661$	7.20591	−	19.7981i	0.280278	−	0.770056i	−0.717052	−	0.697020i	$-0.754509\pi$
$661$	7.20591	−	19.7981i	0.280278	−	0.770056i	0.997329	−	0.0730364i	$-0.0232689\pi$
$662$		0			0
$663$	−1.87324	+	5.00592i	−0.0727507	+	0.194414i
$664$		0			0
$665$	2.12143	−	1.22481i	0.0822656	−	0.0474960i
$666$		0			0
$667$	−19.4828	+	33.7452i	−0.754377	+	1.30662i
$668$		0			0
$669$	6.84674	−	2.42239i	0.264710	−	0.0936549i
$670$		0			0
$671$	5.55448	−	4.66076i	0.214428	−	0.179927i
$672$		0			0
$673$	−22.9145	+	8.34019i	−0.883288	+	0.321491i	−0.743536	−	0.668696i	$-0.766853\pi$
$673$	−22.9145	+	8.34019i	−0.883288	+	0.321491i	−0.139752	+	0.990186i	$0.544631\pi$
$674$		0			0
$675$	−6.27339	−	18.8020i	−0.241463	−	0.723688i
$676$		0			0
$677$	12.7940	−	4.65663i	0.491713	−	0.178969i	−0.0842498	−	0.996445i	$-0.526849\pi$
$677$	12.7940	−	4.65663i	0.491713	−	0.178969i	0.575963	+	0.817476i	$0.304627\pi$
$678$		0			0
$679$	21.8493	+	26.0390i	0.838500	+	0.999285i
$680$		0			0
$681$	20.7059	+	17.6946i	0.793450	+	0.678057i
$682$		0			0
$683$	8.84441	+	5.10632i	0.338422	+	0.195388i	0.659574	−	0.751640i	$-0.270737\pi$
$683$	8.84441	+	5.10632i	0.338422	+	0.195388i	−0.321152	+	0.947028i	$0.604070\pi$
$684$		0			0
$685$	−6.06720	+	3.50290i	−0.231816	+	0.133839i
$686$		0			0
$687$	15.9658	−	13.1536i	0.609131	−	0.501841i
$688$		0			0
$689$	3.71466	−	10.2060i	0.141517	−	0.388816i
$690$		0			0
$691$	−1.00782	+	5.71564i	−0.0383393	+	0.217433i	−0.997958	−	0.0638703i	$-0.979656\pi$
$691$	−1.00782	+	5.71564i	−0.0383393	+	0.217433i	0.959619	+	0.281303i	$0.0907667\pi$
$692$		0			0
$693$	−14.4617	−	5.56067i	−0.549354	−	0.211233i
$694$		0			0
$695$	0.693041	+	0.581531i	0.0262886	+	0.0220587i
$696$		0			0
$697$	−0.958247	−	5.43449i	−0.0362962	−	0.205846i
$698$		0			0
$699$	−19.5822	−	0.176406i	−0.740666	−	0.00667230i
$700$		0			0
$701$	35.3244			1.33418			0.667092	−	0.744975i	$-0.267539\pi$
$701$	35.3244			1.33418			0.667092	+	0.744975i	$0.267539\pi$
$702$		0			0
$703$			5.74657i			0.216736i
$704$		0			0
$705$	11.6807	−	6.60427i	0.439920	−	0.248731i
$706$		0			0
$707$	−20.3399	+	3.58647i	−0.764961	+	0.134883i
$708$		0			0
$709$	19.3240	−	23.0294i	0.725727	−	0.864888i	−0.269447	−	0.963015i	$-0.586841\pi$
$709$	19.3240	−	23.0294i	0.725727	−	0.864888i	0.995174	+	0.0981276i	$0.0312853\pi$
$710$		0			0
$711$	0.737356	−	0.847266i	0.0276530	−	0.0317750i
$712$		0			0
$713$	−28.6161	−	5.04580i	−1.07168	−	0.188967i
$714$		0			0
$715$	−3.05666	−	1.11253i	−0.114313	−	0.0416064i
$716$		0			0
$717$	44.7817	−	7.48093i	1.67240	−	0.279380i
$718$		0			0
$719$	18.9530	+	32.8275i	0.706826	+	1.22426i	0.966028	+	0.258436i	$0.0832070\pi$
$719$	18.9530	+	32.8275i	0.706826	+	1.22426i	−0.259202	+	0.965823i	$0.583460\pi$
$720$		0			0
$721$	−24.5013	+	42.4376i	−0.912478	+	1.58046i
$722$		0			0
$723$	26.9897	+	5.01010i	1.00376	+	0.186328i
$724$		0			0
$725$	−13.8977	+	11.6616i	−0.516148	+	0.433099i
$726$		0			0
$727$	2.51825	+	6.91883i	0.0933966	+	0.256605i	0.977591	−	0.210515i	$-0.0675139\pi$
$727$	2.51825	+	6.91883i	0.0933966	+	0.256605i	−0.884194	+	0.467120i	$0.845292\pi$
$728$		0			0
$729$	−26.9606	−	1.45863i	−0.998540	−	0.0540234i
$730$		0			0
$731$	−5.56634	−	15.2934i	−0.205879	−	0.565647i
$732$		0			0
$733$	−21.3773	−	25.4765i	−0.789590	−	0.940997i	0.209734	−	0.977758i	$-0.432740\pi$
$733$	−21.3773	−	25.4765i	−0.789590	−	0.940997i	−0.999324	+	0.0367619i	$0.988296\pi$
$734$		0			0
$735$	15.2599	+	2.83270i	0.562870	+	0.104486i
$736$		0			0
$737$	−6.65620	−	3.84296i	−0.245184	−	0.141557i
$738$		0			0
$739$	−16.4028	−	28.4106i	−0.603389	−	1.04510i	−0.992304	−	0.123826i	$-0.960483\pi$
$739$	−16.4028	−	28.4106i	−0.603389	−	1.04510i	0.388915	−	0.921273i	$-0.372850\pi$
$740$		0			0
$741$	0.371425	+	2.22339i	0.0136446	+	0.0816784i
$742$		0			0
$743$	−0.667783	−	0.243053i	−0.0244986	−	0.00891676i	0.329742	−	0.944071i	$-0.393038\pi$
$743$	−0.667783	−	0.243053i	−0.0244986	−	0.00891676i	−0.354240	+	0.935154i	$0.615261\pi$
$744$		0			0
$745$	1.94357	−	11.0225i	0.0712070	−	0.403835i
$746$		0			0
$747$	−13.4552	+	15.4608i	−0.492299	+	0.565681i
$748$		0			0
$749$	−4.61322	−	3.87095i	−0.168563	−	0.141441i
$750$		0			0
$751$	21.2525	−	3.74739i	0.775515	−	0.136744i	0.228136	−	0.973629i	$-0.426737\pi$
$751$	21.2525	−	3.74739i	0.775515	−	0.136744i	0.547379	+	0.836885i	$0.315626\pi$
$752$		0			0
$753$	−9.73164	−	17.2119i	−0.354641	−	0.627237i
$754$		0			0
$755$			23.0160i			0.837636i
$756$		0			0
$757$			32.9137i			1.19627i	0.801395	+	0.598135i	$0.204091\pi$
$757$			32.9137i			1.19627i	−0.801395	+	0.598135i	$0.795909\pi$
$758$		0			0
$759$	−18.7787	−	0.169169i	−0.681625	−	0.00614044i
$760$		0			0
$761$	18.9618	−	3.34348i	0.687366	−	0.121201i	0.180952	−	0.983492i	$-0.442082\pi$
$761$	18.9618	−	3.34348i	0.687366	−	0.121201i	0.506414	+	0.862291i	$0.330971\pi$
$762$		0			0
$763$	37.7798	+	31.7011i	1.36772	+	1.14766i
$764$		0			0
$765$	1.60244	−	4.16749i	0.0579365	−	0.150676i
$766$		0			0
$767$	5.27545	−	29.9185i	0.190485	−	1.08030i
$768$		0			0
$769$	30.4645	+	11.0882i	1.09858	+	0.399850i	0.826792	−	0.562508i	$-0.190163\pi$
$769$	30.4645	+	11.0882i	1.09858	+	0.399850i	0.271786	+	0.962358i	$0.412386\pi$
$770$		0			0
$771$	0.857199	−	0.706215i	0.0308713	−	0.0254337i
$772$		0			0
$773$	14.6818	+	25.4296i	0.528067	+	0.914639i	0.999465	+	0.0327179i	$0.0104163\pi$
$773$	14.6818	+	25.4296i	0.528067	+	0.914639i	−0.471398	+	0.881921i	$0.656250\pi$
$774$		0			0
$775$	−11.7165	−	6.76453i	−0.420869	−	0.242989i
$776$		0			0
$777$	−43.7728	+	51.2221i	−1.57034	+	1.83758i
$778$		0			0
$779$	−1.49598	−	1.78284i	−0.0535991	−	0.0638769i
$780$		0			0
$781$	2.69043	+	7.39189i	0.0962711	+	0.264503i
$782$		0			0
$783$	7.82180	+	23.4427i	0.279529	+	0.837774i
$784$		0			0
$785$	6.03819	+	16.5898i	0.215512	+	0.592115i
$786$		0			0
$787$	−28.1631	+	23.6317i	−1.00391	+	0.842378i	−0.987521	−	0.157488i	$-0.949661\pi$
$787$	−28.1631	+	23.6317i	−1.00391	+	0.842378i	−0.0163863	+	0.999866i	$0.505216\pi$
$788$		0			0
$789$	−15.5011	−	43.8131i	−0.551855	−	1.55979i
$790$		0			0
$791$	2.98829	−	5.17587i	0.106251	−	0.184033i
$792$		0			0
$793$	−6.18442	−	10.7117i	−0.219615	−	0.380385i
$794$		0			0
$795$	−3.17977	+	8.49737i	−0.112775	+	0.301371i
$796$		0			0
$797$	44.1868	+	16.0827i	1.56518	+	0.569677i	0.971915	−	0.235333i	$-0.0756181\pi$
$797$	44.1868	+	16.0827i	1.56518	+	0.569677i	0.593261	+	0.805010i	$0.297840\pi$
$798$		0			0
$799$	−9.57860	−	1.68896i	−0.338866	−	0.0597513i
$800$		0			0
$801$	−0.674368	+	37.4264i	−0.0238276	+	1.32240i
$802$		0			0
$803$	10.2905	−	12.2637i	0.363144	−	0.432778i
$804$		0			0
$805$	34.2831	−	6.04504i	1.20832	−	0.213060i
$806$		0			0
$807$	−36.7132	−	21.6396i	−1.29236	−	0.761751i
$808$		0			0
$809$		−	8.15288i		−	0.286640i	−0.989676	−	0.143320i	$-0.954222\pi$
$809$		−	8.15288i		−	0.286640i	0.989676	−	0.143320i	$-0.0457778\pi$
$810$		0			0
$811$	26.4376			0.928351			0.464175	−	0.885743i	$-0.346351\pi$
$811$	26.4376			0.928351			0.464175	+	0.885743i	$0.346351\pi$
$812$		0			0
$813$	−23.0456	+	39.0984i	−0.808243	+	1.37124i
$814$		0			0
$815$	−0.0369612	−	0.209618i	−0.00129470	−	0.00734258i
$816$		0			0
$817$	−5.25804	−	4.41202i	−0.183956	−	0.154357i
$818$		0			0
$819$	−13.6253	+	22.6475i	−0.476108	+	0.791367i
$820$		0			0
$821$	−6.75536	+	38.3116i	−0.235764	+	1.33708i	0.605235	+	0.796047i	$0.293079\pi$
$821$	−6.75536	+	38.3116i	−0.235764	+	1.33708i	−0.840999	+	0.541036i	$0.818032\pi$
$822$		0			0
$823$	−1.90859	+	5.24381i	−0.0665293	+	0.182788i	−0.968502	−	0.249005i	$-0.919897\pi$
$823$	−1.90859	+	5.24381i	−0.0665293	+	0.182788i	0.901973	+	0.431793i	$0.142119\pi$
$824$		0			0
$825$	−8.18906	−	3.06439i	−0.285106	−	0.106688i
$826$		0			0
$827$	4.16244	−	2.40319i	0.144742	−	0.0835670i	−0.425880	−	0.904780i	$-0.640035\pi$
$827$	4.16244	−	2.40319i	0.144742	−	0.0835670i	0.570622	+	0.821213i	$0.306702\pi$
$828$		0			0
$829$	36.2280	+	20.9162i	1.25825	+	0.726451i	0.972734	−	0.231923i	$-0.0745018\pi$
$829$	36.2280	+	20.9162i	1.25825	+	0.726451i	0.285516	+	0.958374i	$0.407835\pi$
$830$		0			0
$831$	−1.43969	+	0.509364i	−0.0499422	+	0.0176696i
$832$		0			0
$833$	−7.23143	−	8.61808i	−0.250554	−	0.298599i
$834$		0			0
$835$	−18.7801	+	6.83541i	−0.649913	+	0.236549i
$836$		0			0
$837$	−14.4326	+	11.4603i	−0.498862	+	0.396125i
$838$		0			0
$839$	20.6528	−	7.51700i	0.713013	−	0.259516i	0.0400566	−	0.999197i	$-0.487246\pi$
$839$	20.6528	−	7.51700i	0.713013	−	0.259516i	0.672957	+	0.739682i	$0.265024\pi$
$840$		0			0
$841$	−4.88732	+	4.10095i	−0.168528	+	0.141412i
$842$		0			0
$843$	10.2486	+	8.75810i	0.352980	+	0.301645i
$844$		0			0
$845$	4.30271	−	7.45251i	0.148018	−	0.256374i
$846$		0			0
$847$	31.2579	−	18.0467i	1.07403	−	0.620093i
$848$		0			0
$849$	2.16659	+	2.62980i	0.0743573	+	0.0902544i
$850$		0			0
$851$	−27.9313	+	76.7405i	−0.957471	+	2.63063i
$852$		0			0
$853$	5.55213	+	0.978991i	0.190101	+	0.0335200i	0.267888	−	0.963450i	$-0.413674\pi$
$853$	5.55213	+	0.978991i	0.190101	+	0.0335200i	−0.0777867	+	0.996970i	$0.524785\pi$
$854$		0			0
$855$	−0.293531	−	1.86006i	−0.0100385	−	0.0636127i
$856$		0			0
$857$	−34.5757	+	41.2057i	−1.18108	+	1.40756i	−0.288023	+	0.957623i	$0.592998\pi$
$857$	−34.5757	+	41.2057i	−1.18108	+	1.40756i	−0.893060	+	0.449937i	$0.851446\pi$
$858$		0			0
$859$	4.50669	+	25.5587i	0.153766	+	0.872051i	0.959905	+	0.280325i	$0.0904422\pi$
$859$	4.50669	+	25.5587i	0.153766	+	0.872051i	−0.806139	+	0.591726i	$0.798447\pi$
$860$		0			0
$861$	0.245812	−	27.2866i	0.00837724	−	0.929924i
$862$		0			0
$863$	6.05406			0.206083			0.103041	−	0.994677i	$-0.467143\pi$
$863$	6.05406			0.206083			0.103041	+	0.994677i	$0.467143\pi$
$864$		0			0
$865$	−2.92119			−0.0993234
$866$		0			0
$867$	22.8143	−	12.8992i	0.774814	−	0.438081i
$868$		0			0
$869$	−0.0860381	−	0.487947i	−0.00291864	−	0.0165525i
$870$		0			0
$871$	−8.42758	+	10.0436i	−0.285558	+	0.340315i
$872$		0			0
$873$	24.7112	−	8.49320i	0.836349	−	0.287451i
$874$		0			0
$875$	36.8846	+	6.50376i	1.24693	+	0.219867i
$876$		0			0
$877$	−5.50910	+	15.1361i	−0.186029	+	0.511111i	−0.997290	−	0.0735739i	$-0.976560\pi$
$877$	−5.50910	+	15.1361i	−0.186029	+	0.511111i	0.811261	+	0.584685i	$0.198782\pi$
$878$		0			0
$879$	14.2158	−	2.37479i	0.479487	−	0.0800998i
$880$		0			0
$881$	−10.9880	+	6.34390i	−0.370194	+	0.213731i	−0.673543	−	0.739148i	$-0.735228\pi$
$881$	−10.9880	+	6.34390i	−0.370194	+	0.213731i	0.303349	+	0.952879i	$0.401895\pi$
$882$		0			0
$883$	5.51804	−	9.55753i	0.185697	−	0.321637i	−0.758114	−	0.652122i	$-0.773879\pi$
$883$	5.51804	−	9.55753i	0.185697	−	0.321637i	0.943811	+	0.330485i	$0.107212\pi$
$884$		0			0
$885$	−4.63187	+	24.9521i	−0.155699	+	0.838757i
$886$		0			0
$887$	16.0941	−	13.5046i	0.540388	−	0.453440i	−0.331282	−	0.943532i	$-0.607481\pi$
$887$	16.0941	−	13.5046i	0.540388	−	0.453440i	0.871671	+	0.490092i	$0.163037\pi$
$888$		0			0
$889$	−53.6991	+	19.5449i	−1.80101	+	0.655513i
$890$		0			0
$891$	−7.97968	+	8.84228i	−0.267329	+	0.296227i
$892$		0			0
$893$	−3.85467	+	1.40299i	−0.128992	+	0.0469492i
$894$		0			0
$895$	16.9820	+	20.2383i	0.567645	+	0.676493i
$896$		0			0
$897$	−5.84677	+	31.4969i	−0.195218	+	1.05165i
$898$		0			0
$899$	14.6084	+	8.43417i	0.487218	+	0.281295i
$900$		0			0
$901$	5.69537	−	3.28822i	0.189740	−	0.109547i
$902$		0			0
$903$	−13.2604	−	79.3781i	−0.441277	−	2.64154i
$904$		0			0
$905$	3.61244	−	9.92510i	0.120082	−	0.329922i
$906$		0			0
$907$	0.111832	−	0.634233i	0.00371333	−	0.0210594i	−0.982895	−	0.184168i	$-0.941041\pi$
$907$	0.111832	−	0.634233i	0.00371333	−	0.0210594i	0.986608	+	0.163109i	$0.0521521\pi$
$908$		0			0
$909$	−3.03825	+	15.5836i	−0.100772	+	0.516874i
$910$		0			0
$911$	24.8500	+	20.8516i	0.823317	+	0.690845i	0.953746	−	0.300613i	$-0.0971912\pi$
$911$	24.8500	+	20.8516i	0.823317	+	0.690845i	−0.130429	+	0.991458i	$0.541636\pi$
$912$		0			0
$913$	1.57001	+	8.90398i	0.0519598	+	0.294679i
$914$		0			0
$915$	5.08542	+	8.99436i	0.168119	+	0.297344i
$916$		0			0
$917$	−47.6339			−1.57301
$918$		0			0
$919$		−	16.7304i		−	0.551885i	−0.961174	−	0.275943i	$-0.911010\pi$
$919$		−	16.7304i		−	0.551885i	0.961174	−	0.275943i	$-0.0889900\pi$
$920$		0			0
$921$	0.0921362	−	10.2277i	0.00303599	−	0.337013i
$922$		0			0
$923$	13.2148	−	2.33013i	0.434971	−	0.0766970i
$924$		0			0
$925$	−24.4407	+	29.1273i	−0.803606	+	0.957701i
$926$		0			0
$927$	23.6897	+	29.2881i	0.778072	+	0.961946i
$928$		0			0
$929$	40.2612	+	7.09914i	1.32093	+	0.232915i	0.789271	−	0.614045i	$-0.210459\pi$
$929$	40.2612	+	7.09914i	1.32093	+	0.232915i	0.531656	+	0.846960i	$0.321570\pi$
$930$		0			0
$931$	−4.45855	−	1.62278i	−0.146123	−	0.0531845i
$932$		0			0
$933$	5.15120	+	6.25249i	0.168643	+	0.204697i
$934$		0			0
$935$	−0.984815	−	1.70575i	−0.0322069	−	0.0557840i
$936$		0			0
$937$	0.950609	−	1.64650i	0.0310550	−	0.0537889i	−0.850080	−	0.526653i	$-0.823447\pi$
$937$	0.950609	−	1.64650i	0.0310550	−	0.0537889i	0.881135	+	0.472864i	$0.156780\pi$
$938$		0			0
$939$	−23.4152	+	27.4001i	−0.764127	+	0.894168i
$940$		0			0
$941$	−43.2329	+	36.2767i	−1.40935	+	1.18259i	−0.452587	+	0.891720i	$0.649499\pi$
$941$	−43.2329	+	36.2767i	−1.40935	+	1.18259i	−0.956764	+	0.290866i	$0.906057\pi$
$942$		0			0
$943$	−11.3120	−	31.0796i	−0.368371	−	1.01209i
$944$		0			0
$945$	11.5521	−	18.8156i	0.375789	−	0.612070i
$946$		0			0
$947$	10.3133	+	28.3357i	0.335139	+	0.920786i	0.986752	+	0.162235i	$0.0518702\pi$
$947$	10.3133	+	28.3357i	0.335139	+	0.920786i	−0.651614	+	0.758551i	$0.725908\pi$
$948$		0			0
$949$	−17.5540	−	20.9200i	−0.569826	−	0.679093i
$950$		0			0
$951$	4.60351	+	13.0116i	0.149279	+	0.421929i
$952$		0			0
$953$	−39.9563	−	23.0688i	−1.29431	−	0.747272i	−0.314897	−	0.949126i	$-0.601970\pi$
$953$	−39.9563	−	23.0688i	−1.29431	−	0.747272i	−0.979416	+	0.201854i	$0.935303\pi$
$954$		0			0
$955$	−8.51814	−	14.7539i	−0.275641	−	0.477424i
$956$		0			0
$957$	10.2103	+	3.82075i	0.330052	+	0.123507i
$958$		0			0
$959$	23.5967	+	8.58850i	0.761977	+	0.277337i
$960$		0			0
$961$	3.19875	−	18.1410i	0.103186	−	0.585194i
$962$		0			0
$963$	−4.05019	+	2.24207i	−0.130515	+	0.0722498i
$964$		0			0
$965$	16.4589	+	13.8107i	0.529832	+	0.444582i
$966$		0			0
$967$	−27.2166	+	4.79902i	−0.875226	+	0.154326i	−0.593175	−	0.805073i	$-0.702126\pi$
$967$	−27.2166	+	4.79902i	−0.875226	+	0.154326i	−0.282051	+	0.959399i	$0.591015\pi$
$968$		0			0
$969$	−0.693096	+	1.17589i	−0.0222654	+	0.0377749i
$970$		0			0
$971$		−	26.9798i		−	0.865824i	−0.901436	−	0.432912i	$-0.857486\pi$
$971$		−	26.9798i		−	0.865824i	0.901436	−	0.432912i	$-0.142514\pi$
$972$		0			0
$973$		−	3.24275i		−	0.103958i
$974$		0			0
$975$	−7.57370	+	12.8493i	−0.242553	+	0.411507i
$976$		0			0
$977$	−21.9678	+	3.87352i	−0.702812	+	0.123925i	−0.513623	−	0.858016i	$-0.671697\pi$
$977$	−21.9678	+	3.87352i	−0.702812	+	0.123925i	−0.189189	+	0.981941i	$0.560586\pi$
$978$		0			0
$979$	12.6494	+	10.6141i	0.404277	+	0.339229i
$980$		0			0
$981$	33.1689	−	18.3614i	1.05900	−	0.586235i
$982$		0			0
$983$	−3.77742	+	21.4228i	−0.120481	+	0.683282i	0.863409	+	0.504505i	$0.168325\pi$
$983$	−3.77742	+	21.4228i	−0.120481	+	0.683282i	−0.983890	+	0.178777i	$0.942786\pi$
$984$		0			0
$985$	−20.1121	−	7.32022i	−0.640826	−	0.233242i
$986$		0			0
$987$	−45.0455	−	16.8563i	−1.43382	−	0.536542i
$988$		0			0
$989$	−48.7720	−	84.4756i	−1.55086	−	2.68617i
$990$		0			0
$991$	−24.1340	−	13.9338i	−0.766642	−	0.442621i	0.0650335	−	0.997883i	$-0.479285\pi$
$991$	−24.1340	−	13.9338i	−0.766642	−	0.442621i	−0.831675	+	0.555262i	$0.812618\pi$
$992$		0			0
$993$	−12.7932	−	36.1592i	−0.405979	−	1.14748i
$994$		0			0
$995$	4.34729	+	5.18090i	0.137818	+	0.164246i
$996$		0			0
$997$	2.31607	+	6.36334i	0.0733506	+	0.201529i	0.970950	−	0.239284i	$-0.0769126\pi$
$997$	2.31607	+	6.36334i	0.0733506	+	0.201529i	−0.897599	+	0.440813i	$0.854690\pi$
$998$		0			0
$999$	24.6759	+	45.5390i	0.780711	+	1.44079i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.bh.b.47.5		192
4.3	odd	2		216.2.v.b.155.18	yes	192
8.3	odd	2	inner	864.2.bh.b.47.6		192
8.5	even	2		216.2.v.b.155.9	yes	192
12.11	even	2		648.2.v.b.467.15		192
24.5	odd	2		648.2.v.b.467.24		192
27.23	odd	18	inner	864.2.bh.b.239.6		192
108.23	even	18		216.2.v.b.131.9	✓	192
108.31	odd	18		648.2.v.b.179.24		192
216.77	odd	18		216.2.v.b.131.18	yes	192
216.85	even	18		648.2.v.b.179.15		192
216.131	even	18	inner	864.2.bh.b.239.5		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.v.b.131.9	✓	192	108.23	even	18
216.2.v.b.131.18	yes	192	216.77	odd	18
216.2.v.b.155.9	yes	192	8.5	even	2
216.2.v.b.155.18	yes	192	4.3	odd	2
648.2.v.b.179.15		192	216.85	even	18
648.2.v.b.179.24		192	108.31	odd	18
648.2.v.b.467.15		192	12.11	even	2
648.2.v.b.467.24		192	24.5	odd	2
864.2.bh.b.47.5		192	1.1	even	1	trivial
864.2.bh.b.47.6		192	8.3	odd	2	inner
864.2.bh.b.239.5		192	216.131	even	18	inner
864.2.bh.b.239.6		192	27.23	odd	18	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.bh (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.49214 - 0.879503i) q^{3} +(-0.189066 - 1.07225i) q^{5} +(-2.50853 + 2.98955i) q^{7} +(1.45295 + 2.62468i) q^{9} +O(q^{10})\)	\(q+(-1.49214 - 0.879503i) q^{3} +(-0.189066 - 1.07225i) q^{5} +(-2.50853 + 2.98955i) q^{7} +(1.45295 + 2.62468i) q^{9} +(1.30329 + 0.229805i) q^{11} +(0.772112 - 2.12136i) q^{13} +(-0.660931 + 1.76622i) q^{15} +(1.18381 - 0.683475i) q^{17} +(0.288253 - 0.499269i) q^{19} +(6.37238 - 2.25456i) q^{21} +(6.27608 - 5.26625i) q^{23} +(3.58450 - 1.30465i) q^{25} +(0.140408 - 5.19426i) q^{27} +(-4.46923 + 1.62667i) q^{29} +(-2.27978 - 2.71694i) q^{31} +(-1.74257 - 1.48915i) q^{33} +(3.67981 + 2.12454i) q^{35} +(-8.63247 + 4.98396i) q^{37} +(-3.01784 + 2.48629i) q^{39} +(1.38072 - 3.79351i) q^{41} +(2.06746 - 11.7251i) q^{43} +(2.53960 - 2.05416i) q^{45} +(-5.45070 - 4.57368i) q^{47} +(-1.42914 - 8.10505i) q^{49} +(-2.36753 - 0.0213279i) q^{51} +4.81104 q^{53} -1.44090i q^{55} +(-0.869221 + 0.491459i) q^{57} +(13.2529 - 2.33685i) q^{59} +(3.52183 - 4.19715i) q^{61} +(-11.4914 - 2.24041i) q^{63} +(-2.42060 - 0.426818i) q^{65} +(-5.45749 - 1.98636i) q^{67} +(-13.9965 + 2.33815i) q^{69} +(2.97201 + 5.14767i) q^{71} +(6.04852 - 10.4764i) q^{73} +(-6.49600 - 1.20586i) q^{75} +(-3.95635 + 3.31977i) q^{77} +(-0.128051 - 0.351818i) q^{79} +(-4.77787 + 7.62706i) q^{81} +(2.33666 + 6.41991i) q^{83} +(-0.956672 - 1.14012i) q^{85} +(8.09936 + 1.50349i) q^{87} +(10.8058 + 6.23875i) q^{89} +(4.40504 + 7.62975i) q^{91} +(1.01219 + 6.05911i) q^{93} +(-0.589838 - 0.214684i) q^{95} +(1.51248 - 8.57770i) q^{97} +(1.29045 + 3.75461i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 12 q^{3} - 12 q^{9}+O(q^{10}) \) 192 * q + 12 * q^3 - 12 * q^9	\( 192 q + 12 q^{3} - 12 q^{9} + 30 q^{11} - 18 q^{17} + 6 q^{19} - 12 q^{25} - 18 q^{27} - 30 q^{33} + 18 q^{35} + 18 q^{41} + 42 q^{43} - 12 q^{49} + 18 q^{51} - 36 q^{57} + 84 q^{59} - 12 q^{65} - 30 q^{67} - 6 q^{73} + 96 q^{75} - 12 q^{81} + 72 q^{83} + 144 q^{89} + 6 q^{91} - 42 q^{97} + 12 q^{99}+O(q^{100}) \) 192 * q + 12 * q^3 - 12 * q^9 + 30 * q^11 - 18 * q^17 + 6 * q^19 - 12 * q^25 - 18 * q^27 - 30 * q^33 + 18 * q^35 + 18 * q^41 + 42 * q^43 - 12 * q^49 + 18 * q^51 - 36 * q^57 + 84 * q^59 - 12 * q^65 - 30 * q^67 - 6 * q^73 + 96 * q^75 - 12 * q^81 + 72 * q^83 + 144 * q^89 + 6 * q^91 - 42 * q^97 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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