LMFDB - Embedded newform 864.2.bh.b.47.17

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			47.17
Character	$\chi$	$=$	864.47
Dual form			864.2.bh.b.239.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.166515 - 1.72403i) q^{3} +(-0.135936 - 0.770931i) q^{5} +(2.51012 - 2.99144i) q^{7} +(-2.94455 - 0.574153i) q^{9} +O(q^{10})$	\(q+(0.166515 - 1.72403i) q^{3} +(-0.135936 - 0.770931i) q^{5} +(2.51012 - 2.99144i) q^{7} +(-2.94455 - 0.574153i) q^{9} +(4.00834 + 0.706778i) q^{11} +(-0.688932 + 1.89283i) q^{13} +(-1.35174 + 0.105986i) q^{15} +(3.24509 - 1.87355i) q^{17} +(2.03521 - 3.52509i) q^{19} +(-4.73936 - 4.82563i) q^{21} +(-1.29440 + 1.08613i) q^{23} +(4.12261 - 1.50051i) q^{25} +(-1.48017 + 4.98087i) q^{27} +(-3.97408 + 1.44645i) q^{29} +(-5.62062 - 6.69839i) q^{31} +(1.88595 - 6.79279i) q^{33} +(-2.64741 - 1.52848i) q^{35} +(-9.04670 + 5.22312i) q^{37} +(3.14857 + 1.50292i) q^{39} +(-3.48236 + 9.56770i) q^{41} +(0.751767 - 4.26348i) q^{43} +(-0.0423626 + 2.34809i) q^{45} +(-1.29698 - 1.08829i) q^{47} +(-1.43250 - 8.12409i) q^{49} +(-2.68970 - 5.90659i) q^{51} +10.8358 q^{53} -3.18622i q^{55} +(-5.73846 - 4.09574i) q^{57} +(-2.48911 + 0.438898i) q^{59} +(2.41745 - 2.88100i) q^{61} +(-9.10870 + 7.36725i) q^{63} +(1.55289 + 0.273816i) q^{65} +(2.89251 + 1.05279i) q^{67} +(1.65698 + 2.41244i) q^{69} +(3.46797 + 6.00671i) q^{71} +(0.963671 - 1.66913i) q^{73} +(-1.90044 - 7.35735i) q^{75} +(12.1757 - 10.2166i) q^{77} +(-2.21520 - 6.08622i) q^{79} +(8.34070 + 3.38124i) q^{81} +(-1.31513 - 3.61329i) q^{83} +(-1.88550 - 2.24705i) q^{85} +(1.83197 + 7.09228i) q^{87} +(-6.55395 - 3.78393i) q^{89} +(3.93298 + 6.81212i) q^{91} +(-12.4841 + 8.57472i) q^{93} +(-2.99426 - 1.08982i) q^{95} +(-0.481780 + 2.73231i) q^{97} +(-11.3969 - 4.38254i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	0.166515	−	1.72403i	0.0961374	−	0.995368i
$3$	0.166515	−	1.72403i	0.0961374	−	0.995368i
$4$		0			0
$5$	−0.135936	−	0.770931i	−0.0607924	−	0.344771i	−0.999999	−	0.00141816i	$-0.999549\pi$
$5$	−0.135936	−	0.770931i	−0.0607924	−	0.344771i	0.939207	−	0.343352i	$-0.111563\pi$
$6$		0			0
$7$	2.51012	−	2.99144i	0.948735	−	1.13066i	−0.0425722	−	0.999093i	$-0.513555\pi$
$7$	2.51012	−	2.99144i	0.948735	−	1.13066i	0.991308	−	0.131565i	$-0.0420003\pi$
$8$		0			0
$9$	−2.94455	−	0.574153i	−0.981515	−	0.191384i
$10$		0			0
$11$	4.00834	+	0.706778i	1.20856	+	0.213101i	0.741395	−	0.671069i	$-0.234165\pi$
$11$	4.00834	+	0.706778i	1.20856	+	0.213101i	0.467164	+	0.884171i	$0.345276\pi$
$12$		0			0
$13$	−0.688932	+	1.89283i	−0.191075	+	0.524976i	−0.997825	−	0.0659179i	$-0.979002\pi$
$13$	−0.688932	+	1.89283i	−0.191075	+	0.524976i	0.806750	+	0.590894i	$0.201225\pi$
$14$		0			0
$15$	−1.35174	+	0.105986i	−0.349018	+	0.0273654i
$16$		0			0
$17$	3.24509	−	1.87355i	0.787049	−	0.454403i	−0.0518736	−	0.998654i	$-0.516519\pi$
$17$	3.24509	−	1.87355i	0.787049	−	0.454403i	0.838923	+	0.544251i	$0.183186\pi$
$18$		0			0
$19$	2.03521	−	3.52509i	0.466909	−	0.808711i	−0.532376	−	0.846508i	$-0.678701\pi$
$19$	2.03521	−	3.52509i	0.466909	−	0.808711i	0.999285	+	0.0377971i	$0.0120341\pi$
$20$		0			0
$21$	−4.73936	−	4.82563i	−1.03421	−	1.05304i
$22$		0			0
$23$	−1.29440	+	1.08613i	−0.269901	+	0.226474i	−0.767685	−	0.640827i	$-0.778591\pi$
$23$	−1.29440	+	1.08613i	−0.269901	+	0.226474i	0.497784	+	0.867301i	$0.334147\pi$
$24$		0			0
$25$	4.12261	−	1.50051i	0.824522	−	0.300101i
$26$		0			0
$27$	−1.48017	+	4.98087i	−0.284858	+	0.958570i
$28$		0			0
$29$	−3.97408	+	1.44645i	−0.737968	+	0.268598i	−0.683534	−	0.729919i	$-0.739558\pi$
$29$	−3.97408	+	1.44645i	−0.737968	+	0.268598i	−0.0544344	+	0.998517i	$0.517336\pi$
$30$		0			0
$31$	−5.62062	−	6.69839i	−1.00949	−	1.20307i	−0.979069	−	0.203530i	$-0.934759\pi$
$31$	−5.62062	−	6.69839i	−1.00949	−	1.20307i	−0.0304242	−	0.999537i	$-0.509686\pi$
$32$		0			0
$33$	1.88595	−	6.79279i	0.328302	−	1.18247i
$34$		0			0
$35$	−2.64741	−	1.52848i	−0.447494	−	0.258361i
$36$		0			0
$37$	−9.04670	+	5.22312i	−1.48727	+	0.858675i	−0.999895	−	0.0145181i	$-0.995379\pi$
$37$	−9.04670	+	5.22312i	−1.48727	+	0.858675i	−0.487374	+	0.873193i	$0.662045\pi$
$38$		0			0
$39$	3.14857	+	1.50292i	0.504174	+	0.240660i
$40$		0			0
$41$	−3.48236	+	9.56770i	−0.543853	+	1.49422i	0.298026	+	0.954558i	$0.403672\pi$
$41$	−3.48236	+	9.56770i	−0.543853	+	1.49422i	−0.841879	+	0.539666i	$0.818550\pi$
$42$		0			0
$43$	0.751767	−	4.26348i	0.114643	−	0.650175i	−0.872283	−	0.489002i	$-0.837361\pi$
$43$	0.751767	−	4.26348i	0.114643	−	0.650175i	0.986926	−	0.161173i	$-0.0515277\pi$
$44$		0			0
$45$	−0.0423626	+	2.34809i	−0.00631505	+	0.350032i
$46$		0			0
$47$	−1.29698	−	1.08829i	−0.189184	−	0.158744i	0.543276	−	0.839554i	$-0.317184\pi$
$47$	−1.29698	−	1.08829i	−0.189184	−	0.158744i	−0.732460	+	0.680810i	$0.761628\pi$
$48$		0			0
$49$	−1.43250	−	8.12409i	−0.204642	−	1.16058i
$50$		0			0
$51$	−2.68970	−	5.90659i	−0.376633	−	0.827089i
$52$		0			0
$53$	10.8358			1.48841			0.744203	−	0.667954i	$-0.232830\pi$
$53$	10.8358			1.48841			0.744203	+	0.667954i	$0.232830\pi$
$54$		0			0
$55$		−	3.18622i		−	0.429630i
$56$		0			0
$57$	−5.73846	−	4.09574i	−0.760078	−	0.542494i
$58$		0			0
$59$	−2.48911	+	0.438898i	−0.324055	+	0.0571396i	−0.333309	−	0.942818i	$-0.608165\pi$
$59$	−2.48911	+	0.438898i	−0.324055	+	0.0571396i	0.00925433	+	0.999957i	$0.497054\pi$
$60$		0			0
$61$	2.41745	−	2.88100i	0.309523	−	0.368875i	−0.588749	−	0.808316i	$-0.700379\pi$
$61$	2.41745	−	2.88100i	0.309523	−	0.368875i	0.898271	+	0.439442i	$0.144824\pi$
$62$		0			0
$63$	−9.10870	+	7.36725i	−1.14759	+	0.928186i
$64$		0			0
$65$	1.55289	+	0.273816i	0.192612	+	0.0339627i
$66$		0			0
$67$	2.89251	+	1.05279i	0.353376	+	0.128618i	0.512608	−	0.858623i	$-0.328680\pi$
$67$	2.89251	+	1.05279i	0.353376	+	0.128618i	−0.159232	+	0.987241i	$0.550902\pi$
$68$		0			0
$69$	1.65698	+	2.41244i	0.199477	+	0.290423i
$70$		0			0
$71$	3.46797	+	6.00671i	0.411573	+	0.712865i	0.995062	−	0.0992558i	$-0.0316462\pi$
$71$	3.46797	+	6.00671i	0.411573	+	0.712865i	−0.583489	+	0.812121i	$0.698313\pi$
$72$		0			0
$73$	0.963671	−	1.66913i	0.112789	−	0.195356i	−0.804105	−	0.594488i	$-0.797355\pi$
$73$	0.963671	−	1.66913i	0.112789	−	0.195356i	0.916894	+	0.399131i	$0.130688\pi$
$74$		0			0
$75$	−1.90044	−	7.35735i	−0.219444	−	0.849553i
$76$		0			0
$77$	12.1757	−	10.2166i	1.38755	−	1.16429i
$78$		0			0
$79$	−2.21520	−	6.08622i	−0.249230	−	0.684753i	−0.999715	−	0.0238663i	$-0.992402\pi$
$79$	−2.21520	−	6.08622i	−0.249230	−	0.684753i	0.750485	−	0.660887i	$-0.229820\pi$
$80$		0			0
$81$	8.34070	+	3.38124i	0.926744	+	0.375693i
$82$		0			0
$83$	−1.31513	−	3.61329i	−0.144354	−	0.396610i	0.846353	−	0.532623i	$-0.178793\pi$
$83$	−1.31513	−	3.61329i	−0.144354	−	0.396610i	−0.990707	+	0.136013i	$0.956571\pi$
$84$		0			0
$85$	−1.88550	−	2.24705i	−0.204511	−	0.243727i
$86$		0			0
$87$	1.83197	+	7.09228i	0.196408	+	0.760372i
$88$		0			0
$89$	−6.55395	−	3.78393i	−0.694718	−	0.401095i	0.110659	−	0.993858i	$-0.464704\pi$
$89$	−6.55395	−	3.78393i	−0.694718	−	0.401095i	−0.805377	+	0.592763i	$0.798037\pi$
$90$		0			0
$91$	3.93298	+	6.81212i	0.412288	+	0.714104i
$92$		0			0
$93$	−12.4841	+	8.57472i	−1.29454	+	0.889157i
$94$		0			0
$95$	−2.99426	−	1.08982i	−0.307204	−	0.111813i
$96$		0			0
$97$	−0.481780	+	2.73231i	−0.0489174	+	0.277424i	−0.999449	−	0.0332049i	$-0.989429\pi$
$97$	−0.481780	+	2.73231i	−0.0489174	+	0.277424i	0.950531	+	0.310629i	$0.100540\pi$
$98$		0			0
$99$	−11.3969	−	4.38254i	−1.14543	−	0.440461i
$100$		0			0
$101$	1.17833	+	0.988733i	0.117248	+	0.0983826i	0.699527	−	0.714607i	$-0.253394\pi$
$101$	1.17833	+	0.988733i	0.117248	+	0.0983826i	−0.582279	+	0.812989i	$0.697839\pi$
$102$		0			0
$103$	−18.3730	+	3.23966i	−1.81035	+	0.319213i	−0.973580	−	0.228348i	$-0.926668\pi$
$103$	−18.3730	+	3.23966i	−1.81035	+	0.319213i	−0.836766	+	0.547561i	$0.815556\pi$
$104$		0			0
$105$	−3.07598	+	4.30969i	−0.300185	+	0.420583i
$106$		0			0
$107$			7.25626i			0.701489i	0.936471	+	0.350745i	$0.114071\pi$
$107$			7.25626i			0.701489i	−0.936471	+	0.350745i	$0.885929\pi$
$108$		0			0
$109$		−	4.50798i		−	0.431786i	−0.976417	−	0.215893i	$-0.930734\pi$
$109$		−	4.50798i		−	0.431786i	0.976417	−	0.215893i	$-0.0692663\pi$
$110$		0			0
$111$	7.49839	+	16.4665i	0.711716	+	1.56293i
$112$		0			0
$113$	3.23012	−	0.569558i	0.303864	−	0.0535795i	−0.0196371	−	0.999807i	$-0.506251\pi$
$113$	3.23012	−	0.569558i	0.303864	−	0.0535795i	0.323501	+	0.946228i	$0.395140\pi$
$114$		0			0
$115$	1.01328	+	0.850247i	0.0944893	+	0.0792859i
$116$		0			0
$117$	3.11536	−	5.17796i	0.288016	−	0.478703i
$118$		0			0
$119$	2.54093	−	14.4103i	0.232927	−	1.32099i
$120$		0			0
$121$	5.23060	+	1.90378i	0.475509	+	0.173071i
$122$		0			0
$123$	15.9151	+	7.59685i	1.43502	+	0.684985i
$124$		0			0
$125$	−3.67425	−	6.36400i	−0.328635	−	0.569213i
$126$		0			0
$127$	17.1332	+	9.89185i	1.52033	+	0.877760i	0.999713	+	0.0239670i	$0.00762968\pi$
$127$	17.1332	+	9.89185i	1.52033	+	0.877760i	0.520612	+	0.853793i	$0.325704\pi$
$128$		0			0
$129$	−7.22518	−	2.00600i	−0.636142	−	0.176618i
$130$		0			0
$131$	11.3636	+	13.5426i	0.992843	+	1.18322i	0.983062	+	0.183272i	$0.0586688\pi$
$131$	11.3636	+	13.5426i	0.992843	+	1.18322i	0.00978049	+	0.999952i	$0.496887\pi$
$132$		0			0
$133$	−5.43648	−	14.9366i	−0.471403	−	1.29517i
$134$		0			0
$135$	4.04112	+	0.464026i	0.347804	+	0.0399370i
$136$		0			0
$137$	4.87855	+	13.4037i	0.416803	+	1.14516i	0.953503	+	0.301383i	$0.0974483\pi$
$137$	4.87855	+	13.4037i	0.416803	+	1.14516i	−0.536701	+	0.843773i	$0.680329\pi$
$138$		0			0
$139$	13.9256	−	11.6849i	1.18115	−	0.991104i	0.181181	−	0.983450i	$-0.442008\pi$
$139$	13.9256	−	11.6849i	1.18115	−	0.991104i	0.999971	−	0.00765422i	$-0.00243644\pi$
$140$		0			0
$141$	−2.09222	+	2.05481i	−0.176196	+	0.173046i
$142$		0			0
$143$	−4.09928	+	7.10016i	−0.342799	+	0.593745i
$144$		0			0
$145$	1.65533	+	2.86712i	0.137468	+	0.238101i
$146$		0			0
$147$	−14.2447	+	1.11688i	−1.17488	+	0.0921188i
$148$		0			0
$149$	18.3251	+	6.66979i	1.50125	+	0.546411i	0.956384	−	0.292112i	$-0.0943578\pi$
$149$	18.3251	+	6.66979i	1.50125	+	0.546411i	0.544867	+	0.838522i	$0.316580\pi$
$150$		0			0
$151$	8.07581	+	1.42398i	0.657200	+	0.115882i	0.492296	−	0.870428i	$-0.336158\pi$
$151$	8.07581	+	1.42398i	0.657200	+	0.115882i	0.164904	+	0.986310i	$0.447269\pi$
$152$		0			0
$153$	−10.6310	+	3.65358i	−0.859466	+	0.295375i
$154$		0			0
$155$	−4.39995	+	5.24366i	−0.353413	+	0.421181i
$156$		0			0
$157$	13.3569	−	2.35518i	1.06600	−	0.187964i	0.386981	−	0.922088i	$-0.373518\pi$
$157$	13.3569	−	2.35518i	1.06600	−	0.187964i	0.679015	+	0.734124i	$0.262407\pi$
$158$		0			0
$159$	1.80432	−	18.6811i	0.143091	−	1.48151i
$160$		0			0
$161$			6.59843i			0.520029i
$162$		0			0
$163$	−13.2904			−1.04098			−0.520492	−	0.853867i	$-0.674251\pi$
$163$	−13.2904			−1.04098			−0.520492	+	0.853867i	$0.674251\pi$
$164$		0			0
$165$	−5.49314	−	0.530554i	−0.427640	−	0.0413036i
$166$		0			0
$167$	1.24589	+	7.06577i	0.0964095	+	0.546765i	0.994306	+	0.106559i	$0.0339834\pi$
$167$	1.24589	+	7.06577i	0.0964095	+	0.546765i	−0.897897	+	0.440206i	$0.854905\pi$
$168$		0			0
$169$	6.85041	+	5.74818i	0.526955	+	0.442168i
$170$		0			0
$171$	−8.01671	+	9.21126i	−0.613053	+	0.704403i
$172$		0			0
$173$	−0.595900	+	3.37951i	−0.0453054	+	0.256940i	−0.999045	−	0.0436944i	$-0.986087\pi$
$173$	−0.595900	+	3.37951i	−0.0453054	+	0.256940i	0.953740	+	0.300634i	$0.0971983\pi$
$174$		0			0
$175$	5.85955	−	16.0990i	0.442941	−	1.21697i
$176$		0			0
$177$	0.342198	+	4.36438i	0.0257212	+	0.328047i
$178$		0			0
$179$	−11.0731	+	6.39304i	−0.827641	+	0.477838i	−0.853044	−	0.521839i	$-0.825246\pi$
$179$	−11.0731	+	6.39304i	−0.827641	+	0.477838i	0.0254036	+	0.999677i	$0.491913\pi$
$180$		0			0
$181$	0.359928	+	0.207804i	0.0267532	+	0.0154460i	0.513317	−	0.858199i	$-0.328417\pi$
$181$	0.359928	+	0.207804i	0.0267532	+	0.0154460i	−0.486564	+	0.873645i	$0.661750\pi$
$182$		0			0
$183$	−4.56439	−	4.64748i	−0.337409	−	0.343551i
$184$		0			0
$185$	5.25643	+	6.26437i	0.386461	+	0.460566i
$186$		0			0
$187$	14.3316	−	5.21627i	1.04803	−	0.381451i
$188$		0			0
$189$	11.1846	+	16.9304i	0.813560	+	1.23151i
$190$		0			0
$191$	24.9508	−	9.08136i	1.80538	−	0.657104i	0.807656	−	0.589654i	$-0.200736\pi$
$191$	24.9508	−	9.08136i	1.80538	−	0.657104i	0.997723	−	0.0674507i	$-0.0214865\pi$
$192$		0			0
$193$	8.97492	−	7.53086i	0.646029	−	0.542083i	−0.259834	−	0.965653i	$-0.583668\pi$
$193$	8.97492	−	7.53086i	0.646029	−	0.542083i	0.905863	+	0.423570i	$0.139223\pi$
$194$		0			0
$195$	0.730646	−	2.63163i	0.0523226	−	0.188455i
$196$		0			0
$197$	−10.8898	+	18.8617i	−0.775866	+	1.34384i	0.158440	+	0.987369i	$0.449354\pi$
$197$	−10.8898	+	18.8617i	−0.775866	+	1.34384i	−0.934306	+	0.356471i	$0.883980\pi$
$198$		0			0
$199$	0.674947	−	0.389681i	0.0478457	−	0.0276237i	−0.475886	−	0.879507i	$-0.657873\pi$
$199$	0.674947	−	0.389681i	0.0478457	−	0.0276237i	0.523732	+	0.851883i	$0.324539\pi$
$200$		0			0
$201$	2.29668	−	4.81146i	0.161995	−	0.339374i
$202$		0			0
$203$	−5.64845	+	15.5190i	−0.396443	+	1.08922i
$204$		0			0
$205$	7.84941	+	1.38406i	0.548227	+	0.0966672i
$206$		0			0
$207$	4.43502	−	2.45497i	0.308255	−	0.170632i
$208$		0			0
$209$	10.6493	−	12.6913i	0.736625	−	0.877875i
$210$		0			0
$211$	−1.44923	−	8.21900i	−0.0997692	−	0.565819i	−0.993181	−	0.116581i	$-0.962807\pi$
$211$	−1.44923	−	8.21900i	−0.0997692	−	0.565819i	0.893412	−	0.449238i	$-0.148305\pi$
$212$		0			0
$213$	10.9332	−	4.97868i	0.749131	−	0.341133i
$214$		0			0
$215$	−3.38904			−0.231131
$216$		0			0
$217$	−34.1463			−2.31800
$218$		0			0
$219$	−2.71716	−	1.93933i	−0.183608	−	0.131048i
$220$		0			0
$221$	1.31066	+	7.43314i	0.0881647	+	0.500007i
$222$		0			0
$223$	−13.5510	+	16.1495i	−0.907444	+	1.08145i	0.0889020	+	0.996040i	$0.471664\pi$
$223$	−13.5510	+	16.1495i	−0.907444	+	1.08145i	−0.996346	+	0.0854092i	$0.972780\pi$
$224$		0			0
$225$	−13.0007	+	2.05130i	−0.866715	+	0.136754i
$226$		0			0
$227$	11.9451	+	2.10624i	0.792824	+	0.139796i	0.555371	−	0.831603i	$-0.312576\pi$
$227$	11.9451	+	2.10624i	0.792824	+	0.139796i	0.237453	+	0.971399i	$0.423687\pi$
$228$		0			0
$229$	−5.11109	+	14.0426i	−0.337751	+	0.927962i	0.648281	+	0.761401i	$0.275488\pi$
$229$	−5.11109	+	14.0426i	−0.337751	+	0.927962i	−0.986031	+	0.166560i	$0.946734\pi$
$230$		0			0
$231$	−15.5863	−	22.6924i	−1.02550	−	1.49305i
$232$		0			0
$233$	−14.7082	+	8.49179i	−0.963567	+	0.556315i	−0.897269	−	0.441484i	$-0.854452\pi$
$233$	−14.7082	+	8.49179i	−0.963567	+	0.556315i	−0.0662977	+	0.997800i	$0.521119\pi$
$234$		0			0
$235$	−0.662693	+	1.14782i	−0.0432293	+	0.0748754i
$236$		0			0
$237$	−10.8617	+	2.80563i	−0.705542	+	0.182245i
$238$		0			0
$239$	9.41696	−	7.90177i	0.609132	−	0.511123i	−0.285234	−	0.958458i	$-0.592071\pi$
$239$	9.41696	−	7.90177i	0.609132	−	0.511123i	0.894366	+	0.447335i	$0.147627\pi$
$240$		0			0
$241$	24.2458	−	8.82476i	1.56181	−	0.568453i	0.590661	−	0.806920i	$-0.298867\pi$
$241$	24.2458	−	8.82476i	1.56181	−	0.568453i	0.971151	+	0.238467i	$0.0766448\pi$
$242$		0			0
$243$	7.21820	−	13.8166i	0.463048	−	0.886333i
$244$		0			0
$245$	−6.06838	+	2.20871i	−0.387695	+	0.141109i
$246$		0			0
$247$	5.27026	+	6.28085i	0.335339	+	0.399641i
$248$		0			0
$249$	−6.44840	+	1.66565i	−0.408651	+	0.105556i
$250$		0			0
$251$	−9.90919	−	5.72107i	−0.625463	−	0.361111i	0.153530	−	0.988144i	$-0.450936\pi$
$251$	−9.90919	−	5.72107i	−0.625463	−	0.361111i	−0.778993	+	0.627033i	$0.784269\pi$
$252$		0			0
$253$	−5.95603	+	3.43872i	−0.374453	+	0.216190i
$254$		0			0
$255$	−4.18795	+	2.87649i	−0.262259	+	0.180133i
$256$		0			0
$257$	−2.38303	+	6.54733i	−0.148650	+	0.408411i	−0.991561	−	0.129641i	$-0.958618\pi$
$257$	−2.38303	+	6.54733i	−0.148650	+	0.408411i	0.842911	+	0.538052i	$0.180840\pi$
$258$		0			0
$259$	−7.08364	+	40.1733i	−0.440156	+	2.49625i
$260$		0			0
$261$	12.5323	−	1.97740i	0.775732	−	0.122398i
$262$		0			0
$263$	−9.78611	−	8.21152i	−0.603437	−	0.506344i	0.289111	−	0.957296i	$-0.406640\pi$
$263$	−9.78611	−	8.21152i	−0.603437	−	0.506344i	−0.892548	+	0.450952i	$0.851085\pi$
$264$		0			0
$265$	−1.47297	−	8.35361i	−0.0904837	−	0.513158i
$266$		0			0
$267$	−7.61493	+	10.6691i	−0.466026	+	0.652939i
$268$		0			0
$269$	−12.2970			−0.749762			−0.374881	−	0.927073i	$-0.622316\pi$
$269$	−12.2970			−0.749762			−0.374881	+	0.927073i	$0.622316\pi$
$270$		0			0
$271$		−	0.0290908i		−	0.00176714i	−1.00000		0.000883569i	$-0.999719\pi$
$271$		−	0.0290908i		−	0.00176714i	1.00000		0.000883569i	$-0.000281249\pi$
$272$		0			0
$273$	12.3992	−	5.64625i	0.750433	−	0.341726i
$274$		0			0
$275$	17.5853	−	3.10077i	1.06043	−	0.186983i
$276$		0			0
$277$	8.42372	−	10.0390i	0.506133	−	0.603185i	−0.451111	−	0.892468i	$-0.648972\pi$
$277$	8.42372	−	10.0390i	0.506133	−	0.603185i	0.957244	+	0.289282i	$0.0934167\pi$
$278$		0			0
$279$	12.7043	+	22.9508i	0.760585	+	1.37403i
$280$		0			0
$281$	−5.87063	−	1.03515i	−0.350213	−	0.0617519i	−0.00422519	−	0.999991i	$-0.501345\pi$
$281$	−5.87063	−	1.03515i	−0.350213	−	0.0617519i	−0.345987	+	0.938239i	$0.612456\pi$
$282$		0			0
$283$	−20.2795	−	7.38115i	−1.20549	−	0.438764i	−0.340355	−	0.940297i	$-0.610547\pi$
$283$	−20.2795	−	7.38115i	−1.20549	−	0.438764i	−0.865139	+	0.501533i	$0.832770\pi$
$284$		0			0
$285$	−2.37747	+	4.98071i	−0.140829	+	0.295032i
$286$		0			0
$287$	19.8801	+	34.4333i	1.17348	+	2.03254i
$288$		0			0
$289$	−1.47961	+	2.56276i	−0.0870359	+	0.150751i
$290$		0			0
$291$	4.63036	+	1.28557i	0.271437	+	0.0753617i
$292$		0			0
$293$	0.243742	−	0.204524i	0.0142396	−	0.0119484i	−0.635640	−	0.771986i	$-0.719264\pi$
$293$	0.243742	−	0.204524i	0.0142396	−	0.0119484i	0.649880	+	0.760037i	$0.274819\pi$
$294$		0			0
$295$	0.676719	+	1.85927i	0.0394001	+	0.108251i
$296$		0			0
$297$	−9.45337	+	18.9189i	−0.548540	+	1.09778i
$298$		0			0
$299$	−1.16410	−	3.19834i	−0.0673217	−	0.184965i
$300$		0			0
$301$	−10.8669	−	12.9507i	−0.626360	−	0.746466i
$302$		0			0
$303$	1.90081	−	1.86683i	0.109199	−	0.107247i
$304$		0			0
$305$	−2.54967	−	1.47205i	−0.145994	−	0.0842895i
$306$		0			0
$307$	−3.67206	−	6.36020i	−0.209576	−	0.362996i	0.742005	−	0.670394i	$-0.233875\pi$
$307$	−3.67206	−	6.36020i	−0.209576	−	0.362996i	−0.951581	+	0.307398i	$0.900542\pi$
$308$		0			0
$309$	2.52588	+	32.2150i	0.143692	+	1.83265i
$310$		0			0
$311$	17.8000	+	6.47869i	1.00935	+	0.367373i	0.793183	−	0.608984i	$-0.208423\pi$
$311$	17.8000	+	6.47869i	1.00935	+	0.367373i	0.216166	+	0.976357i	$0.430645\pi$
$312$		0			0
$313$	−4.61511	+	26.1736i	−0.260861	+	1.47942i	0.519705	+	0.854346i	$0.326042\pi$
$313$	−4.61511	+	26.1736i	−0.260861	+	1.47942i	−0.780566	+	0.625073i	$0.785069\pi$
$314$		0			0
$315$	6.91783	+	6.02070i	0.389776	+	0.339228i
$316$		0			0
$317$	−12.1863	−	10.2255i	−0.684450	−	0.574322i	0.232853	−	0.972512i	$-0.425194\pi$
$317$	−12.1863	−	10.2255i	−0.684450	−	0.574322i	−0.917303	+	0.398190i	$0.869639\pi$
$318$		0			0
$319$	−16.9518	+	2.98905i	−0.949116	+	0.167355i
$320$		0			0
$321$	12.5100	+	1.20828i	0.698240	+	0.0674394i
$322$		0			0
$323$		−	15.2523i		−	0.848660i
$324$		0			0
$325$			8.83713i			0.490196i
$326$		0			0
$327$	−7.77188	−	0.750646i	−0.429786	−	0.0415108i
$328$		0			0
$329$	−6.51114	+	1.14809i	−0.358971	+	0.0632962i
$330$		0			0
$331$	3.81198	+	3.19863i	0.209525	+	0.175813i	0.741511	−	0.670941i	$-0.234110\pi$
$331$	3.81198	+	3.19863i	0.209525	+	0.175813i	−0.531986	+	0.846753i	$0.678554\pi$
$332$		0			0
$333$	29.6373	−	10.1855i	1.62411	−	0.558163i
$334$		0			0
$335$	0.418430	−	2.37303i	0.0228613	−	0.129653i
$336$		0			0
$337$	4.29261	+	1.56238i	0.233834	+	0.0851085i	0.456279	−	0.889837i	$-0.349182\pi$
$337$	4.29261	+	1.56238i	0.233834	+	0.0851085i	−0.222446	+	0.974945i	$0.571404\pi$
$338$		0			0
$339$	−0.444070	−	5.66366i	−0.0241186	−	0.307608i
$340$		0			0
$341$	−17.7950	−	30.8219i	−0.963656	−	1.66910i
$342$		0			0
$343$	−4.22536	−	2.43951i	−0.228148	−	0.131721i
$344$		0			0
$345$	1.63458	−	1.60535i	0.0880027	−	0.0864293i
$346$		0			0
$347$	−16.1321	−	19.2255i	−0.866018	−	1.03208i	−0.999160	−	0.0409830i	$-0.986951\pi$
$347$	−16.1321	−	19.2255i	−0.866018	−	1.03208i	0.133142	−	0.991097i	$-0.457493\pi$
$348$		0			0
$349$	−7.75352	−	21.3026i	−0.415036	−	1.14030i	−0.954478	−	0.298280i	$-0.903587\pi$
$349$	−7.75352	−	21.3026i	−0.415036	−	1.14030i	0.539442	−	0.842023i	$-0.318635\pi$
$350$		0			0
$351$	−8.40820	−	6.23318i	−0.448796	−	0.332703i
$352$		0			0
$353$	−11.8634	−	32.5944i	−0.631425	−	1.73482i	−0.677123	−	0.735869i	$-0.736774\pi$
$353$	−11.8634	−	32.5944i	−0.631425	−	1.73482i	0.0456988	−	0.998955i	$-0.485449\pi$
$354$		0			0
$355$	4.15933	−	3.49009i	0.220754	−	0.185235i
$356$		0			0
$357$	−24.4207	−	6.78017i	−1.29248	−	0.358844i
$358$		0			0
$359$	13.5606	−	23.4877i	0.715702	−	1.23963i	−0.246986	−	0.969019i	$-0.579440\pi$
$359$	13.5606	−	23.4877i	0.715702	−	1.23963i	0.962688	−	0.270613i	$-0.0872263\pi$
$360$		0			0
$361$	1.21583	+	2.10588i	0.0639911	+	0.110836i
$362$		0			0
$363$	4.15315	−	8.70069i	0.217984	−	0.456668i
$364$		0			0
$365$	−1.41778	−	0.516029i	−0.0742099	−	0.0270102i
$366$		0			0
$367$	6.46503	+	1.13996i	0.337472	+	0.0595054i	0.339816	−	0.940492i	$-0.389635\pi$
$367$	6.46503	+	1.13996i	0.337472	+	0.0595054i	−0.00234427	+	0.999997i	$0.500746\pi$
$368$		0			0
$369$	15.7473	−	26.1731i	0.819771	−	1.36252i
$370$		0			0
$371$	27.1990	−	32.4145i	1.41210	−	1.68288i
$372$		0			0
$373$	−10.6886	+	1.88468i	−0.553432	+	0.0975850i	−0.443368	−	0.896339i	$-0.646217\pi$
$373$	−10.6886	+	1.88468i	−0.553432	+	0.0975850i	−0.110064	+	0.993925i	$0.535106\pi$
$374$		0			0
$375$	−11.5835	+	5.27482i	−0.598171	+	0.272390i
$376$		0			0
$377$		−	8.51875i		−	0.438738i
$378$		0			0
$379$	−6.56361			−0.337150			−0.168575	−	0.985689i	$-0.553917\pi$
$379$	−6.56361			−0.337150			−0.168575	+	0.985689i	$0.553917\pi$
$380$		0			0
$381$	19.9068	−	27.8910i	1.01985	−	1.42890i
$382$		0			0
$383$	−2.26029	−	12.8188i	−0.115496	−	0.655008i	−0.986504	−	0.163739i	$-0.947644\pi$
$383$	−2.26029	−	12.8188i	−0.115496	−	0.655008i	0.871008	−	0.491269i	$-0.163467\pi$
$384$		0			0
$385$	−9.53140	−	7.99780i	−0.485765	−	0.407606i
$386$		0			0
$387$	−4.66150	+	12.1224i	−0.236957	+	0.616215i
$388$		0			0
$389$	1.53930	−	8.72982i	0.0780458	−	0.442620i	−0.920596	−	0.390516i	$-0.872296\pi$
$389$	1.53930	−	8.72982i	0.0780458	−	0.442620i	0.998642	−	0.0521031i	$-0.0165924\pi$
$390$		0			0
$391$	−2.16551	+	5.94970i	−0.109515	+	0.300889i
$392$		0			0
$393$	25.2401	−	17.3361i	1.27319	−	0.874492i
$394$		0			0
$395$	−4.39093	+	2.53510i	−0.220932	+	0.127555i
$396$		0			0
$397$	13.3068	+	7.68271i	0.667852	+	0.385584i	0.795262	−	0.606266i	$-0.207333\pi$
$397$	13.3068	+	7.68271i	0.667852	+	0.385584i	−0.127411	+	0.991850i	$0.540667\pi$
$398$		0			0
$399$	−26.6564	+	6.88548i	−1.33449	+	0.344705i
$400$		0			0
$401$	14.4543	+	17.2260i	0.721813	+	0.860224i	0.994806	−	0.101792i	$-0.0324578\pi$
$401$	14.4543	+	17.2260i	0.721813	+	0.860224i	−0.272992	+	0.962016i	$0.588013\pi$
$402$		0			0
$403$	16.5511	−	6.02412i	0.824470	−	0.300083i
$404$		0			0
$405$	1.47290	−	6.88973i	0.0731890	−	0.342353i
$406$		0			0
$407$	−39.9538	+	14.5420i	−1.98044	+	0.720820i
$408$		0			0
$409$	−15.1785	+	12.7363i	−0.750530	+	0.629769i	−0.935643	−	0.352948i	$-0.885179\pi$
$409$	−15.1785	+	12.7363i	−0.750530	+	0.629769i	0.185113	+	0.982717i	$0.440735\pi$
$410$		0			0
$411$	23.9207	−	6.17884i	1.17992	−	0.304780i
$412$		0			0
$413$	−4.93503	+	8.54772i	−0.242837	+	0.420606i
$414$		0			0
$415$	−2.60682	+	1.50505i	−0.127964	+	0.0738799i
$416$		0			0
$417$	−17.8264	−	25.9538i	−0.872960	−	1.27096i
$418$		0			0
$419$	−3.96698	+	10.8992i	−0.193800	+	0.532460i	−0.998090	−	0.0617762i	$-0.980323\pi$
$419$	−3.96698	+	10.8992i	−0.193800	+	0.532460i	0.804290	+	0.594237i	$0.202546\pi$
$420$		0			0
$421$	27.4892	+	4.84709i	1.33974	+	0.236233i	0.797159	−	0.603769i	$-0.206335\pi$
$421$	27.4892	+	4.84709i	1.33974	+	0.236233i	0.542584	+	0.840002i	$0.317446\pi$
$422$		0			0
$423$	3.19417	+	3.94920i	0.155306	+	0.192016i
$424$		0			0
$425$	10.5669	−	12.5932i	0.512572	−	0.610859i
$426$		0			0
$427$	−2.55027	−	14.4633i	−0.123416	−	0.699929i
$428$		0			0
$429$	11.5583	+	8.24956i	0.558039	+	0.398292i
$430$		0			0
$431$	−38.5855			−1.85860			−0.929298	−	0.369330i	$-0.879587\pi$
$431$	−38.5855			−1.85860			−0.929298	+	0.369330i	$0.879587\pi$
$432$		0			0
$433$	27.4071			1.31710			0.658551	−	0.752536i	$-0.271170\pi$
$433$	27.4071			1.31710			0.658551	+	0.752536i	$0.271170\pi$
$434$		0			0
$435$	5.21862	−	2.37642i	0.250214	−	0.113941i
$436$		0			0
$437$	1.19433	+	6.77337i	0.0571325	+	0.324014i
$438$		0			0
$439$	2.90532	−	3.46242i	0.138663	−	0.165252i	−0.692244	−	0.721664i	$-0.743378\pi$
$439$	2.90532	−	3.46242i	0.138663	−	0.165252i	0.830907	+	0.556411i	$0.187822\pi$
$440$		0			0
$441$	−0.446419	+	24.7442i	−0.0212580	+	1.17830i
$442$		0			0
$443$	−7.65023	−	1.34894i	−0.363473	−	0.0640902i	−0.0110709	−	0.999939i	$-0.503524\pi$
$443$	−7.65023	−	1.34894i	−0.363473	−	0.0640902i	−0.352402	+	0.935849i	$0.614635\pi$
$444$		0			0
$445$	−2.02623	+	5.56701i	−0.0960524	+	0.263902i
$446$		0			0
$447$	14.5503	−	30.4824i	0.688206	−	1.44177i
$448$		0			0
$449$	5.99255	−	3.45980i	0.282806	−	0.163278i	−0.351887	−	0.936042i	$-0.614460\pi$
$449$	5.99255	−	3.45980i	0.282806	−	0.163278i	0.634693	+	0.772764i	$0.281127\pi$
$450$		0			0
$451$	−20.7207	+	35.8893i	−0.975700	+	1.68996i
$452$		0			0
$453$	3.79973	−	13.6858i	0.178527	−	0.643015i
$454$		0			0
$455$	4.71704	−	3.95806i	0.221138	−	0.185557i
$456$		0			0
$457$	2.03870	−	0.742024i	0.0953661	−	0.0347104i	−0.293896	−	0.955837i	$-0.594952\pi$
$457$	2.03870	−	0.742024i	0.0953661	−	0.0347104i	0.389263	+	0.921127i	$0.372730\pi$
$458$		0			0
$459$	4.52866	+	18.9365i	0.211380	+	0.883882i
$460$		0			0
$461$	−3.55121	+	1.29254i	−0.165396	+	0.0601994i	−0.423391	−	0.905947i	$-0.639160\pi$
$461$	−3.55121	+	1.29254i	−0.165396	+	0.0601994i	0.257995	+	0.966146i	$0.416938\pi$
$462$		0			0
$463$	−2.61147	−	3.11222i	−0.121365	−	0.144637i	0.701941	−	0.712235i	$-0.252317\pi$
$463$	−2.61147	−	3.11222i	−0.121365	−	0.144637i	−0.823306	+	0.567598i	$0.807873\pi$
$464$		0			0
$465$	8.30756	+	8.45879i	0.385254	+	0.392267i
$466$		0			0
$467$	12.2451	+	7.06974i	0.566638	+	0.327148i	0.755805	−	0.654796i	$-0.227246\pi$
$467$	12.2451	+	7.06974i	0.566638	+	0.327148i	−0.189168	+	0.981945i	$0.560579\pi$
$468$		0			0
$469$	10.4099	−	6.01015i	0.480684	−	0.277523i
$470$		0			0
$471$	−1.83627	−	23.4198i	−0.0846111	−	1.07913i
$472$		0			0
$473$	6.02667	−	16.5581i	0.277106	−	0.761344i
$474$		0			0
$475$	3.10096	−	17.5864i	0.142282	−	0.806920i
$476$		0			0
$477$	−31.9064	−	6.22138i	−1.46089	−	0.284857i
$478$		0			0
$479$	−6.17960	−	5.18530i	−0.282353	−	0.236922i	0.490601	−	0.871384i	$-0.336777\pi$
$479$	−6.17960	−	5.18530i	−0.282353	−	0.236922i	−0.772954	+	0.634462i	$0.781222\pi$
$480$		0			0
$481$	−3.65389	−	20.7222i	−0.166603	−	0.944852i
$482$		0			0
$483$	11.3759	+	1.09874i	0.517620	+	0.0499943i
$484$		0			0
$485$	2.17191			0.0986216
$486$		0			0
$487$			15.8287i			0.717266i	0.933479	+	0.358633i	$0.116757\pi$
$487$			15.8287i			0.717266i	−0.933479	+	0.358633i	$0.883243\pi$
$488$		0			0
$489$	−2.21305	+	22.9130i	−0.100078	+	1.03616i
$490$		0			0
$491$	−22.3135	+	3.93448i	−1.00700	+	0.177561i	−0.652735	−	0.757586i	$-0.726379\pi$
$491$	−22.3135	+	3.93448i	−1.00700	+	0.177561i	−0.354261	+	0.935147i	$0.615268\pi$
$492$		0			0
$493$	−10.1862	+	12.1395i	−0.458765	+	0.546735i
$494$		0			0
$495$	−1.82938	+	9.38198i	−0.0822245	+	0.421689i
$496$		0			0
$497$	26.6737	+	4.70330i	1.19648	+	0.210972i
$498$		0			0
$499$	4.80455	+	1.74871i	0.215081	+	0.0782832i	0.447314	−	0.894377i	$-0.352381\pi$
$499$	4.80455	+	1.74871i	0.215081	+	0.0782832i	−0.232232	+	0.972660i	$0.574603\pi$
$500$		0			0
$501$	12.3890	−	0.971385i	0.553501	−	0.0433983i
$502$		0			0
$503$	5.79569	+	10.0384i	0.258417	+	0.447592i	0.965818	−	0.259221i	$-0.0834658\pi$
$503$	5.79569	+	10.0384i	0.258417	+	0.447592i	−0.707401	+	0.706812i	$0.750132\pi$
$504$		0			0
$505$	0.602068	−	1.04281i	0.0267917	−	0.0464045i
$506$		0			0
$507$	11.0507	−	10.8531i	0.490780	−	0.482005i
$508$		0			0
$509$	1.52773	−	1.28192i	0.0677153	−	0.0568199i	−0.608302	−	0.793706i	$-0.708149\pi$
$509$	1.52773	−	1.28192i	0.0677153	−	0.0568199i	0.676017	+	0.736886i	$0.263705\pi$
$510$		0			0
$511$	−2.57417	−	7.07247i	−0.113874	−	0.312868i
$512$		0			0
$513$	14.5456	+	15.3548i	0.642203	+	0.677933i
$514$		0			0
$515$	4.99510	+	13.7239i	0.220110	+	0.604748i
$516$		0			0
$517$	−4.42954	−	5.27892i	−0.194811	−	0.232167i
$518$		0			0
$519$	5.72715	+	1.59009i	0.251394	+	0.0697971i
$520$		0			0
$521$	−23.0614	−	13.3145i	−1.01034	−	0.583319i	−0.0990474	−	0.995083i	$-0.531580\pi$
$521$	−23.0614	−	13.3145i	−1.01034	−	0.583319i	−0.911291	+	0.411764i	$0.864913\pi$
$522$		0			0
$523$	−12.5145	−	21.6758i	−0.547223	−	0.947818i	−0.998463	−	0.0554155i	$-0.982352\pi$
$523$	−12.5145	−	21.6758i	−0.547223	−	0.947818i	0.451240	−	0.892402i	$-0.350982\pi$
$524$		0			0
$525$	−26.7794	−	12.7828i	−1.16875	−	0.557885i
$526$		0			0
$527$	−30.7892	−	11.2063i	−1.34120	−	0.488156i
$528$		0			0
$529$	−3.49812	+	19.8388i	−0.152092	+	0.862557i
$530$		0			0
$531$	7.58130	+	0.136777i	0.329000	+	0.00593561i
$532$		0			0
$533$	−15.7109	−	13.1830i	−0.680514	−	0.571019i
$534$		0			0
$535$	5.59407	−	0.986386i	0.241853	−	0.0426452i
$536$		0			0
$537$	9.17795	+	20.1548i	0.396058	+	0.869745i
$538$		0			0
$539$		−	33.5765i		−	1.44624i
$540$		0			0
$541$			41.3952i			1.77972i	0.456233	+	0.889860i	$0.349198\pi$
$541$			41.3952i			1.77972i	−0.456233	+	0.889860i	$0.650802\pi$
$542$		0			0
$543$	0.418194	−	0.585923i	0.0179464	−	0.0251443i
$544$		0			0
$545$	−3.47534	+	0.612796i	−0.148867	+	0.0262493i
$546$		0			0
$547$	−13.3233	−	11.1795i	−0.569662	−	0.478003i	0.311872	−	0.950124i	$-0.399044\pi$
$547$	−13.3233	−	11.1795i	−0.569662	−	0.478003i	−0.881534	+	0.472121i	$0.843488\pi$
$548$		0			0
$549$	−8.77242	+	7.09526i	−0.374398	+	0.302818i
$550$		0			0
$551$	−2.98924	+	16.9528i	−0.127346	+	0.722214i
$552$		0			0
$553$	−23.7670	−	8.65048i	−1.01068	−	0.367856i
$554$		0			0
$555$	11.6752	−	8.01912i	0.495586	−	0.340393i
$556$		0			0
$557$	21.0747	+	36.5024i	0.892963	+	1.54666i	0.836306	+	0.548263i	$0.184711\pi$
$557$	21.0747	+	36.5024i	0.892963	+	1.54666i	0.0566567	+	0.998394i	$0.481956\pi$
$558$		0			0
$559$	7.55211	+	4.36021i	0.319420	+	0.184417i
$560$		0			0
$561$	−6.60657	−	25.5766i	−0.278930	−	1.07985i
$562$		0			0
$563$	1.76403	+	2.10229i	0.0743450	+	0.0886009i	0.801935	−	0.597411i	$-0.203804\pi$
$563$	1.76403	+	2.10229i	0.0743450	+	0.0886009i	−0.727590	+	0.686012i	$0.759360\pi$
$564$		0			0
$565$	−0.878179	−	2.41278i	−0.0369453	−	0.101506i
$566$		0			0
$567$	31.0509	−	16.4634i	1.30402	−	0.691398i
$568$		0			0
$569$	−0.717043	−	1.97006i	−0.0300600	−	0.0825892i	0.923755	−	0.382984i	$-0.125104\pi$
$569$	−0.717043	−	1.97006i	−0.0300600	−	0.0825892i	−0.953815	+	0.300395i	$0.902881\pi$
$570$		0			0
$571$	2.63316	−	2.20949i	0.110194	−	0.0924641i	−0.586026	−	0.810293i	$-0.699308\pi$
$571$	2.63316	−	2.20949i	0.110194	−	0.0924641i	0.696220	+	0.717828i	$0.254864\pi$
$572$		0			0
$573$	−11.5018	−	44.5281i	−0.480496	−	1.86019i
$574$		0			0
$575$	−3.70655	+	6.41994i	−0.154574	+	0.267730i
$576$		0			0
$577$	−13.7440	−	23.8053i	−0.572171	−	0.991029i	−0.996343	−	0.0854469i	$-0.972768\pi$
$577$	−13.7440	−	23.8053i	−0.572171	−	0.991029i	0.424172	−	0.905582i	$-0.360565\pi$
$578$		0			0
$579$	−11.4889	−	16.7270i	−0.477464	−	0.695151i
$580$		0			0
$581$	−14.1101	−	5.13565i	−0.585384	−	0.213062i
$582$		0			0
$583$	43.4333	+	7.65847i	1.79883	+	0.317181i
$584$		0			0
$585$	−4.41534	−	1.69786i	−0.182552	−	0.0701978i
$586$		0			0
$587$	−1.95898	+	2.33462i	−0.0808557	+	0.0963600i	−0.804956	−	0.593335i	$-0.797811\pi$
$587$	−1.95898	+	2.33462i	−0.0808557	+	0.0963600i	0.724100	+	0.689695i	$0.242255\pi$
$588$		0			0
$589$	−35.0516	+	6.18054i	−1.44428	+	0.254665i
$590$		0			0
$591$	30.7048	+	21.9151i	1.26303	+	0.901466i
$592$		0			0
$593$		−	35.4432i		−	1.45548i	−0.685854	−	0.727740i	$-0.740571\pi$
$593$		−	35.4432i		−	1.45548i	0.685854	−	0.727740i	$-0.259429\pi$
$594$		0			0
$595$	−11.4548			−0.469599
$596$		0			0
$597$	−0.559432	−	1.22852i	−0.0228960	−	0.0502798i
$598$		0			0
$599$	−0.864787	−	4.90445i	−0.0353342	−	0.200390i	0.962030	−	0.272942i	$-0.0879968\pi$
$599$	−0.864787	−	4.90445i	−0.0353342	−	0.200390i	−0.997365	+	0.0725519i	$0.976886\pi$
$600$		0			0
$601$	−8.85816	−	7.43288i	−0.361332	−	0.303193i	0.443989	−	0.896032i	$-0.353563\pi$
$601$	−8.85816	−	7.43288i	−0.361332	−	0.303193i	−0.805321	+	0.592839i	$0.798007\pi$
$602$		0			0
$603$	−7.91265	−	4.76072i	−0.322228	−	0.193871i
$604$		0			0
$605$	0.756658	−	4.29122i	0.0307625	−	0.174463i
$606$		0			0
$607$	−0.0821746	+	0.225773i	−0.00333536	+	0.00916384i	−0.941349	−	0.337434i	$-0.890441\pi$
$607$	−0.0821746	+	0.225773i	−0.00333536	+	0.00916384i	0.938014	+	0.346598i	$0.112663\pi$
$608$		0			0
$609$	25.8146	+	12.3222i	1.04606	+	0.499322i
$610$		0			0
$611$	2.95348	−	1.70519i	0.119485	−	0.0689848i
$612$		0			0
$613$	22.5946	+	13.0450i	0.912588	+	0.526883i	0.881263	−	0.472626i	$-0.156694\pi$
$613$	22.5946	+	13.0450i	0.912588	+	0.526883i	0.0313252	+	0.999509i	$0.490027\pi$
$614$		0			0
$615$	3.69321	−	13.3021i	0.148925	−	0.536394i
$616$		0			0
$617$	−9.53125	−	11.3589i	−0.383714	−	0.457292i	0.539269	−	0.842134i	$-0.318701\pi$
$617$	−9.53125	−	11.3589i	−0.383714	−	0.457292i	−0.922983	+	0.384841i	$0.874256\pi$
$618$		0			0
$619$	11.2206	−	4.08396i	0.450993	−	0.164148i	−0.106530	−	0.994309i	$-0.533974\pi$
$619$	11.2206	−	4.08396i	0.450993	−	0.164148i	0.557523	+	0.830161i	$0.311752\pi$
$620$		0			0
$621$	−3.49395	−	8.05488i	−0.140207	−	0.323231i
$622$		0			0
$623$	−27.7706	+	10.1077i	−1.11261	+	0.404955i
$624$		0			0
$625$	12.3972	−	10.4025i	0.495887	−	0.416098i
$626$		0			0
$627$	−20.1069	−	20.4729i	−0.802992	−	0.817610i
$628$		0			0
$629$	−19.5716	+	33.8989i	−0.780369	+	1.35164i
$630$		0			0
$631$	−3.14304	+	1.81464i	−0.125122	+	0.0722395i	−0.561255	−	0.827643i	$-0.689681\pi$
$631$	−3.14304	+	1.81464i	−0.125122	+	0.0722395i	0.436132	+	0.899882i	$0.356348\pi$
$632$		0			0
$633$	−14.4111	+	1.12993i	−0.572790	+	0.0449106i
$634$		0			0
$635$	5.29692	−	14.5532i	0.210202	−	0.577525i
$636$		0			0
$637$	16.3644	+	2.88548i	0.648380	+	0.114327i
$638$		0			0
$639$	−6.76284	−	19.6782i	−0.267534	−	0.778457i
$640$		0			0
$641$	−14.6906	+	17.5075i	−0.580242	+	0.691506i	−0.973699	−	0.227837i	$-0.926835\pi$
$641$	−14.6906	+	17.5075i	−0.580242	+	0.691506i	0.393457	+	0.919343i	$0.371279\pi$
$642$		0			0
$643$	7.40620	+	42.0026i	0.292072	+	1.65642i	0.678871	+	0.734258i	$0.262470\pi$
$643$	7.40620	+	42.0026i	0.292072	+	1.65642i	−0.386799	+	0.922164i	$0.626419\pi$
$644$		0			0
$645$	−0.564326	+	5.84280i	−0.0222203	+	0.230060i
$646$		0			0
$647$	−22.8902			−0.899906			−0.449953	−	0.893052i	$-0.648559\pi$
$647$	−22.8902			−0.899906			−0.449953	+	0.893052i	$0.648559\pi$
$648$		0			0
$649$	−10.2874			−0.403816
$650$		0			0
$651$	−5.68586	+	58.8691i	−0.222847	+	2.30726i
$652$		0			0
$653$	−2.77297	−	15.7263i	−0.108515	−	0.615418i	−0.989758	−	0.142755i	$-0.954404\pi$
$653$	−2.77297	−	15.7263i	−0.108515	−	0.615418i	0.881243	−	0.472663i	$-0.156707\pi$
$654$		0			0
$655$	8.89570	−	10.6015i	0.347584	−	0.414234i
$656$		0			0
$657$	−3.79591	+	4.36152i	−0.148092	+	0.170159i
$658$		0			0
$659$	12.3500	+	2.17764i	0.481089	+	0.0848289i	0.408933	−	0.912564i	$-0.365901\pi$
$659$	12.3500	+	2.17764i	0.481089	+	0.0848289i	0.0721558	+	0.997393i	$0.477012\pi$
$660$		0			0
$661$	6.07399	−	16.6881i	0.236251	−	0.649093i	−0.763743	−	0.645521i	$-0.776640\pi$
$661$	6.07399	−	16.6881i	0.236251	−	0.649093i	0.999994	−	0.00357294i	$-0.00113730\pi$
$662$		0			0
$663$	13.0332	−	1.02189i	0.506167	−	0.0396869i
$664$		0			0
$665$	−10.7761	+	6.22157i	−0.417878	+	0.241262i
$666$		0			0
$667$	3.57301	−	6.18864i	0.138348	−	0.239625i
$668$		0			0
$669$	25.5857	+	26.0515i	0.989201	+	1.00721i
$670$		0			0
$671$	11.7262	−	9.83943i	0.452684	−	0.379847i
$672$		0			0
$673$	−31.2988	+	11.3918i	−1.20648	+	0.439122i	−0.865481	−	0.500942i	$-0.832987\pi$
$673$	−31.2988	+	11.3918i	−1.20648	+	0.439122i	−0.340997	+	0.940064i	$0.610765\pi$
$674$		0			0
$675$	1.37169	+	22.7552i	0.0527963	+	0.875848i
$676$		0			0
$677$	25.5846	−	9.31202i	0.983295	−	0.357890i	0.200175	−	0.979760i	$-0.435849\pi$
$677$	25.5846	−	9.31202i	0.983295	−	0.357890i	0.783120	+	0.621870i	$0.213627\pi$
$678$		0			0
$679$	6.96423	+	8.29964i	0.267263	+	0.318511i
$680$		0			0
$681$	5.62026	−	20.2430i	0.215369	−	0.775712i
$682$		0			0
$683$	−34.0275	−	19.6458i	−1.30203	−	0.751725i	−0.321275	−	0.946986i	$-0.604111\pi$
$683$	−34.0275	−	19.6458i	−1.30203	−	0.751725i	−0.980751	+	0.195261i	$0.937445\pi$
$684$		0			0
$685$	9.67016	−	5.58307i	0.369478	−	0.213318i
$686$		0			0
$687$	23.3588	+	11.1500i	0.891193	+	0.425398i
$688$		0			0
$689$	−7.46510	+	20.5102i	−0.284398	+	0.781377i
$690$		0			0
$691$	−7.24693	+	41.0994i	−0.275686	+	1.56349i	0.461087	+	0.887355i	$0.347460\pi$
$691$	−7.24693	+	41.0994i	−0.275686	+	1.56349i	−0.736773	+	0.676140i	$0.763652\pi$
$692$		0			0
$693$	−41.7177	+	23.0926i	−1.58473	+	0.877214i
$694$		0			0
$695$	−10.9013	−	9.14725i	−0.413509	−	0.346975i
$696$		0			0
$697$	6.62503	+	37.5724i	0.250941	+	1.42316i
$698$		0			0
$699$	12.1909	+	26.7714i	0.461104	+	1.01259i
$700$		0			0
$701$	35.6358			1.34594			0.672972	−	0.739668i	$-0.265017\pi$
$701$	35.6358			1.34594			0.672972	+	0.739668i	$0.265017\pi$
$702$		0			0
$703$			42.5206i			1.60369i
$704$		0			0
$705$	1.86852	+	1.33363i	0.0703726	+	0.0502274i
$706$		0			0
$707$	5.91548	−	1.04306i	0.222474	−	0.0392282i
$708$		0			0
$709$	−12.4298	+	14.8132i	−0.466810	+	0.556322i	−0.947163	−	0.320753i	$-0.896064\pi$
$709$	−12.4298	+	14.8132i	−0.466810	+	0.556322i	0.480353	+	0.877075i	$0.340509\pi$
$710$		0			0
$711$	3.02835	+	19.1930i	0.113572	+	0.719795i
$712$		0			0
$713$	14.5506	+	2.56567i	0.544926	+	0.0960851i
$714$		0			0
$715$	6.03097	+	2.19509i	0.225545	+	0.0820918i
$716$		0			0
$717$	−12.0548	−	17.5509i	−0.450195	−	0.655449i
$718$		0			0
$719$	−4.38435	−	7.59391i	−0.163509	−	0.283205i	0.772616	−	0.634873i	$-0.218948\pi$
$719$	−4.38435	−	7.59391i	−0.163509	−	0.283205i	−0.936125	+	0.351668i	$0.885614\pi$
$720$		0			0
$721$	−36.4271	+	63.0937i	−1.35662	+	2.34973i
$722$		0			0
$723$	−11.1768	−	43.2700i	−0.415671	−	1.60923i
$724$		0			0
$725$	−14.2132	+	11.9263i	−0.527864	+	0.442930i
$726$		0			0
$727$	−17.7683	−	48.8179i	−0.658988	−	1.81055i	−0.581477	−	0.813563i	$-0.697525\pi$
$727$	−17.7683	−	48.8179i	−0.658988	−	1.81055i	−0.0775114	−	0.996991i	$-0.524697\pi$
$728$		0			0
$729$	−22.6182	−	14.7450i	−0.837712	−	0.546113i
$730$		0			0
$731$	−5.54830	−	15.2438i	−0.205211	−	0.563814i
$732$		0			0
$733$	3.92115	+	4.67304i	0.144831	+	0.172603i	0.833583	−	0.552394i	$-0.186286\pi$
$733$	3.92115	+	4.67304i	0.144831	+	0.172603i	−0.688752	+	0.724997i	$0.741841\pi$
$734$		0			0
$735$	2.79740	+	10.8298i	0.103184	+	0.399465i
$736$		0			0
$737$	10.8500	+	6.26428i	0.399667	+	0.230748i
$738$		0			0
$739$	17.5953	+	30.4760i	0.647255	+	1.12108i	0.983776	+	0.179402i	$0.0574164\pi$
$739$	17.5953	+	30.4760i	0.647255	+	1.12108i	−0.336521	+	0.941676i	$0.609250\pi$
$740$		0			0
$741$	11.7059	−	8.04022i	0.430028	−	0.295365i
$742$		0			0
$743$	24.6151	+	8.95918i	0.903042	+	0.328681i	0.751471	−	0.659766i	$-0.229345\pi$
$743$	24.6151	+	8.95918i	0.903042	+	0.328681i	0.151571	+	0.988446i	$0.451567\pi$
$744$		0			0
$745$	2.65091	−	15.0340i	0.0971218	−	0.550805i
$746$		0			0
$747$	1.79788	+	11.3946i	0.0657809	+	0.416906i
$748$		0			0
$749$	21.7067	+	18.2141i	0.793145	+	0.665527i
$750$		0			0
$751$	33.0395	−	5.82576i	1.20563	−	0.212585i	0.465499	−	0.885049i	$-0.345875\pi$
$751$	33.0395	−	5.82576i	1.20563	−	0.212585i	0.740130	+	0.672464i	$0.234764\pi$
$752$		0			0
$753$	−11.5133	+	16.1311i	−0.419569	+	0.587849i
$754$		0			0
$755$		−	6.41946i		−	0.233628i
$756$		0			0
$757$			24.5635i			0.892774i	0.894840	+	0.446387i	$0.147289\pi$
$757$			24.5635i			0.892774i	−0.894840	+	0.446387i	$0.852711\pi$
$758$		0			0
$759$	4.93668	+	10.8410i	0.179190	+	0.393502i
$760$		0			0
$761$	31.6026	−	5.57238i	1.14559	−	0.201999i	0.431542	−	0.902093i	$-0.357970\pi$
$761$	31.6026	−	5.57238i	1.14559	−	0.201999i	0.714050	+	0.700094i	$0.246859\pi$
$762$		0			0
$763$	−13.4854	−	11.3156i	−0.488203	−	0.409651i
$764$		0			0
$765$	4.26179	+	7.69912i	0.154085	+	0.278362i
$766$		0			0
$767$	0.884074	−	5.01383i	0.0319220	−	0.181039i
$768$		0			0
$769$	13.6669	+	4.97435i	0.492842	+	0.179380i	0.576472	−	0.817117i	$-0.304429\pi$
$769$	13.6669	+	4.97435i	0.492842	+	0.179380i	−0.0836298	+	0.996497i	$0.526651\pi$
$770$		0			0
$771$	10.8910	+	5.19865i	0.392229	+	0.187225i
$772$		0			0
$773$	−12.4834	−	21.6219i	−0.448997	−	0.777686i	0.549324	−	0.835609i	$-0.314885\pi$
$773$	−12.4834	−	21.6219i	−0.448997	−	0.777686i	−0.998321	+	0.0579237i	$0.981552\pi$
$774$		0			0
$775$	−33.2226	−	19.1811i	−1.19339	−	0.689004i
$776$		0			0
$777$	68.0804	+	18.9019i	2.44237	+	0.678100i
$778$		0			0
$779$	26.6397	+	31.7479i	0.954465	+	1.13749i
$780$		0			0
$781$	9.65540	+	26.5280i	0.345497	+	0.949246i
$782$		0			0
$783$	−1.32227	−	21.9354i	−0.0472541	−	0.783906i
$784$		0			0
$785$	−3.63136	−	9.97708i	−0.129609	−	0.356097i
$786$		0			0
$787$	−19.8410	+	16.6486i	−0.707257	+	0.593459i	−0.923828	−	0.382808i	$-0.874957\pi$
$787$	−19.8410	+	16.6486i	−0.707257	+	0.593459i	0.216571	+	0.976267i	$0.430513\pi$
$788$		0			0
$789$	−15.7864	+	15.5042i	−0.562011	+	0.551964i
$790$		0			0
$791$	6.40419	−	11.0924i	0.227707	−	0.394400i
$792$		0			0
$793$	3.78778	+	6.56063i	0.134508	+	0.232975i
$794$		0			0
$795$	−14.6471	+	1.14844i	−0.519480	+	0.0407308i
$796$		0			0
$797$	4.36086	+	1.58722i	0.154469	+	0.0562223i	0.418098	−	0.908402i	$-0.362697\pi$
$797$	4.36086	+	1.58722i	0.154469	+	0.0562223i	−0.263628	+	0.964624i	$0.584919\pi$
$798$		0			0
$799$	−6.24778	−	1.10165i	−0.221031	−	0.0389737i
$800$		0			0
$801$	17.1259	+	14.9049i	0.605113	+	0.526639i
$802$		0			0
$803$	5.04242	−	6.00932i	0.177943	−	0.212064i
$804$		0			0
$805$	5.08693	−	0.896963i	0.179291	−	0.0316138i
$806$		0			0
$807$	−2.04763	+	21.2004i	−0.0720802	+	0.746289i
$808$		0			0
$809$			26.2974i			0.924566i	0.886732	+	0.462283i	$0.152970\pi$
$809$			26.2974i			0.924566i	−0.886732	+	0.462283i	$0.847030\pi$
$810$		0			0
$811$	19.3273			0.678674			0.339337	−	0.940665i	$-0.389797\pi$
$811$	19.3273			0.678674			0.339337	+	0.940665i	$0.389797\pi$
$812$		0			0
$813$	−0.0501533	−	0.00484405i	−0.00175895	−	0.000169888i
$814$		0			0
$815$	1.80664	+	10.2460i	0.0632839	+	0.358901i
$816$		0			0
$817$	−13.4991	−	11.3271i	−0.472275	−	0.396286i
$818$		0			0
$819$	−7.66964	−	22.3167i	−0.267999	−	0.779809i
$820$		0			0
$821$	3.65700	−	20.7399i	0.127630	−	0.723826i	−0.852081	−	0.523410i	$-0.824660\pi$
$821$	3.65700	−	20.7399i	0.127630	−	0.723826i	0.979711	−	0.200416i	$-0.0642294\pi$
$822$		0			0
$823$	−2.88857	+	7.93629i	−0.100689	+	0.276642i	−0.979801	−	0.199974i	$-0.935914\pi$
$823$	−2.88857	+	7.93629i	−0.100689	+	0.276642i	0.879112	+	0.476615i	$0.158137\pi$
$824$		0			0
$825$	−2.41759	−	30.8339i	−0.0841697	−	1.07350i
$826$		0			0
$827$	−28.5829	+	16.5024i	−0.993926	+	0.573843i	−0.906445	−	0.422323i	$-0.861215\pi$
$827$	−28.5829	+	16.5024i	−0.993926	+	0.573843i	−0.0874801	+	0.996166i	$0.527881\pi$
$828$		0			0
$829$	−35.1395	−	20.2878i	−1.22045	−	0.704624i	−0.255432	−	0.966827i	$-0.582218\pi$
$829$	−35.1395	−	20.2878i	−1.22045	−	0.704624i	−0.965013	+	0.262202i	$0.915551\pi$
$830$		0			0
$831$	−15.9048	−	16.1944i	−0.551733	−	0.561777i
$832$		0			0
$833$	−19.8695	−	23.6795i	−0.688436	−	0.820446i
$834$		0			0
$835$	5.27785	−	1.92098i	0.182648	−	0.0664783i
$836$		0			0
$837$	41.6833	−	18.0809i	1.44079	−	0.624966i
$838$		0			0
$839$	18.0300	−	6.56238i	0.622464	−	0.226558i	−0.0114838	−	0.999934i	$-0.503655\pi$
$839$	18.0300	−	6.56238i	0.622464	−	0.226558i	0.633948	+	0.773376i	$0.281433\pi$
$840$		0			0
$841$	−8.51418	+	7.14425i	−0.293593	+	0.246353i
$842$		0			0
$843$	−2.76218	+	9.94877i	−0.0951345	+	0.342654i
$844$		0			0
$845$	3.50023	−	6.06258i	0.120412	−	0.208559i
$846$		0			0
$847$	18.8245	−	10.8683i	0.646816	−	0.373440i
$848$		0			0
$849$	−16.1022	+	33.7334i	−0.552625	+	1.15773i
$850$		0			0
$851$	6.03706	−	16.5867i	0.206948	−	0.568584i
$852$		0			0
$853$	−0.315761	−	0.0556772i	−0.0108114	−	0.00190635i	0.168240	−	0.985746i	$-0.446192\pi$
$853$	−0.315761	−	0.0556772i	−0.0108114	−	0.00190635i	−0.179051	+	0.983840i	$0.557303\pi$
$854$		0			0
$855$	8.19100	+	4.92819i	0.280126	+	0.168540i
$856$		0			0
$857$	−13.5508	+	16.1492i	−0.462887	+	0.551647i	−0.946108	−	0.323851i	$-0.895022\pi$
$857$	−13.5508	+	16.1492i	−0.462887	+	0.551647i	0.483221	+	0.875498i	$0.339467\pi$
$858$		0			0
$859$	−7.24367	−	41.0809i	−0.247151	−	1.40166i	−0.815444	−	0.578836i	$-0.803507\pi$
$859$	−7.24367	−	41.0809i	−0.247151	−	1.40166i	0.568293	−	0.822826i	$-0.307604\pi$
$860$		0			0
$861$	62.6744	−	28.5402i	2.13594	−	0.972647i
$862$		0			0
$863$	−11.7867			−0.401223			−0.200611	−	0.979671i	$-0.564293\pi$
$863$	−11.7867			−0.401223			−0.200611	+	0.979671i	$0.564293\pi$
$864$		0			0
$865$	2.68637			0.0913395
$866$		0			0
$867$	4.17189	+	2.97763i	0.141685	+	0.101126i
$868$		0			0
$869$	−4.57767	−	25.9613i	−0.155287	−	0.880676i
$870$		0			0
$871$	−3.98548	+	4.74971i	−0.135043	+	0.160938i
$872$		0			0
$873$	2.98739	−	7.76880i	0.101108	−	0.262934i
$874$		0			0
$875$	−28.2603	−	4.98306i	−0.955374	−	0.168458i
$876$		0			0
$877$	−3.87782	+	10.6542i	−0.130945	+	0.359768i	−0.987787	−	0.155811i	$-0.950201\pi$
$877$	−3.87782	+	10.6542i	−0.130945	+	0.359768i	0.856842	+	0.515579i	$0.172423\pi$
$878$		0			0
$879$	−0.312019	−	0.454275i	−0.0105241	−	0.0153223i
$880$		0			0
$881$	24.5990	−	14.2023i	0.828763	−	0.478486i	−0.0246662	−	0.999696i	$-0.507852\pi$
$881$	24.5990	−	14.2023i	0.828763	−	0.478486i	0.853429	+	0.521209i	$0.174519\pi$
$882$		0			0
$883$	−3.49495	+	6.05343i	−0.117614	+	0.203714i	−0.918822	−	0.394673i	$-0.870858\pi$
$883$	−3.49495	+	6.05343i	−0.117614	+	0.203714i	0.801207	+	0.598387i	$0.204191\pi$
$884$		0			0
$885$	3.31812	−	0.857087i	0.111537	−	0.0288107i
$886$		0			0
$887$	−28.6087	+	24.0056i	−0.960587	+	0.806028i	−0.981048	−	0.193763i	$-0.937931\pi$
$887$	−28.6087	+	24.0056i	−0.960587	+	0.806028i	0.0204617	+	0.999791i	$0.493486\pi$
$888$		0			0
$889$	72.5972	−	26.4232i	2.43483	−	0.886207i
$890$		0			0
$891$	31.0425	+	19.4482i	1.03996	+	0.651538i
$892$		0			0
$893$	−6.47596	+	2.35706i	−0.216710	+	0.0788759i
$894$		0			0
$895$	6.43382	+	7.66753i	0.215059	+	0.256297i
$896$		0			0
$897$	−5.70787	+	1.47437i	−0.190580	+	0.0492278i
$898$		0			0
$899$	32.0257	+	18.4900i	1.06812	+	0.616677i
$900$		0			0
$901$	35.1630	−	20.3013i	1.17145	−	0.676336i
$902$		0			0
$903$	−24.1369	+	16.5784i	−0.803225	+	0.551695i
$904$		0			0
$905$	0.111276	−	0.305727i	0.00369893	−	0.0101627i
$906$		0			0
$907$	−7.78756	+	44.1654i	−0.258582	+	1.46649i	0.528127	+	0.849165i	$0.322894\pi$
$907$	−7.78756	+	44.1654i	−0.258582	+	1.46649i	−0.786709	+	0.617324i	$0.788217\pi$
$908$		0			0
$909$	−2.90195	−	3.58791i	−0.0962517	−	0.119003i
$910$		0			0
$911$	33.0561	+	27.7374i	1.09520	+	0.918981i	0.997093	−	0.0761949i	$-0.0242771\pi$
$911$	33.0561	+	27.7374i	1.09520	+	0.918981i	0.0981060	+	0.995176i	$0.468722\pi$
$912$		0			0
$913$	−2.71769	−	15.4128i	−0.0899423	−	0.510088i
$914$		0			0
$915$	−2.96242	+	4.15058i	−0.0979345	+	0.137214i
$916$		0			0
$917$	69.0359			2.27977
$918$		0			0
$919$		−	5.21294i		−	0.171959i	−0.996297	−	0.0859796i	$-0.972598\pi$
$919$		−	5.21294i		−	0.171959i	0.996297	−	0.0859796i	$-0.0274020\pi$
$920$		0			0
$921$	−11.5766	+	5.27167i	−0.381462	+	0.173707i
$922$		0			0
$923$	−13.7589	+	2.42606i	−0.452878	+	0.0798547i
$924$		0			0
$925$	−29.4587	+	35.1075i	−0.968596	+	1.15433i
$926$		0			0
$927$	55.9602	+	1.00960i	1.83797	+	0.0331595i
$928$		0			0
$929$	−20.0093	−	3.52818i	−0.656484	−	0.115756i	−0.164523	−	0.986373i	$-0.552609\pi$
$929$	−20.0093	−	3.52818i	−0.656484	−	0.115756i	−0.491961	+	0.870617i	$0.663720\pi$
$930$		0			0
$931$	−31.5536	−	11.4846i	−1.03413	−	0.376391i
$932$		0			0
$933$	14.1334	−	29.6090i	0.462707	−	0.969355i
$934$		0			0
$935$	−5.96955	−	10.3396i	−0.195225	−	0.338140i
$936$		0			0
$937$	8.65752	−	14.9953i	0.282829	−	0.489874i	−0.689251	−	0.724522i	$-0.742060\pi$
$937$	8.65752	−	14.9953i	0.282829	−	0.489874i	0.972080	+	0.234648i	$0.0753938\pi$
$938$		0			0
$939$	44.3555	+	12.3149i	1.44749	+	0.401881i
$940$		0			0
$941$	−9.65680	+	8.10302i	−0.314803	+	0.264151i	−0.786474	−	0.617624i	$-0.788095\pi$
$941$	−9.65680	+	8.10302i	−0.314803	+	0.264151i	0.471671	+	0.881775i	$0.343651\pi$
$942$		0			0
$943$	−5.88420	−	16.1667i	−0.191616	−	0.526460i
$944$		0			0
$945$	11.5318	−	10.9240i	0.375129	−	0.355358i
$946$		0			0
$947$	0.904890	+	2.48616i	0.0294050	+	0.0807895i	0.953526	−	0.301309i	$-0.0974236\pi$
$947$	0.904890	+	2.48616i	0.0294050	+	0.0807895i	−0.924122	+	0.382099i	$0.875201\pi$
$948$		0			0
$949$	2.49546	+	2.97398i	0.0810061	+	0.0965394i
$950$		0			0
$951$	−19.6583	+	19.3068i	−0.637463	+	0.626066i
$952$		0			0
$953$	−11.5984	−	6.69633i	−0.375708	−	0.216915i	0.300241	−	0.953863i	$-0.402933\pi$
$953$	−11.5984	−	6.69633i	−0.375708	−	0.216915i	−0.675949	+	0.736948i	$0.736266\pi$
$954$		0			0
$955$	−10.3928	−	18.0009i	−0.336303	−	0.582495i
$956$		0			0
$957$	2.33049	+	29.7230i	0.0753340	+	0.960809i
$958$		0			0
$959$	52.3421	+	19.0510i	1.69022	+	0.615188i
$960$		0			0
$961$	−7.89401	+	44.7692i	−0.254646	+	1.44417i
$962$		0			0
$963$	4.16620	−	21.3664i	0.134254	−	0.688522i
$964$		0			0
$965$	−7.02578	−	5.89533i	−0.226168	−	0.189777i
$966$		0			0
$967$	−4.36499	+	0.769665i	−0.140369	+	0.0247508i	−0.243391	−	0.969928i	$-0.578260\pi$
$967$	−4.36499	+	0.769665i	−0.140369	+	0.0247508i	0.103022	+	0.994679i	$0.467149\pi$
$968$		0			0
$969$	−26.2954	−	2.53973i	−0.844729	−	0.0815880i
$970$		0			0
$971$			41.6830i			1.33767i	0.743411	+	0.668835i	$0.233207\pi$
$971$			41.6830i			1.33767i	−0.743411	+	0.668835i	$0.766793\pi$
$972$		0			0
$973$		−	70.9881i		−	2.27577i
$974$		0			0
$975$	15.2355	+	1.47151i	0.487925	+	0.0471262i
$976$		0			0
$977$	−40.5330	+	7.14705i	−1.29676	+	0.228655i	−0.779084	−	0.626920i	$-0.784315\pi$
$977$	−40.5330	+	7.14705i	−1.29676	+	0.228655i	−0.517680	+	0.855574i	$0.673204\pi$
$978$		0			0
$979$	−23.5960	−	19.7994i	−0.754133	−	0.632793i
$980$		0			0
$981$	−2.58827	+	13.2740i	−0.0826371	+	0.423805i
$982$		0			0
$983$	−2.36427	+	13.4084i	−0.0754085	+	0.427663i	0.923609	+	0.383337i	$0.125225\pi$
$983$	−2.36427	+	13.4084i	−0.0754085	+	0.427663i	−0.999017	+	0.0443262i	$0.985886\pi$
$984$		0			0
$985$	16.0214	+	5.83130i	0.510483	+	0.185801i
$986$		0			0
$987$	0.895136	+	11.4166i	0.0284925	+	0.363393i
$988$		0			0
$989$	3.65760	+	6.33516i	0.116305	+	0.201446i
$990$		0			0
$991$	−20.9495	−	12.0952i	−0.665484	−	0.384218i	0.128879	−	0.991660i	$-0.458862\pi$
$991$	−20.9495	−	12.0952i	−0.665484	−	0.384218i	−0.794363	+	0.607443i	$0.792195\pi$
$992$		0			0
$993$	6.14928	−	6.03934i	0.195141	−	0.191653i
$994$		0			0
$995$	−0.392166	−	0.467366i	−0.0124325	−	0.0148165i
$996$		0			0
$997$	2.22417	+	6.11086i	0.0704402	+	0.193533i	0.969917	−	0.243435i	$-0.0782744\pi$
$997$	2.22417	+	6.11086i	0.0704402	+	0.193533i	−0.899477	+	0.436968i	$0.856052\pi$
$998$		0			0
$999$	−12.6251	−	52.7916i	−0.399439	−	1.67025i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.bh.b.47.17		192
4.3	odd	2		216.2.v.b.155.13	yes	192
8.3	odd	2	inner	864.2.bh.b.47.18		192
8.5	even	2		216.2.v.b.155.27	yes	192
12.11	even	2		648.2.v.b.467.20		192
24.5	odd	2		648.2.v.b.467.6		192
27.23	odd	18	inner	864.2.bh.b.239.18		192
108.23	even	18		216.2.v.b.131.27	yes	192
108.31	odd	18		648.2.v.b.179.6		192
216.77	odd	18		216.2.v.b.131.13	✓	192
216.85	even	18		648.2.v.b.179.20		192
216.131	even	18	inner	864.2.bh.b.239.17		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.v.b.131.13	✓	192	216.77	odd	18
216.2.v.b.131.27	yes	192	108.23	even	18
216.2.v.b.155.13	yes	192	4.3	odd	2
216.2.v.b.155.27	yes	192	8.5	even	2
648.2.v.b.179.6		192	108.31	odd	18
648.2.v.b.179.20		192	216.85	even	18
648.2.v.b.467.6		192	24.5	odd	2
648.2.v.b.467.20		192	12.11	even	2
864.2.bh.b.47.17		192	1.1	even	1	trivial
864.2.bh.b.47.18		192	8.3	odd	2	inner
864.2.bh.b.239.17		192	216.131	even	18	inner
864.2.bh.b.239.18		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)

\(f(q)\)	\(=\)	\(q+(0.166515 - 1.72403i) q^{3} +(-0.135936 - 0.770931i) q^{5} +(2.51012 - 2.99144i) q^{7} +(-2.94455 - 0.574153i) q^{9} +O(q^{10})\)	\(q+(0.166515 - 1.72403i) q^{3} +(-0.135936 - 0.770931i) q^{5} +(2.51012 - 2.99144i) q^{7} +(-2.94455 - 0.574153i) q^{9} +(4.00834 + 0.706778i) q^{11} +(-0.688932 + 1.89283i) q^{13} +(-1.35174 + 0.105986i) q^{15} +(3.24509 - 1.87355i) q^{17} +(2.03521 - 3.52509i) q^{19} +(-4.73936 - 4.82563i) q^{21} +(-1.29440 + 1.08613i) q^{23} +(4.12261 - 1.50051i) q^{25} +(-1.48017 + 4.98087i) q^{27} +(-3.97408 + 1.44645i) q^{29} +(-5.62062 - 6.69839i) q^{31} +(1.88595 - 6.79279i) q^{33} +(-2.64741 - 1.52848i) q^{35} +(-9.04670 + 5.22312i) q^{37} +(3.14857 + 1.50292i) q^{39} +(-3.48236 + 9.56770i) q^{41} +(0.751767 - 4.26348i) q^{43} +(-0.0423626 + 2.34809i) q^{45} +(-1.29698 - 1.08829i) q^{47} +(-1.43250 - 8.12409i) q^{49} +(-2.68970 - 5.90659i) q^{51} +10.8358 q^{53} -3.18622i q^{55} +(-5.73846 - 4.09574i) q^{57} +(-2.48911 + 0.438898i) q^{59} +(2.41745 - 2.88100i) q^{61} +(-9.10870 + 7.36725i) q^{63} +(1.55289 + 0.273816i) q^{65} +(2.89251 + 1.05279i) q^{67} +(1.65698 + 2.41244i) q^{69} +(3.46797 + 6.00671i) q^{71} +(0.963671 - 1.66913i) q^{73} +(-1.90044 - 7.35735i) q^{75} +(12.1757 - 10.2166i) q^{77} +(-2.21520 - 6.08622i) q^{79} +(8.34070 + 3.38124i) q^{81} +(-1.31513 - 3.61329i) q^{83} +(-1.88550 - 2.24705i) q^{85} +(1.83197 + 7.09228i) q^{87} +(-6.55395 - 3.78393i) q^{89} +(3.93298 + 6.81212i) q^{91} +(-12.4841 + 8.57472i) q^{93} +(-2.99426 - 1.08982i) q^{95} +(-0.481780 + 2.73231i) q^{97} +(-11.3969 - 4.38254i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 12 q^{3} - 12 q^{9}+O(q^{10}) \) 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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