LMFDB - Embedded newform 864.2.y.b.193.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(97,864)]

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([0, 0, 4]))

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

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

chi := DirichletCharacter("864.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.y (of order $9$, degree $6$, 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:	$54$
Relative dimension:	$9$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			193.3
Character	$\chi$	$=$	864.193
Dual form			864.2.y.b.385.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.661519 - 1.60075i) q^{3} +(0.197119 - 1.11792i) q^{5} +(-0.270013 + 0.226568i) q^{7} +(-2.12478 + 2.11785i) q^{9} +O(q^{10})$	\(q+(-0.661519 - 1.60075i) q^{3} +(0.197119 - 1.11792i) q^{5} +(-0.270013 + 0.226568i) q^{7} +(-2.12478 + 2.11785i) q^{9} +(-0.174455 - 0.989381i) q^{11} +(-5.97001 + 2.17291i) q^{13} +(-1.91990 + 0.423986i) q^{15} +(-3.41720 + 5.91877i) q^{17} +(-1.81718 - 3.14745i) q^{19} +(0.541297 + 0.282344i) q^{21} +(0.200373 + 0.168133i) q^{23} +(3.48758 + 1.26938i) q^{25} +(4.79573 + 2.00024i) q^{27} +(2.52890 + 0.920444i) q^{29} +(-5.72245 - 4.80171i) q^{31} +(-1.46834 + 0.933752i) q^{33} +(0.200059 + 0.346513i) q^{35} +(-0.563717 + 0.976387i) q^{37} +(7.42756 + 8.11906i) q^{39} +(1.79162 - 0.652095i) q^{41} +(-1.06676 - 6.04992i) q^{43} +(1.94874 + 2.79280i) q^{45} +(-8.56245 + 7.18475i) q^{47} +(-1.19396 + 6.77130i) q^{49} +(11.7350 + 1.55470i) q^{51} -8.69660 q^{53} -1.14043 q^{55} +(-3.83617 + 4.99095i) q^{57} +(-1.32731 + 7.52756i) q^{59} +(-0.448757 + 0.376552i) q^{61} +(0.0938827 - 1.05326i) q^{63} +(1.25233 + 7.10230i) q^{65} +(10.0913 - 3.67293i) q^{67} +(0.136587 - 0.431969i) q^{69} +(-5.00739 + 8.67305i) q^{71} +(-2.49979 - 4.32977i) q^{73} +(-0.275152 - 6.42246i) q^{75} +(0.271267 + 0.227620i) q^{77} +(-0.961498 - 0.349957i) q^{79} +(0.0294179 - 8.99995i) q^{81} +(7.77701 + 2.83060i) q^{83} +(5.94309 + 4.98685i) q^{85} +(-0.199517 - 4.65702i) q^{87} +(-3.70362 - 6.41486i) q^{89} +(1.11967 - 1.93933i) q^{91} +(-3.90081 + 12.3366i) q^{93} +(-3.87679 + 1.41104i) q^{95} +(-1.66356 - 9.43453i) q^{97} +(2.46604 + 1.73275i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q+O(q^{10}) $ 54 * q	$ 54 q - 9 q^{11} + 12 q^{17} + 18 q^{19} + 12 q^{21} - 21 q^{27} + 6 q^{29} + 36 q^{31} - 9 q^{33} + 24 q^{39} + 3 q^{41} - 21 q^{43} + 42 q^{45} - 18 q^{49} + 24 q^{51} + 36 q^{53} - 72 q^{55} + 39 q^{57} + 18 q^{59} - 18 q^{61} - 30 q^{63} + 48 q^{65} - 27 q^{67} + 24 q^{69} - 84 q^{75} + 36 q^{77} + 72 q^{79} + 36 q^{81} + 6 q^{87} + 33 q^{89} + 36 q^{91} + 72 q^{93} + 36 q^{95} + 9 q^{97} + 120 q^{99}+O(q^{100}) $ 54 * q - 9 * q^11 + 12 * q^17 + 18 * q^19 + 12 * q^21 - 21 * q^27 + 6 * q^29 + 36 * q^31 - 9 * q^33 + 24 * q^39 + 3 * q^41 - 21 * q^43 + 42 * q^45 - 18 * q^49 + 24 * q^51 + 36 * q^53 - 72 * q^55 + 39 * q^57 + 18 * q^59 - 18 * q^61 - 30 * q^63 + 48 * q^65 - 27 * q^67 + 24 * q^69 - 84 * q^75 + 36 * q^77 + 72 * q^79 + 36 * q^81 + 6 * q^87 + 33 * q^89 + 36 * q^91 + 72 * q^93 + 36 * q^95 + 9 * q^97 + 120 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$325$	$353$	$703$
$\chi(n)$	$1$	$e\left(\frac{1}{9}\right)$	$1$

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
$3$	−0.661519	−	1.60075i	−0.381928	−	0.924192i
$3$	−0.661519	−	1.60075i	−0.381928	−	0.924192i
$4$		0			0
$5$	0.197119	−	1.11792i	0.0881542	−	0.499947i	−0.908477	−	0.417935i	$-0.862754\pi$
$5$	0.197119	−	1.11792i	0.0881542	−	0.499947i	0.996631	−	0.0820126i	$-0.0261348\pi$
$6$		0			0
$7$	−0.270013	+	0.226568i	−0.102055	+	0.0856346i	−0.692388	−	0.721526i	$-0.743441\pi$
$7$	−0.270013	+	0.226568i	−0.102055	+	0.0856346i	0.590332	+	0.807160i	$0.298997\pi$
$8$		0			0
$9$	−2.12478	+	2.11785i	−0.708261	+	0.705950i
$10$		0			0
$11$	−0.174455	−	0.989381i	−0.0526000	−	0.298310i	0.947147	−	0.320800i	$-0.103952\pi$
$11$	−0.174455	−	0.989381i	−0.0526000	−	0.298310i	−0.999747	+	0.0224902i	$0.992841\pi$
$12$		0			0
$13$	−5.97001	+	2.17291i	−1.65578	+	0.602656i	−0.989692	−	0.143213i	$-0.954257\pi$
$13$	−5.97001	+	2.17291i	−1.65578	+	0.602656i	−0.666092	+	0.745869i	$0.732034\pi$
$14$		0			0
$15$	−1.91990	+	0.423986i	−0.495716	+	0.109473i
$16$		0			0
$17$	−3.41720	+	5.91877i	−0.828794	+	1.43551i	0.0701913	+	0.997534i	$0.477639\pi$
$17$	−3.41720	+	5.91877i	−0.828794	+	1.43551i	−0.898985	+	0.437979i	$0.855694\pi$
$18$		0			0
$19$	−1.81718	−	3.14745i	−0.416890	−	0.722075i	0.578735	−	0.815516i	$-0.303547\pi$
$19$	−1.81718	−	3.14745i	−0.416890	−	0.722075i	−0.995625	+	0.0934409i	$0.970213\pi$
$20$		0			0
$21$	0.541297	+	0.282344i	0.118121	+	0.0616125i
$22$		0			0
$23$	0.200373	+	0.168133i	0.0417806	+	0.0350581i	0.663439	−	0.748231i	$-0.269096\pi$
$23$	0.200373	+	0.168133i	0.0417806	+	0.0350581i	−0.621658	+	0.783289i	$0.713541\pi$
$24$		0			0
$25$	3.48758	+	1.26938i	0.697517	+	0.253875i
$26$		0			0
$27$	4.79573	+	2.00024i	0.922939	+	0.384947i
$28$		0			0
$29$	2.52890	+	0.920444i	0.469605	+	0.170922i	0.565973	−	0.824424i	$-0.308500\pi$
$29$	2.52890	+	0.920444i	0.469605	+	0.170922i	−0.0963685	+	0.995346i	$0.530723\pi$
$30$		0			0
$31$	−5.72245	−	4.80171i	−1.02778	−	0.862412i	−0.0371975	−	0.999308i	$-0.511843\pi$
$31$	−5.72245	−	4.80171i	−1.02778	−	0.862412i	−0.990585	+	0.136896i	$0.956288\pi$
$32$		0			0
$33$	−1.46834	+	0.933752i	−0.255606	+	0.162545i
$34$		0			0
$35$	0.200059	+	0.346513i	0.0338162	+	0.0585714i
$36$		0			0
$37$	−0.563717	+	0.976387i	−0.0926746	+	0.160517i	−0.908636	−	0.417590i	$-0.862875\pi$
$37$	−0.563717	+	0.976387i	−0.0926746	+	0.160517i	0.815961	+	0.578107i	$0.196208\pi$
$38$		0			0
$39$	7.42756	+	8.11906i	1.18936	+	1.30009i
$40$		0			0
$41$	1.79162	−	0.652095i	0.279804	−	0.101840i	−0.198307	−	0.980140i	$-0.563544\pi$
$41$	1.79162	−	0.652095i	0.279804	−	0.101840i	0.478110	+	0.878300i	$0.341322\pi$
$42$		0			0
$43$	−1.06676	−	6.04992i	−0.162680	−	0.922605i	−0.951424	−	0.307883i	$-0.900379\pi$
$43$	−1.06676	−	6.04992i	−0.162680	−	0.922605i	0.788744	−	0.614722i	$-0.210732\pi$
$44$		0			0
$45$	1.94874	+	2.79280i	0.290502	+	0.416326i
$46$		0			0
$47$	−8.56245	+	7.18475i	−1.24896	+	1.04800i	−0.252193	+	0.967677i	$0.581152\pi$
$47$	−8.56245	+	7.18475i	−1.24896	+	1.04800i	−0.996769	+	0.0803259i	$0.974404\pi$
$48$		0			0
$49$	−1.19396	+	6.77130i	−0.170566	+	0.967329i
$50$		0			0
$51$	11.7350	+	1.55470i	1.64323	+	0.217701i
$52$		0			0
$53$	−8.69660			−1.19457			−0.597285	−	0.802029i	$-0.703754\pi$
$53$	−8.69660			−1.19457			−0.597285	+	0.802029i	$0.703754\pi$
$54$		0			0
$55$	−1.14043			−0.153776
$56$		0			0
$57$	−3.83617	+	4.99095i	−0.508114	+	0.661067i
$58$		0			0
$59$	−1.32731	+	7.52756i	−0.172801	+	0.980004i	0.767850	+	0.640630i	$0.221327\pi$
$59$	−1.32731	+	7.52756i	−0.172801	+	0.980004i	−0.940651	+	0.339375i	$0.889785\pi$
$60$		0			0
$61$	−0.448757	+	0.376552i	−0.0574574	+	0.0482125i	−0.671064	−	0.741399i	$-0.734162\pi$
$61$	−0.448757	+	0.376552i	−0.0574574	+	0.0482125i	0.613607	+	0.789612i	$0.289718\pi$
$62$		0			0
$63$	0.0938827	−	1.05326i	0.0118281	−	0.132698i
$64$		0			0
$65$	1.25233	+	7.10230i	0.155332	+	0.880931i
$66$		0			0
$67$	10.0913	−	3.67293i	1.23285	−	0.448720i	0.358276	−	0.933616i	$-0.383365\pi$
$67$	10.0913	−	3.67293i	1.23285	−	0.448720i	0.874572	+	0.484896i	$0.161142\pi$
$68$		0			0
$69$	0.136587	−	0.431969i	0.0164432	−	0.0520029i
$70$		0			0
$71$	−5.00739	+	8.67305i	−0.594268	+	1.02930i	0.399382	+	0.916785i	$0.369225\pi$
$71$	−5.00739	+	8.67305i	−0.594268	+	1.02930i	−0.993650	+	0.112517i	$0.964109\pi$
$72$		0			0
$73$	−2.49979	−	4.32977i	−0.292579	−	0.506761i	0.681840	−	0.731501i	$-0.261180\pi$
$73$	−2.49979	−	4.32977i	−0.292579	−	0.506761i	−0.974419	+	0.224740i	$0.927847\pi$
$74$		0			0
$75$	−0.275152	−	6.42246i	−0.0317719	−	0.741601i
$76$		0			0
$77$	0.271267	+	0.227620i	0.0309137	+	0.0259397i
$78$		0			0
$79$	−0.961498	−	0.349957i	−0.108177	−	0.0393732i	0.287365	−	0.957821i	$-0.407221\pi$
$79$	−0.961498	−	0.349957i	−0.108177	−	0.0393732i	−0.395542	+	0.918448i	$0.629443\pi$
$80$		0			0
$81$	0.0294179	−	8.99995i	0.00326866	−	0.999995i
$82$		0			0
$83$	7.77701	+	2.83060i	0.853637	+	0.310699i	0.731522	−	0.681817i	$-0.238810\pi$
$83$	7.77701	+	2.83060i	0.853637	+	0.310699i	0.122115	+	0.992516i	$0.461032\pi$
$84$		0			0
$85$	5.94309	+	4.98685i	0.644619	+	0.540900i
$86$		0			0
$87$	−0.199517	−	4.65702i	−0.0213905	−	0.499285i
$88$		0			0
$89$	−3.70362	−	6.41486i	−0.392583	−	0.679973i	0.600207	−	0.799845i	$-0.295085\pi$
$89$	−3.70362	−	6.41486i	−0.392583	−	0.679973i	−0.992789	+	0.119872i	$0.961752\pi$
$90$		0			0
$91$	1.11967	−	1.93933i	0.117373	−	0.203297i
$92$		0			0
$93$	−3.90081	+	12.3366i	−0.404495	+	1.27925i
$94$		0			0
$95$	−3.87679	+	1.41104i	−0.397750	+	0.144769i
$96$		0			0
$97$	−1.66356	−	9.43453i	−0.168909	−	0.957931i	−0.944942	−	0.327238i	$-0.893882\pi$
$97$	−1.66356	−	9.43453i	−0.168909	−	0.957931i	0.776033	−	0.630693i	$-0.217229\pi$
$98$		0			0
$99$	2.46604	+	1.73275i	0.247846	+	0.174148i
$100$		0			0
$101$	0.904353	−	0.758842i	0.0899865	−	0.0755076i	−0.596685	−	0.802476i	$-0.703516\pi$
$101$	0.904353	−	0.758842i	0.0899865	−	0.0755076i	0.686671	+	0.726968i	$0.259071\pi$
$102$		0			0
$103$	−1.55362	+	8.81102i	−0.153083	+	0.868176i	0.807435	+	0.589957i	$0.200855\pi$
$103$	−1.55362	+	8.81102i	−0.153083	+	0.868176i	−0.960518	+	0.278219i	$0.910256\pi$
$104$		0			0
$105$	0.422336	−	0.549469i	0.0412158	−	0.0536227i
$106$		0			0
$107$	−7.43537			−0.718804			−0.359402	−	0.933183i	$-0.617019\pi$
$107$	−7.43537			−0.718804			−0.359402	+	0.933183i	$0.617019\pi$
$108$		0			0
$109$	−12.1862			−1.16723			−0.583613	−	0.812032i	$-0.698361\pi$
$109$	−12.1862			−1.16723			−0.583613	+	0.812032i	$0.698361\pi$
$110$		0			0
$111$	1.93586	+	0.256470i	0.183744	+	0.0243431i
$112$		0			0
$113$	−0.233045	+	1.32166i	−0.0219230	+	0.124332i	−0.993805	−	0.111136i	$-0.964551\pi$
$113$	−0.233045	+	1.32166i	−0.0219230	+	0.124332i	0.971882	+	0.235468i	$0.0756622\pi$
$114$		0			0
$115$	0.227455	−	0.190858i	0.0212103	−	0.0177976i
$116$		0			0
$117$	8.08310	−	17.2606i	0.747283	−	1.59574i
$118$		0			0
$119$	−0.418314	−	2.37238i	−0.0383468	−	0.217475i
$120$		0			0
$121$	9.38818	−	3.41702i	0.853471	−	0.310638i
$122$		0			0
$123$	−2.22903	−	2.43655i	−0.200985	−	0.219697i
$124$		0			0
$125$	4.94443	−	8.56400i	0.442243	−	0.765987i
$126$		0			0
$127$	−4.94881	−	8.57158i	−0.439136	−	0.760605i	0.558487	−	0.829513i	$-0.311382\pi$
$127$	−4.94881	−	8.57158i	−0.439136	−	0.760605i	−0.997623	+	0.0689078i	$0.978049\pi$
$128$		0			0
$129$	−8.97871	+	5.70976i	−0.790532	+	0.502717i
$130$		0			0
$131$	−8.99616	−	7.54867i	−0.785998	−	0.659530i	0.158754	−	0.987318i	$-0.449252\pi$
$131$	−8.99616	−	7.54867i	−0.785998	−	0.659530i	−0.944751	+	0.327788i	$0.893697\pi$
$132$		0			0
$133$	1.20377	+	0.438138i	0.104381	+	0.0379914i
$134$		0			0
$135$	3.18143	−	4.96694i	0.273814	−	0.427486i
$136$		0			0
$137$	7.84492	+	2.85532i	0.670237	+	0.243946i	0.654650	−	0.755932i	$-0.272816\pi$
$137$	7.84492	+	2.85532i	0.670237	+	0.243946i	0.0155870	+	0.999879i	$0.495038\pi$
$138$		0			0
$139$	−14.5541	−	12.2123i	−1.23446	−	1.03584i	−0.997936	−	0.0642116i	$-0.979547\pi$
$139$	−14.5541	−	12.2123i	−1.23446	−	1.03584i	−0.236526	−	0.971625i	$-0.576009\pi$
$140$		0			0
$141$	17.1652	+	8.95347i	1.44557	+	0.754018i
$142$		0			0
$143$	3.19133	+	5.52754i	0.266872	+	0.462237i
$144$		0			0
$145$	1.52747	−	2.64566i	0.126850	−	0.219710i
$146$		0			0
$147$	11.6290	−	2.56811i	0.959142	−	0.211814i
$148$		0			0
$149$	8.08932	−	2.94427i	0.662703	−	0.241204i	0.0112999	−	0.999936i	$-0.496403\pi$
$149$	8.08932	−	2.94427i	0.662703	−	0.241204i	0.651403	+	0.758732i	$0.274181\pi$
$150$		0			0
$151$	−3.46966	−	19.6774i	−0.282357	−	1.60133i	−0.714575	−	0.699559i	$-0.753380\pi$
$151$	−3.46966	−	19.6774i	−0.282357	−	1.60133i	0.432218	−	0.901769i	$-0.357731\pi$
$152$		0			0
$153$	−5.27425	−	19.8132i	−0.426398	−	1.60181i
$154$		0			0
$155$	−6.49591	+	5.45072i	−0.521764	+	0.437812i
$156$		0			0
$157$	−1.97900	+	11.2234i	−0.157941	+	0.895729i	0.798106	+	0.602517i	$0.205835\pi$
$157$	−1.97900	+	11.2234i	−0.157941	+	0.895729i	−0.956047	+	0.293212i	$0.905276\pi$
$158$		0			0
$159$	5.75297	+	13.9211i	0.456240	+	1.10401i
$160$		0			0
$161$	−0.0921967			−0.00726612
$162$		0			0
$163$	−5.60010			−0.438633			−0.219317	−	0.975654i	$-0.570383\pi$
$163$	−5.60010			−0.438633			−0.219317	+	0.975654i	$0.570383\pi$
$164$		0			0
$165$	0.754418	+	1.82555i	0.0587314	+	0.142118i
$166$		0			0
$167$	−2.66909	+	15.1372i	−0.206541	+	1.17135i	0.688457	+	0.725278i	$0.258289\pi$
$167$	−2.66909	+	15.1372i	−0.206541	+	1.17135i	−0.894997	+	0.446072i	$0.852823\pi$
$168$		0			0
$169$	20.9610	−	17.5883i	1.61238	−	1.35295i
$170$		0			0
$171$	10.5270	+	2.83914i	0.805016	+	0.217114i
$172$		0			0
$173$	−0.450506	−	2.55495i	−0.0342514	−	0.194249i	0.962881	−	0.269926i	$-0.0869993\pi$
$173$	−0.450506	−	2.55495i	−0.0342514	−	0.194249i	−0.997132	+	0.0756771i	$0.975888\pi$
$174$		0			0
$175$	−1.22929	+	0.447426i	−0.0929258	+	0.0338222i
$176$		0			0
$177$	12.9278	−	2.85493i	0.971710	−	0.214590i
$178$		0			0
$179$	1.80474	−	3.12590i	0.134893	−	0.233641i	−0.790664	−	0.612250i	$-0.790264\pi$
$179$	1.80474	−	3.12590i	0.134893	−	0.233641i	0.925556	+	0.378610i	$0.123598\pi$
$180$		0			0
$181$	−5.28962	−	9.16189i	−0.393174	−	0.680998i	0.599692	−	0.800231i	$-0.295290\pi$
$181$	−5.28962	−	9.16189i	−0.393174	−	0.680998i	−0.992866	+	0.119233i	$0.961956\pi$
$182$		0			0
$183$	0.899626	+	0.469250i	0.0665022	+	0.0346880i
$184$		0			0
$185$	0.980400	+	0.822653i	0.0720804	+	0.0604826i
$186$		0			0
$187$	6.45207	+	2.34836i	0.471822	+	0.171729i
$188$		0			0
$189$	−1.74810	+	0.546466i	−0.127156	+	0.0397496i
$190$		0			0
$191$	−18.5529	−	6.75272i	−1.34244	−	0.488610i	−0.431863	−	0.901939i	$-0.642143\pi$
$191$	−18.5529	−	6.75272i	−1.34244	−	0.488610i	−0.910581	+	0.413330i	$0.864366\pi$
$192$		0			0
$193$	−0.305206	−	0.256098i	−0.0219692	−	0.0184343i	0.631737	−	0.775183i	$-0.282342\pi$
$193$	−0.305206	−	0.256098i	−0.0219692	−	0.0184343i	−0.653706	+	0.756749i	$0.726787\pi$
$194$		0			0
$195$	10.5405	−	6.70296i	0.754824	−	0.480009i
$196$		0			0
$197$	−3.80979	−	6.59874i	−0.271436	−	0.470141i	0.697794	−	0.716299i	$-0.254165\pi$
$197$	−3.80979	−	6.59874i	−0.271436	−	0.470141i	−0.969230	+	0.246158i	$0.920832\pi$
$198$		0			0
$199$	9.53510	−	16.5153i	0.675925	−	1.17074i	−0.300272	−	0.953853i	$-0.597078\pi$
$199$	9.53510	−	16.5153i	0.675925	−	1.17074i	0.976198	−	0.216883i	$-0.0695891\pi$
$200$		0			0
$201$	−12.5550	−	13.7239i	−0.885563	−	0.968009i
$202$		0			0
$203$	−0.891380	+	0.324436i	−0.0625626	+	0.0227709i
$204$		0			0
$205$	−0.375826	−	2.13142i	−0.0262489	−	0.148865i
$206$		0			0
$207$	−0.781828	+	0.0671137i	−0.0543408	+	0.00466473i
$208$		0			0
$209$	−2.79701	+	2.34697i	−0.193473	+	0.162343i
$210$		0			0
$211$	3.95089	−	22.4066i	0.271990	−	1.54253i	−0.476372	−	0.879244i	$-0.658049\pi$
$211$	3.95089	−	22.4066i	0.271990	−	1.54253i	0.748363	−	0.663290i	$-0.230840\pi$
$212$		0			0
$213$	17.1958	+	2.27817i	1.17824	+	0.156098i
$214$		0			0
$215$	−6.97359			−0.475595
$216$		0			0
$217$	2.63305			0.178743
$218$		0			0
$219$	−5.27721	+	6.86577i	−0.356601	+	0.463945i
$220$		0			0
$221$	7.53982	−	42.7604i	0.507183	−	2.87638i
$222$		0			0
$223$	−17.8621	+	14.9881i	−1.19613	+	1.00368i	−0.196403	+	0.980523i	$0.562926\pi$
$223$	−17.8621	+	14.9881i	−1.19613	+	1.00368i	−0.999732	+	0.0231532i	$0.992629\pi$
$224$		0			0
$225$	−10.0987	+	4.68903i	−0.673247	+	0.312602i
$226$		0			0
$227$	4.94722	+	28.0571i	0.328358	+	1.86221i	0.484940	+	0.874547i	$0.338841\pi$
$227$	4.94722	+	28.0571i	0.328358	+	1.86221i	−0.156582	+	0.987665i	$0.550048\pi$
$228$		0			0
$229$	−13.0057	+	4.73367i	−0.859438	+	0.312810i	−0.733882	−	0.679277i	$-0.762294\pi$
$229$	−13.0057	+	4.73367i	−0.859438	+	0.312810i	−0.125556	+	0.992087i	$0.540071\pi$
$230$		0			0
$231$	0.184914	−	0.584805i	0.0121664	−	0.0384774i
$232$		0			0
$233$	−14.0225	+	24.2877i	−0.918644	+	1.59114i	−0.117167	+	0.993112i	$0.537381\pi$
$233$	−14.0225	+	24.2877i	−0.918644	+	1.59114i	−0.801477	+	0.598026i	$0.795952\pi$
$234$		0			0
$235$	6.34412	+	10.9883i	0.413845	+	0.716801i
$236$		0			0
$237$	0.0758573	+	1.77062i	0.00492746	+	0.115014i
$238$		0			0
$239$	8.59901	+	7.21542i	0.556224	+	0.466727i	0.877042	−	0.480414i	$-0.159513\pi$
$239$	8.59901	+	7.21542i	0.556224	+	0.466727i	−0.320818	+	0.947141i	$0.603958\pi$
$240$		0			0
$241$	15.1216	+	5.50382i	0.974070	+	0.354533i	0.779532	−	0.626362i	$-0.215457\pi$
$241$	15.1216	+	5.50382i	0.974070	+	0.354533i	0.194538	+	0.980895i	$0.437679\pi$
$242$		0			0
$243$	−14.4261	+	5.90655i	−0.925435	+	0.378905i
$244$		0			0
$245$	7.33439	+	2.66950i	0.468577	+	0.170548i
$246$		0			0
$247$	17.6877	+	14.8418i	1.12544	+	0.944359i
$248$		0			0
$249$	−0.613566	−	14.3215i	−0.0388832	−	0.907589i
$250$		0			0
$251$	−2.38678	−	4.13402i	−0.150652	−	0.260937i	0.780815	−	0.624762i	$-0.214804\pi$
$251$	−2.38678	−	4.13402i	−0.150652	−	0.260937i	−0.931467	+	0.363825i	$0.881471\pi$
$252$		0			0
$253$	0.131391	−	0.227576i	0.00826050	−	0.0143076i
$254$		0			0
$255$	4.05121	−	12.8123i	0.253697	−	0.802337i
$256$		0			0
$257$	22.7312	−	8.27347i	1.41793	−	0.516085i	0.484484	−	0.874800i	$-0.339007\pi$
$257$	22.7312	−	8.27347i	1.41793	−	0.516085i	0.933447	+	0.358715i	$0.116785\pi$
$258$		0			0
$259$	−0.0690069	−	0.391358i	−0.00428788	−	0.0243178i
$260$		0			0
$261$	−7.32273	+	3.40009i	−0.453266	+	0.210460i
$262$		0			0
$263$	24.1834	−	20.2923i	1.49121	−	1.25128i	0.598116	−	0.801409i	$-0.295916\pi$
$263$	24.1834	−	20.2923i	1.49121	−	1.25128i	0.893096	−	0.449866i	$-0.148528\pi$
$264$		0			0
$265$	−1.71426	+	9.72207i	−0.105306	+	0.597222i
$266$		0			0
$267$	−7.81855	+	10.1721i	−0.478487	+	0.622523i
$268$		0			0
$269$	−21.7911			−1.32863			−0.664314	−	0.747454i	$-0.731276\pi$
$269$	−21.7911			−1.32863			−0.664314	+	0.747454i	$0.731276\pi$
$270$		0			0
$271$	5.92553			0.359950			0.179975	−	0.983671i	$-0.442398\pi$
$271$	5.92553			0.359950			0.179975	+	0.983671i	$0.442398\pi$
$272$		0			0
$273$	−3.84506	−	0.509408i	−0.232714	−	0.0308308i
$274$		0			0
$275$	0.647472	−	3.67200i	0.0390440	−	0.221430i
$276$		0			0
$277$	14.0419	−	11.7826i	0.843696	−	0.707945i	−0.114696	−	0.993401i	$-0.536589\pi$
$277$	14.0419	−	11.7826i	0.843696	−	0.707945i	0.958392	+	0.285456i	$0.0921449\pi$
$278$		0			0
$279$	22.3283	−	1.91671i	1.33676	−	0.114750i
$280$		0			0
$281$	5.13446	+	29.1190i	0.306296	+	1.73709i	0.617339	+	0.786697i	$0.288211\pi$
$281$	5.13446	+	29.1190i	0.306296	+	1.73709i	−0.311043	+	0.950396i	$0.600678\pi$
$282$		0			0
$283$	−22.5780	+	8.21771i	−1.34212	+	0.488492i	−0.910480	−	0.413554i	$-0.864287\pi$
$283$	−22.5780	+	8.21771i	−1.34212	+	0.488492i	−0.431641	+	0.902046i	$0.642065\pi$
$284$		0			0
$285$	4.82328	+	5.27233i	0.285706	+	0.312306i
$286$		0			0
$287$	−0.336016	+	0.581997i	−0.0198344	+	0.0343542i
$288$		0			0
$289$	−14.8546	−	25.7289i	−0.873798	−	1.51346i
$290$		0			0
$291$	−14.0018	+	8.90406i	−0.820801	+	0.521966i
$292$		0			0
$293$	−11.6795	−	9.80023i	−0.682321	−	0.572536i	0.234362	−	0.972149i	$-0.424700\pi$
$293$	−11.6795	−	9.80023i	−0.682321	−	0.572536i	−0.916684	+	0.399614i	$0.869144\pi$
$294$		0			0
$295$	8.15354	+	2.96764i	0.474717	+	0.172783i
$296$		0			0
$297$	1.14237	−	5.09376i	0.0662868	−	0.295570i
$298$		0			0
$299$	−1.56156	−	0.568363i	−0.0903076	−	0.0328693i
$300$		0			0
$301$	1.65876	+	1.39186i	0.0956093	+	0.0802257i
$302$		0			0
$303$	−1.81296	−	0.945652i	−0.104152	−	0.0543263i
$304$		0			0
$305$	0.332495	+	0.575898i	0.0190386	+	0.0329758i
$306$		0			0
$307$	−13.4109	+	23.2284i	−0.765401	+	1.32571i	0.174633	+	0.984634i	$0.444126\pi$
$307$	−13.4109	+	23.2284i	−0.765401	+	1.32571i	−0.940034	+	0.341080i	$0.889207\pi$
$308$		0			0
$309$	15.1320	−	3.34171i	0.860828	−	0.190103i
$310$		0			0
$311$	23.5687	−	8.57831i	1.33646	−	0.486431i	0.427763	−	0.903891i	$-0.359302\pi$
$311$	23.5687	−	8.57831i	1.33646	−	0.486431i	0.908696	+	0.417459i	$0.137079\pi$
$312$		0			0
$313$	2.87988	+	16.3326i	0.162780	+	0.923174i	0.951323	+	0.308194i	$0.0997247\pi$
$313$	2.87988	+	16.3326i	0.162780	+	0.923174i	−0.788543	+	0.614980i	$0.789164\pi$
$314$		0			0
$315$	−1.15895	−	0.312569i	−0.0652992	−	0.0176113i
$316$		0			0
$317$	6.64434	−	5.57526i	0.373183	−	0.313138i	−0.436836	−	0.899541i	$-0.643901\pi$
$317$	6.64434	−	5.57526i	0.373183	−	0.313138i	0.810019	+	0.586403i	$0.199457\pi$
$318$		0			0
$319$	0.469492	−	2.66262i	0.0262865	−	0.149078i
$320$		0			0
$321$	4.91864	+	11.9021i	0.274532	+	0.664313i
$322$		0			0
$323$	24.8387			1.38206
$324$		0			0
$325$	−23.5792			−1.30794
$326$		0			0
$327$	8.06141	+	19.5070i	0.445797	+	1.07874i
$328$		0			0
$329$	0.684140	−	3.87995i	0.0377179	−	0.213909i
$330$		0			0
$331$	−2.43549	+	2.04362i	−0.133866	+	0.112327i	−0.707262	−	0.706951i	$-0.750070\pi$
$331$	−2.43549	+	2.04362i	−0.133866	+	0.112327i	0.573396	+	0.819278i	$0.305626\pi$
$332$		0			0
$333$	−0.870064	−	3.26848i	−0.0476792	−	0.179112i
$334$		0			0
$335$	−2.11685	−	12.0052i	−0.115656	−	0.655916i
$336$		0			0
$337$	−11.1370	+	4.05355i	−0.606674	+	0.220811i	−0.627047	−	0.778981i	$-0.715737\pi$
$337$	−11.1370	+	4.05355i	−0.606674	+	0.220811i	0.0203735	+	0.999792i	$0.493514\pi$
$338$		0			0
$339$	2.26982	−	0.501260i	0.123279	−	0.0272247i
$340$		0			0
$341$	−3.75241	+	6.49937i	−0.203204	+	0.351960i
$342$		0			0
$343$	−2.44544	−	4.23563i	−0.132042	−	0.228703i
$344$		0			0
$345$	−0.455981	−	0.237842i	−0.0245492	−	0.0128050i
$346$		0			0
$347$	−15.0597	−	12.6366i	−0.808449	−	0.678369i	0.141788	−	0.989897i	$-0.454715\pi$
$347$	−15.0597	−	12.6366i	−0.808449	−	0.678369i	−0.950237	+	0.311528i	$0.899159\pi$
$348$		0			0
$349$	11.8103	+	4.29860i	0.632192	+	0.230099i	0.638185	−	0.769883i	$-0.279686\pi$
$349$	11.8103	+	4.29860i	0.632192	+	0.230099i	−0.00599329	+	0.999982i	$0.501908\pi$
$350$		0			0
$351$	−32.9769	−	1.52081i	−1.76018	−	0.0811748i
$352$		0			0
$353$	24.8715	+	9.05249i	1.32378	+	0.481815i	0.904667	−	0.426120i	$-0.140120\pi$
$353$	24.8715	+	9.05249i	1.32378	+	0.481815i	0.419110	+	0.907935i	$0.362342\pi$
$354$		0			0
$355$	8.70869	+	7.30746i	0.462209	+	0.387840i
$356$		0			0
$357$	−3.52085	+	2.23899i	−0.186343	+	0.118500i
$358$		0			0
$359$	3.48467	+	6.03563i	0.183914	+	0.318549i	0.943210	−	0.332197i	$-0.107790\pi$
$359$	3.48467	+	6.03563i	0.183914	+	0.318549i	−0.759296	+	0.650745i	$0.774457\pi$
$360$		0			0
$361$	2.89570	−	5.01550i	0.152405	−	0.263973i
$362$		0			0
$363$	−11.6802	−	12.7677i	−0.613054	−	0.670129i
$364$		0			0
$365$	−5.33308	+	1.94108i	−0.279146	+	0.101601i
$366$		0			0
$367$	−2.91583	−	16.5365i	−0.152205	−	0.863197i	−0.961297	−	0.275515i	$-0.911152\pi$
$367$	−2.91583	−	16.5365i	−0.152205	−	0.863197i	0.809092	−	0.587682i	$-0.199959\pi$
$368$		0			0
$369$	−2.42576	+	5.17994i	−0.126280	+	0.269657i
$370$		0			0
$371$	2.34820	−	1.97037i	0.121912	−	0.102297i
$372$		0			0
$373$	−3.03231	+	17.1971i	−0.157007	+	0.890431i	0.799921	+	0.600105i	$0.204875\pi$
$373$	−3.03231	+	17.1971i	−0.157007	+	0.890431i	−0.956928	+	0.290326i	$0.906236\pi$
$374$		0			0
$375$	−16.9796	−	2.24953i	−0.876825	−	0.116165i
$376$		0			0
$377$	−17.0976			−0.880572
$378$		0			0
$379$	−14.5959			−0.749743			−0.374871	−	0.927077i	$-0.622313\pi$
$379$	−14.5959			−0.749743			−0.374871	+	0.927077i	$0.622313\pi$
$380$		0			0
$381$	−10.4472	+	13.5921i	−0.535227	+	0.696342i
$382$		0			0
$383$	3.16033	−	17.9231i	0.161485	−	0.915829i	−0.791129	−	0.611649i	$-0.790506\pi$
$383$	3.16033	−	17.9231i	0.161485	−	0.915829i	0.952615	−	0.304180i	$-0.0983825\pi$
$384$		0			0
$385$	0.307932	−	0.258386i	0.0156937	−	0.0131685i
$386$		0			0
$387$	15.0795	+	10.5955i	0.766533	+	0.538601i
$388$		0			0
$389$	5.49255	+	31.1498i	0.278483	+	1.57936i	0.727675	+	0.685922i	$0.240601\pi$
$389$	5.49255	+	31.1498i	0.278483	+	1.57936i	−0.449191	+	0.893436i	$0.648288\pi$
$390$		0			0
$391$	−1.67985	+	0.611416i	−0.0849538	+	0.0309206i
$392$		0			0
$393$	−6.13239	+	19.3942i	−0.309338	+	0.978306i
$394$		0			0
$395$	−0.580752	+	1.00589i	−0.0292208	+	0.0506119i
$396$		0			0
$397$	−5.80621	−	10.0566i	−0.291405	−	0.504729i	0.682737	−	0.730664i	$-0.260789\pi$
$397$	−5.80621	−	10.0566i	−0.291405	−	0.504729i	−0.974142	+	0.225936i	$0.927456\pi$
$398$		0			0
$399$	−0.0949717	−	2.21678i	−0.00475453	−	0.110978i
$400$		0			0
$401$	−21.8708	−	18.3517i	−1.09217	−	0.916442i	−0.0952991	−	0.995449i	$-0.530381\pi$
$401$	−21.8708	−	18.3517i	−1.09217	−	0.916442i	−0.996874	+	0.0790065i	$0.974825\pi$
$402$		0			0
$403$	44.5968	+	16.2319i	2.22152	+	0.808569i
$404$		0			0
$405$	−10.0554	−	1.80695i	−0.499656	−	0.0897879i
$406$		0			0
$407$	1.06436	+	0.387396i	0.0527585	+	0.0192025i
$408$		0			0
$409$	23.2607	+	19.5181i	1.15017	+	0.965106i	0.999724	−	0.0235126i	$-0.00748497\pi$
$409$	23.2607	+	19.5181i	1.15017	+	0.965106i	0.150445	+	0.988618i	$0.451929\pi$
$410$		0			0
$411$	−0.618924	−	14.4466i	−0.0305293	−	0.712597i
$412$		0			0
$413$	−1.34711	−	2.33327i	−0.0662870	−	0.114812i
$414$		0			0
$415$	4.69737	−	8.13608i	0.230585	−	0.399384i
$416$		0			0
$417$	−9.92105	+	31.3761i	−0.485836	+	1.53650i
$418$		0			0
$419$	−24.7518	+	9.00893i	−1.20921	+	0.440115i	−0.866428	−	0.499301i	$-0.833590\pi$
$419$	−24.7518	+	9.00893i	−1.20921	+	0.440115i	−0.342778	+	0.939417i	$0.611368\pi$
$420$		0			0
$421$	2.58090	+	14.6370i	0.125785	+	0.713364i	0.980838	+	0.194823i	$0.0624134\pi$
$421$	2.58090	+	14.6370i	0.125785	+	0.713364i	−0.855053	+	0.518541i	$0.826476\pi$
$422$		0			0
$423$	2.97714	−	33.4000i	0.144753	−	1.62396i
$424$		0			0
$425$	−19.4309	+	16.3045i	−0.942539	+	0.790884i
$426$		0			0
$427$	0.0358557	−	0.203348i	0.00173518	−	0.00984069i
$428$		0			0
$429$	6.73708	−	8.76509i	0.325269	−	0.423183i
$430$		0			0
$431$	−13.4640			−0.648537			−0.324269	−	0.945965i	$-0.605118\pi$
$431$	−13.4640			−0.648537			−0.324269	+	0.945965i	$0.605118\pi$
$432$		0			0
$433$	−15.7619			−0.757469			−0.378734	−	0.925505i	$-0.623641\pi$
$433$	−15.7619			−0.757469			−0.378734	+	0.925505i	$0.623641\pi$
$434$		0			0
$435$	−5.24549	−	0.694943i	−0.251502	−	0.0333200i
$436$		0			0
$437$	0.165076	−	0.936190i	0.00789664	−	0.0447841i
$438$		0			0
$439$	−16.3515	+	13.7205i	−0.780412	+	0.654844i	−0.943352	−	0.331792i	$-0.892347\pi$
$439$	−16.3515	+	13.7205i	−0.780412	+	0.654844i	0.162940	+	0.986636i	$0.447902\pi$
$440$		0			0
$441$	−11.8037	−	16.9162i	−0.562081	−	0.805533i
$442$		0			0
$443$	−2.06776	−	11.7268i	−0.0982421	−	0.557158i	−0.993706	−	0.112023i	$-0.964267\pi$
$443$	−2.06776	−	11.7268i	−0.0982421	−	0.557158i	0.895464	−	0.445135i	$-0.146844\pi$
$444$		0			0
$445$	−7.90132	+	2.87585i	−0.374559	+	0.136328i
$446$		0			0
$447$	−10.0643	−	11.0013i	−0.476024	−	0.520342i
$448$		0			0
$449$	8.25423	−	14.2967i	0.389541	−	0.674705i	−0.602847	−	0.797857i	$-0.705967\pi$
$449$	8.25423	−	14.2967i	0.389541	−	0.674705i	0.992388	+	0.123152i	$0.0393002\pi$
$450$		0			0
$451$	−0.957726	−	1.65883i	−0.0450976	−	0.0781113i
$452$		0			0
$453$	−29.2034	+	18.5711i	−1.37209	+	0.872545i
$454$		0			0
$455$	−1.94730	−	1.63398i	−0.0912907	−	0.0766020i
$456$		0			0
$457$	6.23844	+	2.27061i	0.291822	+	0.106214i	0.483783	−	0.875188i	$-0.339262\pi$
$457$	6.23844	+	2.27061i	0.291822	+	0.106214i	−0.191961	+	0.981403i	$0.561485\pi$
$458$		0			0
$459$	−28.2270	+	21.5496i	−1.31752	+	1.00585i
$460$		0			0
$461$	9.95197	+	3.62222i	0.463510	+	0.168704i	0.563210	−	0.826314i	$-0.309566\pi$
$461$	9.95197	+	3.62222i	0.463510	+	0.168704i	−0.0997004	+	0.995017i	$0.531788\pi$
$462$		0			0
$463$	18.2070	+	15.2775i	0.846150	+	0.710004i	0.958938	−	0.283615i	$-0.0915337\pi$
$463$	18.2070	+	15.2775i	0.846150	+	0.710004i	−0.112788	+	0.993619i	$0.535978\pi$
$464$		0			0
$465$	13.0224	+	6.79256i	0.603899	+	0.314997i
$466$		0			0
$467$	−11.0232	−	19.0928i	−0.510095	−	0.883510i	−0.999932	−	0.0116961i	$-0.996277\pi$
$467$	−11.0232	−	19.0928i	−0.510095	−	0.883510i	0.489837	−	0.871814i	$-0.337056\pi$
$468$		0			0
$469$	−1.89261	+	3.27810i	−0.0873928	+	0.151369i
$470$		0			0
$471$	19.2751	−	4.25665i	0.888148	−	0.196136i
$472$		0			0
$473$	−5.79958	+	2.11087i	−0.266665	+	0.0970581i
$474$		0			0
$475$	−2.34227	−	13.2837i	−0.107471	−	0.609497i
$476$		0			0
$477$	18.4784	−	18.4181i	0.846068	−	0.843307i
$478$		0			0
$479$	−5.69074	+	4.77510i	−0.260016	+	0.218180i	−0.763471	−	0.645842i	$-0.776507\pi$
$479$	−5.69074	+	4.77510i	−0.260016	+	0.218180i	0.503455	+	0.864022i	$0.332062\pi$
$480$		0			0
$481$	1.24380	−	7.05395i	0.0567125	−	0.321633i
$482$		0			0
$483$	0.0609899	+	0.147584i	0.00277514	+	0.00671529i
$484$		0			0
$485$	−10.8749			−0.493805
$486$		0			0
$487$	35.1968			1.59492			0.797460	−	0.603372i	$-0.206177\pi$
$487$	35.1968			1.59492			0.797460	+	0.603372i	$0.206177\pi$
$488$		0			0
$489$	3.70457	+	8.96434i	0.167527	+	0.405381i
$490$		0			0
$491$	−1.89179	+	10.7289i	−0.0853751	+	0.484186i	0.911900	+	0.410413i	$0.134615\pi$
$491$	−1.89179	+	10.7289i	−0.0853751	+	0.484186i	−0.997275	+	0.0737736i	$0.976496\pi$
$492$		0			0
$493$	−14.0897	+	11.8226i	−0.634567	+	0.532465i
$494$		0			0
$495$	2.42317	−	2.41527i	0.108914	−	0.108558i
$496$		0			0
$497$	−0.612975	−	3.47635i	−0.0274957	−	0.155936i
$498$		0			0
$499$	6.12558	−	2.22953i	0.274219	−	0.0998074i	−0.201251	−	0.979540i	$-0.564501\pi$
$499$	6.12558	−	2.22953i	0.274219	−	0.0998074i	0.475469	+	0.879732i	$0.342278\pi$
$500$		0			0
$501$	25.9964	−	5.74099i	1.16144	−	0.256489i
$502$		0			0
$503$	1.05531	−	1.82784i	0.0470537	−	0.0814995i	−0.841539	−	0.540196i	$-0.818350\pi$
$503$	1.05531	−	1.82784i	0.0470537	−	0.0814995i	0.888593	+	0.458696i	$0.151683\pi$
$504$		0			0
$505$	−0.670057	−	1.16057i	−0.0298171	−	0.0516448i
$506$		0			0
$507$	−42.0206	−	21.9182i	−1.86620	−	0.973421i
$508$		0			0
$509$	26.2708	+	22.0438i	1.16443	+	0.977076i	0.999957	−	0.00930502i	$-0.00296192\pi$
$509$	26.2708	+	22.0438i	1.16443	+	0.977076i	0.164477	+	0.986381i	$0.447406\pi$
$510$		0			0
$511$	1.65596	+	0.602722i	0.0732556	+	0.0266628i
$512$		0			0
$513$	−2.41904	−	18.7291i	−0.106803	−	0.826912i
$514$		0			0
$515$	9.54374	+	3.47364i	0.420547	+	0.153067i
$516$		0			0
$517$	8.60221	+	7.21811i	0.378325	+	0.317452i
$518$		0			0
$519$	−3.79181	+	2.41129i	−0.166442	+	0.105844i
$520$		0			0
$521$	4.72026	+	8.17573i	0.206798	+	0.358185i	0.950704	−	0.310099i	$-0.100362\pi$
$521$	4.72026	+	8.17573i	0.206798	+	0.358185i	−0.743906	+	0.668284i	$0.767029\pi$
$522$		0			0
$523$	−12.9783	+	22.4791i	−0.567502	+	0.982942i	0.429311	+	0.903157i	$0.358757\pi$
$523$	−12.9783	+	22.4791i	−0.567502	+	0.982942i	−0.996812	+	0.0797847i	$0.974577\pi$
$524$		0			0
$525$	1.52942	+	1.67181i	0.0667493	+	0.0729636i
$526$		0			0
$527$	47.9750	−	17.4615i	2.08982	−	0.760634i
$528$		0			0
$529$	−3.98203	−	22.5832i	−0.173132	−	0.981878i
$530$		0			0
$531$	−13.1220	−	18.8055i	−0.569446	−	0.816088i
$532$		0			0
$533$	−9.27904	+	7.78604i	−0.401920	+	0.337251i
$534$		0			0
$535$	−1.46565	+	8.31212i	−0.0633656	+	0.359364i
$536$		0			0
$537$	−6.19765	−	0.821088i	−0.267448	−	0.0354326i
$538$		0			0
$539$	6.90769			0.297535
$540$		0			0
$541$	−31.8373			−1.36879			−0.684396	−	0.729110i	$-0.739934\pi$
$541$	−31.8373			−1.36879			−0.684396	+	0.729110i	$0.739934\pi$
$542$		0			0
$543$	−11.1667	+	14.5281i	−0.479208	+	0.623461i
$544$		0			0
$545$	−2.40213	+	13.6231i	−0.102896	+	0.583551i
$546$		0			0
$547$	−31.2687	+	26.2376i	−1.33695	+	1.12184i	−0.354558	+	0.935034i	$0.615369\pi$
$547$	−31.2687	+	26.2376i	−1.33695	+	1.12184i	−0.982397	+	0.186804i	$0.940187\pi$
$548$		0			0
$549$	0.156031	−	1.75049i	0.00665926	−	0.0747092i
$550$		0			0
$551$	−1.69842	−	9.63221i	−0.0723550	−	0.410346i
$552$		0			0
$553$	0.338906	−	0.123352i	0.0144118	−	0.00524545i
$554$		0			0
$555$	0.668306	−	2.11357i	0.0283680	−	0.0897162i
$556$		0			0
$557$	−0.989874	+	1.71451i	−0.0419423	+	0.0726462i	−0.886234	−	0.463237i	$-0.846688\pi$
$557$	−0.989874	+	1.71451i	−0.0419423	+	0.0726462i	0.844292	+	0.535883i	$0.180021\pi$
$558$		0			0
$559$	19.5145	+	33.8001i	0.825376	+	1.42959i
$560$		0			0
$561$	−0.509035	−	11.8816i	−0.0214915	−	0.501642i
$562$		0			0
$563$	18.7427	+	15.7270i	0.789912	+	0.662815i	0.945724	−	0.324972i	$-0.105355\pi$
$563$	18.7427	+	15.7270i	0.789912	+	0.662815i	−0.155812	+	0.987787i	$0.549799\pi$
$564$		0			0
$565$	1.43157	+	0.521050i	0.0602267	+	0.0219207i
$566$		0			0
$567$	2.03116	+	2.43677i	0.0853006	+	0.102335i
$568$		0			0
$569$	−15.8514	−	5.76944i	−0.664526	−	0.241868i	−0.0123366	−	0.999924i	$-0.503927\pi$
$569$	−15.8514	−	5.76944i	−0.664526	−	0.241868i	−0.652189	+	0.758056i	$0.726149\pi$
$570$		0			0
$571$	12.5783	+	10.5544i	0.526384	+	0.441689i	0.866851	−	0.498568i	$-0.166141\pi$
$571$	12.5783	+	10.5544i	0.526384	+	0.441689i	−0.340467	+	0.940257i	$0.610585\pi$
$572$		0			0
$573$	1.46373	+	34.1656i	0.0611483	+	1.42729i
$574$		0			0
$575$	0.485392	+	0.840724i	0.0202423	+	0.0350606i
$576$		0			0
$577$	−9.17077	+	15.8842i	−0.381784	+	0.661270i	−0.991317	−	0.131491i	$-0.958024\pi$
$577$	−9.17077	+	15.8842i	−0.381784	+	0.661270i	0.609533	+	0.792761i	$0.291357\pi$
$578$		0			0
$579$	−0.208049	+	0.657971i	−0.00864621	+	0.0273443i
$580$		0			0
$581$	−2.74122	+	0.997722i	−0.113725	+	0.0413925i
$582$		0			0
$583$	1.51716	+	8.60425i	0.0628344	+	0.356352i
$584$		0			0
$585$	−17.7025	−	12.4386i	−0.731909	−	0.514273i
$586$		0			0
$587$	15.7449	−	13.2116i	0.649863	−	0.545300i	−0.257166	−	0.966367i	$-0.582789\pi$
$587$	15.7449	−	13.2116i	0.649863	−	0.545300i	0.907029	+	0.421067i	$0.138344\pi$
$588$		0			0
$589$	−4.71441	+	26.7367i	−0.194254	+	1.10167i
$590$		0			0
$591$	−8.04267	+	10.4637i	−0.330831	+	0.430419i
$592$		0			0
$593$	−22.4370			−0.921375			−0.460688	−	0.887562i	$-0.652397\pi$
$593$	−22.4370			−0.921375			−0.460688	+	0.887562i	$0.652397\pi$
$594$		0			0
$595$	−2.73457			−0.112107
$596$		0			0
$597$	−32.7444	−	4.33811i	−1.34014	−	0.177547i
$598$		0			0
$599$	5.17302	−	29.3377i	0.211364	−	1.19871i	−0.675742	−	0.737139i	$-0.736176\pi$
$599$	5.17302	−	29.3377i	0.211364	−	1.19871i	0.887106	−	0.461566i	$-0.152712\pi$
$600$		0			0
$601$	14.0367	−	11.7782i	0.572569	−	0.480442i	−0.309928	−	0.950760i	$-0.600305\pi$
$601$	14.0367	−	11.7782i	0.572569	−	0.480442i	0.882497	+	0.470318i	$0.155861\pi$
$602$		0			0
$603$	−13.6631	+	29.1760i	−0.556405	+	1.18814i
$604$		0			0
$605$	−1.96935	−	11.1688i	−0.0800656	−	0.454074i
$606$		0			0
$607$	−19.6293	+	7.14448i	−0.796729	+	0.289985i	−0.708130	−	0.706082i	$-0.750461\pi$
$607$	−19.6293	+	7.14448i	−0.796729	+	0.289985i	−0.0885984	+	0.996067i	$0.528239\pi$
$608$		0			0
$609$	1.10900	+	1.21225i	0.0449391	+	0.0491230i
$610$		0			0
$611$	35.5061	−	61.4984i	1.43642	−	2.48796i
$612$		0			0
$613$	13.3880	+	23.1887i	0.540737	+	0.936584i	0.998862	+	0.0476964i	$0.0151880\pi$
$613$	13.3880	+	23.1887i	0.540737	+	0.936584i	−0.458125	+	0.888888i	$0.651479\pi$
$614$		0			0
$615$	−3.16324	+	2.01158i	−0.127554	+	0.0811146i
$616$		0			0
$617$	7.19155	+	6.03443i	0.289521	+	0.242937i	0.775967	−	0.630774i	$-0.217262\pi$
$617$	7.19155	+	6.03443i	0.289521	+	0.242937i	−0.486446	+	0.873711i	$0.661707\pi$
$618$		0			0
$619$	46.1099	+	16.7826i	1.85331	+	0.674551i	0.983428	+	0.181298i	$0.0580297\pi$
$619$	46.1099	+	16.7826i	1.85331	+	0.674551i	0.869886	+	0.493254i	$0.164193\pi$
$620$		0			0
$621$	0.624627	+	1.20711i	0.0250654	+	0.0484397i
$622$		0			0
$623$	2.45343	+	0.892974i	0.0982945	+	0.0357763i
$624$		0			0
$625$	5.61632	+	4.71266i	0.224653	+	0.188506i
$626$		0			0
$627$	5.60719	+	2.92474i	0.223930	+	0.116803i
$628$		0			0
$629$	−3.85268	−	6.67303i	−0.153616	−	0.266071i
$630$		0			0
$631$	−4.91387	+	8.51108i	−0.195618	+	0.338821i	−0.947103	−	0.320930i	$-0.896005\pi$
$631$	−4.91387	+	8.51108i	−0.195618	+	0.338821i	0.751485	+	0.659750i	$0.229338\pi$
$632$		0			0
$633$	−38.4809	+	8.49802i	−1.52948	+	0.337766i
$634$		0			0
$635$	−10.5578	+	3.84273i	−0.418974	+	0.152494i
$636$		0			0
$637$	−7.58544	−	43.0191i	−0.300546	−	1.70448i
$638$		0			0
$639$	−7.72861	−	29.0333i	−0.305739	−	1.14854i
$640$		0			0
$641$	15.5954	−	13.0861i	0.615982	−	0.516870i	−0.280556	−	0.959838i	$-0.590519\pi$
$641$	15.5954	−	13.0861i	0.615982	−	0.516870i	0.896538	+	0.442968i	$0.146074\pi$
$642$		0			0
$643$	−1.22411	+	6.94226i	−0.0482741	+	0.273776i	−0.999385	−	0.0350744i	$-0.988833\pi$
$643$	−1.22411	+	6.94226i	−0.0482741	+	0.273776i	0.951111	+	0.308851i	$0.0999443\pi$
$644$		0			0
$645$	4.61316	+	11.1629i	0.181643	+	0.439541i
$646$		0			0
$647$	32.2433			1.26762			0.633808	−	0.773491i	$-0.281491\pi$
$647$	32.2433			1.26762			0.633808	+	0.773491i	$0.281491\pi$
$648$		0			0
$649$	7.67917			0.301434
$650$		0			0
$651$	−1.74181	−	4.21485i	−0.0682671	−	0.165193i
$652$		0			0
$653$	4.63666	−	26.2958i	0.181447	−	1.02903i	−0.748990	−	0.662581i	$-0.769461\pi$
$653$	4.63666	−	26.2958i	0.181447	−	1.02903i	0.930436	−	0.366453i	$-0.119428\pi$
$654$		0			0
$655$	−10.2121	+	8.56896i	−0.399019	+	0.334817i
$656$		0			0
$657$	14.4813	+	3.90564i	0.564970	+	0.152373i
$658$		0			0
$659$	−0.373461	−	2.11800i	−0.0145480	−	0.0825057i	0.976669	−	0.214749i	$-0.0688932\pi$
$659$	−0.373461	−	2.11800i	−0.0145480	−	0.0825057i	−0.991217	+	0.132243i	$0.957782\pi$
$660$		0			0
$661$	28.7031	−	10.4471i	1.11642	−	0.406344i	0.283077	−	0.959097i	$-0.408645\pi$
$661$	28.7031	−	10.4471i	1.11642	−	0.406344i	0.833345	+	0.552753i	$0.186423\pi$
$662$		0			0
$663$	−73.4364	+	16.2175i	−2.85203	+	0.629836i
$664$		0			0
$665$	0.727088	−	1.25935i	0.0281953	−	0.0488357i
$666$		0			0
$667$	0.351966	+	0.609622i	0.0136282	+	0.0236047i
$668$		0			0
$669$	35.8083	+	18.6778i	1.38443	+	0.722126i
$670$		0			0
$671$	0.450841	+	0.378300i	0.0174045	+	0.0146041i
$672$		0			0
$673$	0.282579	+	0.102850i	0.0108926	+	0.00396459i	0.347461	−	0.937695i	$-0.387044\pi$
$673$	0.282579	+	0.102850i	0.0108926	+	0.00396459i	−0.336568	+	0.941659i	$0.609266\pi$
$674$		0			0
$675$	14.1864	+	13.0636i	0.546036	+	0.502818i
$676$		0			0
$677$	−15.0992	−	5.49567i	−0.580311	−	0.211216i	0.0351518	−	0.999382i	$-0.488809\pi$
$677$	−15.0992	−	5.49567i	−0.580311	−	0.211216i	−0.615463	+	0.788166i	$0.711031\pi$
$678$		0			0
$679$	2.58675	+	2.17054i	0.0992702	+	0.0832976i
$680$		0			0
$681$	41.6396	−	26.4795i	1.59563	−	1.01470i
$682$		0			0
$683$	2.62750	+	4.55097i	0.100539	+	0.174138i	0.911907	−	0.410398i	$-0.134610\pi$
$683$	2.62750	+	4.55097i	0.100539	+	0.174138i	−0.811368	+	0.584536i	$0.801277\pi$
$684$		0			0
$685$	4.73839	−	8.20713i	0.181044	−	0.313578i
$686$		0			0
$687$	16.1809	+	17.6874i	0.617340	+	0.674815i
$688$		0			0
$689$	51.9188	−	18.8969i	1.97795	−	0.719915i
$690$		0			0
$691$	0.725322	+	4.11351i	0.0275926	+	0.156485i	0.995491	−	0.0948567i	$-0.0302393\pi$
$691$	0.725322	+	4.11351i	0.0275926	+	0.156485i	−0.967898	+	0.251342i	$0.919128\pi$
$692$		0			0
$693$	−1.05845	+	0.0908595i	−0.0402072	+	0.00345147i
$694$		0			0
$695$	−16.5212	+	13.8630i	−0.626687	+	0.525853i
$696$		0			0
$697$	−2.26272	+	12.8325i	−0.0857066	+	0.486066i
$698$		0			0
$699$	48.1546	+	6.37971i	1.82137	+	0.241303i
$700$		0			0
$701$	35.8425			1.35375			0.676877	−	0.736096i	$-0.263333\pi$
$701$	35.8425			1.35375			0.676877	+	0.736096i	$0.263333\pi$
$702$		0			0
$703$	4.09751			0.154540
$704$		0			0
$705$	13.3928	−	17.4243i	0.504402	−	0.656239i
$706$		0			0
$707$	−0.0722579	+	0.409795i	−0.00271754	+	0.0154119i
$708$		0			0
$709$	28.9098	−	24.2582i	1.08573	−	0.911035i	0.0893450	−	0.996001i	$-0.471523\pi$
$709$	28.9098	−	24.2582i	1.08573	−	0.911035i	0.996384	+	0.0849661i	$0.0270782\pi$
$710$		0			0
$711$	2.78413	−	1.29273i	0.104413	−	0.0484811i
$712$		0			0
$713$	−0.339299	−	1.92426i	−0.0127069	−	0.0720642i
$714$		0			0
$715$	6.80840	−	2.47806i	0.254620	−	0.0926740i
$716$		0			0
$717$	5.86166	−	18.5380i	0.218908	−	0.692314i
$718$		0			0
$719$	−22.2562	+	38.5488i	−0.830015	+	1.43763i	0.0680099	+	0.997685i	$0.478335\pi$
$719$	−22.2562	+	38.5488i	−0.830015	+	1.43763i	−0.898025	+	0.439944i	$0.854998\pi$
$720$		0			0
$721$	−1.57680	−	2.73109i	−0.0587230	−	0.101711i
$722$		0			0
$723$	−1.19302	−	27.8468i	−0.0443689	−	1.03563i
$724$		0			0
$725$	7.65136	+	6.42025i	0.284164	+	0.238442i
$726$		0			0
$727$	12.2017	+	4.44107i	0.452537	+	0.164710i	0.558226	−	0.829689i	$-0.311482\pi$
$727$	12.2017	+	4.44107i	0.452537	+	0.164710i	−0.105688	+	0.994399i	$0.533705\pi$
$728$		0			0
$729$	18.9980	+	19.1853i	0.703631	+	0.710565i
$730$		0			0
$731$	39.4535	+	14.3599i	1.45924	+	0.531120i
$732$		0			0
$733$	−38.8200	−	32.5738i	−1.43385	−	1.20314i	−0.943393	−	0.331677i	$-0.892386\pi$
$733$	−38.8200	−	32.5738i	−1.43385	−	1.20314i	−0.490456	−	0.871466i	$-0.663170\pi$
$734$		0			0
$735$	−0.578646	−	13.5064i	−0.0213437	−	0.498192i
$736$		0			0
$737$	−5.39440	−	9.34338i	−0.198705	−	0.344168i
$738$		0			0
$739$	15.4350	−	26.7342i	0.567786	−	0.983435i	−0.428998	−	0.903305i	$-0.641133\pi$
$739$	15.4350	−	26.7342i	0.567786	−	0.983435i	0.996784	−	0.0801296i	$-0.0255334\pi$
$740$		0			0
$741$	12.0571	−	38.1317i	0.442930	−	1.40080i
$742$		0			0
$743$	−20.8293	+	7.58126i	−0.764155	+	0.278130i	−0.694549	−	0.719445i	$-0.744396\pi$
$743$	−20.8293	+	7.58126i	−0.764155	+	0.278130i	−0.0696052	+	0.997575i	$0.522174\pi$
$744$		0			0
$745$	−1.69689	−	9.62355i	−0.0621693	−	0.352580i
$746$		0			0
$747$	−22.5192	+	10.4561i	−0.823936	+	0.382570i
$748$		0			0
$749$	2.00765	−	1.68462i	0.0733578	−	0.0615545i
$750$		0			0
$751$	−7.16179	+	40.6165i	−0.261337	+	1.48212i	0.517929	+	0.855424i	$0.326703\pi$
$751$	−7.16179	+	40.6165i	−0.261337	+	1.48212i	−0.779266	+	0.626693i	$0.784408\pi$
$752$		0			0
$753$	−5.03863	+	6.55537i	−0.183618	+	0.238891i
$754$		0			0
$755$	−22.6817			−0.825470
$756$		0			0
$757$	53.1131			1.93043			0.965215	−	0.261458i	$-0.0842032\pi$
$757$	53.1131			1.93043			0.965215	+	0.261458i	$0.0842032\pi$
$758$		0			0
$759$	−0.451210	−	0.0597781i	−0.0163779	−	0.00216981i
$760$		0			0
$761$	1.32415	−	7.50962i	0.0480003	−	0.272223i	−0.951356	−	0.308093i	$-0.900309\pi$
$761$	1.32415	−	7.50962i	0.0480003	−	0.272223i	0.999356	+	0.0358700i	$0.0114202\pi$
$762$		0			0
$763$	3.29043	−	2.76100i	0.119122	−	0.0999550i
$764$		0			0
$765$	−23.1892	+	1.99061i	−0.838407	+	0.0719706i
$766$		0			0
$767$	−8.43262	−	47.8237i	−0.304484	−	1.72682i
$768$		0			0
$769$	−31.6268	+	11.5112i	−1.14049	+	0.415104i	−0.842090	−	0.539337i	$-0.818675\pi$
$769$	−31.6268	+	11.5112i	−1.14049	+	0.415104i	−0.298400	+	0.954441i	$0.596453\pi$
$770$		0			0
$771$	−28.2808	−	30.9138i	−1.01851	−	1.11333i
$772$		0			0
$773$	−26.0399	+	45.1024i	−0.936590	+	1.62222i	−0.164815	+	0.986324i	$0.552703\pi$
$773$	−26.0399	+	45.1024i	−0.936590	+	1.62222i	−0.771774	+	0.635896i	$0.780631\pi$
$774$		0			0
$775$	−13.8624	−	24.0103i	−0.497950	−	0.862476i
$776$		0			0
$777$	−0.580816	+	0.369353i	−0.0208366	+	0.0132505i
$778$		0			0
$779$	−5.30813	−	4.45405i	−0.190184	−	0.159583i
$780$		0			0
$781$	9.45451	+	3.44116i	0.338309	+	0.123134i
$782$		0			0
$783$	10.2868	+	9.47262i	0.367620	+	0.338524i
$784$		0			0
$785$	12.1568	+	4.42470i	0.433894	+	0.157924i
$786$		0			0
$787$	−31.0547	−	26.0580i	−1.10698	−	0.928868i	−0.109107	−	0.994030i	$-0.534799\pi$
$787$	−31.0547	−	26.0580i	−1.10698	−	0.928868i	−0.997875	+	0.0651623i	$0.979243\pi$
$788$		0			0
$789$	−48.4806	−	25.2878i	−1.72595	−	0.900269i
$790$		0			0
$791$	−0.236522	−	0.409667i	−0.00840974	−	0.0145661i
$792$		0			0
$793$	1.86087	−	3.22313i	0.0660815	−	0.114457i
$794$		0			0
$795$	16.6966	−	3.68723i	0.592167	−	0.130773i
$796$		0			0
$797$	−9.47037	+	3.44693i	−0.335458	+	0.122097i	−0.504257	−	0.863554i	$-0.668233\pi$
$797$	−9.47037	+	3.44693i	−0.335458	+	0.122097i	0.168799	+	0.985651i	$0.446011\pi$
$798$		0			0
$799$	−13.2652	−	75.2309i	−0.469290	−	2.66148i
$800$		0			0
$801$	21.4551	+	5.78648i	0.758079	+	0.204455i
$802$		0			0
$803$	−3.84769	+	3.22860i	−0.135782	+	0.113935i
$804$		0			0
$805$	−0.0181737	+	0.103068i	−0.000640539	+	0.00363267i
$806$		0			0
$807$	14.4152	+	34.8821i	0.507440	+	1.22791i
$808$		0			0
$809$	−19.5243			−0.686439			−0.343219	−	0.939255i	$-0.611517\pi$
$809$	−19.5243			−0.686439			−0.343219	+	0.939255i	$0.611517\pi$
$810$		0			0
$811$	−11.4755			−0.402960			−0.201480	−	0.979493i	$-0.564575\pi$
$811$	−11.4755			−0.402960			−0.201480	+	0.979493i	$0.564575\pi$
$812$		0			0
$813$	−3.91985	−	9.48528i	−0.137475	−	0.332663i
$814$		0			0
$815$	−1.10388	+	6.26044i	−0.0386674	+	0.219294i
$816$		0			0
$817$	−17.1033	+	14.3514i	−0.598370	+	0.502092i
$818$		0			0
$819$	1.72815	+	6.49195i	0.0603863	+	0.226847i
$820$		0			0
$821$	0.476815	+	2.70415i	0.0166410	+	0.0943755i	0.991997	−	0.126261i	$-0.0402977\pi$
$821$	0.476815	+	2.70415i	0.0166410	+	0.0943755i	−0.975356	+	0.220636i	$0.929187\pi$
$822$		0			0
$823$	35.7815	−	13.0234i	1.24726	−	0.453967i	0.367788	−	0.929910i	$-0.380115\pi$
$823$	35.7815	−	13.0234i	1.24726	−	0.453967i	0.879477	+	0.475942i	$0.157893\pi$
$824$		0			0
$825$	−6.30625	+	1.39266i	−0.219556	+	0.0484861i
$826$		0			0
$827$	1.94797	−	3.37399i	0.0677377	−	0.117325i	−0.830167	−	0.557514i	$-0.811755\pi$
$827$	1.94797	−	3.37399i	0.0677377	−	0.117325i	0.897905	+	0.440189i	$0.145089\pi$
$828$		0			0
$829$	−13.6323	−	23.6118i	−0.473469	−	0.820073i	0.526069	−	0.850442i	$-0.323665\pi$
$829$	−13.6323	−	23.6118i	−0.473469	−	0.820073i	−0.999539	+	0.0303686i	$0.990332\pi$
$830$		0			0
$831$	−28.1499	−	14.6831i	−0.976509	−	0.509353i
$832$		0			0
$833$	−35.9978	−	30.2057i	−1.24725	−	1.04657i
$834$		0			0
$835$	16.3960	+	5.96764i	0.567406	+	0.206519i
$836$		0			0
$837$	−17.8388	−	34.4740i	−0.616597	−	1.19160i
$838$		0			0
$839$	−7.85271	−	2.85815i	−0.271106	−	0.0986745i	0.202890	−	0.979202i	$-0.434967\pi$
$839$	−7.85271	−	2.85815i	−0.271106	−	0.0986745i	−0.473996	+	0.880527i	$0.657189\pi$
$840$		0			0
$841$	−16.6672	−	13.9854i	−0.574730	−	0.482256i
$842$		0			0
$843$	43.2156	−	27.4817i	1.48842	−	0.946522i
$844$		0			0
$845$	−15.5305	−	26.8996i	−0.534265	−	0.925374i
$846$		0			0
$847$	−1.76075	+	3.04970i	−0.0604999	+	0.104789i
$848$		0			0
$849$	28.0902	+	30.7054i	0.964054	+	1.05381i
$850$		0			0
$851$	−0.277116	+	0.100862i	−0.00949941	+	0.00345750i
$852$		0			0
$853$	3.42088	+	19.4008i	0.117129	+	0.664270i	0.985674	+	0.168661i	$0.0539442\pi$
$853$	3.42088	+	19.4008i	0.117129	+	0.664270i	−0.868545	+	0.495610i	$0.834945\pi$
$854$		0			0
$855$	5.24898	−	11.2086i	0.179511	−	0.383326i
$856$		0			0
$857$	29.9664	−	25.1448i	1.02363	−	0.858930i	0.0335529	−	0.999437i	$-0.489318\pi$
$857$	29.9664	−	25.1448i	1.02363	−	0.858930i	0.990080	+	0.140507i	$0.0448733\pi$
$858$		0			0
$859$	1.50602	−	8.54104i	0.0513846	−	0.291417i	−0.948277	−	0.317445i	$-0.897175\pi$
$859$	1.50602	−	8.54104i	0.0513846	−	0.291417i	0.999661	+	0.0260287i	$0.00828611\pi$
$860$		0			0
$861$	1.15391	+	0.152875i	0.0393252	+	0.00520996i
$862$		0			0
$863$	−18.8525			−0.641747			−0.320874	−	0.947122i	$-0.603976\pi$
$863$	−18.8525			−0.641747			−0.320874	+	0.947122i	$0.603976\pi$
$864$		0			0
$865$	−2.94502			−0.100134
$866$		0			0
$867$	−31.3588	+	40.7986i	−1.06500	+	1.38559i
$868$		0			0
$869$	−0.178503	+	1.01234i	−0.00605529	+	0.0343413i
$870$		0			0
$871$	−52.2642	+	43.8549i	−1.77091	+	1.48597i
$872$		0			0
$873$	23.5156	+	16.5232i	0.795884	+	0.559224i
$874$		0			0
$875$	0.605267	+	3.43264i	0.0204618	+	0.116044i
$876$		0			0
$877$	12.2429	−	4.45604i	0.413413	−	0.150470i	−0.126936	−	0.991911i	$-0.540514\pi$
$877$	12.2429	−	4.45604i	0.413413	−	0.150470i	0.540349	+	0.841441i	$0.318292\pi$
$878$		0			0
$879$	−7.96151	+	25.1789i	−0.268535	+	0.849263i
$880$		0			0
$881$	16.5155	−	28.6057i	0.556421	−	0.963749i	−0.441371	−	0.897325i	$-0.645508\pi$
$881$	16.5155	−	28.6057i	0.556421	−	0.963749i	0.997791	−	0.0664243i	$-0.0211591\pi$
$882$		0			0
$883$	9.90985	+	17.1644i	0.333493	+	0.577627i	0.983194	−	0.182563i	$-0.0584394\pi$
$883$	9.90985	+	17.1644i	0.333493	+	0.577627i	−0.649701	+	0.760190i	$0.725106\pi$
$884$		0			0
$885$	−0.643272	−	15.0149i	−0.0216234	−	0.504721i
$886$		0			0
$887$	16.6197	+	13.9456i	0.558035	+	0.468247i	0.877651	−	0.479300i	$-0.159109\pi$
$887$	16.6197	+	13.9456i	0.558035	+	0.468247i	−0.319616	+	0.947547i	$0.603554\pi$
$888$		0			0
$889$	3.27829	+	1.19320i	0.109950	+	0.0400186i
$890$		0			0
$891$	−8.90951	+	1.54098i	−0.298480	+	0.0516247i
$892$		0			0
$893$	38.1732	+	13.8939i	1.27742	+	0.464942i
$894$		0			0
$895$	−3.13875	−	2.63372i	−0.104917	−	0.0880356i
$896$		0			0
$897$	0.123199	+	2.87565i	0.00411351	+	0.0960152i
$898$		0			0
$899$	−10.0518	−	17.4102i	−0.335247	−	0.580664i
$900$		0			0
$901$	29.7181	−	51.4732i	0.990052	−	1.71482i
$902$		0			0
$903$	1.13072	−	3.57600i	0.0376281	−	0.119002i
$904$		0			0
$905$	−11.2849	+	4.10737i	−0.375123	+	0.136534i
$906$		0			0
$907$	−4.38024	−	24.8416i	−0.145443	−	0.824850i	−0.967010	−	0.254738i	$-0.918011\pi$
$907$	−4.38024	−	24.8416i	−0.145443	−	0.824850i	0.821567	−	0.570112i	$-0.193100\pi$
$908$		0			0
$909$	−0.314441	+	3.52766i	−0.0104293	+	0.117005i
$910$		0			0
$911$	15.5370	−	13.0371i	0.514765	−	0.431939i	−0.348037	−	0.937481i	$-0.613152\pi$
$911$	15.5370	−	13.0371i	0.514765	−	0.431939i	0.862802	+	0.505541i	$0.168707\pi$
$912$		0			0
$913$	1.44381	−	8.18823i	0.0477830	−	0.270991i
$914$		0			0
$915$	0.701915	−	0.913208i	0.0232046	−	0.0301897i
$916$		0			0
$917$	4.13937			0.136694
$918$		0			0
$919$	−34.9944			−1.15436			−0.577180	−	0.816617i	$-0.695847\pi$
$919$	−34.9944			−1.15436			−0.577180	+	0.816617i	$0.695847\pi$
$920$		0			0
$921$	46.0543	+	6.10146i	1.51754	+	0.201050i
$922$		0			0
$923$	11.0484	−	62.6588i	0.363664	−	2.06244i
$924$		0			0
$925$	−3.20541	+	2.68966i	−0.105393	+	0.0884355i
$926$		0			0
$927$	−15.3593	−	22.0119i	−0.504466	−	0.722964i
$928$		0			0
$929$	−5.78870	−	32.8293i	−0.189921	−	1.07710i	−0.919468	−	0.393165i	$-0.871380\pi$
$929$	−5.78870	−	32.8293i	−0.189921	−	1.07710i	0.729547	−	0.683931i	$-0.239731\pi$
$930$		0			0
$931$	23.4820	−	8.54675i	0.769591	−	0.280108i
$932$		0			0
$933$	−29.3229	−	32.0528i	−0.959987	−	1.04936i
$934$		0			0
$935$	3.89709	−	6.74996i	0.127449	−	0.220747i
$936$		0			0
$937$	1.96117	+	3.39685i	0.0640687	+	0.110970i	0.896281	−	0.443488i	$-0.146259\pi$
$937$	1.96117	+	3.39685i	0.0640687	+	0.110970i	−0.832212	+	0.554458i	$0.812926\pi$
$938$		0			0
$939$	24.2393	−	15.4143i	0.791019	−	0.503027i
$940$		0			0
$941$	16.4739	+	13.8232i	0.537033	+	0.450625i	0.870522	−	0.492130i	$-0.163781\pi$
$941$	16.4739	+	13.8232i	0.537033	+	0.450625i	−0.333489	+	0.942754i	$0.608226\pi$
$942$		0			0
$943$	0.468629	+	0.170567i	0.0152607	+	0.00555443i
$944$		0			0
$945$	0.266320	+	2.06195i	0.00866339	+	0.0670752i
$946$		0			0
$947$	16.7169	+	6.08445i	0.543226	+	0.197718i	0.599034	−	0.800723i	$-0.295551\pi$
$947$	16.7169	+	6.08445i	0.543226	+	0.197718i	−0.0558084	+	0.998441i	$0.517774\pi$
$948$		0			0
$949$	24.3320	+	20.4170i	0.789850	+	0.662763i
$950$		0			0
$951$	−13.3199	−	6.94776i	−0.431929	−	0.225297i
$952$		0			0
$953$	11.9355	+	20.6729i	0.386629	+	0.669661i	0.991994	−	0.126287i	$-0.0403061\pi$
$953$	11.9355	+	20.6729i	0.386629	+	0.669661i	−0.605365	+	0.795948i	$0.706973\pi$
$954$		0			0
$955$	−11.2061	+	19.4095i	−0.362621	+	0.628078i
$956$		0			0
$957$	−4.57276	+	1.00984i	−0.147816	+	0.0326434i
$958$		0			0
$959$	−2.76516	+	1.00643i	−0.0892915	+	0.0324995i
$960$		0			0
$961$	4.30697	+	24.4261i	0.138935	+	0.787938i
$962$		0			0
$963$	15.7986	−	15.7470i	0.509101	−	0.507440i
$964$		0			0
$965$	−0.346458	+	0.290712i	−0.0111529	+	0.00935836i
$966$		0			0
$967$	−5.32943	+	30.2247i	−0.171383	+	0.971960i	0.770854	+	0.637012i	$0.219830\pi$
$967$	−5.32943	+	30.2247i	−0.171383	+	0.971960i	−0.942237	+	0.334948i	$0.891281\pi$
$968$		0			0
$969$	−16.4313	−	39.7605i	−0.527849	−	1.27729i
$970$		0			0
$971$	42.3837			1.36016			0.680078	−	0.733140i	$-0.261946\pi$
$971$	42.3837			1.36016			0.680078	+	0.733140i	$0.261946\pi$
$972$		0			0
$973$	6.69672			0.214687
$974$		0			0
$975$	15.5981	+	37.7443i	0.499538	+	1.20878i
$976$		0			0
$977$	−4.23952	+	24.0435i	−0.135634	+	0.769220i	0.838782	+	0.544468i	$0.183268\pi$
$977$	−4.23952	+	24.0435i	−0.135634	+	0.769220i	−0.974416	+	0.224752i	$0.927843\pi$
$978$		0			0
$979$	−5.70062	+	4.78339i	−0.182193	+	0.152878i
$980$		0			0
$981$	25.8930	−	25.8085i	0.826701	−	0.824003i
$982$		0			0
$983$	3.27232	+	18.5582i	0.104371	+	0.591915i	0.991470	+	0.130336i	$0.0416058\pi$
$983$	3.27232	+	18.5582i	0.104371	+	0.591915i	−0.887099	+	0.461579i	$0.847283\pi$
$984$		0			0
$985$	−8.12782	+	2.95828i	−0.258974	+	0.0942588i
$986$		0			0
$987$	−6.66340	+	1.47153i	−0.212098	+	0.0468392i
$988$		0			0
$989$	0.803439	−	1.39160i	0.0255479	−	0.0442502i
$990$		0			0
$991$	10.7816	+	18.6742i	0.342488	+	0.593207i	0.984894	−	0.173158i	$-0.0553971\pi$
$991$	10.7816	+	18.6742i	0.342488	+	0.593207i	−0.642406	+	0.766364i	$0.722064\pi$
$992$		0			0
$993$	4.88244	+	2.54671i	0.154939	+	0.0808173i
$994$		0			0
$995$	−16.5831	−	13.9149i	−0.525721	−	0.441132i
$996$		0			0
$997$	3.91532	+	1.42506i	0.123999	+	0.0451321i	0.403275	−	0.915079i	$-0.367872\pi$
$997$	3.91532	+	1.42506i	0.123999	+	0.0451321i	−0.279275	+	0.960211i	$0.590094\pi$
$998$		0			0
$999$	−4.65645	+	3.55492i	−0.147324	+	0.112473i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.y.b.193.3	✓	54
4.3	odd	2		864.2.y.c.193.7	yes	54
27.7	even	9	inner	864.2.y.b.385.3	yes	54
108.7	odd	18		864.2.y.c.385.7	yes	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.y.b.193.3	✓	54	1.1	even	1	trivial
864.2.y.b.385.3	yes	54	27.7	even	9	inner
864.2.y.c.193.7	yes	54	4.3	odd	2
864.2.y.c.385.7	yes	54	108.7	odd	18

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.y (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.661519 - 1.60075i) q^{3} +(0.197119 - 1.11792i) q^{5} +(-0.270013 + 0.226568i) q^{7} +(-2.12478 + 2.11785i) q^{9} +O(q^{10})\)	\(q+(-0.661519 - 1.60075i) q^{3} +(0.197119 - 1.11792i) q^{5} +(-0.270013 + 0.226568i) q^{7} +(-2.12478 + 2.11785i) q^{9} +(-0.174455 - 0.989381i) q^{11} +(-5.97001 + 2.17291i) q^{13} +(-1.91990 + 0.423986i) q^{15} +(-3.41720 + 5.91877i) q^{17} +(-1.81718 - 3.14745i) q^{19} +(0.541297 + 0.282344i) q^{21} +(0.200373 + 0.168133i) q^{23} +(3.48758 + 1.26938i) q^{25} +(4.79573 + 2.00024i) q^{27} +(2.52890 + 0.920444i) q^{29} +(-5.72245 - 4.80171i) q^{31} +(-1.46834 + 0.933752i) q^{33} +(0.200059 + 0.346513i) q^{35} +(-0.563717 + 0.976387i) q^{37} +(7.42756 + 8.11906i) q^{39} +(1.79162 - 0.652095i) q^{41} +(-1.06676 - 6.04992i) q^{43} +(1.94874 + 2.79280i) q^{45} +(-8.56245 + 7.18475i) q^{47} +(-1.19396 + 6.77130i) q^{49} +(11.7350 + 1.55470i) q^{51} -8.69660 q^{53} -1.14043 q^{55} +(-3.83617 + 4.99095i) q^{57} +(-1.32731 + 7.52756i) q^{59} +(-0.448757 + 0.376552i) q^{61} +(0.0938827 - 1.05326i) q^{63} +(1.25233 + 7.10230i) q^{65} +(10.0913 - 3.67293i) q^{67} +(0.136587 - 0.431969i) q^{69} +(-5.00739 + 8.67305i) q^{71} +(-2.49979 - 4.32977i) q^{73} +(-0.275152 - 6.42246i) q^{75} +(0.271267 + 0.227620i) q^{77} +(-0.961498 - 0.349957i) q^{79} +(0.0294179 - 8.99995i) q^{81} +(7.77701 + 2.83060i) q^{83} +(5.94309 + 4.98685i) q^{85} +(-0.199517 - 4.65702i) q^{87} +(-3.70362 - 6.41486i) q^{89} +(1.11967 - 1.93933i) q^{91} +(-3.90081 + 12.3366i) q^{93} +(-3.87679 + 1.41104i) q^{95} +(-1.66356 - 9.43453i) q^{97} +(2.46604 + 1.73275i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q+O(q^{10}) \) 54 * q	\( 54 q - 9 q^{11} + 12 q^{17} + 18 q^{19} + 12 q^{21} - 21 q^{27} + 6 q^{29} + 36 q^{31} - 9 q^{33} + 24 q^{39} + 3 q^{41} - 21 q^{43} + 42 q^{45} - 18 q^{49} + 24 q^{51} + 36 q^{53} - 72 q^{55} + 39 q^{57} + 18 q^{59} - 18 q^{61} - 30 q^{63} + 48 q^{65} - 27 q^{67} + 24 q^{69} - 84 q^{75} + 36 q^{77} + 72 q^{79} + 36 q^{81} + 6 q^{87} + 33 q^{89} + 36 q^{91} + 72 q^{93} + 36 q^{95} + 9 q^{97} + 120 q^{99}+O(q^{100}) \) 54 * q - 9 * q^11 + 12 * q^17 + 18 * q^19 + 12 * q^21 - 21 * q^27 + 6 * q^29 + 36 * q^31 - 9 * q^33 + 24 * q^39 + 3 * q^41 - 21 * q^43 + 42 * q^45 - 18 * q^49 + 24 * q^51 + 36 * q^53 - 72 * q^55 + 39 * q^57 + 18 * q^59 - 18 * q^61 - 30 * q^63 + 48 * q^65 - 27 * q^67 + 24 * q^69 - 84 * q^75 + 36 * q^77 + 72 * q^79 + 36 * q^81 + 6 * q^87 + 33 * q^89 + 36 * q^91 + 72 * q^93 + 36 * q^95 + 9 * q^97 + 120 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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