LMFDB - Embedded newform 576.3.n.c.353.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [576,3,Mod(353,576)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(576, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("576.353");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 576 = 2^{6} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	576.n (of order $6$, degree $2$, 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:	$15.6948632272$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			353.8
Character	$\chi$	$=$	576.353
Dual form			576.3.n.c.545.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.559363 - 2.94739i) q^{3} +(0.920717 + 1.59473i) q^{5} +(-4.56979 + 7.91511i) q^{7} +(-8.37423 + 3.29733i) q^{9} +O(q^{10})$	\(q+(-0.559363 - 2.94739i) q^{3} +(0.920717 + 1.59473i) q^{5} +(-4.56979 + 7.91511i) q^{7} +(-8.37423 + 3.29733i) q^{9} +(-3.81937 + 6.61534i) q^{11} +(15.7478 - 9.09201i) q^{13} +(4.18527 - 3.60575i) q^{15} -30.7770i q^{17} -10.9172i q^{19} +(25.8851 + 9.04153i) q^{21} +(12.5177 - 7.22708i) q^{23} +(10.8046 - 18.7140i) q^{25} +(14.4027 + 22.8377i) q^{27} +(18.9375 - 32.8007i) q^{29} +(-19.9319 - 34.5231i) q^{31} +(21.6344 + 7.55679i) q^{33} -16.8299 q^{35} +7.72657i q^{37} +(-35.6065 - 41.3292i) q^{39} +(-43.1646 + 24.9211i) q^{41} +(7.75029 + 4.47463i) q^{43} +(-12.9686 - 10.3187i) q^{45} +(12.9978 + 7.50427i) q^{47} +(-17.2659 - 29.9055i) q^{49} +(-90.7119 + 17.2155i) q^{51} +20.1038 q^{53} -14.0662 q^{55} +(-32.1771 + 6.10666i) q^{57} +(-19.0494 - 32.9945i) q^{59} +(90.9853 + 52.5304i) q^{61} +(12.1698 - 81.3510i) q^{63} +(28.9986 + 16.7423i) q^{65} +(-18.1407 + 10.4735i) q^{67} +(-28.3030 - 32.8519i) q^{69} -132.111i q^{71} -23.9882 q^{73} +(-61.2013 - 21.3773i) q^{75} +(-34.9074 - 60.4614i) q^{77} +(-21.1445 + 36.6233i) q^{79} +(59.2553 - 55.2251i) q^{81} +(18.7004 - 32.3901i) q^{83} +(49.0810 - 28.3369i) q^{85} +(-107.269 - 37.4687i) q^{87} -45.6700i q^{89} +166.194i q^{91} +(-90.6039 + 78.0582i) q^{93} +(17.4099 - 10.0516i) q^{95} +(41.6001 - 72.0535i) q^{97} +(10.1713 - 67.9921i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 18 q^{5} + 2 q^{9}+O(q^{10}) $ 32 * q - 18 * q^5 + 2 * q^9	$ 32 q - 18 q^{5} + 2 q^{9} + 30 q^{13} + 66 q^{21} - 74 q^{25} - 54 q^{29} - 120 q^{33} - 216 q^{41} - 366 q^{45} - 86 q^{49} + 144 q^{53} + 302 q^{57} - 42 q^{61} + 306 q^{65} + 54 q^{69} + 196 q^{73} - 414 q^{77} + 334 q^{81} - 180 q^{85} + 1002 q^{93} - 64 q^{97}+O(q^{100}) $ 32 * q - 18 * q^5 + 2 * q^9 + 30 * q^13 + 66 * q^21 - 74 * q^25 - 54 * q^29 - 120 * q^33 - 216 * q^41 - 366 * q^45 - 86 * q^49 + 144 * q^53 + 302 * q^57 - 42 * q^61 + 306 * q^65 + 54 * q^69 + 196 * q^73 - 414 * q^77 + 334 * q^81 - 180 * q^85 + 1002 * q^93 - 64 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/576\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$325$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.559363	−	2.94739i	−0.186454	−	0.982464i
$3$	−0.559363	−	2.94739i	−0.186454	−	0.982464i
$4$		0			0
$5$	0.920717	+	1.59473i	0.184143	+	0.318946i	0.943288	−	0.331977i	$-0.107716\pi$
$5$	0.920717	+	1.59473i	0.184143	+	0.318946i	−0.759144	+	0.650923i	$0.774382\pi$
$6$		0			0
$7$	−4.56979	+	7.91511i	−0.652827	+	1.13073i	0.329607	+	0.944118i	$0.393084\pi$
$7$	−4.56979	+	7.91511i	−0.652827	+	1.13073i	−0.982434	+	0.186611i	$0.940250\pi$
$8$		0			0
$9$	−8.37423	+	3.29733i	−0.930469	+	0.366369i
$10$		0			0
$11$	−3.81937	+	6.61534i	−0.347215	+	0.601395i	−0.985754	−	0.168195i	$-0.946206\pi$
$11$	−3.81937	+	6.61534i	−0.347215	+	0.601395i	0.638538	+	0.769590i	$0.279539\pi$
$12$		0			0
$13$	15.7478	−	9.09201i	1.21137	−	0.699385i	0.248313	−	0.968680i	$-0.420124\pi$
$13$	15.7478	−	9.09201i	1.21137	−	0.699385i	0.963058	+	0.269294i	$0.0867905\pi$
$14$		0			0
$15$	4.18527	−	3.60575i	0.279018	−	0.240383i
$16$		0			0
$17$		−	30.7770i		−	1.81041i	−0.424971	−	0.905207i	$-0.639716\pi$
$17$		−	30.7770i		−	1.81041i	0.424971	−	0.905207i	$-0.360284\pi$
$18$		0			0
$19$		−	10.9172i		−	0.574587i	−0.957843	−	0.287294i	$-0.907244\pi$
$19$		−	10.9172i		−	0.574587i	0.957843	−	0.287294i	$-0.0927556\pi$
$20$		0			0
$21$	25.8851	+	9.04153i	1.23262	+	0.430549i
$22$		0			0
$23$	12.5177	−	7.22708i	0.544247	−	0.314221i	−0.202552	−	0.979272i	$-0.564923\pi$
$23$	12.5177	−	7.22708i	0.544247	−	0.314221i	0.746798	+	0.665051i	$0.231590\pi$
$24$		0			0
$25$	10.8046	−	18.7140i	0.432182	−	0.748562i
$26$		0			0
$27$	14.4027	+	22.8377i	0.533435	+	0.845841i
$28$		0			0
$29$	18.9375	−	32.8007i	0.653017	−	1.13106i	−0.329369	−	0.944201i	$-0.606836\pi$
$29$	18.9375	−	32.8007i	0.653017	−	1.13106i	0.982387	−	0.186858i	$-0.0598305\pi$
$30$		0			0
$31$	−19.9319	−	34.5231i	−0.642965	−	1.11365i	−0.984767	−	0.173877i	$-0.944371\pi$
$31$	−19.9319	−	34.5231i	−0.642965	−	1.11365i	0.341802	−	0.939772i	$-0.388963\pi$
$32$		0			0
$33$	21.6344	+	7.55679i	0.655588	+	0.228994i
$34$		0			0
$35$	−16.8299			−0.480855
$36$		0			0
$37$			7.72657i			0.208826i	0.994534	+	0.104413i	$0.0332964\pi$
$37$			7.72657i			0.208826i	−0.994534	+	0.104413i	$0.966704\pi$
$38$		0			0
$39$	−35.6065	−	41.3292i	−0.912986	−	1.05972i
$40$		0			0
$41$	−43.1646	+	24.9211i	−1.05279	+	0.607831i	−0.923430	−	0.383766i	$-0.874627\pi$
$41$	−43.1646	+	24.9211i	−1.05279	+	0.607831i	−0.129364	+	0.991597i	$0.541294\pi$
$42$		0			0
$43$	7.75029	+	4.47463i	0.180239	+	0.104061i	0.587405	−	0.809293i	$-0.300150\pi$
$43$	7.75029	+	4.47463i	0.180239	+	0.104061i	−0.407166	+	0.913354i	$0.633483\pi$
$44$		0			0
$45$	−12.9686	−	10.3187i	−0.288192	−	0.229305i
$46$		0			0
$47$	12.9978	+	7.50427i	0.276548	+	0.159665i	0.631860	−	0.775083i	$-0.282292\pi$
$47$	12.9978	+	7.50427i	0.276548	+	0.159665i	−0.355311	+	0.934748i	$0.615625\pi$
$48$		0			0
$49$	−17.2659	−	29.9055i	−0.352366	−	0.610316i
$50$		0			0
$51$	−90.7119	+	17.2155i	−1.77867	+	0.337560i
$52$		0			0
$53$	20.1038			0.379316			0.189658	−	0.981850i	$-0.439262\pi$
$53$	20.1038			0.379316			0.189658	+	0.981850i	$0.439262\pi$
$54$		0			0
$55$	−14.0662			−0.255750
$56$		0			0
$57$	−32.1771	+	6.10666i	−0.564511	+	0.107134i
$58$		0			0
$59$	−19.0494	−	32.9945i	−0.322871	−	0.559228i	0.658208	−	0.752836i	$-0.271315\pi$
$59$	−19.0494	−	32.9945i	−0.322871	−	0.559228i	−0.981079	+	0.193607i	$0.937981\pi$
$60$		0			0
$61$	90.9853	+	52.5304i	1.49156	+	0.861154i	0.999953	−	0.00966279i	$-0.00307581\pi$
$61$	90.9853	+	52.5304i	1.49156	+	0.861154i	0.491608	+	0.870816i	$0.336409\pi$
$62$		0			0
$63$	12.1698	−	81.3510i	0.193171	−	1.29128i
$64$		0			0
$65$	28.9986	+	16.7423i	0.446132	+	0.257574i
$66$		0			0
$67$	−18.1407	+	10.4735i	−0.270756	+	0.156321i	−0.629231	−	0.777218i	$-0.716630\pi$
$67$	−18.1407	+	10.4735i	−0.270756	+	0.156321i	0.358475	+	0.933539i	$0.383297\pi$
$68$		0			0
$69$	−28.3030	−	32.8519i	−0.410188	−	0.476115i
$70$		0			0
$71$		−	132.111i		−	1.86072i	−0.366652	−	0.930358i	$-0.619496\pi$
$71$		−	132.111i		−	1.86072i	0.366652	−	0.930358i	$-0.380504\pi$
$72$		0			0
$73$	−23.9882			−0.328605			−0.164303	−	0.986410i	$-0.552537\pi$
$73$	−23.9882			−0.328605			−0.164303	+	0.986410i	$0.552537\pi$
$74$		0			0
$75$	−61.2013	−	21.3773i	−0.816017	−	0.285031i
$76$		0			0
$77$	−34.9074	−	60.4614i	−0.453343	−	0.785213i
$78$		0			0
$79$	−21.1445	+	36.6233i	−0.267651	+	0.463586i	−0.968255	−	0.249965i	$-0.919581\pi$
$79$	−21.1445	+	36.6233i	−0.267651	+	0.463586i	0.700604	+	0.713551i	$0.252914\pi$
$80$		0			0
$81$	59.2553	−	55.2251i	0.731547	−	0.681791i
$82$		0			0
$83$	18.7004	−	32.3901i	0.225306	−	0.390242i	−0.731105	−	0.682265i	$-0.760995\pi$
$83$	18.7004	−	32.3901i	0.225306	−	0.390242i	0.956411	+	0.292023i	$0.0943284\pi$
$84$		0			0
$85$	49.0810	−	28.3369i	0.577424	−	0.333376i
$86$		0			0
$87$	−107.269	−	37.4687i	−1.23298	−	0.430675i
$88$		0			0
$89$		−	45.6700i		−	0.513146i	−0.966525	−	0.256573i	$-0.917407\pi$
$89$		−	45.6700i		−	0.513146i	0.966525	−	0.256573i	$-0.0825935\pi$
$90$		0			0
$91$			166.194i			1.82631i
$92$		0			0
$93$	−90.6039	+	78.0582i	−0.974236	+	0.839335i
$94$		0			0
$95$	17.4099	−	10.0516i	0.183262	−	0.105806i
$96$		0			0
$97$	41.6001	−	72.0535i	0.428867	−	0.742820i	−0.567906	−	0.823094i	$-0.692246\pi$
$97$	41.6001	−	72.0535i	0.428867	−	0.742820i	0.996773	+	0.0802740i	$0.0255795\pi$
$98$		0			0
$99$	10.1713	−	67.9921i	0.102741	−	0.686789i
$100$		0			0
$101$	74.5873	−	129.189i	0.738489	−	1.27910i	−0.214687	−	0.976683i	$-0.568873\pi$
$101$	74.5873	−	129.189i	0.738489	−	1.27910i	0.953176	−	0.302417i	$-0.0977934\pi$
$102$		0			0
$103$	66.5665	+	115.296i	0.646276	+	1.11938i	0.984005	+	0.178140i	$0.0570080\pi$
$103$	66.5665	+	115.296i	0.646276	+	1.11938i	−0.337729	+	0.941243i	$0.609659\pi$
$104$		0			0
$105$	9.41405	+	49.6044i	0.0896576	+	0.472423i
$106$		0			0
$107$	104.310			0.974855			0.487428	−	0.873163i	$-0.337935\pi$
$107$	104.310			0.974855			0.487428	+	0.873163i	$0.337935\pi$
$108$		0			0
$109$			51.1660i			0.469413i	0.972066	+	0.234706i	$0.0754129\pi$
$109$			51.1660i			0.469413i	−0.972066	+	0.234706i	$0.924587\pi$
$110$		0			0
$111$	22.7732	−	4.32196i	0.205164	−	0.0389366i
$112$		0			0
$113$	−89.8153	+	51.8549i	−0.794825	+	0.458893i	−0.841659	−	0.540010i	$-0.818420\pi$
$113$	−89.8153	+	51.8549i	−0.794825	+	0.458893i	0.0468333	+	0.998903i	$0.485087\pi$
$114$		0			0
$115$	23.0505	+	13.3082i	0.200439	+	0.115723i
$116$		0			0
$117$	−101.896	+	128.064i	−0.870910	+	1.09457i
$118$		0			0
$119$	243.603	+	140.645i	2.04709	+	1.18189i
$120$		0			0
$121$	31.3248	+	54.2562i	0.258883	+	0.448398i
$122$		0			0
$123$	97.5968	+	113.283i	0.793470	+	0.920999i
$124$		0			0
$125$	85.8276			0.686621
$126$		0			0
$127$	−136.733			−1.07664			−0.538319	−	0.842741i	$-0.680941\pi$
$127$	−136.733			−1.07664			−0.538319	+	0.842741i	$0.680941\pi$
$128$		0			0
$129$	8.85326	−	25.3461i	0.0686299	−	0.196481i
$130$		0			0
$131$	−93.7823	−	162.436i	−0.715895	−	1.23997i	−0.962613	−	0.270879i	$-0.912686\pi$
$131$	−93.7823	−	162.436i	−0.715895	−	1.23997i	0.246718	−	0.969087i	$-0.420648\pi$
$132$		0			0
$133$	86.4105	+	49.8891i	0.649703	+	0.375106i
$134$		0			0
$135$	−23.1591	+	43.9955i	−0.171549	+	0.325893i
$136$		0			0
$137$	−161.057	−	92.9862i	−1.17560	−	0.678732i	−0.220606	−	0.975363i	$-0.570803\pi$
$137$	−161.057	−	92.9862i	−1.17560	−	0.678732i	−0.954992	+	0.296631i	$0.904137\pi$
$138$		0			0
$139$	201.731	−	116.469i	1.45130	−	0.837908i	0.452744	−	0.891641i	$-0.350445\pi$
$139$	201.731	−	116.469i	1.45130	−	0.837908i	0.998555	+	0.0537326i	$0.0171119\pi$
$140$		0			0
$141$	14.8475	−	42.5071i	0.105302	−	0.301469i
$142$		0			0
$143$			138.903i			0.971350i
$144$		0			0
$145$	69.7443			0.480995
$146$		0			0
$147$	−78.4852	+	67.6175i	−0.533913	+	0.459983i
$148$		0			0
$149$	−108.575	−	188.057i	−0.728690	−	1.26213i	−0.957437	−	0.288642i	$-0.906796\pi$
$149$	−108.575	−	188.057i	−0.728690	−	1.26213i	0.228747	−	0.973486i	$-0.426537\pi$
$150$		0			0
$151$	−135.092	+	233.986i	−0.894648	+	1.54957i	−0.0604073	+	0.998174i	$0.519240\pi$
$151$	−135.092	+	233.986i	−0.894648	+	1.54957i	−0.834240	+	0.551401i	$0.814093\pi$
$152$		0			0
$153$	101.482	+	257.734i	0.663280	+	1.68453i
$154$		0			0
$155$	36.7033	−	63.5720i	0.236796	−	0.410142i
$156$		0			0
$157$	71.4453	−	41.2490i	0.455066	−	0.262732i	−0.254901	−	0.966967i	$-0.582043\pi$
$157$	71.4453	−	41.2490i	0.455066	−	0.262732i	0.709967	+	0.704235i	$0.248710\pi$
$158$		0			0
$159$	−11.2453	−	59.2536i	−0.0707252	−	0.372664i
$160$		0			0
$161$			132.105i			0.820527i
$162$		0			0
$163$		−	170.850i		−	1.04816i	−0.851668	−	0.524081i	$-0.824409\pi$
$163$		−	170.850i		−	1.04816i	0.851668	−	0.524081i	$-0.175591\pi$
$164$		0			0
$165$	7.86814	+	41.4587i	0.0476857	+	0.251265i
$166$		0			0
$167$	22.0145	−	12.7101i	0.131823	−	0.0761083i	−0.432638	−	0.901568i	$-0.642417\pi$
$167$	22.0145	−	12.7101i	0.131823	−	0.0761083i	0.564461	+	0.825459i	$0.309084\pi$
$168$		0			0
$169$	80.8293	−	140.000i	0.478280	−	0.828405i
$170$		0			0
$171$	35.9974	+	91.4228i	0.210511	+	0.534636i
$172$		0			0
$173$	−153.244	+	265.426i	−0.885803	+	1.53426i	−0.0410133	+	0.999159i	$0.513059\pi$
$173$	−153.244	+	265.426i	−0.885803	+	1.53426i	−0.844790	+	0.535098i	$0.820275\pi$
$174$		0			0
$175$	98.7491	+	171.038i	0.564281	+	0.977363i
$176$		0			0
$177$	−86.5921	+	74.6018i	−0.489221	+	0.421479i
$178$		0			0
$179$	−220.996			−1.23462			−0.617308	−	0.786722i	$-0.711777\pi$
$179$	−220.996			−1.23462			−0.617308	+	0.786722i	$0.711777\pi$
$180$		0			0
$181$			211.405i			1.16798i	0.811759	+	0.583992i	$0.198510\pi$
$181$			211.405i			1.16798i	−0.811759	+	0.583992i	$0.801490\pi$
$182$		0			0
$183$	103.934	−	297.553i	0.567944	−	1.62597i
$184$		0			0
$185$	−12.3218	+	7.11399i	−0.0666043	+	0.0384540i
$186$		0			0
$187$	203.601	+	117.549i	1.08877	+	0.628604i
$188$		0			0
$189$	−246.580	+	9.63571i	−1.30466	+	0.0509826i
$190$		0			0
$191$	210.554	+	121.563i	1.10238	+	0.636458i	0.936844	−	0.349747i	$-0.113732\pi$
$191$	210.554	+	121.563i	1.10238	+	0.636458i	0.165533	+	0.986204i	$0.447066\pi$
$192$		0			0
$193$	−55.6885	−	96.4553i	−0.288541	−	0.499768i	0.684920	−	0.728618i	$-0.259837\pi$
$193$	−55.6885	−	96.4553i	−0.288541	−	0.499768i	−0.973462	+	0.228850i	$0.926504\pi$
$194$		0			0
$195$	33.1255	−	94.8352i	0.169874	−	0.486334i
$196$		0			0
$197$	−138.054			−0.700782			−0.350391	−	0.936604i	$-0.613951\pi$
$197$	−138.054			−0.700782			−0.350391	+	0.936604i	$0.613951\pi$
$198$		0			0
$199$	33.4917			0.168300			0.0841500	−	0.996453i	$-0.473183\pi$
$199$	33.4917			0.168300			0.0841500	+	0.996453i	$0.473183\pi$
$200$		0			0
$201$	41.0168	+	47.6091i	0.204064	+	0.236861i
$202$		0			0
$203$	173.081	+	299.785i	0.852615	+	1.47677i
$204$		0			0
$205$	−79.4847	−	45.8905i	−0.387730	−	0.223856i
$206$		0			0
$207$	−80.9958	+	101.796i	−0.391284	+	0.491768i
$208$		0			0
$209$	72.2207	+	41.6967i	0.345554	+	0.199506i
$210$		0			0
$211$	−85.4798	+	49.3518i	−0.405117	+	0.233895i	−0.688690	−	0.725056i	$-0.741814\pi$
$211$	−85.4798	+	49.3518i	−0.405117	+	0.233895i	0.283572	+	0.958951i	$0.408480\pi$
$212$		0			0
$213$	−389.382	+	73.8980i	−1.82809	+	0.346939i
$214$		0			0
$215$			16.4795i			0.0766487i
$216$		0			0
$217$	364.339			1.67898
$218$		0			0
$219$	13.4181	+	70.7026i	0.0612699	+	0.322843i
$220$		0			0
$221$	−279.825	−	484.671i	−1.26618	−	2.19308i
$222$		0			0
$223$	−93.0832	+	161.225i	−0.417414	+	0.722981i	−0.995678	−	0.0928676i	$-0.970397\pi$
$223$	−93.0832	+	161.225i	−0.417414	+	0.722981i	0.578265	+	0.815849i	$0.303730\pi$
$224$		0			0
$225$	−28.7735	+	192.342i	−0.127882	+	0.854852i
$226$		0			0
$227$	222.402	−	385.212i	0.979746	−	1.69697i	0.316454	−	0.948608i	$-0.397508\pi$
$227$	222.402	−	385.212i	0.979746	−	1.69697i	0.663291	−	0.748361i	$-0.269159\pi$
$228$		0			0
$229$	−73.3756	+	42.3634i	−0.320418	+	0.184993i	−0.651579	−	0.758581i	$-0.725893\pi$
$229$	−73.3756	+	42.3634i	−0.320418	+	0.184993i	0.331161	+	0.943574i	$0.392560\pi$
$230$		0			0
$231$	−158.678	+	136.706i	−0.686916	+	0.591800i
$232$		0			0
$233$		−	181.796i		−	0.780242i	−0.920764	−	0.390121i	$-0.872433\pi$
$233$		−	181.796i		−	0.780242i	0.920764	−	0.390121i	$-0.127567\pi$
$234$		0			0
$235$			27.6372i			0.117605i
$236$		0			0
$237$	119.771	+	41.8353i	0.505361	+	0.176520i
$238$		0			0
$239$	200.031	−	115.488i	0.836951	−	0.483214i	−0.0192757	−	0.999814i	$-0.506136\pi$
$239$	200.031	−	115.488i	0.836951	−	0.483214i	0.856227	+	0.516600i	$0.172803\pi$
$240$		0			0
$241$	−206.202	+	357.153i	−0.855612	+	1.48196i	0.0204644	+	0.999791i	$0.493486\pi$
$241$	−206.202	+	357.153i	−0.855612	+	1.48196i	−0.876076	+	0.482173i	$0.839848\pi$
$242$		0			0
$243$	−195.915	−	143.758i	−0.806235	−	0.591595i
$244$		0			0
$245$	31.7941	−	55.0689i	0.129772	−	0.224771i
$246$		0			0
$247$	−99.2589	−	171.921i	−0.401858	−	0.696038i
$248$		0			0
$249$	−105.926	−	36.9996i	−0.425408	−	0.148593i
$250$		0			0
$251$	−49.9321			−0.198933			−0.0994663	−	0.995041i	$-0.531714\pi$
$251$	−49.9321			−0.198933			−0.0994663	+	0.995041i	$0.531714\pi$
$252$		0			0
$253$			110.412i			0.436409i
$254$		0			0
$255$	−110.974	−	128.810i	−0.435193	−	0.505138i
$256$		0			0
$257$	−113.337	+	65.4352i	−0.441000	+	0.254612i	−0.704022	−	0.710178i	$-0.748614\pi$
$257$	−113.337	+	65.4352i	−0.441000	+	0.254612i	0.263022	+	0.964790i	$0.415281\pi$
$258$		0			0
$259$	−61.1566	−	35.3088i	−0.236126	−	0.136327i
$260$		0			0
$261$	−50.4323	+	337.124i	−0.193227	+	1.29166i
$262$		0			0
$263$	77.4773	+	44.7316i	0.294591	+	0.170082i	0.640010	−	0.768366i	$-0.278930\pi$
$263$	77.4773	+	44.7316i	0.294591	+	0.170082i	−0.345420	+	0.938448i	$0.612263\pi$
$264$		0			0
$265$	18.5099	+	32.0600i	0.0698486	+	0.120981i
$266$		0			0
$267$	−134.607	+	25.5461i	−0.504148	+	0.0956784i
$268$		0			0
$269$	428.087			1.59140			0.795701	−	0.605690i	$-0.207103\pi$
$269$	428.087			1.59140			0.795701	+	0.605690i	$0.207103\pi$
$270$		0			0
$271$	36.2602			0.133802			0.0669008	−	0.997760i	$-0.478689\pi$
$271$	36.2602			0.133802			0.0669008	+	0.997760i	$0.478689\pi$
$272$		0			0
$273$	489.839	−	92.9630i	1.79428	−	0.340524i
$274$		0			0
$275$	82.5332	+	142.952i	0.300121	+	0.519824i
$276$		0			0
$277$	130.359	+	75.2631i	0.470612	+	0.271708i	0.716496	−	0.697591i	$-0.245745\pi$
$277$	130.359	+	75.2631i	0.470612	+	0.271708i	−0.245884	+	0.969299i	$0.579078\pi$
$278$		0			0
$279$	280.748	+	223.382i	1.00627	+	0.800653i
$280$		0			0
$281$	132.933	+	76.7492i	0.473073	+	0.273129i	0.717525	−	0.696533i	$-0.245275\pi$
$281$	132.933	+	76.7492i	0.473073	+	0.273129i	−0.244452	+	0.969661i	$0.578608\pi$
$282$		0			0
$283$	−61.5307	+	35.5247i	−0.217423	+	0.125529i	−0.604756	−	0.796411i	$-0.706730\pi$
$283$	−61.5307	+	35.5247i	−0.217423	+	0.125529i	0.387334	+	0.921940i	$0.373396\pi$
$284$		0			0
$285$	−39.3645	−	45.6913i	−0.138121	−	0.160320i
$286$		0			0
$287$		−	455.536i		−	1.58723i
$288$		0			0
$289$	−658.226			−2.27760
$290$		0			0
$291$	−235.639	−	82.3077i	−0.809757	−	0.282844i
$292$		0			0
$293$	111.469	+	193.070i	0.380441	+	0.658942i	0.991125	−	0.132931i	$-0.0424390\pi$
$293$	111.469	+	193.070i	0.380441	+	0.658942i	−0.610685	+	0.791874i	$0.709106\pi$
$294$		0			0
$295$	35.0782	−	60.7571i	0.118909	−	0.205956i
$296$		0			0
$297$	−206.089	+	8.05340i	−0.693901	+	0.0271158i
$298$		0			0
$299$	131.417	−	227.622i	0.439523	−	0.761276i
$300$		0			0
$301$	−70.8344	+	40.8962i	−0.235330	+	0.135868i
$302$		0			0
$303$	−422.492	−	147.574i	−1.39436	−	0.487044i
$304$		0			0
$305$			193.462i			0.634303i
$306$		0			0
$307$			285.699i			0.930614i	0.885149	+	0.465307i	$0.154056\pi$
$307$			285.699i			0.930614i	−0.885149	+	0.465307i	$0.845944\pi$
$308$		0			0
$309$	302.589	−	260.690i	0.979252	−	0.843657i
$310$		0			0
$311$	−369.736	+	213.467i	−1.18886	+	0.686390i	−0.958048	−	0.286608i	$-0.907472\pi$
$311$	−369.736	+	213.467i	−1.18886	+	0.686390i	−0.230814	+	0.972998i	$0.574139\pi$
$312$		0			0
$313$	225.712	−	390.944i	0.721124	−	1.24902i	−0.239426	−	0.970915i	$-0.576959\pi$
$313$	225.712	−	390.944i	0.721124	−	1.24902i	0.960550	−	0.278108i	$-0.0897074\pi$
$314$		0			0
$315$	140.938	−	55.4937i	0.447421	−	0.176171i
$316$		0			0
$317$	2.83099	−	4.90342i	0.00893057	−	0.0154682i	−0.861526	−	0.507714i	$-0.830491\pi$
$317$	2.83099	−	4.90342i	0.00893057	−	0.0154682i	0.870456	+	0.492246i	$0.163824\pi$
$318$		0			0
$319$	144.659	+	250.556i	0.453475	+	0.785443i
$320$		0			0
$321$	−58.3469	−	307.441i	−0.181766	−	0.957760i
$322$		0			0
$323$	−335.998			−1.04024
$324$		0			0
$325$		−	392.941i		−	1.20905i
$326$		0			0
$327$	150.806	−	28.6204i	0.461181	−	0.0875241i
$328$		0			0
$329$	−118.794	+	68.5858i	−0.361076	+	0.208468i
$330$		0			0
$331$	255.584	+	147.561i	0.772157	+	0.445805i	0.833643	−	0.552303i	$-0.186251\pi$
$331$	255.584	+	147.561i	0.772157	+	0.445805i	−0.0614867	+	0.998108i	$0.519584\pi$
$332$		0			0
$333$	−25.4770	−	64.7041i	−0.0765076	−	0.194307i
$334$		0			0
$335$	−33.4048	−	19.2863i	−0.0997160	−	0.0575710i
$336$		0			0
$337$	−156.434	−	270.952i	−0.464196	−	0.804012i	0.534968	−	0.844872i	$-0.320323\pi$
$337$	−156.434	−	270.952i	−0.464196	−	0.804012i	−0.999165	+	0.0408603i	$0.986990\pi$
$338$		0			0
$339$	203.076	+	235.715i	0.599044	+	0.695324i
$340$		0			0
$341$	304.510			0.892990
$342$		0			0
$343$	−132.233			−0.385518
$344$		0			0
$345$	26.3309	−	75.3829i	0.0763213	−	0.218501i
$346$		0			0
$347$	30.2492	+	52.3931i	0.0871734	+	0.150989i	0.906315	−	0.422602i	$-0.138883\pi$
$347$	30.2492	+	52.3931i	0.0871734	+	0.150989i	−0.819142	+	0.573591i	$0.805550\pi$
$348$		0			0
$349$	445.021	+	256.933i	1.27513	+	0.736198i	0.975949	−	0.217997i	$-0.0699523\pi$
$349$	445.021	+	256.933i	1.27513	+	0.736198i	0.299184	+	0.954196i	$0.403286\pi$
$350$		0			0
$351$	434.453	+	228.694i	1.23776	+	0.651551i
$352$		0			0
$353$	238.086	+	137.459i	0.674466	+	0.389403i	0.797767	−	0.602966i	$-0.206015\pi$
$353$	238.086	+	137.459i	0.674466	+	0.389403i	−0.123301	+	0.992369i	$0.539348\pi$
$354$		0			0
$355$	210.681	−	121.637i	0.593468	−	0.342639i
$356$		0			0
$357$	278.271	−	796.666i	0.779472	−	2.23156i
$358$		0			0
$359$		−	2.40904i		−	0.00671042i	−0.999994	−	0.00335521i	$-0.998932\pi$
$359$		−	2.40904i		−	0.00671042i	0.999994	−	0.00335521i	$-0.00106800\pi$
$360$		0			0
$361$	241.816			0.669849
$362$		0			0
$363$	142.392	−	122.675i	0.392265	−	0.337949i
$364$		0			0
$365$	−22.0863	−	38.2547i	−0.0605105	−	0.104807i
$366$		0			0
$367$	195.126	−	337.968i	0.531678	−	0.920894i	−0.467638	−	0.883920i	$-0.654895\pi$
$367$	195.126	−	337.968i	0.531678	−	0.920894i	0.999316	−	0.0369739i	$-0.0117718\pi$
$368$		0			0
$369$	279.297	−	351.022i	0.756902	−	0.951280i
$370$		0			0
$371$	−91.8699	+	159.123i	−0.247628	+	0.428904i
$372$		0			0
$373$	98.7732	−	57.0267i	0.264807	−	0.152887i	−0.361718	−	0.932287i	$-0.617810\pi$
$373$	98.7732	−	57.0267i	0.264807	−	0.152887i	0.626526	+	0.779401i	$0.284476\pi$
$374$		0			0
$375$	−48.0088	−	252.968i	−0.128024	−	0.674580i
$376$		0			0
$377$		−	688.720i		−	1.82684i
$378$		0			0
$379$		−	294.626i		−	0.777377i	−0.921369	−	0.388689i	$-0.872928\pi$
$379$		−	294.626i		−	0.777377i	0.921369	−	0.388689i	$-0.127072\pi$
$380$		0			0
$381$	76.4835	+	403.006i	0.200744	+	1.05776i
$382$		0			0
$383$	−413.559	+	238.769i	−1.07979	+	0.623417i	−0.930840	−	0.365428i	$-0.880923\pi$
$383$	−413.559	+	238.769i	−1.07979	+	0.623417i	−0.148950	+	0.988845i	$0.547589\pi$
$384$		0			0
$385$	64.2797	−	111.336i	0.166960	−	0.289184i
$386$		0			0
$387$	−79.6570	−	11.9163i	−0.205832	−	0.0307916i
$388$		0			0
$389$	−200.807	+	347.808i	−0.516213	+	0.894108i	0.483610	+	0.875284i	$0.339325\pi$
$389$	−200.807	+	347.808i	−0.516213	+	0.894108i	−0.999823	+	0.0188238i	$0.994008\pi$
$390$		0			0
$391$	−222.428	−	385.257i	−0.568870	−	0.985311i
$392$		0			0
$393$	−426.303	+	367.274i	−1.08474	+	0.934538i
$394$		0			0
$395$	−77.8722			−0.197145
$396$		0			0
$397$		−	296.399i		−	0.746598i	−0.927711	−	0.373299i	$-0.878227\pi$
$397$		−	296.399i		−	0.746598i	0.927711	−	0.373299i	$-0.121773\pi$
$398$		0			0
$399$	98.7078	−	282.592i	0.247388	−	0.708250i
$400$		0			0
$401$	86.2049	−	49.7704i	0.214975	−	0.124116i	−0.388646	−	0.921387i	$-0.627057\pi$
$401$	86.2049	−	49.7704i	0.214975	−	0.124116i	0.603621	+	0.797271i	$0.293724\pi$
$402$		0			0
$403$	−627.769	−	362.443i	−1.55774	−	0.899361i
$404$		0			0
$405$	142.626	+	43.6494i	0.352164	+	0.107776i
$406$		0			0
$407$	−51.1139	−	29.5106i	−0.125587	−	0.0725077i
$408$		0			0
$409$	216.978	+	375.816i	0.530508	+	0.918867i	0.999366	+	0.0355933i	$0.0113321\pi$
$409$	216.978	+	375.816i	0.530508	+	0.918867i	−0.468858	+	0.883273i	$0.655335\pi$
$410$		0			0
$411$	−183.977	+	526.711i	−0.447634	+	1.28153i
$412$		0			0
$413$	348.206			0.843114
$414$		0			0
$415$	68.8711			0.165955
$416$		0			0
$417$	−456.121	−	529.430i	−1.09382	−	1.26962i
$418$		0			0
$419$	88.3811	+	153.081i	0.210933	+	0.365347i	0.952007	−	0.306076i	$-0.0990163\pi$
$419$	88.3811	+	153.081i	0.210933	+	0.365347i	−0.741073	+	0.671424i	$0.765683\pi$
$420$		0			0
$421$	−296.515	−	171.193i	−0.704312	−	0.406635i	0.104639	−	0.994510i	$-0.466631\pi$
$421$	−296.515	−	171.193i	−0.704312	−	0.406635i	−0.808951	+	0.587876i	$0.799964\pi$
$422$		0			0
$423$	−133.590	−	19.9845i	−0.315816	−	0.0472448i
$424$		0			0
$425$	−575.963	−	332.532i	−1.35521	−	0.782429i
$426$		0			0
$427$	−831.567	+	480.105i	−1.94746	+	1.12437i
$428$		0			0
$429$	409.401	−	77.6972i	0.954316	−	0.181112i
$430$		0			0
$431$		−	613.169i		−	1.42267i	−0.702855	−	0.711333i	$-0.748092\pi$
$431$		−	613.169i		−	1.42267i	0.702855	−	0.711333i	$-0.251908\pi$
$432$		0			0
$433$	172.934			0.399386			0.199693	−	0.979859i	$-0.436006\pi$
$433$	172.934			0.399386			0.199693	+	0.979859i	$0.436006\pi$
$434$		0			0
$435$	−39.0124	−	205.564i	−0.0896837	−	0.472560i
$436$		0			0
$437$	−78.8992	−	136.657i	−0.180547	−	0.312717i
$438$		0			0
$439$	318.835	−	552.239i	0.726276	−	1.25795i	−0.232171	−	0.972675i	$-0.574583\pi$
$439$	318.835	−	552.239i	0.726276	−	1.25795i	0.958447	−	0.285272i	$-0.0920839\pi$
$440$		0			0
$441$	243.197	+	193.504i	0.551467	+	0.438784i
$442$		0			0
$443$	−353.126	+	611.632i	−0.797123	+	1.38066i	0.124359	+	0.992237i	$0.460313\pi$
$443$	−353.126	+	611.632i	−0.797123	+	1.38066i	−0.921482	+	0.388421i	$0.873021\pi$
$444$		0			0
$445$	72.8313	−	42.0492i	0.163666	−	0.0944925i
$446$		0			0
$447$	−493.545	+	425.205i	−1.10413	+	0.951241i
$448$		0			0
$449$			88.2356i			0.196516i	0.995161	+	0.0982579i	$0.0313270\pi$
$449$			88.2356i			0.196516i	−0.995161	+	0.0982579i	$0.968673\pi$
$450$		0			0
$451$		−	380.731i		−	0.844193i
$452$		0			0
$453$	765.213	+	267.285i	1.68921	+	0.590033i
$454$		0			0
$455$	−265.035	+	153.018i	−0.582494	+	0.336303i
$456$		0			0
$457$	−348.107	+	602.939i	−0.761722	+	1.31934i	0.180240	+	0.983623i	$0.442313\pi$
$457$	−348.107	+	602.939i	−0.761722	+	1.31934i	−0.941962	+	0.335719i	$0.891021\pi$
$458$		0			0
$459$	702.877	−	443.274i	1.53132	−	0.965738i
$460$		0			0
$461$	−312.264	+	540.857i	−0.677363	+	1.17323i	0.298410	+	0.954438i	$0.403544\pi$
$461$	−312.264	+	540.857i	−0.677363	+	1.17323i	−0.975772	+	0.218788i	$0.929790\pi$
$462$		0			0
$463$	−261.798	−	453.447i	−0.565438	−	0.979367i	−0.997009	−	0.0772884i	$-0.975374\pi$
$463$	−261.798	−	453.447i	−0.565438	−	0.979367i	0.431571	−	0.902079i	$-0.357960\pi$
$464$		0			0
$465$	−207.902	−	72.6192i	−0.447101	−	0.156170i
$466$		0			0
$467$	−106.125			−0.227248			−0.113624	−	0.993524i	$-0.536246\pi$
$467$	−106.125			−0.227248			−0.113624	+	0.993524i	$0.536246\pi$
$468$		0			0
$469$		−	191.447i		−	0.408203i
$470$		0			0
$471$	−161.541	−	187.504i	−0.342974	−	0.398098i
$472$		0			0
$473$	−59.2024	+	34.1805i	−0.125164	+	0.0722633i
$474$		0			0
$475$	−204.304	−	117.955i	−0.430114	−	0.248327i
$476$		0			0
$477$	−168.353	+	66.2886i	−0.352942	+	0.138970i
$478$		0			0
$479$	291.982	+	168.576i	0.609565	+	0.351933i	0.772795	−	0.634655i	$-0.218858\pi$
$479$	291.982	+	168.576i	0.609565	+	0.351933i	−0.163230	+	0.986588i	$0.552191\pi$
$480$		0			0
$481$	70.2501	+	121.677i	0.146050	+	0.252966i
$482$		0			0
$483$	389.365	−	73.8947i	0.806138	−	0.152991i
$484$		0			0
$485$	153.208			0.315892
$486$		0			0
$487$	89.4910			0.183760			0.0918799	−	0.995770i	$-0.470712\pi$
$487$	89.4910			0.183760			0.0918799	+	0.995770i	$0.470712\pi$
$488$		0			0
$489$	−503.563	+	95.5675i	−1.02978	+	0.195435i
$490$		0			0
$491$	−255.696	−	442.879i	−0.520766	−	0.901993i	−0.999708	−	0.0241469i	$-0.992313\pi$
$491$	−255.696	−	442.879i	−0.520766	−	0.901993i	0.478942	−	0.877846i	$-0.341020\pi$
$492$		0			0
$493$	−1009.51	−	582.840i	−2.04769	−	1.18223i
$494$		0			0
$495$	117.794	−	46.3810i	0.237967	−	0.0936989i
$496$		0			0
$497$	1045.67	+	603.719i	2.10397	+	1.21473i
$498$		0			0
$499$	1.97568	−	1.14066i	0.00395929	−	0.00228590i	−0.498019	−	0.867166i	$-0.665939\pi$
$499$	1.97568	−	1.14066i	0.00395929	−	0.00228590i	0.501978	+	0.864880i	$0.332606\pi$
$500$		0			0
$501$	−49.7757	−	57.7758i	−0.0993526	−	0.115321i
$502$		0			0
$503$		−	702.224i		−	1.39607i	−0.716063	−	0.698036i	$-0.754058\pi$
$503$		−	702.224i		−	1.39607i	0.716063	−	0.698036i	$-0.245942\pi$
$504$		0			0
$505$	274.695			0.543951
$506$		0			0
$507$	−457.849	−	159.924i	−0.903055	−	0.315433i
$508$		0			0
$509$	56.9044	+	98.5614i	0.111797	+	0.193637i	0.916495	−	0.400047i	$-0.131006\pi$
$509$	56.9044	+	98.5614i	0.111797	+	0.193637i	−0.804698	+	0.593684i	$0.797673\pi$
$510$		0			0
$511$	109.621	−	189.869i	0.214522	−	0.371564i
$512$		0			0
$513$	249.323	−	157.237i	0.486010	−	0.306505i
$514$		0			0
$515$	−122.578	+	212.311i	−0.238015	+	0.412254i
$516$		0			0
$517$	−99.2866	+	57.3231i	−0.192044	+	0.110876i
$518$		0			0
$519$	868.034	+	303.200i	1.67251	+	0.584201i
$520$		0			0
$521$		−	766.079i		−	1.47040i	−0.677849	−	0.735201i	$-0.737088\pi$
$521$		−	766.079i		−	1.47040i	0.677849	−	0.735201i	$-0.262912\pi$
$522$		0			0
$523$			28.1668i			0.0538562i	0.999637	+	0.0269281i	$0.00857252\pi$
$523$			28.1668i			0.0538562i	−0.999637	+	0.0269281i	$0.991427\pi$
$524$		0			0
$525$	448.881	−	386.725i	0.855011	−	0.736619i
$526$		0			0
$527$	−1062.52	+	613.446i	−2.01616	+	1.16403i
$528$		0			0
$529$	−160.039	+	277.195i	−0.302530	+	0.523998i
$530$		0			0
$531$	268.317	+	213.491i	0.505305	+	0.402055i
$532$		0			0
$533$	−453.165	+	784.905i	−0.850216	+	1.47262i
$534$		0			0
$535$	96.0396	+	166.345i	0.179513	+	0.310926i
$536$		0			0
$537$	123.617	+	651.362i	0.230200	+	1.21297i
$538$		0			0
$539$	263.780			0.489387
$540$		0			0
$541$			65.6575i			0.121363i	0.998157	+	0.0606816i	$0.0193274\pi$
$541$			65.6575i			0.121363i	−0.998157	+	0.0606816i	$0.980673\pi$
$542$		0			0
$543$	623.094	−	118.252i	1.14750	−	0.217776i
$544$		0			0
$545$	−81.5959	+	47.1094i	−0.149717	+	0.0864393i
$546$		0			0
$547$	442.899	+	255.708i	0.809687	+	0.467473i	0.846847	−	0.531836i	$-0.178498\pi$
$547$	442.899	+	255.708i	0.809687	+	0.467473i	−0.0371602	+	0.999309i	$0.511831\pi$
$548$		0			0
$549$	−935.141	−	139.893i	−1.70335	−	0.254814i
$550$		0			0
$551$	−358.091	−	206.744i	−0.649892	−	0.375216i
$552$		0			0
$553$	−193.251	−	334.721i	−0.349460	−	0.605282i
$554$		0			0
$555$	27.8601	+	32.3378i	0.0501983	+	0.0582664i
$556$		0			0
$557$	70.9792			0.127431			0.0637156	−	0.997968i	$-0.479705\pi$
$557$	70.9792			0.127431			0.0637156	+	0.997968i	$0.479705\pi$
$558$		0			0
$559$	162.734			0.291116
$560$		0			0
$561$	232.576	−	665.843i	0.414573	−	1.18689i
$562$		0			0
$563$	484.898	+	839.869i	0.861276	+	1.49177i	0.870698	+	0.491818i	$0.163668\pi$
$563$	484.898	+	839.869i	0.861276	+	1.49177i	−0.00942163	+	0.999956i	$0.502999\pi$
$564$		0			0
$565$	−165.389	−	95.4873i	−0.292724	−	0.169004i
$566$		0			0
$567$	166.328	+	721.379i	0.293348	+	1.27227i
$568$		0			0
$569$	547.463	+	316.078i	0.962150	+	0.555498i	0.896834	−	0.442367i	$-0.145861\pi$
$569$	547.463	+	316.078i	0.962150	+	0.555498i	0.0653159	+	0.997865i	$0.479194\pi$
$570$		0			0
$571$	805.680	−	465.159i	1.41100	−	0.814640i	0.415515	−	0.909586i	$-0.363601\pi$
$571$	805.680	−	465.159i	1.41100	−	0.814640i	0.995482	+	0.0949465i	$0.0302680\pi$
$572$		0			0
$573$	240.519	−	688.583i	0.419753	−	1.20172i
$574$		0			0
$575$		−	312.342i		−	0.543203i
$576$		0			0
$577$	−1027.79			−1.78127			−0.890636	−	0.454717i	$-0.849741\pi$
$577$	−1027.79			−1.78127			−0.890636	+	0.454717i	$0.849741\pi$
$578$		0			0
$579$	−253.141	+	218.089i	−0.437204	+	0.376665i
$580$		0			0
$581$	170.914	+	296.031i	0.294172	+	0.509521i
$582$		0			0
$583$	−76.7837	+	132.993i	−0.131704	+	0.228119i
$584$		0			0
$585$	−298.046	−	44.5864i	−0.509480	−	0.0762160i
$586$		0			0
$587$	−65.3603	+	113.207i	−0.111346	+	0.192857i	−0.916313	−	0.400462i	$-0.868850\pi$
$587$	−65.3603	+	113.207i	−0.111346	+	0.192857i	0.804967	+	0.593320i	$0.202183\pi$
$588$		0			0
$589$	−376.894	+	217.600i	−0.639889	+	0.369440i
$590$		0			0
$591$	77.2224	+	406.899i	0.130664	+	0.688493i
$592$		0			0
$593$			379.858i			0.640570i	0.947321	+	0.320285i	$0.103779\pi$
$593$			379.858i			0.640570i	−0.947321	+	0.320285i	$0.896221\pi$
$594$		0			0
$595$			517.975i			0.870547i
$596$		0			0
$597$	−18.7340	−	98.7131i	−0.0313803	−	0.165349i
$598$		0			0
$599$	−309.923	+	178.934i	−0.517401	+	0.298721i	−0.735871	−	0.677122i	$-0.763227\pi$
$599$	−309.923	+	178.934i	−0.517401	+	0.298721i	0.218470	+	0.975844i	$0.429893\pi$
$600$		0			0
$601$	1.64207	−	2.84415i	0.00273223	−	0.00473236i	−0.864656	−	0.502364i	$-0.832464\pi$
$601$	1.64207	−	2.84415i	0.00273223	−	0.00473236i	0.867388	+	0.497632i	$0.165797\pi$
$602$		0			0
$603$	117.379	−	147.523i	0.194659	−	0.244649i
$604$		0			0
$605$	−57.6826	+	99.9092i	−0.0953432	+	0.165139i
$606$		0			0
$607$	−226.365	−	392.076i	−0.372925	−	0.645925i	0.617089	−	0.786893i	$-0.288312\pi$
$607$	−226.365	−	392.076i	−0.372925	−	0.645925i	−0.990014	+	0.140969i	$0.954978\pi$
$608$		0			0
$609$	786.768	−	677.825i	1.29190	−	1.11301i
$610$		0			0
$611$	272.915			0.446670
$612$		0			0
$613$			736.259i			1.20108i	0.799597	+	0.600538i	$0.205047\pi$
$613$			736.259i			1.20108i	−0.799597	+	0.600538i	$0.794953\pi$
$614$		0			0
$615$	−90.7964	+	259.942i	−0.147637	+	0.422670i
$616$		0			0
$617$	−384.563	+	222.027i	−0.623278	+	0.359850i	−0.778144	−	0.628086i	$-0.783839\pi$
$617$	−384.563	+	222.027i	−0.623278	+	0.359850i	0.154866	+	0.987935i	$0.450505\pi$
$618$		0			0
$619$	−974.353	−	562.543i	−1.57408	−	0.908793i	−0.995661	−	0.0930494i	$-0.970339\pi$
$619$	−974.353	−	562.543i	−1.57408	−	0.908793i	−0.578414	−	0.815743i	$-0.696328\pi$
$620$		0			0
$621$	345.339	+	181.785i	0.556101	+	0.292730i
$622$		0			0
$623$	361.483	+	208.702i	0.580230	+	0.334996i
$624$		0			0
$625$	−191.091	−	330.979i	−0.305746	−	0.529567i
$626$		0			0
$627$	82.4987	−	236.186i	0.131577	−	0.376693i
$628$		0			0
$629$	237.801			0.378062
$630$		0			0
$631$	1131.60			1.79334			0.896671	−	0.442698i	$-0.145978\pi$
$631$	1131.60			1.79334			0.896671	+	0.442698i	$0.145978\pi$
$632$		0			0
$633$	193.273	+	224.337i	0.305329	+	0.354402i
$634$		0			0
$635$	−125.893	−	218.052i	−0.198256	−	0.343389i
$636$		0			0
$637$	−543.802	−	313.964i	−0.853692	−	0.492879i
$638$		0			0
$639$	435.613	+	1106.33i	0.681710	+	1.73134i
$640$		0			0
$641$	869.162	+	501.811i	1.35595	+	0.782857i	0.989075	−	0.147414i	$-0.0470951\pi$
$641$	869.162	+	501.811i	1.35595	+	0.782857i	0.366873	+	0.930271i	$0.380428\pi$
$642$		0			0
$643$	−202.633	+	116.990i	−0.315137	+	0.181944i	−0.649223	−	0.760598i	$-0.724906\pi$
$643$	−202.633	+	116.990i	−0.315137	+	0.181944i	0.334086	+	0.942543i	$0.391572\pi$
$644$		0			0
$645$	48.5715	−	9.21802i	0.0753046	−	0.0142915i
$646$		0			0
$647$			597.659i			0.923740i	0.886948	+	0.461870i	$0.152821\pi$
$647$			597.659i			0.923740i	−0.886948	+	0.461870i	$0.847179\pi$
$648$		0			0
$649$	291.026			0.448423
$650$		0			0
$651$	−203.798	−	1073.85i	−0.313053	−	1.64954i
$652$		0			0
$653$	162.139	+	280.833i	0.248299	+	0.430067i	0.963054	−	0.269308i	$-0.0867951\pi$
$653$	162.139	+	280.833i	0.248299	+	0.430067i	−0.714755	+	0.699375i	$0.753462\pi$
$654$		0			0
$655$	172.694	−	299.115i	0.263655	−	0.456663i
$656$		0			0
$657$	200.883	−	79.0969i	0.305757	−	0.120391i
$658$		0			0
$659$	596.518	−	1033.20i	0.905186	−	1.56783i	0.0845191	−	0.996422i	$-0.473065\pi$
$659$	596.518	−	1033.20i	0.905186	−	1.56783i	0.820667	−	0.571407i	$-0.193602\pi$
$660$		0			0
$661$	−84.0657	+	48.5353i	−0.127180	+	0.0734271i	−0.562240	−	0.826974i	$-0.690060\pi$
$661$	−84.0657	+	48.5353i	−0.127180	+	0.0734271i	0.435061	+	0.900401i	$0.356727\pi$
$662$		0			0
$663$	−1271.99	+	1095.86i	−1.91854	+	1.65288i
$664$		0			0
$665$			183.735i			0.276293i
$666$		0			0
$667$		−	547.452i		−	0.820767i
$668$		0			0
$669$	527.260	+	184.169i	0.788132	+	0.275290i
$670$		0			0
$671$	−695.013	+	401.266i	−1.03579	+	0.598012i
$672$		0			0
$673$	−299.292	+	518.390i	−0.444714	+	0.770267i	−0.998032	−	0.0627029i	$-0.980028\pi$
$673$	−299.292	+	518.390i	−0.444714	+	0.770267i	0.553318	+	0.832970i	$0.313361\pi$
$674$		0			0
$675$	583.001	−	22.7822i	0.863706	−	0.0337513i
$676$		0			0
$677$	−12.3011	+	21.3061i	−0.0181700	+	0.0314714i	−0.874967	−	0.484182i	$-0.839117\pi$
$677$	−12.3011	+	21.3061i	−0.0181700	+	0.0314714i	0.856797	+	0.515653i	$0.172451\pi$
$678$		0			0
$679$	380.207	+	658.538i	0.559952	+	0.969865i
$680$		0			0
$681$	−1259.77	−	440.033i	−1.84989	−	0.646157i
$682$		0			0
$683$	156.845			0.229641			0.114821	−	0.993386i	$-0.463371\pi$
$683$	156.845			0.229641			0.114821	+	0.993386i	$0.463371\pi$
$684$		0			0
$685$		−	342.456i		−	0.499936i
$686$		0			0
$687$	165.905	+	192.570i	0.241492	+	0.280306i
$688$		0			0
$689$	316.590	−	182.784i	0.459493	−	0.265288i
$690$		0			0
$691$	653.119	+	377.079i	0.945180	+	0.545700i	0.891580	−	0.452863i	$-0.149597\pi$
$691$	653.119	+	377.079i	0.945180	+	0.545700i	0.0535995	+	0.998563i	$0.482931\pi$
$692$		0			0
$693$	491.684	+	391.216i	0.709500	+	0.564526i
$694$		0			0
$695$	371.474	+	214.470i	0.534494	+	0.308590i
$696$		0			0
$697$	766.997	+	1328.48i	1.10043	+	1.90599i
$698$		0			0
$699$	−535.825	+	101.690i	−0.766560	+	0.145480i
$700$		0			0
$701$	−587.766			−0.838468			−0.419234	−	0.907878i	$-0.637701\pi$
$701$	−587.766			−0.838468			−0.419234	+	0.907878i	$0.637701\pi$
$702$		0			0
$703$	84.3522			0.119989
$704$		0			0
$705$	81.4577	−	15.4593i	0.115543	−	0.0219280i
$706$		0			0
$707$	681.697	+	1180.73i	0.964210	+	1.67006i
$708$		0			0
$709$	−394.808	−	227.942i	−0.556851	−	0.321498i	0.195029	−	0.980797i	$-0.437520\pi$
$709$	−394.808	−	227.942i	−0.556851	−	0.321498i	−0.751881	+	0.659299i	$0.770853\pi$
$710$		0			0
$711$	56.3096	−	376.412i	0.0791977	−	0.529412i
$712$		0			0
$713$	−499.003	−	288.099i	−0.699864	−	0.404066i
$714$		0			0
$715$	−221.513	+	127.890i	−0.309808	+	0.178868i
$716$		0			0
$717$	−452.279	−	524.971i	−0.630793	−	0.732176i
$718$		0			0
$719$			1142.22i			1.58862i	0.607509	+	0.794312i	$0.292169\pi$
$719$			1142.22i			1.58862i	−0.607509	+	0.794312i	$0.707831\pi$
$720$		0			0
$721$	−1216.78			−1.68763
$722$		0			0
$723$	1168.01	+	407.981i	1.61551	+	0.564289i
$724$		0			0
$725$	−409.223	−	708.795i	−0.564445	−	0.977648i
$726$		0			0
$727$	−48.3798	+	83.7963i	−0.0665472	+	0.115263i	−0.897379	−	0.441260i	$-0.854532\pi$
$727$	−48.3798	+	83.7963i	−0.0665472	+	0.115263i	0.830832	+	0.556523i	$0.187865\pi$
$728$		0			0
$729$	−314.122	+	657.851i	−0.430894	+	0.902402i
$730$		0			0
$731$	137.716	−	238.531i	0.188394	−	0.326308i
$732$		0			0
$733$	−845.937	+	488.402i	−1.15408	+	0.666306i	−0.949877	−	0.312624i	$-0.898792\pi$
$733$	−845.937	+	488.402i	−1.15408	+	0.666306i	−0.204199	+	0.978929i	$0.565459\pi$
$734$		0			0
$735$	−180.094	−	62.9060i	−0.245026	−	0.0855864i
$736$		0			0
$737$		−	160.009i		−	0.217109i
$738$		0			0
$739$			88.0366i			0.119129i	0.998224	+	0.0595647i	$0.0189713\pi$
$739$			88.0366i			0.119129i	−0.998224	+	0.0595647i	$0.981029\pi$
$740$		0			0
$741$	−451.198	+	388.721i	−0.608904	+	0.524590i
$742$		0			0
$743$	787.884	−	454.885i	1.06041	−	0.612228i	0.134864	−	0.990864i	$-0.456940\pi$
$743$	787.884	−	454.885i	1.06041	−	0.612228i	0.925546	+	0.378636i	$0.123607\pi$
$744$		0			0
$745$	199.933	−	346.295i	0.268367	−	0.464825i
$746$		0			0
$747$	−49.8009	+	332.903i	−0.0666678	+	0.445653i
$748$		0			0
$749$	−476.672	+	825.621i	−0.636412	+	1.10230i
$750$		0			0
$751$	246.537	+	427.015i	0.328279	+	0.568595i	0.982170	−	0.187993i	$-0.0601981\pi$
$751$	246.537	+	427.015i	0.328279	+	0.568595i	−0.653892	+	0.756588i	$0.726865\pi$
$752$		0			0
$753$	27.9302	+	147.169i	0.0370919	+	0.195444i
$754$		0			0
$755$	−497.525			−0.658974
$756$		0			0
$757$		−	477.734i		−	0.631089i	−0.948911	−	0.315544i	$-0.897813\pi$
$757$		−	477.734i		−	0.631089i	0.948911	−	0.315544i	$-0.102187\pi$
$758$		0			0
$759$	325.426	−	61.7602i	0.428756	−	0.0813705i
$760$		0			0
$761$	777.129	−	448.676i	1.02120	−	0.589587i	0.106745	−	0.994286i	$-0.465957\pi$
$761$	777.129	−	448.676i	1.02120	−	0.589587i	0.914450	+	0.404699i	$0.132624\pi$
$762$		0			0
$763$	−404.984	−	233.818i	−0.530779	−	0.306445i
$764$		0			0
$765$	−317.579	+	399.136i	−0.415136	+	0.521746i
$766$		0			0
$767$	−599.972	−	346.394i	−0.782232	−	0.451622i
$768$		0			0
$769$	226.721	+	392.692i	0.294826	+	0.510653i	0.974944	−	0.222449i	$-0.0714051\pi$
$769$	226.721	+	392.692i	0.294826	+	0.510653i	−0.680119	+	0.733102i	$0.738072\pi$
$770$		0			0
$771$	256.260	+	297.446i	0.332373	+	0.385793i
$772$		0			0
$773$	−429.732			−0.555927			−0.277964	−	0.960592i	$-0.589659\pi$
$773$	−429.732			−0.555927			−0.277964	+	0.960592i	$0.589659\pi$
$774$		0			0
$775$	−861.423			−1.11151
$776$		0			0
$777$	−69.8601	+	200.003i	−0.0899100	+	0.257404i
$778$		0			0
$779$	272.067	+	471.234i	0.349252	+	0.604922i
$780$		0			0
$781$	873.959	+	504.580i	1.11903	+	0.646069i
$782$		0			0
$783$	1021.85	−	39.9310i	1.30504	−	0.0509975i
$784$		0			0
$785$	131.562	+	75.9573i	0.167595	+	0.0967609i
$786$		0			0
$787$	127.451	−	73.5837i	0.161945	−	0.0934990i	−0.416837	−	0.908981i	$-0.636861\pi$
$787$	127.451	−	73.5837i	0.161945	−	0.0934990i	0.578782	+	0.815482i	$0.303528\pi$
$788$		0			0
$789$	88.5034	−	253.377i	0.112172	−	0.321137i
$790$		0			0
$791$		−	947.863i		−	1.19831i
$792$		0			0
$793$	1910.43			2.40911
$794$		0			0
$795$	84.1397	−	72.4890i	0.105836	−	0.0911812i
$796$		0			0
$797$	256.948	+	445.047i	0.322394	+	0.558403i	0.980982	−	0.194101i	$-0.0621790\pi$
$797$	256.948	+	445.047i	0.322394	+	0.558403i	−0.658587	+	0.752504i	$0.728846\pi$
$798$		0			0
$799$	230.959	−	400.033i	0.289060	−	0.500667i
$800$		0			0
$801$	150.589	+	382.451i	0.188001	+	0.477467i
$802$		0			0
$803$	91.6198	−	158.690i	0.114097	−	0.197622i
$804$		0			0
$805$	−210.672	+	121.631i	−0.261704	+	0.151095i
$806$		0			0
$807$	−239.456	−	1261.74i	−0.296724	−	1.56349i
$808$		0			0
$809$		−	369.964i		−	0.457311i	−0.973507	−	0.228655i	$-0.926567\pi$
$809$		−	369.964i		−	0.457311i	0.973507	−	0.228655i	$-0.0734329\pi$
$810$		0			0
$811$			42.1364i			0.0519561i	0.999663	+	0.0259781i	$0.00827001\pi$
$811$			42.1364i			0.0519561i	−0.999663	+	0.0259781i	$0.991730\pi$
$812$		0			0
$813$	−20.2826	−	106.873i	−0.0249479	−	0.131455i
$814$		0			0
$815$	272.460	−	157.305i	0.334307	−	0.193012i
$816$		0			0
$817$	48.8503	−	84.6112i	0.0597923	−	0.103563i
$818$		0			0
$819$	−547.996	−	1391.75i	−0.669104	−	1.69933i
$820$		0			0
$821$	−258.078	+	447.005i	−0.314346	+	0.544464i	−0.979298	−	0.202422i	$-0.935119\pi$
$821$	−258.078	+	447.005i	−0.314346	+	0.544464i	0.664952	+	0.746886i	$0.268452\pi$
$822$		0			0
$823$	−169.184	−	293.035i	−0.205569	−	0.356057i	0.744745	−	0.667350i	$-0.232571\pi$
$823$	−169.184	−	293.035i	−0.205569	−	0.356057i	−0.950314	+	0.311293i	$0.899238\pi$
$824$		0			0
$825$	375.169	−	323.220i	0.454750	−	0.391781i
$826$		0			0
$827$	−1283.33			−1.55178			−0.775892	−	0.630866i	$-0.782700\pi$
$827$	−1283.33			−1.55178			−0.775892	+	0.630866i	$0.782700\pi$
$828$		0			0
$829$		−	664.918i		−	0.802072i	−0.916062	−	0.401036i	$-0.868650\pi$
$829$		−	664.918i		−	0.802072i	0.916062	−	0.401036i	$-0.131350\pi$
$830$		0			0
$831$	148.911	−	426.320i	0.179195	−	0.513020i
$832$		0			0
$833$	−920.401	+	531.394i	−1.10492	+	0.637928i
$834$		0			0
$835$	40.5383	+	23.4048i	0.0485488	+	0.0280297i
$836$		0			0
$837$	501.354	−	952.427i	0.598990	−	1.13791i
$838$		0			0
$839$	−145.241	−	83.8547i	−0.173112	−	0.0999460i	0.410941	−	0.911662i	$-0.365200\pi$
$839$	−145.241	−	83.8547i	−0.173112	−	0.0999460i	−0.584052	+	0.811716i	$0.698534\pi$
$840$		0			0
$841$	−296.758	−	514.000i	−0.352864	−	0.611178i
$842$		0			0
$843$	151.852	−	434.738i	0.180132	−	0.515703i
$844$		0			0
$845$	297.684			0.352288
$846$		0			0
$847$	−572.591			−0.676023
$848$		0			0
$849$	139.123	+	161.484i	0.163867	+	0.190205i
$850$		0			0
$851$	55.8406	+	96.7187i	0.0656176	+	0.113653i
$852$		0			0
$853$	−211.425	−	122.066i	−0.247861	−	0.143102i	0.370924	−	0.928663i	$-0.379041\pi$
$853$	−211.425	−	122.066i	−0.247861	−	0.143102i	−0.618784	+	0.785561i	$0.712374\pi$
$854$		0			0
$855$	−112.651	+	141.581i	−0.131756	+	0.165591i
$856$		0			0
$857$	−579.385	−	334.508i	−0.676061	−	0.390324i	0.122308	−	0.992492i	$-0.460970\pi$
$857$	−579.385	−	334.508i	−0.676061	−	0.390324i	−0.798369	+	0.602168i	$0.794304\pi$
$858$		0			0
$859$	626.013	−	361.429i	0.728769	−	0.420755i	−0.0892025	−	0.996014i	$-0.528432\pi$
$859$	626.013	−	361.429i	0.728769	−	0.420755i	0.817972	+	0.575258i	$0.195098\pi$
$860$		0			0
$861$	−1342.64	+	254.810i	−1.55940	+	0.295947i
$862$		0			0
$863$		−	311.048i		−	0.360426i	−0.983628	−	0.180213i	$-0.942321\pi$
$863$		−	311.048i		−	0.360426i	0.983628	−	0.180213i	$-0.0576787\pi$
$864$		0			0
$865$	−564.377			−0.652459
$866$		0			0
$867$	368.187	+	1940.05i	0.424668	+	2.23766i
$868$		0			0
$869$	−161.517	−	279.756i	−0.185865	−	0.321928i
$870$		0			0
$871$	−190.451	+	329.870i	−0.218658	+	0.378726i
$872$		0			0
$873$	−110.785	+	740.561i	−0.126901	+	0.848295i
$874$		0			0
$875$	−392.214	+	679.335i	−0.448245	+	0.776382i
$876$		0			0
$877$	931.826	−	537.990i	1.06252	−	0.613444i	0.136388	−	0.990655i	$-0.456450\pi$
$877$	931.826	−	537.990i	1.06252	−	0.613444i	0.926127	+	0.377212i	$0.123117\pi$
$878$		0			0
$879$	506.701	−	436.539i	0.576452	−	0.496632i
$880$		0			0
$881$			1149.33i			1.30457i	0.757973	+	0.652286i	$0.226190\pi$
$881$			1149.33i			1.30457i	−0.757973	+	0.652286i	$0.773810\pi$
$882$		0			0
$883$		−	457.946i		−	0.518625i	−0.965793	−	0.259313i	$-0.916504\pi$
$883$		−	457.946i		−	0.518625i	0.965793	−	0.259313i	$-0.0834960\pi$
$884$		0			0
$885$	−198.696	−	69.4037i	−0.224516	−	0.0784223i
$886$		0			0
$887$	−1052.34	+	607.568i	−1.18640	+	0.684969i	−0.957487	−	0.288477i	$-0.906851\pi$
$887$	−1052.34	+	607.568i	−1.18640	+	0.684969i	−0.228915	+	0.973447i	$0.573518\pi$
$888$		0			0
$889$	624.841	−	1082.26i	0.702859	−	1.21739i
$890$		0			0
$891$	139.015	+	602.919i	0.156021	+	0.676677i
$892$		0			0
$893$	81.9253	−	141.899i	0.0917416	−	0.158901i
$894$		0			0
$895$	−203.475	−	352.429i	−0.227346	−	0.393775i
$896$		0			0
$897$	−744.400	−	260.015i	−0.829877	−	0.289872i
$898$		0			0
$899$	−1509.84			−1.67947
$900$		0			0
$901$		−	618.734i		−	0.686719i
$902$		0			0
$903$	160.159	+	185.901i	0.177364	+	0.205870i
$904$		0			0
$905$	−337.134	+	194.644i	−0.372524	+	0.215077i
$906$		0			0
$907$	−157.538	−	90.9546i	−0.173691	−	0.100281i	0.410634	−	0.911800i	$-0.365307\pi$
$907$	−157.538	−	90.9546i	−0.173691	−	0.100281i	−0.584325	+	0.811520i	$0.698641\pi$
$908$		0			0
$909$	−198.633	+	1327.80i	−0.218518	+	1.46072i
$910$		0			0
$911$	208.841	+	120.575i	0.229244	+	0.132354i	0.610223	−	0.792229i	$-0.291080\pi$
$911$	208.841	+	120.575i	0.229244	+	0.132354i	−0.380979	+	0.924584i	$0.624413\pi$
$912$		0			0
$913$	142.848	+	247.419i	0.156460	+	0.270996i
$914$		0			0
$915$	570.209	−	108.216i	0.623180	−	0.118269i
$916$		0			0
$917$	1714.26			1.86942
$918$		0			0
$919$	501.923			0.546163			0.273081	−	0.961991i	$-0.411957\pi$
$919$	501.923			0.546163			0.273081	+	0.961991i	$0.411957\pi$
$920$		0			0
$921$	842.065	−	159.809i	0.914295	−	0.173517i
$922$		0			0
$923$	−1201.15	−	2080.46i	−1.30136	−	2.25402i
$924$		0			0
$925$	144.595	+	83.4822i	0.156319	+	0.0902511i
$926$		0			0
$927$	−937.612	−	746.027i	−1.01145	−	0.804776i
$928$		0			0
$929$	−839.922	−	484.929i	−0.904114	−	0.521990i	−0.0255812	−	0.999673i	$-0.508144\pi$
$929$	−839.922	−	484.929i	−0.904114	−	0.521990i	−0.878533	+	0.477682i	$0.841477\pi$
$930$		0			0
$931$	−326.483	+	188.495i	−0.350680	+	0.202465i
$932$		0			0
$933$	835.988	+	970.351i	0.896021	+	1.04003i
$934$		0			0
$935$			432.917i			0.463013i
$936$		0			0
$937$	−700.392			−0.747483			−0.373742	−	0.927533i	$-0.621925\pi$
$937$	−700.392			−0.747483			−0.373742	+	0.927533i	$0.621925\pi$
$938$		0			0
$939$	−1278.52	−	446.581i	−1.36158	−	0.475592i
$940$		0			0
$941$	−679.823	−	1177.49i	−0.722447	−	1.25131i	−0.960016	−	0.279944i	$-0.909684\pi$
$941$	−679.823	−	1177.49i	−0.722447	−	1.25131i	0.237569	−	0.971371i	$-0.423649\pi$
$942$		0			0
$943$	−360.213	+	623.908i	−0.381986	+	0.661620i
$944$		0			0
$945$	−242.397	−	384.357i	−0.256505	−	0.406727i
$946$		0			0
$947$	79.7517	−	138.134i	0.0842151	−	0.145865i	−0.820841	−	0.571156i	$-0.806495\pi$
$947$	79.7517	−	138.134i	0.0842151	−	0.145865i	0.905056	+	0.425291i	$0.139828\pi$
$948$		0			0
$949$	−377.762	+	218.101i	−0.398063	+	0.229822i
$950$		0			0
$951$	−16.0358	−	5.60124i	−0.0168621	−	0.00588984i
$952$		0			0
$953$		−	941.561i		−	0.987997i	−0.869463	−	0.493998i	$-0.835535\pi$
$953$		−	941.561i		−	0.987997i	0.869463	−	0.493998i	$-0.164465\pi$
$954$		0			0
$955$			447.702i			0.468798i
$956$		0			0
$957$	657.570	−	566.518i	0.687116	−	0.591972i
$958$		0			0
$959$	1471.99	−	849.855i	1.53492	−	0.886189i
$960$		0			0
$961$	−314.064	+	543.974i	−0.326809	+	0.566050i
$962$		0			0
$963$	−873.512	+	343.942i	−0.907073	+	0.357157i
$964$		0			0
$965$	102.547	−	177.616i	0.106266	−	0.184058i
$966$		0			0
$967$	−615.116	−	1065.41i	−0.636107	−	1.10177i	−0.986279	−	0.165085i	$-0.947210\pi$
$967$	−615.116	−	1065.41i	−0.636107	−	1.10177i	0.350172	−	0.936685i	$-0.386123\pi$
$968$		0			0
$969$	187.945	+	990.317i	0.193958	+	1.02200i
$970$		0			0
$971$	1584.43			1.63175			0.815876	−	0.578227i	$-0.196255\pi$
$971$	1584.43			1.63175			0.815876	+	0.578227i	$0.196255\pi$
$972$		0			0
$973$			2128.96i			2.18804i
$974$		0			0
$975$	−1158.15	+	219.797i	−1.18785	+	0.225432i
$976$		0			0
$977$	572.558	−	330.567i	0.586037	−	0.338349i	−0.177492	−	0.984122i	$-0.556798\pi$
$977$	572.558	−	330.567i	0.586037	−	0.338349i	0.763529	+	0.645774i	$0.223465\pi$
$978$		0			0
$979$	302.123	+	174.431i	0.308603	+	0.178172i
$980$		0			0
$981$	−168.711	−	428.475i	−0.171978	−	0.436774i
$982$		0			0
$983$	716.470	+	413.654i	0.728861	+	0.420808i	0.818005	−	0.575211i	$-0.195080\pi$
$983$	716.470	+	413.654i	0.728861	+	0.420808i	−0.0891445	+	0.996019i	$0.528413\pi$
$984$		0			0
$985$	−127.109	−	220.159i	−0.129044	−	0.223511i
$986$		0			0
$987$	268.598	+	311.768i	0.272136	+	0.315875i
$988$		0			0
$989$	129.354			0.130793
$990$		0			0
$991$	72.7970			0.0734581			0.0367291	−	0.999325i	$-0.488306\pi$
$991$	72.7970			0.0734581			0.0367291	+	0.999325i	$0.488306\pi$
$992$		0			0
$993$	291.957	−	835.846i	0.294015	−	0.841738i
$994$		0			0
$995$	30.8364	+	53.4101i	0.0309913	+	0.0536785i
$996$		0			0
$997$	676.198	+	390.403i	0.678233	+	0.391578i	0.799189	−	0.601080i	$-0.205263\pi$
$997$	676.198	+	390.403i	0.678233	+	0.391578i	−0.120956	+	0.992658i	$0.538596\pi$
$998$		0			0
$999$	−176.457	+	111.284i	−0.176634	+	0.111395i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	576.3.n.c.353.8	✓	32
3.2	odd	2		1728.3.n.d.737.7		32
4.3	odd	2	inner	576.3.n.c.353.9	yes	32
8.3	odd	2		576.3.n.d.353.8	yes	32
8.5	even	2		576.3.n.d.353.9	yes	32
9.4	even	3		1728.3.n.c.1313.10		32
9.5	odd	6		576.3.n.d.545.9	yes	32
12.11	even	2		1728.3.n.d.737.8		32
24.5	odd	2		1728.3.n.c.737.10		32
24.11	even	2		1728.3.n.c.737.9		32
36.23	even	6		576.3.n.d.545.8	yes	32
36.31	odd	6		1728.3.n.c.1313.9		32
72.5	odd	6	inner	576.3.n.c.545.8	yes	32
72.13	even	6		1728.3.n.d.1313.7		32
72.59	even	6	inner	576.3.n.c.545.9	yes	32
72.67	odd	6		1728.3.n.d.1313.8		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
576.3.n.c.353.8	✓	32	1.1	even	1	trivial
576.3.n.c.353.9	yes	32	4.3	odd	2	inner
576.3.n.c.545.8	yes	32	72.5	odd	6	inner
576.3.n.c.545.9	yes	32	72.59	even	6	inner
576.3.n.d.353.8	yes	32	8.3	odd	2
576.3.n.d.353.9	yes	32	8.5	even	2
576.3.n.d.545.8	yes	32	36.23	even	6
576.3.n.d.545.9	yes	32	9.5	odd	6
1728.3.n.c.737.9		32	24.11	even	2
1728.3.n.c.737.10		32	24.5	odd	2
1728.3.n.c.1313.9		32	36.31	odd	6
1728.3.n.c.1313.10		32	9.4	even	3
1728.3.n.d.737.7		32	3.2	odd	2
1728.3.n.d.737.8		32	12.11	even	2
1728.3.n.d.1313.7		32	72.13	even	6
1728.3.n.d.1313.8		32	72.67	odd	6

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:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	576.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.559363 - 2.94739i) q^{3} +(0.920717 + 1.59473i) q^{5} +(-4.56979 + 7.91511i) q^{7} +(-8.37423 + 3.29733i) q^{9} +O(q^{10})\)	\(q+(-0.559363 - 2.94739i) q^{3} +(0.920717 + 1.59473i) q^{5} +(-4.56979 + 7.91511i) q^{7} +(-8.37423 + 3.29733i) q^{9} +(-3.81937 + 6.61534i) q^{11} +(15.7478 - 9.09201i) q^{13} +(4.18527 - 3.60575i) q^{15} -30.7770i q^{17} -10.9172i q^{19} +(25.8851 + 9.04153i) q^{21} +(12.5177 - 7.22708i) q^{23} +(10.8046 - 18.7140i) q^{25} +(14.4027 + 22.8377i) q^{27} +(18.9375 - 32.8007i) q^{29} +(-19.9319 - 34.5231i) q^{31} +(21.6344 + 7.55679i) q^{33} -16.8299 q^{35} +7.72657i q^{37} +(-35.6065 - 41.3292i) q^{39} +(-43.1646 + 24.9211i) q^{41} +(7.75029 + 4.47463i) q^{43} +(-12.9686 - 10.3187i) q^{45} +(12.9978 + 7.50427i) q^{47} +(-17.2659 - 29.9055i) q^{49} +(-90.7119 + 17.2155i) q^{51} +20.1038 q^{53} -14.0662 q^{55} +(-32.1771 + 6.10666i) q^{57} +(-19.0494 - 32.9945i) q^{59} +(90.9853 + 52.5304i) q^{61} +(12.1698 - 81.3510i) q^{63} +(28.9986 + 16.7423i) q^{65} +(-18.1407 + 10.4735i) q^{67} +(-28.3030 - 32.8519i) q^{69} -132.111i q^{71} -23.9882 q^{73} +(-61.2013 - 21.3773i) q^{75} +(-34.9074 - 60.4614i) q^{77} +(-21.1445 + 36.6233i) q^{79} +(59.2553 - 55.2251i) q^{81} +(18.7004 - 32.3901i) q^{83} +(49.0810 - 28.3369i) q^{85} +(-107.269 - 37.4687i) q^{87} -45.6700i q^{89} +166.194i q^{91} +(-90.6039 + 78.0582i) q^{93} +(17.4099 - 10.0516i) q^{95} +(41.6001 - 72.0535i) q^{97} +(10.1713 - 67.9921i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 18 q^{5} + 2 q^{9}+O(q^{10}) \) 32 * q - 18 * q^5 + 2 * q^9	\( 32 q - 18 q^{5} + 2 q^{9} + 30 q^{13} + 66 q^{21} - 74 q^{25} - 54 q^{29} - 120 q^{33} - 216 q^{41} - 366 q^{45} - 86 q^{49} + 144 q^{53} + 302 q^{57} - 42 q^{61} + 306 q^{65} + 54 q^{69} + 196 q^{73} - 414 q^{77} + 334 q^{81} - 180 q^{85} + 1002 q^{93} - 64 q^{97}+O(q^{100}) \) 32 * q - 18 * q^5 + 2 * q^9 + 30 * q^13 + 66 * q^21 - 74 * q^25 - 54 * q^29 - 120 * q^33 - 216 * q^41 - 366 * q^45 - 86 * q^49 + 144 * q^53 + 302 * q^57 - 42 * q^61 + 306 * q^65 + 54 * q^69 + 196 * q^73 - 414 * q^77 + 334 * q^81 - 180 * q^85 + 1002 * q^93 - 64 * q^97

Introduction

L-functions

Modular forms

Varieties

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Database

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