LMFDB - Embedded newform 576.3.n.d.545.8

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			545.8
Character	$\chi$	$=$	576.545
Dual form			576.3.n.d.353.8

$q$-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 $\left(\mathbb{Z}/576\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$325$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

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	$-0.892284\pi$
$5$	−0.920717	+	1.59473i	−0.184143	+	0.318946i	0.759144	+	0.650923i	$0.225618\pi$
$6$		0			0
$7$	4.56979	+	7.91511i	0.652827	+	1.13073i	0.982434	+	0.186611i	$0.0597504\pi$
$7$	4.56979	+	7.91511i	0.652827	+	1.13073i	−0.329607	+	0.944118i	$0.606916\pi$
$8$		0			0
$9$	−8.37423	−	3.29733i	−0.930469	−	0.366369i
$10$		0			0
$11$	−3.81937	−	6.61534i	−0.347215	−	0.601395i	0.638538	−	0.769590i	$-0.279539\pi$
$11$	−3.81937	−	6.61534i	−0.347215	−	0.601395i	−0.985754	+	0.168195i	$0.946206\pi$
$12$		0			0
$13$	−15.7478	−	9.09201i	−1.21137	−	0.699385i	−0.248313	−	0.968680i	$-0.579876\pi$
$13$	−15.7478	−	9.09201i	−1.21137	−	0.699385i	−0.963058	+	0.269294i	$0.913210\pi$
$14$		0			0
$15$	−4.18527	−	3.60575i	−0.279018	−	0.240383i
$16$		0			0
$17$			30.7770i			1.81041i	0.424971	+	0.905207i	$0.360284\pi$
$17$			30.7770i			1.81041i	−0.424971	+	0.905207i	$0.639716\pi$
$18$		0			0
$19$			10.9172i			0.574587i	0.957843	+	0.287294i	$0.0927556\pi$
$19$			10.9172i			0.574587i	−0.957843	+	0.287294i	$0.907244\pi$
$20$		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	$-0.435077\pi$
$23$	−12.5177	−	7.22708i	−0.544247	−	0.314221i	−0.746798	+	0.665051i	$0.768410\pi$
$24$		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	−0.982387	−	0.186858i	$-0.940169\pi$
$29$	−18.9375	−	32.8007i	−0.653017	−	1.13106i	0.329369	−	0.944201i	$-0.393164\pi$
$30$		0			0
$31$	19.9319	−	34.5231i	0.642965	−	1.11365i	−0.341802	−	0.939772i	$-0.611037\pi$
$31$	19.9319	−	34.5231i	0.642965	−	1.11365i	0.984767	−	0.173877i	$-0.0556295\pi$
$32$		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	−0.129364	−	0.991597i	$-0.541294\pi$
$41$	−43.1646	−	24.9211i	−1.05279	−	0.607831i	−0.923430	+	0.383766i	$0.874627\pi$
$42$		0			0
$43$	7.75029	−	4.47463i	0.180239	−	0.104061i	−0.407166	−	0.913354i	$-0.633483\pi$
$43$	7.75029	−	4.47463i	0.180239	−	0.104061i	0.587405	+	0.809293i	$0.300150\pi$
$44$		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	$-0.717708\pi$
$47$	−12.9978	+	7.50427i	−0.276548	+	0.159665i	0.355311	+	0.934748i	$0.384375\pi$
$48$		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	$-0.560738\pi$
$53$	−20.1038			−0.379316			−0.189658	+	0.981850i	$0.560738\pi$
$54$		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	−0.981079	−	0.193607i	$-0.937981\pi$
$59$	−19.0494	+	32.9945i	−0.322871	+	0.559228i	0.658208	+	0.752836i	$0.271315\pi$
$60$		0			0
$61$	−90.9853	+	52.5304i	−1.49156	+	0.861154i	−0.999953	−	0.00966279i	$-0.996924\pi$
$61$	−90.9853	+	52.5304i	−1.49156	+	0.861154i	−0.491608	+	0.870816i	$0.663591\pi$
$62$		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	0.358475	−	0.933539i	$-0.383297\pi$
$67$	−18.1407	−	10.4735i	−0.270756	−	0.156321i	−0.629231	+	0.777218i	$0.716630\pi$
$68$		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	$-0.0804191\pi$
$79$	21.1445	+	36.6233i	0.267651	+	0.463586i	−0.700604	+	0.713551i	$0.747086\pi$
$80$		0			0
$81$	59.2553	+	55.2251i	0.731547	+	0.681791i
$82$		0			0
$83$	18.7004	+	32.3901i	0.225306	+	0.390242i	0.956411	−	0.292023i	$-0.0943284\pi$
$83$	18.7004	+	32.3901i	0.225306	+	0.390242i	−0.731105	+	0.682265i	$0.760995\pi$
$84$		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	$0.0825935\pi$
$89$			45.6700i			0.513146i	−0.966525	+	0.256573i	$0.917407\pi$
$90$		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	0.996773	−	0.0802740i	$-0.0255795\pi$
$97$	41.6001	+	72.0535i	0.428867	+	0.742820i	−0.567906	+	0.823094i	$0.692246\pi$
$98$		0			0
$99$	10.1713	+	67.9921i	0.102741	+	0.686789i
$100$		0			0
$101$	−74.5873	−	129.189i	−0.738489	−	1.27910i	−0.953176	−	0.302417i	$-0.902207\pi$
$101$	−74.5873	−	129.189i	−0.738489	−	1.27910i	0.214687	−	0.976683i	$-0.431127\pi$
$102$		0			0
$103$	−66.5665	+	115.296i	−0.646276	+	1.11938i	0.337729	+	0.941243i	$0.390341\pi$
$103$	−66.5665	+	115.296i	−0.646276	+	1.11938i	−0.984005	+	0.178140i	$0.942992\pi$
$104$		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	0.0468333	−	0.998903i	$-0.485087\pi$
$113$	−89.8153	−	51.8549i	−0.794825	−	0.458893i	−0.841659	+	0.540010i	$0.818420\pi$
$114$		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	$-0.319059\pi$
$127$	136.733			1.07664			0.538319	+	0.842741i	$0.319059\pi$
$128$		0			0
$129$	8.85326	+	25.3461i	0.0686299	+	0.196481i
$130$		0			0
$131$	−93.7823	+	162.436i	−0.715895	+	1.23997i	0.246718	+	0.969087i	$0.420648\pi$
$131$	−93.7823	+	162.436i	−0.715895	+	1.23997i	−0.962613	+	0.270879i	$0.912686\pi$
$132$		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	−0.954992	−	0.296631i	$-0.904137\pi$
$137$	−161.057	+	92.9862i	−1.17560	+	0.678732i	−0.220606	+	0.975363i	$0.570803\pi$
$138$		0			0
$139$	201.731	+	116.469i	1.45130	+	0.837908i	0.998555	−	0.0537326i	$-0.0171119\pi$
$139$	201.731	+	116.469i	1.45130	+	0.837908i	0.452744	+	0.891641i	$0.350445\pi$
$140$		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	−0.228747	−	0.973486i	$-0.573463\pi$
$149$	108.575	−	188.057i	0.728690	−	1.26213i	0.957437	−	0.288642i	$-0.0932039\pi$
$150$		0			0
$151$	135.092	+	233.986i	0.894648	+	1.54957i	0.834240	+	0.551401i	$0.185907\pi$
$151$	135.092	+	233.986i	0.894648	+	1.54957i	0.0604073	+	0.998174i	$0.480760\pi$
$152$		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	$-0.417957\pi$
$157$	−71.4453	−	41.2490i	−0.455066	−	0.262732i	−0.709967	+	0.704235i	$0.751290\pi$
$158$		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	$0.175591\pi$
$163$			170.850i			1.04816i	−0.851668	+	0.524081i	$0.824409\pi$
$164$		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	$-0.357583\pi$
$167$	−22.0145	−	12.7101i	−0.131823	−	0.0761083i	−0.564461	+	0.825459i	$0.690916\pi$
$168$		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	0.844790	+	0.535098i	$0.179725\pi$
$173$	153.244	+	265.426i	0.885803	+	1.53426i	0.0410133	+	0.999159i	$0.486941\pi$
$174$		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	$-0.886268\pi$
$191$	−210.554	+	121.563i	−1.10238	+	0.636458i	−0.165533	+	0.986204i	$0.552934\pi$
$192$		0			0
$193$	−55.6885	+	96.4553i	−0.288541	+	0.499768i	−0.973462	−	0.228850i	$-0.926504\pi$
$193$	−55.6885	+	96.4553i	−0.288541	+	0.499768i	0.684920	+	0.728618i	$0.259837\pi$
$194$		0			0
$195$	33.1255	+	94.8352i	0.169874	+	0.486334i
$196$		0			0
$197$	138.054			0.700782			0.350391	−	0.936604i	$-0.386049\pi$
$197$	138.054			0.700782			0.350391	+	0.936604i	$0.386049\pi$
$198$		0			0
$199$	−33.4917			−0.168300			−0.0841500	−	0.996453i	$-0.526817\pi$
$199$	−33.4917			−0.168300			−0.0841500	+	0.996453i	$0.526817\pi$
$200$		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	0.283572	−	0.958951i	$-0.408480\pi$
$211$	−85.4798	−	49.3518i	−0.405117	−	0.233895i	−0.688690	+	0.725056i	$0.741814\pi$
$212$		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	$-0.0296033\pi$
$223$	93.0832	+	161.225i	0.417414	+	0.722981i	−0.578265	+	0.815849i	$0.696270\pi$
$224$		0			0
$225$	−28.7735	−	192.342i	−0.127882	−	0.854852i
$226$		0			0
$227$	222.402	+	385.212i	0.979746	+	1.69697i	0.663291	+	0.748361i	$0.269159\pi$
$227$	222.402	+	385.212i	0.979746	+	1.69697i	0.316454	+	0.948608i	$0.397508\pi$
$228$		0			0
$229$	73.3756	+	42.3634i	0.320418	+	0.184993i	0.651579	−	0.758581i	$-0.274107\pi$
$229$	73.3756	+	42.3634i	0.320418	+	0.184993i	−0.331161	+	0.943574i	$0.607440\pi$
$230$		0			0
$231$	158.678	+	136.706i	0.686916	+	0.591800i
$232$		0			0
$233$			181.796i			0.780242i	0.920764	+	0.390121i	$0.127567\pi$
$233$			181.796i			0.780242i	−0.920764	+	0.390121i	$0.872433\pi$
$234$		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	$-0.493864\pi$
$239$	−200.031	−	115.488i	−0.836951	−	0.483214i	−0.856227	+	0.516600i	$0.827197\pi$
$240$		0			0
$241$	−206.202	−	357.153i	−0.855612	−	1.48196i	−0.876076	−	0.482173i	$-0.839848\pi$
$241$	−206.202	−	357.153i	−0.855612	−	1.48196i	0.0204644	−	0.999791i	$-0.493486\pi$
$242$		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	0.263022	−	0.964790i	$-0.415281\pi$
$257$	−113.337	−	65.4352i	−0.441000	−	0.254612i	−0.704022	+	0.710178i	$0.748614\pi$
$258$		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	$-0.721070\pi$
$263$	−77.4773	+	44.7316i	−0.294591	+	0.170082i	0.345420	+	0.938448i	$0.387737\pi$
$264$		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	$-0.792897\pi$
$269$	−428.087			−1.59140			−0.795701	+	0.605690i	$0.792897\pi$
$270$		0			0
$271$	−36.2602			−0.133802			−0.0669008	−	0.997760i	$-0.521311\pi$
$271$	−36.2602			−0.133802			−0.0669008	+	0.997760i	$0.521311\pi$
$272$		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	$-0.754255\pi$
$277$	−130.359	+	75.2631i	−0.470612	+	0.271708i	0.245884	+	0.969299i	$0.420922\pi$
$278$		0			0
$279$	−280.748	+	223.382i	−1.00627	+	0.800653i
$280$		0			0
$281$	132.933	−	76.7492i	0.473073	−	0.273129i	−0.244452	−	0.969661i	$-0.578608\pi$
$281$	132.933	−	76.7492i	0.473073	−	0.273129i	0.717525	+	0.696533i	$0.245275\pi$
$282$		0			0
$283$	−61.5307	−	35.5247i	−0.217423	−	0.125529i	0.387334	−	0.921940i	$-0.373396\pi$
$283$	−61.5307	−	35.5247i	−0.217423	−	0.125529i	−0.604756	+	0.796411i	$0.706730\pi$
$284$		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	$-0.957561\pi$
$293$	−111.469	+	193.070i	−0.380441	+	0.658942i	0.610685	+	0.791874i	$0.290894\pi$
$294$		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	$-0.845944\pi$
$307$		−	285.699i		−	0.930614i	0.885149	−	0.465307i	$-0.154056\pi$
$308$		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	$-0.0925278\pi$
$311$	369.736	+	213.467i	1.18886	+	0.686390i	0.230814	+	0.972998i	$0.425861\pi$
$312$		0			0
$313$	225.712	+	390.944i	0.721124	+	1.24902i	0.960550	+	0.278108i	$0.0897074\pi$
$313$	225.712	+	390.944i	0.721124	+	1.24902i	−0.239426	+	0.970915i	$0.576959\pi$
$314$		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	$-0.169509\pi$
$317$	−2.83099	−	4.90342i	−0.00893057	−	0.0154682i	−0.870456	+	0.492246i	$0.836176\pi$
$318$		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	−0.0614867	−	0.998108i	$-0.519584\pi$
$331$	255.584	−	147.561i	0.772157	−	0.445805i	0.833643	+	0.552303i	$0.186251\pi$
$332$		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	−0.999165	−	0.0408603i	$-0.986990\pi$
$337$	−156.434	+	270.952i	−0.464196	+	0.804012i	0.534968	+	0.844872i	$0.320323\pi$
$338$		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	−0.819142	−	0.573591i	$-0.805550\pi$
$347$	30.2492	−	52.3931i	0.0871734	−	0.150989i	0.906315	+	0.422602i	$0.138883\pi$
$348$		0			0
$349$	−445.021	+	256.933i	−1.27513	+	0.736198i	−0.975949	−	0.217997i	$-0.930048\pi$
$349$	−445.021	+	256.933i	−1.27513	+	0.736198i	−0.299184	+	0.954196i	$0.596714\pi$
$350$		0			0
$351$	−434.453	+	228.694i	−1.23776	+	0.651551i
$352$		0			0
$353$	238.086	−	137.459i	0.674466	−	0.389403i	−0.123301	−	0.992369i	$-0.539348\pi$
$353$	238.086	−	137.459i	0.674466	−	0.389403i	0.797767	+	0.602966i	$0.206015\pi$
$354$		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	−0.999316	−	0.0369739i	$-0.988228\pi$
$367$	−195.126	−	337.968i	−0.531678	−	0.920894i	0.467638	−	0.883920i	$-0.345105\pi$
$368$		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	$-0.382190\pi$
$373$	−98.7732	−	57.0267i	−0.264807	−	0.152887i	−0.626526	+	0.779401i	$0.715524\pi$
$374$		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	$0.127072\pi$
$379$			294.626i			0.777377i	−0.921369	+	0.388689i	$0.872928\pi$
$380$		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	$-0.119077\pi$
$383$	413.559	+	238.769i	1.07979	+	0.623417i	0.148950	+	0.988845i	$0.452411\pi$
$384$		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	0.999823	+	0.0188238i	$0.00599215\pi$
$389$	200.807	+	347.808i	0.516213	+	0.894108i	−0.483610	+	0.875284i	$0.660675\pi$
$390$		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	0.603621	−	0.797271i	$-0.293724\pi$
$401$	86.2049	+	49.7704i	0.214975	+	0.124116i	−0.388646	+	0.921387i	$0.627057\pi$
$402$		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	−0.468858	−	0.883273i	$-0.655335\pi$
$409$	216.978	−	375.816i	0.530508	−	0.918867i	0.999366	−	0.0355933i	$-0.0113321\pi$
$410$		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	−0.741073	−	0.671424i	$-0.765683\pi$
$419$	88.3811	−	153.081i	0.210933	−	0.365347i	0.952007	+	0.306076i	$0.0990163\pi$
$420$		0			0
$421$	296.515	−	171.193i	0.704312	−	0.406635i	−0.104639	−	0.994510i	$-0.533369\pi$
$421$	296.515	−	171.193i	0.704312	−	0.406635i	0.808951	+	0.587876i	$0.200036\pi$
$422$		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	−0.958447	−	0.285272i	$-0.907916\pi$
$439$	−318.835	−	552.239i	−0.726276	−	1.25795i	0.232171	−	0.972675i	$-0.425417\pi$
$440$		0			0
$441$	243.197	−	193.504i	0.551467	−	0.438784i
$442$		0			0
$443$	−353.126	−	611.632i	−0.797123	−	1.38066i	−0.921482	−	0.388421i	$-0.873021\pi$
$443$	−353.126	−	611.632i	−0.797123	−	1.38066i	0.124359	−	0.992237i	$-0.460313\pi$
$444$		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	$-0.968673\pi$
$449$		−	88.2356i		−	0.196516i	0.995161	−	0.0982579i	$-0.0313270\pi$
$450$		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	−0.941962	−	0.335719i	$-0.891021\pi$
$457$	−348.107	−	602.939i	−0.761722	−	1.31934i	0.180240	−	0.983623i	$-0.442313\pi$
$458$		0			0
$459$	702.877	+	443.274i	1.53132	+	0.965738i
$460$		0			0
$461$	312.264	+	540.857i	0.677363	+	1.17323i	0.975772	+	0.218788i	$0.0702105\pi$
$461$	312.264	+	540.857i	0.677363	+	1.17323i	−0.298410	+	0.954438i	$0.596456\pi$
$462$		0			0
$463$	261.798	−	453.447i	0.565438	−	0.979367i	−0.431571	−	0.902079i	$-0.642040\pi$
$463$	261.798	−	453.447i	0.565438	−	0.979367i	0.997009	−	0.0772884i	$-0.0246262\pi$
$464$		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	$-0.781142\pi$
$479$	−291.982	+	168.576i	−0.609565	+	0.351933i	0.163230	+	0.986588i	$0.447809\pi$
$480$		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	$-0.529288\pi$
$487$	−89.4910			−0.183760			−0.0918799	+	0.995770i	$0.529288\pi$
$488$		0			0
$489$	−503.563	−	95.5675i	−1.02978	−	0.195435i
$490$		0			0
$491$	−255.696	+	442.879i	−0.520766	+	0.901993i	0.478942	+	0.877846i	$0.341020\pi$
$491$	−255.696	+	442.879i	−0.520766	+	0.901993i	−0.999708	+	0.0241469i	$0.992313\pi$
$492$		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	0.501978	−	0.864880i	$-0.332606\pi$
$499$	1.97568	+	1.14066i	0.00395929	+	0.00228590i	−0.498019	+	0.867166i	$0.665939\pi$
$500$		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	$-0.868994\pi$
$509$	−56.9044	+	98.5614i	−0.111797	+	0.193637i	0.804698	+	0.593684i	$0.202327\pi$
$510$		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	$0.262912\pi$
$521$			766.079i			1.47040i	−0.677849	+	0.735201i	$0.737088\pi$
$522$		0			0
$523$		−	28.1668i		−	0.0538562i	−0.999637	−	0.0269281i	$-0.991427\pi$
$523$		−	28.1668i		−	0.0538562i	0.999637	−	0.0269281i	$-0.00857252\pi$
$524$		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	−0.0371602	−	0.999309i	$-0.511831\pi$
$547$	442.899	−	255.708i	0.809687	−	0.467473i	0.846847	+	0.531836i	$0.178498\pi$
$548$		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	$-0.520295\pi$
$557$	−70.9792			−0.127431			−0.0637156	+	0.997968i	$0.520295\pi$
$558$		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	−0.00942163	−	0.999956i	$-0.502999\pi$
$563$	484.898	−	839.869i	0.861276	−	1.49177i	0.870698	−	0.491818i	$-0.163668\pi$
$564$		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	0.0653159	−	0.997865i	$-0.479194\pi$
$569$	547.463	−	316.078i	0.962150	−	0.555498i	0.896834	+	0.442367i	$0.145861\pi$
$570$		0			0
$571$	805.680	+	465.159i	1.41100	+	0.814640i	0.995482	−	0.0949465i	$-0.0302680\pi$
$571$	805.680	+	465.159i	1.41100	+	0.814640i	0.415515	+	0.909586i	$0.363601\pi$
$572$		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	0.804967	−	0.593320i	$-0.202183\pi$
$587$	−65.3603	−	113.207i	−0.111346	−	0.192857i	−0.916313	+	0.400462i	$0.868850\pi$
$588$		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	$-0.896221\pi$
$593$		−	379.858i		−	0.640570i	0.947321	−	0.320285i	$-0.103779\pi$
$594$		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	$-0.236773\pi$
$599$	309.923	+	178.934i	0.517401	+	0.298721i	−0.218470	+	0.975844i	$0.570107\pi$
$600$		0			0
$601$	1.64207	+	2.84415i	0.00273223	+	0.00473236i	0.867388	−	0.497632i	$-0.165797\pi$
$601$	1.64207	+	2.84415i	0.00273223	+	0.00473236i	−0.864656	+	0.502364i	$0.832464\pi$
$602$		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	$-0.711688\pi$
$607$	226.365	−	392.076i	0.372925	−	0.645925i	0.990014	+	0.140969i	$0.0450216\pi$
$608$		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	0.154866	−	0.987935i	$-0.450505\pi$
$617$	−384.563	−	222.027i	−0.623278	−	0.359850i	−0.778144	+	0.628086i	$0.783839\pi$
$618$		0			0
$619$	−974.353	+	562.543i	−1.57408	+	0.908793i	−0.578414	+	0.815743i	$0.696328\pi$
$619$	−974.353	+	562.543i	−1.57408	+	0.908793i	−0.995661	+	0.0930494i	$0.970339\pi$
$620$		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	$-0.854022\pi$
$631$	−1131.60			−1.79334			−0.896671	+	0.442698i	$0.854022\pi$
$632$		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	0.366873	−	0.930271i	$-0.380428\pi$
$641$	869.162	−	501.811i	1.35595	−	0.782857i	0.989075	+	0.147414i	$0.0470951\pi$
$642$		0			0
$643$	−202.633	−	116.990i	−0.315137	−	0.181944i	0.334086	−	0.942543i	$-0.391572\pi$
$643$	−202.633	−	116.990i	−0.315137	−	0.181944i	−0.649223	+	0.760598i	$0.724906\pi$
$644$		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	$-0.913205\pi$
$653$	−162.139	+	280.833i	−0.248299	+	0.430067i	0.714755	+	0.699375i	$0.246538\pi$
$654$		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	0.820667	+	0.571407i	$0.193602\pi$
$659$	596.518	+	1033.20i	0.905186	+	1.56783i	0.0845191	+	0.996422i	$0.473065\pi$
$660$		0			0
$661$	84.0657	+	48.5353i	0.127180	+	0.0734271i	0.562240	−	0.826974i	$-0.309940\pi$
$661$	84.0657	+	48.5353i	0.127180	+	0.0734271i	−0.435061	+	0.900401i	$0.643273\pi$
$662$		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	0.553318	−	0.832970i	$-0.313361\pi$
$673$	−299.292	−	518.390i	−0.444714	−	0.770267i	−0.998032	+	0.0627029i	$0.980028\pi$
$674$		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	$-0.160883\pi$
$677$	12.3011	+	21.3061i	0.0181700	+	0.0314714i	−0.856797	+	0.515653i	$0.827549\pi$
$678$		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	0.0535995	−	0.998563i	$-0.482931\pi$
$691$	653.119	−	377.079i	0.945180	−	0.545700i	0.891580	+	0.452863i	$0.149597\pi$
$692$		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	$-0.362299\pi$
$701$	587.766			0.838468			0.419234	+	0.907878i	$0.362299\pi$
$702$		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	$-0.562480\pi$
$709$	394.808	−	227.942i	0.556851	−	0.321498i	0.751881	+	0.659299i	$0.229147\pi$
$710$		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	$-0.145468\pi$
$727$	48.3798	+	83.7963i	0.0665472	+	0.115263i	−0.830832	+	0.556523i	$0.812135\pi$
$728$		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	$-0.101208\pi$
$733$	845.937	+	488.402i	1.15408	+	0.666306i	0.204199	+	0.978929i	$0.434541\pi$
$734$		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	$-0.981029\pi$
$739$		−	88.0366i		−	0.119129i	0.998224	−	0.0595647i	$-0.0189713\pi$
$740$		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	$-0.543060\pi$
$743$	−787.884	−	454.885i	−1.06041	−	0.612228i	−0.925546	+	0.378636i	$0.876393\pi$
$744$		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	$-0.939802\pi$
$751$	−246.537	+	427.015i	−0.328279	+	0.568595i	0.653892	+	0.756588i	$0.273135\pi$
$752$		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	0.914450	−	0.404699i	$-0.132624\pi$
$761$	777.129	+	448.676i	1.02120	+	0.589587i	0.106745	+	0.994286i	$0.465957\pi$
$762$		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	−0.680119	−	0.733102i	$-0.738072\pi$
$769$	226.721	−	392.692i	0.294826	−	0.510653i	0.974944	+	0.222449i	$0.0714051\pi$
$770$		0			0
$771$	256.260	−	297.446i	0.332373	−	0.385793i
$772$		0			0
$773$	429.732			0.555927			0.277964	−	0.960592i	$-0.410341\pi$
$773$	429.732			0.555927			0.277964	+	0.960592i	$0.410341\pi$
$774$		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	0.578782	−	0.815482i	$-0.303528\pi$
$787$	127.451	+	73.5837i	0.161945	+	0.0934990i	−0.416837	+	0.908981i	$0.636861\pi$
$788$		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	$-0.937821\pi$
$797$	−256.948	+	445.047i	−0.322394	+	0.558403i	0.658587	+	0.752504i	$0.271154\pi$
$798$		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	$0.0734329\pi$
$809$			369.964i			0.457311i	−0.973507	+	0.228655i	$0.926567\pi$
$810$		0			0
$811$		−	42.1364i		−	0.0519561i	−0.999663	−	0.0259781i	$-0.991730\pi$
$811$		−	42.1364i		−	0.0519561i	0.999663	−	0.0259781i	$-0.00827001\pi$
$812$		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	$-0.0648814\pi$
$821$	258.078	+	447.005i	0.314346	+	0.544464i	−0.664952	+	0.746886i	$0.731548\pi$
$822$		0			0
$823$	169.184	−	293.035i	0.205569	−	0.356057i	−0.744745	−	0.667350i	$-0.767429\pi$
$823$	169.184	−	293.035i	0.205569	−	0.356057i	0.950314	+	0.311293i	$0.100762\pi$
$824$		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	$-0.634800\pi$
$839$	145.241	−	83.8547i	0.173112	−	0.0999460i	0.584052	+	0.811716i	$0.301466\pi$
$840$		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	$-0.620959\pi$
$853$	211.425	−	122.066i	0.247861	−	0.143102i	0.618784	+	0.785561i	$0.287626\pi$
$854$		0			0
$855$	112.651	+	141.581i	0.131756	+	0.165591i
$856$		0			0
$857$	−579.385	+	334.508i	−0.676061	+	0.390324i	−0.798369	−	0.602168i	$-0.794304\pi$
$857$	−579.385	+	334.508i	−0.676061	+	0.390324i	0.122308	+	0.992492i	$0.460970\pi$
$858$		0			0
$859$	626.013	+	361.429i	0.728769	+	0.420755i	0.817972	−	0.575258i	$-0.195098\pi$
$859$	626.013	+	361.429i	0.728769	+	0.420755i	−0.0892025	+	0.996014i	$0.528432\pi$
$860$		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	$-0.543550\pi$
$877$	−931.826	−	537.990i	−1.06252	−	0.613444i	−0.926127	+	0.377212i	$0.876883\pi$
$878$		0			0
$879$	−506.701	−	436.539i	−0.576452	−	0.496632i
$880$		0			0
$881$		−	1149.33i		−	1.30457i	−0.757973	−	0.652286i	$-0.773810\pi$
$881$		−	1149.33i		−	1.30457i	0.757973	−	0.652286i	$-0.226190\pi$
$882$		0			0
$883$			457.946i			0.518625i	0.965793	+	0.259313i	$0.0834960\pi$
$883$			457.946i			0.518625i	−0.965793	+	0.259313i	$0.916504\pi$
$884$		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	$-0.0931490\pi$
$887$	1052.34	+	607.568i	1.18640	+	0.684969i	0.228915	+	0.973447i	$0.426482\pi$
$888$		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	−0.584325	−	0.811520i	$-0.698641\pi$
$907$	−157.538	+	90.9546i	−0.173691	+	0.100281i	0.410634	+	0.911800i	$0.365307\pi$
$908$		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	$-0.708920\pi$
$911$	−208.841	+	120.575i	−0.229244	+	0.132354i	0.380979	+	0.924584i	$0.375587\pi$
$912$		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	$-0.588043\pi$
$919$	−501.923			−0.546163			−0.273081	+	0.961991i	$0.588043\pi$
$920$		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	−0.878533	−	0.477682i	$-0.841477\pi$
$929$	−839.922	+	484.929i	−0.904114	+	0.521990i	−0.0255812	+	0.999673i	$0.508144\pi$
$930$		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	−0.237569	−	0.971371i	$-0.576351\pi$
$941$	679.823	−	1177.49i	0.722447	−	1.25131i	0.960016	−	0.279944i	$-0.0903160\pi$
$942$		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	0.905056	−	0.425291i	$-0.139828\pi$
$947$	79.7517	+	138.134i	0.0842151	+	0.145865i	−0.820841	+	0.571156i	$0.806495\pi$
$948$		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	$0.164465\pi$
$953$			941.561i			0.987997i	−0.869463	+	0.493998i	$0.835535\pi$
$954$		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	−0.350172	−	0.936685i	$-0.613877\pi$
$967$	615.116	−	1065.41i	0.636107	−	1.10177i	0.986279	−	0.165085i	$-0.0527899\pi$
$968$		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	0.763529	−	0.645774i	$-0.223465\pi$
$977$	572.558	+	330.567i	0.586037	+	0.338349i	−0.177492	+	0.984122i	$0.556798\pi$
$978$		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	$-0.804920\pi$
$983$	−716.470	+	413.654i	−0.728861	+	0.420808i	0.0891445	+	0.996019i	$0.471587\pi$
$984$		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	$-0.511694\pi$
$991$	−72.7970			−0.0734581			−0.0367291	+	0.999325i	$0.511694\pi$
$992$		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	$-0.794737\pi$
$997$	−676.198	+	390.403i	−0.678233	+	0.391578i	0.120956	+	0.992658i	$0.461404\pi$
$998$		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.d.545.8	yes	32
3.2	odd	2		1728.3.n.c.1313.9		32
4.3	odd	2	inner	576.3.n.d.545.9	yes	32
8.3	odd	2		576.3.n.c.545.8	yes	32
8.5	even	2		576.3.n.c.545.9	yes	32
9.2	odd	6		576.3.n.c.353.9	yes	32
9.7	even	3		1728.3.n.d.737.8		32
12.11	even	2		1728.3.n.c.1313.10		32
24.5	odd	2		1728.3.n.d.1313.8		32
24.11	even	2		1728.3.n.d.1313.7		32
36.7	odd	6		1728.3.n.d.737.7		32
36.11	even	6		576.3.n.c.353.8	✓	32
72.11	even	6	inner	576.3.n.d.353.9	yes	32
72.29	odd	6	inner	576.3.n.d.353.8	yes	32
72.43	odd	6		1728.3.n.c.737.10		32
72.61	even	6		1728.3.n.c.737.9		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
576.3.n.c.353.8	✓	32	36.11	even	6
576.3.n.c.353.9	yes	32	9.2	odd	6
576.3.n.c.545.8	yes	32	8.3	odd	2
576.3.n.c.545.9	yes	32	8.5	even	2
576.3.n.d.353.8	yes	32	72.29	odd	6	inner
576.3.n.d.353.9	yes	32	72.11	even	6	inner
576.3.n.d.545.8	yes	32	1.1	even	1	trivial
576.3.n.d.545.9	yes	32	4.3	odd	2	inner
1728.3.n.c.737.9		32	72.61	even	6
1728.3.n.c.737.10		32	72.43	odd	6
1728.3.n.c.1313.9		32	3.2	odd	2
1728.3.n.c.1313.10		32	12.11	even	2
1728.3.n.d.737.7		32	36.7	odd	6
1728.3.n.d.737.8		32	9.7	even	3
1728.3.n.d.1313.7		32	24.11	even	2
1728.3.n.d.1313.8		32	24.5	odd	2

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

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