LMFDB - Embedded newform 288.2.s.a.95.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,2,Mod(95,288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(288, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("288.95");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	288.s (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:	$2.29969157821$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			95.5
Character	$\chi$	$=$	288.95
Dual form			288.2.s.a.191.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.683478 - 1.59150i) q^{3} +(3.40926 + 1.96834i) q^{5} +(0.961325 - 0.555021i) q^{7} +(-2.06572 + 2.17550i) q^{9} +O(q^{10})$	\(q+(-0.683478 - 1.59150i) q^{3} +(3.40926 + 1.96834i) q^{5} +(0.961325 - 0.555021i) q^{7} +(-2.06572 + 2.17550i) q^{9} +(1.63301 + 2.82846i) q^{11} +(0.124912 - 0.216355i) q^{13} +(0.802448 - 6.77114i) q^{15} -5.86838i q^{17} +2.19827i q^{19} +(-1.54036 - 1.15060i) q^{21} +(2.79320 - 4.83797i) q^{23} +(5.24871 + 9.09103i) q^{25} +(4.87417 + 1.80067i) q^{27} +(2.35571 - 1.36007i) q^{29} +(-8.96997 - 5.17882i) q^{31} +(3.38536 - 4.53212i) q^{33} +4.36988 q^{35} -0.333076 q^{37} +(-0.429703 - 0.0509241i) q^{39} +(-5.28400 - 3.05072i) q^{41} +(-8.50982 + 4.91315i) q^{43} +(-11.3247 + 3.35083i) q^{45} +(4.70740 + 8.15346i) q^{47} +(-2.88390 + 4.99507i) q^{49} +(-9.33951 + 4.01091i) q^{51} -4.75157i q^{53} +12.8573i q^{55} +(3.49853 - 1.50247i) q^{57} +(-3.26523 + 5.65555i) q^{59} +(1.07336 + 1.85911i) q^{61} +(-0.778375 + 3.23788i) q^{63} +(0.851719 - 0.491740i) q^{65} +(0.501168 + 0.289349i) q^{67} +(-9.60871 - 1.13873i) q^{69} -3.26444 q^{71} -12.6045 q^{73} +(10.8810 - 14.5668i) q^{75} +(3.13971 + 1.81271i) q^{77} +(7.67063 - 4.42864i) q^{79} +(-0.465627 - 8.98795i) q^{81} +(-2.34056 - 4.05397i) q^{83} +(11.5510 - 20.0069i) q^{85} +(-3.77463 - 2.81953i) q^{87} +4.75157i q^{89} -0.277316i q^{91} +(-2.11129 + 17.8153i) q^{93} +(-4.32693 + 7.49447i) q^{95} +(0.916363 + 1.58719i) q^{97} +(-9.52667 - 2.29018i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{9}+O(q^{10}) $ 24 * q - 4 * q^9	$ 24 q - 4 q^{9} + 8 q^{21} + 12 q^{25} + 24 q^{29} - 20 q^{33} - 36 q^{41} - 8 q^{45} + 12 q^{49} - 36 q^{57} - 48 q^{65} - 16 q^{69} + 24 q^{73} - 48 q^{77} - 20 q^{81} - 64 q^{93} + 12 q^{97}+O(q^{100}) $ 24 * q - 4 * q^9 + 8 * q^21 + 12 * q^25 + 24 * q^29 - 20 * q^33 - 36 * q^41 - 8 * q^45 + 12 * q^49 - 36 * q^57 - 48 * q^65 - 16 * q^69 + 24 * q^73 - 48 * q^77 - 20 * q^81 - 64 * q^93 + 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.683478	−	1.59150i	−0.394606	−	0.918850i
$3$	−0.683478	−	1.59150i	−0.394606	−	0.918850i
$4$		0			0
$5$	3.40926	+	1.96834i	1.52467	+	0.880267i	0.999573	+	0.0292239i	$0.00930359\pi$
$5$	3.40926	+	1.96834i	1.52467	+	0.880267i	0.525095	+	0.851044i	$0.324030\pi$
$6$		0			0
$7$	0.961325	−	0.555021i	0.363347	−	0.209778i	−0.307201	−	0.951645i	$-0.599392\pi$
$7$	0.961325	−	0.555021i	0.363347	−	0.209778i	0.670548	+	0.741866i	$0.266059\pi$
$8$		0			0
$9$	−2.06572	+	2.17550i	−0.688572	+	0.725168i
$10$		0			0
$11$	1.63301	+	2.82846i	0.492372	+	0.852813i	0.999961	−	0.00878589i	$-0.00279667\pi$
$11$	1.63301	+	2.82846i	0.492372	+	0.852813i	−0.507590	+	0.861599i	$0.669463\pi$
$12$		0			0
$13$	0.124912	−	0.216355i	0.0346445	−	0.0600060i	−0.848183	−	0.529703i	$-0.822303\pi$
$13$	0.124912	−	0.216355i	0.0346445	−	0.0600060i	0.882828	+	0.469697i	$0.155637\pi$
$14$		0			0
$15$	0.802448	−	6.77114i	0.207191	−	1.74830i
$16$		0			0
$17$		−	5.86838i		−	1.42329i	−0.702538	−	0.711646i	$-0.747950\pi$
$17$		−	5.86838i		−	1.42329i	0.702538	−	0.711646i	$-0.252050\pi$
$18$		0			0
$19$			2.19827i			0.504317i	0.967686	+	0.252159i	$0.0811405\pi$
$19$			2.19827i			0.504317i	−0.967686	+	0.252159i	$0.918860\pi$
$20$		0			0
$21$	−1.54036	−	1.15060i	−0.336134	−	0.251082i
$22$		0			0
$23$	2.79320	−	4.83797i	0.582423	−	1.00879i	−0.412768	−	0.910836i	$-0.635438\pi$
$23$	2.79320	−	4.83797i	0.582423	−	1.00879i	0.995191	−	0.0979508i	$-0.0312288\pi$
$24$		0			0
$25$	5.24871	+	9.09103i	1.04974	+	1.81821i
$26$		0			0
$27$	4.87417	+	1.80067i	0.938035	+	0.346540i
$28$		0			0
$29$	2.35571	−	1.36007i	0.437445	−	0.252559i	−0.265068	−	0.964230i	$-0.585394\pi$
$29$	2.35571	−	1.36007i	0.437445	−	0.252559i	0.702513	+	0.711671i	$0.252061\pi$
$30$		0			0
$31$	−8.96997	−	5.17882i	−1.61105	−	0.930143i	−0.989126	−	0.147069i	$-0.953016\pi$
$31$	−8.96997	−	5.17882i	−1.61105	−	0.930143i	−0.621929	−	0.783074i	$-0.713651\pi$
$32$		0			0
$33$	3.38536	−	4.53212i	0.589315	−	0.788941i
$34$		0			0
$35$	4.36988			0.738644
$36$		0			0
$37$	−0.333076			−0.0547574			−0.0273787	−	0.999625i	$-0.508716\pi$
$37$	−0.333076			−0.0547574			−0.0273787	+	0.999625i	$0.508716\pi$
$38$		0			0
$39$	−0.429703	−	0.0509241i	−0.0688075	−	0.00815438i
$40$		0			0
$41$	−5.28400	−	3.05072i	−0.825222	−	0.476442i	0.0269919	−	0.999636i	$-0.491407\pi$
$41$	−5.28400	−	3.05072i	−0.825222	−	0.476442i	−0.852214	+	0.523194i	$0.824740\pi$
$42$		0			0
$43$	−8.50982	+	4.91315i	−1.29773	+	0.749248i	−0.980012	−	0.198936i	$-0.936251\pi$
$43$	−8.50982	+	4.91315i	−1.29773	+	0.749248i	−0.317722	+	0.948184i	$0.602918\pi$
$44$		0			0
$45$	−11.3247	+	3.35083i	−1.68819	+	0.499512i
$46$		0			0
$47$	4.70740	+	8.15346i	0.686645	+	1.18930i	0.972917	+	0.231156i	$0.0742507\pi$
$47$	4.70740	+	8.15346i	0.686645	+	1.18930i	−0.286272	+	0.958148i	$0.592416\pi$
$48$		0			0
$49$	−2.88390	+	4.99507i	−0.411986	+	0.713581i
$50$		0			0
$51$	−9.33951	+	4.01091i	−1.30779	+	0.561640i
$52$		0			0
$53$		−	4.75157i		−	0.652678i	−0.945253	−	0.326339i	$-0.894185\pi$
$53$		−	4.75157i		−	0.652678i	0.945253	−	0.326339i	$-0.105815\pi$
$54$		0			0
$55$			12.8573i			1.73368i
$56$		0			0
$57$	3.49853	−	1.50247i	0.463392	−	0.199007i
$58$		0			0
$59$	−3.26523	+	5.65555i	−0.425097	+	0.736290i	−0.996430	−	0.0844287i	$-0.973093\pi$
$59$	−3.26523	+	5.65555i	−0.425097	+	0.736290i	0.571332	+	0.820719i	$0.306427\pi$
$60$		0			0
$61$	1.07336	+	1.85911i	0.137429	+	0.238034i	0.926523	−	0.376239i	$-0.122783\pi$
$61$	1.07336	+	1.85911i	0.137429	+	0.238034i	−0.789094	+	0.614273i	$0.789449\pi$
$62$		0			0
$63$	−0.778375	+	3.23788i	−0.0980660	+	0.407935i
$64$		0			0
$65$	0.851719	−	0.491740i	0.105643	−	0.0609928i
$66$		0			0
$67$	0.501168	+	0.289349i	0.0612274	+	0.0353497i	0.530301	−	0.847809i	$-0.322079\pi$
$67$	0.501168	+	0.289349i	0.0612274	+	0.0353497i	−0.469074	+	0.883159i	$0.655412\pi$
$68$		0			0
$69$	−9.60871	−	1.13873i	−1.15675	−	0.137087i
$70$		0			0
$71$	−3.26444			−0.387418			−0.193709	−	0.981059i	$-0.562052\pi$
$71$	−3.26444			−0.387418			−0.193709	+	0.981059i	$0.562052\pi$
$72$		0			0
$73$	−12.6045			−1.47525			−0.737623	−	0.675213i	$-0.764052\pi$
$73$	−12.6045			−1.47525			−0.737623	+	0.675213i	$0.764052\pi$
$74$		0			0
$75$	10.8810	−	14.5668i	1.25643	−	1.68203i
$76$		0			0
$77$	3.13971	+	1.81271i	0.357803	+	0.206578i
$78$		0			0
$79$	7.67063	−	4.42864i	0.863014	−	0.498261i	−0.00200667	−	0.999998i	$-0.500639\pi$
$79$	7.67063	−	4.42864i	0.863014	−	0.498261i	0.865020	+	0.501737i	$0.167305\pi$
$80$		0			0
$81$	−0.465627	−	8.98795i	−0.0517363	−	0.998661i
$82$		0			0
$83$	−2.34056	−	4.05397i	−0.256910	−	0.444981i	0.708502	−	0.705708i	$-0.249371\pi$
$83$	−2.34056	−	4.05397i	−0.256910	−	0.444981i	−0.965413	+	0.260727i	$0.916038\pi$
$84$		0			0
$85$	11.5510	−	20.0069i	1.25288	−	2.17005i
$86$		0			0
$87$	−3.77463	−	2.81953i	−0.404682	−	0.302285i
$88$		0			0
$89$			4.75157i			0.503665i	0.967771	+	0.251833i	$0.0810333\pi$
$89$			4.75157i			0.503665i	−0.967771	+	0.251833i	$0.918967\pi$
$90$		0			0
$91$		−	0.277316i		−	0.0290707i
$92$		0			0
$93$	−2.11129	+	17.8153i	−0.218930	+	1.84736i
$94$		0			0
$95$	−4.32693	+	7.49447i	−0.443934	+	0.768916i
$96$		0			0
$97$	0.916363	+	1.58719i	0.0930426	+	0.161154i	0.908790	−	0.417254i	$-0.137007\pi$
$97$	0.916363	+	1.58719i	0.0930426	+	0.161154i	−0.815747	+	0.578408i	$0.803674\pi$
$98$		0			0
$99$	−9.52667	−	2.29018i	−0.957466	−	0.230171i
$100$		0			0
$101$	8.30824	−	4.79677i	0.826701	−	0.477296i	−0.0260209	−	0.999661i	$-0.508284\pi$
$101$	8.30824	−	4.79677i	0.826701	−	0.477296i	0.852722	+	0.522365i	$0.174950\pi$
$102$		0			0
$103$	0.338016	+	0.195154i	0.0333057	+	0.0192291i	0.516560	−	0.856251i	$-0.327212\pi$
$103$	0.338016	+	0.195154i	0.0333057	+	0.0192291i	−0.483255	+	0.875480i	$0.660545\pi$
$104$		0			0
$105$	−2.98671	−	6.95464i	−0.291473	−	0.678704i
$106$		0			0
$107$	7.67656			0.742121			0.371060	−	0.928609i	$-0.378994\pi$
$107$	7.67656			0.742121			0.371060	+	0.928609i	$0.378994\pi$
$108$		0			0
$109$	−4.72961			−0.453015			−0.226507	−	0.974009i	$-0.572731\pi$
$109$	−4.72961			−0.453015			−0.226507	+	0.974009i	$0.572731\pi$
$110$		0			0
$111$	0.227650	+	0.530090i	0.0216076	+	0.0503139i
$112$		0			0
$113$	−6.34715	−	3.66453i	−0.597089	−	0.344730i	0.170806	−	0.985305i	$-0.445363\pi$
$113$	−6.34715	−	3.66453i	−0.597089	−	0.344730i	−0.767896	+	0.640575i	$0.778696\pi$
$114$		0			0
$115$	19.0455	−	10.9959i	1.77600	−	1.02538i
$116$		0			0
$117$	0.212647	+	0.718675i	0.0196592	+	0.0664415i
$118$		0			0
$119$	−3.25708	−	5.64143i	−0.298576	−	0.517149i
$120$		0			0
$121$	0.166538	−	0.288453i	0.0151398	−	0.0262230i
$122$		0			0
$123$	−1.24371	+	10.4946i	−0.112142	+	0.946262i
$124$		0			0
$125$			21.6415i			1.93568i
$126$		0			0
$127$			0.116971i			0.0103795i	0.999987	+	0.00518973i	$0.00165195\pi$
$127$			0.116971i			0.0103795i	−0.999987	+	0.00518973i	$0.998348\pi$
$128$		0			0
$129$	13.6355	+	10.1853i	1.20054	+	0.896767i
$130$		0			0
$131$	−1.95887	+	3.39286i	−0.171147	+	0.296436i	−0.938821	−	0.344405i	$-0.888081\pi$
$131$	−1.95887	+	3.39286i	−0.171147	+	0.296436i	0.767674	+	0.640841i	$0.221414\pi$
$132$		0			0
$133$	1.22009	+	2.11325i	0.105795	+	0.183242i
$134$		0			0
$135$	13.0730	+	15.7330i	1.12515	+	1.35408i
$136$		0			0
$137$	−6.43350	+	3.71438i	−0.549651	+	0.317341i	−0.748981	−	0.662591i	$-0.769457\pi$
$137$	−6.43350	+	3.71438i	−0.549651	+	0.317341i	0.199330	+	0.979932i	$0.436123\pi$
$138$		0			0
$139$	−12.9406	−	7.47128i	−1.09761	−	0.633706i	−0.162018	−	0.986788i	$-0.551800\pi$
$139$	−12.9406	−	7.47128i	−1.09761	−	0.633706i	−0.935592	+	0.353082i	$0.885134\pi$
$140$		0			0
$141$	9.75879	−	13.0645i	0.821838	−	1.10023i
$142$		0			0
$143$	0.815935			0.0682319
$144$		0			0
$145$	10.7083			0.889278
$146$		0			0
$147$	9.92071	+	1.17570i	0.818246	+	0.0969704i
$148$		0			0
$149$	1.47576	+	0.852029i	0.120899	+	0.0698010i	0.559230	−	0.829013i	$-0.311097\pi$
$149$	1.47576	+	0.852029i	0.120899	+	0.0698010i	−0.438331	+	0.898814i	$0.644430\pi$
$150$		0			0
$151$	−5.20887	+	3.00734i	−0.423892	+	0.244734i	−0.696741	−	0.717323i	$-0.745367\pi$
$151$	−5.20887	+	3.00734i	−0.423892	+	0.244734i	0.272849	+	0.962057i	$0.412034\pi$
$152$		0			0
$153$	12.7667	+	12.1224i	1.03213	+	0.980040i
$154$		0			0
$155$	−20.3873	−	35.3119i	−1.63755	−	2.83632i
$156$		0			0
$157$	−2.92863	+	5.07254i	−0.233731	+	0.404833i	−0.958903	−	0.283734i	$-0.908427\pi$
$157$	−2.92863	+	5.07254i	−0.233731	+	0.404833i	0.725172	+	0.688567i	$0.241760\pi$
$158$		0			0
$159$	−7.56210	+	3.24759i	−0.599714	+	0.257551i
$160$		0			0
$161$		−	6.20115i		−	0.488719i
$162$		0			0
$163$		−	4.27956i		−	0.335201i	−0.985855	−	0.167601i	$-0.946398\pi$
$163$		−	4.27956i		−	0.335201i	0.985855	−	0.167601i	$-0.0536019\pi$
$164$		0			0
$165$	20.4623	−	8.78766i	1.59299	−	0.684119i
$166$		0			0
$167$	9.31473	−	16.1336i	0.720795	−	1.24845i	−0.239886	−	0.970801i	$-0.577110\pi$
$167$	9.31473	−	16.1336i	0.720795	−	1.24845i	0.960681	−	0.277653i	$-0.0895565\pi$
$168$		0			0
$169$	6.46879	+	11.2043i	0.497600	+	0.861868i
$170$		0			0
$171$	−4.78234	−	4.54100i	−0.365715	−	0.347259i
$172$		0			0
$173$	−7.63503	+	4.40809i	−0.580481	+	0.335141i	−0.761325	−	0.648371i	$-0.775451\pi$
$173$	−7.63503	+	4.40809i	−0.580481	+	0.335141i	0.180844	+	0.983512i	$0.442117\pi$
$174$		0			0
$175$	10.0914	+	5.82629i	0.762840	+	0.440426i
$176$		0			0
$177$	11.2325	+	1.33116i	0.844287	+	0.100056i
$178$		0			0
$179$	6.21764			0.464728			0.232364	−	0.972629i	$-0.425354\pi$
$179$	6.21764			0.464728			0.232364	+	0.972629i	$0.425354\pi$
$180$		0			0
$181$	−20.6618			−1.53578			−0.767888	−	0.640584i	$-0.778692\pi$
$181$	−20.6618			−1.53578			−0.767888	+	0.640584i	$0.778692\pi$
$182$		0			0
$183$	2.22514	−	2.97890i	0.164487	−	0.220206i
$184$		0			0
$185$	−1.13554	−	0.655607i	−0.0834869	−	0.0482012i
$186$		0			0
$187$	16.5985	−	9.58315i	1.21380	−	0.700789i
$188$		0			0
$189$	5.68508	−	0.974240i	0.413529	−	0.0708655i
$190$		0			0
$191$	6.87216	+	11.9029i	0.497252	+	0.861266i	0.999995	−	0.00317001i	$-0.00100905\pi$
$191$	6.87216	+	11.9029i	0.497252	+	0.861266i	−0.502743	+	0.864436i	$0.667676\pi$
$192$		0			0
$193$	8.58105	−	14.8628i	0.617678	−	1.06985i	−0.372231	−	0.928140i	$-0.621407\pi$
$193$	8.58105	−	14.8628i	0.617678	−	1.06985i	0.989908	−	0.141709i	$-0.0452597\pi$
$194$		0			0
$195$	−1.36473	−	1.01941i	−0.0977305	−	0.0730017i
$196$		0			0
$197$			5.65685i			0.403034i	0.979485	+	0.201517i	$0.0645872\pi$
$197$			5.65685i			0.403034i	−0.979485	+	0.201517i	$0.935413\pi$
$198$		0			0
$199$		−	10.8015i		−	0.765700i	−0.923811	−	0.382850i	$-0.874943\pi$
$199$		−	10.8015i		−	0.765700i	0.923811	−	0.382850i	$-0.125057\pi$
$200$		0			0
$201$	0.117961	−	0.995370i	0.00832035	−	0.0702080i
$202$		0			0
$203$	1.50974	−	2.61494i	0.105963	−	0.183533i
$204$		0			0
$205$	−12.0097	−	20.8014i	−0.838793	−	1.45283i
$206$		0			0
$207$	4.75505	+	16.0705i	0.330499	+	1.11698i
$208$		0			0
$209$	−6.21771	+	3.58980i	−0.430088	+	0.248312i
$210$		0			0
$211$	−6.44593	−	3.72156i	−0.443756	−	0.256203i	0.261433	−	0.965221i	$-0.415805\pi$
$211$	−6.44593	−	3.72156i	−0.443756	−	0.256203i	−0.705190	+	0.709019i	$0.749138\pi$
$212$		0			0
$213$	2.23117	+	5.19535i	0.152878	+	0.355979i
$214$		0			0
$215$	−38.6829			−2.63815
$216$		0			0
$217$	−11.4974			−0.780495
$218$		0			0
$219$	8.61490	+	20.0600i	0.582141	+	1.35553i
$220$		0			0
$221$	−1.26965	−	0.733035i	−0.0854061	−	0.0493092i
$222$		0			0
$223$	18.5665	−	10.7194i	1.24330	−	0.717822i	0.273538	−	0.961861i	$-0.411806\pi$
$223$	18.5665	−	10.7194i	1.24330	−	0.717822i	0.969765	+	0.244040i	$0.0784727\pi$
$224$		0			0
$225$	−30.6199	−	7.36091i	−2.04133	−	0.490728i
$226$		0			0
$227$	13.3957	+	23.2020i	0.889104	+	1.53997i	0.840937	+	0.541134i	$0.182005\pi$
$227$	13.3957	+	23.2020i	0.889104	+	1.53997i	0.0481672	+	0.998839i	$0.484662\pi$
$228$		0			0
$229$	0.0416257	−	0.0720978i	0.00275070	−	0.00476436i	−0.864647	−	0.502380i	$-0.832458\pi$
$229$	0.0416257	−	0.0720978i	0.00275070	−	0.00476436i	0.867397	+	0.497616i	$0.165791\pi$
$230$		0			0
$231$	0.739003	−	6.23579i	0.0486229	−	0.410285i
$232$		0			0
$233$			9.29262i			0.608780i	0.952548	+	0.304390i	$0.0984526\pi$
$233$			9.29262i			0.608780i	−0.952548	+	0.304390i	$0.901547\pi$
$234$		0			0
$235$			37.0630i			2.41773i
$236$		0			0
$237$	−12.2909	−	9.18090i	−0.798378	−	0.596364i
$238$		0			0
$239$	7.54478	−	13.0679i	0.488031	−	0.845294i	−0.511874	−	0.859060i	$-0.671049\pi$
$239$	7.54478	−	13.0679i	0.488031	−	0.845294i	0.999905	+	0.0137660i	$0.00438198\pi$
$240$		0			0
$241$	−12.0192	−	20.8179i	−0.774227	−	1.34100i	−0.935228	−	0.354046i	$-0.884806\pi$
$241$	−12.0192	−	20.8179i	−0.774227	−	1.34100i	0.161001	−	0.986954i	$-0.448528\pi$
$242$		0			0
$243$	−13.9860	+	6.88410i	−0.897204	+	0.441615i
$244$		0			0
$245$	−19.6640	+	11.3530i	−1.25628	+	0.725316i
$246$		0			0
$247$	0.475606	+	0.274591i	0.0302621	+	0.0174718i
$248$		0			0
$249$	−4.85216	+	6.49580i	−0.307493	+	0.411654i
$250$		0			0
$251$	−18.4712			−1.16589			−0.582947	−	0.812510i	$-0.698101\pi$
$251$	−18.4712			−1.16589			−0.582947	+	0.812510i	$0.698101\pi$
$252$		0			0
$253$	18.2454			1.14708
$254$		0			0
$255$	−39.7356	−	4.70907i	−2.48834	−	0.294894i
$256$		0			0
$257$	16.5839	+	9.57471i	1.03447	+	0.597254i	0.918263	−	0.395971i	$-0.129592\pi$
$257$	16.5839	+	9.57471i	1.03447	+	0.597254i	0.116211	+	0.993225i	$0.462925\pi$
$258$		0			0
$259$	−0.320195	+	0.184864i	−0.0198959	+	0.0114869i
$260$		0			0
$261$	−1.90740	+	7.93439i	−0.118065	+	0.491126i
$262$		0			0
$263$	1.89930	+	3.28969i	0.117116	+	0.202851i	0.918624	−	0.395134i	$-0.129302\pi$
$263$	1.89930	+	3.28969i	0.117116	+	0.202851i	−0.801508	+	0.597984i	$0.795968\pi$
$264$		0			0
$265$	9.35270	−	16.1993i	0.574532	−	0.995118i
$266$		0			0
$267$	7.56210	−	3.24759i	0.462793	−	0.198749i
$268$		0			0
$269$		−	22.0593i		−	1.34498i	−0.740106	−	0.672490i	$-0.765225\pi$
$269$		−	22.0593i		−	1.34498i	0.740106	−	0.672490i	$-0.234775\pi$
$270$		0			0
$271$		−	16.7153i		−	1.01538i	−0.861540	−	0.507690i	$-0.830499\pi$
$271$		−	16.7153i		−	1.01538i	0.861540	−	0.507690i	$-0.169501\pi$
$272$		0			0
$273$	−0.441348	+	0.189540i	−0.0267116	+	0.0114715i
$274$		0			0
$275$	−17.1424	+	29.6915i	−1.03373	+	1.79047i
$276$		0			0
$277$	9.25752	+	16.0345i	0.556231	+	0.963420i	0.997807	+	0.0661959i	$0.0210862\pi$
$277$	9.25752	+	16.0345i	0.556231	+	0.963420i	−0.441576	+	0.897224i	$0.645580\pi$
$278$		0			0
$279$	29.7960	−	8.81624i	1.78384	−	0.527814i
$280$		0			0
$281$	4.39881	−	2.53965i	0.262411	−	0.151503i	−0.363023	−	0.931780i	$-0.618255\pi$
$281$	4.39881	−	2.53965i	0.262411	−	0.151503i	0.625434	+	0.780277i	$0.284922\pi$
$282$		0			0
$283$	19.8035	+	11.4336i	1.17720	+	0.679656i	0.955365	−	0.295429i	$-0.0954625\pi$
$283$	19.8035	+	11.4336i	1.17720	+	0.679656i	0.221834	+	0.975085i	$0.428796\pi$
$284$		0			0
$285$	14.8848	+	1.76400i	0.881698	+	0.104490i
$286$		0			0
$287$	−6.77285			−0.399789
$288$		0			0
$289$	−17.4379			−1.02576
$290$		0			0
$291$	1.89969	−	2.54320i	0.111362	−	0.149085i
$292$		0			0
$293$	−0.160276	−	0.0925356i	−0.00936344	−	0.00540599i	0.495311	−	0.868716i	$-0.335054\pi$
$293$	−0.160276	−	0.0925356i	−0.00936344	−	0.00540599i	−0.504674	+	0.863310i	$0.668387\pi$
$294$		0			0
$295$	−22.2641	+	12.8542i	−1.29626	+	0.748399i
$296$		0			0
$297$	2.86646	+	16.7269i	0.166329	+	0.970595i
$298$		0			0
$299$	−0.697812	−	1.20865i	−0.0403555	−	0.0698978i
$300$		0			0
$301$	−5.45380	+	9.44626i	−0.314352	+	0.544473i
$302$		0			0
$303$	−13.3125	−	9.94405i	−0.764785	−	0.571271i
$304$		0			0
$305$			8.45090i			0.483897i
$306$		0			0
$307$		−	18.7966i		−	1.07278i	−0.843971	−	0.536388i	$-0.819788\pi$
$307$		−	18.7966i		−	1.07278i	0.843971	−	0.536388i	$-0.180212\pi$
$308$		0			0
$309$	0.0795598	−	0.671334i	0.00452600	−	0.0381909i
$310$		0			0
$311$	−3.65208	+	6.32560i	−0.207091	+	0.358692i	−0.950797	−	0.309815i	$-0.899733\pi$
$311$	−3.65208	+	6.32560i	−0.207091	+	0.358692i	0.743706	+	0.668507i	$0.233066\pi$
$312$		0			0
$313$	−11.2472	−	19.4808i	−0.635732	−	1.10112i	−0.986360	−	0.164605i	$-0.947365\pi$
$313$	−11.2472	−	19.4808i	−0.635732	−	1.10112i	0.350628	−	0.936515i	$-0.385968\pi$
$314$		0			0
$315$	−9.02693	+	9.50668i	−0.508610	+	0.535641i
$316$		0			0
$317$	8.95052	−	5.16758i	0.502711	−	0.290240i	−0.227121	−	0.973866i	$-0.572931\pi$
$317$	8.95052	−	5.16758i	0.502711	−	0.290240i	0.729832	+	0.683626i	$0.239598\pi$
$318$		0			0
$319$	7.69382	+	4.44203i	0.430771	+	0.248706i
$320$		0			0
$321$	−5.24675	−	12.2172i	−0.292845	−	0.681898i
$322$		0			0
$323$	12.9003			0.717791
$324$		0			0
$325$	2.62252			0.145471
$326$		0			0
$327$	3.23258	+	7.52716i	0.178762	+	0.416253i
$328$		0			0
$329$	9.05069	+	5.22542i	0.498981	+	0.288087i
$330$		0			0
$331$	−24.6744	+	14.2458i	−1.35623	+	0.783018i	−0.989113	−	0.147158i	$-0.952988\pi$
$331$	−24.6744	+	14.2458i	−1.35623	+	0.783018i	−0.367114	+	0.930176i	$0.619654\pi$
$332$		0			0
$333$	0.688041	−	0.724609i	0.0377044	−	0.0397083i
$334$		0			0
$335$	1.13907	+	1.97294i	0.0622343	+	0.107793i
$336$		0			0
$337$	−11.7179	+	20.2959i	−0.638312	+	1.10559i	0.347491	+	0.937683i	$0.387034\pi$
$337$	−11.7179	+	20.2959i	−0.638312	+	1.10559i	−0.985803	+	0.167906i	$0.946300\pi$
$338$		0			0
$339$	−1.49395	+	12.6061i	−0.0811400	+	0.684668i
$340$		0			0
$341$		−	33.8283i		−	1.83191i
$342$		0			0
$343$			14.1728i			0.765260i
$344$		0			0
$345$	−30.5172	−	22.7954i	−1.64299	−	1.22726i
$346$		0			0
$347$	10.9531	−	18.9714i	0.587995	−	1.01844i	−0.406500	−	0.913651i	$-0.633251\pi$
$347$	10.9531	−	18.9714i	0.587995	−	1.01844i	0.994495	−	0.104786i	$-0.0334159\pi$
$348$		0			0
$349$	14.4261	+	24.9867i	0.772209	+	1.33750i	0.936350	+	0.351068i	$0.114181\pi$
$349$	14.4261	+	24.9867i	0.772209	+	1.33750i	−0.164141	+	0.986437i	$0.552485\pi$
$350$		0			0
$351$	0.998429	−	0.829625i	0.0532922	−	0.0442821i
$352$		0			0
$353$	−7.24937	+	4.18543i	−0.385845	+	0.222768i	−0.680358	−	0.732880i	$-0.738176\pi$
$353$	−7.24937	+	4.18543i	−0.385845	+	0.222768i	0.294513	+	0.955647i	$0.404842\pi$
$354$		0			0
$355$	−11.1293	−	6.42553i	−0.590684	−	0.341032i
$356$		0			0
$357$	−6.75216	+	9.03941i	−0.357362	+	0.478417i
$358$		0			0
$359$	35.2621			1.86106			0.930532	−	0.366210i	$-0.119345\pi$
$359$	35.2621			1.86106			0.930532	+	0.366210i	$0.119345\pi$
$360$		0			0
$361$	14.1676			0.745664
$362$		0			0
$363$	−0.572896	−	0.0678939i	−0.0300692	−	0.00356351i
$364$		0			0
$365$	−42.9721	−	24.8099i	−2.24926	−	1.29861i
$366$		0			0
$367$	−5.56938	+	3.21548i	−0.290719	+	0.167847i	−0.638266	−	0.769816i	$-0.720348\pi$
$367$	−5.56938	+	3.21548i	−0.290719	+	0.167847i	0.347547	+	0.937663i	$0.387015\pi$
$368$		0			0
$369$	17.5521	−	5.19344i	0.913725	−	0.270359i
$370$		0			0
$371$	−2.63722	−	4.56780i	−0.136918	−	0.237149i
$372$		0			0
$373$	−9.84241	+	17.0476i	−0.509621	+	0.882689i	0.490317	+	0.871544i	$0.336881\pi$
$373$	−9.84241	+	17.0476i	−0.509621	+	0.882689i	−0.999938	+	0.0111451i	$0.996452\pi$
$374$		0			0
$375$	34.4424	−	14.7915i	1.77860	−	0.763830i
$376$		0			0
$377$		−	0.679560i		−	0.0349991i
$378$		0			0
$379$			1.50534i			0.0773240i	0.999252	+	0.0386620i	$0.0123096\pi$
$379$			1.50534i			0.0773240i	−0.999252	+	0.0386620i	$0.987690\pi$
$380$		0			0
$381$	0.186158	−	0.0799467i	0.00953717	−	0.00409580i
$382$		0			0
$383$	14.0663	−	24.3635i	0.718754	−	1.24492i	−0.242739	−	0.970092i	$-0.578046\pi$
$383$	14.0663	−	24.3635i	0.718754	−	1.24492i	0.961494	−	0.274827i	$-0.0886207\pi$
$384$		0			0
$385$	7.13607	+	12.3600i	0.363688	+	0.629926i
$386$		0			0
$387$	6.89031	−	28.6623i	0.350254	−	1.45699i
$388$		0			0
$389$	−13.8804	+	8.01387i	−0.703766	+	0.406319i	−0.808748	−	0.588155i	$-0.799855\pi$
$389$	−13.8804	+	8.01387i	−0.703766	+	0.406319i	0.104983	+	0.994474i	$0.466521\pi$
$390$		0			0
$391$	−28.3911	−	16.3916i	−1.43580	−	0.828959i
$392$		0			0
$393$	6.73857	+	0.798588i	0.339916	+	0.0402835i
$394$		0			0
$395$	34.8683			1.75441
$396$		0			0
$397$	13.7725			0.691224			0.345612	−	0.938377i	$-0.387671\pi$
$397$	13.7725			0.691224			0.345612	+	0.938377i	$0.387671\pi$
$398$		0			0
$399$	2.52933	−	3.38612i	0.126625	−	0.169518i
$400$		0			0
$401$	31.5929	+	18.2402i	1.57767	+	0.910870i	0.995183	+	0.0980324i	$0.0312549\pi$
$401$	31.5929	+	18.2402i	1.57767	+	0.910870i	0.582490	+	0.812838i	$0.302078\pi$
$402$		0			0
$403$	−2.24092	+	1.29380i	−0.111628	+	0.0644487i
$404$		0			0
$405$	16.1039	−	31.5588i	0.800208	−	1.56817i
$406$		0			0
$407$	−0.543918	−	0.942094i	−0.0269610	−	0.0466978i
$408$		0			0
$409$	1.41675	−	2.45388i	0.0700537	−	0.121337i	−0.828871	−	0.559440i	$-0.811016\pi$
$409$	1.41675	−	2.45388i	0.0700537	−	0.121337i	0.898925	+	0.438103i	$0.144350\pi$
$410$		0			0
$411$	10.3086	+	7.70019i	0.508485	+	0.379823i
$412$		0			0
$413$			7.24910i			0.356705i
$414$		0			0
$415$		−	18.4281i		−	0.904599i
$416$		0			0
$417$	−3.04588	+	25.7014i	−0.149157	+	1.25860i
$418$		0			0
$419$	−6.64717	+	11.5132i	−0.324736	+	0.562458i	−0.981459	−	0.191673i	$-0.938609\pi$
$419$	−6.64717	+	11.5132i	−0.324736	+	0.562458i	0.656723	+	0.754132i	$0.271942\pi$
$420$		0			0
$421$	9.90259	+	17.1518i	0.482623	+	0.835927i	0.999801	−	0.0199505i	$-0.00635085\pi$
$421$	9.90259	+	17.1518i	0.482623	+	0.835927i	−0.517178	+	0.855878i	$0.673018\pi$
$422$		0			0
$423$	−27.4620	−	6.60177i	−1.33525	−	0.320989i
$424$		0			0
$425$	53.3497	−	30.8014i	2.58784	−	1.49409i
$426$		0			0
$427$	2.06369	+	1.19147i	0.0998688	+	0.0576593i
$428$		0			0
$429$	−0.557673	−	1.29856i	−0.0269247	−	0.0626949i
$430$		0			0
$431$	−11.7886			−0.567837			−0.283919	−	0.958848i	$-0.591635\pi$
$431$	−11.7886			−0.567837			−0.283919	+	0.958848i	$0.591635\pi$
$432$		0			0
$433$	33.5993			1.61468			0.807341	−	0.590086i	$-0.200906\pi$
$433$	33.5993			1.61468			0.807341	+	0.590086i	$0.200906\pi$
$434$		0			0
$435$	−7.31890	−	17.0423i	−0.350914	−	0.817114i
$436$		0			0
$437$	10.6352	+	6.14021i	0.508749	+	0.293726i
$438$		0			0
$439$	−3.87174	+	2.23535i	−0.184788	+	0.106687i	−0.589540	−	0.807739i	$-0.700691\pi$
$439$	−3.87174	+	2.23535i	−0.184788	+	0.106687i	0.404752	+	0.914426i	$0.367358\pi$
$440$		0			0
$441$	−4.90945	−	16.5923i	−0.233784	−	0.790111i
$442$		0			0
$443$	−1.03420	−	1.79129i	−0.0491363	−	0.0851066i	0.840411	−	0.541949i	$-0.182314\pi$
$443$	−1.03420	−	1.79129i	−0.0491363	−	0.0851066i	−0.889547	+	0.456843i	$0.848980\pi$
$444$		0			0
$445$	−9.35270	+	16.1993i	−0.443360	+	0.767923i
$446$		0			0
$447$	0.347353	−	2.93101i	0.0164293	−	0.138632i
$448$		0			0
$449$		−	0.297420i		−	0.0140361i	−0.999975	−	0.00701807i	$-0.997766\pi$
$449$		−	0.297420i		−	0.0140361i	0.999975	−	0.00701807i	$-0.00223394\pi$
$450$		0			0
$451$		−	19.9274i		−	0.938347i
$452$		0			0
$453$	8.34631	+	6.23444i	0.392144	+	0.292920i
$454$		0			0
$455$	0.545852	−	0.945444i	0.0255900	−	0.0443231i
$456$		0			0
$457$	−1.08489	−	1.87909i	−0.0507491	−	0.0879000i	0.839535	−	0.543306i	$-0.182828\pi$
$457$	−1.08489	−	1.87909i	−0.0507491	−	0.0879000i	−0.890284	+	0.455406i	$0.849494\pi$
$458$		0			0
$459$	10.5670	−	28.6035i	0.493227	−	1.33510i
$460$		0			0
$461$	35.9806	−	20.7734i	1.67578	−	0.967514i	0.711482	−	0.702704i	$-0.248024\pi$
$461$	35.9806	−	20.7734i	1.67578	−	0.967514i	0.964301	−	0.264809i	$-0.0853090\pi$
$462$		0			0
$463$	16.8271	+	9.71513i	0.782022	+	0.451501i	0.837146	−	0.546979i	$-0.184222\pi$
$463$	16.8271	+	9.71513i	0.782022	+	0.451501i	−0.0551244	+	0.998479i	$0.517556\pi$
$464$		0			0
$465$	−42.2644	+	56.5812i	−1.95997	+	2.62389i
$466$		0			0
$467$	14.5573			0.673630			0.336815	−	0.941571i	$-0.390650\pi$
$467$	14.5573			0.673630			0.336815	+	0.941571i	$0.390650\pi$
$468$		0			0
$469$	0.642380			0.0296624
$470$		0			0
$471$	10.0746	+	1.19394i	0.464213	+	0.0550138i
$472$		0			0
$473$	−27.7933	−	16.0465i	−1.27794	−	0.737817i
$474$		0			0
$475$	−19.9845	+	11.5381i	−0.916952	+	0.529403i
$476$		0			0
$477$	10.3371	+	9.81540i	0.473301	+	0.449416i
$478$		0			0
$479$	13.1650	+	22.8025i	0.601526	+	1.04187i	0.992590	+	0.121510i	$0.0387735\pi$
$479$	13.1650	+	22.8025i	0.601526	+	1.04187i	−0.391065	+	0.920363i	$0.627893\pi$
$480$		0			0
$481$	−0.0416054	+	0.0720627i	−0.00189704	+	0.00328577i
$482$		0			0
$483$	−9.86911	+	4.23835i	−0.449060	+	0.192852i
$484$		0			0
$485$			7.21485i			0.327609i
$486$		0			0
$487$			21.6173i			0.979574i	0.871842	+	0.489787i	$0.162926\pi$
$487$			21.6173i			0.979574i	−0.871842	+	0.489787i	$0.837074\pi$
$488$		0			0
$489$	−6.81091	+	2.92499i	−0.308000	+	0.132272i
$490$		0			0
$491$	−8.66258	+	15.0040i	−0.390937	+	0.677122i	−0.992573	−	0.121648i	$-0.961182\pi$
$491$	−8.66258	+	15.0040i	−0.390937	+	0.677122i	0.601637	+	0.798770i	$0.294516\pi$
$492$		0			0
$493$	−7.98143	−	13.8242i	−0.359465	−	0.622612i
$494$		0			0
$495$	−27.9711	−	26.5595i	−1.25721	−	1.19376i
$496$		0			0
$497$	−3.13819	+	1.81184i	−0.140767	+	0.0812720i
$498$		0			0
$499$	21.4481	+	12.3831i	0.960148	+	0.554342i	0.896219	−	0.443613i	$-0.146303\pi$
$499$	21.4481	+	12.3831i	0.960148	+	0.554342i	0.0639294	+	0.997954i	$0.479637\pi$
$500$		0			0
$501$	−32.0429	−	3.79741i	−1.43157	−	0.169656i
$502$		0			0
$503$	−11.4045			−0.508500			−0.254250	−	0.967139i	$-0.581829\pi$
$503$	−11.4045			−0.508500			−0.254250	+	0.967139i	$0.581829\pi$
$504$		0			0
$505$	37.7666			1.68059
$506$		0			0
$507$	13.4103	−	17.9529i	0.595572	−	0.797318i
$508$		0			0
$509$	20.3093	+	11.7256i	0.900192	+	0.519726i	0.877262	−	0.480011i	$-0.159367\pi$
$509$	20.3093	+	11.7256i	0.900192	+	0.519726i	0.0229294	+	0.999737i	$0.492701\pi$
$510$		0			0
$511$	−12.1170	+	6.99577i	−0.536026	+	0.309475i
$512$		0			0
$513$	−3.95836	+	10.7147i	−0.174766	+	0.473067i
$514$		0			0
$515$	0.768257	+	1.33066i	0.0338534	+	0.0586359i
$516$		0			0
$517$	−15.3745	+	26.6294i	−0.676169	+	1.17116i
$518$		0			0
$519$	12.2338	+	9.13830i	0.537006	+	0.401127i
$520$		0			0
$521$			12.9913i			0.569160i	0.958652	+	0.284580i	$0.0918541\pi$
$521$			12.9913i			0.569160i	−0.958652	+	0.284580i	$0.908146\pi$
$522$		0			0
$523$		−	18.8040i		−	0.822243i	−0.911581	−	0.411121i	$-0.865137\pi$
$523$		−	18.8040i		−	0.822243i	0.911581	−	0.411121i	$-0.134863\pi$
$524$		0			0
$525$	2.37525	−	20.0426i	0.103664	−	0.874731i
$526$		0			0
$527$	−30.3913	+	52.6393i	−1.32387	+	2.29300i
$528$		0			0
$529$	−4.10399	−	7.10832i	−0.178434	−	0.309057i
$530$		0			0
$531$	−5.55862	−	18.7863i	−0.241224	−	0.815256i
$532$		0			0
$533$	−1.32007	+	0.762146i	−0.0571788	+	0.0330122i
$534$		0			0
$535$	26.1714	+	15.1101i	1.13149	+	0.653265i
$536$		0			0
$537$	−4.24962	−	9.89535i	−0.183385	−	0.427016i
$538$		0			0
$539$	−18.8378			−0.811401
$540$		0			0
$541$	−9.13908			−0.392920			−0.196460	−	0.980512i	$-0.562945\pi$
$541$	−9.13908			−0.392920			−0.196460	+	0.980512i	$0.562945\pi$
$542$		0			0
$543$	14.1218	+	32.8831i	0.606026	+	1.41115i
$544$		0			0
$545$	−16.1245	−	9.30947i	−0.690697	−	0.398774i
$546$		0			0
$547$	−15.4148	+	8.89976i	−0.659091	+	0.380526i	−0.791930	−	0.610611i	$-0.790924\pi$
$547$	−15.4148	+	8.89976i	−0.659091	+	0.380526i	0.132840	+	0.991138i	$0.457590\pi$
$548$		0			0
$549$	−6.26174	−	1.50530i	−0.267244	−	0.0642446i
$550$		0			0
$551$	2.98980	+	5.17849i	0.127370	+	0.220611i
$552$		0			0
$553$	4.91598	−	8.51473i	0.209049	−	0.362083i
$554$		0			0
$555$	−0.267276	+	2.25531i	−0.0113453	+	0.0957324i
$556$		0			0
$557$			19.4205i			0.822872i	0.911439	+	0.411436i	$0.134973\pi$
$557$			19.4205i			0.822872i	−0.911439	+	0.411436i	$0.865027\pi$
$558$		0			0
$559$			2.45485i			0.103829i
$560$		0			0
$561$	−26.5962	−	19.8666i	−1.12289	−	0.838767i
$562$		0			0
$563$	15.2077	−	26.3406i	0.640930	−	1.11012i	−0.344295	−	0.938861i	$-0.611882\pi$
$563$	15.2077	−	26.3406i	0.640930	−	1.11012i	0.985226	−	0.171262i	$-0.0547845\pi$
$564$		0			0
$565$	−14.4261	−	24.9867i	−0.606909	−	1.05120i
$566$		0			0
$567$	−5.43612	−	8.38191i	−0.228296	−	0.352007i
$568$		0			0
$569$	8.38491	−	4.84103i	0.351514	−	0.202947i	−0.313838	−	0.949477i	$-0.601615\pi$
$569$	8.38491	−	4.84103i	0.351514	−	0.202947i	0.665352	+	0.746530i	$0.268282\pi$
$570$		0			0
$571$	−4.98471	−	2.87792i	−0.208604	−	0.120437i	0.392059	−	0.919940i	$-0.371763\pi$
$571$	−4.98471	−	2.87792i	−0.208604	−	0.120437i	−0.600662	+	0.799503i	$0.705096\pi$
$572$		0			0
$573$	14.2465	−	19.0724i	0.595156	−	0.796761i
$574$		0			0
$575$	58.6429			2.44558
$576$		0			0
$577$	−19.7436			−0.821936			−0.410968	−	0.911650i	$-0.634809\pi$
$577$	−19.7436			−0.821936			−0.410968	+	0.911650i	$0.634809\pi$
$578$		0			0
$579$	−29.5191	−	3.49831i	−1.22677	−	0.145385i
$580$		0			0
$581$	−4.50008	−	2.59813i	−0.186695	−	0.107788i
$582$		0			0
$583$	13.4396	−	7.75938i	0.556613	−	0.321361i
$584$		0			0
$585$	−0.689628	+	2.86871i	−0.0285126	+	0.118607i
$586$		0			0
$587$	−13.6014	−	23.5584i	−0.561392	−	0.972359i	−0.997375	−	0.0724042i	$-0.976933\pi$
$587$	−13.6014	−	23.5584i	−0.561392	−	0.972359i	0.435984	−	0.899955i	$-0.356400\pi$
$588$		0			0
$589$	11.3844	−	19.7184i	0.469087	−	0.812483i
$590$		0			0
$591$	9.00286	−	3.86633i	0.370328	−	0.159040i
$592$		0			0
$593$		−	34.4946i		−	1.41652i	−0.705950	−	0.708261i	$-0.749480\pi$
$593$		−	34.4946i		−	1.41652i	0.705950	−	0.708261i	$-0.250520\pi$
$594$		0			0
$595$		−	25.6441i		−	1.05131i
$596$		0			0
$597$	−17.1906	+	7.38260i	−0.703564	+	0.302150i
$598$		0			0
$599$	3.09709	−	5.36431i	0.126544	−	0.219180i	−0.795792	−	0.605570i	$-0.792945\pi$
$599$	3.09709	−	5.36431i	0.126544	−	0.219180i	0.922335	+	0.386391i	$0.126278\pi$
$600$		0			0
$601$	−12.8844	−	22.3164i	−0.525565	−	0.910306i	−0.999557	−	0.0297762i	$-0.990521\pi$
$601$	−12.8844	−	22.3164i	−0.525565	−	0.910306i	0.473991	−	0.880529i	$-0.342813\pi$
$602$		0			0
$603$	−1.66475	+	0.492578i	−0.0677939	+	0.0200593i
$604$		0			0
$605$	1.13554	−	0.655607i	0.0461664	−	0.0266542i
$606$		0			0
$607$	−37.2241	−	21.4914i	−1.51088	−	0.872307i	−0.999919	−	0.0127033i	$-0.995956\pi$
$607$	−37.2241	−	21.4914i	−1.51088	−	0.872307i	−0.510961	−	0.859604i	$-0.670710\pi$
$608$		0			0
$609$	−5.19354	−	0.615487i	−0.210453	−	0.0249408i
$610$		0			0
$611$	2.35205			0.0951539
$612$		0			0
$613$	33.0975			1.33679			0.668397	−	0.743805i	$-0.266981\pi$
$613$	33.0975			1.33679			0.668397	+	0.743805i	$0.266981\pi$
$614$		0			0
$615$	−24.8970	+	33.3306i	−1.00394	+	1.34402i
$616$		0			0
$617$	−4.02894	−	2.32611i	−0.162199	−	0.0936456i	0.416703	−	0.909043i	$-0.363185\pi$
$617$	−4.02894	−	2.32611i	−0.162199	−	0.0936456i	−0.578902	+	0.815397i	$0.696519\pi$
$618$		0			0
$619$	−6.50736	+	3.75703i	−0.261553	+	0.151008i	−0.625043	−	0.780591i	$-0.714918\pi$
$619$	−6.50736	+	3.75703i	−0.261553	+	0.151008i	0.363490	+	0.931598i	$0.381585\pi$
$620$		0			0
$621$	22.3262	−	18.5515i	0.895918	−	0.744445i
$622$		0			0
$623$	2.63722	+	4.56780i	0.105658	+	0.183005i
$624$		0			0
$625$	−16.3543	+	28.3265i	−0.654173	+	1.13306i
$626$		0			0
$627$	9.96282	+	7.44192i	0.397877	+	0.297202i
$628$		0			0
$629$			1.95462i			0.0779358i
$630$		0			0
$631$			41.0242i			1.63315i	0.577241	+	0.816574i	$0.304129\pi$
$631$			41.0242i			1.63315i	−0.577241	+	0.816574i	$0.695871\pi$
$632$		0			0
$633$	−1.51720	+	12.8023i	−0.0603032	+	0.508845i
$634$		0			0
$635$	−0.230238	+	0.398783i	−0.00913670	+	0.0158252i
$636$		0			0
$637$	0.720471	+	1.24789i	0.0285461	+	0.0494433i
$638$		0			0
$639$	6.74342	−	7.10181i	0.266765	−	0.280943i
$640$		0			0
$641$	−21.0962	+	12.1799i	−0.833249	+	0.481076i	−0.854964	−	0.518688i	$-0.826421\pi$
$641$	−21.0962	+	12.1799i	−0.833249	+	0.481076i	0.0217149	+	0.999764i	$0.493087\pi$
$642$		0			0
$643$	24.3082	+	14.0344i	0.958623	+	0.553461i	0.895749	−	0.444560i	$-0.146640\pi$
$643$	24.3082	+	14.0344i	0.958623	+	0.553461i	0.0628738	+	0.998021i	$0.479973\pi$
$644$		0			0
$645$	26.4389	+	61.5637i	1.04103	+	2.42407i
$646$		0			0
$647$	−18.3596			−0.721791			−0.360895	−	0.932606i	$-0.617529\pi$
$647$	−18.3596			−0.721791			−0.360895	+	0.932606i	$0.617529\pi$
$648$		0			0
$649$	−21.3287			−0.837224
$650$		0			0
$651$	7.85823	+	18.2981i	0.307988	+	0.717159i
$652$		0			0
$653$	−35.6953	−	20.6087i	−1.39687	−	0.806481i	−0.402803	−	0.915287i	$-0.631964\pi$
$653$	−35.6953	−	20.6087i	−1.39687	−	0.806481i	−0.994063	+	0.108806i	$0.965297\pi$
$654$		0			0
$655$	−13.3566	+	7.71144i	−0.521886	+	0.301311i
$656$		0			0
$657$	26.0374	−	27.4212i	1.01581	−	1.06980i
$658$		0			0
$659$	6.77194	+	11.7293i	0.263797	+	0.456910i	0.967248	−	0.253834i	$-0.0816917\pi$
$659$	6.77194	+	11.7293i	0.263797	+	0.456910i	−0.703451	+	0.710744i	$0.748358\pi$
$660$		0			0
$661$	−12.9871	+	22.4944i	−0.505141	+	0.874930i	0.494841	+	0.868983i	$0.335226\pi$
$661$	−12.9871	+	22.4944i	−0.505141	+	0.874930i	−0.999982	+	0.00594652i	$0.998107\pi$
$662$		0			0
$663$	−0.298842	+	2.52166i	−0.0116061	+	0.0979332i
$664$		0			0
$665$			9.60616i			0.372511i
$666$		0			0
$667$		−	15.1958i		−	0.588385i
$668$		0			0
$669$	−29.7496	−	22.2220i	−1.15019	−	0.859153i
$670$		0			0
$671$	−3.50561	+	6.07189i	−0.135332	+	0.234403i
$672$		0			0
$673$	7.20522	+	12.4798i	0.277741	+	0.481061i	0.970823	−	0.239797i	$-0.0770810\pi$
$673$	7.20522	+	12.4798i	0.277741	+	0.481061i	−0.693082	+	0.720859i	$0.743748\pi$
$674$		0			0
$675$	9.21316	+	53.7625i	0.354615	+	2.06932i
$676$		0			0
$677$	−28.6445	+	16.5379i	−1.10090	+	0.635604i	−0.936457	−	0.350782i	$-0.885916\pi$
$677$	−28.6445	+	16.5379i	−1.10090	+	0.635604i	−0.164442	+	0.986387i	$0.552582\pi$
$678$		0			0
$679$	1.76185	+	1.01720i	0.0676134	+	0.0390366i
$680$		0			0
$681$	27.7703	−	37.1773i	1.06416	−	1.42464i
$682$		0			0
$683$	−31.1501			−1.19193			−0.595963	−	0.803012i	$-0.703229\pi$
$683$	−31.1501			−1.19193			−0.595963	+	0.803012i	$0.703229\pi$
$684$		0			0
$685$	−29.2447			−1.11738
$686$		0			0
$687$	−0.143194	−	0.0169699i	−0.00546318	−	0.000647441i
$688$		0			0
$689$	−1.02802	−	0.593531i	−0.0391646	−	0.0226117i
$690$		0			0
$691$	−11.9611	+	6.90572i	−0.455020	+	0.262706i	−0.709948	−	0.704254i	$-0.751282\pi$
$691$	−11.9611	+	6.90572i	−0.455020	+	0.262706i	0.254928	+	0.966960i	$0.417948\pi$
$692$		0			0
$693$	−10.4293	+	3.08590i	−0.396177	+	0.117224i
$694$		0			0
$695$	−29.4120	−	50.9431i	−1.11566	−	1.93238i
$696$		0			0
$697$	−17.9028	+	31.0085i	−0.678116	+	1.17453i
$698$		0			0
$699$	14.7892	−	6.35130i	0.559378	−	0.240228i
$700$		0			0
$701$		−	30.8782i		−	1.16625i	−0.812381	−	0.583127i	$-0.801829\pi$
$701$		−	30.8782i		−	1.16625i	0.812381	−	0.583127i	$-0.198171\pi$
$702$		0			0
$703$		−	0.732191i		−	0.0276151i
$704$		0			0
$705$	58.9856	−	25.3317i	2.22153	−	0.954049i
$706$		0			0
$707$	5.32461	−	9.22250i	0.200253	−	0.346848i
$708$		0			0
$709$	−15.3068	−	26.5122i	−0.574861	−	0.995688i	−0.996057	−	0.0887184i	$-0.971723\pi$
$709$	−15.3068	−	26.5122i	−0.574861	−	0.995688i	0.421196	−	0.906970i	$-0.361610\pi$
$710$		0			0
$711$	−6.21083	+	25.8358i	−0.232924	+	0.968918i
$712$		0			0
$713$	−50.1100	+	28.9310i	−1.87663	+	1.08347i
$714$		0			0
$715$	2.78173	+	1.60604i	0.104031	+	0.0600623i
$716$		0			0
$717$	−25.9542	−	3.07584i	−0.969279	−	0.114869i
$718$		0			0
$719$	−34.2682			−1.27799			−0.638995	−	0.769211i	$-0.720649\pi$
$719$	−34.2682			−1.27799			−0.638995	+	0.769211i	$0.720649\pi$
$720$		0			0
$721$	0.433258			0.0161354
$722$		0			0
$723$	−24.9168	+	33.3571i	−0.926664	+	1.24057i
$724$		0			0
$725$	24.7289	+	14.2772i	0.918409	+	0.530244i
$726$		0			0
$727$	−7.19890	+	4.15628i	−0.266992	+	0.154148i	−0.627520	−	0.778600i	$-0.715930\pi$
$727$	−7.19890	+	4.15628i	−0.266992	+	0.154148i	0.360528	+	0.932748i	$0.382597\pi$
$728$		0			0
$729$	20.5152	+	17.5536i	0.759821	+	0.650133i
$730$		0			0
$731$	28.8322	+	49.9389i	1.06640	+	1.84706i
$732$		0			0
$733$	17.6922	−	30.6438i	0.653477	−	1.13186i	−0.328796	−	0.944401i	$-0.606643\pi$
$733$	17.6922	−	30.6438i	0.653477	−	1.13186i	0.982273	−	0.187454i	$-0.0600237\pi$
$734$		0			0
$735$	31.5081	+	23.5356i	1.16219	+	0.868123i
$736$		0			0
$737$			1.89005i			0.0696207i
$738$		0			0
$739$			30.3812i			1.11759i	0.829305	+	0.558795i	$0.188736\pi$
$739$			30.3812i			1.11759i	−0.829305	+	0.558795i	$0.811264\pi$
$740$		0			0
$741$	0.111945	−	0.944601i	0.00411239	−	0.0347008i
$742$		0			0
$743$	17.2730	−	29.9177i	0.633684	−	1.09757i	−0.353109	−	0.935582i	$-0.614875\pi$
$743$	17.2730	−	29.9177i	0.633684	−	1.09757i	0.986792	−	0.161990i	$-0.0517912\pi$
$744$		0			0
$745$	3.35416	+	5.80958i	0.122887	+	0.212847i
$746$		0			0
$747$	13.6544	+	3.28246i	0.499587	+	0.120099i
$748$		0			0
$749$	7.37967	−	4.26065i	0.269647	−	0.155681i
$750$		0			0
$751$	8.74633	+	5.04970i	0.319158	+	0.184266i	0.651017	−	0.759063i	$-0.274343\pi$
$751$	8.74633	+	5.04970i	0.319158	+	0.184266i	−0.331859	+	0.943329i	$0.607676\pi$
$752$		0			0
$753$	12.6247	+	29.3969i	0.460069	+	1.07128i
$754$		0			0
$755$	−23.6779			−0.861725
$756$		0			0
$757$	38.7446			1.40820			0.704099	−	0.710102i	$-0.251351\pi$
$757$	38.7446			1.40820			0.704099	+	0.710102i	$0.251351\pi$
$758$		0			0
$759$	−12.4703	−	29.0374i	−0.452643	−	1.05399i
$760$		0			0
$761$	30.7016	+	17.7256i	1.11293	+	0.642551i	0.939587	−	0.342310i	$-0.111209\pi$
$761$	30.7016	+	17.7256i	1.11293	+	0.642551i	0.173345	+	0.984861i	$0.444543\pi$
$762$		0			0
$763$	−4.54669	+	2.62504i	−0.164601	+	0.0950327i
$764$		0			0
$765$	19.6640	+	66.4577i	0.710952	+	2.40278i
$766$		0			0
$767$	0.815737	+	1.41290i	0.0294546	+	0.0510168i
$768$		0			0
$769$	17.9368	−	31.0675i	0.646818	−	1.12032i	−0.337060	−	0.941483i	$-0.609433\pi$
$769$	17.9368	−	31.0675i	0.646818	−	1.12032i	0.983878	−	0.178839i	$-0.0572341\pi$
$770$		0			0
$771$	3.90340	−	32.9373i	0.140577	−	1.18621i
$772$		0			0
$773$		−	0.214276i		−	0.00770697i	−0.999993	−	0.00385349i	$-0.998773\pi$
$773$		−	0.214276i		−	0.00770697i	0.999993	−	0.00385349i	$-0.00122661\pi$
$774$		0			0
$775$		−	108.728i		−	3.90564i
$776$		0			0
$777$	0.513057	+	0.383238i	0.0184058	+	0.0137486i
$778$		0			0
$779$	6.70629	−	11.6156i	0.240278	−	0.416174i
$780$		0			0
$781$	−5.33088	−	9.23335i	−0.190754	−	0.330395i
$782$		0			0
$783$	13.9312	−	2.38736i	0.497861	−	0.0853173i
$784$		0			0
$785$	−19.9690	+	11.5291i	−0.712723	+	0.411491i
$786$		0			0
$787$	29.0781	+	16.7883i	1.03652	+	0.598437i	0.918847	−	0.394615i	$-0.129122\pi$
$787$	29.0781	+	16.7883i	1.03652	+	0.598437i	0.117677	+	0.993052i	$0.462455\pi$
$788$		0			0
$789$	3.93739	−	5.27115i	0.140175	−	0.187658i
$790$		0			0
$791$	−8.13556			−0.289267
$792$		0			0
$793$	0.536302			0.0190446
$794$		0			0
$795$	−32.1735	−	3.81289i	−1.14108	−	0.135229i
$796$		0			0
$797$	31.1529	+	17.9861i	1.10349	+	0.637102i	0.937136	−	0.348964i	$-0.113466\pi$
$797$	31.1529	+	17.9861i	1.10349	+	0.637102i	0.166357	+	0.986066i	$0.446800\pi$
$798$		0			0
$799$	47.8476	−	27.6248i	1.69273	−	0.977297i
$800$		0			0
$801$	−10.3371	−	9.81540i	−0.365242	−	0.346810i
$802$		0			0
$803$	−20.5833	−	35.6514i	−0.726370	−	1.25811i
$804$		0			0
$805$	12.2060	−	21.1414i	0.430204	−	0.745135i
$806$		0			0
$807$	−35.1073	+	15.0770i	−1.23584	+	0.530737i
$808$		0			0
$809$		−	7.82300i		−	0.275042i	−0.990499	−	0.137521i	$-0.956087\pi$
$809$		−	7.82300i		−	0.275042i	0.990499	−	0.137521i	$-0.0439135\pi$
$810$		0			0
$811$		−	40.2969i		−	1.41502i	−0.706705	−	0.707508i	$-0.749819\pi$
$811$		−	40.2969i		−	1.41502i	0.706705	−	0.707508i	$-0.250181\pi$
$812$		0			0
$813$	−26.6023	+	11.4245i	−0.932983	+	0.400675i
$814$		0			0
$815$	8.42363	−	14.5902i	0.295067	−	0.511071i
$816$		0			0
$817$	−10.8004	−	18.7069i	−0.377858	−	0.654470i
$818$		0			0
$819$	0.603303	+	0.572857i	0.0210811	+	0.0200173i
$820$		0			0
$821$	−9.96043	+	5.75066i	−0.347621	+	0.200699i	−0.663637	−	0.748055i	$-0.730988\pi$
$821$	−9.96043	+	5.75066i	−0.347621	+	0.200699i	0.316016	+	0.948754i	$0.397655\pi$
$822$		0			0
$823$	47.2358	+	27.2716i	1.64654	+	0.950628i	0.978435	+	0.206557i	$0.0662258\pi$
$823$	47.2358	+	27.2716i	1.64654	+	0.950628i	0.668101	+	0.744071i	$0.267107\pi$
$824$		0			0
$825$	58.9704	+	6.98858i	2.05309	+	0.243311i
$826$		0			0
$827$	2.34342			0.0814887			0.0407443	−	0.999170i	$-0.487027\pi$
$827$	2.34342			0.0814887			0.0407443	+	0.999170i	$0.487027\pi$
$828$		0			0
$829$	15.5991			0.541778			0.270889	−	0.962611i	$-0.412682\pi$
$829$	15.5991			0.541778			0.270889	+	0.962611i	$0.412682\pi$
$830$		0			0
$831$	19.1915	−	25.6925i	0.665747	−	0.891264i
$832$		0			0
$833$	29.3130	+	16.9238i	1.01563	+	0.586377i
$834$		0			0
$835$	63.5127	−	36.6691i	2.19795	−	1.26899i
$836$		0			0
$837$	−34.3959	−	41.3944i	−1.18890	−	1.43080i
$838$		0			0
$839$	1.79725	+	3.11293i	0.0620481	+	0.107470i	0.895381	−	0.445301i	$-0.146903\pi$
$839$	1.79725	+	3.11293i	0.0620481	+	0.107470i	−0.833333	+	0.552772i	$0.813570\pi$
$840$		0			0
$841$	−10.8004	+	18.7069i	−0.372428	+	0.645064i
$842$		0			0
$843$	−7.04833	−	5.26489i	−0.242757	−	0.181332i
$844$		0			0
$845$			50.9311i			1.75208i
$846$		0			0
$847$		−	0.369729i		−	0.0127040i
$848$		0			0
$849$	4.66122	−	39.3318i	0.159973	−	1.34987i
$850$		0			0
$851$	−0.930351	+	1.61141i	−0.0318920	+	0.0552386i
$852$		0			0
$853$	−19.1495	−	33.1679i	−0.655666	−	1.13565i	−0.981726	−	0.190298i	$-0.939055\pi$
$853$	−19.1495	−	33.1679i	−0.655666	−	1.13565i	0.326061	−	0.945349i	$-0.394279\pi$
$854$		0			0
$855$	−7.36602	−	24.8947i	−0.251913	−	0.851381i
$856$		0			0
$857$	26.8867	−	15.5230i	0.918432	−	0.530257i	0.0352975	−	0.999377i	$-0.488762\pi$
$857$	26.8867	−	15.5230i	0.918432	−	0.530257i	0.883134	+	0.469120i	$0.155429\pi$
$858$		0			0
$859$	−37.4925	−	21.6463i	−1.27923	−	0.738562i	−0.302520	−	0.953143i	$-0.597828\pi$
$859$	−37.4925	−	21.6463i	−1.27923	−	0.738562i	−0.976706	+	0.214581i	$0.931161\pi$
$860$		0			0
$861$	4.62909	+	10.7790i	0.157759	+	0.367346i
$862$		0			0
$863$	−28.1206			−0.957237			−0.478619	−	0.878023i	$-0.658862\pi$
$863$	−28.1206			−0.957237			−0.478619	+	0.878023i	$0.658862\pi$
$864$		0			0
$865$	−34.7064			−1.18005
$866$		0			0
$867$	11.9184	+	27.7524i	0.404771	+	0.942521i
$868$		0			0
$869$	25.0525	+	14.4641i	0.849847	+	0.490660i
$870$		0			0
$871$	0.125204	−	0.0722867i	0.00424238	−	0.00244934i
$872$		0			0
$873$	−5.34588	−	1.28513i	−0.180931	−	0.0434950i
$874$		0			0
$875$	12.0115	+	20.8046i	0.406064	+	0.703323i
$876$		0			0
$877$	26.7964	−	46.4127i	0.904849	−	1.56725i	0.0837301	−	0.996488i	$-0.473317\pi$
$877$	26.7964	−	46.4127i	0.904849	−	1.56725i	0.821119	−	0.570757i	$-0.193350\pi$
$878$		0			0
$879$	−0.0377247	+	0.318325i	−0.00127242	+	0.0107368i
$880$		0			0
$881$			26.3409i			0.887449i	0.896163	+	0.443724i	$0.146343\pi$
$881$			26.3409i			0.887449i	−0.896163	+	0.443724i	$0.853657\pi$
$882$		0			0
$883$			47.8523i			1.61036i	0.593032	+	0.805179i	$0.297931\pi$
$883$			47.8523i			1.61036i	−0.593032	+	0.805179i	$0.702069\pi$
$884$		0			0
$885$	35.6744	+	26.6476i	1.19918	+	0.895751i
$886$		0			0
$887$	−9.26690	+	16.0507i	−0.311152	+	0.538931i	−0.978612	−	0.205714i	$-0.934048\pi$
$887$	−9.26690	+	16.0507i	−0.311152	+	0.538931i	0.667460	+	0.744646i	$0.267382\pi$
$888$		0			0
$889$	0.0649212	+	0.112447i	0.00217739	+	0.00377134i
$890$		0			0
$891$	24.6617	−	15.9944i	0.826198	−	0.535834i
$892$		0			0
$893$	−17.9235	+	10.3481i	−0.599786	+	0.346287i
$894$		0			0
$895$	21.1976	+	12.2384i	0.708556	+	0.409085i
$896$		0			0
$897$	−1.44662	+	1.93665i	−0.0483011	+	0.0646628i
$898$		0			0
$899$	−28.1743			−0.939664
$900$		0			0
$901$	−27.8840			−0.928952
$902$		0			0
$903$	18.7612	+	2.22339i	0.624335	+	0.0739899i
$904$		0			0
$905$	−70.4413	−	40.6693i	−2.34155	−	1.35189i
$906$		0			0
$907$	37.8891	−	21.8753i	1.25809	−	0.726357i	0.285385	−	0.958413i	$-0.407879\pi$
$907$	37.8891	−	21.8753i	1.25809	−	0.726357i	0.972702	+	0.232056i	$0.0745452\pi$
$908$		0			0
$909$	−6.72710	+	27.9834i	−0.223124	+	0.928150i
$910$		0			0
$911$	−22.4205	−	38.8334i	−0.742823	−	1.28661i	−0.951205	−	0.308559i	$-0.900153\pi$
$911$	−22.4205	−	38.8334i	−0.742823	−	1.28661i	0.208382	−	0.978047i	$-0.433180\pi$
$912$		0			0
$913$	7.64434	−	13.2404i	0.252991	−	0.438193i
$914$		0			0
$915$	13.4496	−	5.77600i	0.444629	−	0.190949i
$916$		0			0
$917$			4.34886i			0.143612i
$918$		0			0
$919$			13.3225i			0.439469i	0.975560	+	0.219734i	$0.0705191\pi$
$919$			13.3225i			0.439469i	−0.975560	+	0.219734i	$0.929481\pi$
$920$		0			0
$921$	−29.9147	+	12.8470i	−0.985721	+	0.423324i
$922$		0			0
$923$	−0.407770	+	0.706278i	−0.0134219	+	0.0232474i
$924$		0			0
$925$	−1.74822	−	3.02801i	−0.0574811	−	0.0995603i
$926$		0			0
$927$	−1.12280	+	0.332223i	−0.0368777	+	0.0109116i
$928$		0			0
$929$	−16.5850	+	9.57535i	−0.544136	+	0.314157i	−0.746754	−	0.665101i	$-0.768389\pi$
$929$	−16.5850	+	9.57535i	−0.544136	+	0.314157i	0.202618	+	0.979258i	$0.435055\pi$
$930$		0			0
$931$	−10.9805	−	6.33959i	−0.359871	−	0.207772i
$932$		0			0
$933$	12.5633	+	1.48887i	0.411303	+	0.0487436i
$934$		0			0
$935$	75.4515			2.46753
$936$		0			0
$937$	17.6708			0.577281			0.288640	−	0.957438i	$-0.406797\pi$
$937$	17.6708			0.577281			0.288640	+	0.957438i	$0.406797\pi$
$938$		0			0
$939$	−23.3164	+	31.2146i	−0.760901	+	1.01865i
$940$		0			0
$941$	24.1771	+	13.9587i	0.788152	+	0.455040i	0.839312	−	0.543651i	$-0.182958\pi$
$941$	24.1771	+	13.9587i	0.788152	+	0.455040i	−0.0511595	+	0.998690i	$0.516292\pi$
$942$		0			0
$943$	−29.5186	+	17.0426i	−0.961257	+	0.554982i
$944$		0			0
$945$	21.2996	+	7.86872i	0.692874	+	0.255969i
$946$		0			0
$947$	3.15200	+	5.45942i	0.102426	+	0.177407i	0.912684	−	0.408667i	$-0.134006\pi$
$947$	3.15200	+	5.45942i	0.102426	+	0.177407i	−0.810258	+	0.586074i	$0.800673\pi$
$948$		0			0
$949$	−1.57446	+	2.72705i	−0.0511092	+	0.0885237i
$950$		0			0
$951$	−14.3417	−	10.7128i	−0.465060	−	0.347386i
$952$		0			0
$953$			8.17205i			0.264719i	0.991202	+	0.132359i	$0.0422553\pi$
$953$			8.17205i			0.264719i	−0.991202	+	0.132359i	$0.957745\pi$
$954$		0			0
$955$			54.1069i			1.75086i
$956$		0			0
$957$	1.81092	−	15.2807i	0.0585387	−	0.493955i
$958$		0			0
$959$	−4.12313	+	7.14146i	−0.133143	+	0.230610i
$960$		0			0
$961$	38.1403	+	66.0609i	1.23033	+	2.13100i
$962$		0			0
$963$	−15.8576	+	16.7004i	−0.511004	+	0.538162i
$964$		0			0
$965$	58.5101	−	33.7808i	1.88351	−	1.08744i
$966$		0			0
$967$	−23.0033	−	13.2810i	−0.739736	−	0.427087i	0.0822375	−	0.996613i	$-0.473793\pi$
$967$	−23.0033	−	13.2810i	−0.739736	−	0.427087i	−0.821973	+	0.569526i	$0.807127\pi$
$968$		0			0
$969$	−8.81705	−	20.5307i	−0.283244	−	0.659542i
$970$		0			0
$971$	−46.2192			−1.48324			−0.741622	−	0.670818i	$-0.765943\pi$
$971$	−46.2192			−1.48324			−0.741622	+	0.670818i	$0.765943\pi$
$972$		0			0
$973$	−16.5869			−0.531751
$974$		0			0
$975$	−1.79243	−	4.17372i	−0.0574037	−	0.133666i
$976$		0			0
$977$	−31.1382	−	17.9776i	−0.996198	−	0.575155i	−0.0890768	−	0.996025i	$-0.528392\pi$
$977$	−31.1382	−	17.9776i	−0.996198	−	0.575155i	−0.907121	+	0.420870i	$0.861725\pi$
$978$		0			0
$979$	−13.4396	+	7.75938i	−0.429533	+	0.247991i
$980$		0			0
$981$	9.77004	−	10.2893i	0.311933	−	0.328512i
$982$		0			0
$983$	−11.0687	−	19.1716i	−0.353038	−	0.611479i	0.633742	−	0.773544i	$-0.281518\pi$
$983$	−11.0687	−	19.1716i	−0.353038	−	0.611479i	−0.986780	+	0.162065i	$0.948185\pi$
$984$		0			0
$985$	−11.1346	+	19.2857i	−0.354778	+	0.614493i
$986$		0			0
$987$	2.13029	−	17.9756i	0.0678078	−	0.572169i
$988$		0			0
$989$			54.8937i			1.74552i
$990$		0			0
$991$		−	49.0851i		−	1.55924i	−0.626254	−	0.779619i	$-0.715413\pi$
$991$		−	49.0851i		−	1.55924i	0.626254	−	0.779619i	$-0.284587\pi$
$992$		0			0
$993$	39.5365	+	29.5325i	1.25465	+	0.937186i
$994$		0			0
$995$	21.2610	−	36.8252i	0.674021	−	1.16744i
$996$		0			0
$997$	−9.59479	−	16.6187i	−0.303870	−	0.526318i	0.673139	−	0.739516i	$-0.264946\pi$
$997$	−9.59479	−	16.6187i	−0.303870	−	0.526318i	−0.977009	+	0.213198i	$0.931612\pi$
$998$		0			0
$999$	−1.62347	−	0.599761i	−0.0513644	−	0.0189756i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.s.a.95.5	✓	24
3.2	odd	2		864.2.s.a.287.2		24
4.3	odd	2	inner	288.2.s.a.95.8	yes	24
8.3	odd	2		576.2.s.g.383.5		24
8.5	even	2		576.2.s.g.383.8		24
9.2	odd	6	inner	288.2.s.a.191.8	yes	24
9.4	even	3		2592.2.c.c.2591.2		24
9.5	odd	6		2592.2.c.c.2591.24		24
9.7	even	3		864.2.s.a.575.1		24
12.11	even	2		864.2.s.a.287.1		24
24.5	odd	2		1728.2.s.g.1151.12		24
24.11	even	2		1728.2.s.g.1151.11		24
36.7	odd	6		864.2.s.a.575.2		24
36.11	even	6	inner	288.2.s.a.191.5	yes	24
36.23	even	6		2592.2.c.c.2591.23		24
36.31	odd	6		2592.2.c.c.2591.1		24
72.5	odd	6		5184.2.c.m.5183.2		24
72.11	even	6		576.2.s.g.191.8		24
72.13	even	6		5184.2.c.m.5183.24		24
72.29	odd	6		576.2.s.g.191.5		24
72.43	odd	6		1728.2.s.g.575.12		24
72.59	even	6		5184.2.c.m.5183.1		24
72.61	even	6		1728.2.s.g.575.11		24
72.67	odd	6		5184.2.c.m.5183.23		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.s.a.95.5	✓	24	1.1	even	1	trivial
288.2.s.a.95.8	yes	24	4.3	odd	2	inner
288.2.s.a.191.5	yes	24	36.11	even	6	inner
288.2.s.a.191.8	yes	24	9.2	odd	6	inner
576.2.s.g.191.5		24	72.29	odd	6
576.2.s.g.191.8		24	72.11	even	6
576.2.s.g.383.5		24	8.3	odd	2
576.2.s.g.383.8		24	8.5	even	2
864.2.s.a.287.1		24	12.11	even	2
864.2.s.a.287.2		24	3.2	odd	2
864.2.s.a.575.1		24	9.7	even	3
864.2.s.a.575.2		24	36.7	odd	6
1728.2.s.g.575.11		24	72.61	even	6
1728.2.s.g.575.12		24	72.43	odd	6
1728.2.s.g.1151.11		24	24.11	even	2
1728.2.s.g.1151.12		24	24.5	odd	2
2592.2.c.c.2591.1		24	36.31	odd	6
2592.2.c.c.2591.2		24	9.4	even	3
2592.2.c.c.2591.23		24	36.23	even	6
2592.2.c.c.2591.24		24	9.5	odd	6
5184.2.c.m.5183.1		24	72.59	even	6
5184.2.c.m.5183.2		24	72.5	odd	6
5184.2.c.m.5183.23		24	72.67	odd	6
5184.2.c.m.5183.24		24	72.13	even	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:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	288.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.683478 - 1.59150i) q^{3} +(3.40926 + 1.96834i) q^{5} +(0.961325 - 0.555021i) q^{7} +(-2.06572 + 2.17550i) q^{9} +O(q^{10})\)	\(q+(-0.683478 - 1.59150i) q^{3} +(3.40926 + 1.96834i) q^{5} +(0.961325 - 0.555021i) q^{7} +(-2.06572 + 2.17550i) q^{9} +(1.63301 + 2.82846i) q^{11} +(0.124912 - 0.216355i) q^{13} +(0.802448 - 6.77114i) q^{15} -5.86838i q^{17} +2.19827i q^{19} +(-1.54036 - 1.15060i) q^{21} +(2.79320 - 4.83797i) q^{23} +(5.24871 + 9.09103i) q^{25} +(4.87417 + 1.80067i) q^{27} +(2.35571 - 1.36007i) q^{29} +(-8.96997 - 5.17882i) q^{31} +(3.38536 - 4.53212i) q^{33} +4.36988 q^{35} -0.333076 q^{37} +(-0.429703 - 0.0509241i) q^{39} +(-5.28400 - 3.05072i) q^{41} +(-8.50982 + 4.91315i) q^{43} +(-11.3247 + 3.35083i) q^{45} +(4.70740 + 8.15346i) q^{47} +(-2.88390 + 4.99507i) q^{49} +(-9.33951 + 4.01091i) q^{51} -4.75157i q^{53} +12.8573i q^{55} +(3.49853 - 1.50247i) q^{57} +(-3.26523 + 5.65555i) q^{59} +(1.07336 + 1.85911i) q^{61} +(-0.778375 + 3.23788i) q^{63} +(0.851719 - 0.491740i) q^{65} +(0.501168 + 0.289349i) q^{67} +(-9.60871 - 1.13873i) q^{69} -3.26444 q^{71} -12.6045 q^{73} +(10.8810 - 14.5668i) q^{75} +(3.13971 + 1.81271i) q^{77} +(7.67063 - 4.42864i) q^{79} +(-0.465627 - 8.98795i) q^{81} +(-2.34056 - 4.05397i) q^{83} +(11.5510 - 20.0069i) q^{85} +(-3.77463 - 2.81953i) q^{87} +4.75157i q^{89} -0.277316i q^{91} +(-2.11129 + 17.8153i) q^{93} +(-4.32693 + 7.49447i) q^{95} +(0.916363 + 1.58719i) q^{97} +(-9.52667 - 2.29018i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{9}+O(q^{10}) \) 24 * q - 4 * q^9	\( 24 q - 4 q^{9} + 8 q^{21} + 12 q^{25} + 24 q^{29} - 20 q^{33} - 36 q^{41} - 8 q^{45} + 12 q^{49} - 36 q^{57} - 48 q^{65} - 16 q^{69} + 24 q^{73} - 48 q^{77} - 20 q^{81} - 64 q^{93} + 12 q^{97}+O(q^{100}) \) 24 * q - 4 * q^9 + 8 * q^21 + 12 * q^25 + 24 * q^29 - 20 * q^33 - 36 * q^41 - 8 * q^45 + 12 * q^49 - 36 * q^57 - 48 * q^65 - 16 * q^69 + 24 * q^73 - 48 * q^77 - 20 * q^81 - 64 * q^93 + 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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