LMFDB - Embedded newform 384.2.n.a.241.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [384,2,Mod(49,384)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(384, base_ring=CyclotomicField(8))

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

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

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

chi := DirichletCharacter("384.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 384 = 2^{7} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	384.n (of order $8$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.06625543762$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 96)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			241.1
Character	$\chi$	$=$	384.241
Dual form			384.2.n.a.145.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.382683 - 0.923880i) q^{3} +(-1.46213 - 0.605634i) q^{5} +(3.54889 + 3.54889i) q^{7} +(-0.707107 + 0.707107i) q^{9} +O(q^{10})$	\(q+(-0.382683 - 0.923880i) q^{3} +(-1.46213 - 0.605634i) q^{5} +(3.54889 + 3.54889i) q^{7} +(-0.707107 + 0.707107i) q^{9} +(0.471165 - 1.13749i) q^{11} +(4.97028 - 2.05876i) q^{13} +1.58260i q^{15} +0.419142i q^{17} +(0.721541 - 0.298872i) q^{19} +(1.92065 - 4.63685i) q^{21} +(5.76431 - 5.76431i) q^{23} +(-1.76450 - 1.76450i) q^{25} +(0.923880 + 0.382683i) q^{27} +(1.26426 + 3.05219i) q^{29} -0.702664 q^{31} -1.23121 q^{33} +(-3.03961 - 7.33827i) q^{35} +(1.86641 + 0.773092i) q^{37} +(-3.80408 - 3.80408i) q^{39} +(1.76678 - 1.76678i) q^{41} +(-1.70666 + 4.12024i) q^{43} +(1.46213 - 0.605634i) q^{45} +9.64136i q^{47} +18.1893i q^{49} +(0.387237 - 0.160399i) q^{51} +(-0.729689 + 1.76163i) q^{53} +(-1.37781 + 1.37781i) q^{55} +(-0.552244 - 0.552244i) q^{57} +(-9.04676 - 3.74729i) q^{59} +(0.0348835 + 0.0842161i) q^{61} -5.01889 q^{63} -8.51404 q^{65} +(-1.84116 - 4.44495i) q^{67} +(-7.53144 - 3.11962i) q^{69} +(4.81608 + 4.81608i) q^{71} +(4.70238 - 4.70238i) q^{73} +(-0.954942 + 2.30543i) q^{75} +(5.70896 - 2.36473i) q^{77} -2.83705i q^{79} -1.00000i q^{81} +(-8.15085 + 3.37619i) q^{83} +(0.253847 - 0.612841i) q^{85} +(2.33605 - 2.33605i) q^{87} +(-5.34580 - 5.34580i) q^{89} +(24.9453 + 10.3327i) q^{91} +(0.268898 + 0.649177i) q^{93} -1.23599 q^{95} -10.5490 q^{97} +(0.471165 + 1.13749i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q + 16 q^{23} + 48 q^{31} + 48 q^{35} + 16 q^{43} - 16 q^{51} - 32 q^{53} - 32 q^{55} - 64 q^{59} - 32 q^{61} - 16 q^{63} - 16 q^{67} - 32 q^{69} - 64 q^{71} - 32 q^{75} - 32 q^{77} + 48 q^{91}+O(q^{100}) $ 32 * q + 16 * q^23 + 48 * q^31 + 48 * q^35 + 16 * q^43 - 16 * q^51 - 32 * q^53 - 32 * q^55 - 64 * q^59 - 32 * q^61 - 16 * q^63 - 16 * q^67 - 32 * q^69 - 64 * q^71 - 32 * q^75 - 32 * q^77 + 48 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{1}{8}\right)$	$1$

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
$3$	−0.382683	−	0.923880i	−0.220942	−	0.533402i
$3$	−0.382683	−	0.923880i	−0.220942	−	0.533402i
$4$		0			0
$5$	−1.46213	−	0.605634i	−0.653884	−	0.270848i	0.0309782	−	0.999520i	$-0.490138\pi$
$5$	−1.46213	−	0.605634i	−0.653884	−	0.270848i	−0.684863	+	0.728672i	$0.740138\pi$
$6$		0			0
$7$	3.54889	+	3.54889i	1.34136	+	1.34136i	0.894712	+	0.446643i	$0.147381\pi$
$7$	3.54889	+	3.54889i	1.34136	+	1.34136i	0.446643	+	0.894712i	$0.352619\pi$
$8$		0			0
$9$	−0.707107	+	0.707107i	−0.235702	+	0.235702i
$10$		0			0
$11$	0.471165	−	1.13749i	0.142062	−	0.342967i	−0.836794	−	0.547517i	$-0.815573\pi$
$11$	0.471165	−	1.13749i	0.142062	−	0.342967i	0.978856	+	0.204550i	$0.0655731\pi$
$12$		0			0
$13$	4.97028	−	2.05876i	1.37851	−	0.570996i	0.434425	−	0.900708i	$-0.356952\pi$
$13$	4.97028	−	2.05876i	1.37851	−	0.570996i	0.944082	+	0.329712i	$0.106952\pi$
$14$		0			0
$15$			1.58260i			0.408625i
$16$		0			0
$17$			0.419142i			0.101657i	0.998707	+	0.0508285i	$0.0161862\pi$
$17$			0.419142i			0.101657i	−0.998707	+	0.0508285i	$0.983814\pi$
$18$		0			0
$19$	0.721541	−	0.298872i	0.165533	−	0.0685660i	−0.298378	−	0.954448i	$-0.596446\pi$
$19$	0.721541	−	0.298872i	0.165533	−	0.0685660i	0.463911	+	0.885882i	$0.346446\pi$
$20$		0			0
$21$	1.92065	−	4.63685i	0.419120	−	1.01184i
$22$		0			0
$23$	5.76431	−	5.76431i	1.20194	−	1.20194i	0.228367	−	0.973575i	$-0.426661\pi$
$23$	5.76431	−	5.76431i	1.20194	−	1.20194i	0.973575	−	0.228367i	$-0.0733387\pi$
$24$		0			0
$25$	−1.76450	−	1.76450i	−0.352901	−	0.352901i
$26$		0			0
$27$	0.923880	+	0.382683i	0.177801	+	0.0736475i
$28$		0			0
$29$	1.26426	+	3.05219i	0.234767	+	0.566778i	0.996727	−	0.0808468i	$-0.0257625\pi$
$29$	1.26426	+	3.05219i	0.234767	+	0.566778i	−0.761959	+	0.647625i	$0.775762\pi$
$30$		0			0
$31$	−0.702664			−0.126202			−0.0631011	−	0.998007i	$-0.520099\pi$
$31$	−0.702664			−0.126202			−0.0631011	+	0.998007i	$0.520099\pi$
$32$		0			0
$33$	−1.23121			−0.214327
$34$		0			0
$35$	−3.03961	−	7.33827i	−0.513788	−	1.24039i
$36$		0			0
$37$	1.86641	+	0.773092i	0.306836	+	0.127096i	0.530788	−	0.847505i	$-0.321896\pi$
$37$	1.86641	+	0.773092i	0.306836	+	0.127096i	−0.223952	+	0.974600i	$0.571896\pi$
$38$		0			0
$39$	−3.80408	−	3.80408i	−0.609141	−	0.609141i
$40$		0			0
$41$	1.76678	−	1.76678i	0.275925	−	0.275925i	−0.555555	−	0.831480i	$-0.687494\pi$
$41$	1.76678	−	1.76678i	0.275925	−	0.275925i	0.831480	+	0.555555i	$0.187494\pi$
$42$		0			0
$43$	−1.70666	+	4.12024i	−0.260263	+	0.628330i	−0.998955	−	0.0457131i	$-0.985444\pi$
$43$	−1.70666	+	4.12024i	−0.260263	+	0.628330i	0.738692	+	0.674044i	$0.235444\pi$
$44$		0			0
$45$	1.46213	−	0.605634i	0.217961	−	0.0902826i
$46$		0			0
$47$			9.64136i			1.40634i	0.711023	+	0.703169i	$0.248232\pi$
$47$			9.64136i			1.40634i	−0.711023	+	0.703169i	$0.751768\pi$
$48$		0			0
$49$			18.1893i			2.59847i
$50$		0			0
$51$	0.387237	−	0.160399i	0.0542240	−	0.0224603i
$52$		0			0
$53$	−0.729689	+	1.76163i	−0.100230	+	0.241978i	−0.966038	−	0.258399i	$-0.916805\pi$
$53$	−0.729689	+	1.76163i	−0.100230	+	0.241978i	0.865808	+	0.500377i	$0.166805\pi$
$54$		0			0
$55$	−1.37781	+	1.37781i	−0.185784	+	0.185784i
$56$		0			0
$57$	−0.552244	−	0.552244i	−0.0731464	−	0.0731464i
$58$		0			0
$59$	−9.04676	−	3.74729i	−1.17779	−	0.487856i	−0.294028	−	0.955797i	$-0.594996\pi$
$59$	−9.04676	−	3.74729i	−1.17779	−	0.487856i	−0.883760	+	0.467941i	$0.844996\pi$
$60$		0			0
$61$	0.0348835	+	0.0842161i	0.00446637	+	0.0107828i	0.926097	−	0.377286i	$-0.123142\pi$
$61$	0.0348835	+	0.0842161i	0.00446637	+	0.0107828i	−0.921631	+	0.388068i	$0.873142\pi$
$62$		0			0
$63$	−5.01889			−0.632321
$64$		0			0
$65$	−8.51404			−1.05604
$66$		0			0
$67$	−1.84116	−	4.44495i	−0.224933	−	0.543037i	0.770614	−	0.637303i	$-0.219950\pi$
$67$	−1.84116	−	4.44495i	−0.224933	−	0.543037i	−0.995547	+	0.0942652i	$0.969950\pi$
$68$		0			0
$69$	−7.53144	−	3.11962i	−0.906679	−	0.375559i
$70$		0			0
$71$	4.81608	+	4.81608i	0.571564	+	0.571564i	0.932565	−	0.361001i	$-0.117565\pi$
$71$	4.81608	+	4.81608i	0.571564	+	0.571564i	−0.361001	+	0.932565i	$0.617565\pi$
$72$		0			0
$73$	4.70238	−	4.70238i	0.550372	−	0.550372i	−0.376176	−	0.926548i	$-0.622761\pi$
$73$	4.70238	−	4.70238i	0.550372	−	0.550372i	0.926548	+	0.376176i	$0.122761\pi$
$74$		0			0
$75$	−0.954942	+	2.30543i	−0.110267	+	0.266209i
$76$		0			0
$77$	5.70896	−	2.36473i	0.650596	−	0.269486i
$78$		0			0
$79$		−	2.83705i		−	0.319193i	−0.987182	−	0.159597i	$-0.948981\pi$
$79$		−	2.83705i		−	0.319193i	0.987182	−	0.159597i	$-0.0510194\pi$
$80$		0			0
$81$		−	1.00000i		−	0.111111i
$82$		0			0
$83$	−8.15085	+	3.37619i	−0.894672	+	0.370585i	−0.782169	−	0.623066i	$-0.785887\pi$
$83$	−8.15085	+	3.37619i	−0.894672	+	0.370585i	−0.112503	+	0.993651i	$0.535887\pi$
$84$		0			0
$85$	0.253847	−	0.612841i	0.0275336	−	0.0664719i
$86$		0			0
$87$	2.33605	−	2.33605i	0.250451	−	0.250451i
$88$		0			0
$89$	−5.34580	−	5.34580i	−0.566654	−	0.566654i	0.364536	−	0.931189i	$-0.381228\pi$
$89$	−5.34580	−	5.34580i	−0.566654	−	0.566654i	−0.931189	+	0.364536i	$0.881228\pi$
$90$		0			0
$91$	24.9453	+	10.3327i	2.61498	+	1.08316i
$92$		0			0
$93$	0.268898	+	0.649177i	0.0278834	+	0.0673165i
$94$		0			0
$95$	−1.23599			−0.126810
$96$		0			0
$97$	−10.5490			−1.07109			−0.535544	−	0.844507i	$-0.679893\pi$
$97$	−10.5490			−1.07109			−0.535544	+	0.844507i	$0.679893\pi$
$98$		0			0
$99$	0.471165	+	1.13749i	0.0473539	+	0.114322i
$100$		0			0
$101$	−14.7491	−	6.10929i	−1.46759	−	0.607897i	−0.501285	−	0.865282i	$-0.667139\pi$
$101$	−14.7491	−	6.10929i	−1.46759	−	0.607897i	−0.966309	+	0.257385i	$0.917139\pi$
$102$		0			0
$103$	0.180630	+	0.180630i	0.0177980	+	0.0177980i	0.715950	−	0.698152i	$-0.245994\pi$
$103$	0.180630	+	0.180630i	0.0177980	+	0.0177980i	−0.698152	+	0.715950i	$0.745994\pi$
$104$		0			0
$105$	−5.61647	+	5.61647i	−0.548111	+	0.548111i
$106$		0			0
$107$	−3.57306	+	8.62613i	−0.345421	+	0.833919i	0.651728	+	0.758453i	$0.274044\pi$
$107$	−3.57306	+	8.62613i	−0.345421	+	0.833919i	−0.997148	+	0.0754662i	$0.975956\pi$
$108$		0			0
$109$	−7.71934	+	3.19745i	−0.739378	+	0.306261i	−0.720400	−	0.693559i	$-0.756042\pi$
$109$	−7.71934	+	3.19745i	−0.739378	+	0.306261i	−0.0189789	+	0.999820i	$0.506042\pi$
$110$		0			0
$111$		−	2.02019i		−	0.191748i
$112$		0			0
$113$		−	12.8803i		−	1.21168i	−0.795587	−	0.605839i	$-0.792838\pi$
$113$		−	12.8803i		−	1.21168i	0.795587	−	0.605839i	$-0.207162\pi$
$114$		0			0
$115$	−11.9192	+	4.93711i	−1.11147	+	0.460388i
$116$		0			0
$117$	−2.05876	+	4.97028i	−0.190332	+	0.459502i
$118$		0			0
$119$	−1.48749	+	1.48749i	−0.136358	+	0.136358i
$120$		0			0
$121$	6.70628	+	6.70628i	0.609662	+	0.609662i
$122$		0			0
$123$	−2.30841	−	0.956175i	−0.208142	−	0.0862154i
$124$		0			0
$125$	4.53946	+	10.9592i	0.406022	+	0.980223i
$126$		0			0
$127$	−14.5951			−1.29510			−0.647552	−	0.762021i	$-0.724207\pi$
$127$	−14.5951			−1.29510			−0.647552	+	0.762021i	$0.724207\pi$
$128$		0			0
$129$	4.45971			0.392656
$130$		0			0
$131$	−1.05197	−	2.53967i	−0.0919108	−	0.221892i	0.871238	−	0.490860i	$-0.163317\pi$
$131$	−1.05197	−	2.53967i	−0.0919108	−	0.221892i	−0.963149	+	0.268968i	$0.913317\pi$
$132$		0			0
$133$	3.62134	+	1.50001i	0.314010	+	0.130067i
$134$		0			0
$135$	−1.11907	−	1.11907i	−0.0963139	−	0.0963139i
$136$		0			0
$137$	10.5319	−	10.5319i	0.899805	−	0.899805i	−0.0956134	−	0.995419i	$-0.530481\pi$
$137$	10.5319	−	10.5319i	0.899805	−	0.899805i	0.995419	+	0.0956134i	$0.0304812\pi$
$138$		0			0
$139$	4.34181	−	10.4820i	0.368267	−	0.889076i	−0.625767	−	0.780010i	$-0.715214\pi$
$139$	4.34181	−	10.4820i	0.368267	−	0.889076i	0.994035	−	0.109066i	$-0.0347859\pi$
$140$		0			0
$141$	8.90746	−	3.68959i	0.750143	−	0.310719i
$142$		0			0
$143$		−	6.62367i		−	0.553899i
$144$		0			0
$145$		−	5.22838i		−	0.434193i
$146$		0			0
$147$	16.8047	−	6.96074i	1.38603	−	0.574112i
$148$		0			0
$149$	−7.35637	+	17.7598i	−0.602657	+	1.45494i	0.268179	+	0.963369i	$0.413578\pi$
$149$	−7.35637	+	17.7598i	−0.602657	+	1.45494i	−0.870836	+	0.491574i	$0.836422\pi$
$150$		0			0
$151$	−1.67484	+	1.67484i	−0.136297	+	0.136297i	−0.771964	−	0.635667i	$-0.780725\pi$
$151$	−1.67484	+	1.67484i	−0.136297	+	0.136297i	0.635667	+	0.771964i	$0.280725\pi$
$152$		0			0
$153$	−0.296378	−	0.296378i	−0.0239608	−	0.0239608i
$154$		0			0
$155$	1.02739	+	0.425557i	0.0825216	+	0.0341816i
$156$		0			0
$157$	−5.88393	−	14.2051i	−0.469589	−	1.13369i	−0.964343	−	0.264654i	$-0.914742\pi$
$157$	−5.88393	−	14.2051i	−0.469589	−	1.13369i	0.494755	−	0.869033i	$-0.335258\pi$
$158$		0			0
$159$	1.90677			0.151217
$160$		0			0
$161$	40.9139			3.22446
$162$		0			0
$163$	0.0308652	+	0.0745152i	0.00241755	+	0.00583648i	0.925084	−	0.379763i	$-0.123995\pi$
$163$	0.0308652	+	0.0745152i	0.00241755	+	0.00583648i	−0.922666	+	0.385600i	$0.873995\pi$
$164$		0			0
$165$	1.80020	+	0.745665i	0.140145	+	0.0580500i
$166$		0			0
$167$	−3.70781	−	3.70781i	−0.286919	−	0.286919i	0.548942	−	0.835861i	$-0.315031\pi$
$167$	−3.70781	−	3.70781i	−0.286919	−	0.286919i	−0.835861	+	0.548942i	$0.815031\pi$
$168$		0			0
$169$	11.2728	−	11.2728i	0.867136	−	0.867136i
$170$		0			0
$171$	−0.298872	+	0.721541i	−0.0228553	+	0.0551776i
$172$		0			0
$173$	−14.4940	+	6.00361i	−1.10196	+	0.456446i	−0.858161	−	0.513380i	$-0.828393\pi$
$173$	−14.4940	+	6.00361i	−1.10196	+	0.456446i	−0.243797	+	0.969826i	$0.578393\pi$
$174$		0			0
$175$		−	12.5241i		−	0.946730i
$176$		0			0
$177$			9.79214i			0.736022i
$178$		0			0
$179$	21.2978	−	8.82184i	1.59187	−	0.659376i	0.601637	−	0.798770i	$-0.294516\pi$
$179$	21.2978	−	8.82184i	1.59187	−	0.659376i	0.990237	+	0.139394i	$0.0445155\pi$
$180$		0			0
$181$	−0.843844	+	2.03722i	−0.0627224	+	0.151425i	−0.952133	−	0.305684i	$-0.901115\pi$
$181$	−0.843844	+	2.03722i	−0.0627224	+	0.151425i	0.889411	+	0.457109i	$0.151115\pi$
$182$		0			0
$183$	0.0644562	−	0.0644562i	0.00476474	−	0.00476474i
$184$		0			0
$185$	−2.26072	−	2.26072i	−0.166212	−	0.166212i
$186$		0			0
$187$	0.476772	+	0.197485i	0.0348650	+	0.0144416i
$188$		0			0
$189$	1.92065	+	4.63685i	0.139707	+	0.337281i
$190$		0			0
$191$	10.5263			0.761656			0.380828	−	0.924646i	$-0.375639\pi$
$191$	10.5263			0.761656			0.380828	+	0.924646i	$0.375639\pi$
$192$		0			0
$193$	−14.4005			−1.03657			−0.518285	−	0.855208i	$-0.673429\pi$
$193$	−14.4005			−1.03657			−0.518285	+	0.855208i	$0.673429\pi$
$194$		0			0
$195$	3.25818	+	7.86595i	0.233323	+	0.563292i
$196$		0			0
$197$	15.2594	+	6.32063i	1.08718	+	0.450326i	0.853024	−	0.521872i	$-0.174766\pi$
$197$	15.2594	+	6.32063i	1.08718	+	0.450326i	0.234160	+	0.972198i	$0.424766\pi$
$198$		0			0
$199$	−4.42484	−	4.42484i	−0.313668	−	0.313668i	0.532661	−	0.846329i	$-0.321192\pi$
$199$	−4.42484	−	4.42484i	−0.313668	−	0.313668i	−0.846329	+	0.532661i	$0.821192\pi$
$200$		0			0
$201$	−3.40202	+	3.40202i	−0.239960	+	0.239960i
$202$		0			0
$203$	−6.34518	+	15.3186i	−0.445345	+	1.07516i
$204$		0			0
$205$	−3.65329	+	1.51324i	−0.255157	+	0.105689i
$206$		0			0
$207$			8.15197i			0.566601i
$208$		0			0
$209$		−	0.961566i		−	0.0665129i
$210$		0			0
$211$	−5.03490	+	2.08552i	−0.346617	+	0.143573i	−0.549198	−	0.835692i	$-0.685067\pi$
$211$	−5.03490	+	2.08552i	−0.346617	+	0.143573i	0.202582	+	0.979265i	$0.435067\pi$
$212$		0			0
$213$	2.60644	−	6.29251i	0.178591	−	0.431156i
$214$		0			0
$215$	4.99071	−	4.99071i	0.340364	−	0.340364i
$216$		0			0
$217$	−2.49368	−	2.49368i	−0.169282	−	0.169282i
$218$		0			0
$219$	−6.14396	−	2.54491i	−0.415170	−	0.171969i
$220$		0			0
$221$	0.862912	+	2.08325i	0.0580457	+	0.140135i
$222$		0			0
$223$	6.55302			0.438823			0.219411	−	0.975632i	$-0.429586\pi$
$223$	6.55302			0.438823			0.219411	+	0.975632i	$0.429586\pi$
$224$		0			0
$225$	2.49538			0.166359
$226$		0			0
$227$	7.13682	+	17.2298i	0.473687	+	1.14358i	0.962521	+	0.271206i	$0.0874224\pi$
$227$	7.13682	+	17.2298i	0.473687	+	1.14358i	−0.488834	+	0.872377i	$0.662578\pi$
$228$		0			0
$229$	19.5161	+	8.08385i	1.28966	+	0.534196i	0.918885	−	0.394526i	$-0.129091\pi$
$229$	19.5161	+	8.08385i	1.28966	+	0.534196i	0.370778	+	0.928721i	$0.379091\pi$
$230$		0			0
$231$	−4.36945	−	4.36945i	−0.287489	−	0.287489i
$232$		0			0
$233$	−12.3229	+	12.3229i	−0.807303	+	0.807303i	−0.984225	−	0.176922i	$-0.943386\pi$
$233$	−12.3229	+	12.3229i	−0.807303	+	0.807303i	0.176922	+	0.984225i	$0.443386\pi$
$234$		0			0
$235$	5.83914	−	14.0969i	0.380903	−	0.919582i
$236$		0			0
$237$	−2.62109	+	1.08569i	−0.170258	+	0.0705233i
$238$		0			0
$239$			9.89811i			0.640256i	0.947374	+	0.320128i	$0.103726\pi$
$239$			9.89811i			0.640256i	−0.947374	+	0.320128i	$0.896274\pi$
$240$		0			0
$241$		−	4.48193i		−	0.288706i	−0.989526	−	0.144353i	$-0.953890\pi$
$241$		−	4.48193i		−	0.288706i	0.989526	−	0.144353i	$-0.0461101\pi$
$242$		0			0
$243$	−0.923880	+	0.382683i	−0.0592669	+	0.0245492i
$244$		0			0
$245$	11.0160	−	26.5951i	0.703790	−	1.69910i
$246$		0			0
$247$	2.97095	−	2.97095i	0.189037	−	0.189037i
$248$		0			0
$249$	6.23839	+	6.23839i	0.395342	+	0.395342i
$250$		0			0
$251$	4.74357	+	1.96485i	0.299412	+	0.124020i	0.527332	−	0.849659i	$-0.323192\pi$
$251$	4.74357	+	1.96485i	0.299412	+	0.124020i	−0.227920	+	0.973680i	$0.573192\pi$
$252$		0			0
$253$	−3.84093	−	9.27281i	−0.241477	−	0.582977i
$254$		0			0
$255$	−0.663334			−0.0415396
$256$		0			0
$257$	−21.8091			−1.36042			−0.680208	−	0.733019i	$-0.738111\pi$
$257$	−21.8091			−1.36042			−0.680208	+	0.733019i	$0.738111\pi$
$258$		0			0
$259$	3.88007	+	9.36731i	0.241096	+	0.582056i
$260$		0			0
$261$	−3.05219	−	1.26426i	−0.188926	−	0.0782557i
$262$		0			0
$263$	−12.6621	−	12.6621i	−0.780776	−	0.780776i	0.199186	−	0.979962i	$-0.436170\pi$
$263$	−12.6621	−	12.6621i	−0.780776	−	0.780776i	−0.979962	+	0.199186i	$0.936170\pi$
$264$		0			0
$265$	2.13380	−	2.13380i	0.131078	−	0.131078i
$266$		0			0
$267$	−2.89313	+	6.98463i	−0.177056	+	0.427452i
$268$		0			0
$269$	11.0354	−	4.57101i	0.672840	−	0.278699i	−0.0199903	−	0.999800i	$-0.506364\pi$
$269$	11.0354	−	4.57101i	0.672840	−	0.278699i	0.692830	+	0.721101i	$0.256364\pi$
$270$		0			0
$271$		−	24.7890i		−	1.50582i	−0.658121	−	0.752912i	$-0.728648\pi$
$271$		−	24.7890i		−	1.50582i	0.658121	−	0.752912i	$-0.271352\pi$
$272$		0			0
$273$		−	27.0006i		−	1.63415i
$274$		0			0
$275$	−2.83848	+	1.17574i	−0.171167	+	0.0708997i
$276$		0			0
$277$	0.490227	−	1.18351i	0.0294549	−	0.0711104i	−0.908468	−	0.417955i	$-0.862747\pi$
$277$	0.490227	−	1.18351i	0.0294549	−	0.0711104i	0.937923	+	0.346845i	$0.112747\pi$
$278$		0			0
$279$	0.496859	−	0.496859i	0.0297461	−	0.0297461i
$280$		0			0
$281$	11.2732	+	11.2732i	0.672504	+	0.672504i	0.958293	−	0.285789i	$-0.0922556\pi$
$281$	11.2732	+	11.2732i	0.672504	+	0.672504i	−0.285789	+	0.958293i	$0.592256\pi$
$282$		0			0
$283$	−19.6457	−	8.13751i	−1.16782	−	0.483725i	−0.287345	−	0.957827i	$-0.592773\pi$
$283$	−19.6457	−	8.13751i	−1.16782	−	0.483725i	−0.880470	+	0.474102i	$0.842773\pi$
$284$		0			0
$285$	0.472994	+	1.14191i	0.0280178	+	0.0676409i
$286$		0			0
$287$	12.5402			0.740227
$288$		0			0
$289$	16.8243			0.989666
$290$		0			0
$291$	4.03693	+	9.74600i	0.236649	+	0.571321i
$292$		0			0
$293$	−12.9966	−	5.38336i	−0.759269	−	0.314499i	−0.0307516	−	0.999527i	$-0.509790\pi$
$293$	−12.9966	−	5.38336i	−0.759269	−	0.314499i	−0.728517	+	0.685028i	$0.759790\pi$
$294$		0			0
$295$	10.9581	+	10.9581i	0.638002	+	0.638002i
$296$		0			0
$297$	0.870600	−	0.870600i	0.0505173	−	0.0505173i
$298$		0			0
$299$	16.7829	−	40.5175i	0.970581	−	2.34319i
$300$		0			0
$301$	−20.6790	+	8.56553i	−1.19192	+	0.493709i
$302$		0			0
$303$			15.9644i			0.917128i
$304$		0			0
$305$		−	0.144262i		−	0.00826039i
$306$		0			0
$307$	−5.44024	+	2.25342i	−0.310491	+	0.128609i	−0.532487	−	0.846438i	$-0.678743\pi$
$307$	−5.44024	+	2.25342i	−0.310491	+	0.128609i	0.221997	+	0.975047i	$0.428743\pi$
$308$		0			0
$309$	0.0977562	−	0.236004i	0.00556116	−	0.0134258i
$310$		0			0
$311$	−12.0286	+	12.0286i	−0.682077	+	0.682077i	−0.960468	−	0.278391i	$-0.910199\pi$
$311$	−12.0286	+	12.0286i	−0.682077	+	0.682077i	0.278391	+	0.960468i	$0.410199\pi$
$312$		0			0
$313$	−18.0892	−	18.0892i	−1.02246	−	1.02246i	−0.999742	−	0.0227184i	$-0.992768\pi$
$313$	−18.0892	−	18.0892i	−1.02246	−	1.02246i	−0.0227184	−	0.999742i	$-0.507232\pi$
$314$		0			0
$315$	7.33827	+	3.03961i	0.413465	+	0.171263i
$316$		0			0
$317$	6.30035	+	15.2104i	0.353863	+	0.854300i	0.996136	+	0.0878245i	$0.0279915\pi$
$317$	6.30035	+	15.2104i	0.353863	+	0.854300i	−0.642273	+	0.766476i	$0.722009\pi$
$318$		0			0
$319$	4.06752			0.227738
$320$		0			0
$321$	9.33685			0.521132
$322$		0			0
$323$	0.125270	+	0.302428i	0.00697021	+	0.0168276i
$324$		0			0
$325$	−12.4027	−	5.13738i	−0.687980	−	0.284971i
$326$		0			0
$327$	5.90812	+	5.90812i	0.326720	+	0.326720i
$328$		0			0
$329$	−34.2162	+	34.2162i	−1.88640	+	1.88640i
$330$		0			0
$331$	−3.57821	+	8.63857i	−0.196676	+	0.474819i	−0.991193	−	0.132423i	$-0.957724\pi$
$331$	−3.57821	+	8.63857i	−0.196676	+	0.474819i	0.794517	+	0.607242i	$0.207724\pi$
$332$		0			0
$333$	−1.86641	+	0.773092i	−0.102279	+	0.0423652i
$334$		0			0
$335$			7.61417i			0.416006i
$336$		0			0
$337$		−	7.95561i		−	0.433370i	−0.976242	−	0.216685i	$-0.930476\pi$
$337$		−	7.95561i		−	0.433370i	0.976242	−	0.216685i	$-0.0695244\pi$
$338$		0			0
$339$	−11.8999	+	4.92908i	−0.646312	+	0.267711i
$340$		0			0
$341$	−0.331071	+	0.799276i	−0.0179285	+	0.0432832i
$342$		0			0
$343$	−39.7096	+	39.7096i	−2.14412	+	2.14412i
$344$		0			0
$345$	9.12259	+	9.12259i	0.491144	+	0.491144i
$346$		0			0
$347$	−24.7595	−	10.2557i	−1.32916	−	0.550557i	−0.398745	−	0.917062i	$-0.630554\pi$
$347$	−24.7595	−	10.2557i	−1.32916	−	0.550557i	−0.930416	+	0.366505i	$0.880554\pi$
$348$		0			0
$349$	−9.76660	−	23.5787i	−0.522794	−	1.26214i	−0.936161	−	0.351572i	$-0.885647\pi$
$349$	−9.76660	−	23.5787i	−0.522794	−	1.26214i	0.413366	−	0.910565i	$-0.364353\pi$
$350$		0			0
$351$	5.37979			0.287152
$352$		0			0
$353$	−6.97022			−0.370987			−0.185494	−	0.982645i	$-0.559388\pi$
$353$	−6.97022			−0.370987			−0.185494	+	0.982645i	$0.559388\pi$
$354$		0			0
$355$	−4.12495	−	9.95852i	−0.218930	−	0.528543i
$356$		0			0
$357$	1.94350	+	0.805025i	0.102861	+	0.0426064i
$358$		0			0
$359$	17.8636	+	17.8636i	0.942805	+	0.942805i	0.998451	−	0.0556457i	$-0.0177217\pi$
$359$	17.8636	+	17.8636i	0.942805	+	0.942805i	−0.0556457	+	0.998451i	$0.517722\pi$
$360$		0			0
$361$	−13.0037	+	13.0037i	−0.684407	+	0.684407i
$362$		0			0
$363$	3.62941	−	8.76218i	0.190495	−	0.459895i
$364$		0			0
$365$	−9.72341	+	4.02757i	−0.508947	+	0.210813i
$366$		0			0
$367$		−	5.77401i		−	0.301401i	−0.988579	−	0.150700i	$-0.951847\pi$
$367$		−	5.77401i		−	0.301401i	0.988579	−	0.150700i	$-0.0481529\pi$
$368$		0			0
$369$			2.49861i			0.130072i
$370$		0			0
$371$	−8.84141	+	3.66223i	−0.459023	+	0.190134i
$372$		0			0
$373$	−6.93394	+	16.7400i	−0.359026	+	0.866766i	0.636411	+	0.771350i	$0.280418\pi$
$373$	−6.93394	+	16.7400i	−0.359026	+	0.866766i	−0.995438	+	0.0954158i	$0.969582\pi$
$374$		0			0
$375$	8.38783	−	8.38783i	0.433146	−	0.433146i
$376$		0			0
$377$	12.5674	+	12.5674i	0.647256	+	0.647256i
$378$		0			0
$379$	−17.3937	−	7.20472i	−0.893456	−	0.370082i	−0.111755	−	0.993736i	$-0.535647\pi$
$379$	−17.3937	−	7.20472i	−0.893456	−	0.370082i	−0.781700	+	0.623654i	$0.785647\pi$
$380$		0			0
$381$	5.58529	+	13.4841i	0.286143	+	0.690811i
$382$		0			0
$383$	−7.76327			−0.396685			−0.198342	−	0.980133i	$-0.563556\pi$
$383$	−7.76327			−0.396685			−0.198342	+	0.980133i	$0.563556\pi$
$384$		0			0
$385$	−9.77940			−0.498404
$386$		0			0
$387$	−1.70666	−	4.12024i	−0.0867543	−	0.209443i
$388$		0			0
$389$	22.1262	+	9.16496i	1.12184	+	0.464682i	0.865000	−	0.501772i	$-0.167318\pi$
$389$	22.1262	+	9.16496i	1.12184	+	0.464682i	0.256841	+	0.966454i	$0.417318\pi$
$390$		0			0
$391$	2.41607	+	2.41607i	0.122186	+	0.122186i
$392$		0			0
$393$	−1.94378	+	1.94378i	−0.0980508	+	0.0980508i
$394$		0			0
$395$	−1.71822	+	4.14814i	−0.0864528	+	0.208715i
$396$		0			0
$397$	17.1908	−	7.12064i	0.862779	−	0.357375i	0.0929854	−	0.995667i	$-0.470359\pi$
$397$	17.1908	−	7.12064i	0.862779	−	0.357375i	0.769794	+	0.638293i	$0.220359\pi$
$398$		0			0
$399$		−	3.91971i		−	0.196231i
$400$		0			0
$401$		−	13.4861i		−	0.673466i	−0.941600	−	0.336733i	$-0.890678\pi$
$401$		−	13.4861i		−	0.673466i	0.941600	−	0.336733i	$-0.109322\pi$
$402$		0			0
$403$	−3.49243	+	1.44661i	−0.173971	+	0.0720610i
$404$		0			0
$405$	−0.605634	+	1.46213i	−0.0300942	+	0.0726538i
$406$		0			0
$407$	1.75877	−	1.75877i	0.0871792	−	0.0871792i
$408$		0			0
$409$	2.39993	+	2.39993i	0.118669	+	0.118669i	0.763948	−	0.645278i	$-0.223259\pi$
$409$	2.39993	+	2.39993i	0.118669	+	0.118669i	−0.645278	+	0.763948i	$0.723259\pi$
$410$		0			0
$411$	−13.7607	−	5.69985i	−0.678763	−	0.281153i
$412$		0			0
$413$	−18.8072	−	45.4047i	−0.925444	−	2.23422i
$414$		0			0
$415$	13.9623			0.685384
$416$		0			0
$417$	−11.3457			−0.555601
$418$		0			0
$419$	3.43963	+	8.30401i	0.168037	+	0.405677i	0.985356	−	0.170508i	$-0.0545408\pi$
$419$	3.43963	+	8.30401i	0.168037	+	0.405677i	−0.817319	+	0.576185i	$0.804541\pi$
$420$		0			0
$421$	27.1820	+	11.2592i	1.32477	+	0.548738i	0.929159	−	0.369680i	$-0.120533\pi$
$421$	27.1820	+	11.2592i	1.32477	+	0.548738i	0.395612	+	0.918418i	$0.370533\pi$
$422$		0			0
$423$	−6.81747	−	6.81747i	−0.331477	−	0.331477i
$424$		0			0
$425$	0.739578	−	0.739578i	0.0358748	−	0.0358748i
$426$		0			0
$427$	−0.175076	+	0.422672i	−0.00847254	+	0.0204545i
$428$		0			0
$429$	−6.11947	+	2.53477i	−0.295451	+	0.122380i
$430$		0			0
$431$		−	11.2962i		−	0.544119i	−0.962280	−	0.272060i	$-0.912295\pi$
$431$		−	11.2962i		−	0.544119i	0.962280	−	0.272060i	$-0.0877048\pi$
$432$		0			0
$433$			38.7244i			1.86098i	0.366323	+	0.930488i	$0.380617\pi$
$433$			38.7244i			1.86098i	−0.366323	+	0.930488i	$0.619383\pi$
$434$		0			0
$435$	−4.83039	+	2.00081i	−0.231600	+	0.0959317i
$436$		0			0
$437$	2.43640	−	5.88198i	0.116549	−	0.281373i
$438$		0			0
$439$	12.1768	−	12.1768i	0.581166	−	0.581166i	−0.354058	−	0.935223i	$-0.615198\pi$
$439$	12.1768	−	12.1768i	0.581166	−	0.581166i	0.935223	+	0.354058i	$0.115198\pi$
$440$		0			0
$441$	−12.8618	−	12.8618i	−0.612465	−	0.612465i
$442$		0			0
$443$	5.56969	+	2.30704i	0.264624	+	0.109611i	0.511051	−	0.859551i	$-0.329256\pi$
$443$	5.56969	+	2.30704i	0.264624	+	0.109611i	−0.246427	+	0.969161i	$0.579256\pi$
$444$		0			0
$445$	4.57866	+	11.0539i	0.217049	+	0.524003i
$446$		0			0
$447$	19.2231			0.909222
$448$		0			0
$449$	−13.4725			−0.635805			−0.317903	−	0.948123i	$-0.602978\pi$
$449$	−13.4725			−0.635805			−0.317903	+	0.948123i	$0.602978\pi$
$450$		0			0
$451$	−1.17726	−	2.84215i	−0.0554348	−	0.133832i
$452$		0			0
$453$	2.18829	+	0.906419i	0.102815	+	0.0425873i
$454$		0			0
$455$	−30.2154	−	30.2154i	−1.41652	−	1.41652i
$456$		0			0
$457$	−0.807356	+	0.807356i	−0.0377665	+	0.0377665i	−0.725738	−	0.687971i	$-0.758501\pi$
$457$	−0.807356	+	0.807356i	−0.0377665	+	0.0377665i	0.687971	+	0.725738i	$0.258501\pi$
$458$		0			0
$459$	−0.160399	+	0.387237i	−0.00748678	+	0.0180747i
$460$		0			0
$461$	4.82041	−	1.99668i	0.224509	−	0.0929945i	−0.267594	−	0.963532i	$-0.586229\pi$
$461$	4.82041	−	1.99668i	0.224509	−	0.0929945i	0.492102	+	0.870537i	$0.336229\pi$
$462$		0			0
$463$			15.0849i			0.701053i	0.936553	+	0.350526i	$0.113997\pi$
$463$			15.0849i			0.701053i	−0.936553	+	0.350526i	$0.886003\pi$
$464$		0			0
$465$		−	1.11203i		−	0.0515694i
$466$		0			0
$467$	17.1432	−	7.10095i	0.793294	−	0.328593i	0.0510266	−	0.998697i	$-0.483751\pi$
$467$	17.1432	−	7.10095i	0.793294	−	0.328593i	0.742267	+	0.670104i	$0.233751\pi$
$468$		0			0
$469$	9.24058	−	22.3087i	0.426690	−	1.03012i
$470$		0			0
$471$	−10.8721	+	10.8721i	−0.500959	+	0.500959i
$472$		0			0
$473$	3.88263	+	3.88263i	0.178523	+	0.178523i
$474$		0			0
$475$	−1.80052	−	0.745800i	−0.0826136	−	0.0342197i
$476$		0			0
$477$	−0.729689	−	1.76163i	−0.0334102	−	0.0806593i
$478$		0			0
$479$	−13.4984			−0.616757			−0.308379	−	0.951264i	$-0.599786\pi$
$479$	−13.4984			−0.616757			−0.308379	+	0.951264i	$0.599786\pi$
$480$		0			0
$481$	10.8682			0.495546
$482$		0			0
$483$	−15.6571	−	37.7995i	−0.712421	−	1.71994i
$484$		0			0
$485$	15.4240	+	6.38883i	0.700368	+	0.290102i
$486$		0			0
$487$	18.9270	+	18.9270i	0.857666	+	0.857666i	0.991063	−	0.133397i	$-0.0425884\pi$
$487$	18.9270	+	18.9270i	0.857666	+	0.857666i	−0.133397	+	0.991063i	$0.542588\pi$
$488$		0			0
$489$	0.0570315	−	0.0570315i	0.00257905	−	0.00257905i
$490$		0			0
$491$	−11.5298	+	27.8355i	−0.520335	+	1.25620i	0.417361	+	0.908741i	$0.362955\pi$
$491$	−11.5298	+	27.8355i	−0.520335	+	1.25620i	−0.937695	+	0.347458i	$0.887045\pi$
$492$		0			0
$493$	−1.27930	+	0.529905i	−0.0576169	+	0.0238657i
$494$		0			0
$495$		−	1.94852i		−	0.0875793i
$496$		0			0
$497$			34.1835i			1.53334i
$498$		0			0
$499$	4.77450	−	1.97766i	0.213736	−	0.0885323i	−0.273247	−	0.961944i	$-0.588098\pi$
$499$	4.77450	−	1.97766i	0.213736	−	0.0885323i	0.486983	+	0.873412i	$0.338098\pi$
$500$		0			0
$501$	−2.00665	+	4.84448i	−0.0896505	+	0.216435i
$502$		0			0
$503$	−0.935522	+	0.935522i	−0.0417129	+	0.0417129i	−0.727656	−	0.685943i	$-0.759390\pi$
$503$	−0.935522	+	0.935522i	−0.0417129	+	0.0417129i	0.685943	+	0.727656i	$0.259390\pi$
$504$		0			0
$505$	17.8652	+	17.8652i	0.794989	+	0.794989i
$506$		0			0
$507$	−14.7286	−	6.10078i	−0.654120	−	0.270945i
$508$		0			0
$509$	−3.46080	−	8.35510i	−0.153397	−	0.370333i	0.828435	−	0.560085i	$-0.189232\pi$
$509$	−3.46080	−	8.35510i	−0.153397	−	0.370333i	−0.981832	+	0.189752i	$0.939232\pi$
$510$		0			0
$511$	33.3765			1.47649
$512$		0			0
$513$	0.780990			0.0344816
$514$		0			0
$515$	−0.154709	−	0.373500i	−0.00681729	−	0.0164584i
$516$		0			0
$517$	10.9670	+	4.54267i	0.482328	+	0.199787i
$518$		0			0
$519$	11.0932	+	11.0932i	0.486938	+	0.486938i
$520$		0			0
$521$	18.6279	−	18.6279i	0.816103	−	0.816103i	−0.169438	−	0.985541i	$-0.554195\pi$
$521$	18.6279	−	18.6279i	0.816103	−	0.816103i	0.985541	+	0.169438i	$0.0541953\pi$
$522$		0			0
$523$	6.71157	−	16.2032i	0.293476	−	0.708514i	−0.706523	−	0.707690i	$-0.749737\pi$
$523$	6.71157	−	16.2032i	0.293476	−	0.708514i	1.00000		0.000824669i	$-0.000262500\pi$
$524$		0			0
$525$	−11.5707	+	4.79275i	−0.504988	+	0.209173i
$526$		0			0
$527$		−	0.294516i		−	0.0128293i
$528$		0			0
$529$		−	43.4546i		−	1.88933i
$530$		0			0
$531$	9.04676	−	3.74729i	0.392596	−	0.162619i
$532$		0			0
$533$	5.14402	−	12.4188i	0.222812	−	0.537916i
$534$		0			0
$535$	10.4486	−	10.4486i	0.451730	−	0.451730i
$536$		0			0
$537$	−16.3006	−	16.3006i	−0.703425	−	0.703425i
$538$		0			0
$539$	20.6902	+	8.57016i	0.891190	+	0.369143i
$540$		0			0
$541$	−1.92568	−	4.64901i	−0.0827916	−	0.199877i	0.877063	−	0.480376i	$-0.159500\pi$
$541$	−1.92568	−	4.64901i	−0.0827916	−	0.199877i	−0.959854	+	0.280500i	$0.909500\pi$
$542$		0			0
$543$	2.20507			0.0946286
$544$		0			0
$545$	13.2232			0.566418
$546$		0			0
$547$	−3.16571	−	7.64271i	−0.135356	−	0.326779i	0.841639	−	0.540041i	$-0.181591\pi$
$547$	−3.16571	−	7.64271i	−0.135356	−	0.326779i	−0.976995	+	0.213262i	$0.931591\pi$
$548$		0			0
$549$	−0.0842161	−	0.0348835i	−0.00359426	−	0.00148879i
$550$		0			0
$551$	1.82443	+	1.82443i	0.0777233	+	0.0777233i
$552$		0			0
$553$	10.0684	−	10.0684i	0.428152	−	0.428152i
$554$		0			0
$555$	−1.22349	+	2.95378i	−0.0519344	+	0.125381i
$556$		0			0
$557$	27.6378	−	11.4479i	1.17105	−	0.485065i	0.289511	−	0.957175i	$-0.406507\pi$
$557$	27.6378	−	11.4479i	1.17105	−	0.485065i	0.881540	+	0.472110i	$0.156507\pi$
$558$		0			0
$559$			23.9923i			1.01477i
$560$		0			0
$561$		−	0.516054i		−	0.0217878i
$562$		0			0
$563$	23.2024	−	9.61075i	0.977865	−	0.405045i	0.164231	−	0.986422i	$-0.447486\pi$
$563$	23.2024	−	9.61075i	0.977865	−	0.405045i	0.813634	+	0.581377i	$0.197486\pi$
$564$		0			0
$565$	−7.80076	+	18.8327i	−0.328180	+	0.792297i
$566$		0			0
$567$	3.54889	−	3.54889i	0.149039	−	0.149039i
$568$		0			0
$569$	−17.3917	−	17.3917i	−0.729097	−	0.729097i	0.241343	−	0.970440i	$-0.422412\pi$
$569$	−17.3917	−	17.3917i	−0.729097	−	0.729097i	−0.970440	+	0.241343i	$0.922412\pi$
$570$		0			0
$571$	37.7837	+	15.6505i	1.58120	+	0.654954i	0.988603	−	0.150546i	$-0.0481031\pi$
$571$	37.7837	+	15.6505i	1.58120	+	0.654954i	0.592596	+	0.805500i	$0.298103\pi$
$572$		0			0
$573$	−4.02824	−	9.72503i	−0.168282	−	0.406269i
$574$		0			0
$575$	−20.3423			−0.848332
$576$		0			0
$577$	−13.8026			−0.574610			−0.287305	−	0.957839i	$-0.592759\pi$
$577$	−13.8026			−0.574610			−0.287305	+	0.957839i	$0.592759\pi$
$578$		0			0
$579$	5.51083	+	13.3043i	0.229022	+	0.552909i
$580$		0			0
$581$	−40.9082	−	16.9447i	−1.69716	−	0.702987i
$582$		0			0
$583$	1.66003	+	1.66003i	0.0687515	+	0.0687515i
$584$		0			0
$585$	6.02034	−	6.02034i	0.248910	−	0.248910i
$586$		0			0
$587$	3.50667	−	8.46586i	0.144736	−	0.349423i	−0.834842	−	0.550490i	$-0.814441\pi$
$587$	3.50667	−	8.46586i	0.144736	−	0.349423i	0.979578	+	0.201067i	$0.0644408\pi$
$588$		0			0
$589$	−0.507001	+	0.210007i	−0.0208906	+	0.00865317i
$590$		0			0
$591$		−	16.5166i		−	0.679403i
$592$		0			0
$593$		−	9.94303i		−	0.408311i	−0.978938	−	0.204156i	$-0.934555\pi$
$593$		−	9.94303i		−	0.408311i	0.978938	−	0.204156i	$-0.0654449\pi$
$594$		0			0
$595$	3.07578	−	1.27403i	0.126095	−	0.0522302i
$596$		0			0
$597$	−2.39470	+	5.78133i	−0.0980087	+	0.236614i
$598$		0			0
$599$	−7.33034	+	7.33034i	−0.299510	+	0.299510i	−0.840822	−	0.541312i	$-0.817928\pi$
$599$	−7.33034	+	7.33034i	−0.299510	+	0.299510i	0.541312	+	0.840822i	$0.317928\pi$
$600$		0			0
$601$	13.1690	+	13.1690i	0.537174	+	0.537174i	0.922698	−	0.385524i	$-0.125979\pi$
$601$	13.1690	+	13.1690i	0.537174	+	0.537174i	−0.385524	+	0.922698i	$0.625979\pi$
$602$		0			0
$603$	4.44495	+	1.84116i	0.181012	+	0.0749778i
$604$		0			0
$605$	−5.74390	−	13.8670i	−0.233523	−	0.563774i
$606$		0			0
$607$	−26.6851			−1.08312			−0.541558	−	0.840663i	$-0.682165\pi$
$607$	−26.6851			−1.08312			−0.541558	+	0.840663i	$0.682165\pi$
$608$		0			0
$609$	16.5808			0.671886
$610$		0			0
$611$	19.8492	+	47.9202i	0.803013	+	1.93864i
$612$		0			0
$613$	−32.3066	−	13.3818i	−1.30485	−	0.540487i	−0.381473	−	0.924380i	$-0.624583\pi$
$613$	−32.3066	−	13.3818i	−1.30485	−	0.540487i	−0.923378	+	0.383893i	$0.874583\pi$
$614$		0			0
$615$	2.79610	+	2.79610i	0.112750	+	0.112750i
$616$		0			0
$617$	8.69424	−	8.69424i	0.350017	−	0.350017i	−0.510099	−	0.860116i	$-0.670391\pi$
$617$	8.69424	−	8.69424i	0.350017	−	0.350017i	0.860116	+	0.510099i	$0.170391\pi$
$618$		0			0
$619$	−4.36939	+	10.5486i	−0.175621	+	0.423986i	−0.987039	−	0.160480i	$-0.948696\pi$
$619$	−4.36939	+	10.5486i	−0.175621	+	0.423986i	0.811418	+	0.584466i	$0.198696\pi$
$620$		0			0
$621$	7.53144	−	3.11962i	0.302226	−	0.125186i
$622$		0			0
$623$		−	37.9434i		−	1.52017i
$624$		0			0
$625$		−	6.29614i		−	0.251846i
$626$		0			0
$627$	−0.888371	+	0.367976i	−0.0354781	+	0.0146955i
$628$		0			0
$629$	−0.324036	+	0.782291i	−0.0129201	+	0.0311920i
$630$		0			0
$631$	25.2614	−	25.2614i	1.00564	−	1.00564i	0.00565528	−	0.999984i	$-0.498200\pi$
$631$	25.2614	−	25.2614i	1.00564	−	1.00564i	0.999984	−	0.00565528i	$-0.00180014\pi$
$632$		0			0
$633$	3.85355	+	3.85355i	0.153165	+	0.153165i
$634$		0			0
$635$	21.3399	+	8.83928i	0.846848	+	0.350776i
$636$		0			0
$637$	37.4473	+	90.4057i	1.48372	+	3.58201i
$638$		0			0
$639$	−6.81097			−0.269438
$640$		0			0
$641$	−5.16034			−0.203821			−0.101911	−	0.994794i	$-0.532496\pi$
$641$	−5.16034			−0.203821			−0.101911	+	0.994794i	$0.532496\pi$
$642$		0			0
$643$	11.5208	+	27.8137i	0.454336	+	1.09686i	0.970657	+	0.240469i	$0.0773012\pi$
$643$	11.5208	+	27.8137i	0.454336	+	1.09686i	−0.516321	+	0.856395i	$0.672699\pi$
$644$		0			0
$645$	−6.52068	−	2.70095i	−0.256752	−	0.106350i
$646$		0			0
$647$	10.2546	+	10.2546i	0.403152	+	0.403152i	0.879342	−	0.476190i	$-0.157983\pi$
$647$	10.2546	+	10.2546i	0.403152	+	0.403152i	−0.476190	+	0.879342i	$0.657983\pi$
$648$		0			0
$649$	−8.52504	+	8.52504i	−0.334637	+	0.334637i
$650$		0			0
$651$	−1.34957	+	3.25815i	−0.0528938	+	0.127697i
$652$		0			0
$653$	33.9760	−	14.0733i	1.32958	−	0.550732i	0.399048	−	0.916930i	$-0.369341\pi$
$653$	33.9760	−	14.0733i	1.32958	−	0.550732i	0.930537	+	0.366198i	$0.119341\pi$
$654$		0			0
$655$			4.35044i			0.169986i
$656$		0			0
$657$			6.65017i			0.259448i
$658$		0			0
$659$	−37.0134	+	15.3315i	−1.44184	+	0.597229i	−0.960243	−	0.279164i	$-0.909943\pi$
$659$	−37.0134	+	15.3315i	−1.44184	+	0.597229i	−0.481596	+	0.876393i	$0.659943\pi$
$660$		0			0
$661$	−5.34519	+	12.9044i	−0.207904	+	0.501924i	−0.993093	−	0.117332i	$-0.962566\pi$
$661$	−5.34519	+	12.9044i	−0.207904	+	0.501924i	0.785189	+	0.619256i	$0.212566\pi$
$662$		0			0
$663$	1.59445	−	1.59445i	0.0619234	−	0.0619234i
$664$		0			0
$665$	−4.38641	−	4.38641i	−0.170098	−	0.170098i
$666$		0			0
$667$	24.8814	+	10.3062i	0.963411	+	0.399058i
$668$		0			0
$669$	−2.50773	−	6.05420i	−0.0969545	−	0.234069i
$670$		0			0
$671$	0.112231			0.00433264
$672$		0			0
$673$	22.7067			0.875278			0.437639	−	0.899151i	$-0.355815\pi$
$673$	22.7067			0.875278			0.437639	+	0.899151i	$0.355815\pi$
$674$		0			0
$675$	−0.954942	−	2.30543i	−0.0367557	−	0.0887362i
$676$		0			0
$677$	2.47043	+	1.02328i	0.0949462	+	0.0393280i	0.429651	−	0.902995i	$-0.358637\pi$
$677$	2.47043	+	1.02328i	0.0949462	+	0.0393280i	−0.334705	+	0.942323i	$0.608637\pi$
$678$		0			0
$679$	−37.4373	−	37.4373i	−1.43671	−	1.43671i
$680$		0			0
$681$	13.1871	−	13.1871i	0.505332	−	0.505332i
$682$		0			0
$683$	7.12261	−	17.1955i	0.272539	−	0.657967i	−0.727052	−	0.686583i	$-0.759110\pi$
$683$	7.12261	−	17.1955i	0.272539	−	0.657967i	0.999590	+	0.0286156i	$0.00910988\pi$
$684$		0			0
$685$	−21.7776	+	9.02057i	−0.832079	+	0.344658i
$686$		0			0
$687$		−	21.1241i		−	0.805936i
$688$		0			0
$689$			10.2580i			0.390799i
$690$		0			0
$691$	−27.2224	+	11.2759i	−1.03559	+	0.428956i	−0.834727	−	0.550664i	$-0.814375\pi$
$691$	−27.2224	+	11.2759i	−1.03559	+	0.428956i	−0.200863	+	0.979619i	$0.564375\pi$
$692$		0			0
$693$	−2.36473	+	5.70896i	−0.0898286	+	0.216865i
$694$		0			0
$695$	−12.6966	+	12.6966i	−0.481608	+	0.481608i
$696$		0			0
$697$	0.740533	+	0.740533i	0.0280497	+	0.0280497i
$698$		0			0
$699$	16.1007	+	6.66913i	0.608984	+	0.252250i
$700$		0			0
$701$	10.0320	+	24.2193i	0.378902	+	0.914750i	0.992172	+	0.124877i	$0.0398536\pi$
$701$	10.0320	+	24.2193i	0.378902	+	0.914750i	−0.613271	+	0.789873i	$0.710146\pi$
$702$		0			0
$703$	1.57775			0.0595058
$704$		0			0
$705$	−15.2584			−0.574665
$706$		0			0
$707$	−30.6619	−	74.0244i	−1.15316	−	2.78397i
$708$		0			0
$709$	2.86478	+	1.18663i	0.107589	+	0.0445648i	0.435829	−	0.900030i	$-0.356455\pi$
$709$	2.86478	+	1.18663i	0.107589	+	0.0445648i	−0.328240	+	0.944594i	$0.606455\pi$
$710$		0			0
$711$	2.00610	+	2.00610i	0.0752346	+	0.0752346i
$712$		0			0
$713$	−4.05038	+	4.05038i	−0.151688	+	0.151688i
$714$		0			0
$715$	−4.01152	+	9.68467i	−0.150022	+	0.362186i
$716$		0			0
$717$	9.14466	−	3.78784i	0.341514	−	0.141460i
$718$		0			0
$719$			28.8542i			1.07608i	0.842920	+	0.538040i	$0.180835\pi$
$719$			28.8542i			1.07608i	−0.842920	+	0.538040i	$0.819165\pi$
$720$		0			0
$721$			1.28207i			0.0477469i
$722$		0			0
$723$	−4.14076	+	1.71516i	−0.153997	+	0.0637874i
$724$		0			0
$725$	3.15481	−	7.61639i	0.117167	−	0.282866i
$726$		0			0
$727$	27.0018	−	27.0018i	1.00144	−	1.00144i	0.00144152	−	0.999999i	$-0.499541\pi$
$727$	27.0018	−	27.0018i	1.00144	−	1.00144i	0.999999	−	0.00144152i	$-0.000458852\pi$
$728$		0			0
$729$	0.707107	+	0.707107i	0.0261891	+	0.0261891i
$730$		0			0
$731$	−1.72697	−	0.715333i	−0.0638742	−	0.0264575i
$732$		0			0
$733$	5.85715	+	14.1404i	0.216339	+	0.522288i	0.994373	−	0.105934i	$-0.0337831\pi$
$733$	5.85715	+	14.1404i	0.216339	+	0.522288i	−0.778034	+	0.628222i	$0.783783\pi$
$734$		0			0
$735$	−28.7863			−1.06180
$736$		0			0
$737$	−5.92360			−0.218198
$738$		0			0
$739$	−9.07639	−	21.9124i	−0.333881	−	0.806059i	−0.998277	−	0.0586786i	$-0.981311\pi$
$739$	−9.07639	−	21.9124i	−0.333881	−	0.806059i	0.664396	−	0.747380i	$-0.268689\pi$
$740$		0			0
$741$	−3.88174	−	1.60787i	−0.142599	−	0.0590665i
$742$		0			0
$743$	−8.23952	−	8.23952i	−0.302279	−	0.302279i	0.539626	−	0.841905i	$-0.318566\pi$
$743$	−8.23952	−	8.23952i	−0.302279	−	0.302279i	−0.841905	+	0.539626i	$0.818566\pi$
$744$		0			0
$745$	21.5119	−	21.5119i	0.788136	−	0.788136i
$746$		0			0
$747$	3.37619	−	8.15085i	0.123528	−	0.298224i
$748$		0			0
$749$	−43.2936	+	17.9328i	−1.58191	+	0.655250i
$750$		0			0
$751$			28.2969i			1.03257i	0.856417	+	0.516285i	$0.172685\pi$
$751$			28.2969i			1.03257i	−0.856417	+	0.516285i	$0.827315\pi$
$752$		0			0
$753$		−	5.13441i		−	0.187108i
$754$		0			0
$755$	3.46318	−	1.43450i	0.126038	−	0.0522067i
$756$		0			0
$757$	16.0550	−	38.7601i	0.583527	−	1.40876i	−0.306068	−	0.952010i	$-0.599013\pi$
$757$	16.0550	−	38.7601i	0.583527	−	1.40876i	0.889595	−	0.456750i	$-0.150987\pi$
$758$		0			0
$759$	−7.09710	+	7.09710i	−0.257609	+	0.257609i
$760$		0			0
$761$	−0.792041	−	0.792041i	−0.0287115	−	0.0287115i	0.692605	−	0.721317i	$-0.256463\pi$
$761$	−0.792041	−	0.792041i	−0.0287115	−	0.0287115i	−0.721317	+	0.692605i	$0.756463\pi$
$762$		0			0
$763$	−38.7425	−	16.0477i	−1.40257	−	0.580965i
$764$		0			0
$765$	0.253847	+	0.612841i	0.00917785	+	0.0221573i
$766$		0			0
$767$	−52.6796			−1.90215
$768$		0			0
$769$	17.0970			0.616534			0.308267	−	0.951300i	$-0.400251\pi$
$769$	17.0970			0.616534			0.308267	+	0.951300i	$0.400251\pi$
$770$		0			0
$771$	8.34600	+	20.1490i	0.300574	+	0.725649i
$772$		0			0
$773$	−11.0550	−	4.57913i	−0.397621	−	0.164700i	0.174908	−	0.984585i	$-0.444037\pi$
$773$	−11.0550	−	4.57913i	−0.397621	−	0.164700i	−0.572528	+	0.819885i	$0.694037\pi$
$774$		0			0
$775$	1.23985	+	1.23985i	0.0445368	+	0.0445368i
$776$		0			0
$777$	7.16943	−	7.16943i	0.257202	−	0.257202i
$778$		0			0
$779$	0.746764	−	1.80285i	0.0267556	−	0.0645937i
$780$		0			0
$781$	7.74743	−	3.20909i	0.277225	−	0.114830i
$782$		0			0
$783$			3.30367i			0.118064i
$784$		0			0
$785$			24.3331i			0.868487i
$786$		0			0
$787$	48.0613	−	19.9077i	1.71320	−	0.709631i	0.713239	−	0.700921i	$-0.247227\pi$
$787$	48.0613	−	19.9077i	1.71320	−	0.709631i	0.999962	−	0.00871015i	$-0.00277256\pi$
$788$		0			0
$789$	−6.85266	+	16.5438i	−0.243961	+	0.588974i
$790$		0			0
$791$	45.7109	−	45.7109i	1.62529	−	1.62529i
$792$		0			0
$793$	0.346761	+	0.346761i	0.0123138	+	0.0123138i
$794$		0			0
$795$	−2.78794	−	1.15480i	−0.0988782	−	0.0409567i
$796$		0			0
$797$	2.54297	+	6.13928i	0.0900767	+	0.217464i	0.962497	−	0.271292i	$-0.0874508\pi$
$797$	2.54297	+	6.13928i	0.0900767	+	0.217464i	−0.872420	+	0.488756i	$0.837451\pi$
$798$		0			0
$799$	−4.04110			−0.142964
$800$		0			0
$801$	7.56011			0.267123
$802$		0			0
$803$	−3.13333	−	7.56452i	−0.110573	−	0.266946i
$804$		0			0
$805$	−59.8214	−	24.7788i	−2.10843	−	0.873339i
$806$		0			0
$807$	−8.44613	−	8.44613i	−0.297318	−	0.297318i
$808$		0			0
$809$	10.3014	−	10.3014i	0.362178	−	0.362178i	−0.502436	−	0.864614i	$-0.667563\pi$
$809$	10.3014	−	10.3014i	0.362178	−	0.362178i	0.864614	+	0.502436i	$0.167563\pi$
$810$		0			0
$811$	−20.6691	+	49.8997i	−0.725791	+	1.75221i	−0.0696566	+	0.997571i	$0.522190\pi$
$811$	−20.6691	+	49.8997i	−0.725791	+	1.75221i	−0.656135	+	0.754644i	$0.727810\pi$
$812$		0			0
$813$	−22.9020	+	9.48634i	−0.803210	+	0.332700i
$814$		0			0
$815$		−	0.127644i		−	0.00447117i
$816$		0			0
$817$			3.48299i			0.121854i
$818$		0			0
$819$	−24.9453	+	10.3327i	−0.871659	+	0.361053i
$820$		0			0
$821$	−19.8645	+	47.9571i	−0.693275	+	1.67371i	0.0448018	+	0.998996i	$0.485734\pi$
$821$	−19.8645	+	47.9571i	−0.693275	+	1.67371i	−0.738076	+	0.674717i	$0.764266\pi$
$822$		0			0
$823$	−20.2460	+	20.2460i	−0.705732	+	0.705732i	−0.965635	−	0.259903i	$-0.916310\pi$
$823$	−20.2460	+	20.2460i	−0.705732	+	0.705732i	0.259903	+	0.965635i	$0.416310\pi$
$824$		0			0
$825$	2.17248	+	2.17248i	0.0756361	+	0.0756361i
$826$		0			0
$827$	3.66959	+	1.51999i	0.127604	+	0.0528554i	0.445572	−	0.895246i	$-0.353000\pi$
$827$	3.66959	+	1.51999i	0.127604	+	0.0528554i	−0.317968	+	0.948102i	$0.603000\pi$
$828$		0			0
$829$	−9.44957	−	22.8133i	−0.328197	−	0.792338i	−0.998726	−	0.0504548i	$-0.983933\pi$
$829$	−9.44957	−	22.8133i	−0.328197	−	0.792338i	0.670529	−	0.741883i	$-0.266067\pi$
$830$		0			0
$831$	−1.28103			−0.0444383
$832$		0			0
$833$	−7.62390			−0.264152
$834$		0			0
$835$	3.17572	+	7.66687i	0.109900	+	0.265323i
$836$		0			0
$837$	−0.649177	−	0.268898i	−0.0224388	−	0.00929447i
$838$		0			0
$839$	11.4170	+	11.4170i	0.394157	+	0.394157i	0.876166	−	0.482009i	$-0.160093\pi$
$839$	11.4170	+	11.4170i	0.394157	+	0.394157i	−0.482009	+	0.876166i	$0.660093\pi$
$840$		0			0
$841$	12.7886	−	12.7886i	0.440985	−	0.440985i
$842$		0			0
$843$	6.10102	−	14.7292i	0.210130	−	0.507299i
$844$		0			0
$845$	−23.3094	+	9.65508i	−0.801869	+	0.332145i
$846$		0			0
$847$			47.5997i			1.63555i
$848$		0			0
$849$			21.2643i			0.729790i
$850$		0			0
$851$	15.2149	−	6.30222i	0.521561	−	0.216037i
$852$		0			0
$853$	−19.3307	+	46.6685i	−0.661871	+	1.59790i	0.132997	+	0.991116i	$0.457540\pi$
$853$	−19.3307	+	46.6685i	−0.661871	+	1.59790i	−0.794868	+	0.606782i	$0.792460\pi$
$854$		0			0
$855$	0.873980	−	0.873980i	0.0298895	−	0.0298895i
$856$		0			0
$857$	−24.3711	−	24.3711i	−0.832500	−	0.832500i	0.155358	−	0.987858i	$-0.450347\pi$
$857$	−24.3711	−	24.3711i	−0.832500	−	0.832500i	−0.987858	+	0.155358i	$0.950347\pi$
$858$		0			0
$859$	−17.9730	−	7.44465i	−0.613230	−	0.254008i	0.0543788	−	0.998520i	$-0.482682\pi$
$859$	−17.9730	−	7.44465i	−0.613230	−	0.254008i	−0.667609	+	0.744512i	$0.732682\pi$
$860$		0			0
$861$	−4.79894	−	11.5857i	−0.163547	−	0.394838i
$862$		0			0
$863$	−0.390207			−0.0132828			−0.00664139	−	0.999978i	$-0.502114\pi$
$863$	−0.390207			−0.0132828			−0.00664139	+	0.999978i	$0.502114\pi$
$864$		0			0
$865$	24.8281			0.844180
$866$		0			0
$867$	−6.43839	−	15.5436i	−0.218659	−	0.527890i
$868$		0			0
$869$	−3.22713	−	1.33672i	−0.109473	−	0.0453451i
$870$		0			0
$871$	−18.3021	−	18.3021i	−0.620144	−	0.620144i
$872$		0			0
$873$	7.45927	−	7.45927i	0.252458	−	0.252458i
$874$		0			0
$875$	−22.7831	+	55.0032i	−0.770208	+	1.85945i
$876$		0			0
$877$	28.8582	−	11.9535i	0.974472	−	0.403640i	0.162097	−	0.986775i	$-0.448174\pi$
$877$	28.8582	−	11.9535i	0.974472	−	0.403640i	0.812375	+	0.583135i	$0.198174\pi$
$878$		0			0
$879$			14.0674i			0.474482i
$880$		0			0
$881$			48.5009i			1.63404i	0.576611	+	0.817019i	$0.304375\pi$
$881$			48.5009i			1.63404i	−0.576611	+	0.817019i	$0.695625\pi$
$882$		0			0
$883$	37.6860	−	15.6101i	1.26824	−	0.525320i	0.355808	−	0.934559i	$-0.384206\pi$
$883$	37.6860	−	15.6101i	1.26824	−	0.525320i	0.912427	+	0.409238i	$0.134206\pi$
$884$		0			0
$885$	5.93045	−	14.3174i	0.199350	−	0.481274i
$886$		0			0
$887$	−25.0095	+	25.0095i	−0.839736	+	0.839736i	−0.988824	−	0.149088i	$-0.952366\pi$
$887$	−25.0095	+	25.0095i	−0.839736	+	0.839736i	0.149088	+	0.988824i	$0.452366\pi$
$888$		0			0
$889$	−51.7964	−	51.7964i	−1.73719	−	1.73719i
$890$		0			0
$891$	−1.13749	−	0.471165i	−0.0381075	−	0.0157846i
$892$		0			0
$893$	2.88153	+	6.95664i	0.0964268	+	0.232795i
$894$		0			0
$895$	−36.4830			−1.21949
$896$		0			0
$897$	−43.8559			−1.46430
$898$		0			0
$899$	−0.888350	−	2.14467i	−0.0296281	−	0.0715286i
$900$		0			0
$901$	−0.738372	−	0.305844i	−0.0245987	−	0.0101891i
$902$		0			0
$903$	15.8270	+	15.8270i	0.526691	+	0.526691i
$904$		0			0
$905$	2.46762	−	2.46762i	0.0820264	−	0.0820264i
$906$		0			0
$907$	−9.23765	+	22.3017i	−0.306731	+	0.740514i	0.693076	+	0.720865i	$0.256255\pi$
$907$	−9.23765	+	22.3017i	−0.306731	+	0.740514i	−0.999807	+	0.0196496i	$0.993745\pi$
$908$		0			0
$909$	14.7491	−	6.10929i	0.489198	−	0.202632i
$910$		0			0
$911$		−	38.5220i		−	1.27629i	−0.769915	−	0.638146i	$-0.779702\pi$
$911$		−	38.5220i		−	1.27629i	0.769915	−	0.638146i	$-0.220298\pi$
$912$		0			0
$913$			10.8623i			0.359489i
$914$		0			0
$915$	−0.133280	+	0.0552065i	−0.00440611	+	0.00182507i
$916$		0			0
$917$	5.27971	−	12.7464i	0.174351	−	0.420922i
$918$		0			0
$919$	4.31853	−	4.31853i	0.142455	−	0.142455i	−0.632283	−	0.774738i	$-0.717882\pi$
$919$	4.31853	−	4.31853i	0.142455	−	0.142455i	0.774738	+	0.632283i	$0.217882\pi$
$920$		0			0
$921$	4.16378	+	4.16378i	0.137201	+	0.137201i
$922$		0			0
$923$	33.8524	+	14.0221i	1.11426	+	0.461544i
$924$		0			0
$925$	−1.92916	−	4.65741i	−0.0634304	−	0.153135i
$926$		0			0
$927$	−0.255449			−0.00839006
$928$		0			0
$929$	6.77754			0.222364			0.111182	−	0.993800i	$-0.464536\pi$
$929$	6.77754			0.222364			0.111182	+	0.993800i	$0.464536\pi$
$930$		0			0
$931$	5.43627	+	13.1243i	0.178167	+	0.430132i
$932$		0			0
$933$	15.7161	+	6.50981i	0.514521	+	0.213122i
$934$		0			0
$935$	−0.577498	−	0.577498i	−0.0188862	−	0.0188862i
$936$		0			0
$937$	−39.7932	+	39.7932i	−1.29999	+	1.29999i	−0.371593	+	0.928396i	$0.621188\pi$
$937$	−39.7932	+	39.7932i	−1.29999	+	1.29999i	−0.928396	+	0.371593i	$0.878812\pi$
$938$		0			0
$939$	−9.78979	+	23.6346i	−0.319478	+	0.771287i
$940$		0			0
$941$	−16.5648	+	6.86138i	−0.539998	+	0.223675i	−0.635976	−	0.771709i	$-0.719402\pi$
$941$	−16.5648	+	6.86138i	−0.539998	+	0.223675i	0.0959776	+	0.995383i	$0.469402\pi$
$942$		0			0
$943$		−	20.3686i		−	0.663292i
$944$		0			0
$945$		−	7.94289i		−	0.258382i
$946$		0			0
$947$	−1.69908	+	0.703781i	−0.0552126	+	0.0228698i	−0.410119	−	0.912032i	$-0.634513\pi$
$947$	−1.69908	+	0.703781i	−0.0552126	+	0.0228698i	0.354906	+	0.934902i	$0.384513\pi$
$948$		0			0
$949$	13.6911	−	33.0532i	0.444431	−	1.07295i
$950$		0			0
$951$	11.6415	−	11.6415i	0.377502	−	0.377502i
$952$		0			0
$953$	14.7617	+	14.7617i	0.478177	+	0.478177i	0.904548	−	0.426371i	$-0.140208\pi$
$953$	14.7617	+	14.7617i	0.478177	+	0.478177i	−0.426371	+	0.904548i	$0.640208\pi$
$954$		0			0
$955$	−15.3908	−	6.37508i	−0.498035	−	0.206293i
$956$		0			0
$957$	−1.55657	−	3.75790i	−0.0503169	−	0.121476i
$958$		0			0
$959$	74.7535			2.41392
$960$		0			0
$961$	−30.5063			−0.984073
$962$		0			0
$963$	−3.57306	−	8.62613i	−0.115140	−	0.277973i
$964$		0			0
$965$	21.0554	+	8.72143i	0.677797	+	0.280753i
$966$		0			0
$967$	31.0181	+	31.0181i	0.997474	+	0.997474i	0.999997	−	0.00252299i	$-0.000803093\pi$
$967$	31.0181	+	31.0181i	0.997474	+	0.997474i	−0.00252299	+	0.999997i	$0.500803\pi$
$968$		0			0
$969$	0.231469	−	0.231469i	0.00743585	−	0.00743585i
$970$		0			0
$971$	15.9371	−	38.4755i	0.511444	−	1.23474i	−0.431599	−	0.902066i	$-0.642050\pi$
$971$	15.9371	−	38.4755i	0.511444	−	1.23474i	0.943043	−	0.332670i	$-0.107950\pi$
$972$		0			0
$973$	52.6083	−	21.7911i	1.68654	−	0.698589i
$974$		0			0
$975$			13.4246i			0.429932i
$976$		0			0
$977$		−	55.3040i		−	1.76933i	−0.466225	−	0.884666i	$-0.654386\pi$
$977$		−	55.3040i		−	1.76933i	0.466225	−	0.884666i	$-0.345614\pi$
$978$		0			0
$979$	−8.59957	+	3.56206i	−0.274843	+	0.113844i
$980$		0			0
$981$	3.19745	−	7.71934i	0.102087	−	0.246459i
$982$		0			0
$983$	25.0055	−	25.0055i	0.797553	−	0.797553i	−0.185156	−	0.982709i	$-0.559279\pi$
$983$	25.0055	−	25.0055i	0.797553	−	0.797553i	0.982709	+	0.185156i	$0.0592791\pi$
$984$		0			0
$985$	−18.4832	−	18.4832i	−0.588923	−	0.588923i
$986$		0			0
$987$	44.7056	+	18.5177i	1.42299	+	0.589423i
$988$		0			0
$989$	13.9126	+	33.5881i	0.442396	+	1.06804i
$990$		0			0
$991$	−59.9489			−1.90434			−0.952169	−	0.305572i	$-0.901152\pi$
$991$	−59.9489			−1.90434			−0.952169	+	0.305572i	$0.901152\pi$
$992$		0			0
$993$	9.35032			0.296723
$994$		0			0
$995$	3.78985	+	9.14952i	0.120146	+	0.290059i
$996$		0			0
$997$	−32.0316	−	13.2679i	−1.01445	−	0.420199i	−0.187374	−	0.982289i	$-0.559998\pi$
$997$	−32.0316	−	13.2679i	−1.01445	−	0.420199i	−0.827076	+	0.562090i	$0.809998\pi$
$998$		0			0
$999$	1.42849	+	1.42849i	0.0451954	+	0.0451954i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.n.a.241.1		32
3.2	odd	2		1152.2.v.c.1009.6		32
4.3	odd	2		96.2.n.a.37.7	yes	32
8.3	odd	2		768.2.n.a.481.4		32
8.5	even	2		768.2.n.b.481.8		32
12.11	even	2		288.2.v.d.37.2		32
32.3	odd	8		768.2.n.a.289.4		32
32.13	even	8	inner	384.2.n.a.145.1		32
32.19	odd	8		96.2.n.a.13.7	✓	32
32.29	even	8		768.2.n.b.289.8		32
96.77	odd	8		1152.2.v.c.145.6		32
96.83	even	8		288.2.v.d.109.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
96.2.n.a.13.7	✓	32	32.19	odd	8
96.2.n.a.37.7	yes	32	4.3	odd	2
288.2.v.d.37.2		32	12.11	even	2
288.2.v.d.109.2		32	96.83	even	8
384.2.n.a.145.1		32	32.13	even	8	inner
384.2.n.a.241.1		32	1.1	even	1	trivial
768.2.n.a.289.4		32	32.3	odd	8
768.2.n.a.481.4		32	8.3	odd	2
768.2.n.b.289.8		32	32.29	even	8
768.2.n.b.481.8		32	8.5	even	2
1152.2.v.c.145.6		32	96.77	odd	8
1152.2.v.c.1009.6		32	3.2	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:	\( N \)	\(=\)	\( 384 = 2^{7} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	384.n (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.382683 - 0.923880i) q^{3} +(-1.46213 - 0.605634i) q^{5} +(3.54889 + 3.54889i) q^{7} +(-0.707107 + 0.707107i) q^{9} +O(q^{10})\)	\(q+(-0.382683 - 0.923880i) q^{3} +(-1.46213 - 0.605634i) q^{5} +(3.54889 + 3.54889i) q^{7} +(-0.707107 + 0.707107i) q^{9} +(0.471165 - 1.13749i) q^{11} +(4.97028 - 2.05876i) q^{13} +1.58260i q^{15} +0.419142i q^{17} +(0.721541 - 0.298872i) q^{19} +(1.92065 - 4.63685i) q^{21} +(5.76431 - 5.76431i) q^{23} +(-1.76450 - 1.76450i) q^{25} +(0.923880 + 0.382683i) q^{27} +(1.26426 + 3.05219i) q^{29} -0.702664 q^{31} -1.23121 q^{33} +(-3.03961 - 7.33827i) q^{35} +(1.86641 + 0.773092i) q^{37} +(-3.80408 - 3.80408i) q^{39} +(1.76678 - 1.76678i) q^{41} +(-1.70666 + 4.12024i) q^{43} +(1.46213 - 0.605634i) q^{45} +9.64136i q^{47} +18.1893i q^{49} +(0.387237 - 0.160399i) q^{51} +(-0.729689 + 1.76163i) q^{53} +(-1.37781 + 1.37781i) q^{55} +(-0.552244 - 0.552244i) q^{57} +(-9.04676 - 3.74729i) q^{59} +(0.0348835 + 0.0842161i) q^{61} -5.01889 q^{63} -8.51404 q^{65} +(-1.84116 - 4.44495i) q^{67} +(-7.53144 - 3.11962i) q^{69} +(4.81608 + 4.81608i) q^{71} +(4.70238 - 4.70238i) q^{73} +(-0.954942 + 2.30543i) q^{75} +(5.70896 - 2.36473i) q^{77} -2.83705i q^{79} -1.00000i q^{81} +(-8.15085 + 3.37619i) q^{83} +(0.253847 - 0.612841i) q^{85} +(2.33605 - 2.33605i) q^{87} +(-5.34580 - 5.34580i) q^{89} +(24.9453 + 10.3327i) q^{91} +(0.268898 + 0.649177i) q^{93} -1.23599 q^{95} -10.5490 q^{97} +(0.471165 + 1.13749i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q + 16 q^{23} + 48 q^{31} + 48 q^{35} + 16 q^{43} - 16 q^{51} - 32 q^{53} - 32 q^{55} - 64 q^{59} - 32 q^{61} - 16 q^{63} - 16 q^{67} - 32 q^{69} - 64 q^{71} - 32 q^{75} - 32 q^{77} + 48 q^{91}+O(q^{100}) \) 32 * q + 16 * q^23 + 48 * q^31 + 48 * q^35 + 16 * q^43 - 16 * q^51 - 32 * q^53 - 32 * q^55 - 64 * q^59 - 32 * q^61 - 16 * q^63 - 16 * q^67 - 32 * q^69 - 64 * q^71 - 32 * q^75 - 32 * q^77 + 48 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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