LMFDB - Embedded newform 572.2.p.a.485.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(309,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 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("572.309");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.p (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:	$4.56744299562$
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			485.1
Character	$\chi$	$=$	572.485
Dual form			572.2.p.a.309.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.63981 + 2.84024i) q^{3} -0.829371i q^{5} +(0.846479 - 0.488715i) q^{7} +(-3.87798 - 6.71686i) q^{9} +O(q^{10})$	\(q+(-1.63981 + 2.84024i) q^{3} -0.829371i q^{5} +(0.846479 - 0.488715i) q^{7} +(-3.87798 - 6.71686i) q^{9} +(-0.866025 - 0.500000i) q^{11} +(-3.45912 - 1.01710i) q^{13} +(2.35561 + 1.36001i) q^{15} +(-3.15739 - 5.46876i) q^{17} +(-4.34888 + 2.51083i) q^{19} +3.20561i q^{21} +(1.02646 - 1.77787i) q^{23} +4.31214 q^{25} +15.5978 q^{27} +(1.13645 - 1.96840i) q^{29} -5.42545i q^{31} +(2.84024 - 1.63981i) q^{33} +(-0.405326 - 0.702045i) q^{35} +(-7.63322 - 4.40704i) q^{37} +(8.56112 - 8.15689i) q^{39} +(9.81305 + 5.66557i) q^{41} +(2.21697 + 3.83991i) q^{43} +(-5.57077 + 3.21629i) q^{45} -3.90757i q^{47} +(-3.02232 + 5.23480i) q^{49} +20.7102 q^{51} -9.52011 q^{53} +(-0.414685 + 0.718256i) q^{55} -16.4692i q^{57} +(-0.137643 + 0.0794680i) q^{59} +(-2.64132 - 4.57490i) q^{61} +(-6.56526 - 3.79046i) q^{63} +(-0.843550 + 2.86889i) q^{65} +(-7.71908 - 4.45661i) q^{67} +(3.36640 + 5.83077i) q^{69} +(6.21829 - 3.59013i) q^{71} -1.90626i q^{73} +(-7.07112 + 12.2475i) q^{75} -0.977430 q^{77} -0.910363 q^{79} +(-13.9436 + 24.1510i) q^{81} +7.90962i q^{83} +(-4.53563 + 2.61865i) q^{85} +(3.72715 + 6.45561i) q^{87} +(-9.13322 - 5.27307i) q^{89} +(-3.42514 + 0.829573i) q^{91} +(15.4096 + 8.89673i) q^{93} +(2.08241 + 3.60683i) q^{95} +(-7.21545 + 4.16584i) q^{97} +7.75597i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{3} + 6 q^{7} - 14 q^{9}+O(q^{10}) $ 24 * q - 2 * q^3 + 6 * q^7 - 14 * q^9	$ 24 q - 2 q^{3} + 6 q^{7} - 14 q^{9} - 2 q^{13} - 6 q^{19} + 10 q^{23} - 40 q^{25} - 8 q^{27} - 8 q^{29} + 8 q^{35} + 18 q^{37} + 36 q^{41} + 10 q^{43} - 30 q^{45} + 14 q^{49} + 44 q^{51} + 16 q^{53} - 24 q^{59} + 6 q^{61} - 6 q^{63} - 24 q^{65} - 54 q^{67} + 10 q^{69} + 18 q^{71} + 6 q^{75} - 16 q^{77} - 32 q^{79} - 4 q^{81} + 52 q^{87} - 18 q^{89} - 18 q^{91} + 30 q^{93} - 12 q^{95} + 42 q^{97}+O(q^{100}) $ 24 * q - 2 * q^3 + 6 * q^7 - 14 * q^9 - 2 * q^13 - 6 * q^19 + 10 * q^23 - 40 * q^25 - 8 * q^27 - 8 * q^29 + 8 * q^35 + 18 * q^37 + 36 * q^41 + 10 * q^43 - 30 * q^45 + 14 * q^49 + 44 * q^51 + 16 * q^53 - 24 * q^59 + 6 * q^61 - 6 * q^63 - 24 * q^65 - 54 * q^67 + 10 * q^69 + 18 * q^71 + 6 * q^75 - 16 * q^77 - 32 * q^79 - 4 * q^81 + 52 * q^87 - 18 * q^89 - 18 * q^91 + 30 * q^93 - 12 * q^95 + 42 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$1$

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
$3$	−1.63981	+	2.84024i	−0.946747	+	1.63981i	−0.194533	+	0.980896i	$0.562319\pi$
$3$	−1.63981	+	2.84024i	−0.946747	+	1.63981i	−0.752214	+	0.658919i	$0.771014\pi$
$4$		0			0
$5$		−	0.829371i		−	0.370906i	−0.982653	−	0.185453i	$-0.940625\pi$
$5$		−	0.829371i		−	0.370906i	0.982653	−	0.185453i	$-0.0593752\pi$
$6$		0			0
$7$	0.846479	−	0.488715i	0.319939	−	0.184717i	−0.331426	−	0.943481i	$-0.607530\pi$
$7$	0.846479	−	0.488715i	0.319939	−	0.184717i	0.651365	+	0.758764i	$0.274197\pi$
$8$		0			0
$9$	−3.87798	−	6.71686i	−1.29266	−	2.23895i
$10$		0			0
$11$	−0.866025	−	0.500000i	−0.261116	−	0.150756i
$11$	−0.866025	−	0.500000i	−0.261116	−	0.150756i
$12$		0			0
$13$	−3.45912	−	1.01710i	−0.959387	−	0.282092i
$13$	−3.45912	−	1.01710i	−0.959387	−	0.282092i
$14$		0			0
$15$	2.35561	+	1.36001i	0.608217	+	0.351154i
$16$		0			0
$17$	−3.15739	−	5.46876i	−0.765780	−	1.32637i	−0.939833	−	0.341634i	$-0.889020\pi$
$17$	−3.15739	−	5.46876i	−0.765780	−	1.32637i	0.174053	−	0.984736i	$-0.444314\pi$
$18$		0			0
$19$	−4.34888	+	2.51083i	−0.997701	+	0.576023i	−0.907567	−	0.419906i	$-0.862063\pi$
$19$	−4.34888	+	2.51083i	−0.997701	+	0.576023i	−0.0901340	+	0.995930i	$0.528730\pi$
$20$		0			0
$21$			3.20561i			0.699521i
$22$		0			0
$23$	1.02646	−	1.77787i	0.214031	−	0.370712i	−0.738941	−	0.673770i	$-0.764674\pi$
$23$	1.02646	−	1.77787i	0.214031	−	0.370712i	0.952972	+	0.303057i	$0.0980073\pi$
$24$		0			0
$25$	4.31214			0.862429
$26$		0			0
$27$	15.5978			3.00180
$28$		0			0
$29$	1.13645	−	1.96840i	0.211034	−	0.365522i	−0.741004	−	0.671500i	$-0.765650\pi$
$29$	1.13645	−	1.96840i	0.211034	−	0.365522i	0.952039	+	0.305978i	$0.0989835\pi$
$30$		0			0
$31$		−	5.42545i		−	0.974440i	−0.873279	−	0.487220i	$-0.838011\pi$
$31$		−	5.42545i		−	0.974440i	0.873279	−	0.487220i	$-0.161989\pi$
$32$		0			0
$33$	2.84024	−	1.63981i	0.494423	−	0.285455i
$34$		0			0
$35$	−0.405326	−	0.702045i	−0.0685125	−	0.118667i
$36$		0			0
$37$	−7.63322	−	4.40704i	−1.25489	−	0.724513i	−0.282816	−	0.959174i	$-0.591269\pi$
$37$	−7.63322	−	4.40704i	−1.25489	−	0.724513i	−0.972077	+	0.234661i	$0.924602\pi$
$38$		0			0
$39$	8.56112	−	8.15689i	1.37088	−	1.30615i
$40$		0			0
$41$	9.81305	+	5.66557i	1.53254	+	0.884813i	0.999244	+	0.0388852i	$0.0123807\pi$
$41$	9.81305	+	5.66557i	1.53254	+	0.884813i	0.533297	+	0.845928i	$0.320953\pi$
$42$		0			0
$43$	2.21697	+	3.83991i	0.338085	+	0.585580i	0.984072	−	0.177768i	$-0.0568876\pi$
$43$	2.21697	+	3.83991i	0.338085	+	0.585580i	−0.645988	+	0.763348i	$0.723554\pi$
$44$		0			0
$45$	−5.57077	+	3.21629i	−0.830441	+	0.479456i
$46$		0			0
$47$		−	3.90757i		−	0.569978i	−0.958531	−	0.284989i	$-0.908010\pi$
$47$		−	3.90757i		−	0.569978i	0.958531	−	0.284989i	$-0.0919899\pi$
$48$		0			0
$49$	−3.02232	+	5.23480i	−0.431759	+	0.747829i
$50$		0			0
$51$	20.7102			2.90000
$52$		0			0
$53$	−9.52011			−1.30769			−0.653844	−	0.756630i	$-0.726845\pi$
$53$	−9.52011			−1.30769			−0.653844	+	0.756630i	$0.726845\pi$
$54$		0			0
$55$	−0.414685	+	0.718256i	−0.0559162	+	0.0968496i
$56$		0			0
$57$		−	16.4692i		−	2.18139i
$58$		0			0
$59$	−0.137643	+	0.0794680i	−0.0179195	+	0.0103458i	−0.508933	−	0.860806i	$-0.669960\pi$
$59$	−0.137643	+	0.0794680i	−0.0179195	+	0.0103458i	0.491013	+	0.871152i	$0.336627\pi$
$60$		0			0
$61$	−2.64132	−	4.57490i	−0.338186	−	0.585756i	0.645905	−	0.763418i	$-0.276480\pi$
$61$	−2.64132	−	4.57490i	−0.338186	−	0.585756i	−0.984092	+	0.177662i	$0.943147\pi$
$62$		0			0
$63$	−6.56526	−	3.79046i	−0.827145	−	0.477553i
$64$		0			0
$65$	−0.843550	+	2.86889i	−0.104630	+	0.355842i
$66$		0			0
$67$	−7.71908	−	4.45661i	−0.943035	−	0.544462i	−0.0521247	−	0.998641i	$-0.516599\pi$
$67$	−7.71908	−	4.45661i	−0.943035	−	0.544462i	−0.890910	+	0.454179i	$0.849933\pi$
$68$		0			0
$69$	3.36640	+	5.83077i	0.405266	+	0.701942i
$70$		0			0
$71$	6.21829	−	3.59013i	0.737976	−	0.426070i	−0.0833572	−	0.996520i	$-0.526564\pi$
$71$	6.21829	−	3.59013i	0.737976	−	0.426070i	0.821333	+	0.570449i	$0.193231\pi$
$72$		0			0
$73$		−	1.90626i		−	0.223110i	−0.993758	−	0.111555i	$-0.964417\pi$
$73$		−	1.90626i		−	0.223110i	0.993758	−	0.111555i	$-0.0355832\pi$
$74$		0			0
$75$	−7.07112	+	12.2475i	−0.816502	+	1.41422i
$76$		0			0
$77$	−0.977430			−0.111388
$78$		0			0
$79$	−0.910363			−0.102424			−0.0512119	−	0.998688i	$-0.516308\pi$
$79$	−0.910363			−0.102424			−0.0512119	+	0.998688i	$0.516308\pi$
$80$		0			0
$81$	−13.9436	+	24.1510i	−1.54928	+	2.68344i
$82$		0			0
$83$			7.90962i			0.868193i	0.900866	+	0.434097i	$0.142932\pi$
$83$			7.90962i			0.868193i	−0.900866	+	0.434097i	$0.857068\pi$
$84$		0			0
$85$	−4.53563	+	2.61865i	−0.491958	+	0.284032i
$86$		0			0
$87$	3.72715	+	6.45561i	0.399592	+	0.692114i
$88$		0			0
$89$	−9.13322	−	5.27307i	−0.968119	−	0.558944i	−0.0694568	−	0.997585i	$-0.522127\pi$
$89$	−9.13322	−	5.27307i	−0.968119	−	0.558944i	−0.898662	+	0.438641i	$0.855460\pi$
$90$		0			0
$91$	−3.42514	+	0.829573i	−0.359052	+	0.0869628i
$92$		0			0
$93$	15.4096	+	8.89673i	1.59790	+	0.922548i
$94$		0			0
$95$	2.08241	+	3.60683i	0.213650	+	0.370053i
$96$		0			0
$97$	−7.21545	+	4.16584i	−0.732617	+	0.422977i	−0.819379	−	0.573252i	$-0.805682\pi$
$97$	−7.21545	+	4.16584i	−0.732617	+	0.422977i	0.0867615	+	0.996229i	$0.472348\pi$
$98$		0			0
$99$			7.75597i			0.779504i
$100$		0			0
$101$	−3.83825	+	6.64805i	−0.381920	+	0.661506i	−0.991337	−	0.131345i	$-0.958070\pi$
$101$	−3.83825	+	6.64805i	−0.381920	+	0.661506i	0.609416	+	0.792850i	$0.291404\pi$
$102$		0			0
$103$	−18.4320			−1.81616			−0.908079	−	0.418799i	$-0.862451\pi$
$103$	−18.4320			−1.81616			−0.908079	+	0.418799i	$0.862451\pi$
$104$		0			0
$105$	2.65864			0.259456
$106$		0			0
$107$	2.77623	−	4.80857i	0.268388	−	0.464862i	−0.700058	−	0.714086i	$-0.746842\pi$
$107$	2.77623	−	4.80857i	0.268388	−	0.464862i	0.968446	+	0.249224i	$0.0801757\pi$
$108$		0			0
$109$		−	12.6617i		−	1.21278i	−0.795169	−	0.606388i	$-0.792618\pi$
$109$		−	12.6617i		−	1.21278i	0.795169	−	0.606388i	$-0.207382\pi$
$110$		0			0
$111$	25.0341	−	14.4535i	2.37613	−	1.37186i
$112$		0			0
$113$	−7.59366	−	13.1526i	−0.714351	−	1.23729i	−0.963209	−	0.268753i	$-0.913389\pi$
$113$	−7.59366	−	13.1526i	−0.714351	−	1.23729i	0.248858	−	0.968540i	$-0.419945\pi$
$114$		0			0
$115$	−1.47452	−	0.851313i	−0.137499	−	0.0793853i
$116$		0			0
$117$	6.58271	+	27.1787i	0.608572	+	2.51267i
$118$		0			0
$119$	−5.34533	−	3.08613i	−0.490006	−	0.282905i
$120$		0			0
$121$	0.500000	+	0.866025i	0.0454545	+	0.0787296i
$122$		0			0
$123$	−32.1832	+	18.5810i	−2.90186	+	1.67539i
$124$		0			0
$125$		−	7.72322i		−	0.690786i
$126$		0			0
$127$	−10.4870	+	18.1640i	−0.930570	+	1.61179i	−0.148220	+	0.988954i	$0.547354\pi$
$127$	−10.4870	+	18.1640i	−0.930570	+	1.61179i	−0.782350	+	0.622839i	$0.785979\pi$
$128$		0			0
$129$	−14.5417			−1.28032
$130$		0			0
$131$	−0.690951			−0.0603687			−0.0301843	−	0.999544i	$-0.509609\pi$
$131$	−0.690951			−0.0603687			−0.0301843	+	0.999544i	$0.509609\pi$
$132$		0			0
$133$	−2.45416	+	4.25072i	−0.212802	+	0.368584i
$134$		0			0
$135$		−	12.9364i		−	1.11338i
$136$		0			0
$137$	10.9658	−	6.33111i	0.936873	−	0.540904i	0.0478940	−	0.998852i	$-0.484749\pi$
$137$	10.9658	−	6.33111i	0.936873	−	0.540904i	0.888979	+	0.457949i	$0.151416\pi$
$138$		0			0
$139$	2.23357	+	3.86865i	0.189449	+	0.328135i	0.945067	−	0.326878i	$-0.105997\pi$
$139$	2.23357	+	3.86865i	0.189449	+	0.328135i	−0.755618	+	0.655013i	$0.772663\pi$
$140$		0			0
$141$	11.0984	+	6.40769i	0.934657	+	0.539625i
$142$		0			0
$143$	2.48714	+	2.61039i	0.207985	+	0.218292i
$144$		0			0
$145$	−1.63253	−	0.942542i	−0.135574	−	0.0782739i
$146$		0			0
$147$	−9.91207	−	17.1682i	−0.817534	−	1.41601i
$148$		0			0
$149$	17.7537	−	10.2501i	1.45444	−	0.839723i	0.455714	−	0.890126i	$-0.349384\pi$
$149$	17.7537	−	10.2501i	1.45444	−	0.839723i	0.998729	+	0.0504031i	$0.0160506\pi$
$150$		0			0
$151$		−	4.34306i		−	0.353433i	−0.984262	−	0.176716i	$-0.943452\pi$
$151$		−	4.34306i		−	0.353433i	0.984262	−	0.176716i	$-0.0565476\pi$
$152$		0			0
$153$	−24.4886	+	42.4156i	−1.97979	+	3.42909i
$154$		0			0
$155$	−4.49971			−0.361425
$156$		0			0
$157$	14.9973			1.19691			0.598457	−	0.801155i	$-0.295781\pi$
$157$	14.9973			1.19691			0.598457	+	0.801155i	$0.295781\pi$
$158$		0			0
$159$	15.6112	−	27.0394i	1.23805	−	2.14436i
$160$		0			0
$161$		−	2.00658i		−	0.158140i
$162$		0			0
$163$	2.67981	−	1.54719i	0.209899	−	0.121185i	−0.391366	−	0.920235i	$-0.627997\pi$
$163$	2.67981	−	1.54719i	0.209899	−	0.121185i	0.601264	+	0.799050i	$0.294664\pi$
$164$		0			0
$165$	−1.36001	−	2.35561i	−0.105877	−	0.183384i
$166$		0			0
$167$	10.8054	+	6.23851i	0.836148	+	0.482750i	0.855953	−	0.517053i	$-0.172971\pi$
$167$	10.8054	+	6.23851i	0.836148	+	0.482750i	−0.0198048	+	0.999804i	$0.506304\pi$
$168$		0			0
$169$	10.9310	+	7.03652i	0.840848	+	0.541271i
$170$		0			0
$171$	33.7298	+	19.4739i	2.57938	+	1.48921i
$172$		0			0
$173$	2.06635	+	3.57902i	0.157102	+	0.272108i	0.933822	−	0.357737i	$-0.116452\pi$
$173$	2.06635	+	3.57902i	0.157102	+	0.272108i	−0.776721	+	0.629845i	$0.783118\pi$
$174$		0			0
$175$	3.65014	−	2.10741i	0.275925	−	0.159305i
$176$		0			0
$177$		−	0.521251i		−	0.0391796i
$178$		0			0
$179$	0.0382804	−	0.0663035i	0.00286121	−	0.00495576i	−0.864591	−	0.502476i	$-0.832423\pi$
$179$	0.0382804	−	0.0663035i	0.00286121	−	0.00495576i	0.867452	+	0.497520i	$0.165756\pi$
$180$		0			0
$181$	−6.74860			−0.501619			−0.250810	−	0.968036i	$-0.580697\pi$
$181$	−6.74860			−0.501619			−0.250810	+	0.968036i	$0.580697\pi$
$182$		0			0
$183$	17.3251			1.28071
$184$		0			0
$185$	−3.65507	+	6.33077i	−0.268726	+	0.465447i
$186$		0			0
$187$			6.31478i			0.461783i
$188$		0			0
$189$	13.2032	−	7.62288i	0.960393	−	0.554483i
$190$		0			0
$191$	−5.46568	−	9.46684i	−0.395483	−	0.684997i	0.597680	−	0.801735i	$-0.296089\pi$
$191$	−5.46568	−	9.46684i	−0.395483	−	0.684997i	−0.993163	+	0.116738i	$0.962756\pi$
$192$		0			0
$193$	−5.80047	−	3.34890i	−0.417527	−	0.241059i	0.276492	−	0.961016i	$-0.410828\pi$
$193$	−5.80047	−	3.34890i	−0.417527	−	0.241059i	−0.694019	+	0.719957i	$0.744162\pi$
$194$		0			0
$195$	−6.76508	−	7.10034i	−0.484458	−	0.508466i
$196$		0			0
$197$	−2.32093	−	1.33999i	−0.165359	−	0.0954703i	0.415036	−	0.909805i	$-0.363769\pi$
$197$	−2.32093	−	1.33999i	−0.165359	−	0.0954703i	−0.580396	+	0.814334i	$0.697102\pi$
$198$		0			0
$199$	8.22561	+	14.2472i	0.583098	+	1.00996i	0.995110	+	0.0987766i	$0.0314929\pi$
$199$	8.22561	+	14.2472i	0.583098	+	1.00996i	−0.412012	+	0.911179i	$0.635174\pi$
$200$		0			0
$201$	25.3157	−	14.6160i	1.78563	−	1.03094i
$202$		0			0
$203$		−	2.22161i		−	0.155926i
$204$		0			0
$205$	4.69885	−	8.13866i	0.328182	−	0.568428i
$206$		0			0
$207$	−15.9223			−1.10668
$208$		0			0
$209$	5.02165			0.347355
$210$		0			0
$211$	4.44712	−	7.70264i	0.306152	−	0.530271i	−0.671365	−	0.741127i	$-0.734292\pi$
$211$	4.44712	−	7.70264i	0.306152	−	0.530271i	0.977517	+	0.210856i	$0.0676250\pi$
$212$		0			0
$213$			23.5486i			1.61352i
$214$		0			0
$215$	3.18470	−	1.83869i	0.217195	−	0.125398i
$216$		0			0
$217$	−2.65150	−	4.59253i	−0.179995	−	0.311761i
$218$		0			0
$219$	5.41423	+	3.12591i	0.365860	+	0.211229i
$220$		0			0
$221$	5.35954	+	22.1285i	0.360522	+	1.48852i
$222$		0			0
$223$	−25.5459	−	14.7489i	−1.71068	−	0.987660i	−0.933646	−	0.358197i	$-0.883392\pi$
$223$	−25.5459	−	14.7489i	−1.71068	−	0.987660i	−0.777031	−	0.629462i	$-0.783275\pi$
$224$		0			0
$225$	−16.7224	−	28.9641i	−1.11483	−	1.93094i
$226$		0			0
$227$	−21.3668	+	12.3361i	−1.41816	+	0.818777i	−0.996137	−	0.0878074i	$-0.972014\pi$
$227$	−21.3668	+	12.3361i	−1.41816	+	0.818777i	−0.422025	+	0.906584i	$0.638681\pi$
$228$		0			0
$229$		−	8.82971i		−	0.583484i	−0.956497	−	0.291742i	$-0.905765\pi$
$229$		−	8.82971i		−	0.583484i	0.956497	−	0.291742i	$-0.0942348\pi$
$230$		0			0
$231$	1.60280	−	2.77614i	0.105457	−	0.182656i
$232$		0			0
$233$	20.6355			1.35188			0.675939	−	0.736958i	$-0.263738\pi$
$233$	20.6355			1.35188			0.675939	+	0.736958i	$0.263738\pi$
$234$		0			0
$235$	−3.24082			−0.211408
$236$		0			0
$237$	1.49283	−	2.58565i	0.0969695	−	0.167956i
$238$		0			0
$239$			12.5043i			0.808835i	0.914574	+	0.404418i	$0.132526\pi$
$239$			12.5043i			0.808835i	−0.914574	+	0.404418i	$0.867474\pi$
$240$		0			0
$241$	−11.2767	+	6.51061i	−0.726397	+	0.419385i	−0.817103	−	0.576492i	$-0.804421\pi$
$241$	−11.2767	+	6.51061i	−0.726397	+	0.419385i	0.0907057	+	0.995878i	$0.471088\pi$
$242$		0			0
$243$	−22.3330	−	38.6819i	−1.43266	−	2.48144i
$244$		0			0
$245$	4.34159	+	2.50662i	0.277374	+	0.160142i
$246$		0			0
$247$	17.5971	−	4.26202i	1.11967	−	0.271186i
$248$		0			0
$249$	−22.4652	−	12.9703i	−1.42368	−	0.821960i
$250$		0			0
$251$	2.61446	+	4.52837i	0.165023	+	0.285828i	0.936663	−	0.350231i	$-0.113897\pi$
$251$	2.61446	+	4.52837i	0.165023	+	0.285828i	−0.771640	+	0.636059i	$0.780564\pi$
$252$		0			0
$253$	−1.77787	+	1.02646i	−0.111774	+	0.0645328i
$254$		0			0
$255$		−	17.1764i		−	1.07563i
$256$		0			0
$257$	1.49262	−	2.58529i	0.0931069	−	0.161266i	−0.815710	−	0.578461i	$-0.803653\pi$
$257$	1.49262	−	2.58529i	0.0931069	−	0.161266i	0.908817	+	0.417195i	$0.136987\pi$
$258$		0			0
$259$	−8.61514			−0.535319
$260$		0			0
$261$	−17.6286			−1.09118
$262$		0			0
$263$	5.87389	−	10.1739i	0.362200	−	0.627348i	−0.626123	−	0.779724i	$-0.715359\pi$
$263$	5.87389	−	10.1739i	0.362200	−	0.627348i	0.988323	+	0.152376i	$0.0486925\pi$
$264$		0			0
$265$			7.89570i			0.485029i
$266$		0			0
$267$	29.9536	−	17.2937i	1.83313	−	1.05836i
$268$		0			0
$269$	15.4585	+	26.7749i	0.942522	+	1.63250i	0.760637	+	0.649177i	$0.224887\pi$
$269$	15.4585	+	26.7749i	0.942522	+	1.63250i	0.181885	+	0.983320i	$0.441780\pi$
$270$		0			0
$271$	−12.4126	−	7.16643i	−0.754013	−	0.435329i	0.0731292	−	0.997322i	$-0.476701\pi$
$271$	−12.4126	−	7.16643i	−0.754013	−	0.435329i	−0.827142	+	0.561993i	$0.810035\pi$
$272$		0			0
$273$	3.26041	−	11.0886i	0.197329	−	0.671111i
$274$		0			0
$275$	−3.73443	−	2.15607i	−0.225194	−	0.130016i
$276$		0			0
$277$	−4.87125	−	8.43724i	−0.292685	−	0.506945i	0.681759	−	0.731577i	$-0.261215\pi$
$277$	−4.87125	−	8.43724i	−0.292685	−	0.506945i	−0.974444	+	0.224632i	$0.927882\pi$
$278$		0			0
$279$	−36.4420	+	21.0398i	−2.18173	+	1.25962i
$280$		0			0
$281$		−	23.2777i		−	1.38863i	−0.719669	−	0.694317i	$-0.755707\pi$
$281$		−	23.2777i		−	1.38863i	0.719669	−	0.694317i	$-0.244293\pi$
$282$		0			0
$283$	−12.3243	+	21.3463i	−0.732604	+	1.26891i	0.223163	+	0.974781i	$0.428362\pi$
$283$	−12.3243	+	21.3463i	−0.732604	+	1.26891i	−0.955767	+	0.294126i	$0.904972\pi$
$284$		0			0
$285$	−13.6590			−0.809092
$286$		0			0
$287$	11.0754			0.653759
$288$		0			0
$289$	−11.4383	+	19.8116i	−0.672838	+	1.16539i
$290$		0			0
$291$		−	27.3248i		−	1.60181i
$292$		0			0
$293$	1.45095	−	0.837709i	0.0847657	−	0.0489395i	−0.457018	−	0.889457i	$-0.651083\pi$
$293$	1.45095	−	0.837709i	0.0847657	−	0.0489395i	0.541784	+	0.840518i	$0.317749\pi$
$294$		0			0
$295$	0.0659084	+	0.114157i	0.00383733	+	0.00664646i
$296$		0			0
$297$	−13.5081	−	7.79890i	−0.783819	−	0.452538i
$298$		0			0
$299$	−5.35891	+	5.10588i	−0.309914	+	0.295280i
$300$		0			0
$301$	3.75324	+	2.16693i	0.216333	+	0.124900i
$302$		0			0
$303$	−12.5880	−	21.8031i	−0.723164	−	1.25256i
$304$		0			0
$305$	−3.79429	+	2.19063i	−0.217260	+	0.125435i
$306$		0			0
$307$			21.8488i			1.24698i	0.781833	+	0.623488i	$0.214285\pi$
$307$			21.8488i			1.24698i	−0.781833	+	0.623488i	$0.785715\pi$
$308$		0			0
$309$	30.2250	−	52.3513i	1.71944	−	2.97816i
$310$		0			0
$311$	8.78745			0.498291			0.249145	−	0.968466i	$-0.419850\pi$
$311$	8.78745			0.498291			0.249145	+	0.968466i	$0.419850\pi$
$312$		0			0
$313$	−18.6613			−1.05480			−0.527399	−	0.849618i	$-0.676833\pi$
$313$	−18.6613			−1.05480			−0.527399	+	0.849618i	$0.676833\pi$
$314$		0			0
$315$	−3.14369	+	5.44504i	−0.177127	+	0.306793i
$316$		0			0
$317$		−	21.3723i		−	1.20039i	−0.799855	−	0.600193i	$-0.795090\pi$
$317$		−	21.3723i		−	1.20039i	0.799855	−	0.600193i	$-0.204910\pi$
$318$		0			0
$319$	−1.96840	+	1.13645i	−0.110209	+	0.0636292i
$320$		0			0
$321$	9.10500	+	15.7703i	0.508192	+	0.880214i
$322$		0			0
$323$	27.4622	+	15.8553i	1.52804	+	0.882214i
$324$		0			0
$325$	−14.9162	−	4.38587i	−0.827403	−	0.243284i
$326$		0			0
$327$	35.9624	+	20.7629i	1.98873	+	1.14819i
$328$		0			0
$329$	−1.90969	−	3.30767i	−0.105284	−	0.182358i
$330$		0			0
$331$	−5.20296	+	3.00393i	−0.285980	+	0.165111i	−0.636128	−	0.771584i	$-0.719465\pi$
$331$	−5.20296	+	3.00393i	−0.285980	+	0.165111i	0.350147	+	0.936695i	$0.386132\pi$
$332$		0			0
$333$			68.3617i			3.74620i
$334$		0			0
$335$	−3.69618	+	6.40197i	−0.201944	+	0.349777i
$336$		0			0
$337$	−1.79804			−0.0979454			−0.0489727	−	0.998800i	$-0.515595\pi$
$337$	−1.79804			−0.0979454			−0.0489727	+	0.998800i	$0.515595\pi$
$338$		0			0
$339$	49.8088			2.70524
$340$		0			0
$341$	−2.71273	+	4.69858i	−0.146902	+	0.254442i
$342$		0			0
$343$			12.7502i			0.688447i
$344$		0			0
$345$	4.83587	−	2.79199i	0.260354	−	0.150316i
$346$		0			0
$347$	13.2242	+	22.9050i	0.709913	+	1.22961i	0.964889	+	0.262659i	$0.0845993\pi$
$347$	13.2242	+	22.9050i	0.709913	+	1.22961i	−0.254975	+	0.966948i	$0.582067\pi$
$348$		0			0
$349$	29.8061	+	17.2086i	1.59549	+	0.921154i	0.992342	+	0.123522i	$0.0394188\pi$
$349$	29.8061	+	17.2086i	1.59549	+	0.921154i	0.603144	+	0.797632i	$0.293915\pi$
$350$		0			0
$351$	−53.9547	−	15.8645i	−2.87989	−	0.846783i
$352$		0			0
$353$	−18.9264	−	10.9271i	−1.00735	−	0.581593i	−0.0969342	−	0.995291i	$-0.530904\pi$
$353$	−18.9264	−	10.9271i	−1.00735	−	0.581593i	−0.910414	+	0.413698i	$0.864237\pi$
$354$		0			0
$355$	−2.97755	−	5.15727i	−0.158032	−	0.273719i
$356$		0			0
$357$	17.5307	−	10.1214i	0.927823	−	0.535679i
$358$		0			0
$359$		−	18.0628i		−	0.953316i	−0.879089	−	0.476658i	$-0.841848\pi$
$359$		−	18.0628i		−	0.953316i	0.879089	−	0.476658i	$-0.158152\pi$
$360$		0			0
$361$	3.10850	−	5.38408i	0.163605	−	0.283373i
$362$		0			0
$363$	−3.27963			−0.172136
$364$		0			0
$365$	−1.58099			−0.0827529
$366$		0			0
$367$	7.80391	−	13.5168i	0.407361	−	0.705569i	−0.587232	−	0.809418i	$-0.699783\pi$
$367$	7.80391	−	13.5168i	0.407361	−	0.705569i	0.994593	+	0.103849i	$0.0331158\pi$
$368$		0			0
$369$		−	87.8839i		−	4.57505i
$370$		0			0
$371$	−8.05857	+	4.65262i	−0.418380	+	0.241552i
$372$		0			0
$373$	−0.720554	−	1.24804i	−0.0373089	−	0.0646209i	0.846768	−	0.531962i	$-0.178545\pi$
$373$	−0.720554	−	1.24804i	−0.0373089	−	0.0646209i	−0.884077	+	0.467341i	$0.845212\pi$
$374$		0			0
$375$	21.9358	+	12.6646i	1.13276	+	0.654000i
$376$		0			0
$377$	−5.93318	+	5.65304i	−0.305574	+	0.291146i
$378$		0			0
$379$	3.52072	+	2.03269i	0.180847	+	0.104412i	0.587691	−	0.809086i	$-0.300037\pi$
$379$	3.52072	+	2.03269i	0.180847	+	0.104412i	−0.406843	+	0.913498i	$0.633371\pi$
$380$		0			0
$381$	−34.3934	−	59.5712i	−1.76203	−	3.05192i
$382$		0			0
$383$	7.87338	−	4.54570i	0.402311	−	0.232274i	−0.285170	−	0.958477i	$-0.592050\pi$
$383$	7.87338	−	4.54570i	0.402311	−	0.232274i	0.687481	+	0.726203i	$0.258717\pi$
$384$		0			0
$385$			0.810651i			0.0413146i
$386$		0			0
$387$	17.1948	−	29.7822i	0.874058	−	1.51391i
$388$		0			0
$389$	0.119791			0.00607364			0.00303682	−	0.999995i	$-0.499033\pi$
$389$	0.119791			0.00607364			0.00303682	+	0.999995i	$0.499033\pi$
$390$		0			0
$391$	−12.9637			−0.655602
$392$		0			0
$393$	1.13303	−	1.96247i	0.0571539	−	0.0989934i
$394$		0			0
$395$			0.755028i			0.0379896i
$396$		0			0
$397$	32.6280	−	18.8378i	1.63755	−	0.945442i	0.655883	−	0.754863i	$-0.272297\pi$
$397$	32.6280	−	18.8378i	1.63755	−	0.945442i	0.981672	−	0.190580i	$-0.0610368\pi$
$398$		0			0
$399$	−8.04872	−	13.9408i	−0.402940	−	0.697913i
$400$		0			0
$401$	−5.39911	−	3.11718i	−0.269619	−	0.155665i	0.359096	−	0.933301i	$-0.383085\pi$
$401$	−5.39911	−	3.11718i	−0.269619	−	0.155665i	−0.628714	+	0.777636i	$0.716419\pi$
$402$		0			0
$403$	−5.51821	+	18.7673i	−0.274882	+	0.934865i
$404$		0			0
$405$	20.0301	+	11.5644i	0.995303	+	0.574639i
$406$		0			0
$407$	4.40704	+	7.63322i	0.218449	+	0.378365i
$408$		0			0
$409$	11.9146	−	6.87893i	0.589142	−	0.340141i	−0.175616	−	0.984459i	$-0.556192\pi$
$409$	11.9146	−	6.87893i	0.589142	−	0.340141i	0.764758	+	0.644318i	$0.222859\pi$
$410$		0			0
$411$			41.5274i			2.04840i
$412$		0			0
$413$	−0.0776743	+	0.134536i	−0.00382210	+	0.00662008i
$414$		0			0
$415$	6.56000			0.322018
$416$		0			0
$417$	−14.6505			−0.717440
$418$		0			0
$419$	−7.13313	+	12.3550i	−0.348476	+	0.603579i	−0.985979	−	0.166869i	$-0.946634\pi$
$419$	−7.13313	+	12.3550i	−0.348476	+	0.603579i	0.637503	+	0.770448i	$0.279968\pi$
$420$		0			0
$421$		−	5.85527i		−	0.285368i	−0.989768	−	0.142684i	$-0.954427\pi$
$421$		−	5.85527i		−	0.285368i	0.989768	−	0.142684i	$-0.0455733\pi$
$422$		0			0
$423$	−26.2466	+	15.1535i	−1.27615	+	0.736788i
$424$		0			0
$425$	−13.6151	−	23.5821i	−0.660431	−	1.14390i
$426$		0			0
$427$	−4.47164	−	2.58170i	−0.216398	−	0.124937i
$428$		0			0
$429$	−11.4926	+	2.78352i	−0.554867	+	0.134389i
$430$		0			0
$431$	30.4355	+	17.5719i	1.46602	+	0.846410i	0.999278	−	0.0379815i	$-0.0120928\pi$
$431$	30.4355	+	17.5719i	1.46602	+	0.846410i	0.466746	+	0.884391i	$0.345426\pi$
$432$		0			0
$433$	4.22667	+	7.32081i	0.203121	+	0.351816i	0.949532	−	0.313669i	$-0.101558\pi$
$433$	4.22667	+	7.32081i	0.203121	+	0.351816i	−0.746411	+	0.665485i	$0.768225\pi$
$434$		0			0
$435$	5.35409	−	3.09119i	0.256709	−	0.148211i
$436$		0			0
$437$			10.3090i			0.493147i
$438$		0			0
$439$	−12.1376	+	21.0229i	−0.579294	+	1.00337i	0.416266	+	0.909243i	$0.363338\pi$
$439$	−12.1376	+	21.0229i	−0.579294	+	1.00337i	−0.995560	+	0.0941243i	$0.969995\pi$
$440$		0			0
$441$	46.8820			2.23247
$442$		0			0
$443$	29.9293			1.42198			0.710992	−	0.703200i	$-0.248246\pi$
$443$	29.9293			1.42198			0.710992	+	0.703200i	$0.248246\pi$
$444$		0			0
$445$	−4.37333	+	7.57482i	−0.207315	+	0.359081i
$446$		0			0
$447$			67.2332i			3.18002i
$448$		0			0
$449$	25.3652	−	14.6446i	1.19706	−	0.691122i	0.237160	−	0.971471i	$-0.423783\pi$
$449$	25.3652	−	14.6446i	1.19706	−	0.691122i	0.959898	+	0.280349i	$0.0904501\pi$
$450$		0			0
$451$	−5.66557	−	9.81305i	−0.266781	−	0.462079i
$452$		0			0
$453$	12.3353	+	7.12181i	0.579565	+	0.334612i
$454$		0			0
$455$	0.688023	+	2.84071i	0.0322550	+	0.133175i
$456$		0			0
$457$	26.2747	+	15.1697i	1.22908	+	0.709608i	0.966837	−	0.255395i	$-0.0822055\pi$
$457$	26.2747	+	15.1697i	1.22908	+	0.709608i	0.262240	+	0.965003i	$0.415539\pi$
$458$		0			0
$459$	−49.2484	−	85.3007i	−2.29872	−	3.98150i
$460$		0			0
$461$	16.6615	−	9.61951i	0.776003	−	0.448025i	−0.0590090	−	0.998257i	$-0.518794\pi$
$461$	16.6615	−	9.61951i	0.776003	−	0.448025i	0.835012	+	0.550232i	$0.185461\pi$
$462$		0			0
$463$			14.3549i			0.667127i	0.942728	+	0.333564i	$0.108251\pi$
$463$			14.3549i			0.667127i	−0.942728	+	0.333564i	$0.891749\pi$
$464$		0			0
$465$	7.37869	−	12.7803i	0.342179	−	0.592671i
$466$		0			0
$467$	−21.1819			−0.980180			−0.490090	−	0.871672i	$-0.663036\pi$
$467$	−21.1819			−0.980180			−0.490090	+	0.871672i	$0.663036\pi$
$468$		0			0
$469$	−8.71205			−0.402285
$470$		0			0
$471$	−24.5928	+	42.5959i	−1.13317	+	1.96272i
$472$		0			0
$473$		−	4.43394i		−	0.203873i
$474$		0			0
$475$	−18.7530	+	10.8270i	−0.860447	+	0.496779i
$476$		0			0
$477$	36.9188	+	63.9453i	1.69040	+	2.92785i
$478$		0			0
$479$	20.9113	+	12.0731i	0.955461	+	0.551636i	0.894773	−	0.446521i	$-0.147337\pi$
$479$	20.9113	+	12.0731i	0.955461	+	0.551636i	0.0606880	+	0.998157i	$0.480671\pi$
$480$		0			0
$481$	21.9218	+	23.0082i	0.999550	+	1.04908i
$482$		0			0
$483$	5.69917	+	3.29041i	0.259321	+	0.149719i
$484$		0			0
$485$	3.45502	+	5.98428i	0.156885	+	0.271732i
$486$		0			0
$487$	13.8787	−	8.01289i	0.628905	−	0.363099i	−0.151423	−	0.988469i	$-0.548386\pi$
$487$	13.8787	−	8.01289i	0.628905	−	0.363099i	0.780328	+	0.625371i	$0.215052\pi$
$488$		0			0
$489$			10.1484i			0.458926i
$490$		0			0
$491$	19.0655	−	33.0224i	0.860414	−	1.49028i	−0.0111168	−	0.999938i	$-0.503539\pi$
$491$	19.0655	−	33.0224i	0.860414	−	1.49028i	0.871530	−	0.490342i	$-0.163128\pi$
$492$		0			0
$493$	−14.3529			−0.646424
$494$		0			0
$495$	6.43257			0.289123
$496$		0			0
$497$	3.50910	−	6.07794i	0.157405	−	0.272633i
$498$		0			0
$499$		−	35.3892i		−	1.58424i	−0.610365	−	0.792120i	$-0.708977\pi$
$499$		−	35.3892i		−	1.58424i	0.610365	−	0.792120i	$-0.291023\pi$
$500$		0			0
$501$	−35.4378	+	20.4600i	−1.58324	+	0.914086i
$502$		0			0
$503$	8.02161	+	13.8938i	0.357666	+	0.619496i	0.987570	−	0.157177i	$-0.0502393\pi$
$503$	8.02161	+	13.8938i	0.357666	+	0.619496i	−0.629904	+	0.776673i	$0.716906\pi$
$504$		0			0
$505$	5.51370	+	3.18333i	0.245356	+	0.141656i
$506$		0			0
$507$	−37.9103	+	19.5082i	−1.68365	+	0.866389i
$508$		0			0
$509$	−16.9340	−	9.77684i	−0.750585	−	0.433351i	0.0753200	−	0.997159i	$-0.476002\pi$
$509$	−16.9340	−	9.77684i	−0.750585	−	0.433351i	−0.825905	+	0.563809i	$0.809336\pi$
$510$		0			0
$511$	−0.931615	−	1.61361i	−0.0412122	−	0.0713817i
$512$		0			0
$513$	−67.8330	+	39.1634i	−2.99490	+	1.72911i
$514$		0			0
$515$			15.2869i			0.673623i
$516$		0			0
$517$	−1.95378	+	3.38405i	−0.0859273	+	0.148831i
$518$		0			0
$519$	−13.5537			−0.594942
$520$		0			0
$521$	−12.1223			−0.531089			−0.265544	−	0.964099i	$-0.585552\pi$
$521$	−12.1223			−0.531089			−0.265544	+	0.964099i	$0.585552\pi$
$522$		0			0
$523$	21.6024	−	37.4165i	0.944608	−	1.63611i	0.188073	−	0.982155i	$-0.439776\pi$
$523$	21.6024	−	37.4165i	0.944608	−	1.63611i	0.756534	−	0.653954i	$-0.226891\pi$
$524$		0			0
$525$			13.8230i			0.603287i
$526$		0			0
$527$	−29.6705	+	17.1303i	−1.29247	+	0.746207i
$528$		0			0
$529$	9.39278	+	16.2688i	0.408382	+	0.707338i
$530$		0			0
$531$	1.06755	+	0.616351i	0.0463278	+	0.0267473i
$532$		0			0
$533$	−28.1821	−	29.5787i	−1.22070	−	1.28120i
$534$		0			0
$535$	−3.98809	−	2.30252i	−0.172420	−	0.0995467i
$536$		0			0
$537$	0.125545	+	0.217451i	0.00541768	+	0.00938370i
$538$		0			0
$539$	5.23480	−	3.02232i	0.225479	−	0.130180i
$540$		0			0
$541$			16.2055i			0.696727i	0.937359	+	0.348364i	$0.113263\pi$
$541$			16.2055i			0.696727i	−0.937359	+	0.348364i	$0.886737\pi$
$542$		0			0
$543$	11.0664	−	19.1676i	0.474907	−	0.822562i
$544$		0			0
$545$	−10.5013			−0.449825
$546$		0			0
$547$	−32.3546			−1.38338			−0.691692	−	0.722193i	$-0.743134\pi$
$547$	−32.3546			−1.38338			−0.691692	+	0.722193i	$0.743134\pi$
$548$		0			0
$549$	−20.4860	+	35.4828i	−0.874321	+	1.51437i
$550$		0			0
$551$			11.4138i			0.486243i
$552$		0			0
$553$	−0.770603	+	0.444908i	−0.0327694	+	0.0189194i
$554$		0			0
$555$	−11.9873	−	20.7626i	−0.508831	−	0.881322i
$556$		0			0
$557$	−11.8748	−	6.85592i	−0.503152	−	0.290495i	0.226863	−	0.973927i	$-0.427153\pi$
$557$	−11.8748	−	6.85592i	−0.503152	−	0.290495i	−0.730014	+	0.683432i	$0.760487\pi$
$558$		0			0
$559$	−3.76321	−	15.5376i	−0.159167	−	0.657169i
$560$		0			0
$561$	−17.9355	−	10.3551i	−0.757238	−	0.437192i
$562$		0			0
$563$	−3.22479	−	5.58549i	−0.135909	−	0.235401i	0.790036	−	0.613061i	$-0.210062\pi$
$563$	−3.22479	−	5.58549i	−0.135909	−	0.235401i	−0.925944	+	0.377660i	$0.876729\pi$
$564$		0			0
$565$	−10.9084	+	6.29796i	−0.458919	+	0.264957i
$566$		0			0
$567$			27.2577i			1.14472i
$568$		0			0
$569$	12.5392	−	21.7185i	0.525670	−	0.910488i	−0.473882	−	0.880588i	$-0.657148\pi$
$569$	12.5392	−	21.7185i	0.525670	−	0.910488i	0.999553	−	0.0298998i	$-0.00951881\pi$
$570$		0			0
$571$	−41.9724			−1.75649			−0.878245	−	0.478210i	$-0.841286\pi$
$571$	−41.9724			−1.75649			−0.878245	+	0.478210i	$0.841286\pi$
$572$		0			0
$573$	35.8508			1.49769
$574$		0			0
$575$	4.42623	−	7.66645i	0.184586	−	0.319713i
$576$		0			0
$577$			6.75537i			0.281230i	0.990064	+	0.140615i	$0.0449079\pi$
$577$			6.75537i			0.281230i	−0.990064	+	0.140615i	$0.955092\pi$
$578$		0			0
$579$	19.0234	−	10.9832i	0.790586	−	0.456445i
$580$		0			0
$581$	3.86555	+	6.69532i	0.160370	+	0.277769i
$582$		0			0
$583$	8.24465	+	4.76005i	0.341459	+	0.197141i
$584$		0			0
$585$	22.5412	−	5.45951i	0.931965	−	0.225723i
$586$		0			0
$587$	−29.8992	−	17.2623i	−1.23407	−	0.712491i	−0.266195	−	0.963919i	$-0.585767\pi$
$587$	−29.8992	−	17.2623i	−1.23407	−	0.712491i	−0.967876	+	0.251428i	$0.919100\pi$
$588$		0			0
$589$	13.6224	+	23.5946i	0.561300	+	0.972200i
$590$		0			0
$591$	7.61179	−	4.39467i	0.313107	−	0.180773i
$592$		0			0
$593$			20.8562i			0.856460i	0.903670	+	0.428230i	$0.140863\pi$
$593$			20.8562i			0.856460i	−0.903670	+	0.428230i	$0.859137\pi$
$594$		0			0
$595$	−2.55954	+	4.43326i	−0.104931	+	0.181746i
$596$		0			0
$597$	−53.9539			−2.20819
$598$		0			0
$599$	−11.2370			−0.459133			−0.229566	−	0.973293i	$-0.573731\pi$
$599$	−11.2370			−0.459133			−0.229566	+	0.973293i	$0.573731\pi$
$600$		0			0
$601$	7.63121	−	13.2176i	0.311284	−	0.539159i	−0.667357	−	0.744738i	$-0.732574\pi$
$601$	7.63121	−	13.2176i	0.311284	−	0.539159i	0.978641	+	0.205579i	$0.0659078\pi$
$602$		0			0
$603$			69.1306i			2.81522i
$604$		0			0
$605$	0.718256	−	0.414685i	0.0292013	−	0.0168594i
$606$		0			0
$607$	−9.37382	−	16.2359i	−0.380472	−	0.658996i	0.610658	−	0.791894i	$-0.290905\pi$
$607$	−9.37382	−	16.2359i	−0.380472	−	0.658996i	−0.991130	+	0.132898i	$0.957572\pi$
$608$		0			0
$609$	6.30991	+	3.64303i	0.255690	+	0.147623i
$610$		0			0
$611$	−3.97438	+	13.5168i	−0.160786	+	0.546829i
$612$		0			0
$613$	22.2758	+	12.8610i	0.899713	+	0.519449i	0.877107	−	0.480295i	$-0.159470\pi$
$613$	22.2758	+	12.8610i	0.899713	+	0.519449i	0.0226059	+	0.999744i	$0.492804\pi$
$614$		0			0
$615$	15.4105	+	26.6918i	0.621411	+	1.07632i
$616$		0			0
$617$	−15.5002	+	8.94904i	−0.624014	+	0.360275i	−0.778430	−	0.627731i	$-0.783984\pi$
$617$	−15.5002	+	8.94904i	−0.624014	+	0.360275i	0.154416	+	0.988006i	$0.450650\pi$
$618$		0			0
$619$		−	40.5095i		−	1.62822i	−0.580714	−	0.814108i	$-0.697226\pi$
$619$		−	40.5095i		−	1.62822i	0.580714	−	0.814108i	$-0.302774\pi$
$620$		0			0
$621$	16.0105	−	27.7309i	0.642478	−	1.11280i
$622$		0			0
$623$	−10.3081			−0.412985
$624$		0			0
$625$	15.1553			0.606212
$626$		0			0
$627$	−8.23458	+	14.2627i	−0.328857	+	0.569598i
$628$		0			0
$629$			55.6590i			2.21927i
$630$		0			0
$631$	−13.2588	+	7.65497i	−0.527824	+	0.304739i	−0.740130	−	0.672464i	$-0.765236\pi$
$631$	−13.2588	+	7.65497i	−0.527824	+	0.304739i	0.212306	+	0.977203i	$0.431903\pi$
$632$		0			0
$633$	14.5849	+	25.2618i	0.579698	+	1.00407i
$634$		0			0
$635$	15.0647	+	8.69760i	0.597824	+	0.345154i
$636$		0			0
$637$	15.7789	−	15.0338i	0.625181	−	0.595662i
$638$		0			0
$639$	−48.2289	−	27.8450i	−1.90790	−	1.10153i
$640$		0			0
$641$	13.3822	+	23.1786i	0.528565	+	0.915501i	0.999445	+	0.0333042i	$0.0106030\pi$
$641$	13.3822	+	23.1786i	0.528565	+	0.915501i	−0.470880	+	0.882197i	$0.656064\pi$
$642$		0			0
$643$	3.58722	−	2.07108i	0.141466	−	0.0816756i	−0.427596	−	0.903970i	$-0.640640\pi$
$643$	3.58722	−	2.07108i	0.141466	−	0.0816756i	0.569063	+	0.822294i	$0.307306\pi$
$644$		0			0
$645$			12.0604i			0.474879i
$646$		0			0
$647$	−1.20082	+	2.07987i	−0.0472089	+	0.0817683i	−0.888664	−	0.458558i	$-0.848366\pi$
$647$	−1.20082	+	2.07987i	−0.0472089	+	0.0817683i	0.841455	+	0.540327i	$0.181699\pi$
$648$		0			0
$649$	0.158936			0.00623878
$650$		0			0
$651$	17.3919			0.681641
$652$		0			0
$653$	14.2105	−	24.6134i	0.556102	−	0.963196i	−0.441715	−	0.897155i	$-0.645630\pi$
$653$	14.2105	−	24.6134i	0.556102	−	0.963196i	0.997817	−	0.0660410i	$-0.0210368\pi$
$654$		0			0
$655$			0.573054i			0.0223911i
$656$		0			0
$657$	−12.8041	+	7.39243i	−0.499534	+	0.288406i
$658$		0			0
$659$	1.49517	+	2.58971i	0.0582436	+	0.100881i	0.893677	−	0.448711i	$-0.148117\pi$
$659$	1.49517	+	2.58971i	0.0582436	+	0.100881i	−0.835433	+	0.549592i	$0.814783\pi$
$660$		0			0
$661$	17.6557	+	10.1935i	0.686726	+	0.396481i	0.802384	−	0.596808i	$-0.203565\pi$
$661$	17.6557	+	10.1935i	0.686726	+	0.396481i	−0.115659	+	0.993289i	$0.536898\pi$
$662$		0			0
$663$	−71.6389	−	21.0642i	−2.78222	−	0.818067i
$664$		0			0
$665$	3.52542	+	2.03541i	0.136710	+	0.0789296i
$666$		0			0
$667$	−2.33304	−	4.04095i	−0.0903357	−	0.156466i
$668$		0			0
$669$	83.7809	−	48.3709i	3.23916	−	1.87013i
$670$		0			0
$671$			5.28264i			0.203934i
$672$		0			0
$673$	−14.4113	+	24.9610i	−0.555513	+	0.962177i	0.442350	+	0.896842i	$0.354145\pi$
$673$	−14.4113	+	24.9610i	−0.555513	+	0.962177i	−0.997863	+	0.0653348i	$0.979188\pi$
$674$		0			0
$675$	67.2600			2.58884
$676$		0			0
$677$	−28.8863			−1.11019			−0.555095	−	0.831787i	$-0.687318\pi$
$677$	−28.8863			−1.11019			−0.555095	+	0.831787i	$0.687318\pi$
$678$		0			0
$679$	−4.07181	+	7.05259i	−0.156262	+	0.270654i
$680$		0			0
$681$		−	80.9158i		−	3.10070i
$682$		0			0
$683$	4.89153	−	2.82413i	0.187169	−	0.108062i	−0.403487	−	0.914985i	$-0.632202\pi$
$683$	4.89153	−	2.82413i	0.187169	−	0.108062i	0.590657	+	0.806923i	$0.298869\pi$
$684$		0			0
$685$	−5.25084	−	9.09472i	−0.200624	−	0.347491i
$686$		0			0
$687$	25.0785	+	14.4791i	0.956805	+	0.552412i
$688$		0			0
$689$	32.9312	+	9.68287i	1.25458	+	0.368888i
$690$		0			0
$691$	29.1279	+	16.8170i	1.10808	+	0.639748i	0.938330	−	0.345740i	$-0.112372\pi$
$691$	29.1279	+	16.8170i	1.10808	+	0.639748i	0.169746	+	0.985488i	$0.445705\pi$
$692$		0			0
$693$	3.79046	+	6.56526i	0.143988	+	0.249394i
$694$		0			0
$695$	3.20855	−	1.85246i	0.121707	−	0.0702676i
$696$		0			0
$697$		−	71.5537i		−	2.71029i
$698$		0			0
$699$	−33.8384	+	58.6099i	−1.27989	+	2.21683i
$700$		0			0
$701$	−51.4110			−1.94177			−0.970883	−	0.239553i	$-0.922999\pi$
$701$	−51.4110			−1.94177			−0.970883	+	0.239553i	$0.922999\pi$
$702$		0			0
$703$	44.2613			1.66934
$704$		0			0
$705$	5.31435	−	9.20472i	0.200150	−	0.346670i
$706$		0			0
$707$			7.50324i			0.282188i
$708$		0			0
$709$	1.03708	−	0.598758i	0.0389483	−	0.0224868i	−0.480399	−	0.877050i	$-0.659508\pi$
$709$	1.03708	−	0.598758i	0.0389483	−	0.0224868i	0.519348	+	0.854563i	$0.326175\pi$
$710$		0			0
$711$	3.53037	+	6.11478i	0.132399	+	0.229322i
$712$		0			0
$713$	−9.64577	−	5.56899i	−0.361237	−	0.208560i
$714$		0			0
$715$	2.16498	−	2.06276i	0.0809657	−	0.0771428i
$716$		0			0
$717$	−35.5152	−	20.5047i	−1.32634	−	0.765763i
$718$		0			0
$719$	−10.9295	−	18.9305i	−0.407603	−	0.705989i	0.587018	−	0.809574i	$-0.300302\pi$
$719$	−10.9295	−	18.9305i	−0.407603	−	0.705989i	−0.994621	+	0.103585i	$0.966969\pi$
$720$		0			0
$721$	−15.6023	+	9.00798i	−0.581060	+	0.335475i
$722$		0			0
$723$		−	42.7048i		−	1.58821i
$724$		0			0
$725$	4.90056	−	8.48801i	0.182002	−	0.315237i
$726$		0			0
$727$	26.7904			0.993601			0.496800	−	0.867865i	$-0.334508\pi$
$727$	26.7904			0.993601			0.496800	+	0.867865i	$0.334508\pi$
$728$		0			0
$729$	62.8265			2.32691
$730$		0			0
$731$	13.9997	−	24.2482i	0.517797	−	0.896851i
$732$		0			0
$733$			36.0274i			1.33070i	0.746531	+	0.665351i	$0.231718\pi$
$733$			36.0274i			1.33070i	−0.746531	+	0.665351i	$0.768282\pi$
$734$		0			0
$735$	−14.2388	+	8.22078i	−0.525207	+	0.303228i
$736$		0			0
$737$	4.45661	+	7.71908i	0.164161	+	0.284336i
$738$		0			0
$739$	−12.1926	−	7.03940i	−0.448512	−	0.258949i	0.258689	−	0.965961i	$-0.416709\pi$
$739$	−12.1926	−	7.03940i	−0.448512	−	0.258949i	−0.707202	+	0.707012i	$0.750043\pi$
$740$		0			0
$741$	−16.7507	+	56.9688i	−0.615353	+	2.09280i
$742$		0			0
$743$	−24.4238	−	14.1011i	−0.896024	−	0.517320i	−0.0201160	−	0.999798i	$-0.506404\pi$
$743$	−24.4238	−	14.1011i	−0.896024	−	0.517320i	−0.875908	+	0.482478i	$0.839737\pi$
$744$		0			0
$745$	−8.50115	−	14.7244i	−0.311458	−	0.539461i
$746$		0			0
$747$	53.1278	−	30.6734i	1.94385	−	1.12228i
$748$		0			0
$749$		−	5.42714i		−	0.198303i
$750$		0			0
$751$	−1.69016	+	2.92744i	−0.0616747	+	0.106824i	−0.895214	−	0.445636i	$-0.852977\pi$
$751$	−1.69016	+	2.92744i	−0.0616747	+	0.106824i	0.833539	+	0.552460i	$0.186311\pi$
$752$		0			0
$753$	−17.1489			−0.624940
$754$		0			0
$755$	−3.60200			−0.131090
$756$		0			0
$757$	17.7435	−	30.7326i	0.644897	−	1.11699i	−0.339428	−	0.940632i	$-0.610234\pi$
$757$	17.7435	−	30.7326i	0.644897	−	1.11699i	0.984325	−	0.176363i	$-0.0564331\pi$
$758$		0			0
$759$		−	6.73279i		−	0.244385i
$760$		0			0
$761$	30.1078	−	17.3827i	1.09141	−	0.630124i	0.157456	−	0.987526i	$-0.449671\pi$
$761$	30.1078	−	17.3827i	1.09141	−	0.630124i	0.933951	+	0.357402i	$0.116337\pi$
$762$		0			0
$763$	−6.18798	−	10.7179i	−0.224020	−	0.388014i
$764$		0			0
$765$	35.1782	+	20.3101i	1.27187	+	0.734315i
$766$		0			0
$767$	0.556949	−	0.134893i	0.0201103	−	0.00487072i
$768$		0			0
$769$	−4.63462	−	2.67580i	−0.167129	−	0.0964917i	0.414103	−	0.910230i	$-0.364095\pi$
$769$	−4.63462	−	2.67580i	−0.167129	−	0.0964917i	−0.581231	+	0.813738i	$0.697429\pi$
$770$		0			0
$771$	4.89523	+	8.47879i	0.176297	+	0.305356i
$772$		0			0
$773$	42.1637	−	24.3432i	1.51652	−	0.875564i	0.516710	−	0.856160i	$-0.327156\pi$
$773$	42.1637	−	24.3432i	1.51652	−	0.875564i	0.999812	−	0.0194040i	$-0.00617686\pi$
$774$		0			0
$775$		−	23.3953i		−	0.840385i
$776$		0			0
$777$	14.1272	−	24.4691i	0.506812	−	0.877824i
$778$		0			0
$779$	−56.9010			−2.03869
$780$		0			0
$781$	−7.18027			−0.256930
$782$		0			0
$783$	17.7262	−	30.7027i	0.633483	−	1.09722i
$784$		0			0
$785$		−	12.4383i		−	0.443942i
$786$		0			0
$787$	46.1260	−	26.6309i	1.64421	−	0.949287i	0.664902	−	0.746930i	$-0.268473\pi$
$787$	46.1260	−	26.6309i	1.64421	−	0.949287i	0.979312	−	0.202357i	$-0.0648602\pi$
$788$		0			0
$789$	19.2642	+	33.3665i	0.685823	+	1.18788i
$790$		0			0
$791$	−12.8557	−	7.42227i	−0.457098	−	0.263905i
$792$		0			0
$793$	4.48353	+	18.5116i	0.159215	+	0.657367i
$794$		0			0
$795$	−22.4257	−	12.9475i	−0.795357	−	0.459200i
$796$		0			0
$797$	−12.7278	−	22.0452i	−0.450842	−	0.780881i	0.547597	−	0.836742i	$-0.315543\pi$
$797$	−12.7278	−	22.0452i	−0.450842	−	0.780881i	−0.998439	+	0.0558617i	$0.982209\pi$
$798$		0			0
$799$	−21.3696	+	12.3377i	−0.756001	+	0.436477i
$800$		0			0
$801$			81.7954i			2.89010i
$802$		0			0
$803$	−0.953128	+	1.65087i	−0.0336352	+	0.0582578i
$804$		0			0
$805$	−1.66420			−0.0586552
$806$		0			0
$807$	−101.396			−3.56932
$808$		0			0
$809$	−8.01969	+	13.8905i	−0.281957	+	0.488364i	−0.971867	−	0.235531i	$-0.924317\pi$
$809$	−8.01969	+	13.8905i	−0.281957	+	0.488364i	0.689910	+	0.723896i	$0.257650\pi$
$810$		0			0
$811$			12.8798i			0.452271i	0.974096	+	0.226136i	$0.0726093\pi$
$811$			12.8798i			0.452271i	−0.974096	+	0.226136i	$0.927391\pi$
$812$		0			0
$813$	40.7088	−	23.5032i	1.42772	−	0.824294i
$814$		0			0
$815$	−1.28319	−	2.22255i	−0.0449482	−	0.0778526i
$816$		0			0
$817$	−19.2827	−	11.1329i	−0.674615	−	0.389489i
$818$		0			0
$819$	18.8548	+	19.7891i	0.658839	+	0.691489i
$820$		0			0
$821$	−20.5490	−	11.8640i	−0.717165	−	0.414055i	0.0965434	−	0.995329i	$-0.469221\pi$
$821$	−20.5490	−	11.8640i	−0.717165	−	0.414055i	−0.813708	+	0.581273i	$0.802555\pi$
$822$		0			0
$823$	−0.414091	−	0.717226i	−0.0144343	−	0.0250009i	0.858718	−	0.512448i	$-0.171261\pi$
$823$	−0.414091	−	0.717226i	−0.0144343	−	0.0250009i	−0.873152	+	0.487447i	$0.837928\pi$
$824$		0			0
$825$	12.2475	−	7.07112i	0.426404	−	0.246185i
$826$		0			0
$827$		−	34.1022i		−	1.18585i	−0.805258	−	0.592925i	$-0.797973\pi$
$827$		−	34.1022i		−	1.18585i	0.805258	−	0.592925i	$-0.202027\pi$
$828$		0			0
$829$	12.7715	−	22.1209i	0.443572	−	0.768290i	−0.554379	−	0.832264i	$-0.687044\pi$
$829$	12.7715	−	22.1209i	0.443572	−	0.768290i	0.997952	+	0.0639744i	$0.0203776\pi$
$830$		0			0
$831$	31.9518			1.10839
$832$		0			0
$833$	38.1705			1.32253
$834$		0			0
$835$	5.17404	−	8.96170i	0.179055	−	0.310132i
$836$		0			0
$837$		−	84.6251i		−	2.92507i
$838$		0			0
$839$	26.3718	−	15.2257i	0.910454	−	0.525651i	0.0298768	−	0.999554i	$-0.490489\pi$
$839$	26.3718	−	15.2257i	0.910454	−	0.525651i	0.880577	+	0.473903i	$0.157155\pi$
$840$		0			0
$841$	11.9169	+	20.6407i	0.410929	+	0.711750i
$842$		0			0
$843$	66.1144	+	38.1712i	2.27710	+	1.31469i
$844$		0			0
$845$	5.83588	−	9.06587i	0.200760	−	0.311876i
$846$		0			0
$847$	0.846479	+	0.488715i	0.0290854	+	0.0167924i
$848$		0			0
$849$	−40.4191	−	70.0080i	−1.38718	−	2.40267i
$850$		0			0
$851$	−15.6703	+	9.04727i	−0.537172	+	0.310136i
$852$		0			0
$853$		−	28.4668i		−	0.974684i	−0.873211	−	0.487342i	$-0.837966\pi$
$853$		−	28.4668i		−	0.974684i	0.873211	−	0.487342i	$-0.162034\pi$
$854$		0			0
$855$	16.1511	−	27.9745i	0.552355	−	0.956707i
$856$		0			0
$857$	−38.6939			−1.32176			−0.660879	−	0.750492i	$-0.729817\pi$
$857$	−38.6939			−1.32176			−0.660879	+	0.750492i	$0.729817\pi$
$858$		0			0
$859$	−3.69241			−0.125983			−0.0629916	−	0.998014i	$-0.520064\pi$
$859$	−3.69241			−0.125983			−0.0629916	+	0.998014i	$0.520064\pi$
$860$		0			0
$861$	−18.1616	+	31.4568i	−0.618945	+	1.07204i
$862$		0			0
$863$			45.8787i			1.56173i	0.624700	+	0.780865i	$0.285221\pi$
$863$			45.8787i			1.56173i	−0.624700	+	0.780865i	$0.714779\pi$
$864$		0			0
$865$	2.96834	−	1.71377i	0.100926	−	0.0582699i
$866$		0			0
$867$	−37.5132	−	64.9748i	−1.27402	−	2.20666i
$868$		0			0
$869$	0.788397	+	0.455181i	0.0267445	+	0.0154410i
$870$		0			0
$871$	22.1684	+	23.2670i	0.751148	+	0.788372i
$872$		0			0
$873$	55.9628	+	32.3101i	1.89405	+	1.09353i
$874$		0			0
$875$	−3.77445	−	6.53754i	−0.127600	−	0.221009i
$876$		0			0
$877$	−9.88137	+	5.70501i	−0.333670	+	0.192645i	−0.657469	−	0.753481i	$-0.728373\pi$
$877$	−9.88137	+	5.70501i	−0.333670	+	0.192645i	0.323799	+	0.946126i	$0.395040\pi$
$878$		0			0
$879$			5.49475i			0.185333i
$880$		0			0
$881$	−24.7539	+	42.8749i	−0.833979	+	1.44449i	0.0608809	+	0.998145i	$0.480609\pi$
$881$	−24.7539	+	42.8749i	−0.833979	+	1.44449i	−0.894859	+	0.446348i	$0.852724\pi$
$882$		0			0
$883$	−42.1670			−1.41903			−0.709516	−	0.704690i	$-0.751086\pi$
$883$	−42.1670			−1.41903			−0.709516	+	0.704690i	$0.751086\pi$
$884$		0			0
$885$	−0.432310			−0.0145319
$886$		0			0
$887$	−2.27370	+	3.93817i	−0.0763435	+	0.132231i	−0.901670	−	0.432425i	$-0.857658\pi$
$887$	−2.27370	+	3.93817i	−0.0763435	+	0.132231i	0.825326	+	0.564656i	$0.190991\pi$
$888$		0			0
$889$			20.5006i			0.687568i
$890$		0			0
$891$	24.1510	−	13.9436i	0.809088	−	0.467127i
$892$		0			0
$893$	9.81123	+	16.9935i	0.328320	+	0.568667i
$894$		0			0
$895$	−0.0549902	−	0.0317486i	−0.00183812	−	0.00106124i
$896$		0			0
$897$	−5.71431	−	23.5933i	−0.190795	−	0.787757i
$898$		0			0
$899$	−10.6794	−	6.16578i	−0.356179	−	0.205640i
$900$		0			0
$901$	30.0587	+	52.0632i	1.00140	+	1.73448i
$902$		0			0
$903$	−12.3092	+	7.10674i	−0.409625	+	0.236497i
$904$		0			0
$905$			5.59709i			0.186053i
$906$		0			0
$907$	−9.14435	+	15.8385i	−0.303633	+	0.525908i	−0.976956	−	0.213440i	$-0.931533\pi$
$907$	−9.14435	+	15.8385i	−0.303633	+	0.525908i	0.673323	+	0.739349i	$0.264866\pi$
$908$		0			0
$909$	59.5387			1.97477
$910$		0			0
$911$	−14.6463			−0.485254			−0.242627	−	0.970120i	$-0.578009\pi$
$911$	−14.6463			−0.485254			−0.242627	+	0.970120i	$0.578009\pi$
$912$		0			0
$913$	3.95481	−	6.84993i	0.130885	−	0.226700i
$914$		0			0
$915$		−	14.3689i		−	0.475022i
$916$		0			0
$917$	−0.584875	+	0.337678i	−0.0193143	+	0.0111511i
$918$		0			0
$919$	−14.4963	−	25.1083i	−0.478189	−	0.828247i	0.521499	−	0.853252i	$-0.325373\pi$
$919$	−14.4963	−	25.1083i	−0.478189	−	0.828247i	−0.999687	+	0.0250049i	$0.992040\pi$
$920$		0			0
$921$	−62.0559	−	35.8280i	−2.04481	−	1.18057i
$922$		0			0
$923$	−25.1613	+	6.09410i	−0.828195	+	0.200590i
$924$		0			0
$925$	−32.9155	−	19.0038i	−1.08226	−	0.624841i
$926$		0			0
$927$	71.4789	+	123.805i	2.34768	+	4.06629i
$928$		0			0
$929$	−24.0635	+	13.8931i	−0.789498	+	0.455817i	−0.839786	−	0.542918i	$-0.817319\pi$
$929$	−24.0635	+	13.8931i	−0.789498	+	0.455817i	0.0502881	+	0.998735i	$0.483986\pi$
$930$		0			0
$931$		−	30.3540i		−	0.994814i
$932$		0			0
$933$	−14.4098	+	24.9585i	−0.471756	+	0.817105i
$934$		0			0
$935$	5.23730			0.171278
$936$		0			0
$937$	−32.7763			−1.07076			−0.535378	−	0.844613i	$-0.679831\pi$
$937$	−32.7763			−1.07076			−0.535378	+	0.844613i	$0.679831\pi$
$938$		0			0
$939$	30.6010	−	53.0025i	0.998626	−	1.72967i
$940$		0			0
$941$		−	34.7292i		−	1.13214i	−0.824357	−	0.566070i	$-0.808463\pi$
$941$		−	34.7292i		−	1.13214i	0.824357	−	0.566070i	$-0.191537\pi$
$942$		0			0
$943$	20.1453	−	11.6309i	0.656022	−	0.378755i
$944$		0			0
$945$	−6.32219	−	10.9504i	−0.205661	−	0.356215i
$946$		0			0
$947$	−14.0416	−	8.10693i	−0.456291	−	0.263440i	0.254192	−	0.967154i	$-0.418190\pi$
$947$	−14.0416	−	8.10693i	−0.456291	−	0.263440i	−0.710484	+	0.703714i	$0.751524\pi$
$948$		0			0
$949$	−1.93885	+	6.59397i	−0.0629376	+	0.214049i
$950$		0			0
$951$	60.7024	+	35.0466i	1.96841	+	1.13646i
$952$		0			0
$953$	3.01548	+	5.22296i	0.0976809	+	0.169188i	0.910724	−	0.413015i	$-0.135524\pi$
$953$	3.01548	+	5.22296i	0.0976809	+	0.169188i	−0.813043	+	0.582203i	$0.802191\pi$
$954$		0			0
$955$	−7.85152	+	4.53308i	−0.254069	+	0.146687i
$956$		0			0
$957$		−	7.45430i		−	0.240963i
$958$		0			0
$959$	6.18822	−	10.7183i	0.199828	−	0.346112i
$960$		0			0
$961$	1.56448			0.0504671
$962$		0			0
$963$	−43.0647			−1.38774
$964$		0			0
$965$	−2.77748	+	4.81074i	−0.0894103	+	0.154863i
$966$		0			0
$967$		−	27.8774i		−	0.896475i	−0.893914	−	0.448238i	$-0.852052\pi$
$967$		−	27.8774i		−	0.896475i	0.893914	−	0.448238i	$-0.147948\pi$
$968$		0			0
$969$	−90.0660	+	51.9996i	−2.89334	+	1.67047i
$970$		0			0
$971$	−4.89097	−	8.47140i	−0.156959	−	0.271860i	0.776812	−	0.629733i	$-0.216836\pi$
$971$	−4.89097	−	8.47140i	−0.156959	−	0.271860i	−0.933770	+	0.357872i	$0.883502\pi$
$972$		0			0
$973$	3.78134	+	2.18316i	0.121224	+	0.0699887i
$974$		0			0
$975$	36.9168	−	35.1737i	1.18228	−	1.12646i
$976$		0			0
$977$	−50.8997	−	29.3870i	−1.62843	−	0.940172i	−0.984563	−	0.175031i	$-0.943997\pi$
$977$	−50.8997	−	29.3870i	−1.62843	−	0.940172i	−0.643863	−	0.765141i	$-0.722669\pi$
$978$		0			0
$979$	5.27307	+	9.13322i	0.168528	+	0.291899i
$980$		0			0
$981$	−85.0472	+	49.1020i	−2.71535	+	1.56771i
$982$		0			0
$983$			24.2599i			0.773772i	0.922128	+	0.386886i	$0.126449\pi$
$983$			24.2599i			0.773772i	−0.922128	+	0.386886i	$0.873551\pi$
$984$		0			0
$985$	−1.11135	+	1.92491i	−0.0354105	+	0.0613328i
$986$		0			0
$987$	12.5261			0.398711
$988$		0			0
$989$	9.10249			0.289442
$990$		0			0
$991$	1.01891	−	1.76481i	0.0323668	−	0.0560609i	−0.849388	−	0.527768i	$-0.823029\pi$
$991$	1.01891	−	1.76481i	0.0323668	−	0.0560609i	0.881755	+	0.471708i	$0.156362\pi$
$992$		0			0
$993$		−	19.7035i		−	0.625273i
$994$		0			0
$995$	11.8162	−	6.82208i	0.374598	−	0.216274i
$996$		0			0
$997$	−6.84978	−	11.8642i	−0.216935	−	0.375742i	0.736935	−	0.675964i	$-0.236273\pi$
$997$	−6.84978	−	11.8642i	−0.216935	−	0.375742i	−0.953869	+	0.300222i	$0.902939\pi$
$998$		0			0
$999$	−119.061	−	68.7402i	−3.76694	−	2.17484i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.p.a.485.1	yes	24
13.6	odd	12		7436.2.a.u.1.12		12
13.7	odd	12		7436.2.a.v.1.12		12
13.10	even	6	inner	572.2.p.a.309.1	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.p.a.309.1	✓	24	13.10	even	6	inner
572.2.p.a.485.1	yes	24	1.1	even	1	trivial
7436.2.a.u.1.12		12	13.6	odd	12
7436.2.a.v.1.12		12	13.7	odd	12

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:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.63981 + 2.84024i) q^{3} -0.829371i q^{5} +(0.846479 - 0.488715i) q^{7} +(-3.87798 - 6.71686i) q^{9} +O(q^{10})\)	\(q+(-1.63981 + 2.84024i) q^{3} -0.829371i q^{5} +(0.846479 - 0.488715i) q^{7} +(-3.87798 - 6.71686i) q^{9} +(-0.866025 - 0.500000i) q^{11} +(-3.45912 - 1.01710i) q^{13} +(2.35561 + 1.36001i) q^{15} +(-3.15739 - 5.46876i) q^{17} +(-4.34888 + 2.51083i) q^{19} +3.20561i q^{21} +(1.02646 - 1.77787i) q^{23} +4.31214 q^{25} +15.5978 q^{27} +(1.13645 - 1.96840i) q^{29} -5.42545i q^{31} +(2.84024 - 1.63981i) q^{33} +(-0.405326 - 0.702045i) q^{35} +(-7.63322 - 4.40704i) q^{37} +(8.56112 - 8.15689i) q^{39} +(9.81305 + 5.66557i) q^{41} +(2.21697 + 3.83991i) q^{43} +(-5.57077 + 3.21629i) q^{45} -3.90757i q^{47} +(-3.02232 + 5.23480i) q^{49} +20.7102 q^{51} -9.52011 q^{53} +(-0.414685 + 0.718256i) q^{55} -16.4692i q^{57} +(-0.137643 + 0.0794680i) q^{59} +(-2.64132 - 4.57490i) q^{61} +(-6.56526 - 3.79046i) q^{63} +(-0.843550 + 2.86889i) q^{65} +(-7.71908 - 4.45661i) q^{67} +(3.36640 + 5.83077i) q^{69} +(6.21829 - 3.59013i) q^{71} -1.90626i q^{73} +(-7.07112 + 12.2475i) q^{75} -0.977430 q^{77} -0.910363 q^{79} +(-13.9436 + 24.1510i) q^{81} +7.90962i q^{83} +(-4.53563 + 2.61865i) q^{85} +(3.72715 + 6.45561i) q^{87} +(-9.13322 - 5.27307i) q^{89} +(-3.42514 + 0.829573i) q^{91} +(15.4096 + 8.89673i) q^{93} +(2.08241 + 3.60683i) q^{95} +(-7.21545 + 4.16584i) q^{97} +7.75597i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{3} + 6 q^{7} - 14 q^{9}+O(q^{10}) \) 24 * q - 2 * q^3 + 6 * q^7 - 14 * q^9	\( 24 q - 2 q^{3} + 6 q^{7} - 14 q^{9} - 2 q^{13} - 6 q^{19} + 10 q^{23} - 40 q^{25} - 8 q^{27} - 8 q^{29} + 8 q^{35} + 18 q^{37} + 36 q^{41} + 10 q^{43} - 30 q^{45} + 14 q^{49} + 44 q^{51} + 16 q^{53} - 24 q^{59} + 6 q^{61} - 6 q^{63} - 24 q^{65} - 54 q^{67} + 10 q^{69} + 18 q^{71} + 6 q^{75} - 16 q^{77} - 32 q^{79} - 4 q^{81} + 52 q^{87} - 18 q^{89} - 18 q^{91} + 30 q^{93} - 12 q^{95} + 42 q^{97}+O(q^{100}) \) 24 * q - 2 * q^3 + 6 * q^7 - 14 * q^9 - 2 * q^13 - 6 * q^19 + 10 * q^23 - 40 * q^25 - 8 * q^27 - 8 * q^29 + 8 * q^35 + 18 * q^37 + 36 * q^41 + 10 * q^43 - 30 * q^45 + 14 * q^49 + 44 * q^51 + 16 * q^53 - 24 * q^59 + 6 * q^61 - 6 * q^63 - 24 * q^65 - 54 * q^67 + 10 * q^69 + 18 * q^71 + 6 * q^75 - 16 * q^77 - 32 * q^79 - 4 * q^81 + 52 * q^87 - 18 * q^89 - 18 * q^91 + 30 * q^93 - 12 * q^95 + 42 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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