LMFDB - Embedded newform 576.3.o.h.511.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [576,3,Mod(319,576)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([3, 0, 2]))

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

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

chi := DirichletCharacter("576.319");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 576 = 2^{6} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	576.o (of order $6$, degree $2$, 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:	$15.6948632272$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 10 x^{19} + 50 x^{18} - 130 x^{17} + 203 x^{16} - 296 x^{15} + 1260 x^{14} - 3380 x^{13} + \cdots + 64 $ x^20 - 10x^19 + 50x^18 - 130x^17 + 203x^16 - 296x^15 + 1260x^14 - 3380x^13 + 4843x^12 - 2370x^11 + 8978x^10 - 23570x^9 + 32213x^8 - 6940x^7 + 11856x^6 - 30488x^5 + 41556x^4 - 6096x^3 + 288x^2 + 192*x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{26}\cdot 3^{4} $
Twist minimal:	no (minimal twist has level 288)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			511.6
Root			$-1.24258 + 1.24258i$ of defining polynomial
Character	$\chi$	$=$	576.511
Dual form			576.3.o.h.319.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.998802 - 2.82885i) q^{3} +(-1.18939 - 2.06008i) q^{5} +(6.27165 + 3.62094i) q^{7} +(-7.00479 - 5.65092i) q^{9} +O(q^{10})$	\(q+(0.998802 - 2.82885i) q^{3} +(-1.18939 - 2.06008i) q^{5} +(6.27165 + 3.62094i) q^{7} +(-7.00479 - 5.65092i) q^{9} +(-12.4835 - 7.20734i) q^{11} +(-0.702060 - 1.21600i) q^{13} +(-7.01562 + 1.30699i) q^{15} -13.0349 q^{17} -14.1455i q^{19} +(16.5072 - 14.1249i) q^{21} +(-26.2946 + 15.1812i) q^{23} +(9.67071 - 16.7502i) q^{25} +(-22.9820 + 14.1713i) q^{27} +(14.5940 - 25.2775i) q^{29} +(-3.44515 + 1.98906i) q^{31} +(-32.8570 + 28.1152i) q^{33} -17.2268i q^{35} +51.6925 q^{37} +(-4.14111 + 0.771476i) q^{39} +(12.7135 + 22.0205i) q^{41} +(-64.0557 - 36.9826i) q^{43} +(-3.30994 + 21.1516i) q^{45} +(-40.7870 - 23.5484i) q^{47} +(1.72236 + 2.98321i) q^{49} +(-13.0193 + 36.8738i) q^{51} -73.1369 q^{53} +34.2893i q^{55} +(-40.0155 - 14.1286i) q^{57} +(44.3650 - 25.6142i) q^{59} +(-46.7652 + 80.9998i) q^{61} +(-23.4699 - 60.8045i) q^{63} +(-1.67004 + 2.89260i) q^{65} +(-71.4356 + 41.2433i) q^{67} +(16.6823 + 89.5466i) q^{69} +46.6086i q^{71} +120.245 q^{73} +(-37.7246 - 44.0871i) q^{75} +(-52.1946 - 90.4037i) q^{77} +(-57.4052 - 33.1429i) q^{79} +(17.1341 + 79.1670i) q^{81} +(16.1314 + 9.31346i) q^{83} +(15.5036 + 26.8530i) q^{85} +(-56.9298 - 66.5314i) q^{87} +38.2794 q^{89} -10.1685i q^{91} +(2.18573 + 11.7325i) q^{93} +(-29.1409 + 16.8245i) q^{95} +(86.1636 - 149.240i) q^{97} +(46.7160 + 121.029i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 14 q^{5} + 48 q^{9}+O(q^{10}) $ 20 * q - 14 * q^5 + 48 * q^9	$ 20 q - 14 q^{5} + 48 q^{9} - 26 q^{13} + 72 q^{17} + 42 q^{21} + 36 q^{25} + 134 q^{29} - 42 q^{33} - 96 q^{37} - 26 q^{41} - 306 q^{45} + 348 q^{49} + 192 q^{53} - 612 q^{57} - 386 q^{61} - 106 q^{65} - 78 q^{69} - 168 q^{73} - 58 q^{77} + 264 q^{81} - 192 q^{85} - 240 q^{89} + 642 q^{93} + 374 q^{97}+O(q^{100}) $ 20 * q - 14 * q^5 + 48 * q^9 - 26 * q^13 + 72 * q^17 + 42 * q^21 + 36 * q^25 + 134 * q^29 - 42 * q^33 - 96 * q^37 - 26 * q^41 - 306 * q^45 + 348 * q^49 + 192 * q^53 - 612 * q^57 - 386 * q^61 - 106 * q^65 - 78 * q^69 - 168 * q^73 - 58 * q^77 + 264 * q^81 - 192 * q^85 - 240 * q^89 + 642 * q^93 + 374 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$65$	$127$	$325$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.998802	−	2.82885i	0.332934	−	0.942950i
$3$	0.998802	−	2.82885i	0.332934	−	0.942950i
$4$		0			0
$5$	−1.18939	−	2.06008i	−0.237878	−	0.412016i	0.722228	−	0.691656i	$-0.243118\pi$
$5$	−1.18939	−	2.06008i	−0.237878	−	0.412016i	−0.960105	+	0.279640i	$0.909785\pi$
$6$		0			0
$7$	6.27165	+	3.62094i	0.895949	+	0.517277i	0.875884	−	0.482522i	$-0.160279\pi$
$7$	6.27165	+	3.62094i	0.895949	+	0.517277i	0.0200655	+	0.999799i	$0.493613\pi$
$8$		0			0
$9$	−7.00479	−	5.65092i	−0.778310	−	0.627880i
$10$		0			0
$11$	−12.4835	−	7.20734i	−1.13486	−	0.655212i	−0.189708	−	0.981840i	$-0.560754\pi$
$11$	−12.4835	−	7.20734i	−1.13486	−	0.655212i	−0.945153	+	0.326628i	$0.894088\pi$
$12$		0			0
$13$	−0.702060	−	1.21600i	−0.0540046	−	0.0935388i	0.837759	−	0.546040i	$-0.183865\pi$
$13$	−0.702060	−	1.21600i	−0.0540046	−	0.0935388i	−0.891764	+	0.452501i	$0.850532\pi$
$14$		0			0
$15$	−7.01562	+	1.30699i	−0.467708	+	0.0871325i
$16$		0			0
$17$	−13.0349			−0.766760			−0.383380	−	0.923591i	$-0.625240\pi$
$17$	−13.0349			−0.766760			−0.383380	+	0.923591i	$0.625240\pi$
$18$		0			0
$19$		−	14.1455i		−	0.744500i	−0.928132	−	0.372250i	$-0.878586\pi$
$19$		−	14.1455i		−	0.744500i	0.928132	−	0.372250i	$-0.121414\pi$
$20$		0			0
$21$	16.5072	−	14.1249i	0.786058	−	0.672617i
$22$		0			0
$23$	−26.2946	+	15.1812i	−1.14325	+	0.660053i	−0.947232	−	0.320548i	$-0.896133\pi$
$23$	−26.2946	+	15.1812i	−1.14325	+	0.660053i	−0.196013	+	0.980601i	$0.562799\pi$
$24$		0			0
$25$	9.67071	−	16.7502i	0.386829	−	0.670007i
$26$		0			0
$27$	−22.9820	+	14.1713i	−0.851186	+	0.524865i
$28$		0			0
$29$	14.5940	−	25.2775i	0.503241	−	0.871639i	−0.496752	−	0.867892i	$-0.665474\pi$
$29$	14.5940	−	25.2775i	0.503241	−	0.871639i	0.999993	−	0.00374634i	$-0.00119250\pi$
$30$		0			0
$31$	−3.44515	+	1.98906i	−0.111134	+	0.0641632i	−0.554537	−	0.832159i	$-0.687104\pi$
$31$	−3.44515	+	1.98906i	−0.111134	+	0.0641632i	0.443403	+	0.896322i	$0.353771\pi$
$32$		0			0
$33$	−32.8570	+	28.1152i	−0.995667	+	0.851975i
$34$		0			0
$35$		−	17.2268i		−	0.492194i
$36$		0			0
$37$	51.6925			1.39710			0.698548	−	0.715563i	$-0.253830\pi$
$37$	51.6925			1.39710			0.698548	+	0.715563i	$0.253830\pi$
$38$		0			0
$39$	−4.14111	+	0.771476i	−0.106182	+	0.0197814i
$40$		0			0
$41$	12.7135	+	22.0205i	0.310086	+	0.537084i	0.978381	−	0.206812i	$-0.0663089\pi$
$41$	12.7135	+	22.0205i	0.310086	+	0.537084i	−0.668295	+	0.743897i	$0.732976\pi$
$42$		0			0
$43$	−64.0557	−	36.9826i	−1.48967	−	0.860060i	−0.489738	−	0.871870i	$-0.662908\pi$
$43$	−64.0557	−	36.9826i	−1.48967	−	0.860060i	−0.999930	+	0.0118095i	$0.996241\pi$
$44$		0			0
$45$	−3.30994	+	21.1516i	−0.0735543	+	0.470035i
$46$		0			0
$47$	−40.7870	−	23.5484i	−0.867808	−	0.501029i	−0.00118860	−	0.999999i	$-0.500378\pi$
$47$	−40.7870	−	23.5484i	−0.867808	−	0.501029i	−0.866619	+	0.498970i	$0.833712\pi$
$48$		0			0
$49$	1.72236	+	2.98321i	0.0351501	+	0.0608818i
$50$		0			0
$51$	−13.0193	+	36.8738i	−0.255281	+	0.723017i
$52$		0			0
$53$	−73.1369			−1.37994			−0.689970	−	0.723838i	$-0.742376\pi$
$53$	−73.1369			−1.37994			−0.689970	+	0.723838i	$0.742376\pi$
$54$		0			0
$55$			34.2893i			0.623441i
$56$		0			0
$57$	−40.0155	−	14.1286i	−0.702027	−	0.247869i
$58$		0			0
$59$	44.3650	−	25.6142i	0.751950	−	0.434138i	−0.0744481	−	0.997225i	$-0.523720\pi$
$59$	44.3650	−	25.6142i	0.751950	−	0.434138i	0.826398	+	0.563086i	$0.190386\pi$
$60$		0			0
$61$	−46.7652	+	80.9998i	−0.766643	+	1.32787i	0.172730	+	0.984969i	$0.444741\pi$
$61$	−46.7652	+	80.9998i	−0.766643	+	1.32787i	−0.939373	+	0.342896i	$0.888592\pi$
$62$		0			0
$63$	−23.4699	−	60.8045i	−0.372538	−	0.965150i
$64$		0			0
$65$	−1.67004	+	2.89260i	−0.0256930	+	0.0445015i
$66$		0			0
$67$	−71.4356	+	41.2433i	−1.06620	+	0.615572i	−0.927141	−	0.374712i	$-0.877742\pi$
$67$	−71.4356	+	41.2433i	−1.06620	+	0.615572i	−0.139061	+	0.990284i	$0.544408\pi$
$68$		0			0
$69$	16.6823	+	89.5466i	0.241772	+	1.29778i
$70$		0			0
$71$			46.6086i			0.656459i	0.944598	+	0.328229i	$0.106452\pi$
$71$			46.6086i			0.656459i	−0.944598	+	0.328229i	$0.893548\pi$
$72$		0			0
$73$	120.245			1.64720			0.823599	−	0.567173i	$-0.191963\pi$
$73$	120.245			1.64720			0.823599	+	0.567173i	$0.191963\pi$
$74$		0			0
$75$	−37.7246	−	44.0871i	−0.502995	−	0.587828i
$76$		0			0
$77$	−52.1946	−	90.4037i	−0.677852	−	1.17407i
$78$		0			0
$79$	−57.4052	−	33.1429i	−0.726648	−	0.419530i	0.0905466	−	0.995892i	$-0.471139\pi$
$79$	−57.4052	−	33.1429i	−0.726648	−	0.419530i	−0.817195	+	0.576362i	$0.804472\pi$
$80$		0			0
$81$	17.1341	+	79.1670i	0.211533	+	0.977371i
$82$		0			0
$83$	16.1314	+	9.31346i	0.194354	+	0.112210i	0.594019	−	0.804451i	$-0.297540\pi$
$83$	16.1314	+	9.31346i	0.194354	+	0.112210i	−0.399665	+	0.916661i	$0.630874\pi$
$84$		0			0
$85$	15.5036	+	26.8530i	0.182395	+	0.315917i
$86$		0			0
$87$	−56.9298	−	66.5314i	−0.654366	−	0.764729i
$88$		0			0
$89$	38.2794			0.430106			0.215053	−	0.976602i	$-0.431008\pi$
$89$	38.2794			0.430106			0.215053	+	0.976602i	$0.431008\pi$
$90$		0			0
$91$		−	10.1685i		−	0.111741i
$92$		0			0
$93$	2.18573	+	11.7325i	0.0235024	+	0.126156i
$94$		0			0
$95$	−29.1409	+	16.8245i	−0.306746	+	0.177100i
$96$		0			0
$97$	86.1636	−	149.240i	0.888285	−	1.53855i	0.0463833	−	0.998924i	$-0.485230\pi$
$97$	86.1636	−	149.240i	0.888285	−	1.53855i	0.841902	−	0.539631i	$-0.181436\pi$
$98$		0			0
$99$	46.7160	+	121.029i	0.471879	+	1.22252i
$100$		0			0
$101$	63.6148	−	110.184i	0.629849	−	1.09093i	−0.357733	−	0.933824i	$-0.616450\pi$
$101$	63.6148	−	110.184i	0.629849	−	1.09093i	0.987582	−	0.157107i	$-0.0502166\pi$
$102$		0			0
$103$	118.904	−	68.6494i	1.15441	−	0.666499i	0.204452	−	0.978877i	$-0.434459\pi$
$103$	118.904	−	68.6494i	1.15441	−	0.666499i	0.949958	+	0.312378i	$0.101125\pi$
$104$		0			0
$105$	−48.7320	−	17.2061i	−0.464114	−	0.163868i
$106$		0			0
$107$			74.0998i			0.692521i	0.938138	+	0.346261i	$0.112549\pi$
$107$			74.0998i			0.692521i	−0.938138	+	0.346261i	$0.887451\pi$
$108$		0			0
$109$	−6.48932			−0.0595350			−0.0297675	−	0.999557i	$-0.509477\pi$
$109$	−6.48932			−0.0595350			−0.0297675	+	0.999557i	$0.509477\pi$
$110$		0			0
$111$	51.6306	−	146.230i	0.465141	−	1.31739i
$112$		0			0
$113$	−45.8811	−	79.4685i	−0.406028	−	0.703261i	0.588413	−	0.808561i	$-0.299753\pi$
$113$	−45.8811	−	79.4685i	−0.406028	−	0.703261i	−0.994441	+	0.105300i	$0.966420\pi$
$114$		0			0
$115$	62.5490	+	36.1127i	0.543905	+	0.314023i
$116$		0			0
$117$	−1.95376	+	12.4851i	−0.0166988	+	0.106711i
$118$		0			0
$119$	−81.7504	−	47.1986i	−0.686978	−	0.396627i
$120$		0			0
$121$	43.3914	+	75.1561i	0.358607	+	0.621125i
$122$		0			0
$123$	74.9909	−	13.9706i	0.609682	−	0.113582i
$124$		0			0
$125$	−105.478			−0.843826
$126$		0			0
$127$			177.581i			1.39827i	0.714987	+	0.699137i	$0.246432\pi$
$127$			177.581i			1.39827i	−0.714987	+	0.699137i	$0.753568\pi$
$128$		0			0
$129$	−168.597	+	144.266i	−1.30696	+	1.11834i
$130$		0			0
$131$	41.4781	−	23.9474i	0.316626	−	0.182804i	−0.333261	−	0.942834i	$-0.608149\pi$
$131$	41.4781	−	23.9474i	0.316626	−	0.182804i	0.649888	+	0.760030i	$0.274816\pi$
$132$		0			0
$133$	51.2200	−	88.7156i	0.385113	−	0.667035i
$134$		0			0
$135$	56.5286	+	30.4896i	0.418731	+	0.225849i
$136$		0			0
$137$	102.336	−	177.250i	0.746975	−	1.29380i	−0.202291	−	0.979325i	$-0.564839\pi$
$137$	102.336	−	177.250i	0.746975	−	1.29380i	0.949266	−	0.314474i	$-0.101828\pi$
$138$		0			0
$139$	−3.63366	+	2.09789i	−0.0261414	+	0.0150928i	−0.513014	−	0.858380i	$-0.671471\pi$
$139$	−3.63366	+	2.09789i	−0.0261414	+	0.0150928i	0.486872	+	0.873473i	$0.338138\pi$
$140$		0			0
$141$	−107.353	+	91.8601i	−0.761368	+	0.651490i
$142$		0			0
$143$			20.2399i			0.141538i
$144$		0			0
$145$	−69.4316			−0.478839
$146$		0			0
$147$	10.1593	−	1.89265i	0.0691112	−	0.0128752i
$148$		0			0
$149$	−109.832	−	190.235i	−0.737131	−	1.27675i	−0.953782	−	0.300499i	$-0.902847\pi$
$149$	−109.832	−	190.235i	−0.737131	−	1.27675i	0.216651	−	0.976249i	$-0.430487\pi$
$150$		0			0
$151$	56.3773	+	32.5494i	0.373359	+	0.215559i	0.674925	−	0.737886i	$-0.264176\pi$
$151$	56.3773	+	32.5494i	0.373359	+	0.215559i	−0.301566	+	0.953445i	$0.597509\pi$
$152$		0			0
$153$	91.3069	+	73.6593i	0.596777	+	0.481434i
$154$		0			0
$155$	8.19524	+	4.73152i	0.0528725	+	0.0305260i
$156$		0			0
$157$	37.5262	+	64.9972i	0.239020	+	0.413995i	0.960433	−	0.278510i	$-0.0898405\pi$
$157$	37.5262	+	64.9972i	0.239020	+	0.413995i	−0.721413	+	0.692505i	$0.756507\pi$
$158$		0			0
$159$	−73.0492	+	206.893i	−0.459429	+	1.30122i
$160$		0			0
$161$	−219.881			−1.36572
$162$		0			0
$163$		−	198.926i		−	1.22040i	−0.792246	−	0.610202i	$-0.791088\pi$
$163$		−	198.926i		−	1.22040i	0.792246	−	0.610202i	$-0.208912\pi$
$164$		0			0
$165$	96.9992	+	34.2482i	0.587874	+	0.207565i
$166$		0			0
$167$	126.219	−	72.8727i	0.755803	−	0.436363i	−0.0719837	−	0.997406i	$-0.522933\pi$
$167$	126.219	−	72.8727i	0.755803	−	0.436363i	0.827787	+	0.561043i	$0.189600\pi$
$168$		0			0
$169$	83.5142	−	144.651i	0.494167	−	0.855922i
$170$		0			0
$171$	−79.9352	+	99.0863i	−0.467457	+	0.579452i
$172$		0			0
$173$	−39.1409	+	67.7941i	−0.226248	+	0.391873i	−0.956693	−	0.291098i	$-0.905979\pi$
$173$	−39.1409	+	67.7941i	−0.226248	+	0.391873i	0.730445	+	0.682972i	$0.239313\pi$
$174$		0			0
$175$	121.303	−	70.0341i	0.693158	−	0.400195i
$176$		0			0
$177$	−28.1468	−	151.086i	−0.159021	−	0.853591i
$178$		0			0
$179$		−	107.176i		−	0.598747i	−0.954136	−	0.299373i	$-0.903222\pi$
$179$		−	107.176i		−	0.598747i	0.954136	−	0.299373i	$-0.0967776\pi$
$180$		0			0
$181$	352.497			1.94750			0.973748	−	0.227628i	$-0.0730970\pi$
$181$	352.497			1.94750			0.973748	+	0.227628i	$0.0730970\pi$
$182$		0			0
$183$	182.427	+	213.195i	0.996869	+	1.16500i
$184$		0			0
$185$	−61.4825	−	106.491i	−0.332338	−	0.575626i
$186$		0			0
$187$	162.721	+	93.9471i	0.870166	+	0.502391i
$188$		0			0
$189$	−195.449	+	5.66127i	−1.03412	+	0.0299538i
$190$		0			0
$191$	199.812	+	115.362i	1.04614	+	0.603988i	0.921565	−	0.388223i	$-0.126911\pi$
$191$	199.812	+	115.362i	1.04614	+	0.603988i	0.124572	+	0.992211i	$0.460244\pi$
$192$		0			0
$193$	157.504	+	272.805i	0.816082	+	1.41350i	0.908548	+	0.417779i	$0.137192\pi$
$193$	157.504	+	272.805i	0.816082	+	1.41350i	−0.0924666	+	0.995716i	$0.529475\pi$
$194$		0			0
$195$	6.51469	+	7.61344i	0.0334087	+	0.0390433i
$196$		0			0
$197$	258.685			1.31312			0.656560	−	0.754273i	$-0.272011\pi$
$197$	258.685			1.31312			0.656560	+	0.754273i	$0.272011\pi$
$198$		0			0
$199$		−	103.542i		−	0.520310i	−0.965567	−	0.260155i	$-0.916226\pi$
$199$		−	103.542i		−	0.520310i	0.965567	−	0.260155i	$-0.0837736\pi$
$200$		0			0
$201$	45.3213	+	243.274i	0.225479	+	1.21032i
$202$		0			0
$203$	183.057	−	105.688i	0.901757	−	0.520629i
$204$		0			0
$205$	30.2426	−	52.3817i	0.147525	−	0.255521i
$206$		0			0
$207$	269.976	+	42.2477i	1.30423	+	0.204095i
$208$		0			0
$209$	−101.951	+	176.585i	−0.487806	+	0.844905i
$210$		0			0
$211$	87.9065	−	50.7528i	0.416618	−	0.240535i	−0.277011	−	0.960867i	$-0.589344\pi$
$211$	87.9065	−	50.7528i	0.416618	−	0.240535i	0.693629	+	0.720332i	$0.256011\pi$
$212$		0			0
$213$	131.849	+	46.5527i	0.619008	+	0.218558i
$214$		0			0
$215$			175.947i			0.818356i
$216$		0			0
$217$	−28.8090			−0.132760
$218$		0			0
$219$	120.101	−	340.156i	0.548408	−	1.55323i
$220$		0			0
$221$	9.15130	+	15.8505i	0.0414086	+	0.0717218i
$222$		0			0
$223$	−143.820	−	83.0344i	−0.644932	−	0.372352i	0.141580	−	0.989927i	$-0.454782\pi$
$223$	−143.820	−	83.0344i	−0.644932	−	0.372352i	−0.786512	+	0.617575i	$0.788115\pi$
$224$		0			0
$225$	−162.395	+	62.6829i	−0.721757	+	0.278591i
$226$		0			0
$227$	−236.336	−	136.449i	−1.04113	−	0.601096i	−0.120976	−	0.992655i	$-0.538602\pi$
$227$	−236.336	−	136.449i	−1.04113	−	0.601096i	−0.920153	+	0.391559i	$0.871936\pi$
$228$		0			0
$229$	−59.7267	−	103.450i	−0.260815	−	0.451745i	0.705644	−	0.708567i	$-0.250658\pi$
$229$	−59.7267	−	103.450i	−0.260815	−	0.451745i	−0.966459	+	0.256822i	$0.917325\pi$
$230$		0			0
$231$	−307.871	+	57.3553i	−1.33277	+	0.248292i
$232$		0			0
$233$	−18.0809			−0.0776006			−0.0388003	−	0.999247i	$-0.512354\pi$
$233$	−18.0809			−0.0776006			−0.0388003	+	0.999247i	$0.512354\pi$
$234$		0			0
$235$			112.033i			0.476734i
$236$		0			0
$237$	−151.093	+	129.288i	−0.637522	+	0.545517i
$238$		0			0
$239$	356.651	−	205.913i	1.49226	−	0.861559i	0.492303	−	0.870424i	$-0.336155\pi$
$239$	356.651	−	205.913i	1.49226	−	0.861559i	0.999961	+	0.00886544i	$0.00282199\pi$
$240$		0			0
$241$	−96.8685	+	167.781i	−0.401944	+	0.696188i	−0.993961	−	0.109738i	$-0.964999\pi$
$241$	−96.8685	+	167.781i	−0.401944	+	0.696188i	0.592016	+	0.805926i	$0.298332\pi$
$242$		0			0
$243$	241.065	+	30.6023i	0.992038	+	0.125935i
$244$		0			0
$245$	4.09710	−	7.09638i	0.0167228	−	0.0289648i
$246$		0			0
$247$	−17.2010	+	9.93100i	−0.0696396	+	0.0402065i
$248$		0			0
$249$	42.4584	−	36.3310i	0.170516	−	0.145907i
$250$		0			0
$251$			475.263i			1.89348i	0.322001	+	0.946739i	$0.395645\pi$
$251$			475.263i			1.89348i	−0.322001	+	0.946739i	$0.604355\pi$
$252$		0			0
$253$	437.665			1.72990
$254$		0			0
$255$	91.4481	−	17.0365i	0.358620	−	0.0668098i
$256$		0			0
$257$	−172.988	−	299.624i	−0.673106	−	1.16585i	−0.977019	−	0.213154i	$-0.931626\pi$
$257$	−172.988	−	299.624i	−0.673106	−	1.16585i	0.303913	−	0.952700i	$-0.401707\pi$
$258$		0			0
$259$	324.197	+	187.175i	1.25173	+	0.722685i
$260$		0			0
$261$	−245.069	+	94.5943i	−0.938962	+	0.362430i
$262$		0			0
$263$	−337.008	−	194.572i	−1.28140	−	0.739816i	−0.304294	−	0.952578i	$-0.598421\pi$
$263$	−337.008	−	194.572i	−1.28140	−	0.739816i	−0.977104	+	0.212762i	$0.931754\pi$
$264$		0			0
$265$	86.9881	+	150.668i	0.328257	+	0.568558i
$266$		0			0
$267$	38.2336	−	108.287i	0.143197	−	0.405568i
$268$		0			0
$269$	−182.696			−0.679167			−0.339584	−	0.940576i	$-0.610286\pi$
$269$	−182.696			−0.679167			−0.339584	+	0.940576i	$0.610286\pi$
$270$		0			0
$271$			194.807i			0.718844i	0.933175	+	0.359422i	$0.117026\pi$
$271$			194.807i			0.718844i	−0.933175	+	0.359422i	$0.882974\pi$
$272$		0			0
$273$	−28.7651	−	10.1563i	−0.105367	−	0.0372025i
$274$		0			0
$275$	−241.448	+	139.400i	−0.877994	+	0.506910i
$276$		0			0
$277$	−48.0171	+	83.1680i	−0.173347	+	0.300246i	−0.939588	−	0.342308i	$-0.888791\pi$
$277$	−48.0171	+	83.1680i	−0.173347	+	0.300246i	0.766241	+	0.642553i	$0.222125\pi$
$278$		0			0
$279$	35.3726	+	5.53534i	0.126783	+	0.0198399i
$280$		0			0
$281$	28.1712	−	48.7940i	0.100254	−	0.173644i	−0.811536	−	0.584303i	$-0.801368\pi$
$281$	28.1712	−	48.7940i	0.100254	−	0.173644i	0.911789	+	0.410659i	$0.134701\pi$
$282$		0			0
$283$	−264.050	+	152.449i	−0.933039	+	0.538690i	−0.887771	−	0.460285i	$-0.847747\pi$
$283$	−264.050	+	152.449i	−0.933039	+	0.538690i	−0.0452674	+	0.998975i	$0.514414\pi$
$284$		0			0
$285$	18.4880	+	99.2395i	0.0648702	+	0.348209i
$286$		0			0
$287$			184.139i			0.641601i
$288$		0			0
$289$	−119.091			−0.412079
$290$		0			0
$291$	−336.117	−	392.805i	−1.15504	−	1.34985i
$292$		0			0
$293$	182.627	+	316.319i	0.623299	+	1.07959i	0.988867	+	0.148802i	$0.0475416\pi$
$293$	182.627	+	316.319i	0.623299	+	1.07959i	−0.365568	+	0.930785i	$0.619125\pi$
$294$		0			0
$295$	−105.534	−	60.9304i	−0.357744	−	0.206544i
$296$		0			0
$297$	389.033	−	11.2686i	1.30988	−	0.0379413i
$298$		0			0
$299$	36.9208	+	21.3163i	0.123481	+	0.0712918i
$300$		0			0
$301$	−267.823	−	463.883i	−0.889778	−	1.54114i
$302$		0			0
$303$	−248.155	−	290.009i	−0.818995	−	0.957124i
$304$		0			0
$305$	222.488			0.729469
$306$		0			0
$307$		−	49.0342i		−	0.159721i	−0.996806	−	0.0798603i	$-0.974553\pi$
$307$		−	49.0342i		−	0.159721i	0.996806	−	0.0798603i	$-0.0254474\pi$
$308$		0			0
$309$	−75.4371	−	404.929i	−0.244133	−	1.31045i
$310$		0			0
$311$	198.275	−	114.474i	0.637540	−	0.368084i	−0.146126	−	0.989266i	$-0.546681\pi$
$311$	198.275	−	114.474i	0.637540	−	0.368084i	0.783666	+	0.621182i	$0.213347\pi$
$312$		0			0
$313$	89.7831	−	155.509i	0.286847	−	0.496834i	−0.686208	−	0.727405i	$-0.740726\pi$
$313$	89.7831	−	155.509i	0.286847	−	0.496834i	0.973055	+	0.230571i	$0.0740595\pi$
$314$		0			0
$315$	−97.3472	+	120.670i	−0.309039	+	0.383079i
$316$		0			0
$317$	−164.943	+	285.690i	−0.520326	+	0.901231i	0.479395	+	0.877599i	$0.340856\pi$
$317$	−164.943	+	285.690i	−0.520326	+	0.901231i	−0.999721	+	0.0236317i	$0.992477\pi$
$318$		0			0
$319$	−364.367	+	210.368i	−1.14222	+	0.659459i
$320$		0			0
$321$	209.617	+	74.0110i	0.653013	+	0.230564i
$322$		0			0
$323$			184.386i			0.570853i
$324$		0			0
$325$	−27.1577			−0.0835621
$326$		0			0
$327$	−6.48154	+	18.3573i	−0.0198212	+	0.0561386i
$328$		0			0
$329$	−170.534	−	295.374i	−0.518341	−	0.897793i
$330$		0			0
$331$	−10.7647	−	6.21499i	−0.0325217	−	0.0187764i	0.483651	−	0.875261i	$-0.339310\pi$
$331$	−10.7647	−	6.21499i	−0.0325217	−	0.0187764i	−0.516173	+	0.856485i	$0.672644\pi$
$332$		0			0
$333$	−362.095	−	292.111i	−1.08737	−	0.877209i
$334$		0			0
$335$	169.929	+	98.1086i	0.507251	+	0.292862i
$336$		0			0
$337$	−65.3200	−	113.138i	−0.193828	−	0.335720i	0.752688	−	0.658378i	$-0.228757\pi$
$337$	−65.3200	−	113.138i	−0.193828	−	0.335720i	−0.946516	+	0.322658i	$0.895424\pi$
$338$		0			0
$339$	−270.631	+	50.4176i	−0.798320	+	0.148725i
$340$		0			0
$341$	57.3433			0.168162
$342$		0			0
$343$		−	329.906i		−	0.961824i
$344$		0			0
$345$	164.632	−	140.872i	0.477193	−	0.408326i
$346$		0			0
$347$	130.337	−	75.2502i	0.375611	−	0.216859i	−0.300296	−	0.953846i	$-0.597085\pi$
$347$	130.337	−	75.2502i	0.375611	−	0.216859i	0.675907	+	0.736987i	$0.263752\pi$
$348$		0			0
$349$	−112.573	+	194.983i	−0.322560	+	0.558691i	−0.981016	−	0.193929i	$-0.937877\pi$
$349$	−112.573	+	194.983i	−0.322560	+	0.558691i	0.658455	+	0.752620i	$0.271210\pi$
$350$		0			0
$351$	33.3672	+	17.9971i	0.0950632	+	0.0512737i
$352$		0			0
$353$	158.550	−	274.617i	0.449150	−	0.777951i	−0.549181	−	0.835704i	$-0.685060\pi$
$353$	158.550	−	274.617i	0.449150	−	0.777951i	0.998331	+	0.0577528i	$0.0183935\pi$
$354$		0			0
$355$	96.0174	−	55.4357i	0.270472	−	0.156157i
$356$		0			0
$357$	−215.170	+	184.118i	−0.602718	+	0.515736i
$358$		0			0
$359$		−	410.024i		−	1.14213i	−0.820906	−	0.571064i	$-0.806531\pi$
$359$		−	410.024i		−	1.14213i	0.820906	−	0.571064i	$-0.193469\pi$
$360$		0			0
$361$	160.905			0.445719
$362$		0			0
$363$	255.945	−	47.6817i	0.705082	−	0.131355i
$364$		0			0
$365$	−143.018	−	247.715i	−0.391831	−	0.678672i
$366$		0			0
$367$	−547.260	−	315.961i	−1.49117	−	0.860928i	−0.491222	−	0.871034i	$-0.663450\pi$
$367$	−547.260	−	315.961i	−1.49117	−	0.860928i	−0.999949	+	0.0101064i	$0.996783\pi$
$368$		0			0
$369$	35.3804	−	226.092i	0.0958819	−	0.612715i
$370$		0			0
$371$	−458.688	−	264.824i	−1.23636	−	0.713811i
$372$		0			0
$373$	22.6159	+	39.1719i	0.0606325	+	0.105019i	0.894748	−	0.446571i	$-0.147355\pi$
$373$	22.6159	+	39.1719i	0.0606325	+	0.105019i	−0.834116	+	0.551589i	$0.814022\pi$
$374$		0			0
$375$	−105.352	+	298.382i	−0.280938	+	0.795686i
$376$		0			0
$377$	−40.9834			−0.108709
$378$		0			0
$379$			0.949486i			0.00250524i	0.999999	+	0.00125262i	$0.000398721\pi$
$379$			0.949486i			0.00250524i	−0.999999	+	0.00125262i	$0.999601\pi$
$380$		0			0
$381$	502.350	+	177.368i	1.31850	+	0.465533i
$382$		0			0
$383$	−125.604	+	72.5178i	−0.327949	+	0.189341i	−0.654930	−	0.755689i	$-0.727302\pi$
$383$	−125.604	+	72.5178i	−0.327949	+	0.189341i	0.326981	+	0.945031i	$0.393969\pi$
$384$		0			0
$385$	−124.159	+	215.050i	−0.322492	+	0.558572i
$386$		0			0
$387$	239.711	+	621.029i	0.619409	+	1.60473i
$388$		0			0
$389$	85.2005	−	147.572i	0.219024	−	0.379361i	−0.735486	−	0.677540i	$-0.763046\pi$
$389$	85.2005	−	147.572i	0.219024	−	0.379361i	0.954510	+	0.298179i	$0.0963792\pi$
$390$		0			0
$391$	342.749	−	197.886i	0.876595	−	0.506102i
$392$		0			0
$393$	−26.3152	−	141.254i	−0.0669597	−	0.359425i
$394$		0			0
$395$			157.679i			0.399187i
$396$		0			0
$397$	−397.412			−1.00104			−0.500519	−	0.865726i	$-0.666857\pi$
$397$	−397.412			−1.00104			−0.500519	+	0.865726i	$0.666857\pi$
$398$		0			0
$399$	−199.805	−	233.503i	−0.500763	−	0.585220i
$400$		0			0
$401$	267.688	+	463.650i	0.667552	+	1.15623i	0.978587	+	0.205836i	$0.0659913\pi$
$401$	267.688	+	463.650i	0.667552	+	1.15623i	−0.311034	+	0.950399i	$0.600675\pi$
$402$		0			0
$403$	4.83741	+	2.79288i	0.0120035	+	0.00693022i
$404$		0			0
$405$	142.711	−	129.458i	0.352374	−	0.319649i
$406$		0			0
$407$	−645.303	−	372.566i	−1.58551	−	0.915395i
$408$		0			0
$409$	−73.9349	−	128.059i	−0.180770	−	0.313103i	0.761373	−	0.648314i	$-0.224526\pi$
$409$	−73.9349	−	128.059i	−0.180770	−	0.313103i	−0.942143	+	0.335211i	$0.891192\pi$
$410$		0			0
$411$	−399.202	−	466.530i	−0.971295	−	1.13511i
$412$		0			0
$413$	370.989			0.898279
$414$		0			0
$415$		−	44.3092i		−	0.106769i
$416$		0			0
$417$	2.30532	+	12.3745i	0.00552835	+	0.0296749i
$418$		0			0
$419$	82.5163	−	47.6408i	0.196936	−	0.113701i	−0.398289	−	0.917260i	$-0.630396\pi$
$419$	82.5163	−	47.6408i	0.196936	−	0.113701i	0.595226	+	0.803559i	$0.297063\pi$
$420$		0			0
$421$	107.222	−	185.714i	0.254685	−	0.441127i	−0.710125	−	0.704076i	$-0.751362\pi$
$421$	107.222	−	185.714i	0.254685	−	0.441127i	0.964810	+	0.262949i	$0.0846950\pi$
$422$		0			0
$423$	152.634	+	395.435i	0.360837	+	0.934835i
$424$		0			0
$425$	−126.057	+	218.337i	−0.296605	+	0.513735i
$426$		0			0
$427$	−586.590	+	338.668i	−1.37375	+	0.793133i
$428$		0			0
$429$	57.2558	+	20.2157i	0.133463	+	0.0471228i
$430$		0			0
$431$			208.782i			0.484412i	0.970225	+	0.242206i	$0.0778710\pi$
$431$			208.782i			0.484412i	−0.970225	+	0.242206i	$0.922129\pi$
$432$		0			0
$433$	−736.209			−1.70025			−0.850126	−	0.526580i	$-0.823474\pi$
$433$	−736.209			−1.70025			−0.850126	+	0.526580i	$0.823474\pi$
$434$		0			0
$435$	−69.3484	+	196.412i	−0.159422	+	0.451521i
$436$		0			0
$437$	214.746	+	371.951i	0.491410	+	0.851146i
$438$		0			0
$439$	−84.2082	−	48.6176i	−0.191818	−	0.110746i	0.401015	−	0.916071i	$-0.368657\pi$
$439$	−84.2082	−	48.6176i	−0.191818	−	0.110746i	−0.592833	+	0.805325i	$0.701991\pi$
$440$		0			0
$441$	4.79314	−	30.6296i	0.0108688	−	0.0694550i
$442$		0			0
$443$	−450.111	−	259.872i	−1.01605	−	0.586618i	−0.103095	−	0.994672i	$-0.532875\pi$
$443$	−450.111	−	259.872i	−1.01605	−	0.586618i	−0.912958	+	0.408053i	$0.866208\pi$
$444$		0			0
$445$	−45.5291	−	78.8587i	−0.102313	−	0.177210i
$446$		0			0
$447$	−647.849	+	120.692i	−1.44933	+	0.270005i
$448$		0			0
$449$	54.0051			0.120279			0.0601394	−	0.998190i	$-0.480845\pi$
$449$	54.0051			0.120279			0.0601394	+	0.998190i	$0.480845\pi$
$450$		0			0
$451$		−	366.523i		−	0.812689i
$452$		0			0
$453$	148.387	−	126.972i	0.327566	−	0.280292i
$454$		0			0
$455$	−20.9478	+	12.0942i	−0.0460392	+	0.0265808i
$456$		0			0
$457$	−132.757	+	229.941i	−0.290496	+	0.503154i	−0.973927	−	0.226861i	$-0.927154\pi$
$457$	−132.757	+	229.941i	−0.290496	+	0.503154i	0.683431	+	0.730015i	$0.260487\pi$
$458$		0			0
$459$	299.569	−	184.722i	0.652655	−	0.402445i
$460$		0			0
$461$	56.3955	−	97.6799i	0.122333	−	0.211887i	−0.798354	−	0.602188i	$-0.794296\pi$
$461$	56.3955	−	97.6799i	0.122333	−	0.211887i	0.920687	+	0.390301i	$0.127629\pi$
$462$		0			0
$463$	30.9268	−	17.8556i	0.0667966	−	0.0385650i	−0.466230	−	0.884664i	$-0.654388\pi$
$463$	30.9268	−	17.8556i	0.0667966	−	0.0385650i	0.533026	+	0.846099i	$0.321055\pi$
$464$		0			0
$465$	21.5702	−	18.4573i	0.0463875	−	0.0396930i
$466$		0			0
$467$			11.4087i			0.0244298i	0.999925	+	0.0122149i	$0.00388821\pi$
$467$			11.4087i			0.0244298i	−0.999925	+	0.0122149i	$0.996112\pi$
$468$		0			0
$469$	−597.358			−1.27368
$470$		0			0
$471$	221.349	−	41.2365i	0.469954	−	0.0875510i
$472$		0			0
$473$	533.092	+	923.342i	1.12704	+	1.95210i
$474$		0			0
$475$	−236.940	−	136.797i	−0.498820	−	0.287994i
$476$		0			0
$477$	512.308	+	413.291i	1.07402	+	0.866438i
$478$		0			0
$479$	−140.486	−	81.1094i	−0.293289	−	0.169331i	0.346135	−	0.938185i	$-0.387494\pi$
$479$	−140.486	−	81.1094i	−0.293289	−	0.169331i	−0.639424	+	0.768854i	$0.720827\pi$
$480$		0			0
$481$	−36.2913	−	62.8583i	−0.0754497	−	0.130683i
$482$		0			0
$483$	−219.617	+	622.010i	−0.454694	+	1.28781i
$484$		0			0
$485$	−409.928			−0.845212
$486$		0			0
$487$			561.542i			1.15306i	0.817074	+	0.576532i	$0.195594\pi$
$487$			561.542i			1.15306i	−0.817074	+	0.576532i	$0.804406\pi$
$488$		0			0
$489$	−562.731	−	198.687i	−1.15078	−	0.406314i
$490$		0			0
$491$	551.001	−	318.121i	1.12220	−	0.647904i	0.180240	−	0.983623i	$-0.442312\pi$
$491$	551.001	−	318.121i	1.12220	−	0.647904i	0.941962	+	0.335719i	$0.108979\pi$
$492$		0			0
$493$	−190.232	+	329.491i	−0.385865	+	0.668338i
$494$		0			0
$495$	193.766	−	240.189i	0.391447	−	0.485231i
$496$		0			0
$497$	−168.767	+	292.313i	−0.339571	+	0.588154i
$498$		0			0
$499$	526.821	−	304.160i	1.05575	−	0.609539i	0.131499	−	0.991316i	$-0.458021\pi$
$499$	526.821	−	304.160i	1.05575	−	0.609539i	0.924255	+	0.381777i	$0.124688\pi$
$500$		0			0
$501$	−80.0779	−	429.840i	−0.159836	−	0.857965i
$502$		0			0
$503$			951.976i			1.89260i	0.323295	+	0.946298i	$0.395209\pi$
$503$			951.976i			1.89260i	−0.323295	+	0.946298i	$0.604791\pi$
$504$		0			0
$505$	−302.650			−0.599308
$506$		0			0
$507$	−325.782	−	380.727i	−0.642567	−	0.750940i
$508$		0			0
$509$	310.568	+	537.919i	0.610152	+	1.05682i	0.991214	+	0.132266i	$0.0422252\pi$
$509$	310.568	+	537.919i	0.610152	+	1.05682i	−0.381062	+	0.924550i	$0.624442\pi$
$510$		0			0
$511$	754.137	+	435.401i	1.47581	+	0.852057i
$512$		0			0
$513$	200.461	+	325.092i	0.390762	+	0.633708i
$514$		0			0
$515$	−282.846	−	163.301i	−0.549216	−	0.317090i
$516$		0			0
$517$	339.442	+	587.931i	0.656561	+	1.13720i
$518$		0			0
$519$	152.685	+	178.437i	0.294191	+	0.343809i
$520$		0			0
$521$	−197.708			−0.379478			−0.189739	−	0.981835i	$-0.560764\pi$
$521$	−197.708			−0.379478			−0.189739	+	0.981835i	$0.560764\pi$
$522$		0			0
$523$		−	291.212i		−	0.556811i	−0.960464	−	0.278406i	$-0.910194\pi$
$523$		−	291.212i		−	0.556811i	0.960464	−	0.278406i	$-0.0898060\pi$
$524$		0			0
$525$	−76.9587	−	413.097i	−0.146588	−	0.786851i
$526$		0			0
$527$	44.9073	−	25.9272i	0.0852131	−	0.0491978i
$528$		0			0
$529$	196.439	−	340.242i	0.371340	−	0.643179i
$530$		0			0
$531$	−455.511	−	71.2816i	−0.857837	−	0.134240i
$532$		0			0
$533$	17.8513	−	30.9194i	0.0334921	−	0.0580101i
$534$		0			0
$535$	152.651	−	88.1334i	0.285330	−	0.164735i
$536$		0			0
$537$	−303.184	−	107.047i	−0.564588	−	0.199343i
$538$		0			0
$539$		−	49.6544i		−	0.0921232i
$540$		0			0
$541$	−110.859			−0.204915			−0.102457	−	0.994737i	$-0.532670\pi$
$541$	−110.859			−0.204915			−0.102457	+	0.994737i	$0.532670\pi$
$542$		0			0
$543$	352.075	−	997.161i	0.648388	−	1.83639i
$544$		0			0
$545$	7.71831	+	13.3685i	0.0141620	+	0.0245294i
$546$		0			0
$547$	−137.984	−	79.6653i	−0.252256	−	0.145640i	0.368541	−	0.929612i	$-0.379858\pi$
$547$	−137.984	−	79.6653i	−0.252256	−	0.145640i	−0.620797	+	0.783971i	$0.713191\pi$
$548$		0			0
$549$	785.304	−	303.120i	1.43043	−	0.552130i
$550$		0			0
$551$	−357.563	−	206.439i	−0.648935	−	0.374663i
$552$		0			0
$553$	−240.017	−	415.721i	−0.434027	−	0.751756i
$554$		0			0
$555$	−362.655	+	67.5615i	−0.653433	+	0.121733i
$556$		0			0
$557$	310.714			0.557834			0.278917	−	0.960315i	$-0.410025\pi$
$557$	310.714			0.557834			0.278917	+	0.960315i	$0.410025\pi$
$558$		0			0
$559$			103.856i			0.185789i
$560$		0			0
$561$	428.288	−	366.479i	0.763438	−	0.653261i
$562$		0			0
$563$	194.057	−	112.039i	0.344683	−	0.199003i	−0.317658	−	0.948205i	$-0.602896\pi$
$563$	194.057	−	112.039i	0.344683	−	0.199003i	0.662341	+	0.749202i	$0.269563\pi$
$564$		0			0
$565$	−109.141	+	189.038i	−0.193170	+	0.334580i
$566$		0			0
$567$	−179.200	+	558.549i	−0.316049	+	0.985096i
$568$		0			0
$569$	29.7555	−	51.5380i	0.0522944	−	0.0905765i	−0.838693	−	0.544604i	$-0.816680\pi$
$569$	29.7555	−	51.5380i	0.0522944	−	0.0905765i	0.890988	+	0.454028i	$0.150013\pi$
$570$		0			0
$571$	−317.284	+	183.184i	−0.555663	+	0.320812i	−0.751403	−	0.659843i	$-0.770623\pi$
$571$	−317.284	+	183.184i	−0.555663	+	0.320812i	0.195740	+	0.980656i	$0.437289\pi$
$572$		0			0
$573$	525.914	−	450.015i	0.917825	−	0.785367i
$574$		0			0
$575$			587.253i			1.02131i
$576$		0			0
$577$	474.120			0.821698			0.410849	−	0.911703i	$-0.365232\pi$
$577$	474.120			0.821698			0.410849	+	0.911703i	$0.365232\pi$
$578$		0			0
$579$	929.038	−	173.077i	1.60456	−	0.298924i
$580$		0			0
$581$	67.4469	+	116.821i	0.116088	+	0.201070i
$582$		0			0
$583$	913.002	+	527.122i	1.56604	+	0.904154i
$584$		0			0
$585$	28.0442	−	10.8248i	0.0479387	−	0.0185039i
$586$		0			0
$587$	815.632	+	470.905i	1.38949	+	0.802224i	0.993258	−	0.115926i	$-0.0369835\pi$
$587$	815.632	+	470.905i	1.38949	+	0.802224i	0.396234	+	0.918150i	$0.370317\pi$
$588$		0			0
$589$	28.1362	+	48.7334i	0.0477695	+	0.0827392i
$590$		0			0
$591$	258.375	−	731.781i	0.437183	−	1.23821i
$592$		0			0
$593$	556.568			0.938564			0.469282	−	0.883048i	$-0.344513\pi$
$593$	556.568			0.938564			0.469282	+	0.883048i	$0.344513\pi$
$594$		0			0
$595$			224.550i			0.377395i
$596$		0			0
$597$	−292.904	−	103.418i	−0.490626	−	0.173229i
$598$		0			0
$599$	−113.317	+	65.4234i	−0.189176	+	0.109221i	−0.591597	−	0.806234i	$-0.701502\pi$
$599$	−113.317	+	65.4234i	−0.189176	+	0.109221i	0.402421	+	0.915455i	$0.368169\pi$
$600$		0			0
$601$	−214.716	+	371.899i	−0.357265	+	0.618801i	−0.987503	−	0.157601i	$-0.949624\pi$
$601$	−214.716	+	371.899i	−0.357265	+	0.618801i	0.630238	+	0.776402i	$0.282957\pi$
$602$		0			0
$603$	733.454	+	114.776i	1.21634	+	0.190341i
$604$		0			0
$605$	103.218	−	178.780i	0.170609	−	0.295503i
$606$		0			0
$607$	−848.940	+	490.136i	−1.39858	+	0.807473i	−0.994244	−	0.107136i	$-0.965832\pi$
$607$	−848.940	+	490.136i	−1.39858	+	0.807473i	−0.404340	+	0.914609i	$0.632499\pi$
$608$		0			0
$609$	−116.138	−	623.401i	−0.190702	−	1.02365i
$610$		0			0
$611$			66.1295i			0.108232i
$612$		0			0
$613$	−650.932			−1.06188			−0.530940	−	0.847409i	$-0.678161\pi$
$613$	−650.932			−1.06188			−0.530940	+	0.847409i	$0.678161\pi$
$614$		0			0
$615$	−117.974	−	137.871i	−0.191827	−	0.224180i
$616$		0			0
$617$	513.017	+	888.571i	0.831470	+	1.44015i	0.896873	+	0.442289i	$0.145834\pi$
$617$	513.017	+	888.571i	0.831470	+	1.44015i	−0.0654026	+	0.997859i	$0.520833\pi$
$618$		0			0
$619$	−789.043	−	455.554i	−1.27471	−	0.735952i	−0.298836	−	0.954305i	$-0.596598\pi$
$619$	−789.043	−	455.554i	−1.27471	−	0.735952i	−0.975870	+	0.218353i	$0.929932\pi$
$620$		0			0
$621$	389.165	−	721.525i	0.626675	−	1.16188i
$622$		0			0
$623$	240.075	+	138.607i	0.385353	+	0.222484i
$624$		0			0
$625$	−116.313	−	201.460i	−0.186101	−	0.322337i
$626$		0			0
$627$	397.703	+	464.779i	0.634296	+	0.741274i
$628$		0			0
$629$	−673.808			−1.07124
$630$		0			0
$631$		−	235.962i		−	0.373950i	−0.982365	−	0.186975i	$-0.940132\pi$
$631$		−	235.962i		−	0.373950i	0.982365	−	0.186975i	$-0.0598683\pi$
$632$		0			0
$633$	−55.7710	−	299.366i	−0.0881059	−	0.472933i
$634$		0			0
$635$	365.831	−	211.213i	0.576112	−	0.332618i
$636$		0			0
$637$	2.41840	−	4.18878i	0.00379654	−	0.00657580i
$638$		0			0
$639$	263.382	−	326.483i	0.412178	−	0.510929i
$640$		0			0
$641$	−372.360	+	644.946i	−0.580905	+	1.00616i	0.414468	+	0.910064i	$0.363968\pi$
$641$	−372.360	+	644.946i	−0.580905	+	1.00616i	−0.995372	+	0.0960922i	$0.969366\pi$
$642$		0			0
$643$	542.878	−	313.430i	0.844289	−	0.487450i	−0.0144311	−	0.999896i	$-0.504594\pi$
$643$	542.878	−	313.430i	0.844289	−	0.487450i	0.858720	+	0.512446i	$0.171260\pi$
$644$		0			0
$645$	497.726	+	175.736i	0.771669	+	0.272459i
$646$		0			0
$647$		−	516.051i		−	0.797606i	−0.917037	−	0.398803i	$-0.869426\pi$
$647$		−	516.051i		−	0.797606i	0.917037	−	0.398803i	$-0.130574\pi$
$648$		0			0
$649$	−738.440			−1.13781
$650$		0			0
$651$	−28.7745	+	81.4964i	−0.0442005	+	0.125186i
$652$		0			0
$653$	−247.780	−	429.167i	−0.379448	−	0.657223i	0.611534	−	0.791218i	$-0.290553\pi$
$653$	−247.780	−	429.167i	−0.379448	−	0.657223i	−0.990982	+	0.133995i	$0.957219\pi$
$654$		0			0
$655$	−98.6670	−	56.9654i	−0.150637	−	0.0869701i
$656$		0			0
$657$	−842.294	−	679.498i	−1.28203	−	1.03424i
$658$		0			0
$659$	181.631	+	104.865i	0.275616	+	0.159127i	0.631437	−	0.775427i	$-0.282465\pi$
$659$	181.631	+	104.865i	0.275616	+	0.159127i	−0.355821	+	0.934554i	$0.615799\pi$
$660$		0			0
$661$	−639.718	−	1108.02i	−0.967804	−	1.67629i	−0.701886	−	0.712289i	$-0.747658\pi$
$661$	−639.718	−	1108.02i	−0.967804	−	1.67629i	−0.265918	−	0.963996i	$-0.585675\pi$
$662$		0			0
$663$	53.9791	−	10.0561i	0.0814164	−	0.0151676i
$664$		0			0
$665$	−243.682			−0.366439
$666$		0			0
$667$			886.218i			1.32866i
$668$		0			0
$669$	−378.540	+	323.910i	−0.565829	+	0.484170i
$670$		0			0
$671$	1167.59	−	674.106i	1.74007	−	1.00463i
$672$		0			0
$673$	530.868	−	919.490i	0.788808	−	1.36626i	−0.137890	−	0.990448i	$-0.544032\pi$
$673$	530.868	−	919.490i	0.788808	−	1.36626i	0.926698	−	0.375808i	$-0.122635\pi$
$674$		0			0
$675$	15.1200	+	522.000i	0.0224000	+	0.773333i
$676$		0			0
$677$	−297.754	+	515.724i	−0.439813	+	0.761779i	−0.997675	−	0.0681552i	$-0.978289\pi$
$677$	−297.754	+	515.724i	−0.439813	+	0.761779i	0.557861	+	0.829934i	$0.311622\pi$
$678$		0			0
$679$	1080.78	−	623.986i	1.59172	−	0.918978i
$680$		0			0
$681$	−622.046	+	532.275i	−0.913431	+	0.781607i
$682$		0			0
$683$			275.097i			0.402778i	0.979511	+	0.201389i	$0.0645455\pi$
$683$			275.097i			0.402778i	−0.979511	+	0.201389i	$0.935454\pi$
$684$		0			0
$685$	−486.867			−0.710755
$686$		0			0
$687$	−352.299	+	65.6321i	−0.512807	+	0.0955344i
$688$		0			0
$689$	51.3465	+	88.9347i	0.0745232	+	0.129078i
$690$		0			0
$691$	146.569	+	84.6218i	0.212112	+	0.122463i	0.602292	−	0.798276i	$-0.294254\pi$
$691$	146.569	+	84.6218i	0.212112	+	0.122463i	−0.390181	+	0.920738i	$0.627587\pi$
$692$		0			0
$693$	−145.252	+	928.207i	−0.209599	+	1.33940i
$694$		0			0
$695$	8.64365	+	4.99042i	0.0124369	+	0.00718045i
$696$		0			0
$697$	−165.720	−	287.035i	−0.237762	−	0.411815i
$698$		0			0
$699$	−18.0593	+	51.1483i	−0.0258359	+	0.0731735i
$700$		0			0
$701$	1051.23			1.49962			0.749811	−	0.661652i	$-0.230145\pi$
$701$	1051.23			1.49962			0.749811	+	0.661652i	$0.230145\pi$
$702$		0			0
$703$		−	731.217i		−	1.04014i
$704$		0			0
$705$	316.923	+	111.898i	0.449537	+	0.158721i
$706$		0			0
$707$	797.938	−	460.690i	1.12863	−	0.651612i
$708$		0			0
$709$	−330.089	+	571.731i	−0.465570	+	0.806390i	−0.999227	−	0.0393106i	$-0.987484\pi$
$709$	−330.089	+	571.731i	−0.465570	+	0.806390i	0.533657	+	0.845701i	$0.320817\pi$
$710$		0			0
$711$	214.823	+	556.551i	0.302142	+	0.782773i
$712$		0			0
$713$	60.3927	−	104.603i	0.0847022	−	0.146708i
$714$		0			0
$715$	41.6959	−	24.0731i	0.0583159	−	0.0336687i
$716$		0			0
$717$	−226.272	−	1214.58i	−0.315582	−	1.69397i
$718$		0			0
$719$			959.400i			1.33435i	0.744900	+	0.667176i	$0.232497\pi$
$719$			959.400i			1.33435i	−0.744900	+	0.667176i	$0.767503\pi$
$720$		0			0
$721$	994.300			1.37906
$722$		0			0
$723$	377.876	+	441.607i	0.522649	+	0.610798i
$724$		0			0
$725$	−282.269	−	488.903i	−0.389336	−	0.674350i
$726$		0			0
$727$	−191.443	−	110.530i	−0.263333	−	0.152035i	0.362521	−	0.931976i	$-0.381916\pi$
$727$	−191.443	−	110.530i	−0.263333	−	0.152035i	−0.625854	+	0.779940i	$0.715249\pi$
$728$		0			0
$729$	327.346	−	651.372i	0.449034	−	0.893515i
$730$		0			0
$731$	834.962	+	482.065i	1.14222	+	0.659460i
$732$		0			0
$733$	708.705	+	1227.51i	0.966855	+	1.67464i	0.704546	+	0.709658i	$0.251151\pi$
$733$	708.705	+	1227.51i	0.966855	+	1.67464i	0.262309	+	0.964984i	$0.415516\pi$
$734$		0			0
$735$	−15.9824	−	18.6780i	−0.0217448	−	0.0254122i
$736$		0			0
$737$	1189.02			1.61332
$738$		0			0
$739$			404.556i			0.547437i	0.961810	+	0.273718i	$0.0882536\pi$
$739$			404.556i			0.547437i	−0.961810	+	0.273718i	$0.911746\pi$
$740$		0			0
$741$	10.9129	+	58.5781i	0.0147273	+	0.0790528i
$742$		0			0
$743$	−243.500	+	140.585i	−0.327725	+	0.189212i	−0.654831	−	0.755775i	$-0.727260\pi$
$743$	−243.500	+	140.585i	−0.327725	+	0.189212i	0.327105	+	0.944988i	$0.393927\pi$
$744$		0			0
$745$	−261.267	+	452.527i	−0.350694	+	0.607419i
$746$		0			0
$747$	−60.3673	−	156.396i	−0.0808130	−	0.209365i
$748$		0			0
$749$	−268.311	+	464.728i	−0.358225	+	0.620464i
$750$		0			0
$751$	−567.143	+	327.440i	−0.755184	+	0.436006i	−0.827564	−	0.561371i	$-0.810274\pi$
$751$	−567.143	+	327.440i	−0.755184	+	0.436006i	0.0723797	+	0.997377i	$0.476941\pi$
$752$		0			0
$753$	1344.45	+	474.694i	1.78546	+	0.630403i
$754$		0			0
$755$		−	154.856i		−	0.205107i
$756$		0			0
$757$	−952.611			−1.25840			−0.629201	−	0.777242i	$-0.716618\pi$
$757$	−952.611			−1.25840			−0.629201	+	0.777242i	$0.716618\pi$
$758$		0			0
$759$	437.140	−	1238.09i	0.575942	−	1.63121i
$760$		0			0
$761$	−144.934	−	251.032i	−0.190452	−	0.329872i	0.754948	−	0.655784i	$-0.227662\pi$
$761$	−144.934	−	251.032i	−0.190452	−	0.329872i	−0.945400	+	0.325912i	$0.894329\pi$
$762$		0			0
$763$	−40.6987	−	23.4974i	−0.0533404	−	0.0307961i
$764$		0			0
$765$	43.1448	−	275.709i	0.0563985	−	0.360404i
$766$		0			0
$767$	−62.2939	−	35.9654i	−0.0812176	−	0.0468910i
$768$		0			0
$769$	−166.962	−	289.186i	−0.217115	−	0.376055i	0.736809	−	0.676100i	$-0.236331\pi$
$769$	−166.962	−	289.186i	−0.217115	−	0.376055i	−0.953925	+	0.300046i	$0.902998\pi$
$770$		0			0
$771$	−1020.37	+	190.092i	−1.32344	+	0.246553i
$772$		0			0
$773$	−285.777			−0.369698			−0.184849	−	0.982767i	$-0.559180\pi$
$773$	−285.777			−0.369698			−0.184849	+	0.982767i	$0.559180\pi$
$774$		0			0
$775$			76.9425i			0.0992806i
$776$		0			0
$777$	853.300	−	730.155i	1.09820	−	0.939710i
$778$		0			0
$779$	311.491	−	179.839i	0.399860	−	0.230859i
$780$		0			0
$781$	335.924	−	581.837i	0.430120	−	0.744990i
$782$		0			0
$783$	22.8175	+	787.745i	0.0291411	+	1.00606i
$784$		0			0
$785$	89.2663	−	154.614i	0.113715	−	0.196960i
$786$		0			0
$787$	919.316	−	530.767i	1.16813	−	0.674419i	0.214889	−	0.976638i	$-0.431061\pi$
$787$	919.316	−	530.767i	1.16813	−	0.674419i	0.953238	+	0.302220i	$0.0977276\pi$
$788$		0			0
$789$	−887.018	+	759.006i	−1.12423	+	0.961985i
$790$		0			0
$791$		−	664.531i		−	0.840115i
$792$		0			0
$793$	131.328			0.165609
$794$		0			0
$795$	513.100	−	95.5890i	0.645409	−	0.120238i
$796$		0			0
$797$	191.807	+	332.220i	0.240661	+	0.416838i	0.960903	−	0.276886i	$-0.0893023\pi$
$797$	191.807	+	332.220i	0.240661	+	0.416838i	−0.720241	+	0.693723i	$0.755969\pi$
$798$		0			0
$799$	531.655	+	306.951i	0.665400	+	0.384169i
$800$		0			0
$801$	−268.139	−	216.314i	−0.334756	−	0.270055i
$802$		0			0
$803$	−1501.08	−	866.649i	−1.86934	−	1.07926i
$804$		0			0
$805$	261.524	+	452.972i	0.324874	+	0.562698i
$806$		0			0
$807$	−182.477	+	516.820i	−0.226118	+	0.640421i
$808$		0			0
$809$	48.0973			0.0594528			0.0297264	−	0.999558i	$-0.490536\pi$
$809$	48.0973			0.0594528			0.0297264	+	0.999558i	$0.490536\pi$
$810$		0			0
$811$			632.783i			0.780251i	0.920762	+	0.390125i	$0.127568\pi$
$811$			632.783i			0.780251i	−0.920762	+	0.390125i	$0.872432\pi$
$812$		0			0
$813$	551.079	+	194.573i	0.677834	+	0.239328i
$814$		0			0
$815$	−409.803	+	236.600i	−0.502826	+	0.290307i
$816$		0			0
$817$	−523.137	+	906.101i	−0.640315	+	1.10906i
$818$		0			0
$819$	−57.4612	+	71.2279i	−0.0701602	+	0.0869694i
$820$		0			0
$821$	192.156	−	332.824i	0.234051	−	0.405388i	−0.724945	−	0.688806i	$-0.758135\pi$
$821$	192.156	−	332.824i	0.234051	−	0.405388i	0.958996	+	0.283418i	$0.0914684\pi$
$822$		0			0
$823$	403.246	−	232.814i	0.489971	−	0.282885i	−0.234591	−	0.972094i	$-0.575375\pi$
$823$	403.246	−	232.814i	0.489971	−	0.282885i	0.724563	+	0.689209i	$0.242042\pi$
$824$		0			0
$825$	153.183	+	822.254i	0.185677	+	0.996672i
$826$		0			0
$827$			1077.08i			1.30239i	0.758910	+	0.651196i	$0.225732\pi$
$827$			1077.08i			1.30239i	−0.758910	+	0.651196i	$0.774268\pi$
$828$		0			0
$829$	483.566			0.583313			0.291656	−	0.956523i	$-0.405794\pi$
$829$	483.566			0.583313			0.291656	+	0.956523i	$0.405794\pi$
$830$		0			0
$831$	187.310	+	218.902i	0.225404	+	0.263419i
$832$		0			0
$833$	−22.4508	−	38.8859i	−0.0269517	−	0.0466817i
$834$		0			0
$835$	−300.247	−	173.348i	−0.359577	−	0.207602i
$836$		0			0
$837$	50.9889	−	94.5350i	0.0609186	−	0.112945i
$838$		0			0
$839$	−774.684	−	447.264i	−0.923342	−	0.533092i	−0.0386422	−	0.999253i	$-0.512303\pi$
$839$	−774.684	−	447.264i	−0.923342	−	0.533092i	−0.884700	+	0.466161i	$0.845637\pi$
$840$		0			0
$841$	−5.46889	−	9.47239i	−0.00650284	−	0.0112632i
$842$		0			0
$843$	−109.893	−	128.428i	−0.130360	−	0.152346i
$844$		0			0
$845$	−397.323			−0.470205
$846$		0			0
$847$			628.470i			0.741995i
$848$		0			0
$849$	167.523	+	899.225i	0.197318	+	1.05916i
$850$		0			0
$851$	−1359.24	+	784.756i	−1.59722	+	0.922157i
$852$		0			0
$853$	142.742	−	247.236i	0.167341	−	0.289843i	−0.770143	−	0.637871i	$-0.779815\pi$
$853$	142.742	−	247.236i	0.167341	−	0.289843i	0.937484	+	0.348028i	$0.113149\pi$
$854$		0			0
$855$	299.200	+	46.8208i	0.349941	+	0.0547612i
$856$		0			0
$857$	216.497	−	374.984i	0.252622	−	0.437555i	−0.711625	−	0.702560i	$-0.752040\pi$
$857$	216.497	−	374.984i	0.252622	−	0.437555i	0.964247	+	0.265005i	$0.0853736\pi$
$858$		0			0
$859$	548.031	−	316.406i	0.637987	−	0.368342i	−0.145852	−	0.989306i	$-0.546592\pi$
$859$	548.031	−	316.406i	0.637987	−	0.368342i	0.783839	+	0.620965i	$0.213259\pi$
$860$		0			0
$861$	520.903	+	183.919i	0.604997	+	0.213611i
$862$		0			0
$863$		−	574.237i		−	0.665396i	−0.943033	−	0.332698i	$-0.892041\pi$
$863$		−	574.237i		−	0.665396i	0.943033	−	0.332698i	$-0.107959\pi$
$864$		0			0
$865$	186.215			0.215278
$866$		0			0
$867$	−118.948	+	336.890i	−0.137195	+	0.388570i
$868$		0			0
$869$	477.744	+	827.477i	0.549763	+	0.952218i
$870$		0			0
$871$	100.304	+	57.9106i	0.115160	+	0.0664875i
$872$		0			0
$873$	−1446.90	+	558.489i	−1.65739	+	0.639736i
$874$		0			0
$875$	−661.522	−	381.930i	−0.756026	−	0.436492i
$876$		0			0
$877$	−293.952	−	509.139i	−0.335179	−	0.580546i	0.648341	−	0.761350i	$-0.275463\pi$
$877$	−293.952	−	509.139i	−0.335179	−	0.580546i	−0.983519	+	0.180804i	$0.942130\pi$
$878$		0			0
$879$	1077.23	−	200.684i	1.22551	−	0.228309i
$880$		0			0
$881$	−938.429			−1.06519			−0.532593	−	0.846371i	$-0.678782\pi$
$881$	−938.429			−1.06519			−0.532593	+	0.846371i	$0.678782\pi$
$882$		0			0
$883$		−	192.855i		−	0.218408i	−0.994019	−	0.109204i	$-0.965170\pi$
$883$		−	192.855i		−	0.218408i	0.994019	−	0.109204i	$-0.0348303\pi$
$884$		0			0
$885$	−277.771	+	237.684i	−0.313865	+	0.268569i
$886$		0			0
$887$	−740.478	+	427.515i	−0.834812	+	0.481979i	−0.855497	−	0.517807i	$-0.826748\pi$
$887$	−740.478	+	427.515i	−0.834812	+	0.481979i	0.0206856	+	0.999786i	$0.493415\pi$
$888$		0			0
$889$	−643.009	+	1113.72i	−0.723295	+	1.25278i
$890$		0			0
$891$	356.690	−	1111.77i	0.400325	−	1.24778i
$892$		0			0
$893$	−333.104	+	576.952i	−0.373016	+	0.646083i
$894$		0			0
$895$	−220.790	+	127.473i	−0.246693	+	0.142428i
$896$		0			0
$897$	97.1771	−	83.1528i	0.108336	−	0.0927010i
$898$		0			0
$899$			116.113i			0.129158i
$900$		0			0
$901$	953.333			1.05808
$902$		0			0
$903$	−1579.76	+	294.304i	−1.74946	+	0.325918i
$904$		0			0
$905$	−419.255	−	726.172i	−0.463266	−	0.802400i
$906$		0			0
$907$	571.938	+	330.209i	0.630582	+	0.364067i	0.780978	−	0.624559i	$-0.214721\pi$
$907$	571.938	+	330.209i	0.630582	+	0.364067i	−0.150395	+	0.988626i	$0.548055\pi$
$908$		0			0
$909$	−1068.25	+	412.334i	−1.17519	+	0.453612i
$910$		0			0
$911$	472.759	+	272.947i	0.518945	+	0.299613i	0.736503	−	0.676434i	$-0.236476\pi$
$911$	472.759	+	272.947i	0.518945	+	0.299613i	−0.217558	+	0.976047i	$0.569809\pi$
$912$		0			0
$913$	−134.250	−	232.529i	−0.147043	−	0.254686i
$914$		0			0
$915$	222.221	−	629.385i	0.242865	−	0.687853i
$916$		0			0
$917$	346.848			0.378242
$918$		0			0
$919$		−	1399.13i		−	1.52245i	−0.648490	−	0.761223i	$-0.724599\pi$
$919$		−	1399.13i		−	1.52245i	0.648490	−	0.761223i	$-0.275401\pi$
$920$		0			0
$921$	−138.710	−	48.9755i	−0.150609	−	0.0531764i
$922$		0			0
$923$	56.6762	−	32.7220i	0.0614044	−	0.0354518i
$924$		0			0
$925$	499.904	−	865.859i	0.540437	−	0.936064i
$926$		0			0
$927$	−1220.83	−	191.044i	−1.31697	−	0.206089i
$928$		0			0
$929$	−267.898	+	464.014i	−0.288373	+	0.499476i	−0.973422	−	0.229021i	$-0.926448\pi$
$929$	−267.898	+	464.014i	−0.288373	+	0.499476i	0.685049	+	0.728497i	$0.259781\pi$
$930$		0			0
$931$	42.1990	−	24.3636i	0.0453265	−	0.0261693i
$932$		0			0
$933$	−125.793	−	675.227i	−0.134826	−	0.723716i
$934$		0			0
$935$		−	446.958i		−	0.478030i
$936$		0			0
$937$	125.571			0.134014			0.0670072	−	0.997752i	$-0.478655\pi$
$937$	125.571			0.134014			0.0670072	+	0.997752i	$0.478655\pi$
$938$		0			0
$939$	−350.236	−	409.306i	−0.372988	−	0.435895i
$940$		0			0
$941$	−540.991	−	937.024i	−0.574911	−	0.995774i	−0.996051	−	0.0887791i	$-0.971703\pi$
$941$	−540.991	−	937.024i	−0.574911	−	0.995774i	0.421141	−	0.906995i	$-0.361630\pi$
$942$		0			0
$943$	−668.595	−	386.013i	−0.709008	−	0.409346i
$944$		0			0
$945$	244.127	+	395.906i	0.258335	+	0.418948i
$946$		0			0
$947$	−156.473	−	90.3395i	−0.165230	−	0.0953954i	0.415105	−	0.909774i	$-0.363745\pi$
$947$	−156.473	−	90.3395i	−0.165230	−	0.0953954i	−0.580335	+	0.814378i	$0.697078\pi$
$948$		0			0
$949$	−84.4195	−	146.219i	−0.0889563	−	0.154077i
$950$		0			0
$951$	643.429	+	751.948i	0.676582	+	0.790692i
$952$		0			0
$953$	−494.689			−0.519086			−0.259543	−	0.965732i	$-0.583572\pi$
$953$	−494.689			−0.519086			−0.259543	+	0.965732i	$0.583572\pi$
$954$		0			0
$955$		−	548.839i		−	0.574700i
$956$		0			0
$957$	231.168	+	1240.86i	0.241554	+	1.29661i
$958$		0			0
$959$	1283.63	−	741.101i	1.33850	−	0.772786i
$960$		0			0
$961$	−472.587	+	818.545i	−0.491766	+	0.851764i
$962$		0			0
$963$	418.732	−	519.053i	0.434821	−	0.538996i
$964$		0			0
$965$	374.666	−	648.941i	0.388255	−	0.672478i
$966$		0			0
$967$	−1017.10	+	587.221i	−1.05181	+	0.607261i	−0.923155	−	0.384429i	$-0.874398\pi$
$967$	−1017.10	+	587.221i	−1.05181	+	0.607261i	−0.128652	+	0.991690i	$0.541065\pi$
$968$		0			0
$969$	521.599	+	184.165i	0.538286	+	0.190056i
$970$		0			0
$971$		−	523.380i		−	0.539011i	−0.962999	−	0.269506i	$-0.913140\pi$
$971$		−	523.380i		−	0.539011i	0.962999	−	0.269506i	$-0.0868603\pi$
$972$		0			0
$973$	−30.3853			−0.0312285
$974$		0			0
$975$	−27.1252	+	76.8251i	−0.0278207	+	0.0787949i
$976$		0			0
$977$	−936.160	−	1621.48i	−0.958199	−	1.65965i	−0.726872	−	0.686773i	$-0.759027\pi$
$977$	−936.160	−	1621.48i	−0.958199	−	1.65965i	−0.231327	−	0.972876i	$-0.574307\pi$
$978$		0			0
$979$	−477.860	−	275.893i	−0.488111	−	0.281811i
$980$		0			0
$981$	45.4563	+	36.6706i	0.0463367	+	0.0373809i
$982$		0			0
$983$	1017.61	+	587.519i	1.03521	+	0.597680i	0.918473	−	0.395483i	$-0.129423\pi$
$983$	1017.61	+	587.519i	1.03521	+	0.597680i	0.116738	+	0.993163i	$0.462756\pi$
$984$		0			0
$985$	−307.677	−	532.911i	−0.312362	−	0.541027i
$986$		0			0
$987$	−1005.90	+	187.396i	−1.01915	+	0.189864i
$988$		0			0
$989$	2245.76			2.27074
$990$		0			0
$991$			333.706i			0.336737i	0.985724	+	0.168368i	$0.0538498\pi$
$991$			333.706i			0.336737i	−0.985724	+	0.168368i	$0.946150\pi$
$992$		0			0
$993$	−28.3331	+	24.2441i	−0.0285328	+	0.0244150i
$994$		0			0
$995$	−213.304	+	123.151i	−0.214376	+	0.123770i
$996$		0			0
$997$	231.571	−	401.092i	0.232267	−	0.402299i	−0.726208	−	0.687475i	$-0.758719\pi$
$997$	231.571	−	401.092i	0.232267	−	0.402299i	0.958475	+	0.285177i	$0.0920522\pi$
$998$		0			0
$999$	−1188.00	+	732.553i	−1.18919	+	0.733286i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	576.3.o.h.511.6		20
3.2	odd	2		1728.3.o.h.127.8		20
4.3	odd	2	inner	576.3.o.h.511.5		20
8.3	odd	2		288.3.o.b.223.6	yes	20
8.5	even	2		288.3.o.b.223.5	yes	20
9.4	even	3	inner	576.3.o.h.319.5		20
9.5	odd	6		1728.3.o.h.1279.7		20
12.11	even	2		1728.3.o.h.127.7		20
24.5	odd	2		864.3.o.b.127.4		20
24.11	even	2		864.3.o.b.127.3		20
36.23	even	6		1728.3.o.h.1279.8		20
36.31	odd	6	inner	576.3.o.h.319.6		20
72.5	odd	6		864.3.o.b.415.3		20
72.11	even	6		2592.3.g.h.2431.8		10
72.13	even	6		288.3.o.b.31.6	yes	20
72.29	odd	6		2592.3.g.h.2431.7		10
72.43	odd	6		2592.3.g.g.2431.4		10
72.59	even	6		864.3.o.b.415.4		20
72.61	even	6		2592.3.g.g.2431.3		10
72.67	odd	6		288.3.o.b.31.5	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.3.o.b.31.5	✓	20	72.67	odd	6
288.3.o.b.31.6	yes	20	72.13	even	6
288.3.o.b.223.5	yes	20	8.5	even	2
288.3.o.b.223.6	yes	20	8.3	odd	2
576.3.o.h.319.5		20	9.4	even	3	inner
576.3.o.h.319.6		20	36.31	odd	6	inner
576.3.o.h.511.5		20	4.3	odd	2	inner
576.3.o.h.511.6		20	1.1	even	1	trivial
864.3.o.b.127.3		20	24.11	even	2
864.3.o.b.127.4		20	24.5	odd	2
864.3.o.b.415.3		20	72.5	odd	6
864.3.o.b.415.4		20	72.59	even	6
1728.3.o.h.127.7		20	12.11	even	2
1728.3.o.h.127.8		20	3.2	odd	2
1728.3.o.h.1279.7		20	9.5	odd	6
1728.3.o.h.1279.8		20	36.23	even	6
2592.3.g.g.2431.3		10	72.61	even	6
2592.3.g.g.2431.4		10	72.43	odd	6
2592.3.g.h.2431.7		10	72.29	odd	6
2592.3.g.h.2431.8		10	72.11	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	576.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.998802 - 2.82885i) q^{3} +(-1.18939 - 2.06008i) q^{5} +(6.27165 + 3.62094i) q^{7} +(-7.00479 - 5.65092i) q^{9} +O(q^{10})\)	\(q+(0.998802 - 2.82885i) q^{3} +(-1.18939 - 2.06008i) q^{5} +(6.27165 + 3.62094i) q^{7} +(-7.00479 - 5.65092i) q^{9} +(-12.4835 - 7.20734i) q^{11} +(-0.702060 - 1.21600i) q^{13} +(-7.01562 + 1.30699i) q^{15} -13.0349 q^{17} -14.1455i q^{19} +(16.5072 - 14.1249i) q^{21} +(-26.2946 + 15.1812i) q^{23} +(9.67071 - 16.7502i) q^{25} +(-22.9820 + 14.1713i) q^{27} +(14.5940 - 25.2775i) q^{29} +(-3.44515 + 1.98906i) q^{31} +(-32.8570 + 28.1152i) q^{33} -17.2268i q^{35} +51.6925 q^{37} +(-4.14111 + 0.771476i) q^{39} +(12.7135 + 22.0205i) q^{41} +(-64.0557 - 36.9826i) q^{43} +(-3.30994 + 21.1516i) q^{45} +(-40.7870 - 23.5484i) q^{47} +(1.72236 + 2.98321i) q^{49} +(-13.0193 + 36.8738i) q^{51} -73.1369 q^{53} +34.2893i q^{55} +(-40.0155 - 14.1286i) q^{57} +(44.3650 - 25.6142i) q^{59} +(-46.7652 + 80.9998i) q^{61} +(-23.4699 - 60.8045i) q^{63} +(-1.67004 + 2.89260i) q^{65} +(-71.4356 + 41.2433i) q^{67} +(16.6823 + 89.5466i) q^{69} +46.6086i q^{71} +120.245 q^{73} +(-37.7246 - 44.0871i) q^{75} +(-52.1946 - 90.4037i) q^{77} +(-57.4052 - 33.1429i) q^{79} +(17.1341 + 79.1670i) q^{81} +(16.1314 + 9.31346i) q^{83} +(15.5036 + 26.8530i) q^{85} +(-56.9298 - 66.5314i) q^{87} +38.2794 q^{89} -10.1685i q^{91} +(2.18573 + 11.7325i) q^{93} +(-29.1409 + 16.8245i) q^{95} +(86.1636 - 149.240i) q^{97} +(46.7160 + 121.029i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 14 q^{5} + 48 q^{9}+O(q^{10}) \) 20 * q - 14 * q^5 + 48 * q^9	\( 20 q - 14 q^{5} + 48 q^{9} - 26 q^{13} + 72 q^{17} + 42 q^{21} + 36 q^{25} + 134 q^{29} - 42 q^{33} - 96 q^{37} - 26 q^{41} - 306 q^{45} + 348 q^{49} + 192 q^{53} - 612 q^{57} - 386 q^{61} - 106 q^{65} - 78 q^{69} - 168 q^{73} - 58 q^{77} + 264 q^{81} - 192 q^{85} - 240 q^{89} + 642 q^{93} + 374 q^{97}+O(q^{100}) \) 20 * q - 14 * q^5 + 48 * q^9 - 26 * q^13 + 72 * q^17 + 42 * q^21 + 36 * q^25 + 134 * q^29 - 42 * q^33 - 96 * q^37 - 26 * q^41 - 306 * q^45 + 348 * q^49 + 192 * q^53 - 612 * q^57 - 386 * q^61 - 106 * q^65 - 78 * q^69 - 168 * q^73 - 58 * q^77 + 264 * q^81 - 192 * q^85 - 240 * q^89 + 642 * q^93 + 374 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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