LMFDB - Embedded newform 288.3.q.b.257.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,3,Mod(65,288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 0, 1]))

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

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

chi := DirichletCharacter("288.65");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	288.q (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:	$7.84743161358$
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			257.4
Character	$\chi$	$=$	288.257
Dual form			288.3.q.b.65.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.92817 - 2.29830i) q^{3} +(7.02261 + 4.05450i) q^{5} +(1.65619 + 2.86860i) q^{7} +(-1.56434 + 8.86300i) q^{9} +O(q^{10})$	\(q+(-1.92817 - 2.29830i) q^{3} +(7.02261 + 4.05450i) q^{5} +(1.65619 + 2.86860i) q^{7} +(-1.56434 + 8.86300i) q^{9} +(-17.0190 + 9.82591i) q^{11} +(-2.62735 + 4.55070i) q^{13} +(-4.22230 - 23.9578i) q^{15} +1.23020i q^{17} +6.71738 q^{19} +(3.39949 - 9.33754i) q^{21} +(28.4732 + 16.4390i) q^{23} +(20.3780 + 35.2957i) q^{25} +(23.3861 - 13.4940i) q^{27} +(-27.6899 + 15.9868i) q^{29} +(-15.4197 + 26.7077i) q^{31} +(55.3983 + 20.1687i) q^{33} +26.8600i q^{35} -0.751729 q^{37} +(15.5248 - 2.73608i) q^{39} +(63.5333 + 36.6810i) q^{41} +(-23.7200 - 41.0843i) q^{43} +(-46.9208 + 55.8988i) q^{45} +(67.3986 - 38.9126i) q^{47} +(19.0141 - 32.9334i) q^{49} +(2.82738 - 2.37204i) q^{51} -52.1167i q^{53} -159.357 q^{55} +(-12.9522 - 15.4385i) q^{57} +(50.8455 + 29.3557i) q^{59} +(-26.5511 - 45.9879i) q^{61} +(-28.0152 + 10.1913i) q^{63} +(-36.9017 + 21.3052i) q^{65} +(-38.9099 + 67.3939i) q^{67} +(-17.1194 - 97.1371i) q^{69} +60.3747i q^{71} -59.6798 q^{73} +(41.8279 - 114.891i) q^{75} +(-56.3732 - 32.5471i) q^{77} +(-42.2143 - 73.1172i) q^{79} +(-76.1057 - 27.7295i) q^{81} +(-1.70956 + 0.987014i) q^{83} +(-4.98787 + 8.63924i) q^{85} +(90.1332 + 32.8145i) q^{87} -83.5607i q^{89} -17.4055 q^{91} +(91.1140 - 16.0579i) q^{93} +(47.1735 + 27.2357i) q^{95} +(48.3304 + 83.7107i) q^{97} +(-60.4636 - 166.210i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{9}+O(q^{10}) $ 24 * q + 12 * q^9	$ 24 q + 12 q^{9} + 24 q^{21} + 60 q^{25} + 72 q^{29} + 108 q^{33} + 252 q^{41} + 72 q^{45} - 36 q^{49} + 12 q^{57} - 96 q^{61} - 288 q^{65} - 432 q^{69} + 24 q^{73} - 720 q^{77} - 372 q^{81} + 96 q^{85} - 132 q^{97}+O(q^{100}) $ 24 * q + 12 * q^9 + 24 * q^21 + 60 * q^25 + 72 * q^29 + 108 * q^33 + 252 * q^41 + 72 * q^45 - 36 * q^49 + 12 * q^57 - 96 * q^61 - 288 * q^65 - 432 * q^69 + 24 * q^73 - 720 * q^77 - 372 * q^81 + 96 * q^85 - 132 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.92817	−	2.29830i	−0.642722	−	0.766099i
$3$	−1.92817	−	2.29830i	−0.642722	−	0.766099i
$4$		0			0
$5$	7.02261	+	4.05450i	1.40452	+	0.810901i	0.994853	−	0.101333i	$-0.0323109\pi$
$5$	7.02261	+	4.05450i	1.40452	+	0.810901i	0.409669	+	0.912234i	$0.365644\pi$
$6$		0			0
$7$	1.65619	+	2.86860i	0.236598	+	0.409800i	0.959736	−	0.280904i	$-0.0906343\pi$
$7$	1.65619	+	2.86860i	0.236598	+	0.409800i	−0.723138	+	0.690704i	$0.757301\pi$
$8$		0			0
$9$	−1.56434	+	8.86300i	−0.173816	+	0.984778i
$10$		0			0
$11$	−17.0190	+	9.82591i	−1.54718	+	0.893265i	−0.548825	+	0.835938i	$0.684925\pi$
$11$	−17.0190	+	9.82591i	−1.54718	+	0.893265i	−0.998355	+	0.0573273i	$0.981742\pi$
$12$		0			0
$13$	−2.62735	+	4.55070i	−0.202104	+	0.350054i	−0.949206	−	0.314655i	$-0.898111\pi$
$13$	−2.62735	+	4.55070i	−0.202104	+	0.350054i	0.747102	+	0.664709i	$0.231444\pi$
$14$		0			0
$15$	−4.22230	−	23.9578i	−0.281487	−	1.59719i
$16$		0			0
$17$			1.23020i			0.0723650i	0.999345	+	0.0361825i	$0.0115198\pi$
$17$			1.23020i			0.0723650i	−0.999345	+	0.0361825i	$0.988480\pi$
$18$		0			0
$19$	6.71738			0.353546			0.176773	−	0.984252i	$-0.443434\pi$
$19$	6.71738			0.353546			0.176773	+	0.984252i	$0.443434\pi$
$20$		0			0
$21$	3.39949	−	9.33754i	0.161880	−	0.444645i
$22$		0			0
$23$	28.4732	+	16.4390i	1.23797	+	0.714740i	0.968678	−	0.248320i	$-0.0798783\pi$
$23$	28.4732	+	16.4390i	1.23797	+	0.714740i	0.269288	+	0.963060i	$0.413212\pi$
$24$		0			0
$25$	20.3780	+	35.2957i	0.815120	+	1.41183i
$26$		0			0
$27$	23.3861	−	13.4940i	0.866153	−	0.499779i
$28$		0			0
$29$	−27.6899	+	15.9868i	−0.954825	+	0.551268i	−0.894576	−	0.446915i	$-0.852523\pi$
$29$	−27.6899	+	15.9868i	−0.954825	+	0.551268i	−0.0602486	+	0.998183i	$0.519189\pi$
$30$		0			0
$31$	−15.4197	+	26.7077i	−0.497410	+	0.861539i	−0.999996	−	0.00298830i	$-0.999049\pi$
$31$	−15.4197	+	26.7077i	−0.497410	+	0.861539i	0.502586	+	0.864527i	$0.332382\pi$
$32$		0			0
$33$	55.3983	+	20.1687i	1.67874	+	0.611172i
$34$		0			0
$35$			26.8600i			0.767430i
$36$		0			0
$37$	−0.751729			−0.0203170			−0.0101585	−	0.999948i	$-0.503234\pi$
$37$	−0.751729			−0.0203170			−0.0101585	+	0.999948i	$0.503234\pi$
$38$		0			0
$39$	15.5248	−	2.73608i	0.398072	−	0.0701560i
$40$		0			0
$41$	63.5333	+	36.6810i	1.54959	+	0.894658i	0.998172	+	0.0604315i	$0.0192477\pi$
$41$	63.5333	+	36.6810i	1.54959	+	0.894658i	0.551421	+	0.834227i	$0.314086\pi$
$42$		0			0
$43$	−23.7200	−	41.0843i	−0.551628	−	0.955448i	−0.998157	−	0.0606787i	$-0.980673\pi$
$43$	−23.7200	−	41.0843i	−0.551628	−	0.955448i	0.446529	−	0.894769i	$-0.352660\pi$
$44$		0			0
$45$	−46.9208	+	55.8988i	−1.04269	+	1.24219i
$46$		0			0
$47$	67.3986	−	38.9126i	1.43401	−	0.827927i	0.436588	−	0.899661i	$-0.356187\pi$
$47$	67.3986	−	38.9126i	1.43401	−	0.827927i	0.997424	+	0.0717341i	$0.0228533\pi$
$48$		0			0
$49$	19.0141	−	32.9334i	0.388043	−	0.672110i
$50$		0			0
$51$	2.82738	−	2.37204i	0.0554387	−	0.0465106i
$52$		0			0
$53$		−	52.1167i		−	0.983333i	−0.870783	−	0.491667i	$-0.836388\pi$
$53$		−	52.1167i		−	0.983333i	0.870783	−	0.491667i	$-0.163612\pi$
$54$		0			0
$55$	−159.357			−2.89740
$56$		0			0
$57$	−12.9522	−	15.4385i	−0.227232	−	0.270852i
$58$		0			0
$59$	50.8455	+	29.3557i	0.861788	+	0.497554i	0.864611	−	0.502442i	$-0.167565\pi$
$59$	50.8455	+	29.3557i	0.861788	+	0.497554i	−0.00282234	+	0.999996i	$0.500898\pi$
$60$		0			0
$61$	−26.5511	−	45.9879i	−0.435264	−	0.753900i	0.562053	−	0.827101i	$-0.310012\pi$
$61$	−26.5511	−	45.9879i	−0.435264	−	0.753900i	−0.997317	+	0.0732013i	$0.976678\pi$
$62$		0			0
$63$	−28.0152	+	10.1913i	−0.444686	+	0.161767i
$64$		0			0
$65$	−36.9017	+	21.3052i	−0.567718	+	0.327772i
$66$		0			0
$67$	−38.9099	+	67.3939i	−0.580745	+	1.00588i	0.414647	+	0.909983i	$0.363905\pi$
$67$	−38.9099	+	67.3939i	−0.580745	+	1.00588i	−0.995391	+	0.0958967i	$0.969428\pi$
$68$		0			0
$69$	−17.1194	−	97.1371i	−0.248107	−	1.40778i
$70$		0			0
$71$			60.3747i			0.850347i	0.905112	+	0.425174i	$0.139787\pi$
$71$			60.3747i			0.850347i	−0.905112	+	0.425174i	$0.860213\pi$
$72$		0			0
$73$	−59.6798			−0.817532			−0.408766	−	0.912639i	$-0.634041\pi$
$73$	−59.6798			−0.817532			−0.408766	+	0.912639i	$0.634041\pi$
$74$		0			0
$75$	41.8279	−	114.891i	0.557705	−	1.53188i
$76$		0			0
$77$	−56.3732	−	32.5471i	−0.732119	−	0.422689i
$78$		0			0
$79$	−42.2143	−	73.1172i	−0.534358	−	0.925535i	−0.999194	−	0.0401381i	$-0.987220\pi$
$79$	−42.2143	−	73.1172i	−0.534358	−	0.925535i	0.464836	−	0.885397i	$-0.346113\pi$
$80$		0			0
$81$	−76.1057	−	27.7295i	−0.939576	−	0.342340i
$82$		0			0
$83$	−1.70956	+	0.987014i	−0.0205971	+	0.0118917i	−0.510263	−	0.860018i	$-0.670452\pi$
$83$	−1.70956	+	0.987014i	−0.0205971	+	0.0118917i	0.489666	+	0.871910i	$0.337119\pi$
$84$		0			0
$85$	−4.98787	+	8.63924i	−0.0586808	+	0.101638i
$86$		0			0
$87$	90.1332	+	32.8145i	1.03601	+	0.377178i
$88$		0			0
$89$		−	83.5607i		−	0.938884i	−0.882963	−	0.469442i	$-0.844455\pi$
$89$		−	83.5607i		−	0.938884i	0.882963	−	0.469442i	$-0.155545\pi$
$90$		0			0
$91$	−17.4055			−0.191269
$92$		0			0
$93$	91.1140	−	16.0579i	0.979721	−	0.172665i
$94$		0			0
$95$	47.1735	+	27.2357i	0.496564	+	0.286691i
$96$		0			0
$97$	48.3304	+	83.7107i	0.498252	+	0.862997i	0.999998	−	0.00201760i	$-0.000642222\pi$
$97$	48.3304	+	83.7107i	0.498252	+	0.862997i	−0.501746	+	0.865015i	$0.667309\pi$
$98$		0			0
$99$	−60.4636	−	166.210i	−0.610743	−	1.67889i
$100$		0			0
$101$	53.6448	−	30.9719i	0.531137	−	0.306652i	−0.210342	−	0.977628i	$-0.567458\pi$
$101$	53.6448	−	30.9719i	0.531137	−	0.306652i	0.741479	+	0.670976i	$0.234125\pi$
$102$		0			0
$103$	4.47610	−	7.75284i	0.0434573	−	0.0752703i	−0.843479	−	0.537163i	$-0.819496\pi$
$103$	4.47610	−	7.75284i	0.0434573	−	0.0752703i	0.886936	+	0.461892i	$0.152829\pi$
$104$		0			0
$105$	61.7324	−	51.7907i	0.587927	−	0.493244i
$106$		0			0
$107$			202.958i			1.89681i	0.317067	+	0.948403i	$0.397302\pi$
$107$			202.958i			1.89681i	−0.317067	+	0.948403i	$0.602698\pi$
$108$		0			0
$109$	−86.4001			−0.792661			−0.396331	−	0.918108i	$-0.629717\pi$
$109$	−86.4001			−0.792661			−0.396331	+	0.918108i	$0.629717\pi$
$110$		0			0
$111$	1.44946	+	1.72770i	0.0130582	+	0.0155648i
$112$		0			0
$113$	−76.1110	−	43.9427i	−0.673549	−	0.388873i	0.123871	−	0.992298i	$-0.460469\pi$
$113$	−76.1110	−	43.9427i	−0.673549	−	0.388873i	−0.797420	+	0.603425i	$0.793802\pi$
$114$		0			0
$115$	133.304	+	230.890i	1.15917	+	2.00774i
$116$		0			0
$117$	−36.2228	−	30.4050i	−0.309597	−	0.259872i
$118$		0			0
$119$	−3.52896	+	2.03745i	−0.0296551	+	0.0171214i
$120$		0			0
$121$	132.597	−	229.665i	1.09584	−	1.89806i
$122$		0			0
$123$	−38.1991	−	216.746i	−0.310562	−	1.76216i
$124$		0			0
$125$			127.766i			1.02213i
$126$		0			0
$127$	38.5783			0.303766			0.151883	−	0.988398i	$-0.451466\pi$
$127$	38.5783			0.303766			0.151883	+	0.988398i	$0.451466\pi$
$128$		0			0
$129$	−48.6877	+	133.733i	−0.377424	+	1.03669i
$130$		0			0
$131$	20.3214	+	11.7326i	0.155125	+	0.0895617i	0.575553	−	0.817764i	$-0.304787\pi$
$131$	20.3214	+	11.7326i	0.155125	+	0.0895617i	−0.420428	+	0.907326i	$0.638120\pi$
$132$		0			0
$133$	11.1252	+	19.2695i	0.0836484	+	0.144883i
$134$		0			0
$135$	218.943	+	0.0558951i	1.62180	+	0.000414038i
$136$		0			0
$137$	38.0442	−	21.9648i	0.277695	−	0.160327i	−0.354685	−	0.934986i	$-0.615412\pi$
$137$	38.0442	−	21.9648i	0.277695	−	0.160327i	0.632379	+	0.774659i	$0.282078\pi$
$138$		0			0
$139$	24.4904	−	42.4186i	0.176190	−	0.305170i	−0.764383	−	0.644763i	$-0.776956\pi$
$139$	24.4904	−	42.4186i	0.176190	−	0.305170i	0.940572	+	0.339593i	$0.110289\pi$
$140$		0			0
$141$	−219.388	−	79.8720i	−1.55595	−	0.566468i
$142$		0			0
$143$		−	103.264i		−	0.722128i
$144$		0			0
$145$	−259.274			−1.78810
$146$		0			0
$147$	−112.353	+	19.8010i	−0.764307	+	0.134701i
$148$		0			0
$149$	−31.9046	−	18.4202i	−0.214125	−	0.123625i	0.389102	−	0.921195i	$-0.372785\pi$
$149$	−31.9046	−	18.4202i	−0.214125	−	0.123625i	−0.603227	+	0.797570i	$0.706119\pi$
$150$		0			0
$151$	−109.254	−	189.234i	−0.723537	−	1.25320i	−0.959573	−	0.281459i	$-0.909182\pi$
$151$	−109.254	−	189.234i	−0.723537	−	1.25320i	0.236036	−	0.971744i	$-0.424152\pi$
$152$		0			0
$153$	−10.9033	−	1.92446i	−0.0712634	−	0.0125782i
$154$		0			0
$155$	−216.573	+	125.039i	−1.39725	+	0.806700i
$156$		0			0
$157$	47.7861	−	82.7680i	0.304370	−	0.527185i	−0.672751	−	0.739869i	$-0.734887\pi$
$157$	47.7861	−	82.7680i	0.304370	−	0.527185i	0.977121	+	0.212684i	$0.0682206\pi$
$158$		0			0
$159$	−119.780	+	100.490i	−0.753331	+	0.632010i
$160$		0			0
$161$			108.904i			0.676424i
$162$		0			0
$163$	−25.5141			−0.156528			−0.0782640	−	0.996933i	$-0.524938\pi$
$163$	−25.5141			−0.156528			−0.0782640	+	0.996933i	$0.524938\pi$
$164$		0			0
$165$	307.267	+	366.249i	1.86222	+	2.21969i
$166$		0			0
$167$	58.7293	+	33.9074i	0.351672	+	0.203038i	0.665422	−	0.746468i	$-0.268252\pi$
$167$	58.7293	+	33.9074i	0.351672	+	0.203038i	−0.313749	+	0.949506i	$0.601585\pi$
$168$		0			0
$169$	70.6941	+	122.446i	0.418308	+	0.724531i
$170$		0			0
$171$	−10.5083	+	59.5362i	−0.0614520	+	0.348165i
$172$		0			0
$173$	161.030	−	92.9710i	0.930812	−	0.537404i	0.0437435	−	0.999043i	$-0.486072\pi$
$173$	161.030	−	92.9710i	0.930812	−	0.537404i	0.887068	+	0.461638i	$0.152738\pi$
$174$		0			0
$175$	−67.4995	+	116.913i	−0.385712	+	0.668072i
$176$		0			0
$177$	−30.5706	−	173.461i	−0.172715	−	0.980004i
$178$		0			0
$179$		−	210.607i		−	1.17657i	−0.808653	−	0.588286i	$-0.799803\pi$
$179$		−	210.607i		−	1.17657i	0.808653	−	0.588286i	$-0.200197\pi$
$180$		0			0
$181$	243.392			1.34471			0.672353	−	0.740231i	$-0.265284\pi$
$181$	243.392			1.34471			0.672353	+	0.740231i	$0.265284\pi$
$182$		0			0
$183$	−54.4989	+	149.695i	−0.297808	+	0.818004i
$184$		0			0
$185$	−5.27910	−	3.04789i	−0.0285357	−	0.0164751i
$186$		0			0
$187$	−12.0879	−	20.9368i	−0.0646411	−	0.111962i
$188$		0			0
$189$	77.4407	+	44.7368i	0.409739	+	0.236703i
$190$		0			0
$191$	202.446	−	116.882i	1.05993	−	0.611949i	0.134515	−	0.990912i	$-0.457052\pi$
$191$	202.446	−	116.882i	1.05993	−	0.611949i	0.925412	+	0.378963i	$0.123719\pi$
$192$		0			0
$193$	−123.176	+	213.347i	−0.638217	+	1.10542i	0.347607	+	0.937640i	$0.386994\pi$
$193$	−123.176	+	213.347i	−0.638217	+	1.10542i	−0.985824	+	0.167784i	$0.946339\pi$
$194$		0			0
$195$	120.118	+	43.7310i	0.615991	+	0.224262i
$196$		0			0
$197$			320.112i			1.62494i	0.583006	+	0.812468i	$0.301876\pi$
$197$			320.112i			1.62494i	−0.583006	+	0.812468i	$0.698124\pi$
$198$		0			0
$199$	−221.676			−1.11395			−0.556974	−	0.830530i	$-0.688038\pi$
$199$	−221.676			−1.11395			−0.556974	+	0.830530i	$0.688038\pi$
$200$		0			0
$201$	229.916	−	40.5202i	1.14386	−	0.201593i
$202$		0			0
$203$	−91.7193	−	52.9542i	−0.451819	−	0.260858i
$204$		0			0
$205$	297.446	+	515.192i	1.45096	+	2.51313i
$206$		0			0
$207$	−190.241	+	226.642i	−0.919039	+	1.09489i
$208$		0			0
$209$	−114.323	+	66.0044i	−0.547000	+	0.315811i
$210$		0			0
$211$	140.237	−	242.898i	0.664630	−	1.15117i	−0.314755	−	0.949173i	$-0.601922\pi$
$211$	140.237	−	242.898i	0.664630	−	1.15117i	0.979385	−	0.202000i	$-0.0647442\pi$
$212$		0			0
$213$	138.759	−	116.412i	0.651450	−	0.546537i
$214$		0			0
$215$		−	384.691i		−	1.78926i
$216$		0			0
$217$	−102.152			−0.470744
$218$		0			0
$219$	115.073	+	137.162i	0.525446	+	0.626310i
$220$		0			0
$221$	−5.59829	−	3.23217i	−0.0253316	−	0.0146252i
$222$		0			0
$223$	15.0168	+	26.0099i	0.0673400	+	0.116636i	0.897730	−	0.440547i	$-0.145215\pi$
$223$	15.0168	+	26.0099i	0.0673400	+	0.116636i	−0.830390	+	0.557183i	$0.811882\pi$
$224$		0			0
$225$	−344.704	+	125.396i	−1.53202	+	0.557314i
$226$		0			0
$227$	9.28260	−	5.35931i	0.0408925	−	0.0236093i	−0.479414	−	0.877589i	$-0.659151\pi$
$227$	9.28260	−	5.35931i	0.0408925	−	0.0236093i	0.520307	+	0.853979i	$0.325818\pi$
$228$		0			0
$229$	115.416	−	199.906i	0.503999	−	0.872952i	−0.495990	−	0.868328i	$-0.665195\pi$
$229$	115.416	−	199.906i	0.503999	−	0.872952i	0.999989	−	0.00462381i	$-0.00147181\pi$
$230$		0			0
$231$	33.8941	+	192.319i	0.146728	+	0.832548i
$232$		0			0
$233$		−	151.505i		−	0.650235i	−0.945674	−	0.325118i	$-0.894596\pi$
$233$		−	151.505i		−	0.650235i	0.945674	−	0.325118i	$-0.105404\pi$
$234$		0			0
$235$	631.085			2.68547
$236$		0			0
$237$	−86.6490	+	238.003i	−0.365608	+	1.00423i
$238$		0			0
$239$	−20.7366	−	11.9723i	−0.0867640	−	0.0500932i	0.455990	−	0.889985i	$-0.349285\pi$
$239$	−20.7366	−	11.9723i	−0.0867640	−	0.0500932i	−0.542754	+	0.839892i	$0.682619\pi$
$240$		0			0
$241$	−60.6287	−	105.012i	−0.251571	−	0.435734i	0.712387	−	0.701786i	$-0.247614\pi$
$241$	−60.6287	−	105.012i	−0.251571	−	0.435734i	−0.963959	+	0.266052i	$0.914281\pi$
$242$		0			0
$243$	83.0137	+	228.381i	0.341620	+	0.939838i
$244$		0			0
$245$	267.057	−	154.185i	1.09003	−	0.629329i
$246$		0			0
$247$	−17.6489	+	30.5688i	−0.0714530	+	0.123760i
$248$		0			0
$249$	5.56476	+	2.02594i	0.0223484	+	0.00813632i
$250$		0			0
$251$			188.807i			0.752220i	0.926575	+	0.376110i	$0.122739\pi$
$251$			188.807i			0.752220i	−0.926575	+	0.376110i	$0.877261\pi$
$252$		0			0
$253$	−646.114			−2.55381
$254$		0			0
$255$	29.4730	−	5.19430i	0.115580	−	0.0203698i
$256$		0			0
$257$	160.701	+	92.7809i	0.625297	+	0.361015i	0.778928	−	0.627113i	$-0.215764\pi$
$257$	160.701	+	92.7809i	0.625297	+	0.361015i	−0.153632	+	0.988128i	$0.549097\pi$
$258$		0			0
$259$	−1.24500	−	2.15641i	−0.00480696	−	0.00832590i
$260$		0			0
$261$	−98.3744	−	270.425i	−0.376914	−	1.03611i
$262$		0			0
$263$	180.894	−	104.439i	0.687809	−	0.397107i	−0.114982	−	0.993368i	$-0.536681\pi$
$263$	180.894	−	104.439i	0.687809	−	0.397107i	0.802791	+	0.596261i	$0.203348\pi$
$264$		0			0
$265$	211.307	−	365.995i	0.797386	−	1.38111i
$266$		0			0
$267$	−192.047	+	161.119i	−0.719278	+	0.603442i
$268$		0			0
$269$			95.7103i			0.355801i	0.984049	+	0.177900i	$0.0569304\pi$
$269$			95.7103i			0.355801i	−0.984049	+	0.177900i	$0.943070\pi$
$270$		0			0
$271$	278.965			1.02939			0.514696	−	0.857373i	$-0.327905\pi$
$271$	278.965			1.02939			0.514696	+	0.857373i	$0.327905\pi$
$272$		0			0
$273$	33.5607	+	40.0030i	0.122933	+	0.146531i
$274$		0			0
$275$	−693.626	−	400.465i	−2.52228	−	1.45624i
$276$		0			0
$277$	−70.5229	−	122.149i	−0.254595	−	0.440972i	0.710190	−	0.704010i	$-0.248609\pi$
$277$	−70.5229	−	122.149i	−0.254595	−	0.440972i	−0.964786	+	0.263038i	$0.915276\pi$
$278$		0			0
$279$	−212.589	−	178.445i	−0.761967	−	0.639587i
$280$		0			0
$281$	−197.330	+	113.929i	−0.702243	+	0.405440i	−0.808182	−	0.588932i	$-0.799548\pi$
$281$	−197.330	+	113.929i	−0.702243	+	0.405440i	0.105939	+	0.994373i	$0.466215\pi$
$282$		0			0
$283$	45.3792	−	78.5990i	0.160350	−	0.277735i	−0.774644	−	0.632398i	$-0.782071\pi$
$283$	45.3792	−	78.5990i	0.160350	−	0.277735i	0.934994	+	0.354663i	$0.115404\pi$
$284$		0			0
$285$	−28.3628	−	160.934i	−0.0995187	−	0.564680i
$286$		0			0
$287$			243.002i			0.846697i
$288$		0			0
$289$	287.487			0.994763
$290$		0			0
$291$	99.2030	−	272.486i	0.340904	−	0.936378i
$292$		0			0
$293$	−107.798	−	62.2372i	−0.367911	−	0.212414i	0.304634	−	0.952469i	$-0.401466\pi$
$293$	−107.798	−	62.2372i	−0.367911	−	0.212414i	−0.672545	+	0.740056i	$0.734799\pi$
$294$		0			0
$295$	238.045	+	412.307i	0.806934	+	1.39765i
$296$		0			0
$297$	−265.417	+	459.445i	−0.893660	+	1.54695i
$298$		0			0
$299$	−149.618	+	86.3821i	−0.500395	+	0.288903i
$300$		0			0
$301$	78.5694	−	136.086i	0.261028	−	0.452114i
$302$		0			0
$303$	−174.619	−	63.5729i	−0.576300	−	0.209811i
$304$		0			0
$305$		−	430.607i		−	1.41183i
$306$		0			0
$307$	210.821			0.686714			0.343357	−	0.939205i	$-0.388436\pi$
$307$	210.821			0.686714			0.343357	+	0.939205i	$0.388436\pi$
$308$		0			0
$309$	−26.4490	+	4.66135i	−0.0855955	+	0.0150853i
$310$		0			0
$311$	−437.181	−	252.406i	−1.40573	−	0.811596i	−0.410753	−	0.911747i	$-0.634734\pi$
$311$	−437.181	−	252.406i	−1.40573	−	0.811596i	−0.994972	+	0.100150i	$0.968068\pi$
$312$		0			0
$313$	147.444	+	255.380i	0.471066	+	0.815911i	0.999452	−	0.0330936i	$-0.0105359\pi$
$313$	147.444	+	255.380i	0.471066	+	0.815911i	−0.528386	+	0.849004i	$0.677203\pi$
$314$		0			0
$315$	−238.061	−	42.0183i	−0.755748	−	0.133391i
$316$		0			0
$317$	−386.798	+	223.318i	−1.22018	+	0.704472i	−0.964957	−	0.262409i	$-0.915483\pi$
$317$	−386.798	+	223.318i	−1.22018	+	0.704472i	−0.255225	+	0.966882i	$0.582150\pi$
$318$		0			0
$319$	314.170	−	544.158i	0.984858	−	1.70582i
$320$		0			0
$321$	466.459	−	391.338i	1.45314	−	1.21912i
$322$		0			0
$323$			8.26375i			0.0255844i
$324$		0			0
$325$	−214.160			−0.658955
$326$		0			0
$327$	166.594	+	198.573i	0.509461	+	0.607257i
$328$		0			0
$329$	223.249	+	128.893i	0.678569	+	0.391772i
$330$		0			0
$331$	0.557483	+	0.965590i	0.00168424	+	0.00291719i	0.866866	−	0.498541i	$-0.166131\pi$
$331$	0.557483	+	0.965590i	0.00168424	+	0.00291719i	−0.865182	+	0.501458i	$0.832797\pi$
$332$		0			0
$333$	1.17596	−	6.66258i	0.00353142	−	0.0200077i
$334$		0			0
$335$	−546.498	+	315.521i	−1.63134	+	0.941853i
$336$		0			0
$337$	−19.3776	+	33.5630i	−0.0575004	+	0.0995935i	−0.893343	−	0.449376i	$-0.851646\pi$
$337$	−19.3776	+	33.5630i	−0.0575004	+	0.0995935i	0.835842	+	0.548970i	$0.184980\pi$
$338$		0			0
$339$	45.7613	+	259.655i	0.134989	+	0.765943i
$340$		0			0
$341$		−	606.051i		−	1.77727i
$342$		0			0
$343$	288.270			0.840436
$344$		0			0
$345$	273.620	−	751.566i	0.793102	−	2.17845i
$346$		0			0
$347$	238.530	+	137.715i	0.687407	+	0.396875i	0.802640	−	0.596464i	$-0.203428\pi$
$347$	238.530	+	137.715i	0.687407	+	0.396875i	−0.115233	+	0.993338i	$0.536761\pi$
$348$		0			0
$349$	0.705163	+	1.22138i	0.00202052	+	0.00349965i	0.867034	−	0.498249i	$-0.166024\pi$
$349$	0.705163	+	1.22138i	0.00202052	+	0.00349965i	−0.865013	+	0.501749i	$0.832690\pi$
$350$		0			0
$351$	−0.0362204	+	141.877i	−0.000103192	+	0.404207i
$352$		0			0
$353$	−230.195	+	132.903i	−0.652112	+	0.376497i	−0.789265	−	0.614053i	$-0.789538\pi$
$353$	−230.195	+	132.903i	−0.652112	+	0.376497i	0.137153	+	0.990550i	$0.456205\pi$
$354$		0			0
$355$	−244.789	+	423.988i	−0.689547	+	1.19433i
$356$		0			0
$357$	11.4871	+	4.18206i	0.0321767	+	0.0117145i
$358$		0			0
$359$		−	525.038i		−	1.46250i	−0.682109	−	0.731251i	$-0.738937\pi$
$359$		−	525.038i		−	1.46250i	0.682109	−	0.731251i	$-0.261063\pi$
$360$		0			0
$361$	−315.877			−0.875005
$362$		0			0
$363$	−783.508	+	138.085i	−2.15842	+	0.380399i
$364$		0			0
$365$	−419.108	−	241.972i	−1.14824	−	0.662937i
$366$		0			0
$367$	−46.2379	−	80.0864i	−0.125989	−	0.218219i	0.796130	−	0.605125i	$-0.206877\pi$
$367$	−46.2379	−	80.0864i	−0.125989	−	0.218219i	−0.922119	+	0.386906i	$0.873544\pi$
$368$		0			0
$369$	−424.492	+	505.715i	−1.15038	+	1.37050i
$370$		0			0
$371$	149.502	−	86.3149i	0.402970	−	0.232655i
$372$		0			0
$373$	167.069	−	289.372i	0.447907	−	0.775797i	−0.550343	−	0.834939i	$-0.685503\pi$
$373$	167.069	−	289.372i	0.447907	−	0.775797i	0.998250	+	0.0591414i	$0.0188363\pi$
$374$		0			0
$375$	293.643	−	246.354i	0.783049	−	0.656943i
$376$		0			0
$377$		−	168.011i		−	0.445653i
$378$		0			0
$379$	−33.4125			−0.0881596			−0.0440798	−	0.999028i	$-0.514036\pi$
$379$	−33.4125			−0.0881596			−0.0440798	+	0.999028i	$0.514036\pi$
$380$		0			0
$381$	−74.3853	−	88.6643i	−0.195237	−	0.232715i
$382$		0			0
$383$	173.467	+	100.151i	0.452916	+	0.261491i	0.709061	−	0.705147i	$-0.249119\pi$
$383$	173.467	+	100.151i	0.452916	+	0.261491i	−0.256145	+	0.966638i	$0.582452\pi$
$384$		0			0
$385$	−263.924	−	457.131i	−0.685518	−	1.18735i
$386$		0			0
$387$	401.236	−	145.961i	1.03679	−	0.377159i
$388$		0			0
$389$	114.791	−	66.2746i	0.295093	−	0.170372i	−0.345144	−	0.938550i	$-0.612170\pi$
$389$	114.791	−	66.2746i	0.295093	−	0.170372i	0.640236	+	0.768178i	$0.278836\pi$
$390$		0			0
$391$	−20.2234	+	35.0279i	−0.0517222	+	0.0895854i
$392$		0			0
$393$	−12.2181	−	69.3271i	−0.0310894	−	0.176405i
$394$		0			0
$395$		−	684.632i		−	1.73324i
$396$		0			0
$397$	−216.148			−0.544453			−0.272227	−	0.962233i	$-0.587760\pi$
$397$	−216.148			−0.544453			−0.272227	+	0.962233i	$0.587760\pi$
$398$		0			0
$399$	22.8357	−	62.7238i	0.0572322	−	0.157203i
$400$		0			0
$401$	360.413	+	208.085i	0.898786	+	0.518914i	0.876806	−	0.480844i	$-0.159670\pi$
$401$	360.413	+	208.085i	0.898786	+	0.518914i	0.0219796	+	0.999758i	$0.493003\pi$
$402$		0			0
$403$	−81.0258	−	140.341i	−0.201057	−	0.348240i
$404$		0			0
$405$	−422.031	−	503.304i	−1.04205	−	1.24273i
$406$		0			0
$407$	12.7937	−	7.38643i	0.0314341	−	0.0181485i
$408$		0			0
$409$	−230.325	+	398.935i	−0.563143	+	0.975392i	0.434077	+	0.900876i	$0.357075\pi$
$409$	−230.325	+	398.935i	−0.563143	+	0.975392i	−0.997220	+	0.0745161i	$0.976259\pi$
$410$		0			0
$411$	−123.837	−	45.0850i	−0.301307	−	0.109696i
$412$		0			0
$413$			194.474i			0.470881i
$414$		0			0
$415$	−16.0074			−0.0385721
$416$		0			0
$417$	−144.712	+	25.5039i	−0.347031	+	0.0611605i
$418$		0			0
$419$	682.995	+	394.327i	1.63006	+	0.941116i	0.984073	+	0.177768i	$0.0568875\pi$
$419$	682.995	+	394.327i	1.63006	+	0.941116i	0.645987	+	0.763348i	$0.276446\pi$
$420$		0			0
$421$	172.003	+	297.918i	0.408558	+	0.707644i	0.994728	−	0.102544i	$-0.0326983\pi$
$421$	172.003	+	297.918i	0.408558	+	0.707644i	−0.586170	+	0.810188i	$0.699365\pi$
$422$		0			0
$423$	239.448	+	658.226i	0.566071	+	1.55609i
$424$		0			0
$425$	−43.4210	+	25.0691i	−0.102167	+	0.0589862i
$426$		0			0
$427$	87.9472	−	152.329i	0.205965	−	0.356742i
$428$		0			0
$429$	−237.332	+	199.111i	−0.553222	+	0.464128i
$430$		0			0
$431$			639.752i			1.48434i	0.670210	+	0.742172i	$0.266204\pi$
$431$			639.752i			1.48434i	−0.670210	+	0.742172i	$0.733796\pi$
$432$		0			0
$433$	379.659			0.876811			0.438405	−	0.898777i	$-0.355543\pi$
$433$	379.659			0.876811			0.438405	+	0.898777i	$0.355543\pi$
$434$		0			0
$435$	499.924	+	595.889i	1.14925	+	1.36986i
$436$		0			0
$437$	191.266	+	110.427i	0.437679	+	0.252694i
$438$		0			0
$439$	−73.3930	−	127.120i	−0.167182	−	0.289568i	0.770246	−	0.637747i	$-0.220133\pi$
$439$	−73.3930	−	127.120i	−0.167182	−	0.289568i	−0.937428	+	0.348179i	$0.886800\pi$
$440$		0			0
$441$	262.144	+	220.041i	0.594431	+	0.498959i
$442$		0			0
$443$	675.366	−	389.923i	1.52453	−	0.880187i	0.524950	−	0.851133i	$-0.324084\pi$
$443$	675.366	−	389.923i	1.52453	−	0.880187i	0.999578	−	0.0290537i	$-0.00924938\pi$
$444$		0			0
$445$	338.797	−	586.814i	0.761342	−	1.31868i
$446$		0			0
$447$	19.1825	+	108.844i	0.0429139	+	0.243498i
$448$		0			0
$449$			95.1178i			0.211844i	0.994374	+	0.105922i	$0.0337793\pi$
$449$			95.1178i			0.211844i	−0.994374	+	0.105922i	$0.966221\pi$
$450$		0			0
$451$	−1441.70			−3.19667
$452$		0			0
$453$	−224.255	+	615.973i	−0.495044	+	1.35976i
$454$		0			0
$455$	−122.232	−	70.5707i	−0.268642	−	0.155100i
$456$		0			0
$457$	235.838	+	408.484i	0.516057	+	0.893837i	0.999826	+	0.0186415i	$0.00593413\pi$
$457$	235.838	+	408.484i	0.516057	+	0.893837i	−0.483769	+	0.875196i	$0.660733\pi$
$458$		0			0
$459$	16.6004	+	28.7697i	0.0361665	+	0.0626791i
$460$		0			0
$461$	441.560	−	254.935i	0.957832	−	0.553004i	0.0623266	−	0.998056i	$-0.480148\pi$
$461$	441.560	−	254.935i	0.957832	−	0.553004i	0.895505	+	0.445052i	$0.146815\pi$
$462$		0			0
$463$	199.010	−	344.696i	0.429828	−	0.744484i	−0.567030	−	0.823697i	$-0.691907\pi$
$463$	199.010	−	344.696i	0.429828	−	0.744484i	0.996858	+	0.0792133i	$0.0252408\pi$
$464$		0			0
$465$	704.965	+	256.654i	1.51605	+	0.551944i
$466$		0			0
$467$		−	328.797i		−	0.704062i	−0.935988	−	0.352031i	$-0.885491\pi$
$467$		−	328.797i		−	0.704062i	0.935988	−	0.352031i	$-0.114509\pi$
$468$		0			0
$469$	−257.768			−0.549612
$470$		0			0
$471$	−282.365	+	49.7638i	−0.599501	+	0.105656i
$472$		0			0
$473$	807.381	+	466.141i	1.70694	+	0.985500i
$474$		0			0
$475$	136.887	+	237.095i	0.288183	+	0.499147i
$476$		0			0
$477$	461.910	+	81.5283i	0.968365	+	0.170919i
$478$		0			0
$479$	−310.579	+	179.313i	−0.648391	+	0.374349i	−0.787839	−	0.615881i	$-0.788800\pi$
$479$	−310.579	+	179.313i	−0.648391	+	0.374349i	0.139449	+	0.990229i	$0.455467\pi$
$480$		0			0
$481$	1.97505	−	3.42089i	0.00410614	−	0.00711205i
$482$		0			0
$483$	250.294	−	209.986i	0.518208	−	0.434753i
$484$		0			0
$485$			783.823i			1.61613i
$486$		0			0
$487$	−87.6240			−0.179926			−0.0899630	−	0.995945i	$-0.528675\pi$
$487$	−87.6240			−0.179926			−0.0899630	+	0.995945i	$0.528675\pi$
$488$		0			0
$489$	49.1954	+	58.6389i	0.100604	+	0.119916i
$490$		0			0
$491$	403.944	+	233.217i	0.822698	+	0.474985i	0.851346	−	0.524605i	$-0.175787\pi$
$491$	403.944	+	233.217i	0.822698	+	0.474985i	−0.0286483	+	0.999590i	$0.509120\pi$
$492$		0			0
$493$	−19.6670	−	34.0643i	−0.0398925	−	0.0690959i
$494$		0			0
$495$	249.289	−	1412.38i	0.503613	−	2.85329i
$496$		0			0
$497$	−173.191	+	99.9916i	−0.348472	+	0.201190i
$498$		0			0
$499$	−148.171	+	256.640i	−0.296936	+	0.514309i	−0.975433	−	0.220294i	$-0.929298\pi$
$499$	−148.171	+	256.640i	−0.296936	+	0.514309i	0.678497	+	0.734603i	$0.262632\pi$
$500$		0			0
$501$	−35.3107	−	200.356i	−0.0704804	−	0.399913i
$502$		0			0
$503$			218.468i			0.434331i	0.976135	+	0.217165i	$0.0696811\pi$
$503$			218.468i			0.434331i	−0.976135	+	0.217165i	$0.930319\pi$
$504$		0			0
$505$	502.302			0.994658
$506$		0			0
$507$	145.107	−	398.572i	0.286207	−	0.786138i
$508$		0			0
$509$	−657.975	−	379.882i	−1.29268	−	0.746330i	−0.313553	−	0.949571i	$-0.601519\pi$
$509$	−657.975	−	379.882i	−1.29268	−	0.746330i	−0.979129	+	0.203240i	$0.934853\pi$
$510$		0			0
$511$	−98.8408	−	171.197i	−0.193426	−	0.335024i
$512$		0			0
$513$	157.094	−	90.6446i	0.306225	−	0.176695i
$514$		0			0
$515$	62.8678	−	36.2968i	0.122073	−	0.0704792i
$516$		0			0
$517$	−764.703	+	1324.50i	−1.47912	+	2.56191i
$518$		0			0
$519$	−524.169	−	190.832i	−1.00996	−	0.367692i
$520$		0			0
$521$		−	719.772i		−	1.38152i	−0.723084	−	0.690760i	$-0.757276\pi$
$521$		−	719.772i		−	1.38152i	0.723084	−	0.690760i	$-0.242724\pi$
$522$		0			0
$523$	−144.308			−0.275924			−0.137962	−	0.990437i	$-0.544055\pi$
$523$	−144.308			−0.275924			−0.137962	+	0.990437i	$0.544055\pi$
$524$		0			0
$525$	398.850	−	70.2931i	0.759715	−	0.133892i
$526$		0			0
$527$	−32.8559	−	18.9694i	−0.0623453	−	0.0359950i
$528$		0			0
$529$	275.983	+	478.017i	0.521707	+	0.903623i
$530$		0			0
$531$	−339.719	+	404.722i	−0.639773	+	0.762188i
$532$		0			0
$533$	−333.848	+	192.747i	−0.626357	+	0.361627i
$534$		0			0
$535$	−822.895	+	1425.30i	−1.53812	+	2.66411i
$536$		0			0
$537$	−484.036	+	406.085i	−0.901371	+	0.756210i
$538$		0			0
$539$			747.324i			1.38650i
$540$		0			0
$541$	596.733			1.10302			0.551509	−	0.834169i	$-0.314052\pi$
$541$	596.733			1.10302			0.551509	+	0.834169i	$0.314052\pi$
$542$		0			0
$543$	−469.300	−	559.386i	−0.864272	−	1.03018i
$544$		0			0
$545$	−606.754	−	350.309i	−1.11331	−	0.642770i
$546$		0			0
$547$	−438.017	−	758.668i	−0.800762	−	1.38696i	−0.919115	−	0.393989i	$-0.871095\pi$
$547$	−438.017	−	758.668i	−0.800762	−	1.38696i	0.118353	−	0.992972i	$-0.462239\pi$
$548$		0			0
$549$	449.126	−	163.382i	0.818080	−	0.297599i
$550$		0			0
$551$	−186.004	+	107.389i	−0.337575	+	0.194899i
$552$		0			0
$553$	139.829	−	242.191i	0.252856	−	0.437959i
$554$		0			0
$555$	3.17403	+	18.0098i	0.00571897	+	0.0324501i
$556$		0			0
$557$			937.435i			1.68301i	0.540251	+	0.841504i	$0.318329\pi$
$557$			937.435i			1.68301i	−0.540251	+	0.841504i	$0.681671\pi$
$558$		0			0
$559$	249.283			0.445944
$560$		0			0
$561$	−24.8116	+	68.1513i	−0.0442274	+	0.121482i
$562$		0			0
$563$	−381.150	−	220.057i	−0.676999	−	0.390865i	0.121725	−	0.992564i	$-0.461158\pi$
$563$	−381.150	−	220.057i	−0.676999	−	0.390865i	−0.798723	+	0.601698i	$0.794491\pi$
$564$		0			0
$565$	−356.332	−	617.185i	−0.630676	−	1.09236i
$566$		0			0
$567$	−46.5002	−	264.242i	−0.0820110	−	0.466035i
$568$		0			0
$569$	−417.616	+	241.111i	−0.733947	+	0.423744i	−0.819864	−	0.572558i	$-0.805951\pi$
$569$	−417.616	+	241.111i	−0.733947	+	0.423744i	0.0859175	+	0.996302i	$0.472618\pi$
$570$		0			0
$571$	341.490	−	591.478i	0.598056	−	1.03586i	−0.395052	−	0.918659i	$-0.629273\pi$
$571$	341.490	−	591.478i	0.598056	−	1.03586i	0.993108	−	0.117204i	$-0.0373932\pi$
$572$		0			0
$573$	−658.980	−	239.913i	−1.15005	−	0.418696i
$574$		0			0
$575$			1339.98i			2.33040i
$576$		0			0
$577$	−155.714			−0.269867			−0.134934	−	0.990855i	$-0.543082\pi$
$577$	−155.714			−0.269867			−0.134934	+	0.990855i	$0.543082\pi$
$578$		0			0
$579$	727.839	−	128.274i	1.25706	−	0.221544i
$580$		0			0
$581$	−5.66269	−	3.26935i	−0.00974645	−	0.00562712i
$582$		0			0
$583$	512.094	+	886.973i	0.878377	+	1.52139i
$584$		0			0
$585$	−131.101	−	360.388i	−0.224104	−	0.616048i
$586$		0			0
$587$	−101.636	+	58.6798i	−0.173145	+	0.0999656i	−0.584068	−	0.811705i	$-0.698540\pi$
$587$	−101.636	+	58.6798i	−0.173145	+	0.0999656i	0.410923	+	0.911670i	$0.365207\pi$
$588$		0			0
$589$	−103.580	+	179.406i	−0.175857	+	0.304594i
$590$		0			0
$591$	735.713	−	617.230i	1.24486	−	1.04438i
$592$		0			0
$593$			805.727i			1.35873i	0.733801	+	0.679365i	$0.237745\pi$
$593$			805.727i			1.35873i	−0.733801	+	0.679365i	$0.762255\pi$
$594$		0			0
$595$	−33.0433			−0.0555350
$596$		0			0
$597$	427.428	+	509.477i	0.715960	+	0.853395i
$598$		0			0
$599$	383.876	+	221.631i	0.640862	+	0.370002i	0.784947	−	0.619563i	$-0.212690\pi$
$599$	383.876	+	221.631i	0.640862	+	0.370002i	−0.144084	+	0.989565i	$0.546024\pi$
$600$		0			0
$601$	−424.198	−	734.733i	−0.705821	−	1.22252i	−0.966394	−	0.257064i	$-0.917245\pi$
$601$	−424.198	−	734.733i	−0.705821	−	1.22252i	0.260573	−	0.965454i	$-0.416088\pi$
$602$		0			0
$603$	−536.444	−	450.286i	−0.889625	−	0.746742i
$604$		0			0
$605$	1862.36	−	1075.23i	3.07827	−	1.77724i
$606$		0			0
$607$	217.239	−	376.269i	0.357890	−	0.619884i	−0.629718	−	0.776824i	$-0.716830\pi$
$607$	217.239	−	376.269i	0.357890	−	0.619884i	0.987608	+	0.156940i	$0.0501629\pi$
$608$		0			0
$609$	55.1457	+	312.903i	0.0905513	+	0.513798i
$610$		0			0
$611$			408.947i			0.669308i
$612$		0			0
$613$	1108.99			1.80912			0.904561	−	0.426345i	$-0.140199\pi$
$613$	1108.99			1.80912			0.904561	+	0.426345i	$0.140199\pi$
$614$		0			0
$615$	610.539	−	1677.00i	0.992746	−	2.72683i
$616$		0			0
$617$	−404.667	−	233.635i	−0.655863	−	0.378662i	0.134836	−	0.990868i	$-0.456949\pi$
$617$	−404.667	−	233.635i	−0.655863	−	0.378662i	−0.790699	+	0.612205i	$0.790283\pi$
$618$		0			0
$619$	−137.847	−	238.758i	−0.222693	−	0.385716i	0.732932	−	0.680302i	$-0.238152\pi$
$619$	−137.847	−	238.758i	−0.222693	−	0.385716i	−0.955625	+	0.294586i	$0.904818\pi$
$620$		0			0
$621$	887.707	+	0.226627i	1.42948	+	0.000364939i
$622$		0			0
$623$	239.702	−	138.392i	0.384754	−	0.222138i
$624$		0			0
$625$	−8.57618	+	14.8544i	−0.0137219	+	0.0237670i
$626$		0			0
$627$	372.132	+	135.481i	0.593511	+	0.216078i
$628$		0			0
$629$		−	0.924781i		−	0.00147024i
$630$		0			0
$631$	308.627			0.489108			0.244554	−	0.969636i	$-0.421359\pi$
$631$	308.627			0.489108			0.244554	+	0.969636i	$0.421359\pi$
$632$		0			0
$633$	−828.651	+	146.041i	−1.30909	+	0.230712i
$634$		0			0
$635$	270.920	+	156.416i	0.426646	+	0.246324i
$636$		0			0
$637$	99.9133	+	173.055i	0.156850	+	0.271672i
$638$		0			0
$639$	−535.101	−	94.4466i	−0.837403	−	0.147804i
$640$		0			0
$641$	791.012	−	456.691i	1.23403	−	0.712467i	0.266162	−	0.963928i	$-0.414245\pi$
$641$	791.012	−	456.691i	1.23403	−	0.712467i	0.967867	+	0.251462i	$0.0809112\pi$
$642$		0			0
$643$	−624.662	+	1081.95i	−0.971480	+	1.68265i	−0.280388	+	0.959887i	$0.590463\pi$
$643$	−624.662	+	1081.95i	−0.971480	+	1.68265i	−0.691092	+	0.722767i	$0.742870\pi$
$644$		0			0
$645$	−884.135	+	741.749i	−1.37075	+	1.15000i
$646$		0			0
$647$		−	90.8741i		−	0.140455i	−0.997531	−	0.0702273i	$-0.977628\pi$
$647$		−	90.8741i		−	0.140455i	0.997531	−	0.0702273i	$-0.0223725\pi$
$648$		0			0
$649$	−1153.79			−1.77779
$650$		0			0
$651$	196.965	+	234.775i	0.302558	+	0.360637i
$652$		0			0
$653$	351.248	+	202.793i	0.537898	+	0.310556i	0.744227	−	0.667927i	$-0.232818\pi$
$653$	351.248	+	202.793i	0.537898	+	0.310556i	−0.206328	+	0.978483i	$0.566152\pi$
$654$		0			0
$655$	95.1396	+	164.787i	0.145251	+	0.251583i
$656$		0			0
$657$	93.3597	−	528.942i	0.142100	−	0.805087i
$658$		0			0
$659$	115.959	−	66.9491i	0.175962	−	0.101592i	−0.409432	−	0.912341i	$-0.634273\pi$
$659$	115.959	−	66.9491i	0.175962	−	0.101592i	0.585394	+	0.810749i	$0.300940\pi$
$660$		0			0
$661$	105.598	−	182.901i	0.159755	−	0.276704i	−0.775025	−	0.631930i	$-0.782263\pi$
$661$	105.598	−	182.901i	0.159755	−	0.276704i	0.934780	+	0.355227i	$0.115596\pi$
$662$		0			0
$663$	3.36594	+	19.0987i	0.00507684	+	0.0288065i
$664$		0			0
$665$			180.429i			0.271322i
$666$		0			0
$667$	−1051.23			−1.57605
$668$		0			0
$669$	30.8236	−	84.6646i	0.0460741	−	0.126554i
$670$		0			0
$671$	903.746	+	521.778i	1.34686	+	0.777613i
$672$		0			0
$673$	−216.932	−	375.738i	−0.322336	−	0.558303i	0.658633	−	0.752464i	$-0.271135\pi$
$673$	−216.932	−	375.738i	−0.322336	−	0.558303i	−0.980970	+	0.194161i	$0.937802\pi$
$674$		0			0
$675$	952.845	+	550.449i	1.41162	+	0.815481i
$676$		0			0
$677$	−548.653	+	316.765i	−0.810418	+	0.467895i	−0.847101	−	0.531432i	$-0.821654\pi$
$677$	−548.653	+	316.765i	−0.810418	+	0.467895i	0.0366831	+	0.999327i	$0.488321\pi$
$678$		0			0
$679$	−160.088	+	277.281i	−0.235771	+	0.408367i
$680$		0			0
$681$	−30.2157	−	11.0005i	−0.0443696	−	0.0161535i
$682$		0			0
$683$			258.998i			0.379206i	0.981861	+	0.189603i	$0.0607200\pi$
$683$			258.998i			0.379206i	−0.981861	+	0.189603i	$0.939280\pi$
$684$		0			0
$685$	356.226			0.520038
$686$		0			0
$687$	−681.984	+	120.192i	−0.992699	+	0.174953i
$688$		0			0
$689$	237.167	+	136.929i	0.344220	+	0.198735i
$690$		0			0
$691$	−226.262	−	391.897i	−0.327441	−	0.567144i	0.654562	−	0.756008i	$-0.272853\pi$
$691$	−226.262	−	391.897i	−0.327441	−	0.567144i	−0.982003	+	0.188864i	$0.939520\pi$
$692$		0			0
$693$	376.652	−	448.721i	0.543509	−	0.647505i
$694$		0			0
$695$	343.973	−	198.593i	0.494925	−	0.285745i
$696$		0			0
$697$	−45.1251	+	78.1590i	−0.0647419	+	0.112136i
$698$		0			0
$699$	−348.203	+	292.127i	−0.498145	+	0.417921i
$700$		0			0
$701$		−	480.386i		−	0.685287i	−0.939466	−	0.342643i	$-0.888678\pi$
$701$		−	480.386i		−	0.685287i	0.939466	−	0.342643i	$-0.111322\pi$
$702$		0			0
$703$	−5.04965			−0.00718301
$704$		0			0
$705$	−1216.84	−	1450.42i	−1.72601	−	2.05733i
$706$		0			0
$707$	177.692	+	102.590i	0.251332	+	0.145107i
$708$		0			0
$709$	−175.153	−	303.374i	−0.247042	−	0.427890i	0.715662	−	0.698447i	$-0.246125\pi$
$709$	−175.153	−	303.374i	−0.247042	−	0.427890i	−0.962704	+	0.270557i	$0.912792\pi$
$710$		0			0
$711$	714.076	−	259.765i	1.00433	−	0.365351i
$712$		0			0
$713$	−878.097	+	506.970i	−1.23155	+	0.711038i
$714$		0			0
$715$	418.686	−	725.185i	0.585574	−	1.01424i
$716$		0			0
$717$	12.4678	+	70.7435i	0.0173888	+	0.0986659i
$718$		0			0
$719$		−	114.619i		−	0.159415i	−0.996818	−	0.0797074i	$-0.974601\pi$
$719$		−	114.619i		−	0.159415i	0.996818	−	0.0797074i	$-0.0253986\pi$
$720$		0			0
$721$	29.6530			0.0411276
$722$		0			0
$723$	−124.446	+	341.823i	−0.172125	+	0.472785i
$724$		0			0
$725$	−1128.53	−	651.558i	−1.55659	−	0.898700i
$726$		0			0
$727$	−445.588	−	771.782i	−0.612914	−	1.06160i	−0.990747	−	0.135724i	$-0.956664\pi$
$727$	−445.588	−	771.782i	−0.612914	−	1.06160i	0.377833	−	0.925874i	$-0.376669\pi$
$728$		0			0
$729$	364.822	−	631.146i	0.500442	−	0.865770i
$730$		0			0
$731$	50.5420	−	29.1805i	0.0691409	−	0.0399185i
$732$		0			0
$733$	−253.765	+	439.534i	−0.346200	+	0.599637i	−0.985571	−	0.169262i	$-0.945862\pi$
$733$	−253.765	+	439.534i	−0.346200	+	0.599637i	0.639371	+	0.768899i	$0.279195\pi$
$734$		0			0
$735$	−869.295	−	316.481i	−1.18271	−	0.430587i
$736$		0			0
$737$		−	1529.30i		−	2.07504i
$738$		0			0
$739$	−385.114			−0.521129			−0.260564	−	0.965456i	$-0.583909\pi$
$739$	−385.114			−0.521129			−0.260564	+	0.965456i	$0.583909\pi$
$740$		0			0
$741$	104.286	−	18.3793i	0.140737	−	0.0248034i
$742$		0			0
$743$	−557.320	−	321.769i	−0.750094	−	0.433067i	0.0756336	−	0.997136i	$-0.475902\pi$
$743$	−557.320	−	321.769i	−0.750094	−	0.433067i	−0.825728	+	0.564068i	$0.809235\pi$
$744$		0			0
$745$	−149.369	−	258.715i	−0.200496	−	0.347268i
$746$		0			0
$747$	−6.07357	−	16.6958i	−0.00813062	−	0.0223505i
$748$		0			0
$749$	−582.206	+	336.137i	−0.777311	+	0.448780i
$750$		0			0
$751$	−197.669	+	342.372i	−0.263207	+	0.455888i	−0.967092	−	0.254426i	$-0.918114\pi$
$751$	−197.669	+	342.372i	−0.263207	+	0.455888i	0.703885	+	0.710314i	$0.251447\pi$
$752$		0			0
$753$	433.935	−	364.052i	0.576275	−	0.483469i
$754$		0			0
$755$		−	1771.89i		−	2.34687i
$756$		0			0
$757$	120.960			0.159789			0.0798944	−	0.996803i	$-0.474542\pi$
$757$	120.960			0.159789			0.0798944	+	0.996803i	$0.474542\pi$
$758$		0			0
$759$	1245.82	+	1484.96i	1.64139	+	1.95647i
$760$		0			0
$761$	−759.093	−	438.262i	−0.997494	−	0.575903i	−0.0899878	−	0.995943i	$-0.528683\pi$
$761$	−759.093	−	438.262i	−0.997494	−	0.575903i	−0.907506	+	0.420040i	$0.862016\pi$
$762$		0			0
$763$	−143.095	−	247.847i	−0.187542	−	0.324832i
$764$		0			0
$765$	−68.7669	−	57.7222i	−0.0898914	−	0.0754539i
$766$		0			0
$767$	−267.178	+	154.255i	−0.348341	+	0.201115i
$768$		0			0
$769$	−152.027	+	263.319i	−0.197694	+	0.342417i	−0.947780	−	0.318923i	$-0.896679\pi$
$769$	−152.027	+	263.319i	−0.197694	+	0.342417i	0.750086	+	0.661340i	$0.230012\pi$
$770$		0			0
$771$	−96.6208	−	548.237i	−0.125319	−	0.711072i
$772$		0			0
$773$		−	485.869i		−	0.628550i	−0.949332	−	0.314275i	$-0.898239\pi$
$773$		−	485.869i		−	0.628550i	0.949332	−	0.314275i	$-0.101761\pi$
$774$		0			0
$775$	−1256.89			−1.62180
$776$		0			0
$777$	−2.55549	+	7.01930i	−0.00328892	+	0.00903385i
$778$		0			0
$779$	426.778	+	246.400i	0.547853	+	0.316303i
$780$		0			0
$781$	−593.236	−	1027.52i	−0.759585	−	1.31564i
$782$		0			0
$783$	−431.834	+	747.518i	−0.551512	+	0.954684i
$784$		0			0
$785$	671.167	−	387.498i	0.854989	−	0.493628i
$786$		0			0
$787$	−387.359	+	670.925i	−0.492197	+	0.852510i	−0.999960	−	0.00898689i	$-0.997139\pi$
$787$	−387.359	+	670.925i	−0.492197	+	0.852510i	0.507763	+	0.861497i	$0.330473\pi$
$788$		0			0
$789$	−588.825	−	214.372i	−0.746293	−	0.271700i
$790$		0			0
$791$		−	291.109i		−	0.368027i
$792$		0			0
$793$	279.036			0.351874
$794$		0			0
$795$	−1248.60	+	220.052i	−1.57057	+	0.276796i
$796$		0			0
$797$	345.517	+	199.485i	0.433523	+	0.250294i	0.700846	−	0.713312i	$-0.252806\pi$
$797$	345.517	+	199.485i	0.433523	+	0.250294i	−0.267324	+	0.963607i	$0.586139\pi$
$798$		0			0
$799$	47.8704	+	82.9140i	0.0599129	+	0.103772i
$800$		0			0
$801$	740.599	+	130.717i	0.924593	+	0.163193i
$802$		0			0
$803$	1015.69	−	586.409i	1.26487	−	0.730272i
$804$		0			0
$805$	−441.553	+	764.792i	−0.548513	+	0.950052i
$806$		0			0
$807$	219.971	−	184.546i	0.272578	−	0.228681i
$808$		0			0
$809$			536.898i			0.663656i	0.943340	+	0.331828i	$0.107665\pi$
$809$			536.898i			0.663656i	−0.943340	+	0.331828i	$0.892335\pi$
$810$		0			0
$811$	278.092			0.342900			0.171450	−	0.985193i	$-0.445155\pi$
$811$	278.092			0.342900			0.171450	+	0.985193i	$0.445155\pi$
$812$		0			0
$813$	−537.892	−	641.145i	−0.661613	−	0.788616i
$814$		0			0
$815$	−179.175	−	103.447i	−0.219847	−	0.126929i
$816$		0			0
$817$	−159.336	−	275.979i	−0.195026	−	0.337795i
$818$		0			0
$819$	27.2282	−	154.265i	0.0332456	−	0.188358i
$820$		0			0
$821$	338.349	−	195.346i	0.412118	−	0.237936i	−0.279581	−	0.960122i	$-0.590196\pi$
$821$	338.349	−	195.346i	0.412118	−	0.237936i	0.691699	+	0.722186i	$0.256862\pi$
$822$		0			0
$823$	399.600	−	692.127i	0.485541	−	0.840981i	−0.514321	−	0.857598i	$-0.671956\pi$
$823$	399.600	−	692.127i	0.485541	−	0.840981i	0.999862	+	0.0166166i	$0.00528947\pi$
$824$		0			0
$825$	417.039	+	2366.32i	0.505502	+	2.86827i
$826$		0			0
$827$			989.841i			1.19691i	0.801158	+	0.598453i	$0.204218\pi$
$827$			989.841i			1.19691i	−0.801158	+	0.598453i	$0.795782\pi$
$828$		0			0
$829$	1060.24			1.27894			0.639472	−	0.768814i	$-0.279153\pi$
$829$	1060.24			1.27894			0.639472	+	0.768814i	$0.279153\pi$
$830$		0			0
$831$	−144.755	+	397.607i	−0.174194	+	0.478468i
$832$		0			0
$833$	40.5148	+	23.3912i	0.0486372	+	0.0280807i
$834$		0			0
$835$	274.955	+	476.236i	0.329288	+	0.570343i
$836$		0			0
$837$	−0.212575	+	832.664i	−0.000253972	+	0.994820i
$838$		0			0
$839$	−968.557	+	559.197i	−1.15442	+	0.666504i	−0.949960	−	0.312371i	$-0.898877\pi$
$839$	−968.557	+	559.197i	−1.15442	+	0.666504i	−0.204458	+	0.978875i	$0.565543\pi$
$840$		0			0
$841$	90.6547	−	157.018i	0.107794	−	0.186705i
$842$		0			0
$843$	642.328	+	233.850i	0.761955	+	0.277402i
$844$		0			0
$845$			1146.52i			1.35683i
$846$		0			0
$847$	878.422			1.03710
$848$		0			0
$849$	−268.143	+	47.2572i	−0.315833	+	0.0556622i
$850$		0			0
$851$	−21.4042	−	12.3577i	−0.0251518	−	0.0145214i
$852$		0			0
$853$	−499.172	−	864.591i	−0.585196	−	1.01359i	−0.994851	−	0.101348i	$-0.967684\pi$
$853$	−499.172	−	864.591i	−0.585196	−	1.01359i	0.409655	−	0.912240i	$-0.365649\pi$
$854$		0			0
$855$	−315.185	+	375.493i	−0.368638	+	0.439174i
$856$		0			0
$857$	−1078.87	+	622.884i	−1.25889	+	0.726819i	−0.972858	−	0.231402i	$-0.925669\pi$
$857$	−1078.87	+	622.884i	−1.25889	+	0.726819i	−0.286029	+	0.958221i	$0.592335\pi$
$858$		0			0
$859$	−91.7405	+	158.899i	−0.106799	+	0.184982i	−0.914472	−	0.404649i	$-0.867394\pi$
$859$	−91.7405	+	158.899i	−0.106799	+	0.184982i	0.807673	+	0.589631i	$0.200727\pi$
$860$		0			0
$861$	558.491	−	468.549i	0.648654	−	0.544191i
$862$		0			0
$863$		−	874.132i		−	1.01290i	−0.862269	−	0.506450i	$-0.830958\pi$
$863$		−	874.132i		−	1.01290i	0.862269	−	0.506450i	$-0.169042\pi$
$864$		0			0
$865$	1507.80			1.74313
$866$		0			0
$867$	−554.322	−	660.730i	−0.639357	−	0.762087i
$868$		0			0
$869$	1436.89	+	829.587i	1.65350	+	0.954646i
$870$		0			0
$871$	−204.460	−	354.134i	−0.234741	−	0.406584i
$872$		0			0
$873$	−817.534	+	297.400i	−0.936465	+	0.340665i
$874$		0			0
$875$	−366.508	+	211.604i	−0.418867	+	0.241833i
$876$		0			0
$877$	−383.954	+	665.028i	−0.437804	+	0.758299i	−0.997520	−	0.0703855i	$-0.977577\pi$
$877$	−383.954	+	665.028i	−0.437804	+	0.758299i	0.559716	+	0.828685i	$0.310910\pi$
$878$		0			0
$879$	64.8129	+	367.755i	0.0737348	+	0.418379i
$880$		0			0
$881$		−	616.132i		−	0.699355i	−0.936870	−	0.349677i	$-0.886291\pi$
$881$		−	616.132i		−	0.699355i	0.936870	−	0.349677i	$-0.113709\pi$
$882$		0			0
$883$	1534.01			1.73727			0.868637	−	0.495448i	$-0.164996\pi$
$883$	1534.01			1.73727			0.868637	+	0.495448i	$0.164996\pi$
$884$		0			0
$885$	488.612	−	1342.10i	0.552104	−	1.51649i
$886$		0			0
$887$	−632.469	−	365.156i	−0.713042	−	0.411675i	0.0991441	−	0.995073i	$-0.468390\pi$
$887$	−632.469	−	365.156i	−0.713042	−	0.411675i	−0.812187	+	0.583398i	$0.801723\pi$
$888$		0			0
$889$	63.8928	+	110.665i	0.0718704	+	0.124483i
$890$		0			0
$891$	1567.71	−	275.879i	1.75949	−	0.309629i
$892$		0			0
$893$	452.742	−	261.391i	0.506990	−	0.292711i
$894$		0			0
$895$	853.905	−	1479.01i	0.954084	−	1.65252i
$896$		0			0
$897$	487.020	+	177.308i	0.542944	+	0.197668i
$898$		0			0
$899$		−	986.046i		−	1.09683i
$900$		0			0
$901$	64.1142			0.0711589
$902$		0			0
$903$	−464.262	+	81.8211i	−0.514133	+	0.0906103i
$904$		0			0
$905$	1709.24	+	986.833i	1.88867	+	1.09042i
$906$		0			0
$907$	280.478	+	485.802i	0.309237	+	0.535614i	0.978196	−	0.207685i	$-0.0665930\pi$
$907$	280.478	+	485.802i	0.309237	+	0.535614i	−0.668959	+	0.743300i	$0.733260\pi$
$908$		0			0
$909$	190.585	+	523.905i	0.209664	+	0.576353i
$910$		0			0
$911$	−1367.97	+	789.798i	−1.50161	+	0.866958i	−0.501616	+	0.865090i	$0.667261\pi$
$911$	−1367.97	+	789.798i	−1.50161	+	0.866958i	−0.999998	+	0.00186727i	$0.999406\pi$
$912$		0			0
$913$	19.3966	−	33.5959i	0.0212449	−	0.0367973i
$914$		0			0
$915$	−989.662	+	830.282i	−1.08160	+	0.907412i
$916$		0			0
$917$			77.7253i			0.0847604i
$918$		0			0
$919$	318.950			0.347062			0.173531	−	0.984828i	$-0.444482\pi$
$919$	318.950			0.347062			0.173531	+	0.984828i	$0.444482\pi$
$920$		0			0
$921$	−406.499	−	484.530i	−0.441367	−	0.526091i
$922$		0			0
$923$	−274.747	−	158.625i	−0.297667	−	0.171858i
$924$		0			0
$925$	−15.3187	−	26.5328i	−0.0165608	−	0.0286842i
$926$		0			0
$927$	61.7113	+	51.7998i	0.0665710	+	0.0558790i
$928$		0			0
$929$	−341.278	+	197.037i	−0.367361	+	0.212096i	−0.672305	−	0.740274i	$-0.734696\pi$
$929$	−341.278	+	197.037i	−0.367361	+	0.212096i	0.304944	+	0.952370i	$0.401362\pi$
$930$		0			0
$931$	127.725	−	221.226i	0.137191	−	0.237622i
$932$		0			0
$933$	262.853	+	1491.45i	0.281728	+	1.59856i
$934$		0			0
$935$		−	196.041i		−	0.209670i
$936$		0			0
$937$	−289.080			−0.308516			−0.154258	−	0.988031i	$-0.549299\pi$
$937$	−289.080			−0.308516			−0.154258	+	0.988031i	$0.549299\pi$
$938$		0			0
$939$	302.643	−	831.285i	0.322304	−	0.885288i
$940$		0			0
$941$	−315.358	−	182.072i	−0.335130	−	0.193488i	0.322986	−	0.946404i	$-0.395313\pi$
$941$	−315.358	−	182.072i	−0.335130	−	0.193488i	−0.658116	+	0.752916i	$0.728647\pi$
$942$		0			0
$943$	1206.00	+	2088.85i	1.27890	+	2.21511i
$944$		0			0
$945$	362.450	+	628.152i	0.383545	+	0.664712i
$946$		0			0
$947$	−348.750	+	201.351i	−0.368268	+	0.212620i	−0.672702	−	0.739914i	$-0.734866\pi$
$947$	−348.750	+	201.351i	−0.368268	+	0.212620i	0.304434	+	0.952534i	$0.401533\pi$
$948$		0			0
$949$	156.800	−	271.585i	0.165226	−	0.286180i
$950$		0			0
$951$	1259.06	+	458.382i	1.32393	+	0.482000i
$952$		0			0
$953$		−	1417.46i		−	1.48737i	−0.668532	−	0.743683i	$-0.733077\pi$
$953$		−	1417.46i		−	1.48737i	0.668532	−	0.743683i	$-0.266923\pi$
$954$		0			0
$955$	1895.60			1.98492
$956$		0			0
$957$	−1856.41	+	327.172i	−1.93982	+	0.341872i
$958$		0			0
$959$	126.016	+	72.7556i	0.131404	+	0.0758661i
$960$		0			0
$961$	4.96543	+	8.60038i	0.00516694	+	0.00894941i
$962$		0			0
$963$	−1798.82	−	317.496i	−1.86793	−	0.329695i
$964$		0			0
$965$	−1730.03	+	998.835i	−1.79278	+	1.03506i
$966$		0			0
$967$	530.591	−	919.010i	0.548698	−	0.950373i	−0.449666	−	0.893197i	$-0.648457\pi$
$967$	530.591	−	919.010i	0.548698	−	0.950373i	0.998364	−	0.0571760i	$-0.0182096\pi$
$968$		0			0
$969$	18.9926	−	15.9339i	0.0196002	−	0.0164437i
$970$		0			0
$971$			1210.22i			1.24637i	0.782076	+	0.623184i	$0.214161\pi$
$971$			1210.22i			1.24637i	−0.782076	+	0.623184i	$0.785839\pi$
$972$		0			0
$973$	162.242			0.166745
$974$		0			0
$975$	412.937	+	492.204i	0.423525	+	0.504825i
$976$		0			0
$977$	454.102	+	262.176i	0.464792	+	0.268348i	0.714057	−	0.700087i	$-0.246856\pi$
$977$	454.102	+	262.176i	0.464792	+	0.268348i	−0.249265	+	0.968435i	$0.580189\pi$
$978$		0			0
$979$	821.060	+	1422.12i	0.838672	+	1.45262i
$980$		0			0
$981$	135.159	−	765.764i	0.137777	−	0.780595i
$982$		0			0
$983$	1293.30	−	746.685i	1.31566	−	0.759598i	0.332634	−	0.943056i	$-0.392063\pi$
$983$	1293.30	−	746.685i	1.31566	−	0.759598i	0.983028	+	0.183458i	$0.0587292\pi$
$984$		0			0
$985$	−1297.90	+	2248.02i	−1.31766	+	2.28226i
$986$		0			0
$987$	−134.227	−	761.620i	−0.135995	−	0.771651i
$988$		0			0
$989$		−	1559.73i		−	1.57708i
$990$		0			0
$991$	568.621			0.573785			0.286892	−	0.957963i	$-0.407378\pi$
$991$	568.621			0.573785			0.286892	+	0.957963i	$0.407378\pi$
$992$		0			0
$993$	1.14429	−	3.14308i	0.00115236	−	0.00316524i
$994$		0			0
$995$	−1556.74	−	898.786i	−1.56457	−	0.903302i
$996$		0			0
$997$	665.743	+	1153.10i	0.667746	+	1.15657i	0.978533	+	0.206091i	$0.0660742\pi$
$997$	665.743	+	1153.10i	0.667746	+	1.15657i	−0.310787	+	0.950480i	$0.600592\pi$
$998$		0			0
$999$	−17.5800	+	10.1439i	−0.0175976	+	0.0101540i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.3.q.b.257.4	yes	24
3.2	odd	2		864.3.q.a.449.1		24
4.3	odd	2	inner	288.3.q.b.257.9	yes	24
8.3	odd	2		576.3.q.l.257.4		24
8.5	even	2		576.3.q.l.257.9		24
9.2	odd	6	inner	288.3.q.b.65.4	✓	24
9.4	even	3		2592.3.e.i.161.7		24
9.5	odd	6		2592.3.e.i.161.8		24
9.7	even	3		864.3.q.a.737.1		24
12.11	even	2		864.3.q.a.449.2		24
24.5	odd	2		1728.3.q.k.449.11		24
24.11	even	2		1728.3.q.k.449.12		24
36.7	odd	6		864.3.q.a.737.2		24
36.11	even	6	inner	288.3.q.b.65.9	yes	24
36.23	even	6		2592.3.e.i.161.18		24
36.31	odd	6		2592.3.e.i.161.17		24
72.11	even	6		576.3.q.l.65.4		24
72.29	odd	6		576.3.q.l.65.9		24
72.43	odd	6		1728.3.q.k.1601.12		24
72.61	even	6		1728.3.q.k.1601.11		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.3.q.b.65.4	✓	24	9.2	odd	6	inner
288.3.q.b.65.9	yes	24	36.11	even	6	inner
288.3.q.b.257.4	yes	24	1.1	even	1	trivial
288.3.q.b.257.9	yes	24	4.3	odd	2	inner
576.3.q.l.65.4		24	72.11	even	6
576.3.q.l.65.9		24	72.29	odd	6
576.3.q.l.257.4		24	8.3	odd	2
576.3.q.l.257.9		24	8.5	even	2
864.3.q.a.449.1		24	3.2	odd	2
864.3.q.a.449.2		24	12.11	even	2
864.3.q.a.737.1		24	9.7	even	3
864.3.q.a.737.2		24	36.7	odd	6
1728.3.q.k.449.11		24	24.5	odd	2
1728.3.q.k.449.12		24	24.11	even	2
1728.3.q.k.1601.11		24	72.61	even	6
1728.3.q.k.1601.12		24	72.43	odd	6
2592.3.e.i.161.7		24	9.4	even	3
2592.3.e.i.161.8		24	9.5	odd	6
2592.3.e.i.161.17		24	36.31	odd	6
2592.3.e.i.161.18		24	36.23	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	288.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.92817 - 2.29830i) q^{3} +(7.02261 + 4.05450i) q^{5} +(1.65619 + 2.86860i) q^{7} +(-1.56434 + 8.86300i) q^{9} +O(q^{10})\)	\(q+(-1.92817 - 2.29830i) q^{3} +(7.02261 + 4.05450i) q^{5} +(1.65619 + 2.86860i) q^{7} +(-1.56434 + 8.86300i) q^{9} +(-17.0190 + 9.82591i) q^{11} +(-2.62735 + 4.55070i) q^{13} +(-4.22230 - 23.9578i) q^{15} +1.23020i q^{17} +6.71738 q^{19} +(3.39949 - 9.33754i) q^{21} +(28.4732 + 16.4390i) q^{23} +(20.3780 + 35.2957i) q^{25} +(23.3861 - 13.4940i) q^{27} +(-27.6899 + 15.9868i) q^{29} +(-15.4197 + 26.7077i) q^{31} +(55.3983 + 20.1687i) q^{33} +26.8600i q^{35} -0.751729 q^{37} +(15.5248 - 2.73608i) q^{39} +(63.5333 + 36.6810i) q^{41} +(-23.7200 - 41.0843i) q^{43} +(-46.9208 + 55.8988i) q^{45} +(67.3986 - 38.9126i) q^{47} +(19.0141 - 32.9334i) q^{49} +(2.82738 - 2.37204i) q^{51} -52.1167i q^{53} -159.357 q^{55} +(-12.9522 - 15.4385i) q^{57} +(50.8455 + 29.3557i) q^{59} +(-26.5511 - 45.9879i) q^{61} +(-28.0152 + 10.1913i) q^{63} +(-36.9017 + 21.3052i) q^{65} +(-38.9099 + 67.3939i) q^{67} +(-17.1194 - 97.1371i) q^{69} +60.3747i q^{71} -59.6798 q^{73} +(41.8279 - 114.891i) q^{75} +(-56.3732 - 32.5471i) q^{77} +(-42.2143 - 73.1172i) q^{79} +(-76.1057 - 27.7295i) q^{81} +(-1.70956 + 0.987014i) q^{83} +(-4.98787 + 8.63924i) q^{85} +(90.1332 + 32.8145i) q^{87} -83.5607i q^{89} -17.4055 q^{91} +(91.1140 - 16.0579i) q^{93} +(47.1735 + 27.2357i) q^{95} +(48.3304 + 83.7107i) q^{97} +(-60.4636 - 166.210i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{9}+O(q^{10}) \) 24 * q + 12 * q^9	\( 24 q + 12 q^{9} + 24 q^{21} + 60 q^{25} + 72 q^{29} + 108 q^{33} + 252 q^{41} + 72 q^{45} - 36 q^{49} + 12 q^{57} - 96 q^{61} - 288 q^{65} - 432 q^{69} + 24 q^{73} - 720 q^{77} - 372 q^{81} + 96 q^{85} - 132 q^{97}+O(q^{100}) \) 24 * q + 12 * q^9 + 24 * q^21 + 60 * q^25 + 72 * q^29 + 108 * q^33 + 252 * q^41 + 72 * q^45 - 36 * q^49 + 12 * q^57 - 96 * q^61 - 288 * q^65 - 432 * q^69 + 24 * q^73 - 720 * q^77 - 372 * q^81 + 96 * q^85 - 132 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more