LMFDB - Embedded newform 288.5.t.b.79.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,5,Mod(79,288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([3, 3, 4]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("288.79");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	288.t (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:	$29.7705493681$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$44$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 72)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			79.16
Character	$\chi$	$=$	288.79
Dual form			288.5.t.b.175.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.44945 + 7.82320i) q^{3} +(2.53773 - 1.46516i) q^{5} +(-39.8426 - 23.0032i) q^{7} +(-41.4048 - 69.6178i) q^{9} +O(q^{10})$	\(q+(-4.44945 + 7.82320i) q^{3} +(2.53773 - 1.46516i) q^{5} +(-39.8426 - 23.0032i) q^{7} +(-41.4048 - 69.6178i) q^{9} +(-27.1224 + 46.9774i) q^{11} +(174.611 - 100.811i) q^{13} +(0.170730 + 26.3723i) q^{15} -88.7146 q^{17} +357.083 q^{19} +(357.236 - 209.345i) q^{21} +(214.383 - 123.774i) q^{23} +(-308.207 + 533.830i) q^{25} +(728.863 - 14.1572i) q^{27} +(-18.7746 - 10.8395i) q^{29} +(349.016 - 201.504i) q^{31} +(-246.834 - 421.207i) q^{33} -134.813 q^{35} +1263.37i q^{37} +(11.7472 + 1814.57i) q^{39} +(-1106.42 - 1916.37i) q^{41} +(-678.384 + 1175.00i) q^{43} +(-207.075 - 116.007i) q^{45} +(3120.48 + 1801.61i) q^{47} +(-142.209 - 246.314i) q^{49} +(394.731 - 694.032i) q^{51} +4122.82i q^{53} +158.955i q^{55} +(-1588.82 + 2793.53i) q^{57} +(2643.76 + 4579.12i) q^{59} +(4778.25 + 2758.72i) q^{61} +(48.2476 + 3726.20i) q^{63} +(295.410 - 511.664i) q^{65} +(-3090.68 - 5353.21i) q^{67} +(14.4230 + 2227.89i) q^{69} +4832.30i q^{71} +9435.38 q^{73} +(-2804.90 - 4786.41i) q^{75} +(2161.26 - 1247.80i) q^{77} +(-1099.86 - 635.004i) q^{79} +(-3132.28 + 5765.03i) q^{81} +(-1266.75 + 2194.08i) q^{83} +(-225.134 + 129.981i) q^{85} +(168.337 - 98.6477i) q^{87} +5907.27 q^{89} -9275.93 q^{91} +(23.4806 + 3627.00i) q^{93} +(906.180 - 523.183i) q^{95} +(-928.999 + 1609.07i) q^{97} +(4393.46 - 56.8874i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 18 q^{3} + 30 q^{9}+O(q^{10}) $ 88 * q + 18 * q^3 + 30 * q^9	$ 88 q + 18 q^{3} + 30 q^{9} - 44 q^{11} - 1156 q^{17} - 860 q^{19} + 5998 q^{25} - 504 q^{27} - 3204 q^{33} + 2508 q^{35} + 2348 q^{41} - 3500 q^{43} + 16462 q^{49} + 12378 q^{51} - 6522 q^{57} + 3508 q^{59} - 2502 q^{65} - 5132 q^{67} + 19004 q^{73} + 39858 q^{75} - 11346 q^{81} - 17090 q^{83} - 8272 q^{89} + 9612 q^{91} + 9980 q^{97} + 11742 q^{99}+O(q^{100}) $ 88 * q + 18 * q^3 + 30 * q^9 - 44 * q^11 - 1156 * q^17 - 860 * q^19 + 5998 * q^25 - 504 * q^27 - 3204 * q^33 + 2508 * q^35 + 2348 * q^41 - 3500 * q^43 + 16462 * q^49 + 12378 * q^51 - 6522 * q^57 + 3508 * q^59 - 2502 * q^65 - 5132 * q^67 + 19004 * q^73 + 39858 * q^75 - 11346 * q^81 - 17090 * q^83 - 8272 * q^89 + 9612 * q^91 + 9980 * q^97 + 11742 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$37$	$65$	$127$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$-1$

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
$3$	−4.44945	+	7.82320i	−0.494383	+	0.869244i
$3$	−4.44945	+	7.82320i	−0.494383	+	0.869244i
$4$		0			0
$5$	2.53773	−	1.46516i	0.101509	−	0.0586064i	−0.448386	−	0.893840i	$-0.648001\pi$
$5$	2.53773	−	1.46516i	0.101509	−	0.0586064i	0.549895	+	0.835234i	$0.314668\pi$
$6$		0			0
$7$	−39.8426	−	23.0032i	−0.813115	−	0.469452i	0.0349214	−	0.999390i	$-0.488882\pi$
$7$	−39.8426	−	23.0032i	−0.813115	−	0.469452i	−0.848036	+	0.529938i	$0.822215\pi$
$8$		0			0
$9$	−41.4048	−	69.6178i	−0.511171	−	0.859479i
$10$		0			0
$11$	−27.1224	+	46.9774i	−0.224152	+	0.388243i	−0.956065	−	0.293156i	$-0.905295\pi$
$11$	−27.1224	+	46.9774i	−0.224152	+	0.388243i	0.731913	+	0.681398i	$0.238628\pi$
$12$		0			0
$13$	174.611	−	100.811i	1.03320	−	0.596517i	0.115299	−	0.993331i	$-0.463217\pi$
$13$	174.611	−	100.811i	1.03320	−	0.596517i	0.917899	+	0.396813i	$0.129884\pi$
$14$		0			0
$15$	0.170730	+	26.3723i	0.000758800	+	0.117210i
$16$		0			0
$17$	−88.7146			−0.306971			−0.153485	−	0.988151i	$-0.549050\pi$
$17$	−88.7146			−0.306971			−0.153485	+	0.988151i	$0.549050\pi$
$18$		0			0
$19$	357.083			0.989149			0.494575	−	0.869135i	$-0.335324\pi$
$19$	357.083			0.989149			0.494575	+	0.869135i	$0.335324\pi$
$20$		0			0
$21$	357.236	−	209.345i	0.810059	−	0.474706i
$22$		0			0
$23$	214.383	−	123.774i	0.405261	−	0.233977i	−0.283491	−	0.958975i	$-0.591492\pi$
$23$	214.383	−	123.774i	0.405261	−	0.233977i	0.688751	+	0.724998i	$0.258159\pi$
$24$		0			0
$25$	−308.207	+	533.830i	−0.493131	+	0.854127i
$26$		0			0
$27$	728.863	−	14.1572i	0.999811	−	0.0194200i
$28$		0			0
$29$	−18.7746	−	10.8395i	−0.0223242	−	0.0128889i	0.488796	−	0.872398i	$-0.337436\pi$
$29$	−18.7746	−	10.8395i	−0.0223242	−	0.0128889i	−0.511121	+	0.859509i	$0.670769\pi$
$30$		0			0
$31$	349.016	−	201.504i	0.363180	−	0.209682i	−0.307295	−	0.951614i	$-0.599424\pi$
$31$	349.016	−	201.504i	0.363180	−	0.209682i	0.670475	+	0.741932i	$0.266090\pi$
$32$		0			0
$33$	−246.834	−	421.207i	−0.226661	−	0.386784i
$34$		0			0
$35$	−134.813			−0.110052
$36$		0			0
$37$			1263.37i			0.922839i	0.887182	+	0.461419i	$0.152660\pi$
$37$			1263.37i			0.922839i	−0.887182	+	0.461419i	$0.847340\pi$
$38$		0			0
$39$	11.7472	+	1814.57i	0.00772334	+	1.19301i
$40$		0			0
$41$	−1106.42	−	1916.37i	−0.658189	−	1.14002i	−0.981084	−	0.193582i	$-0.937989\pi$
$41$	−1106.42	−	1916.37i	−0.658189	−	1.14002i	0.322895	−	0.946435i	$-0.395344\pi$
$42$		0			0
$43$	−678.384	+	1175.00i	−0.366892	+	0.635476i	−0.989078	−	0.147393i	$-0.952912\pi$
$43$	−678.384	+	1175.00i	−0.366892	+	0.635476i	0.622185	+	0.782870i	$0.286245\pi$
$44$		0			0
$45$	−207.075	−	116.007i	−0.102259	−	0.0572872i
$46$		0			0
$47$	3120.48	+	1801.61i	1.41262	+	0.815577i	0.995635	−	0.0933366i	$-0.0297533\pi$
$47$	3120.48	+	1801.61i	1.41262	+	0.815577i	0.416985	+	0.908913i	$0.363087\pi$
$48$		0			0
$49$	−142.209	−	246.314i	−0.0592292	−	0.102588i
$50$		0			0
$51$	394.731	−	694.032i	0.151761	−	0.266833i
$52$		0			0
$53$			4122.82i			1.46772i	0.679303	+	0.733858i	$0.262282\pi$
$53$			4122.82i			1.46772i	−0.679303	+	0.733858i	$0.737718\pi$
$54$		0			0
$55$			158.955i			0.0525469i
$56$		0			0
$57$	−1588.82	+	2793.53i	−0.489019	+	0.859812i
$58$		0			0
$59$	2643.76	+	4579.12i	0.759482	+	1.31546i	0.943115	+	0.332466i	$0.107881\pi$
$59$	2643.76	+	4579.12i	0.759482	+	1.31546i	−0.183634	+	0.982995i	$0.558786\pi$
$60$		0			0
$61$	4778.25	+	2758.72i	1.28413	+	0.741393i	0.977601	−	0.210468i	$-0.0674987\pi$
$61$	4778.25	+	2758.72i	1.28413	+	0.741393i	0.306530	+	0.951861i	$0.400832\pi$
$62$		0			0
$63$	48.2476	+	3726.20i	0.0121561	+	0.938826i
$64$		0			0
$65$	295.410	−	511.664i	0.0699194	−	0.121104i
$66$		0			0
$67$	−3090.68	−	5353.21i	−0.688500	−	1.19252i	−0.972323	−	0.233641i	$-0.924936\pi$
$67$	−3090.68	−	5353.21i	−0.688500	−	1.19252i	0.283822	−	0.958877i	$-0.408397\pi$
$68$		0			0
$69$	14.4230	+	2227.89i	0.00302940	+	0.467945i
$70$		0			0
$71$			4832.30i			0.958600i	0.877651	+	0.479300i	$0.159109\pi$
$71$			4832.30i			0.958600i	−0.877651	+	0.479300i	$0.840891\pi$
$72$		0			0
$73$	9435.38			1.77057			0.885286	−	0.465047i	$-0.153963\pi$
$73$	9435.38			1.77057			0.885286	+	0.465047i	$0.153963\pi$
$74$		0			0
$75$	−2804.90	−	4786.41i	−0.498650	−	0.850917i
$76$		0			0
$77$	2161.26	−	1247.80i	0.364523	−	0.210457i
$78$		0			0
$79$	−1099.86	−	635.004i	−0.176231	−	0.101747i	0.409290	−	0.912405i	$-0.365777\pi$
$79$	−1099.86	−	635.004i	−0.176231	−	0.101747i	−0.585521	+	0.810657i	$0.699110\pi$
$80$		0			0
$81$	−3132.28	+	5765.03i	−0.477409	+	0.878681i
$82$		0			0
$83$	−1266.75	+	2194.08i	−0.183881	+	0.318490i	−0.943199	−	0.332229i	$-0.892199\pi$
$83$	−1266.75	+	2194.08i	−0.183881	+	0.318490i	0.759318	+	0.650720i	$0.225533\pi$
$84$		0			0
$85$	−225.134	+	129.981i	−0.0311604	+	0.0179904i
$86$		0			0
$87$	168.337	−	98.6477i	0.0222403	−	0.0130331i
$88$		0			0
$89$	5907.27			0.745773			0.372887	−	0.927877i	$-0.378368\pi$
$89$	5907.27			0.745773			0.372887	+	0.927877i	$0.378368\pi$
$90$		0			0
$91$	−9275.93			−1.12015
$92$		0			0
$93$	23.4806	+	3627.00i	0.00271484	+	0.419355i
$94$		0			0
$95$	906.180	−	523.183i	0.100408	−	0.0579704i
$96$		0			0
$97$	−928.999	+	1609.07i	−0.0987351	+	0.171014i	−0.911161	−	0.412050i	$-0.864813\pi$
$97$	−928.999	+	1609.07i	−0.0987351	+	0.171014i	0.812426	+	0.583064i	$0.198146\pi$
$98$		0			0
$99$	4393.46	−	56.8874i	0.448267	−	0.00580425i
$100$		0			0
$101$	13841.8	+	7991.56i	1.35690	+	0.783409i	0.989205	−	0.146536i	$-0.0468123\pi$
$101$	13841.8	+	7991.56i	1.35690	+	0.783409i	0.367699	+	0.929945i	$0.380146\pi$
$102$		0			0
$103$	17094.2	−	9869.37i	1.61130	−	0.930283i	0.622227	−	0.782837i	$-0.286228\pi$
$103$	17094.2	−	9869.37i	1.61130	−	0.930283i	0.989070	−	0.147445i	$-0.0471051\pi$
$104$		0			0
$105$	599.844	−	1054.67i	0.0544076	−	0.0956617i
$106$		0			0
$107$	−8611.81			−0.752189			−0.376095	−	0.926581i	$-0.622733\pi$
$107$	−8611.81			−0.752189			−0.376095	+	0.926581i	$0.622733\pi$
$108$		0			0
$109$		−	19759.0i		−	1.66307i	−0.555470	−	0.831537i	$-0.687461\pi$
$109$		−	19759.0i		−	1.66307i	0.555470	−	0.831537i	$-0.312539\pi$
$110$		0			0
$111$	−9883.56	−	5621.28i	−0.802172	−	0.456236i
$112$		0			0
$113$	−8203.89	−	14209.6i	−0.642485	−	1.11282i	−0.984876	−	0.173259i	$-0.944570\pi$
$113$	−8203.89	−	14209.6i	−0.642485	−	1.11282i	0.342392	−	0.939557i	$-0.388763\pi$
$114$		0			0
$115$	362.697	−	628.210i	0.0274251	−	0.0475017i
$116$		0			0
$117$	−14248.0	−	7981.92i	−1.04083	−	0.583090i
$118$		0			0
$119$	3534.62	+	2040.72i	0.249603	+	0.144108i
$120$		0			0
$121$	5849.25	+	10131.2i	0.399512	+	0.691975i
$122$		0			0
$123$	19915.1	−	128.927i	1.31635	−	0.00852183i
$124$		0			0
$125$			3637.74i			0.232815i
$126$		0			0
$127$			190.402i			0.0118049i	0.999983	+	0.00590247i	$0.00187883\pi$
$127$			190.402i			0.0118049i	−0.999983	+	0.00590247i	$0.998121\pi$
$128$		0			0
$129$	−6173.79	−	10535.2i	−0.370999	−	0.633088i
$130$		0			0
$131$	5339.62	+	9248.49i	0.311148	+	0.538925i	0.978611	−	0.205718i	$-0.0659530\pi$
$131$	5339.62	+	9248.49i	0.311148	+	0.538925i	−0.667463	+	0.744643i	$0.732620\pi$
$132$		0			0
$133$	−14227.1	−	8214.03i	−0.804292	−	0.464358i
$134$		0			0
$135$	1828.91	−	1103.83i	0.100352	−	0.0605666i
$136$		0			0
$137$	−2673.96	+	4631.43i	−0.142467	+	0.246759i	−0.928425	−	0.371520i	$-0.878837\pi$
$137$	−2673.96	+	4631.43i	−0.142467	+	0.246759i	0.785958	+	0.618280i	$0.212170\pi$
$138$		0			0
$139$	4160.16	+	7205.61i	0.215318	+	0.372942i	0.953371	−	0.301801i	$-0.0975878\pi$
$139$	4160.16	+	7205.61i	0.215318	+	0.372942i	−0.738053	+	0.674743i	$0.764254\pi$
$140$		0			0
$141$	−27978.7	+	16395.9i	−1.40731	+	0.824704i
$142$		0			0
$143$			10937.0i			0.534842i
$144$		0			0
$145$	−63.5266			−0.00302148
$146$		0			0
$147$	2559.72	−	16.5712i	0.118456	−	0.000766864i
$148$		0			0
$149$	8232.13	−	4752.82i	0.370800	−	0.214082i	−0.303008	−	0.952988i	$-0.597991\pi$
$149$	8232.13	−	4752.82i	0.370800	−	0.214082i	0.673808	+	0.738907i	$0.264658\pi$
$150$		0			0
$151$	−23033.8	−	13298.5i	−1.01021	−	0.583244i	−0.0989556	−	0.995092i	$-0.531550\pi$
$151$	−23033.8	−	13298.5i	−1.01021	−	0.583244i	−0.911253	+	0.411848i	$0.864884\pi$
$152$		0			0
$153$	3673.21	+	6176.12i	0.156914	+	0.263835i
$154$		0			0
$155$	590.472	−	1022.73i	0.0245774	−	0.0425693i
$156$		0			0
$157$	14257.2	−	8231.41i	0.578410	−	0.333945i	−0.182091	−	0.983282i	$-0.558287\pi$
$157$	14257.2	−	8231.41i	0.578410	−	0.333945i	0.760501	+	0.649336i	$0.224953\pi$
$158$		0			0
$159$	−32253.6	−	18344.3i	−1.27580	−	0.725614i
$160$		0			0
$161$	−11388.8			−0.439365
$162$		0			0
$163$	6664.66			0.250843			0.125422	−	0.992104i	$-0.459972\pi$
$163$	6664.66			0.250843			0.125422	+	0.992104i	$0.459972\pi$
$164$		0			0
$165$	−1243.53	−	707.260i	−0.0456761	−	0.0259783i
$166$		0			0
$167$	−19196.1	+	11082.8i	−0.688302	+	0.397391i	−0.802976	−	0.596012i	$-0.796751\pi$
$167$	−19196.1	+	11082.8i	−0.688302	+	0.397391i	0.114674	+	0.993403i	$0.463418\pi$
$168$		0			0
$169$	6045.39	−	10470.9i	0.211666	−	0.366616i
$170$		0			0
$171$	−14785.0	−	24859.3i	−0.505624	−	0.850153i
$172$		0			0
$173$	9709.71	+	5605.90i	0.324425	+	0.187307i	0.653363	−	0.757045i	$-0.273357\pi$
$173$	9709.71	+	5605.90i	0.324425	+	0.187307i	−0.328938	+	0.944351i	$0.606691\pi$
$174$		0			0
$175$	24559.5	−	14179.5i	0.801944	−	0.463002i
$176$		0			0
$177$	−47586.6	+	308.068i	−1.51893	+	0.00983331i
$178$		0			0
$179$	16987.5			0.530179			0.265090	−	0.964224i	$-0.414598\pi$
$179$	16987.5			0.530179			0.265090	+	0.964224i	$0.414598\pi$
$180$		0			0
$181$		−	48494.7i		−	1.48026i	−0.672465	−	0.740129i	$-0.734764\pi$
$181$		−	48494.7i		−	1.48026i	0.672465	−	0.740129i	$-0.265236\pi$
$182$		0			0
$183$	−42842.6	+	25106.4i	−1.27930	+	0.749691i
$184$		0			0
$185$	1851.03	+	3206.08i	0.0540842	+	0.0936766i
$186$		0			0
$187$	2406.15	−	4167.58i	0.0688082	−	0.119179i
$188$		0			0
$189$	−29365.5	−	16202.1i	−0.822079	−	0.453573i
$190$		0			0
$191$	31625.9	+	18259.2i	0.866915	+	0.500514i	0.866322	−	0.499486i	$-0.166478\pi$
$191$	31625.9	+	18259.2i	0.866915	+	0.500514i	0.000593302		1.00000i	$0.499811\pi$
$192$		0			0
$193$	−12557.9	−	21750.9i	−0.337133	−	0.583932i	0.646759	−	0.762694i	$-0.276124\pi$
$193$	−12557.9	−	21750.9i	−0.337133	−	0.583932i	−0.983892	+	0.178762i	$0.942791\pi$
$194$		0			0
$195$	2688.44	+	4587.67i	0.0707019	+	0.120649i
$196$		0			0
$197$			28539.7i			0.735388i	0.929947	+	0.367694i	$0.119853\pi$
$197$			28539.7i			0.735388i	−0.929947	+	0.367694i	$0.880147\pi$
$198$		0			0
$199$		−	63914.2i		−	1.61395i	−0.590583	−	0.806977i	$-0.701102\pi$
$199$		−	63914.2i		−	1.61395i	0.590583	−	0.806977i	$-0.298898\pi$
$200$		0			0
$201$	55631.0	−	360.146i	1.37697	−	0.00891429i
$202$		0			0
$203$	498.687	+	863.752i	0.0121014	+	0.0209603i
$204$		0			0
$205$	−5615.57	−	3242.15i	−0.133624	−	0.0771481i
$206$		0			0
$207$	−17493.4	−	9800.03i	−0.408256	−	0.228711i
$208$		0			0
$209$	−9684.94	+	16774.8i	−0.221720	+	0.384030i
$210$		0			0
$211$	7822.71	+	13549.3i	0.175708	+	0.304336i	0.940406	−	0.340053i	$-0.110445\pi$
$211$	7822.71	+	13549.3i	0.175708	+	0.304336i	−0.764698	+	0.644389i	$0.777112\pi$
$212$		0			0
$213$	−37804.0	−	21501.1i	−0.833257	−	0.473916i
$214$		0			0
$215$			3975.76i			0.0860089i
$216$		0			0
$217$	−18541.0			−0.393743
$218$		0			0
$219$	−41982.2	+	73814.8i	−0.875341	+	1.53906i
$220$		0			0
$221$	−15490.5	+	8943.44i	−0.317162	+	0.183113i
$222$		0			0
$223$	−44835.1	−	25885.6i	−0.901589	−	0.520532i	−0.0238733	−	0.999715i	$-0.507600\pi$
$223$	−44835.1	−	25885.6i	−0.901589	−	0.520532i	−0.877715	+	0.479183i	$0.840933\pi$
$224$		0			0
$225$	49925.3	−	646.443i	0.986179	−	0.0127692i
$226$		0			0
$227$	28229.2	−	48894.4i	0.547831	−	0.948871i	−0.450592	−	0.892730i	$-0.648787\pi$
$227$	28229.2	−	48894.4i	0.547831	−	0.948871i	0.998423	−	0.0561410i	$-0.0178797\pi$
$228$		0			0
$229$	48956.6	−	28265.1i	0.933556	−	0.538989i	0.0456218	−	0.998959i	$-0.485473\pi$
$229$	48956.6	−	28265.1i	0.933556	−	0.538989i	0.887935	+	0.459970i	$0.152140\pi$
$230$		0			0
$231$	145.402	+	22460.0i	0.00272487	+	0.420906i
$232$		0			0
$233$	72322.4			1.33217			0.666087	−	0.745874i	$-0.267968\pi$
$233$	72322.4			1.33217			0.666087	+	0.745874i	$0.267968\pi$
$234$		0			0
$235$	10558.6			0.191192
$236$		0			0
$237$	9861.52	−	5778.99i	0.175569	−	0.102886i
$238$		0			0
$239$	86456.7	−	49915.8i	1.51357	−	0.873861i	0.513698	−	0.857971i	$-0.328275\pi$
$239$	86456.7	−	49915.8i	1.51357	−	0.873861i	0.999874	−	0.0158894i	$-0.00505797\pi$
$240$		0			0
$241$	−13108.7	+	22704.9i	−0.225697	+	0.390918i	−0.956528	−	0.291640i	$-0.905799\pi$
$241$	−13108.7	+	22704.9i	−0.225697	+	0.390918i	0.730832	+	0.682558i	$0.239132\pi$
$242$		0			0
$243$	−31164.0	−	50155.6i	−0.527765	−	0.849390i
$244$		0			0
$245$	−721.778	−	416.719i	−0.0120246	−	0.00694242i
$246$		0			0
$247$	62350.4	−	35998.0i	1.02199	−	0.590045i
$248$		0			0
$249$	−11528.4	−	19672.5i	−0.185939	−	0.317293i
$250$		0			0
$251$	−110168.			−1.74866			−0.874332	−	0.485328i	$-0.838700\pi$
$251$	−110168.			−1.74866			−0.874332	+	0.485328i	$0.838700\pi$
$252$		0			0
$253$			13428.2i			0.209786i
$254$		0			0
$255$	−15.1462	−	2339.61i	−0.000232929	−	0.0359801i
$256$		0			0
$257$	21395.2	+	37057.7i	0.323930	+	0.561063i	0.981295	−	0.192509i	$-0.0616625\pi$
$257$	21395.2	+	37057.7i	0.323930	+	0.561063i	−0.657365	+	0.753572i	$0.728329\pi$
$258$		0			0
$259$	29061.4	−	50335.8i	0.433229	−	0.750374i
$260$		0			0
$261$	22.7352	+	1755.86i	0.000333748	+	0.0257756i
$262$		0			0
$263$	70761.8	+	40854.3i	1.02303	+	0.590645i	0.914979	−	0.403501i	$-0.132207\pi$
$263$	70761.8	+	40854.3i	1.02303	+	0.590645i	0.108048	+	0.994146i	$0.465540\pi$
$264$		0			0
$265$	6040.58	+	10462.6i	0.0860175	+	0.148987i
$266$		0			0
$267$	−26284.1	+	46213.7i	−0.368698	+	0.648259i
$268$		0			0
$269$			71867.3i			0.993177i	0.867986	+	0.496589i	$0.165414\pi$
$269$			71867.3i			0.993177i	−0.867986	+	0.496589i	$0.834586\pi$
$270$		0			0
$271$			57719.4i			0.785929i	0.919554	+	0.392964i	$0.128550\pi$
$271$			57719.4i			0.785929i	−0.919554	+	0.392964i	$0.871450\pi$
$272$		0			0
$273$	41272.8	−	72567.4i	0.553781	−	0.973680i
$274$		0			0
$275$	−16718.6	−	28957.5i	−0.221072	−	0.382909i
$276$		0			0
$277$	17169.2	+	9912.65i	0.223764	+	0.129190i	0.607692	−	0.794173i	$-0.292095\pi$
$277$	17169.2	+	9912.65i	0.223764	+	0.129190i	−0.383928	+	0.923363i	$0.625429\pi$
$278$		0			0
$279$	−28479.2	−	15954.5i	−0.365864	−	0.204962i
$280$		0			0
$281$	−62271.1	+	107857.i	−0.788631	+	1.36595i	0.138175	+	0.990408i	$0.455876\pi$
$281$	−62271.1	+	107857.i	−0.788631	+	1.36595i	−0.926806	+	0.375541i	$0.877457\pi$
$282$		0			0
$283$	28575.7	+	49494.6i	0.356799	+	0.617995i	0.987424	−	0.158093i	$-0.0505347\pi$
$283$	28575.7	+	49494.6i	0.356799	+	0.617995i	−0.630625	+	0.776088i	$0.717201\pi$
$284$		0			0
$285$	60.9647	+	9417.10i	0.000750566	+	0.115938i
$286$		0			0
$287$			101804.i			1.23595i
$288$		0			0
$289$	−75650.7			−0.905769
$290$		0			0
$291$	−8454.56	−	14427.2i	−0.0998401	−	0.170371i
$292$		0			0
$293$	25459.0	−	14698.8i	0.296555	−	0.171216i	−0.344339	−	0.938845i	$-0.611897\pi$
$293$	25459.0	−	14698.8i	0.296555	−	0.171216i	0.640894	+	0.767629i	$0.278564\pi$
$294$		0			0
$295$	13418.3	+	7747.04i	0.154189	+	0.0890209i
$296$		0			0
$297$	−19103.4	+	34624.0i	−0.216570	+	0.392523i
$298$		0			0
$299$	24955.7	−	43224.5i	0.279143	−	0.483490i
$300$		0			0
$301$	54057.2	−	31210.0i	0.596652	−	0.344477i
$302$		0			0
$303$	−124108.	+	72729.0i	−1.35180	+	0.792177i
$304$		0			0
$305$	16167.9			0.173801
$306$		0			0
$307$	77280.8			0.819964			0.409982	−	0.912094i	$-0.365535\pi$
$307$	77280.8			0.819964			0.409982	+	0.912094i	$0.365535\pi$
$308$		0			0
$309$	1150.04	+	177645.i	0.0120447	+	1.86053i
$310$		0			0
$311$	−88843.4	+	51293.7i	−0.918553	+	0.530327i	−0.883173	−	0.469047i	$-0.844597\pi$
$311$	−88843.4	+	51293.7i	−0.918553	+	0.530327i	−0.0353799	+	0.999374i	$0.511264\pi$
$312$		0			0
$313$	20566.6	−	35622.4i	0.209930	−	0.363609i	−0.741762	−	0.670663i	$-0.766010\pi$
$313$	20566.6	−	35622.4i	0.209930	−	0.363609i	0.951692	+	0.307054i	$0.0993431\pi$
$314$		0			0
$315$	5581.91	+	9385.40i	0.0562551	+	0.0945870i
$316$		0			0
$317$	109026.	+	62945.9i	1.08495	+	0.626396i	0.932227	−	0.361873i	$-0.117863\pi$
$317$	109026.	+	62945.9i	1.08495	+	0.626396i	0.152723	+	0.988269i	$0.451196\pi$
$318$		0			0
$319$	1018.43	−	587.989i	0.0100080	−	0.00577813i
$320$		0			0
$321$	38317.8	−	67371.9i	0.371870	−	0.653836i
$322$		0			0
$323$	−31678.5			−0.303640
$324$		0			0
$325$			124283.i			1.17664i
$326$		0			0
$327$	154578.	+	87916.6i	1.44562	+	0.822196i
$328$		0			0
$329$	−82885.4	−	143562.i	−0.765748	−	1.32632i
$330$		0			0
$331$	−54232.0	+	93932.5i	−0.494993	+	0.857354i	−0.999983	−	0.00577154i	$-0.998163\pi$
$331$	−54232.0	+	93932.5i	−0.494993	+	0.857354i	0.504990	+	0.863125i	$0.331496\pi$
$332$		0			0
$333$	87952.8	−	52309.4i	0.793161	−	0.471728i
$334$		0			0
$335$	−15686.6	−	9056.67i	−0.139778	−	0.0807010i
$336$		0			0
$337$	−1823.71	−	3158.77i	−0.0160582	−	0.0278136i	0.857885	−	0.513842i	$-0.171778\pi$
$337$	−1823.71	−	3158.77i	−0.0160582	−	0.0278136i	−0.873943	+	0.486029i	$0.838445\pi$
$338$		0			0
$339$	147667.	−	955.971i	1.28494	−	0.00831850i
$340$		0			0
$341$			21861.1i			0.188003i
$342$		0			0
$343$			123546.i			1.05013i
$344$		0			0
$345$	3300.81	+	5632.64i	0.0277321	+	0.0473232i
$346$		0			0
$347$	86264.4	+	149414.i	0.716428	+	1.24089i	0.962406	+	0.271615i	$0.0875576\pi$
$347$	86264.4	+	149414.i	0.716428	+	1.24089i	−0.245978	+	0.969275i	$0.579109\pi$
$348$		0			0
$349$	−138147.	−	79759.0i	−1.13420	−	0.654831i	−0.189212	−	0.981936i	$-0.560593\pi$
$349$	−138147.	−	79759.0i	−1.13420	−	0.654831i	−0.944988	+	0.327106i	$0.893927\pi$
$350$		0			0
$351$	125840.	−	75949.7i	1.02142	−	0.616470i
$352$		0			0
$353$	−20555.4	+	35603.0i	−0.164959	+	0.285718i	−0.936641	−	0.350291i	$-0.886083\pi$
$353$	−20555.4	+	35603.0i	−0.164959	+	0.285718i	0.771681	+	0.636009i	$0.219416\pi$
$354$		0			0
$355$	7080.09	+	12263.1i	0.0561800	+	0.0973067i
$356$		0			0
$357$	−31692.0	+	18572.0i	−0.248664	+	0.145721i
$358$		0			0
$359$		−	76360.8i		−	0.592491i	−0.955112	−	0.296245i	$-0.904265\pi$
$359$		−	76360.8i		−	0.592491i	0.955112	−	0.296245i	$-0.0957346\pi$
$360$		0			0
$361$	−2812.82			−0.0215838
$362$		0			0
$363$	−105284.	+	681.593i	−0.799007	+	0.00517263i
$364$		0			0
$365$	23944.4	−	13824.3i	0.179729	−	0.103767i
$366$		0			0
$367$	102925.	+	59423.6i	0.764165	+	0.441191i	0.830789	−	0.556587i	$-0.187889\pi$
$367$	102925.	+	59423.6i	0.764165	+	0.441191i	−0.0666239	+	0.997778i	$0.521223\pi$
$368$		0			0
$369$	−87602.4	+	156373.i	−0.643374	+	1.14844i
$370$		0			0
$371$	94837.8	−	164264.i	0.689023	−	1.19342i
$372$		0			0
$373$	115434.	−	66645.9i	0.829691	−	0.479023i	−0.0240556	−	0.999711i	$-0.507658\pi$
$373$	115434.	−	66645.9i	0.829691	−	0.479023i	0.853747	+	0.520688i	$0.174325\pi$
$374$		0			0
$375$	−28458.7	−	16185.9i	−0.202373	−	0.115100i
$376$		0			0
$377$	−4371.00			−0.0307537
$378$		0			0
$379$	−141694.			−0.986447			−0.493224	−	0.869902i	$-0.664182\pi$
$379$	−141694.			−0.986447			−0.493224	+	0.869902i	$0.664182\pi$
$380$		0			0
$381$	−1489.55	−	847.183i	−0.0102614	−	0.00583616i
$382$		0			0
$383$	−43983.8	+	25394.1i	−0.299844	+	0.173115i	−0.642373	−	0.766392i	$-0.722050\pi$
$383$	−43983.8	+	25394.1i	−0.299844	+	0.173115i	0.342529	+	0.939507i	$0.388717\pi$
$384$		0			0
$385$	3656.46	−	6333.17i	0.0246683	−	0.0427267i
$386$		0			0
$387$	109889.	−	1422.87i	0.733723	−	0.00950040i
$388$		0			0
$389$	−103180.	−	59570.8i	−0.681860	−	0.393672i	0.118696	−	0.992931i	$-0.462129\pi$
$389$	−103180.	−	59570.8i	−0.681860	−	0.393672i	−0.800555	+	0.599259i	$0.795462\pi$
$390$		0			0
$391$	−19018.9	+	10980.6i	−0.124403	+	0.0718242i
$392$		0			0
$393$	−96111.1	+	622.207i	−0.622284	+	0.00402856i
$394$		0			0
$395$	−3721.53			−0.0238521
$396$		0			0
$397$			200049.i			1.26927i	0.772812	+	0.634635i	$0.218850\pi$
$397$			200049.i			1.26927i	−0.772812	+	0.634635i	$0.781150\pi$
$398$		0			0
$399$	127563.	−	74753.7i	0.801269	−	0.469555i
$400$		0			0
$401$	−13977.6	−	24209.9i	−0.0869248	−	0.150558i	0.819285	−	0.573387i	$-0.194371\pi$
$401$	−13977.6	−	24209.9i	−0.0869248	−	0.150558i	−0.906210	+	0.422828i	$0.861037\pi$
$402$		0			0
$403$	40627.9	−	70369.6i	0.250158	−	0.433286i
$404$		0			0
$405$	497.796	+	19219.4i	0.00303488	+	0.117173i
$406$		0			0
$407$	−59349.6	−	34265.5i	−0.358285	−	0.206856i
$408$		0			0
$409$	−27650.2	−	47891.6i	−0.165292	−	0.286294i	0.771467	−	0.636270i	$-0.219523\pi$
$409$	−27650.2	−	47891.6i	−0.165292	−	0.286294i	−0.936759	+	0.349975i	$0.886190\pi$
$410$		0			0
$411$	−24334.9	−	41526.2i	−0.144061	−	0.245832i
$412$		0			0
$413$		−	243259.i		−	1.42616i
$414$		0			0
$415$			7423.98i			0.0431063i
$416$		0			0
$417$	−74881.3	+	484.769i	−0.430627	+	0.00278781i
$418$		0			0
$419$	76753.4	+	132941.i	0.437189	+	0.757234i	0.997472	−	0.0710675i	$-0.0226406\pi$
$419$	76753.4	+	132941.i	0.437189	+	0.757234i	−0.560282	+	0.828302i	$0.689307\pi$
$420$		0			0
$421$	−230275.	−	132949.i	−1.29922	−	0.750105i	−0.318950	−	0.947771i	$-0.603330\pi$
$421$	−230275.	−	132949.i	−1.29922	−	0.750105i	−0.980269	+	0.197667i	$0.936664\pi$
$422$		0			0
$423$	−3778.75	−	291836.i	−0.0211187	−	1.63102i
$424$		0			0
$425$	27342.4	−	47358.5i	0.151377	−	0.262192i
$426$		0			0
$427$	−126919.	−	219830.i	−0.696097	−	1.20568i
$428$		0			0
$429$	−85562.2	−	48663.6i	−0.464909	−	0.264417i
$430$		0			0
$431$		−	187074.i		−	1.00707i	−0.863976	−	0.503533i	$-0.832033\pi$
$431$		−	187074.i		−	1.00707i	0.863976	−	0.503533i	$-0.167967\pi$
$432$		0			0
$433$	252526.			1.34688			0.673441	−	0.739241i	$-0.264815\pi$
$433$	252526.			1.34688			0.673441	+	0.739241i	$0.264815\pi$
$434$		0			0
$435$	282.658	−	496.981i	0.00149377	−	0.00262640i
$436$		0			0
$437$	76552.5	−	44197.6i	0.400863	−	0.231439i
$438$		0			0
$439$	−138415.	−	79914.0i	−0.718215	−	0.414662i	0.0958801	−	0.995393i	$-0.469433\pi$
$439$	−138415.	−	79914.0i	−0.718215	−	0.414662i	−0.814095	+	0.580731i	$0.802767\pi$
$440$		0			0
$441$	−11259.7	+	20098.9i	−0.0578960	+	0.103346i
$442$		0			0
$443$	−152813.	+	264680.i	−0.778670	+	1.34870i	0.154038	+	0.988065i	$0.450772\pi$
$443$	−152813.	+	264680.i	−0.778670	+	1.34870i	−0.932708	+	0.360632i	$0.882561\pi$
$444$		0			0
$445$	14991.1	−	8655.09i	0.0757028	−	0.0437070i
$446$		0			0
$447$	553.830	+	85549.0i	0.00277180	+	0.428154i
$448$		0			0
$449$	338152.			1.67733			0.838667	−	0.544645i	$-0.183336\pi$
$449$	338152.			1.67733			0.838667	+	0.544645i	$0.183336\pi$
$450$		0			0
$451$	120035.			0.590138
$452$		0			0
$453$	206525.	−	121026.i	1.00641	−	0.589772i
$454$		0			0
$455$	−23539.8	+	13590.7i	−0.113705	+	0.0656477i
$456$		0			0
$457$	−1641.07	+	2842.42i	−0.00785770	+	0.0136099i	−0.869928	−	0.493180i	$-0.835835\pi$
$457$	−1641.07	+	2842.42i	−0.00785770	+	0.0136099i	0.862070	+	0.506790i	$0.169168\pi$
$458$		0			0
$459$	−64660.7	+	1255.95i	−0.306913	+	0.00596137i
$460$		0			0
$461$	−215070.	−	124171.i	−1.01199	−	0.584275i	−0.100220	−	0.994965i	$-0.531955\pi$
$461$	−215070.	−	124171.i	−1.01199	−	0.584275i	−0.911775	+	0.410690i	$0.865288\pi$
$462$		0			0
$463$	−42958.9	+	24802.3i	−0.200397	+	0.115699i	−0.596841	−	0.802360i	$-0.703578\pi$
$463$	−42958.9	+	24802.3i	−0.200397	+	0.115699i	0.396444	+	0.918059i	$0.370244\pi$
$464$		0			0
$465$	5373.72	+	9169.95i	0.0248525	+	0.0424093i
$466$		0			0
$467$	−18727.6			−0.0858712			−0.0429356	−	0.999078i	$-0.513671\pi$
$467$	−18727.6			−0.0858712			−0.0429356	+	0.999078i	$0.513671\pi$
$468$		0			0
$469$			284381.i			1.29287i
$470$		0			0
$471$	959.178	+	148162.i	0.00432372	+	0.667876i
$472$		0			0
$473$	−36798.8	−	63737.4i	−0.164479	−	0.284887i
$474$		0			0
$475$	−110055.	+	190621.i	−0.487780	+	0.844859i
$476$		0			0
$477$	287021.	−	170704.i	1.26147	−	0.750254i
$478$		0			0
$479$	−343234.	−	198166.i	−1.49596	−	0.863691i	−0.495967	−	0.868341i	$-0.665186\pi$
$479$	−343234.	−	198166.i	−1.49596	−	0.863691i	−0.999989	+	0.00465021i	$0.998520\pi$
$480$		0			0
$481$	127362.	+	220597.i	0.550489	+	0.953475i
$482$		0			0
$483$	50673.8	−	89096.6i	0.217215	−	0.381915i
$484$		0			0
$485$			5444.52i			0.0231460i
$486$		0			0
$487$			240262.i			1.01304i	0.862228	+	0.506520i	$0.169068\pi$
$487$			240262.i			1.01304i	−0.862228	+	0.506520i	$0.830932\pi$
$488$		0			0
$489$	−29654.0	+	52138.9i	−0.124013	+	0.218044i
$490$		0			0
$491$	−98040.3	−	169811.i	−0.406670	−	0.704372i	0.587845	−	0.808974i	$-0.299977\pi$
$491$	−98040.3	−	169811.i	−0.406670	−	0.704372i	−0.994514	+	0.104601i	$0.966643\pi$
$492$		0			0
$493$	1665.58	+	961.625i	0.00685287	+	0.00395651i
$494$		0			0
$495$	11066.1	−	6581.48i	0.0451630	−	0.0268605i
$496$		0			0
$497$	111158.	−	192532.i	0.450017	−	0.779452i
$498$		0			0
$499$	−130948.	−	226808.i	−0.525892	−	0.910871i	−0.999545	−	0.0301596i	$-0.990398\pi$
$499$	−130948.	−	226808.i	−0.525892	−	0.910871i	0.473654	−	0.880711i	$-0.342935\pi$
$500$		0			0
$501$	−1291.45	−	199487.i	−0.00514518	−	0.794766i
$502$		0			0
$503$		−	311251.i		−	1.23020i	−0.788450	−	0.615099i	$-0.789116\pi$
$503$		−	311251.i		−	1.23020i	0.788450	−	0.615099i	$-0.210884\pi$
$504$		0			0
$505$	46835.6			0.183651
$506$		0			0
$507$	55017.4	+	93884.1i	0.214035	+	0.365238i
$508$		0			0
$509$	−317446.	+	183278.i	−1.22528	+	0.707415i	−0.966039	−	0.258398i	$-0.916805\pi$
$509$	−317446.	+	183278.i	−1.22528	+	0.707415i	−0.259240	+	0.965813i	$0.583472\pi$
$510$		0			0
$511$	−375930.	−	217043.i	−1.43968	−	0.831199i
$512$		0			0
$513$	260264.	−	5055.29i	0.988963	−	0.0192093i
$514$		0			0
$515$	28920.4	−	50091.6i	0.109041	−	0.188864i
$516$		0			0
$517$	−169270.	+	97727.9i	−0.633283	+	0.365626i
$518$		0			0
$519$	−87058.9	+	51017.8i	−0.323205	+	0.189403i
$520$		0			0
$521$	−526988.			−1.94145			−0.970723	−	0.240203i	$-0.922786\pi$
$521$	−526988.			−1.94145			−0.970723	+	0.240203i	$0.922786\pi$
$522$		0			0
$523$	−311012.			−1.13703			−0.568517	−	0.822671i	$-0.692483\pi$
$523$	−311012.			−1.13703			−0.568517	+	0.822671i	$0.692483\pi$
$524$		0			0
$525$	1652.28	+	255225.i	0.00599467	+	0.925986i
$526$		0			0
$527$	−30962.8	+	17876.4i	−0.111486	+	0.0643663i
$528$		0			0
$529$	−109280.	+	189279.i	−0.390509	+	0.676382i
$530$		0			0
$531$	209324.	−	373650.i	0.742386	−	1.32518i
$532$		0			0
$533$	−386384.	−	223079.i	−1.36008	−	0.785242i
$534$		0			0
$535$	−21854.5	+	12617.7i	−0.0763541	+	0.0440831i
$536$		0			0
$537$	−75584.9	+	132896.i	−0.262112	+	0.460855i
$538$		0			0
$539$	15428.2			0.0531054
$540$		0			0
$541$			377631.i			1.29025i	0.764078	+	0.645124i	$0.223194\pi$
$541$			377631.i			1.29025i	−0.764078	+	0.645124i	$0.776806\pi$
$542$		0			0
$543$	379384.	+	215775.i	1.28671	+	0.731815i
$544$		0			0
$545$	−28950.0	−	50143.0i	−0.0974667	−	0.168817i
$546$		0			0
$547$	51766.7	−	89662.5i	0.173012	−	0.299665i	−0.766460	−	0.642292i	$-0.777983\pi$
$547$	51766.7	−	89662.5i	0.173012	−	0.299665i	0.939471	+	0.342627i	$0.111317\pi$
$548$		0			0
$549$	−5786.24	−	446876.i	−0.0191978	−	1.48266i
$550$		0			0
$551$	−6704.10	−	3870.61i	−0.0220819	−	0.0127490i
$552$		0			0
$553$	29214.2	+	50600.4i	0.0955308	+	0.165464i
$554$		0			0
$555$	−33317.9	+	215.694i	−0.108166	+	0.000700249i
$556$		0			0
$557$		−	321643.i		−	1.03673i	−0.855161	−	0.518363i	$-0.826542\pi$
$557$		−	321643.i		−	1.03673i	0.855161	−	0.518363i	$-0.173458\pi$
$558$		0			0
$559$			273556.i			0.875431i
$560$		0			0
$561$	21897.7	+	37367.2i	0.0695782	+	0.118731i
$562$		0			0
$563$	15717.8	+	27224.0i	0.0495878	+	0.0858885i	0.889754	−	0.456441i	$-0.150876\pi$
$563$	15717.8	+	27224.0i	0.0495878	+	0.0858885i	−0.840166	+	0.542329i	$0.817543\pi$
$564$		0			0
$565$	−41638.5	−	24040.0i	−0.130436	−	0.0753074i
$566$		0			0
$567$	257412.	−	157642.i	0.800687	−	0.490348i
$568$		0			0
$569$	118855.	−	205862.i	0.367106	−	0.635846i	−0.622006	−	0.783013i	$-0.713682\pi$
$569$	118855.	−	205862.i	0.367106	−	0.635846i	0.989112	+	0.147166i	$0.0470153\pi$
$570$		0			0
$571$	259870.	+	450108.i	0.797047	+	1.38053i	0.921531	+	0.388304i	$0.126939\pi$
$571$	259870.	+	450108.i	0.797047	+	1.38053i	−0.124484	+	0.992222i	$0.539728\pi$
$572$		0			0
$573$	−283564.	+	166172.i	−0.863657	+	0.506115i
$574$		0			0
$575$			152592.i			0.461526i
$576$		0			0
$577$	−150655.			−0.452513			−0.226257	−	0.974068i	$-0.572649\pi$
$577$	−150655.			−0.452513			−0.226257	+	0.974068i	$0.572649\pi$
$578$		0			0
$579$	226037.	−	1463.33i	0.674252	−	0.00436500i
$580$		0			0
$581$	100942.	−	58278.7i	0.299032	−	0.172646i
$582$		0			0
$583$	−193679.	−	111821.i	−0.569830	−	0.328992i
$584$		0			0
$585$	−47852.3	+	619.602i	−0.139827	+	0.00181051i
$586$		0			0
$587$	−222883.	+	386045.i	−0.646846	+	1.12037i	0.337025	+	0.941496i	$0.390579\pi$
$587$	−222883.	+	386045.i	−0.646846	+	1.12037i	−0.983872	+	0.178875i	$0.942754\pi$
$588$		0			0
$589$	124628.	−	71953.8i	0.359239	−	0.207407i
$590$		0			0
$591$	−223272.	−	126986.i	−0.639232	−	0.363563i
$592$		0			0
$593$	−59064.6			−0.167965			−0.0839823	−	0.996467i	$-0.526764\pi$
$593$	−59064.6			−0.167965			−0.0839823	+	0.996467i	$0.526764\pi$
$594$		0			0
$595$	11959.9			0.0337826
$596$		0			0
$597$	500013.	+	284383.i	1.40292	+	0.797911i
$598$		0			0
$599$	354748.	−	204814.i	0.988703	−	0.570828i	0.0838164	−	0.996481i	$-0.473289\pi$
$599$	354748.	−	204814.i	0.988703	−	0.570828i	0.904886	+	0.425653i	$0.139956\pi$
$600$		0			0
$601$	268772.	−	465527.i	0.744107	−	1.28883i	−0.206505	−	0.978446i	$-0.566209\pi$
$601$	268772.	−	465527.i	0.744107	−	1.28883i	0.950611	−	0.310385i	$-0.100458\pi$
$602$		0			0
$603$	−244710.	+	436815.i	−0.673003	+	1.20133i
$604$		0			0
$605$	29687.6	+	17140.2i	0.0811082	+	0.0468279i
$606$		0			0
$607$	377551.	−	217979.i	1.02470	−	0.591614i	0.109242	−	0.994015i	$-0.465158\pi$
$607$	377551.	−	217979.i	1.02470	−	0.591614i	0.915463	+	0.402402i	$0.131824\pi$
$608$		0			0
$609$	−8976.18	+	58.1103i	−0.0242023	+	0.000156682i
$610$		0			0
$611$	726491.			1.94602
$612$		0			0
$613$			184751.i			0.491662i	0.969313	+	0.245831i	$0.0790608\pi$
$613$			184751.i			0.491662i	−0.969313	+	0.245831i	$0.920939\pi$
$614$		0			0
$615$	50350.2	−	29505.9i	0.133122	−	0.0780116i
$616$		0			0
$617$	70628.6	+	122332.i	0.185528	+	0.321344i	0.943754	−	0.330647i	$-0.107267\pi$
$617$	70628.6	+	122332.i	0.185528	+	0.321344i	−0.758226	+	0.651992i	$0.773934\pi$
$618$		0			0
$619$	132429.	−	229374.i	0.345623	−	0.598637i	−0.639844	−	0.768505i	$-0.721001\pi$
$619$	132429.	−	229374.i	0.345623	−	0.598637i	0.985467	+	0.169868i	$0.0543342\pi$
$620$		0			0
$621$	154503.	−	93249.3i	0.400640	−	0.241803i
$622$		0			0
$623$	−235361.	−	135886.i	−0.606399	−	0.350105i
$624$		0			0
$625$	−187299.	−	324412.i	−0.479486	−	0.830494i
$626$		0			0
$627$	−88140.0	−	150406.i	−0.224201	−	0.382587i
$628$		0			0
$629$		−	112079.i		−	0.283285i
$630$		0			0
$631$			699879.i			1.75778i	0.477026	+	0.878889i	$0.341715\pi$
$631$			699879.i			1.75778i	−0.477026	+	0.878889i	$0.658285\pi$
$632$		0			0
$633$	−140806.	+	911.553i	−0.351409	+	0.00227496i
$634$		0			0
$635$	278.969	+	483.188i	0.000691844	+	0.00119831i
$636$		0			0
$637$	−49662.5	−	28672.7i	−0.122391	−	0.0706625i
$638$		0			0
$639$	336414.	−	200081.i	0.823897	−	0.490008i
$640$		0			0
$641$	−159686.	+	276584.i	−0.388643	+	0.673149i	−0.992267	−	0.124120i	$-0.960389\pi$
$641$	−159686.	+	276584.i	−0.388643	+	0.673149i	0.603625	+	0.797269i	$0.293723\pi$
$642$		0			0
$643$	120033.	+	207903.i	0.290321	+	0.502850i	0.973886	−	0.227040i	$-0.0729047\pi$
$643$	120033.	+	207903.i	0.290321	+	0.502850i	−0.683565	+	0.729890i	$0.739571\pi$
$644$		0			0
$645$	−31103.2	−	17689.9i	−0.0747627	−	0.0425214i
$646$		0			0
$647$			160526.i			0.383475i	0.981446	+	0.191737i	$0.0614122\pi$
$647$			160526.i			0.383475i	−0.981446	+	0.191737i	$0.938588\pi$
$648$		0			0
$649$	−286820.			−0.680957
$650$		0			0
$651$	82497.0	−	145050.i	0.194660	−	0.342259i
$652$		0			0
$653$	23755.5	−	13715.3i	0.0557107	−	0.0321646i	−0.471886	−	0.881660i	$-0.656427\pi$
$653$	23755.5	−	13715.3i	0.0557107	−	0.0321646i	0.527597	+	0.849495i	$0.323093\pi$
$654$		0			0
$655$	27101.0	+	15646.8i	0.0631689	+	0.0364706i
$656$		0			0
$657$	−390670.	−	656870.i	−0.905064	−	1.52177i
$658$		0			0
$659$	215117.	−	372594.i	0.495341	−	0.857957i	−0.504644	−	0.863327i	$-0.668376\pi$
$659$	215117.	−	372594.i	0.495341	−	0.857957i	0.999986	+	0.00537093i	$0.00170963\pi$
$660$		0			0
$661$	122972.	−	70998.0i	0.281451	−	0.162496i	−0.352629	−	0.935763i	$-0.614712\pi$
$661$	122972.	−	70998.0i	0.281451	−	0.162496i	0.634080	+	0.773267i	$0.281379\pi$
$662$		0			0
$663$	−1042.15	−	160979.i	−0.00237084	−	0.366219i
$664$		0			0
$665$	−48139.5			−0.108857
$666$		0			0
$667$	−5366.61			−0.0120628
$668$		0			0
$669$	401999.	−	235577.i	0.898200	−	0.526358i
$670$		0			0
$671$	−259195.	+	149646.i	−0.575681	+	0.332370i
$672$		0			0
$673$	−78759.2	+	136415.i	−0.173889	+	0.301184i	−0.939776	−	0.341791i	$-0.888967\pi$
$673$	−78759.2	+	136415.i	−0.173889	+	0.301184i	0.765887	+	0.642975i	$0.222300\pi$
$674$		0			0
$675$	−217083.	+	393452.i	−0.476450	+	0.863543i
$676$		0			0
$677$	606737.	+	350300.i	1.32380	+	0.764298i	0.984333	−	0.176319i	$-0.0564190\pi$
$677$	606737.	+	350300.i	1.32380	+	0.764298i	0.339470	+	0.940617i	$0.389752\pi$
$678$		0			0
$679$	74027.5	−	42739.8i	0.160566	−	0.0927028i
$680$		0			0
$681$	256906.	+	438395.i	0.553962	+	0.945305i
$682$		0			0
$683$	−408773.			−0.876275			−0.438137	−	0.898908i	$-0.644362\pi$
$683$	−408773.			−0.876275			−0.438137	+	0.898908i	$0.644362\pi$
$684$		0			0
$685$			15671.1i			0.0333978i
$686$		0			0
$687$	3293.64	+	508762.i	0.00697850	+	1.07796i
$688$		0			0
$689$	415627.	+	719887.i	0.875518	+	1.51644i
$690$		0			0
$691$	309805.	−	536598.i	0.648832	−	1.12381i	−0.334570	−	0.942371i	$-0.608591\pi$
$691$	309805.	−	536598.i	0.648832	−	1.12381i	0.983402	−	0.181439i	$-0.0580756\pi$
$692$		0			0
$693$	−176356.	−	98796.9i	−0.367217	−	0.205720i
$694$		0			0
$695$	21114.7	+	12190.6i	0.0437135	+	0.0252380i
$696$		0			0
$697$	98155.2	+	170010.i	0.202045	+	0.349952i
$698$		0			0
$699$	−321795.	+	565792.i	−0.658604	+	1.15798i
$700$		0			0
$701$			98886.5i			0.201234i	0.994925	+	0.100617i	$0.0320816\pi$
$701$			98886.5i			0.201234i	−0.994925	+	0.100617i	$0.967918\pi$
$702$		0			0
$703$			451126.i			0.912825i
$704$		0			0
$705$	−46979.8	+	82601.8i	−0.0945220	+	0.166192i
$706$		0			0
$707$	−367662.	−	636809.i	−0.735546	−	1.27400i
$708$		0			0
$709$	−16701.3	−	9642.51i	−0.0332245	−	0.0191822i	0.483296	−	0.875457i	$-0.339440\pi$
$709$	−16701.3	−	9642.51i	−0.0332245	−	0.0191822i	−0.516520	+	0.856275i	$0.672773\pi$
$710$		0			0
$711$	1331.88	+	102862.i	0.00263466	+	0.203477i
$712$		0			0
$713$	49882.0	−	86398.2i	0.0981217	−	0.169952i
$714$		0			0
$715$	16024.4	+	27755.1i	0.0313452	+	0.0542914i
$716$		0			0
$717$	5816.52	+	898466.i	0.0113142	+	1.74768i
$718$		0			0
$719$		−	124940.i		−	0.241681i	−0.992672	−	0.120841i	$-0.961441\pi$
$719$		−	124940.i		−	0.241681i	0.992672	−	0.120841i	$-0.0385590\pi$
$720$		0			0
$721$	−908107.			−1.74689
$722$		0			0
$723$	−119299.	−	203576.i	−0.228223	−	0.389449i
$724$		0			0
$725$	11572.9	−	6681.64i	0.0220175	−	0.0127118i
$726$		0			0
$727$	237638.	+	137200.i	0.449621	+	0.259589i	0.707670	−	0.706543i	$-0.249746\pi$
$727$	237638.	+	137200.i	0.449621	+	0.259589i	−0.258049	+	0.966132i	$0.583080\pi$
$728$		0			0
$729$	531040.	−	20637.3i	0.999246	−	0.0388327i
$730$		0			0
$731$	60182.6	−	104239.i	0.112625	−	0.195073i
$732$		0			0
$733$	196395.	−	113389.i	0.365530	−	0.211039i	−0.305974	−	0.952040i	$-0.598982\pi$
$733$	196395.	−	113389.i	0.365530	−	0.211039i	0.671504	+	0.741001i	$0.265649\pi$
$734$		0			0
$735$	6471.59	−	3792.44i	0.0119794	−	0.00702012i
$736$		0			0
$737$	335306.			0.617315
$738$		0			0
$739$	173966.			0.318549			0.159274	−	0.987234i	$-0.449085\pi$
$739$	173966.			0.318549			0.159274	+	0.987234i	$0.449085\pi$
$740$		0			0
$741$	4194.73	+	647951.i	0.00763954	+	1.18006i
$742$		0			0
$743$	−223552.	+	129068.i	−0.404949	+	0.233797i	−0.688617	−	0.725125i	$-0.741782\pi$
$743$	−223552.	+	129068.i	−0.404949	+	0.233797i	0.283668	+	0.958923i	$0.408449\pi$
$744$		0			0
$745$	13927.3	−	24122.8i	0.0250931	−	0.0434625i
$746$		0			0
$747$	205197.	−	2656.93i	0.367730	−	0.00476145i
$748$		0			0
$749$	343117.	+	198099.i	0.611616	+	0.353117i
$750$		0			0
$751$	439854.	−	253950.i	0.779881	−	0.450264i	−0.0565073	−	0.998402i	$-0.517996\pi$
$751$	439854.	−	253950.i	0.779881	−	0.450264i	0.836388	+	0.548138i	$0.184663\pi$
$752$		0			0
$753$	490185.	−	861863.i	0.864510	−	1.52002i
$754$		0			0
$755$	−77937.9			−0.136727
$756$		0			0
$757$		−	146756.i		−	0.256097i	−0.991768	−	0.128048i	$-0.959129\pi$
$757$		−	146756.i		−	0.256097i	0.991768	−	0.128048i	$-0.0408713\pi$
$758$		0			0
$759$	−105051.	−	59748.1i	−0.182355	−	0.103715i
$760$		0			0
$761$	106335.	+	184178.i	0.183615	+	0.318030i	0.943109	−	0.332484i	$-0.107887\pi$
$761$	106335.	+	184178.i	0.183615	+	0.318030i	−0.759494	+	0.650514i	$0.774553\pi$
$762$		0			0
$763$	−454519.	+	787250.i	−0.780734	+	1.35227i
$764$		0			0
$765$	18370.6	+	10291.5i	0.0313907	+	0.0175855i
$766$		0			0
$767$	923255.	+	533042.i	1.56939	+	0.906088i
$768$		0			0
$769$	44021.9	+	76248.2i	0.0744417	+	0.128937i	0.900843	−	0.434144i	$-0.142949\pi$
$769$	44021.9	+	76248.2i	0.0744417	+	0.128937i	−0.826402	+	0.563081i	$0.809616\pi$
$770$		0			0
$771$	−385106.	+	2493.11i	−0.647846	+	0.00419405i
$772$		0			0
$773$			956337.i			1.60049i	0.599675	+	0.800243i	$0.295296\pi$
$773$			956337.i			1.60049i	−0.599675	+	0.800243i	$0.704704\pi$
$774$		0			0
$775$			248420.i			0.413602i
$776$		0			0
$777$	264480.	+	451320.i	0.438077	+	0.747554i
$778$		0			0
$779$	−395082.	−	684302.i	−0.651047	−	1.12765i
$780$		0			0
$781$	−227009.	−	131064.i	−0.372169	−	0.214872i
$782$		0			0
$783$	−13837.6	−	7634.74i	−0.0225703	−	0.0124529i
$784$		0			0
$785$	24120.7	−	41778.2i	0.0391426	−	0.0677970i
$786$		0			0
$787$	150134.	+	260040.i	0.242398	+	0.419846i	0.961397	−	0.275165i	$-0.0887326\pi$
$787$	150134.	+	260040.i	0.242398	+	0.419846i	−0.718999	+	0.695012i	$0.755399\pi$
$788$		0			0
$789$	−634462.	+	371804.i	−1.01918	+	0.597255i
$790$		0			0
$791$			754861.i			1.20646i
$792$		0			0
$793$	1.11244e6			1.76902
$794$		0			0
$795$	−108728.	+	703.888i	−0.172031	+	0.00111370i
$796$		0			0
$797$	189436.	−	109371.i	0.298226	−	0.172181i	−0.343420	−	0.939182i	$-0.611585\pi$
$797$	189436.	−	109371.i	0.298226	−	0.172181i	0.641646	+	0.767001i	$0.278252\pi$
$798$		0			0
$799$	−276832.	−	159829.i	−0.433633	−	0.250358i
$800$		0			0
$801$	−244589.	−	411251.i	−0.381217	−	0.640977i
$802$		0			0
$803$	−255910.	+	443249.i	−0.396877	+	0.687412i
$804$		0			0
$805$	−28901.6	+	16686.4i	−0.0445996	+	0.0257496i
$806$		0			0
$807$	−562232.	−	319770.i	−0.863313	−	0.491010i
$808$		0			0
$809$	−373854.			−0.571223			−0.285611	−	0.958346i	$-0.592197\pi$
$809$	−373854.			−0.571223			−0.285611	+	0.958346i	$0.592197\pi$
$810$		0			0
$811$	389516.			0.592220			0.296110	−	0.955154i	$-0.404310\pi$
$811$	389516.			0.592220			0.296110	+	0.955154i	$0.404310\pi$
$812$		0			0
$813$	−451550.	−	256819.i	−0.683164	−	0.388550i
$814$		0			0
$815$	16913.1	−	9764.78i	0.0254629	−	0.0147010i
$816$		0			0
$817$	−242239.	+	419571.i	−0.362911	+	0.628581i
$818$		0			0
$819$	384068.	+	645770.i	0.572586	+	0.962742i
$820$		0			0
$821$	−766580.	−	442585.i	−1.13729	−	0.656614i	−0.191531	−	0.981486i	$-0.561345\pi$
$821$	−766580.	−	442585.i	−1.13729	−	0.656614i	−0.945758	+	0.324872i	$0.894679\pi$
$822$		0			0
$823$	556310.	−	321186.i	0.821329	−	0.474195i	−0.0295455	−	0.999563i	$-0.509406\pi$
$823$	556310.	−	321186.i	0.821329	−	0.474195i	0.850875	+	0.525369i	$0.176073\pi$
$824$		0			0
$825$	300929.	−	1948.16i	0.442136	−	0.00286231i
$826$		0			0
$827$	144563.			0.211372			0.105686	−	0.994400i	$-0.466296\pi$
$827$	144563.			0.211372			0.105686	+	0.994400i	$0.466296\pi$
$828$		0			0
$829$		−	390583.i		−	0.568335i	−0.958775	−	0.284167i	$-0.908283\pi$
$829$		−	390583.i		−	0.568335i	0.958775	−	0.284167i	$-0.0917171\pi$
$830$		0			0
$831$	−153942.	+	90212.3i	−0.222923	+	0.130636i
$832$		0			0
$833$	12616.0	+	21851.6i	0.0181816	+	0.0314915i
$834$		0			0
$835$	−32476.3	+	56250.6i	−0.0465793	+	0.0806778i
$836$		0			0
$837$	251532.	−	151810.i	0.359039	−	0.216695i
$838$		0			0
$839$	−21529.2	−	12429.9i	−0.0305846	−	0.0176580i	0.484630	−	0.874719i	$-0.338954\pi$
$839$	−21529.2	−	12429.9i	−0.0305846	−	0.0176580i	−0.515214	+	0.857061i	$0.672288\pi$
$840$		0			0
$841$	−353406.	−	612116.i	−0.499668	−	0.865450i
$842$		0			0
$843$	−566712.	−	967062.i	−0.797457	−	1.36081i
$844$		0			0
$845$		−	35429.8i		−	0.0496199i
$846$		0			0
$847$		−	538205.i		−	0.750207i
$848$		0			0
$849$	−514352.	+	3329.83i	−0.713584	+	0.00461962i
$850$		0			0
$851$	156372.	+	270844.i	0.215923	+	0.373990i
$852$		0			0
$853$	264635.	+	152787.i	0.363705	+	0.209985i	0.670705	−	0.741724i	$-0.265992\pi$
$853$	264635.	+	152787.i	0.363705	+	0.209985i	−0.307000	+	0.951710i	$0.599325\pi$
$854$		0			0
$855$	−73943.1	−	41424.0i	−0.101150	−	0.0566656i
$856$		0			0
$857$	−221670.	+	383944.i	−0.301818	+	0.522764i	−0.976548	−	0.215301i	$-0.930927\pi$
$857$	−221670.	+	383944.i	−0.301818	+	0.522764i	0.674730	+	0.738065i	$0.264260\pi$
$858$		0			0
$859$	−228055.	−	395003.i	−0.309067	−	0.535320i	0.669091	−	0.743180i	$-0.266683\pi$
$859$	−228055.	−	395003.i	−0.309067	−	0.535320i	−0.978159	+	0.207860i	$0.933350\pi$
$860$		0			0
$861$	−796435.	−	452973.i	−1.07435	−	0.611034i
$862$		0			0
$863$		−	432830.i		−	0.581160i	−0.956851	−	0.290580i	$-0.906152\pi$
$863$		−	432830.i		−	0.581160i	0.956851	−	0.290580i	$-0.0938483\pi$
$864$		0			0
$865$	32854.2			0.0439095
$866$		0			0
$867$	336604.	−	591831.i	0.447797	−	0.787334i
$868$		0			0
$869$	59661.6	−	34445.6i	0.0790052	−	0.0456136i
$870$		0			0
$871$	−1.07933e6	−	623151.i	−1.42272	−	0.821405i
$872$		0			0
$873$	150485.	−	1948.51i	0.197454	−	0.00255667i
$874$		0			0
$875$	83679.4	−	144937.i	0.109296	−	0.189305i
$876$		0			0
$877$	439842.	−	253943.i	0.571870	−	0.330169i	−0.186026	−	0.982545i	$-0.559561\pi$
$877$	439842.	−	253943.i	0.571870	−	0.330169i	0.757896	+	0.652376i	$0.226227\pi$
$878$		0			0
$879$	1712.79	+	264572.i	0.00221681	+	0.342426i
$880$		0			0
$881$	−630033.			−0.811730			−0.405865	−	0.913933i	$-0.633030\pi$
$881$	−630033.			−0.811730			−0.405865	+	0.913933i	$0.633030\pi$
$882$		0			0
$883$	111488.			0.142990			0.0714950	−	0.997441i	$-0.477223\pi$
$883$	111488.			0.142990			0.0714950	+	0.997441i	$0.477223\pi$
$884$		0			0
$885$	−120311.	+	70503.7i	−0.153609	+	0.0900172i
$886$		0			0
$887$	642963.	−	371215.i	0.817220	−	0.471822i	−0.0322369	−	0.999480i	$-0.510263\pi$
$887$	642963.	−	371215.i	0.817220	−	0.471822i	0.849457	+	0.527658i	$0.176930\pi$
$888$		0			0
$889$	4379.84	−	7586.11i	0.00554185	−	0.00959877i
$890$		0			0
$891$	−185871.	−	303508.i	−0.234129	−	0.382309i
$892$		0			0
$893$	1.11427e6	+	643324.i	1.39729	+	0.806727i
$894$		0			0
$895$	43109.6	−	24889.4i	0.0538181	−	0.0310719i
$896$		0			0
$897$	227115.	+	387558.i	0.282267	+	0.481673i
$898$		0			0
$899$	−8736.86			−0.0108103
$900$		0			0
$901$		−	365754.i		−	0.450546i
$902$		0			0
$903$	3636.79	+	561767.i	0.00446008	+	0.688939i
$904$		0			0
$905$	−71052.5	−	123067.i	−0.0867525	−	0.150260i
$906$		0			0
$907$	120922.	−	209443.i	0.146991	−	0.254596i	−0.783123	−	0.621867i	$-0.786374\pi$
$907$	120922.	−	209443.i	0.146991	−	0.254596i	0.930114	+	0.367271i	$0.119708\pi$
$908$		0			0
$909$	−16761.8	−	1.29452e6i	−0.0202858	−	1.56669i
$910$		0			0
$911$	276542.	+	159661.i	0.333214	+	0.192381i	0.657267	−	0.753658i	$-0.271712\pi$
$911$	276542.	+	159661.i	0.333214	+	0.192381i	−0.324053	+	0.946039i	$0.605046\pi$
$912$		0			0
$913$	−68714.8	−	119017.i	−0.0824344	−	0.142781i
$914$		0			0
$915$	−71938.1	+	126485.i	−0.0859245	+	0.151076i
$916$		0			0
$917$		−	491312.i		−	0.584277i
$918$		0			0
$919$		−	1.48790e6i		−	1.76175i	−0.473350	−	0.880875i	$-0.656955\pi$
$919$		−	1.48790e6i		−	1.76175i	0.473350	−	0.880875i	$-0.343045\pi$
$920$		0			0
$921$	−343857.	+	604583.i	−0.405376	+	0.712749i
$922$		0			0
$923$	487151.	+	843771.i	0.571821	+	0.990424i
$924$		0			0
$925$	−674422.	−	389378.i	−0.788222	−	0.455080i
$926$		0			0
$927$	−1.39487e6	−	781425.i	−1.62321	−	0.909343i
$928$		0			0
$929$	588618.	−	1.01952e6i	0.682028	−	1.18131i	−0.292333	−	0.956317i	$-0.594431\pi$
$929$	588618.	−	1.01952e6i	0.682028	−	1.18131i	0.974361	−	0.224991i	$-0.0722352\pi$
$930$		0			0
$931$	−50780.5	−	87954.5i	−0.0585865	−	0.101475i
$932$		0			0
$933$	−5977.08	−	923268.i	−0.00686635	−	1.06063i
$934$		0			0
$935$		−	14101.6i		−	0.0161304i
$936$		0			0
$937$	904036.			1.02969			0.514845	−	0.857283i	$-0.327849\pi$
$937$	904036.			1.02969			0.514845	+	0.857283i	$0.327849\pi$
$938$		0			0
$939$	187171.	+	319397.i	0.212279	+	0.362243i
$940$		0			0
$941$	−569128.	+	328586.i	−0.642733	+	0.371082i	−0.785666	−	0.618650i	$-0.787680\pi$
$941$	−569128.	+	328586.i	−0.642733	+	0.371082i	0.142934	+	0.989732i	$0.454346\pi$
$942$		0			0
$943$	−474393.	−	273891.i	−0.533476	−	0.308003i
$944$		0			0
$945$	−98260.2	+	1908.57i	−0.110031	+	0.00213720i
$946$		0			0
$947$	−100820.	+	174625.i	−0.112420	+	0.194718i	−0.916746	−	0.399471i	$-0.869194\pi$
$947$	−100820.	+	174625.i	−0.112420	+	0.194718i	0.804325	+	0.594189i	$0.202527\pi$
$948$		0			0
$949$	1.64752e6	−	951194.i	1.82935	−	1.05618i
$950$		0			0
$951$	−977542.	+	572854.i	−1.08087	+	0.633407i
$952$		0			0
$953$	−638389.			−0.702910			−0.351455	−	0.936205i	$-0.614313\pi$
$953$	−638389.			−0.702910			−0.351455	+	0.936205i	$0.614313\pi$
$954$		0			0
$955$	107011.			0.117333
$956$		0			0
$957$	68.5163	+	10583.6i	7.48118e−5	+	0.0115560i
$958$		0			0
$959$	213075.	−	123019.i	0.231684	−	0.133763i
$960$		0			0
$961$	−380552.	+	659136.i	−0.412067	+	0.713721i
$962$		0			0
$963$	356571.	+	599536.i	0.384497	+	0.646491i
$964$		0			0
$965$	−63737.0	−	36798.6i	−0.0684443	−	0.0395163i
$966$		0			0
$967$	961591.	−	555175.i	1.02834	−	0.593714i	0.111833	−	0.993727i	$-0.464328\pi$
$967$	961591.	−	555175.i	1.02834	−	0.593714i	0.916509	+	0.400013i	$0.130995\pi$
$968$		0			0
$969$	140952.	−	247827.i	0.150114	−	0.263937i
$970$		0			0
$971$	1.25193e6			1.32783			0.663913	−	0.747810i	$-0.268895\pi$
$971$	1.25193e6			1.32783			0.663913	+	0.747810i	$0.268895\pi$
$972$		0			0
$973$		−	382787.i		−	0.404326i
$974$		0			0
$975$	−972290.	−	552991.i	−1.02279	−	0.581713i
$976$		0			0
$977$	33214.5	+	57529.3i	0.0347968	+	0.0602698i	0.882899	−	0.469562i	$-0.155588\pi$
$977$	33214.5	+	57529.3i	0.0347968	+	0.0602698i	−0.848103	+	0.529832i	$0.822255\pi$
$978$		0			0
$979$	−160219.	+	277508.i	−0.167167	+	0.289541i
$980$		0			0
$981$	−1.37558e6	+	818117.i	−1.42938	+	0.850114i
$982$		0			0
$983$	−130314.	−	75236.9i	−0.134860	−	0.0778617i	0.431052	−	0.902327i	$-0.358143\pi$
$983$	−130314.	−	75236.9i	−0.134860	−	0.0778617i	−0.565912	+	0.824465i	$0.691476\pi$
$984$		0			0
$985$	41815.2	+	72426.0i	0.0430984	+	0.0746487i
$986$		0			0
$987$	1.49191e6	−	9658.35i	1.53146	−	0.00991445i
$988$		0			0
$989$			335865.i			0.343378i
$990$		0			0
$991$		−	795870.i		−	0.810391i	−0.914230	−	0.405196i	$-0.867203\pi$
$991$		−	795870.i		−	0.810391i	0.914230	−	0.405196i	$-0.132797\pi$
$992$		0			0
$993$	−493550.	−	842215.i	−0.500533	−	0.854131i
$994$		0			0
$995$	−93644.4	−	162197.i	−0.0945879	−	0.163831i
$996$		0			0
$997$	−674456.	−	389398.i	−0.678521	−	0.391745i	0.120776	−	0.992680i	$-0.461462\pi$
$997$	−674456.	−	389398.i	−0.678521	−	0.391745i	−0.799298	+	0.600935i	$0.794795\pi$
$998$		0			0
$999$	17885.7	+	920820.i	0.0179215	+	0.922664i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.5.t.b.79.16		88
3.2	odd	2		864.5.t.b.559.20		88
4.3	odd	2		72.5.p.b.43.39	yes	88
8.3	odd	2	inner	288.5.t.b.79.15		88
8.5	even	2		72.5.p.b.43.10	✓	88
9.4	even	3	inner	288.5.t.b.175.15		88
9.5	odd	6		864.5.t.b.847.25		88
12.11	even	2		216.5.p.b.19.6		88
24.5	odd	2		216.5.p.b.19.35		88
24.11	even	2		864.5.t.b.559.25		88
36.23	even	6		216.5.p.b.91.35		88
36.31	odd	6		72.5.p.b.67.10	yes	88
72.5	odd	6		216.5.p.b.91.6		88
72.13	even	6		72.5.p.b.67.39	yes	88
72.59	even	6		864.5.t.b.847.20		88
72.67	odd	6	inner	288.5.t.b.175.16		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.5.p.b.43.10	✓	88	8.5	even	2
72.5.p.b.43.39	yes	88	4.3	odd	2
72.5.p.b.67.10	yes	88	36.31	odd	6
72.5.p.b.67.39	yes	88	72.13	even	6
216.5.p.b.19.6		88	12.11	even	2
216.5.p.b.19.35		88	24.5	odd	2
216.5.p.b.91.6		88	72.5	odd	6
216.5.p.b.91.35		88	36.23	even	6
288.5.t.b.79.15		88	8.3	odd	2	inner
288.5.t.b.79.16		88	1.1	even	1	trivial
288.5.t.b.175.15		88	9.4	even	3	inner
288.5.t.b.175.16		88	72.67	odd	6	inner
864.5.t.b.559.20		88	3.2	odd	2
864.5.t.b.559.25		88	24.11	even	2
864.5.t.b.847.20		88	72.59	even	6
864.5.t.b.847.25		88	9.5	odd	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:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	288.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-4.44945 + 7.82320i) q^{3} +(2.53773 - 1.46516i) q^{5} +(-39.8426 - 23.0032i) q^{7} +(-41.4048 - 69.6178i) q^{9} +O(q^{10})\)	\(q+(-4.44945 + 7.82320i) q^{3} +(2.53773 - 1.46516i) q^{5} +(-39.8426 - 23.0032i) q^{7} +(-41.4048 - 69.6178i) q^{9} +(-27.1224 + 46.9774i) q^{11} +(174.611 - 100.811i) q^{13} +(0.170730 + 26.3723i) q^{15} -88.7146 q^{17} +357.083 q^{19} +(357.236 - 209.345i) q^{21} +(214.383 - 123.774i) q^{23} +(-308.207 + 533.830i) q^{25} +(728.863 - 14.1572i) q^{27} +(-18.7746 - 10.8395i) q^{29} +(349.016 - 201.504i) q^{31} +(-246.834 - 421.207i) q^{33} -134.813 q^{35} +1263.37i q^{37} +(11.7472 + 1814.57i) q^{39} +(-1106.42 - 1916.37i) q^{41} +(-678.384 + 1175.00i) q^{43} +(-207.075 - 116.007i) q^{45} +(3120.48 + 1801.61i) q^{47} +(-142.209 - 246.314i) q^{49} +(394.731 - 694.032i) q^{51} +4122.82i q^{53} +158.955i q^{55} +(-1588.82 + 2793.53i) q^{57} +(2643.76 + 4579.12i) q^{59} +(4778.25 + 2758.72i) q^{61} +(48.2476 + 3726.20i) q^{63} +(295.410 - 511.664i) q^{65} +(-3090.68 - 5353.21i) q^{67} +(14.4230 + 2227.89i) q^{69} +4832.30i q^{71} +9435.38 q^{73} +(-2804.90 - 4786.41i) q^{75} +(2161.26 - 1247.80i) q^{77} +(-1099.86 - 635.004i) q^{79} +(-3132.28 + 5765.03i) q^{81} +(-1266.75 + 2194.08i) q^{83} +(-225.134 + 129.981i) q^{85} +(168.337 - 98.6477i) q^{87} +5907.27 q^{89} -9275.93 q^{91} +(23.4806 + 3627.00i) q^{93} +(906.180 - 523.183i) q^{95} +(-928.999 + 1609.07i) q^{97} +(4393.46 - 56.8874i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 18 q^{3} + 30 q^{9}+O(q^{10}) \) 88 * q + 18 * q^3 + 30 * q^9	\( 88 q + 18 q^{3} + 30 q^{9} - 44 q^{11} - 1156 q^{17} - 860 q^{19} + 5998 q^{25} - 504 q^{27} - 3204 q^{33} + 2508 q^{35} + 2348 q^{41} - 3500 q^{43} + 16462 q^{49} + 12378 q^{51} - 6522 q^{57} + 3508 q^{59} - 2502 q^{65} - 5132 q^{67} + 19004 q^{73} + 39858 q^{75} - 11346 q^{81} - 17090 q^{83} - 8272 q^{89} + 9612 q^{91} + 9980 q^{97} + 11742 q^{99}+O(q^{100}) \) 88 * q + 18 * q^3 + 30 * q^9 - 44 * q^11 - 1156 * q^17 - 860 * q^19 + 5998 * q^25 - 504 * q^27 - 3204 * q^33 + 2508 * q^35 + 2348 * q^41 - 3500 * q^43 + 16462 * q^49 + 12378 * q^51 - 6522 * q^57 + 3508 * q^59 - 2502 * q^65 - 5132 * q^67 + 19004 * q^73 + 39858 * q^75 - 11346 * q^81 - 17090 * q^83 - 8272 * q^89 + 9612 * q^91 + 9980 * q^97 + 11742 * q^99

Introduction

L-functions

Modular forms

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Database

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