LMFDB - Embedded newform 144.3.m.c.19.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [144,3,Mod(19,144)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(144, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("144.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	144.m (of order $4$, 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:	$3.92371580679$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{14} - 4 x^{13} + 10 x^{12} + 56 x^{11} + 88 x^{10} - 128 x^{9} - 496 x^{8} - 512 x^{7} + \cdots + 65536 $ x^16 - 6x^14 - 4x^13 + 10x^12 + 56x^11 + 88x^10 - 128x^9 - 496x^8 - 512x^7 + 1408x^6 + 3584x^5 + 2560x^4 - 4096x^3 - 24576*x^2 + 65536
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	no (minimal twist has level 48)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			19.8
Root			$1.84258 + 0.777752i$ of defining polynomial
Character	$\chi$	$=$	144.19
Dual form			144.3.m.c.91.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.84258 - 0.777752i) q^{2} +(2.79020 - 2.86614i) q^{4} +(4.78830 - 4.78830i) q^{5} -10.3302 q^{7} +(2.91202 - 7.45118i) q^{8} +O(q^{10})$	\(q+(1.84258 - 0.777752i) q^{2} +(2.79020 - 2.86614i) q^{4} +(4.78830 - 4.78830i) q^{5} -10.3302 q^{7} +(2.91202 - 7.45118i) q^{8} +(5.09872 - 12.5469i) q^{10} +(0.526169 + 0.526169i) q^{11} +(17.2840 + 17.2840i) q^{13} +(-19.0343 + 8.03437i) q^{14} +(-0.429536 - 15.9942i) q^{16} -4.71650 q^{17} +(-2.53604 + 2.53604i) q^{19} +(-0.363618 - 27.0843i) q^{20} +(1.37874 + 0.560279i) q^{22} +12.5864 q^{23} -20.8557i q^{25} +(45.2897 + 18.4044i) q^{26} +(-28.8235 + 29.6080i) q^{28} +(2.19683 + 2.19683i) q^{29} +28.0521i q^{31} +(-13.2310 - 29.1366i) q^{32} +(-8.69052 + 3.66827i) q^{34} +(-49.4644 + 49.4644i) q^{35} +(-32.1128 + 32.1128i) q^{37} +(-2.70044 + 6.64526i) q^{38} +(-21.7349 - 49.6222i) q^{40} +23.1145i q^{41} +(4.79441 + 4.79441i) q^{43} +(2.97619 - 0.0399566i) q^{44} +(23.1915 - 9.78913i) q^{46} +39.0095i q^{47} +57.7141 q^{49} +(-16.2206 - 38.4283i) q^{50} +(97.7640 - 1.31252i) q^{52} +(27.9768 - 27.9768i) q^{53} +5.03891 q^{55} +(-30.0819 + 76.9726i) q^{56} +(5.75642 + 2.33924i) q^{58} +(-79.8538 - 79.8538i) q^{59} +(-36.7762 - 36.7762i) q^{61} +(21.8176 + 51.6883i) q^{62} +(-47.0402 - 43.3960i) q^{64} +165.522 q^{65} +(-10.9869 + 10.9869i) q^{67} +(-13.1600 + 13.5181i) q^{68} +(-52.6711 + 129.613i) q^{70} -52.6605 q^{71} -67.8061i q^{73} +(-34.1946 + 84.1462i) q^{74} +(0.192584 + 14.3447i) q^{76} +(-5.43545 - 5.43545i) q^{77} +56.4602i q^{79} +(-78.6420 - 74.5285i) q^{80} +(17.9773 + 42.5903i) q^{82} +(58.3697 - 58.3697i) q^{83} +(-22.5840 + 22.5840i) q^{85} +(12.5629 + 5.10522i) q^{86} +(5.45279 - 2.38836i) q^{88} -131.566i q^{89} +(-178.548 - 178.548i) q^{91} +(35.1187 - 36.0745i) q^{92} +(30.3397 + 71.8781i) q^{94} +24.2866i q^{95} +60.9413 q^{97} +(106.343 - 44.8872i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 12 q^{4} + 12 q^{8}+O(q^{10}) $ 16 * q + 12 * q^4 + 12 * q^8	$ 16 q + 12 q^{4} + 12 q^{8} - 56 q^{10} - 32 q^{11} + 44 q^{14} + 32 q^{16} - 32 q^{19} - 80 q^{20} + 32 q^{22} + 128 q^{23} + 100 q^{26} - 120 q^{28} - 32 q^{29} - 160 q^{32} + 96 q^{34} - 96 q^{35} - 96 q^{37} - 168 q^{38} + 48 q^{40} + 160 q^{43} - 88 q^{44} + 136 q^{46} + 112 q^{49} + 236 q^{50} - 48 q^{52} + 160 q^{53} - 256 q^{55} + 224 q^{56} + 144 q^{58} + 128 q^{59} - 32 q^{61} + 276 q^{62} - 408 q^{64} + 32 q^{65} + 320 q^{67} + 448 q^{68} - 384 q^{70} - 512 q^{71} - 348 q^{74} + 72 q^{76} - 224 q^{77} - 552 q^{80} - 40 q^{82} + 160 q^{83} + 160 q^{85} - 528 q^{86} + 480 q^{88} - 480 q^{91} - 496 q^{92} + 312 q^{94} + 440 q^{98}+O(q^{100}) $ 16 * q + 12 * q^4 + 12 * q^8 - 56 * q^10 - 32 * q^11 + 44 * q^14 + 32 * q^16 - 32 * q^19 - 80 * q^20 + 32 * q^22 + 128 * q^23 + 100 * q^26 - 120 * q^28 - 32 * q^29 - 160 * q^32 + 96 * q^34 - 96 * q^35 - 96 * q^37 - 168 * q^38 + 48 * q^40 + 160 * q^43 - 88 * q^44 + 136 * q^46 + 112 * q^49 + 236 * q^50 - 48 * q^52 + 160 * q^53 - 256 * q^55 + 224 * q^56 + 144 * q^58 + 128 * q^59 - 32 * q^61 + 276 * q^62 - 408 * q^64 + 32 * q^65 + 320 * q^67 + 448 * q^68 - 384 * q^70 - 512 * q^71 - 348 * q^74 + 72 * q^76 - 224 * q^77 - 552 * q^80 - 40 * q^82 + 160 * q^83 + 160 * q^85 - 528 * q^86 + 480 * q^88 - 480 * q^91 - 496 * q^92 + 312 * q^94 + 440 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	1.84258	−	0.777752i	0.921290	−	0.388876i
$2$	1.84258	−	0.777752i	0.921290	−	0.388876i
$3$		0			0
$3$		0			0
$4$	2.79020	−	2.86614i	0.697551	−	0.716535i
$5$	4.78830	−	4.78830i	0.957661	−	0.957661i	−0.0414785	−	0.999139i	$-0.513207\pi$
$5$	4.78830	−	4.78830i	0.957661	−	0.957661i	0.999139	+	0.0414785i	$0.0132068\pi$
$6$		0			0
$7$	−10.3302			−1.47575			−0.737875	−	0.674937i	$-0.764171\pi$
$7$	−10.3302			−1.47575			−0.737875	+	0.674937i	$0.764171\pi$
$8$	2.91202	−	7.45118i	0.364003	−	0.931398i
$9$		0			0
$10$	5.09872	−	12.5469i	0.509872	−	1.25469i
$11$	0.526169	+	0.526169i	0.0478335	+	0.0478335i	0.730619	−	0.682785i	$-0.239232\pi$
$11$	0.526169	+	0.526169i	0.0478335	+	0.0478335i	−0.682785	+	0.730619i	$0.739232\pi$
$12$		0			0
$13$	17.2840	+	17.2840i	1.32953	+	1.32953i	0.905774	+	0.423761i	$0.139290\pi$
$13$	17.2840	+	17.2840i	1.32953	+	1.32953i	0.423761	+	0.905774i	$0.360710\pi$
$14$	−19.0343	+	8.03437i	−1.35959	+	0.573884i
$15$		0			0
$16$	−0.429536	−	15.9942i	−0.0268460	−	0.999640i
$17$	−4.71650			−0.277441			−0.138721	−	0.990332i	$-0.544299\pi$
$17$	−4.71650			−0.277441			−0.138721	+	0.990332i	$0.544299\pi$
$18$		0			0
$19$	−2.53604	+	2.53604i	−0.133476	+	0.133476i	−0.770688	−	0.637213i	$-0.780087\pi$
$19$	−2.53604	+	2.53604i	−0.133476	+	0.133476i	0.637213	+	0.770688i	$0.280087\pi$
$20$	−0.363618	−	27.0843i	−0.0181809	−	1.35422i
$21$		0			0
$22$	1.37874	+	0.560279i	0.0626698	+	0.0254672i
$23$	12.5864			0.547236			0.273618	−	0.961838i	$-0.411780\pi$
$23$	12.5864			0.547236			0.273618	+	0.961838i	$0.411780\pi$
$24$		0			0
$25$		−	20.8557i		−	0.834229i
$26$	45.2897	+	18.4044i	1.74191	+	0.707863i
$27$		0			0
$28$	−28.8235	+	29.6080i	−1.02941	+	1.05743i
$29$	2.19683	+	2.19683i	0.0757526	+	0.0757526i	0.743968	−	0.668215i	$-0.232942\pi$
$29$	2.19683	+	2.19683i	0.0757526	+	0.0757526i	−0.668215	+	0.743968i	$0.732942\pi$
$30$		0			0
$31$			28.0521i			0.904908i	0.891788	+	0.452454i	$0.149451\pi$
$31$			28.0521i			0.904908i	−0.891788	+	0.452454i	$0.850549\pi$
$32$	−13.2310	−	29.1366i	−0.413469	−	0.910518i
$33$		0			0
$34$	−8.69052	+	3.66827i	−0.255604	+	0.107890i
$35$	−49.4644	+	49.4644i	−1.41327	+	1.41327i
$36$		0			0
$37$	−32.1128	+	32.1128i	−0.867914	+	0.867914i	−0.992241	−	0.124327i	$-0.960323\pi$
$37$	−32.1128	+	32.1128i	−0.867914	+	0.867914i	0.124327	+	0.992241i	$0.460323\pi$
$38$	−2.70044	+	6.64526i	−0.0710643	+	0.174875i
$39$		0			0
$40$	−21.7349	−	49.6222i	−0.543372	−	1.24055i
$41$			23.1145i			0.563768i	0.959449	+	0.281884i	$0.0909593\pi$
$41$			23.1145i			0.563768i	−0.959449	+	0.281884i	$0.909041\pi$
$42$		0			0
$43$	4.79441	+	4.79441i	0.111498	+	0.111498i	0.760655	−	0.649157i	$-0.224878\pi$
$43$	4.79441	+	4.79441i	0.111498	+	0.111498i	−0.649157	+	0.760655i	$0.724878\pi$
$44$	2.97619	−	0.0399566i	0.0676407	−	0.000908104i
$45$		0			0
$46$	23.1915	−	9.78913i	0.504163	−	0.212807i
$47$			39.0095i			0.829989i	0.909824	+	0.414994i	$0.136216\pi$
$47$			39.0095i			0.829989i	−0.909824	+	0.414994i	$0.863784\pi$
$48$		0			0
$49$	57.7141			1.17784
$50$	−16.2206	−	38.4283i	−0.324412	−	0.768567i
$51$		0			0
$52$	97.7640	−	1.31252i	1.88008	−	0.0252408i
$53$	27.9768	−	27.9768i	0.527864	−	0.527864i	−0.392071	−	0.919935i	$-0.628241\pi$
$53$	27.9768	−	27.9768i	0.527864	−	0.527864i	0.919935	+	0.392071i	$0.128241\pi$
$54$		0			0
$55$	5.03891			0.0916166
$56$	−30.0819	+	76.9726i	−0.537177	+	1.37451i
$57$		0			0
$58$	5.75642	+	2.33924i	0.0992485	+	0.0403318i
$59$	−79.8538	−	79.8538i	−1.35345	−	1.35345i	−0.881764	−	0.471691i	$-0.843644\pi$
$59$	−79.8538	−	79.8538i	−1.35345	−	1.35345i	−0.471691	−	0.881764i	$-0.656356\pi$
$60$		0			0
$61$	−36.7762	−	36.7762i	−0.602888	−	0.602888i	0.338190	−	0.941078i	$-0.390185\pi$
$61$	−36.7762	−	36.7762i	−0.602888	−	0.602888i	−0.941078	+	0.338190i	$0.890185\pi$
$62$	21.8176	+	51.6883i	0.351897	+	0.833682i
$63$		0			0
$64$	−47.0402	−	43.3960i	−0.735004	−	0.678063i
$65$	165.522			2.54649
$66$		0			0
$67$	−10.9869	+	10.9869i	−0.163984	+	0.163984i	−0.784329	−	0.620345i	$-0.786992\pi$
$67$	−10.9869	+	10.9869i	−0.163984	+	0.163984i	0.620345	+	0.784329i	$0.286992\pi$
$68$	−13.1600	+	13.5181i	−0.193529	+	0.198796i
$69$		0			0
$70$	−52.6711	+	129.613i	−0.752444	+	1.85162i
$71$	−52.6605			−0.741697			−0.370849	−	0.928693i	$-0.620933\pi$
$71$	−52.6605			−0.741697			−0.370849	+	0.928693i	$0.620933\pi$
$72$		0			0
$73$		−	67.8061i		−	0.928850i	−0.885612	−	0.464425i	$-0.846261\pi$
$73$		−	67.8061i		−	0.928850i	0.885612	−	0.464425i	$-0.153739\pi$
$74$	−34.1946	+	84.1462i	−0.462089	+	1.13711i
$75$		0			0
$76$	0.192584	+	14.3447i	0.00253399	+	0.188746i
$77$	−5.43545	−	5.43545i	−0.0705903	−	0.0705903i
$78$		0			0
$79$			56.4602i			0.714686i	0.933973	+	0.357343i	$0.116317\pi$
$79$			56.4602i			0.714686i	−0.933973	+	0.357343i	$0.883683\pi$
$80$	−78.6420	−	74.5285i	−0.983025	−	0.931606i
$81$		0			0
$82$	17.9773	+	42.5903i	0.219236	+	0.519394i
$83$	58.3697	−	58.3697i	0.703249	−	0.703249i	−0.261857	−	0.965107i	$-0.584335\pi$
$83$	58.3697	−	58.3697i	0.703249	−	0.703249i	0.965107	+	0.261857i	$0.0843349\pi$
$84$		0			0
$85$	−22.5840	+	22.5840i	−0.265694	+	0.265694i
$86$	12.5629	+	5.10522i	0.146081	+	0.0593630i
$87$		0			0
$88$	5.45279	−	2.38836i	0.0619636	−	0.0271405i
$89$		−	131.566i		−	1.47827i	−0.673558	−	0.739135i	$-0.735235\pi$
$89$		−	131.566i		−	1.47827i	0.673558	−	0.739135i	$-0.264765\pi$
$90$		0			0
$91$	−178.548	−	178.548i	−1.96206	−	1.96206i
$92$	35.1187	−	36.0745i	0.381725	−	0.392114i
$93$		0			0
$94$	30.3397	+	71.8781i	0.322763	+	0.764661i
$95$			24.2866i			0.255649i
$96$		0			0
$97$	60.9413			0.628261			0.314131	−	0.949380i	$-0.398287\pi$
$97$	60.9413			0.628261			0.314131	+	0.949380i	$0.398287\pi$
$98$	106.343	−	44.8872i	1.08513	−	0.458033i
$99$		0			0
$100$	−59.7755	−	58.1917i	−0.597755	−	0.581917i
$101$	−109.986	+	109.986i	−1.08897	+	1.08897i	−0.0933326	+	0.995635i	$0.529752\pi$
$101$	−109.986	+	109.986i	−1.08897	+	1.08897i	−0.995635	+	0.0933326i	$0.970248\pi$
$102$		0			0
$103$	173.295			1.68248			0.841239	−	0.540663i	$-0.181826\pi$
$103$	173.295			1.68248			0.841239	+	0.540663i	$0.181826\pi$
$104$	179.117	−	78.4546i	1.72228	−	0.754371i
$105$		0			0
$106$	29.7905	−	73.3085i	0.281042	−	0.691589i
$107$	25.4747	+	25.4747i	0.238081	+	0.238081i	0.816055	−	0.577974i	$-0.196156\pi$
$107$	25.4747	+	25.4747i	0.238081	+	0.238081i	−0.577974	+	0.816055i	$0.696156\pi$
$108$		0			0
$109$	33.0605	+	33.0605i	0.303307	+	0.303307i	0.842306	−	0.538999i	$-0.181197\pi$
$109$	33.0605	+	33.0605i	0.303307	+	0.303307i	−0.538999	+	0.842306i	$0.681197\pi$
$110$	9.28460	−	3.91902i	0.0844054	−	0.0356275i
$111$		0			0
$112$	4.43721	+	165.224i	0.0396180	+	1.47522i
$113$	−140.159			−1.24034			−0.620171	−	0.784466i	$-0.712937\pi$
$113$	−140.159			−1.24034			−0.620171	+	0.784466i	$0.712937\pi$
$114$		0			0
$115$	60.2677	−	60.2677i	0.524067	−	0.524067i
$116$	12.4260	−	0.166824i	0.107121	−	0.00143814i
$117$		0			0
$118$	−209.244	−	85.0306i	−1.77325	−	0.720598i
$119$	48.7226			0.409434
$120$		0			0
$121$		−	120.446i		−	0.995424i
$122$	−96.3658	−	39.1603i	−0.789883	−	0.320986i
$123$		0			0
$124$	80.4014	+	78.2712i	0.648398	+	0.631219i
$125$	19.8441	+	19.8441i	0.158752	+	0.158752i
$126$		0			0
$127$		−	40.8458i		−	0.321620i	−0.986985	−	0.160810i	$-0.948589\pi$
$127$		−	40.8458i		−	0.321620i	0.986985	−	0.160810i	$-0.0514107\pi$
$128$	−120.427	−	43.3750i	−0.940834	−	0.338868i
$129$		0			0
$130$	304.987	−	128.735i	2.34605	−	0.990268i
$131$	75.0168	−	75.0168i	0.572647	−	0.572647i	−0.360220	−	0.932867i	$-0.617298\pi$
$131$	75.0168	−	75.0168i	0.572647	−	0.572647i	0.932867	+	0.360220i	$0.117298\pi$
$132$		0			0
$133$	26.1979	−	26.1979i	0.196977	−	0.196977i
$134$	−11.6992	+	28.7893i	−0.0873071	+	0.214846i
$135$		0			0
$136$	−13.7346	+	35.1435i	−0.100989	+	0.258408i
$137$		−	134.028i		−	0.978308i	−0.872197	−	0.489154i	$-0.837306\pi$
$137$		−	134.028i		−	0.978308i	0.872197	−	0.489154i	$-0.162694\pi$
$138$		0			0
$139$	22.8798	+	22.8798i	0.164603	+	0.164603i	0.784602	−	0.619999i	$-0.212867\pi$
$139$	22.8798	+	22.8798i	0.164603	+	0.164603i	−0.619999	+	0.784602i	$0.712867\pi$
$140$	3.75626	+	279.788i	0.0268305	+	1.99848i
$141$		0			0
$142$	−97.0312	+	40.9568i	−0.683318	+	0.288428i
$143$			18.1885i			0.127193i
$144$		0			0
$145$	21.0381			0.145091
$146$	−52.7363	−	124.938i	−0.361208	−	0.855740i
$147$		0			0
$148$	2.43861	+	181.641i	0.0164771	+	1.22730i
$149$	9.32124	−	9.32124i	0.0625587	−	0.0625587i	−0.675135	−	0.737694i	$-0.735915\pi$
$149$	9.32124	−	9.32124i	0.0625587	−	0.0625587i	0.737694	+	0.675135i	$0.235915\pi$
$150$		0			0
$151$	−50.5403			−0.334704			−0.167352	−	0.985897i	$-0.553522\pi$
$151$	−50.5403			−0.334704			−0.167352	+	0.985897i	$0.553522\pi$
$152$	11.5115	+	26.2815i	0.0757334	+	0.172904i
$153$		0			0
$154$	−14.2427	−	5.78782i	−0.0924850	−	0.0375833i
$155$	134.322	+	134.322i	0.866595	+	0.866595i
$156$		0			0
$157$	−95.8844	−	95.8844i	−0.610729	−	0.610729i	0.332407	−	0.943136i	$-0.392139\pi$
$157$	−95.8844	−	95.8844i	−0.610729	−	0.610729i	−0.943136	+	0.332407i	$0.892139\pi$
$158$	43.9120	+	104.032i	0.277924	+	0.658433i
$159$		0			0
$160$	−202.869	−	76.1608i	−1.26793	−	0.476005i
$161$	−130.021			−0.807584
$162$		0			0
$163$	−140.885	+	140.885i	−0.864324	+	0.864324i	−0.991837	−	0.127513i	$-0.959301\pi$
$163$	−140.885	+	140.885i	−0.864324	+	0.864324i	0.127513	+	0.991837i	$0.459301\pi$
$164$	66.2494	+	64.4941i	0.403959	+	0.393257i
$165$		0			0
$166$	62.1537	−	152.948i	0.374420	−	0.921374i
$167$	107.849			0.645800			0.322900	−	0.946433i	$-0.395342\pi$
$167$	107.849			0.645800			0.322900	+	0.946433i	$0.395342\pi$
$168$		0			0
$169$			428.470i			2.53533i
$170$	−24.0481	+	59.1777i	−0.141459	+	0.348104i
$171$		0			0
$172$	27.1188	−	0.364082i	0.157668	−	0.00211675i
$173$	53.8845	+	53.8845i	0.311471	+	0.311471i	0.845479	−	0.534008i	$-0.179315\pi$
$173$	53.8845	+	53.8845i	0.311471	+	0.311471i	−0.534008	+	0.845479i	$0.679315\pi$
$174$		0			0
$175$			215.445i			1.23111i
$176$	8.18965	−	8.64167i	0.0465321	−	0.0491004i
$177$		0			0
$178$	−102.326	−	242.421i	−0.574864	−	1.36191i
$179$	−104.178	+	104.178i	−0.582002	+	0.582002i	−0.935453	−	0.353451i	$-0.885008\pi$
$179$	−104.178	+	104.178i	−0.582002	+	0.582002i	0.353451	+	0.935453i	$0.385008\pi$
$180$		0			0
$181$	−205.498	+	205.498i	−1.13535	+	1.13535i	−0.146073	+	0.989274i	$0.546664\pi$
$181$	−205.498	+	205.498i	−1.13535	+	1.13535i	−0.989274	+	0.146073i	$0.953336\pi$
$182$	−467.854	−	190.122i	−2.57063	−	1.04463i
$183$		0			0
$184$	36.6520	−	93.7838i	0.199196	−	0.509695i
$185$			307.532i			1.66233i
$186$		0			0
$187$	−2.48167	−	2.48167i	−0.0132710	−	0.0132710i
$188$	111.807	+	108.844i	0.594716	+	0.578959i
$189$		0			0
$190$	18.8890	+	44.7501i	0.0994157	+	0.235527i
$191$		−	248.255i		−	1.29977i	−0.760034	−	0.649883i	$-0.774818\pi$
$191$		−	248.255i		−	1.29977i	0.760034	−	0.649883i	$-0.225182\pi$
$192$		0			0
$193$	−129.921			−0.673166			−0.336583	−	0.941654i	$-0.609271\pi$
$193$	−129.921			−0.673166			−0.336583	+	0.941654i	$0.609271\pi$
$194$	112.289	−	47.3973i	0.578811	−	0.244316i
$195$		0			0
$196$	161.034	−	165.417i	0.821602	−	0.843963i
$197$	−237.001	+	237.001i	−1.20305	+	1.20305i	−0.229816	+	0.973234i	$0.573812\pi$
$197$	−237.001	+	237.001i	−1.20305	+	1.20305i	−0.973234	+	0.229816i	$0.926188\pi$
$198$		0			0
$199$	246.508			1.23873			0.619366	−	0.785102i	$-0.287390\pi$
$199$	246.508			1.23873			0.619366	+	0.785102i	$0.287390\pi$
$200$	−155.400	−	60.7324i	−0.776999	−	0.303662i
$201$		0			0
$202$	−117.116	+	288.199i	−0.579781	+	1.42673i
$203$	−22.6938	−	22.6938i	−0.111792	−	0.111792i
$204$		0			0
$205$	110.679	+	110.679i	0.539898	+	0.539898i
$206$	319.311	−	134.781i	1.55005	−	0.654276i
$207$		0			0
$208$	269.020	−	283.868i	1.29336	−	1.36475i
$209$	−2.66877			−0.0127692
$210$		0			0
$211$	−13.4139	+	13.4139i	−0.0635728	+	0.0635728i	−0.738178	−	0.674606i	$-0.764314\pi$
$211$	−13.4139	+	13.4139i	−0.0635728	+	0.0635728i	0.674606	+	0.738178i	$0.264314\pi$
$212$	−2.12452	−	158.246i	−0.0100213	−	0.746445i
$213$		0			0
$214$	66.7522	+	27.1262i	0.311926	+	0.126758i
$215$	45.9142			0.213554
$216$		0			0
$217$		−	289.786i		−	1.33542i
$218$	86.6295	+	35.2037i	0.397383	+	0.161485i
$219$		0			0
$220$	14.0596	−	14.4422i	0.0639072	−	0.0656465i
$221$	−81.5197	−	81.5197i	−0.368867	−	0.368867i
$222$		0			0
$223$		−	295.580i		−	1.32547i	−0.748854	−	0.662735i	$-0.769396\pi$
$223$		−	295.580i		−	1.32547i	0.748854	−	0.662735i	$-0.230604\pi$
$224$	136.680	+	300.988i	0.610177	+	1.34370i
$225$		0			0
$226$	−258.254	+	109.009i	−1.14272	+	0.482340i
$227$	97.0742	−	97.0742i	0.427640	−	0.427640i	−0.460184	−	0.887824i	$-0.652217\pi$
$227$	97.0742	−	97.0742i	0.427640	−	0.427640i	0.887824	+	0.460184i	$0.152217\pi$
$228$		0			0
$229$	34.2565	−	34.2565i	0.149592	−	0.149592i	−0.628344	−	0.777936i	$-0.716267\pi$
$229$	34.2565	−	34.2565i	0.149592	−	0.149592i	0.777936	+	0.628344i	$0.216267\pi$
$230$	64.1747	−	157.921i	0.279021	−	0.686615i
$231$		0			0
$232$	22.7662	−	9.97174i	0.0981300	−	0.0429816i
$233$			62.8176i			0.269604i	0.990873	+	0.134802i	$0.0430398\pi$
$233$			62.8176i			0.269604i	−0.990873	+	0.134802i	$0.956960\pi$
$234$		0			0
$235$	186.789	+	186.789i	0.794848	+	0.794848i
$236$	−451.681	+	6.06400i	−1.91390	+	0.0256949i
$237$		0			0
$238$	89.7753	−	37.8941i	0.377207	−	0.159219i
$239$			355.910i			1.48916i	0.667532	+	0.744581i	$0.267351\pi$
$239$			355.910i			1.48916i	−0.667532	+	0.744581i	$0.732649\pi$
$240$		0			0
$241$	66.2545			0.274915			0.137458	−	0.990508i	$-0.456107\pi$
$241$	66.2545			0.274915			0.137458	+	0.990508i	$0.456107\pi$
$242$	−93.6774	−	221.932i	−0.387097	−	0.917074i
$243$		0			0
$244$	−208.019	+	2.79274i	−0.852535	+	0.0114456i
$245$	276.352	−	276.352i	1.12797	−	1.12797i
$246$		0			0
$247$	−87.6655			−0.354921
$248$	209.022	+	81.6885i	0.842829	+	0.329389i
$249$		0			0
$250$	51.9980	+	21.1305i	0.207992	+	0.0845220i
$251$	−325.395	−	325.395i	−1.29640	−	1.29640i	−0.930757	−	0.365638i	$-0.880851\pi$
$251$	−325.395	−	325.395i	−1.29640	−	1.29640i	−0.365638	−	0.930757i	$-0.619149\pi$
$252$		0			0
$253$	6.62259	+	6.62259i	0.0261762	+	0.0261762i
$254$	−31.7679	−	75.2616i	−0.125070	−	0.296306i
$255$		0			0
$256$	−255.631	+	13.7402i	−0.998559	+	0.0536726i
$257$	312.011			1.21405			0.607026	−	0.794682i	$-0.292362\pi$
$257$	312.011			1.21405			0.607026	+	0.794682i	$0.292362\pi$
$258$		0			0
$259$	331.733	−	331.733i	1.28082	−	1.28082i
$260$	461.839	−	474.409i	1.77630	−	1.82465i
$261$		0			0
$262$	79.8800	−	196.569i	0.304885	−	0.750263i
$263$	168.163			0.639403			0.319702	−	0.947518i	$-0.396417\pi$
$263$	168.163			0.639403			0.319702	+	0.947518i	$0.396417\pi$
$264$		0			0
$265$		−	267.923i		−	1.01103i
$266$	27.8962	−	68.6472i	0.104873	−	0.258072i
$267$		0			0
$268$	0.834331	+	62.1457i	0.00311318	+	0.231887i
$269$	−212.116	−	212.116i	−0.788535	−	0.788535i	0.192719	−	0.981254i	$-0.438269\pi$
$269$	−212.116	−	212.116i	−0.788535	−	0.788535i	−0.981254	+	0.192719i	$0.938269\pi$
$270$		0			0
$271$			173.450i			0.640037i	0.947411	+	0.320019i	$0.103689\pi$
$271$			173.450i			0.640037i	−0.947411	+	0.320019i	$0.896311\pi$
$272$	2.02590	+	75.4368i	0.00744818	+	0.277341i
$273$		0			0
$274$	−104.241	−	246.958i	−0.380441	−	0.901305i
$275$	10.9736	−	10.9736i	0.0399041	−	0.0399041i
$276$		0			0
$277$	−38.4049	+	38.4049i	−0.138646	+	0.138646i	−0.773023	−	0.634377i	$-0.781257\pi$
$277$	−38.4049	+	38.4049i	−0.138646	+	0.138646i	0.634377	+	0.773023i	$0.281257\pi$
$278$	59.9526	+	24.3630i	0.215657	+	0.0876368i
$279$		0			0
$280$	224.527	+	512.610i	0.801881	+	1.83075i
$281$			223.573i			0.795632i	0.917465	+	0.397816i	$0.130232\pi$
$281$			223.573i			0.795632i	−0.917465	+	0.397816i	$0.869768\pi$
$282$		0			0
$283$	247.755	+	247.755i	0.875459	+	0.875459i	0.993061	−	0.117602i	$-0.0375206\pi$
$283$	247.755	+	247.755i	0.875459	+	0.875459i	−0.117602	+	0.993061i	$0.537521\pi$
$284$	−146.933	+	150.932i	−0.517371	+	0.531452i
$285$		0			0
$286$	14.1462	+	33.5139i	0.0494622	+	0.117181i
$287$		−	238.778i		−	0.831980i
$288$		0			0
$289$	−266.755			−0.923026
$290$	38.7645	−	16.3625i	0.133671	−	0.0564223i
$291$		0			0
$292$	−194.342	−	189.193i	−0.665554	−	0.647920i
$293$	102.262	−	102.262i	0.349016	−	0.349016i	−0.510727	−	0.859743i	$-0.670624\pi$
$293$	102.262	−	102.262i	0.349016	−	0.349016i	0.859743	+	0.510727i	$0.170624\pi$
$294$		0			0
$295$	−764.729			−2.59230
$296$	145.765	+	332.792i	0.492450	+	1.12430i
$297$		0			0
$298$	9.92552	−	24.4247i	0.0333071	−	0.0819622i
$299$	217.543	+	217.543i	0.727570	+	0.727570i
$300$		0			0
$301$	−49.5275	−	49.5275i	−0.164543	−	0.164543i
$302$	−93.1246	+	39.3079i	−0.308360	+	0.130158i
$303$		0			0
$304$	41.6513	+	39.4726i	0.137011	+	0.129844i
$305$	−352.191			−1.15472
$306$		0			0
$307$	138.292	−	138.292i	0.450463	−	0.450463i	−0.445045	−	0.895508i	$-0.646812\pi$
$307$	138.292	−	138.292i	0.450463	−	0.450463i	0.895508	+	0.445045i	$0.146812\pi$
$308$	−30.7448	+	0.412762i	−0.0998208	+	0.00134014i
$309$		0			0
$310$	351.969	+	143.030i	1.13538	+	0.461387i
$311$	−205.789			−0.661702			−0.330851	−	0.943683i	$-0.607336\pi$
$311$	−205.789			−0.661702			−0.330851	+	0.943683i	$0.607336\pi$
$312$		0			0
$313$			223.861i			0.715209i	0.933873	+	0.357605i	$0.116406\pi$
$313$			223.861i			0.715209i	−0.933873	+	0.357605i	$0.883594\pi$
$314$	−251.249	−	102.100i	−0.800156	−	0.325161i
$315$		0			0
$316$	161.823	+	157.535i	0.512098	+	0.498530i
$317$	176.488	+	176.488i	0.556744	+	0.556744i	0.928379	−	0.371635i	$-0.121203\pi$
$317$	176.488	+	176.488i	0.556744	+	0.556744i	−0.371635	+	0.928379i	$0.621203\pi$
$318$		0			0
$319$			2.31180i			0.00724703i
$320$	−433.036	+	17.4495i	−1.35324	+	0.0545296i
$321$		0			0
$322$	−239.574	+	101.124i	−0.744019	+	0.314050i
$323$	11.9612	−	11.9612i	0.0370316	−	0.0370316i
$324$		0			0
$325$	360.469	−	360.469i	1.10914	−	1.10914i
$326$	−150.018	+	369.165i	−0.460178	+	1.13241i
$327$		0			0
$328$	172.230	+	67.3099i	0.525092	+	0.205213i
$329$		−	402.978i		−	1.22486i
$330$		0			0
$331$	−183.939	−	183.939i	−0.555706	−	0.555706i	0.372376	−	0.928082i	$-0.378543\pi$
$331$	−183.939	−	183.939i	−0.555706	−	0.555706i	−0.928082	+	0.372376i	$0.878543\pi$
$332$	−4.43252	−	330.159i	−0.0133510	−	0.994455i
$333$		0			0
$334$	198.720	−	83.8795i	0.594969	−	0.251136i
$335$			105.217i			0.314081i
$336$		0			0
$337$	12.7162			0.0377336			0.0188668	−	0.999822i	$-0.493994\pi$
$337$	12.7162			0.0377336			0.0188668	+	0.999822i	$0.493994\pi$
$338$	333.244	+	789.490i	0.985928	+	2.33577i
$339$		0			0
$340$	1.71500	+	127.743i	0.00504413	+	0.375715i
$341$	−14.7602	+	14.7602i	−0.0432849	+	0.0432849i
$342$		0			0
$343$	−90.0184			−0.262444
$344$	49.6855	−	21.7626i	0.144435	−	0.0632633i
$345$		0			0
$346$	141.195	+	57.3777i	0.408079	+	0.165831i
$347$	113.546	+	113.546i	0.327221	+	0.327221i	0.851529	−	0.524308i	$-0.175676\pi$
$347$	113.546	+	113.546i	0.327221	+	0.327221i	−0.524308	+	0.851529i	$0.675676\pi$
$348$		0			0
$349$	90.9653	+	90.9653i	0.260645	+	0.260645i	0.825316	−	0.564671i	$-0.190997\pi$
$349$	90.9653	+	90.9653i	0.260645	+	0.260645i	−0.564671	+	0.825316i	$0.690997\pi$
$350$	167.563	+	396.974i	0.478751	+	1.13421i
$351$		0			0
$352$	8.36902	−	22.2925i	0.0237756	−	0.0633309i
$353$	−36.2208			−0.102609			−0.0513043	−	0.998683i	$-0.516338\pi$
$353$	−36.2208			−0.102609			−0.0513043	+	0.998683i	$0.516338\pi$
$354$		0			0
$355$	−252.155	+	252.155i	−0.710294	+	0.710294i
$356$	−377.087	−	367.096i	−1.05923	−	1.03117i
$357$		0			0
$358$	−110.932	+	272.982i	−0.309866	+	0.762520i
$359$	−142.121			−0.395880			−0.197940	−	0.980214i	$-0.563425\pi$
$359$	−142.121			−0.395880			−0.197940	+	0.980214i	$0.563425\pi$
$360$		0			0
$361$			348.137i			0.964369i
$362$	−218.820	+	538.473i	−0.604475	+	1.48749i
$363$		0			0
$364$	−1009.93	+	13.5587i	−2.77452	+	0.0372491i
$365$	−324.676	−	324.676i	−0.889523	−	0.889523i
$366$		0			0
$367$		−	654.218i		−	1.78261i	−0.453404	−	0.891305i	$-0.649791\pi$
$367$		−	654.218i		−	1.78261i	0.453404	−	0.891305i	$-0.350209\pi$
$368$	−5.40633	−	201.310i	−0.0146911	−	0.547039i
$369$		0			0
$370$	239.184	+	566.652i	0.646442	+	1.53149i
$371$	−289.007	+	289.007i	−0.778995	+	0.778995i
$372$		0			0
$373$	335.277	−	335.277i	0.898867	−	0.898867i	−0.0964690	−	0.995336i	$-0.530755\pi$
$373$	335.277	−	335.277i	0.898867	−	0.898867i	0.995336	+	0.0964690i	$0.0307549\pi$
$374$	−6.50281	−	2.64255i	−0.0173872	−	0.00706565i
$375$		0			0
$376$	290.667	+	113.597i	0.773050	+	0.302118i
$377$			75.9397i			0.201432i
$378$		0			0
$379$	−98.7497	−	98.7497i	−0.260553	−	0.260553i	0.564725	−	0.825279i	$-0.308982\pi$
$379$	−98.7497	−	98.7497i	−0.260553	−	0.260553i	−0.825279	+	0.564725i	$0.808982\pi$
$380$	69.6089	+	67.7646i	0.183181	+	0.178328i
$381$		0			0
$382$	−193.081	−	457.430i	−0.505448	−	1.19746i
$383$		−	156.144i		−	0.407687i	−0.979003	−	0.203844i	$-0.934657\pi$
$383$		−	156.144i		−	0.407687i	0.979003	−	0.203844i	$-0.0653434\pi$
$384$		0			0
$385$	−52.0532			−0.135203
$386$	−239.390	+	101.046i	−0.620181	+	0.261778i
$387$		0			0
$388$	170.039	−	174.667i	0.438244	−	0.450171i
$389$	391.047	−	391.047i	1.00526	−	1.00526i	0.00527486	−	0.999986i	$-0.498321\pi$
$389$	391.047	−	391.047i	1.00526	−	1.00526i	0.999986	−	0.00527486i	$-0.00167905\pi$
$390$		0			0
$391$	−59.3639			−0.151826
$392$	168.065	−	430.038i	0.428737	−	1.09704i
$393$		0			0
$394$	−252.365	+	621.021i	−0.640520	+	1.57620i
$395$	270.349	+	270.349i	0.684427	+	0.684427i
$396$		0			0
$397$	243.862	+	243.862i	0.614262	+	0.614262i	0.944054	−	0.329791i	$-0.106978\pi$
$397$	243.862	+	243.862i	0.614262	+	0.614262i	−0.329791	+	0.944054i	$0.606978\pi$
$398$	454.210	−	191.722i	1.14123	−	0.481713i
$399$		0			0
$400$	−333.571	+	8.95828i	−0.833928	+	0.0223957i
$401$	175.261			0.437059			0.218529	−	0.975830i	$-0.429874\pi$
$401$	175.261			0.437059			0.218529	+	0.975830i	$0.429874\pi$
$402$		0			0
$403$	−484.852	+	484.852i	−1.20311	+	1.20311i
$404$	8.35218	+	622.117i	0.0206737	+	1.53989i
$405$		0			0
$406$	−59.4652	−	24.1650i	−0.146466	−	0.0595196i
$407$	−33.7935			−0.0830307
$408$		0			0
$409$		−	44.4504i		−	0.108681i	−0.998522	−	0.0543404i	$-0.982694\pi$
$409$		−	44.4504i		−	0.108681i	0.998522	−	0.0543404i	$-0.0173056\pi$
$410$	290.016	+	117.854i	0.707356	+	0.287449i
$411$		0			0
$412$	483.529	−	496.689i	1.17361	−	1.20556i
$413$	824.910	+	824.910i	1.99736	+	1.99736i
$414$		0			0
$415$		−	558.984i		−	1.34695i
$416$	274.911	−	732.279i	0.660844	−	1.76029i
$417$		0			0
$418$	−4.91741	+	2.07564i	−0.0117641	+	0.00496564i
$419$	−14.9985	+	14.9985i	−0.0357959	+	0.0357959i	−0.724778	−	0.688982i	$-0.758058\pi$
$419$	−14.9985	+	14.9985i	−0.0357959	+	0.0357959i	0.688982	+	0.724778i	$0.258058\pi$
$420$		0			0
$421$	312.907	−	312.907i	0.743247	−	0.743247i	−0.229954	−	0.973201i	$-0.573858\pi$
$421$	312.907	−	312.907i	0.743247	−	0.743247i	0.973201	+	0.229954i	$0.0738576\pi$
$422$	−14.2834	+	35.1488i	−0.0338470	+	0.0832909i
$423$		0			0
$424$	−126.991	−	289.929i	−0.299507	−	0.683795i
$425$			98.3660i			0.231449i
$426$		0			0
$427$	379.907	+	379.907i	0.889712	+	0.889712i
$428$	144.094	−	1.93452i	0.336667	−	0.00451990i
$429$		0			0
$430$	84.6006	−	35.7099i	0.196746	−	0.0830462i
$431$		−	532.400i		−	1.23527i	−0.786466	−	0.617633i	$-0.788092\pi$
$431$		−	532.400i		−	1.23527i	0.786466	−	0.617633i	$-0.211908\pi$
$432$		0			0
$433$	553.451			1.27818			0.639089	−	0.769133i	$-0.279312\pi$
$433$	553.451			1.27818			0.639089	+	0.769133i	$0.279312\pi$
$434$	−225.381	−	533.953i	−0.519312	−	1.23031i
$435$		0			0
$436$	187.001	−	2.51057i	0.428903	−	0.00575819i
$437$	−31.9197	+	31.9197i	−0.0730427	+	0.0730427i
$438$		0			0
$439$	645.291			1.46991			0.734956	−	0.678115i	$-0.237203\pi$
$439$	645.291			1.46991			0.734956	+	0.678115i	$0.237203\pi$
$440$	14.6734	−	37.5458i	0.0333487	−	0.0853315i
$441$		0			0
$442$	−213.609	−	86.8045i	−0.483278	−	0.196390i
$443$	−315.833	−	315.833i	−0.712941	−	0.712941i	0.254208	−	0.967149i	$-0.418185\pi$
$443$	−315.833	−	315.833i	−0.712941	−	0.712941i	−0.967149	+	0.254208i	$0.918185\pi$
$444$		0			0
$445$	−629.978	−	629.978i	−1.41568	−	1.41568i
$446$	−229.888	−	544.630i	−0.515444	−	1.22114i
$447$		0			0
$448$	485.937	+	448.292i	1.08468	+	1.00065i
$449$	−218.589			−0.486835			−0.243417	−	0.969922i	$-0.578268\pi$
$449$	−218.589			−0.486835			−0.243417	+	0.969922i	$0.578268\pi$
$450$		0			0
$451$	−12.1621	+	12.1621i	−0.0269670	+	0.0269670i
$452$	−391.071	+	401.715i	−0.865202	+	0.888749i
$453$		0			0
$454$	103.367	−	254.367i	0.227681	−	0.560279i
$455$	−1709.88			−3.75798
$456$		0			0
$457$			296.561i			0.648930i	0.945898	+	0.324465i	$0.105184\pi$
$457$			296.561i			0.648930i	−0.945898	+	0.324465i	$0.894816\pi$
$458$	36.4773	−	89.7634i	0.0796447	−	0.195990i
$459$		0			0
$460$	−4.57665	−	340.895i	−0.00994925	−	0.741076i
$461$	−118.061	−	118.061i	−0.256097	−	0.256097i	0.567368	−	0.823465i	$-0.307962\pi$
$461$	−118.061	−	118.061i	−0.256097	−	0.256097i	−0.823465	+	0.567368i	$0.807962\pi$
$462$		0			0
$463$			409.453i			0.884348i	0.896929	+	0.442174i	$0.145793\pi$
$463$			409.453i			0.884348i	−0.896929	+	0.442174i	$0.854207\pi$
$464$	34.1929	−	36.0802i	0.0736917	−	0.0777590i
$465$		0			0
$466$	48.8565	+	115.747i	0.104842	+	0.248383i
$467$	−494.764	+	494.764i	−1.05945	+	1.05945i	−0.0613343	+	0.998117i	$0.519536\pi$
$467$	−494.764	+	494.764i	−1.05945	+	1.05945i	−0.998117	+	0.0613343i	$0.980464\pi$
$468$		0			0
$469$	113.497	−	113.497i	0.241999	−	0.241999i
$470$	489.450	+	198.898i	1.04138	+	0.423188i
$471$		0			0
$472$	−827.542	+	362.469i	−1.75327	+	0.767943i
$473$			5.04534i			0.0106667i
$474$		0			0
$475$	52.8909	+	52.8909i	0.111349	+	0.111349i
$476$	135.946	−	139.646i	0.285601	−	0.293374i
$477$		0			0
$478$	276.810	+	655.792i	0.579100	+	1.37195i
$479$			558.806i			1.16661i	0.812254	+	0.583305i	$0.198241\pi$
$479$			558.806i			1.16661i	−0.812254	+	0.583305i	$0.801759\pi$
$480$		0			0
$481$	−1110.07			−2.30784
$482$	122.079	−	51.5296i	0.253277	−	0.106908i
$483$		0			0
$484$	−345.216	−	336.070i	−0.713256	−	0.694359i
$485$	291.806	−	291.806i	0.601661	−	0.601661i
$486$		0			0
$487$	−361.328			−0.741946			−0.370973	−	0.928644i	$-0.620976\pi$
$487$	−361.328			−0.741946			−0.370973	+	0.928644i	$0.620976\pi$
$488$	−381.119	+	166.933i	−0.780981	+	0.342075i
$489$		0			0
$490$	294.268	−	724.135i	0.600547	−	1.47783i
$491$	488.975	+	488.975i	0.995876	+	0.995876i	0.999992	−	0.00411514i	$-0.00130989\pi$
$491$	488.975	+	488.975i	0.995876	+	0.995876i	−0.00411514	+	0.999992i	$0.501310\pi$
$492$		0			0
$493$	−10.3613	−	10.3613i	−0.0210169	−	0.0210169i
$494$	−161.531	+	68.1820i	−0.326985	+	0.138020i
$495$		0			0
$496$	448.672	−	12.0494i	0.904582	−	0.0242931i
$497$	543.996			1.09456
$498$		0			0
$499$	−102.895	+	102.895i	−0.206203	+	0.206203i	−0.802652	−	0.596448i	$-0.796578\pi$
$499$	−102.895	+	102.895i	−0.206203	+	0.206203i	0.596448	+	0.802652i	$0.296578\pi$
$500$	112.245	−	1.50693i	0.224490	−	0.00301387i
$501$		0			0
$502$	−852.643	−	346.490i	−1.69849	−	0.690219i
$503$	881.975			1.75343			0.876715	−	0.481011i	$-0.159730\pi$
$503$	881.975			1.75343			0.876715	+	0.481011i	$0.159730\pi$
$504$		0			0
$505$			1053.29i			2.08572i
$506$	17.3534	+	7.05192i	0.0342952	+	0.0139366i
$507$		0			0
$508$	−117.070	−	113.968i	−0.230452	−	0.224346i
$509$	−161.639	−	161.639i	−0.317563	−	0.317563i	0.530268	−	0.847830i	$-0.322091\pi$
$509$	−161.639	−	161.639i	−0.317563	−	0.317563i	−0.847830	+	0.530268i	$0.822091\pi$
$510$		0			0
$511$			700.454i			1.37075i
$512$	−460.334	+	224.135i	−0.899090	+	0.437764i
$513$		0			0
$514$	574.906	−	242.668i	1.11849	−	0.472116i
$515$	829.791	−	829.791i	1.61124	−	1.61124i
$516$		0			0
$517$	−20.5256	+	20.5256i	−0.0397013	+	0.0397013i
$518$	353.239	−	869.252i	0.681928	−	1.67809i
$519$		0			0
$520$	482.003	−	1233.33i	0.926929	−	2.37179i
$521$		−	763.931i		−	1.46628i	−0.680078	−	0.733140i	$-0.738054\pi$
$521$		−	763.931i		−	1.46628i	0.680078	−	0.733140i	$-0.261946\pi$
$522$		0			0
$523$	295.573	+	295.573i	0.565150	+	0.565150i	0.930766	−	0.365616i	$-0.119142\pi$
$523$	295.573	+	295.573i	0.565150	+	0.565150i	−0.365616	+	0.930766i	$0.619142\pi$
$524$	−5.69668	−	424.321i	−0.0108715	−	0.809773i
$525$		0			0
$526$	309.854	−	130.789i	0.589076	−	0.248649i
$527$		−	132.308i		−	0.251059i
$528$		0			0
$529$	−370.582			−0.700532
$530$	−208.377	−	493.669i	−0.393165	−	0.931451i
$531$		0			0
$532$	−1.98944	−	148.184i	−0.00373954	−	0.278542i
$533$	−399.509	+	399.509i	−0.749549	+	0.749549i
$534$		0			0
$535$	243.961			0.456002
$536$	49.8713	+	113.859i	0.0930434	+	0.212424i
$537$		0			0
$538$	−555.814	−	225.867i	−1.03311	−	0.419827i
$539$	30.3673	+	30.3673i	0.0563401	+	0.0563401i
$540$		0			0
$541$	243.037	+	243.037i	0.449236	+	0.449236i	0.895100	−	0.445865i	$-0.147104\pi$
$541$	243.037	+	243.037i	0.449236	+	0.449236i	−0.445865	+	0.895100i	$0.647104\pi$
$542$	134.901	+	319.596i	0.248895	+	0.589660i
$543$		0			0
$544$	62.4040	+	137.423i	0.114713	+	0.252615i
$545$	316.607			0.580931
$546$		0			0
$547$	424.574	−	424.574i	0.776187	−	0.776187i	−0.202993	−	0.979180i	$-0.565067\pi$
$547$	424.574	−	424.574i	0.776187	−	0.776187i	0.979180	+	0.202993i	$0.0650669\pi$
$548$	−384.144	−	373.966i	−0.700992	−	0.682419i
$549$		0			0
$550$	11.6850	−	28.7545i	0.0212455	−	0.0522810i
$551$	−11.1425			−0.0202223
$552$		0			0
$553$		−	583.248i		−	1.05470i
$554$	−40.8946	+	100.634i	−0.0738171	+	0.181649i
$555$		0			0
$556$	129.416	−	1.73746i	0.232763	−	0.00312493i
$557$	445.773	+	445.773i	0.800311	+	0.800311i	0.983144	−	0.182833i	$-0.0585268\pi$
$557$	445.773	+	445.773i	0.800311	+	0.800311i	−0.182833	+	0.983144i	$0.558527\pi$
$558$		0			0
$559$			165.733i			0.296481i
$560$	812.392	+	769.898i	1.45070	+	1.37482i
$561$		0			0
$562$	173.884	+	411.951i	0.309402	+	0.733008i
$563$	529.295	−	529.295i	0.940133	−	0.940133i	−0.0581732	−	0.998307i	$-0.518528\pi$
$563$	529.295	−	529.295i	0.940133	−	0.940133i	0.998307	+	0.0581732i	$0.0185276\pi$
$564$		0			0
$565$	−671.123	+	671.123i	−1.18783	+	1.18783i
$566$	649.200	+	263.816i	1.14700	+	0.466107i
$567$		0			0
$568$	−153.349	+	392.383i	−0.269980	+	0.690815i
$569$			346.814i			0.609516i	0.952430	+	0.304758i	$0.0985755\pi$
$569$			346.814i			0.609516i	−0.952430	+	0.304758i	$0.901424\pi$
$570$		0			0
$571$	−155.711	−	155.711i	−0.272699	−	0.272699i	0.557487	−	0.830186i	$-0.311766\pi$
$571$	−155.711	−	155.711i	−0.272699	−	0.272699i	−0.830186	+	0.557487i	$0.811766\pi$
$572$	52.1309	+	50.7497i	0.0911380	+	0.0887233i
$573$		0			0
$574$	−185.710	−	439.968i	−0.323537	−	0.766495i
$575$		−	262.499i		−	0.456520i
$576$		0			0
$577$	620.510			1.07541			0.537704	−	0.843134i	$-0.319292\pi$
$577$	620.510			1.07541			0.537704	+	0.843134i	$0.319292\pi$
$578$	−491.517	+	207.469i	−0.850375	+	0.358943i
$579$		0			0
$580$	58.7007	−	60.2983i	0.101208	−	0.103963i
$581$	−602.974	+	602.974i	−1.03782	+	1.03782i
$582$		0			0
$583$	29.4410			0.0504992
$584$	−505.235	−	197.453i	−0.865129	−	0.338104i
$585$		0			0
$586$	108.891	−	267.960i	0.185821	−	0.457269i
$587$	−561.656	−	561.656i	−0.956825	−	0.956825i	0.0422810	−	0.999106i	$-0.486538\pi$
$587$	−561.656	−	561.656i	−0.956825	−	0.956825i	−0.999106	+	0.0422810i	$0.986538\pi$
$588$		0			0
$589$	−71.1413	−	71.1413i	−0.120783	−	0.120783i
$590$	−1409.07	+	594.770i	−2.38826	+	1.00808i
$591$		0			0
$592$	527.413	+	499.826i	0.890901	+	0.844301i
$593$	−851.739			−1.43632			−0.718161	−	0.695877i	$-0.755016\pi$
$593$	−851.739			−1.43632			−0.718161	+	0.695877i	$0.755016\pi$
$594$		0			0
$595$	233.299	−	233.299i	0.392099	−	0.392099i
$596$	−0.707843	−	52.7241i	−0.00118766	−	0.0884633i
$597$		0			0
$598$	570.036	+	231.646i	0.953237	+	0.387368i
$599$	1001.69			1.67228			0.836138	−	0.548519i	$-0.184808\pi$
$599$	1001.69			1.67228			0.836138	+	0.548519i	$0.184808\pi$
$600$		0			0
$601$		−	955.182i		−	1.58932i	−0.607054	−	0.794661i	$-0.707649\pi$
$601$		−	955.182i		−	1.58932i	0.607054	−	0.794661i	$-0.292351\pi$
$602$	−129.778	−	52.7382i	−0.215579	−	0.0876050i
$603$		0			0
$604$	−141.018	+	144.856i	−0.233473	+	0.239827i
$605$	−576.734	−	576.734i	−0.953279	−	0.953279i
$606$		0			0
$607$			291.885i			0.480865i	0.970666	+	0.240432i	$0.0772892\pi$
$607$			291.885i			0.480865i	−0.970666	+	0.240432i	$0.922711\pi$
$608$	107.446	+	40.3371i	0.176720	+	0.0663440i
$609$		0			0
$610$	−648.940	+	273.917i	−1.06384	+	0.449045i
$611$	−674.238	+	674.238i	−1.10350	+	1.10350i
$612$		0			0
$613$	−332.933	+	332.933i	−0.543121	+	0.543121i	−0.924442	−	0.381322i	$-0.875469\pi$
$613$	−332.933	+	332.933i	−0.543121	+	0.543121i	0.381322	+	0.924442i	$0.375469\pi$
$614$	147.257	−	362.371i	0.239833	−	0.590181i
$615$		0			0
$616$	−56.3287	+	24.6724i	−0.0914427	+	0.0400526i
$617$			970.864i			1.57352i	0.617257	+	0.786762i	$0.288244\pi$
$617$			970.864i			1.57352i	−0.617257	+	0.786762i	$0.711756\pi$
$618$		0			0
$619$	−696.761	−	696.761i	−1.12562	−	1.12562i	−0.990881	−	0.134744i	$-0.956979\pi$
$619$	−696.761	−	696.761i	−1.12562	−	1.12562i	−0.134744	−	0.990881i	$-0.543021\pi$
$620$	759.773	−	10.2003i	1.22544	−	0.0164520i
$621$		0			0
$622$	−379.183	+	160.053i	−0.609619	+	0.257320i
$623$			1359.11i			2.18156i
$624$		0			0
$625$	711.432			1.13829
$626$	174.108	+	412.481i	0.278128	+	0.658915i
$627$		0			0
$628$	−542.355	+	7.28135i	−0.863623	+	0.0115945i
$629$	151.460	−	151.460i	0.240795	−	0.240795i
$630$		0			0
$631$	−377.591			−0.598401			−0.299200	−	0.954190i	$-0.596720\pi$
$631$	−377.591			−0.598401			−0.299200	+	0.954190i	$0.596720\pi$
$632$	420.695	+	164.413i	0.665657	+	0.260148i
$633$		0			0
$634$	462.457	+	187.929i	0.729427	+	0.296418i
$635$	−195.582	−	195.582i	−0.308003	−	0.308003i
$636$		0			0
$637$	997.527	+	997.527i	1.56598	+	1.56598i
$638$	1.79801	+	4.25968i	0.00281820	+	0.00667661i
$639$		0			0
$640$	−784.333	+	368.947i	−1.22552	+	0.576480i
$641$	−729.200			−1.13760			−0.568799	−	0.822477i	$-0.692592\pi$
$641$	−729.200			−1.13760			−0.568799	+	0.822477i	$0.692592\pi$
$642$		0			0
$643$	243.958	−	243.958i	0.379406	−	0.379406i	−0.491482	−	0.870888i	$-0.663545\pi$
$643$	243.958	−	243.958i	0.379406	−	0.379406i	0.870888	+	0.491482i	$0.163545\pi$
$644$	−362.785	+	372.659i	−0.563331	+	0.578663i
$645$		0			0
$646$	12.7366	−	31.3423i	0.0197161	−	0.0485176i
$647$	281.594			0.435230			0.217615	−	0.976035i	$-0.430172\pi$
$647$	281.594			0.435230			0.217615	+	0.976035i	$0.430172\pi$
$648$		0			0
$649$		−	84.0331i		−	0.129481i
$650$	383.838	−	944.549i	0.590520	−	1.45315i
$651$		0			0
$652$	10.6986	+	796.893i	0.0164089	+	1.22223i
$653$	−323.704	−	323.704i	−0.495718	−	0.495718i	0.414384	−	0.910102i	$-0.363997\pi$
$653$	−323.704	−	323.704i	−0.495718	−	0.495718i	−0.910102	+	0.414384i	$0.863997\pi$
$654$		0			0
$655$		−	718.407i		−	1.09680i
$656$	369.698	−	9.92850i	0.563564	−	0.0151349i
$657$		0			0
$658$	−313.417	−	742.519i	−0.476317	−	1.12845i
$659$	−507.811	+	507.811i	−0.770578	+	0.770578i	−0.978208	−	0.207629i	$-0.933425\pi$
$659$	−507.811	+	507.811i	−0.770578	+	0.770578i	0.207629	+	0.978208i	$0.433425\pi$
$660$		0			0
$661$	57.1593	−	57.1593i	0.0864741	−	0.0864741i	−0.662547	−	0.749021i	$-0.730524\pi$
$661$	57.1593	−	57.1593i	0.0864741	−	0.0864741i	0.749021	+	0.662547i	$0.230524\pi$
$662$	−481.981	−	195.863i	−0.728068	−	0.295866i
$663$		0			0
$664$	−264.949	−	604.897i	−0.399020	−	0.910990i
$665$		−	250.887i		−	0.377274i
$666$		0			0
$667$	27.6502	+	27.6502i	0.0414546	+	0.0414546i
$668$	300.919	−	309.109i	0.450478	−	0.462739i
$669$		0			0
$670$	81.8329	+	193.871i	0.122139	+	0.289360i
$671$		−	38.7009i		−	0.0576765i
$672$		0			0
$673$	1110.84			1.65059			0.825293	−	0.564705i	$-0.191010\pi$
$673$	1110.84			1.65059			0.825293	+	0.564705i	$0.191010\pi$
$674$	23.4307	−	9.89007i	0.0347636	−	0.0146737i
$675$		0			0
$676$	1228.06	+	1195.52i	1.81665	+	1.76852i
$677$	−397.465	+	397.465i	−0.587097	+	0.587097i	−0.936844	−	0.349747i	$-0.886268\pi$
$677$	−397.465	+	397.465i	−0.587097	+	0.587097i	0.349747	+	0.936844i	$0.386268\pi$
$678$		0			0
$679$	−629.539			−0.927156
$680$	102.512	+	234.043i	0.150754	+	0.344181i
$681$		0			0
$682$	−15.7170	+	38.6765i	−0.0230455	+	0.0567104i
$683$	238.015	+	238.015i	0.348485	+	0.348485i	0.859545	−	0.511060i	$-0.170747\pi$
$683$	238.015	+	238.015i	0.348485	+	0.348485i	−0.511060	+	0.859545i	$0.670747\pi$
$684$		0			0
$685$	−641.768	−	641.768i	−0.936887	−	0.936887i
$686$	−165.866	+	70.0120i	−0.241787	+	0.102058i
$687$		0			0
$688$	74.6236	−	78.7423i	0.108464	−	0.114451i
$689$	967.099			1.40363
$690$		0			0
$691$	−685.172	+	685.172i	−0.991565	+	0.991565i	−0.999965	−	0.00839951i	$-0.997326\pi$
$691$	−685.172	+	685.172i	−0.991565	+	0.991565i	0.00839951	+	0.999965i	$0.497326\pi$
$692$	304.789	−	4.09192i	0.440447	−	0.00591318i
$693$		0			0
$694$	297.528	+	120.907i	0.428714	+	0.174217i
$695$	219.111			0.315267
$696$		0			0
$697$		−	109.019i		−	0.156412i
$698$	238.359	+	96.8624i	0.341489	+	0.138771i
$699$		0			0
$700$	617.495	+	601.135i	0.882136	+	0.858764i
$701$	−543.074	−	543.074i	−0.774713	−	0.774713i	0.204214	−	0.978926i	$-0.434536\pi$
$701$	−543.074	−	543.074i	−0.774713	−	0.774713i	−0.978926	+	0.204214i	$0.934536\pi$
$702$		0			0
$703$		−	162.879i		−	0.231691i
$704$	−1.91746	−	47.5847i	−0.00272366	−	0.0675919i
$705$		0			0
$706$	−66.7398	+	28.1708i	−0.0945323	+	0.0399020i
$707$	1136.18	−	1136.18i	1.60704	−	1.60704i
$708$		0			0
$709$	−488.019	+	488.019i	−0.688320	+	0.688320i	−0.961860	−	0.273541i	$-0.911805\pi$
$709$	−488.019	+	488.019i	−0.688320	+	0.688320i	0.273541	+	0.961860i	$0.411805\pi$
$710$	−268.501	+	660.729i	−0.378171	+	0.930604i
$711$		0			0
$712$	−980.322	−	383.123i	−1.37686	−	0.538094i
$713$			353.076i			0.495198i
$714$		0			0
$715$	87.0923	+	87.0923i	0.121807	+	0.121807i
$716$	7.91118	+	589.269i	0.0110491	+	0.823002i
$717$		0			0
$718$	−261.869	+	110.535i	−0.364721	+	0.153948i
$719$		−	297.369i		−	0.413587i	−0.978385	−	0.206793i	$-0.933697\pi$
$719$		−	297.369i		−	0.413587i	0.978385	−	0.206793i	$-0.0663028\pi$
$720$		0			0
$721$	−1790.18			−2.48292
$722$	270.764	+	641.470i	0.375020	+	0.888463i
$723$		0			0
$724$	15.6053	+	1162.37i	0.0215542	+	1.60548i
$725$	45.8164	−	45.8164i	0.0631950	−	0.0631950i
$726$		0			0
$727$	1158.85			1.59402			0.797009	−	0.603967i	$-0.206414\pi$
$727$	1158.85			1.59402			0.797009	+	0.603967i	$0.206414\pi$
$728$	−1850.33	+	810.456i	−2.54166	+	1.11326i
$729$		0			0
$730$	−850.759	−	345.724i	−1.16542	−	0.473595i
$731$	−22.6128	−	22.6128i	−0.0309341	−	0.0309341i
$732$		0			0
$733$	−348.835	−	348.835i	−0.475901	−	0.475901i	0.427917	−	0.903818i	$-0.359248\pi$
$733$	−348.835	−	348.835i	−0.475901	−	0.475901i	−0.903818	+	0.427917i	$0.859248\pi$
$734$	−508.819	−	1205.45i	−0.693215	−	1.64230i
$735$		0			0
$736$	−166.531	−	366.726i	−0.226265	−	0.498269i
$737$	−11.5619			−0.0156878
$738$		0			0
$739$	825.489	−	825.489i	1.11703	−	1.11703i	0.124860	−	0.992174i	$-0.460152\pi$
$739$	825.489	−	825.489i	1.11703	−	1.11703i	0.992174	−	0.124860i	$-0.0398482\pi$
$740$	881.430	+	858.076i	1.19112	+	1.15956i
$741$		0			0
$742$	−307.743	+	757.295i	−0.414748	+	1.02061i
$743$	899.725			1.21094			0.605468	−	0.795870i	$-0.292986\pi$
$743$	899.725			1.21094			0.605468	+	0.795870i	$0.292986\pi$
$744$		0			0
$745$		−	89.2659i		−	0.119820i
$746$	357.013	−	878.538i	0.478569	−	1.17767i
$747$		0			0
$748$	−14.0372	+	0.188455i	−0.0187663	+	0.000251945i
$749$	−263.160	−	263.160i	−0.351348	−	0.351348i
$750$		0			0
$751$		−	80.4386i		−	0.107109i	−0.998565	−	0.0535543i	$-0.982945\pi$
$751$		−	80.4386i		−	0.107109i	0.998565	−	0.0535543i	$-0.0170550\pi$
$752$	623.927	−	16.7560i	0.829690	−	0.0222819i
$753$		0			0
$754$	59.0623	+	139.925i	0.0783319	+	0.185577i
$755$	−242.003	+	242.003i	−0.320533	+	0.320533i
$756$		0			0
$757$	233.298	−	233.298i	0.308187	−	0.308187i	−0.536019	−	0.844206i	$-0.680072\pi$
$757$	233.298	−	233.298i	0.308187	−	0.308187i	0.844206	+	0.536019i	$0.180072\pi$
$758$	−258.757	−	105.151i	−0.341368	−	0.138722i
$759$		0			0
$760$	180.964	+	70.7233i	0.238111	+	0.0930569i
$761$			56.1906i			0.0738378i	0.999318	+	0.0369189i	$0.0117543\pi$
$761$			56.1906i			0.0738378i	−0.999318	+	0.0369189i	$0.988246\pi$
$762$		0			0
$763$	−341.523	−	341.523i	−0.447606	−	0.447606i
$764$	−711.535	−	692.682i	−0.931328	−	0.906652i
$765$		0			0
$766$	−121.441	−	287.708i	−0.158540	−	0.375598i
$767$		−	2760.38i		−	3.59893i
$768$		0			0
$769$	517.343			0.672748			0.336374	−	0.941728i	$-0.390799\pi$
$769$	517.343			0.672748			0.336374	+	0.941728i	$0.390799\pi$
$770$	−95.9122	+	40.4845i	−0.124561	+	0.0525773i
$771$		0			0
$772$	−362.506	+	372.372i	−0.469567	+	0.482347i
$773$	523.925	−	523.925i	0.677781	−	0.677781i	−0.281716	−	0.959498i	$-0.590904\pi$
$773$	523.925	−	523.925i	0.677781	−	0.677781i	0.959498	+	0.281716i	$0.0909037\pi$
$774$		0			0
$775$	585.048			0.754900
$776$	177.463	−	454.085i	0.228689	−	0.585161i
$777$		0			0
$778$	416.397	−	1024.67i	0.535215	−	1.31706i
$779$	−58.6192	−	58.6192i	−0.0752492	−	0.0752492i
$780$		0			0
$781$	−27.7083	−	27.7083i	−0.0354780	−	0.0354780i
$782$	−109.383	+	46.1704i	−0.139876	+	0.0590414i
$783$		0			0
$784$	−24.7903	−	923.092i	−0.0316202	−	1.17741i
$785$	−918.248			−1.16974
$786$		0			0
$787$	−46.6965	+	46.6965i	−0.0593348	+	0.0593348i	−0.736152	−	0.676817i	$-0.763359\pi$
$787$	−46.6965	+	46.6965i	−0.0593348	+	0.0593348i	0.676817	+	0.736152i	$0.263359\pi$
$788$	17.9975	+	1340.56i	0.0228395	+	1.70122i
$789$		0			0
$790$	708.403	+	287.875i	0.896713	+	0.364398i
$791$	1447.87			1.83044
$792$		0			0
$793$		−	1271.27i		−	1.60312i
$794$	639.000	+	259.671i	0.804786	+	0.327042i
$795$		0			0
$796$	687.806	−	706.526i	0.864078	−	0.887595i
$797$	−127.126	−	127.126i	−0.159505	−	0.159505i	0.622842	−	0.782348i	$-0.285978\pi$
$797$	−127.126	−	127.126i	−0.159505	−	0.159505i	−0.782348	+	0.622842i	$0.785978\pi$
$798$		0			0
$799$		−	183.988i		−	0.230273i
$800$	−607.665	+	275.942i	−0.759581	+	0.344928i
$801$		0			0
$802$	322.932	−	136.309i	0.402658	−	0.169962i
$803$	35.6774	−	35.6774i	0.0444302	−	0.0444302i
$804$		0			0
$805$	−622.580	+	622.580i	−0.773392	+	0.773392i
$806$	−516.284	+	1270.47i	−0.640551	+	1.57627i
$807$		0			0
$808$	499.243	+	1139.80i	0.617874	+	1.41065i
$809$		−	1047.16i		−	1.29439i	−0.762325	−	0.647194i	$-0.775942\pi$
$809$		−	1047.16i		−	1.29439i	0.762325	−	0.647194i	$-0.224058\pi$
$810$		0			0
$811$	−112.206	−	112.206i	−0.138356	−	0.138356i	0.634537	−	0.772893i	$-0.281191\pi$
$811$	−112.206	−	112.206i	−0.138356	−	0.138356i	−0.772893	+	0.634537i	$0.781191\pi$
$812$	−128.364	+	1.72334i	−0.158083	+	0.00212234i
$813$		0			0
$814$	−62.2672	+	26.2830i	−0.0764954	+	0.0322887i
$815$			1349.20i			1.65546i
$816$		0			0
$817$	−24.3176			−0.0297645
$818$	−34.5714	−	81.9035i	−0.0422633	−	0.100126i
$819$		0			0
$820$	626.039	−	8.40484i	0.763463	−	0.0102498i
$821$	7.63080	−	7.63080i	0.00929452	−	0.00929452i	−0.702444	−	0.711739i	$-0.747908\pi$
$821$	7.63080	−	7.63080i	0.00929452	−	0.00929452i	0.711739	+	0.702444i	$0.247908\pi$
$822$		0			0
$823$	1316.28			1.59937			0.799687	−	0.600417i	$-0.204999\pi$
$823$	1316.28			1.59937			0.799687	+	0.600417i	$0.204999\pi$
$824$	504.640	−	1291.26i	0.612427	−	1.56706i
$825$		0			0
$826$	2161.54	+	878.387i	2.61687	+	1.06342i
$827$	−341.515	−	341.515i	−0.412957	−	0.412957i	0.469810	−	0.882767i	$-0.344322\pi$
$827$	−341.515	−	341.515i	−0.412957	−	0.412957i	−0.882767	+	0.469810i	$0.844322\pi$
$828$		0			0
$829$	−621.672	−	621.672i	−0.749905	−	0.749905i	0.224556	−	0.974461i	$-0.427907\pi$
$829$	−621.672	−	621.672i	−0.749905	−	0.749905i	−0.974461	+	0.224556i	$0.927907\pi$
$830$	−434.751	−	1029.97i	−0.523796	−	1.24093i
$831$		0			0
$832$	−62.9859	−	1563.10i	−0.0757042	−	1.87872i
$833$	−272.208			−0.326781
$834$		0			0
$835$	516.412	−	516.412i	0.618457	−	0.618457i
$836$	−7.44640	+	7.64906i	−0.00890717	+	0.00914959i
$837$		0			0
$838$	−15.9708	+	39.3010i	−0.0190582	+	0.0468986i
$839$	−1440.49			−1.71692			−0.858459	−	0.512883i	$-0.828578\pi$
$839$	−1440.49			−1.71692			−0.858459	+	0.512883i	$0.828578\pi$
$840$		0			0
$841$		−	831.348i		−	0.988523i
$842$	333.192	−	819.921i	0.395715	−	0.973778i
$843$		0			0
$844$	1.01863	+	75.8734i	0.00120691	+	0.0898974i
$845$	2051.65	+	2051.65i	2.42798	+	2.42798i
$846$		0			0
$847$			1244.24i			1.46900i
$848$	−459.484	−	435.450i	−0.541845	−	0.513503i
$849$		0			0
$850$	76.5043	+	181.247i	0.0900051	+	0.213232i
$851$	−404.186	+	404.186i	−0.474954	+	0.474954i
$852$		0			0
$853$	−625.193	+	625.193i	−0.732934	+	0.732934i	−0.971200	−	0.238266i	$-0.923421\pi$
$853$	−625.193	+	625.193i	−0.732934	+	0.732934i	0.238266	+	0.971200i	$0.423421\pi$
$854$	995.482	+	404.535i	1.16567	+	0.473695i
$855$		0			0
$856$	264.000	−	115.634i	0.308411	−	0.135086i
$857$		−	1105.18i		−	1.28959i	−0.764356	−	0.644794i	$-0.776943\pi$
$857$		−	1105.18i		−	1.28959i	0.764356	−	0.644794i	$-0.223057\pi$
$858$		0			0
$859$	379.841	+	379.841i	0.442190	+	0.442190i	0.892747	−	0.450558i	$-0.148775\pi$
$859$	379.841	+	379.841i	0.442190	+	0.442190i	−0.450558	+	0.892747i	$0.648775\pi$
$860$	128.110	−	131.597i	0.148965	−	0.153019i
$861$		0			0
$862$	−414.075	−	980.989i	−0.480365	−	1.13804i
$863$			381.969i			0.442606i	0.975205	+	0.221303i	$0.0710311\pi$
$863$			381.969i			0.442606i	−0.975205	+	0.221303i	$0.928969\pi$
$864$		0			0
$865$	516.031			0.596567
$866$	1019.78	−	430.448i	1.17757	−	0.497053i
$867$		0			0
$868$	−830.567	−	808.561i	−0.956874	−	0.931521i
$869$	−29.7076	+	29.7076i	−0.0341859	+	0.0341859i
$870$		0			0
$871$	−379.794			−0.436044
$872$	342.613	−	150.067i	0.392904	−	0.172095i
$873$		0			0
$874$	−33.9890	+	83.6401i	−0.0388890	+	0.0956981i
$875$	−204.994	−	204.994i	−0.234279	−	0.234279i
$876$		0			0
$877$	638.602	+	638.602i	0.728166	+	0.728166i	0.970254	−	0.242088i	$-0.0778323\pi$
$877$	638.602	+	638.602i	0.728166	+	0.728166i	−0.242088	+	0.970254i	$0.577832\pi$
$878$	1189.00	−	501.877i	1.35421	−	0.571614i
$879$		0			0
$880$	−2.16439	−	80.5935i	−0.00245954	−	0.0915835i
$881$	1362.97			1.54707			0.773533	−	0.633756i	$-0.218488\pi$
$881$	1362.97			1.54707			0.773533	+	0.633756i	$0.218488\pi$
$882$		0			0
$883$	−897.988	+	897.988i	−1.01697	+	1.01697i	−0.0171209	+	0.999853i	$0.505450\pi$
$883$	−897.988	+	897.988i	−1.01697	+	1.01697i	−0.999853	+	0.0171209i	$0.994550\pi$
$884$	−461.104	+	6.19051i	−0.521610	+	0.00700284i
$885$		0			0
$886$	−827.587	−	336.308i	−0.934071	−	0.379580i
$887$	−1343.56			−1.51472			−0.757359	−	0.652998i	$-0.773511\pi$
$887$	−1343.56			−1.51472			−0.757359	+	0.652998i	$0.773511\pi$
$888$		0			0
$889$			421.947i			0.474631i
$890$	−1650.75	−	670.818i	−1.85478	−	0.753728i
$891$		0			0
$892$	−847.174	−	824.728i	−0.949746	−	0.924583i
$893$	−98.9295	−	98.9295i	−0.110783	−	0.110783i
$894$		0			0
$895$			997.676i			1.11472i
$896$	1244.04	+	448.075i	1.38844	+	0.500084i
$897$		0			0
$898$	−402.767	+	170.008i	−0.448516	+	0.189318i
$899$	−61.6257	+	61.6257i	−0.0685491	+	0.0685491i
$900$		0			0
$901$	−131.952	+	131.952i	−0.146451	+	0.146451i
$902$	−12.9506	+	31.8688i	−0.0143576	+	0.0353312i
$903$		0			0
$904$	−408.146	+	1044.35i	−0.451488	+	1.15525i
$905$			1967.97i			2.17456i
$906$		0			0
$907$	−671.651	−	671.651i	−0.740519	−	0.740519i	0.232159	−	0.972678i	$-0.425421\pi$
$907$	−671.651	−	671.651i	−0.740519	−	0.740519i	−0.972678	+	0.232159i	$0.925421\pi$
$908$	−7.37170	−	549.085i	−0.00811861	−	0.604720i
$909$		0			0
$910$	−3150.59	+	1329.86i	−3.46219	+	1.46139i
$911$			770.729i			0.846025i	0.906124	+	0.423012i	$0.139027\pi$
$911$			770.729i			0.846025i	−0.906124	+	0.423012i	$0.860973\pi$
$912$		0			0
$913$	61.4246			0.0672778
$914$	230.651	+	546.438i	0.252354	+	0.597853i
$915$		0			0
$916$	−2.60140	−	193.767i	−0.00283995	−	0.211536i
$917$	−774.942	+	774.942i	−0.845084	+	0.845084i
$918$		0			0
$919$	−1153.98			−1.25569			−0.627843	−	0.778340i	$-0.716062\pi$
$919$	−1153.98			−1.25569			−0.627843	+	0.778340i	$0.716062\pi$
$920$	−273.565	−	624.567i	−0.297353	−	0.678877i
$921$		0			0
$922$	−309.358	−	125.714i	−0.335529	−	0.136350i
$923$	−910.182	−	910.182i	−0.986112	−	0.986112i
$924$		0			0
$925$	669.736	+	669.736i	0.724039	+	0.724039i
$926$	318.453	+	754.450i	0.343902	+	0.814741i
$927$		0			0
$928$	34.9418	−	93.0742i	0.0376528	−	0.100296i
$929$	652.736			0.702622			0.351311	−	0.936259i	$-0.385736\pi$
$929$	652.736			0.702622			0.351311	+	0.936259i	$0.385736\pi$
$930$		0			0
$931$	−146.365	+	146.365i	−0.157213	+	0.157213i
$932$	180.044	+	175.274i	0.193180	+	0.188062i
$933$		0			0
$934$	−526.838	+	1296.45i	−0.564067	+	1.38806i
$935$	−23.7660			−0.0254182
$936$		0			0
$937$			644.074i			0.687378i	0.939083	+	0.343689i	$0.111677\pi$
$937$			644.074i			0.687378i	−0.939083	+	0.343689i	$0.888323\pi$
$938$	120.855	−	297.401i	0.128843	−	0.317059i
$939$		0			0
$940$	1056.54	−	14.1845i	1.12398	−	0.0150899i
$941$	−171.348	−	171.348i	−0.182092	−	0.182092i	0.610175	−	0.792267i	$-0.291099\pi$
$941$	−171.348	−	171.348i	−0.182092	−	0.182092i	−0.792267	+	0.610175i	$0.791099\pi$
$942$		0			0
$943$			290.929i			0.308514i
$944$	−1242.90	+	1311.50i	−1.31663	+	1.38930i
$945$		0			0
$946$	3.92402	+	9.29644i	0.00414801	+	0.00982710i
$947$	−731.249	+	731.249i	−0.772174	+	0.772174i	−0.978486	−	0.206312i	$-0.933854\pi$
$947$	−731.249	+	731.249i	−0.772174	+	0.772174i	0.206312	+	0.978486i	$0.433854\pi$
$948$		0			0
$949$	1171.96	−	1171.96i	1.23494	−	1.23494i
$950$	138.592	+	56.3197i	0.145886	+	0.0592839i
$951$		0			0
$952$	141.881	−	363.041i	0.149035	−	0.381345i
$953$		−	1745.08i		−	1.83115i	−0.402152	−	0.915573i	$-0.631738\pi$
$953$		−	1745.08i		−	1.83115i	0.402152	−	0.915573i	$-0.368262\pi$
$954$		0			0
$955$	−1188.72	−	1188.72i	−1.24473	−	1.24473i
$956$	1020.09	+	993.060i	1.06704	+	1.03877i
$957$		0			0
$958$	434.612	+	1029.64i	0.453666	+	1.07479i
$959$			1384.54i			1.44374i
$960$		0			0
$961$	174.077			0.181142
$962$	−2045.40	+	863.362i	−2.12619	+	0.897465i
$963$		0			0
$964$	184.864	−	189.895i	0.191767	−	0.196986i
$965$	−622.102	+	622.102i	−0.644665	+	0.644665i
$966$		0			0
$967$	904.237			0.935095			0.467548	−	0.883968i	$-0.345138\pi$
$967$	904.237			0.935095			0.467548	+	0.883968i	$0.345138\pi$
$968$	−897.467	−	350.743i	−0.927136	−	0.362337i
$969$		0			0
$970$	310.723	−	764.628i	0.320333	−	0.788276i
$971$	1010.37	+	1010.37i	1.04055	+	1.04055i	0.999143	+	0.0414029i	$0.0131827\pi$
$971$	1010.37	+	1010.37i	1.04055	+	1.04055i	0.0414029	+	0.999143i	$0.486817\pi$
$972$		0			0
$973$	−236.354	−	236.354i	−0.242913	−	0.242913i
$974$	−665.775	+	281.023i	−0.683547	+	0.288525i
$975$		0			0
$976$	−572.410	+	604.003i	−0.586485	+	0.618856i
$977$	396.922			0.406266			0.203133	−	0.979151i	$-0.434888\pi$
$977$	396.922			0.406266			0.203133	+	0.979151i	$0.434888\pi$
$978$		0			0
$979$	69.2259	−	69.2259i	0.0707108	−	0.0707108i
$980$	−20.9859	−	1563.14i	−0.0214142	−	1.59505i
$981$		0			0
$982$	1281.28	+	520.675i	1.30476	+	0.530218i
$983$	−1672.52			−1.70145			−0.850724	−	0.525612i	$-0.823836\pi$
$983$	−1672.52			−1.70145			−0.850724	+	0.525612i	$0.823836\pi$
$984$		0			0
$985$			2269.66i			2.30423i
$986$	−27.1501	−	11.0330i	−0.0275356	−	0.0111897i
$987$		0			0
$988$	−244.604	+	251.262i	−0.247575	+	0.254313i
$989$	60.3446	+	60.3446i	0.0610157	+	0.0610157i
$990$		0			0
$991$		−	775.801i		−	0.782847i	−0.920211	−	0.391423i	$-0.871983\pi$
$991$		−	775.801i		−	0.782847i	0.920211	−	0.391423i	$-0.128017\pi$
$992$	817.343	−	371.158i	0.823935	−	0.374151i
$993$		0			0
$994$	1002.36	−	423.094i	1.00841	−	0.425648i
$995$	1180.35	−	1180.35i	1.18629	−	1.18629i
$996$		0			0
$997$	201.495	−	201.495i	0.202101	−	0.202101i	−0.598799	−	0.800900i	$-0.704355\pi$
$997$	201.495	−	201.495i	0.202101	−	0.202101i	0.800900	+	0.598799i	$0.204355\pi$
$998$	−109.566	+	269.620i	−0.109786	+	0.270161i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.3.m.c.19.8		16
3.2	odd	2		48.3.l.a.19.1	✓	16
4.3	odd	2		576.3.m.c.559.7		16
8.3	odd	2		1152.3.m.c.991.2		16
8.5	even	2		1152.3.m.f.991.2		16
12.11	even	2		192.3.l.a.175.5		16
16.3	odd	4		1152.3.m.f.415.2		16
16.5	even	4		576.3.m.c.271.7		16
16.11	odd	4	inner	144.3.m.c.91.8		16
16.13	even	4		1152.3.m.c.415.2		16
24.5	odd	2		384.3.l.a.223.8		16
24.11	even	2		384.3.l.b.223.4		16
48.5	odd	4		192.3.l.a.79.5		16
48.11	even	4		48.3.l.a.43.1	yes	16
48.29	odd	4		384.3.l.b.31.4		16
48.35	even	4		384.3.l.a.31.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.3.l.a.19.1	✓	16	3.2	odd	2
48.3.l.a.43.1	yes	16	48.11	even	4
144.3.m.c.19.8		16	1.1	even	1	trivial
144.3.m.c.91.8		16	16.11	odd	4	inner
192.3.l.a.79.5		16	48.5	odd	4
192.3.l.a.175.5		16	12.11	even	2
384.3.l.a.31.8		16	48.35	even	4
384.3.l.a.223.8		16	24.5	odd	2
384.3.l.b.31.4		16	48.29	odd	4
384.3.l.b.223.4		16	24.11	even	2
576.3.m.c.271.7		16	16.5	even	4
576.3.m.c.559.7		16	4.3	odd	2
1152.3.m.c.415.2		16	16.13	even	4
1152.3.m.c.991.2		16	8.3	odd	2
1152.3.m.f.415.2		16	16.3	odd	4
1152.3.m.f.991.2		16	8.5	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	144.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.84258 - 0.777752i) q^{2} +(2.79020 - 2.86614i) q^{4} +(4.78830 - 4.78830i) q^{5} -10.3302 q^{7} +(2.91202 - 7.45118i) q^{8} +O(q^{10})\)	\(q+(1.84258 - 0.777752i) q^{2} +(2.79020 - 2.86614i) q^{4} +(4.78830 - 4.78830i) q^{5} -10.3302 q^{7} +(2.91202 - 7.45118i) q^{8} +(5.09872 - 12.5469i) q^{10} +(0.526169 + 0.526169i) q^{11} +(17.2840 + 17.2840i) q^{13} +(-19.0343 + 8.03437i) q^{14} +(-0.429536 - 15.9942i) q^{16} -4.71650 q^{17} +(-2.53604 + 2.53604i) q^{19} +(-0.363618 - 27.0843i) q^{20} +(1.37874 + 0.560279i) q^{22} +12.5864 q^{23} -20.8557i q^{25} +(45.2897 + 18.4044i) q^{26} +(-28.8235 + 29.6080i) q^{28} +(2.19683 + 2.19683i) q^{29} +28.0521i q^{31} +(-13.2310 - 29.1366i) q^{32} +(-8.69052 + 3.66827i) q^{34} +(-49.4644 + 49.4644i) q^{35} +(-32.1128 + 32.1128i) q^{37} +(-2.70044 + 6.64526i) q^{38} +(-21.7349 - 49.6222i) q^{40} +23.1145i q^{41} +(4.79441 + 4.79441i) q^{43} +(2.97619 - 0.0399566i) q^{44} +(23.1915 - 9.78913i) q^{46} +39.0095i q^{47} +57.7141 q^{49} +(-16.2206 - 38.4283i) q^{50} +(97.7640 - 1.31252i) q^{52} +(27.9768 - 27.9768i) q^{53} +5.03891 q^{55} +(-30.0819 + 76.9726i) q^{56} +(5.75642 + 2.33924i) q^{58} +(-79.8538 - 79.8538i) q^{59} +(-36.7762 - 36.7762i) q^{61} +(21.8176 + 51.6883i) q^{62} +(-47.0402 - 43.3960i) q^{64} +165.522 q^{65} +(-10.9869 + 10.9869i) q^{67} +(-13.1600 + 13.5181i) q^{68} +(-52.6711 + 129.613i) q^{70} -52.6605 q^{71} -67.8061i q^{73} +(-34.1946 + 84.1462i) q^{74} +(0.192584 + 14.3447i) q^{76} +(-5.43545 - 5.43545i) q^{77} +56.4602i q^{79} +(-78.6420 - 74.5285i) q^{80} +(17.9773 + 42.5903i) q^{82} +(58.3697 - 58.3697i) q^{83} +(-22.5840 + 22.5840i) q^{85} +(12.5629 + 5.10522i) q^{86} +(5.45279 - 2.38836i) q^{88} -131.566i q^{89} +(-178.548 - 178.548i) q^{91} +(35.1187 - 36.0745i) q^{92} +(30.3397 + 71.8781i) q^{94} +24.2866i q^{95} +60.9413 q^{97} +(106.343 - 44.8872i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{4} + 12 q^{8}+O(q^{10}) \) 16 * q + 12 * q^4 + 12 * q^8	\( 16 q + 12 q^{4} + 12 q^{8} - 56 q^{10} - 32 q^{11} + 44 q^{14} + 32 q^{16} - 32 q^{19} - 80 q^{20} + 32 q^{22} + 128 q^{23} + 100 q^{26} - 120 q^{28} - 32 q^{29} - 160 q^{32} + 96 q^{34} - 96 q^{35} - 96 q^{37} - 168 q^{38} + 48 q^{40} + 160 q^{43} - 88 q^{44} + 136 q^{46} + 112 q^{49} + 236 q^{50} - 48 q^{52} + 160 q^{53} - 256 q^{55} + 224 q^{56} + 144 q^{58} + 128 q^{59} - 32 q^{61} + 276 q^{62} - 408 q^{64} + 32 q^{65} + 320 q^{67} + 448 q^{68} - 384 q^{70} - 512 q^{71} - 348 q^{74} + 72 q^{76} - 224 q^{77} - 552 q^{80} - 40 q^{82} + 160 q^{83} + 160 q^{85} - 528 q^{86} + 480 q^{88} - 480 q^{91} - 496 q^{92} + 312 q^{94} + 440 q^{98}+O(q^{100}) \) 16 * q + 12 * q^4 + 12 * q^8 - 56 * q^10 - 32 * q^11 + 44 * q^14 + 32 * q^16 - 32 * q^19 - 80 * q^20 + 32 * q^22 + 128 * q^23 + 100 * q^26 - 120 * q^28 - 32 * q^29 - 160 * q^32 + 96 * q^34 - 96 * q^35 - 96 * q^37 - 168 * q^38 + 48 * q^40 + 160 * q^43 - 88 * q^44 + 136 * q^46 + 112 * q^49 + 236 * q^50 - 48 * q^52 + 160 * q^53 - 256 * q^55 + 224 * q^56 + 144 * q^58 + 128 * q^59 - 32 * q^61 + 276 * q^62 - 408 * q^64 + 32 * q^65 + 320 * q^67 + 448 * q^68 - 384 * q^70 - 512 * q^71 - 348 * q^74 + 72 * q^76 - 224 * q^77 - 552 * q^80 - 40 * q^82 + 160 * q^83 + 160 * q^85 - 528 * q^86 + 480 * q^88 - 480 * q^91 - 496 * q^92 + 312 * q^94 + 440 * q^98

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