LMFDB - Embedded newform 144.3.m.c.91.8

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			91.8
Root			$1.84258 - 0.777752i$ of defining polynomial
Character	$\chi$	$=$	144.91
Dual form			144.3.m.c.19.8

$q$-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 $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

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

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	0.999139	−	0.0414785i	$-0.0132068\pi$
$5$	4.78830	+	4.78830i	0.957661	+	0.957661i	−0.0414785	+	0.999139i	$0.513207\pi$
$6$		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	−0.682785	−	0.730619i	$-0.739232\pi$
$11$	0.526169	−	0.526169i	0.0478335	−	0.0478335i	0.730619	+	0.682785i	$0.239232\pi$
$12$		0			0
$13$	17.2840	−	17.2840i	1.32953	−	1.32953i	0.423761	−	0.905774i	$-0.360710\pi$
$13$	17.2840	−	17.2840i	1.32953	−	1.32953i	0.905774	−	0.423761i	$-0.139290\pi$
$14$	−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	0.637213	−	0.770688i	$-0.280087\pi$
$19$	−2.53604	−	2.53604i	−0.133476	−	0.133476i	−0.770688	+	0.637213i	$0.780087\pi$
$20$	−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	−0.668215	−	0.743968i	$-0.732942\pi$
$29$	2.19683	−	2.19683i	0.0757526	−	0.0757526i	0.743968	+	0.668215i	$0.232942\pi$
$30$		0			0
$31$		−	28.0521i		−	0.904908i	−0.891788	−	0.452454i	$-0.850549\pi$
$31$		−	28.0521i		−	0.904908i	0.891788	−	0.452454i	$-0.149451\pi$
$32$	−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	0.124327	−	0.992241i	$-0.460323\pi$
$37$	−32.1128	−	32.1128i	−0.867914	−	0.867914i	−0.992241	+	0.124327i	$0.960323\pi$
$38$	−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	$-0.909041\pi$
$41$		−	23.1145i		−	0.563768i	0.959449	−	0.281884i	$-0.0909593\pi$
$42$		0			0
$43$	4.79441	−	4.79441i	0.111498	−	0.111498i	−0.649157	−	0.760655i	$-0.724878\pi$
$43$	4.79441	−	4.79441i	0.111498	−	0.111498i	0.760655	+	0.649157i	$0.224878\pi$
$44$	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	$-0.863784\pi$
$47$		−	39.0095i		−	0.829989i	0.909824	−	0.414994i	$-0.136216\pi$
$48$		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	0.919935	−	0.392071i	$-0.128241\pi$
$53$	27.9768	+	27.9768i	0.527864	+	0.527864i	−0.392071	+	0.919935i	$0.628241\pi$
$54$		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	−0.471691	+	0.881764i	$0.656356\pi$
$59$	−79.8538	+	79.8538i	−1.35345	+	1.35345i	−0.881764	+	0.471691i	$0.843644\pi$
$60$		0			0
$61$	−36.7762	+	36.7762i	−0.602888	+	0.602888i	−0.941078	−	0.338190i	$-0.890185\pi$
$61$	−36.7762	+	36.7762i	−0.602888	+	0.602888i	0.338190	+	0.941078i	$0.390185\pi$
$62$	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	0.620345	−	0.784329i	$-0.286992\pi$
$67$	−10.9869	−	10.9869i	−0.163984	−	0.163984i	−0.784329	+	0.620345i	$0.786992\pi$
$68$	−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	$0.153739\pi$
$73$			67.8061i			0.928850i	−0.885612	+	0.464425i	$0.846261\pi$
$74$	−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	$-0.883683\pi$
$79$		−	56.4602i		−	0.714686i	0.933973	−	0.357343i	$-0.116317\pi$
$80$	−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	0.965107	−	0.261857i	$-0.0843349\pi$
$83$	58.3697	+	58.3697i	0.703249	+	0.703249i	−0.261857	+	0.965107i	$0.584335\pi$
$84$		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	$0.264765\pi$
$89$			131.566i			1.47827i	−0.673558	+	0.739135i	$0.735235\pi$
$90$		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	−0.995635	−	0.0933326i	$-0.970248\pi$
$101$	−109.986	−	109.986i	−1.08897	−	1.08897i	−0.0933326	−	0.995635i	$-0.529752\pi$
$102$		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	−0.577974	−	0.816055i	$-0.696156\pi$
$107$	25.4747	−	25.4747i	0.238081	−	0.238081i	0.816055	+	0.577974i	$0.196156\pi$
$108$		0			0
$109$	33.0605	−	33.0605i	0.303307	−	0.303307i	−0.538999	−	0.842306i	$-0.681197\pi$
$109$	33.0605	−	33.0605i	0.303307	−	0.303307i	0.842306	+	0.538999i	$0.181197\pi$
$110$	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	$0.0514107\pi$
$127$			40.8458i			0.321620i	−0.986985	+	0.160810i	$0.948589\pi$
$128$	−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	0.932867	−	0.360220i	$-0.117298\pi$
$131$	75.0168	+	75.0168i	0.572647	+	0.572647i	−0.360220	+	0.932867i	$0.617298\pi$
$132$		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	$0.162694\pi$
$137$			134.028i			0.978308i	−0.872197	+	0.489154i	$0.837306\pi$
$138$		0			0
$139$	22.8798	−	22.8798i	0.164603	−	0.164603i	−0.619999	−	0.784602i	$-0.712867\pi$
$139$	22.8798	−	22.8798i	0.164603	−	0.164603i	0.784602	+	0.619999i	$0.212867\pi$
$140$	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	0.737694	−	0.675135i	$-0.235915\pi$
$149$	9.32124	+	9.32124i	0.0625587	+	0.0625587i	−0.675135	+	0.737694i	$0.735915\pi$
$150$		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	−0.943136	−	0.332407i	$-0.892139\pi$
$157$	−95.8844	+	95.8844i	−0.610729	+	0.610729i	0.332407	+	0.943136i	$0.392139\pi$
$158$	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	0.127513	−	0.991837i	$-0.459301\pi$
$163$	−140.885	−	140.885i	−0.864324	−	0.864324i	−0.991837	+	0.127513i	$0.959301\pi$
$164$	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	−0.534008	−	0.845479i	$-0.679315\pi$
$173$	53.8845	−	53.8845i	0.311471	−	0.311471i	0.845479	+	0.534008i	$0.179315\pi$
$174$		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	0.353451	−	0.935453i	$-0.385008\pi$
$179$	−104.178	−	104.178i	−0.582002	−	0.582002i	−0.935453	+	0.353451i	$0.885008\pi$
$180$		0			0
$181$	−205.498	−	205.498i	−1.13535	−	1.13535i	−0.989274	−	0.146073i	$-0.953336\pi$
$181$	−205.498	−	205.498i	−1.13535	−	1.13535i	−0.146073	−	0.989274i	$-0.546664\pi$
$182$	−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	$0.225182\pi$
$191$			248.255i			1.29977i	−0.760034	+	0.649883i	$0.774818\pi$
$192$		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	−0.973234	−	0.229816i	$-0.926188\pi$
$197$	−237.001	−	237.001i	−1.20305	−	1.20305i	−0.229816	−	0.973234i	$-0.573812\pi$
$198$		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	0.674606	−	0.738178i	$-0.264314\pi$
$211$	−13.4139	−	13.4139i	−0.0635728	−	0.0635728i	−0.738178	+	0.674606i	$0.764314\pi$
$212$	−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	$0.230604\pi$
$223$			295.580i			1.32547i	−0.748854	+	0.662735i	$0.769396\pi$
$224$	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	0.887824	−	0.460184i	$-0.152217\pi$
$227$	97.0742	+	97.0742i	0.427640	+	0.427640i	−0.460184	+	0.887824i	$0.652217\pi$
$228$		0			0
$229$	34.2565	+	34.2565i	0.149592	+	0.149592i	0.777936	−	0.628344i	$-0.216267\pi$
$229$	34.2565	+	34.2565i	0.149592	+	0.149592i	−0.628344	+	0.777936i	$0.716267\pi$
$230$	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	$-0.956960\pi$
$233$		−	62.8176i		−	0.269604i	0.990873	−	0.134802i	$-0.0430398\pi$
$234$		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	$-0.732649\pi$
$239$		−	355.910i		−	1.48916i	0.667532	−	0.744581i	$-0.267351\pi$
$240$		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	−0.365638	+	0.930757i	$0.619149\pi$
$251$	−325.395	+	325.395i	−1.29640	+	1.29640i	−0.930757	+	0.365638i	$0.880851\pi$
$252$		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	−0.981254	−	0.192719i	$-0.938269\pi$
$269$	−212.116	+	212.116i	−0.788535	+	0.788535i	0.192719	+	0.981254i	$0.438269\pi$
$270$		0			0
$271$		−	173.450i		−	0.640037i	−0.947411	−	0.320019i	$-0.896311\pi$
$271$		−	173.450i		−	0.640037i	0.947411	−	0.320019i	$-0.103689\pi$
$272$	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	0.634377	−	0.773023i	$-0.281257\pi$
$277$	−38.4049	−	38.4049i	−0.138646	−	0.138646i	−0.773023	+	0.634377i	$0.781257\pi$
$278$	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	$-0.869768\pi$
$281$		−	223.573i		−	0.795632i	0.917465	−	0.397816i	$-0.130232\pi$
$282$		0			0
$283$	247.755	−	247.755i	0.875459	−	0.875459i	−0.117602	−	0.993061i	$-0.537521\pi$
$283$	247.755	−	247.755i	0.875459	−	0.875459i	0.993061	+	0.117602i	$0.0375206\pi$
$284$	−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	0.859743	−	0.510727i	$-0.170624\pi$
$293$	102.262	+	102.262i	0.349016	+	0.349016i	−0.510727	+	0.859743i	$0.670624\pi$
$294$		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	0.895508	−	0.445045i	$-0.146812\pi$
$307$	138.292	+	138.292i	0.450463	+	0.450463i	−0.445045	+	0.895508i	$0.646812\pi$
$308$	−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	$-0.883594\pi$
$313$		−	223.861i		−	0.715209i	0.933873	−	0.357605i	$-0.116406\pi$
$314$	−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	−0.371635	−	0.928379i	$-0.621203\pi$
$317$	176.488	−	176.488i	0.556744	−	0.556744i	0.928379	+	0.371635i	$0.121203\pi$
$318$		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	−0.928082	−	0.372376i	$-0.878543\pi$
$331$	−183.939	+	183.939i	−0.555706	+	0.555706i	0.372376	+	0.928082i	$0.378543\pi$
$332$	−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	−0.524308	−	0.851529i	$-0.675676\pi$
$347$	113.546	−	113.546i	0.327221	−	0.327221i	0.851529	+	0.524308i	$0.175676\pi$
$348$		0			0
$349$	90.9653	−	90.9653i	0.260645	−	0.260645i	−0.564671	−	0.825316i	$-0.690997\pi$
$349$	90.9653	−	90.9653i	0.260645	−	0.260645i	0.825316	+	0.564671i	$0.190997\pi$
$350$	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	$0.350209\pi$
$367$			654.218i			1.78261i	−0.453404	+	0.891305i	$0.649791\pi$
$368$	−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	0.995336	−	0.0964690i	$-0.0307549\pi$
$373$	335.277	+	335.277i	0.898867	+	0.898867i	−0.0964690	+	0.995336i	$0.530755\pi$
$374$	−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	−0.825279	−	0.564725i	$-0.808982\pi$
$379$	−98.7497	+	98.7497i	−0.260553	+	0.260553i	0.564725	+	0.825279i	$0.308982\pi$
$380$	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	$0.0653434\pi$
$383$			156.144i			0.407687i	−0.979003	+	0.203844i	$0.934657\pi$
$384$		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	0.999986	+	0.00527486i	$0.00167905\pi$
$389$	391.047	+	391.047i	1.00526	+	1.00526i	0.00527486	+	0.999986i	$0.498321\pi$
$390$		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	−0.329791	−	0.944054i	$-0.606978\pi$
$397$	243.862	−	243.862i	0.614262	−	0.614262i	0.944054	+	0.329791i	$0.106978\pi$
$398$	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	$0.0173056\pi$
$409$			44.4504i			0.108681i	−0.998522	+	0.0543404i	$0.982694\pi$
$410$	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	0.688982	−	0.724778i	$-0.258058\pi$
$419$	−14.9985	−	14.9985i	−0.0357959	−	0.0357959i	−0.724778	+	0.688982i	$0.758058\pi$
$420$		0			0
$421$	312.907	+	312.907i	0.743247	+	0.743247i	0.973201	−	0.229954i	$-0.0738576\pi$
$421$	312.907	+	312.907i	0.743247	+	0.743247i	−0.229954	+	0.973201i	$0.573858\pi$
$422$	−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	$0.211908\pi$
$431$			532.400i			1.23527i	−0.786466	+	0.617633i	$0.788092\pi$
$432$		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	−0.967149	−	0.254208i	$-0.918185\pi$
$443$	−315.833	+	315.833i	−0.712941	+	0.712941i	0.254208	+	0.967149i	$0.418185\pi$
$444$		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	$-0.894816\pi$
$457$		−	296.561i		−	0.648930i	0.945898	−	0.324465i	$-0.105184\pi$
$458$	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	−0.823465	−	0.567368i	$-0.807962\pi$
$461$	−118.061	+	118.061i	−0.256097	+	0.256097i	0.567368	+	0.823465i	$0.307962\pi$
$462$		0			0
$463$		−	409.453i		−	0.884348i	−0.896929	−	0.442174i	$-0.854207\pi$
$463$		−	409.453i		−	0.884348i	0.896929	−	0.442174i	$-0.145793\pi$
$464$	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	−0.998117	−	0.0613343i	$-0.980464\pi$
$467$	−494.764	−	494.764i	−1.05945	−	1.05945i	−0.0613343	−	0.998117i	$-0.519536\pi$
$468$		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	$-0.801759\pi$
$479$		−	558.806i		−	1.16661i	0.812254	−	0.583305i	$-0.198241\pi$
$480$		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	−0.00411514	−	0.999992i	$-0.501310\pi$
$491$	488.975	−	488.975i	0.995876	−	0.995876i	0.999992	+	0.00411514i	$0.00130989\pi$
$492$		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	0.596448	−	0.802652i	$-0.296578\pi$
$499$	−102.895	−	102.895i	−0.206203	−	0.206203i	−0.802652	+	0.596448i	$0.796578\pi$
$500$	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	−0.847830	−	0.530268i	$-0.822091\pi$
$509$	−161.639	+	161.639i	−0.317563	+	0.317563i	0.530268	+	0.847830i	$0.322091\pi$
$510$		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	$0.261946\pi$
$521$			763.931i			1.46628i	−0.680078	+	0.733140i	$0.738054\pi$
$522$		0			0
$523$	295.573	−	295.573i	0.565150	−	0.565150i	−0.365616	−	0.930766i	$-0.619142\pi$
$523$	295.573	−	295.573i	0.565150	−	0.565150i	0.930766	+	0.365616i	$0.119142\pi$
$524$	−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	−0.445865	−	0.895100i	$-0.647104\pi$
$541$	243.037	−	243.037i	0.449236	−	0.449236i	0.895100	+	0.445865i	$0.147104\pi$
$542$	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	0.979180	−	0.202993i	$-0.0650669\pi$
$547$	424.574	+	424.574i	0.776187	+	0.776187i	−0.202993	+	0.979180i	$0.565067\pi$
$548$	−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	−0.182833	−	0.983144i	$-0.558527\pi$
$557$	445.773	−	445.773i	0.800311	−	0.800311i	0.983144	+	0.182833i	$0.0585268\pi$
$558$		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	0.998307	−	0.0581732i	$-0.0185276\pi$
$563$	529.295	+	529.295i	0.940133	+	0.940133i	−0.0581732	+	0.998307i	$0.518528\pi$
$564$		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	$-0.901424\pi$
$569$		−	346.814i		−	0.609516i	0.952430	−	0.304758i	$-0.0985755\pi$
$570$		0			0
$571$	−155.711	+	155.711i	−0.272699	+	0.272699i	−0.830186	−	0.557487i	$-0.811766\pi$
$571$	−155.711	+	155.711i	−0.272699	+	0.272699i	0.557487	+	0.830186i	$0.311766\pi$
$572$	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	−0.999106	−	0.0422810i	$-0.986538\pi$
$587$	−561.656	+	561.656i	−0.956825	+	0.956825i	0.0422810	+	0.999106i	$0.486538\pi$
$588$		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	$0.292351\pi$
$601$			955.182i			1.58932i	−0.607054	+	0.794661i	$0.707649\pi$
$602$	−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	$-0.922711\pi$
$607$		−	291.885i		−	0.480865i	0.970666	−	0.240432i	$-0.0772892\pi$
$608$	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	0.381322	−	0.924442i	$-0.375469\pi$
$613$	−332.933	−	332.933i	−0.543121	−	0.543121i	−0.924442	+	0.381322i	$0.875469\pi$
$614$	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	$-0.711756\pi$
$617$		−	970.864i		−	1.57352i	0.617257	−	0.786762i	$-0.288244\pi$
$618$		0			0
$619$	−696.761	+	696.761i	−1.12562	+	1.12562i	−0.134744	+	0.990881i	$0.543021\pi$
$619$	−696.761	+	696.761i	−1.12562	+	1.12562i	−0.990881	+	0.134744i	$0.956979\pi$
$620$	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	0.870888	−	0.491482i	$-0.163545\pi$
$643$	243.958	+	243.958i	0.379406	+	0.379406i	−0.491482	+	0.870888i	$0.663545\pi$
$644$	−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	−0.910102	−	0.414384i	$-0.863997\pi$
$653$	−323.704	+	323.704i	−0.495718	+	0.495718i	0.414384	+	0.910102i	$0.363997\pi$
$654$		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	0.207629	−	0.978208i	$-0.433425\pi$
$659$	−507.811	−	507.811i	−0.770578	−	0.770578i	−0.978208	+	0.207629i	$0.933425\pi$
$660$		0			0
$661$	57.1593	+	57.1593i	0.0864741	+	0.0864741i	0.749021	−	0.662547i	$-0.230524\pi$
$661$	57.1593	+	57.1593i	0.0864741	+	0.0864741i	−0.662547	+	0.749021i	$0.730524\pi$
$662$	−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	0.349747	−	0.936844i	$-0.386268\pi$
$677$	−397.465	−	397.465i	−0.587097	−	0.587097i	−0.936844	+	0.349747i	$0.886268\pi$
$678$		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	−0.511060	−	0.859545i	$-0.670747\pi$
$683$	238.015	−	238.015i	0.348485	−	0.348485i	0.859545	+	0.511060i	$0.170747\pi$
$684$		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	0.00839951	−	0.999965i	$-0.497326\pi$
$691$	−685.172	−	685.172i	−0.991565	−	0.991565i	−0.999965	+	0.00839951i	$0.997326\pi$
$692$	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	−0.978926	−	0.204214i	$-0.934536\pi$
$701$	−543.074	+	543.074i	−0.774713	+	0.774713i	0.204214	+	0.978926i	$0.434536\pi$
$702$		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	0.273541	−	0.961860i	$-0.411805\pi$
$709$	−488.019	−	488.019i	−0.688320	−	0.688320i	−0.961860	+	0.273541i	$0.911805\pi$
$710$	−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	$0.0663028\pi$
$719$			297.369i			0.413587i	−0.978385	+	0.206793i	$0.933697\pi$
$720$		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	−0.903818	−	0.427917i	$-0.859248\pi$
$733$	−348.835	+	348.835i	−0.475901	+	0.475901i	0.427917	+	0.903818i	$0.359248\pi$
$734$	−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	0.992174	+	0.124860i	$0.0398482\pi$
$739$	825.489	+	825.489i	1.11703	+	1.11703i	0.124860	+	0.992174i	$0.460152\pi$
$740$	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	$0.0170550\pi$
$751$			80.4386i			0.107109i	−0.998565	+	0.0535543i	$0.982945\pi$
$752$	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	0.844206	−	0.536019i	$-0.180072\pi$
$757$	233.298	+	233.298i	0.308187	+	0.308187i	−0.536019	+	0.844206i	$0.680072\pi$
$758$	−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	$-0.988246\pi$
$761$		−	56.1906i		−	0.0738378i	0.999318	−	0.0369189i	$-0.0117543\pi$
$762$		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	0.959498	−	0.281716i	$-0.0909037\pi$
$773$	523.925	+	523.925i	0.677781	+	0.677781i	−0.281716	+	0.959498i	$0.590904\pi$
$774$		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	0.676817	−	0.736152i	$-0.263359\pi$
$787$	−46.6965	−	46.6965i	−0.0593348	−	0.0593348i	−0.736152	+	0.676817i	$0.763359\pi$
$788$	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	−0.782348	−	0.622842i	$-0.785978\pi$
$797$	−127.126	+	127.126i	−0.159505	+	0.159505i	0.622842	+	0.782348i	$0.285978\pi$
$798$		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	$0.224058\pi$
$809$			1047.16i			1.29439i	−0.762325	+	0.647194i	$0.775942\pi$
$810$		0			0
$811$	−112.206	+	112.206i	−0.138356	+	0.138356i	−0.772893	−	0.634537i	$-0.781191\pi$
$811$	−112.206	+	112.206i	−0.138356	+	0.138356i	0.634537	+	0.772893i	$0.281191\pi$
$812$	−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	0.711739	−	0.702444i	$-0.247908\pi$
$821$	7.63080	+	7.63080i	0.00929452	+	0.00929452i	−0.702444	+	0.711739i	$0.747908\pi$
$822$		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	−0.882767	−	0.469810i	$-0.844322\pi$
$827$	−341.515	+	341.515i	−0.412957	+	0.412957i	0.469810	+	0.882767i	$0.344322\pi$
$828$		0			0
$829$	−621.672	+	621.672i	−0.749905	+	0.749905i	−0.974461	−	0.224556i	$-0.927907\pi$
$829$	−621.672	+	621.672i	−0.749905	+	0.749905i	0.224556	+	0.974461i	$0.427907\pi$
$830$	−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	0.238266	−	0.971200i	$-0.423421\pi$
$853$	−625.193	−	625.193i	−0.732934	−	0.732934i	−0.971200	+	0.238266i	$0.923421\pi$
$854$	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	$0.223057\pi$
$857$			1105.18i			1.28959i	−0.764356	+	0.644794i	$0.776943\pi$
$858$		0			0
$859$	379.841	−	379.841i	0.442190	−	0.442190i	−0.450558	−	0.892747i	$-0.648775\pi$
$859$	379.841	−	379.841i	0.442190	−	0.442190i	0.892747	+	0.450558i	$0.148775\pi$
$860$	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	$-0.928969\pi$
$863$		−	381.969i		−	0.442606i	0.975205	−	0.221303i	$-0.0710311\pi$
$864$		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	−0.242088	−	0.970254i	$-0.577832\pi$
$877$	638.602	−	638.602i	0.728166	−	0.728166i	0.970254	+	0.242088i	$0.0778323\pi$
$878$	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	−0.999853	−	0.0171209i	$-0.994550\pi$
$883$	−897.988	−	897.988i	−1.01697	−	1.01697i	−0.0171209	−	0.999853i	$-0.505450\pi$
$884$	−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	−0.972678	−	0.232159i	$-0.925421\pi$
$907$	−671.651	+	671.651i	−0.740519	+	0.740519i	0.232159	+	0.972678i	$0.425421\pi$
$908$	−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	$-0.860973\pi$
$911$		−	770.729i		−	0.846025i	0.906124	−	0.423012i	$-0.139027\pi$
$912$		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	$-0.888323\pi$
$937$		−	644.074i		−	0.687378i	0.939083	−	0.343689i	$-0.111677\pi$
$938$	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	−0.792267	−	0.610175i	$-0.791099\pi$
$941$	−171.348	+	171.348i	−0.182092	+	0.182092i	0.610175	+	0.792267i	$0.291099\pi$
$942$		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	0.206312	−	0.978486i	$-0.433854\pi$
$947$	−731.249	−	731.249i	−0.772174	−	0.772174i	−0.978486	+	0.206312i	$0.933854\pi$
$948$		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	$0.368262\pi$
$953$			1745.08i			1.83115i	−0.402152	+	0.915573i	$0.631738\pi$
$954$		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	0.0414029	−	0.999143i	$-0.486817\pi$
$971$	1010.37	−	1010.37i	1.04055	−	1.04055i	0.999143	−	0.0414029i	$-0.0131827\pi$
$972$		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	$0.128017\pi$
$991$			775.801i			0.782847i	−0.920211	+	0.391423i	$0.871983\pi$
$992$	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	0.800900	−	0.598799i	$-0.204355\pi$
$997$	201.495	+	201.495i	0.202101	+	0.202101i	−0.598799	+	0.800900i	$0.704355\pi$
$998$	−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.91.8		16
3.2	odd	2		48.3.l.a.43.1	yes	16
4.3	odd	2		576.3.m.c.271.7		16
8.3	odd	2		1152.3.m.c.415.2		16
8.5	even	2		1152.3.m.f.415.2		16
12.11	even	2		192.3.l.a.79.5		16
16.3	odd	4	inner	144.3.m.c.19.8		16
16.5	even	4		1152.3.m.c.991.2		16
16.11	odd	4		1152.3.m.f.991.2		16
16.13	even	4		576.3.m.c.559.7		16
24.5	odd	2		384.3.l.a.31.8		16
24.11	even	2		384.3.l.b.31.4		16
48.5	odd	4		384.3.l.b.223.4		16
48.11	even	4		384.3.l.a.223.8		16
48.29	odd	4		192.3.l.a.175.5		16
48.35	even	4		48.3.l.a.19.1	✓	16

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

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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