LMFDB - Embedded newform 405.3.l.j.298.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [405,3,Mod(28,405)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(405, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([4, 9]))

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

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

chi := DirichletCharacter("405.28");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	405.l (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$11.0354507066$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
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} + 256x^{12} + 15630x^{8} + 235936x^{4} + 28561 $ x^16 + 256x^12 + 15630x^8 + 235936*x^4 + 28561
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			298.2
Root			$1.54374 - 1.54374i$ of defining polynomial
Character	$\chi$	$=$	405.298
Dual form			405.3.l.j.352.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.565047 - 2.10878i) q^{2} +(-0.663588 + 0.383123i) q^{4} +(-2.48091 - 4.34109i) q^{5} +(0.528192 + 1.97124i) q^{7} +(-4.99206 - 4.99206i) q^{8} +(-7.75259 + 7.68463i) q^{10} +(6.33336 - 10.9697i) q^{11} +(3.44531 - 12.8581i) q^{13} +(3.85846 - 2.22768i) q^{14} +(-9.23893 + 16.0023i) q^{16} +(-16.3208 + 16.3208i) q^{17} +9.12517i q^{19} +(3.30948 + 1.93020i) q^{20} +(-26.7114 - 7.15730i) q^{22} +(5.73162 - 21.3907i) q^{23} +(-12.6901 + 21.5397i) q^{25} -29.0616 q^{26} +(-1.10573 - 1.10573i) q^{28} +(-16.6416 - 9.60806i) q^{29} +(-9.32320 - 16.1483i) q^{31} +(11.6886 + 3.13196i) q^{32} +(43.6390 + 25.1950i) q^{34} +(7.24692 - 7.18340i) q^{35} +(-32.6377 + 32.6377i) q^{37} +(19.2430 - 5.15615i) q^{38} +(-9.28611 + 34.0559i) q^{40} +(25.8234 + 44.7275i) q^{41} +(-46.1316 + 12.3609i) q^{43} +9.70583i q^{44} -48.3470 q^{46} +(-13.7731 - 51.4021i) q^{47} +(38.8285 - 22.4176i) q^{49} +(52.5932 + 14.5898i) q^{50} +(2.63995 + 9.85244i) q^{52} +(18.2998 + 18.2998i) q^{53} +(-63.3330 - 0.278790i) q^{55} +(7.20378 - 12.4773i) q^{56} +(-10.8580 + 40.5226i) q^{58} +(-85.9329 + 49.6134i) q^{59} +(51.7677 - 89.6644i) q^{61} +(-28.7851 + 28.7851i) q^{62} +47.4929i q^{64} +(-64.3655 + 16.9434i) q^{65} +(-18.9237 - 5.07060i) q^{67} +(4.57742 - 17.0832i) q^{68} +(-19.2431 - 11.2232i) q^{70} +54.5913 q^{71} +(-8.13786 - 8.13786i) q^{73} +(87.2677 + 50.3840i) q^{74} +(-3.49606 - 6.05535i) q^{76} +(24.9691 + 6.69046i) q^{77} +(122.145 + 70.5203i) q^{79} +(92.3884 + 0.406690i) q^{80} +(79.7291 - 79.7291i) q^{82} +(-65.8143 + 17.6349i) q^{83} +(111.341 + 30.3595i) q^{85} +(52.1330 + 90.2970i) q^{86} +(-86.3781 + 23.1449i) q^{88} -59.3859i q^{89} +27.1661 q^{91} +(4.39183 + 16.3905i) q^{92} +(-100.613 + 58.0892i) q^{94} +(39.6132 - 22.6388i) q^{95} +(-29.4385 - 109.866i) q^{97} +(-69.2138 - 69.2138i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{2} + 12 q^{5} - 20 q^{7} - 56 q^{10} + 22 q^{13} - 168 q^{14} + 16 q^{16} - 96 q^{20} - 16 q^{22} + 36 q^{23} + 46 q^{25} + 176 q^{28} - 252 q^{29} - 160 q^{31} - 114 q^{32} + 4 q^{37} + 192 q^{38}+ \cdots - 152 q^{97}+O(q^{100}) $ 16 * q - 6 * q^2 + 12 * q^5 - 20 * q^7 - 56 * q^10 + 22 * q^13 - 168 * q^14 + 16 * q^16 - 96 * q^20 - 16 * q^22 + 36 * q^23 + 46 * q^25 + 176 * q^28 - 252 * q^29 - 160 * q^31 - 114 * q^32 + 4 * q^37 + 192 * q^38 + 264 * q^40 - 128 * q^43 - 16 * q^46 + 204 * q^47 + 540 * q^50 + 154 * q^52 - 364 * q^55 - 246 * q^58 + 36 * q^59 - 4 * q^61 + 24 * q^65 - 44 * q^67 + 966 * q^68 + 18 * q^70 + 364 * q^73 + 288 * q^74 + 456 * q^76 - 204 * q^77 + 32 * q^82 + 12 * q^83 - 32 * q^85 - 420 * q^88 + 224 * q^91 - 960 * q^92 + 114 * q^95 - 152 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.565047	−	2.10878i	−0.282523	−	1.05439i	−0.950630	−	0.310326i	$-0.899562\pi$
$2$	−0.565047	−	2.10878i	−0.282523	−	1.05439i	0.668107	−	0.744065i	$-0.267105\pi$
$3$		0			0
$3$		0			0
$4$	−0.663588	+	0.383123i	−0.165897	+	0.0957807i
$5$	−2.48091	−	4.34109i	−0.496183	−	0.868218i
$5$	−2.48091	−	4.34109i	−0.496183	−	0.868218i
$6$		0			0
$7$	0.528192	+	1.97124i	0.0754560	+	0.281605i	0.993336	−	0.115252i	$-0.0367675\pi$
$7$	0.528192	+	1.97124i	0.0754560	+	0.281605i	−0.917880	+	0.396857i	$0.870101\pi$
$8$	−4.99206	−	4.99206i	−0.624008	−	0.624008i
$9$		0			0
$10$	−7.75259	+	7.68463i	−0.775259	+	0.768463i
$11$	6.33336	−	10.9697i	0.575760	−	0.997246i	−0.420198	−	0.907432i	$-0.638039\pi$
$11$	6.33336	−	10.9697i	0.575760	−	0.997246i	0.995959	−	0.0898139i	$-0.0286272\pi$
$12$		0			0
$13$	3.44531	−	12.8581i	0.265024	−	0.989082i	−0.697212	−	0.716865i	$-0.745576\pi$
$13$	3.44531	−	12.8581i	0.265024	−	0.989082i	0.962236	−	0.272217i	$-0.0877569\pi$
$14$	3.85846	−	2.22768i	0.275604	−	0.159120i
$15$		0			0
$16$	−9.23893	+	16.0023i	−0.577433	+	1.00014i
$17$	−16.3208	+	16.3208i	−0.960047	+	0.960047i	−0.999232	−	0.0391852i	$-0.987524\pi$
$17$	−16.3208	+	16.3208i	−0.960047	+	0.960047i	0.0391852	+	0.999232i	$0.487524\pi$
$18$		0			0
$19$			9.12517i			0.480272i	0.970739	+	0.240136i	$0.0771920\pi$
$19$			9.12517i			0.480272i	−0.970739	+	0.240136i	$0.922808\pi$
$20$	3.30948	+	1.93020i	0.165474	+	0.0965101i
$21$		0			0
$22$	−26.7114	−	7.15730i	−1.21415	−	0.325332i
$23$	5.73162	−	21.3907i	0.249201	−	0.930030i	−0.722025	−	0.691867i	$-0.756788\pi$
$23$	5.73162	−	21.3907i	0.249201	−	0.930030i	0.971225	−	0.238163i	$-0.0765451\pi$
$24$		0			0
$25$	−12.6901	+	21.5397i	−0.507605	+	0.861590i
$26$	−29.0616			−1.11776
$27$		0			0
$28$	−1.10573	−	1.10573i	−0.0394903	−	0.0394903i
$29$	−16.6416	−	9.60806i	−0.573850	−	0.331312i	0.184836	−	0.982769i	$-0.440825\pi$
$29$	−16.6416	−	9.60806i	−0.573850	−	0.331312i	−0.758686	+	0.651457i	$0.774158\pi$
$30$		0			0
$31$	−9.32320	−	16.1483i	−0.300748	−	0.520911i	0.675557	−	0.737307i	$-0.263903\pi$
$31$	−9.32320	−	16.1483i	−0.300748	−	0.520911i	−0.976306	+	0.216396i	$0.930570\pi$
$32$	11.6886	+	3.13196i	0.365270	+	0.0978738i
$33$		0			0
$34$	43.6390	+	25.1950i	1.28350	+	0.741030i
$35$	7.24692	−	7.18340i	0.207055	−	0.205240i
$36$		0			0
$37$	−32.6377	+	32.6377i	−0.882100	+	0.882100i	−0.993748	−	0.111648i	$-0.964387\pi$
$37$	−32.6377	+	32.6377i	−0.882100	+	0.882100i	0.111648	+	0.993748i	$0.464387\pi$
$38$	19.2430	−	5.15615i	0.506395	−	0.135688i
$39$		0			0
$40$	−9.28611	+	34.0559i	−0.232153	+	0.851397i
$41$	25.8234	+	44.7275i	0.629839	+	1.09091i	0.987584	+	0.157094i	$0.0502126\pi$
$41$	25.8234	+	44.7275i	0.629839	+	1.09091i	−0.357744	+	0.933820i	$0.616454\pi$
$42$		0			0
$43$	−46.1316	+	12.3609i	−1.07283	+	0.287463i	−0.751654	−	0.659557i	$-0.770744\pi$
$43$	−46.1316	+	12.3609i	−1.07283	+	0.287463i	−0.321173	+	0.947021i	$0.604077\pi$
$44$			9.70583i			0.220587i
$45$		0			0
$46$	−48.3470			−1.05102
$47$	−13.7731	−	51.4021i	−0.293046	−	1.09366i	−0.942757	−	0.333480i	$-0.891777\pi$
$47$	−13.7731	−	51.4021i	−0.293046	−	1.09366i	0.649711	−	0.760181i	$-0.274890\pi$
$48$		0			0
$49$	38.8285	−	22.4176i	0.792417	−	0.457502i
$50$	52.5932	+	14.5898i	1.05186	+	0.291795i
$51$		0			0
$52$	2.63995	+	9.85244i	0.0507683	+	0.189470i
$53$	18.2998	+	18.2998i	0.345280	+	0.345280i	0.858348	−	0.513068i	$-0.171491\pi$
$53$	18.2998	+	18.2998i	0.345280	+	0.345280i	−0.513068	+	0.858348i	$0.671491\pi$
$54$		0			0
$55$	−63.3330	−	0.278790i	−1.15151	−	0.00506890i
$56$	7.20378	−	12.4773i	0.128639	−	0.222809i
$57$		0			0
$58$	−10.8580	+	40.5226i	−0.187207	+	0.698666i
$59$	−85.9329	+	49.6134i	−1.45649	+	0.840905i	−0.998836	−	0.0482263i	$-0.984643\pi$
$59$	−85.9329	+	49.6134i	−1.45649	+	0.840905i	−0.457653	+	0.889131i	$0.651310\pi$
$60$		0			0
$61$	51.7677	−	89.6644i	0.848651	−	1.46991i	−0.0337606	−	0.999430i	$-0.510748\pi$
$61$	51.7677	−	89.6644i	0.848651	−	1.46991i	0.882412	−	0.470477i	$-0.155918\pi$
$62$	−28.7851	+	28.7851i	−0.464276	+	0.464276i
$63$		0			0
$64$			47.4929i			0.742076i
$65$	−64.3655	+	16.9434i	−0.990239	+	0.260667i
$66$		0			0
$67$	−18.9237	−	5.07060i	−0.282444	−	0.0756805i	0.114816	−	0.993387i	$-0.463372\pi$
$67$	−18.9237	−	5.07060i	−0.282444	−	0.0756805i	−0.397260	+	0.917706i	$0.630039\pi$
$68$	4.57742	−	17.0832i	0.0673150	−	0.251223i
$69$		0			0
$70$	−19.2431	−	11.2232i	−0.274901	−	0.160332i
$71$	54.5913			0.768892			0.384446	−	0.923148i	$-0.374393\pi$
$71$	54.5913			0.768892			0.384446	+	0.923148i	$0.374393\pi$
$72$		0			0
$73$	−8.13786	−	8.13786i	−0.111478	−	0.111478i	0.649168	−	0.760645i	$-0.275117\pi$
$73$	−8.13786	−	8.13786i	−0.111478	−	0.111478i	−0.760645	+	0.649168i	$0.775117\pi$
$74$	87.2677	+	50.3840i	1.17929	+	0.680865i
$75$		0			0
$76$	−3.49606	−	6.05535i	−0.0460008	−	0.0796757i
$77$	24.9691	+	6.69046i	0.324275	+	0.0868891i
$78$		0			0
$79$	122.145	+	70.5203i	1.54614	+	0.892662i	0.998431	+	0.0559909i	$0.0178318\pi$
$79$	122.145	+	70.5203i	1.54614	+	0.892662i	0.547705	+	0.836671i	$0.315502\pi$
$80$	92.3884	+	0.406690i	1.15485	+	0.00508363i
$81$		0			0
$82$	79.7291	−	79.7291i	0.972306	−	0.972306i
$83$	−65.8143	+	17.6349i	−0.792944	+	0.212469i	−0.632484	−	0.774574i	$-0.717964\pi$
$83$	−65.8143	+	17.6349i	−0.792944	+	0.212469i	−0.160460	+	0.987042i	$0.551298\pi$
$84$		0			0
$85$	111.341	+	30.3595i	1.30989	+	0.357171i
$86$	52.1330	+	90.2970i	0.606198	+	1.04996i
$87$		0			0
$88$	−86.3781	+	23.1449i	−0.981569	+	0.263011i
$89$		−	59.3859i		−	0.667257i	−0.942705	−	0.333629i	$-0.891727\pi$
$89$		−	59.3859i		−	0.667257i	0.942705	−	0.333629i	$-0.108273\pi$
$90$		0			0
$91$	27.1661			0.298528
$92$	4.39183	+	16.3905i	0.0477373	+	0.178158i
$93$		0			0
$94$	−100.613	+	58.0892i	−1.07036	+	0.617970i
$95$	39.6132	−	22.6388i	0.416981	−	0.238303i
$96$		0			0
$97$	−29.4385	−	109.866i	−0.303490	−	1.13264i	−0.934238	−	0.356651i	$-0.883918\pi$
$97$	−29.4385	−	109.866i	−0.303490	−	1.13264i	0.630748	−	0.775988i	$-0.282748\pi$
$98$	−69.2138	−	69.2138i	−0.706263	−	0.706263i
$99$		0			0
$100$	0.168646	−	19.1554i	0.00168646	−	0.191554i
$101$	−8.95268	+	15.5065i	−0.0886404	+	0.153530i	−0.906937	−	0.421267i	$-0.861586\pi$
$101$	−8.95268	+	15.5065i	−0.0886404	+	0.153530i	0.818296	+	0.574797i	$0.194919\pi$
$102$		0			0
$103$	20.5961	−	76.8655i	0.199962	−	0.746267i	−0.790965	−	0.611862i	$-0.790421\pi$
$103$	20.5961	−	76.8655i	0.199962	−	0.746267i	0.990926	−	0.134406i	$-0.0429125\pi$
$104$	−81.3875	+	46.9891i	−0.782572	+	0.451818i
$105$		0			0
$106$	28.2501	−	48.9307i	0.266511	−	0.461610i
$107$	−59.3250	+	59.3250i	−0.554439	+	0.554439i	−0.927719	−	0.373280i	$-0.878233\pi$
$107$	−59.3250	+	59.3250i	−0.554439	+	0.554439i	0.373280	+	0.927719i	$0.378233\pi$
$108$		0			0
$109$		−	140.876i		−	1.29244i	−0.763153	−	0.646218i	$-0.776350\pi$
$109$		−	140.876i		−	1.29244i	0.763153	−	0.646218i	$-0.223650\pi$
$110$	35.1982	+	133.713i	0.319984	+	1.21557i
$111$		0			0
$112$	−36.4242	−	9.75985i	−0.325217	−	0.0871415i
$113$	52.1216	−	194.521i	0.461253	−	1.72142i	−0.207769	−	0.978178i	$-0.566620\pi$
$113$	52.1216	−	194.521i	0.461253	−	1.72142i	0.669022	−	0.743243i	$-0.266713\pi$
$114$		0			0
$115$	−107.079	+	28.1870i	−0.931118	+	0.245104i
$116$	14.7243			0.126933
$117$		0			0
$118$	153.180	+	153.180i	1.29814	+	1.29814i
$119$	−40.7927	−	23.5517i	−0.342796	−	0.197913i
$120$		0			0
$121$	−19.7230	−	34.1613i	−0.163000	−	0.282324i
$122$	−218.334	−	58.5024i	−1.78962	−	0.479528i
$123$		0			0
$124$	12.3735	+	7.14386i	0.0997866	+	0.0576118i
$125$	124.989	+	1.65068i	0.999913	+	0.0132054i
$126$		0			0
$127$	145.343	−	145.343i	1.14443	−	1.14443i	0.156799	−	0.987631i	$-0.449882\pi$
$127$	145.343	−	145.343i	1.14443	−	1.14443i	0.987631	−	0.156799i	$-0.0501175\pi$
$128$	146.907	−	39.3636i	1.14771	−	0.307528i
$129$		0			0
$130$	72.0994	+	126.159i	0.554611	+	0.970455i
$131$	−110.153	−	190.791i	−0.840865	−	1.45642i	−0.889164	−	0.457588i	$-0.848713\pi$
$131$	−110.153	−	190.791i	−0.840865	−	1.45642i	0.0482993	−	0.998833i	$-0.484620\pi$
$132$		0			0
$133$	−17.9879	+	4.81984i	−0.135247	+	0.0362394i
$134$			42.7712i			0.319188i
$135$		0			0
$136$	162.949			1.19815
$137$	−21.0181	−	78.4408i	−0.153417	−	0.572560i	−0.999236	−	0.0390898i	$-0.987554\pi$
$137$	−21.0181	−	78.4408i	−0.153417	−	0.572560i	0.845819	−	0.533471i	$-0.179113\pi$
$138$		0			0
$139$	224.304	−	129.502i	1.61369	−	0.931667i	0.625191	−	0.780472i	$-0.285021\pi$
$139$	224.304	−	129.502i	1.61369	−	0.931667i	0.988504	−	0.151195i	$-0.0483121\pi$
$140$	−2.05685	+	7.54329i	−0.0146918	+	0.0538806i
$141$		0			0
$142$	−30.8467	−	115.121i	−0.217230	−	0.810713i
$143$	−119.229	−	119.229i	−0.833768	−	0.833768i
$144$		0			0
$145$	−0.422939	+	96.0797i	−0.00291682	+	0.662618i
$146$	−12.5627	+	21.7593i	−0.0860460	+	0.149036i
$147$		0			0
$148$	9.15375	−	34.1623i	0.0618497	−	0.230826i
$149$	−113.230	+	65.3731i	−0.759930	+	0.438746i	−0.829271	−	0.558847i	$-0.811244\pi$
$149$	−113.230	+	65.3731i	−0.759930	+	0.438746i	0.0693405	+	0.997593i	$0.477910\pi$
$150$		0			0
$151$	63.1475	−	109.375i	0.418195	−	0.724335i	−0.577563	−	0.816346i	$-0.695996\pi$
$151$	63.1475	−	109.375i	0.418195	−	0.724335i	0.995758	+	0.0920110i	$0.0293295\pi$
$152$	45.5534	−	45.5534i	0.299694	−	0.299694i
$153$		0			0
$154$		−	56.4349i		−	0.366461i
$155$	−46.9710	+	80.5353i	−0.303038	+	0.519583i
$156$		0			0
$157$	−178.457	−	47.8175i	−1.13667	−	0.304570i	−0.359060	−	0.933315i	$-0.616903\pi$
$157$	−178.457	−	47.8175i	−1.13667	−	0.304570i	−0.777612	+	0.628744i	$0.783569\pi$
$158$	79.6946	−	297.424i	0.504396	−	1.88243i
$159$		0			0
$160$	−15.4024	−	58.5116i	−0.0962649	−	0.365697i
$161$	45.1935			0.280705
$162$		0			0
$163$	−70.0370	−	70.0370i	−0.429675	−	0.429675i	0.458843	−	0.888518i	$-0.348264\pi$
$163$	−70.0370	−	70.0370i	−0.429675	−	0.429675i	−0.888518	+	0.458843i	$0.848264\pi$
$164$	−34.2722	−	19.7871i	−0.208977	−	0.120653i
$165$		0			0
$166$	74.3763	+	128.824i	0.448050	+	0.776046i
$167$	−93.7589	−	25.1226i	−0.561431	−	0.150435i	−0.0330670	−	0.999453i	$-0.510527\pi$
$167$	−93.7589	−	25.1226i	−0.561431	−	0.150435i	−0.528363	+	0.849018i	$0.677194\pi$
$168$		0			0
$169$	−7.10136	−	4.09997i	−0.0420199	−	0.0242602i
$170$	1.10906	−	251.948i	0.00652391	−	1.48205i
$171$		0			0
$172$	25.8766	−	25.8766i	0.150445	−	0.150445i
$173$	66.6187	−	17.8504i	0.385079	−	0.103182i	−0.0610854	−	0.998133i	$-0.519456\pi$
$173$	66.6187	−	17.8504i	0.385079	−	0.103182i	0.446165	+	0.894951i	$0.352790\pi$
$174$		0			0
$175$	−49.1628	−	13.6381i	−0.280930	−	0.0779322i
$176$	117.027	+	202.697i	0.664926	+	1.15169i
$177$		0			0
$178$	−125.232	+	33.5558i	−0.703550	+	0.188516i
$179$			159.099i			0.888822i	0.895823	+	0.444411i	$0.146587\pi$
$179$			159.099i			0.888822i	−0.895823	+	0.444411i	$0.853413\pi$
$180$		0			0
$181$	63.3929			0.350237			0.175119	−	0.984547i	$-0.443969\pi$
$181$	63.3929			0.350237			0.175119	+	0.984547i	$0.443969\pi$
$182$	−15.3501	−	57.2874i	−0.0843413	−	0.314766i
$183$		0			0
$184$	−135.396	+	78.1711i	−0.735850	+	0.424843i
$185$	222.655	+	60.7119i	1.20354	+	0.328172i
$186$		0			0
$187$	75.6688	+	282.400i	0.404646	+	1.51016i
$188$	28.8330	+	28.8330i	0.153367	+	0.153367i
$189$		0			0
$190$	−70.1235	−	70.7436i	−0.369071	−	0.372335i
$191$	−61.7475	+	106.950i	−0.323285	+	0.559947i	−0.981164	−	0.193177i	$-0.938121\pi$
$191$	−61.7475	+	106.950i	−0.323285	+	0.559947i	0.657878	+	0.753124i	$0.271454\pi$
$192$		0			0
$193$	64.3390	−	240.116i	0.333363	−	1.24413i	−0.572271	−	0.820065i	$-0.693937\pi$
$193$	64.3390	−	240.116i	0.333363	−	1.24413i	0.905633	−	0.424062i	$-0.139396\pi$
$194$	−215.050	+	124.159i	−1.10850	+	0.639994i
$195$		0			0
$196$	−17.1774	+	29.7521i	−0.0876398	+	0.151797i
$197$	−53.2469	+	53.2469i	−0.270289	+	0.270289i	−0.829217	−	0.558928i	$-0.811213\pi$
$197$	−53.2469	+	53.2469i	−0.270289	+	0.270289i	0.558928	+	0.829217i	$0.311213\pi$
$198$		0			0
$199$		−	31.6979i		−	0.159286i	−0.996823	−	0.0796430i	$-0.974622\pi$
$199$		−	31.6979i		−	0.159286i	0.996823	−	0.0796430i	$-0.0253780\pi$
$200$	170.878	−	44.1779i	0.854389	−	0.220890i
$201$		0			0
$202$	37.7585	+	10.1174i	0.186923	+	0.0500860i
$203$	10.1498	−	37.8796i	0.0499990	−	0.186599i
$204$		0			0
$205$	130.100	−	223.067i	0.634635	−	1.08813i
$206$	−173.731			−0.843352
$207$		0			0
$208$	173.927	+	173.927i	0.836190	+	0.836190i
$209$	100.100	+	57.7930i	0.478949	+	0.276522i
$210$		0			0
$211$	101.246	+	175.363i	0.479838	+	0.831103i	0.999733	−	0.0231271i	$-0.00736225\pi$
$211$	101.246	+	175.363i	0.479838	+	0.831103i	−0.519895	+	0.854230i	$0.674029\pi$
$212$	−19.1546	−	5.13247i	−0.0903521	−	0.0242098i
$213$		0			0
$214$	158.625	+	91.5822i	0.741238	+	0.427954i
$215$	168.108	+	169.595i	0.781899	+	0.788813i
$216$		0			0
$217$	26.9076	−	26.9076i	0.123998	−	0.123998i
$218$	−297.076	+	79.6013i	−1.36273	+	0.365144i
$219$		0			0
$220$	42.1339	−	24.0793i	0.191518	−	0.109452i
$221$	153.624	+	266.084i	0.695130	+	1.20400i
$222$		0			0
$223$	−64.0039	+	17.1498i	−0.287013	+	0.0769049i	−0.399453	−	0.916754i	$-0.630800\pi$
$223$	−64.0039	+	17.1498i	−0.287013	+	0.0769049i	0.112440	+	0.993658i	$0.464133\pi$
$224$			24.6954i			0.110247i
$225$		0			0
$226$	−439.653			−1.94537
$227$	75.6965	+	282.503i	0.333465	+	1.24451i	0.905524	+	0.424295i	$0.139478\pi$
$227$	75.6965	+	282.503i	0.333465	+	1.24451i	−0.572059	+	0.820212i	$0.693855\pi$
$228$		0			0
$229$	−229.797	+	132.673i	−1.00348	+	0.579358i	−0.909276	−	0.416195i	$-0.863364\pi$
$229$	−229.797	+	132.673i	−1.00348	+	0.579358i	−0.0942027	+	0.995553i	$0.530030\pi$
$230$	119.945	+	209.879i	0.521499	+	0.912515i
$231$		0			0
$232$	35.1121	+	131.040i	0.151345	+	0.564829i
$233$	59.9258	+	59.9258i	0.257192	+	0.257192i	0.823911	−	0.566719i	$-0.191787\pi$
$233$	59.9258	+	59.9258i	0.257192	+	0.257192i	−0.566719	+	0.823911i	$0.691787\pi$
$234$		0			0
$235$	−188.971	+	187.315i	−0.804132	+	0.797084i
$236$	38.0160	−	65.8457i	0.161085	−	0.279007i
$237$		0			0
$238$	−26.6156	+	99.3307i	−0.111830	+	0.417356i
$239$	168.749	−	97.4274i	0.706063	−	0.407646i	−0.103538	−	0.994625i	$-0.533016\pi$
$239$	168.749	−	97.4274i	0.706063	−	0.407646i	0.809602	+	0.586980i	$0.199683\pi$
$240$		0			0
$241$	9.02748	−	15.6361i	0.0374584	−	0.0648799i	−0.846688	−	0.532089i	$-0.821407\pi$
$241$	9.02748	−	15.6361i	0.0374584	−	0.0648799i	0.884147	+	0.467209i	$0.154740\pi$
$242$	−60.8943	+	60.8943i	−0.251629	+	0.251629i
$243$		0			0
$244$			79.3336i			0.325138i
$245$	−193.647	−	112.942i	−0.790396	−	0.460986i
$246$		0			0
$247$	117.332	+	31.4390i	0.475028	+	0.127283i
$248$	−34.0711	+	127.155i	−0.137384	+	0.512722i
$249$		0			0
$250$	−67.1438	−	264.508i	−0.268575	−	1.05803i
$251$	319.556			1.27313			0.636566	−	0.771223i	$-0.280354\pi$
$251$	319.556			1.27313			0.636566	+	0.771223i	$0.280354\pi$
$252$		0			0
$253$	−198.349	−	198.349i	−0.783989	−	0.783989i
$254$	−388.621	−	224.371i	−1.53001	−	0.883349i
$255$		0			0
$256$	−71.0326	−	123.032i	−0.277471	−	0.480594i
$257$	126.459	+	33.8846i	0.492058	+	0.131847i	0.496312	−	0.868144i	$-0.334687\pi$
$257$	126.459	+	33.8846i	0.492058	+	0.131847i	−0.00425348	+	0.999991i	$0.501354\pi$
$258$		0			0
$259$	−81.5757	−	47.0977i	−0.314964	−	0.181845i
$260$	36.2208	−	35.9033i	0.139311	−	0.138090i
$261$		0			0
$262$	−340.095	+	340.095i	−1.29807	+	1.29807i
$263$	494.002	−	132.368i	1.87834	−	0.503299i	0.878671	−	0.477428i	$-0.158431\pi$
$263$	494.002	−	132.368i	1.87834	−	0.503299i	0.999665	−	0.0258709i	$-0.00823588\pi$
$264$		0			0
$265$	34.0409	−	124.842i	0.128456	−	0.471100i
$266$	20.3280	+	35.2091i	0.0764210	+	0.132365i
$267$		0			0
$268$	14.5002	−	3.88532i	0.0541053	−	0.0144975i
$269$			220.179i			0.818508i	0.912421	+	0.409254i	$0.134211\pi$
$269$			220.179i			0.818508i	−0.912421	+	0.409254i	$0.865789\pi$
$270$		0			0
$271$	−298.400			−1.10111			−0.550553	−	0.834800i	$-0.685583\pi$
$271$	−298.400			−1.10111			−0.550553	+	0.834800i	$0.685583\pi$
$272$	−110.383	−	411.957i	−0.405822	−	1.51455i
$273$		0			0
$274$	−153.538	+	88.6454i	−0.560359	+	0.323523i
$275$	155.914	+	275.626i	0.566959	+	1.00228i
$276$		0			0
$277$	93.2365	+	347.963i	0.336594	+	1.25619i	0.902131	+	0.431462i	$0.142002\pi$
$277$	93.2365	+	347.963i	0.336594	+	1.25619i	−0.565537	+	0.824723i	$0.691331\pi$
$278$	−399.833	−	399.833i	−1.43825	−	1.43825i
$279$		0			0
$280$	−72.0371	−	0.317105i	−0.257275	−	0.00113252i
$281$	34.8739	−	60.4033i	0.124106	−	0.214959i	−0.797277	−	0.603614i	$-0.793727\pi$
$281$	34.8739	−	60.4033i	0.124106	−	0.214959i	0.921383	+	0.388655i	$0.127060\pi$
$282$		0			0
$283$	−16.5108	+	61.6190i	−0.0583419	+	0.217735i	−0.988942	−	0.148302i	$-0.952619\pi$
$283$	−16.5108	+	61.6190i	−0.0583419	+	0.217735i	0.930600	+	0.366037i	$0.119286\pi$
$284$	−36.2262	+	20.9152i	−0.127557	+	0.0736450i
$285$		0			0
$286$	−184.058	+	318.798i	−0.643559	+	1.11468i
$287$	−74.5288	+	74.5288i	−0.259682	+	0.259682i
$288$		0			0
$289$		−	243.737i		−	0.843380i
$290$	202.850	−	53.3976i	0.699484	−	0.184130i
$291$		0			0
$292$	8.51799	+	2.28239i	0.0291712	+	0.00781640i
$293$	34.3019	−	128.016i	0.117071	−	0.436916i	−0.882362	−	0.470571i	$-0.844048\pi$
$293$	34.3019	−	128.016i	0.117071	−	0.436916i	0.999434	+	0.0336549i	$0.0107147\pi$
$294$		0			0
$295$	428.568	+	249.956i	1.45277	+	0.847308i
$296$	325.859			1.10088
$297$		0			0
$298$	201.838	+	201.838i	0.677308	+	0.677308i
$299$	−255.296	−	147.395i	−0.853832	−	0.492960i
$300$		0			0
$301$	−48.7326	−	84.4074i	−0.161902	−	0.280423i
$302$	−266.329	−	71.3626i	−0.881883	−	0.236300i
$303$		0			0
$304$	−146.024	−	84.3067i	−0.480341	−	0.277325i
$305$	−517.672	−	2.27877i	−1.69729	−	0.00747139i
$306$		0			0
$307$	−110.408	+	110.408i	−0.359634	+	0.359634i	−0.863678	−	0.504044i	$-0.831845\pi$
$307$	−110.408	+	110.408i	−0.359634	+	0.359634i	0.504044	+	0.863678i	$0.331845\pi$
$308$	−19.1325	+	5.12654i	−0.0621185	+	0.0166446i
$309$		0			0
$310$	196.372	+	53.5454i	0.633459	+	0.172727i
$311$	−151.964	−	263.209i	−0.488630	−	0.846331i	0.511285	−	0.859411i	$-0.329170\pi$
$311$	−151.964	−	263.209i	−0.488630	−	0.846331i	−0.999914	+	0.0130800i	$0.995836\pi$
$312$		0			0
$313$	70.0305	−	18.7646i	0.223740	−	0.0599508i	−0.145208	−	0.989401i	$-0.546385\pi$
$313$	70.0305	−	18.7646i	0.223740	−	0.0599508i	0.368947	+	0.929450i	$0.379718\pi$
$314$			403.347i			1.28455i
$315$		0			0
$316$	−108.072			−0.341999
$317$	22.3631	+	83.4604i	0.0705462	+	0.263282i	0.992187	−	0.124763i	$-0.0398171\pi$
$317$	22.3631	+	83.4604i	0.0705462	+	0.263282i	−0.921640	+	0.388045i	$0.873150\pi$
$318$		0			0
$319$	−210.795	+	121.703i	−0.660800	+	0.381513i
$320$	206.171	−	117.826i	0.644284	−	0.368206i
$321$		0			0
$322$	−25.5365	−	95.3034i	−0.0793058	−	0.295973i
$323$	−148.930	−	148.930i	−0.461084	−	0.461084i
$324$		0			0
$325$	233.238	+	237.381i	0.717656	+	0.730405i
$326$	−108.119	+	187.267i	−0.331653	+	0.574439i
$327$		0			0
$328$	94.3703	−	352.195i	0.287714	−	1.07376i
$329$	94.0509	−	54.3003i	0.285869	−	0.165047i
$330$		0			0
$331$	−124.188	+	215.101i	−0.375192	+	0.649851i	−0.990356	−	0.138548i	$-0.955756\pi$
$331$	−124.188	+	215.101i	−0.375192	+	0.649851i	0.615164	+	0.788399i	$0.289090\pi$
$332$	36.9173	−	36.9173i	0.111197	−	0.111197i
$333$		0			0
$334$			211.913i			0.634469i
$335$	24.9362	+	94.7293i	0.0744365	+	0.282774i
$336$		0			0
$337$	−190.227	−	50.9712i	−0.564472	−	0.151250i	−0.0347120	−	0.999397i	$-0.511051\pi$
$337$	−190.227	−	50.9712i	−0.564472	−	0.151250i	−0.529760	+	0.848147i	$0.677718\pi$
$338$	−4.63335	+	17.2919i	−0.0137081	+	0.0511595i
$339$		0			0
$340$	−85.5157	+	22.5109i	−0.251517	+	0.0662085i
$341$	−236.189			−0.692636
$342$		0			0
$343$	135.409	+	135.409i	0.394777	+	0.394777i
$344$	291.998	+	168.585i	0.848832	+	0.490073i
$345$		0			0
$346$	−75.2854	−	130.398i	−0.217588	−	0.376873i
$347$	−27.4777	−	7.36263i	−0.0791865	−	0.0212180i	0.219008	−	0.975723i	$-0.429718\pi$
$347$	−27.4777	−	7.36263i	−0.0791865	−	0.0212180i	−0.298195	+	0.954505i	$0.596384\pi$
$348$		0			0
$349$	−515.156	−	297.426i	−1.47609	−	0.852222i	−0.476456	−	0.879198i	$-0.658079\pi$
$349$	−515.156	−	297.426i	−1.47609	−	0.852222i	−0.999636	+	0.0269761i	$0.991412\pi$
$350$	−0.980599	+	111.380i	−0.00280171	+	0.318228i
$351$		0			0
$352$	108.385	−	108.385i	0.307912	−	0.307912i
$353$	315.597	−	84.5639i	0.894042	−	0.239558i	0.217586	−	0.976041i	$-0.430182\pi$
$353$	315.597	−	84.5639i	0.894042	−	0.239558i	0.676456	+	0.736483i	$0.263515\pi$
$354$		0			0
$355$	−135.436	−	236.986i	−0.381511	−	0.667566i
$356$	22.7521	+	39.4078i	0.0639104	+	0.110696i
$357$		0			0
$358$	335.506	−	89.8985i	0.937166	−	0.251113i
$359$		−	245.484i		−	0.683799i	−0.939736	−	0.341900i	$-0.888930\pi$
$359$		−	245.484i		−	0.683799i	0.939736	−	0.341900i	$-0.111070\pi$
$360$		0			0
$361$	277.731			0.769339
$362$	−35.8200	−	133.682i	−0.0989502	−	0.369287i
$363$		0			0
$364$	−18.0271	+	10.4080i	−0.0495250	+	0.0285933i
$365$	−15.1378	+	55.5165i	−0.0414735	+	0.152100i
$366$		0			0
$367$	114.721	+	428.144i	0.312591	+	1.16660i	0.926212	+	0.377004i	$0.123046\pi$
$367$	114.721	+	428.144i	0.312591	+	1.16660i	−0.613621	+	0.789601i	$0.710288\pi$
$368$	289.346	+	289.346i	0.786266	+	0.786266i
$369$		0			0
$370$	2.21786	−	503.835i	0.00599423	−	1.36172i
$371$	−26.4075	+	45.7392i	−0.0711793	+	0.123286i
$372$		0			0
$373$	51.4256	−	191.923i	0.137870	−	0.514539i	−0.862099	−	0.506739i	$-0.830851\pi$
$373$	51.4256	−	191.923i	0.137870	−	0.514539i	0.999970	−	0.00779940i	$-0.00248265\pi$
$374$	552.764	−	319.138i	1.47798	−	0.853311i
$375$		0			0
$376$	−187.846	+	325.359i	−0.499591	+	0.865316i
$377$	−180.877	+	180.877i	−0.479779	+	0.479779i
$378$		0			0
$379$		−	177.166i		−	0.467456i	−0.972302	−	0.233728i	$-0.924908\pi$
$379$		−	177.166i		−	0.467456i	0.972302	−	0.233728i	$-0.0750925\pi$
$380$	−17.6134	+	30.1995i	−0.0463511	+	0.0794725i
$381$		0			0
$382$	260.424	+	69.7805i	0.681739	+	0.182671i
$383$	−4.44480	+	16.5882i	−0.0116052	+	0.0433113i	−0.971486	−	0.237098i	$-0.923804\pi$
$383$	−4.44480	+	16.5882i	−0.0116052	+	0.0433113i	0.959880	+	0.280410i	$0.0904703\pi$
$384$		0			0
$385$	−32.9024	−	124.992i	−0.0854608	−	0.324654i
$386$	−542.708			−1.40598
$387$		0			0
$388$	61.6273	+	61.6273i	0.158833	+	0.158833i
$389$	−149.347	−	86.2254i	−0.383925	−	0.221659i	0.295600	−	0.955312i	$-0.404481\pi$
$389$	−149.347	−	86.2254i	−0.383925	−	0.221659i	−0.679524	+	0.733653i	$0.737814\pi$
$390$		0			0
$391$	255.569	+	442.658i	0.653628	+	1.13212i
$392$	−305.744	−	81.9239i	−0.779960	−	0.208990i
$393$		0			0
$394$	142.373	+	82.1992i	0.361353	+	0.208628i
$395$	3.10425	−	705.196i	0.00785886	−	1.78531i
$396$		0			0
$397$	4.98532	−	4.98532i	0.0125575	−	0.0125575i	−0.700800	−	0.713358i	$-0.747174\pi$
$397$	4.98532	−	4.98532i	0.0125575	−	0.0125575i	0.713358	+	0.700800i	$0.247174\pi$
$398$	−66.8440	+	17.9108i	−0.167950	+	0.0450020i
$399$		0			0
$400$	−227.442	−	402.075i	−0.568605	−	1.00519i
$401$	−354.129	−	613.369i	−0.883115	−	1.52960i	−0.847859	−	0.530221i	$-0.822109\pi$
$401$	−354.129	−	613.369i	−0.883115	−	1.52960i	−0.0352554	−	0.999378i	$-0.511224\pi$
$402$		0			0
$403$	−239.757	+	64.2426i	−0.594929	+	0.159411i
$404$		−	13.7199i		−	0.0339602i
$405$		0			0
$406$	−85.6149			−0.210874
$407$	151.320	+	564.733i	0.371793	+	1.38755i
$408$		0			0
$409$	−344.913	+	199.136i	−0.843309	+	0.486885i	−0.858388	−	0.513002i	$-0.828533\pi$
$409$	−344.913	+	199.136i	−0.843309	+	0.486885i	0.0150787	+	0.999886i	$0.495200\pi$
$410$	−543.912	−	148.310i	−1.32662	−	0.361732i
$411$		0			0
$412$	15.7816	+	58.8979i	0.0383050	+	0.142956i
$413$	−143.189	−	143.189i	−0.346704	−	0.346704i
$414$		0			0
$415$	239.834	+	241.955i	0.577914	+	0.583025i
$416$	80.5419	−	139.503i	0.193610	−	0.335343i
$417$		0			0
$418$	65.3115	−	243.746i	0.156248	−	0.583124i
$419$	−411.732	+	237.714i	−0.982654	+	0.567336i	−0.903070	−	0.429493i	$-0.858692\pi$
$419$	−411.732	+	237.714i	−0.982654	+	0.567336i	−0.0795838	+	0.996828i	$0.525359\pi$
$420$		0			0
$421$	285.120	−	493.842i	0.677245	−	1.17302i	−0.298563	−	0.954390i	$-0.596507\pi$
$421$	285.120	−	493.842i	0.677245	−	1.17302i	0.975807	−	0.218632i	$-0.0701595\pi$
$422$	312.593	−	312.593i	0.740743	−	0.740743i
$423$		0			0
$424$		−	182.708i		−	0.430915i
$425$	−144.433	−	558.659i	−0.339842	−	1.31449i
$426$		0			0
$427$	204.093	+	54.6866i	0.477970	+	0.128072i
$428$	16.6386	−	62.0961i	0.0388753	−	0.145084i
$429$		0			0
$430$	262.650	−	450.333i	0.610814	−	1.04729i
$431$	565.177			1.31131			0.655657	−	0.755059i	$-0.272392\pi$
$431$	565.177			1.31131			0.655657	+	0.755059i	$0.272392\pi$
$432$		0			0
$433$	−34.7884	−	34.7884i	−0.0803428	−	0.0803428i	0.665793	−	0.746136i	$-0.268093\pi$
$433$	−34.7884	−	34.7884i	−0.0803428	−	0.0803428i	−0.746136	+	0.665793i	$0.768093\pi$
$434$	−71.9464	−	41.5383i	−0.165775	−	0.0957103i
$435$		0			0
$436$	53.9727	+	93.4834i	0.123791	+	0.214411i
$437$	195.194	+	52.3020i	0.446667	+	0.119684i
$438$		0			0
$439$	−271.216	−	156.587i	−0.617804	−	0.356689i	0.158209	−	0.987406i	$-0.449428\pi$
$439$	−271.216	−	156.587i	−0.617804	−	0.356689i	−0.776014	+	0.630716i	$0.782761\pi$
$440$	314.771	+	317.554i	0.715388	+	0.721714i
$441$		0			0
$442$	474.309	−	474.309i	1.07310	−	1.07310i
$443$	−446.109	+	119.535i	−1.00702	+	0.269830i	−0.724383	−	0.689397i	$-0.757875\pi$
$443$	−446.109	+	119.535i	−1.00702	+	0.269830i	−0.282636	+	0.959227i	$0.591209\pi$
$444$		0			0
$445$	−257.799	+	147.331i	−0.579325	+	0.331082i
$446$	72.3304	+	125.280i	0.162176	+	0.280897i
$447$		0			0
$448$	−93.6198	+	25.0854i	−0.208973	+	0.0559941i
$449$			3.80236i			0.00846851i	0.999991	+	0.00423425i	$0.00134781\pi$
$449$			3.80236i			0.00846851i	−0.999991	+	0.00423425i	$0.998652\pi$
$450$		0			0
$451$	654.196			1.45055
$452$	39.9380	+	149.051i	0.0883584	+	0.329758i
$453$		0			0
$454$	552.966	−	319.255i	1.21799	−	0.703205i
$455$	−67.3968	−	117.930i	−0.148125	−	0.259188i
$456$		0			0
$457$	−183.873	−	686.222i	−0.402347	−	1.50158i	−0.808896	−	0.587951i	$-0.799935\pi$
$457$	−183.873	−	686.222i	−0.402347	−	1.50158i	0.406549	−	0.913629i	$-0.366732\pi$
$458$	409.625	+	409.625i	0.894377	+	0.894377i
$459$		0			0
$460$	60.2570	−	59.7288i	0.130993	−	0.129845i
$461$	52.8552	−	91.5479i	0.114653	−	0.198586i	−0.802988	−	0.595996i	$-0.796758\pi$
$461$	52.8552	−	91.5479i	0.114653	−	0.198586i	0.917641	+	0.397410i	$0.130091\pi$
$462$		0			0
$463$	−224.884	+	839.277i	−0.485710	+	1.81269i	0.0911330	+	0.995839i	$0.470951\pi$
$463$	−224.884	+	839.277i	−0.485710	+	1.81269i	−0.576843	+	0.816855i	$0.695716\pi$
$464$	307.502	−	177.536i	0.662720	−	0.382621i
$465$		0			0
$466$	92.5096	−	160.231i	0.198519	−	0.343844i
$467$	476.135	−	476.135i	1.01956	−	1.01956i	0.0197563	−	0.999805i	$-0.493711\pi$
$467$	476.135	−	476.135i	1.01956	−	1.01956i	0.999805	−	0.0197563i	$-0.00628905\pi$
$468$		0			0
$469$		−	39.9814i		−	0.0852482i
$470$	501.784	+	292.658i	1.06762	+	0.622676i
$471$		0			0
$472$	676.656	+	181.309i	1.43359	+	0.384130i
$473$	−156.572	+	584.336i	−0.331020	+	1.23538i
$474$		0			0
$475$	−196.554	−	115.799i	−0.413797	−	0.243788i
$476$	36.0927			0.0758251
$477$		0			0
$478$	−300.804	−	300.804i	−0.629298	−	0.629298i
$479$	458.453	+	264.688i	0.957105	+	0.552585i	0.895281	−	0.445502i	$-0.146975\pi$
$479$	458.453	+	264.688i	0.957105	+	0.552585i	0.0618243	+	0.998087i	$0.480308\pi$
$480$		0			0
$481$	307.211	+	532.105i	0.638692	+	1.10625i
$482$	−38.0740	−	10.2019i	−0.0789917	−	0.0211658i
$483$		0			0
$484$	26.1759	+	15.1127i	0.0540825	+	0.0312245i
$485$	−403.904	+	400.363i	−0.832791	+	0.825492i
$486$		0			0
$487$	−386.577	+	386.577i	−0.793793	+	0.793793i	−0.982109	−	0.188315i	$-0.939697\pi$
$487$	−386.577	+	386.577i	−0.793793	+	0.793793i	0.188315	+	0.982109i	$0.439697\pi$
$488$	−706.038	+	189.182i	−1.44680	+	0.387669i
$489$		0			0
$490$	−128.750	+	472.177i	−0.262755	+	0.963626i
$491$	147.395	+	255.296i	0.300194	+	0.519951i	0.976180	−	0.216963i	$-0.0696152\pi$
$491$	147.395	+	255.296i	0.300194	+	0.519951i	−0.675986	+	0.736915i	$0.736282\pi$
$492$		0			0
$493$	428.416	−	114.794i	0.868998	−	0.232847i
$494$		−	265.192i		−	0.536826i
$495$		0			0
$496$	344.545			0.694648
$497$	28.8347	+	107.613i	0.0580175	+	0.216524i
$498$		0			0
$499$	747.810	−	431.748i	1.49862	−	0.865227i	0.498619	−	0.866821i	$-0.333841\pi$
$499$	747.810	−	431.748i	1.49862	−	0.865227i	0.999999	+	0.00159434i	$0.000507494\pi$
$500$	−83.5737	+	46.7908i	−0.167147	+	0.0935816i
$501$		0			0
$502$	−180.564	−	673.874i	−0.359689	−	1.34238i
$503$	336.760	+	336.760i	0.669503	+	0.669503i	0.957601	−	0.288098i	$-0.0930228\pi$
$503$	336.760	+	336.760i	0.669503	+	0.669503i	−0.288098	+	0.957601i	$0.593023\pi$
$504$		0			0
$505$	89.5259	+	0.394090i	0.177279	+	0.000780376i
$506$	−306.199	+	530.352i	−0.605136	+	1.04813i
$507$		0			0
$508$	−40.7636	+	152.132i	−0.0802433	+	0.299472i
$509$	−429.289	+	247.850i	−0.843397	+	0.486935i	−0.858417	−	0.512952i	$-0.828552\pi$
$509$	−429.289	+	247.850i	−0.843397	+	0.486935i	0.0150207	+	0.999887i	$0.495219\pi$
$510$		0			0
$511$	11.7433	−	20.3400i	0.0229810	−	0.0398043i
$512$	210.862	−	210.862i	0.411839	−	0.411839i
$513$		0			0
$514$		−	285.821i		−	0.556072i
$515$	−384.777	+	101.288i	−0.747140	+	0.196675i
$516$		0			0
$517$	−651.096	−	174.461i	−1.25937	−	0.337448i
$518$	−53.2249	+	198.638i	−0.102751	+	0.383471i
$519$		0			0
$520$	405.899	+	236.734i	0.780576	+	0.455259i
$521$	225.358			0.432550			0.216275	−	0.976333i	$-0.430609\pi$
$521$	225.358			0.432550			0.216275	+	0.976333i	$0.430609\pi$
$522$		0			0
$523$	−442.494	−	442.494i	−0.846069	−	0.846069i	0.143571	−	0.989640i	$-0.454142\pi$
$523$	−442.494	−	442.494i	−0.846069	−	0.846069i	−0.989640	+	0.143571i	$0.954142\pi$
$524$	146.193	+	84.4045i	0.278994	+	0.161077i
$525$		0			0
$526$	−558.269	−	966.950i	−1.06135	−	1.83831i
$527$	415.714	+	111.390i	0.788832	+	0.211367i
$528$		0			0
$529$	33.4173	+	19.2935i	0.0631707	+	0.0364716i
$530$	−282.499	−	1.24355i	−0.533016	−	0.00234632i
$531$		0			0
$532$	10.0900	−	10.0900i	0.0189661	−	0.0189661i
$533$	664.078	−	177.939i	1.24593	−	0.333845i
$534$		0			0
$535$	404.715	+	110.355i	0.756477	+	0.206271i
$536$	69.1557	+	119.781i	0.129022	+	0.223472i
$537$		0			0
$538$	464.309	−	124.411i	0.863028	−	0.231248i
$539$		−	567.916i		−	1.05365i
$540$		0			0
$541$	223.593			0.413295			0.206647	−	0.978415i	$-0.433745\pi$
$541$	223.593			0.413295			0.206647	+	0.978415i	$0.433745\pi$
$542$	168.610	+	629.260i	0.311088	+	1.16100i
$543$		0			0
$544$	−241.884	+	139.652i	−0.444640	+	0.256713i
$545$	−611.554	+	349.500i	−1.12212	+	0.641285i
$546$		0			0
$547$	149.145	+	556.615i	0.272659	+	1.01758i	0.957394	+	0.288785i	$0.0932514\pi$
$547$	149.145	+	556.615i	0.272659	+	1.01758i	−0.684735	+	0.728792i	$0.740082\pi$
$548$	43.9999	+	43.9999i	0.0802917	+	0.0802917i
$549$		0			0
$550$	493.137	−	484.530i	0.896613	−	0.880963i
$551$	87.6752	−	151.858i	0.159120	−	0.275604i
$552$		0			0
$553$	−74.4965	+	278.025i	−0.134713	+	0.502757i
$554$	681.096	−	393.231i	1.22942	−	0.709804i
$555$		0			0
$556$	−99.2302	+	171.872i	−0.178472	+	0.309122i
$557$	42.5030	−	42.5030i	0.0763070	−	0.0763070i	−0.667923	−	0.744230i	$-0.732817\pi$
$557$	42.5030	−	42.5030i	0.0763070	−	0.0763070i	0.744230	+	0.667923i	$0.232817\pi$
$558$		0			0
$559$			635.750i			1.13730i
$560$	47.9971	+	182.334i	0.0857091	+	0.325597i
$561$		0			0
$562$	−147.083	−	39.4108i	−0.261713	−	0.0701259i
$563$	−162.816	+	607.639i	−0.289194	+	1.07929i	0.656525	+	0.754304i	$0.272026\pi$
$563$	−162.816	+	607.639i	−0.289194	+	1.07929i	−0.945719	+	0.324984i	$0.894641\pi$
$564$		0			0
$565$	−973.740	+	256.324i	−1.72343	+	0.453671i
$566$	139.270			0.246061
$567$		0			0
$568$	−272.523	−	272.523i	−0.479795	−	0.479795i
$569$	−523.215	−	302.078i	−0.919535	−	0.530894i	−0.0360482	−	0.999350i	$-0.511477\pi$
$569$	−523.215	−	302.078i	−0.919535	−	0.530894i	−0.883487	+	0.468456i	$0.844810\pi$
$570$		0			0
$571$	16.4403	+	28.4755i	0.0287921	+	0.0498695i	0.880062	−	0.474858i	$-0.157501\pi$
$571$	16.4403	+	28.4755i	0.0287921	+	0.0498695i	−0.851270	+	0.524727i	$0.824167\pi$
$572$	124.798	+	33.4396i	0.218179	+	0.0584608i
$573$		0			0
$574$	199.277	+	115.053i	0.347173	+	0.200440i
$575$	388.015	+	394.908i	0.674809	+	0.686797i
$576$		0			0
$577$	536.453	−	536.453i	0.929729	−	0.929729i	−0.0679593	−	0.997688i	$-0.521649\pi$
$577$	536.453	−	536.453i	0.929729	−	0.929729i	0.997688	+	0.0679593i	$0.0216488\pi$
$578$	−513.988	+	137.723i	−0.889253	+	0.238275i
$579$		0			0
$580$	−36.5297	−	63.9194i	−0.0629822	−	0.110206i
$581$	−69.5252	−	120.421i	−0.119665	−	0.207265i
$582$		0			0
$583$	316.643	−	84.8443i	0.543128	−	0.145531i
$584$			81.2494i			0.139126i
$585$		0			0
$586$	−289.341			−0.493756
$587$	−77.4800	−	289.159i	−0.131993	−	0.492605i	0.867999	−	0.496566i	$-0.165406\pi$
$587$	−77.4800	−	289.159i	−0.131993	−	0.492605i	−0.999992	+	0.00396077i	$0.998739\pi$
$588$		0			0
$589$	147.356	−	85.0757i	0.250179	−	0.144441i
$590$	284.942	−	1044.99i	0.482952	−	1.77118i
$591$		0			0
$592$	−220.741	−	823.815i	−0.372873	−	1.39158i
$593$	9.85573	+	9.85573i	0.0166201	+	0.0166201i	0.715368	−	0.698748i	$-0.246259\pi$
$593$	9.85573	+	9.85573i	0.0166201	+	0.0166201i	−0.698748	+	0.715368i	$0.746259\pi$
$594$		0			0
$595$	−1.03673	+	235.514i	−0.00174240	+	0.395823i
$596$	50.0919	−	86.7617i	0.0840468	−	0.145573i
$597$		0			0
$598$	−166.570	+	621.648i	−0.278545	+	1.03955i
$599$	−98.0614	+	56.6158i	−0.163709	+	0.0945172i	−0.579616	−	0.814890i	$-0.696797\pi$
$599$	−98.0614	+	56.6158i	−0.163709	+	0.0945172i	0.415907	+	0.909407i	$0.363464\pi$
$600$		0			0
$601$	408.039	−	706.744i	0.678933	−	1.17595i	−0.296370	−	0.955073i	$-0.595776\pi$
$601$	408.039	−	706.744i	0.678933	−	1.17595i	0.975303	−	0.220873i	$-0.0708907\pi$
$602$	−150.461	+	150.461i	−0.249935	+	0.249935i
$603$		0			0
$604$			96.7730i			0.160220i
$605$	−99.3660	+	170.371i	−0.164241	+	0.281604i
$606$		0			0
$607$	578.568	+	155.027i	0.953161	+	0.255399i	0.701703	−	0.712470i	$-0.252423\pi$
$607$	578.568	+	155.027i	0.953161	+	0.255399i	0.251458	+	0.967868i	$0.419090\pi$
$608$	−28.5797	+	106.661i	−0.0470060	+	0.175429i
$609$		0			0
$610$	287.704	+	1092.95i	0.471645	+	1.79172i
$611$	−708.384			−1.15938
$612$		0			0
$613$	567.736	+	567.736i	0.926160	+	0.926160i	0.997455	−	0.0712948i	$-0.0227131\pi$
$613$	567.736	+	567.736i	0.926160	+	0.926160i	−0.0712948	+	0.997455i	$0.522713\pi$
$614$	295.211	+	170.440i	0.480800	+	0.277590i
$615$		0			0
$616$	−91.2484	−	158.047i	−0.148130	−	0.256569i
$617$	927.600	+	248.550i	1.50340	+	0.402836i	0.914238	−	0.405177i	$-0.132790\pi$
$617$	927.600	+	248.550i	1.50340	+	0.402836i	0.589165	+	0.808012i	$0.299457\pi$
$618$		0			0
$619$	−248.631	−	143.547i	−0.401665	−	0.231902i	0.285537	−	0.958368i	$-0.407828\pi$
$619$	−248.631	−	143.547i	−0.401665	−	0.231902i	−0.687202	+	0.726466i	$0.741161\pi$
$620$	0.314467	−	71.4379i	0.000507205	−	0.115222i
$621$		0			0
$622$	−469.184	+	469.184i	−0.754315	+	0.754315i
$623$	117.064	−	31.3671i	0.187903	−	0.0503485i
$624$		0			0
$625$	−302.922	−	546.684i	−0.484675	−	0.874695i
$626$	−79.1410	−	137.076i	−0.126423	−	0.218972i
$627$		0			0
$628$	136.742	−	36.6400i	0.217743	−	0.0583439i
$629$		−	1065.35i		−	1.69372i
$630$		0			0
$631$	−431.640			−0.684057			−0.342029	−	0.939690i	$-0.611114\pi$
$631$	−431.640			−0.684057			−0.342029	+	0.939690i	$0.611114\pi$
$632$	−257.713	−	961.797i	−0.407773	−	1.52183i
$633$		0			0
$634$	163.364	−	94.3181i	0.257671	−	0.148767i
$635$	−991.528	−	270.363i	−1.56146	−	0.425768i
$636$		0			0
$637$	−154.471	−	576.494i	−0.242498	−	0.905015i
$638$	375.754	+	375.754i	0.588956	+	0.588956i
$639$		0			0
$640$	−535.344	−	540.078i	−0.836475	−	0.843872i
$641$	169.961	−	294.381i	0.265150	−	0.459253i	−0.702453	−	0.711730i	$-0.747912\pi$
$641$	169.961	−	294.381i	0.265150	−	0.459253i	0.967603	+	0.252477i	$0.0812453\pi$
$642$		0			0
$643$	−54.8829	+	204.826i	−0.0853544	+	0.318547i	−0.995381	−	0.0960027i	$-0.969394\pi$
$643$	−54.8829	+	204.826i	−0.0853544	+	0.318547i	0.910027	+	0.414550i	$0.136061\pi$
$644$	−29.9899	+	17.3147i	−0.0465682	+	0.0268862i
$645$		0			0
$646$	−229.909	+	398.213i	−0.355896	+	0.616430i
$647$	−575.066	+	575.066i	−0.888819	+	0.888819i	−0.994410	−	0.105591i	$-0.966327\pi$
$647$	−575.066	+	575.066i	−0.888819	+	0.888819i	0.105591	+	0.994410i	$0.466327\pi$
$648$		0			0
$649$			1256.88i			1.93664i
$650$	368.796	−	625.980i	0.567378	−	0.963047i
$651$		0			0
$652$	73.3086	+	19.6430i	0.112436	+	0.0301273i
$653$	−17.1844	+	64.1329i	−0.0263160	+	0.0982128i	−0.977835	−	0.209378i	$-0.932856\pi$
$653$	−17.1844	+	64.1329i	−0.0263160	+	0.0982128i	0.951519	+	0.307591i	$0.0995228\pi$
$654$		0			0
$655$	−554.960	+	951.522i	−0.847268	+	1.45271i
$656$	−954.322			−1.45476
$657$		0			0
$658$	−167.651	−	167.651i	−0.254788	−	0.254788i
$659$	958.773	+	553.548i	1.45489	+	0.839981i	0.998753	−	0.0499281i	$-0.0158992\pi$
$659$	958.773	+	553.548i	1.45489	+	0.839981i	0.456137	+	0.889909i	$0.349233\pi$
$660$		0			0
$661$	−168.964	−	292.654i	−0.255619	−	0.442745i	0.709445	−	0.704761i	$-0.248946\pi$
$661$	−168.964	−	292.654i	−0.255619	−	0.442745i	−0.965063	+	0.262016i	$0.915613\pi$
$662$	523.773	+	140.345i	0.791198	+	0.212001i
$663$		0			0
$664$	416.584	+	240.515i	0.627385	+	0.362221i
$665$	65.5497	+	66.1294i	0.0985710	+	0.0994427i
$666$		0			0
$667$	−300.907	+	300.907i	−0.451134	+	0.451134i
$668$	71.8424	−	19.2501i	0.107548	−	0.0288175i
$669$		0			0
$670$	185.673	−	106.112i	0.277125	−	0.158376i
$671$	−655.728	−	1135.75i	−0.977240	−	1.69263i
$672$		0			0
$673$	−881.503	+	236.198i	−1.30981	+	0.350963i	−0.845152	−	0.534527i	$-0.820490\pi$
$673$	−881.503	+	236.198i	−1.30981	+	0.350963i	−0.464660	+	0.885489i	$0.653823\pi$
$674$			429.949i			0.637906i
$675$		0			0
$676$	6.28317			0.00929464
$677$	−170.665	−	636.930i	−0.252090	−	0.940812i	−0.969686	−	0.244353i	$-0.921424\pi$
$677$	−170.665	−	636.930i	−0.252090	−	0.940812i	0.717597	−	0.696459i	$-0.245242\pi$
$678$		0			0
$679$	201.023	−	116.061i	0.296057	−	0.170929i
$680$	−404.262	−	707.376i	−0.594504	−	1.04026i
$681$		0			0
$682$	133.458	+	498.071i	0.195686	+	0.730310i
$683$	−88.3335	−	88.3335i	−0.129332	−	0.129332i	0.639478	−	0.768810i	$-0.279151\pi$
$683$	−88.3335	−	88.3335i	−0.129332	−	0.129332i	−0.768810	+	0.639478i	$0.779151\pi$
$684$		0			0
$685$	−288.374	+	285.847i	−0.420984	+	0.417294i
$686$	209.035	−	362.060i	0.304716	−	0.527784i
$687$		0			0
$688$	228.403	−	852.412i	0.331981	−	1.23897i
$689$	298.349	−	172.252i	0.433017	−	0.250003i
$690$		0			0
$691$	−408.588	+	707.695i	−0.591300	+	1.02416i	0.402758	+	0.915307i	$0.368052\pi$
$691$	−408.588	+	707.695i	−0.591300	+	1.02416i	−0.994058	+	0.108855i	$0.965282\pi$
$692$	−37.3685	+	37.3685i	−0.0540007	+	0.0540007i
$693$		0			0
$694$			62.1048i			0.0894882i
$695$	−1118.66	−	652.439i	−1.60958	−	0.938761i
$696$		0			0
$697$	−1151.45	−	308.529i	−1.65200	−	0.442653i
$698$	−336.119	+	1254.41i	−0.481545	+	1.79715i
$699$		0			0
$700$	37.8489	−	9.78529i	0.0540699	−	0.0139790i
$701$	−626.425			−0.893616			−0.446808	−	0.894630i	$-0.647439\pi$
$701$	−626.425			−0.893616			−0.446808	+	0.894630i	$0.647439\pi$
$702$		0			0
$703$	−297.825	−	297.825i	−0.423648	−	0.423648i
$704$	520.983	+	300.790i	0.740033	+	0.427258i
$705$		0			0
$706$	−356.654	−	617.743i	−0.505175	−	0.874990i
$707$	−35.2957	−	9.45746i	−0.0499232	−	0.0133769i
$708$		0			0
$709$	82.1961	+	47.4559i	0.115932	+	0.0669336i	0.556845	−	0.830616i	$-0.312012\pi$
$709$	82.1961	+	47.4559i	0.115932	+	0.0669336i	−0.440912	+	0.897550i	$0.645345\pi$
$710$	−423.224	+	419.514i	−0.596090	+	0.590865i
$711$		0			0
$712$	−296.458	+	296.458i	−0.416374	+	0.416374i
$713$	−398.859	+	106.874i	−0.559410	+	0.149893i
$714$		0			0
$715$	−221.786	+	813.380i	−0.310191	+	1.13759i
$716$	−60.9545	−	105.576i	−0.0851320	−	0.147453i
$717$		0			0
$718$	−517.673	+	138.710i	−0.720992	+	0.193189i
$719$		−	377.998i		−	0.525727i	−0.964833	−	0.262864i	$-0.915333\pi$
$719$		−	377.998i		−	0.525727i	0.964833	−	0.262864i	$-0.0846670\pi$
$720$		0			0
$721$	162.399			0.225241
$722$	−156.931	−	585.675i	−0.217356	−	0.811185i
$723$		0			0
$724$	−42.0668	+	24.2873i	−0.0581033	+	0.0335460i
$725$	418.140	−	236.529i	0.576745	−	0.326248i
$726$		0			0
$727$	71.4219	+	266.550i	0.0982419	+	0.366644i	0.997491	−	0.0707930i	$-0.0225530\pi$
$727$	71.4219	+	266.550i	0.0982419	+	0.366644i	−0.899249	+	0.437437i	$0.855886\pi$
$728$	−135.615	−	135.615i	−0.186284	−	0.186284i
$729$		0			0
$730$	125.626	+	0.553000i	0.172090	+	0.000757535i
$731$	551.164	−	954.644i	0.753986	−	1.30594i
$732$		0			0
$733$	−130.531	+	487.149i	−0.178078	+	0.664596i	0.817929	+	0.575319i	$0.195122\pi$
$733$	−130.531	+	487.149i	−0.178078	+	0.664596i	−0.996007	+	0.0892766i	$0.971544\pi$
$734$	838.040	−	483.843i	1.14174	−	0.659186i
$735$		0			0
$736$	133.990	−	232.077i	0.182051	−	0.315322i
$737$	−175.474	+	175.474i	−0.238092	+	0.238092i
$738$		0			0
$739$			347.915i			0.470791i	0.971900	+	0.235396i	$0.0756386\pi$
$739$			347.915i			0.470791i	−0.971900	+	0.235396i	$0.924361\pi$
$740$	−171.011	+	45.0164i	−0.231096	+	0.0608330i
$741$		0			0
$742$	111.375	+	29.8430i	0.150102	+	0.0402196i
$743$	252.285	−	941.541i	0.339550	−	1.26722i	−0.559302	−	0.828964i	$-0.688931\pi$
$743$	252.285	−	941.541i	0.339550	−	1.26722i	0.898852	−	0.438252i	$-0.144402\pi$
$744$		0			0
$745$	564.704	+	329.355i	0.757991	+	0.442087i
$746$	−433.782			−0.581477
$747$		0			0
$748$	−158.407	−	158.407i	−0.211774	−	0.211774i
$749$	−148.279	−	85.6087i	−0.197969	−	0.114297i
$750$		0			0
$751$	−254.883	−	441.471i	−0.339392	−	0.587844i	0.644927	−	0.764244i	$-0.276888\pi$
$751$	−254.883	−	441.471i	−0.339392	−	0.587844i	−0.984318	+	0.176401i	$0.943555\pi$
$752$	949.800	+	254.498i	1.26303	+	0.338428i
$753$		0			0
$754$	483.634	+	279.226i	0.641424	+	0.370326i
$755$	−631.469	−	2.77970i	−0.836382	−	0.00368172i
$756$		0			0
$757$	280.253	−	280.253i	0.370215	−	0.370215i	−0.497340	−	0.867555i	$-0.665690\pi$
$757$	280.253	−	280.253i	0.370215	−	0.370215i	0.867555	+	0.497340i	$0.165690\pi$
$758$	−373.604	+	100.107i	−0.492881	+	0.132067i
$759$		0			0
$760$	−310.766	−	84.7373i	−0.408902	−	0.111496i
$761$	404.473	+	700.568i	0.531502	+	0.920589i	0.999324	+	0.0367662i	$0.0117057\pi$
$761$	404.473	+	700.568i	0.531502	+	0.920589i	−0.467822	+	0.883823i	$0.654961\pi$
$762$		0			0
$763$	277.699	−	74.4093i	0.363957	−	0.0975220i
$764$		−	94.6276i		−	0.123858i
$765$		0			0
$766$	37.4925			0.0489458
$767$	341.867	+	1275.86i	0.445719	+	1.66345i
$768$		0			0
$769$	449.923	−	259.763i	0.585075	−	0.337793i	−0.178073	−	0.984017i	$-0.556986\pi$
$769$	449.923	−	259.763i	0.585075	−	0.337793i	0.763148	+	0.646224i	$0.223653\pi$
$770$	−244.989	+	140.010i	−0.318168	+	0.181832i
$771$		0			0
$772$	49.2995	+	183.988i	0.0638595	+	0.238327i
$773$	436.114	+	436.114i	0.564184	+	0.564184i	0.930493	−	0.366309i	$-0.119379\pi$
$773$	436.114	+	436.114i	0.564184	+	0.564184i	−0.366309	+	0.930493i	$0.619379\pi$
$774$		0			0
$775$	466.142	+	4.10396i	0.601473	+	0.00529543i
$776$	−401.499	+	695.417i	−0.517396	+	0.896156i
$777$		0			0
$778$	−97.4427	+	363.661i	−0.125248	+	0.467431i
$779$	−408.146	+	235.643i	−0.523935	+	0.302494i
$780$		0			0
$781$	345.747	−	598.851i	0.442697	−	0.766775i
$782$	789.061	−	789.061i	1.00903	−	1.00903i
$783$		0			0
$784$			828.459i			1.05671i
$785$	235.158	+	893.331i	0.299564	+	1.13800i
$786$		0			0
$787$	−782.335	−	209.626i	−0.994073	−	0.266361i	−0.275112	−	0.961412i	$-0.588715\pi$
$787$	−782.335	−	209.626i	−0.994073	−	0.266361i	−0.718960	+	0.695051i	$0.755382\pi$
$788$	14.9339	−	55.7342i	0.0189517	−	0.0707286i
$789$		0			0
$790$	−1488.86	+	391.923i	−1.88463	+	0.496105i
$791$	410.977			0.519566
$792$		0			0
$793$	−974.554	−	974.554i	−1.22895	−	1.22895i
$794$	−13.3299	−	7.69602i	−0.0167883	−	0.00969271i
$795$		0			0
$796$	12.1442	+	21.0344i	0.0152565	+	0.0264251i
$797$	755.517	+	202.440i	0.947951	+	0.254003i	0.699492	−	0.714640i	$-0.253409\pi$
$797$	755.517	+	202.440i	0.947951	+	0.254003i	0.248458	+	0.968643i	$0.420076\pi$
$798$		0			0
$799$	1063.71	+	614.134i	1.33130	+	0.768629i
$800$	−215.792	+	212.025i	−0.269740	+	0.265032i
$801$		0			0
$802$	−1093.36	+	1093.36i	−1.36330	+	1.36330i
$803$	−140.810	+	37.7299i	−0.175355	+	0.0469862i
$804$		0			0
$805$	−112.121	−	196.189i	−0.139281	−	0.243713i
$806$	270.947	+	469.295i	0.336163	+	0.582251i
$807$		0			0
$808$	122.102	−	32.7171i	0.151116	−	0.0404914i
$809$		−	12.8828i		−	0.0159243i	−0.999968	−	0.00796215i	$-0.997466\pi$
$809$		−	12.8828i		−	0.0159243i	0.999968	−	0.00796215i	$-0.00253446\pi$
$810$		0			0
$811$	−513.954			−0.633729			−0.316864	−	0.948471i	$-0.602630\pi$
$811$	−513.954			−0.633729			−0.316864	+	0.948471i	$0.602630\pi$
$812$	7.77724	+	29.0251i	0.00957788	+	0.0357451i
$813$		0			0
$814$	1105.40	−	638.201i	1.35798	−	0.784031i
$815$	−130.281	+	477.793i	−0.159854	+	0.586249i
$816$		0			0
$817$	−112.795	−	420.958i	−0.138060	−	0.515249i
$818$	614.827	+	614.827i	0.751622	+	0.751622i
$819$		0			0
$820$	−0.871012	+	197.869i	−0.00106221	+	0.241304i
$821$	656.487	−	1137.07i	0.799619	−	1.38498i	−0.120246	−	0.992744i	$-0.538368\pi$
$821$	656.487	−	1137.07i	0.799619	−	1.38498i	0.919865	−	0.392236i	$-0.128298\pi$
$822$		0			0
$823$	−233.948	+	873.104i	−0.284262	+	1.06088i	0.665115	+	0.746741i	$0.268383\pi$
$823$	−233.948	+	873.104i	−0.284262	+	1.06088i	−0.949377	+	0.314139i	$0.898284\pi$
$824$	−486.535	+	280.901i	−0.590455	+	0.340899i
$825$		0			0
$826$	−221.046	+	382.863i	−0.267610	+	0.463514i
$827$	−117.925	+	117.925i	−0.142594	+	0.142594i	−0.774800	−	0.632206i	$-0.782150\pi$
$827$	−117.925	+	117.925i	−0.142594	+	0.142594i	0.632206	+	0.774800i	$0.282150\pi$
$828$		0			0
$829$		−	579.532i		−	0.699073i	−0.936923	−	0.349537i	$-0.886339\pi$
$829$		−	579.532i		−	0.699073i	0.936923	−	0.349537i	$-0.113661\pi$
$830$	374.713	−	642.475i	0.451462	−	0.774066i
$831$		0			0
$832$	610.667	+	163.628i	0.733974	+	0.196668i
$833$	−267.838	+	999.585i	−0.321534	+	1.19998i
$834$		0			0
$835$	123.548	+	469.343i	0.147962	+	0.562087i
$836$	−88.5673			−0.105942
$837$		0			0
$838$	733.935	+	733.935i	0.875817	+	0.875817i
$839$	−251.639	−	145.284i	−0.299928	−	0.173163i	0.342483	−	0.939524i	$-0.388732\pi$
$839$	−251.639	−	145.284i	−0.299928	−	0.173163i	−0.642410	+	0.766361i	$0.722065\pi$
$840$		0			0
$841$	−235.870	−	408.539i	−0.280464	−	0.485778i
$842$	−1202.51	−	322.212i	−1.42816	−	0.382675i
$843$		0			0
$844$	−134.371	−	77.5791i	−0.159207	−	0.0919184i
$845$	−0.180477	+	40.9993i	−0.000213583	+	0.0485199i
$846$		0			0
$847$	56.9225	−	56.9225i	0.0672048	−	0.0672048i
$848$	−461.910	+	123.768i	−0.544705	+	0.145953i
$849$		0			0
$850$	−1096.48	+	620.246i	−1.28998	+	0.729701i
$851$	511.076	+	885.210i	0.600560	+	1.04020i
$852$		0			0
$853$	359.918	−	96.4397i	0.421943	−	0.113059i	−0.0415985	−	0.999134i	$-0.513245\pi$
$853$	359.918	−	96.4397i	0.421943	−	0.113059i	0.463542	+	0.886075i	$0.346578\pi$
$854$		−	461.289i		−	0.540151i
$855$		0			0
$856$	592.308			0.691949
$857$	128.091	+	478.041i	0.149464	+	0.557807i	0.999516	+	0.0311085i	$0.00990374\pi$
$857$	128.091	+	478.041i	0.149464	+	0.557807i	−0.850052	+	0.526699i	$0.823430\pi$
$858$		0			0
$859$	510.012	−	294.456i	0.593728	−	0.342789i	−0.172842	−	0.984950i	$-0.555295\pi$
$859$	510.012	−	294.456i	0.593728	−	0.342789i	0.766570	+	0.642161i	$0.221962\pi$
$860$	−176.530	−	48.1350i	−0.205268	−	0.0559710i
$861$		0			0
$862$	−319.351	−	1191.84i	−0.370477	−	1.38264i
$863$	142.644	+	142.644i	0.165288	+	0.165288i	0.784905	−	0.619616i	$-0.212712\pi$
$863$	142.644	+	142.644i	0.165288	+	0.165288i	−0.619616	+	0.784905i	$0.712712\pi$
$864$		0			0
$865$	−242.766	−	244.912i	−0.280654	−	0.283136i
$866$	−53.7041	+	93.0183i	−0.0620140	+	0.107411i
$867$		0			0
$868$	−7.54666	+	28.1645i	−0.00869431	+	0.0324476i
$869$	1547.17	−	893.262i	1.78041	−	1.02792i
$870$		0			0
$871$	−130.396	+	225.853i	−0.149709	+	0.259303i
$872$	−703.260	+	703.260i	−0.806491	+	0.806491i
$873$		0			0
$874$		−	441.174i		−	0.504776i
$875$	62.7643	+	247.255i	0.0717307	+	0.282577i
$876$		0			0
$877$	1509.15	+	404.375i	1.72081	+	0.461089i	0.978033	−	0.208451i	$-0.0668423\pi$
$877$	1509.15	+	404.375i	1.72081	+	0.461089i	0.742775	+	0.669541i	$0.233509\pi$
$878$	−176.958	+	660.415i	−0.201546	+	0.752181i
$879$		0			0
$880$	589.590	−	1010.90i	0.669989	−	1.14875i
$881$	−395.302			−0.448697			−0.224349	−	0.974509i	$-0.572025\pi$
$881$	−395.302			−0.448697			−0.224349	+	0.974509i	$0.572025\pi$
$882$		0			0
$883$	−827.610	−	827.610i	−0.937271	−	0.937271i	0.0608748	−	0.998145i	$-0.480611\pi$
$883$	−827.610	−	827.610i	−0.937271	−	0.937271i	−0.998145	+	0.0608748i	$0.980611\pi$
$884$	−203.886	−	117.714i	−0.230640	−	0.133160i
$885$		0			0
$886$	504.145	+	873.205i	0.569013	+	0.985559i
$887$	−292.997	−	78.5084i	−0.330324	−	0.0885100i	0.0898455	−	0.995956i	$-0.471363\pi$
$887$	−292.997	−	78.5084i	−0.330324	−	0.0885100i	−0.420169	+	0.907446i	$0.638029\pi$
$888$		0			0
$889$	363.274	+	209.736i	0.408632	+	0.235924i
$890$	456.359	+	460.394i	0.512763	+	0.517297i
$891$		0			0
$892$	35.9018	−	35.9018i	0.0402486	−	0.0402486i
$893$	469.053	−	125.682i	0.525255	−	0.140742i
$894$		0			0
$895$	690.664	−	394.711i	0.771691	−	0.441018i
$896$	155.190	+	268.797i	0.173203	+	0.299996i
$897$		0			0
$898$	8.01835	−	2.14851i	0.00892912	−	0.00239255i
$899$			358.311i			0.398567i
$900$		0			0
$901$	−597.336			−0.662970
$902$	−369.652	−	1379.56i	−0.409813	−	1.52944i
$903$		0			0
$904$	−1231.25	+	710.865i	−1.36201	+	0.786355i
$905$	−157.272	−	275.194i	−0.173782	−	0.304082i
$906$		0			0
$907$	−143.164	−	534.296i	−0.157844	−	0.589080i	−0.998845	−	0.0480474i	$-0.984700\pi$
$907$	−143.164	−	534.296i	−0.157844	−	0.589080i	0.841002	−	0.541033i	$-0.181967\pi$
$908$	−158.465	−	158.465i	−0.174521	−	0.174521i
$909$		0			0
$910$	−210.607	+	208.761i	−0.231437	+	0.229408i
$911$	−622.627	+	1078.42i	−0.683454	+	1.18378i	0.290466	+	0.956885i	$0.406190\pi$
$911$	−622.627	+	1078.42i	−0.683454	+	1.18378i	−0.973920	+	0.226892i	$0.927144\pi$
$912$		0			0
$913$	−223.376	+	833.652i	−0.244662	+	0.913091i
$914$	−1343.20	+	775.495i	−1.46958	+	0.848463i
$915$		0			0
$916$	101.660	−	176.081i	0.110983	−	0.192228i
$917$	317.913	−	317.913i	0.346688	−	0.346688i
$918$		0			0
$919$		−	123.047i		−	0.133892i	−0.997757	−	0.0669462i	$-0.978674\pi$
$919$		−	123.047i		−	0.133892i	0.997757	−	0.0669462i	$-0.0213256\pi$
$920$	675.255	+	393.832i	0.733972	+	0.428078i
$921$		0			0
$922$	−222.920	−	59.7314i	−0.241779	−	0.0647845i
$923$	188.084	−	701.939i	0.203775	−	0.760497i
$924$		0			0
$925$	−288.832	−	1117.18i	−0.312250	−	1.20777i
$926$	1896.92			2.04851
$927$		0			0
$928$	−164.426	−	164.426i	−0.177183	−	0.177183i
$929$	−998.545	−	576.510i	−1.07486	−	0.620571i	−0.145355	−	0.989380i	$-0.546432\pi$
$929$	−998.545	−	576.510i	−1.07486	−	0.620571i	−0.929505	+	0.368809i	$0.879766\pi$
$930$		0			0
$931$	204.564	+	354.316i	0.219726	+	0.380576i
$932$	−62.7250	−	16.8071i	−0.0673015	−	0.0180334i
$933$		0			0
$934$	−1273.10	−	735.027i	−1.36307	−	0.786967i
$935$	1038.20	−	1029.10i	1.11037	−	1.10064i
$936$		0			0
$937$	315.317	−	315.317i	0.336518	−	0.336518i	−0.518537	−	0.855055i	$-0.673523\pi$
$937$	315.317	−	315.317i	0.336518	−	0.336518i	0.855055	+	0.518537i	$0.173523\pi$
$938$	−84.3122	+	22.5914i	−0.0898850	+	0.0240846i
$939$		0			0
$940$	53.6345	−	196.699i	0.0570579	−	0.209254i
$941$	−311.898	−	540.224i	−0.331454	−	0.574095i	0.651343	−	0.758783i	$-0.274206\pi$
$941$	−311.898	−	540.224i	−0.331454	−	0.574095i	−0.982797	+	0.184688i	$0.940873\pi$
$942$		0			0
$943$	1104.76	−	296.020i	1.17154	−	0.313913i
$944$		−	1833.50i		−	1.94226i
$945$		0			0
$946$	1320.71			1.39610
$947$	324.936	+	1212.68i	0.343121	+	1.28055i	0.894792	+	0.446484i	$0.147324\pi$
$947$	324.936	+	1212.68i	0.343121	+	1.28055i	−0.551670	+	0.834062i	$0.686009\pi$
$948$		0			0
$949$	−132.675	+	76.5997i	−0.139805	+	0.0807162i
$950$	−133.134	+	479.922i	−0.140141	+	0.505181i
$951$		0			0
$952$	86.0683	+	321.211i	0.0904079	+	0.337407i
$953$	1156.15	+	1156.15i	1.21317	+	1.21317i	0.969979	+	0.243188i	$0.0781933\pi$
$953$	1156.15	+	1156.15i	1.21317	+	1.21317i	0.243188	+	0.969979i	$0.421807\pi$
$954$		0			0
$955$	617.469	+	2.71808i	0.646565	+	0.00284615i
$956$	−74.6533	+	129.303i	−0.0780892	+	0.135255i
$957$		0			0
$958$	299.122	−	1116.34i	0.312236	−	1.16528i
$959$	143.524	−	82.8636i	0.149660	−	0.0864062i
$960$		0			0
$961$	306.656	−	531.144i	0.319101	−	0.552699i
$962$	948.505	−	948.505i	0.985972	−	0.985972i
$963$		0			0
$964$			13.8345i			0.0143512i
$965$	−1201.99	+	316.407i	−1.24558	+	0.327883i
$966$		0			0
$967$	−564.461	−	151.247i	−0.583724	−	0.156408i	−0.0451407	−	0.998981i	$-0.514374\pi$
$967$	−564.461	−	151.247i	−0.583724	−	0.156408i	−0.538583	+	0.842572i	$0.681040\pi$
$968$	−72.0767	+	268.994i	−0.0744594	+	0.277886i
$969$		0			0
$970$	1072.50	+	625.522i	1.10567	+	0.644868i
$971$	755.109			0.777662			0.388831	−	0.921309i	$-0.372879\pi$
$971$	755.109			0.777662			0.388831	+	0.921309i	$0.372879\pi$
$972$		0			0
$973$	373.754	+	373.754i	0.384125	+	0.384125i
$974$	1033.64	+	596.774i	1.06123	+	0.612704i
$975$		0			0
$976$	956.557	+	1656.80i	0.980078	+	1.69755i
$977$	1053.61	+	282.315i	1.07842	+	0.288961i	0.753947	−	0.656935i	$-0.228147\pi$
$977$	1053.61	+	282.315i	1.07842	+	0.288961i	0.324470	+	0.945896i	$0.394814\pi$
$978$		0			0
$979$	−651.446	−	376.112i	−0.665420	−	0.384180i
$980$	171.772	+	0.756136i	0.175278	+	0.000771567i
$981$		0			0
$982$	455.079	−	455.079i	0.463421	−	0.463421i
$983$	−144.353	+	38.6793i	−0.146850	+	0.0393482i	−0.331495	−	0.943457i	$-0.607553\pi$
$983$	−144.353	+	38.6793i	−0.146850	+	0.0393482i	0.184645	+	0.982805i	$0.440886\pi$
$984$		0			0
$985$	363.251	+	99.0486i	0.368783	+	0.100557i
$986$	−484.150	−	838.573i	−0.491025	−	0.850480i
$987$		0			0
$988$	−89.9051	+	24.0900i	−0.0909971	+	0.0243826i
$989$			1057.63i			1.06940i
$990$		0			0
$991$	961.090			0.969819			0.484909	−	0.874564i	$-0.338853\pi$
$991$	961.090			0.969819			0.484909	+	0.874564i	$0.338853\pi$
$992$	−58.3998	−	217.951i	−0.0588708	−	0.219709i
$993$		0			0
$994$	210.639	−	121.612i	0.211910	−	0.122346i
$995$	−137.603	+	78.6398i	−0.138295	+	0.0790350i
$996$		0			0
$997$	263.082	+	981.834i	0.263873	+	0.984788i	0.962936	+	0.269728i	$0.0869339\pi$
$997$	263.082	+	981.834i	0.263873	+	0.984788i	−0.699063	+	0.715060i	$0.746399\pi$
$998$	−1333.01	−	1333.01i	−1.33568	−	1.33568i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.3.l.j.298.2		16
3.2	odd	2		405.3.l.m.298.3		16
5.2	odd	4		405.3.l.m.217.3		16
9.2	odd	6		405.3.g.f.163.6	yes	16
9.4	even	3		405.3.l.m.28.3		16
9.5	odd	6	inner	405.3.l.j.28.2		16
9.7	even	3		405.3.g.f.163.3	yes	16
15.2	even	4	inner	405.3.l.j.217.2		16
45.2	even	12		405.3.g.f.82.6	yes	16
45.7	odd	12		405.3.g.f.82.3	✓	16
45.22	odd	12	inner	405.3.l.j.352.2		16
45.32	even	12		405.3.l.m.352.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
405.3.g.f.82.3	✓	16	45.7	odd	12
405.3.g.f.82.6	yes	16	45.2	even	12
405.3.g.f.163.3	yes	16	9.7	even	3
405.3.g.f.163.6	yes	16	9.2	odd	6
405.3.l.j.28.2		16	9.5	odd	6	inner
405.3.l.j.217.2		16	15.2	even	4	inner
405.3.l.j.298.2		16	1.1	even	1	trivial
405.3.l.j.352.2		16	45.22	odd	12	inner
405.3.l.m.28.3		16	9.4	even	3
405.3.l.m.217.3		16	5.2	odd	4
405.3.l.m.298.3		16	3.2	odd	2
405.3.l.m.352.3		16	45.32	even	12

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:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	405.l (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.565047 - 2.10878i) q^{2} +(-0.663588 + 0.383123i) q^{4} +(-2.48091 - 4.34109i) q^{5} +(0.528192 + 1.97124i) q^{7} +(-4.99206 - 4.99206i) q^{8} +(-7.75259 + 7.68463i) q^{10} +(6.33336 - 10.9697i) q^{11} +(3.44531 - 12.8581i) q^{13} +(3.85846 - 2.22768i) q^{14} +(-9.23893 + 16.0023i) q^{16} +(-16.3208 + 16.3208i) q^{17} +9.12517i q^{19} +(3.30948 + 1.93020i) q^{20} +(-26.7114 - 7.15730i) q^{22} +(5.73162 - 21.3907i) q^{23} +(-12.6901 + 21.5397i) q^{25} -29.0616 q^{26} +(-1.10573 - 1.10573i) q^{28} +(-16.6416 - 9.60806i) q^{29} +(-9.32320 - 16.1483i) q^{31} +(11.6886 + 3.13196i) q^{32} +(43.6390 + 25.1950i) q^{34} +(7.24692 - 7.18340i) q^{35} +(-32.6377 + 32.6377i) q^{37} +(19.2430 - 5.15615i) q^{38} +(-9.28611 + 34.0559i) q^{40} +(25.8234 + 44.7275i) q^{41} +(-46.1316 + 12.3609i) q^{43} +9.70583i q^{44} -48.3470 q^{46} +(-13.7731 - 51.4021i) q^{47} +(38.8285 - 22.4176i) q^{49} +(52.5932 + 14.5898i) q^{50} +(2.63995 + 9.85244i) q^{52} +(18.2998 + 18.2998i) q^{53} +(-63.3330 - 0.278790i) q^{55} +(7.20378 - 12.4773i) q^{56} +(-10.8580 + 40.5226i) q^{58} +(-85.9329 + 49.6134i) q^{59} +(51.7677 - 89.6644i) q^{61} +(-28.7851 + 28.7851i) q^{62} +47.4929i q^{64} +(-64.3655 + 16.9434i) q^{65} +(-18.9237 - 5.07060i) q^{67} +(4.57742 - 17.0832i) q^{68} +(-19.2431 - 11.2232i) q^{70} +54.5913 q^{71} +(-8.13786 - 8.13786i) q^{73} +(87.2677 + 50.3840i) q^{74} +(-3.49606 - 6.05535i) q^{76} +(24.9691 + 6.69046i) q^{77} +(122.145 + 70.5203i) q^{79} +(92.3884 + 0.406690i) q^{80} +(79.7291 - 79.7291i) q^{82} +(-65.8143 + 17.6349i) q^{83} +(111.341 + 30.3595i) q^{85} +(52.1330 + 90.2970i) q^{86} +(-86.3781 + 23.1449i) q^{88} -59.3859i q^{89} +27.1661 q^{91} +(4.39183 + 16.3905i) q^{92} +(-100.613 + 58.0892i) q^{94} +(39.6132 - 22.6388i) q^{95} +(-29.4385 - 109.866i) q^{97} +(-69.2138 - 69.2138i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{2} + 12 q^{5} - 20 q^{7} - 56 q^{10} + 22 q^{13} - 168 q^{14} + 16 q^{16} - 96 q^{20} - 16 q^{22} + 36 q^{23} + 46 q^{25} + 176 q^{28} - 252 q^{29} - 160 q^{31} - 114 q^{32} + 4 q^{37} + 192 q^{38}+ \cdots - 152 q^{97}+O(q^{100}) \) 16 * q - 6 * q^2 + 12 * q^5 - 20 * q^7 - 56 * q^10 + 22 * q^13 - 168 * q^14 + 16 * q^16 - 96 * q^20 - 16 * q^22 + 36 * q^23 + 46 * q^25 + 176 * q^28 - 252 * q^29 - 160 * q^31 - 114 * q^32 + 4 * q^37 + 192 * q^38 + 264 * q^40 - 128 * q^43 - 16 * q^46 + 204 * q^47 + 540 * q^50 + 154 * q^52 - 364 * q^55 - 246 * q^58 + 36 * q^59 - 4 * q^61 + 24 * q^65 - 44 * q^67 + 966 * q^68 + 18 * q^70 + 364 * q^73 + 288 * q^74 + 456 * q^76 - 204 * q^77 + 32 * q^82 + 12 * q^83 - 32 * q^85 - 420 * q^88 + 224 * q^91 - 960 * q^92 + 114 * q^95 - 152 * q^97

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