LMFDB - Embedded newform 405.3.l.m.298.3

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			298.3
Root			$-1.54374 + 1.54374i$ of defining polynomial
Character	$\chi$	$=$	405.298
Dual form			405.3.l.m.352.3

$q$-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	$0.100438\pi$
$2$	0.565047	+	2.10878i	0.282523	+	1.05439i	−0.668107	+	0.744065i	$0.732895\pi$
$3$		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	$0.361961\pi$
$11$	−6.33336	+	10.9697i	−0.575760	+	0.997246i	−0.995959	+	0.0898139i	$0.971373\pi$
$12$		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	−0.0391852	−	0.999232i	$-0.512476\pi$
$17$	16.3208	−	16.3208i	0.960047	−	0.960047i	0.999232	+	0.0391852i	$0.0124762\pi$
$18$		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	$0.243212\pi$
$23$	−5.73162	+	21.3907i	−0.249201	+	0.930030i	−0.971225	+	0.238163i	$0.923455\pi$
$24$		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	0.758686	−	0.651457i	$-0.225842\pi$
$29$	16.6416	+	9.60806i	0.573850	+	0.331312i	−0.184836	+	0.982769i	$0.559175\pi$
$30$		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	$-0.949787\pi$
$41$	−25.8234	−	44.7275i	−0.629839	−	1.09091i	0.357744	−	0.933820i	$-0.383546\pi$
$42$		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	$0.108223\pi$
$47$	13.7731	+	51.4021i	0.293046	+	1.09366i	−0.649711	+	0.760181i	$0.725110\pi$
$48$		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	0.513068	−	0.858348i	$-0.328509\pi$
$53$	−18.2998	−	18.2998i	−0.345280	−	0.345280i	−0.858348	+	0.513068i	$0.828509\pi$
$54$		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	0.457653	−	0.889131i	$-0.348690\pi$
$59$	85.9329	−	49.6134i	1.45649	−	0.840905i	0.998836	+	0.0482263i	$0.0153569\pi$
$60$		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	$-0.625607\pi$
$71$	−54.5913			−0.768892			−0.384446	+	0.923148i	$0.625607\pi$
$72$		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	0.160460	−	0.987042i	$-0.448702\pi$
$83$	65.8143	−	17.6349i	0.792944	−	0.212469i	0.632484	+	0.774574i	$0.282036\pi$
$84$		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	$0.108273\pi$
$89$			59.3859i			0.667257i	−0.942705	+	0.333629i	$0.891727\pi$
$90$		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	−0.818296	−	0.574797i	$-0.805081\pi$
$101$	8.95268	−	15.5065i	0.0886404	−	0.153530i	0.906937	+	0.421267i	$0.138414\pi$
$102$		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	−0.373280	−	0.927719i	$-0.621767\pi$
$107$	59.3250	−	59.3250i	0.554439	−	0.554439i	0.927719	+	0.373280i	$0.121767\pi$
$108$		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	$0.433380\pi$
$113$	−52.1216	+	194.521i	−0.461253	+	1.72142i	−0.669022	+	0.743243i	$0.733287\pi$
$114$		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	$0.151287\pi$
$131$	110.153	+	190.791i	0.840865	+	1.45642i	−0.0482993	+	0.998833i	$0.515380\pi$
$132$		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	$0.0124459\pi$
$137$	21.0181	+	78.4408i	0.153417	+	0.572560i	−0.845819	+	0.533471i	$0.820887\pi$
$138$		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	−0.0693405	−	0.997593i	$-0.522090\pi$
$149$	113.230	−	65.3731i	0.759930	−	0.438746i	0.829271	+	0.558847i	$0.188756\pi$
$150$		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	0.528363	−	0.849018i	$-0.322806\pi$
$167$	93.7589	+	25.1226i	0.561431	+	0.150435i	0.0330670	+	0.999453i	$0.489473\pi$
$168$		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	−0.446165	−	0.894951i	$-0.647210\pi$
$173$	−66.6187	+	17.8504i	−0.385079	+	0.103182i	0.0610854	+	0.998133i	$0.480544\pi$
$174$		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	$-0.853413\pi$
$179$		−	159.099i		−	0.888822i	0.895823	−	0.444411i	$-0.146587\pi$
$180$		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	−0.657878	−	0.753124i	$-0.728546\pi$
$191$	61.7475	−	106.950i	0.323285	−	0.559947i	0.981164	+	0.193177i	$0.0618793\pi$
$192$		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	−0.558928	−	0.829217i	$-0.688787\pi$
$197$	53.2469	−	53.2469i	0.270289	−	0.270289i	0.829217	+	0.558928i	$0.188787\pi$
$198$		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	$-0.860522\pi$
$227$	−75.6965	−	282.503i	−0.333465	−	1.24451i	0.572059	−	0.820212i	$-0.306145\pi$
$228$		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	0.566719	−	0.823911i	$-0.308213\pi$
$233$	−59.9258	−	59.9258i	−0.257192	−	0.257192i	−0.823911	+	0.566719i	$0.808213\pi$
$234$		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	−0.809602	−	0.586980i	$-0.800317\pi$
$239$	−168.749	+	97.4274i	−0.706063	+	0.407646i	0.103538	+	0.994625i	$0.466984\pi$
$240$		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	$-0.719646\pi$
$251$	−319.556			−1.27313			−0.636566	+	0.771223i	$0.719646\pi$
$252$		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	0.00425348	−	0.999991i	$-0.498646\pi$
$257$	−126.459	−	33.8846i	−0.492058	−	0.131847i	−0.496312	+	0.868144i	$0.665313\pi$
$258$		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	$0.841569\pi$
$263$	−494.002	+	132.368i	−1.87834	+	0.503299i	−0.999665	+	0.0258709i	$0.991764\pi$
$264$		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	$-0.865789\pi$
$269$		−	220.179i		−	0.818508i	0.912421	−	0.409254i	$-0.134211\pi$
$270$		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	−0.921383	−	0.388655i	$-0.872940\pi$
$281$	−34.8739	+	60.4033i	−0.124106	+	0.214959i	0.797277	+	0.603614i	$0.206273\pi$
$282$		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	−0.999434	−	0.0336549i	$-0.989285\pi$
$293$	−34.3019	+	128.016i	−0.117071	+	0.436916i	0.882362	+	0.470571i	$0.155952\pi$
$294$		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	0.999914	−	0.0130800i	$-0.00416361\pi$
$311$	151.964	+	263.209i	0.488630	+	0.846331i	−0.511285	+	0.859411i	$0.670830\pi$
$312$		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	0.921640	−	0.388045i	$-0.126850\pi$
$317$	−22.3631	−	83.4604i	−0.0705462	−	0.263282i	−0.992187	+	0.124763i	$0.960183\pi$
$318$		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	0.298195	−	0.954505i	$-0.403616\pi$
$347$	27.4777	+	7.36263i	0.0791865	+	0.0212180i	−0.219008	+	0.975723i	$0.570282\pi$
$348$		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	−0.676456	−	0.736483i	$-0.736485\pi$
$353$	−315.597	+	84.5639i	−0.894042	+	0.239558i	−0.217586	+	0.976041i	$0.569818\pi$
$354$		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	$0.111070\pi$
$359$			245.484i			0.683799i	−0.939736	+	0.341900i	$0.888930\pi$
$360$		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	−0.959880	−	0.280410i	$-0.909530\pi$
$383$	4.44480	−	16.5882i	0.0116052	−	0.0433113i	0.971486	+	0.237098i	$0.0761964\pi$
$384$		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	0.679524	−	0.733653i	$-0.262186\pi$
$389$	149.347	+	86.2254i	0.383925	+	0.221659i	−0.295600	+	0.955312i	$0.595519\pi$
$390$		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	$0.177891\pi$
$401$	354.129	+	613.369i	0.883115	+	1.52960i	0.0352554	+	0.999378i	$0.488776\pi$
$402$		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	0.0795838	−	0.996828i	$-0.474641\pi$
$419$	411.732	−	237.714i	0.982654	−	0.567336i	0.903070	+	0.429493i	$0.141308\pi$
$420$		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	$-0.727608\pi$
$431$	−565.177			−1.31131			−0.655657	+	0.755059i	$0.727608\pi$
$432$		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	0.282636	−	0.959227i	$-0.408791\pi$
$443$	446.109	−	119.535i	1.00702	−	0.269830i	0.724383	+	0.689397i	$0.242125\pi$
$444$		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	$-0.998652\pi$
$449$		−	3.80236i		−	0.00846851i	0.999991	−	0.00423425i	$-0.00134781\pi$
$450$		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	−0.917641	−	0.397410i	$-0.869909\pi$
$461$	−52.8552	+	91.5479i	−0.114653	+	0.198586i	0.802988	+	0.595996i	$0.203242\pi$
$462$		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	$0.506289\pi$
$467$	−476.135	+	476.135i	−1.01956	+	1.01956i	−0.999805	+	0.0197563i	$0.993711\pi$
$468$		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	−0.0618243	−	0.998087i	$-0.519692\pi$
$479$	−458.453	−	264.688i	−0.957105	−	0.552585i	−0.895281	+	0.445502i	$0.853025\pi$
$480$		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	0.675986	−	0.736915i	$-0.263718\pi$
$491$	−147.395	−	255.296i	−0.300194	−	0.519951i	−0.976180	+	0.216963i	$0.930385\pi$
$492$		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	0.288098	−	0.957601i	$-0.406977\pi$
$503$	−336.760	−	336.760i	−0.669503	−	0.669503i	−0.957601	+	0.288098i	$0.906977\pi$
$504$		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	−0.0150207	−	0.999887i	$-0.504781\pi$
$509$	429.289	−	247.850i	0.843397	−	0.486935i	0.858417	+	0.512952i	$0.171448\pi$
$510$		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	$-0.569391\pi$
$521$	−225.358			−0.432550			−0.216275	+	0.976333i	$0.569391\pi$
$522$		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	−0.744230	−	0.667923i	$-0.767183\pi$
$557$	−42.5030	+	42.5030i	−0.0763070	+	0.0763070i	0.667923	+	0.744230i	$0.267183\pi$
$558$		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	$-0.727974\pi$
$563$	162.816	−	607.639i	0.289194	−	1.07929i	0.945719	−	0.324984i	$-0.105359\pi$
$564$		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	0.883487	−	0.468456i	$-0.155190\pi$
$569$	523.215	+	302.078i	0.919535	+	0.530894i	0.0360482	+	0.999350i	$0.488523\pi$
$570$		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	0.999992	−	0.00396077i	$-0.00126075\pi$
$587$	77.4800	+	289.159i	0.131993	+	0.492605i	−0.867999	+	0.496566i	$0.834594\pi$
$588$		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	0.698748	−	0.715368i	$-0.253741\pi$
$593$	−9.85573	−	9.85573i	−0.0166201	−	0.0166201i	−0.715368	+	0.698748i	$0.753741\pi$
$594$		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	−0.415907	−	0.909407i	$-0.636536\pi$
$599$	98.0614	−	56.6158i	0.163709	−	0.0945172i	0.579616	+	0.814890i	$0.303203\pi$
$600$		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	−0.589165	−	0.808012i	$-0.700543\pi$
$617$	−927.600	−	248.550i	−1.50340	−	0.402836i	−0.914238	+	0.405177i	$0.867210\pi$
$618$		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	−0.967603	−	0.252477i	$-0.918755\pi$
$641$	−169.961	+	294.381i	−0.265150	+	0.459253i	0.702453	+	0.711730i	$0.252088\pi$
$642$		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	−0.105591	−	0.994410i	$-0.533673\pi$
$647$	575.066	−	575.066i	0.888819	−	0.888819i	0.994410	+	0.105591i	$0.0336734\pi$
$648$		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	−0.951519	−	0.307591i	$-0.900477\pi$
$653$	17.1844	−	64.1329i	0.0263160	−	0.0982128i	0.977835	+	0.209378i	$0.0671439\pi$
$654$		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	−0.456137	−	0.889909i	$-0.650767\pi$
$659$	−958.773	−	553.548i	−1.45489	−	0.839981i	−0.998753	+	0.0499281i	$0.984101\pi$
$660$		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	$0.0785755\pi$
$677$	170.665	+	636.930i	0.252090	+	0.940812i	−0.717597	+	0.696459i	$0.754758\pi$
$678$		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	0.768810	−	0.639478i	$-0.220849\pi$
$683$	88.3335	+	88.3335i	0.129332	+	0.129332i	−0.639478	+	0.768810i	$0.720849\pi$
$684$		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	$-0.352561\pi$
$701$	626.425			0.893616			0.446808	+	0.894630i	$0.352561\pi$
$702$		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	$0.0846670\pi$
$719$			377.998i			0.525727i	−0.964833	+	0.262864i	$0.915333\pi$
$720$		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	$0.311069\pi$
$743$	−252.285	+	941.541i	−0.339550	+	1.26722i	−0.898852	+	0.438252i	$0.855598\pi$
$744$		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	$-0.988294\pi$
$761$	−404.473	−	700.568i	−0.531502	−	0.920589i	0.467822	−	0.883823i	$-0.345039\pi$
$762$		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	0.366309	−	0.930493i	$-0.380621\pi$
$773$	−436.114	−	436.114i	−0.564184	−	0.564184i	−0.930493	+	0.366309i	$0.880621\pi$
$774$		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	−0.248458	−	0.968643i	$-0.579924\pi$
$797$	−755.517	−	202.440i	−0.947951	−	0.254003i	−0.699492	+	0.714640i	$0.746591\pi$
$798$		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	$0.00253446\pi$
$809$			12.8828i			0.0159243i	−0.999968	+	0.00796215i	$0.997466\pi$
$810$		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	$0.461632\pi$
$821$	−656.487	+	1137.07i	−0.799619	+	1.38498i	−0.919865	+	0.392236i	$0.871702\pi$
$822$		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	−0.632206	−	0.774800i	$-0.717850\pi$
$827$	117.925	−	117.925i	0.142594	−	0.142594i	0.774800	+	0.632206i	$0.217850\pi$
$828$		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	0.642410	−	0.766361i	$-0.277935\pi$
$839$	251.639	+	145.284i	0.299928	+	0.173163i	−0.342483	+	0.939524i	$0.611268\pi$
$840$		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	$-0.990096\pi$
$857$	−128.091	−	478.041i	−0.149464	−	0.557807i	0.850052	−	0.526699i	$-0.176570\pi$
$858$		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	0.619616	−	0.784905i	$-0.287288\pi$
$863$	−142.644	−	142.644i	−0.165288	−	0.165288i	−0.784905	+	0.619616i	$0.787288\pi$
$864$		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	$-0.427975\pi$
$881$	395.302			0.448697			0.224349	+	0.974509i	$0.427975\pi$
$882$		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	0.420169	−	0.907446i	$-0.361971\pi$
$887$	292.997	+	78.5084i	0.330324	+	0.0885100i	−0.0898455	+	0.995956i	$0.528637\pi$
$888$		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	$-0.593810\pi$
$911$	622.627	−	1078.42i	0.683454	−	1.18378i	0.973920	−	0.226892i	$-0.0728564\pi$
$912$		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	0.929505	−	0.368809i	$-0.120234\pi$
$929$	998.545	+	576.510i	1.07486	+	0.620571i	0.145355	+	0.989380i	$0.453568\pi$
$930$		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	0.982797	−	0.184688i	$-0.0591275\pi$
$941$	311.898	+	540.224i	0.331454	+	0.574095i	−0.651343	+	0.758783i	$0.725794\pi$
$942$		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	$-0.852676\pi$
$947$	−324.936	−	1212.68i	−0.343121	−	1.28055i	0.551670	−	0.834062i	$-0.313991\pi$
$948$		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	$-0.921807\pi$
$953$	−1156.15	−	1156.15i	−1.21317	−	1.21317i	−0.243188	−	0.969979i	$-0.578193\pi$
$954$		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	$-0.627121\pi$
$971$	−755.109			−0.777662			−0.388831	+	0.921309i	$0.627121\pi$
$972$		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	−0.324470	−	0.945896i	$-0.605186\pi$
$977$	−1053.61	−	282.315i	−1.07842	−	0.288961i	−0.753947	+	0.656935i	$0.771853\pi$
$978$		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	−0.184645	−	0.982805i	$-0.559114\pi$
$983$	144.353	−	38.6793i	0.146850	−	0.0393482i	0.331495	+	0.943457i	$0.392447\pi$
$984$		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.m.298.3		16
3.2	odd	2		405.3.l.j.298.2		16
5.2	odd	4		405.3.l.j.217.2		16
9.2	odd	6		405.3.g.f.163.3	yes	16
9.4	even	3		405.3.l.j.28.2		16
9.5	odd	6	inner	405.3.l.m.28.3		16
9.7	even	3		405.3.g.f.163.6	yes	16
15.2	even	4	inner	405.3.l.m.217.3		16
45.2	even	12		405.3.g.f.82.3	✓	16
45.7	odd	12		405.3.g.f.82.6	yes	16
45.22	odd	12	inner	405.3.l.m.352.3		16
45.32	even	12		405.3.l.j.352.2		16

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

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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