LMFDB - Embedded newform 405.3.l.m.352.3

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			352.3
Root			$-1.54374 - 1.54374i$ of defining polynomial
Character	$\chi$	$=$	405.352
Dual form			405.3.l.m.298.3

$q$-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 $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{3}\right)$

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	−0.668107	−	0.744065i	$-0.732895\pi$
$2$	0.565047	−	2.10878i	0.282523	−	1.05439i	0.950630	−	0.310326i	$-0.100438\pi$
$3$		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	−0.917880	−	0.396857i	$-0.870101\pi$
$7$	0.528192	−	1.97124i	0.0754560	−	0.281605i	0.993336	+	0.115252i	$0.0367675\pi$
$8$	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	−0.995959	−	0.0898139i	$-0.971373\pi$
$11$	−6.33336	−	10.9697i	−0.575760	−	0.997246i	0.420198	−	0.907432i	$-0.361961\pi$
$12$		0			0
$13$	3.44531	+	12.8581i	0.265024	+	0.989082i	0.962236	+	0.272217i	$0.0877569\pi$
$13$	3.44531	+	12.8581i	0.265024	+	0.989082i	−0.697212	+	0.716865i	$0.745576\pi$
$14$	−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	$-0.0124762\pi$
$17$	16.3208	+	16.3208i	0.960047	+	0.960047i	−0.0391852	+	0.999232i	$0.512476\pi$
$18$		0			0
$19$		−	9.12517i		−	0.480272i	−0.970739	−	0.240136i	$-0.922808\pi$
$19$		−	9.12517i		−	0.480272i	0.970739	−	0.240136i	$-0.0771920\pi$
$20$	−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	−0.971225	−	0.238163i	$-0.923455\pi$
$23$	−5.73162	−	21.3907i	−0.249201	−	0.930030i	0.722025	−	0.691867i	$-0.243212\pi$
$24$		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	$-0.559175\pi$
$29$	16.6416	−	9.60806i	0.573850	−	0.331312i	0.758686	+	0.651457i	$0.225842\pi$
$30$		0			0
$31$	−9.32320	+	16.1483i	−0.300748	+	0.520911i	−0.976306	−	0.216396i	$-0.930570\pi$
$31$	−9.32320	+	16.1483i	−0.300748	+	0.520911i	0.675557	+	0.737307i	$0.263903\pi$
$32$	−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	0.111648	−	0.993748i	$-0.464387\pi$
$37$	−32.6377	−	32.6377i	−0.882100	−	0.882100i	−0.993748	+	0.111648i	$0.964387\pi$
$38$	−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	0.357744	+	0.933820i	$0.383546\pi$
$41$	−25.8234	+	44.7275i	−0.629839	+	1.09091i	−0.987584	+	0.157094i	$0.949787\pi$
$42$		0			0
$43$	−46.1316	−	12.3609i	−1.07283	−	0.287463i	−0.321173	−	0.947021i	$-0.604077\pi$
$43$	−46.1316	−	12.3609i	−1.07283	−	0.287463i	−0.751654	+	0.659557i	$0.770744\pi$
$44$			9.70583i			0.220587i
$45$		0			0
$46$	−48.3470			−1.05102
$47$	13.7731	−	51.4021i	0.293046	−	1.09366i	−0.649711	−	0.760181i	$-0.725110\pi$
$47$	13.7731	−	51.4021i	0.293046	−	1.09366i	0.942757	−	0.333480i	$-0.108223\pi$
$48$		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	$-0.828509\pi$
$53$	−18.2998	+	18.2998i	−0.345280	+	0.345280i	0.513068	+	0.858348i	$0.328509\pi$
$54$		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	$-0.0153569\pi$
$59$	85.9329	+	49.6134i	1.45649	+	0.840905i	0.457653	+	0.889131i	$0.348690\pi$
$60$		0			0
$61$	51.7677	+	89.6644i	0.848651	+	1.46991i	0.882412	+	0.470477i	$0.155918\pi$
$61$	51.7677	+	89.6644i	0.848651	+	1.46991i	−0.0337606	+	0.999430i	$0.510748\pi$
$62$	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	−0.397260	−	0.917706i	$-0.630039\pi$
$67$	−18.9237	+	5.07060i	−0.282444	+	0.0756805i	0.114816	+	0.993387i	$0.463372\pi$
$68$	−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	−0.760645	−	0.649168i	$-0.775117\pi$
$73$	−8.13786	+	8.13786i	−0.111478	+	0.111478i	0.649168	+	0.760645i	$0.275117\pi$
$74$	−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	0.547705	−	0.836671i	$-0.315502\pi$
$79$	122.145	−	70.5203i	1.54614	−	0.892662i	0.998431	−	0.0559909i	$-0.0178318\pi$
$80$	−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	$-0.282036\pi$
$83$	65.8143	+	17.6349i	0.792944	+	0.212469i	0.160460	+	0.987042i	$0.448702\pi$
$84$		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	0.630748	+	0.775988i	$0.282748\pi$
$97$	−29.4385	+	109.866i	−0.303490	+	1.13264i	−0.934238	+	0.356651i	$0.883918\pi$
$98$	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	$-0.138414\pi$
$101$	8.95268	+	15.5065i	0.0886404	+	0.153530i	−0.818296	+	0.574797i	$0.805081\pi$
$102$		0			0
$103$	20.5961	+	76.8655i	0.199962	+	0.746267i	0.990926	+	0.134406i	$0.0429125\pi$
$103$	20.5961	+	76.8655i	0.199962	+	0.746267i	−0.790965	+	0.611862i	$0.790421\pi$
$104$	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	$-0.121767\pi$
$107$	59.3250	+	59.3250i	0.554439	+	0.554439i	−0.373280	+	0.927719i	$0.621767\pi$
$108$		0			0
$109$			140.876i			1.29244i	0.763153	+	0.646218i	$0.223650\pi$
$109$			140.876i			1.29244i	−0.763153	+	0.646218i	$0.776350\pi$
$110$	−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	−0.669022	−	0.743243i	$-0.733287\pi$
$113$	−52.1216	−	194.521i	−0.461253	−	1.72142i	0.207769	−	0.978178i	$-0.433380\pi$
$114$		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	0.987631	+	0.156799i	$0.0501175\pi$
$127$	145.343	+	145.343i	1.14443	+	1.14443i	0.156799	+	0.987631i	$0.449882\pi$
$128$	−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	−0.0482993	−	0.998833i	$-0.515380\pi$
$131$	110.153	−	190.791i	0.840865	−	1.45642i	0.889164	−	0.457588i	$-0.151287\pi$
$132$		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	−0.845819	−	0.533471i	$-0.820887\pi$
$137$	21.0181	−	78.4408i	0.153417	−	0.572560i	0.999236	−	0.0390898i	$-0.0124459\pi$
$138$		0			0
$139$	224.304	+	129.502i	1.61369	+	0.931667i	0.988504	+	0.151195i	$0.0483121\pi$
$139$	224.304	+	129.502i	1.61369	+	0.931667i	0.625191	+	0.780472i	$0.285021\pi$
$140$	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	$-0.188756\pi$
$149$	113.230	+	65.3731i	0.759930	+	0.438746i	−0.0693405	+	0.997593i	$0.522090\pi$
$150$		0			0
$151$	63.1475	+	109.375i	0.418195	+	0.724335i	0.995758	−	0.0920110i	$-0.0293295\pi$
$151$	63.1475	+	109.375i	0.418195	+	0.724335i	−0.577563	+	0.816346i	$0.695996\pi$
$152$	−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	−0.777612	−	0.628744i	$-0.783569\pi$
$157$	−178.457	+	47.8175i	−1.13667	+	0.304570i	−0.359060	+	0.933315i	$0.616903\pi$
$158$	−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	−0.888518	−	0.458843i	$-0.848264\pi$
$163$	−70.0370	+	70.0370i	−0.429675	+	0.429675i	0.458843	+	0.888518i	$0.348264\pi$
$164$	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	$-0.489473\pi$
$167$	93.7589	−	25.1226i	0.561431	−	0.150435i	0.528363	+	0.849018i	$0.322806\pi$
$168$		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	$-0.480544\pi$
$173$	−66.6187	−	17.8504i	−0.385079	−	0.103182i	−0.446165	+	0.894951i	$0.647210\pi$
$174$		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	$-0.0618793\pi$
$191$	61.7475	+	106.950i	0.323285	+	0.559947i	−0.657878	+	0.753124i	$0.728546\pi$
$192$		0			0
$193$	64.3390	+	240.116i	0.333363	+	1.24413i	0.905633	+	0.424062i	$0.139396\pi$
$193$	64.3390	+	240.116i	0.333363	+	1.24413i	−0.572271	+	0.820065i	$0.693937\pi$
$194$	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	$-0.188787\pi$
$197$	53.2469	+	53.2469i	0.270289	+	0.270289i	−0.558928	+	0.829217i	$0.688787\pi$
$198$		0			0
$199$			31.6979i			0.159286i	0.996823	+	0.0796430i	$0.0253780\pi$
$199$			31.6979i			0.159286i	−0.996823	+	0.0796430i	$0.974622\pi$
$200$	−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	−0.519895	−	0.854230i	$-0.674029\pi$
$211$	101.246	−	175.363i	0.479838	−	0.831103i	0.999733	+	0.0231271i	$0.00736225\pi$
$212$	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	0.112440	−	0.993658i	$-0.464133\pi$
$223$	−64.0039	−	17.1498i	−0.287013	−	0.0769049i	−0.399453	+	0.916754i	$0.630800\pi$
$224$			24.6954i			0.110247i
$225$		0			0
$226$	−439.653			−1.94537
$227$	−75.6965	+	282.503i	−0.333465	+	1.24451i	0.572059	+	0.820212i	$0.306145\pi$
$227$	−75.6965	+	282.503i	−0.333465	+	1.24451i	−0.905524	+	0.424295i	$0.860522\pi$
$228$		0			0
$229$	−229.797	−	132.673i	−1.00348	−	0.579358i	−0.0942027	−	0.995553i	$-0.530030\pi$
$229$	−229.797	−	132.673i	−1.00348	−	0.579358i	−0.909276	+	0.416195i	$0.863364\pi$
$230$	−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	$-0.808213\pi$
$233$	−59.9258	+	59.9258i	−0.257192	+	0.257192i	0.566719	+	0.823911i	$0.308213\pi$
$234$		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	$-0.466984\pi$
$239$	−168.749	−	97.4274i	−0.706063	−	0.407646i	−0.809602	+	0.586980i	$0.800317\pi$
$240$		0			0
$241$	9.02748	+	15.6361i	0.0374584	+	0.0648799i	0.884147	−	0.467209i	$-0.154740\pi$
$241$	9.02748	+	15.6361i	0.0374584	+	0.0648799i	−0.846688	+	0.532089i	$0.821407\pi$
$242$	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	−0.496312	−	0.868144i	$-0.665313\pi$
$257$	−126.459	+	33.8846i	−0.492058	+	0.131847i	0.00425348	+	0.999991i	$0.498646\pi$
$258$		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	−0.999665	−	0.0258709i	$-0.991764\pi$
$263$	−494.002	−	132.368i	−1.87834	−	0.503299i	−0.878671	−	0.477428i	$-0.841569\pi$
$264$		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	−0.565537	−	0.824723i	$-0.691331\pi$
$277$	93.2365	−	347.963i	0.336594	−	1.25619i	0.902131	−	0.431462i	$-0.142002\pi$
$278$	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	$-0.206273\pi$
$281$	−34.8739	−	60.4033i	−0.124106	−	0.214959i	−0.921383	+	0.388655i	$0.872940\pi$
$282$		0			0
$283$	−16.5108	−	61.6190i	−0.0583419	−	0.217735i	0.930600	−	0.366037i	$-0.119286\pi$
$283$	−16.5108	−	61.6190i	−0.0583419	−	0.217735i	−0.988942	+	0.148302i	$0.952619\pi$
$284$	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	$-0.155952\pi$
$293$	−34.3019	−	128.016i	−0.117071	−	0.436916i	−0.999434	+	0.0336549i	$0.989285\pi$
$294$		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	0.504044	−	0.863678i	$-0.331845\pi$
$307$	−110.408	−	110.408i	−0.359634	−	0.359634i	−0.863678	+	0.504044i	$0.831845\pi$
$308$	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	$-0.670830\pi$
$311$	151.964	−	263.209i	0.488630	−	0.846331i	0.999914	+	0.0130800i	$0.00416361\pi$
$312$		0			0
$313$	70.0305	+	18.7646i	0.223740	+	0.0599508i	0.368947	−	0.929450i	$-0.379718\pi$
$313$	70.0305	+	18.7646i	0.223740	+	0.0599508i	−0.145208	+	0.989401i	$0.546385\pi$
$314$			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	$-0.960183\pi$
$317$	−22.3631	+	83.4604i	−0.0705462	+	0.263282i	0.921640	+	0.388045i	$0.126850\pi$
$318$		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	0.615164	−	0.788399i	$-0.289090\pi$
$331$	−124.188	−	215.101i	−0.375192	−	0.649851i	−0.990356	+	0.138548i	$0.955756\pi$
$332$	−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	−0.529760	−	0.848147i	$-0.677718\pi$
$337$	−190.227	+	50.9712i	−0.564472	+	0.151250i	−0.0347120	+	0.999397i	$0.511051\pi$
$338$	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	$-0.570282\pi$
$347$	27.4777	−	7.36263i	0.0791865	−	0.0212180i	0.298195	+	0.954505i	$0.403616\pi$
$348$		0			0
$349$	−515.156	+	297.426i	−1.47609	+	0.852222i	−0.999636	−	0.0269761i	$-0.991412\pi$
$349$	−515.156	+	297.426i	−1.47609	+	0.852222i	−0.476456	+	0.879198i	$0.658079\pi$
$350$	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	$-0.569818\pi$
$353$	−315.597	−	84.5639i	−0.894042	−	0.239558i	−0.676456	+	0.736483i	$0.736485\pi$
$354$		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	−0.613621	−	0.789601i	$-0.710288\pi$
$367$	114.721	−	428.144i	0.312591	−	1.16660i	0.926212	−	0.377004i	$-0.123046\pi$
$368$	−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	0.999970	+	0.00779940i	$0.00248265\pi$
$373$	51.4256	+	191.923i	0.137870	+	0.514539i	−0.862099	+	0.506739i	$0.830851\pi$
$374$	−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	$0.0750925\pi$
$379$			177.166i			0.467456i	−0.972302	+	0.233728i	$0.924908\pi$
$380$	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	$-0.0761964\pi$
$383$	4.44480	+	16.5882i	0.0116052	+	0.0433113i	−0.959880	+	0.280410i	$0.909530\pi$
$384$		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	$-0.595519\pi$
$389$	149.347	−	86.2254i	0.383925	−	0.221659i	0.679524	+	0.733653i	$0.262186\pi$
$390$		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	0.713358	−	0.700800i	$-0.247174\pi$
$397$	4.98532	+	4.98532i	0.0125575	+	0.0125575i	−0.700800	+	0.713358i	$0.747174\pi$
$398$	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	0.0352554	−	0.999378i	$-0.488776\pi$
$401$	354.129	−	613.369i	0.883115	−	1.52960i	0.847859	−	0.530221i	$-0.177891\pi$
$402$		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	0.0150787	−	0.999886i	$-0.495200\pi$
$409$	−344.913	−	199.136i	−0.843309	−	0.486885i	−0.858388	+	0.513002i	$0.828533\pi$
$410$	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	$-0.141308\pi$
$419$	411.732	+	237.714i	0.982654	+	0.567336i	0.0795838	+	0.996828i	$0.474641\pi$
$420$		0			0
$421$	285.120	+	493.842i	0.677245	+	1.17302i	0.975807	+	0.218632i	$0.0701595\pi$
$421$	285.120	+	493.842i	0.677245	+	1.17302i	−0.298563	+	0.954390i	$0.596507\pi$
$422$	−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	−0.746136	−	0.665793i	$-0.768093\pi$
$433$	−34.7884	+	34.7884i	−0.0803428	+	0.0803428i	0.665793	+	0.746136i	$0.268093\pi$
$434$	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	−0.776014	−	0.630716i	$-0.782761\pi$
$439$	−271.216	+	156.587i	−0.617804	+	0.356689i	0.158209	+	0.987406i	$0.449428\pi$
$440$	−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	$-0.242125\pi$
$443$	446.109	+	119.535i	1.00702	+	0.269830i	0.282636	+	0.959227i	$0.408791\pi$
$444$		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	0.406549	+	0.913629i	$0.366732\pi$
$457$	−183.873	+	686.222i	−0.402347	+	1.50158i	−0.808896	+	0.587951i	$0.799935\pi$
$458$	−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	$-0.203242\pi$
$461$	−52.8552	−	91.5479i	−0.114653	−	0.198586i	−0.917641	+	0.397410i	$0.869909\pi$
$462$		0			0
$463$	−224.884	−	839.277i	−0.485710	−	1.81269i	−0.576843	−	0.816855i	$-0.695716\pi$
$463$	−224.884	−	839.277i	−0.485710	−	1.81269i	0.0911330	−	0.995839i	$-0.470951\pi$
$464$	−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	−0.999805	−	0.0197563i	$-0.993711\pi$
$467$	−476.135	−	476.135i	−1.01956	−	1.01956i	−0.0197563	−	0.999805i	$-0.506289\pi$
$468$		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	$-0.853025\pi$
$479$	−458.453	+	264.688i	−0.957105	+	0.552585i	−0.0618243	+	0.998087i	$0.519692\pi$
$480$		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	0.188315	−	0.982109i	$-0.439697\pi$
$487$	−386.577	−	386.577i	−0.793793	−	0.793793i	−0.982109	+	0.188315i	$0.939697\pi$
$488$	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	$-0.930385\pi$
$491$	−147.395	+	255.296i	−0.300194	+	0.519951i	0.675986	+	0.736915i	$0.263718\pi$
$492$		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	0.999999	−	0.00159434i	$-0.000507494\pi$
$499$	747.810	+	431.748i	1.49862	+	0.865227i	0.498619	+	0.866821i	$0.333841\pi$
$500$	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	$-0.906977\pi$
$503$	−336.760	+	336.760i	−0.669503	+	0.669503i	0.288098	+	0.957601i	$0.406977\pi$
$504$		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	$-0.171448\pi$
$509$	429.289	+	247.850i	0.843397	+	0.486935i	−0.0150207	+	0.999887i	$0.504781\pi$
$510$		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	−0.989640	−	0.143571i	$-0.954142\pi$
$523$	−442.494	+	442.494i	−0.846069	+	0.846069i	0.143571	+	0.989640i	$0.454142\pi$
$524$	−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	−0.684735	−	0.728792i	$-0.740082\pi$
$547$	149.145	−	556.615i	0.272659	−	1.01758i	0.957394	−	0.288785i	$-0.0932514\pi$
$548$	−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	$-0.267183\pi$
$557$	−42.5030	−	42.5030i	−0.0763070	−	0.0763070i	−0.744230	+	0.667923i	$0.767183\pi$
$558$		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	0.945719	+	0.324984i	$0.105359\pi$
$563$	162.816	+	607.639i	0.289194	+	1.07929i	−0.656525	+	0.754304i	$0.727974\pi$
$564$		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	$-0.488523\pi$
$569$	523.215	−	302.078i	0.919535	−	0.530894i	0.883487	+	0.468456i	$0.155190\pi$
$570$		0			0
$571$	16.4403	−	28.4755i	0.0287921	−	0.0498695i	−0.851270	−	0.524727i	$-0.824167\pi$
$571$	16.4403	−	28.4755i	0.0287921	−	0.0498695i	0.880062	+	0.474858i	$0.157501\pi$
$572$	−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	0.997688	−	0.0679593i	$-0.0216488\pi$
$577$	536.453	+	536.453i	0.929729	+	0.929729i	−0.0679593	+	0.997688i	$0.521649\pi$
$578$	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	$-0.834594\pi$
$587$	77.4800	−	289.159i	0.131993	−	0.492605i	0.999992	+	0.00396077i	$0.00126075\pi$
$588$		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	$-0.753741\pi$
$593$	−9.85573	+	9.85573i	−0.0166201	+	0.0166201i	0.698748	+	0.715368i	$0.253741\pi$
$594$		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	$-0.303203\pi$
$599$	98.0614	+	56.6158i	0.163709	+	0.0945172i	−0.415907	+	0.909407i	$0.636536\pi$
$600$		0			0
$601$	408.039	+	706.744i	0.678933	+	1.17595i	0.975303	+	0.220873i	$0.0708907\pi$
$601$	408.039	+	706.744i	0.678933	+	1.17595i	−0.296370	+	0.955073i	$0.595776\pi$
$602$	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	0.251458	−	0.967868i	$-0.419090\pi$
$607$	578.568	−	155.027i	0.953161	−	0.255399i	0.701703	+	0.712470i	$0.252423\pi$
$608$	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	−0.0712948	−	0.997455i	$-0.522713\pi$
$613$	567.736	−	567.736i	0.926160	−	0.926160i	0.997455	+	0.0712948i	$0.0227131\pi$
$614$	−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	$-0.867210\pi$
$617$	−927.600	+	248.550i	−1.50340	+	0.402836i	−0.589165	+	0.808012i	$0.700543\pi$
$618$		0			0
$619$	−248.631	+	143.547i	−0.401665	+	0.231902i	−0.687202	−	0.726466i	$-0.741161\pi$
$619$	−248.631	+	143.547i	−0.401665	+	0.231902i	0.285537	+	0.958368i	$0.407828\pi$
$620$	−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	$-0.252088\pi$
$641$	−169.961	−	294.381i	−0.265150	−	0.459253i	−0.967603	+	0.252477i	$0.918755\pi$
$642$		0			0
$643$	−54.8829	−	204.826i	−0.0853544	−	0.318547i	0.910027	−	0.414550i	$-0.136061\pi$
$643$	−54.8829	−	204.826i	−0.0853544	−	0.318547i	−0.995381	+	0.0960027i	$0.969394\pi$
$644$	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	$-0.0336734\pi$
$647$	575.066	+	575.066i	0.888819	+	0.888819i	−0.105591	+	0.994410i	$0.533673\pi$
$648$		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	$-0.0671439\pi$
$653$	17.1844	+	64.1329i	0.0263160	+	0.0982128i	−0.951519	+	0.307591i	$0.900477\pi$
$654$		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	$-0.984101\pi$
$659$	−958.773	+	553.548i	−1.45489	+	0.839981i	−0.456137	+	0.889909i	$0.650767\pi$
$660$		0			0
$661$	−168.964	+	292.654i	−0.255619	+	0.442745i	−0.965063	−	0.262016i	$-0.915613\pi$
$661$	−168.964	+	292.654i	−0.255619	+	0.442745i	0.709445	+	0.704761i	$0.248946\pi$
$662$	−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	−0.464660	−	0.885489i	$-0.653823\pi$
$673$	−881.503	−	236.198i	−1.30981	−	0.350963i	−0.845152	+	0.534527i	$0.820490\pi$
$674$			429.949i			0.637906i
$675$		0			0
$676$	6.28317			0.00929464
$677$	170.665	−	636.930i	0.252090	−	0.940812i	−0.717597	−	0.696459i	$-0.754758\pi$
$677$	170.665	−	636.930i	0.252090	−	0.940812i	0.969686	−	0.244353i	$-0.0785755\pi$
$678$		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	$-0.720849\pi$
$683$	88.3335	−	88.3335i	0.129332	−	0.129332i	0.768810	+	0.639478i	$0.220849\pi$
$684$		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	−0.994058	−	0.108855i	$-0.965282\pi$
$691$	−408.588	−	707.695i	−0.591300	−	1.02416i	0.402758	−	0.915307i	$-0.368052\pi$
$692$	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	−0.440912	−	0.897550i	$-0.645345\pi$
$709$	82.1961	−	47.4559i	0.115932	−	0.0669336i	0.556845	+	0.830616i	$0.312012\pi$
$710$	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	−0.899249	−	0.437437i	$-0.855886\pi$
$727$	71.4219	−	266.550i	0.0982419	−	0.366644i	0.997491	+	0.0707930i	$0.0225530\pi$
$728$	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	−0.996007	−	0.0892766i	$-0.971544\pi$
$733$	−130.531	−	487.149i	−0.178078	−	0.664596i	0.817929	−	0.575319i	$-0.195122\pi$
$734$	−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	$-0.924361\pi$
$739$		−	347.915i		−	0.470791i	0.971900	−	0.235396i	$-0.0756386\pi$
$740$	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	−0.898852	−	0.438252i	$-0.855598\pi$
$743$	−252.285	−	941.541i	−0.339550	−	1.26722i	0.559302	−	0.828964i	$-0.311069\pi$
$744$		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	−0.984318	−	0.176401i	$-0.943555\pi$
$751$	−254.883	+	441.471i	−0.339392	+	0.587844i	0.644927	+	0.764244i	$0.276888\pi$
$752$	−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	0.867555	−	0.497340i	$-0.165690\pi$
$757$	280.253	+	280.253i	0.370215	+	0.370215i	−0.497340	+	0.867555i	$0.665690\pi$
$758$	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	0.467822	+	0.883823i	$0.345039\pi$
$761$	−404.473	+	700.568i	−0.531502	+	0.920589i	−0.999324	+	0.0367662i	$0.988294\pi$
$762$		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	0.763148	−	0.646224i	$-0.223653\pi$
$769$	449.923	+	259.763i	0.585075	+	0.337793i	−0.178073	+	0.984017i	$0.556986\pi$
$770$	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	$-0.880621\pi$
$773$	−436.114	+	436.114i	−0.564184	+	0.564184i	0.366309	+	0.930493i	$0.380621\pi$
$774$		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	−0.718960	−	0.695051i	$-0.755382\pi$
$787$	−782.335	+	209.626i	−0.994073	+	0.266361i	−0.275112	+	0.961412i	$0.588715\pi$
$788$	−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	$-0.746591\pi$
$797$	−755.517	+	202.440i	−0.947951	+	0.254003i	−0.248458	+	0.968643i	$0.579924\pi$
$798$		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	−0.919865	−	0.392236i	$-0.871702\pi$
$821$	−656.487	−	1137.07i	−0.799619	−	1.38498i	0.120246	−	0.992744i	$-0.461632\pi$
$822$		0			0
$823$	−233.948	−	873.104i	−0.284262	−	1.06088i	−0.949377	−	0.314139i	$-0.898284\pi$
$823$	−233.948	−	873.104i	−0.284262	−	1.06088i	0.665115	−	0.746741i	$-0.268383\pi$
$824$	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	$-0.217850\pi$
$827$	117.925	+	117.925i	0.142594	+	0.142594i	−0.632206	+	0.774800i	$0.717850\pi$
$828$		0			0
$829$			579.532i			0.699073i	0.936923	+	0.349537i	$0.113661\pi$
$829$			579.532i			0.699073i	−0.936923	+	0.349537i	$0.886339\pi$
$830$	−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	$-0.611268\pi$
$839$	251.639	−	145.284i	0.299928	−	0.173163i	0.642410	+	0.766361i	$0.277935\pi$
$840$		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	0.463542	−	0.886075i	$-0.346578\pi$
$853$	359.918	+	96.4397i	0.421943	+	0.113059i	−0.0415985	+	0.999134i	$0.513245\pi$
$854$		−	461.289i		−	0.540151i
$855$		0			0
$856$	592.308			0.691949
$857$	−128.091	+	478.041i	−0.149464	+	0.557807i	0.850052	+	0.526699i	$0.176570\pi$
$857$	−128.091	+	478.041i	−0.149464	+	0.557807i	−0.999516	+	0.0311085i	$0.990096\pi$
$858$		0			0
$859$	510.012	+	294.456i	0.593728	+	0.342789i	0.766570	−	0.642161i	$-0.221962\pi$
$859$	510.012	+	294.456i	0.593728	+	0.342789i	−0.172842	+	0.984950i	$0.555295\pi$
$860$	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	$-0.787288\pi$
$863$	−142.644	+	142.644i	−0.165288	+	0.165288i	0.619616	+	0.784905i	$0.287288\pi$
$864$		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	0.742775	−	0.669541i	$-0.233509\pi$
$877$	1509.15	−	404.375i	1.72081	−	0.461089i	0.978033	+	0.208451i	$0.0668423\pi$
$878$	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	−0.998145	−	0.0608748i	$-0.980611\pi$
$883$	−827.610	+	827.610i	−0.937271	+	0.937271i	0.0608748	+	0.998145i	$0.480611\pi$
$884$	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	$-0.528637\pi$
$887$	292.997	−	78.5084i	0.330324	−	0.0885100i	0.420169	+	0.907446i	$0.361971\pi$
$888$		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	0.841002	+	0.541033i	$0.181967\pi$
$907$	−143.164	+	534.296i	−0.157844	+	0.589080i	−0.998845	+	0.0480474i	$0.984700\pi$
$908$	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	0.973920	+	0.226892i	$0.0728564\pi$
$911$	622.627	+	1078.42i	0.683454	+	1.18378i	−0.290466	+	0.956885i	$0.593810\pi$
$912$		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	$0.0213256\pi$
$919$			123.047i			0.133892i	−0.997757	+	0.0669462i	$0.978674\pi$
$920$	−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	$-0.453568\pi$
$929$	998.545	−	576.510i	1.07486	−	0.620571i	0.929505	+	0.368809i	$0.120234\pi$
$930$		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	0.855055	−	0.518537i	$-0.173523\pi$
$937$	315.317	+	315.317i	0.336518	+	0.336518i	−0.518537	+	0.855055i	$0.673523\pi$
$938$	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	$-0.725794\pi$
$941$	311.898	−	540.224i	0.331454	−	0.574095i	0.982797	+	0.184688i	$0.0591275\pi$
$942$		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	0.551670	+	0.834062i	$0.313991\pi$
$947$	−324.936	+	1212.68i	−0.343121	+	1.28055i	−0.894792	+	0.446484i	$0.852676\pi$
$948$		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	−0.243188	+	0.969979i	$0.578193\pi$
$953$	−1156.15	+	1156.15i	−1.21317	+	1.21317i	−0.969979	+	0.243188i	$0.921807\pi$
$954$		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	−0.538583	−	0.842572i	$-0.681040\pi$
$967$	−564.461	+	151.247i	−0.583724	+	0.156408i	−0.0451407	+	0.998981i	$0.514374\pi$
$968$	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	−0.753947	−	0.656935i	$-0.771853\pi$
$977$	−1053.61	+	282.315i	−1.07842	+	0.288961i	−0.324470	+	0.945896i	$0.605186\pi$
$978$		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	$-0.392447\pi$
$983$	144.353	+	38.6793i	0.146850	+	0.0393482i	−0.184645	+	0.982805i	$0.559114\pi$
$984$		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	−0.699063	−	0.715060i	$-0.746399\pi$
$997$	263.082	−	981.834i	0.263873	−	0.984788i	0.962936	−	0.269728i	$-0.0869339\pi$
$998$	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.352.3		16
3.2	odd	2		405.3.l.j.352.2		16
5.3	odd	4		405.3.l.j.28.2		16
9.2	odd	6	inner	405.3.l.m.217.3		16
9.4	even	3		405.3.g.f.82.6	yes	16
9.5	odd	6		405.3.g.f.82.3	✓	16
9.7	even	3		405.3.l.j.217.2		16
15.8	even	4	inner	405.3.l.m.28.3		16
45.13	odd	12		405.3.g.f.163.6	yes	16
45.23	even	12		405.3.g.f.163.3	yes	16
45.38	even	12		405.3.l.j.298.2		16
45.43	odd	12	inner	405.3.l.m.298.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
405.3.g.f.82.3	✓	16	9.5	odd	6
405.3.g.f.82.6	yes	16	9.4	even	3
405.3.g.f.163.3	yes	16	45.23	even	12
405.3.g.f.163.6	yes	16	45.13	odd	12
405.3.l.j.28.2		16	5.3	odd	4
405.3.l.j.217.2		16	9.7	even	3
405.3.l.j.298.2		16	45.38	even	12
405.3.l.j.352.2		16	3.2	odd	2
405.3.l.m.28.3		16	15.8	even	4	inner
405.3.l.m.217.3		16	9.2	odd	6	inner
405.3.l.m.298.3		16	45.43	odd	12	inner
405.3.l.m.352.3		16	1.1	even	1	trivial

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more