LMFDB - Embedded newform 135.3.g.a.28.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [135,3,Mod(28,135)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(135, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("135.28");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	135.g (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.67848356886$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 217x^{12} + 9264x^{8} + 59497x^{4} + 28561 $ x^16 + 217x^12 + 9264x^8 + 59497*x^4 + 28561
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			28.5
Root			$0.601022 - 0.601022i$ of defining polynomial
Character	$\chi$	$=$	135.28
Dual form			135.3.g.a.82.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.601022 - 0.601022i) q^{2} +3.27754i q^{4} +(-4.98774 + 0.349865i) q^{5} +(-7.13454 + 7.13454i) q^{7} +(4.37397 + 4.37397i) q^{8} +(-2.78747 + 3.20802i) q^{10} -6.84616 q^{11} +(5.13850 + 5.13850i) q^{13} +8.57603i q^{14} -7.85248 q^{16} +(17.0856 - 17.0856i) q^{17} +21.9632i q^{19} +(-1.14670 - 16.3476i) q^{20} +(-4.11469 + 4.11469i) q^{22} +(-3.06284 - 3.06284i) q^{23} +(24.7552 - 3.49008i) q^{25} +6.17670 q^{26} +(-23.3838 - 23.3838i) q^{28} +41.1349i q^{29} +20.3793 q^{31} +(-22.2154 + 22.2154i) q^{32} -20.5376i q^{34} +(33.0891 - 38.0814i) q^{35} +(30.7953 - 30.7953i) q^{37} +(13.2004 + 13.2004i) q^{38} +(-23.3465 - 20.2859i) q^{40} -79.7736 q^{41} +(-16.8417 - 16.8417i) q^{43} -22.4386i q^{44} -3.68166 q^{46} +(21.1840 - 21.1840i) q^{47} -52.8032i q^{49} +(12.7808 - 16.9760i) q^{50} +(-16.8417 + 16.8417i) q^{52} +(48.1359 + 48.1359i) q^{53} +(34.1469 - 2.39523i) q^{55} -62.4124 q^{56} +(24.7230 + 24.7230i) q^{58} +32.3498i q^{59} +53.3901 q^{61} +(12.2484 - 12.2484i) q^{62} -4.70606i q^{64} +(-27.4273 - 23.8317i) q^{65} +(7.43409 - 7.43409i) q^{67} +(55.9987 + 55.9987i) q^{68} +(-3.00045 - 42.7750i) q^{70} -62.5131 q^{71} +(16.4036 + 16.4036i) q^{73} -37.0173i q^{74} -71.9854 q^{76} +(48.8441 - 48.8441i) q^{77} +141.870i q^{79} +(39.1662 - 2.74731i) q^{80} +(-47.9457 + 47.9457i) q^{82} +(18.7813 + 18.7813i) q^{83} +(-79.2408 + 91.1960i) q^{85} -20.2444 q^{86} +(-29.9448 - 29.9448i) q^{88} +48.7354i q^{89} -73.3216 q^{91} +(10.0386 - 10.0386i) q^{92} -25.4641i q^{94} +(-7.68416 - 109.547i) q^{95} +(6.96035 - 6.96035i) q^{97} +(-31.7359 - 31.7359i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{7} - 32 q^{10} + 28 q^{13} - 20 q^{16} + 176 q^{22} + 64 q^{25} + 80 q^{28} - 208 q^{31} - 176 q^{37} - 252 q^{40} - 188 q^{43} + 188 q^{46} - 188 q^{52} - 136 q^{55} + 504 q^{58} + 296 q^{61}+ \cdots - 284 q^{97}+O(q^{100}) $ 16 * q - 8 * q^7 - 32 * q^10 + 28 * q^13 - 20 * q^16 + 176 * q^22 + 64 * q^25 + 80 * q^28 - 208 * q^31 - 176 * q^37 - 252 * q^40 - 188 * q^43 + 188 * q^46 - 188 * q^52 - 136 * q^55 + 504 * q^58 + 296 * q^61 + 304 * q^67 + 684 * q^70 - 56 * q^73 - 732 * q^76 - 76 * q^82 - 788 * q^85 - 1128 * q^88 + 200 * q^91 - 284 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.601022	−	0.601022i	0.300511	−	0.300511i	−0.540703	−	0.841214i	$-0.681842\pi$
$2$	0.601022	−	0.601022i	0.300511	−	0.300511i	0.841214	+	0.540703i	$0.181842\pi$
$3$		0			0
$3$		0			0
$4$			3.27754i			0.819386i
$5$	−4.98774	+	0.349865i	−0.997549	+	0.0699731i
$5$	−4.98774	+	0.349865i	−0.997549	+	0.0699731i
$6$		0			0
$7$	−7.13454	+	7.13454i	−1.01922	+	1.01922i	−0.0194078	+	0.999812i	$0.506178\pi$
$7$	−7.13454	+	7.13454i	−1.01922	+	1.01922i	−0.999812	+	0.0194078i	$0.993822\pi$
$8$	4.37397	+	4.37397i	0.546746	+	0.546746i
$9$		0			0
$10$	−2.78747	+	3.20802i	−0.278747	+	0.320802i
$11$	−6.84616			−0.622378			−0.311189	−	0.950348i	$-0.600727\pi$
$11$	−6.84616			−0.622378			−0.311189	+	0.950348i	$0.600727\pi$
$12$		0			0
$13$	5.13850	+	5.13850i	0.395269	+	0.395269i	0.876561	−	0.481292i	$-0.159832\pi$
$13$	5.13850	+	5.13850i	0.395269	+	0.395269i	−0.481292	+	0.876561i	$0.659832\pi$
$14$			8.57603i			0.612573i
$15$		0			0
$16$	−7.85248			−0.490780
$17$	17.0856	−	17.0856i	1.00503	−	1.00503i	0.00504558	−	0.999987i	$-0.498394\pi$
$17$	17.0856	−	17.0856i	1.00503	−	1.00503i	0.999987	−	0.00504558i	$-0.00160606\pi$
$18$		0			0
$19$			21.9632i			1.15596i	0.816051	+	0.577979i	$0.196159\pi$
$19$			21.9632i			1.15596i	−0.816051	+	0.577979i	$0.803841\pi$
$20$	−1.14670	−	16.3476i	−0.0573350	−	0.817378i
$21$		0			0
$22$	−4.11469	+	4.11469i	−0.187031	+	0.187031i
$23$	−3.06284	−	3.06284i	−0.133167	−	0.133167i	0.637382	−	0.770548i	$-0.280018\pi$
$23$	−3.06284	−	3.06284i	−0.133167	−	0.133167i	−0.770548	+	0.637382i	$0.780018\pi$
$24$		0			0
$25$	24.7552	−	3.49008i	0.990208	−	0.139603i
$26$	6.17670			0.237565
$27$		0			0
$28$	−23.3838	−	23.3838i	−0.835134	−	0.835134i
$29$			41.1349i			1.41845i	0.704984	+	0.709223i	$0.250954\pi$
$29$			41.1349i			1.41845i	−0.704984	+	0.709223i	$0.749046\pi$
$30$		0			0
$31$	20.3793			0.657395			0.328698	−	0.944435i	$-0.393390\pi$
$31$	20.3793			0.657395			0.328698	+	0.944435i	$0.393390\pi$
$32$	−22.2154	+	22.2154i	−0.694230	+	0.694230i
$33$		0			0
$34$		−	20.5376i		−	0.604047i
$35$	33.0891	−	38.0814i	0.945403	−	1.08804i
$36$		0			0
$37$	30.7953	−	30.7953i	0.832305	−	0.832305i	−0.155526	−	0.987832i	$-0.549707\pi$
$37$	30.7953	−	30.7953i	0.832305	−	0.832305i	0.987832	+	0.155526i	$0.0497074\pi$
$38$	13.2004	+	13.2004i	0.347378	+	0.347378i
$39$		0			0
$40$	−23.3465	−	20.2859i	−0.583663	−	0.507148i
$41$	−79.7736			−1.94570			−0.972849	−	0.231440i	$-0.925656\pi$
$41$	−79.7736			−1.94570			−0.972849	+	0.231440i	$0.925656\pi$
$42$		0			0
$43$	−16.8417	−	16.8417i	−0.391666	−	0.391666i	0.483615	−	0.875281i	$-0.339324\pi$
$43$	−16.8417	−	16.8417i	−0.391666	−	0.391666i	−0.875281	+	0.483615i	$0.839324\pi$
$44$		−	22.4386i		−	0.509968i
$45$		0			0
$46$	−3.68166			−0.0800362
$47$	21.1840	−	21.1840i	0.450723	−	0.450723i	−0.444872	−	0.895594i	$-0.646751\pi$
$47$	21.1840	−	21.1840i	0.450723	−	0.450723i	0.895594	+	0.444872i	$0.146751\pi$
$48$		0			0
$49$		−	52.8032i		−	1.07762i
$50$	12.7808	−	16.9760i	0.255616	−	0.339521i
$51$		0			0
$52$	−16.8417	+	16.8417i	−0.323878	+	0.323878i
$53$	48.1359	+	48.1359i	0.908225	+	0.908225i	0.996129	−	0.0879040i	$-0.0280169\pi$
$53$	48.1359	+	48.1359i	0.908225	+	0.908225i	−0.0879040	+	0.996129i	$0.528017\pi$
$54$		0			0
$55$	34.1469	−	2.39523i	0.620852	−	0.0435497i
$56$	−62.4124			−1.11451
$57$		0			0
$58$	24.7230	+	24.7230i	0.426259	+	0.426259i
$59$			32.3498i			0.548301i	0.961687	+	0.274150i	$0.0883966\pi$
$59$			32.3498i			0.548301i	−0.961687	+	0.274150i	$0.911603\pi$
$60$		0			0
$61$	53.3901			0.875247			0.437624	−	0.899158i	$-0.355820\pi$
$61$	53.3901			0.875247			0.437624	+	0.899158i	$0.355820\pi$
$62$	12.2484	−	12.2484i	0.197555	−	0.197555i
$63$		0			0
$64$		−	4.70606i		−	0.0735322i
$65$	−27.4273	−	23.8317i	−0.421958	−	0.366642i
$66$		0			0
$67$	7.43409	−	7.43409i	0.110957	−	0.110957i	−0.649449	−	0.760405i	$-0.725000\pi$
$67$	7.43409	−	7.43409i	0.110957	−	0.110957i	0.760405	+	0.649449i	$0.225000\pi$
$68$	55.9987	+	55.9987i	0.823510	+	0.823510i
$69$		0			0
$70$	−3.00045	−	42.7750i	−0.0428636	−	0.611072i
$71$	−62.5131			−0.880466			−0.440233	−	0.897884i	$-0.645104\pi$
$71$	−62.5131			−0.880466			−0.440233	+	0.897884i	$0.645104\pi$
$72$		0			0
$73$	16.4036	+	16.4036i	0.224707	+	0.224707i	0.810477	−	0.585770i	$-0.199208\pi$
$73$	16.4036	+	16.4036i	0.224707	+	0.224707i	−0.585770	+	0.810477i	$0.699208\pi$
$74$		−	37.0173i		−	0.500234i
$75$		0			0
$76$	−71.9854			−0.947176
$77$	48.8441	−	48.8441i	0.634340	−	0.634340i
$78$		0			0
$79$			141.870i			1.79583i	0.440170	+	0.897914i	$0.354918\pi$
$79$			141.870i			1.79583i	−0.440170	+	0.897914i	$0.645082\pi$
$80$	39.1662	−	2.74731i	0.489577	−	0.0343414i
$81$		0			0
$82$	−47.9457	+	47.9457i	−0.584704	+	0.584704i
$83$	18.7813	+	18.7813i	0.226281	+	0.226281i	0.811137	−	0.584856i	$-0.198849\pi$
$83$	18.7813	+	18.7813i	0.226281	+	0.226281i	−0.584856	+	0.811137i	$0.698849\pi$
$84$		0			0
$85$	−79.2408	+	91.1960i	−0.932244	+	1.07289i
$86$	−20.2444			−0.235400
$87$		0			0
$88$	−29.9448	−	29.9448i	−0.340282	−	0.340282i
$89$			48.7354i			0.547589i	0.961788	+	0.273795i	$0.0882789\pi$
$89$			48.7354i			0.547589i	−0.961788	+	0.273795i	$0.911721\pi$
$90$		0			0
$91$	−73.3216			−0.805732
$92$	10.0386	−	10.0386i	0.109115	−	0.109115i
$93$		0			0
$94$		−	25.4641i		−	0.270894i
$95$	−7.68416	−	109.547i	−0.0808859	−	1.15313i
$96$		0			0
$97$	6.96035	−	6.96035i	0.0717562	−	0.0717562i	−0.670318	−	0.742074i	$-0.733842\pi$
$97$	6.96035	−	6.96035i	0.0717562	−	0.0717562i	0.742074	+	0.670318i	$0.233842\pi$
$98$	−31.7359	−	31.7359i	−0.323836	−	0.323836i
$99$		0			0
$100$	11.4389	+	81.1362i	0.114389	+	0.811362i
$101$	105.583			1.04538			0.522690	−	0.852523i	$-0.324929\pi$
$101$	105.583			1.04538			0.522690	+	0.852523i	$0.324929\pi$
$102$		0			0
$103$	119.756	+	119.756i	1.16268	+	1.16268i	0.983888	+	0.178788i	$0.0572177\pi$
$103$	119.756	+	119.756i	1.16268	+	1.16268i	0.178788	+	0.983888i	$0.442782\pi$
$104$			44.9512i			0.432223i
$105$		0			0
$106$	57.8615			0.545863
$107$	−66.8231	+	66.8231i	−0.624515	+	0.624515i	−0.946683	−	0.322168i	$-0.895589\pi$
$107$	−66.8231	+	66.8231i	−0.624515	+	0.624515i	0.322168	+	0.946683i	$0.395589\pi$
$108$		0			0
$109$		−	48.2233i		−	0.442415i	−0.975227	−	0.221208i	$-0.929000\pi$
$109$		−	48.2233i		−	0.442415i	0.975227	−	0.221208i	$-0.0709998\pi$
$110$	19.0834	−	21.9626i	0.173486	−	0.199660i
$111$		0			0
$112$	56.0238	−	56.0238i	0.500213	−	0.500213i
$113$	−35.7855	−	35.7855i	−0.316686	−	0.316686i	0.530807	−	0.847493i	$-0.321889\pi$
$113$	−35.7855	−	35.7855i	−0.316686	−	0.316686i	−0.847493	+	0.530807i	$0.821889\pi$
$114$		0			0
$115$	16.3482	+	14.2051i	0.142158	+	0.123522i
$116$	−134.822			−1.16226
$117$		0			0
$118$	19.4429	+	19.4429i	0.164770	+	0.164770i
$119$			243.795i			2.04870i
$120$		0			0
$121$	−74.1302			−0.612646
$122$	32.0886	−	32.0886i	0.263021	−	0.263021i
$123$		0			0
$124$			66.7939i			0.538661i
$125$	−122.251	+	26.0686i	−0.978012	+	0.208549i
$126$		0			0
$127$	−48.1040	+	48.1040i	−0.378772	+	0.378772i	−0.870659	−	0.491887i	$-0.836307\pi$
$127$	−48.1040	+	48.1040i	−0.378772	+	0.378772i	0.491887	+	0.870659i	$0.336307\pi$
$128$	−91.6899	−	91.6899i	−0.716328	−	0.716328i
$129$		0			0
$130$	−30.8078	+	2.16101i	−0.236983	+	0.0166232i
$131$	178.550			1.36297			0.681487	−	0.731830i	$-0.261333\pi$
$131$	178.550			1.36297			0.681487	+	0.731830i	$0.261333\pi$
$132$		0			0
$133$	−156.697	−	156.697i	−1.17818	−	1.17818i
$134$		−	8.93610i		−	0.0666873i
$135$		0			0
$136$	149.463			1.09899
$137$	57.1514	−	57.1514i	0.417164	−	0.417164i	−0.467061	−	0.884225i	$-0.654687\pi$
$137$	57.1514	−	57.1514i	0.417164	−	0.417164i	0.884225	+	0.467061i	$0.154687\pi$
$138$		0			0
$139$		−	169.100i		−	1.21655i	−0.793727	−	0.608274i	$-0.791862\pi$
$139$		−	169.100i		−	1.21655i	0.793727	−	0.608274i	$-0.208138\pi$
$140$	124.813	+	108.451i	0.891524	+	0.774650i
$141$		0			0
$142$	−37.5718	+	37.5718i	−0.264590	+	0.264590i
$143$	−35.1790	−	35.1790i	−0.246007	−	0.246007i
$144$		0			0
$145$	−14.3917	−	205.171i	−0.0992530	−	1.41497i
$146$	19.7179			0.135054
$147$		0			0
$148$	100.933	+	100.933i	0.681979	+	0.681979i
$149$		−	252.758i		−	1.69636i	−0.529705	−	0.848182i	$-0.677697\pi$
$149$		−	252.758i		−	1.69636i	0.529705	−	0.848182i	$-0.322303\pi$
$150$		0			0
$151$	−95.1486			−0.630123			−0.315062	−	0.949071i	$-0.602025\pi$
$151$	−95.1486			−0.630123			−0.315062	+	0.949071i	$0.602025\pi$
$152$	−96.0663	+	96.0663i	−0.632015	+	0.632015i
$153$		0			0
$154$		−	58.7128i		−	0.381252i
$155$	−101.647	+	7.12999i	−0.655784	+	0.0460000i
$156$		0			0
$157$	202.553	−	202.553i	1.29015	−	1.29015i	0.355453	−	0.934694i	$-0.384327\pi$
$157$	202.553	−	202.553i	1.29015	−	1.29015i	0.934694	−	0.355453i	$-0.115673\pi$
$158$	85.2673	+	85.2673i	0.539666	+	0.539666i
$159$		0			0
$160$	103.032	−	118.577i	0.643951	−	0.741106i
$161$	43.7038			0.271452
$162$		0			0
$163$	−34.5104	−	34.5104i	−0.211720	−	0.211720i	0.593278	−	0.804998i	$-0.297834\pi$
$163$	−34.5104	−	34.5104i	−0.211720	−	0.211720i	−0.804998	+	0.593278i	$0.797834\pi$
$164$		−	261.462i		−	1.59428i
$165$		0			0
$166$	22.5760			0.136000
$167$	36.8934	−	36.8934i	0.220918	−	0.220918i	−0.587967	−	0.808885i	$-0.700071\pi$
$167$	36.8934	−	36.8934i	0.220918	−	0.220918i	0.808885	+	0.587967i	$0.200071\pi$
$168$		0			0
$169$		−	116.192i		−	0.687525i
$170$	7.18539	+	102.436i	0.0422670	+	0.602566i
$171$		0			0
$172$	55.1993	−	55.1993i	0.320926	−	0.320926i
$173$	76.7538	+	76.7538i	0.443663	+	0.443663i	0.893241	−	0.449578i	$-0.148426\pi$
$173$	76.7538	+	76.7538i	0.443663	+	0.443663i	−0.449578	+	0.893241i	$0.648426\pi$
$174$		0			0
$175$	−151.717	+	201.517i	−0.866953	+	1.15152i
$176$	53.7593			0.305451
$177$		0			0
$178$	29.2911	+	29.2911i	0.164557	+	0.164557i
$179$			0.472314i			0.00263862i	0.999999	+	0.00131931i	$0.000419950\pi$
$179$			0.472314i			0.00263862i	−0.999999	+	0.00131931i	$0.999580\pi$
$180$		0			0
$181$	71.0814			0.392715			0.196357	−	0.980532i	$-0.437089\pi$
$181$	71.0814			0.392715			0.196357	+	0.980532i	$0.437089\pi$
$182$	−44.0679	+	44.0679i	−0.242131	+	0.242131i
$183$		0			0
$184$		−	26.7935i		−	0.145617i
$185$	−142.825	+	164.373i	−0.772026	+	0.888504i
$186$		0			0
$187$	−116.970	+	116.970i	−0.625510	+	0.625510i
$188$	69.4314	+	69.4314i	0.369316	+	0.369316i
$189$		0			0
$190$	−70.4584	−	61.2217i	−0.370834	−	0.322220i
$191$	37.9492			0.198687			0.0993435	−	0.995053i	$-0.468326\pi$
$191$	37.9492			0.198687			0.0993435	+	0.995053i	$0.468326\pi$
$192$		0			0
$193$	−72.2919	−	72.2919i	−0.374570	−	0.374570i	0.494569	−	0.869138i	$-0.335326\pi$
$193$	−72.2919	−	72.2919i	−0.374570	−	0.374570i	−0.869138	+	0.494569i	$0.835326\pi$
$194$		−	8.36665i		−	0.0431270i
$195$		0			0
$196$	173.065			0.882984
$197$	2.95917	−	2.95917i	0.0150212	−	0.0150212i	−0.699556	−	0.714577i	$-0.746619\pi$
$197$	2.95917	−	2.95917i	0.0150212	−	0.0150212i	0.714577	+	0.699556i	$0.246619\pi$
$198$		0			0
$199$			250.929i			1.26095i	0.776210	+	0.630475i	$0.217140\pi$
$199$			250.929i			1.26095i	−0.776210	+	0.630475i	$0.782860\pi$
$200$	123.544	+	93.0129i	0.617719	+	0.465064i
$201$		0			0
$202$	63.4579	−	63.4579i	0.314148	−	0.314148i
$203$	−293.479	−	293.479i	−1.44571	−	1.44571i
$204$		0			0
$205$	397.890	−	27.9100i	1.94093	−	0.136146i
$206$	143.952			0.698794
$207$		0			0
$208$	−40.3500	−	40.3500i	−0.193990	−	0.193990i
$209$		−	150.364i		−	0.719443i
$210$		0			0
$211$	−242.283			−1.14826			−0.574131	−	0.818764i	$-0.694660\pi$
$211$	−242.283			−1.14826			−0.574131	+	0.818764i	$0.694660\pi$
$212$	−157.768	+	157.768i	−0.744187	+	0.744187i
$213$		0			0
$214$			80.3243i			0.375347i
$215$	89.8942	+	78.1096i	0.418113	+	0.363300i
$216$		0			0
$217$	−145.397	+	145.397i	−0.670030	+	0.670030i
$218$	−28.9832	−	28.9832i	−0.132951	−	0.132951i
$219$		0			0
$220$	7.85048	+	111.918i	0.0356840	+	0.508718i
$221$	175.588			0.794517
$222$		0			0
$223$	−173.530	−	173.530i	−0.778163	−	0.778163i	0.201355	−	0.979518i	$-0.435465\pi$
$223$	−173.530	−	173.530i	−0.778163	−	0.778163i	−0.979518	+	0.201355i	$0.935465\pi$
$224$		−	316.993i		−	1.41515i
$225$		0			0
$226$	−43.0158			−0.190335
$227$	−111.249	+	111.249i	−0.490082	+	0.490082i	−0.908332	−	0.418250i	$-0.862644\pi$
$227$	−111.249	+	111.249i	−0.490082	+	0.490082i	0.418250	+	0.908332i	$0.362644\pi$
$228$		0			0
$229$			10.3095i			0.0450198i	0.999747	+	0.0225099i	$0.00716574\pi$
$229$			10.3095i			0.0450198i	−0.999747	+	0.0225099i	$0.992834\pi$
$230$	18.3632	−	1.28809i	0.0798400	−	0.00560038i
$231$		0			0
$232$	−179.923	+	179.923i	−0.775529	+	0.775529i
$233$	−224.189	−	224.189i	−0.962184	−	0.962184i	0.0371270	−	0.999311i	$-0.488179\pi$
$233$	−224.189	−	224.189i	−0.962184	−	0.962184i	−0.999311	+	0.0371270i	$0.988179\pi$
$234$		0			0
$235$	−98.2486	+	113.072i	−0.418079	+	0.481156i
$236$	−106.028			−0.449270
$237$		0			0
$238$	146.526	+	146.526i	0.615656	+	0.615656i
$239$			209.920i			0.878327i	0.898407	+	0.439164i	$0.144725\pi$
$239$			209.920i			0.878327i	−0.898407	+	0.439164i	$0.855275\pi$
$240$		0			0
$241$	−12.3229			−0.0511323			−0.0255662	−	0.999673i	$-0.508139\pi$
$241$	−12.3229			−0.0511323			−0.0255662	+	0.999673i	$0.508139\pi$
$242$	−44.5539	+	44.5539i	−0.184107	+	0.184107i
$243$		0			0
$244$			174.988i			0.717165i
$245$	18.4740	+	263.369i	0.0754041	+	1.07498i
$246$		0			0
$247$	−112.858	+	112.858i	−0.456915	+	0.456915i
$248$	89.1381	+	89.1381i	0.359428	+	0.359428i
$249$		0			0
$250$	−57.8080	+	89.1436i	−0.231232	+	0.356575i
$251$	396.814			1.58093			0.790466	−	0.612506i	$-0.209839\pi$
$251$	396.814			1.58093			0.790466	+	0.612506i	$0.209839\pi$
$252$		0			0
$253$	20.9687	+	20.9687i	0.0828801	+	0.0828801i
$254$			57.8232i			0.227650i
$255$		0			0
$256$	−91.3911			−0.356997
$257$	−133.629	+	133.629i	−0.519957	+	0.519957i	−0.917558	−	0.397601i	$-0.869843\pi$
$257$	−133.629	+	133.629i	−0.519957	+	0.519957i	0.397601	+	0.917558i	$0.369843\pi$
$258$		0			0
$259$			439.420i			1.69660i
$260$	78.1096	−	89.8942i	0.300421	−	0.345747i
$261$		0			0
$262$	107.312	−	107.312i	0.409589	−	0.409589i
$263$	−185.126	−	185.126i	−0.703903	−	0.703903i	0.261343	−	0.965246i	$-0.415835\pi$
$263$	−185.126	−	185.126i	−0.703903	−	0.703903i	−0.965246	+	0.261343i	$0.915835\pi$
$264$		0			0
$265$	−256.931	−	223.249i	−0.969550	−	0.842447i
$266$	−188.357			−0.708109
$267$		0			0
$268$	24.3656	+	24.3656i	0.0909162	+	0.0909162i
$269$			289.745i			1.07712i	0.842588	+	0.538559i	$0.181031\pi$
$269$			289.745i			1.07712i	−0.842588	+	0.538559i	$0.818969\pi$
$270$		0			0
$271$	253.543			0.935582			0.467791	−	0.883839i	$-0.345050\pi$
$271$	253.543			0.935582			0.467791	+	0.883839i	$0.345050\pi$
$272$	−134.164	+	134.164i	−0.493250	+	0.493250i
$273$		0			0
$274$		−	68.6986i		−	0.250725i
$275$	−169.478	+	23.8936i	−0.616283	+	0.0868859i
$276$		0			0
$277$	58.8124	−	58.8124i	0.212319	−	0.212319i	−0.592933	−	0.805252i	$-0.702030\pi$
$277$	58.8124	−	58.8124i	0.212319	−	0.212319i	0.805252	+	0.592933i	$0.202030\pi$
$278$	−101.633	−	101.633i	−0.365586	−	0.365586i
$279$		0			0
$280$	311.297	−	21.8359i	1.11178	−	0.0779855i
$281$	428.466			1.52479			0.762395	−	0.647112i	$-0.224023\pi$
$281$	428.466			1.52479			0.762395	+	0.647112i	$0.224023\pi$
$282$		0			0
$283$	320.183	+	320.183i	1.13139	+	1.13139i	0.989946	+	0.141444i	$0.0451744\pi$
$283$	320.183	+	320.183i	1.13139	+	1.13139i	0.141444	+	0.989946i	$0.454826\pi$
$284$		−	204.889i		−	0.721442i
$285$		0			0
$286$	−42.2867			−0.147855
$287$	569.148	−	569.148i	1.98309	−	1.98309i
$288$		0			0
$289$		−	294.833i		−	1.02018i
$290$	−131.962	−	114.662i	−0.455041	−	0.395387i
$291$		0			0
$292$	−53.7636	+	53.7636i	−0.184122	+	0.184122i
$293$	−7.37108	−	7.37108i	−0.0251573	−	0.0251573i	0.694416	−	0.719574i	$-0.255663\pi$
$293$	−7.37108	−	7.37108i	−0.0251573	−	0.0251573i	−0.719574	+	0.694416i	$0.755663\pi$
$294$		0			0
$295$	−11.3181	−	161.352i	−0.0383663	−	0.546957i
$296$	269.395			0.910119
$297$		0			0
$298$	−151.913	−	151.913i	−0.509776	−	0.509776i
$299$		−	31.4768i		−	0.105273i
$300$		0			0
$301$	240.315			0.798388
$302$	−57.1864	+	57.1864i	−0.189359	+	0.189359i
$303$		0			0
$304$		−	172.466i		−	0.567321i
$305$	−266.296	+	18.6793i	−0.873102	+	0.0612437i
$306$		0			0
$307$	−75.2762	+	75.2762i	−0.245199	+	0.245199i	−0.818997	−	0.573798i	$-0.805470\pi$
$307$	−75.2762	+	75.2762i	−0.245199	+	0.245199i	0.573798	+	0.818997i	$0.305470\pi$
$308$	160.089	+	160.089i	0.519769	+	0.519769i
$309$		0			0
$310$	−56.8065	+	65.3771i	−0.183247	+	0.210894i
$311$	−307.264			−0.987988			−0.493994	−	0.869465i	$-0.664463\pi$
$311$	−307.264			−0.987988			−0.493994	+	0.869465i	$0.664463\pi$
$312$		0			0
$313$	−150.851	−	150.851i	−0.481951	−	0.481951i	0.423803	−	0.905754i	$-0.360695\pi$
$313$	−150.851	−	150.851i	−0.481951	−	0.481951i	−0.905754	+	0.423803i	$0.860695\pi$
$314$		−	243.478i		−	0.775407i
$315$		0			0
$316$	−464.987			−1.47148
$317$	80.7274	−	80.7274i	0.254661	−	0.254661i	−0.568218	−	0.822878i	$-0.692367\pi$
$317$	80.7274	−	80.7274i	0.254661	−	0.254661i	0.822878	+	0.568218i	$0.192367\pi$
$318$		0			0
$319$		−	281.616i		−	0.882809i
$320$	1.64649	+	23.4726i	0.00514527	+	0.0733520i
$321$		0			0
$322$	26.2670	−	26.2670i	0.0815744	−	0.0815744i
$323$	375.254	+	375.254i	1.16178	+	1.16178i
$324$		0			0
$325$	145.138	+	109.271i	0.446579	+	0.336218i
$326$	−41.4830			−0.127248
$327$		0			0
$328$	−348.927	−	348.927i	−1.06380	−	1.06380i
$329$			302.275i			0.918770i
$330$		0			0
$331$	310.505			0.938080			0.469040	−	0.883177i	$-0.344600\pi$
$331$	310.505			0.938080			0.469040	+	0.883177i	$0.344600\pi$
$332$	−61.5567	+	61.5567i	−0.185412	+	0.185412i
$333$		0			0
$334$		−	44.3474i		−	0.132777i
$335$	−34.4784	+	39.6803i	−0.102921	+	0.118449i
$336$		0			0
$337$	173.720	−	173.720i	0.515489	−	0.515489i	−0.400714	−	0.916203i	$-0.631238\pi$
$337$	173.720	−	173.720i	0.515489	−	0.515489i	0.916203	+	0.400714i	$0.131238\pi$
$338$	−69.8338	−	69.8338i	−0.206609	−	0.206609i
$339$		0			0
$340$	−298.899	−	259.715i	−0.879115	−	0.763868i
$341$	−139.520			−0.409148
$342$		0			0
$343$	27.1342	+	27.1342i	0.0791084	+	0.0791084i
$344$		−	147.330i		−	0.428284i
$345$		0			0
$346$	92.2614			0.266651
$347$	108.486	−	108.486i	0.312639	−	0.312639i	−0.533292	−	0.845931i	$-0.679045\pi$
$347$	108.486	−	108.486i	0.312639	−	0.312639i	0.845931	+	0.533292i	$0.179045\pi$
$348$		0			0
$349$		−	0.0961855i		−	0.000275603i	−1.00000		0.000137802i	$-0.999956\pi$
$349$		−	0.0961855i		−	0.000275603i	1.00000		0.000137802i	$-4.38636e-5\pi$
$350$	29.9310	+	212.301i	0.0855171	+	0.606575i
$351$		0			0
$352$	152.090	−	152.090i	0.432074	−	0.432074i
$353$	−191.489	−	191.489i	−0.542461	−	0.542461i	0.381789	−	0.924250i	$-0.375308\pi$
$353$	−191.489	−	191.489i	−0.542461	−	0.542461i	−0.924250	+	0.381789i	$0.875308\pi$
$354$		0			0
$355$	311.799	−	21.8712i	0.878308	−	0.0616089i
$356$	−159.733			−0.448687
$357$		0			0
$358$	0.283871	+	0.283871i	0.000792936	+	0.000792936i
$359$			147.318i			0.410356i	0.978725	+	0.205178i	$0.0657774\pi$
$359$			147.318i			0.410356i	−0.978725	+	0.205178i	$0.934223\pi$
$360$		0			0
$361$	−121.383			−0.336240
$362$	42.7215	−	42.7215i	0.118015	−	0.118015i
$363$		0			0
$364$		−	240.315i		−	0.660206i
$365$	−87.5561	−	76.0780i	−0.239880	−	0.208433i
$366$		0			0
$367$	480.412	−	480.412i	1.30902	−	1.30902i	0.386904	−	0.922120i	$-0.373544\pi$
$367$	480.412	−	480.412i	1.30902	−	1.30902i	0.922120	−	0.386904i	$-0.126456\pi$
$368$	24.0509	+	24.0509i	0.0653556	+	0.0653556i
$369$		0			0
$370$	12.9511	+	184.633i	0.0350029	+	0.499008i
$371$	−686.855			−1.85136
$372$		0			0
$373$	387.842	+	387.842i	1.03979	+	1.03979i	0.999175	+	0.0406159i	$0.0129320\pi$
$373$	387.842	+	387.842i	1.03979	+	1.03979i	0.0406159	+	0.999175i	$0.487068\pi$
$374$			140.604i			0.375945i
$375$		0			0
$376$	185.316			0.492861
$377$	−211.372	+	211.372i	−0.560668	+	0.560668i
$378$		0			0
$379$		−	306.368i		−	0.808358i	−0.914680	−	0.404179i	$-0.867557\pi$
$379$		−	306.368i		−	0.808358i	0.914680	−	0.404179i	$-0.132443\pi$
$380$	359.045	−	25.1852i	0.944855	−	0.0662768i
$381$		0			0
$382$	22.8083	−	22.8083i	0.0597076	−	0.0597076i
$383$	316.156	+	316.156i	0.825474	+	0.825474i	0.986887	−	0.161413i	$-0.0516052\pi$
$383$	316.156	+	316.156i	0.825474	+	0.825474i	−0.161413	+	0.986887i	$0.551605\pi$
$384$		0			0
$385$	−226.533	+	260.711i	−0.588398	+	0.677171i
$386$	−86.8981			−0.225125
$387$		0			0
$388$	22.8129	+	22.8129i	0.0587960	+	0.0587960i
$389$		−	20.6616i		−	0.0531145i	−0.999647	−	0.0265573i	$-0.991546\pi$
$389$		−	20.6616i		−	0.0531145i	0.999647	−	0.0265573i	$-0.00845443\pi$
$390$		0			0
$391$	−104.661			−0.267674
$392$	230.959	−	230.959i	0.589182	−	0.589182i
$393$		0			0
$394$		−	3.55706i		−	0.00902806i
$395$	−49.6356	−	707.614i	−0.125660	−	1.79143i
$396$		0			0
$397$	144.786	−	144.786i	0.364701	−	0.364701i	−0.500839	−	0.865540i	$-0.666975\pi$
$397$	144.786	−	144.786i	0.364701	−	0.364701i	0.865540	+	0.500839i	$0.166975\pi$
$398$	150.814	+	150.814i	0.378929	+	0.378929i
$399$		0			0
$400$	−194.390	+	27.4058i	−0.485974	+	0.0685144i
$401$	509.332			1.27016			0.635078	−	0.772448i	$-0.280968\pi$
$401$	509.332			1.27016			0.635078	+	0.772448i	$0.280968\pi$
$402$		0			0
$403$	104.719	+	104.719i	0.259848	+	0.259848i
$404$			346.054i			0.856569i
$405$		0			0
$406$	−352.774			−0.868902
$407$	−210.829	+	210.829i	−0.518008	+	0.518008i
$408$		0			0
$409$			446.139i			1.09080i	0.838174	+	0.545402i	$0.183623\pi$
$409$			446.139i			1.09080i	−0.838174	+	0.545402i	$0.816377\pi$
$410$	222.366	−	255.916i	0.542357	−	0.624184i
$411$		0			0
$412$	−392.504	+	392.504i	−0.952681	+	0.952681i
$413$	−230.801	−	230.801i	−0.558839	−	0.558839i
$414$		0			0
$415$	−100.247	−	87.1056i	−0.241560	−	0.209893i
$416$	−228.307			−0.548816
$417$		0			0
$418$	−90.3718	−	90.3718i	−0.216201	−	0.216201i
$419$		−	53.7826i		−	0.128359i	−0.997938	−	0.0641797i	$-0.979557\pi$
$419$		−	53.7826i		−	0.128359i	0.997938	−	0.0641797i	$-0.0204431\pi$
$420$		0			0
$421$	−499.578			−1.18665			−0.593323	−	0.804965i	$-0.702184\pi$
$421$	−499.578			−1.18665			−0.593323	+	0.804965i	$0.702184\pi$
$422$	−145.618	+	145.618i	−0.345065	+	0.345065i
$423$		0			0
$424$			421.090i			0.993136i
$425$	363.326	−	482.586i	0.854885	−	1.13550i
$426$		0			0
$427$	−380.913	+	380.913i	−0.892069	+	0.892069i
$428$	−219.016	−	219.016i	−0.511719	−	0.511719i
$429$		0			0
$430$	100.974	−	7.08282i	0.234823	−	0.0164717i
$431$	−618.642			−1.43536			−0.717682	−	0.696371i	$-0.754797\pi$
$431$	−618.642			−1.43536			−0.717682	+	0.696371i	$0.754797\pi$
$432$		0			0
$433$	170.934	+	170.934i	0.394768	+	0.394768i	0.876383	−	0.481615i	$-0.159950\pi$
$433$	170.934	+	170.934i	0.394768	+	0.394768i	−0.481615	+	0.876383i	$0.659950\pi$
$434$			174.773i			0.402703i
$435$		0			0
$436$	158.054			0.362509
$437$	67.2697	−	67.2697i	0.153935	−	0.153935i
$438$		0			0
$439$		−	14.7887i		−	0.0336872i	−0.999858	−	0.0168436i	$-0.994638\pi$
$439$		−	14.7887i		−	0.0336872i	0.999858	−	0.0168436i	$-0.00536174\pi$
$440$	159.834	+	138.881i	0.363259	+	0.315638i
$441$		0			0
$442$	105.532	−	105.532i	0.238761	−	0.238761i
$443$	584.922	+	584.922i	1.32037	+	1.32037i	0.913478	+	0.406888i	$0.133386\pi$
$443$	584.922	+	584.922i	1.32037	+	1.32037i	0.406888	+	0.913478i	$0.366614\pi$
$444$		0			0
$445$	−17.0508	−	243.080i	−0.0383165	−	0.546247i
$446$	−208.591			−0.467693
$447$		0			0
$448$	33.5756	+	33.5756i	0.0749454	+	0.0749454i
$449$			227.191i			0.505993i	0.967467	+	0.252997i	$0.0814162\pi$
$449$			227.191i			0.505993i	−0.967467	+	0.252997i	$0.918584\pi$
$450$		0			0
$451$	546.143			1.21096
$452$	117.289	−	117.289i	0.259488	−	0.259488i
$453$		0			0
$454$			133.726i			0.294550i
$455$	365.709	−	25.6527i	0.803757	−	0.0563795i
$456$		0			0
$457$	−234.242	+	234.242i	−0.512565	+	0.512565i	−0.915311	−	0.402747i	$-0.868055\pi$
$457$	−234.242	+	234.242i	−0.512565	+	0.512565i	0.402747	+	0.915311i	$0.368055\pi$
$458$	6.19626	+	6.19626i	0.0135290	+	0.0135290i
$459$		0			0
$460$	−46.5577	+	53.5820i	−0.101212	+	0.116483i
$461$	138.139			0.299651			0.149826	−	0.988712i	$-0.452129\pi$
$461$	138.139			0.299651			0.149826	+	0.988712i	$0.452129\pi$
$462$		0			0
$463$	−222.375	−	222.375i	−0.480291	−	0.480291i	0.424934	−	0.905225i	$-0.360297\pi$
$463$	−222.375	−	222.375i	−0.480291	−	0.480291i	−0.905225	+	0.424934i	$0.860297\pi$
$464$		−	323.011i		−	0.696145i
$465$		0			0
$466$	−269.485			−0.578294
$467$	−108.181	+	108.181i	−0.231651	+	0.231651i	−0.813382	−	0.581730i	$-0.802376\pi$
$467$	−108.181	+	108.181i	−0.231651	+	0.231651i	0.581730	+	0.813382i	$0.302376\pi$
$468$		0			0
$469$			106.078i			0.226178i
$470$	8.90899	+	127.008i	0.0189553	+	0.270230i
$471$		0			0
$472$	−141.497	+	141.497i	−0.299781	+	0.299781i
$473$	115.301	+	115.301i	0.243764	+	0.243764i
$474$		0			0
$475$	76.6533	+	543.703i	0.161375	+	1.14464i
$476$	−799.049			−1.67868
$477$		0			0
$478$	126.167	+	126.167i	0.263947	+	0.263947i
$479$		−	44.0316i		−	0.0919239i	−0.998943	−	0.0459620i	$-0.985365\pi$
$479$		−	44.0316i		−	0.0919239i	0.998943	−	0.0459620i	$-0.0146353\pi$
$480$		0			0
$481$	316.483			0.657969
$482$	−7.40633	+	7.40633i	−0.0153658	+	0.0153658i
$483$		0			0
$484$		−	242.965i		−	0.501994i
$485$	−32.2813	+	37.1516i	−0.0665593	+	0.0766013i
$486$		0			0
$487$	−491.002	+	491.002i	−1.00822	+	1.00822i	−0.00825217	+	0.999966i	$0.502627\pi$
$487$	−491.002	+	491.002i	−1.00822	+	1.00822i	−0.999966	+	0.00825217i	$0.997373\pi$
$488$	233.526	+	233.526i	0.478538	+	0.478538i
$489$		0			0
$490$	169.394	+	147.187i	0.345702	+	0.300382i
$491$	120.685			0.245795			0.122897	−	0.992419i	$-0.460781\pi$
$491$	120.685			0.245795			0.122897	+	0.992419i	$0.460781\pi$
$492$		0			0
$493$	702.813	+	702.813i	1.42558	+	1.42558i
$494$			135.660i			0.274616i
$495$		0			0
$496$	−160.028			−0.322636
$497$	446.002	−	446.002i	0.897388	−	0.897388i
$498$		0			0
$499$			37.0345i			0.0742174i	0.999311	+	0.0371087i	$0.0118148\pi$
$499$			37.0345i			0.0742174i	−0.999311	+	0.0371087i	$0.988185\pi$
$500$	−85.4410	−	400.685i	−0.170882	−	0.801370i
$501$		0			0
$502$	238.494	−	238.494i	0.475087	−	0.475087i
$503$	105.860	+	105.860i	0.210458	+	0.210458i	0.804462	−	0.594004i	$-0.202454\pi$
$503$	105.860	+	105.860i	0.210458	+	0.210458i	−0.594004	+	0.804462i	$0.702454\pi$
$504$		0			0
$505$	−526.623	+	36.9399i	−1.04282	+	0.0731484i
$506$	25.2052			0.0498127
$507$		0			0
$508$	−157.663	−	157.663i	−0.310360	−	0.310360i
$509$		−	55.5038i		−	0.109045i	−0.998513	−	0.0545224i	$-0.982636\pi$
$509$		−	55.5038i		−	0.109045i	0.998513	−	0.0545224i	$-0.0173636\pi$
$510$		0			0
$511$	−234.064			−0.458051
$512$	311.832	−	311.832i	0.609046	−	0.609046i
$513$		0			0
$514$			160.628i			0.312506i
$515$	−639.209	−	555.412i	−1.24118	−	1.07847i
$516$		0			0
$517$	−145.029	+	145.029i	−0.280520	+	0.280520i
$518$	264.101	+	264.101i	0.509848	+	0.509848i
$519$		0			0
$520$	−15.7269	−	224.205i	−0.0302440	−	0.431164i
$521$	−297.883			−0.571753			−0.285876	−	0.958266i	$-0.592285\pi$
$521$	−297.883			−0.571753			−0.285876	+	0.958266i	$0.592285\pi$
$522$		0			0
$523$	−172.407	−	172.407i	−0.329650	−	0.329650i	0.522803	−	0.852453i	$-0.324886\pi$
$523$	−172.407	−	172.407i	−0.329650	−	0.329650i	−0.852453	+	0.522803i	$0.824886\pi$
$524$			585.205i			1.11680i
$525$		0			0
$526$	−222.530			−0.423061
$527$	348.191	−	348.191i	0.660704	−	0.660704i
$528$		0			0
$529$		−	510.238i		−	0.964533i
$530$	−288.598	+	20.2437i	−0.544525	+	0.0381957i
$531$		0			0
$532$	513.583	−	513.583i	0.965381	−	0.965381i
$533$	−409.917	−	409.917i	−0.769074	−	0.769074i
$534$		0			0
$535$	309.918	−	356.676i	0.579285	−	0.666684i
$536$	65.0329			0.121330
$537$		0			0
$538$	174.143	+	174.143i	0.323686	+	0.323686i
$539$			361.499i			0.670685i
$540$		0			0
$541$	659.182			1.21845			0.609225	−	0.792997i	$-0.291481\pi$
$541$	659.182			1.21845			0.609225	+	0.792997i	$0.291481\pi$
$542$	152.385	−	152.385i	0.281153	−	0.281153i
$543$		0			0
$544$			759.124i			1.39545i
$545$	16.8716	+	240.525i	0.0309571	+	0.441331i
$546$		0			0
$547$	521.656	−	521.656i	0.953667	−	0.953667i	−0.0453063	−	0.998973i	$-0.514426\pi$
$547$	521.656	−	521.656i	0.953667	−	0.953667i	0.998973	+	0.0453063i	$0.0144264\pi$
$548$	187.316	+	187.316i	0.341818	+	0.341818i
$549$		0			0
$550$	−87.4994	+	116.221i	−0.159090	+	0.211310i
$551$	−903.455			−1.63966
$552$		0			0
$553$	−1012.18	−	1012.18i	−1.83034	−	1.83034i
$554$		−	70.6951i		−	0.127608i
$555$		0			0
$556$	554.233			0.996822
$557$	−612.302	+	612.302i	−1.09929	+	1.09929i	−0.104792	+	0.994494i	$0.533418\pi$
$557$	−612.302	+	612.302i	−1.09929	+	1.09929i	−0.994494	+	0.104792i	$0.966582\pi$
$558$		0			0
$559$		−	173.082i		−	0.309627i
$560$	−259.832	+	299.033i	−0.463985	+	0.533988i
$561$		0			0
$562$	257.518	−	257.518i	0.458216	−	0.458216i
$563$	589.642	+	589.642i	1.04732	+	1.04732i	0.998823	+	0.0484975i	$0.0154433\pi$
$563$	589.642	+	589.642i	1.04732	+	1.04732i	0.0484975	+	0.998823i	$0.484557\pi$
$564$		0			0
$565$	191.009	+	165.969i	0.338069	+	0.293750i
$566$	384.875			0.679990
$567$		0			0
$568$	−273.430	−	273.430i	−0.481391	−	0.481391i
$569$		−	224.057i		−	0.393773i	−0.980426	−	0.196886i	$-0.936917\pi$
$569$		−	224.057i		−	0.393773i	0.980426	−	0.196886i	$-0.0630830\pi$
$570$		0			0
$571$	−513.775			−0.899781			−0.449891	−	0.893084i	$-0.648537\pi$
$571$	−513.775			−0.899781			−0.449891	+	0.893084i	$0.648537\pi$
$572$	115.301	−	115.301i	0.201574	−	0.201574i
$573$		0			0
$574$		−	684.141i		−	1.19188i
$575$	−86.5106	−	65.1316i	−0.150453	−	0.113272i
$576$		0			0
$577$	−264.261	+	264.261i	−0.457991	+	0.457991i	−0.897996	−	0.440004i	$-0.854977\pi$
$577$	−264.261	+	264.261i	−0.457991	+	0.457991i	0.440004	+	0.897996i	$0.354977\pi$
$578$	−177.201	−	177.201i	−0.306576	−	0.306576i
$579$		0			0
$580$	672.456	−	47.1694i	1.15941	−	0.0813265i
$581$	−267.992			−0.461260
$582$		0			0
$583$	−329.546	−	329.546i	−0.565259	−	0.565259i
$584$			143.498i			0.245715i
$585$		0			0
$586$	−8.86036			−0.0151201
$587$	147.347	−	147.347i	0.251016	−	0.251016i	−0.570371	−	0.821387i	$-0.693201\pi$
$587$	147.347	−	147.347i	0.251016	−	0.251016i	0.821387	+	0.570371i	$0.193201\pi$
$588$		0			0
$589$			447.594i			0.759922i
$590$	−103.779	−	90.1739i	−0.175896	−	0.152837i
$591$		0			0
$592$	−241.819	+	241.819i	−0.408479	+	0.408479i
$593$	120.017	+	120.017i	0.202389	+	0.202389i	0.801023	−	0.598634i	$-0.204289\pi$
$593$	120.017	+	120.017i	0.202389	+	0.202389i	−0.598634	+	0.801023i	$0.704289\pi$
$594$		0			0
$595$	−85.2954	−	1215.99i	−0.143354	−	2.04368i
$596$	828.427			1.38998
$597$		0			0
$598$	−18.9182	−	18.9182i	−0.0316358	−	0.0316358i
$599$			603.402i			1.00735i	0.863894	+	0.503674i	$0.168019\pi$
$599$			603.402i			1.00735i	−0.863894	+	0.503674i	$0.831981\pi$
$600$		0			0
$601$	−891.282			−1.48300			−0.741499	−	0.670954i	$-0.765885\pi$
$601$	−891.282			−1.48300			−0.741499	+	0.670954i	$0.765885\pi$
$602$	144.435	−	144.435i	0.239924	−	0.239924i
$603$		0			0
$604$		−	311.854i		−	0.516314i
$605$	369.742	−	25.9356i	0.611144	−	0.0428687i
$606$		0			0
$607$	272.546	−	272.546i	0.449004	−	0.449004i	−0.446019	−	0.895023i	$-0.647159\pi$
$607$	272.546	−	272.546i	0.449004	−	0.449004i	0.895023	+	0.446019i	$0.147159\pi$
$608$	−487.921	−	487.921i	−0.802502	−	0.802502i
$609$		0			0
$610$	−148.823	+	171.276i	−0.243972	+	0.280781i
$611$	217.707			0.356313
$612$		0			0
$613$	280.729	+	280.729i	0.457960	+	0.457960i	0.897985	−	0.440025i	$-0.145031\pi$
$613$	280.729	+	280.729i	0.457960	+	0.457960i	−0.440025	+	0.897985i	$0.645031\pi$
$614$			90.4853i			0.147370i
$615$		0			0
$616$	427.285			0.693645
$617$	−323.273	+	323.273i	−0.523943	+	0.523943i	−0.918760	−	0.394817i	$-0.870808\pi$
$617$	−323.273	+	323.273i	−0.523943	+	0.523943i	0.394817	+	0.918760i	$0.370808\pi$
$618$		0			0
$619$		−	229.642i		−	0.370989i	−0.982645	−	0.185494i	$-0.940611\pi$
$619$		−	229.642i		−	0.370989i	0.982645	−	0.185494i	$-0.0593887\pi$
$620$	−23.3689	−	333.151i	−0.0376917	−	0.537340i
$621$		0			0
$622$	−184.673	+	184.673i	−0.296901	+	0.296901i
$623$	−347.705	−	347.705i	−0.558114	−	0.558114i
$624$		0			0
$625$	600.639	−	172.795i	0.961022	−	0.276472i
$626$	−181.329			−0.289663
$627$		0			0
$628$	663.877	+	663.877i	1.05713	+	1.05713i
$629$		−	1052.31i		−	1.67299i
$630$		0			0
$631$	69.8714			0.110731			0.0553656	−	0.998466i	$-0.482368\pi$
$631$	69.8714			0.110731			0.0553656	+	0.998466i	$0.482368\pi$
$632$	−620.537	+	620.537i	−0.981862	+	0.981862i
$633$		0			0
$634$		−	97.0379i		−	0.153057i
$635$	223.101	−	256.760i	0.351340	−	0.404347i
$636$		0			0
$637$	271.329	−	271.329i	0.425949	−	0.425949i
$638$	−169.258	−	169.258i	−0.265294	−	0.265294i
$639$		0			0
$640$	489.405	+	425.247i	0.764696	+	0.664448i
$641$	1087.22			1.69613			0.848065	−	0.529892i	$-0.177768\pi$
$641$	1087.22			1.69613			0.848065	+	0.529892i	$0.177768\pi$
$642$		0			0
$643$	−554.713	−	554.713i	−0.862695	−	0.862695i	0.128955	−	0.991650i	$-0.458838\pi$
$643$	−554.713	−	554.713i	−0.862695	−	0.862695i	−0.991650	+	0.128955i	$0.958838\pi$
$644$			143.241i			0.222424i
$645$		0			0
$646$	451.072			0.698253
$647$	646.211	−	646.211i	0.998780	−	0.998780i	−0.00121929	−	0.999999i	$-0.500388\pi$
$647$	646.211	−	646.211i	0.998780	−	0.998780i	0.999999	+	0.00121929i	$0.000388112\pi$
$648$		0			0
$649$		−	221.471i		−	0.341250i
$650$	152.905	−	21.5572i	0.235239	−	0.0331649i
$651$		0			0
$652$	113.109	−	113.109i	0.173481	−	0.173481i
$653$	−725.130	−	725.130i	−1.11046	−	1.11046i	−0.993088	−	0.117371i	$-0.962553\pi$
$653$	−725.130	−	725.130i	−1.11046	−	1.11046i	−0.117371	−	0.993088i	$-0.537447\pi$
$654$		0			0
$655$	−890.560	+	62.4683i	−1.35963	+	0.0953715i
$656$	626.421			0.954910
$657$		0			0
$658$	181.674	+	181.674i	0.276101	+	0.276101i
$659$			393.373i			0.596924i	0.954421	+	0.298462i	$0.0964737\pi$
$659$			393.373i			0.596924i	−0.954421	+	0.298462i	$0.903526\pi$
$660$		0			0
$661$	1035.22			1.56614			0.783070	−	0.621934i	$-0.213653\pi$
$661$	1035.22			1.56614			0.783070	+	0.621934i	$0.213653\pi$
$662$	186.620	−	186.620i	0.281903	−	0.281903i
$663$		0			0
$664$			164.298i			0.247436i
$665$	836.389	+	726.743i	1.25773	+	1.09285i
$666$		0			0
$667$	125.990	−	125.990i	0.188890	−	0.188890i
$668$	120.920	+	120.920i	0.181017	+	0.181017i
$669$		0			0
$670$	3.12643	+	44.5710i	0.00466632	+	0.0665239i
$671$	−365.517			−0.544734
$672$		0			0
$673$	−463.125	−	463.125i	−0.688151	−	0.688151i	0.273672	−	0.961823i	$-0.411762\pi$
$673$	−463.125	−	463.125i	−0.688151	−	0.688151i	−0.961823	+	0.273672i	$0.911762\pi$
$674$		−	208.819i		−	0.309820i
$675$		0			0
$676$	380.823			0.563348
$677$	−103.341	+	103.341i	−0.152645	+	0.152645i	−0.779298	−	0.626653i	$-0.784424\pi$
$677$	−103.341	+	103.341i	−0.152645	+	0.152645i	0.626653	+	0.779298i	$0.284424\pi$
$678$		0			0
$679$			99.3177i			0.146271i
$680$	−745.485	+	52.2920i	−1.09630	+	0.0769000i
$681$		0			0
$682$	−83.8543	+	83.8543i	−0.122954	+	0.122954i
$683$	68.3094	+	68.3094i	0.100014	+	0.100014i	0.755343	−	0.655329i	$-0.227470\pi$
$683$	68.3094	+	68.3094i	0.100014	+	0.100014i	−0.655329	+	0.755343i	$0.727470\pi$
$684$		0			0
$685$	−265.061	+	305.052i	−0.386951	+	0.445332i
$686$	32.6165			0.0475459
$687$		0			0
$688$	132.249	+	132.249i	0.192222	+	0.192222i
$689$			494.693i			0.717986i
$690$		0			0
$691$	−608.394			−0.880454			−0.440227	−	0.897887i	$-0.645102\pi$
$691$	−608.394			−0.880454			−0.440227	+	0.897887i	$0.645102\pi$
$692$	−251.564	+	251.564i	−0.363532	+	0.363532i
$693$		0			0
$694$		−	130.405i		−	0.187903i
$695$	59.1623	+	843.428i	0.0851256	+	1.21357i
$696$		0			0
$697$	−1362.98	+	1362.98i	−1.95549	+	1.95549i
$698$	−0.0578096	−	0.0578096i	−8.28218e−5	−	8.28218e-5i
$699$		0			0
$700$	−660.481	−	497.258i	−0.943544	−	0.710369i
$701$	147.038			0.209755			0.104877	−	0.994485i	$-0.466555\pi$
$701$	147.038			0.209755			0.104877	+	0.994485i	$0.466555\pi$
$702$		0			0
$703$	676.364	+	676.364i	0.962110	+	0.962110i
$704$			32.2184i			0.0457648i
$705$		0			0
$706$	−230.178			−0.326031
$707$	−753.288	+	753.288i	−1.06547	+	1.06547i
$708$		0			0
$709$			1093.46i			1.54225i	0.636682	+	0.771127i	$0.280307\pi$
$709$			1093.46i			1.54225i	−0.636682	+	0.771127i	$0.719693\pi$
$710$	174.253	−	200.543i	0.245427	−	0.282455i
$711$		0			0
$712$	−213.167	+	213.167i	−0.299392	+	0.299392i
$713$	−62.4183	−	62.4183i	−0.0875432	−	0.0875432i
$714$		0			0
$715$	187.772	+	163.156i	0.262618	+	0.228190i
$716$	−1.54803			−0.00216205
$717$		0			0
$718$	88.5413	+	88.5413i	0.123317	+	0.123317i
$719$		−	1213.55i		−	1.68783i	−0.536476	−	0.843916i	$-0.680245\pi$
$719$		−	1213.55i		−	1.68783i	0.536476	−	0.843916i	$-0.319755\pi$
$720$		0			0
$721$	−1708.80			−2.37004
$722$	−72.9536	+	72.9536i	−0.101044	+	0.101044i
$723$		0			0
$724$			232.972i			0.321785i
$725$	143.564	+	1018.30i	0.198019	+	1.40456i
$726$		0			0
$727$	508.711	−	508.711i	0.699740	−	0.699740i	−0.264615	−	0.964354i	$-0.585245\pi$
$727$	508.711	−	508.711i	0.699740	−	0.699740i	0.964354	+	0.264615i	$0.0852447\pi$
$728$	−320.706	−	320.706i	−0.440530	−	0.440530i
$729$		0			0
$730$	−98.3477	+	6.89860i	−0.134723	+	0.00945013i
$731$	−575.498			−0.787275
$732$		0			0
$733$	−173.434	−	173.434i	−0.236608	−	0.236608i	0.578836	−	0.815444i	$-0.303507\pi$
$733$	−173.434	−	173.434i	−0.236608	−	0.236608i	−0.815444	+	0.578836i	$0.803507\pi$
$734$		−	577.476i		−	0.786752i
$735$		0			0
$736$	136.084			0.184897
$737$	−50.8949	+	50.8949i	−0.0690569	+	0.0690569i
$738$		0			0
$739$		−	346.404i		−	0.468747i	−0.972147	−	0.234374i	$-0.924696\pi$
$739$		−	346.404i		−	0.468747i	0.972147	−	0.234374i	$-0.0753039\pi$
$740$	−538.741	−	468.115i	−0.728028	−	0.632588i
$741$		0			0
$742$	−412.815	+	412.815i	−0.556354	+	0.556354i
$743$	537.923	+	537.923i	0.723987	+	0.723987i	0.969415	−	0.245428i	$-0.0789284\pi$
$743$	537.923	+	537.923i	0.723987	+	0.723987i	−0.245428	+	0.969415i	$0.578928\pi$
$744$		0			0
$745$	88.4314	+	1260.69i	0.118700	+	1.69221i
$746$	466.203			0.624937
$747$		0			0
$748$	−383.376	−	383.376i	−0.512534	−	0.512534i
$749$		−	953.504i		−	1.27304i
$750$		0			0
$751$	806.139			1.07342			0.536710	−	0.843767i	$-0.319667\pi$
$751$	806.139			1.07342			0.536710	+	0.843767i	$0.319667\pi$
$752$	−166.347	+	166.347i	−0.221206	+	0.221206i
$753$		0			0
$754$			254.078i			0.336974i
$755$	474.577	−	33.2892i	0.628579	−	0.0440916i
$756$		0			0
$757$	−588.844	+	588.844i	−0.777866	+	0.777866i	−0.979468	−	0.201602i	$-0.935385\pi$
$757$	−588.844	+	588.844i	−0.777866	+	0.777866i	0.201602	+	0.979468i	$0.435385\pi$
$758$	−184.134	−	184.134i	−0.242921	−	0.242921i
$759$		0			0
$760$	445.544	−	512.764i	0.586242	−	0.674690i
$761$	317.363			0.417035			0.208517	−	0.978019i	$-0.433136\pi$
$761$	317.363			0.417035			0.208517	+	0.978019i	$0.433136\pi$
$762$		0			0
$763$	344.051	+	344.051i	0.450918	+	0.450918i
$764$			124.380i			0.162801i
$765$		0			0
$766$	380.034			0.496128
$767$	−166.229	+	166.229i	−0.216726	+	0.216726i
$768$		0			0
$769$			1060.67i			1.37929i	0.724149	+	0.689644i	$0.242233\pi$
$769$			1060.67i			1.37929i	−0.724149	+	0.689644i	$0.757767\pi$
$770$	20.5416	+	292.845i	0.0266774	+	0.380318i
$771$		0			0
$772$	236.940	−	236.940i	0.306917	−	0.306917i
$773$	273.893	+	273.893i	0.354325	+	0.354325i	0.861716	−	0.507391i	$-0.169390\pi$
$773$	273.893	+	273.893i	0.354325	+	0.354325i	−0.507391	+	0.861716i	$0.669390\pi$
$774$		0			0
$775$	504.492	−	71.1252i	0.650958	−	0.0917744i
$776$	60.8886			0.0784647
$777$		0			0
$778$	−12.4181	−	12.4181i	−0.0159615	−	0.0159615i
$779$		−	1752.09i		−	2.24915i
$780$		0			0
$781$	427.974			0.547983
$782$	−62.9033	+	62.9033i	−0.0804390	+	0.0804390i
$783$		0			0
$784$			414.636i			0.528873i
$785$	−939.417	+	1081.15i	−1.19671	+	1.37726i
$786$		0			0
$787$	539.840	−	539.840i	0.685947	−	0.685947i	−0.275386	−	0.961334i	$-0.588806\pi$
$787$	539.840	−	539.840i	0.685947	−	0.685947i	0.961334	+	0.275386i	$0.0888058\pi$
$788$	9.69882	+	9.69882i	0.0123082	+	0.0123082i
$789$		0			0
$790$	−455.124	−	395.459i	−0.576106	−	0.500582i
$791$	510.626			0.645545
$792$		0			0
$793$	274.345	+	274.345i	0.345958	+	0.345958i
$794$		−	174.040i		−	0.219193i
$795$		0			0
$796$	−822.431			−1.03320
$797$	−807.143	+	807.143i	−1.01273	+	1.01273i	−0.0128090	+	0.999918i	$0.504077\pi$
$797$	−807.143	+	807.143i	−1.01273	+	1.01273i	−0.999918	+	0.0128090i	$0.995923\pi$
$798$		0			0
$799$		−	723.880i		−	0.905982i
$800$	−472.412	+	627.479i	−0.590516	+	0.784349i
$801$		0			0
$802$	306.120	−	306.120i	0.381696	−	0.381696i
$803$	−112.302	−	112.302i	−0.139853	−	0.139853i
$804$		0			0
$805$	−217.984	+	15.2905i	−0.270787	+	0.0189944i
$806$	125.877			0.156174
$807$		0			0
$808$	461.818	+	461.818i	0.571557	+	0.571557i
$809$		−	483.669i		−	0.597861i	−0.954275	−	0.298930i	$-0.903370\pi$
$809$		−	483.669i		−	0.597861i	0.954275	−	0.298930i	$-0.0966298\pi$
$810$		0			0
$811$	−303.549			−0.374289			−0.187145	−	0.982332i	$-0.559923\pi$
$811$	−303.549			−0.374289			−0.187145	+	0.982332i	$0.559923\pi$
$812$	961.890	−	961.890i	1.18459	−	1.18459i
$813$		0			0
$814$			253.426i			0.311334i
$815$	184.203	+	160.055i	0.226016	+	0.196386i
$816$		0			0
$817$	369.897	−	369.897i	0.452750	−	0.452750i
$818$	268.139	+	268.139i	0.327799	+	0.327799i
$819$		0			0
$820$	91.4764	+	1304.10i	0.111557	+	1.59037i
$821$	694.915			0.846425			0.423213	−	0.906030i	$-0.360902\pi$
$821$	694.915			0.846425			0.423213	+	0.906030i	$0.360902\pi$
$822$		0			0
$823$	216.871	+	216.871i	0.263513	+	0.263513i	0.826480	−	0.562967i	$-0.190340\pi$
$823$	216.871	+	216.871i	0.263513	+	0.263513i	−0.562967	+	0.826480i	$0.690340\pi$
$824$			1047.61i			1.27138i
$825$		0			0
$826$	−277.432			−0.335875
$827$	418.921	−	418.921i	0.506555	−	0.506555i	−0.406912	−	0.913467i	$-0.633395\pi$
$827$	418.921	−	418.921i	0.506555	−	0.506555i	0.913467	+	0.406912i	$0.133395\pi$
$828$		0			0
$829$		−	282.787i		−	0.341119i	−0.985347	−	0.170559i	$-0.945443\pi$
$829$		−	282.787i		−	0.341119i	0.985347	−	0.170559i	$-0.0545574\pi$
$830$	−112.603	+	7.89856i	−0.135667	+	0.00951633i
$831$		0			0
$832$	24.1821	−	24.1821i	0.0290650	−	0.0290650i
$833$	−902.172	−	902.172i	−1.08304	−	1.08304i
$834$		0			0
$835$	−171.107	+	196.922i	−0.204918	+	0.235835i
$836$	492.823			0.589502
$837$		0			0
$838$	−32.3245	−	32.3245i	−0.0385734	−	0.0385734i
$839$			537.577i			0.640735i	0.947293	+	0.320368i	$0.103806\pi$
$839$			537.577i			0.640735i	−0.947293	+	0.320368i	$0.896194\pi$
$840$		0			0
$841$	−851.083			−1.01199
$842$	−300.257	+	300.257i	−0.356600	+	0.356600i
$843$		0			0
$844$		−	794.094i		−	0.940869i
$845$	40.6514	+	579.534i	0.0481082	+	0.685840i
$846$		0			0
$847$	528.884	−	528.884i	0.624421	−	0.624421i
$848$	−377.986	−	377.986i	−0.445739	−	0.445739i
$849$		0			0
$850$	−71.6778	−	508.412i	−0.0843268	−	0.598132i
$851$	−188.642			−0.221671
$852$		0			0
$853$	311.281	+	311.281i	0.364925	+	0.364925i	0.865623	−	0.500697i	$-0.166923\pi$
$853$	311.281	+	311.281i	0.364925	+	0.364925i	−0.500697	+	0.865623i	$0.666923\pi$
$854$			457.875i			0.536153i
$855$		0			0
$856$	−584.564			−0.682902
$857$	−395.094	+	395.094i	−0.461020	+	0.461020i	−0.898990	−	0.437970i	$-0.855698\pi$
$857$	−395.094	+	395.094i	−0.461020	+	0.461020i	0.437970	+	0.898990i	$0.355698\pi$
$858$		0			0
$859$		−	1392.98i		−	1.62163i	−0.585301	−	0.810816i	$-0.699024\pi$
$859$		−	1392.98i		−	1.62163i	0.585301	−	0.810816i	$-0.300976\pi$
$860$	−256.008	+	294.632i	−0.297683	+	0.342596i
$861$		0			0
$862$	−371.817	+	371.817i	−0.431343	+	0.431343i
$863$	−489.876	−	489.876i	−0.567643	−	0.567643i	0.363824	−	0.931468i	$-0.381471\pi$
$863$	−489.876	−	489.876i	−0.567643	−	0.567643i	−0.931468	+	0.363824i	$0.881471\pi$
$864$		0			0
$865$	−409.682	−	355.975i	−0.473620	−	0.411531i
$866$	205.471			0.237264
$867$		0			0
$868$	−476.544	−	476.544i	−0.549013	−	0.549013i
$869$		−	971.267i		−	1.11768i
$870$		0			0
$871$	76.4001			0.0877154
$872$	210.927	−	210.927i	0.241889	−	0.241889i
$873$		0			0
$874$		−	80.8612i		−	0.0925185i
$875$	686.220	−	1058.20i	0.784252	−	1.20937i
$876$		0			0
$877$	−77.0982	+	77.0982i	−0.0879112	+	0.0879112i	−0.749695	−	0.661784i	$-0.769800\pi$
$877$	−77.0982	+	77.0982i	−0.0879112	+	0.0879112i	0.661784	+	0.749695i	$0.269800\pi$
$878$	−8.88833	−	8.88833i	−0.0101234	−	0.0101234i
$879$		0			0
$880$	−268.138	+	18.8085i	−0.304702	+	0.0213733i
$881$	76.9529			0.0873473			0.0436736	−	0.999046i	$-0.486094\pi$
$881$	76.9529			0.0873473			0.0436736	+	0.999046i	$0.486094\pi$
$882$		0			0
$883$	−583.159	−	583.159i	−0.660430	−	0.660430i	0.295052	−	0.955481i	$-0.404663\pi$
$883$	−583.159	−	583.159i	−0.660430	−	0.660430i	−0.955481	+	0.295052i	$0.904663\pi$
$884$			575.498i			0.651016i
$885$		0			0
$886$	703.102			0.793569
$887$	488.552	−	488.552i	0.550792	−	0.550792i	−0.375878	−	0.926669i	$-0.622659\pi$
$887$	488.552	−	488.552i	0.550792	−	0.550792i	0.926669	+	0.375878i	$0.122659\pi$
$888$		0			0
$889$		−	686.400i		−	0.772103i
$890$	−156.344	−	135.848i	−0.175668	−	0.152639i
$891$		0			0
$892$	568.753	−	568.753i	0.637616	−	0.637616i
$893$	465.268	+	465.268i	0.521016	+	0.521016i
$894$		0			0
$895$	−0.165246	−	2.35578i	−0.000184633	−	0.00263216i
$896$	1308.33			1.46019
$897$		0			0
$898$	136.547	+	136.547i	0.152057	+	0.152057i
$899$			838.299i			0.932480i
$900$		0			0
$901$	1644.86			1.82559
$902$	328.244	−	328.244i	0.363907	−	0.363907i
$903$		0			0
$904$		−	313.049i		−	0.346294i
$905$	−354.536	+	24.8689i	−0.391752	+	0.0274795i
$906$		0			0
$907$	292.322	−	292.322i	0.322295	−	0.322295i	−0.527352	−	0.849647i	$-0.676815\pi$
$907$	292.322	−	292.322i	0.322295	−	0.322295i	0.849647	+	0.527352i	$0.176815\pi$
$908$	−364.622	−	364.622i	−0.401566	−	0.401566i
$909$		0			0
$910$	204.382	−	235.217i	0.224595	−	0.258480i
$911$	406.514			0.446229			0.223114	−	0.974792i	$-0.428378\pi$
$911$	406.514			0.446229			0.223114	+	0.974792i	$0.428378\pi$
$912$		0			0
$913$	−128.580	−	128.580i	−0.140832	−	0.140832i
$914$			281.569i			0.308063i
$915$		0			0
$916$	−33.7900			−0.0368886
$917$	−1273.87	+	1273.87i	−1.38917	+	1.38917i
$918$		0			0
$919$			250.621i			0.272710i	0.990660	+	0.136355i	$0.0435388\pi$
$919$			250.621i			0.272710i	−0.990660	+	0.136355i	$0.956461\pi$
$920$	9.37411	+	133.639i	0.0101892	+	0.145260i
$921$		0			0
$922$	83.0247	−	83.0247i	0.0900484	−	0.0900484i
$923$	−321.223	−	321.223i	−0.348021	−	0.348021i
$924$		0			0
$925$	654.865	−	869.821i	0.707963	−	0.940347i
$926$	−267.304			−0.288666
$927$		0			0
$928$	−913.828	−	913.828i	−0.984728	−	0.984728i
$929$		−	1099.09i		−	1.18309i	−0.806274	−	0.591543i	$-0.798519\pi$
$929$		−	1099.09i		−	1.18309i	0.806274	−	0.591543i	$-0.201481\pi$
$930$		0			0
$931$	1159.73			1.24568
$932$	734.789	−	734.789i	0.788400	−	0.788400i
$933$		0			0
$934$			130.039i			0.139228i
$935$	542.495	−	624.342i	0.580208	−	0.667746i
$936$		0			0
$937$	999.231	−	999.231i	1.06642	−	1.06642i	0.0687838	−	0.997632i	$-0.478088\pi$
$937$	999.231	−	999.231i	1.06642	−	1.06642i	0.997632	−	0.0687838i	$-0.0219119\pi$
$938$	63.7549	+	63.7549i	0.0679690	+	0.0679690i
$939$		0			0
$940$	−370.598	−	322.014i	−0.394253	−	0.342568i
$941$	1082.29			1.15015			0.575074	−	0.818101i	$-0.304973\pi$
$941$	1082.29			1.15015			0.575074	+	0.818101i	$0.304973\pi$
$942$		0			0
$943$	244.334	+	244.334i	0.259102	+	0.259102i
$944$		−	254.026i		−	0.269095i
$945$		0			0
$946$	138.596			0.146508
$947$	−888.185	+	888.185i	−0.937893	+	0.937893i	−0.998181	−	0.0602880i	$-0.980798\pi$
$947$	−888.185	+	888.185i	−0.937893	+	0.937893i	0.0602880	+	0.998181i	$0.480798\pi$
$948$		0			0
$949$			168.580i			0.177639i
$950$	372.848	+	280.707i	0.392472	+	0.295481i
$951$		0			0
$952$	−1066.35	+	1066.35i	−1.12012	+	1.12012i
$953$	−819.972	−	819.972i	−0.860411	−	0.860411i	0.130974	−	0.991386i	$-0.458189\pi$
$953$	−819.972	−	819.972i	−0.860411	−	0.860411i	−0.991386	+	0.130974i	$0.958189\pi$
$954$		0			0
$955$	−189.281	+	13.2771i	−0.198200	+	0.0139027i
$956$	−688.023			−0.719689
$957$		0			0
$958$	−26.4639	−	26.4639i	−0.0276242	−	0.0276242i
$959$			815.498i			0.850363i
$960$		0			0
$961$	−545.686			−0.567832
$962$	190.213	−	190.213i	0.197727	−	0.197727i
$963$		0			0
$964$		−	40.3888i		−	0.0418971i
$965$	385.866	+	335.281i	0.399861	+	0.347442i
$966$		0			0
$967$	−628.270	+	628.270i	−0.649711	+	0.649711i	−0.952923	−	0.303212i	$-0.901941\pi$
$967$	−628.270	+	628.270i	−0.649711	+	0.649711i	0.303212	+	0.952923i	$0.401941\pi$
$968$	−324.243	−	324.243i	−0.334961	−	0.334961i
$969$		0			0
$970$	2.92720	+	41.7307i	0.00301773	+	0.0430213i
$971$	−1286.55			−1.32497			−0.662486	−	0.749074i	$-0.730499\pi$
$971$	−1286.55			−1.32497			−0.662486	+	0.749074i	$0.730499\pi$
$972$		0			0
$973$	1206.45	+	1206.45i	1.23993	+	1.23993i
$974$			590.206i			0.605961i
$975$		0			0
$976$	−419.245			−0.429554
$977$	1038.76	−	1038.76i	1.06321	−	1.06321i	0.0653473	−	0.997863i	$-0.479184\pi$
$977$	1038.76	−	1038.76i	1.06321	−	1.06321i	0.997863	−	0.0653473i	$-0.0208155\pi$
$978$		0			0
$979$		−	333.650i		−	0.340807i
$980$	−863.204	+	60.5494i	−0.880820	+	0.0617851i
$981$		0			0
$982$	72.5345	−	72.5345i	0.0738640	−	0.0738640i
$983$	−335.407	−	335.407i	−0.341207	−	0.341207i	0.515614	−	0.856821i	$-0.327564\pi$
$983$	−335.407	−	335.407i	−0.341207	−	0.341207i	−0.856821	+	0.515614i	$0.827564\pi$
$984$		0			0
$985$	−13.7243	+	15.7949i	−0.0139333	+	0.0160354i
$986$	844.813			0.856808
$987$		0			0
$988$	−369.897	−	369.897i	−0.374390	−	0.374390i
$989$			103.166i			0.104314i
$990$		0			0
$991$	−361.054			−0.364333			−0.182167	−	0.983268i	$-0.558311\pi$
$991$	−361.054			−0.364333			−0.182167	+	0.983268i	$0.558311\pi$
$992$	−452.733	+	452.733i	−0.456384	+	0.456384i
$993$		0			0
$994$		−	536.114i		−	0.539350i
$995$	−87.7913	−	1251.57i	−0.0882325	−	1.25786i
$996$		0			0
$997$	535.002	−	535.002i	0.536612	−	0.536612i	−0.385920	−	0.922532i	$-0.626116\pi$
$997$	535.002	−	535.002i	0.536612	−	0.536612i	0.922532	+	0.385920i	$0.126116\pi$
$998$	22.2585	+	22.2585i	0.0223032	+	0.0223032i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.3.g.a.28.5	yes	16
3.2	odd	2	inner	135.3.g.a.28.4	✓	16
5.2	odd	4	inner	135.3.g.a.82.5	yes	16
5.3	odd	4		675.3.g.k.82.4		16
5.4	even	2		675.3.g.k.568.4		16
9.2	odd	6		405.3.l.o.28.5		32
9.4	even	3		405.3.l.o.298.5		32
9.5	odd	6		405.3.l.o.298.4		32
9.7	even	3		405.3.l.o.28.4		32
15.2	even	4	inner	135.3.g.a.82.4	yes	16
15.8	even	4		675.3.g.k.82.5		16
15.14	odd	2		675.3.g.k.568.5		16
45.2	even	12		405.3.l.o.352.4		32
45.7	odd	12		405.3.l.o.352.5		32
45.22	odd	12		405.3.l.o.217.4		32
45.32	even	12		405.3.l.o.217.5		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.3.g.a.28.4	✓	16	3.2	odd	2	inner
135.3.g.a.28.5	yes	16	1.1	even	1	trivial
135.3.g.a.82.4	yes	16	15.2	even	4	inner
135.3.g.a.82.5	yes	16	5.2	odd	4	inner
405.3.l.o.28.4		32	9.7	even	3
405.3.l.o.28.5		32	9.2	odd	6
405.3.l.o.217.4		32	45.22	odd	12
405.3.l.o.217.5		32	45.32	even	12
405.3.l.o.298.4		32	9.5	odd	6
405.3.l.o.298.5		32	9.4	even	3
405.3.l.o.352.4		32	45.2	even	12
405.3.l.o.352.5		32	45.7	odd	12
675.3.g.k.82.4		16	5.3	odd	4
675.3.g.k.82.5		16	15.8	even	4
675.3.g.k.568.4		16	5.4	even	2
675.3.g.k.568.5		16	15.14	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	135.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.601022 - 0.601022i) q^{2} +3.27754i q^{4} +(-4.98774 + 0.349865i) q^{5} +(-7.13454 + 7.13454i) q^{7} +(4.37397 + 4.37397i) q^{8} +(-2.78747 + 3.20802i) q^{10} -6.84616 q^{11} +(5.13850 + 5.13850i) q^{13} +8.57603i q^{14} -7.85248 q^{16} +(17.0856 - 17.0856i) q^{17} +21.9632i q^{19} +(-1.14670 - 16.3476i) q^{20} +(-4.11469 + 4.11469i) q^{22} +(-3.06284 - 3.06284i) q^{23} +(24.7552 - 3.49008i) q^{25} +6.17670 q^{26} +(-23.3838 - 23.3838i) q^{28} +41.1349i q^{29} +20.3793 q^{31} +(-22.2154 + 22.2154i) q^{32} -20.5376i q^{34} +(33.0891 - 38.0814i) q^{35} +(30.7953 - 30.7953i) q^{37} +(13.2004 + 13.2004i) q^{38} +(-23.3465 - 20.2859i) q^{40} -79.7736 q^{41} +(-16.8417 - 16.8417i) q^{43} -22.4386i q^{44} -3.68166 q^{46} +(21.1840 - 21.1840i) q^{47} -52.8032i q^{49} +(12.7808 - 16.9760i) q^{50} +(-16.8417 + 16.8417i) q^{52} +(48.1359 + 48.1359i) q^{53} +(34.1469 - 2.39523i) q^{55} -62.4124 q^{56} +(24.7230 + 24.7230i) q^{58} +32.3498i q^{59} +53.3901 q^{61} +(12.2484 - 12.2484i) q^{62} -4.70606i q^{64} +(-27.4273 - 23.8317i) q^{65} +(7.43409 - 7.43409i) q^{67} +(55.9987 + 55.9987i) q^{68} +(-3.00045 - 42.7750i) q^{70} -62.5131 q^{71} +(16.4036 + 16.4036i) q^{73} -37.0173i q^{74} -71.9854 q^{76} +(48.8441 - 48.8441i) q^{77} +141.870i q^{79} +(39.1662 - 2.74731i) q^{80} +(-47.9457 + 47.9457i) q^{82} +(18.7813 + 18.7813i) q^{83} +(-79.2408 + 91.1960i) q^{85} -20.2444 q^{86} +(-29.9448 - 29.9448i) q^{88} +48.7354i q^{89} -73.3216 q^{91} +(10.0386 - 10.0386i) q^{92} -25.4641i q^{94} +(-7.68416 - 109.547i) q^{95} +(6.96035 - 6.96035i) q^{97} +(-31.7359 - 31.7359i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{7} - 32 q^{10} + 28 q^{13} - 20 q^{16} + 176 q^{22} + 64 q^{25} + 80 q^{28} - 208 q^{31} - 176 q^{37} - 252 q^{40} - 188 q^{43} + 188 q^{46} - 188 q^{52} - 136 q^{55} + 504 q^{58} + 296 q^{61}+ \cdots - 284 q^{97}+O(q^{100}) \) 16 * q - 8 * q^7 - 32 * q^10 + 28 * q^13 - 20 * q^16 + 176 * q^22 + 64 * q^25 + 80 * q^28 - 208 * q^31 - 176 * q^37 - 252 * q^40 - 188 * q^43 + 188 * q^46 - 188 * q^52 - 136 * q^55 + 504 * q^58 + 296 * q^61 + 304 * q^67 + 684 * q^70 - 56 * q^73 - 732 * q^76 - 76 * q^82 - 788 * q^85 - 1128 * q^88 + 200 * q^91 - 284 * q^97

Introduction

L-functions

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