LMFDB - Embedded newform 270.3.l.b.73.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [270,3,Mod(37,270)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(270, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([4, 3]))

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

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

chi := DirichletCharacter("270.37");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 270 = 2 \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	270.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:	$7.35696713773$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 90)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			73.1
Character	$\chi$	$=$	270.73
Dual form			270.3.l.b.37.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.366025 - 1.36603i) q^{2} +(-1.73205 + 1.00000i) q^{4} +(-4.34994 - 2.46536i) q^{5} +(-0.882779 - 3.29458i) q^{7} +(2.00000 + 2.00000i) q^{8} +(-1.77556 + 6.84452i) q^{10} +(0.641369 - 1.11088i) q^{11} +(-1.05805 + 3.94868i) q^{13} +(-4.17735 + 2.41180i) q^{14} +(2.00000 - 3.46410i) q^{16} +(-19.6659 + 19.6659i) q^{17} +17.2032i q^{19} +(9.99968 - 0.0798070i) q^{20} +(-1.75225 - 0.469515i) q^{22} +(-7.98597 + 29.8041i) q^{23} +(12.8440 + 21.4484i) q^{25} +5.78128 q^{26} +(4.82359 + 4.82359i) q^{28} +(-46.0987 - 26.6151i) q^{29} +(-13.3765 - 23.1688i) q^{31} +(-5.46410 - 1.46410i) q^{32} +(34.0624 + 19.6659i) q^{34} +(-4.28229 + 16.5076i) q^{35} +(6.39867 - 6.39867i) q^{37} +(23.5001 - 6.29683i) q^{38} +(-3.76916 - 13.6306i) q^{40} +(24.7520 + 42.8716i) q^{41} +(-44.1156 + 11.8207i) q^{43} +2.56548i q^{44} +43.6362 q^{46} +(-2.93580 - 10.9565i) q^{47} +(32.3603 - 18.6832i) q^{49} +(24.5978 - 25.3958i) q^{50} +(-2.11609 - 7.89737i) q^{52} +(-0.174975 - 0.174975i) q^{53} +(-5.52865 + 3.25107i) q^{55} +(4.82359 - 8.35471i) q^{56} +(-19.4836 + 72.7138i) q^{58} +(88.3973 - 51.0362i) q^{59} +(-26.3420 + 45.6258i) q^{61} +(-26.7530 + 26.7530i) q^{62} +8.00000i q^{64} +(14.3374 - 14.5681i) q^{65} +(-57.3947 - 15.3789i) q^{67} +(14.3965 - 53.7283i) q^{68} +(24.1172 - 0.192478i) q^{70} -5.54275 q^{71} +(-48.9018 - 48.9018i) q^{73} +(-11.0828 - 6.39867i) q^{74} +(-17.2032 - 29.7969i) q^{76} +(-4.22608 - 1.13237i) q^{77} +(-84.7222 - 48.9144i) q^{79} +(-17.2401 + 10.1379i) q^{80} +(49.5039 - 49.5039i) q^{82} +(-69.6231 + 18.6555i) q^{83} +(134.029 - 37.0620i) q^{85} +(32.2949 + 55.9363i) q^{86} +(3.50450 - 0.939029i) q^{88} -46.9573i q^{89} +13.9433 q^{91} +(-15.9719 - 59.6081i) q^{92} +(-13.8923 + 8.02075i) q^{94} +(42.4122 - 74.8331i) q^{95} +(-41.3179 - 154.200i) q^{97} +(-37.3665 - 37.3665i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{2} - 6 q^{7} + 48 q^{8} - 12 q^{10} + 12 q^{11} + 48 q^{16} + 36 q^{17} - 12 q^{20} - 12 q^{22} + 54 q^{23} + 54 q^{25} - 24 q^{28} - 72 q^{31} - 48 q^{32} + 336 q^{35} + 132 q^{37} + 36 q^{38}+ \cdots - 24 q^{98}+O(q^{100}) $ 24 * q + 12 * q^2 - 6 * q^7 + 48 * q^8 - 12 * q^10 + 12 * q^11 + 48 * q^16 + 36 * q^17 - 12 * q^20 - 12 * q^22 + 54 * q^23 + 54 * q^25 - 24 * q^28 - 72 * q^31 - 48 * q^32 + 336 * q^35 + 132 * q^37 + 36 * q^38 + 12 * q^40 - 24 * q^41 + 108 * q^43 + 216 * q^46 - 48 * q^47 - 54 * q^50 - 384 * q^53 - 552 * q^55 - 24 * q^56 + 60 * q^58 - 456 * q^61 - 144 * q^62 - 264 * q^65 + 12 * q^67 + 36 * q^68 + 174 * q^70 + 168 * q^71 - 432 * q^73 - 72 * q^76 + 48 * q^77 - 48 * q^82 + 246 * q^83 + 324 * q^85 - 216 * q^86 + 24 * q^88 + 1224 * q^91 + 108 * q^92 - 432 * q^95 - 102 * q^97 - 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/270\mathbb{Z}\right)^\times$.

$n$	$191$	$217$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.366025	−	1.36603i	−0.183013	−	0.683013i
$2$	−0.366025	−	1.36603i	−0.183013	−	0.683013i
$3$		0			0
$3$		0			0
$4$	−1.73205	+	1.00000i	−0.433013	+	0.250000i
$5$	−4.34994	−	2.46536i	−0.869988	−	0.493073i
$5$	−4.34994	−	2.46536i	−0.869988	−	0.493073i
$6$		0			0
$7$	−0.882779	−	3.29458i	−0.126111	−	0.470654i	0.873766	−	0.486347i	$-0.161671\pi$
$7$	−0.882779	−	3.29458i	−0.126111	−	0.470654i	−0.999877	+	0.0156937i	$0.995004\pi$
$8$	2.00000	+	2.00000i	0.250000	+	0.250000i
$9$		0			0
$10$	−1.77556	+	6.84452i	−0.177556	+	0.684452i
$11$	0.641369	−	1.11088i	0.0583063	−	0.100989i	−0.835399	−	0.549644i	$-0.814763\pi$
$11$	0.641369	−	1.11088i	0.0583063	−	0.100989i	0.893705	+	0.448655i	$0.148097\pi$
$12$		0			0
$13$	−1.05805	+	3.94868i	−0.0813882	+	0.303745i	−0.994606	−	0.103727i	$-0.966923\pi$
$13$	−1.05805	+	3.94868i	−0.0813882	+	0.303745i	0.913218	+	0.407472i	$0.133590\pi$
$14$	−4.17735	+	2.41180i	−0.298382	+	0.172271i
$15$		0			0
$16$	2.00000	−	3.46410i	0.125000	−	0.216506i
$17$	−19.6659	+	19.6659i	−1.15682	+	1.15682i	−0.171664	+	0.985156i	$0.554914\pi$
$17$	−19.6659	+	19.6659i	−1.15682	+	1.15682i	−0.985156	+	0.171664i	$0.945086\pi$
$18$		0			0
$19$			17.2032i			0.905434i	0.891654	+	0.452717i	$0.149545\pi$
$19$			17.2032i			0.905434i	−0.891654	+	0.452717i	$0.850455\pi$
$20$	9.99968	−	0.0798070i	0.499984	−	0.00399035i
$21$		0			0
$22$	−1.75225	−	0.469515i	−0.0796478	−	0.0213416i
$23$	−7.98597	+	29.8041i	−0.347216	+	1.29583i	0.542785	+	0.839871i	$0.317370\pi$
$23$	−7.98597	+	29.8041i	−0.347216	+	1.29583i	−0.890002	+	0.455957i	$0.849297\pi$
$24$		0			0
$25$	12.8440	+	21.4484i	0.513759	+	0.857935i
$26$	5.78128			0.222357
$27$		0			0
$28$	4.82359	+	4.82359i	0.172271	+	0.172271i
$29$	−46.0987	−	26.6151i	−1.58961	−	0.917762i	−0.993371	−	0.114956i	$-0.963327\pi$
$29$	−46.0987	−	26.6151i	−1.58961	−	0.917762i	−0.596240	−	0.802806i	$-0.703339\pi$
$30$		0			0
$31$	−13.3765	−	23.1688i	−0.431501	−	0.747381i	0.565502	−	0.824747i	$-0.308682\pi$
$31$	−13.3765	−	23.1688i	−0.431501	−	0.747381i	−0.997003	+	0.0773657i	$0.975349\pi$
$32$	−5.46410	−	1.46410i	−0.170753	−	0.0457532i
$33$		0			0
$34$	34.0624	+	19.6659i	1.00183	+	0.578410i
$35$	−4.28229	+	16.5076i	−0.122351	+	0.471645i
$36$		0			0
$37$	6.39867	−	6.39867i	0.172937	−	0.172937i	−0.615332	−	0.788268i	$-0.710978\pi$
$37$	6.39867	−	6.39867i	0.172937	−	0.172937i	0.788268	+	0.615332i	$0.210978\pi$
$38$	23.5001	−	6.29683i	0.618423	−	0.165706i
$39$		0			0
$40$	−3.76916	−	13.6306i	−0.0942289	−	0.340765i
$41$	24.7520	+	42.8716i	0.603706	+	1.04565i	0.992255	+	0.124222i	$0.0396433\pi$
$41$	24.7520	+	42.8716i	0.603706	+	1.04565i	−0.388548	+	0.921428i	$0.627023\pi$
$42$		0			0
$43$	−44.1156	+	11.8207i	−1.02594	+	0.274901i	−0.732277	−	0.681007i	$-0.761542\pi$
$43$	−44.1156	+	11.8207i	−1.02594	+	0.274901i	−0.293667	+	0.955908i	$0.594876\pi$
$44$			2.56548i			0.0583063i
$45$		0			0
$46$	43.6362			0.948613
$47$	−2.93580	−	10.9565i	−0.0624638	−	0.233118i	0.927636	−	0.373487i	$-0.121838\pi$
$47$	−2.93580	−	10.9565i	−0.0624638	−	0.233118i	−0.990099	+	0.140369i	$0.955171\pi$
$48$		0			0
$49$	32.3603	−	18.6832i	0.660415	−	0.381291i
$50$	24.5978	−	25.3958i	0.491956	−	0.507917i
$51$		0			0
$52$	−2.11609	−	7.89737i	−0.0406941	−	0.151872i
$53$	−0.174975	−	0.174975i	−0.00330142	−	0.00330142i	0.705454	−	0.708756i	$-0.250743\pi$
$53$	−0.174975	−	0.174975i	−0.00330142	−	0.00330142i	−0.708756	+	0.705454i	$0.750743\pi$
$54$		0			0
$55$	−5.52865	+	3.25107i	−0.100521	+	0.0591104i
$56$	4.82359	−	8.35471i	0.0861356	−	0.149191i
$57$		0			0
$58$	−19.4836	+	72.7138i	−0.335924	+	1.25369i
$59$	88.3973	−	51.0362i	1.49826	−	0.865020i	0.498261	−	0.867027i	$-0.333972\pi$
$59$	88.3973	−	51.0362i	1.49826	−	0.865020i	0.999998	+	0.00200725i	$0.000638929\pi$
$60$		0			0
$61$	−26.3420	+	45.6258i	−0.431837	+	0.747963i	−0.997032	−	0.0769943i	$-0.975468\pi$
$61$	−26.3420	+	45.6258i	−0.431837	+	0.747963i	0.565195	+	0.824958i	$0.308801\pi$
$62$	−26.7530	+	26.7530i	−0.431501	+	0.431501i
$63$		0			0
$64$			8.00000i			0.125000i
$65$	14.3374	−	14.5681i	0.220575	−	0.224124i
$66$		0			0
$67$	−57.3947	−	15.3789i	−0.856637	−	0.229535i	−0.196337	−	0.980537i	$-0.562905\pi$
$67$	−57.3947	−	15.3789i	−0.856637	−	0.229535i	−0.660301	+	0.751001i	$0.729571\pi$
$68$	14.3965	−	53.7283i	0.211713	−	0.790122i
$69$		0			0
$70$	24.1172	−	0.192478i	0.344531	−	0.00274969i
$71$	−5.54275			−0.0780669			−0.0390335	−	0.999238i	$-0.512428\pi$
$71$	−5.54275			−0.0780669			−0.0390335	+	0.999238i	$0.512428\pi$
$72$		0			0
$73$	−48.9018	−	48.9018i	−0.669888	−	0.669888i	0.287802	−	0.957690i	$-0.407075\pi$
$73$	−48.9018	−	48.9018i	−0.669888	−	0.669888i	−0.957690	+	0.287802i	$0.907075\pi$
$74$	−11.0828	−	6.39867i	−0.149768	−	0.0864685i
$75$		0			0
$76$	−17.2032	−	29.7969i	−0.226359	−	0.392064i
$77$	−4.22608	−	1.13237i	−0.0548841	−	0.0147062i
$78$		0			0
$79$	−84.7222	−	48.9144i	−1.07243	−	0.619169i	−0.143587	−	0.989638i	$-0.545864\pi$
$79$	−84.7222	−	48.9144i	−1.07243	−	0.619169i	−0.928845	+	0.370468i	$0.879197\pi$
$80$	−17.2401	+	10.1379i	−0.215502	+	0.126724i
$81$		0			0
$82$	49.5039	−	49.5039i	0.603706	−	0.603706i
$83$	−69.6231	+	18.6555i	−0.838833	+	0.224765i	−0.652563	−	0.757734i	$-0.726306\pi$
$83$	−69.6231	+	18.6555i	−0.838833	+	0.224765i	−0.186269	+	0.982499i	$0.559640\pi$
$84$		0			0
$85$	134.029	−	37.0620i	1.57681	−	0.436023i
$86$	32.2949	+	55.9363i	0.375522	+	0.650423i
$87$		0			0
$88$	3.50450	−	0.939029i	0.0398239	−	0.0106708i
$89$		−	46.9573i		−	0.527610i	−0.964576	−	0.263805i	$-0.915022\pi$
$89$		−	46.9573i		−	0.527610i	0.964576	−	0.263805i	$-0.0849776\pi$
$90$		0			0
$91$	13.9433			0.153223
$92$	−15.9719	−	59.6081i	−0.173608	−	0.647914i
$93$		0			0
$94$	−13.8923	+	8.02075i	−0.147791	+	0.0853271i
$95$	42.4122	−	74.8331i	0.446445	−	0.787717i
$96$		0			0
$97$	−41.3179	−	154.200i	−0.425958	−	1.58970i	−0.761823	−	0.647786i	$-0.775695\pi$
$97$	−41.3179	−	154.200i	−0.425958	−	1.58970i	0.335865	−	0.941910i	$-0.390971\pi$
$98$	−37.3665	−	37.3665i	−0.381291	−	0.381291i
$99$		0			0
$100$	−43.6948	−	24.3057i	−0.436948	−	0.243057i
$101$	37.1675	−	64.3761i	0.367995	−	0.637387i	−0.621257	−	0.783607i	$-0.713378\pi$
$101$	37.1675	−	64.3761i	0.367995	−	0.637387i	0.989252	+	0.146220i	$0.0467109\pi$
$102$		0			0
$103$	−4.10992	+	15.3384i	−0.0399022	+	0.148917i	−0.983003	−	0.183590i	$-0.941228\pi$
$103$	−4.10992	+	15.3384i	−0.0399022	+	0.148917i	0.943101	+	0.332507i	$0.107895\pi$
$104$	−10.0135	+	5.78128i	−0.0962833	+	0.0555892i
$105$		0			0
$106$	−0.174975	+	0.303066i	−0.00165071	+	0.00285911i
$107$	−114.528	+	114.528i	−1.07035	+	1.07035i	−0.0730234	+	0.997330i	$0.523265\pi$
$107$	−114.528	+	114.528i	−1.07035	+	1.07035i	−0.997330	+	0.0730234i	$0.976735\pi$
$108$		0			0
$109$		−	80.1875i		−	0.735665i	−0.929892	−	0.367833i	$-0.880100\pi$
$109$		−	80.1875i		−	0.735665i	0.929892	−	0.367833i	$-0.119900\pi$
$110$	6.46467	+	6.36230i	0.0587697	+	0.0578391i
$111$		0			0
$112$	−13.1783	−	3.53112i	−0.117663	−	0.0315278i
$113$	−38.6740	+	144.333i	−0.342247	+	1.27728i	0.553548	+	0.832818i	$0.313274\pi$
$113$	−38.6740	+	144.333i	−0.342247	+	1.27728i	−0.895795	+	0.444467i	$0.853393\pi$
$114$		0			0
$115$	108.216	−	109.958i	0.941012	−	0.956153i
$116$	106.460			0.917762
$117$		0			0
$118$	−102.072	−	102.072i	−0.865020	−	0.865020i
$119$	82.1515	+	47.4302i	0.690349	+	0.398573i
$120$		0			0
$121$	59.6773	+	103.364i	0.493201	+	0.854249i
$122$	71.9678	+	19.2837i	0.589900	+	0.158063i
$123$		0			0
$124$	46.3376	+	26.7530i	0.373691	+	0.215750i
$125$	−2.99251	−	124.964i	−0.0239401	−	0.999713i
$126$		0			0
$127$	−111.415	+	111.415i	−0.877284	+	0.877284i	−0.993253	−	0.115969i	$-0.963003\pi$
$127$	−111.415	+	111.415i	−0.877284	+	0.877284i	0.115969	+	0.993253i	$0.463003\pi$
$128$	10.9282	−	2.92820i	0.0853766	−	0.0228766i
$129$		0			0
$130$	−25.1482	−	14.2529i	−0.193448	−	0.109638i
$131$	−2.05048	−	3.55154i	−0.0156525	−	0.0271110i	0.858093	−	0.513494i	$-0.171649\pi$
$131$	−2.05048	−	3.55154i	−0.0156525	−	0.0271110i	−0.873746	+	0.486383i	$0.838316\pi$
$132$		0			0
$133$	56.6774	−	15.1867i	0.426146	−	0.114185i
$134$			84.0317i			0.627102i
$135$		0			0
$136$	−78.6637			−0.578410
$137$	−36.0575	−	134.568i	−0.263194	−	0.982252i	−0.963347	−	0.268259i	$-0.913552\pi$
$137$	−36.0575	−	134.568i	−0.263194	−	0.982252i	0.700153	−	0.713993i	$-0.253115\pi$
$138$		0			0
$139$	−20.2625	+	11.6985i	−0.145773	+	0.0841621i	−0.571113	−	0.820872i	$-0.693488\pi$
$139$	−20.2625	+	11.6985i	−0.145773	+	0.0841621i	0.425339	+	0.905034i	$0.360155\pi$
$140$	−9.09044	−	32.8743i	−0.0649317	−	0.234816i
$141$		0			0
$142$	2.02879	+	7.57154i	0.0142872	+	0.0533207i
$143$	3.70793	+	3.70793i	0.0259296	+	0.0259296i
$144$		0			0
$145$	134.911	+	229.424i	0.930419	+	1.58224i
$146$	−48.9018	+	84.7004i	−0.334944	+	0.580140i
$147$		0			0
$148$	−4.68415	+	17.4815i	−0.0316497	+	0.118118i
$149$	195.281	−	112.746i	1.31061	−	0.756683i	0.328416	−	0.944533i	$-0.393485\pi$
$149$	195.281	−	112.746i	1.31061	−	0.756683i	0.982198	+	0.187850i	$0.0601519\pi$
$150$		0			0
$151$	−124.344	+	215.370i	−0.823470	+	1.42629i	0.0796138	+	0.996826i	$0.474631\pi$
$151$	−124.344	+	215.370i	−0.823470	+	1.42629i	−0.903083	+	0.429465i	$0.858702\pi$
$152$	−34.4065	+	34.4065i	−0.226359	+	0.226359i
$153$		0			0
$154$			6.18740i			0.0401780i
$155$	1.06754	+	133.761i	0.00688735	+	0.862974i
$156$		0			0
$157$	52.1651	+	13.9776i	0.332261	+	0.0890292i	0.421093	−	0.907017i	$-0.361647\pi$
$157$	52.1651	+	13.9776i	0.332261	+	0.0890292i	−0.0888315	+	0.996047i	$0.528313\pi$
$158$	−35.8078	+	133.637i	−0.226632	+	0.845801i
$159$		0			0
$160$	20.1590	+	19.8397i	0.125994	+	0.123998i
$161$	105.242			0.653674
$162$		0			0
$163$	115.074	+	115.074i	0.705977	+	0.705977i	0.965687	−	0.259709i	$-0.0836268\pi$
$163$	115.074	+	115.074i	0.705977	+	0.705977i	−0.259709	+	0.965687i	$0.583627\pi$
$164$	−85.7433	−	49.5039i	−0.522825	−	0.301853i
$165$		0			0
$166$	50.9676	+	88.2786i	0.307034	+	0.531799i
$167$	−302.380	−	81.0225i	−1.81066	−	0.485164i	−0.815101	−	0.579319i	$-0.803318\pi$
$167$	−302.380	−	81.0225i	−1.81066	−	0.485164i	−0.995558	+	0.0941548i	$0.969985\pi$
$168$		0			0
$169$	131.886	+	76.1442i	0.780388	+	0.450557i
$170$	−99.6857	−	169.522i	−0.586387	−	0.997187i
$171$		0			0
$172$	64.5897	−	64.5897i	0.375522	−	0.375522i
$173$	209.321	−	56.0873i	1.20995	−	0.324204i	0.403205	−	0.915110i	$-0.367896\pi$
$173$	209.321	−	56.0873i	1.20995	−	0.324204i	0.806741	+	0.590906i	$0.201230\pi$
$174$		0			0
$175$	59.3249	−	61.2496i	0.338999	−	0.349998i
$176$	−2.56548	−	4.44353i	−0.0145766	−	0.0252473i
$177$		0			0
$178$	−64.1449	+	17.1876i	−0.360364	+	0.0965593i
$179$			164.771i			0.920507i	0.887788	+	0.460254i	$0.152241\pi$
$179$			164.771i			0.920507i	−0.887788	+	0.460254i	$0.847759\pi$
$180$		0			0
$181$	−5.29281			−0.0292421			−0.0146210	−	0.999893i	$-0.504654\pi$
$181$	−5.29281			−0.0292421			−0.0146210	+	0.999893i	$0.504654\pi$
$182$	−5.10359	−	19.0468i	−0.0280417	−	0.104653i
$183$		0			0
$184$	−75.5801	+	43.6362i	−0.410761	+	0.237153i
$185$	−43.6088	+	12.0588i	−0.235724	+	0.0651826i
$186$		0			0
$187$	9.23344	+	34.4597i	0.0493767	+	0.184276i
$188$	16.0415	+	16.0415i	0.0853271	+	0.0853271i
$189$		0			0
$190$	−117.748	−	30.5454i	−0.619726	−	0.160765i
$191$	−39.7078	+	68.7759i	−0.207894	+	0.360083i	−0.951051	−	0.309034i	$-0.899994\pi$
$191$	−39.7078	+	68.7759i	−0.207894	+	0.360083i	0.743157	+	0.669117i	$0.233328\pi$
$192$		0			0
$193$	−43.9766	+	164.123i	−0.227858	+	0.850377i	0.753381	+	0.657584i	$0.228421\pi$
$193$	−43.9766	+	164.123i	−0.227858	+	0.850377i	−0.981239	+	0.192794i	$0.938245\pi$
$194$	−195.518	+	112.883i	−1.00783	+	0.581869i
$195$		0			0
$196$	−37.3665	+	64.7206i	−0.190645	+	0.330207i
$197$	38.1732	−	38.1732i	0.193773	−	0.193773i	−0.603551	−	0.797324i	$-0.706248\pi$
$197$	38.1732	−	38.1732i	0.193773	−	0.193773i	0.797324	+	0.603551i	$0.206248\pi$
$198$		0			0
$199$			90.0401i			0.452463i	0.974074	+	0.226231i	$0.0726405\pi$
$199$			90.0401i			0.452463i	−0.974074	+	0.226231i	$0.927359\pi$
$200$	−17.2088	+	68.5847i	−0.0860440	+	0.342923i
$201$		0			0
$202$	−101.544	−	27.2085i	−0.502691	−	0.134696i
$203$	−46.9905	+	175.371i	−0.231480	+	0.863896i
$204$		0			0
$205$	−1.97538	−	247.512i	−0.00963599	−	1.20737i
$206$	22.4570			0.109015
$207$		0			0
$208$	11.5626	+	11.5626i	0.0555892	+	0.0555892i
$209$	19.1108	+	11.0336i	0.0914392	+	0.0527925i
$210$		0			0
$211$	−185.810	−	321.832i	−0.880614	−	1.52527i	−0.850659	−	0.525718i	$-0.823797\pi$
$211$	−185.810	−	321.832i	−0.880614	−	1.52527i	−0.0299553	−	0.999551i	$-0.509536\pi$
$212$	0.478042	+	0.128091i	0.00225491	+	0.000604202i
$213$		0			0
$214$	198.368	+	114.528i	0.926953	+	0.535177i
$215$	221.043	+	57.3415i	1.02811	+	0.266704i
$216$		0			0
$217$	−64.5229	+	64.5229i	−0.297341	+	0.297341i
$218$	−109.538	+	29.3507i	−0.502469	+	0.134636i
$219$		0			0
$220$	6.32483	−	11.1597i	0.0287492	−	0.0507258i
$221$	−56.8471	−	98.4620i	−0.257227	−	0.445529i
$222$		0			0
$223$	210.286	−	56.3460i	0.942988	−	0.252673i	0.245604	−	0.969370i	$-0.421014\pi$
$223$	210.286	−	56.3460i	0.942988	−	0.252673i	0.697384	+	0.716698i	$0.254347\pi$
$224$			19.2944i			0.0861356i
$225$		0			0
$226$	211.318			0.935037
$227$	9.09000	+	33.9243i	0.0400440	+	0.149446i	0.983053	−	0.183320i	$-0.0586845\pi$
$227$	9.09000	+	33.9243i	0.0400440	+	0.149446i	−0.943009	+	0.332767i	$0.892018\pi$
$228$		0			0
$229$	121.286	−	70.0246i	0.529634	−	0.305784i	−0.211233	−	0.977436i	$-0.567748\pi$
$229$	121.286	−	70.0246i	0.529634	−	0.305784i	0.740867	+	0.671651i	$0.234415\pi$
$230$	−189.815	−	107.579i	−0.825282	−	0.467735i
$231$		0			0
$232$	−38.9672	−	145.428i	−0.167962	−	0.626843i
$233$	127.973	+	127.973i	0.549239	+	0.549239i	0.926221	−	0.376982i	$-0.123038\pi$
$233$	127.973	+	127.973i	0.549239	+	0.549239i	−0.376982	+	0.926221i	$0.623038\pi$
$234$		0			0
$235$	−14.2413	+	54.8981i	−0.0606013	+	0.233609i
$236$	−102.072	+	176.795i	−0.432510	+	0.749129i
$237$		0			0
$238$	34.7213	−	129.582i	0.145888	−	0.544461i
$239$	−62.3945	+	36.0235i	−0.261065	+	0.150726i	−0.624820	−	0.780769i	$-0.714828\pi$
$239$	−62.3945	+	36.0235i	−0.261065	+	0.150726i	0.363755	+	0.931495i	$0.381494\pi$
$240$		0			0
$241$	−134.240	+	232.511i	−0.557014	+	0.964776i	0.440730	+	0.897640i	$0.354720\pi$
$241$	−134.240	+	232.511i	−0.557014	+	0.964776i	−0.997744	+	0.0671366i	$0.978614\pi$
$242$	119.355	−	119.355i	0.493201	−	0.493201i
$243$		0			0
$244$		−	105.368i		−	0.431837i
$245$	−186.826	+	1.49105i	−0.762557	+	0.00608593i
$246$		0			0
$247$	−67.9302	−	18.2018i	−0.275021	−	0.0736917i
$248$	19.5846	−	73.0907i	0.0789701	−	0.294720i
$249$		0			0
$250$	−169.609	+	49.8279i	−0.678436	+	0.199312i
$251$	−251.209			−1.00083			−0.500416	−	0.865785i	$-0.666820\pi$
$251$	−251.209			−1.00083			−0.500416	+	0.865785i	$0.666820\pi$
$252$		0			0
$253$	27.9869	+	27.9869i	0.110620	+	0.110620i
$254$	192.977	+	111.415i	0.759751	+	0.438642i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	−78.0244	−	20.9066i	−0.303597	−	0.0813485i	0.103805	−	0.994598i	$-0.466898\pi$
$257$	−78.0244	−	20.9066i	−0.303597	−	0.0813485i	−0.407401	+	0.913249i	$0.633565\pi$
$258$		0			0
$259$	−26.7295	−	15.4323i	−0.103203	−	0.0595841i
$260$	−10.2650	+	39.5700i	−0.0394808	+	0.152192i
$261$		0			0
$262$	−4.10096	+	4.10096i	−0.0156525	+	0.0156525i
$263$	138.594	−	37.1361i	0.526973	−	0.141202i	0.0144826	−	0.999895i	$-0.495390\pi$
$263$	138.594	−	37.1361i	0.526973	−	0.141202i	0.512490	+	0.858693i	$0.328723\pi$
$264$		0			0
$265$	0.329755	+	1.19251i	0.00124436	+	0.00450004i
$266$	−41.4907	−	71.8641i	−0.155980	−	0.270166i
$267$		0			0
$268$	114.789	−	30.7577i	0.428319	−	0.114768i
$269$		−	341.458i		−	1.26936i	−0.772775	−	0.634680i	$-0.781132\pi$
$269$		−	341.458i		−	1.26936i	0.772775	−	0.634680i	$-0.218868\pi$
$270$		0			0
$271$	157.125			0.579798			0.289899	−	0.957057i	$-0.406378\pi$
$271$	157.125			0.579798			0.289899	+	0.957057i	$0.406378\pi$
$272$	28.7929	+	107.457i	0.105856	+	0.395061i
$273$		0			0
$274$	−170.626	+	98.5110i	−0.622723	+	0.359529i
$275$	32.0644	−	0.511841i	0.116598	−	0.00186124i
$276$		0			0
$277$	−43.2604	−	161.450i	−0.156175	−	0.582851i	−0.999002	−	0.0446674i	$-0.985777\pi$
$277$	−43.2604	−	161.450i	−0.156175	−	0.582851i	0.842827	−	0.538184i	$-0.180889\pi$
$278$	23.3971	+	23.3971i	0.0841621	+	0.0841621i
$279$		0			0
$280$	−41.5797	+	24.4506i	−0.148499	+	0.0873235i
$281$	−100.731	+	174.471i	−0.358473	+	0.620893i	−0.987706	−	0.156324i	$-0.950036\pi$
$281$	−100.731	+	174.471i	−0.358473	+	0.620893i	0.629233	+	0.777217i	$0.283369\pi$
$282$		0			0
$283$	−15.3918	+	57.4430i	−0.0543880	+	0.202979i	−0.987773	−	0.155897i	$-0.950173\pi$
$283$	−15.3918	+	57.4430i	−0.0543880	+	0.202979i	0.933385	+	0.358876i	$0.116840\pi$
$284$	9.60033	−	5.54275i	0.0338040	−	0.0195167i
$285$		0			0
$286$	3.70793	−	6.42232i	0.0129648	−	0.0224557i
$287$	119.393	−	119.393i	0.416005	−	0.416005i
$288$		0			0
$289$		−	484.497i		−	1.67646i
$290$	264.018	−	268.267i	0.910408	−	0.925057i
$291$		0			0
$292$	133.602	+	35.7986i	0.457542	+	0.122598i
$293$	83.4199	−	311.327i	0.284709	−	1.06255i	−0.664342	−	0.747429i	$-0.731288\pi$
$293$	83.4199	−	311.327i	0.284709	−	1.06255i	0.949051	−	0.315121i	$-0.102045\pi$
$294$		0			0
$295$	−510.346	+	4.07304i	−1.72998	+	0.0138069i
$296$	25.5947			0.0864685
$297$		0			0
$298$	−225.492	−	225.492i	−0.756683	−	0.756683i
$299$	−109.237	−	63.0682i	−0.365342	−	0.210930i
$300$		0			0
$301$	77.8886	+	134.907i	0.258766	+	0.448196i
$302$	339.714	+	91.0261i	1.12488	+	0.301411i
$303$		0			0
$304$	59.5938	+	34.4065i	0.196032	+	0.113179i
$305$	227.070	−	133.527i	0.744493	−	0.437792i
$306$		0			0
$307$	65.6054	−	65.6054i	0.213698	−	0.213698i	−0.592138	−	0.805837i	$-0.701716\pi$
$307$	65.6054	−	65.6054i	0.213698	−	0.213698i	0.805837	+	0.592138i	$0.201716\pi$
$308$	8.45215	−	2.26475i	0.0274421	−	0.00735308i
$309$		0			0
$310$	182.330	−	50.4182i	0.588162	−	0.162639i
$311$	−121.899	−	211.135i	−0.391957	−	0.678890i	0.600751	−	0.799437i	$-0.294869\pi$
$311$	−121.899	−	211.135i	−0.391957	−	0.678890i	−0.992708	+	0.120547i	$0.961535\pi$
$312$		0			0
$313$	−227.421	+	60.9372i	−0.726584	+	0.194688i	−0.603108	−	0.797660i	$-0.706071\pi$
$313$	−227.421	+	60.9372i	−0.726584	+	0.194688i	−0.123477	+	0.992347i	$0.539404\pi$
$314$		−	76.3749i		−	0.243232i
$315$		0			0
$316$	195.657			0.619169
$317$	122.564	+	457.413i	0.386636	+	1.44294i	0.835572	+	0.549380i	$0.185136\pi$
$317$	122.564	+	457.413i	0.386636	+	1.44294i	−0.448937	+	0.893564i	$0.648197\pi$
$318$		0			0
$319$	−59.1325	+	34.1402i	−0.185368	+	0.107023i
$320$	19.7229	−	34.7995i	0.0616341	−	0.108749i
$321$		0			0
$322$	−38.5211	−	143.763i	−0.119631	−	0.446468i
$323$	−338.318	−	338.318i	−1.04742	−	1.04742i
$324$		0			0
$325$	−98.2824	+	28.0234i	−0.302407	+	0.0862259i
$326$	115.074	−	199.315i	0.352989	−	0.611394i
$327$		0			0
$328$	−36.2394	+	135.247i	−0.110486	+	0.412339i
$329$	−33.5055	+	19.3444i	−0.101840	+	0.0587976i
$330$		0			0
$331$	123.081	−	213.182i	0.371845	−	0.644054i	−0.618004	−	0.786175i	$-0.712059\pi$
$331$	123.081	−	213.182i	0.371845	−	0.644054i	0.989849	+	0.142120i	$0.0453920\pi$
$332$	101.935	−	101.935i	0.307034	−	0.307034i
$333$		0			0
$334$			442.715i			1.32549i
$335$	211.749	+	208.396i	0.632087	+	0.622077i
$336$		0			0
$337$	435.441	+	116.676i	1.29211	+	0.346220i	0.838461	−	0.544962i	$-0.183456\pi$
$337$	435.441	+	116.676i	1.29211	+	0.346220i	0.453648	+	0.891181i	$0.350122\pi$
$338$	55.7414	−	208.030i	0.164915	−	0.615473i
$339$		0			0
$340$	−195.084	+	198.222i	−0.573775	+	0.583007i
$341$	−34.3171			−0.100637
$342$		0			0
$343$	−208.298	−	208.298i	−0.607284	−	0.607284i
$344$	−111.873	−	64.5897i	−0.325211	−	0.187761i
$345$		0			0
$346$	−153.233	−	265.408i	−0.442871	−	0.767075i
$347$	257.007	+	68.8649i	0.740655	+	0.198458i	0.609369	−	0.792887i	$-0.291423\pi$
$347$	257.007	+	68.8649i	0.740655	+	0.198458i	0.131286	+	0.991345i	$0.458089\pi$
$348$		0			0
$349$	99.2693	+	57.3131i	0.284439	+	0.164221i	0.635431	−	0.772157i	$-0.280822\pi$
$349$	99.2693	+	57.3131i	0.284439	+	0.164221i	−0.350992	+	0.936378i	$0.614156\pi$
$350$	−105.383	−	58.6204i	−0.301094	−	0.167487i
$351$		0			0
$352$	−5.13095	+	5.13095i	−0.0145766	+	0.0145766i
$353$	99.3009	−	26.6076i	0.281306	−	0.0753757i	−0.115408	−	0.993318i	$-0.536817\pi$
$353$	99.3009	−	26.6076i	0.281306	−	0.0753757i	0.396713	+	0.917943i	$0.370151\pi$
$354$		0			0
$355$	24.1106	+	13.6649i	0.0679173	+	0.0384927i
$356$	46.9573	+	81.3324i	0.131903	+	0.228462i
$357$		0			0
$358$	225.081	−	60.3103i	0.628718	−	0.168464i
$359$		−	190.904i		−	0.531767i	−0.964005	−	0.265883i	$-0.914336\pi$
$359$		−	190.904i		−	0.531767i	0.964005	−	0.265883i	$-0.0856636\pi$
$360$		0			0
$361$	65.0483			0.180189
$362$	1.93730	+	7.23012i	0.00535167	+	0.0199727i
$363$		0			0
$364$	−24.1504	+	13.9433i	−0.0663474	+	0.0383057i
$365$	92.1593	+	333.281i	0.252491	+	0.913098i
$366$		0			0
$367$	135.622	+	506.147i	0.369542	+	1.37915i	0.861159	+	0.508336i	$0.169739\pi$
$367$	135.622	+	506.147i	0.369542	+	1.37915i	−0.491617	+	0.870812i	$0.663594\pi$
$368$	87.2724	+	87.2724i	0.237153	+	0.237153i
$369$		0			0
$370$	32.4346	+	55.1570i	0.0876610	+	0.149073i
$371$	−0.422005	+	0.730934i	−0.00113748	+	0.00197017i
$372$		0			0
$373$	56.8529	−	212.178i	0.152421	−	0.568842i	−0.846892	−	0.531765i	$-0.821529\pi$
$373$	56.8529	−	212.178i	0.152421	−	0.568842i	0.999312	−	0.0370764i	$-0.0118045\pi$
$374$	43.6931	−	25.2262i	0.116826	−	0.0674498i
$375$		0			0
$376$	16.0415	−	27.7847i	0.0426635	−	0.0738954i
$377$	153.869	−	153.869i	0.408141	−	0.408141i
$378$		0			0
$379$		−	542.378i		−	1.43108i	−0.698574	−	0.715538i	$-0.746181\pi$
$379$		−	542.378i		−	1.43108i	0.698574	−	0.715538i	$-0.253819\pi$
$380$	1.37294	+	172.027i	0.00361300	+	0.452703i
$381$		0			0
$382$	108.484	+	29.0681i	0.283989	+	0.0760946i
$383$	−87.3480	+	325.987i	−0.228063	+	0.851141i	0.753092	+	0.657916i	$0.228562\pi$
$383$	−87.3480	+	325.987i	−0.228063	+	0.851141i	−0.981154	+	0.193226i	$0.938105\pi$
$384$		0			0
$385$	15.5915	+	15.3446i	0.0404973	+	0.0398560i
$386$	240.292			0.622519
$387$		0			0
$388$	225.765	+	225.765i	0.581869	+	0.581869i
$389$	−151.351	−	87.3827i	−0.389078	−	0.224634i	0.292683	−	0.956210i	$-0.405452\pi$
$389$	−151.351	−	87.3827i	−0.389078	−	0.224634i	−0.681761	+	0.731575i	$0.738785\pi$
$390$		0			0
$391$	−429.073	−	743.176i	−1.09737	−	1.90071i
$392$	102.087	+	27.3542i	0.260426	+	0.0697810i
$393$		0			0
$394$	−66.1180	−	38.1732i	−0.167812	−	0.0968864i
$395$	247.945	+	421.645i	0.627708	+	1.06746i
$396$		0			0
$397$	−249.989	+	249.989i	−0.629695	+	0.629695i	−0.947991	−	0.318296i	$-0.896889\pi$
$397$	−249.989	+	249.989i	−0.629695	+	0.629695i	0.318296	+	0.947991i	$0.396889\pi$
$398$	122.997	−	32.9570i	0.309038	−	0.0828064i
$399$		0			0
$400$	99.9873	−	1.59609i	0.249968	−	0.00399022i
$401$	65.7803	+	113.935i	0.164041	+	0.284127i	0.936314	−	0.351163i	$-0.114214\pi$
$401$	65.7803	+	113.935i	0.164041	+	0.284127i	−0.772274	+	0.635290i	$0.780880\pi$
$402$		0			0
$403$	105.639	−	28.3060i	0.262132	−	0.0702382i
$404$			148.670i			0.367995i
$405$		0			0
$406$	256.761			0.632416
$407$	−3.00427	−	11.2121i	−0.00738149	−	0.0275481i
$408$		0			0
$409$	−396.466	+	228.899i	−0.969353	+	0.559656i	−0.899039	−	0.437868i	$-0.855734\pi$
$409$	−396.466	+	228.899i	−0.969353	+	0.559656i	−0.0703144	+	0.997525i	$0.522400\pi$
$410$	−337.384	+	93.2940i	−0.822888	+	0.227546i
$411$		0			0
$412$	−8.21984	−	30.6769i	−0.0199511	−	0.0744584i
$413$	−246.178	−	246.178i	−0.596072	−	0.596072i
$414$		0			0
$415$	348.849	+	90.4961i	0.840600	+	0.218063i
$416$	11.5626	−	20.0269i	0.0277946	−	0.0481417i
$417$		0			0
$418$	8.07718	−	30.1444i	0.0193234	−	0.0721159i
$419$	−178.018	+	102.779i	−0.424864	+	0.245295i	−0.697156	−	0.716919i	$-0.745552\pi$
$419$	−178.018	+	102.779i	−0.424864	+	0.245295i	0.272292	+	0.962215i	$0.412218\pi$
$420$		0			0
$421$	33.9869	−	58.8671i	0.0807291	−	0.139827i	−0.822834	−	0.568281i	$-0.807608\pi$
$421$	33.9869	−	58.8671i	0.0807291	−	0.139827i	0.903563	+	0.428455i	$0.140942\pi$
$422$	−371.619	+	371.619i	−0.880614	+	0.880614i
$423$		0			0
$424$		−	0.699901i		−	0.00165071i
$425$	−674.391	−	169.213i	−1.58680	−	0.398149i
$426$		0			0
$427$	173.572	+	46.5084i	0.406491	+	0.108919i
$428$	83.8402	−	312.896i	0.195888	−	0.731065i
$429$		0			0
$430$	−2.57736	−	322.938i	−0.00599385	−	0.751019i
$431$	−99.6045			−0.231101			−0.115550	−	0.993302i	$-0.536863\pi$
$431$	−99.6045			−0.231101			−0.115550	+	0.993302i	$0.536863\pi$
$432$		0			0
$433$	−459.635	−	459.635i	−1.06151	−	1.06151i	−0.997980	−	0.0635322i	$-0.979763\pi$
$433$	−459.635	−	459.635i	−1.06151	−	1.06151i	−0.0635322	−	0.997980i	$-0.520237\pi$
$434$	111.757	+	64.5229i	0.257504	+	0.148670i
$435$		0			0
$436$	80.1875	+	138.889i	0.183916	+	0.318552i
$437$	−512.727	−	137.385i	−1.17329	−	0.314381i
$438$		0			0
$439$	50.5174	+	29.1662i	0.115074	+	0.0664379i	0.556432	−	0.830893i	$-0.312170\pi$
$439$	50.5174	+	29.1662i	0.115074	+	0.0664379i	−0.441358	+	0.897331i	$0.645503\pi$
$440$	−17.5594	−	4.55515i	−0.0399078	−	0.0103526i
$441$		0			0
$442$	−113.694	+	113.694i	−0.257227	+	0.257227i
$443$	−233.923	+	62.6794i	−0.528042	+	0.141489i	−0.512984	−	0.858398i	$-0.671460\pi$
$443$	−233.923	+	62.6794i	−0.528042	+	0.141489i	−0.0150582	+	0.999887i	$0.504793\pi$
$444$		0			0
$445$	−115.767	+	204.261i	−0.260150	+	0.459015i
$446$	−153.940	−	266.632i	−0.345157	−	0.597830i
$447$		0			0
$448$	26.3566	−	7.06223i	0.0588317	−	0.0157639i
$449$			769.773i			1.71442i	0.514970	+	0.857208i	$0.327803\pi$
$449$			769.773i			1.71442i	−0.514970	+	0.857208i	$0.672197\pi$
$450$		0			0
$451$	63.5005			0.140799
$452$	−77.3479	−	288.666i	−0.171124	−	0.638642i
$453$		0			0
$454$	43.0143	−	24.8343i	0.0947452	−	0.0547012i
$455$	−60.6524	−	34.3752i	−0.133302	−	0.0755499i
$456$		0			0
$457$	−4.67380	−	17.4429i	−0.0102271	−	0.0381682i	0.960624	−	0.277853i	$-0.0896227\pi$
$457$	−4.67380	−	17.4429i	−0.0102271	−	0.0381682i	−0.970851	+	0.239684i	$0.922956\pi$
$458$	−140.049	−	140.049i	−0.305784	−	0.305784i
$459$		0			0
$460$	−77.4786	+	298.668i	−0.168432	+	0.649279i
$461$	294.578	−	510.225i	0.638999	−	1.10678i	−0.346654	−	0.937993i	$-0.612682\pi$
$461$	294.578	−	510.225i	0.638999	−	1.10678i	0.985653	−	0.168785i	$-0.0539844\pi$
$462$		0			0
$463$	−169.498	+	632.574i	−0.366086	+	1.36625i	0.499857	+	0.866108i	$0.333386\pi$
$463$	−169.498	+	632.574i	−0.366086	+	1.36625i	−0.865943	+	0.500143i	$0.833281\pi$
$464$	−184.395	+	106.460i	−0.397403	+	0.229441i
$465$		0			0
$466$	127.973	−	221.655i	0.274619	−	0.475655i
$467$	61.7235	−	61.7235i	0.132170	−	0.132170i	−0.637927	−	0.770097i	$-0.720208\pi$
$467$	61.7235	−	61.7235i	0.132170	−	0.132170i	0.770097	+	0.637927i	$0.220208\pi$
$468$		0			0
$469$			202.667i			0.432126i
$470$	80.2049	−	0.640111i	0.170649	−	0.00136194i
$471$		0			0
$472$	278.867	+	74.7222i	0.590820	+	0.158310i
$473$	−15.1629	+	56.5887i	−0.0320569	+	0.119638i
$474$		0			0
$475$	−368.982	+	220.958i	−0.776803	+	0.465175i
$476$	−189.721			−0.398573
$477$		0			0
$478$	72.0469	+	72.0469i	0.150726	+	0.150726i
$479$	−141.705	−	81.8136i	−0.295836	−	0.170801i	0.344735	−	0.938700i	$-0.387969\pi$
$479$	−141.705	−	81.8136i	−0.295836	−	0.170801i	−0.640571	+	0.767899i	$0.721302\pi$
$480$		0			0
$481$	18.4962	+	32.0364i	0.0384537	+	0.0666037i
$482$	366.751	+	98.2708i	0.760895	+	0.203881i
$483$		0			0
$484$	−206.728	−	119.355i	−0.427124	−	0.246600i
$485$	−200.430	+	772.627i	−0.413257	+	1.59304i
$486$		0			0
$487$	−359.366	+	359.366i	−0.737918	+	0.737918i	−0.972175	−	0.234257i	$-0.924734\pi$
$487$	−359.366	+	359.366i	−0.737918	+	0.737918i	0.234257	+	0.972175i	$0.424734\pi$
$488$	−143.936	+	38.5674i	−0.294950	+	0.0790316i
$489$		0			0
$490$	70.4200	+	254.664i	0.143714	+	0.519722i
$491$	28.5143	+	49.3883i	0.0580740	+	0.100587i	0.893601	−	0.448863i	$-0.148171\pi$
$491$	28.5143	+	49.3883i	0.0580740	+	0.100587i	−0.835527	+	0.549450i	$0.814837\pi$
$492$		0			0
$493$	1429.98	−	383.163i	2.90058	−	0.777207i
$494$			99.4567i			0.201329i
$495$		0			0
$496$	−107.012			−0.215750
$497$	4.89303	+	18.2610i	0.00984512	+	0.0367425i
$498$		0			0
$499$	−767.997	+	443.403i	−1.53907	+	0.888584i	−0.540179	+	0.841550i	$0.681643\pi$
$499$	−767.997	+	443.403i	−1.53907	+	0.888584i	−0.998893	+	0.0470334i	$0.985023\pi$
$500$	130.147	+	213.452i	0.260295	+	0.426904i
$501$		0			0
$502$	91.9488	+	343.158i	0.183165	+	0.683581i
$503$	70.9445	+	70.9445i	0.141043	+	0.141043i	0.774103	−	0.633060i	$-0.218201\pi$
$503$	70.9445	+	70.9445i	0.141043	+	0.141043i	−0.633060	+	0.774103i	$0.718201\pi$
$504$		0			0
$505$	−320.387	+	188.401i	−0.634429	+	0.373070i
$506$	27.9869	−	48.4747i	0.0553100	−	0.0957998i
$507$		0			0
$508$	81.5615	−	304.392i	0.160554	−	0.599196i
$509$	190.984	−	110.265i	0.375214	−	0.216630i	−0.300520	−	0.953776i	$-0.597160\pi$
$509$	190.984	−	110.265i	0.375214	−	0.216630i	0.675734	+	0.737146i	$0.263827\pi$
$510$		0			0
$511$	−117.941	+	204.280i	−0.230805	+	0.399765i
$512$	−16.0000	+	16.0000i	−0.0312500	+	0.0312500i
$513$		0			0
$514$			114.236i			0.222248i
$515$	55.6927	−	56.5889i	0.108141	−	0.109881i
$516$		0			0
$517$	−14.0544	−	3.76586i	−0.0271845	−	0.00728406i
$518$	−11.2972	+	42.1618i	−0.0218093	+	0.0813934i
$519$		0			0
$520$	57.8109	−	0.461386i	0.111175	−	0.000887281i
$521$	−315.280			−0.605144			−0.302572	−	0.953127i	$-0.597845\pi$
$521$	−315.280			−0.605144			−0.302572	+	0.953127i	$0.597845\pi$
$522$		0			0
$523$	550.337	+	550.337i	1.05227	+	1.05227i	0.998556	+	0.0537127i	$0.0171055\pi$
$523$	550.337	+	550.337i	1.05227	+	1.05227i	0.0537127	+	0.998556i	$0.482894\pi$
$524$	7.10308	+	4.10096i	0.0135555	+	0.00782627i
$525$		0			0
$526$	−101.458	−	175.730i	−0.192885	−	0.334087i
$527$	718.698	+	192.575i	1.36375	+	0.365417i
$528$		0			0
$529$	−366.379	−	211.529i	−0.692588	−	0.399866i
$530$	1.50830	−	0.886942i	0.00284585	−	0.00167348i
$531$		0			0
$532$	−82.9815	+	82.9815i	−0.155980	+	0.155980i
$533$	−195.475	+	52.3775i	−0.366745	+	0.0982692i
$534$		0			0
$535$	780.542	−	215.837i	1.45896	−	0.403433i
$536$	−84.0317	−	145.547i	−0.156776	−	0.271543i
$537$		0			0
$538$	−466.440	+	124.982i	−0.866989	+	0.232309i
$539$		−	47.9314i		−	0.0889265i
$540$		0			0
$541$	86.5875			0.160051			0.0800254	−	0.996793i	$-0.474500\pi$
$541$	86.5875			0.160051			0.0800254	+	0.996793i	$0.474500\pi$
$542$	−57.5119	−	214.637i	−0.106110	−	0.396010i
$543$		0			0
$544$	136.250	−	78.6637i	0.250459	−	0.144602i
$545$	−197.691	+	348.811i	−0.362736	+	0.640020i
$546$		0			0
$547$	131.665	+	491.379i	0.240703	+	0.898317i	0.975495	+	0.220024i	$0.0706135\pi$
$547$	131.665	+	491.379i	0.240703	+	0.898317i	−0.734791	+	0.678293i	$0.762720\pi$
$548$	197.022	+	197.022i	0.359529	+	0.359529i
$549$		0			0
$550$	−12.4356	−	43.6134i	−0.0226101	−	0.0792971i
$551$	457.866	−	793.047i	0.830973	−	1.43929i
$552$		0			0
$553$	−86.3611	+	322.304i	−0.156168	+	0.582828i
$554$	−204.710	+	118.189i	−0.369513	+	0.213338i
$555$		0			0
$556$	23.3971	−	40.5249i	0.0420811	−	0.0728865i
$557$	145.517	−	145.517i	0.261252	−	0.261252i	−0.564311	−	0.825563i	$-0.690858\pi$
$557$	145.517	−	145.517i	0.261252	−	0.261252i	0.825563	+	0.564311i	$0.190858\pi$
$558$		0			0
$559$		−	186.706i		−	0.333999i
$560$	48.6194	+	47.8494i	0.0868203	+	0.0854454i
$561$		0			0
$562$	275.202	+	73.7401i	0.489683	+	0.131210i
$563$	132.511	−	494.539i	0.235366	−	0.878399i	−0.742617	−	0.669716i	$-0.766416\pi$
$563$	132.511	−	494.539i	0.235366	−	0.878399i	0.977983	−	0.208683i	$-0.0669177\pi$
$564$		0			0
$565$	524.063	−	532.496i	0.927545	−	0.942470i
$566$	84.1024			0.148591
$567$		0			0
$568$	−11.0855	−	11.0855i	−0.0195167	−	0.0195167i
$569$	334.415	+	193.075i	0.587724	+	0.339323i	0.764197	−	0.644983i	$-0.223135\pi$
$569$	334.415	+	193.075i	0.587724	+	0.339323i	−0.176473	+	0.984306i	$0.556469\pi$
$570$		0			0
$571$	−76.7904	−	133.005i	−0.134484	−	0.232933i	0.790916	−	0.611924i	$-0.209604\pi$
$571$	−76.7904	−	133.005i	−0.134484	−	0.232933i	−0.925400	+	0.378991i	$0.876271\pi$
$572$	−10.1303	−	2.71439i	−0.0177102	−	0.00474544i
$573$		0			0
$574$	−206.795	−	119.393i	−0.360271	−	0.208002i
$575$	−741.820	+	211.516i	−1.29012	+	0.367855i
$576$		0			0
$577$	−115.299	+	115.299i	−0.199825	+	0.199825i	−0.799925	−	0.600100i	$-0.795127\pi$
$577$	−115.299	+	115.299i	−0.199825	+	0.199825i	0.600100	+	0.799925i	$0.295127\pi$
$578$	−661.836	+	177.338i	−1.14504	+	0.306814i
$579$		0			0
$580$	−463.096	−	262.464i	−0.798442	−	0.452523i
$581$	122.924	+	212.910i	0.211572	+	0.366454i
$582$		0			0
$583$	−0.306601	+	0.0821535i	−0.000525902	+	0.000140915i
$584$		−	195.607i		−	0.334944i
$585$		0			0
$586$	−455.815			−0.777841
$587$	−58.3833	−	217.890i	−0.0994606	−	0.371192i	0.898197	−	0.439592i	$-0.144877\pi$
$587$	−58.3833	−	217.890i	−0.0994606	−	0.371192i	−0.997658	+	0.0684005i	$0.978210\pi$
$588$		0			0
$589$	398.579	−	230.120i	0.676704	−	0.390695i
$590$	192.363	+	695.654i	0.326040	+	1.17907i
$591$		0			0
$592$	−9.36830	−	34.9630i	−0.0158248	−	0.0590591i
$593$	250.553	+	250.553i	0.422518	+	0.422518i	0.886070	−	0.463552i	$-0.153425\pi$
$593$	250.553	+	250.553i	0.422518	+	0.422518i	−0.463552	+	0.886070i	$0.653425\pi$
$594$		0			0
$595$	−240.422	−	408.852i	−0.404070	−	0.687146i
$596$	−225.492	+	390.563i	−0.378342	+	0.655307i
$597$		0			0
$598$	−46.1691	+	172.306i	−0.0772059	+	0.288136i
$599$	390.471	−	225.439i	0.651871	−	0.376358i	−0.137301	−	0.990529i	$-0.543843\pi$
$599$	390.471	−	225.439i	0.651871	−	0.376358i	0.789173	+	0.614171i	$0.210510\pi$
$600$		0			0
$601$	184.215	−	319.070i	0.306514	−	0.530898i	−0.671083	−	0.741382i	$-0.734171\pi$
$601$	184.215	−	319.070i	0.306514	−	0.530898i	0.977597	+	0.210484i	$0.0675040\pi$
$602$	155.777	−	155.777i	0.258766	−	0.258766i
$603$		0			0
$604$		−	497.376i		−	0.823470i
$605$	−4.76266	−	596.754i	−0.00787217	−	0.986370i
$606$		0			0
$607$	606.509	+	162.514i	0.999191	+	0.267733i	0.721107	−	0.692824i	$-0.243634\pi$
$607$	606.509	+	162.514i	0.999191	+	0.267733i	0.278085	+	0.960557i	$0.410300\pi$
$608$	25.1873	−	94.0003i	0.0414265	−	0.154606i
$609$		0			0
$610$	−265.514	−	261.310i	−0.435269	−	0.428377i
$611$	46.3701			0.0758922
$612$		0			0
$613$	−530.799	−	530.799i	−0.865904	−	0.865904i	0.126112	−	0.992016i	$-0.459750\pi$
$613$	−530.799	−	530.799i	−0.865904	−	0.865904i	−0.992016	+	0.126112i	$0.959750\pi$
$614$	−113.632	−	65.6054i	−0.185068	−	0.106849i
$615$		0			0
$616$	−6.18740	−	10.7169i	−0.0100445	−	0.0173976i
$617$	399.394	+	107.017i	0.647316	+	0.173448i	0.567515	−	0.823363i	$-0.307905\pi$
$617$	399.394	+	107.017i	0.647316	+	0.173448i	0.0798010	+	0.996811i	$0.474572\pi$
$618$		0			0
$619$	311.398	+	179.786i	0.503066	+	0.290445i	0.729979	−	0.683470i	$-0.239530\pi$
$619$	311.398	+	179.786i	0.503066	+	0.290445i	−0.226913	+	0.973915i	$0.572863\pi$
$620$	−135.610	−	230.613i	−0.218726	−	0.371957i
$621$		0			0
$622$	−243.797	+	243.797i	−0.391957	+	0.391957i
$623$	−154.704	+	41.4529i	−0.248322	+	0.0665376i
$624$		0			0
$625$	−295.065	+	550.964i	−0.472104	+	0.881543i
$626$	166.484	+	288.358i	0.265948	+	0.460636i
$627$		0			0
$628$	−104.330	+	27.9552i	−0.166131	+	0.0445146i
$629$			251.671i			0.400113i
$630$		0			0
$631$	1215.94			1.92701			0.963505	−	0.267690i	$-0.0862602\pi$
$631$	1215.94			1.92701			0.963505	+	0.267690i	$0.0862602\pi$
$632$	−71.6156	−	267.273i	−0.113316	−	0.422900i
$633$		0			0
$634$	579.977	−	334.850i	0.914790	−	0.528154i
$635$	759.328	−	209.970i	1.19579	−	0.330662i
$636$		0			0
$637$	39.5355	+	147.548i	0.0620651	+	0.231630i
$638$	68.2804	+	68.2804i	0.107023	+	0.107023i
$639$		0			0
$640$	−54.7561	−	14.2045i	−0.0855564	−	0.0221945i
$641$	−273.901	+	474.411i	−0.427303	+	0.740111i	−0.996632	−	0.0819986i	$-0.973870\pi$
$641$	−273.901	+	474.411i	−0.427303	+	0.740111i	0.569329	+	0.822110i	$0.307203\pi$
$642$		0			0
$643$	189.239	−	706.250i	0.294306	−	1.09837i	−0.647460	−	0.762099i	$-0.724169\pi$
$643$	189.239	−	706.250i	0.294306	−	1.09837i	0.941767	−	0.336267i	$-0.109165\pi$
$644$	−182.284	+	105.242i	−0.283049	+	0.163419i
$645$		0			0
$646$	−338.318	+	585.984i	−0.523712	+	0.907095i
$647$	374.569	−	374.569i	0.578932	−	0.578932i	−0.355677	−	0.934609i	$-0.615750\pi$
$647$	374.569	−	374.569i	0.578932	−	0.578932i	0.934609	+	0.355677i	$0.115750\pi$
$648$		0			0
$649$		−	130.932i		−	0.201744i
$650$	74.2545	+	123.999i	0.114238	+	0.190768i
$651$		0			0
$652$	−314.389	−	84.2403i	−0.482192	−	0.129203i
$653$	233.065	−	869.812i	0.356915	−	1.33202i	−0.521143	−	0.853470i	$-0.674494\pi$
$653$	233.065	−	869.812i	0.356915	−	1.33202i	0.878058	−	0.478555i	$-0.158839\pi$
$654$		0			0
$655$	0.163643	+	20.5042i	0.000249836	+	0.0313041i
$656$	198.016			0.301853
$657$		0			0
$658$	38.6888	+	38.6888i	0.0587976	+	0.0587976i
$659$	−131.147	−	75.7178i	−0.199009	−	0.114898i	0.397184	−	0.917739i	$-0.369987\pi$
$659$	−131.147	−	75.7178i	−0.199009	−	0.114898i	−0.596193	+	0.802841i	$0.703321\pi$
$660$		0			0
$661$	−26.7023	−	46.2498i	−0.0403969	−	0.0699695i	0.845120	−	0.534577i	$-0.179529\pi$
$661$	−26.7023	−	46.2498i	−0.0403969	−	0.0699695i	−0.885517	+	0.464607i	$0.846196\pi$
$662$	−336.263	−	90.1013i	−0.507950	−	0.136105i
$663$		0			0
$664$	−176.557	−	101.935i	−0.265899	−	0.153517i
$665$	−283.984	−	73.6693i	−0.427044	−	0.110781i
$666$		0			0
$667$	1161.38	−	1161.38i	1.74120	−	1.74120i
$668$	604.760	−	162.045i	0.905329	−	0.242582i
$669$		0			0
$670$	207.169	−	365.533i	0.309207	−	0.545571i
$671$	33.7899	+	58.5259i	0.0503576	+	0.0872219i
$672$		0			0
$673$	−645.366	+	172.925i	−0.958939	+	0.256947i	−0.704151	−	0.710050i	$-0.748672\pi$
$673$	−645.366	+	172.925i	−0.958939	+	0.256947i	−0.254788	+	0.966997i	$0.582006\pi$
$674$		−	637.529i		−	0.945889i
$675$		0			0
$676$	−304.577			−0.450557
$677$	139.481	+	520.551i	0.206028	+	0.768908i	0.989134	+	0.147019i	$0.0469678\pi$
$677$	139.481	+	520.551i	0.206028	+	0.768908i	−0.783105	+	0.621889i	$0.786365\pi$
$678$		0			0
$679$	−471.551	+	272.250i	−0.694478	+	0.400957i
$680$	342.182	+	193.935i	0.503210	+	0.285198i
$681$		0			0
$682$	12.5609	+	46.8781i	0.0184178	+	0.0687362i
$683$	−40.8892	−	40.8892i	−0.0598670	−	0.0598670i	0.676539	−	0.736406i	$-0.263479\pi$
$683$	−40.8892	−	40.8892i	−0.0598670	−	0.0598670i	−0.736406	+	0.676539i	$0.763479\pi$
$684$		0			0
$685$	−174.912	+	674.260i	−0.255346	+	0.984321i
$686$	−208.298	+	360.783i	−0.303642	+	0.525923i
$687$		0			0
$688$	−47.2830	+	176.462i	−0.0687252	+	0.256486i
$689$	0.876055	−	0.505790i	0.00127149	−	0.000734093i
$690$		0			0
$691$	−402.556	+	697.247i	−0.582570	+	1.00904i	0.412604	+	0.910911i	$0.364619\pi$
$691$	−402.556	+	697.247i	−0.582570	+	1.00904i	−0.995174	+	0.0981299i	$0.968714\pi$
$692$	−306.467	+	306.467i	−0.442871	+	0.442871i
$693$		0			0
$694$		−	376.285i		−	0.542197i
$695$	116.982	−	0.933625i	0.168319	−	0.00134335i
$696$		0			0
$697$	−1329.88	−	356.340i	−1.90801	−	0.511249i
$698$	41.9561	−	156.582i	0.0601091	−	0.224330i
$699$		0			0
$700$	−41.5041	+	165.412i	−0.0592916	+	0.236303i
$701$	−1140.79			−1.62738			−0.813690	−	0.581299i	$-0.802545\pi$
$701$	−1140.79			−1.62738			−0.813690	+	0.581299i	$0.802545\pi$
$702$		0			0
$703$	110.078	+	110.078i	0.156583	+	0.156583i
$704$	8.88707	+	5.13095i	0.0126237	+	0.00728828i
$705$		0			0
$706$	−72.6933	−	125.909i	−0.102965	−	0.178341i
$707$	−244.902	−	65.6214i	−0.346397	−	0.0928167i
$708$		0			0
$709$	641.044	+	370.107i	0.904152	+	0.522013i	0.878545	−	0.477659i	$-0.158515\pi$
$709$	641.044	+	370.107i	0.904152	+	0.522013i	0.0256073	+	0.999672i	$0.491848\pi$
$710$	9.84149	−	37.9375i	0.0138613	−	0.0534330i
$711$		0			0
$712$	93.9146	−	93.9146i	0.131903	−	0.131903i
$713$	797.349	−	213.649i	1.11830	−	0.299648i
$714$		0			0
$715$	−6.98788	−	25.2707i	−0.00977326	−	0.0353436i
$716$	−164.771	−	285.391i	−0.230127	−	0.398591i
$717$		0			0
$718$	−260.780	+	69.8758i	−0.363203	+	0.0973201i
$719$		−	595.037i		−	0.827590i	−0.910370	−	0.413795i	$-0.864203\pi$
$719$		−	595.037i		−	0.827590i	0.910370	−	0.413795i	$-0.135797\pi$
$720$		0			0
$721$	54.1618			0.0751204
$722$	−23.8093	−	88.8576i	−0.0329769	−	0.123071i
$723$		0			0
$724$	9.16742	−	5.29281i	0.0126622	−	0.00731052i
$725$	−21.2400	−	1330.59i	−0.0292966	−	1.83529i
$726$		0			0
$727$	−285.714	−	1066.30i	−0.393004	−	1.46671i	−0.825153	−	0.564910i	$-0.808911\pi$
$727$	−285.714	−	1066.30i	−0.393004	−	1.46671i	0.432148	−	0.901803i	$-0.357756\pi$
$728$	27.8865	+	27.8865i	0.0383057	+	0.0383057i
$729$		0			0
$730$	421.537	−	247.881i	0.577448	−	0.339563i
$731$	635.108	−	1100.04i	0.868821	−	1.50484i
$732$		0			0
$733$	−56.5121	+	210.906i	−0.0770970	+	0.287730i	−0.993701	−	0.112067i	$-0.964253\pi$
$733$	−56.5121	+	210.906i	−0.0770970	+	0.287730i	0.916604	+	0.399797i	$0.130919\pi$
$734$	641.769	−	370.526i	0.874345	−	0.504803i
$735$		0			0
$736$	87.2724	−	151.160i	0.118577	−	0.205381i
$737$	−53.8953	+	53.8953i	−0.0731279	+	0.0731279i
$738$		0			0
$739$			393.578i			0.532583i	0.963893	+	0.266291i	$0.0857983\pi$
$739$			393.578i			0.532583i	−0.963893	+	0.266291i	$0.914202\pi$
$740$	63.4740	−	64.4953i	0.0857756	−	0.0871558i
$741$		0			0
$742$	1.15294	+	0.308929i	0.00155383	+	0.000416346i
$743$	−249.966	+	932.885i	−0.336428	+	1.25557i	0.565885	+	0.824484i	$0.308535\pi$
$743$	−249.966	+	932.885i	−0.336428	+	1.25557i	−0.902313	+	0.431082i	$0.858132\pi$
$744$		0			0
$745$	−1127.42	+	8.99790i	−1.51332	+	0.0120777i
$746$	−310.650			−0.416421
$747$		0			0
$748$	−50.4524	−	50.4524i	−0.0674498	−	0.0674498i
$749$	478.423	+	276.218i	0.638749	+	0.368782i
$750$		0			0
$751$	−112.720	−	195.237i	−0.150093	−	0.259969i	0.781168	−	0.624320i	$-0.214624\pi$
$751$	−112.720	−	195.237i	−0.150093	−	0.259969i	−0.931262	+	0.364351i	$0.881291\pi$
$752$	−43.8262	−	11.7432i	−0.0582795	−	0.0156159i
$753$		0			0
$754$	−266.509	−	153.869i	−0.353461	−	0.204071i
$755$	1071.85	−	630.294i	1.41967	−	0.834826i
$756$		0			0
$757$	257.146	−	257.146i	0.339691	−	0.339691i	−0.516560	−	0.856251i	$-0.672788\pi$
$757$	257.146	−	257.146i	0.339691	−	0.339691i	0.856251	+	0.516560i	$0.172788\pi$
$758$	−740.902	+	198.524i	−0.977443	+	0.261905i
$759$		0			0
$760$	234.491	−	64.8417i	0.308540	−	0.0853181i
$761$	405.656	+	702.618i	0.533057	+	0.923282i	0.999255	+	0.0386014i	$0.0122903\pi$
$761$	405.656	+	702.618i	0.533057	+	0.923282i	−0.466198	+	0.884681i	$0.654376\pi$
$762$		0			0
$763$	−264.184	+	70.7878i	−0.346243	+	0.0927757i
$764$		−	158.831i		−	0.207894i
$765$		0			0
$766$	477.278			0.623079
$767$	107.997	+	403.052i	0.140805	+	0.525491i
$768$		0			0
$769$	239.236	−	138.123i	0.311100	−	0.179614i	−0.336318	−	0.941748i	$-0.609182\pi$
$769$	239.236	−	138.123i	0.311100	−	0.179614i	0.647419	+	0.762134i	$0.275848\pi$
$770$	15.2542	−	26.9148i	0.0198106	−	0.0349543i
$771$		0			0
$772$	−87.9532	−	328.246i	−0.113929	−	0.425189i
$773$	246.810	+	246.810i	0.319288	+	0.319288i	0.848494	−	0.529205i	$-0.177510\pi$
$773$	246.810	+	246.810i	0.319288	+	0.319288i	−0.529205	+	0.848494i	$0.677510\pi$
$774$		0			0
$775$	325.126	−	584.484i	0.419517	−	0.754173i
$776$	225.765	−	391.037i	0.290934	−	0.503913i
$777$		0			0
$778$	−63.9686	+	238.734i	−0.0822219	+	0.306856i
$779$	−737.532	+	425.814i	−0.946767	+	0.546616i
$780$		0			0
$781$	−3.55495	+	6.15735i	−0.00455179	+	0.00788393i
$782$	−858.146	+	858.146i	−1.09737	+	1.09737i
$783$		0			0
$784$		−	149.466i		−	0.190645i
$785$	−192.455	−	189.407i	−0.245166	−	0.241283i
$786$		0			0
$787$	−324.226	−	86.8762i	−0.411978	−	0.110389i	0.0468765	−	0.998901i	$-0.485073\pi$
$787$	−324.226	−	86.8762i	−0.411978	−	0.110389i	−0.458854	+	0.888512i	$0.651740\pi$
$788$	−27.9447	+	104.291i	−0.0354629	+	0.132349i
$789$		0			0
$790$	485.224	−	493.032i	0.614208	−	0.624091i
$791$	509.657			0.644320
$792$		0			0
$793$	−152.291	−	152.291i	−0.192044	−	0.192044i
$794$	432.993	+	249.989i	0.545332	+	0.314847i
$795$		0			0
$796$	−90.0401	−	155.954i	−0.113116	−	0.195922i
$797$	−737.163	−	197.522i	−0.924922	−	0.247832i	−0.235234	−	0.971939i	$-0.575586\pi$
$797$	−737.163	−	197.522i	−0.924922	−	0.247832i	−0.689688	+	0.724107i	$0.742252\pi$
$798$		0			0
$799$	273.206	+	157.735i	0.341935	+	0.197416i
$800$	−38.7782	−	136.001i	−0.0484727	−	0.170001i
$801$		0			0
$802$	131.561	−	131.561i	0.164041	−	0.164041i
$803$	−85.6883	+	22.9601i	−0.106710	+	0.0285929i
$804$		0			0
$805$	−457.795	−	259.459i	−0.568689	−	0.322309i
$806$	−77.3334	−	133.945i	−0.0959471	−	0.166185i
$807$		0			0
$808$	203.087	−	54.4170i	0.251346	−	0.0673478i
$809$			195.169i			0.241248i	0.992698	+	0.120624i	$0.0384895\pi$
$809$			195.169i			0.241248i	−0.992698	+	0.120624i	$0.961511\pi$
$810$		0			0
$811$	−1111.22			−1.37018			−0.685090	−	0.728459i	$-0.740237\pi$
$811$	−1111.22			−1.37018			−0.685090	+	0.728459i	$0.740237\pi$
$812$	−93.9810	−	350.742i	−0.115740	−	0.431948i
$813$		0			0
$814$	−14.2163	+	8.20781i	−0.0174648	+	0.0100833i
$815$	−216.867	−	784.267i	−0.266094	−	0.962290i
$816$		0			0
$817$	−203.355	−	758.932i	−0.248905	−	0.928925i
$818$	457.799	+	457.799i	0.559656	+	0.559656i
$819$		0			0
$820$	250.933	+	426.727i	0.306016	+	0.520399i
$821$	−679.281	+	1176.55i	−0.827382	+	1.43307i	0.0727025	+	0.997354i	$0.476838\pi$
$821$	−679.281	+	1176.55i	−0.827382	+	1.43307i	−0.900085	+	0.435715i	$0.856496\pi$
$822$		0			0
$823$	289.667	−	1081.05i	0.351965	−	1.31355i	−0.532295	−	0.846559i	$-0.678670\pi$
$823$	289.667	−	1081.05i	0.351965	−	1.31355i	0.884261	−	0.466994i	$-0.154663\pi$
$824$	−38.8967	+	22.4570i	−0.0472048	+	0.0272537i
$825$		0			0
$826$	−246.178	+	426.392i	−0.298036	+	0.516214i
$827$	346.428	−	346.428i	0.418897	−	0.418897i	−0.465926	−	0.884823i	$-0.654279\pi$
$827$	346.428	−	346.428i	0.418897	−	0.418897i	0.884823	+	0.465926i	$0.154279\pi$
$828$		0			0
$829$			1353.95i			1.63324i	0.577178	+	0.816618i	$0.304154\pi$
$829$			1353.95i			1.63324i	−0.577178	+	0.816618i	$0.695846\pi$
$830$	−4.06757	−	509.660i	−0.00490069	−	0.614048i
$831$		0			0
$832$	−31.5895	−	8.46438i	−0.0379681	−	0.0101735i
$833$	−268.972	+	1003.82i	−0.322896	+	1.20506i
$834$		0			0
$835$	1115.59	+	1097.92i	1.33603	+	1.31487i
$836$	−44.1345			−0.0527925
$837$		0			0
$838$	205.557	+	205.557i	0.245295	+	0.245295i
$839$	−953.073	−	550.257i	−1.13596	−	0.655849i	−0.190535	−	0.981680i	$-0.561022\pi$
$839$	−953.073	−	550.257i	−1.13596	−	0.655849i	−0.945428	+	0.325832i	$0.894356\pi$
$840$		0			0
$841$	996.227	+	1725.52i	1.18457	+	2.05174i
$842$	−92.8541	−	24.8802i	−0.110278	−	0.0295489i
$843$		0			0
$844$	643.663	+	371.619i	0.762634	+	0.440307i
$845$	−385.972	−	656.369i	−0.456771	−	0.776768i
$846$		0			0
$847$	287.859	−	287.859i	0.339857	−	0.339857i
$848$	−0.956083	+	0.256182i	−0.00112746	+	0.000302101i
$849$		0			0
$850$	15.6943	+	983.171i	0.0184639	+	1.15667i
$851$	139.607	+	241.806i	0.164050	+	0.284143i
$852$		0			0
$853$	37.7424	−	10.1130i	0.0442467	−	0.0118559i	−0.236628	−	0.971600i	$-0.576042\pi$
$853$	37.7424	−	10.1130i	0.0442467	−	0.0118559i	0.280874	+	0.959745i	$0.409376\pi$
$854$		−	254.127i		−	0.297572i
$855$		0			0
$856$	−458.111			−0.535177
$857$	235.052	+	877.224i	0.274273	+	1.02360i	0.956327	+	0.292298i	$0.0944199\pi$
$857$	235.052	+	877.224i	0.274273	+	1.02360i	−0.682055	+	0.731301i	$0.738913\pi$
$858$		0			0
$859$	1116.53	−	644.631i	1.29981	−	0.750443i	0.319436	−	0.947608i	$-0.396507\pi$
$859$	1116.53	−	644.631i	1.29981	−	0.750443i	0.980370	+	0.197165i	$0.0631733\pi$
$860$	−440.199	+	121.724i	−0.511859	+	0.141540i
$861$		0			0
$862$	36.4578	+	136.062i	0.0422944	+	0.157845i
$863$	230.587	+	230.587i	0.267193	+	0.267193i	0.827968	−	0.560775i	$-0.189497\pi$
$863$	230.587	+	230.587i	0.267193	+	0.267193i	−0.560775	+	0.827968i	$0.689497\pi$
$864$		0			0
$865$	−1048.81	−	272.075i	−1.21249	−	0.314537i
$866$	−459.635	+	796.111i	−0.530756	+	0.919296i
$867$		0			0
$868$	47.2340	−	176.280i	0.0544171	−	0.203087i
$869$	−108.676	+	62.7443i	−0.125059	+	0.0722029i
$870$		0			0
$871$	121.453	−	210.362i	0.139440	−	0.241518i
$872$	160.375	−	160.375i	0.183916	−	0.183916i
$873$		0			0
$874$			750.684i			0.858906i
$875$	−409.062	+	120.175i	−0.467500	+	0.137343i
$876$		0			0
$877$	−763.671	−	204.625i	−0.870777	−	0.233324i	−0.204353	−	0.978897i	$-0.565509\pi$
$877$	−763.671	−	204.625i	−0.870777	−	0.233324i	−0.666424	+	0.745573i	$0.732176\pi$
$878$	21.3512	−	79.6837i	0.0243180	−	0.0907559i
$879$		0			0
$880$	0.204743	+	25.6539i	0.000232662	+	0.0291522i
$881$	569.305			0.646204			0.323102	−	0.946364i	$-0.395274\pi$
$881$	569.305			0.646204			0.323102	+	0.946364i	$0.395274\pi$
$882$		0			0
$883$	34.5889	+	34.5889i	0.0391720	+	0.0391720i	0.726421	−	0.687249i	$-0.241182\pi$
$883$	34.5889	+	34.5889i	0.0391720	+	0.0391720i	−0.687249	+	0.726421i	$0.741182\pi$
$884$	196.924	+	113.694i	0.222765	+	0.128613i
$885$		0			0
$886$	171.243	+	296.602i	0.193277	+	0.334765i
$887$	−1248.03	−	334.410i	−1.40703	−	0.377012i	−0.526165	−	0.850382i	$-0.676371\pi$
$887$	−1248.03	−	334.410i	−1.40703	−	0.377012i	−0.880864	+	0.473370i	$0.843037\pi$
$888$		0			0
$889$	465.420	+	268.711i	0.523532	+	0.302262i
$890$	321.400	+	83.3755i	0.361124	+	0.0936803i
$891$		0			0
$892$	−307.880	+	307.880i	−0.345157	+	0.345157i
$893$	188.488	−	50.5052i	0.211073	−	0.0565568i
$894$		0			0
$895$	406.220	−	716.743i	0.453877	−	0.800830i
$896$	−19.2944	−	33.4188i	−0.0215339	−	0.0372978i
$897$		0			0
$898$	1051.53	−	281.756i	1.17097	−	0.313760i
$899$			1424.07i			1.58406i
$900$		0			0
$901$	6.88210			0.00763830
$902$	−23.2428	−	86.7433i	−0.0257681	−	0.0961678i
$903$		0			0
$904$	−366.014	+	211.318i	−0.404883	+	0.233759i
$905$	23.0234	+	13.0487i	0.0254402	+	0.0144185i
$906$		0			0
$907$	33.2750	+	124.184i	0.0366869	+	0.136917i	0.981840	−	0.189709i	$-0.0607546\pi$
$907$	33.2750	+	124.184i	0.0366869	+	0.136917i	−0.945153	+	0.326627i	$0.894088\pi$
$908$	−49.6687	−	49.6687i	−0.0547012	−	0.0547012i
$909$		0			0
$910$	−24.7571	+	95.4349i	−0.0272056	+	0.104873i
$911$	−756.019	+	1309.46i	−0.829878	+	1.43739i	0.0682558	+	0.997668i	$0.478257\pi$
$911$	−756.019	+	1309.46i	−0.829878	+	1.43739i	−0.898134	+	0.439723i	$0.855077\pi$
$912$		0			0
$913$	−23.9301	+	89.3082i	−0.0262104	+	0.0978184i
$914$	−22.1167	+	12.7691i	−0.0241977	+	0.0139705i
$915$		0			0
$916$	−140.049	+	242.572i	−0.152892	+	0.264817i
$917$	−9.89069	+	9.89069i	−0.0107859	+	0.0107859i
$918$		0			0
$919$			1310.73i			1.42626i	0.701031	+	0.713131i	$0.252724\pi$
$919$			1310.73i			1.42626i	−0.701031	+	0.713131i	$0.747276\pi$
$920$	436.348	−	3.48247i	0.474291	−	0.00378530i
$921$		0			0
$922$	−804.803	−	215.646i	−0.872888	−	0.233890i
$923$	5.86449	−	21.8866i	0.00635373	−	0.0237124i
$924$		0			0
$925$	219.425	+	55.0566i	0.237216	+	0.0595207i
$926$	926.153			1.00017
$927$		0			0
$928$	212.921	+	212.921i	0.229441	+	0.229441i
$929$	450.427	+	260.054i	0.484851	+	0.279929i	0.722436	−	0.691438i	$-0.243022\pi$
$929$	450.427	+	260.054i	0.484851	+	0.279929i	−0.237585	+	0.971367i	$0.576356\pi$
$930$		0			0
$931$	321.412	+	556.703i	0.345233	+	0.597962i
$932$	−349.628	−	93.6824i	−0.375137	−	0.100518i
$933$		0			0
$934$	−106.908	−	61.7235i	−0.114463	−	0.0660851i
$935$	44.7907	−	172.661i	0.0479045	−	0.184664i
$936$		0			0
$937$	−845.208	+	845.208i	−0.902037	+	0.902037i	−0.995612	−	0.0935755i	$-0.970170\pi$
$937$	−845.208	+	845.208i	−0.902037	+	0.902037i	0.0935755	+	0.995612i	$0.470170\pi$
$938$	276.849	−	74.1814i	0.295148	−	0.0790846i
$939$		0			0
$940$	−30.2314	−	109.328i	−0.0321611	−	0.116306i
$941$	630.493	+	1092.05i	0.670025	+	1.16052i	0.977897	+	0.209089i	$0.0670498\pi$
$941$	630.493	+	1092.05i	0.670025	+	1.16052i	−0.307872	+	0.951428i	$0.599617\pi$
$942$		0			0
$943$	−1475.42	+	395.337i	−1.56460	+	0.419233i
$944$		−	408.289i		−	0.432510i
$945$		0			0
$946$	82.8517			0.0875810
$947$	155.755	+	581.287i	0.164472	+	0.613819i	0.998107	+	0.0615028i	$0.0195893\pi$
$947$	155.755	+	581.287i	0.164472	+	0.613819i	−0.833635	+	0.552316i	$0.813744\pi$
$948$		0			0
$949$	244.838	−	141.357i	0.257996	−	0.148954i
$950$	436.891	+	423.162i	0.459885	+	0.445434i
$951$		0			0
$952$	69.4427	+	259.164i	0.0729440	+	0.272231i
$953$	−211.288	−	211.288i	−0.221708	−	0.221708i	0.587509	−	0.809217i	$-0.300109\pi$
$953$	−211.288	−	211.288i	−0.221708	−	0.221708i	−0.809217	+	0.587509i	$0.800109\pi$
$954$		0			0
$955$	342.284	−	201.277i	0.358413	−	0.210761i
$956$	72.0469	−	124.789i	0.0753629	−	0.130532i
$957$		0			0
$958$	−59.8917	+	223.519i	−0.0625174	+	0.233318i
$959$	−411.515	+	237.588i	−0.429109	+	0.247746i
$960$		0			0
$961$	122.637	−	212.414i	0.127614	−	0.221034i
$962$	36.9925	−	36.9925i	0.0384537	−	0.0384537i
$963$		0			0
$964$		−	536.961i		−	0.557014i
$965$	595.918	−	605.506i	0.617531	−	0.627468i
$966$		0			0
$967$	672.007	+	180.064i	0.694940	+	0.186209i	0.588963	−	0.808160i	$-0.299536\pi$
$967$	672.007	+	180.064i	0.694940	+	0.186209i	0.105977	+	0.994369i	$0.466203\pi$
$968$	−87.3736	+	326.083i	−0.0902620	+	0.336862i
$969$		0			0
$970$	1128.79	−	9.00882i	1.16370	−	0.00928744i
$971$	1004.59			1.03459			0.517297	−	0.855806i	$-0.326938\pi$
$971$	1004.59			1.03459			0.517297	+	0.855806i	$0.326938\pi$
$972$		0			0
$973$	56.4290	+	56.4290i	0.0579948	+	0.0579948i
$974$	622.440	+	359.366i	0.639056	+	0.368959i
$975$		0			0
$976$	105.368	+	182.503i	0.107959	+	0.186991i
$977$	−1528.90	−	409.667i	−1.56489	−	0.419311i	−0.630682	−	0.776041i	$-0.717225\pi$
$977$	−1528.90	−	409.667i	−1.56489	−	0.419311i	−0.934208	+	0.356730i	$0.883892\pi$
$978$		0			0
$979$	−52.1641	−	30.1169i	−0.0532830	−	0.0307630i
$980$	322.102	−	189.409i	0.328675	−	0.193274i
$981$		0			0
$982$	57.0287	−	57.0287i	0.0580740	−	0.0580740i
$983$	−791.759	+	212.151i	−0.805451	+	0.215820i	−0.637976	−	0.770056i	$-0.720228\pi$
$983$	−791.759	+	212.151i	−0.805451	+	0.215820i	−0.167475	+	0.985876i	$0.553561\pi$
$984$		0			0
$985$	−260.162	+	71.9404i	−0.264124	+	0.0730360i
$986$	−1046.82	−	1813.15i	−1.06168	−	1.83889i
$987$		0			0
$988$	135.860	−	36.4037i	0.137511	−	0.0368458i
$989$		−	1409.22i		−	1.42490i
$990$		0			0
$991$	−570.979			−0.576164			−0.288082	−	0.957606i	$-0.593018\pi$
$991$	−570.979			−0.576164			−0.288082	+	0.957606i	$0.593018\pi$
$992$	39.1692	+	146.181i	0.0394851	+	0.147360i
$993$		0			0
$994$	23.1540	−	13.3680i	0.0232938	−	0.0134487i
$995$	221.981	−	391.669i	0.223097	−	0.393637i
$996$		0			0
$997$	−305.672	−	1140.78i	−0.306592	−	1.14422i	−0.931567	−	0.363571i	$-0.881557\pi$
$997$	−305.672	−	1140.78i	−0.306592	−	1.14422i	0.624975	−	0.780645i	$-0.285109\pi$
$998$	886.807	+	886.807i	0.888584	+	0.888584i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	270.3.l.b.73.1		24
3.2	odd	2		90.3.k.a.43.4	yes	24
5.2	odd	4	inner	270.3.l.b.127.4		24
9.2	odd	6		810.3.g.k.163.1		12
9.4	even	3	inner	270.3.l.b.253.4		24
9.5	odd	6		90.3.k.a.13.6	yes	24
9.7	even	3		810.3.g.i.163.6		12
15.2	even	4		90.3.k.a.7.6	✓	24
45.2	even	12		810.3.g.k.487.1		12
45.7	odd	12		810.3.g.i.487.6		12
45.22	odd	12	inner	270.3.l.b.37.1		24
45.32	even	12		90.3.k.a.67.4	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.3.k.a.7.6	✓	24	15.2	even	4
90.3.k.a.13.6	yes	24	9.5	odd	6
90.3.k.a.43.4	yes	24	3.2	odd	2
90.3.k.a.67.4	yes	24	45.32	even	12
270.3.l.b.37.1		24	45.22	odd	12	inner
270.3.l.b.73.1		24	1.1	even	1	trivial
270.3.l.b.127.4		24	5.2	odd	4	inner
270.3.l.b.253.4		24	9.4	even	3	inner
810.3.g.i.163.6		12	9.7	even	3
810.3.g.i.487.6		12	45.7	odd	12
810.3.g.k.163.1		12	9.2	odd	6
810.3.g.k.487.1		12	45.2	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 270 = 2 \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	270.l (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.366025 - 1.36603i) q^{2} +(-1.73205 + 1.00000i) q^{4} +(-4.34994 - 2.46536i) q^{5} +(-0.882779 - 3.29458i) q^{7} +(2.00000 + 2.00000i) q^{8} +(-1.77556 + 6.84452i) q^{10} +(0.641369 - 1.11088i) q^{11} +(-1.05805 + 3.94868i) q^{13} +(-4.17735 + 2.41180i) q^{14} +(2.00000 - 3.46410i) q^{16} +(-19.6659 + 19.6659i) q^{17} +17.2032i q^{19} +(9.99968 - 0.0798070i) q^{20} +(-1.75225 - 0.469515i) q^{22} +(-7.98597 + 29.8041i) q^{23} +(12.8440 + 21.4484i) q^{25} +5.78128 q^{26} +(4.82359 + 4.82359i) q^{28} +(-46.0987 - 26.6151i) q^{29} +(-13.3765 - 23.1688i) q^{31} +(-5.46410 - 1.46410i) q^{32} +(34.0624 + 19.6659i) q^{34} +(-4.28229 + 16.5076i) q^{35} +(6.39867 - 6.39867i) q^{37} +(23.5001 - 6.29683i) q^{38} +(-3.76916 - 13.6306i) q^{40} +(24.7520 + 42.8716i) q^{41} +(-44.1156 + 11.8207i) q^{43} +2.56548i q^{44} +43.6362 q^{46} +(-2.93580 - 10.9565i) q^{47} +(32.3603 - 18.6832i) q^{49} +(24.5978 - 25.3958i) q^{50} +(-2.11609 - 7.89737i) q^{52} +(-0.174975 - 0.174975i) q^{53} +(-5.52865 + 3.25107i) q^{55} +(4.82359 - 8.35471i) q^{56} +(-19.4836 + 72.7138i) q^{58} +(88.3973 - 51.0362i) q^{59} +(-26.3420 + 45.6258i) q^{61} +(-26.7530 + 26.7530i) q^{62} +8.00000i q^{64} +(14.3374 - 14.5681i) q^{65} +(-57.3947 - 15.3789i) q^{67} +(14.3965 - 53.7283i) q^{68} +(24.1172 - 0.192478i) q^{70} -5.54275 q^{71} +(-48.9018 - 48.9018i) q^{73} +(-11.0828 - 6.39867i) q^{74} +(-17.2032 - 29.7969i) q^{76} +(-4.22608 - 1.13237i) q^{77} +(-84.7222 - 48.9144i) q^{79} +(-17.2401 + 10.1379i) q^{80} +(49.5039 - 49.5039i) q^{82} +(-69.6231 + 18.6555i) q^{83} +(134.029 - 37.0620i) q^{85} +(32.2949 + 55.9363i) q^{86} +(3.50450 - 0.939029i) q^{88} -46.9573i q^{89} +13.9433 q^{91} +(-15.9719 - 59.6081i) q^{92} +(-13.8923 + 8.02075i) q^{94} +(42.4122 - 74.8331i) q^{95} +(-41.3179 - 154.200i) q^{97} +(-37.3665 - 37.3665i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{2} - 6 q^{7} + 48 q^{8} - 12 q^{10} + 12 q^{11} + 48 q^{16} + 36 q^{17} - 12 q^{20} - 12 q^{22} + 54 q^{23} + 54 q^{25} - 24 q^{28} - 72 q^{31} - 48 q^{32} + 336 q^{35} + 132 q^{37} + 36 q^{38}+ \cdots - 24 q^{98}+O(q^{100}) \) 24 * q + 12 * q^2 - 6 * q^7 + 48 * q^8 - 12 * q^10 + 12 * q^11 + 48 * q^16 + 36 * q^17 - 12 * q^20 - 12 * q^22 + 54 * q^23 + 54 * q^25 - 24 * q^28 - 72 * q^31 - 48 * q^32 + 336 * q^35 + 132 * q^37 + 36 * q^38 + 12 * q^40 - 24 * q^41 + 108 * q^43 + 216 * q^46 - 48 * q^47 - 54 * q^50 - 384 * q^53 - 552 * q^55 - 24 * q^56 + 60 * q^58 - 456 * q^61 - 144 * q^62 - 264 * q^65 + 12 * q^67 + 36 * q^68 + 174 * q^70 + 168 * q^71 - 432 * q^73 - 72 * q^76 + 48 * q^77 - 48 * q^82 + 246 * q^83 + 324 * q^85 - 216 * q^86 + 24 * q^88 + 1224 * q^91 + 108 * q^92 - 432 * q^95 - 102 * q^97 - 24 * q^98

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