LMFDB - Embedded newform 760.2.cg.a.9.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [760,2,Mod(9,760)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(760, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 9, 8]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("760.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 760 = 2^{3} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	760.cg (of order $18$, degree $6$, 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:	$6.06863055362$
Analytic rank:	$0$
Dimension:	$180$
Relative dimension:	$30$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			9.13
Character	$\chi$	$=$	760.9
Dual form			760.2.cg.a.169.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.248287 - 0.295897i) q^{3} +(2.19862 - 0.407498i) q^{5} +(-1.75773 - 1.01483i) q^{7} +(0.495036 - 2.80749i) q^{9} +O(q^{10})$	\(q+(-0.248287 - 0.295897i) q^{3} +(2.19862 - 0.407498i) q^{5} +(-1.75773 - 1.01483i) q^{7} +(0.495036 - 2.80749i) q^{9} +(-2.49808 - 4.32679i) q^{11} +(-3.32037 + 3.95706i) q^{13} +(-0.666467 - 0.549389i) q^{15} +(-2.75531 + 0.485835i) q^{17} +(2.11103 - 3.81360i) q^{19} +(0.136138 + 0.772075i) q^{21} +(-2.36723 - 6.50391i) q^{23} +(4.66789 - 1.79187i) q^{25} +(-1.95719 + 1.12998i) q^{27} +(-0.923331 + 5.23647i) q^{29} +(-3.07542 + 5.32678i) q^{31} +(-0.660045 + 1.81346i) q^{33} +(-4.27813 - 1.51495i) q^{35} +0.614404i q^{37} +1.99529 q^{39} +(3.88992 - 3.26403i) q^{41} +(1.00644 - 2.76516i) q^{43} +(-0.0556491 - 6.37434i) q^{45} +(10.7185 + 1.88996i) q^{47} +(-1.44026 - 2.49460i) q^{49} +(0.827865 + 0.694661i) q^{51} +(-4.43998 - 12.1987i) q^{53} +(-7.25549 - 8.49503i) q^{55} +(-1.65257 + 0.322219i) q^{57} +(0.214362 + 1.21571i) q^{59} +(11.9813 - 4.36085i) q^{61} +(-3.71925 + 4.43243i) q^{63} +(-5.68775 + 10.0531i) q^{65} +(0.339144 + 0.0598002i) q^{67} +(-1.33673 + 2.31529i) q^{69} +(-12.3969 - 4.51209i) q^{71} +(2.77452 + 3.30654i) q^{73} +(-1.68919 - 0.936316i) q^{75} +10.1404i q^{77} +(-1.12187 + 0.941358i) q^{79} +(-7.21632 - 2.62653i) q^{81} +(-6.12427 - 3.53585i) q^{83} +(-5.85991 + 2.19095i) q^{85} +(1.77871 - 1.02694i) q^{87} +(-2.07556 - 1.74160i) q^{89} +(9.85205 - 3.58585i) q^{91} +(2.33976 - 0.412563i) q^{93} +(3.08733 - 9.24491i) q^{95} +(10.4928 - 1.85016i) q^{97} +(-13.3841 + 4.87140i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 180 q+O(q^{10}) $ 180 * q	$ 180 q - 12 q^{15} + 12 q^{25} + 24 q^{35} - 18 q^{41} + 18 q^{45} + 90 q^{49} + 36 q^{51} - 36 q^{55} - 12 q^{59} + 48 q^{69} - 24 q^{71} - 156 q^{79} + 24 q^{81} + 12 q^{85} - 36 q^{89} + 36 q^{91} + 78 q^{95} + 42 q^{99}+O(q^{100}) $ 180 * q - 12 * q^15 + 12 * q^25 + 24 * q^35 - 18 * q^41 + 18 * q^45 + 90 * q^49 + 36 * q^51 - 36 * q^55 - 12 * q^59 + 48 * q^69 - 24 * q^71 - 156 * q^79 + 24 * q^81 + 12 * q^85 - 36 * q^89 + 36 * q^91 + 78 * q^95 + 42 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/760\mathbb{Z}\right)^\times$.

$n$	$191$	$381$	$401$	$457$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{9}\right)$	$-1$

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			0
$2$		0			0
$3$	−0.248287	−	0.295897i	−0.143349	−	0.170836i	0.689593	−	0.724197i	$-0.257789\pi$
$3$	−0.248287	−	0.295897i	−0.143349	−	0.170836i	−0.832942	+	0.553361i	$0.813345\pi$
$4$		0			0
$5$	2.19862	−	0.407498i	0.983254	−	0.182239i
$5$	2.19862	−	0.407498i	0.983254	−	0.182239i
$6$		0			0
$7$	−1.75773	−	1.01483i	−0.664360	−	0.383568i	0.129576	−	0.991569i	$-0.458638\pi$
$7$	−1.75773	−	1.01483i	−0.664360	−	0.383568i	−0.793936	+	0.608001i	$0.791972\pi$
$8$		0			0
$9$	0.495036	−	2.80749i	0.165012	−	0.935829i
$10$		0			0
$11$	−2.49808	−	4.32679i	−0.753198	−	1.30458i	−0.946265	−	0.323392i	$-0.895177\pi$
$11$	−2.49808	−	4.32679i	−0.753198	−	1.30458i	0.193067	−	0.981186i	$-0.438156\pi$
$12$		0			0
$13$	−3.32037	+	3.95706i	−0.920905	+	1.09749i	0.0740581	+	0.997254i	$0.476405\pi$
$13$	−3.32037	+	3.95706i	−0.920905	+	1.09749i	−0.994963	+	0.100238i	$0.968039\pi$
$14$		0			0
$15$	−0.666467	−	0.549389i	−0.172081	−	0.141852i
$16$		0			0
$17$	−2.75531	+	0.485835i	−0.668261	+	0.117832i	−0.497478	−	0.867476i	$-0.665741\pi$
$17$	−2.75531	+	0.485835i	−0.668261	+	0.117832i	−0.170782	+	0.985309i	$0.554630\pi$
$18$		0			0
$19$	2.11103	−	3.81360i	0.484304	−	0.874900i
$19$	2.11103	−	3.81360i	0.484304	−	0.874900i
$20$		0			0
$21$	0.136138	+	0.772075i	0.0297077	+	0.168481i
$22$		0			0
$23$	−2.36723	−	6.50391i	−0.493601	−	1.35616i	−0.897362	−	0.441294i	$-0.854520\pi$
$23$	−2.36723	−	6.50391i	−0.493601	−	1.35616i	0.403761	−	0.914864i	$-0.367703\pi$
$24$		0			0
$25$	4.66789	−	1.79187i	0.933578	−	0.358374i
$26$		0			0
$27$	−1.95719	+	1.12998i	−0.376661	+	0.217465i
$28$		0			0
$29$	−0.923331	+	5.23647i	−0.171458	+	0.972388i	0.770695	+	0.637205i	$0.219909\pi$
$29$	−0.923331	+	5.23647i	−0.171458	+	0.972388i	−0.942153	+	0.335183i	$0.891202\pi$
$30$		0			0
$31$	−3.07542	+	5.32678i	−0.552361	+	0.956717i	0.445743	+	0.895161i	$0.352940\pi$
$31$	−3.07542	+	5.32678i	−0.552361	+	0.956717i	−0.998104	+	0.0615562i	$0.980394\pi$
$32$		0			0
$33$	−0.660045	+	1.81346i	−0.114899	+	0.315683i
$34$		0			0
$35$	−4.27813	−	1.51495i	−0.723136	−	0.256073i
$36$		0			0
$37$			0.614404i			0.101007i	0.998724	+	0.0505037i	$0.0160827\pi$
$37$			0.614404i			0.101007i	−0.998724	+	0.0505037i	$0.983917\pi$
$38$		0			0
$39$	1.99529			0.319502
$40$		0			0
$41$	3.88992	−	3.26403i	0.607503	−	0.509756i	−0.286344	−	0.958127i	$-0.592440\pi$
$41$	3.88992	−	3.26403i	0.607503	−	0.509756i	0.893847	+	0.448371i	$0.147996\pi$
$42$		0			0
$43$	1.00644	−	2.76516i	0.153480	−	0.421683i	−0.838994	−	0.544141i	$-0.816856\pi$
$43$	1.00644	−	2.76516i	0.153480	−	0.421683i	0.992474	+	0.122458i	$0.0390777\pi$
$44$		0			0
$45$	−0.0556491	−	6.37434i	−0.00829568	−	0.950230i
$46$		0			0
$47$	10.7185	+	1.88996i	1.56346	+	0.275679i	0.887340	−	0.461116i	$-0.152551\pi$
$47$	10.7185	+	1.88996i	1.56346	+	0.275679i	0.676115	+	0.736796i	$0.263662\pi$
$48$		0			0
$49$	−1.44026	−	2.49460i	−0.205751	−	0.356371i
$50$		0			0
$51$	0.827865	+	0.694661i	0.115924	+	0.0972720i
$52$		0			0
$53$	−4.43998	−	12.1987i	−0.609878	−	1.67562i	−0.730488	−	0.682925i	$-0.760708\pi$
$53$	−4.43998	−	12.1987i	−0.609878	−	1.67562i	0.120611	−	0.992700i	$-0.461515\pi$
$54$		0			0
$55$	−7.25549	−	8.49503i	−0.978330	−	1.14547i
$56$		0			0
$57$	−1.65257	+	0.322219i	−0.218889	+	0.0426790i
$58$		0			0
$59$	0.214362	+	1.21571i	0.0279076	+	0.158272i	0.995577	−	0.0939508i	$-0.0299496\pi$
$59$	0.214362	+	1.21571i	0.0279076	+	0.158272i	−0.967669	+	0.252222i	$0.918839\pi$
$60$		0			0
$61$	11.9813	−	4.36085i	1.53405	−	0.558350i	0.569444	−	0.822030i	$-0.307159\pi$
$61$	11.9813	−	4.36085i	1.53405	−	0.558350i	0.964610	+	0.263680i	$0.0849364\pi$
$62$		0			0
$63$	−3.71925	+	4.43243i	−0.468582	+	0.558434i
$64$		0			0
$65$	−5.68775	+	10.0531i	−0.705478	+	1.24694i
$66$		0			0
$67$	0.339144	+	0.0598002i	0.0414330	+	0.00730575i	0.194326	−	0.980937i	$-0.437748\pi$
$67$	0.339144	+	0.0598002i	0.0414330	+	0.00730575i	−0.152893	+	0.988243i	$0.548859\pi$
$68$		0			0
$69$	−1.33673	+	2.31529i	−0.160924	+	0.278728i
$70$		0			0
$71$	−12.3969	−	4.51209i	−1.47124	−	0.535487i	−0.522802	−	0.852454i	$-0.675113\pi$
$71$	−12.3969	−	4.51209i	−1.47124	−	0.535487i	−0.948436	+	0.316967i	$0.897335\pi$
$72$		0			0
$73$	2.77452	+	3.30654i	0.324733	+	0.387001i	0.903569	−	0.428442i	$-0.140937\pi$
$73$	2.77452	+	3.30654i	0.324733	+	0.387001i	−0.578836	+	0.815444i	$0.696493\pi$
$74$		0			0
$75$	−1.68919	−	0.936316i	−0.195050	−	0.108116i
$76$		0			0
$77$			10.1404i			1.15561i
$78$		0			0
$79$	−1.12187	+	0.941358i	−0.126220	+	0.105911i	−0.703713	−	0.710485i	$-0.748476\pi$
$79$	−1.12187	+	0.941358i	−0.126220	+	0.105911i	0.577493	+	0.816396i	$0.304031\pi$
$80$		0			0
$81$	−7.21632	−	2.62653i	−0.801813	−	0.291836i
$82$		0			0
$83$	−6.12427	−	3.53585i	−0.672226	−	0.388110i	0.124694	−	0.992195i	$-0.460205\pi$
$83$	−6.12427	−	3.53585i	−0.672226	−	0.388110i	−0.796920	+	0.604086i	$0.793539\pi$
$84$		0			0
$85$	−5.85991	+	2.19095i	−0.635597	+	0.237642i
$86$		0			0
$87$	1.77871	−	1.02694i	0.190697	−	0.110099i
$88$		0			0
$89$	−2.07556	−	1.74160i	−0.220009	−	0.184609i	0.526121	−	0.850410i	$-0.323646\pi$
$89$	−2.07556	−	1.74160i	−0.220009	−	0.184609i	−0.746130	+	0.665800i	$0.768090\pi$
$90$		0			0
$91$	9.85205	−	3.58585i	1.03278	−	0.375900i
$92$		0			0
$93$	2.33976	−	0.412563i	0.242622	−	0.0427808i
$94$		0			0
$95$	3.08733	−	9.24491i	0.316753	−	0.948508i
$96$		0			0
$97$	10.4928	−	1.85016i	1.06538	−	0.187855i	0.386638	−	0.922232i	$-0.373636\pi$
$97$	10.4928	−	1.85016i	1.06538	−	0.187855i	0.678742	+	0.734377i	$0.262525\pi$
$98$		0			0
$99$	−13.3841	+	4.87140i	−1.34515	+	0.489594i
$100$		0			0
$101$	11.0280	+	9.25358i	1.09733	+	0.920765i	0.997242	−	0.0742138i	$-0.0236447\pi$
$101$	11.0280	+	9.25358i	1.09733	+	0.920765i	0.100083	+	0.994979i	$0.468089\pi$
$102$		0			0
$103$	5.65583	−	3.26540i	0.557286	−	0.321749i	−0.194769	−	0.980849i	$-0.562396\pi$
$103$	5.65583	−	3.26540i	0.557286	−	0.321749i	0.752055	+	0.659100i	$0.229063\pi$
$104$		0			0
$105$	0.613935	+	1.64203i	0.0599139	+	0.160245i
$106$		0			0
$107$	16.7052	+	9.64476i	1.61495	+	0.932394i	0.988199	+	0.153179i	$0.0489510\pi$
$107$	16.7052	+	9.64476i	1.61495	+	0.932394i	0.626756	+	0.779216i	$0.284382\pi$
$108$		0			0
$109$	−2.61682	−	0.952444i	−0.250646	−	0.0912276i	0.213642	−	0.976912i	$-0.431467\pi$
$109$	−2.61682	−	0.952444i	−0.250646	−	0.0912276i	−0.464288	+	0.885684i	$0.653690\pi$
$110$		0			0
$111$	0.181800	−	0.152548i	0.0172557	−	0.0144793i
$112$		0			0
$113$		−	4.77780i		−	0.449458i	−0.974421	−	0.224729i	$-0.927850\pi$
$113$		−	4.77780i		−	0.449458i	0.974421	−	0.224729i	$-0.0721497\pi$
$114$		0			0
$115$	−7.85498	−	13.3350i	−0.732480	−	1.24350i
$116$		0			0
$117$	9.46571	+	11.2808i	0.875105	+	1.04291i
$118$		0			0
$119$	5.33613	+	1.94219i	0.489162	+	0.178041i
$120$		0			0
$121$	−6.98076	+	12.0910i	−0.634615	+	1.09918i
$122$		0			0
$123$	−1.93163	−	0.340599i	−0.174169	−	0.0307108i
$124$		0			0
$125$	9.53275	−	5.84181i	0.852635	−	0.522507i
$126$		0			0
$127$	−3.91649	+	4.66749i	−0.347532	+	0.414173i	−0.911289	−	0.411768i	$-0.864911\pi$
$127$	−3.91649	+	4.66749i	−0.347532	+	0.414173i	0.563756	+	0.825941i	$0.309356\pi$
$128$		0			0
$129$	−1.06809	+	0.388752i	−0.0940399	+	0.0342277i
$130$		0			0
$131$	0.760180	+	4.31119i	0.0664172	+	0.376671i	0.999840	+	0.0178921i	$0.00569555\pi$
$131$	0.760180	+	4.31119i	0.0664172	+	0.376671i	−0.933423	+	0.358778i	$0.883193\pi$
$132$		0			0
$133$	−7.58077	+	4.56095i	−0.657336	+	0.395485i
$134$		0			0
$135$	−3.84265	+	3.28196i	−0.330723	+	0.282466i
$136$		0			0
$137$	−0.0429522	−	0.118010i	−0.00366966	−	0.0100823i	0.937844	−	0.347056i	$-0.112819\pi$
$137$	−0.0429522	−	0.118010i	−0.00366966	−	0.0100823i	−0.941514	+	0.336974i	$0.890597\pi$
$138$		0			0
$139$	1.18573	+	0.994942i	0.100572	+	0.0843899i	0.691687	−	0.722197i	$-0.256868\pi$
$139$	1.18573	+	0.994942i	0.100572	+	0.0843899i	−0.591115	+	0.806587i	$0.701312\pi$
$140$		0			0
$141$	−2.10203	−	3.64083i	−0.177023	−	0.306613i
$142$		0			0
$143$	25.4159	+	4.48152i	2.12539	+	0.374763i
$144$		0			0
$145$	0.103796	+	11.8893i	0.00861976	+	0.987351i
$146$		0			0
$147$	−0.380546	+	1.04554i	−0.0313869	+	0.0862349i
$148$		0			0
$149$	17.0194	−	14.2810i	1.39428	−	1.16994i	0.430713	−	0.902489i	$-0.358262\pi$
$149$	17.0194	−	14.2810i	1.39428	−	1.16994i	0.963571	−	0.267454i	$-0.0861825\pi$
$150$		0			0
$151$	7.67004			0.624179			0.312089	−	0.950053i	$-0.398971\pi$
$151$	7.67004			0.624179			0.312089	+	0.950053i	$0.398971\pi$
$152$		0			0
$153$			7.97601i			0.644822i
$154$		0			0
$155$	−4.59103	+	12.9648i	−0.368760	+	1.04136i
$156$		0			0
$157$	−5.95316	+	16.3562i	−0.475114	+	1.30537i	0.438481	+	0.898741i	$0.355517\pi$
$157$	−5.95316	+	16.3562i	−0.475114	+	1.30537i	−0.913595	+	0.406625i	$0.866705\pi$
$158$		0			0
$159$	−2.50718	+	4.34256i	−0.198832	+	0.344388i
$160$		0			0
$161$	−2.43939	+	13.8344i	−0.192251	+	1.09031i
$162$		0			0
$163$	−5.74508	+	3.31692i	−0.449989	+	0.259801i	−0.707826	−	0.706387i	$-0.750324\pi$
$163$	−5.74508	+	3.31692i	−0.449989	+	0.259801i	0.257837	+	0.966189i	$0.416990\pi$
$164$		0			0
$165$	−0.712209	+	4.25608i	−0.0554454	+	0.331336i
$166$		0			0
$167$	2.44159	+	6.70822i	0.188936	+	0.519098i	0.997605	−	0.0691662i	$-0.0220339\pi$
$167$	2.44159	+	6.70822i	0.188936	+	0.519098i	−0.808669	+	0.588264i	$0.799812\pi$
$168$		0			0
$169$	−2.37607	−	13.4753i	−0.182774	−	1.03657i
$170$		0			0
$171$	−9.66160	−	7.81457i	−0.738841	−	0.597595i
$172$		0			0
$173$	12.3799	−	2.18291i	0.941228	−	0.165964i	0.318077	−	0.948065i	$-0.396963\pi$
$173$	12.3799	−	2.18291i	0.941228	−	0.165964i	0.623152	+	0.782101i	$0.285852\pi$
$174$		0			0
$175$	−10.0233	−	1.58747i	−0.757693	−	0.120002i
$176$		0			0
$177$	0.306501	−	0.365274i	0.0230380	−	0.0274557i
$178$		0			0
$179$	9.59664	+	16.6219i	0.717286	+	1.24238i	0.962071	+	0.272799i	$0.0879494\pi$
$179$	9.59664	+	16.6219i	0.717286	+	1.24238i	−0.244785	+	0.969577i	$0.578717\pi$
$180$		0			0
$181$	−2.30052	+	13.0469i	−0.170996	+	0.969769i	0.771668	+	0.636026i	$0.219423\pi$
$181$	−2.30052	+	13.0469i	−0.170996	+	0.969769i	−0.942664	+	0.333743i	$0.891688\pi$
$182$		0			0
$183$	−4.26518	−	2.46250i	−0.315291	−	0.182033i
$184$		0			0
$185$	0.250368	+	1.35084i	0.0184075	+	0.0993159i
$186$		0			0
$187$	8.98508	+	10.7080i	0.657054	+	0.783047i
$188$		0			0
$189$	4.58694			0.333651
$190$		0			0
$191$	−7.92695			−0.573574			−0.286787	−	0.957994i	$-0.592587\pi$
$191$	−7.92695			−0.573574			−0.286787	+	0.957994i	$0.592587\pi$
$192$		0			0
$193$	−9.67275	−	11.5275i	−0.696260	−	0.829770i	0.295838	−	0.955238i	$-0.404401\pi$
$193$	−9.67275	−	11.5275i	−0.696260	−	0.829770i	−0.992098	+	0.125468i	$0.959957\pi$
$194$		0			0
$195$	4.38689	−	0.813077i	0.314152	−	0.0582256i
$196$		0			0
$197$	22.8011	+	13.1642i	1.62451	+	0.937913i	0.985692	+	0.168559i	$0.0539113\pi$
$197$	22.8011	+	13.1642i	1.62451	+	0.937913i	0.638822	+	0.769355i	$0.279422\pi$
$198$		0			0
$199$	−0.0152846	+	0.0866835i	−0.00108350	+	0.00614483i	−0.985345	−	0.170575i	$-0.945438\pi$
$199$	−0.0152846	+	0.0866835i	−0.00108350	+	0.00614483i	0.984261	+	0.176720i	$0.0565486\pi$
$200$		0			0
$201$	−0.0665103	−	0.115199i	−0.00469127	−	0.00812552i
$202$		0			0
$203$	6.93707	−	8.26728i	0.486887	−	0.580249i
$204$		0			0
$205$	7.22238	−	8.76150i	0.504433	−	0.611930i
$206$		0			0
$207$	−19.4315	+	3.42630i	−1.35058	+	0.238144i
$208$		0			0
$209$	−21.7742	+	0.392659i	−1.50615	+	0.0271608i
$210$		0			0
$211$	0.921667	+	5.22703i	0.0634502	+	0.359844i	0.999958	+	0.00919637i	$0.00292734\pi$
$211$	0.921667	+	5.22703i	0.0634502	+	0.359844i	−0.936508	+	0.350647i	$0.885962\pi$
$212$		0			0
$213$	1.74287	+	4.78849i	0.119419	+	0.328102i
$214$		0			0
$215$	1.08598	−	6.48967i	0.0740630	−	0.442592i
$216$		0			0
$217$	10.8115	−	6.24203i	0.733933	−	0.423736i
$218$		0			0
$219$	0.289519	−	1.64194i	0.0195639	−	0.110952i
$220$		0			0
$221$	7.22617	−	12.5161i	0.486085	−	0.841923i
$222$		0			0
$223$	−3.27745	+	9.00472i	−0.219474	+	0.603000i	−0.999748	−	0.0224374i	$-0.992857\pi$
$223$	−3.27745	+	9.00472i	−0.219474	+	0.603000i	0.780274	+	0.625438i	$0.215080\pi$
$224$		0			0
$225$	−2.71988	−	13.9921i	−0.181326	−	0.932806i
$226$		0			0
$227$		−	25.0428i		−	1.66215i	−0.556162	−	0.831074i	$-0.687727\pi$
$227$		−	25.0428i		−	1.66215i	0.556162	−	0.831074i	$-0.312273\pi$
$228$		0			0
$229$	−15.2215			−1.00587			−0.502933	−	0.864325i	$-0.667746\pi$
$229$	−15.2215			−1.00587			−0.502933	+	0.864325i	$0.667746\pi$
$230$		0			0
$231$	3.00053	−	2.51774i	0.197420	−	0.165655i
$232$		0			0
$233$	7.01594	−	19.2761i	0.459629	−	1.26282i	−0.466133	−	0.884715i	$-0.654353\pi$
$233$	7.01594	−	19.2761i	0.459629	−	1.26282i	0.925762	−	0.378106i	$-0.123425\pi$
$234$		0			0
$235$	24.3361	−	0.212459i	1.58751	−	0.0138593i
$236$		0			0
$237$	0.557090	+	0.0982300i	0.0361869	+	0.00638073i
$238$		0			0
$239$	3.71465	+	6.43396i	0.240281	+	0.416178i	0.960794	−	0.277262i	$-0.0894272\pi$
$239$	3.71465	+	6.43396i	0.240281	+	0.416178i	−0.720513	+	0.693441i	$0.756094\pi$
$240$		0			0
$241$	−18.0617	−	15.1556i	−1.16346	−	0.976257i	−0.163510	−	0.986542i	$-0.552282\pi$
$241$	−18.0617	−	15.1556i	−1.16346	−	0.976257i	−0.999947	+	0.0102849i	$0.996726\pi$
$242$		0			0
$243$	3.33340	+	9.15844i	0.213838	+	0.587514i
$244$		0			0
$245$	−4.18312	−	4.89777i	−0.267250	−	0.312907i
$246$		0			0
$247$	8.08125	+	21.0161i	0.514198	+	1.33722i
$248$		0			0
$249$	0.474330	+	2.69006i	0.0300594	+	0.170475i
$250$		0			0
$251$	19.2048	−	6.98998i	1.21220	−	0.441204i	0.344732	−	0.938701i	$-0.387970\pi$
$251$	19.2048	−	6.98998i	1.21220	−	0.441204i	0.867465	+	0.497498i	$0.165748\pi$
$252$		0			0
$253$	−22.2276	+	26.4898i	−1.39743	+	1.66540i
$254$		0			0
$255$	2.10324	+	1.18994i	0.131710	+	0.0745172i
$256$		0			0
$257$	−4.93687	−	0.870503i	−0.307953	−	0.0543005i	0.0175359	−	0.999846i	$-0.494418\pi$
$257$	−4.93687	−	0.870503i	−0.307953	−	0.0543005i	−0.325489	+	0.945546i	$0.605529\pi$
$258$		0			0
$259$	0.623513	−	1.07996i	0.0387432	−	0.0671052i
$260$		0			0
$261$	14.2442	+	5.18448i	0.881697	+	0.320911i
$262$		0			0
$263$	−9.96981	−	11.8816i	−0.614765	−	0.732648i	0.365396	−	0.930852i	$-0.380934\pi$
$263$	−9.96981	−	11.8816i	−0.614765	−	0.732648i	−0.980161	+	0.198204i	$0.936489\pi$
$264$		0			0
$265$	−14.7328	−	25.0111i	−0.905029	−	1.53642i
$266$		0			0
$267$			1.04657i			0.0640489i
$268$		0			0
$269$	−8.83952	+	7.41724i	−0.538955	+	0.452237i	−0.871180	−	0.490963i	$-0.836645\pi$
$269$	−8.83952	+	7.41724i	−0.538955	+	0.452237i	0.332225	+	0.943200i	$0.392201\pi$
$270$		0			0
$271$	−11.6772	−	4.25016i	−0.709341	−	0.258179i	−0.0379471	−	0.999280i	$-0.512082\pi$
$271$	−11.6772	−	4.25016i	−0.709341	−	0.258179i	−0.671394	+	0.741101i	$0.734304\pi$
$272$		0			0
$273$	−3.50718	−	2.02487i	−0.212264	−	0.122551i
$274$		0			0
$275$	−19.4138	−	15.7208i	−1.17070	−	0.947998i
$276$		0			0
$277$	3.30673	−	1.90914i	0.198682	−	0.114709i	−0.397358	−	0.917663i	$-0.630073\pi$
$277$	3.30673	−	1.90914i	0.198682	−	0.114709i	0.596041	+	0.802954i	$0.296740\pi$
$278$		0			0
$279$	13.4324	+	11.2711i	0.804178	+	0.674786i
$280$		0			0
$281$	−26.4742	+	9.63584i	−1.57932	+	0.574826i	−0.975056	−	0.221958i	$-0.928755\pi$
$281$	−26.4742	+	9.63584i	−1.57932	+	0.574826i	−0.604265	+	0.796784i	$0.706533\pi$
$282$		0			0
$283$	−18.2545	+	3.21877i	−1.08512	+	0.191336i	−0.687478	−	0.726205i	$-0.741282\pi$
$283$	−18.2545	+	3.21877i	−1.08512	+	0.191336i	−0.397641	+	0.917541i	$0.630171\pi$
$284$		0			0
$285$	−3.50209	+	1.38186i	−0.207446	+	0.0818543i
$286$		0			0
$287$	−10.1498	+	1.78969i	−0.599127	+	0.105642i
$288$		0			0
$289$	−8.61908	+	3.13709i	−0.507005	+	0.184535i
$290$		0			0
$291$	−3.15268	−	2.64541i	−0.184813	−	0.155077i
$292$		0			0
$293$	14.9665	−	8.64092i	0.874353	−	0.504808i	0.00556039	−	0.999985i	$-0.498230\pi$
$293$	14.9665	−	8.64092i	0.874353	−	0.504808i	0.868792	+	0.495177i	$0.164897\pi$
$294$		0			0
$295$	0.966701	+	2.58553i	0.0562835	+	0.150536i
$296$		0			0
$297$	9.77840	+	5.64556i	0.567400	+	0.327589i
$298$		0			0
$299$	33.5965	+	12.2281i	1.94293	+	0.707170i
$300$		0			0
$301$	−4.57520	+	3.83905i	−0.263710	+	0.221279i
$302$		0			0
$303$		−	5.56069i		−	0.319453i
$304$		0			0
$305$	24.5654	−	14.4702i	1.40661	−	0.828564i
$306$		0			0
$307$	16.8445	+	20.0745i	0.961369	+	1.14571i	0.989269	+	0.146104i	$0.0466734\pi$
$307$	16.8445	+	20.0745i	0.961369	+	1.14571i	−0.0279006	+	0.999611i	$0.508882\pi$
$308$		0			0
$309$	−2.37049	−	0.862788i	−0.134853	−	0.0490823i
$310$		0			0
$311$	−2.13376	+	3.69578i	−0.120994	+	0.209568i	−0.920160	−	0.391542i	$-0.871942\pi$
$311$	−2.13376	+	3.69578i	−0.120994	+	0.209568i	0.799166	+	0.601111i	$0.205275\pi$
$312$		0			0
$313$	−22.4255	−	3.95422i	−1.26757	−	0.223506i	−0.500873	−	0.865521i	$-0.666988\pi$
$313$	−22.4255	−	3.95422i	−1.26757	−	0.223506i	−0.766692	+	0.642015i	$0.778099\pi$
$314$		0			0
$315$	−6.37103	+	11.2608i	−0.358967	+	0.634476i
$316$		0			0
$317$	13.0144	−	15.5100i	0.730963	−	0.871127i	−0.264684	−	0.964335i	$-0.585268\pi$
$317$	13.0144	−	15.5100i	0.730963	−	0.871127i	0.995647	+	0.0932079i	$0.0297121\pi$
$318$		0			0
$319$	24.9637	−	9.08603i	1.39770	−	0.508720i
$320$		0			0
$321$	−1.29383	−	7.33769i	−0.0722147	−	0.409550i
$322$		0			0
$323$	−3.96377	+	11.5333i	−0.220550	+	0.641728i
$324$		0			0
$325$	−8.40858	+	24.4208i	−0.466424	+	1.35462i
$326$		0			0
$327$	0.367897	+	1.01079i	0.0203447	+	0.0558967i
$328$		0			0
$329$	−16.9223	−	14.1995i	−0.932955	−	0.782842i
$330$		0			0
$331$	−8.22049	−	14.2383i	−0.451839	−	0.782608i	0.546661	−	0.837354i	$-0.315898\pi$
$331$	−8.22049	−	14.2383i	−0.451839	−	0.782608i	−0.998500	+	0.0547458i	$0.982565\pi$
$332$		0			0
$333$	1.72493	+	0.304152i	0.0945256	+	0.0166674i
$334$		0			0
$335$	0.770018	−	0.00672240i	0.0420706	−	0.000367284i
$336$		0			0
$337$	3.46485	−	9.51959i	0.188742	−	0.518565i	−0.808842	−	0.588025i	$-0.799906\pi$
$337$	3.46485	−	9.51959i	0.188742	−	0.518565i	0.997585	+	0.0694603i	$0.0221277\pi$
$338$		0			0
$339$	−1.41374	+	1.18627i	−0.0767837	+	0.0644291i
$340$		0			0
$341$	30.7305			1.66415
$342$		0			0
$343$			20.0540i			1.08281i
$344$		0			0
$345$	−1.99550	+	5.63517i	−0.107434	+	0.303387i
$346$		0			0
$347$	−0.284237	+	0.780935i	−0.0152587	+	0.0419228i	−0.947088	−	0.320974i	$-0.895990\pi$
$347$	−0.284237	+	0.780935i	−0.0152587	+	0.0419228i	0.931829	+	0.362896i	$0.118212\pi$
$348$		0			0
$349$	−1.52695	+	2.64475i	−0.0817355	+	0.141570i	−0.903995	−	0.427542i	$-0.859380\pi$
$349$	−1.52695	+	2.64475i	−0.0817355	+	0.141570i	0.822260	+	0.569112i	$0.192713\pi$
$350$		0			0
$351$	2.02717	−	11.4967i	0.108203	−	0.613647i
$352$		0			0
$353$	24.3150	−	14.0383i	1.29416	−	0.747182i	0.314769	−	0.949168i	$-0.398073\pi$
$353$	24.3150	−	14.0383i	1.29416	−	0.747182i	0.979388	+	0.201986i	$0.0647397\pi$
$354$		0			0
$355$	−29.0947	−	4.86869i	−1.54419	−	0.258403i
$356$		0			0
$357$	−0.750203	−	2.06117i	−0.0397050	−	0.109088i
$358$		0			0
$359$	2.57960	+	14.6296i	0.136146	+	0.772122i	0.974055	+	0.226312i	$0.0726668\pi$
$359$	2.57960	+	14.6296i	0.136146	+	0.772122i	−0.837909	+	0.545810i	$0.816222\pi$
$360$		0			0
$361$	−10.0871	−	16.1013i	−0.530899	−	0.847435i
$362$		0			0
$363$	5.31093	−	0.936461i	0.278752	−	0.0491514i
$364$		0			0
$365$	7.44753	+	6.13923i	0.389822	+	0.321342i
$366$		0			0
$367$	3.60318	−	4.29410i	0.188084	−	0.224150i	−0.663759	−	0.747946i	$-0.731040\pi$
$367$	3.60318	−	4.29410i	0.188084	−	0.224150i	0.851844	+	0.523796i	$0.175485\pi$
$368$		0			0
$369$	−7.23807	−	12.5367i	−0.376799	−	0.652635i
$370$		0			0
$371$	−4.57531	+	25.9479i	−0.237538	+	1.34715i
$372$		0			0
$373$	4.33340	+	2.50189i	0.224375	+	0.129543i	0.607974	−	0.793957i	$-0.291982\pi$
$373$	4.33340	+	2.50189i	0.224375	+	0.129543i	−0.383599	+	0.923500i	$0.625316\pi$
$374$		0			0
$375$	−4.09543	−	1.37027i	−0.211487	−	0.0707603i
$376$		0			0
$377$	−17.6552	−	21.0407i	−0.909291	−	1.08365i
$378$		0			0
$379$	27.2579			1.40014			0.700072	−	0.714072i	$-0.253151\pi$
$379$	27.2579			1.40014			0.700072	+	0.714072i	$0.253151\pi$
$380$		0			0
$381$	2.35351			0.120574
$382$		0			0
$383$	−24.2773	−	28.9326i	−1.24051	−	1.47839i	−0.821300	−	0.570497i	$-0.806751\pi$
$383$	−24.2773	−	28.9326i	−1.24051	−	1.47839i	−0.419213	−	0.907888i	$-0.637694\pi$
$384$		0			0
$385$	4.13222	+	22.2950i	0.210597	+	1.13626i
$386$		0			0
$387$	−7.26494	−	4.19441i	−0.369298	−	0.213214i
$388$		0			0
$389$	5.41583	−	30.7147i	0.274593	−	1.55730i	−0.465657	−	0.884965i	$-0.654182\pi$
$389$	5.41583	−	30.7147i	0.274593	−	1.55730i	0.740251	−	0.672331i	$-0.234707\pi$
$390$		0			0
$391$	9.68228	+	16.7702i	0.489654	+	0.848105i
$392$		0			0
$393$	1.08693	−	1.29535i	0.0548282	−	0.0653417i
$394$		0			0
$395$	−2.08296	+	2.52685i	−0.104805	+	0.127140i
$396$		0			0
$397$	−9.88334	+	1.74270i	−0.496030	+	0.0874636i	−0.416066	−	0.909334i	$-0.636592\pi$
$397$	−9.88334	+	1.74270i	−0.496030	+	0.0874636i	−0.0799640	+	0.996798i	$0.525481\pi$
$398$		0			0
$399$	3.23178	+	1.11070i	0.161791	+	0.0556046i
$400$		0			0
$401$	−3.98188	−	22.5824i	−0.198846	−	1.12771i	−0.906835	−	0.421486i	$-0.861509\pi$
$401$	−3.98188	−	22.5824i	−0.198846	−	1.12771i	0.707989	−	0.706223i	$-0.249602\pi$
$402$		0			0
$403$	−10.8669	−	29.8565i	−0.541318	−	1.48726i
$404$		0			0
$405$	−16.9363	−	2.83410i	−0.841570	−	0.140828i
$406$		0			0
$407$	2.65840	−	1.53483i	0.131772	−	0.0760785i
$408$		0			0
$409$	1.91380	−	10.8537i	0.0946314	−	0.536681i	−0.900228	−	0.435418i	$-0.856601\pi$
$409$	1.91380	−	10.8537i	0.0946314	−	0.536681i	0.994860	−	0.101263i	$-0.0322884\pi$
$410$		0			0
$411$	−0.0242544	+	0.0420098i	−0.00119638	+	0.00207219i
$412$		0			0
$413$	0.856942	−	2.35443i	0.0421673	−	0.115854i
$414$		0			0
$415$	−14.9058	−	5.27837i	−0.731698	−	0.259105i
$416$		0			0
$417$		−	0.597884i		−	0.0292785i
$418$		0			0
$419$	−4.91341			−0.240036			−0.120018	−	0.992772i	$-0.538295\pi$
$419$	−4.91341			−0.240036			−0.120018	+	0.992772i	$0.538295\pi$
$420$		0			0
$421$	7.65017	−	6.41925i	0.372846	−	0.312855i	−0.437040	−	0.899442i	$-0.643973\pi$
$421$	7.65017	−	6.41925i	0.372846	−	0.312855i	0.809886	+	0.586587i	$0.199529\pi$
$422$		0			0
$423$	10.6121	−	29.1565i	0.515978	−	1.41764i
$424$		0			0
$425$	−11.9909	+	7.20498i	−0.581645	+	0.349493i
$426$		0			0
$427$	−25.4855	−	4.49378i	−1.23333	−	0.217469i
$428$		0			0
$429$	−4.98438	−	8.63320i	−0.240648	−	0.416815i
$430$		0			0
$431$	13.7070	+	11.5015i	0.660241	+	0.554008i	0.910159	−	0.414259i	$-0.135959\pi$
$431$	13.7070	+	11.5015i	0.660241	+	0.554008i	−0.249918	+	0.968267i	$0.580404\pi$
$432$		0			0
$433$	−4.08986	−	11.2368i	−0.196546	−	0.540006i	0.801794	−	0.597601i	$-0.203879\pi$
$433$	−4.08986	−	11.2368i	−0.196546	−	0.540006i	−0.998340	+	0.0575945i	$0.981657\pi$
$434$		0			0
$435$	3.49223	−	2.98267i	0.167440	−	0.143008i
$436$		0			0
$437$	−29.8006	−	4.70230i	−1.42556	−	0.224941i
$438$		0			0
$439$	−5.93574	−	33.6632i	−0.283297	−	1.60666i	−0.711305	−	0.702883i	$-0.751896\pi$
$439$	−5.93574	−	33.6632i	−0.283297	−	1.60666i	0.428008	−	0.903775i	$-0.359215\pi$
$440$		0			0
$441$	−7.71653	+	2.80859i	−0.367454	+	0.133742i
$442$		0			0
$443$	−17.3354	+	20.6595i	−0.823631	+	0.981565i	−0.999996	−	0.00276007i	$-0.999121\pi$
$443$	−17.3354	+	20.6595i	−0.823631	+	0.981565i	0.176366	+	0.984325i	$0.443566\pi$
$444$		0			0
$445$	−5.27307	−	2.98333i	−0.249967	−	0.141424i
$446$		0			0
$447$	−8.45140	−	1.49021i	−0.399737	−	0.0704845i
$448$		0			0
$449$	−6.24310	+	10.8134i	−0.294630	+	0.510315i	−0.974899	−	0.222648i	$-0.928530\pi$
$449$	−6.24310	+	10.8134i	−0.294630	+	0.510315i	0.680269	+	0.732963i	$0.261863\pi$
$450$		0			0
$451$	−23.8401	−	8.67708i	−1.12259	−	0.408588i
$452$		0			0
$453$	−1.90437	−	2.26954i	−0.0894752	−	0.106632i
$454$		0			0
$455$	20.1997	−	11.8986i	0.946978	−	0.557817i
$456$		0			0
$457$			37.2242i			1.74127i	0.491926	+	0.870637i	$0.336293\pi$
$457$			37.2242i			1.74127i	−0.491926	+	0.870637i	$0.663707\pi$
$458$		0			0
$459$	4.84367	−	4.06432i	0.226083	−	0.189706i
$460$		0			0
$461$	38.7689	+	14.1107i	1.80565	+	0.657203i	0.997688	+	0.0679675i	$0.0216514\pi$
$461$	38.7689	+	14.1107i	1.80565	+	0.657203i	0.807962	+	0.589235i	$0.200571\pi$
$462$		0			0
$463$	36.7591	+	21.2229i	1.70834	+	0.986311i	0.936619	+	0.350349i	$0.113937\pi$
$463$	36.7591	+	21.2229i	1.70834	+	0.986311i	0.771721	+	0.635961i	$0.219396\pi$
$464$		0			0
$465$	4.97614	−	1.86052i	0.230763	−	0.0862796i
$466$		0			0
$467$	7.73715	−	4.46704i	0.358032	−	0.206710i	−0.310185	−	0.950676i	$-0.600391\pi$
$467$	7.73715	−	4.46704i	0.358032	−	0.206710i	0.668217	+	0.743966i	$0.267058\pi$
$468$		0			0
$469$	−0.535436	−	0.449284i	−0.0247242	−	0.0207460i
$470$		0			0
$471$	6.31784	−	2.29951i	0.291111	−	0.105956i
$472$		0			0
$473$	−14.4784	+	2.55294i	−0.665719	+	0.117384i
$474$		0			0
$475$	3.02059	−	21.5842i	0.138594	−	0.990349i
$476$		0			0
$477$	−36.4458	+	6.42637i	−1.66874	+	0.294243i
$478$		0			0
$479$	3.82965	−	1.39388i	0.174981	−	0.0636879i	−0.253044	−	0.967455i	$-0.581432\pi$
$479$	3.82965	−	1.39388i	0.174981	−	0.0636879i	0.428025	+	0.903767i	$0.359210\pi$
$480$		0			0
$481$	−2.43123	−	2.04005i	−0.110855	−	0.0930182i
$482$		0			0
$483$	4.69924	−	2.71311i	0.213823	−	0.123451i
$484$		0			0
$485$	22.3157	−	8.34359i	1.01330	−	0.378863i
$486$		0			0
$487$	−5.29459	−	3.05683i	−0.239921	−	0.138518i	0.375220	−	0.926936i	$-0.377567\pi$
$487$	−5.29459	−	3.05683i	−0.239921	−	0.138518i	−0.615140	+	0.788418i	$0.710901\pi$
$488$		0			0
$489$	2.40789	+	0.876402i	0.108889	+	0.0396323i
$490$		0			0
$491$	8.96177	−	7.51982i	0.404439	−	0.339365i	−0.417767	−	0.908554i	$-0.637187\pi$
$491$	8.96177	−	7.51982i	0.404439	−	0.339365i	0.822206	+	0.569189i	$0.192743\pi$
$492$		0			0
$493$		−	14.8767i		−	0.670012i
$494$		0			0
$495$	−27.4414	+	16.1644i	−1.23340	+	0.726534i
$496$		0			0
$497$	17.2114	+	20.5117i	0.772036	+	0.920076i
$498$		0			0
$499$	−7.99418	−	2.90964i	−0.357869	−	0.130254i	0.156828	−	0.987626i	$-0.449873\pi$
$499$	−7.99418	−	2.90964i	−0.357869	−	0.130254i	−0.514697	+	0.857372i	$0.672095\pi$
$500$		0			0
$501$	1.37873	−	2.38802i	0.0615969	−	0.106689i
$502$		0			0
$503$	9.55700	+	1.68516i	0.426125	+	0.0751374i	0.382598	−	0.923915i	$-0.375029\pi$
$503$	9.55700	+	1.68516i	0.426125	+	0.0751374i	0.0435272	+	0.999052i	$0.486140\pi$
$504$		0			0
$505$	28.0172	+	15.8512i	1.24675	+	0.705371i
$506$		0			0
$507$	−3.39737	+	4.04883i	−0.150882	+	0.179815i
$508$		0			0
$509$	−29.4562	+	10.7212i	−1.30562	+	0.475208i	−0.898824	−	0.438309i	$-0.855578\pi$
$509$	−29.4562	+	10.7212i	−1.30562	+	0.475208i	−0.406800	+	0.913517i	$0.633355\pi$
$510$		0			0
$511$	−1.52129	−	8.62766i	−0.0672979	−	0.381665i
$512$		0			0
$513$	0.177616	+	9.84936i	0.00784192	+	0.434860i
$514$		0			0
$515$	11.1044	−	9.48412i	0.489319	−	0.417920i
$516$		0			0
$517$	−18.5982	−	51.0980i	−0.817946	−	2.24729i
$518$		0			0
$519$	−3.71969	−	3.12119i	−0.163276	−	0.137005i
$520$		0			0
$521$	3.69071	+	6.39250i	0.161693	+	0.280060i	0.935476	−	0.353390i	$-0.114971\pi$
$521$	3.69071	+	6.39250i	0.161693	+	0.280060i	−0.773783	+	0.633451i	$0.781638\pi$
$522$		0			0
$523$	−10.6860	−	1.88424i	−0.467268	−	0.0823919i	−0.0649432	−	0.997889i	$-0.520687\pi$
$523$	−10.6860	−	1.88424i	−0.467268	−	0.0823919i	−0.402325	+	0.915497i	$0.631798\pi$
$524$		0			0
$525$	2.01894	+	3.36002i	0.0881136	+	0.146643i
$526$		0			0
$527$	5.88579	−	16.1711i	0.256389	−	0.704423i
$528$		0			0
$529$	−19.0780	+	16.0084i	−0.829480	+	0.696016i
$530$		0			0
$531$	3.51920			0.152720
$532$		0			0
$533$			26.2304i			1.13617i
$534$		0			0
$535$	40.6587	+	14.3979i	1.75783	+	0.622473i
$536$		0			0
$537$	2.53564	−	6.96661i	0.109421	−	0.300631i
$538$		0			0
$539$	−7.19573	+	12.4634i	−0.309942	+	0.536836i
$540$		0			0
$541$	−2.19629	+	12.4558i	−0.0944257	+	0.535515i	0.900496	+	0.434864i	$0.143204\pi$
$541$	−2.19629	+	12.4558i	−0.0944257	+	0.535515i	−0.994922	+	0.100651i	$0.967908\pi$
$542$		0			0
$543$	4.43173	−	2.55866i	0.190184	−	0.109803i
$544$		0			0
$545$	−6.14152	−	1.02772i	−0.263074	−	0.0440225i
$546$		0			0
$547$	−5.41331	−	14.8730i	−0.231457	−	0.635922i	0.768536	−	0.639807i	$-0.220986\pi$
$547$	−5.41331	−	14.8730i	−0.231457	−	0.635922i	−0.999992	+	0.00388494i	$0.998763\pi$
$548$		0			0
$549$	−6.31185	−	35.7963i	−0.269383	−	1.52775i
$550$		0			0
$551$	18.0206	+	14.5756i	0.767704	+	0.620940i
$552$		0			0
$553$	2.92726	−	0.516154i	0.124480	−	0.0219491i
$554$		0			0
$555$	0.337547	−	0.409480i	0.0143281	−	0.0173815i
$556$		0			0
$557$	9.31207	−	11.0977i	0.394565	−	0.470224i	−0.531790	−	0.846876i	$-0.678480\pi$
$557$	9.31207	−	11.0977i	0.394565	−	0.470224i	0.926355	+	0.376652i	$0.122925\pi$
$558$		0			0
$559$	7.60018	+	13.1639i	0.321453	+	0.556774i
$560$		0			0
$561$	0.937586	−	5.31732i	0.0395849	−	0.224497i
$562$		0			0
$563$	35.3172	+	20.3904i	1.48844	+	0.859354i	0.999913	−	0.0131930i	$-0.00419959\pi$
$563$	35.3172	+	20.3904i	1.48844	+	0.859354i	0.488531	+	0.872547i	$0.337533\pi$
$564$		0			0
$565$	−1.94695	−	10.5046i	−0.0819087	−	0.441931i
$566$		0			0
$567$	10.0189	+	11.9400i	0.420753	+	0.501434i
$568$		0			0
$569$	20.1384			0.844246			0.422123	−	0.906539i	$-0.361285\pi$
$569$	20.1384			0.844246			0.422123	+	0.906539i	$0.361285\pi$
$570$		0			0
$571$	−6.07939			−0.254415			−0.127207	−	0.991876i	$-0.540601\pi$
$571$	−6.07939			−0.254415			−0.127207	+	0.991876i	$0.540601\pi$
$572$		0			0
$573$	1.96816	+	2.34556i	0.0822211	+	0.0979872i
$574$		0			0
$575$	−22.7041	−	26.1178i	−0.946828	−	1.08919i
$576$		0			0
$577$	−9.61953	−	5.55384i	−0.400466	−	0.231209i	0.286219	−	0.958164i	$-0.407602\pi$
$577$	−9.61953	−	5.55384i	−0.400466	−	0.231209i	−0.686685	+	0.726955i	$0.740935\pi$
$578$		0			0
$579$	−1.00934	+	5.72428i	−0.0419469	+	0.237893i
$580$		0			0
$581$	7.17654	+	12.4301i	0.297733	+	0.515689i
$582$		0			0
$583$	−41.6900	+	49.6842i	−1.72662	+	2.05771i
$584$		0			0
$585$	25.4084	+	20.9450i	1.05051	+	0.865967i
$586$		0			0
$587$	−12.3374	+	2.17542i	−0.509220	+	0.0897893i	−0.422355	−	0.906431i	$-0.638796\pi$
$587$	−12.3374	+	2.17542i	−0.509220	+	0.0897893i	−0.0868659	+	0.996220i	$0.527685\pi$
$588$		0			0
$589$	13.8219	+	22.9734i	0.569521	+	0.946603i
$590$		0			0
$591$	−1.76597	−	10.0153i	−0.0726422	−	0.411974i
$592$		0			0
$593$	4.12938	+	11.3454i	0.169573	+	0.465899i	0.995147	−	0.0983948i	$-0.0313708\pi$
$593$	4.12938	+	11.3454i	0.169573	+	0.465899i	−0.825574	+	0.564294i	$0.809149\pi$
$594$		0			0
$595$	12.5236	+	2.09569i	0.513417	+	0.0859148i
$596$		0			0
$597$	0.0294444	−	0.0169997i	0.00120508	−	0.000695752i
$598$		0			0
$599$	−3.49998	+	19.8494i	−0.143005	+	0.811024i	0.825942	+	0.563755i	$0.190644\pi$
$599$	−3.49998	+	19.8494i	−0.143005	+	0.811024i	−0.968947	+	0.247268i	$0.920467\pi$
$600$		0			0
$601$	−8.65639	+	14.9933i	−0.353102	+	0.611590i	−0.986791	−	0.161997i	$-0.948206\pi$
$601$	−8.65639	+	14.9933i	−0.353102	+	0.611590i	0.633689	+	0.773588i	$0.281540\pi$
$602$		0			0
$603$	0.335777	−	0.922539i	0.0136739	−	0.0375687i
$604$		0			0
$605$	−10.4210	+	29.4283i	−0.423673	+	1.19643i
$606$		0			0
$607$		−	32.2776i		−	1.31011i	−0.755582	−	0.655054i	$-0.772646\pi$
$607$		−	32.2776i		−	1.31011i	0.755582	−	0.655054i	$-0.227354\pi$
$608$		0			0
$609$	−4.16865			−0.168922
$610$		0			0
$611$	−43.0681	+	36.1385i	−1.74235	+	1.46201i
$612$		0			0
$613$	4.33958	−	11.9229i	0.175274	−	0.481561i	−0.820684	−	0.571382i	$-0.806407\pi$
$613$	4.33958	−	11.9229i	0.175274	−	0.481561i	0.995958	+	0.0898212i	$0.0286296\pi$
$614$		0			0
$615$	−4.38573	+	0.0382882i	−0.176850	+	0.00154393i
$616$		0			0
$617$	−22.8772	−	4.03388i	−0.921003	−	0.162398i	−0.307008	−	0.951707i	$-0.599328\pi$
$617$	−22.8772	−	4.03388i	−0.921003	−	0.162398i	−0.613996	+	0.789309i	$0.710439\pi$
$618$		0			0
$619$	9.94737	+	17.2294i	0.399819	+	0.692506i	0.993703	−	0.112044i	$-0.0357398\pi$
$619$	9.94737	+	17.2294i	0.399819	+	0.692506i	−0.593885	+	0.804550i	$0.702406\pi$
$620$		0			0
$621$	11.9824	+	10.0544i	0.480838	+	0.403471i
$622$		0			0
$623$	1.88085	+	5.16759i	0.0753546	+	0.207035i
$624$		0			0
$625$	18.5784	−	16.7285i	0.743136	−	0.669140i
$626$		0			0
$627$	5.52243	+	6.34542i	0.220545	+	0.253412i
$628$		0			0
$629$	−0.298499	−	1.69287i	−0.0119019	−	0.0674992i
$630$		0			0
$631$	40.2762	−	14.6593i	1.60337	−	0.583579i	0.623258	−	0.782016i	$-0.285809\pi$
$631$	40.2762	−	14.6593i	1.60337	−	0.583579i	0.980114	+	0.198437i	$0.0635865\pi$
$632$		0			0
$633$	1.31783	−	1.57052i	0.0523789	−	0.0624227i
$634$		0			0
$635$	−6.70889	+	11.8580i	−0.266234	+	0.470571i
$636$		0			0
$637$	14.6535	+	2.58380i	0.580591	+	0.102374i
$638$		0			0
$639$	−18.8045	+	32.5704i	−0.743896	+	1.28847i
$640$		0			0
$641$	4.37943	+	1.59398i	0.172977	+	0.0629585i	0.427057	−	0.904225i	$-0.359550\pi$
$641$	4.37943	+	1.59398i	0.172977	+	0.0629585i	−0.254080	+	0.967183i	$0.581773\pi$
$642$		0			0
$643$	−3.04048	−	3.62351i	−0.119905	−	0.142897i	0.702753	−	0.711434i	$-0.251954\pi$
$643$	−3.04048	−	3.62351i	−0.119905	−	0.142897i	−0.822658	+	0.568537i	$0.807510\pi$
$644$		0			0
$645$	−2.18991	+	1.28996i	−0.0862275	+	0.0507923i
$646$		0			0
$647$			0.286876i			0.0112783i	0.999984	+	0.00563914i	$0.00179500\pi$
$647$			0.286876i			0.0112783i	−0.999984	+	0.00563914i	$0.998205\pi$
$648$		0			0
$649$	4.72463	−	3.96443i	0.185458	−	0.155618i
$650$		0			0
$651$	−4.53135	−	1.64928i	−0.177598	−	0.0646403i
$652$		0			0
$653$	9.39185	+	5.42238i	0.367531	+	0.212194i	0.672379	−	0.740207i	$-0.265272\pi$
$653$	9.39185	+	5.42238i	0.367531	+	0.212194i	−0.304848	+	0.952401i	$0.598606\pi$
$654$		0			0
$655$	3.42815	+	9.16892i	0.133949	+	0.358259i
$656$		0			0
$657$	10.6566	−	6.15257i	0.415752	−	0.240035i
$658$		0			0
$659$	−32.4787	−	27.2529i	−1.26519	−	1.06162i	−0.995109	−	0.0987834i	$-0.968505\pi$
$659$	−32.4787	−	27.2529i	−1.26519	−	1.06162i	−0.270082	−	0.962837i	$-0.587051\pi$
$660$		0			0
$661$	−22.7802	+	8.29133i	−0.886049	+	0.322495i	−0.744648	−	0.667457i	$-0.767383\pi$
$661$	−22.7802	+	8.29133i	−0.886049	+	0.322495i	−0.141400	+	0.989952i	$0.545161\pi$
$662$		0			0
$663$	−5.49764	+	0.969382i	−0.213511	+	0.0376477i
$664$		0			0
$665$	−14.8087	+	13.1170i	−0.574256	+	0.508654i
$666$		0			0
$667$	36.2433	−	6.39066i	1.40334	−	0.247447i
$668$		0			0
$669$	3.47822	−	1.26597i	0.134476	−	0.0489451i
$670$		0			0
$671$	−48.7988	−	40.9471i	−1.88386	−	1.58074i
$672$		0			0
$673$	8.00813	−	4.62349i	0.308691	−	0.178223i	−0.337650	−	0.941272i	$-0.609632\pi$
$673$	8.00813	−	4.62349i	0.308691	−	0.178223i	0.646340	+	0.763049i	$0.276299\pi$
$674$		0			0
$675$	−7.11115	+	8.78166i	−0.273708	+	0.338006i
$676$		0			0
$677$	17.3070	+	9.99219i	0.665161	+	0.384031i	0.794241	−	0.607603i	$-0.207869\pi$
$677$	17.3070	+	9.99219i	0.665161	+	0.384031i	−0.129079	+	0.991634i	$0.541202\pi$
$678$		0			0
$679$	−20.3211	−	7.39626i	−0.779851	−	0.283842i
$680$		0			0
$681$	−7.41008	+	6.21780i	−0.283955	+	0.238267i
$682$		0			0
$683$			7.54136i			0.288562i	0.989537	+	0.144281i	$0.0460869\pi$
$683$			7.54136i			0.288562i	−0.989537	+	0.144281i	$0.953913\pi$
$684$		0			0
$685$	−0.142525	−	0.241957i	−0.00544559	−	0.00924471i
$686$		0			0
$687$	3.77930	+	4.50400i	0.144189	+	0.171838i
$688$		0			0
$689$	63.0135	+	22.9351i	2.40062	+	0.873756i
$690$		0			0
$691$	13.4982	−	23.3795i	0.513495	−	0.889399i	−0.486383	−	0.873746i	$-0.661684\pi$
$691$	13.4982	−	23.3795i	0.513495	−	0.889399i	0.999877	−	0.0156532i	$-0.00498276\pi$
$692$		0			0
$693$	28.4692	+	5.01989i	1.08146	+	0.190690i
$694$		0			0
$695$	3.01240	+	1.70432i	0.114267	+	0.0646486i
$696$		0			0
$697$	−9.13215	+	10.8833i	−0.345905	+	0.412233i
$698$		0			0
$699$	−7.44571	+	2.71002i	−0.281623	+	0.102502i
$700$		0			0
$701$	−7.13387	−	40.4582i	−0.269443	−	1.52809i	−0.756079	−	0.654481i	$-0.772887\pi$
$701$	−7.13387	−	40.4582i	−0.269443	−	1.52809i	0.486636	−	0.873605i	$-0.338224\pi$
$702$		0			0
$703$	2.34309	+	1.29703i	0.0883713	+	0.0489183i
$704$		0			0
$705$	−6.10521	−	7.14823i	−0.229935	−	0.269218i
$706$		0			0
$707$	−9.99345	−	27.4568i	−0.375842	−	1.03262i
$708$		0			0
$709$	8.86041	+	7.43476i	0.332760	+	0.279218i	0.793823	−	0.608149i	$-0.208088\pi$
$709$	8.86041	+	7.43476i	0.332760	+	0.279218i	−0.461064	+	0.887367i	$0.652532\pi$
$710$		0			0
$711$	2.08749	+	3.61564i	0.0782869	+	0.135597i
$712$		0			0
$713$	41.9251	+	7.39252i	1.57011	+	0.276852i
$714$		0			0
$715$	57.7063	−	0.503786i	2.15809	−	0.0188405i
$716$		0			0
$717$	0.981491	−	2.69662i	0.0366544	−	0.100707i
$718$		0			0
$719$	−15.3867	+	12.9110i	−0.573829	+	0.481499i	−0.882914	−	0.469535i	$-0.844422\pi$
$719$	−15.3867	+	12.9110i	−0.573829	+	0.481499i	0.309085	+	0.951034i	$0.399977\pi$
$720$		0			0
$721$	−13.2552			−0.493651
$722$		0			0
$723$			9.10734i			0.338706i
$724$		0			0
$725$	5.07307	+	26.0978i	0.188409	+	0.969246i
$726$		0			0
$727$	10.8824	−	29.8991i	0.403605	−	1.10890i	−0.556887	−	0.830588i	$-0.688004\pi$
$727$	10.8824	−	29.8991i	0.403605	−	1.10890i	0.960492	−	0.278307i	$-0.0897734\pi$
$728$		0			0
$729$	−9.63686	+	16.6915i	−0.356921	+	0.618205i
$730$		0			0
$731$	−1.42963	+	8.10784i	−0.0528768	+	0.299879i
$732$		0			0
$733$	4.51550	−	2.60703i	0.166784	−	0.0962927i	−0.414285	−	0.910147i	$-0.635968\pi$
$733$	4.51550	−	2.60703i	0.166784	−	0.0962927i	0.581068	+	0.813855i	$0.302635\pi$
$734$		0			0
$735$	−0.410621	+	2.45383i	−0.0151460	+	0.0905108i
$736$		0			0
$737$	−0.588463	−	1.61679i	−0.0216763	−	0.0595552i
$738$		0			0
$739$	4.28406	+	24.2961i	0.157592	+	0.893746i	0.956378	+	0.292132i	$0.0943646\pi$
$739$	4.28406	+	24.2961i	0.157592	+	0.893746i	−0.798786	+	0.601615i	$0.794524\pi$
$740$		0			0
$741$	4.21212	−	7.60923i	0.154736	−	0.279532i
$742$		0			0
$743$	−2.06863	+	0.364755i	−0.0758907	+	0.0133816i	−0.211465	−	0.977386i	$-0.567823\pi$
$743$	−2.06863	+	0.364755i	−0.0758907	+	0.0133816i	0.135574	+	0.990767i	$0.456712\pi$
$744$		0			0
$745$	31.5998	−	38.3339i	1.15773	−	1.40444i
$746$		0			0
$747$	−12.9586	+	15.4434i	−0.474130	+	0.565046i
$748$		0			0
$749$	−19.5755	−	33.9058i	−0.715274	−	1.23889i
$750$		0			0
$751$	3.55434	−	20.1577i	0.129700	−	0.735564i	−0.848705	−	0.528866i	$-0.822617\pi$
$751$	3.55434	−	20.1577i	0.129700	−	0.735564i	0.978405	−	0.206697i	$-0.0662716\pi$
$752$		0			0
$753$	−6.83662	−	3.94712i	−0.249140	−	0.143841i
$754$		0			0
$755$	16.8635	−	3.12553i	0.613727	−	0.113750i
$756$		0			0
$757$	11.3376	+	13.5116i	0.412072	+	0.491088i	0.931661	−	0.363328i	$-0.118360\pi$
$757$	11.3376	+	13.5116i	0.412072	+	0.491088i	−0.519590	+	0.854416i	$0.673915\pi$
$758$		0			0
$759$	13.3571			0.484830
$760$		0			0
$761$	13.3795			0.485006			0.242503	−	0.970151i	$-0.422032\pi$
$761$	13.3795			0.485006			0.242503	+	0.970151i	$0.422032\pi$
$762$		0			0
$763$	3.63310	+	4.32976i	0.131527	+	0.156748i
$764$		0			0
$765$	3.25021	+	17.5362i	0.117512	+	0.634024i
$766$		0			0
$767$	−5.52240	−	3.18836i	−0.199402	−	0.115125i
$768$		0			0
$769$	2.71812	−	15.4152i	0.0980179	−	0.555887i	−0.895763	−	0.444532i	$-0.853370\pi$
$769$	2.71812	−	15.4152i	0.0980179	−	0.555887i	0.993781	−	0.111355i	$-0.0355190\pi$
$770$		0			0
$771$	0.968181	+	1.67694i	0.0348682	+	0.0603935i
$772$		0			0
$773$	−16.0681	+	19.1492i	−0.577930	+	0.688750i	−0.973238	−	0.229799i	$-0.926193\pi$
$773$	−16.0681	+	19.1492i	−0.577930	+	0.688750i	0.395309	+	0.918548i	$0.370638\pi$
$774$		0			0
$775$	−4.81081	+	30.3756i	−0.172809	+	1.09112i
$776$		0			0
$777$	−0.474366	+	0.0836435i	−0.0170178	+	0.00300069i
$778$		0			0
$779$	−4.23596	−	21.7251i	−0.151769	−	0.778381i
$780$		0			0
$781$	11.4454	+	64.9103i	0.409550	+	2.32267i
$782$		0			0
$783$	−4.10999	−	11.2921i	−0.146879	−	0.403547i
$784$		0			0
$785$	−6.42365	+	38.3870i	−0.229270	+	1.37009i
$786$		0			0
$787$	−21.3578	+	12.3309i	−0.761323	+	0.439550i	−0.829770	−	0.558105i	$-0.811529\pi$
$787$	−21.3578	+	12.3309i	−0.761323	+	0.439550i	0.0684479	+	0.997655i	$0.478195\pi$
$788$		0			0
$789$	−1.04034	+	5.90007i	−0.0370372	+	0.210048i
$790$		0			0
$791$	−4.84864	+	8.39809i	−0.172398	+	0.298602i
$792$		0			0
$793$	−22.5263	+	61.8906i	−0.799934	+	2.19780i
$794$		0			0
$795$	−3.74276	+	10.5693i	−0.132742	+	0.374856i
$796$		0			0
$797$		−	10.7215i		−	0.379776i	−0.981806	−	0.189888i	$-0.939188\pi$
$797$		−	10.7215i		−	0.379776i	0.981806	−	0.189888i	$-0.0608125\pi$
$798$		0			0
$799$	−30.4510			−1.07728
$800$		0			0
$801$	−5.91699	+	4.96495i	−0.209067	+	0.175428i
$802$		0			0
$803$	7.37577	−	20.2648i	0.260285	−	0.715128i
$804$		0			0
$805$	0.274222	+	31.4108i	0.00966505	+	1.10708i
$806$		0			0
$807$	4.38948	+	0.773983i	0.154517	+	0.0272455i
$808$		0			0
$809$	−0.174831	−	0.302817i	−0.00614674	−	0.0106465i	0.862936	−	0.505314i	$-0.168623\pi$
$809$	−0.174831	−	0.302817i	−0.00614674	−	0.0106465i	−0.869082	+	0.494667i	$0.835290\pi$
$810$		0			0
$811$	0.144079	+	0.120897i	0.00505930	+	0.00424526i	0.645314	−	0.763918i	$-0.276727\pi$
$811$	0.144079	+	0.120897i	0.00505930	+	0.00424526i	−0.640254	+	0.768163i	$0.721171\pi$
$812$		0			0
$813$	1.64169	+	4.51052i	0.0575767	+	0.158191i
$814$		0			0
$815$	−11.2796	+	9.63377i	−0.395108	+	0.337456i
$816$		0			0
$817$	−8.42060	−	9.67549i	−0.294600	−	0.338503i
$818$		0			0
$819$	−5.19012	−	29.4346i	−0.181358	−	1.02853i
$820$		0			0
$821$	−10.1467	+	3.69308i	−0.354121	+	0.128889i	−0.512954	−	0.858416i	$-0.671449\pi$
$821$	−10.1467	+	3.69308i	−0.354121	+	0.128889i	0.158833	+	0.987305i	$0.449227\pi$
$822$		0			0
$823$	20.7215	−	24.6950i	0.722307	−	0.860812i	−0.272546	−	0.962143i	$-0.587866\pi$
$823$	20.7215	−	24.6950i	0.722307	−	0.860812i	0.994853	+	0.101331i	$0.0323100\pi$
$824$		0			0
$825$	0.168466	+	9.64775i	0.00586523	+	0.335891i
$826$		0			0
$827$	0.955921	+	0.168555i	0.0332406	+	0.00586122i	0.190244	−	0.981737i	$-0.439072\pi$
$827$	0.955921	+	0.168555i	0.0332406	+	0.00586122i	−0.157003	+	0.987598i	$0.550183\pi$
$828$		0			0
$829$	−7.94069	+	13.7537i	−0.275791	+	0.477685i	−0.970334	−	0.241766i	$-0.922273\pi$
$829$	−7.94069	+	13.7537i	−0.275791	+	0.477685i	0.694543	+	0.719451i	$0.255607\pi$
$830$		0			0
$831$	−1.38593	−	0.504436i	−0.0480773	−	0.0174987i
$832$		0			0
$833$	5.18031	+	6.17366i	0.179487	+	0.213904i
$834$		0			0
$835$	8.10173	+	13.7539i	0.280372	+	0.475974i
$836$		0			0
$837$		−	13.9007i		−	0.480477i
$838$		0			0
$839$	14.8550	−	12.4648i	0.512850	−	0.430333i	−0.349280	−	0.937018i	$-0.613574\pi$
$839$	14.8550	−	12.4648i	0.512850	−	0.430333i	0.862131	+	0.506686i	$0.169130\pi$
$840$		0			0
$841$	0.683015	+	0.248597i	0.0235522	+	0.00857232i
$842$		0			0
$843$	9.42443	+	5.44119i	0.324594	+	0.187405i
$844$		0			0
$845$	−10.7153	−	28.6590i	−0.368616	−	0.985899i
$846$		0			0
$847$	24.5406	−	14.1685i	0.843225	−	0.486836i
$848$		0			0
$849$	5.48479	+	4.60228i	0.188237	+	0.157950i
$850$		0			0
$851$	3.99602	−	1.45443i	0.136982	−	0.0498574i
$852$		0			0
$853$	−46.5514	+	8.20827i	−1.59389	+	0.281046i	−0.898960	−	0.438031i	$-0.855676\pi$
$853$	−46.5514	+	8.20827i	−1.59389	+	0.281046i	−0.694931	+	0.719077i	$0.744565\pi$
$854$		0			0
$855$	−24.4266	−	13.2442i	−0.835374	−	0.452942i
$856$		0			0
$857$	−14.4190	+	2.54245i	−0.492543	+	0.0868486i	−0.414402	−	0.910094i	$-0.636009\pi$
$857$	−14.4190	+	2.54245i	−0.492543	+	0.0868486i	−0.0781404	+	0.996942i	$0.524898\pi$
$858$		0			0
$859$	27.7553	−	10.1021i	0.946997	−	0.344679i	0.178072	−	0.984017i	$-0.443014\pi$
$859$	27.7553	−	10.1021i	0.946997	−	0.344679i	0.768925	+	0.639339i	$0.220792\pi$
$860$		0			0
$861$	3.04964	+	2.55895i	0.103931	+	0.0872089i
$862$		0			0
$863$	−6.58447	+	3.80155i	−0.224138	+	0.129406i	−0.607865	−	0.794040i	$-0.707974\pi$
$863$	−6.58447	+	3.80155i	−0.224138	+	0.129406i	0.383727	+	0.923447i	$0.374640\pi$
$864$		0			0
$865$	26.3293	−	9.84420i	0.895222	−	0.334713i
$866$		0			0
$867$	3.06826	+	1.77146i	0.104204	+	0.0601620i
$868$		0			0
$869$	6.87557	+	2.50250i	0.233238	+	0.0848916i
$870$		0			0
$871$	−1.36272	+	1.14345i	−0.0461739	+	0.0387445i
$872$		0			0
$873$		−	30.3742i		−	1.02801i
$874$		0			0
$875$	−22.6844	+	0.594238i	−0.766873	+	0.0200889i
$876$		0			0
$877$	−13.3391	−	15.8969i	−0.450430	−	0.536801i	0.492270	−	0.870442i	$-0.336167\pi$
$877$	−13.3391	−	15.8969i	−0.450430	−	0.536801i	−0.942700	+	0.333641i	$0.891723\pi$
$878$		0			0
$879$	−6.27281	−	2.28312i	−0.211577	−	0.0770076i
$880$		0			0
$881$	6.17836	−	10.7012i	0.208154	−	0.360534i	−0.742979	−	0.669315i	$-0.766588\pi$
$881$	6.17836	−	10.7012i	0.208154	−	0.360534i	0.951133	+	0.308781i	$0.0999211\pi$
$882$		0			0
$883$	36.5445	+	6.44379i	1.22982	+	0.216851i	0.750548	−	0.660815i	$-0.229789\pi$
$883$	36.5445	+	6.44379i	1.22982	+	0.216851i	0.479273	+	0.877666i	$0.340900\pi$
$884$		0			0
$885$	0.525032	−	0.927998i	0.0176488	−	0.0311943i
$886$		0			0
$887$	−13.5613	+	16.1617i	−0.455343	+	0.542656i	−0.944055	−	0.329789i	$-0.893022\pi$
$887$	−13.5613	+	16.1617i	−0.455343	+	0.542656i	0.488712	+	0.872445i	$0.337467\pi$
$888$		0			0
$889$	11.6208	−	4.22964i	0.389750	−	0.141857i
$890$		0			0
$891$	6.66248	+	37.7848i	0.223201	+	1.26584i
$892$		0			0
$893$	29.8347	−	36.8863i	0.998379	−	1.23435i
$894$		0			0
$895$	27.8728	+	32.6346i	0.931684	+	1.09085i
$896$		0			0
$897$	−4.72331	−	12.9772i	−0.157707	−	0.433295i
$898$		0			0
$899$	−25.0539	−	21.0227i	−0.835594	−	0.701146i
$900$		0			0
$901$	18.1601	+	31.4542i	0.605000	+	1.04789i
$902$		0			0
$903$	2.27193	+	0.400602i	0.0756050	+	0.0133312i
$904$		0			0
$905$	0.258612	+	29.6227i	0.00859654	+	0.984691i
$906$		0			0
$907$	10.7770	−	29.6094i	0.357843	−	0.983165i	−0.621934	−	0.783070i	$-0.713653\pi$
$907$	10.7770	−	29.6094i	0.357843	−	0.983165i	0.979776	−	0.200095i	$-0.0641252\pi$
$908$		0			0
$909$	31.4386	−	26.3801i	1.04275	−	0.874972i
$910$		0			0
$911$	−27.0162			−0.895085			−0.447543	−	0.894263i	$-0.647701\pi$
$911$	−27.0162			−0.895085			−0.447543	+	0.894263i	$0.647701\pi$
$912$		0			0
$913$			35.3313i			1.16929i
$914$		0			0
$915$	−10.3810	−	3.67606i	−0.343185	−	0.121527i
$916$		0			0
$917$	3.03892	−	8.34937i	0.100354	−	0.275720i
$918$		0			0
$919$	−1.94333	+	3.36595i	−0.0641045	+	0.111032i	−0.896296	−	0.443455i	$-0.853752\pi$
$919$	−1.94333	+	3.36595i	−0.0641045	+	0.111032i	0.832192	+	0.554488i	$0.187086\pi$
$920$		0			0
$921$	1.75771	−	9.96850i	0.0579187	−	0.328473i
$922$		0			0
$923$	59.0169	−	34.0734i	1.94256	−	1.12154i
$924$		0			0
$925$	1.10093	+	2.86797i	0.0361984	+	0.0942982i
$926$		0			0
$927$	−6.36772	−	17.4952i	−0.209144	−	0.574617i
$928$		0			0
$929$	5.87379	+	33.3119i	0.192713	+	1.09293i	0.915638	+	0.402003i	$0.131686\pi$
$929$	5.87379	+	33.3119i	0.192713	+	1.09293i	−0.722926	+	0.690926i	$0.757203\pi$
$930$		0			0
$931$	−12.5538	+	0.226386i	−0.411435	+	0.00741949i
$932$		0			0
$933$	1.62335	−	0.286241i	0.0531462	−	0.00937111i
$934$		0			0
$935$	24.1183	+	19.8815i	0.788753	+	0.650193i
$936$		0			0
$937$	−4.26094	+	5.07798i	−0.139199	+	0.165891i	−0.831140	−	0.556063i	$-0.812311\pi$
$937$	−4.26094	+	5.07798i	−0.139199	+	0.165891i	0.691941	+	0.721954i	$0.256756\pi$
$938$		0			0
$939$	4.39792	+	7.61743i	0.143521	+	0.248585i
$940$		0			0
$941$	3.66372	−	20.7780i	0.119434	−	0.677344i	−0.865025	−	0.501729i	$-0.832698\pi$
$941$	3.66372	−	20.7780i	0.119434	−	0.677344i	0.984459	−	0.175615i	$-0.0561913\pi$
$942$		0			0
$943$	−30.4373	−	17.5730i	−0.991174	−	0.572254i
$944$		0			0
$945$	10.0850	−	1.86917i	0.328064	−	0.0608042i
$946$		0			0
$947$	−17.0313	−	20.2971i	−0.553442	−	0.659567i	0.414703	−	0.909957i	$-0.363886\pi$
$947$	−17.0313	−	20.2971i	−0.553442	−	0.659567i	−0.968145	+	0.250390i	$0.919441\pi$
$948$		0			0
$949$	−22.2966			−0.723779
$950$		0			0
$951$	−7.82067			−0.253603
$952$		0			0
$953$	24.6105	+	29.3297i	0.797214	+	0.950083i	0.999573	−	0.0292289i	$-0.00930518\pi$
$953$	24.6105	+	29.3297i	0.797214	+	0.950083i	−0.202359	+	0.979311i	$0.564861\pi$
$954$		0			0
$955$	−17.4284	+	3.23022i	−0.563969	+	0.104527i
$956$		0			0
$957$	−8.88669	−	5.13073i	−0.287266	−	0.165853i
$958$		0			0
$959$	−0.0442615	+	0.251019i	−0.00142928	+	0.00810583i
$960$		0			0
$961$	−3.41637	−	5.91733i	−0.110206	−	0.190882i
$962$		0			0
$963$	35.3472	−	42.1252i	1.13905	−	1.35747i
$964$		0			0
$965$	−25.9642	−	21.4031i	−0.835817	−	0.688990i
$966$		0			0
$967$	−48.8965	+	8.62177i	−1.57241	+	0.277257i	−0.890777	−	0.454441i	$-0.849839\pi$
$967$	−48.8965	+	8.62177i	−1.57241	+	0.277257i	−0.681628	+	0.731699i	$0.738728\pi$
$968$		0			0
$969$	4.39681	−	1.69069i	0.141246	−	0.0543129i
$970$		0			0
$971$	−7.62257	−	43.2298i	−0.244620	−	1.38731i	−0.821374	−	0.570391i	$-0.806792\pi$
$971$	−7.62257	−	43.2298i	−0.244620	−	1.38731i	0.576754	−	0.816918i	$-0.304319\pi$
$972$		0			0
$973$	−1.07449	−	2.95215i	−0.0344467	−	0.0946415i
$974$		0			0
$975$	9.31379	−	3.57530i	0.298280	−	0.114501i
$976$		0			0
$977$	25.7948	−	14.8927i	0.825250	−	0.476458i	−0.0269734	−	0.999636i	$-0.508587\pi$
$977$	25.7948	−	14.8927i	0.825250	−	0.476458i	0.852224	+	0.523178i	$0.175254\pi$
$978$		0			0
$979$	−2.35064	+	13.3311i	−0.0751268	+	0.426065i
$980$		0			0
$981$	−3.96939	+	6.87519i	−0.126733	+	0.219508i
$982$		0			0
$983$	−14.8621	+	40.8333i	−0.474028	+	1.30238i	0.440462	+	0.897771i	$0.354815\pi$
$983$	−14.8621	+	40.8333i	−0.474028	+	1.30238i	−0.914490	+	0.404610i	$0.867407\pi$
$984$		0			0
$985$	55.4955	+	19.6518i	1.76823	+	0.626158i
$986$		0			0
$987$			8.53279i			0.271602i
$988$		0			0
$989$	−20.3668			−0.647627
$990$		0			0
$991$	−45.0781	+	37.8250i	−1.43195	+	1.20155i	−0.487407	+	0.873175i	$0.662057\pi$
$991$	−45.0781	+	37.8250i	−1.43195	+	1.20155i	−0.944547	+	0.328377i	$0.893498\pi$
$992$		0			0
$993$	−2.17203	+	5.96760i	−0.0689273	+	0.189376i
$994$		0			0
$995$	0.00171821	+	0.196813i	5.44710e−5	+	0.00623939i
$996$		0			0
$997$	−29.2085	−	5.15024i	−0.925042	−	0.163110i	−0.309216	−	0.950992i	$-0.600067\pi$
$997$	−29.2085	−	5.15024i	−0.925042	−	0.163110i	−0.615826	+	0.787882i	$0.711178\pi$
$998$		0			0
$999$	−0.694265	−	1.20250i	−0.0219656	−	0.0380455i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	760.2.cg.a.9.13	✓	180
5.4	even	2	inner	760.2.cg.a.9.18	yes	180
19.17	even	9	inner	760.2.cg.a.169.18	yes	180
95.74	even	18	inner	760.2.cg.a.169.13	yes	180

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
760.2.cg.a.9.13	✓	180	1.1	even	1	trivial
760.2.cg.a.9.18	yes	180	5.4	even	2	inner
760.2.cg.a.169.13	yes	180	95.74	even	18	inner
760.2.cg.a.169.18	yes	180	19.17	even	9	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 760 = 2^{3} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	760.cg (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.248287 - 0.295897i) q^{3} +(2.19862 - 0.407498i) q^{5} +(-1.75773 - 1.01483i) q^{7} +(0.495036 - 2.80749i) q^{9} +O(q^{10})\)	\(q+(-0.248287 - 0.295897i) q^{3} +(2.19862 - 0.407498i) q^{5} +(-1.75773 - 1.01483i) q^{7} +(0.495036 - 2.80749i) q^{9} +(-2.49808 - 4.32679i) q^{11} +(-3.32037 + 3.95706i) q^{13} +(-0.666467 - 0.549389i) q^{15} +(-2.75531 + 0.485835i) q^{17} +(2.11103 - 3.81360i) q^{19} +(0.136138 + 0.772075i) q^{21} +(-2.36723 - 6.50391i) q^{23} +(4.66789 - 1.79187i) q^{25} +(-1.95719 + 1.12998i) q^{27} +(-0.923331 + 5.23647i) q^{29} +(-3.07542 + 5.32678i) q^{31} +(-0.660045 + 1.81346i) q^{33} +(-4.27813 - 1.51495i) q^{35} +0.614404i q^{37} +1.99529 q^{39} +(3.88992 - 3.26403i) q^{41} +(1.00644 - 2.76516i) q^{43} +(-0.0556491 - 6.37434i) q^{45} +(10.7185 + 1.88996i) q^{47} +(-1.44026 - 2.49460i) q^{49} +(0.827865 + 0.694661i) q^{51} +(-4.43998 - 12.1987i) q^{53} +(-7.25549 - 8.49503i) q^{55} +(-1.65257 + 0.322219i) q^{57} +(0.214362 + 1.21571i) q^{59} +(11.9813 - 4.36085i) q^{61} +(-3.71925 + 4.43243i) q^{63} +(-5.68775 + 10.0531i) q^{65} +(0.339144 + 0.0598002i) q^{67} +(-1.33673 + 2.31529i) q^{69} +(-12.3969 - 4.51209i) q^{71} +(2.77452 + 3.30654i) q^{73} +(-1.68919 - 0.936316i) q^{75} +10.1404i q^{77} +(-1.12187 + 0.941358i) q^{79} +(-7.21632 - 2.62653i) q^{81} +(-6.12427 - 3.53585i) q^{83} +(-5.85991 + 2.19095i) q^{85} +(1.77871 - 1.02694i) q^{87} +(-2.07556 - 1.74160i) q^{89} +(9.85205 - 3.58585i) q^{91} +(2.33976 - 0.412563i) q^{93} +(3.08733 - 9.24491i) q^{95} +(10.4928 - 1.85016i) q^{97} +(-13.3841 + 4.87140i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 180 q+O(q^{10}) \) 180 * q	\( 180 q - 12 q^{15} + 12 q^{25} + 24 q^{35} - 18 q^{41} + 18 q^{45} + 90 q^{49} + 36 q^{51} - 36 q^{55} - 12 q^{59} + 48 q^{69} - 24 q^{71} - 156 q^{79} + 24 q^{81} + 12 q^{85} - 36 q^{89} + 36 q^{91} + 78 q^{95} + 42 q^{99}+O(q^{100}) \) 180 * q - 12 * q^15 + 12 * q^25 + 24 * q^35 - 18 * q^41 + 18 * q^45 + 90 * q^49 + 36 * q^51 - 36 * q^55 - 12 * q^59 + 48 * q^69 - 24 * q^71 - 156 * q^79 + 24 * q^81 + 12 * q^85 - 36 * q^89 + 36 * q^91 + 78 * q^95 + 42 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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