LMFDB - Embedded newform 288.2.s.a.95.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,2,Mod(95,288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(288, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("288.95");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	288.s (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.29969157821$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			95.10
Character	$\chi$	$=$	288.95
Dual form			288.2.s.a.191.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.20567 + 1.24353i) q^{3} +(-0.398132 - 0.229862i) q^{5} +(4.28309 - 2.47284i) q^{7} +(-0.0927324 + 2.99857i) q^{9} +O(q^{10})$	\(q+(1.20567 + 1.24353i) q^{3} +(-0.398132 - 0.229862i) q^{5} +(4.28309 - 2.47284i) q^{7} +(-0.0927324 + 2.99857i) q^{9} +(-1.17474 - 2.03471i) q^{11} +(-0.0384586 + 0.0666122i) q^{13} +(-0.194175 - 0.772226i) q^{15} +5.92857i q^{17} +3.59561i q^{19} +(8.23903 + 2.34472i) q^{21} +(2.41469 - 4.18237i) q^{23} +(-2.39433 - 4.14710i) q^{25} +(-3.84061 + 3.49996i) q^{27} +(-6.54954 + 3.78138i) q^{29} +(0.663421 + 0.383026i) q^{31} +(1.11388 - 3.91401i) q^{33} -2.27365 q^{35} -5.47993 q^{37} +(-0.129203 + 0.0324878i) q^{39} +(-0.986492 - 0.569551i) q^{41} +(6.79101 - 3.92079i) q^{43} +(0.726176 - 1.17251i) q^{45} +(-3.01076 - 5.21479i) q^{47} +(8.72990 - 15.1206i) q^{49} +(-7.37235 + 7.14788i) q^{51} -9.71390i q^{53} +1.08011i q^{55} +(-4.47124 + 4.33511i) q^{57} +(-4.15776 + 7.20145i) q^{59} +(2.63407 + 4.56234i) q^{61} +(7.01780 + 13.0724i) q^{63} +(0.0306232 - 0.0176803i) q^{65} +(-1.84450 - 1.06492i) q^{67} +(8.11221 - 2.03980i) q^{69} -10.6650 q^{71} -7.51416 q^{73} +(2.27028 - 7.97744i) q^{75} +(-10.0630 - 5.80990i) q^{77} +(-2.52870 + 1.45994i) q^{79} +(-8.98280 - 0.556128i) q^{81} +(-4.44322 - 7.69588i) q^{83} +(1.36275 - 2.36035i) q^{85} +(-12.5988 - 3.58546i) q^{87} +9.71390i q^{89} +0.380408i q^{91} +(0.323560 + 1.28679i) q^{93} +(0.826493 - 1.43153i) q^{95} +(3.16305 + 5.47856i) q^{97} +(6.21016 - 3.33386i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{9}+O(q^{10}) $ 24 * q - 4 * q^9	$ 24 q - 4 q^{9} + 8 q^{21} + 12 q^{25} + 24 q^{29} - 20 q^{33} - 36 q^{41} - 8 q^{45} + 12 q^{49} - 36 q^{57} - 48 q^{65} - 16 q^{69} + 24 q^{73} - 48 q^{77} - 20 q^{81} - 64 q^{93} + 12 q^{97}+O(q^{100}) $ 24 * q - 4 * q^9 + 8 * q^21 + 12 * q^25 + 24 * q^29 - 20 * q^33 - 36 * q^41 - 8 * q^45 + 12 * q^49 - 36 * q^57 - 48 * q^65 - 16 * q^69 + 24 * q^73 - 48 * q^77 - 20 * q^81 - 64 * q^93 + 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

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
$3$	1.20567	+	1.24353i	0.696092	+	0.717952i
$3$	1.20567	+	1.24353i	0.696092	+	0.717952i
$4$		0			0
$5$	−0.398132	−	0.229862i	−0.178050	−	0.102797i	0.408326	−	0.912836i	$-0.366113\pi$
$5$	−0.398132	−	0.229862i	−0.178050	−	0.102797i	−0.586376	+	0.810039i	$0.699446\pi$
$6$		0			0
$7$	4.28309	−	2.47284i	1.61886	−	0.934647i	0.631638	−	0.775263i	$-0.282383\pi$
$7$	4.28309	−	2.47284i	1.61886	−	0.934647i	0.987217	−	0.159383i	$-0.0509506\pi$
$8$		0			0
$9$	−0.0927324	+	2.99857i	−0.0309108	+	0.999522i
$10$		0			0
$11$	−1.17474	−	2.03471i	−0.354198	−	0.613489i	0.632782	−	0.774330i	$-0.281913\pi$
$11$	−1.17474	−	2.03471i	−0.354198	−	0.613489i	−0.986980	+	0.160841i	$0.948579\pi$
$12$		0			0
$13$	−0.0384586	+	0.0666122i	−0.0106665	+	0.0184749i	−0.871309	−	0.490734i	$-0.836729\pi$
$13$	−0.0384586	+	0.0666122i	−0.0106665	+	0.0184749i	0.860643	+	0.509209i	$0.170062\pi$
$14$		0			0
$15$	−0.194175	−	0.772226i	−0.0501358	−	0.199388i
$16$		0			0
$17$			5.92857i			1.43789i	0.695068	+	0.718944i	$0.255374\pi$
$17$			5.92857i			1.43789i	−0.695068	+	0.718944i	$0.744626\pi$
$18$		0			0
$19$			3.59561i			0.824889i	0.910983	+	0.412444i	$0.135325\pi$
$19$			3.59561i			0.824889i	−0.910983	+	0.412444i	$0.864675\pi$
$20$		0			0
$21$	8.23903	+	2.34472i	1.79790	+	0.511660i
$22$		0			0
$23$	2.41469	−	4.18237i	0.503498	−	0.872084i	−0.496494	−	0.868040i	$-0.665379\pi$
$23$	2.41469	−	4.18237i	0.503498	−	0.872084i	0.999992	−	0.00404388i	$-0.00128721\pi$
$24$		0			0
$25$	−2.39433	−	4.14710i	−0.478865	−	0.829419i
$26$		0			0
$27$	−3.84061	+	3.49996i	−0.739126	+	0.673567i
$28$		0			0
$29$	−6.54954	+	3.78138i	−1.21622	+	0.702184i	−0.964107	−	0.265514i	$-0.914458\pi$
$29$	−6.54954	+	3.78138i	−1.21622	+	0.702184i	−0.252112	+	0.967698i	$0.581125\pi$
$30$		0			0
$31$	0.663421	+	0.383026i	0.119154	+	0.0687935i	0.558392	−	0.829577i	$-0.311418\pi$
$31$	0.663421	+	0.383026i	0.119154	+	0.0687935i	−0.439238	+	0.898370i	$0.644752\pi$
$32$		0			0
$33$	1.11388	−	3.91401i	0.193901	−	0.681342i
$34$		0			0
$35$	−2.27365			−0.384317
$36$		0			0
$37$	−5.47993			−0.900894			−0.450447	−	0.892803i	$-0.648735\pi$
$37$	−5.47993			−0.900894			−0.450447	+	0.892803i	$0.648735\pi$
$38$		0			0
$39$	−0.129203	+	0.0324878i	−0.0206890	+	0.00520221i
$40$		0			0
$41$	−0.986492	−	0.569551i	−0.154064	−	0.0889490i	0.420986	−	0.907067i	$-0.361684\pi$
$41$	−0.986492	−	0.569551i	−0.154064	−	0.0889490i	−0.575050	+	0.818118i	$0.695017\pi$
$42$		0			0
$43$	6.79101	−	3.92079i	1.03562	−	0.597915i	0.117030	−	0.993128i	$-0.462663\pi$
$43$	6.79101	−	3.92079i	1.03562	−	0.597915i	0.918590	+	0.395213i	$0.129329\pi$
$44$		0			0
$45$	0.726176	−	1.17251i	0.108252	−	0.174788i
$46$		0			0
$47$	−3.01076	−	5.21479i	−0.439165	−	0.760656i	0.558461	−	0.829531i	$-0.311392\pi$
$47$	−3.01076	−	5.21479i	−0.439165	−	0.760656i	−0.997625	+	0.0688755i	$0.978059\pi$
$48$		0			0
$49$	8.72990	−	15.1206i	1.24713	−	2.16009i
$50$		0			0
$51$	−7.37235	+	7.14788i	−1.03234	+	1.00090i
$52$		0			0
$53$		−	9.71390i		−	1.33431i	−0.744920	−	0.667154i	$-0.767512\pi$
$53$		−	9.71390i		−	1.33431i	0.744920	−	0.667154i	$-0.232488\pi$
$54$		0			0
$55$			1.08011i			0.145642i
$56$		0			0
$57$	−4.47124	+	4.33511i	−0.592231	+	0.574199i
$58$		0			0
$59$	−4.15776	+	7.20145i	−0.541294	+	0.937548i	0.457536	+	0.889191i	$0.348732\pi$
$59$	−4.15776	+	7.20145i	−0.541294	+	0.937548i	−0.998830	+	0.0483574i	$0.984601\pi$
$60$		0			0
$61$	2.63407	+	4.56234i	0.337258	+	0.584147i	0.983916	−	0.178633i	$-0.0571674\pi$
$61$	2.63407	+	4.56234i	0.337258	+	0.584147i	−0.646658	+	0.762780i	$0.723834\pi$
$62$		0			0
$63$	7.01780	+	13.0724i	0.884160	+	1.64697i
$64$		0			0
$65$	0.0306232	−	0.0176803i	0.00379834	−	0.00219297i
$66$		0			0
$67$	−1.84450	−	1.06492i	−0.225342	−	0.130101i	0.383079	−	0.923715i	$-0.374864\pi$
$67$	−1.84450	−	1.06492i	−0.225342	−	0.130101i	−0.608421	+	0.793614i	$0.708197\pi$
$68$		0			0
$69$	8.11221	−	2.03980i	0.976596	−	0.245564i
$70$		0			0
$71$	−10.6650			−1.26570			−0.632851	−	0.774273i	$-0.718115\pi$
$71$	−10.6650			−1.26570			−0.632851	+	0.774273i	$0.718115\pi$
$72$		0			0
$73$	−7.51416			−0.879466			−0.439733	−	0.898129i	$-0.644927\pi$
$73$	−7.51416			−0.879466			−0.439733	+	0.898129i	$0.644927\pi$
$74$		0			0
$75$	2.27028	−	7.97744i	0.262149	−	0.921155i
$76$		0			0
$77$	−10.0630	−	5.80990i	−1.14679	−	0.662100i
$78$		0			0
$79$	−2.52870	+	1.45994i	−0.284501	+	0.164256i	−0.635459	−	0.772135i	$-0.719189\pi$
$79$	−2.52870	+	1.45994i	−0.284501	+	0.164256i	0.350959	+	0.936391i	$0.385856\pi$
$80$		0			0
$81$	−8.98280	−	0.556128i	−0.998089	−	0.0617920i
$82$		0			0
$83$	−4.44322	−	7.69588i	−0.487706	−	0.844732i	0.512194	−	0.858870i	$-0.328833\pi$
$83$	−4.44322	−	7.69588i	−0.487706	−	0.844732i	−0.999900	+	0.0141378i	$0.995500\pi$
$84$		0			0
$85$	1.36275	−	2.36035i	0.147811	−	0.256016i
$86$		0			0
$87$	−12.5988	−	3.58546i	−1.35074	−	0.384402i
$88$		0			0
$89$			9.71390i			1.02967i	0.857289	+	0.514836i	$0.172147\pi$
$89$			9.71390i			1.02967i	−0.857289	+	0.514836i	$0.827853\pi$
$90$		0			0
$91$			0.380408i			0.0398776i
$92$		0			0
$93$	0.323560	+	1.28679i	0.0335517	+	0.133433i
$94$		0			0
$95$	0.826493	−	1.43153i	0.0847964	−	0.146872i
$96$		0			0
$97$	3.16305	+	5.47856i	0.321159	+	0.556263i	0.980727	−	0.195381i	$-0.0625944\pi$
$97$	3.16305	+	5.47856i	0.321159	+	0.556263i	−0.659569	+	0.751644i	$0.729261\pi$
$98$		0			0
$99$	6.21016	−	3.33386i	0.624144	−	0.335065i
$100$		0			0
$101$	4.50085	−	2.59857i	0.447851	−	0.258567i	−0.259071	−	0.965858i	$-0.583416\pi$
$101$	4.50085	−	2.59857i	0.447851	−	0.258567i	0.706922	+	0.707291i	$0.250083\pi$
$102$		0			0
$103$	−2.41781	−	1.39593i	−0.238234	−	0.137545i	0.376131	−	0.926567i	$-0.377254\pi$
$103$	−2.41781	−	1.39593i	−0.238234	−	0.137545i	−0.614365	+	0.789022i	$0.710588\pi$
$104$		0			0
$105$	−2.74126	−	2.82735i	−0.267520	−	0.275921i
$106$		0			0
$107$	14.5911			1.41057			0.705286	−	0.708923i	$-0.250819\pi$
$107$	14.5911			1.41057			0.705286	+	0.708923i	$0.250819\pi$
$108$		0			0
$109$	−12.6711			−1.21368			−0.606838	−	0.794826i	$-0.707562\pi$
$109$	−12.6711			−1.21368			−0.606838	+	0.794826i	$0.707562\pi$
$110$		0			0
$111$	−6.60697	−	6.81445i	−0.627106	−	0.646799i
$112$		0			0
$113$	16.5820	+	9.57360i	1.55990	+	0.900608i	0.997265	+	0.0739025i	$0.0235454\pi$
$113$	16.5820	+	9.57360i	1.55990	+	0.900608i	0.562634	+	0.826706i	$0.309788\pi$
$114$		0			0
$115$	−1.92273	+	1.11009i	−0.179296	+	0.103517i
$116$		0			0
$117$	−0.196175	−	0.121498i	−0.0181364	−	0.0112325i
$118$		0			0
$119$	14.6604	+	25.3926i	1.34392	+	2.32773i
$120$		0			0
$121$	2.73996	−	4.74576i	0.249088	−	0.431432i
$122$		0			0
$123$	−0.481127	−	1.91342i	−0.0433818	−	0.172527i
$124$		0			0
$125$			4.50008i			0.402499i
$126$		0			0
$127$			11.2364i			0.997071i	0.866869	+	0.498535i	$0.166129\pi$
$127$			11.2364i			0.997071i	−0.866869	+	0.498535i	$0.833871\pi$
$128$		0			0
$129$	13.0633	+	3.71765i	1.15016	+	0.327321i
$130$		0			0
$131$	7.54434	−	13.0672i	0.659152	−	1.14168i	−0.321684	−	0.946847i	$-0.604249\pi$
$131$	7.54434	−	13.0672i	0.659152	−	1.14168i	0.980836	−	0.194837i	$-0.0624178\pi$
$132$		0			0
$133$	8.89137	+	15.4003i	0.770979	+	1.33538i
$134$		0			0
$135$	2.33358	−	0.510637i	0.200842	−	0.0439486i
$136$		0			0
$137$	−3.11622	+	1.79915i	−0.266237	+	0.153712i	−0.627176	−	0.778877i	$-0.715789\pi$
$137$	−3.11622	+	1.79915i	−0.266237	+	0.153712i	0.360939	+	0.932589i	$0.382456\pi$
$138$		0			0
$139$	−6.13766	−	3.54358i	−0.520590	−	0.300563i	0.216586	−	0.976264i	$-0.430508\pi$
$139$	−6.13766	−	3.54358i	−0.520590	−	0.300563i	−0.737176	+	0.675701i	$0.763841\pi$
$140$		0			0
$141$	2.85477	−	10.0313i	0.240415	−	0.844786i
$142$		0			0
$143$	0.180716			0.0151122
$144$		0			0
$145$	3.47678			0.288731
$146$		0			0
$147$	29.3283	−	7.37456i	2.41896	−	0.608243i
$148$		0			0
$149$	0.985645	+	0.569062i	0.0807472	+	0.0466194i	0.539830	−	0.841774i	$-0.318489\pi$
$149$	0.985645	+	0.569062i	0.0807472	+	0.0466194i	−0.459083	+	0.888393i	$0.651822\pi$
$150$		0			0
$151$	9.68181	−	5.58979i	0.787894	−	0.454891i	−0.0513265	−	0.998682i	$-0.516345\pi$
$151$	9.68181	−	5.58979i	0.787894	−	0.454891i	0.839221	+	0.543791i	$0.183012\pi$
$152$		0			0
$153$	−17.7772	−	0.549770i	−1.43720	−	0.0444463i
$154$		0			0
$155$	−0.176086	−	0.304990i	−0.0141436	−	0.0244974i
$156$		0			0
$157$	−8.18986	+	14.1853i	−0.653622	+	1.13211i	0.328615	+	0.944464i	$0.393418\pi$
$157$	−8.18986	+	14.1853i	−0.653622	+	1.13211i	−0.982237	+	0.187643i	$0.939915\pi$
$158$		0			0
$159$	12.0795	−	11.7117i	0.957969	−	0.928801i
$160$		0			0
$161$		−	23.8846i		−	1.88237i
$162$		0			0
$163$			4.04520i			0.316845i	0.987371	+	0.158422i	$0.0506408\pi$
$163$			4.04520i			0.316845i	−0.987371	+	0.158422i	$0.949359\pi$
$164$		0			0
$165$	−1.34315	+	1.30226i	−0.104564	+	0.101381i
$166$		0			0
$167$	−1.58072	+	2.73790i	−0.122320	+	0.211865i	−0.920682	−	0.390313i	$-0.872367\pi$
$167$	−1.58072	+	2.73790i	−0.122320	+	0.211865i	0.798362	+	0.602178i	$0.205700\pi$
$168$		0			0
$169$	6.49704	+	11.2532i	0.499772	+	0.865631i
$170$		0			0
$171$	−10.7817	−	0.333429i	−0.824495	−	0.0254980i
$172$		0			0
$173$	17.4056	−	10.0491i	1.32333	−	0.764022i	0.339068	−	0.940762i	$-0.389888\pi$
$173$	17.4056	−	10.0491i	1.32333	−	0.764022i	0.984258	+	0.176739i	$0.0565550\pi$
$174$		0			0
$175$	−20.5102	−	11.8416i	−1.55043	−	0.895140i
$176$		0			0
$177$	−13.9681	+	3.51225i	−1.04991	+	0.263997i
$178$		0			0
$179$	10.1699			0.760135			0.380067	−	0.924959i	$-0.375901\pi$
$179$	10.1699			0.760135			0.380067	+	0.924959i	$0.375901\pi$
$180$		0			0
$181$	15.0572			1.11920			0.559598	−	0.828764i	$-0.310956\pi$
$181$	15.0572			1.11920			0.559598	+	0.828764i	$0.310956\pi$
$182$		0			0
$183$	−2.49759	+	8.77620i	−0.184627	+	0.648755i
$184$		0			0
$185$	2.18174	+	1.25963i	0.160404	+	0.0926095i
$186$		0			0
$187$	12.0629	−	6.96454i	0.882129	−	0.509297i
$188$		0			0
$189$	−7.79483	+	24.4879i	−0.566991	+	1.78123i
$190$		0			0
$191$	−1.41193	−	2.44554i	−0.102164	−	0.176953i	0.810412	−	0.585860i	$-0.199243\pi$
$191$	−1.41193	−	2.44554i	−0.102164	−	0.176953i	−0.912576	+	0.408907i	$0.865910\pi$
$192$		0			0
$193$	−8.95170	+	15.5048i	−0.644357	+	1.11606i	0.340092	+	0.940392i	$0.389542\pi$
$193$	−8.95170	+	15.5048i	−0.644357	+	1.11606i	−0.984450	+	0.175668i	$0.943792\pi$
$194$		0			0
$195$	0.0589074	+	0.0167643i	0.00421845	+	0.00120052i
$196$		0			0
$197$			5.65685i			0.403034i	0.979485	+	0.201517i	$0.0645872\pi$
$197$			5.65685i			0.403034i	−0.979485	+	0.201517i	$0.935413\pi$
$198$		0			0
$199$			6.78022i			0.480637i	0.970694	+	0.240319i	$0.0772519\pi$
$199$			6.78022i			0.480637i	−0.970694	+	0.240319i	$0.922748\pi$
$200$		0			0
$201$	−0.899592	−	3.57764i	−0.0634524	−	0.252347i
$202$		0			0
$203$	−18.7015	+	32.3919i	−1.31259	+	2.27347i
$204$		0			0
$205$	0.261836	+	0.453514i	0.0182874	+	0.0316748i
$206$		0			0
$207$	12.3172	+	7.62845i	0.856104	+	0.530214i
$208$		0			0
$209$	7.31603	−	4.22391i	0.506060	−	0.292174i
$210$		0			0
$211$	−14.2250	−	8.21281i	−0.979289	−	0.565393i	−0.0772337	−	0.997013i	$-0.524609\pi$
$211$	−14.2250	−	8.21281i	−0.979289	−	0.565393i	−0.902055	+	0.431620i	$0.857942\pi$
$212$		0			0
$213$	−12.8584	−	13.2622i	−0.881046	−	0.908714i
$214$		0			0
$215$	−3.60496			−0.245856
$216$		0			0
$217$	3.78865			0.257191
$218$		0			0
$219$	−9.05957	−	9.34408i	−0.612189	−	0.631414i
$220$		0			0
$221$	−0.394915	−	0.228004i	−0.0265649	−	0.0153372i
$222$		0			0
$223$	−13.5026	+	7.79574i	−0.904202	+	0.522041i	−0.878561	−	0.477630i	$-0.841496\pi$
$223$	−13.5026	+	7.79574i	−0.904202	+	0.522041i	−0.0256409	+	0.999671i	$0.508163\pi$
$224$		0			0
$225$	12.6574	−	6.79498i	0.843825	−	0.452999i
$226$		0			0
$227$	2.25723	+	3.90964i	0.149818	+	0.259492i	0.931160	−	0.364611i	$-0.118798\pi$
$227$	2.25723	+	3.90964i	0.149818	+	0.259492i	−0.781342	+	0.624103i	$0.785465\pi$
$228$		0			0
$229$	2.77842	−	4.81237i	0.183603	−	0.318010i	−0.759502	−	0.650505i	$-0.774557\pi$
$229$	2.77842	−	4.81237i	0.183603	−	0.318010i	0.943105	+	0.332495i	$0.107890\pi$
$230$		0			0
$231$	−4.90790	−	19.5185i	−0.322916	−	1.28422i
$232$		0			0
$233$			1.32613i			0.0868780i	0.999056	+	0.0434390i	$0.0138314\pi$
$233$			1.32613i			0.0868780i	−0.999056	+	0.0434390i	$0.986169\pi$
$234$		0			0
$235$			2.76824i			0.180580i
$236$		0			0
$237$	−4.86425	−	1.38430i	−0.315967	−	0.0899201i
$238$		0			0
$239$	12.1286	−	21.0073i	0.784534	−	1.35885i	−0.144744	−	0.989469i	$-0.546236\pi$
$239$	12.1286	−	21.0073i	0.784534	−	1.35885i	0.929277	−	0.369383i	$-0.120431\pi$
$240$		0			0
$241$	−3.00711	−	5.20846i	−0.193705	−	0.335507i	0.752770	−	0.658283i	$-0.228717\pi$
$241$	−3.00711	−	5.20846i	−0.193705	−	0.335507i	−0.946475	+	0.322777i	$0.895384\pi$
$242$		0			0
$243$	−10.1387	−	11.8409i	−0.650398	−	0.759593i
$244$		0			0
$245$	−6.95131	+	4.01334i	−0.444103	+	0.256403i
$246$		0			0
$247$	−0.239511	−	0.138282i	−0.0152397	−	0.00879867i
$248$		0			0
$249$	4.21301	−	14.8039i	0.266989	−	0.938162i
$250$		0			0
$251$	12.7656			0.805760			0.402880	−	0.915253i	$-0.368009\pi$
$251$	12.7656			0.805760			0.402880	+	0.915253i	$0.368009\pi$
$252$		0			0
$253$	−11.3466			−0.713352
$254$		0			0
$255$	4.57820	−	1.15118i	0.286698	−	0.0720897i
$256$		0			0
$257$	−11.4638	−	6.61864i	−0.715094	−	0.412860i	0.0978505	−	0.995201i	$-0.468803\pi$
$257$	−11.4638	−	6.61864i	−0.715094	−	0.412860i	−0.812944	+	0.582342i	$0.802137\pi$
$258$		0			0
$259$	−23.4710	+	13.5510i	−1.45842	+	0.842018i
$260$		0			0
$261$	−10.7314	−	19.9899i	−0.664254	−	1.23734i
$262$		0			0
$263$	3.76791	+	6.52622i	0.232340	+	0.402424i	0.958496	−	0.285105i	$-0.0920286\pi$
$263$	3.76791	+	6.52622i	0.232340	+	0.402424i	−0.726157	+	0.687529i	$0.758695\pi$
$264$		0			0
$265$	−2.23286	+	3.86742i	−0.137163	+	0.237574i
$266$		0			0
$267$	−12.0795	+	11.7117i	−0.739255	+	0.716747i
$268$		0			0
$269$		−	6.40793i		−	0.390699i	−0.980734	−	0.195349i	$-0.937416\pi$
$269$		−	6.40793i		−	0.390699i	0.980734	−	0.195349i	$-0.0625840\pi$
$270$		0			0
$271$			5.53211i			0.336051i	0.985783	+	0.168026i	$0.0537392\pi$
$271$			5.53211i			0.336051i	−0.985783	+	0.168026i	$0.946261\pi$
$272$		0			0
$273$	−0.473049	+	0.458645i	−0.0286302	+	0.0277585i
$274$		0			0
$275$	−5.62543	+	9.74353i	−0.339226	+	0.587557i
$276$		0			0
$277$	−10.1627	−	17.6023i	−0.610616	−	1.05762i	−0.991137	−	0.132846i	$-0.957588\pi$
$277$	−10.1627	−	17.6023i	−0.610616	−	1.05762i	0.380520	−	0.924773i	$-0.375745\pi$
$278$		0			0
$279$	−1.21005	+	1.95379i	−0.0724438	+	0.116971i
$280$		0			0
$281$	6.20013	−	3.57965i	0.369869	−	0.213544i	−0.303532	−	0.952821i	$-0.598166\pi$
$281$	6.20013	−	3.57965i	0.369869	−	0.213544i	0.673401	+	0.739277i	$0.264833\pi$
$282$		0			0
$283$	10.4042	+	6.00686i	0.618465	+	0.357071i	0.776271	−	0.630399i	$-0.217109\pi$
$283$	10.4042	+	6.00686i	0.618465	+	0.357071i	−0.157806	+	0.987470i	$0.550442\pi$
$284$		0			0
$285$	2.77662	−	0.698178i	0.164473	−	0.0413565i
$286$		0			0
$287$	−5.63364			−0.332543
$288$		0			0
$289$	−18.1479			−1.06752
$290$		0			0
$291$	−2.99917	+	10.5387i	−0.175814	+	0.617787i
$292$		0			0
$293$	20.6573	+	11.9265i	1.20681	+	0.696752i	0.962061	−	0.272834i	$-0.0879610\pi$
$293$	20.6573	+	11.9265i	1.20681	+	0.696752i	0.244749	+	0.969586i	$0.421294\pi$
$294$		0			0
$295$	3.31067	−	1.91142i	0.192755	−	0.111287i
$296$		0			0
$297$	11.6331	+	3.70299i	0.675023	+	0.214869i
$298$		0			0
$299$	0.185731	+	0.321696i	0.0107411	+	0.0186042i
$300$		0			0
$301$	19.3910	−	33.5862i	1.11768	−	1.93588i
$302$		0			0
$303$	8.65792	+	2.46393i	0.497384	+	0.141549i
$304$		0			0
$305$		−	2.42188i		−	0.138677i
$306$		0			0
$307$			13.1729i			0.751818i	0.926657	+	0.375909i	$0.122669\pi$
$307$			13.1729i			0.751818i	−0.926657	+	0.375909i	$0.877331\pi$
$308$		0			0
$309$	−1.17920	−	4.68964i	−0.0670826	−	0.266785i
$310$		0			0
$311$	−1.14825	+	1.98883i	−0.0651114	+	0.112776i	−0.896743	−	0.442551i	$-0.854074\pi$
$311$	−1.14825	+	1.98883i	−0.0651114	+	0.112776i	0.831632	+	0.555327i	$0.187407\pi$
$312$		0			0
$313$	4.36557	+	7.56139i	0.246757	+	0.427395i	0.962624	−	0.270841i	$-0.0873018\pi$
$313$	4.36557	+	7.56139i	0.246757	+	0.427395i	−0.715867	+	0.698236i	$0.753968\pi$
$314$		0			0
$315$	0.210841	−	6.81768i	0.0118795	−	0.384133i
$316$		0			0
$317$	4.23728	−	2.44640i	0.237990	−	0.137403i	−0.376263	−	0.926513i	$-0.622791\pi$
$317$	4.23728	−	2.44640i	0.237990	−	0.137403i	0.614252	+	0.789110i	$0.289458\pi$
$318$		0			0
$319$	15.3880	+	8.88428i	0.861564	+	0.497424i
$320$		0			0
$321$	17.5920	+	18.1444i	0.981889	+	1.01272i
$322$		0			0
$323$	−21.3168			−1.18610
$324$		0			0
$325$	0.368330			0.0204313
$326$		0			0
$327$	−15.2772	−	15.7569i	−0.844830	−	0.871361i
$328$		0			0
$329$	−25.7907	−	14.8903i	−1.42189	−	0.820927i
$330$		0			0
$331$	−3.14019	+	1.81299i	−0.172601	+	0.0996511i	−0.583812	−	0.811889i	$-0.698439\pi$
$331$	−3.14019	+	1.81299i	−0.172601	+	0.0996511i	0.411211	+	0.911540i	$0.365106\pi$
$332$		0			0
$333$	0.508167	−	16.4319i	0.0278474	−	0.900464i
$334$		0			0
$335$	0.489571	+	0.847962i	0.0267481	+	0.0463291i
$336$		0			0
$337$	−4.75655	+	8.23858i	−0.259106	+	0.448784i	−0.966003	−	0.258532i	$-0.916761\pi$
$337$	−4.75655	+	8.23858i	−0.259106	+	0.448784i	0.706897	+	0.707317i	$0.250094\pi$
$338$		0			0
$339$	8.08727	+	32.1627i	0.439240	+	1.74684i
$340$		0			0
$341$		−	1.79983i		−	0.0974661i
$342$		0			0
$343$		−	51.7308i		−	2.79320i
$344$		0			0
$345$	−3.69861	−	1.05258i	−0.199126	−	0.0566688i
$346$		0			0
$347$	2.42602	−	4.20199i	0.130236	−	0.225575i	−0.793532	−	0.608529i	$-0.791760\pi$
$347$	2.42602	−	4.20199i	0.130236	−	0.225575i	0.923767	+	0.382954i	$0.125093\pi$
$348$		0			0
$349$	4.40121	+	7.62312i	0.235591	+	0.408056i	0.959444	−	0.281898i	$-0.0909640\pi$
$349$	4.40121	+	7.62312i	0.235591	+	0.408056i	−0.723853	+	0.689954i	$0.757631\pi$
$350$		0			0
$351$	−0.0854355	−	0.390435i	−0.00456021	−	0.0208399i
$352$		0			0
$353$	−16.5392	+	9.54894i	−0.880295	+	0.508239i	−0.870756	−	0.491716i	$-0.836370\pi$
$353$	−16.5392	+	9.54894i	−0.880295	+	0.508239i	−0.00953954	+	0.999954i	$0.503037\pi$
$354$		0			0
$355$	4.24608	+	2.45148i	0.225359	+	0.130111i
$356$		0			0
$357$	−13.9008	+	48.8457i	−0.735711	+	2.58519i
$358$		0			0
$359$	−4.99319			−0.263531			−0.131765	−	0.991281i	$-0.542065\pi$
$359$	−4.99319			−0.263531			−0.131765	+	0.991281i	$0.542065\pi$
$360$		0			0
$361$	6.07161			0.319558
$362$		0			0
$363$	9.20497	−	2.31458i	0.483136	−	0.121484i
$364$		0			0
$365$	2.99163	+	1.72722i	0.156589	+	0.0904067i
$366$		0			0
$367$	5.30108	−	3.06058i	0.276714	−	0.159761i	−0.355221	−	0.934782i	$-0.615594\pi$
$367$	5.30108	−	3.06058i	0.276714	−	0.159761i	0.631935	+	0.775021i	$0.282261\pi$
$368$		0			0
$369$	1.79932	−	2.90525i	0.0936687	−	0.151241i
$370$		0			0
$371$	−24.0210	−	41.6055i	−1.24711	−	2.16005i
$372$		0			0
$373$	−2.06426	+	3.57540i	−0.106883	+	0.185127i	−0.914506	−	0.404572i	$-0.867420\pi$
$373$	−2.06426	+	3.57540i	−0.106883	+	0.185127i	0.807623	+	0.589699i	$0.200754\pi$
$374$		0			0
$375$	−5.59598	+	5.42559i	−0.288975	+	0.280176i
$376$		0			0
$377$		−	0.581706i		−	0.0299594i
$378$		0			0
$379$		−	28.0527i		−	1.44097i	−0.693470	−	0.720485i	$-0.743919\pi$
$379$		−	28.0527i		−	1.44097i	0.693470	−	0.720485i	$-0.256081\pi$
$380$		0			0
$381$	−13.9728	+	13.5474i	−0.715849	+	0.694053i
$382$		0			0
$383$	8.13318	−	14.0871i	0.415586	−	0.719816i	−0.579904	−	0.814685i	$-0.696910\pi$
$383$	8.13318	−	14.0871i	0.415586	−	0.719816i	0.995490	+	0.0948689i	$0.0302432\pi$
$384$		0			0
$385$	2.67095	+	4.62622i	0.136124	+	0.235774i
$386$		0			0
$387$	11.1270	+	20.7269i	0.565618	+	1.05361i
$388$		0			0
$389$	−31.3063	+	18.0747i	−1.58729	+	0.916424i	−0.593542	+	0.804803i	$0.702271\pi$
$389$	−31.3063	+	18.0747i	−1.58729	+	0.916424i	−0.993751	+	0.111621i	$0.964396\pi$
$390$		0			0
$391$	24.7955	+	14.3157i	1.25396	+	0.723974i
$392$		0			0
$393$	25.3454	−	6.37306i	1.27851	−	0.321478i
$394$		0			0
$395$	1.34234			0.0675405
$396$		0			0
$397$	32.9550			1.65396			0.826982	−	0.562229i	$-0.190056\pi$
$397$	32.9550			1.65396			0.826982	+	0.562229i	$0.190056\pi$
$398$		0			0
$399$	−8.43070	+	29.6243i	−0.422063	+	1.48307i
$400$		0			0
$401$	−6.54505	−	3.77879i	−0.326844	−	0.188704i	0.327595	−	0.944818i	$-0.393762\pi$
$401$	−6.54505	−	3.77879i	−0.326844	−	0.188704i	−0.654439	+	0.756115i	$0.727095\pi$
$402$		0			0
$403$	−0.0510285	+	0.0294613i	−0.00254191	+	0.00146757i
$404$		0			0
$405$	3.44851	+	2.28622i	0.171358	+	0.113603i
$406$		0			0
$407$	6.43750	+	11.1501i	0.319095	+	0.552689i
$408$		0			0
$409$	−4.05684	+	7.02666i	−0.200598	+	0.347446i	−0.948721	−	0.316114i	$-0.897622\pi$
$409$	−4.05684	+	7.02666i	−0.200598	+	0.347446i	0.748123	+	0.663560i	$0.230955\pi$
$410$		0			0
$411$	−5.99443	−	1.70594i	−0.295683	−	0.0841477i
$412$		0			0
$413$			41.1259i			2.02367i
$414$		0			0
$415$			4.08530i			0.200540i
$416$		0			0
$417$	−2.99343	−	11.9047i	−0.146589	−	0.582978i
$418$		0			0
$419$	5.99038	−	10.3756i	0.292649	−	0.506883i	−0.681786	−	0.731552i	$-0.738797\pi$
$419$	5.99038	−	10.3756i	0.292649	−	0.506883i	0.974435	+	0.224668i	$0.0721299\pi$
$420$		0			0
$421$	−12.5646	−	21.7626i	−0.612363	−	1.06064i	−0.990841	−	0.135034i	$-0.956886\pi$
$421$	−12.5646	−	21.7626i	−0.612363	−	1.06064i	0.378478	−	0.925610i	$-0.376448\pi$
$422$		0			0
$423$	15.9161	−	8.54439i	0.773867	−	0.415442i
$424$		0			0
$425$	24.5863	−	14.1949i	1.19261	−	0.688555i
$426$		0			0
$427$	22.5639	+	13.0273i	1.09194	+	0.630433i
$428$		0			0
$429$	0.217883	+	0.224725i	0.0105195	+	0.0108498i
$430$		0			0
$431$	−18.7211			−0.901763			−0.450881	−	0.892584i	$-0.648890\pi$
$431$	−18.7211			−0.901763			−0.450881	+	0.892584i	$0.648890\pi$
$432$		0			0
$433$	−2.06315			−0.0991487			−0.0495744	−	0.998770i	$-0.515786\pi$
$433$	−2.06315			−0.0991487			−0.0495744	+	0.998770i	$0.515786\pi$
$434$		0			0
$435$	4.19184	+	4.32348i	0.200983	+	0.207295i
$436$		0			0
$437$	15.0382	+	8.68228i	0.719372	+	0.415330i
$438$		0			0
$439$	22.4517	−	12.9625i	1.07156	−	0.618665i	0.142952	−	0.989730i	$-0.454340\pi$
$439$	22.4517	−	12.9625i	1.07156	−	0.618665i	0.928607	+	0.371065i	$0.121007\pi$
$440$		0			0
$441$	44.5307	+	27.5793i	2.12051	+	1.31330i
$442$		0			0
$443$	7.25888	+	12.5727i	0.344880	+	0.597349i	0.985332	−	0.170649i	$-0.0545864\pi$
$443$	7.25888	+	12.5727i	0.344880	+	0.597349i	−0.640452	+	0.767998i	$0.721253\pi$
$444$		0			0
$445$	2.23286	−	3.86742i	0.105848	−	0.183333i
$446$		0			0
$447$	0.480714	+	1.91178i	0.0227370	+	0.0904240i
$448$		0			0
$449$			14.4797i			0.683341i	0.939820	+	0.341670i	$0.110993\pi$
$449$			14.4797i			0.683341i	−0.939820	+	0.341670i	$0.889007\pi$
$450$		0			0
$451$			2.67630i			0.126022i
$452$		0			0
$453$	18.6241	+	5.30018i	0.875037	+	0.249024i
$454$		0			0
$455$	0.0874413	−	0.151453i	0.00409931	−	0.00710021i
$456$		0			0
$457$	−12.7269	−	22.0437i	−0.595341	−	1.03116i	−0.993499	−	0.113844i	$-0.963684\pi$
$457$	−12.7269	−	22.0437i	−0.595341	−	1.03116i	0.398158	−	0.917317i	$-0.369650\pi$
$458$		0			0
$459$	−20.7497	−	22.7693i	−0.968515	−	1.06278i
$460$		0			0
$461$	−1.81422	+	1.04744i	−0.0844966	+	0.0487841i	−0.541653	−	0.840602i	$-0.682201\pi$
$461$	−1.81422	+	1.04744i	−0.0844966	+	0.0487841i	0.457156	+	0.889386i	$0.348868\pi$
$462$		0			0
$463$	4.82478	+	2.78559i	0.224226	+	0.129457i	0.607906	−	0.794009i	$-0.292010\pi$
$463$	4.82478	+	2.78559i	0.224226	+	0.129457i	−0.383679	+	0.923466i	$0.625343\pi$
$464$		0			0
$465$	0.166963	−	0.586685i	0.00774273	−	0.0272069i
$466$		0			0
$467$	39.0574			1.80736			0.903680	−	0.428208i	$-0.140855\pi$
$467$	39.0574			1.80736			0.903680	+	0.428208i	$0.140855\pi$
$468$		0			0
$469$	−10.5336			−0.486395
$470$		0			0
$471$	−27.5140	+	6.91837i	−1.26778	+	0.318782i
$472$		0			0
$473$	−15.9554	−	9.21184i	−0.733629	−	0.423561i
$474$		0			0
$475$	14.9113	−	8.60906i	0.684179	−	0.395011i
$476$		0			0
$477$	29.1278	+	0.900793i	1.33367	+	0.0412445i
$478$		0			0
$479$	−15.8390	−	27.4340i	−0.723703	−	1.25349i	−0.959506	−	0.281689i	$-0.909105\pi$
$479$	−15.8390	−	27.4340i	−0.723703	−	1.25349i	0.235803	−	0.971801i	$-0.424228\pi$
$480$		0			0
$481$	0.210750	−	0.365030i	0.00960938	−	0.0166439i
$482$		0			0
$483$	29.7012	−	28.7969i	1.35145	−	1.31030i
$484$		0			0
$485$		−	2.90825i		−	0.132057i
$486$		0			0
$487$			33.3903i			1.51306i	0.653961	+	0.756528i	$0.273106\pi$
$487$			33.3903i			1.51306i	−0.653961	+	0.756528i	$0.726894\pi$
$488$		0			0
$489$	−5.03033	+	4.87717i	−0.227479	+	0.220553i
$490$		0			0
$491$	9.52060	−	16.4902i	0.429659	−	0.744190i	−0.567184	−	0.823591i	$-0.691967\pi$
$491$	9.52060	−	16.4902i	0.429659	−	0.744190i	0.996843	+	0.0794005i	$0.0253006\pi$
$492$		0			0
$493$	−22.4182	−	38.8294i	−1.00966	−	1.74879i
$494$		0			0
$495$	−3.23879	−	0.100161i	−0.145573	−	0.00450192i
$496$		0			0
$497$	−45.6791	+	26.3729i	−2.04899	+	1.18298i
$498$		0			0
$499$	18.8684	+	10.8937i	0.844664	+	0.487667i	0.858847	−	0.512232i	$-0.171181\pi$
$499$	18.8684	+	10.8937i	0.844664	+	0.487667i	−0.0141827	+	0.999899i	$0.504515\pi$
$500$		0			0
$501$	−5.31048	+	1.33531i	−0.237255	+	0.0596574i
$502$		0			0
$503$	21.6101			0.963547			0.481774	−	0.876296i	$-0.339993\pi$
$503$	21.6101			0.963547			0.481774	+	0.876296i	$0.339993\pi$
$504$		0			0
$505$	−2.38924			−0.106320
$506$		0			0
$507$	−6.16043	+	21.6469i	−0.273594	+	0.961372i
$508$		0			0
$509$	22.5799	+	13.0365i	1.00084	+	0.577834i	0.908496	−	0.417893i	$-0.137231\pi$
$509$	22.5799	+	13.0365i	1.00084	+	0.577834i	0.0923421	+	0.995727i	$0.470565\pi$
$510$		0			0
$511$	−32.1838	+	18.5813i	−1.42373	+	0.821989i
$512$		0			0
$513$	−12.5845	−	13.8093i	−0.555618	−	0.609697i
$514$		0			0
$515$	0.641740	+	1.11153i	0.0282784	+	0.0489797i
$516$		0			0
$517$	−7.07373	+	12.2521i	−0.311102	+	0.538845i
$518$		0			0
$519$	33.4818	+	9.52849i	1.46969	+	0.418254i
$520$		0			0
$521$			0.184295i			0.00807410i	0.999992	+	0.00403705i	$0.00128504\pi$
$521$			0.184295i			0.00807410i	−0.999992	+	0.00403705i	$0.998715\pi$
$522$		0			0
$523$		−	28.9997i		−	1.26807i	−0.773304	−	0.634035i	$-0.781397\pi$
$523$		−	28.9997i		−	1.26807i	0.773304	−	0.634035i	$-0.218603\pi$
$524$		0			0
$525$	−10.0031	−	39.7821i	−0.436573	−	1.73623i
$526$		0			0
$527$	−2.27080	+	3.93314i	−0.0989175	+	0.171330i
$528$		0			0
$529$	−0.161471	−	0.279677i	−0.00702050	−	0.0121599i
$530$		0			0
$531$	−21.2085	−	13.1351i	−0.920369	−	0.570016i
$532$		0			0
$533$	0.0758781	−	0.0438083i	0.00328665	−	0.00189755i
$534$		0			0
$535$	−5.80918	−	3.35393i	−0.251153	−	0.145003i
$536$		0			0
$537$	12.2615	+	12.6466i	0.529124	+	0.545741i
$538$		0			0
$539$	−41.0215			−1.76692
$540$		0			0
$541$	40.1108			1.72450			0.862249	−	0.506484i	$-0.169055\pi$
$541$	40.1108			1.72450			0.862249	+	0.506484i	$0.169055\pi$
$542$		0			0
$543$	18.1540	+	18.7241i	0.779063	+	0.803529i
$544$		0			0
$545$	5.04479	+	2.91261i	0.216095	+	0.124763i
$546$		0			0
$547$	17.7795	−	10.2650i	0.760198	−	0.438901i	−0.0691687	−	0.997605i	$-0.522035\pi$
$547$	17.7795	−	10.2650i	0.760198	−	0.438901i	0.829367	+	0.558704i	$0.188701\pi$
$548$		0			0
$549$	−13.9247	+	7.47534i	−0.594293	+	0.319040i
$550$		0			0
$551$	−13.5963	−	23.5496i	−0.579224	−	1.00325i
$552$		0			0
$553$	−7.22042	+	12.5061i	−0.307043	+	0.531815i
$554$		0			0
$555$	1.06407	+	4.23174i	0.0451671	+	0.179628i
$556$		0			0
$557$		−	1.23121i		−	0.0521682i	−0.999660	−	0.0260841i	$-0.991696\pi$
$557$		−	1.23121i		−	0.0521682i	0.999660	−	0.0260841i	$-0.00830378\pi$
$558$		0			0
$559$			0.603152i			0.0255106i
$560$		0			0
$561$	23.2045	+	6.60370i	0.979694	+	0.278808i
$562$		0			0
$563$	−10.8990	+	18.8776i	−0.459337	+	0.795595i	−0.998926	−	0.0463337i	$-0.985246\pi$
$563$	−10.8990	+	18.8776i	−0.459337	+	0.795595i	0.539589	+	0.841928i	$0.318580\pi$
$564$		0			0
$565$	−4.40121	−	7.62312i	−0.185160	−	0.320707i
$566$		0			0
$567$	−39.8494	+	19.8311i	−1.67352	+	0.832828i
$568$		0			0
$569$	14.3575	−	8.28931i	0.601898	−	0.347506i	−0.167890	−	0.985806i	$-0.553695\pi$
$569$	14.3575	−	8.28931i	0.601898	−	0.347506i	0.769788	+	0.638300i	$0.220362\pi$
$570$		0			0
$571$	0.452356	+	0.261168i	0.0189305	+	0.0109295i	0.509435	−	0.860509i	$-0.329854\pi$
$571$	0.452356	+	0.261168i	0.0189305	+	0.0109295i	−0.490505	+	0.871438i	$0.663188\pi$
$572$		0			0
$573$	1.33878	−	4.70429i	0.0559284	−	0.196525i
$574$		0			0
$575$	−23.1262			−0.964431
$576$		0			0
$577$	34.5966			1.44028			0.720139	−	0.693830i	$-0.244078\pi$
$577$	34.5966			1.44028			0.720139	+	0.693830i	$0.244078\pi$
$578$		0			0
$579$	−30.0735	+	7.56193i	−1.24981	+	0.314263i
$580$		0			0
$581$	−38.0614	−	21.9747i	−1.57905	−	0.911666i
$582$		0			0
$583$	−19.7650	+	11.4113i	−0.818583	+	0.472609i
$584$		0			0
$585$	0.0501758	+	0.0934653i	0.00207452	+	0.00386431i
$586$		0			0
$587$	0.942362	+	1.63222i	0.0388955	+	0.0673689i	0.884818	−	0.465937i	$-0.154283\pi$
$587$	0.942362	+	1.63222i	0.0388955	+	0.0673689i	−0.845922	+	0.533306i	$0.820949\pi$
$588$		0			0
$589$	−1.37721	+	2.38540i	−0.0567470	+	0.0982887i
$590$		0			0
$591$	−7.03447	+	6.82028i	−0.289359	+	0.280549i
$592$		0			0
$593$		−	26.7478i		−	1.09840i	−0.835691	−	0.549199i	$-0.814933\pi$
$593$		−	26.7478i		−	1.09840i	0.835691	−	0.549199i	$-0.185067\pi$
$594$		0			0
$595$		−	13.4795i		−	0.552605i
$596$		0			0
$597$	−8.43141	+	8.17469i	−0.345075	+	0.334568i
$598$		0			0
$599$	−11.7506	+	20.3527i	−0.480118	+	0.831589i	−0.999740	−	0.0228075i	$-0.992740\pi$
$599$	−11.7506	+	20.3527i	−0.480118	+	0.831589i	0.519622	+	0.854396i	$0.326073\pi$
$600$		0			0
$601$	−8.49651	−	14.7164i	−0.346580	−	0.600294i	0.639060	−	0.769157i	$-0.279324\pi$
$601$	−8.49651	−	14.7164i	−0.346580	−	0.600294i	−0.985640	+	0.168863i	$0.945990\pi$
$602$		0			0
$603$	3.36429	−	5.43211i	0.137005	−	0.221213i
$604$		0			0
$605$	−2.18174	+	1.25963i	−0.0887002	+	0.0512111i
$606$		0			0
$607$	−16.5877	−	9.57694i	−0.673276	−	0.388716i	0.124041	−	0.992277i	$-0.460415\pi$
$607$	−16.5877	−	9.57694i	−0.673276	−	0.388716i	−0.797317	+	0.603561i	$0.793748\pi$
$608$		0			0
$609$	−62.8281	+	15.7980i	−2.54592	+	0.640169i
$610$		0			0
$611$	0.463158			0.0187374
$612$		0			0
$613$	−16.5441			−0.668211			−0.334106	−	0.942536i	$-0.608434\pi$
$613$	−16.5441			−0.668211			−0.334106	+	0.942536i	$0.608434\pi$
$614$		0			0
$615$	−0.248270	+	0.872388i	−0.0100112	+	0.0351781i
$616$		0			0
$617$	27.4744	+	15.8624i	1.10608	+	0.638595i	0.937811	−	0.347146i	$-0.112849\pi$
$617$	27.4744	+	15.8624i	1.10608	+	0.638595i	0.168268	+	0.985741i	$0.446183\pi$
$618$		0			0
$619$	8.46158	−	4.88529i	0.340099	−	0.196356i	−0.320217	−	0.947344i	$-0.603756\pi$
$619$	8.46158	−	4.88529i	0.340099	−	0.196356i	0.660316	+	0.750988i	$0.270422\pi$
$620$		0			0
$621$	5.36422	+	24.5142i	0.215259	+	0.983720i
$622$		0			0
$623$	24.0210	+	41.6055i	0.962379	+	1.66689i
$624$		0			0
$625$	−10.9372	+	18.9439i	−0.437490	+	0.757754i
$626$		0			0
$627$	14.0733	+	4.00507i	0.562032	+	0.159947i
$628$		0			0
$629$		−	32.4881i		−	1.29539i
$630$		0			0
$631$		−	23.9365i		−	0.952896i	−0.879203	−	0.476448i	$-0.841924\pi$
$631$		−	23.9365i		−	0.952896i	0.879203	−	0.476448i	$-0.158076\pi$
$632$		0			0
$633$	−6.93775	−	27.5911i	−0.275751	−	1.09665i
$634$		0			0
$635$	2.58282	−	4.47358i	0.102496	−	0.177529i
$636$		0			0
$637$	0.671479	+	1.16304i	0.0266050	+	0.0460811i
$638$		0			0
$639$	0.988990	−	31.9797i	0.0391239	−	1.26510i
$640$		0			0
$641$	0.947835	−	0.547233i	0.0374372	−	0.0216144i	−0.481165	−	0.876630i	$-0.659786\pi$
$641$	0.947835	−	0.547233i	0.0374372	−	0.0216144i	0.518602	+	0.855016i	$0.326453\pi$
$642$		0			0
$643$	−30.4240	−	17.5653i	−1.19981	−	0.692708i	−0.239294	−	0.970947i	$-0.576916\pi$
$643$	−30.4240	−	17.5653i	−1.19981	−	0.692708i	−0.960512	+	0.278239i	$0.910249\pi$
$644$		0			0
$645$	−4.34639	−	4.48288i	−0.171139	−	0.176513i
$646$		0			0
$647$	−37.2369			−1.46393			−0.731966	−	0.681341i	$-0.761397\pi$
$647$	−37.2369			−1.46393			−0.731966	+	0.681341i	$0.761397\pi$
$648$		0			0
$649$	19.5372			0.766901
$650$		0			0
$651$	4.56786	+	4.71130i	0.179028	+	0.184651i
$652$		0			0
$653$	−35.6290	−	20.5704i	−1.39427	−	0.804982i	−0.400484	−	0.916304i	$-0.631158\pi$
$653$	−35.6290	−	20.5704i	−1.39427	−	0.804982i	−0.993784	+	0.111322i	$0.964491\pi$
$654$		0			0
$655$	−6.00729	+	3.46831i	−0.234724	+	0.135518i
$656$		0			0
$657$	0.696806	−	22.5317i	0.0271850	−	0.879045i
$658$		0			0
$659$	−9.31389	−	16.1321i	−0.362818	−	0.628419i	0.625606	−	0.780139i	$-0.284852\pi$
$659$	−9.31389	−	16.1321i	−0.362818	−	0.628419i	−0.988423	+	0.151721i	$0.951519\pi$
$660$		0			0
$661$	−1.50846	+	2.61273i	−0.0586722	+	0.101623i	−0.893870	−	0.448327i	$-0.852020\pi$
$661$	−1.50846	+	2.61273i	−0.0586722	+	0.101623i	0.835197	+	0.549950i	$0.185353\pi$
$662$		0			0
$663$	−0.192606	−	0.765986i	−0.00748020	−	0.0297484i
$664$		0			0
$665$		−	8.17514i		−	0.317019i
$666$		0			0
$667$			36.5234i			1.41419i
$668$		0			0
$669$	−25.9739	−	7.39184i	−1.00421	−	0.285785i
$670$		0			0
$671$	6.18869	−	10.7191i	0.238912	−	0.413808i
$672$		0			0
$673$	−14.1646	−	24.5337i	−0.546004	−	0.945706i	−0.998543	−	0.0539618i	$-0.982815\pi$
$673$	−14.1646	−	24.5337i	−0.546004	−	0.945706i	0.452539	−	0.891744i	$-0.350518\pi$
$674$		0			0
$675$	23.7103	+	7.54734i	0.912611	+	0.290497i
$676$		0			0
$677$	21.8629	−	12.6226i	0.840260	−	0.485124i	−0.0170927	−	0.999854i	$-0.505441\pi$
$677$	21.8629	−	12.6226i	0.840260	−	0.485124i	0.857353	+	0.514730i	$0.172108\pi$
$678$		0			0
$679$	27.0952	+	15.6434i	1.03982	+	0.600340i
$680$		0			0
$681$	−2.14028	+	7.52065i	−0.0820157	+	0.288192i
$682$		0			0
$683$	9.12320			0.349089			0.174545	−	0.984649i	$-0.444155\pi$
$683$	9.12320			0.349089			0.174545	+	0.984649i	$0.444155\pi$
$684$		0			0
$685$	1.65423			0.0632047
$686$		0			0
$687$	9.33418	−	2.34706i	0.356121	−	0.0895461i
$688$		0			0
$689$	0.647065	+	0.373583i	0.0246512	+	0.0142324i
$690$		0			0
$691$	−40.6272	+	23.4561i	−1.54553	+	0.892313i	−0.547058	+	0.837095i	$0.684252\pi$
$691$	−40.6272	+	23.4561i	−1.54553	+	0.892313i	−0.998474	+	0.0552184i	$0.982415\pi$
$692$		0			0
$693$	18.3545	−	29.6359i	0.697232	−	1.12578i
$694$		0			0
$695$	1.62907	+	2.82163i	0.0617941	+	0.107030i
$696$		0			0
$697$	3.37662	−	5.84848i	0.127899	−	0.221527i
$698$		0			0
$699$	−1.64909	+	1.59888i	−0.0623742	+	0.0604751i
$700$		0			0
$701$			14.2915i			0.539783i	0.962891	+	0.269892i	$0.0869879\pi$
$701$			14.2915i			0.539783i	−0.962891	+	0.269892i	$0.913012\pi$
$702$		0			0
$703$		−	19.7037i		−	0.743138i
$704$		0			0
$705$	−3.44238	+	3.33757i	−0.129648	+	0.125700i
$706$		0			0
$707$	12.8517	−	22.2598i	0.483337	−	0.837165i
$708$		0			0
$709$	20.4700	+	35.4551i	0.768768	+	1.33155i	0.938231	+	0.346009i	$0.112463\pi$
$709$	20.4700	+	35.4551i	0.768768	+	1.33155i	−0.169463	+	0.985537i	$0.554203\pi$
$710$		0			0
$711$	−4.14325	−	7.71785i	−0.155384	−	0.289442i
$712$		0			0
$713$	3.20391	−	1.84978i	0.119988	−	0.0692748i
$714$		0			0
$715$	−0.0719487	−	0.0415396i	−0.00269073	−	0.00155349i
$716$		0			0
$717$	40.7463	−	10.2456i	1.52170	−	0.382629i
$718$		0			0
$719$	51.0710			1.90463			0.952313	−	0.305123i	$-0.0986974\pi$
$719$	51.0710			1.90463			0.952313	+	0.305123i	$0.0986974\pi$
$720$		0			0
$721$	−13.8076			−0.514222
$722$		0			0
$723$	2.85131	−	10.0191i	0.106041	−	0.372614i
$724$		0			0
$725$	31.3635	+	18.1077i	1.16481	+	0.672503i
$726$		0			0
$727$	−23.0591	+	13.3132i	−0.855213	+	0.493758i	−0.862406	−	0.506216i	$-0.831044\pi$
$727$	−23.0591	+	13.3132i	−0.855213	+	0.493758i	0.00719304	+	0.999974i	$0.497710\pi$
$728$		0			0
$729$	2.50058	−	26.8840i	0.0926142	−	0.995702i
$730$		0			0
$731$	23.2447	+	40.2610i	0.859736	+	1.48911i
$732$		0			0
$733$	−21.7287	+	37.6352i	−0.802567	+	1.39009i	0.115354	+	0.993324i	$0.463200\pi$
$733$	−21.7287	+	37.6352i	−0.802567	+	1.39009i	−0.917921	+	0.396763i	$0.870134\pi$
$734$		0			0
$735$	−13.3717	−	3.80541i	−0.493222	−	0.140365i
$736$		0			0
$737$			5.00405i			0.184326i
$738$		0			0
$739$			2.24313i			0.0825150i	0.999149	+	0.0412575i	$0.0131364\pi$
$739$			2.24313i			0.0825150i	−0.999149	+	0.0412575i	$0.986864\pi$
$740$		0			0
$741$	−0.116813	−	0.464561i	−0.00429124	−	0.0170661i
$742$		0			0
$743$	−22.4331	+	38.8553i	−0.822991	+	1.42546i	0.0804542	+	0.996758i	$0.474363\pi$
$743$	−22.4331	+	38.8553i	−0.822991	+	1.42546i	−0.903445	+	0.428704i	$0.858970\pi$
$744$		0			0
$745$	−0.261611	−	0.453124i	−0.00958470	−	0.0166012i
$746$		0			0
$747$	23.4886	−	12.6096i	0.859404	−	0.461362i
$748$		0			0
$749$	62.4949	−	36.0814i	2.28351	−	1.31839i
$750$		0			0
$751$	24.6400	+	14.2259i	0.899128	+	0.519112i	0.876917	−	0.480642i	$-0.159596\pi$
$751$	24.6400	+	14.2259i	0.899128	+	0.519112i	0.0222105	+	0.999753i	$0.492930\pi$
$752$		0			0
$753$	15.3911	+	15.8744i	0.560883	+	0.578497i
$754$		0			0
$755$	−5.13952			−0.187046
$756$		0			0
$757$	−17.8913			−0.650269			−0.325135	−	0.945668i	$-0.605410\pi$
$757$	−17.8913			−0.650269			−0.325135	+	0.945668i	$0.605410\pi$
$758$		0			0
$759$	−13.6802	−	14.1098i	−0.496559	−	0.512153i
$760$		0			0
$761$	−4.80178	−	2.77231i	−0.174064	−	0.100496i	0.410437	−	0.911889i	$-0.365376\pi$
$761$	−4.80178	−	2.77231i	−0.174064	−	0.100496i	−0.584501	+	0.811393i	$0.698710\pi$
$762$		0			0
$763$	−54.2716	+	31.3337i	−1.96476	+	1.13436i
$764$		0			0
$765$	6.95131	+	4.30518i	0.251325	+	0.155654i
$766$		0			0
$767$	−0.319803	−	0.553915i	−0.0115474	−	0.0200007i
$768$		0			0
$769$	11.3305	−	19.6250i	0.408589	−	0.707696i	−0.586143	−	0.810207i	$-0.699354\pi$
$769$	11.3305	−	19.6250i	0.408589	−	0.707696i	0.994732	+	0.102511i	$0.0326878\pi$
$770$		0			0
$771$	−5.59108	−	22.2355i	−0.201358	−	0.800792i
$772$		0			0
$773$			20.9941i			0.755105i	0.925988	+	0.377552i	$0.123234\pi$
$773$			20.9941i			0.755105i	−0.925988	+	0.377552i	$0.876766\pi$
$774$		0			0
$775$		−	3.66836i		−	0.131771i
$776$		0			0
$777$	−45.1493	−	12.8489i	−1.61972	−	0.460952i
$778$		0			0
$779$	2.04788	−	3.54704i	0.0733730	−	0.127086i
$780$		0			0
$781$	12.5286	+	21.7002i	0.448309	+	0.776494i
$782$		0			0
$783$	11.9196	−	37.4459i	0.425970	−	1.33821i
$784$		0			0
$785$	6.52130	−	3.76507i	0.232755	−	0.134381i
$786$		0			0
$787$	11.4280	+	6.59793i	0.407363	+	0.235191i	0.689656	−	0.724137i	$-0.257762\pi$
$787$	11.4280	+	6.59793i	0.407363	+	0.235191i	−0.282293	+	0.959328i	$0.591095\pi$
$788$		0			0
$789$	−3.57270	+	12.5540i	−0.127191	+	0.446933i
$790$		0			0
$791$	94.6960			3.36700
$792$		0			0
$793$	−0.405210			−0.0143894
$794$		0			0
$795$	−7.50133	+	1.88620i	−0.266045	+	0.0668966i
$796$		0			0
$797$	−43.2431	−	24.9664i	−1.53175	−	0.884356i	−0.999281	−	0.0379066i	$-0.987931\pi$
$797$	−43.2431	−	24.9664i	−1.53175	−	0.884356i	−0.532469	−	0.846450i	$-0.678736\pi$
$798$		0			0
$799$	30.9162	−	17.8495i	1.09374	−	0.631470i
$800$		0			0
$801$	−29.1278	−	0.900793i	−1.02918	−	0.0318280i
$802$		0			0
$803$	8.82719	+	15.2891i	0.311505	+	0.539542i
$804$		0			0
$805$	−5.49016	+	9.50923i	−0.193503	+	0.335156i
$806$		0			0
$807$	7.96845	−	7.72584i	0.280503	−	0.271962i
$808$		0			0
$809$			38.4167i			1.35066i	0.737516	+	0.675329i	$0.235999\pi$
$809$			38.4167i			1.35066i	−0.737516	+	0.675329i	$0.764001\pi$
$810$		0			0
$811$		−	8.98092i		−	0.315363i	−0.987490	−	0.157681i	$-0.949598\pi$
$811$		−	8.98092i		−	0.315363i	0.987490	−	0.157681i	$-0.0504019\pi$
$812$		0			0
$813$	−6.87934	+	6.66988i	−0.241269	+	0.233923i
$814$		0			0
$815$	0.929838	−	1.61053i	0.0325708	−	0.0564143i
$816$		0			0
$817$	14.0976	+	24.4178i	0.493214	+	0.854271i
$818$		0			0
$819$	−1.14068	−	0.0352761i	−0.0398585	−	0.00123265i
$820$		0			0
$821$	−48.8738	+	28.2173i	−1.70571	+	0.984792i	−0.765984	+	0.642859i	$0.777748\pi$
$821$	−48.8738	+	28.2173i	−1.70571	+	0.984792i	−0.939725	+	0.341932i	$0.888919\pi$
$822$		0			0
$823$	−35.6509	−	20.5831i	−1.24271	−	0.717481i	−0.273068	−	0.961995i	$-0.588038\pi$
$823$	−35.6509	−	20.5831i	−1.24271	−	0.717481i	−0.969646	+	0.244514i	$0.921372\pi$
$824$		0			0
$825$	−18.8988	+	4.75207i	−0.657971	+	0.165446i
$826$		0			0
$827$	−6.24168			−0.217044			−0.108522	−	0.994094i	$-0.534612\pi$
$827$	−6.24168			−0.217044			−0.108522	+	0.994094i	$0.534612\pi$
$828$		0			0
$829$	−33.2083			−1.15337			−0.576686	−	0.816966i	$-0.695654\pi$
$829$	−33.2083			−1.15337			−0.576686	+	0.816966i	$0.695654\pi$
$830$		0			0
$831$	9.63615	−	33.8601i	0.334274	−	1.17459i
$832$		0			0
$833$	89.6437	+	51.7558i	3.10597	+	1.79323i
$834$		0			0
$835$	1.25868	−	0.726697i	0.0435583	−	0.0251484i
$836$		0			0
$837$	−3.88852	+	0.850891i	−0.134407	+	0.0294111i
$838$		0			0
$839$	−11.9352	−	20.6724i	−0.412049	−	0.713690i	0.583064	−	0.812426i	$-0.301854\pi$
$839$	−11.9352	−	20.6724i	−0.412049	−	0.713690i	−0.995114	+	0.0987356i	$0.968520\pi$
$840$		0			0
$841$	14.0976	−	24.4178i	0.486125	−	0.841994i
$842$		0			0
$843$	11.9267	+	3.39418i	0.410777	+	0.116902i
$844$		0			0
$845$		−	5.97369i		−	0.205501i
$846$		0			0
$847$		−	27.1020i		−	0.931235i
$848$		0			0
$849$	5.07428	+	20.1802i	0.174149	+	0.692582i
$850$		0			0
$851$	−13.2323	+	22.9191i	−0.453599	+	0.785656i
$852$		0			0
$853$	19.5841	+	33.9206i	0.670545	+	1.16142i	0.977750	+	0.209775i	$0.0672731\pi$
$853$	19.5841	+	33.9206i	0.670545	+	1.16142i	−0.307205	+	0.951644i	$0.599394\pi$
$854$		0			0
$855$	4.21589	+	2.61104i	0.144180	+	0.0892958i
$856$		0			0
$857$	8.87557	−	5.12431i	0.303184	−	0.175043i	−0.340689	−	0.940176i	$-0.610660\pi$
$857$	8.87557	−	5.12431i	0.303184	−	0.175043i	0.643872	+	0.765133i	$0.277327\pi$
$858$		0			0
$859$	−13.6163	−	7.86135i	−0.464581	−	0.268226i	0.249388	−	0.968404i	$-0.419771\pi$
$859$	−13.6163	−	7.86135i	−0.464581	−	0.268226i	−0.713968	+	0.700178i	$0.753104\pi$
$860$		0			0
$861$	−6.79230	−	7.00560i	−0.231481	−	0.238750i
$862$		0			0
$863$	−32.0370			−1.09055			−0.545276	−	0.838257i	$-0.683575\pi$
$863$	−32.0370			−1.09055			−0.545276	+	0.838257i	$0.683575\pi$
$864$		0			0
$865$	−9.23966			−0.314158
$866$		0			0
$867$	−21.8804	−	22.5675i	−0.743096	−	0.766432i
$868$		0			0
$869$	5.94113	+	3.43011i	0.201539	+	0.116359i
$870$		0			0
$871$	0.141874	−	0.0819110i	0.00480722	−	0.00277545i
$872$		0			0
$873$	−16.7211	+	8.97656i	−0.565925	+	0.303811i
$874$		0			0
$875$	11.1280	+	19.2742i	0.376194	+	0.651588i
$876$		0			0
$877$	−18.3684	+	31.8149i	−0.620255	+	1.07431i	0.369183	+	0.929357i	$0.379638\pi$
$877$	−18.3684	+	31.8149i	−0.620255	+	1.07431i	−0.989438	+	0.144957i	$0.953696\pi$
$878$		0			0
$879$	10.0749	+	40.0673i	0.339817	+	1.35144i
$880$		0			0
$881$		−	44.9995i		−	1.51607i	−0.652213	−	0.758036i	$-0.726159\pi$
$881$		−	44.9995i		−	1.51607i	0.652213	−	0.758036i	$-0.273841\pi$
$882$		0			0
$883$		−	28.0715i		−	0.944680i	−0.881416	−	0.472340i	$-0.843409\pi$
$883$		−	28.0715i		−	0.944680i	0.881416	−	0.472340i	$-0.156591\pi$
$884$		0			0
$885$	6.36848	+	1.81239i	0.214074	+	0.0609227i
$886$		0			0
$887$	13.4625	−	23.3177i	0.452025	−	0.782930i	−0.546487	−	0.837468i	$-0.684035\pi$
$887$	13.4625	−	23.3177i	0.452025	−	0.782930i	0.998512	+	0.0545375i	$0.0173685\pi$
$888$		0			0
$889$	27.7859	+	48.1266i	0.931909	+	1.61411i
$890$		0			0
$891$	9.42091	+	18.9307i	0.315612	+	0.634203i
$892$		0			0
$893$	18.7503	−	10.8255i	0.627456	−	0.362262i
$894$		0			0
$895$	−4.04897	−	2.33767i	−0.135342	−	0.0781398i
$896$		0			0
$897$	−0.176108	+	0.618820i	−0.00588009	+	0.0206618i
$898$		0			0
$899$	−5.79347			−0.193223
$900$		0			0
$901$	57.5895			1.91859
$902$		0			0
$903$	65.1446	−	16.3805i	2.16787	−	0.545109i
$904$		0			0
$905$	−5.99477	−	3.46108i	−0.199273	−	0.115050i
$906$		0			0
$907$	−5.49526	+	3.17269i	−0.182467	+	0.105347i	−0.588451	−	0.808533i	$-0.700262\pi$
$907$	−5.49526	+	3.17269i	−0.182467	+	0.105347i	0.405984	+	0.913880i	$0.366929\pi$
$908$		0			0
$909$	7.37460	+	13.7371i	0.244600	+	0.455630i
$910$		0			0
$911$	−11.6552	−	20.1874i	−0.386154	−	0.668838i	0.605775	−	0.795636i	$-0.292863\pi$
$911$	−11.6552	−	20.1874i	−0.386154	−	0.668838i	−0.991929	+	0.126798i	$0.959530\pi$
$912$		0			0
$913$	−10.4393	+	18.0813i	−0.345489	+	0.598405i
$914$		0			0
$915$	3.01169	−	2.91999i	0.0995632	−	0.0965318i
$916$		0			0
$917$		−	74.6238i		−	2.46430i
$918$		0			0
$919$			16.2387i			0.535664i	0.963466	+	0.267832i	$0.0863072\pi$
$919$			16.2387i			0.535664i	−0.963466	+	0.267832i	$0.913693\pi$
$920$		0			0
$921$	−16.3809	+	15.8822i	−0.539769	+	0.523335i
$922$		0			0
$923$	0.410161	−	0.710419i	0.0135006	−	0.0233837i
$924$		0			0
$925$	13.1207	+	22.7258i	0.431407	+	0.747219i
$926$		0			0
$927$	4.40998	−	7.12053i	0.144843	−	0.233869i
$928$		0			0
$929$	3.64731	−	2.10577i	0.119664	−	0.0690882i	−0.438973	−	0.898500i	$-0.644658\pi$
$929$	3.64731	−	2.10577i	0.119664	−	0.0690882i	0.558637	+	0.829412i	$0.311324\pi$
$930$		0			0
$931$	54.3678	+	31.3893i	1.78183	+	1.02874i
$932$		0			0
$933$	−3.85758	+	0.969983i	−0.126291	+	0.0317558i
$934$		0			0
$935$	−6.40352			−0.209418
$936$		0			0
$937$	42.9154			1.40198			0.700992	−	0.713169i	$-0.252741\pi$
$937$	42.9154			1.40198			0.700992	+	0.713169i	$0.252741\pi$
$938$		0			0
$939$	−4.13939	+	14.5452i	−0.135084	+	0.474666i
$940$		0			0
$941$	−5.89739	−	3.40486i	−0.192249	−	0.110995i	0.400786	−	0.916172i	$-0.368737\pi$
$941$	−5.89739	−	3.40486i	−0.192249	−	0.110995i	−0.593035	+	0.805177i	$0.702071\pi$
$942$		0			0
$943$	−4.76415	+	2.75058i	−0.155142	+	0.0895713i
$944$		0			0
$945$	8.73220	−	7.95767i	0.284058	−	0.258863i
$946$		0			0
$947$	23.8163	+	41.2511i	0.773927	+	1.34048i	0.935395	+	0.353603i	$0.115044\pi$
$947$	23.8163	+	41.2511i	0.773927	+	1.34048i	−0.161468	+	0.986878i	$0.551623\pi$
$948$		0			0
$949$	0.288984	−	0.500535i	0.00938081	−	0.0162480i
$950$		0			0
$951$	8.15092	+	2.31965i	0.264312	+	0.0752197i
$952$		0			0
$953$			56.0644i			1.81610i	0.418859	+	0.908051i	$0.362430\pi$
$953$			56.0644i			1.81610i	−0.418859	+	0.908051i	$0.637570\pi$
$954$		0			0
$955$			1.29820i			0.0420088i
$956$		0			0
$957$	7.50498	+	29.8470i	0.242601	+	0.964815i
$958$		0			0
$959$	−8.89804	+	15.4119i	−0.287333	+	0.497675i
$960$		0			0
$961$	−15.2066	−	26.3386i	−0.490535	−	0.849631i
$962$		0			0
$963$	−1.35306	+	43.7523i	−0.0436019	+	1.40990i
$964$		0			0
$965$	7.12792	−	4.11531i	0.229456	−	0.132476i
$966$		0			0
$967$	−6.10910	−	3.52709i	−0.196455	−	0.113424i	0.398546	−	0.917149i	$-0.369515\pi$
$967$	−6.10910	−	3.52709i	−0.196455	−	0.113424i	−0.595001	+	0.803725i	$0.702848\pi$
$968$		0			0
$969$	−25.7010	−	26.5081i	−0.825634	−	0.851562i
$970$		0			0
$971$	−33.2137			−1.06588			−0.532939	−	0.846153i	$-0.678913\pi$
$971$	−33.2137			−1.06588			−0.532939	+	0.846153i	$0.678913\pi$
$972$		0			0
$973$	−35.0509			−1.12368
$974$		0			0
$975$	0.444083	+	0.458029i	0.0142220	+	0.0146687i
$976$		0			0
$977$	−11.7166	−	6.76456i	−0.374846	−	0.216418i	0.300727	−	0.953710i	$-0.402771\pi$
$977$	−11.7166	−	6.76456i	−0.374846	−	0.216418i	−0.675574	+	0.737293i	$0.736104\pi$
$978$		0			0
$979$	19.7650	−	11.4113i	0.631692	−	0.364708i
$980$		0			0
$981$	1.17502	−	37.9953i	0.0375157	−	1.21310i
$982$		0			0
$983$	4.59692	+	7.96210i	0.146619	+	0.253952i	0.929976	−	0.367621i	$-0.119828\pi$
$983$	4.59692	+	7.96210i	0.146619	+	0.253952i	−0.783357	+	0.621572i	$0.786494\pi$
$984$		0			0
$985$	1.30029	−	2.25218i	0.0414308	−	0.0717603i
$986$		0			0
$987$	−12.5785	−	50.0242i	−0.400379	−	1.59229i
$988$		0			0
$989$		−	37.8700i		−	1.20420i
$990$		0			0
$991$			29.2577i			0.929402i	0.885468	+	0.464701i	$0.153838\pi$
$991$			29.2577i			0.929402i	−0.885468	+	0.464701i	$0.846162\pi$
$992$		0			0
$993$	−6.04054	−	1.71906i	−0.191691	−	0.0545527i
$994$		0			0
$995$	1.55851	−	2.69943i	0.0494082	−	0.0855775i
$996$		0			0
$997$	−25.1497	−	43.5606i	−0.796500	−	1.37958i	−0.921883	−	0.387469i	$-0.873349\pi$
$997$	−25.1497	−	43.5606i	−0.796500	−	1.37958i	0.125383	−	0.992108i	$-0.459984\pi$
$998$		0			0
$999$	21.0463	−	19.1795i	0.665874	−	0.606813i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.s.a.95.10	yes	24
3.2	odd	2		864.2.s.a.287.8		24
4.3	odd	2	inner	288.2.s.a.95.3	✓	24
8.3	odd	2		576.2.s.g.383.10		24
8.5	even	2		576.2.s.g.383.3		24
9.2	odd	6	inner	288.2.s.a.191.3	yes	24
9.4	even	3		2592.2.c.c.2591.16		24
9.5	odd	6		2592.2.c.c.2591.10		24
9.7	even	3		864.2.s.a.575.7		24
12.11	even	2		864.2.s.a.287.7		24
24.5	odd	2		1728.2.s.g.1151.5		24
24.11	even	2		1728.2.s.g.1151.6		24
36.7	odd	6		864.2.s.a.575.8		24
36.11	even	6	inner	288.2.s.a.191.10	yes	24
36.23	even	6		2592.2.c.c.2591.9		24
36.31	odd	6		2592.2.c.c.2591.15		24
72.5	odd	6		5184.2.c.m.5183.16		24
72.11	even	6		576.2.s.g.191.3		24
72.13	even	6		5184.2.c.m.5183.10		24
72.29	odd	6		576.2.s.g.191.10		24
72.43	odd	6		1728.2.s.g.575.5		24
72.59	even	6		5184.2.c.m.5183.15		24
72.61	even	6		1728.2.s.g.575.6		24
72.67	odd	6		5184.2.c.m.5183.9		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.s.a.95.3	✓	24	4.3	odd	2	inner
288.2.s.a.95.10	yes	24	1.1	even	1	trivial
288.2.s.a.191.3	yes	24	9.2	odd	6	inner
288.2.s.a.191.10	yes	24	36.11	even	6	inner
576.2.s.g.191.3		24	72.11	even	6
576.2.s.g.191.10		24	72.29	odd	6
576.2.s.g.383.3		24	8.5	even	2
576.2.s.g.383.10		24	8.3	odd	2
864.2.s.a.287.7		24	12.11	even	2
864.2.s.a.287.8		24	3.2	odd	2
864.2.s.a.575.7		24	9.7	even	3
864.2.s.a.575.8		24	36.7	odd	6
1728.2.s.g.575.5		24	72.43	odd	6
1728.2.s.g.575.6		24	72.61	even	6
1728.2.s.g.1151.5		24	24.5	odd	2
1728.2.s.g.1151.6		24	24.11	even	2
2592.2.c.c.2591.9		24	36.23	even	6
2592.2.c.c.2591.10		24	9.5	odd	6
2592.2.c.c.2591.15		24	36.31	odd	6
2592.2.c.c.2591.16		24	9.4	even	3
5184.2.c.m.5183.9		24	72.67	odd	6
5184.2.c.m.5183.10		24	72.13	even	6
5184.2.c.m.5183.15		24	72.59	even	6
5184.2.c.m.5183.16		24	72.5	odd	6

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:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	288.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.20567 + 1.24353i) q^{3} +(-0.398132 - 0.229862i) q^{5} +(4.28309 - 2.47284i) q^{7} +(-0.0927324 + 2.99857i) q^{9} +O(q^{10})\)	\(q+(1.20567 + 1.24353i) q^{3} +(-0.398132 - 0.229862i) q^{5} +(4.28309 - 2.47284i) q^{7} +(-0.0927324 + 2.99857i) q^{9} +(-1.17474 - 2.03471i) q^{11} +(-0.0384586 + 0.0666122i) q^{13} +(-0.194175 - 0.772226i) q^{15} +5.92857i q^{17} +3.59561i q^{19} +(8.23903 + 2.34472i) q^{21} +(2.41469 - 4.18237i) q^{23} +(-2.39433 - 4.14710i) q^{25} +(-3.84061 + 3.49996i) q^{27} +(-6.54954 + 3.78138i) q^{29} +(0.663421 + 0.383026i) q^{31} +(1.11388 - 3.91401i) q^{33} -2.27365 q^{35} -5.47993 q^{37} +(-0.129203 + 0.0324878i) q^{39} +(-0.986492 - 0.569551i) q^{41} +(6.79101 - 3.92079i) q^{43} +(0.726176 - 1.17251i) q^{45} +(-3.01076 - 5.21479i) q^{47} +(8.72990 - 15.1206i) q^{49} +(-7.37235 + 7.14788i) q^{51} -9.71390i q^{53} +1.08011i q^{55} +(-4.47124 + 4.33511i) q^{57} +(-4.15776 + 7.20145i) q^{59} +(2.63407 + 4.56234i) q^{61} +(7.01780 + 13.0724i) q^{63} +(0.0306232 - 0.0176803i) q^{65} +(-1.84450 - 1.06492i) q^{67} +(8.11221 - 2.03980i) q^{69} -10.6650 q^{71} -7.51416 q^{73} +(2.27028 - 7.97744i) q^{75} +(-10.0630 - 5.80990i) q^{77} +(-2.52870 + 1.45994i) q^{79} +(-8.98280 - 0.556128i) q^{81} +(-4.44322 - 7.69588i) q^{83} +(1.36275 - 2.36035i) q^{85} +(-12.5988 - 3.58546i) q^{87} +9.71390i q^{89} +0.380408i q^{91} +(0.323560 + 1.28679i) q^{93} +(0.826493 - 1.43153i) q^{95} +(3.16305 + 5.47856i) q^{97} +(6.21016 - 3.33386i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{9}+O(q^{10}) \) 24 * q - 4 * q^9	\( 24 q - 4 q^{9} + 8 q^{21} + 12 q^{25} + 24 q^{29} - 20 q^{33} - 36 q^{41} - 8 q^{45} + 12 q^{49} - 36 q^{57} - 48 q^{65} - 16 q^{69} + 24 q^{73} - 48 q^{77} - 20 q^{81} - 64 q^{93} + 12 q^{97}+O(q^{100}) \) 24 * q - 4 * q^9 + 8 * q^21 + 12 * q^25 + 24 * q^29 - 20 * q^33 - 36 * q^41 - 8 * q^45 + 12 * q^49 - 36 * q^57 - 48 * q^65 - 16 * q^69 + 24 * q^73 - 48 * q^77 - 20 * q^81 - 64 * q^93 + 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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