LMFDB - Embedded newform 576.2.r.e.481.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [576,2,Mod(97,576)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(576, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("576.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 576 = 2^{6} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	576.r (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:	$4.59938315643$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 16x^{8} - 24x^{7} + 96x^{5} + 304x^{4} + 384x^{3} + 288x^{2} + 144x + 36 $ x^12 - 16x^8 - 24x^7 + 96x^5 + 304x^4 + 384x^3 + 288x^2 + 144*x + 36
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			481.5
Root			$-0.403293 - 1.50511i$ of defining polynomial
Character	$\chi$	$=$	576.481
Dual form			576.2.r.e.97.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.10182 - 1.33641i) q^{3} +(-1.50000 - 0.866025i) q^{5} +(-0.495361 - 0.857990i) q^{7} +(-0.571993 - 2.94497i) q^{9} +O(q^{10})$	\(q+(1.10182 - 1.33641i) q^{3} +(-1.50000 - 0.866025i) q^{5} +(-0.495361 - 0.857990i) q^{7} +(-0.571993 - 2.94497i) q^{9} +(-1.81937 + 1.05042i) q^{11} +(-5.50924 - 3.18076i) q^{13} +(-2.81009 + 1.05042i) q^{15} +3.81681 q^{17} -2.00000i q^{19} +(-1.69243 - 0.283343i) q^{21} +(-3.55142 + 6.15125i) q^{23} +(-1.00000 - 1.73205i) q^{25} +(-4.56592 - 2.48040i) q^{27} +(7.22522 - 4.17148i) q^{29} +(1.07804 - 1.86723i) q^{31} +(-0.600830 + 3.58880i) q^{33} +1.71598i q^{35} -4.62947i q^{37} +(-10.3210 + 3.85799i) q^{39} +(-0.408405 + 0.707378i) q^{41} +(-1.97802 + 1.14201i) q^{43} +(-1.69243 + 4.91281i) q^{45} +(3.39278 + 5.87646i) q^{47} +(3.00924 - 5.21215i) q^{49} +(4.20543 - 5.10083i) q^{51} -3.14681i q^{53} +3.63875 q^{55} +(-2.67282 - 2.20364i) q^{57} +(-10.3210 - 5.95882i) q^{59} +(-4.22522 + 2.43943i) q^{61} +(-2.24341 + 1.94958i) q^{63} +(5.50924 + 9.54228i) q^{65} +(11.8944 + 6.86723i) q^{67} +(4.30757 + 11.5237i) q^{69} +13.5391 q^{71} +10.0185 q^{73} +(-3.41655 - 0.571993i) q^{75} +(1.80249 + 1.04067i) q^{77} +(-4.54214 - 7.86723i) q^{79} +(-8.34565 + 3.36900i) q^{81} +(3.71007 - 2.14201i) q^{83} +(-5.72522 - 3.30545i) q^{85} +(2.38606 - 14.2521i) q^{87} -14.0185 q^{89} +6.30249i q^{91} +(-1.30757 - 3.49805i) q^{93} +(-1.73205 + 3.00000i) q^{95} +(-6.22522 - 10.7824i) q^{97} +(4.13411 + 4.75716i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 18 q^{5} - 4 q^{9}+O(q^{10}) $ 12 * q - 18 * q^5 - 4 * q^9	$ 12 q - 18 q^{5} - 4 q^{9} - 6 q^{13} - 6 q^{21} - 12 q^{25} + 18 q^{29} + 30 q^{33} + 18 q^{41} - 6 q^{45} - 24 q^{49} + 8 q^{57} + 18 q^{61} + 6 q^{65} + 66 q^{69} - 90 q^{77} - 20 q^{81} - 48 q^{89} - 30 q^{93} - 6 q^{97}+O(q^{100}) $ 12 * q - 18 * q^5 - 4 * q^9 - 6 * q^13 - 6 * q^21 - 12 * q^25 + 18 * q^29 + 30 * q^33 + 18 * q^41 - 6 * q^45 - 24 * q^49 + 8 * q^57 + 18 * q^61 + 6 * q^65 + 66 * q^69 - 90 * q^77 - 20 * q^81 - 48 * q^89 - 30 * q^93 - 6 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/576\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$325$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$-1$

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
$3$	1.10182	−	1.33641i	0.636135	−	0.771578i
$3$	1.10182	−	1.33641i	0.636135	−	0.771578i
$4$		0			0
$5$	−1.50000	−	0.866025i	−0.670820	−	0.387298i	0.125567	−	0.992085i	$-0.459925\pi$
$5$	−1.50000	−	0.866025i	−0.670820	−	0.387298i	−0.796387	+	0.604787i	$0.793258\pi$
$6$		0			0
$7$	−0.495361	−	0.857990i	−0.187229	−	0.324290i	0.757097	−	0.653303i	$-0.226617\pi$
$7$	−0.495361	−	0.857990i	−0.187229	−	0.324290i	−0.944325	+	0.329013i	$0.893284\pi$
$8$		0			0
$9$	−0.571993	−	2.94497i	−0.190664	−	0.981655i
$10$		0			0
$11$	−1.81937	+	1.05042i	−0.548561	+	0.316712i	−0.748542	−	0.663088i	$-0.769246\pi$
$11$	−1.81937	+	1.05042i	−0.548561	+	0.316712i	0.199980	+	0.979800i	$0.435912\pi$
$12$		0			0
$13$	−5.50924	−	3.18076i	−1.52799	−	0.882184i	−0.999446	−	0.0332758i	$-0.989406\pi$
$13$	−5.50924	−	3.18076i	−1.52799	−	0.882184i	−0.528541	−	0.848908i	$-0.677261\pi$
$14$		0			0
$15$	−2.81009	+	1.05042i	−0.725563	+	0.271216i
$16$		0			0
$17$	3.81681			0.925712			0.462856	−	0.886433i	$-0.346825\pi$
$17$	3.81681			0.925712			0.462856	+	0.886433i	$0.346825\pi$
$18$		0			0
$19$		−	2.00000i		−	0.458831i	−0.973329	−	0.229416i	$-0.926318\pi$
$19$		−	2.00000i		−	0.458831i	0.973329	−	0.229416i	$-0.0736815\pi$
$20$		0			0
$21$	−1.69243	−	0.283343i	−0.369317	−	0.0618305i
$22$		0			0
$23$	−3.55142	+	6.15125i	−0.740523	+	1.28262i	0.211734	+	0.977327i	$0.432089\pi$
$23$	−3.55142	+	6.15125i	−0.740523	+	1.28262i	−0.952257	+	0.305296i	$0.901245\pi$
$24$		0			0
$25$	−1.00000	−	1.73205i	−0.200000	−	0.346410i
$26$		0			0
$27$	−4.56592	−	2.48040i	−0.878712	−	0.477353i
$28$		0			0
$29$	7.22522	−	4.17148i	1.34169	−	0.774624i	0.354634	−	0.935005i	$-0.384606\pi$
$29$	7.22522	−	4.17148i	1.34169	−	0.774624i	0.987055	+	0.160381i	$0.0512723\pi$
$30$		0			0
$31$	1.07804	−	1.86723i	0.193622	−	0.335364i	−0.752826	−	0.658220i	$-0.771310\pi$
$31$	1.07804	−	1.86723i	0.193622	−	0.335364i	0.946448	+	0.322856i	$0.104643\pi$
$32$		0			0
$33$	−0.600830	+	3.58880i	−0.104591	+	0.624729i
$34$		0			0
$35$			1.71598i			0.290054i
$36$		0			0
$37$		−	4.62947i		−	0.761080i	−0.924765	−	0.380540i	$-0.875738\pi$
$37$		−	4.62947i		−	0.761080i	0.924765	−	0.380540i	$-0.124262\pi$
$38$		0			0
$39$	−10.3210	+	3.85799i	−1.65268	+	0.617773i
$40$		0			0
$41$	−0.408405	+	0.707378i	−0.0637822	+	0.110474i	−0.896153	−	0.443745i	$-0.853650\pi$
$41$	−0.408405	+	0.707378i	−0.0637822	+	0.110474i	0.832371	+	0.554219i	$0.186983\pi$
$42$		0			0
$43$	−1.97802	+	1.14201i	−0.301645	+	0.174155i	−0.643182	−	0.765714i	$-0.722386\pi$
$43$	−1.97802	+	1.14201i	−0.301645	+	0.174155i	0.341537	+	0.939868i	$0.389053\pi$
$44$		0			0
$45$	−1.69243	+	4.91281i	−0.252292	+	0.732358i
$46$		0			0
$47$	3.39278	+	5.87646i	0.494887	+	0.857170i	0.999983	−	0.00589362i	$-0.00187601\pi$
$47$	3.39278	+	5.87646i	0.494887	+	0.857170i	−0.505095	+	0.863064i	$0.668543\pi$
$48$		0			0
$49$	3.00924	−	5.21215i	0.429891	−	0.744593i
$50$		0			0
$51$	4.20543	−	5.10083i	0.588878	−	0.714259i
$52$		0			0
$53$		−	3.14681i		−	0.432247i	−0.976366	−	0.216124i	$-0.930659\pi$
$53$		−	3.14681i		−	0.432247i	0.976366	−	0.216124i	$-0.0693414\pi$
$54$		0			0
$55$	3.63875			0.490648
$56$		0			0
$57$	−2.67282	−	2.20364i	−0.354024	−	0.291879i
$58$		0			0
$59$	−10.3210	−	5.95882i	−1.34368	−	0.775772i	−0.356332	−	0.934359i	$-0.615973\pi$
$59$	−10.3210	−	5.95882i	−1.34368	−	0.775772i	−0.987345	+	0.158587i	$0.949306\pi$
$60$		0			0
$61$	−4.22522	+	2.43943i	−0.540983	+	0.312337i	−0.745477	−	0.666531i	$-0.767778\pi$
$61$	−4.22522	+	2.43943i	−0.540983	+	0.312337i	0.204494	+	0.978868i	$0.434445\pi$
$62$		0			0
$63$	−2.24341	+	1.94958i	−0.282643	+	0.245625i
$64$		0			0
$65$	5.50924	+	9.54228i	0.683337	+	1.18357i
$66$		0			0
$67$	11.8944	+	6.86723i	1.45313	+	0.838965i	0.998658	−	0.0517956i	$-0.0164944\pi$
$67$	11.8944	+	6.86723i	1.45313	+	0.838965i	0.454473	+	0.890761i	$0.349828\pi$
$68$		0			0
$69$	4.30757	+	11.5237i	0.518571	+	1.38729i
$70$		0			0
$71$	13.5391			1.60680			0.803399	−	0.595442i	$-0.203023\pi$
$71$	13.5391			1.60680			0.803399	+	0.595442i	$0.203023\pi$
$72$		0			0
$73$	10.0185			1.17257			0.586287	−	0.810104i	$-0.300589\pi$
$73$	10.0185			1.17257			0.586287	+	0.810104i	$0.300589\pi$
$74$		0			0
$75$	−3.41655	−	0.571993i	−0.394509	−	0.0660481i
$76$		0			0
$77$	1.80249	+	1.04067i	0.205413	+	0.118595i
$78$		0			0
$79$	−4.54214	−	7.86723i	−0.511031	−	0.885132i	−0.999918	−	0.0127849i	$-0.995930\pi$
$79$	−4.54214	−	7.86723i	−0.511031	−	0.885132i	0.488887	−	0.872347i	$-0.337403\pi$
$80$		0			0
$81$	−8.34565	+	3.36900i	−0.927294	+	0.374333i
$82$		0			0
$83$	3.71007	−	2.14201i	0.407233	−	0.235116i	−0.282367	−	0.959306i	$-0.591120\pi$
$83$	3.71007	−	2.14201i	0.407233	−	0.235116i	0.689600	+	0.724190i	$0.257786\pi$
$84$		0			0
$85$	−5.72522	−	3.30545i	−0.620987	−	0.358527i
$86$		0			0
$87$	2.38606	−	14.2521i	0.255812	−	1.52798i
$88$		0			0
$89$	−14.0185			−1.48595			−0.742977	−	0.669316i	$-0.766587\pi$
$89$	−14.0185			−1.48595			−0.742977	+	0.669316i	$0.766587\pi$
$90$		0			0
$91$			6.30249i			0.660681i
$92$		0			0
$93$	−1.30757	−	3.49805i	−0.135589	−	0.362731i
$94$		0			0
$95$	−1.73205	+	3.00000i	−0.177705	+	0.307794i
$96$		0			0
$97$	−6.22522	−	10.7824i	−0.632075	−	1.09479i	−0.987127	−	0.159939i	$-0.948870\pi$
$97$	−6.22522	−	10.7824i	−0.632075	−	1.09479i	0.355052	−	0.934847i	$-0.384463\pi$
$98$		0			0
$99$	4.13411	+	4.75716i	0.415493	+	0.478113i
$100$		0			0
$101$	13.8025	−	7.96887i	1.37340	−	0.792932i	0.382045	−	0.924144i	$-0.375220\pi$
$101$	13.8025	−	7.96887i	1.37340	−	0.792932i	0.991354	+	0.131211i	$0.0418867\pi$
$102$		0			0
$103$	8.58893	−	14.8765i	0.846292	−	1.46582i	−0.0382019	−	0.999270i	$-0.512163\pi$
$103$	8.58893	−	14.8765i	0.846292	−	1.46582i	0.884494	−	0.466551i	$-0.154504\pi$
$104$		0			0
$105$	2.29326	+	1.89070i	0.223799	+	0.184513i
$106$		0			0
$107$			16.2017i			1.56627i	0.621849	+	0.783137i	$0.286382\pi$
$107$			16.2017i			1.56627i	−0.621849	+	0.783137i	$0.713618\pi$
$108$		0			0
$109$			0.816078i			0.0781661i	0.999236	+	0.0390830i	$0.0124437\pi$
$109$			0.816078i			0.0781661i	−0.999236	+	0.0390830i	$0.987556\pi$
$110$		0			0
$111$	−6.18687	−	5.10083i	−0.587232	−	0.484149i
$112$		0			0
$113$	3.21598	−	5.57024i	0.302534	−	0.524004i	−0.674175	−	0.738571i	$-0.735501\pi$
$113$	3.21598	−	5.57024i	0.302534	−	0.524004i	0.976709	+	0.214567i	$0.0688341\pi$
$114$		0			0
$115$	10.6543	−	6.15125i	0.993516	−	0.573607i
$116$		0			0
$117$	−6.21598	+	18.0439i	−0.574668	+	1.66816i
$118$		0			0
$119$	−1.89070	−	3.27478i	−0.173320	−	0.300199i
$120$		0			0
$121$	−3.29326	+	5.70409i	−0.299387	+	0.518553i
$122$		0			0
$123$	0.495361	+	1.32520i	0.0446652	+	0.119489i
$124$		0			0
$125$			12.1244i			1.08444i
$126$		0			0
$127$	16.1871			1.43638			0.718188	−	0.695849i	$-0.244972\pi$
$127$	16.1871			1.43638			0.718188	+	0.695849i	$0.244972\pi$
$128$		0			0
$129$	−0.653222	+	3.90174i	−0.0575130	+	0.343529i
$130$		0			0
$131$	6.68223	+	3.85799i	0.583830	+	0.337074i	0.762654	−	0.646807i	$-0.223896\pi$
$131$	6.68223	+	3.85799i	0.583830	+	0.337074i	−0.178824	+	0.983881i	$0.557229\pi$
$132$		0			0
$133$	−1.71598	+	0.990721i	−0.148794	+	0.0859064i
$134$		0			0
$135$	4.70079	+	7.67480i	0.404580	+	0.660542i
$136$		0			0
$137$	4.30757	+	7.46094i	0.368021	+	0.637431i	0.989256	−	0.146193i	$-0.0467021\pi$
$137$	4.30757	+	7.46094i	0.368021	+	0.637431i	−0.621235	+	0.783624i	$0.713369\pi$
$138$		0			0
$139$	−4.95018	−	2.85799i	−0.419869	−	0.242412i	0.275152	−	0.961401i	$-0.411272\pi$
$139$	−4.95018	−	2.85799i	−0.419869	−	0.242412i	−0.695021	+	0.718989i	$0.744605\pi$
$140$		0			0
$141$	11.5916	+	1.94065i	0.976188	+	0.163432i
$142$		0			0
$143$	13.3645			1.11759
$144$		0			0
$145$	−14.4504			−1.20004
$146$		0			0
$147$	−3.64995	−	9.76442i	−0.301043	−	0.805356i
$148$		0			0
$149$	1.22522	+	0.707378i	0.100374	+	0.0579507i	0.549346	−	0.835595i	$-0.314877\pi$
$149$	1.22522	+	0.707378i	0.100374	+	0.0579507i	−0.448973	+	0.893545i	$0.648210\pi$
$150$		0			0
$151$	1.64473	+	2.84875i	0.133846	+	0.231828i	0.925156	−	0.379587i	$-0.123934\pi$
$151$	1.64473	+	2.84875i	0.133846	+	0.231828i	−0.791310	+	0.611415i	$0.790601\pi$
$152$		0			0
$153$	−2.18319	−	11.2404i	−0.176500	−	0.908731i
$154$		0			0
$155$	−3.23413	+	1.86723i	−0.259772	+	0.149979i
$156$		0			0
$157$	5.78402	+	3.33941i	0.461615	+	0.266514i	0.712723	−	0.701445i	$-0.247462\pi$
$157$	5.78402	+	3.33941i	0.461615	+	0.266514i	−0.251108	+	0.967959i	$0.580795\pi$
$158$		0			0
$159$	−4.20543	−	3.46721i	−0.333512	−	0.274968i
$160$		0			0
$161$	7.03694			0.554589
$162$		0			0
$163$			7.43196i			0.582116i	0.956705	+	0.291058i	$0.0940073\pi$
$163$			7.43196i			0.582116i	−0.956705	+	0.291058i	$0.905993\pi$
$164$		0			0
$165$	4.00924	−	4.86286i	0.312119	−	0.378573i
$166$		0			0
$167$	−4.95018	+	8.57397i	−0.383057	+	0.663474i	−0.991498	−	0.130126i	$-0.958462\pi$
$167$	−4.95018	+	8.57397i	−0.383057	+	0.663474i	0.608441	+	0.793599i	$0.291795\pi$
$168$		0			0
$169$	13.7345	+	23.7888i	1.05650	+	1.82991i
$170$		0			0
$171$	−5.88993	+	1.14399i	−0.450414	+	0.0874828i
$172$		0			0
$173$	10.5000	−	6.06218i	0.798300	−	0.460899i	−0.0445762	−	0.999006i	$-0.514194\pi$
$173$	10.5000	−	6.06218i	0.798300	−	0.460899i	0.842876	+	0.538107i	$0.180860\pi$
$174$		0			0
$175$	−0.990721	+	1.71598i	−0.0748915	+	0.129716i
$176$		0			0
$177$	−19.3353	+	7.22754i	−1.45333	+	0.543255i
$178$		0			0
$179$		−	6.00000i		−	0.448461i	−0.974536	−	0.224231i	$-0.928013\pi$
$179$		−	6.00000i		−	0.448461i	0.974536	−	0.224231i	$-0.0719869\pi$
$180$		0			0
$181$			4.62947i			0.344106i	0.985088	+	0.172053i	$0.0550400\pi$
$181$			4.62947i			0.344106i	−0.985088	+	0.172053i	$0.944960\pi$
$182$		0			0
$183$	−1.39534	+	8.33444i	−0.103146	+	0.616099i
$184$		0			0
$185$	−4.00924	+	6.94420i	−0.294765	+	0.510548i
$186$		0			0
$187$	−6.94420	+	4.00924i	−0.507810	+	0.293184i
$188$		0			0
$189$	0.133620	+	5.14620i	0.00971946	+	0.374331i
$190$		0			0
$191$	−8.58893	−	14.8765i	−0.621473	−	1.07642i	−0.989212	−	0.146494i	$-0.953201\pi$
$191$	−8.58893	−	14.8765i	−0.621473	−	1.07642i	0.367739	−	0.929929i	$-0.380132\pi$
$192$		0			0
$193$	5.79326	−	10.0342i	0.417008	−	0.722278i	−0.578629	−	0.815591i	$-0.696412\pi$
$193$	5.79326	−	10.0342i	0.417008	−	0.722278i	0.995637	+	0.0933122i	$0.0297455\pi$
$194$		0			0
$195$	18.8226	+	3.15125i	1.34791	+	0.225665i
$196$		0			0
$197$			17.6698i			1.25892i	0.777033	+	0.629460i	$0.216724\pi$
$197$			17.6698i			1.25892i	−0.777033	+	0.629460i	$0.783276\pi$
$198$		0			0
$199$	−16.5044			−1.16997			−0.584984	−	0.811045i	$-0.698899\pi$
$199$	−16.5044			−1.16997			−0.584984	+	0.811045i	$0.698899\pi$
$200$		0			0
$201$	22.2829	−	8.32936i	1.57171	−	0.587508i
$202$		0			0
$203$	−7.15818	−	4.13277i	−0.502405	−	0.290064i
$204$		0			0
$205$	1.22522	−	0.707378i	0.0855728	−	0.0494055i
$206$		0			0
$207$	20.1466	+	6.94035i	1.40029	+	0.482388i
$208$		0			0
$209$	2.10083	+	3.63875i	0.145317	+	0.251697i
$210$		0			0
$211$	−10.1623	−	5.86723i	−0.699604	−	0.403916i	0.107596	−	0.994195i	$-0.465685\pi$
$211$	−10.1623	−	5.86723i	−0.699604	−	0.403916i	−0.807200	+	0.590278i	$0.799018\pi$
$212$		0			0
$213$	14.9176	−	18.0938i	1.02214	−	1.23977i
$214$		0			0
$215$	3.95604			0.269800
$216$		0			0
$217$	−2.13608			−0.145007
$218$		0			0
$219$	11.0385	−	13.3888i	0.745915	−	0.904731i
$220$		0			0
$221$	−21.0277	−	12.1404i	−1.41448	−	0.816648i
$222$		0			0
$223$	0.670004	+	1.16048i	0.0448668	+	0.0777116i	0.887587	−	0.460641i	$-0.152380\pi$
$223$	0.670004	+	1.16048i	0.0448668	+	0.0777116i	−0.842720	+	0.538352i	$0.819047\pi$
$224$		0			0
$225$	−4.52884	+	3.93569i	−0.301922	+	0.262379i
$226$		0			0
$227$	−3.37678	+	1.94958i	−0.224125	+	0.129398i	−0.607859	−	0.794045i	$-0.707971\pi$
$227$	−3.37678	+	1.94958i	−0.224125	+	0.129398i	0.383734	+	0.923444i	$0.374638\pi$
$228$		0			0
$229$	1.93196	+	1.11542i	0.127667	+	0.0737089i	0.562474	−	0.826815i	$-0.309850\pi$
$229$	1.93196	+	1.11542i	0.127667	+	0.0737089i	−0.434806	+	0.900524i	$0.643183\pi$
$230$		0			0
$231$	3.37678	−	1.26224i	0.222176	−	0.0830495i
$232$		0			0
$233$	−9.26724			−0.607117			−0.303559	−	0.952813i	$-0.598175\pi$
$233$	−9.26724			−0.607117			−0.303559	+	0.952813i	$0.598175\pi$
$234$		0			0
$235$		−	11.7529i		−	0.766676i
$236$		0			0
$237$	−15.5185	−	2.59808i	−1.00803	−	0.168763i
$238$		0			0
$239$	−10.4796	+	18.1512i	−0.677871	+	1.17411i	0.297750	+	0.954644i	$0.403764\pi$
$239$	−10.4796	+	18.1512i	−0.677871	+	1.17411i	−0.975621	+	0.219463i	$0.929570\pi$
$240$		0			0
$241$	−7.51847	−	13.0224i	−0.484307	−	0.838845i	0.515530	−	0.856871i	$-0.327595\pi$
$241$	−7.51847	−	13.0224i	−0.484307	−	0.838845i	−0.999838	+	0.0180266i	$0.994262\pi$
$242$		0			0
$243$	−4.69301	+	14.8652i	−0.301057	+	0.953606i
$244$		0			0
$245$	−9.02771	+	5.21215i	−0.576759	+	0.332992i
$246$		0			0
$247$	−6.36152	+	11.0185i	−0.404774	+	0.701089i
$248$		0			0
$249$	1.22522	−	7.31829i	0.0776449	−	0.463778i
$250$		0			0
$251$			0.164719i			0.0103969i	0.999986	+	0.00519847i	$0.00165473\pi$
$251$			0.164719i			0.0103969i	−0.999986	+	0.00519847i	$0.998345\pi$
$252$		0			0
$253$		−	14.9219i		−	0.938130i
$254$		0			0
$255$	−10.7256	+	4.00924i	−0.671663	+	0.251068i
$256$		0			0
$257$	13.4176	−	23.2400i	0.836969	−	1.44967i	−0.0554474	−	0.998462i	$-0.517659\pi$
$257$	13.4176	−	23.2400i	0.836969	−	1.44967i	0.892417	−	0.451212i	$-0.149008\pi$
$258$		0			0
$259$	−3.97204	+	2.29326i	−0.246810	+	0.142496i
$260$		0			0
$261$	−16.4176	−	18.8920i	−1.01623	−	1.16938i
$262$		0			0
$263$	−9.98769	−	17.2992i	−0.615867	−	1.06671i	−0.990232	−	0.139432i	$-0.955472\pi$
$263$	−9.98769	−	17.2992i	−0.615867	−	1.06671i	0.374364	−	0.927282i	$-0.377861\pi$
$264$		0			0
$265$	−2.72522	+	4.72021i	−0.167409	+	0.289960i
$266$		0			0
$267$	−15.4458	+	18.7345i	−0.945268	+	1.14653i
$268$		0			0
$269$		−	0.666581i		−	0.0406422i	−0.999794	−	0.0203211i	$-0.993531\pi$
$269$		−	0.666581i		−	0.0406422i	0.999794	−	0.0203211i	$-0.00646884\pi$
$270$		0			0
$271$	−17.0352			−1.03482			−0.517408	−	0.855739i	$-0.673103\pi$
$271$	−17.0352			−1.03482			−0.517408	+	0.855739i	$0.673103\pi$
$272$		0			0
$273$	8.42272	+	6.94420i	0.509766	+	0.420282i
$274$		0			0
$275$	3.63875	+	2.10083i	0.219425	+	0.126685i
$276$		0			0
$277$	3.21598	−	1.85675i	0.193229	−	0.111561i	−0.400264	−	0.916400i	$-0.631082\pi$
$277$	3.21598	−	1.85675i	0.193229	−	0.111561i	0.593494	+	0.804839i	$0.297748\pi$
$278$		0			0
$279$	−6.11555	−	2.10676i	−0.366128	−	0.126128i
$280$		0			0
$281$	−13.5277	−	23.4307i	−0.806995	−	1.39776i	−0.914936	−	0.403600i	$-0.867759\pi$
$281$	−13.5277	−	23.4307i	−0.806995	−	1.39776i	0.107940	−	0.994157i	$-0.465574\pi$
$282$		0			0
$283$	0.994145	+	0.573970i	0.0590958	+	0.0341190i	0.529257	−	0.848462i	$-0.322471\pi$
$283$	0.994145	+	0.573970i	0.0590958	+	0.0341190i	−0.470161	+	0.882581i	$0.655804\pi$
$284$		0			0
$285$	2.10083	+	5.62019i	0.124442	+	0.332911i
$286$		0			0
$287$	0.809231			0.0477674
$288$		0			0
$289$	−2.43196			−0.143056
$290$		0			0
$291$	−21.2688	−	3.56078i	−1.24680	−	0.208737i
$292$		0			0
$293$	−22.8025	−	13.1650i	−1.33214	−	0.769109i	−0.346509	−	0.938047i	$-0.612633\pi$
$293$	−22.8025	−	13.1650i	−1.33214	−	0.769109i	−0.985627	+	0.168938i	$0.945966\pi$
$294$		0			0
$295$	10.3210	+	17.8765i	0.600911	+	1.04081i
$296$		0			0
$297$	10.9126	−	0.283343i	0.633211	−	0.0164412i
$298$		0			0
$299$	39.1313	−	22.5924i	2.26302	−	1.30655i
$300$		0			0
$301$	1.95967	+	1.13141i	0.112953	+	0.0652136i
$302$		0			0
$303$	4.55814	−	27.2261i	0.261858	−	1.56410i
$304$		0			0
$305$	8.45043			0.483870
$306$		0			0
$307$		−	7.43196i		−	0.424164i	−0.977252	−	0.212082i	$-0.931976\pi$
$307$		−	7.43196i		−	0.424164i	0.977252	−	0.212082i	$-0.0680244\pi$
$308$		0			0
$309$	−10.4176	−	27.8695i	−0.592639	−	1.58544i
$310$		0			0
$311$	4.96618	−	8.60168i	0.281606	−	0.487756i	−0.690174	−	0.723643i	$-0.742466\pi$
$311$	4.96618	−	8.60168i	0.281606	−	0.487756i	0.971781	+	0.235887i	$0.0757995\pi$
$312$		0			0
$313$	4.51847	+	7.82622i	0.255399	+	0.442364i	0.965004	−	0.262236i	$-0.0844598\pi$
$313$	4.51847	+	7.82622i	0.255399	+	0.442364i	−0.709605	+	0.704600i	$0.751126\pi$
$314$		0			0
$315$	5.05350	−	0.981529i	0.284733	−	0.0553029i
$316$		0			0
$317$	−7.52771	+	4.34612i	−0.422798	+	0.244103i	−0.696274	−	0.717776i	$-0.745160\pi$
$317$	−7.52771	+	4.34612i	−0.422798	+	0.244103i	0.273476	+	0.961879i	$0.411827\pi$
$318$		0			0
$319$	−8.76357	+	15.1790i	−0.490666	+	0.849858i
$320$		0			0
$321$	21.6521	+	17.8513i	1.20850	+	0.996362i
$322$		0			0
$323$		−	7.63362i		−	0.424746i
$324$		0			0
$325$			12.7230i			0.705747i
$326$		0			0
$327$	1.09062	+	0.899170i	0.0603112	+	0.0497242i
$328$		0			0
$329$	3.36130	−	5.82194i	0.185314	−	0.320974i
$330$		0			0
$331$	11.1462	−	6.43527i	0.612651	−	0.353714i	−0.161351	−	0.986897i	$-0.551585\pi$
$331$	11.1462	−	6.43527i	0.612651	−	0.353714i	0.774002	+	0.633183i	$0.218252\pi$
$332$		0			0
$333$	−13.6336	+	2.64802i	−0.747118	+	0.145111i
$334$		0			0
$335$	−11.8944	−	20.6017i	−0.649860	−	1.12559i
$336$		0			0
$337$	1.21598	−	2.10614i	0.0662386	−	0.114729i	−0.831004	−	0.556266i	$-0.812233\pi$
$337$	1.21598	−	2.10614i	0.0662386	−	0.114729i	0.897243	+	0.441538i	$0.145567\pi$
$338$		0			0
$339$	−3.90071	−	10.4353i	−0.211857	−	0.566766i
$340$		0			0
$341$			4.52957i			0.245290i
$342$		0			0
$343$	−12.8977			−0.696409
$344$		0			0
$345$	3.51847	−	21.0160i	0.189428	−	1.13147i
$346$		0			0
$347$	−20.2373	−	11.6840i	−1.08640	−	0.627232i	−0.153782	−	0.988105i	$-0.549146\pi$
$347$	−20.2373	−	11.6840i	−1.08640	−	0.627232i	−0.932615	+	0.360873i	$0.882479\pi$
$348$		0			0
$349$	8.66641	−	5.00355i	0.463902	−	0.267834i	−0.249781	−	0.968302i	$-0.580359\pi$
$349$	8.66641	−	5.00355i	0.463902	−	0.267834i	0.713684	+	0.700468i	$0.247025\pi$
$350$		0			0
$351$	17.2652	+	28.1882i	0.921547	+	1.50457i
$352$		0			0
$353$	10.6924	+	18.5198i	0.569100	+	0.985711i	0.996655	+	0.0817214i	$0.0260418\pi$
$353$	10.6924	+	18.5198i	0.569100	+	0.985711i	−0.427555	+	0.903989i	$0.640625\pi$
$354$		0			0
$355$	−20.3087	−	11.7252i	−1.07787	−	0.622310i
$356$		0			0
$357$	−6.45967	−	1.08147i	−0.341882	−	0.0572373i
$358$		0			0
$359$	−23.9634			−1.26474			−0.632370	−	0.774666i	$-0.717918\pi$
$359$	−23.9634			−1.26474			−0.632370	+	0.774666i	$0.717918\pi$
$360$		0			0
$361$	15.0000			0.789474
$362$		0			0
$363$	3.99444	+	10.6860i	0.209654	+	0.560870i
$364$		0			0
$365$	−15.0277	−	8.67625i	−0.786586	−	0.454136i
$366$		0			0
$367$	8.25564	+	14.2992i	0.430941	+	0.746411i	0.996955	−	0.0779844i	$-0.0248484\pi$
$367$	8.25564	+	14.2992i	0.430941	+	0.746411i	−0.566014	+	0.824396i	$0.691515\pi$
$368$		0			0
$369$	2.31681	+	0.798123i	0.120608	+	0.0415486i
$370$		0			0
$371$	−2.69993	+	1.55880i	−0.140173	+	0.0809291i
$372$		0			0
$373$	21.2437	+	12.2650i	1.09996	+	0.635060i	0.936210	−	0.351442i	$-0.114309\pi$
$373$	21.2437	+	12.2650i	1.09996	+	0.635060i	0.163747	+	0.986502i	$0.447642\pi$
$374$		0			0
$375$	16.2031	+	13.3588i	0.836726	+	0.689847i
$376$		0			0
$377$	−53.0739			−2.73344
$378$		0			0
$379$			10.8824i			0.558991i	0.960147	+	0.279495i	$0.0901672\pi$
$379$			10.8824i			0.558991i	−0.960147	+	0.279495i	$0.909833\pi$
$380$		0			0
$381$	17.8353	−	21.6327i	0.913729	−	1.10828i
$382$		0			0
$383$	1.66073	−	2.87646i	0.0848591	−	0.146980i	−0.820472	−	0.571687i	$-0.806289\pi$
$383$	1.66073	−	2.87646i	0.0848591	−	0.146980i	0.905331	+	0.424706i	$0.139623\pi$
$384$		0			0
$385$	−1.80249	−	3.12201i	−0.0918635	−	0.159112i
$386$		0			0
$387$	4.49459	+	5.17198i	0.228473	+	0.262906i
$388$		0			0
$389$	1.19751	−	0.691382i	0.0607161	−	0.0350545i	−0.469335	−	0.883020i	$-0.655506\pi$
$389$	1.19751	−	0.691382i	0.0607161	−	0.0350545i	0.530051	+	0.847966i	$0.322173\pi$
$390$		0			0
$391$	−13.5551	+	23.4781i	−0.685511	+	1.18734i
$392$		0			0
$393$	12.5185	−	4.67941i	0.631473	−	0.236045i
$394$		0			0
$395$			15.7345i			0.791686i
$396$		0			0
$397$			19.9685i			1.00219i	0.865392	+	0.501096i	$0.167070\pi$
$397$			19.9685i			1.00219i	−0.865392	+	0.501096i	$0.832930\pi$
$398$		0			0
$399$	−0.566686	+	3.38485i	−0.0283698	+	0.169454i
$400$		0			0
$401$	0.326046	−	0.564728i	0.0162819	−	0.0282012i	−0.857770	−	0.514034i	$-0.828150\pi$
$401$	0.326046	−	0.564728i	0.0162819	−	0.0282012i	0.874052	+	0.485833i	$0.161484\pi$
$402$		0			0
$403$	−11.8784	+	6.85799i	−0.591705	+	0.341621i
$404$		0			0
$405$	15.4361	+	2.17404i	0.767027	+	0.108029i
$406$		0			0
$407$	4.86286	+	8.42272i	0.241043	+	0.417499i
$408$		0			0
$409$	−7.51847	+	13.0224i	−0.371764	+	0.643915i	−0.989837	−	0.142206i	$-0.954580\pi$
$409$	−7.51847	+	13.0224i	−0.371764	+	0.643915i	0.618073	+	0.786121i	$0.287914\pi$
$410$		0			0
$411$	14.7171	+	2.46390i	0.725939	+	0.121535i
$412$		0			0
$413$			11.8071i			0.580988i
$414$		0			0
$415$	−7.42014			−0.364240
$416$		0			0
$417$	−9.27365	+	3.46650i	−0.454133	+	0.169755i
$418$		0			0
$419$	−11.4024	−	6.58321i	−0.557046	−	0.321611i	0.194913	−	0.980821i	$-0.437558\pi$
$419$	−11.4024	−	6.58321i	−0.557046	−	0.321611i	−0.751959	+	0.659210i	$0.770891\pi$
$420$		0			0
$421$	−3.36130	+	1.94065i	−0.163820	+	0.0945813i	−0.579668	−	0.814853i	$-0.696818\pi$
$421$	−3.36130	+	1.94065i	−0.163820	+	0.0945813i	0.415849	+	0.909434i	$0.363485\pi$
$422$		0			0
$423$	15.3653	−	13.3529i	0.747088	−	0.649241i
$424$		0			0
$425$	−3.81681	−	6.61091i	−0.185142	−	0.320676i
$426$		0			0
$427$	4.18601	+	2.41679i	0.202575	+	0.116957i
$428$		0			0
$429$	14.7252	−	17.8604i	0.710940	−	0.862310i
$430$		0			0
$431$	3.81339			0.183684			0.0918422	−	0.995774i	$-0.470724\pi$
$431$	3.81339			0.183684			0.0918422	+	0.995774i	$0.470724\pi$
$432$		0			0
$433$	−10.0185			−0.481457			−0.240728	−	0.970592i	$-0.577386\pi$
$433$	−10.0185			−0.481457			−0.240728	+	0.970592i	$0.577386\pi$
$434$		0			0
$435$	−15.9217	+	19.3117i	−0.763389	+	0.925926i
$436$		0			0
$437$	12.3025	+	7.10285i	0.588508	+	0.339775i
$438$		0			0
$439$	−12.2117	−	21.1512i	−0.582832	−	1.00949i	−0.995142	−	0.0984504i	$-0.968611\pi$
$439$	−12.2117	−	21.1512i	−0.582832	−	1.00949i	0.412310	−	0.911043i	$-0.364722\pi$
$440$		0			0
$441$	−17.0709	−	5.88078i	−0.812898	−	0.280037i
$442$		0			0
$443$	21.3799	−	12.3437i	1.01579	−	0.586466i	0.102907	−	0.994691i	$-0.467186\pi$
$443$	21.3799	−	12.3437i	1.01579	−	0.586466i	0.912881	+	0.408225i	$0.133852\pi$
$444$		0			0
$445$	21.0277	+	12.1404i	0.996809	+	0.575508i
$446$		0			0
$447$	2.29531	−	0.857990i	0.108565	−	0.0405815i
$448$		0			0
$449$	21.6521			1.02183			0.510913	−	0.859633i	$-0.329308\pi$
$449$	21.6521			1.02183			0.510913	+	0.859633i	$0.329308\pi$
$450$		0			0
$451$		−	1.71598i		−	0.0808023i
$452$		0			0
$453$	5.61930	+	0.940774i	0.264018	+	0.0442014i
$454$		0			0
$455$	5.45812	−	9.45374i	0.255880	−	0.443198i
$456$		0			0
$457$	11.2437	+	19.4746i	0.525957	+	0.910985i	0.999543	+	0.0302371i	$0.00962623\pi$
$457$	11.2437	+	19.4746i	0.525957	+	0.910985i	−0.473585	+	0.880748i	$0.657040\pi$
$458$		0			0
$459$	−17.4272	−	9.46721i	−0.813434	−	0.441892i
$460$		0			0
$461$	−21.6756	+	12.5144i	−1.00954	+	0.582856i	−0.911056	−	0.412283i	$-0.864731\pi$
$461$	−21.6756	+	12.5144i	−1.00954	+	0.582856i	−0.0984799	+	0.995139i	$0.531398\pi$
$462$		0			0
$463$	−9.73830	+	16.8672i	−0.452577	+	0.783886i	−0.998545	−	0.0539194i	$-0.982829\pi$
$463$	−9.73830	+	16.8672i	−0.452577	+	0.783886i	0.545968	+	0.837806i	$0.316162\pi$
$464$		0			0
$465$	−1.06804	+	6.37947i	−0.0495292	+	0.295841i
$466$		0			0
$467$			2.40332i			0.111212i	0.998453	+	0.0556062i	$0.0177091\pi$
$467$			2.40332i			0.111212i	−0.998453	+	0.0556062i	$0.982291\pi$
$468$		0			0
$469$		−	13.6070i		−	0.628314i
$470$		0			0
$471$	10.8358	−	4.05042i	0.499285	−	0.186633i
$472$		0			0
$473$	2.39917	−	4.15548i	0.110314	−	0.191069i
$474$		0			0
$475$	−3.46410	+	2.00000i	−0.158944	+	0.0917663i
$476$		0			0
$477$	−9.26724	+	1.79995i	−0.424318	+	0.0824142i
$478$		0			0
$479$	−10.6543	−	18.4537i	−0.486806	−	0.843173i	0.513079	−	0.858341i	$-0.328505\pi$
$479$	−10.6543	−	18.4537i	−0.486806	−	0.843173i	−0.999885	+	0.0151687i	$0.995171\pi$
$480$		0			0
$481$	−14.7252	+	25.5048i	−0.671412	+	1.16292i
$482$		0			0
$483$	7.75343	−	9.40425i	0.352793	−	0.427908i
$484$		0			0
$485$			21.5648i			0.979206i
$486$		0			0
$487$	40.7851			1.84815			0.924075	−	0.382210i	$-0.124837\pi$
$487$	40.7851			1.84815			0.924075	+	0.382210i	$0.124837\pi$
$488$		0			0
$489$	9.93216	+	8.18867i	0.449148	+	0.370304i
$490$		0			0
$491$	30.6776	+	17.7117i	1.38446	+	0.799320i	0.992684	−	0.120740i	$-0.0385267\pi$
$491$	30.6776	+	17.7117i	1.38446	+	0.799320i	0.391778	+	0.920060i	$0.371860\pi$
$492$		0			0
$493$	27.5773	−	15.9217i	1.24202	−	0.717079i
$494$		0			0
$495$	−2.08134	−	10.7160i	−0.0935492	−	0.481647i
$496$		0			0
$497$	−6.70674	−	11.6164i	−0.300839	−	0.521068i
$498$		0			0
$499$	−3.74206	−	2.16048i	−0.167518	−	0.0967164i	0.413897	−	0.910324i	$-0.364167\pi$
$499$	−3.74206	−	2.16048i	−0.167518	−	0.0967164i	−0.581415	+	0.813607i	$0.697501\pi$
$500$		0			0
$501$	6.00415	+	16.0624i	0.268246	+	0.717617i
$502$		0			0
$503$	7.24550			0.323061			0.161530	−	0.986868i	$-0.448357\pi$
$503$	7.24550			0.323061			0.161530	+	0.986868i	$0.448357\pi$
$504$		0			0
$505$	−27.6050			−1.22841
$506$		0			0
$507$	46.9245	+	7.85601i	2.08399	+	0.348898i
$508$		0			0
$509$	7.22522	+	4.17148i	0.320252	+	0.184898i	0.651505	−	0.758644i	$-0.274138\pi$
$509$	7.22522	+	4.17148i	0.320252	+	0.184898i	−0.331253	+	0.943542i	$0.607471\pi$
$510$		0			0
$511$	−4.96276	−	8.59575i	−0.219539	−	0.380253i
$512$		0			0
$513$	−4.96080	+	9.13184i	−0.219025	+	0.403181i
$514$		0			0
$515$	−25.7668	+	14.8765i	−1.13542	+	0.655535i
$516$		0			0
$517$	−12.3454	−	7.12765i	−0.542952	−	0.313474i
$518$		0			0
$519$	3.46752	−	20.7117i	0.152207	−	0.909145i
$520$		0			0
$521$	16.9714			0.743529			0.371764	−	0.928327i	$-0.378753\pi$
$521$	16.9714			0.743529			0.371764	+	0.928327i	$0.378753\pi$
$522$		0			0
$523$		−	40.0554i		−	1.75150i	−0.482764	−	0.875750i	$-0.660367\pi$
$523$		−	40.0554i		−	1.75150i	0.482764	−	0.875750i	$-0.339633\pi$
$524$		0			0
$525$	1.20166	+	3.21471i	0.0524448	+	0.140301i
$526$		0			0
$527$	4.11469	−	7.12685i	0.179239	−	0.310450i
$528$		0			0
$529$	−13.7252	−	23.7728i	−0.596748	−	1.03360i
$530$		0			0
$531$	−11.6450	+	33.8033i	−0.505350	+	1.46694i
$532$		0			0
$533$	4.50000	−	2.59808i	0.194917	−	0.112535i
$534$		0			0
$535$	14.0310	−	24.3025i	0.606615	−	1.05069i
$536$		0			0
$537$	−8.01847	−	6.61091i	−0.346023	−	0.285282i
$538$		0			0
$539$			12.6438i			0.544606i
$540$		0			0
$541$			25.5956i			1.10044i	0.835020	+	0.550220i	$0.185456\pi$
$541$			25.5956i			1.10044i	−0.835020	+	0.550220i	$0.814544\pi$
$542$		0			0
$543$	6.18687	+	5.10083i	0.265504	+	0.218898i
$544$		0			0
$545$	0.706744	−	1.22412i	0.0302736	−	0.0524354i
$546$		0			0
$547$	−29.2469	+	16.8857i	−1.25051	+	0.721980i	−0.971210	−	0.238225i	$-0.923435\pi$
$547$	−29.2469	+	16.8857i	−1.25051	+	0.721980i	−0.279296	+	0.960205i	$0.590101\pi$
$548$		0			0
$549$	9.60083	+	11.0478i	0.409753	+	0.471508i
$550$		0			0
$551$	−8.34296	−	14.4504i	−0.355422	−	0.615609i
$552$		0			0
$553$	−4.50000	+	7.79423i	−0.191359	+	0.331444i
$554$		0			0
$555$	4.86286	+	13.0092i	0.206417	+	0.552211i
$556$		0			0
$557$			18.3364i			0.776937i	0.921462	+	0.388469i	$0.126996\pi$
$557$			18.3364i			0.776937i	−0.921462	+	0.388469i	$0.873004\pi$
$558$		0			0
$559$	14.5298			0.614546
$560$		0			0
$561$	−2.29326	+	13.6978i	−0.0968213	+	0.578320i
$562$		0			0
$563$	35.8258	+	20.6840i	1.50988	+	0.871728i	0.999934	+	0.0115205i	$0.00366716\pi$
$563$	35.8258	+	20.6840i	1.50988	+	0.871728i	0.509944	+	0.860208i	$0.329666\pi$
$564$		0			0
$565$	−9.64794	+	5.57024i	−0.405892	+	0.234342i
$566$		0			0
$567$	7.02467	+	5.49161i	0.295009	+	0.230626i
$568$		0			0
$569$	0.683190	+	1.18332i	0.0286408	+	0.0496073i	0.879991	−	0.474991i	$-0.157549\pi$
$569$	0.683190	+	1.18332i	0.0286408	+	0.0496073i	−0.851350	+	0.524599i	$0.824215\pi$
$570$		0			0
$571$	15.3585	+	8.86723i	0.642733	+	0.371082i	0.785666	−	0.618650i	$-0.212320\pi$
$571$	15.3585	+	8.86723i	0.642733	+	0.371082i	−0.142934	+	0.989732i	$0.545654\pi$
$572$		0			0
$573$	−29.3445	−	4.91281i	−1.22588	−	0.205236i
$574$		0			0
$575$	14.2057			0.592418
$576$		0			0
$577$	20.5865			0.857028			0.428514	−	0.903535i	$-0.359037\pi$
$577$	20.5865			0.857028			0.428514	+	0.903535i	$0.359037\pi$
$578$		0			0
$579$	−7.02673	−	18.7981i	−0.292021	−	0.781220i
$580$		0			0
$581$	−3.67565	−	2.12214i	−0.152491	−	0.0880410i
$582$		0			0
$583$	3.30545	+	5.72522i	0.136898	+	0.237114i
$584$		0			0
$585$	24.9504	−	21.6826i	1.03157	−	0.896466i
$586$		0			0
$587$	12.5450	−	7.24284i	0.517786	−	0.298944i	−0.218242	−	0.975895i	$-0.570032\pi$
$587$	12.5450	−	7.24284i	0.517786	−	0.298944i	0.736028	+	0.676951i	$0.236699\pi$
$588$		0			0
$589$	−3.73445	−	2.15609i	−0.153875	−	0.0888400i
$590$		0			0
$591$	23.6141	+	19.4689i	0.971355	+	0.800844i
$592$		0			0
$593$	4.58651			0.188345			0.0941727	−	0.995556i	$-0.469979\pi$
$593$	4.58651			0.188345			0.0941727	+	0.995556i	$0.469979\pi$
$594$		0			0
$595$			6.54957i			0.268506i
$596$		0			0
$597$	−18.1849	+	22.0567i	−0.744258	+	0.902721i
$598$		0			0
$599$	1.31144	−	2.27148i	0.0535839	−	0.0928101i	−0.837989	−	0.545687i	$-0.816269\pi$
$599$	1.31144	−	2.27148i	0.0535839	−	0.0928101i	0.891573	+	0.452877i	$0.149602\pi$
$600$		0			0
$601$	−3.50924	−	6.07817i	−0.143145	−	0.247934i	0.785535	−	0.618818i	$-0.212388\pi$
$601$	−3.50924	−	6.07817i	−0.143145	−	0.247934i	−0.928679	+	0.370884i	$0.879055\pi$
$602$		0			0
$603$	13.4202	−	38.9566i	0.546514	−	1.58643i
$604$		0			0
$605$	9.87977	−	5.70409i	0.401670	−	0.231904i
$606$		0			0
$607$	18.5892	−	32.1974i	0.754512	−	1.30685i	−0.191105	−	0.981570i	$-0.561207\pi$
$607$	18.5892	−	32.1974i	0.754512	−	1.30685i	0.945617	−	0.325283i	$-0.105460\pi$
$608$		0			0
$609$	−13.4101	+	5.01270i	−0.543405	+	0.203125i
$610$		0			0
$611$		−	43.1664i		−	1.74633i
$612$		0			0
$613$			10.7096i			0.432557i	0.976332	+	0.216278i	$0.0693919\pi$
$613$			10.7096i			0.432557i	−0.976332	+	0.216278i	$0.930608\pi$
$614$		0			0
$615$	0.404616	−	2.41679i	0.0163157	−	0.0974546i
$616$		0			0
$617$	−16.6101	+	28.7695i	−0.668696	+	1.15822i	0.309573	+	0.950876i	$0.399814\pi$
$617$	−16.6101	+	28.7695i	−0.668696	+	1.15822i	−0.978269	+	0.207340i	$0.933519\pi$
$618$		0			0
$619$	22.8106	−	13.1697i	0.916836	−	0.529336i	0.0342118	−	0.999415i	$-0.489108\pi$
$619$	22.8106	−	13.1697i	0.916836	−	0.529336i	0.882624	+	0.470079i	$0.155775\pi$
$620$		0			0
$621$	31.4731	−	19.2771i	1.26297	−	0.773565i
$622$		0			0
$623$	6.94420	+	12.0277i	0.278213	+	0.481880i
$624$		0			0
$625$	5.50000	−	9.52628i	0.220000	−	0.381051i
$626$		0			0
$627$	7.17760	+	1.20166i	0.286646	+	0.0479897i
$628$		0			0
$629$		−	17.6698i		−	0.704541i
$630$		0			0
$631$	−21.6327			−0.861183			−0.430592	−	0.902547i	$-0.641695\pi$
$631$	−21.6327			−0.861183			−0.430592	+	0.902547i	$0.641695\pi$
$632$		0			0
$633$	−19.0381	+	7.11645i	−0.756695	+	0.282853i
$634$		0			0
$635$	−24.2807	−	14.0185i	−0.963550	−	0.556306i
$636$		0			0
$637$	−33.1572	+	19.1433i	−1.31374	+	0.758485i
$638$		0			0
$639$	−7.74428	−	39.8722i	−0.306359	−	1.57732i
$640$		0			0
$641$	−1.88485	−	3.26466i	−0.0744471	−	0.128946i	0.826399	−	0.563086i	$-0.190386\pi$
$641$	−1.88485	−	3.26466i	−0.0744471	−	0.128946i	−0.900846	+	0.434139i	$0.857053\pi$
$642$		0			0
$643$	29.2469	+	16.8857i	1.15338	+	0.665907i	0.949710	−	0.313132i	$-0.101378\pi$
$643$	29.2469	+	16.8857i	1.15338	+	0.665907i	0.203675	+	0.979039i	$0.434711\pi$
$644$		0			0
$645$	4.35884	−	5.28690i	0.171629	−	0.208171i
$646$		0			0
$647$	15.7020			0.617311			0.308656	−	0.951174i	$-0.400121\pi$
$647$	15.7020			0.617311			0.308656	+	0.951174i	$0.400121\pi$
$648$		0			0
$649$	25.0369			0.982786
$650$		0			0
$651$	−2.35357	+	2.85468i	−0.0922438	+	0.111884i
$652$		0			0
$653$	27.4009	+	15.8199i	1.07228	+	0.619080i	0.928803	−	0.370574i	$-0.120839\pi$
$653$	27.4009	+	15.8199i	1.07228	+	0.619080i	0.143475	+	0.989654i	$0.454172\pi$
$654$		0			0
$655$	−6.68223	−	11.5740i	−0.261097	−	0.452232i
$656$		0			0
$657$	−5.73050	−	29.5041i	−0.223568	−	1.15106i
$658$		0			0
$659$	−31.4389	+	18.1512i	−1.22468	+	0.707072i	−0.965913	−	0.258866i	$-0.916651\pi$
$659$	−31.4389	+	18.1512i	−1.22468	+	0.707072i	−0.258772	+	0.965939i	$0.583318\pi$
$660$		0			0
$661$	12.6479	+	7.30229i	0.491948	+	0.284026i	0.725382	−	0.688346i	$-0.241663\pi$
$661$	12.6479	+	7.30229i	0.491948	+	0.284026i	−0.233434	+	0.972373i	$0.574996\pi$
$662$		0			0
$663$	−39.3932	+	14.7252i	−1.52991	+	0.571880i
$664$		0			0
$665$	3.43196			0.133086
$666$		0			0
$667$			59.2588i			2.29451i
$668$		0			0
$669$	2.28910	+	0.383238i	0.0885019	+	0.0148168i
$670$		0			0
$671$	5.12483	−	8.87646i	0.197842	−	0.342672i
$672$		0			0
$673$	1.79326	+	3.10601i	0.0691249	+	0.119728i	0.898516	−	0.438940i	$-0.144646\pi$
$673$	1.79326	+	3.10601i	0.0691249	+	0.119728i	−0.829391	+	0.558668i	$0.811313\pi$
$674$		0			0
$675$	0.269744	+	10.3888i	0.0103824	+	0.399865i
$676$		0			0
$677$	1.25292	−	0.723375i	0.0481537	−	0.0278016i	−0.475730	−	0.879591i	$-0.657816\pi$
$677$	1.25292	−	0.723375i	0.0481537	−	0.0278016i	0.523884	+	0.851790i	$0.324483\pi$
$678$		0			0
$679$	−6.16745	+	10.6823i	−0.236685	+	0.409951i
$680$		0			0
$681$	−1.11515	+	6.66086i	−0.0427326	+	0.255245i
$682$		0			0
$683$			16.9714i			0.649391i	0.945819	+	0.324696i	$0.105262\pi$
$683$			16.9714i			0.649391i	−0.945819	+	0.324696i	$0.894738\pi$
$684$		0			0
$685$		−	14.9219i		−	0.570136i
$686$		0			0
$687$	3.61933	−	1.35291i	0.138086	−	0.0516166i
$688$		0			0
$689$	−10.0092	+	17.3365i	−0.381322	+	0.660468i
$690$		0			0
$691$	8.44628	−	4.87646i	0.321312	−	0.185509i	−0.330665	−	0.943748i	$-0.607273\pi$
$691$	8.44628	−	4.87646i	0.321312	−	0.185509i	0.651977	+	0.758239i	$0.273940\pi$
$692$		0			0
$693$	2.03372	−	5.90353i	0.0772547	−	0.224257i
$694$		0			0
$695$	4.95018	+	8.57397i	0.187771	+	0.325229i
$696$		0			0
$697$	−1.55880	+	2.69993i	−0.0590439	+	0.102267i
$698$		0			0
$699$	−10.2108	+	12.3849i	−0.386208	+	0.468438i
$700$		0			0
$701$		−	33.3398i		−	1.25923i	−0.776908	−	0.629614i	$-0.783213\pi$
$701$		−	33.3398i		−	1.25923i	0.776908	−	0.629614i	$-0.216787\pi$
$702$		0			0
$703$	−9.25893			−0.349207
$704$		0			0
$705$	−15.7067	−	12.9496i	−0.591550	−	0.487710i
$706$		0			0
$707$	−13.6744	−	7.89493i	−0.514280	−	0.296919i
$708$		0			0
$709$	44.5369	−	25.7134i	1.67262	−	0.965688i	0.706457	−	0.707756i	$-0.250292\pi$
$709$	44.5369	−	25.7134i	1.67262	−	0.965688i	0.966163	−	0.257931i	$-0.0830408\pi$
$710$		0			0
$711$	−20.5706	+	17.8765i	−0.771459	+	0.670420i
$712$		0			0
$713$	7.65717	+	13.2626i	0.286763	+	0.496689i
$714$		0			0
$715$	−20.0467	−	11.5740i	−0.749704	−	0.432842i
$716$		0			0
$717$	12.7109	+	34.0045i	0.474697	+	1.26992i
$718$		0			0
$719$	−22.1178			−0.824854			−0.412427	−	0.910991i	$-0.635319\pi$
$719$	−22.1178			−0.824854			−0.412427	+	0.910991i	$0.635319\pi$
$720$		0			0
$721$	−17.0185			−0.633801
$722$		0			0
$723$	−25.6872	−	4.30051i	−0.955319	−	0.159938i
$724$		0			0
$725$	−14.4504	−	8.34296i	−0.536676	−	0.309850i
$726$		0			0
$727$	14.2930	+	24.7562i	0.530099	+	0.918158i	0.999383	+	0.0351108i	$0.0111784\pi$
$727$	14.2930	+	24.7562i	0.530099	+	0.918158i	−0.469285	+	0.883047i	$0.655488\pi$
$728$		0			0
$729$	14.6952	+	22.6506i	0.544268	+	0.838911i
$730$		0			0
$731$	−7.54973	+	4.35884i	−0.279237	+	0.161217i
$732$		0			0
$733$	−39.4167	−	22.7572i	−1.45589	−	0.840558i	−0.457084	−	0.889424i	$-0.651106\pi$
$733$	−39.4167	−	22.7572i	−1.45589	−	0.840558i	−0.998805	+	0.0488654i	$0.984439\pi$
$734$		0			0
$735$	−2.98131	+	17.8076i	−0.109967	+	0.656842i
$736$		0			0
$737$	−28.8538			−1.06284
$738$		0			0
$739$		−	19.9815i		−	0.735032i	−0.930017	−	0.367516i	$-0.880208\pi$
$739$		−	19.9815i		−	0.735032i	0.930017	−	0.367516i	$-0.119792\pi$
$740$		0			0
$741$	7.71598	+	20.6420i	0.283454	+	0.758301i
$742$		0			0
$743$	−18.8386	+	32.6294i	−0.691121	+	1.19706i	0.280350	+	0.959898i	$0.409549\pi$
$743$	−18.8386	+	32.6294i	−0.691121	+	1.19706i	−0.971471	+	0.237158i	$0.923784\pi$
$744$		0			0
$745$	−1.22522	−	2.12214i	−0.0448884	−	0.0777490i
$746$		0			0
$747$	−8.43028	−	9.70081i	−0.308448	−	0.354934i
$748$		0			0
$749$	13.9009	−	8.02567i	0.507926	−	0.293251i
$750$		0			0
$751$	6.25820	−	10.8395i	0.228365	−	0.395540i	−0.728959	−	0.684558i	$-0.759995\pi$
$751$	6.25820	−	10.8395i	0.228365	−	0.395540i	0.957324	+	0.289018i	$0.0933287\pi$
$752$		0			0
$753$	0.220132	+	0.181490i	0.00802205	+	0.00661386i
$754$		0			0
$755$		−	5.69751i		−	0.207354i
$756$		0			0
$757$		−	12.5872i		−	0.457491i	−0.973486	−	0.228745i	$-0.926538\pi$
$757$		−	12.5872i		−	0.457491i	0.973486	−	0.228745i	$-0.0734623\pi$
$758$		0			0
$759$	−19.9418	−	16.4412i	−0.723840	−	0.596778i
$760$		0			0
$761$	5.94120	−	10.2905i	0.215368	−	0.373029i	−0.738018	−	0.674781i	$-0.764238\pi$
$761$	5.94120	−	10.2905i	0.215368	−	0.373029i	0.953386	+	0.301752i	$0.0975715\pi$
$762$		0			0
$763$	0.700187	−	0.404253i	0.0253485	−	0.0146349i
$764$		0			0
$765$	−6.45967	+	18.7513i	−0.233550	+	0.677953i
$766$		0			0
$767$	37.9071	+	65.6571i	1.36875	+	2.37074i
$768$		0			0
$769$	22.5369	−	39.0351i	0.812703	−	1.40764i	−0.0982627	−	0.995161i	$-0.531329\pi$
$769$	22.5369	−	39.0351i	0.812703	−	1.40764i	0.910966	−	0.412482i	$-0.135338\pi$
$770$		0			0
$771$	−16.2745	−	43.5378i	−0.586110	−	1.56798i
$772$		0			0
$773$		−	34.0384i		−	1.22428i	−0.790751	−	0.612138i	$-0.790310\pi$
$773$		−	34.0384i		−	1.22428i	0.790751	−	0.612138i	$-0.209690\pi$
$774$		0			0
$775$	−4.31217			−0.154898
$776$		0			0
$777$	−1.31173	+	7.83503i	−0.0470579	+	0.281080i
$778$		0			0
$779$	1.41476	+	0.816810i	0.0506889	+	0.0292653i
$780$		0			0
$781$	−24.6327	+	14.2217i	−0.881427	+	0.508892i
$782$		0			0
$783$	−43.3367	+	1.12523i	−1.54873	+	0.0402125i
$784$		0			0
$785$	−5.78402	−	10.0182i	−0.206441	−	0.357565i
$786$		0			0
$787$	−3.67808	−	2.12354i	−0.131109	−	0.0756960i	0.433011	−	0.901389i	$-0.357451\pi$
$787$	−3.67808	−	2.12354i	−0.131109	−	0.0756960i	−0.564120	+	0.825693i	$0.690785\pi$
$788$		0			0
$789$	−34.1235	−	5.71289i	−1.21483	−	0.203384i
$790$		0			0
$791$	−6.37228			−0.226572
$792$		0			0
$793$	31.0369			1.10215
$794$		0			0
$795$	3.30545	+	8.84283i	0.117232	+	0.313623i
$796$		0			0
$797$	37.2806	+	21.5240i	1.32055	+	0.762419i	0.983816	−	0.179182i	$-0.0573451\pi$
$797$	37.2806	+	21.5240i	1.32055	+	0.762419i	0.336732	+	0.941601i	$0.390678\pi$
$798$		0			0
$799$	12.9496	+	22.4293i	0.458123	+	0.793493i
$800$		0			0
$801$	8.01847	+	41.2839i	0.283319	+	1.45870i
$802$		0			0
$803$	−18.2273	+	10.5236i	−0.643229	+	0.371368i
$804$		0			0
$805$	−10.5554	−	6.09417i	−0.372029	−	0.214791i
$806$		0			0
$807$	−0.890827	−	0.734451i	−0.0313586	−	0.0258539i
$808$		0			0
$809$	25.2488			0.887699			0.443850	−	0.896101i	$-0.353612\pi$
$809$	25.2488			0.887699			0.443850	+	0.896101i	$0.353612\pi$
$810$		0			0
$811$		−	36.9378i		−	1.29706i	−0.761188	−	0.648531i	$-0.775384\pi$
$811$		−	36.9378i		−	1.29706i	0.761188	−	0.648531i	$-0.224616\pi$
$812$		0			0
$813$	−18.7697	+	22.7661i	−0.658282	+	0.798440i
$814$		0			0
$815$	6.43627	−	11.1479i	0.225453	−	0.390495i
$816$		0			0
$817$	2.28402	+	3.95604i	0.0799078	+	0.138404i
$818$		0			0
$819$	18.5606	−	3.60498i	0.648561	−	0.125968i
$820$		0			0
$821$	−10.7748	+	6.22082i	−0.376043	+	0.217108i	−0.676095	−	0.736814i	$-0.736329\pi$
$821$	−10.7748	+	6.22082i	−0.376043	+	0.217108i	0.300052	+	0.953923i	$0.402996\pi$
$822$		0			0
$823$	0.760749	−	1.31766i	0.0265180	−	0.0459306i	−0.852462	−	0.522789i	$-0.824891\pi$
$823$	0.760749	−	1.31766i	0.0265180	−	0.0459306i	0.878980	+	0.476859i	$0.158225\pi$
$824$		0			0
$825$	6.81681	−	2.54813i	0.237331	−	0.0887145i
$826$		0			0
$827$		−	10.0369i		−	0.349019i	−0.984656	−	0.174509i	$-0.944166\pi$
$827$		−	10.0369i		−	0.349019i	0.984656	−	0.174509i	$-0.0558339\pi$
$828$		0			0
$829$		−	43.7824i		−	1.52063i	−0.649556	−	0.760314i	$-0.725045\pi$
$829$		−	43.7824i		−	1.52063i	0.649556	−	0.760314i	$-0.274955\pi$
$830$		0			0
$831$	1.06205	−	6.34367i	0.0368420	−	0.220060i
$832$		0			0
$833$	11.4857	−	19.8938i	0.397955	−	0.689279i
$834$		0			0
$835$	14.8506	−	8.57397i	0.513925	−	0.296714i
$836$		0			0
$837$	−9.55372	+	5.85163i	−0.330225	+	0.202262i
$838$		0			0
$839$	21.0626	+	36.4814i	0.727161	+	1.25948i	0.958078	+	0.286506i	$0.0924938\pi$
$839$	21.0626	+	36.4814i	0.727161	+	1.25948i	−0.230918	+	0.972973i	$0.574173\pi$
$840$		0			0
$841$	20.3025	−	35.1649i	0.700086	−	1.21258i
$842$		0			0
$843$	−46.2181	−	7.73776i	−1.59184	−	0.266503i
$844$		0			0
$845$		−	47.5775i		−	1.63672i
$846$		0			0
$847$	6.52540			0.224215
$848$		0			0
$849$	1.86243	−	0.696176i	0.0639183	−	0.0238927i
$850$		0			0
$851$	28.4770	+	16.4412i	0.976178	+	0.563597i
$852$		0			0
$853$	−22.7748	+	13.1490i	−0.779794	+	0.450214i	−0.836357	−	0.548185i	$-0.815319\pi$
$853$	−22.7748	+	13.1490i	−0.779794	+	0.450214i	0.0565634	+	0.998399i	$0.481986\pi$
$854$		0			0
$855$	9.82562	+	3.38485i	0.336029	+	0.115759i
$856$		0			0
$857$	9.24369	+	16.0105i	0.315758	+	0.546909i	0.979598	−	0.200965i	$-0.0644078\pi$
$857$	9.24369	+	16.0105i	0.315758	+	0.546909i	−0.663840	+	0.747875i	$0.731074\pi$
$858$		0			0
$859$	39.8954	+	23.0336i	1.36121	+	0.785898i	0.989786	−	0.142564i	$-0.0455346\pi$
$859$	39.8954	+	23.0336i	1.36121	+	0.785898i	0.371429	+	0.928461i	$0.378868\pi$
$860$		0			0
$861$	0.891626	−	1.08147i	0.0303865	−	0.0368563i
$862$		0			0
$863$	−46.0812			−1.56862			−0.784311	−	0.620368i	$-0.786983\pi$
$863$	−46.0812			−1.56862			−0.784311	+	0.620368i	$0.786983\pi$
$864$		0			0
$865$	−21.0000			−0.714021
$866$		0			0
$867$	−2.67958	+	3.25010i	−0.0910032	+	0.110379i
$868$		0			0
$869$	16.5277	+	9.54228i	0.560664	+	0.323700i
$870$		0			0
$871$	−43.6860	−	75.6663i	−1.48024	−	2.56386i
$872$		0			0
$873$	−28.1930	+	24.5005i	−0.954188	+	0.829216i
$874$		0			0
$875$	10.4026	−	6.00593i	0.351671	−	0.203037i
$876$		0			0
$877$	−28.5396	−	16.4773i	−0.963713	−	0.556400i	−0.0663989	−	0.997793i	$-0.521151\pi$
$877$	−28.5396	−	16.4773i	−0.963713	−	0.556400i	−0.897314	+	0.441393i	$0.854484\pi$
$878$		0			0
$879$	−42.7181	+	15.9681i	−1.44085	+	0.538589i
$880$		0			0
$881$	21.9815			0.740577			0.370288	−	0.928917i	$-0.379259\pi$
$881$	21.9815			0.740577			0.370288	+	0.928917i	$0.379259\pi$
$882$		0			0
$883$			10.0000i			0.336527i	0.985742	+	0.168263i	$0.0538159\pi$
$883$			10.0000i			0.336527i	−0.985742	+	0.168263i	$0.946184\pi$
$884$		0			0
$885$	35.2622	+	5.90353i	1.18532	+	0.198445i
$886$		0			0
$887$	−1.67672	+	2.90417i	−0.0562988	+	0.0975124i	−0.892801	−	0.450451i	$-0.851263\pi$
$887$	−1.67672	+	2.90417i	−0.0562988	+	0.0975124i	0.836502	+	0.547963i	$0.184597\pi$
$888$		0			0
$889$	−8.01847	−	13.8884i	−0.268931	−	0.465802i
$890$		0			0
$891$	11.6450	−	14.8959i	0.390122	−	0.499030i
$892$		0			0
$893$	11.7529	−	6.78555i	0.393297	−	0.227070i
$894$		0			0
$895$	−5.19615	+	9.00000i	−0.173688	+	0.300837i
$896$		0			0
$897$	12.9227	−	77.1882i	0.431477	−	2.57724i
$898$		0			0
$899$		−	17.9881i		−	0.599938i
$900$		0			0
$901$		−	12.0108i		−	0.400137i
$902$		0			0
$903$	3.67123	−	1.37231i	0.122171	−	0.0456676i
$904$		0			0
$905$	4.00924	−	6.94420i	0.133271	−	0.230833i
$906$		0			0
$907$	−8.87423	+	5.12354i	−0.294664	+	0.170124i	−0.640043	−	0.768339i	$-0.721084\pi$
$907$	−8.87423	+	5.12354i	−0.294664	+	0.170124i	0.345379	+	0.938463i	$0.387750\pi$
$908$		0			0
$909$	−31.3630	−	36.0897i	−1.04024	−	1.19702i
$910$		0			0
$911$	12.7036	+	22.0033i	0.420890	+	0.729002i	0.996027	−	0.0890549i	$-0.0283847\pi$
$911$	12.7036	+	22.0033i	0.420890	+	0.729002i	−0.575137	+	0.818057i	$0.695051\pi$
$912$		0			0
$913$	−4.50000	+	7.79423i	−0.148928	+	0.257951i
$914$		0			0
$915$	9.31084	−	11.2933i	0.307807	−	0.373344i
$916$		0			0
$917$		−	7.64439i		−	0.252440i
$918$		0			0
$919$	44.1134			1.45517			0.727584	−	0.686019i	$-0.240643\pi$
$919$	44.1134			1.45517			0.727584	+	0.686019i	$0.240643\pi$
$920$		0			0
$921$	−9.93216	−	8.18867i	−0.327276	−	0.269826i
$922$		0			0
$923$	−74.5902	−	43.0646i	−2.45517	−	1.41749i
$924$		0			0
$925$	−8.01847	+	4.62947i	−0.263646	+	0.152216i
$926$		0			0
$927$	−48.7235	−	16.7849i	−1.60029	−	0.551287i
$928$		0			0
$929$	17.8117	+	30.8508i	0.584384	+	1.01218i	0.994952	+	0.100353i	$0.0319971\pi$
$929$	17.8117	+	30.8508i	0.584384	+	1.01218i	−0.410568	+	0.911830i	$0.634670\pi$
$930$		0			0
$931$	−10.4243	−	6.01847i	−0.341643	−	0.197247i
$932$		0			0
$933$	−6.02355	−	16.1143i	−0.197202	−	0.527560i
$934$		0			0
$935$	13.8884			0.454199
$936$		0			0
$937$	−15.4135			−0.503537			−0.251768	−	0.967788i	$-0.581012\pi$
$937$	−15.4135			−0.503537			−0.251768	+	0.967788i	$0.581012\pi$
$938$		0			0
$939$	15.4376	+	2.58454i	0.503787	+	0.0843431i
$940$		0			0
$941$	−7.55541	−	4.36212i	−0.246299	−	0.142201i	0.371769	−	0.928325i	$-0.378751\pi$
$941$	−7.55541	−	4.36212i	−0.246299	−	0.142201i	−0.618069	+	0.786124i	$0.712085\pi$
$942$		0			0
$943$	−2.90084	−	5.02440i	−0.0944643	−	0.163617i
$944$		0			0
$945$	4.25631	−	7.83503i	0.138458	−	0.254873i
$946$		0			0
$947$	−13.7691	+	7.94958i	−0.447435	+	0.258327i	−0.706746	−	0.707467i	$-0.749838\pi$
$947$	−13.7691	+	7.94958i	−0.447435	+	0.258327i	0.259311	+	0.965794i	$0.416504\pi$
$948$		0			0
$949$	−55.1941	−	31.8663i	−1.79168	−	1.03443i
$950$		0			0
$951$	−2.48595	+	14.8488i	−0.0806126	+	0.481504i
$952$		0			0
$953$	25.6890			0.832149			0.416075	−	0.909330i	$-0.363405\pi$
$953$	25.6890			0.832149			0.416075	+	0.909330i	$0.363405\pi$
$954$		0			0
$955$			29.7529i			0.962782i
$956$		0			0
$957$	10.6295	+	28.4362i	0.343602	+	0.919211i
$958$		0			0
$959$	4.26761	−	7.39171i	0.137808	−	0.238691i
$960$		0			0
$961$	13.1756	+	22.8209i	0.425021	+	0.736158i
$962$		0			0
$963$	47.7133	−	9.26724i	1.53754	−	0.298633i
$964$		0			0
$965$	−17.3798	+	10.0342i	−0.559475	+	0.323013i
$966$		0			0
$967$	15.3585	−	26.6017i	0.493896	−	0.855452i	−0.506080	−	0.862487i	$-0.668906\pi$
$967$	15.3585	−	26.6017i	0.493896	−	0.855452i	0.999975	+	0.00703449i	$0.00223917\pi$
$968$		0			0
$969$	−10.2017	−	8.41086i	−0.327725	−	0.270196i
$970$		0			0
$971$			40.0924i			1.28662i	0.765604	+	0.643312i	$0.222440\pi$
$971$			40.0924i			1.28662i	−0.765604	+	0.643312i	$0.777560\pi$
$972$		0			0
$973$			5.66294i			0.181546i
$974$		0			0
$975$	17.0032	+	14.0185i	0.544539	+	0.448950i
$976$		0			0
$977$	−24.4361	+	42.3246i	−0.781780	+	1.35408i	0.149123	+	0.988819i	$0.452355\pi$
$977$	−24.4361	+	42.3246i	−0.781780	+	1.35408i	−0.930904	+	0.365265i	$0.880978\pi$
$978$		0			0
$979$	25.5048	−	14.7252i	0.815138	−	0.470620i
$980$		0			0
$981$	2.40332	−	0.466791i	0.0767322	−	0.0149035i
$982$		0			0
$983$	−5.60077	−	9.70081i	−0.178637	−	0.309408i	0.762777	−	0.646662i	$-0.223835\pi$
$983$	−5.60077	−	9.70081i	−0.178637	−	0.309408i	−0.941414	+	0.337254i	$0.890502\pi$
$984$		0			0
$985$	15.3025	−	26.5047i	0.487578	−	0.844510i
$986$		0			0
$987$	−4.07697	−	10.9068i	−0.129771	−	0.347167i
$988$		0			0
$989$		−	16.2230i		−	0.515863i
$990$		0			0
$991$	−15.7020			−0.498792			−0.249396	−	0.968402i	$-0.580232\pi$
$991$	−15.7020			−0.498792			−0.249396	+	0.968402i	$0.580232\pi$
$992$		0			0
$993$	3.68093	−	21.9864i	0.116811	−	0.697718i
$994$		0			0
$995$	24.7566	+	14.2933i	0.784838	+	0.453127i
$996$		0			0
$997$	−21.0984	+	12.1811i	−0.668192	+	0.385781i	−0.795391	−	0.606096i	$-0.792735\pi$
$997$	−21.0984	+	12.1811i	−0.668192	+	0.385781i	0.127199	+	0.991877i	$0.459401\pi$
$998$		0			0
$999$	−11.4829	+	21.1378i	−0.363304	+	0.668770i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	576.2.r.e.481.5	yes	12
3.2	odd	2		1728.2.r.f.1441.3		12
4.3	odd	2	inner	576.2.r.e.481.2	yes	12
8.3	odd	2		576.2.r.f.481.5	yes	12
8.5	even	2		576.2.r.f.481.2	yes	12
9.2	odd	6		1728.2.r.e.289.3		12
9.4	even	3		5184.2.d.q.2593.10		12
9.5	odd	6		5184.2.d.r.2593.4		12
9.7	even	3		576.2.r.f.97.2	yes	12
12.11	even	2		1728.2.r.f.1441.4		12
24.5	odd	2		1728.2.r.e.1441.3		12
24.11	even	2		1728.2.r.e.1441.4		12
36.7	odd	6		576.2.r.f.97.5	yes	12
36.11	even	6		1728.2.r.e.289.4		12
36.23	even	6		5184.2.d.r.2593.3		12
36.31	odd	6		5184.2.d.q.2593.9		12
72.5	odd	6		5184.2.d.r.2593.10		12
72.11	even	6		1728.2.r.f.289.4		12
72.13	even	6		5184.2.d.q.2593.4		12
72.29	odd	6		1728.2.r.f.289.3		12
72.43	odd	6	inner	576.2.r.e.97.2	✓	12
72.59	even	6		5184.2.d.r.2593.9		12
72.61	even	6	inner	576.2.r.e.97.5	yes	12
72.67	odd	6		5184.2.d.q.2593.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
576.2.r.e.97.2	✓	12	72.43	odd	6	inner
576.2.r.e.97.5	yes	12	72.61	even	6	inner
576.2.r.e.481.2	yes	12	4.3	odd	2	inner
576.2.r.e.481.5	yes	12	1.1	even	1	trivial
576.2.r.f.97.2	yes	12	9.7	even	3
576.2.r.f.97.5	yes	12	36.7	odd	6
576.2.r.f.481.2	yes	12	8.5	even	2
576.2.r.f.481.5	yes	12	8.3	odd	2
1728.2.r.e.289.3		12	9.2	odd	6
1728.2.r.e.289.4		12	36.11	even	6
1728.2.r.e.1441.3		12	24.5	odd	2
1728.2.r.e.1441.4		12	24.11	even	2
1728.2.r.f.289.3		12	72.29	odd	6
1728.2.r.f.289.4		12	72.11	even	6
1728.2.r.f.1441.3		12	3.2	odd	2
1728.2.r.f.1441.4		12	12.11	even	2
5184.2.d.q.2593.3		12	72.67	odd	6
5184.2.d.q.2593.4		12	72.13	even	6
5184.2.d.q.2593.9		12	36.31	odd	6
5184.2.d.q.2593.10		12	9.4	even	3
5184.2.d.r.2593.3		12	36.23	even	6
5184.2.d.r.2593.4		12	9.5	odd	6
5184.2.d.r.2593.9		12	72.59	even	6
5184.2.d.r.2593.10		12	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:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	576.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.10182 - 1.33641i) q^{3} +(-1.50000 - 0.866025i) q^{5} +(-0.495361 - 0.857990i) q^{7} +(-0.571993 - 2.94497i) q^{9} +O(q^{10})\)	\(q+(1.10182 - 1.33641i) q^{3} +(-1.50000 - 0.866025i) q^{5} +(-0.495361 - 0.857990i) q^{7} +(-0.571993 - 2.94497i) q^{9} +(-1.81937 + 1.05042i) q^{11} +(-5.50924 - 3.18076i) q^{13} +(-2.81009 + 1.05042i) q^{15} +3.81681 q^{17} -2.00000i q^{19} +(-1.69243 - 0.283343i) q^{21} +(-3.55142 + 6.15125i) q^{23} +(-1.00000 - 1.73205i) q^{25} +(-4.56592 - 2.48040i) q^{27} +(7.22522 - 4.17148i) q^{29} +(1.07804 - 1.86723i) q^{31} +(-0.600830 + 3.58880i) q^{33} +1.71598i q^{35} -4.62947i q^{37} +(-10.3210 + 3.85799i) q^{39} +(-0.408405 + 0.707378i) q^{41} +(-1.97802 + 1.14201i) q^{43} +(-1.69243 + 4.91281i) q^{45} +(3.39278 + 5.87646i) q^{47} +(3.00924 - 5.21215i) q^{49} +(4.20543 - 5.10083i) q^{51} -3.14681i q^{53} +3.63875 q^{55} +(-2.67282 - 2.20364i) q^{57} +(-10.3210 - 5.95882i) q^{59} +(-4.22522 + 2.43943i) q^{61} +(-2.24341 + 1.94958i) q^{63} +(5.50924 + 9.54228i) q^{65} +(11.8944 + 6.86723i) q^{67} +(4.30757 + 11.5237i) q^{69} +13.5391 q^{71} +10.0185 q^{73} +(-3.41655 - 0.571993i) q^{75} +(1.80249 + 1.04067i) q^{77} +(-4.54214 - 7.86723i) q^{79} +(-8.34565 + 3.36900i) q^{81} +(3.71007 - 2.14201i) q^{83} +(-5.72522 - 3.30545i) q^{85} +(2.38606 - 14.2521i) q^{87} -14.0185 q^{89} +6.30249i q^{91} +(-1.30757 - 3.49805i) q^{93} +(-1.73205 + 3.00000i) q^{95} +(-6.22522 - 10.7824i) q^{97} +(4.13411 + 4.75716i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 18 q^{5} - 4 q^{9}+O(q^{10}) \) 12 * q - 18 * q^5 - 4 * q^9	\( 12 q - 18 q^{5} - 4 q^{9} - 6 q^{13} - 6 q^{21} - 12 q^{25} + 18 q^{29} + 30 q^{33} + 18 q^{41} - 6 q^{45} - 24 q^{49} + 8 q^{57} + 18 q^{61} + 6 q^{65} + 66 q^{69} - 90 q^{77} - 20 q^{81} - 48 q^{89} - 30 q^{93} - 6 q^{97}+O(q^{100}) \) 12 * q - 18 * q^5 - 4 * q^9 - 6 * q^13 - 6 * q^21 - 12 * q^25 + 18 * q^29 + 30 * q^33 + 18 * q^41 - 6 * q^45 - 24 * q^49 + 8 * q^57 + 18 * q^61 + 6 * q^65 + 66 * q^69 - 90 * q^77 - 20 * q^81 - 48 * q^89 - 30 * q^93 - 6 * q^97

Introduction

L-functions

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Groups

Database

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