LMFDB - Embedded newform 572.2.n.a.313.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(53,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6, 0]))

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

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

chi := DirichletCharacter("572.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.n (of order $5$, degree $4$, 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:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 4 x^{19} + 22 x^{18} - 72 x^{17} + 236 x^{16} - 556 x^{15} + 1232 x^{14} - 1981 x^{13} + \cdots + 400 $ x^20 - 4x^19 + 22x^18 - 72x^17 + 236x^16 - 556x^15 + 1232x^14 - 1981x^13 + 3407x^12 - 4130x^11 + 5358x^10 - 6093x^9 + 10112x^8 - 14136x^7 + 17259x^6 - 10035x^5 + 2921x^4 + 440x^3 + 560x^2 - 200*x + 400
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			313.5
Root			$0.758867 + 2.33555i$ of defining polynomial
Character	$\chi$	$=$	572.313
Dual form			572.2.n.a.53.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.98674 + 1.44345i) q^{3} +(0.248052 - 0.763424i) q^{5} +(0.0617615 - 0.0448724i) q^{7} +(0.936532 + 2.88235i) q^{9} +O(q^{10})$	\(q+(1.98674 + 1.44345i) q^{3} +(0.248052 - 0.763424i) q^{5} +(0.0617615 - 0.0448724i) q^{7} +(0.936532 + 2.88235i) q^{9} +(2.51492 + 2.16221i) q^{11} +(0.309017 + 0.951057i) q^{13} +(1.59478 - 1.15868i) q^{15} +(-0.810966 + 2.49590i) q^{17} +(-1.14980 - 0.835375i) q^{19} +0.187475 q^{21} +4.13353 q^{23} +(3.52380 + 2.56019i) q^{25} +(-0.0232835 + 0.0716592i) q^{27} +(0.681561 - 0.495183i) q^{29} +(-1.48641 - 4.57469i) q^{31} +(1.87545 + 7.92592i) q^{33} +(-0.0189366 - 0.0582809i) q^{35} +(0.734098 - 0.533353i) q^{37} +(-0.758867 + 2.33555i) q^{39} +(-6.84307 - 4.97178i) q^{41} -3.94904 q^{43} +2.43276 q^{45} +(-3.07681 - 2.23543i) q^{47} +(-2.16132 + 6.65185i) q^{49} +(-5.21388 + 3.78811i) q^{51} +(-1.95792 - 6.02585i) q^{53} +(2.27452 - 1.38361i) q^{55} +(-1.07852 - 3.31934i) q^{57} +(-3.82683 + 2.78036i) q^{59} +(-2.30648 + 7.09863i) q^{61} +(0.187180 + 0.135994i) q^{63} +0.802712 q^{65} -0.998118 q^{67} +(8.21225 + 5.96655i) q^{69} +(4.29264 - 13.2114i) q^{71} +(-3.97283 + 2.88643i) q^{73} +(3.30536 + 10.1729i) q^{75} +(0.252349 + 0.0206909i) q^{77} +(-2.68220 - 8.25497i) q^{79} +(7.20592 - 5.23541i) q^{81} +(0.752569 - 2.31617i) q^{83} +(1.70427 + 1.23822i) q^{85} +2.06886 q^{87} +6.86890 q^{89} +(0.0617615 + 0.0448724i) q^{91} +(3.65023 - 11.2343i) q^{93} +(-0.922954 + 0.670566i) q^{95} +(-3.53266 - 10.8724i) q^{97} +(-3.87694 + 9.27387i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + q^{3} + q^{5} + 3 q^{7} + 12 q^{9}+O(q^{10}) $ 20 * q + q^3 + q^5 + 3 * q^7 + 12 * q^9	$ 20 q + q^{3} + q^{5} + 3 q^{7} + 12 q^{9} - q^{11} - 5 q^{13} + 14 q^{15} - 3 q^{17} - 7 q^{19} - 32 q^{21} - 30 q^{23} - 12 q^{25} + 13 q^{27} - 14 q^{29} + 11 q^{31} - 10 q^{33} - 10 q^{35} + 45 q^{37} - 4 q^{39} + 9 q^{41} - 8 q^{43} - 34 q^{45} + 39 q^{47} + 30 q^{49} - 55 q^{51} + 36 q^{53} + 11 q^{55} - 31 q^{57} - 31 q^{59} - 7 q^{61} + 14 q^{63} - 14 q^{65} + 26 q^{67} + 32 q^{69} + 33 q^{71} - 44 q^{73} + 37 q^{75} - 73 q^{77} + 21 q^{79} + 16 q^{81} - 25 q^{83} + 15 q^{85} + 32 q^{87} - 2 q^{89} + 3 q^{91} + 33 q^{93} - 37 q^{95} + 52 q^{97} - 8 q^{99}+O(q^{100}) $ 20 * q + q^3 + q^5 + 3 * q^7 + 12 * q^9 - q^11 - 5 * q^13 + 14 * q^15 - 3 * q^17 - 7 * q^19 - 32 * q^21 - 30 * q^23 - 12 * q^25 + 13 * q^27 - 14 * q^29 + 11 * q^31 - 10 * q^33 - 10 * q^35 + 45 * q^37 - 4 * q^39 + 9 * q^41 - 8 * q^43 - 34 * q^45 + 39 * q^47 + 30 * q^49 - 55 * q^51 + 36 * q^53 + 11 * q^55 - 31 * q^57 - 31 * q^59 - 7 * q^61 + 14 * q^63 - 14 * q^65 + 26 * q^67 + 32 * q^69 + 33 * q^71 - 44 * q^73 + 37 * q^75 - 73 * q^77 + 21 * q^79 + 16 * q^81 - 25 * q^83 + 15 * q^85 + 32 * q^87 - 2 * q^89 + 3 * q^91 + 33 * q^93 - 37 * q^95 + 52 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	1.98674	+	1.44345i	1.14704	+	0.833377i	0.988085	−	0.153909i	$-0.0491861\pi$
$3$	1.98674	+	1.44345i	1.14704	+	0.833377i	0.158959	+	0.987285i	$0.449186\pi$
$4$		0			0
$5$	0.248052	−	0.763424i	0.110932	−	0.341414i	−0.880145	−	0.474705i	$-0.842555\pi$
$5$	0.248052	−	0.763424i	0.110932	−	0.341414i	0.991077	+	0.133291i	$0.0425546\pi$
$6$		0			0
$7$	0.0617615	−	0.0448724i	0.0233437	−	0.0169602i	−0.576052	−	0.817413i	$-0.695408\pi$
$7$	0.0617615	−	0.0448724i	0.0233437	−	0.0169602i	0.599396	+	0.800453i	$0.295408\pi$
$8$		0			0
$9$	0.936532	+	2.88235i	0.312177	+	0.960783i
$10$		0			0
$11$	2.51492	+	2.16221i	0.758278	+	0.651931i
$11$	2.51492	+	2.16221i	0.758278	+	0.651931i
$12$		0			0
$13$	0.309017	+	0.951057i	0.0857059	+	0.263776i
$13$	0.309017	+	0.951057i	0.0857059	+	0.263776i
$14$		0			0
$15$	1.59478	−	1.15868i	0.411770	−	0.299169i
$16$		0			0
$17$	−0.810966	+	2.49590i	−0.196688	+	0.605344i	0.803265	+	0.595622i	$0.203095\pi$
$17$	−0.810966	+	2.49590i	−0.196688	+	0.605344i	−0.999953	+	0.00972157i	$0.996905\pi$
$18$		0			0
$19$	−1.14980	−	0.835375i	−0.263781	−	0.191648i	0.448031	−	0.894018i	$-0.352125\pi$
$19$	−1.14980	−	0.835375i	−0.263781	−	0.191648i	−0.711812	+	0.702370i	$0.752125\pi$
$20$		0			0
$21$	0.187475			0.0409104
$22$		0			0
$23$	4.13353			0.861901			0.430950	−	0.902376i	$-0.358178\pi$
$23$	4.13353			0.861901			0.430950	+	0.902376i	$0.358178\pi$
$24$		0			0
$25$	3.52380	+	2.56019i	0.704760	+	0.512038i
$26$		0			0
$27$	−0.0232835	+	0.0716592i	−0.00448091	+	0.0137908i
$28$		0			0
$29$	0.681561	−	0.495183i	0.126563	−	0.0919532i	−0.522703	−	0.852515i	$-0.675076\pi$
$29$	0.681561	−	0.495183i	0.126563	−	0.0919532i	0.649266	+	0.760562i	$0.275076\pi$
$30$		0			0
$31$	−1.48641	−	4.57469i	−0.266966	−	0.821638i	−0.991234	−	0.132119i	$-0.957822\pi$
$31$	−1.48641	−	4.57469i	−0.266966	−	0.821638i	0.724268	−	0.689519i	$-0.242178\pi$
$32$		0			0
$33$	1.87545	+	7.92592i	0.326474	+	1.37973i
$34$		0			0
$35$	−0.0189366	−	0.0582809i	−0.00320087	−	0.00985128i
$36$		0			0
$37$	0.734098	−	0.533353i	0.120685	−	0.0876827i	−0.525806	−	0.850605i	$-0.676236\pi$
$37$	0.734098	−	0.533353i	0.120685	−	0.0876827i	0.646490	+	0.762922i	$0.276236\pi$
$38$		0			0
$39$	−0.758867	+	2.33555i	−0.121516	+	0.373988i
$40$		0			0
$41$	−6.84307	−	4.97178i	−1.06871	−	0.776462i	−0.0930286	−	0.995663i	$-0.529655\pi$
$41$	−6.84307	−	4.97178i	−1.06871	−	0.776462i	−0.975680	+	0.219201i	$0.929655\pi$
$42$		0			0
$43$	−3.94904			−0.602223			−0.301111	−	0.953589i	$-0.597358\pi$
$43$	−3.94904			−0.602223			−0.301111	+	0.953589i	$0.597358\pi$
$44$		0			0
$45$	2.43276			0.362655
$46$		0			0
$47$	−3.07681	−	2.23543i	−0.448799	−	0.326072i	0.340322	−	0.940309i	$-0.389464\pi$
$47$	−3.07681	−	2.23543i	−0.448799	−	0.326072i	−0.789121	+	0.614237i	$0.789464\pi$
$48$		0			0
$49$	−2.16132	+	6.65185i	−0.308760	+	0.950265i
$50$		0			0
$51$	−5.21388	+	3.78811i	−0.730090	+	0.530441i
$52$		0			0
$53$	−1.95792	−	6.02585i	−0.268940	−	0.827714i	−0.990759	−	0.135632i	$-0.956694\pi$
$53$	−1.95792	−	6.02585i	−0.268940	−	0.827714i	0.721819	−	0.692082i	$-0.243306\pi$
$54$		0			0
$55$	2.27452	−	1.38361i	0.306696	−	0.186567i
$56$		0			0
$57$	−1.07852	−	3.31934i	−0.142854	−	0.439658i
$58$		0			0
$59$	−3.82683	+	2.78036i	−0.498211	+	0.361971i	−0.808333	−	0.588725i	$-0.799630\pi$
$59$	−3.82683	+	2.78036i	−0.498211	+	0.361971i	0.310122	+	0.950697i	$0.399630\pi$
$60$		0			0
$61$	−2.30648	+	7.09863i	−0.295315	+	0.908886i	0.687800	+	0.725900i	$0.258576\pi$
$61$	−2.30648	+	7.09863i	−0.295315	+	0.908886i	−0.983115	+	0.182986i	$0.941424\pi$
$62$		0			0
$63$	0.187180	+	0.135994i	0.0235824	+	0.0171336i
$64$		0			0
$65$	0.802712			0.0995642
$66$		0			0
$67$	−0.998118			−0.121939			−0.0609697	−	0.998140i	$-0.519419\pi$
$67$	−0.998118			−0.121939			−0.0609697	+	0.998140i	$0.519419\pi$
$68$		0			0
$69$	8.21225	+	5.96655i	0.988638	+	0.718288i
$70$		0			0
$71$	4.29264	−	13.2114i	0.509443	−	1.56790i	−0.283727	−	0.958905i	$-0.591571\pi$
$71$	4.29264	−	13.2114i	0.509443	−	1.56790i	0.793170	−	0.609000i	$-0.208429\pi$
$72$		0			0
$73$	−3.97283	+	2.88643i	−0.464984	+	0.337831i	−0.795483	−	0.605975i	$-0.792783\pi$
$73$	−3.97283	+	2.88643i	−0.464984	+	0.337831i	0.330499	+	0.943806i	$0.392783\pi$
$74$		0			0
$75$	3.30536	+	10.1729i	0.381670	+	1.17466i
$76$		0			0
$77$	0.252349	+	0.0206909i	0.0287579	+	0.00235794i
$78$		0			0
$79$	−2.68220	−	8.25497i	−0.301771	−	0.928757i	−0.980862	−	0.194703i	$-0.937626\pi$
$79$	−2.68220	−	8.25497i	−0.301771	−	0.928757i	0.679091	−	0.734054i	$-0.262374\pi$
$80$		0			0
$81$	7.20592	−	5.23541i	0.800658	−	0.581712i
$82$		0			0
$83$	0.752569	−	2.31617i	0.0826052	−	0.254233i	−0.901221	−	0.433361i	$-0.857328\pi$
$83$	0.752569	−	2.31617i	0.0826052	−	0.254233i	0.983826	+	0.179128i	$0.0573276\pi$
$84$		0			0
$85$	1.70427	+	1.23822i	0.184854	+	0.134304i
$86$		0			0
$87$	2.06886			0.221805
$88$		0			0
$89$	6.86890			0.728102			0.364051	−	0.931379i	$-0.381393\pi$
$89$	6.86890			0.728102			0.364051	+	0.931379i	$0.381393\pi$
$90$		0			0
$91$	0.0617615	+	0.0448724i	0.00647437	+	0.00470390i
$92$		0			0
$93$	3.65023	−	11.2343i	0.378511	−	1.16494i
$94$		0			0
$95$	−0.922954	+	0.670566i	−0.0946931	+	0.0687986i
$96$		0			0
$97$	−3.53266	−	10.8724i	−0.358687	−	1.10393i	−0.953840	−	0.300314i	$-0.902909\pi$
$97$	−3.53266	−	10.8724i	−0.358687	−	1.10393i	0.595153	−	0.803612i	$-0.297091\pi$
$98$		0			0
$99$	−3.87694	+	9.27387i	−0.389647	+	0.932059i
$100$		0			0
$101$	−3.05829	−	9.41245i	−0.304311	−	0.936574i	−0.979933	−	0.199326i	$-0.936125\pi$
$101$	−3.05829	−	9.41245i	−0.304311	−	0.936574i	0.675622	−	0.737248i	$-0.263875\pi$
$102$		0			0
$103$	−4.74500	+	3.44744i	−0.467539	+	0.339687i	−0.796481	−	0.604663i	$-0.793308\pi$
$103$	−4.74500	+	3.44744i	−0.467539	+	0.339687i	0.328943	+	0.944350i	$0.393308\pi$
$104$		0			0
$105$	0.0465035	−	0.143123i	0.00453828	−	0.0139674i
$106$		0			0
$107$	−8.48316	−	6.16337i	−0.820098	−	0.595836i	0.0966428	−	0.995319i	$-0.469190\pi$
$107$	−8.48316	−	6.16337i	−0.820098	−	0.595836i	−0.916740	+	0.399483i	$0.869190\pi$
$108$		0			0
$109$	10.0664			0.964187			0.482094	−	0.876120i	$-0.339876\pi$
$109$	10.0664			0.964187			0.482094	+	0.876120i	$0.339876\pi$
$110$		0			0
$111$	2.22833			0.211504
$112$		0			0
$113$	8.94205	+	6.49678i	0.841197	+	0.611166i	0.922705	−	0.385507i	$-0.125973\pi$
$113$	8.94205	+	6.49678i	0.841197	+	0.611166i	−0.0815074	+	0.996673i	$0.525973\pi$
$114$		0			0
$115$	1.02533	−	3.15564i	0.0956124	−	0.294265i
$116$		0			0
$117$	−2.45187	+	1.78139i	−0.226676	+	0.164690i
$118$		0			0
$119$	0.0619103	+	0.190540i	0.00567531	+	0.0174668i
$120$		0			0
$121$	1.64968	+	10.8756i	0.149971	+	0.988690i
$122$		0			0
$123$	−6.41888	−	19.7553i	−0.578771	−	1.78127i
$124$		0			0
$125$	6.07563	−	4.41421i	0.543421	−	0.394819i
$126$		0			0
$127$	−1.83338	+	5.64257i	−0.162686	+	0.500697i	−0.998858	−	0.0477702i	$-0.984788\pi$
$127$	−1.83338	+	5.64257i	−0.162686	+	0.500697i	0.836172	+	0.548467i	$0.184788\pi$
$128$		0			0
$129$	−7.84571	−	5.70024i	−0.690776	−	0.501878i
$130$		0			0
$131$	−7.70033			−0.672781			−0.336391	−	0.941723i	$-0.609206\pi$
$131$	−7.70033			−0.672781			−0.336391	+	0.941723i	$0.609206\pi$
$132$		0			0
$133$	−0.108498			−0.00940800
$134$		0			0
$135$	0.0489309	+	0.0355504i	0.00421130	+	0.00305969i
$136$		0			0
$137$	1.34881	−	4.15121i	0.115237	−	0.354662i	−0.876760	−	0.480929i	$-0.840300\pi$
$137$	1.34881	−	4.15121i	0.115237	−	0.354662i	0.991996	+	0.126267i	$0.0402996\pi$
$138$		0			0
$139$	−16.4082	+	11.9213i	−1.39173	+	1.01115i	−0.396053	+	0.918228i	$0.629620\pi$
$139$	−16.4082	+	11.9213i	−1.39173	+	1.01115i	−0.995673	+	0.0929208i	$0.970380\pi$
$140$		0			0
$141$	−2.88608	−	8.88245i	−0.243052	−	0.748037i
$142$		0			0
$143$	−1.27923	+	3.05999i	−0.106975	+	0.255890i
$144$		0			0
$145$	−0.208973	−	0.643152i	−0.0173542	−	0.0534108i
$146$		0			0
$147$	−13.8956	+	10.0957i	−1.14609	+	0.832683i
$148$		0			0
$149$	2.92371	−	8.99825i	0.239520	−	0.737165i	−0.756970	−	0.653449i	$-0.773321\pi$
$149$	2.92371	−	8.99825i	0.239520	−	0.737165i	0.996490	−	0.0837158i	$-0.0266788\pi$
$150$		0			0
$151$	−11.1598	−	8.10806i	−0.908170	−	0.659824i	0.0323810	−	0.999476i	$-0.489691\pi$
$151$	−11.1598	−	8.10806i	−0.908170	−	0.659824i	−0.940551	+	0.339651i	$0.889691\pi$
$152$		0			0
$153$	−7.95354			−0.643006
$154$		0			0
$155$	−3.86113			−0.310134
$156$		0			0
$157$	3.49032	+	2.53587i	0.278558	+	0.202384i	0.718288	−	0.695746i	$-0.244926\pi$
$157$	3.49032	+	2.53587i	0.278558	+	0.202384i	−0.439730	+	0.898130i	$0.644926\pi$
$158$		0			0
$159$	4.80814	−	14.7979i	0.381311	−	1.17355i
$160$		0			0
$161$	0.255293	−	0.185481i	0.0201199	−	0.0146180i
$162$		0			0
$163$	2.91066	+	8.95809i	0.227980	+	0.701652i	0.997975	+	0.0636016i	$0.0202587\pi$
$163$	2.91066	+	8.95809i	0.227980	+	0.701652i	−0.769995	+	0.638050i	$0.779741\pi$
$164$		0			0
$165$	6.51605	+	0.534270i	0.507274	+	0.0415929i
$166$		0			0
$167$	−6.16251	−	18.9663i	−0.476870	−	1.46765i	−0.843420	−	0.537255i	$-0.819461\pi$
$167$	−6.16251	−	18.9663i	−0.476870	−	1.46765i	0.366550	−	0.930398i	$-0.380539\pi$
$168$		0			0
$169$	−0.809017	+	0.587785i	−0.0622321	+	0.0452143i
$170$		0			0
$171$	1.33102	−	4.09647i	0.101786	−	0.313265i
$172$		0			0
$173$	12.4111	+	9.01718i	0.943597	+	0.685563i	0.949284	−	0.314421i	$-0.101810\pi$
$173$	12.4111	+	9.01718i	0.943597	+	0.685563i	−0.00568700	+	0.999984i	$0.501810\pi$
$174$		0			0
$175$	0.332517			0.0251359
$176$		0			0
$177$	−11.6162			−0.873129
$178$		0			0
$179$	6.99105	+	5.07929i	0.522535	+	0.379644i	0.817558	−	0.575846i	$-0.195327\pi$
$179$	6.99105	+	5.07929i	0.522535	+	0.379644i	−0.295023	+	0.955490i	$0.595327\pi$
$180$		0			0
$181$	0.951446	−	2.92825i	0.0707204	−	0.217655i	−0.909449	−	0.415815i	$-0.863496\pi$
$181$	0.951446	−	2.92825i	0.0707204	−	0.217655i	0.980170	+	0.198160i	$0.0634964\pi$
$182$		0			0
$183$	−14.8289	+	10.7738i	−1.09618	+	0.796424i
$184$		0			0
$185$	−0.225081	−	0.692727i	−0.0165483	−	0.0509303i
$186$		0			0
$187$	−7.43617	+	4.52351i	−0.543787	+	0.330792i
$188$		0			0
$189$	0.00177750	+	0.00547057i	0.000129294	+	0.000397925i
$190$		0			0
$191$	−1.19943	+	0.871440i	−0.0867880	+	0.0630552i	−0.630333	−	0.776325i	$-0.717082\pi$
$191$	−1.19943	+	0.871440i	−0.0867880	+	0.0630552i	0.543545	+	0.839380i	$0.317082\pi$
$192$		0			0
$193$	1.68877	−	5.19751i	0.121561	−	0.374125i	−0.871698	−	0.490043i	$-0.836981\pi$
$193$	1.68877	−	5.19751i	0.121561	−	0.374125i	0.993259	+	0.115918i	$0.0369811\pi$
$194$		0			0
$195$	1.59478	+	1.15868i	0.114205	+	0.0829744i
$196$		0			0
$197$	−7.48686			−0.533417			−0.266708	−	0.963777i	$-0.585936\pi$
$197$	−7.48686			−0.533417			−0.266708	+	0.963777i	$0.585936\pi$
$198$		0			0
$199$	−18.4279			−1.30632			−0.653158	−	0.757221i	$-0.726556\pi$
$199$	−18.4279			−1.30632			−0.653158	+	0.757221i	$0.726556\pi$
$200$		0			0
$201$	−1.98300	−	1.44073i	−0.139870	−	0.101621i
$202$		0			0
$203$	0.0198742	−	0.0611666i	0.00139490	−	0.00429305i
$204$		0			0
$205$	−5.49302	+	3.99091i	−0.383649	+	0.278737i
$206$		0			0
$207$	3.87118	+	11.9143i	0.269066	+	0.828100i
$208$		0			0
$209$	−1.08539	−	4.58700i	−0.0750780	−	0.317290i
$210$		0			0
$211$	−2.76944	−	8.52346i	−0.190656	−	0.586779i	0.809344	−	0.587335i	$-0.199823\pi$
$211$	−2.76944	−	8.52346i	−0.190656	−	0.586779i	−1.00000		0.000556240i	$0.999823\pi$
$212$		0			0
$213$	27.5984	−	20.0514i	1.89101	−	1.37390i
$214$		0			0
$215$	−0.979566	+	3.01479i	−0.0668058	+	0.205607i
$216$		0			0
$217$	−0.297080	−	0.215841i	−0.0201671	−	0.0146522i
$218$		0			0
$219$	−12.0594			−0.814898
$220$		0			0
$221$	−2.62434			−0.176532
$222$		0			0
$223$	6.81419	+	4.95080i	0.456312	+	0.331530i	0.792083	−	0.610414i	$-0.208997\pi$
$223$	6.81419	+	4.95080i	0.456312	+	0.331530i	−0.335771	+	0.941944i	$0.608997\pi$
$224$		0			0
$225$	−4.07921	+	12.5545i	−0.271947	+	0.836968i
$226$		0			0
$227$	9.02077	−	6.55397i	0.598729	−	0.435002i	−0.246698	−	0.969092i	$-0.579346\pi$
$227$	9.02077	−	6.55397i	0.598729	−	0.435002i	0.845428	+	0.534090i	$0.179346\pi$
$228$		0			0
$229$	7.49326	+	23.0619i	0.495168	+	1.52397i	0.816694	+	0.577071i	$0.195804\pi$
$229$	7.49326	+	23.0619i	0.495168	+	1.52397i	−0.321526	+	0.946901i	$0.604196\pi$
$230$		0			0
$231$	0.471486	+	0.405361i	0.0310215	+	0.0266708i
$232$		0			0
$233$	3.54820	+	10.9203i	0.232451	+	0.715409i	0.997449	+	0.0713777i	$0.0227396\pi$
$233$	3.54820	+	10.9203i	0.232451	+	0.715409i	−0.764999	+	0.644032i	$0.777260\pi$
$234$		0			0
$235$	−2.46979	+	1.79441i	−0.161112	+	0.117054i
$236$		0			0
$237$	6.58680	−	20.2721i	0.427859	−	1.31681i
$238$		0			0
$239$	6.53712	+	4.74949i	0.422851	+	0.307219i	0.778784	−	0.627292i	$-0.215837\pi$
$239$	6.53712	+	4.74949i	0.422851	+	0.307219i	−0.355933	+	0.934511i	$0.615837\pi$
$240$		0			0
$241$	−12.4939			−0.804803			−0.402402	−	0.915463i	$-0.631824\pi$
$241$	−12.4939			−0.804803			−0.402402	+	0.915463i	$0.631824\pi$
$242$		0			0
$243$	22.0994			1.41768
$244$		0			0
$245$	4.54207	+	3.30001i	0.290182	+	0.210830i
$246$		0			0
$247$	0.439183	−	1.35167i	0.0279445	−	0.0860044i
$248$		0			0
$249$	4.83843	−	3.51533i	0.306623	−	0.222775i
$250$		0			0
$251$	−2.92237	−	8.99412i	−0.184458	−	0.567704i	0.815480	−	0.578785i	$-0.196473\pi$
$251$	−2.92237	−	8.99412i	−0.184458	−	0.567704i	−0.999939	+	0.0110809i	$0.996473\pi$
$252$		0			0
$253$	10.3955	+	8.93757i	0.653560	+	0.561900i
$254$		0			0
$255$	1.59862	+	4.92005i	0.100110	+	0.308106i
$256$		0			0
$257$	12.1428	−	8.82226i	0.757447	−	0.550318i	−0.140679	−	0.990055i	$-0.544929\pi$
$257$	12.1428	−	8.82226i	0.757447	−	0.550318i	0.898126	+	0.439738i	$0.144929\pi$
$258$		0			0
$259$	0.0214062	−	0.0658814i	0.00133011	−	0.00409367i
$260$		0			0
$261$	2.06560	+	1.50074i	0.127857	+	0.0928936i
$262$		0			0
$263$	23.0684			1.42246			0.711230	−	0.702959i	$-0.248138\pi$
$263$	23.0684			1.42246			0.711230	+	0.702959i	$0.248138\pi$
$264$		0			0
$265$	−5.08594			−0.312427
$266$		0			0
$267$	13.6467	+	9.91492i	0.835165	+	0.606783i
$268$		0			0
$269$	−6.36681	+	19.5950i	−0.388191	+	1.19473i	0.545948	+	0.837819i	$0.316170\pi$
$269$	−6.36681	+	19.5950i	−0.388191	+	1.19473i	−0.934139	+	0.356910i	$0.883830\pi$
$270$		0			0
$271$	−5.17931	+	3.76299i	−0.314621	+	0.228585i	−0.733877	−	0.679283i	$-0.762291\pi$
$271$	−5.17931	+	3.76299i	−0.314621	+	0.228585i	0.419256	+	0.907868i	$0.362291\pi$
$272$		0			0
$273$	0.0579330	+	0.178299i	0.00350626	+	0.0107912i
$274$		0			0
$275$	3.32641	+	14.0579i	0.200590	+	0.847722i
$276$		0			0
$277$	5.93502	+	18.2661i	0.356601	+	1.09751i	0.955075	+	0.296363i	$0.0957739\pi$
$277$	5.93502	+	18.2661i	0.356601	+	1.09751i	−0.598474	+	0.801142i	$0.704226\pi$
$278$		0			0
$279$	11.7938	−	8.56868i	0.706075	−	0.512993i
$280$		0			0
$281$	−7.49726	+	23.0742i	−0.447249	+	1.37649i	0.432749	+	0.901514i	$0.357544\pi$
$281$	−7.49726	+	23.0742i	−0.447249	+	1.37649i	−0.879998	+	0.474977i	$0.842456\pi$
$282$		0			0
$283$	11.6438	+	8.45974i	0.692154	+	0.502879i	0.877367	−	0.479819i	$-0.159298\pi$
$283$	11.6438	+	8.45974i	0.692154	+	0.502879i	−0.185214	+	0.982698i	$0.559298\pi$
$284$		0			0
$285$	−2.80160			−0.165952
$286$		0			0
$287$	−0.645734			−0.0381165
$288$		0			0
$289$	8.18145	+	5.94417i	0.481262	+	0.349657i
$290$		0			0
$291$	8.67532	−	26.6999i	0.508556	−	1.56517i
$292$		0			0
$293$	7.43502	−	5.40186i	0.434358	−	0.315580i	−0.349031	−	0.937111i	$-0.613489\pi$
$293$	7.43502	−	5.40186i	0.434358	−	0.315580i	0.783389	+	0.621531i	$0.213489\pi$
$294$		0			0
$295$	1.17334	+	3.61117i	0.0683145	+	0.210250i
$296$		0			0
$297$	−0.213499	+	0.129874i	−0.0123884	+	0.00753603i
$298$		0			0
$299$	1.27733	+	3.93122i	0.0738700	+	0.227348i
$300$		0			0
$301$	−0.243899	+	0.177203i	−0.0140581	+	0.0102138i
$302$		0			0
$303$	7.51038	−	23.1146i	0.431460	−	1.32790i
$304$		0			0
$305$	4.84714	+	3.52165i	0.277546	+	0.201649i
$306$		0			0
$307$	25.9103			1.47878			0.739390	−	0.673277i	$-0.235114\pi$
$307$	25.9103			1.47878			0.739390	+	0.673277i	$0.235114\pi$
$308$		0			0
$309$	−14.4033			−0.819375
$310$		0			0
$311$	9.30261	+	6.75874i	0.527503	+	0.383253i	0.819423	−	0.573190i	$-0.194294\pi$
$311$	9.30261	+	6.75874i	0.527503	+	0.383253i	−0.291920	+	0.956443i	$0.594294\pi$
$312$		0			0
$313$	−8.99719	+	27.6905i	−0.508551	+	1.56516i	0.286166	+	0.958180i	$0.407619\pi$
$313$	−8.99719	+	27.6905i	−0.508551	+	1.56516i	−0.794717	+	0.606980i	$0.792381\pi$
$314$		0			0
$315$	0.150251	−	0.109164i	0.00846570	−	0.00615069i
$316$		0			0
$317$	−1.85334	−	5.70398i	−0.104094	−	0.320367i	0.885423	−	0.464786i	$-0.153869\pi$
$317$	−1.85334	−	5.70398i	−0.104094	−	0.320367i	−0.989517	+	0.144419i	$0.953869\pi$
$318$		0			0
$319$	2.78477	+	0.228331i	0.155917	+	0.0127841i
$320$		0			0
$321$	−7.95729	−	24.4900i	−0.444133	−	1.36690i
$322$		0			0
$323$	3.01746	−	2.19231i	0.167896	−	0.121983i
$324$		0			0
$325$	−1.34597	+	4.14247i	−0.0746610	+	0.229783i
$326$		0			0
$327$	19.9993	+	14.5304i	1.10597	+	0.803531i
$328$		0			0
$329$	−0.290338			−0.0160068
$330$		0			0
$331$	−7.99409			−0.439395			−0.219697	−	0.975568i	$-0.570507\pi$
$331$	−7.99409			−0.439395			−0.219697	+	0.975568i	$0.570507\pi$
$332$		0			0
$333$	2.22482	+	1.61642i	0.121919	+	0.0885795i
$334$		0			0
$335$	−0.247585	+	0.761987i	−0.0135270	+	0.0416318i
$336$		0			0
$337$	−11.1933	+	8.13243i	−0.609740	+	0.443002i	−0.849323	−	0.527874i	$-0.822989\pi$
$337$	−11.1933	+	8.13243i	−0.609740	+	0.443002i	0.239583	+	0.970876i	$0.422989\pi$
$338$		0			0
$339$	8.38774	+	25.8148i	0.455560	+	1.40207i
$340$		0			0
$341$	6.15324	−	14.7189i	0.333217	−	0.797074i
$342$		0			0
$343$	0.330134	+	1.01605i	0.0178256	+	0.0548614i
$344$		0			0
$345$	6.59207	−	4.78942i	0.354905	−	0.257854i
$346$		0			0
$347$	2.88259	−	8.87170i	0.154746	−	0.476258i	−0.843389	−	0.537303i	$-0.819443\pi$
$347$	2.88259	−	8.87170i	0.154746	−	0.476258i	0.998135	+	0.0610447i	$0.0194432\pi$
$348$		0			0
$349$	25.7265	+	18.6914i	1.37711	+	1.00053i	0.997144	+	0.0755284i	$0.0240643\pi$
$349$	25.7265	+	18.6914i	1.37711	+	1.00053i	0.379966	+	0.925000i	$0.375936\pi$
$350$		0			0
$351$	−0.0753470			−0.00402172
$352$		0			0
$353$	−27.1244			−1.44369			−0.721843	−	0.692056i	$-0.756705\pi$
$353$	−27.1244			−1.44369			−0.721843	+	0.692056i	$0.756705\pi$
$354$		0			0
$355$	−9.02111	−	6.55422i	−0.478791	−	0.347862i
$356$		0			0
$357$	−0.152036	+	0.467919i	−0.00804660	+	0.0247649i
$358$		0			0
$359$	−24.7905	+	18.0113i	−1.30839	+	0.950601i	−1.00000		0.000658371i	$-0.999790\pi$
$359$	−24.7905	+	18.0113i	−1.30839	+	0.950601i	−0.308391	+	0.951260i	$0.599790\pi$
$360$		0			0
$361$	−5.24715	−	16.1491i	−0.276166	−	0.849950i
$362$		0			0
$363$	−12.4209	+	23.9882i	−0.651928	+	1.25905i
$364$		0			0
$365$	1.21810	+	3.74894i	0.0637585	+	0.196228i
$366$		0			0
$367$	17.6290	−	12.8082i	0.920227	−	0.668584i	−0.0233536	−	0.999727i	$-0.507434\pi$
$367$	17.6290	−	12.8082i	0.920227	−	0.668584i	0.943580	+	0.331143i	$0.107434\pi$
$368$		0			0
$369$	7.92166	−	24.3804i	0.412385	−	1.26919i
$370$		0			0
$371$	−0.391318	−	0.284309i	−0.0203162	−	0.0147606i
$372$		0			0
$373$	−25.7757			−1.33461			−0.667307	−	0.744783i	$-0.732553\pi$
$373$	−25.7757			−1.33461			−0.667307	+	0.744783i	$0.732553\pi$
$374$		0			0
$375$	18.4424			0.952361
$376$		0			0
$377$	0.681561	+	0.495183i	0.0351022	+	0.0255032i
$378$		0			0
$379$	−4.26371	+	13.1223i	−0.219012	+	0.674050i	0.779832	+	0.625988i	$0.215304\pi$
$379$	−4.26371	+	13.1223i	−0.219012	+	0.674050i	−0.998844	+	0.0480612i	$0.984696\pi$
$380$		0			0
$381$	−11.7872	+	8.56392i	−0.603878	+	0.438743i
$382$		0			0
$383$	−2.71524	−	8.35664i	−0.138742	−	0.427004i	0.857411	−	0.514632i	$-0.172071\pi$
$383$	−2.71524	−	8.35664i	−0.138742	−	0.427004i	−0.996153	+	0.0876277i	$0.972071\pi$
$384$		0			0
$385$	0.0783915	−	0.187517i	0.00399520	−	0.00955676i
$386$		0			0
$387$	−3.69840	−	11.3825i	−0.188000	−	0.578606i
$388$		0			0
$389$	23.7434	−	17.2506i	1.20384	−	0.874640i	0.209182	−	0.977877i	$-0.432920\pi$
$389$	23.7434	−	17.2506i	1.20384	−	0.874640i	0.994657	+	0.103236i	$0.0329198\pi$
$390$		0			0
$391$	−3.35215	+	10.3169i	−0.169526	+	0.521746i
$392$		0			0
$393$	−15.2986	−	11.1151i	−0.771710	−	0.560680i
$394$		0			0
$395$	−6.96737			−0.350566
$396$		0			0
$397$	−30.1631			−1.51384			−0.756922	−	0.653505i	$-0.773298\pi$
$397$	−30.1631			−1.51384			−0.756922	+	0.653505i	$0.773298\pi$
$398$		0			0
$399$	−0.215558	−	0.156612i	−0.0107914	−	0.00784041i
$400$		0			0
$401$	−6.91633	+	21.2863i	−0.345385	+	1.06299i	0.615993	+	0.787752i	$0.288755\pi$
$401$	−6.91633	+	21.2863i	−0.345385	+	1.06299i	−0.961377	+	0.275233i	$0.911245\pi$
$402$		0			0
$403$	3.89146	−	2.82731i	0.193847	−	0.140838i
$404$		0			0
$405$	−2.20940	−	6.79983i	−0.109786	−	0.337886i
$406$		0			0
$407$	2.99942	+	0.245932i	0.148676	+	0.0121904i
$408$		0			0
$409$	11.6420	+	35.8305i	0.575661	+	1.77170i	0.633916	+	0.773402i	$0.281447\pi$
$409$	11.6420	+	35.8305i	0.575661	+	1.77170i	−0.0582543	+	0.998302i	$0.518553\pi$
$410$		0			0
$411$	8.67180	−	6.30043i	0.427748	−	0.310777i
$412$		0			0
$413$	−0.111590	+	0.343438i	−0.00549097	+	0.0168995i
$414$		0			0
$415$	−1.58154	−	1.14906i	−0.0776349	−	0.0564051i
$416$		0			0
$417$	−49.8066			−2.43904
$418$		0			0
$419$	−2.92003			−0.142653			−0.0713264	−	0.997453i	$-0.522723\pi$
$419$	−2.92003			−0.142653			−0.0713264	+	0.997453i	$0.522723\pi$
$420$		0			0
$421$	−9.69975	−	7.04728i	−0.472737	−	0.343463i	0.325770	−	0.945449i	$-0.394376\pi$
$421$	−9.69975	−	7.04728i	−0.472737	−	0.343463i	−0.798507	+	0.601986i	$0.794376\pi$
$422$		0			0
$423$	3.56177	−	10.9620i	0.173179	−	0.532991i
$424$		0			0
$425$	−9.24765	+	6.71881i	−0.448577	+	0.325910i
$426$		0			0
$427$	0.176080	+	0.541920i	0.00852113	+	0.0262253i
$428$		0			0
$429$	−6.95845	+	4.23291i	−0.335957	+	0.204367i
$430$		0			0
$431$	−4.25494	−	13.0954i	−0.204953	−	0.630781i	−0.999715	−	0.0238599i	$-0.992404\pi$
$431$	−4.25494	−	13.0954i	−0.204953	−	0.630781i	0.794762	−	0.606921i	$-0.207596\pi$
$432$		0			0
$433$	7.55725	−	5.49066i	0.363178	−	0.263864i	−0.391198	−	0.920306i	$-0.627939\pi$
$433$	7.55725	−	5.49066i	0.363178	−	0.263864i	0.754376	+	0.656442i	$0.227939\pi$
$434$		0			0
$435$	0.513183	−	1.57942i	0.0246053	−	0.0757272i
$436$		0			0
$437$	−4.75271	−	3.45305i	−0.227353	−	0.165182i
$438$		0			0
$439$	−8.76321			−0.418245			−0.209122	−	0.977889i	$-0.567061\pi$
$439$	−8.76321			−0.418245			−0.209122	+	0.977889i	$0.567061\pi$
$440$		0			0
$441$	−21.1971			−1.00939
$442$		0			0
$443$	30.2940	+	22.0099i	1.43931	+	1.04572i	0.988186	+	0.153261i	$0.0489774\pi$
$443$	30.2940	+	22.0099i	1.43931	+	1.04572i	0.451126	+	0.892460i	$0.351023\pi$
$444$		0			0
$445$	1.70384	−	5.24389i	0.0807699	−	0.248584i
$446$		0			0
$447$	18.7972	−	13.6569i	0.889076	−	0.645951i
$448$		0			0
$449$	−10.8338	−	33.3431i	−0.511280	−	1.57356i	−0.789950	−	0.613171i	$-0.789894\pi$
$449$	−10.8338	−	33.3431i	−0.511280	−	1.57356i	0.278670	−	0.960387i	$-0.410106\pi$
$450$		0			0
$451$	−6.45976	−	27.2998i	−0.304178	−	1.28550i
$452$		0			0
$453$	−10.4680	−	32.2172i	−0.491830	−	1.51370i
$454$		0			0
$455$	0.0495767	−	0.0360196i	0.00232419	−	0.00168863i
$456$		0			0
$457$	−2.68355	+	8.25912i	−0.125531	+	0.386345i	−0.993997	−	0.109403i	$-0.965106\pi$
$457$	−2.68355	+	8.25912i	−0.125531	+	0.386345i	0.868466	+	0.495748i	$0.165106\pi$
$458$		0			0
$459$	−0.159972	−	0.116226i	−0.00746685	−	0.00542498i
$460$		0			0
$461$	24.8498			1.15737			0.578685	−	0.815551i	$-0.303566\pi$
$461$	24.8498			1.15737			0.578685	+	0.815551i	$0.303566\pi$
$462$		0			0
$463$	−31.0661			−1.44376			−0.721882	−	0.692016i	$-0.756723\pi$
$463$	−31.0661			−1.44376			−0.721882	+	0.692016i	$0.756723\pi$
$464$		0			0
$465$	−7.67106	−	5.57335i	−0.355737	−	0.258458i
$466$		0			0
$467$	−0.0202189	+	0.0622273i	−0.000935618	+	0.00287954i	−0.951523	−	0.307577i	$-0.900482\pi$
$467$	−0.0202189	+	0.0622273i	−0.000935618	+	0.00287954i	0.950588	+	0.310456i	$0.100482\pi$
$468$		0			0
$469$	−0.0616453	+	0.0447879i	−0.00284651	+	0.00206811i
$470$		0			0
$471$	3.27396	+	10.0762i	0.150856	+	0.464287i
$472$		0			0
$473$	−9.93153	−	8.53866i	−0.456652	−	0.392608i
$474$		0			0
$475$	−1.91293	−	5.88739i	−0.0877711	−	0.270132i
$476$		0			0
$477$	15.5349	−	11.2868i	0.711296	−	0.516787i
$478$		0			0
$479$	1.45785	−	4.48681i	0.0666110	−	0.205008i	−0.912211	−	0.409721i	$-0.865626\pi$
$479$	1.45785	−	4.48681i	0.0666110	−	0.205008i	0.978822	+	0.204713i	$0.0656261\pi$
$480$		0			0
$481$	0.734098	+	0.533353i	0.0334720	+	0.0243188i
$482$		0			0
$483$	0.774934			0.0352607
$484$		0			0
$485$	−9.17655			−0.416686
$486$		0			0
$487$	15.0523	+	10.9362i	0.682087	+	0.495565i	0.874049	−	0.485837i	$-0.161485\pi$
$487$	15.0523	+	10.9362i	0.682087	+	0.495565i	−0.191963	+	0.981402i	$0.561485\pi$
$488$		0			0
$489$	−7.14784	+	21.9988i	−0.323236	+	0.994819i
$490$		0			0
$491$	10.3340	−	7.50810i	0.466367	−	0.338836i	−0.329656	−	0.944101i	$-0.606933\pi$
$491$	10.3340	−	7.50810i	0.466367	−	0.338836i	0.796024	+	0.605265i	$0.206933\pi$
$492$		0			0
$493$	0.683203	+	2.10268i	0.0307699	+	0.0947001i
$494$		0			0
$495$	6.11822	+	5.26015i	0.274993	+	0.236426i
$496$		0			0
$497$	−0.327707	−	1.00858i	−0.0146997	−	0.0452409i
$498$		0			0
$499$	4.10103	−	2.97957i	0.183587	−	0.133384i	−0.492196	−	0.870485i	$-0.663806\pi$
$499$	4.10103	−	2.97957i	0.183587	−	0.133384i	0.675783	+	0.737100i	$0.263806\pi$
$500$		0			0
$501$	15.1336	−	46.5763i	0.676117	−	2.08088i
$502$		0			0
$503$	−19.8230	−	14.4023i	−0.883865	−	0.642166i	0.0504059	−	0.998729i	$-0.483949\pi$
$503$	−19.8230	−	14.4023i	−0.883865	−	0.642166i	−0.934271	+	0.356563i	$0.883949\pi$
$504$		0			0
$505$	−7.94431			−0.353517
$506$		0			0
$507$	−2.45574			−0.109063
$508$		0			0
$509$	2.64945	+	1.92494i	0.117435	+	0.0853213i	0.644952	−	0.764223i	$-0.276877\pi$
$509$	2.64945	+	1.92494i	0.117435	+	0.0853213i	−0.527518	+	0.849544i	$0.676877\pi$
$510$		0			0
$511$	−0.115847	+	0.356541i	−0.00512477	+	0.0157724i
$512$		0			0
$513$	0.0866336	−	0.0629430i	0.00382497	−	0.00277900i
$514$		0			0
$515$	1.45486	+	4.47759i	0.0641087	+	0.197306i
$516$		0			0
$517$	−2.90447	−	12.2747i	−0.127738	−	0.539839i
$518$		0			0
$519$	11.6417	+	35.8296i	0.511015	+	1.57274i
$520$		0			0
$521$	−29.8883	+	21.7151i	−1.30943	+	0.951357i	−0.309431	+	0.950922i	$0.600138\pi$
$521$	−29.8883	+	21.7151i	−1.30943	+	0.951357i	−1.00000		0.000434844i	$0.999862\pi$
$522$		0			0
$523$	10.1798	−	31.3302i	0.445131	−	1.36997i	−0.437209	−	0.899360i	$-0.644033\pi$
$523$	10.1798	−	31.3302i	0.445131	−	1.36997i	0.882340	−	0.470613i	$-0.155967\pi$
$524$		0			0
$525$	0.660624	+	0.479972i	0.0288320	+	0.0209477i
$526$		0			0
$527$	12.6234			0.549883
$528$		0			0
$529$	−5.91393			−0.257127
$530$		0			0
$531$	−11.5979	−	8.42637i	−0.503306	−	0.365673i
$532$		0			0
$533$	2.61382	−	8.04451i	0.113217	−	0.348447i
$534$		0			0
$535$	−6.80953	+	4.94741i	−0.294402	+	0.213895i
$536$		0			0
$537$	6.55768	+	20.1825i	0.282985	+	0.870937i
$538$		0			0
$539$	−19.8183	+	12.0557i	−0.853633	+	0.519275i
$540$		0			0
$541$	10.4485	+	32.1571i	0.449214	+	1.38254i	0.877795	+	0.479036i	$0.159014\pi$
$541$	10.4485	+	32.1571i	0.449214	+	1.38254i	−0.428581	+	0.903503i	$0.640986\pi$
$542$		0			0
$543$	6.11706	−	4.44430i	0.262508	−	0.190723i
$544$		0			0
$545$	2.49699	−	7.68495i	0.106959	−	0.329187i
$546$		0			0
$547$	32.4659	+	23.5878i	1.38814	+	1.00854i	0.996066	+	0.0886098i	$0.0282424\pi$
$547$	32.4659	+	23.5878i	1.38814	+	1.00854i	0.392074	+	0.919934i	$0.371758\pi$
$548$		0			0
$549$	−22.6208			−0.965433
$550$		0			0
$551$	−1.19732			−0.0510075
$552$		0			0
$553$	−0.536077	−	0.389483i	−0.0227963	−	0.0165625i
$554$		0			0
$555$	0.552741	−	1.70116i	0.0234625	−	0.0722103i
$556$		0			0
$557$	5.96037	−	4.33046i	0.252549	−	0.183488i	−0.454307	−	0.890845i	$-0.650113\pi$
$557$	5.96037	−	4.33046i	0.252549	−	0.183488i	0.706856	+	0.707358i	$0.250113\pi$
$558$		0			0
$559$	−1.22032	−	3.75576i	−0.0516141	−	0.158852i
$560$		0			0
$561$	−21.3032	−	1.74671i	−0.899422	−	0.0737463i
$562$		0			0
$563$	−14.6349	−	45.0417i	−0.616788	−	1.89828i	−0.368746	−	0.929530i	$-0.620213\pi$
$563$	−14.6349	−	45.0417i	−0.616788	−	1.89828i	−0.248042	−	0.968749i	$-0.579787\pi$
$564$		0			0
$565$	7.17789	−	5.21504i	0.301976	−	0.219399i
$566$		0			0
$567$	0.210124	−	0.646694i	0.00882436	−	0.0271586i
$568$		0			0
$569$	14.6428	+	10.6386i	0.613859	+	0.445995i	0.850771	−	0.525536i	$-0.176135\pi$
$569$	14.6428	+	10.6386i	0.613859	+	0.445995i	−0.236912	+	0.971531i	$0.576135\pi$
$570$		0			0
$571$	31.8111			1.33125			0.665626	−	0.746285i	$-0.268165\pi$
$571$	31.8111			1.33125			0.665626	+	0.746285i	$0.268165\pi$
$572$		0			0
$573$	−3.64084			−0.152098
$574$		0			0
$575$	14.5657	+	10.5826i	0.607433	+	0.441326i
$576$		0			0
$577$	0.0585889	−	0.180318i	0.00243909	−	0.00750674i	−0.949830	−	0.312768i	$-0.898744\pi$
$577$	0.0585889	−	0.180318i	0.00243909	−	0.00750674i	0.952269	+	0.305261i	$0.0987438\pi$
$578$		0			0
$579$	10.8575	−	7.88843i	0.451222	−	0.327832i
$580$		0			0
$581$	−0.0574522	−	0.176820i	−0.00238352	−	0.00733572i
$582$		0			0
$583$	8.10514	−	19.3880i	0.335681	−	0.802968i
$584$		0			0
$585$	0.751766	+	2.31370i	0.0310817	+	0.0956596i
$586$		0			0
$587$	−4.88752	+	3.55099i	−0.201729	+	0.146565i	−0.684064	−	0.729422i	$-0.739789\pi$
$587$	−4.88752	+	3.55099i	−0.201729	+	0.146565i	0.482334	+	0.875987i	$0.339789\pi$
$588$		0			0
$589$	−2.11252	+	6.50166i	−0.0870447	+	0.267896i
$590$		0			0
$591$	−14.8744	−	10.8069i	−0.611852	−	0.444537i
$592$		0			0
$593$	17.7680			0.729644			0.364822	−	0.931077i	$-0.381130\pi$
$593$	17.7680			0.729644			0.364822	+	0.931077i	$0.381130\pi$
$594$		0			0
$595$	0.160820			0.00659299
$596$		0			0
$597$	−36.6114	−	26.5997i	−1.49840	−	1.08865i
$598$		0			0
$599$	−9.39722	+	28.9217i	−0.383960	+	1.18171i	0.553272	+	0.833001i	$0.313379\pi$
$599$	−9.39722	+	28.9217i	−0.383960	+	1.18171i	−0.937232	+	0.348707i	$0.886621\pi$
$600$		0			0
$601$	6.89222	−	5.00749i	0.281139	−	0.204260i	−0.438275	−	0.898841i	$-0.644410\pi$
$601$	6.89222	−	5.00749i	0.281139	−	0.204260i	0.719414	+	0.694581i	$0.244410\pi$
$602$		0			0
$603$	−0.934769	−	2.87692i	−0.0380667	−	0.117157i
$604$		0			0
$605$	8.71190	+	1.43830i	0.354189	+	0.0584752i
$606$		0			0
$607$	−8.23929	−	25.3579i	−0.334423	−	1.02925i	−0.967006	−	0.254755i	$-0.918005\pi$
$607$	−8.23929	−	25.3579i	−0.334423	−	1.02925i	0.632583	−	0.774492i	$-0.281995\pi$
$608$		0			0
$609$	0.127776	−	0.0928345i	0.00517774	−	0.00376185i
$610$		0			0
$611$	1.17524	−	3.61701i	0.0475450	−	0.146329i
$612$		0			0
$613$	24.9382	+	18.1187i	1.00725	+	0.731807i	0.963630	−	0.267242i	$-0.0861122\pi$
$613$	24.9382	+	18.1187i	1.00725	+	0.731807i	0.0436161	+	0.999048i	$0.486112\pi$
$614$		0			0
$615$	−16.6739			−0.672355
$616$		0			0
$617$	−31.5361			−1.26960			−0.634798	−	0.772678i	$-0.718917\pi$
$617$	−31.5361			−1.26960			−0.634798	+	0.772678i	$0.718917\pi$
$618$		0			0
$619$	−9.01513	−	6.54987i	−0.362348	−	0.263262i	0.391682	−	0.920100i	$-0.371893\pi$
$619$	−9.01513	−	6.54987i	−0.362348	−	0.263262i	−0.754031	+	0.656839i	$0.771893\pi$
$620$		0			0
$621$	−0.0962430	+	0.296206i	−0.00386210	+	0.0118863i
$622$		0			0
$623$	0.424234	−	0.308224i	0.0169966	−	0.0123487i
$624$		0			0
$625$	4.86701	+	14.9791i	0.194681	+	0.599165i
$626$		0			0
$627$	4.46473	−	10.6799i	0.178304	−	0.426514i
$628$		0			0
$629$	0.735866	+	2.26476i	0.0293409	+	0.0903020i
$630$		0			0
$631$	−37.0193	+	26.8961i	−1.47371	+	1.07072i	−0.494197	+	0.869350i	$0.664538\pi$
$631$	−37.0193	+	26.8961i	−1.47371	+	1.07072i	−0.979516	+	0.201366i	$0.935462\pi$
$632$		0			0
$633$	6.80103	−	20.9314i	0.270317	−	0.831950i
$634$		0			0
$635$	3.85290	+	2.79930i	0.152898	+	0.111087i
$636$		0			0
$637$	−6.99417			−0.277119
$638$		0			0
$639$	42.1001			1.66545
$640$		0			0
$641$	13.2797	+	9.64824i	0.524515	+	0.381082i	0.818302	−	0.574788i	$-0.194916\pi$
$641$	13.2797	+	9.64824i	0.524515	+	0.381082i	−0.293787	+	0.955871i	$0.594916\pi$
$642$		0			0
$643$	11.5514	−	35.5515i	0.455542	−	1.40201i	−0.414956	−	0.909842i	$-0.636203\pi$
$643$	11.5514	−	35.5515i	0.455542	−	1.40201i	0.870498	−	0.492173i	$-0.163797\pi$
$644$		0			0
$645$	−6.29785	+	4.57565i	−0.247977	+	0.180166i
$646$		0			0
$647$	−2.84563	−	8.75796i	−0.111873	−	0.344311i	0.879409	−	0.476068i	$-0.157938\pi$
$647$	−2.84563	−	8.75796i	−0.111873	−	0.344311i	−0.991282	+	0.131757i	$0.957938\pi$
$648$		0			0
$649$	−15.6359	−	1.28203i	−0.613763	−	0.0503243i
$650$		0			0
$651$	−0.278664	−	0.857640i	−0.0109217	−	0.0336136i
$652$		0			0
$653$	5.60133	−	4.06960i	0.219197	−	0.159256i	−0.472768	−	0.881187i	$-0.656745\pi$
$653$	5.60133	−	4.06960i	0.219197	−	0.159256i	0.691965	+	0.721931i	$0.256745\pi$
$654$		0			0
$655$	−1.91008	+	5.87862i	−0.0746330	+	0.229697i
$656$		0			0
$657$	−12.0404	−	8.74785i	−0.469740	−	0.341286i
$658$		0			0
$659$	10.5867			0.412400			0.206200	−	0.978510i	$-0.433890\pi$
$659$	10.5867			0.412400			0.206200	+	0.978510i	$0.433890\pi$
$660$		0			0
$661$	28.1239			1.09389			0.546946	−	0.837168i	$-0.315790\pi$
$661$	28.1239			1.09389			0.546946	+	0.837168i	$0.315790\pi$
$662$		0			0
$663$	−5.21388	−	3.78811i	−0.202490	−	0.147118i
$664$		0			0
$665$	−0.0269132	+	0.0828303i	−0.00104365	+	0.00321202i
$666$		0			0
$667$	2.81725	−	2.04685i	0.109085	−	0.0792545i
$668$		0			0
$669$	6.39178	+	19.6719i	0.247121	+	0.760559i
$670$		0			0
$671$	−21.1494	+	12.8654i	−0.816462	+	0.496663i
$672$		0			0
$673$	−7.57205	−	23.3044i	−0.291881	−	0.898317i	−0.984251	−	0.176775i	$-0.943434\pi$
$673$	−7.57205	−	23.3044i	−0.291881	−	0.898317i	0.692370	−	0.721542i	$-0.256566\pi$
$674$		0			0
$675$	−0.265507	+	0.192902i	−0.0102194	+	0.00742482i
$676$		0			0
$677$	5.26960	−	16.2182i	0.202527	−	0.623315i	−0.797279	−	0.603612i	$-0.793728\pi$
$677$	5.26960	−	16.2182i	0.202527	−	0.623315i	0.999806	−	0.0197034i	$-0.00627219\pi$
$678$		0			0
$679$	−0.706054	−	0.512978i	−0.0270959	−	0.0196863i
$680$		0			0
$681$	27.3822			1.04929
$682$		0			0
$683$	−14.8342			−0.567615			−0.283808	−	0.958881i	$-0.591598\pi$
$683$	−14.8342			−0.567615			−0.283808	+	0.958881i	$0.591598\pi$
$684$		0			0
$685$	−2.83456	−	2.05943i	−0.108303	−	0.0786868i
$686$		0			0
$687$	−18.4015	+	56.6341i	−0.702062	+	2.16073i
$688$		0			0
$689$	5.12589	−	3.72418i	0.195281	−	0.141880i
$690$		0			0
$691$	1.83192	+	5.63806i	0.0696894	+	0.214482i	0.979836	−	0.199805i	$-0.0640309\pi$
$691$	1.83192	+	5.63806i	0.0696894	+	0.214482i	−0.910146	+	0.414287i	$0.864031\pi$
$692$		0			0
$693$	0.176695	+	0.746736i	0.00671208	+	0.0283662i
$694$		0			0
$695$	5.03090	+	15.4835i	0.190833	+	0.587323i
$696$		0			0
$697$	17.9586	−	13.0477i	0.680229	−	0.494215i
$698$		0			0
$699$	−8.71348	+	26.8173i	−0.329574	+	1.01433i
$700$		0			0
$701$	−25.8448	−	18.7774i	−0.976146	−	0.709211i	−0.0193019	−	0.999814i	$-0.506144\pi$
$701$	−25.8448	−	18.7774i	−0.976146	−	0.709211i	−0.956844	+	0.290602i	$0.906144\pi$
$702$		0			0
$703$	−1.28961			−0.0486386
$704$		0			0
$705$	−7.49698			−0.282353
$706$		0			0
$707$	−0.611244	−	0.444095i	−0.0229882	−	0.0167019i
$708$		0			0
$709$	6.63506	−	20.4206i	0.249185	−	0.766913i	−0.745735	−	0.666243i	$-0.767901\pi$
$709$	6.63506	−	20.4206i	0.249185	−	0.766913i	0.994920	−	0.100670i	$-0.0320986\pi$
$710$		0			0
$711$	21.2817	−	15.4621i	0.798128	−	0.579874i
$712$		0			0
$713$	−6.14410	−	18.9096i	−0.230098	−	0.708170i
$714$		0			0
$715$	2.01876	+	1.73563i	0.0754973	+	0.0649090i
$716$		0			0
$717$	6.13189	+	18.8720i	0.229000	+	0.704788i
$718$		0			0
$719$	−20.8822	+	15.1718i	−0.778775	+	0.565813i	−0.904611	−	0.426238i	$-0.859839\pi$
$719$	−20.8822	+	15.1718i	−0.778775	+	0.565813i	0.125836	+	0.992051i	$0.459839\pi$
$720$		0			0
$721$	−0.138363	+	0.425839i	−0.00515293	+	0.0158591i
$722$		0			0
$723$	−24.8221	−	18.0343i	−0.923145	−	0.670704i
$724$		0			0
$725$	3.66945			0.136280
$726$		0			0
$727$	−20.9442			−0.776776			−0.388388	−	0.921496i	$-0.626968\pi$
$727$	−20.9442			−0.776776			−0.388388	+	0.921496i	$0.626968\pi$
$728$		0			0
$729$	22.2880	+	16.1931i	0.825480	+	0.599746i
$730$		0			0
$731$	3.20254	−	9.85640i	0.118450	−	0.364552i
$732$		0			0
$733$	−20.0572	+	14.5724i	−0.740828	+	0.538243i	−0.892970	−	0.450116i	$-0.851383\pi$
$733$	−20.0572	+	14.5724i	−0.740828	+	0.538243i	0.152142	+	0.988359i	$0.451383\pi$
$734$		0			0
$735$	4.26051	+	13.1125i	0.157151	+	0.483662i
$736$		0			0
$737$	−2.51019	−	2.15814i	−0.0924640	−	0.0794962i
$738$		0			0
$739$	−14.4308	−	44.4133i	−0.530844	−	1.63377i	−0.752461	−	0.658637i	$-0.771133\pi$
$739$	−14.4308	−	44.4133i	−0.530844	−	1.63377i	0.221616	−	0.975134i	$-0.428867\pi$
$740$		0			0
$741$	2.82360	−	2.05147i	0.103728	−	0.0753626i
$742$		0			0
$743$	−16.5556	+	50.9528i	−0.607365	+	1.86928i	−0.127727	+	0.991809i	$0.540768\pi$
$743$	−16.5556	+	50.9528i	−0.607365	+	1.86928i	−0.479638	+	0.877467i	$0.659232\pi$
$744$		0			0
$745$	−6.14425	−	4.46406i	−0.225108	−	0.163551i
$746$		0			0
$747$	7.38081			0.270050
$748$		0			0
$749$	−0.800498			−0.0292496
$750$		0			0
$751$	−0.866159	−	0.629302i	−0.0316066	−	0.0229635i	0.571870	−	0.820344i	$-0.306218\pi$
$751$	−0.866159	−	0.629302i	−0.0316066	−	0.0229635i	−0.603476	+	0.797381i	$0.706218\pi$
$752$		0			0
$753$	7.17659	−	22.0873i	0.261529	−	0.804904i
$754$		0			0
$755$	−8.95809	+	6.50844i	−0.326018	+	0.236866i
$756$		0			0
$757$	−2.99137	−	9.20648i	−0.108723	−	0.334615i	0.881863	−	0.471506i	$-0.156289\pi$
$757$	−2.99137	−	9.20648i	−0.108723	−	0.334615i	−0.990586	+	0.136890i	$0.956289\pi$
$758$		0			0
$759$	7.75224	+	32.7620i	0.281389	+	1.18919i
$760$		0			0
$761$	5.56532	+	17.1283i	0.201743	+	0.620900i	0.999831	+	0.0183601i	$0.00584453\pi$
$761$	5.56532	+	17.1283i	0.201743	+	0.620900i	−0.798089	+	0.602540i	$0.794155\pi$
$762$		0			0
$763$	0.621717	−	0.451704i	0.0225077	−	0.0163528i
$764$		0			0
$765$	−1.97289	+	6.07193i	−0.0713300	+	0.219531i
$766$		0			0
$767$	−3.82683	−	2.78036i	−0.138179	−	0.100393i
$768$		0			0
$769$	−21.7229			−0.783350			−0.391675	−	0.920104i	$-0.628104\pi$
$769$	−21.7229			−0.783350			−0.391675	+	0.920104i	$0.628104\pi$
$770$		0			0
$771$	36.8591			1.32745
$772$		0			0
$773$	−16.5958	−	12.0575i	−0.596908	−	0.433679i	0.247872	−	0.968793i	$-0.420269\pi$
$773$	−16.5958	−	12.0575i	−0.596908	−	0.433679i	−0.844780	+	0.535114i	$0.820269\pi$
$774$		0			0
$775$	6.47427	−	19.9257i	0.232563	−	0.715754i
$776$		0			0
$777$	0.137625	−	0.0999904i	0.00493727	−	0.00358714i
$778$		0			0
$779$	3.71483	+	11.4331i	0.133098	+	0.409632i
$780$		0			0
$781$	39.3615	−	23.9441i	1.40847	−	0.856786i
$782$		0			0
$783$	0.0196153	+	0.0603697i	0.000700994	+	0.00215744i
$784$		0			0
$785$	2.80172	−	2.03557i	0.0999978	−	0.0726526i
$786$		0			0
$787$	3.42592	−	10.5439i	0.122121	−	0.375850i	−0.871245	−	0.490849i	$-0.836687\pi$
$787$	3.42592	−	10.5439i	0.122121	−	0.375850i	0.993366	+	0.114999i	$0.0366866\pi$
$788$		0			0
$789$	45.8310	+	33.2981i	1.63163	+	1.18545i
$790$		0			0
$791$	0.843801			0.0300021
$792$		0			0
$793$	−7.46394			−0.265052
$794$		0			0
$795$	−10.1044	−	7.34131i	−0.358368	−	0.260369i
$796$		0			0
$797$	−4.17894	+	12.8614i	−0.148026	+	0.455576i	−0.997388	−	0.0722348i	$-0.976987\pi$
$797$	−4.17894	+	12.8614i	−0.148026	+	0.455576i	0.849362	+	0.527811i	$0.176987\pi$
$798$		0			0
$799$	8.07461	−	5.86654i	0.285659	−	0.207543i
$800$		0			0
$801$	6.43295	+	19.7986i	0.227297	+	0.699548i
$802$		0			0
$803$	−16.2324	−	1.33095i	−0.572830	−	0.0469680i
$804$		0			0
$805$	−0.0782751	−	0.240906i	−0.00275884	−	0.00849082i
$806$		0			0
$807$	−40.9336	+	29.7400i	−1.44093	+	1.04690i
$808$		0			0
$809$	−5.24897	+	16.1547i	−0.184544	+	0.567968i	−0.999940	−	0.0109352i	$-0.996519\pi$
$809$	−5.24897	+	16.1547i	−0.184544	+	0.567968i	0.815396	+	0.578903i	$0.196519\pi$
$810$		0			0
$811$	−13.9079	−	10.1047i	−0.488372	−	0.354823i	0.316186	−	0.948697i	$-0.397598\pi$
$811$	−13.9079	−	10.1047i	−0.488372	−	0.354823i	−0.804558	+	0.593874i	$0.797598\pi$
$812$		0			0
$813$	−15.7216			−0.551382
$814$		0			0
$815$	7.56082			0.264844
$816$		0			0
$817$	4.54059	+	3.29893i	0.158855	+	0.115415i
$818$		0			0
$819$	−0.0714962	+	0.220043i	−0.00249828	+	0.00768892i
$820$		0			0
$821$	17.8865	−	12.9953i	0.624244	−	0.453540i	−0.230157	−	0.973153i	$-0.573924\pi$
$821$	17.8865	−	12.9953i	0.624244	−	0.453540i	0.854401	+	0.519614i	$0.173924\pi$
$822$		0			0
$823$	−14.6675	−	45.1421i	−0.511279	−	1.57355i	−0.789953	−	0.613168i	$-0.789895\pi$
$823$	−14.6675	−	45.1421i	−0.511279	−	1.57355i	0.278674	−	0.960386i	$-0.410105\pi$
$824$		0			0
$825$	−13.6831	+	32.7308i	−0.476385	+	1.13954i
$826$		0			0
$827$	8.34177	+	25.6733i	0.290072	+	0.892749i	0.984832	+	0.173508i	$0.0555103\pi$
$827$	8.34177	+	25.6733i	0.290072	+	0.892749i	−0.694761	+	0.719241i	$0.744490\pi$
$828$		0			0
$829$	−4.47032	+	3.24788i	−0.155261	+	0.112803i	−0.662703	−	0.748882i	$-0.730591\pi$
$829$	−4.47032	+	3.24788i	−0.155261	+	0.112803i	0.507443	+	0.861686i	$0.330591\pi$
$830$		0			0
$831$	−14.5749	+	44.8569i	−0.505598	+	1.55607i
$832$		0			0
$833$	−14.8496	−	10.7889i	−0.514508	−	0.373812i
$834$		0			0
$835$	−16.0079			−0.553977
$836$		0			0
$837$	0.362427			0.0125273
$838$		0			0
$839$	20.0093	+	14.5376i	0.690798	+	0.501894i	0.876922	−	0.480632i	$-0.159593\pi$
$839$	20.0093	+	14.5376i	0.690798	+	0.501894i	−0.186125	+	0.982526i	$0.559593\pi$
$840$		0			0
$841$	−8.74217	+	26.9056i	−0.301454	+	0.927781i
$842$		0			0
$843$	−48.2016	+	35.0205i	−1.66015	+	1.20617i
$844$		0			0
$845$	0.248052	+	0.763424i	0.00853324	+	0.0262626i
$846$		0			0
$847$	0.589901	+	0.597668i	0.0202692	+	0.0205361i
$848$		0			0
$849$	10.9220	+	33.6146i	0.374843	+	1.15365i
$850$		0			0
$851$	3.03441	−	2.20463i	0.104018	−	0.0755738i
$852$		0			0
$853$	6.15239	−	18.9351i	0.210654	−	0.648326i	−0.788780	−	0.614676i	$-0.789287\pi$
$853$	6.15239	−	18.9351i	0.210654	−	0.648326i	0.999434	−	0.0336499i	$-0.0107131\pi$
$854$		0			0
$855$	−2.79718	−	2.03227i	−0.0956616	−	0.0695022i
$856$		0			0
$857$	38.1677			1.30378			0.651892	−	0.758312i	$-0.273975\pi$
$857$	38.1677			1.30378			0.651892	+	0.758312i	$0.273975\pi$
$858$		0			0
$859$	51.0250			1.74095			0.870475	−	0.492213i	$-0.163812\pi$
$859$	51.0250			1.74095			0.870475	+	0.492213i	$0.163812\pi$
$860$		0			0
$861$	−1.28291	−	0.932086i	−0.0437213	−	0.0317654i
$862$		0			0
$863$	2.02435	−	6.23030i	0.0689096	−	0.212082i	−0.910672	−	0.413131i	$-0.864435\pi$
$863$	2.02435	−	6.23030i	0.0689096	−	0.212082i	0.979581	+	0.201049i	$0.0644351\pi$
$864$		0			0
$865$	9.96252	−	7.23820i	0.338736	−	0.246106i
$866$		0			0
$867$	7.67429	+	23.6190i	0.260633	+	0.802145i
$868$		0			0
$869$	11.1035	−	26.5601i	0.376659	−	0.900990i
$870$		0			0
$871$	−0.308435	−	0.949266i	−0.0104509	−	0.0321647i
$872$		0			0
$873$	28.0297	−	20.3647i	0.948660	−	0.689242i
$874$		0			0
$875$	0.177165	−	0.545256i	0.00598925	−	0.0184330i
$876$		0			0
$877$	15.2891	+	11.1082i	0.516276	+	0.375096i	0.815199	−	0.579181i	$-0.196627\pi$
$877$	15.2891	+	11.1082i	0.516276	+	0.375096i	−0.298923	+	0.954277i	$0.596627\pi$
$878$		0			0
$879$	22.5688			0.761225
$880$		0			0
$881$	53.0305			1.78664			0.893322	−	0.449418i	$-0.148369\pi$
$881$	53.0305			1.78664			0.893322	+	0.449418i	$0.148369\pi$
$882$		0			0
$883$	18.7048	+	13.5898i	0.629466	+	0.457334i	0.856215	−	0.516619i	$-0.172810\pi$
$883$	18.7048	+	13.5898i	0.629466	+	0.457334i	−0.226749	+	0.973953i	$0.572810\pi$
$884$		0			0
$885$	−2.88142	+	8.86811i	−0.0968580	+	0.298098i
$886$		0			0
$887$	16.7275	−	12.1532i	0.561653	−	0.408065i	−0.270410	−	0.962745i	$-0.587159\pi$
$887$	16.7275	−	12.1532i	0.561653	−	0.408065i	0.832064	+	0.554680i	$0.187159\pi$
$888$		0			0
$889$	0.139963	+	0.430762i	0.00469421	+	0.0144473i
$890$		0			0
$891$	29.4424	+	2.41407i	0.986358	+	0.0808745i
$892$		0			0
$893$	1.67028	+	5.14058i	0.0558937	+	0.172023i
$894$		0			0
$895$	5.61180	−	4.07721i	0.187582	−	0.136286i
$896$		0			0
$897$	−3.13680	+	9.65407i	−0.104735	+	0.322340i
$898$		0			0
$899$	−3.27838	−	2.38188i	−0.109340	−	0.0794403i
$900$		0			0
$901$	16.6277			0.553949
$902$		0			0
$903$	−0.740347			−0.0246372
$904$		0			0
$905$	−1.99949	−	1.45271i	−0.0664653	−	0.0482899i
$906$		0			0
$907$	9.18739	−	28.2759i	0.305062	−	0.938885i	−0.674592	−	0.738191i	$-0.735680\pi$
$907$	9.18739	−	28.2759i	0.305062	−	0.938885i	0.979654	−	0.200694i	$-0.0643198\pi$
$908$		0			0
$909$	24.2658	−	17.6301i	0.804845	−	0.584754i
$910$		0			0
$911$	−12.1376	−	37.3558i	−0.402138	−	1.23765i	−0.923262	−	0.384171i	$-0.874487\pi$
$911$	−12.1376	−	37.3558i	−0.402138	−	1.23765i	0.521124	−	0.853481i	$-0.325513\pi$
$912$		0			0
$913$	6.90070	−	4.19778i	0.228380	−	0.138926i
$914$		0			0
$915$	4.54667	+	13.9932i	0.150308	+	0.462601i
$916$		0			0
$917$	−0.475584	+	0.345532i	−0.0157052	+	0.0114105i
$918$		0			0
$919$	−10.7963	+	33.2275i	−0.356136	+	1.09607i	0.599212	+	0.800591i	$0.295481\pi$
$919$	−10.7963	+	33.2275i	−0.356136	+	1.09607i	−0.955348	+	0.295484i	$0.904519\pi$
$920$		0			0
$921$	51.4771	+	37.4003i	1.69623	+	1.23238i
$922$		0			0
$923$	13.8913			0.457237
$924$		0			0
$925$	3.95230			0.129951
$926$		0			0
$927$	−14.3806	−	10.4481i	−0.472320	−	0.343161i
$928$		0			0
$929$	−3.17452	+	9.77017i	−0.104153	+	0.320549i	−0.989531	−	0.144323i	$-0.953900\pi$
$929$	−3.17452	+	9.77017i	−0.104153	+	0.320549i	0.885378	+	0.464872i	$0.153900\pi$
$930$		0			0
$931$	8.04187	−	5.84276i	0.263561	−	0.191489i
$932$		0			0
$933$	8.72595	+	26.8557i	0.285675	+	0.879217i
$934$		0			0
$935$	1.60880	+	6.79902i	0.0526135	+	0.222352i
$936$		0			0
$937$	−8.26364	−	25.4329i	−0.269961	−	0.830856i	−0.990509	−	0.137450i	$-0.956109\pi$
$937$	−8.26364	−	25.4329i	−0.269961	−	0.830856i	0.720547	−	0.693406i	$-0.243891\pi$
$938$		0			0
$939$	−57.8449	+	42.0268i	−1.88770	+	1.37149i
$940$		0			0
$941$	−13.2549	+	40.7943i	−0.432096	+	1.32986i	0.463937	+	0.885868i	$0.346436\pi$
$941$	−13.2549	+	40.7943i	−0.432096	+	1.32986i	−0.896033	+	0.443987i	$0.853564\pi$
$942$		0			0
$943$	−28.2860	−	20.5510i	−0.921120	−	0.669233i
$944$		0			0
$945$	0.00461728			0.000150200
$946$		0			0
$947$	57.7191			1.87562			0.937810	−	0.347150i	$-0.112851\pi$
$947$	57.7191			1.87562			0.937810	+	0.347150i	$0.112851\pi$
$948$		0			0
$949$	−3.97283	−	2.88643i	−0.128963	−	0.0936974i
$950$		0			0
$951$	4.55132	−	14.0075i	0.147587	−	0.454225i
$952$		0			0
$953$	18.0348	−	13.1030i	0.584203	−	0.424449i	−0.256034	−	0.966668i	$-0.582416\pi$
$953$	18.0348	−	13.1030i	0.584203	−	0.424449i	0.840237	+	0.542219i	$0.182416\pi$
$954$		0			0
$955$	0.367757	+	1.13184i	0.0119003	+	0.0366255i
$956$		0			0
$957$	5.20302	+	4.47331i	0.168190	+	0.144601i
$958$		0			0
$959$	−0.102970	−	0.316910i	−0.00332508	−	0.0102335i
$960$		0			0
$961$	6.36118	−	4.62167i	0.205199	−	0.149086i
$962$		0			0
$963$	9.82025	−	30.2236i	0.316453	−	0.973943i
$964$		0			0
$965$	−3.54900	−	2.57850i	−0.114246	−	0.0830049i
$966$		0			0
$967$	43.4144			1.39611			0.698057	−	0.716043i	$-0.254048\pi$
$967$	43.4144			1.39611			0.698057	+	0.716043i	$0.254048\pi$
$968$		0			0
$969$	9.15939			0.294242
$970$		0			0
$971$	3.40020	+	2.47039i	0.109118	+	0.0792786i	0.641006	−	0.767536i	$-0.278517\pi$
$971$	3.40020	+	2.47039i	0.109118	+	0.0792786i	−0.531888	+	0.846815i	$0.678517\pi$
$972$		0			0
$973$	−0.478461	+	1.47255i	−0.0153388	+	0.0472078i
$974$		0			0
$975$	−8.65355	+	6.28717i	−0.277135	+	0.201351i
$976$		0			0
$977$	−5.61442	−	17.2794i	−0.179621	−	0.552817i	0.820193	−	0.572087i	$-0.193866\pi$
$977$	−5.61442	−	17.2794i	−0.179621	−	0.552817i	−0.999814	+	0.0192695i	$0.993866\pi$
$978$		0			0
$979$	17.2748	+	14.8520i	0.552104	+	0.474672i
$980$		0			0
$981$	9.42752	+	29.0149i	0.300998	+	0.926375i
$982$		0			0
$983$	−2.33456	+	1.69616i	−0.0744608	+	0.0540990i	−0.624393	−	0.781110i	$-0.714654\pi$
$983$	−2.33456	+	1.69616i	−0.0744608	+	0.0540990i	0.549932	+	0.835209i	$0.314654\pi$
$984$		0			0
$985$	−1.85713	+	5.71565i	−0.0591730	+	0.182116i
$986$		0			0
$987$	−0.576826	−	0.419088i	−0.0183606	−	0.0133397i
$988$		0			0
$989$	−16.3235			−0.519056
$990$		0			0
$991$	20.0936			0.638295			0.319147	−	0.947705i	$-0.396604\pi$
$991$	20.0936			0.638295			0.319147	+	0.947705i	$0.396604\pi$
$992$		0			0
$993$	−15.8822	−	11.5391i	−0.504006	−	0.366181i
$994$		0			0
$995$	−4.57106	+	14.0683i	−0.144912	+	0.445995i
$996$		0			0
$997$	−18.8652	+	13.7064i	−0.597468	+	0.434086i	−0.844979	−	0.534799i	$-0.820387\pi$
$997$	−18.8652	+	13.7064i	−0.597468	+	0.434086i	0.247512	+	0.968885i	$0.420387\pi$
$998$		0			0
$999$	0.0211273	+	0.0650232i	0.000668439	+	0.00205724i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.n.a.313.5	yes	20
11.3	even	5		6292.2.a.w.1.1		10
11.8	odd	10		6292.2.a.x.1.1		10
11.9	even	5	inner	572.2.n.a.53.5	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.n.a.53.5	✓	20	11.9	even	5	inner
572.2.n.a.313.5	yes	20	1.1	even	1	trivial
6292.2.a.w.1.1		10	11.3	even	5
6292.2.a.x.1.1		10	11.8	odd	10

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:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.98674 + 1.44345i) q^{3} +(0.248052 - 0.763424i) q^{5} +(0.0617615 - 0.0448724i) q^{7} +(0.936532 + 2.88235i) q^{9} +O(q^{10})\)	\(q+(1.98674 + 1.44345i) q^{3} +(0.248052 - 0.763424i) q^{5} +(0.0617615 - 0.0448724i) q^{7} +(0.936532 + 2.88235i) q^{9} +(2.51492 + 2.16221i) q^{11} +(0.309017 + 0.951057i) q^{13} +(1.59478 - 1.15868i) q^{15} +(-0.810966 + 2.49590i) q^{17} +(-1.14980 - 0.835375i) q^{19} +0.187475 q^{21} +4.13353 q^{23} +(3.52380 + 2.56019i) q^{25} +(-0.0232835 + 0.0716592i) q^{27} +(0.681561 - 0.495183i) q^{29} +(-1.48641 - 4.57469i) q^{31} +(1.87545 + 7.92592i) q^{33} +(-0.0189366 - 0.0582809i) q^{35} +(0.734098 - 0.533353i) q^{37} +(-0.758867 + 2.33555i) q^{39} +(-6.84307 - 4.97178i) q^{41} -3.94904 q^{43} +2.43276 q^{45} +(-3.07681 - 2.23543i) q^{47} +(-2.16132 + 6.65185i) q^{49} +(-5.21388 + 3.78811i) q^{51} +(-1.95792 - 6.02585i) q^{53} +(2.27452 - 1.38361i) q^{55} +(-1.07852 - 3.31934i) q^{57} +(-3.82683 + 2.78036i) q^{59} +(-2.30648 + 7.09863i) q^{61} +(0.187180 + 0.135994i) q^{63} +0.802712 q^{65} -0.998118 q^{67} +(8.21225 + 5.96655i) q^{69} +(4.29264 - 13.2114i) q^{71} +(-3.97283 + 2.88643i) q^{73} +(3.30536 + 10.1729i) q^{75} +(0.252349 + 0.0206909i) q^{77} +(-2.68220 - 8.25497i) q^{79} +(7.20592 - 5.23541i) q^{81} +(0.752569 - 2.31617i) q^{83} +(1.70427 + 1.23822i) q^{85} +2.06886 q^{87} +6.86890 q^{89} +(0.0617615 + 0.0448724i) q^{91} +(3.65023 - 11.2343i) q^{93} +(-0.922954 + 0.670566i) q^{95} +(-3.53266 - 10.8724i) q^{97} +(-3.87694 + 9.27387i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + q^{3} + q^{5} + 3 q^{7} + 12 q^{9}+O(q^{10}) \) 20 * q + q^3 + q^5 + 3 * q^7 + 12 * q^9	\( 20 q + q^{3} + q^{5} + 3 q^{7} + 12 q^{9} - q^{11} - 5 q^{13} + 14 q^{15} - 3 q^{17} - 7 q^{19} - 32 q^{21} - 30 q^{23} - 12 q^{25} + 13 q^{27} - 14 q^{29} + 11 q^{31} - 10 q^{33} - 10 q^{35} + 45 q^{37} - 4 q^{39} + 9 q^{41} - 8 q^{43} - 34 q^{45} + 39 q^{47} + 30 q^{49} - 55 q^{51} + 36 q^{53} + 11 q^{55} - 31 q^{57} - 31 q^{59} - 7 q^{61} + 14 q^{63} - 14 q^{65} + 26 q^{67} + 32 q^{69} + 33 q^{71} - 44 q^{73} + 37 q^{75} - 73 q^{77} + 21 q^{79} + 16 q^{81} - 25 q^{83} + 15 q^{85} + 32 q^{87} - 2 q^{89} + 3 q^{91} + 33 q^{93} - 37 q^{95} + 52 q^{97} - 8 q^{99}+O(q^{100}) \) 20 * q + q^3 + q^5 + 3 * q^7 + 12 * q^9 - q^11 - 5 * q^13 + 14 * q^15 - 3 * q^17 - 7 * q^19 - 32 * q^21 - 30 * q^23 - 12 * q^25 + 13 * q^27 - 14 * q^29 + 11 * q^31 - 10 * q^33 - 10 * q^35 + 45 * q^37 - 4 * q^39 + 9 * q^41 - 8 * q^43 - 34 * q^45 + 39 * q^47 + 30 * q^49 - 55 * q^51 + 36 * q^53 + 11 * q^55 - 31 * q^57 - 31 * q^59 - 7 * q^61 + 14 * q^63 - 14 * q^65 + 26 * q^67 + 32 * q^69 + 33 * q^71 - 44 * q^73 + 37 * q^75 - 73 * q^77 + 21 * q^79 + 16 * q^81 - 25 * q^83 + 15 * q^85 + 32 * q^87 - 2 * q^89 + 3 * q^91 + 33 * q^93 - 37 * q^95 + 52 * q^97 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more