LMFDB - Embedded newform 1008.2.r.k.673.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(337,1008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2, 0]))

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

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

chi := DirichletCharacter("1008.337");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.r (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			673.1
Root			$0.500000 - 0.224437i$ of defining polynomial
Character	$\chi$	$=$	1008.673
Dual form			1008.2.r.k.337.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.349814 + 1.69636i) q^{3} +(1.79418 + 3.10761i) q^{5} +(-0.500000 + 0.866025i) q^{7} +(-2.75526 - 1.18682i) q^{9} +O(q^{10})$	\(q+(-0.349814 + 1.69636i) q^{3} +(1.79418 + 3.10761i) q^{5} +(-0.500000 + 0.866025i) q^{7} +(-2.75526 - 1.18682i) q^{9} +(-1.40545 + 2.43430i) q^{11} +(-0.500000 - 0.866025i) q^{13} +(-5.89926 + 1.95649i) q^{15} -4.11126 q^{17} +0.888736 q^{19} +(-1.29418 - 1.15113i) q^{21} +(2.93818 + 5.08907i) q^{23} +(-3.93818 + 6.82112i) q^{25} +(2.97710 - 4.25874i) q^{27} +(0.849814 - 1.47192i) q^{29} +(-3.49381 - 6.05146i) q^{31} +(-3.63781 - 3.23569i) q^{33} -3.58836 q^{35} +4.76509 q^{37} +(1.64400 - 0.545231i) q^{39} +(2.70582 + 4.68661i) q^{41} +(2.60507 - 4.51212i) q^{43} +(-1.25526 - 10.6917i) q^{45} +(-1.33310 + 2.30900i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(1.43818 - 6.97418i) q^{51} -0.123644 q^{53} -10.0865 q^{55} +(-0.310892 + 1.50761i) q^{57} +(-4.43818 - 7.68715i) q^{59} +(-1.93818 + 3.35702i) q^{61} +(2.40545 - 1.79272i) q^{63} +(1.79418 - 3.10761i) q^{65} +(6.15452 + 10.6599i) q^{67} +(-9.66071 + 3.20397i) q^{69} +2.87636 q^{71} -10.6414 q^{73} +(-10.1934 - 9.06668i) q^{75} +(-1.40545 - 2.43430i) q^{77} +(-3.54325 + 6.13709i) q^{79} +(6.18292 + 6.53999i) q^{81} +(-2.05563 + 3.56046i) q^{83} +(-7.37636 - 12.7762i) q^{85} +(2.19963 + 1.95649i) q^{87} +9.60940 q^{89} +1.00000 q^{91} +(11.4876 - 3.80987i) q^{93} +(1.59455 + 2.76185i) q^{95} +(-3.66071 + 6.34053i) q^{97} +(6.76145 - 5.03913i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 4 q^{3} + 5 q^{5} - 3 q^{7} - 4 q^{9}+O(q^{10}) $ 6 * q + 4 * q^3 + 5 * q^5 - 3 * q^7 - 4 * q^9	$ 6 q + 4 q^{3} + 5 q^{5} - 3 q^{7} - 4 q^{9} - 2 q^{11} - 3 q^{13} - 11 q^{15} - 24 q^{17} + 6 q^{19} - 2 q^{21} - 6 q^{25} + 7 q^{27} - q^{29} - 3 q^{31} + 8 q^{33} - 10 q^{35} - 6 q^{37} - 2 q^{39} + 22 q^{41} - 3 q^{43} + 5 q^{45} - 9 q^{47} - 3 q^{49} - 9 q^{51} - 36 q^{53} + 12 q^{55} + 11 q^{57} - 9 q^{59} + 6 q^{61} + 8 q^{63} + 5 q^{65} - 39 q^{69} - 18 q^{71} + 6 q^{73} - 31 q^{75} - 2 q^{77} + 15 q^{79} + 32 q^{81} - 12 q^{83} - 9 q^{85} + q^{87} - 4 q^{89} + 6 q^{91} + 33 q^{93} + 16 q^{95} - 3 q^{97} + 46 q^{99}+O(q^{100}) $ 6 * q + 4 * q^3 + 5 * q^5 - 3 * q^7 - 4 * q^9 - 2 * q^11 - 3 * q^13 - 11 * q^15 - 24 * q^17 + 6 * q^19 - 2 * q^21 - 6 * q^25 + 7 * q^27 - q^29 - 3 * q^31 + 8 * q^33 - 10 * q^35 - 6 * q^37 - 2 * q^39 + 22 * q^41 - 3 * q^43 + 5 * q^45 - 9 * q^47 - 3 * q^49 - 9 * q^51 - 36 * q^53 + 12 * q^55 + 11 * q^57 - 9 * q^59 + 6 * q^61 + 8 * q^63 + 5 * q^65 - 39 * q^69 - 18 * q^71 + 6 * q^73 - 31 * q^75 - 2 * q^77 + 15 * q^79 + 32 * q^81 - 12 * q^83 - 9 * q^85 + q^87 - 4 * q^89 + 6 * q^91 + 33 * q^93 + 16 * q^95 - 3 * q^97 + 46 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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
$3$	−0.349814	+	1.69636i	−0.201965	+	0.979393i
$3$	−0.349814	+	1.69636i	−0.201965	+	0.979393i
$4$		0			0
$5$	1.79418	+	3.10761i	0.802383	+	1.38977i	0.918044	+	0.396479i	$0.129768\pi$
$5$	1.79418	+	3.10761i	0.802383	+	1.38977i	−0.115661	+	0.993289i	$0.536899\pi$
$6$		0			0
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$8$		0			0
$9$	−2.75526	−	1.18682i	−0.918420	−	0.395607i
$10$		0			0
$11$	−1.40545	+	2.43430i	−0.423758	+	0.733970i	−0.996304	−	0.0859026i	$-0.972623\pi$
$11$	−1.40545	+	2.43430i	−0.423758	+	0.733970i	0.572546	+	0.819873i	$0.305956\pi$
$12$		0			0
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i	0.788320	−	0.615265i	$-0.210951\pi$
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i	−0.926995	+	0.375073i	$0.877618\pi$
$14$		0			0
$15$	−5.89926	+	1.95649i	−1.52318	+	0.505163i
$16$		0			0
$17$	−4.11126			−0.997128			−0.498564	−	0.866853i	$-0.666139\pi$
$17$	−4.11126			−0.997128			−0.498564	+	0.866853i	$0.666139\pi$
$18$		0			0
$19$	0.888736			0.203890			0.101945	−	0.994790i	$-0.467493\pi$
$19$	0.888736			0.203890			0.101945	+	0.994790i	$0.467493\pi$
$20$		0			0
$21$	−1.29418	−	1.15113i	−0.282414	−	0.251196i
$22$		0			0
$23$	2.93818	+	5.08907i	0.612652	+	1.06115i	0.990792	+	0.135396i	$0.0432308\pi$
$23$	2.93818	+	5.08907i	0.612652	+	1.06115i	−0.378139	+	0.925749i	$0.623436\pi$
$24$		0			0
$25$	−3.93818	+	6.82112i	−0.787636	+	1.36422i
$26$		0			0
$27$	2.97710	−	4.25874i	0.572943	−	0.819595i
$28$		0			0
$29$	0.849814	−	1.47192i	0.157807	−	0.273329i	−0.776271	−	0.630399i	$-0.782891\pi$
$29$	0.849814	−	1.47192i	0.157807	−	0.273329i	0.934077	+	0.357071i	$0.116224\pi$
$30$		0			0
$31$	−3.49381	−	6.05146i	−0.627507	−	1.08687i	−0.988050	−	0.154131i	$-0.950742\pi$
$31$	−3.49381	−	6.05146i	−0.627507	−	1.08687i	0.360544	−	0.932742i	$-0.382591\pi$
$32$		0			0
$33$	−3.63781	−	3.23569i	−0.633261	−	0.563262i
$34$		0			0
$35$	−3.58836			−0.606544
$36$		0			0
$37$	4.76509			0.783376			0.391688	−	0.920098i	$-0.371891\pi$
$37$	4.76509			0.783376			0.391688	+	0.920098i	$0.371891\pi$
$38$		0			0
$39$	1.64400	−	0.545231i	0.263250	−	0.0873068i
$40$		0			0
$41$	2.70582	+	4.68661i	0.422578	+	0.731926i	0.996191	−	0.0872002i	$-0.0277920\pi$
$41$	2.70582	+	4.68661i	0.422578	+	0.731926i	−0.573613	+	0.819126i	$0.694459\pi$
$42$		0			0
$43$	2.60507	−	4.51212i	0.397270	−	0.688092i	−0.596118	−	0.802897i	$-0.703291\pi$
$43$	2.60507	−	4.51212i	0.397270	−	0.688092i	0.993388	+	0.114805i	$0.0366243\pi$
$44$		0			0
$45$	−1.25526	−	10.6917i	−0.187123	−	1.59382i
$46$		0			0
$47$	−1.33310	+	2.30900i	−0.194453	+	0.336803i	−0.946721	−	0.322055i	$-0.895627\pi$
$47$	−1.33310	+	2.30900i	−0.194453	+	0.336803i	0.752268	+	0.658857i	$0.228960\pi$
$48$		0			0
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$		0			0
$51$	1.43818	−	6.97418i	0.201385	−	0.976580i
$52$		0			0
$53$	−0.123644			−0.0169838			−0.00849190	−	0.999964i	$-0.502703\pi$
$53$	−0.123644			−0.0169838			−0.00849190	+	0.999964i	$0.502703\pi$
$54$		0			0
$55$	−10.0865			−1.36006
$56$		0			0
$57$	−0.310892	+	1.50761i	−0.0411787	+	0.199688i
$58$		0			0
$59$	−4.43818	−	7.68715i	−0.577802	−	1.00078i	−0.995731	−	0.0923022i	$-0.970577\pi$
$59$	−4.43818	−	7.68715i	−0.577802	−	1.00078i	0.417929	−	0.908479i	$-0.362756\pi$
$60$		0			0
$61$	−1.93818	+	3.35702i	−0.248158	+	0.429823i	−0.963015	−	0.269448i	$-0.913159\pi$
$61$	−1.93818	+	3.35702i	−0.248158	+	0.429823i	0.714857	+	0.699271i	$0.246492\pi$
$62$		0			0
$63$	2.40545	−	1.79272i	0.303058	−	0.225861i
$64$		0			0
$65$	1.79418	−	3.10761i	0.222541	−	0.385452i
$66$		0			0
$67$	6.15452	+	10.6599i	0.751894	+	1.30232i	0.946904	+	0.321517i	$0.104193\pi$
$67$	6.15452	+	10.6599i	0.751894	+	1.30232i	−0.195010	+	0.980801i	$0.562474\pi$
$68$		0			0
$69$	−9.66071	+	3.20397i	−1.16301	+	0.385713i
$70$		0			0
$71$	2.87636			0.341361			0.170680	−	0.985326i	$-0.445403\pi$
$71$	2.87636			0.341361			0.170680	+	0.985326i	$0.445403\pi$
$72$		0			0
$73$	−10.6414			−1.24549			−0.622744	−	0.782426i	$-0.713982\pi$
$73$	−10.6414			−1.24549			−0.622744	+	0.782426i	$0.713982\pi$
$74$		0			0
$75$	−10.1934	−	9.06668i	−1.17704	−	1.04693i
$76$		0			0
$77$	−1.40545	−	2.43430i	−0.160165	−	0.277415i
$78$		0			0
$79$	−3.54325	+	6.13709i	−0.398647	+	0.690477i	−0.993559	−	0.113314i	$-0.963853\pi$
$79$	−3.54325	+	6.13709i	−0.398647	+	0.690477i	0.594912	+	0.803791i	$0.297187\pi$
$80$		0			0
$81$	6.18292	+	6.53999i	0.686991	+	0.726666i
$82$		0			0
$83$	−2.05563	+	3.56046i	−0.225635	+	0.390811i	−0.956510	−	0.291700i	$-0.905779\pi$
$83$	−2.05563	+	3.56046i	−0.225635	+	0.390811i	0.730875	+	0.682512i	$0.239112\pi$
$84$		0			0
$85$	−7.37636	−	12.7762i	−0.800078	−	1.38578i
$86$		0			0
$87$	2.19963	+	1.95649i	0.235825	+	0.209757i
$88$		0			0
$89$	9.60940			1.01859			0.509297	−	0.860591i	$-0.329905\pi$
$89$	9.60940			1.01859			0.509297	+	0.860591i	$0.329905\pi$
$90$		0			0
$91$	1.00000			0.104828
$92$		0			0
$93$	11.4876	−	3.80987i	1.19121	−	0.395065i
$94$		0			0
$95$	1.59455	+	2.76185i	0.163598	+	0.283360i
$96$		0			0
$97$	−3.66071	+	6.34053i	−0.371688	+	0.643783i	−0.989825	−	0.142287i	$-0.954554\pi$
$97$	−3.66071	+	6.34053i	−0.371688	+	0.643783i	0.618137	+	0.786070i	$0.287888\pi$
$98$		0			0
$99$	6.76145	−	5.03913i	0.679551	−	0.506452i
$100$		0			0
$101$	−1.73236	+	3.00054i	−0.172376	+	0.298564i	−0.939250	−	0.343233i	$-0.888478\pi$
$101$	−1.73236	+	3.00054i	−0.172376	+	0.298564i	0.766874	+	0.641798i	$0.221811\pi$
$102$		0			0
$103$	−7.93818	−	13.7493i	−0.782172	−	1.35476i	−0.930674	−	0.365849i	$-0.880779\pi$
$103$	−7.93818	−	13.7493i	−0.782172	−	1.35476i	0.148502	−	0.988912i	$-0.452555\pi$
$104$		0			0
$105$	1.25526	−	6.08715i	0.122501	−	0.594045i
$106$		0			0
$107$	5.35346			0.517538			0.258769	−	0.965939i	$-0.416683\pi$
$107$	5.35346			0.517538			0.258769	+	0.965939i	$0.416683\pi$
$108$		0			0
$109$	−18.8640			−1.80684			−0.903421	−	0.428755i	$-0.858952\pi$
$109$	−18.8640			−1.80684			−0.903421	+	0.428755i	$0.858952\pi$
$110$		0			0
$111$	−1.66690	+	8.08330i	−0.158215	+	0.767233i
$112$		0			0
$113$	9.27561	+	16.0658i	0.872576	+	1.51135i	0.859322	+	0.511434i	$0.170886\pi$
$113$	9.27561	+	16.0658i	0.872576	+	1.51135i	0.0132538	+	0.999912i	$0.495781\pi$
$114$		0			0
$115$	−10.5433	+	18.2614i	−0.983163	+	1.70289i
$116$		0			0
$117$	0.349814	+	2.97954i	0.0323403	+	0.275458i
$118$		0			0
$119$	2.05563	−	3.56046i	0.188439	−	0.326387i
$120$		0			0
$121$	1.54944	+	2.68371i	0.140858	+	0.243974i
$122$		0			0
$123$	−8.89671	+	2.95059i	−0.802189	+	0.266046i
$124$		0			0
$125$	−10.3214			−0.923175
$126$		0			0
$127$	−9.98762			−0.886258			−0.443129	−	0.896458i	$-0.646132\pi$
$127$	−9.98762			−0.886258			−0.443129	+	0.896458i	$0.646132\pi$
$128$		0			0
$129$	6.74288	+	5.99754i	0.593678	+	0.528054i
$130$		0			0
$131$	8.02654	+	13.9024i	0.701282	+	1.21466i	0.968017	+	0.250886i	$0.0807220\pi$
$131$	8.02654	+	13.9024i	0.701282	+	1.21466i	−0.266734	+	0.963770i	$0.585945\pi$
$132$		0			0
$133$	−0.444368	+	0.769668i	−0.0385316	+	0.0667387i
$134$		0			0
$135$	18.5760	+	1.61072i	1.59877	+	0.138629i
$136$		0			0
$137$	6.49381	−	11.2476i	0.554804	−	0.960948i	−0.443115	−	0.896465i	$-0.646127\pi$
$137$	6.49381	−	11.2476i	0.554804	−	0.960948i	0.997919	−	0.0644834i	$-0.0205400\pi$
$138$		0			0
$139$	0.555632	+	0.962383i	0.0471281	+	0.0816283i	0.888627	−	0.458630i	$-0.151660\pi$
$139$	0.555632	+	0.962383i	0.0471281	+	0.0816283i	−0.841499	+	0.540259i	$0.818326\pi$
$140$		0			0
$141$	−3.45056	−	3.06914i	−0.290589	−	0.258468i
$142$		0			0
$143$	2.81089			0.235059
$144$		0			0
$145$	6.09888			0.506485
$146$		0			0
$147$	1.64400	−	0.545231i	0.135595	−	0.0449699i
$148$		0			0
$149$	−4.21634	−	7.30291i	−0.345416	−	0.598278i	0.640013	−	0.768364i	$-0.278929\pi$
$149$	−4.21634	−	7.30291i	−0.345416	−	0.598278i	−0.985429	+	0.170086i	$0.945595\pi$
$150$		0			0
$151$	−7.42580	+	12.8619i	−0.604303	+	1.04668i	0.387858	+	0.921719i	$0.373215\pi$
$151$	−7.42580	+	12.8619i	−0.604303	+	1.04668i	−0.992161	+	0.124964i	$0.960118\pi$
$152$		0			0
$153$	11.3276	+	4.87933i	0.915782	+	0.394470i
$154$		0			0
$155$	12.5371	−	21.7148i	1.00700	−	1.74418i
$156$		0			0
$157$	−1.44437	−	2.50172i	−0.115273	−	0.199659i	0.802616	−	0.596496i	$-0.203441\pi$
$157$	−1.44437	−	2.50172i	−0.115273	−	0.199659i	−0.917889	+	0.396837i	$0.870108\pi$
$158$		0			0
$159$	0.0432524	−	0.209744i	0.00343014	−	0.0166338i
$160$		0			0
$161$	−5.87636			−0.463122
$162$		0			0
$163$	10.3090			0.807466			0.403733	−	0.914877i	$-0.367713\pi$
$163$	10.3090			0.807466			0.403733	+	0.914877i	$0.367713\pi$
$164$		0			0
$165$	3.52840	−	17.1103i	0.274686	−	1.33204i
$166$		0			0
$167$	6.07598	+	10.5239i	0.470174	+	0.814365i	0.999418	−	0.0341045i	$-0.0108579\pi$
$167$	6.07598	+	10.5239i	0.470174	+	0.814365i	−0.529244	+	0.848469i	$0.677525\pi$
$168$		0			0
$169$	6.00000	−	10.3923i	0.461538	−	0.799408i
$170$		0			0
$171$	−2.44870	−	1.05477i	−0.187257	−	0.0806602i
$172$		0			0
$173$	3.30470	−	5.72391i	0.251252	−	0.435181i	−0.712619	−	0.701551i	$-0.752491\pi$
$173$	3.30470	−	5.72391i	0.251252	−	0.435181i	0.963871	+	0.266370i	$0.0858244\pi$
$174$		0			0
$175$	−3.93818	−	6.82112i	−0.297698	−	0.515629i
$176$		0			0
$177$	14.5927	−	4.83967i	1.09685	−	0.363772i
$178$		0			0
$179$	3.84294			0.287234			0.143617	−	0.989633i	$-0.454127\pi$
$179$	3.84294			0.287234			0.143617	+	0.989633i	$0.454127\pi$
$180$		0			0
$181$	18.5426			1.37826			0.689129	−	0.724639i	$-0.257993\pi$
$181$	18.5426			1.37826			0.689129	+	0.724639i	$0.257993\pi$
$182$		0			0
$183$	−5.01671	−	4.46218i	−0.370846	−	0.329854i
$184$		0			0
$185$	8.54944	+	14.8081i	0.628567	+	1.08871i
$186$		0			0
$187$	5.77816	−	10.0081i	0.422541	−	0.731862i
$188$		0			0
$189$	2.19963	+	4.70761i	0.159999	+	0.342429i
$190$		0			0
$191$	2.31708	−	4.01330i	0.167658	−	0.290392i	−0.769938	−	0.638119i	$-0.779713\pi$
$191$	2.31708	−	4.01330i	0.167658	−	0.290392i	0.937596	+	0.347726i	$0.113046\pi$
$192$		0			0
$193$	12.6483	+	21.9075i	0.910446	+	1.57694i	0.813435	+	0.581656i	$0.197595\pi$
$193$	12.6483	+	21.9075i	0.910446	+	1.57694i	0.0970118	+	0.995283i	$0.469072\pi$
$194$		0			0
$195$	4.64400	+	4.13066i	0.332563	+	0.295803i
$196$		0			0
$197$	10.7207			0.763816			0.381908	−	0.924200i	$-0.375267\pi$
$197$	10.7207			0.763816			0.381908	+	0.924200i	$0.375267\pi$
$198$		0			0
$199$	8.76647			0.621439			0.310719	−	0.950502i	$-0.399430\pi$
$199$	8.76647			0.621439			0.310719	+	0.950502i	$0.399430\pi$
$200$		0			0
$201$	−20.2360	+	6.71127i	−1.42734	+	0.473376i
$202$		0			0
$203$	0.849814	+	1.47192i	0.0596453	+	0.103309i
$204$		0			0
$205$	−9.70946	+	16.8173i	−0.678138	+	1.17457i
$206$		0			0
$207$	−2.05563	−	17.5088i	−0.142876	−	1.21695i
$208$		0			0
$209$	−1.24907	+	2.16345i	−0.0864000	+	0.149649i
$210$		0			0
$211$	5.26509	+	9.11941i	0.362464	+	0.627806i	0.988366	−	0.152096i	$-0.0486023\pi$
$211$	5.26509	+	9.11941i	0.362464	+	0.627806i	−0.625902	+	0.779902i	$0.715269\pi$
$212$		0			0
$213$	−1.00619	+	4.87933i	−0.0689430	+	0.334326i
$214$		0			0
$215$	18.6959			1.27505
$216$		0			0
$217$	6.98762			0.474351
$218$		0			0
$219$	3.72253	−	18.0517i	0.251545	−	1.21982i
$220$		0			0
$221$	2.05563	+	3.56046i	0.138277	+	0.239502i
$222$		0			0
$223$	−2.83379	+	4.90827i	−0.189765	+	0.328682i	−0.945172	−	0.326574i	$-0.894106\pi$
$223$	−2.83379	+	4.90827i	−0.189765	+	0.328682i	0.755407	+	0.655256i	$0.227439\pi$
$224$		0			0
$225$	18.9462	−	14.1201i	1.26308	−	0.941338i
$226$		0			0
$227$	−5.54944	+	9.61192i	−0.368329	+	0.637965i	−0.989304	−	0.145865i	$-0.953403\pi$
$227$	−5.54944	+	9.61192i	−0.368329	+	0.637965i	0.620975	+	0.783830i	$0.286737\pi$
$228$		0			0
$229$	−9.82141	−	17.0112i	−0.649017	−	1.12413i	−0.983358	−	0.181679i	$-0.941847\pi$
$229$	−9.82141	−	17.0112i	−0.649017	−	1.12413i	0.334341	−	0.942452i	$-0.391486\pi$
$230$		0			0
$231$	4.62110	−	1.53259i	0.304046	−	0.100837i
$232$		0			0
$233$	8.96286			0.587177			0.293588	−	0.955932i	$-0.405151\pi$
$233$	8.96286			0.587177			0.293588	+	0.955932i	$0.405151\pi$
$234$		0			0
$235$	−9.56732			−0.624103
$236$		0			0
$237$	−9.17123	−	8.15747i	−0.595735	−	0.529884i
$238$		0			0
$239$	5.61126	+	9.71899i	0.362963	+	0.628670i	0.988447	−	0.151567i	$-0.0484320\pi$
$239$	5.61126	+	9.71899i	0.362963	+	0.628670i	−0.625484	+	0.780237i	$0.715099\pi$
$240$		0			0
$241$	3.49312	−	6.05026i	0.225012	−	0.389732i	−0.731311	−	0.682044i	$-0.761091\pi$
$241$	3.49312	−	6.05026i	0.225012	−	0.389732i	0.956323	+	0.292312i	$0.0944246\pi$
$242$		0			0
$243$	−13.2570	+	8.20066i	−0.850440	+	0.526073i
$244$		0			0
$245$	1.79418	−	3.10761i	0.114626	−	0.198538i
$246$		0			0
$247$	−0.444368	−	0.769668i	−0.0282745	−	0.0489728i
$248$		0			0
$249$	−5.32072	−	4.73259i	−0.337187	−	0.299915i
$250$		0			0
$251$	−4.62041			−0.291638			−0.145819	−	0.989311i	$-0.546582\pi$
$251$	−4.62041			−0.291638			−0.145819	+	0.989311i	$0.546582\pi$
$252$		0			0
$253$	−16.5178			−1.03847
$254$		0			0
$255$	24.2534	−	8.04364i	1.51881	−	0.503712i
$256$		0			0
$257$	0.712008	+	1.23323i	0.0444138	+	0.0769270i	0.887378	−	0.461043i	$-0.152525\pi$
$257$	0.712008	+	1.23323i	0.0444138	+	0.0769270i	−0.842964	+	0.537970i	$0.819191\pi$
$258$		0			0
$259$	−2.38255	+	4.12669i	−0.148044	+	0.256420i
$260$		0			0
$261$	−4.08836	+	3.04695i	−0.253063	+	0.188601i
$262$		0			0
$263$	8.13162	−	14.0844i	0.501417	−	0.868480i	−0.498582	−	0.866843i	$-0.666146\pi$
$263$	8.13162	−	14.0844i	0.501417	−	0.868480i	0.999999	−	0.00163692i	$-0.000521048\pi$
$264$		0			0
$265$	−0.221840	−	0.384237i	−0.0136275	−	0.0236035i
$266$		0			0
$267$	−3.36151	+	16.3010i	−0.205721	+	0.997604i
$268$		0			0
$269$	−18.6538			−1.13734			−0.568672	−	0.822564i	$-0.692543\pi$
$269$	−18.6538			−1.13734			−0.568672	+	0.822564i	$0.692543\pi$
$270$		0			0
$271$	−3.96286			−0.240727			−0.120363	−	0.992730i	$-0.538406\pi$
$271$	−3.96286			−0.240727			−0.120363	+	0.992730i	$0.538406\pi$
$272$		0			0
$273$	−0.349814	+	1.69636i	−0.0211717	+	0.102668i
$274$		0			0
$275$	−11.0698	−	19.1734i	−0.667534	−	1.15620i
$276$		0			0
$277$	1.16690	−	2.02112i	0.0701120	−	0.121438i	−0.828838	−	0.559488i	$-0.810998\pi$
$277$	1.16690	−	2.02112i	0.0701120	−	0.121438i	0.898950	+	0.438051i	$0.144331\pi$
$278$		0			0
$279$	2.44437	+	20.8199i	0.146340	+	1.24645i
$280$		0			0
$281$	−13.9975	+	24.2443i	−0.835018	+	1.44629i	0.0589978	+	0.998258i	$0.481210\pi$
$281$	−13.9975	+	24.2443i	−0.835018	+	1.44629i	−0.894016	+	0.448035i	$0.852124\pi$
$282$		0			0
$283$	5.16002	+	8.93741i	0.306731	+	0.531274i	0.977645	−	0.210261i	$-0.0674314\pi$
$283$	5.16002	+	8.93741i	0.306731	+	0.531274i	−0.670914	+	0.741535i	$0.734098\pi$
$284$		0			0
$285$	−5.24288	+	1.73880i	−0.310561	+	0.102998i
$286$		0			0
$287$	−5.41164			−0.319439
$288$		0			0
$289$	−0.0975070			−0.00573571
$290$		0			0
$291$	−9.47524	−	8.42787i	−0.555448	−	0.494051i
$292$		0			0
$293$	15.3480	+	26.5834i	0.896637	+	1.55302i	0.831765	+	0.555127i	$0.187330\pi$
$293$	15.3480	+	26.5834i	0.896637	+	1.55302i	0.0648718	+	0.997894i	$0.479336\pi$
$294$		0			0
$295$	15.9258	−	27.5843i	0.927236	−	1.60602i
$296$		0			0
$297$	6.18292	+	13.2326i	0.358769	+	0.767833i
$298$		0			0
$299$	2.93818	−	5.08907i	0.169919	−	0.294309i
$300$		0			0
$301$	2.60507	+	4.51212i	0.150154	+	0.260074i
$302$		0			0
$303$	−4.48398	−	3.98833i	−0.257598	−	0.229124i
$304$		0			0
$305$	−13.9098			−0.796471
$306$		0			0
$307$	11.4437			0.653125			0.326563	−	0.945176i	$-0.394110\pi$
$307$	11.4437			0.653125			0.326563	+	0.945176i	$0.394110\pi$
$308$		0			0
$309$	26.1007	−	8.65628i	1.48482	−	0.492439i
$310$		0			0
$311$	5.98143	+	10.3601i	0.339176	+	0.587470i	0.984278	−	0.176627i	$-0.0565185\pi$
$311$	5.98143	+	10.3601i	0.339176	+	0.587470i	−0.645102	+	0.764096i	$0.723185\pi$
$312$		0			0
$313$	6.77197	−	11.7294i	0.382774	−	0.662985i	−0.608683	−	0.793413i	$-0.708302\pi$
$313$	6.77197	−	11.7294i	0.382774	−	0.662985i	0.991458	+	0.130429i	$0.0416353\pi$
$314$		0			0
$315$	9.88688	+	4.25874i	0.557062	+	0.239953i
$316$		0			0
$317$	14.9814	−	25.9486i	0.841441	−	1.45742i	−0.0472355	−	0.998884i	$-0.515041\pi$
$317$	14.9814	−	25.9486i	0.841441	−	1.45742i	0.888676	−	0.458535i	$-0.151626\pi$
$318$		0			0
$319$	2.38874	+	4.13741i	0.133744	+	0.231651i
$320$		0			0
$321$	−1.87271	+	9.08138i	−0.104525	+	0.506873i
$322$		0			0
$323$	−3.65383			−0.203304
$324$		0			0
$325$	7.87636			0.436902
$326$		0			0
$327$	6.59888	−	32.0001i	0.364919	−	1.76961i
$328$		0			0
$329$	−1.33310	−	2.30900i	−0.0734964	−	0.127299i
$330$		0			0
$331$	1.04325	−	1.80697i	0.0573423	−	0.0993198i	−0.835929	−	0.548837i	$-0.815071\pi$
$331$	1.04325	−	1.80697i	0.0573423	−	0.0993198i	0.893272	+	0.449517i	$0.148404\pi$
$332$		0			0
$333$	−13.1291	−	5.65531i	−0.719469	−	0.309909i
$334$		0			0
$335$	−22.0846	+	38.2517i	−1.20661	+	2.08992i
$336$		0			0
$337$	8.10439	+	14.0372i	0.441474	+	0.764655i	0.997799	−	0.0663093i	$-0.0211224\pi$
$337$	8.10439	+	14.0372i	0.441474	+	0.764655i	−0.556325	+	0.830965i	$0.687789\pi$
$338$		0			0
$339$	−30.4981	+	10.1147i	−1.65643	+	0.549355i
$340$		0			0
$341$	19.6414			1.06364
$342$		0			0
$343$	1.00000			0.0539949
$344$		0			0
$345$	−27.2898	−	24.2732i	−1.46923	−	1.30683i
$346$		0			0
$347$	5.63348	+	9.75747i	0.302421	+	0.523808i	0.976684	−	0.214683i	$-0.0688719\pi$
$347$	5.63348	+	9.75747i	0.302421	+	0.523808i	−0.674263	+	0.738491i	$0.735539\pi$
$348$		0			0
$349$	0.0988844	−	0.171273i	0.00529316	−	0.00916803i	−0.863367	−	0.504577i	$-0.831648\pi$
$349$	0.0988844	−	0.171273i	0.00529316	−	0.00916803i	0.868660	+	0.495409i	$0.164982\pi$
$350$		0			0
$351$	−5.17673	−	0.448873i	−0.276313	−	0.0239591i
$352$		0			0
$353$	6.25093	−	10.8269i	0.332703	−	0.576259i	−0.650338	−	0.759645i	$-0.725373\pi$
$353$	6.25093	−	10.8269i	0.332703	−	0.576259i	0.983041	+	0.183386i	$0.0587059\pi$
$354$		0			0
$355$	5.16071	+	8.93861i	0.273902	+	0.474412i
$356$		0			0
$357$	5.32072	+	4.73259i	0.281603	+	0.250475i
$358$		0			0
$359$	−20.0197			−1.05660			−0.528299	−	0.849059i	$-0.677170\pi$
$359$	−20.0197			−1.05660			−0.528299	+	0.849059i	$0.677170\pi$
$360$		0			0
$361$	−18.2101			−0.958429
$362$		0			0
$363$	−5.09455	+	1.68961i	−0.267395	+	0.0886814i
$364$		0			0
$365$	−19.0927	−	33.0695i	−0.999357	−	1.73094i
$366$		0			0
$367$	15.0364	−	26.0438i	0.784892	−	1.35947i	−0.144171	−	0.989553i	$-0.546052\pi$
$367$	15.0364	−	26.0438i	0.784892	−	1.35947i	0.929063	−	0.369921i	$-0.120615\pi$
$368$		0			0
$369$	−1.89307	−	16.1242i	−0.0985491	−	0.839390i
$370$		0			0
$371$	0.0618219	−	0.107079i	0.00320963	−	0.00555925i
$372$		0			0
$373$	−3.50619	−	6.07290i	−0.181544	−	0.314443i	0.760863	−	0.648913i	$-0.224776\pi$
$373$	−3.50619	−	6.07290i	−0.181544	−	0.314443i	−0.942406	+	0.334470i	$0.891443\pi$
$374$		0			0
$375$	3.61058	−	17.5088i	0.186449	−	0.904151i
$376$		0			0
$377$	−1.69963			−0.0875353
$378$		0			0
$379$	19.0741			0.979772			0.489886	−	0.871787i	$-0.337038\pi$
$379$	19.0741			0.979772			0.489886	+	0.871787i	$0.337038\pi$
$380$		0			0
$381$	3.49381	−	16.9426i	0.178993	−	0.867995i
$382$		0			0
$383$	1.60507	+	2.78007i	0.0820155	+	0.142055i	0.904116	−	0.427288i	$-0.140531\pi$
$383$	1.60507	+	2.78007i	0.0820155	+	0.142055i	−0.822100	+	0.569343i	$0.807198\pi$
$384$		0			0
$385$	5.04325	−	8.73517i	0.257028	−	0.445185i
$386$		0			0
$387$	−12.5327	+	9.34031i	−0.637075	+	0.474795i
$388$		0			0
$389$	−2.56801	+	4.44793i	−0.130203	+	0.225519i	−0.923755	−	0.382984i	$-0.874896\pi$
$389$	−2.56801	+	4.44793i	−0.130203	+	0.225519i	0.793552	+	0.608503i	$0.208230\pi$
$390$		0			0
$391$	−12.0796	−	20.9225i	−0.610893	−	1.05810i
$392$		0			0
$393$	−26.3912	+	8.75264i	−1.33126	+	0.441512i
$394$		0			0
$395$	−25.4290			−1.27947
$396$		0			0
$397$	22.9381			1.15123			0.575615	−	0.817721i	$-0.304763\pi$
$397$	22.9381			1.15123			0.575615	+	0.817721i	$0.304763\pi$
$398$		0			0
$399$	−1.15019	−	1.02305i	−0.0575813	−	0.0512164i
$400$		0			0
$401$	9.10507	+	15.7705i	0.454686	+	0.787539i	0.998670	−	0.0515566i	$-0.0164183\pi$
$401$	9.10507	+	15.7705i	0.454686	+	0.787539i	−0.543984	+	0.839095i	$0.683085\pi$
$402$		0			0
$403$	−3.49381	+	6.05146i	−0.174039	+	0.301445i
$404$		0			0
$405$	−9.23050	+	30.9481i	−0.458667	+	1.53782i
$406$		0			0
$407$	−6.69708	+	11.5997i	−0.331962	+	0.574975i
$408$		0			0
$409$	7.66621	+	13.2783i	0.379070	+	0.656568i	0.990927	−	0.134400i	$-0.0429108\pi$
$409$	7.66621	+	13.2783i	0.379070	+	0.656568i	−0.611858	+	0.790968i	$0.709577\pi$
$410$		0			0
$411$	16.8083	+	14.9504i	0.829094	+	0.737449i
$412$		0			0
$413$	8.87636			0.436777
$414$		0			0
$415$	−14.7527			−0.724182
$416$		0			0
$417$	−1.82691	+	0.605896i	−0.0894644	+	0.0296708i
$418$		0			0
$419$	5.28435	+	9.15276i	0.258157	+	0.447142i	0.965748	−	0.259481i	$-0.0835513\pi$
$419$	5.28435	+	9.15276i	0.258157	+	0.447142i	−0.707591	+	0.706622i	$0.750218\pi$
$420$		0			0
$421$	18.0858	−	31.3256i	0.881449	−	1.52671i	0.0317181	−	0.999497i	$-0.489902\pi$
$421$	18.0858	−	31.3256i	0.881449	−	1.52671i	0.849731	−	0.527217i	$-0.176765\pi$
$422$		0			0
$423$	6.41342	−	4.77975i	0.311831	−	0.232399i
$424$		0			0
$425$	16.1909	−	28.0434i	0.785374	−	1.36031i
$426$		0			0
$427$	−1.93818	−	3.35702i	−0.0937950	−	0.162458i
$428$		0			0
$429$	−0.983290	+	4.76828i	−0.0474737	+	0.230215i
$430$		0			0
$431$	−35.0989			−1.69065			−0.845327	−	0.534249i	$-0.820594\pi$
$431$	−35.0989			−1.69065			−0.845327	+	0.534249i	$0.820594\pi$
$432$		0			0
$433$	−41.1730			−1.97865			−0.989324	−	0.145731i	$-0.953447\pi$
$433$	−41.1730			−1.97865			−0.989324	+	0.145731i	$0.953447\pi$
$434$		0			0
$435$	−2.13348	+	10.3459i	−0.102292	+	0.496047i
$436$		0			0
$437$	2.61126	+	4.52284i	0.124914	+	0.216357i
$438$		0			0
$439$	−2.33929	+	4.05178i	−0.111648	+	0.193381i	−0.916435	−	0.400184i	$-0.868946\pi$
$439$	−2.33929	+	4.05178i	−0.111648	+	0.193381i	0.804787	+	0.593564i	$0.202280\pi$
$440$		0			0
$441$	0.349814	+	2.97954i	0.0166578	+	0.141883i
$442$		0			0
$443$	15.0865	−	26.1306i	0.716781	−	1.24150i	−0.245487	−	0.969400i	$-0.578948\pi$
$443$	15.0865	−	26.1306i	0.716781	−	1.24150i	0.962268	−	0.272102i	$-0.0877188\pi$
$444$		0			0
$445$	17.2410	+	29.8623i	0.817303	+	1.41561i
$446$		0			0
$447$	13.8633	−	4.59776i	0.655711	−	0.217466i
$448$		0			0
$449$	0.333792			0.0157526			0.00787632	−	0.999969i	$-0.497493\pi$
$449$	0.333792			0.0157526			0.00787632	+	0.999969i	$0.497493\pi$
$450$		0			0
$451$	−15.2115			−0.716283
$452$		0			0
$453$	−19.2207	−	17.0961i	−0.903066	−	0.803244i
$454$		0			0
$455$	1.79418	+	3.10761i	0.0841125	+	0.145687i
$456$		0			0
$457$	9.65452	−	16.7221i	0.451619	−	0.782227i	−0.546868	−	0.837219i	$-0.684180\pi$
$457$	9.65452	−	16.7221i	0.451619	−	0.782227i	0.998487	+	0.0549917i	$0.0175132\pi$
$458$		0			0
$459$	−12.2396	+	17.5088i	−0.571298	+	0.817241i
$460$		0			0
$461$	−19.5538	+	33.8681i	−0.910710	+	1.57740i	−0.0976463	+	0.995221i	$0.531131\pi$
$461$	−19.5538	+	33.8681i	−0.910710	+	1.57740i	−0.813064	+	0.582175i	$0.802202\pi$
$462$		0			0
$463$	10.9382	+	18.9455i	0.508340	+	0.880471i	0.999953	+	0.00965741i	$0.00307410\pi$
$463$	10.9382	+	18.9455i	0.508340	+	0.880471i	−0.491613	+	0.870814i	$0.663593\pi$
$464$		0			0
$465$	32.4505	+	28.8635i	1.50486	+	1.33851i
$466$		0			0
$467$	12.3200			0.570103			0.285052	−	0.958512i	$-0.407989\pi$
$467$	12.3200			0.570103			0.285052	+	0.958512i	$0.407989\pi$
$468$		0			0
$469$	−12.3090			−0.568378
$470$		0			0
$471$	4.74907	−	1.57503i	0.218826	−	0.0725735i
$472$		0			0
$473$	7.32258	+	12.6831i	0.336693	+	0.583169i
$474$		0			0
$475$	−3.50000	+	6.06218i	−0.160591	+	0.278152i
$476$		0			0
$477$	0.340671	+	0.146743i	0.0155983	+	0.00671890i
$478$		0			0
$479$	6.74474	−	11.6822i	0.308175	−	0.533775i	−0.669788	−	0.742552i	$-0.733615\pi$
$479$	6.74474	−	11.6822i	0.308175	−	0.533775i	0.977963	+	0.208777i	$0.0669484\pi$
$480$		0			0
$481$	−2.38255	−	4.12669i	−0.108635	−	0.188161i
$482$		0			0
$483$	2.05563	−	9.96840i	0.0935345	−	0.453578i
$484$		0			0
$485$	−26.2719			−1.19295
$486$		0			0
$487$	−7.54394			−0.341849			−0.170924	−	0.985284i	$-0.554675\pi$
$487$	−7.54394			−0.341849			−0.170924	+	0.985284i	$0.554675\pi$
$488$		0			0
$489$	−3.60624	+	17.4878i	−0.163080	+	0.790826i
$490$		0			0
$491$	−8.06979	−	13.9773i	−0.364185	−	0.630786i	0.624460	−	0.781057i	$-0.285319\pi$
$491$	−8.06979	−	13.9773i	−0.364185	−	0.630786i	−0.988645	+	0.150270i	$0.951986\pi$
$492$		0			0
$493$	−3.49381	+	6.05146i	−0.157353	+	0.272544i
$494$		0			0
$495$	27.7909	+	11.9709i	1.24911	+	0.538050i
$496$		0			0
$497$	−1.43818	+	2.49100i	−0.0645111	+	0.111737i
$498$		0			0
$499$	−15.4327	−	26.7302i	−0.690862	−	1.19661i	−0.971556	−	0.236810i	$-0.923898\pi$
$499$	−15.4327	−	26.7302i	−0.690862	−	1.19661i	0.280694	−	0.959797i	$-0.409435\pi$
$500$		0			0
$501$	−19.9778	+	6.62563i	−0.892542	+	0.296011i
$502$		0			0
$503$	−24.6304			−1.09822			−0.549109	−	0.835751i	$-0.685033\pi$
$503$	−24.6304			−1.09822			−0.549109	+	0.835751i	$0.685033\pi$
$504$		0			0
$505$	−12.4327			−0.553247
$506$		0			0
$507$	15.5302	+	13.8135i	0.689720	+	0.613480i
$508$		0			0
$509$	−6.79487	−	11.7691i	−0.301177	−	0.521654i	0.675226	−	0.737611i	$-0.264046\pi$
$509$	−6.79487	−	11.7691i	−0.301177	−	0.521654i	−0.976403	+	0.215957i	$0.930713\pi$
$510$		0			0
$511$	5.32072	−	9.21576i	0.235375	−	0.407681i
$512$		0			0
$513$	2.64586	−	3.78490i	0.116817	−	0.167107i
$514$		0			0
$515$	28.4851	−	49.3376i	1.25520	−	2.17407i
$516$		0			0
$517$	−3.74721	−	6.49036i	−0.164802	−	0.285446i
$518$		0			0
$519$	8.55377	+	7.60826i	0.375469	+	0.333966i
$520$		0			0
$521$	−39.1730			−1.71620			−0.858100	−	0.513482i	$-0.828355\pi$
$521$	−39.1730			−1.71620			−0.858100	+	0.513482i	$0.828355\pi$
$522$		0			0
$523$	−19.1236			−0.836219			−0.418109	−	0.908397i	$-0.637307\pi$
$523$	−19.1236			−0.836219			−0.418109	+	0.908397i	$0.637307\pi$
$524$		0			0
$525$	12.9487	−	4.29443i	0.565128	−	0.187424i
$526$		0			0
$527$	14.3640	+	24.8791i	0.625705	+	1.08375i
$528$		0			0
$529$	−5.76578	+	9.98663i	−0.250686	+	0.434201i
$530$		0			0
$531$	3.10507	+	26.4474i	0.134749	+	1.14772i
$532$		0			0
$533$	2.70582	−	4.68661i	0.117202	−	0.203000i
$534$		0			0
$535$	9.60507	+	16.6365i	0.415264	+	0.719258i
$536$		0			0
$537$	−1.34431	+	6.51899i	−0.0580114	+	0.281315i
$538$		0			0
$539$	2.81089			0.121074
$540$		0			0
$541$	2.53018			0.108781			0.0543906	−	0.998520i	$-0.482678\pi$
$541$	2.53018			0.108781			0.0543906	+	0.998520i	$0.482678\pi$
$542$		0			0
$543$	−6.48645	+	31.4548i	−0.278360	+	1.34986i
$544$		0			0
$545$	−33.8454	−	58.6220i	−1.44978	−	2.51109i
$546$		0			0
$547$	8.92580	−	15.4599i	0.381640	−	0.661019i	−0.609657	−	0.792665i	$-0.708693\pi$
$547$	8.92580	−	15.4599i	0.381640	−	0.661019i	0.991297	+	0.131646i	$0.0420262\pi$
$548$		0			0
$549$	9.32437	−	6.94920i	0.397954	−	0.296585i
$550$		0			0
$551$	0.755260	−	1.30815i	0.0321752	−	0.0557290i
$552$		0			0
$553$	−3.54325	−	6.13709i	−0.150674	−	0.260976i
$554$		0			0
$555$	−28.1105	+	9.32284i	−1.19322	+	0.395733i
$556$		0			0
$557$	41.3607			1.75251			0.876255	−	0.481847i	$-0.160034\pi$
$557$	41.3607			1.75251			0.876255	+	0.481847i	$0.160034\pi$
$558$		0			0
$559$	−5.21015			−0.220366
$560$		0			0
$561$	14.9560	+	13.3028i	0.631442	+	0.561644i
$562$		0			0
$563$	−10.3683	−	17.9584i	−0.436972	−	0.756858i	0.560482	−	0.828166i	$-0.310616\pi$
$563$	−10.3683	−	17.9584i	−0.436972	−	0.756858i	−0.997454	+	0.0713087i	$0.977282\pi$
$564$		0			0
$565$	−33.2843	+	57.6501i	−1.40028	+	2.42536i
$566$		0			0
$567$	−8.75526	+	2.08457i	−0.367686	+	0.0875436i
$568$		0			0
$569$	0.134164	−	0.232379i	0.00562446	−	0.00974185i	−0.863199	−	0.504863i	$-0.831543\pi$
$569$	0.134164	−	0.232379i	0.00562446	−	0.00974185i	0.868824	+	0.495121i	$0.164876\pi$
$570$		0			0
$571$	17.9684	+	31.1221i	0.751953	+	1.30242i	0.946875	+	0.321601i	$0.104221\pi$
$571$	17.9684	+	31.1221i	0.751953	+	1.30242i	−0.194923	+	0.980819i	$0.562446\pi$
$572$		0			0
$573$	5.99745	+	5.33451i	0.250547	+	0.222852i
$574$		0			0
$575$	−46.2843			−1.93019
$576$		0			0
$577$	5.43130			0.226108			0.113054	−	0.993589i	$-0.463937\pi$
$577$	5.43130			0.226108			0.113054	+	0.993589i	$0.463937\pi$
$578$		0			0
$579$	−41.5876	+	13.7925i	−1.72832	+	0.573198i
$580$		0			0
$581$	−2.05563	−	3.56046i	−0.0852820	−	0.147713i
$582$		0			0
$583$	0.173775	−	0.300987i	0.00719702	−	0.0124656i
$584$		0			0
$585$	−8.63162	+	6.43292i	−0.356873	+	0.265968i
$586$		0			0
$587$	17.5822	−	30.4532i	0.725694	−	1.25694i	−0.232994	−	0.972478i	$-0.574852\pi$
$587$	17.5822	−	30.4532i	0.725694	−	1.25694i	0.958688	−	0.284461i	$-0.0918145\pi$
$588$		0			0
$589$	−3.10507	−	5.37815i	−0.127942	−	0.221603i
$590$		0			0
$591$	−3.75024	+	18.1861i	−0.154264	+	0.748076i
$592$		0			0
$593$	−33.5068			−1.37596			−0.687980	−	0.725730i	$-0.741502\pi$
$593$	−33.5068			−1.37596			−0.687980	+	0.725730i	$0.741502\pi$
$594$		0			0
$595$	14.7527			0.604802
$596$		0			0
$597$	−3.06663	+	14.8711i	−0.125509	+	0.608632i
$598$		0			0
$599$	3.12364	+	5.41031i	0.127629	+	0.221059i	0.922757	−	0.385381i	$-0.125930\pi$
$599$	3.12364	+	5.41031i	0.127629	+	0.221059i	−0.795129	+	0.606441i	$0.792597\pi$
$600$		0			0
$601$	−11.2040	+	19.4058i	−0.457019	+	0.791580i	−0.998802	−	0.0489384i	$-0.984416\pi$
$601$	−11.2040	+	19.4058i	−0.457019	+	0.791580i	0.541783	+	0.840519i	$0.317750\pi$
$602$		0			0
$603$	−4.30587	−	36.6752i	−0.175349	−	1.49353i
$604$		0			0
$605$	−5.55996	+	9.63014i	−0.226045	+	0.391521i
$606$		0			0
$607$	7.47524	+	12.9475i	0.303411	+	0.525523i	0.976906	−	0.213669i	$-0.0685413\pi$
$607$	7.47524	+	12.9475i	0.303411	+	0.525523i	−0.673496	+	0.739191i	$0.735208\pi$
$608$		0			0
$609$	−2.79418	+	0.926690i	−0.113226	+	0.0375514i
$610$		0			0
$611$	2.66621			0.107863
$612$		0			0
$613$	35.1978			1.42162			0.710812	−	0.703382i	$-0.248328\pi$
$613$	35.1978			1.42162			0.710812	+	0.703382i	$0.248328\pi$
$614$		0			0
$615$	−25.1316	−	22.3536i	−1.01340	−	0.901386i
$616$		0			0
$617$	1.00619	+	1.74277i	0.0405077	+	0.0701614i	0.885568	−	0.464509i	$-0.153769\pi$
$617$	1.00619	+	1.74277i	0.0405077	+	0.0701614i	−0.845061	+	0.534670i	$0.820436\pi$
$618$		0			0
$619$	19.6909	−	34.1056i	0.791444	−	1.37082i	−0.133629	−	0.991031i	$-0.542663\pi$
$619$	19.6909	−	34.1056i	0.791444	−	1.37082i	0.925073	−	0.379789i	$-0.124004\pi$
$620$		0			0
$621$	30.4203	+	2.63774i	1.22072	+	0.105849i
$622$		0			0
$623$	−4.80470	+	8.32199i	−0.192496	+	0.333413i
$624$		0			0
$625$	1.17240	+	2.03065i	0.0468959	+	0.0812261i
$626$		0			0
$627$	−3.23305	−	2.87568i	−0.129116	−	0.114843i
$628$		0			0
$629$	−19.5906			−0.781126
$630$		0			0
$631$	−44.3832			−1.76687			−0.883433	−	0.468558i	$-0.844774\pi$
$631$	−44.3832			−1.76687			−0.883433	+	0.468558i	$0.844774\pi$
$632$		0			0
$633$	−17.3116	+	5.74138i	−0.688074	+	0.228200i
$634$		0			0
$635$	−17.9196	−	31.0377i	−0.711118	−	1.23169i
$636$		0			0
$637$	−0.500000	+	0.866025i	−0.0198107	+	0.0343132i
$638$		0			0
$639$	−7.92511	−	3.41372i	−0.313512	−	0.135045i
$640$		0			0
$641$	7.49312	−	12.9785i	0.295961	−	0.512619i	−0.679247	−	0.733909i	$-0.737694\pi$
$641$	7.49312	−	12.9785i	0.295961	−	0.512619i	0.975208	+	0.221291i	$0.0710270\pi$
$642$		0			0
$643$	−5.32691	−	9.22649i	−0.210073	−	0.363857i	0.741664	−	0.670771i	$-0.234037\pi$
$643$	−5.32691	−	9.22649i	−0.210073	−	0.363857i	−0.951737	+	0.306914i	$0.900703\pi$
$644$		0			0
$645$	−6.54009	+	31.7150i	−0.257516	+	1.24878i
$646$		0			0
$647$	−2.12955			−0.0837213			−0.0418606	−	0.999123i	$-0.513329\pi$
$647$	−2.12955			−0.0837213			−0.0418606	+	0.999123i	$0.513329\pi$
$648$		0			0
$649$	24.9505			0.979392
$650$		0			0
$651$	−2.44437	+	11.8535i	−0.0958023	+	0.464575i
$652$		0			0
$653$	−5.58582	−	9.67492i	−0.218590	−	0.378609i	0.735787	−	0.677213i	$-0.236812\pi$
$653$	−5.58582	−	9.67492i	−0.218590	−	0.378609i	−0.954377	+	0.298604i	$0.903479\pi$
$654$		0			0
$655$	−28.8022	+	49.8868i	−1.12539	+	1.94924i
$656$		0			0
$657$	29.3200	+	12.6295i	1.14388	+	0.492723i
$658$		0			0
$659$	−5.65452	+	9.79391i	−0.220269	+	0.381517i	−0.954890	−	0.296961i	$-0.904027\pi$
$659$	−5.65452	+	9.79391i	−0.220269	+	0.381517i	0.734621	+	0.678478i	$0.237360\pi$
$660$		0			0
$661$	−16.1785	−	28.0220i	−0.629271	−	1.08993i	−0.987698	−	0.156372i	$-0.950020\pi$
$661$	−16.1785	−	28.0220i	−0.629271	−	1.08993i	0.358427	−	0.933558i	$-0.383313\pi$
$662$		0			0
$663$	−6.75890	+	2.24159i	−0.262494	+	0.0870561i
$664$		0			0
$665$	−3.18911			−0.123668
$666$		0			0
$667$	9.98762			0.386722
$668$		0			0
$669$	−7.33489	−	6.52411i	−0.283583	−	0.252237i
$670$		0			0
$671$	−5.44801	−	9.43623i	−0.210318	−	0.364282i
$672$		0			0
$673$	12.0803	−	20.9237i	0.465662	−	0.806550i	−0.533569	−	0.845756i	$-0.679150\pi$
$673$	12.0803	−	20.9237i	0.465662	−	0.806550i	0.999231	+	0.0392063i	$0.0124830\pi$
$674$		0			0
$675$	17.3251	+	37.0788i	0.666842	+	1.42717i
$676$		0			0
$677$	−12.5371	+	21.7148i	−0.481838	+	0.834569i	−0.999783	−	0.0208457i	$-0.993364\pi$
$677$	−12.5371	+	21.7148i	−0.481838	+	0.834569i	0.517944	+	0.855414i	$0.326697\pi$
$678$		0			0
$679$	−3.66071	−	6.34053i	−0.140485	−	0.243327i
$680$		0			0
$681$	−14.3640	−	12.7762i	−0.550429	−	0.489586i
$682$		0			0
$683$	47.6784			1.82436			0.912182	−	0.409785i	$-0.134396\pi$
$683$	47.6784			1.82436			0.912182	+	0.409785i	$0.134396\pi$
$684$		0			0
$685$	46.6043			1.78066
$686$		0			0
$687$	32.2927	−	10.7099i	1.23204	−	0.408607i
$688$		0			0
$689$	0.0618219	+	0.107079i	0.00235523	+	0.00407937i
$690$		0			0
$691$	−12.3400	+	21.3735i	−0.469435	+	0.813085i	−0.999389	−	0.0349408i	$-0.988876\pi$
$691$	−12.3400	+	21.3735i	−0.469435	+	0.813085i	0.529954	+	0.848026i	$0.322209\pi$
$692$		0			0
$693$	0.983290	+	8.37515i	0.0373521	+	0.318146i
$694$		0			0
$695$	−1.99381	+	3.45338i	−0.0756295	+	0.130994i
$696$		0			0
$697$	−11.1243	−	19.2679i	−0.421364	−	0.729824i
$698$		0			0
$699$	−3.13533	+	15.2042i	−0.118589	+	0.575076i
$700$		0			0
$701$	−29.6784			−1.12094			−0.560469	−	0.828175i	$-0.689379\pi$
$701$	−29.6784			−1.12094			−0.560469	+	0.828175i	$0.689379\pi$
$702$		0			0
$703$	4.23491			0.159723
$704$		0			0
$705$	3.34678	−	16.2296i	0.126047	−	0.611242i
$706$		0			0
$707$	−1.73236	−	3.00054i	−0.0651521	−	0.112847i
$708$		0			0
$709$	14.6291	−	25.3383i	0.549406	−	0.951599i	−0.448909	−	0.893577i	$-0.648187\pi$
$709$	14.6291	−	25.3383i	0.549406	−	0.951599i	0.998315	−	0.0580220i	$-0.0184794\pi$
$710$		0			0
$711$	17.0462	−	12.7041i	0.639283	−	0.476440i
$712$		0			0
$713$	20.5309	−	35.5605i	0.768887	−	1.33175i
$714$		0			0
$715$	5.04325	+	8.73517i	0.188607	+	0.326677i
$716$		0			0
$717$	−18.4498	+	6.11887i	−0.689020	+	0.228513i
$718$		0			0
$719$	−1.07413			−0.0400581			−0.0200291	−	0.999799i	$-0.506376\pi$
$719$	−1.07413			−0.0400581			−0.0200291	+	0.999799i	$0.506376\pi$
$720$		0			0
$721$	15.8764			0.591266
$722$		0			0
$723$	9.04147	+	8.04205i	0.336256	+	0.299087i
$724$		0			0
$725$	6.69344	+	11.5934i	0.248588	+	0.430567i
$726$		0			0
$727$	12.7163	−	22.0253i	0.471623	−	0.816875i	−0.527850	−	0.849338i	$-0.677002\pi$
$727$	12.7163	−	22.0253i	0.471623	−	0.816875i	0.999473	+	0.0324628i	$0.0103350\pi$
$728$		0			0
$729$	−9.27375	−	25.3574i	−0.343472	−	0.939163i
$730$		0			0
$731$	−10.7101	+	18.5505i	−0.396129	+	0.686116i
$732$		0			0
$733$	5.69777	+	9.86883i	0.210452	+	0.364513i	0.951856	−	0.306545i	$-0.0991731\pi$
$733$	5.69777	+	9.86883i	0.210452	+	0.364513i	−0.741404	+	0.671059i	$0.765840\pi$
$734$		0			0
$735$	4.64400	+	4.13066i	0.171296	+	0.152362i
$736$		0			0
$737$	−34.5994			−1.27448
$738$		0			0
$739$	29.9395			1.10134			0.550671	−	0.834723i	$-0.314372\pi$
$739$	29.9395			1.10134			0.550671	+	0.834723i	$0.314372\pi$
$740$		0			0
$741$	1.46108	−	0.484566i	0.0536740	−	0.0178010i
$742$		0			0
$743$	−9.50069	−	16.4557i	−0.348546	−	0.603700i	0.637445	−	0.770496i	$-0.279991\pi$
$743$	−9.50069	−	16.4557i	−0.348546	−	0.603700i	−0.985991	+	0.166796i	$0.946658\pi$
$744$		0			0
$745$	15.1298	−	26.2055i	0.554311	−	0.960096i
$746$		0			0
$747$	9.88942	−	7.37033i	0.361835	−	0.269666i
$748$		0			0
$749$	−2.67673	+	4.63623i	−0.0978055	+	0.169404i
$750$		0			0
$751$	0.0130684	+	0.0226352i	0.000476873	+	0.000825969i	0.866264	−	0.499587i	$-0.166515\pi$
$751$	0.0130684	+	0.0226352i	0.000476873	+	0.000825969i	−0.865787	+	0.500413i	$0.833182\pi$
$752$		0			0
$753$	1.61628	−	7.83786i	0.0589006	−	0.285628i
$754$		0			0
$755$	−53.2929			−1.93953
$756$		0			0
$757$	−13.6910			−0.497607			−0.248803	−	0.968554i	$-0.580037\pi$
$757$	−13.6910			−0.497607			−0.248803	+	0.968554i	$0.580037\pi$
$758$		0			0
$759$	5.77816	−	28.0201i	0.209734	−	1.01707i
$760$		0			0
$761$	7.32141	+	12.6811i	0.265401	+	0.459688i	0.967669	−	0.252225i	$-0.0811623\pi$
$761$	7.32141	+	12.6811i	0.265401	+	0.459688i	−0.702268	+	0.711913i	$0.747829\pi$
$762$		0			0
$763$	9.43199	−	16.3367i	0.341461	−	0.591428i
$764$		0			0
$765$	5.16071	+	43.9562i	0.186586	+	1.58924i
$766$		0			0
$767$	−4.43818	+	7.68715i	−0.160253	+	0.277567i
$768$		0			0
$769$	−24.5672	−	42.5517i	−0.885918	−	1.53445i	−0.844658	−	0.535306i	$-0.820196\pi$
$769$	−24.5672	−	42.5517i	−0.885918	−	1.53445i	−0.0412592	−	0.999148i	$-0.513137\pi$
$770$		0			0
$771$	−2.34108	+	0.776418i	−0.0843118	+	0.0279620i
$772$		0			0
$773$	12.4413			0.447484			0.223742	−	0.974648i	$-0.428173\pi$
$773$	12.4413			0.447484			0.223742	+	0.974648i	$0.428173\pi$
$774$		0			0
$775$	55.0370			1.97699
$776$		0			0
$777$	−6.16690	−	5.48523i	−0.221236	−	0.196781i
$778$		0			0
$779$	2.40476	+	4.16516i	0.0861594	+	0.149232i
$780$		0			0
$781$	−4.04256	+	7.00193i	−0.144654	+	0.250549i
$782$		0			0
$783$	−3.73855	−	8.00119i	−0.133605	−	0.285939i
$784$		0			0
$785$	5.18292	−	8.97708i	0.184986	−	0.320406i
$786$		0			0
$787$	−16.4567	−	28.5038i	−0.586617	−	1.01605i	−0.994672	−	0.103093i	$-0.967126\pi$
$787$	−16.4567	−	28.5038i	−0.586617	−	1.01605i	0.408055	−	0.912957i	$-0.366207\pi$
$788$		0			0
$789$	21.0476	+	18.7210i	0.749314	+	0.666487i
$790$		0			0
$791$	−18.5512			−0.659606
$792$		0			0
$793$	3.87636			0.137653
$794$		0			0
$795$	0.729407	−	0.241908i	0.0258694	−	0.00857958i
$796$		0			0
$797$	−13.1989	−	22.8612i	−0.467530	−	0.809786i	0.531781	−	0.846882i	$-0.321523\pi$
$797$	−13.1989	−	22.8612i	−0.467530	−	0.809786i	−0.999312	+	0.0370953i	$0.988189\pi$
$798$		0			0
$799$	5.48074	−	9.49292i	0.193895	−	0.335835i
$800$		0			0
$801$	−26.4764	−	11.4046i	−0.935498	−	0.402963i
$802$		0			0
$803$	14.9560	−	25.9045i	0.527785	−	0.914151i
$804$		0			0
$805$	−10.5433	−	18.2614i	−0.371601	−	0.643631i
$806$		0			0
$807$	6.52537	−	31.6436i	0.229704	−	1.11391i
$808$		0			0
$809$	35.5919			1.25135			0.625673	−	0.780086i	$-0.284825\pi$
$809$	35.5919			1.25135			0.625673	+	0.780086i	$0.284825\pi$
$810$		0			0
$811$	37.8268			1.32828			0.664140	−	0.747608i	$-0.268798\pi$
$811$	37.8268			1.32828			0.664140	+	0.747608i	$0.268798\pi$
$812$		0			0
$813$	1.38626	−	6.72243i	0.0486184	−	0.235766i
$814$		0			0
$815$	18.4963	+	32.0365i	0.647896	+	1.12219i
$816$		0			0
$817$	2.31522	−	4.01008i	0.0809994	−	0.140295i
$818$		0			0
$819$	−2.75526	−	1.18682i	−0.0962766	−	0.0414708i
$820$		0			0
$821$	9.15638	−	15.8593i	0.319560	−	0.553494i	−0.660836	−	0.750530i	$-0.729798\pi$
$821$	9.15638	−	15.8593i	0.319560	−	0.553494i	0.980396	+	0.197036i	$0.0631317\pi$
$822$		0			0
$823$	−18.0000	−	31.1769i	−0.627441	−	1.08676i	−0.988063	−	0.154047i	$-0.950769\pi$
$823$	−18.0000	−	31.1769i	−0.627441	−	1.08676i	0.360623	−	0.932712i	$-0.382564\pi$
$824$		0			0
$825$	36.3974	−	12.0712i	1.26719	−	0.420265i
$826$		0			0
$827$	28.2115			0.981011			0.490505	−	0.871438i	$-0.336812\pi$
$827$	28.2115			0.981011			0.490505	+	0.871438i	$0.336812\pi$
$828$		0			0
$829$	−11.2843			−0.391919			−0.195960	−	0.980612i	$-0.562782\pi$
$829$	−11.2843			−0.391919			−0.195960	+	0.980612i	$0.562782\pi$
$830$		0			0
$831$	3.02035	+	2.68649i	0.104775	+	0.0931933i
$832$		0			0
$833$	2.05563	+	3.56046i	0.0712234	+	0.123363i
$834$		0			0
$835$	−21.8028	+	37.7636i	−0.754519	+	1.30686i
$836$		0			0
$837$	−36.1730	−	3.13656i	−1.25032	−	0.108415i
$838$		0			0
$839$	−1.02152	+	1.76933i	−0.0352669	+	0.0610840i	−0.883120	−	0.469147i	$-0.844561\pi$
$839$	−1.02152	+	1.76933i	−0.0352669	+	0.0610840i	0.847853	+	0.530231i	$0.177895\pi$
$840$		0			0
$841$	13.0556	+	22.6130i	0.450194	+	0.779759i
$842$		0			0
$843$	−36.2305	−	32.2257i	−1.24784	−	1.10991i
$844$		0			0
$845$	43.0604			1.48132
$846$		0			0
$847$	−3.09888			−0.106479
$848$		0			0
$849$	−16.9661	+	5.62680i	−0.582275	+	0.193111i
$850$		0			0
$851$	14.0007	+	24.2499i	0.479937	+	0.831276i
$852$		0			0
$853$	24.2960	−	42.0818i	0.831878	−	1.44085i	−0.0646692	−	0.997907i	$-0.520599\pi$
$853$	24.2960	−	42.0818i	0.831878	−	1.44085i	0.896547	−	0.442948i	$-0.146067\pi$
$854$		0			0
$855$	−1.11559	−	9.50206i	−0.0381525	−	0.324964i
$856$		0			0
$857$	22.4487	−	38.8823i	0.766833	−	1.32819i	−0.172439	−	0.985020i	$-0.555165\pi$
$857$	22.4487	−	38.8823i	0.766833	−	1.32819i	0.939272	−	0.343173i	$-0.111502\pi$
$858$		0			0
$859$	14.9065	+	25.8189i	0.508605	+	0.880929i	0.999950	+	0.00996438i	$0.00317181\pi$
$859$	14.9065	+	25.8189i	0.508605	+	0.880929i	−0.491346	+	0.870965i	$0.663495\pi$
$860$		0			0
$861$	1.89307	−	9.18007i	0.0645155	−	0.312856i
$862$		0			0
$863$	42.2595			1.43853			0.719265	−	0.694736i	$-0.244479\pi$
$863$	42.2595			1.43853			0.719265	+	0.694736i	$0.244479\pi$
$864$		0			0
$865$	23.7170			0.806401
$866$		0			0
$867$	0.0341093	−	0.165407i	0.00115841	−	0.00561751i
$868$		0			0
$869$	−9.95970	−	17.2507i	−0.337860	−	0.585190i
$870$		0			0
$871$	6.15452	−	10.6599i	0.208538	−	0.361198i
$872$		0			0
$873$	17.6113	−	13.1252i	0.596051	−	0.444221i
$874$		0			0
$875$	5.16071	−	8.93861i	0.174464	−	0.302180i
$876$		0			0
$877$	15.2658	+	26.4411i	0.515489	+	0.892853i	0.999838	+	0.0179782i	$0.00572295\pi$
$877$	15.2658	+	26.4411i	0.515489	+	0.892853i	−0.484350	+	0.874875i	$0.660944\pi$
$878$		0			0
$879$	−50.4640	+	16.7364i	−1.70211	+	0.564504i
$880$		0			0
$881$	−13.4079			−0.451724			−0.225862	−	0.974159i	$-0.572520\pi$
$881$	−13.4079			−0.451724			−0.225862	+	0.974159i	$0.572520\pi$
$882$		0			0
$883$	14.1250			0.475345			0.237672	−	0.971345i	$-0.423616\pi$
$883$	14.1250			0.475345			0.237672	+	0.971345i	$0.423616\pi$
$884$		0			0
$885$	41.2218	+	36.6652i	1.38565	+	1.23249i
$886$		0			0
$887$	−19.9716	−	34.5918i	−0.670581	−	1.16148i	−0.977740	−	0.209822i	$-0.932712\pi$
$887$	−19.9716	−	34.5918i	−0.670581	−	1.16148i	0.307159	−	0.951658i	$-0.400622\pi$
$888$		0			0
$889$	4.99381	−	8.64953i	0.167487	−	0.290096i
$890$		0			0
$891$	−24.6101	+	5.85949i	−0.824469	+	0.196300i
$892$		0			0
$893$	−1.18478	+	2.05209i	−0.0396471	+	0.0686707i
$894$		0			0
$895$	6.89493	+	11.9424i	0.230472	+	0.399189i
$896$		0			0
$897$	7.60507	+	6.76443i	0.253926	+	0.225858i
$898$		0			0
$899$	−11.8764			−0.396099
$900$		0			0
$901$	0.508333			0.0169350
$902$		0			0
$903$	−8.56546	+	2.84073i	−0.285041	+	0.0945337i
$904$		0			0
$905$	33.2687	+	57.6231i	1.10589	+	1.91546i
$906$		0			0
$907$	20.7101	−	35.8710i	0.687669	−	1.19108i	−0.284921	−	0.958551i	$-0.591967\pi$
$907$	20.7101	−	35.8710i	0.687669	−	1.19108i	0.972590	−	0.232527i	$-0.0746994\pi$
$908$		0			0
$909$	8.33420	−	6.21126i	0.276428	−	0.206014i
$910$		0			0
$911$	0.894237	−	1.54886i	0.0296274	−	0.0513162i	−0.850832	−	0.525439i	$-0.823901\pi$
$911$	0.894237	−	1.54886i	0.0296274	−	0.0513162i	0.880459	+	0.474122i	$0.157235\pi$
$912$		0			0
$913$	−5.77816	−	10.0081i	−0.191229	−	0.331219i
$914$		0			0
$915$	4.86584	−	23.5960i	0.160860	−	0.780058i
$916$		0			0
$917$	−16.0531			−0.530120
$918$		0			0
$919$	57.4683			1.89570			0.947852	−	0.318711i	$-0.103250\pi$
$919$	57.4683			1.89570			0.947852	+	0.318711i	$0.103250\pi$
$920$		0			0
$921$	−4.00316	+	19.4126i	−0.131909	+	0.639666i
$922$		0			0
$923$	−1.43818	−	2.49100i	−0.0473382	−	0.0819922i
$924$		0			0
$925$	−18.7658	+	32.5033i	−0.617015	+	1.06870i
$926$		0			0
$927$	5.55377	+	47.3042i	0.182410	+	1.55367i
$928$		0			0
$929$	−17.3676	+	30.0816i	−0.569813	+	0.986945i	0.426771	+	0.904360i	$0.359651\pi$
$929$	−17.3676	+	30.0816i	−0.569813	+	0.986945i	−0.996584	+	0.0825854i	$0.973682\pi$
$930$		0			0
$931$	−0.444368	−	0.769668i	−0.0145636	−	0.0252248i
$932$		0			0
$933$	−19.6669	+	6.52252i	−0.643865	+	0.213538i
$934$		0			0
$935$	41.4683			1.35616
$936$		0			0
$937$	11.6662			0.381118			0.190559	−	0.981676i	$-0.438970\pi$
$937$	11.6662			0.381118			0.190559	+	0.981676i	$0.438970\pi$
$938$		0			0
$939$	17.5283	+	15.5908i	0.572015	+	0.508786i
$940$		0			0
$941$	25.1687	+	43.5934i	0.820475	+	1.42111i	0.905329	+	0.424712i	$0.139625\pi$
$941$	25.1687	+	43.5934i	0.820475	+	1.42111i	−0.0848531	+	0.996393i	$0.527042\pi$
$942$		0			0
$943$	−15.9004	+	27.5402i	−0.517787	+	0.896833i
$944$		0			0
$945$	−10.6829	+	15.2819i	−0.347515	+	0.497121i
$946$		0			0
$947$	−16.1941	+	28.0491i	−0.526238	+	0.911472i	0.473294	+	0.880904i	$0.343065\pi$
$947$	−16.1941	+	28.0491i	−0.526238	+	0.911472i	−0.999533	+	0.0305673i	$0.990269\pi$
$948$		0			0
$949$	5.32072	+	9.21576i	0.172718	+	0.299156i
$950$		0			0
$951$	38.7774	+	34.4911i	1.25744	+	1.11845i
$952$		0			0
$953$	−12.5367			−0.406102			−0.203051	−	0.979168i	$-0.565086\pi$
$953$	−12.5367			−0.406102			−0.203051	+	0.979168i	$0.565086\pi$
$954$		0			0
$955$	16.6291			0.538104
$956$		0			0
$957$	−7.85414	+	2.60483i	−0.253888	+	0.0842021i
$958$		0			0
$959$	6.49381	+	11.2476i	0.209696	+	0.363204i
$960$		0			0
$961$	−8.91342	+	15.4385i	−0.287530	+	0.498016i
$962$		0			0
$963$	−14.7502	−	6.35359i	−0.475317	−	0.204741i
$964$		0			0
$965$	−45.3868	+	78.6122i	−1.46105	+	2.53062i
$966$		0			0
$967$	−28.9937	−	50.2186i	−0.932376	−	1.61492i	−0.779248	−	0.626715i	$-0.784399\pi$
$967$	−28.9937	−	50.2186i	−0.932376	−	1.61492i	−0.153127	−	0.988206i	$-0.548935\pi$
$968$		0			0
$969$	1.27816	−	6.19820i	0.0410604	−	0.199115i
$970$		0			0
$971$	−28.0370			−0.899750			−0.449875	−	0.893092i	$-0.648531\pi$
$971$	−28.0370			−0.899750			−0.449875	+	0.893092i	$0.648531\pi$
$972$		0			0
$973$	−1.11126			−0.0356255
$974$		0			0
$975$	−2.75526	+	13.3611i	−0.0882389	+	0.427898i
$976$		0			0
$977$	−4.92030	−	8.52220i	−0.157414	−	0.272649i	0.776521	−	0.630091i	$-0.216982\pi$
$977$	−4.92030	−	8.52220i	−0.157414	−	0.272649i	−0.933935	+	0.357442i	$0.883649\pi$
$978$		0			0
$979$	−13.5055	+	23.3922i	−0.431638	+	0.747618i
$980$		0			0
$981$	51.9752	+	22.3881i	1.65944	+	0.714798i
$982$		0			0
$983$	−24.3447	+	42.1663i	−0.776476	+	1.34490i	0.157485	+	0.987521i	$0.449661\pi$
$983$	−24.3447	+	42.1663i	−0.776476	+	1.34490i	−0.933961	+	0.357374i	$0.883672\pi$
$984$		0			0
$985$	19.2348	+	33.3157i	0.612873	+	1.06153i
$986$		0			0
$987$	4.38323	−	1.45370i	0.139520	−	0.0462718i
$988$		0			0
$989$	30.6167			0.973554
$990$		0			0
$991$	−2.86398			−0.0909772			−0.0454886	−	0.998965i	$-0.514484\pi$
$991$	−2.86398			−0.0909772			−0.0454886	+	0.998965i	$0.514484\pi$
$992$		0			0
$993$	2.70032	+	2.40183i	0.0856920	+	0.0762198i
$994$		0			0
$995$	15.7286	+	27.2428i	0.498631	+	0.863655i
$996$		0			0
$997$	25.4203	−	44.0292i	0.805069	−	1.39442i	−0.111176	−	0.993801i	$-0.535462\pi$
$997$	25.4203	−	44.0292i	0.805069	−	1.39442i	0.916245	−	0.400619i	$-0.131205\pi$
$998$		0			0
$999$	14.1862	−	20.2933i	0.448830	−	0.642051i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.r.k.673.1		6
3.2	odd	2		3024.2.r.g.2017.1		6
4.3	odd	2		63.2.f.b.43.1	yes	6
9.2	odd	6		9072.2.a.cd.1.3		3
9.4	even	3	inner	1008.2.r.k.337.1		6
9.5	odd	6		3024.2.r.g.1009.1		6
9.7	even	3		9072.2.a.bq.1.1		3
12.11	even	2		189.2.f.a.127.3		6
28.3	even	6		441.2.g.d.79.1		6
28.11	odd	6		441.2.g.e.79.1		6
28.19	even	6		441.2.h.b.214.3		6
28.23	odd	6		441.2.h.c.214.3		6
28.27	even	2		441.2.f.d.295.1		6
36.7	odd	6		567.2.a.d.1.3		3
36.11	even	6		567.2.a.g.1.1		3
36.23	even	6		189.2.f.a.64.3		6
36.31	odd	6		63.2.f.b.22.1	✓	6
84.11	even	6		1323.2.g.c.667.3		6
84.23	even	6		1323.2.h.d.802.1		6
84.47	odd	6		1323.2.h.e.802.1		6
84.59	odd	6		1323.2.g.b.667.3		6
84.83	odd	2		1323.2.f.c.883.3		6
252.23	even	6		1323.2.g.c.361.3		6
252.31	even	6		441.2.h.b.373.3		6
252.59	odd	6		1323.2.h.e.226.1		6
252.67	odd	6		441.2.h.c.373.3		6
252.83	odd	6		3969.2.a.p.1.1		3
252.95	even	6		1323.2.h.d.226.1		6
252.103	even	6		441.2.g.d.67.1		6
252.131	odd	6		1323.2.g.b.361.3		6
252.139	even	6		441.2.f.d.148.1		6
252.167	odd	6		1323.2.f.c.442.3		6
252.223	even	6		3969.2.a.m.1.3		3
252.247	odd	6		441.2.g.e.67.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.f.b.22.1	✓	6	36.31	odd	6
63.2.f.b.43.1	yes	6	4.3	odd	2
189.2.f.a.64.3		6	36.23	even	6
189.2.f.a.127.3		6	12.11	even	2
441.2.f.d.148.1		6	252.139	even	6
441.2.f.d.295.1		6	28.27	even	2
441.2.g.d.67.1		6	252.103	even	6
441.2.g.d.79.1		6	28.3	even	6
441.2.g.e.67.1		6	252.247	odd	6
441.2.g.e.79.1		6	28.11	odd	6
441.2.h.b.214.3		6	28.19	even	6
441.2.h.b.373.3		6	252.31	even	6
441.2.h.c.214.3		6	28.23	odd	6
441.2.h.c.373.3		6	252.67	odd	6
567.2.a.d.1.3		3	36.7	odd	6
567.2.a.g.1.1		3	36.11	even	6
1008.2.r.k.337.1		6	9.4	even	3	inner
1008.2.r.k.673.1		6	1.1	even	1	trivial
1323.2.f.c.442.3		6	252.167	odd	6
1323.2.f.c.883.3		6	84.83	odd	2
1323.2.g.b.361.3		6	252.131	odd	6
1323.2.g.b.667.3		6	84.59	odd	6
1323.2.g.c.361.3		6	252.23	even	6
1323.2.g.c.667.3		6	84.11	even	6
1323.2.h.d.226.1		6	252.95	even	6
1323.2.h.d.802.1		6	84.23	even	6
1323.2.h.e.226.1		6	252.59	odd	6
1323.2.h.e.802.1		6	84.47	odd	6
3024.2.r.g.1009.1		6	9.5	odd	6
3024.2.r.g.2017.1		6	3.2	odd	2
3969.2.a.m.1.3		3	252.223	even	6
3969.2.a.p.1.1		3	252.83	odd	6
9072.2.a.bq.1.1		3	9.7	even	3
9072.2.a.cd.1.3		3	9.2	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:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.r (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.349814 + 1.69636i) q^{3} +(1.79418 + 3.10761i) q^{5} +(-0.500000 + 0.866025i) q^{7} +(-2.75526 - 1.18682i) q^{9} +O(q^{10})\)	\(q+(-0.349814 + 1.69636i) q^{3} +(1.79418 + 3.10761i) q^{5} +(-0.500000 + 0.866025i) q^{7} +(-2.75526 - 1.18682i) q^{9} +(-1.40545 + 2.43430i) q^{11} +(-0.500000 - 0.866025i) q^{13} +(-5.89926 + 1.95649i) q^{15} -4.11126 q^{17} +0.888736 q^{19} +(-1.29418 - 1.15113i) q^{21} +(2.93818 + 5.08907i) q^{23} +(-3.93818 + 6.82112i) q^{25} +(2.97710 - 4.25874i) q^{27} +(0.849814 - 1.47192i) q^{29} +(-3.49381 - 6.05146i) q^{31} +(-3.63781 - 3.23569i) q^{33} -3.58836 q^{35} +4.76509 q^{37} +(1.64400 - 0.545231i) q^{39} +(2.70582 + 4.68661i) q^{41} +(2.60507 - 4.51212i) q^{43} +(-1.25526 - 10.6917i) q^{45} +(-1.33310 + 2.30900i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(1.43818 - 6.97418i) q^{51} -0.123644 q^{53} -10.0865 q^{55} +(-0.310892 + 1.50761i) q^{57} +(-4.43818 - 7.68715i) q^{59} +(-1.93818 + 3.35702i) q^{61} +(2.40545 - 1.79272i) q^{63} +(1.79418 - 3.10761i) q^{65} +(6.15452 + 10.6599i) q^{67} +(-9.66071 + 3.20397i) q^{69} +2.87636 q^{71} -10.6414 q^{73} +(-10.1934 - 9.06668i) q^{75} +(-1.40545 - 2.43430i) q^{77} +(-3.54325 + 6.13709i) q^{79} +(6.18292 + 6.53999i) q^{81} +(-2.05563 + 3.56046i) q^{83} +(-7.37636 - 12.7762i) q^{85} +(2.19963 + 1.95649i) q^{87} +9.60940 q^{89} +1.00000 q^{91} +(11.4876 - 3.80987i) q^{93} +(1.59455 + 2.76185i) q^{95} +(-3.66071 + 6.34053i) q^{97} +(6.76145 - 5.03913i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 4 q^{3} + 5 q^{5} - 3 q^{7} - 4 q^{9}+O(q^{10}) \) 6 * q + 4 * q^3 + 5 * q^5 - 3 * q^7 - 4 * q^9	\( 6 q + 4 q^{3} + 5 q^{5} - 3 q^{7} - 4 q^{9} - 2 q^{11} - 3 q^{13} - 11 q^{15} - 24 q^{17} + 6 q^{19} - 2 q^{21} - 6 q^{25} + 7 q^{27} - q^{29} - 3 q^{31} + 8 q^{33} - 10 q^{35} - 6 q^{37} - 2 q^{39} + 22 q^{41} - 3 q^{43} + 5 q^{45} - 9 q^{47} - 3 q^{49} - 9 q^{51} - 36 q^{53} + 12 q^{55} + 11 q^{57} - 9 q^{59} + 6 q^{61} + 8 q^{63} + 5 q^{65} - 39 q^{69} - 18 q^{71} + 6 q^{73} - 31 q^{75} - 2 q^{77} + 15 q^{79} + 32 q^{81} - 12 q^{83} - 9 q^{85} + q^{87} - 4 q^{89} + 6 q^{91} + 33 q^{93} + 16 q^{95} - 3 q^{97} + 46 q^{99}+O(q^{100}) \) 6 * q + 4 * q^3 + 5 * q^5 - 3 * q^7 - 4 * q^9 - 2 * q^11 - 3 * q^13 - 11 * q^15 - 24 * q^17 + 6 * q^19 - 2 * q^21 - 6 * q^25 + 7 * q^27 - q^29 - 3 * q^31 + 8 * q^33 - 10 * q^35 - 6 * q^37 - 2 * q^39 + 22 * q^41 - 3 * q^43 + 5 * q^45 - 9 * q^47 - 3 * q^49 - 9 * q^51 - 36 * q^53 + 12 * q^55 + 11 * q^57 - 9 * q^59 + 6 * q^61 + 8 * q^63 + 5 * q^65 - 39 * q^69 - 18 * q^71 + 6 * q^73 - 31 * q^75 - 2 * q^77 + 15 * q^79 + 32 * q^81 - 12 * q^83 - 9 * q^85 + q^87 - 4 * q^89 + 6 * q^91 + 33 * q^93 + 16 * q^95 - 3 * q^97 + 46 * q^99

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