LMFDB - Embedded newform 456.2.q.f.49.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [456,2,Mod(49,456)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(456, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("456.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 456 = 2^{3} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	456.q (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.64117833217$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			49.2
Root			$-0.173648 + 0.984808i$ of defining polynomial
Character	$\chi$	$=$	456.49
Dual form			456.2.q.f.121.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{3} +(-0.347296 + 0.601535i) q^{5} +0.305407 q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{3} +(-0.347296 + 0.601535i) q^{5} +0.305407 q^{7} +(-0.500000 - 0.866025i) q^{9} +4.82295 q^{11} +(-0.500000 - 0.866025i) q^{13} +(0.347296 + 0.601535i) q^{15} +(3.75877 - 6.51038i) q^{17} +(3.06418 + 3.10013i) q^{19} +(0.152704 - 0.264490i) q^{21} +(-0.347296 - 0.601535i) q^{23} +(2.25877 + 3.91231i) q^{25} -1.00000 q^{27} +(-5.06418 - 8.77141i) q^{29} -1.82295 q^{31} +(2.41147 - 4.17680i) q^{33} +(-0.106067 + 0.183713i) q^{35} +6.51754 q^{37} -1.00000 q^{39} +(-2.69459 + 4.66717i) q^{41} +(-1.84730 + 3.19961i) q^{43} +0.694593 q^{45} +(3.00000 + 5.19615i) q^{47} -6.90673 q^{49} +(-3.75877 - 6.51038i) q^{51} +(-2.71688 - 4.70578i) q^{53} +(-1.67499 + 2.90117i) q^{55} +(4.21688 - 1.10359i) q^{57} +(2.04189 - 3.53666i) q^{59} +(-0.194593 - 0.337044i) q^{61} +(-0.152704 - 0.264490i) q^{63} +0.694593 q^{65} +(3.91147 + 6.77487i) q^{67} -0.694593 q^{69} +(-5.45336 + 9.44550i) q^{71} +(2.19459 - 3.80115i) q^{73} +4.51754 q^{75} +1.47296 q^{77} +(-7.21688 + 12.5000i) q^{79} +(-0.500000 + 0.866025i) q^{81} +0.739170 q^{83} +(2.61081 + 4.52206i) q^{85} -10.1284 q^{87} +(0.411474 + 0.712694i) q^{89} +(-0.152704 - 0.264490i) q^{91} +(-0.911474 + 1.57872i) q^{93} +(-2.92902 + 0.766546i) q^{95} +(-5.45336 + 9.44550i) q^{97} +(-2.41147 - 4.17680i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{3} + 6 q^{7} - 3 q^{9}+O(q^{10}) $ 6 * q + 3 * q^3 + 6 * q^7 - 3 * q^9	$ 6 q + 3 q^{3} + 6 q^{7} - 3 q^{9} - 12 q^{11} - 3 q^{13} + 3 q^{21} - 9 q^{25} - 6 q^{27} - 12 q^{29} + 30 q^{31} - 6 q^{33} + 24 q^{35} - 6 q^{37} - 6 q^{39} - 12 q^{41} - 9 q^{43} + 18 q^{47} + 12 q^{49} + 9 q^{57} + 6 q^{59} + 3 q^{61} - 3 q^{63} + 3 q^{67} - 6 q^{71} + 9 q^{73} - 18 q^{75} - 12 q^{77} - 27 q^{79} - 3 q^{81} - 24 q^{83} + 24 q^{85} - 24 q^{87} - 18 q^{89} - 3 q^{91} + 15 q^{93} + 48 q^{95} - 6 q^{97} + 6 q^{99}+O(q^{100}) $ 6 * q + 3 * q^3 + 6 * q^7 - 3 * q^9 - 12 * q^11 - 3 * q^13 + 3 * q^21 - 9 * q^25 - 6 * q^27 - 12 * q^29 + 30 * q^31 - 6 * q^33 + 24 * q^35 - 6 * q^37 - 6 * q^39 - 12 * q^41 - 9 * q^43 + 18 * q^47 + 12 * q^49 + 9 * q^57 + 6 * q^59 + 3 * q^61 - 3 * q^63 + 3 * q^67 - 6 * q^71 + 9 * q^73 - 18 * q^75 - 12 * q^77 - 27 * q^79 - 3 * q^81 - 24 * q^83 + 24 * q^85 - 24 * q^87 - 18 * q^89 - 3 * q^91 + 15 * q^93 + 48 * q^95 - 6 * q^97 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/456\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$343$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$		0			0
$5$	−0.347296	+	0.601535i	−0.155316	+	0.269015i	−0.933174	−	0.359425i	$-0.882973\pi$
$5$	−0.347296	+	0.601535i	−0.155316	+	0.269015i	0.777858	+	0.628440i	$0.216306\pi$
$6$		0			0
$7$	0.305407			0.115433			0.0577166	−	0.998333i	$-0.481618\pi$
$7$	0.305407			0.115433			0.0577166	+	0.998333i	$0.481618\pi$
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	4.82295			1.45417			0.727087	−	0.686546i	$-0.240874\pi$
$11$	4.82295			1.45417			0.727087	+	0.686546i	$0.240874\pi$
$12$		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
$15$	0.347296	+	0.601535i	0.0896715	+	0.155316i
$16$		0			0
$17$	3.75877	−	6.51038i	0.911636	−	1.57900i	0.0998822	−	0.994999i	$-0.468153\pi$
$17$	3.75877	−	6.51038i	0.911636	−	1.57900i	0.811754	−	0.584000i	$-0.198513\pi$
$18$		0			0
$19$	3.06418	+	3.10013i	0.702971	+	0.711219i
$19$	3.06418	+	3.10013i	0.702971	+	0.711219i
$20$		0			0
$21$	0.152704	−	0.264490i	0.0333227	−	0.0577166i
$22$		0			0
$23$	−0.347296	−	0.601535i	−0.0724163	−	0.125429i	0.827544	−	0.561402i	$-0.189738\pi$
$23$	−0.347296	−	0.601535i	−0.0724163	−	0.125429i	−0.899960	+	0.435973i	$0.856404\pi$
$24$		0			0
$25$	2.25877	+	3.91231i	0.451754	+	0.782461i
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	−5.06418	−	8.77141i	−0.940394	−	1.62881i	−0.764721	−	0.644362i	$-0.777123\pi$
$29$	−5.06418	−	8.77141i	−0.940394	−	1.62881i	−0.175674	−	0.984448i	$-0.556210\pi$
$30$		0			0
$31$	−1.82295			−0.327411			−0.163706	−	0.986509i	$-0.552345\pi$
$31$	−1.82295			−0.327411			−0.163706	+	0.986509i	$0.552345\pi$
$32$		0			0
$33$	2.41147	−	4.17680i	0.419784	−	0.727087i
$34$		0			0
$35$	−0.106067	+	0.183713i	−0.0179286	+	0.0310532i
$36$		0			0
$37$	6.51754			1.07148			0.535739	−	0.844384i	$-0.320033\pi$
$37$	6.51754			1.07148			0.535739	+	0.844384i	$0.320033\pi$
$38$		0			0
$39$	−1.00000			−0.160128
$40$		0			0
$41$	−2.69459	+	4.66717i	−0.420825	+	0.728890i	−0.996020	−	0.0891261i	$-0.971593\pi$
$41$	−2.69459	+	4.66717i	−0.420825	+	0.728890i	0.575196	+	0.818016i	$0.304926\pi$
$42$		0			0
$43$	−1.84730	+	3.19961i	−0.281710	+	0.487936i	−0.971806	−	0.235782i	$-0.924235\pi$
$43$	−1.84730	+	3.19961i	−0.281710	+	0.487936i	0.690096	+	0.723718i	$0.257568\pi$
$44$		0			0
$45$	0.694593			0.103544
$46$		0			0
$47$	3.00000	+	5.19615i	0.437595	+	0.757937i	0.997503	−	0.0706177i	$-0.0224970\pi$
$47$	3.00000	+	5.19615i	0.437595	+	0.757937i	−0.559908	+	0.828554i	$0.689164\pi$
$48$		0			0
$49$	−6.90673			−0.986675
$50$		0			0
$51$	−3.75877	−	6.51038i	−0.526333	−	0.911636i
$52$		0			0
$53$	−2.71688	−	4.70578i	−0.373192	−	0.646388i	0.616862	−	0.787071i	$-0.288404\pi$
$53$	−2.71688	−	4.70578i	−0.373192	−	0.646388i	−0.990055	+	0.140683i	$0.955070\pi$
$54$		0			0
$55$	−1.67499	+	2.90117i	−0.225856	+	0.391194i
$56$		0			0
$57$	4.21688	−	1.10359i	0.558540	−	0.146174i
$58$		0			0
$59$	2.04189	−	3.53666i	0.265831	−	0.460433i	−0.701950	−	0.712226i	$-0.747687\pi$
$59$	2.04189	−	3.53666i	0.265831	−	0.460433i	0.967781	+	0.251793i	$0.0810202\pi$
$60$		0			0
$61$	−0.194593	−	0.337044i	−0.0249150	−	0.0431541i	0.853299	−	0.521422i	$-0.174598\pi$
$61$	−0.194593	−	0.337044i	−0.0249150	−	0.0431541i	−0.878214	+	0.478268i	$0.841265\pi$
$62$		0			0
$63$	−0.152704	−	0.264490i	−0.0192389	−	0.0333227i
$64$		0			0
$65$	0.694593			0.0861536
$66$		0			0
$67$	3.91147	+	6.77487i	0.477863	+	0.827682i	0.999678	−	0.0253761i	$-0.00807834\pi$
$67$	3.91147	+	6.77487i	0.477863	+	0.827682i	−0.521815	+	0.853058i	$0.674745\pi$
$68$		0			0
$69$	−0.694593			−0.0836191
$70$		0			0
$71$	−5.45336	+	9.44550i	−0.647195	+	1.12097i	0.336595	+	0.941650i	$0.390725\pi$
$71$	−5.45336	+	9.44550i	−0.647195	+	1.12097i	−0.983790	+	0.179325i	$0.942609\pi$
$72$		0			0
$73$	2.19459	−	3.80115i	0.256858	−	0.444890i	−0.708541	−	0.705670i	$-0.750646\pi$
$73$	2.19459	−	3.80115i	0.256858	−	0.444890i	0.965398	+	0.260779i	$0.0839795\pi$
$74$		0			0
$75$	4.51754			0.521641
$76$		0			0
$77$	1.47296			0.167860
$78$		0			0
$79$	−7.21688	+	12.5000i	−0.811963	+	1.40636i	0.0995259	+	0.995035i	$0.468267\pi$
$79$	−7.21688	+	12.5000i	−0.811963	+	1.40636i	−0.911489	+	0.411326i	$0.865066\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	0.739170			0.0811345			0.0405672	−	0.999177i	$-0.487084\pi$
$83$	0.739170			0.0811345			0.0405672	+	0.999177i	$0.487084\pi$
$84$		0			0
$85$	2.61081	+	4.52206i	0.283183	+	0.490487i
$86$		0			0
$87$	−10.1284			−1.08587
$88$		0			0
$89$	0.411474	+	0.712694i	0.0436162	+	0.0755454i	0.887009	−	0.461751i	$-0.152779\pi$
$89$	0.411474	+	0.712694i	0.0436162	+	0.0755454i	−0.843393	+	0.537297i	$0.819445\pi$
$90$		0			0
$91$	−0.152704	−	0.264490i	−0.0160077	−	0.0277261i
$92$		0			0
$93$	−0.911474	+	1.57872i	−0.0945155	+	0.163706i
$94$		0			0
$95$	−2.92902	+	0.766546i	−0.300511	+	0.0786459i
$96$		0			0
$97$	−5.45336	+	9.44550i	−0.553705	+	0.959045i	0.444298	+	0.895879i	$0.353453\pi$
$97$	−5.45336	+	9.44550i	−0.553705	+	0.959045i	−0.998003	+	0.0631663i	$0.979880\pi$
$98$		0			0
$99$	−2.41147	−	4.17680i	−0.242362	−	0.419784i
$100$		0			0
$101$	−4.75877	−	8.24243i	−0.473515	−	0.820153i	0.526025	−	0.850469i	$-0.323682\pi$
$101$	−4.75877	−	8.24243i	−0.473515	−	0.820153i	−0.999540	+	0.0303164i	$0.990348\pi$
$102$		0			0
$103$	−2.30541			−0.227159			−0.113579	−	0.993529i	$-0.536232\pi$
$103$	−2.30541			−0.227159			−0.113579	+	0.993529i	$0.536232\pi$
$104$		0			0
$105$	0.106067	+	0.183713i	0.0103511	+	0.0179286i
$106$		0			0
$107$	9.51754			0.920095			0.460048	−	0.887894i	$-0.347832\pi$
$107$	9.51754			0.920095			0.460048	+	0.887894i	$0.347832\pi$
$108$		0			0
$109$	−6.75877	+	11.7065i	−0.647373	+	1.12128i	0.336375	+	0.941728i	$0.390799\pi$
$109$	−6.75877	+	11.7065i	−0.647373	+	1.12128i	−0.983748	+	0.179555i	$0.942534\pi$
$110$		0			0
$111$	3.25877	−	5.64436i	0.309309	−	0.535739i
$112$		0			0
$113$	−21.0797			−1.98301			−0.991504	−	0.130078i	$-0.958477\pi$
$113$	−21.0797			−1.98301			−0.991504	+	0.130078i	$0.958477\pi$
$114$		0			0
$115$	0.482459			0.0449895
$116$		0			0
$117$	−0.500000	+	0.866025i	−0.0462250	+	0.0800641i
$118$		0			0
$119$	1.14796	−	1.98832i	0.105233	−	0.182269i
$120$		0			0
$121$	12.2608			1.11462
$122$		0			0
$123$	2.69459	+	4.66717i	0.242963	+	0.420825i
$124$		0			0
$125$	−6.61081			−0.591289
$126$		0			0
$127$	−4.69459	−	8.13127i	−0.416578	−	0.721534i	0.579015	−	0.815317i	$-0.303437\pi$
$127$	−4.69459	−	8.13127i	−0.416578	−	0.721534i	−0.995593	+	0.0937831i	$0.970104\pi$
$128$		0			0
$129$	1.84730	+	3.19961i	0.162645	+	0.281710i
$130$		0			0
$131$	4.06418	−	7.03936i	0.355089	−	0.615032i	−0.632044	−	0.774932i	$-0.717784\pi$
$131$	4.06418	−	7.03936i	0.355089	−	0.615032i	0.987133	+	0.159900i	$0.0511173\pi$
$132$		0			0
$133$	0.935822	+	0.946803i	0.0811461	+	0.0820982i
$134$		0			0
$135$	0.347296	−	0.601535i	0.0298905	−	0.0517719i
$136$		0			0
$137$	2.67499	+	4.63322i	0.228540	+	0.395843i	0.957376	−	0.288846i	$-0.0932715\pi$
$137$	2.67499	+	4.63322i	0.228540	+	0.395843i	−0.728836	+	0.684689i	$0.759938\pi$
$138$		0			0
$139$	−6.97565	−	12.0822i	−0.591667	−	1.02480i	−0.994008	−	0.109308i	$-0.965137\pi$
$139$	−6.97565	−	12.0822i	−0.591667	−	1.02480i	0.402341	−	0.915490i	$-0.368197\pi$
$140$		0			0
$141$	6.00000			0.505291
$142$		0			0
$143$	−2.41147	−	4.17680i	−0.201658	−	0.349281i
$144$		0			0
$145$	7.03508			0.584232
$146$		0			0
$147$	−3.45336	+	5.98140i	−0.284829	+	0.493338i
$148$		0			0
$149$	−5.34730	+	9.26179i	−0.438068	+	0.758755i	−0.997540	−	0.0700934i	$-0.977670\pi$
$149$	−5.34730	+	9.26179i	−0.438068	+	0.758755i	0.559473	+	0.828849i	$0.311004\pi$
$150$		0			0
$151$	−17.6459			−1.43600			−0.718001	−	0.696042i	$-0.754943\pi$
$151$	−17.6459			−1.43600			−0.718001	+	0.696042i	$0.754943\pi$
$152$		0			0
$153$	−7.51754			−0.607757
$154$		0			0
$155$	0.633103	−	1.09657i	0.0508521	−	0.0880784i
$156$		0			0
$157$	−7.95336	+	13.7756i	−0.634747	+	1.09941i	0.351821	+	0.936067i	$0.385563\pi$
$157$	−7.95336	+	13.7756i	−0.634747	+	1.09941i	−0.986569	+	0.163348i	$0.947771\pi$
$158$		0			0
$159$	−5.43376			−0.430925
$160$		0			0
$161$	−0.106067	−	0.183713i	−0.00835924	−	0.0144786i
$162$		0			0
$163$	−2.17705			−0.170520			−0.0852599	−	0.996359i	$-0.527172\pi$
$163$	−2.17705			−0.170520			−0.0852599	+	0.996359i	$0.527172\pi$
$164$		0			0
$165$	1.67499	+	2.90117i	0.130398	+	0.225856i
$166$		0			0
$167$	5.47565	+	9.48411i	0.423719	+	0.733902i	0.996300	−	0.0859458i	$-0.0273912\pi$
$167$	5.47565	+	9.48411i	0.423719	+	0.733902i	−0.572581	+	0.819848i	$0.694058\pi$
$168$		0			0
$169$	6.00000	−	10.3923i	0.461538	−	0.799408i
$170$		0			0
$171$	1.15270	−	4.20372i	0.0881495	−	0.321467i
$172$		0			0
$173$	5.06418	−	8.77141i	0.385022	−	0.666878i	−0.606750	−	0.794893i	$-0.707527\pi$
$173$	5.06418	−	8.77141i	0.385022	−	0.666878i	0.991772	+	0.128015i	$0.0408604\pi$
$174$		0			0
$175$	0.689845	+	1.19485i	0.0521474	+	0.0903219i
$176$		0			0
$177$	−2.04189	−	3.53666i	−0.153478	−	0.265831i
$178$		0			0
$179$	8.69459			0.649864			0.324932	−	0.945737i	$-0.394659\pi$
$179$	8.69459			0.649864			0.324932	+	0.945737i	$0.394659\pi$
$180$		0			0
$181$	−3.93582	−	6.81704i	−0.292547	−	0.506707i	0.681864	−	0.731479i	$-0.261170\pi$
$181$	−3.93582	−	6.81704i	−0.292547	−	0.506707i	−0.974411	+	0.224772i	$0.927836\pi$
$182$		0			0
$183$	−0.389185			−0.0287694
$184$		0			0
$185$	−2.26352	+	3.92053i	−0.166417	+	0.288243i
$186$		0			0
$187$	18.1284	−	31.3992i	1.32568	−	2.29614i
$188$		0			0
$189$	−0.305407			−0.0222151
$190$		0			0
$191$	13.8580			1.00273			0.501366	−	0.865235i	$-0.332831\pi$
$191$	13.8580			1.00273			0.501366	+	0.865235i	$0.332831\pi$
$192$		0			0
$193$	−1.04664	+	1.81283i	−0.0753386	+	0.130490i	−0.901233	−	0.433334i	$-0.857337\pi$
$193$	−1.04664	+	1.81283i	−0.0753386	+	0.130490i	0.825895	+	0.563824i	$0.190670\pi$
$194$		0			0
$195$	0.347296	−	0.601535i	0.0248704	−	0.0430768i
$196$		0			0
$197$	14.0446			1.00063			0.500317	−	0.865842i	$-0.333217\pi$
$197$	14.0446			1.00063			0.500317	+	0.865842i	$0.333217\pi$
$198$		0			0
$199$	10.9953	+	19.0443i	0.779433	+	1.35002i	0.932269	+	0.361766i	$0.117826\pi$
$199$	10.9953	+	19.0443i	0.779433	+	1.35002i	−0.152836	+	0.988252i	$0.548841\pi$
$200$		0			0
$201$	7.82295			0.551788
$202$		0			0
$203$	−1.54664	−	2.67885i	−0.108553	−	0.188019i
$204$		0			0
$205$	−1.87164	−	3.24178i	−0.130721	−	0.226416i
$206$		0			0
$207$	−0.347296	+	0.601535i	−0.0241388	+	0.0418096i
$208$		0			0
$209$	14.7784	+	14.9518i	1.02224	+	1.03424i
$210$		0			0
$211$	7.97565	−	13.8142i	0.549067	−	0.951011i	−0.449272	−	0.893395i	$-0.648317\pi$
$211$	7.97565	−	13.8142i	0.549067	−	0.951011i	0.998339	−	0.0576162i	$-0.0183500\pi$
$212$		0			0
$213$	5.45336	+	9.44550i	0.373658	+	0.647195i
$214$		0			0
$215$	−1.28312	−	2.22243i	−0.0875080	−	0.151568i
$216$		0			0
$217$	−0.556742			−0.0377941
$218$		0			0
$219$	−2.19459	−	3.80115i	−0.148297	−	0.256858i
$220$		0			0
$221$	−7.51754			−0.505685
$222$		0			0
$223$	13.2520	−	22.9531i	0.887417	−	1.53705i	0.0444991	−	0.999009i	$-0.485831\pi$
$223$	13.2520	−	22.9531i	0.887417	−	1.53705i	0.842918	−	0.538042i	$-0.180836\pi$
$224$		0			0
$225$	2.25877	−	3.91231i	0.150585	−	0.260820i
$226$		0			0
$227$	2.65539			0.176245			0.0881223	−	0.996110i	$-0.471913\pi$
$227$	2.65539			0.176245			0.0881223	+	0.996110i	$0.471913\pi$
$228$		0			0
$229$	21.2567			1.40468			0.702342	−	0.711840i	$-0.252138\pi$
$229$	21.2567			1.40468			0.702342	+	0.711840i	$0.252138\pi$
$230$		0			0
$231$	0.736482	−	1.27562i	0.0484569	−	0.0839299i
$232$		0			0
$233$	−6.75877	+	11.7065i	−0.442782	+	0.766921i	−0.997895	−	0.0648544i	$-0.979342\pi$
$233$	−6.75877	+	11.7065i	−0.442782	+	0.766921i	0.555113	+	0.831775i	$0.312675\pi$
$234$		0			0
$235$	−4.16756			−0.271861
$236$		0			0
$237$	7.21688	+	12.5000i	0.468787	+	0.811963i
$238$		0			0
$239$	−24.4688			−1.58276			−0.791379	−	0.611326i	$-0.790636\pi$
$239$	−24.4688			−1.58276			−0.791379	+	0.611326i	$0.790636\pi$
$240$		0			0
$241$	−5.93376	−	10.2776i	−0.382227	−	0.662037i	0.609153	−	0.793053i	$-0.291510\pi$
$241$	−5.93376	−	10.2776i	−0.382227	−	0.662037i	−0.991380	+	0.131016i	$0.958176\pi$
$242$		0			0
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$		0			0
$245$	2.39868	−	4.15464i	0.153246	−	0.265430i
$246$		0			0
$247$	1.15270	−	4.20372i	0.0733448	−	0.267476i
$248$		0			0
$249$	0.369585	−	0.640140i	0.0234215	−	0.0405672i
$250$		0			0
$251$	−3.69459	−	6.39922i	−0.233201	−	0.403915i	0.725548	−	0.688172i	$-0.241587\pi$
$251$	−3.69459	−	6.39922i	−0.233201	−	0.403915i	−0.958748	+	0.284257i	$0.908253\pi$
$252$		0			0
$253$	−1.67499	−	2.90117i	−0.105306	−	0.182395i
$254$		0			0
$255$	5.22163			0.326991
$256$		0			0
$257$	−2.67230	−	4.62857i	−0.166694	−	0.288722i	0.770562	−	0.637365i	$-0.219976\pi$
$257$	−2.67230	−	4.62857i	−0.166694	−	0.288722i	−0.937255	+	0.348643i	$0.886642\pi$
$258$		0			0
$259$	1.99050			0.123684
$260$		0			0
$261$	−5.06418	+	8.77141i	−0.313465	+	0.542937i
$262$		0			0
$263$	12.0642	−	20.8958i	0.743909	−	1.28849i	−0.206794	−	0.978385i	$-0.566303\pi$
$263$	12.0642	−	20.8958i	0.743909	−	1.28849i	0.950703	−	0.310104i	$-0.100364\pi$
$264$		0			0
$265$	3.77425			0.231850
$266$		0			0
$267$	0.822948			0.0503636
$268$		0			0
$269$	1.80066	−	3.11883i	0.109788	−	0.190159i	−0.805896	−	0.592057i	$-0.798316\pi$
$269$	1.80066	−	3.11883i	0.109788	−	0.190159i	0.915684	+	0.401898i	$0.131649\pi$
$270$		0			0
$271$	−9.38919	+	16.2625i	−0.570352	+	0.987879i	0.426177	+	0.904640i	$0.359860\pi$
$271$	−9.38919	+	16.2625i	−0.570352	+	0.987879i	−0.996530	+	0.0832396i	$0.973473\pi$
$272$		0			0
$273$	−0.305407			−0.0184841
$274$		0			0
$275$	10.8939	+	18.8688i	0.656929	+	1.13783i
$276$		0			0
$277$	20.1284			1.20940			0.604698	−	0.796455i	$-0.293294\pi$
$277$	20.1284			1.20940			0.604698	+	0.796455i	$0.293294\pi$
$278$		0			0
$279$	0.911474	+	1.57872i	0.0545685	+	0.0945155i
$280$		0			0
$281$	7.17024	+	12.4192i	0.427741	+	0.740869i	0.996672	−	0.0815162i	$-0.0259762\pi$
$281$	7.17024	+	12.4192i	0.427741	+	0.740869i	−0.568931	+	0.822385i	$0.692643\pi$
$282$		0			0
$283$	−3.38919	+	5.87024i	−0.201466	+	0.348950i	−0.949001	−	0.315273i	$-0.897904\pi$
$283$	−3.38919	+	5.87024i	−0.201466	+	0.348950i	0.747535	+	0.664223i	$0.231237\pi$
$284$		0			0
$285$	−0.800660	+	2.91987i	−0.0474270	+	0.172958i
$286$		0			0
$287$	−0.822948	+	1.42539i	−0.0485771	+	0.0841380i
$288$		0			0
$289$	−19.7567	−	34.2196i	−1.16216	−	2.01292i
$290$		0			0
$291$	5.45336	+	9.44550i	0.319682	+	0.553705i
$292$		0			0
$293$	16.7784			0.980203			0.490101	−	0.871665i	$-0.336960\pi$
$293$	16.7784			0.980203			0.490101	+	0.871665i	$0.336960\pi$
$294$		0			0
$295$	1.41828	+	2.45654i	0.0825755	+	0.143025i
$296$		0			0
$297$	−4.82295			−0.279856
$298$		0			0
$299$	−0.347296	+	0.601535i	−0.0200847	+	0.0347877i
$300$		0			0
$301$	−0.564178	+	0.977185i	−0.0325187	+	0.0563240i
$302$		0			0
$303$	−9.51754			−0.546768
$304$		0			0
$305$	0.270325			0.0154788
$306$		0			0
$307$	8.58172	−	14.8640i	0.489785	−	0.848332i	−0.510146	−	0.860088i	$-0.670409\pi$
$307$	8.58172	−	14.8640i	0.489785	−	0.848332i	0.999931	+	0.0117559i	$0.00374210\pi$
$308$		0			0
$309$	−1.15270	+	1.99654i	−0.0655750	+	0.113579i
$310$		0			0
$311$	−12.1729			−0.690264			−0.345132	−	0.938554i	$-0.612166\pi$
$311$	−12.1729			−0.690264			−0.345132	+	0.938554i	$0.612166\pi$
$312$		0			0
$313$	−1.85204	−	3.20783i	−0.104684	−	0.181318i	0.808925	−	0.587912i	$-0.200050\pi$
$313$	−1.85204	−	3.20783i	−0.104684	−	0.181318i	−0.913609	+	0.406594i	$0.866716\pi$
$314$		0			0
$315$	0.212134			0.0119524
$316$		0			0
$317$	−11.7811	−	20.4054i	−0.661690	−	1.14608i	−0.980171	−	0.198152i	$-0.936506\pi$
$317$	−11.7811	−	20.4054i	−0.661690	−	1.14608i	0.318481	−	0.947929i	$-0.396827\pi$
$318$		0			0
$319$	−24.4243	−	42.3041i	−1.36750	−	2.36857i
$320$		0			0
$321$	4.75877	−	8.24243i	0.265609	−	0.460048i
$322$		0			0
$323$	31.7006	−	8.29628i	1.76387	−	0.461618i
$324$		0			0
$325$	2.25877	−	3.91231i	0.125294	−	0.217016i
$326$		0			0
$327$	6.75877	+	11.7065i	0.373761	+	0.647373i
$328$		0			0
$329$	0.916222	+	1.58694i	0.0505129	+	0.0874910i
$330$		0			0
$331$	−4.30541			−0.236647			−0.118323	−	0.992975i	$-0.537752\pi$
$331$	−4.30541			−0.236647			−0.118323	+	0.992975i	$0.537752\pi$
$332$		0			0
$333$	−3.25877	−	5.64436i	−0.178580	−	0.309309i
$334$		0			0
$335$	−5.43376			−0.296878
$336$		0			0
$337$	−9.77631	+	16.9331i	−0.532550	+	0.922403i	0.466728	+	0.884401i	$0.345433\pi$
$337$	−9.77631	+	16.9331i	−0.532550	+	0.922403i	−0.999278	+	0.0380021i	$0.987901\pi$
$338$		0			0
$339$	−10.5398	+	18.2555i	−0.572445	+	0.991504i
$340$		0			0
$341$	−8.79199			−0.476113
$342$		0			0
$343$	−4.24722			−0.229328
$344$		0			0
$345$	0.241230	−	0.417822i	0.0129874	−	0.0224948i
$346$		0			0
$347$	−16.8452	+	29.1768i	−0.904300	+	1.56629i	−0.0824452	+	0.996596i	$0.526273\pi$
$347$	−16.8452	+	29.1768i	−0.904300	+	1.56629i	−0.821855	+	0.569697i	$0.807060\pi$
$348$		0			0
$349$	12.5567			0.672147			0.336073	−	0.941836i	$-0.390901\pi$
$349$	12.5567			0.672147			0.336073	+	0.941836i	$0.390901\pi$
$350$		0			0
$351$	0.500000	+	0.866025i	0.0266880	+	0.0462250i
$352$		0			0
$353$	−5.65951			−0.301225			−0.150613	−	0.988593i	$-0.548125\pi$
$353$	−5.65951			−0.301225			−0.150613	+	0.988593i	$0.548125\pi$
$354$		0			0
$355$	−3.78787	−	6.56078i	−0.201039	−	0.348210i
$356$		0			0
$357$	−1.14796	−	1.98832i	−0.0607563	−	0.105233i
$358$		0			0
$359$	−11.3892	+	19.7266i	−0.601098	+	1.04113i	0.391557	+	0.920154i	$0.371937\pi$
$359$	−11.3892	+	19.7266i	−0.601098	+	1.04113i	−0.992655	+	0.120979i	$0.961397\pi$
$360$		0			0
$361$	−0.221629	+	18.9987i	−0.0116647	+	0.999932i
$362$		0			0
$363$	6.13041	−	10.6182i	0.321763	−	0.557310i
$364$		0			0
$365$	1.52435	+	2.64025i	0.0797880	+	0.138197i
$366$		0			0
$367$	13.5574	+	23.4821i	0.707689	+	1.22575i	0.965712	+	0.259615i	$0.0835955\pi$
$367$	13.5574	+	23.4821i	0.707689	+	1.22575i	−0.258023	+	0.966139i	$0.583071\pi$
$368$		0			0
$369$	5.38919			0.280550
$370$		0			0
$371$	−0.829755	−	1.43718i	−0.0430788	−	0.0746146i
$372$		0			0
$373$	−13.9418			−0.721879			−0.360940	−	0.932589i	$-0.617544\pi$
$373$	−13.9418			−0.721879			−0.360940	+	0.932589i	$0.617544\pi$
$374$		0			0
$375$	−3.30541	+	5.72513i	−0.170690	+	0.295645i
$376$		0			0
$377$	−5.06418	+	8.77141i	−0.260818	+	0.451751i
$378$		0			0
$379$	1.08378			0.0556699			0.0278350	−	0.999613i	$-0.491139\pi$
$379$	1.08378			0.0556699			0.0278350	+	0.999613i	$0.491139\pi$
$380$		0			0
$381$	−9.38919			−0.481023
$382$		0			0
$383$	−16.5398	+	28.6478i	−0.845146	+	1.46384i	0.0403487	+	0.999186i	$0.487153\pi$
$383$	−16.5398	+	28.6478i	−0.845146	+	1.46384i	−0.885495	+	0.464650i	$0.846180\pi$
$384$		0			0
$385$	−0.511555	+	0.886039i	−0.0260713	+	0.0451567i
$386$		0			0
$387$	3.69459			0.187807
$388$		0			0
$389$	1.41147	+	2.44474i	0.0715646	+	0.123953i	0.899587	−	0.436741i	$-0.143867\pi$
$389$	1.41147	+	2.44474i	0.0715646	+	0.123953i	−0.828023	+	0.560695i	$0.810534\pi$
$390$		0			0
$391$	−5.22163			−0.264069
$392$		0			0
$393$	−4.06418	−	7.03936i	−0.205011	−	0.355089i
$394$		0			0
$395$	−5.01279	−	8.68241i	−0.252221	−	0.436860i
$396$		0			0
$397$	14.7567	−	25.5594i	0.740618	−	1.28279i	−0.211596	−	0.977357i	$-0.567866\pi$
$397$	14.7567	−	25.5594i	0.740618	−	1.28279i	0.952214	−	0.305431i	$-0.0988005\pi$
$398$		0			0
$399$	1.28787	−	0.337044i	0.0644740	−	0.0168733i
$400$		0			0
$401$	−11.1506	+	19.3135i	−0.556837	+	0.964469i	0.440922	+	0.897546i	$0.354652\pi$
$401$	−11.1506	+	19.3135i	−0.556837	+	0.964469i	−0.997758	+	0.0669236i	$0.978682\pi$
$402$		0			0
$403$	0.911474	+	1.57872i	0.0454038	+	0.0786416i
$404$		0			0
$405$	−0.347296	−	0.601535i	−0.0172573	−	0.0298905i
$406$		0			0
$407$	31.4338			1.55811
$408$		0			0
$409$	−14.8871	−	25.7853i	−0.736121	−	1.27500i	−0.954230	−	0.299075i	$-0.903322\pi$
$409$	−14.8871	−	25.7853i	−0.736121	−	1.27500i	0.218109	−	0.975924i	$-0.430011\pi$
$410$		0			0
$411$	5.34998			0.263895
$412$		0			0
$413$	0.623608	−	1.08012i	0.0306857	−	0.0531493i
$414$		0			0
$415$	−0.256711	+	0.444637i	−0.0126015	+	0.0218264i
$416$		0			0
$417$	−13.9513			−0.683198
$418$		0			0
$419$	−40.1147			−1.95973			−0.979867	−	0.199653i	$-0.936019\pi$
$419$	−40.1147			−1.95973			−0.979867	+	0.199653i	$0.936019\pi$
$420$		0			0
$421$	−17.0155	+	29.4717i	−0.829284	+	1.43636i	0.0693170	+	0.997595i	$0.477918\pi$
$421$	−17.0155	+	29.4717i	−0.829284	+	1.43636i	−0.898601	+	0.438767i	$0.855415\pi$
$422$		0			0
$423$	3.00000	−	5.19615i	0.145865	−	0.252646i
$424$		0			0
$425$	33.9608			1.64734
$426$		0			0
$427$	−0.0594300	−	0.102936i	−0.00287602	−	0.00498141i
$428$		0			0
$429$	−4.82295			−0.232854
$430$		0			0
$431$	−5.12836	−	8.88257i	−0.247024	−	0.427858i	0.715675	−	0.698434i	$-0.246119\pi$
$431$	−5.12836	−	8.88257i	−0.247024	−	0.427858i	−0.962699	+	0.270575i	$0.912786\pi$
$432$		0			0
$433$	−15.9979	−	27.7092i	−0.768812	−	1.33162i	−0.938208	−	0.346073i	$-0.887515\pi$
$433$	−15.9979	−	27.7092i	−0.768812	−	1.33162i	0.169396	−	0.985548i	$-0.445818\pi$
$434$		0			0
$435$	3.51754	−	6.09256i	0.168653	−	0.292116i
$436$		0			0
$437$	0.800660	−	2.91987i	0.0383007	−	0.139677i
$438$		0			0
$439$	−6.05943	+	10.4952i	−0.289201	+	0.500911i	−0.973619	−	0.228179i	$-0.926723\pi$
$439$	−6.05943	+	10.4952i	−0.289201	+	0.500911i	0.684418	+	0.729089i	$0.260056\pi$
$440$		0			0
$441$	3.45336	+	5.98140i	0.164446	+	0.284829i
$442$		0			0
$443$	−2.45336	−	4.24935i	−0.116563	−	0.201893i	0.801841	−	0.597538i	$-0.203854\pi$
$443$	−2.45336	−	4.24935i	−0.116563	−	0.201893i	−0.918403	+	0.395645i	$0.870521\pi$
$444$		0			0
$445$	−0.571614			−0.0270971
$446$		0			0
$447$	5.34730	+	9.26179i	0.252918	+	0.438068i
$448$		0			0
$449$	−6.12836			−0.289215			−0.144607	−	0.989489i	$-0.546192\pi$
$449$	−6.12836			−0.289215			−0.144607	+	0.989489i	$0.546192\pi$
$450$		0			0
$451$	−12.9959	+	22.5095i	−0.611952	+	1.05993i
$452$		0			0
$453$	−8.82295	+	15.2818i	−0.414538	+	0.718001i
$454$		0			0
$455$	0.212134			0.00994498
$456$		0			0
$457$	29.9959			1.40315			0.701574	−	0.712597i	$-0.252481\pi$
$457$	29.9959			1.40315			0.701574	+	0.712597i	$0.252481\pi$
$458$		0			0
$459$	−3.75877	+	6.51038i	−0.175444	+	0.303879i
$460$		0			0
$461$	8.53983	−	14.7914i	0.397740	−	0.688905i	−0.595707	−	0.803202i	$-0.703128\pi$
$461$	8.53983	−	14.7914i	0.397740	−	0.688905i	0.993447	+	0.114297i	$0.0364614\pi$
$462$		0			0
$463$	28.3756			1.31872			0.659362	−	0.751825i	$-0.270826\pi$
$463$	28.3756			1.31872			0.659362	+	0.751825i	$0.270826\pi$
$464$		0			0
$465$	−0.633103	−	1.09657i	−0.0293595	−	0.0508521i
$466$		0			0
$467$	6.61081			0.305912			0.152956	−	0.988233i	$-0.451121\pi$
$467$	6.61081			0.305912			0.152956	+	0.988233i	$0.451121\pi$
$468$		0			0
$469$	1.19459	+	2.06910i	0.0551612	+	0.0955419i
$470$		0			0
$471$	7.95336	+	13.7756i	0.366472	+	0.634747i
$472$		0			0
$473$	−8.90941	+	15.4316i	−0.409655	+	0.709544i
$474$		0			0
$475$	−5.20739	+	18.9905i	−0.238931	+	0.871343i
$476$		0			0
$477$	−2.71688	+	4.70578i	−0.124397	+	0.215463i
$478$		0			0
$479$	−5.45336	−	9.44550i	−0.249171	−	0.431576i	0.714125	−	0.700018i	$-0.246825\pi$
$479$	−5.45336	−	9.44550i	−0.249171	−	0.431576i	−0.963296	+	0.268442i	$0.913491\pi$
$480$		0			0
$481$	−3.25877	−	5.64436i	−0.148587	−	0.257360i
$482$		0			0
$483$	−0.212134			−0.00965242
$484$		0			0
$485$	−3.78787	−	6.56078i	−0.171998	−	0.297910i
$486$		0			0
$487$	11.8324			0.536179			0.268090	−	0.963394i	$-0.413608\pi$
$487$	11.8324			0.536179			0.268090	+	0.963394i	$0.413608\pi$
$488$		0			0
$489$	−1.08853	+	1.88538i	−0.0492248	+	0.0852599i
$490$		0			0
$491$	7.45336	−	12.9096i	0.336366	−	0.582602i	−0.647381	−	0.762167i	$-0.724136\pi$
$491$	7.45336	−	12.9096i	0.336366	−	0.582602i	0.983746	+	0.179565i	$0.0574689\pi$
$492$		0			0
$493$	−76.1403			−3.42919
$494$		0			0
$495$	3.34998			0.150571
$496$		0			0
$497$	−1.66550	+	2.88473i	−0.0747077	+	0.129398i
$498$		0			0
$499$	−19.9115	+	34.4877i	−0.891360	+	1.54388i	−0.0531141	+	0.998588i	$0.516915\pi$
$499$	−19.9115	+	34.4877i	−0.891360	+	1.54388i	−0.838246	+	0.545292i	$0.816419\pi$
$500$		0			0
$501$	10.9513			0.489268
$502$		0			0
$503$	5.06418	+	8.77141i	0.225801	+	0.391098i	0.956559	−	0.291538i	$-0.0941669\pi$
$503$	5.06418	+	8.77141i	0.225801	+	0.391098i	−0.730759	+	0.682636i	$0.760834\pi$
$504$		0			0
$505$	6.61081			0.294177
$506$		0			0
$507$	−6.00000	−	10.3923i	−0.266469	−	0.461538i
$508$		0			0
$509$	−12.5175	−	21.6810i	−0.554830	−	0.960994i	−0.997917	−	0.0645153i	$-0.979450\pi$
$509$	−12.5175	−	21.6810i	−0.554830	−	0.960994i	0.443086	−	0.896479i	$-0.353883\pi$
$510$		0			0
$511$	0.670245	−	1.16090i	0.0296499	−	0.0513551i
$512$		0			0
$513$	−3.06418	−	3.10013i	−0.135287	−	0.136874i
$514$		0			0
$515$	0.800660	−	1.38678i	0.0352813	−	0.0611090i
$516$		0			0
$517$	14.4688	+	25.0608i	0.636339	+	1.10217i
$518$		0			0
$519$	−5.06418	−	8.77141i	−0.222293	−	0.385022i
$520$		0			0
$521$	23.9162			1.04779			0.523894	−	0.851783i	$-0.324479\pi$
$521$	23.9162			1.04779			0.523894	+	0.851783i	$0.324479\pi$
$522$		0			0
$523$	18.4290	+	31.9200i	0.805845	+	1.39576i	0.915719	+	0.401818i	$0.131622\pi$
$523$	18.4290	+	31.9200i	0.805845	+	1.39576i	−0.109875	+	0.993945i	$0.535045\pi$
$524$		0			0
$525$	1.37969			0.0602146
$526$		0			0
$527$	−6.85204	+	11.8681i	−0.298480	+	0.516982i
$528$		0			0
$529$	11.2588	−	19.5008i	0.489512	−	0.847859i
$530$		0			0
$531$	−4.08378			−0.177221
$532$		0			0
$533$	5.38919			0.233432
$534$		0			0
$535$	−3.30541	+	5.72513i	−0.142905	+	0.247519i
$536$		0			0
$537$	4.34730	−	7.52974i	0.187600	−	0.324932i
$538$		0			0
$539$	−33.3108			−1.43480
$540$		0			0
$541$	−11.2101	−	19.4164i	−0.481959	−	0.834777i	0.517827	−	0.855485i	$-0.326741\pi$
$541$	−11.2101	−	19.4164i	−0.481959	−	0.834777i	−0.999786	+	0.0207084i	$0.993408\pi$
$542$		0			0
$543$	−7.87164			−0.337805
$544$		0			0
$545$	−4.69459	−	8.13127i	−0.201094	−	0.348305i
$546$		0			0
$547$	3.18779	+	5.52141i	0.136300	+	0.236078i	0.926093	−	0.377295i	$-0.123146\pi$
$547$	3.18779	+	5.52141i	0.136300	+	0.236078i	−0.789793	+	0.613373i	$0.789812\pi$
$548$		0			0
$549$	−0.194593	+	0.337044i	−0.00830501	+	0.0143847i
$550$		0			0
$551$	11.6750	−	42.5768i	0.497371	−	1.81383i
$552$		0			0
$553$	−2.20409	+	3.81759i	−0.0937274	+	0.162341i
$554$		0			0
$555$	2.26352	+	3.92053i	0.0960810	+	0.166417i
$556$		0			0
$557$	8.97090	+	15.5381i	0.380109	+	0.658369i	0.991078	−	0.133286i	$-0.0425530\pi$
$557$	8.97090	+	15.5381i	0.380109	+	0.658369i	−0.610968	+	0.791655i	$0.709220\pi$
$558$		0			0
$559$	3.69459			0.156265
$560$		0			0
$561$	−18.1284	−	31.3992i	−0.765380	−	1.32568i
$562$		0			0
$563$	−17.5175			−0.738276			−0.369138	−	0.929375i	$-0.620347\pi$
$563$	−17.5175			−0.738276			−0.369138	+	0.929375i	$0.620347\pi$
$564$		0			0
$565$	7.32089	−	12.6802i	0.307992	−	0.533458i
$566$		0			0
$567$	−0.152704	+	0.264490i	−0.00641295	+	0.0111076i
$568$		0			0
$569$	12.6810			0.531614			0.265807	−	0.964026i	$-0.414362\pi$
$569$	12.6810			0.531614			0.265807	+	0.964026i	$0.414362\pi$
$570$		0			0
$571$	39.0256			1.63317			0.816585	−	0.577225i	$-0.195865\pi$
$571$	39.0256			1.63317			0.816585	+	0.577225i	$0.195865\pi$
$572$		0			0
$573$	6.92902	−	12.0014i	0.289464	−	0.501366i
$574$		0			0
$575$	1.56893	−	2.71746i	0.0654287	−	0.113326i
$576$		0			0
$577$	28.2959			1.17797			0.588987	−	0.808142i	$-0.299527\pi$
$577$	28.2959			1.17797			0.588987	+	0.808142i	$0.299527\pi$
$578$		0			0
$579$	1.04664	+	1.81283i	0.0434967	+	0.0753386i
$580$		0			0
$581$	0.225748			0.00936560
$582$		0			0
$583$	−13.1034	−	22.6957i	−0.542686	−	0.939961i
$584$		0			0
$585$	−0.347296	−	0.601535i	−0.0143589	−	0.0248704i
$586$		0			0
$587$	−12.8648	+	22.2826i	−0.530989	+	0.919699i	0.468357	+	0.883539i	$0.344846\pi$
$587$	−12.8648	+	22.2826i	−0.530989	+	0.919699i	−0.999346	+	0.0361602i	$0.988487\pi$
$588$		0			0
$589$	−5.58584	−	5.65138i	−0.230160	−	0.232861i
$590$		0			0
$591$	7.02229	−	12.1630i	0.288858	−	0.500317i
$592$		0			0
$593$	6.49525	+	11.2501i	0.266728	+	0.461987i	0.968015	−	0.250893i	$-0.0807241\pi$
$593$	6.49525	+	11.2501i	0.266728	+	0.461987i	−0.701287	+	0.712879i	$0.747391\pi$
$594$		0			0
$595$	0.797362	+	1.38107i	0.0326886	+	0.0566184i
$596$		0			0
$597$	21.9905			0.900011
$598$		0			0
$599$	5.18984	+	8.98908i	0.212051	+	0.367284i	0.952356	−	0.304987i	$-0.0986523\pi$
$599$	5.18984	+	8.98908i	0.212051	+	0.367284i	−0.740305	+	0.672271i	$0.765319\pi$
$600$		0			0
$601$	−7.29591			−0.297606			−0.148803	−	0.988867i	$-0.547542\pi$
$601$	−7.29591			−0.297606			−0.148803	+	0.988867i	$0.547542\pi$
$602$		0			0
$603$	3.91147	−	6.77487i	0.159288	−	0.275894i
$604$		0			0
$605$	−4.25814	+	7.37532i	−0.173118	+	0.299849i
$606$		0			0
$607$	39.1147			1.58762			0.793809	−	0.608167i	$-0.208095\pi$
$607$	39.1147			1.58762			0.793809	+	0.608167i	$0.208095\pi$
$608$		0			0
$609$	−3.09327			−0.125346
$610$		0			0
$611$	3.00000	−	5.19615i	0.121367	−	0.210214i
$612$		0			0
$613$	−20.3209	+	35.1968i	−0.820753	+	1.42159i	0.0843693	+	0.996435i	$0.473112\pi$
$613$	−20.3209	+	35.1968i	−0.820753	+	1.42159i	−0.905122	+	0.425151i	$0.860221\pi$
$614$		0			0
$615$	−3.74329			−0.150944
$616$		0			0
$617$	8.38238	+	14.5187i	0.337462	+	0.584501i	0.983955	−	0.178419i	$-0.0570983\pi$
$617$	8.38238	+	14.5187i	0.337462	+	0.584501i	−0.646493	+	0.762920i	$0.723765\pi$
$618$		0			0
$619$	−14.0797			−0.565909			−0.282955	−	0.959133i	$-0.591315\pi$
$619$	−14.0797			−0.565909			−0.282955	+	0.959133i	$0.591315\pi$
$620$		0			0
$621$	0.347296	+	0.601535i	0.0139365	+	0.0241388i
$622$		0			0
$623$	0.125667	+	0.217662i	0.00503475	+	0.00872044i
$624$		0			0
$625$	−8.99794	+	15.5849i	−0.359918	+	0.623396i
$626$		0			0
$627$	20.3378	−	5.32256i	0.812214	−	0.212562i
$628$		0			0
$629$	24.4979	−	42.4317i	0.976797	−	1.69186i
$630$		0			0
$631$	−10.4486	−	18.0975i	−0.415953	−	0.720451i	0.579575	−	0.814919i	$-0.303219\pi$
$631$	−10.4486	−	18.0975i	−0.415953	−	0.720451i	−0.995528	+	0.0944674i	$0.969885\pi$
$632$		0			0
$633$	−7.97565	−	13.8142i	−0.317004	−	0.549067i
$634$		0			0
$635$	6.52166			0.258804
$636$		0			0
$637$	3.45336	+	5.98140i	0.136827	+	0.236992i
$638$		0			0
$639$	10.9067			0.431463
$640$		0			0
$641$	−1.69459	+	2.93512i	−0.0669324	+	0.115930i	−0.897550	−	0.440914i	$-0.854655\pi$
$641$	−1.69459	+	2.93512i	−0.0669324	+	0.115930i	0.830617	+	0.556844i	$0.187988\pi$
$642$		0			0
$643$	8.82770	−	15.2900i	0.348130	−	0.602979i	−0.637787	−	0.770213i	$-0.720150\pi$
$643$	8.82770	−	15.2900i	0.348130	−	0.602979i	0.985917	+	0.167233i	$0.0534833\pi$
$644$		0			0
$645$	−2.56624			−0.101045
$646$		0			0
$647$	−16.6500			−0.654580			−0.327290	−	0.944924i	$-0.606135\pi$
$647$	−16.6500			−0.654580			−0.327290	+	0.944924i	$0.606135\pi$
$648$		0			0
$649$	9.84793	−	17.0571i	0.386565	−	0.669550i
$650$		0			0
$651$	−0.278371	+	0.482152i	−0.0109102	+	0.0188970i
$652$		0			0
$653$	−35.5877			−1.39265			−0.696327	−	0.717724i	$-0.745184\pi$
$653$	−35.5877			−1.39265			−0.696327	+	0.717724i	$0.745184\pi$
$654$		0			0
$655$	2.82295	+	4.88949i	0.110302	+	0.191048i
$656$		0			0
$657$	−4.38919			−0.171238
$658$		0			0
$659$	−20.4561	−	35.4309i	−0.796855	−	1.38019i	−0.921655	−	0.388011i	$-0.873162\pi$
$659$	−20.4561	−	35.4309i	−0.796855	−	1.38019i	0.124800	−	0.992182i	$-0.460171\pi$
$660$		0			0
$661$	0.645897	+	1.11873i	0.0251225	+	0.0435134i	0.878313	−	0.478085i	$-0.158669\pi$
$661$	0.645897	+	1.11873i	0.0251225	+	0.0435134i	−0.853191	+	0.521599i	$0.825336\pi$
$662$		0			0
$663$	−3.75877	+	6.51038i	−0.145979	+	0.252842i
$664$		0			0
$665$	−0.894543	+	0.234109i	−0.0346889	+	0.00907834i
$666$		0			0
$667$	−3.51754	+	6.09256i	−0.136200	+	0.235905i
$668$		0			0
$669$	−13.2520	−	22.9531i	−0.512351	−	0.887417i
$670$		0			0
$671$	−0.938511	−	1.62555i	−0.0362308	−	0.0627536i
$672$		0			0
$673$	7.99588			0.308219			0.154109	−	0.988054i	$-0.450749\pi$
$673$	7.99588			0.308219			0.154109	+	0.988054i	$0.450749\pi$
$674$		0			0
$675$	−2.25877	−	3.91231i	−0.0869401	−	0.150585i
$676$		0			0
$677$	46.7701			1.79752			0.898761	−	0.438439i	$-0.144468\pi$
$677$	46.7701			1.79752			0.898761	+	0.438439i	$0.144468\pi$
$678$		0			0
$679$	−1.66550	+	2.88473i	−0.0639159	+	0.110706i
$680$		0			0
$681$	1.32770	−	2.29964i	0.0508774	−	0.0881223i
$682$		0			0
$683$	−5.69047			−0.217740			−0.108870	−	0.994056i	$-0.534723\pi$
$683$	−5.69047			−0.217740			−0.108870	+	0.994056i	$0.534723\pi$
$684$		0			0
$685$	−3.71606			−0.141983
$686$		0			0
$687$	10.6284	−	18.4089i	0.405497	−	0.702342i
$688$		0			0
$689$	−2.71688	+	4.70578i	−0.103505	+	0.179276i
$690$		0			0
$691$	−28.8485			−1.09745			−0.548725	−	0.836003i	$-0.684887\pi$
$691$	−28.8485			−1.09745			−0.548725	+	0.836003i	$0.684887\pi$
$692$		0			0
$693$	−0.736482	−	1.27562i	−0.0279766	−	0.0484569i
$694$		0			0
$695$	9.69047			0.367581
$696$		0			0
$697$	20.2567	+	35.0857i	0.767278	+	1.32896i
$698$		0			0
$699$	6.75877	+	11.7065i	0.255640	+	0.442782i
$700$		0			0
$701$	22.7716	−	39.4415i	0.860070	−	1.48969i	−0.0117902	−	0.999930i	$-0.503753\pi$
$701$	22.7716	−	39.4415i	0.860070	−	1.48969i	0.871860	−	0.489755i	$-0.162914\pi$
$702$		0			0
$703$	19.9709	+	20.2052i	0.753217	+	0.762055i
$704$		0			0
$705$	−2.08378	+	3.60921i	−0.0784796	+	0.135931i
$706$		0			0
$707$	−1.45336	−	2.51730i	−0.0546593	−	0.0946728i
$708$		0			0
$709$	15.1013	+	26.1563i	0.567142	+	0.982319i	0.996847	+	0.0793493i	$0.0252842\pi$
$709$	15.1013	+	26.1563i	0.567142	+	0.982319i	−0.429705	+	0.902969i	$0.641382\pi$
$710$		0			0
$711$	14.4338			0.541308
$712$		0			0
$713$	0.633103	+	1.09657i	0.0237099	+	0.0410668i
$714$		0			0
$715$	3.34998			0.125282
$716$		0			0
$717$	−12.2344	+	21.1906i	−0.456903	+	0.791379i
$718$		0			0
$719$	18.0770	−	31.3102i	0.674157	−	1.16767i	−0.302557	−	0.953131i	$-0.597840\pi$
$719$	18.0770	−	31.3102i	0.674157	−	1.16767i	0.976714	−	0.214543i	$-0.0688263\pi$
$720$		0			0
$721$	−0.704088			−0.0262216
$722$		0			0
$723$	−11.8675			−0.441358
$724$		0			0
$725$	22.8776	−	39.6252i	0.849654	−	1.47164i
$726$		0			0
$727$	3.65064	−	6.32310i	0.135395	−	0.234511i	−0.790353	−	0.612651i	$-0.790103\pi$
$727$	3.65064	−	6.32310i	0.135395	−	0.234511i	0.925748	+	0.378140i	$0.123436\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	13.8871	+	24.0532i	0.513634	+	0.889640i
$732$		0			0
$733$	51.4986			1.90214			0.951071	−	0.308972i	$-0.0999849\pi$
$733$	51.4986			1.90214			0.951071	+	0.308972i	$0.0999849\pi$
$734$		0			0
$735$	−2.39868	−	4.15464i	−0.0884767	−	0.153246i
$736$		0			0
$737$	18.8648	+	32.6749i	0.694895	+	1.20359i
$738$		0			0
$739$	−16.3452	+	28.3108i	−0.601269	+	1.04143i	0.391360	+	0.920238i	$0.372005\pi$
$739$	−16.3452	+	28.3108i	−0.601269	+	1.04143i	−0.992629	+	0.121191i	$0.961329\pi$
$740$		0			0
$741$	−3.06418	−	3.10013i	−0.112565	−	0.113886i
$742$		0			0
$743$	22.7965	−	39.4848i	0.836324	−	1.44856i	−0.0566239	−	0.998396i	$-0.518034\pi$
$743$	22.7965	−	39.4848i	0.836324	−	1.44856i	0.892948	−	0.450160i	$-0.148633\pi$
$744$		0			0
$745$	−3.71419	−	6.43317i	−0.136078	−	0.235693i
$746$		0			0
$747$	−0.369585	−	0.640140i	−0.0135224	−	0.0234215i
$748$		0			0
$749$	2.90673			0.106209
$750$		0			0
$751$	9.15270	+	15.8529i	0.333987	+	0.578482i	0.983290	−	0.182048i	$-0.0582725\pi$
$751$	9.15270	+	15.8529i	0.333987	+	0.578482i	−0.649303	+	0.760530i	$0.724939\pi$
$752$		0			0
$753$	−7.38919			−0.269277
$754$		0			0
$755$	6.12836	−	10.6146i	0.223034	−	0.386306i
$756$		0			0
$757$	15.7121	−	27.2142i	0.571067	−	0.989117i	−0.425390	−	0.905010i	$-0.639863\pi$
$757$	15.7121	−	27.2142i	0.571067	−	0.989117i	0.996457	−	0.0841071i	$-0.0268038\pi$
$758$		0			0
$759$	−3.34998			−0.121597
$760$		0			0
$761$	38.5580			1.39773			0.698863	−	0.715255i	$-0.253690\pi$
$761$	38.5580			1.39773			0.698863	+	0.715255i	$0.253690\pi$
$762$		0			0
$763$	−2.06418	+	3.57526i	−0.0747283	+	0.129433i
$764$		0			0
$765$	2.61081	−	4.52206i	0.0943942	−	0.163496i
$766$		0			0
$767$	−4.08378			−0.147457
$768$		0			0
$769$	−7.37164	−	12.7681i	−0.265828	−	0.460428i	0.701952	−	0.712224i	$-0.252312\pi$
$769$	−7.37164	−	12.7681i	−0.265828	−	0.460428i	−0.967780	+	0.251796i	$0.918979\pi$
$770$		0			0
$771$	−5.34461			−0.192481
$772$		0			0
$773$	1.95130	+	3.37976i	0.0701835	+	0.121561i	0.898982	−	0.437986i	$-0.144308\pi$
$773$	1.95130	+	3.37976i	0.0701835	+	0.121561i	−0.828798	+	0.559548i	$0.810975\pi$
$774$		0			0
$775$	−4.11762	−	7.13193i	−0.147909	−	0.256186i
$776$		0			0
$777$	0.995252	−	1.72383i	0.0357045	−	0.0618420i
$778$		0			0
$779$	−22.7256	+	5.94745i	−0.814228	+	0.213090i
$780$		0			0
$781$	−26.3013	+	45.5552i	−0.941134	+	1.63009i
$782$		0			0
$783$	5.06418	+	8.77141i	0.180979	+	0.313465i
$784$		0			0
$785$	−5.52435	−	9.56845i	−0.197172	−	0.341513i
$786$		0			0
$787$	−10.7879			−0.384546			−0.192273	−	0.981341i	$-0.561586\pi$
$787$	−10.7879			−0.384546			−0.192273	+	0.981341i	$0.561586\pi$
$788$		0			0
$789$	−12.0642	−	20.8958i	−0.429496	−	0.743909i
$790$		0			0
$791$	−6.43788			−0.228905
$792$		0			0
$793$	−0.194593	+	0.337044i	−0.00691019	+	0.0119688i
$794$		0			0
$795$	1.88713	−	3.26860i	0.0669295	−	0.115925i
$796$		0			0
$797$	−48.5526			−1.71982			−0.859911	−	0.510444i	$-0.829481\pi$
$797$	−48.5526			−1.71982			−0.859911	+	0.510444i	$0.829481\pi$
$798$		0			0
$799$	45.1052			1.59571
$800$		0			0
$801$	0.411474	−	0.712694i	0.0145387	−	0.0251818i
$802$		0			0
$803$	10.5844	−	18.3327i	0.373516	−	0.646948i
$804$		0			0
$805$	0.147347			0.00519328
$806$		0			0
$807$	−1.80066	−	3.11883i	−0.0633862	−	0.109788i
$808$		0			0
$809$	−35.8972			−1.26208			−0.631040	−	0.775751i	$-0.717372\pi$
$809$	−35.8972			−1.26208			−0.631040	+	0.775751i	$0.717372\pi$
$810$		0			0
$811$	3.17705	+	5.50282i	0.111561	+	0.193230i	0.916400	−	0.400264i	$-0.131082\pi$
$811$	3.17705	+	5.50282i	0.111561	+	0.193230i	−0.804839	+	0.593494i	$0.797748\pi$
$812$		0			0
$813$	9.38919	+	16.2625i	0.329293	+	0.570352i
$814$		0			0
$815$	0.756082	−	1.30957i	0.0264844	−	0.0458723i
$816$		0			0
$817$	−15.5797	+	4.07732i	−0.545063	+	0.142647i
$818$		0			0
$819$	−0.152704	+	0.264490i	−0.00533590	+	0.00924205i
$820$		0			0
$821$	6.93582	+	12.0132i	0.242062	+	0.419263i	0.961301	−	0.275499i	$-0.0888430\pi$
$821$	6.93582	+	12.0132i	0.242062	+	0.419263i	−0.719240	+	0.694762i	$0.755510\pi$
$822$		0			0
$823$	−2.95130	−	5.11181i	−0.102876	−	0.178186i	0.809992	−	0.586440i	$-0.199471\pi$
$823$	−2.95130	−	5.11181i	−0.102876	−	0.178186i	−0.912868	+	0.408254i	$0.866138\pi$
$824$		0			0
$825$	21.7879			0.758556
$826$		0			0
$827$	−11.9709	−	20.7342i	−0.416269	−	0.720999i	0.579292	−	0.815120i	$-0.303329\pi$
$827$	−11.9709	−	20.7342i	−0.416269	−	0.720999i	−0.995561	+	0.0941211i	$0.969996\pi$
$828$		0			0
$829$	20.4593			0.710583			0.355291	−	0.934756i	$-0.384382\pi$
$829$	20.4593			0.710583			0.355291	+	0.934756i	$0.384382\pi$
$830$		0			0
$831$	10.0642	−	17.4317i	0.349122	−	0.604698i
$832$		0			0
$833$	−25.9608	+	44.9654i	−0.899488	+	1.55796i
$834$		0			0
$835$	−7.60670			−0.263241
$836$		0			0
$837$	1.82295			0.0630103
$838$		0			0
$839$	14.3628	−	24.8771i	0.495858	−	0.858852i	−0.504130	−	0.863628i	$-0.668187\pi$
$839$	14.3628	−	24.8771i	0.495858	−	0.858852i	0.999989	+	0.00477600i	$0.00152025\pi$
$840$		0			0
$841$	−36.7918	+	63.7253i	−1.26868	+	2.19742i
$842$		0			0
$843$	14.3405			0.493913
$844$		0			0
$845$	4.16756	+	7.21842i	0.143368	+	0.248321i
$846$		0			0
$847$	3.74455			0.128664
$848$		0			0
$849$	3.38919	+	5.87024i	0.116317	+	0.201466i
$850$		0			0
$851$	−2.26352	−	3.92053i	−0.0775924	−	0.134394i
$852$		0			0
$853$	1.22369	−	2.11949i	0.0418983	−	0.0725700i	−0.844316	−	0.535846i	$-0.819993\pi$
$853$	1.22369	−	2.11949i	0.0418983	−	0.0725700i	0.886214	+	0.463276i	$0.153326\pi$
$854$		0			0
$855$	2.12836	+	2.15333i	0.0727882	+	0.0736423i
$856$		0			0
$857$	10.0351	−	17.3813i	0.342792	−	0.593733i	−0.642158	−	0.766572i	$-0.721961\pi$
$857$	10.0351	−	17.3813i	0.342792	−	0.593733i	0.984950	+	0.172839i	$0.0552941\pi$
$858$		0			0
$859$	−22.5128	−	38.9933i	−0.768127	−	1.33043i	−0.938578	−	0.345068i	$-0.887856\pi$
$859$	−22.5128	−	38.9933i	−0.768127	−	1.33043i	0.170451	−	0.985366i	$-0.445478\pi$
$860$		0			0
$861$	0.822948	+	1.42539i	0.0280460	+	0.0485771i
$862$		0			0
$863$	−18.5918			−0.632873			−0.316437	−	0.948614i	$-0.602486\pi$
$863$	−18.5918			−0.632873			−0.316437	+	0.948614i	$0.602486\pi$
$864$		0			0
$865$	3.51754	+	6.09256i	0.119600	+	0.207153i
$866$		0			0
$867$	−39.5134			−1.34195
$868$		0			0
$869$	−34.8066	+	60.2869i	−1.18073	+	2.04509i
$870$		0			0
$871$	3.91147	−	6.77487i	0.132535	−	0.229558i
$872$		0			0
$873$	10.9067			0.369137
$874$		0			0
$875$	−2.01899			−0.0682544
$876$		0			0
$877$	−3.86959	+	6.70232i	−0.130667	+	0.226321i	−0.923934	−	0.382553i	$-0.875045\pi$
$877$	−3.86959	+	6.70232i	−0.130667	+	0.226321i	0.793267	+	0.608874i	$0.208378\pi$
$878$		0			0
$879$	8.38919	−	14.5305i	0.282960	−	0.490101i
$880$		0			0
$881$	15.0487			0.507003			0.253502	−	0.967335i	$-0.418418\pi$
$881$	15.0487			0.507003			0.253502	+	0.967335i	$0.418418\pi$
$882$		0			0
$883$	0.281059	+	0.486809i	0.00945839	+	0.0163824i	0.870716	−	0.491786i	$-0.163656\pi$
$883$	0.281059	+	0.486809i	0.00945839	+	0.0163824i	−0.861257	+	0.508169i	$0.830323\pi$
$884$		0			0
$885$	2.83656			0.0953500
$886$		0			0
$887$	−1.43107	−	2.47869i	−0.0480508	−	0.0832264i	0.841000	−	0.541036i	$-0.181968\pi$
$887$	−1.43107	−	2.47869i	−0.0480508	−	0.0832264i	−0.889050	+	0.457809i	$0.848634\pi$
$888$		0			0
$889$	−1.43376	−	2.48335i	−0.0480869	−	0.0832889i
$890$		0			0
$891$	−2.41147	+	4.17680i	−0.0807874	+	0.139928i
$892$		0			0
$893$	−6.91622	+	25.2223i	−0.231443	+	0.844033i
$894$		0			0
$895$	−3.01960	+	5.23010i	−0.100934	+	0.174823i
$896$		0			0
$897$	0.347296	+	0.601535i	0.0115959	+	0.0200847i
$898$		0			0
$899$	9.23173	+	15.9898i	0.307896	+	0.533291i
$900$		0			0
$901$	−40.8485			−1.36086
$902$		0			0
$903$	0.564178	+	0.977185i	0.0187747	+	0.0325187i
$904$		0			0
$905$	5.46759			0.181749
$906$		0			0
$907$	17.0351	−	29.5056i	0.565641	−	0.979718i	−0.431349	−	0.902185i	$-0.641962\pi$
$907$	17.0351	−	29.5056i	0.565641	−	0.979718i	0.996990	−	0.0775332i	$-0.0247044\pi$
$908$		0			0
$909$	−4.75877	+	8.24243i	−0.157838	+	0.273384i
$910$		0			0
$911$	−5.90261			−0.195562			−0.0977811	−	0.995208i	$-0.531174\pi$
$911$	−5.90261			−0.195562			−0.0977811	+	0.995208i	$0.531174\pi$
$912$		0			0
$913$	3.56498			0.117984
$914$		0			0
$915$	0.135163	−	0.234109i	0.00446834	−	0.00773939i
$916$		0			0
$917$	1.24123	−	2.14987i	0.0409890	−	0.0709950i
$918$		0			0
$919$	−0.394562			−0.0130154			−0.00650770	−	0.999979i	$-0.502071\pi$
$919$	−0.394562			−0.0130154			−0.00650770	+	0.999979i	$0.502071\pi$
$920$		0			0
$921$	−8.58172	−	14.8640i	−0.282777	−	0.489785i
$922$		0			0
$923$	10.9067			0.358999
$924$		0			0
$925$	14.7216	+	25.4986i	0.484044	+	0.838389i
$926$		0			0
$927$	1.15270	+	1.99654i	0.0378598	+	0.0655750i
$928$		0			0
$929$	16.8999	−	29.2715i	0.554468	−	0.960367i	−0.443476	−	0.896286i	$-0.646255\pi$
$929$	16.8999	−	29.2715i	0.554468	−	0.960367i	0.997945	−	0.0640813i	$-0.0204117\pi$
$930$		0			0
$931$	−21.1634	−	21.4118i	−0.693604	−	0.701742i
$932$		0			0
$933$	−6.08647	+	10.5421i	−0.199262	+	0.345132i
$934$		0			0
$935$	12.5918	+	21.8097i	0.411797	+	0.713253i
$936$		0			0
$937$	−20.8601	−	36.1307i	−0.681469	−	1.18034i	−0.974532	−	0.224247i	$-0.928008\pi$
$937$	−20.8601	−	36.1307i	−0.681469	−	1.18034i	0.293063	−	0.956093i	$-0.405325\pi$
$938$		0			0
$939$	−3.70409			−0.120878
$940$		0			0
$941$	−4.73917	−	8.20848i	−0.154493	−	0.267589i	0.778382	−	0.627791i	$-0.216041\pi$
$941$	−4.73917	−	8.20848i	−0.154493	−	0.267589i	−0.932874	+	0.360203i	$0.882708\pi$
$942$		0			0
$943$	3.74329			0.121898
$944$		0			0
$945$	0.106067	−	0.183713i	0.00345035	−	0.00597619i
$946$		0			0
$947$	−3.71007	+	6.42604i	−0.120561	+	0.208818i	−0.919989	−	0.391944i	$-0.871803\pi$
$947$	−3.71007	+	6.42604i	−0.120561	+	0.208818i	0.799428	+	0.600762i	$0.205136\pi$
$948$		0			0
$949$	−4.38919			−0.142479
$950$		0			0
$951$	−23.5621			−0.764054
$952$		0			0
$953$	−0.909415	+	1.57515i	−0.0294588	+	0.0510242i	−0.880379	−	0.474271i	$-0.842712\pi$
$953$	−0.909415	+	1.57515i	−0.0294588	+	0.0510242i	0.850920	+	0.525295i	$0.176045\pi$
$954$		0			0
$955$	−4.81284	+	8.33609i	−0.155740	+	0.269750i
$956$		0			0
$957$	−48.8485			−1.57905
$958$		0			0
$959$	0.816962	+	1.41502i	0.0263811	+	0.0456934i
$960$		0			0
$961$	−27.6769			−0.892802
$962$		0			0
$963$	−4.75877	−	8.24243i	−0.153349	−	0.265609i
$964$		0			0
$965$	−0.726986	−	1.25918i	−0.0234025	−	0.0405343i
$966$		0			0
$967$	−2.95067	+	5.11072i	−0.0948873	+	0.164350i	−0.909562	−	0.415569i	$-0.863582\pi$
$967$	−2.95067	+	5.11072i	−0.0948873	+	0.164350i	0.814674	+	0.579919i	$0.196916\pi$
$968$		0			0
$969$	8.66550	−	31.6016i	0.278376	−	1.01519i
$970$		0			0
$971$	−22.6851	+	39.2917i	−0.727999	+	1.26093i	0.229728	+	0.973255i	$0.426216\pi$
$971$	−22.6851	+	39.2917i	−0.727999	+	1.26093i	−0.957727	+	0.287677i	$0.907117\pi$
$972$		0			0
$973$	−2.13041	−	3.68999i	−0.0682980	−	0.118296i
$974$		0			0
$975$	−2.25877	−	3.91231i	−0.0723385	−	0.125294i
$976$		0			0
$977$	−36.2377			−1.15935			−0.579674	−	0.814849i	$-0.696820\pi$
$977$	−36.2377			−1.15935			−0.579674	+	0.814849i	$0.696820\pi$
$978$		0			0
$979$	1.98452	+	3.43729i	0.0634255	+	0.109856i
$980$		0			0
$981$	13.5175			0.431582
$982$		0			0
$983$	4.32770	−	7.49579i	0.138032	−	0.239079i	−0.788720	−	0.614753i	$-0.789256\pi$
$983$	4.32770	−	7.49579i	0.138032	−	0.239079i	0.926752	+	0.375675i	$0.122589\pi$
$984$		0			0
$985$	−4.87763	+	8.44830i	−0.155414	+	0.269185i
$986$		0			0
$987$	1.83244			0.0583273
$988$		0			0
$989$	2.56624			0.0816016
$990$		0			0
$991$	−29.9020	+	51.7917i	−0.949868	+	1.64522i	−0.204169	+	0.978936i	$0.565449\pi$
$991$	−29.9020	+	51.7917i	−0.949868	+	1.64522i	−0.745699	+	0.666283i	$0.767884\pi$
$992$		0			0
$993$	−2.15270	+	3.72859i	−0.0683140	+	0.118323i
$994$		0			0
$995$	−15.2744			−0.484232
$996$		0			0
$997$	7.52498	+	13.0336i	0.238318	+	0.412780i	0.960232	−	0.279204i	$-0.0900705\pi$
$997$	7.52498	+	13.0336i	0.238318	+	0.412780i	−0.721913	+	0.691983i	$0.756737\pi$
$998$		0			0
$999$	−6.51754			−0.206206

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	456.2.q.f.49.2	✓	6
3.2	odd	2		1368.2.s.j.505.2		6
4.3	odd	2		912.2.q.k.49.2		6
12.11	even	2		2736.2.s.x.1873.2		6
19.7	even	3	inner	456.2.q.f.121.2	yes	6
19.8	odd	6		8664.2.a.z.1.2		3
19.11	even	3		8664.2.a.x.1.2		3
57.26	odd	6		1368.2.s.j.577.2		6
76.7	odd	6		912.2.q.k.577.2		6
228.83	even	6		2736.2.s.x.577.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.2.q.f.49.2	✓	6	1.1	even	1	trivial
456.2.q.f.121.2	yes	6	19.7	even	3	inner
912.2.q.k.49.2		6	4.3	odd	2
912.2.q.k.577.2		6	76.7	odd	6
1368.2.s.j.505.2		6	3.2	odd	2
1368.2.s.j.577.2		6	57.26	odd	6
2736.2.s.x.577.2		6	228.83	even	6
2736.2.s.x.1873.2		6	12.11	even	2
8664.2.a.x.1.2		3	19.11	even	3
8664.2.a.z.1.2		3	19.8	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:	\( N \)	\(=\)	\( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	456.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{3} +(-0.347296 + 0.601535i) q^{5} +0.305407 q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{3} +(-0.347296 + 0.601535i) q^{5} +0.305407 q^{7} +(-0.500000 - 0.866025i) q^{9} +4.82295 q^{11} +(-0.500000 - 0.866025i) q^{13} +(0.347296 + 0.601535i) q^{15} +(3.75877 - 6.51038i) q^{17} +(3.06418 + 3.10013i) q^{19} +(0.152704 - 0.264490i) q^{21} +(-0.347296 - 0.601535i) q^{23} +(2.25877 + 3.91231i) q^{25} -1.00000 q^{27} +(-5.06418 - 8.77141i) q^{29} -1.82295 q^{31} +(2.41147 - 4.17680i) q^{33} +(-0.106067 + 0.183713i) q^{35} +6.51754 q^{37} -1.00000 q^{39} +(-2.69459 + 4.66717i) q^{41} +(-1.84730 + 3.19961i) q^{43} +0.694593 q^{45} +(3.00000 + 5.19615i) q^{47} -6.90673 q^{49} +(-3.75877 - 6.51038i) q^{51} +(-2.71688 - 4.70578i) q^{53} +(-1.67499 + 2.90117i) q^{55} +(4.21688 - 1.10359i) q^{57} +(2.04189 - 3.53666i) q^{59} +(-0.194593 - 0.337044i) q^{61} +(-0.152704 - 0.264490i) q^{63} +0.694593 q^{65} +(3.91147 + 6.77487i) q^{67} -0.694593 q^{69} +(-5.45336 + 9.44550i) q^{71} +(2.19459 - 3.80115i) q^{73} +4.51754 q^{75} +1.47296 q^{77} +(-7.21688 + 12.5000i) q^{79} +(-0.500000 + 0.866025i) q^{81} +0.739170 q^{83} +(2.61081 + 4.52206i) q^{85} -10.1284 q^{87} +(0.411474 + 0.712694i) q^{89} +(-0.152704 - 0.264490i) q^{91} +(-0.911474 + 1.57872i) q^{93} +(-2.92902 + 0.766546i) q^{95} +(-5.45336 + 9.44550i) q^{97} +(-2.41147 - 4.17680i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{3} + 6 q^{7} - 3 q^{9}+O(q^{10}) \) 6 * q + 3 * q^3 + 6 * q^7 - 3 * q^9	\( 6 q + 3 q^{3} + 6 q^{7} - 3 q^{9} - 12 q^{11} - 3 q^{13} + 3 q^{21} - 9 q^{25} - 6 q^{27} - 12 q^{29} + 30 q^{31} - 6 q^{33} + 24 q^{35} - 6 q^{37} - 6 q^{39} - 12 q^{41} - 9 q^{43} + 18 q^{47} + 12 q^{49} + 9 q^{57} + 6 q^{59} + 3 q^{61} - 3 q^{63} + 3 q^{67} - 6 q^{71} + 9 q^{73} - 18 q^{75} - 12 q^{77} - 27 q^{79} - 3 q^{81} - 24 q^{83} + 24 q^{85} - 24 q^{87} - 18 q^{89} - 3 q^{91} + 15 q^{93} + 48 q^{95} - 6 q^{97} + 6 q^{99}+O(q^{100}) \) 6 * q + 3 * q^3 + 6 * q^7 - 3 * q^9 - 12 * q^11 - 3 * q^13 + 3 * q^21 - 9 * q^25 - 6 * q^27 - 12 * q^29 + 30 * q^31 - 6 * q^33 + 24 * q^35 - 6 * q^37 - 6 * q^39 - 12 * q^41 - 9 * q^43 + 18 * q^47 + 12 * q^49 + 9 * q^57 + 6 * q^59 + 3 * q^61 - 3 * q^63 + 3 * q^67 - 6 * q^71 + 9 * q^73 - 18 * q^75 - 12 * q^77 - 27 * q^79 - 3 * q^81 - 24 * q^83 + 24 * q^85 - 24 * q^87 - 18 * q^89 - 3 * q^91 + 15 * q^93 + 48 * q^95 - 6 * q^97 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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