LMFDB - Embedded newform 1092.2.q.d.625.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1092,2,Mod(625,1092)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1092, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 2, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1092.625"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1092 = 2^{2} \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1092.q (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [6,0,3,0,-5] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$8.71966390072$
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:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			625.1
Root			$0.500000 - 0.224437i$ of defining polynomial
Character	$\chi$	$=$	1092.625
Dual form			1092.2.q.d.781.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 + 0.866025i) q^{3} +(-1.84981 + 3.20397i) q^{5} +(1.23855 - 2.33795i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(0.794182 + 1.37556i) q^{11} -1.00000 q^{13} -3.69963 q^{15} +(0.444368 + 0.769668i) q^{17} +(-3.08836 + 5.34920i) q^{19} +(2.64400 - 0.0963576i) q^{21} +(-3.34362 + 5.79133i) q^{23} +(-4.34362 - 7.52338i) q^{25} -1.00000 q^{27} +5.87636 q^{29} +(-0.761450 - 1.31887i) q^{31} +(-0.794182 + 1.37556i) q^{33} +(5.19963 + 8.29305i) q^{35} +(1.55563 - 2.69443i) q^{37} +(-0.500000 - 0.866025i) q^{39} -11.4981 q^{41} -5.06546 q^{43} +(-1.84981 - 3.20397i) q^{45} +(-3.00000 + 5.19615i) q^{47} +(-3.93199 - 5.79133i) q^{49} +(-0.444368 + 0.769668i) q^{51} +(0.382546 + 0.662589i) q^{53} -5.87636 q^{55} -6.17673 q^{57} +(-2.73855 - 4.74331i) q^{59} +(0.0327319 - 0.0566933i) q^{61} +(1.40545 + 2.24159i) q^{63} +(1.84981 - 3.20397i) q^{65} +(-5.30470 - 9.18801i) q^{67} -6.68725 q^{69} -5.09888 q^{71} +(4.52654 + 7.84020i) q^{73} +(4.34362 - 7.52338i) q^{75} +(4.19963 - 0.153051i) q^{77} +(-2.82691 + 4.89636i) q^{79} +(-0.500000 - 0.866025i) q^{81} +13.1643 q^{83} -3.28799 q^{85} +(2.93818 + 5.08907i) q^{87} +(-3.90545 + 6.76443i) q^{89} +(-1.23855 + 2.33795i) q^{91} +(0.761450 - 1.31887i) q^{93} +(-11.4258 - 19.7901i) q^{95} +1.11126 q^{97} -1.58836 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{3} - 5 q^{5} + 2 q^{7} - 3 q^{9} - q^{11} - 6 q^{13} - 10 q^{15} + 3 q^{17} - 7 q^{19} + 4 q^{21} + 4 q^{23} - 2 q^{25} - 6 q^{27} - 10 q^{31} + q^{33} + 19 q^{35} + 9 q^{37} - 3 q^{39} - 8 q^{41}+ \cdots + 2 q^{99}+O(q^{100}) $ 6 * q + 3 * q^3 - 5 * q^5 + 2 * q^7 - 3 * q^9 - q^11 - 6 * q^13 - 10 * q^15 + 3 * q^17 - 7 * q^19 + 4 * q^21 + 4 * q^23 - 2 * q^25 - 6 * q^27 - 10 * q^31 + q^33 + 19 * q^35 + 9 * q^37 - 3 * q^39 - 8 * q^41 - 8 * q^43 - 5 * q^45 - 18 * q^47 + 12 * q^49 - 3 * q^51 - 15 * q^53 - 14 * q^57 - 11 * q^59 - 11 * q^61 + 2 * q^63 + 5 * q^65 - q^67 + 8 * q^69 + 6 * q^71 - 2 * q^73 + 2 * q^75 + 13 * q^77 - 3 * q^81 + 20 * q^83 + 4 * q^85 - 17 * q^89 - 2 * q^91 + 10 * q^93 - 15 * q^95 + 6 * q^97 + 2 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1092\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$547$	$925$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$	$1$

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
$5$	−1.84981	+	3.20397i	−0.827262	+	1.43286i	0.0729162	+	0.997338i	$0.476769\pi$
$5$	−1.84981	+	3.20397i	−0.827262	+	1.43286i	−0.900178	+	0.435522i	$0.856564\pi$
$6$		0			0
$7$	1.23855	−	2.33795i	0.468128	−	0.883661i
$7$	1.23855	−	2.33795i	0.468128	−	0.883661i
$8$		0			0
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	0.794182	+	1.37556i	0.239455	+	0.414748i	0.960558	−	0.278080i	$-0.0896979\pi$
$11$	0.794182	+	1.37556i	0.239455	+	0.414748i	−0.721103	+	0.692828i	$0.756365\pi$
$12$		0			0
$13$	−1.00000			−0.277350
$13$	−1.00000			−0.277350
$14$		0			0
$15$	−3.69963			−0.955240
$16$		0			0
$17$	0.444368	+	0.769668i	0.107775	+	0.186672i	0.914869	−	0.403752i	$-0.132294\pi$
$17$	0.444368	+	0.769668i	0.107775	+	0.186672i	−0.807094	+	0.590424i	$0.798961\pi$
$18$		0			0
$19$	−3.08836	+	5.34920i	−0.708519	+	1.22719i	0.256887	+	0.966441i	$0.417303\pi$
$19$	−3.08836	+	5.34920i	−0.708519	+	1.22719i	−0.965406	+	0.260750i	$0.916030\pi$
$20$		0			0
$21$	2.64400	−	0.0963576i	0.576967	−	0.0210269i
$22$		0			0
$23$	−3.34362	+	5.79133i	−0.697194	+	1.20758i	0.272242	+	0.962229i	$0.412235\pi$
$23$	−3.34362	+	5.79133i	−0.697194	+	1.20758i	−0.969436	+	0.245346i	$0.921098\pi$
$24$		0			0
$25$	−4.34362	−	7.52338i	−0.868725	−	1.50468i
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	5.87636			1.09121			0.545606	−	0.838042i	$-0.316300\pi$
$29$	5.87636			1.09121			0.545606	+	0.838042i	$0.316300\pi$
$30$		0			0
$31$	−0.761450	−	1.31887i	−0.136760	−	0.236876i	0.789508	−	0.613740i	$-0.210336\pi$
$31$	−0.761450	−	1.31887i	−0.136760	−	0.236876i	−0.926269	+	0.376864i	$0.877002\pi$
$32$		0			0
$33$	−0.794182	+	1.37556i	−0.138249	+	0.239455i
$34$		0			0
$35$	5.19963	+	8.29305i	0.878898	+	1.40178i
$36$		0			0
$37$	1.55563	−	2.69443i	0.255744	−	0.442962i	−0.709353	−	0.704853i	$-0.751013\pi$
$37$	1.55563	−	2.69443i	0.255744	−	0.442962i	0.965097	+	0.261891i	$0.0843461\pi$
$38$		0			0
$39$	−0.500000	−	0.866025i	−0.0800641	−	0.138675i
$40$		0			0
$41$	−11.4981			−1.79571			−0.897854	−	0.440293i	$-0.854874\pi$
$41$	−11.4981			−1.79571			−0.897854	+	0.440293i	$0.854874\pi$
$42$		0			0
$43$	−5.06546			−0.772476			−0.386238	−	0.922399i	$-0.626226\pi$
$43$	−5.06546			−0.772476			−0.386238	+	0.922399i	$0.626226\pi$
$44$		0			0
$45$	−1.84981	−	3.20397i	−0.275754	−	0.477620i
$46$		0			0
$47$	−3.00000	+	5.19615i	−0.437595	+	0.757937i	−0.997503	−	0.0706177i	$-0.977503\pi$
$47$	−3.00000	+	5.19615i	−0.437595	+	0.757937i	0.559908	+	0.828554i	$0.310836\pi$
$48$		0			0
$49$	−3.93199	−	5.79133i	−0.561713	−	0.827332i
$50$		0			0
$51$	−0.444368	+	0.769668i	−0.0622240	+	0.107775i
$52$		0			0
$53$	0.382546	+	0.662589i	0.0525467	+	0.0910136i	0.891102	−	0.453802i	$-0.149933\pi$
$53$	0.382546	+	0.662589i	0.0525467	+	0.0910136i	−0.838556	+	0.544816i	$0.816599\pi$
$54$		0			0
$55$	−5.87636			−0.792368
$56$		0			0
$57$	−6.17673			−0.818128
$58$		0			0
$59$	−2.73855	−	4.74331i	−0.356529	−	0.617526i	0.630850	−	0.775905i	$-0.282707\pi$
$59$	−2.73855	−	4.74331i	−0.356529	−	0.617526i	−0.987378	+	0.158379i	$0.949373\pi$
$60$		0			0
$61$	0.0327319	−	0.0566933i	0.00419089	−	0.00725884i	−0.863922	−	0.503625i	$-0.831999\pi$
$61$	0.0327319	−	0.0566933i	0.00419089	−	0.00725884i	0.868113	+	0.496366i	$0.165333\pi$
$62$		0			0
$63$	1.40545	+	2.24159i	0.177070	+	0.282414i
$64$		0			0
$65$	1.84981	−	3.20397i	0.229441	−	0.397404i
$66$		0			0
$67$	−5.30470	−	9.18801i	−0.648073	−	1.12249i	−0.983583	−	0.180458i	$-0.942242\pi$
$67$	−5.30470	−	9.18801i	−0.648073	−	1.12249i	0.335510	−	0.942037i	$-0.391091\pi$
$68$		0			0
$69$	−6.68725			−0.805050
$70$		0			0
$71$	−5.09888			−0.605126			−0.302563	−	0.953129i	$-0.597842\pi$
$71$	−5.09888			−0.605126			−0.302563	+	0.953129i	$0.597842\pi$
$72$		0			0
$73$	4.52654	+	7.84020i	0.529792	+	0.917626i	0.999396	+	0.0347491i	$0.0110632\pi$
$73$	4.52654	+	7.84020i	0.529792	+	0.917626i	−0.469604	+	0.882877i	$0.655603\pi$
$74$		0			0
$75$	4.34362	−	7.52338i	0.501559	−	0.868725i
$76$		0			0
$77$	4.19963	−	0.153051i	0.478592	−	0.0174418i
$78$		0			0
$79$	−2.82691	+	4.89636i	−0.318053	+	0.550883i	−0.980082	−	0.198595i	$-0.936362\pi$
$79$	−2.82691	+	4.89636i	−0.318053	+	0.550883i	0.662029	+	0.749478i	$0.269696\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	13.1643			1.44497			0.722487	−	0.691384i	$-0.242999\pi$
$83$	13.1643			1.44497			0.722487	+	0.691384i	$0.242999\pi$
$84$		0			0
$85$	−3.28799			−0.356633
$86$		0			0
$87$	2.93818	+	5.08907i	0.315006	+	0.545606i
$88$		0			0
$89$	−3.90545	+	6.76443i	−0.413976	+	0.717028i	−0.995320	−	0.0966297i	$-0.969194\pi$
$89$	−3.90545	+	6.76443i	−0.413976	+	0.717028i	0.581344	+	0.813658i	$0.302527\pi$
$90$		0			0
$91$	−1.23855	+	2.33795i	−0.129835	+	0.245083i
$92$		0			0
$93$	0.761450	−	1.31887i	0.0789587	−	0.136760i
$94$		0			0
$95$	−11.4258	−	19.7901i	−1.17226	−	2.03042i
$96$		0			0
$97$	1.11126			0.112832			0.0564159	−	0.998407i	$-0.482033\pi$
$97$	1.11126			0.112832			0.0564159	+	0.998407i	$0.482033\pi$
$98$		0			0
$99$	−1.58836			−0.159637
$100$		0			0
$101$	9.24907	+	16.0199i	0.920317	+	1.59404i	0.798925	+	0.601431i	$0.205403\pi$
$101$	9.24907	+	16.0199i	0.920317	+	1.59404i	0.121392	+	0.992605i	$0.461264\pi$
$102$		0			0
$103$	−9.48762	+	16.4330i	−0.934843	+	1.61920i	−0.159929	+	0.987128i	$0.551127\pi$
$103$	−9.48762	+	16.4330i	−0.934843	+	1.61920i	−0.774914	+	0.632067i	$0.782207\pi$
$104$		0			0
$105$	−4.58217	+	8.64953i	−0.447174	+	0.844108i
$106$		0			0
$107$	10.1087	−	17.5088i	0.977246	−	1.69264i	0.304933	−	0.952374i	$-0.401366\pi$
$107$	10.1087	−	17.5088i	0.977246	−	1.69264i	0.672313	−	0.740267i	$-0.265301\pi$
$108$		0			0
$109$	5.78180	+	10.0144i	0.553796	+	0.959203i	0.997996	+	0.0632755i	$0.0201547\pi$
$109$	5.78180	+	10.0144i	0.553796	+	0.959203i	−0.444200	+	0.895928i	$0.646512\pi$
$110$		0			0
$111$	3.11126			0.295308
$112$		0			0
$113$	16.8182			1.58212			0.791060	−	0.611738i	$-0.209529\pi$
$113$	16.8182			1.58212			0.791060	+	0.611738i	$0.209529\pi$
$114$		0			0
$115$	−12.3702	−	21.4258i	−1.15352	−	1.99796i
$116$		0			0
$117$	0.500000	−	0.866025i	0.0462250	−	0.0800641i
$118$		0			0
$119$	2.34981	−	0.0856364i	0.215407	−	0.00785028i
$120$		0			0
$121$	4.23855	−	7.34138i	0.385323	−	0.667399i
$122$		0			0
$123$	−5.74907	−	9.95768i	−0.518376	−	0.897854i
$124$		0			0
$125$	13.6414			1.22013
$126$		0			0
$127$	7.78613			0.690908			0.345454	−	0.938436i	$-0.387725\pi$
$127$	7.78613			0.690908			0.345454	+	0.938436i	$0.387725\pi$
$128$		0			0
$129$	−2.53273	−	4.38682i	−0.222995	−	0.386238i
$130$		0			0
$131$	−1.33310	+	2.30900i	−0.116474	+	0.201739i	−0.918368	−	0.395728i	$-0.870492\pi$
$131$	−1.33310	+	2.30900i	−0.116474	+	0.201739i	0.801894	+	0.597466i	$0.203826\pi$
$132$		0			0
$133$	8.68106	+	13.8457i	0.752743	+	1.20057i
$134$		0			0
$135$	1.84981	−	3.20397i	0.159207	−	0.275754i
$136$		0			0
$137$	3.04325	+	5.27107i	0.260003	+	0.450338i	0.966242	−	0.257635i	$-0.0829432\pi$
$137$	3.04325	+	5.27107i	0.260003	+	0.450338i	−0.706240	+	0.707973i	$0.749610\pi$
$138$		0			0
$139$	12.0989			1.02621			0.513107	−	0.858325i	$-0.328494\pi$
$139$	12.0989			1.02621			0.513107	+	0.858325i	$0.328494\pi$
$140$		0			0
$141$	−6.00000			−0.505291
$142$		0			0
$143$	−0.794182	−	1.37556i	−0.0664128	−	0.115030i
$144$		0			0
$145$	−10.8702	+	18.8277i	−0.902718	+	1.56355i
$146$		0			0
$147$	3.04944	−	6.30087i	0.251514	−	0.519687i
$148$		0			0
$149$	−3.68725	+	6.38650i	−0.302071	+	0.523203i	−0.976605	−	0.215041i	$-0.931011\pi$
$149$	−3.68725	+	6.38650i	−0.302071	+	0.523203i	0.674534	+	0.738244i	$0.264345\pi$
$150$		0			0
$151$	11.9752	+	20.7417i	0.974531	+	1.68794i	0.681473	+	0.731843i	$0.261340\pi$
$151$	11.9752	+	20.7417i	0.974531	+	1.68794i	0.293058	+	0.956095i	$0.405327\pi$
$152$		0			0
$153$	−0.888736			−0.0718500
$154$		0			0
$155$	5.63416			0.452547
$156$		0			0
$157$	−4.24907	−	7.35961i	−0.339113	−	0.587360i	0.645153	−	0.764053i	$-0.276793\pi$
$157$	−4.24907	−	7.35961i	−0.339113	−	0.587360i	−0.984266	+	0.176693i	$0.943460\pi$
$158$		0			0
$159$	−0.382546	+	0.662589i	−0.0303379	+	0.0525467i
$160$		0			0
$161$	9.39857	+	14.9901i	0.740711	+	1.18138i
$162$		0			0
$163$	−0.849814	+	1.47192i	−0.0665626	+	0.115290i	−0.897386	−	0.441246i	$-0.854537\pi$
$163$	−0.849814	+	1.47192i	−0.0665626	+	0.115290i	0.830823	+	0.556536i	$0.187870\pi$
$164$		0			0
$165$	−2.93818	−	5.08907i	−0.228737	−	0.396184i
$166$		0			0
$167$	1.82327			0.141089			0.0705445	−	0.997509i	$-0.477526\pi$
$167$	1.82327			0.141089			0.0705445	+	0.997509i	$0.477526\pi$
$168$		0			0
$169$	1.00000			0.0769231
$170$		0			0
$171$	−3.08836	−	5.34920i	−0.236173	−	0.409064i
$172$		0			0
$173$	−3.53342	+	6.12006i	−0.268641	+	0.465300i	−0.968511	−	0.248970i	$-0.919908\pi$
$173$	−3.53342	+	6.12006i	−0.268641	+	0.465300i	0.699870	+	0.714270i	$0.253241\pi$
$174$		0			0
$175$	−22.9691	+	0.837082i	−1.73630	+	0.0632775i
$176$		0			0
$177$	2.73855	−	4.74331i	0.205842	−	0.356529i
$178$		0			0
$179$	−6.07165	−	10.5164i	−0.453817	−	0.786034i	0.544803	−	0.838564i	$-0.316605\pi$
$179$	−6.07165	−	10.5164i	−0.453817	−	0.786034i	−0.998619	+	0.0525307i	$0.983271\pi$
$180$		0			0
$181$	25.7403			1.91326			0.956632	−	0.291299i	$-0.0940876\pi$
$181$	25.7403			1.91326			0.956632	+	0.291299i	$0.0940876\pi$
$182$		0			0
$183$	0.0654638			0.00483923
$184$		0			0
$185$	5.75526	+	9.96840i	0.423135	+	0.732892i
$186$		0			0
$187$	−0.705818	+	1.22251i	−0.0516145	+	0.0893990i
$188$		0			0
$189$	−1.23855	+	2.33795i	−0.0900912	+	0.170061i
$190$		0			0
$191$	−4.77197	+	8.26530i	−0.345288	+	0.598056i	−0.985406	−	0.170221i	$-0.945552\pi$
$191$	−4.77197	+	8.26530i	−0.345288	+	0.598056i	0.640118	+	0.768276i	$0.278885\pi$
$192$		0			0
$193$	−3.27128	−	5.66603i	−0.235472	−	0.407849i	0.723938	−	0.689865i	$-0.242330\pi$
$193$	−3.27128	−	5.66603i	−0.235472	−	0.407849i	−0.959410	+	0.282016i	$0.908997\pi$
$194$		0			0
$195$	3.69963			0.264936
$196$		0			0
$197$	−5.74543			−0.409345			−0.204672	−	0.978831i	$-0.565613\pi$
$197$	−5.74543			−0.409345			−0.204672	+	0.978831i	$0.565613\pi$
$198$		0			0
$199$	−10.2163	−	17.6952i	−0.724217	−	1.25438i	−0.959295	−	0.282404i	$-0.908868\pi$
$199$	−10.2163	−	17.6952i	−0.724217	−	1.25438i	0.235078	−	0.971976i	$-0.424465\pi$
$200$		0			0
$201$	5.30470	−	9.18801i	0.374165	−	0.648073i
$202$		0			0
$203$	7.27816	−	13.7386i	0.510827	−	0.964261i
$204$		0			0
$205$	21.2694	−	36.8397i	1.48552	−	2.57300i
$206$		0			0
$207$	−3.34362	−	5.79133i	−0.232398	−	0.402525i
$208$		0			0
$209$	−9.81089			−0.678634
$210$		0			0
$211$	4.04580			0.278524			0.139262	−	0.990256i	$-0.455527\pi$
$211$	4.04580			0.278524			0.139262	+	0.990256i	$0.455527\pi$
$212$		0			0
$213$	−2.54944	−	4.41576i	−0.174685	−	0.302563i
$214$		0			0
$215$	9.37017	−	16.2296i	0.639040	−	1.10685i
$216$		0			0
$217$	−4.02654	+	0.146743i	−0.273339	+	0.00996156i
$218$		0			0
$219$	−4.52654	+	7.84020i	−0.305875	+	0.529792i
$220$		0			0
$221$	−0.444368	−	0.769668i	−0.0298914	−	0.0517735i
$222$		0			0
$223$	−10.2967			−0.689515			−0.344757	−	0.938692i	$-0.612039\pi$
$223$	−10.2967			−0.689515			−0.344757	+	0.938692i	$0.612039\pi$
$224$		0			0
$225$	8.68725			0.579150
$226$		0			0
$227$	9.16435	+	15.8731i	0.608259	+	1.05354i	0.991527	+	0.129899i	$0.0414652\pi$
$227$	9.16435	+	15.8731i	0.608259	+	1.05354i	−0.383268	+	0.923637i	$0.625201\pi$
$228$		0			0
$229$	−7.91164	+	13.7034i	−0.522816	+	0.905543i	0.476832	+	0.878995i	$0.341785\pi$
$229$	−7.91164	+	13.7034i	−0.522816	+	0.905543i	−0.999648	+	0.0265487i	$0.991548\pi$
$230$		0			0
$231$	2.23236	+	3.56046i	0.146879	+	0.234261i
$232$		0			0
$233$	−0.843624	+	1.46120i	−0.0552677	+	0.0957264i	−0.892336	−	0.451373i	$-0.850935\pi$
$233$	−0.843624	+	1.46120i	−0.0552677	+	0.0957264i	0.837068	+	0.547099i	$0.184268\pi$
$234$		0			0
$235$	−11.0989	−	19.2238i	−0.724011	−	1.25402i
$236$		0			0
$237$	−5.65383			−0.367256
$238$		0			0
$239$	−9.46472			−0.612222			−0.306111	−	0.951996i	$-0.599028\pi$
$239$	−9.46472			−0.612222			−0.306111	+	0.951996i	$0.599028\pi$
$240$		0			0
$241$	−7.10439	−	12.3052i	−0.457634	−	0.792645i	0.541202	−	0.840893i	$-0.317970\pi$
$241$	−7.10439	−	12.3052i	−0.457634	−	0.792645i	−0.998835	+	0.0482480i	$0.984636\pi$
$242$		0			0
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$		0			0
$245$	25.8287	−	1.88510i	1.65013	−	0.120435i
$246$		0			0
$247$	3.08836	−	5.34920i	0.196508	−	0.340362i
$248$		0			0
$249$	6.58217	+	11.4007i	0.417128	+	0.722487i
$250$		0			0
$251$	19.1657			1.20973			0.604865	−	0.796328i	$-0.293227\pi$
$251$	19.1657			1.20973			0.604865	+	0.796328i	$0.293227\pi$
$252$		0			0
$253$	−10.6218			−0.667786
$254$		0			0
$255$	−1.64400	−	2.84748i	−0.102951	−	0.178316i
$256$		0			0
$257$	1.88255	−	3.26067i	0.117430	−	0.203395i	−0.801319	−	0.598238i	$-0.795868\pi$
$257$	1.88255	−	3.26067i	0.117430	−	0.203395i	0.918749	+	0.394843i	$0.129201\pi$
$258$		0			0
$259$	−4.37271	−	6.97418i	−0.271707	−	0.433354i
$260$		0			0
$261$	−2.93818	+	5.08907i	−0.181869	+	0.315006i
$262$		0			0
$263$	0.954888	+	1.65392i	0.0588809	+	0.101985i	0.893963	−	0.448140i	$-0.147913\pi$
$263$	0.954888	+	1.65392i	0.0588809	+	0.101985i	−0.835082	+	0.550125i	$0.814580\pi$
$264$		0			0
$265$	−2.83056			−0.173880
$266$		0			0
$267$	−7.81089			−0.478019
$268$		0			0
$269$	9.52723	+	16.5016i	0.580886	+	1.00612i	0.995375	+	0.0960690i	$0.0306269\pi$
$269$	9.52723	+	16.5016i	0.580886	+	1.00612i	−0.414489	+	0.910054i	$0.636040\pi$
$270$		0			0
$271$	11.2040	−	19.4058i	0.680592	−	1.17882i	−0.294208	−	0.955741i	$-0.595056\pi$
$271$	11.2040	−	19.4058i	0.680592	−	1.17882i	0.974800	−	0.223079i	$-0.0716107\pi$
$272$		0			0
$273$	−2.64400	+	0.0963576i	−0.160022	+	0.00583183i
$274$		0			0
$275$	6.89926	−	11.9499i	0.416041	−	0.720604i
$276$		0			0
$277$	14.0767	+	24.3815i	0.845785	+	1.46494i	0.884937	+	0.465710i	$0.154201\pi$
$277$	14.0767	+	24.3815i	0.845785	+	1.46494i	−0.0391522	+	0.999233i	$0.512466\pi$
$278$		0			0
$279$	1.52290			0.0911736
$280$		0			0
$281$	−12.0865			−0.721020			−0.360510	−	0.932755i	$-0.617397\pi$
$281$	−12.0865			−0.721020			−0.360510	+	0.932755i	$0.617397\pi$
$282$		0			0
$283$	7.71634	+	13.3651i	0.458689	+	0.794472i	0.998892	−	0.0470624i	$-0.0149860\pi$
$283$	7.71634	+	13.3651i	0.458689	+	0.794472i	−0.540203	+	0.841535i	$0.681653\pi$
$284$		0			0
$285$	11.4258	−	19.7901i	0.676806	−	1.17226i
$286$		0			0
$287$	−14.2410	+	26.8820i	−0.840621	+	1.58680i
$288$		0			0
$289$	8.10507	−	14.0384i	0.476769	−	0.825788i
$290$		0			0
$291$	0.555632	+	0.962383i	0.0325717	+	0.0564159i
$292$		0			0
$293$	13.4313			0.784665			0.392332	−	0.919823i	$-0.371668\pi$
$293$	13.4313			0.784665			0.392332	+	0.919823i	$0.371668\pi$
$294$		0			0
$295$	20.2632			1.17977
$296$		0			0
$297$	−0.794182	−	1.37556i	−0.0460831	−	0.0798183i
$298$		0			0
$299$	3.34362	−	5.79133i	0.193367	−	0.334921i
$300$		0			0
$301$	−6.27383	+	11.8428i	−0.361618	+	0.682607i
$302$		0			0
$303$	−9.24907	+	16.0199i	−0.531345	+	0.920317i
$304$		0			0
$305$	0.121096	+	0.209744i	0.00693393	+	0.0120099i
$306$		0			0
$307$	4.53528			0.258842			0.129421	−	0.991590i	$-0.458688\pi$
$307$	4.53528			0.258842			0.129421	+	0.991590i	$0.458688\pi$
$308$		0			0
$309$	−18.9752			−1.07946
$310$		0			0
$311$	−8.00619	−	13.8671i	−0.453989	−	0.786333i	0.544640	−	0.838670i	$-0.316666\pi$
$311$	−8.00619	−	13.8671i	−0.453989	−	0.786333i	−0.998629	+	0.0523372i	$0.983333\pi$
$312$		0			0
$313$	7.64400	−	13.2398i	0.432064	−	0.748357i	−0.564987	−	0.825100i	$-0.691119\pi$
$313$	7.64400	−	13.2398i	0.432064	−	0.748357i	0.997051	+	0.0767428i	$0.0244520\pi$
$314$		0			0
$315$	−9.78180	+	0.356487i	−0.551142	+	0.0200858i
$316$		0			0
$317$	8.79782	−	15.2383i	0.494135	−	0.855867i	−0.505842	−	0.862626i	$-0.668818\pi$
$317$	8.79782	−	15.2383i	0.494135	−	0.855867i	0.999977	+	0.00675911i	$0.00215151\pi$
$318$		0			0
$319$	4.66690	+	8.08330i	0.261296	+	0.452578i
$320$		0			0
$321$	20.2174			1.12843
$322$		0			0
$323$	−5.48948			−0.305443
$324$		0			0
$325$	4.34362	+	7.52338i	0.240941	+	0.417322i
$326$		0			0
$327$	−5.78180	+	10.0144i	−0.319734	+	0.553796i
$328$		0			0
$329$	8.43268	+	13.4495i	0.464909	+	0.741497i
$330$		0			0
$331$	−0.806562	+	1.39701i	−0.0443326	+	0.0767864i	−0.887340	−	0.461115i	$-0.847449\pi$
$331$	−0.806562	+	1.39701i	−0.0443326	+	0.0767864i	0.843008	+	0.537902i	$0.180783\pi$
$332$		0			0
$333$	1.55563	+	2.69443i	0.0852481	+	0.147654i
$334$		0			0
$335$	39.2509			2.14450
$336$		0			0
$337$	18.0952			0.985706			0.492853	−	0.870112i	$-0.335954\pi$
$337$	18.0952			0.985706			0.492853	+	0.870112i	$0.335954\pi$
$338$		0			0
$339$	8.40909	+	14.5650i	0.456719	+	0.791060i
$340$		0			0
$341$	1.20946	−	2.09485i	0.0654959	−	0.113442i
$342$		0			0
$343$	−18.4098	+	2.01993i	−0.994035	+	0.109066i
$344$		0			0
$345$	12.3702	−	21.4258i	0.665987	−	1.15352i
$346$		0			0
$347$	1.59269	+	2.75863i	0.0855003	+	0.148091i	0.905604	−	0.424124i	$-0.139418\pi$
$347$	1.59269	+	2.75863i	0.0855003	+	0.148091i	−0.820104	+	0.572215i	$0.806084\pi$
$348$		0			0
$349$	31.4327			1.68255			0.841276	−	0.540605i	$-0.181805\pi$
$349$	31.4327			1.68255			0.841276	+	0.540605i	$0.181805\pi$
$350$		0			0
$351$	1.00000			0.0533761
$352$		0			0
$353$	14.3040	+	24.7753i	0.761326	+	1.31866i	0.942167	+	0.335143i	$0.108785\pi$
$353$	14.3040	+	24.7753i	0.761326	+	1.31866i	−0.180842	+	0.983512i	$0.557882\pi$
$354$		0			0
$355$	9.43199	−	16.3367i	0.500598	−	0.867061i
$356$		0			0
$357$	1.24907	+	1.99218i	0.0661078	+	0.105437i
$358$		0			0
$359$	−3.23786	+	5.60814i	−0.170888	+	0.295986i	−0.938730	−	0.344652i	$-0.887997\pi$
$359$	−3.23786	+	5.60814i	−0.170888	+	0.295986i	0.767843	+	0.640638i	$0.221330\pi$
$360$		0			0
$361$	−9.57598	−	16.5861i	−0.503999	−	0.872952i
$362$		0			0
$363$	8.47710			0.444932
$364$		0			0
$365$	−33.4930			−1.75311
$366$		0			0
$367$	−6.62729	−	11.4788i	−0.345942	−	0.599188i	0.639583	−	0.768722i	$-0.279107\pi$
$367$	−6.62729	−	11.4788i	−0.345942	−	0.599188i	−0.985524	+	0.169534i	$0.945774\pi$
$368$		0			0
$369$	5.74907	−	9.95768i	0.299285	−	0.518376i
$370$		0			0
$371$	2.02290	−	0.0737224i	0.105024	−	0.00382748i
$372$		0			0
$373$	18.9647	−	32.8479i	0.981956	−	1.70080i	0.327204	−	0.944954i	$-0.393893\pi$
$373$	18.9647	−	32.8479i	0.981956	−	1.70080i	0.654752	−	0.755844i	$-0.272773\pi$
$374$		0			0
$375$	6.82072	+	11.8138i	0.352221	+	0.610064i
$376$		0			0
$377$	−5.87636			−0.302648
$378$		0			0
$379$	−14.0655			−0.722494			−0.361247	−	0.932470i	$-0.617649\pi$
$379$	−14.0655			−0.722494			−0.361247	+	0.932470i	$0.617649\pi$
$380$		0			0
$381$	3.89307	+	6.74299i	0.199448	+	0.345454i
$382$		0			0
$383$	−10.5327	+	18.2432i	−0.538197	+	0.932185i	0.460804	+	0.887502i	$0.347561\pi$
$383$	−10.5327	+	18.2432i	−0.538197	+	0.932185i	−0.999001	+	0.0446833i	$0.985772\pi$
$384$		0			0
$385$	−7.27816	+	13.7386i	−0.370929	+	0.700184i
$386$		0			0
$387$	2.53273	−	4.38682i	0.128746	−	0.222995i
$388$		0			0
$389$	−6.99381	−	12.1136i	−0.354600	−	0.614186i	0.632449	−	0.774602i	$-0.282050\pi$
$389$	−6.99381	−	12.1136i	−0.354600	−	0.614186i	−0.987049	+	0.160416i	$0.948716\pi$
$390$		0			0
$391$	−5.94320			−0.300560
$392$		0			0
$393$	−2.66621			−0.134492
$394$		0			0
$395$	−10.4585	−	18.1147i	−0.526226	−	0.911450i
$396$		0			0
$397$	−4.54944	+	7.87987i	−0.228330	+	0.395479i	−0.957313	−	0.289052i	$-0.906660\pi$
$397$	−4.54944	+	7.87987i	−0.228330	+	0.395479i	0.728983	+	0.684531i	$0.239993\pi$
$398$		0			0
$399$	−7.65019	+	14.4409i	−0.382988	+	0.722947i
$400$		0			0
$401$	−9.42216	+	16.3197i	−0.470520	+	0.814965i	−0.999432	−	0.0337123i	$-0.989267\pi$
$401$	−9.42216	+	16.3197i	−0.470520	+	0.814965i	0.528912	+	0.848677i	$0.322600\pi$
$402$		0			0
$403$	0.761450	+	1.31887i	0.0379305	+	0.0656976i
$404$		0			0
$405$	3.69963			0.183836
$406$		0			0
$407$	4.94182			0.244957
$408$		0			0
$409$	−19.1756	−	33.2130i	−0.948170	−	1.64228i	−0.749276	−	0.662258i	$-0.769598\pi$
$409$	−19.1756	−	33.2130i	−0.948170	−	1.64228i	−0.198895	−	0.980021i	$-0.563735\pi$
$410$		0			0
$411$	−3.04325	+	5.27107i	−0.150113	+	0.260003i
$412$		0			0
$413$	−14.4814	+	0.527760i	−0.712585	+	0.0259694i
$414$		0			0
$415$	−24.3516	+	42.1782i	−1.19537	+	2.07045i
$416$		0			0
$417$	6.04944	+	10.4779i	0.296242	+	0.513107i
$418$		0			0
$419$	−0.176728			−0.00863373			−0.00431686	−	0.999991i	$-0.501374\pi$
$419$	−0.176728			−0.00863373			−0.00431686	+	0.999991i	$0.501374\pi$
$420$		0			0
$421$	9.35346			0.455860			0.227930	−	0.973678i	$-0.426804\pi$
$421$	9.35346			0.455860			0.227930	+	0.973678i	$0.426804\pi$
$422$		0			0
$423$	−3.00000	−	5.19615i	−0.145865	−	0.252646i
$424$		0			0
$425$	3.86033	−	6.68630i	0.187254	−	0.324333i
$426$		0			0
$427$	−0.0920059	−	0.146743i	−0.00445248	−	0.00710139i
$428$		0			0
$429$	0.794182	−	1.37556i	0.0383435	−	0.0664128i
$430$		0			0
$431$	−12.1607	−	21.0630i	−0.585761	−	1.01457i	−0.994780	−	0.102042i	$-0.967463\pi$
$431$	−12.1607	−	21.0630i	−0.585761	−	1.01457i	0.409020	−	0.912526i	$-0.365871\pi$
$432$		0			0
$433$	35.3942			1.70093			0.850467	−	0.526028i	$-0.176319\pi$
$433$	35.3942			1.70093			0.850467	+	0.526028i	$0.176319\pi$
$434$		0			0
$435$	−21.7403			−1.04237
$436$		0			0
$437$	−20.6527	−	35.7715i	−0.987951	−	1.71118i
$438$		0			0
$439$	−4.02723	+	6.97537i	−0.192209	+	0.332916i	−0.945982	−	0.324219i	$-0.894899\pi$
$439$	−4.02723	+	6.97537i	−0.192209	+	0.332916i	0.753773	+	0.657135i	$0.228232\pi$
$440$		0			0
$441$	6.98143	−	0.509538i	0.332449	−	0.0242637i
$442$		0			0
$443$	−9.72548	+	16.8450i	−0.462072	+	0.800331i	−0.999064	−	0.0432556i	$-0.986227\pi$
$443$	−9.72548	+	16.8450i	−0.462072	+	0.800331i	0.536992	+	0.843587i	$0.319560\pi$
$444$		0			0
$445$	−14.4487	−	25.0259i	−0.684934	−	1.18634i
$446$		0			0
$447$	−7.37450			−0.348802
$448$		0			0
$449$	23.0334			1.08701			0.543507	−	0.839405i	$-0.317096\pi$
$449$	23.0334			1.08701			0.543507	+	0.839405i	$0.317096\pi$
$450$		0			0
$451$	−9.13162	−	15.8164i	−0.429991	−	0.744766i
$452$		0			0
$453$	−11.9752	+	20.7417i	−0.562646	+	0.974531i
$454$		0			0
$455$	−5.19963	−	8.29305i	−0.243762	−	0.388784i
$456$		0			0
$457$	2.08472	−	3.61084i	0.0975192	−	0.168908i	−0.813138	−	0.582071i	$-0.802243\pi$
$457$	2.08472	−	3.61084i	0.0975192	−	0.168908i	0.910657	+	0.413163i	$0.135576\pi$
$458$		0			0
$459$	−0.444368	−	0.769668i	−0.0207413	−	0.0359250i
$460$		0			0
$461$	−15.9381			−0.742311			−0.371156	−	0.928571i	$-0.621038\pi$
$461$	−15.9381			−0.742311			−0.371156	+	0.928571i	$0.621038\pi$
$462$		0			0
$463$	−42.5278			−1.97644			−0.988218	−	0.153051i	$-0.951090\pi$
$463$	−42.5278			−1.97644			−0.988218	+	0.153051i	$0.951090\pi$
$464$		0			0
$465$	2.81708	+	4.87933i	0.130639	+	0.226273i
$466$		0			0
$467$	−4.22803	+	7.32316i	−0.195650	+	0.338876i	−0.947113	−	0.320899i	$-0.896015\pi$
$467$	−4.22803	+	7.32316i	−0.195650	+	0.338876i	0.751463	+	0.659775i	$0.229348\pi$
$468$		0			0
$469$	−28.0512	+	1.02230i	−1.29529	+	0.0472053i
$470$		0			0
$471$	4.24907	−	7.35961i	0.195787	−	0.339113i
$472$		0			0
$473$	−4.02290	−	6.96787i	−0.184973	−	0.320383i
$474$		0			0
$475$	53.6588			2.46203
$476$		0			0
$477$	−0.765092			−0.0350312
$478$		0			0
$479$	−17.2305	−	29.8441i	−0.787282	−	1.36361i	−0.927626	−	0.373509i	$-0.878154\pi$
$479$	−17.2305	−	29.8441i	−0.787282	−	1.36361i	0.140345	−	0.990103i	$-0.455179\pi$
$480$		0			0
$481$	−1.55563	+	2.69443i	−0.0709307	+	0.122856i
$482$		0			0
$483$	−8.28249	+	15.6344i	−0.376866	+	0.711391i
$484$		0			0
$485$	−2.05563	+	3.56046i	−0.0933414	+	0.161672i
$486$		0			0
$487$	14.3306	+	24.8213i	0.649379	+	1.12476i	0.983271	+	0.182147i	$0.0583046\pi$
$487$	14.3306	+	24.8213i	0.649379	+	1.12476i	−0.333892	+	0.942611i	$0.608362\pi$
$488$		0			0
$489$	−1.69963			−0.0768598
$490$		0			0
$491$	−6.58836			−0.297329			−0.148664	−	0.988888i	$-0.547497\pi$
$491$	−6.58836			−0.297329			−0.148664	+	0.988888i	$0.547497\pi$
$492$		0			0
$493$	2.61126	+	4.52284i	0.117605	+	0.203699i
$494$		0			0
$495$	2.93818	−	5.08907i	0.132061	−	0.228737i
$496$		0			0
$497$	−6.31522	+	11.9209i	−0.283276	+	0.534726i
$498$		0			0
$499$	−16.7527	+	29.0165i	−0.749954	+	1.29896i	0.197890	+	0.980224i	$0.436591\pi$
$499$	−16.7527	+	29.0165i	−0.749954	+	1.29896i	−0.947844	+	0.318735i	$0.896742\pi$
$500$		0			0
$501$	0.911636	+	1.57900i	0.0407289	+	0.0705445i
$502$		0			0
$503$	−14.2632			−0.635966			−0.317983	−	0.948096i	$-0.603006\pi$
$503$	−14.2632			−0.635966			−0.317983	+	0.948096i	$0.603006\pi$
$504$		0			0
$505$	−68.4362			−3.04537
$506$		0			0
$507$	0.500000	+	0.866025i	0.0222058	+	0.0384615i
$508$		0			0
$509$	−10.0426	+	17.3942i	−0.445129	+	0.770986i	−0.998061	−	0.0622404i	$-0.980175\pi$
$509$	−10.0426	+	17.3942i	−0.445129	+	0.770986i	0.552932	+	0.833226i	$0.313509\pi$
$510$		0			0
$511$	23.9363	−	0.872333i	1.05888	−	0.0385898i
$512$		0			0
$513$	3.08836	−	5.34920i	0.136355	−	0.236173i
$514$		0			0
$515$	−35.1007	−	60.7961i	−1.54672	−	2.67900i
$516$		0			0
$517$	−9.53018			−0.419137
$518$		0			0
$519$	−7.06684			−0.310200
$520$		0			0
$521$	0.888047	+	1.53814i	0.0389061	+	0.0673873i	0.884823	−	0.465928i	$-0.154279\pi$
$521$	0.888047	+	1.53814i	0.0389061	+	0.0673873i	−0.845917	+	0.533315i	$0.820946\pi$
$522$		0			0
$523$	−3.95420	+	6.84887i	−0.172905	+	0.299480i	−0.939434	−	0.342729i	$-0.888649\pi$
$523$	−3.95420	+	6.84887i	−0.172905	+	0.299480i	0.766529	+	0.642209i	$0.221982\pi$
$524$		0			0
$525$	−12.2095	−	19.4732i	−0.532865	−	0.849882i
$526$		0			0
$527$	0.676728	−	1.17213i	0.0294787	−	0.0510587i
$528$		0			0
$529$	−10.8596	−	18.8095i	−0.472159	−	0.817803i
$530$		0			0
$531$	5.47710			0.237686
$532$		0			0
$533$	11.4981			0.498040
$534$		0			0
$535$	37.3985	+	64.7761i	1.61688	+	2.80051i
$536$		0			0
$537$	6.07165	−	10.5164i	0.262011	−	0.453817i
$538$		0			0
$539$	4.84362	−	10.0081i	0.208630	−	0.431078i
$540$		0			0
$541$	−15.4629	+	26.7825i	−0.664800	+	1.15147i	0.314539	+	0.949245i	$0.398150\pi$
$541$	−15.4629	+	26.7825i	−0.664800	+	1.15147i	−0.979339	+	0.202223i	$0.935183\pi$
$542$		0			0
$543$	12.8702	+	22.2918i	0.552312	+	0.956632i
$544$		0			0
$545$	−42.7810			−1.83254
$546$		0			0
$547$	5.14331			0.219912			0.109956	−	0.993936i	$-0.464929\pi$
$547$	5.14331			0.219912			0.109956	+	0.993936i	$0.464929\pi$
$548$		0			0
$549$	0.0327319	+	0.0566933i	0.00139696	+	0.00241961i
$550$		0			0
$551$	−18.1483	+	31.4338i	−0.773145	+	1.33913i
$552$		0			0
$553$	7.94615	+	12.6736i	0.337905	+	0.538935i
$554$		0			0
$555$	−5.75526	+	9.96840i	−0.244297	+	0.423135i
$556$		0			0
$557$	7.54070	+	13.0609i	0.319510	+	0.553407i	0.980386	−	0.197088i	$-0.0631484\pi$
$557$	7.54070	+	13.0609i	0.319510	+	0.553407i	−0.660876	+	0.750495i	$0.729815\pi$
$558$		0			0
$559$	5.06546			0.214246
$560$		0			0
$561$	−1.41164			−0.0595993
$562$		0			0
$563$	−13.8702	−	24.0238i	−0.584558	−	1.01248i	−0.994930	−	0.100566i	$-0.967935\pi$
$563$	−13.8702	−	24.0238i	−0.584558	−	1.01248i	0.410373	−	0.911918i	$-0.365399\pi$
$564$		0			0
$565$	−31.1105	+	53.8850i	−1.30883	+	2.26696i
$566$		0			0
$567$	−2.64400	+	0.0963576i	−0.111037	+	0.00404664i
$568$		0			0
$569$	10.8054	−	18.7155i	0.452986	−	0.784594i	−0.545584	−	0.838056i	$-0.683692\pi$
$569$	10.8054	−	18.7155i	0.452986	−	0.784594i	0.998570	+	0.0534619i	$0.0170256\pi$
$570$		0			0
$571$	14.1130	+	24.4445i	0.590613	+	1.02297i	0.994150	+	0.108008i	$0.0344472\pi$
$571$	14.1130	+	24.4445i	0.590613	+	1.02297i	−0.403537	+	0.914963i	$0.632219\pi$
$572$		0			0
$573$	−9.54394			−0.398704
$574$		0			0
$575$	58.0938			2.42268
$576$		0			0
$577$	4.51671	+	7.82317i	0.188033	+	0.325683i	0.944594	−	0.328240i	$-0.106455\pi$
$577$	4.51671	+	7.82317i	0.188033	+	0.325683i	−0.756561	+	0.653923i	$0.773122\pi$
$578$		0			0
$579$	3.27128	−	5.66603i	0.135950	−	0.235472i
$580$		0			0
$581$	16.3047	−	30.7775i	0.676433	−	1.27687i
$582$		0			0
$583$	−0.607622	+	1.05243i	−0.0251651	+	0.0435873i
$584$		0			0
$585$	1.84981	+	3.20397i	0.0764804	+	0.132468i
$586$		0			0
$587$	6.74033			0.278203			0.139102	−	0.990278i	$-0.455579\pi$
$587$	6.74033			0.278203			0.139102	+	0.990278i	$0.455579\pi$
$588$		0			0
$589$	9.40654			0.387590
$590$		0			0
$591$	−2.87271	−	4.97569i	−0.118168	−	0.204672i
$592$		0			0
$593$	−13.8040	+	23.9093i	−0.566863	+	0.981835i	0.430011	+	0.902824i	$0.358510\pi$
$593$	−13.8040	+	23.9093i	−0.566863	+	0.981835i	−0.996874	+	0.0790116i	$0.974824\pi$
$594$		0			0
$595$	−4.07234	+	7.68715i	−0.166950	+	0.315142i
$596$		0			0
$597$	10.2163	−	17.6952i	0.418127	−	0.724217i
$598$		0			0
$599$	−20.8814	−	36.1676i	−0.853190	−	1.47777i	−0.878314	−	0.478084i	$-0.841331\pi$
$599$	−20.8814	−	36.1676i	−0.853190	−	1.47777i	0.0251243	−	0.999684i	$-0.492002\pi$
$600$		0			0
$601$	−24.1978			−0.987048			−0.493524	−	0.869732i	$-0.664291\pi$
$601$	−24.1978			−0.987048			−0.493524	+	0.869732i	$0.664291\pi$
$602$		0			0
$603$	10.6094			0.432048
$604$		0			0
$605$	15.6811	+	27.1604i	0.637526	+	1.10423i
$606$		0			0
$607$	14.5982	−	25.2848i	0.592522	−	1.02628i	−0.401369	−	0.915916i	$-0.631465\pi$
$607$	14.5982	−	25.2848i	0.592522	−	1.02628i	0.993891	−	0.110363i	$-0.0352012\pi$
$608$		0			0
$609$	15.5371	−	0.566231i	0.629594	−	0.0229449i
$610$		0			0
$611$	3.00000	−	5.19615i	0.121367	−	0.210214i
$612$		0			0
$613$	7.37567	+	12.7750i	0.297900	+	0.515979i	0.975655	−	0.219309i	$-0.0703803\pi$
$613$	7.37567	+	12.7750i	0.297900	+	0.515979i	−0.677755	+	0.735288i	$0.737047\pi$
$614$		0			0
$615$	42.5388			1.71533
$616$		0			0
$617$	3.80951			0.153365			0.0766826	−	0.997056i	$-0.475567\pi$
$617$	3.80951			0.153365			0.0766826	+	0.997056i	$0.475567\pi$
$618$		0			0
$619$	−8.34981	−	14.4623i	−0.335607	−	0.581289i	0.647994	−	0.761645i	$-0.275608\pi$
$619$	−8.34981	−	14.4623i	−0.335607	−	0.581289i	−0.983601	+	0.180356i	$0.942275\pi$
$620$		0			0
$621$	3.34362	−	5.79133i	0.134175	−	0.232398i
$622$		0			0
$623$	10.9778	+	17.5088i	0.439816	+	0.701476i
$624$		0			0
$625$	−3.51602	+	6.08993i	−0.140641	+	0.243597i
$626$		0			0
$627$	−4.90545	−	8.49648i	−0.195905	−	0.339317i
$628$		0			0
$629$	2.76509			0.110251
$630$		0			0
$631$	33.3942			1.32940			0.664700	−	0.747110i	$-0.268559\pi$
$631$	33.3942			1.32940			0.664700	+	0.747110i	$0.268559\pi$
$632$		0			0
$633$	2.02290	+	3.50377i	0.0804031	+	0.139262i
$634$		0			0
$635$	−14.4029	+	24.9466i	−0.571562	+	0.989974i
$636$		0			0
$637$	3.93199	+	5.79133i	0.155791	+	0.229461i
$638$		0			0
$639$	2.54944	−	4.41576i	0.100854	−	0.174685i
$640$		0			0
$641$	−0.345483	−	0.598395i	−0.0136458	−	0.0236352i	0.859122	−	0.511771i	$-0.171010\pi$
$641$	−0.345483	−	0.598395i	−0.0136458	−	0.0236352i	−0.872768	+	0.488136i	$0.837677\pi$
$642$		0			0
$643$	−4.73305			−0.186653			−0.0933266	−	0.995636i	$-0.529750\pi$
$643$	−4.73305			−0.186653			−0.0933266	+	0.995636i	$0.529750\pi$
$644$		0			0
$645$	18.7403			0.737900
$646$		0			0
$647$	19.2596	+	33.3586i	0.757173	+	1.31146i	0.944287	+	0.329123i	$0.106753\pi$
$647$	19.2596	+	33.3586i	0.757173	+	1.31146i	−0.187114	+	0.982338i	$0.559913\pi$
$648$		0			0
$649$	4.34981	−	7.53410i	0.170745	−	0.295739i
$650$		0			0
$651$	−2.14035	−	3.41372i	−0.0838871	−	0.133794i
$652$		0			0
$653$	−13.5600	+	23.4865i	−0.530642	+	0.919100i	0.468718	+	0.883348i	$0.344716\pi$
$653$	−13.5600	+	23.4865i	−0.530642	+	0.919100i	−0.999361	+	0.0357518i	$0.988617\pi$
$654$		0			0
$655$	−4.93199	−	8.54245i	−0.192709	−	0.333781i
$656$		0			0
$657$	−9.05308			−0.353194
$658$		0			0
$659$	−44.3680			−1.72833			−0.864166	−	0.503206i	$-0.832154\pi$
$659$	−44.3680			−1.72833			−0.864166	+	0.503206i	$0.832154\pi$
$660$		0			0
$661$	21.6414	+	37.4841i	0.841755	+	1.45796i	0.888410	+	0.459051i	$0.151810\pi$
$661$	21.6414	+	37.4841i	0.841755	+	1.45796i	−0.0466552	+	0.998911i	$0.514856\pi$
$662$		0			0
$663$	0.444368	−	0.769668i	0.0172578	−	0.0298914i
$664$		0			0
$665$	−60.4195	+	2.20192i	−2.34297	+	0.0853870i
$666$		0			0
$667$	−19.6483	+	34.0319i	−0.760786	+	1.31772i
$668$		0			0
$669$	−5.14833	−	8.91716i	−0.199046	−	0.344757i
$670$		0			0
$671$	0.103980			0.00401412
$672$		0			0
$673$	16.2188			0.625189			0.312595	−	0.949887i	$-0.398802\pi$
$673$	16.2188			0.625189			0.312595	+	0.949887i	$0.398802\pi$
$674$		0			0
$675$	4.34362	+	7.52338i	0.167186	+	0.289575i
$676$		0			0
$677$	−17.6902	+	30.6403i	−0.679890	+	1.17760i	0.295124	+	0.955459i	$0.404639\pi$
$677$	−17.6902	+	30.6403i	−0.679890	+	1.17760i	−0.975014	+	0.222145i	$0.928694\pi$
$678$		0			0
$679$	1.37636	−	2.59808i	0.0528197	−	0.0997050i
$680$		0			0
$681$	−9.16435	+	15.8731i	−0.351179	+	0.608259i
$682$		0			0
$683$	−12.6866	−	21.9738i	−0.485438	−	0.840803i	0.514422	−	0.857537i	$-0.328006\pi$
$683$	−12.6866	−	21.9738i	−0.485438	−	0.840803i	−0.999860	+	0.0167342i	$0.994673\pi$
$684$		0			0
$685$	−22.5178			−0.860361
$686$		0			0
$687$	−15.8233			−0.603695
$688$		0			0
$689$	−0.382546	−	0.662589i	−0.0145738	−	0.0252426i
$690$		0			0
$691$	25.1599	−	43.5783i	0.957129	−	1.65780i	0.227711	−	0.973729i	$-0.426876\pi$
$691$	25.1599	−	43.5783i	0.957129	−	1.65780i	0.729419	−	0.684068i	$-0.239791\pi$
$692$		0			0
$693$	−1.96727	+	3.71351i	−0.0747303	+	0.141065i
$694$		0			0
$695$	−22.3807	+	38.7645i	−0.848948	+	1.47042i
$696$		0			0
$697$	−5.10940	−	8.84975i	−0.193533	−	0.335208i
$698$		0			0
$699$	−1.68725			−0.0638176
$700$		0			0
$701$	6.49458			0.245297			0.122648	−	0.992450i	$-0.460861\pi$
$701$	6.49458			0.245297			0.122648	+	0.992450i	$0.460861\pi$
$702$		0			0
$703$	9.60872	+	16.6428i	0.362400	+	0.627695i
$704$		0			0
$705$	11.0989	−	19.2238i	0.418008	−	0.724011i
$706$		0			0
$707$	48.9090	−	1.78244i	1.83941	−	0.0670354i
$708$		0			0
$709$	−2.87271	+	4.97569i	−0.107887	+	0.186866i	−0.914914	−	0.403649i	$-0.867742\pi$
$709$	−2.87271	+	4.97569i	−0.107887	+	0.186866i	0.807027	+	0.590515i	$0.201075\pi$
$710$		0			0
$711$	−2.82691	−	4.89636i	−0.106018	−	0.183628i
$712$		0			0
$713$	10.1840			0.381394
$714$		0			0
$715$	5.87636			0.219763
$716$		0			0
$717$	−4.73236	−	8.19669i	−0.176733	−	0.306111i
$718$		0			0
$719$	−5.47641	+	9.48542i	−0.204236	+	0.353747i	−0.949889	−	0.312588i	$-0.898804\pi$
$719$	−5.47641	+	9.48542i	−0.204236	+	0.353747i	0.745653	+	0.666334i	$0.232138\pi$
$720$		0			0
$721$	26.6687	+	42.5347i	0.993194	+	1.58407i
$722$		0			0
$723$	7.10439	−	12.3052i	0.264215	−	0.457634i
$724$		0			0
$725$	−25.5247	−	44.2100i	−0.947963	−	1.64192i
$726$		0			0
$727$	9.41026			0.349007			0.174504	−	0.984657i	$-0.444168\pi$
$727$	9.41026			0.349007			0.174504	+	0.984657i	$0.444168\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−2.25093	−	3.89872i	−0.0832536	−	0.144200i
$732$		0			0
$733$	12.5407	−	21.7211i	0.463201	−	0.802289i	−0.535917	−	0.844271i	$-0.680034\pi$
$733$	12.5407	−	21.7211i	0.463201	−	0.802289i	0.999118	+	0.0419822i	$0.0133673\pi$
$734$		0			0
$735$	14.5469	+	21.4258i	0.536570	+	0.790301i
$736$		0			0
$737$	8.42580	−	14.5939i	0.310368	−	0.537574i
$738$		0			0
$739$	−20.0352	−	34.7020i	−0.737007	−	1.27653i	−0.953837	−	0.300324i	$-0.902905\pi$
$739$	−20.0352	−	34.7020i	−0.737007	−	1.27653i	0.216830	−	0.976209i	$-0.430428\pi$
$740$		0			0
$741$	6.17673			0.226908
$742$		0			0
$743$	17.1113			0.627751			0.313876	−	0.949464i	$-0.398372\pi$
$743$	17.1113			0.627751			0.313876	+	0.949464i	$0.398372\pi$
$744$		0			0
$745$	−13.6414	−	23.6277i	−0.499784	−	0.865651i
$746$		0			0
$747$	−6.58217	+	11.4007i	−0.240829	+	0.417128i
$748$		0			0
$749$	−28.4145	−	45.3192i	−1.03824	−	1.65593i
$750$		0			0
$751$	21.2069	−	36.7314i	0.773851	−	1.34035i	−0.161587	−	0.986859i	$-0.551661\pi$
$751$	21.2069	−	36.7314i	0.773851	−	1.34035i	0.935438	−	0.353491i	$-0.115006\pi$
$752$		0			0
$753$	9.58286	+	16.5980i	0.349219	+	0.604865i
$754$		0			0
$755$	−88.6079			−3.22477
$756$		0			0
$757$	−28.0814			−1.02064			−0.510318	−	0.859986i	$-0.670472\pi$
$757$	−28.0814			−1.02064			−0.510318	+	0.859986i	$0.670472\pi$
$758$		0			0
$759$	−5.31089	−	9.19874i	−0.192773	−	0.333893i
$760$		0			0
$761$	−3.54325	+	6.13709i	−0.128443	+	0.222469i	−0.923073	−	0.384624i	$-0.874331\pi$
$761$	−3.54325	+	6.13709i	−0.128443	+	0.222469i	0.794631	+	0.607093i	$0.207665\pi$
$762$		0			0
$763$	30.5741	−	1.11424i	1.10686	−	0.0403382i
$764$		0			0
$765$	1.64400	−	2.84748i	0.0594388	−	0.102951i
$766$		0			0
$767$	2.73855	+	4.74331i	0.0988833	+	0.171271i
$768$		0			0
$769$	−29.3942			−1.05998			−0.529990	−	0.848004i	$-0.677804\pi$
$769$	−29.3942			−1.05998			−0.529990	+	0.848004i	$0.677804\pi$
$770$		0			0
$771$	3.76509			0.135596
$772$		0			0
$773$	2.88509	+	4.99713i	0.103770	+	0.179734i	0.913235	−	0.407434i	$-0.133576\pi$
$773$	2.88509	+	4.99713i	0.103770	+	0.179734i	−0.809465	+	0.587168i	$0.800243\pi$
$774$		0			0
$775$	−6.61491	+	11.4574i	−0.237614	+	0.411560i
$776$		0			0
$777$	3.85346	−	7.27397i	0.138242	−	0.260952i
$778$		0			0
$779$	35.5104	−	61.5059i	1.27229	−	2.20368i
$780$		0			0
$781$	−4.04944	−	7.01384i	−0.144900	−	0.250975i
$782$		0			0
$783$	−5.87636			−0.210004
$784$		0			0
$785$	31.4400			1.12214
$786$		0			0
$787$	−6.08768	−	10.5442i	−0.217002	−	0.375859i	0.736888	−	0.676015i	$-0.236295\pi$
$787$	−6.08768	−	10.5442i	−0.217002	−	0.375859i	−0.953890	+	0.300156i	$0.902961\pi$
$788$		0			0
$789$	−0.954888	+	1.65392i	−0.0339949	+	0.0588809i
$790$		0			0
$791$	20.8302	−	39.3200i	0.740635	−	1.39806i
$792$		0			0
$793$	−0.0327319	+	0.0566933i	−0.00116234	+	0.00201324i
$794$		0			0
$795$	−1.41528	−	2.45133i	−0.0501947	−	0.0869398i
$796$		0			0
$797$	32.6377			1.15609			0.578044	−	0.816006i	$-0.303816\pi$
$797$	32.6377			1.15609			0.578044	+	0.816006i	$0.303816\pi$
$798$		0			0
$799$	−5.33242			−0.188647
$800$		0			0
$801$	−3.90545	−	6.76443i	−0.137992	−	0.239009i
$802$		0			0
$803$	−7.18980	+	12.4531i	−0.253722	+	0.439460i
$804$		0			0
$805$	−65.4133	+	2.38392i	−2.30552	+	0.0840221i
$806$		0			0
$807$	−9.52723	+	16.5016i	−0.335374	+	0.580886i
$808$		0			0
$809$	−12.1731	−	21.0844i	−0.427983	−	0.741288i	0.568711	−	0.822537i	$-0.307442\pi$
$809$	−12.1731	−	21.0844i	−0.427983	−	0.741288i	−0.996694	+	0.0812493i	$0.974109\pi$
$810$		0			0
$811$	−14.7156			−0.516734			−0.258367	−	0.966047i	$-0.583184\pi$
$811$	−14.7156			−0.516734			−0.258367	+	0.966047i	$0.583184\pi$
$812$		0			0
$813$	22.4079			0.785880
$814$		0			0
$815$	−3.14400	−	5.44556i	−0.110129	−	0.190750i
$816$		0			0
$817$	15.6440	−	27.0962i	0.547314	−	0.947976i
$818$		0			0
$819$	−1.40545	−	2.24159i	−0.0491103	−	0.0783275i
$820$		0			0
$821$	1.52359	−	2.63893i	0.0531736	−	0.0920994i	−0.838213	−	0.545342i	$-0.816400\pi$
$821$	1.52359	−	2.63893i	0.0531736	−	0.0920994i	0.891387	+	0.453243i	$0.149733\pi$
$822$		0			0
$823$	22.2305	+	38.5044i	0.774907	+	1.34218i	0.934847	+	0.355051i	$0.115536\pi$
$823$	22.2305	+	38.5044i	0.774907	+	1.34218i	−0.159940	+	0.987127i	$0.551130\pi$
$824$		0			0
$825$	13.7985			0.480403
$826$		0			0
$827$	−16.8750			−0.586801			−0.293400	−	0.955990i	$-0.594787\pi$
$827$	−16.8750			−0.586801			−0.293400	+	0.955990i	$0.594787\pi$
$828$		0			0
$829$	11.3171	+	19.6018i	0.393059	+	0.680797i	0.992851	−	0.119358i	$-0.0380836\pi$
$829$	11.3171	+	19.6018i	0.393059	+	0.680797i	−0.599793	+	0.800155i	$0.704750\pi$
$830$		0			0
$831$	−14.0767	+	24.3815i	−0.488314	+	0.845785i
$832$		0			0
$833$	2.71015	−	5.59980i	0.0939011	−	0.194022i
$834$		0			0
$835$	−3.37271	+	5.84171i	−0.116718	+	0.202161i
$836$		0			0
$837$	0.761450	+	1.31887i	0.0263196	+	0.0455868i
$838$		0			0
$839$	−9.57970			−0.330728			−0.165364	−	0.986233i	$-0.552880\pi$
$839$	−9.57970			−0.330728			−0.165364	+	0.986233i	$0.552880\pi$
$840$		0			0
$841$	5.53156			0.190743
$842$		0			0
$843$	−6.04325	−	10.4672i	−0.208141	−	0.360510i
$844$		0			0
$845$	−1.84981	+	3.20397i	−0.0636355	+	0.110220i
$846$		0			0
$847$	−11.9141	−	19.0022i	−0.409374	−	0.652922i
$848$		0			0
$849$	−7.71634	+	13.3651i	−0.264824	+	0.458689i
$850$		0			0
$851$	10.4029	+	18.0183i	0.356607	+	0.617661i
$852$		0			0
$853$	33.9788			1.16341			0.581706	−	0.813399i	$-0.302385\pi$
$853$	33.9788			1.16341			0.581706	+	0.813399i	$0.302385\pi$
$854$		0			0
$855$	22.8516			0.781508
$856$		0			0
$857$	−19.3523	−	33.5191i	−0.661061	−	1.14499i	−0.980337	−	0.197330i	$-0.936773\pi$
$857$	−19.3523	−	33.5191i	−0.661061	−	1.14499i	0.319276	−	0.947662i	$-0.396560\pi$
$858$		0			0
$859$	−10.3454	+	17.9188i	−0.352981	+	0.611381i	−0.986770	−	0.162125i	$-0.948165\pi$
$859$	−10.3454	+	17.9188i	−0.352981	+	0.611381i	0.633789	+	0.773506i	$0.281499\pi$
$860$		0			0
$861$	−30.4010	+	1.10793i	−1.03606	+	0.0377583i
$862$		0			0
$863$	27.5073	−	47.6440i	0.936359	−	1.62182i	0.164166	−	0.986433i	$-0.447507\pi$
$863$	27.5073	−	47.6440i	0.936359	−	1.62182i	0.772193	−	0.635388i	$-0.219160\pi$
$864$		0			0
$865$	−13.0723	−	22.6420i	−0.444473	−	0.769850i
$866$		0			0
$867$	16.2101			0.550526
$868$		0			0
$869$	−8.98034			−0.304637
$870$		0			0
$871$	5.30470	+	9.18801i	0.179743	+	0.311324i
$872$		0			0
$873$	−0.555632	+	0.962383i	−0.0188053	+	0.0325717i
$874$		0			0
$875$	16.8956	−	31.8930i	0.571176	−	1.07818i
$876$		0			0
$877$	11.6614	−	20.1981i	0.393777	−	0.682042i	−0.599167	−	0.800624i	$-0.704501\pi$
$877$	11.6614	−	20.1981i	0.393777	−	0.682042i	0.992944	+	0.118582i	$0.0378348\pi$
$878$		0			0
$879$	6.71565	+	11.6318i	0.226513	+	0.392332i
$880$		0			0
$881$	−31.5105			−1.06162			−0.530808	−	0.847492i	$-0.678112\pi$
$881$	−31.5105			−1.06162			−0.530808	+	0.847492i	$0.678112\pi$
$882$		0			0
$883$	15.2990			0.514852			0.257426	−	0.966298i	$-0.417126\pi$
$883$	15.2990			0.514852			0.257426	+	0.966298i	$0.417126\pi$
$884$		0			0
$885$	10.1316	+	17.5485i	0.340571	+	0.589886i
$886$		0			0
$887$	−15.4272	+	26.7207i	−0.517994	+	0.897192i	0.481788	+	0.876288i	$0.339988\pi$
$887$	−15.4272	+	26.7207i	−0.517994	+	0.897192i	−0.999781	+	0.0209037i	$0.993346\pi$
$888$		0			0
$889$	9.64351	−	18.2036i	0.323433	−	0.610528i
$890$		0			0
$891$	0.794182	−	1.37556i	0.0266061	−	0.0460831i
$892$		0			0
$893$	−18.5302	−	32.0952i	−0.620089	−	1.07403i
$894$		0			0
$895$	44.9257			1.50170
$896$		0			0
$897$	6.68725			0.223281
$898$		0			0
$899$	−4.47455	−	7.75015i	−0.149235	−	0.258482i
$900$		0			0
$901$	−0.339982	+	0.588867i	−0.0113265	+	0.0196180i
$902$		0			0
$903$	−13.3931	+	0.488096i	−0.445693	+	0.0162428i
$904$		0			0
$905$	−47.6148	+	82.4713i	−1.58277	+	2.74144i
$906$		0			0
$907$	18.1756	+	31.4810i	0.603509	+	1.04531i	0.992285	+	0.123977i	$0.0395648\pi$
$907$	18.1756	+	31.4810i	0.603509	+	1.04531i	−0.388776	+	0.921332i	$0.627102\pi$
$908$		0			0
$909$	−18.4981			−0.613545
$910$		0			0
$911$	17.6749			0.585595			0.292797	−	0.956175i	$-0.405414\pi$
$911$	17.6749			0.585595			0.292797	+	0.956175i	$0.405414\pi$
$912$		0			0
$913$	10.4549	+	18.1084i	0.346006	+	0.599300i
$914$		0			0
$915$	−0.121096	+	0.209744i	−0.00400331	+	0.00693393i
$916$		0			0
$917$	3.74721	+	5.97654i	0.123744	+	0.197363i
$918$		0			0
$919$	11.8585	−	20.5395i	0.391175	−	0.677535i	−0.601430	−	0.798926i	$-0.705402\pi$
$919$	11.8585	−	20.5395i	0.391175	−	0.677535i	0.992605	+	0.121391i	$0.0387354\pi$
$920$		0			0
$921$	2.26764	+	3.92767i	0.0747213	+	0.129421i
$922$		0			0
$923$	5.09888			0.167832
$924$		0			0
$925$	−27.0283			−0.888686
$926$		0			0
$927$	−9.48762	−	16.4330i	−0.311614	−	0.539732i
$928$		0			0
$929$	13.8287	−	23.9520i	0.453705	−	0.785840i	−0.544908	−	0.838496i	$-0.683435\pi$
$929$	13.8287	−	23.9520i	0.453705	−	0.785840i	0.998613	+	0.0526561i	$0.0167687\pi$
$930$		0			0
$931$	43.1224	−	3.14728i	1.41328	−	0.103148i
$932$		0			0
$933$	8.00619	−	13.8671i	0.262111	−	0.453989i
$934$		0			0
$935$	−2.61126	−	4.52284i	−0.0853975	−	0.147913i
$936$		0			0
$937$	−19.5439			−0.638473			−0.319236	−	0.947675i	$-0.603426\pi$
$937$	−19.5439			−0.638473			−0.319236	+	0.947675i	$0.603426\pi$
$938$		0			0
$939$	15.2880			0.498905
$940$		0			0
$941$	22.0476	+	38.1875i	0.718731	+	1.24488i	0.961503	+	0.274795i	$0.0886099\pi$
$941$	22.0476	+	38.1875i	0.718731	+	1.24488i	−0.242772	+	0.970083i	$0.578057\pi$
$942$		0			0
$943$	38.4455	−	66.5895i	1.25196	−	2.16845i
$944$		0			0
$945$	−5.19963	−	8.29305i	−0.169144	−	0.269773i
$946$		0			0
$947$	−19.0388	+	32.9762i	−0.618679	+	1.07158i	0.371048	+	0.928614i	$0.378999\pi$
$947$	−19.0388	+	32.9762i	−0.618679	+	1.07158i	−0.989727	+	0.142970i	$0.954335\pi$
$948$		0			0
$949$	−4.52654	−	7.84020i	−0.146938	−	0.254504i
$950$		0			0
$951$	17.5956			0.570578
$952$		0			0
$953$	−17.2581			−0.559046			−0.279523	−	0.960139i	$-0.590176\pi$
$953$	−17.2581			−0.559046			−0.279523	+	0.960139i	$0.590176\pi$
$954$		0			0
$955$	−17.6545	−	30.5785i	−0.571287	−	0.989498i
$956$		0			0
$957$	−4.66690	+	8.08330i	−0.150859	+	0.261296i
$958$		0			0
$959$	16.0927	−	0.586481i	0.519660	−	0.0189385i
$960$		0			0
$961$	14.3404	−	24.8383i	0.462593	−	0.801235i
$962$		0			0
$963$	10.1087	+	17.5088i	0.325749	+	0.564214i
$964$		0			0
$965$	24.2051			0.779188
$966$		0			0
$967$	−38.5760			−1.24052			−0.620260	−	0.784396i	$-0.712973\pi$
$967$	−38.5760			−1.24052			−0.620260	+	0.784396i	$0.712973\pi$
$968$		0			0
$969$	−2.74474	−	4.75403i	−0.0881737	−	0.152721i
$970$		0			0
$971$	14.7298	−	25.5128i	0.472702	−	0.818744i	−0.526810	−	0.849983i	$-0.676612\pi$
$971$	14.7298	−	25.5128i	0.472702	−	0.818744i	0.999512	+	0.0312390i	$0.00994531\pi$
$972$		0			0
$973$	14.9851	−	28.2865i	0.480399	−	0.906825i
$974$		0			0
$975$	−4.34362	+	7.52338i	−0.139107	+	0.240941i
$976$		0			0
$977$	−12.4258	−	21.5221i	−0.397537	−	0.688553i	0.595885	−	0.803070i	$-0.296801\pi$
$977$	−12.4258	−	21.5221i	−0.397537	−	0.688553i	−0.993421	+	0.114516i	$0.963468\pi$
$978$		0			0
$979$	−12.4065			−0.396515
$980$		0			0
$981$	−11.5636			−0.369197
$982$		0			0
$983$	−19.6836	−	34.0930i	−0.627810	−	1.08740i	−0.987990	−	0.154516i	$-0.950618\pi$
$983$	−19.6836	−	34.0930i	−0.627810	−	1.08740i	0.360181	−	0.932883i	$-0.382715\pi$
$984$		0			0
$985$	10.6280	−	18.4082i	0.338635	−	0.586534i
$986$		0			0
$987$	−7.43130	+	14.0277i	−0.236541	+	0.446506i
$988$		0			0
$989$	16.9370	−	29.3358i	0.538566	−	0.932823i
$990$		0			0
$991$	7.41164	+	12.8373i	0.235438	+	0.407791i	0.959400	−	0.282049i	$-0.0910141\pi$
$991$	7.41164	+	12.8373i	0.235438	+	0.407791i	−0.723962	+	0.689840i	$0.757681\pi$
$992$		0			0
$993$	−1.61312			−0.0511909
$994$		0			0
$995$	75.5933			2.39647
$996$		0			0
$997$	10.2825	+	17.8098i	0.325650	+	0.564042i	0.981644	−	0.190724i	$-0.0610836\pi$
$997$	10.2825	+	17.8098i	0.325650	+	0.564042i	−0.655994	+	0.754766i	$0.727750\pi$
$998$		0			0
$999$	−1.55563	+	2.69443i	−0.0492180	+	0.0852481i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1092.2.q.d.625.1	✓	6
3.2	odd	2		3276.2.r.i.2809.3		6
7.2	even	3		7644.2.a.w.1.3		3
7.4	even	3	inner	1092.2.q.d.781.1	yes	6
7.5	odd	6		7644.2.a.x.1.1		3
21.11	odd	6		3276.2.r.i.1873.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1092.2.q.d.625.1	✓	6	1.1	even	1	trivial
1092.2.q.d.781.1	yes	6	7.4	even	3	inner
3276.2.r.i.1873.3		6	21.11	odd	6
3276.2.r.i.2809.3		6	3.2	odd	2
7644.2.a.w.1.3		3	7.2	even	3
7644.2.a.x.1.1		3	7.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1092 = 2^{2} \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1092.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{3} +(-1.84981 + 3.20397i) q^{5} +(1.23855 - 2.33795i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(0.794182 + 1.37556i) q^{11} -1.00000 q^{13} -3.69963 q^{15} +(0.444368 + 0.769668i) q^{17} +(-3.08836 + 5.34920i) q^{19} +(2.64400 - 0.0963576i) q^{21} +(-3.34362 + 5.79133i) q^{23} +(-4.34362 - 7.52338i) q^{25} -1.00000 q^{27} +5.87636 q^{29} +(-0.761450 - 1.31887i) q^{31} +(-0.794182 + 1.37556i) q^{33} +(5.19963 + 8.29305i) q^{35} +(1.55563 - 2.69443i) q^{37} +(-0.500000 - 0.866025i) q^{39} -11.4981 q^{41} -5.06546 q^{43} +(-1.84981 - 3.20397i) q^{45} +(-3.00000 + 5.19615i) q^{47} +(-3.93199 - 5.79133i) q^{49} +(-0.444368 + 0.769668i) q^{51} +(0.382546 + 0.662589i) q^{53} -5.87636 q^{55} -6.17673 q^{57} +(-2.73855 - 4.74331i) q^{59} +(0.0327319 - 0.0566933i) q^{61} +(1.40545 + 2.24159i) q^{63} +(1.84981 - 3.20397i) q^{65} +(-5.30470 - 9.18801i) q^{67} -6.68725 q^{69} -5.09888 q^{71} +(4.52654 + 7.84020i) q^{73} +(4.34362 - 7.52338i) q^{75} +(4.19963 - 0.153051i) q^{77} +(-2.82691 + 4.89636i) q^{79} +(-0.500000 - 0.866025i) q^{81} +13.1643 q^{83} -3.28799 q^{85} +(2.93818 + 5.08907i) q^{87} +(-3.90545 + 6.76443i) q^{89} +(-1.23855 + 2.33795i) q^{91} +(0.761450 - 1.31887i) q^{93} +(-11.4258 - 19.7901i) q^{95} +1.11126 q^{97} -1.58836 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{3} - 5 q^{5} + 2 q^{7} - 3 q^{9} - q^{11} - 6 q^{13} - 10 q^{15} + 3 q^{17} - 7 q^{19} + 4 q^{21} + 4 q^{23} - 2 q^{25} - 6 q^{27} - 10 q^{31} + q^{33} + 19 q^{35} + 9 q^{37} - 3 q^{39} - 8 q^{41}+ \cdots + 2 q^{99}+O(q^{100}) \) 6 * q + 3 * q^3 - 5 * q^5 + 2 * q^7 - 3 * q^9 - q^11 - 6 * q^13 - 10 * q^15 + 3 * q^17 - 7 * q^19 + 4 * q^21 + 4 * q^23 - 2 * q^25 - 6 * q^27 - 10 * q^31 + q^33 + 19 * q^35 + 9 * q^37 - 3 * q^39 - 8 * q^41 - 8 * q^43 - 5 * q^45 - 18 * q^47 + 12 * q^49 - 3 * q^51 - 15 * q^53 - 14 * q^57 - 11 * q^59 - 11 * q^61 + 2 * q^63 + 5 * q^65 - q^67 + 8 * q^69 + 6 * q^71 - 2 * q^73 + 2 * q^75 + 13 * q^77 - 3 * q^81 + 20 * q^83 + 4 * q^85 - 17 * q^89 - 2 * q^91 + 10 * q^93 - 15 * q^95 + 6 * q^97 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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