LMFDB - Embedded newform 1040.2.dh.a.529.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1040,2,Mod(289,1040)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1040.289"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1040, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 3, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1040 = 2^{4} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1040.dh (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,0,-6,0,0,0,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	no
Analytic conductor:	$8.30444181021$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 8x^{10} + 54x^{8} - 78x^{6} + 92x^{4} - 10x^{2} + 1 $ x^12 - 8x^10 + 54x^8 - 78x^6 + 92x^4 - 10*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			529.6
Root			$-0.286513 + 0.165418i$ of defining polynomial
Character	$\chi$	$=$	1040.529
Dual form			1040.2.dh.a.289.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.33117 + 1.34590i) q^{3} +(-2.12291 + 0.702335i) q^{5} +(-2.90420 + 1.67674i) q^{7} +(2.12291 + 3.67698i) q^{9} +(-1.62291 + 2.81095i) q^{11} +(-1.21648 - 3.39414i) q^{13} +(-5.89413 - 1.21996i) q^{15} +(-1.68772 + 0.974404i) q^{17} +(0.622905 + 1.07890i) q^{19} -9.02690 q^{21} +(-2.33117 - 1.34590i) q^{23} +(4.01345 - 2.98198i) q^{25} +3.35348i q^{27} +(1.50000 - 2.59808i) q^{29} -3.78109 q^{31} +(-7.56654 + 4.36854i) q^{33} +(4.98770 - 5.59927i) q^{35} +(-1.68772 - 0.974404i) q^{37} +(1.73236 - 9.54958i) q^{39} +(-1.39055 + 2.40850i) q^{41} +(-7.56654 + 4.36854i) q^{43} +(-7.08920 - 6.31489i) q^{45} +6.86960i q^{47} +(2.12291 - 3.67698i) q^{49} -5.24581 q^{51} +12.8336i q^{53} +(1.47104 - 7.10721i) q^{55} +3.35348i q^{57} +(1.26764 + 2.19562i) q^{59} +(3.74581 + 6.48793i) q^{61} +(-12.3307 - 7.11911i) q^{63} +(4.96629 + 6.35106i) q^{65} +(-3.47722 - 2.00758i) q^{67} +(-3.62291 - 6.27506i) q^{69} +(2.62291 + 4.54300i) q^{71} +5.46493i q^{73} +(13.3695 - 1.54979i) q^{75} -10.8848i q^{77} +13.7811 q^{79} +(1.85526 - 3.21341i) q^{81} +8.61955i q^{83} +(2.89851 - 3.25391i) q^{85} +(6.99351 - 4.03771i) q^{87} +(5.15819 - 8.93425i) q^{89} +(9.22398 + 7.81753i) q^{91} +(-8.81438 - 5.08898i) q^{93} +(-2.08012 - 1.85292i) q^{95} +(-4.56055 + 2.63304i) q^{97} -13.7811 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{5} + 6 q^{9} + 4 q^{15} - 12 q^{19} - 8 q^{21} - 2 q^{25} + 18 q^{29} + 16 q^{31} - 10 q^{35} + 32 q^{39} + 14 q^{41} - 29 q^{45} + 6 q^{49} - 24 q^{51} + 26 q^{55} + 4 q^{59} + 6 q^{61} + 23 q^{65}+ \cdots - 104 q^{99}+O(q^{100}) $ 12 * q - 6 * q^5 + 6 * q^9 + 4 * q^15 - 12 * q^19 - 8 * q^21 - 2 * q^25 + 18 * q^29 + 16 * q^31 - 10 * q^35 + 32 * q^39 + 14 * q^41 - 29 * q^45 + 6 * q^49 - 24 * q^51 + 26 * q^55 + 4 * q^59 + 6 * q^61 + 23 * q^65 - 24 * q^69 + 12 * q^71 - 2 * q^75 + 104 * q^79 + 14 * q^81 + 21 * q^85 + 20 * q^89 + 44 * q^91 - 20 * q^95 - 104 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1040\mathbb{Z}\right)^\times$.

$n$	$261$	$417$	$561$	$911$
$\chi(n)$	$1$	$-1$	$e\left(\frac{2}{3}\right)$	$1$

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
$3$	2.33117	+	1.34590i	1.34590	+	0.777057i	0.987666	−	0.156574i	$-0.0500450\pi$
$3$	2.33117	+	1.34590i	1.34590	+	0.777057i	0.358236	+	0.933631i	$0.383378\pi$
$4$		0			0
$5$	−2.12291	+	0.702335i	−0.949392	+	0.314094i
$5$	−2.12291	+	0.702335i	−0.949392	+	0.314094i
$6$		0			0
$7$	−2.90420	+	1.67674i	−1.09768	+	0.633748i	−0.935611	−	0.353031i	$-0.885151\pi$
$7$	−2.90420	+	1.67674i	−1.09768	+	0.633748i	−0.162072	+	0.986779i	$0.551818\pi$
$8$		0			0
$9$	2.12291	+	3.67698i	0.707635	+	1.22566i
$10$		0			0
$11$	−1.62291	+	2.81095i	−0.489324	+	0.847535i	−0.999925	−	0.0122837i	$-0.996090\pi$
$11$	−1.62291	+	2.81095i	−0.489324	+	0.847535i	0.510600	+	0.859818i	$0.329423\pi$
$12$		0			0
$13$	−1.21648	−	3.39414i	−0.337391	−	0.941365i
$13$	−1.21648	−	3.39414i	−0.337391	−	0.941365i
$14$		0			0
$15$	−5.89413	−	1.21996i	−1.52186	−	0.314992i
$16$		0			0
$17$	−1.68772	+	0.974404i	−0.409332	+	0.236328i	−0.690503	−	0.723330i	$-0.742611\pi$
$17$	−1.68772	+	0.974404i	−0.409332	+	0.236328i	0.281171	+	0.959658i	$0.409277\pi$
$18$		0			0
$19$	0.622905	+	1.07890i	0.142904	+	0.247517i	0.928589	−	0.371110i	$-0.121023\pi$
$19$	0.622905	+	1.07890i	0.142904	+	0.247517i	−0.785685	+	0.618627i	$0.787689\pi$
$20$		0			0
$21$	−9.02690			−1.96983
$22$		0			0
$23$	−2.33117	−	1.34590i	−0.486083	−	0.280640i	0.236865	−	0.971543i	$-0.423880\pi$
$23$	−2.33117	−	1.34590i	−0.486083	−	0.280640i	−0.722948	+	0.690903i	$0.757213\pi$
$24$		0			0
$25$	4.01345	−	2.98198i	0.802690	−	0.596396i
$26$		0			0
$27$			3.35348i			0.645377i
$28$		0			0
$29$	1.50000	−	2.59808i	0.278543	−	0.482451i	−0.692480	−	0.721437i	$-0.743482\pi$
$29$	1.50000	−	2.59808i	0.278543	−	0.482451i	0.971023	+	0.238987i	$0.0768152\pi$
$30$		0			0
$31$	−3.78109			−0.679105			−0.339552	−	0.940587i	$-0.610276\pi$
$31$	−3.78109			−0.679105			−0.339552	+	0.940587i	$0.610276\pi$
$32$		0			0
$33$	−7.56654	+	4.36854i	−1.31717	+	0.760466i
$34$		0			0
$35$	4.98770	−	5.59927i	0.843076	−	0.946450i
$36$		0			0
$37$	−1.68772	−	0.974404i	−0.277459	−	0.160191i	0.354813	−	0.934937i	$-0.384544\pi$
$37$	−1.68772	−	0.974404i	−0.277459	−	0.160191i	−0.632273	+	0.774746i	$0.717878\pi$
$38$		0			0
$39$	1.73236	−	9.54958i	0.277399	−	1.52916i
$40$		0			0
$41$	−1.39055	+	2.40850i	−0.217167	+	0.376144i	−0.953941	−	0.299995i	$-0.903015\pi$
$41$	−1.39055	+	2.40850i	−0.217167	+	0.376144i	0.736774	+	0.676139i	$0.236348\pi$
$42$		0			0
$43$	−7.56654	+	4.36854i	−1.15389	+	0.666197i	−0.949831	−	0.312763i	$-0.898745\pi$
$43$	−7.56654	+	4.36854i	−1.15389	+	0.666197i	−0.204055	+	0.978959i	$0.565412\pi$
$44$		0			0
$45$	−7.08920	−	6.31489i	−1.05679	−	0.941368i
$46$		0			0
$47$			6.86960i			1.00203i	0.865437	+	0.501017i	$0.167041\pi$
$47$			6.86960i			1.00203i	−0.865437	+	0.501017i	$0.832959\pi$
$48$		0			0
$49$	2.12291	−	3.67698i	0.303272	−	0.525283i
$50$		0			0
$51$	−5.24581			−0.734560
$52$		0			0
$53$			12.8336i			1.76282i	0.472347	+	0.881412i	$0.343407\pi$
$53$			12.8336i			1.76282i	−0.472347	+	0.881412i	$0.656593\pi$
$54$		0			0
$55$	1.47104	−	7.10721i	0.198355	−	0.958336i
$56$		0			0
$57$			3.35348i			0.444179i
$58$		0			0
$59$	1.26764	+	2.19562i	0.165033	+	0.285845i	0.936667	−	0.350221i	$-0.113894\pi$
$59$	1.26764	+	2.19562i	0.165033	+	0.285845i	−0.771634	+	0.636067i	$0.780560\pi$
$60$		0			0
$61$	3.74581	+	6.48793i	0.479602	+	0.830695i	0.999726	−	0.0233957i	$-0.00744777\pi$
$61$	3.74581	+	6.48793i	0.479602	+	0.830695i	−0.520124	+	0.854090i	$0.674114\pi$
$62$		0			0
$63$	−12.3307	−	7.11911i	−1.55352	−	0.896924i
$64$		0			0
$65$	4.96629	+	6.35106i	0.615993	+	0.787752i
$66$		0			0
$67$	−3.47722	−	2.00758i	−0.424810	−	0.245264i	0.272323	−	0.962206i	$-0.412208\pi$
$67$	−3.47722	−	2.00758i	−0.424810	−	0.245264i	−0.697133	+	0.716942i	$0.745541\pi$
$68$		0			0
$69$	−3.62291	−	6.27506i	−0.436147	−	0.755428i
$70$		0			0
$71$	2.62291	+	4.54300i	0.311282	+	0.539155i	0.978640	−	0.205581i	$-0.0659084\pi$
$71$	2.62291	+	4.54300i	0.311282	+	0.539155i	−0.667359	+	0.744737i	$0.732575\pi$
$72$		0			0
$73$			5.46493i			0.639622i	0.947481	+	0.319811i	$0.103619\pi$
$73$			5.46493i			0.639622i	−0.947481	+	0.319811i	$0.896381\pi$
$74$		0			0
$75$	13.3695	−	1.54979i	1.54378	−	0.178954i
$76$		0			0
$77$		−	10.8848i		−	1.24043i
$78$		0			0
$79$	13.7811			1.55049			0.775247	−	0.631658i	$-0.217625\pi$
$79$	13.7811			1.55049			0.775247	+	0.631658i	$0.217625\pi$
$80$		0			0
$81$	1.85526	−	3.21341i	0.206140	−	0.357046i
$82$		0			0
$83$			8.61955i			0.946119i	0.881031	+	0.473059i	$0.156850\pi$
$83$			8.61955i			0.946119i	−0.881031	+	0.473059i	$0.843150\pi$
$84$		0			0
$85$	2.89851	−	3.25391i	0.314387	−	0.352936i
$86$		0			0
$87$	6.99351	−	4.03771i	0.749783	−	0.432888i
$88$		0			0
$89$	5.15819	−	8.93425i	0.546767	−	0.947028i	−0.451726	−	0.892156i	$-0.649192\pi$
$89$	5.15819	−	8.93425i	0.546767	−	0.947028i	0.998493	−	0.0548717i	$-0.0174750\pi$
$90$		0			0
$91$	9.22398	+	7.81753i	0.966936	+	0.819500i
$92$		0			0
$93$	−8.81438	−	5.08898i	−0.914008	−	0.527703i
$94$		0			0
$95$	−2.08012	−	1.85292i	−0.213416	−	0.190106i
$96$		0			0
$97$	−4.56055	+	2.63304i	−0.463054	+	0.267344i	−0.713328	−	0.700831i	$-0.752813\pi$
$97$	−4.56055	+	2.63304i	−0.463054	+	0.267344i	0.250273	+	0.968175i	$0.419479\pi$
$98$		0			0
$99$	−13.7811			−1.38505
$100$		0			0
$101$	−2.85526	+	4.94546i	−0.284109	+	0.492092i	−0.972393	−	0.233350i	$-0.925031\pi$
$101$	−2.85526	+	4.94546i	−0.284109	+	0.492092i	0.688283	+	0.725442i	$0.258365\pi$
$102$		0			0
$103$		−	7.36863i		−	0.726052i	−0.931779	−	0.363026i	$-0.881744\pi$
$103$		−	7.36863i		−	0.726052i	0.931779	−	0.363026i	$-0.118256\pi$
$104$		0			0
$105$	19.1633	−	6.33991i	1.87014	−	0.618712i
$106$		0			0
$107$	7.42568	+	4.28722i	0.717868	+	0.414461i	0.813967	−	0.580911i	$-0.197303\pi$
$107$	7.42568	+	4.28722i	0.717868	+	0.414461i	−0.0960996	+	0.995372i	$0.530637\pi$
$108$		0			0
$109$	8.49162			0.813350			0.406675	−	0.913573i	$-0.366688\pi$
$109$	8.49162			0.813350			0.406675	+	0.913573i	$0.366688\pi$
$110$		0			0
$111$	−2.62291	−	4.54300i	−0.248955	−	0.431203i
$112$		0			0
$113$	6.35006	−	3.66621i	0.597363	−	0.344888i	−0.170640	−	0.985333i	$-0.554584\pi$
$113$	6.35006	−	3.66621i	0.597363	−	0.344888i	0.768004	+	0.640446i	$0.221250\pi$
$114$		0			0
$115$	5.89413	+	1.21996i	0.549630	+	0.113762i
$116$		0			0
$117$	9.89771	−	11.6784i	0.915044	−	1.07967i
$118$		0			0
$119$	3.26764	−	5.65972i	0.299544	−	0.518826i
$120$		0			0
$121$	0.232358	+	0.402456i	0.0211234	+	0.0365869i
$122$		0			0
$123$	−6.48321	+	3.74308i	−0.584571	+	0.337502i
$124$		0			0
$125$	−6.42583	+	9.14925i	−0.574744	+	0.818333i
$126$		0			0
$127$	−7.93599	−	4.58185i	−0.704205	−	0.406573i	0.104707	−	0.994503i	$-0.466610\pi$
$127$	−7.93599	−	4.58185i	−0.704205	−	0.406573i	−0.808912	+	0.587930i	$0.799943\pi$
$128$		0			0
$129$	−23.5185			−2.07069
$130$		0			0
$131$	−10.0000			−0.873704			−0.436852	−	0.899533i	$-0.643907\pi$
$131$	−10.0000			−0.873704			−0.436852	+	0.899533i	$0.643907\pi$
$132$		0			0
$133$	−3.61808	−	2.08890i	−0.313727	−	0.181130i
$134$		0			0
$135$	−2.35526	−	7.11911i	−0.202709	−	0.612716i
$136$		0			0
$137$	14.5914	−	8.42435i	1.24663	−	0.719741i	0.276193	−	0.961102i	$-0.410927\pi$
$137$	14.5914	−	8.42435i	1.24663	−	0.719741i	0.970435	+	0.241361i	$0.0775938\pi$
$138$		0			0
$139$	0.513452	+	0.889325i	0.0435505	+	0.0754316i	0.886979	−	0.461810i	$-0.152800\pi$
$139$	0.513452	+	0.889325i	0.0435505	+	0.0754316i	−0.843429	+	0.537241i	$0.819466\pi$
$140$		0			0
$141$	−9.24581	+	16.0142i	−0.778638	+	1.34864i
$142$		0			0
$143$	11.5150	+	2.08890i	0.962933	+	0.174682i
$144$		0			0
$145$	−1.35964	+	6.56897i	−0.112912	+	0.545523i
$146$		0			0
$147$	9.89771	−	5.71445i	0.816349	−	0.471319i
$148$		0			0
$149$	7.92583	+	13.7279i	0.649309	+	1.12464i	0.983288	+	0.182056i	$0.0582753\pi$
$149$	7.92583	+	13.7279i	0.649309	+	1.12464i	−0.333979	+	0.942581i	$0.608391\pi$
$150$		0			0
$151$	−14.5454			−1.18369			−0.591845	−	0.806052i	$-0.701600\pi$
$151$	−14.5454			−1.18369			−0.591845	+	0.806052i	$0.701600\pi$
$152$		0			0
$153$	−7.16573	−	4.13713i	−0.579315	−	0.334468i
$154$		0			0
$155$	8.02690	−	2.65559i	0.644736	−	0.213302i
$156$		0			0
$157$			10.9210i			0.871588i	0.900047	+	0.435794i	$0.143532\pi$
$157$			10.9210i			0.871588i	−0.900047	+	0.435794i	$0.856468\pi$
$158$		0			0
$159$	−17.2727	+	29.9172i	−1.36982	+	2.37259i
$160$		0			0
$161$	9.02690			0.711420
$162$		0			0
$163$	−3.61808	+	2.08890i	−0.283390	+	0.163615i	−0.634957	−	0.772547i	$-0.718982\pi$
$163$	−3.61808	+	2.08890i	−0.283390	+	0.163615i	0.351567	+	0.936163i	$0.385649\pi$
$164$		0			0
$165$	12.9949	−	14.5882i	1.01165	−	1.13569i
$166$		0			0
$167$	−2.90420	−	1.67674i	−0.224733	−	0.129750i	0.383407	−	0.923580i	$-0.374751\pi$
$167$	−2.90420	−	1.67674i	−0.224733	−	0.129750i	−0.608140	+	0.793830i	$0.708084\pi$
$168$		0			0
$169$	−10.0404	+	8.25780i	−0.772335	+	0.635215i
$170$		0			0
$171$	−2.64474	+	4.58082i	−0.202248	+	0.350304i
$172$		0			0
$173$	−7.56654	+	4.36854i	−0.575273	+	0.332134i	−0.759253	−	0.650796i	$-0.774435\pi$
$173$	−7.56654	+	4.36854i	−0.575273	+	0.332134i	0.183979	+	0.982930i	$0.441102\pi$
$174$		0			0
$175$	−6.65585	+	15.3898i	−0.503135	+	1.16336i
$176$		0			0
$177$			6.82449i			0.512960i
$178$		0			0
$179$	9.00507	−	15.5972i	0.673071	−	1.16579i	−0.303958	−	0.952685i	$-0.598308\pi$
$179$	9.00507	−	15.5972i	0.673071	−	1.16579i	0.977029	−	0.213107i	$-0.0683584\pi$
$180$		0			0
$181$	1.04366			0.0775749			0.0387875	−	0.999247i	$-0.487650\pi$
$181$	1.04366			0.0775749			0.0387875	+	0.999247i	$0.487650\pi$
$182$		0			0
$183$			20.1660i			1.49071i
$184$		0			0
$185$	4.26722	+	0.883225i	0.313732	+	0.0649360i
$186$		0			0
$187$		−	6.32546i		−	0.462564i
$188$		0			0
$189$	−5.62291	−	9.73916i	−0.409006	−	0.708419i
$190$		0			0
$191$	12.7593	+	22.0997i	0.923228	+	1.59908i	0.794387	+	0.607412i	$0.207792\pi$
$191$	12.7593	+	22.0997i	0.923228	+	1.59908i	0.128841	+	0.991665i	$0.458874\pi$
$192$		0			0
$193$	−17.1652	−	9.91035i	−1.23558	−	0.713362i	−0.267392	−	0.963588i	$-0.586162\pi$
$193$	−17.1652	−	9.91035i	−1.23558	−	0.713362i	−0.968188	+	0.250225i	$0.919495\pi$
$194$		0			0
$195$	3.02937	+	21.4895i	0.216938	+	1.53890i
$196$		0			0
$197$	−18.7512	−	10.8260i	−1.33596	−	0.771319i	−0.349758	−	0.936840i	$-0.613736\pi$
$197$	−18.7512	−	10.8260i	−1.33596	−	0.771319i	−0.986206	+	0.165521i	$0.947070\pi$
$198$		0			0
$199$	−9.11453	−	15.7868i	−0.646112	−	1.11910i	−0.984044	−	0.177928i	$-0.943061\pi$
$199$	−9.11453	−	15.7868i	−0.646112	−	1.11910i	0.337932	−	0.941171i	$-0.390273\pi$
$200$		0			0
$201$	−5.40400	−	9.36000i	−0.381169	−	0.660204i
$202$		0			0
$203$			10.0604i			0.706104i
$204$		0			0
$205$	1.26043	−	6.08964i	0.0880321	−	0.425319i
$206$		0			0
$207$		−	11.4289i		−	0.794363i
$208$		0			0
$209$	−4.04366			−0.279706
$210$		0			0
$211$	9.64981	−	16.7140i	0.664320	−	1.15064i	−0.315149	−	0.949042i	$-0.602054\pi$
$211$	9.64981	−	16.7140i	0.664320	−	1.15064i	0.979469	−	0.201594i	$-0.0646122\pi$
$212$		0			0
$213$			14.1207i			0.967534i
$214$		0			0
$215$	12.9949	−	14.5882i	0.886242	−	0.994910i
$216$		0			0
$217$	10.9810	−	6.33991i	0.745442	−	0.430381i
$218$		0			0
$219$	−7.35526	+	12.7397i	−0.497023	+	0.860868i
$220$		0			0
$221$	5.36034	+	4.54300i	0.360575	+	0.305596i
$222$		0			0
$223$	−10.7134	−	6.18537i	−0.717421	−	0.414203i	0.0963818	−	0.995344i	$-0.469273\pi$
$223$	−10.7134	−	6.18537i	−0.717421	−	0.414203i	−0.813803	+	0.581141i	$0.802606\pi$
$224$		0			0
$225$	19.4849	+	8.42692i	1.29899	+	0.561795i
$226$		0			0
$227$	5.33715	−	3.08141i	0.354239	−	0.204520i	−0.312311	−	0.949980i	$-0.601103\pi$
$227$	5.33715	−	3.08141i	0.354239	−	0.204520i	0.666551	+	0.745460i	$0.267770\pi$
$228$		0			0
$229$	26.9832			1.78310			0.891551	−	0.452920i	$-0.149618\pi$
$229$	26.9832			1.78310			0.891551	+	0.452920i	$0.149618\pi$
$230$		0			0
$231$	14.6498	−	25.3742i	0.963887	−	1.66950i
$232$		0			0
$233$		−	0.824319i		−	0.0540029i	−0.999635	−	0.0270015i	$-0.991404\pi$
$233$		−	0.824319i		−	0.0540029i	0.999635	−	0.0270015i	$-0.00859588\pi$
$234$		0			0
$235$	−4.82476	−	14.5835i	−0.314733	−	0.951323i
$236$		0			0
$237$	32.1261	+	18.5480i	2.08681	+	1.20482i
$238$		0			0
$239$	4.00000			0.258738			0.129369	−	0.991596i	$-0.458705\pi$
$239$	4.00000			0.258738			0.129369	+	0.991596i	$0.458705\pi$
$240$		0			0
$241$	−11.3469	−	19.6534i	−0.730917	−	1.26599i	−0.956492	−	0.291760i	$-0.905759\pi$
$241$	−11.3469	−	19.6534i	−0.730917	−	1.26599i	0.225575	−	0.974226i	$-0.427574\pi$
$242$		0			0
$243$	17.3625	−	10.0242i	1.11380	−	0.643054i
$244$		0			0
$245$	−1.92426	+	9.29687i	−0.122936	+	0.593955i
$246$		0			0
$247$	2.90420	−	3.42669i	0.184790	−	0.218035i
$248$		0			0
$249$	−11.6011	+	20.0936i	−0.735188	+	1.27338i
$250$		0			0
$251$	9.51345	+	16.4778i	0.600484	+	1.04007i	0.992748	+	0.120216i	$0.0383586\pi$
$251$	9.51345	+	16.4778i	0.600484	+	1.04007i	−0.392264	+	0.919853i	$0.628308\pi$
$252$		0			0
$253$	7.56654	−	4.36854i	0.475704	−	0.274648i
$254$		0			0
$255$	11.1364	−	3.68431i	0.697386	−	0.230721i
$256$		0			0
$257$	1.82857	+	1.05573i	0.114063	+	0.0658544i	0.555946	−	0.831218i	$-0.312356\pi$
$257$	1.82857	+	1.05573i	0.114063	+	0.0658544i	−0.441883	+	0.897073i	$0.645689\pi$
$258$		0			0
$259$	6.53528			0.406083
$260$		0			0
$261$	12.7374			0.788427
$262$		0			0
$263$	−25.9092	−	14.9587i	−1.59763	−	0.922391i	−0.991943	−	0.126687i	$-0.959566\pi$
$263$	−25.9092	−	14.9587i	−1.59763	−	0.922391i	−0.605685	−	0.795704i	$-0.707101\pi$
$264$		0			0
$265$	−9.01345	−	27.2444i	−0.553692	−	1.67361i
$266$		0			0
$267$	24.0492	−	13.8848i	1.47179	−	0.849738i
$268$		0			0
$269$	9.29455	+	16.0986i	0.566699	+	0.981551i	0.996889	+	0.0788127i	$0.0251129\pi$
$269$	9.29455	+	16.0986i	0.566699	+	0.981551i	−0.430191	+	0.902738i	$0.641554\pi$
$270$		0			0
$271$	2.91238	−	5.04439i	0.176914	−	0.306425i	−0.763908	−	0.645326i	$-0.776722\pi$
$271$	2.91238	−	5.04439i	0.176914	−	0.306425i	0.940822	+	0.338901i	$0.110055\pi$
$272$		0			0
$273$	10.9810	+	30.6386i	0.664603	+	1.85433i
$274$		0			0
$275$	1.86875	+	16.1211i	0.112690	+	0.972139i
$276$		0			0
$277$	−11.7263	+	6.77017i	−0.704564	+	0.406780i	−0.809045	−	0.587747i	$-0.800015\pi$
$277$	−11.7263	+	6.77017i	−0.704564	+	0.406780i	0.104481	+	0.994527i	$0.466682\pi$
$278$		0			0
$279$	−8.02690	−	13.9030i	−0.480558	−	0.832351i
$280$		0			0
$281$	−0.464716			−0.0277226			−0.0138613	−	0.999904i	$-0.504412\pi$
$281$	−0.464716			−0.0277226			−0.0138613	+	0.999904i	$0.504412\pi$
$282$		0			0
$283$	8.71259	+	5.03022i	0.517910	+	0.299015i	0.736079	−	0.676896i	$-0.236675\pi$
$283$	8.71259	+	5.03022i	0.517910	+	0.299015i	−0.218169	+	0.975911i	$0.570009\pi$
$284$		0			0
$285$	−2.35526	−	7.11911i	−0.139514	−	0.421700i
$286$		0			0
$287$		−	9.32634i		−	0.550516i
$288$		0			0
$289$	−6.60107	+	11.4334i	−0.388298	+	0.672553i
$290$		0			0
$291$	−14.1752			−0.830967
$292$		0			0
$293$	11.6481	−	6.72506i	0.680492	−	0.392882i	−0.119548	−	0.992828i	$-0.538145\pi$
$293$	11.6481	−	6.72506i	0.680492	−	0.392882i	0.800040	+	0.599946i	$0.204811\pi$
$294$		0			0
$295$	−4.23314	−	3.77079i	−0.246463	−	0.219544i
$296$		0			0
$297$	−9.42647	−	5.44238i	−0.546979	−	0.315799i
$298$		0			0
$299$	−1.73236	+	9.54958i	−0.100185	+	0.552266i
$300$		0			0
$301$	14.6498	−	25.3742i	0.844401	−	1.46255i
$302$		0			0
$303$	−13.3122	+	7.68581i	−0.764767	+	0.441538i
$304$		0			0
$305$	−12.5087	−	11.1425i	−0.716246	−	0.638015i
$306$		0			0
$307$			24.6077i			1.40444i	0.711961	+	0.702219i	$0.247807\pi$
$307$			24.6077i			1.40444i	−0.711961	+	0.702219i	$0.752193\pi$
$308$		0			0
$309$	9.91745	−	17.1775i	0.564184	−	0.977196i
$310$		0			0
$311$	−2.43781			−0.138236			−0.0691178	−	0.997609i	$-0.522018\pi$
$311$	−2.43781			−0.138236			−0.0691178	+	0.997609i	$0.522018\pi$
$312$		0			0
$313$		−	19.2965i		−	1.09071i	−0.838207	−	0.545353i	$-0.816396\pi$
$313$		−	19.2965i		−	1.09071i	0.838207	−	0.545353i	$-0.183604\pi$
$314$		0			0
$315$	31.1768	+	6.45295i	1.75662	+	0.363583i
$316$		0			0
$317$			28.8217i			1.61879i	0.587265	+	0.809395i	$0.300205\pi$
$317$			28.8217i			1.61879i	−0.587265	+	0.809395i	$0.699795\pi$
$318$		0			0
$319$	4.86872	+	8.43286i	0.272596	+	0.472150i
$320$		0			0
$321$	11.5404	+	19.9885i	0.644120	+	1.11565i
$322$		0			0
$323$	−2.10258	−	1.21392i	−0.116990	−	0.0675445i
$324$		0			0
$325$	−15.0035	−	9.99470i	−0.832246	−	0.554406i
$326$		0			0
$327$	19.7954	+	11.4289i	1.09469	+	0.632019i
$328$		0			0
$329$	−11.5185	−	19.9507i	−0.635037	−	1.09992i
$330$		0			0
$331$	−1.48655	−	2.57478i	−0.0817081	−	0.141522i	0.822276	−	0.569089i	$-0.192704\pi$
$331$	−1.48655	−	2.57478i	−0.0817081	−	0.141522i	−0.903984	+	0.427567i	$0.859371\pi$
$332$		0			0
$333$		−	8.27427i		−	0.453427i
$334$		0			0
$335$	8.79180	+	1.81972i	0.480347	+	0.0994218i
$336$		0			0
$337$		−	1.90370i		−	0.103701i	−0.998655	−	0.0518505i	$-0.983488\pi$
$337$		−	1.90370i		−	0.103701i	0.998655	−	0.0518505i	$-0.0165119\pi$
$338$		0			0
$339$	19.7374			1.07199
$340$		0			0
$341$	6.13636	−	10.6285i	0.332302	−	0.575565i
$342$		0			0
$343$		−	9.23611i		−	0.498703i
$344$		0			0
$345$	12.0983	+	10.7769i	0.651349	+	0.580206i
$346$		0			0
$347$	−10.9420	+	6.31735i	−0.587396	+	0.339133i	−0.764067	−	0.645137i	$-0.776800\pi$
$347$	−10.9420	+	6.31735i	−0.587396	+	0.339133i	0.176671	+	0.984270i	$0.443467\pi$
$348$		0			0
$349$	4.48655	−	7.77093i	0.240159	−	0.415968i	−0.720600	−	0.693351i	$-0.756134\pi$
$349$	4.48655	−	7.77093i	0.240159	−	0.415968i	0.960760	+	0.277383i	$0.0894670\pi$
$350$		0			0
$351$	11.3822	−	4.07944i	0.607535	−	0.217744i
$352$		0			0
$353$	29.6618	+	17.1252i	1.57874	+	0.911484i	0.995036	+	0.0995150i	$0.0317291\pi$
$353$	29.6618	+	17.1252i	1.57874	+	0.911484i	0.583701	+	0.811969i	$0.301604\pi$
$354$		0			0
$355$	−8.75889	−	7.80221i	−0.464874	−	0.414098i
$356$		0			0
$357$	15.2349	−	8.79585i	0.806315	−	0.465526i
$358$		0			0
$359$	22.4043			1.18245			0.591227	−	0.806505i	$-0.298644\pi$
$359$	22.4043			1.18245			0.591227	+	0.806505i	$0.298644\pi$
$360$		0			0
$361$	8.72398	−	15.1104i	0.459157	−	0.795283i
$362$		0			0
$363$			1.25092i			0.0656565i
$364$		0			0
$365$	−3.83821	−	11.6015i	−0.200901	−	0.607252i
$366$		0			0
$367$	11.4273	+	6.59753i	0.596498	+	0.344388i	0.767663	−	0.640854i	$-0.221420\pi$
$367$	11.4273	+	6.59753i	0.596498	+	0.344388i	−0.171165	+	0.985242i	$0.554753\pi$
$368$		0			0
$369$	−11.8080			−0.614700
$370$		0			0
$371$	−21.5185	−	37.2712i	−1.11719	−	1.93502i
$372$		0			0
$373$	−13.2168	+	7.63070i	−0.684338	+	0.395103i	−0.801488	−	0.598012i	$-0.795958\pi$
$373$	−13.2168	+	7.63070i	−0.684338	+	0.395103i	0.117149	+	0.993114i	$0.462624\pi$
$374$		0			0
$375$	−27.2937	+	12.6799i	−1.40944	+	0.654788i
$376$		0			0
$377$	−10.6430	−	1.93070i	−0.548140	−	0.0994362i
$378$		0			0
$379$	−9.11453	+	15.7868i	−0.468182	+	0.810915i	−0.999339	−	0.0363588i	$-0.988424\pi$
$379$	−9.11453	+	15.7868i	−0.468182	+	0.810915i	0.531157	+	0.847273i	$0.321757\pi$
$380$		0			0
$381$	−12.3334	−	21.3621i	−0.631861	−	1.09442i
$382$		0			0
$383$	−1.24784	+	0.720440i	−0.0637616	+	0.0368128i	−0.531542	−	0.847032i	$-0.678387\pi$
$383$	−1.24784	+	0.720440i	−0.0637616	+	0.0368128i	0.467780	+	0.883845i	$0.345054\pi$
$384$		0			0
$385$	7.64474	+	23.1073i	0.389612	+	1.17766i
$386$		0			0
$387$	−32.1261	−	18.5480i	−1.63306	−	0.942848i
$388$		0			0
$389$	18.7912			0.952754			0.476377	−	0.879241i	$-0.341950\pi$
$389$	18.7912			0.952754			0.476377	+	0.879241i	$0.341950\pi$
$390$		0			0
$391$	5.24581			0.265292
$392$		0			0
$393$	−23.3117	−	13.4590i	−1.17592	−	0.678918i
$394$		0			0
$395$	−29.2560	+	9.67894i	−1.47203	+	0.487000i
$396$		0			0
$397$	14.8027	−	8.54634i	0.742926	−	0.428928i	−0.0802063	−	0.996778i	$-0.525558\pi$
$397$	14.8027	−	8.54634i	0.742926	−	0.428928i	0.823132	+	0.567850i	$0.192225\pi$
$398$		0			0
$399$	−5.62291	−	9.73916i	−0.281497	−	0.487568i
$400$		0			0
$401$	−11.1011	+	19.2276i	−0.554361	+	0.960182i	0.443592	+	0.896229i	$0.353704\pi$
$401$	−11.1011	+	19.2276i	−0.554361	+	0.960182i	−0.997953	+	0.0639527i	$0.979629\pi$
$402$		0			0
$403$	4.59962	+	12.8336i	0.229124	+	0.639285i
$404$		0			0
$405$	−1.68166	+	8.12478i	−0.0835623	+	0.403724i
$406$		0			0
$407$	5.47801	−	3.16273i	0.271535	−	0.156771i
$408$		0			0
$409$	−4.81638	−	8.34221i	−0.238155	−	0.412496i	0.722030	−	0.691862i	$-0.243209\pi$
$409$	−4.81638	−	8.34221i	−0.238155	−	0.412496i	−0.960185	+	0.279366i	$0.909876\pi$
$410$		0			0
$411$	45.3534			2.23712
$412$		0			0
$413$	−7.36296	−	4.25101i	−0.362308	−	0.209178i
$414$		0			0
$415$	−6.05381	−	18.2985i	−0.297170	−	0.898238i
$416$		0			0
$417$			2.76423i			0.135365i
$418$		0			0
$419$	0.978168	−	1.69424i	0.0477866	−	0.0827689i	−0.841143	−	0.540813i	$-0.818117\pi$
$419$	0.978168	−	1.69424i	0.0477866	−	0.0827689i	0.888929	+	0.458044i	$0.151450\pi$
$420$		0			0
$421$	−12.0807			−0.588778			−0.294389	−	0.955686i	$-0.595116\pi$
$421$	−12.0807			−0.588778			−0.294389	+	0.955686i	$0.595116\pi$
$422$		0			0
$423$	−25.2594	+	14.5835i	−1.22815	+	0.709075i
$424$		0			0
$425$	−3.86792	+	8.94346i	−0.187622	+	0.433822i
$426$		0			0
$427$	−21.7571	−	12.5615i	−1.05290	−	0.607893i
$428$		0			0
$429$	24.0320	+	20.3676i	1.16027	+	0.983359i
$430$		0			0
$431$	12.2945	−	21.2948i	0.592207	−	1.02573i	−0.401727	−	0.915759i	$-0.631590\pi$
$431$	12.2945	−	21.2948i	0.592207	−	1.02573i	0.993934	−	0.109974i	$-0.0350767\pi$
$432$		0			0
$433$	−31.2400	+	18.0364i	−1.50130	+	0.866775i	−0.501299	+	0.865274i	$0.667144\pi$
$433$	−31.2400	+	18.0364i	−1.50130	+	0.866775i	−0.999999	+	0.00150085i	$0.999522\pi$
$434$		0			0
$435$	−12.0107	+	13.4835i	−0.575871	+	0.646482i
$436$		0			0
$437$		−	3.35348i		−	0.160419i
$438$		0			0
$439$	−1.26764	+	2.19562i	−0.0605013	+	0.104791i	−0.894690	−	0.446688i	$-0.852603\pi$
$439$	−1.26764	+	2.19562i	−0.0605013	+	0.104791i	0.834188	+	0.551480i	$0.185937\pi$
$440$		0			0
$441$	18.0269			0.858424
$442$		0			0
$443$			19.3579i			0.919721i	0.887991	+	0.459860i	$0.152101\pi$
$443$			19.3579i			0.919721i	−0.887991	+	0.459860i	$0.847899\pi$
$444$		0			0
$445$	−4.67552	+	22.5893i	−0.221641	+	1.07084i
$446$		0			0
$447$			42.6696i			2.01820i
$448$		0			0
$449$	−12.4040	−	21.4844i	−0.585381	−	1.01391i	−0.994828	−	0.101576i	$-0.967612\pi$
$449$	−12.4040	−	21.4844i	−0.585381	−	1.01391i	0.409447	−	0.912334i	$-0.365722\pi$
$450$		0			0
$451$	−4.51345	−	7.81753i	−0.212530	−	0.368113i
$452$		0			0
$453$	−33.9079	−	19.5767i	−1.59313	−	0.919795i
$454$		0			0
$455$	−25.0722	−	10.1176i	−1.17540	−	0.474318i
$456$		0			0
$457$	6.55363	+	3.78374i	0.306566	+	0.176996i	0.645389	−	0.763854i	$-0.276695\pi$
$457$	6.55363	+	3.78374i	0.306566	+	0.176996i	−0.338823	+	0.940850i	$0.610029\pi$
$458$		0			0
$459$	−3.26764	−	5.65972i	−0.152520	−	0.264173i
$460$		0			0
$461$	6.17164	+	10.6896i	0.287442	+	0.497864i	0.973198	−	0.229967i	$-0.0738618\pi$
$461$	6.17164	+	10.6896i	0.287442	+	0.497864i	−0.685756	+	0.727831i	$0.740528\pi$
$462$		0			0
$463$		−	22.8578i		−	1.06229i	−0.847281	−	0.531146i	$-0.821762\pi$
$463$		−	22.8578i		−	1.06229i	0.847281	−	0.531146i	$-0.178238\pi$
$464$		0			0
$465$	22.2863	+	4.61279i	1.03350	+	0.213913i
$466$		0			0
$467$		−	15.2976i		−	0.707889i	−0.935266	−	0.353945i	$-0.884840\pi$
$467$		−	15.2976i		−	0.707889i	0.935266	−	0.353945i	$-0.115160\pi$
$468$		0			0
$469$	13.4647			0.621743
$470$		0			0
$471$	−14.6985	+	25.4586i	−0.677273	+	1.17307i
$472$		0			0
$473$		−	28.3589i		−	1.30394i
$474$		0			0
$475$	5.71727	+	2.47264i	0.262326	+	0.113452i
$476$		0			0
$477$	−47.1887	+	27.2444i	−2.16062	+	1.24744i
$478$		0			0
$479$	−12.1414	+	21.0296i	−0.554756	+	0.960866i	0.443166	+	0.896439i	$0.353855\pi$
$479$	−12.1414	+	21.0296i	−0.554756	+	0.960866i	−0.997922	+	0.0644264i	$0.979478\pi$
$480$		0			0
$481$	−1.25419	+	6.91369i	−0.0571861	+	0.315237i
$482$		0			0
$483$	21.0433	+	12.1493i	0.957501	+	0.552814i
$484$		0			0
$485$	7.83235	−	8.79272i	0.355649	−	0.399257i
$486$		0			0
$487$	31.9462	−	18.4441i	1.44762	−	0.835783i	0.449280	−	0.893391i	$-0.351681\pi$
$487$	31.9462	−	18.4441i	1.44762	−	0.835783i	0.998339	+	0.0576081i	$0.0183474\pi$
$488$		0			0
$489$	−11.2458			−0.508553
$490$		0			0
$491$	−17.6767	+	30.6170i	−0.797739	+	1.38172i	0.123346	+	0.992364i	$0.460637\pi$
$491$	−17.6767	+	30.6170i	−0.797739	+	1.38172i	−0.921085	+	0.389361i	$0.872696\pi$
$492$		0			0
$493$			5.84642i			0.263310i
$494$		0			0
$495$	29.2560	−	9.67894i	1.31496	−	0.435036i
$496$		0			0
$497$	−15.2349	−	8.79585i	−0.683377	−	0.394548i
$498$		0			0
$499$	16.2189			0.726058			0.363029	−	0.931778i	$-0.381743\pi$
$499$	16.2189			0.726058			0.363029	+	0.931778i	$0.381743\pi$
$500$		0			0
$501$	−4.51345	−	7.81753i	−0.201646	−	0.349261i
$502$		0			0
$503$	−17.5270	+	10.1192i	−0.781489	+	0.451193i	−0.836958	−	0.547268i	$-0.815668\pi$
$503$	−17.5270	+	10.1192i	−0.781489	+	0.451193i	0.0554688	+	0.998460i	$0.482335\pi$
$504$		0			0
$505$	2.58808	−	12.5041i	0.115168	−	0.556425i
$506$		0			0
$507$	−34.5200	+	5.73700i	−1.53309	+	0.254789i
$508$		0			0
$509$	−10.0185	+	17.3526i	−0.444063	+	0.769140i	−0.997986	−	0.0634276i	$-0.979797\pi$
$509$	−10.0185	+	17.3526i	−0.444063	+	0.769140i	0.553923	+	0.832568i	$0.313130\pi$
$510$		0			0
$511$	−9.16326	−	15.8712i	−0.405359	−	0.702102i
$512$		0			0
$513$	−3.61808	+	2.08890i	−0.159742	+	0.0922271i
$514$		0			0
$515$	5.17524	+	15.6429i	0.228048	+	0.689308i
$516$		0			0
$517$	−19.3101	−	11.1487i	−0.849259	−	0.490320i
$518$		0			0
$519$	−23.5185			−1.03235
$520$		0			0
$521$	16.0269			0.702151			0.351076	−	0.936347i	$-0.385816\pi$
$521$	16.0269			0.702151			0.351076	+	0.936347i	$0.385816\pi$
$522$		0			0
$523$	−10.1654	−	5.86898i	−0.444501	−	0.256633i	0.261004	−	0.965338i	$-0.415946\pi$
$523$	−10.1654	−	5.86898i	−0.444501	−	0.256633i	−0.705505	+	0.708705i	$0.749280\pi$
$524$		0			0
$525$	−36.2291	+	26.9180i	−1.58117	+	1.17480i
$526$		0			0
$527$	6.38142	−	3.68431i	0.277979	−	0.160491i
$528$		0			0
$529$	−7.87709	−	13.6435i	−0.342482	−	0.593197i
$530$		0			0
$531$	−5.38217	+	9.32219i	−0.233566	+	0.404548i
$532$		0			0
$533$	9.86635	+	1.78982i	0.427359	+	0.0775258i
$534$		0			0
$535$	−18.7751	−	3.88605i	−0.811718	−	0.168008i
$536$		0			0
$537$	41.9847	−	24.2399i	1.81177	−	1.04603i
$538$		0			0
$539$	6.89055	+	11.9348i	0.296797	+	0.514067i
$540$		0			0
$541$	−21.8080			−0.937599			−0.468800	−	0.883305i	$-0.655313\pi$
$541$	−21.8080			−0.937599			−0.468800	+	0.883305i	$0.655313\pi$
$542$		0			0
$543$	2.43296	+	1.40467i	0.104408	+	0.0602801i
$544$		0			0
$545$	−18.0269	+	5.96396i	−0.772188	+	0.255468i
$546$		0			0
$547$		−	6.30924i		−	0.269764i	−0.990862	−	0.134882i	$-0.956935\pi$
$547$		−	6.30924i		−	0.269764i	0.990862	−	0.134882i	$-0.0430655\pi$
$548$		0			0
$549$	−15.9040	+	27.5465i	−0.678766	+	1.17566i
$550$		0			0
$551$	3.73743			0.159220
$552$		0			0
$553$	−40.0230	+	23.1073i	−1.70195	+	0.982622i
$554$		0			0
$555$	8.75889	+	7.80221i	0.371794	+	0.331185i
$556$		0			0
$557$	31.0364	+	17.9189i	1.31506	+	0.759247i	0.982929	−	0.183987i	$-0.0589006\pi$
$557$	31.0364	+	17.9189i	1.31506	+	0.759247i	0.332126	+	0.943235i	$0.392234\pi$
$558$		0			0
$559$	24.0320	+	20.3676i	1.01644	+	0.861459i
$560$		0			0
$561$	8.51345	−	14.7457i	0.359438	−	0.622565i
$562$		0			0
$563$	−4.33196	+	2.50106i	−0.182570	+	0.105407i	−0.588500	−	0.808497i	$-0.700281\pi$
$563$	−4.33196	+	2.50106i	−0.182570	+	0.105407i	0.405929	+	0.913904i	$0.366948\pi$
$564$		0			0
$565$	−10.9057	+	12.2429i	−0.458805	+	0.515062i
$566$		0			0
$567$			12.4432i			0.522564i
$568$		0			0
$569$	−6.58402	+	11.4039i	−0.276017	+	0.478075i	−0.970391	−	0.241539i	$-0.922348\pi$
$569$	−6.58402	+	11.4039i	−0.276017	+	0.478075i	0.694375	+	0.719614i	$0.255681\pi$
$570$		0			0
$571$	−19.8349			−0.830065			−0.415032	−	0.909807i	$-0.636230\pi$
$571$	−19.8349			−0.830065			−0.415032	+	0.909807i	$0.636230\pi$
$572$		0			0
$573$			68.6909i			2.86960i
$574$		0			0
$575$	−13.3695	+	1.54979i	−0.557547	+	0.0646307i
$576$		0			0
$577$		−	10.9210i		−	0.454646i	−0.973819	−	0.227323i	$-0.927003\pi$
$577$		−	10.9210i		−	0.454646i	0.973819	−	0.227323i	$-0.0729972\pi$
$578$		0			0
$579$	−26.6767	−	46.2054i	−1.10865	−	1.92023i
$580$		0			0
$581$	−14.4527	−	25.0329i	−0.599601	−	1.03854i
$582$		0			0
$583$	−36.0745	−	20.8276i	−1.49406	−	0.862593i
$584$		0			0
$585$	−12.8098	+	31.7436i	−0.529618	+	1.31244i
$586$		0			0
$587$	−35.0303	−	20.2247i	−1.44585	−	0.834764i	−0.447624	−	0.894222i	$-0.647730\pi$
$587$	−35.0303	−	20.2247i	−1.44585	−	0.834764i	−0.998231	+	0.0594576i	$0.981063\pi$
$588$		0			0
$589$	−2.35526	−	4.07944i	−0.0970469	−	0.168090i
$590$		0			0
$591$	−29.1414	−	50.4744i	−1.19872	−	2.07624i
$592$		0			0
$593$			1.47709i			0.0606569i	0.999540	+	0.0303284i	$0.00965532\pi$
$593$			1.47709i			0.0606569i	−0.999540	+	0.0303284i	$0.990345\pi$
$594$		0			0
$595$	−2.96188	+	14.3100i	−0.121425	+	0.586654i
$596$		0			0
$597$		−	49.0690i		−	2.00826i
$598$		0			0
$599$	2.27271			0.0928606			0.0464303	−	0.998922i	$-0.485215\pi$
$599$	2.27271			0.0928606			0.0464303	+	0.998922i	$0.485215\pi$
$600$		0			0
$601$	−3.70215	+	6.41231i	−0.151014	+	0.261563i	−0.931600	−	0.363484i	$-0.881587\pi$
$601$	−3.70215	+	6.41231i	−0.151014	+	0.261563i	0.780587	+	0.625048i	$0.214920\pi$
$602$		0			0
$603$		−	17.0476i		−	0.694231i
$604$		0			0
$605$	−0.775932	−	0.691182i	−0.0315461	−	0.0281006i
$606$		0			0
$607$	−9.26059	+	5.34661i	−0.375876	+	0.217012i	−0.676022	−	0.736881i	$-0.736298\pi$
$607$	−9.26059	+	5.34661i	−0.375876	+	0.217012i	0.300146	+	0.953893i	$0.402964\pi$
$608$		0			0
$609$	−13.5404	+	23.4526i	−0.548683	+	0.950347i
$610$		0			0
$611$	23.3164	−	8.35673i	0.943280	−	0.338077i
$612$		0			0
$613$	−5.26673	−	3.04075i	−0.212721	−	0.122815i	0.389854	−	0.920877i	$-0.372525\pi$
$613$	−5.26673	−	3.04075i	−0.212721	−	0.122815i	−0.602575	+	0.798062i	$0.705859\pi$
$614$		0			0
$615$	11.1343	−	12.4996i	0.448980	−	0.504032i
$616$		0			0
$617$	−27.5732	+	15.9194i	−1.11006	+	0.640892i	−0.938844	−	0.344342i	$-0.888102\pi$
$617$	−27.5732	+	15.9194i	−1.11006	+	0.640892i	−0.171213	+	0.985234i	$0.554769\pi$
$618$		0			0
$619$	−26.4043			−1.06128			−0.530639	−	0.847598i	$-0.678048\pi$
$619$	−26.4043			−1.06128			−0.530639	+	0.847598i	$0.678048\pi$
$620$		0			0
$621$	4.51345	−	7.81753i	0.181119	−	0.313707i
$622$		0			0
$623$			34.5957i			1.38605i
$624$		0			0
$625$	7.21560	−	23.9361i	0.288624	−	0.957443i
$626$		0			0
$627$	−9.42647	−	5.44238i	−0.376457	−	0.217348i
$628$		0			0
$629$	3.79785			0.151430
$630$		0			0
$631$	17.5840	+	30.4564i	0.700009	+	1.21245i	0.968463	+	0.249158i	$0.0801539\pi$
$631$	17.5840	+	30.4564i	0.700009	+	1.21245i	−0.268454	+	0.963293i	$0.586513\pi$
$632$		0			0
$633$	44.9907	−	25.9754i	1.78822	−	1.03243i
$634$		0			0
$635$	20.0653	+	4.15310i	0.796269	+	0.164811i
$636$		0			0
$637$	−15.0626	−	2.73247i	−0.596804	−	0.108264i
$638$		0			0
$639$	−11.1364	+	19.2887i	−0.440547	+	0.763051i
$640$		0			0
$641$	−2.76257	−	4.78491i	−0.109115	−	0.188993i	0.806297	−	0.591511i	$-0.201468\pi$
$641$	−2.76257	−	4.78491i	−0.109115	−	0.188993i	−0.915412	+	0.402518i	$0.868135\pi$
$642$		0			0
$643$	27.8472	−	16.0776i	1.09819	−	0.634039i	0.162444	−	0.986718i	$-0.448062\pi$
$643$	27.8472	−	16.0776i	1.09819	−	0.634039i	0.935744	+	0.352679i	$0.114729\pi$
$644$		0			0
$645$	49.9276	−	16.5179i	1.96590	−	0.650391i
$646$		0			0
$647$	11.9376	+	6.89216i	0.469314	+	0.270959i	0.715953	−	0.698149i	$-0.245993\pi$
$647$	11.9376	+	6.89216i	0.469314	+	0.270959i	−0.246638	+	0.969108i	$0.579326\pi$
$648$		0			0
$649$	−8.22905			−0.323019
$650$		0			0
$651$	34.1316			1.33772
$652$		0			0
$653$	−7.36296	−	4.25101i	−0.288135	−	0.166355i	0.348965	−	0.937136i	$-0.386533\pi$
$653$	−7.36296	−	4.25101i	−0.288135	−	0.166355i	−0.637100	+	0.770781i	$0.719866\pi$
$654$		0			0
$655$	21.2291	−	7.02335i	0.829488	−	0.274425i
$656$		0			0
$657$	−20.0944	+	11.6015i	−0.783959	+	0.452619i
$658$		0			0
$659$	−2.02183	−	3.50192i	−0.0787594	−	0.136415i	0.823956	−	0.566654i	$-0.191763\pi$
$659$	−2.02183	−	3.50192i	−0.0787594	−	0.136415i	−0.902715	+	0.430239i	$0.858429\pi$
$660$		0			0
$661$	−15.6364	+	27.0830i	−0.608184	+	1.05341i	0.383356	+	0.923601i	$0.374768\pi$
$661$	−15.6364	+	27.0830i	−0.608184	+	1.05341i	−0.991540	+	0.129805i	$0.958565\pi$
$662$		0			0
$663$	6.38142	+	17.8050i	0.247834	+	0.691489i
$664$		0			0
$665$	9.14794	+	1.89343i	0.354742	+	0.0734241i
$666$		0			0
$667$	−6.99351	+	4.03771i	−0.270790	+	0.156341i
$668$		0			0
$669$	−16.6498	−	28.8383i	−0.643719	−	1.11495i
$670$		0			0
$671$	−24.3164			−0.938723
$672$		0			0
$673$	27.7768	+	16.0370i	1.07072	+	0.618179i	0.928377	−	0.371639i	$-0.121204\pi$
$673$	27.7768	+	16.0370i	1.07072	+	0.618179i	0.142340	+	0.989818i	$0.454537\pi$
$674$		0			0
$675$	10.0000	+	13.4590i	0.384900	+	0.518038i
$676$		0			0
$677$		−	14.2382i		−	0.547220i	−0.961841	−	0.273610i	$-0.911782\pi$
$677$		−	14.2382i		−	0.547220i	0.961841	−	0.273610i	$-0.0882177\pi$
$678$		0			0
$679$	8.82983	−	15.2937i	0.338858	−	0.586919i
$680$		0			0
$681$	16.5891			0.635695
$682$		0			0
$683$	22.3302	−	12.8923i	0.854440	−	0.493311i	−0.00770647	−	0.999970i	$-0.502453\pi$
$683$	22.3302	−	12.8923i	0.854440	−	0.493311i	0.862146	+	0.506659i	$0.169120\pi$
$684$		0			0
$685$	−25.0595	+	28.1322i	−0.957473	+	1.07487i
$686$		0			0
$687$	62.9025	+	36.3168i	2.39988	+	1.38557i
$688$		0			0
$689$	43.5589	−	15.6118i	1.65946	−	0.594761i
$690$		0			0
$691$	−0.0218318	+	0.0378138i	−0.000830522	+	0.00143851i	−0.866440	−	0.499281i	$-0.833598\pi$
$691$	−0.0218318	+	0.0378138i	−0.000830522	+	0.00143851i	0.865610	+	0.500719i	$0.166931\pi$
$692$		0			0
$693$	40.0230	−	23.1073i	1.52035	−	0.877774i
$694$		0			0
$695$	−1.71461	−	1.52734i	−0.0650390	−	0.0579352i
$696$		0			0
$697$		−	5.41982i		−	0.205290i
$698$		0			0
$699$	1.10945	−	1.92163i	0.0419634	−	0.0726827i
$700$		0			0
$701$	−14.5454			−0.549373			−0.274687	−	0.961534i	$-0.588574\pi$
$701$	−14.5454			−0.549373			−0.274687	+	0.961534i	$0.588574\pi$
$702$		0			0
$703$		−	2.42785i		−	0.0915679i
$704$		0			0
$705$	8.38064	−	40.4903i	0.315633	−	1.52495i
$706$		0			0
$707$		−	19.1501i		−	0.720214i
$708$		0			0
$709$	9.81638	+	17.0025i	0.368662	+	0.638541i	0.989357	−	0.145511i	$-0.0464827\pi$
$709$	9.81638	+	17.0025i	0.368662	+	0.638541i	−0.620695	+	0.784052i	$0.713149\pi$
$710$		0			0
$711$	29.2560	+	50.6728i	1.09718	+	1.90038i
$712$		0			0
$713$	8.81438	+	5.08898i	0.330101	+	0.190584i
$714$		0			0
$715$	−25.9124	+	3.65285i	−0.969067	+	0.136609i
$716$		0			0
$717$	9.32468	+	5.38361i	0.348237	+	0.201055i
$718$		0			0
$719$	−23.7156	−	41.0766i	−0.884443	−	1.53190i	−0.846351	−	0.532625i	$-0.821206\pi$
$719$	−23.7156	−	41.0766i	−0.884443	−	1.53190i	−0.0380914	−	0.999274i	$-0.512128\pi$
$720$		0			0
$721$	12.3553	+	21.3999i	0.460134	+	0.796976i
$722$		0			0
$723$		−	61.0872i		−	2.27186i
$724$		0			0
$725$	−1.72723	−	14.9002i	−0.0641477	−	0.553380i
$726$		0			0
$727$			34.0951i			1.26452i	0.774757	+	0.632259i	$0.217872\pi$
$727$			34.0951i			1.26452i	−0.774757	+	0.632259i	$0.782128\pi$
$728$		0			0
$729$	42.8349			1.58648
$730$		0			0
$731$	8.51345	−	14.7457i	0.314881	−	0.545391i
$732$		0			0
$733$		−	14.3920i		−	0.531580i	−0.964031	−	0.265790i	$-0.914367\pi$
$733$		−	14.3920i		−	0.531580i	0.964031	−	0.265790i	$-0.0856327\pi$
$734$		0			0
$735$	−16.9984	+	19.0827i	−0.626997	+	0.703877i
$736$		0			0
$737$	11.2864	−	6.51621i	0.415740	−	0.240028i
$738$		0			0
$739$	17.2240	−	29.8328i	0.633594	−	1.09742i	−0.353217	−	0.935541i	$-0.614912\pi$
$739$	17.2240	−	29.8328i	0.633594	−	1.09742i	0.986811	−	0.161876i	$-0.0517545\pi$
$740$		0			0
$741$	11.3822	−	4.07944i	0.418134	−	0.149862i
$742$		0			0
$743$	35.2589	+	20.3567i	1.29352	+	0.746816i	0.979277	−	0.202526i	$-0.0649150\pi$
$743$	35.2589	+	20.3567i	1.29352	+	0.746816i	0.314246	+	0.949342i	$0.398248\pi$
$744$		0			0
$745$	−26.4674	−	23.5765i	−0.969690	−	0.863777i
$746$		0			0
$747$	−31.6939	+	18.2985i	−1.15962	+	0.669507i
$748$		0			0
$749$	−28.7542			−1.05066
$750$		0			0
$751$	16.2509	−	28.1474i	0.593003	−	1.02711i	−0.400822	−	0.916156i	$-0.631275\pi$
$751$	16.2509	−	28.1474i	0.593003	−	1.02711i	0.993825	−	0.110956i	$-0.0353912\pi$
$752$		0			0
$753$			51.2167i			1.86644i
$754$		0			0
$755$	30.8786	−	10.2158i	1.12379	−	0.371790i
$756$		0			0
$757$	−11.2864	−	6.51621i	−0.410211	−	0.236836i	0.280669	−	0.959805i	$-0.409444\pi$
$757$	−11.2864	−	6.51621i	−0.410211	−	0.236836i	−0.690881	+	0.722969i	$0.742777\pi$
$758$		0			0
$759$	23.5185			0.853668
$760$		0			0
$761$	1.99493	+	3.45532i	0.0723161	+	0.125255i	0.899916	−	0.436063i	$-0.143628\pi$
$761$	1.99493	+	3.45532i	0.0723161	+	0.125255i	−0.827600	+	0.561318i	$0.810294\pi$
$762$		0			0
$763$	−24.6613	+	14.2382i	−0.892800	+	0.515458i
$764$		0			0
$765$	18.1178	+	3.75001i	0.655051	+	0.135582i
$766$		0			0
$767$	5.91018	−	6.97348i	0.213404	−	0.251798i
$768$		0			0
$769$	3.33343	−	5.77367i	0.120207	−	0.208204i	−0.799642	−	0.600476i	$-0.794978\pi$
$769$	3.33343	−	5.77367i	0.120207	−	0.208204i	0.919849	+	0.392272i	$0.128311\pi$
$770$		0			0
$771$	2.84181	+	4.92216i	0.102345	+	0.177267i
$772$		0			0
$773$	41.8593	−	24.1675i	1.50557	−	0.869244i	0.505595	−	0.862771i	$-0.331273\pi$
$773$	41.8593	−	24.1675i	1.50557	−	0.869244i	0.999979	−	0.00647254i	$-0.00206029\pi$
$774$		0			0
$775$	−15.1752	+	11.2751i	−0.545111	+	0.405015i
$776$		0			0
$777$	15.2349	+	8.79585i	0.546548	+	0.315549i
$778$		0			0
$779$	−3.46472			−0.124136
$780$		0			0
$781$	−17.0269			−0.609271
$782$		0			0
$783$	8.71259	+	5.03022i	0.311363	+	0.179765i
$784$		0			0
$785$	−7.67017	−	23.1842i	−0.273760	−	0.827478i
$786$		0			0
$787$	−24.2151	+	13.9806i	−0.863176	+	0.498355i	−0.865074	−	0.501643i	$-0.832729\pi$
$787$	−24.2151	+	13.9806i	−0.863176	+	0.498355i	0.00189876	+	0.999998i	$0.499396\pi$
$788$		0			0
$789$	−40.2658	−	69.7424i	−1.43350	−	2.48290i
$790$		0			0
$791$	−12.2945	+	21.2948i	−0.437144	+	0.757155i
$792$		0			0
$793$	17.4642	−	20.6062i	0.620174	−	0.731749i
$794$		0			0
$795$	15.6564	−	75.6426i	0.555277	−	2.68277i
$796$		0			0
$797$	−32.2529	+	18.6212i	−1.14246	+	0.659597i	−0.947038	−	0.321123i	$-0.895940\pi$
$797$	−32.2529	+	18.6212i	−1.14246	+	0.659597i	−0.195418	+	0.980720i	$0.562607\pi$
$798$		0			0
$799$	−6.69377	−	11.5939i	−0.236808	−	0.410164i
$800$		0			0
$801$	43.8014			1.54765
$802$		0			0
$803$	−15.3617	−	8.86907i	−0.542102	−	0.312983i
$804$		0			0
$805$	−19.1633	+	6.33991i	−0.675416	+	0.223452i
$806$		0			0
$807$			50.0382i			1.76143i
$808$		0			0
$809$	7.26434	−	12.5822i	0.255400	−	0.442367i	−0.709604	−	0.704601i	$-0.751126\pi$
$809$	7.26434	−	12.5822i	0.255400	−	0.442367i	0.965004	+	0.262234i	$0.0844594\pi$
$810$		0			0
$811$	−44.0538			−1.54694			−0.773469	−	0.633834i	$-0.781480\pi$
$811$	−44.0538			−1.54694			−0.773469	+	0.633834i	$0.781480\pi$
$812$		0			0
$813$	13.5785	−	7.83955i	0.476219	−	0.274945i
$814$		0			0
$815$	6.21373	−	6.97563i	0.217657	−	0.244346i
$816$		0			0
$817$	−9.42647	−	5.44238i	−0.329790	−	0.190405i
$818$		0			0
$819$	−9.16326	+	50.5123i	−0.320190	+	1.76504i
$820$		0			0
$821$	−13.5135	+	23.4060i	−0.471623	+	0.816875i	−0.999473	−	0.0324629i	$-0.989665\pi$
$821$	−13.5135	+	23.4060i	−0.471623	+	0.816875i	0.527850	+	0.849337i	$0.322998\pi$
$822$		0			0
$823$	34.2914	−	19.7981i	1.19532	−	0.690120i	0.235814	−	0.971798i	$-0.424225\pi$
$823$	34.2914	−	19.7981i	1.19532	−	0.690120i	0.959509	+	0.281679i	$0.0908912\pi$
$824$		0			0
$825$	−17.3410	+	40.0962i	−0.603737	+	1.39597i
$826$		0			0
$827$		−	26.5639i		−	0.923716i	−0.886954	−	0.461858i	$-0.847183\pi$
$827$		−	26.5639i		−	0.923716i	0.886954	−	0.461858i	$-0.152817\pi$
$828$		0			0
$829$	6.99162	−	12.1098i	0.242829	−	0.420592i	−0.718690	−	0.695331i	$-0.755258\pi$
$829$	6.99162	−	12.1098i	0.242829	−	0.420592i	0.961519	+	0.274738i	$0.0885913\pi$
$830$		0			0
$831$	−36.4480			−1.26437
$832$		0			0
$833$			8.27427i			0.286686i
$834$		0			0
$835$	7.34297	+	1.51984i	0.254114	+	0.0525962i
$836$		0			0
$837$		−	12.6798i		−	0.438278i
$838$		0			0
$839$	−7.19707	−	12.4657i	−0.248471	−	0.430364i	0.714631	−	0.699502i	$-0.246595\pi$
$839$	−7.19707	−	12.4657i	−0.248471	−	0.430364i	−0.963102	+	0.269138i	$0.913261\pi$
$840$		0			0
$841$	10.0000	+	17.3205i	0.344828	+	0.597259i
$842$		0			0
$843$	−1.08333	−	0.625462i	−0.0373119	−	0.0215421i
$844$		0			0
$845$	15.5150	−	24.5822i	0.533732	−	0.845654i
$846$		0			0
$847$	−1.34963	−	0.779207i	−0.0463737	−	0.0267739i
$848$		0			0
$849$	13.5404	+	23.4526i	0.464704	+	0.804891i
$850$		0			0
$851$	2.62291	+	4.54300i	0.0899120	+	0.155732i
$852$		0			0
$853$		−	27.2633i		−	0.933478i	−0.884395	−	0.466739i	$-0.845429\pi$
$853$		−	27.2633i		−	0.933478i	0.884395	−	0.466739i	$-0.154571\pi$
$854$		0			0
$855$	2.39726	−	11.5821i	0.0819845	−	0.396101i
$856$		0			0
$857$			50.6201i			1.72915i	0.502503	+	0.864575i	$0.332413\pi$
$857$			50.6201i			1.72915i	−0.502503	+	0.864575i	$0.667587\pi$
$858$		0			0
$859$	1.27992			0.0436702			0.0218351	−	0.999762i	$-0.493049\pi$
$859$	1.27992			0.0436702			0.0218351	+	0.999762i	$0.493049\pi$
$860$		0			0
$861$	12.5523	−	21.7413i	0.427782	−	0.740941i
$862$		0			0
$863$		−	8.38448i		−	0.285411i	−0.989765	−	0.142706i	$-0.954420\pi$
$863$		−	8.38448i		−	0.285411i	0.989765	−	0.142706i	$-0.0455802\pi$
$864$		0			0
$865$	12.9949	−	14.5882i	0.441839	−	0.496015i
$866$		0			0
$867$	−30.7765	+	17.7688i	−1.04522	+	0.603460i
$868$		0			0
$869$	−22.3654	+	38.7380i	−0.758695	+	1.31410i
$870$		0			0
$871$	−2.58402	+	14.2443i	−0.0875562	+	0.482651i
$872$		0			0
$873$	−19.3632	−	11.1794i	−0.655347	−	0.378365i
$874$		0			0
$875$	3.32098	−	37.3456i	0.112270	−	1.26251i
$876$		0			0
$877$	48.3989	−	27.9431i	1.63431	−	0.943572i	0.651573	−	0.758586i	$-0.274110\pi$
$877$	48.3989	−	27.9431i	1.63431	−	0.943572i	0.982741	−	0.184985i	$-0.0592237\pi$
$878$		0			0
$879$	36.2051			1.22117
$880$		0			0
$881$	−12.5975	+	21.8195i	−0.424420	+	0.735116i	−0.996366	−	0.0851746i	$-0.972855\pi$
$881$	−12.5975	+	21.8195i	−0.424420	+	0.735116i	0.571946	+	0.820291i	$0.306189\pi$
$882$		0			0
$883$			30.7868i			1.03606i	0.855363	+	0.518029i	$0.173334\pi$
$883$			30.7868i			1.03606i	−0.855363	+	0.518029i	$0.826666\pi$
$884$		0			0
$885$	−4.79307	−	14.4877i	−0.161117	−	0.487000i
$886$		0			0
$887$	10.8011	+	6.23603i	0.362666	+	0.209385i	0.670250	−	0.742136i	$-0.266187\pi$
$887$	10.8011	+	6.23603i	0.362666	+	0.209385i	−0.307584	+	0.951521i	$0.599520\pi$
$888$		0			0
$889$	30.7302			1.03066
$890$		0			0
$891$	6.02183	+	10.4301i	0.201739	+	0.349422i
$892$		0			0
$893$	−7.41163	+	4.27911i	−0.248021	+	0.143195i
$894$		0			0
$895$	−8.16243	+	39.4360i	−0.272840	+	1.31820i
$896$		0			0
$897$	−16.8912	+	19.9301i	−0.563981	+	0.665447i
$898$		0			0
$899$	−5.67164	+	9.82357i	−0.189160	+	0.327634i
$900$		0			0
$901$	−12.5051	−	21.6594i	−0.416604	−	0.721580i
$902$		0			0
$903$	68.3024	−	39.4344i	2.27296	−	1.31230i
$904$		0			0
$905$	−2.21560	+	0.733001i	−0.0736490	+	0.0243658i
$906$		0			0
$907$	33.6807	+	19.4455i	1.11835	+	0.645678i	0.940979	−	0.338466i	$-0.109908\pi$
$907$	33.6807	+	19.4455i	1.11835	+	0.645678i	0.177369	+	0.984144i	$0.443241\pi$
$908$		0			0
$909$	−24.2458			−0.804183
$910$		0			0
$911$	−0.165096			−0.00546989			−0.00273494	−	0.999996i	$-0.500871\pi$
$911$	−0.165096			−0.00546989			−0.00273494	+	0.999996i	$0.500871\pi$
$912$		0			0
$913$	−24.2292	−	13.9887i	−0.801868	−	0.462959i
$914$		0			0
$915$	−14.1633	−	42.8105i	−0.468223	−	1.41527i
$916$		0			0
$917$	29.0420	−	16.7674i	0.959050	−	0.553708i
$918$		0			0
$919$	−0.447663	−	0.775375i	−0.0147670	−	0.0255773i	0.858547	−	0.512734i	$-0.171367\pi$
$919$	−0.447663	−	0.775375i	−0.0147670	−	0.0255773i	−0.873314	+	0.487157i	$0.838034\pi$
$920$		0			0
$921$	−33.1196	+	57.3648i	−1.09133	+	1.89024i
$922$		0			0
$923$	12.2289	−	14.4290i	0.402518	−	0.474935i
$924$		0			0
$925$	−9.67923	+	1.12201i	−0.318251	+	0.0368916i
$926$		0			0
$927$	27.0943	−	15.6429i	0.889893	−	0.513780i
$928$		0			0
$929$	−6.14474	−	10.6430i	−0.201602	−	0.349185i	0.747443	−	0.664326i	$-0.231282\pi$
$929$	−6.14474	−	10.6430i	−0.201602	−	0.349185i	−0.949045	+	0.315141i	$0.897948\pi$
$930$		0			0
$931$	5.28947			0.173356
$932$		0			0
$933$	−5.68295	−	3.28106i	−0.186052	−	0.107417i
$934$		0			0
$935$	4.44259	+	13.4284i	0.145288	+	0.439154i
$936$		0			0
$937$			5.77242i			0.188577i	0.995545	+	0.0942884i	$0.0300576\pi$
$937$			5.77242i			0.188577i	−0.995545	+	0.0942884i	$0.969942\pi$
$938$		0			0
$939$	25.9713	−	44.9835i	0.847540	−	1.46798i
$940$		0			0
$941$	−55.8887			−1.82192			−0.910960	−	0.412495i	$-0.864658\pi$
$941$	−55.8887			−1.82192			−0.910960	+	0.412495i	$0.864658\pi$
$942$		0			0
$943$	6.48321	−	3.74308i	0.211122	−	0.121891i
$944$		0			0
$945$	18.7770	+	16.7261i	0.610817	+	0.544102i
$946$		0			0
$947$	1.64231	+	0.948188i	0.0533679	+	0.0308120i	0.526447	−	0.850208i	$-0.323524\pi$
$947$	1.64231	+	0.948188i	0.0533679	+	0.0308120i	−0.473079	+	0.881020i	$0.656857\pi$
$948$		0			0
$949$	18.5487	−	6.64798i	0.602117	−	0.215802i
$950$		0			0
$951$	−38.7912	+	67.1884i	−1.25789	+	2.17873i
$952$		0			0
$953$	29.1438	−	16.8262i	0.944059	−	0.545053i	0.0528285	−	0.998604i	$-0.483176\pi$
$953$	29.1438	−	16.8262i	0.944059	−	0.545053i	0.891230	+	0.453551i	$0.149843\pi$
$954$		0			0
$955$	−42.6081	−	37.9543i	−1.37877	−	1.22817i
$956$		0			0
$957$			26.2113i			0.847290i
$958$		0			0
$959$	−28.2509	+	48.9320i	−0.912269	+	1.58010i
$960$		0			0
$961$	−16.7033			−0.538817
$962$		0			0
$963$			36.4054i			1.17315i
$964$		0			0
$965$	43.4005	+	8.98300i	1.39711	+	0.289173i
$966$		0			0
$967$		−	23.0493i		−	0.741216i	−0.928789	−	0.370608i	$-0.879149\pi$
$967$		−	23.0493i		−	0.741216i	0.928789	−	0.370608i	$-0.120851\pi$
$968$		0			0
$969$	−3.26764	−	5.65972i	−0.104972	−	0.181816i
$970$		0			0
$971$	7.45964	+	12.9205i	0.239391	+	0.414638i	0.960540	−	0.278143i	$-0.0897188\pi$
$971$	7.45964	+	12.9205i	0.239391	+	0.414638i	−0.721148	+	0.692781i	$0.756385\pi$
$972$		0			0
$973$	−2.98233	−	1.72185i	−0.0956092	−	0.0552000i
$974$		0			0
$975$	−21.5239	−	43.4926i	−0.689317	−	1.39288i
$976$		0			0
$977$	−20.2339	−	11.6821i	−0.647341	−	0.373742i	0.140096	−	0.990138i	$-0.455259\pi$
$977$	−20.2339	−	11.6821i	−0.647341	−	0.373742i	−0.787437	+	0.616396i	$0.788592\pi$
$978$		0			0
$979$	16.7425	+	28.9989i	0.535093	+	0.926808i
$980$		0			0
$981$	18.0269	+	31.2235i	0.575555	+	0.996890i
$982$		0			0
$983$		−	5.31119i		−	0.169401i	−0.996406	−	0.0847003i	$-0.973007\pi$
$983$		−	5.31119i		−	0.169401i	0.996406	−	0.0847003i	$-0.0269933\pi$
$984$		0			0
$985$	47.4104	+	9.81295i	1.51062	+	0.312667i
$986$		0			0
$987$		−	62.0112i		−	1.97384i
$988$		0			0
$989$	23.5185			0.747846
$990$		0			0
$991$	−12.0440	+	20.8607i	−0.382589	+	0.662663i	−0.991432	−	0.130628i	$-0.958301\pi$
$991$	−12.0440	+	20.8607i	−0.382589	+	0.662663i	0.608843	+	0.793291i	$0.291634\pi$
$992$		0			0
$993$		−	8.00299i		−	0.253967i
$994$		0			0
$995$	30.4369	+	27.1125i	0.964915	+	0.859523i
$996$		0			0
$997$	−17.6755	+	10.2050i	−0.559790	+	0.323195i	−0.753061	−	0.657951i	$-0.771424\pi$
$997$	−17.6755	+	10.2050i	−0.559790	+	0.323195i	0.193271	+	0.981145i	$0.438090\pi$
$998$		0			0
$999$	3.26764	−	5.65972i	0.103384	−	0.179066i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1040.2.dh.a.529.6		12
4.3	odd	2		65.2.n.a.9.3	✓	12
5.4	even	2	inner	1040.2.dh.a.529.1		12
12.11	even	2		585.2.bs.a.334.4		12
13.3	even	3	inner	1040.2.dh.a.289.1		12
20.3	even	4		325.2.e.e.126.3		12
20.7	even	4		325.2.e.e.126.4		12
20.19	odd	2		65.2.n.a.9.4	yes	12
52.3	odd	6		65.2.n.a.29.4	yes	12
52.7	even	12		845.2.d.d.844.6		12
52.11	even	12		845.2.l.f.699.8		24
52.15	even	12		845.2.l.f.699.6		24
52.19	even	12		845.2.d.d.844.8		12
52.23	odd	6		845.2.n.e.484.3		12
52.31	even	4		845.2.l.f.654.5		24
52.35	odd	6		845.2.b.d.339.4		6
52.43	odd	6		845.2.b.e.339.3		6
52.47	even	4		845.2.l.f.654.7		24
52.51	odd	2		845.2.n.e.529.4		12
60.59	even	2		585.2.bs.a.334.3		12
65.29	even	6	inner	1040.2.dh.a.289.6		12
156.107	even	6		585.2.bs.a.289.3		12
260.3	even	12		325.2.e.e.276.3		12
260.19	even	12		845.2.d.d.844.5		12
260.43	even	12		4225.2.a.bq.1.3		6
260.59	even	12		845.2.d.d.844.7		12
260.87	even	12		4225.2.a.br.1.3		6
260.99	even	4		845.2.l.f.654.6		24
260.107	even	12		325.2.e.e.276.4		12
260.119	even	12		845.2.l.f.699.7		24
260.139	odd	6		845.2.b.d.339.3		6
260.147	even	12		4225.2.a.bq.1.4		6
260.159	odd	6		65.2.n.a.29.3	yes	12
260.179	odd	6		845.2.n.e.484.4		12
260.199	odd	6		845.2.b.e.339.4		6
260.219	even	12		845.2.l.f.699.5		24
260.239	even	4		845.2.l.f.654.8		24
260.243	even	12		4225.2.a.br.1.4		6
260.259	odd	2		845.2.n.e.529.3		12
780.419	even	6		585.2.bs.a.289.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.n.a.9.3	✓	12	4.3	odd	2
65.2.n.a.9.4	yes	12	20.19	odd	2
65.2.n.a.29.3	yes	12	260.159	odd	6
65.2.n.a.29.4	yes	12	52.3	odd	6
325.2.e.e.126.3		12	20.3	even	4
325.2.e.e.126.4		12	20.7	even	4
325.2.e.e.276.3		12	260.3	even	12
325.2.e.e.276.4		12	260.107	even	12
585.2.bs.a.289.3		12	156.107	even	6
585.2.bs.a.289.4		12	780.419	even	6
585.2.bs.a.334.3		12	60.59	even	2
585.2.bs.a.334.4		12	12.11	even	2
845.2.b.d.339.3		6	260.139	odd	6
845.2.b.d.339.4		6	52.35	odd	6
845.2.b.e.339.3		6	52.43	odd	6
845.2.b.e.339.4		6	260.199	odd	6
845.2.d.d.844.5		12	260.19	even	12
845.2.d.d.844.6		12	52.7	even	12
845.2.d.d.844.7		12	260.59	even	12
845.2.d.d.844.8		12	52.19	even	12
845.2.l.f.654.5		24	52.31	even	4
845.2.l.f.654.6		24	260.99	even	4
845.2.l.f.654.7		24	52.47	even	4
845.2.l.f.654.8		24	260.239	even	4
845.2.l.f.699.5		24	260.219	even	12
845.2.l.f.699.6		24	52.15	even	12
845.2.l.f.699.7		24	260.119	even	12
845.2.l.f.699.8		24	52.11	even	12
845.2.n.e.484.3		12	52.23	odd	6
845.2.n.e.484.4		12	260.179	odd	6
845.2.n.e.529.3		12	260.259	odd	2
845.2.n.e.529.4		12	52.51	odd	2
1040.2.dh.a.289.1		12	13.3	even	3	inner
1040.2.dh.a.289.6		12	65.29	even	6	inner
1040.2.dh.a.529.1		12	5.4	even	2	inner
1040.2.dh.a.529.6		12	1.1	even	1	trivial
4225.2.a.bq.1.3		6	260.43	even	12
4225.2.a.bq.1.4		6	260.147	even	12
4225.2.a.br.1.3		6	260.87	even	12
4225.2.a.br.1.4		6	260.243	even	12

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:	\( N \)	\(=\)	\( 1040 = 2^{4} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1040.dh (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.33117 + 1.34590i) q^{3} +(-2.12291 + 0.702335i) q^{5} +(-2.90420 + 1.67674i) q^{7} +(2.12291 + 3.67698i) q^{9} +(-1.62291 + 2.81095i) q^{11} +(-1.21648 - 3.39414i) q^{13} +(-5.89413 - 1.21996i) q^{15} +(-1.68772 + 0.974404i) q^{17} +(0.622905 + 1.07890i) q^{19} -9.02690 q^{21} +(-2.33117 - 1.34590i) q^{23} +(4.01345 - 2.98198i) q^{25} +3.35348i q^{27} +(1.50000 - 2.59808i) q^{29} -3.78109 q^{31} +(-7.56654 + 4.36854i) q^{33} +(4.98770 - 5.59927i) q^{35} +(-1.68772 - 0.974404i) q^{37} +(1.73236 - 9.54958i) q^{39} +(-1.39055 + 2.40850i) q^{41} +(-7.56654 + 4.36854i) q^{43} +(-7.08920 - 6.31489i) q^{45} +6.86960i q^{47} +(2.12291 - 3.67698i) q^{49} -5.24581 q^{51} +12.8336i q^{53} +(1.47104 - 7.10721i) q^{55} +3.35348i q^{57} +(1.26764 + 2.19562i) q^{59} +(3.74581 + 6.48793i) q^{61} +(-12.3307 - 7.11911i) q^{63} +(4.96629 + 6.35106i) q^{65} +(-3.47722 - 2.00758i) q^{67} +(-3.62291 - 6.27506i) q^{69} +(2.62291 + 4.54300i) q^{71} +5.46493i q^{73} +(13.3695 - 1.54979i) q^{75} -10.8848i q^{77} +13.7811 q^{79} +(1.85526 - 3.21341i) q^{81} +8.61955i q^{83} +(2.89851 - 3.25391i) q^{85} +(6.99351 - 4.03771i) q^{87} +(5.15819 - 8.93425i) q^{89} +(9.22398 + 7.81753i) q^{91} +(-8.81438 - 5.08898i) q^{93} +(-2.08012 - 1.85292i) q^{95} +(-4.56055 + 2.63304i) q^{97} -13.7811 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{5} + 6 q^{9} + 4 q^{15} - 12 q^{19} - 8 q^{21} - 2 q^{25} + 18 q^{29} + 16 q^{31} - 10 q^{35} + 32 q^{39} + 14 q^{41} - 29 q^{45} + 6 q^{49} - 24 q^{51} + 26 q^{55} + 4 q^{59} + 6 q^{61} + 23 q^{65}+ \cdots - 104 q^{99}+O(q^{100}) \) 12 * q - 6 * q^5 + 6 * q^9 + 4 * q^15 - 12 * q^19 - 8 * q^21 - 2 * q^25 + 18 * q^29 + 16 * q^31 - 10 * q^35 + 32 * q^39 + 14 * q^41 - 29 * q^45 + 6 * q^49 - 24 * q^51 + 26 * q^55 + 4 * q^59 + 6 * q^61 + 23 * q^65 - 24 * q^69 + 12 * q^71 - 2 * q^75 + 104 * q^79 + 14 * q^81 + 21 * q^85 + 20 * q^89 + 44 * q^91 - 20 * q^95 - 104 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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