LMFDB - Embedded newform 440.2.y.b.81.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [440,2,Mod(81,440)] 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("440.81"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(440, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 440 = 2^{3} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	440.y (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,-1,0,3,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$3.51341768894$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
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} - 2 x^{11} + 15 x^{10} - 22 x^{9} + 89 x^{8} - 118 x^{7} + 205 x^{6} - 68 x^{5} + 1061 x^{4} + \cdots + 400 $ x^12 - 2x^11 + 15x^10 - 22x^9 + 89x^8 - 118x^7 + 205x^6 - 68x^5 + 1061x^4 - 1490x^3 + 2760x^2 - 1600*x + 400
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			81.1
Root			$-0.866917 - 2.66810i$ of defining polynomial
Character	$\chi$	$=$	440.81
Dual form			440.2.y.b.201.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.535784 + 1.64897i) q^{3} +(0.809017 - 0.587785i) q^{5} +(-0.386966 - 1.19096i) q^{7} +(-0.00499969 - 0.00363249i) q^{9} +(2.45751 + 2.22725i) q^{11} +(2.02882 + 1.47403i) q^{13} +(0.535784 + 1.64897i) q^{15} +(2.91579 - 2.11845i) q^{17} +(-2.18093 + 6.71222i) q^{19} +2.17119 q^{21} -2.20737 q^{23} +(0.309017 - 0.951057i) q^{25} +(-4.19943 + 3.05107i) q^{27} +(0.834223 + 2.56747i) q^{29} +(2.29231 + 1.66546i) q^{31} +(-4.98937 + 2.85905i) q^{33} +(-1.01309 - 0.736053i) q^{35} +(-2.49468 - 7.67782i) q^{37} +(-3.51765 + 2.55572i) q^{39} +(-3.19109 + 9.82117i) q^{41} +6.88581 q^{43} -0.00617996 q^{45} +(0.493365 - 1.51842i) q^{47} +(4.39448 - 3.19278i) q^{49} +(1.93103 + 5.94309i) q^{51} +(-1.43514 - 1.04269i) q^{53} +(3.29731 + 0.357394i) q^{55} +(-9.89977 - 7.19261i) q^{57} +(-1.35006 - 4.15504i) q^{59} +(6.74173 - 4.89816i) q^{61} +(-0.00239143 + 0.00736007i) q^{63} +2.50777 q^{65} +5.43293 q^{67} +(1.18267 - 3.63989i) q^{69} +(3.75112 - 2.72535i) q^{71} +(-0.628770 - 1.93515i) q^{73} +(1.40270 + 1.01912i) q^{75} +(1.70159 - 3.78866i) q^{77} +(-13.5612 - 9.85278i) q^{79} +(-2.78687 - 8.57710i) q^{81} +(4.55121 - 3.30665i) q^{83} +(1.11373 - 3.42772i) q^{85} -4.68066 q^{87} -4.72832 q^{89} +(0.970419 - 2.98664i) q^{91} +(-3.97449 + 2.88764i) q^{93} +(2.18093 + 6.71222i) q^{95} +(-15.4476 - 11.2233i) q^{97} +(-0.00419634 - 0.0200624i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - q^{3} + 3 q^{5} - 8 q^{7} + 10 q^{9} - 4 q^{11} - 7 q^{13} + q^{15} + 7 q^{17} + 3 q^{19} + 4 q^{21} + 36 q^{23} - 3 q^{25} + 8 q^{27} + 13 q^{29} + 2 q^{31} - 19 q^{33} - 2 q^{35} - 22 q^{37}+ \cdots - 79 q^{99}+O(q^{100}) $ 12 * q - q^3 + 3 * q^5 - 8 * q^7 + 10 * q^9 - 4 * q^11 - 7 * q^13 + q^15 + 7 * q^17 + 3 * q^19 + 4 * q^21 + 36 * q^23 - 3 * q^25 + 8 * q^27 + 13 * q^29 + 2 * q^31 - 19 * q^33 - 2 * q^35 - 22 * q^37 - q^39 + 7 * q^41 + 6 * q^43 - 20 * q^45 - 2 * q^47 - 19 * q^49 - 33 * q^51 + 3 * q^53 + 4 * q^55 - 25 * q^57 + 19 * q^59 + 22 * q^61 - 2 * q^63 + 12 * q^65 + 22 * q^67 + 21 * q^69 + 44 * q^71 + 17 * q^73 - q^75 - 38 * q^77 - 43 * q^79 - 85 * q^81 - 15 * q^83 + 18 * q^85 + 50 * q^87 + 2 * q^89 + 59 * q^91 + 5 * q^93 - 3 * q^95 - 20 * q^97 - 79 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/440\mathbb{Z}\right)^\times$.

$n$	$111$	$177$	$221$	$321$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{1}{5}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.535784	+	1.64897i	−0.309335	+	0.952036i	0.668689	+	0.743542i	$0.266856\pi$
$3$	−0.535784	+	1.64897i	−0.309335	+	0.952036i	−0.978024	+	0.208493i	$0.933144\pi$
$4$		0			0
$5$	0.809017	−	0.587785i	0.361803	−	0.262866i
$5$	0.809017	−	0.587785i	0.361803	−	0.262866i
$6$		0			0
$7$	−0.386966	−	1.19096i	−0.146259	−	0.450140i	0.850912	−	0.525309i	$-0.176050\pi$
$7$	−0.386966	−	1.19096i	−0.146259	−	0.450140i	−0.997171	+	0.0751693i	$0.976050\pi$
$8$		0			0
$9$	−0.00499969	−	0.00363249i	−0.00166656	−	0.00121083i
$10$		0			0
$11$	2.45751	+	2.22725i	0.740967	+	0.671541i
$11$	2.45751	+	2.22725i	0.740967	+	0.671541i
$12$		0			0
$13$	2.02882	+	1.47403i	0.562695	+	0.408822i	0.832444	−	0.554109i	$-0.186941\pi$
$13$	2.02882	+	1.47403i	0.562695	+	0.408822i	−0.269749	+	0.962931i	$0.586941\pi$
$14$		0			0
$15$	0.535784	+	1.64897i	0.138339	+	0.425763i
$16$		0			0
$17$	2.91579	−	2.11845i	0.707183	−	0.513799i	−0.175081	−	0.984554i	$-0.556019\pi$
$17$	2.91579	−	2.11845i	0.707183	−	0.513799i	0.882264	+	0.470756i	$0.156019\pi$
$18$		0			0
$19$	−2.18093	+	6.71222i	−0.500340	+	1.53989i	0.308125	+	0.951346i	$0.400299\pi$
$19$	−2.18093	+	6.71222i	−0.500340	+	1.53989i	−0.808465	+	0.588544i	$0.799701\pi$
$20$		0			0
$21$	2.17119			0.473792
$22$		0			0
$23$	−2.20737			−0.460268			−0.230134	−	0.973159i	$-0.573916\pi$
$23$	−2.20737			−0.460268			−0.230134	+	0.973159i	$0.573916\pi$
$24$		0			0
$25$	0.309017	−	0.951057i	0.0618034	−	0.190211i
$26$		0			0
$27$	−4.19943	+	3.05107i	−0.808182	+	0.587178i
$28$		0			0
$29$	0.834223	+	2.56747i	0.154911	+	0.476768i	0.998152	−	0.0607684i	$-0.0193551\pi$
$29$	0.834223	+	2.56747i	0.154911	+	0.476768i	−0.843241	+	0.537536i	$0.819355\pi$
$30$		0			0
$31$	2.29231	+	1.66546i	0.411712	+	0.299126i	0.774294	−	0.632826i	$-0.218105\pi$
$31$	2.29231	+	1.66546i	0.411712	+	0.299126i	−0.362583	+	0.931952i	$0.618105\pi$
$32$		0			0
$33$	−4.98937	+	2.85905i	−0.868538	+	0.497696i
$34$		0			0
$35$	−1.01309	−	0.736053i	−0.171243	−	0.124416i
$36$		0			0
$37$	−2.49468	−	7.67782i	−0.410122	−	1.26223i	−0.916542	−	0.399939i	$-0.869031\pi$
$37$	−2.49468	−	7.67782i	−0.410122	−	1.26223i	0.506420	−	0.862287i	$-0.330969\pi$
$38$		0			0
$39$	−3.51765	+	2.55572i	−0.563274	+	0.409243i
$40$		0			0
$41$	−3.19109	+	9.82117i	−0.498365	+	1.53381i	0.313282	+	0.949660i	$0.398571\pi$
$41$	−3.19109	+	9.82117i	−0.498365	+	1.53381i	−0.811647	+	0.584148i	$0.801429\pi$
$42$		0			0
$43$	6.88581			1.05008			0.525038	−	0.851079i	$-0.324051\pi$
$43$	6.88581			1.05008			0.525038	+	0.851079i	$0.324051\pi$
$44$		0			0
$45$	−0.00617996			−0.000921254
$46$		0			0
$47$	0.493365	−	1.51842i	0.0719647	−	0.221485i	−0.908605	−	0.417657i	$-0.862851\pi$
$47$	0.493365	−	1.51842i	0.0719647	−	0.221485i	0.980569	+	0.196173i	$0.0628513\pi$
$48$		0			0
$49$	4.39448	−	3.19278i	0.627783	−	0.456111i
$50$		0			0
$51$	1.93103	+	5.94309i	0.270398	+	0.832199i
$52$		0			0
$53$	−1.43514	−	1.04269i	−0.197132	−	0.143225i	0.484841	−	0.874602i	$-0.338878\pi$
$53$	−1.43514	−	1.04269i	−0.197132	−	0.143225i	−0.681972	+	0.731378i	$0.738878\pi$
$54$		0			0
$55$	3.29731	+	0.357394i	0.444610	+	0.0481910i
$56$		0			0
$57$	−9.89977	−	7.19261i	−1.31126	−	0.952684i
$58$		0			0
$59$	−1.35006	−	4.15504i	−0.175762	−	0.540941i	0.823905	−	0.566728i	$-0.191791\pi$
$59$	−1.35006	−	4.15504i	−0.175762	−	0.540941i	−0.999667	+	0.0257871i	$0.991791\pi$
$60$		0			0
$61$	6.74173	−	4.89816i	0.863191	−	0.627145i	−0.0655605	−	0.997849i	$-0.520884\pi$
$61$	6.74173	−	4.89816i	0.863191	−	0.627145i	0.928751	+	0.370704i	$0.120884\pi$
$62$		0			0
$63$	−0.00239143	+	0.00736007i	−0.000301292	+	0.000927282i
$64$		0			0
$65$	2.50777			0.311050
$66$		0			0
$67$	5.43293			0.663738			0.331869	−	0.943326i	$-0.392321\pi$
$67$	5.43293			0.663738			0.331869	+	0.943326i	$0.392321\pi$
$68$		0			0
$69$	1.18267	−	3.63989i	0.142377	−	0.438191i
$70$		0			0
$71$	3.75112	−	2.72535i	0.445176	−	0.323439i	−0.342512	−	0.939513i	$-0.611278\pi$
$71$	3.75112	−	2.72535i	0.445176	−	0.323439i	0.787688	+	0.616074i	$0.211278\pi$
$72$		0			0
$73$	−0.628770	−	1.93515i	−0.0735919	−	0.226493i	0.907494	−	0.420065i	$-0.137993\pi$
$73$	−0.628770	−	1.93515i	−0.0735919	−	0.226493i	−0.981086	+	0.193572i	$0.937993\pi$
$74$		0			0
$75$	1.40270	+	1.01912i	0.161970	+	0.117678i
$76$		0			0
$77$	1.70159	−	3.78866i	0.193914	−	0.431758i
$78$		0			0
$79$	−13.5612	−	9.85278i	−1.52575	−	1.10852i	−0.958542	−	0.284951i	$-0.908023\pi$
$79$	−13.5612	−	9.85278i	−1.52575	−	1.10852i	−0.567210	−	0.823573i	$-0.691977\pi$
$80$		0			0
$81$	−2.78687	−	8.57710i	−0.309652	−	0.953012i
$82$		0			0
$83$	4.55121	−	3.30665i	0.499561	−	0.362952i	−0.309288	−	0.950968i	$-0.600091\pi$
$83$	4.55121	−	3.30665i	0.499561	−	0.362952i	0.808849	+	0.588016i	$0.200091\pi$
$84$		0			0
$85$	1.11373	−	3.42772i	0.120801	−	0.371788i
$86$		0			0
$87$	−4.68066			−0.501820
$88$		0			0
$89$	−4.72832			−0.501200			−0.250600	−	0.968091i	$-0.580628\pi$
$89$	−4.72832			−0.501200			−0.250600	+	0.968091i	$0.580628\pi$
$90$		0			0
$91$	0.970419	−	2.98664i	0.101728	−	0.313085i
$92$		0			0
$93$	−3.97449	+	2.88764i	−0.412135	+	0.299434i
$94$		0			0
$95$	2.18093	+	6.71222i	0.223759	+	0.688660i
$96$		0			0
$97$	−15.4476	−	11.2233i	−1.56847	−	1.13956i	−0.928608	−	0.371063i	$-0.878993\pi$
$97$	−15.4476	−	11.2233i	−1.56847	−	1.13956i	−0.639858	−	0.768493i	$-0.721007\pi$
$98$		0			0
$99$	−0.00419634	−	0.0200624i	−0.000421748	−	0.00201635i
$100$		0			0
$101$	11.5085	+	8.36138i	1.14513	+	0.831989i	0.987826	−	0.155561i	$-0.0497185\pi$
$101$	11.5085	+	8.36138i	1.14513	+	0.831989i	0.157308	+	0.987550i	$0.449719\pi$
$102$		0			0
$103$	−4.90766	−	15.1042i	−0.483566	−	1.48826i	−0.834047	−	0.551693i	$-0.813982\pi$
$103$	−4.90766	−	15.1042i	−0.483566	−	1.48826i	0.350481	−	0.936570i	$-0.386018\pi$
$104$		0			0
$105$	1.75653	−	1.27619i	0.171420	−	0.124544i
$106$		0			0
$107$	−1.25132	+	3.85116i	−0.120969	+	0.372306i	−0.993145	−	0.116887i	$-0.962708\pi$
$107$	−1.25132	+	3.85116i	−0.120969	+	0.372306i	0.872176	+	0.489193i	$0.162708\pi$
$108$		0			0
$109$	5.89844			0.564968			0.282484	−	0.959272i	$-0.408842\pi$
$109$	5.89844			0.564968			0.282484	+	0.959272i	$0.408842\pi$
$110$		0			0
$111$	13.9971			1.32855
$112$		0			0
$113$	1.05499	−	3.24692i	0.0992448	−	0.305444i	−0.889092	−	0.457729i	$-0.848663\pi$
$113$	1.05499	−	3.24692i	0.0992448	−	0.305444i	0.988337	+	0.152285i	$0.0486630\pi$
$114$		0			0
$115$	−1.78580	+	1.29746i	−0.166526	+	0.120989i
$116$		0			0
$117$	−0.00478911	−	0.0147394i	−0.000442753	−	0.00136265i
$118$		0			0
$119$	−3.65129	−	2.65282i	−0.334713	−	0.243183i
$120$		0			0
$121$	1.07872	+	10.9470i	0.0980656	+	0.995180i
$122$		0			0
$123$	−14.4851	−	10.5241i	−1.30608	−	0.948922i
$124$		0			0
$125$	−0.309017	−	0.951057i	−0.0276393	−	0.0850651i
$126$		0			0
$127$	−5.00949	+	3.63961i	−0.444521	+	0.322963i	−0.787429	−	0.616406i	$-0.788588\pi$
$127$	−5.00949	+	3.63961i	−0.444521	+	0.322963i	0.342908	+	0.939369i	$0.388588\pi$
$128$		0			0
$129$	−3.68931	+	11.3545i	−0.324826	+	0.999710i
$130$		0			0
$131$	−7.39924			−0.646475			−0.323237	−	0.946318i	$-0.604771\pi$
$131$	−7.39924			−0.646475			−0.323237	+	0.946318i	$0.604771\pi$
$132$		0			0
$133$	8.83792			0.766345
$134$		0			0
$135$	−1.60404	+	4.93673i	−0.138054	+	0.424886i
$136$		0			0
$137$	−14.9530	+	10.8640i	−1.27752	+	0.928175i	−0.999475	−	0.0323920i	$-0.989687\pi$
$137$	−14.9530	+	10.8640i	−1.27752	+	0.928175i	−0.278048	+	0.960567i	$0.589687\pi$
$138$		0			0
$139$	−5.51361	−	16.9691i	−0.467658	−	1.43930i	−0.855608	−	0.517624i	$-0.826817\pi$
$139$	−5.51361	−	16.9691i	−0.467658	−	1.43930i	0.387950	−	0.921680i	$-0.373183\pi$
$140$		0			0
$141$	2.23950	+	1.62709i	0.188600	+	0.137026i
$142$		0			0
$143$	1.70283	+	8.14114i	0.142398	+	0.680796i
$144$		0			0
$145$	2.18402	+	1.58679i	0.181373	+	0.131775i
$146$		0			0
$147$	2.91031	+	8.95702i	0.240039	+	0.738763i
$148$		0			0
$149$	5.98599	−	4.34908i	0.490392	−	0.356290i	−0.314943	−	0.949111i	$-0.601985\pi$
$149$	5.98599	−	4.34908i	0.490392	−	0.356290i	0.805335	+	0.592820i	$0.201985\pi$
$150$		0			0
$151$	1.36436	−	4.19906i	0.111030	−	0.341714i	−0.880069	−	0.474847i	$-0.842504\pi$
$151$	1.36436	−	4.19906i	0.111030	−	0.341714i	0.991098	+	0.133132i	$0.0425035\pi$
$152$		0			0
$153$	−0.0222733			−0.00180069
$154$		0			0
$155$	2.83345			0.227589
$156$		0			0
$157$	−0.720185	+	2.21650i	−0.0574770	+	0.176896i	−0.975673	−	0.219230i	$-0.929646\pi$
$157$	−0.720185	+	2.21650i	−0.0574770	+	0.176896i	0.918196	+	0.396126i	$0.129646\pi$
$158$		0			0
$159$	2.48830	−	1.80785i	0.197335	−	0.143372i
$160$		0			0
$161$	0.854175	+	2.62888i	0.0673184	+	0.207185i
$162$		0			0
$163$	−1.21850	−	0.885295i	−0.0954406	−	0.0693416i	0.539042	−	0.842279i	$-0.318787\pi$
$163$	−1.21850	−	0.885295i	−0.0954406	−	0.0693416i	−0.634482	+	0.772938i	$0.718787\pi$
$164$		0			0
$165$	−2.35598	+	5.24570i	−0.183413	+	0.408377i
$166$		0			0
$167$	−7.92620	−	5.75872i	−0.613347	−	0.445623i	0.237244	−	0.971450i	$-0.423756\pi$
$167$	−7.92620	−	5.75872i	−0.613347	−	0.445623i	−0.850591	+	0.525827i	$0.823756\pi$
$168$		0			0
$169$	−2.07385	−	6.38265i	−0.159527	−	0.490973i
$170$		0			0
$171$	0.0352861	−	0.0256368i	0.00269839	−	0.00196050i
$172$		0			0
$173$	−6.20927	+	19.1102i	−0.472082	+	1.45292i	0.377771	+	0.925899i	$0.376691\pi$
$173$	−6.20927	+	19.1102i	−0.472082	+	1.45292i	−0.849853	+	0.527020i	$0.823309\pi$
$174$		0			0
$175$	−1.25225			−0.0946610
$176$		0			0
$177$	7.57490			0.569364
$178$		0			0
$179$	5.00760	−	15.4118i	0.374285	−	1.15193i	−0.569674	−	0.821871i	$-0.692931\pi$
$179$	5.00760	−	15.4118i	0.374285	−	1.15193i	0.943960	−	0.330061i	$-0.107069\pi$
$180$		0			0
$181$	7.62800	−	5.54207i	0.566985	−	0.411939i	−0.267024	−	0.963690i	$-0.586040\pi$
$181$	7.62800	−	5.54207i	0.566985	−	0.411939i	0.834009	+	0.551751i	$0.186040\pi$
$182$		0			0
$183$	4.46482	+	13.7413i	0.330049	+	1.01579i
$184$		0			0
$185$	−6.53115	−	4.74516i	−0.480179	−	0.348871i
$186$		0			0
$187$	11.8839	+	1.28809i	0.869036	+	0.0941943i
$188$		0			0
$189$	5.25873	+	3.82069i	0.382516	+	0.277914i
$190$		0			0
$191$	2.52639	+	7.77542i	0.182803	+	0.562610i	0.999904	−	0.0138853i	$-0.00441998\pi$
$191$	2.52639	+	7.77542i	0.182803	+	0.562610i	−0.817101	+	0.576495i	$0.804420\pi$
$192$		0			0
$193$	4.04119	−	2.93610i	0.290891	−	0.211345i	−0.432763	−	0.901508i	$-0.642461\pi$
$193$	4.04119	−	2.93610i	0.290891	−	0.211345i	0.723654	+	0.690163i	$0.242461\pi$
$194$		0			0
$195$	−1.34362	+	4.13524i	−0.0962187	+	0.296131i
$196$		0			0
$197$	−7.00790			−0.499292			−0.249646	−	0.968337i	$-0.580314\pi$
$197$	−7.00790			−0.499292			−0.249646	+	0.968337i	$0.580314\pi$
$198$		0			0
$199$	18.8762			1.33810			0.669050	−	0.743217i	$-0.266701\pi$
$199$	18.8762			1.33810			0.669050	+	0.743217i	$0.266701\pi$
$200$		0			0
$201$	−2.91088	+	8.95875i	−0.205317	+	0.631902i
$202$		0			0
$203$	2.73494	−	1.98705i	0.191955	−	0.139463i
$204$		0			0
$205$	3.19109	+	9.82117i	0.222875	+	0.685940i
$206$		0			0
$207$	0.0110362	+	0.00801823i	0.000767066	+	0.000557306i
$208$		0			0
$209$	−20.3095	+	11.6379i	−1.40483	+	0.805009i
$210$		0			0
$211$	−11.1392	−	8.09308i	−0.766852	−	0.557150i	0.134153	−	0.990961i	$-0.457169\pi$
$211$	−11.1392	−	8.09308i	−0.766852	−	0.557150i	−0.901004	+	0.433810i	$0.857169\pi$
$212$		0			0
$213$	2.48424	+	7.64569i	0.170217	+	0.523874i
$214$		0			0
$215$	5.57074	−	4.04738i	0.379921	−	0.276029i
$216$		0			0
$217$	1.09645	−	3.37453i	0.0744319	−	0.229078i
$218$		0			0
$219$	3.52790			0.238394
$220$		0			0
$221$	9.03828			0.607980
$222$		0			0
$223$	8.89894	−	27.3881i	0.595917	−	1.83404i	0.0458095	−	0.998950i	$-0.485413\pi$
$223$	8.89894	−	27.3881i	0.595917	−	1.83404i	0.550108	−	0.835094i	$-0.314587\pi$
$224$		0			0
$225$	−0.00499969	+	0.00363249i	−0.000333313	+	0.000242166i
$226$		0			0
$227$	7.50197	+	23.0887i	0.497923	+	1.53245i	0.812351	+	0.583168i	$0.198187\pi$
$227$	7.50197	+	23.0887i	0.497923	+	1.53245i	−0.314428	+	0.949281i	$0.601813\pi$
$228$		0			0
$229$	13.2625	+	9.63574i	0.876408	+	0.636748i	0.932299	−	0.361689i	$-0.117800\pi$
$229$	13.2625	+	9.63574i	0.876408	+	0.636748i	−0.0558905	+	0.998437i	$0.517800\pi$
$230$		0			0
$231$	5.33572	+	4.83578i	0.351065	+	0.318171i
$232$		0			0
$233$	2.03746	+	1.48030i	0.133478	+	0.0969776i	0.652521	−	0.757771i	$-0.273711\pi$
$233$	2.03746	+	1.48030i	0.133478	+	0.0969776i	−0.519043	+	0.854748i	$0.673711\pi$
$234$		0			0
$235$	−0.493365	−	1.51842i	−0.0321836	−	0.0990509i
$236$		0			0
$237$	23.5128	−	17.0831i	1.52732	−	1.10967i
$238$		0			0
$239$	2.06369	−	6.35138i	0.133489	−	0.410837i	−0.861863	−	0.507141i	$-0.830702\pi$
$239$	2.06369	−	6.35138i	0.133489	−	0.410837i	0.995352	+	0.0963045i	$0.0307022\pi$
$240$		0			0
$241$	−2.14310			−0.138049			−0.0690247	−	0.997615i	$-0.521989\pi$
$241$	−2.14310			−0.138049			−0.0690247	+	0.997615i	$0.521989\pi$
$242$		0			0
$243$	0.0642239			0.00411997
$244$		0			0
$245$	1.67854	−	5.16602i	0.107238	−	0.330045i
$246$		0			0
$247$	−14.3187	+	10.4032i	−0.911079	+	0.661938i
$248$		0			0
$249$	3.01411	+	9.27649i	0.191012	+	0.587873i
$250$		0			0
$251$	−11.6422	−	8.45856i	−0.734850	−	0.533900i	0.156244	−	0.987718i	$-0.450061\pi$
$251$	−11.6422	−	8.45856i	−0.734850	−	0.533900i	−0.891094	+	0.453819i	$0.850061\pi$
$252$		0			0
$253$	−5.42463	−	4.91636i	−0.341043	−	0.309089i
$254$		0			0
$255$	5.05550	+	3.67303i	0.316587	+	0.230014i
$256$		0			0
$257$	7.54105	+	23.2090i	0.470398	+	1.44774i	0.852065	+	0.523436i	$0.175350\pi$
$257$	7.54105	+	23.2090i	0.470398	+	1.44774i	−0.381667	+	0.924300i	$0.624650\pi$
$258$		0			0
$259$	−8.17861	+	5.94211i	−0.508194	+	0.369225i
$260$		0			0
$261$	0.00515546	−	0.0158669i	0.000319115	−	0.000982135i
$262$		0			0
$263$	0.992957			0.0612283			0.0306142	−	0.999531i	$-0.490254\pi$
$263$	0.992957			0.0612283			0.0306142	+	0.999531i	$0.490254\pi$
$264$		0			0
$265$	−1.77393			−0.108972
$266$		0			0
$267$	2.53336	−	7.79687i	0.155039	−	0.477161i
$268$		0			0
$269$	−24.6128	+	17.8822i	−1.50067	+	1.09030i	−0.530551	+	0.847653i	$0.678015\pi$
$269$	−24.6128	+	17.8822i	−1.50067	+	1.09030i	−0.970115	+	0.242645i	$0.921985\pi$
$270$		0			0
$271$	8.01666	+	24.6728i	0.486978	+	1.49876i	0.829096	+	0.559106i	$0.188856\pi$
$271$	8.01666	+	24.6728i	0.486978	+	1.49876i	−0.342119	+	0.939657i	$0.611144\pi$
$272$		0			0
$273$	4.40496	+	3.20039i	0.266600	+	0.193697i
$274$		0			0
$275$	2.87765	−	1.64897i	0.173529	−	0.0994369i
$276$		0			0
$277$	4.07624	+	2.96156i	0.244917	+	0.177943i	0.703471	−	0.710724i	$-0.251632\pi$
$277$	4.07624	+	2.96156i	0.244917	+	0.177943i	−0.458554	+	0.888667i	$0.651632\pi$
$278$		0			0
$279$	−0.00541108	−	0.0166536i	−0.000323953	−	0.000997025i
$280$		0			0
$281$	−16.8065	+	12.2106i	−1.00259	+	0.728424i	−0.962642	−	0.270778i	$-0.912719\pi$
$281$	−16.8065	+	12.2106i	−1.00259	+	0.728424i	−0.0399476	+	0.999202i	$0.512719\pi$
$282$		0			0
$283$	−1.40797	+	4.33329i	−0.0836952	+	0.257587i	−0.984143	−	0.177377i	$-0.943239\pi$
$283$	−1.40797	+	4.33329i	−0.0836952	+	0.257587i	0.900448	+	0.434964i	$0.143239\pi$
$284$		0			0
$285$	−12.2368			−0.724845
$286$		0			0
$287$	12.9314			0.763319
$288$		0			0
$289$	−1.23927	+	3.81407i	−0.0728981	+	0.224357i
$290$		0			0
$291$	26.7836	−	19.4594i	1.57008	−	1.14073i
$292$		0			0
$293$	−0.738834	−	2.27390i	−0.0431631	−	0.132842i	0.927153	−	0.374684i	$-0.122249\pi$
$293$	−0.738834	−	2.27390i	−0.0431631	−	0.132842i	−0.970316	+	0.241841i	$0.922249\pi$
$294$		0			0
$295$	−3.53449	−	2.56796i	−0.205786	−	0.149512i
$296$		0			0
$297$	−17.1156	−	1.85515i	−0.993150	−	0.107647i
$298$		0			0
$299$	−4.47836	−	3.25372i	−0.258990	−	0.188167i
$300$		0			0
$301$	−2.66457	−	8.20071i	−0.153583	−	0.472681i
$302$		0			0
$303$	−19.9538	+	14.4972i	−1.14631	+	0.832845i
$304$		0			0
$305$	2.57511	−	7.92538i	0.147451	−	0.453806i
$306$		0			0
$307$	3.26648			0.186428			0.0932138	−	0.995646i	$-0.470286\pi$
$307$	3.26648			0.186428			0.0932138	+	0.995646i	$0.470286\pi$
$308$		0			0
$309$	27.5359			1.56646
$310$		0			0
$311$	0.845368	−	2.60177i	0.0479364	−	0.147533i	−0.924223	−	0.381853i	$-0.875286\pi$
$311$	0.845368	−	2.60177i	0.0479364	−	0.147533i	0.972160	+	0.234320i	$0.0752862\pi$
$312$		0			0
$313$	8.38026	−	6.08861i	0.473680	−	0.344149i	−0.325194	−	0.945647i	$-0.605430\pi$
$313$	8.38026	−	6.08861i	0.473680	−	0.344149i	0.798874	+	0.601499i	$0.205430\pi$
$314$		0			0
$315$	0.00239143	+	0.00736007i	0.000134742	+	0.000414693i
$316$		0			0
$317$	−25.2866	−	18.3718i	−1.42024	−	1.03186i	−0.991732	−	0.128323i	$-0.959041\pi$
$317$	−25.2866	−	18.3718i	−1.42024	−	1.03186i	−0.428504	−	0.903540i	$-0.640959\pi$
$318$		0			0
$319$	−3.66829	+	8.16762i	−0.205385	+	0.457299i
$320$		0			0
$321$	−5.68003	−	4.12678i	−0.317028	−	0.230334i
$322$		0			0
$323$	7.86034	+	24.1916i	0.437361	+	1.34606i
$324$		0			0
$325$	2.02882	−	1.47403i	0.112539	−	0.0817643i
$326$		0			0
$327$	−3.16029	+	9.72638i	−0.174765	+	0.537870i
$328$		0			0
$329$	−1.99929			−0.110224
$330$		0			0
$331$	−29.7878			−1.63729			−0.818644	−	0.574302i	$-0.805274\pi$
$331$	−29.7878			−1.63729			−0.818644	+	0.574302i	$0.805274\pi$
$332$		0			0
$333$	−0.0154170	+	0.0474486i	−0.000844846	+	0.00260017i
$334$		0			0
$335$	4.39533	−	3.19339i	0.240143	−	0.174474i
$336$		0			0
$337$	−9.21954	−	28.3748i	−0.502220	−	1.54568i	−0.805394	−	0.592740i	$-0.798046\pi$
$337$	−9.21954	−	28.3748i	−0.502220	−	1.54568i	0.303173	−	0.952935i	$-0.401954\pi$
$338$		0			0
$339$	4.78884	+	3.47929i	0.260094	+	0.188969i
$340$		0			0
$341$	1.92398	+	9.19845i	0.104190	+	0.498124i
$342$		0			0
$343$	−12.5946	−	9.15051i	−0.680045	−	0.494081i
$344$		0			0
$345$	−1.18267	−	3.63989i	−0.0636729	−	0.195965i
$346$		0			0
$347$	17.9739	−	13.0588i	0.964891	−	0.701035i	0.0106099	−	0.999944i	$-0.496623\pi$
$347$	17.9739	−	13.0588i	0.964891	−	0.701035i	0.954282	+	0.298909i	$0.0966227\pi$
$348$		0			0
$349$	−5.93726	+	18.2730i	−0.317814	+	0.978132i	0.656766	+	0.754094i	$0.271924\pi$
$349$	−5.93726	+	18.2730i	−0.317814	+	0.978132i	−0.974581	+	0.224038i	$0.928076\pi$
$350$		0			0
$351$	−13.0173			−0.694811
$352$		0			0
$353$	31.0691			1.65364			0.826821	−	0.562466i	$-0.190147\pi$
$353$	31.0691			1.65364			0.826821	+	0.562466i	$0.190147\pi$
$354$		0			0
$355$	1.43280	−	4.40970i	0.0760451	−	0.234043i
$356$		0			0
$357$	6.33073	−	4.59955i	0.335058	−	0.243434i
$358$		0			0
$359$	−8.50924	−	26.1887i	−0.449100	−	1.38219i	−0.877924	−	0.478801i	$-0.841072\pi$
$359$	−8.50924	−	26.1887i	−0.449100	−	1.38219i	0.428823	−	0.903388i	$-0.358928\pi$
$360$		0			0
$361$	−24.9262	−	18.1099i	−1.31190	−	0.953153i
$362$		0			0
$363$	−18.6292	−	4.08643i	−0.977782	−	0.214482i
$364$		0			0
$365$	−1.64614	−	1.19599i	−0.0861629	−	0.0626010i
$366$		0			0
$367$	7.35123	+	22.6248i	0.383731	+	1.18100i	0.937397	+	0.348264i	$0.113229\pi$
$367$	7.35123	+	22.6248i	0.383731	+	1.18100i	−0.553665	+	0.832739i	$0.686771\pi$
$368$		0			0
$369$	0.0516297	−	0.0375112i	0.00268774	−	0.00195275i
$370$		0			0
$371$	−0.686451	+	2.11268i	−0.0356387	+	0.109685i
$372$		0			0
$373$	−15.5085			−0.803000			−0.401500	−	0.915859i	$-0.631511\pi$
$373$	−15.5085			−0.803000			−0.401500	+	0.915859i	$0.631511\pi$
$374$		0			0
$375$	1.73383			0.0895348
$376$		0			0
$377$	−2.09203	+	6.43862i	−0.107745	+	0.331606i
$378$		0			0
$379$	15.4087	−	11.1950i	0.791489	−	0.575051i	−0.116916	−	0.993142i	$-0.537301\pi$
$379$	15.4087	−	11.1950i	0.791489	−	0.575051i	0.908405	+	0.418091i	$0.137301\pi$
$380$		0			0
$381$	−3.31762	−	10.2106i	−0.169967	−	0.523103i
$382$		0			0
$383$	12.8006	+	9.30018i	0.654080	+	0.475217i	0.864659	−	0.502360i	$-0.167535\pi$
$383$	12.8006	+	9.30018i	0.654080	+	0.475217i	−0.210578	+	0.977577i	$0.567535\pi$
$384$		0			0
$385$	−0.850306	−	4.06526i	−0.0433356	−	0.207185i
$386$		0			0
$387$	−0.0344269	−	0.0250126i	−0.00175002	−	0.00127146i
$388$		0			0
$389$	−5.01448	−	15.4330i	−0.254244	−	0.782483i	−0.993978	−	0.109583i	$-0.965048\pi$
$389$	−5.01448	−	15.4330i	−0.254244	−	0.782483i	0.739733	−	0.672900i	$-0.234952\pi$
$390$		0			0
$391$	−6.43622	+	4.67619i	−0.325494	+	0.236485i
$392$		0			0
$393$	3.96440	−	12.2012i	0.199977	−	0.615467i
$394$		0			0
$395$	−16.7625			−0.843415
$396$		0			0
$397$	31.3002			1.57091			0.785455	−	0.618919i	$-0.212429\pi$
$397$	31.3002			1.57091			0.785455	+	0.618919i	$0.212429\pi$
$398$		0			0
$399$	−4.73522	+	14.5735i	−0.237057	+	0.729588i
$400$		0			0
$401$	5.55064	−	4.03277i	0.277186	−	0.201387i	−0.440503	−	0.897751i	$-0.645200\pi$
$401$	5.55064	−	4.03277i	0.277186	−	0.201387i	0.717689	+	0.696364i	$0.245200\pi$
$402$		0			0
$403$	2.19576	+	6.75786i	0.109379	+	0.336633i
$404$		0			0
$405$	−7.29612	−	5.30094i	−0.362547	−	0.263406i
$406$		0			0
$407$	10.9697	−	24.4246i	0.543749	−	1.21068i
$408$		0			0
$409$	18.4691	+	13.4186i	0.913238	+	0.663506i	0.941832	−	0.336085i	$-0.109103\pi$
$409$	18.4691	+	13.4186i	0.913238	+	0.663506i	−0.0285937	+	0.999591i	$0.509103\pi$
$410$		0			0
$411$	−9.90288	−	30.4779i	−0.488473	−	1.50336i
$412$		0			0
$413$	−4.42606	+	3.21572i	−0.217792	+	0.158235i
$414$		0			0
$415$	1.73841	−	5.35027i	0.0853352	−	0.262635i
$416$		0			0
$417$	30.9358			1.51493
$418$		0			0
$419$	5.98106			0.292194			0.146097	−	0.989270i	$-0.453329\pi$
$419$	5.98106			0.292194			0.146097	+	0.989270i	$0.453329\pi$
$420$		0			0
$421$	11.6887	−	35.9742i	0.569674	−	1.75328i	−0.0839652	−	0.996469i	$-0.526758\pi$
$421$	11.6887	−	35.9742i	0.569674	−	1.75328i	0.653639	−	0.756807i	$-0.273242\pi$
$422$		0			0
$423$	−0.00798232	+	0.00579949i	−0.000388114	+	0.000281981i
$424$		0			0
$425$	−1.11373	−	3.42772i	−0.0540240	−	0.166269i
$426$		0			0
$427$	−8.44232	−	6.13370i	−0.408552	−	0.296831i
$428$		0			0
$429$	−14.3369	−	1.55397i	−0.692191	−	0.0750262i
$430$		0			0
$431$	−5.27409	−	3.83185i	−0.254044	−	0.184574i	0.453473	−	0.891270i	$-0.350185\pi$
$431$	−5.27409	−	3.83185i	−0.254044	−	0.184574i	−0.707517	+	0.706696i	$0.750185\pi$
$432$		0			0
$433$	−8.96761	−	27.5995i	−0.430956	−	1.32635i	−0.897175	−	0.441676i	$-0.854384\pi$
$433$	−8.96761	−	27.5995i	−0.430956	−	1.32635i	0.466219	−	0.884669i	$-0.345616\pi$
$434$		0			0
$435$	−3.78673	+	2.75122i	−0.181560	+	0.131911i
$436$		0			0
$437$	4.81412	−	14.8163i	0.230291	−	0.708762i
$438$		0			0
$439$	12.2777			0.585984			0.292992	−	0.956115i	$-0.405349\pi$
$439$	12.2777			0.585984			0.292992	+	0.956115i	$0.405349\pi$
$440$		0			0
$441$	−0.0335688			−0.00159851
$442$		0			0
$443$	2.70527	−	8.32598i	0.128531	−	0.395579i	−0.865996	−	0.500050i	$-0.833315\pi$
$443$	2.70527	−	8.32598i	0.128531	−	0.395579i	0.994528	+	0.104471i	$0.0333149\pi$
$444$		0			0
$445$	−3.82529	+	2.77923i	−0.181336	+	0.131748i
$446$		0			0
$447$	3.96432	+	12.2009i	0.187506	+	0.577084i
$448$		0			0
$449$	16.9978	+	12.3496i	0.802175	+	0.582814i	0.911551	−	0.411186i	$-0.134885\pi$
$449$	16.9978	+	12.3496i	0.802175	+	0.582814i	−0.109376	+	0.994000i	$0.534885\pi$
$450$		0			0
$451$	−29.7163	+	17.0283i	−1.39929	+	0.801830i
$452$		0			0
$453$	6.19313	+	4.49957i	0.290979	+	0.211408i
$454$		0			0
$455$	−0.970419	−	2.98664i	−0.0454940	−	0.140016i
$456$		0			0
$457$	11.1794	−	8.12230i	0.522950	−	0.379945i	−0.294764	−	0.955570i	$-0.595241\pi$
$457$	11.1794	−	8.12230i	0.522950	−	0.379945i	0.817714	+	0.575625i	$0.195241\pi$
$458$		0			0
$459$	−5.78115	+	17.7925i	−0.269841	+	0.830485i
$460$		0			0
$461$	−38.6522			−1.80021			−0.900106	−	0.435672i	$-0.856511\pi$
$461$	−38.6522			−1.80021			−0.900106	+	0.435672i	$0.856511\pi$
$462$		0			0
$463$	−15.0206			−0.698066			−0.349033	−	0.937110i	$-0.613490\pi$
$463$	−15.0206			−0.698066			−0.349033	+	0.937110i	$0.613490\pi$
$464$		0			0
$465$	−1.51812	+	4.67229i	−0.0704011	+	0.216672i
$466$		0			0
$467$	−9.53857	+	6.93018i	−0.441393	+	0.320690i	−0.786188	−	0.617987i	$-0.787948\pi$
$467$	−9.53857	+	6.93018i	−0.441393	+	0.320690i	0.344795	+	0.938678i	$0.387948\pi$
$468$		0			0
$469$	−2.10236	−	6.47039i	−0.0970778	−	0.298775i
$470$		0			0
$471$	−3.26909	−	2.37513i	−0.150632	−	0.109440i
$472$		0			0
$473$	16.9220	+	15.3364i	0.778072	+	0.705169i
$474$		0			0
$475$	5.70976	+	4.14838i	0.261982	+	0.190341i
$476$		0			0
$477$	0.00338770	+	0.0104263i	0.000155112	+	0.000477386i
$478$		0			0
$479$	−14.8577	+	10.7948i	−0.678866	+	0.493225i	−0.872981	−	0.487754i	$-0.837816\pi$
$479$	−14.8577	+	10.7948i	−0.678866	+	0.493225i	0.194115	+	0.980979i	$0.437816\pi$
$480$		0			0
$481$	6.25606	−	19.2542i	0.285252	−	0.877915i
$482$		0			0
$483$	−4.79261			−0.218071
$484$		0			0
$485$	−19.0943			−0.867026
$486$		0			0
$487$	6.90222	−	21.2428i	0.312769	−	0.962605i	−0.663893	−	0.747827i	$-0.731097\pi$
$487$	6.90222	−	21.2428i	0.312769	−	0.962605i	0.976663	−	0.214778i	$-0.0689028\pi$
$488$		0			0
$489$	2.11268	−	1.53495i	0.0955388	−	0.0694130i
$490$		0			0
$491$	2.69256	+	8.28684i	0.121513	+	0.373980i	0.993250	−	0.115995i	$-0.0370058\pi$
$491$	2.69256	+	8.28684i	0.121513	+	0.373980i	−0.871736	+	0.489975i	$0.837006\pi$
$492$		0			0
$493$	7.87147	+	5.71896i	0.354513	+	0.257569i
$494$		0			0
$495$	−0.0151873	−	0.0137643i	−0.000682619	−	0.000618660i
$496$		0			0
$497$	−4.69733	−	3.41281i	−0.210704	−	0.153085i
$498$		0			0
$499$	12.0473	+	37.0779i	0.539312	+	1.65983i	0.734142	+	0.678996i	$0.237585\pi$
$499$	12.0473	+	37.0779i	0.539312	+	1.65983i	−0.194830	+	0.980837i	$0.562415\pi$
$500$		0			0
$501$	13.7427	−	9.98466i	0.613979	−	0.446082i
$502$		0			0
$503$	3.94916	−	12.1543i	0.176084	−	0.541932i	−0.823597	−	0.567175i	$-0.808036\pi$
$503$	3.94916	−	12.1543i	0.176084	−	0.541932i	0.999681	+	0.0252436i	$0.00803613\pi$
$504$		0			0
$505$	14.2252			0.633015
$506$		0			0
$507$	11.6360			0.516771
$508$		0			0
$509$	11.4262	−	35.1664i	0.506459	−	1.55872i	−0.291844	−	0.956466i	$-0.594269\pi$
$509$	11.4262	−	35.1664i	0.506459	−	1.55872i	0.798303	−	0.602256i	$-0.205731\pi$
$510$		0			0
$511$	−2.06137	+	1.49768i	−0.0911899	+	0.0662533i
$512$		0			0
$513$	−11.3208	−	34.8417i	−0.499824	−	1.53830i
$514$		0			0
$515$	−12.8484	−	9.33492i	−0.566169	−	0.411346i
$516$		0			0
$517$	4.59435	−	2.63269i	0.202059	−	0.115786i
$518$		0			0
$519$	−28.1853	−	20.4779i	−1.23720	−	0.898878i
$520$		0			0
$521$	−2.77225	−	8.53211i	−0.121454	−	0.373798i	0.871784	−	0.489891i	$-0.162963\pi$
$521$	−2.77225	−	8.53211i	−0.121454	−	0.373798i	−0.993238	+	0.116092i	$0.962963\pi$
$522$		0			0
$523$	−2.50362	+	1.81899i	−0.109476	+	0.0795387i	−0.641176	−	0.767394i	$-0.721553\pi$
$523$	−2.50362	+	1.81899i	−0.109476	+	0.0795387i	0.531701	+	0.846932i	$0.321553\pi$
$524$		0			0
$525$	0.670934	−	2.06492i	0.0292820	−	0.0901206i
$526$		0			0
$527$	10.2121			0.444846
$528$		0			0
$529$	−18.1275			−0.788154
$530$		0			0
$531$	−0.00834329	+	0.0256780i	−0.000362068	+	0.00111433i
$532$		0			0
$533$	−20.9508	+	15.2217i	−0.907481	+	0.659324i
$534$		0			0
$535$	1.25132	+	3.85116i	0.0540992	+	0.166500i
$536$		0			0
$537$	22.7307	+	16.5148i	0.980900	+	0.712666i
$538$		0			0
$539$	17.9106	+	1.94132i	0.771464	+	0.0836185i
$540$		0			0
$541$	15.2808	+	11.1022i	0.656974	+	0.477320i	0.865640	−	0.500667i	$-0.166912\pi$
$541$	15.2808	+	11.1022i	0.656974	+	0.477320i	−0.208665	+	0.977987i	$0.566912\pi$
$542$		0			0
$543$	5.05176	+	15.5477i	0.216792	+	0.667217i
$544$		0			0
$545$	4.77194	−	3.46702i	0.204407	−	0.148511i
$546$		0			0
$547$	−10.5202	+	32.3777i	−0.449810	+	1.38437i	0.427312	+	0.904104i	$0.359461\pi$
$547$	−10.5202	+	32.3777i	−0.449810	+	1.38437i	−0.877122	+	0.480268i	$0.840539\pi$
$548$		0			0
$549$	−0.0514991			−0.00219793
$550$		0			0
$551$	−19.0528			−0.811678
$552$		0			0
$553$	−6.48653	+	19.9635i	−0.275835	+	0.848934i
$554$		0			0
$555$	11.3239	−	8.22731i	0.480674	−	0.349230i
$556$		0			0
$557$	6.13777	+	18.8901i	0.260065	+	0.800399i	0.992789	+	0.119873i	$0.0382487\pi$
$557$	6.13777	+	18.8901i	0.260065	+	0.800399i	−0.732724	+	0.680526i	$0.761751\pi$
$558$		0			0
$559$	13.9701	+	10.1499i	0.590873	+	0.429294i
$560$		0			0
$561$	−8.49123	+	18.9061i	−0.358500	+	0.798216i
$562$		0			0
$563$	19.2154	+	13.9608i	0.809834	+	0.588379i	0.913782	−	0.406204i	$-0.133148\pi$
$563$	19.2154	+	13.9608i	0.809834	+	0.588379i	−0.103949	+	0.994583i	$0.533148\pi$
$564$		0			0
$565$	−1.05499	−	3.24692i	−0.0443836	−	0.136599i
$566$		0			0
$567$	−9.13655	+	6.63809i	−0.383699	+	0.278774i
$568$		0			0
$569$	11.2508	−	34.6264i	0.471658	−	1.45161i	−0.378755	−	0.925497i	$-0.623648\pi$
$569$	11.2508	−	34.6264i	0.471658	−	1.45161i	0.850413	−	0.526116i	$-0.176352\pi$
$570$		0			0
$571$	−1.49673			−0.0626362			−0.0313181	−	0.999509i	$-0.509970\pi$
$571$	−1.49673			−0.0626362			−0.0313181	+	0.999509i	$0.509970\pi$
$572$		0			0
$573$	−14.1751			−0.592172
$574$		0			0
$575$	−0.682114	+	2.09933i	−0.0284461	+	0.0875481i
$576$		0			0
$577$	−33.3772	+	24.2500i	−1.38951	+	1.00954i	−0.393594	+	0.919284i	$0.628768\pi$
$577$	−33.3772	+	24.2500i	−1.38951	+	1.00954i	−0.995919	+	0.0902557i	$0.971232\pi$
$578$		0			0
$579$	2.67634	+	8.23693i	0.111225	+	0.342315i
$580$		0			0
$581$	−5.69925	−	4.14075i	−0.236445	−	0.171787i
$582$		0			0
$583$	−1.20454	−	5.75884i	−0.0498870	−	0.238507i
$584$		0			0
$585$	−0.0125381	−	0.00910943i	−0.000518385	−	0.000376628i
$586$		0			0
$587$	12.8847	+	39.6551i	0.531810	+	1.63674i	0.750443	+	0.660935i	$0.229840\pi$
$587$	12.8847	+	39.6551i	0.531810	+	1.63674i	−0.218634	+	0.975807i	$0.570160\pi$
$588$		0			0
$589$	−16.1783	+	11.7543i	−0.666617	+	0.484326i
$590$		0			0
$591$	3.75472	−	11.5558i	0.154449	−	0.475344i
$592$		0			0
$593$	16.0656			0.659736			0.329868	−	0.944027i	$-0.392996\pi$
$593$	16.0656			0.659736			0.329868	+	0.944027i	$0.392996\pi$
$594$		0			0
$595$	−4.51324			−0.185025
$596$		0			0
$597$	−10.1136	+	31.1264i	−0.413921	+	1.27392i
$598$		0			0
$599$	20.5746	−	14.9483i	0.840655	−	0.610771i	−0.0818988	−	0.996641i	$-0.526098\pi$
$599$	20.5746	−	14.9483i	0.840655	−	0.610771i	0.922553	+	0.385869i	$0.126098\pi$
$600$		0			0
$601$	4.15982	+	12.8026i	0.169682	+	0.522229i	0.999351	−	0.0360277i	$-0.0114704\pi$
$601$	4.15982	+	12.8026i	0.169682	+	0.522229i	−0.829668	+	0.558257i	$0.811470\pi$
$602$		0			0
$603$	−0.0271630	−	0.0197350i	−0.00110616	−	0.000803673i
$604$		0			0
$605$	7.30718	+	8.22224i	0.297079	+	0.334281i
$606$		0			0
$607$	1.66478	+	1.20953i	0.0675712	+	0.0490933i	0.621058	−	0.783765i	$-0.286703\pi$
$607$	1.66478	+	1.20953i	0.0675712	+	0.0490933i	−0.553487	+	0.832858i	$0.686703\pi$
$608$		0			0
$609$	1.81126	+	5.57447i	0.0733958	+	0.225889i
$610$		0			0
$611$	3.23915	−	2.35338i	0.131042	−	0.0952074i
$612$		0			0
$613$	−11.8489	+	36.4670i	−0.478571	+	1.47289i	0.362510	+	0.931980i	$0.381920\pi$
$613$	−11.8489	+	36.4670i	−0.478571	+	1.47289i	−0.841081	+	0.540909i	$0.818080\pi$
$614$		0			0
$615$	−17.9046			−0.721982
$616$		0			0
$617$	7.25724			0.292166			0.146083	−	0.989272i	$-0.453333\pi$
$617$	7.25724			0.292166			0.146083	+	0.989272i	$0.453333\pi$
$618$		0			0
$619$	−5.44221	+	16.7494i	−0.218741	+	0.673215i	0.780126	+	0.625622i	$0.215155\pi$
$619$	−5.44221	+	16.7494i	−0.218741	+	0.673215i	−0.998867	+	0.0475925i	$0.984845\pi$
$620$		0			0
$621$	9.26969	−	6.73483i	0.371980	−	0.270259i
$622$		0			0
$623$	1.82970	+	5.63123i	0.0733052	+	0.225610i
$624$		0			0
$625$	−0.809017	−	0.587785i	−0.0323607	−	0.0235114i
$626$		0			0
$627$	−8.30907	−	39.7252i	−0.331832	−	1.58647i
$628$		0			0
$629$	−23.5390	−	17.1021i	−0.938562	−	0.681905i
$630$		0			0
$631$	−8.78700	−	27.0436i	−0.349805	−	1.07659i	−0.958961	−	0.283539i	$-0.908492\pi$
$631$	−8.78700	−	27.0436i	−0.349805	−	1.07659i	0.609156	−	0.793051i	$-0.291508\pi$
$632$		0			0
$633$	19.3135	−	14.0320i	0.767641	−	0.557724i
$634$		0			0
$635$	−1.91346	+	5.88901i	−0.0759332	+	0.233698i
$636$		0			0
$637$	13.6219			0.539718
$638$		0			0
$639$	−0.0286542			−0.00113354
$640$		0			0
$641$	−13.1372	+	40.4322i	−0.518889	+	1.59698i	0.257205	+	0.966357i	$0.417199\pi$
$641$	−13.1372	+	40.4322i	−0.518889	+	1.59698i	−0.776093	+	0.630618i	$0.782801\pi$
$642$		0			0
$643$	18.5865	−	13.5039i	0.732981	−	0.532542i	−0.157524	−	0.987515i	$-0.550351\pi$
$643$	18.5865	−	13.5039i	0.732981	−	0.532542i	0.890505	+	0.454973i	$0.150351\pi$
$644$		0			0
$645$	3.68931	+	11.3545i	0.145266	+	0.447084i
$646$		0			0
$647$	11.5392	+	8.38372i	0.453653	+	0.329598i	0.791036	−	0.611769i	$-0.209542\pi$
$647$	11.5392	+	8.38372i	0.453653	+	0.329598i	−0.337383	+	0.941367i	$0.609542\pi$
$648$		0			0
$649$	5.93654	−	13.2180i	0.233030	−	0.518851i
$650$		0			0
$651$	4.97704	+	3.61603i	0.195066	+	0.141724i
$652$		0			0
$653$	−8.29334	−	25.5243i	−0.324543	−	0.998842i	−0.971646	−	0.236439i	$-0.924020\pi$
$653$	−8.29334	−	25.5243i	−0.324543	−	0.998842i	0.647103	−	0.762403i	$-0.275980\pi$
$654$		0			0
$655$	−5.98611	+	4.34917i	−0.233897	+	0.169936i
$656$		0			0
$657$	−0.00388577	+	0.0119592i	−0.000151598	+	0.000466572i
$658$		0			0
$659$	28.8747			1.12480			0.562400	−	0.826865i	$-0.309878\pi$
$659$	28.8747			1.12480			0.562400	+	0.826865i	$0.309878\pi$
$660$		0			0
$661$	−23.6938			−0.921582			−0.460791	−	0.887509i	$-0.652434\pi$
$661$	−23.6938			−0.921582			−0.460791	+	0.887509i	$0.652434\pi$
$662$		0			0
$663$	−4.84256	+	14.9039i	−0.188070	+	0.578819i
$664$		0			0
$665$	7.15003	−	5.19480i	0.277266	−	0.201446i
$666$		0			0
$667$	−1.84144	−	5.66736i	−0.0713007	−	0.219441i
$668$		0			0
$669$	40.3944	+	29.3482i	1.56174	+	1.13467i
$670$		0			0
$671$	27.4773	+	2.97825i	1.06075	+	0.114974i
$672$		0			0
$673$	4.77758	+	3.47111i	0.184162	+	0.133802i	0.676047	−	0.736859i	$-0.263692\pi$
$673$	4.77758	+	3.47111i	0.184162	+	0.133802i	−0.491885	+	0.870660i	$0.663692\pi$
$674$		0			0
$675$	1.60404	+	4.93673i	0.0617396	+	0.190015i
$676$		0			0
$677$	−24.6423	+	17.9036i	−0.947079	+	0.688093i	−0.950114	−	0.311903i	$-0.899034\pi$
$677$	−24.6423	+	17.9036i	−0.947079	+	0.688093i	0.00303550	+	0.999995i	$0.499034\pi$
$678$		0			0
$679$	−7.38883	+	22.7405i	−0.283557	+	0.872699i
$680$		0			0
$681$	−42.0921			−1.61297
$682$		0			0
$683$	−2.95068			−0.112905			−0.0564524	−	0.998405i	$-0.517979\pi$
$683$	−2.95068			−0.112905			−0.0564524	+	0.998405i	$0.517979\pi$
$684$		0			0
$685$	−5.71155	+	17.5783i	−0.218227	+	0.671634i
$686$		0			0
$687$	−22.9949	+	16.7068i	−0.877310	+	0.637403i
$688$		0			0
$689$	−1.37469	−	4.23087i	−0.0523717	−	0.161183i
$690$		0			0
$691$	31.2400	+	22.6972i	1.18842	+	0.863441i	0.993097	−	0.117297i	$-0.0374231\pi$
$691$	31.2400	+	22.6972i	1.18842	+	0.863441i	0.195327	+	0.980738i	$0.437423\pi$
$692$		0			0
$693$	−0.0222697	+	0.0127611i	−0.000845955	+	0.000484756i
$694$		0			0
$695$	−14.4348	−	10.4875i	−0.547544	−	0.397814i
$696$		0			0
$697$	11.5011	+	35.3966i	0.435634	+	1.34074i
$698$		0			0
$699$	−3.53261	+	2.56659i	−0.133616	+	0.0970775i
$700$		0			0
$701$	10.2324	−	31.4922i	0.386474	−	1.18944i	−0.548931	−	0.835867i	$-0.684965\pi$
$701$	10.2324	−	31.4922i	0.386474	−	1.18944i	0.935405	−	0.353577i	$-0.115035\pi$
$702$		0			0
$703$	56.9760			2.14889
$704$		0			0
$705$	2.76817			0.104255
$706$		0			0
$707$	5.50468	−	16.9417i	0.207025	−	0.637157i
$708$		0			0
$709$	−17.7941	+	12.9282i	−0.668272	+	0.485528i	−0.869446	−	0.494027i	$-0.835524\pi$
$709$	−17.7941	+	12.9282i	−0.668272	+	0.485528i	0.201174	+	0.979555i	$0.435524\pi$
$710$		0			0
$711$	0.0320116	+	0.0985217i	0.00120053	+	0.00369485i
$712$		0			0
$713$	−5.05998	−	3.67629i	−0.189498	−	0.137678i
$714$		0			0
$715$	6.16286	+	5.58542i	0.230478	+	0.208883i
$716$		0			0
$717$	9.36757	+	6.80594i	0.349838	+	0.254172i
$718$		0			0
$719$	−1.85139	−	5.69798i	−0.0690450	−	0.212499i	0.910580	−	0.413332i	$-0.135635\pi$
$719$	−1.85139	−	5.69798i	−0.0690450	−	0.212499i	−0.979625	+	0.200833i	$0.935635\pi$
$720$		0			0
$721$	−16.0894	+	11.6896i	−0.599200	+	0.435344i
$722$		0			0
$723$	1.14824	−	3.53392i	0.0427035	−	0.131428i
$724$		0			0
$725$	2.69960			0.100261
$726$		0			0
$727$	−4.06512			−0.150767			−0.0753834	−	0.997155i	$-0.524018\pi$
$727$	−4.06512			−0.150767			−0.0753834	+	0.997155i	$0.524018\pi$
$728$		0			0
$729$	8.32620	−	25.6254i	0.308378	−	0.949089i
$730$		0			0
$731$	20.0776	−	14.5872i	0.742596	−	0.539528i
$732$		0			0
$733$	−9.24807	−	28.4626i	−0.341585	−	1.05129i	−0.963386	−	0.268117i	$-0.913599\pi$
$733$	−9.24807	−	28.4626i	−0.341585	−	1.05129i	0.621801	−	0.783175i	$-0.286401\pi$
$734$		0			0
$735$	7.61930	+	5.53574i	0.281042	+	0.204189i
$736$		0			0
$737$	13.3515	+	12.1005i	0.491808	+	0.445727i
$738$		0			0
$739$	15.9174	+	11.5646i	0.585530	+	0.425412i	0.840713	−	0.541480i	$-0.182136\pi$
$739$	15.9174	+	11.5646i	0.585530	+	0.425412i	−0.255184	+	0.966893i	$0.582136\pi$
$740$		0			0
$741$	−9.48281	−	29.1851i	−0.348360	−	1.07214i
$742$		0			0
$743$	21.5791	−	15.6782i	0.791662	−	0.575176i	−0.116794	−	0.993156i	$-0.537262\pi$
$743$	21.5791	−	15.6782i	0.791662	−	0.575176i	0.908456	+	0.417980i	$0.137262\pi$
$744$		0			0
$745$	2.28645	−	7.03696i	0.0837689	−	0.257814i
$746$		0			0
$747$	−0.0347660			−0.00127202
$748$		0			0
$749$	5.07079			0.185282
$750$		0			0
$751$	2.43053	−	7.48041i	0.0886914	−	0.272964i	−0.896867	−	0.442301i	$-0.854162\pi$
$751$	2.43053	−	7.48041i	0.0886914	−	0.272964i	0.985558	+	0.169336i	$0.0541625\pi$
$752$		0			0
$753$	20.1857	−	14.6657i	0.735607	−	0.534449i
$754$		0			0
$755$	−1.36436	−	4.19906i	−0.0496540	−	0.152819i
$756$		0			0
$757$	19.7853	+	14.3748i	0.719108	+	0.522463i	0.886099	−	0.463496i	$-0.153405\pi$
$757$	19.7853	+	14.3748i	0.719108	+	0.522463i	−0.166991	+	0.985958i	$0.553405\pi$
$758$		0			0
$759$	11.0134	−	6.31097i	0.399760	−	0.229074i
$760$		0			0
$761$	42.2329	+	30.6840i	1.53094	+	1.11229i	0.955712	+	0.294302i	$0.0950873\pi$
$761$	42.2329	+	30.6840i	1.53094	+	1.11229i	0.575230	+	0.817992i	$0.304913\pi$
$762$		0			0
$763$	−2.28249	−	7.02480i	−0.0826319	−	0.254315i
$764$		0			0
$765$	−0.0180195	+	0.0130919i	−0.000651495	+	0.000473339i
$766$		0			0
$767$	3.38562	−	10.4199i	0.122248	−	0.376240i
$768$		0			0
$769$	26.7480			0.964558			0.482279	−	0.876018i	$-0.339809\pi$
$769$	26.7480			0.964558			0.482279	+	0.876018i	$0.339809\pi$
$770$		0			0
$771$	−42.3114			−1.52381
$772$		0			0
$773$	−15.5257	+	47.7833i	−0.558422	+	1.71865i	0.128307	+	0.991734i	$0.459046\pi$
$773$	−15.5257	+	47.7833i	−0.558422	+	1.71865i	−0.686730	+	0.726913i	$0.740954\pi$
$774$		0			0
$775$	2.29231	−	1.66546i	0.0823423	−	0.0598252i
$776$		0			0
$777$	−5.41641	−	16.6700i	−0.194313	−	0.598033i
$778$		0			0
$779$	−58.9623	−	42.8386i	−2.11254	−	1.53485i
$780$		0			0
$781$	15.2884	+	1.65710i	0.547063	+	0.0592959i
$782$		0			0
$783$	−11.3368	−	8.23667i	−0.405144	−	0.294354i
$784$		0			0
$785$	0.720185	+	2.21650i	0.0257045	+	0.0791104i
$786$		0			0
$787$	26.1647	−	19.0098i	0.932672	−	0.677626i	−0.0139739	−	0.999902i	$-0.504448\pi$
$787$	26.1647	−	19.0098i	0.932672	−	0.677626i	0.946645	+	0.322277i	$0.104448\pi$
$788$		0			0
$789$	−0.532010	+	1.63736i	−0.0189401	+	0.0582915i
$790$		0			0
$791$	−4.27518			−0.152008
$792$		0			0
$793$	20.8978			0.742103
$794$		0			0
$795$	0.950444	−	2.92517i	0.0337088	−	0.103745i
$796$		0			0
$797$	−31.2484	+	22.7033i	−1.10688	+	0.804193i	−0.982169	−	0.188001i	$-0.939799\pi$
$797$	−31.2484	+	22.7033i	−1.10688	+	0.804193i	−0.124707	+	0.992194i	$0.539799\pi$
$798$		0			0
$799$	−1.77814	−	5.47257i	−0.0629062	−	0.193605i
$800$		0			0
$801$	0.0236401	+	0.0171756i	0.000835283	+	0.000606868i
$802$		0			0
$803$	2.76486	−	6.15609i	0.0975699	−	0.217244i
$804$		0			0
$805$	2.23626	+	1.62474i	0.0788178	+	0.0572645i
$806$		0			0
$807$	−16.3002	−	50.1668i	−0.573794	−	1.76596i
$808$		0			0
$809$	23.9627	−	17.4099i	0.842484	−	0.612101i	−0.0805792	−	0.996748i	$-0.525677\pi$
$809$	23.9627	−	17.4099i	0.842484	−	0.612101i	0.923064	+	0.384648i	$0.125677\pi$
$810$		0			0
$811$	−4.51727	+	13.9027i	−0.158623	+	0.488191i	−0.998510	−	0.0545700i	$-0.982621\pi$
$811$	−4.51727	+	13.9027i	−0.158623	+	0.488191i	0.839887	+	0.542761i	$0.182621\pi$
$812$		0			0
$813$	−44.9799			−1.57751
$814$		0			0
$815$	−1.50615			−0.0527583
$816$		0			0
$817$	−15.0175	+	46.2191i	−0.525396	+	1.61700i
$818$		0			0
$819$	−0.0157007	+	0.0114073i	−0.000548628	+	0.000398602i
$820$		0			0
$821$	8.64907	+	26.6191i	0.301855	+	0.929013i	0.980832	+	0.194854i	$0.0624233\pi$
$821$	8.64907	+	26.6191i	0.301855	+	0.929013i	−0.678978	+	0.734159i	$0.737577\pi$
$822$		0			0
$823$	−14.2865	−	10.3797i	−0.497995	−	0.361815i	0.310256	−	0.950653i	$-0.399585\pi$
$823$	−14.2865	−	10.3797i	−0.497995	−	0.361815i	−0.808251	+	0.588839i	$0.799585\pi$
$824$		0			0
$825$	1.17731	+	5.62867i	0.0409888	+	0.195965i
$826$		0			0
$827$	3.13665	+	2.27891i	0.109072	+	0.0792455i	0.640984	−	0.767554i	$-0.278526\pi$
$827$	3.13665	+	2.27891i	0.109072	+	0.0792455i	−0.531912	+	0.846800i	$0.678526\pi$
$828$		0			0
$829$	−6.43603	−	19.8081i	−0.223532	−	0.687962i	−0.998437	−	0.0558842i	$-0.982202\pi$
$829$	−6.43603	−	19.8081i	−0.223532	−	0.687962i	0.774905	−	0.632078i	$-0.217798\pi$
$830$		0			0
$831$	−7.06752	+	5.13485i	−0.245170	+	0.178126i
$832$		0			0
$833$	6.04966	−	18.6189i	0.209608	−	0.645108i
$834$		0			0
$835$	−9.79732			−0.339050
$836$		0			0
$837$	−14.7079			−0.508378
$838$		0			0
$839$	−9.02525	+	27.7769i	−0.311586	+	0.958964i	0.665551	+	0.746353i	$0.268197\pi$
$839$	−9.02525	+	27.7769i	−0.311586	+	0.958964i	−0.977137	+	0.212611i	$0.931803\pi$
$840$		0			0
$841$	17.5655	−	12.7621i	0.605707	−	0.440072i
$842$		0			0
$843$	−11.1303	−	34.2557i	−0.383349	−	1.17983i
$844$		0			0
$845$	−5.42940	−	3.94469i	−0.186777	−	0.135702i
$846$		0			0
$847$	12.6200	−	5.52082i	0.433627	−	0.189698i
$848$		0			0
$849$	−6.39111	−	4.64342i	−0.219342	−	0.159362i
$850$		0			0
$851$	5.50667	+	16.9478i	0.188766	+	0.580962i
$852$		0			0
$853$	−46.3786	+	33.6960i	−1.58797	+	1.15373i	−0.681207	+	0.732091i	$0.738545\pi$
$853$	−46.3786	+	33.6960i	−1.58797	+	1.15373i	−0.906764	+	0.421638i	$0.861455\pi$
$854$		0			0
$855$	0.0134781	−	0.0414813i	0.000460941	−	0.00141863i
$856$		0			0
$857$	43.7938			1.49597			0.747984	−	0.663717i	$-0.231022\pi$
$857$	43.7938			1.49597			0.747984	+	0.663717i	$0.231022\pi$
$858$		0			0
$859$	−32.0382			−1.09313			−0.546564	−	0.837417i	$-0.684065\pi$
$859$	−32.0382			−1.09313			−0.546564	+	0.837417i	$0.684065\pi$
$860$		0			0
$861$	−6.92846	+	21.3236i	−0.236121	+	0.726707i
$862$		0			0
$863$	−40.9055	+	29.7196i	−1.39244	+	1.01167i	−0.396846	+	0.917885i	$0.629895\pi$
$863$	−40.9055	+	29.7196i	−1.39244	+	1.01167i	−0.995593	+	0.0937806i	$0.970105\pi$
$864$		0			0
$865$	6.20927	+	19.1102i	0.211122	+	0.649765i
$866$		0			0
$867$	−5.62533	−	4.08704i	−0.191046	−	0.138803i
$868$		0			0
$869$	−11.3822	−	54.4174i	−0.386114	−	1.84599i
$870$		0			0
$871$	11.0225	+	8.00828i	0.373482	+	0.271350i
$872$		0			0
$873$	0.0364646	+	0.112226i	0.00123414	+	0.00379829i
$874$		0			0
$875$	−1.01309	+	0.736053i	−0.0342487	+	0.0248831i
$876$		0			0
$877$	6.17959	−	19.0188i	0.208670	−	0.642220i	−0.790873	−	0.611981i	$-0.790373\pi$
$877$	6.17959	−	19.0188i	0.208670	−	0.642220i	0.999543	−	0.0302393i	$-0.00962694\pi$
$878$		0			0
$879$	4.14545			0.139823
$880$		0			0
$881$	−19.7712			−0.666108			−0.333054	−	0.942908i	$-0.608079\pi$
$881$	−19.7712			−0.666108			−0.333054	+	0.942908i	$0.608079\pi$
$882$		0			0
$883$	−2.69759	+	8.30232i	−0.0907810	+	0.279395i	−0.986131	−	0.165968i	$-0.946925\pi$
$883$	−2.69759	+	8.30232i	−0.0907810	+	0.279395i	0.895350	+	0.445363i	$0.146925\pi$
$884$		0			0
$885$	6.12822	−	4.45241i	0.205998	−	0.149666i
$886$		0			0
$887$	−15.4955	−	47.6902i	−0.520287	−	1.60128i	−0.773452	−	0.633855i	$-0.781471\pi$
$887$	−15.4955	−	47.6902i	−0.520287	−	1.60128i	0.253165	−	0.967423i	$-0.418529\pi$
$888$		0			0
$889$	6.27313	+	4.55769i	0.210394	+	0.152860i
$890$		0			0
$891$	12.2546	−	27.2854i	0.410544	−	0.914095i
$892$		0			0
$893$	9.11599	+	6.62315i	0.305055	+	0.221635i
$894$		0			0
$895$	−5.00760	−	15.4118i	−0.167385	−	0.515159i
$896$		0			0
$897$	7.76473	−	5.64141i	0.259257	−	0.188361i
$898$		0			0
$899$	−2.36373	+	7.27482i	−0.0788349	+	0.242629i
$900$		0			0
$901$	−6.39345			−0.212997
$902$		0			0
$903$	14.9504			0.497518
$904$		0			0
$905$	2.91364	−	8.96725i	0.0968526	−	0.298082i
$906$		0			0
$907$	−17.4459	+	12.6752i	−0.579281	+	0.420872i	−0.838465	−	0.544956i	$-0.816547\pi$
$907$	−17.4459	+	12.6752i	−0.579281	+	0.420872i	0.259184	+	0.965828i	$0.416547\pi$
$908$		0			0
$909$	−0.0271661	−	0.0836087i	−0.000901043	−	0.00277312i
$910$		0			0
$911$	−20.9688	−	15.2347i	−0.694728	−	0.504749i	0.183483	−	0.983023i	$-0.441263\pi$
$911$	−20.9688	−	15.2347i	−0.694728	−	0.504749i	−0.878211	+	0.478274i	$0.841263\pi$
$912$		0			0
$913$	18.5494	+	2.01056i	0.613895	+	0.0665398i
$914$		0			0
$915$	11.6890	+	8.49259i	0.386428	+	0.280756i
$916$		0			0
$917$	2.86325	+	8.81219i	0.0945530	+	0.291004i
$918$		0			0
$919$	−10.6510	+	7.73843i	−0.351345	+	0.255267i	−0.749433	−	0.662080i	$-0.769674\pi$
$919$	−10.6510	+	7.73843i	−0.351345	+	0.255267i	0.398088	+	0.917347i	$0.369674\pi$
$920$		0			0
$921$	−1.75013	+	5.38633i	−0.0576686	+	0.177486i
$922$		0			0
$923$	11.6276			0.382727
$924$		0			0
$925$	−8.07294			−0.265437
$926$		0			0
$927$	−0.0303291	+	0.0933434i	−0.000996139	+	0.00306580i
$928$		0			0
$929$	−32.5849	+	23.6743i	−1.06908	+	0.776728i	−0.975746	−	0.218907i	$-0.929751\pi$
$929$	−32.5849	+	23.6743i	−1.06908	+	0.776728i	−0.0933293	+	0.995635i	$0.529751\pi$
$930$		0			0
$931$	11.8466	+	36.4600i	0.388255	+	1.19493i
$932$		0			0
$933$	3.83732	+	2.78798i	0.125628	+	0.0912743i
$934$		0			0
$935$	10.3714	−	5.94309i	0.339181	−	0.194360i
$936$		0			0
$937$	−30.2387	−	21.9697i	−0.987855	−	0.717719i	−0.0284047	−	0.999597i	$-0.509043\pi$
$937$	−30.2387	−	21.9697i	−0.987855	−	0.717719i	−0.959450	+	0.281878i	$0.909043\pi$
$938$		0			0
$939$	5.54995	+	17.0810i	0.181116	+	0.557418i
$940$		0			0
$941$	30.9226	−	22.4666i	1.00805	−	0.732389i	0.0442485	−	0.999021i	$-0.485911\pi$
$941$	30.9226	−	22.4666i	1.00805	−	0.732389i	0.963799	+	0.266632i	$0.0859107\pi$
$942$		0			0
$943$	7.04391	−	21.6789i	0.229381	−	0.705963i
$944$		0			0
$945$	6.50015			0.211450
$946$		0			0
$947$	−58.9505			−1.91564			−0.957818	−	0.287377i	$-0.907217\pi$
$947$	−58.9505			−1.91564			−0.957818	+	0.287377i	$0.907217\pi$
$948$		0			0
$949$	1.57681	−	4.85291i	0.0511853	−	0.157532i
$950$		0			0
$951$	43.8428	−	31.8536i	1.42170	−	1.03292i
$952$		0			0
$953$	6.37363	+	19.6160i	0.206462	+	0.635425i	0.999650	+	0.0264484i	$0.00841976\pi$
$953$	6.37363	+	19.6160i	0.206462	+	0.635425i	−0.793188	+	0.608977i	$0.791580\pi$
$954$		0			0
$955$	6.61417	+	4.80547i	0.214029	+	0.155502i
$956$		0			0
$957$	−11.5028	−	10.4250i	−0.371832	−	0.336992i
$958$		0			0
$959$	18.7249	+	13.6044i	0.604658	+	0.439310i
$960$		0			0
$961$	−7.09859	−	21.8472i	−0.228987	−	0.704749i
$962$		0			0
$963$	0.0202455	−	0.0147092i	0.000652402	−	0.000473998i
$964$		0			0
$965$	1.54360	−	4.75070i	0.0496901	−	0.152931i
$966$		0			0
$967$	−35.8174			−1.15181			−0.575904	−	0.817517i	$-0.695350\pi$
$967$	−35.8174			−1.15181			−0.575904	+	0.817517i	$0.695350\pi$
$968$		0			0
$969$	−44.1028			−1.41679
$970$		0			0
$971$	3.49481	−	10.7559i	0.112154	−	0.345174i	−0.879189	−	0.476473i	$-0.841915\pi$
$971$	3.49481	−	10.7559i	0.112154	−	0.345174i	0.991343	+	0.131299i	$0.0419149\pi$
$972$		0			0
$973$	−18.0760	+	13.1330i	−0.579489	+	0.421023i
$974$		0			0
$975$	1.34362	+	4.13524i	0.0430303	+	0.132434i
$976$		0			0
$977$	−18.7803	−	13.6447i	−0.600834	−	0.436531i	0.245341	−	0.969437i	$-0.421100\pi$
$977$	−18.7803	−	13.6447i	−0.600834	−	0.436531i	−0.846175	+	0.532906i	$0.821100\pi$
$978$		0			0
$979$	−11.6199	−	10.5311i	−0.371373	−	0.336577i
$980$		0			0
$981$	−0.0294904	−	0.0214260i	−0.000941556	−	0.000684080i
$982$		0			0
$983$	10.5567	+	32.4901i	0.336706	+	1.03627i	0.965876	+	0.259006i	$0.0833949\pi$
$983$	10.5567	+	32.4901i	0.336706	+	1.03627i	−0.629170	+	0.777268i	$0.716605\pi$
$984$		0			0
$985$	−5.66951	+	4.11914i	−0.180646	+	0.131247i
$986$		0			0
$987$	1.07119	−	3.29678i	0.0340963	−	0.104938i
$988$		0			0
$989$	−15.1995			−0.483316
$990$		0			0
$991$	−27.7516			−0.881560			−0.440780	−	0.897615i	$-0.645298\pi$
$991$	−27.7516			−0.881560			−0.440780	+	0.897615i	$0.645298\pi$
$992$		0			0
$993$	15.9598	−	49.1194i	0.506470	−	1.55876i
$994$		0			0
$995$	15.2712	−	11.0952i	0.484129	−	0.351740i
$996$		0			0
$997$	−13.3489	−	41.0836i	−0.422763	−	1.30113i	−0.905120	−	0.425155i	$-0.860219\pi$
$997$	−13.3489	−	41.0836i	−0.422763	−	1.30113i	0.482358	−	0.875974i	$-0.339781\pi$
$998$		0			0
$999$	33.9018	+	24.6311i	1.07261	+	0.779293i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	440.2.y.b.81.1	✓	12
4.3	odd	2		880.2.bo.j.81.3		12
11.3	even	5	inner	440.2.y.b.201.1	yes	12
11.5	even	5		4840.2.a.bf.1.2		6
11.6	odd	10		4840.2.a.be.1.2		6
44.3	odd	10		880.2.bo.j.641.3		12
44.27	odd	10		9680.2.a.cx.1.5		6
44.39	even	10		9680.2.a.cy.1.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
440.2.y.b.81.1	✓	12	1.1	even	1	trivial
440.2.y.b.201.1	yes	12	11.3	even	5	inner
880.2.bo.j.81.3		12	4.3	odd	2
880.2.bo.j.641.3		12	44.3	odd	10
4840.2.a.be.1.2		6	11.6	odd	10
4840.2.a.bf.1.2		6	11.5	even	5
9680.2.a.cx.1.5		6	44.27	odd	10
9680.2.a.cy.1.5		6	44.39	even	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 440 = 2^{3} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	440.y (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.535784 + 1.64897i) q^{3} +(0.809017 - 0.587785i) q^{5} +(-0.386966 - 1.19096i) q^{7} +(-0.00499969 - 0.00363249i) q^{9} +(2.45751 + 2.22725i) q^{11} +(2.02882 + 1.47403i) q^{13} +(0.535784 + 1.64897i) q^{15} +(2.91579 - 2.11845i) q^{17} +(-2.18093 + 6.71222i) q^{19} +2.17119 q^{21} -2.20737 q^{23} +(0.309017 - 0.951057i) q^{25} +(-4.19943 + 3.05107i) q^{27} +(0.834223 + 2.56747i) q^{29} +(2.29231 + 1.66546i) q^{31} +(-4.98937 + 2.85905i) q^{33} +(-1.01309 - 0.736053i) q^{35} +(-2.49468 - 7.67782i) q^{37} +(-3.51765 + 2.55572i) q^{39} +(-3.19109 + 9.82117i) q^{41} +6.88581 q^{43} -0.00617996 q^{45} +(0.493365 - 1.51842i) q^{47} +(4.39448 - 3.19278i) q^{49} +(1.93103 + 5.94309i) q^{51} +(-1.43514 - 1.04269i) q^{53} +(3.29731 + 0.357394i) q^{55} +(-9.89977 - 7.19261i) q^{57} +(-1.35006 - 4.15504i) q^{59} +(6.74173 - 4.89816i) q^{61} +(-0.00239143 + 0.00736007i) q^{63} +2.50777 q^{65} +5.43293 q^{67} +(1.18267 - 3.63989i) q^{69} +(3.75112 - 2.72535i) q^{71} +(-0.628770 - 1.93515i) q^{73} +(1.40270 + 1.01912i) q^{75} +(1.70159 - 3.78866i) q^{77} +(-13.5612 - 9.85278i) q^{79} +(-2.78687 - 8.57710i) q^{81} +(4.55121 - 3.30665i) q^{83} +(1.11373 - 3.42772i) q^{85} -4.68066 q^{87} -4.72832 q^{89} +(0.970419 - 2.98664i) q^{91} +(-3.97449 + 2.88764i) q^{93} +(2.18093 + 6.71222i) q^{95} +(-15.4476 - 11.2233i) q^{97} +(-0.00419634 - 0.0200624i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - q^{3} + 3 q^{5} - 8 q^{7} + 10 q^{9} - 4 q^{11} - 7 q^{13} + q^{15} + 7 q^{17} + 3 q^{19} + 4 q^{21} + 36 q^{23} - 3 q^{25} + 8 q^{27} + 13 q^{29} + 2 q^{31} - 19 q^{33} - 2 q^{35} - 22 q^{37}+ \cdots - 79 q^{99}+O(q^{100}) \) 12 * q - q^3 + 3 * q^5 - 8 * q^7 + 10 * q^9 - 4 * q^11 - 7 * q^13 + q^15 + 7 * q^17 + 3 * q^19 + 4 * q^21 + 36 * q^23 - 3 * q^25 + 8 * q^27 + 13 * q^29 + 2 * q^31 - 19 * q^33 - 2 * q^35 - 22 * q^37 - q^39 + 7 * q^41 + 6 * q^43 - 20 * q^45 - 2 * q^47 - 19 * q^49 - 33 * q^51 + 3 * q^53 + 4 * q^55 - 25 * q^57 + 19 * q^59 + 22 * q^61 - 2 * q^63 + 12 * q^65 + 22 * q^67 + 21 * q^69 + 44 * q^71 + 17 * q^73 - q^75 - 38 * q^77 - 43 * q^79 - 85 * q^81 - 15 * q^83 + 18 * q^85 + 50 * q^87 + 2 * q^89 + 59 * q^91 + 5 * q^93 - 3 * q^95 - 20 * q^97 - 79 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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