LMFDB - Embedded newform 1100.2.q.b.221.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1100,2,Mod(221,1100)] 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("1100.221"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1100, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 6, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1100 = 2^{2} \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1100.q (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [52] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$8.78354422234$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$13$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			221.5
Character	$\chi$	$=$	1100.221
Dual form			1100.2.q.b.881.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.19952 - 0.871501i) q^{3} +(1.53725 - 1.62384i) q^{5} +0.464093 q^{7} +(-0.247722 - 0.762409i) q^{9} +(-0.309017 + 0.951057i) q^{11} +(0.419514 + 1.29113i) q^{13} +(-3.25914 + 0.608119i) q^{15} +(5.73729 - 4.16839i) q^{17} +(3.40865 - 2.47653i) q^{19} +(-0.556688 - 0.404457i) q^{21} +(-0.518801 + 1.59671i) q^{23} +(-0.273745 - 4.99250i) q^{25} +(-1.74182 + 5.36077i) q^{27} +(-4.31755 - 3.13688i) q^{29} +(-1.06809 + 0.776016i) q^{31} +(1.19952 - 0.871501i) q^{33} +(0.713425 - 0.753615i) q^{35} +(-2.80832 - 8.64313i) q^{37} +(0.622007 - 1.91434i) q^{39} +(0.909817 + 2.80013i) q^{41} +3.48609 q^{43} +(-1.61884 - 0.769749i) q^{45} +(1.28006 + 0.930016i) q^{47} -6.78462 q^{49} -10.5147 q^{51} +(0.855660 + 0.621674i) q^{53} +(1.06933 + 1.96380i) q^{55} -6.24704 q^{57} +(-0.00145915 - 0.00449081i) q^{59} +(-2.14181 + 6.59180i) q^{61} +(-0.114966 - 0.353829i) q^{63} +(2.74149 + 1.30356i) q^{65} +(2.74254 - 1.99258i) q^{67} +(2.01384 - 1.46314i) q^{69} +(-7.57077 - 5.50048i) q^{71} +(4.04155 - 12.4386i) q^{73} +(-4.02261 + 6.22716i) q^{75} +(-0.143413 + 0.441379i) q^{77} +(-14.2967 - 10.3872i) q^{79} +(4.81562 - 3.49875i) q^{81} +(4.42841 - 3.21743i) q^{83} +(2.05082 - 15.7243i) q^{85} +(2.44518 + 7.52549i) q^{87} +(4.35847 - 13.4140i) q^{89} +(0.194694 + 0.599205i) q^{91} +1.95750 q^{93} +(1.21844 - 9.34216i) q^{95} +(-3.89601 - 2.83062i) q^{97} +0.801644 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - 3 q^{5} - 9 q^{9} + 13 q^{11} + 12 q^{13} - 15 q^{15} + 8 q^{17} - 10 q^{19} - 6 q^{21} + 22 q^{23} + 5 q^{25} + 21 q^{27} + 12 q^{29} - 12 q^{31} + 30 q^{35} + 15 q^{37} - 20 q^{39} - 68 q^{43}+ \cdots - 56 q^{99}+O(q^{100}) $ 52 * q - 3 * q^5 - 9 * q^9 + 13 * q^11 + 12 * q^13 - 15 * q^15 + 8 * q^17 - 10 * q^19 - 6 * q^21 + 22 * q^23 + 5 * q^25 + 21 * q^27 + 12 * q^29 - 12 * q^31 + 30 * q^35 + 15 * q^37 - 20 * q^39 - 68 * q^43 - 7 * q^45 + 19 * q^47 + 68 * q^49 + 34 * q^51 + 3 * q^53 - 2 * q^55 - 24 * q^57 - 37 * q^59 + 10 * q^61 - 8 * q^63 + 12 * q^65 + 2 * q^67 + 27 * q^69 - 3 * q^71 + 4 * q^73 + 68 * q^75 - 17 * q^79 - 39 * q^81 + 78 * q^83 + 13 * q^85 + 13 * q^87 - 7 * q^89 - 2 * q^91 - 94 * q^93 + 18 * q^95 + 15 * q^97 - 56 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1100\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$551$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$	$1$

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
$3$	−1.19952	−	0.871501i	−0.692542	−	0.503161i	0.184953	−	0.982747i	$-0.440787\pi$
$3$	−1.19952	−	0.871501i	−0.692542	−	0.503161i	−0.877495	+	0.479586i	$0.840787\pi$
$4$		0			0
$5$	1.53725	−	1.62384i	0.687478	−	0.726206i
$5$	1.53725	−	1.62384i	0.687478	−	0.726206i
$6$		0			0
$7$	0.464093			0.175411			0.0877053	−	0.996146i	$-0.472047\pi$
$7$	0.464093			0.175411			0.0877053	+	0.996146i	$0.472047\pi$
$8$		0			0
$9$	−0.247722	−	0.762409i	−0.0825739	−	0.254136i
$10$		0			0
$11$	−0.309017	+	0.951057i	−0.0931721	+	0.286754i
$11$	−0.309017	+	0.951057i	−0.0931721	+	0.286754i
$12$		0			0
$13$	0.419514	+	1.29113i	0.116352	+	0.358096i	0.992227	−	0.124444i	$-0.0397146\pi$
$13$	0.419514	+	1.29113i	0.116352	+	0.358096i	−0.875874	+	0.482539i	$0.839715\pi$
$14$		0			0
$15$	−3.25914	+	0.608119i	−0.841505	+	0.157016i
$16$		0			0
$17$	5.73729	−	4.16839i	1.39150	−	1.01098i	0.395798	−	0.918338i	$-0.370468\pi$
$17$	5.73729	−	4.16839i	1.39150	−	1.01098i	0.995699	−	0.0926445i	$-0.0295320\pi$
$18$		0			0
$19$	3.40865	−	2.47653i	0.781998	−	0.568155i	−0.123580	−	0.992335i	$-0.539437\pi$
$19$	3.40865	−	2.47653i	0.781998	−	0.568155i	0.905578	+	0.424180i	$0.139437\pi$
$20$		0			0
$21$	−0.556688	−	0.404457i	−0.121479	−	0.0882598i
$22$		0			0
$23$	−0.518801	+	1.59671i	−0.108178	+	0.332936i	−0.990463	−	0.137778i	$-0.956004\pi$
$23$	−0.518801	+	1.59671i	−0.108178	+	0.332936i	0.882286	+	0.470715i	$0.156004\pi$
$24$		0			0
$25$	−0.273745	−	4.99250i	−0.0547490	−	0.998500i
$26$		0			0
$27$	−1.74182	+	5.36077i	−0.335213	+	1.03168i
$28$		0			0
$29$	−4.31755	−	3.13688i	−0.801749	−	0.582504i	0.109678	−	0.993967i	$-0.465018\pi$
$29$	−4.31755	−	3.13688i	−0.801749	−	0.582504i	−0.911427	+	0.411463i	$0.865018\pi$
$30$		0			0
$31$	−1.06809	+	0.776016i	−0.191835	+	0.139377i	−0.679557	−	0.733623i	$-0.737828\pi$
$31$	−1.06809	+	0.776016i	−0.191835	+	0.139377i	0.487722	+	0.872999i	$0.337828\pi$
$32$		0			0
$33$	1.19952	−	0.871501i	0.208809	−	0.151709i
$34$		0			0
$35$	0.713425	−	0.753615i	0.120591	−	0.127384i
$36$		0			0
$37$	−2.80832	−	8.64313i	−0.461685	−	1.42092i	−0.863104	−	0.505027i	$-0.831483\pi$
$37$	−2.80832	−	8.64313i	−0.461685	−	1.42092i	0.401418	−	0.915895i	$-0.368517\pi$
$38$		0			0
$39$	0.622007	−	1.91434i	0.0996009	−	0.306540i
$40$		0			0
$41$	0.909817	+	2.80013i	0.142090	+	0.437307i	0.996625	−	0.0820860i	$-0.0261582\pi$
$41$	0.909817	+	2.80013i	0.142090	+	0.437307i	−0.854536	+	0.519393i	$0.826158\pi$
$42$		0			0
$43$	3.48609			0.531624			0.265812	−	0.964025i	$-0.414360\pi$
$43$	3.48609			0.531624			0.265812	+	0.964025i	$0.414360\pi$
$44$		0			0
$45$	−1.61884	−	0.769749i	−0.241323	−	0.114747i
$46$		0			0
$47$	1.28006	+	0.930016i	0.186716	+	0.135657i	0.677216	−	0.735784i	$-0.263186\pi$
$47$	1.28006	+	0.930016i	0.186716	+	0.135657i	−0.490501	+	0.871441i	$0.663186\pi$
$48$		0			0
$49$	−6.78462			−0.969231
$50$		0			0
$51$	−10.5147			−1.47236
$52$		0			0
$53$	0.855660	+	0.621674i	0.117534	+	0.0853934i	0.644999	−	0.764183i	$-0.276858\pi$
$53$	0.855660	+	0.621674i	0.117534	+	0.0853934i	−0.527465	+	0.849576i	$0.676858\pi$
$54$		0			0
$55$	1.06933	+	1.96380i	0.144189	+	0.264799i
$56$		0			0
$57$	−6.24704			−0.827440
$58$		0			0
$59$	−0.00145915	−	0.00449081i	−0.000189966	−	0.000584654i	0.950961	−	0.309309i	$-0.100098\pi$
$59$	−0.00145915	−	0.00449081i	−0.000189966	−	0.000584654i	−0.951151	+	0.308725i	$0.900098\pi$
$60$		0			0
$61$	−2.14181	+	6.59180i	−0.274230	+	0.843994i	0.715192	+	0.698928i	$0.246339\pi$
$61$	−2.14181	+	6.59180i	−0.274230	+	0.843994i	−0.989422	+	0.145066i	$0.953661\pi$
$62$		0			0
$63$	−0.114966	−	0.353829i	−0.0144843	−	0.0445782i
$64$		0			0
$65$	2.74149	+	1.30356i	0.340041	+	0.161687i
$66$		0			0
$67$	2.74254	−	1.99258i	0.335055	−	0.243432i	−0.407517	−	0.913197i	$-0.633605\pi$
$67$	2.74254	−	1.99258i	0.335055	−	0.243432i	0.742573	+	0.669766i	$0.233605\pi$
$68$		0			0
$69$	2.01384	−	1.46314i	0.242438	−	0.176142i
$70$		0			0
$71$	−7.57077	−	5.50048i	−0.898485	−	0.652787i	0.0395917	−	0.999216i	$-0.487394\pi$
$71$	−7.57077	−	5.50048i	−0.898485	−	0.652787i	−0.938076	+	0.346429i	$0.887394\pi$
$72$		0			0
$73$	4.04155	−	12.4386i	0.473028	−	1.45583i	−0.375572	−	0.926793i	$-0.622554\pi$
$73$	4.04155	−	12.4386i	0.473028	−	1.45583i	0.848599	−	0.529036i	$-0.177446\pi$
$74$		0			0
$75$	−4.02261	+	6.22716i	−0.464490	+	0.719051i
$76$		0			0
$77$	−0.143413	+	0.441379i	−0.0163434	+	0.0502998i
$78$		0			0
$79$	−14.2967	−	10.3872i	−1.60851	−	1.16865i	−0.867945	−	0.496660i	$-0.834560\pi$
$79$	−14.2967	−	10.3872i	−1.60851	−	1.16865i	−0.740562	−	0.671989i	$-0.765440\pi$
$80$		0			0
$81$	4.81562	−	3.49875i	0.535069	−	0.388750i
$82$		0			0
$83$	4.42841	−	3.21743i	0.486081	−	0.353159i	−0.317594	−	0.948227i	$-0.602875\pi$
$83$	4.42841	−	3.21743i	0.486081	−	0.353159i	0.803675	+	0.595068i	$0.202875\pi$
$84$		0			0
$85$	2.05082	−	15.7243i	0.222443	−	1.70554i
$86$		0			0
$87$	2.44518	+	7.52549i	0.262151	+	0.806817i
$88$		0			0
$89$	4.35847	−	13.4140i	0.461997	−	1.42188i	−0.400724	−	0.916199i	$-0.631241\pi$
$89$	4.35847	−	13.4140i	0.461997	−	1.42188i	0.862721	−	0.505681i	$-0.168759\pi$
$90$		0			0
$91$	0.194694	+	0.599205i	0.0204094	+	0.0628138i
$92$		0			0
$93$	1.95750			0.202983
$94$		0			0
$95$	1.21844	−	9.34216i	0.125009	−	0.958486i
$96$		0			0
$97$	−3.89601	−	2.83062i	−0.395580	−	0.287406i	0.372158	−	0.928169i	$-0.378618\pi$
$97$	−3.89601	−	2.83062i	−0.395580	−	0.287406i	−0.767738	+	0.640764i	$0.778618\pi$
$98$		0			0
$99$	0.801644			0.0805683
$100$		0			0
$101$	−5.90169			−0.587240			−0.293620	−	0.955922i	$-0.594860\pi$
$101$	−5.90169			−0.587240			−0.293620	+	0.955922i	$0.594860\pi$
$102$		0			0
$103$	11.0885	+	8.05629i	1.09258	+	0.793809i	0.979834	−	0.199814i	$-0.0640337\pi$
$103$	11.0885	+	8.05629i	1.09258	+	0.793809i	0.112751	+	0.993623i	$0.464034\pi$
$104$		0			0
$105$	−1.51254	+	0.282224i	−0.147609	+	0.0275422i
$106$		0			0
$107$	−4.64193			−0.448752			−0.224376	−	0.974503i	$-0.572034\pi$
$107$	−4.64193			−0.448752			−0.224376	+	0.974503i	$0.572034\pi$
$108$		0			0
$109$	−2.49803	−	7.68815i	−0.239268	−	0.736391i	−0.996527	−	0.0832760i	$-0.973462\pi$
$109$	−2.49803	−	7.68815i	−0.239268	−	0.736391i	0.757258	−	0.653115i	$-0.226538\pi$
$110$		0			0
$111$	−4.16386	+	12.8150i	−0.395216	+	1.21635i
$112$		0			0
$113$	5.08634	+	15.6542i	0.478483	+	1.47262i	0.841202	+	0.540721i	$0.181848\pi$
$113$	5.08634	+	15.6542i	0.478483	+	1.47262i	−0.362719	+	0.931898i	$0.618152\pi$
$114$		0			0
$115$	1.79528	+	3.29698i	0.167411	+	0.307445i
$116$		0			0
$117$	0.880448	−	0.639683i	0.0813974	−	0.0591387i
$118$		0			0
$119$	2.66264	−	1.93452i	0.244083	−	0.177337i
$120$		0			0
$121$	−0.809017	−	0.587785i	−0.0735470	−	0.0534350i
$122$		0			0
$123$	1.34897	−	4.15171i	0.121633	−	0.374347i
$124$		0			0
$125$	−8.52786	−	7.23019i	−0.762755	−	0.646688i
$126$		0			0
$127$	2.72976	−	8.40134i	0.242227	−	0.745498i	−0.753853	−	0.657043i	$-0.771807\pi$
$127$	2.72976	−	8.40134i	0.242227	−	0.745498i	0.996080	−	0.0884552i	$-0.0281930\pi$
$128$		0			0
$129$	−4.18163	−	3.03813i	−0.368172	−	0.267493i
$130$		0			0
$131$	−6.66283	+	4.84083i	−0.582134	+	0.422945i	−0.839493	−	0.543371i	$-0.817148\pi$
$131$	−6.66283	+	4.84083i	−0.582134	+	0.422945i	0.257359	+	0.966316i	$0.417148\pi$
$132$		0			0
$133$	1.58193	−	1.14934i	0.137171	−	0.0996604i
$134$		0			0
$135$	6.02745	+	11.0693i	0.518760	+	0.952690i
$136$		0			0
$137$	2.34688	+	7.22296i	0.200508	+	0.617099i	0.999868	+	0.0162471i	$0.00517185\pi$
$137$	2.34688	+	7.22296i	0.200508	+	0.617099i	−0.799360	+	0.600852i	$0.794828\pi$
$138$		0			0
$139$	−4.73085	+	14.5601i	−0.401266	+	1.23497i	0.522708	+	0.852512i	$0.324922\pi$
$139$	−4.73085	+	14.5601i	−0.401266	+	1.23497i	−0.923973	+	0.382457i	$0.875078\pi$
$140$		0			0
$141$	−0.724942	−	2.23114i	−0.0610511	−	0.187896i
$142$		0			0
$143$	−1.35758			−0.113526
$144$		0			0
$145$	−11.7309	+	2.18887i	−0.974202	+	0.181775i
$146$		0			0
$147$	8.13827	+	5.91280i	0.671233	+	0.487679i
$148$		0			0
$149$	12.2718			1.00535			0.502673	−	0.864477i	$-0.332350\pi$
$149$	12.2718			1.00535			0.502673	+	0.864477i	$0.332350\pi$
$150$		0			0
$151$	7.21724			0.587331			0.293666	−	0.955908i	$-0.405125\pi$
$151$	7.21724			0.587331			0.293666	+	0.955908i	$0.405125\pi$
$152$		0			0
$153$	−4.59927	−	3.34156i	−0.371829	−	0.270149i
$154$		0			0
$155$	−0.381795	+	2.92735i	−0.0306665	+	0.235130i
$156$		0			0
$157$	24.7873			1.97824			0.989121	−	0.147102i	$-0.0469947\pi$
$157$	24.7873			1.97824			0.989121	+	0.147102i	$0.0469947\pi$
$158$		0			0
$159$	−0.484591	−	1.49142i	−0.0384305	−	0.118277i
$160$		0			0
$161$	−0.240772	+	0.741020i	−0.0189755	+	0.0584006i
$162$		0			0
$163$	4.68678	+	14.4244i	0.367097	+	1.12981i	0.948658	+	0.316305i	$0.102442\pi$
$163$	4.68678	+	14.4244i	0.367097	+	1.12981i	−0.581561	+	0.813503i	$0.697558\pi$
$164$		0			0
$165$	0.428773	−	3.28754i	0.0333799	−	0.255935i
$166$		0			0
$167$	−7.55182	+	5.48672i	−0.584377	+	0.424575i	−0.840300	−	0.542122i	$-0.817621\pi$
$167$	−7.55182	+	5.48672i	−0.584377	+	0.424575i	0.255922	+	0.966697i	$0.417621\pi$
$168$		0			0
$169$	9.02619	−	6.55791i	0.694322	−	0.504455i
$170$		0			0
$171$	−2.73253	−	1.98530i	−0.208962	−	0.151819i
$172$		0			0
$173$	−1.79500	+	5.52445i	−0.136471	+	0.420016i	−0.995816	−	0.0913812i	$-0.970872\pi$
$173$	−1.79500	+	5.52445i	−0.136471	+	0.420016i	0.859345	+	0.511397i	$0.170872\pi$
$174$		0			0
$175$	−0.127043	−	2.31698i	−0.00960355	−	0.175148i
$176$		0			0
$177$	−0.00216347	+	0.00665846i	−0.000162616	+	0.000500481i
$178$		0			0
$179$	2.56435	+	1.86311i	0.191668	+	0.139255i	0.679481	−	0.733693i	$-0.262205\pi$
$179$	2.56435	+	1.86311i	0.191668	+	0.139255i	−0.487813	+	0.872948i	$0.662205\pi$
$180$		0			0
$181$	−9.77354	+	7.10089i	−0.726462	+	0.527805i	−0.888442	−	0.458989i	$-0.848212\pi$
$181$	−9.77354	+	7.10089i	−0.726462	+	0.527805i	0.161980	+	0.986794i	$0.448212\pi$
$182$		0			0
$183$	8.31389	−	6.04040i	0.614581	−	0.446519i
$184$		0			0
$185$	−18.3522	−	8.72634i	−1.34928	−	0.641573i
$186$		0			0
$187$	2.19145	+	6.74459i	0.160255	+	0.493213i
$188$		0			0
$189$	−0.808365	+	2.48789i	−0.0587999	+	0.180968i
$190$		0			0
$191$	7.97758	+	24.5525i	0.577237	+	1.77655i	0.628431	+	0.777865i	$0.283697\pi$
$191$	7.97758	+	24.5525i	0.577237	+	1.77655i	−0.0511934	+	0.998689i	$0.516303\pi$
$192$		0			0
$193$	8.58958			0.618291			0.309146	−	0.951015i	$-0.399957\pi$
$193$	8.58958			0.618291			0.309146	+	0.951015i	$0.399957\pi$
$194$		0			0
$195$	−2.15242	−	3.95286i	−0.154138	−	0.283070i
$196$		0			0
$197$	14.1885	+	10.3086i	1.01089	+	0.734456i	0.964396	−	0.264462i	$-0.0851945\pi$
$197$	14.1885	+	10.3086i	1.01089	+	0.734456i	0.0464960	+	0.998918i	$0.485195\pi$
$198$		0			0
$199$	14.8242			1.05086			0.525429	−	0.850837i	$-0.323905\pi$
$199$	14.8242			1.05086			0.525429	+	0.850837i	$0.323905\pi$
$200$		0			0
$201$	−5.02626			−0.354525
$202$		0			0
$203$	−2.00374	−	1.45581i	−0.140635	−	0.102177i
$204$		0			0
$205$	5.94559	+	2.82709i	0.415258	+	0.197452i
$206$		0			0
$207$	1.34586			0.0935439
$208$		0			0
$209$	1.30199	+	4.00711i	0.0900605	+	0.277178i
$210$		0			0
$211$	−7.27321	+	22.3847i	−0.500709	+	1.54102i	0.307158	+	0.951658i	$0.400622\pi$
$211$	−7.27321	+	22.3847i	−0.500709	+	1.54102i	−0.807867	+	0.589365i	$0.799378\pi$
$212$		0			0
$213$	4.28759	+	13.1959i	0.293781	+	0.904165i
$214$		0			0
$215$	5.35899	−	5.66088i	0.365480	−	0.386068i
$216$		0			0
$217$	−0.495695	+	0.360144i	−0.0336500	+	0.0244481i
$218$		0			0
$219$	−15.6882	+	11.3981i	−1.06011	+	0.770214i
$220$		0			0
$221$	7.78881	+	5.65890i	0.523932	+	0.380659i
$222$		0			0
$223$	6.40140	−	19.7015i	0.428669	−	1.31931i	−0.470767	−	0.882257i	$-0.656023\pi$
$223$	6.40140	−	19.7015i	0.428669	−	1.31931i	0.899437	−	0.437051i	$-0.143977\pi$
$224$		0			0
$225$	−3.73852	+	1.44546i	−0.249234	+	0.0963638i
$226$		0			0
$227$	−4.26135	+	13.1151i	−0.282836	+	0.870478i	0.704203	+	0.709998i	$0.251304\pi$
$227$	−4.26135	+	13.1151i	−0.282836	+	0.870478i	−0.987039	+	0.160480i	$0.948696\pi$
$228$		0			0
$229$	11.3640	+	8.25640i	0.750952	+	0.545599i	0.896122	−	0.443808i	$-0.146373\pi$
$229$	11.3640	+	8.25640i	0.750952	+	0.545599i	−0.145170	+	0.989407i	$0.546373\pi$
$230$		0			0
$231$	0.556688	−	0.404457i	0.0366274	−	0.0266113i
$232$		0			0
$233$	−7.38833	+	5.36793i	−0.484025	+	0.351665i	−0.802882	−	0.596138i	$-0.796701\pi$
$233$	−7.38833	+	5.36793i	−0.484025	+	0.351665i	0.318857	+	0.947803i	$0.396701\pi$
$234$		0			0
$235$	3.47797	−	0.648951i	0.226878	−	0.0423329i
$236$		0			0
$237$	8.09674	+	24.9192i	0.525940	+	1.61868i
$238$		0			0
$239$	4.01964	−	12.3712i	0.260009	−	0.800225i	−0.732793	−	0.680452i	$-0.761783\pi$
$239$	4.01964	−	12.3712i	0.260009	−	0.800225i	0.992801	−	0.119773i	$-0.0382166\pi$
$240$		0			0
$241$	−0.636734	−	1.95967i	−0.0410156	−	0.126233i	0.928452	−	0.371452i	$-0.121140\pi$
$241$	−0.636734	−	1.95967i	−0.0410156	−	0.126233i	−0.969468	+	0.245219i	$0.921140\pi$
$242$		0			0
$243$	8.08434			0.518611
$244$		0			0
$245$	−10.4296	+	11.0172i	−0.666325	+	0.703861i
$246$		0			0
$247$	4.62751	+	3.36208i	0.294441	+	0.213924i
$248$		0			0
$249$	−8.11594			−0.514327
$250$		0			0
$251$	−10.5583			−0.666433			−0.333217	−	0.942850i	$-0.608134\pi$
$251$	−10.5583			−0.666433			−0.333217	+	0.942850i	$0.608134\pi$
$252$		0			0
$253$	−1.35824	−	0.986819i	−0.0853918	−	0.0620408i
$254$		0			0
$255$	−16.1637	+	17.0743i	−1.01221	+	1.06923i
$256$		0			0
$257$	7.48673			0.467009			0.233505	−	0.972356i	$-0.424981\pi$
$257$	7.48673			0.467009			0.233505	+	0.972356i	$0.424981\pi$
$258$		0			0
$259$	−1.30332	−	4.01121i	−0.0809845	−	0.249245i
$260$		0			0
$261$	−1.32204	+	4.06881i	−0.0818321	+	0.251853i
$262$		0			0
$263$	−2.71213	−	8.34707i	−0.167237	−	0.514702i	0.831957	−	0.554840i	$-0.187220\pi$
$263$	−2.71213	−	8.34707i	−0.167237	−	0.514702i	−0.999194	+	0.0401375i	$0.987220\pi$
$264$		0			0
$265$	2.32486	−	0.433794i	0.142815	−	0.0266477i
$266$		0			0
$267$	−16.9184	+	12.2919i	−1.03539	+	0.752252i
$268$		0			0
$269$	−7.57051	+	5.50029i	−0.461582	+	0.335359i	−0.794151	−	0.607720i	$-0.792084\pi$
$269$	−7.57051	+	5.50029i	−0.461582	+	0.335359i	0.332570	+	0.943079i	$0.392084\pi$
$270$		0			0
$271$	−11.7867	−	8.56351i	−0.715988	−	0.520196i	0.169112	−	0.985597i	$-0.445910\pi$
$271$	−11.7867	−	8.56351i	−0.715988	−	0.520196i	−0.885100	+	0.465401i	$0.845910\pi$
$272$		0			0
$273$	0.288669	−	0.888433i	0.0174711	−	0.0537704i
$274$		0			0
$275$	4.83274	+	1.28242i	0.291425	+	0.0773329i
$276$		0			0
$277$	1.45279	−	4.47123i	0.0872897	−	0.268650i	−0.897878	−	0.440244i	$-0.854892\pi$
$277$	1.45279	−	4.47123i	0.0872897	−	0.268650i	0.985168	+	0.171594i	$0.0548918\pi$
$278$		0			0
$279$	0.856232	+	0.622089i	0.0512613	+	0.0372435i
$280$		0			0
$281$	17.6607	−	12.8313i	1.05355	−	0.765449i	0.0806656	−	0.996741i	$-0.474295\pi$
$281$	17.6607	−	12.8313i	1.05355	−	0.765449i	0.972884	+	0.231292i	$0.0742954\pi$
$282$		0			0
$283$	17.6250	−	12.8053i	1.04770	−	0.761198i	0.0759253	−	0.997114i	$-0.475809\pi$
$283$	17.6250	−	12.8053i	1.04770	−	0.761198i	0.971774	+	0.235916i	$0.0758089\pi$
$284$		0			0
$285$	−9.60324	+	10.1442i	−0.568847	+	0.600892i
$286$		0			0
$287$	0.422240	+	1.29952i	0.0249240	+	0.0767082i
$288$		0			0
$289$	10.2878	−	31.6625i	0.605163	−	1.86250i
$290$		0			0
$291$	2.20645	+	6.79075i	0.129344	+	0.398081i
$292$		0			0
$293$	3.73427			0.218158			0.109079	−	0.994033i	$-0.465210\pi$
$293$	3.73427			0.218158			0.109079	+	0.994033i	$0.465210\pi$
$294$		0			0
$295$	−0.00953547	−	0.00453405i	−0.000555176	−	0.000263983i
$296$		0			0
$297$	−4.56014	−	3.31314i	−0.264606	−	0.192248i
$298$		0			0
$299$	−2.27920			−0.131810
$300$		0			0
$301$	1.61787			0.0932525
$302$		0			0
$303$	7.07918	+	5.14333i	0.406688	+	0.295476i
$304$		0			0
$305$	7.41158	+	13.6112i	0.424386	+	0.779374i
$306$		0			0
$307$	−11.1056			−0.633829			−0.316915	−	0.948454i	$-0.602647\pi$
$307$	−11.1056			−0.633829			−0.316915	+	0.948454i	$0.602647\pi$
$308$		0			0
$309$	−6.27982	−	19.3273i	−0.357247	−	1.09949i
$310$		0			0
$311$	3.45869	−	10.6448i	0.196124	−	0.603609i	−0.803837	−	0.594849i	$-0.797212\pi$
$311$	3.45869	−	10.6448i	0.196124	−	0.603609i	0.999962	−	0.00875962i	$-0.00278831\pi$
$312$		0			0
$313$	3.05799	+	9.41152i	0.172848	+	0.531970i	0.999529	−	0.0307005i	$-0.00977380\pi$
$313$	3.05799	+	9.41152i	0.172848	+	0.531970i	−0.826681	+	0.562671i	$0.809774\pi$
$314$		0			0
$315$	−0.751294	−	0.357235i	−0.0423306	−	0.0201279i
$316$		0			0
$317$	−19.0324	+	13.8279i	−1.06897	+	0.776650i	−0.975726	−	0.218994i	$-0.929722\pi$
$317$	−19.0324	+	13.8279i	−1.06897	+	0.776650i	−0.0932403	+	0.995644i	$0.529722\pi$
$318$		0			0
$319$	4.31755	−	3.13688i	0.241736	−	0.175632i
$320$		0			0
$321$	5.56807	+	4.04544i	0.310780	+	0.225795i
$322$		0			0
$323$	9.23329	−	28.4172i	0.513754	−	1.58117i
$324$		0			0
$325$	6.33114	−	2.44787i	0.351188	−	0.135783i
$326$		0			0
$327$	−3.70380	+	11.3991i	−0.204820	+	0.630372i
$328$		0			0
$329$	0.594066	+	0.431614i	0.0327519	+	0.0237956i
$330$		0			0
$331$	12.6001	−	9.15449i	0.692563	−	0.503176i	−0.184939	−	0.982750i	$-0.559209\pi$
$331$	12.6001	−	9.15449i	0.692563	−	0.503176i	0.877502	+	0.479574i	$0.159209\pi$
$332$		0			0
$333$	−5.89392	+	4.28218i	−0.322985	+	0.234662i
$334$		0			0
$335$	0.980335	−	7.51655i	0.0535614	−	0.410673i
$336$		0			0
$337$	0.000528103		0.00162533i	2.87676e−5		8.85376e-5i	0.951071	−	0.308973i	$-0.0999852\pi$
$337$	0.000528103		0.00162533i	2.87676e−5		8.85376e-5i	−0.951042	+	0.309061i	$0.899985\pi$
$338$		0			0
$339$	7.54145	−	23.2102i	0.409595	−	1.26060i
$340$		0			0
$341$	−0.407976	−	1.25562i	−0.0220931	−	0.0679957i
$342$		0			0
$343$	−6.39734			−0.345424
$344$		0			0
$345$	0.719857	−	5.51938i	0.0387558	−	0.297153i
$346$		0			0
$347$	10.9991	+	7.99134i	0.590464	+	0.428997i	0.842481	−	0.538725i	$-0.181094\pi$
$347$	10.9991	+	7.99134i	0.590464	+	0.428997i	−0.252017	+	0.967723i	$0.581094\pi$
$348$		0			0
$349$	3.83836			0.205463			0.102731	−	0.994709i	$-0.467242\pi$
$349$	3.83836			0.205463			0.102731	+	0.994709i	$0.467242\pi$
$350$		0			0
$351$	−7.65217			−0.408443
$352$		0			0
$353$	1.76474	+	1.28216i	0.0939277	+	0.0682425i	0.633758	−	0.773531i	$-0.281512\pi$
$353$	1.76474	+	1.28216i	0.0939277	+	0.0682425i	−0.539830	+	0.841774i	$0.681512\pi$
$354$		0			0
$355$	−20.5701	+	3.83815i	−1.09175	+	0.203708i
$356$		0			0
$357$	−4.87981			−0.258267
$358$		0			0
$359$	−0.0459288	−	0.141354i	−0.00242403	−	0.00746039i	0.949837	−	0.312745i	$-0.101248\pi$
$359$	−0.0459288	−	0.141354i	−0.00242403	−	0.00746039i	−0.952261	+	0.305284i	$0.901248\pi$
$360$		0			0
$361$	−0.385618	+	1.18681i	−0.0202957	+	0.0624637i
$362$		0			0
$363$	0.458175	+	1.41012i	0.0240479	+	0.0740120i
$364$		0			0
$365$	−13.9855	−	25.6841i	−0.732035	−	1.34437i
$366$		0			0
$367$	−7.09040	+	5.15148i	−0.370116	+	0.268905i	−0.757259	−	0.653115i	$-0.773462\pi$
$367$	−7.09040	+	5.15148i	−0.370116	+	0.268905i	0.387143	+	0.922020i	$0.373462\pi$
$368$		0			0
$369$	1.90946	−	1.38731i	0.0994026	−	0.0722202i
$370$		0			0
$371$	0.397106	+	0.288514i	0.0206167	+	0.0149789i
$372$		0			0
$373$	1.56652	−	4.82125i	0.0811113	−	0.249635i	−0.902275	−	0.431162i	$-0.858104\pi$
$373$	1.56652	−	4.82125i	0.0811113	−	0.249635i	0.983386	+	0.181527i	$0.0581039\pi$
$374$		0			0
$375$	3.92821	+	16.1048i	0.202852	+	0.831647i
$376$		0			0
$377$	2.23886	−	6.89049i	0.115307	−	0.354878i
$378$		0			0
$379$	14.9583	+	10.8678i	0.768355	+	0.558242i	0.901462	−	0.432859i	$-0.142495\pi$
$379$	14.9583	+	10.8678i	0.768355	+	0.558242i	−0.133107	+	0.991102i	$0.542495\pi$
$380$		0			0
$381$	−10.5962	+	7.69857i	−0.542858	+	0.394409i
$382$		0			0
$383$	−15.6123	+	11.3430i	−0.797750	+	0.579599i	−0.910253	−	0.414052i	$-0.864113\pi$
$383$	−15.6123	+	11.3430i	−0.797750	+	0.579599i	0.112503	+	0.993651i	$0.464113\pi$
$384$		0			0
$385$	0.496270	+	0.911388i	0.0252923	+	0.0464486i
$386$		0			0
$387$	−0.863581	−	2.65783i	−0.0438983	−	0.135105i
$388$		0			0
$389$	−3.94872	+	12.1529i	−0.200208	+	0.616177i	0.799668	+	0.600442i	$0.205009\pi$
$389$	−3.94872	+	12.1529i	−0.200208	+	0.616177i	−0.999876	+	0.0157348i	$0.994991\pi$
$390$		0			0
$391$	3.67917	+	11.3233i	0.186064	+	0.572646i
$392$		0			0
$393$	12.2110			0.615962
$394$		0			0
$395$	−38.8447	+	7.24801i	−1.95449	+	0.364687i
$396$		0			0
$397$	23.3412	+	16.9584i	1.17146	+	0.851117i	0.991183	−	0.132498i	$-0.0422998\pi$
$397$	23.3412	+	16.9584i	1.17146	+	0.851117i	0.180279	+	0.983615i	$0.442300\pi$
$398$		0			0
$399$	−2.89921			−0.145142
$400$		0			0
$401$	6.67777			0.333472			0.166736	−	0.986002i	$-0.446677\pi$
$401$	6.67777			0.333472			0.166736	+	0.986002i	$0.446677\pi$
$402$		0			0
$403$	−1.45002	−	1.05350i	−0.0722306	−	0.0524786i
$404$		0			0
$405$	1.72136	−	13.1983i	0.0855353	−	0.655827i
$406$		0			0
$407$	9.08792			0.450472
$408$		0			0
$409$	6.45462	+	19.8653i	0.319160	+	0.982274i	0.974008	+	0.226514i	$0.0727328\pi$
$409$	6.45462	+	19.8653i	0.319160	+	0.982274i	−0.654848	+	0.755761i	$0.727267\pi$
$410$		0			0
$411$	3.47969	−	10.7094i	0.171640	−	0.528254i
$412$		0			0
$413$	−0.000677183	−	0.00208416i	−3.33220e−5	−	0.000102555i
$414$		0			0
$415$	1.58295	−	12.1370i	0.0777042	−	0.595783i
$416$		0			0
$417$	18.3638	−	13.3421i	0.899281	−	0.653366i
$418$		0			0
$419$	−19.2113	+	13.9578i	−0.938532	+	0.681884i	−0.948067	−	0.318071i	$-0.896965\pi$
$419$	−19.2113	+	13.9578i	−0.938532	+	0.681884i	0.00953449	+	0.999955i	$0.496965\pi$
$420$		0			0
$421$	−25.0706	−	18.2148i	−1.22186	−	0.887736i	−0.225611	−	0.974218i	$-0.572438\pi$
$421$	−25.0706	−	18.2148i	−1.22186	−	0.887736i	−0.996253	+	0.0864811i	$0.972438\pi$
$422$		0			0
$423$	0.391955	−	1.20631i	0.0190575	−	0.0586529i
$424$		0			0
$425$	−22.3812	−	27.5024i	−1.08565	−	1.33406i
$426$		0			0
$427$	−0.993997	+	3.05921i	−0.0481029	+	0.148045i
$428$		0			0
$429$	1.62844	+	1.18313i	0.0786217	+	0.0571220i
$430$		0			0
$431$	−6.38370	+	4.63803i	−0.307492	+	0.223406i	−0.730820	−	0.682571i	$-0.760862\pi$
$431$	−6.38370	+	4.63803i	−0.307492	+	0.223406i	0.423328	+	0.905977i	$0.360862\pi$
$432$		0			0
$433$	19.9149	−	14.4690i	0.957048	−	0.695336i	0.00458476	−	0.999989i	$-0.498541\pi$
$433$	19.9149	−	14.4690i	0.957048	−	0.695336i	0.952463	+	0.304653i	$0.0985406\pi$
$434$		0			0
$435$	15.9791	+	7.59794i	0.766138	+	0.364294i
$436$		0			0
$437$	2.18588	+	6.72744i	0.104565	+	0.321817i
$438$		0			0
$439$	10.4697	−	32.2223i	0.499690	−	1.53789i	−0.309829	−	0.950792i	$-0.600272\pi$
$439$	10.4697	−	32.2223i	0.499690	−	1.53789i	0.809519	−	0.587094i	$-0.199728\pi$
$440$		0			0
$441$	1.68070	+	5.17265i	0.0800332	+	0.246317i
$442$		0			0
$443$	−24.4482			−1.16157			−0.580784	−	0.814058i	$-0.697254\pi$
$443$	−24.4482			−1.16157			−0.580784	+	0.814058i	$0.697254\pi$
$444$		0			0
$445$	−15.0822	−	27.6981i	−0.714964	−	1.31301i
$446$		0			0
$447$	−14.7203	−	10.6949i	−0.696244	−	0.505851i
$448$		0			0
$449$	−7.72167			−0.364408			−0.182204	−	0.983261i	$-0.558323\pi$
$449$	−7.72167			−0.364408			−0.182204	+	0.983261i	$0.558323\pi$
$450$		0			0
$451$	−2.94423			−0.138638
$452$		0			0
$453$	−8.65721	−	6.28983i	−0.406751	−	0.295522i
$454$		0			0
$455$	1.27231	+	0.604974i	0.0596467	+	0.0283616i
$456$		0			0
$457$	35.8445			1.67674			0.838368	−	0.545105i	$-0.183510\pi$
$457$	35.8445			1.67674			0.838368	+	0.545105i	$0.183510\pi$
$458$		0			0
$459$	12.3524	+	38.0168i	0.576562	+	1.77447i
$460$		0			0
$461$	−2.06504	+	6.35554i	−0.0961785	+	0.296007i	−0.987559	−	0.157249i	$-0.949738\pi$
$461$	−2.06504	+	6.35554i	−0.0961785	+	0.296007i	0.891381	+	0.453256i	$0.149738\pi$
$462$		0			0
$463$	−2.77816	−	8.55031i	−0.129112	−	0.397367i	0.865516	−	0.500882i	$-0.166991\pi$
$463$	−2.77816	−	8.55031i	−0.129112	−	0.397367i	−0.994628	+	0.103515i	$0.966991\pi$
$464$		0			0
$465$	3.00916	−	3.17867i	0.139546	−	0.147407i
$466$		0			0
$467$	8.45021	−	6.13944i	0.391029	−	0.284099i	−0.374848	−	0.927086i	$-0.622305\pi$
$467$	8.45021	−	6.13944i	0.391029	−	0.284099i	0.765877	+	0.642987i	$0.222305\pi$
$468$		0			0
$469$	1.27280	−	0.924740i	0.0587722	−	0.0427005i
$470$		0			0
$471$	−29.7328	−	21.6022i	−1.37002	−	0.995375i
$472$		0			0
$473$	−1.07726	+	3.31547i	−0.0495326	+	0.152446i
$474$		0			0
$475$	−13.2972	−	16.3398i	−0.610117	−	0.749720i
$476$		0			0
$477$	0.262004	−	0.806365i	0.0119963	−	0.0369209i
$478$		0			0
$479$	−27.4603	−	19.9511i	−1.25469	−	0.911589i	−0.256210	−	0.966621i	$-0.582474\pi$
$479$	−27.4603	−	19.9511i	−1.25469	−	0.911589i	−0.998485	+	0.0550323i	$0.982474\pi$
$480$		0			0
$481$	9.98129	−	7.25183i	0.455107	−	0.330655i
$482$		0			0
$483$	0.934610	−	0.679034i	0.0425262	−	0.0308971i
$484$		0			0
$485$	−10.5856	+	1.97516i	−0.480668	+	0.0896874i
$486$		0			0
$487$	5.59364	+	17.2155i	0.253472	+	0.780107i	0.994127	+	0.108221i	$0.0345155\pi$
$487$	5.59364	+	17.2155i	0.253472	+	0.780107i	−0.740655	+	0.671886i	$0.765485\pi$
$488$		0			0
$489$	6.94901	−	21.3869i	0.314245	−	0.967148i
$490$		0			0
$491$	12.4829	+	38.4184i	0.563345	+	1.73380i	0.672818	+	0.739808i	$0.265084\pi$
$491$	12.4829	+	38.4184i	0.563345	+	1.73380i	−0.109473	+	0.993990i	$0.534916\pi$
$492$		0			0
$493$	−37.8468			−1.70453
$494$		0			0
$495$	1.23233	−	1.30175i	0.0553889	−	0.0585091i
$496$		0			0
$497$	−3.51354	−	2.55274i	−0.157604	−	0.114506i
$498$		0			0
$499$	26.4824			1.18551			0.592757	−	0.805382i	$-0.298040\pi$
$499$	26.4824			1.18551			0.592757	+	0.805382i	$0.298040\pi$
$500$		0			0
$501$	13.8402			0.618335
$502$		0			0
$503$	5.03971	+	3.66156i	0.224710	+	0.163261i	0.694444	−	0.719547i	$-0.255650\pi$
$503$	5.03971	+	3.66156i	0.224710	+	0.163261i	−0.469735	+	0.882808i	$0.655650\pi$
$504$		0			0
$505$	−9.07236	+	9.58343i	−0.403715	+	0.426457i
$506$		0			0
$507$	−16.5423			−0.734669
$508$		0			0
$509$	4.49613	+	13.8377i	0.199288	+	0.613344i	0.999900	+	0.0141611i	$0.00450776\pi$
$509$	4.49613	+	13.8377i	0.199288	+	0.613344i	−0.800612	+	0.599183i	$0.795492\pi$
$510$		0			0
$511$	1.87565	−	5.77267i	0.0829741	−	0.255368i
$512$		0			0
$513$	7.33885	+	22.5866i	0.324018	+	0.997225i
$514$		0			0
$515$	30.1280	−	5.62155i	1.32760	−	0.247715i
$516$		0			0
$517$	−1.28006	+	0.930016i	−0.0562969	+	0.0409021i
$518$		0			0
$519$	6.96769	−	5.06232i	0.305848	−	0.222211i
$520$		0			0
$521$	20.6718	+	15.0190i	0.905649	+	0.657992i	0.939911	−	0.341420i	$-0.110908\pi$
$521$	20.6718	+	15.0190i	0.905649	+	0.657992i	−0.0342617	+	0.999413i	$0.510908\pi$
$522$		0			0
$523$	6.89220	−	21.2120i	0.301375	−	0.927537i	−0.679630	−	0.733555i	$-0.737860\pi$
$523$	6.89220	−	21.2120i	0.301375	−	0.927537i	0.981005	−	0.193982i	$-0.0621403\pi$
$524$		0			0
$525$	−1.86686	+	2.88998i	−0.0814766	+	0.126129i
$526$		0			0
$527$	−2.89323	+	8.90446i	−0.126031	+	0.387884i
$528$		0			0
$529$	16.3271	+	11.8623i	0.709873	+	0.515753i
$530$		0			0
$531$	−0.00306237	+	0.00222495i	−0.000132896	+	9.65544e-5i
$532$		0			0
$533$	−3.23365	+	2.34939i	−0.140065	+	0.101763i
$534$		0			0
$535$	−7.13579	+	7.53777i	−0.308507	+	0.325886i
$536$		0			0
$537$	−1.45228	−	4.46966i	−0.0626706	−	0.192880i
$538$		0			0
$539$	2.09656	−	6.45255i	0.0903053	−	0.277931i
$540$		0			0
$541$	0.656452	+	2.02035i	0.0282231	+	0.0868617i	0.964176	−	0.265264i	$-0.0854590\pi$
$541$	0.656452	+	2.02035i	0.0282231	+	0.0868617i	−0.935953	+	0.352125i	$0.885459\pi$
$542$		0			0
$543$	17.9120			0.768676
$544$		0			0
$545$	−16.3245	−	7.76217i	−0.699263	−	0.332495i
$546$		0			0
$547$	−31.5061	−	22.8905i	−1.34710	−	0.978727i	−0.999150	−	0.0412153i	$-0.986877\pi$
$547$	−31.5061	−	22.8905i	−1.34710	−	0.978727i	−0.347952	−	0.937512i	$-0.613123\pi$
$548$		0			0
$549$	5.55622			0.237134
$550$		0			0
$551$	−22.4856			−0.957919
$552$		0			0
$553$	−6.63501	−	4.82061i	−0.282149	−	0.204993i
$554$		0			0
$555$	14.4088	+	26.4613i	0.611618	+	1.12322i
$556$		0			0
$557$	−35.8809			−1.52032			−0.760160	−	0.649736i	$-0.774880\pi$
$557$	−35.8809			−1.52032			−0.760160	+	0.649736i	$0.774880\pi$
$558$		0			0
$559$	1.46247	+	4.50101i	0.0618557	+	0.190372i
$560$		0			0
$561$	3.24923	−	10.0001i	0.137183	−	0.422205i
$562$		0			0
$563$	1.48314	+	4.56463i	0.0625069	+	0.192376i	0.977433	−	0.211244i	$-0.0677516\pi$
$563$	1.48314	+	4.56463i	0.0625069	+	0.192376i	−0.914926	+	0.403621i	$0.867752\pi$
$564$		0			0
$565$	33.2389	+	15.8049i	1.39837	+	0.664916i
$566$		0			0
$567$	2.23489	−	1.62375i	0.0938568	−	0.0681909i
$568$		0			0
$569$	−8.25293	+	5.99611i	−0.345981	+	0.251370i	−0.747181	−	0.664621i	$-0.768593\pi$
$569$	−8.25293	+	5.99611i	−0.345981	+	0.251370i	0.401200	+	0.915990i	$0.368593\pi$
$570$		0			0
$571$	−5.11710	−	3.71779i	−0.214144	−	0.155585i	0.475543	−	0.879693i	$-0.342252\pi$
$571$	−5.11710	−	3.71779i	−0.214144	−	0.155585i	−0.689687	+	0.724108i	$0.742252\pi$
$572$		0			0
$573$	11.8282	−	36.4036i	0.494132	−	1.52078i
$574$		0			0
$575$	8.11358	+	2.15303i	0.338360	+	0.0897874i
$576$		0			0
$577$	−1.80069	+	5.54195i	−0.0749637	+	0.230714i	−0.981516	−	0.191378i	$-0.938704\pi$
$577$	−1.80069	+	5.54195i	−0.0749637	+	0.230714i	0.906553	+	0.422093i	$0.138704\pi$
$578$		0			0
$579$	−10.3034	−	7.48582i	−0.428193	−	0.311100i
$580$		0			0
$581$	2.05519	−	1.49319i	0.0852638	−	0.0619478i
$582$		0			0
$583$	−0.855660	+	0.621674i	−0.0354378	+	0.0257471i
$584$		0			0
$585$	0.314720	−	2.41306i	0.0130121	−	0.0997678i
$586$		0			0
$587$	0.686308	+	2.11224i	0.0283270	+	0.0871814i	0.964221	−	0.265102i	$-0.0854055\pi$
$587$	0.686308	+	2.11224i	0.0283270	+	0.0871814i	−0.935894	+	0.352283i	$0.885405\pi$
$588$		0			0
$589$	−1.71893	+	5.29034i	−0.0708275	+	0.217985i
$590$		0			0
$591$	−8.03548	−	24.7306i	−0.330535	−	1.01728i
$592$		0			0
$593$	−41.1776			−1.69096			−0.845480	−	0.534007i	$-0.820686\pi$
$593$	−41.1776			−1.69096			−0.845480	+	0.534007i	$0.820686\pi$
$594$		0			0
$595$	0.951771	−	7.29754i	0.0390188	−	0.299170i
$596$		0			0
$597$	−17.7819	−	12.9193i	−0.727764	−	0.528751i
$598$		0			0
$599$	29.1938			1.19283			0.596413	−	0.802677i	$-0.296592\pi$
$599$	29.1938			1.19283			0.596413	+	0.802677i	$0.296592\pi$
$600$		0			0
$601$	43.1993			1.76214			0.881068	−	0.472990i	$-0.156825\pi$
$601$	43.1993			1.76214			0.881068	+	0.472990i	$0.156825\pi$
$602$		0			0
$603$	−2.19855	−	1.59734i	−0.0895317	−	0.0650486i
$604$		0			0
$605$	−2.19813	+	0.410147i	−0.0893667	+	0.0166749i
$606$		0			0
$607$	6.05817			0.245894			0.122947	−	0.992413i	$-0.460766\pi$
$607$	6.05817			0.245894			0.122947	+	0.992413i	$0.460766\pi$
$608$		0			0
$609$	1.13479	+	3.49253i	0.0459840	+	0.141524i
$610$		0			0
$611$	−0.663771	+	2.04288i	−0.0268533	+	0.0826460i
$612$		0			0
$613$	14.2749	+	43.9336i	0.576558	+	1.77446i	0.630813	+	0.775935i	$0.282722\pi$
$613$	14.2749	+	43.9336i	0.576558	+	1.77446i	−0.0542548	+	0.998527i	$0.517278\pi$
$614$		0			0
$615$	−4.66803	−	8.57272i	−0.188233	−	0.345686i
$616$		0			0
$617$	35.9868	−	26.1459i	1.44877	−	1.05260i	0.462657	−	0.886537i	$-0.346896\pi$
$617$	35.9868	−	26.1459i	1.44877	−	1.05260i	0.986116	−	0.166058i	$-0.0531039\pi$
$618$		0			0
$619$	37.6527	−	27.3563i	1.51339	−	1.09954i	0.548747	−	0.835988i	$-0.315105\pi$
$619$	37.6527	−	27.3563i	1.51339	−	1.09954i	0.964644	−	0.263555i	$-0.0848950\pi$
$620$		0			0
$621$	−7.65591	−	5.56234i	−0.307221	−	0.223209i
$622$		0			0
$623$	2.02273	−	6.22533i	0.0810391	−	0.249413i
$624$		0			0
$625$	−24.8501	+	2.73334i	−0.994005	+	0.109334i
$626$		0			0
$627$	1.93044	−	5.94128i	0.0770944	−	0.237272i
$628$		0			0
$629$	−52.1401	−	37.8820i	−2.07896	−	1.51045i
$630$		0			0
$631$	8.28172	−	6.01702i	0.329690	−	0.239534i	−0.410609	−	0.911811i	$-0.634684\pi$
$631$	8.28172	−	6.01702i	0.329690	−	0.239534i	0.740299	+	0.672278i	$0.234684\pi$
$632$		0			0
$633$	28.2326	−	20.5122i	1.12214	−	0.815286i
$634$		0			0
$635$	−9.44616	−	17.3476i	−0.374859	−	0.688420i
$636$		0			0
$637$	−2.84624	−	8.75984i	−0.112772	−	0.347077i
$638$		0			0
$639$	−2.31818	+	7.13461i	−0.0917056	+	0.282241i
$640$		0			0
$641$	−3.84526	−	11.8345i	−0.151878	−	0.467434i	0.845953	−	0.533258i	$-0.179032\pi$
$641$	−3.84526	−	11.8345i	−0.151878	−	0.467434i	−0.997831	+	0.0658240i	$0.979032\pi$
$642$		0			0
$643$	14.3537			0.566055			0.283027	−	0.959112i	$-0.408661\pi$
$643$	14.3537			0.566055			0.283027	+	0.959112i	$0.408661\pi$
$644$		0			0
$645$	−11.3617	+	2.11996i	−0.447365	+	0.0834734i
$646$		0			0
$647$	13.6902	+	9.94652i	0.538218	+	0.391038i	0.823423	−	0.567428i	$-0.192062\pi$
$647$	13.6902	+	9.94652i	0.538218	+	0.391038i	−0.285205	+	0.958467i	$0.592062\pi$
$648$		0			0
$649$	0.00472192			0.000185352
$650$		0			0
$651$	0.908460			0.0356054
$652$		0			0
$653$	12.9015	+	9.37352i	0.504877	+	0.366814i	0.810877	−	0.585217i	$-0.198991\pi$
$653$	12.9015	+	9.37352i	0.504877	+	0.366814i	−0.306000	+	0.952032i	$0.598991\pi$
$654$		0			0
$655$	−2.38166	+	18.2609i	−0.0930590	+	0.713514i
$656$		0			0
$657$	−10.4845			−0.409039
$658$		0			0
$659$	−15.0666	−	46.3701i	−0.586910	−	1.80632i	−0.591463	−	0.806332i	$-0.701449\pi$
$659$	−15.0666	−	46.3701i	−0.586910	−	1.80632i	0.00455338	−	0.999990i	$-0.498551\pi$
$660$		0			0
$661$	3.76122	−	11.5758i	0.146294	−	0.450248i	−0.850881	−	0.525359i	$-0.823931\pi$
$661$	3.76122	−	11.5758i	0.146294	−	0.450248i	0.997175	+	0.0751110i	$0.0239311\pi$
$662$		0			0
$663$	−4.41108	−	13.5759i	−0.171312	−	0.527244i
$664$		0			0
$665$	0.565468	−	4.33563i	0.0219279	−	0.168129i
$666$		0			0
$667$	7.24863	−	5.26644i	0.280668	−	0.203917i
$668$		0			0
$669$	−24.8484	+	18.0534i	−0.960696	+	0.697987i
$670$		0			0
$671$	−5.60732	−	4.07396i	−0.216468	−	0.157273i
$672$		0			0
$673$	11.2093	−	34.4986i	0.432086	−	1.32982i	−0.463958	−	0.885857i	$-0.653571\pi$
$673$	11.2093	−	34.4986i	0.432086	−	1.32982i	0.896044	−	0.443966i	$-0.146429\pi$
$674$		0			0
$675$	27.2404	+	7.22855i	1.04848	+	0.278227i
$676$		0			0
$677$	−5.61193	+	17.2718i	−0.215684	+	0.663808i	0.783420	+	0.621492i	$0.213473\pi$
$677$	−5.61193	+	17.2718i	−0.215684	+	0.663808i	−0.999104	+	0.0423152i	$0.986527\pi$
$678$		0			0
$679$	−1.80811	−	1.31367i	−0.0693889	−	0.0504140i
$680$		0			0
$681$	16.5414	−	12.0180i	0.633866	−	0.460531i
$682$		0			0
$683$	9.82577	−	7.13884i	0.375973	−	0.273160i	−0.383711	−	0.923453i	$-0.625354\pi$
$683$	9.82577	−	7.13884i	0.375973	−	0.273160i	0.759683	+	0.650293i	$0.225354\pi$
$684$		0			0
$685$	15.3367	+	7.29250i	0.585985	+	0.278632i
$686$		0			0
$687$	−6.43582	−	19.8074i	−0.245542	−	0.755700i
$688$		0			0
$689$	−0.443701	+	1.36557i	−0.0169037	+	0.0520241i
$690$		0			0
$691$	−9.32734	−	28.7066i	−0.354829	−	1.09205i	−0.956109	−	0.293012i	$-0.905342\pi$
$691$	−9.32734	−	28.7066i	−0.354829	−	1.09205i	0.601280	−	0.799039i	$-0.294658\pi$
$692$		0			0
$693$	0.372038			0.0141325
$694$		0			0
$695$	16.3708	+	30.0646i	0.620980	+	1.14041i
$696$		0			0
$697$	16.8919	+	12.2727i	0.639826	+	0.464861i
$698$		0			0
$699$	13.5406			0.512152
$700$		0			0
$701$	−48.4020			−1.82812			−0.914060	−	0.405580i	$-0.867070\pi$
$701$	−48.4020			−1.82812			−0.914060	+	0.405580i	$0.867070\pi$
$702$		0			0
$703$	−30.9776	−	22.5065i	−1.16834	−	0.848850i
$704$		0			0
$705$	−4.73744	−	2.25262i	−0.178422	−	0.0848387i
$706$		0			0
$707$	−2.73893			−0.103008
$708$		0			0
$709$	2.28124	+	7.02092i	0.0856736	+	0.263676i	0.984711	−	0.174195i	$-0.0557324\pi$
$709$	2.28124	+	7.02092i	0.0856736	+	0.263676i	−0.899037	+	0.437872i	$0.855732\pi$
$710$		0			0
$711$	−4.37767	+	13.4731i	−0.164175	+	0.505280i
$712$		0			0
$713$	−0.684941	−	2.10803i	−0.0256512	−	0.0789464i
$714$		0			0
$715$	−2.08693	+	2.20449i	−0.0780467	+	0.0824434i
$716$		0			0
$717$	−15.6031	+	11.3363i	−0.582709	+	0.423363i
$718$		0			0
$719$	−15.8385	+	11.5073i	−0.590675	+	0.429150i	−0.842557	−	0.538608i	$-0.818950\pi$
$719$	−15.8385	+	11.5073i	−0.590675	+	0.429150i	0.251882	+	0.967758i	$0.418950\pi$
$720$		0			0
$721$	5.14611	+	3.73887i	0.191651	+	0.139243i
$722$		0			0
$723$	−0.944076	+	2.90557i	−0.0351106	+	0.108059i
$724$		0			0
$725$	−14.4790	+	22.4141i	−0.537736	+	0.832438i
$726$		0			0
$727$	−0.712156	+	2.19179i	−0.0264124	+	0.0812890i	−0.963394	−	0.268090i	$-0.913607\pi$
$727$	−0.712156	+	2.19179i	−0.0264124	+	0.0812890i	0.936981	+	0.349379i	$0.113607\pi$
$728$		0			0
$729$	−24.1442	−	17.5418i	−0.894228	−	0.649695i
$730$		0			0
$731$	20.0007	−	14.5314i	0.739754	−	0.537463i
$732$		0			0
$733$	−17.5796	+	12.7723i	−0.649316	+	0.471756i	−0.863038	−	0.505139i	$-0.831441\pi$
$733$	−17.5796	+	12.7723i	−0.649316	+	0.471756i	0.213722	+	0.976894i	$0.431441\pi$
$734$		0			0
$735$	22.1120	−	4.12586i	0.815613	−	0.152184i
$736$		0			0
$737$	1.04756	+	3.22405i	0.0385873	+	0.118760i
$738$		0			0
$739$	−15.4525	+	47.5580i	−0.568431	+	1.74945i	0.0890998	+	0.996023i	$0.471601\pi$
$739$	−15.4525	+	47.5580i	−0.568431	+	1.74945i	−0.657531	+	0.753428i	$0.728399\pi$
$740$		0			0
$741$	−2.62072	−	8.06575i	−0.0962745	−	0.296303i
$742$		0			0
$743$	−30.3527			−1.11353			−0.556767	−	0.830669i	$-0.687958\pi$
$743$	−30.3527			−1.11353			−0.556767	+	0.830669i	$0.687958\pi$
$744$		0			0
$745$	18.8648	−	19.9275i	0.691153	−	0.730088i
$746$		0			0
$747$	−3.55001	−	2.57923i	−0.129888	−	0.0943692i
$748$		0			0
$749$	−2.15429			−0.0787159
$750$		0			0
$751$	−23.4049			−0.854057			−0.427028	−	0.904238i	$-0.640440\pi$
$751$	−23.4049			−0.854057			−0.427028	+	0.904238i	$0.640440\pi$
$752$		0			0
$753$	12.6649	+	9.20155i	0.461533	+	0.335323i
$754$		0			0
$755$	11.0947	−	11.7197i	0.403777	−	0.426523i
$756$		0			0
$757$	−0.172890			−0.00628380			−0.00314190	−	0.999995i	$-0.501000\pi$
$757$	−0.172890			−0.00628380			−0.00314190	+	0.999995i	$0.501000\pi$
$758$		0			0
$759$	0.769219	+	2.36741i	0.0279209	+	0.0859316i
$760$		0			0
$761$	−1.53270	+	4.71717i	−0.0555604	+	0.170997i	−0.974986	−	0.222267i	$-0.928654\pi$
$761$	−1.53270	+	4.71717i	−0.0555604	+	0.170997i	0.919425	+	0.393264i	$0.128654\pi$
$762$		0			0
$763$	−1.15932	−	3.56802i	−0.0419702	−	0.129171i
$764$		0			0
$765$	−12.4964	+	2.33169i	−0.451808	+	0.0843024i
$766$		0			0
$767$	0.00518610	−	0.00376792i	0.000187259	−	0.000136052i
$768$		0			0
$769$	−25.2285	+	18.3296i	−0.909762	+	0.660981i	−0.940955	−	0.338533i	$-0.890069\pi$
$769$	−25.2285	+	18.3296i	−0.909762	+	0.660981i	0.0311928	+	0.999513i	$0.490069\pi$
$770$		0			0
$771$	−8.98046	−	6.52469i	−0.323424	−	0.234981i
$772$		0			0
$773$	−12.1236	+	37.3127i	−0.436057	+	1.34204i	0.455944	+	0.890009i	$0.349302\pi$
$773$	−12.1236	+	37.3127i	−0.436057	+	1.34204i	−0.892000	+	0.452035i	$0.850698\pi$
$774$		0			0
$775$	4.16665	+	5.12003i	0.149670	+	0.183917i
$776$		0			0
$777$	−1.93242	+	5.94737i	−0.0693251	+	0.213361i
$778$		0			0
$779$	10.0359	+	7.29147i	0.359572	+	0.261244i
$780$		0			0
$781$	7.57077	−	5.50048i	0.270903	−	0.196823i
$782$		0			0
$783$	24.3365	−	17.6815i	0.869715	−	0.631885i
$784$		0			0
$785$	38.1042	−	40.2507i	1.36000	−	1.43661i
$786$		0			0
$787$	−16.2734	−	50.0842i	−0.580082	−	1.78531i	−0.618181	−	0.786036i	$-0.712130\pi$
$787$	−16.2734	−	50.0842i	−0.580082	−	1.78531i	0.0380983	−	0.999274i	$-0.487870\pi$
$788$		0			0
$789$	−4.02123	+	12.3761i	−0.143160	+	0.440600i
$790$		0			0
$791$	2.36054	+	7.26498i	0.0839310	+	0.258313i
$792$		0			0
$793$	−9.40940			−0.334138
$794$		0			0
$795$	−3.16677	−	1.50578i	−0.112314	−	0.0534044i
$796$		0			0
$797$	−27.3574	−	19.8763i	−0.969047	−	0.704054i	−0.0138129	−	0.999905i	$-0.504397\pi$
$797$	−27.3574	−	19.8763i	−0.969047	−	0.704054i	−0.955234	+	0.295851i	$0.904397\pi$
$798$		0			0
$799$	11.2207			0.396961
$800$		0			0
$801$	−11.3066			−0.399500
$802$		0			0
$803$	10.5809	+	7.68748i	0.373392	+	0.271285i
$804$		0			0
$805$	0.833176	+	1.53011i	0.0293656	+	0.0539292i
$806$		0			0
$807$	13.8745			0.488404
$808$		0			0
$809$	12.5401	+	38.5946i	0.440888	+	1.35691i	0.886931	+	0.461901i	$0.152833\pi$
$809$	12.5401	+	38.5946i	0.440888	+	1.35691i	−0.446044	+	0.895011i	$0.647167\pi$
$810$		0			0
$811$	−3.02716	+	9.31663i	−0.106298	+	0.327151i	−0.990033	−	0.140837i	$-0.955021\pi$
$811$	−3.02716	+	9.31663i	−0.106298	+	0.327151i	0.883735	+	0.467988i	$0.155021\pi$
$812$		0			0
$813$	6.67520	+	20.5442i	0.234110	+	0.720515i
$814$		0			0
$815$	30.6277	+	14.5633i	1.07284	+	0.510130i
$816$		0			0
$817$	11.8829	−	8.63342i	0.415729	−	0.302045i
$818$		0			0
$819$	0.408610	−	0.296872i	0.0142780	−	0.0103736i
$820$		0			0
$821$	24.7622	+	17.9908i	0.864208	+	0.627884i	0.929027	−	0.370013i	$-0.120647\pi$
$821$	24.7622	+	17.9908i	0.864208	+	0.627884i	−0.0648183	+	0.997897i	$0.520647\pi$
$822$		0			0
$823$	−1.60741	+	4.94710i	−0.0560308	+	0.172445i	−0.975155	−	0.221522i	$-0.928898\pi$
$823$	−1.60741	+	4.94710i	−0.0560308	+	0.172445i	0.919125	+	0.393967i	$0.128898\pi$
$824$		0			0
$825$	−4.67933	−	5.75002i	−0.162913	−	0.200190i
$826$		0			0
$827$	7.53349	−	23.1857i	0.261965	−	0.806246i	−0.730412	−	0.683007i	$-0.760672\pi$
$827$	7.53349	−	23.1857i	0.261965	−	0.806246i	0.992377	−	0.123239i	$-0.0393282\pi$
$828$		0			0
$829$	−14.5777	−	10.5913i	−0.506305	−	0.367852i	0.305115	−	0.952316i	$-0.401305\pi$
$829$	−14.5777	−	10.5913i	−0.506305	−	0.367852i	−0.811420	+	0.584463i	$0.801305\pi$
$830$		0			0
$831$	−5.63933	+	4.09721i	−0.195626	+	0.142131i
$832$		0			0
$833$	−38.9253	+	28.2809i	−1.34868	+	0.979875i
$834$		0			0
$835$	−2.69943	+	20.6974i	−0.0934177	+	0.716264i
$836$		0			0
$837$	−2.29961	−	7.07748i	−0.0794863	−	0.244634i
$838$		0			0
$839$	−10.4430	+	32.1402i	−0.360532	+	1.10960i	0.592200	+	0.805791i	$0.298260\pi$
$839$	−10.4430	+	32.1402i	−0.360532	+	1.10960i	−0.952732	+	0.303812i	$0.901740\pi$
$840$		0			0
$841$	−0.160300	−	0.493353i	−0.00552759	−	0.0170122i
$842$		0			0
$843$	−32.3668			−1.11477
$844$		0			0
$845$	3.22645	−	24.7383i	0.110993	−	0.851022i
$846$		0			0
$847$	−0.375459	−	0.272787i	−0.0129009	−	0.00937307i
$848$		0			0
$849$	−32.3014			−1.10858
$850$		0			0
$851$	15.2575			0.523020
$852$		0			0
$853$	−0.867634	−	0.630373i	−0.0297072	−	0.0215836i	0.572833	−	0.819672i	$-0.305845\pi$
$853$	−0.867634	−	0.630373i	−0.0297072	−	0.0215836i	−0.602540	+	0.798089i	$0.705845\pi$
$854$		0			0
$855$	−7.42438	+	1.38531i	−0.253909	+	0.0473766i
$856$		0			0
$857$	46.2028			1.57826			0.789129	−	0.614227i	$-0.210532\pi$
$857$	46.2028			1.57826			0.789129	+	0.614227i	$0.210532\pi$
$858$		0			0
$859$	−4.44234	−	13.6721i	−0.151571	−	0.466487i	0.846227	−	0.532823i	$-0.178869\pi$
$859$	−4.44234	−	13.6721i	−0.151571	−	0.466487i	−0.997797	+	0.0663366i	$0.978869\pi$
$860$		0			0
$861$	0.626048	−	1.92678i	0.0213357	−	0.0656644i
$862$		0			0
$863$	9.20537	+	28.3312i	0.313354	+	0.964406i	0.976426	+	0.215850i	$0.0692523\pi$
$863$	9.20537	+	28.3312i	0.313354	+	0.964406i	−0.663072	+	0.748556i	$0.730748\pi$
$864$		0			0
$865$	6.21148	+	11.4072i	0.211197	+	0.387858i
$866$		0			0
$867$	−39.9343	+	29.0139i	−1.35624	+	0.985365i
$868$		0			0
$869$	14.2967	−	10.3872i	0.484983	−	0.352361i
$870$		0			0
$871$	3.72321	+	2.70507i	0.126156	+	0.0916579i
$872$		0			0
$873$	−1.19296	+	3.67156i	−0.0403756	+	0.124263i
$874$		0			0
$875$	−3.95772	−	3.35548i	−0.133795	−	0.113436i
$876$		0			0
$877$	2.63780	−	8.11831i	0.0890722	−	0.274136i	−0.896591	−	0.442859i	$-0.853964\pi$
$877$	2.63780	−	8.11831i	0.0890722	−	0.274136i	0.985664	+	0.168723i	$0.0539643\pi$
$878$		0			0
$879$	−4.47932	−	3.25441i	−0.151084	−	0.109769i
$880$		0			0
$881$	17.1509	−	12.4609i	0.577829	−	0.419817i	−0.260112	−	0.965578i	$-0.583759\pi$
$881$	17.1509	−	12.4609i	0.577829	−	0.419817i	0.837941	+	0.545761i	$0.183759\pi$
$882$		0			0
$883$	−33.2676	+	24.1703i	−1.11954	+	0.813395i	−0.984140	−	0.177395i	$-0.943233\pi$
$883$	−33.2676	+	24.1703i	−1.11954	+	0.813395i	−0.135403	+	0.990791i	$0.543233\pi$
$884$		0			0
$885$	0.00748653	+	0.0137488i	0.000251657	+	0.000462162i
$886$		0			0
$887$	−13.3900	−	41.2103i	−0.449594	−	1.38371i	−0.877367	−	0.479821i	$-0.840702\pi$
$887$	−13.3900	−	41.2103i	−0.449594	−	1.38371i	0.427773	−	0.903886i	$-0.359298\pi$
$888$		0			0
$889$	1.26686	−	3.89900i	0.0424892	−	0.130768i
$890$		0			0
$891$	1.83940	+	5.66110i	0.0616223	+	0.189654i
$892$		0			0
$893$	6.66648			0.223085
$894$		0			0
$895$	6.96744	−	1.30005i	0.232896	−	0.0434558i
$896$		0			0
$897$	2.73394	+	1.98633i	0.0912837	+	0.0663215i
$898$		0			0
$899$	7.04582			0.234991
$900$		0			0
$901$	7.50055			0.249879
$902$		0			0
$903$	−1.94067	−	1.40998i	−0.0645813	−	0.0469211i
$904$		0			0
$905$	−3.49360	+	26.7865i	−0.116131	+	0.890415i
$906$		0			0
$907$	−40.7634			−1.35353			−0.676764	−	0.736200i	$-0.736618\pi$
$907$	−40.7634			−1.35353			−0.676764	+	0.736200i	$0.736618\pi$
$908$		0			0
$909$	1.46198	+	4.49950i	0.0484907	+	0.149239i
$910$		0			0
$911$	1.49594	−	4.60402i	0.0495626	−	0.152538i	−0.923212	−	0.384291i	$-0.874446\pi$
$911$	1.49594	−	4.60402i	0.0495626	−	0.152538i	0.972775	+	0.231753i	$0.0744460\pi$
$912$		0			0
$913$	1.69150	+	5.20591i	0.0559805	+	0.172290i
$914$		0			0
$915$	2.97184	−	22.7861i	0.0982459	−	0.753284i
$916$		0			0
$917$	−3.09217	+	2.24659i	−0.102113	+	0.0741891i
$918$		0			0
$919$	3.56227	−	2.58814i	0.117508	−	0.0853749i	−0.527479	−	0.849568i	$-0.676863\pi$
$919$	3.56227	−	2.58814i	0.117508	−	0.0853749i	0.644987	+	0.764193i	$0.276863\pi$
$920$		0			0
$921$	13.3214	+	9.67853i	0.438953	+	0.318918i
$922$		0			0
$923$	3.92581	−	12.0824i	0.129219	−	0.397697i
$924$		0			0
$925$	−42.3821	+	16.3866i	−1.39351	+	0.538787i
$926$		0			0
$927$	3.39532	−	10.4497i	0.111517	−	0.343214i
$928$		0			0
$929$	−21.4271	−	15.5677i	−0.703001	−	0.510760i	0.177907	−	0.984047i	$-0.443067\pi$
$929$	−21.4271	−	15.5677i	−0.703001	−	0.510760i	−0.880908	+	0.473287i	$0.843067\pi$
$930$		0			0
$931$	−23.1264	+	16.8023i	−0.757937	+	0.550674i
$932$		0			0
$933$	−13.4257	+	9.75433i	−0.439537	+	0.319342i
$934$		0			0
$935$	14.3210	+	6.80952i	0.468346	+	0.222695i
$936$		0			0
$937$	1.36826	+	4.21108i	0.0446992	+	0.137570i	0.970915	−	0.239423i	$-0.0769582\pi$
$937$	1.36826	+	4.21108i	0.0446992	+	0.137570i	−0.926216	+	0.376993i	$0.876958\pi$
$938$		0			0
$939$	4.53403	−	13.9543i	0.147963	−	0.455382i
$940$		0			0
$941$	11.7507	+	36.1651i	0.383063	+	1.17895i	0.937875	+	0.346972i	$0.112790\pi$
$941$	11.7507	+	36.1651i	0.383063	+	1.17895i	−0.554812	+	0.831976i	$0.687210\pi$
$942$		0			0
$943$	−4.94300			−0.160966
$944$		0			0
$945$	2.79730	+	5.13717i	0.0909960	+	0.167112i
$946$		0			0
$947$	35.5912	+	25.8585i	1.15656	+	0.840289i	0.989339	−	0.145631i	$-0.0465213\pi$
$947$	35.5912	+	25.8585i	1.15656	+	0.840289i	0.167219	+	0.985920i	$0.446521\pi$
$948$		0			0
$949$	17.7554			0.576364
$950$		0			0
$951$	34.8807			1.13108
$952$		0			0
$953$	10.4998	+	7.62855i	0.340122	+	0.247113i	0.744713	−	0.667385i	$-0.232586\pi$
$953$	10.4998	+	7.62855i	0.340122	+	0.247113i	−0.404591	+	0.914498i	$0.632586\pi$
$954$		0			0
$955$	52.1329	+	24.7888i	1.68698	+	0.802148i
$956$		0			0
$957$	−7.91277			−0.255784
$958$		0			0
$959$	1.08917	+	3.35212i	0.0351712	+	0.108246i
$960$		0			0
$961$	−9.04090	+	27.8250i	−0.291642	+	0.897582i
$962$		0			0
$963$	1.14991	+	3.53905i	0.0370552	+	0.114044i
$964$		0			0
$965$	13.2043	−	13.9481i	0.425062	−	0.449007i
$966$		0			0
$967$	36.4732	−	26.4993i	1.17290	−	0.852160i	0.181545	−	0.983383i	$-0.441890\pi$
$967$	36.4732	−	26.4993i	1.17290	−	0.852160i	0.991353	+	0.131223i	$0.0418903\pi$
$968$		0			0
$969$	−35.8411	+	26.0401i	−1.15138	+	0.836527i
$970$		0			0
$971$	28.5664	+	20.7547i	0.916739	+	0.666050i	0.942710	−	0.333613i	$-0.108268\pi$
$971$	28.5664	+	20.7547i	0.916739	+	0.666050i	−0.0259710	+	0.999663i	$0.508268\pi$
$972$		0			0
$973$	−2.19556	+	6.75722i	−0.0703863	+	0.216627i
$974$		0			0
$975$	−9.72763	−	2.58133i	−0.311533	−	0.0826688i
$976$		0			0
$977$	−8.78133	+	27.0262i	−0.280940	+	0.864643i	0.706647	+	0.707567i	$0.250207\pi$
$977$	−8.78133	+	27.0262i	−0.280940	+	0.864643i	−0.987586	+	0.157077i	$0.949793\pi$
$978$		0			0
$979$	11.4106	+	8.29030i	0.364685	+	0.264959i
$980$		0			0
$981$	−5.24270	+	3.80904i	−0.167387	+	0.121613i
$982$		0			0
$983$	29.3225	−	21.3041i	0.935244	−	0.679494i	−0.0120274	−	0.999928i	$-0.503829\pi$
$983$	29.3225	−	21.3041i	0.935244	−	0.679494i	0.947271	+	0.320433i	$0.103829\pi$
$984$		0			0
$985$	38.5508	−	7.19316i	1.22833	−	0.229193i
$986$		0			0
$987$	−0.336440	−	1.03546i	−0.0107090	−	0.0329590i
$988$		0			0
$989$	−1.80859	+	5.56627i	−0.0575098	+	0.176997i
$990$		0			0
$991$	13.1758	+	40.5511i	0.418545	+	1.28815i	0.909042	+	0.416705i	$0.136815\pi$
$991$	13.1758	+	40.5511i	0.418545	+	1.28815i	−0.490497	+	0.871443i	$0.663185\pi$
$992$		0			0
$993$	−23.0922			−0.732807
$994$		0			0
$995$	22.7884	−	24.0722i	0.722442	−	0.763140i
$996$		0			0
$997$	−43.8347	−	31.8478i	−1.38826	−	1.00863i	−0.996054	−	0.0887521i	$-0.971712\pi$
$997$	−43.8347	−	31.8478i	−1.38826	−	1.00863i	−0.392206	−	0.919877i	$-0.628288\pi$
$998$		0			0
$999$	51.2254			1.62070

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1100.2.q.b.221.5	✓	52
25.6	even	5	inner	1100.2.q.b.881.5	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1100.2.q.b.221.5	✓	52	1.1	even	1	trivial
1100.2.q.b.881.5	yes	52	25.6	even	5	inner

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:	\( N \)	\(=\)	\( 1100 = 2^{2} \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1100.q (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.19952 - 0.871501i) q^{3} +(1.53725 - 1.62384i) q^{5} +0.464093 q^{7} +(-0.247722 - 0.762409i) q^{9} +(-0.309017 + 0.951057i) q^{11} +(0.419514 + 1.29113i) q^{13} +(-3.25914 + 0.608119i) q^{15} +(5.73729 - 4.16839i) q^{17} +(3.40865 - 2.47653i) q^{19} +(-0.556688 - 0.404457i) q^{21} +(-0.518801 + 1.59671i) q^{23} +(-0.273745 - 4.99250i) q^{25} +(-1.74182 + 5.36077i) q^{27} +(-4.31755 - 3.13688i) q^{29} +(-1.06809 + 0.776016i) q^{31} +(1.19952 - 0.871501i) q^{33} +(0.713425 - 0.753615i) q^{35} +(-2.80832 - 8.64313i) q^{37} +(0.622007 - 1.91434i) q^{39} +(0.909817 + 2.80013i) q^{41} +3.48609 q^{43} +(-1.61884 - 0.769749i) q^{45} +(1.28006 + 0.930016i) q^{47} -6.78462 q^{49} -10.5147 q^{51} +(0.855660 + 0.621674i) q^{53} +(1.06933 + 1.96380i) q^{55} -6.24704 q^{57} +(-0.00145915 - 0.00449081i) q^{59} +(-2.14181 + 6.59180i) q^{61} +(-0.114966 - 0.353829i) q^{63} +(2.74149 + 1.30356i) q^{65} +(2.74254 - 1.99258i) q^{67} +(2.01384 - 1.46314i) q^{69} +(-7.57077 - 5.50048i) q^{71} +(4.04155 - 12.4386i) q^{73} +(-4.02261 + 6.22716i) q^{75} +(-0.143413 + 0.441379i) q^{77} +(-14.2967 - 10.3872i) q^{79} +(4.81562 - 3.49875i) q^{81} +(4.42841 - 3.21743i) q^{83} +(2.05082 - 15.7243i) q^{85} +(2.44518 + 7.52549i) q^{87} +(4.35847 - 13.4140i) q^{89} +(0.194694 + 0.599205i) q^{91} +1.95750 q^{93} +(1.21844 - 9.34216i) q^{95} +(-3.89601 - 2.83062i) q^{97} +0.801644 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 3 q^{5} - 9 q^{9} + 13 q^{11} + 12 q^{13} - 15 q^{15} + 8 q^{17} - 10 q^{19} - 6 q^{21} + 22 q^{23} + 5 q^{25} + 21 q^{27} + 12 q^{29} - 12 q^{31} + 30 q^{35} + 15 q^{37} - 20 q^{39} - 68 q^{43}+ \cdots - 56 q^{99}+O(q^{100}) \) 52 * q - 3 * q^5 - 9 * q^9 + 13 * q^11 + 12 * q^13 - 15 * q^15 + 8 * q^17 - 10 * q^19 - 6 * q^21 + 22 * q^23 + 5 * q^25 + 21 * q^27 + 12 * q^29 - 12 * q^31 + 30 * q^35 + 15 * q^37 - 20 * q^39 - 68 * q^43 - 7 * q^45 + 19 * q^47 + 68 * q^49 + 34 * q^51 + 3 * q^53 - 2 * q^55 - 24 * q^57 - 37 * q^59 + 10 * q^61 - 8 * q^63 + 12 * q^65 + 2 * q^67 + 27 * q^69 - 3 * q^71 + 4 * q^73 + 68 * q^75 - 17 * q^79 - 39 * q^81 + 78 * q^83 + 13 * q^85 + 13 * q^87 - 7 * q^89 - 2 * q^91 - 94 * q^93 + 18 * q^95 + 15 * q^97 - 56 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more