LMFDB - Embedded newform 572.2.bq.a.49.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(49,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 12, 25]))

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

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

chi := DirichletCharacter("572.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.bq (of order $30$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$14$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			49.7
Character	$\chi$	$=$	572.49
Dual form			572.2.bq.a.537.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0476950 + 0.453788i) q^{3} +(-3.72881 - 1.21156i) q^{5} +(0.128901 - 0.0135480i) q^{7} +(2.73079 + 0.580448i) q^{9} +O(q^{10})$	\(q+(-0.0476950 + 0.453788i) q^{3} +(-3.72881 - 1.21156i) q^{5} +(0.128901 - 0.0135480i) q^{7} +(2.73079 + 0.580448i) q^{9} +(3.18108 + 0.938485i) q^{11} +(-2.13957 + 2.90211i) q^{13} +(0.727638 - 1.63430i) q^{15} +(2.49450 + 2.77042i) q^{17} +(-1.96575 - 4.41515i) q^{19} +0.0591397i q^{21} +(3.42619 + 5.93434i) q^{23} +(8.39104 + 6.09645i) q^{25} +(-0.816647 + 2.51338i) q^{27} +(6.80110 + 3.02804i) q^{29} +(4.74701 - 1.54240i) q^{31} +(-0.577595 + 1.39877i) q^{33} +(-0.497060 - 0.105653i) q^{35} +(1.23304 - 2.76946i) q^{37} +(-1.21489 - 1.10933i) q^{39} +(8.74488 + 0.919124i) q^{41} +(-4.73852 + 8.20736i) q^{43} +(-9.47936 - 5.47291i) q^{45} +(-5.37278 + 7.39500i) q^{47} +(-6.83060 + 1.45189i) q^{49} +(-1.37616 + 0.999837i) q^{51} +(-1.51016 - 4.64779i) q^{53} +(-10.7246 - 7.35351i) q^{55} +(2.09730 - 0.681453i) q^{57} +(6.51121 - 0.684356i) q^{59} +(-7.25934 - 8.06231i) q^{61} +(0.359865 + 0.0378234i) q^{63} +(11.4941 - 8.22918i) q^{65} +(5.04304 - 2.91160i) q^{67} +(-2.85634 + 1.27173i) q^{69} +(-8.48501 + 7.63994i) q^{71} +(1.01482 + 1.39678i) q^{73} +(-3.16670 + 3.51698i) q^{75} +(0.422758 + 0.0778742i) q^{77} +(-3.87049 - 11.9121i) q^{79} +(6.54972 + 2.91612i) q^{81} +(4.35448 + 1.41486i) q^{83} +(-5.94496 - 13.3526i) q^{85} +(-1.69847 + 2.94183i) q^{87} +(-7.27757 + 4.20171i) q^{89} +(-0.236475 + 0.403071i) q^{91} +(0.473512 + 2.22770i) q^{93} +(1.98068 + 18.8449i) q^{95} +(2.19971 - 10.3488i) q^{97} +(8.14212 + 4.40926i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q + 20 q^{9}+O(q^{10}) $ 112 * q + 20 * q^9	$ 112 q + 20 q^{9} - 6 q^{11} + 11 q^{13} + 30 q^{15} + 16 q^{17} - 12 q^{19} + 6 q^{23} + 40 q^{25} - 12 q^{27} - 5 q^{29} + 9 q^{33} - 33 q^{35} - 45 q^{39} - 18 q^{41} + 30 q^{45} - 16 q^{49} + 48 q^{51} - 2 q^{53} - 20 q^{55} - 39 q^{59} + 4 q^{61} - 102 q^{63} - 6 q^{65} + 48 q^{67} + 34 q^{69} + 84 q^{71} - 56 q^{75} - 22 q^{77} - 24 q^{79} + 16 q^{81} + 60 q^{85} - 34 q^{87} - 66 q^{89} - 41 q^{91} + 123 q^{93} + 12 q^{95} - 15 q^{97}+O(q^{100}) $ 112 * q + 20 * q^9 - 6 * q^11 + 11 * q^13 + 30 * q^15 + 16 * q^17 - 12 * q^19 + 6 * q^23 + 40 * q^25 - 12 * q^27 - 5 * q^29 + 9 * q^33 - 33 * q^35 - 45 * q^39 - 18 * q^41 + 30 * q^45 - 16 * q^49 + 48 * q^51 - 2 * q^53 - 20 * q^55 - 39 * q^59 + 4 * q^61 - 102 * q^63 - 6 * q^65 + 48 * q^67 + 34 * q^69 + 84 * q^71 - 56 * q^75 - 22 * q^77 - 24 * q^79 + 16 * q^81 + 60 * q^85 - 34 * q^87 - 66 * q^89 - 41 * q^91 + 123 * q^93 + 12 * q^95 - 15 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{5}\right)$

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
$3$	−0.0476950	+	0.453788i	−0.0275367	+	0.261994i	0.972088	+	0.234615i	$0.0753829\pi$
$3$	−0.0476950	+	0.453788i	−0.0275367	+	0.261994i	−0.999625	+	0.0273795i	$0.991284\pi$
$4$		0			0
$5$	−3.72881	−	1.21156i	−1.66757	−	0.541828i	−0.685136	−	0.728416i	$-0.740257\pi$
$5$	−3.72881	−	1.21156i	−1.66757	−	0.541828i	−0.982438	+	0.186588i	$0.940257\pi$
$6$		0			0
$7$	0.128901	−	0.0135480i	0.0487199	−	0.00512067i	−0.0801372	−	0.996784i	$-0.525536\pi$
$7$	0.128901	−	0.0135480i	0.0487199	−	0.00512067i	0.128857	+	0.991663i	$0.458869\pi$
$8$		0			0
$9$	2.73079	+	0.580448i	0.910265	+	0.193483i
$10$		0			0
$11$	3.18108	+	0.938485i	0.959131	+	0.282964i
$11$	3.18108	+	0.938485i	0.959131	+	0.282964i
$12$		0			0
$13$	−2.13957	+	2.90211i	−0.593411	+	0.804900i
$13$	−2.13957	+	2.90211i	−0.593411	+	0.804900i
$14$		0			0
$15$	0.727638	−	1.63430i	0.187875	−	0.421975i
$16$		0			0
$17$	2.49450	+	2.77042i	0.605005	+	0.671926i	0.965370	−	0.260886i	$-0.0840146\pi$
$17$	2.49450	+	2.77042i	0.605005	+	0.671926i	−0.360365	+	0.932811i	$0.617348\pi$
$18$		0			0
$19$	−1.96575	−	4.41515i	−0.450974	−	1.01291i	−0.985797	−	0.167941i	$-0.946288\pi$
$19$	−1.96575	−	4.41515i	−0.450974	−	1.01291i	0.534823	−	0.844964i	$-0.320378\pi$
$20$		0			0
$21$			0.0591397i			0.0129053i
$22$		0			0
$23$	3.42619	+	5.93434i	0.714411	+	1.23740i	0.963186	+	0.268835i	$0.0866386\pi$
$23$	3.42619	+	5.93434i	0.714411	+	1.23740i	−0.248775	+	0.968561i	$0.580028\pi$
$24$		0			0
$25$	8.39104	+	6.09645i	1.67821	+	1.21929i
$26$		0			0
$27$	−0.816647	+	2.51338i	−0.157164	+	0.483700i
$28$		0			0
$29$	6.80110	+	3.02804i	1.26293	+	0.562293i	0.925390	−	0.379017i	$-0.123738\pi$
$29$	6.80110	+	3.02804i	1.26293	+	0.562293i	0.337542	+	0.941310i	$0.390404\pi$
$30$		0			0
$31$	4.74701	−	1.54240i	0.852588	−	0.277023i	0.150059	−	0.988677i	$-0.452054\pi$
$31$	4.74701	−	1.54240i	0.852588	−	0.277023i	0.702530	+	0.711654i	$0.252054\pi$
$32$		0			0
$33$	−0.577595	+	1.39877i	−0.100546	+	0.243495i
$34$		0			0
$35$	−0.497060	−	0.105653i	−0.0840185	−	0.0178587i
$36$		0			0
$37$	1.23304	−	2.76946i	0.202711	−	0.455296i	−0.783372	−	0.621554i	$-0.786502\pi$
$37$	1.23304	−	2.76946i	0.202711	−	0.455296i	0.986082	+	0.166258i	$0.0531684\pi$
$38$		0			0
$39$	−1.21489	−	1.10933i	−0.194539	−	0.177635i
$40$		0			0
$41$	8.74488	+	0.919124i	1.36572	+	0.143543i	0.758854	−	0.651260i	$-0.225759\pi$
$41$	8.74488	+	0.919124i	1.36572	+	0.143543i	0.606867	+	0.794803i	$0.292426\pi$
$42$		0			0
$43$	−4.73852	+	8.20736i	−0.722618	+	1.25161i	0.237329	+	0.971429i	$0.423728\pi$
$43$	−4.73852	+	8.20736i	−0.722618	+	1.25161i	−0.959947	+	0.280181i	$0.909605\pi$
$44$		0			0
$45$	−9.47936	−	5.47291i	−1.41310	−	0.815853i
$46$		0			0
$47$	−5.37278	+	7.39500i	−0.783700	+	1.07867i	0.211164	+	0.977451i	$0.432275\pi$
$47$	−5.37278	+	7.39500i	−0.783700	+	1.07867i	−0.994864	+	0.101220i	$0.967725\pi$
$48$		0			0
$49$	−6.83060	+	1.45189i	−0.975800	+	0.207413i
$50$		0			0
$51$	−1.37616	+	0.999837i	−0.192701	+	0.140005i
$52$		0			0
$53$	−1.51016	−	4.64779i	−0.207436	−	0.638424i	−0.999605	−	0.0281206i	$-0.991048\pi$
$53$	−1.51016	−	4.64779i	−0.207436	−	0.638424i	0.792168	−	0.610303i	$-0.208952\pi$
$54$		0			0
$55$	−10.7246	−	7.35351i	−1.44610	−	0.991547i
$56$		0			0
$57$	2.09730	−	0.681453i	0.277794	−	0.0902607i
$58$		0			0
$59$	6.51121	−	0.684356i	0.847688	−	0.0890956i	0.329283	−	0.944231i	$-0.393193\pi$
$59$	6.51121	−	0.684356i	0.847688	−	0.0890956i	0.518404	+	0.855136i	$0.326526\pi$
$60$		0			0
$61$	−7.25934	−	8.06231i	−0.929463	−	1.03227i	−0.999397	−	0.0347218i	$-0.988946\pi$
$61$	−7.25934	−	8.06231i	−0.929463	−	1.03227i	0.0699339	−	0.997552i	$-0.477721\pi$
$62$		0			0
$63$	0.359865	+	0.0378234i	0.0453388	+	0.00476529i
$64$		0			0
$65$	11.4941	−	8.22918i	1.42567	−	1.02070i
$66$		0			0
$67$	5.04304	−	2.91160i	0.616105	−	0.355708i	−0.159246	−	0.987239i	$-0.550906\pi$
$67$	5.04304	−	2.91160i	0.616105	−	0.355708i	0.775351	+	0.631531i	$0.217573\pi$
$68$		0			0
$69$	−2.85634	+	1.27173i	−0.343863	+	0.153098i
$70$		0			0
$71$	−8.48501	+	7.63994i	−1.00699	+	0.906694i	−0.995643	−	0.0932419i	$-0.970277\pi$
$71$	−8.48501	+	7.63994i	−1.00699	+	0.906694i	−0.0113420	+	0.999936i	$0.503610\pi$
$72$		0			0
$73$	1.01482	+	1.39678i	0.118776	+	0.163481i	0.864265	−	0.503037i	$-0.167784\pi$
$73$	1.01482	+	1.39678i	0.118776	+	0.163481i	−0.745489	+	0.666518i	$0.767784\pi$
$74$		0			0
$75$	−3.16670	+	3.51698i	−0.365659	+	0.406106i
$76$		0			0
$77$	0.422758	+	0.0778742i	0.0481777	+	0.00887458i
$78$		0			0
$79$	−3.87049	−	11.9121i	−0.435464	−	1.34022i	−0.892610	−	0.450830i	$-0.851128\pi$
$79$	−3.87049	−	11.9121i	−0.435464	−	1.34022i	0.457146	−	0.889392i	$-0.348872\pi$
$80$		0			0
$81$	6.54972	+	2.91612i	0.727747	+	0.324014i
$82$		0			0
$83$	4.35448	+	1.41486i	0.477966	+	0.155301i	0.538085	−	0.842891i	$-0.319148\pi$
$83$	4.35448	+	1.41486i	0.477966	+	0.155301i	−0.0601186	+	0.998191i	$0.519148\pi$
$84$		0			0
$85$	−5.94496	−	13.3526i	−0.644822	−	1.44829i
$86$		0			0
$87$	−1.69847	+	2.94183i	−0.182095	+	0.315397i
$88$		0			0
$89$	−7.27757	+	4.20171i	−0.771421	+	0.445380i	−0.833381	−	0.552698i	$-0.813598\pi$
$89$	−7.27757	+	4.20171i	−0.771421	+	0.445380i	0.0619601	+	0.998079i	$0.480265\pi$
$90$		0			0
$91$	−0.236475	+	0.403071i	−0.0247893	+	0.0422533i
$92$		0			0
$93$	0.473512	+	2.22770i	0.0491009	+	0.231002i
$94$		0			0
$95$	1.98068	+	18.8449i	0.203213	+	1.93344i
$96$		0			0
$97$	2.19971	−	10.3488i	0.223347	−	1.05076i	−0.713400	−	0.700757i	$-0.752846\pi$
$97$	2.19971	−	10.3488i	0.223347	−	1.05076i	0.936747	−	0.350007i	$-0.113821\pi$
$98$		0			0
$99$	8.14212	+	4.40926i	0.818314	+	0.443147i
$100$		0			0
$101$	8.29268	−	9.20996i	0.825153	−	0.916425i	−0.172493	−	0.985011i	$-0.555182\pi$
$101$	8.29268	−	9.20996i	0.825153	−	0.916425i	0.997645	+	0.0685860i	$0.0218488\pi$
$102$		0			0
$103$	−2.39578	+	1.74064i	−0.236064	+	0.171510i	−0.699528	−	0.714605i	$-0.746606\pi$
$103$	−2.39578	+	1.74064i	−0.236064	+	0.171510i	0.463464	+	0.886116i	$0.346606\pi$
$104$		0			0
$105$	0.0716515	−	0.220521i	0.00699247	−	0.0215206i
$106$		0			0
$107$	−0.718594	+	6.83696i	−0.0694691	+	0.660954i	0.903273	+	0.429066i	$0.141157\pi$
$107$	−0.718594	+	6.83696i	−0.0694691	+	0.660954i	−0.972742	+	0.231888i	$0.925510\pi$
$108$		0			0
$109$			1.59460i			0.152735i	0.997080	+	0.0763674i	$0.0243322\pi$
$109$			1.59460i			0.152735i	−0.997080	+	0.0763674i	$0.975668\pi$
$110$		0			0
$111$	1.19794	+	0.691628i	0.113703	+	0.0656465i
$112$		0			0
$113$	13.2615	−	5.90438i	1.24753	−	0.555438i	0.326602	−	0.945162i	$-0.394096\pi$
$113$	13.2615	−	5.90438i	1.24753	−	0.555438i	0.920932	+	0.389724i	$0.127430\pi$
$114$		0			0
$115$	−5.58579	−	26.2791i	−0.520878	−	2.45054i
$116$		0			0
$117$	−7.52726	+	6.68315i	−0.695895	+	0.617857i
$118$		0			0
$119$	0.359076	+	0.323314i	0.0329165	+	0.0296381i
$120$		0			0
$121$	9.23849	+	5.97079i	0.839863	+	0.542799i
$122$		0			0
$123$	−0.834174	+	3.92448i	−0.0752150	+	0.353859i
$124$		0			0
$125$	−12.3797	−	17.0392i	−1.10727	−	1.52403i
$126$		0			0
$127$	−0.824264	+	0.175203i	−0.0731416	+	0.0155467i	−0.244337	−	0.969690i	$-0.578570\pi$
$127$	−0.824264	+	0.175203i	−0.0731416	+	0.0155467i	0.171196	+	0.985237i	$0.445237\pi$
$128$		0			0
$129$	−3.49839	−	2.54173i	−0.308016	−	0.223787i
$130$		0			0
$131$	−22.4525			−1.96168			−0.980840	−	0.194814i	$-0.937590\pi$
$131$	−22.4525			−1.96168			−0.980840	+	0.194814i	$0.937590\pi$
$132$		0			0
$133$	−0.313203	−	0.542484i	−0.0271582	−	0.0470393i
$134$		0			0
$135$	6.09024	−	8.38250i	0.524164	−	0.721451i
$136$		0			0
$137$	10.3655	−	9.33312i	0.885583	−	0.797383i	−0.0945920	−	0.995516i	$-0.530155\pi$
$137$	10.3655	−	9.33312i	0.885583	−	0.797383i	0.980175	+	0.198134i	$0.0634880\pi$
$138$		0			0
$139$	0.729018	+	6.93614i	0.0618345	+	0.588316i	0.980941	+	0.194306i	$0.0622456\pi$
$139$	0.729018	+	6.93614i	0.0618345	+	0.588316i	−0.919106	+	0.394009i	$0.871088\pi$
$140$		0			0
$141$	−3.09950	−	2.79081i	−0.261025	−	0.235028i
$142$		0			0
$143$	−9.52973	+	7.22387i	−0.796916	+	0.604090i
$144$		0			0
$145$	−21.6913	−	19.5309i	−1.80137	−	1.62196i
$146$		0			0
$147$	−0.333064	−	3.16889i	−0.0274706	−	0.261366i
$148$		0			0
$149$	−0.217589	+	0.195918i	−0.0178256	+	0.0160502i	−0.677995	−	0.735066i	$-0.737151\pi$
$149$	−0.217589	+	0.195918i	−0.0178256	+	0.0160502i	0.660170	+	0.751116i	$0.270484\pi$
$150$		0			0
$151$	−5.50212	+	7.57302i	−0.447756	+	0.616284i	−0.971914	−	0.235338i	$-0.924380\pi$
$151$	−5.50212	+	7.57302i	−0.447756	+	0.616284i	0.524157	+	0.851621i	$0.324380\pi$
$152$		0			0
$153$	5.20387	+	9.01337i	0.420708	+	0.728688i
$154$		0			0
$155$	−19.5694			−1.57185
$156$		0			0
$157$	17.6109	+	12.7950i	1.40550	+	1.02116i	0.993957	+	0.109766i	$0.0350100\pi$
$157$	17.6109	+	12.7950i	1.40550	+	1.02116i	0.411543	+	0.911390i	$0.364990\pi$
$158$		0			0
$159$	2.18114	−	0.463615i	0.172976	−	0.0367671i
$160$		0			0
$161$	0.522037	+	0.718523i	0.0411423	+	0.0566275i
$162$		0			0
$163$	−1.69848	+	7.99072i	−0.133035	+	0.625881i	0.860219	+	0.509925i	$0.170327\pi$
$163$	−1.69848	+	7.99072i	−0.133035	+	0.625881i	−0.993254	+	0.115957i	$0.963007\pi$
$164$		0			0
$165$	3.84844	−	4.51596i	0.299601	−	0.351567i
$166$		0			0
$167$	−8.41762	−	7.57925i	−0.651375	−	0.586500i	0.275761	−	0.961226i	$-0.411070\pi$
$167$	−8.41762	−	7.57925i	−0.651375	−	0.586500i	−0.927136	+	0.374726i	$0.877737\pi$
$168$		0			0
$169$	−3.84446	−	12.4185i	−0.295728	−	0.955272i
$170$		0			0
$171$	−2.80530	−	13.1979i	−0.214526	−	1.00927i
$172$		0			0
$173$	−0.0481805	+	0.0214513i	−0.00366310	+	0.00163092i	−0.408567	−	0.912728i	$-0.633972\pi$
$173$	−0.0481805	+	0.0214513i	−0.00366310	+	0.00163092i	0.404904	+	0.914359i	$0.367305\pi$
$174$		0			0
$175$	1.16421	+	0.672155i	0.0880057	+	0.0508101i
$176$		0			0
$177$			2.98735i			0.224543i
$178$		0			0
$179$	1.44005	−	13.7012i	0.107635	−	1.02408i	−0.798762	−	0.601648i	$-0.794511\pi$
$179$	1.44005	−	13.7012i	0.107635	−	1.02408i	0.906396	−	0.422428i	$-0.138822\pi$
$180$		0			0
$181$	0.370716	−	1.14095i	0.0275551	−	0.0848059i	−0.936333	−	0.351113i	$-0.885803\pi$
$181$	0.370716	−	1.14095i	0.0275551	−	0.0848059i	0.963888	+	0.266307i	$0.0858034\pi$
$182$		0			0
$183$	4.00481	−	2.90967i	0.296044	−	0.215089i
$184$		0			0
$185$	−7.95315	+	8.83287i	−0.584727	+	0.649405i
$186$		0			0
$187$	5.33519	+	11.1540i	0.390148	+	0.815659i
$188$		0			0
$189$	−0.0712151	+	0.335041i	−0.00518013	+	0.0243706i
$190$		0			0
$191$	1.79021	+	17.0327i	0.129535	+	1.23244i	0.845373	+	0.534176i	$0.179378\pi$
$191$	1.79021	+	17.0327i	0.129535	+	1.23244i	−0.715838	+	0.698266i	$0.753955\pi$
$192$		0			0
$193$	2.49319	+	11.7296i	0.179464	+	0.844312i	0.972091	+	0.234605i	$0.0753796\pi$
$193$	2.49319	+	11.7296i	0.179464	+	0.844312i	−0.792627	+	0.609707i	$0.791287\pi$
$194$		0			0
$195$	3.18609	+	5.60839i	0.228160	+	0.401625i
$196$		0			0
$197$	−5.04666	+	2.91369i	−0.359560	+	0.207592i	−0.668888	−	0.743363i	$-0.733229\pi$
$197$	−5.04666	+	2.91369i	−0.359560	+	0.207592i	0.309328	+	0.950955i	$0.399896\pi$
$198$		0			0
$199$	7.70425	−	13.3441i	0.546140	−	0.945941i	−0.452395	−	0.891818i	$-0.649430\pi$
$199$	7.70425	−	13.3441i	0.546140	−	0.945941i	0.998534	−	0.0541236i	$-0.0172365\pi$
$200$		0			0
$201$	1.08072	+	2.42734i	0.0762281	+	0.171211i
$202$		0			0
$203$	0.917690	+	0.298175i	0.0644092	+	0.0209278i
$204$		0			0
$205$	−31.4944	−	14.0222i	−2.19967	−	0.979354i
$206$		0			0
$207$	5.91165	+	18.1942i	0.410888	+	1.26458i
$208$		0			0
$209$	−2.10965	−	15.8898i	−0.145928	−	1.09912i
$210$		0			0
$211$	−9.89951	+	10.9945i	−0.681510	+	0.756894i	−0.980319	−	0.197419i	$-0.936744\pi$
$211$	−9.89951	+	10.9945i	−0.681510	+	0.756894i	0.298809	+	0.954313i	$0.403411\pi$
$212$		0			0
$213$	−3.06222	−	4.21478i	−0.209820	−	0.288792i
$214$		0			0
$215$	27.6128	−	24.8627i	1.88318	−	1.69562i
$216$		0			0
$217$	0.590997	−	0.263129i	0.0401195	−	0.0178623i
$218$		0			0
$219$	−0.682245	+	0.393894i	−0.0461018	+	0.0266169i
$220$		0			0
$221$	−13.3772	+	1.31179i	−0.899849	+	0.0882403i
$222$		0			0
$223$	−3.40614	−	0.357999i	−0.228092	−	0.0239734i	−0.0102070	−	0.999948i	$-0.503249\pi$
$223$	−3.40614	−	0.357999i	−0.228092	−	0.0239734i	−0.217885	+	0.975975i	$0.569916\pi$
$224$		0			0
$225$	19.3755	+	21.5187i	1.29170	+	1.43458i
$226$		0			0
$227$	−14.0024	+	1.47171i	−0.929370	+	0.0976807i	−0.557102	−	0.830444i	$-0.688087\pi$
$227$	−14.0024	+	1.47171i	−0.929370	+	0.0976807i	−0.372269	+	0.928125i	$0.621420\pi$
$228$		0			0
$229$	−10.0362	+	3.26095i	−0.663209	+	0.215490i	−0.621229	−	0.783629i	$-0.713366\pi$
$229$	−10.0362	+	3.26095i	−0.663209	+	0.215490i	−0.0419797	+	0.999118i	$0.513366\pi$
$230$		0			0
$231$	−0.0555018	+	0.188128i	−0.00365175	+	0.0123779i
$232$		0			0
$233$	2.54917	+	7.84553i	0.167002	+	0.513978i	0.999178	−	0.0405326i	$-0.0129055\pi$
$233$	2.54917	+	7.84553i	0.167002	+	0.513978i	−0.832177	+	0.554511i	$0.812905\pi$
$234$		0			0
$235$	28.9936	−	21.0651i	1.89133	−	1.37413i
$236$		0			0
$237$	5.59019	−	1.18823i	0.363122	−	0.0771839i
$238$		0			0
$239$	−2.02574	+	2.78819i	−0.131034	+	0.180353i	−0.869493	−	0.493946i	$-0.835554\pi$
$239$	−2.02574	+	2.78819i	−0.131034	+	0.180353i	0.738459	+	0.674299i	$0.235554\pi$
$240$		0			0
$241$	14.7070	+	8.49110i	0.947362	+	0.546960i	0.892261	−	0.451521i	$-0.149118\pi$
$241$	14.7070	+	8.49110i	0.947362	+	0.546960i	0.0551017	+	0.998481i	$0.482452\pi$
$242$		0			0
$243$	−5.59978	+	9.69910i	−0.359226	+	0.622198i
$244$		0			0
$245$	27.2291	+	2.86189i	1.73960	+	0.182839i
$246$		0			0
$247$	17.0191	+	3.74171i	1.08290	+	0.238079i
$248$		0			0
$249$	−0.849732	+	1.90853i	−0.0538496	+	0.120948i
$250$		0			0
$251$	20.8462	+	4.43101i	1.31580	+	0.279683i	0.811758	−	0.583994i	$-0.198511\pi$
$251$	20.8462	+	4.43101i	1.31580	+	0.279683i	0.504046	+	0.863677i	$0.331844\pi$
$252$		0			0
$253$	5.32969	+	22.0930i	0.335075	+	1.38898i
$254$		0			0
$255$	6.34279	−	2.06090i	0.397201	−	0.129058i
$256$		0			0
$257$	0.541688	+	0.241175i	0.0337896	+	0.0150441i	0.423562	−	0.905867i	$-0.360780\pi$
$257$	0.541688	+	0.241175i	0.0337896	+	0.0150441i	−0.389772	+	0.920911i	$0.627446\pi$
$258$		0			0
$259$	0.121419	−	0.373690i	0.00754463	−	0.0232200i
$260$		0			0
$261$	16.8148	+	12.2166i	1.04081	+	0.756191i
$262$		0			0
$263$	−12.9855	−	22.4916i	−0.800722	−	1.38689i	−0.919142	−	0.393927i	$-0.871116\pi$
$263$	−12.9855	−	22.4916i	−0.800722	−	1.38689i	0.118420	−	0.992964i	$-0.462217\pi$
$264$		0			0
$265$			19.1604i			1.17701i
$266$		0			0
$267$	−1.55958	−	3.50287i	−0.0954447	−	0.214372i
$268$		0			0
$269$	9.58052	+	10.6402i	0.584135	+	0.648747i	0.960682	−	0.277650i	$-0.0895556\pi$
$269$	9.58052	+	10.6402i	0.584135	+	0.648747i	−0.376548	+	0.926397i	$0.622889\pi$
$270$		0			0
$271$	2.43644	−	5.47233i	0.148003	−	0.332421i	−0.824296	−	0.566158i	$-0.808429\pi$
$271$	2.43644	−	5.47233i	0.148003	−	0.332421i	0.972300	+	0.233738i	$0.0750957\pi$
$272$		0			0
$273$	−0.171630	−	0.126534i	−0.0103875	−	0.00765817i
$274$		0			0
$275$	20.9711	+	27.2681i	1.26461	+	1.64433i
$276$		0			0
$277$	−1.08853	−	0.231374i	−0.0654034	−	0.0139019i	0.175094	−	0.984552i	$-0.443977\pi$
$277$	−1.08853	−	0.231374i	−0.0654034	−	0.0139019i	−0.240497	+	0.970650i	$0.577310\pi$
$278$		0			0
$279$	13.8584	−	1.45658i	0.829680	−	0.0872029i
$280$		0			0
$281$	−23.9515	−	7.78232i	−1.42883	−	0.464254i	−0.510432	−	0.859918i	$-0.670514\pi$
$281$	−23.9515	−	7.78232i	−1.42883	−	0.464254i	−0.918395	+	0.395664i	$0.870514\pi$
$282$		0			0
$283$	−0.280088	+	2.66486i	−0.0166495	+	0.158410i	−0.999688	−	0.0249916i	$-0.992044\pi$
$283$	−0.280088	+	2.66486i	−0.0166495	+	0.158410i	0.983038	+	0.183401i	$0.0587108\pi$
$284$		0			0
$285$	−8.64605			−0.512148
$286$		0			0
$287$	1.13967			0.0672728
$288$		0			0
$289$	0.324274	−	3.08526i	0.0190749	−	0.181486i
$290$		0			0
$291$	4.59125	+	1.49179i	0.269144	+	0.0874502i
$292$		0			0
$293$	−10.9402	+	1.14986i	−0.639134	+	0.0671757i	−0.418552	−	0.908193i	$-0.637462\pi$
$293$	−10.9402	+	1.14986i	−0.639134	+	0.0671757i	−0.220582	+	0.975368i	$0.570796\pi$
$294$		0			0
$295$	−25.1082	−	5.33691i	−1.46186	−	0.310727i
$296$		0			0
$297$	−4.95659	+	7.22885i	−0.287610	+	0.419460i
$298$		0			0
$299$	−24.5527	−	2.75377i	−1.41992	−	0.159255i
$300$		0			0
$301$	−0.499605	+	1.12213i	−0.0287968	+	0.0646786i
$302$		0			0
$303$	3.78384	+	4.20239i	0.217376	+	0.241421i
$304$		0			0
$305$	17.3007	+	38.8580i	0.990634	+	2.22500i
$306$		0			0
$307$		−	32.2744i		−	1.84200i	−0.389563	−	0.921000i	$-0.627374\pi$
$307$		−	32.2744i		−	1.84200i	0.389563	−	0.921000i	$-0.372626\pi$
$308$		0			0
$309$	−0.675613	−	1.17020i	−0.0384343	−	0.0665702i
$310$		0			0
$311$	9.66441	+	7.02161i	0.548018	+	0.398159i	0.827054	−	0.562122i	$-0.190015\pi$
$311$	9.66441	+	7.02161i	0.548018	+	0.398159i	−0.279036	+	0.960281i	$0.590015\pi$
$312$		0			0
$313$	10.3639	−	31.8967i	0.585800	−	1.80291i	−0.0102351	−	0.999948i	$-0.503258\pi$
$313$	10.3639	−	31.8967i	0.585800	−	1.80291i	0.596035	−	0.802959i	$-0.296742\pi$
$314$		0			0
$315$	−1.29604	−	0.577035i	−0.0730237	−	0.0325123i
$316$		0			0
$317$	22.2667	−	7.23487i	1.25062	−	0.406351i	0.392477	−	0.919762i	$-0.371618\pi$
$317$	22.2667	−	7.23487i	1.25062	−	0.406351i	0.858143	+	0.513411i	$0.171618\pi$
$318$		0			0
$319$	18.7930	+	16.0152i	1.05221	+	0.896677i
$320$		0			0
$321$	−3.06826	−	0.652178i	−0.171253	−	0.0364010i
$322$		0			0
$323$	7.32826	−	16.4595i	0.407755	−	0.915834i
$324$		0			0
$325$	−35.6458	+	11.3079i	−1.97727	+	0.627250i
$326$		0			0
$327$	−0.723609	−	0.0760544i	−0.0400157	−	0.00420582i
$328$		0			0
$329$	−0.592367	+	1.02601i	−0.0326583	+	0.0565658i
$330$		0			0
$331$	6.63199	+	3.82898i	0.364527	+	0.210460i	0.671065	−	0.741399i	$-0.265837\pi$
$331$	6.63199	+	3.82898i	0.364527	+	0.210460i	−0.306538	+	0.951859i	$0.599171\pi$
$332$		0			0
$333$	4.97471	−	6.84710i	0.272612	−	0.375219i
$334$		0			0
$335$	−22.3321	+	4.74684i	−1.22013	+	0.259347i
$336$		0			0
$337$	−16.2573	+	11.8116i	−0.885592	+	0.643420i	−0.934725	−	0.355372i	$-0.884354\pi$
$337$	−16.2573	+	11.8116i	−0.885592	+	0.643420i	0.0491332	+	0.998792i	$0.484354\pi$
$338$		0			0
$339$	2.04683	+	6.29950i	0.111169	+	0.342142i
$340$		0			0
$341$	16.5481	−	0.451483i	0.896131	−	0.0244492i
$342$		0			0
$343$	−1.72367	+	0.560054i	−0.0930694	+	0.0302401i
$344$		0			0
$345$	12.1915	−	1.28138i	0.656370	−	0.0689873i
$346$		0			0
$347$	−9.53781	−	10.5928i	−0.512017	−	0.568652i	0.430594	−	0.902546i	$-0.358304\pi$
$347$	−9.53781	−	10.5928i	−0.512017	−	0.568652i	−0.942611	+	0.333894i	$0.891637\pi$
$348$		0			0
$349$	−21.8064	−	2.29194i	−1.16727	−	0.122685i	−0.498998	−	0.866603i	$-0.666299\pi$
$349$	−21.8064	−	2.29194i	−1.16727	−	0.122685i	−0.668271	+	0.743918i	$0.732965\pi$
$350$		0			0
$351$	−5.54683	−	7.74756i	−0.296068	−	0.413534i
$352$		0			0
$353$	−6.14385	+	3.54715i	−0.327004	+	0.188796i	−0.654510	−	0.756053i	$-0.727125\pi$
$353$	−6.14385	+	3.54715i	−0.327004	+	0.188796i	0.327506	+	0.944849i	$0.393792\pi$
$354$		0			0
$355$	40.8952	−	18.2077i	2.17049	−	0.966366i
$356$		0			0
$357$	−0.163842	+	0.147524i	−0.00867143	+	0.00780779i
$358$		0			0
$359$	2.27858	+	3.13619i	0.120259	+	0.165522i	0.864902	−	0.501941i	$-0.167380\pi$
$359$	2.27858	+	3.13619i	0.120259	+	0.165522i	−0.744643	+	0.667463i	$0.767380\pi$
$360$		0			0
$361$	−2.91590	+	3.23844i	−0.153469	+	0.170444i
$362$		0			0
$363$	−3.15010	+	3.90754i	−0.165337	+	0.205092i
$364$		0			0
$365$	−2.09179	−	6.43786i	−0.109489	−	0.336973i
$366$		0			0
$367$	−19.0353	−	8.47508i	−0.993637	−	0.442396i	−0.155488	−	0.987838i	$-0.549695\pi$
$367$	−19.0353	−	8.47508i	−0.993637	−	0.442396i	−0.838148	+	0.545442i	$0.816362\pi$
$368$		0			0
$369$	23.3470	+	7.58589i	1.21539	+	0.394906i
$370$		0			0
$371$	−0.257629	−	0.578644i	−0.0133754	−	0.0300417i
$372$		0			0
$373$	6.60827	−	11.4459i	0.342163	−	0.592644i	−0.642671	−	0.766142i	$-0.722174\pi$
$373$	6.60827	−	11.4459i	0.342163	−	0.592644i	0.984834	+	0.173498i	$0.0555071\pi$
$374$		0			0
$375$	8.32263	−	4.80507i	0.429779	−	0.248133i
$376$		0			0
$377$	−23.3391	+	13.2588i	−1.20203	+	0.682863i
$378$		0			0
$379$	−3.68119	−	17.3186i	−0.189090	−	0.889599i	−0.965709	−	0.259628i	$-0.916400\pi$
$379$	−3.68119	−	17.3186i	−0.189090	−	0.889599i	0.776619	−	0.629971i	$-0.216933\pi$
$380$		0			0
$381$	−0.0401916	−	0.382397i	−0.00205908	−	0.0195908i
$382$		0			0
$383$	−3.26577	+	15.3643i	−0.166873	+	0.785077i	0.812491	+	0.582974i	$0.198111\pi$
$383$	−3.26577	+	15.3643i	−0.166873	+	0.785077i	−0.979364	+	0.202103i	$0.935222\pi$
$384$		0			0
$385$	−1.48203	−	0.802575i	−0.0755314	−	0.0409030i
$386$		0			0
$387$	−17.7039	+	19.6621i	−0.899938	+	0.999483i
$388$		0			0
$389$	15.5579	−	11.3034i	0.788814	−	0.573107i	−0.118797	−	0.992919i	$-0.537904\pi$
$389$	15.5579	−	11.3034i	0.788814	−	0.573107i	0.907611	+	0.419811i	$0.137904\pi$
$390$		0			0
$391$	−7.89399	+	24.2952i	−0.399216	+	1.22866i
$392$		0			0
$393$	1.07087	−	10.1886i	0.0540183	−	0.513949i
$394$		0			0
$395$			49.1075i			2.47086i
$396$		0			0
$397$	11.4293	+	6.59873i	0.573622	+	0.331181i	0.758594	−	0.651563i	$-0.225886\pi$
$397$	11.4293	+	6.59873i	0.573622	+	0.331181i	−0.184973	+	0.982744i	$0.559220\pi$
$398$		0			0
$399$	0.261111	−	0.116254i	0.0130719	−	0.00581998i
$400$		0			0
$401$	0.144950	+	0.681934i	0.00723844	+	0.0340542i	0.981619	−	0.190853i	$-0.0611254\pi$
$401$	0.144950	+	0.681934i	0.00723844	+	0.0340542i	−0.974380	+	0.224907i	$0.927792\pi$
$402$		0			0
$403$	−5.68037	+	17.0764i	−0.282959	+	0.850637i
$404$		0			0
$405$	−20.8896	−	18.8091i	−1.03801	−	0.934630i
$406$		0			0
$407$	6.52149	−	7.65266i	0.323258	−	0.379328i
$408$		0			0
$409$	4.82700	−	22.7092i	0.238680	−	1.12290i	−0.681627	−	0.731700i	$-0.738727\pi$
$409$	4.82700	−	22.7092i	0.238680	−	1.12290i	0.920306	−	0.391199i	$-0.127940\pi$
$410$		0			0
$411$	3.74087	+	5.14887i	0.184524	+	0.253975i
$412$		0			0
$413$	0.830028	−	0.176428i	0.0408430	−	0.00868145i
$414$		0			0
$415$	−14.5228	−	10.5515i	−0.712898	−	0.517951i
$416$		0			0
$417$	−3.18231			−0.155838
$418$		0			0
$419$	−10.8179	−	18.7372i	−0.528490	−	0.915371i	−0.999448	−	0.0332159i	$-0.989425\pi$
$419$	−10.8179	−	18.7372i	−0.528490	−	0.915371i	0.470958	−	0.882155i	$-0.343908\pi$
$420$		0			0
$421$	6.18637	−	8.51481i	0.301505	−	0.414987i	−0.631203	−	0.775618i	$-0.717439\pi$
$421$	6.18637	−	8.51481i	0.301505	−	0.414987i	0.932709	+	0.360631i	$0.117439\pi$
$422$		0			0
$423$	−18.9644	+	17.0756i	−0.922079	+	0.830244i
$424$		0			0
$425$	4.04171	+	38.4543i	0.196052	+	1.86531i
$426$		0			0
$427$	−1.04496	−	0.940888i	−0.0505693	−	0.0455328i
$428$		0			0
$429$	−2.82358	−	4.66902i	−0.136324	−	0.225422i
$430$		0			0
$431$	15.6513	+	14.0925i	0.753895	+	0.678811i	0.953610	−	0.301044i	$-0.0973349\pi$
$431$	15.6513	+	14.0925i	0.753895	+	0.678811i	−0.199715	+	0.979854i	$0.564002\pi$
$432$		0			0
$433$	2.25456	+	21.4507i	0.108347	+	1.03086i	0.904708	+	0.426033i	$0.140089\pi$
$433$	2.25456	+	21.4507i	0.108347	+	1.03086i	−0.796360	+	0.604822i	$0.793244\pi$
$434$		0			0
$435$	9.89747	−	8.91172i	0.474547	−	0.427284i
$436$		0			0
$437$	19.4660	−	26.7926i	0.931184	−	1.28166i
$438$		0			0
$439$	2.24407	+	3.88685i	0.107104	+	0.185509i	0.914596	−	0.404369i	$-0.132509\pi$
$439$	2.24407	+	3.88685i	0.107104	+	0.185509i	−0.807492	+	0.589879i	$0.799176\pi$
$440$		0			0
$441$	−19.4957			−0.928367
$442$		0			0
$443$	18.2096	+	13.2301i	0.865165	+	0.628579i	0.929285	−	0.369363i	$-0.120424\pi$
$443$	18.2096	+	13.2301i	0.865165	+	0.628579i	−0.0641199	+	0.997942i	$0.520424\pi$
$444$		0			0
$445$	32.2273	−	6.85013i	1.52772	−	0.324727i
$446$		0			0
$447$	−0.0785274	−	0.108084i	−0.00371422	−	0.00511218i
$448$		0			0
$449$	8.53530	−	40.1554i	0.402806	−	1.89505i	−0.0414302	−	0.999141i	$-0.513191\pi$
$449$	8.53530	−	40.1554i	0.402806	−	1.89505i	0.444236	−	0.895910i	$-0.353475\pi$
$450$		0			0
$451$	26.9556	+	11.1307i	1.26929	+	0.524126i
$452$		0			0
$453$	−3.17412	−	2.85799i	−0.149133	−	0.134280i
$454$		0			0
$455$	1.37011	−	1.21647i	0.0642319	−	0.0570290i
$456$		0			0
$457$	−5.67429	−	26.6954i	−0.265432	−	1.24876i	−0.885659	−	0.464337i	$-0.846293\pi$
$457$	−5.67429	−	26.6954i	−0.265432	−	1.24876i	0.620227	−	0.784423i	$-0.287041\pi$
$458$		0			0
$459$	−9.00025	+	4.00717i	−0.420096	+	0.187039i
$460$		0			0
$461$	2.39426	+	1.38233i	0.111512	+	0.0643813i	0.554719	−	0.832038i	$-0.312826\pi$
$461$	2.39426	+	1.38233i	0.111512	+	0.0643813i	−0.443207	+	0.896419i	$0.646159\pi$
$462$		0			0
$463$		−	9.64522i		−	0.448251i	−0.974560	−	0.224126i	$-0.928047\pi$
$463$		−	9.64522i		−	0.448251i	0.974560	−	0.224126i	$-0.0719526\pi$
$464$		0			0
$465$	0.933363	−	8.88036i	0.0432837	−	0.411817i
$466$		0			0
$467$	−1.25216	+	3.85376i	−0.0579431	+	0.178331i	−0.975839	−	0.218491i	$-0.929887\pi$
$467$	−1.25216	+	3.85376i	−0.0579431	+	0.178331i	0.917896	+	0.396821i	$0.129887\pi$
$468$		0			0
$469$	0.610605	−	0.443630i	0.0281951	−	0.0204849i
$470$		0			0
$471$	−6.64619	+	7.38134i	−0.306240	+	0.340114i
$472$		0			0
$473$	−22.7761	+	21.6612i	−1.04725	+	0.995983i
$474$		0			0
$475$	10.4220	−	49.0318i	0.478196	−	2.24973i
$476$		0			0
$477$	−1.42613	−	13.5687i	−0.0652981	−	0.621270i
$478$		0			0
$479$	−1.95143	−	9.18075i	−0.0891630	−	0.419479i	−0.999978	−	0.00666383i	$-0.997879\pi$
$479$	−1.95143	−	9.18075i	−0.0891630	−	0.419479i	0.910815	−	0.412815i	$-0.135455\pi$
$480$		0			0
$481$	5.39908	+	9.50387i	0.246177	+	0.433339i
$482$		0			0
$483$	−0.350955	+	0.202624i	−0.0159690	+	0.00921972i
$484$		0			0
$485$	−20.7405	+	35.9237i	−0.941780	+	1.63121i
$486$		0			0
$487$	−9.49384	−	21.3235i	−0.430207	−	0.966260i	−0.990442	−	0.137927i	$-0.955956\pi$
$487$	−9.49384	−	21.3235i	−0.430207	−	0.966260i	0.560236	−	0.828333i	$-0.310711\pi$
$488$		0			0
$489$	−3.54508	−	1.15187i	−0.160314	−	0.0520892i
$490$		0			0
$491$	5.72504	+	2.54895i	0.258368	+	0.115033i	0.531833	−	0.846849i	$-0.321503\pi$
$491$	5.72504	+	2.54895i	0.258368	+	0.115033i	−0.273466	+	0.961882i	$0.588170\pi$
$492$		0			0
$493$	8.57637	+	26.3953i	0.386260	+	1.18879i
$494$		0			0
$495$	−25.0183	−	26.3060i	−1.12449	−	1.18237i
$496$		0			0
$497$	−0.990218	+	1.09975i	−0.0444173	+	0.0493304i
$498$		0			0
$499$	−13.9632	−	19.2187i	−0.625079	−	0.860347i	0.372631	−	0.927979i	$-0.378456\pi$
$499$	−13.9632	−	19.2187i	−0.625079	−	0.860347i	−0.997710	+	0.0676321i	$0.978456\pi$
$500$		0			0
$501$	3.84085	−	3.45832i	0.171597	−	0.154506i
$502$		0			0
$503$	20.4742	−	9.11568i	0.912898	−	0.406448i	0.104121	−	0.994565i	$-0.466797\pi$
$503$	20.4742	−	9.11568i	0.912898	−	0.406448i	0.808776	+	0.588116i	$0.200130\pi$
$504$		0			0
$505$	−42.0803	+	24.2951i	−1.87255	+	1.08112i
$506$		0			0
$507$	5.81874	−	1.15227i	0.258419	−	0.0511739i
$508$		0			0
$509$	−4.87461	−	0.512342i	−0.216063	−	0.0227092i	−0.00412175	−	0.999992i	$-0.501312\pi$
$509$	−4.87461	−	0.512342i	−0.216063	−	0.0227092i	−0.211942	+	0.977282i	$0.567979\pi$
$510$		0			0
$511$	0.149735	+	0.166298i	0.00662388	+	0.00735657i
$512$		0			0
$513$	12.7023	−	1.33506i	0.560820	−	0.0589445i
$514$		0			0
$515$	11.0423	−	3.58786i	0.486582	−	0.158100i
$516$		0			0
$517$	−24.0313	+	18.4818i	−1.05690	+	0.812827i
$518$		0			0
$519$	−0.00743638	−	0.0228868i	−0.000326421	−	0.00100462i
$520$		0			0
$521$	20.6067	−	14.9716i	0.902795	−	0.655919i	−0.0363875	−	0.999338i	$-0.511585\pi$
$521$	20.6067	−	14.9716i	0.902795	−	0.655919i	0.939182	+	0.343419i	$0.111585\pi$
$522$		0			0
$523$	−4.80418	+	1.02116i	−0.210072	+	0.0446522i	−0.311745	−	0.950166i	$-0.600914\pi$
$523$	−4.80418	+	1.02116i	−0.210072	+	0.0446522i	0.101674	+	0.994818i	$0.467580\pi$
$524$		0			0
$525$	−0.360542	+	0.496244i	−0.0157354	+	0.0216579i
$526$		0			0
$527$	16.1145	+	9.30371i	0.701959	+	0.405276i
$528$		0			0
$529$	−11.9776	+	20.7458i	−0.520766	+	0.901993i
$530$		0			0
$531$	18.1780	+	1.91059i	0.788859	+	0.0829124i
$532$		0			0
$533$	−21.3777	+	23.4121i	−0.925971	+	1.01409i
$534$		0			0
$535$	10.9629	−	24.6231i	0.473968	−	1.06455i
$536$		0			0
$537$	6.14875	+	1.30696i	0.265338	+	0.0563994i
$538$		0			0
$539$	−23.0912	−	1.79185i	−0.994610	−	0.0771804i
$540$		0			0
$541$	−29.9955	+	9.74613i	−1.28961	+	0.419019i	−0.871954	−	0.489588i	$-0.837147\pi$
$541$	−29.9955	+	9.74613i	−1.28961	+	0.419019i	−0.417653	+	0.908607i	$0.637147\pi$
$542$		0			0
$543$	0.500066	+	0.222644i	0.0214599	+	0.00955456i
$544$		0			0
$545$	1.93196	−	5.94595i	0.0827560	−	0.254697i
$546$		0			0
$547$	−31.4333	−	22.8377i	−1.34399	−	0.976468i	−0.999287	−	0.0377571i	$-0.987979\pi$
$547$	−31.4333	−	22.8377i	−1.34399	−	0.976468i	−0.344706	−	0.938711i	$-0.612021\pi$
$548$		0			0
$549$	−15.1440	−	26.2302i	−0.646330	−	1.11948i
$550$		0			0
$551$		−	35.9803i		−	1.53281i
$552$		0			0
$553$	−0.660295	−	1.48305i	−0.0280786	−	0.0630656i
$554$		0			0
$555$	−3.62892	−	4.03032i	−0.154039	−	0.171078i
$556$		0			0
$557$	5.73927	−	12.8906i	0.243181	−	0.546193i	−0.750180	−	0.661234i	$-0.770033\pi$
$557$	5.73927	−	12.8906i	0.243181	−	0.546193i	0.993361	+	0.115041i	$0.0366998\pi$
$558$		0			0
$559$	−13.6802	−	31.3119i	−0.578612	−	1.32435i
$560$		0			0
$561$	−5.31599	+	1.88905i	−0.224441	+	0.0797559i
$562$		0			0
$563$	−0.503262	−	0.106972i	−0.0212100	−	0.00450832i	0.197294	−	0.980344i	$-0.436784\pi$
$563$	−0.503262	−	0.106972i	−0.0212100	−	0.00450832i	−0.218504	+	0.975836i	$0.570118\pi$
$564$		0			0
$565$	−56.6030	+	5.94921i	−2.38131	+	0.250285i
$566$		0			0
$567$	0.883771	+	0.287155i	0.0371149	+	0.0120594i
$568$		0			0
$569$	4.69343	−	44.6550i	0.196759	−	1.87203i	−0.237695	−	0.971340i	$-0.576392\pi$
$569$	4.69343	−	44.6550i	0.196759	−	1.87203i	0.434454	−	0.900694i	$-0.356941\pi$
$570$		0			0
$571$	−1.76143			−0.0737134			−0.0368567	−	0.999321i	$-0.511735\pi$
$571$	−1.76143			−0.0737134			−0.0368567	+	0.999321i	$0.511735\pi$
$572$		0			0
$573$	−7.81461			−0.326460
$574$		0			0
$575$	−7.42908	+	70.6829i	−0.309814	+	2.94768i
$576$		0			0
$577$	−19.6043	−	6.36984i	−0.816139	−	0.265180i	−0.128943	−	0.991652i	$-0.541159\pi$
$577$	−19.6043	−	6.36984i	−0.816139	−	0.265180i	−0.687196	+	0.726472i	$0.741159\pi$
$578$		0			0
$579$	−5.44164	+	0.571939i	−0.226147	+	0.0237690i
$580$		0			0
$581$	0.580464	+	0.123381i	0.0240817	+	0.00511873i
$582$		0			0
$583$	−0.442047	−	16.2022i	−0.0183077	−	0.671029i
$584$		0			0
$585$	36.1648	−	15.8004i	1.49523	−	0.653268i
$586$		0			0
$587$	4.15818	−	9.33942i	0.171626	−	0.385479i	−0.807169	−	0.590321i	$-0.799001\pi$
$587$	4.15818	−	9.33942i	0.171626	−	0.385479i	0.978795	+	0.204842i	$0.0656680\pi$
$588$		0			0
$589$	−16.1414	−	17.9268i	−0.665093	−	0.738661i
$590$		0			0
$591$	−1.08150	−	2.42908i	−0.0444869	−	0.0999191i
$592$		0			0
$593$			35.2373i			1.44702i	0.690312	+	0.723512i	$0.257473\pi$
$593$			35.2373i			1.44702i	−0.690312	+	0.723512i	$0.742527\pi$
$594$		0			0
$595$	−0.947211	−	1.64062i	−0.0388319	−	0.0672588i
$596$		0			0
$597$	5.68795	+	4.13254i	0.232792	+	0.169134i
$598$		0			0
$599$	14.1882	−	43.6667i	0.579713	−	1.78417i	−0.0398230	−	0.999207i	$-0.512679\pi$
$599$	14.1882	−	43.6667i	0.579713	−	1.78417i	0.619536	−	0.784968i	$-0.287321\pi$
$600$		0			0
$601$	5.60509	+	2.49555i	0.228637	+	0.101796i	0.517858	−	0.855467i	$-0.326730\pi$
$601$	5.60509	+	2.49555i	0.228637	+	0.101796i	−0.289221	+	0.957262i	$0.593396\pi$
$602$		0			0
$603$	15.4615	−	5.02376i	0.629642	−	0.204583i
$604$		0			0
$605$	−27.2146	−	33.4569i	−1.10643	−	1.36022i
$606$		0			0
$607$	8.47529	+	1.80148i	0.344001	+	0.0731197i	0.376673	−	0.926346i	$-0.377068\pi$
$607$	8.47529	+	1.80148i	0.344001	+	0.0731197i	−0.0326714	+	0.999466i	$0.510401\pi$
$608$		0			0
$609$	−0.179078	+	0.402215i	−0.00725659	+	0.0162986i
$610$		0			0
$611$	−9.96562	−	31.4145i	−0.403166	−	1.27090i
$612$		0			0
$613$	17.0537	+	1.79242i	0.688794	+	0.0723952i	0.442458	−	0.896789i	$-0.354107\pi$
$613$	17.0537	+	1.79242i	0.688794	+	0.0723952i	0.246336	+	0.969184i	$0.420773\pi$
$614$		0			0
$615$	7.86524	−	13.6230i	0.317157	−	0.549332i
$616$		0			0
$617$	5.89730	+	3.40481i	0.237416	+	0.137072i	0.613989	−	0.789315i	$-0.289564\pi$
$617$	5.89730	+	3.40481i	0.237416	+	0.137072i	−0.376572	+	0.926387i	$0.622897\pi$
$618$		0			0
$619$	−10.4079	+	14.3252i	−0.418327	+	0.575778i	−0.965225	−	0.261422i	$-0.915809\pi$
$619$	−10.4079	+	14.3252i	−0.418327	+	0.575778i	0.546898	+	0.837199i	$0.315809\pi$
$620$		0			0
$621$	−17.7133	+	3.76507i	−0.710809	+	0.151087i
$622$		0			0
$623$	−0.881160	+	0.640200i	−0.0353029	+	0.0256491i
$624$		0			0
$625$	9.49201	+	29.2134i	0.379680	+	1.16854i
$626$		0			0
$627$	7.31120	−	0.199472i	0.291981	−	0.00796613i
$628$		0			0
$629$	10.7484	−	3.49236i	0.428566	−	0.139250i
$630$		0			0
$631$	7.25629	−	0.762666i	0.288868	−	0.0303613i	0.0410138	−	0.999159i	$-0.486941\pi$
$631$	7.25629	−	0.762666i	0.288868	−	0.0303613i	0.247854	+	0.968797i	$0.420275\pi$
$632$		0			0
$633$	−4.51702	−	5.01666i	−0.179535	−	0.199394i
$634$		0			0
$635$	3.28579	+	0.345351i	0.130393	+	0.0137048i
$636$		0			0
$637$	10.4010	−	22.9296i	0.412104	−	0.908502i
$638$		0			0
$639$	−27.6054	+	15.9380i	−1.09205	+	0.630497i
$640$		0			0
$641$	−33.1380	+	14.7540i	−1.30887	+	0.582748i	−0.938225	−	0.346025i	$-0.887531\pi$
$641$	−33.1380	+	14.7540i	−1.30887	+	0.582748i	−0.370649	+	0.928773i	$0.620865\pi$
$642$		0			0
$643$	−29.8161	+	26.8465i	−1.17583	+	1.05872i	−0.178634	+	0.983916i	$0.557168\pi$
$643$	−29.8161	+	26.8465i	−1.17583	+	1.05872i	−0.997198	+	0.0748079i	$0.976166\pi$
$644$		0			0
$645$	9.96537	+	13.7162i	0.392386	+	0.540073i
$646$		0			0
$647$	10.9752	−	12.1892i	0.431478	−	0.479205i	−0.487720	−	0.873000i	$-0.662171\pi$
$647$	10.9752	−	12.1892i	0.431478	−	0.479205i	0.919198	+	0.393795i	$0.128838\pi$
$648$		0			0
$649$	21.3549	+	3.93369i	0.838254	+	0.154411i
$650$		0			0
$651$	0.0912170	+	0.280737i	0.00357507	+	0.0110029i
$652$		0			0
$653$	5.78828	+	2.57711i	0.226513	+	0.100850i	0.516855	−	0.856073i	$-0.327103\pi$
$653$	5.78828	+	2.57711i	0.226513	+	0.100850i	−0.290342	+	0.956923i	$0.593769\pi$
$654$		0			0
$655$	83.7209	+	27.2026i	3.27125	+	1.06289i
$656$		0			0
$657$	1.96051	+	4.40338i	0.0764868	+	0.171792i
$658$		0			0
$659$	11.5113	−	19.9381i	0.448416	−	0.776678i	−0.549868	−	0.835252i	$-0.685322\pi$
$659$	11.5113	−	19.9381i	0.448416	−	0.776678i	0.998283	+	0.0585734i	$0.0186552\pi$
$660$		0			0
$661$	−1.82838	+	1.05562i	−0.0711159	+	0.0410588i	−0.535136	−	0.844766i	$-0.679740\pi$
$661$	−1.82838	+	1.05562i	−0.0711159	+	0.0410588i	0.464020	+	0.885824i	$0.346406\pi$
$662$		0			0
$663$	0.0427542	−	6.13298i	0.00166043	−	0.238185i
$664$		0			0
$665$	0.510621	+	2.40228i	0.0198010	+	0.0931566i
$666$		0			0
$667$	5.33243	+	50.7347i	0.206473	+	1.96446i
$668$		0			0
$669$	0.324911	−	1.52859i	0.0125618	−	0.0590986i
$670$		0			0
$671$	−15.5261	−	32.4596i	−0.599380	−	1.25309i
$672$		0			0
$673$	4.67197	−	5.18874i	0.180091	−	0.200011i	−0.646340	−	0.763050i	$-0.723701\pi$
$673$	4.67197	−	5.18874i	0.180091	−	0.200011i	0.826431	+	0.563039i	$0.190368\pi$
$674$		0			0
$675$	−22.1752	+	16.1112i	−0.853525	+	0.620122i
$676$		0			0
$677$	−9.90760	+	30.4925i	−0.380780	+	1.17192i	0.558715	+	0.829359i	$0.311294\pi$
$677$	−9.90760	+	30.4925i	−0.380780	+	1.17192i	−0.939496	+	0.342561i	$0.888706\pi$
$678$		0			0
$679$	0.143338	−	1.36377i	0.00550081	−	0.0523368i
$680$		0			0
$681$		−	6.42430i		−	0.246180i
$682$		0			0
$683$	14.9677	+	8.64162i	0.572724	+	0.330662i	0.758236	−	0.651980i	$-0.226061\pi$
$683$	14.9677	+	8.64162i	0.572724	+	0.330662i	−0.185513	+	0.982642i	$0.559395\pi$
$684$		0			0
$685$	−49.9586	+	22.2430i	−1.90882	+	0.849861i
$686$		0			0
$687$	−1.00110	−	4.70982i	−0.0381945	−	0.179691i
$688$		0			0
$689$	16.7195	+	5.56165i	0.636962	+	0.211882i
$690$		0			0
$691$	−10.0544	−	9.05302i	−0.382487	−	0.344393i	0.455351	−	0.890312i	$-0.349514\pi$
$691$	−10.0544	−	9.05302i	−0.382487	−	0.344393i	−0.837838	+	0.545919i	$0.816181\pi$
$692$		0			0
$693$	1.10926	+	0.458047i	0.0421374	+	0.0173998i
$694$		0			0
$695$	5.68521	−	26.7468i	0.215652	−	1.01456i
$696$		0			0
$697$	19.2677	+	26.5198i	0.729817	+	1.00451i
$698$		0			0
$699$	−3.68179	+	0.782589i	−0.139258	+	0.0296002i
$700$		0			0
$701$	−8.44189	−	6.13339i	−0.318846	−	0.231655i	0.416837	−	0.908981i	$-0.363139\pi$
$701$	−8.44189	−	6.13339i	−0.318846	−	0.231655i	−0.735683	+	0.677326i	$0.763139\pi$
$702$		0			0
$703$	−14.6514			−0.552589
$704$		0			0
$705$	8.17622	+	14.1616i	0.307934	+	0.533358i
$706$		0			0
$707$	0.944156	−	1.29952i	0.0355086	−	0.0488734i
$708$		0			0
$709$	10.7116	−	9.64481i	0.402284	−	0.362218i	−0.443012	−	0.896515i	$-0.646090\pi$
$709$	10.7116	−	9.64481i	0.402284	−	0.362218i	0.845297	+	0.534297i	$0.179424\pi$
$710$		0			0
$711$	−3.65513	−	34.7762i	−0.137078	−	1.30421i
$712$		0			0
$713$	25.4173	+	22.8858i	0.951885	+	0.857081i
$714$		0			0
$715$	44.2867	−	15.3906i	1.65623	−	0.575574i
$716$		0			0
$717$	−1.16863	−	1.05224i	−0.0436432	−	0.0392965i
$718$		0			0
$719$	3.90557	+	37.1590i	0.145653	+	1.38580i	0.786244	+	0.617916i	$0.212023\pi$
$719$	3.90557	+	37.1590i	0.145653	+	1.38580i	−0.640591	+	0.767882i	$0.721311\pi$
$720$		0			0
$721$	−0.285236	+	0.256828i	−0.0106227	+	0.00956476i
$722$		0			0
$723$	−4.55461	+	6.26888i	−0.169388	+	0.233142i
$724$		0			0
$725$	38.6080	+	66.8710i	1.43386	+	2.48353i
$726$		0			0
$727$	46.8427			1.73730			0.868650	−	0.495426i	$-0.164988\pi$
$727$	46.8427			1.73730			0.868650	+	0.495426i	$0.164988\pi$
$728$		0			0
$729$	13.2666	+	9.63878i	0.491357	+	0.356992i
$730$		0			0
$731$	−34.5581	+	7.34554i	−1.27818	+	0.271685i
$732$		0			0
$733$	−5.41904	−	7.45867i	−0.200157	−	0.275492i	0.697126	−	0.716949i	$-0.254462\pi$
$733$	−5.41904	−	7.45867i	−0.200157	−	0.275492i	−0.897283	+	0.441457i	$0.854462\pi$
$734$		0			0
$735$	−2.59738	+	12.2197i	−0.0958058	+	0.450731i
$736$		0			0
$737$	18.7748	−	4.52920i	0.691578	−	0.166835i
$738$		0			0
$739$	1.42219	+	1.28054i	0.0523160	+	0.0471055i	0.694874	−	0.719132i	$-0.255460\pi$
$739$	1.42219	+	1.28054i	0.0523160	+	0.0471055i	−0.642558	+	0.766237i	$0.722127\pi$
$740$		0			0
$741$	−2.50967	+	7.54460i	−0.0921950	+	0.277158i
$742$		0			0
$743$	7.70528	+	36.2505i	0.282679	+	1.32990i	0.858705	+	0.512470i	$0.171269\pi$
$743$	7.70528	+	36.2505i	0.282679	+	1.32990i	−0.576026	+	0.817431i	$0.695397\pi$
$744$		0			0
$745$	1.04872	−	0.466918i	0.0384220	−	0.0171066i
$746$		0			0
$747$	11.0699	+	6.39123i	0.405028	+	0.233843i
$748$		0			0
$749$			0.891025i			0.0325573i
$750$		0			0
$751$	1.47535	−	14.0370i	0.0538363	−	0.512218i	−0.934062	−	0.357112i	$-0.883761\pi$
$751$	1.47535	−	14.0370i	0.0538363	−	0.512218i	0.987898	−	0.155106i	$-0.0495719\pi$
$752$		0			0
$753$	−3.00500	+	9.24843i	−0.109508	+	0.337032i
$754$		0			0
$755$	29.6915	−	21.5722i	1.08059	−	0.785092i
$756$		0			0
$757$	15.5470	−	17.2667i	0.565067	−	0.627570i	−0.391116	−	0.920341i	$-0.627911\pi$
$757$	15.5470	−	17.2667i	0.565067	−	0.627570i	0.956182	+	0.292771i	$0.0945775\pi$
$758$		0			0
$759$	−10.2797	+	1.36482i	−0.373131	+	0.0495399i
$760$		0			0
$761$	−1.88880	+	8.88610i	−0.0684689	+	0.322121i	−0.999031	−	0.0440133i	$-0.985986\pi$
$761$	−1.88880	+	8.88610i	−0.0684689	+	0.322121i	0.930562	+	0.366134i	$0.119319\pi$
$762$		0			0
$763$	0.0216036	+	0.205545i	0.000782104	+	0.00744122i
$764$		0			0
$765$	−8.48398	−	39.9140i	−0.306739	−	1.44309i
$766$		0			0
$767$	−11.9451	+	20.3605i	−0.431314	+	0.735174i
$768$		0			0
$769$	32.2586	−	18.6245i	1.16328	−	0.671617i	0.211188	−	0.977445i	$-0.432267\pi$
$769$	32.2586	−	18.6245i	1.16328	−	0.671617i	0.952087	+	0.305828i	$0.0989333\pi$
$770$		0			0
$771$	−0.135278	+	0.234309i	−0.00487192	+	0.00843842i
$772$		0			0
$773$	−6.28285	−	14.1115i	−0.225978	−	0.507556i	0.764600	−	0.644506i	$-0.222937\pi$
$773$	−6.28285	−	14.1115i	−0.225978	−	0.507556i	−0.990578	+	0.136950i	$0.956270\pi$
$774$		0			0
$775$	49.2355	+	15.9976i	1.76859	+	0.574650i
$776$		0			0
$777$	0.163785	+	0.0729217i	0.00587575	+	0.00261605i
$778$		0			0
$779$	−13.1322	−	40.4168i	−0.470510	−	1.44808i
$780$		0			0
$781$	−34.1614	+	16.3402i	−1.22239	+	0.584697i
$782$		0			0
$783$	−13.1647	+	14.6209i	−0.470469	+	0.522508i
$784$		0			0
$785$	−50.1656	−	69.0470i	−1.79049	−	2.46439i
$786$		0			0
$787$	−39.8725	+	35.9014i	−1.42130	+	1.27975i	−0.514953	+	0.857218i	$0.672191\pi$
$787$	−39.8725	+	35.9014i	−1.42130	+	1.27975i	−0.906350	+	0.422529i	$0.861143\pi$
$788$		0			0
$789$	10.8257	−	4.81993i	0.385407	−	0.171594i
$790$		0			0
$791$	1.62942	−	0.940745i	0.0579355	−	0.0334491i
$792$		0			0
$793$	38.9296	−	3.81748i	1.38243	−	0.135563i
$794$		0			0
$795$	−8.69475	−	0.913855i	−0.308371	−	0.0324111i
$796$		0			0
$797$	−6.45162	−	7.16525i	−0.228528	−	0.253806i	0.617965	−	0.786205i	$-0.287957\pi$
$797$	−6.45162	−	7.16525i	−0.228528	−	0.253806i	−0.846493	+	0.532399i	$0.821291\pi$
$798$		0			0
$799$	−33.8896	+	3.56194i	−1.19893	+	0.126013i
$800$		0			0
$801$	−22.3124	+	7.24975i	−0.788371	+	0.256157i
$802$		0			0
$803$	1.91737	+	5.39567i	0.0676624	+	0.190409i
$804$		0			0
$805$	−1.07604	−	3.31172i	−0.0379255	−	0.116723i
$806$		0			0
$807$	−5.28536	+	3.84004i	−0.186053	+	0.135176i
$808$		0			0
$809$	−35.2718	+	7.49725i	−1.24009	+	0.263589i	−0.780847	−	0.624722i	$-0.785212\pi$
$809$	−35.2718	+	7.49725i	−1.24009	+	0.263589i	−0.459242	+	0.888311i	$0.651879\pi$
$810$		0			0
$811$	17.3537	−	23.8853i	0.609371	−	0.838727i	−0.387155	−	0.922015i	$-0.626542\pi$
$811$	17.3537	−	23.8853i	0.609371	−	0.838727i	0.996526	+	0.0832878i	$0.0265421\pi$
$812$		0			0
$813$	2.36707	+	1.36663i	0.0830168	+	0.0479298i
$814$		0			0
$815$	16.0146	−	27.7380i	0.560966	−	0.971621i
$816$		0			0
$817$	45.5515	+	4.78765i	1.59365	+	0.167499i
$818$		0			0
$819$	−0.879725	+	0.963442i	−0.0307401	+	0.0336654i
$820$		0			0
$821$	−10.1972	+	22.9032i	−0.355884	+	0.799328i	0.643541	+	0.765412i	$0.277465\pi$
$821$	−10.1972	+	22.9032i	−0.355884	+	0.799328i	−0.999425	+	0.0339165i	$0.989202\pi$
$822$		0			0
$823$	4.54660	+	0.966409i	0.158484	+	0.0336869i	0.286471	−	0.958089i	$-0.407518\pi$
$823$	4.54660	+	0.966409i	0.158484	+	0.0336869i	−0.127986	+	0.991776i	$0.540851\pi$
$824$		0			0
$825$	−13.3742	+	8.21588i	−0.465629	+	0.286040i
$826$		0			0
$827$	−44.0869	+	14.3247i	−1.53305	+	0.498119i	−0.949449	−	0.313920i	$-0.898358\pi$
$827$	−44.0869	+	14.3247i	−1.53305	+	0.498119i	−0.583603	+	0.812039i	$0.698358\pi$
$828$		0			0
$829$	12.8199	+	5.70777i	0.445252	+	0.198239i	0.617100	−	0.786884i	$-0.288307\pi$
$829$	12.8199	+	5.70777i	0.445252	+	0.198239i	−0.171848	+	0.985123i	$0.554974\pi$
$830$		0			0
$831$	0.156912	−	0.482926i	0.00544322	−	0.0167525i
$832$		0			0
$833$	−21.0613	−	15.3019i	−0.729729	−	0.530179i
$834$		0			0
$835$	22.2049	+	38.4601i	0.768433	+	1.33097i
$836$		0			0
$837$			13.1906i			0.455935i
$838$		0			0
$839$	−14.1994	−	31.8925i	−0.490219	−	1.10105i	−0.974141	−	0.225939i	$-0.927455\pi$
$839$	−14.1994	−	31.8925i	−0.490219	−	1.10105i	0.483923	−	0.875111i	$-0.339212\pi$
$840$		0			0
$841$	17.6811	+	19.6368i	0.609692	+	0.677132i
$842$		0			0
$843$	4.67389	−	10.4977i	0.160977	−	0.361561i
$844$		0			0
$845$	−0.710596	+	50.9642i	−0.0244453	+	1.75322i
$846$		0			0
$847$	1.27174	+	0.644475i	0.0436975	+	0.0221444i
$848$		0			0
$849$	−1.19592	−	0.254201i	−0.0410440	−	0.00872417i
$850$		0			0
$851$	20.6595	−	2.17141i	0.708200	−	0.0744348i
$852$		0			0
$853$	−7.88798	−	2.56296i	−0.270079	−	0.0877540i	0.170847	−	0.985298i	$-0.445350\pi$
$853$	−7.88798	−	2.56296i	−0.270079	−	0.0877540i	−0.440926	+	0.897544i	$0.645350\pi$
$854$		0			0
$855$	−5.52966	+	52.6112i	−0.189110	+	1.79926i
$856$		0			0
$857$	−27.7135			−0.946676			−0.473338	−	0.880881i	$-0.656951\pi$
$857$	−27.7135			−0.946676			−0.473338	+	0.880881i	$0.656951\pi$
$858$		0			0
$859$	−7.36434			−0.251268			−0.125634	−	0.992077i	$-0.540097\pi$
$859$	−7.36434			−0.251268			−0.125634	+	0.992077i	$0.540097\pi$
$860$		0			0
$861$	−0.0543567	+	0.517170i	−0.00185247	+	0.0176251i
$862$		0			0
$863$	−39.7857	−	12.9271i	−1.35432	−	0.440045i	−0.460177	−	0.887827i	$-0.652214\pi$
$863$	−39.7857	−	12.9271i	−1.35432	−	0.440045i	−0.894143	+	0.447782i	$0.852214\pi$
$864$		0			0
$865$	0.205646	−	0.0216142i	0.00699216	−	0.000734905i
$866$		0			0
$867$	1.38459	+	0.294303i	0.0470230	+	0.00999505i
$868$		0			0
$869$	−1.13295	−	41.5259i	−0.0384327	−	1.40867i
$870$		0			0
$871$	−2.34017	+	20.8650i	−0.0792936	+	0.706984i
$872$		0			0
$873$	12.0139	−	26.9837i	0.406609	−	0.913259i
$874$		0			0
$875$	−1.82660	−	2.02864i	−0.0617503	−	0.0685807i
$876$		0			0
$877$	0.620414	+	1.39347i	0.0209499	+	0.0470543i	0.923717	−	0.383075i	$-0.125135\pi$
$877$	0.620414	+	1.39347i	0.0209499	+	0.0470543i	−0.902767	+	0.430129i	$0.858468\pi$
$878$		0			0
$879$		−	5.01938i		−	0.169299i
$880$		0			0
$881$	−5.91335	−	10.2422i	−0.199226	−	0.345069i	0.749052	−	0.662511i	$-0.230509\pi$
$881$	−5.91335	−	10.2422i	−0.199226	−	0.345069i	−0.948278	+	0.317442i	$0.897176\pi$
$882$		0			0
$883$	25.9734	+	18.8708i	0.874073	+	0.635051i	0.931677	−	0.363288i	$-0.118346\pi$
$883$	25.9734	+	18.8708i	0.874073	+	0.635051i	−0.0576036	+	0.998340i	$0.518346\pi$
$884$		0			0
$885$	3.61936	−	11.1392i	0.121664	−	0.374442i
$886$		0			0
$887$	35.3232	+	15.7269i	1.18604	+	0.528058i	0.902411	−	0.430877i	$-0.141796\pi$
$887$	35.3232	+	15.7269i	1.18604	+	0.528058i	0.283627	+	0.958935i	$0.408462\pi$
$888$		0			0
$889$	−0.103875	+	0.0337509i	−0.00348384	+	0.00113197i
$890$		0			0
$891$	18.0984	+	15.4232i	0.606320	+	0.516698i
$892$		0			0
$893$	43.2116	+	9.18490i	1.44602	+	0.307361i
$894$		0			0
$895$	−21.9696	+	49.3445i	−0.734362	+	1.64940i
$896$		0			0
$897$	2.42067	−	11.0104i	0.0808238	−	0.367626i
$898$		0			0
$899$	36.9553	+	3.88416i	1.23253	+	0.129544i
$900$		0			0
$901$	9.10925	−	15.7777i	0.303473	−	0.525631i
$902$		0			0
$903$	−0.485381	−	0.280235i	−0.0161525	−	0.00932563i
$904$		0			0
$905$	−2.76466	+	3.80523i	−0.0919003	+	0.126490i
$906$		0			0
$907$	−1.26162	+	0.268165i	−0.0418913	+	0.00890428i	−0.228810	−	0.973471i	$-0.573483\pi$
$907$	−1.26162	+	0.268165i	−0.0418913	+	0.00890428i	0.186918	+	0.982375i	$0.440150\pi$
$908$		0			0
$909$	27.9915	−	20.3370i	0.928420	−	0.674536i
$910$		0			0
$911$	8.73142	+	26.8725i	0.289285	+	0.890327i	0.985082	+	0.172088i	$0.0550515\pi$
$911$	8.73142	+	26.8725i	0.289285	+	0.890327i	−0.695797	+	0.718239i	$0.744949\pi$
$912$		0			0
$913$	12.5241	+	8.58738i	0.414488	+	0.284201i
$914$		0			0
$915$	−18.4584	+	5.99751i	−0.610217	+	0.198271i
$916$		0			0
$917$	−2.89414	+	0.304186i	−0.0955728	+	0.0100451i
$918$		0			0
$919$	6.19796	+	6.88353i	0.204452	+	0.227067i	0.836647	−	0.547742i	$-0.184513\pi$
$919$	6.19796	+	6.88353i	0.204452	+	0.227067i	−0.632195	+	0.774809i	$0.717846\pi$
$920$		0			0
$921$	14.6457	+	1.53933i	0.482594	+	0.0507226i
$922$		0			0
$923$	−4.01763	−	40.9706i	−0.132242	−	1.34856i
$924$		0			0
$925$	27.2304	−	15.7215i	0.895329	−	0.516918i
$926$		0			0
$927$	−7.55274	+	3.36270i	−0.248065	+	0.110445i
$928$		0			0
$929$	−0.442203	+	0.398161i	−0.0145082	+	0.0130632i	−0.676353	−	0.736578i	$-0.736441\pi$
$929$	−0.442203	+	0.398161i	−0.0145082	+	0.0130632i	0.661845	+	0.749641i	$0.269774\pi$
$930$		0			0
$931$	19.8376	+	27.3041i	0.650150	+	0.894855i
$932$		0			0
$933$	−3.64726	+	4.05069i	−0.119406	+	0.132614i
$934$		0			0
$935$	−6.38016	−	48.0549i	−0.208653	−	1.57156i
$936$		0			0
$937$	12.6165	+	38.8295i	0.412162	+	1.26850i	0.914765	+	0.403987i	$0.132376\pi$
$937$	12.6165	+	38.8295i	0.412162	+	1.26850i	−0.502603	+	0.864517i	$0.667624\pi$
$938$		0			0
$939$	13.9800	+	6.22430i	0.456220	+	0.203122i
$940$		0			0
$941$	54.0463	+	17.5607i	1.76186	+	0.572462i	0.997390	−	0.0721993i	$-0.0230018\pi$
$941$	54.0463	+	17.5607i	1.76186	+	0.572462i	0.764468	+	0.644662i	$0.223002\pi$
$942$		0			0
$943$	24.5073	+	55.0442i	0.798067	+	1.79249i
$944$		0			0
$945$	0.671470	−	1.16302i	0.0218429	−	0.0378331i
$946$		0			0
$947$	−45.1135	+	26.0463i	−1.46599	+	0.846390i	−0.999277	−	0.0380189i	$-0.987895\pi$
$947$	−45.1135	+	26.0463i	−1.46599	+	0.846390i	−0.466713	+	0.884409i	$0.654562\pi$
$948$		0			0
$949$	−6.22490	−	0.0433950i	−0.202069	−	0.00140866i
$950$		0			0
$951$	2.22109	+	10.4494i	0.0720237	+	0.338845i
$952$		0			0
$953$	−5.49672	−	52.2978i	−0.178056	−	1.69409i	−0.610168	−	0.792272i	$-0.708898\pi$
$953$	−5.49672	−	52.2978i	−0.178056	−	1.69409i	0.432111	−	0.901820i	$-0.357769\pi$
$954$		0			0
$955$	13.9608	−	65.6806i	0.451762	−	2.12537i
$956$		0			0
$957$	−8.16382	+	7.76420i	−0.263899	+	0.250981i
$958$		0			0
$959$	1.20967	−	1.34348i	0.0390624	−	0.0433832i
$960$		0			0
$961$	−4.92440	+	3.57778i	−0.158852	+	0.115412i
$962$		0			0
$963$	−5.93084	+	18.2532i	−0.191118	+	0.588202i
$964$		0			0
$965$	4.91446	−	46.7579i	0.158202	−	1.50519i
$966$		0			0
$967$			12.8220i			0.412328i	0.978517	+	0.206164i	$0.0660981\pi$
$967$			12.8220i			0.412328i	−0.978517	+	0.206164i	$0.933902\pi$
$968$		0			0
$969$	7.11962	+	4.11051i	0.228715	+	0.132049i
$970$		0			0
$971$	5.51607	−	2.45591i	0.177019	−	0.0788139i	−0.316314	−	0.948655i	$-0.602445\pi$
$971$	5.51607	−	2.45591i	0.177019	−	0.0788139i	0.493333	+	0.869841i	$0.335779\pi$
$972$		0			0
$973$	0.187942	+	0.884197i	0.00602514	+	0.0283460i
$974$		0			0
$975$	−3.43127	−	16.7150i	−0.109888	−	0.535307i
$976$		0			0
$977$	−17.8953	−	16.1130i	−0.572522	−	0.515501i	0.331234	−	0.943549i	$-0.392535\pi$
$977$	−17.8953	−	16.1130i	−0.572522	−	0.515501i	−0.903756	+	0.428048i	$0.859202\pi$
$978$		0			0
$979$	−27.0938	+	6.53606i	−0.865920	+	0.208893i
$980$		0			0
$981$	−0.925582	+	4.35452i	−0.0295516	+	0.139029i
$982$		0			0
$983$	16.7360	+	23.0351i	0.533795	+	0.734705i	0.987703	−	0.156343i	$-0.0499706\pi$
$983$	16.7360	+	23.0351i	0.533795	+	0.734705i	−0.453908	+	0.891048i	$0.649971\pi$
$984$		0			0
$985$	22.3482	−	4.75025i	0.712072	−	0.151356i
$986$		0			0
$987$	−0.437338	−	0.317745i	−0.0139206	−	0.0101139i
$988$		0			0
$989$	−64.9404			−2.06498
$990$		0			0
$991$	−11.2997	−	19.5716i	−0.358945	−	0.621711i	0.628840	−	0.777535i	$-0.283530\pi$
$991$	−11.2997	−	19.5716i	−0.358945	−	0.621711i	−0.987785	+	0.155824i	$0.950197\pi$
$992$		0			0
$993$	−2.05386	+	2.82689i	−0.0651772	+	0.0897087i
$994$		0			0
$995$	−44.8949	+	40.4236i	−1.42327	+	1.28151i
$996$		0			0
$997$	−5.52908	−	52.6057i	−0.175108	−	1.66604i	−0.630834	−	0.775918i	$-0.717287\pi$
$997$	−5.52908	−	52.6057i	−0.175108	−	1.66604i	0.455726	−	0.890120i	$-0.349380\pi$
$998$		0			0
$999$	5.95374	+	5.36077i	0.188368	+	0.169607i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.bq.a.49.7	✓	112
11.9	even	5	inner	572.2.bq.a.361.8	yes	112
13.4	even	6	inner	572.2.bq.a.225.8	yes	112
143.108	even	30	inner	572.2.bq.a.537.7	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.bq.a.49.7	✓	112	1.1	even	1	trivial
572.2.bq.a.225.8	yes	112	13.4	even	6	inner
572.2.bq.a.361.8	yes	112	11.9	even	5	inner
572.2.bq.a.537.7	yes	112	143.108	even	30	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.bq (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0476950 + 0.453788i) q^{3} +(-3.72881 - 1.21156i) q^{5} +(0.128901 - 0.0135480i) q^{7} +(2.73079 + 0.580448i) q^{9} +O(q^{10})\)	\(q+(-0.0476950 + 0.453788i) q^{3} +(-3.72881 - 1.21156i) q^{5} +(0.128901 - 0.0135480i) q^{7} +(2.73079 + 0.580448i) q^{9} +(3.18108 + 0.938485i) q^{11} +(-2.13957 + 2.90211i) q^{13} +(0.727638 - 1.63430i) q^{15} +(2.49450 + 2.77042i) q^{17} +(-1.96575 - 4.41515i) q^{19} +0.0591397i q^{21} +(3.42619 + 5.93434i) q^{23} +(8.39104 + 6.09645i) q^{25} +(-0.816647 + 2.51338i) q^{27} +(6.80110 + 3.02804i) q^{29} +(4.74701 - 1.54240i) q^{31} +(-0.577595 + 1.39877i) q^{33} +(-0.497060 - 0.105653i) q^{35} +(1.23304 - 2.76946i) q^{37} +(-1.21489 - 1.10933i) q^{39} +(8.74488 + 0.919124i) q^{41} +(-4.73852 + 8.20736i) q^{43} +(-9.47936 - 5.47291i) q^{45} +(-5.37278 + 7.39500i) q^{47} +(-6.83060 + 1.45189i) q^{49} +(-1.37616 + 0.999837i) q^{51} +(-1.51016 - 4.64779i) q^{53} +(-10.7246 - 7.35351i) q^{55} +(2.09730 - 0.681453i) q^{57} +(6.51121 - 0.684356i) q^{59} +(-7.25934 - 8.06231i) q^{61} +(0.359865 + 0.0378234i) q^{63} +(11.4941 - 8.22918i) q^{65} +(5.04304 - 2.91160i) q^{67} +(-2.85634 + 1.27173i) q^{69} +(-8.48501 + 7.63994i) q^{71} +(1.01482 + 1.39678i) q^{73} +(-3.16670 + 3.51698i) q^{75} +(0.422758 + 0.0778742i) q^{77} +(-3.87049 - 11.9121i) q^{79} +(6.54972 + 2.91612i) q^{81} +(4.35448 + 1.41486i) q^{83} +(-5.94496 - 13.3526i) q^{85} +(-1.69847 + 2.94183i) q^{87} +(-7.27757 + 4.20171i) q^{89} +(-0.236475 + 0.403071i) q^{91} +(0.473512 + 2.22770i) q^{93} +(1.98068 + 18.8449i) q^{95} +(2.19971 - 10.3488i) q^{97} +(8.14212 + 4.40926i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q + 20 q^{9}+O(q^{10}) \) 112 * q + 20 * q^9	\( 112 q + 20 q^{9} - 6 q^{11} + 11 q^{13} + 30 q^{15} + 16 q^{17} - 12 q^{19} + 6 q^{23} + 40 q^{25} - 12 q^{27} - 5 q^{29} + 9 q^{33} - 33 q^{35} - 45 q^{39} - 18 q^{41} + 30 q^{45} - 16 q^{49} + 48 q^{51} - 2 q^{53} - 20 q^{55} - 39 q^{59} + 4 q^{61} - 102 q^{63} - 6 q^{65} + 48 q^{67} + 34 q^{69} + 84 q^{71} - 56 q^{75} - 22 q^{77} - 24 q^{79} + 16 q^{81} + 60 q^{85} - 34 q^{87} - 66 q^{89} - 41 q^{91} + 123 q^{93} + 12 q^{95} - 15 q^{97}+O(q^{100}) \) 112 * q + 20 * q^9 - 6 * q^11 + 11 * q^13 + 30 * q^15 + 16 * q^17 - 12 * q^19 + 6 * q^23 + 40 * q^25 - 12 * q^27 - 5 * q^29 + 9 * q^33 - 33 * q^35 - 45 * q^39 - 18 * q^41 + 30 * q^45 - 16 * q^49 + 48 * q^51 - 2 * q^53 - 20 * q^55 - 39 * q^59 + 4 * q^61 - 102 * q^63 - 6 * q^65 + 48 * q^67 + 34 * q^69 + 84 * q^71 - 56 * q^75 - 22 * q^77 - 24 * q^79 + 16 * q^81 + 60 * q^85 - 34 * q^87 - 66 * q^89 - 41 * q^91 + 123 * q^93 + 12 * q^95 - 15 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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