LMFDB - Embedded newform 572.2.bv.a.41.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(41,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([0, 18, 5]))

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

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

chi := DirichletCharacter("572.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.bv (of order $60$, degree $16$, 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:	$224$
Relative dimension:	$14$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			41.3
Character	$\chi$	$=$	572.41
Dual form			572.2.bv.a.293.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.57791 + 1.75245i) q^{3} +(-0.871666 + 0.138058i) q^{5} +(1.64722 + 0.0863272i) q^{7} +(-0.267683 - 2.54684i) q^{9} +O(q^{10})$	\(q+(-1.57791 + 1.75245i) q^{3} +(-0.871666 + 0.138058i) q^{5} +(1.64722 + 0.0863272i) q^{7} +(-0.267683 - 2.54684i) q^{9} +(-1.51846 + 2.94860i) q^{11} +(-3.02315 + 1.96482i) q^{13} +(1.13347 - 1.74539i) q^{15} +(-1.58869 + 0.707329i) q^{17} +(-1.31821 - 2.02987i) q^{19} +(-2.75045 + 2.75045i) q^{21} +(5.16837 - 2.98396i) q^{23} +(-4.01454 + 1.30440i) q^{25} +(-0.837775 - 0.608679i) q^{27} +(-2.05446 - 9.66548i) q^{29} +(-1.46591 + 9.25538i) q^{31} +(-2.77127 - 7.31366i) q^{33} +(-1.44774 + 0.152164i) q^{35} +(-9.35068 - 6.07240i) q^{37} +(1.32701 - 8.39823i) q^{39} +(-0.632569 + 0.0331515i) q^{41} +(-2.31861 + 4.01596i) q^{43} +(0.584942 + 2.18303i) q^{45} +(5.38665 - 10.5719i) q^{47} +(-4.25577 - 0.447300i) q^{49} +(1.26725 - 3.90019i) q^{51} +(-7.21879 + 5.24476i) q^{53} +(0.916515 - 2.77983i) q^{55} +(5.63725 + 0.892853i) q^{57} +(-0.155108 + 2.95963i) q^{59} +(3.77315 + 8.47463i) q^{61} +(-0.221072 - 4.21831i) q^{63} +(2.36392 - 2.13004i) q^{65} +(-0.625682 - 0.167651i) q^{67} +(-2.92599 + 13.7657i) q^{69} +(-0.106450 + 0.277311i) q^{71} +(3.71569 + 7.29246i) q^{73} +(4.04869 - 9.09350i) q^{75} +(-2.75579 + 4.72592i) q^{77} +(6.86049 + 9.44265i) q^{79} +(9.90332 - 2.10502i) q^{81} +(-0.258118 - 1.62969i) q^{83} +(1.28715 - 0.835886i) q^{85} +(20.1800 + 11.6509i) q^{87} +(-1.89945 + 7.08886i) q^{89} +(-5.14942 + 2.97552i) q^{91} +(-13.9065 - 17.1731i) q^{93} +(1.42928 + 1.58738i) q^{95} +(6.43891 + 5.21413i) q^{97} +(7.91608 + 3.07799i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q + 28 q^{9}+O(q^{10}) $ 224 * q + 28 * q^9	$ 224 q + 28 q^{9} + 16 q^{11} + 10 q^{13} - 28 q^{15} - 48 q^{23} + 24 q^{27} + 20 q^{29} + 4 q^{31} + 60 q^{33} + 50 q^{35} + 12 q^{37} - 40 q^{39} + 20 q^{41} + 64 q^{45} - 62 q^{47} + 100 q^{53} - 22 q^{55} + 12 q^{59} - 40 q^{61} - 80 q^{63} - 44 q^{67} - 152 q^{71} + 30 q^{73} - 120 q^{75} + 80 q^{79} + 72 q^{81} + 90 q^{83} - 40 q^{85} - 8 q^{89} - 36 q^{91} - 90 q^{93} - 42 q^{97} + 144 q^{99}+O(q^{100}) $ 224 * q + 28 * q^9 + 16 * q^11 + 10 * q^13 - 28 * q^15 - 48 * q^23 + 24 * q^27 + 20 * q^29 + 4 * q^31 + 60 * q^33 + 50 * q^35 + 12 * q^37 - 40 * q^39 + 20 * q^41 + 64 * q^45 - 62 * q^47 + 100 * q^53 - 22 * q^55 + 12 * q^59 - 40 * q^61 - 80 * q^63 - 44 * q^67 - 152 * q^71 + 30 * q^73 - 120 * q^75 + 80 * q^79 + 72 * q^81 + 90 * q^83 - 40 * q^85 - 8 * q^89 - 36 * q^91 - 90 * q^93 - 42 * q^97 + 144 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{3}{10}\right)$

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
$3$	−1.57791	+	1.75245i	−0.911006	+	1.01178i	0.0888698	+	0.996043i	$0.471674\pi$
$3$	−1.57791	+	1.75245i	−0.911006	+	1.01178i	−0.999876	+	0.0157319i	$0.994992\pi$
$4$		0			0
$5$	−0.871666	+	0.138058i	−0.389821	+	0.0617416i	−0.348269	−	0.937395i	$-0.613230\pi$
$5$	−0.871666	+	0.138058i	−0.389821	+	0.0617416i	−0.0415523	+	0.999136i	$0.513230\pi$
$6$		0			0
$7$	1.64722	+	0.0863272i	0.622591	+	0.0326286i	0.361024	−	0.932557i	$-0.382427\pi$
$7$	1.64722	+	0.0863272i	0.622591	+	0.0326286i	0.261567	+	0.965185i	$0.415761\pi$
$8$		0			0
$9$	−0.267683	−	2.54684i	−0.0892277	−	0.848945i
$10$		0			0
$11$	−1.51846	+	2.94860i	−0.457834	+	0.889038i
$11$	−1.51846	+	2.94860i	−0.457834	+	0.889038i
$12$		0			0
$13$	−3.02315	+	1.96482i	−0.838472	+	0.544944i
$13$	−3.02315	+	1.96482i	−0.838472	+	0.544944i
$14$		0			0
$15$	1.13347	−	1.74539i	0.292661	−	0.450658i
$16$		0			0
$17$	−1.58869	+	0.707329i	−0.385313	+	0.171552i	−0.590246	−	0.807224i	$-0.700969\pi$
$17$	−1.58869	+	0.707329i	−0.385313	+	0.171552i	0.204933	+	0.978776i	$0.434302\pi$
$18$		0			0
$19$	−1.31821	−	2.02987i	−0.302419	−	0.465684i	0.654491	−	0.756070i	$-0.272883\pi$
$19$	−1.31821	−	2.02987i	−0.302419	−	0.465684i	−0.956910	+	0.290386i	$0.906216\pi$
$20$		0			0
$21$	−2.75045	+	2.75045i	−0.600197	+	0.600197i
$22$		0			0
$23$	5.16837	−	2.98396i	1.07768	−	0.622199i	0.147410	−	0.989075i	$-0.452906\pi$
$23$	5.16837	−	2.98396i	1.07768	−	0.622199i	0.930270	+	0.366877i	$0.119573\pi$
$24$		0			0
$25$	−4.01454	+	1.30440i	−0.802908	+	0.260881i
$26$		0			0
$27$	−0.837775	−	0.608679i	−0.161230	−	0.117140i
$28$		0			0
$29$	−2.05446	−	9.66548i	−0.381504	−	1.79484i	−0.579872	−	0.814708i	$-0.696897\pi$
$29$	−2.05446	−	9.66548i	−0.381504	−	1.79484i	0.198368	−	0.980128i	$-0.436436\pi$
$30$		0			0
$31$	−1.46591	+	9.25538i	−0.263285	+	1.66231i	0.401936	+	0.915668i	$0.368338\pi$
$31$	−1.46591	+	9.25538i	−0.263285	+	1.66231i	−0.665221	+	0.746647i	$0.731662\pi$
$32$		0			0
$33$	−2.77127	−	7.31366i	−0.482416	−	1.27314i
$34$		0			0
$35$	−1.44774	+	0.152164i	−0.244713	+	0.0257204i
$36$		0			0
$37$	−9.35068	−	6.07240i	−1.53724	−	0.998297i	−0.986526	−	0.163605i	$-0.947688\pi$
$37$	−9.35068	−	6.07240i	−1.53724	−	0.998297i	−0.550717	−	0.834692i	$-0.685646\pi$
$38$		0			0
$39$	1.32701	−	8.39823i	0.212492	−	1.34479i
$40$		0			0
$41$	−0.632569	+	0.0331515i	−0.0987907	+	0.00517740i	−0.101667	−	0.994818i	$-0.532418\pi$
$41$	−0.632569	+	0.0331515i	−0.0987907	+	0.00517740i	0.00287654	+	0.999996i	$0.499084\pi$
$42$		0			0
$43$	−2.31861	+	4.01596i	−0.353585	+	0.612428i	−0.986875	−	0.161487i	$-0.948371\pi$
$43$	−2.31861	+	4.01596i	−0.353585	+	0.612428i	0.633289	+	0.773915i	$0.281704\pi$
$44$		0			0
$45$	0.584942	+	2.18303i	0.0871981	+	0.325428i
$46$		0			0
$47$	5.38665	−	10.5719i	0.785723	−	1.54207i	−0.0536797	−	0.998558i	$-0.517095\pi$
$47$	5.38665	−	10.5719i	0.785723	−	1.54207i	0.839403	−	0.543510i	$-0.182905\pi$
$48$		0			0
$49$	−4.25577	−	0.447300i	−0.607967	−	0.0638999i
$50$		0			0
$51$	1.26725	−	3.90019i	0.177450	−	0.546136i
$52$		0			0
$53$	−7.21879	+	5.24476i	−0.991578	+	0.720423i	−0.960266	−	0.279086i	$-0.909968\pi$
$53$	−7.21879	+	5.24476i	−0.991578	+	0.720423i	−0.0313116	+	0.999510i	$0.509968\pi$
$54$		0			0
$55$	0.916515	−	2.77983i	0.123583	−	0.374833i
$56$		0			0
$57$	5.63725	+	0.892853i	0.746672	+	0.118261i
$58$		0			0
$59$	−0.155108	+	2.95963i	−0.0201933	+	0.385311i	0.969773	+	0.244009i	$0.0784625\pi$
$59$	−0.155108	+	2.95963i	−0.0201933	+	0.385311i	−0.989966	+	0.141303i	$0.954871\pi$
$60$		0			0
$61$	3.77315	+	8.47463i	0.483102	+	1.08507i	0.976550	+	0.215290i	$0.0690696\pi$
$61$	3.77315	+	8.47463i	0.483102	+	1.08507i	−0.493448	+	0.869775i	$0.664264\pi$
$62$		0			0
$63$	−0.221072	−	4.21831i	−0.0278525	−	0.531457i
$64$		0			0
$65$	2.36392	−	2.13004i	0.293208	−	0.264199i
$66$		0			0
$67$	−0.625682	−	0.167651i	−0.0764392	−	0.0204818i	0.220397	−	0.975410i	$-0.429265\pi$
$67$	−0.625682	−	0.167651i	−0.0764392	−	0.0204818i	−0.296836	+	0.954928i	$0.595931\pi$
$68$		0			0
$69$	−2.92599	+	13.7657i	−0.352248	+	1.65720i
$70$		0			0
$71$	−0.106450	+	0.277311i	−0.0126333	+	0.0329108i	−0.939752	−	0.341857i	$-0.888944\pi$
$71$	−0.106450	+	0.277311i	−0.0126333	+	0.0329108i	0.927119	+	0.374768i	$0.122278\pi$
$72$		0			0
$73$	3.71569	+	7.29246i	0.434889	+	0.853518i	0.999601	+	0.0282302i	$0.00898716\pi$
$73$	3.71569	+	7.29246i	0.434889	+	0.853518i	−0.564712	+	0.825288i	$0.691013\pi$
$74$		0			0
$75$	4.04869	−	9.09350i	0.467502	−	1.05003i
$76$		0			0
$77$	−2.75579	+	4.72592i	−0.314051	+	0.538568i
$78$		0			0
$79$	6.86049	+	9.44265i	0.771865	+	1.06238i	0.996133	+	0.0878540i	$0.0280009\pi$
$79$	6.86049	+	9.44265i	0.771865	+	1.06238i	−0.224268	+	0.974528i	$0.571999\pi$
$80$		0			0
$81$	9.90332	−	2.10502i	1.10037	−	0.233891i
$82$		0			0
$83$	−0.258118	−	1.62969i	−0.0283321	−	0.178882i	0.969464	−	0.245233i	$-0.0788644\pi$
$83$	−0.258118	−	1.62969i	−0.0283321	−	0.178882i	−0.997796	+	0.0663508i	$0.978864\pi$
$84$		0			0
$85$	1.28715	−	0.835886i	0.139611	−	0.0906646i
$86$		0			0
$87$	20.1800	+	11.6509i	2.16352	+	1.24911i
$88$		0			0
$89$	−1.89945	+	7.08886i	−0.201342	+	0.751418i	0.789192	+	0.614147i	$0.210500\pi$
$89$	−1.89945	+	7.08886i	−0.201342	+	0.751418i	−0.990534	+	0.137271i	$0.956167\pi$
$90$		0			0
$91$	−5.14942	+	2.97552i	−0.539806	+	0.311919i
$92$		0			0
$93$	−13.9065	−	17.1731i	−1.44203	−	1.78076i
$94$		0			0
$95$	1.42928	+	1.58738i	0.146641	+	0.162861i
$96$		0			0
$97$	6.43891	+	5.21413i	0.653773	+	0.529415i	0.897828	−	0.440347i	$-0.145144\pi$
$97$	6.43891	+	5.21413i	0.653773	+	0.529415i	−0.244055	+	0.969761i	$0.578478\pi$
$98$		0			0
$99$	7.91608	+	3.07799i	0.795596	+	0.309349i
$100$		0			0
$101$	−4.25259	−	1.89337i	−0.423148	−	0.188398i	0.184104	−	0.982907i	$-0.441062\pi$
$101$	−4.25259	−	1.89337i	−0.423148	−	0.188398i	−0.607252	+	0.794509i	$0.707728\pi$
$102$		0			0
$103$	−1.20199	−	0.390552i	−0.118436	−	0.0384822i	0.249199	−	0.968452i	$-0.419833\pi$
$103$	−1.20199	−	0.390552i	−0.118436	−	0.0384822i	−0.367635	+	0.929970i	$0.619833\pi$
$104$		0			0
$105$	2.01775	−	2.77719i	0.196912	−	0.271026i
$106$		0			0
$107$	−0.882676	−	0.794765i	−0.0853316	−	0.0768329i	0.625361	−	0.780335i	$-0.284952\pi$
$107$	−0.882676	−	0.794765i	−0.0853316	−	0.0768329i	−0.710693	+	0.703503i	$0.751618\pi$
$108$		0			0
$109$	6.49259	+	6.49259i	0.621877	+	0.621877i	0.946011	−	0.324134i	$-0.105073\pi$
$109$	6.49259	+	6.49259i	0.621877	+	0.621877i	−0.324134	+	0.946011i	$0.605073\pi$
$110$		0			0
$111$	25.3961	−	6.80486i	2.41049	−	0.645889i
$112$		0			0
$113$	−12.3942	−	2.63447i	−1.16595	−	0.247830i	−0.416025	−	0.909353i	$-0.636577\pi$
$113$	−12.3942	−	2.63447i	−1.16595	−	0.247830i	−0.749925	+	0.661523i	$0.769910\pi$
$114$		0			0
$115$	−4.09313	+	3.31455i	−0.381687	+	0.309084i
$116$		0			0
$117$	5.81333	+	7.17353i	0.537443	+	0.663193i
$118$		0			0
$119$	−2.67798	+	1.02798i	−0.245490	+	0.0942348i
$120$		0			0
$121$	−6.38853	−	8.95470i	−0.580775	−	0.814064i
$122$		0			0
$123$	0.940041	−	1.16085i	0.0847606	−	0.104671i
$124$		0			0
$125$	7.25096	−	3.69455i	0.648546	−	0.330451i
$126$		0			0
$127$	−1.66805	+	15.8704i	−0.148015	+	1.40827i	0.628321	+	0.777954i	$0.283742\pi$
$127$	−1.66805	+	15.8704i	−0.148015	+	1.40827i	−0.776337	+	0.630318i	$0.782924\pi$
$128$		0			0
$129$	−3.37919	−	10.4001i	−0.297521	−	0.915675i
$130$		0			0
$131$			20.5642i			1.79670i	0.439281	+	0.898350i	$0.355233\pi$
$131$			20.5642i			1.79670i	−0.439281	+	0.898350i	$0.644767\pi$
$132$		0			0
$133$	−1.99615	−	3.45744i	−0.173088	−	0.299798i
$134$		0			0
$135$	0.814293	+	0.414903i	0.0700832	+	0.0357092i
$136$		0			0
$137$	−4.00569	−	1.53764i	−0.342229	−	0.131369i	0.181182	−	0.983450i	$-0.442008\pi$
$137$	−4.00569	−	1.53764i	−0.342229	−	0.131369i	−0.523411	+	0.852080i	$0.675341\pi$
$138$		0			0
$139$	−3.72984	+	3.35836i	−0.316360	+	0.284852i	−0.811977	−	0.583689i	$-0.801609\pi$
$139$	−3.72984	+	3.35836i	−0.316360	+	0.284852i	0.495617	+	0.868541i	$0.334942\pi$
$140$		0			0
$141$	10.0270	+	26.1213i	0.844428	+	2.19981i
$142$		0			0
$143$	−1.20294	−	11.8976i	−0.100595	−	0.994927i
$144$		0			0
$145$	3.12521	+	8.14144i	0.259534	+	0.676110i
$146$		0			0
$147$	7.49909	−	6.75221i	0.618514	−	0.556913i
$148$		0			0
$149$	20.5375	+	7.88361i	1.68250	+	0.645851i	0.996642	−	0.0818854i	$-0.0260942\pi$
$149$	20.5375	+	7.88361i	1.68250	+	0.645851i	0.685857	+	0.727736i	$0.259427\pi$
$150$		0			0
$151$	−16.9468	−	8.63485i	−1.37911	−	0.702694i	−0.402046	−	0.915619i	$-0.631701\pi$
$151$	−16.9468	−	8.63485i	−1.37911	−	0.702694i	−0.977069	+	0.212925i	$0.931701\pi$
$152$		0			0
$153$	2.22672	+	3.85678i	0.180019	+	0.311803i
$154$		0			0
$155$		−	8.26998i		−	0.664261i
$156$		0			0
$157$	3.74123	+	11.5143i	0.298583	+	0.918944i	0.981994	+	0.188910i	$0.0604956\pi$
$157$	3.74123	+	11.5143i	0.298583	+	0.918944i	−0.683411	+	0.730034i	$0.739504\pi$
$158$		0			0
$159$	2.19944	−	20.9263i	0.174427	−	1.65956i
$160$		0			0
$161$	8.77104	−	4.46907i	0.691255	−	0.352212i
$162$		0			0
$163$	9.29129	−	11.4738i	0.727750	−	0.898696i	−0.270193	−	0.962806i	$-0.587088\pi$
$163$	9.29129	−	11.4738i	0.727750	−	0.898696i	0.997943	+	0.0641100i	$0.0204209\pi$
$164$		0			0
$165$	3.42533	+	5.99247i	0.266662	+	0.466513i
$166$		0			0
$167$	1.79508	−	0.689065i	0.138907	−	0.0533215i	−0.287921	−	0.957654i	$-0.592964\pi$
$167$	1.79508	−	0.689065i	0.138907	−	0.0533215i	0.426828	+	0.904333i	$0.359631\pi$
$168$		0			0
$169$	5.27893	−	11.8799i	0.406071	−	0.913841i
$170$		0			0
$171$	−4.81688	+	3.90063i	−0.368356	+	0.298289i
$172$		0			0
$173$	−16.9523	−	3.60331i	−1.28886	−	0.273955i	−0.488017	−	0.872834i	$-0.662280\pi$
$173$	−16.9523	−	3.60331i	−1.28886	−	0.273955i	−0.800839	+	0.598879i	$0.795613\pi$
$174$		0			0
$175$	−6.72544	+	1.80208i	−0.508395	+	0.136224i
$176$		0			0
$177$	−4.94185	−	4.94185i	−0.371452	−	0.371452i
$178$		0			0
$179$	6.24857	+	5.62624i	0.467040	+	0.420525i	0.868757	−	0.495239i	$-0.164920\pi$
$179$	6.24857	+	5.62624i	0.467040	+	0.420525i	−0.401717	+	0.915764i	$0.631586\pi$
$180$		0			0
$181$	0.125931	−	0.173330i	0.00936041	−	0.0128835i	−0.804311	−	0.594208i	$-0.797465\pi$
$181$	0.125931	−	0.173330i	0.00936041	−	0.0128835i	0.813672	+	0.581325i	$0.197465\pi$
$182$		0			0
$183$	−20.8050	−	6.75996i	−1.53795	−	0.499711i
$184$		0			0
$185$	8.98902	+	4.00217i	0.660886	+	0.294245i
$186$		0			0
$187$	0.326732	−	5.75846i	0.0238930	−	0.421100i
$188$		0			0
$189$	−1.32745	−	1.07495i	−0.0965581	−	0.0781912i
$190$		0			0
$191$	4.31679	+	4.79428i	0.312352	+	0.346902i	0.878795	−	0.477199i	$-0.158348\pi$
$191$	4.31679	+	4.79428i	0.312352	+	0.346902i	−0.566444	+	0.824100i	$0.691681\pi$
$192$		0			0
$193$	−12.3285	−	15.2245i	−0.887426	−	1.09588i	−0.994819	−	0.101664i	$-0.967583\pi$
$193$	−12.3285	−	15.2245i	−0.887426	−	1.09588i	0.107392	−	0.994217i	$-0.465750\pi$
$194$		0			0
$195$	0.00273195	+	7.50366i	0.000195639	+	0.537348i
$196$		0			0
$197$	4.82305	−	17.9999i	0.343628	−	1.28244i	−0.550579	−	0.834783i	$-0.685593\pi$
$197$	4.82305	−	17.9999i	0.343628	−	1.28244i	0.894207	−	0.447654i	$-0.147740\pi$
$198$		0			0
$199$	10.3658	+	5.98467i	0.734809	+	0.424242i	0.820179	−	0.572107i	$-0.193874\pi$
$199$	10.3658	+	5.98467i	0.734809	+	0.424242i	−0.0853700	+	0.996349i	$0.527207\pi$
$200$		0			0
$201$	1.28107	−	0.831936i	0.0903596	−	0.0586802i
$202$		0			0
$203$	−2.54976	−	16.0985i	−0.178958	−	1.12990i
$204$		0			0
$205$	0.546812	−	0.116229i	0.0381910	−	0.00811775i
$206$		0			0
$207$	−8.98315	−	12.3642i	−0.624372	−	0.859374i
$208$		0			0
$209$	7.98694	−	0.804602i	0.552468	−	0.0556555i
$210$		0			0
$211$	3.59875	−	8.08292i	0.247748	−	0.556451i	−0.746273	−	0.665640i	$-0.768159\pi$
$211$	3.59875	−	8.08292i	0.247748	−	0.556451i	0.994021	+	0.109189i	$0.0348253\pi$
$212$		0			0
$213$	−0.318005	−	0.624120i	−0.0217893	−	0.0427640i
$214$		0			0
$215$	1.46662	−	3.82068i	0.100023	−	0.260568i
$216$		0			0
$217$	−3.21366	+	15.1191i	−0.218158	+	1.02635i
$218$		0			0
$219$	−18.6427	−	4.99529i	−1.25976	−	0.337550i
$220$		0			0
$221$	3.41307	−	5.25986i	0.229588	−	0.353816i
$222$		0			0
$223$	0.806448	+	15.3879i	0.0540038	+	1.03045i	0.882456	+	0.470394i	$0.155888\pi$
$223$	0.806448	+	15.3879i	0.0540038	+	1.03045i	−0.828453	+	0.560059i	$0.810778\pi$
$224$		0			0
$225$	4.39673	+	9.87521i	0.293115	+	0.658347i
$226$		0			0
$227$	−0.528698	+	10.0882i	−0.0350909	+	0.669575i	0.923294	+	0.384095i	$0.125486\pi$
$227$	−0.528698	+	10.0882i	−0.0350909	+	0.669575i	−0.958385	+	0.285480i	$0.907847\pi$
$228$		0			0
$229$	8.27601	+	1.31079i	0.546894	+	0.0866195i	0.423767	−	0.905771i	$-0.360708\pi$
$229$	8.27601	+	1.31079i	0.546894	+	0.0866195i	0.123127	+	0.992391i	$0.460708\pi$
$230$		0			0
$231$	−3.93352	−	12.2864i	−0.258807	−	0.808388i
$232$		0			0
$233$	−5.77756	+	4.19764i	−0.378500	+	0.274997i	−0.760727	−	0.649072i	$-0.775157\pi$
$233$	−5.77756	+	4.19764i	−0.378500	+	0.274997i	0.382227	+	0.924069i	$0.375157\pi$
$234$		0			0
$235$	−3.23582	+	9.95883i	−0.211082	+	0.649642i
$236$		0			0
$237$	−27.3730	−	2.87701i	−1.77807	−	0.186882i
$238$		0			0
$239$	−0.260454	+	0.511171i	−0.0168474	+	0.0330649i	−0.899277	−	0.437380i	$-0.855907\pi$
$239$	−0.260454	+	0.511171i	−0.0168474	+	0.0330649i	0.882429	+	0.470445i	$0.155907\pi$
$240$		0			0
$241$	0.685277	+	2.55749i	0.0441426	+	0.164742i	0.984479	−	0.175505i	$-0.0561559\pi$
$241$	0.685277	+	2.55749i	0.0441426	+	0.164742i	−0.940336	+	0.340247i	$0.889489\pi$
$242$		0			0
$243$	−10.3843	+	17.9861i	−0.666153	+	1.15381i
$244$		0			0
$245$	3.77136	−	0.197649i	0.240944	−	0.0126273i
$246$		0			0
$247$	7.97349	+	3.54655i	0.507341	+	0.225662i
$248$		0			0
$249$	3.26323	+	2.11917i	0.206799	+	0.134297i
$250$		0			0
$251$	−3.50883	+	0.368793i	−0.221476	+	0.0232780i	−0.214616	−	0.976698i	$-0.568850\pi$
$251$	−3.50883	+	0.368793i	−0.221476	+	0.0232780i	−0.00685937	+	0.999976i	$0.502183\pi$
$252$		0			0
$253$	0.950529	+	19.7705i	0.0597592	+	1.24296i
$254$		0			0
$255$	−0.566164	+	3.57462i	−0.0354545	+	0.223851i
$256$		0			0
$257$	−3.71577	−	17.4813i	−0.231783	−	1.09045i	−0.927988	−	0.372611i	$-0.878463\pi$
$257$	−3.71577	−	17.4813i	−0.231783	−	1.09045i	0.696204	−	0.717844i	$-0.254871\pi$
$258$		0			0
$259$	−14.8784	−	10.8098i	−0.924500	−	0.671689i
$260$		0			0
$261$	−24.0665	+	7.81967i	−1.48968	+	0.484025i
$262$		0			0
$263$	−21.2111	+	12.2462i	−1.30793	+	0.755134i	−0.981750	−	0.190174i	$-0.939095\pi$
$263$	−21.2111	+	12.2462i	−1.30793	+	0.755134i	−0.326179	+	0.945308i	$0.605761\pi$
$264$		0			0
$265$	5.56829	−	5.56829i	0.342058	−	0.342058i
$266$		0			0
$267$	−9.42568	−	14.5143i	−0.576842	−	0.888259i
$268$		0			0
$269$	−4.38596	+	1.95275i	−0.267416	+	0.119061i	−0.536065	−	0.844177i	$-0.680090\pi$
$269$	−4.38596	+	1.95275i	−0.267416	+	0.119061i	0.268648	+	0.963238i	$0.413423\pi$
$270$		0			0
$271$	−1.75376	+	2.70055i	−0.106533	+	0.164047i	−0.887916	−	0.460005i	$-0.847848\pi$
$271$	−1.75376	+	2.70055i	−0.106533	+	0.164047i	0.781383	+	0.624051i	$0.214514\pi$
$272$		0			0
$273$	2.91088	−	13.7192i	0.176175	−	0.830322i
$274$		0			0
$275$	2.24977	−	13.8180i	0.135666	−	0.833256i
$276$		0			0
$277$	2.11132	+	20.0879i	0.126857	+	1.20696i	0.853925	+	0.520397i	$0.174216\pi$
$277$	2.11132	+	20.0879i	0.126857	+	1.20696i	−0.727068	+	0.686566i	$0.759117\pi$
$278$		0			0
$279$	23.9643	+	1.25592i	1.43471	+	0.0751898i
$280$		0			0
$281$	4.29432	−	0.680153i	0.256177	−	0.0405745i	−0.0270247	−	0.999635i	$-0.508603\pi$
$281$	4.29432	−	0.680153i	0.256177	−	0.0405745i	0.283202	+	0.959060i	$0.408603\pi$
$282$		0			0
$283$	11.3890	−	12.6488i	0.677007	−	0.751892i	−0.302534	−	0.953139i	$-0.597833\pi$
$283$	11.3890	−	12.6488i	0.677007	−	0.751892i	0.979541	+	0.201246i	$0.0644992\pi$
$284$		0			0
$285$	−5.03707			−0.298370
$286$		0			0
$287$	−1.04484			−0.0616751
$288$		0			0
$289$	−9.35161	+	10.3860i	−0.550095	+	0.610942i
$290$		0			0
$291$	−19.2975	+	3.05642i	−1.13124	+	0.179171i
$292$		0			0
$293$	26.4832	+	1.38793i	1.54717	+	0.0810835i	0.806680	−	0.590988i	$-0.201262\pi$
$293$	26.4832	+	1.38793i	1.54717	+	0.0810835i	0.740486	+	0.672072i	$0.234595\pi$
$294$		0			0
$295$	−0.273400	−	2.60123i	−0.0159180	−	0.151449i
$296$		0			0
$297$	3.06688	−	1.54601i	0.177959	−	0.0897085i
$298$		0			0
$299$	−9.76183	+	19.1759i	−0.564541	+	1.10897i
$300$		0			0
$301$	−4.16596	+	6.41501i	−0.240122	+	0.369755i
$302$		0			0
$303$	10.0282	−	4.46486i	0.576107	−	0.256499i
$304$		0			0
$305$	−4.45892	−	6.86613i	−0.255317	−	0.393154i
$306$		0			0
$307$	−11.7822	+	11.7822i	−0.672443	+	0.672443i	−0.958279	−	0.285836i	$-0.907729\pi$
$307$	−11.7822	+	11.7822i	−0.672443	+	0.672443i	0.285836	+	0.958279i	$0.407729\pi$
$308$		0			0
$309$	2.58106	−	1.49018i	0.146831	−	0.0847731i
$310$		0			0
$311$	0.548968	−	0.178370i	0.0311291	−	0.0101145i	−0.293411	−	0.955986i	$-0.594790\pi$
$311$	0.548968	−	0.178370i	0.0311291	−	0.0101145i	0.324540	+	0.945872i	$0.394790\pi$
$312$		0			0
$313$	−11.8412	−	8.60313i	−0.669304	−	0.486278i	0.200488	−	0.979696i	$-0.435747\pi$
$313$	−11.8412	−	8.60313i	−0.669304	−	0.486278i	−0.869792	+	0.493418i	$0.835747\pi$
$314$		0			0
$315$	0.775074	+	3.64644i	0.0436705	+	0.205453i
$316$		0			0
$317$	1.17171	−	7.39791i	0.0658100	−	0.415508i	−0.932686	−	0.360689i	$-0.882542\pi$
$317$	1.17171	−	7.39791i	0.0658100	−	0.415508i	0.998496	−	0.0548194i	$-0.0174583\pi$
$318$		0			0
$319$	31.6193	+	8.61890i	1.77034	+	0.482566i
$320$		0			0
$321$	2.78557	−	0.292775i	0.155475	−	0.0163411i
$322$		0			0
$323$	3.53001	+	2.29242i	0.196415	+	0.127553i
$324$		0			0
$325$	9.57365	−	11.8313i	0.531051	−	0.656281i
$326$		0			0
$327$	−21.6226	+	1.13319i	−1.19573	+	0.0626658i
$328$		0			0
$329$	9.78563	−	16.9492i	0.539499	−	0.934440i
$330$		0			0
$331$	0.625292	+	2.33362i	0.0343692	+	0.128268i	0.980979	−	0.194114i	$-0.0621832\pi$
$331$	0.625292	+	2.33362i	0.0343692	+	0.128268i	−0.946610	+	0.322382i	$0.895517\pi$
$332$		0			0
$333$	−12.9624	+	25.4401i	−0.710335	+	1.39411i
$334$		0			0
$335$	0.568531	+	0.0597550i	0.0310622	+	0.00326477i
$336$		0			0
$337$	0.771616	−	2.37479i	0.0420326	−	0.129363i	−0.927838	−	0.372983i	$-0.878335\pi$
$337$	0.771616	−	2.37479i	0.0420326	−	0.129363i	0.969871	+	0.243620i	$0.0783350\pi$
$338$		0			0
$339$	24.1737	−	17.5632i	1.31294	−	0.953904i
$340$		0			0
$341$	−25.0645	−	18.3763i	−1.35732	−	0.995135i
$342$		0			0
$343$	−18.3758	−	2.91044i	−0.992199	−	0.157149i
$344$		0			0
$345$	0.650017	−	12.4031i	0.0349957	−	0.667758i
$346$		0			0
$347$	3.72149	+	8.35861i	0.199780	+	0.448714i	0.985457	−	0.169923i	$-0.0543519\pi$
$347$	3.72149	+	8.35861i	0.199780	+	0.448714i	−0.785677	+	0.618637i	$0.787685\pi$
$348$		0			0
$349$	1.15251	+	21.9913i	0.0616927	+	1.17717i	0.837587	+	0.546304i	$0.183966\pi$
$349$	1.15251	+	21.9913i	0.0616927	+	1.17717i	−0.775894	+	0.630863i	$0.782701\pi$
$350$		0			0
$351$	3.72867	+	0.194050i	0.199022	+	0.0103576i
$352$		0			0
$353$	−18.9110	−	5.06718i	−1.00653	−	0.269699i	−0.282351	−	0.959311i	$-0.591114\pi$
$353$	−18.9110	−	5.06718i	−1.00653	−	0.269699i	−0.724179	+	0.689612i	$0.757781\pi$
$354$		0			0
$355$	0.0545036	−	0.256419i	0.00289275	−	0.0136093i
$356$		0			0
$357$	2.42413	−	6.31507i	0.128299	−	0.334229i
$358$		0			0
$359$	3.38217	+	6.63789i	0.178504	+	0.350334i	0.962871	−	0.269964i	$-0.0870117\pi$
$359$	3.38217	+	6.63789i	0.178504	+	0.350334i	−0.784366	+	0.620298i	$0.787012\pi$
$360$		0			0
$361$	5.34531	−	12.0058i	0.281332	−	0.631883i
$362$		0			0
$363$	25.7732	+	2.93415i	1.35274	+	0.154003i
$364$		0			0
$365$	−4.24563	−	5.84361i	−0.222226	−	0.305868i
$366$		0			0
$367$	−17.2578	+	3.66825i	−0.900849	+	0.191481i	−0.634980	−	0.772528i	$-0.718992\pi$
$367$	−17.2578	+	3.66825i	−0.900849	+	0.191481i	−0.265868	+	0.964009i	$0.585659\pi$
$368$		0			0
$369$	0.253760	+	1.60218i	0.0132102	+	0.0834059i
$370$		0			0
$371$	−12.3437	+	8.01610i	−0.640853	+	0.416175i
$372$		0			0
$373$	−18.0801	−	10.4386i	−0.936154	−	0.540489i	−0.0474013	−	0.998876i	$-0.515094\pi$
$373$	−18.0801	−	10.4386i	−0.936154	−	0.540489i	−0.888753	+	0.458387i	$0.848427\pi$
$374$		0			0
$375$	−4.96686	+	18.5366i	−0.256488	+	0.957225i
$376$		0			0
$377$	25.2019	+	25.1836i	1.29797	+	1.29702i
$378$		0			0
$379$	5.55983	+	6.86582i	0.285589	+	0.352673i	0.899671	−	0.436569i	$-0.143807\pi$
$379$	5.55983	+	6.86582i	0.285589	+	0.352673i	−0.614081	+	0.789243i	$0.710473\pi$
$380$		0			0
$381$	−25.1800	−	27.9653i	−1.29001	−	1.43270i
$382$		0			0
$383$	13.1887	+	10.6800i	0.673910	+	0.545722i	0.904045	−	0.427437i	$-0.140583\pi$
$383$	13.1887	+	10.6800i	0.673910	+	0.545722i	−0.230135	+	0.973159i	$0.573917\pi$
$384$		0			0
$385$	1.74968	−	4.49988i	0.0891718	−	0.229335i
$386$		0			0
$387$	10.8486	+	4.83013i	0.551467	+	0.245529i
$388$		0			0
$389$	−25.5590	−	8.30462i	−1.29589	−	0.421061i	−0.421742	−	0.906716i	$-0.638581\pi$
$389$	−25.5590	−	8.30462i	−1.29589	−	0.421061i	−0.874151	+	0.485655i	$0.838581\pi$
$390$		0			0
$391$	−6.10028	+	8.39632i	−0.308505	+	0.424620i
$392$		0			0
$393$	−36.0376	−	32.4484i	−1.81786	−	1.63680i
$394$		0			0
$395$	−7.28369	−	7.28369i	−0.366482	−	0.366482i
$396$		0			0
$397$	−16.5594	+	4.43707i	−0.831091	+	0.222690i	−0.649189	−	0.760627i	$-0.724892\pi$
$397$	−16.5594	+	4.43707i	−0.831091	+	0.222690i	−0.181901	+	0.983317i	$0.558225\pi$
$398$		0			0
$399$	9.20872	+	1.95737i	0.461013	+	0.0979913i
$400$		0			0
$401$	22.9918	−	18.6184i	1.14816	−	0.929759i	0.149895	−	0.988702i	$-0.452106\pi$
$401$	22.9918	−	18.6184i	1.14816	−	0.929759i	0.998261	+	0.0589431i	$0.0187731\pi$
$402$		0			0
$403$	−13.7535	−	30.8607i	−0.685112	−	1.53728i
$404$		0			0
$405$	−8.34177	+	3.20211i	−0.414506	+	0.159114i
$406$		0			0
$407$	32.1038	−	18.3507i	1.59133	−	0.909612i
$408$		0			0
$409$	−16.3835	+	20.2320i	−0.810114	+	1.00041i	0.189713	+	0.981840i	$0.439244\pi$
$409$	−16.3835	+	20.2320i	−0.810114	+	1.00041i	−0.999828	+	0.0185684i	$0.994089\pi$
$410$		0			0
$411$	9.01525	−	4.59350i	0.444689	−	0.226581i
$412$		0			0
$413$	−0.510993	+	4.86178i	−0.0251443	+	0.239232i
$414$		0			0
$415$	0.449985	+	1.38491i	0.0220889	+	0.0679827i
$416$		0			0
$417$		−	11.8355i		−	0.579588i
$418$		0			0
$419$	7.05742	+	12.2238i	0.344777	+	0.597172i	0.985313	−	0.170756i	$-0.0546211\pi$
$419$	7.05742	+	12.2238i	0.344777	+	0.597172i	−0.640536	+	0.767928i	$0.721288\pi$
$420$		0			0
$421$	27.1392	+	13.8281i	1.32268	+	0.673940i	0.965575	−	0.260124i	$-0.0837633\pi$
$421$	27.1392	+	13.8281i	1.32268	+	0.673940i	0.357107	+	0.934064i	$0.383763\pi$
$422$		0			0
$423$	−28.3668	−	10.8890i	−1.37924	−	0.529441i
$424$		0			0
$425$	5.45521	−	4.91189i	0.264616	−	0.238262i
$426$		0			0
$427$	5.48362	+	14.2853i	0.265371	+	0.691314i
$428$		0			0
$429$	22.7480	+	16.6653i	1.09829	+	0.804606i
$430$		0			0
$431$	7.28873	+	18.9878i	0.351086	+	0.914610i	0.989450	+	0.144875i	$0.0462782\pi$
$431$	7.28873	+	18.9878i	0.351086	+	0.914610i	−0.638364	+	0.769735i	$0.720389\pi$
$432$		0			0
$433$	−0.568070	+	0.511492i	−0.0272997	+	0.0245808i	−0.682668	−	0.730729i	$-0.739180\pi$
$433$	−0.568070	+	0.511492i	−0.0272997	+	0.0245808i	0.655368	+	0.755310i	$0.272514\pi$
$434$		0			0
$435$	−19.1987	−	7.36970i	−0.920508	−	0.353350i
$436$		0			0
$437$	−12.8701	−	6.55762i	−0.615658	−	0.313694i
$438$		0			0
$439$	−15.5896	−	27.0019i	−0.744050	−	1.28873i	−0.950637	−	0.310304i	$-0.899569\pi$
$439$	−15.5896	−	27.0019i	−0.744050	−	1.28873i	0.206587	−	0.978428i	$-0.433764\pi$
$440$		0			0
$441$			10.9585i			0.521833i
$442$		0			0
$443$	−9.43603	−	29.0411i	−0.448319	−	1.37979i	−0.878802	−	0.477186i	$-0.841657\pi$
$443$	−9.43603	−	29.0411i	−0.448319	−	1.37979i	0.430483	−	0.902599i	$-0.358343\pi$
$444$		0			0
$445$	0.677014	−	6.44136i	0.0320935	−	0.305350i
$446$		0			0
$447$	−46.2219	+	23.5513i	−2.18622	+	1.11394i
$448$		0			0
$449$	25.0804	−	30.9717i	1.18362	−	1.46164i	0.327505	−	0.944850i	$-0.393792\pi$
$449$	25.0804	−	30.9717i	1.18362	−	1.46164i	0.856110	−	0.516793i	$-0.172874\pi$
$450$		0			0
$451$	0.862783	−	1.91554i	0.0406269	−	0.0901990i
$452$		0			0
$453$	41.8727	−	16.0734i	1.96735	−	0.755195i
$454$		0			0
$455$	4.07778	−	3.30458i	0.191169	−	0.154921i
$456$		0			0
$457$	11.3965	−	9.22867i	0.533104	−	0.431699i	−0.324594	−	0.945854i	$-0.605228\pi$
$457$	11.3965	−	9.22867i	0.533104	−	0.431699i	0.857698	+	0.514155i	$0.171894\pi$
$458$		0			0
$459$	1.76150	+	0.374418i	0.0822197	+	0.0174763i
$460$		0			0
$461$	7.02615	−	1.88265i	0.327240	−	0.0876838i	−0.0914586	−	0.995809i	$-0.529153\pi$
$461$	7.02615	−	1.88265i	0.327240	−	0.0876838i	0.418699	+	0.908125i	$0.362486\pi$
$462$		0			0
$463$	−3.14771	−	3.14771i	−0.146287	−	0.146287i	0.630170	−	0.776457i	$-0.282985\pi$
$463$	−3.14771	−	3.14771i	−0.146287	−	0.146287i	−0.776457	+	0.630170i	$0.782985\pi$
$464$		0			0
$465$	14.4927	+	13.0493i	0.672082	+	0.605146i
$466$		0			0
$467$	24.2807	−	33.4195i	1.12357	−	1.54647i	0.323843	−	0.946111i	$-0.395025\pi$
$467$	24.2807	−	33.4195i	1.12357	−	1.54647i	0.799732	−	0.600357i	$-0.204975\pi$
$468$		0			0
$469$	−1.01616	−	0.330171i	−0.0469220	−	0.0152459i
$470$		0			0
$471$	−26.0816	−	11.6123i	−1.20178	−	0.535065i
$472$		0			0
$473$	−8.32074	−	12.9348i	−0.382588	−	0.594741i
$474$		0			0
$475$	7.93978	+	6.42951i	0.364302	+	0.295006i
$476$		0			0
$477$	15.2899	+	16.9811i	0.700076	+	0.777513i
$478$		0			0
$479$	11.8153	+	14.5907i	0.539854	+	0.666664i	0.971957	−	0.235160i	$-0.0755615\pi$
$479$	11.8153	+	14.5907i	0.539854	+	0.666664i	−0.432103	+	0.901824i	$0.642228\pi$
$480$		0			0
$481$	40.1998	−	0.0146360i	1.83295	−	0.000667346i
$482$		0			0
$483$	−6.00811	+	22.4226i	−0.273378	+	1.02026i
$484$		0			0
$485$	−6.33244	−	3.65603i	−0.287541	−	0.166012i
$486$		0			0
$487$	−0.715852	+	0.464880i	−0.0324383	+	0.0210657i	−0.560756	−	0.827981i	$-0.689490\pi$
$487$	−0.715852	+	0.464880i	−0.0324383	+	0.0210657i	0.528318	+	0.849047i	$0.322823\pi$
$488$		0			0
$489$	5.44638	+	34.3871i	0.246294	+	1.55504i
$490$		0			0
$491$	−11.4735	+	2.43876i	−0.517790	+	0.110060i	−0.459392	−	0.888234i	$-0.651933\pi$
$491$	−11.4735	+	2.43876i	−0.517790	+	0.110060i	−0.0583979	+	0.998293i	$0.518599\pi$
$492$		0			0
$493$	10.1006	+	13.9022i	0.454907	+	0.626126i
$494$		0			0
$495$	−7.32512	−	1.59010i	−0.329240	−	0.0714696i
$496$		0			0
$497$	−0.199286	+	0.447603i	−0.00893919	+	0.0200777i
$498$		0			0
$499$	9.67514	+	18.9885i	0.433119	+	0.850043i	0.999662	+	0.0260112i	$0.00828054\pi$
$499$	9.67514	+	18.9885i	0.433119	+	0.850043i	−0.566543	+	0.824032i	$0.691719\pi$
$500$		0			0
$501$	−1.62492	+	4.23306i	−0.0725960	+	0.189119i
$502$		0			0
$503$	−6.15909	+	28.9763i	−0.274620	+	1.29199i	0.597172	+	0.802113i	$0.296291\pi$
$503$	−6.15909	+	28.9763i	−0.274620	+	1.29199i	−0.871793	+	0.489875i	$0.837043\pi$
$504$		0			0
$505$	3.96823	+	1.06328i	0.176584	+	0.0473155i
$506$		0			0
$507$	12.4893	+	27.9965i	0.554668	+	1.24337i
$508$		0			0
$509$	0.866679	+	16.5372i	0.0384149	+	0.733000i	0.948152	+	0.317816i	$0.102949\pi$
$509$	0.866679	+	16.5372i	0.0384149	+	0.733000i	−0.909738	+	0.415184i	$0.863717\pi$
$510$		0			0
$511$	5.49103	+	12.3331i	0.242909	+	0.545582i
$512$		0			0
$513$	−0.131174	+	2.50294i	−0.00579145	+	0.110508i
$514$		0			0
$515$	1.10166	+	0.174485i	0.0485448	+	0.00768874i
$516$		0			0
$517$	22.9929	+	31.9361i	1.01123	+	1.40455i
$518$		0			0
$519$	33.0637	−	24.0222i	1.45134	−	1.05446i
$520$		0			0
$521$	6.74337	−	20.7540i	0.295433	−	0.909248i	−0.687643	−	0.726049i	$-0.741355\pi$
$521$	6.74337	−	20.7540i	0.295433	−	0.909248i	0.983076	−	0.183199i	$-0.0586453\pi$
$522$		0			0
$523$	16.3254	+	1.71587i	0.713861	+	0.0750298i	0.454495	−	0.890749i	$-0.349820\pi$
$523$	16.3254	+	1.71587i	0.713861	+	0.0750298i	0.259366	+	0.965779i	$0.416486\pi$
$524$		0			0
$525$	7.45409	−	14.6295i	0.325323	−	0.638483i
$526$		0			0
$527$	−4.21773	−	15.7408i	−0.183727	−	0.685679i
$528$		0			0
$529$	6.30805	−	10.9259i	0.274263	−	0.475037i
$530$		0			0
$531$	7.57922	−	0.397210i	0.328910	−	0.0172374i
$532$		0			0
$533$	1.84722	−	1.34311i	0.0800119	−	0.0581765i
$534$		0			0
$535$	0.879123	+	0.570909i	0.0380078	+	0.0246826i
$536$		0			0
$537$	−19.7194	+	2.07259i	−0.850953	+	0.0894388i
$538$		0			0
$539$	7.78115	−	11.8694i	0.335158	−	0.511250i
$540$		0			0
$541$	0.170933	−	1.07923i	0.00734900	−	0.0463998i	−0.983741	−	0.179591i	$-0.942523\pi$
$541$	0.170933	−	1.07923i	0.00734900	−	0.0463998i	0.991090	+	0.133191i	$0.0425225\pi$
$542$		0			0
$543$	0.105043	+	0.494187i	0.00450781	+	0.0212076i
$544$		0			0
$545$	−6.55573	−	4.76301i	−0.280816	−	0.204025i
$546$		0			0
$547$	−29.1568	+	9.47363i	−1.24666	+	0.405063i	−0.856722	−	0.515779i	$-0.827503\pi$
$547$	−29.1568	+	9.47363i	−1.24666	+	0.405063i	−0.389935	+	0.920842i	$0.627503\pi$
$548$		0			0
$549$	20.5735	−	11.8781i	0.878055	−	0.506945i
$550$		0			0
$551$	−16.9114	+	16.9114i	−0.720452	+	0.720452i
$552$		0			0
$553$	10.4856	+	16.1464i	0.445892	+	0.686614i
$554$		0			0
$555$	−21.1974	+	9.43771i	−0.899781	+	0.400608i
$556$		0			0
$557$	−4.80342	+	7.39661i	−0.203527	+	0.313405i	−0.925665	−	0.378345i	$-0.876493\pi$
$557$	−4.80342	+	7.39661i	−0.203527	+	0.313405i	0.722137	+	0.691750i	$0.243160\pi$
$558$		0			0
$559$	−0.881124	−	16.6965i	−0.0372676	−	0.706188i
$560$		0			0
$561$	9.57584	+	9.65891i	0.404292	+	0.407800i
$562$		0			0
$563$	2.73594	+	26.0307i	0.115306	+	1.09706i	0.887223	+	0.461340i	$0.152631\pi$
$563$	2.73594	+	26.0307i	0.115306	+	1.09706i	−0.771917	+	0.635723i	$0.780702\pi$
$564$		0			0
$565$	11.1673	+	0.585255i	0.469813	+	0.0246219i
$566$		0			0
$567$	16.4947	−	2.61250i	0.692711	−	0.109715i
$568$		0			0
$569$	−18.2276	+	20.2438i	−0.764140	+	0.848663i	−0.992158	−	0.124994i	$-0.960109\pi$
$569$	−18.2276	+	20.2438i	−0.764140	+	0.848663i	0.228018	+	0.973657i	$0.426776\pi$
$570$		0			0
$571$	16.6534			0.696925			0.348462	−	0.937323i	$-0.386704\pi$
$571$	16.6534			0.696925			0.348462	+	0.937323i	$0.386704\pi$
$572$		0			0
$573$	−15.2132			−0.635541
$574$		0			0
$575$	−16.8564	+	18.7209i	−0.702959	+	0.780715i
$576$		0			0
$577$	40.5643	−	6.42476i	1.68872	−	0.267466i	0.763196	−	0.646167i	$-0.223629\pi$
$577$	40.5643	−	6.42476i	1.68872	−	0.267466i	0.925519	+	0.378701i	$0.123629\pi$
$578$		0			0
$579$	46.1333	+	2.41775i	1.91724	+	0.100478i
$580$		0			0
$581$	−0.284490	−	2.70674i	−0.0118026	−	0.112295i
$582$		0			0
$583$	−4.50324	−	29.2493i	−0.186505	−	1.21138i
$584$		0			0
$585$	−6.05765	−	5.45034i	−0.250453	−	0.225344i
$586$		0			0
$587$	−7.86538	+	12.1116i	−0.324639	+	0.499900i	−0.962878	−	0.269938i	$-0.912997\pi$
$587$	−7.86538	+	12.1116i	−0.324639	+	0.499900i	0.638239	+	0.769839i	$0.279663\pi$
$588$		0			0
$589$	20.7196	−	9.22495i	0.853735	−	0.380107i
$590$		0			0
$591$	23.9334	+	36.8543i	0.984490	+	1.51598i
$592$		0			0
$593$	−7.07282	+	7.07282i	−0.290446	+	0.290446i	−0.837256	−	0.546810i	$-0.815842\pi$
$593$	−7.07282	+	7.07282i	−0.290446	+	0.290446i	0.546810	+	0.837256i	$0.315842\pi$
$594$		0			0
$595$	2.19238	−	1.26577i	0.0898789	−	0.0518916i
$596$		0			0
$597$	−26.8440	+	8.72216i	−1.09865	+	0.356974i
$598$		0			0
$599$	21.7788	+	15.8232i	0.889859	+	0.646520i	0.935841	−	0.352422i	$-0.114642\pi$
$599$	21.7788	+	15.8232i	0.889859	+	0.646520i	−0.0459826	+	0.998942i	$0.514642\pi$
$600$		0			0
$601$	8.98739	+	42.2823i	0.366603	+	1.72473i	0.644926	+	0.764245i	$0.276888\pi$
$601$	8.98739	+	42.2823i	0.366603	+	1.72473i	−0.278323	+	0.960488i	$0.589778\pi$
$602$		0			0
$603$	−0.259495	+	1.63839i	−0.0105674	+	0.0667202i
$604$		0			0
$605$	6.80494	+	6.92352i	0.276660	+	0.281481i
$606$		0			0
$607$	−47.4229	+	4.98435i	−1.92484	+	0.202308i	−0.988762	−	0.149496i	$-0.952235\pi$
$607$	−47.4229	+	4.98435i	−1.92484	+	0.202308i	−0.936073	+	0.351805i	$0.885568\pi$
$608$		0			0
$609$	32.2351	+	20.9337i	1.30623	+	0.848277i
$610$		0			0
$611$	4.48724	+	42.5443i	0.181534	+	1.72116i
$612$		0			0
$613$	−28.3243	+	1.48441i	−1.14401	+	0.0599548i	−0.614903	−	0.788603i	$-0.710805\pi$
$613$	−28.3243	+	1.48441i	−1.14401	+	0.0599548i	−0.529103	+	0.848557i	$0.677472\pi$
$614$		0			0
$615$	−0.659136	+	1.14166i	−0.0265789	+	0.0460360i
$616$		0			0
$617$	−0.0834352	−	0.311384i	−0.00335897	−	0.0125359i	0.964226	−	0.265082i	$-0.0853989\pi$
$617$	−0.0834352	−	0.311384i	−0.00335897	−	0.0125359i	−0.967585	+	0.252546i	$0.918732\pi$
$618$		0			0
$619$	5.14609	−	10.0998i	0.206839	−	0.405944i	−0.764161	−	0.645026i	$-0.776847\pi$
$619$	5.14609	−	10.0998i	0.206839	−	0.405944i	0.970999	+	0.239082i	$0.0768465\pi$
$620$		0			0
$621$	−6.14621	−	0.645992i	−0.246639	−	0.0259228i
$622$		0			0
$623$	−3.74078	+	11.5129i	−0.149871	+	0.461256i
$624$		0			0
$625$	11.2645	−	8.18414i	0.450580	−	0.327366i
$626$		0			0
$627$	−11.1926	+	15.2663i	−0.446991	+	0.609676i
$628$		0			0
$629$	19.1505	+	3.03314i	0.763580	+	0.120939i
$630$		0			0
$631$	1.42516	−	27.1936i	0.0567346	−	1.08256i	−0.810845	−	0.585261i	$-0.800992\pi$
$631$	1.42516	−	27.1936i	0.0567346	−	1.08256i	0.867579	−	0.497299i	$-0.165675\pi$
$632$		0			0
$633$	8.48638	+	19.0607i	0.337303	+	0.757596i
$634$		0			0
$635$	−0.737063	−	14.0640i	−0.0292494	−	0.558113i
$636$		0			0
$637$	13.7447	−	7.00959i	0.544586	−	0.277730i
$638$		0			0
$639$	0.734761	+	0.196879i	0.0290667	+	0.00778840i
$640$		0			0
$641$	7.95195	−	37.4110i	0.314083	−	1.47764i	−0.483985	−	0.875076i	$-0.660811\pi$
$641$	7.95195	−	37.4110i	0.314083	−	1.47764i	0.798068	−	0.602568i	$-0.205856\pi$
$642$		0			0
$643$	12.1032	−	31.5298i	0.477302	−	1.24342i	−0.457806	−	0.889052i	$-0.651364\pi$
$643$	12.1032	−	31.5298i	0.477302	−	1.24342i	0.935108	−	0.354363i	$-0.115302\pi$
$644$		0			0
$645$	4.38134	+	8.59886i	0.172515	+	0.338580i
$646$		0			0
$647$	15.3849	−	34.5551i	0.604844	−	1.35850i	−0.308465	−	0.951236i	$-0.599815\pi$
$647$	15.3849	−	34.5551i	0.604844	−	1.35850i	0.913309	−	0.407267i	$-0.133518\pi$
$648$		0			0
$649$	−8.49126	−	4.95145i	−0.333311	−	0.194361i
$650$		0			0
$651$	−21.4245	−	29.4883i	−0.839694	−	1.15574i
$652$		0			0
$653$	−0.105687	+	0.0224645i	−0.00413585	+	0.000879103i	−0.209979	−	0.977706i	$-0.567340\pi$
$653$	−0.105687	+	0.0224645i	−0.00413585	+	0.000879103i	0.205843	+	0.978585i	$0.434006\pi$
$654$		0			0
$655$	−2.83905	−	17.9251i	−0.110931	−	0.700391i
$656$		0			0
$657$	17.5781	−	11.4153i	0.685786	−	0.445355i
$658$		0			0
$659$	−5.44158	−	3.14170i	−0.211974	−	0.122383i	0.390255	−	0.920707i	$-0.372387\pi$
$659$	−5.44158	−	3.14170i	−0.211974	−	0.122383i	−0.602228	+	0.798324i	$0.705720\pi$
$660$		0			0
$661$	3.50770	−	13.0909i	0.136434	−	0.509178i	−0.863554	−	0.504256i	$-0.831767\pi$
$661$	3.50770	−	13.0909i	0.136434	−	0.509178i	0.999988	−	0.00492160i	$-0.00156660\pi$
$662$		0			0
$663$	3.83210	+	14.2808i	0.148826	+	0.554620i
$664$		0			0
$665$	2.21731	+	2.73815i	0.0859835	+	0.106181i
$666$		0			0
$667$	−39.4597	−	43.8244i	−1.52788	−	1.69689i
$668$		0			0
$669$	−28.2390	−	22.8675i	−1.09178	−	0.884110i
$670$		0			0
$671$	−30.7177	−	1.74291i	−1.18584	−	0.0672841i
$672$		0			0
$673$	−26.8799	−	11.9677i	−1.03614	−	0.461321i	−0.183063	−	0.983101i	$-0.558601\pi$
$673$	−26.8799	−	11.9677i	−1.03614	−	0.461321i	−0.853080	+	0.521780i	$0.825268\pi$
$674$		0			0
$675$	4.15724	+	1.35077i	0.160012	+	0.0519912i
$676$		0			0
$677$	16.4598	−	22.6550i	0.632602	−	0.870703i	−0.365592	−	0.930775i	$-0.619133\pi$
$677$	16.4598	−	22.6550i	0.632602	−	0.870703i	0.998194	+	0.0600729i	$0.0191333\pi$
$678$		0			0
$679$	10.1562	+	9.14467i	0.389759	+	0.350940i
$680$		0			0
$681$	−16.8447	−	16.8447i	−0.645491	−	0.645491i
$682$		0			0
$683$	10.2809	−	2.75475i	0.393386	−	0.105407i	−0.0567033	−	0.998391i	$-0.518059\pi$
$683$	10.2809	−	2.75475i	0.393386	−	0.105407i	0.450089	+	0.892984i	$0.351392\pi$
$684$		0			0
$685$	3.70391	+	0.787290i	0.141519	+	0.0300808i
$686$		0			0
$687$	−15.3559	+	12.4349i	−0.585864	+	0.474423i
$688$		0			0
$689$	11.5185	−	30.0394i	0.438820	−	1.14441i
$690$		0			0
$691$	−28.3909	+	10.8982i	−1.08004	+	0.414588i	−0.832350	−	0.554251i	$-0.813005\pi$
$691$	−28.3909	+	10.8982i	−1.08004	+	0.414588i	−0.247690	+	0.968839i	$0.579671\pi$
$692$		0			0
$693$	12.7738	+	5.75350i	0.485237	+	0.218557i
$694$		0			0
$695$	2.78752	−	3.44230i	0.105737	−	0.130574i
$696$		0			0
$697$	0.981505	−	0.500102i	0.0371772	−	0.0189427i
$698$		0			0
$699$	1.76032	−	16.7484i	0.0665815	−	0.633481i
$700$		0			0
$701$	9.98281	+	30.7239i	0.377046	+	1.16043i	0.942088	+	0.335365i	$0.108860\pi$
$701$	9.98281	+	30.7239i	0.377046	+	1.16043i	−0.565042	+	0.825062i	$0.691140\pi$
$702$		0			0
$703$			26.9854i			1.01777i
$704$		0			0
$705$	−12.3465	−	21.3847i	−0.464995	−	0.805395i
$706$		0			0
$707$	−6.84150	−	3.48592i	−0.257301	−	0.131101i
$708$		0			0
$709$	−31.5156	−	12.0977i	−1.18359	−	0.454339i	−0.314630	−	0.949214i	$-0.601881\pi$
$709$	−31.5156	−	12.0977i	−1.18359	−	0.454339i	−0.868964	+	0.494875i	$0.835214\pi$
$710$		0			0
$711$	22.2125	−	20.0002i	0.833032	−	0.750065i
$712$		0			0
$713$	20.0413	+	52.2094i	0.750554	+	1.95526i
$714$		0			0
$715$	2.69112	+	10.2047i	0.100642	+	0.381633i
$716$		0			0
$717$	−0.484825	−	1.26301i	−0.0181061	−	0.0471681i
$718$		0			0
$719$	−16.1748	+	14.5638i	−0.603217	+	0.543139i	−0.913152	−	0.407619i	$-0.866359\pi$
$719$	−16.1748	+	14.5638i	−0.603217	+	0.543139i	0.309935	+	0.950758i	$0.399693\pi$
$720$		0			0
$721$	−1.94623	−	0.747089i	−0.0724816	−	0.0278231i
$722$		0			0
$723$	−5.56316	−	2.83457i	−0.206896	−	0.105419i
$724$		0			0
$725$	20.8554	+	36.1226i	0.774551	+	1.34156i
$726$		0			0
$727$		−	10.1689i		−	0.377145i	−0.982059	−	0.188573i	$-0.939614\pi$
$727$		−	10.1689i		−	0.377145i	0.982059	−	0.188573i	$-0.0603861\pi$
$728$		0			0
$729$	−5.74825	−	17.6913i	−0.212898	−	0.655233i
$730$		0			0
$731$	0.842949	−	8.02012i	0.0311776	−	0.296635i
$732$		0			0
$733$	−32.8601	+	16.7431i	−1.21372	+	0.618419i	−0.939269	−	0.343183i	$-0.888495\pi$
$733$	−32.8601	+	16.7431i	−1.21372	+	0.618419i	−0.274448	+	0.961602i	$0.588495\pi$
$734$		0			0
$735$	−5.60450	+	6.92098i	−0.206725	+	0.255284i
$736$		0			0
$737$	1.44441	−	1.59032i	0.0532056	−	0.0585800i
$738$		0			0
$739$	20.1673	−	7.74152i	0.741868	−	0.284776i	0.0420675	−	0.999115i	$-0.486606\pi$
$739$	20.1673	−	7.74152i	0.741868	−	0.284776i	0.699800	+	0.714338i	$0.253272\pi$
$740$		0			0
$741$	−18.7966	+	8.37698i	−0.690510	+	0.307736i
$742$		0			0
$743$	−34.2667	+	27.7486i	−1.25712	+	1.01800i	−0.258475	+	0.966018i	$0.583220\pi$
$743$	−34.2667	+	27.7486i	−1.25712	+	1.01800i	−0.998648	+	0.0519798i	$0.983447\pi$
$744$		0			0
$745$	−18.9903	−	4.03650i	−0.695749	−	0.147886i
$746$		0			0
$747$	−4.08146	+	1.09363i	−0.149333	+	0.0400137i
$748$		0			0
$749$	−1.38535	−	1.38535i	−0.0506197	−	0.0506197i
$750$		0			0
$751$	−20.1474	−	18.1408i	−0.735190	−	0.661968i	0.213942	−	0.976846i	$-0.431370\pi$
$751$	−20.1474	−	18.1408i	−0.735190	−	0.661968i	−0.949132	+	0.314878i	$0.898036\pi$
$752$		0			0
$753$	4.89033	−	6.73096i	0.178214	−	0.245290i
$754$		0			0
$755$	15.9641	+	5.18705i	0.580993	+	0.188776i
$756$		0			0
$757$	22.3305	+	9.94216i	0.811614	+	0.361354i	0.770211	−	0.637789i	$-0.220151\pi$
$757$	22.3305	+	9.94216i	0.811614	+	0.361354i	0.0414027	+	0.999143i	$0.486817\pi$
$758$		0			0
$759$	−36.1466	−	29.5303i	−1.31204	−	1.07188i
$760$		0			0
$761$	−1.28954	−	1.04425i	−0.0467458	−	0.0378540i	0.605663	−	0.795721i	$-0.292908\pi$
$761$	−1.28954	−	1.04425i	−0.0467458	−	0.0378540i	−0.652409	+	0.757867i	$0.726241\pi$
$762$		0			0
$763$	10.1342	+	11.2552i	0.366884	+	0.407466i
$764$		0			0
$765$	−2.47341	−	3.05441i	−0.0894265	−	0.110432i
$766$		0			0
$767$	−5.34625	−	9.25219i	−0.193042	−	0.334077i
$768$		0			0
$769$	9.33663	−	34.8448i	0.336687	−	1.25653i	−0.565341	−	0.824857i	$-0.691255\pi$
$769$	9.33663	−	34.8448i	0.336687	−	1.25653i	0.902028	−	0.431677i	$-0.142078\pi$
$770$		0			0
$771$	36.4982	+	21.0723i	1.31445	+	0.758899i
$772$		0			0
$773$	−17.2861	+	11.2257i	−0.621737	+	0.403761i	−0.816710	−	0.577048i	$-0.804205\pi$
$773$	−17.2861	+	11.2257i	−0.621737	+	0.403761i	0.194973	+	0.980809i	$0.437538\pi$
$774$		0			0
$775$	−6.18780	−	39.0682i	−0.222272	−	1.40337i
$776$		0			0
$777$	42.4204	−	9.01673i	1.52182	−	0.323474i
$778$		0			0
$779$	0.901154	+	1.24033i	0.0322872	+	0.0444395i
$780$		0			0
$781$	−0.656041	−	0.734966i	−0.0234750	−	0.0262991i
$782$		0			0
$783$	−4.16200	+	9.34801i	−0.148738	+	0.334071i
$784$		0			0
$785$	−4.85076	−	9.52015i	−0.173131	−	0.339789i
$786$		0			0
$787$	−3.98060	+	10.3698i	−0.141893	+	0.369644i	−0.986049	−	0.166453i	$-0.946769\pi$
$787$	−3.98060	+	10.3698i	−0.141893	+	0.369644i	0.844156	+	0.536097i	$0.180102\pi$
$788$		0			0
$789$	12.0083	−	56.4946i	0.427507	−	2.01126i
$790$		0			0
$791$	−20.1886	−	5.40951i	−0.717823	−	0.192340i
$792$		0			0
$793$	−28.0580	−	18.2065i	−0.996368	−	0.646533i
$794$		0			0
$795$	0.971871	+	18.5444i	0.0344687	+	0.657702i
$796$		0			0
$797$	5.23626	+	11.7608i	0.185478	+	0.416590i	0.982221	−	0.187728i	$-0.0601124\pi$
$797$	5.23626	+	11.7608i	0.185478	+	0.416590i	−0.796743	+	0.604318i	$0.793446\pi$
$798$		0			0
$799$	−1.07989	+	20.6055i	−0.0382038	+	0.728972i
$800$		0			0
$801$	18.5626	+	2.94003i	0.655878	+	0.103881i
$802$		0			0
$803$	−27.1447	−	0.117233i	−0.957917	−	0.00413707i
$804$		0			0
$805$	−7.02843	+	5.10645i	−0.247720	+	0.179979i
$806$		0			0
$807$	3.49855	−	10.7674i	0.123155	−	0.379031i
$808$		0			0
$809$	−52.0707	−	5.47285i	−1.83071	−	0.192415i	−0.874486	−	0.485051i	$-0.838801\pi$
$809$	−52.0707	−	5.47285i	−1.83071	−	0.192415i	−0.956224	+	0.292636i	$0.905468\pi$
$810$		0			0
$811$	9.11748	−	17.8941i	0.320158	−	0.628346i	−0.673700	−	0.739005i	$-0.735296\pi$
$811$	9.11748	−	17.8941i	0.320158	−	0.628346i	0.993858	+	0.110659i	$0.0352961\pi$
$812$		0			0
$813$	−1.96529	−	7.33458i	−0.0689259	−	0.257235i
$814$		0			0
$815$	−6.51485	+	11.2840i	−0.228205	+	0.395263i
$816$		0			0
$817$	11.2083	−	0.587402i	0.392129	−	0.0205506i
$818$		0			0
$819$	8.95657	+	12.3182i	0.312968	+	0.430434i
$820$		0			0
$821$	−22.5508	−	14.6447i	−0.787030	−	0.511103i	0.0874477	−	0.996169i	$-0.472129\pi$
$821$	−22.5508	−	14.6447i	−0.787030	−	0.511103i	−0.874478	+	0.485066i	$0.838796\pi$
$822$		0			0
$823$	−32.9415	+	3.46229i	−1.14827	+	0.120688i	−0.659486	−	0.751717i	$-0.729226\pi$
$823$	−32.9415	+	3.46229i	−1.14827	+	0.120688i	−0.488784	+	0.872405i	$0.662559\pi$
$824$		0			0
$825$	20.6653	+	25.7461i	0.719475	+	0.896365i
$826$		0			0
$827$	7.63295	−	48.1925i	0.265424	−	1.67582i	−0.390199	−	0.920730i	$-0.627594\pi$
$827$	7.63295	−	48.1925i	0.265424	−	1.67582i	0.655623	−	0.755088i	$-0.272406\pi$
$828$		0			0
$829$	2.73925	+	12.8872i	0.0951383	+	0.447590i	0.999771	+	0.0213984i	$0.00681184\pi$
$829$	2.73925	+	12.8872i	0.0951383	+	0.447590i	−0.904633	+	0.426192i	$0.859855\pi$
$830$		0			0
$831$	−38.5344	−	27.9969i	−1.33674	−	0.971200i
$832$		0			0
$833$	7.07748	−	2.29961i	0.245220	−	0.0796768i
$834$		0			0
$835$	−1.46958	+	0.848460i	−0.0508568	+	0.0293622i
$836$		0			0
$837$	6.86165	−	6.86165i	0.237173	−	0.237173i
$838$		0			0
$839$	−26.3789	−	40.6200i	−0.910702	−	1.40236i	−0.915478	−	0.402369i	$-0.868187\pi$
$839$	−26.3789	−	40.6200i	−0.910702	−	1.40236i	0.00477610	−	0.999989i	$-0.498480\pi$
$840$		0			0
$841$	−62.7080	+	27.9194i	−2.16234	+	0.962737i
$842$		0			0
$843$	−5.58411	+	8.59877i	−0.192327	+	0.296158i
$844$		0			0
$845$	−2.96134	+	11.0841i	−0.101873	+	0.381306i
$846$		0			0
$847$	−9.75028	−	15.3019i	−0.335024	−	0.525778i
$848$		0			0
$849$	4.19547	+	39.9173i	0.143988	+	1.36996i
$850$		0			0
$851$	−66.4476	−	3.48237i	−2.27780	−	0.119374i
$852$		0			0
$853$	41.1209	−	6.51292i	1.40795	−	0.222998i	0.594252	−	0.804279i	$-0.297448\pi$
$853$	41.1209	−	6.51292i	1.40795	−	0.222998i	0.813703	+	0.581281i	$0.197448\pi$
$854$		0			0
$855$	3.66019	−	4.06506i	0.125176	−	0.139022i
$856$		0			0
$857$	1.09802			0.0375075			0.0187538	−	0.999824i	$-0.494030\pi$
$857$	1.09802			0.0375075			0.0187538	+	0.999824i	$0.494030\pi$
$858$		0			0
$859$	28.2393			0.963512			0.481756	−	0.876305i	$-0.339999\pi$
$859$	28.2393			0.963512			0.481756	+	0.876305i	$0.339999\pi$
$860$		0			0
$861$	1.64867	−	1.83103i	0.0561864	−	0.0624013i
$862$		0			0
$863$	57.2206	−	9.06286i	1.94781	−	0.308503i	0.947865	−	0.318672i	$-0.103237\pi$
$863$	57.2206	−	9.06286i	1.94781	−	0.308503i	0.999948	+	0.0101683i	$0.00323673\pi$
$864$		0			0
$865$	15.2742	+	0.800486i	0.519338	+	0.0272173i
$866$		0			0
$867$	−3.44494	−	32.7764i	−0.116996	−	1.11314i
$868$		0			0
$869$	−38.2601	+	5.89053i	−1.29788	+	0.199823i
$870$		0			0
$871$	2.22094	−	0.722520i	0.0752536	−	0.0244817i
$872$		0			0
$873$	11.5559	−	17.7946i	0.391109	−	0.602256i
$874$		0			0
$875$	12.2629	−	5.45978i	0.414561	−	0.184574i
$876$		0			0
$877$	−0.210659	−	0.324386i	−0.00711344	−	0.0109537i	0.835096	−	0.550104i	$-0.185412\pi$
$877$	−0.210659	−	0.324386i	−0.00711344	−	0.0109537i	−0.842209	+	0.539151i	$0.818745\pi$
$878$		0			0
$879$	−44.2204	+	44.2204i	−1.49152	+	1.49152i
$880$		0			0
$881$	−6.73690	+	3.88955i	−0.226972	+	0.131042i	−0.609174	−	0.793036i	$-0.708499\pi$
$881$	−6.73690	+	3.88955i	−0.226972	+	0.131042i	0.382202	+	0.924079i	$0.375166\pi$
$882$		0			0
$883$	28.3309	−	9.20528i	0.953412	−	0.309782i	0.209311	−	0.977849i	$-0.432878\pi$
$883$	28.3309	−	9.20528i	0.953412	−	0.309782i	0.744101	+	0.668067i	$0.232878\pi$
$884$		0			0
$885$	4.98991	+	3.62538i	0.167734	+	0.121866i
$886$		0			0
$887$	2.58314	+	12.1527i	0.0867335	+	0.408049i	1.00000		0.000685863i	$0.000218317\pi$
$887$	2.58314	+	12.1527i	0.0867335	+	0.408049i	−0.913266	+	0.407363i	$0.866448\pi$
$888$		0			0
$889$	−4.11769	+	25.9981i	−0.138103	+	0.871948i
$890$		0			0
$891$	−8.83098	+	32.3974i	−0.295849	+	1.08535i
$892$		0			0
$893$	−28.5603	+	3.00181i	−0.955733	+	0.100452i
$894$		0			0
$895$	−6.22342	−	4.04153i	−0.208026	−	0.135094i
$896$		0			0
$897$	−18.2015	−	47.3649i	−0.607730	−	1.58147i
$898$		0			0
$899$	92.4694	−	4.84611i	3.08403	−	0.161627i
$900$		0			0
$901$	7.75863	−	13.4383i	0.258477	−	0.447696i
$902$		0			0
$903$	−4.66846	−	17.4229i	−0.155356	−	0.579798i
$904$		0			0
$905$	−0.0858406	+	0.168472i	−0.00285344	+	0.00560019i
$906$		0			0
$907$	−23.0622	−	2.42393i	−0.765766	−	0.0804853i	−0.286412	−	0.958107i	$-0.592463\pi$
$907$	−23.0622	−	2.42393i	−0.765766	−	0.0804853i	−0.479355	+	0.877621i	$0.659129\pi$
$908$		0			0
$909$	−3.68377	+	11.3375i	−0.122183	+	0.376040i
$910$		0			0
$911$	−17.6634	+	12.8332i	−0.585214	+	0.425183i	−0.840600	−	0.541657i	$-0.817797\pi$
$911$	−17.6634	+	12.8332i	−0.585214	+	0.425183i	0.255386	+	0.966839i	$0.417797\pi$
$912$		0			0
$913$	5.19726	+	1.71354i	0.172004	+	0.0567100i
$914$		0			0
$915$	19.0683	+	3.02012i	0.630378	+	0.0998421i
$916$		0			0
$917$	−1.77525	+	33.8737i	−0.0586238	+	1.11861i
$918$		0			0
$919$	12.0936	+	27.1626i	0.398931	+	0.896013i	0.995616	+	0.0935374i	$0.0298175\pi$
$919$	12.0936	+	27.1626i	0.398931	+	0.896013i	−0.596685	+	0.802475i	$0.703516\pi$
$920$		0			0
$921$	−2.05642	−	39.2388i	−0.0677612	−	1.29296i
$922$		0			0
$923$	−0.223054	−	1.04751i	−0.00734190	−	0.0344792i
$924$		0			0
$925$	45.4596	+	12.1809i	1.49470	+	0.400504i
$926$		0			0
$927$	−0.672917	+	3.16583i	−0.0221015	+	0.103979i
$928$		0			0
$929$	−15.5739	+	40.5713i	−0.510962	+	1.33110i	0.399206	+	0.916861i	$0.369286\pi$
$929$	−15.5739	+	40.5713i	−0.510962	+	1.33110i	−0.910168	+	0.414240i	$0.864047\pi$
$930$		0			0
$931$	4.70205	+	9.22829i	0.154103	+	0.302445i
$932$		0			0
$933$	−0.553637	+	1.24349i	−0.0181252	+	0.0407100i
$934$		0			0
$935$	0.510203	+	5.06456i	0.0166854	+	0.165629i
$936$		0			0
$937$	11.1359	+	15.3272i	0.363793	+	0.500718i	0.951201	−	0.308573i	$-0.0998514\pi$
$937$	11.1359	+	15.3272i	0.363793	+	0.500718i	−0.587408	+	0.809291i	$0.699851\pi$
$938$		0			0
$939$	33.7609	−	7.17609i	1.10174	−	0.234183i
$940$		0			0
$941$	3.88260	+	24.5138i	0.126569	+	0.799127i	0.966544	+	0.256501i	$0.0825698\pi$
$941$	3.88260	+	24.5138i	0.126569	+	0.799127i	−0.839975	+	0.542626i	$0.817430\pi$
$942$		0			0
$943$	−3.17043	+	2.05890i	−0.103243	+	0.0670471i
$944$		0			0
$945$	1.30550	+	0.753732i	0.0424680	+	0.0245189i
$946$		0			0
$947$	−1.42306	+	5.31092i	−0.0462432	+	0.172582i	−0.985185	−	0.171493i	$-0.945141\pi$
$947$	−1.42306	+	5.31092i	−0.0462432	+	0.172582i	0.938942	+	0.344075i	$0.111807\pi$
$948$		0			0
$949$	−25.5615	−	14.7456i	−0.829762	−	0.478661i
$950$		0			0
$951$	11.1156	+	13.7266i	0.360447	+	0.445116i
$952$		0			0
$953$	−2.23954	−	2.48726i	−0.0725457	−	0.0805701i	0.705779	−	0.708432i	$-0.250597\pi$
$953$	−2.23954	−	2.48726i	−0.0725457	−	0.0805701i	−0.778325	+	0.627862i	$0.783930\pi$
$954$		0			0
$955$	−4.42469	−	3.58304i	−0.143180	−	0.115944i
$956$		0			0
$957$	−64.9966	+	41.8113i	−2.10104	+	1.35157i
$958$		0			0
$959$	−6.46551	−	2.87863i	−0.208782	−	0.0929559i
$960$		0			0
$961$	−54.0304	−	17.5555i	−1.74292	−	0.566307i
$962$		0			0
$963$	−1.78786	+	2.46078i	−0.0576130	+	0.0792974i
$964$		0			0
$965$	12.8482	+	11.5686i	0.413599	+	0.372406i
$966$		0			0
$967$	17.7731	+	17.7731i	0.571544	+	0.571544i	0.932560	−	0.361016i	$-0.117570\pi$
$967$	17.7731	+	17.7731i	0.571544	+	0.571544i	−0.361016	+	0.932560i	$0.617570\pi$
$968$		0			0
$969$	−9.58737	+	2.56893i	−0.307991	+	0.0825259i
$970$		0			0
$971$	−20.9327	−	4.44938i	−0.671762	−	0.142787i	−0.140611	−	0.990065i	$-0.544907\pi$
$971$	−20.9327	−	4.44938i	−0.671762	−	0.142787i	−0.531150	+	0.847277i	$0.678240\pi$
$972$		0			0
$973$	−6.43378	+	5.20997i	−0.206257	+	0.167024i
$974$		0			0
$975$	5.62733	+	35.4460i	0.180219	+	1.13518i
$976$		0			0
$977$	−14.8519	+	5.70110i	−0.475153	+	0.182394i	−0.584147	−	0.811648i	$-0.698571\pi$
$977$	−14.8519	+	5.70110i	−0.475153	+	0.182394i	0.108993	+	0.994043i	$0.465237\pi$
$978$		0			0
$979$	−18.0180	−	16.3649i	−0.575858	−	0.523025i
$980$		0			0
$981$	14.7976	−	18.2735i	0.472451	−	0.583429i
$982$		0			0
$983$	18.2584	−	9.30314i	0.582354	−	0.296724i	−0.137887	−	0.990448i	$-0.544031\pi$
$983$	18.2584	−	9.30314i	0.582354	−	0.296724i	0.720241	+	0.693724i	$0.244031\pi$
$984$		0			0
$985$	−1.71906	+	16.3557i	−0.0547737	+	0.521137i
$986$		0			0
$987$	14.2617	+	43.8931i	0.453956	+	1.39713i
$988$		0			0
$989$			27.6746i			0.880002i
$990$		0			0
$991$	−12.1082	−	20.9721i	−0.384631	−	0.666200i	0.607087	−	0.794635i	$-0.292338\pi$
$991$	−12.1082	−	20.9721i	−0.384631	−	0.666200i	−0.991718	+	0.128435i	$0.959005\pi$
$992$		0			0
$993$	−5.07620	−	2.58645i	−0.161088	−	0.0820786i
$994$		0			0
$995$	−9.86171	−	3.78556i	−0.312637	−	0.120010i
$996$		0			0
$997$	23.8068	−	21.4357i	0.753969	−	0.678877i	−0.199659	−	0.979866i	$-0.563983\pi$
$997$	23.8068	−	21.4357i	0.753969	−	0.678877i	0.953628	+	0.300989i	$0.0973166\pi$
$998$		0			0
$999$	4.13762	+	10.7789i	0.130909	+	0.341028i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.bv.a.41.3	✓	224
11.7	odd	10	inner	572.2.bv.a.249.12	yes	224
13.7	odd	12	inner	572.2.bv.a.85.12	yes	224
143.7	even	60	inner	572.2.bv.a.293.3	yes	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.bv.a.41.3	✓	224	1.1	even	1	trivial
572.2.bv.a.85.12	yes	224	13.7	odd	12	inner
572.2.bv.a.249.12	yes	224	11.7	odd	10	inner
572.2.bv.a.293.3	yes	224	143.7	even	60	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.bv (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.57791 + 1.75245i) q^{3} +(-0.871666 + 0.138058i) q^{5} +(1.64722 + 0.0863272i) q^{7} +(-0.267683 - 2.54684i) q^{9} +O(q^{10})\)	\(q+(-1.57791 + 1.75245i) q^{3} +(-0.871666 + 0.138058i) q^{5} +(1.64722 + 0.0863272i) q^{7} +(-0.267683 - 2.54684i) q^{9} +(-1.51846 + 2.94860i) q^{11} +(-3.02315 + 1.96482i) q^{13} +(1.13347 - 1.74539i) q^{15} +(-1.58869 + 0.707329i) q^{17} +(-1.31821 - 2.02987i) q^{19} +(-2.75045 + 2.75045i) q^{21} +(5.16837 - 2.98396i) q^{23} +(-4.01454 + 1.30440i) q^{25} +(-0.837775 - 0.608679i) q^{27} +(-2.05446 - 9.66548i) q^{29} +(-1.46591 + 9.25538i) q^{31} +(-2.77127 - 7.31366i) q^{33} +(-1.44774 + 0.152164i) q^{35} +(-9.35068 - 6.07240i) q^{37} +(1.32701 - 8.39823i) q^{39} +(-0.632569 + 0.0331515i) q^{41} +(-2.31861 + 4.01596i) q^{43} +(0.584942 + 2.18303i) q^{45} +(5.38665 - 10.5719i) q^{47} +(-4.25577 - 0.447300i) q^{49} +(1.26725 - 3.90019i) q^{51} +(-7.21879 + 5.24476i) q^{53} +(0.916515 - 2.77983i) q^{55} +(5.63725 + 0.892853i) q^{57} +(-0.155108 + 2.95963i) q^{59} +(3.77315 + 8.47463i) q^{61} +(-0.221072 - 4.21831i) q^{63} +(2.36392 - 2.13004i) q^{65} +(-0.625682 - 0.167651i) q^{67} +(-2.92599 + 13.7657i) q^{69} +(-0.106450 + 0.277311i) q^{71} +(3.71569 + 7.29246i) q^{73} +(4.04869 - 9.09350i) q^{75} +(-2.75579 + 4.72592i) q^{77} +(6.86049 + 9.44265i) q^{79} +(9.90332 - 2.10502i) q^{81} +(-0.258118 - 1.62969i) q^{83} +(1.28715 - 0.835886i) q^{85} +(20.1800 + 11.6509i) q^{87} +(-1.89945 + 7.08886i) q^{89} +(-5.14942 + 2.97552i) q^{91} +(-13.9065 - 17.1731i) q^{93} +(1.42928 + 1.58738i) q^{95} +(6.43891 + 5.21413i) q^{97} +(7.91608 + 3.07799i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q + 28 q^{9}+O(q^{10}) \) 224 * q + 28 * q^9	\( 224 q + 28 q^{9} + 16 q^{11} + 10 q^{13} - 28 q^{15} - 48 q^{23} + 24 q^{27} + 20 q^{29} + 4 q^{31} + 60 q^{33} + 50 q^{35} + 12 q^{37} - 40 q^{39} + 20 q^{41} + 64 q^{45} - 62 q^{47} + 100 q^{53} - 22 q^{55} + 12 q^{59} - 40 q^{61} - 80 q^{63} - 44 q^{67} - 152 q^{71} + 30 q^{73} - 120 q^{75} + 80 q^{79} + 72 q^{81} + 90 q^{83} - 40 q^{85} - 8 q^{89} - 36 q^{91} - 90 q^{93} - 42 q^{97} + 144 q^{99}+O(q^{100}) \) 224 * q + 28 * q^9 + 16 * q^11 + 10 * q^13 - 28 * q^15 - 48 * q^23 + 24 * q^27 + 20 * q^29 + 4 * q^31 + 60 * q^33 + 50 * q^35 + 12 * q^37 - 40 * q^39 + 20 * q^41 + 64 * q^45 - 62 * q^47 + 100 * q^53 - 22 * q^55 + 12 * q^59 - 40 * q^61 - 80 * q^63 - 44 * q^67 - 152 * q^71 + 30 * q^73 - 120 * q^75 + 80 * q^79 + 72 * q^81 + 90 * q^83 - 40 * q^85 - 8 * q^89 - 36 * q^91 - 90 * q^93 - 42 * q^97 + 144 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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