LMFDB - Embedded newform 572.2.bv.a.249.1

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			249.1
Character	$\chi$	$=$	572.249
Dual form			572.2.bv.a.85.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.18098 + 0.676138i) q^{3} +(-0.412038 + 2.60150i) q^{5} +(-3.92487 + 2.54884i) q^{7} +(6.92083 - 3.08135i) q^{9} +O(q^{10})$	\(q+(-3.18098 + 0.676138i) q^{3} +(-0.412038 + 2.60150i) q^{5} +(-3.92487 + 2.54884i) q^{7} +(6.92083 - 3.08135i) q^{9} +(-2.46258 + 2.22165i) q^{11} +(-0.584728 + 3.55782i) q^{13} +(-0.448292 - 8.55392i) q^{15} +(0.189345 + 1.80150i) q^{17} +(0.154824 - 2.95422i) q^{19} +(10.7616 - 10.7616i) q^{21} +(1.36235 - 0.786555i) q^{23} +(-1.84276 - 0.598749i) q^{25} +(-12.0387 + 8.74664i) q^{27} +(-4.29846 - 3.87035i) q^{29} +(7.06231 - 1.11856i) q^{31} +(6.33127 - 8.73205i) q^{33} +(-5.01362 - 11.2608i) q^{35} +(-7.37274 + 0.386389i) q^{37} +(-0.545572 - 11.7127i) q^{39} +(-1.28127 - 0.832069i) q^{41} +(2.46467 - 4.26893i) q^{43} +(5.16450 + 19.2742i) q^{45} +(-0.733754 + 0.373867i) q^{47} +(6.06086 - 13.6129i) q^{49} +(-1.82037 - 5.60251i) q^{51} +(-0.294980 - 0.214316i) q^{53} +(-4.76494 - 7.32181i) q^{55} +(1.50497 + 9.50201i) q^{57} +(8.30975 + 12.7959i) q^{59} +(-8.12559 + 0.854034i) q^{61} +(-19.3095 + 29.7340i) q^{63} +(-9.01475 - 2.98713i) q^{65} +(2.65162 + 0.710499i) q^{67} +(-3.80180 + 3.42315i) q^{69} +(-1.48136 - 1.19959i) q^{71} +(5.78905 + 2.94967i) q^{73} +(6.26662 + 0.658648i) q^{75} +(4.00268 - 14.9964i) q^{77} +(-3.48647 + 4.79872i) q^{79} +(17.1734 - 19.0730i) q^{81} +(10.1398 + 1.60599i) q^{83} +(-4.76462 - 0.249703i) q^{85} +(16.2902 + 9.40516i) q^{87} +(0.136159 - 0.508151i) q^{89} +(-6.77334 - 15.4544i) q^{91} +(-21.7087 + 8.33321i) q^{93} +(7.62163 + 1.62003i) q^{95} +(4.65373 - 12.1234i) q^{97} +(-10.1974 + 22.9637i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{10}\right)$

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
$3$	−3.18098	+	0.676138i	−1.83654	+	0.390368i	−0.989896	−	0.141793i	$-0.954713\pi$
$3$	−3.18098	+	0.676138i	−1.83654	+	0.390368i	−0.846643	+	0.532162i	$0.821380\pi$
$4$		0			0
$5$	−0.412038	+	2.60150i	−0.184269	+	1.16343i	0.706074	+	0.708138i	$0.250464\pi$
$5$	−0.412038	+	2.60150i	−0.184269	+	1.16343i	−0.890343	+	0.455290i	$0.849536\pi$
$6$		0			0
$7$	−3.92487	+	2.54884i	−1.48346	+	0.963371i	−0.487544	+	0.873098i	$0.662107\pi$
$7$	−3.92487	+	2.54884i	−1.48346	+	0.963371i	−0.995917	+	0.0902724i	$0.971226\pi$
$8$		0			0
$9$	6.92083	−	3.08135i	2.30694	−	1.02712i
$10$		0			0
$11$	−2.46258	+	2.22165i	−0.742495	+	0.669851i
$11$	−2.46258	+	2.22165i	−0.742495	+	0.669851i
$12$		0			0
$13$	−0.584728	+	3.55782i	−0.162174	+	0.986762i
$13$	−0.584728	+	3.55782i	−0.162174	+	0.986762i
$14$		0			0
$15$	−0.448292	−	8.55392i	−0.115748	−	2.20861i
$16$		0			0
$17$	0.189345	+	1.80150i	0.0459230	+	0.436928i	0.993192	+	0.116489i	$0.0371639\pi$
$17$	0.189345	+	1.80150i	0.0459230	+	0.436928i	−0.947269	+	0.320439i	$0.896169\pi$
$18$		0			0
$19$	0.154824	−	2.95422i	0.0355191	−	0.677746i	−0.921616	−	0.388103i	$-0.873130\pi$
$19$	0.154824	−	2.95422i	0.0355191	−	0.677746i	0.957135	−	0.289642i	$-0.0935363\pi$
$20$		0			0
$21$	10.7616	−	10.7616i	2.34836	−	2.34836i
$22$		0			0
$23$	1.36235	−	0.786555i	0.284070	−	0.164008i	−0.351194	−	0.936303i	$-0.614224\pi$
$23$	1.36235	−	0.786555i	0.284070	−	0.164008i	0.635265	+	0.772295i	$0.280891\pi$
$24$		0			0
$25$	−1.84276	−	0.598749i	−0.368552	−	0.119750i
$26$		0			0
$27$	−12.0387	+	8.74664i	−2.31685	+	1.68329i
$28$		0			0
$29$	−4.29846	−	3.87035i	−0.798204	−	0.718707i	0.165345	−	0.986236i	$-0.447126\pi$
$29$	−4.29846	−	3.87035i	−0.798204	−	0.718707i	−0.963550	+	0.267529i	$0.913793\pi$
$30$		0			0
$31$	7.06231	−	1.11856i	1.26843	−	0.200899i	0.514290	−	0.857616i	$-0.328055\pi$
$31$	7.06231	−	1.11856i	1.26843	−	0.200899i	0.754137	+	0.656717i	$0.228055\pi$
$32$		0			0
$33$	6.33127	−	8.73205i	1.10213	−	1.52005i
$34$		0			0
$35$	−5.01362	−	11.2608i	−0.847457	−	1.90342i
$36$		0			0
$37$	−7.37274	+	0.386389i	−1.21207	+	0.0635219i	−0.647632	−	0.761953i	$-0.724241\pi$
$37$	−7.37274	+	0.386389i	−1.21207	+	0.0635219i	−0.564439	+	0.825475i	$0.690907\pi$
$38$		0			0
$39$	−0.545572	−	11.7127i	−0.0873614	−	1.87553i
$40$		0			0
$41$	−1.28127	−	0.832069i	−0.200101	−	0.129947i	0.440699	−	0.897655i	$-0.354731\pi$
$41$	−1.28127	−	0.832069i	−0.200101	−	0.129947i	−0.640800	+	0.767708i	$0.721397\pi$
$42$		0			0
$43$	2.46467	−	4.26893i	0.375859	−	0.651006i	−0.614597	−	0.788842i	$-0.710681\pi$
$43$	2.46467	−	4.26893i	0.375859	−	0.651006i	0.990455	+	0.137835i	$0.0440145\pi$
$44$		0			0
$45$	5.16450	+	19.2742i	0.769879	+	2.87323i
$46$		0			0
$47$	−0.733754	+	0.373867i	−0.107029	+	0.0545340i	−0.506685	−	0.862131i	$-0.669129\pi$
$47$	−0.733754	+	0.373867i	−0.107029	+	0.0545340i	0.399656	+	0.916665i	$0.369129\pi$
$48$		0			0
$49$	6.06086	−	13.6129i	0.865837	−	1.94470i
$50$		0			0
$51$	−1.82037	−	5.60251i	−0.254902	−	0.784508i
$52$		0			0
$53$	−0.294980	−	0.214316i	−0.0405186	−	0.0294385i	0.567342	−	0.823483i	$-0.307972\pi$
$53$	−0.294980	−	0.214316i	−0.0405186	−	0.0294385i	−0.607860	+	0.794044i	$0.707972\pi$
$54$		0			0
$55$	−4.76494	−	7.32181i	−0.642505	−	0.987272i
$56$		0			0
$57$	1.50497	+	9.50201i	0.199338	+	1.25857i
$58$		0			0
$59$	8.30975	+	12.7959i	1.08184	+	1.66588i	0.638781	+	0.769389i	$0.279439\pi$
$59$	8.30975	+	12.7959i	1.08184	+	1.66588i	0.443056	+	0.896494i	$0.353894\pi$
$60$		0			0
$61$	−8.12559	+	0.854034i	−1.04038	+	0.109348i	−0.609277	−	0.792957i	$-0.708540\pi$
$61$	−8.12559	+	0.854034i	−1.04038	+	0.109348i	−0.431098	+	0.902305i	$0.641874\pi$
$62$		0			0
$63$	−19.3095	+	29.7340i	−2.43276	+	3.74613i
$64$		0			0
$65$	−9.01475	−	2.98713i	−1.11814	−	0.370507i
$66$		0			0
$67$	2.65162	+	0.710499i	0.323947	+	0.0868013i	0.417128	−	0.908848i	$-0.363037\pi$
$67$	2.65162	+	0.710499i	0.323947	+	0.0868013i	−0.0931809	+	0.995649i	$0.529703\pi$
$68$		0			0
$69$	−3.80180	+	3.42315i	−0.457682	+	0.412099i
$70$		0			0
$71$	−1.48136	−	1.19959i	−0.175806	−	0.142365i	0.537379	−	0.843341i	$-0.319415\pi$
$71$	−1.48136	−	1.19959i	−0.175806	−	0.142365i	−0.713185	+	0.700976i	$0.752748\pi$
$72$		0			0
$73$	5.78905	+	2.94967i	0.677557	+	0.345233i	0.758673	−	0.651472i	$-0.225848\pi$
$73$	5.78905	+	2.94967i	0.677557	+	0.345233i	−0.0811152	+	0.996705i	$0.525848\pi$
$74$		0			0
$75$	6.26662	+	0.658648i	0.723606	+	0.0760541i
$76$		0			0
$77$	4.00268	−	14.9964i	0.456148	−	1.70900i
$78$		0			0
$79$	−3.48647	+	4.79872i	−0.392259	+	0.539898i	−0.958780	−	0.284149i	$-0.908289\pi$
$79$	−3.48647	+	4.79872i	−0.392259	+	0.539898i	0.566521	+	0.824047i	$0.308289\pi$
$80$		0			0
$81$	17.1734	−	19.0730i	1.90815	−	2.11922i
$82$		0			0
$83$	10.1398	+	1.60599i	1.11299	+	0.176280i	0.685734	−	0.727852i	$-0.259481\pi$
$83$	10.1398	+	1.60599i	1.11299	+	0.176280i	0.427253	+	0.904132i	$0.359481\pi$
$84$		0			0
$85$	−4.76462	−	0.249703i	−0.516796	−	0.0270841i
$86$		0			0
$87$	16.2902	+	9.40516i	1.74649	+	1.00834i
$88$		0			0
$89$	0.136159	−	0.508151i	0.0144328	−	0.0538639i	−0.958334	−	0.285650i	$-0.907790\pi$
$89$	0.136159	−	0.508151i	0.0144328	−	0.0538639i	0.972767	+	0.231786i	$0.0744571\pi$
$90$		0			0
$91$	−6.77334	−	15.4544i	−0.710039	−	1.62006i
$92$		0			0
$93$	−21.7087	+	8.33321i	−2.25109	+	0.864113i
$94$		0			0
$95$	7.62163	+	1.62003i	0.781963	+	0.166211i
$96$		0			0
$97$	4.65373	−	12.1234i	0.472515	−	1.23094i	−0.465717	−	0.884934i	$-0.654203\pi$
$97$	4.65373	−	12.1234i	0.472515	−	1.23094i	0.938231	−	0.346009i	$-0.112463\pi$
$98$		0			0
$99$	−10.1974	+	22.9637i	−1.02488	+	2.30794i
$100$		0			0
$101$	−0.963154	+	9.16380i	−0.0958374	+	0.911832i	0.835945	+	0.548814i	$0.184920\pi$
$101$	−0.963154	+	9.16380i	−0.0958374	+	0.911832i	−0.931782	+	0.363018i	$0.881746\pi$
$102$		0			0
$103$	−14.6287	+	4.75316i	−1.44141	+	0.468343i	−0.922337	−	0.386387i	$-0.873723\pi$
$103$	−14.6287	+	4.75316i	−1.44141	+	0.468343i	−0.519074	+	0.854729i	$0.673723\pi$
$104$		0			0
$105$	23.5621	+	32.4304i	2.29942	+	3.16488i
$106$		0			0
$107$	−0.649698	−	3.05659i	−0.0628087	−	0.295492i	0.935521	−	0.353272i	$-0.114931\pi$
$107$	−0.649698	−	3.05659i	−0.0628087	−	0.295492i	−0.998329	+	0.0577804i	$0.981598\pi$
$108$		0			0
$109$	4.29312	+	4.29312i	0.411207	+	0.411207i	0.882159	−	0.470952i	$-0.156090\pi$
$109$	4.29312	+	4.29312i	0.411207	+	0.411207i	−0.470952	+	0.882159i	$0.656090\pi$
$110$		0			0
$111$	23.1913	−	6.21408i	2.20122	−	0.589815i
$112$		0			0
$113$	7.03720	+	7.81560i	0.662004	+	0.735230i	0.976853	−	0.213912i	$-0.0686205\pi$
$113$	7.03720	+	7.81560i	0.662004	+	0.735230i	−0.314849	+	0.949142i	$0.601954\pi$
$114$		0			0
$115$	1.48488	+	3.86825i	0.138466	+	0.360717i
$116$		0			0
$117$	6.91610	+	26.4248i	0.639393	+	2.44298i
$118$		0			0
$119$	−5.33489	−	6.58804i	−0.489049	−	0.603925i
$120$		0			0
$121$	1.12858	−	10.9420i	0.102599	−	0.994723i
$122$		0			0
$123$	4.63830	+	1.78048i	0.418221	+	0.160540i
$124$		0			0
$125$	−3.66197	+	7.18701i	−0.327536	+	0.642826i
$126$		0			0
$127$	−10.3296	−	4.59901i	−0.916600	−	0.408097i	−0.106449	−	0.994318i	$-0.533948\pi$
$127$	−10.3296	−	4.59901i	−0.916600	−	0.408097i	−0.810151	+	0.586222i	$0.800615\pi$
$128$		0			0
$129$	−4.95367	+	15.2458i	−0.436147	+	1.34232i
$130$		0			0
$131$			3.18477i			0.278255i	0.990274	+	0.139127i	$0.0444297\pi$
$131$			3.18477i			0.278255i	−0.990274	+	0.139127i	$0.955570\pi$
$132$		0			0
$133$	6.92218	+	11.9896i	0.600229	+	1.03963i
$134$		0			0
$135$	−17.7940	−	34.9227i	−1.53146	−	3.00567i
$136$		0			0
$137$	−2.36845	+	2.92480i	−0.202351	+	0.249882i	−0.868212	−	0.496193i	$-0.834731\pi$
$137$	−2.36845	+	2.92480i	−0.202351	+	0.249882i	0.665861	+	0.746075i	$0.268064\pi$
$138$		0			0
$139$	−0.138760	+	0.652816i	−0.0117695	+	0.0553712i	−0.983640	−	0.180143i	$-0.942344\pi$
$139$	−0.138760	+	0.652816i	−0.0117695	+	0.0553712i	0.971871	+	0.235514i	$0.0756773\pi$
$140$		0			0
$141$	2.08127	−	1.68538i	0.175275	−	0.141935i
$142$		0			0
$143$	−6.46428	−	10.0605i	−0.540570	−	0.841299i
$144$		0			0
$145$	11.8399	−	9.58773i	0.983247	−	0.796218i
$146$		0			0
$147$	−10.0753	+	47.4003i	−0.830993	+	3.90951i
$148$		0			0
$149$	−12.8660	+	15.8882i	−1.05403	+	1.30162i	−0.102273	+	0.994756i	$0.532611\pi$
$149$	−12.8660	+	15.8882i	−1.05403	+	1.30162i	−0.951755	+	0.306859i	$0.900722\pi$
$150$		0			0
$151$	−6.82352	−	13.3919i	−0.555290	−	1.08982i	−0.982604	−	0.185714i	$-0.940540\pi$
$151$	−6.82352	−	13.3919i	−0.555290	−	1.08982i	0.427314	−	0.904103i	$-0.359460\pi$
$152$		0			0
$153$	6.86148	+	11.8844i	0.554718	+	0.960799i
$154$		0			0
$155$			18.8335i			1.51274i
$156$		0			0
$157$	6.25585	−	19.2535i	0.499271	−	1.53660i	−0.310923	−	0.950435i	$-0.600638\pi$
$157$	6.25585	−	19.2535i	0.499271	−	1.53660i	0.810194	−	0.586162i	$-0.199362\pi$
$158$		0			0
$159$	1.08323	+	0.482286i	0.0859059	+	0.0382478i
$160$		0			0
$161$	−3.34225	+	6.55954i	−0.263407	+	0.516964i
$162$		0			0
$163$	−4.62415	−	1.77505i	−0.362192	−	0.139032i	0.170465	−	0.985364i	$-0.445473\pi$
$163$	−4.62415	−	1.77505i	−0.362192	−	0.139032i	−0.532657	+	0.846331i	$0.678806\pi$
$164$		0			0
$165$	20.1077	+	20.0688i	1.56538	+	1.56235i
$166$		0			0
$167$	−5.18330	−	6.40084i	−0.401096	−	0.495312i	0.536081	−	0.844166i	$-0.319904\pi$
$167$	−5.18330	−	6.40084i	−0.401096	−	0.495312i	−0.937177	+	0.348854i	$0.886571\pi$
$168$		0			0
$169$	−12.3162	−	4.16071i	−0.947399	−	0.320055i
$170$		0			0
$171$	−8.03149	−	20.9227i	−0.614183	−	1.60000i
$172$		0			0
$173$	−0.124257	−	0.138002i	−0.00944711	−	0.0104921i	0.738403	−	0.674360i	$-0.235580\pi$
$173$	−0.124257	−	0.138002i	−0.00944711	−	0.0104921i	−0.747850	+	0.663868i	$0.768914\pi$
$174$		0			0
$175$	8.75870	−	2.34689i	0.662096	−	0.177408i
$176$		0			0
$177$	−35.0849	−	35.0849i	−2.63714	−	2.63714i
$178$		0			0
$179$	−4.05952	−	19.0985i	−0.303423	−	1.42749i	−0.820546	−	0.571581i	$-0.806330\pi$
$179$	−4.05952	−	19.0985i	−0.303423	−	1.42749i	0.517123	−	0.855911i	$-0.327003\pi$
$180$		0			0
$181$	−3.47335	−	4.78065i	−0.258172	−	0.355343i	0.660180	−	0.751107i	$-0.270480\pi$
$181$	−3.47335	−	4.78065i	−0.258172	−	0.355343i	−0.918352	+	0.395764i	$0.870480\pi$
$182$		0			0
$183$	25.2699	−	8.21068i	1.86800	−	0.606951i
$184$		0			0
$185$	2.03265	−	19.3394i	0.149444	−	1.42186i
$186$		0			0
$187$	−4.46857	−	4.01568i	−0.326774	−	0.293655i
$188$		0			0
$189$	24.9566	−	65.0142i	1.81533	−	4.72908i
$190$		0			0
$191$	22.2568	+	4.73083i	1.61044	+	0.342311i	0.923261	−	0.384173i	$-0.125513\pi$
$191$	22.2568	+	4.73083i	1.61044	+	0.342311i	0.687184	+	0.726484i	$0.258847\pi$
$192$		0			0
$193$	−11.4088	+	4.37941i	−0.821221	+	0.315237i	−0.732455	−	0.680816i	$-0.761626\pi$
$193$	−11.4088	+	4.37941i	−0.821221	+	0.315237i	−0.0887656	+	0.996053i	$0.528292\pi$
$194$		0			0
$195$	30.6954	+	3.40677i	2.19815	+	0.243964i
$196$		0			0
$197$	2.77949	−	10.3732i	0.198030	−	0.739059i	−0.793431	−	0.608660i	$-0.791708\pi$
$197$	2.77949	−	10.3732i	0.198030	−	0.739059i	0.991462	−	0.130399i	$-0.0416258\pi$
$198$		0			0
$199$	−16.3836	−	9.45908i	−1.16140	−	0.670536i	−0.209763	−	0.977752i	$-0.567269\pi$
$199$	−16.3836	−	9.45908i	−1.16140	−	0.670536i	−0.951640	+	0.307216i	$0.900603\pi$
$200$		0			0
$201$	−8.91514	−	0.467223i	−0.628825	−	0.0329553i
$202$		0			0
$203$	26.7358	+	4.23454i	1.87649	+	0.297206i
$204$		0			0
$205$	2.69256	−	2.99039i	0.188057	−	0.208858i
$206$		0			0
$207$	7.00496	−	9.64150i	0.486878	−	0.670130i
$208$		0			0
$209$	6.18197	+	7.61897i	0.427616	+	0.527015i
$210$		0			0
$211$	−26.0656	−	2.73961i	−1.79443	−	0.188602i	−0.852122	−	0.523343i	$-0.824684\pi$
$211$	−26.0656	−	2.73961i	−1.79443	−	0.188602i	−0.942310	+	0.334741i	$0.891351\pi$
$212$		0			0
$213$	5.52328	+	2.81425i	0.378449	+	0.192829i
$214$		0			0
$215$	10.0901	+	8.17081i	0.688139	+	0.557244i
$216$		0			0
$217$	−24.8676	+	22.3909i	−1.68812	+	1.51999i
$218$		0			0
$219$	−20.4092	−	5.46864i	−1.37913	−	0.369536i
$220$		0			0
$221$	−6.52013	−	0.379730i	−0.438591	−	0.0255434i
$222$		0			0
$223$	−9.21909	+	14.1962i	−0.617356	+	0.950645i	0.382290	+	0.924042i	$0.375136\pi$
$223$	−9.21909	+	14.1962i	−0.617356	+	0.950645i	−0.999646	+	0.0266027i	$0.991531\pi$
$224$		0			0
$225$	−14.5984	+	1.53435i	−0.973225	+	0.102290i
$226$		0			0
$227$	13.3781	+	20.6005i	0.887936	+	1.36730i	0.929756	+	0.368177i	$0.120018\pi$
$227$	13.3781	+	20.6005i	0.887936	+	1.36730i	−0.0418195	+	0.999125i	$0.513315\pi$
$228$		0			0
$229$	−1.28526	−	8.11481i	−0.0849324	−	0.536242i	−0.993066	−	0.117561i	$-0.962492\pi$
$229$	−1.28526	−	8.11481i	−0.0849324	−	0.536242i	0.908133	−	0.418681i	$-0.137508\pi$
$230$		0			0
$231$	−2.59282	+	50.4095i	−0.170595	+	3.31670i
$232$		0			0
$233$	−21.9726	−	15.9640i	−1.43947	−	1.04584i	−0.988152	−	0.153476i	$-0.950953\pi$
$233$	−21.9726	−	15.9640i	−1.43947	−	1.04584i	−0.451321	−	0.892362i	$-0.649047\pi$
$234$		0			0
$235$	−0.670280	−	2.06291i	−0.0437243	−	0.134569i
$236$		0			0
$237$	7.84580	−	17.6220i	0.509639	−	1.14467i
$238$		0			0
$239$	6.80628	−	3.46797i	0.440261	−	0.224324i	−0.219786	−	0.975548i	$-0.570536\pi$
$239$	6.80628	−	3.46797i	0.440261	−	0.224324i	0.660048	+	0.751224i	$0.270536\pi$
$240$		0			0
$241$	1.78778	+	6.67208i	0.115161	+	0.429787i	0.999299	−	0.0374394i	$-0.0119201\pi$
$241$	1.78778	+	6.67208i	0.115161	+	0.429787i	−0.884138	+	0.467226i	$0.845253\pi$
$242$		0			0
$243$	−19.4112	+	33.6212i	−1.24523	+	2.15680i
$244$		0			0
$245$	32.9167	+	21.3764i	2.10297	+	1.36569i
$246$		0			0
$247$	10.4201	+	2.27825i	0.663013	+	0.144962i
$248$		0			0
$249$	−33.3404	+	1.74729i	−2.11286	+	0.110730i
$250$		0			0
$251$	5.57408	+	12.5196i	0.351833	+	0.790229i	0.999597	+	0.0283884i	$0.00903753\pi$
$251$	5.57408	+	12.5196i	0.351833	+	0.790229i	−0.647764	+	0.761841i	$0.724296\pi$
$252$		0			0
$253$	−1.60745	+	4.96362i	−0.101060	+	0.312060i
$254$		0			0
$255$	15.3250	−	2.42724i	0.959689	−	0.152000i
$256$		0			0
$257$	−7.96177	−	7.16881i	−0.496642	−	0.447178i	0.382348	−	0.924018i	$-0.375115\pi$
$257$	−7.96177	−	7.16881i	−0.496642	−	0.447178i	−0.878990	+	0.476840i	$0.841782\pi$
$258$		0			0
$259$	27.9522	−	20.3085i	1.73686	−	1.26191i
$260$		0			0
$261$	−41.6748	−	13.5410i	−2.57961	−	0.838165i
$262$		0			0
$263$	−7.35100	+	4.24410i	−0.453282	+	0.261703i	−0.709215	−	0.704992i	$-0.750951\pi$
$263$	−7.35100	+	4.24410i	−0.453282	+	0.261703i	0.255933	+	0.966694i	$0.417617\pi$
$264$		0			0
$265$	0.679086	−	0.679086i	0.0417159	−	0.0417159i
$266$		0			0
$267$	−0.0895376	+	1.70848i	−0.00547961	+	0.104557i
$268$		0			0
$269$	−1.08290	−	10.3031i	−0.0660257	−	0.628193i	−0.976632	−	0.214918i	$-0.931052\pi$
$269$	−1.08290	−	10.3031i	−0.0660257	−	0.628193i	0.910606	−	0.413275i	$-0.135615\pi$
$270$		0			0
$271$	−0.630741	−	12.0352i	−0.0383148	−	0.731089i	−0.948479	−	0.316841i	$-0.897378\pi$
$271$	−0.630741	−	12.0352i	−0.0383148	−	0.731089i	0.910164	−	0.414248i	$-0.135955\pi$
$272$		0			0
$273$	31.9951	+	44.5803i	1.93643	+	2.69812i
$274$		0			0
$275$	5.86815	−	2.61949i	0.353863	−	0.157961i
$276$		0			0
$277$	15.0257	−	6.68987i	0.902807	−	0.401955i	0.0977897	−	0.995207i	$-0.468823\pi$
$277$	15.0257	−	6.68987i	0.902807	−	0.401955i	0.805017	+	0.593252i	$0.202156\pi$
$278$		0			0
$279$	45.4303	−	29.5028i	2.71984	−	1.76629i
$280$		0			0
$281$	0.414131	−	2.61472i	0.0247050	−	0.155981i	−0.972252	−	0.233937i	$-0.924839\pi$
$281$	0.414131	−	2.61472i	0.0247050	−	0.155981i	0.996957	+	0.0779555i	$0.0248392\pi$
$282$		0			0
$283$	−3.27661	+	0.696465i	−0.194774	+	0.0414006i	−0.304266	−	0.952587i	$-0.598411\pi$
$283$	−3.27661	+	0.696465i	−0.194774	+	0.0414006i	0.109491	+	0.993988i	$0.465078\pi$
$284$		0			0
$285$	−25.3396			−1.50099
$286$		0			0
$287$	7.14964			0.422030
$288$		0			0
$289$	13.4190	−	2.85229i	0.789350	−	0.167782i
$290$		0			0
$291$	−6.60634	+	41.7108i	−0.387270	+	2.44513i
$292$		0			0
$293$	−13.8461	+	8.99179i	−0.808900	+	0.525306i	−0.881572	−	0.472050i	$-0.843514\pi$
$293$	−13.8461	+	8.99179i	−0.808900	+	0.525306i	0.0726715	+	0.997356i	$0.476848\pi$
$294$		0			0
$295$	−36.7125	+	16.3454i	−2.13748	+	0.951669i
$296$		0			0
$297$	10.2143	−	48.2850i	0.592697	−	2.80178i
$298$		0			0
$299$	2.00182	+	5.30693i	0.115768	+	0.306908i
$300$		0			0
$301$	1.20732	+	23.0370i	0.0695888	+	1.32783i
$302$		0			0
$303$	−3.13222	−	29.8011i	−0.179941	−	1.71203i
$304$		0			0
$305$	1.12628	−	21.4906i	0.0644904	−	1.23055i
$306$		0			0
$307$	9.08621	−	9.08621i	0.518578	−	0.518578i	−0.398563	−	0.917141i	$-0.630491\pi$
$307$	9.08621	−	9.08621i	0.518578	−	0.518578i	0.917141	+	0.398563i	$0.130491\pi$
$308$		0			0
$309$	43.3199	−	25.0107i	2.46438	−	1.42281i
$310$		0			0
$311$	15.1449	+	4.92089i	0.858790	+	0.279038i	0.705123	−	0.709085i	$-0.250892\pi$
$311$	15.1449	+	4.92089i	0.858790	+	0.279038i	0.153667	+	0.988123i	$0.450892\pi$
$312$		0			0
$313$	1.73720	−	1.26215i	0.0981921	−	0.0713407i	−0.537606	−	0.843196i	$-0.680671\pi$
$313$	1.73720	−	1.26215i	0.0981921	−	0.0713407i	0.635798	+	0.771856i	$0.280671\pi$
$314$		0			0
$315$	−69.3968	−	62.4852i	−3.91007	−	3.52064i
$316$		0			0
$317$	6.28660	−	0.995700i	0.353091	−	0.0559241i	0.0226302	−	0.999744i	$-0.492796\pi$
$317$	6.28660	−	0.995700i	0.353091	−	0.0559241i	0.330460	+	0.943820i	$0.392796\pi$
$318$		0			0
$319$	19.1839	−	0.0186113i	1.07409	−	0.00104203i
$320$		0			0
$321$	4.13335	+	9.28366i	0.230701	+	0.518163i
$322$		0			0
$323$	5.35135	−	0.280452i	0.297757	−	0.0156048i
$324$		0			0
$325$	3.20775	−	6.20610i	0.177934	−	0.344253i
$326$		0			0
$327$	−16.5591	−	10.7536i	−0.915719	−	0.594675i
$328$		0			0
$329$	1.92696	−	3.33760i	0.106237	−	0.184008i
$330$		0			0
$331$	−6.20304	−	23.1501i	−0.340950	−	1.27244i	−0.897273	−	0.441476i	$-0.854455\pi$
$331$	−6.20304	−	23.1501i	−0.340950	−	1.27244i	0.556323	−	0.830966i	$-0.312212\pi$
$332$		0			0
$333$	−49.8349	+	25.3921i	−2.73093	+	1.39148i
$334$		0			0
$335$	−2.94093	+	6.60544i	−0.160680	+	0.360894i
$336$		0			0
$337$	1.16426	+	3.58321i	0.0634211	+	0.195190i	0.977746	−	0.209791i	$-0.0672782\pi$
$337$	1.16426	+	3.58321i	0.0634211	+	0.195190i	−0.914325	+	0.404981i	$0.867278\pi$
$338$		0			0
$339$	−27.6696	−	20.1032i	−1.50281	−	1.09185i
$340$		0			0
$341$	−14.9064	+	18.4445i	−0.807229	+	0.998825i
$342$		0			0
$343$	5.78440	+	36.5213i	0.312328	+	1.97196i
$344$		0			0
$345$	−7.33886	−	11.3008i	−0.395111	−	0.608417i
$346$		0			0
$347$	−2.09576	+	0.220274i	−0.112506	+	0.0118249i	−0.160614	−	0.987017i	$-0.551348\pi$
$347$	−2.09576	+	0.220274i	−0.112506	+	0.0118249i	0.0481079	+	0.998842i	$0.484681\pi$
$348$		0			0
$349$	−9.14270	+	14.0785i	−0.489398	+	0.753606i	−0.993957	−	0.109771i	$-0.964988\pi$
$349$	−9.14270	+	14.0785i	−0.489398	+	0.753606i	0.504559	+	0.863377i	$0.331655\pi$
$350$		0			0
$351$	−24.0796	−	47.9460i	−1.28527	−	2.55917i
$352$		0			0
$353$	7.40555	+	1.98431i	0.394158	+	0.105614i	0.450454	−	0.892800i	$-0.351262\pi$
$353$	7.40555	+	1.98431i	0.394158	+	0.105614i	−0.0562957	+	0.998414i	$0.517929\pi$
$354$		0			0
$355$	3.73110	−	3.35950i	0.198026	−	0.178304i
$356$		0			0
$357$	21.4246	+	17.3493i	1.13391	+	0.918222i
$358$		0			0
$359$	−1.14843	−	0.585152i	−0.0606116	−	0.0308831i	0.423422	−	0.905933i	$-0.360829\pi$
$359$	−1.14843	−	0.585152i	−0.0606116	−	0.0308831i	−0.484034	+	0.875049i	$0.660829\pi$
$360$		0			0
$361$	10.1924	+	1.07127i	0.536444	+	0.0563826i
$362$		0			0
$363$	3.80826	+	35.5692i	0.199882	+	1.86690i
$364$		0			0
$365$	−10.0589	+	13.8449i	−0.526506	+	0.724673i
$366$		0			0
$367$	−10.8275	+	12.0251i	−0.565190	+	0.627707i	−0.956212	−	0.292674i	$-0.905455\pi$
$367$	−10.8275	+	12.0251i	−0.565190	+	0.627707i	0.391022	+	0.920381i	$0.372122\pi$
$368$		0			0
$369$	−11.4314	−	1.81055i	−0.595093	−	0.0942535i
$370$		0			0
$371$	1.70401	+	0.0893036i	0.0884680	+	0.00463641i
$372$		0			0
$373$	−17.5343	−	10.1234i	−0.907890	−	0.524171i	−0.0281386	−	0.999604i	$-0.508958\pi$
$373$	−17.5343	−	10.1234i	−0.907890	−	0.524171i	−0.879752	+	0.475433i	$0.842291\pi$
$374$		0			0
$375$	6.78922	−	25.3377i	0.350594	−	1.30843i
$376$		0			0
$377$	16.2835	−	13.0301i	0.838641	−	0.671082i
$378$		0			0
$379$	13.4515	−	5.16354i	0.690956	−	0.265233i	0.0125509	−	0.999921i	$-0.496005\pi$
$379$	13.4515	−	5.16354i	0.690956	−	0.265233i	0.678405	+	0.734688i	$0.262672\pi$
$380$		0			0
$381$	35.9677	+	7.64516i	1.84268	+	0.391674i
$382$		0			0
$383$	−6.36860	+	16.5908i	−0.325420	+	0.847749i	0.669097	+	0.743175i	$0.266681\pi$
$383$	−6.36860	+	16.5908i	−0.325420	+	0.847749i	−0.994517	+	0.104574i	$0.966652\pi$
$384$		0			0
$385$	37.3639	+	16.5921i	1.90424	+	0.845610i
$386$		0			0
$387$	3.90347	−	37.1391i	0.198425	−	1.88788i
$388$		0			0
$389$	20.4678	−	6.65040i	1.03776	−	0.337189i	0.259906	−	0.965634i	$-0.416308\pi$
$389$	20.4678	−	6.65040i	1.03776	−	0.337189i	0.777854	+	0.628445i	$0.216308\pi$
$390$		0			0
$391$	1.67493	+	2.30535i	0.0847050	+	0.116586i
$392$		0			0
$393$	−2.15334	−	10.1307i	−0.108622	−	0.511026i
$394$		0			0
$395$	−11.0473	−	11.0473i	−0.555851	−	0.555851i
$396$		0			0
$397$	−21.7569	+	5.82974i	−1.09195	+	0.292586i	−0.759481	−	0.650529i	$-0.774547\pi$
$397$	−21.7569	+	5.82974i	−1.09195	+	0.292586i	−0.332465	+	0.943115i	$0.607880\pi$
$398$		0			0
$399$	−30.1259	−	33.4582i	−1.50818	−	1.67501i
$400$		0			0
$401$	11.2264	+	29.2458i	0.560621	+	1.46047i	0.861973	+	0.506954i	$0.169229\pi$
$401$	11.2264	+	29.2458i	0.560621	+	1.46047i	−0.301352	+	0.953513i	$0.597438\pi$
$402$		0			0
$403$	−0.149891	+	25.7805i	−0.00746663	+	1.28422i
$404$		0			0
$405$	42.5423	+	52.5354i	2.11394	+	2.61050i
$406$		0			0
$407$	17.2975	−	17.3311i	0.857407	−	0.859072i
$408$		0			0
$409$	−12.4459	−	4.77754i	−0.615411	−	0.236234i	0.0306375	−	0.999531i	$-0.490246\pi$
$409$	−12.4459	−	4.77754i	−0.615411	−	0.236234i	−0.646048	+	0.763296i	$0.723580\pi$
$410$		0			0
$411$	5.55644	−	10.9051i	0.274079	−	0.537910i
$412$		0			0
$413$	−65.2293	−	29.0420i	−3.20973	−	1.42906i
$414$		0			0
$415$	−8.35596	+	25.7170i	−0.410178	+	1.26240i
$416$		0			0
$417$		−	2.17042i		−	0.106286i
$418$		0			0
$419$	8.05356	+	13.9492i	0.393442	+	0.681462i	0.992901	−	0.118944i	$-0.0379508\pi$
$419$	8.05356	+	13.9492i	0.393442	+	0.681462i	−0.599459	+	0.800406i	$0.704617\pi$
$420$		0			0
$421$	0.806020	+	1.58190i	0.0392830	+	0.0770972i	0.909814	−	0.415017i	$-0.136224\pi$
$421$	0.806020	+	1.58190i	0.0392830	+	0.0770972i	−0.870531	+	0.492114i	$0.836224\pi$
$422$		0			0
$423$	−3.92617	+	4.84842i	−0.190897	+	0.235738i
$424$		0			0
$425$	0.729728	−	3.43310i	0.0353970	−	0.166530i
$426$		0			0
$427$	29.7151	−	24.0628i	1.43801	−	1.16448i
$428$		0			0
$429$	27.3650	+	27.6314i	1.32119	+	1.33406i
$430$		0			0
$431$	−20.4638	+	16.5712i	−0.985706	+	0.798209i	−0.979433	−	0.201771i	$-0.935330\pi$
$431$	−20.4638	+	16.5712i	−0.985706	+	0.798209i	−0.00627323	+	0.999980i	$0.501997\pi$
$432$		0			0
$433$	4.03612	−	18.9884i	0.193963	−	0.912526i	−0.768233	−	0.640170i	$-0.778864\pi$
$433$	4.03612	−	18.9884i	0.193963	−	0.912526i	0.962197	−	0.272356i	$-0.0878028\pi$
$434$		0			0
$435$	−31.1797	+	38.5038i	−1.49495	+	1.84611i
$436$		0			0
$437$	−2.11273	−	4.14647i	−0.101066	−	0.198353i
$438$		0			0
$439$	14.3772	+	24.9020i	0.686186	+	1.18851i	0.973063	+	0.230541i	$0.0740496\pi$
$439$	14.3772	+	24.9020i	0.686186	+	1.18851i	−0.286877	+	0.957967i	$0.592617\pi$
$440$		0			0
$441$		−	112.888i		−	5.37563i
$442$		0			0
$443$	−8.25228	+	25.3979i	−0.392078	+	1.20669i	0.539137	+	0.842218i	$0.318751\pi$
$443$	−8.25228	+	25.3979i	−0.392078	+	1.20669i	−0.931214	+	0.364472i	$0.881249\pi$
$444$		0			0
$445$	1.26585	+	0.563594i	0.0600072	+	0.0267169i
$446$		0			0
$447$	30.1840	−	59.2394i	1.42765	−	2.80193i
$448$		0			0
$449$	−14.2663	−	5.47631i	−0.673267	−	0.258443i	−0.00237422	−	0.999997i	$-0.500756\pi$
$449$	−14.2663	−	5.47631i	−0.673267	−	0.258443i	−0.670893	+	0.741554i	$0.734089\pi$
$450$		0			0
$451$	5.00380	−	0.797501i	0.235620	−	0.0375528i
$452$		0			0
$453$	30.7602	+	37.9857i	1.44524	+	1.78472i
$454$		0			0
$455$	42.9954	−	11.2531i	2.01566	−	0.527552i
$456$		0			0
$457$	1.77927	+	4.63516i	0.0832308	+	0.216824i	0.968880	−	0.247532i	$-0.0796194\pi$
$457$	1.77927	+	4.63516i	0.0832308	+	0.216824i	−0.885649	+	0.464355i	$0.846286\pi$
$458$		0			0
$459$	−18.0365	−	20.0316i	−0.841874	−	0.934995i
$460$		0			0
$461$	−38.0836	+	10.2045i	−1.77373	+	0.475270i	−0.989418	−	0.145094i	$-0.953652\pi$
$461$	−38.0836	+	10.2045i	−1.77373	+	0.475270i	−0.784314	+	0.620364i	$0.786985\pi$
$462$		0			0
$463$	16.6972	+	16.6972i	0.775984	+	0.775984i	0.979145	−	0.203162i	$-0.0651217\pi$
$463$	16.6972	+	16.6972i	0.775984	+	0.775984i	−0.203162	+	0.979145i	$0.565122\pi$
$464$		0			0
$465$	−12.7340	−	59.9090i	−0.590527	−	2.77821i
$466$		0			0
$467$	−19.9135	−	27.4086i	−0.921487	−	1.26832i	−0.963089	−	0.269184i	$-0.913246\pi$
$467$	−19.9135	−	27.4086i	−0.921487	−	1.26832i	0.0416019	−	0.999134i	$-0.486754\pi$
$468$		0			0
$469$	−12.2182	+	3.96993i	−0.564184	+	0.183315i
$470$		0			0
$471$	−6.88168	+	65.4748i	−0.317091	+	3.01692i
$472$		0			0
$473$	3.41461	+	15.9882i	0.157004	+	0.735138i
$474$		0			0
$475$	−2.05414	+	5.35122i	−0.0942505	+	0.245531i
$476$		0			0
$477$	−2.70189	−	0.574304i	−0.123711	−	0.0262956i
$478$		0			0
$479$	16.7916	−	6.44567i	0.767226	−	0.294510i	0.0568966	−	0.998380i	$-0.481879\pi$
$479$	16.7916	−	6.44567i	0.767226	−	0.294510i	0.710329	+	0.703870i	$0.248546\pi$
$480$		0			0
$481$	2.93634	−	26.4568i	0.133886	−	1.20633i
$482$		0			0
$483$	6.19648	−	23.1256i	0.281950	−	1.05225i
$484$		0			0
$485$	29.6215	+	17.1020i	1.34504	+	0.776561i
$486$		0			0
$487$	−12.2191	−	0.640376i	−0.553700	−	0.0290182i	−0.226565	−	0.973996i	$-0.572750\pi$
$487$	−12.2191	−	0.640376i	−0.553700	−	0.0290182i	−0.327135	+	0.944978i	$0.606083\pi$
$488$		0			0
$489$	15.9095	+	2.51982i	0.719453	+	0.113950i
$490$		0			0
$491$	0.578036	−	0.641974i	0.0260864	−	0.0289719i	−0.729960	−	0.683489i	$-0.760462\pi$
$491$	0.578036	−	0.641974i	0.0260864	−	0.0289719i	0.756047	+	0.654518i	$0.227128\pi$
$492$		0			0
$493$	6.15855	−	8.47651i	0.277367	−	0.381763i
$494$		0			0
$495$	−55.5384	−	35.9905i	−2.49627	−	1.61765i
$496$		0			0
$497$	8.87171	+	0.932455i	0.397951	+	0.0418263i
$498$		0			0
$499$	−15.0810	−	7.68414i	−0.675117	−	0.343989i	0.0825904	−	0.996584i	$-0.473681\pi$
$499$	−15.0810	−	7.68414i	−0.675117	−	0.343989i	−0.757708	+	0.652594i	$0.773681\pi$
$500$		0			0
$501$	20.8158	+	16.8563i	0.929982	+	0.753085i
$502$		0			0
$503$	32.1535	−	28.9511i	1.43365	−	1.29087i	0.540331	−	0.841453i	$-0.318299\pi$
$503$	32.1535	−	28.9511i	1.43365	−	1.29087i	0.893323	−	0.449415i	$-0.148368\pi$
$504$		0			0
$505$	−23.4428	−	6.28147i	−1.04319	−	0.279522i
$506$		0			0
$507$	41.9907	+	4.90770i	1.86487	+	0.217959i
$508$		0			0
$509$	−14.7770	+	22.7546i	−0.654980	+	1.00858i	0.342629	+	0.939471i	$0.388683\pi$
$509$	−14.7770	+	22.7546i	−0.654980	+	1.00858i	−0.997609	+	0.0691099i	$0.977984\pi$
$510$		0			0
$511$	−30.2395	+	3.17830i	−1.33772	+	0.140600i
$512$		0			0
$513$	23.9756	+	36.9193i	1.05855	+	1.63002i
$514$		0			0
$515$	−6.33778	−	40.0151i	−0.279276	−	1.76328i
$516$		0			0
$517$	0.976329	−	2.55082i	0.0429389	−	0.112185i
$518$		0			0
$519$	0.488568	+	0.354966i	0.0214458	+	0.0155813i
$520$		0			0
$521$	12.7542	+	39.2535i	0.558773	+	1.71973i	0.685767	+	0.727822i	$0.259467\pi$
$521$	12.7542	+	39.2535i	0.558773	+	1.71973i	−0.126994	+	0.991903i	$0.540533\pi$
$522$		0			0
$523$	8.07195	−	18.1299i	0.352962	−	0.792765i	−0.646591	−	0.762837i	$-0.723806\pi$
$523$	8.07195	−	18.1299i	0.352962	−	0.792765i	0.999552	−	0.0299274i	$-0.00952760\pi$
$524$		0			0
$525$	−26.2744	+	13.3875i	−1.14671	+	0.584278i
$526$		0			0
$527$	3.35230	+	12.5110i	0.146028	+	0.544986i
$528$		0			0
$529$	−10.2627	+	17.7755i	−0.446203	+	0.772846i
$530$		0			0
$531$	96.9390	+	62.9529i	4.20679	+	2.73192i
$532$		0			0
$533$	3.70955	−	4.07201i	0.160678	−	0.176378i
$534$		0			0
$535$	8.21943	−	0.430762i	0.355357	−	0.0186235i
$536$		0			0
$537$	25.8265	+	58.0073i	1.11450	+	2.50320i
$538$		0			0
$539$	15.3177	+	46.9879i	0.659781	+	2.02391i
$540$		0			0
$541$	25.3378	−	4.01312i	1.08936	−	0.172537i	0.414182	−	0.910194i	$-0.364068\pi$
$541$	25.3378	−	4.01312i	1.08936	−	0.172537i	0.675176	+	0.737656i	$0.264068\pi$
$542$		0			0
$543$	14.2810	+	12.8587i	0.612857	+	0.551819i
$544$		0			0
$545$	−12.9375	+	9.39964i	−0.554182	+	0.402636i
$546$		0			0
$547$	−34.1003	−	11.0798i	−1.45802	−	0.473740i	−0.530557	−	0.847649i	$-0.678017\pi$
$547$	−34.1003	−	11.0798i	−1.45802	−	0.473740i	−0.927465	+	0.373909i	$0.878017\pi$
$548$		0			0
$549$	−53.6042	+	30.9484i	−2.28777	+	1.32085i
$550$		0			0
$551$	−12.0994	+	12.0994i	−0.515452	+	0.515452i
$552$		0			0
$553$	1.45279	−	27.7208i	0.0617787	−	1.17881i
$554$		0			0
$555$	6.61028	+	62.8926i	0.280591	+	2.66964i
$556$		0			0
$557$	−1.28267	−	24.4748i	−0.0543484	−	1.03703i	−0.880640	−	0.473786i	$-0.842887\pi$
$557$	−1.28267	−	24.4748i	−0.0543484	−	1.03703i	0.826291	−	0.563243i	$-0.190446\pi$
$558$		0			0
$559$	13.7469	+	11.2650i	0.581434	+	0.476459i
$560$		0			0
$561$	16.9296	+	9.75241i	0.714768	+	0.411747i
$562$		0			0
$563$	−35.8104	+	15.9438i	−1.50923	+	0.671951i	−0.983862	−	0.178927i	$-0.942738\pi$
$563$	−35.8104	+	15.9438i	−1.50923	+	0.671951i	−0.525364	+	0.850877i	$0.676071\pi$
$564$		0			0
$565$	−23.2319	+	15.0870i	−0.977374	+	0.634714i
$566$		0			0
$567$	−18.7893	+	118.631i	−0.789077	+	4.98204i
$568$		0			0
$569$	8.04559	−	1.71014i	0.337289	−	0.0716930i	−0.0361538	−	0.999346i	$-0.511511\pi$
$569$	8.04559	−	1.71014i	0.337289	−	0.0716930i	0.373443	+	0.927653i	$0.378177\pi$
$570$		0			0
$571$	12.5687			0.525986			0.262993	−	0.964798i	$-0.415290\pi$
$571$	12.5687			0.525986			0.262993	+	0.964798i	$0.415290\pi$
$572$		0			0
$573$	−73.9971			−3.09127
$574$		0			0
$575$	−2.98144	+	0.633724i	−0.124335	+	0.0264281i
$576$		0			0
$577$	−1.67735	+	10.5904i	−0.0698292	+	0.440884i	0.927859	+	0.372930i	$0.121647\pi$
$577$	−1.67735	+	10.5904i	−0.0698292	+	0.440884i	−0.997688	+	0.0679537i	$0.978353\pi$
$578$		0			0
$579$	33.3299	−	21.6447i	1.38514	−	0.899524i
$580$		0			0
$581$	−43.8908	+	19.5414i	−1.82090	+	0.810716i
$582$		0			0
$583$	1.20254	−	0.127572i	0.0498043	−	0.00528350i
$584$		0			0
$585$	−71.5939	+	7.10423i	−2.96005	+	0.293724i
$586$		0			0
$587$	−1.07743	−	20.5587i	−0.0444704	−	0.848546i	−0.926256	−	0.376895i	$-0.876992\pi$
$587$	−1.07743	−	20.5587i	−0.0444704	−	0.848546i	0.881785	−	0.471651i	$-0.156342\pi$
$588$		0			0
$589$	−2.21106	−	21.0368i	−0.0911051	−	0.866807i
$590$		0			0
$591$	−1.82778	+	34.8762i	−0.0751850	+	1.43461i
$592$		0			0
$593$	−17.0737	+	17.0737i	−0.701133	+	0.701133i	−0.964654	−	0.263521i	$-0.915116\pi$
$593$	−17.0737	+	17.0737i	−0.701133	+	0.701133i	0.263521	+	0.964654i	$0.415116\pi$
$594$		0			0
$595$	19.3370	−	11.1642i	0.792739	−	0.457688i
$596$		0			0
$597$	58.5115	+	19.0116i	2.39472	+	0.778091i
$598$		0			0
$599$	−16.1898	+	11.7626i	−0.661498	+	0.480606i	−0.867169	−	0.498015i	$-0.834063\pi$
$599$	−16.1898	+	11.7626i	−0.661498	+	0.480606i	0.205670	+	0.978621i	$0.434063\pi$
$600$		0			0
$601$	1.09017	+	0.981597i	0.0444691	+	0.0400402i	0.691066	−	0.722792i	$-0.257142\pi$
$601$	1.09017	+	0.981597i	0.0444691	+	0.0400402i	−0.646596	+	0.762832i	$0.723808\pi$
$602$		0			0
$603$	20.5407	−	3.25333i	0.836482	−	0.132486i
$604$		0			0
$605$	28.0005	+	7.44451i	1.13838	+	0.302662i
$606$		0			0
$607$	−14.8774	−	33.4153i	−0.603856	−	1.35628i	−0.914047	−	0.405609i	$-0.867059\pi$
$607$	−14.8774	−	33.4153i	−0.603856	−	1.35628i	0.310190	−	0.950674i	$-0.399607\pi$
$608$		0			0
$609$	−87.9092	+	4.60713i	−3.56226	+	0.186690i
$610$		0			0
$611$	−0.901104	−	2.82918i	−0.0364548	−	0.114456i
$612$		0			0
$613$	34.1180	+	22.1565i	1.37801	+	0.894891i	0.999528	−	0.0307171i	$-0.00977909\pi$
$613$	34.1180	+	22.1565i	1.37801	+	0.894891i	0.378483	+	0.925608i	$0.376446\pi$
$614$		0			0
$615$	−6.54306	+	11.3329i	−0.263842	+	0.456987i
$616$		0			0
$617$	1.37552	+	5.13350i	0.0553763	+	0.206667i	0.988071	−	0.154000i	$-0.0492156\pi$
$617$	1.37552	+	5.13350i	0.0553763	+	0.206667i	−0.932695	+	0.360667i	$0.882549\pi$
$618$		0			0
$619$	4.59787	−	2.34273i	0.184804	−	0.0941623i	−0.359141	−	0.933283i	$-0.616930\pi$
$619$	4.59787	−	2.34273i	0.184804	−	0.0941623i	0.543945	+	0.839121i	$0.316930\pi$
$620$		0			0
$621$	−9.52126	+	21.3851i	−0.382075	+	0.858155i
$622$		0			0
$623$	0.760791	+	2.34147i	0.0304804	+	0.0938091i
$624$		0			0
$625$	−25.0259	−	18.1824i	−1.00104	−	0.727295i
$626$		0			0
$627$	−24.8162	−	20.0559i	−0.991063	−	0.800957i
$628$		0			0
$629$	−2.09207	−	13.2088i	−0.0834164	−	0.526671i
$630$		0			0
$631$	11.8427	+	18.2361i	0.471449	+	0.725967i	0.991774	−	0.128001i	$-0.0408561\pi$
$631$	11.8427	+	18.2361i	0.471449	+	0.725967i	−0.520326	+	0.853968i	$0.674189\pi$
$632$		0			0
$633$	84.7666	−	8.90933i	3.36917	−	0.354114i
$634$		0			0
$635$	16.2205	−	24.9774i	0.643691	−	0.991198i
$636$		0			0
$637$	44.8883	+	29.5233i	1.77854	+	1.16976i
$638$		0			0
$639$	−13.9486	−	3.73752i	−0.551799	−	0.147854i
$640$		0			0
$641$	11.2883	−	10.1640i	0.445860	−	0.401454i	−0.415384	−	0.909646i	$-0.636353\pi$
$641$	11.2883	−	10.1640i	0.445860	−	0.401454i	0.861244	+	0.508192i	$0.169686\pi$
$642$		0			0
$643$	14.0280	+	11.3597i	0.553211	+	0.447982i	0.864715	−	0.502263i	$-0.167499\pi$
$643$	14.0280	+	11.3597i	0.553211	+	0.447982i	−0.311504	+	0.950245i	$0.600833\pi$
$644$		0			0
$645$	−37.6210	−	19.1689i	−1.48133	−	0.754773i
$646$		0			0
$647$	7.58185	+	0.796884i	0.298073	+	0.0313288i	0.252385	−	0.967627i	$-0.418785\pi$
$647$	7.58185	+	0.796884i	0.298073	+	0.0313288i	0.0456885	+	0.998956i	$0.485452\pi$
$648$		0			0
$649$	−48.8913	−	13.0496i	−1.91915	−	0.512240i
$650$		0			0
$651$	63.9640	−	88.0389i	2.50695	−	3.45052i
$652$		0			0
$653$	8.98587	−	9.97982i	0.351644	−	0.390540i	−0.541209	−	0.840888i	$-0.682033\pi$
$653$	8.98587	−	9.97982i	0.351644	−	0.390540i	0.892853	+	0.450348i	$0.148700\pi$
$654$		0			0
$655$	−8.28519	−	1.31225i	−0.323729	−	0.0512737i
$656$		0			0
$657$	49.1540	+	2.57605i	1.91768	+	0.100501i
$658$		0			0
$659$	−20.5911	−	11.8883i	−0.802115	−	0.463101i	0.0420953	−	0.999114i	$-0.486597\pi$
$659$	−20.5911	−	11.8883i	−0.802115	−	0.463101i	−0.844210	+	0.536012i	$0.819930\pi$
$660$		0			0
$661$	0.103978	−	0.388053i	0.00404429	−	0.0150935i	−0.963874	−	0.266358i	$-0.914180\pi$
$661$	0.103978	−	0.388053i	0.00404429	−	0.0150935i	0.967918	+	0.251264i	$0.0808464\pi$
$662$		0			0
$663$	20.9971	−	3.20059i	0.815462	−	0.124301i
$664$		0			0
$665$	−34.0431	+	13.0679i	−1.32013	+	0.506752i
$666$		0			0
$667$	−8.90027	−	1.89181i	−0.344620	−	0.0732512i
$668$		0			0
$669$	19.7272	−	51.3911i	0.762697	−	1.98689i
$670$		0			0
$671$	18.1125	−	20.1553i	0.699227	−	0.778087i
$672$		0			0
$673$	−3.57274	+	33.9923i	−0.137719	+	1.31031i	0.679370	+	0.733796i	$0.262253\pi$
$673$	−3.57274	+	33.9923i	−0.137719	+	1.31031i	−0.817089	+	0.576512i	$0.804413\pi$
$674$		0			0
$675$	27.4215	−	8.90978i	1.05545	−	0.342938i
$676$		0			0
$677$	−6.17935	−	8.50514i	−0.237492	−	0.326879i	0.673590	−	0.739105i	$-0.264751\pi$
$677$	−6.17935	−	8.50514i	−0.237492	−	0.326879i	−0.911082	+	0.412226i	$0.864751\pi$
$678$		0			0
$679$	12.6353	+	59.4443i	0.484897	+	2.28126i
$680$		0			0
$681$	−56.4843	−	56.4843i	−2.16448	−	2.16448i
$682$		0			0
$683$	16.0980	−	4.31345i	0.615973	−	0.165050i	0.0626768	−	0.998034i	$-0.480036\pi$
$683$	16.0980	−	4.31345i	0.615973	−	0.165050i	0.553297	+	0.832984i	$0.313370\pi$
$684$		0			0
$685$	−6.63298	−	7.36667i	−0.253433	−	0.281466i
$686$		0			0
$687$	9.57512	+	24.9440i	0.365314	+	0.951675i
$688$		0			0
$689$	0.934980	−	0.924170i	0.0356199	−	0.0352081i
$690$		0			0
$691$	−7.80888	−	9.64317i	−0.297064	−	0.366843i	0.606658	−	0.794963i	$-0.292510\pi$
$691$	−7.80888	−	9.64317i	−0.297064	−	0.366843i	−0.903722	+	0.428119i	$0.859176\pi$
$692$		0			0
$693$	−18.5073	−	116.121i	−0.703033	−	4.41107i
$694$		0			0
$695$	−1.64113	−	0.629970i	−0.0622516	−	0.0238961i
$696$		0			0
$697$	1.25637	−	2.46576i	0.0475884	−	0.0933974i
$698$		0			0
$699$	80.6883	+	35.9247i	3.05191	+	1.35880i
$700$		0			0
$701$	−3.66568	+	11.2818i	−0.138451	+	0.426107i	−0.996111	−	0.0881096i	$-0.971917\pi$
$701$	−3.66568	+	11.2818i	−0.138451	+	0.426107i	0.857660	+	0.514217i	$0.171917\pi$
$702$		0			0
$703$			21.8406i			0.823732i
$704$		0			0
$705$	3.52696	+	6.10887i	0.132833	+	0.230074i
$706$		0			0
$707$	−19.5768	−	38.4216i	−0.736261	−	1.44499i
$708$		0			0
$709$	29.8169	−	36.8208i	1.11980	−	1.38284i	0.205080	−	0.978745i	$-0.434255\pi$
$709$	29.8169	−	36.8208i	1.11980	−	1.38284i	0.914719	−	0.404091i	$-0.132412\pi$
$710$		0			0
$711$	−9.34274	+	43.9541i	−0.350380	+	1.64841i
$712$		0			0
$713$	8.74154	−	7.07876i	0.327373	−	0.265102i
$714$		0			0
$715$	28.8359	−	12.6715i	1.07840	−	0.473889i
$716$		0			0
$717$	−19.3058	+	15.6335i	−0.720988	+	0.583845i
$718$		0			0
$719$	−4.08370	+	19.2123i	−0.152296	+	0.716498i	0.834033	+	0.551714i	$0.186026\pi$
$719$	−4.08370	+	19.2123i	−0.152296	+	0.716498i	−0.986330	+	0.164784i	$0.947307\pi$
$720$		0			0
$721$	45.3008	−	55.9418i	1.68709	−	2.08338i
$722$		0			0
$723$	−10.1981	−	20.0150i	−0.379273	−	0.744365i
$724$		0			0
$725$	5.60366	+	9.70583i	0.208115	+	0.360465i
$726$		0			0
$727$		−	4.22288i		−	0.156618i	−0.996929	−	0.0783089i	$-0.975048\pi$
$727$		−	4.22288i		−	0.156618i	0.996929	−	0.0783089i	$-0.0249520\pi$
$728$		0			0
$729$	15.2211	−	46.8457i	0.563744	−	1.73503i
$730$		0			0
$731$	8.15716	+	3.63180i	0.301703	+	0.134327i
$732$		0			0
$733$	4.69250	−	9.20955i	0.173322	−	0.340163i	−0.787962	−	0.615724i	$-0.788864\pi$
$733$	4.69250	−	9.20955i	0.173322	−	0.340163i	0.961284	+	0.275561i	$0.0888637\pi$
$734$		0			0
$735$	−119.161	−	45.7415i	−4.39531	−	1.68720i
$736$		0			0
$737$	−8.10829	+	4.14130i	−0.298673	+	0.152547i
$738$		0			0
$739$	2.60843	+	3.22115i	0.0959528	+	0.118492i	0.822861	−	0.568243i	$-0.192377\pi$
$739$	2.60843	+	3.22115i	0.0959528	+	0.118492i	−0.726908	+	0.686735i	$0.759043\pi$
$740$		0			0
$741$	−34.6864	−	0.201672i	−1.27424	−	0.00740861i
$742$		0			0
$743$	6.54534	+	17.0512i	0.240125	+	0.625548i	0.999690	−	0.0248837i	$-0.00792154\pi$
$743$	6.54534	+	17.0512i	0.240125	+	0.625548i	−0.759565	+	0.650431i	$0.774588\pi$
$744$		0			0
$745$	−36.0320	−	40.0176i	−1.32011	−	1.46613i
$746$		0			0
$747$	75.1244	−	20.1295i	2.74866	−	0.736501i
$748$		0			0
$749$	10.3407	+	10.3407i	0.377842	+	0.377842i
$750$		0			0
$751$	−4.95511	−	23.3119i	−0.180814	−	0.850665i	−0.971239	−	0.238106i	$-0.923474\pi$
$751$	−4.95511	−	23.3119i	−0.180814	−	0.850665i	0.790425	−	0.612559i	$-0.209860\pi$
$752$		0			0
$753$	−26.1960	−	36.0557i	−0.954635	−	1.31394i
$754$		0			0
$755$	37.6506	−	12.2334i	1.37025	−	0.445220i
$756$		0			0
$757$	0.379271	−	3.60852i	0.0137848	−	0.131154i	−0.985465	−	0.169878i	$-0.945663\pi$
$757$	0.379271	−	3.60852i	0.0137848	−	0.131154i	0.999250	+	0.0387240i	$0.0123293\pi$
$758$		0			0
$759$	1.75719	−	16.8760i	0.0637820	−	0.612561i
$760$		0			0
$761$	7.85950	−	20.4747i	0.284907	−	0.742207i	−0.714200	−	0.699942i	$-0.753209\pi$
$761$	7.85950	−	20.4747i	0.284907	−	0.742207i	0.999106	−	0.0422653i	$-0.0134575\pi$
$762$		0			0
$763$	−27.7924	−	5.90746i	−1.00615	−	0.213864i
$764$		0			0
$765$	−33.7446	+	12.9533i	−1.22004	+	0.468329i
$766$		0			0
$767$	−50.3844	+	22.0825i	−1.81928	+	0.797352i
$768$		0			0
$769$	−7.09767	+	26.4889i	−0.255949	+	0.955213i	0.711612	+	0.702573i	$0.247966\pi$
$769$	−7.09767	+	26.4889i	−0.255949	+	0.955213i	−0.967560	+	0.252640i	$0.918701\pi$
$770$		0			0
$771$	30.1733	+	17.4206i	1.08667	+	0.627387i
$772$		0			0
$773$	−7.47980	−	0.392000i	−0.269030	−	0.0140993i	−0.0826559	−	0.996578i	$-0.526340\pi$
$773$	−7.47980	−	0.392000i	−0.269030	−	0.0140993i	−0.186374	+	0.982479i	$0.559674\pi$
$774$		0			0
$775$	−13.6839	−	2.16731i	−0.491539	−	0.0778521i
$776$		0			0
$777$	−75.1840	+	83.5003i	−2.69721	+	2.99556i
$778$		0			0
$779$	−2.65649	+	3.65634i	−0.0951786	+	0.131002i
$780$		0			0
$781$	6.31303	−	0.336994i	0.225898	−	0.0120586i
$782$		0			0
$783$	85.6005	+	8.99698i	3.05911	+	0.321526i
$784$		0			0
$785$	47.5104	+	24.2078i	1.69572	+	0.864012i
$786$		0			0
$787$	−26.1005	−	21.1358i	−0.930383	−	0.753410i	0.0389289	−	0.999242i	$-0.487605\pi$
$787$	−26.1005	−	21.1358i	−0.930383	−	0.753410i	−0.969312	+	0.245832i	$0.920939\pi$
$788$		0			0
$789$	20.5138	−	18.4707i	0.730310	−	0.657574i
$790$		0			0
$791$	−47.5408	−	12.7385i	−1.69036	−	0.452930i
$792$		0			0
$793$	1.71276	−	29.4088i	0.0608218	−	1.04434i
$794$		0			0
$795$	−1.70100	+	2.61931i	−0.0603283	+	0.0928974i
$796$		0			0
$797$	0.910111	−	0.0956565i	0.0322378	−	0.00338833i	−0.0883958	−	0.996085i	$-0.528174\pi$
$797$	0.910111	−	0.0956565i	0.0322378	−	0.00338833i	0.120634	+	0.992697i	$0.461507\pi$
$798$		0			0
$799$	−0.812453	−	1.25107i	−0.0287425	−	0.0442596i
$800$		0			0
$801$	−0.623461	−	3.93638i	−0.0220289	−	0.139085i
$802$		0			0
$803$	−20.8091	+	5.59743i	−0.734338	+	0.197529i
$804$		0			0
$805$	−15.6875	−	11.3977i	−0.552913	−	0.401715i
$806$		0			0
$807$	10.4110	+	32.0419i	0.366486	+	1.12793i
$808$		0			0
$809$	−2.87400	+	6.45510i	−0.101044	+	0.226949i	−0.956993	−	0.290112i	$-0.906307\pi$
$809$	−2.87400	+	6.45510i	−0.101044	+	0.226949i	0.855948	+	0.517061i	$0.172974\pi$
$810$		0			0
$811$	41.8555	−	21.3264i	1.46975	−	0.748873i	0.478153	−	0.878276i	$-0.341306\pi$
$811$	41.8555	−	21.3264i	1.46975	−	0.748873i	0.991592	+	0.129404i	$0.0413064\pi$
$812$		0			0
$813$	10.1439	+	37.8574i	0.355761	+	1.32772i
$814$		0			0
$815$	6.52311	−	11.2984i	0.228495	−	0.395764i
$816$		0			0
$817$	−12.2298	−	7.94212i	−0.427866	−	0.277860i
$818$		0			0
$819$	−94.4974	−	86.0859i	−3.30201	−	3.00809i
$820$		0			0
$821$	27.1640	−	1.42361i	0.948032	−	0.0496842i	0.427952	−	0.903802i	$-0.359235\pi$
$821$	27.1640	−	1.42361i	0.948032	−	0.0496842i	0.520080	+	0.854117i	$0.325902\pi$
$822$		0			0
$823$	−9.17587	−	20.6093i	−0.319851	−	0.718397i	0.680040	−	0.733175i	$-0.261962\pi$
$823$	−9.17587	−	20.6093i	−0.319851	−	0.718397i	−0.999891	+	0.0147785i	$0.995296\pi$
$824$		0			0
$825$	−16.8953	+	12.3002i	−0.588219	+	0.428239i
$826$		0			0
$827$	−31.3458	+	4.96469i	−1.09000	+	0.172639i	−0.675463	−	0.737394i	$-0.736056\pi$
$827$	−31.3458	+	4.96469i	−1.09000	+	0.172639i	−0.414537	+	0.910033i	$0.636056\pi$
$828$		0			0
$829$	1.31861	+	1.18729i	0.0457974	+	0.0412361i	0.691712	−	0.722174i	$-0.256857\pi$
$829$	1.31861	+	1.18729i	0.0457974	+	0.0412361i	−0.645914	+	0.763410i	$0.723524\pi$
$830$		0			0
$831$	−43.2732	+	31.4398i	−1.50113	+	1.09063i
$832$		0			0
$833$	25.6712	+	8.34109i	0.889456	+	0.289002i
$834$		0			0
$835$	18.7875	−	10.8470i	0.650169	−	0.375375i
$836$		0			0
$837$	−75.2374	+	75.2374i	−2.60059	+	2.60059i
$838$		0			0
$839$	0.200637	−	3.82838i	0.00692676	−	0.132170i	−0.992977	−	0.118306i	$-0.962253\pi$
$839$	0.200637	−	3.82838i	0.00692676	−	0.132170i	0.999904	−	0.0138640i	$-0.00441319\pi$
$840$		0			0
$841$	0.465822	+	4.43200i	0.0160628	+	0.152828i
$842$		0			0
$843$	0.450569	+	8.59738i	0.0155184	+	0.296109i
$844$		0			0
$845$	15.8988	−	30.3262i	0.546937	−	1.04325i
$846$		0			0
$847$	23.4597	+	45.8223i	0.806086	+	1.57447i
$848$		0			0
$849$	9.95192	−	4.43088i	0.341549	−	0.152067i
$850$		0			0
$851$	−9.74036	+	6.32546i	−0.333895	+	0.216834i
$852$		0			0
$853$	−7.32001	+	46.2167i	−0.250632	+	1.58243i	0.465875	+	0.884851i	$0.345740\pi$
$853$	−7.32001	+	46.2167i	−0.250632	+	1.58243i	−0.716507	+	0.697580i	$0.754260\pi$
$854$		0			0
$855$	57.7399	−	12.2730i	1.97466	−	0.419727i
$856$		0			0
$857$	54.3944			1.85808			0.929038	−	0.369985i	$-0.120637\pi$
$857$	54.3944			1.85808			0.929038	+	0.369985i	$0.120637\pi$
$858$		0			0
$859$	−0.493353			−0.0168330			−0.00841650	−	0.999965i	$-0.502679\pi$
$859$	−0.493353			−0.0168330			−0.00841650	+	0.999965i	$0.502679\pi$
$860$		0			0
$861$	−22.7429	+	4.83414i	−0.775074	+	0.164747i
$862$		0			0
$863$	2.00802	−	12.6781i	0.0683537	−	0.431568i	−0.929652	−	0.368440i	$-0.879892\pi$
$863$	2.00802	−	12.6781i	0.0683537	−	0.431568i	0.998005	−	0.0631287i	$-0.0201078\pi$
$864$		0			0
$865$	0.410211	−	0.266394i	0.0139476	−	0.00905766i
$866$		0			0
$867$	−40.7569	+	18.1461i	−1.38418	+	0.616275i
$868$		0			0
$869$	−2.07534	−	19.5629i	−0.0704010	−	0.663627i
$870$		0			0
$871$	−4.07830	+	9.01854i	−0.138188	+	0.305581i
$872$		0			0
$873$	−5.14873	−	98.2436i	−0.174258	−	3.32504i
$874$		0			0
$875$	−3.94581	−	37.5418i	−0.133393	−	1.26915i
$876$		0			0
$877$	0.766735	−	14.6302i	0.0258908	−	0.494026i	−0.954652	−	0.297723i	$-0.903773\pi$
$877$	0.766735	−	14.6302i	0.0258908	−	0.494026i	0.980543	−	0.196303i	$-0.0628938\pi$
$878$		0			0
$879$	37.9646	−	37.9646i	1.28051	−	1.28051i
$880$		0			0
$881$	−5.44643	+	3.14450i	−0.183495	+	0.105941i	−0.588934	−	0.808181i	$-0.700452\pi$
$881$	−5.44643	+	3.14450i	−0.183495	+	0.105941i	0.405439	+	0.914122i	$0.367119\pi$
$882$		0			0
$883$	−12.2630	−	3.98450i	−0.412684	−	0.134089i	0.0953141	−	0.995447i	$-0.469614\pi$
$883$	−12.2630	−	3.98450i	−0.412684	−	0.134089i	−0.507998	+	0.861358i	$0.669614\pi$
$884$		0			0
$885$	105.730	−	76.8172i	3.55407	−	2.58218i
$886$		0			0
$887$	−21.8568	−	19.6799i	−0.733878	−	0.660787i	0.214934	−	0.976629i	$-0.431046\pi$
$887$	−21.8568	−	19.6799i	−0.733878	−	0.660787i	−0.948812	+	0.315842i	$0.897713\pi$
$888$		0			0
$889$	52.2643	−	8.27785i	1.75289	−	0.277630i
$890$		0			0
$891$	0.0825813	+	85.1218i	0.00276658	+	2.85169i
$892$		0			0
$893$	0.990883	+	2.22556i	0.0331586	+	0.0744755i
$894$		0			0
$895$	51.3576	−	2.69154i	1.71669	−	0.0899682i
$896$		0			0
$897$	−9.95595	−	15.5277i	−0.332419	−	0.518456i
$898$		0			0
$899$	−34.6863	−	22.5255i	−1.15685	−	0.751269i
$900$		0			0
$901$	0.330236	−	0.571986i	0.0110018	−	0.0190556i
$902$		0			0
$903$	−19.4167	−	72.4641i	−0.646147	−	2.41145i
$904$		0			0
$905$	13.8680	−	7.06611i	0.460989	−	0.234886i
$906$		0			0
$907$	13.8475	−	31.1019i	0.459798	−	1.03272i	−0.523717	−	0.851892i	$-0.675455\pi$
$907$	13.8475	−	31.1019i	0.459798	−	1.03272i	0.983514	−	0.180830i	$-0.0578784\pi$
$908$		0			0
$909$	21.5710	+	66.3889i	0.715467	+	2.20198i
$910$		0			0
$911$	−7.57628	−	5.50449i	−0.251013	−	0.182372i	0.455162	−	0.890408i	$-0.349581\pi$
$911$	−7.57628	−	5.50449i	−0.251013	−	0.182372i	−0.706176	+	0.708037i	$0.749581\pi$
$912$		0			0
$913$	−28.5380	+	18.5722i	−0.944470	+	0.614649i
$914$		0			0
$915$	10.9480	+	69.1228i	0.361929	+	2.28513i
$916$		0			0
$917$	−8.11747	−	12.4998i	−0.268063	−	0.412780i
$918$		0			0
$919$	16.6162	−	1.74644i	0.548119	−	0.0576096i	0.173578	−	0.984820i	$-0.444467\pi$
$919$	16.6162	−	1.74644i	0.548119	−	0.0576096i	0.374541	+	0.927210i	$0.377800\pi$
$920$		0			0
$921$	−22.7595	+	35.0466i	−0.749952	+	1.15482i
$922$		0			0
$923$	5.13411	−	4.56900i	0.168991	−	0.150390i
$924$		0			0
$925$	13.8175	+	3.70240i	0.454318	+	0.121734i
$926$		0			0
$927$	−86.5967	+	77.9720i	−2.84421	+	2.56094i
$928$		0			0
$929$	−36.2451	−	29.3507i	−1.18916	−	0.962966i	−0.189343	−	0.981911i	$-0.560636\pi$
$929$	−36.2451	−	29.3507i	−1.18916	−	0.962966i	−0.999821	+	0.0189450i	$0.993969\pi$
$930$		0			0
$931$	−39.2772	−	20.0127i	−1.28726	−	0.655891i
$932$		0			0
$933$	−51.5029	−	5.41317i	−1.68613	−	0.177219i
$934$		0			0
$935$	12.2880	−	9.97039i	0.401861	−	0.326067i
$936$		0			0
$937$	−30.1325	+	41.4738i	−0.984384	+	1.35489i	−0.0499505	+	0.998752i	$0.515906\pi$
$937$	−30.1325	+	41.4738i	−0.984384	+	1.35489i	−0.934434	+	0.356137i	$0.884094\pi$
$938$		0			0
$939$	−4.67260	+	5.18944i	−0.152484	+	0.169351i
$940$		0			0
$941$	−58.3132	−	9.23590i	−1.90096	−	0.301082i	−0.907943	−	0.419093i	$-0.862348\pi$
$941$	−58.3132	−	9.23590i	−1.90096	−	0.301082i	−0.993012	+	0.118011i	$0.962348\pi$
$942$		0			0
$943$	−2.40001	−	0.125779i	−0.0781552	−	0.00409594i
$944$		0			0
$945$	158.851	+	91.7129i	5.16744	+	2.98342i
$946$		0			0
$947$	−7.69828	+	28.7304i	−0.250161	+	0.933612i	0.720559	+	0.693394i	$0.243885\pi$
$947$	−7.69828	+	28.7304i	−0.250161	+	0.933612i	−0.970719	+	0.240218i	$0.922781\pi$
$948$		0			0
$949$	−13.8794	+	18.8717i	−0.450545	+	0.612600i
$950$		0			0
$951$	−19.3243	+	7.41791i	−0.626634	+	0.240542i
$952$		0			0
$953$	−23.3176	−	4.95631i	−0.755331	−	0.160551i	−0.185876	−	0.982573i	$-0.559512\pi$
$953$	−23.3176	−	4.95631i	−0.755331	−	0.160551i	−0.569455	+	0.822023i	$0.692846\pi$
$954$		0			0
$955$	−21.4779	+	55.9518i	−0.695008	+	1.81056i
$956$		0			0
$957$	−61.0108	+	13.0301i	−1.97220	+	0.421204i
$958$		0			0
$959$	1.84103	−	17.5163i	0.0594501	−	0.565630i
$960$		0			0
$961$	19.1422	−	6.21969i	0.617492	−	0.200635i
$962$		0			0
$963$	−13.9149	−	19.1522i	−0.448401	−	0.617170i
$964$		0			0
$965$	−6.69222	−	31.4844i	−0.215430	−	1.01352i
$966$		0			0
$967$	−1.93195	−	1.93195i	−0.0621274	−	0.0621274i	0.675360	−	0.737488i	$-0.263988\pi$
$967$	−1.93195	−	1.93195i	−0.0621274	−	0.0621274i	−0.737488	+	0.675360i	$0.763988\pi$
$968$		0			0
$969$	−16.8329	+	4.51036i	−0.540751	+	0.144894i
$970$		0			0
$971$	−24.1549	−	26.8268i	−0.775169	−	0.860912i	0.218197	−	0.975905i	$-0.429982\pi$
$971$	−24.1549	−	26.8268i	−0.775169	−	0.860912i	−0.993366	+	0.114992i	$0.963316\pi$
$972$		0			0
$973$	−1.11931	−	2.91590i	−0.0358834	−	0.0934793i
$974$		0			0
$975$	−6.00762	+	21.9104i	−0.192398	+	0.701693i
$976$		0			0
$977$	−3.94019	−	4.86572i	−0.126058	−	0.155668i	0.710210	−	0.703990i	$-0.248600\pi$
$977$	−3.94019	−	4.86572i	−0.126058	−	0.155668i	−0.836267	+	0.548322i	$0.815267\pi$
$978$		0			0
$979$	0.793630	+	1.55386i	0.0253645	+	0.0496615i
$980$		0			0
$981$	42.9406	+	16.4833i	1.37099	+	0.526273i
$982$		0			0
$983$	5.16132	−	10.1297i	0.164621	−	0.323086i	−0.793930	−	0.608010i	$-0.791968\pi$
$983$	5.16132	−	10.1297i	0.164621	−	0.323086i	0.958550	+	0.284924i	$0.0919682\pi$
$984$		0			0
$985$	25.8406	+	11.5050i	0.823350	+	0.366579i
$986$		0			0
$987$	−3.87295	+	11.9197i	−0.123277	+	0.379409i
$988$		0			0
$989$		−	7.75439i		−	0.246575i
$990$		0			0
$991$	15.5533	+	26.9391i	0.494067	+	0.855750i	0.999977	−	0.00683691i	$-0.00217627\pi$
$991$	15.5533	+	26.9391i	0.494067	+	0.855750i	−0.505909	+	0.862587i	$0.668843\pi$
$992$		0			0
$993$	35.3844	+	69.4458i	1.12289	+	2.20379i
$994$		0			0
$995$	31.3585	−	38.7245i	0.994131	−	1.22765i
$996$		0			0
$997$	2.93938	−	13.8287i	0.0930910	−	0.437959i	−0.906775	−	0.421614i	$-0.861464\pi$
$997$	2.93938	−	13.8287i	0.0930910	−	0.437959i	0.999866	−	0.0163446i	$-0.00520289\pi$
$998$		0			0
$999$	85.3787	−	69.1383i	2.70126	−	2.18744i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.bv.a.249.1	yes	224
11.8	odd	10	inner	572.2.bv.a.41.14	✓	224
13.7	odd	12	inner	572.2.bv.a.293.14	yes	224
143.85	even	60	inner	572.2.bv.a.85.1	yes	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.bv.a.41.14	✓	224	11.8	odd	10	inner
572.2.bv.a.85.1	yes	224	143.85	even	60	inner
572.2.bv.a.249.1	yes	224	1.1	even	1	trivial
572.2.bv.a.293.14	yes	224	13.7	odd	12	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)

\(f(q)\)	\(=\)	\(q+(-3.18098 + 0.676138i) q^{3} +(-0.412038 + 2.60150i) q^{5} +(-3.92487 + 2.54884i) q^{7} +(6.92083 - 3.08135i) q^{9} +O(q^{10})\)	\(q+(-3.18098 + 0.676138i) q^{3} +(-0.412038 + 2.60150i) q^{5} +(-3.92487 + 2.54884i) q^{7} +(6.92083 - 3.08135i) q^{9} +(-2.46258 + 2.22165i) q^{11} +(-0.584728 + 3.55782i) q^{13} +(-0.448292 - 8.55392i) q^{15} +(0.189345 + 1.80150i) q^{17} +(0.154824 - 2.95422i) q^{19} +(10.7616 - 10.7616i) q^{21} +(1.36235 - 0.786555i) q^{23} +(-1.84276 - 0.598749i) q^{25} +(-12.0387 + 8.74664i) q^{27} +(-4.29846 - 3.87035i) q^{29} +(7.06231 - 1.11856i) q^{31} +(6.33127 - 8.73205i) q^{33} +(-5.01362 - 11.2608i) q^{35} +(-7.37274 + 0.386389i) q^{37} +(-0.545572 - 11.7127i) q^{39} +(-1.28127 - 0.832069i) q^{41} +(2.46467 - 4.26893i) q^{43} +(5.16450 + 19.2742i) q^{45} +(-0.733754 + 0.373867i) q^{47} +(6.06086 - 13.6129i) q^{49} +(-1.82037 - 5.60251i) q^{51} +(-0.294980 - 0.214316i) q^{53} +(-4.76494 - 7.32181i) q^{55} +(1.50497 + 9.50201i) q^{57} +(8.30975 + 12.7959i) q^{59} +(-8.12559 + 0.854034i) q^{61} +(-19.3095 + 29.7340i) q^{63} +(-9.01475 - 2.98713i) q^{65} +(2.65162 + 0.710499i) q^{67} +(-3.80180 + 3.42315i) q^{69} +(-1.48136 - 1.19959i) q^{71} +(5.78905 + 2.94967i) q^{73} +(6.26662 + 0.658648i) q^{75} +(4.00268 - 14.9964i) q^{77} +(-3.48647 + 4.79872i) q^{79} +(17.1734 - 19.0730i) q^{81} +(10.1398 + 1.60599i) q^{83} +(-4.76462 - 0.249703i) q^{85} +(16.2902 + 9.40516i) q^{87} +(0.136159 - 0.508151i) q^{89} +(-6.77334 - 15.4544i) q^{91} +(-21.7087 + 8.33321i) q^{93} +(7.62163 + 1.62003i) q^{95} +(4.65373 - 12.1234i) q^{97} +(-10.1974 + 22.9637i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q + 28 q^{9}+O(q^{10}) \) 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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