LMFDB - Embedded newform 567.2.e.g.163.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(163,567)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(567, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("567.163");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.e (of order $3$, degree $2$, 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:	$4.52751779461$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4x^{14} + 14x^{12} - 39x^{10} + 77x^{8} - 156x^{6} + 224x^{4} - 256x^{2} + 256 $ x^16 - 4x^14 + 14x^12 - 39x^10 + 77x^8 - 156x^6 + 224x^4 - 256*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			163.7
Root			$1.41264 - 0.0667052i$ of defining polynomial
Character	$\chi$	$=$	567.163
Dual form			567.2.e.g.487.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.764088 - 1.32344i) q^{2} +(-0.167661 - 0.290398i) q^{4} +(1.41264 - 2.44676i) q^{5} +(1.65876 - 2.06119i) q^{7} +2.54392 q^{8} +(-2.15876 - 3.73909i) q^{10} +(1.81857 + 3.14986i) q^{11} -5.62908 q^{13} +(-1.46042 - 3.77020i) q^{14} +(2.27910 - 3.94752i) q^{16} +(1.60110 + 2.77319i) q^{17} +(-2.03544 + 3.52548i) q^{19} -0.947380 q^{20} +5.55820 q^{22} +(2.35159 - 4.07307i) q^{23} +(-1.49110 - 2.58266i) q^{25} +(-4.30111 + 7.44975i) q^{26} +(-0.876676 - 0.136119i) q^{28} -4.32626 q^{29} +(-1.79099 - 3.10208i) q^{31} +(-0.938949 - 1.62631i) q^{32} +4.89353 q^{34} +(-2.70001 - 6.97032i) q^{35} +(2.15578 - 3.73392i) q^{37} +(3.11051 + 5.38756i) q^{38} +(3.59364 - 6.22437i) q^{40} -3.15192 q^{41} -9.19325 q^{43} +(0.609809 - 1.05622i) q^{44} +(-3.59364 - 6.22437i) q^{46} +(2.42321 - 4.19713i) q^{47} +(-1.49702 - 6.83805i) q^{49} -4.55733 q^{50} +(0.943779 + 1.63467i) q^{52} +(7.06707 + 12.2405i) q^{53} +10.2760 q^{55} +(4.21976 - 5.24351i) q^{56} +(-3.30564 + 5.72554i) q^{58} +(0.750489 + 1.29988i) q^{59} +(-6.60254 + 11.4359i) q^{61} -5.47388 q^{62} +6.24665 q^{64} +(-7.95186 + 13.7730i) q^{65} +(6.34108 + 10.9831i) q^{67} +(0.536885 - 0.929913i) q^{68} +(-11.2878 - 1.75263i) q^{70} +2.91413 q^{71} +(-1.46456 - 2.53670i) q^{73} +(-3.29441 - 5.70608i) q^{74} +1.36506 q^{76} +(9.50905 + 1.47644i) q^{77} +(-0.446763 + 0.773817i) q^{79} +(-6.43910 - 11.1528i) q^{80} +(-2.40834 + 4.17137i) q^{82} -8.04863 q^{83} +9.04711 q^{85} +(-7.02446 + 12.1667i) q^{86} +(4.62631 + 8.01300i) q^{88} +(2.82863 - 4.89934i) q^{89} +(-9.33731 + 11.6026i) q^{91} -1.57708 q^{92} +(-3.70310 - 6.41396i) q^{94} +(5.75068 + 9.96047i) q^{95} +5.13578 q^{97} +(-10.1936 - 3.24366i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{4} + 6 q^{7} - 14 q^{10} + 12 q^{13} - 6 q^{16} - 24 q^{19} + 4 q^{22} - 26 q^{28} - 20 q^{31} + 4 q^{37} - 36 q^{40} + 20 q^{43} + 36 q^{46} - 14 q^{49} - 34 q^{52} + 8 q^{55} + 22 q^{58} - 36 q^{61}+ \cdots + 28 q^{97}+O(q^{100}) $ 16 * q - 6 * q^4 + 6 * q^7 - 14 * q^10 + 12 * q^13 - 6 * q^16 - 24 * q^19 + 4 * q^22 - 26 * q^28 - 20 * q^31 + 4 * q^37 - 36 * q^40 + 20 * q^43 + 36 * q^46 - 14 * q^49 - 34 * q^52 + 8 * q^55 + 22 * q^58 - 36 * q^61 + 76 * q^64 + 18 * q^67 - 58 * q^70 - 32 * q^73 + 116 * q^76 + 32 * q^79 + 2 * q^82 + 60 * q^85 + 72 * q^88 - 22 * q^91 - 54 * q^94 + 28 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.764088	−	1.32344i	0.540292	−	0.935813i	−0.458595	−	0.888645i	$-0.651647\pi$
$2$	0.764088	−	1.32344i	0.540292	−	0.935813i	0.998887	−	0.0471677i	$-0.0150195\pi$
$3$		0			0
$3$		0			0
$4$	−0.167661	−	0.290398i	−0.0838307	−	0.145199i
$5$	1.41264	−	2.44676i	0.631752	−	1.09423i	−0.355442	−	0.934698i	$-0.615670\pi$
$5$	1.41264	−	2.44676i	0.631752	−	1.09423i	0.987193	−	0.159527i	$-0.0509971\pi$
$6$		0			0
$7$	1.65876	−	2.06119i	0.626953	−	0.779057i
$7$	1.65876	−	2.06119i	0.626953	−	0.779057i
$8$	2.54392			0.899412
$9$		0			0
$10$	−2.15876	−	3.73909i	−0.682661	−	1.18240i
$11$	1.81857	+	3.14986i	0.548321	+	0.949719i	0.998390	+	0.0567257i	$0.0180660\pi$
$11$	1.81857	+	3.14986i	0.548321	+	0.949719i	−0.450069	+	0.892994i	$0.648601\pi$
$12$		0			0
$13$	−5.62908			−1.56123			−0.780613	−	0.625015i	$-0.785093\pi$
$13$	−5.62908			−1.56123			−0.780613	+	0.625015i	$0.785093\pi$
$14$	−1.46042	−	3.77020i	−0.390314	−	1.00763i
$15$		0			0
$16$	2.27910	−	3.94752i	0.569776	−	0.986880i
$17$	1.60110	+	2.77319i	0.388324	+	0.672597i	0.992224	−	0.124463i	$-0.0397209\pi$
$17$	1.60110	+	2.77319i	0.388324	+	0.672597i	−0.603900	+	0.797060i	$0.706388\pi$
$18$		0			0
$19$	−2.03544	+	3.52548i	−0.466962	+	0.808801i	−0.999288	−	0.0377382i	$-0.987985\pi$
$19$	−2.03544	+	3.52548i	−0.466962	+	0.808801i	0.532326	+	0.846539i	$0.321318\pi$
$20$	−0.947380			−0.211841
$21$		0			0
$22$	5.55820			1.18501
$23$	2.35159	−	4.07307i	0.490340	−	0.849294i	−0.509598	−	0.860413i	$-0.670206\pi$
$23$	2.35159	−	4.07307i	0.490340	−	0.849294i	0.999938	+	0.0111185i	$0.00353920\pi$
$24$		0			0
$25$	−1.49110	−	2.58266i	−0.298220	−	0.516532i
$26$	−4.30111	+	7.44975i	−0.843518	+	1.46102i
$27$		0			0
$28$	−0.876676	−	0.136119i	−0.165676	−	0.0257241i
$29$	−4.32626			−0.803366			−0.401683	−	0.915779i	$-0.631575\pi$
$29$	−4.32626			−0.803366			−0.401683	+	0.915779i	$0.631575\pi$
$30$		0			0
$31$	−1.79099	−	3.10208i	−0.321670	−	0.557150i	0.659162	−	0.752001i	$-0.270911\pi$
$31$	−1.79099	−	3.10208i	−0.321670	−	0.557150i	−0.980833	+	0.194851i	$0.937578\pi$
$32$	−0.938949	−	1.62631i	−0.165984	−	0.287493i
$33$		0			0
$34$	4.89353			0.839233
$35$	−2.70001	−	6.97032i	−0.456386	−	1.17820i
$36$		0			0
$37$	2.15578	−	3.73392i	0.354408	−	0.613852i	−0.632609	−	0.774472i	$-0.718016\pi$
$37$	2.15578	−	3.73392i	0.354408	−	0.613852i	0.987016	+	0.160619i	$0.0513492\pi$
$38$	3.11051	+	5.38756i	0.504591	+	0.873977i
$39$		0			0
$40$	3.59364	−	6.22437i	0.568205	−	0.984159i
$41$	−3.15192			−0.492246			−0.246123	−	0.969239i	$-0.579157\pi$
$41$	−3.15192			−0.492246			−0.246123	+	0.969239i	$0.579157\pi$
$42$		0			0
$43$	−9.19325			−1.40196			−0.700979	−	0.713182i	$-0.747253\pi$
$43$	−9.19325			−1.40196			−0.700979	+	0.713182i	$0.747253\pi$
$44$	0.609809	−	1.05622i	0.0919322	−	0.159231i
$45$		0			0
$46$	−3.59364	−	6.22437i	−0.529854	−	0.917733i
$47$	2.42321	−	4.19713i	0.353462	−	0.612215i	−0.633391	−	0.773832i	$-0.718338\pi$
$47$	2.42321	−	4.19713i	0.353462	−	0.612215i	0.986854	+	0.161617i	$0.0516710\pi$
$48$		0			0
$49$	−1.49702	−	6.83805i	−0.213859	−	0.976864i
$50$	−4.55733			−0.644504
$51$		0			0
$52$	0.943779	+	1.63467i	0.130879	+	0.226688i
$53$	7.06707	+	12.2405i	0.970736	+	1.68136i	0.693342	+	0.720609i	$0.256138\pi$
$53$	7.06707	+	12.2405i	0.970736	+	1.68136i	0.277395	+	0.960756i	$0.410529\pi$
$54$		0			0
$55$	10.2760			1.38561
$56$	4.21976	−	5.24351i	0.563889	−	0.700693i
$57$		0			0
$58$	−3.30564	+	5.72554i	−0.434052	+	0.751800i
$59$	0.750489	+	1.29988i	0.0977053	+	0.169231i	0.910734	−	0.412992i	$-0.135516\pi$
$59$	0.750489	+	1.29988i	0.0977053	+	0.169231i	−0.813029	+	0.582223i	$0.802183\pi$
$60$		0			0
$61$	−6.60254	+	11.4359i	−0.845369	+	1.46422i	0.0399317	+	0.999202i	$0.487286\pi$
$61$	−6.60254	+	11.4359i	−0.845369	+	1.46422i	−0.885301	+	0.465019i	$0.846047\pi$
$62$	−5.47388			−0.695184
$63$		0			0
$64$	6.24665			0.780831
$65$	−7.95186	+	13.7730i	−0.986307	+	1.70833i
$66$		0			0
$67$	6.34108	+	10.9831i	0.774686	+	1.34180i	0.934971	+	0.354725i	$0.115425\pi$
$67$	6.34108	+	10.9831i	0.774686	+	1.34180i	−0.160285	+	0.987071i	$0.551241\pi$
$68$	0.536885	−	0.929913i	0.0651069	−	0.112768i
$69$		0			0
$70$	−11.2878	−	1.75263i	−1.34916	−	0.209480i
$71$	2.91413			0.345844			0.172922	−	0.984936i	$-0.444679\pi$
$71$	2.91413			0.345844			0.172922	+	0.984936i	$0.444679\pi$
$72$		0			0
$73$	−1.46456	−	2.53670i	−0.171414	−	0.296898i	0.767500	−	0.641048i	$-0.221500\pi$
$73$	−1.46456	−	2.53670i	−0.171414	−	0.296898i	−0.938914	+	0.344151i	$0.888167\pi$
$74$	−3.29441	−	5.70608i	−0.382967	−	0.663319i
$75$		0			0
$76$	1.36506			0.156583
$77$	9.50905	+	1.47644i	1.08366	+	0.168257i
$78$		0			0
$79$	−0.446763	+	0.773817i	−0.0502648	+	0.0870612i	−0.890063	−	0.455837i	$-0.849340\pi$
$79$	−0.446763	+	0.773817i	−0.0502648	+	0.0870612i	0.839798	+	0.542899i	$0.182673\pi$
$80$	−6.43910	−	11.1528i	−0.719913	−	1.24693i
$81$		0			0
$82$	−2.40834	+	4.17137i	−0.265957	+	0.460651i
$83$	−8.04863			−0.883452			−0.441726	−	0.897150i	$-0.645634\pi$
$83$	−8.04863			−0.883452			−0.441726	+	0.897150i	$0.645634\pi$
$84$		0			0
$85$	9.04711			0.981297
$86$	−7.02446	+	12.1667i	−0.757467	+	1.31197i
$87$		0			0
$88$	4.62631	+	8.01300i	0.493166	+	0.854189i
$89$	2.82863	−	4.89934i	0.299835	−	0.519329i	−0.676263	−	0.736660i	$-0.736402\pi$
$89$	2.82863	−	4.89934i	0.299835	−	0.519329i	0.976098	+	0.217331i	$0.0697352\pi$
$90$		0			0
$91$	−9.33731	+	11.6026i	−0.978816	+	1.21628i
$92$	−1.57708			−0.164422
$93$		0			0
$94$	−3.70310	−	6.41396i	−0.381946	−	0.661549i
$95$	5.75068	+	9.96047i	0.590007	+	1.02192i
$96$		0			0
$97$	5.13578			0.521460			0.260730	−	0.965412i	$-0.416037\pi$
$97$	5.13578			0.521460			0.260730	+	0.965412i	$0.416037\pi$
$98$	−10.1936	−	3.24366i	−1.02971	−	0.327660i
$99$		0			0
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	1.26223	+	2.18625i	0.125597	+	0.217540i	0.921966	−	0.387271i	$-0.126582\pi$
$101$	1.26223	+	2.18625i	0.125597	+	0.217540i	−0.796369	+	0.604811i	$0.793249\pi$
$102$		0			0
$103$	−4.92321	+	8.52725i	−0.485098	+	0.840215i	−0.999853	−	0.0171225i	$-0.994549\pi$
$103$	−4.92321	+	8.52725i	−0.485098	+	0.840215i	0.514755	+	0.857337i	$0.327883\pi$
$104$	−14.3199			−1.40418
$105$		0			0
$106$	21.5995			2.09792
$107$	1.35126	−	2.34045i	0.130631	−	0.226260i	−0.793289	−	0.608845i	$-0.791633\pi$
$107$	1.35126	−	2.34045i	0.130631	−	0.226260i	0.923920	+	0.382586i	$0.124966\pi$
$108$		0			0
$109$	4.52873	+	7.84400i	0.433774	+	0.751319i	0.997195	−	0.0748515i	$-0.0238483\pi$
$109$	4.52873	+	7.84400i	0.433774	+	0.751319i	−0.563421	+	0.826170i	$0.690515\pi$
$110$	7.85174	−	13.5996i	0.748634	−	1.29667i
$111$		0			0
$112$	−4.35611	−	11.2457i	−0.411613	−	1.06262i
$113$	−0.465776			−0.0438165			−0.0219082	−	0.999760i	$-0.506974\pi$
$113$	−0.465776			−0.0438165			−0.0219082	+	0.999760i	$0.506974\pi$
$114$		0			0
$115$	−6.64389	−	11.5076i	−0.619546	−	1.07309i
$116$	0.725346	+	1.25634i	0.0673467	+	0.116648i
$117$		0			0
$118$	2.29376			0.211158
$119$	8.37191	+	1.29988i	0.767452	+	0.119160i
$120$		0			0
$121$	−1.11442	+	1.93024i	−0.101311	+	0.175476i
$122$	10.0898	+	17.4761i	0.913492	+	1.58221i
$123$		0			0
$124$	−0.600558	+	1.04020i	−0.0539317	+	0.0934125i
$125$	5.70084			0.509899
$126$		0			0
$127$	−15.7574			−1.39825			−0.699123	−	0.715002i	$-0.746426\pi$
$127$	−15.7574			−1.39825			−0.699123	+	0.715002i	$0.746426\pi$
$128$	6.65089	−	11.5197i	0.587861	−	1.01821i
$129$		0			0
$130$	12.1518	+	21.0476i	1.06579	+	1.84600i
$131$	6.07396	−	10.5204i	0.530685	−	0.919173i	−0.468674	−	0.883371i	$-0.655268\pi$
$131$	6.07396	−	10.5204i	0.530685	−	0.919173i	0.999359	−	0.0358017i	$-0.0113985\pi$
$132$		0			0
$133$	3.89038	+	10.0434i	0.337339	+	0.870870i
$134$	19.3806			1.67423
$135$		0			0
$136$	4.07307	+	7.05477i	0.349263	+	0.604941i
$137$	1.08169	+	1.87353i	0.0924146	+	0.160067i	0.908527	−	0.417827i	$-0.137208\pi$
$137$	1.08169	+	1.87353i	0.0924146	+	0.160067i	−0.816112	+	0.577894i	$0.803875\pi$
$138$		0			0
$139$	−21.4514			−1.81949			−0.909743	−	0.415173i	$-0.863721\pi$
$139$	−21.4514			−1.81949			−0.909743	+	0.415173i	$0.863721\pi$
$140$	−1.57148	+	1.95273i	−0.132814	+	0.165036i
$141$		0			0
$142$	2.22665	−	3.85668i	0.186857	−	0.323645i
$143$	−10.2369	−	17.7308i	−0.856053	−	1.48273i
$144$		0			0
$145$	−6.11144	+	10.5853i	−0.507528	+	0.879063i
$146$	−4.47622			−0.370454
$147$		0			0
$148$	−1.44576			−0.118841
$149$	−5.54862	+	9.61049i	−0.454561	+	0.787322i	−0.998663	−	0.0516967i	$-0.983537\pi$
$149$	−5.54862	+	9.61049i	−0.454561	+	0.787322i	0.544102	+	0.839019i	$0.316870\pi$
$150$		0			0
$151$	−1.04355	−	1.80748i	−0.0849228	−	0.147091i	0.820436	−	0.571739i	$-0.193731\pi$
$151$	−1.04355	−	1.80748i	−0.0849228	−	0.147091i	−0.905358	+	0.424649i	$0.860398\pi$
$152$	−5.17799	+	8.96855i	−0.419991	+	0.727445i
$153$		0			0
$154$	9.21974	−	11.4565i	0.742948	−	0.923193i
$155$	−10.1201			−0.812863
$156$		0			0
$157$	10.8077	+	18.7194i	0.862547	+	1.49397i	0.869463	+	0.493998i	$0.164465\pi$
$157$	10.8077	+	18.7194i	0.862547	+	1.49397i	−0.00691621	+	0.999976i	$0.502202\pi$
$158$	0.682733	+	1.18253i	0.0543153	+	0.0940769i
$159$		0			0
$160$	−5.30559			−0.419444
$161$	−4.49465	−	11.6033i	−0.354228	−	0.914471i
$162$		0			0
$163$	4.69122	−	8.12543i	0.367444	−	0.636432i	−0.621721	−	0.783239i	$-0.713566\pi$
$163$	4.69122	−	8.12543i	0.367444	−	0.636432i	0.989165	+	0.146807i	$0.0468995\pi$
$164$	0.528454	+	0.915310i	0.0412654	+	0.0714737i
$165$		0			0
$166$	−6.14986	+	10.6519i	−0.477322	+	0.826746i
$167$	17.4047			1.34682			0.673408	−	0.739271i	$-0.264830\pi$
$167$	17.4047			1.34682			0.673408	+	0.739271i	$0.264830\pi$
$168$		0			0
$169$	18.6865			1.43743
$170$	6.91279	−	11.9733i	0.530187	−	0.918310i
$171$		0			0
$172$	1.54135	+	2.66970i	0.117527	+	0.203563i
$173$	10.7738	−	18.6607i	0.819116	−	1.41875i	−0.0872187	−	0.996189i	$-0.527798\pi$
$173$	10.7738	−	18.6607i	0.819116	−	1.41875i	0.906334	−	0.422561i	$-0.138869\pi$
$174$		0			0
$175$	−7.79674	−	1.21058i	−0.589378	−	0.0915112i
$176$	16.5789			1.24968
$177$		0			0
$178$	−4.32265	−	7.48705i	−0.323996	−	0.561178i
$179$	−2.82863	−	4.89934i	−0.211422	−	0.366194i	0.740738	−	0.671794i	$-0.234476\pi$
$179$	−2.82863	−	4.89934i	−0.211422	−	0.366194i	−0.952160	+	0.305601i	$0.901143\pi$
$180$		0			0
$181$	1.12427			0.0835664			0.0417832	−	0.999127i	$-0.486696\pi$
$181$	1.12427			0.0835664			0.0417832	+	0.999127i	$0.486696\pi$
$182$	8.22083	+	21.2228i	0.609368	+	1.57314i
$183$		0			0
$184$	5.98225	−	10.3616i	0.441018	−	0.763865i
$185$	−6.09067	−	10.5494i	−0.447795	−	0.775604i
$186$		0			0
$187$	−5.82344	+	10.0865i	−0.425852	+	0.737597i
$188$	−1.62512			−0.118524
$189$		0			0
$190$	17.5761			1.27510
$191$	−1.96950	+	3.41127i	−0.142508	+	0.246831i	−0.928440	−	0.371481i	$-0.878850\pi$
$191$	−1.96950	+	3.41127i	−0.142508	+	0.246831i	0.785932	+	0.618312i	$0.212183\pi$
$192$		0			0
$193$	−9.04339	−	15.6636i	−0.650957	−	1.12749i	−0.982891	−	0.184189i	$-0.941034\pi$
$193$	−9.04339	−	15.6636i	−0.650957	−	1.12749i	0.331933	−	0.943303i	$-0.392299\pi$
$194$	3.92419	−	6.79690i	0.281741	−	0.487989i
$195$		0			0
$196$	−1.73476	+	1.58121i	−0.123912	+	0.112943i
$197$	25.4842			1.81567			0.907836	−	0.419326i	$-0.137734\pi$
$197$	25.4842			1.81567			0.907836	+	0.419326i	$0.137734\pi$
$198$		0			0
$199$	−6.31454	−	10.9371i	−0.447626	−	0.775311i	0.550605	−	0.834766i	$-0.314397\pi$
$199$	−6.31454	−	10.9371i	−0.447626	−	0.775311i	−0.998231	+	0.0594551i	$0.981064\pi$
$200$	−3.79324	−	6.57009i	−0.268223	−	0.464575i
$201$		0			0
$202$	3.85782			0.271436
$203$	−7.17623	+	8.91724i	−0.503673	+	0.625868i
$204$		0			0
$205$	−4.45252	+	7.71199i	−0.310977	+	0.538629i
$206$	7.52353	+	13.0311i	0.524189	+	0.907922i
$207$		0			0
$208$	−12.8292	+	22.2209i	−0.889548	+	1.54074i
$209$	−14.8064			−1.02418
$210$		0			0
$211$	2.31156			0.159134			0.0795670	−	0.996830i	$-0.474646\pi$
$211$	2.31156			0.159134			0.0795670	+	0.996830i	$0.474646\pi$
$212$	2.36975	−	4.10452i	0.162755	−	0.281900i
$213$		0			0
$214$	−2.06496	−	3.57662i	−0.141158	−	0.244493i
$215$	−12.9868	+	22.4937i	−0.885689	+	1.53406i
$216$		0			0
$217$	−9.36479	−	1.45405i	−0.635724	−	0.0987071i
$218$	13.8414			0.937458
$219$		0			0
$220$	−1.72288	−	2.98412i	−0.116157	−	0.201189i
$221$	−9.01272	−	15.6105i	−0.606261	−	1.05008i
$222$		0			0
$223$	9.29962			0.622749			0.311374	−	0.950287i	$-0.399211\pi$
$223$	9.29962			0.622749			0.311374	+	0.950287i	$0.399211\pi$
$224$	−4.90963	−	0.762304i	−0.328038	−	0.0509336i
$225$		0			0
$226$	−0.355894	+	0.616426i	−0.0236737	+	0.0410040i
$227$	0.964092	+	1.66986i	0.0639890	+	0.110832i	0.896245	−	0.443559i	$-0.146284\pi$
$227$	0.964092	+	1.66986i	0.0639890	+	0.110832i	−0.832256	+	0.554391i	$0.812951\pi$
$228$		0			0
$229$	−1.67059	+	2.89355i	−0.110396	+	0.191211i	−0.915930	−	0.401338i	$-0.868545\pi$
$229$	−1.67059	+	2.89355i	−0.110396	+	0.191211i	0.805534	+	0.592549i	$0.201879\pi$
$230$	−20.3061			−1.33894
$231$		0			0
$232$	−11.0057			−0.722556
$233$	−10.5758	+	18.3178i	−0.692842	+	1.20004i	0.278061	+	0.960563i	$0.410308\pi$
$233$	−10.5758	+	18.3178i	−0.692842	+	1.20004i	−0.970903	+	0.239474i	$0.923025\pi$
$234$		0			0
$235$	−6.84626	−	11.8581i	−0.446601	−	0.773535i
$236$	0.251656	−	0.435881i	0.0163814	−	0.0283734i
$237$		0			0
$238$	8.11720	−	10.0865i	0.526160	−	0.653810i
$239$	−24.1151			−1.55987			−0.779937	−	0.625858i	$-0.784749\pi$
$239$	−24.1151			−1.55987			−0.779937	+	0.625858i	$0.784749\pi$
$240$		0			0
$241$	−4.61720	−	7.99722i	−0.297420	−	0.515146i	0.678125	−	0.734947i	$-0.262793\pi$
$241$	−4.61720	−	7.99722i	−0.297420	−	0.515146i	−0.975545	+	0.219800i	$0.929459\pi$
$242$	1.70304	+	2.94975i	0.109475	+	0.189617i
$243$		0			0
$244$	4.42796			0.283471
$245$	−18.8458	−	5.99686i	−1.20402	−	0.383125i
$246$		0			0
$247$	11.4576	−	19.8452i	0.729033	−	1.26272i
$248$	−4.55612	−	7.89144i	−0.289314	−	0.501107i
$249$		0			0
$250$	4.35595	−	7.54472i	0.275494	−	0.477170i
$251$	−18.5790			−1.17270			−0.586349	−	0.810058i	$-0.699435\pi$
$251$	−18.5790			−1.17270			−0.586349	+	0.810058i	$0.699435\pi$
$252$		0			0
$253$	17.1062			1.07545
$254$	−12.0401	+	20.8540i	−0.755461	+	1.30850i
$255$		0			0
$256$	−3.91708	−	6.78458i	−0.244818	−	0.424037i
$257$	−5.10987	+	8.85056i	−0.318745	+	0.552083i	−0.980226	−	0.197879i	$-0.936595\pi$
$257$	−5.10987	+	8.85056i	−0.318745	+	0.552083i	0.661481	+	0.749962i	$0.269928\pi$
$258$		0			0
$259$	−4.12039	−	10.6372i	−0.256029	−	0.660960i
$260$	5.33288			0.330731
$261$		0			0
$262$	−9.28209	−	16.0770i	−0.573449	−	0.993243i
$263$	4.56887	+	7.91352i	0.281729	+	0.487969i	0.971811	−	0.235763i	$-0.0757588\pi$
$263$	4.56887	+	7.91352i	0.281729	+	0.487969i	−0.690082	+	0.723731i	$0.742425\pi$
$264$		0			0
$265$	39.9329			2.45306
$266$	16.2644	+	2.52533i	0.997233	+	0.154838i
$267$		0			0
$268$	2.12631	−	3.68287i	0.129885	−	0.224967i
$269$	−11.4606	−	19.8504i	−0.698767	−	1.21030i	−0.968894	−	0.247475i	$-0.920399\pi$
$269$	−11.4606	−	19.8504i	−0.698767	−	1.21030i	0.270127	−	0.962825i	$-0.412934\pi$
$270$		0			0
$271$	4.65781	−	8.06757i	0.282942	−	0.490070i	−0.689166	−	0.724604i	$-0.742023\pi$
$271$	4.65781	−	8.06757i	0.282942	−	0.490070i	0.972108	+	0.234533i	$0.0753562\pi$
$272$	14.5963			0.885030
$273$		0			0
$274$	3.30601			0.199723
$275$	5.42336	−	9.39353i	0.327041	−	0.566451i
$276$		0			0
$277$	−0.0916589	−	0.158758i	−0.00550725	−	0.00953884i	0.863259	−	0.504762i	$-0.168420\pi$
$277$	−0.0916589	−	0.158758i	−0.00550725	−	0.00953884i	−0.868766	+	0.495223i	$0.835086\pi$
$278$	−16.3908	+	28.3896i	−0.983053	+	1.70270i
$279$		0			0
$280$	−6.86862	−	17.7319i	−0.410479	−	1.05969i
$281$	−16.2019			−0.966527			−0.483263	−	0.875475i	$-0.660549\pi$
$281$	−16.2019			−0.966527			−0.483263	+	0.875475i	$0.660549\pi$
$282$		0			0
$283$	−10.3492	−	17.9253i	−0.615195	−	1.06555i	−0.990350	−	0.138588i	$-0.955744\pi$
$283$	−10.3492	−	17.9253i	−0.615195	−	1.06555i	0.375155	−	0.926962i	$-0.377590\pi$
$284$	−0.488588	−	0.846258i	−0.0289923	−	0.0502162i
$285$		0			0
$286$	−31.2876			−1.85007
$287$	−5.22828	+	6.49670i	−0.308615	+	0.383488i
$288$		0			0
$289$	3.37296	−	5.84213i	0.198409	−	0.343655i
$290$	9.33936	+	16.1762i	0.548426	+	0.949902i
$291$		0			0
$292$	−0.491101	+	0.850612i	−0.0287395	+	0.0497783i
$293$	16.0234			0.936097			0.468049	−	0.883703i	$-0.344957\pi$
$293$	16.0234			0.936097			0.468049	+	0.883703i	$0.344957\pi$
$294$		0			0
$295$	4.24068			0.246902
$296$	5.48413	−	9.49879i	0.318758	−	0.552106i
$297$		0			0
$298$	8.47927	+	14.6865i	0.491191	+	0.850768i
$299$	−13.2373	+	22.9276i	−0.765532	+	1.32594i
$300$		0			0
$301$	−15.2494	+	18.9490i	−0.878962	+	1.09221i
$302$	−3.18945			−0.183532
$303$		0			0
$304$	9.27794	+	16.0699i	0.532127	+	0.921670i
$305$	18.6540	+	32.3097i	1.06813	+	1.85005i
$306$		0			0
$307$	−5.32307			−0.303804			−0.151902	−	0.988396i	$-0.548540\pi$
$307$	−5.32307			−0.303804			−0.151902	+	0.988396i	$0.548540\pi$
$308$	−1.16554	−	3.00895i	−0.0664130	−	0.171451i
$309$		0			0
$310$	−7.73262	+	13.3933i	−0.439183	+	0.760688i
$311$	−9.21297	−	15.9573i	−0.522420	−	0.904857i	−0.999660	−	0.0260843i	$-0.991696\pi$
$311$	−9.21297	−	15.9573i	−0.522420	−	0.904857i	0.477240	−	0.878773i	$-0.341637\pi$
$312$		0			0
$313$	−2.32344	+	4.02432i	−0.131329	+	0.227468i	−0.924189	−	0.381936i	$-0.875258\pi$
$313$	−2.32344	+	4.02432i	−0.131329	+	0.227468i	0.792860	+	0.609403i	$0.208591\pi$
$314$	33.0321			1.86411
$315$		0			0
$316$	0.299620			0.0168549
$317$	5.24006	−	9.07606i	0.294311	−	0.509762i	−0.680513	−	0.732736i	$-0.738243\pi$
$317$	5.24006	−	9.07606i	0.294311	−	0.509762i	0.974824	+	0.222974i	$0.0715764\pi$
$318$		0			0
$319$	−7.86762	−	13.6271i	−0.440502	−	0.762972i
$320$	8.82426	−	15.2841i	0.493291	−	0.854405i
$321$		0			0
$322$	−18.7906	−	2.91757i	−1.04716	−	0.162590i
$323$	−13.0358			−0.725329
$324$		0			0
$325$	8.39353	+	14.5380i	0.465589	+	0.806424i
$326$	−7.16901	−	12.4171i	−0.397054	−	0.687719i
$327$		0			0
$328$	−8.01822			−0.442732
$329$	−4.63155	−	11.9568i	−0.255346	−	0.659197i
$330$		0			0
$331$	−6.42677	+	11.1315i	−0.353247	+	0.611842i	−0.986816	−	0.161844i	$-0.948256\pi$
$331$	−6.42677	+	11.1315i	−0.353247	+	0.611842i	0.633569	+	0.773686i	$0.281589\pi$
$332$	1.34944	+	2.33731i	0.0740604	+	0.128276i
$333$		0			0
$334$	13.2987	−	23.0341i	0.727674	−	1.26037i
$335$	35.8306			1.95764
$336$		0			0
$337$	7.29218			0.397230			0.198615	−	0.980078i	$-0.436356\pi$
$337$	7.29218			0.397230			0.198615	+	0.980078i	$0.436356\pi$
$338$	14.2782	−	24.7305i	0.776630	−	1.34516i
$339$		0			0
$340$	−1.51685	−	2.62726i	−0.0822628	−	0.142483i
$341$	6.51408	−	11.2827i	0.352757	−	0.610993i
$342$		0			0
$343$	−16.5777	−	8.25707i	−0.895113	−	0.445840i
$344$	−23.3869			−1.26094
$345$		0			0
$346$	−16.4642	−	28.5169i	−0.885123	−	1.53308i
$347$	−8.76942	−	15.1891i	−0.470767	−	0.815392i	0.528674	−	0.848825i	$-0.322689\pi$
$347$	−8.76942	−	15.1891i	−0.470767	−	0.815392i	−0.999441	+	0.0334327i	$0.989356\pi$
$348$		0			0
$349$	21.0160			1.12496			0.562481	−	0.826810i	$-0.309847\pi$
$349$	21.0160			1.12496			0.562481	+	0.826810i	$0.309847\pi$
$350$	−7.55953	+	9.39353i	−0.404074	+	0.502105i
$351$		0			0
$352$	3.41510	−	5.91512i	0.182025	−	0.315277i
$353$	−2.52669	−	4.37636i	−0.134482	−	0.232930i	0.790917	−	0.611923i	$-0.209604\pi$
$353$	−2.52669	−	4.37636i	−0.134482	−	0.232930i	−0.925400	+	0.378993i	$0.876270\pi$
$354$		0			0
$355$	4.11662	−	7.13019i	0.218487	−	0.378431i
$356$	−1.89701			−0.100541
$357$		0			0
$358$	−8.64530			−0.456918
$359$	7.23806	−	12.5367i	0.382010	−	0.661661i	−0.609339	−	0.792910i	$-0.708565\pi$
$359$	7.23806	−	12.5367i	0.382010	−	0.661661i	0.991349	+	0.131249i	$0.0418986\pi$
$360$		0			0
$361$	1.21398	+	2.10268i	0.0638938	+	0.110667i
$362$	0.859042	−	1.48791i	0.0451503	−	0.0782026i
$363$		0			0
$364$	4.93488	+	0.766226i	0.258658	+	0.0401611i
$365$	−8.27559			−0.433164
$366$		0			0
$367$	−7.46142	−	12.9236i	−0.389483	−	0.674604i	0.602897	−	0.797819i	$-0.294013\pi$
$367$	−7.46142	−	12.9236i	−0.389483	−	0.674604i	−0.992380	+	0.123215i	$0.960680\pi$
$368$	−10.7190	−	18.5659i	−0.558768	−	0.967814i
$369$		0			0
$370$	−18.6152			−0.967761
$371$	36.9526	+	5.73754i	1.91849	+	0.297878i
$372$		0			0
$373$	−3.91054	+	6.77325i	−0.202480	+	0.350705i	−0.949327	−	0.314290i	$-0.898233\pi$
$373$	−3.91054	+	6.77325i	−0.202480	+	0.350705i	0.746847	+	0.664996i	$0.231567\pi$
$374$	8.89924	+	15.4139i	0.460169	+	0.797036i
$375$		0			0
$376$	6.16447	−	10.6772i	0.317908	−	0.550633i
$377$	24.3528			1.25424
$378$		0			0
$379$	11.6097			0.596350			0.298175	−	0.954511i	$-0.403622\pi$
$379$	11.6097			0.596350			0.298175	+	0.954511i	$0.403622\pi$
$380$	1.92833	−	3.33997i	0.0989214	−	0.171337i
$381$		0			0
$382$	3.00974	+	5.21303i	0.153992	+	0.266722i
$383$	−12.5382	+	21.7168i	−0.640672	+	1.10968i	0.344611	+	0.938746i	$0.388011\pi$
$383$	−12.5382	+	21.7168i	−0.640672	+	1.10968i	−0.985283	+	0.170931i	$0.945322\pi$
$384$		0			0
$385$	17.0454	−	21.1807i	0.868713	−	1.07947i
$386$	−27.6398			−1.40683
$387$		0			0
$388$	−0.861073	−	1.49142i	−0.0437143	−	0.0757155i
$389$	−11.7497	−	20.3510i	−0.595732	−	1.03184i	−0.993443	−	0.114327i	$-0.963529\pi$
$389$	−11.7497	−	20.3510i	−0.595732	−	1.03184i	0.397712	−	0.917510i	$-0.369804\pi$
$390$		0			0
$391$	15.0605			0.761643
$392$	−3.80829	−	17.3955i	−0.192348	−	0.878603i
$393$		0			0
$394$	19.4721	−	33.7267i	0.980992	−	1.69913i
$395$	1.26223	+	2.18625i	0.0635098	+	0.110002i
$396$		0			0
$397$	9.86170	−	17.0810i	0.494945	−	0.857269i	−0.505038	−	0.863097i	$-0.668522\pi$
$397$	9.86170	−	17.0810i	0.494945	−	0.857269i	0.999983	+	0.00582755i	$0.00185498\pi$
$398$	−19.2995			−0.967395
$399$		0			0
$400$	−13.5935			−0.679674
$401$	−7.18983	+	12.4532i	−0.359043	+	0.621881i	−0.987801	−	0.155720i	$-0.950230\pi$
$401$	−7.18983	+	12.4532i	−0.359043	+	0.621881i	0.628758	+	0.777601i	$0.283564\pi$
$402$		0			0
$403$	10.0816	+	17.4618i	0.502200	+	0.869836i
$404$	0.423255	−	0.733099i	0.0210577	−	0.0364730i
$405$		0			0
$406$	6.31816	+	16.3109i	0.313565	+	0.809495i
$407$	15.6818			0.777317
$408$		0			0
$409$	5.78795	+	10.0250i	0.286196	+	0.495705i	0.972898	−	0.231233i	$-0.0742759\pi$
$409$	5.78795	+	10.0250i	0.286196	+	0.495705i	−0.686703	+	0.726938i	$0.740943\pi$
$410$	6.80424	+	11.7853i	0.336037	+	0.582034i
$411$		0			0
$412$	3.30173			0.162664
$413$	3.92419	+	0.609299i	0.193097	+	0.0299816i
$414$		0			0
$415$	−11.3698	+	19.6931i	−0.558122	+	0.966696i
$416$	5.28542	+	9.15462i	0.259139	+	0.448842i
$417$		0			0
$418$	−11.3134	+	19.5954i	−0.553356	+	0.958440i
$419$	34.1721			1.66942			0.834708	−	0.550693i	$-0.185636\pi$
$419$	34.1721			1.66942			0.834708	+	0.550693i	$0.185636\pi$
$420$		0			0
$421$	−10.2213			−0.498156			−0.249078	−	0.968483i	$-0.580128\pi$
$421$	−10.2213			−0.498156			−0.249078	+	0.968483i	$0.580128\pi$
$422$	1.76623	−	3.05920i	0.0859789	−	0.148920i
$423$		0			0
$424$	17.9781	+	31.1389i	0.873092	+	1.51224i
$425$	4.77480	−	8.27020i	0.231612	−	0.401164i
$426$		0			0
$427$	12.6196	+	32.5786i	0.610705	+	1.57659i
$428$	−0.906215			−0.0438036
$429$		0			0
$430$	19.8460	+	34.3744i	0.957061	+	1.65768i
$431$	0.0380526	+	0.0659090i	0.00183293	+	0.00317472i	0.866940	−	0.498412i	$-0.166083\pi$
$431$	0.0380526	+	0.0659090i	0.00183293	+	0.00317472i	−0.865107	+	0.501587i	$0.832750\pi$
$432$		0			0
$433$	−29.2697			−1.40661			−0.703305	−	0.710888i	$-0.748293\pi$
$433$	−29.2697			−1.40661			−0.703305	+	0.710888i	$0.748293\pi$
$434$	−9.07987	+	11.2827i	−0.435848	+	0.541588i
$435$		0			0
$436$	1.51859	−	2.63027i	0.0727271	−	0.125967i
$437$	9.57303	+	16.5810i	0.457940	+	0.793175i
$438$		0			0
$439$	2.17263	−	3.76310i	0.103694	−	0.179603i	−0.809510	−	0.587106i	$-0.800267\pi$
$439$	2.17263	−	3.76310i	0.103694	−	0.179603i	0.913204	+	0.407503i	$0.133600\pi$
$440$	26.1412			1.24623
$441$		0			0
$442$	−27.5461			−1.31023
$443$	10.2772	−	17.8006i	0.488284	−	0.845732i	−0.511625	−	0.859209i	$-0.670956\pi$
$443$	10.2772	−	17.8006i	0.488284	−	0.845732i	0.999909	+	0.0134764i	$0.00428979\pi$
$444$		0			0
$445$	−7.99168	−	13.8420i	−0.378842	−	0.656173i
$446$	7.10573	−	12.3075i	0.336466	−	0.582776i
$447$		0			0
$448$	10.3617	−	12.8755i	0.489544	−	0.608312i
$449$	−12.4720			−0.588588			−0.294294	−	0.955715i	$-0.595085\pi$
$449$	−12.4720			−0.588588			−0.294294	+	0.955715i	$0.595085\pi$
$450$		0			0
$451$	−5.73199	−	9.92810i	−0.269909	−	0.467496i
$452$	0.0780926	+	0.135260i	0.00367317	+	0.00636211i
$453$		0			0
$454$	2.94661			0.138291
$455$	15.1986	+	39.2365i	0.712521	+	1.83943i
$456$		0			0
$457$	15.4674	−	26.7903i	0.723534	−	1.25320i	−0.236041	−	0.971743i	$-0.575850\pi$
$457$	15.4674	−	26.7903i	0.723534	−	1.25320i	0.959575	−	0.281454i	$-0.0908168\pi$
$458$	2.55296	+	4.42186i	0.119292	+	0.206620i
$459$		0			0
$460$	−2.22785	+	3.85875i	−0.103874	+	0.179915i
$461$	8.02281			0.373660			0.186830	−	0.982392i	$-0.440179\pi$
$461$	8.02281			0.373660			0.186830	+	0.982392i	$0.440179\pi$
$462$		0			0
$463$	−16.8223			−0.781800			−0.390900	−	0.920433i	$-0.627836\pi$
$463$	−16.8223			−0.781800			−0.390900	+	0.920433i	$0.627836\pi$
$464$	−9.85998	+	17.0780i	−0.457738	+	0.792826i
$465$		0			0
$466$	16.1616	+	27.9928i	0.748674	+	1.29674i
$467$	−0.480399	+	0.832075i	−0.0222302	+	0.0385038i	−0.876926	−	0.480625i	$-0.840410\pi$
$467$	−0.480399	+	0.832075i	−0.0222302	+	0.0385038i	0.854696	+	0.519128i	$0.173743\pi$
$468$		0			0
$469$	33.1566	+	5.14813i	1.53103	+	0.237719i
$470$	−20.9246			−0.965179
$471$		0			0
$472$	1.90918	+	3.30680i	0.0878773	+	0.152208i
$473$	−16.7186	−	28.9575i	−0.768723	−	1.33147i
$474$		0			0
$475$	12.1402			0.557029
$476$	−1.02616	−	2.64913i	−0.0470341	−	0.121423i
$477$		0			0
$478$	−18.4260	+	31.9148i	−0.842787	+	1.45975i
$479$	−12.0645	−	20.8964i	−0.551242	−	0.954779i	−0.998185	−	0.0602166i	$-0.980821\pi$
$479$	−12.0645	−	20.8964i	−0.551242	−	0.954779i	0.446944	−	0.894562i	$-0.352512\pi$
$480$		0			0
$481$	−12.1350	+	21.0185i	−0.553311	+	0.958362i
$482$	−14.1118			−0.642774
$483$		0			0
$484$	0.747384			0.0339720
$485$	7.25501	−	12.5661i	0.329433	−	0.570595i
$486$		0			0
$487$	−7.39944	−	12.8162i	−0.335301	−	0.580758i	0.648242	−	0.761435i	$-0.275505\pi$
$487$	−7.39944	−	12.8162i	−0.335301	−	0.580758i	−0.983543	+	0.180677i	$0.942171\pi$
$488$	−16.7963	+	29.0921i	−0.760335	+	1.31694i
$489$		0			0
$490$	−22.3364	+	20.3592i	−1.00905	+	0.919735i
$491$	6.30383			0.284488			0.142244	−	0.989832i	$-0.454568\pi$
$491$	6.30383			0.284488			0.142244	+	0.989832i	$0.454568\pi$
$492$		0			0
$493$	−6.92677	−	11.9975i	−0.311966	−	0.540341i
$494$	−17.5093	−	30.3270i	−0.787781	−	1.36448i
$495$		0			0
$496$	−16.3274			−0.733120
$497$	4.83385	−	6.00658i	0.216828	−	0.269432i
$498$		0			0
$499$	14.2986	−	24.7658i	0.640092	−	1.10867i	−0.345320	−	0.938485i	$-0.612230\pi$
$499$	14.2986	−	24.7658i	0.640092	−	1.10867i	0.985412	−	0.170187i	$-0.0544370\pi$
$500$	−0.955811	−	1.65551i	−0.0427452	−	0.0740368i
$501$		0			0
$502$	−14.1960	+	24.5882i	−0.633600	+	1.09743i
$503$	−35.4133			−1.57900			−0.789500	−	0.613750i	$-0.789660\pi$
$503$	−35.4133			−1.57900			−0.789500	+	0.613750i	$0.789660\pi$
$504$		0			0
$505$	7.13231			0.317384
$506$	13.0706	−	22.6390i	0.581060	−	1.00642i
$507$		0			0
$508$	2.64191	+	4.57592i	0.117216	+	0.203024i
$509$	−16.2442	+	28.1357i	−0.720010	+	1.24709i	0.240985	+	0.970529i	$0.422529\pi$
$509$	−16.2442	+	28.1357i	−0.720010	+	1.24709i	−0.960995	+	0.276565i	$0.910804\pi$
$510$		0			0
$511$	−7.65797	−	1.18903i	−0.338769	−	0.0525997i
$512$	14.6316			0.646630
$513$		0			0
$514$	7.80878	+	13.5252i	0.344431	+	0.596571i
$515$	13.9094	+	24.0919i	0.612923	+	1.06161i
$516$		0			0
$517$	17.6272			0.775243
$518$	−17.2260	−	2.67463i	−0.756866	−	0.117517i
$519$		0			0
$520$	−20.2289	+	35.0375i	−0.887096	+	1.53650i
$521$	16.4909	+	28.5631i	0.722479	+	1.25137i	0.960003	+	0.279989i	$0.0903308\pi$
$521$	16.4909	+	28.5631i	0.722479	+	1.25137i	−0.237524	+	0.971382i	$0.576336\pi$
$522$		0			0
$523$	−7.13133	+	12.3518i	−0.311831	+	0.540108i	−0.978759	−	0.205015i	$-0.934276\pi$
$523$	−7.13133	+	12.3518i	−0.311831	+	0.540108i	0.666928	+	0.745123i	$0.267609\pi$
$524$	−4.07348			−0.177951
$525$		0			0
$526$	13.9641			0.608863
$527$	5.73509	−	9.93347i	0.249825	−	0.432709i
$528$		0			0
$529$	0.440059	+	0.762205i	0.0191330	+	0.0331393i
$530$	30.5122	−	52.8487i	1.32537	−	2.29560i
$531$		0			0
$532$	2.26431	−	2.81364i	0.0981701	−	0.121987i
$533$	17.7424			0.768508
$534$		0			0
$535$	−3.81768	−	6.61242i	−0.165053	−	0.285880i
$536$	16.1312	+	27.9401i	0.696762	+	1.20683i
$537$		0			0
$538$	−35.0277			−1.51015
$539$	18.8165	−	17.1509i	0.810484	−	0.738742i
$540$		0			0
$541$	7.99105	−	13.8409i	0.343562	−	0.595067i	−0.641529	−	0.767098i	$-0.721700\pi$
$541$	7.99105	−	13.8409i	0.343562	−	0.595067i	0.985091	+	0.172032i	$0.0550331\pi$
$542$	−7.11796	−	12.3287i	−0.305743	−	0.529562i
$543$		0			0
$544$	3.00670	−	5.20776i	0.128911	−	0.223281i
$545$	25.5899			1.09615
$546$		0			0
$547$	−32.0570			−1.37066			−0.685330	−	0.728233i	$-0.740342\pi$
$547$	−32.0570			−1.37066			−0.685330	+	0.728233i	$0.740342\pi$
$548$	0.362714	−	0.628238i	0.0154944	−	0.0268370i
$549$		0			0
$550$	−8.28784	−	14.3550i	−0.353395	−	0.612098i
$551$	8.80583	−	15.2521i	0.375141	−	0.649763i
$552$		0			0
$553$	0.853910	+	2.20444i	0.0363120	+	0.0937425i
$554$	−0.280142			−0.0119021
$555$		0			0
$556$	3.59657	+	6.22945i	0.152529	+	0.264187i
$557$	−19.6474	−	34.0302i	−0.832486	−	1.44191i	−0.896061	−	0.443931i	$-0.853584\pi$
$557$	−19.6474	−	34.0302i	−0.832486	−	1.44191i	0.0635754	−	0.997977i	$-0.479750\pi$
$558$		0			0
$559$	51.7496			2.18877
$560$	−33.6691	−	5.22771i	−1.42278	−	0.220911i
$561$		0			0
$562$	−12.3797	+	21.4423i	−0.522207	+	0.904489i
$563$	17.2532	+	29.8834i	0.727134	+	1.25943i	0.958089	+	0.286469i	$0.0924816\pi$
$563$	17.2532	+	29.8834i	0.727134	+	1.25943i	−0.230955	+	0.972964i	$0.574185\pi$
$564$		0			0
$565$	−0.657973	+	1.13964i	−0.0276811	+	0.0479451i
$566$	−31.6308			−1.32954
$567$		0			0
$568$	7.41332			0.311056
$569$	−2.14203	+	3.71010i	−0.0897985	+	0.155536i	−0.907426	−	0.420212i	$-0.861956\pi$
$569$	−2.14203	+	3.71010i	−0.0897985	+	0.155536i	0.817627	+	0.575748i	$0.195289\pi$
$570$		0			0
$571$	−12.5798	−	21.7888i	−0.526447	−	0.911833i	−0.999525	−	0.0308128i	$-0.990190\pi$
$571$	−12.5798	−	21.7888i	−0.526447	−	0.911833i	0.473078	−	0.881021i	$-0.343143\pi$
$572$	−3.43267	+	5.94555i	−0.143527	+	0.248596i
$573$		0			0
$574$	4.60312	+	11.8834i	0.192131	+	0.496002i
$575$	−14.0258			−0.584917
$576$		0			0
$577$	22.1281	+	38.3271i	0.921206	+	1.59558i	0.797552	+	0.603251i	$0.206128\pi$
$577$	22.1281	+	38.3271i	0.921206	+	1.59558i	0.123655	+	0.992325i	$0.460539\pi$
$578$	−5.15447	−	8.92781i	−0.214398	−	0.371348i
$579$		0			0
$580$	4.09861			0.170186
$581$	−13.3508	+	16.5898i	−0.553883	+	0.688259i
$582$		0			0
$583$	−25.7040	+	44.5206i	−1.06455	+	1.84385i
$584$	−3.72573	−	6.45315i	−0.154172	−	0.267033i
$585$		0			0
$586$	12.2433	−	21.2060i	0.505766	−	0.876012i
$587$	13.0046			0.536757			0.268378	−	0.963314i	$-0.413512\pi$
$587$	13.0046			0.536757			0.268378	+	0.963314i	$0.413512\pi$
$588$		0			0
$589$	14.5818			0.600831
$590$	3.24025	−	5.61228i	0.133399	−	0.231054i
$591$		0			0
$592$	−9.82648	−	17.0200i	−0.403866	−	0.699516i
$593$	−14.1164	+	24.4503i	−0.579691	+	1.00405i	0.415824	+	0.909445i	$0.363493\pi$
$593$	−14.1164	+	24.4503i	−0.579691	+	1.00405i	−0.995515	+	0.0946086i	$0.969840\pi$
$594$		0			0
$595$	15.0070	−	18.6478i	0.615227	−	0.764486i
$596$	3.72116			0.152425
$597$		0			0
$598$	20.2289	+	35.0375i	0.827221	+	1.43279i
$599$	2.49768	+	4.32611i	0.102052	+	0.176760i	0.912530	−	0.409010i	$-0.134126\pi$
$599$	2.49768	+	4.32611i	0.102052	+	0.176760i	−0.810478	+	0.585769i	$0.800792\pi$
$600$		0			0
$601$	8.15787			0.332766			0.166383	−	0.986061i	$-0.446791\pi$
$601$	8.15787			0.332766			0.166383	+	0.986061i	$0.446791\pi$
$602$	13.4260	+	34.6604i	0.547204	+	1.41265i
$603$		0			0
$604$	−0.349925	+	0.606089i	−0.0142383	+	0.0246614i
$605$	3.14856	+	5.45347i	0.128007	+	0.221715i
$606$		0			0
$607$	−8.36385	+	14.4866i	−0.339478	+	0.587993i	−0.984335	−	0.176310i	$-0.943584\pi$
$607$	−8.36385	+	14.4866i	−0.339478	+	0.587993i	0.644857	+	0.764304i	$0.276917\pi$
$608$	7.64469			0.310033
$609$		0			0
$610$	57.0133			2.30840
$611$	−13.6405	+	23.6260i	−0.551834	+	0.955805i
$612$		0			0
$613$	8.29381	+	14.3653i	0.334984	+	0.580209i	0.983482	−	0.181007i	$-0.0579358\pi$
$613$	8.29381	+	14.3653i	0.334984	+	0.580209i	−0.648498	+	0.761216i	$0.724602\pi$
$614$	−4.06729	+	7.04476i	−0.164143	+	0.284303i
$615$		0			0
$616$	24.1903	+	3.75596i	0.974654	+	0.151332i
$617$	−23.7085			−0.954470			−0.477235	−	0.878776i	$-0.658361\pi$
$617$	−23.7085			−0.954470			−0.477235	+	0.878776i	$0.658361\pi$
$618$		0			0
$619$	3.91206	+	6.77589i	0.157239	+	0.272346i	0.933872	−	0.357607i	$-0.116407\pi$
$619$	3.91206	+	6.77589i	0.157239	+	0.272346i	−0.776633	+	0.629953i	$0.783074\pi$
$620$	1.69674	+	2.93885i	0.0681429	+	0.118027i
$621$		0			0
$622$	−28.1581			−1.12904
$623$	−5.40644	−	13.9572i	−0.216604	−	0.559183i
$624$		0			0
$625$	15.5087	−	26.8619i	0.620350	−	1.07448i
$626$	3.55063	+	6.14986i	0.141912	+	0.245798i
$627$		0			0
$628$	3.62406	−	6.27706i	0.144616	−	0.250482i
$629$	13.8065			0.550500
$630$		0			0
$631$	−2.54669			−0.101382			−0.0506911	−	0.998714i	$-0.516142\pi$
$631$	−2.54669			−0.101382			−0.0506911	+	0.998714i	$0.516142\pi$
$632$	−1.13653	+	1.96853i	−0.0452088	+	0.0783039i
$633$		0			0
$634$	−8.00774	−	13.8698i	−0.318028	−	0.550841i
$635$	−22.2596	+	38.5547i	−0.883344	+	1.53000i
$636$		0			0
$637$	8.42682	+	38.4919i	0.333883	+	1.52511i
$638$	−24.0462			−0.951999
$639$		0			0
$640$	−18.7906	−	32.5463i	−0.742764	−	1.28651i
$641$	−5.14269	−	8.90739i	−0.203124	−	0.351821i	0.746409	−	0.665487i	$-0.231776\pi$
$641$	−5.14269	−	8.90739i	−0.203124	−	0.351821i	−0.949533	+	0.313666i	$0.898443\pi$
$642$		0			0
$643$	−4.92126			−0.194076			−0.0970378	−	0.995281i	$-0.530937\pi$
$643$	−4.92126			−0.194076			−0.0970378	+	0.995281i	$0.530937\pi$
$644$	−2.61600	+	3.25067i	−0.103085	+	0.128094i
$645$		0			0
$646$	−9.96047	+	17.2520i	−0.391890	+	0.678773i
$647$	−4.39168	−	7.60661i	−0.172655	−	0.299047i	0.766692	−	0.642015i	$-0.221901\pi$
$647$	−4.39168	−	7.60661i	−0.172655	−	0.299047i	−0.939347	+	0.342968i	$0.888568\pi$
$648$		0			0
$649$	−2.72964	+	4.72787i	−0.107148	+	0.185585i
$650$	25.6536			1.00622
$651$		0			0
$652$	−3.14614			−0.123212
$653$	−0.887297	+	1.53684i	−0.0347226	+	0.0601414i	−0.882864	−	0.469628i	$-0.844388\pi$
$653$	−0.887297	+	1.53684i	−0.0347226	+	0.0601414i	0.848142	+	0.529769i	$0.177721\pi$
$654$		0			0
$655$	−17.1606	−	29.7231i	−0.670522	−	1.16138i
$656$	−7.18354	+	12.4423i	−0.280470	+	0.485788i
$657$		0			0
$658$	−19.3630	−	3.00643i	−0.754846	−	0.117203i
$659$	2.34367			0.0912966			0.0456483	−	0.998958i	$-0.485465\pi$
$659$	2.34367			0.0912966			0.0456483	+	0.998958i	$0.485465\pi$
$660$		0			0
$661$	11.4547	+	19.8401i	0.445537	+	0.771692i	0.998089	−	0.0617856i	$-0.0196795\pi$
$661$	11.4547	+	19.8401i	0.445537	+	0.771692i	−0.552553	+	0.833478i	$0.686346\pi$
$662$	9.82124	+	17.0109i	0.381713	+	0.661147i
$663$		0			0
$664$	−20.4751			−0.794587
$665$	30.0694	+	4.66880i	1.16604	+	0.181048i
$666$		0			0
$667$	−10.1736	+	17.6212i	−0.393922	+	0.682294i
$668$	−2.91810	−	5.05429i	−0.112905	−	0.195556i
$669$		0			0
$670$	27.3778	−	47.4197i	1.05770	−	1.83198i
$671$	−48.0288			−1.85413
$672$		0			0
$673$	−29.7349			−1.14620			−0.573098	−	0.819487i	$-0.694259\pi$
$673$	−29.7349			−1.14620			−0.573098	+	0.819487i	$0.694259\pi$
$674$	5.57187	−	9.65076i	0.214620	−	0.371733i
$675$		0			0
$676$	−3.13301	−	5.42654i	−0.120500	−	0.208713i
$677$	−12.7480	+	22.0802i	−0.489946	+	0.848611i	−0.999933	−	0.0115711i	$-0.996317\pi$
$677$	−12.7480	+	22.0802i	−0.489946	+	0.848611i	0.509987	+	0.860182i	$0.329650\pi$
$678$		0			0
$679$	8.51905	−	10.5858i	0.326931	−	0.406247i
$680$	23.0151			0.882590
$681$		0			0
$682$	−9.95466	−	17.2420i	−0.381184	−	0.660230i
$683$	−5.69293	−	9.86044i	−0.217834	−	0.377299i	0.736312	−	0.676643i	$-0.236566\pi$
$683$	−5.69293	−	9.86044i	−0.217834	−	0.377299i	−0.954145	+	0.299343i	$0.903232\pi$
$684$		0			0
$685$	6.11212			0.233532
$686$	−23.5946	+	15.6305i	−0.900845	+	0.596775i
$687$		0			0
$688$	−20.9524	+	36.2906i	−0.798801	+	1.38356i
$689$	−39.7811	−	68.9029i	−1.51554	−	2.62499i
$690$		0			0
$691$	16.1261	−	27.9313i	0.613468	−	1.06256i	−0.377184	−	0.926138i	$-0.623107\pi$
$691$	16.1261	−	27.9313i	0.613468	−	1.06256i	0.990651	−	0.136419i	$-0.0435592\pi$
$692$	−7.22539			−0.274668
$693$		0			0
$694$	−26.8024			−1.01741
$695$	−30.3031	+	52.4865i	−1.14946	+	1.99093i
$696$		0			0
$697$	−5.04653	−	8.74085i	−0.191151	−	0.331083i
$698$	16.0581	−	27.8134i	0.607807	−	1.05275i
$699$		0			0
$700$	0.955663	+	2.46713i	0.0361207	+	0.0932486i
$701$	15.6291			0.590302			0.295151	−	0.955451i	$-0.404630\pi$
$701$	15.6291			0.590302			0.295151	+	0.955451i	$0.404630\pi$
$702$		0			0
$703$	8.77591	+	15.2003i	0.330990	+	0.573291i
$704$	11.3600	+	19.6761i	0.428146	+	0.741570i
$705$		0			0
$706$	−7.72246			−0.290639
$707$	6.60002	+	1.02477i	0.248219	+	0.0385403i
$708$		0			0
$709$	5.90824	−	10.2334i	0.221888	−	0.384322i	−0.733493	−	0.679697i	$-0.762111\pi$
$709$	5.90824	−	10.2334i	0.221888	−	0.384322i	0.955381	+	0.295375i	$0.0954446\pi$
$710$	−6.29092	−	10.8962i	−0.236094	−	0.408927i
$711$		0			0
$712$	7.19582	−	12.4635i	0.269675	−	0.467090i
$713$	−16.8466			−0.630912
$714$		0			0
$715$	−57.8442			−2.16325
$716$	−0.948505	+	1.64286i	−0.0354473	+	0.0613965i
$717$		0			0
$718$	−11.0610	−	19.1583i	−0.412794	−	0.714980i
$719$	25.3616	−	43.9276i	0.945830	−	1.63822i	0.191748	−	0.981444i	$-0.438584\pi$
$719$	25.3616	−	43.9276i	0.945830	−	1.63822i	0.754082	−	0.656781i	$-0.228082\pi$
$720$		0			0
$721$	9.40985	+	24.2923i	0.350441	+	0.904694i
$722$	3.71036			0.138085
$723$		0			0
$724$	−0.188497	−	0.326486i	−0.00700543	−	0.0121338i
$725$	6.45088	+	11.1733i	0.239580	+	0.414964i
$726$		0			0
$727$	2.26602			0.0840422			0.0420211	−	0.999117i	$-0.486620\pi$
$727$	2.26602			0.0840422			0.0420211	+	0.999117i	$0.486620\pi$
$728$	−23.7534	+	29.5161i	−0.880358	+	1.09394i
$729$		0			0
$730$	−6.32328	+	10.9522i	−0.234035	+	0.405361i
$731$	−14.7193	−	25.4946i	−0.544414	−	0.942952i
$732$		0			0
$733$	16.8262	−	29.1439i	0.621490	−	1.07645i	−0.367718	−	0.929937i	$-0.619861\pi$
$733$	16.8262	−	29.1439i	0.621490	−	1.07645i	0.989208	−	0.146515i	$-0.0468058\pi$
$734$	−22.8047			−0.841738
$735$		0			0
$736$	−8.83209			−0.325555
$737$	−23.0634	+	39.9471i	−0.849553	+	1.47147i
$738$		0			0
$739$	−9.80187	−	16.9773i	−0.360568	−	0.624521i	0.627487	−	0.778627i	$-0.284084\pi$
$739$	−9.80187	−	16.9773i	−0.360568	−	0.624521i	−0.988054	+	0.154106i	$0.950750\pi$
$740$	−2.04234	+	3.53744i	−0.0750780	+	0.130039i
$741$		0			0
$742$	35.8284	−	44.5206i	1.31530	−	1.63440i
$743$	48.8390			1.79173			0.895865	−	0.444327i	$-0.146557\pi$
$743$	48.8390			1.79173			0.895865	+	0.444327i	$0.146557\pi$
$744$		0			0
$745$	15.6764	+	27.1523i	0.574339	+	0.994784i
$746$	5.97599	+	10.3507i	0.218796	+	0.378967i
$747$		0			0
$748$	3.90546			0.142798
$749$	−2.58269	−	6.66745i	−0.0943696	−	0.243623i
$750$		0			0
$751$	−7.91269	+	13.7052i	−0.288738	+	0.500109i	−0.973509	−	0.228649i	$-0.926569\pi$
$751$	−7.91269	+	13.7052i	−0.288738	+	0.500109i	0.684771	+	0.728759i	$0.259902\pi$
$752$	−11.0455	−	19.1314i	−0.402788	−	0.697650i
$753$		0			0
$754$	18.6077	−	32.2295i	0.677653	−	1.17373i
$755$	−5.89663			−0.214600
$756$		0			0
$757$	−2.18728			−0.0794982			−0.0397491	−	0.999210i	$-0.512656\pi$
$757$	−2.18728			−0.0794982			−0.0397491	+	0.999210i	$0.512656\pi$
$758$	8.87084	−	15.3647i	0.322203	−	0.558073i
$759$		0			0
$760$	14.6293	+	25.3386i	0.530660	+	0.919129i
$761$	13.8781	−	24.0376i	0.503081	−	0.871361i	−0.496913	−	0.867800i	$-0.665533\pi$
$761$	13.8781	−	24.0376i	0.503081	−	0.871361i	0.999994	−	0.00356072i	$-0.00113341\pi$
$762$		0			0
$763$	23.6801	+	3.67674i	0.857276	+	0.133107i
$764$	1.32084			0.0477861
$765$		0			0
$766$	19.1606	+	33.1871i	0.692300	+	1.19910i
$767$	−4.22456	−	7.31715i	−0.152540	−	0.264207i
$768$		0			0
$769$	10.0206			0.361352			0.180676	−	0.983543i	$-0.442171\pi$
$769$	10.0206			0.361352			0.180676	+	0.983543i	$0.442171\pi$
$770$	−15.0072	−	38.7425i	−0.540823	−	1.39618i
$771$		0			0
$772$	−3.03245	+	5.25236i	−0.109140	+	0.189037i
$773$	21.7596	+	37.6887i	0.782639	+	1.35557i	0.930400	+	0.366547i	$0.119460\pi$
$773$	21.7596	+	37.6887i	0.782639	+	1.35557i	−0.147761	+	0.989023i	$0.547207\pi$
$774$		0			0
$775$	−5.34108	+	9.25102i	−0.191857	+	0.332306i
$776$	13.0650			0.469007
$777$		0			0
$778$	−35.9111			−1.28748
$779$	6.41553	−	11.1120i	0.229860	−	0.398130i
$780$		0			0
$781$	5.29957	+	9.17912i	0.189633	+	0.328455i
$782$	11.5076	−	19.9317i	0.411510	−	0.712756i
$783$		0			0
$784$	−30.4052	−	9.67512i	−1.08590	−	0.345540i
$785$	61.0694			2.17966
$786$		0			0
$787$	2.91819	+	5.05445i	0.104022	+	0.180172i	0.913338	−	0.407202i	$-0.133495\pi$
$787$	2.91819	+	5.05445i	0.104022	+	0.180172i	−0.809316	+	0.587373i	$0.800162\pi$
$788$	−4.27271	−	7.40055i	−0.152209	−	0.263634i
$789$		0			0
$790$	3.85782			0.137255
$791$	−0.772611	+	0.960053i	−0.0274709	+	0.0341355i
$792$		0			0
$793$	37.1662	−	64.3738i	1.31981	−	2.28598i
$794$	−15.0704	−	26.1027i	−0.534829	−	0.926351i
$795$		0			0
$796$	−2.11741	+	3.66746i	−0.0750496	+	0.129990i
$797$	36.5800			1.29573			0.647865	−	0.761755i	$-0.275662\pi$
$797$	36.5800			1.29573			0.647865	+	0.761755i	$0.275662\pi$
$798$		0			0
$799$	15.5192			0.549031
$800$	−2.80014	+	4.84998i	−0.0989998	+	0.171473i
$801$		0			0
$802$	10.9873	+	19.0306i	0.387976	+	0.671994i
$803$	5.32683	−	9.22634i	0.187980	−	0.325590i
$804$		0			0
$805$	−34.7399	−	5.39398i	−1.22442	−	0.190113i
$806$	30.8129			1.08534
$807$		0			0
$808$	3.21102	+	5.56164i	0.112963	+	0.195658i
$809$	11.0249	+	19.0957i	0.387616	+	0.671370i	0.992128	−	0.125225i	$-0.0399654\pi$
$809$	11.0249	+	19.0957i	0.387616	+	0.671370i	−0.604513	+	0.796596i	$0.706632\pi$
$810$		0			0
$811$	−12.6451			−0.444029			−0.222015	−	0.975043i	$-0.571263\pi$
$811$	−12.6451			−0.444029			−0.222015	+	0.975043i	$0.571263\pi$
$812$	3.79273	+	0.588886i	0.133099	+	0.0206659i
$813$		0			0
$814$	11.9823	−	20.7539i	0.419978	−	0.727423i
$815$	−13.2540	−	22.9566i	−0.464267	−	0.804134i
$816$		0			0
$817$	18.7123	−	32.4107i	0.654660	−	1.13391i
$818$	17.6900			0.618517
$819$		0			0
$820$	2.98606			0.104278
$821$	15.5479	−	26.9298i	0.542625	−	0.939855i	−0.456127	−	0.889915i	$-0.650764\pi$
$821$	15.5479	−	26.9298i	0.542625	−	0.939855i	0.998752	−	0.0499401i	$-0.0159030\pi$
$822$		0			0
$823$	24.4819	+	42.4039i	0.853385	+	1.47811i	0.878135	+	0.478412i	$0.158788\pi$
$823$	24.4819	+	42.4039i	0.853385	+	1.47811i	−0.0247505	+	0.999694i	$0.507879\pi$
$824$	−12.5242	+	21.6926i	−0.436303	+	0.755699i
$825$		0			0
$826$	3.80480	−	4.72787i	0.132386	−	0.164504i
$827$	−36.3827			−1.26515			−0.632575	−	0.774499i	$-0.718002\pi$
$827$	−36.3827			−1.26515			−0.632575	+	0.774499i	$0.718002\pi$
$828$		0			0
$829$	−22.8702	−	39.6124i	−0.794316	−	1.37580i	−0.923273	−	0.384145i	$-0.874496\pi$
$829$	−22.8702	−	39.6124i	−0.794316	−	1.37580i	0.128957	−	0.991650i	$-0.458837\pi$
$830$	17.3751	+	30.0945i	0.603098	+	1.04460i
$831$		0			0
$832$	−35.1629			−1.21905
$833$	16.5663	−	15.0999i	0.573989	−	0.523181i
$834$		0			0
$835$	24.5866	−	42.5852i	0.850853	−	1.47372i
$836$	2.48246	+	4.29974i	0.0858576	+	0.148710i
$837$		0			0
$838$	26.1105	−	45.2247i	0.901972	−	1.56226i
$839$	−25.5348			−0.881559			−0.440779	−	0.897615i	$-0.645298\pi$
$839$	−25.5348			−0.881559			−0.440779	+	0.897615i	$0.645298\pi$
$840$		0			0
$841$	−10.2835			−0.354604
$842$	−7.80998	+	13.5273i	−0.269150	+	0.466181i
$843$		0			0
$844$	−0.387559	−	0.671271i	−0.0133403	−	0.0231061i
$845$	26.3974	−	45.7216i	0.908097	−	1.57287i
$846$		0			0
$847$	2.13003	+	5.49885i	0.0731886	+	0.188943i
$848$	64.4263			2.21241
$849$		0			0
$850$	−7.29674	−	12.6383i	−0.250276	−	0.433491i
$851$	−10.1390	−	17.5613i	−0.347561	−	0.601993i
$852$		0			0
$853$	−1.84673			−0.0632310			−0.0316155	−	0.999500i	$-0.510065\pi$
$853$	−1.84673			−0.0632310			−0.0316155	+	0.999500i	$0.510065\pi$
$854$	52.7583	+	8.19164i	1.80535	+	0.280312i
$855$		0			0
$856$	3.43749	−	5.95391i	0.117491	−	0.203501i
$857$	11.2424	+	19.4724i	0.384033	+	0.665165i	0.991635	−	0.129077i	$-0.0412015\pi$
$857$	11.2424	+	19.4724i	0.384033	+	0.665165i	−0.607601	+	0.794242i	$0.707868\pi$
$858$		0			0
$859$	0.573807	−	0.993864i	0.0195781	−	0.0339102i	−0.856070	−	0.516859i	$-0.827101\pi$
$859$	0.573807	−	0.993864i	0.0195781	−	0.0339102i	0.875648	+	0.482949i	$0.160434\pi$
$860$	8.70951			0.296992
$861$		0			0
$862$	0.116302			0.00396126
$863$	−0.897635	+	1.55475i	−0.0305558	+	0.0529243i	−0.880899	−	0.473304i	$-0.843061\pi$
$863$	−0.897635	+	1.55475i	−0.0305558	+	0.0529243i	0.850343	+	0.526229i	$0.176394\pi$
$864$		0			0
$865$	−30.4390	−	52.7218i	−1.03496	−	1.79260i
$866$	−22.3646	+	38.7366i	−0.759980	+	1.31632i
$867$		0			0
$868$	1.14786	+	2.96330i	0.0389610	+	0.100581i
$869$	−3.24989			−0.110245
$870$		0			0
$871$	−35.6944	−	61.8246i	−1.20946	−	2.09485i
$872$	11.5207	+	19.9545i	0.390141	+	0.675745i
$873$		0			0
$874$	29.2585			0.989685
$875$	9.45634	−	11.7505i	0.319683	−	0.397240i
$876$		0			0
$877$	−4.28998	+	7.43047i	−0.144862	+	0.250909i	−0.929322	−	0.369271i	$-0.879607\pi$
$877$	−4.28998	+	7.43047i	−0.144862	+	0.250909i	0.784459	+	0.620180i	$0.212941\pi$
$878$	−3.32016	−	5.75069i	−0.112050	−	0.194076i
$879$		0			0
$880$	23.4200	−	40.5646i	0.789487	−	1.36743i
$881$	−16.5346			−0.557066			−0.278533	−	0.960427i	$-0.589848\pi$
$881$	−16.5346			−0.557066			−0.278533	+	0.960427i	$0.589848\pi$
$882$		0			0
$883$	−27.4948			−0.925273			−0.462636	−	0.886548i	$-0.653096\pi$
$883$	−27.4948			−0.925273			−0.462636	+	0.886548i	$0.653096\pi$
$884$	−3.02217	+	5.23455i	−0.101647	+	0.176057i
$885$		0			0
$886$	−15.7053	−	27.2025i	−0.527631	−	0.913885i
$887$	21.7210	−	37.6218i	0.729318	−	1.26322i	−0.227853	−	0.973695i	$-0.573171\pi$
$887$	21.7210	−	37.6218i	0.729318	−	1.26322i	0.957172	−	0.289521i	$-0.0934960\pi$
$888$		0			0
$889$	−26.1378	+	32.4791i	−0.876634	+	1.08931i
$890$	−24.4254			−0.818741
$891$		0			0
$892$	−1.55919	−	2.70059i	−0.0522054	−	0.0904225i
$893$	9.86461	+	17.0860i	0.330107	+	0.571761i
$894$		0			0
$895$	−15.9834			−0.534265
$896$	−12.7120	−	32.8172i	−0.424678	−	1.09634i
$897$		0			0
$898$	−9.52968	+	16.5059i	−0.318010	+	0.550809i
$899$	7.74826	+	13.4204i	0.258419	+	0.447595i
$900$		0			0
$901$	−22.6302	+	39.1966i	−0.753920	+	1.30583i
$902$	−17.5190			−0.583319
$903$		0			0
$904$	−1.18490			−0.0394091
$905$	1.58819	−	2.75083i	0.0527932	−	0.0914406i
$906$		0			0
$907$	−5.64761	−	9.78196i	−0.187526	−	0.324805i	0.756899	−	0.653532i	$-0.226714\pi$
$907$	−5.64761	−	9.78196i	−0.187526	−	0.324805i	−0.944425	+	0.328728i	$0.893380\pi$
$908$	0.323282	−	0.559941i	0.0107285	−	0.0185823i
$909$		0			0
$910$	63.5402	+	9.86571i	2.10634	+	0.327045i
$911$	10.0338			0.332435			0.166217	−	0.986089i	$-0.446845\pi$
$911$	10.0338			0.332435			0.166217	+	0.986089i	$0.446845\pi$
$912$		0			0
$913$	−14.6370	−	25.3521i	−0.484415	−	0.839032i
$914$	−23.6369	−	40.9403i	−0.781839	−	1.35418i
$915$		0			0
$916$	1.12038			0.0370182
$917$	−11.6093	−	29.9705i	−0.383373	−	0.989712i
$918$		0			0
$919$	0.178967	−	0.309980i	0.00590358	−	0.0102253i	−0.863059	−	0.505104i	$-0.831454\pi$
$919$	0.178967	−	0.309980i	0.00590358	−	0.0102253i	0.868962	+	0.494879i	$0.164787\pi$
$920$	−16.9015	−	29.2743i	−0.557227	−	0.965146i
$921$		0			0
$922$	6.13013	−	10.6177i	0.201885	−	0.349675i
$923$	−16.4039			−0.539941
$924$		0			0
$925$	−12.8579			−0.422766
$926$	−12.8537	+	22.2633i	−0.422400	+	0.731619i
$927$		0			0
$928$	4.06214	+	7.03583i	0.133346	+	0.230962i
$929$	−16.7632	+	29.0347i	−0.549983	+	0.952599i	0.448292	+	0.893887i	$0.352033\pi$
$929$	−16.7632	+	29.0347i	−0.549983	+	0.952599i	−0.998275	+	0.0587116i	$0.981301\pi$
$930$		0			0
$931$	27.1545	+	8.64073i	0.889953	+	0.283188i
$932$	7.09259			0.232326
$933$		0			0
$934$	0.734134	+	1.27156i	0.0240216	+	0.0416066i
$935$	16.4528	+	28.4972i	0.538065	+	0.931957i
$936$		0			0
$937$	12.8772			0.420680			0.210340	−	0.977628i	$-0.432543\pi$
$937$	12.8772			0.420680			0.210340	+	0.977628i	$0.432543\pi$
$938$	32.1478	−	39.9471i	1.04966	−	1.30432i
$939$		0			0
$940$	−2.29571	+	3.97628i	−0.0748777	+	0.129692i
$941$	16.0492	+	27.7980i	0.523189	+	0.906190i	0.999636	+	0.0269868i	$0.00859120\pi$
$941$	16.0492	+	27.7980i	0.523189	+	0.906190i	−0.476447	+	0.879203i	$0.658075\pi$
$942$		0			0
$943$	−7.41201	+	12.8380i	−0.241368	+	0.418062i
$944$	6.84176			0.222680
$945$		0			0
$946$	−51.0980			−1.66134
$947$	8.39928	−	14.5480i	0.272940	−	0.472746i	−0.696673	−	0.717389i	$-0.745337\pi$
$947$	8.39928	−	14.5480i	0.272940	−	0.472746i	0.969613	+	0.244642i	$0.0786706\pi$
$948$		0			0
$949$	8.24414	+	14.2793i	0.267616	+	0.463524i
$950$	9.27616	−	16.0668i	0.300958	−	0.521275i
$951$		0			0
$952$	21.2975	+	3.30680i	0.690255	+	0.107174i
$953$	2.69574			0.0873237			0.0436619	−	0.999046i	$-0.486098\pi$
$953$	2.69574			0.0873237			0.0436619	+	0.999046i	$0.486098\pi$
$954$		0			0
$955$	5.56438	+	9.63780i	0.180059	+	0.311872i
$956$	4.04316	+	7.00297i	0.130765	+	0.226492i
$957$		0			0
$958$	−36.8734			−1.19133
$959$	5.65597	+	0.878187i	0.182641	+	0.0283581i
$960$		0			0
$961$	9.08474	−	15.7352i	0.293056	−	0.507588i
$962$	18.5445	+	32.1200i	0.597898	+	1.03559i
$963$		0			0
$964$	−1.54825	+	2.68165i	−0.0498658	+	0.0863701i
$965$	−51.1002			−1.64497
$966$		0			0
$967$	13.6775			0.439837			0.219919	−	0.975518i	$-0.429421\pi$
$967$	13.6775			0.439837			0.219919	+	0.975518i	$0.429421\pi$
$968$	−2.83501	+	4.91038i	−0.0911206	+	0.157826i
$969$		0			0
$970$	−11.0869	−	19.2031i	−0.355980	−	0.616576i
$971$	21.3133	−	36.9157i	0.683977	−	1.18468i	−0.289781	−	0.957093i	$-0.593582\pi$
$971$	21.3133	−	36.9157i	0.683977	−	1.18468i	0.973757	−	0.227589i	$-0.0730843\pi$
$972$		0			0
$973$	−35.5828	+	44.2155i	−1.14073	+	1.41748i
$974$	−22.6153			−0.724641
$975$		0			0
$976$	30.0957	+	52.1273i	0.963341	+	1.66856i
$977$	2.52841	+	4.37934i	0.0808911	+	0.140108i	0.903633	−	0.428308i	$-0.140890\pi$
$977$	2.52841	+	4.37934i	0.0808911	+	0.140108i	−0.822742	+	0.568415i	$0.807557\pi$
$978$		0			0
$979$	20.5763			0.657622
$980$	1.41824	+	6.47823i	0.0453041	+	0.206940i
$981$		0			0
$982$	4.81668	−	8.34274i	0.153707	−	0.266227i
$983$	16.6442	+	28.8286i	0.530868	+	0.919490i	0.999351	+	0.0360177i	$0.0114673\pi$
$983$	16.6442	+	28.8286i	0.530868	+	0.919490i	−0.468483	+	0.883472i	$0.655199\pi$
$984$		0			0
$985$	35.9999	−	62.3537i	1.14705	−	1.98675i
$986$	−21.1707			−0.674211
$987$		0			0
$988$	−7.68402			−0.244461
$989$	−21.6188	+	37.4448i	−0.687436	+	1.19067i
$990$		0			0
$991$	−16.0440	−	27.7890i	−0.509653	−	0.882746i	−0.999937	−	0.0111829i	$-0.996440\pi$
$991$	−16.0440	−	27.7890i	−0.509653	−	0.882746i	0.490284	−	0.871563i	$-0.336893\pi$
$992$	−3.36329	+	5.82539i	−0.106785	+	0.184956i
$993$		0			0
$994$	−4.25586	−	10.9869i	−0.134988	−	0.348482i
$995$	−35.6807			−1.13115
$996$		0			0
$997$	21.6283	+	37.4613i	0.684975	+	1.18641i	0.973445	+	0.228922i	$0.0735202\pi$
$997$	21.6283	+	37.4613i	0.684975	+	1.18641i	−0.288470	+	0.957489i	$0.593146\pi$
$998$	−21.8507	−	37.8466i	−0.691673	−	1.19801i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.e.g.163.7	yes	16
3.2	odd	2	inner	567.2.e.g.163.2	✓	16
7.2	even	3		3969.2.a.bg.1.2		8
7.4	even	3	inner	567.2.e.g.487.7	yes	16
7.5	odd	6		3969.2.a.bf.1.2		8
9.2	odd	6		567.2.h.l.352.7		16
9.4	even	3		567.2.g.l.541.7		16
9.5	odd	6		567.2.g.l.541.2		16
9.7	even	3		567.2.h.l.352.2		16
21.2	odd	6		3969.2.a.bg.1.7		8
21.5	even	6		3969.2.a.bf.1.7		8
21.11	odd	6	inner	567.2.e.g.487.2	yes	16
63.4	even	3		567.2.h.l.298.2		16
63.11	odd	6		567.2.g.l.109.2		16
63.25	even	3		567.2.g.l.109.7		16
63.32	odd	6		567.2.h.l.298.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
567.2.e.g.163.2	✓	16	3.2	odd	2	inner
567.2.e.g.163.7	yes	16	1.1	even	1	trivial
567.2.e.g.487.2	yes	16	21.11	odd	6	inner
567.2.e.g.487.7	yes	16	7.4	even	3	inner
567.2.g.l.109.2		16	63.11	odd	6
567.2.g.l.109.7		16	63.25	even	3
567.2.g.l.541.2		16	9.5	odd	6
567.2.g.l.541.7		16	9.4	even	3
567.2.h.l.298.2		16	63.4	even	3
567.2.h.l.298.7		16	63.32	odd	6
567.2.h.l.352.2		16	9.7	even	3
567.2.h.l.352.7		16	9.2	odd	6
3969.2.a.bf.1.2		8	7.5	odd	6
3969.2.a.bf.1.7		8	21.5	even	6
3969.2.a.bg.1.2		8	7.2	even	3
3969.2.a.bg.1.7		8	21.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.764088 - 1.32344i) q^{2} +(-0.167661 - 0.290398i) q^{4} +(1.41264 - 2.44676i) q^{5} +(1.65876 - 2.06119i) q^{7} +2.54392 q^{8} +(-2.15876 - 3.73909i) q^{10} +(1.81857 + 3.14986i) q^{11} -5.62908 q^{13} +(-1.46042 - 3.77020i) q^{14} +(2.27910 - 3.94752i) q^{16} +(1.60110 + 2.77319i) q^{17} +(-2.03544 + 3.52548i) q^{19} -0.947380 q^{20} +5.55820 q^{22} +(2.35159 - 4.07307i) q^{23} +(-1.49110 - 2.58266i) q^{25} +(-4.30111 + 7.44975i) q^{26} +(-0.876676 - 0.136119i) q^{28} -4.32626 q^{29} +(-1.79099 - 3.10208i) q^{31} +(-0.938949 - 1.62631i) q^{32} +4.89353 q^{34} +(-2.70001 - 6.97032i) q^{35} +(2.15578 - 3.73392i) q^{37} +(3.11051 + 5.38756i) q^{38} +(3.59364 - 6.22437i) q^{40} -3.15192 q^{41} -9.19325 q^{43} +(0.609809 - 1.05622i) q^{44} +(-3.59364 - 6.22437i) q^{46} +(2.42321 - 4.19713i) q^{47} +(-1.49702 - 6.83805i) q^{49} -4.55733 q^{50} +(0.943779 + 1.63467i) q^{52} +(7.06707 + 12.2405i) q^{53} +10.2760 q^{55} +(4.21976 - 5.24351i) q^{56} +(-3.30564 + 5.72554i) q^{58} +(0.750489 + 1.29988i) q^{59} +(-6.60254 + 11.4359i) q^{61} -5.47388 q^{62} +6.24665 q^{64} +(-7.95186 + 13.7730i) q^{65} +(6.34108 + 10.9831i) q^{67} +(0.536885 - 0.929913i) q^{68} +(-11.2878 - 1.75263i) q^{70} +2.91413 q^{71} +(-1.46456 - 2.53670i) q^{73} +(-3.29441 - 5.70608i) q^{74} +1.36506 q^{76} +(9.50905 + 1.47644i) q^{77} +(-0.446763 + 0.773817i) q^{79} +(-6.43910 - 11.1528i) q^{80} +(-2.40834 + 4.17137i) q^{82} -8.04863 q^{83} +9.04711 q^{85} +(-7.02446 + 12.1667i) q^{86} +(4.62631 + 8.01300i) q^{88} +(2.82863 - 4.89934i) q^{89} +(-9.33731 + 11.6026i) q^{91} -1.57708 q^{92} +(-3.70310 - 6.41396i) q^{94} +(5.75068 + 9.96047i) q^{95} +5.13578 q^{97} +(-10.1936 - 3.24366i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{4} + 6 q^{7} - 14 q^{10} + 12 q^{13} - 6 q^{16} - 24 q^{19} + 4 q^{22} - 26 q^{28} - 20 q^{31} + 4 q^{37} - 36 q^{40} + 20 q^{43} + 36 q^{46} - 14 q^{49} - 34 q^{52} + 8 q^{55} + 22 q^{58} - 36 q^{61}+ \cdots + 28 q^{97}+O(q^{100}) \) 16 * q - 6 * q^4 + 6 * q^7 - 14 * q^10 + 12 * q^13 - 6 * q^16 - 24 * q^19 + 4 * q^22 - 26 * q^28 - 20 * q^31 + 4 * q^37 - 36 * q^40 + 20 * q^43 + 36 * q^46 - 14 * q^49 - 34 * q^52 + 8 * q^55 + 22 * q^58 - 36 * q^61 + 76 * q^64 + 18 * q^67 - 58 * q^70 - 32 * q^73 + 116 * q^76 + 32 * q^79 + 2 * q^82 + 60 * q^85 + 72 * q^88 - 22 * q^91 - 54 * q^94 + 28 * q^97

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