LMFDB - Embedded newform 567.2.g.l.109.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(109,567)]

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([2, 4]))

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

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

chi := DirichletCharacter("567.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.g (of order $3$, degree $2$, not 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			109.8
Root			$1.14160 - 0.834713i$ of defining polynomial
Character	$\chi$	$=$	567.109
Dual form			567.2.g.l.541.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.29368 - 2.24073i) q^{2} +(-2.34723 - 4.06553i) q^{4} -2.28320 q^{5} +(-2.08382 - 1.63024i) q^{7} -6.97158 q^{8} +(-2.95374 + 5.11603i) q^{10} +2.95632 q^{11} +(-2.13422 + 3.69657i) q^{13} +(-6.34873 + 2.56025i) q^{14} +(-4.32455 + 7.49033i) q^{16} +(-0.764218 + 1.32366i) q^{17} +(-3.69033 - 6.39184i) q^{19} +(5.35921 + 9.28243i) q^{20} +(3.82455 - 6.62431i) q^{22} +6.15202 q^{23} +0.213017 q^{25} +(5.52200 + 9.56439i) q^{26} +(-1.73659 + 12.2984i) q^{28} +(-1.17019 - 2.02683i) q^{29} +(-3.11065 - 5.38780i) q^{31} +(4.21761 + 7.30512i) q^{32} +(1.97731 + 3.42480i) q^{34} +(4.75779 + 3.72218i) q^{35} +(-3.58796 - 6.21453i) q^{37} -19.0965 q^{38} +15.9175 q^{40} +(-3.94584 + 6.83440i) q^{41} +(-0.417061 - 0.722372i) q^{43} +(-6.93918 - 12.0190i) q^{44} +(7.95876 - 13.7850i) q^{46} +(2.91322 - 5.04584i) q^{47} +(1.68461 + 6.79427i) q^{49} +(0.275576 - 0.477312i) q^{50} +20.0380 q^{52} +(3.71826 - 6.44021i) q^{53} -6.74989 q^{55} +(14.5275 + 11.3654i) q^{56} -6.05542 q^{58} +(-2.31179 - 4.00414i) q^{59} +(3.56527 - 6.17523i) q^{61} -16.0968 q^{62} +4.52683 q^{64} +(4.87285 - 8.44003i) q^{65} +(1.66262 + 2.87974i) q^{67} +7.17519 q^{68} +(14.4954 - 5.84557i) q^{70} -0.160242 q^{71} +(0.190329 - 0.329659i) q^{73} -18.5667 q^{74} +(-17.3241 + 30.0063i) q^{76} +(-6.16045 - 4.81953i) q^{77} +(3.97731 - 6.88891i) q^{79} +(9.87382 - 17.1020i) q^{80} +(10.2093 + 17.6831i) q^{82} +(2.14900 + 3.72218i) q^{83} +(1.74486 - 3.02219i) q^{85} -2.15818 q^{86} -20.6102 q^{88} +(-3.02828 - 5.24514i) q^{89} +(10.4736 - 4.22370i) q^{91} +(-14.4402 - 25.0112i) q^{92} +(-7.53756 - 13.0554i) q^{94} +(8.42577 + 14.5939i) q^{95} +(0.661044 + 1.14496i) q^{97} +(17.4034 + 5.01487i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{4} - 14 q^{10} - 6 q^{13} - 6 q^{16} - 24 q^{19} - 2 q^{22} - 26 q^{28} - 20 q^{31} + 4 q^{37} + 72 q^{40} - 10 q^{43} + 36 q^{46} + 4 q^{49} + 68 q^{52} + 8 q^{55} - 44 q^{58} - 36 q^{61} + 76 q^{64}+ \cdots - 14 q^{97}+O(q^{100}) $ 16 * q - 6 * q^4 - 14 * q^10 - 6 * q^13 - 6 * q^16 - 24 * q^19 - 2 * q^22 - 26 * q^28 - 20 * q^31 + 4 * q^37 + 72 * q^40 - 10 * q^43 + 36 * q^46 + 4 * q^49 + 68 * q^52 + 8 * q^55 - 44 * q^58 - 36 * q^61 + 76 * q^64 + 18 * q^67 + 104 * q^70 - 32 * q^73 - 58 * q^76 + 32 * q^79 + 2 * q^82 - 30 * q^85 - 144 * q^88 - 22 * q^91 - 54 * q^94 - 14 * q^97

Character values

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

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.29368	−	2.24073i	0.914772	−	1.58443i	0.107538	−	0.994201i	$-0.465703\pi$
$2$	1.29368	−	2.24073i	0.914772	−	1.58443i	0.807234	−	0.590231i	$-0.200963\pi$
$3$		0			0
$3$		0			0
$4$	−2.34723	−	4.06553i	−1.17362	−	2.03276i
$5$	−2.28320			−1.02108			−0.510540	−	0.859854i	$-0.670554\pi$
$5$	−2.28320			−1.02108			−0.510540	+	0.859854i	$0.670554\pi$
$6$		0			0
$7$	−2.08382	−	1.63024i	−0.787610	−	0.616174i
$7$	−2.08382	−	1.63024i	−0.787610	−	0.616174i
$8$	−6.97158			−2.46482
$9$		0			0
$10$	−2.95374	+	5.11603i	−0.934055	+	1.61783i
$11$	2.95632			0.891365			0.445682	−	0.895191i	$-0.352961\pi$
$11$	2.95632			0.891365			0.445682	+	0.895191i	$0.352961\pi$
$12$		0			0
$13$	−2.13422	+	3.69657i	−0.591925	+	1.02524i	0.402048	+	0.915619i	$0.368299\pi$
$13$	−2.13422	+	3.69657i	−0.591925	+	1.02524i	−0.993973	+	0.109626i	$0.965035\pi$
$14$	−6.34873	+	2.56025i	−1.69677	+	0.684256i
$15$		0			0
$16$	−4.32455	+	7.49033i	−1.08114	+	1.87258i
$17$	−0.764218	+	1.32366i	−0.185350	+	0.321036i	−0.943694	−	0.330818i	$-0.892675\pi$
$17$	−0.764218	+	1.32366i	−0.185350	+	0.321036i	0.758344	+	0.651854i	$0.226009\pi$
$18$		0			0
$19$	−3.69033	−	6.39184i	−0.846619	−	1.46639i	−0.884207	−	0.467095i	$-0.845301\pi$
$19$	−3.69033	−	6.39184i	−0.846619	−	1.46639i	0.0375879	−	0.999293i	$-0.488033\pi$
$20$	5.35921	+	9.28243i	1.19836	+	2.07561i
$21$		0			0
$22$	3.82455	−	6.62431i	0.815396	−	1.41231i
$23$	6.15202			1.28278			0.641392	−	0.767213i	$-0.278357\pi$
$23$	6.15202			1.28278			0.641392	+	0.767213i	$0.278357\pi$
$24$		0			0
$25$	0.213017			0.0426033
$26$	5.52200	+	9.56439i	1.08295	+	1.87573i
$27$		0			0
$28$	−1.73659	+	12.2984i	−0.328184	+	2.32418i
$29$	−1.17019	−	2.02683i	−0.217299	−	0.376372i	0.736683	−	0.676239i	$-0.236391\pi$
$29$	−1.17019	−	2.02683i	−0.217299	−	0.376372i	−0.953981	+	0.299866i	$0.903058\pi$
$30$		0			0
$31$	−3.11065	−	5.38780i	−0.558689	−	0.967677i	−0.997606	−	0.0691500i	$-0.977971\pi$
$31$	−3.11065	−	5.38780i	−0.558689	−	0.967677i	0.438918	−	0.898527i	$-0.355362\pi$
$32$	4.21761	+	7.30512i	0.745575	+	1.29137i
$33$		0			0
$34$	1.97731	+	3.42480i	0.339106	+	0.587349i
$35$	4.75779	+	3.72218i	0.804212	+	0.629163i
$36$		0			0
$37$	−3.58796	−	6.21453i	−0.589857	−	1.02166i	−0.994251	−	0.107077i	$-0.965851\pi$
$37$	−3.58796	−	6.21453i	−0.589857	−	1.02166i	0.404394	−	0.914585i	$-0.367483\pi$
$38$	−19.0965			−3.09786
$39$		0			0
$40$	15.9175			2.51678
$41$	−3.94584	+	6.83440i	−0.616237	+	1.06735i	0.373929	+	0.927457i	$0.378010\pi$
$41$	−3.94584	+	6.83440i	−0.616237	+	1.06735i	−0.990166	+	0.139897i	$0.955323\pi$
$42$		0			0
$43$	−0.417061	−	0.722372i	−0.0636013	−	0.110161i	0.832471	−	0.554068i	$-0.186925\pi$
$43$	−0.417061	−	0.722372i	−0.0636013	−	0.110161i	−0.896073	+	0.443907i	$0.853592\pi$
$44$	−6.93918	−	12.0190i	−1.04612	−	1.81193i
$45$		0			0
$46$	7.95876	−	13.7850i	1.17346	−	2.03248i
$47$	2.91322	−	5.04584i	0.424936	−	0.736011i	−0.571478	−	0.820617i	$-0.693630\pi$
$47$	2.91322	−	5.04584i	0.424936	−	0.736011i	0.996414	+	0.0846058i	$0.0269631\pi$
$48$		0			0
$49$	1.68461	+	6.79427i	0.240659	+	0.970610i
$50$	0.275576	−	0.477312i	0.0389724	−	0.0675021i
$51$		0			0
$52$	20.0380			2.77877
$53$	3.71826	−	6.44021i	0.510742	−	0.884631i	−0.489180	−	0.872183i	$-0.662704\pi$
$53$	3.71826	−	6.44021i	0.510742	−	0.884631i	0.999923	−	0.0124487i	$-0.00396266\pi$
$54$		0			0
$55$	−6.74989			−0.910154
$56$	14.5275	+	11.3654i	1.94132	+	1.51876i
$57$		0			0
$58$	−6.05542			−0.795115
$59$	−2.31179	−	4.00414i	−0.300970	−	0.521295i	0.675386	−	0.737464i	$-0.263977\pi$
$59$	−2.31179	−	4.00414i	−0.300970	−	0.521295i	−0.976356	+	0.216170i	$0.930644\pi$
$60$		0			0
$61$	3.56527	−	6.17523i	0.456486	−	0.790657i	−0.542286	−	0.840194i	$-0.682441\pi$
$61$	3.56527	−	6.17523i	0.456486	−	0.790657i	0.998772	+	0.0495366i	$0.0157744\pi$
$62$	−16.0968			−2.04429
$63$		0			0
$64$	4.52683			0.565853
$65$	4.87285	−	8.44003i	0.604403	−	1.04686i
$66$		0			0
$67$	1.66262	+	2.87974i	0.203121	+	0.351816i	0.949533	−	0.313669i	$-0.101558\pi$
$67$	1.66262	+	2.87974i	0.203121	+	0.351816i	−0.746411	+	0.665485i	$0.768225\pi$
$68$	7.17519			0.870120
$69$		0			0
$70$	14.4954	−	5.84557i	1.73254	−	0.698680i
$71$	−0.160242			−0.0190172			−0.00950860	−	0.999955i	$-0.503027\pi$
$71$	−0.160242			−0.0190172			−0.00950860	+	0.999955i	$0.503027\pi$
$72$		0			0
$73$	0.190329	−	0.329659i	0.0222763	−	0.0385837i	−0.854672	−	0.519168i	$-0.826242\pi$
$73$	0.190329	−	0.329659i	0.0222763	−	0.0385837i	0.876949	+	0.480584i	$0.159575\pi$
$74$	−18.5667			−2.15834
$75$		0			0
$76$	−17.3241	+	30.0063i	−1.98721	+	3.44196i
$77$	−6.16045	−	4.81953i	−0.702048	−	0.549236i
$78$		0			0
$79$	3.97731	−	6.88891i	0.447483	−	0.775063i	−0.550739	−	0.834678i	$-0.685654\pi$
$79$	3.97731	−	6.88891i	0.447483	−	0.775063i	0.998221	+	0.0596151i	$0.0189873\pi$
$80$	9.87382	−	17.1020i	1.10393	−	1.91206i
$81$		0			0
$82$	10.2093	+	17.6831i	1.12743	+	1.95277i
$83$	2.14900	+	3.72218i	0.235883	+	0.408562i	0.959529	−	0.281610i	$-0.0908683\pi$
$83$	2.14900	+	3.72218i	0.235883	+	0.408562i	−0.723646	+	0.690172i	$0.757535\pi$
$84$		0			0
$85$	1.74486	−	3.02219i	0.189257	−	0.327803i
$86$	−2.15818			−0.232723
$87$		0			0
$88$	−20.6102			−2.19706
$89$	−3.02828	−	5.24514i	−0.320997	−	0.555984i	0.659697	−	0.751532i	$-0.270685\pi$
$89$	−3.02828	−	5.24514i	−0.320997	−	0.555984i	−0.980694	+	0.195548i	$0.937351\pi$
$90$		0			0
$91$	10.4736	−	4.22370i	1.09794	−	0.442764i
$92$	−14.4402	−	25.0112i	−1.50550	−	2.60760i
$93$		0			0
$94$	−7.53756	−	13.0554i	−0.777440	−	1.34657i
$95$	8.42577	+	14.5939i	0.864466	+	1.49730i
$96$		0			0
$97$	0.661044	+	1.14496i	0.0671189	+	0.116253i	0.897632	−	0.440746i	$-0.145286\pi$
$97$	0.661044	+	1.14496i	0.0671189	+	0.116253i	−0.830513	+	0.556999i	$0.811953\pi$
$98$	17.4034	+	5.01487i	1.75801	+	0.506579i
$99$		0			0
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	18.1620			1.80719			0.903594	−	0.428389i	$-0.140919\pi$
$101$	18.1620			1.80719			0.903594	+	0.428389i	$0.140919\pi$
$102$		0			0
$103$	13.5351			1.33365			0.666827	−	0.745213i	$-0.267652\pi$
$103$	13.5351			1.33365			0.666827	+	0.745213i	$0.267652\pi$
$104$	14.8789	−	25.7709i	1.45899	−	2.52705i
$105$		0			0
$106$	−9.62050	−	16.6632i	−0.934426	−	1.61847i
$107$	4.06934	+	7.04830i	0.393398	+	0.681385i	0.992895	−	0.118992i	$-0.0379662\pi$
$107$	4.06934	+	7.04830i	0.393398	+	0.681385i	−0.599498	+	0.800377i	$0.704633\pi$
$108$		0			0
$109$	2.74398	−	4.75272i	0.262826	−	0.455228i	−0.704166	−	0.710036i	$-0.748679\pi$
$109$	2.74398	−	4.75272i	0.262826	−	0.455228i	0.966992	+	0.254808i	$0.0820122\pi$
$110$	−8.73222	+	15.1246i	−0.832584	+	1.44208i
$111$		0			0
$112$	21.2226	−	8.55845i	2.00535	−	0.808697i
$113$	−3.12754	+	5.41706i	−0.294214	+	0.509594i	−0.974802	−	0.223073i	$-0.928391\pi$
$113$	−3.12754	+	5.41706i	−0.294214	+	0.509594i	0.680587	+	0.732667i	$0.261725\pi$
$114$		0			0
$115$	−14.0463			−1.30982
$116$	−5.49342	+	9.51487i	−0.510051	+	0.883434i
$117$		0			0
$118$	−11.9629			−1.10127
$119$	3.75039	−	1.51242i	0.343797	−	0.138643i
$120$		0			0
$121$	−2.26016			−0.205469
$122$	−9.22467	−	15.9776i	−0.835162	−	1.44654i
$123$		0			0
$124$	−14.6028	+	25.2929i	−1.31137	+	2.27136i
$125$	10.9297			0.977578
$126$		0			0
$127$	−5.60019			−0.496936			−0.248468	−	0.968640i	$-0.579927\pi$
$127$	−5.60019			−0.496936			−0.248468	+	0.968640i	$0.579927\pi$
$128$	−2.57894	+	4.46685i	−0.227948	+	0.394818i
$129$		0			0
$130$	−12.6079	−	21.8374i	−1.10578	−	1.91527i
$131$	−7.12474			−0.622491			−0.311246	−	0.950330i	$-0.600746\pi$
$131$	−7.12474			−0.622491			−0.311246	+	0.950330i	$0.600746\pi$
$132$		0			0
$133$	−2.73027	+	19.3356i	−0.236744	+	1.67661i
$134$	8.60362			0.743239
$135$		0			0
$136$	5.32780	−	9.22803i	0.456855	−	0.791297i
$137$	−8.87821			−0.758516			−0.379258	−	0.925291i	$-0.623821\pi$
$137$	−8.87821			−0.758516			−0.379258	+	0.925291i	$0.623821\pi$
$138$		0			0
$139$	−4.18550	+	7.24949i	−0.355009	+	0.614894i	−0.987120	−	0.159985i	$-0.948856\pi$
$139$	−4.18550	+	7.24949i	−0.355009	+	0.614894i	0.632110	+	0.774878i	$0.282189\pi$
$140$	3.96498	−	28.0797i	0.335102	−	2.37317i
$141$		0			0
$142$	−0.207302	+	0.359058i	−0.0173964	+	0.0301315i
$143$	−6.30943	+	10.9283i	−0.527621	+	0.913867i
$144$		0			0
$145$	2.67178	+	4.62766i	0.221879	+	0.384306i
$146$	−0.492450	−	0.852948i	−0.0407555	−	0.0705905i
$147$		0			0
$148$	−16.8436	+	29.1739i	−1.38453	+	2.39808i
$149$	13.4522			1.10205			0.551025	−	0.834489i	$-0.314237\pi$
$149$	13.4522			1.10205			0.551025	+	0.834489i	$0.314237\pi$
$150$		0			0
$151$	−9.02147			−0.734157			−0.367078	−	0.930190i	$-0.619642\pi$
$151$	−9.02147			−0.734157			−0.367078	+	0.930190i	$0.619642\pi$
$152$	25.7274	+	44.5612i	2.08677	+	3.61439i
$153$		0			0
$154$	−18.7689	+	7.56893i	−1.51244	+	0.609922i
$155$	7.10224	+	12.3014i	0.570466	+	0.988075i
$156$		0			0
$157$	−1.46420	−	2.53607i	−0.116856	−	0.202400i	0.801664	−	0.597775i	$-0.203948\pi$
$157$	−1.46420	−	2.53607i	−0.116856	−	0.202400i	−0.918520	+	0.395374i	$0.870615\pi$
$158$	−10.2908	−	17.8241i	−0.818689	−	1.41801i
$159$		0			0
$160$	−9.62966	−	16.6791i	−0.761292	−	1.31860i
$161$	−12.8197	−	10.0293i	−1.01033	−	0.790418i
$162$		0			0
$163$	0.602369	+	1.04333i	0.0471812	+	0.0817202i	0.888652	−	0.458583i	$-0.151643\pi$
$163$	0.602369	+	1.04333i	0.0471812	+	0.0817202i	−0.841470	+	0.540303i	$0.818310\pi$
$164$	37.0473			2.89290
$165$		0			0
$166$	11.1205			0.863118
$167$	7.18464	−	12.4442i	0.555964	−	0.962958i	−0.441864	−	0.897082i	$-0.645682\pi$
$167$	7.18464	−	12.4442i	0.555964	−	0.962958i	0.997828	−	0.0658761i	$-0.0209842\pi$
$168$		0			0
$169$	−2.60977	−	4.52025i	−0.200751	−	0.347711i
$170$	−4.51460	−	7.81953i	−0.346254	−	0.599730i
$171$		0			0
$172$	−1.95788	+	3.39115i	−0.149287	+	0.258573i
$173$	2.72184	−	4.71436i	0.206938	−	0.358426i	−0.743811	−	0.668390i	$-0.766984\pi$
$173$	2.72184	−	4.71436i	0.206938	−	0.358426i	0.950748	+	0.309964i	$0.100317\pi$
$174$		0			0
$175$	−0.443889	−	0.347269i	−0.0335548	−	0.0262511i
$176$	−12.7848	+	22.1438i	−0.963687	+	1.66915i
$177$		0			0
$178$	−15.6706			−1.17456
$179$	3.02828	−	5.24514i	0.226345	−	0.392040i	−0.730377	−	0.683044i	$-0.760656\pi$
$179$	3.02828	−	5.24514i	0.226345	−	0.392040i	0.956722	+	0.291004i	$0.0939891\pi$
$180$		0			0
$181$	12.7416			0.947076			0.473538	−	0.880773i	$-0.342977\pi$
$181$	12.7416			0.947076			0.473538	+	0.880773i	$0.342977\pi$
$182$	4.08542	−	28.9327i	0.302831	−	2.14463i
$183$		0			0
$184$	−42.8893			−3.16184
$185$	8.19204	+	14.1890i	0.602291	+	1.04320i
$186$		0			0
$187$	−2.25927	+	3.91318i	−0.165215	+	0.286160i
$188$	−27.3520			−1.99485
$189$		0			0
$190$	43.6011			3.16316
$191$	−12.0662	+	20.8993i	−0.873079	+	1.51222i	−0.0142836	+	0.999898i	$0.504547\pi$
$191$	−12.0662	+	20.8993i	−0.873079	+	1.51222i	−0.858795	+	0.512319i	$0.828787\pi$
$192$		0			0
$193$	0.394373	+	0.683075i	0.0283876	+	0.0491688i	0.879870	−	0.475214i	$-0.157629\pi$
$193$	0.394373	+	0.683075i	0.0283876	+	0.0491688i	−0.851483	+	0.524383i	$0.824296\pi$
$194$	3.42073			0.245594
$195$		0			0
$196$	23.6681	−	22.7966i	1.69058	−	1.62833i
$197$	−14.8985			−1.06147			−0.530736	−	0.847537i	$-0.678085\pi$
$197$	−14.8985			−1.06147			−0.530736	+	0.847537i	$0.678085\pi$
$198$		0			0
$199$	−1.36578	+	2.36561i	−0.0968178	+	0.167693i	−0.910366	−	0.413804i	$-0.864200\pi$
$199$	−1.36578	+	2.36561i	−0.0968178	+	0.167693i	0.813548	+	0.581498i	$0.197533\pi$
$200$	−1.48506			−0.105010
$201$		0			0
$202$	23.4959	−	40.6961i	1.65317	−	2.86337i
$203$	−0.865757	+	6.13124i	−0.0607642	+	0.430328i
$204$		0			0
$205$	9.00916	−	15.6043i	0.629227	−	1.08985i
$206$	17.5101	−	30.3285i	1.21999	−	2.11308i
$207$		0			0
$208$	−18.4590	−	31.9720i	−1.27990	−	2.21686i
$209$	−10.9098	−	18.8963i	−0.754647	−	1.30709i
$210$		0			0
$211$	4.58796	−	7.94658i	0.315848	−	0.547065i	−0.663769	−	0.747937i	$-0.731044\pi$
$211$	4.58796	−	7.94658i	0.315848	−	0.547065i	0.979617	+	0.200872i	$0.0643776\pi$
$212$	−34.9105			−2.39766
$213$		0			0
$214$	21.0577			1.43948
$215$	0.952236	+	1.64932i	0.0649419	+	0.112483i
$216$		0			0
$217$	−2.30139	+	16.2983i	−0.156229	+	1.10640i
$218$	−7.09969	−	12.2970i	−0.480852	−	0.832860i
$219$		0			0
$220$	15.8436	+	27.4418i	1.06817	+	1.85013i
$221$	−3.26201	−	5.64997i	−0.219427	−	0.380058i
$222$		0			0
$223$	14.1714	+	24.5455i	0.948985	+	1.64369i	0.747569	+	0.664184i	$0.231221\pi$
$223$	14.1714	+	24.5455i	0.948985	+	1.64369i	0.201415	+	0.979506i	$0.435446\pi$
$224$	3.12037	−	22.0983i	0.208489	−	1.47650i
$225$		0			0
$226$	8.09210	+	14.0159i	0.538278	+	0.932326i
$227$	2.07197			0.137522			0.0687608	−	0.997633i	$-0.478095\pi$
$227$	2.07197			0.137522			0.0687608	+	0.997633i	$0.478095\pi$
$228$		0			0
$229$	−15.6854			−1.03652			−0.518259	−	0.855224i	$-0.673420\pi$
$229$	−15.6854			−1.03652			−0.518259	+	0.855224i	$0.673420\pi$
$230$	−18.1715	+	31.4739i	−1.19819	+	2.07533i
$231$		0			0
$232$	8.15806	+	14.1302i	0.535603	+	0.927692i
$233$	−14.6262	−	25.3334i	−0.958196	−	1.65964i	−0.726879	−	0.686766i	$-0.759030\pi$
$233$	−14.6262	−	25.3334i	−0.958196	−	1.65964i	−0.231317	−	0.972878i	$-0.574304\pi$
$234$		0			0
$235$	−6.65147	+	11.5207i	−0.433894	+	0.751526i
$236$	−10.8526	+	18.7973i	−0.706446	+	1.22360i
$237$		0			0
$238$	1.46290	−	10.3602i	0.0948259	−	0.671551i
$239$	8.86060	−	15.3470i	0.573144	−	0.992715i	−0.423096	−	0.906085i	$-0.639057\pi$
$239$	8.86060	−	15.3470i	0.573144	−	0.992715i	0.996241	−	0.0866304i	$-0.0276099\pi$
$240$		0			0
$241$	−26.4073			−1.70104			−0.850520	−	0.525942i	$-0.823713\pi$
$241$	−26.4073			−1.70104			−0.850520	+	0.525942i	$0.823713\pi$
$242$	−2.92393	+	5.06439i	−0.187957	+	0.325551i
$243$		0			0
$244$	−33.4741			−2.14296
$245$	−3.84632	−	15.5127i	−0.245732	−	0.991070i
$246$		0			0
$247$	31.5039			2.00454
$248$	21.6861	+	37.5615i	1.37707	+	2.38515i
$249$		0			0
$250$	14.1395	−	24.4904i	0.894261	−	1.54891i
$251$	8.81798			0.556586			0.278293	−	0.960496i	$-0.410231\pi$
$251$	8.81798			0.556586			0.278293	+	0.960496i	$0.410231\pi$
$252$		0			0
$253$	18.1873			1.14343
$254$	−7.24487	+	12.5485i	−0.454584	+	0.787362i
$255$		0			0
$256$	11.1995	+	19.3981i	0.699968	+	1.21238i
$257$	9.19671			0.573675			0.286837	−	0.957979i	$-0.407396\pi$
$257$	9.19671			0.573675			0.286837	+	0.957979i	$0.407396\pi$
$258$		0			0
$259$	−2.65453	+	18.7992i	−0.164944	+	1.16813i
$260$	−45.7509			−2.83735
$261$		0			0
$262$	−9.21716	+	15.9646i	−0.569438	+	0.986295i
$263$	−0.254605			−0.0156996			−0.00784982	−	0.999969i	$-0.502499\pi$
$263$	−0.254605			−0.0156996			−0.00784982	+	0.999969i	$0.502499\pi$
$264$		0			0
$265$	−8.48954	+	14.7043i	−0.521508	+	0.903279i
$266$	39.7936	+	31.1319i	2.43990	+	1.90882i
$267$		0			0
$268$	7.80512	−	13.5189i	0.476773	−	0.825796i
$269$	−0.489721	+	0.848222i	−0.0298588	+	0.0517170i	−0.880569	−	0.473919i	$-0.842839\pi$
$269$	−0.489721	+	0.848222i	−0.0298588	+	0.0517170i	0.850710	+	0.525636i	$0.176172\pi$
$270$		0			0
$271$	−7.02445	−	12.1667i	−0.426705	−	0.739075i	0.569873	−	0.821733i	$-0.306992\pi$
$271$	−7.02445	−	12.1667i	−0.426705	−	0.739075i	−0.996578	+	0.0826580i	$0.973659\pi$
$272$	−6.60979	−	11.4485i	−0.400777	−	0.694167i
$273$		0			0
$274$	−11.4856	+	19.8936i	−0.693870	+	1.20182i
$275$	0.629746			0.0379751
$276$		0			0
$277$	25.4187			1.52726			0.763630	−	0.645654i	$-0.223415\pi$
$277$	25.4187			1.52726			0.763630	+	0.645654i	$0.223415\pi$
$278$	10.8294	+	18.7571i	0.649505	+	1.12498i
$279$		0			0
$280$	−33.1693	−	25.9494i	−1.98224	−	1.55078i
$281$	14.6906	+	25.4448i	0.876366	+	1.51791i	0.855300	+	0.518132i	$0.173373\pi$
$281$	14.6906	+	25.4448i	0.876366	+	1.51791i	0.0210657	+	0.999778i	$0.493294\pi$
$282$		0			0
$283$	1.53844	+	2.66466i	0.0914510	+	0.158398i	0.908122	−	0.418706i	$-0.137516\pi$
$283$	1.53844	+	2.66466i	0.0914510	+	0.158398i	−0.816671	+	0.577104i	$0.804183\pi$
$284$	0.376125	+	0.651467i	0.0223189	+	0.0386575i
$285$		0			0
$286$	16.3248	+	28.2754i	0.965307	+	1.67196i
$287$	19.3642	−	7.80898i	1.14303	−	0.460949i
$288$		0			0
$289$	7.33194	+	12.6993i	0.431291	+	0.747017i
$290$	13.8257			0.811876
$291$		0			0
$292$	−1.78698			−0.104575
$293$	8.50817	−	14.7366i	0.497053	−	0.860921i	−0.502941	−	0.864320i	$-0.667749\pi$
$293$	8.50817	−	14.7366i	0.497053	−	0.860921i	0.999994	+	0.00339988i	$0.00108222\pi$
$294$		0			0
$295$	5.27829	+	9.14226i	0.307314	+	0.532283i
$296$	25.0137	+	43.3251i	1.45389	+	2.51822i
$297$		0			0
$298$	17.4029	−	30.1428i	1.00812	−	1.74612i
$299$	−13.1297	+	22.7414i	−0.759313	+	1.31517i
$300$		0			0
$301$	−0.308560	+	2.18520i	−0.0177851	+	0.125953i
$302$	−11.6709	+	20.2146i	−0.671586	+	1.16322i
$303$		0			0
$304$	63.8360			3.66124
$305$	−8.14024	+	14.0993i	−0.466109	+	0.807324i
$306$		0			0
$307$	24.2396			1.38343			0.691714	−	0.722172i	$-0.256856\pi$
$307$	24.2396			1.38343			0.691714	+	0.722172i	$0.256856\pi$
$308$	−5.13391	+	36.3580i	−0.292532	+	2.07169i
$309$		0			0
$310$	36.7522			2.08738
$311$	−10.9807	−	19.0192i	−0.622661	−	1.07848i	−0.988988	−	0.147994i	$-0.952718\pi$
$311$	−10.9807	−	19.0192i	−0.622661	−	1.07848i	0.366328	−	0.930486i	$-0.380615\pi$
$312$		0			0
$313$	1.24073	−	2.14900i	0.0701300	−	0.121469i	−0.828828	−	0.559503i	$-0.810992\pi$
$313$	1.24073	−	2.14900i	0.0701300	−	0.121469i	0.898958	+	0.438035i	$0.144325\pi$
$314$	−7.57685			−0.427586
$315$		0			0
$316$	−37.3427			−2.10069
$317$	−9.73961	+	16.8695i	−0.547031	+	0.947486i	0.451445	+	0.892299i	$0.350909\pi$
$317$	−9.73961	+	16.8695i	−0.547031	+	0.947486i	−0.998476	+	0.0551868i	$0.982425\pi$
$318$		0			0
$319$	−3.45946	−	5.99195i	−0.193692	−	0.335485i
$320$	−10.3357			−0.577781
$321$		0			0
$322$	−39.0575	+	15.7507i	−2.17659	+	0.877752i
$323$	11.2809			0.627684
$324$		0			0
$325$	−0.454624	+	0.787432i	−0.0252180	+	0.0436789i
$326$	3.11710			0.172640
$327$		0			0
$328$	27.5087	−	47.6465i	1.51892	−	2.63084i
$329$	−14.2966	+	5.76537i	−0.788195	+	0.317855i
$330$		0			0
$331$	−1.28856	+	2.23185i	−0.0708256	+	0.122674i	−0.899263	−	0.437408i	$-0.855897\pi$
$331$	−1.28856	+	2.23185i	−0.0708256	+	0.122674i	0.828438	+	0.560081i	$0.189230\pi$
$332$	10.0884	−	17.4736i	0.553673	−	0.958990i
$333$		0			0
$334$	−18.5893	−	32.1976i	−1.01716	−	1.76178i
$335$	−3.79610	−	6.57504i	−0.207403	−	0.359233i
$336$		0			0
$337$	12.0760	−	20.9163i	0.657822	−	1.13938i	−0.323356	−	0.946277i	$-0.604811\pi$
$337$	12.0760	−	20.9163i	0.657822	−	1.13938i	0.981178	−	0.193104i	$-0.0618554\pi$
$338$	−13.5048			−0.734567
$339$		0			0
$340$	−16.3824			−0.888462
$341$	−9.19608	−	15.9281i	−0.497996	−	0.862554i
$342$		0			0
$343$	7.56588	−	16.9044i	0.408519	−	0.912750i
$344$	2.90758	+	5.03607i	0.156766	+	0.271527i
$345$		0			0
$346$	−7.04240	−	12.1978i	−0.378602	−	0.655757i
$347$	18.1212	+	31.3868i	0.972797	+	1.68493i	0.687022	+	0.726637i	$0.258918\pi$
$347$	18.1212	+	31.3868i	0.972797	+	1.68493i	0.285775	+	0.958297i	$0.407749\pi$
$348$		0			0
$349$	−17.6469	−	30.5653i	−0.944617	−	1.63613i	−0.756515	−	0.653976i	$-0.773100\pi$
$349$	−17.6469	−	30.5653i	−0.944617	−	1.63613i	−0.188102	−	0.982149i	$-0.560234\pi$
$350$	−1.35239	+	0.545376i	−0.0722881	+	0.0291516i
$351$		0			0
$352$	12.4686	+	21.5963i	0.664579	+	1.15109i
$353$	2.92219			0.155532			0.0777662	−	0.996972i	$-0.475221\pi$
$353$	2.92219			0.155532			0.0777662	+	0.996972i	$0.475221\pi$
$354$		0			0
$355$	0.365864			0.0194181
$356$	−14.2162	+	24.6231i	−0.753456	+	1.30502i
$357$		0			0
$358$	−7.83528	−	13.5711i	−0.414107	−	0.717255i
$359$	0.196714	+	0.340719i	0.0103822	+	0.0179825i	0.871170	−	0.490982i	$-0.163362\pi$
$359$	0.196714	+	0.340719i	0.0103822	+	0.0179825i	−0.860788	+	0.508964i	$0.830029\pi$
$360$		0			0
$361$	−17.7371	+	30.7215i	−0.933529	+	1.61692i
$362$	16.4836	−	28.5504i	0.866359	−	1.50058i
$363$		0			0
$364$	−41.7556	−	32.6669i	−2.18859	−	1.71221i
$365$	−0.434559	+	0.752678i	−0.0227459	+	0.0393970i
$366$		0			0
$367$	−9.23134			−0.481872			−0.240936	−	0.970541i	$-0.577454\pi$
$367$	−9.23134			−0.481872			−0.240936	+	0.970541i	$0.577454\pi$
$368$	−26.6047	+	46.0807i	−1.38686	+	2.40212i
$369$		0			0
$370$	42.3916			2.20384
$371$	−18.2473	+	7.35858i	−0.947353	+	0.382039i
$372$		0			0
$373$	−21.5244			−1.11449			−0.557245	−	0.830348i	$-0.688142\pi$
$373$	−21.5244			−1.11449			−0.557245	+	0.830348i	$0.688142\pi$
$374$	5.84557	+	10.1248i	0.302267	+	0.523542i
$375$		0			0
$376$	−20.3097	+	35.1775i	−1.04739	+	1.81414i
$377$	9.98975			0.514498
$378$		0			0
$379$	−18.2445			−0.937159			−0.468579	−	0.883421i	$-0.655234\pi$
$379$	−18.2445			−0.937159			−0.468579	+	0.883421i	$0.655234\pi$
$380$	39.5545	−	68.5104i	2.02910	−	3.51451i
$381$		0			0
$382$	31.2197	+	54.0740i	1.59734	+	2.76667i
$383$	−6.25965			−0.319853			−0.159926	−	0.987129i	$-0.551126\pi$
$383$	−6.25965			−0.319853			−0.159926	+	0.987129i	$0.551126\pi$
$384$		0			0
$385$	14.0655	+	11.0040i	0.716847	+	0.560813i
$386$	2.04078			0.103873
$387$		0			0
$388$	3.10325	−	5.37499i	0.157544	−	0.272874i
$389$	22.6208			1.14692			0.573460	−	0.819234i	$-0.305601\pi$
$389$	22.6208			1.14692			0.573460	+	0.819234i	$0.305601\pi$
$390$		0			0
$391$	−4.70148	+	8.14320i	−0.237764	+	0.411820i
$392$	−11.7444	−	47.3668i	−0.593183	−	2.39238i
$393$		0			0
$394$	−19.2739	+	33.3834i	−0.971006	+	1.68183i
$395$	−9.08101	+	15.7288i	−0.456915	+	0.791400i
$396$		0			0
$397$	10.6077	+	18.3730i	0.532384	+	0.922115i	0.999285	+	0.0378060i	$0.0120369\pi$
$397$	10.6077	+	18.3730i	0.532384	+	0.922115i	−0.466902	+	0.884309i	$0.654630\pi$
$398$	3.53378	+	6.12069i	0.177132	+	0.306802i
$399$		0			0
$400$	−0.921200	+	1.59557i	−0.0460600	+	0.0797783i
$401$	−4.27442			−0.213454			−0.106727	−	0.994288i	$-0.534037\pi$
$401$	−4.27442			−0.213454			−0.106727	+	0.994288i	$0.534037\pi$
$402$		0			0
$403$	26.5552			1.32281
$404$	−42.6305	−	73.8382i	−2.12095	−	3.67359i
$405$		0			0
$406$	12.6184	+	9.87180i	0.626241	+	0.489929i
$407$	−10.6072	−	18.3721i	−0.525778	−	0.910674i
$408$		0			0
$409$	−17.6627	−	30.5926i	−0.873363	−	1.51271i	−0.858497	−	0.512819i	$-0.828601\pi$
$409$	−17.6627	−	30.5926i	−0.873363	−	1.51271i	−0.0148660	−	0.999889i	$-0.504732\pi$
$410$	−23.3100	−	40.3741i	−1.15120	−	1.99394i
$411$		0			0
$412$	−31.7701	−	55.0274i	−1.56520	−	2.71100i
$413$	−1.71036	+	12.1127i	−0.0841615	+	0.596026i
$414$		0			0
$415$	−4.90660	−	8.49849i	−0.240856	−	0.417174i
$416$	−36.0052			−1.76530
$417$		0			0
$418$	−56.4553			−2.76132
$419$	−1.87450	+	3.24673i	−0.0915755	+	0.158613i	−0.908174	−	0.418592i	$-0.862524\pi$
$419$	−1.87450	+	3.24673i	−0.0915755	+	0.158613i	0.816599	+	0.577206i	$0.195857\pi$
$420$		0			0
$421$	−12.2663	−	21.2459i	−0.597825	−	1.03546i	−0.993142	−	0.116918i	$-0.962699\pi$
$421$	−12.2663	−	21.2459i	−0.597825	−	1.03546i	0.395317	−	0.918545i	$-0.370635\pi$
$422$	−11.8707	−	20.5607i	−0.577858	−	1.00088i
$423$		0			0
$424$	−25.9221	+	44.8984i	−1.25889	+	2.18046i
$425$	−0.162791	+	0.281963i	−0.00789653	+	0.0136772i
$426$		0			0
$427$	−17.4965	+	7.05581i	−0.846716	+	0.341455i
$428$	19.1034	−	33.0880i	0.923396	−	1.59937i
$429$		0			0
$430$	4.92757			0.237628
$431$	−12.1284	+	21.0071i	−0.584206	+	1.01187i	0.410768	+	0.911740i	$0.365261\pi$
$431$	−12.1284	+	21.0071i	−0.584206	+	1.01187i	−0.994974	+	0.100135i	$0.968073\pi$
$432$		0			0
$433$	8.60056			0.413317			0.206658	−	0.978413i	$-0.433741\pi$
$433$	8.60056			0.413317			0.206658	+	0.978413i	$0.433741\pi$
$434$	33.5428	+	26.2417i	1.61011	+	1.25964i
$435$		0			0
$436$	−25.7631			−1.23383
$437$	−22.7030	−	39.3227i	−1.08603	−	1.88106i
$438$		0			0
$439$	−13.2792	+	23.0002i	−0.633780	+	1.09774i	0.352992	+	0.935626i	$0.385164\pi$
$439$	−13.2792	+	23.0002i	−0.633780	+	1.09774i	−0.986772	+	0.162113i	$0.948169\pi$
$440$	47.0573			2.24337
$441$		0			0
$442$	−16.8801			−0.802902
$443$	13.8041	−	23.9094i	0.655853	−	1.13597i	−0.325826	−	0.945430i	$-0.605642\pi$
$443$	13.8041	−	23.9094i	0.655853	−	1.13597i	0.981679	−	0.190542i	$-0.0610244\pi$
$444$		0			0
$445$	6.91419	+	11.9757i	0.327764	+	0.567704i
$446$	73.3330			3.47242
$447$		0			0
$448$	−9.43309	−	7.37983i	−0.445672	−	0.348664i
$449$	−15.6315			−0.737695			−0.368847	−	0.929490i	$-0.620247\pi$
$449$	−15.6315			−0.737695			−0.368847	+	0.929490i	$0.620247\pi$
$450$		0			0
$451$	−11.6652	+	20.2047i	−0.549292	+	0.951402i
$452$	29.3643			1.38118
$453$		0			0
$454$	2.68047	−	4.64272i	0.125801	−	0.217894i
$455$	−23.9134	+	9.64356i	−1.12108	+	0.452097i
$456$		0			0
$457$	16.4677	−	28.5230i	0.770328	−	1.33425i	−0.167055	−	0.985948i	$-0.553426\pi$
$457$	16.4677	−	28.5230i	0.770328	−	1.33425i	0.937383	−	0.348300i	$-0.113241\pi$
$458$	−20.2919	+	35.1466i	−0.948178	+	1.64229i
$459$		0			0
$460$	32.9700	+	57.1057i	1.53723	+	2.66256i
$461$	−17.4591	−	30.2400i	−0.813149	−	1.40842i	−0.910649	−	0.413180i	$-0.864418\pi$
$461$	−17.4591	−	30.2400i	−0.813149	−	1.40842i	0.0974999	−	0.995236i	$-0.468915\pi$
$462$		0			0
$463$	−1.55128	+	2.68689i	−0.0720940	+	0.124871i	−0.899819	−	0.436264i	$-0.856302\pi$
$463$	−1.55128	+	2.68689i	−0.0720940	+	0.124871i	0.827725	+	0.561134i	$0.189635\pi$
$464$	20.2421			0.939718
$465$		0			0
$466$	−75.6868			−3.50613
$467$	5.26376	+	9.11710i	0.243578	+	0.421889i	0.961731	−	0.273996i	$-0.0883455\pi$
$467$	5.26376	+	9.11710i	0.243578	+	0.421889i	−0.718153	+	0.695885i	$0.755012\pi$
$468$		0			0
$469$	1.23008	−	8.71134i	0.0567998	−	0.402252i
$470$	17.2098	+	29.8082i	0.793828	+	1.37495i
$471$		0			0
$472$	16.1168	+	27.9152i	0.741837	+	1.28490i
$473$	−1.23297	−	2.13556i	−0.0566919	−	0.0981933i
$474$		0			0
$475$	−0.786102	−	1.36157i	−0.0360688	−	0.0624730i
$476$	−14.9518	−	11.6973i	−0.685315	−	0.536145i
$477$		0			0
$478$	−22.9256	−	39.7083i	−1.04859	−	1.81622i
$479$	−16.9781			−0.775748			−0.387874	−	0.921712i	$-0.626790\pi$
$479$	−16.9781			−0.775748			−0.387874	+	0.921712i	$0.626790\pi$
$480$		0			0
$481$	30.6299			1.39660
$482$	−34.1626	+	59.1714i	−1.55607	+	2.69518i
$483$		0			0
$484$	5.30512	+	9.18873i	0.241142	+	0.417669i
$485$	−1.50930	−	2.61418i	−0.0685337	−	0.118704i
$486$		0			0
$487$	6.60283	−	11.4364i	0.299203	−	0.518235i	−0.676751	−	0.736212i	$-0.736613\pi$
$487$	6.60283	−	11.4364i	0.299203	−	0.518235i	0.975954	+	0.217977i	$0.0699459\pi$
$488$	−24.8556	+	43.0511i	−1.12516	+	1.94883i
$489$		0			0
$490$	−39.7356	−	11.4500i	−1.79507	−	0.517257i
$491$	7.89168	−	13.6688i	0.356147	−	0.616864i	−0.631167	−	0.775647i	$-0.717424\pi$
$491$	7.89168	−	13.6688i	0.356147	−	0.616864i	0.987314	+	0.158783i	$0.0507570\pi$
$492$		0			0
$493$	3.57712			0.161105
$494$	40.7560	−	70.5915i	1.83370	−	3.17606i
$495$		0			0
$496$	53.8085			2.41608
$497$	0.333915	+	0.261233i	0.0149781	+	0.0117179i
$498$		0			0
$499$	42.9459			1.92252			0.961261	−	0.275640i	$-0.0888897\pi$
$499$	42.9459			1.92252			0.961261	+	0.275640i	$0.0888897\pi$
$500$	−25.6545	−	44.4348i	−1.14730	−	1.98719i
$501$		0			0
$502$	11.4077	−	19.7587i	0.509149	−	0.881873i
$503$	37.7173			1.68173			0.840866	−	0.541243i	$-0.182046\pi$
$503$	37.7173			1.68173			0.840866	+	0.541243i	$0.182046\pi$
$504$		0			0
$505$	−41.4676			−1.84528
$506$	23.5287	−	40.7529i	1.04598	−	1.81169i
$507$		0			0
$508$	13.1450	+	22.7677i	0.583213	+	1.01015i
$509$	−34.9928			−1.55103			−0.775513	−	0.631331i	$-0.782509\pi$
$509$	−34.9928			−1.55103			−0.775513	+	0.631331i	$0.782509\pi$
$510$		0			0
$511$	−0.934035	+	0.376668i	−0.0413193	+	0.0166628i
$512$	47.6386			2.10535
$513$		0			0
$514$	11.8976	−	20.6073i	0.524782	−	0.908949i
$515$	−30.9034			−1.36177
$516$		0			0
$517$	8.61241	−	14.9171i	0.378773	−	0.656055i
$518$	38.6897	+	30.2683i	1.69993	+	1.32991i
$519$		0			0
$520$	−33.9715	+	58.8403i	−1.48975	+	2.58032i
$521$	−6.97005	+	12.0725i	−0.305363	+	0.528905i	−0.977342	−	0.211665i	$-0.932111\pi$
$521$	−6.97005	+	12.0725i	−0.305363	+	0.528905i	0.671979	+	0.740570i	$0.265445\pi$
$522$		0			0
$523$	−13.4103	−	23.2274i	−0.586393	−	1.01566i	−0.994700	−	0.102817i	$-0.967214\pi$
$523$	−13.4103	−	23.2274i	−0.586393	−	1.01566i	0.408308	−	0.912844i	$-0.366119\pi$
$524$	16.7234	+	28.9658i	0.730566	+	1.26538i
$525$		0			0
$526$	−0.329379	+	0.570501i	−0.0143616	+	0.0248750i
$527$	9.50885			0.414212
$528$		0			0
$529$	14.8473			0.645535
$530$	21.9656	+	38.0455i	0.954123	+	1.65259i
$531$		0			0
$532$	85.0179	−	34.2851i	3.68599	−	1.48645i
$533$	−16.8426	−	29.1722i	−0.729533	−	1.26359i
$534$		0			0
$535$	−9.29112	−	16.0927i	−0.401690	−	0.695748i
$536$	−11.5911	−	20.0763i	−0.500658	−	0.867166i
$537$		0			0
$538$	1.26709	+	2.19466i	0.0546280	+	0.0946186i
$539$	4.98026	+	20.0860i	0.214515	+	0.865167i
$540$		0			0
$541$	−11.6251	−	20.1353i	−0.499802	−	0.865683i	0.500198	−	0.865911i	$-0.333261\pi$
$541$	−11.6251	−	20.1353i	−0.499802	−	0.865683i	−1.00000		0.000228285i	$0.999927\pi$
$542$	−36.3497			−1.56135
$543$		0			0
$544$	−12.8927			−0.552770
$545$	−6.26507	+	10.8514i	−0.268366	+	0.464824i
$546$		0			0
$547$	−7.87127	−	13.6334i	−0.336551	−	0.582924i	0.647230	−	0.762294i	$-0.275927\pi$
$547$	−7.87127	−	13.6334i	−0.336551	−	0.582924i	−0.983782	+	0.179371i	$0.942594\pi$
$548$	20.8392	+	36.0946i	0.890208	+	1.54189i
$549$		0			0
$550$	0.814692	−	1.41109i	0.0347386	−	0.0601690i
$551$	−8.63677	+	14.9593i	−0.367939	+	0.637288i
$552$		0			0
$553$	−19.5186	+	7.87126i	−0.830015	+	0.334720i
$554$	32.8837	−	56.9563i	1.39710	−	2.41984i
$555$		0			0
$556$	39.2973			1.66658
$557$	−2.06405	+	3.57504i	−0.0874565	+	0.151479i	−0.906435	−	0.422345i	$-0.861207\pi$
$557$	−2.06405	+	3.57504i	−0.0874565	+	0.151479i	0.818979	+	0.573824i	$0.194541\pi$
$558$		0			0
$559$	3.56040			0.150589
$560$	−48.4556	+	19.5407i	−2.04762	+	0.825744i
$561$		0			0
$562$	76.0198			3.20670
$563$	0.342707	+	0.593585i	0.0144434	+	0.0250166i	0.873157	−	0.487440i	$-0.162069\pi$
$563$	0.342707	+	0.593585i	0.0144434	+	0.0250166i	−0.858713	+	0.512456i	$0.828736\pi$
$564$		0			0
$565$	7.14081	−	12.3683i	0.300416	−	0.520336i
$566$	7.96104			0.334627
$567$		0			0
$568$	1.11714			0.0468740
$569$	−9.25223	+	16.0253i	−0.387874	+	0.671817i	−0.992163	−	0.124948i	$-0.960124\pi$
$569$	−9.25223	+	16.0253i	−0.387874	+	0.671817i	0.604290	+	0.796765i	$0.293457\pi$
$570$		0			0
$571$	−17.2741	−	29.9197i	−0.722901	−	1.25210i	−0.959832	−	0.280574i	$-0.909475\pi$
$571$	−17.2741	−	29.9197i	−0.722901	−	1.25210i	0.236932	−	0.971526i	$-0.423858\pi$
$572$	59.2389			2.47690
$573$		0			0
$574$	7.55332	−	53.4921i	0.315269	−	2.23272i
$575$	1.31048			0.0546509
$576$		0			0
$577$	−0.246628	+	0.427172i	−0.0102673	+	0.0177834i	−0.871113	−	0.491082i	$-0.836602\pi$
$577$	−0.246628	+	0.427172i	−0.0102673	+	0.0177834i	0.860846	+	0.508865i	$0.169935\pi$
$578$	37.9408			1.57813
$579$		0			0
$580$	12.5426	−	21.7244i	0.520802	−	0.902056i
$581$	1.58992	−	11.2597i	0.0659612	−	0.467133i
$582$		0			0
$583$	10.9924	−	19.0394i	0.455258	−	0.788529i
$584$	−1.32689	+	2.29824i	−0.0549071	+	0.0951019i
$585$		0			0
$586$	−22.0138	−	38.1290i	−0.909380	−	1.57509i
$587$	18.8206	+	32.5983i	0.776810	+	1.34547i	0.933771	+	0.357870i	$0.116497\pi$
$587$	18.8206	+	32.5983i	0.776810	+	1.34547i	−0.156961	+	0.987605i	$0.550170\pi$
$588$		0			0
$589$	−22.9586	+	39.7655i	−0.945994	+	1.63851i
$590$	27.3137			1.12449
$591$		0			0
$592$	62.0652			2.55086
$593$	−12.5475	−	21.7328i	−0.515262	−	0.892460i	−0.999843	−	0.0177137i	$-0.994361\pi$
$593$	−12.5475	−	21.7328i	−0.515262	−	0.892460i	0.484581	−	0.874746i	$-0.338972\pi$
$594$		0			0
$595$	−8.56290	+	3.45316i	−0.351044	+	0.141566i
$596$	−31.5755	−	54.6904i	−1.29338	−	2.24021i
$597$		0			0
$598$	33.9715	+	58.8403i	1.38920	+	2.40616i
$599$	0.269218	+	0.466300i	0.0110000	+	0.0190525i	0.871473	−	0.490444i	$-0.163165\pi$
$599$	0.269218	+	0.466300i	0.0110000	+	0.0190525i	−0.860473	+	0.509496i	$0.829832\pi$
$600$		0			0
$601$	18.0520	+	31.2670i	0.736357	+	1.27541i	0.954125	+	0.299408i	$0.0967890\pi$
$601$	18.0520	+	31.2670i	0.736357	+	1.27541i	−0.217768	+	0.976001i	$0.569878\pi$
$602$	4.49726	+	3.51836i	0.183295	+	0.143398i
$603$		0			0
$604$	21.1755	+	36.6770i	0.861619	+	1.49237i
$605$	5.16040			0.209800
$606$		0			0
$607$	−22.3536			−0.907305			−0.453652	−	0.891179i	$-0.649879\pi$
$607$	−22.3536			−0.907305			−0.453652	+	0.891179i	$0.649879\pi$
$608$	31.1287	−	53.9166i	1.26244	−	2.18660i
$609$		0			0
$610$	21.0618	+	36.4801i	0.852767	+	1.47704i
$611$	12.4349	+	21.5378i	0.503061	+	0.871328i
$612$		0			0
$613$	12.2687	−	21.2500i	0.495529	−	0.858281i	−0.504458	−	0.863436i	$-0.668308\pi$
$613$	12.2687	−	21.2500i	0.495529	−	0.858281i	0.999987	+	0.00515549i	$0.00164105\pi$
$614$	31.3584	−	54.3143i	1.26552	−	2.19195i
$615$		0			0
$616$	42.9480	+	33.5997i	1.73042	+	1.35377i
$617$	−15.0763	+	26.1130i	−0.606950	+	1.05127i	0.384790	+	0.923004i	$0.374274\pi$
$617$	−15.0763	+	26.1130i	−0.606950	+	1.05127i	−0.991740	+	0.128264i	$0.959059\pi$
$618$		0			0
$619$	23.6094			0.948942			0.474471	−	0.880271i	$-0.342639\pi$
$619$	23.6094			0.948942			0.474471	+	0.880271i	$0.342639\pi$
$620$	33.3412	−	57.7487i	1.33902	−	2.31924i
$621$		0			0
$622$	−56.8224			−2.27837
$623$	−2.24046	+	15.8668i	−0.0897620	+	0.635689i
$624$		0			0
$625$	−26.0197			−1.04079
$626$	−3.21021	−	5.56025i	−0.128306	−	0.222232i
$627$		0			0
$628$	−6.87364	+	11.9055i	−0.274288	+	0.475081i
$629$	10.9679			0.437320
$630$		0			0
$631$	−7.41460			−0.295171			−0.147585	−	0.989049i	$-0.547150\pi$
$631$	−7.41460			−0.295171			−0.147585	+	0.989049i	$0.547150\pi$
$632$	−27.7281	+	48.0265i	−1.10297	+	1.91039i
$633$		0			0
$634$	25.2000	+	43.6476i	1.00082	+	1.73347i
$635$	12.7864			0.507412
$636$		0			0
$637$	−28.7108	−	8.27315i	−1.13756	−	0.327794i
$638$	−17.9018			−0.708738
$639$		0			0
$640$	5.88824	−	10.1987i	0.232753	−	0.403140i
$641$	18.6918			0.738280			0.369140	−	0.929374i	$-0.379652\pi$
$641$	18.6918			0.738280			0.369140	+	0.929374i	$0.379652\pi$
$642$		0			0
$643$	−18.2102	+	31.5410i	−0.718141	+	1.24386i	0.243594	+	0.969877i	$0.421673\pi$
$643$	−18.2102	+	31.5410i	−0.718141	+	1.24386i	−0.961735	+	0.273980i	$0.911660\pi$
$644$	−10.6835	+	75.6599i	−0.420989	+	2.98142i
$645$		0			0
$646$	14.5939	−	25.2773i	0.574188	−	0.994522i
$647$	−8.33593	+	14.4383i	−0.327719	+	0.567626i	−0.982059	−	0.188574i	$-0.939613\pi$
$647$	−8.33593	+	14.4383i	−0.327719	+	0.567626i	0.654340	+	0.756201i	$0.272947\pi$
$648$		0			0
$649$	−6.83440	−	11.8375i	−0.268274	−	0.464664i
$650$	1.17628	+	2.03737i	0.0461375	+	0.0799124i
$651$		0			0
$652$	2.82780	−	4.89790i	0.110745	−	0.191817i
$653$	8.61070			0.336963			0.168481	−	0.985705i	$-0.446114\pi$
$653$	8.61070			0.336963			0.168481	+	0.985705i	$0.446114\pi$
$654$		0			0
$655$	16.2672			0.635613
$656$	−34.1280	−	59.1113i	−1.33247	−	2.30791i
$657$		0			0
$658$	−5.57662	+	39.4933i	−0.217399	+	1.53961i
$659$	7.34515	+	12.7222i	0.286126	+	0.495586i	0.972882	−	0.231303i	$-0.0742989\pi$
$659$	7.34515	+	12.7222i	0.286126	+	0.495586i	−0.686755	+	0.726889i	$0.740966\pi$
$660$		0			0
$661$	−4.06201	−	7.03561i	−0.157994	−	0.273654i	0.776151	−	0.630547i	$-0.217169\pi$
$661$	−4.06201	−	7.03561i	−0.157994	−	0.273654i	−0.934145	+	0.356893i	$0.883836\pi$
$662$	3.33397	+	5.77461i	0.129579	+	0.224437i
$663$		0			0
$664$	−14.9819	−	25.9494i	−0.581411	−	1.00703i
$665$	6.23375	−	44.1470i	0.241735	−	1.71195i
$666$		0			0
$667$	−7.19902	−	12.4691i	−0.278747	−	0.482805i
$668$	−67.4561			−2.60996
$669$		0			0
$670$	−19.6438			−0.758906
$671$	10.5401	−	18.2560i	0.406896	−	0.704764i
$672$		0			0
$673$	6.57582	+	11.3897i	0.253479	+	0.439039i	0.964481	−	0.264151i	$-0.0850917\pi$
$673$	6.57582	+	11.3897i	0.253479	+	0.439039i	−0.711002	+	0.703190i	$0.751758\pi$
$674$	−31.2451	−	54.1180i	−1.20351	−	2.08455i
$675$		0			0
$676$	−12.2515	+	21.2202i	−0.471210	+	0.816160i
$677$	5.40967	−	9.36982i	0.207910	−	0.360111i	−0.743146	−	0.669130i	$-0.766667\pi$
$677$	5.40967	−	9.36982i	0.207910	−	0.360111i	0.951056	+	0.309018i	$0.100000\pi$
$678$		0			0
$679$	0.489070	−	3.46356i	0.0187688	−	0.132919i
$680$	−12.1645	+	21.0695i	−0.466486	+	0.807977i
$681$		0			0
$682$	−47.5873			−1.82221
$683$	0.684640	−	1.18583i	0.0261970	−	0.0453746i	−0.852630	−	0.522516i	$-0.824994\pi$
$683$	0.684640	−	1.18583i	0.0261970	−	0.0453746i	0.878827	+	0.477141i	$0.158327\pi$
$684$		0			0
$685$	20.2708			0.774506
$686$	−28.0902	−	38.8219i	−1.07249	−	1.48223i
$687$		0			0
$688$	7.21440			0.275047
$689$	15.8711	+	27.4896i	0.604642	+	1.04727i
$690$		0			0
$691$	17.9215	−	31.0409i	0.681765	−	1.18085i	−0.292677	−	0.956211i	$-0.594546\pi$
$691$	17.9215	−	31.0409i	0.681765	−	1.18085i	0.974442	−	0.224640i	$-0.0721207\pi$
$692$	−25.5552			−0.971462
$693$		0			0
$694$	93.7724			3.55955
$695$	9.55634	−	16.5521i	0.362493	−	0.627855i
$696$		0			0
$697$	−6.03097	−	10.4459i	−0.228439	−	0.395668i
$698$	−91.3181			−3.45644
$699$		0			0
$700$	−0.369922	+	2.61976i	−0.0139817	+	0.0990177i
$701$	−29.6235			−1.11886			−0.559431	−	0.828877i	$-0.688980\pi$
$701$	−29.6235			−1.11886			−0.559431	+	0.828877i	$0.688980\pi$
$702$		0			0
$703$	−26.4815	+	45.8673i	−0.998769	+	1.72992i
$704$	13.3828			0.504382
$705$		0			0
$706$	3.78039	−	6.54782i	0.142277	−	0.246431i
$707$	−37.8464	−	29.6085i	−1.42336	−	1.11354i
$708$		0			0
$709$	7.63863	−	13.2305i	0.286875	−	0.496882i	−0.686187	−	0.727425i	$-0.740717\pi$
$709$	7.63863	−	13.2305i	0.286875	−	0.496882i	0.973062	+	0.230543i	$0.0740503\pi$
$710$	0.473313	−	0.819802i	0.0177631	−	0.0307666i
$711$		0			0
$712$	21.1119	+	36.5669i	0.791202	+	1.37040i
$713$	−19.1368	−	33.1458i	−0.716677	−	1.24132i
$714$		0			0
$715$	14.4057	−	24.9514i	0.538743	−	0.933131i
$716$	−28.4324			−1.06257
$717$		0			0
$718$	1.01794			0.0379893
$719$	1.00538	+	1.74138i	0.0374945	+	0.0649424i	0.884164	−	0.467177i	$-0.154729\pi$
$719$	1.00538	+	1.74138i	0.0374945	+	0.0649424i	−0.846669	+	0.532120i	$0.821396\pi$
$720$		0			0
$721$	−28.2047	−	22.0655i	−1.05040	−	0.821763i
$722$	45.8923	+	79.4877i	1.70793	+	2.95823i
$723$		0			0
$724$	−29.9075	−	51.8014i	−1.11150	−	1.92518i
$725$	−0.249270	−	0.431748i	−0.00925765	−	0.0160347i
$726$		0			0
$727$	−10.2515	−	17.7561i	−0.380206	−	0.658535i	0.610886	−	0.791719i	$-0.290813\pi$
$727$	−10.2515	−	17.7561i	−0.380206	−	0.658535i	−0.991091	+	0.133183i	$0.957480\pi$
$728$	−73.0178	+	29.4458i	−2.70622	+	1.09134i
$729$		0			0
$730$	1.12436	+	1.94745i	0.0416146	+	0.0720785i
$731$	1.27490			0.0471540
$732$		0			0
$733$	4.62855			0.170959			0.0854797	−	0.996340i	$-0.472758\pi$
$733$	4.62855			0.170959			0.0854797	+	0.996340i	$0.472758\pi$
$734$	−11.9424	+	20.6849i	−0.440803	+	0.763493i
$735$		0			0
$736$	25.9468	+	44.9412i	0.956412	+	1.65655i
$737$	4.91524	+	8.51345i	0.181055	+	0.313597i
$738$		0			0
$739$	11.6640	−	20.2026i	0.429066	−	0.743164i	−0.567725	−	0.823219i	$-0.692176\pi$
$739$	11.6640	−	20.2026i	0.429066	−	0.743164i	0.996790	+	0.0800546i	$0.0255095\pi$
$740$	38.4573	−	66.6099i	1.41372	−	2.44863i
$741$		0			0
$742$	−7.11767	+	50.4069i	−0.261298	+	1.85049i
$743$	−26.1283	+	45.2555i	−0.958553	+	1.66026i	−0.232535	+	0.972588i	$0.574702\pi$
$743$	−26.1283	+	45.2555i	−0.958553	+	1.66026i	−0.726018	+	0.687675i	$0.758631\pi$
$744$		0			0
$745$	−30.7142			−1.12528
$746$	−27.8458	+	48.2303i	−1.01951	+	1.76584i
$747$		0			0
$748$	21.2122			0.775594
$749$	3.01067	−	21.3214i	0.110008	−	0.779067i
$750$		0			0
$751$	−6.18756			−0.225787			−0.112894	−	0.993607i	$-0.536012\pi$
$751$	−6.18756			−0.225787			−0.112894	+	0.993607i	$0.536012\pi$
$752$	25.1967	+	43.6419i	0.918829	+	1.59146i
$753$		0			0
$754$	12.9236	−	22.3843i	0.470649	−	0.815188i
$755$	20.5979			0.749633
$756$		0			0
$757$	20.9175			0.760260			0.380130	−	0.924933i	$-0.375879\pi$
$757$	20.9175			0.760260			0.380130	+	0.924933i	$0.375879\pi$
$758$	−23.6026	+	40.8810i	−0.857287	+	1.48486i
$759$		0			0
$760$	−58.7409	−	101.742i	−2.13076	−	3.69058i
$761$	−33.9143			−1.22939			−0.614696	−	0.788764i	$-0.710721\pi$
$761$	−33.9143			−1.22939			−0.614696	+	0.788764i	$0.710721\pi$
$762$		0			0
$763$	−13.4661	+	5.43045i	−0.487504	+	0.196595i
$764$	113.289			4.09864
$765$		0			0
$766$	−8.09800	+	14.0261i	−0.292593	+	0.506785i
$767$	19.7355			0.712606
$768$		0			0
$769$	4.25392	−	7.36800i	0.153400	−	0.265697i	−0.779075	−	0.626931i	$-0.784311\pi$
$769$	4.25392	−	7.36800i	0.153400	−	0.265697i	0.932475	+	0.361234i	$0.117644\pi$
$770$	42.8532	−	17.2814i	1.54432	−	0.622778i
$771$		0			0
$772$	1.85137	−	3.20667i	0.0666324	−	0.115411i
$773$	22.7870	−	39.4682i	0.819590	−	1.41957i	−0.0863952	−	0.996261i	$-0.527535\pi$
$773$	22.7870	−	39.4682i	0.819590	−	1.41957i	0.905985	−	0.423310i	$-0.139132\pi$
$774$		0			0
$775$	−0.662620	−	1.14769i	−0.0238020	−	0.0412263i
$776$	−4.60852	−	7.98219i	−0.165436	−	0.286544i
$777$		0			0
$778$	29.2642	−	50.6870i	1.04917	−	1.81722i
$779$	58.2458			2.08687
$780$		0			0
$781$	−0.473726			−0.0169513
$782$	12.1645	+	21.0695i	0.435000	+	0.753442i
$783$		0			0
$784$	−58.1765	−	16.7638i	−2.07773	−	0.598707i
$785$	3.34307	+	5.79036i	0.119319	+	0.206667i
$786$		0			0
$787$	4.16234	+	7.20939i	0.148372	+	0.256987i	0.930626	−	0.365972i	$-0.119264\pi$
$787$	4.16234	+	7.20939i	0.148372	+	0.256987i	−0.782254	+	0.622959i	$0.785930\pi$
$788$	34.9702	+	60.5702i	1.24576	+	2.15772i
$789$		0			0
$790$	23.4959	+	40.6961i	0.835947	+	1.44790i
$791$	15.3484	−	6.18953i	0.545725	−	0.220074i
$792$		0			0
$793$	15.2181	+	26.3586i	0.540412	+	0.936020i
$794$	54.8919			1.94804
$795$		0			0
$796$	12.8232			0.454508
$797$	19.6387	−	34.0152i	0.695637	−	1.20488i	−0.274329	−	0.961636i	$-0.588456\pi$
$797$	19.6387	−	34.0152i	0.695637	−	1.20488i	0.969966	−	0.243242i	$-0.0782111\pi$
$798$		0			0
$799$	4.45267	+	7.71224i	0.157524	+	0.272840i
$800$	0.898421	+	1.55611i	0.0317640	+	0.0550168i
$801$		0			0
$802$	−5.52975	+	9.57781i	−0.195262	+	0.338204i
$803$	0.562673	−	0.974578i	0.0198563	−	0.0343921i
$804$		0			0
$805$	29.2700	+	22.8989i	1.03163	+	0.807080i
$806$	34.3540	−	59.5029i	1.21007	−	2.09590i
$807$		0			0
$808$	−126.618			−4.45440
$809$	−11.4525	+	19.8364i	−0.402649	+	0.697409i	−0.994045	−	0.108973i	$-0.965244\pi$
$809$	−11.4525	+	19.8364i	−0.402649	+	0.697409i	0.591395	+	0.806382i	$0.298577\pi$
$810$		0			0
$811$	−17.0254			−0.597842			−0.298921	−	0.954278i	$-0.596627\pi$
$811$	−17.0254			−0.597842			−0.298921	+	0.954278i	$0.596627\pi$
$812$	26.9588	−	10.8717i	0.946070	−	0.381521i
$813$		0			0
$814$	−54.8893			−1.92387
$815$	−1.37533	−	2.38214i	−0.0481758	−	0.0834429i
$816$		0			0
$817$	−3.07819	+	5.33158i	−0.107692	+	0.186528i
$818$	−91.3996			−3.19571
$819$		0			0
$820$	−84.5864			−2.95389
$821$	−16.3565	+	28.3303i	−0.570845	+	0.988733i	0.425634	+	0.904895i	$0.360051\pi$
$821$	−16.3565	+	28.3303i	−0.570845	+	0.988733i	−0.996479	+	0.0838376i	$0.973282\pi$
$822$		0			0
$823$	13.9457	+	24.1547i	0.486118	+	0.841981i	0.999873	−	0.0159561i	$-0.00507920\pi$
$823$	13.9457	+	24.1547i	0.486118	+	0.841981i	−0.513755	+	0.857937i	$0.671746\pi$
$824$	−94.3610			−3.28722
$825$		0			0
$826$	24.9285	+	19.5024i	0.867375	+	0.678577i
$827$	−17.5753			−0.611153			−0.305576	−	0.952168i	$-0.598849\pi$
$827$	−17.5753			−0.611153			−0.305576	+	0.952168i	$0.598849\pi$
$828$		0			0
$829$	0.997731	−	1.72812i	0.0346526	−	0.0600201i	−0.848179	−	0.529710i	$-0.822301\pi$
$829$	0.997731	−	1.72812i	0.0346526	−	0.0600201i	0.882832	+	0.469690i	$0.155634\pi$
$830$	−25.3904			−0.881312
$831$		0			0
$832$	−9.66123	+	16.7337i	−0.334943	+	0.580138i
$833$	−10.2807	−	2.96244i	−0.356207	−	0.102642i
$834$		0			0
$835$	−16.4040	+	28.4126i	−0.567684	+	0.983257i
$836$	−51.2157	+	88.7082i	−1.77133	+	3.06804i
$837$		0			0
$838$	4.85003	+	8.40049i	0.167541	+	0.290190i
$839$	11.3262	+	19.6175i	0.391023	+	0.677272i	0.992585	−	0.121555i	$-0.0387879\pi$
$839$	11.3262	+	19.6175i	0.391023	+	0.677272i	−0.601562	+	0.798826i	$0.705455\pi$
$840$		0			0
$841$	11.7613	−	20.3712i	0.405563	−	0.702455i
$842$	−63.4750			−2.18749
$843$		0			0
$844$	−43.0761			−1.48274
$845$	5.95863	+	10.3206i	0.204983	+	0.355041i
$846$		0			0
$847$	4.70976	+	3.68460i	0.161829	+	0.126605i
$848$	32.1596	+	55.7020i	1.10436	+	1.91281i
$849$		0			0
$850$	0.421200	+	0.729541i	0.0144471	+	0.0250230i
$851$	−22.0732	−	38.2319i	−0.756659	−	1.31057i
$852$		0			0
$853$	6.65119	+	11.5202i	0.227732	+	0.394444i	0.957136	−	0.289640i	$-0.0935355\pi$
$853$	6.65119	+	11.5202i	0.227732	+	0.394444i	−0.729403	+	0.684084i	$0.760202\pi$
$854$	−6.82481	+	48.3329i	−0.233540	+	1.65392i
$855$		0			0
$856$	−28.3697	−	49.1377i	−0.969656	−	1.67949i
$857$	24.3329			0.831197			0.415599	−	0.909548i	$-0.363572\pi$
$857$	24.3329			0.831197			0.415599	+	0.909548i	$0.363572\pi$
$858$		0			0
$859$	15.6185			0.532897			0.266448	−	0.963849i	$-0.414150\pi$
$859$	15.6185			0.532897			0.266448	+	0.963849i	$0.414150\pi$
$860$	4.47024	−	7.74268i	0.152434	−	0.264023i
$861$		0			0
$862$	31.3807	+	54.3530i	1.06883	+	1.85127i
$863$	18.3558	+	31.7931i	0.624838	+	1.08225i	0.988572	+	0.150748i	$0.0481682\pi$
$863$	18.3558	+	31.7931i	0.624838	+	1.08225i	−0.363735	+	0.931503i	$0.618498\pi$
$864$		0			0
$865$	−6.21451	+	10.7638i	−0.211300	+	0.365982i
$866$	11.1264	−	19.2715i	0.378091	−	0.654872i
$867$		0			0
$868$	71.6632	−	28.8996i	2.43241	−	0.980916i
$869$	11.7582	−	20.3658i	0.398870	−	0.690863i
$870$		0			0
$871$	−14.1936			−0.480931
$872$	−19.1299	+	33.1339i	−0.647820	+	1.12206i
$873$		0			0
$874$	−117.482			−3.97388
$875$	−22.7754	−	17.8180i	−0.769950	−	0.602358i
$876$		0			0
$877$	−50.1983			−1.69508			−0.847538	−	0.530734i	$-0.821916\pi$
$877$	−50.1983			−1.69508			−0.847538	+	0.530734i	$0.821916\pi$
$878$	34.3581	+	59.5099i	1.15953	+	2.00836i
$879$		0			0
$880$	29.1902	−	50.5589i	0.984001	−	1.70434i
$881$	−51.6426			−1.73989			−0.869943	−	0.493153i	$-0.835844\pi$
$881$	−51.6426			−1.73989			−0.869943	+	0.493153i	$0.835844\pi$
$882$		0			0
$883$	−4.77954			−0.160844			−0.0804222	−	0.996761i	$-0.525627\pi$
$883$	−4.77954			−0.160844			−0.0804222	+	0.996761i	$0.525627\pi$
$884$	−15.3134	+	26.5236i	−0.515046	+	0.892086i
$885$		0			0
$886$	−35.7163	−	61.8625i	−1.19991	−	2.07831i
$887$	31.1565			1.04613			0.523066	−	0.852292i	$-0.324788\pi$
$887$	31.1565			1.04613			0.523066	+	0.852292i	$0.324788\pi$
$888$		0			0
$889$	11.6698	+	9.12967i	0.391392	+	0.306199i
$890$	35.7791			1.19932
$891$		0			0
$892$	66.5270	−	115.228i	2.22749	−	3.85812i
$893$	−43.0029			−1.43904
$894$		0			0
$895$	−6.91419	+	11.9757i	−0.231116	+	0.400304i
$896$	12.6561	−	5.10382i	0.422811	−	0.170507i
$897$		0			0
$898$	−20.2222	+	35.0258i	−0.674823	+	1.16883i
$899$	−7.28009	+	12.6095i	−0.242805	+	0.420550i
$900$		0			0
$901$	5.68312	+	9.84345i	0.189332	+	0.327933i
$902$	30.1821	+	52.2769i	1.00495	+	1.74063i
$903$		0			0
$904$	21.8039	−	37.7655i	0.725187	−	1.25606i
$905$	−29.0917			−0.967040
$906$		0			0
$907$	−22.2370			−0.738368			−0.369184	−	0.929356i	$-0.620363\pi$
$907$	−22.2370			−0.738368			−0.369184	+	0.929356i	$0.620363\pi$
$908$	−4.86340	−	8.42366i	−0.161398	−	0.279549i
$909$		0			0
$910$	−9.32784	+	66.0592i	−0.309215	+	2.18984i
$911$	1.01685	+	1.76123i	0.0336897	+	0.0583523i	0.882379	−	0.470540i	$-0.155941\pi$
$911$	1.01685	+	1.76123i	0.0336897	+	0.0583523i	−0.848689	+	0.528892i	$0.822608\pi$
$912$		0			0
$913$	6.35314	+	11.0040i	0.210258	+	0.364178i
$914$	−42.6081	−	73.7993i	−1.40935	−	2.44107i
$915$		0			0
$916$	36.8172	+	63.7693i	1.21647	+	2.10700i
$917$	14.8467	+	11.6151i	0.490280	+	0.383563i
$918$		0			0
$919$	23.8031	+	41.2282i	0.785193	+	1.35999i	0.928884	+	0.370371i	$0.120769\pi$
$919$	23.8031	+	41.2282i	0.785193	+	1.35999i	−0.143691	+	0.989623i	$0.545897\pi$
$920$	97.9249			3.22849
$921$		0			0
$922$	−90.3460			−2.97539
$923$	0.341991	−	0.592345i	0.0112568	−	0.0194973i
$924$		0			0
$925$	−0.764295	−	1.32380i	−0.0251299	−	0.0435262i
$926$	4.01373	+	6.95198i	0.131899	+	0.228456i
$927$		0			0
$928$	9.87080	−	17.0967i	0.324025	−	0.561228i
$929$	−15.6050	+	27.0287i	−0.511985	+	0.886784i	0.487919	+	0.872889i	$0.337756\pi$
$929$	−15.6050	+	27.0287i	−0.511985	+	0.886784i	−0.999903	+	0.0138945i	$0.995577\pi$
$930$		0			0
$931$	37.2111	−	35.8409i	1.21954	−	1.17464i
$932$	−68.6624	+	118.927i	−2.24911	+	3.89557i
$933$		0			0
$934$	27.2386			0.891273
$935$	5.15838	−	8.93458i	0.168697	−	0.292192i
$936$		0			0
$937$	−18.0157			−0.588548			−0.294274	−	0.955721i	$-0.595078\pi$
$937$	−18.0157			−0.588548			−0.294274	+	0.955721i	$0.595078\pi$
$938$	−17.9284	−	14.0260i	−0.585383	−	0.457965i
$939$		0			0
$940$	62.4502			2.03690
$941$	21.8559	+	37.8555i	0.712481	+	1.23405i	0.963923	+	0.266181i	$0.0857618\pi$
$941$	21.8559	+	37.8555i	0.712481	+	1.23405i	−0.251442	+	0.967872i	$0.580905\pi$
$942$		0			0
$943$	−24.2749	+	42.0453i	−0.790499	+	1.36918i
$944$	39.9898			1.30156
$945$		0			0
$946$	−6.38028			−0.207441
$947$	22.2393	−	38.5197i	0.722681	−	1.25172i	−0.237240	−	0.971451i	$-0.576243\pi$
$947$	22.2393	−	38.5197i	0.722681	−	1.25172i	0.959921	−	0.280270i	$-0.0904239\pi$
$948$		0			0
$949$	0.812405	+	1.40713i	0.0263718	+	0.0456773i
$950$	−4.06787			−0.131979
$951$		0			0
$952$	−26.1461	+	10.5439i	−0.847400	+	0.341731i
$953$	52.3118			1.69454			0.847272	−	0.531159i	$-0.178243\pi$
$953$	52.3118			1.69454			0.847272	+	0.531159i	$0.178243\pi$
$954$		0			0
$955$	27.5496	−	47.7172i	0.891483	−	1.54409i
$956$	−83.1916			−2.69061
$957$		0			0
$958$	−21.9642	+	38.0432i	−0.709633	+	1.22912i
$959$	18.5006	+	14.4736i	0.597415	+	0.467378i
$960$		0			0
$961$	−3.85225	+	6.67230i	−0.124266	+	0.215236i
$962$	39.6254	−	68.6333i	1.27758	−	2.21283i
$963$		0			0
$964$	61.9840	+	107.359i	1.99637	+	3.45781i
$965$	−0.900434	−	1.55960i	−0.0289860	−	0.0502052i
$966$		0			0
$967$	−0.331836	+	0.574757i	−0.0106711	+	0.0184829i	−0.871312	−	0.490730i	$-0.836730\pi$
$967$	−0.331836	+	0.574757i	−0.0106711	+	0.0184829i	0.860641	+	0.509213i	$0.170063\pi$
$968$	15.7569			0.506444
$969$		0			0
$970$	−7.81022			−0.250771
$971$	−29.2598	−	50.6795i	−0.938993	−	1.62638i	−0.767354	−	0.641224i	$-0.778427\pi$
$971$	−29.2598	−	50.6795i	−0.938993	−	1.62638i	−0.171639	−	0.985160i	$-0.554906\pi$
$972$		0			0
$973$	20.5403	−	8.28326i	0.658490	−	0.265549i
$974$	−17.0840	−	29.5903i	−0.547405	−	0.948134i
$975$		0			0
$976$	30.8364	+	53.4101i	0.987048	+	1.70962i
$977$	27.0201	+	46.8002i	0.864450	+	1.49727i	0.867593	+	0.497276i	$0.165666\pi$
$977$	27.0201	+	46.8002i	0.864450	+	1.49727i	−0.00314297	+	0.999995i	$0.501000\pi$
$978$		0			0
$979$	−8.95258	−	15.5063i	−0.286126	−	0.495584i
$980$	−54.0391	+	52.0492i	−1.72622	+	1.66265i
$981$		0			0
$982$	−20.4187	−	35.3662i	−0.651586	−	1.12858i
$983$	21.8521			0.696974			0.348487	−	0.937314i	$-0.386696\pi$
$983$	21.8521			0.696974			0.348487	+	0.937314i	$0.386696\pi$
$984$		0			0
$985$	34.0163			1.08385
$986$	4.62766	−	8.01534i	0.147375	−	0.255260i
$987$		0			0
$988$	−73.9469	−	128.080i	−2.35256	−	4.07476i
$989$	−2.56577	−	4.44404i	−0.0815867	−	0.141312i
$990$		0			0
$991$	6.91507	−	11.9773i	0.219664	−	0.380470i	−0.735041	−	0.678023i	$-0.762837\pi$
$991$	6.91507	−	11.9773i	0.219664	−	0.380470i	0.954705	+	0.297553i	$0.0961704\pi$
$992$	26.2390	−	45.4473i	0.833089	−	1.44295i
$993$		0			0
$994$	1.01733	−	0.410259i	0.0322678	−	0.0130126i
$995$	3.11836	−	5.40116i	0.0988586	−	0.171228i
$996$		0			0
$997$	−6.27402			−0.198700			−0.0993501	−	0.995053i	$-0.531676\pi$
$997$	−6.27402			−0.198700			−0.0993501	+	0.995053i	$0.531676\pi$
$998$	55.5584	−	96.2299i	1.75867	−	3.04611i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.g.l.109.8		16
3.2	odd	2	inner	567.2.g.l.109.1		16
7.2	even	3		567.2.h.l.352.1		16
9.2	odd	6		567.2.h.l.298.8		16
9.4	even	3		567.2.e.g.487.8	yes	16
9.5	odd	6		567.2.e.g.487.1	yes	16
9.7	even	3		567.2.h.l.298.1		16
21.2	odd	6		567.2.h.l.352.8		16
63.2	odd	6	inner	567.2.g.l.541.1		16
63.4	even	3		3969.2.a.bg.1.1		8
63.16	even	3	inner	567.2.g.l.541.8		16
63.23	odd	6		567.2.e.g.163.1	✓	16
63.31	odd	6		3969.2.a.bf.1.1		8
63.32	odd	6		3969.2.a.bg.1.8		8
63.58	even	3		567.2.e.g.163.8	yes	16
63.59	even	6		3969.2.a.bf.1.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
567.2.e.g.163.1	✓	16	63.23	odd	6
567.2.e.g.163.8	yes	16	63.58	even	3
567.2.e.g.487.1	yes	16	9.5	odd	6
567.2.e.g.487.8	yes	16	9.4	even	3
567.2.g.l.109.1		16	3.2	odd	2	inner
567.2.g.l.109.8		16	1.1	even	1	trivial
567.2.g.l.541.1		16	63.2	odd	6	inner
567.2.g.l.541.8		16	63.16	even	3	inner
567.2.h.l.298.1		16	9.7	even	3
567.2.h.l.298.8		16	9.2	odd	6
567.2.h.l.352.1		16	7.2	even	3
567.2.h.l.352.8		16	21.2	odd	6
3969.2.a.bf.1.1		8	63.31	odd	6
3969.2.a.bf.1.8		8	63.59	even	6
3969.2.a.bg.1.1		8	63.4	even	3
3969.2.a.bg.1.8		8	63.32	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.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.29368 - 2.24073i) q^{2} +(-2.34723 - 4.06553i) q^{4} -2.28320 q^{5} +(-2.08382 - 1.63024i) q^{7} -6.97158 q^{8} +(-2.95374 + 5.11603i) q^{10} +2.95632 q^{11} +(-2.13422 + 3.69657i) q^{13} +(-6.34873 + 2.56025i) q^{14} +(-4.32455 + 7.49033i) q^{16} +(-0.764218 + 1.32366i) q^{17} +(-3.69033 - 6.39184i) q^{19} +(5.35921 + 9.28243i) q^{20} +(3.82455 - 6.62431i) q^{22} +6.15202 q^{23} +0.213017 q^{25} +(5.52200 + 9.56439i) q^{26} +(-1.73659 + 12.2984i) q^{28} +(-1.17019 - 2.02683i) q^{29} +(-3.11065 - 5.38780i) q^{31} +(4.21761 + 7.30512i) q^{32} +(1.97731 + 3.42480i) q^{34} +(4.75779 + 3.72218i) q^{35} +(-3.58796 - 6.21453i) q^{37} -19.0965 q^{38} +15.9175 q^{40} +(-3.94584 + 6.83440i) q^{41} +(-0.417061 - 0.722372i) q^{43} +(-6.93918 - 12.0190i) q^{44} +(7.95876 - 13.7850i) q^{46} +(2.91322 - 5.04584i) q^{47} +(1.68461 + 6.79427i) q^{49} +(0.275576 - 0.477312i) q^{50} +20.0380 q^{52} +(3.71826 - 6.44021i) q^{53} -6.74989 q^{55} +(14.5275 + 11.3654i) q^{56} -6.05542 q^{58} +(-2.31179 - 4.00414i) q^{59} +(3.56527 - 6.17523i) q^{61} -16.0968 q^{62} +4.52683 q^{64} +(4.87285 - 8.44003i) q^{65} +(1.66262 + 2.87974i) q^{67} +7.17519 q^{68} +(14.4954 - 5.84557i) q^{70} -0.160242 q^{71} +(0.190329 - 0.329659i) q^{73} -18.5667 q^{74} +(-17.3241 + 30.0063i) q^{76} +(-6.16045 - 4.81953i) q^{77} +(3.97731 - 6.88891i) q^{79} +(9.87382 - 17.1020i) q^{80} +(10.2093 + 17.6831i) q^{82} +(2.14900 + 3.72218i) q^{83} +(1.74486 - 3.02219i) q^{85} -2.15818 q^{86} -20.6102 q^{88} +(-3.02828 - 5.24514i) q^{89} +(10.4736 - 4.22370i) q^{91} +(-14.4402 - 25.0112i) q^{92} +(-7.53756 - 13.0554i) q^{94} +(8.42577 + 14.5939i) q^{95} +(0.661044 + 1.14496i) q^{97} +(17.4034 + 5.01487i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{4} - 14 q^{10} - 6 q^{13} - 6 q^{16} - 24 q^{19} - 2 q^{22} - 26 q^{28} - 20 q^{31} + 4 q^{37} + 72 q^{40} - 10 q^{43} + 36 q^{46} + 4 q^{49} + 68 q^{52} + 8 q^{55} - 44 q^{58} - 36 q^{61} + 76 q^{64}+ \cdots - 14 q^{97}+O(q^{100}) \) 16 * q - 6 * q^4 - 14 * q^10 - 6 * q^13 - 6 * q^16 - 24 * q^19 - 2 * q^22 - 26 * q^28 - 20 * q^31 + 4 * q^37 + 72 * q^40 - 10 * q^43 + 36 * q^46 + 4 * q^49 + 68 * q^52 + 8 * q^55 - 44 * q^58 - 36 * q^61 + 76 * q^64 + 18 * q^67 + 104 * q^70 - 32 * q^73 - 58 * q^76 + 32 * q^79 + 2 * q^82 - 30 * q^85 - 144 * q^88 - 22 * q^91 - 54 * q^94 - 14 * q^97

Introduction

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