LMFDB - Embedded newform 560.2.ci.c.17.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [560,2,Mod(17,560)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(560, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 0, 3, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("560.17"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.ci (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,0,-12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
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} + 10x^{14} + 61x^{12} + 266x^{10} + 852x^{8} + 1438x^{6} + 1933x^{4} + 3038x^{2} + 2401 $ x^16 + 10x^14 + 61x^12 + 266x^10 + 852x^8 + 1438x^6 + 1933x^4 + 3038*x^2 + 2401
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			17.1
Root			$0.144868 - 1.25092i$ of defining polynomial
Character	$\chi$	$=$	560.17
Dual form			560.2.ci.c.33.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.95290 + 0.523277i) q^{3} +(-1.82591 + 1.29076i) q^{5} +(1.90155 - 1.83959i) q^{7} +(0.941911 - 0.543813i) q^{9} +(-2.01999 + 3.49872i) q^{11} +(-0.204875 - 0.204875i) q^{13} +(2.89039 - 3.47617i) q^{15} +(-0.527924 - 1.97024i) q^{17} +(-3.10166 - 5.37224i) q^{19} +(-2.75092 + 4.58757i) q^{21} +(4.38350 + 1.17456i) q^{23} +(1.66789 - 4.71361i) q^{25} +(2.73397 - 2.73397i) q^{27} -7.15869i q^{29} +(-6.33287 - 3.65628i) q^{31} +(2.11403 - 7.88965i) q^{33} +(-1.09759 + 5.81337i) q^{35} +(1.19723 - 4.46814i) q^{37} +(0.507306 + 0.292893i) q^{39} -2.58745i q^{41} +(4.97801 - 4.97801i) q^{43} +(-1.01791 + 2.20873i) q^{45} +(0.304388 + 0.0815604i) q^{47} +(0.231803 - 6.99616i) q^{49} +(2.06196 + 3.57142i) q^{51} +(2.14370 + 8.00039i) q^{53} +(-0.827689 - 8.99566i) q^{55} +(8.86840 + 8.86840i) q^{57} +(0.427702 - 0.740802i) q^{59} +(-5.99356 + 3.46038i) q^{61} +(0.790700 - 2.76682i) q^{63} +(0.638527 + 0.109639i) q^{65} +(-3.05106 + 0.817530i) q^{67} -9.17514 q^{69} -7.12240 q^{71} +(-11.1331 + 2.98311i) q^{73} +(-0.790684 + 10.0780i) q^{75} +(2.59511 + 10.3690i) q^{77} +(-4.39618 + 2.53813i) q^{79} +(-5.53997 + 9.59552i) q^{81} +(-3.85372 - 3.85372i) q^{83} +(3.50704 + 2.91605i) q^{85} +(3.74598 + 13.9802i) q^{87} +(1.53615 + 2.66069i) q^{89} +(-0.766467 - 0.0126942i) q^{91} +(14.2807 + 3.82650i) q^{93} +(12.5976 + 5.80572i) q^{95} +(6.63103 - 6.63103i) q^{97} +4.39398i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 12 q^{5} - 8 q^{7} + 12 q^{11} - 16 q^{15} - 36 q^{17} - 28 q^{21} + 4 q^{23} + 12 q^{25} - 24 q^{31} + 48 q^{33} - 8 q^{35} + 4 q^{37} + 8 q^{43} - 12 q^{45} - 12 q^{47} + 16 q^{51} - 28 q^{53}+ \cdots - 20 q^{95}+O(q^{100}) $ 16 * q - 12 * q^5 - 8 * q^7 + 12 * q^11 - 16 * q^15 - 36 * q^17 - 28 * q^21 + 4 * q^23 + 12 * q^25 - 24 * q^31 + 48 * q^33 - 8 * q^35 + 4 * q^37 + 8 * q^43 - 12 * q^45 - 12 * q^47 + 16 * q^51 - 28 * q^53 + 8 * q^57 - 12 * q^61 + 36 * q^63 - 8 * q^65 - 32 * q^67 - 16 * q^71 - 12 * q^73 + 48 * q^75 + 16 * q^77 + 24 * q^85 + 24 * q^87 + 16 * q^91 + 28 * q^93 - 20 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{4}\right)$	$1$	$1$

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			0
$2$		0			0
$3$	−1.95290	+	0.523277i	−1.12751	+	0.302114i	−0.773917	−	0.633287i	$-0.781705\pi$
$3$	−1.95290	+	0.523277i	−1.12751	+	0.302114i	−0.353588	+	0.935401i	$0.615039\pi$
$4$		0			0
$5$	−1.82591	+	1.29076i	−0.816571	+	0.577245i
$5$	−1.82591	+	1.29076i	−0.816571	+	0.577245i
$6$		0			0
$7$	1.90155	−	1.83959i	0.718719	−	0.695300i
$7$	1.90155	−	1.83959i	0.718719	−	0.695300i
$8$		0			0
$9$	0.941911	−	0.543813i	0.313970	−	0.181271i
$10$		0			0
$11$	−2.01999	+	3.49872i	−0.609049	+	1.05490i	0.382349	+	0.924018i	$0.375115\pi$
$11$	−2.01999	+	3.49872i	−0.609049	+	1.05490i	−0.991397	+	0.130886i	$0.958218\pi$
$12$		0			0
$13$	−0.204875	−	0.204875i	−0.0568221	−	0.0568221i	0.678125	−	0.734947i	$-0.262793\pi$
$13$	−0.204875	−	0.204875i	−0.0568221	−	0.0568221i	−0.734947	+	0.678125i	$0.762793\pi$
$14$		0			0
$15$	2.89039	−	3.47617i	0.746295	−	0.897544i
$16$		0			0
$17$	−0.527924	−	1.97024i	−0.128040	−	0.477853i	0.871890	−	0.489703i	$-0.162895\pi$
$17$	−0.527924	−	1.97024i	−0.128040	−	0.477853i	−0.999930	+	0.0118498i	$0.996228\pi$
$18$		0			0
$19$	−3.10166	−	5.37224i	−0.711571	−	1.23248i	−0.964267	−	0.264931i	$-0.914651\pi$
$19$	−3.10166	−	5.37224i	−0.711571	−	1.23248i	0.252697	−	0.967545i	$-0.418682\pi$
$20$		0			0
$21$	−2.75092	+	4.58757i	−0.600300	+	1.00109i
$22$		0			0
$23$	4.38350	+	1.17456i	0.914023	+	0.244912i	0.685029	−	0.728516i	$-0.259790\pi$
$23$	4.38350	+	1.17456i	0.914023	+	0.244912i	0.228994	+	0.973428i	$0.426456\pi$
$24$		0			0
$25$	1.66789	−	4.71361i	0.333577	−	0.942723i
$26$		0			0
$27$	2.73397	−	2.73397i	0.526152	−	0.526152i
$28$		0			0
$29$		−	7.15869i		−	1.32934i	−0.747139	−	0.664668i	$-0.768573\pi$
$29$		−	7.15869i		−	1.32934i	0.747139	−	0.664668i	$-0.231427\pi$
$30$		0			0
$31$	−6.33287	−	3.65628i	−1.13742	−	0.656688i	−0.191627	−	0.981468i	$-0.561376\pi$
$31$	−6.33287	−	3.65628i	−1.13742	−	0.656688i	−0.945790	+	0.324780i	$0.894710\pi$
$32$		0			0
$33$	2.11403	−	7.88965i	0.368005	−	1.37341i
$34$		0			0
$35$	−1.09759	+	5.81337i	−0.185527	+	0.982639i
$36$		0			0
$37$	1.19723	−	4.46814i	0.196824	−	0.734558i	−0.794963	−	0.606658i	$-0.792510\pi$
$37$	1.19723	−	4.46814i	0.196824	−	0.734558i	0.991787	−	0.127900i	$-0.0408236\pi$
$38$		0			0
$39$	0.507306	+	0.292893i	0.0812340	+	0.0469005i
$40$		0			0
$41$		−	2.58745i		−	0.404093i	−0.979376	−	0.202046i	$-0.935241\pi$
$41$		−	2.58745i		−	0.404093i	0.979376	−	0.202046i	$-0.0647591\pi$
$42$		0			0
$43$	4.97801	−	4.97801i	0.759140	−	0.759140i	−0.217026	−	0.976166i	$-0.569636\pi$
$43$	4.97801	−	4.97801i	0.759140	−	0.759140i	0.976166	+	0.217026i	$0.0696356\pi$
$44$		0			0
$45$	−1.01791	+	2.20873i	−0.151742	+	0.329258i
$46$		0			0
$47$	0.304388	+	0.0815604i	0.0443995	+	0.0118968i	0.280950	−	0.959722i	$-0.409350\pi$
$47$	0.304388	+	0.0815604i	0.0443995	+	0.0118968i	−0.236551	+	0.971619i	$0.576017\pi$
$48$		0			0
$49$	0.231803	−	6.99616i	0.0331148	−	0.999452i
$50$		0			0
$51$	2.06196	+	3.57142i	0.288732	+	0.500099i
$52$		0			0
$53$	2.14370	+	8.00039i	0.294460	+	1.09894i	0.941646	+	0.336606i	$0.109279\pi$
$53$	2.14370	+	8.00039i	0.294460	+	1.09894i	−0.647186	+	0.762332i	$0.724054\pi$
$54$		0			0
$55$	−0.827689	−	8.99566i	−0.111606	−	1.21297i
$56$		0			0
$57$	8.86840	+	8.86840i	1.17465	+	1.17465i
$58$		0			0
$59$	0.427702	−	0.740802i	0.0556821	−	0.0964442i	−0.836841	−	0.547446i	$-0.815600\pi$
$59$	0.427702	−	0.740802i	0.0556821	−	0.0964442i	0.892523	+	0.451002i	$0.148933\pi$
$60$		0			0
$61$	−5.99356	+	3.46038i	−0.767397	+	0.443057i	−0.831945	−	0.554858i	$-0.812773\pi$
$61$	−5.99356	+	3.46038i	−0.767397	+	0.443057i	0.0645484	+	0.997915i	$0.479439\pi$
$62$		0			0
$63$	0.790700	−	2.76682i	0.0996189	−	0.348587i
$64$		0			0
$65$	0.638527	+	0.109639i	0.0791995	+	0.0135990i
$66$		0			0
$67$	−3.05106	+	0.817530i	−0.372747	+	0.0998772i	−0.440329	−	0.897837i	$-0.645138\pi$
$67$	−3.05106	+	0.817530i	−0.372747	+	0.0998772i	0.0675822	+	0.997714i	$0.478472\pi$
$68$		0			0
$69$	−9.17514			−1.10456
$70$		0			0
$71$	−7.12240			−0.845273			−0.422637	−	0.906299i	$-0.638895\pi$
$71$	−7.12240			−0.845273			−0.422637	+	0.906299i	$0.638895\pi$
$72$		0			0
$73$	−11.1331	+	2.98311i	−1.30303	+	0.349147i	−0.842597	−	0.538545i	$-0.818974\pi$
$73$	−11.1331	+	2.98311i	−1.30303	+	0.349147i	−0.460438	+	0.887692i	$0.652307\pi$
$74$		0			0
$75$	−0.790684	+	10.0780i	−0.0913004	+	1.16370i
$76$		0			0
$77$	2.59511	+	10.3690i	0.295740	+	1.18165i
$78$		0			0
$79$	−4.39618	+	2.53813i	−0.494609	+	0.285562i	−0.726484	−	0.687183i	$-0.758847\pi$
$79$	−4.39618	+	2.53813i	−0.494609	+	0.285562i	0.231876	+	0.972745i	$0.425514\pi$
$80$		0			0
$81$	−5.53997	+	9.59552i	−0.615553	+	1.06617i
$82$		0			0
$83$	−3.85372	−	3.85372i	−0.423001	−	0.423001i	0.463235	−	0.886236i	$-0.346689\pi$
$83$	−3.85372	−	3.85372i	−0.423001	−	0.423001i	−0.886236	+	0.463235i	$0.846689\pi$
$84$		0			0
$85$	3.50704	+	2.91605i	0.380392	+	0.316290i
$86$		0			0
$87$	3.74598	+	13.9802i	0.401611	+	1.49883i
$88$		0			0
$89$	1.53615	+	2.66069i	0.162832	+	0.282033i	0.935883	−	0.352310i	$-0.114604\pi$
$89$	1.53615	+	2.66069i	0.162832	+	0.282033i	−0.773051	+	0.634343i	$0.781271\pi$
$90$		0			0
$91$	−0.766467	−	0.0126942i	−0.0803475	−	0.00133071i
$92$		0			0
$93$	14.2807	+	3.82650i	1.48084	+	0.396789i
$94$		0			0
$95$	12.5976	+	5.80572i	1.29249	+	0.595655i
$96$		0			0
$97$	6.63103	−	6.63103i	0.673279	−	0.673279i	−0.285191	−	0.958471i	$-0.592057\pi$
$97$	6.63103	−	6.63103i	0.673279	−	0.673279i	0.958471	+	0.285191i	$0.0920572\pi$
$98$		0			0
$99$			4.39398i			0.441611i
$100$		0			0
$101$	−8.56364	−	4.94422i	−0.852114	−	0.491968i	0.00924966	−	0.999957i	$-0.497056\pi$
$101$	−8.56364	−	4.94422i	−0.852114	−	0.491968i	−0.861364	+	0.507989i	$0.830389\pi$
$102$		0			0
$103$	−1.10827	+	4.13612i	−0.109201	+	0.407544i	−0.998788	−	0.0492221i	$-0.984326\pi$
$103$	−1.10827	+	4.13612i	−0.109201	+	0.407544i	0.889587	+	0.456766i	$0.150992\pi$
$104$		0			0
$105$	−0.898518	−	11.9273i	−0.0876864	−	1.16398i
$106$		0			0
$107$	3.84918	−	14.3653i	0.372114	−	1.38875i	−0.485402	−	0.874291i	$-0.661327\pi$
$107$	3.84918	−	14.3653i	0.372114	−	1.38875i	0.857516	−	0.514457i	$-0.172007\pi$
$108$		0			0
$109$	11.4586	+	6.61564i	1.09754	+	0.633664i	0.935573	−	0.353133i	$-0.114884\pi$
$109$	11.4586	+	6.61564i	1.09754	+	0.633664i	0.161964	+	0.986797i	$0.448217\pi$
$110$		0			0
$111$			9.35230i			0.887681i
$112$		0			0
$113$	9.75336	−	9.75336i	0.917519	−	0.917519i	−0.0793296	−	0.996848i	$-0.525278\pi$
$113$	9.75336	−	9.75336i	0.917519	−	0.917519i	0.996848	+	0.0793296i	$0.0252780\pi$
$114$		0			0
$115$	−9.51994	+	3.51341i	−0.887739	+	0.327627i
$116$		0			0
$117$	−0.304388	−	0.0815604i	−0.0281406	−	0.00754026i
$118$		0			0
$119$	−4.62831	−	2.77535i	−0.424276	−	0.254416i
$120$		0			0
$121$	−2.66069	−	4.60846i	−0.241881	−	0.418951i
$122$		0			0
$123$	1.35396	+	5.05303i	0.122082	+	0.455617i
$124$		0			0
$125$	3.03873	+	10.7595i	0.271792	+	0.962356i
$126$		0			0
$127$	2.19984	+	2.19984i	0.195204	+	0.195204i	0.797940	−	0.602736i	$-0.205923\pi$
$127$	2.19984	+	2.19984i	0.195204	+	0.195204i	−0.602736	+	0.797940i	$0.705923\pi$
$128$		0			0
$129$	−7.11667	+	12.3264i	−0.626587	+	1.08528i
$130$		0			0
$131$	6.32091	−	3.64938i	0.552260	−	0.318848i	−0.197773	−	0.980248i	$-0.563371\pi$
$131$	6.32091	−	3.64938i	0.552260	−	0.318848i	0.750033	+	0.661400i	$0.230037\pi$
$132$		0			0
$133$	−15.7807	−	4.50980i	−1.36836	−	0.391049i
$134$		0			0
$135$	−1.46309	+	8.52087i	−0.125922	+	0.733360i
$136$		0			0
$137$	−6.93431	+	1.85804i	−0.592438	+	0.158743i	−0.542567	−	0.840012i	$-0.682548\pi$
$137$	−6.93431	+	1.85804i	−0.592438	+	0.158743i	−0.0498710	+	0.998756i	$0.515881\pi$
$138$		0			0
$139$	12.4172			1.05321			0.526605	−	0.850110i	$-0.323465\pi$
$139$	12.4172			1.05321			0.526605	+	0.850110i	$0.323465\pi$
$140$		0			0
$141$	−0.637116			−0.0536549
$142$		0			0
$143$	1.13064	−	0.302955i	0.0945492	−	0.0253344i
$144$		0			0
$145$	9.24014	+	13.0711i	0.767352	+	1.08550i
$146$		0			0
$147$	3.20824	+	13.7841i	0.264611	+	1.13689i
$148$		0			0
$149$	−20.7399	+	11.9742i	−1.69908	+	0.980963i	−0.752440	+	0.658661i	$0.771123\pi$
$149$	−20.7399	+	11.9742i	−1.69908	+	0.980963i	−0.946637	+	0.322302i	$0.895543\pi$
$150$		0			0
$151$	−1.77167	+	3.06862i	−0.144176	+	0.249721i	−0.929065	−	0.369916i	$-0.879387\pi$
$151$	−1.77167	+	3.06862i	−0.144176	+	0.249721i	0.784889	+	0.619636i	$0.212720\pi$
$152$		0			0
$153$	−1.56870	−	1.56870i	−0.126822	−	0.126822i
$154$		0			0
$155$	16.2826	−	1.49816i	1.30785	−	0.120335i
$156$		0			0
$157$	−1.58462	−	5.91389i	−0.126467	−	0.471980i	0.873421	−	0.486966i	$-0.161896\pi$
$157$	−1.58462	−	5.91389i	−0.126467	−	0.471980i	−0.999888	+	0.0149859i	$0.995230\pi$
$158$		0			0
$159$	−8.37284	−	14.5022i	−0.664010	−	1.15010i
$160$		0			0
$161$	10.4962	−	5.83037i	0.827213	−	0.459498i
$162$		0			0
$163$	−15.9937	−	4.28549i	−1.25272	−	0.335666i	−0.429334	−	0.903146i	$-0.641252\pi$
$163$	−15.9937	−	4.28549i	−1.25272	−	0.335666i	−0.823387	+	0.567480i	$0.807918\pi$
$164$		0			0
$165$	6.32361	+	17.1345i	0.492293	+	1.33392i
$166$		0			0
$167$	−10.2873	+	10.2873i	−0.796056	+	0.796056i	−0.982471	−	0.186415i	$-0.940313\pi$
$167$	−10.2873	+	10.2873i	−0.796056	+	0.796056i	0.186415	+	0.982471i	$0.440313\pi$
$168$		0			0
$169$		−	12.9161i		−	0.993543i
$170$		0			0
$171$	−5.84298	−	3.37345i	−0.446824	−	0.257974i
$172$		0			0
$173$	2.01155	−	7.50720i	0.152935	−	0.570762i	−0.846338	−	0.532646i	$-0.821198\pi$
$173$	2.01155	−	7.50720i	0.152935	−	0.570762i	0.999273	−	0.0381159i	$-0.0121356\pi$
$174$		0			0
$175$	−5.49955	−	12.0314i	−0.415727	−	0.909489i
$176$		0			0
$177$	−0.447613	+	1.67052i	−0.0336447	+	0.125564i
$178$		0			0
$179$	3.34695	+	1.93236i	0.250163	+	0.144431i	0.619839	−	0.784729i	$-0.287198\pi$
$179$	3.34695	+	1.93236i	0.250163	+	0.144431i	−0.369676	+	0.929161i	$0.620531\pi$
$180$		0			0
$181$			6.99107i			0.519642i	0.965657	+	0.259821i	$0.0836636\pi$
$181$			6.99107i			0.519642i	−0.965657	+	0.259821i	$0.916336\pi$
$182$		0			0
$183$	9.89407	−	9.89407i	0.731390	−	0.731390i
$184$		0			0
$185$	3.58125	+	9.70376i	0.263299	+	0.713435i
$186$		0			0
$187$	7.95971	+	2.13280i	0.582071	+	0.155966i
$188$		0			0
$189$	0.169398	−	10.2282i	0.0123219	−	0.743990i
$190$		0			0
$191$	2.23721	+	3.87496i	0.161879	+	0.280383i	0.935543	−	0.353214i	$-0.114911\pi$
$191$	2.23721	+	3.87496i	0.161879	+	0.280383i	−0.773664	+	0.633597i	$0.781578\pi$
$192$		0			0
$193$	−5.19573	−	19.3907i	−0.373997	−	1.39577i	−0.854805	−	0.518949i	$-0.826324\pi$
$193$	−5.19573	−	19.3907i	−0.373997	−	1.39577i	0.480809	−	0.876825i	$-0.340343\pi$
$194$		0			0
$195$	−1.30435	+	0.120013i	−0.0934064	+	0.00859431i
$196$		0			0
$197$	−7.84901	−	7.84901i	−0.559219	−	0.559219i	0.369866	−	0.929085i	$-0.379404\pi$
$197$	−7.84901	−	7.84901i	−0.559219	−	0.559219i	−0.929085	+	0.369866i	$0.879404\pi$
$198$		0			0
$199$	−5.40103	+	9.35485i	−0.382869	+	0.663148i	−0.991471	−	0.130327i	$-0.958397\pi$
$199$	−5.40103	+	9.35485i	−0.382869	+	0.663148i	0.608602	+	0.793475i	$0.291730\pi$
$200$		0			0
$201$	5.53062	−	3.19310i	0.390100	−	0.225224i
$202$		0			0
$203$	−13.1691	−	13.6126i	−0.924288	−	0.955419i
$204$		0			0
$205$	3.33978	+	4.72446i	0.233260	+	0.329970i
$206$		0			0
$207$	4.76761	−	1.27748i	0.331372	−	0.0887908i
$208$		0			0
$209$	25.0613			1.73353
$210$		0			0
$211$	−7.56555			−0.520834			−0.260417	−	0.965496i	$-0.583860\pi$
$211$	−7.56555			−0.520834			−0.260417	+	0.965496i	$0.583860\pi$
$212$		0			0
$213$	13.9093	−	3.72699i	0.953050	−	0.255369i
$214$		0			0
$215$	−2.66399	+	15.5148i	−0.181682	+	1.05810i
$216$		0			0
$217$	−18.7683	+	4.69728i	−1.27408	+	0.318872i
$218$		0			0
$219$	20.1809	−	11.6514i	1.36370	−	0.787330i
$220$		0			0
$221$	−0.295494	+	0.511811i	−0.0198771	+	0.0344281i
$222$		0			0
$223$	9.35230	+	9.35230i	0.626277	+	0.626277i	0.947129	−	0.320853i	$-0.103969\pi$
$223$	9.35230	+	9.35230i	0.626277	+	0.626277i	−0.320853	+	0.947129i	$0.603969\pi$
$224$		0			0
$225$	−0.992322	−	5.34682i	−0.0661548	−	0.356455i
$226$		0			0
$227$	−4.19127	−	15.6420i	−0.278184	−	1.03820i	−0.953677	−	0.300832i	$-0.902736\pi$
$227$	−4.19127	−	15.6420i	−0.278184	−	1.03820i	0.675493	−	0.737367i	$-0.263931\pi$
$228$		0			0
$229$	−5.88820	−	10.1987i	−0.389103	−	0.673947i	0.603226	−	0.797570i	$-0.293882\pi$
$229$	−5.88820	−	10.1987i	−0.389103	−	0.673947i	−0.992329	+	0.123624i	$0.960548\pi$
$230$		0			0
$231$	−10.4938	−	18.8915i	−0.690442	−	1.24297i
$232$		0			0
$233$	5.52920	+	1.48154i	0.362230	+	0.0970591i	0.435343	−	0.900264i	$-0.356627\pi$
$233$	5.52920	+	1.48154i	0.362230	+	0.0970591i	−0.0731138	+	0.997324i	$0.523294\pi$
$234$		0			0
$235$	−0.661059	+	0.243969i	−0.0431227	+	0.0159148i
$236$		0			0
$237$	7.25713	−	7.25713i	0.471402	−	0.471402i
$238$		0			0
$239$		−	8.33794i		−	0.539337i	−0.962953	−	0.269668i	$-0.913086\pi$
$239$		−	8.33794i		−	0.539337i	0.962953	−	0.269668i	$-0.0869141\pi$
$240$		0			0
$241$	2.56723	+	1.48219i	0.165370	+	0.0954763i	0.580401	−	0.814331i	$-0.302896\pi$
$241$	2.56723	+	1.48219i	0.165370	+	0.0954763i	−0.415031	+	0.909807i	$0.636229\pi$
$242$		0			0
$243$	2.79578	−	10.4340i	0.179349	−	0.669340i
$244$		0			0
$245$	8.60710	+	13.0736i	0.549887	+	0.835239i
$246$		0			0
$247$	−0.465184	+	1.73609i	−0.0295989	+	0.110465i
$248$		0			0
$249$	9.54248	+	5.50936i	0.604730	+	0.349141i
$250$		0			0
$251$			16.1800i			1.02127i	0.859796	+	0.510637i	$0.170590\pi$
$251$			16.1800i			1.02127i	−0.859796	+	0.510637i	$0.829410\pi$
$252$		0			0
$253$	−12.9641	+	12.9641i	−0.815043	+	0.815043i
$254$		0			0
$255$	−8.37479	−	3.85960i	−0.524450	−	0.241697i
$256$		0			0
$257$	−5.62621	−	1.50754i	−0.350954	−	0.0940377i	0.0790355	−	0.996872i	$-0.474816\pi$
$257$	−5.62621	−	1.50754i	−0.350954	−	0.0940377i	−0.429989	+	0.902834i	$0.641483\pi$
$258$		0			0
$259$	−5.94295	−	10.6988i	−0.369277	−	0.664793i
$260$		0			0
$261$	−3.89299	−	6.74285i	−0.240970	−	0.417372i
$262$		0			0
$263$	−0.449601	−	1.67793i	−0.0277236	−	0.103466i	0.950678	−	0.310180i	$-0.100389\pi$
$263$	−0.449601	−	1.67793i	−0.0277236	−	0.103466i	−0.978401	+	0.206715i	$0.933723\pi$
$264$		0			0
$265$	−14.2408	−	11.8410i	−0.874803	−	0.727386i
$266$		0			0
$267$	−4.39223	−	4.39223i	−0.268800	−	0.268800i
$268$		0			0
$269$	1.89169	−	3.27650i	0.115338	−	0.199772i	−0.802577	−	0.596549i	$-0.796538\pi$
$269$	1.89169	−	3.27650i	0.115338	−	0.199772i	0.917915	+	0.396777i	$0.129872\pi$
$270$		0			0
$271$	18.4029	−	10.6249i	1.11789	−	0.645416i	0.177032	−	0.984205i	$-0.443351\pi$
$271$	18.4029	−	10.6249i	1.11789	−	0.645416i	0.940862	+	0.338789i	$0.110017\pi$
$272$		0			0
$273$	1.50347	−	0.376284i	0.0909943	−	0.0227737i
$274$		0			0
$275$	13.1225	+	15.3569i	0.791317	+	0.926056i
$276$		0			0
$277$	4.72353	−	1.26567i	0.283810	−	0.0760465i	−0.114106	−	0.993469i	$-0.536400\pi$
$277$	4.72353	−	1.26567i	0.283810	−	0.0760465i	0.397916	+	0.917422i	$0.369734\pi$
$278$		0			0
$279$	−7.95333			−0.476153
$280$		0			0
$281$	−29.4776			−1.75849			−0.879243	−	0.476373i	$-0.841951\pi$
$281$	−29.4776			−1.75849			−0.879243	+	0.476373i	$0.841951\pi$
$282$		0			0
$283$	10.8991	−	2.92041i	0.647886	−	0.173601i	0.0801133	−	0.996786i	$-0.474472\pi$
$283$	10.8991	−	2.92041i	0.647886	−	0.173601i	0.567773	+	0.823185i	$0.307805\pi$
$284$		0			0
$285$	−27.6399	−	4.74593i	−1.63724	−	0.281125i
$286$		0			0
$287$	−4.75986	−	4.92018i	−0.280966	−	0.290429i
$288$		0			0
$289$	11.1193	−	6.41973i	0.654076	−	0.377631i
$290$		0			0
$291$	−9.47985	+	16.4196i	−0.555719	+	0.962533i
$292$		0			0
$293$	7.23407	+	7.23407i	0.422619	+	0.422619i	0.886105	−	0.463485i	$-0.153401\pi$
$293$	7.23407	+	7.23407i	0.422619	+	0.422619i	−0.463485	+	0.886105i	$0.653401\pi$
$294$		0			0
$295$	0.175251	+	1.90470i	0.0102035	+	0.110896i
$296$		0			0
$297$	4.04281	+	15.0880i	0.234588	+	0.875493i
$298$		0			0
$299$	−0.657432	−	1.13871i	−0.0380203	−	0.0658531i
$300$		0			0
$301$	0.308440	−	18.6235i	0.0177782	−	1.07344i
$302$		0			0
$303$	19.3111	+	5.17439i	1.10939	+	0.297261i
$304$		0			0
$305$	6.47718	−	14.0546i	0.370882	−	0.804763i
$306$		0			0
$307$	−1.07859	+	1.07859i	−0.0615584	+	0.0615584i	−0.737216	−	0.675657i	$-0.763860\pi$
$307$	−1.07859	+	1.07859i	−0.0615584	+	0.0615584i	0.675657	+	0.737216i	$0.263860\pi$
$308$		0			0
$309$		−	8.65735i		−	0.492500i
$310$		0			0
$311$	8.33830	+	4.81412i	0.472821	+	0.272984i	0.717420	−	0.696641i	$-0.245323\pi$
$311$	8.33830	+	4.81412i	0.472821	+	0.272984i	−0.244599	+	0.969624i	$0.578656\pi$
$312$		0			0
$313$	0.783378	−	2.92361i	0.0442791	−	0.165252i	−0.940246	−	0.340496i	$-0.889405\pi$
$313$	0.783378	−	2.92361i	0.0442791	−	0.165252i	0.984525	+	0.175244i	$0.0560716\pi$
$314$		0			0
$315$	2.12755	+	6.07257i	0.119874	+	0.342150i
$316$		0			0
$317$	0.504353	−	1.88227i	0.0283273	−	0.105719i	−0.950315	−	0.311291i	$-0.899239\pi$
$317$	0.504353	−	1.88227i	0.0283273	−	0.105719i	0.978642	+	0.205572i	$0.0659054\pi$
$318$		0			0
$319$	25.0463	+	14.4605i	1.40232	+	0.809631i
$320$		0			0
$321$			30.0682i			1.67824i
$322$		0			0
$323$	−8.94715	+	8.94715i	−0.497833	+	0.497833i
$324$		0			0
$325$	−1.30741	+	0.623993i	−0.0725220	+	0.0346129i
$326$		0			0
$327$	−25.8393	−	6.92363i	−1.42892	−	0.382878i
$328$		0			0
$329$	0.728847	−	0.404858i	0.0401826	−	0.0223205i
$330$		0			0
$331$	−14.4468	−	25.0225i	−0.794066	−	1.37536i	−0.923431	−	0.383765i	$-0.874627\pi$
$331$	−14.4468	−	25.0225i	−0.794066	−	1.37536i	0.129365	−	0.991597i	$-0.458706\pi$
$332$		0			0
$333$	−1.30214	−	4.85966i	−0.0713570	−	0.266308i
$334$		0			0
$335$	4.51573	−	5.43092i	0.246721	−	0.296723i
$336$		0			0
$337$	−0.823226	−	0.823226i	−0.0448440	−	0.0448440i	0.684329	−	0.729173i	$-0.260095\pi$
$337$	−0.823226	−	0.823226i	−0.0448440	−	0.0448440i	−0.729173	+	0.684329i	$0.760095\pi$
$338$		0			0
$339$	−13.9436	+	24.1510i	−0.757312	+	1.31170i
$340$		0			0
$341$	25.5846	−	14.7713i	1.38548	−	0.799910i
$342$		0			0
$343$	−12.4293	−	13.7300i	−0.671119	−	0.741350i
$344$		0			0
$345$	16.7530	−	11.8429i	0.901950	−	0.637600i
$346$		0			0
$347$	−16.1350	+	4.32336i	−0.866172	+	0.232090i	−0.664432	−	0.747349i	$-0.731326\pi$
$347$	−16.1350	+	4.32336i	−0.866172	+	0.232090i	−0.201740	+	0.979439i	$0.564660\pi$
$348$		0			0
$349$	−36.7146			−1.96529			−0.982644	−	0.185503i	$-0.940608\pi$
$349$	−36.7146			−1.96529			−0.982644	+	0.185503i	$0.940608\pi$
$350$		0			0
$351$	−1.12024			−0.0597942
$352$		0			0
$353$	−13.7845	+	3.69356i	−0.733677	+	0.196588i	−0.606266	−	0.795262i	$-0.707333\pi$
$353$	−13.7845	+	3.69356i	−0.733677	+	0.196588i	−0.127411	+	0.991850i	$0.540667\pi$
$354$		0			0
$355$	13.0048	−	9.19329i	0.690226	−	0.487929i
$356$		0			0
$357$	10.4909	+	2.99808i	0.555236	+	0.158675i
$358$		0			0
$359$	−23.4596	+	13.5444i	−1.23815	+	0.714847i	−0.968716	−	0.248172i	$-0.920170\pi$
$359$	−23.4596	+	13.5444i	−1.23815	+	0.714847i	−0.269435	+	0.963019i	$0.586837\pi$
$360$		0			0
$361$	−9.74064	+	16.8713i	−0.512665	+	0.887962i
$362$		0			0
$363$	7.60756	+	7.60756i	0.399293	+	0.399293i
$364$		0			0
$365$	16.4776	−	19.8171i	0.862477	−	1.03727i
$366$		0			0
$367$	−5.86782	−	21.8990i	−0.306298	−	1.14312i	−0.931823	−	0.362914i	$-0.881782\pi$
$367$	−5.86782	−	21.8990i	−0.306298	−	1.14312i	0.625525	−	0.780204i	$-0.284885\pi$
$368$		0			0
$369$	−1.40709	−	2.43715i	−0.0732502	−	0.126873i
$370$		0			0
$371$	18.7938	+	11.2696i	0.975726	+	0.585090i
$372$		0			0
$373$	12.3984	+	3.32215i	0.641966	+	0.172014i	0.565094	−	0.825027i	$-0.308840\pi$
$373$	12.3984	+	3.32215i	0.641966	+	0.172014i	0.0768720	+	0.997041i	$0.475507\pi$
$374$		0			0
$375$	−11.5645	−	19.4220i	−0.597188	−	1.00295i
$376$		0			0
$377$	−1.46664	+	1.46664i	−0.0755356	+	0.0755356i
$378$		0			0
$379$		−	14.4739i		−	0.743476i	−0.928338	−	0.371738i	$-0.878762\pi$
$379$		−	14.4739i		−	0.743476i	0.928338	−	0.371738i	$-0.121238\pi$
$380$		0			0
$381$	−5.44718	−	3.14493i	−0.279068	−	0.161120i
$382$		0			0
$383$	−0.453341	+	1.69189i	−0.0231647	+	0.0864517i	−0.976540	−	0.215334i	$-0.930916\pi$
$383$	−0.453341	+	1.69189i	−0.0231647	+	0.0864517i	0.953376	+	0.301786i	$0.0975827\pi$
$384$		0			0
$385$	−18.1222	−	15.5831i	−0.923595	−	0.794189i
$386$		0			0
$387$	1.98174	−	7.39595i	0.100737	−	0.375957i
$388$		0			0
$389$	2.40954	+	1.39115i	0.122169	+	0.0705341i	0.559839	−	0.828601i	$-0.310863\pi$
$389$	2.40954	+	1.39115i	0.122169	+	0.0705341i	−0.437670	+	0.899135i	$0.644196\pi$
$390$		0			0
$391$		−	9.25661i		−	0.468127i
$392$		0			0
$393$	−10.4344	+	10.4344i	−0.526348	+	0.526348i
$394$		0			0
$395$	4.75090	−	10.3088i	0.239044	−	0.518692i
$396$		0			0
$397$	38.3163	+	10.2668i	1.92304	+	0.515277i	0.986212	+	0.165486i	$0.0529193\pi$
$397$	38.3163	+	10.2668i	1.92304	+	0.515277i	0.936828	+	0.349791i	$0.113747\pi$
$398$		0			0
$399$	33.1780	+	0.549491i	1.66098	+	0.0275089i
$400$		0			0
$401$	9.98528	+	17.2950i	0.498641	+	0.863672i	0.999999	−	0.00156835i	$-0.000499221\pi$
$401$	9.98528	+	17.2950i	0.498641	+	0.863672i	−0.501358	+	0.865240i	$0.667166\pi$
$402$		0			0
$403$	0.548365	+	2.04653i	0.0273160	+	0.101945i
$404$		0			0
$405$	−2.27000	−	24.6713i	−0.112797	−	1.22593i
$406$		0			0
$407$	13.2144	+	13.2144i	0.655012	+	0.655012i
$408$		0			0
$409$	7.65280	−	13.2550i	0.378407	−	0.655419i	−0.612424	−	0.790529i	$-0.709805\pi$
$409$	7.65280	−	13.2550i	0.378407	−	0.655419i	0.990831	+	0.135110i	$0.0431388\pi$
$410$		0			0
$411$	12.5697	−	7.25713i	0.620019	−	0.357968i
$412$		0			0
$413$	−0.549475	−	2.19547i	−0.0270379	−	0.108032i
$414$		0			0
$415$	12.0108	+	2.06232i	0.589585	+	0.101235i
$416$		0			0
$417$	−24.2495	+	6.49762i	−1.18750	+	0.318190i
$418$		0			0
$419$	−27.7027			−1.35337			−0.676684	−	0.736274i	$-0.736584\pi$
$419$	−27.7027			−1.35337			−0.676684	+	0.736274i	$0.736584\pi$
$420$		0			0
$421$	33.0159			1.60910			0.804549	−	0.593887i	$-0.202407\pi$
$421$	33.0159			1.60910			0.804549	+	0.593887i	$0.202407\pi$
$422$		0			0
$423$	0.331060	−	0.0887072i	0.0160967	−	0.00431309i
$424$		0			0
$425$	−10.1675	−	0.797705i	−0.493194	−	0.0386944i
$426$		0			0
$427$	−5.03138	+	17.6058i	−0.243485	+	0.852005i
$428$		0			0
$429$	−2.04950	+	1.18328i	−0.0989509	+	0.0571293i
$430$		0			0
$431$	11.9586	−	20.7129i	0.576027	−	0.997708i	−0.419902	−	0.907569i	$-0.637936\pi$
$431$	11.9586	−	20.7129i	0.576027	−	0.997708i	0.995929	−	0.0901384i	$-0.0287309\pi$
$432$		0			0
$433$	13.2515	+	13.2515i	0.636829	+	0.636829i	0.949772	−	0.312943i	$-0.101315\pi$
$433$	13.2515	+	13.2515i	0.636829	+	0.636829i	−0.312943	+	0.949772i	$0.601315\pi$
$434$		0			0
$435$	−24.8849	−	20.6914i	−1.19314	−	0.992077i
$436$		0			0
$437$	−7.28615	−	27.1923i	−0.348544	−	1.30078i
$438$		0			0
$439$	−7.05383	−	12.2176i	−0.336661	−	0.583114i	0.647141	−	0.762370i	$-0.275964\pi$
$439$	−7.05383	−	12.2176i	−0.336661	−	0.583114i	−0.983802	+	0.179256i	$0.942631\pi$
$440$		0			0
$441$	−3.58626	−	6.71582i	−0.170774	−	0.319801i
$442$		0			0
$443$	20.3457	+	5.45161i	0.966652	+	0.259014i	0.707414	−	0.706800i	$-0.249862\pi$
$443$	20.3457	+	5.45161i	0.966652	+	0.259014i	0.259238	+	0.965813i	$0.416528\pi$
$444$		0			0
$445$	−6.23919	−	2.87538i	−0.295766	−	0.136306i
$446$		0			0
$447$	34.2370	−	34.2370i	1.61936	−	1.61936i
$448$		0			0
$449$			31.3247i			1.47831i	0.673538	+	0.739153i	$0.264774\pi$
$449$			31.3247i			1.47831i	−0.673538	+	0.739153i	$0.735226\pi$
$450$		0			0
$451$	9.05278	+	5.22662i	0.426279	+	0.246112i
$452$		0			0
$453$	1.85415	−	6.91977i	0.0871154	−	0.325119i
$454$		0			0
$455$	1.41588	−	0.966145i	0.0663776	−	0.0452936i
$456$		0			0
$457$	−0.740622	+	2.76404i	−0.0346448	+	0.129296i	−0.981082	−	0.193591i	$-0.937987\pi$
$457$	−0.740622	+	2.76404i	−0.0346448	+	0.129296i	0.946438	+	0.322887i	$0.104653\pi$
$458$		0			0
$459$	−6.82989	−	3.94324i	−0.318792	−	0.184055i
$460$		0			0
$461$			3.02674i			0.140969i	0.997513	+	0.0704846i	$0.0224546\pi$
$461$			3.02674i			0.140969i	−0.997513	+	0.0704846i	$0.977545\pi$
$462$		0			0
$463$	−19.2889	+	19.2889i	−0.896431	+	0.896431i	−0.995118	−	0.0986876i	$-0.968536\pi$
$463$	−19.2889	+	19.2889i	−0.896431	+	0.896431i	0.0986876	+	0.995118i	$0.468536\pi$
$464$		0			0
$465$	−31.0143	+	11.4461i	−1.43825	+	0.530799i
$466$		0			0
$467$	24.2727	+	6.50385i	1.12321	+	0.300962i	0.772180	−	0.635403i	$-0.219166\pi$
$467$	24.2727	+	6.50385i	1.12321	+	0.300962i	0.351026	+	0.936366i	$0.385833\pi$
$468$		0			0
$469$	−4.29784	+	7.16729i	−0.198456	+	0.330955i
$470$		0			0
$471$	6.18921	+	10.7200i	0.285184	+	0.493953i
$472$		0			0
$473$	7.36115	+	27.4722i	0.338466	+	1.26317i
$474$		0			0
$475$	−30.4959	+	5.65976i	−1.39925	+	0.259688i
$476$		0			0
$477$	6.36989	+	6.36989i	0.291657	+	0.291657i
$478$		0			0
$479$	−4.14346	+	7.17668i	−0.189319	+	0.327911i	−0.945024	−	0.327002i	$-0.893961\pi$
$479$	−4.14346	+	7.17668i	−0.189319	+	0.327911i	0.755704	+	0.654913i	$0.227295\pi$
$480$		0			0
$481$	−1.16069	+	0.670127i	−0.0529231	+	0.0305551i
$482$		0			0
$483$	−17.4470	+	16.8785i	−0.793867	+	0.767999i
$484$		0			0
$485$	−3.54860	+	20.6667i	−0.161134	+	0.938427i
$486$		0			0
$487$	10.3144	−	2.76375i	0.467392	−	0.125237i	−0.0174340	−	0.999848i	$-0.505550\pi$
$487$	10.3144	−	2.76375i	0.467392	−	0.125237i	0.484826	+	0.874611i	$0.338883\pi$
$488$		0			0
$489$	33.4765			1.51386
$490$		0			0
$491$	−25.7259			−1.16100			−0.580498	−	0.814262i	$-0.697142\pi$
$491$	−25.7259			−1.16100			−0.580498	+	0.814262i	$0.697142\pi$
$492$		0			0
$493$	−14.1043	+	3.77924i	−0.635227	+	0.170209i
$494$		0			0
$495$	−5.67156	−	8.02300i	−0.254918	−	0.360607i
$496$		0			0
$497$	−13.5436	+	13.1023i	−0.607514	+	0.587719i
$498$		0			0
$499$	−12.6429	+	7.29940i	−0.565975	+	0.326766i	−0.755540	−	0.655102i	$-0.772626\pi$
$499$	−12.6429	+	7.29940i	−0.565975	+	0.326766i	0.189565	+	0.981868i	$0.439292\pi$
$500$		0			0
$501$	14.7069	−	25.4732i	0.657058	−	1.13806i
$502$		0			0
$503$	13.9891	+	13.9891i	0.623744	+	0.623744i	0.946487	−	0.322743i	$-0.104605\pi$
$503$	13.9891	+	13.9891i	0.623744	+	0.623744i	−0.322743	+	0.946487i	$0.604605\pi$
$504$		0			0
$505$	22.0182	−	2.02589i	0.979798	−	0.0901510i
$506$		0			0
$507$	6.75868	+	25.2237i	0.300163	+	1.12022i
$508$		0			0
$509$	−1.42883	−	2.47481i	−0.0633319	−	0.109694i	0.832621	−	0.553843i	$-0.186839\pi$
$509$	−1.42883	−	2.47481i	−0.0633319	−	0.109694i	−0.895953	+	0.444149i	$0.853506\pi$
$510$		0			0
$511$	−15.6825	+	26.1530i	−0.693754	+	1.15694i
$512$		0			0
$513$	−23.1674	−	6.20768i	−1.02287	−	0.274076i
$514$		0			0
$515$	−3.31513	−	8.98269i	−0.146082	−	0.395825i
$516$		0			0
$517$	−0.900216	+	0.900216i	−0.0395914	+	0.0395914i
$518$		0			0
$519$			15.7134i			0.689741i
$520$		0			0
$521$	24.7917	+	14.3135i	1.08614	+	0.627084i	0.932547	−	0.361049i	$-0.117581\pi$
$521$	24.7917	+	14.3135i	1.08614	+	0.627084i	0.153595	+	0.988134i	$0.450915\pi$
$522$		0			0
$523$	−8.17429	+	30.5069i	−0.357437	+	1.33397i	0.519954	+	0.854195i	$0.325949\pi$
$523$	−8.17429	+	30.5069i	−0.357437	+	1.33397i	−0.877390	+	0.479777i	$0.840717\pi$
$524$		0			0
$525$	17.0358	+	20.6183i	0.743504	+	0.899857i
$526$		0			0
$527$	−3.86048	+	14.4075i	−0.168165	+	0.627600i
$528$		0			0
$529$	−2.08308	−	1.20267i	−0.0905687	−	0.0522899i
$530$		0			0
$531$		−	0.930359i		−	0.0403742i
$532$		0			0
$533$	−0.530105	+	0.530105i	−0.0229614	+	0.0229614i
$534$		0			0
$535$	11.5139	+	31.1981i	0.497790	+	1.34881i
$536$		0			0
$537$	−7.54741	−	2.02232i	−0.325695	−	0.0872696i
$538$		0			0
$539$	24.0094	+	14.9432i	1.03416	+	0.643648i
$540$		0			0
$541$	−18.4994	−	32.0420i	−0.795353	−	1.37759i	−0.922615	−	0.385722i	$-0.873952\pi$
$541$	−18.4994	−	32.0420i	−0.795353	−	1.37759i	0.127262	−	0.991869i	$-0.459381\pi$
$542$		0			0
$543$	−3.65827	−	13.6528i	−0.156991	−	0.585899i
$544$		0			0
$545$	−29.4616	+	2.71076i	−1.26200	+	0.116116i
$546$		0			0
$547$	20.0765	+	20.0765i	0.858409	+	0.858409i	0.991151	−	0.132742i	$-0.0423781\pi$
$547$	20.0765	+	20.0765i	0.858409	+	0.858409i	−0.132742	+	0.991151i	$0.542378\pi$
$548$		0			0
$549$	−3.76360	+	6.51875i	−0.160627	+	0.278213i
$550$		0			0
$551$	−38.4582	+	22.2039i	−1.63838	+	0.945916i
$552$		0			0
$553$	−3.69043	+	12.9136i	−0.156933	+	0.549141i
$554$		0			0
$555$	−12.0716	−	17.0765i	−0.512409	−	0.724855i
$556$		0			0
$557$	24.8367	−	6.65499i	1.05237	−	0.281981i	0.309137	−	0.951017i	$-0.399960\pi$
$557$	24.8367	−	6.65499i	1.05237	−	0.281981i	0.743229	+	0.669037i	$0.233293\pi$
$558$		0			0
$559$	−2.03974			−0.0862718
$560$		0			0
$561$	−16.6605			−0.703408
$562$		0			0
$563$	−5.18407	+	1.38907i	−0.218482	+	0.0585422i	−0.366400	−	0.930458i	$-0.619410\pi$
$563$	−5.18407	+	1.38907i	−0.218482	+	0.0585422i	0.147917	+	0.989000i	$0.452743\pi$
$564$		0			0
$565$	−5.21952	+	30.3980i	−0.219587	+	1.27885i
$566$		0			0
$567$	7.11728	+	28.4377i	0.298898	+	1.19427i
$568$		0			0
$569$	−22.0839	+	12.7502i	−0.925806	+	0.534514i	−0.885483	−	0.464672i	$-0.846172\pi$
$569$	−22.0839	+	12.7502i	−0.925806	+	0.534514i	−0.0403234	+	0.999187i	$0.512839\pi$
$570$		0			0
$571$	7.95235	−	13.7739i	0.332795	−	0.576419i	−0.650263	−	0.759709i	$-0.725341\pi$
$571$	7.95235	−	13.7739i	0.332795	−	0.576419i	0.983059	+	0.183290i	$0.0586748\pi$
$572$		0			0
$573$	−6.39672	−	6.39672i	−0.267227	−	0.267227i
$574$		0			0
$575$	12.8476	−	18.7031i	0.535781	−	0.779973i
$576$		0			0
$577$	−5.96565	−	22.2641i	−0.248353	−	0.926867i	−0.971668	−	0.236349i	$-0.924049\pi$
$577$	−5.96565	−	22.2641i	−0.248353	−	0.926867i	0.723315	−	0.690518i	$-0.242617\pi$
$578$		0			0
$579$	20.2934	+	35.1493i	0.843366	+	1.46075i
$580$		0			0
$581$	−14.4173	−	0.238779i	−0.598132	−	0.00990621i
$582$		0			0
$583$	−32.3214	−	8.66048i	−1.33861	−	0.358681i
$584$		0			0
$585$	0.661059	−	0.243969i	0.0273314	−	0.0100869i
$586$		0			0
$587$	28.2277	−	28.2277i	1.16508	−	1.16508i	0.181734	−	0.983348i	$-0.441829\pi$
$587$	28.2277	−	28.2277i	1.16508	−	1.16508i	0.983348	−	0.181734i	$-0.0581711\pi$
$588$		0			0
$589$			45.3622i			1.86912i
$590$		0			0
$591$	19.4355	+	11.2211i	0.799471	+	0.461575i
$592$		0			0
$593$	−9.16977	+	34.2220i	−0.376557	+	1.40533i	0.474499	+	0.880256i	$0.342629\pi$
$593$	−9.16977	+	34.2220i	−0.376557	+	1.40533i	−0.851056	+	0.525075i	$0.824037\pi$
$594$		0			0
$595$	12.0332	−	0.906496i	0.493312	−	0.0371627i
$596$		0			0
$597$	5.65247	−	21.0953i	0.231340	−	0.863373i
$598$		0			0
$599$	14.5339	+	8.39115i	0.593839	+	0.342853i	0.766614	−	0.642108i	$-0.221940\pi$
$599$	14.5339	+	8.39115i	0.593839	+	0.342853i	−0.172775	+	0.984961i	$0.555273\pi$
$600$		0			0
$601$			1.73528i			0.0707833i	0.999374	+	0.0353917i	$0.0112679\pi$
$601$			1.73528i			0.0707833i	−0.999374	+	0.0353917i	$0.988732\pi$
$602$		0			0
$603$	−2.42925	+	2.42925i	−0.0989266	+	0.0989266i
$604$		0			0
$605$	10.8066	+	4.98031i	0.439350	+	0.202478i
$606$		0			0
$607$	−38.0930	−	10.2070i	−1.54615	−	0.414288i	−0.617900	−	0.786257i	$-0.712016\pi$
$607$	−38.0930	−	10.2070i	−1.54615	−	0.414288i	−0.928245	+	0.371968i	$0.878683\pi$
$608$		0			0
$609$	32.8410	+	19.6930i	1.33079	+	0.798000i
$610$		0			0
$611$	−0.0456517	−	0.0790711i	−0.00184687	−	0.00319887i
$612$		0			0
$613$	0.0885018	+	0.330293i	0.00357455	+	0.0133404i	0.967690	−	0.252143i	$-0.0811352\pi$
$613$	0.0885018	+	0.330293i	0.00357455	+	0.0133404i	−0.964116	+	0.265483i	$0.914469\pi$
$614$		0			0
$615$	−8.99444	−	7.47875i	−0.362691	−	0.301572i
$616$		0			0
$617$	11.1876	+	11.1876i	0.450397	+	0.450397i	0.895486	−	0.445089i	$-0.146828\pi$
$617$	11.1876	+	11.1876i	0.450397	+	0.450397i	−0.445089	+	0.895486i	$0.646828\pi$
$618$		0			0
$619$	18.2682	−	31.6414i	0.734260	−	1.27178i	−0.220787	−	0.975322i	$-0.570862\pi$
$619$	18.2682	−	31.6414i	0.734260	−	1.27178i	0.955047	−	0.296454i	$-0.0958042\pi$
$620$		0			0
$621$	15.1956	−	8.77316i	0.609777	−	0.352055i
$622$		0			0
$623$	7.81566	+	2.23356i	0.313128	+	0.0894855i
$624$		0			0
$625$	−19.4363	−	15.7235i	−0.777452	−	0.628942i
$626$		0			0
$627$	−48.9421	+	13.1140i	−1.95456	+	0.523723i
$628$		0			0
$629$	−9.43535			−0.376212
$630$		0			0
$631$	35.8189			1.42593			0.712964	−	0.701201i	$-0.247352\pi$
$631$	35.8189			1.42593			0.712964	+	0.701201i	$0.247352\pi$
$632$		0			0
$633$	14.7747	−	3.95888i	0.587243	−	0.157351i
$634$		0			0
$635$	−6.85616	−	1.17725i	−0.272079	−	0.0467176i
$636$		0			0
$637$	−1.48083	+	1.38585i	−0.0586726	+	0.0549093i
$638$		0			0
$639$	−6.70867	+	3.87325i	−0.265391	+	0.153223i
$640$		0			0
$641$	7.16573	−	12.4114i	0.283029	−	0.490221i	−0.689100	−	0.724666i	$-0.741994\pi$
$641$	7.16573	−	12.4114i	0.283029	−	0.490221i	0.972129	+	0.234445i	$0.0753272\pi$
$642$		0			0
$643$	7.65201	+	7.65201i	0.301766	+	0.301766i	0.841704	−	0.539939i	$-0.181553\pi$
$643$	7.65201	+	7.65201i	0.301766	+	0.301766i	−0.539939	+	0.841704i	$0.681553\pi$
$644$		0			0
$645$	−2.91605	−	31.6928i	−0.114819	−	1.24790i
$646$		0			0
$647$	−8.37254	−	31.2468i	−0.329159	−	1.22844i	−0.910065	−	0.414466i	$-0.863968\pi$
$647$	−8.37254	−	31.2468i	−0.329159	−	1.22844i	0.580906	−	0.813971i	$-0.302698\pi$
$648$		0			0
$649$	1.72791	+	2.99282i	0.0678262	+	0.117478i
$650$		0			0
$651$	34.1947	−	18.9943i	1.34019	−	0.744447i
$652$		0			0
$653$	0.494788	+	0.132578i	0.0193625	+	0.00518818i	0.268487	−	0.963283i	$-0.413476\pi$
$653$	0.494788	+	0.132578i	0.0193625	+	0.00518818i	−0.249125	+	0.968471i	$0.580143\pi$
$654$		0			0
$655$	−6.83094	+	14.8222i	−0.266907	+	0.579151i
$656$		0			0
$657$	−8.86417	+	8.86417i	−0.345824	+	0.345824i
$658$		0			0
$659$		−	19.5542i		−	0.761723i	−0.924632	−	0.380862i	$-0.875627\pi$
$659$		−	19.5542i		−	0.761723i	0.924632	−	0.380862i	$-0.124373\pi$
$660$		0			0
$661$	34.0324	+	19.6486i	1.32371	+	0.764242i	0.984318	−	0.176405i	$-0.0564468\pi$
$661$	34.0324	+	19.6486i	1.32371	+	0.764242i	0.339388	+	0.940647i	$0.389780\pi$
$662$		0			0
$663$	0.309250	−	1.15414i	0.0120103	−	0.0448230i
$664$		0			0
$665$	34.6352	−	12.1346i	1.34310	−	0.470559i
$666$		0			0
$667$	8.40828	−	31.3801i	0.325570	−	1.21504i
$668$		0			0
$669$	−23.1579	−	13.3702i	−0.895337	−	0.516923i
$670$		0			0
$671$		−	27.9597i		−	1.07937i
$672$		0			0
$673$	18.4813	−	18.4813i	0.712401	−	0.712401i	−0.254636	−	0.967037i	$-0.581956\pi$
$673$	18.4813	−	18.4813i	0.712401	−	0.712401i	0.967037	+	0.254636i	$0.0819556\pi$
$674$		0			0
$675$	−8.32692	−	17.4468i	−0.320503	−	0.671528i
$676$		0			0
$677$	−39.7951	−	10.6631i	−1.52945	−	0.409815i	−0.606611	−	0.794999i	$-0.707472\pi$
$677$	−39.7951	−	10.6631i	−1.52945	−	0.409815i	−0.922840	+	0.385183i	$0.874138\pi$
$678$		0			0
$679$	0.410862	−	24.8076i	0.0157674	−	0.952030i
$680$		0			0
$681$	16.3702	+	28.3541i	0.627309	+	1.08653i
$682$		0			0
$683$	2.36248	+	8.81689i	0.0903978	+	0.337369i	0.996282	−	0.0861573i	$-0.0274588\pi$
$683$	2.36248	+	8.81689i	0.0903978	+	0.337369i	−0.905884	+	0.423526i	$0.860792\pi$
$684$		0			0
$685$	10.2631	−	12.3431i	0.392134	−	0.471607i
$686$		0			0
$687$	16.8358	+	16.8358i	0.642325	+	0.642325i
$688$		0			0
$689$	1.19989	−	2.07827i	0.0457121	−	0.0791758i
$690$		0			0
$691$	41.9971	−	24.2470i	1.59765	−	0.922401i	0.605706	−	0.795689i	$-0.292891\pi$
$691$	41.9971	−	24.2470i	1.59765	−	0.922401i	0.991940	−	0.126712i	$-0.0404424\pi$
$692$		0			0
$693$	8.08313	+	8.35538i	0.307053	+	0.317395i
$694$		0			0
$695$	−22.6726	+	16.0276i	−0.860022	+	0.607960i
$696$		0			0
$697$	−5.09790	+	1.36598i	−0.193097	+	0.0517401i
$698$		0			0
$699$	−11.5732			−0.437739
$700$		0			0
$701$	−30.8898			−1.16669			−0.583347	−	0.812223i	$-0.698257\pi$
$701$	−30.8898			−1.16669			−0.583347	+	0.812223i	$0.698257\pi$
$702$		0			0
$703$	−27.7173	+	7.42684i	−1.04538	+	0.280109i
$704$		0			0
$705$	1.16332	−	0.822363i	0.0438130	−	0.0309720i
$706$		0			0
$707$	−25.3796	+	6.35191i	−0.954496	+	0.238888i
$708$		0			0
$709$	12.7354	−	7.35277i	0.478287	−	0.276139i	−0.241416	−	0.970422i	$-0.577612\pi$
$709$	12.7354	−	7.35277i	0.478287	−	0.276139i	0.719702	+	0.694283i	$0.244278\pi$
$710$		0			0
$711$	−2.76054	+	4.78140i	−0.103528	+	0.179316i
$712$		0			0
$713$	−23.4656	−	23.4656i	−0.878795	−	0.878795i
$714$		0			0
$715$	−1.67341	+	2.01256i	−0.0625821	+	0.0752654i
$716$		0			0
$717$	4.36306	+	16.2831i	0.162941	+	0.608105i
$718$		0			0
$719$	11.7360	+	20.3273i	0.437679	+	0.758082i	0.997510	−	0.0705247i	$-0.0224674\pi$
$719$	11.7360	+	20.3273i	0.437679	+	0.758082i	−0.559831	+	0.828607i	$0.689134\pi$
$720$		0			0
$721$	5.50134	+	9.90382i	0.204881	+	0.368837i
$722$		0			0
$723$	−5.78913	−	1.55119i	−0.215300	−	0.0576895i
$724$		0			0
$725$	−33.7433	−	11.9399i	−1.25320	−	0.443436i
$726$		0			0
$727$	−14.1380	+	14.1380i	−0.524349	+	0.524349i	−0.918882	−	0.394533i	$-0.870907\pi$
$727$	−14.1380	+	14.1380i	−0.524349	+	0.524349i	0.394533	+	0.918882i	$0.370907\pi$
$728$		0			0
$729$		−	11.4004i		−	0.422236i
$730$		0			0
$731$	−12.4359	−	7.17986i	−0.459958	−	0.265557i
$732$		0			0
$733$	−7.17859	+	26.7908i	−0.265147	+	0.989543i	0.697013	+	0.717058i	$0.254512\pi$
$733$	−7.17859	+	26.7908i	−0.265147	+	0.989543i	−0.962160	+	0.272484i	$0.912155\pi$
$734$		0			0
$735$	−23.6499	−	21.0274i	−0.872339	−	0.775608i
$736$		0			0
$737$	3.30280	−	12.3262i	0.121660	−	0.454042i
$738$		0			0
$739$	−11.7451	−	6.78102i	−0.432050	−	0.249444i	0.268170	−	0.963372i	$-0.413581\pi$
$739$	−11.7451	−	6.78102i	−0.432050	−	0.249444i	−0.700219	+	0.713928i	$0.746915\pi$
$740$		0			0
$741$		−	3.63383i		−	0.133492i
$742$		0			0
$743$	−13.5961	+	13.5961i	−0.498791	+	0.498791i	−0.911062	−	0.412270i	$-0.864736\pi$
$743$	−13.5961	+	13.5961i	−0.498791	+	0.498791i	0.412270	+	0.911062i	$0.364736\pi$
$744$		0			0
$745$	22.4134	−	48.6339i	0.821162	−	1.78181i
$746$		0			0
$747$	−5.72557	−	1.53416i	−0.209488	−	0.0561320i
$748$		0			0
$749$	−19.1069	−	34.3973i	−0.698152	−	1.25685i
$750$		0			0
$751$	21.8309	+	37.8123i	0.796622	+	1.37979i	0.921804	+	0.387656i	$0.126715\pi$
$751$	21.8309	+	37.8123i	0.796622	+	1.37979i	−0.125182	+	0.992134i	$0.539951\pi$
$752$		0			0
$753$	−8.46663	−	31.5979i	−0.308541	−	1.15149i
$754$		0			0
$755$	−0.725941	−	7.88981i	−0.0264197	−	0.287140i
$756$		0			0
$757$	7.88896	+	7.88896i	0.286729	+	0.286729i	0.835785	−	0.549056i	$-0.185013\pi$
$757$	7.88896	+	7.88896i	0.286729	+	0.286729i	−0.549056	+	0.835785i	$0.685013\pi$
$758$		0			0
$759$	18.5337	−	32.1013i	0.672730	−	1.16520i
$760$		0			0
$761$	−1.70923	+	0.986825i	−0.0619596	+	0.0357724i	−0.530660	−	0.847585i	$-0.678056\pi$
$761$	−1.70923	+	0.986825i	−0.0619596	+	0.0357724i	0.468700	+	0.883357i	$0.344722\pi$
$762$		0			0
$763$	33.9593	−	8.49921i	1.22941	−	0.307692i
$764$		0			0
$765$	4.88911	+	0.839490i	0.176766	+	0.0303518i
$766$		0			0
$767$	−0.239397	+	0.0641463i	−0.00864413	+	0.00231619i
$768$		0			0
$769$	17.4914			0.630756			0.315378	−	0.948966i	$-0.397869\pi$
$769$	17.4914			0.630756			0.315378	+	0.948966i	$0.397869\pi$
$770$		0			0
$771$	11.7763			0.424112
$772$		0			0
$773$	43.1933	−	11.5736i	1.55355	−	0.416274i	0.622939	−	0.782271i	$-0.285939\pi$
$773$	43.1933	−	11.5736i	1.55355	−	0.416274i	0.930616	+	0.365997i	$0.119272\pi$
$774$		0			0
$775$	−27.7968	+	23.7524i	−0.998491	+	0.853212i
$776$		0			0
$777$	17.2044	+	17.7839i	0.617205	+	0.637994i
$778$		0			0
$779$	−13.9004	+	8.02542i	−0.498035	+	0.287540i
$780$		0			0
$781$	14.3871	−	24.9193i	0.514813	−	0.891682i
$782$		0			0
$783$	−19.5716	−	19.5716i	−0.699433	−	0.699433i
$784$		0			0
$785$	10.5268	+	8.75286i	0.375717	+	0.312403i
$786$		0			0
$787$	−6.71595	−	25.0643i	−0.239398	−	0.893445i	−0.976117	−	0.217246i	$-0.930293\pi$
$787$	−6.71595	−	25.0643i	−0.239398	−	0.893445i	0.736719	−	0.676199i	$-0.236374\pi$
$788$		0			0
$789$	1.75605	+	3.04156i	0.0625170	+	0.108283i
$790$		0			0
$791$	0.604323	−	36.4887i	0.0214873	−	1.29739i
$792$		0			0
$793$	1.93688	+	0.518984i	0.0687805	+	0.0184297i
$794$		0			0
$795$	34.0069	+	15.6724i	1.20610	+	0.555841i
$796$		0			0
$797$	37.3374	−	37.3374i	1.32256	−	1.32256i	0.410861	−	0.911698i	$-0.365228\pi$
$797$	37.3374	−	37.3374i	1.32256	−	1.32256i	0.911698	−	0.410861i	$-0.134772\pi$
$798$		0			0
$799$		−	0.642773i		−	0.0227397i
$800$		0			0
$801$	2.89384	+	1.67076i	0.102249	+	0.0590333i
$802$		0			0
$803$	12.0517	−	44.9776i	0.425295	−	1.58722i
$804$		0			0
$805$	−11.6394	+	24.1937i	−0.410236	+	0.852717i
$806$		0			0
$807$	−1.97975	+	7.38854i	−0.0696906	+	0.260089i
$808$		0			0
$809$	13.9001	+	8.02525i	0.488703	+	0.282153i	0.724036	−	0.689762i	$-0.242285\pi$
$809$	13.9001	+	8.02525i	0.488703	+	0.282153i	−0.235333	+	0.971915i	$0.575618\pi$
$810$		0			0
$811$			35.4040i			1.24320i	0.783334	+	0.621602i	$0.213518\pi$
$811$			35.4040i			1.24320i	−0.783334	+	0.621602i	$0.786482\pi$
$812$		0			0
$813$	−30.3791	+	30.3791i	−1.06544	+	1.06544i
$814$		0			0
$815$	34.7345	−	12.8190i	1.21670	−	0.449032i
$816$		0			0
$817$	−42.1832	−	11.3030i	−1.47580	−	0.395440i
$818$		0			0
$819$	−0.728847	+	0.404858i	−0.0254680	+	0.0141469i
$820$		0			0
$821$	−13.4231	−	23.2495i	−0.468469	−	0.811412i	0.530881	−	0.847446i	$-0.321861\pi$
$821$	−13.4231	−	23.2495i	−0.468469	−	0.811412i	−0.999351	+	0.0360337i	$0.988528\pi$
$822$		0			0
$823$	−7.24225	−	27.0285i	−0.252449	−	0.942153i	−0.969492	−	0.245124i	$-0.921171\pi$
$823$	−7.24225	−	27.0285i	−0.252449	−	0.942153i	0.717043	−	0.697029i	$-0.245495\pi$
$824$		0			0
$825$	−33.6628	−	23.1237i	−1.17199	−	0.805066i
$826$		0			0
$827$	−16.8901	−	16.8901i	−0.587325	−	0.587325i	0.349581	−	0.936906i	$-0.386324\pi$
$827$	−16.8901	−	16.8901i	−0.587325	−	0.587325i	−0.936906	+	0.349581i	$0.886324\pi$
$828$		0			0
$829$	−7.08412	+	12.2701i	−0.246042	+	0.426157i	−0.962424	−	0.271551i	$-0.912463\pi$
$829$	−7.08412	+	12.2701i	−0.246042	+	0.426157i	0.716382	+	0.697708i	$0.245797\pi$
$830$		0			0
$831$	−8.56228	+	4.94343i	−0.297022	+	0.171486i
$832$		0			0
$833$	−13.9065	+	3.23673i	−0.481831	+	0.112146i
$834$		0			0
$835$	5.50526	−	32.0621i	0.190517	−	1.10956i
$836$		0			0
$837$	−27.3100	+	7.31770i	−0.943972	+	0.252937i
$838$		0			0
$839$	18.1874			0.627900			0.313950	−	0.949439i	$-0.398348\pi$
$839$	18.1874			0.627900			0.313950	+	0.949439i	$0.398348\pi$
$840$		0			0
$841$	−22.2469			−0.767134
$842$		0			0
$843$	57.5667	−	15.4250i	1.98270	−	0.531264i
$844$		0			0
$845$	16.6715	+	23.5835i	0.573517	+	0.811298i
$846$		0			0
$847$	−13.5371	−	3.86863i	−0.465141	−	0.132928i
$848$		0			0
$849$	−19.7567	+	11.4065i	−0.678048	+	0.391471i
$850$		0			0
$851$	10.4962	−	18.1799i	0.359804	−	0.623198i
$852$		0			0
$853$	17.4820	+	17.4820i	0.598574	+	0.598574i	0.939933	−	0.341359i	$-0.110887\pi$
$853$	17.4820	+	17.4820i	0.598574	+	0.598574i	−0.341359	+	0.939933i	$0.610887\pi$
$854$		0			0
$855$	15.0231	−	1.38227i	0.513778	−	0.0472726i
$856$		0			0
$857$	−6.76932	−	25.2634i	−0.231235	−	0.862982i	−0.979810	−	0.199932i	$-0.935928\pi$
$857$	−6.76932	−	25.2634i	−0.231235	−	0.862982i	0.748574	−	0.663051i	$-0.230739\pi$
$858$		0			0
$859$	24.4126	+	42.2838i	0.832946	+	1.44271i	0.895692	+	0.444676i	$0.146681\pi$
$859$	24.4126	+	42.2838i	0.832946	+	1.44271i	−0.0627455	+	0.998030i	$0.519986\pi$
$860$		0			0
$861$	11.8701	+	7.11788i	0.404533	+	0.242577i
$862$		0			0
$863$	14.8258	+	3.97256i	0.504676	+	0.135228i	0.502169	−	0.864769i	$-0.332535\pi$
$863$	14.8258	+	3.97256i	0.504676	+	0.135228i	0.00250685	+	0.999997i	$0.499202\pi$
$864$		0			0
$865$	6.01708	+	16.3039i	0.204587	+	0.554349i
$866$		0			0
$867$	−18.3555	+	18.3555i	−0.623387	+	0.623387i
$868$		0			0
$869$		−	20.5080i		−	0.695686i
$870$		0			0
$871$	0.792578	+	0.457595i	0.0268555	+	0.0155050i
$872$		0			0
$873$	2.63980	−	9.85188i	0.0893438	−	0.333436i
$874$		0			0
$875$	25.5713	+	14.8697i	0.864469	+	0.502687i
$876$		0			0
$877$	−10.2134	+	38.1169i	−0.344882	+	1.28712i	0.547868	+	0.836565i	$0.315440\pi$
$877$	−10.2134	+	38.1169i	−0.344882	+	1.28712i	−0.892750	+	0.450552i	$0.851227\pi$
$878$		0			0
$879$	−17.9128	−	10.3420i	−0.604185	−	0.348826i
$880$		0			0
$881$		−	52.5926i		−	1.77189i	−0.463791	−	0.885945i	$-0.653511\pi$
$881$		−	52.5926i		−	1.77189i	0.463791	−	0.885945i	$-0.346489\pi$
$882$		0			0
$883$	−13.0940	+	13.0940i	−0.440649	+	0.440649i	−0.892230	−	0.451581i	$-0.850860\pi$
$883$	−13.0940	+	13.0940i	−0.440649	+	0.440649i	0.451581	+	0.892230i	$0.350860\pi$
$884$		0			0
$885$	−1.33893	−	3.62797i	−0.0450077	−	0.121953i
$886$		0			0
$887$	−35.6990	−	9.56553i	−1.19866	−	0.321179i	−0.396354	−	0.918098i	$-0.629725\pi$
$887$	−35.6990	−	9.56553i	−1.19866	−	0.321179i	−0.802302	+	0.596919i	$0.796391\pi$
$888$		0			0
$889$	8.22991	+	0.136303i	0.276022	+	0.00457146i
$890$		0			0
$891$	−22.3813	−	38.7656i	−0.749803	−	1.29870i
$892$		0			0
$893$	−0.505946	−	1.88822i	−0.0169308	−	0.0631867i
$894$		0			0
$895$	−8.60543	+	0.791785i	−0.287648	+	0.0264664i
$896$		0			0
$897$	1.87976	+	1.87976i	0.0627633	+	0.0627633i
$898$		0			0
$899$	−26.1742	+	45.3351i	−0.872959	+	1.51201i
$900$		0			0
$901$	14.6310	−	8.44719i	0.487428	−	0.281417i
$902$		0			0
$903$	9.14288	+	36.5311i	0.304256	+	1.21568i
$904$		0			0
$905$	−9.02378	−	12.7651i	−0.299961	−	0.424325i
$906$		0			0
$907$	−16.0061	+	4.28883i	−0.531474	+	0.142408i	−0.514569	−	0.857449i	$-0.672048\pi$
$907$	−16.0061	+	4.28883i	−0.531474	+	0.142408i	−0.0169054	+	0.999857i	$0.505381\pi$
$908$		0			0
$909$	−10.7549			−0.356718
$910$		0			0
$911$	1.46770			0.0486270			0.0243135	−	0.999704i	$-0.492260\pi$
$911$	1.46770			0.0486270			0.0243135	+	0.999704i	$0.492260\pi$
$912$		0			0
$913$	21.2676	−	5.69862i	0.703853	−	0.188597i
$914$		0			0
$915$	−5.29482	+	30.8365i	−0.175041	+	1.01942i
$916$		0			0
$917$	5.30617	−	18.5674i	0.175225	−	0.613149i
$918$		0			0
$919$	24.1523	−	13.9443i	0.796710	−	0.459981i	−0.0456096	−	0.998959i	$-0.514523\pi$
$919$	24.1523	−	13.9443i	0.796710	−	0.459981i	0.842319	+	0.538979i	$0.181190\pi$
$920$		0			0
$921$	1.54197	−	2.67078i	0.0508098	−	0.0880051i
$922$		0			0
$923$	1.45920	+	1.45920i	0.0480302	+	0.0480302i
$924$		0			0
$925$	−19.0642	−	13.0957i	−0.626828	−	0.430582i
$926$		0			0
$927$	1.20538	+	4.49855i	0.0395900	+	0.147752i
$928$		0			0
$929$	16.6468	+	28.8331i	0.546164	+	0.945984i	0.998533	+	0.0541530i	$0.0172459\pi$
$929$	16.6468	+	28.8331i	0.546164	+	0.945984i	−0.452368	+	0.891831i	$0.649421\pi$
$930$		0			0
$931$	−38.3040	+	20.4544i	−1.25536	+	0.670367i
$932$		0			0
$933$	−18.8030	−	5.03824i	−0.615581	−	0.164944i
$934$		0			0
$935$	−17.2866	+	6.37976i	−0.565333	+	0.208641i
$936$		0			0
$937$	−25.6651	+	25.6651i	−0.838442	+	0.838442i	−0.988654	−	0.150212i	$-0.952004\pi$
$937$	−25.6651	+	25.6651i	−0.838442	+	0.838442i	0.150212	+	0.988654i	$0.452004\pi$
$938$		0			0
$939$			6.11942i			0.199700i
$940$		0			0
$941$	−21.0732	−	12.1666i	−0.686967	−	0.396621i	0.115508	−	0.993307i	$-0.463151\pi$
$941$	−21.0732	−	12.1666i	−0.686967	−	0.396621i	−0.802475	+	0.596686i	$0.796484\pi$
$942$		0			0
$943$	3.03911	−	11.3421i	0.0989670	−	0.369350i
$944$		0			0
$945$	12.8928	+	18.8944i	0.419402	+	0.614634i
$946$		0			0
$947$	0.556477	−	2.07680i	0.0180831	−	0.0674869i	−0.956295	−	0.292405i	$-0.905545\pi$
$947$	0.556477	−	2.07680i	0.0180831	−	0.0674869i	0.974378	+	0.224918i	$0.0722113\pi$
$948$		0			0
$949$	2.89206	+	1.66973i	0.0938804	+	0.0542019i
$950$		0			0
$951$			3.93980i			0.127757i
$952$		0			0
$953$	−13.1863	+	13.1863i	−0.427146	+	0.427146i	−0.887655	−	0.460509i	$-0.847667\pi$
$953$	−13.1863	+	13.1863i	−0.427146	+	0.427146i	0.460509	+	0.887655i	$0.347667\pi$
$954$		0			0
$955$	−9.08659	−	4.18763i	−0.294035	−	0.135509i
$956$		0			0
$957$	−56.4796	−	15.1337i	−1.82573	−	0.489202i
$958$		0			0
$959$	−9.76792	+	16.2895i	−0.315423	+	0.526015i
$960$		0			0
$961$	11.2368	+	19.4627i	0.362477	+	0.627829i
$962$		0			0
$963$	−4.18646	−	15.6241i	−0.134907	−	0.503479i
$964$		0			0
$965$	34.5156	+	28.6993i	1.11110	+	0.923862i
$966$		0			0
$967$	27.7931	+	27.7931i	0.893766	+	0.893766i	0.994875	−	0.101109i	$-0.0322392\pi$
$967$	27.7931	+	27.7931i	0.893766	+	0.893766i	−0.101109	+	0.994875i	$0.532239\pi$
$968$		0			0
$969$	12.7910	−	22.1547i	0.410907	−	0.711711i
$970$		0			0
$971$	−12.1029	+	6.98760i	−0.388400	+	0.224243i	−0.681467	−	0.731849i	$-0.738658\pi$
$971$	−12.1029	+	6.98760i	−0.388400	+	0.224243i	0.293067	+	0.956092i	$0.405324\pi$
$972$		0			0
$973$	23.6119	−	22.8425i	0.756963	−	0.732298i
$974$		0			0
$975$	2.22671	−	1.90273i	0.0713119	−	0.0609362i
$976$		0			0
$977$	−8.06456	+	2.16089i	−0.258008	+	0.0691331i	−0.385505	−	0.922706i	$-0.625973\pi$
$977$	−8.06456	+	2.16089i	−0.258008	+	0.0691331i	0.127496	+	0.991839i	$0.459306\pi$
$978$		0			0
$979$	−12.4120			−0.396690
$980$		0			0
$981$	14.3907			0.459459
$982$		0			0
$983$	23.5262	−	6.30383i	0.750370	−	0.201061i	0.136688	−	0.990614i	$-0.456354\pi$
$983$	23.5262	−	6.30383i	0.750370	−	0.201061i	0.613682	+	0.789553i	$0.289688\pi$
$984$		0			0
$985$	24.4628	+	4.20041i	0.779449	+	0.133836i
$986$		0			0
$987$	−1.21151	+	1.17203i	−0.0385628	+	0.0373062i
$988$		0			0
$989$	27.6681	−	15.9742i	0.879794	−	0.507949i
$990$		0			0
$991$	8.72002	−	15.1035i	0.277000	−	0.479779i	−0.693637	−	0.720324i	$-0.743993\pi$
$991$	8.72002	−	15.1035i	0.277000	−	0.479779i	0.970638	+	0.240545i	$0.0773263\pi$
$992$		0			0
$993$	41.3067	+	41.3067i	1.31083	+	1.31083i
$994$		0			0
$995$	−2.21307	−	24.0525i	−0.0701590	−	0.762516i
$996$		0			0
$997$	6.77324	+	25.2781i	0.214511	+	0.800565i	0.986338	+	0.164733i	$0.0526762\pi$
$997$	6.77324	+	25.2781i	0.214511	+	0.800565i	−0.771827	+	0.635832i	$0.780657\pi$
$998$		0			0
$999$	−8.94255	−	15.4890i	−0.282930	−	0.490049i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.ci.c.17.1		16
4.3	odd	2		70.2.k.a.17.4	yes	16
5.3	odd	4	inner	560.2.ci.c.353.1		16
7.5	odd	6	inner	560.2.ci.c.257.1		16
12.11	even	2		630.2.bv.c.577.2		16
20.3	even	4		70.2.k.a.3.2	✓	16
20.7	even	4		350.2.o.c.143.3		16
20.19	odd	2		350.2.o.c.157.1		16
28.3	even	6		490.2.g.c.97.8		16
28.11	odd	6		490.2.g.c.97.5		16
28.19	even	6		70.2.k.a.47.2	yes	16
28.23	odd	6		490.2.l.c.117.1		16
28.27	even	2		490.2.l.c.227.3		16
35.33	even	12	inner	560.2.ci.c.33.1		16
60.23	odd	4		630.2.bv.c.73.4		16
84.47	odd	6		630.2.bv.c.397.4		16
140.3	odd	12		490.2.g.c.293.5		16
140.19	even	6		350.2.o.c.257.3		16
140.23	even	12		490.2.l.c.313.3		16
140.47	odd	12		350.2.o.c.243.1		16
140.83	odd	4		490.2.l.c.423.1		16
140.103	odd	12		70.2.k.a.33.4	yes	16
140.123	even	12		490.2.g.c.293.8		16
420.383	even	12		630.2.bv.c.523.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.2.k.a.3.2	✓	16	20.3	even	4
70.2.k.a.17.4	yes	16	4.3	odd	2
70.2.k.a.33.4	yes	16	140.103	odd	12
70.2.k.a.47.2	yes	16	28.19	even	6
350.2.o.c.143.3		16	20.7	even	4
350.2.o.c.157.1		16	20.19	odd	2
350.2.o.c.243.1		16	140.47	odd	12
350.2.o.c.257.3		16	140.19	even	6
490.2.g.c.97.5		16	28.11	odd	6
490.2.g.c.97.8		16	28.3	even	6
490.2.g.c.293.5		16	140.3	odd	12
490.2.g.c.293.8		16	140.123	even	12
490.2.l.c.117.1		16	28.23	odd	6
490.2.l.c.227.3		16	28.27	even	2
490.2.l.c.313.3		16	140.23	even	12
490.2.l.c.423.1		16	140.83	odd	4
560.2.ci.c.17.1		16	1.1	even	1	trivial
560.2.ci.c.33.1		16	35.33	even	12	inner
560.2.ci.c.257.1		16	7.5	odd	6	inner
560.2.ci.c.353.1		16	5.3	odd	4	inner
630.2.bv.c.73.4		16	60.23	odd	4
630.2.bv.c.397.4		16	84.47	odd	6
630.2.bv.c.523.2		16	420.383	even	12
630.2.bv.c.577.2		16	12.11	even	2

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:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.ci (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.95290 + 0.523277i) q^{3} +(-1.82591 + 1.29076i) q^{5} +(1.90155 - 1.83959i) q^{7} +(0.941911 - 0.543813i) q^{9} +(-2.01999 + 3.49872i) q^{11} +(-0.204875 - 0.204875i) q^{13} +(2.89039 - 3.47617i) q^{15} +(-0.527924 - 1.97024i) q^{17} +(-3.10166 - 5.37224i) q^{19} +(-2.75092 + 4.58757i) q^{21} +(4.38350 + 1.17456i) q^{23} +(1.66789 - 4.71361i) q^{25} +(2.73397 - 2.73397i) q^{27} -7.15869i q^{29} +(-6.33287 - 3.65628i) q^{31} +(2.11403 - 7.88965i) q^{33} +(-1.09759 + 5.81337i) q^{35} +(1.19723 - 4.46814i) q^{37} +(0.507306 + 0.292893i) q^{39} -2.58745i q^{41} +(4.97801 - 4.97801i) q^{43} +(-1.01791 + 2.20873i) q^{45} +(0.304388 + 0.0815604i) q^{47} +(0.231803 - 6.99616i) q^{49} +(2.06196 + 3.57142i) q^{51} +(2.14370 + 8.00039i) q^{53} +(-0.827689 - 8.99566i) q^{55} +(8.86840 + 8.86840i) q^{57} +(0.427702 - 0.740802i) q^{59} +(-5.99356 + 3.46038i) q^{61} +(0.790700 - 2.76682i) q^{63} +(0.638527 + 0.109639i) q^{65} +(-3.05106 + 0.817530i) q^{67} -9.17514 q^{69} -7.12240 q^{71} +(-11.1331 + 2.98311i) q^{73} +(-0.790684 + 10.0780i) q^{75} +(2.59511 + 10.3690i) q^{77} +(-4.39618 + 2.53813i) q^{79} +(-5.53997 + 9.59552i) q^{81} +(-3.85372 - 3.85372i) q^{83} +(3.50704 + 2.91605i) q^{85} +(3.74598 + 13.9802i) q^{87} +(1.53615 + 2.66069i) q^{89} +(-0.766467 - 0.0126942i) q^{91} +(14.2807 + 3.82650i) q^{93} +(12.5976 + 5.80572i) q^{95} +(6.63103 - 6.63103i) q^{97} +4.39398i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 12 q^{5} - 8 q^{7} + 12 q^{11} - 16 q^{15} - 36 q^{17} - 28 q^{21} + 4 q^{23} + 12 q^{25} - 24 q^{31} + 48 q^{33} - 8 q^{35} + 4 q^{37} + 8 q^{43} - 12 q^{45} - 12 q^{47} + 16 q^{51} - 28 q^{53}+ \cdots - 20 q^{95}+O(q^{100}) \) 16 * q - 12 * q^5 - 8 * q^7 + 12 * q^11 - 16 * q^15 - 36 * q^17 - 28 * q^21 + 4 * q^23 + 12 * q^25 - 24 * q^31 + 48 * q^33 - 8 * q^35 + 4 * q^37 + 8 * q^43 - 12 * q^45 - 12 * q^47 + 16 * q^51 - 28 * q^53 + 8 * q^57 - 12 * q^61 + 36 * q^63 - 8 * q^65 - 32 * q^67 - 16 * q^71 - 12 * q^73 + 48 * q^75 + 16 * q^77 + 24 * q^85 + 24 * q^87 + 16 * q^91 + 28 * q^93 - 20 * q^95

Introduction

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