LMFDB - Embedded newform 560.2.bs.c.271.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [560,2,Mod(31,560)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(560, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 0, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("560.31"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.bs (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 43 x^{10} - 160 x^{9} + 572 x^{8} - 1394 x^{7} + 3039 x^{6} - 4844 x^{5} + \cdots + 657 $ x^12 - 6x^11 + 43x^10 - 160x^9 + 572x^8 - 1394x^7 + 3039x^6 - 4844x^5 + 6526x^4 - 6318x^3 + 4737x^2 - 2196*x + 657
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			271.5
Root			$0.500000 - 1.58132i$ of defining polynomial
Character	$\chi$	$=$	560.271
Dual form			560.2.bs.c.31.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.22368 + 2.11947i) q^{3} +(-0.866025 - 0.500000i) q^{5} +(-2.49406 + 0.882973i) q^{7} +(-1.49476 + 2.58900i) q^{9} +(-5.60385 + 3.23538i) q^{11} -2.30812i q^{13} -2.44735i q^{15} +(-4.70726 + 2.71774i) q^{17} +(-0.494762 + 0.856953i) q^{19} +(-4.92336 - 4.20562i) q^{21} +(5.17680 + 2.98883i) q^{23} +(0.500000 + 0.866025i) q^{25} +0.0256392 q^{27} +3.02424 q^{29} +(2.62784 + 4.55156i) q^{31} +(-13.7146 - 7.91812i) q^{33} +(2.60141 + 0.482355i) q^{35} +(-0.211966 + 0.367136i) q^{37} +(4.89198 - 2.82439i) q^{39} +9.84894i q^{41} -5.22517i q^{43} +(2.58900 - 1.49476i) q^{45} +(1.96499 - 3.40347i) q^{47} +(5.44072 - 4.40438i) q^{49} +(-11.5203 - 6.65126i) q^{51} +(-4.50577 - 7.80423i) q^{53} +6.47077 q^{55} -2.42171 q^{57} +(4.11048 + 7.11956i) q^{59} +(-5.74509 - 3.31693i) q^{61} +(1.44201 - 7.77698i) q^{63} +(-1.15406 + 1.99889i) q^{65} +(-12.6354 + 7.29503i) q^{67} +14.6294i q^{69} +2.28875i q^{71} +(10.4552 - 6.03634i) q^{73} +(-1.22368 + 2.11947i) q^{75} +(11.1196 - 13.0173i) q^{77} +(-7.02943 - 4.05844i) q^{79} +(4.51566 + 7.82135i) q^{81} +2.94129 q^{83} +5.43548 q^{85} +(3.70069 + 6.40979i) q^{87} +(15.2613 + 8.81111i) q^{89} +(2.03801 + 5.75660i) q^{91} +(-6.43125 + 11.1393i) q^{93} +(0.856953 - 0.494762i) q^{95} +4.96528i q^{97} -19.3445i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{3} - 2 q^{7} - 10 q^{9} + 6 q^{11} + 2 q^{19} + 12 q^{21} - 18 q^{23} + 6 q^{25} + 20 q^{27} + 16 q^{29} + 4 q^{31} - 6 q^{35} - 4 q^{37} + 24 q^{39} - 12 q^{45} + 12 q^{47} - 8 q^{49} - 12 q^{51}+ \cdots - 12 q^{95}+O(q^{100}) $ 12 * q + 2 * q^3 - 2 * q^7 - 10 * q^9 + 6 * q^11 + 2 * q^19 + 12 * q^21 - 18 * q^23 + 6 * q^25 + 20 * q^27 + 16 * q^29 + 4 * q^31 - 6 * q^35 - 4 * q^37 + 24 * q^39 - 12 * q^45 + 12 * q^47 - 8 * q^49 - 12 * q^51 - 12 * q^53 + 24 * q^55 + 16 * q^57 + 24 * q^59 - 48 * q^61 - 56 * q^63 - 2 * q^65 - 42 * q^67 + 24 * q^73 - 2 * q^75 + 40 * q^77 + 12 * q^79 - 6 * q^81 + 36 * q^83 - 16 * q^85 - 30 * q^87 + 12 * q^89 + 36 * q^91 + 28 * q^93 - 12 * q^95

Character values

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

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$	$1$

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
$3$	1.22368	+	2.11947i	0.706489	+	1.22368i	0.966151	+	0.257976i	$0.0830554\pi$
$3$	1.22368	+	2.11947i	0.706489	+	1.22368i	−0.259662	+	0.965700i	$0.583611\pi$
$4$		0			0
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$6$		0			0
$7$	−2.49406	+	0.882973i	−0.942668	+	0.333732i
$7$	−2.49406	+	0.882973i	−0.942668	+	0.333732i
$8$		0			0
$9$	−1.49476	+	2.58900i	−0.498254	+	0.863001i
$10$		0			0
$11$	−5.60385	+	3.23538i	−1.68962	+	0.975505i	−0.734824	+	0.678258i	$0.762735\pi$
$11$	−5.60385	+	3.23538i	−1.68962	+	0.975505i	−0.954801	+	0.297247i	$0.903931\pi$
$12$		0			0
$13$		−	2.30812i		−	0.640157i	−0.947391	−	0.320079i	$-0.896291\pi$
$13$		−	2.30812i		−	0.640157i	0.947391	−	0.320079i	$-0.103709\pi$
$14$		0			0
$15$		−	2.44735i		−	0.631903i
$16$		0			0
$17$	−4.70726	+	2.71774i	−1.14168	+	0.659149i	−0.946846	−	0.321688i	$-0.895750\pi$
$17$	−4.70726	+	2.71774i	−1.14168	+	0.659149i	−0.194833	+	0.980836i	$0.562417\pi$
$18$		0			0
$19$	−0.494762	+	0.856953i	−0.113506	+	0.196598i	−0.917182	−	0.398469i	$-0.869541\pi$
$19$	−0.494762	+	0.856953i	−0.113506	+	0.196598i	0.803675	+	0.595068i	$0.202875\pi$
$20$		0			0
$21$	−4.92336	−	4.20562i	−1.07436	−	0.917741i
$22$		0			0
$23$	5.17680	+	2.98883i	1.07944	+	0.623213i	0.930745	−	0.365670i	$-0.119160\pi$
$23$	5.17680	+	2.98883i	1.07944	+	0.623213i	0.148693	+	0.988883i	$0.452493\pi$
$24$		0			0
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$		0			0
$27$	0.0256392			0.00493426
$28$		0			0
$29$	3.02424			0.561588			0.280794	−	0.959768i	$-0.409402\pi$
$29$	3.02424			0.561588			0.280794	+	0.959768i	$0.409402\pi$
$30$		0			0
$31$	2.62784	+	4.55156i	0.471975	+	0.817484i	0.999486	−	0.0320641i	$-0.0102081\pi$
$31$	2.62784	+	4.55156i	0.471975	+	0.817484i	−0.527511	+	0.849548i	$0.676875\pi$
$32$		0			0
$33$	−13.7146	−	7.91812i	−2.38740	−	1.37837i
$34$		0			0
$35$	2.60141	+	0.482355i	0.439719	+	0.0815330i
$36$		0			0
$37$	−0.211966	+	0.367136i	−0.0348470	+	0.0603567i	−0.882923	−	0.469518i	$-0.844428\pi$
$37$	−0.211966	+	0.367136i	−0.0348470	+	0.0603567i	0.848076	+	0.529875i	$0.177761\pi$
$38$		0			0
$39$	4.89198	−	2.82439i	0.783344	−	0.452264i
$40$		0			0
$41$			9.84894i			1.53815i	0.639161	+	0.769073i	$0.279282\pi$
$41$			9.84894i			1.53815i	−0.639161	+	0.769073i	$0.720718\pi$
$42$		0			0
$43$		−	5.22517i		−	0.796830i	−0.917205	−	0.398415i	$-0.869560\pi$
$43$		−	5.22517i		−	0.796830i	0.917205	−	0.398415i	$-0.130440\pi$
$44$		0			0
$45$	2.58900	−	1.49476i	0.385946	−	0.222826i
$46$		0			0
$47$	1.96499	−	3.40347i	0.286624	−	0.496447i	−0.686378	−	0.727245i	$-0.740800\pi$
$47$	1.96499	−	3.40347i	0.286624	−	0.496447i	0.973002	+	0.230798i	$0.0741336\pi$
$48$		0			0
$49$	5.44072	−	4.40438i	0.777245	−	0.629198i
$50$		0			0
$51$	−11.5203	−	6.65126i	−1.61317	−	0.931363i
$52$		0			0
$53$	−4.50577	−	7.80423i	−0.618916	−	1.07199i	−0.989684	−	0.143268i	$-0.954239\pi$
$53$	−4.50577	−	7.80423i	−0.618916	−	1.07199i	0.370768	−	0.928725i	$-0.379094\pi$
$54$		0			0
$55$	6.47077			0.872518
$56$		0			0
$57$	−2.42171			−0.320763
$58$		0			0
$59$	4.11048	+	7.11956i	0.535139	+	0.926888i	0.999157	+	0.0410623i	$0.0130742\pi$
$59$	4.11048	+	7.11956i	0.535139	+	0.926888i	−0.464017	+	0.885826i	$0.653592\pi$
$60$		0			0
$61$	−5.74509	−	3.31693i	−0.735583	−	0.424689i	0.0848783	−	0.996391i	$-0.472950\pi$
$61$	−5.74509	−	3.31693i	−0.735583	−	0.424689i	−0.820461	+	0.571702i	$0.806283\pi$
$62$		0			0
$63$	1.44201	−	7.77698i	0.181677	−	0.979807i
$64$		0			0
$65$	−1.15406	+	1.99889i	−0.143143	+	0.247932i
$66$		0			0
$67$	−12.6354	+	7.29503i	−1.54366	+	0.891230i	−0.545052	+	0.838402i	$0.683490\pi$
$67$	−12.6354	+	7.29503i	−1.54366	+	0.891230i	−0.998604	+	0.0528283i	$0.983176\pi$
$68$		0			0
$69$			14.6294i			1.76117i
$70$		0			0
$71$			2.28875i			0.271625i	0.990735	+	0.135813i	$0.0433645\pi$
$71$			2.28875i			0.271625i	−0.990735	+	0.135813i	$0.956635\pi$
$72$		0			0
$73$	10.4552	−	6.03634i	1.22369	−	0.706500i	0.257990	−	0.966148i	$-0.416940\pi$
$73$	10.4552	−	6.03634i	1.22369	−	0.706500i	0.965703	+	0.259648i	$0.0836065\pi$
$74$		0			0
$75$	−1.22368	+	2.11947i	−0.141298	+	0.244735i
$76$		0			0
$77$	11.1196	−	13.0173i	1.26720	−	1.48346i
$78$		0			0
$79$	−7.02943	−	4.05844i	−0.790872	−	0.456610i	0.0493971	−	0.998779i	$-0.484270\pi$
$79$	−7.02943	−	4.05844i	−0.790872	−	0.456610i	−0.840270	+	0.542169i	$0.817603\pi$
$80$		0			0
$81$	4.51566	+	7.82135i	0.501740	+	0.869039i
$82$		0			0
$83$	2.94129			0.322849			0.161424	−	0.986885i	$-0.448391\pi$
$83$	2.94129			0.322849			0.161424	+	0.986885i	$0.448391\pi$
$84$		0			0
$85$	5.43548			0.589561
$86$		0			0
$87$	3.70069	+	6.40979i	0.396756	+	0.687202i
$88$		0			0
$89$	15.2613	+	8.81111i	1.61769	+	0.933976i	0.987515	+	0.157527i	$0.0503520\pi$
$89$	15.2613	+	8.81111i	1.61769	+	0.933976i	0.630180	+	0.776449i	$0.282981\pi$
$90$		0			0
$91$	2.03801	+	5.75660i	0.213641	+	0.603455i
$92$		0			0
$93$	−6.43125	+	11.1393i	−0.666890	+	1.15509i
$94$		0			0
$95$	0.856953	−	0.494762i	0.0879215	−	0.0507615i
$96$		0			0
$97$			4.96528i			0.504148i	0.967708	+	0.252074i	$0.0811126\pi$
$97$			4.96528i			0.504148i	−0.967708	+	0.252074i	$0.918887\pi$
$98$		0			0
$99$		−	19.3445i		−	1.94420i
$100$		0			0
$101$	−5.53415	+	3.19514i	−0.550668	+	0.317928i	−0.749391	−	0.662127i	$-0.769654\pi$
$101$	−5.53415	+	3.19514i	−0.550668	+	0.317928i	0.198723	+	0.980056i	$0.436321\pi$
$102$		0			0
$103$	−6.76445	+	11.7164i	−0.666521	+	1.15445i	0.312349	+	0.949967i	$0.398884\pi$
$103$	−6.76445	+	11.7164i	−0.666521	+	1.15445i	−0.978870	+	0.204482i	$0.934449\pi$
$104$		0			0
$105$	2.16094	+	6.10385i	0.210887	+	0.595675i
$106$		0			0
$107$	3.67525	+	2.12191i	0.355300	+	0.205133i	0.667017	−	0.745042i	$-0.267571\pi$
$107$	3.67525	+	2.12191i	0.355300	+	0.205133i	−0.311717	+	0.950175i	$0.600904\pi$
$108$		0			0
$109$	4.69039	+	8.12400i	0.449258	+	0.778138i	0.998338	−	0.0576318i	$-0.0183549\pi$
$109$	4.69039	+	8.12400i	0.449258	+	0.778138i	−0.549080	+	0.835770i	$0.685022\pi$
$110$		0			0
$111$	−1.03751			−0.0984761
$112$		0			0
$113$	−7.45643			−0.701442			−0.350721	−	0.936480i	$-0.614063\pi$
$113$	−7.45643			−0.701442			−0.350721	+	0.936480i	$0.614063\pi$
$114$		0			0
$115$	−2.98883	−	5.17680i	−0.278710	−	0.482739i
$116$		0			0
$117$	5.97573	+	3.45009i	0.552456	+	0.318961i
$118$		0			0
$119$	9.34053	−	10.9346i	0.856245	−	1.00237i
$120$		0			0
$121$	15.4354	−	26.7349i	1.40322	−	2.43045i
$122$		0			0
$123$	−20.8745	+	12.0519i	−1.88219	+	1.08668i
$124$		0			0
$125$		−	1.00000i		−	0.0894427i
$126$		0			0
$127$		−	13.8065i		−	1.22513i	−0.790420	−	0.612565i	$-0.790138\pi$
$127$		−	13.8065i		−	1.22513i	0.790420	−	0.612565i	$-0.209862\pi$
$128$		0			0
$129$	11.0746	−	6.39391i	0.975062	−	0.562952i
$130$		0			0
$131$	−1.27898	+	2.21526i	−0.111745	+	0.193548i	−0.916474	−	0.400094i	$-0.868977\pi$
$131$	−1.27898	+	2.21526i	−0.111745	+	0.193548i	0.804729	+	0.593642i	$0.202311\pi$
$132$		0			0
$133$	0.477302	−	2.57416i	0.0413873	−	0.223208i
$134$		0			0
$135$	−0.0222042	−	0.0128196i	−0.00191103	−	0.00110333i
$136$		0			0
$137$	−0.156375	−	0.270849i	−0.0133600	−	0.0231402i	0.859268	−	0.511525i	$-0.170919\pi$
$137$	−0.156375	−	0.270849i	−0.0133600	−	0.0231402i	−0.872628	+	0.488385i	$0.837586\pi$
$138$		0			0
$139$	0.186858			0.0158491			0.00792453	−	0.999969i	$-0.497478\pi$
$139$	0.186858			0.0158491			0.00792453	+	0.999969i	$0.497478\pi$
$140$		0			0
$141$	9.61806			0.809987
$142$		0			0
$143$	7.46765	+	12.9344i	0.624476	+	1.08162i
$144$		0			0
$145$	−2.61907	−	1.51212i	−0.217502	−	0.125575i
$146$		0			0
$147$	15.9926	+	6.14189i	1.31905	+	0.506575i
$148$		0			0
$149$	−7.07961	+	12.2622i	−0.579984	+	1.00456i	0.415497	+	0.909595i	$0.363608\pi$
$149$	−7.07961	+	12.2622i	−0.579984	+	1.00456i	−0.995480	+	0.0949668i	$0.969726\pi$
$150$		0			0
$151$	18.1869	−	10.5002i	1.48003	−	0.854494i	0.480283	−	0.877114i	$-0.340534\pi$
$151$	18.1869	−	10.5002i	1.48003	−	0.854494i	0.999744	+	0.0226198i	$0.00720072\pi$
$152$		0			0
$153$		−	16.2495i		−	1.31369i
$154$		0			0
$155$		−	5.25569i		−	0.422147i
$156$		0			0
$157$	5.90231	−	3.40770i	0.471055	−	0.271964i	−0.245626	−	0.969365i	$-0.578994\pi$
$157$	5.90231	−	3.40770i	0.471055	−	0.271964i	0.716681	+	0.697401i	$0.245660\pi$
$158$		0			0
$159$	11.0272	−	19.0997i	0.874514	−	1.51470i
$160$		0			0
$161$	−15.5503	−	2.88335i	−1.22554	−	0.227240i
$162$		0			0
$163$	−6.60114	−	3.81117i	−0.517041	−	0.298514i	0.218682	−	0.975796i	$-0.429824\pi$
$163$	−6.60114	−	3.81117i	−0.517041	−	0.298514i	−0.735723	+	0.677282i	$0.763158\pi$
$164$		0			0
$165$	7.91812	+	13.7146i	0.616425	+	1.06768i
$166$		0			0
$167$	−5.01130			−0.387786			−0.193893	−	0.981023i	$-0.562112\pi$
$167$	−5.01130			−0.387786			−0.193893	+	0.981023i	$0.562112\pi$
$168$		0			0
$169$	7.67259			0.590199
$170$		0			0
$171$	−1.47910	−	2.56188i	−0.113110	−	0.195912i
$172$		0			0
$173$	10.4586	+	6.03826i	0.795150	+	0.459080i	0.841773	−	0.539832i	$-0.181512\pi$
$173$	10.4586	+	6.03826i	0.795150	+	0.459080i	−0.0466222	+	0.998913i	$0.514846\pi$
$174$		0			0
$175$	−2.01171	−	1.71844i	−0.152071	−	0.129902i
$176$		0			0
$177$	−10.0598	+	17.4241i	−0.756140	+	1.30967i
$178$		0			0
$179$	−8.81788	+	5.09101i	−0.659080	+	0.380520i	−0.791926	−	0.610617i	$-0.790922\pi$
$179$	−8.81788	+	5.09101i	−0.659080	+	0.380520i	0.132847	+	0.991137i	$0.457588\pi$
$180$		0			0
$181$		−	6.35399i		−	0.472288i	−0.971718	−	0.236144i	$-0.924116\pi$
$181$		−	6.35399i		−	0.472288i	0.971718	−	0.236144i	$-0.0758838\pi$
$182$		0			0
$183$		−	16.2354i		−	1.20015i
$184$		0			0
$185$	0.367136	−	0.211966i	0.0269924	−	0.0155840i
$186$		0			0
$187$	17.5859	−	30.4596i	1.28601	−	2.22743i
$188$		0			0
$189$	−0.0639457	+	0.0226387i	−0.00465137	+	0.00164672i
$190$		0			0
$191$	−5.09447	−	2.94129i	−0.368623	−	0.212824i	0.304234	−	0.952597i	$-0.401600\pi$
$191$	−5.09447	−	2.94129i	−0.368623	−	0.212824i	−0.672857	+	0.739773i	$0.734933\pi$
$192$		0			0
$193$	4.20663	+	7.28609i	0.302800	+	0.524465i	0.976769	−	0.214295i	$-0.0687453\pi$
$193$	4.20663	+	7.28609i	0.302800	+	0.524465i	−0.673969	+	0.738759i	$0.735412\pi$
$194$		0			0
$195$	−5.64878			−0.404517
$196$		0			0
$197$	−15.8091			−1.12635			−0.563174	−	0.826338i	$-0.690420\pi$
$197$	−15.8091			−1.12635			−0.563174	+	0.826338i	$0.690420\pi$
$198$		0			0
$199$	6.18568	+	10.7139i	0.438491	+	0.759489i	0.997573	−	0.0696235i	$-0.0221798\pi$
$199$	6.18568	+	10.7139i	0.438491	+	0.759489i	−0.559082	+	0.829112i	$0.688846\pi$
$200$		0			0
$201$	−30.9232	−	17.8535i	−2.18115	−	1.25929i
$202$		0			0
$203$	−7.54266	+	2.67033i	−0.529391	+	0.187420i
$204$		0			0
$205$	4.92447	−	8.52943i	0.343940	−	0.595721i
$206$		0			0
$207$	−15.4762	+	8.93517i	−1.07567	+	0.621037i
$208$		0			0
$209$		−	6.40298i		−	0.442903i
$210$		0			0
$211$		−	3.49347i		−	0.240500i	−0.992744	−	0.120250i	$-0.961630\pi$
$211$		−	3.49347i		−	0.240500i	0.992744	−	0.120250i	$-0.0383697\pi$
$212$		0			0
$213$	−4.85094	+	2.80069i	−0.332381	+	0.191900i
$214$		0			0
$215$	−2.61258	+	4.52513i	−0.178177	+	0.308611i
$216$		0			0
$217$	−10.5729	−	9.03157i	−0.717736	−	0.613103i
$218$		0			0
$219$	25.5876	+	14.7730i	1.72905	+	0.998269i
$220$		0			0
$221$	6.27287	+	10.8649i	0.421959	+	0.730854i
$222$		0			0
$223$	−22.6778			−1.51862			−0.759309	−	0.650731i	$-0.774463\pi$
$223$	−22.6778			−1.51862			−0.759309	+	0.650731i	$0.774463\pi$
$224$		0			0
$225$	−2.98952			−0.199302
$226$		0			0
$227$	−3.77727	−	6.54243i	−0.250706	−	0.434236i	0.713014	−	0.701150i	$-0.247330\pi$
$227$	−3.77727	−	6.54243i	−0.250706	−	0.434236i	−0.963721	+	0.266913i	$0.913996\pi$
$228$		0			0
$229$	10.6443	+	6.14551i	0.703397	+	0.406106i	0.808611	−	0.588343i	$-0.200220\pi$
$229$	10.6443	+	6.14551i	0.703397	+	0.406106i	−0.105214	+	0.994450i	$0.533553\pi$
$230$		0			0
$231$	41.1965	+	7.63870i	2.71053	+	0.502589i
$232$		0			0
$233$	1.58232	−	2.74065i	0.103661	−	0.179546i	−0.809529	−	0.587079i	$-0.800278\pi$
$233$	1.58232	−	2.74065i	0.103661	−	0.179546i	0.913190	+	0.407533i	$0.133611\pi$
$234$		0			0
$235$	−3.40347	+	1.96499i	−0.222018	+	0.128182i
$236$		0			0
$237$		−	19.8649i		−	1.29036i
$238$		0			0
$239$			27.0004i			1.74651i	0.487263	+	0.873255i	$0.337995\pi$
$239$			27.0004i			1.74651i	−0.487263	+	0.873255i	$0.662005\pi$
$240$		0			0
$241$	11.7391	−	6.77756i	0.756180	−	0.436581i	−0.0717424	−	0.997423i	$-0.522856\pi$
$241$	11.7391	−	6.77756i	0.756180	−	0.436581i	0.827923	+	0.560842i	$0.189523\pi$
$242$		0			0
$243$	−11.0129	+	19.0750i	−0.706481	+	1.22366i
$244$		0			0
$245$	−6.91399	+	1.09395i	−0.441719	+	0.0698898i
$246$		0			0
$247$	1.97795	+	1.14197i	0.125854	+	0.0726618i
$248$		0			0
$249$	3.59919	+	6.23397i	0.228089	+	0.395062i
$250$		0			0
$251$	−14.2304			−0.898215			−0.449108	−	0.893478i	$-0.648258\pi$
$251$	−14.2304			−0.898215			−0.449108	+	0.893478i	$0.648258\pi$
$252$		0			0
$253$	−38.6800			−2.43179
$254$		0			0
$255$	6.65126	+	11.5203i	0.416518	+	0.721431i
$256$		0			0
$257$	16.5626	+	9.56245i	1.03315	+	0.596489i	0.917885	−	0.396846i	$-0.129895\pi$
$257$	16.5626	+	9.56245i	1.03315	+	0.596489i	0.115264	+	0.993335i	$0.463229\pi$
$258$		0			0
$259$	0.204486	−	1.10282i	0.0127061	−	0.0685259i
$260$		0			0
$261$	−4.52053	+	7.82978i	−0.279814	+	0.484651i
$262$		0			0
$263$	−6.01602	+	3.47335i	−0.370964	+	0.214176i	−0.673879	−	0.738841i	$-0.735373\pi$
$263$	−6.01602	+	3.47335i	−0.370964	+	0.214176i	0.302916	+	0.953017i	$0.402040\pi$
$264$		0			0
$265$			9.01155i			0.553575i
$266$		0			0
$267$			43.1278i			2.63938i
$268$		0			0
$269$	6.70087	−	3.86875i	0.408559	−	0.235882i	−0.281611	−	0.959529i	$-0.590869\pi$
$269$	6.70087	−	3.86875i	0.408559	−	0.235882i	0.690171	+	0.723647i	$0.257536\pi$
$270$		0			0
$271$	1.26098	−	2.18408i	0.0765990	−	0.132673i	−0.825181	−	0.564868i	$-0.808927\pi$
$271$	1.26098	−	2.18408i	0.0765990	−	0.132673i	0.901781	+	0.432194i	$0.142261\pi$
$272$		0			0
$273$	−9.70707	+	11.3637i	−0.587498	+	0.687762i
$274$		0			0
$275$	−5.60385	−	3.23538i	−0.337925	−	0.195101i
$276$		0			0
$277$	−14.8320	−	25.6898i	−0.891169	−	1.54355i	−0.838475	−	0.544940i	$-0.816553\pi$
$277$	−14.8320	−	25.6898i	−0.891169	−	1.54355i	−0.0526939	−	0.998611i	$-0.516781\pi$
$278$		0			0
$279$	−15.7120			−0.940653
$280$		0			0
$281$	−15.3527			−0.915862			−0.457931	−	0.888988i	$-0.651409\pi$
$281$	−15.3527			−0.915862			−0.457931	+	0.888988i	$0.651409\pi$
$282$		0			0
$283$	4.51231	+	7.81555i	0.268229	+	0.464586i	0.968405	−	0.249385i	$-0.0802283\pi$
$283$	4.51231	+	7.81555i	0.268229	+	0.464586i	−0.700176	+	0.713971i	$0.746895\pi$
$284$		0			0
$285$	2.09726	+	1.21086i	0.124231	+	0.0717249i
$286$		0			0
$287$	−8.69634	−	24.5639i	−0.513329	−	1.44996i
$288$		0			0
$289$	6.27222	−	10.8638i	0.368954	−	0.639047i
$290$		0			0
$291$	−10.5237	+	6.07589i	−0.616913	+	0.356175i
$292$		0			0
$293$			0.815396i			0.0476359i	0.999716	+	0.0238180i	$0.00758221\pi$
$293$			0.815396i			0.0476359i	−0.999716	+	0.0238180i	$0.992418\pi$
$294$		0			0
$295$		−	8.22097i		−	0.478643i
$296$		0			0
$297$	−0.143678	+	0.0829525i	−0.00833704	+	0.00481339i
$298$		0			0
$299$	6.89857	−	11.9487i	0.398954	−	0.691009i
$300$		0			0
$301$	4.61368	+	13.0319i	0.265928	+	0.751146i
$302$		0			0
$303$	−13.5440	−	7.81963i	−0.778082	−	0.449226i
$304$		0			0
$305$	3.31693	+	5.74509i	0.189927	+	0.328963i
$306$		0			0
$307$	−8.42073			−0.480597			−0.240298	−	0.970699i	$-0.577245\pi$
$307$	−8.42073			−0.480597			−0.240298	+	0.970699i	$0.577245\pi$
$308$		0			0
$309$	−33.1100			−1.88356
$310$		0			0
$311$	10.1220	+	17.5319i	0.573968	+	0.994141i	0.996153	+	0.0876316i	$0.0279298\pi$
$311$	10.1220	+	17.5319i	0.573968	+	0.994141i	−0.422185	+	0.906510i	$0.638737\pi$
$312$		0			0
$313$	21.4103	+	12.3613i	1.21018	+	0.698700i	0.962799	−	0.270217i	$-0.0870955\pi$
$313$	21.4103	+	12.3613i	1.21018	+	0.698700i	0.247385	+	0.968917i	$0.420429\pi$
$314$		0			0
$315$	−5.13731	+	6.01405i	−0.289455	+	0.338853i
$316$		0			0
$317$	−9.30310	+	16.1134i	−0.522514	+	0.905021i	0.477143	+	0.878826i	$0.341673\pi$
$317$	−9.30310	+	16.1134i	−0.522514	+	0.905021i	−0.999657	+	0.0261954i	$0.991661\pi$
$318$		0			0
$319$	−16.9474	+	9.78460i	−0.948873	+	0.547832i
$320$		0			0
$321$			10.3861i			0.579696i
$322$		0			0
$323$		−	5.37854i		−	0.299270i
$324$		0			0
$325$	1.99889	−	1.15406i	0.110878	−	0.0640157i
$326$		0			0
$327$	−11.4790	+	19.8823i	−0.634792	+	1.09949i
$328$		0			0
$329$	−1.89565	+	10.2235i	−0.104511	+	0.563641i
$330$		0			0
$331$	−18.5243	−	10.6950i	−1.01819	−	0.587851i	−0.104610	−	0.994513i	$-0.533359\pi$
$331$	−18.5243	−	10.6950i	−1.01819	−	0.587851i	−0.913579	+	0.406662i	$0.866693\pi$
$332$		0			0
$333$	−0.633677	−	1.09756i	−0.0347253	−	0.0601460i
$334$		0			0
$335$	14.5901			0.797141
$336$		0			0
$337$	−11.2762			−0.614252			−0.307126	−	0.951669i	$-0.599367\pi$
$337$	−11.2762			−0.614252			−0.307126	+	0.951669i	$0.599367\pi$
$338$		0			0
$339$	−9.12425	−	15.8037i	−0.495561	−	0.858337i
$340$		0			0
$341$	−29.4521	−	17.0042i	−1.59492	−	0.920827i
$342$		0			0
$343$	−9.68055	+	15.7888i	−0.522701	+	0.852516i
$344$		0			0
$345$	7.31471	−	12.6694i	0.393811	−	0.682100i
$346$		0			0
$347$	22.4623	−	12.9686i	1.20584	−	0.696192i	0.243992	−	0.969777i	$-0.421543\pi$
$347$	22.4623	−	12.9686i	1.20584	−	0.696192i	0.961848	+	0.273585i	$0.0882095\pi$
$348$		0			0
$349$		−	15.3031i		−	0.819159i	−0.912274	−	0.409579i	$-0.865675\pi$
$349$		−	15.3031i		−	0.819159i	0.912274	−	0.409579i	$-0.134325\pi$
$350$		0			0
$351$		−	0.0591782i		−	0.00315870i
$352$		0			0
$353$	3.43863	−	1.98530i	0.183020	−	0.105667i	−0.405691	−	0.914010i	$-0.632969\pi$
$353$	3.43863	−	1.98530i	0.183020	−	0.105667i	0.588711	+	0.808344i	$0.299636\pi$
$354$		0			0
$355$	1.14438	−	1.98212i	0.0607372	−	0.105200i
$356$		0			0
$357$	34.6053	+	6.41655i	1.83151	+	0.339600i
$358$		0			0
$359$	−24.9641	−	14.4130i	−1.31755	−	0.760689i	−0.334218	−	0.942496i	$-0.608472\pi$
$359$	−24.9641	−	14.4130i	−1.31755	−	0.760689i	−0.983334	+	0.181806i	$0.941806\pi$
$360$		0			0
$361$	9.01042	+	15.6065i	0.474233	+	0.821395i
$362$		0			0
$363$	75.5518			3.96544
$364$		0			0
$365$	−12.0727			−0.631912
$366$		0			0
$367$	5.13465	+	8.89347i	0.268026	+	0.464236i	0.968352	−	0.249588i	$-0.0802952\pi$
$367$	5.13465	+	8.89347i	0.268026	+	0.464236i	−0.700326	+	0.713824i	$0.746962\pi$
$368$		0			0
$369$	−25.4989	−	14.7218i	−1.32742	−	0.766387i
$370$		0			0
$371$	18.1286	+	15.4858i	0.941191	+	0.803982i
$372$		0			0
$373$	17.2110	−	29.8103i	0.891151	−	1.54352i	0.0526548	−	0.998613i	$-0.483232\pi$
$373$	17.2110	−	29.8103i	0.891151	−	1.54352i	0.838497	−	0.544907i	$-0.183435\pi$
$374$		0			0
$375$	2.11947	−	1.22368i	0.109449	−	0.0631903i
$376$		0			0
$377$		−	6.98032i		−	0.359505i
$378$		0			0
$379$		−	10.7999i		−	0.554754i	−0.960761	−	0.277377i	$-0.910535\pi$
$379$		−	10.7999i		−	0.554754i	0.960761	−	0.277377i	$-0.0894651\pi$
$380$		0			0
$381$	29.2624	−	16.8947i	1.49916	−	0.865541i
$382$		0			0
$383$	12.4793	−	21.6148i	0.637664	−	1.10447i	−0.348280	−	0.937390i	$-0.613234\pi$
$383$	12.4793	−	21.6148i	0.637664	−	1.10447i	0.985944	−	0.167075i	$-0.0534323\pi$
$384$		0			0
$385$	−16.1385	+	5.71351i	−0.822495	+	0.291188i
$386$		0			0
$387$	13.5280	+	7.81038i	0.687666	+	0.397024i
$388$		0			0
$389$	−14.6421	−	25.3609i	−0.742384	−	1.28585i	−0.951407	−	0.307937i	$-0.900362\pi$
$389$	−14.6421	−	25.3609i	−0.742384	−	1.28585i	0.209022	−	0.977911i	$-0.432972\pi$
$390$		0			0
$391$	−32.4914			−1.64316
$392$		0			0
$393$	−6.26022			−0.315787
$394$		0			0
$395$	4.05844	+	7.02943i	0.204202	+	0.353689i
$396$		0			0
$397$	11.1825	+	6.45624i	0.561235	+	0.324029i	0.753641	−	0.657286i	$-0.228296\pi$
$397$	11.1825	+	6.45624i	0.561235	+	0.324029i	−0.192406	+	0.981315i	$0.561629\pi$
$398$		0			0
$399$	6.03990	−	2.13831i	0.302373	−	0.107049i
$400$		0			0
$401$	0.880955	−	1.52586i	0.0439928	−	0.0761977i	−0.843191	−	0.537615i	$-0.819325\pi$
$401$	0.880955	−	1.52586i	0.0439928	−	0.0761977i	0.887183	+	0.461417i	$0.152659\pi$
$402$		0			0
$403$	10.5055	−	6.06537i	0.523318	−	0.302138i
$404$		0			0
$405$		−	9.03132i		−	0.448770i
$406$		0			0
$407$		−	2.74316i		−	0.135974i
$408$		0			0
$409$	−34.7367	+	20.0552i	−1.71762	+	0.991667i	−0.794397	+	0.607399i	$0.792213\pi$
$409$	−34.7367	+	20.0552i	−1.71762	+	0.991667i	−0.923221	+	0.384268i	$0.874454\pi$
$410$		0			0
$411$	0.382704	−	0.662863i	0.0188774	−	0.0326966i
$412$		0			0
$413$	−16.5382	−	14.1272i	−0.813791	−	0.695155i
$414$		0			0
$415$	−2.54723	−	1.47065i	−0.125039	−	0.0721912i
$416$		0			0
$417$	0.228653	+	0.396039i	0.0111972	+	0.0193941i
$418$		0			0
$419$	12.0471			0.588539			0.294269	−	0.955723i	$-0.404924\pi$
$419$	12.0471			0.588539			0.294269	+	0.955723i	$0.404924\pi$
$420$		0			0
$421$	28.6654			1.39707			0.698533	−	0.715578i	$-0.253836\pi$
$421$	28.6654			1.39707			0.698533	+	0.715578i	$0.253836\pi$
$422$		0			0
$423$	5.87440	+	10.1748i	0.285623	+	0.494714i
$424$		0			0
$425$	−4.70726	−	2.71774i	−0.228336	−	0.131830i
$426$		0			0
$427$	17.2574	+	3.19988i	0.835143	+	0.154853i
$428$		0			0
$429$	−18.2760	+	31.6549i	−0.882372	+	1.52831i
$430$		0			0
$431$	14.8354	−	8.56524i	0.714597	−	0.412573i	−0.0981636	−	0.995170i	$-0.531297\pi$
$431$	14.8354	−	8.56524i	0.714597	−	0.412573i	0.812761	+	0.582597i	$0.197964\pi$
$432$		0			0
$433$		−	12.4485i		−	0.598235i	−0.954216	−	0.299117i	$-0.903308\pi$
$433$		−	12.4485i		−	0.598235i	0.954216	−	0.299117i	$-0.0966923\pi$
$434$		0			0
$435$		−	7.40139i		−	0.354869i
$436$		0			0
$437$	−5.12257	+	2.95751i	−0.245046	+	0.141477i
$438$		0			0
$439$	−5.40019	+	9.35340i	−0.257737	+	0.446414i	−0.965635	−	0.259901i	$-0.916310\pi$
$439$	−5.40019	+	9.35340i	−0.257737	+	0.446414i	0.707898	+	0.706314i	$0.249643\pi$
$440$		0			0
$441$	3.27038	+	20.6695i	0.155733	+	0.984264i
$442$		0			0
$443$	0.0831833	+	0.0480259i	0.00395216	+	0.00228178i	0.501975	−	0.864882i	$-0.332607\pi$
$443$	0.0831833	+	0.0480259i	0.00395216	+	0.00228178i	−0.498023	+	0.867164i	$0.665940\pi$
$444$		0			0
$445$	−8.81111	−	15.2613i	−0.417687	−	0.723455i
$446$		0			0
$447$	−34.6525			−1.63901
$448$		0			0
$449$	13.7048			0.646770			0.323385	−	0.946268i	$-0.395179\pi$
$449$	13.7048			0.646770			0.323385	+	0.946268i	$0.395179\pi$
$450$		0			0
$451$	−31.8651	−	55.1920i	−1.50047	−	2.59889i
$452$		0			0
$453$	44.5097	+	25.6977i	2.09125	+	1.20738i
$454$		0			0
$455$	1.11333	−	6.00436i	0.0521939	−	0.281489i
$456$		0			0
$457$	−10.7440	+	18.6091i	−0.502583	+	0.870499i	0.497413	+	0.867514i	$0.334283\pi$
$457$	−10.7440	+	18.6091i	−0.502583	+	0.870499i	−0.999996	+	0.00298483i	$0.999050\pi$
$458$		0			0
$459$	−0.120690	+	0.0696806i	−0.00563334	+	0.00325241i
$460$		0			0
$461$			27.2004i			1.26685i	0.773804	+	0.633425i	$0.218351\pi$
$461$			27.2004i			1.26685i	−0.773804	+	0.633425i	$0.781649\pi$
$462$		0			0
$463$		−	30.2578i		−	1.40620i	−0.711092	−	0.703099i	$-0.751799\pi$
$463$		−	30.2578i		−	1.40620i	0.711092	−	0.703099i	$-0.248201\pi$
$464$		0			0
$465$	11.1393	−	6.43125i	0.516571	−	0.298242i
$466$		0			0
$467$	8.38737	−	14.5274i	0.388121	−	0.672246i	−0.604076	−	0.796927i	$-0.706458\pi$
$467$	8.38737	−	14.5274i	0.388121	−	0.672246i	0.992197	+	0.124681i	$0.0397908\pi$
$468$		0			0
$469$	25.0721	−	29.3510i	1.15772	−	1.35530i
$470$		0			0
$471$	14.4450	+	8.33983i	0.665591	+	0.384279i
$472$		0			0
$473$	16.9054	+	29.2811i	0.777312	+	1.34634i
$474$		0			0
$475$	−0.989524			−0.0454025
$476$		0			0
$477$	26.9402			1.23351
$478$		0			0
$479$	−8.56995	−	14.8436i	−0.391571	−	0.678221i	0.601086	−	0.799184i	$-0.294735\pi$
$479$	−8.56995	−	14.8436i	−0.391571	−	0.678221i	−0.992657	+	0.120964i	$0.961402\pi$
$480$		0			0
$481$	0.847393	+	0.489243i	0.0386378	+	0.0223075i
$482$		0			0
$483$	−12.9174	−	36.4867i	−0.587761	−	1.66020i
$484$		0			0
$485$	2.48264	−	4.30006i	0.112731	−	0.195256i
$486$		0			0
$487$	−9.77556	+	5.64392i	−0.442973	+	0.255750i	−0.704858	−	0.709349i	$-0.748989\pi$
$487$	−9.77556	+	5.64392i	−0.442973	+	0.255750i	0.261885	+	0.965099i	$0.415656\pi$
$488$		0			0
$489$		−	18.6545i		−	0.843587i
$490$		0			0
$491$			25.5317i			1.15223i	0.817369	+	0.576115i	$0.195432\pi$
$491$			25.5317i			1.15223i	−0.817369	+	0.576115i	$0.804568\pi$
$492$		0			0
$493$	−14.2359	+	8.21911i	−0.641154	+	0.370170i
$494$		0			0
$495$	−9.67226	+	16.7528i	−0.434736	+	0.752984i
$496$		0			0
$497$	−2.02091	−	5.70830i	−0.0906501	−	0.256052i
$498$		0			0
$499$	14.7658	+	8.52503i	0.661007	+	0.381633i	0.792661	−	0.609663i	$-0.208695\pi$
$499$	14.7658	+	8.52503i	0.661007	+	0.381633i	−0.131653	+	0.991296i	$0.542029\pi$
$500$		0			0
$501$	−6.13221	−	10.6213i	−0.273967	−	0.474524i
$502$		0			0
$503$	29.6588			1.32242			0.661211	−	0.750200i	$-0.270043\pi$
$503$	29.6588			1.32242			0.661211	+	0.750200i	$0.270043\pi$
$504$		0			0
$505$	6.39028			0.284364
$506$		0			0
$507$	9.38875	+	16.2618i	0.416969	+	0.722212i
$508$		0			0
$509$	20.4666	+	11.8164i	0.907167	+	0.523753i	0.879519	−	0.475865i	$-0.157865\pi$
$509$	20.4666	+	11.8164i	0.907167	+	0.523753i	0.0276483	+	0.999618i	$0.491198\pi$
$510$		0			0
$511$	−20.7461	+	24.2867i	−0.917754	+	1.07438i
$512$		0			0
$513$	−0.0126853	+	0.0219715i	−0.000560069	+	0.000970067i
$514$		0			0
$515$	11.7164	−	6.76445i	0.516285	−	0.298077i
$516$		0			0
$517$			25.4301i			1.11841i
$518$		0			0
$519$			29.5555i			1.29734i
$520$		0			0
$521$	−15.2756	+	8.81935i	−0.669235	+	0.386383i	−0.795787	−	0.605577i	$-0.792942\pi$
$521$	−15.2756	+	8.81935i	−0.669235	+	0.386383i	0.126552	+	0.991960i	$0.459609\pi$
$522$		0			0
$523$	10.9640	−	18.9902i	0.479423	−	0.830385i	−0.520298	−	0.853985i	$-0.674179\pi$
$523$	10.9640	−	18.9902i	0.479423	−	0.830385i	0.999721	+	0.0235992i	$0.00751257\pi$
$524$		0			0
$525$	1.18049	−	6.36656i	0.0515209	−	0.277860i
$526$		0			0
$527$	−24.7399	−	14.2836i	−1.07769	−	0.622203i
$528$		0			0
$529$	6.36617	+	11.0265i	0.276790	+	0.479414i
$530$		0			0
$531$	−24.5768			−1.06654
$532$		0			0
$533$	22.7325			0.984655
$534$		0			0
$535$	−2.12191	−	3.67525i	−0.0917381	−	0.158895i
$536$		0			0
$537$	−21.5804	−	12.4595i	−0.931265	−	0.537666i
$538$		0			0
$539$	−16.2391	+	42.2843i	−0.699467	+	1.82131i
$540$		0			0
$541$	−1.03970	+	1.80081i	−0.0447002	+	0.0774231i	−0.887510	−	0.460789i	$-0.847567\pi$
$541$	−1.03970	+	1.80081i	−0.0447002	+	0.0774231i	0.842810	+	0.538212i	$0.180900\pi$
$542$		0			0
$543$	13.4671	−	7.77522i	0.577928	−	0.333667i
$544$		0			0
$545$		−	9.38079i		−	0.401829i
$546$		0			0
$547$		−	9.15708i		−	0.391528i	−0.980651	−	0.195764i	$-0.937281\pi$
$547$		−	9.15708i		−	0.391528i	0.980651	−	0.195764i	$-0.0627187\pi$
$548$		0			0
$549$	17.1751	−	9.91603i	0.733014	−	0.423206i
$550$		0			0
$551$	−1.49628	+	2.59163i	−0.0637437	+	0.110407i
$552$		0			0
$553$	21.1153	+	3.91522i	0.897916	+	0.166492i
$554$		0			0
$555$	0.898510	+	0.518755i	0.0381396	+	0.0220199i
$556$		0			0
$557$	7.88972	+	13.6654i	0.334298	+	0.579021i	0.983350	−	0.181723i	$-0.0581674\pi$
$557$	7.88972	+	13.6654i	0.334298	+	0.579021i	−0.649052	+	0.760744i	$0.724834\pi$
$558$		0			0
$559$	−12.0603			−0.510097
$560$		0			0
$561$	86.0776			3.63420
$562$		0			0
$563$	2.40099	+	4.15864i	0.101190	+	0.175266i	0.912175	−	0.409801i	$-0.134402\pi$
$563$	2.40099	+	4.15864i	0.101190	+	0.175266i	−0.810985	+	0.585066i	$0.801068\pi$
$564$		0			0
$565$	6.45746	+	3.72822i	0.271667	+	0.156847i
$566$		0			0
$567$	−18.1684	−	15.5198i	−0.763001	−	0.651768i
$568$		0			0
$569$	12.8609	−	22.2758i	0.539158	−	0.933850i	−0.459791	−	0.888027i	$-0.652076\pi$
$569$	12.8609	−	22.2758i	0.539158	−	0.933850i	0.998950	−	0.0458225i	$-0.0145909\pi$
$570$		0			0
$571$	15.4404	−	8.91452i	0.646161	−	0.373061i	−0.140823	−	0.990035i	$-0.544975\pi$
$571$	15.4404	−	8.91452i	0.646161	−	0.373061i	0.786984	+	0.616974i	$0.211641\pi$
$572$		0			0
$573$		−	14.3967i		−	0.601433i
$574$		0			0
$575$			5.97765i			0.249285i
$576$		0			0
$577$	28.6062	−	16.5158i	1.19089	−	0.687563i	0.232384	−	0.972624i	$-0.425347\pi$
$577$	28.6062	−	16.5158i	1.19089	−	0.687563i	0.958509	+	0.285062i	$0.0920140\pi$
$578$		0			0
$579$	−10.2951	+	17.8316i	−0.427850	+	0.741057i
$580$		0			0
$581$	−7.33577	+	2.59708i	−0.304339	+	0.107745i
$582$		0			0
$583$	50.4994	+	29.1558i	2.09147	+	1.20751i
$584$		0			0
$585$	−3.45009	−	5.97573i	−0.142644	−	0.247066i
$586$		0			0
$587$	−14.6086			−0.602960			−0.301480	−	0.953472i	$-0.597481\pi$
$587$	−14.6086			−0.602960			−0.301480	+	0.953472i	$0.597481\pi$
$588$		0			0
$589$	−5.20063			−0.214288
$590$		0			0
$591$	−19.3451	−	33.5068i	−0.795753	−	1.37828i
$592$		0			0
$593$	−9.24743	−	5.33901i	−0.379746	−	0.219247i	0.297962	−	0.954578i	$-0.403693\pi$
$593$	−9.24743	−	5.33901i	−0.379746	−	0.219247i	−0.677708	+	0.735331i	$0.737027\pi$
$594$		0			0
$595$	−13.5564	+	4.79938i	−0.555760	+	0.196755i
$596$		0			0
$597$	−15.1385	+	26.2207i	−0.619578	+	1.07314i
$598$		0			0
$599$	−12.5607	+	7.25191i	−0.513216	+	0.296305i	−0.734154	−	0.678982i	$-0.762421\pi$
$599$	−12.5607	+	7.25191i	−0.513216	+	0.296305i	0.220939	+	0.975288i	$0.429088\pi$
$600$		0			0
$601$			38.6998i			1.57860i	0.614008	+	0.789299i	$0.289556\pi$
$601$			38.6998i			1.57860i	−0.614008	+	0.789299i	$0.710444\pi$
$602$		0			0
$603$		−	43.6174i		−	1.77624i
$604$		0			0
$605$	−26.7349	+	15.4354i	−1.08693	+	0.627539i
$606$		0			0
$607$	8.72945	−	15.1198i	0.354317	−	0.613696i	−0.632683	−	0.774410i	$-0.718047\pi$
$607$	8.72945	−	15.1198i	0.354317	−	0.613696i	0.987001	+	0.160715i	$0.0513799\pi$
$608$		0			0
$609$	−14.8894	−	12.7188i	−0.603351	−	0.515392i
$610$		0			0
$611$	−7.85562	−	4.53544i	−0.317804	−	0.183484i
$612$		0			0
$613$	8.97395	+	15.5433i	0.362455	+	0.627790i	0.988364	−	0.152106i	$-0.0486055\pi$
$613$	8.97395	+	15.5433i	0.362455	+	0.627790i	−0.625910	+	0.779896i	$0.715272\pi$
$614$		0			0
$615$	24.1038			0.971959
$616$		0			0
$617$	47.2698			1.90301			0.951506	−	0.307629i	$-0.0995357\pi$
$617$	47.2698			1.90301			0.951506	+	0.307629i	$0.0995357\pi$
$618$		0			0
$619$	23.4615	+	40.6366i	0.942999	+	1.63332i	0.759709	+	0.650264i	$0.225342\pi$
$619$	23.4615	+	40.6366i	0.942999	+	1.63332i	0.183290	+	0.983059i	$0.441325\pi$
$620$		0			0
$621$	0.132729	+	0.0766310i	0.00532622	+	0.00307510i
$622$		0			0
$623$	−45.8426	−	8.50018i	−1.83665	−	0.340552i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$	13.5709	−	7.83517i	0.541970	−	0.312906i
$628$		0			0
$629$		−	2.30427i		−	0.0918774i
$630$		0			0
$631$			26.1192i			1.03979i	0.854231	+	0.519894i	$0.174028\pi$
$631$			26.1192i			1.03979i	−0.854231	+	0.519894i	$0.825972\pi$
$632$		0			0
$633$	7.40430	−	4.27487i	0.294294	−	0.169911i
$634$		0			0
$635$	−6.90325	+	11.9568i	−0.273947	+	0.474491i
$636$		0			0
$637$	−10.1658	−	12.5578i	−0.402785	−	0.497559i
$638$		0			0
$639$	−5.92559	−	3.42114i	−0.234413	−	0.135338i
$640$		0			0
$641$	8.97538	+	15.5458i	0.354506	+	0.614023i	0.987033	−	0.160515i	$-0.0513156\pi$
$641$	8.97538	+	15.5458i	0.354506	+	0.614023i	−0.632527	+	0.774538i	$0.717982\pi$
$642$		0			0
$643$	28.8535			1.13787			0.568936	−	0.822382i	$-0.307355\pi$
$643$	28.8535			1.13787			0.568936	+	0.822382i	$0.307355\pi$
$644$		0			0
$645$	−12.7878			−0.503520
$646$		0			0
$647$	−15.9361	−	27.6021i	−0.626512	−	1.08515i	−0.988246	−	0.152869i	$-0.951149\pi$
$647$	−15.9361	−	27.6021i	−0.626512	−	1.08515i	0.361735	−	0.932281i	$-0.382185\pi$
$648$		0			0
$649$	−46.0691	−	26.5980i	−1.80837	−	1.04406i
$650$		0			0
$651$	6.20430	−	33.4606i	0.243166	−	1.31143i
$652$		0			0
$653$	−0.534003	+	0.924921i	−0.0208972	+	0.0361950i	−0.876285	−	0.481793i	$-0.839986\pi$
$653$	−0.534003	+	0.924921i	−0.0208972	+	0.0361950i	0.855388	+	0.517988i	$0.173319\pi$
$654$		0			0
$655$	2.21526	−	1.27898i	0.0865573	−	0.0499739i
$656$		0			0
$657$			36.0915i			1.40806i
$658$		0			0
$659$		−	27.6777i		−	1.07817i	−0.842252	−	0.539085i	$-0.818770\pi$
$659$		−	27.6777i		−	1.07817i	0.842252	−	0.539085i	$-0.181230\pi$
$660$		0			0
$661$	−25.2579	+	14.5827i	−0.982418	+	0.567200i	−0.902999	−	0.429642i	$-0.858640\pi$
$661$	−25.2579	+	14.5827i	−0.982418	+	0.567200i	−0.0794190	+	0.996841i	$0.525307\pi$
$662$		0			0
$663$	−15.3519	+	26.5903i	−0.596219	+	1.03268i
$664$		0			0
$665$	−1.70043	+	1.99063i	−0.0659400	+	0.0771935i
$666$		0			0
$667$	15.6559	+	9.03894i	0.606199	+	0.349989i
$668$		0			0
$669$	−27.7503	−	48.0648i	−1.07289	−	1.85829i
$670$		0			0
$671$	42.9261			1.65714
$672$		0			0
$673$	5.57642			0.214955			0.107478	−	0.994208i	$-0.465723\pi$
$673$	5.57642			0.214955			0.107478	+	0.994208i	$0.465723\pi$
$674$		0			0
$675$	0.0128196	+	0.0222042i	0.000493426	+	0.000854639i
$676$		0			0
$677$	10.2275	+	5.90484i	0.393074	+	0.226942i	0.683491	−	0.729959i	$-0.260461\pi$
$677$	10.2275	+	5.90484i	0.393074	+	0.226942i	−0.290417	+	0.956900i	$0.593794\pi$
$678$		0			0
$679$	−4.38421	−	12.3837i	−0.168250	−	0.475244i
$680$		0			0
$681$	9.24431	−	16.0116i	0.354243	−	0.613567i
$682$		0			0
$683$	−17.1263	+	9.88788i	−0.655320	+	0.378349i	−0.790491	−	0.612473i	$-0.790175\pi$
$683$	−17.1263	+	9.88788i	−0.655320	+	0.378349i	0.135171	+	0.990822i	$0.456841\pi$
$684$		0			0
$685$			0.312750i			0.0119496i
$686$		0			0
$687$			30.0804i			1.14764i
$688$		0			0
$689$	−18.0131	+	10.3999i	−0.686244	+	0.396203i
$690$		0			0
$691$	5.06918	−	8.78008i	0.192841	−	0.334010i	−0.753350	−	0.657620i	$-0.771563\pi$
$691$	5.06918	−	8.78008i	0.192841	−	0.334010i	0.946191	+	0.323610i	$0.104897\pi$
$692$		0			0
$693$	17.0807	+	48.2465i	0.648841	+	1.83273i
$694$		0			0
$695$	−0.161823	−	0.0934288i	−0.00613831	−	0.00354396i
$696$		0			0
$697$	−26.7668	−	46.3615i	−1.01387	−	1.75607i
$698$		0			0
$699$	7.74497			0.292942
$700$		0			0
$701$	−0.203655			−0.00769196			−0.00384598	−	0.999993i	$-0.501224\pi$
$701$	−0.203655			−0.00769196			−0.00384598	+	0.999993i	$0.501224\pi$
$702$		0			0
$703$	−0.209745	−	0.363289i	−0.00791069	−	0.0137017i
$704$		0			0
$705$	−8.32949	−	4.80903i	−0.313707	−	0.181119i
$706$		0			0
$707$	10.9813	−	12.8554i	0.412994	−	0.483477i
$708$		0			0
$709$	7.27057	−	12.5930i	0.273052	−	0.472940i	−0.696590	−	0.717470i	$-0.745300\pi$
$709$	7.27057	−	12.5930i	0.273052	−	0.472940i	0.969642	+	0.244530i	$0.0786335\pi$
$710$		0			0
$711$	21.0146	−	12.1328i	0.788111	−	0.455016i
$712$		0			0
$713$			31.4167i			1.17656i
$714$		0			0
$715$		−	14.9353i		−	0.558549i
$716$		0			0
$717$	−57.2265	+	33.0397i	−2.13716	+	1.23389i
$718$		0			0
$719$	−20.2951	+	35.1522i	−0.756881	+	1.31096i	0.187553	+	0.982254i	$0.439944\pi$
$719$	−20.2951	+	35.1522i	−0.756881	+	1.31096i	−0.944434	+	0.328702i	$0.893389\pi$
$720$		0			0
$721$	6.52574	−	35.1942i	0.243031	−	1.31070i
$722$		0			0
$723$	28.7296	+	16.5871i	1.06847	+	0.616879i
$724$		0			0
$725$	1.51212	+	2.61907i	0.0561588	+	0.0972699i
$726$		0			0
$727$	7.75162			0.287491			0.143746	−	0.989615i	$-0.454085\pi$
$727$	7.75162			0.287491			0.143746	+	0.989615i	$0.454085\pi$
$728$		0			0
$729$	−26.8111			−0.993004
$730$		0			0
$731$	14.2006	+	24.5962i	0.525230	+	0.909725i
$732$		0			0
$733$	5.77541	+	3.33444i	0.213320	+	0.123160i	0.602853	−	0.797852i	$-0.294030\pi$
$733$	5.77541	+	3.33444i	0.213320	+	0.123160i	−0.389534	+	0.921012i	$0.627364\pi$
$734$		0			0
$735$	−10.7791	−	13.3153i	−0.397592	−	0.491144i
$736$		0			0
$737$	47.2045	−	81.7606i	1.73880	−	3.01169i
$738$		0			0
$739$	24.9563	−	14.4085i	0.918031	−	0.530026i	0.0350249	−	0.999386i	$-0.488849\pi$
$739$	24.9563	−	14.4085i	0.918031	−	0.530026i	0.883006	+	0.469361i	$0.155516\pi$
$740$		0			0
$741$			5.58960i			0.205339i
$742$		0			0
$743$		−	17.9238i		−	0.657560i	−0.944406	−	0.328780i	$-0.893362\pi$
$743$		−	17.9238i		−	0.657560i	0.944406	−	0.328780i	$-0.106638\pi$
$744$		0			0
$745$	12.2622	−	7.07961i	0.449254	−	0.259377i
$746$		0			0
$747$	−4.39653	+	7.61502i	−0.160861	+	0.278619i
$748$		0			0
$749$	−11.0399	−	2.04703i	−0.403389	−	0.0747968i
$750$		0			0
$751$	19.7943	+	11.4282i	0.722304	+	0.417023i	0.815600	−	0.578616i	$-0.196407\pi$
$751$	19.7943	+	11.4282i	0.722304	+	0.417023i	−0.0932959	+	0.995638i	$0.529740\pi$
$752$		0			0
$753$	−17.4134	−	30.1609i	−0.634579	−	1.09912i
$754$		0			0
$755$	−21.0004			−0.764283
$756$		0			0
$757$	−42.7423			−1.55349			−0.776747	−	0.629812i	$-0.783132\pi$
$757$	−42.7423			−1.55349			−0.776747	+	0.629812i	$0.783132\pi$
$758$		0			0
$759$	−47.3318	−	81.9810i	−1.71803	−	2.97572i
$760$		0			0
$761$	−29.0191	−	16.7542i	−1.05194	−	0.607339i	−0.128749	−	0.991677i	$-0.541096\pi$
$761$	−29.0191	−	16.7542i	−1.05194	−	0.607339i	−0.923192	+	0.384338i	$0.874430\pi$
$762$		0			0
$763$	−18.8714	−	16.1203i	−0.683191	−	0.583594i
$764$		0			0
$765$	−8.12475	+	14.0725i	−0.293751	+	0.508791i
$766$		0			0
$767$	16.4328	−	9.48748i	0.593354	−	0.342573i
$768$		0			0
$769$			29.5287i			1.06483i	0.846483	+	0.532415i	$0.178716\pi$
$769$			29.5287i			1.06483i	−0.846483	+	0.532415i	$0.821284\pi$
$770$		0			0
$771$			46.8053i			1.68565i
$772$		0			0
$773$	36.1864	−	20.8922i	1.30154	−	0.751442i	0.320868	−	0.947124i	$-0.396026\pi$
$773$	36.1864	−	20.8922i	1.30154	−	0.751442i	0.980667	+	0.195682i	$0.0626922\pi$
$774$		0			0
$775$	−2.62784	+	4.55156i	−0.0943949	+	0.163497i
$776$		0			0
$777$	2.58762	−	0.916093i	0.0928302	−	0.0328646i
$778$		0			0
$779$	−8.44007	−	4.87288i	−0.302397	−	0.174589i
$780$		0			0
$781$	−7.40500	−	12.8258i	−0.264972	−	0.458945i
$782$		0			0
$783$	0.0775391			0.00277102
$784$		0			0
$785$	−6.81540			−0.243252
$786$		0			0
$787$	−5.51042	−	9.54433i	−0.196425	−	0.340219i	0.750941	−	0.660369i	$-0.229600\pi$
$787$	−5.51042	−	9.54433i	−0.196425	−	0.340219i	−0.947367	+	0.320150i	$0.896267\pi$
$788$		0			0
$789$	−14.7233	−	8.50051i	−0.524164	−	0.302626i
$790$		0			0
$791$	18.5968	−	6.58383i	0.661227	−	0.234094i
$792$		0			0
$793$	−7.65586	+	13.2603i	−0.271868	+	0.470888i
$794$		0			0
$795$	−19.0997	+	11.0272i	−0.677396	+	0.391095i
$796$		0			0
$797$		−	12.9488i		−	0.458669i	−0.973348	−	0.229334i	$-0.926345\pi$
$797$		−	12.9488i		−	0.458669i	0.973348	−	0.229334i	$-0.0736549\pi$
$798$		0			0
$799$			21.3614i			0.755711i
$800$		0			0
$801$	−45.6240	+	26.3410i	−1.61205	+	0.930715i
$802$		0			0
$803$	−39.0597	+	67.6534i	−1.37839	+	2.38744i
$804$		0			0
$805$	12.0253	+	10.2722i	0.423836	+	0.362048i
$806$		0			0
$807$	16.3994	+	9.46819i	0.577285	+	0.333296i
$808$		0			0
$809$	−12.7612	−	22.1031i	−0.448661	−	0.777104i	0.549638	−	0.835403i	$-0.314766\pi$
$809$	−12.7612	−	22.1031i	−0.448661	−	0.777104i	−0.998299	+	0.0582988i	$0.981432\pi$
$810$		0			0
$811$	−6.60292			−0.231860			−0.115930	−	0.993257i	$-0.536985\pi$
$811$	−6.60292			−0.231860			−0.115930	+	0.993257i	$0.536985\pi$
$812$		0			0
$813$	6.17212			0.216466
$814$		0			0
$815$	3.81117	+	6.60114i	0.133499	+	0.231228i
$816$		0			0
$817$	4.47772	+	2.58521i	0.156656	+	0.0904452i
$818$		0			0
$819$	−17.9502	−	3.32834i	−0.627230	−	0.116302i
$820$		0			0
$821$	−2.88258	+	4.99278i	−0.100603	+	0.174249i	−0.911933	−	0.410339i	$-0.865410\pi$
$821$	−2.88258	+	4.99278i	−0.100603	+	0.174249i	0.811330	+	0.584588i	$0.198744\pi$
$822$		0			0
$823$	−2.71517	+	1.56761i	−0.0946450	+	0.0546433i	−0.546575	−	0.837410i	$-0.684069\pi$
$823$	−2.71517	+	1.56761i	−0.0946450	+	0.0546433i	0.451930	+	0.892053i	$0.350736\pi$
$824$		0			0
$825$		−	15.8362i		−	0.551347i
$826$		0			0
$827$			22.0174i			0.765621i	0.923827	+	0.382811i	$0.125044\pi$
$827$			22.0174i			0.765621i	−0.923827	+	0.382811i	$0.874956\pi$
$828$		0			0
$829$	−40.5056	+	23.3859i	−1.40682	+	0.812226i	−0.995080	−	0.0990766i	$-0.968411\pi$
$829$	−40.5056	+	23.3859i	−1.40682	+	0.812226i	−0.411737	+	0.911303i	$0.635078\pi$
$830$		0			0
$831$	36.2991	−	62.8719i	1.25920	−	2.18100i
$832$		0			0
$833$	−13.6409	+	35.5190i	−0.472630	+	1.23066i
$834$		0			0
$835$	4.33992	+	2.50565i	0.150189	+	0.0867116i
$836$		0			0
$837$	0.0673757	+	0.116698i	0.00232884	+	0.00403368i
$838$		0			0
$839$	36.3872			1.25622			0.628112	−	0.778123i	$-0.283828\pi$
$839$	36.3872			1.25622			0.628112	+	0.778123i	$0.283828\pi$
$840$		0			0
$841$	−19.8539			−0.684619
$842$		0			0
$843$	−18.7867	−	32.5395i	−0.647047	−	1.12072i
$844$		0			0
$845$	−6.64465	−	3.83629i	−0.228583	−	0.131973i
$846$		0			0
$847$	−14.8907	+	80.3077i	−0.511651	+	2.75941i
$848$		0			0
$849$	−11.0432	+	19.1274i	−0.379002	+	0.656450i
$850$		0			0
$851$	−2.19461	+	1.26706i	−0.0752303	+	0.0434342i
$852$		0			0
$853$			5.80981i			0.198924i	0.995041	+	0.0994621i	$0.0317122\pi$
$853$			5.80981i			0.198924i	−0.995041	+	0.0994621i	$0.968288\pi$
$854$		0			0
$855$			2.95820i			0.101168i
$856$		0			0
$857$	−0.283292	+	0.163559i	−0.00967708	+	0.00558706i	−0.504831	−	0.863218i	$-0.668445\pi$
$857$	−0.283292	+	0.163559i	−0.00967708	+	0.00558706i	0.495154	+	0.868805i	$0.335112\pi$
$858$		0			0
$859$	4.81365	−	8.33748i	0.164239	−	0.284471i	−0.772145	−	0.635446i	$-0.780816\pi$
$859$	4.81365	−	8.33748i	0.164239	−	0.284471i	0.936385	+	0.350975i	$0.114150\pi$
$860$		0			0
$861$	41.4209	−	48.4898i	1.41162	−	1.65253i
$862$		0			0
$863$	−17.7605	−	10.2541i	−0.604576	−	0.349052i	0.166264	−	0.986081i	$-0.446830\pi$
$863$	−17.7605	−	10.2541i	−0.604576	−	0.349052i	−0.770840	+	0.637029i	$0.780163\pi$
$864$		0			0
$865$	−6.03826	−	10.4586i	−0.205307	−	0.355602i
$866$		0			0
$867$	30.7006			1.04265
$868$		0			0
$869$	52.5225			1.78170
$870$		0			0
$871$	16.8378	+	29.1639i	0.570527	+	0.988182i
$872$		0			0
$873$	−12.8551	−	7.42191i	−0.435080	−	0.251194i
$874$		0			0
$875$	0.882973	+	2.49406i	0.0298499	+	0.0843148i
$876$		0			0
$877$	−8.70522	+	15.0779i	−0.293954	+	0.509144i	−0.974741	−	0.223338i	$-0.928305\pi$
$877$	−8.70522	+	15.0779i	−0.293954	+	0.509144i	0.680787	+	0.732482i	$0.261638\pi$
$878$		0			0
$879$	−1.72820	+	0.997779i	−0.0582909	+	0.0336543i
$880$		0			0
$881$		−	25.3913i		−	0.855455i	−0.903908	−	0.427727i	$-0.859314\pi$
$881$		−	25.3913i		−	0.855455i	0.903908	−	0.427727i	$-0.140686\pi$
$882$		0			0
$883$			24.0260i			0.808541i	0.914639	+	0.404270i	$0.132475\pi$
$883$			24.0260i			0.808541i	−0.914639	+	0.404270i	$0.867525\pi$
$884$		0			0
$885$	17.4241	−	10.0598i	0.585704	−	0.338156i
$886$		0			0
$887$	−2.28322	+	3.95465i	−0.0766631	+	0.132784i	−0.901808	−	0.432136i	$-0.857760\pi$
$887$	−2.28322	+	3.95465i	−0.0766631	+	0.132784i	0.825145	+	0.564921i	$0.191093\pi$
$888$		0			0
$889$	12.1908	+	34.4343i	0.408865	+	1.15489i
$890$		0			0
$891$	−50.6102	−	29.2198i	−1.69550	−	0.978900i
$892$		0			0
$893$	1.94441	+	3.36782i	0.0650672	+	0.112700i
$894$		0			0
$895$	10.1820			0.340347
$896$		0			0
$897$	33.7664			1.12743
$898$		0			0
$899$	7.94724	+	13.7650i	0.265055	+	0.459089i
$900$		0			0
$901$	42.4197	+	24.4910i	1.41321	+	0.815915i
$902$		0			0
$903$	−21.9751	+	25.7254i	−0.731284	+	0.856086i
$904$		0			0
$905$	−3.17700	+	5.50272i	−0.105607	+	0.182917i
$906$		0			0
$907$	36.2439	−	20.9254i	1.20346	−	0.694817i	0.242136	−	0.970242i	$-0.422152\pi$
$907$	36.2439	−	20.9254i	1.20346	−	0.694817i	0.961323	+	0.275425i	$0.0888185\pi$
$908$		0			0
$909$		−	19.1039i		−	0.633636i
$910$		0			0
$911$			33.5744i			1.11237i	0.831059	+	0.556184i	$0.187735\pi$
$911$			33.5744i			1.11237i	−0.831059	+	0.556184i	$0.812265\pi$
$912$		0			0
$913$	−16.4826	+	9.51621i	−0.545493	+	0.314941i
$914$		0			0
$915$	−8.11768	+	14.0602i	−0.268362	+	0.464817i
$916$		0			0
$917$	1.23385	−	6.65430i	0.0407452	−	0.219744i
$918$		0			0
$919$	31.2275	+	18.0292i	1.03010	+	0.594728i	0.917013	−	0.398857i	$-0.130593\pi$
$919$	31.2275	+	18.0292i	1.03010	+	0.594728i	0.113086	+	0.993585i	$0.463926\pi$
$920$		0			0
$921$	−10.3042	−	17.8475i	−0.339536	−	0.588094i
$922$		0			0
$923$	5.28272			0.173883
$924$		0			0
$925$	−0.423932			−0.0139388
$926$		0			0
$927$	−20.2225	−	35.0264i	−0.664194	−	1.15042i
$928$		0			0
$929$	1.21564	+	0.701850i	0.0398838	+	0.0230269i	0.519809	−	0.854282i	$-0.326003\pi$
$929$	1.21564	+	0.701850i	0.0398838	+	0.0230269i	−0.479926	+	0.877309i	$0.659336\pi$
$930$		0			0
$931$	1.08249	+	6.84156i	0.0354771	+	0.224223i
$932$		0			0
$933$	−24.7722	+	42.9066i	−0.811004	+	1.40470i
$934$		0			0
$935$	−30.4596	+	17.5859i	−0.996136	+	0.575119i
$936$		0			0
$937$			58.7549i			1.91944i	0.280960	+	0.959720i	$0.409347\pi$
$937$			58.7549i			1.91944i	−0.280960	+	0.959720i	$0.590653\pi$
$938$		0			0
$939$			60.5047i			1.97450i
$940$		0			0
$941$	−24.9066	+	14.3798i	−0.811930	+	0.468768i	−0.847626	−	0.530594i	$-0.821969\pi$
$941$	−24.9066	+	14.3798i	−0.811930	+	0.468768i	0.0356954	+	0.999363i	$0.488635\pi$
$942$		0			0
$943$	−29.4368	+	50.9860i	−0.958593	+	1.66033i
$944$		0			0
$945$	0.0666980	+	0.0123672i	0.00216968	+	0.000402305i
$946$		0			0
$947$	14.3605	+	8.29103i	0.466653	+	0.269422i	0.714838	−	0.699291i	$-0.246501\pi$
$947$	14.3605	+	8.29103i	0.466653	+	0.269422i	−0.248185	+	0.968713i	$0.579834\pi$
$948$		0			0
$949$	−13.9326	−	24.1319i	−0.452271	−	0.783356i
$950$		0			0
$951$	−45.5359			−1.47660
$952$		0			0
$953$	−6.47062			−0.209604			−0.104802	−	0.994493i	$-0.533421\pi$
$953$	−6.47062			−0.209604			−0.104802	+	0.994493i	$0.533421\pi$
$954$		0			0
$955$	2.94129	+	5.09447i	0.0951780	+	0.164853i
$956$		0			0
$957$	−41.4763	−	23.9463i	−1.34074	−	0.774075i
$958$		0			0
$959$	0.629162	+	0.537441i	0.0203167	+	0.0173549i
$960$		0			0
$961$	1.68888	−	2.92523i	0.0544800	−	0.0943621i
$962$		0			0
$963$	−10.9873	+	6.34349i	−0.354059	+	0.204416i
$964$		0			0
$965$		−	8.41326i		−	0.270832i
$966$		0			0
$967$			7.89312i			0.253826i	0.991914	+	0.126913i	$0.0405069\pi$
$967$			7.89312i			0.253826i	−0.991914	+	0.126913i	$0.959493\pi$
$968$		0			0
$969$	11.3996	−	6.58158i	0.366209	−	0.211431i
$970$		0			0
$971$	9.39678	−	16.2757i	0.301557	−	0.522312i	−0.674932	−	0.737880i	$-0.735827\pi$
$971$	9.39678	−	16.2757i	0.301557	−	0.522312i	0.976489	+	0.215568i	$0.0691603\pi$
$972$		0			0
$973$	−0.466035	+	0.164990i	−0.0149404	+	0.00528934i
$974$		0			0
$975$	4.89198	+	2.82439i	0.156669	+	0.0904528i
$976$		0			0
$977$	4.83820	+	8.38001i	0.154788	+	0.268100i	0.932982	−	0.359924i	$-0.117197\pi$
$977$	4.83820	+	8.38001i	0.154788	+	0.268100i	−0.778194	+	0.628024i	$0.783864\pi$
$978$		0			0
$979$	−114.029			−3.64439
$980$		0			0
$981$	−28.0441			−0.895379
$982$		0			0
$983$	−18.0155	−	31.2038i	−0.574606	−	0.995247i	−0.996084	−	0.0884081i	$-0.971822\pi$
$983$	−18.0155	−	31.2038i	−0.574606	−	0.995247i	0.421478	−	0.906838i	$-0.361511\pi$
$984$		0			0
$985$	13.6910	+	7.90453i	0.436233	+	0.251859i
$986$		0			0
$987$	−23.9881	+	8.49249i	−0.763549	+	0.270319i
$988$		0			0
$989$	15.6171	−	27.0496i	0.496595	−	0.860128i
$990$		0			0
$991$	31.5064	−	18.1903i	1.00084	−	0.577832i	0.0923399	−	0.995728i	$-0.470565\pi$
$991$	31.5064	−	18.1903i	1.00084	−	0.577832i	0.908495	+	0.417895i	$0.137232\pi$
$992$		0			0
$993$		−	52.3489i		−	1.66124i
$994$		0			0
$995$		−	12.3714i		−	0.392198i
$996$		0			0
$997$	−20.7365	+	11.9722i	−0.656731	+	0.379164i	−0.791030	−	0.611777i	$-0.790455\pi$
$997$	−20.7365	+	11.9722i	−0.656731	+	0.379164i	0.134299	+	0.990941i	$0.457122\pi$
$998$		0			0
$999$	−0.00543463	+	0.00941305i	−0.000171944	+	0.000297816i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.bs.c.271.5	yes	12
4.3	odd	2		560.2.bs.b.271.2	yes	12
7.2	even	3		3920.2.k.d.2351.4		12
7.3	odd	6		560.2.bs.b.31.2	✓	12
7.5	odd	6		3920.2.k.e.2351.9		12
28.3	even	6	inner	560.2.bs.c.31.5	yes	12
28.19	even	6		3920.2.k.d.2351.3		12
28.23	odd	6		3920.2.k.e.2351.10		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.bs.b.31.2	✓	12	7.3	odd	6
560.2.bs.b.271.2	yes	12	4.3	odd	2
560.2.bs.c.31.5	yes	12	28.3	even	6	inner
560.2.bs.c.271.5	yes	12	1.1	even	1	trivial
3920.2.k.d.2351.3		12	28.19	even	6
3920.2.k.d.2351.4		12	7.2	even	3
3920.2.k.e.2351.9		12	7.5	odd	6
3920.2.k.e.2351.10		12	28.23	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:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.bs (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.22368 + 2.11947i) q^{3} +(-0.866025 - 0.500000i) q^{5} +(-2.49406 + 0.882973i) q^{7} +(-1.49476 + 2.58900i) q^{9} +(-5.60385 + 3.23538i) q^{11} -2.30812i q^{13} -2.44735i q^{15} +(-4.70726 + 2.71774i) q^{17} +(-0.494762 + 0.856953i) q^{19} +(-4.92336 - 4.20562i) q^{21} +(5.17680 + 2.98883i) q^{23} +(0.500000 + 0.866025i) q^{25} +0.0256392 q^{27} +3.02424 q^{29} +(2.62784 + 4.55156i) q^{31} +(-13.7146 - 7.91812i) q^{33} +(2.60141 + 0.482355i) q^{35} +(-0.211966 + 0.367136i) q^{37} +(4.89198 - 2.82439i) q^{39} +9.84894i q^{41} -5.22517i q^{43} +(2.58900 - 1.49476i) q^{45} +(1.96499 - 3.40347i) q^{47} +(5.44072 - 4.40438i) q^{49} +(-11.5203 - 6.65126i) q^{51} +(-4.50577 - 7.80423i) q^{53} +6.47077 q^{55} -2.42171 q^{57} +(4.11048 + 7.11956i) q^{59} +(-5.74509 - 3.31693i) q^{61} +(1.44201 - 7.77698i) q^{63} +(-1.15406 + 1.99889i) q^{65} +(-12.6354 + 7.29503i) q^{67} +14.6294i q^{69} +2.28875i q^{71} +(10.4552 - 6.03634i) q^{73} +(-1.22368 + 2.11947i) q^{75} +(11.1196 - 13.0173i) q^{77} +(-7.02943 - 4.05844i) q^{79} +(4.51566 + 7.82135i) q^{81} +2.94129 q^{83} +5.43548 q^{85} +(3.70069 + 6.40979i) q^{87} +(15.2613 + 8.81111i) q^{89} +(2.03801 + 5.75660i) q^{91} +(-6.43125 + 11.1393i) q^{93} +(0.856953 - 0.494762i) q^{95} +4.96528i q^{97} -19.3445i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{3} - 2 q^{7} - 10 q^{9} + 6 q^{11} + 2 q^{19} + 12 q^{21} - 18 q^{23} + 6 q^{25} + 20 q^{27} + 16 q^{29} + 4 q^{31} - 6 q^{35} - 4 q^{37} + 24 q^{39} - 12 q^{45} + 12 q^{47} - 8 q^{49} - 12 q^{51}+ \cdots - 12 q^{95}+O(q^{100}) \) 12 * q + 2 * q^3 - 2 * q^7 - 10 * q^9 + 6 * q^11 + 2 * q^19 + 12 * q^21 - 18 * q^23 + 6 * q^25 + 20 * q^27 + 16 * q^29 + 4 * q^31 - 6 * q^35 - 4 * q^37 + 24 * q^39 - 12 * q^45 + 12 * q^47 - 8 * q^49 - 12 * q^51 - 12 * q^53 + 24 * q^55 + 16 * q^57 + 24 * q^59 - 48 * q^61 - 56 * q^63 - 2 * q^65 - 42 * q^67 + 24 * q^73 - 2 * q^75 + 40 * q^77 + 12 * q^79 - 6 * q^81 + 36 * q^83 - 16 * q^85 - 30 * q^87 + 12 * q^89 + 36 * q^91 + 28 * q^93 - 12 * q^95

Introduction

L-functions

Modular forms

Varieties

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