LMFDB - Embedded newform 1764.2.i.f.373.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1764,2,Mod(373,1764)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1764, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2, 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("1764.373"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1764.i (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [6,0,2,0,3] 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:	$14.0856109166$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			373.3
Root			$0.500000 + 1.41036i$ of defining polynomial
Character	$\chi$	$=$	1764.373
Dual form			1764.2.i.f.1537.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.71053 + 0.272169i) q^{3} +(1.97141 + 3.41458i) q^{5} +(2.85185 + 0.931107i) q^{9} +(-0.471410 + 0.816506i) q^{11} +(0.500000 - 0.866025i) q^{13} +(2.44282 + 6.37731i) q^{15} +(-2.80150 - 4.85235i) q^{17} +(-0.641315 + 1.11079i) q^{19} +(2.33009 + 4.03584i) q^{23} +(-5.27292 + 9.13296i) q^{25} +(4.62476 + 2.36887i) q^{27} +(3.83009 + 6.63392i) q^{29} +7.82846 q^{31} +(-1.02859 + 1.26836i) q^{33} +(4.91423 - 8.51170i) q^{37} +(1.09097 - 1.34528i) q^{39} +(-0.471410 + 0.816506i) q^{41} +(-4.63160 - 8.02217i) q^{43} +(2.44282 + 11.5735i) q^{45} -5.28263 q^{47} +(-3.47141 - 9.06259i) q^{51} +(4.61273 + 7.98947i) q^{53} -3.71737 q^{55} +(-1.39931 + 1.72550i) q^{57} -9.54583 q^{59} -10.5458 q^{61} +3.94282 q^{65} -1.71737 q^{67} +(2.88727 + 7.53762i) q^{69} +3.54583 q^{71} +(-1.35868 - 2.35331i) q^{73} +(-11.5052 + 14.1871i) q^{75} -16.3743 q^{79} +(7.26608 + 5.31075i) q^{81} +(0.198495 + 0.343803i) q^{83} +(11.0458 - 19.1319i) q^{85} +(4.74596 + 12.3900i) q^{87} +(-2.75404 + 4.77014i) q^{89} +(13.3908 + 2.13066i) q^{93} -5.05718 q^{95} +(6.77292 + 11.7310i) q^{97} +(-2.10464 + 1.88962i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 2 q^{3} + 3 q^{5} + 8 q^{9} + 6 q^{11} + 3 q^{13} - 3 q^{15} - 3 q^{19} + 6 q^{23} - 6 q^{25} - 7 q^{27} + 15 q^{29} - 6 q^{31} - 15 q^{33} + 3 q^{37} - 2 q^{39} + 6 q^{41} - 3 q^{43} - 3 q^{45} - 30 q^{47}+ \cdots - 24 q^{99}+O(q^{100}) $ 6 * q + 2 * q^3 + 3 * q^5 + 8 * q^9 + 6 * q^11 + 3 * q^13 - 3 * q^15 - 3 * q^19 + 6 * q^23 - 6 * q^25 - 7 * q^27 + 15 * q^29 - 6 * q^31 - 15 * q^33 + 3 * q^37 - 2 * q^39 + 6 * q^41 - 3 * q^43 - 3 * q^45 - 30 * q^47 - 12 * q^51 + 18 * q^53 - 24 * q^55 + 7 * q^57 - 6 * q^59 - 12 * q^61 + 6 * q^65 - 12 * q^67 + 27 * q^69 - 30 * q^71 - 9 * q^73 - 34 * q^75 + 6 * q^79 + 8 * q^81 + 18 * q^83 + 15 * q^85 + 39 * q^87 - 6 * q^89 + 10 * q^93 - 48 * q^95 + 15 * q^97 - 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times$.

$n$	$785$	$883$	$1081$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.71053	+	0.272169i	0.987577	+	0.157137i
$3$	1.71053	+	0.272169i	0.987577	+	0.157137i
$4$		0			0
$5$	1.97141	+	3.41458i	0.881641	+	1.52705i	0.849515	+	0.527564i	$0.176894\pi$
$5$	1.97141	+	3.41458i	0.881641	+	1.52705i	0.0321260	+	0.999484i	$0.489772\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	2.85185	+	0.931107i	0.950616	+	0.310369i
$10$		0			0
$11$	−0.471410	+	0.816506i	−0.142135	+	0.246186i	−0.928301	−	0.371831i	$-0.878730\pi$
$11$	−0.471410	+	0.816506i	−0.142135	+	0.246186i	0.786165	+	0.618017i	$0.212064\pi$
$12$		0			0
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i	−0.788320	−	0.615265i	$-0.789049\pi$
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i	0.926995	+	0.375073i	$0.122382\pi$
$14$		0			0
$15$	2.44282	+	6.37731i	0.630733	+	1.64662i
$16$		0			0
$17$	−2.80150	−	4.85235i	−0.679465	−	1.17687i	−0.975142	−	0.221580i	$-0.928879\pi$
$17$	−2.80150	−	4.85235i	−0.679465	−	1.17687i	0.295678	−	0.955288i	$-0.404455\pi$
$18$		0			0
$19$	−0.641315	+	1.11079i	−0.147128	+	0.254833i	−0.930165	−	0.367142i	$-0.880336\pi$
$19$	−0.641315	+	1.11079i	−0.147128	+	0.254833i	0.783037	+	0.621975i	$0.213670\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.33009	+	4.03584i	0.485858	+	0.841531i	0.999868	−	0.0162531i	$-0.00517374\pi$
$23$	2.33009	+	4.03584i	0.485858	+	0.841531i	−0.514010	+	0.857784i	$0.671840\pi$
$24$		0			0
$25$	−5.27292	+	9.13296i	−1.05458	+	1.82659i
$26$		0			0
$27$	4.62476	+	2.36887i	0.890036	+	0.455890i
$28$		0			0
$29$	3.83009	+	6.63392i	0.711231	+	1.23189i	0.964395	+	0.264465i	$0.0851952\pi$
$29$	3.83009	+	6.63392i	0.711231	+	1.23189i	−0.253165	+	0.967423i	$0.581471\pi$
$30$		0			0
$31$	7.82846			1.40603			0.703016	−	0.711174i	$-0.251836\pi$
$31$	7.82846			1.40603			0.703016	+	0.711174i	$0.251836\pi$
$32$		0			0
$33$	−1.02859	+	1.26836i	−0.179055	+	0.220793i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	4.91423	−	8.51170i	0.807894	−	1.39931i	−0.106425	−	0.994321i	$-0.533940\pi$
$37$	4.91423	−	8.51170i	0.807894	−	1.39931i	0.914320	−	0.404994i	$-0.132726\pi$
$38$		0			0
$39$	1.09097	−	1.34528i	0.174695	−	0.215417i
$40$		0			0
$41$	−0.471410	+	0.816506i	−0.0736219	+	0.127517i	−0.900486	−	0.434885i	$-0.856789\pi$
$41$	−0.471410	+	0.816506i	−0.0736219	+	0.127517i	0.826864	+	0.562402i	$0.190122\pi$
$42$		0			0
$43$	−4.63160	−	8.02217i	−0.706312	−	1.22337i	−0.966216	−	0.257734i	$-0.917024\pi$
$43$	−4.63160	−	8.02217i	−0.706312	−	1.22337i	0.259903	−	0.965635i	$-0.416309\pi$
$44$		0			0
$45$	2.44282	+	11.5735i	0.364154	+	1.72527i
$46$		0			0
$47$	−5.28263			−0.770551			−0.385275	−	0.922802i	$-0.625894\pi$
$47$	−5.28263			−0.770551			−0.385275	+	0.922802i	$0.625894\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−3.47141	−	9.06259i	−0.486095	−	1.26902i
$52$		0			0
$53$	4.61273	+	7.98947i	0.633607	+	1.09744i	0.986809	+	0.161892i	$0.0517595\pi$
$53$	4.61273	+	7.98947i	0.633607	+	1.09744i	−0.353202	+	0.935547i	$0.614907\pi$
$54$		0			0
$55$	−3.71737			−0.501250
$56$		0			0
$57$	−1.39931	+	1.72550i	−0.185344	+	0.228548i
$58$		0			0
$59$	−9.54583			−1.24276			−0.621381	−	0.783509i	$-0.713428\pi$
$59$	−9.54583			−1.24276			−0.621381	+	0.783509i	$0.713428\pi$
$60$		0			0
$61$	−10.5458			−1.35026			−0.675128	−	0.737701i	$-0.735911\pi$
$61$	−10.5458			−1.35026			−0.675128	+	0.737701i	$0.735911\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	3.94282			0.489047
$66$		0			0
$67$	−1.71737			−0.209810			−0.104905	−	0.994482i	$-0.533454\pi$
$67$	−1.71737			−0.209810			−0.104905	+	0.994482i	$0.533454\pi$
$68$		0			0
$69$	2.88727	+	7.53762i	0.347587	+	0.907423i
$70$		0			0
$71$	3.54583			0.420813			0.210406	−	0.977614i	$-0.432521\pi$
$71$	3.54583			0.420813			0.210406	+	0.977614i	$0.432521\pi$
$72$		0			0
$73$	−1.35868	−	2.35331i	−0.159022	−	0.275434i	0.775494	−	0.631355i	$-0.217501\pi$
$73$	−1.35868	−	2.35331i	−0.159022	−	0.275434i	−0.934516	+	0.355920i	$0.884167\pi$
$74$		0			0
$75$	−11.5052	+	14.1871i	−1.32851	+	1.63819i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−16.3743			−1.84225			−0.921126	−	0.389265i	$-0.872729\pi$
$79$	−16.3743			−1.84225			−0.921126	+	0.389265i	$0.872729\pi$
$80$		0			0
$81$	7.26608	+	5.31075i	0.807342	+	0.590084i
$82$		0			0
$83$	0.198495	+	0.343803i	0.0217877	+	0.0377373i	0.876714	−	0.481013i	$-0.159731\pi$
$83$	0.198495	+	0.343803i	0.0217877	+	0.0377373i	−0.854926	+	0.518750i	$0.826398\pi$
$84$		0			0
$85$	11.0458	−	19.1319i	1.19809	−	2.07515i
$86$		0			0
$87$	4.74596	+	12.3900i	0.508820	+	1.32834i
$88$		0			0
$89$	−2.75404	+	4.77014i	−0.291928	+	0.505634i	−0.974266	−	0.225403i	$-0.927630\pi$
$89$	−2.75404	+	4.77014i	−0.291928	+	0.505634i	0.682338	+	0.731037i	$0.260963\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	13.3908	+	2.13066i	1.38857	+	0.220939i
$94$		0			0
$95$	−5.05718			−0.518856
$96$		0			0
$97$	6.77292	+	11.7310i	0.687685	+	1.19111i	0.972585	+	0.232549i	$0.0747064\pi$
$97$	6.77292	+	11.7310i	0.687685	+	1.19111i	−0.284899	+	0.958557i	$0.591960\pi$
$98$		0			0
$99$	−2.10464	+	1.88962i	−0.211525	+	0.189914i
$100$		0			0
$101$	1.30150	−	2.25427i	0.129505	−	0.224309i	−0.793980	−	0.607944i	$-0.791995\pi$
$101$	1.30150	−	2.25427i	0.129505	−	0.224309i	0.923485	+	0.383635i	$0.125328\pi$
$102$		0			0
$103$	−7.99028	−	13.8396i	−0.787306	−	1.36365i	−0.927612	−	0.373546i	$-0.878142\pi$
$103$	−7.99028	−	13.8396i	−0.787306	−	1.36365i	0.140305	−	0.990108i	$-0.455192\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	5.44282	−	9.42724i	0.526177	−	0.911366i	−0.473358	−	0.880870i	$-0.656958\pi$
$107$	5.44282	−	9.42724i	0.526177	−	0.911366i	0.999535	−	0.0304954i	$-0.00970850\pi$
$108$		0			0
$109$	1.64132	+	2.84284i	0.157209	+	0.272295i	0.933861	−	0.357635i	$-0.116417\pi$
$109$	1.64132	+	2.84284i	0.157209	+	0.272295i	−0.776652	+	0.629930i	$0.783084\pi$
$110$		0			0
$111$	10.7226	−	13.2220i	1.01774	−	1.25498i
$112$		0			0
$113$	3.22545	−	5.58664i	0.303425	−	0.525547i	−0.673485	−	0.739201i	$-0.735203\pi$
$113$	3.22545	−	5.58664i	0.303425	−	0.525547i	0.976909	+	0.213654i	$0.0685365\pi$
$114$		0			0
$115$	−9.18715	+	15.9126i	−0.856706	+	1.48386i
$116$		0			0
$117$	2.23229	−	2.00422i	0.206375	−	0.185290i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	5.05555	+	8.75646i	0.459595	+	0.796042i
$122$		0			0
$123$	−1.02859	+	1.26836i	−0.0927448	+	0.114364i
$124$		0			0
$125$	−21.8662			−1.95577
$126$		0			0
$127$	−0.828460			−0.0735140			−0.0367570	−	0.999324i	$-0.511703\pi$
$127$	−0.828460			−0.0735140			−0.0367570	+	0.999324i	$0.511703\pi$
$128$		0			0
$129$	−5.73912	−	14.9828i	−0.505302	−	1.31916i
$130$		0			0
$131$	−2.71574	−	4.70379i	−0.237275	−	0.410972i	0.722656	−	0.691207i	$-0.242921\pi$
$131$	−2.71574	−	4.70379i	−0.237275	−	0.410972i	−0.959931	+	0.280235i	$0.909588\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	1.02859	+	20.4617i	0.0885269	+	1.76106i
$136$		0			0
$137$	10.5744	−	18.3154i	0.903434	−	1.56479i	0.0804276	−	0.996760i	$-0.474371\pi$
$137$	10.5744	−	18.3154i	0.903434	−	1.56479i	0.823006	−	0.568033i	$-0.192295\pi$
$138$		0			0
$139$	0.923945	−	1.60032i	0.0783680	−	0.135737i	−0.824178	−	0.566331i	$-0.808362\pi$
$139$	0.923945	−	1.60032i	0.0783680	−	0.135737i	0.902546	+	0.430594i	$0.141696\pi$
$140$		0			0
$141$	−9.03611	−	1.43777i	−0.760978	−	0.121082i
$142$		0			0
$143$	0.471410	+	0.816506i	0.0394213	+	0.0682797i
$144$		0			0
$145$	−15.1014	+	26.1563i	−1.25410	+	2.17217i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−6.07442	−	10.5212i	−0.497636	−	0.861931i	0.502360	−	0.864658i	$-0.332465\pi$
$149$	−6.07442	−	10.5212i	−0.497636	−	0.861931i	−0.999996	+	0.00272771i	$0.999132\pi$
$150$		0			0
$151$	4.49028	−	7.77740i	0.365414	−	0.632916i	−0.623428	−	0.781880i	$-0.714261\pi$
$151$	4.49028	−	7.77740i	0.365414	−	0.632916i	0.988843	+	0.148965i	$0.0475940\pi$
$152$		0			0
$153$	−3.47141	−	16.4467i	−0.280647	−	1.32963i
$154$		0			0
$155$	15.4331	+	26.7309i	1.23962	+	2.14708i
$156$		0			0
$157$	−11.8090			−0.942463			−0.471232	−	0.882010i	$-0.656190\pi$
$157$	−11.8090			−0.942463			−0.471232	+	0.882010i	$0.656190\pi$
$158$		0			0
$159$	5.71574	+	14.9217i	0.453287	+	1.18337i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	6.14132	−	10.6371i	0.481025	−	0.833160i	−0.518738	−	0.854933i	$-0.673598\pi$
$163$	6.14132	−	10.6371i	0.481025	−	0.833160i	0.999763	+	0.0217737i	$0.00693132\pi$
$164$		0			0
$165$	−6.35868	−	1.01175i	−0.495023	−	0.0787648i
$166$		0			0
$167$	11.4428	−	19.8195i	0.885472	−	1.53368i	0.0403003	−	0.999188i	$-0.487169\pi$
$167$	11.4428	−	19.8195i	0.885472	−	1.53368i	0.845172	−	0.534495i	$-0.179498\pi$
$168$		0			0
$169$	6.00000	+	10.3923i	0.461538	+	0.799408i
$170$		0			0
$171$	−2.86320	+	2.57067i	−0.218954	+	0.196584i
$172$		0			0
$173$	19.2632			1.46455			0.732277	−	0.681007i	$-0.238458\pi$
$173$	19.2632			1.46455			0.732277	+	0.681007i	$0.238458\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−16.3285	−	2.59808i	−1.22732	−	0.195283i
$178$		0			0
$179$	2.41586	+	4.18440i	0.180570	+	0.312757i	0.942075	−	0.335403i	$-0.108872\pi$
$179$	2.41586	+	4.18440i	0.180570	+	0.312757i	−0.761505	+	0.648159i	$0.775539\pi$
$180$		0			0
$181$	3.26320			0.242552			0.121276	−	0.992619i	$-0.461301\pi$
$181$	3.26320			0.242552			0.121276	+	0.992619i	$0.461301\pi$
$182$		0			0
$183$	−18.0390	−	2.87024i	−1.33348	−	0.212175i
$184$		0			0
$185$	38.7518			2.84909
$186$		0			0
$187$	5.28263			0.386304
$188$		0			0
$189$		0			0
$190$		0			0
$191$	14.6979			1.06351			0.531753	−	0.846900i	$-0.321534\pi$
$191$	14.6979			1.06351			0.531753	+	0.846900i	$0.321534\pi$
$192$		0			0
$193$	10.1111			0.727812			0.363906	−	0.931436i	$-0.381443\pi$
$193$	10.1111			0.727812			0.363906	+	0.931436i	$0.381443\pi$
$194$		0			0
$195$	6.74433	+	1.07311i	0.482971	+	0.0768472i
$196$		0			0
$197$	16.6375			1.18537			0.592686	−	0.805434i	$-0.298067\pi$
$197$	16.6375			1.18537			0.592686	+	0.805434i	$0.298067\pi$
$198$		0			0
$199$	−6.55555	−	11.3545i	−0.464710	−	0.804902i	0.534478	−	0.845182i	$-0.320508\pi$
$199$	−6.55555	−	11.3545i	−0.464710	−	0.804902i	−0.999188	+	0.0402805i	$0.987175\pi$
$200$		0			0
$201$	−2.93762	−	0.467414i	−0.207204	−	0.0329689i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−3.71737			−0.259632
$206$		0			0
$207$	2.88727	+	13.6792i	0.200679	+	0.950769i
$208$		0			0
$209$	−0.604645	−	1.04728i	−0.0418242	−	0.0724416i
$210$		0			0
$211$	−1.06526	+	1.84509i	−0.0733355	+	0.127021i	−0.900361	−	0.435143i	$-0.856698\pi$
$211$	−1.06526	+	1.84509i	−0.0733355	+	0.127021i	0.827026	+	0.562164i	$0.190031\pi$
$212$		0			0
$213$	6.06526	+	0.965064i	0.415585	+	0.0661251i
$214$		0			0
$215$	18.2616	−	31.6300i	1.24543	−	2.15715i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−1.68358	−	4.39521i	−0.113766	−	0.297001i
$220$		0			0
$221$	−5.60301			−0.376899
$222$		0			0
$223$	7.04583	+	12.2037i	0.471824	+	0.817223i	0.999480	−	0.0322352i	$-0.0102626\pi$
$223$	7.04583	+	12.2037i	0.471824	+	0.817223i	−0.527657	+	0.849458i	$0.676929\pi$
$224$		0			0
$225$	−23.5413	+	21.1362i	−1.56942	+	1.40908i
$226$		0			0
$227$	−2.39536	+	4.14888i	−0.158985	+	0.275371i	−0.934503	−	0.355955i	$-0.884156\pi$
$227$	−2.39536	+	4.14888i	−0.158985	+	0.275371i	0.775518	+	0.631326i	$0.217489\pi$
$228$		0			0
$229$	−9.04583	−	15.6678i	−0.597765	−	1.03536i	−0.993150	−	0.116844i	$-0.962722\pi$
$229$	−9.04583	−	15.6678i	−0.597765	−	1.03536i	0.395385	−	0.918516i	$-0.370611\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	1.57442	−	2.72698i	0.103144	−	0.178650i	−0.809835	−	0.586658i	$-0.800443\pi$
$233$	1.57442	−	2.72698i	0.103144	−	0.178650i	0.912978	+	0.408008i	$0.133777\pi$
$234$		0			0
$235$	−10.4142	−	18.0380i	−0.679349	−	1.17667i
$236$		0			0
$237$	−28.0088	−	4.45657i	−1.81937	−	0.289485i
$238$		0			0
$239$	6.16019	−	10.6698i	0.398470	−	0.690170i	−0.595068	−	0.803676i	$-0.702875\pi$
$239$	6.16019	−	10.6698i	0.398470	−	0.690170i	0.993537	+	0.113506i	$0.0362081\pi$
$240$		0			0
$241$	−7.27292	+	12.5971i	−0.468490	+	0.811448i	−0.999351	−	0.0360106i	$-0.988535\pi$
$241$	−7.27292	+	12.5971i	−0.468490	+	0.811448i	0.530862	+	0.847458i	$0.321868\pi$
$242$		0			0
$243$	10.9834	+	11.0618i	0.704589	+	0.709616i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	0.641315	+	1.11079i	0.0408059	+	0.0706779i
$248$		0			0
$249$	0.245960	+	0.642111i	0.0155871	+	0.0406922i
$250$		0			0
$251$	−2.28263			−0.144078			−0.0720392	−	0.997402i	$-0.522951\pi$
$251$	−2.28263			−0.144078			−0.0720392	+	0.997402i	$0.522951\pi$
$252$		0			0
$253$	−4.39372			−0.276231
$254$		0			0
$255$	24.1014	−	29.7195i	1.50929	−	1.86111i
$256$		0			0
$257$	−0.396990	−	0.687607i	−0.0247636	−	0.0428917i	0.853378	−	0.521293i	$-0.174550\pi$
$257$	−0.396990	−	0.687607i	−0.0247636	−	0.0428917i	−0.878142	+	0.478401i	$0.841217\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	4.74596	+	22.4852i	0.293768	+	1.39180i
$262$		0			0
$263$	−5.24433	+	9.08344i	−0.323379	+	0.560109i	−0.981183	−	0.193080i	$-0.938152\pi$
$263$	−5.24433	+	9.08344i	−0.323379	+	0.560109i	0.657804	+	0.753189i	$0.271486\pi$
$264$		0			0
$265$	−18.1871	+	31.5011i	−1.11723	+	1.93509i
$266$		0			0
$267$	−6.00916	+	7.40992i	−0.367755	+	0.453479i
$268$		0			0
$269$	−5.16991	−	8.95454i	−0.315215	−	0.545968i	0.664268	−	0.747494i	$-0.268743\pi$
$269$	−5.16991	−	8.95454i	−0.315215	−	0.545968i	−0.979483	+	0.201526i	$0.935410\pi$
$270$		0			0
$271$	15.4142	−	26.6982i	0.936348	−	1.62180i	0.164135	−	0.986438i	$-0.447517\pi$
$271$	15.4142	−	26.6982i	0.936348	−	1.62180i	0.772213	−	0.635364i	$-0.219150\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−4.97141	−	8.61073i	−0.299787	−	0.519247i
$276$		0			0
$277$	−7.12188	+	12.3355i	−0.427913	+	0.741166i	−0.996687	−	0.0813269i	$-0.974084\pi$
$277$	−7.12188	+	12.3355i	−0.427913	+	0.741166i	0.568775	+	0.822493i	$0.307418\pi$
$278$		0			0
$279$	22.3256	+	7.28914i	1.33660	+	0.436389i
$280$		0			0
$281$	4.46169	+	7.72788i	0.266162	+	0.461007i	0.967868	−	0.251461i	$-0.0809109\pi$
$281$	4.46169	+	7.72788i	0.266162	+	0.461007i	−0.701705	+	0.712468i	$0.747578\pi$
$282$		0			0
$283$	−23.2632			−1.38285			−0.691427	−	0.722446i	$-0.743018\pi$
$283$	−23.2632			−1.38285			−0.691427	+	0.722446i	$0.743018\pi$
$284$		0			0
$285$	−8.65047	−	1.37641i	−0.512410	−	0.0815313i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−7.19686	+	12.4653i	−0.423345	+	0.733255i
$290$		0			0
$291$	8.39248	+	21.9097i	0.491976	+	1.28437i
$292$		0			0
$293$	−11.9412	+	20.6827i	−0.697611	+	1.20830i	0.271681	+	0.962387i	$0.412420\pi$
$293$	−11.9412	+	20.6827i	−0.697611	+	1.20830i	−0.969292	+	0.245911i	$0.920913\pi$
$294$		0			0
$295$	−18.8187	−	32.5950i	−1.09567	−	1.89776i
$296$		0			0
$297$	−4.11436	+	2.65944i	−0.238739	+	0.154316i
$298$		0			0
$299$	4.66019			0.269506
$300$		0			0
$301$		0			0
$302$		0			0
$303$	2.83981	−	3.50178i	0.163143	−	0.201172i
$304$		0			0
$305$	−20.7902	−	36.0096i	−1.19044	−	2.06190i
$306$		0			0
$307$	−7.37429			−0.420873			−0.210436	−	0.977608i	$-0.567489\pi$
$307$	−7.37429			−0.420873			−0.210436	+	0.977608i	$0.567489\pi$
$308$		0			0
$309$	−9.90095	−	25.8478i	−0.563245	−	1.47043i
$310$		0			0
$311$	9.17154			0.520070			0.260035	−	0.965599i	$-0.416266\pi$
$311$	9.17154			0.520070			0.260035	+	0.965599i	$0.416266\pi$
$312$		0			0
$313$	16.1111			0.910653			0.455326	−	0.890325i	$-0.349523\pi$
$313$	16.1111			0.910653			0.455326	+	0.890325i	$0.349523\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−4.26320			−0.239445			−0.119723	−	0.992807i	$-0.538201\pi$
$317$	−4.26320			−0.239445			−0.119723	+	0.992807i	$0.538201\pi$
$318$		0			0
$319$	−7.22218			−0.404364
$320$		0			0
$321$	11.8759	−	14.6442i	0.662849	−	0.817362i
$322$		0			0
$323$	7.18659			0.399873
$324$		0			0
$325$	5.27292	+	9.13296i	0.292489	+	0.506605i
$326$		0			0
$327$	2.03379	+	5.30949i	0.112469	+	0.293615i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−12.2826			−0.675114			−0.337557	−	0.941305i	$-0.609601\pi$
$331$	−12.2826			−0.675114			−0.337557	+	0.941305i	$0.609601\pi$
$332$		0			0
$333$	21.9399	−	19.6984i	1.20230	−	1.07947i
$334$		0			0
$335$	−3.38564	−	5.86410i	−0.184977	−	0.320390i
$336$		0			0
$337$	13.4903	−	23.3659i	0.734863	−	1.27282i	−0.219921	−	0.975518i	$-0.570580\pi$
$337$	13.4903	−	23.3659i	0.734863	−	1.27282i	0.954784	−	0.297302i	$-0.0960867\pi$
$338$		0			0
$339$	7.03775	−	8.67827i	0.382238	−	0.471339i
$340$		0			0
$341$	−3.69041	+	6.39199i	−0.199847	+	0.346145i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−20.0458	+	24.7186i	−1.07923	+	1.33080i
$346$		0			0
$347$	−21.5048			−1.15444			−0.577219	−	0.816589i	$-0.695862\pi$
$347$	−21.5048			−1.15444			−0.577219	+	0.816589i	$0.695862\pi$
$348$		0			0
$349$	2.54583	+	4.40951i	0.136275	+	0.236035i	0.926084	−	0.377318i	$-0.123154\pi$
$349$	2.54583	+	4.40951i	0.136275	+	0.236035i	−0.789809	+	0.613353i	$0.789820\pi$
$350$		0			0
$351$	4.36389	−	2.82073i	0.232927	−	0.150559i
$352$		0			0
$353$	−4.78426	+	8.28659i	−0.254641	+	0.441051i	−0.964798	−	0.262993i	$-0.915291\pi$
$353$	−4.78426	+	8.28659i	−0.254641	+	0.441051i	0.710157	+	0.704043i	$0.248624\pi$
$354$		0			0
$355$	6.99028	+	12.1075i	0.371006	+	0.642601i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−5.48113	+	9.49359i	−0.289283	+	0.501052i	−0.973639	−	0.228096i	$-0.926750\pi$
$359$	−5.48113	+	9.49359i	−0.289283	+	0.501052i	0.684356	+	0.729148i	$0.260083\pi$
$360$		0			0
$361$	8.67743	+	15.0297i	0.456707	+	0.791039i
$362$		0			0
$363$	6.26444	+	16.3542i	0.328798	+	0.858372i
$364$		0			0
$365$	5.35705	−	9.27868i	0.280401	−	0.485668i
$366$		0			0
$367$	−2.34897	+	4.06853i	−0.122615	+	0.212376i	−0.920798	−	0.390039i	$-0.872461\pi$
$367$	−2.34897	+	4.06853i	−0.122615	+	0.212376i	0.798183	+	0.602415i	$0.205795\pi$
$368$		0			0
$369$	−2.10464	+	1.88962i	−0.109563	+	0.0983696i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−4.63160	−	8.02217i	−0.239815	−	0.415372i	0.720846	−	0.693095i	$-0.243754\pi$
$373$	−4.63160	−	8.02217i	−0.239815	−	0.415372i	−0.960661	+	0.277723i	$0.910420\pi$
$374$		0			0
$375$	−37.4029	−	5.95130i	−1.93148	−	0.307324i
$376$		0			0
$377$	7.66019			0.394520
$378$		0			0
$379$	−13.5458			−0.695803			−0.347901	−	0.937531i	$-0.613106\pi$
$379$	−13.5458			−0.695803			−0.347901	+	0.937531i	$0.613106\pi$
$380$		0			0
$381$	−1.41711	−	0.225481i	−0.0726007	−	0.0115517i
$382$		0			0
$383$	−6.13968	−	10.6342i	−0.313723	−	0.543384i	0.665442	−	0.746449i	$-0.268243\pi$
$383$	−6.13968	−	10.6342i	−0.313723	−	0.543384i	−0.979165	+	0.203065i	$0.934910\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−5.73912	−	27.1905i	−0.291736	−	1.38217i
$388$		0			0
$389$	3.75567	−	6.50502i	0.190420	−	0.329818i	−0.754969	−	0.655760i	$-0.772348\pi$
$389$	3.75567	−	6.50502i	0.190420	−	0.329818i	0.945390	+	0.325943i	$0.105682\pi$
$390$		0			0
$391$	13.0555	−	22.6129i	0.660247	−	1.14358i
$392$		0			0
$393$	−3.36513	−	8.78513i	−0.169748	−	0.443151i
$394$		0			0
$395$	−32.2804	−	55.9114i	−1.62421	−	2.81321i
$396$		0			0
$397$	11.4601	−	19.8494i	0.575164	−	0.996213i	−0.420860	−	0.907126i	$-0.638272\pi$
$397$	11.4601	−	19.8494i	0.575164	−	0.996213i	0.996024	−	0.0890875i	$-0.0283951\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	10.5631	+	18.2958i	0.527495	+	0.913647i	0.999486	+	0.0320445i	$0.0102018\pi$
$401$	10.5631	+	18.2958i	0.527495	+	0.913647i	−0.471992	+	0.881603i	$0.656465\pi$
$402$		0			0
$403$	3.91423	−	6.77965i	0.194982	−	0.337718i
$404$		0			0
$405$	−3.80959	+	35.2803i	−0.189300	+	1.75309i
$406$		0			0
$407$	4.63323	+	8.02500i	0.229661	+	0.397784i
$408$		0			0
$409$	3.43474			0.169837			0.0849185	−	0.996388i	$-0.472937\pi$
$409$	3.43474			0.169837			0.0849185	+	0.996388i	$0.472937\pi$
$410$		0			0
$411$	23.0728	−	28.4511i	1.13810	−	1.40339i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−0.782630	+	1.35556i	−0.0384178	+	0.0665416i
$416$		0			0
$417$	2.01600	−	2.48593i	0.0987238	−	0.121737i
$418$		0			0
$419$	10.2157	−	17.6942i	0.499071	−	0.864417i	−0.500928	−	0.865489i	$-0.667008\pi$
$419$	10.2157	−	17.6942i	0.499071	−	0.864417i	0.999999	+	0.00107202i	$0.000341235\pi$
$420$		0			0
$421$	−7.90451	−	13.6910i	−0.385242	−	0.667260i	0.606560	−	0.795037i	$-0.292549\pi$
$421$	−7.90451	−	13.6910i	−0.385242	−	0.667260i	−0.991803	+	0.127778i	$0.959216\pi$
$422$		0			0
$423$	−15.0653	−	4.91870i	−0.732498	−	0.239155i
$424$		0			0
$425$	59.0884			2.86621
$426$		0			0
$427$		0			0
$428$		0			0
$429$	0.584135	+	1.52496i	0.0282023	+	0.0736260i
$430$		0			0
$431$	13.3759	+	23.1678i	0.644296	+	1.11595i	0.984464	+	0.175588i	$0.0561827\pi$
$431$	13.3759	+	23.1678i	0.644296	+	1.11595i	−0.340168	+	0.940365i	$0.610484\pi$
$432$		0			0
$433$	−14.4347			−0.693689			−0.346845	−	0.937923i	$-0.612747\pi$
$433$	−14.4347			−0.693689			−0.346845	+	0.937923i	$0.612747\pi$
$434$		0			0
$435$	−32.9503	+	40.6312i	−1.57985	+	1.94812i
$436$		0			0
$437$	−5.97730			−0.285933
$438$		0			0
$439$	−38.6375			−1.84407			−0.922033	−	0.387110i	$-0.873473\pi$
$439$	−38.6375			−1.84407			−0.922033	+	0.387110i	$0.873473\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	10.5653			0.501971			0.250985	−	0.967991i	$-0.419245\pi$
$443$	10.5653			0.501971			0.250985	+	0.967991i	$0.419245\pi$
$444$		0			0
$445$	−21.7174			−1.02950
$446$		0			0
$447$	−7.52696	−	19.6501i	−0.356013	−	0.929420i
$448$		0			0
$449$	−9.37429			−0.442400			−0.221200	−	0.975228i	$-0.570997\pi$
$449$	−9.37429			−0.442400			−0.221200	+	0.975228i	$0.570997\pi$
$450$		0			0
$451$	−0.444455	−	0.769818i	−0.0209286	−	0.0362493i
$452$		0			0
$453$	9.79755	−	12.0814i	0.460329	−	0.567633i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	20.7174			0.969118			0.484559	−	0.874759i	$-0.338980\pi$
$457$	20.7174			0.969118			0.484559	+	0.874759i	$0.338980\pi$
$458$		0			0
$459$	−1.46169	−	29.0774i	−0.0682261	−	1.35722i
$460$		0			0
$461$	−17.6300	−	30.5360i	−0.821109	−	1.42220i	−0.904857	−	0.425716i	$-0.860022\pi$
$461$	−17.6300	−	30.5360i	−0.821109	−	1.42220i	0.0837475	−	0.996487i	$-0.473311\pi$
$462$		0			0
$463$	−3.55555	+	6.15838i	−0.165240	+	0.286204i	−0.936741	−	0.350024i	$-0.886173\pi$
$463$	−3.55555	+	6.15838i	−0.165240	+	0.286204i	0.771500	+	0.636229i	$0.219507\pi$
$464$		0			0
$465$	19.1235	+	49.9245i	0.886832	+	2.31520i
$466$		0			0
$467$	−2.51724	+	4.35999i	−0.116484	+	0.201756i	−0.918372	−	0.395718i	$-0.870496\pi$
$467$	−2.51724	+	4.35999i	−0.116484	+	0.201756i	0.801888	+	0.597474i	$0.203829\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−20.1997	−	3.21405i	−0.930755	−	0.148096i
$472$		0			0
$473$	8.73353			0.401568
$474$		0			0
$475$	−6.76320	−	11.7142i	−0.310317	−	0.537485i
$476$		0			0
$477$	5.71574	+	27.0797i	0.261706	+	1.23989i
$478$		0			0
$479$	−3.13323	+	5.42692i	−0.143161	+	0.247962i	−0.928685	−	0.370869i	$-0.879060\pi$
$479$	−3.13323	+	5.42692i	−0.143161	+	0.247962i	0.785524	+	0.618831i	$0.212393\pi$
$480$		0			0
$481$	−4.91423	−	8.51170i	−0.224070	−	0.388100i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−26.7044	+	46.2534i	−1.21258	+	2.10026i
$486$		0			0
$487$	−7.03611	−	12.1869i	−0.318837	−	0.552242i	0.661409	−	0.750026i	$-0.269959\pi$
$487$	−7.03611	−	12.1869i	−0.318837	−	0.552242i	−0.980246	+	0.197784i	$0.936626\pi$
$488$		0			0
$489$	13.4000	−	16.5236i	0.605969	−	0.747222i
$490$		0			0
$491$	−1.97141	+	3.41458i	−0.0889685	+	0.154098i	−0.907075	−	0.420968i	$-0.861690\pi$
$491$	−1.97141	+	3.41458i	−0.0889685	+	0.154098i	0.818107	+	0.575066i	$0.195024\pi$
$492$		0			0
$493$	21.4601	−	37.1699i	0.966512	−	1.67405i
$494$		0			0
$495$	−10.6014	−	3.46127i	−0.476496	−	0.155573i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−9.82846	−	17.0234i	−0.439982	−	0.762072i	0.557705	−	0.830039i	$-0.311682\pi$
$499$	−9.82846	−	17.0234i	−0.439982	−	0.762072i	−0.997688	+	0.0679674i	$0.978349\pi$
$500$		0			0
$501$	24.9676	−	30.7876i	1.11547	−	1.37549i
$502$		0			0
$503$	−10.2632			−0.457613			−0.228807	−	0.973472i	$-0.573482\pi$
$503$	−10.2632			−0.457613			−0.228807	+	0.973472i	$0.573482\pi$
$504$		0			0
$505$	10.2632			0.456706
$506$		0			0
$507$	7.43474	+	19.4094i	0.330188	+	0.862002i
$508$		0			0
$509$	−0.669905	−	1.16031i	−0.0296930	−	0.0514298i	0.850797	−	0.525494i	$-0.176120\pi$
$509$	−0.669905	−	1.16031i	−0.0296930	−	0.0514298i	−0.880490	+	0.474065i	$0.842786\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−5.59725	+	3.61795i	−0.247125	+	0.159736i
$514$		0			0
$515$	31.5043	−	54.5670i	1.38824	−	2.40451i
$516$		0			0
$517$	2.49028	−	4.31330i	0.109523	−	0.189699i
$518$		0			0
$519$	32.9503	+	5.24284i	1.44636	+	0.230135i
$520$		0			0
$521$	−7.89699	−	13.6780i	−0.345973	−	0.599244i	0.639557	−	0.768744i	$-0.279118\pi$
$521$	−7.89699	−	13.6780i	−0.345973	−	0.599244i	−0.985530	+	0.169500i	$0.945785\pi$
$522$		0			0
$523$	5.33818	−	9.24599i	0.233422	−	0.404299i	−0.725391	−	0.688337i	$-0.758341\pi$
$523$	5.33818	−	9.24599i	0.233422	−	0.404299i	0.958813	+	0.284038i	$0.0916743\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−21.9315	−	37.9864i	−0.955350	−	1.65471i
$528$		0			0
$529$	0.641315	−	1.11079i	0.0278833	−	0.0482952i
$530$		0			0
$531$	−27.2233	−	8.88819i	−1.18139	−	0.385715i
$532$		0			0
$533$	0.471410	+	0.816506i	0.0204190	+	0.0353668i
$534$		0			0
$535$	42.9201			1.85560
$536$		0			0
$537$	2.99355	+	7.81508i	0.129181	+	0.337246i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−8.32846	+	14.4253i	−0.358068	+	0.620193i	−0.987638	−	0.156751i	$-0.949898\pi$
$541$	−8.32846	+	14.4253i	−0.358068	+	0.620193i	0.629570	+	0.776944i	$0.283231\pi$
$542$		0			0
$543$	5.58181	+	0.888141i	0.239538	+	0.0381138i
$544$		0			0
$545$	−6.47141	+	11.2088i	−0.277205	+	0.480133i
$546$		0			0
$547$	−7.81875	−	13.5425i	−0.334305	−	0.579034i	0.649046	−	0.760749i	$-0.275168\pi$
$547$	−7.81875	−	13.5425i	−0.334305	−	0.579034i	−0.983351	+	0.181715i	$0.941835\pi$
$548$		0			0
$549$	−30.0751	−	9.81930i	−1.28357	−	0.419077i
$550$		0			0
$551$	−9.82519			−0.418567
$552$		0			0
$553$		0			0
$554$		0			0
$555$	66.2863	+	10.5470i	2.81370	+	0.447697i
$556$		0			0
$557$	8.39536	+	14.5412i	0.355723	+	0.616130i	0.987241	−	0.159231i	$-0.0509015\pi$
$557$	8.39536	+	14.5412i	0.355723	+	0.616130i	−0.631519	+	0.775361i	$0.717568\pi$
$558$		0			0
$559$	−9.26320			−0.391792
$560$		0			0
$561$	9.03611	+	1.43777i	0.381505	+	0.0607026i
$562$		0			0
$563$	15.1715			0.639404			0.319702	−	0.947518i	$-0.396417\pi$
$563$	15.1715			0.639404			0.319702	+	0.947518i	$0.396417\pi$
$564$		0			0
$565$	25.4347			1.07005
$566$		0			0
$567$		0			0
$568$		0			0
$569$	35.5264			1.48934			0.744672	−	0.667431i	$-0.232606\pi$
$569$	35.5264			1.48934			0.744672	+	0.667431i	$0.232606\pi$
$570$		0			0
$571$	−1.54583			−0.0646910			−0.0323455	−	0.999477i	$-0.510298\pi$
$571$	−1.54583			−0.0646910			−0.0323455	+	0.999477i	$0.510298\pi$
$572$		0			0
$573$	25.1413	+	4.00032i	1.05029	+	0.167116i
$574$		0			0
$575$	−49.1456			−2.04951
$576$		0			0
$577$	0.838175	+	1.45176i	0.0348937	+	0.0604377i	0.882945	−	0.469477i	$-0.155557\pi$
$577$	0.838175	+	1.45176i	0.0348937	+	0.0604377i	−0.848051	+	0.529914i	$0.822224\pi$
$578$		0			0
$579$	17.2954	+	2.75192i	0.718770	+	0.114366i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−8.69794			−0.360232
$584$		0			0
$585$	11.2443	+	3.67119i	0.464896	+	0.151785i
$586$		0			0
$587$	19.7346	+	34.1813i	0.814535	+	1.41082i	0.909662	+	0.415350i	$0.136341\pi$
$587$	19.7346	+	34.1813i	0.814535	+	1.41082i	−0.0951271	+	0.995465i	$0.530326\pi$
$588$		0			0
$589$	−5.02051	+	8.69578i	−0.206866	+	0.358303i
$590$		0			0
$591$	28.4590	+	4.52820i	1.17065	+	0.186265i
$592$		0			0
$593$	−11.4159	+	19.7729i	−0.468793	+	0.811974i	−0.999364	−	0.0356669i	$-0.988644\pi$
$593$	−11.4159	+	19.7729i	−0.468793	+	0.811974i	0.530570	+	0.847641i	$0.321978\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−8.12313	−	21.2065i	−0.332458	−	0.867925i
$598$		0			0
$599$	45.2750			1.84989			0.924943	−	0.380106i	$-0.124113\pi$
$599$	45.2750			1.84989			0.924943	+	0.380106i	$0.124113\pi$
$600$		0			0
$601$	−13.5253	−	23.4265i	−0.551709	−	0.955589i	−0.998151	−	0.0607761i	$-0.980642\pi$
$601$	−13.5253	−	23.4265i	−0.551709	−	0.955589i	0.446442	−	0.894813i	$-0.352691\pi$
$602$		0			0
$603$	−4.89768	−	1.59906i	−0.199449	−	0.0651186i
$604$		0			0
$605$	−19.9331	+	34.5252i	−0.810396	+	1.40365i
$606$		0			0
$607$	9.32846	+	16.1574i	0.378631	+	0.655807i	0.990863	−	0.134870i	$-0.0430618\pi$
$607$	9.32846	+	16.1574i	0.378631	+	0.655807i	−0.612233	+	0.790678i	$0.709728\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−2.64132	+	4.57489i	−0.106856	+	0.185080i
$612$		0			0
$613$	14.4806	+	25.0811i	0.584865	+	1.01302i	0.994892	+	0.100942i	$0.0321857\pi$
$613$	14.4806	+	25.0811i	0.584865	+	1.01302i	−0.410028	+	0.912073i	$0.634481\pi$
$614$		0			0
$615$	−6.35868	−	1.01175i	−0.256407	−	0.0407978i
$616$		0			0
$617$	−18.8457	+	32.6417i	−0.758699	+	1.31411i	0.184815	+	0.982773i	$0.440831\pi$
$617$	−18.8457	+	32.6417i	−0.758699	+	1.31411i	−0.943514	+	0.331332i	$0.892502\pi$
$618$		0			0
$619$	−0.00971516	+	0.0168272i	−0.000390485	+	0.000676340i	−0.866221	−	0.499662i	$-0.833458\pi$
$619$	−0.00971516	+	0.0168272i	−0.000390485	+	0.000676340i	0.865830	+	0.500338i	$0.166791\pi$
$620$		0			0
$621$	1.21574	+	24.1845i	0.0487858	+	0.970491i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−16.7427	−	28.9992i	−0.669708	−	1.15997i
$626$		0			0
$627$	−0.749229	−	1.95596i	−0.0299213	−	0.0781137i
$628$		0			0
$629$	−55.0690			−2.19574
$630$		0			0
$631$	28.4854			1.13399			0.566993	−	0.823723i	$-0.308107\pi$
$631$	28.4854			1.13399			0.566993	+	0.823723i	$0.308107\pi$
$632$		0			0
$633$	−2.32434	+	2.86615i	−0.0923841	+	0.113919i
$634$		0			0
$635$	−1.63323	−	2.82885i	−0.0648129	−	0.112259i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	10.1122	+	3.30155i	0.400031	+	0.130607i
$640$		0			0
$641$	−22.2696	+	38.5722i	−0.879598	+	1.52351i	−0.0278156	+	0.999613i	$0.508855\pi$
$641$	−22.2696	+	38.5722i	−0.879598	+	1.52351i	−0.851783	+	0.523896i	$0.824478\pi$
$642$		0			0
$643$	−4.50972	+	7.81106i	−0.177846	+	0.308038i	−0.941142	−	0.338010i	$-0.890246\pi$
$643$	−4.50972	+	7.81106i	−0.177846	+	0.308038i	0.763297	+	0.646048i	$0.223579\pi$
$644$		0			0
$645$	39.8457	−	49.1339i	1.56892	−	1.93464i
$646$		0			0
$647$	−21.4126	−	37.0877i	−0.841816	−	1.45807i	−0.888358	−	0.459152i	$-0.848153\pi$
$647$	−21.4126	−	37.0877i	−0.841816	−	1.45807i	0.0465419	−	0.998916i	$-0.485180\pi$
$648$		0			0
$649$	4.50000	−	7.79423i	0.176640	−	0.305950i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−2.80150	−	4.85235i	−0.109631	−	0.189887i	0.805990	−	0.591930i	$-0.201634\pi$
$653$	−2.80150	−	4.85235i	−0.109631	−	0.189887i	−0.915621	+	0.402043i	$0.868300\pi$
$654$		0			0
$655$	10.7077	−	18.5462i	0.418383	−	0.724660i
$656$		0			0
$657$	−1.68358	−	7.97637i	−0.0656826	−	0.311188i
$658$		0			0
$659$	3.26376	+	5.65299i	0.127138	+	0.220209i	0.922567	−	0.385838i	$-0.126088\pi$
$659$	3.26376	+	5.65299i	0.127138	+	0.220209i	−0.795429	+	0.606047i	$0.792754\pi$
$660$		0			0
$661$	−11.0194			−0.428606			−0.214303	−	0.976767i	$-0.568748\pi$
$661$	−11.0194			−0.428606			−0.214303	+	0.976767i	$0.568748\pi$
$662$		0			0
$663$	−9.58414	−	1.52496i	−0.372217	−	0.0592247i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−17.8490	+	30.9153i	−0.691115	+	1.19705i
$668$		0			0
$669$	8.73065	+	22.7926i	0.337547	+	0.881211i
$670$		0			0
$671$	4.97141	−	8.61073i	0.191919	−	0.332414i
$672$		0			0
$673$	1.67743	+	2.90539i	0.0646602	+	0.111995i	0.896543	−	0.442956i	$-0.146070\pi$
$673$	1.67743	+	2.90539i	0.0646602	+	0.111995i	−0.831883	+	0.554951i	$0.812737\pi$
$674$		0			0
$675$	−46.0208	+	29.7469i	−1.77134	+	1.14496i
$676$		0			0
$677$	−40.6375			−1.56183			−0.780913	−	0.624640i	$-0.785246\pi$
$677$	−40.6375			−1.56183			−0.780913	+	0.624640i	$0.785246\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−5.22653	+	6.44485i	−0.200281	+	0.246967i
$682$		0			0
$683$	7.03775	+	12.1897i	0.269292	+	0.466427i	0.968679	−	0.248316i	$-0.0798770\pi$
$683$	7.03775	+	12.1897i	0.269292	+	0.466427i	−0.699387	+	0.714743i	$0.746544\pi$
$684$		0			0
$685$	83.3861			3.18602
$686$		0			0
$687$	−11.2089	−	29.2623i	−0.427646	−	1.11643i
$688$		0			0
$689$	9.22545			0.351462
$690$		0			0
$691$	−43.9201			−1.67080			−0.835400	−	0.549642i	$-0.814764\pi$
$691$	−43.9201			−1.67080			−0.835400	+	0.549642i	$0.814764\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	7.28590			0.276370
$696$		0			0
$697$	5.28263			0.200094
$698$		0			0
$699$	3.43530	−	4.23607i	0.129935	−	0.160223i
$700$		0			0
$701$	7.69578			0.290666			0.145333	−	0.989383i	$-0.453575\pi$
$701$	7.69578			0.290666			0.145333	+	0.989383i	$0.453575\pi$
$702$		0			0
$703$	6.30314	+	10.9174i	0.237727	+	0.411756i
$704$		0			0
$705$	−12.9045	−	33.6890i	−0.486012	−	1.26880i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	0.222181			0.00834417			0.00417209	−	0.999991i	$-0.498672\pi$
$709$	0.222181			0.00834417			0.00417209	+	0.999991i	$0.498672\pi$
$710$		0			0
$711$	−46.6970	−	15.2462i	−1.75127	−	0.571778i
$712$		0			0
$713$	18.2411	+	31.5944i	0.683133	+	1.18322i
$714$		0			0
$715$	−1.85868	+	3.21934i	−0.0695109	+	0.120396i
$716$		0			0
$717$	13.4412	−	16.5744i	0.501970	−	0.618981i
$718$		0			0
$719$	1.32201	−	2.28980i	0.0493028	−	0.0853950i	−0.840321	−	0.542089i	$-0.817633\pi$
$719$	1.32201	−	2.28980i	0.0493028	−	0.0853950i	0.889624	+	0.456694i	$0.150967\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−15.8691	+	19.5682i	−0.590178	+	0.727750i
$724$		0			0
$725$	−80.7831			−3.00021
$726$		0			0
$727$	−12.7427	−	22.0710i	−0.472600	−	0.818568i	0.526908	−	0.849922i	$-0.323351\pi$
$727$	−12.7427	−	22.0710i	−0.472600	−	0.818568i	−0.999508	+	0.0313547i	$0.990018\pi$
$728$		0			0
$729$	15.7769	+	21.9110i	0.584329	+	0.811517i
$730$		0			0
$731$	−25.9509	+	44.9483i	−0.959829	+	1.66247i
$732$		0			0
$733$	−0.934740	−	1.61902i	−0.0345254	−	0.0597997i	0.848246	−	0.529602i	$-0.177659\pi$
$733$	−0.934740	−	1.61902i	−0.0345254	−	0.0597997i	−0.882772	+	0.469802i	$0.844325\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	0.809585	−	1.40224i	0.0298215	−	0.0516523i
$738$		0			0
$739$	−25.5819	−	44.3092i	−0.941047	−	1.62994i	−0.763479	−	0.645833i	$-0.776510\pi$
$739$	−25.5819	−	44.3092i	−0.941047	−	1.62994i	−0.177568	−	0.984108i	$-0.556823\pi$
$740$		0			0
$741$	0.794668	+	2.07459i	0.0291929	+	0.0762120i
$742$		0			0
$743$	19.3668	−	33.5442i	0.710498	−	1.23062i	−0.254173	−	0.967159i	$-0.581803\pi$
$743$	19.3668	−	33.5442i	0.710498	−	1.23062i	0.964671	−	0.263459i	$-0.0848635\pi$
$744$		0			0
$745$	23.9503	−	41.4832i	0.877473	−	1.51983i
$746$		0			0
$747$	0.245960	+	1.16530i	0.00899920	+	0.0426359i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−3.09549	−	5.36154i	−0.112956	−	0.195645i	0.804005	−	0.594623i	$-0.202699\pi$
$751$	−3.09549	−	5.36154i	−0.112956	−	0.195645i	−0.916961	+	0.398977i	$0.869365\pi$
$752$		0			0
$753$	−3.90451	−	0.621261i	−0.142288	−	0.0226400i
$754$		0			0
$755$	35.4088			1.28866
$756$		0			0
$757$	−13.7174			−0.498566			−0.249283	−	0.968431i	$-0.580195\pi$
$757$	−13.7174			−0.498566			−0.249283	+	0.968431i	$0.580195\pi$
$758$		0			0
$759$	−7.51561	−	1.19583i	−0.272799	−	0.0434060i
$760$		0			0
$761$	−19.6602	−	34.0524i	−0.712681	−	1.23440i	−0.963847	−	0.266456i	$-0.914147\pi$
$761$	−19.6602	−	34.0524i	−0.712681	−	1.23440i	0.251166	−	0.967944i	$-0.419186\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	49.3149	−	44.2765i	1.78298	−	1.60082i
$766$		0			0
$767$	−4.77292	+	8.26693i	−0.172340	+	0.298502i
$768$		0			0
$769$	−11.3646	+	19.6840i	−0.409817	+	0.709824i	−0.994869	−	0.101172i	$-0.967741\pi$
$769$	−11.3646	+	19.6840i	−0.409817	+	0.709824i	0.585052	+	0.810996i	$0.301074\pi$
$770$		0			0
$771$	−0.491920	−	1.28422i	−0.0177161	−	0.0462502i
$772$		0			0
$773$	14.3662	+	24.8830i	0.516717	+	0.894979i	0.999812	+	0.0194115i	$0.00617926\pi$
$773$	14.3662	+	24.8830i	0.516717	+	0.894979i	−0.483095	+	0.875568i	$0.660487\pi$
$774$		0			0
$775$	−41.2788	+	71.4970i	−1.48278	+	2.56825i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−0.604645	−	1.04728i	−0.0216636	−	0.0375225i
$780$		0			0
$781$	−1.67154	+	2.89519i	−0.0598124	+	0.103598i
$782$		0			0
$783$	1.99837	+	39.7533i	0.0714157	+	1.42067i
$784$		0			0
$785$	−23.2804	−	40.3229i	−0.830915	−	1.43919i
$786$		0			0
$787$	−54.0118			−1.92531			−0.962656	−	0.270728i	$-0.912736\pi$
$787$	−54.0118			−1.92531			−0.962656	+	0.270728i	$0.912736\pi$
$788$		0			0
$789$	−11.4428	+	14.1102i	−0.407375	+	0.502336i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−5.27292	+	9.13296i	−0.187247	+	0.324321i
$794$		0			0
$795$	−39.6833	+	48.9336i	−1.40742	+	1.73550i
$796$		0			0
$797$	0.103565	−	0.179381i	0.00366848	−	0.00635399i	−0.864185	−	0.503174i	$-0.832166\pi$
$797$	0.103565	−	0.179381i	0.00366848	−	0.00635399i	0.867854	+	0.496820i	$0.165499\pi$
$798$		0			0
$799$	14.7993	+	25.6332i	0.523562	+	0.906836i
$800$		0			0
$801$	−12.2956	+	11.0394i	−0.434444	+	0.390058i
$802$		0			0
$803$	2.56199			0.0904107
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−6.40615	−	16.7241i	−0.225507	−	0.588717i
$808$		0			0
$809$	18.0270	+	31.2236i	0.633794	+	1.09776i	0.986769	+	0.162131i	$0.0518366\pi$
$809$	18.0270	+	31.2236i	0.633794	+	1.09776i	−0.352975	+	0.935633i	$0.614830\pi$
$810$		0			0
$811$	−2.01943			−0.0709118			−0.0354559	−	0.999371i	$-0.511288\pi$
$811$	−2.01943			−0.0709118			−0.0354559	+	0.999371i	$0.511288\pi$
$812$		0			0
$813$	33.6330	−	41.4729i	1.17956	−	1.45452i
$814$		0			0
$815$	48.4282			1.69637
$816$		0			0
$817$	11.8813			0.415673
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−30.3743			−1.06007			−0.530035	−	0.847976i	$-0.677821\pi$
$821$	−30.3743			−1.06007			−0.530035	+	0.847976i	$0.677821\pi$
$822$		0			0
$823$	−13.1305			−0.457701			−0.228851	−	0.973462i	$-0.573497\pi$
$823$	−13.1305			−0.457701			−0.228851	+	0.973462i	$0.573497\pi$
$824$		0			0
$825$	−6.16019	−	16.0820i	−0.214470	−	0.559904i
$826$		0			0
$827$	−11.3236			−0.393762			−0.196881	−	0.980427i	$-0.563081\pi$
$827$	−11.3236			−0.393762			−0.196881	+	0.980427i	$0.563081\pi$
$828$		0			0
$829$	5.53022	+	9.57863i	0.192073	+	0.332680i	0.945937	−	0.324351i	$-0.105146\pi$
$829$	5.53022	+	9.57863i	0.192073	+	0.332680i	−0.753864	+	0.657030i	$0.771812\pi$
$830$		0			0
$831$	−15.5395	+	19.1619i	−0.539061	+	0.664718i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	90.2340			3.12267
$836$		0			0
$837$	36.2048	+	18.5446i	1.25142	+	0.640996i
$838$		0			0
$839$	−5.27128	−	9.13013i	−0.181985	−	0.315207i	0.760572	−	0.649254i	$-0.224919\pi$
$839$	−5.27128	−	9.13013i	−0.181985	−	0.315207i	−0.942556	+	0.334047i	$0.891586\pi$
$840$		0			0
$841$	−14.8393	+	25.7023i	−0.511698	+	0.886288i
$842$		0			0
$843$	5.52859	+	14.4331i	0.190415	+	0.497104i
$844$		0			0
$845$	−23.6569	+	40.9750i	−0.813823	+	1.40958i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−39.7925	−	6.33152i	−1.36567	−	0.217297i
$850$		0			0
$851$	45.8025			1.57009
$852$		0			0
$853$	13.6413	+	23.6275i	0.467070	+	0.808989i	0.999292	−	0.0376160i	$-0.0119764\pi$
$853$	13.6413	+	23.6275i	0.467070	+	0.808989i	−0.532223	+	0.846604i	$0.678643\pi$
$854$		0			0
$855$	−14.4223	−	4.70878i	−0.493233	−	0.161037i
$856$		0			0
$857$	1.21574	−	2.10571i	0.0415287	−	0.0719299i	−0.844514	−	0.535534i	$-0.820111\pi$
$857$	1.21574	−	2.10571i	0.0415287	−	0.0719299i	0.886043	+	0.463604i	$0.153444\pi$
$858$		0			0
$859$	15.8743	+	27.4951i	0.541624	+	0.938120i	0.998811	+	0.0487495i	$0.0155236\pi$
$859$	15.8743	+	27.4951i	0.541624	+	0.938120i	−0.457187	+	0.889370i	$0.651143\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	13.9126	−	24.0973i	0.473590	−	0.820282i	−0.525953	−	0.850514i	$-0.676291\pi$
$863$	13.9126	−	24.0973i	0.473590	−	0.820282i	0.999543	+	0.0302315i	$0.00962444\pi$
$864$		0			0
$865$	37.9757	+	65.7758i	1.29121	+	2.23644i
$866$		0			0
$867$	−15.7031	+	19.3636i	−0.533307	+	0.657622i
$868$		0			0
$869$	7.71900	−	13.3697i	0.261849	−	0.453536i
$870$		0			0
$871$	−0.858685	+	1.48729i	−0.0290954	+	0.0503948i
$872$		0			0
$873$	8.39248	+	39.7614i	0.284042	+	1.34572i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	2.29342	+	3.97233i	0.0774434	+	0.134136i	0.902146	−	0.431430i	$-0.141991\pi$
$877$	2.29342	+	3.97233i	0.0774434	+	0.134136i	−0.824703	+	0.565566i	$0.808658\pi$
$878$		0			0
$879$	−26.0550	+	32.1285i	−0.878813	+	1.08367i
$880$		0			0
$881$	57.4465			1.93542			0.967711	−	0.252062i	$-0.0811085\pi$
$881$	57.4465			1.93542			0.967711	+	0.252062i	$0.0811085\pi$
$882$		0			0
$883$	36.3937			1.22475			0.612373	−	0.790569i	$-0.290215\pi$
$883$	36.3937			1.22475			0.612373	+	0.790569i	$0.290215\pi$
$884$		0			0
$885$	−23.3187	−	60.8767i	−0.783851	−	2.04635i
$886$		0			0
$887$	21.7238	+	37.6268i	0.729414	+	1.26338i	0.957131	+	0.289655i	$0.0935407\pi$
$887$	21.7238	+	37.6268i	0.729414	+	1.26338i	−0.227717	+	0.973727i	$0.573126\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−7.76157	+	3.42926i	−0.260022	+	0.114884i
$892$		0			0
$893$	3.38783	−	5.86789i	0.113369	−	0.196362i
$894$		0			0
$895$	−9.52532	+	16.4983i	−0.318396	+	0.551479i
$896$		0			0
$897$	7.97141	+	1.26836i	0.266158	+	0.0423492i
$898$		0			0
$899$	29.9837	+	51.9334i	1.00001	+	1.73207i
$900$		0			0
$901$	25.8451	−	44.7651i	0.861027	−	1.49134i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	6.43310	+	11.1425i	0.213844	+	0.370388i
$906$		0			0
$907$	−11.1569	+	19.3244i	−0.370459	+	0.641655i	−0.989636	−	0.143597i	$-0.954133\pi$
$907$	−11.1569	+	19.3244i	−0.370459	+	0.641655i	0.619177	+	0.785252i	$0.287466\pi$
$908$		0			0
$909$	5.81066	−	5.21700i	0.192728	−	0.173037i
$910$		0			0
$911$	7.67799	+	13.2987i	0.254383	+	0.440604i	0.964728	−	0.263250i	$-0.0847943\pi$
$911$	7.67799	+	13.2987i	0.254383	+	0.440604i	−0.710345	+	0.703854i	$0.751461\pi$
$912$		0			0
$913$	−0.374290			−0.0123872
$914$		0			0
$915$	−25.7616	−	67.2541i	−0.851651	−	2.22335i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	18.4142	−	31.8944i	0.607429	−	1.05210i	−0.384233	−	0.923236i	$-0.625534\pi$
$919$	18.4142	−	31.8944i	0.607429	−	1.05210i	0.991662	−	0.128862i	$-0.0411326\pi$
$920$		0			0
$921$	−12.6140	−	2.00705i	−0.415644	−	0.0661346i
$922$		0			0
$923$	1.77292	−	3.07078i	0.0583562	−	0.101076i
$924$		0			0
$925$	51.8246	+	89.7629i	1.70398	+	2.95139i
$926$		0			0
$927$	−9.90095	−	46.9082i	−0.325190	−	1.54067i
$928$		0			0
$929$	−41.7292			−1.36909			−0.684545	−	0.728971i	$-0.739999\pi$
$929$	−41.7292			−1.36909			−0.684545	+	0.728971i	$0.739999\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	15.6882	+	2.49621i	0.513609	+	0.0817221i
$934$		0			0
$935$	10.4142	+	18.0380i	0.340582	+	0.589905i
$936$		0			0
$937$	−25.3743			−0.828942			−0.414471	−	0.910063i	$-0.636033\pi$
$937$	−25.3743			−0.828942			−0.414471	+	0.910063i	$0.636033\pi$
$938$		0			0
$939$	27.5586	+	4.38493i	0.899340	+	0.143097i
$940$		0			0
$941$	47.1423			1.53680			0.768398	−	0.639973i	$-0.221054\pi$
$941$	47.1423			1.53680			0.768398	+	0.639973i	$0.221054\pi$
$942$		0			0
$943$	−4.39372			−0.143079
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−34.5070			−1.12133			−0.560663	−	0.828044i	$-0.689454\pi$
$947$	−34.5070			−1.12133			−0.560663	+	0.828044i	$0.689454\pi$
$948$		0			0
$949$	−2.71737			−0.0882096
$950$		0			0
$951$	−7.29235	−	1.16031i	−0.236470	−	0.0376256i
$952$		0			0
$953$	−44.1833			−1.43124			−0.715619	−	0.698491i	$-0.753855\pi$
$953$	−44.1833			−1.43124			−0.715619	+	0.698491i	$0.753855\pi$
$954$		0			0
$955$	28.9757	+	50.1873i	0.937631	+	1.62402i
$956$		0			0
$957$	−12.3538	−	1.96565i	−0.399341	−	0.0635405i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	30.2848			0.976929
$962$		0			0
$963$	24.2999	−	21.8172i	0.783052	−	0.703050i
$964$		0			0
$965$	19.9331	+	34.5252i	0.641669	+	1.11140i
$966$		0			0
$967$	−21.2330	+	36.7766i	−0.682806	+	1.18266i	0.291314	+	0.956627i	$0.405907\pi$
$967$	−21.2330	+	36.7766i	−0.682806	+	1.18266i	−0.974121	+	0.226028i	$0.927426\pi$
$968$		0			0
$969$	12.2929	+	1.95596i	0.394905	+	0.0628346i
$970$		0			0
$971$	−3.02696	+	5.24284i	−0.0971396	+	0.168251i	−0.910500	−	0.413510i	$-0.864303\pi$
$971$	−3.02696	+	5.24284i	−0.0971396	+	0.168251i	0.813360	+	0.581761i	$0.197636\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	6.53379	+	17.0573i	0.209249	+	0.546272i
$976$		0			0
$977$	−44.0528			−1.40937			−0.704687	−	0.709518i	$-0.748913\pi$
$977$	−44.0528			−1.40937			−0.704687	+	0.709518i	$0.748913\pi$
$978$		0			0
$979$	−2.59656	−	4.49738i	−0.0829866	−	0.143737i
$980$		0			0
$981$	2.03379	+	9.63559i	0.0649340	+	0.307641i
$982$		0			0
$983$	2.23517	−	3.87142i	0.0712907	−	0.123479i	−0.828177	−	0.560467i	$-0.810622\pi$
$983$	2.23517	−	3.87142i	0.0712907	−	0.123479i	0.899467	+	0.436988i	$0.143955\pi$
$984$		0			0
$985$	32.7993	+	56.8101i	1.04507	+	1.81012i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	21.5841	−	37.3848i	0.686336	−	1.18877i
$990$		0			0
$991$	15.7524	+	27.2840i	0.500392	+	0.866704i	1.00000		0.000452297i	$0.000143971\pi$
$991$	15.7524	+	27.2840i	0.500392	+	0.866704i	−0.499608	+	0.866251i	$0.666523\pi$
$992$		0			0
$993$	−21.0098	−	3.34295i	−0.666727	−	0.106085i
$994$		0			0
$995$	25.8473	−	44.7689i	0.819416	−	1.41927i
$996$		0			0
$997$	−13.0000	+	22.5167i	−0.411714	+	0.713110i	−0.995077	−	0.0991016i	$-0.968403\pi$
$997$	−13.0000	+	22.5167i	−0.411714	+	0.713110i	0.583363	+	0.812211i	$0.301736\pi$
$998$		0			0
$999$	42.8903	−	27.7234i	1.35699	−	0.877129i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1764.2.i.f.373.3		6
3.2	odd	2		5292.2.i.d.1549.1		6
7.2	even	3		252.2.j.b.85.1	✓	6
7.3	odd	6		1764.2.l.g.949.2		6
7.4	even	3		1764.2.l.d.949.2		6
7.5	odd	6		1764.2.j.d.589.3		6
7.6	odd	2		1764.2.i.e.373.1		6
9.2	odd	6		5292.2.l.g.3313.3		6
9.7	even	3		1764.2.l.d.961.2		6
21.2	odd	6		756.2.j.a.253.1		6
21.5	even	6		5292.2.j.e.1765.3		6
21.11	odd	6		5292.2.l.g.361.3		6
21.17	even	6		5292.2.l.d.361.1		6
21.20	even	2		5292.2.i.g.1549.3		6
28.23	odd	6		1008.2.r.g.337.3		6
63.2	odd	6		756.2.j.a.505.1		6
63.11	odd	6		5292.2.i.d.2125.1		6
63.16	even	3		252.2.j.b.169.1	yes	6
63.20	even	6		5292.2.l.d.3313.1		6
63.23	odd	6		2268.2.a.j.1.3		3
63.25	even	3	inner	1764.2.i.f.1537.3		6
63.34	odd	6		1764.2.l.g.961.2		6
63.38	even	6		5292.2.i.g.2125.3		6
63.47	even	6		5292.2.j.e.3529.3		6
63.52	odd	6		1764.2.i.e.1537.1		6
63.58	even	3		2268.2.a.g.1.1		3
63.61	odd	6		1764.2.j.d.1177.3		6
84.23	even	6		3024.2.r.i.1009.1		6
252.23	even	6		9072.2.a.bz.1.3		3
252.79	odd	6		1008.2.r.g.673.3		6
252.191	even	6		3024.2.r.i.2017.1		6
252.247	odd	6		9072.2.a.bt.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.j.b.85.1	✓	6	7.2	even	3
252.2.j.b.169.1	yes	6	63.16	even	3
756.2.j.a.253.1		6	21.2	odd	6
756.2.j.a.505.1		6	63.2	odd	6
1008.2.r.g.337.3		6	28.23	odd	6
1008.2.r.g.673.3		6	252.79	odd	6
1764.2.i.e.373.1		6	7.6	odd	2
1764.2.i.e.1537.1		6	63.52	odd	6
1764.2.i.f.373.3		6	1.1	even	1	trivial
1764.2.i.f.1537.3		6	63.25	even	3	inner
1764.2.j.d.589.3		6	7.5	odd	6
1764.2.j.d.1177.3		6	63.61	odd	6
1764.2.l.d.949.2		6	7.4	even	3
1764.2.l.d.961.2		6	9.7	even	3
1764.2.l.g.949.2		6	7.3	odd	6
1764.2.l.g.961.2		6	63.34	odd	6
2268.2.a.g.1.1		3	63.58	even	3
2268.2.a.j.1.3		3	63.23	odd	6
3024.2.r.i.1009.1		6	84.23	even	6
3024.2.r.i.2017.1		6	252.191	even	6
5292.2.i.d.1549.1		6	3.2	odd	2
5292.2.i.d.2125.1		6	63.11	odd	6
5292.2.i.g.1549.3		6	21.20	even	2
5292.2.i.g.2125.3		6	63.38	even	6
5292.2.j.e.1765.3		6	21.5	even	6
5292.2.j.e.3529.3		6	63.47	even	6
5292.2.l.d.361.1		6	21.17	even	6
5292.2.l.d.3313.1		6	63.20	even	6
5292.2.l.g.361.3		6	21.11	odd	6
5292.2.l.g.3313.3		6	9.2	odd	6
9072.2.a.bt.1.1		3	252.247	odd	6
9072.2.a.bz.1.3		3	252.23	even	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:	\( N \)	\(=\)	\( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1764.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.71053 + 0.272169i) q^{3} +(1.97141 + 3.41458i) q^{5} +(2.85185 + 0.931107i) q^{9} +(-0.471410 + 0.816506i) q^{11} +(0.500000 - 0.866025i) q^{13} +(2.44282 + 6.37731i) q^{15} +(-2.80150 - 4.85235i) q^{17} +(-0.641315 + 1.11079i) q^{19} +(2.33009 + 4.03584i) q^{23} +(-5.27292 + 9.13296i) q^{25} +(4.62476 + 2.36887i) q^{27} +(3.83009 + 6.63392i) q^{29} +7.82846 q^{31} +(-1.02859 + 1.26836i) q^{33} +(4.91423 - 8.51170i) q^{37} +(1.09097 - 1.34528i) q^{39} +(-0.471410 + 0.816506i) q^{41} +(-4.63160 - 8.02217i) q^{43} +(2.44282 + 11.5735i) q^{45} -5.28263 q^{47} +(-3.47141 - 9.06259i) q^{51} +(4.61273 + 7.98947i) q^{53} -3.71737 q^{55} +(-1.39931 + 1.72550i) q^{57} -9.54583 q^{59} -10.5458 q^{61} +3.94282 q^{65} -1.71737 q^{67} +(2.88727 + 7.53762i) q^{69} +3.54583 q^{71} +(-1.35868 - 2.35331i) q^{73} +(-11.5052 + 14.1871i) q^{75} -16.3743 q^{79} +(7.26608 + 5.31075i) q^{81} +(0.198495 + 0.343803i) q^{83} +(11.0458 - 19.1319i) q^{85} +(4.74596 + 12.3900i) q^{87} +(-2.75404 + 4.77014i) q^{89} +(13.3908 + 2.13066i) q^{93} -5.05718 q^{95} +(6.77292 + 11.7310i) q^{97} +(-2.10464 + 1.88962i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{3} + 3 q^{5} + 8 q^{9} + 6 q^{11} + 3 q^{13} - 3 q^{15} - 3 q^{19} + 6 q^{23} - 6 q^{25} - 7 q^{27} + 15 q^{29} - 6 q^{31} - 15 q^{33} + 3 q^{37} - 2 q^{39} + 6 q^{41} - 3 q^{43} - 3 q^{45} - 30 q^{47}+ \cdots - 24 q^{99}+O(q^{100}) \) 6 * q + 2 * q^3 + 3 * q^5 + 8 * q^9 + 6 * q^11 + 3 * q^13 - 3 * q^15 - 3 * q^19 + 6 * q^23 - 6 * q^25 - 7 * q^27 + 15 * q^29 - 6 * q^31 - 15 * q^33 + 3 * q^37 - 2 * q^39 + 6 * q^41 - 3 * q^43 - 3 * q^45 - 30 * q^47 - 12 * q^51 + 18 * q^53 - 24 * q^55 + 7 * q^57 - 6 * q^59 - 12 * q^61 + 6 * q^65 - 12 * q^67 + 27 * q^69 - 30 * q^71 - 9 * q^73 - 34 * q^75 + 6 * q^79 + 8 * q^81 + 18 * q^83 + 15 * q^85 + 39 * q^87 - 6 * q^89 + 10 * q^93 - 48 * q^95 + 15 * q^97 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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