LMFDB - Embedded newform 900.3.p.d.101.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [900,3,Mod(101,900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(900, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("900.101");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	900.p (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$24.5232237924$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 10 x^{14} - 12 x^{13} + 6 x^{12} - 27 x^{11} - 585 x^{10} + 3618 x^{9} + \cdots + 43046721 $ x^16 - 2x^15 + 10x^14 - 12x^13 + 6x^12 - 27x^11 - 585x^10 + 3618x^9 - 12150x^8 + 32562x^7 - 47385x^6 - 19683x^5 + 39366x^4 - 708588x^3 + 5314410x^2 - 9565938*x + 43046721
Coefficient ring:	$\Z[a_1, \ldots, a_{41}]$
Coefficient ring index:	$ 3^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.8
Root			$0.844479 - 2.87869i$ of defining polynomial
Character	$\chi$	$=$	900.101
Dual form			900.3.p.d.401.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.91526 - 0.708005i) q^{3} +(-4.96248 + 8.59526i) q^{7} +(7.99746 - 4.12804i) q^{9} +O(q^{10})$	\(q+(2.91526 - 0.708005i) q^{3} +(-4.96248 + 8.59526i) q^{7} +(7.99746 - 4.12804i) q^{9} +(3.59076 + 2.07313i) q^{11} +(-0.613246 - 1.06217i) q^{13} +21.0247i q^{17} -9.84025 q^{19} +(-8.38141 + 28.5709i) q^{21} +(2.32213 - 1.34068i) q^{23} +(20.3920 - 17.6965i) q^{27} +(-0.321704 - 0.185736i) q^{29} +(22.1854 + 38.4263i) q^{31} +(11.9358 + 3.50142i) q^{33} -33.0624 q^{37} +(-2.53980 - 2.66233i) q^{39} +(-34.2494 + 19.7739i) q^{41} +(-14.5886 + 25.2682i) q^{43} +(68.6012 + 39.6069i) q^{47} +(-24.7524 - 42.8724i) q^{49} +(14.8856 + 61.2924i) q^{51} +92.8471i q^{53} +(-28.6869 + 6.96695i) q^{57} +(-53.3228 + 30.7859i) q^{59} +(12.6725 - 21.9495i) q^{61} +(-4.20566 + 89.2255i) q^{63} +(17.9426 + 31.0774i) q^{67} +(5.82040 - 5.55252i) q^{69} -16.7821i q^{71} +62.4649 q^{73} +(-35.6382 + 20.5757i) q^{77} +(71.9430 - 124.609i) q^{79} +(46.9187 - 66.0276i) q^{81} +(-14.2118 - 8.20517i) q^{83} +(-1.06935 - 0.313699i) q^{87} -155.682i q^{89} +12.1729 q^{91} +(91.8823 + 96.3152i) q^{93} +(-52.3390 + 90.6538i) q^{97} +(37.2749 + 1.75696i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{3} + q^{7} + 14 q^{9}+O(q^{10}) $ 16 * q - 2 * q^3 + q^7 + 14 * q^9	$ 16 q - 2 q^{3} + q^{7} + 14 q^{9} + 10 q^{13} + 2 q^{19} + q^{21} - 27 q^{23} + 16 q^{27} + 9 q^{29} + 8 q^{31} - 36 q^{33} + 22 q^{37} + 19 q^{39} + 54 q^{41} - 44 q^{43} + 108 q^{47} - 45 q^{49} + 90 q^{51} + 68 q^{57} + 9 q^{59} - 55 q^{61} + 107 q^{63} + 28 q^{67} - 147 q^{69} - 86 q^{73} - 342 q^{77} + 11 q^{79} - 130 q^{81} + 306 q^{83} - 375 q^{87} - 134 q^{91} + 83 q^{93} - 41 q^{97} + 252 q^{99}+O(q^{100}) $ 16 * q - 2 * q^3 + q^7 + 14 * q^9 + 10 * q^13 + 2 * q^19 + q^21 - 27 * q^23 + 16 * q^27 + 9 * q^29 + 8 * q^31 - 36 * q^33 + 22 * q^37 + 19 * q^39 + 54 * q^41 - 44 * q^43 + 108 * q^47 - 45 * q^49 + 90 * q^51 + 68 * q^57 + 9 * q^59 - 55 * q^61 + 107 * q^63 + 28 * q^67 - 147 * q^69 - 86 * q^73 - 342 * q^77 + 11 * q^79 - 130 * q^81 + 306 * q^83 - 375 * q^87 - 134 * q^91 + 83 * q^93 - 41 * q^97 + 252 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.91526	−	0.708005i	0.971753	−	0.236002i
$3$	2.91526	−	0.708005i	0.971753	−	0.236002i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−4.96248	+	8.59526i	−0.708925	+	1.22789i	0.256331	+	0.966589i	$0.417486\pi$
$7$	−4.96248	+	8.59526i	−0.708925	+	1.22789i	−0.965256	+	0.261306i	$0.915847\pi$
$8$		0			0
$9$	7.99746	−	4.12804i	0.888606	−	0.458671i
$10$		0			0
$11$	3.59076	+	2.07313i	0.326433	+	0.188466i	0.654256	−	0.756273i	$-0.272982\pi$
$11$	3.59076	+	2.07313i	0.326433	+	0.188466i	−0.327823	+	0.944739i	$0.606315\pi$
$12$		0			0
$13$	−0.613246	−	1.06217i	−0.0471728	−	0.0817057i	0.841475	−	0.540296i	$-0.181688\pi$
$13$	−0.613246	−	1.06217i	−0.0471728	−	0.0817057i	−0.888648	+	0.458591i	$0.848354\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$			21.0247i			1.23675i	0.785885	+	0.618373i	$0.212208\pi$
$17$			21.0247i			1.23675i	−0.785885	+	0.618373i	$0.787792\pi$
$18$		0			0
$19$	−9.84025			−0.517908			−0.258954	−	0.965890i	$-0.583378\pi$
$19$	−9.84025			−0.517908			−0.258954	+	0.965890i	$0.583378\pi$
$20$		0			0
$21$	−8.38141	+	28.5709i	−0.399115	+	1.36052i
$22$		0			0
$23$	2.32213	−	1.34068i	0.100962	−	0.0582906i	−0.448669	−	0.893698i	$-0.648102\pi$
$23$	2.32213	−	1.34068i	0.100962	−	0.0582906i	0.549631	+	0.835408i	$0.314768\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	20.3920	−	17.6965i	0.755259	−	0.655427i
$28$		0			0
$29$	−0.321704	−	0.185736i	−0.0110932	−	0.00640468i	0.494443	−	0.869210i	$-0.335372\pi$
$29$	−0.321704	−	0.185736i	−0.0110932	−	0.00640468i	−0.505536	+	0.862805i	$0.668705\pi$
$30$		0			0
$31$	22.1854	+	38.4263i	0.715659	+	1.23956i	0.962705	+	0.270554i	$0.0872069\pi$
$31$	22.1854	+	38.4263i	0.715659	+	1.23956i	−0.247046	+	0.969004i	$0.579460\pi$
$32$		0			0
$33$	11.9358	+	3.50142i	0.361690	+	0.106104i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−33.0624			−0.893579			−0.446790	−	0.894639i	$-0.647433\pi$
$37$	−33.0624			−0.893579			−0.446790	+	0.894639i	$0.647433\pi$
$38$		0			0
$39$	−2.53980	−	2.66233i	−0.0651230	−	0.0682649i
$40$		0			0
$41$	−34.2494	+	19.7739i	−0.835351	+	0.482290i	−0.855681	−	0.517503i	$-0.826862\pi$
$41$	−34.2494	+	19.7739i	−0.835351	+	0.482290i	0.0203301	+	0.999793i	$0.493528\pi$
$42$		0			0
$43$	−14.5886	+	25.2682i	−0.339270	+	0.587633i	−0.984296	−	0.176528i	$-0.943513\pi$
$43$	−14.5886	+	25.2682i	−0.339270	+	0.587633i	0.645026	+	0.764161i	$0.276847\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	68.6012	+	39.6069i	1.45960	+	0.842700i	0.998991	−	0.0449040i	$-0.0142982\pi$
$47$	68.6012	+	39.6069i	1.45960	+	0.842700i	0.460608	+	0.887604i	$0.347632\pi$
$48$		0			0
$49$	−24.7524	−	42.8724i	−0.505150	−	0.874946i
$50$		0			0
$51$	14.8856	+	61.2924i	0.291874	+	1.20181i
$52$		0			0
$53$			92.8471i			1.75183i	0.482463	+	0.875916i	$0.339742\pi$
$53$			92.8471i			1.75183i	−0.482463	+	0.875916i	$0.660258\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−28.6869	+	6.96695i	−0.503279	+	0.122227i
$58$		0			0
$59$	−53.3228	+	30.7859i	−0.903776	+	0.521796i	−0.878424	−	0.477883i	$-0.841404\pi$
$59$	−53.3228	+	30.7859i	−0.903776	+	0.521796i	−0.0253530	+	0.999679i	$0.508071\pi$
$60$		0			0
$61$	12.6725	−	21.9495i	0.207747	−	0.359828i	−0.743258	−	0.669005i	$-0.766720\pi$
$61$	12.6725	−	21.9495i	0.207747	−	0.359828i	0.951004	+	0.309177i	$0.100054\pi$
$62$		0			0
$63$	−4.20566	+	89.2255i	−0.0667564	+	1.41628i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	17.9426	+	31.0774i	0.267799	+	0.463842i	0.968293	−	0.249816i	$-0.0803703\pi$
$67$	17.9426	+	31.0774i	0.267799	+	0.463842i	−0.700494	+	0.713658i	$0.747037\pi$
$68$		0			0
$69$	5.82040	−	5.55252i	0.0843537	−	0.0804713i
$70$		0			0
$71$		−	16.7821i		−	0.236368i	−0.992992	−	0.118184i	$-0.962293\pi$
$71$		−	16.7821i		−	0.236368i	0.992992	−	0.118184i	$-0.0377073\pi$
$72$		0			0
$73$	62.4649			0.855684			0.427842	−	0.903854i	$-0.359274\pi$
$73$	62.4649			0.855684			0.427842	+	0.903854i	$0.359274\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−35.6382	+	20.5757i	−0.462833	+	0.267217i
$78$		0			0
$79$	71.9430	−	124.609i	0.910671	−	1.57733i	0.0975527	−	0.995230i	$-0.468899\pi$
$79$	71.9430	−	124.609i	0.910671	−	1.57733i	0.813118	−	0.582098i	$-0.197768\pi$
$80$		0			0
$81$	46.9187	−	66.0276i	0.579243	−	0.815155i
$82$		0			0
$83$	−14.2118	−	8.20517i	−0.171226	−	0.0988575i	0.411938	−	0.911212i	$-0.364852\pi$
$83$	−14.2118	−	8.20517i	−0.171226	−	0.0988575i	−0.583164	+	0.812355i	$0.698185\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−1.06935	−	0.313699i	−0.0122914	−	0.00360574i
$88$		0			0
$89$		−	155.682i		−	1.74924i	−0.484809	−	0.874620i	$-0.661111\pi$
$89$		−	155.682i		−	1.74924i	0.484809	−	0.874620i	$-0.338889\pi$
$90$		0			0
$91$	12.1729			0.133768
$92$		0			0
$93$	91.8823	+	96.3152i	0.987981	+	1.03565i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−52.3390	+	90.6538i	−0.539577	+	0.934576i	0.459349	+	0.888256i	$0.348083\pi$
$97$	−52.3390	+	90.6538i	−0.539577	+	0.934576i	−0.998927	+	0.0463198i	$0.985251\pi$
$98$		0			0
$99$	37.2749	+	1.75696i	0.376514	+	0.0177470i
$100$		0			0
$101$	89.5942	+	51.7272i	0.887071	+	0.512151i	0.872983	−	0.487750i	$-0.162182\pi$
$101$	89.5942	+	51.7272i	0.887071	+	0.512151i	0.0140876	+	0.999901i	$0.495516\pi$
$102$		0			0
$103$	58.1660	+	100.747i	0.564719	+	0.978122i	0.997076	+	0.0764192i	$0.0243487\pi$
$103$	58.1660	+	100.747i	0.564719	+	0.978122i	−0.432357	+	0.901703i	$0.642318\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	191.681i		−	1.79141i	−0.444651	−	0.895704i	$-0.646672\pi$
$107$		−	191.681i		−	1.79141i	0.444651	−	0.895704i	$-0.353328\pi$
$108$		0			0
$109$	140.403			1.28810			0.644050	−	0.764983i	$-0.277253\pi$
$109$	140.403			1.28810			0.644050	+	0.764983i	$0.277253\pi$
$110$		0			0
$111$	−96.3855	+	23.4084i	−0.868338	+	0.210886i
$112$		0			0
$113$	−102.898	+	59.4080i	−0.910599	+	0.525735i	−0.880624	−	0.473816i	$-0.842876\pi$
$113$	−102.898	+	59.4080i	−0.910599	+	0.525735i	−0.0299752	+	0.999551i	$0.509543\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−9.28910	−	5.96319i	−0.0793940	−	0.0509674i
$118$		0			0
$119$	−180.713	−	104.335i	−1.51859	−	0.876761i
$120$		0			0
$121$	−51.9043	−	89.9009i	−0.428961	−	0.742982i
$122$		0			0
$123$	−85.8458	+	81.8948i	−0.697933	+	0.665811i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	135.134			1.06405			0.532025	−	0.846729i	$-0.321431\pi$
$127$	135.134			1.06405			0.532025	+	0.846729i	$0.321431\pi$
$128$		0			0
$129$	−24.6395	+	83.9922i	−0.191004	+	0.651102i
$130$		0			0
$131$	−125.310	+	72.3475i	−0.956561	+	0.552271i	−0.895113	−	0.445839i	$-0.852905\pi$
$131$	−125.310	+	72.3475i	−0.956561	+	0.552271i	−0.0614484	+	0.998110i	$0.519572\pi$
$132$		0			0
$133$	48.8320	−	84.5796i	0.367158	−	0.635937i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	102.935	+	59.4296i	0.751351	+	0.433793i	0.826182	−	0.563404i	$-0.190508\pi$
$137$	102.935	+	59.4296i	0.751351	+	0.433793i	−0.0748310	+	0.997196i	$0.523842\pi$
$138$		0			0
$139$	−69.8533	−	120.989i	−0.502542	−	0.870428i	−0.999996	−	0.00293743i	$-0.999065\pi$
$139$	−69.8533	−	120.989i	−0.502542	−	0.870428i	0.497454	−	0.867490i	$-0.334268\pi$
$140$		0			0
$141$	228.032	+	66.8943i	1.61725	+	0.474428i
$142$		0			0
$143$		−	5.08535i		−	0.0355619i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−102.513	−	107.459i	−0.697370	−	0.731015i
$148$		0			0
$149$	−207.246	+	119.654i	−1.39091	+	0.803045i	−0.993417	−	0.114558i	$-0.963455\pi$
$149$	−207.246	+	119.654i	−1.39091	+	0.803045i	−0.397498	+	0.917603i	$0.630121\pi$
$150$		0			0
$151$	−26.5794	+	46.0369i	−0.176022	+	0.304880i	−0.940515	−	0.339753i	$-0.889656\pi$
$151$	−26.5794	+	46.0369i	−0.176022	+	0.304880i	0.764492	+	0.644633i	$0.222990\pi$
$152$		0			0
$153$	86.7906	+	168.144i	0.567259	+	1.09898i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	43.4721	+	75.2959i	0.276892	+	0.479591i	0.970611	−	0.240655i	$-0.0773622\pi$
$157$	43.4721	+	75.2959i	0.276892	+	0.479591i	−0.693719	+	0.720246i	$0.744029\pi$
$158$		0			0
$159$	65.7362	+	270.673i	0.413436	+	1.70235i
$160$		0			0
$161$			26.6124i			0.165295i
$162$		0			0
$163$	45.5616			0.279519			0.139760	−	0.990185i	$-0.455367\pi$
$163$	45.5616			0.279519			0.139760	+	0.990185i	$0.455367\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	70.8458	−	40.9028i	0.424226	−	0.244927i	−0.272658	−	0.962111i	$-0.587903\pi$
$167$	70.8458	−	40.9028i	0.424226	−	0.244927i	0.696884	+	0.717184i	$0.254569\pi$
$168$		0			0
$169$	83.7479	−	145.056i	0.495549	−	0.858317i
$170$		0			0
$171$	−78.6970	+	40.6209i	−0.460216	+	0.237549i
$172$		0			0
$173$	−185.787	−	107.264i	−1.07391	−	0.620025i	−0.144666	−	0.989481i	$-0.546211\pi$
$173$	−185.787	−	107.264i	−1.07391	−	0.620025i	−0.929248	+	0.369456i	$0.879544\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−133.653	+	127.502i	−0.755103	+	0.720349i
$178$		0			0
$179$			14.6923i			0.0820800i	0.999158	+	0.0410400i	$0.0130671\pi$
$179$			14.6923i			0.0820800i	−0.999158	+	0.0410400i	$0.986933\pi$
$180$		0			0
$181$	93.0954			0.514339			0.257170	−	0.966366i	$-0.417210\pi$
$181$	93.0954			0.514339			0.257170	+	0.966366i	$0.417210\pi$
$182$		0			0
$183$	21.4034	−	72.9607i	0.116958	−	0.398692i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−43.5869	+	75.4947i	−0.233085	+	0.403715i
$188$		0			0
$189$	50.9116	+	263.093i	0.269373	+	1.39203i
$190$		0			0
$191$	−179.363	−	103.555i	−0.939072	−	0.542173i	−0.0494024	−	0.998779i	$-0.515732\pi$
$191$	−179.363	−	103.555i	−0.939072	−	0.542173i	−0.889669	+	0.456606i	$0.849065\pi$
$192$		0			0
$193$	−130.282	−	225.655i	−0.675037	−	1.16920i	−0.976458	−	0.215708i	$-0.930794\pi$
$193$	−130.282	−	225.655i	−0.675037	−	1.16920i	0.301421	−	0.953491i	$-0.402539\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			156.721i			0.795537i	0.917486	+	0.397768i	$0.130215\pi$
$197$			156.721i			0.795537i	−0.917486	+	0.397768i	$0.869785\pi$
$198$		0			0
$199$	144.623			0.726748			0.363374	−	0.931643i	$-0.381625\pi$
$199$	144.623			0.726748			0.363374	+	0.931643i	$0.381625\pi$
$200$		0			0
$201$	74.3101	+	77.8953i	0.369702	+	0.387539i
$202$		0			0
$203$	3.19289	−	1.84342i	0.0157285	−	0.00908087i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	13.0368	−	20.3079i	0.0629795	−	0.0981058i
$208$		0			0
$209$	−35.3340	−	20.4001i	−0.169062	−	0.0976082i
$210$		0			0
$211$	11.9568	+	20.7098i	0.0566673	+	0.0981506i	0.892967	−	0.450121i	$-0.148619\pi$
$211$	11.9568	+	20.7098i	0.0566673	+	0.0981506i	−0.836300	+	0.548272i	$0.815286\pi$
$212$		0			0
$213$	−11.8818	−	48.9243i	−0.0557833	−	0.229691i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−440.379			−2.02940
$218$		0			0
$219$	182.101	−	44.2255i	0.831513	−	0.201943i
$220$		0			0
$221$	22.3319	−	12.8933i	0.101049	−	0.0583408i
$222$		0			0
$223$	219.308	−	379.853i	0.983446	−	1.70338i	0.334796	−	0.942291i	$-0.391333\pi$
$223$	219.308	−	379.853i	0.983446	−	1.70338i	0.648650	−	0.761087i	$-0.275334\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	371.191	+	214.307i	1.63520	+	0.944085i	0.982453	+	0.186512i	$0.0597183\pi$
$227$	371.191	+	214.307i	1.63520	+	0.944085i	0.652750	+	0.757573i	$0.273615\pi$
$228$		0			0
$229$	29.1308	+	50.4560i	0.127209	+	0.220332i	0.922594	−	0.385772i	$-0.126065\pi$
$229$	29.1308	+	50.4560i	0.127209	+	0.220332i	−0.795386	+	0.606104i	$0.792732\pi$
$230$		0			0
$231$	−89.3267	+	85.2155i	−0.386696	+	0.368898i
$232$		0			0
$233$		−	283.668i		−	1.21746i	−0.793378	−	0.608730i	$-0.791679\pi$
$233$		−	283.668i		−	1.21746i	0.793378	−	0.608730i	$-0.208321\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	121.509	−	414.203i	0.512695	−	1.74769i
$238$		0			0
$239$	−218.485	+	126.142i	−0.914161	+	0.527791i	−0.881768	−	0.471684i	$-0.843646\pi$
$239$	−218.485	+	126.142i	−0.914161	+	0.527791i	−0.0323937	+	0.999475i	$0.510313\pi$
$240$		0			0
$241$	119.975	−	207.803i	0.497822	−	0.862253i	−0.502175	−	0.864766i	$-0.667467\pi$
$241$	119.975	−	207.803i	0.497822	−	0.862253i	0.999997	+	0.00251337i	$0.000800031\pi$
$242$		0			0
$243$	90.0321	−	225.706i	0.370503	−	0.928831i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	6.03450	+	10.4521i	0.0244312	+	0.0423160i
$248$		0			0
$249$	−47.2403	−	13.8582i	−0.189720	−	0.0556553i
$250$		0			0
$251$		−	21.5862i		−	0.0860008i	−0.999075	−	0.0430004i	$-0.986308\pi$
$251$		−	21.5862i		−	0.0860008i	0.999075	−	0.0430004i	$-0.0136917\pi$
$252$		0			0
$253$	11.1176			0.0439432
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−47.6487	+	27.5100i	−0.185403	+	0.107043i	−0.589829	−	0.807528i	$-0.700805\pi$
$257$	−47.6487	+	27.5100i	−0.185403	+	0.107043i	0.404426	+	0.914571i	$0.367471\pi$
$258$		0			0
$259$	164.072	−	284.180i	0.633481	−	1.09722i
$260$		0			0
$261$	−3.33953	−	0.157409i	−0.0127951	−	0.000603101i
$262$		0			0
$263$	−149.330	−	86.2155i	−0.567793	−	0.327815i	0.188474	−	0.982078i	$-0.439646\pi$
$263$	−149.330	−	86.2155i	−0.567793	−	0.327815i	−0.756267	+	0.654263i	$0.772979\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−110.224	−	453.854i	−0.412824	−	1.69983i
$268$		0			0
$269$			220.556i			0.819910i	0.912106	+	0.409955i	$0.134456\pi$
$269$			220.556i			0.819910i	−0.912106	+	0.409955i	$0.865544\pi$
$270$		0			0
$271$	176.241			0.650337			0.325168	−	0.945656i	$-0.394579\pi$
$271$	176.241			0.650337			0.325168	+	0.945656i	$0.394579\pi$
$272$		0			0
$273$	35.4871	−	8.61846i	0.129989	−	0.0315695i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−190.788	+	330.454i	−0.688764	+	1.19297i	0.283474	+	0.958980i	$0.408513\pi$
$277$	−190.788	+	330.454i	−0.688764	+	1.19297i	−0.972238	+	0.233994i	$0.924820\pi$
$278$		0			0
$279$	336.052	+	215.730i	1.20449	+	0.773227i
$280$		0			0
$281$	−435.222	−	251.276i	−1.54883	−	0.894219i	−0.998231	−	0.0594516i	$-0.981065\pi$
$281$	−435.222	−	251.276i	−1.54883	−	0.894219i	−0.550602	−	0.834768i	$-0.685602\pi$
$282$		0			0
$283$	−171.577	−	297.181i	−0.606280	−	1.05011i	−0.991848	−	0.127428i	$-0.959328\pi$
$283$	−171.577	−	297.181i	−0.606280	−	1.05011i	0.385568	−	0.922680i	$-0.374006\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		−	392.510i		−	1.36763i
$288$		0			0
$289$	−153.037			−0.529541
$290$		0			0
$291$	−88.3983	+	301.336i	−0.303774	+	1.03552i
$292$		0			0
$293$	−415.522	+	239.902i	−1.41816	+	0.818777i	−0.996138	−	0.0878060i	$-0.972014\pi$
$293$	−415.522	+	239.902i	−1.41816	+	0.818777i	−0.422027	+	0.906583i	$0.638681\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	109.910	−	21.2688i	0.370067	−	0.0716123i
$298$		0			0
$299$	−2.84808	−	1.64434i	−0.00952534	−	0.00549946i
$300$		0			0
$301$	−144.791	−	250.786i	−0.481034	−	0.833176i
$302$		0			0
$303$	297.813	+	87.3650i	0.982882	+	0.288333i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−170.593			−0.555679			−0.277840	−	0.960627i	$-0.589618\pi$
$307$	−170.593			−0.555679			−0.277840	+	0.960627i	$0.589618\pi$
$308$		0			0
$309$	240.898	+	252.520i	0.779605	+	0.817218i
$310$		0			0
$311$	360.862	−	208.344i	1.16033	−	0.669916i	0.208946	−	0.977927i	$-0.432997\pi$
$311$	360.862	−	208.344i	1.16033	−	0.669916i	0.951383	+	0.308011i	$0.0996634\pi$
$312$		0			0
$313$	39.5306	−	68.4691i	0.126296	−	0.218751i	−0.795943	−	0.605372i	$-0.793024\pi$
$313$	39.5306	−	68.4691i	0.126296	−	0.218751i	0.922239	+	0.386621i	$0.126358\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	182.089	+	105.129i	0.574413	+	0.331637i	0.758910	−	0.651196i	$-0.225732\pi$
$317$	182.089	+	105.129i	0.574413	+	0.331637i	−0.184497	+	0.982833i	$0.559066\pi$
$318$		0			0
$319$	−0.770107	−	1.33387i	−0.00241413	−	0.00418140i
$320$		0			0
$321$	−135.711	−	558.798i	−0.422775	−	1.74081i
$322$		0			0
$323$		−	206.888i		−	0.640521i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	409.311	−	99.4060i	1.25171	−	0.303994i
$328$		0			0
$329$	−680.863	+	393.097i	−2.06949	+	1.19482i
$330$		0			0
$331$	285.288	−	494.133i	0.861896	−	1.49285i	−0.00820039	−	0.999966i	$-0.502610\pi$
$331$	285.288	−	494.133i	0.861896	−	1.49285i	0.870096	−	0.492881i	$-0.164056\pi$
$332$		0			0
$333$	−264.415	+	136.483i	−0.794040	+	0.409858i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−66.3441	−	114.911i	−0.196867	−	0.340983i	0.750644	−	0.660707i	$-0.229743\pi$
$337$	−66.3441	−	114.911i	−0.196867	−	0.340983i	−0.947511	+	0.319723i	$0.896410\pi$
$338$		0			0
$339$	−257.912	+	246.042i	−0.760803	+	0.725787i
$340$		0			0
$341$			183.973i			0.539510i
$342$		0			0
$343$	5.00939			0.0146046
$344$		0			0
$345$		0			0
$346$		0			0
$347$	160.519	−	92.6758i	0.462591	−	0.267077i	−0.250542	−	0.968106i	$-0.580609\pi$
$347$	160.519	−	92.6758i	0.462591	−	0.267077i	0.713133	+	0.701029i	$0.247275\pi$
$348$		0			0
$349$	−36.8894	+	63.8943i	−0.105700	+	0.183078i	−0.914024	−	0.405660i	$-0.867042\pi$
$349$	−36.8894	+	63.8943i	−0.105700	+	0.183078i	0.808324	+	0.588738i	$0.200375\pi$
$350$		0			0
$351$	−31.3021	−	10.8075i	−0.0891798	−	0.0307906i
$352$		0			0
$353$	123.744	+	71.4437i	0.350550	+	0.202390i	0.664928	−	0.746908i	$-0.268462\pi$
$353$	123.744	+	71.4437i	0.350550	+	0.202390i	−0.314377	+	0.949298i	$0.601796\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−600.694	−	176.217i	−1.68262	−	0.493604i
$358$		0			0
$359$		−	275.684i		−	0.767923i	−0.923349	−	0.383961i	$-0.874560\pi$
$359$		−	275.684i		−	0.767923i	0.923349	−	0.383961i	$-0.125440\pi$
$360$		0			0
$361$	−264.169			−0.731771
$362$		0			0
$363$	−214.965	−	225.336i	−0.592189	−	0.620759i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	250.968	−	434.689i	0.683836	−	1.18444i	−0.289965	−	0.957037i	$-0.593644\pi$
$367$	250.968	−	434.689i	0.683836	−	1.18444i	0.973801	−	0.227401i	$-0.0730229\pi$
$368$		0			0
$369$	−192.281	+	299.524i	−0.521086	+	0.811717i
$370$		0			0
$371$	−798.046	−	460.752i	−2.15107	−	1.24192i
$372$		0			0
$373$	3.48399	+	6.03444i	0.00934045	+	0.0161781i	0.870658	−	0.491889i	$-0.163693\pi$
$373$	3.48399	+	6.03444i	0.00934045	+	0.0161781i	−0.861317	+	0.508067i	$0.830360\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			0.455607i			0.00120851i
$378$		0			0
$379$	682.804			1.80159			0.900797	−	0.434240i	$-0.142983\pi$
$379$	682.804			1.80159			0.900797	+	0.434240i	$0.142983\pi$
$380$		0			0
$381$	393.951	−	95.6757i	1.03399	−	0.251117i
$382$		0			0
$383$	−160.047	+	92.4032i	−0.417877	+	0.241262i	−0.694169	−	0.719812i	$-0.744228\pi$
$383$	−160.047	+	92.4032i	−0.417877	+	0.241262i	0.276291	+	0.961074i	$0.410895\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−12.3637	+	262.304i	−0.0319476	+	0.677787i
$388$		0			0
$389$	−18.7375	−	10.8181i	−0.0481683	−	0.0278100i	0.475722	−	0.879595i	$-0.342187\pi$
$389$	−18.7375	−	10.8181i	−0.0481683	−	0.0278100i	−0.523891	+	0.851785i	$0.675520\pi$
$390$		0			0
$391$	28.1875	+	48.8221i	0.0720907	+	0.124865i
$392$		0			0
$393$	−314.087	+	299.631i	−0.799204	+	0.762421i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	113.001			0.284637			0.142318	−	0.989821i	$-0.454544\pi$
$397$	113.001			0.284637			0.142318	+	0.989821i	$0.454544\pi$
$398$		0			0
$399$	82.4752	−	281.145i	0.206705	−	0.704623i
$400$		0			0
$401$	407.847	−	235.471i	1.01708	−	0.587209i	0.103820	−	0.994596i	$-0.466893\pi$
$401$	407.847	−	235.471i	1.01708	−	0.587209i	0.913256	+	0.407387i	$0.133560\pi$
$402$		0			0
$403$	27.2103	−	47.1296i	0.0675193	−	0.116947i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−118.719	−	68.5426i	−0.291694	−	0.168409i
$408$		0			0
$409$	−160.550	−	278.081i	−0.392543	−	0.679904i	0.600241	−	0.799819i	$-0.295071\pi$
$409$	−160.550	−	278.081i	−0.392543	−	0.679904i	−0.992784	+	0.119915i	$0.961738\pi$
$410$		0			0
$411$	342.159	+	100.374i	0.832503	+	0.244219i
$412$		0			0
$413$		−	611.098i		−	1.47966i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−289.302	−	303.259i	−0.693769	−	0.727240i
$418$		0			0
$419$	608.628	−	351.391i	1.45257	−	0.838643i	0.453945	−	0.891030i	$-0.350016\pi$
$419$	608.628	−	351.391i	1.45257	−	0.838643i	0.998627	+	0.0523870i	$0.0166829\pi$
$420$		0			0
$421$	−100.762	+	174.525i	−0.239340	+	0.414549i	−0.960525	−	0.278193i	$-0.910264\pi$
$421$	−100.762	+	174.525i	−0.239340	+	0.414549i	0.721185	+	0.692742i	$0.243598\pi$
$422$		0			0
$423$	712.133	+	33.5665i	1.68353	+	0.0793534i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	125.774	+	217.848i	0.294554	+	0.510182i
$428$		0			0
$429$	−3.60046	−	14.8251i	−0.00839267	−	0.0345574i
$430$		0			0
$431$			499.638i			1.15925i	0.814883	+	0.579626i	$0.196801\pi$
$431$			499.638i			1.15925i	−0.814883	+	0.579626i	$0.803199\pi$
$432$		0			0
$433$	552.323			1.27557			0.637786	−	0.770213i	$-0.279850\pi$
$433$	552.323			1.27557			0.637786	+	0.770213i	$0.279850\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−22.8504	+	13.1927i	−0.0522892	+	0.0301892i
$438$		0			0
$439$	295.077	−	511.088i	0.672157	−	1.16421i	−0.305134	−	0.952309i	$-0.598701\pi$
$439$	295.077	−	511.088i	0.672157	−	1.16421i	0.977291	−	0.211901i	$-0.0679653\pi$
$440$		0			0
$441$	−374.935	−	240.691i	−0.850192	−	0.545785i
$442$		0			0
$443$	147.755	+	85.3062i	0.333532	+	0.192565i	0.657408	−	0.753535i	$-0.271653\pi$
$443$	147.755	+	85.3062i	0.333532	+	0.192565i	−0.323876	+	0.946100i	$0.604986\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−519.461	+	495.553i	−1.16211	+	1.10862i
$448$		0			0
$449$		−	285.994i		−	0.636957i	−0.947930	−	0.318478i	$-0.896828\pi$
$449$		−	285.994i		−	0.636957i	0.947930	−	0.318478i	$-0.103172\pi$
$450$		0			0
$451$	−163.975			−0.363582
$452$		0			0
$453$	−44.8915	+	153.028i	−0.0990981	+	0.337809i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−118.487	+	205.226i	−0.259272	+	0.449073i	−0.966047	−	0.258366i	$-0.916816\pi$
$457$	−118.487	+	205.226i	−0.259272	+	0.449073i	0.706775	+	0.707438i	$0.250149\pi$
$458$		0			0
$459$	372.064	+	428.735i	0.810597	+	0.934063i
$460$		0			0
$461$	562.490	+	324.754i	1.22015	+	0.704455i	0.964950	−	0.262432i	$-0.0845247\pi$
$461$	562.490	+	324.754i	1.22015	+	0.704455i	0.255202	+	0.966888i	$0.417858\pi$
$462$		0			0
$463$	−138.962	−	240.689i	−0.300133	−	0.519846i	0.676033	−	0.736872i	$-0.263698\pi$
$463$	−138.962	−	240.689i	−0.300133	−	0.519846i	−0.976166	+	0.217026i	$0.930364\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		−	593.440i		−	1.27075i	−0.772204	−	0.635375i	$-0.780846\pi$
$467$		−	593.440i		−	1.27075i	0.772204	−	0.635375i	$-0.219154\pi$
$468$		0			0
$469$	−356.158			−0.759399
$470$		0			0
$471$	180.042	+	188.728i	0.382255	+	0.400697i
$472$		0			0
$473$	−104.768	+	60.4881i	−0.221498	+	0.127882i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	383.276	+	742.541i	0.803514	+	1.55669i
$478$		0			0
$479$	−490.726	−	283.321i	−1.02448	−	0.591484i	−0.109082	−	0.994033i	$-0.534791\pi$
$479$	−490.726	−	283.321i	−1.02448	−	0.591484i	−0.915399	+	0.402549i	$0.868124\pi$
$480$		0			0
$481$	20.2754	+	35.1181i	0.0421526	+	0.0730105i
$482$		0			0
$483$	18.8417	+	77.5821i	0.0390098	+	0.160626i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	651.371			1.33752			0.668759	−	0.743479i	$-0.266826\pi$
$487$	651.371			1.33752			0.668759	+	0.743479i	$0.266826\pi$
$488$		0			0
$489$	132.824	−	32.2578i	0.271623	−	0.0659670i
$490$		0			0
$491$	−138.817	+	80.1462i	−0.282724	+	0.163231i	−0.634656	−	0.772795i	$-0.718858\pi$
$491$	−138.817	+	80.1462i	−0.282724	+	0.163231i	0.351932	+	0.936025i	$0.385525\pi$
$492$		0			0
$493$	3.90503	−	6.76372i	0.00792096	−	0.0137195i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	144.247	+	83.2810i	0.290235	+	0.167567i
$498$		0			0
$499$	278.706	+	482.733i	0.558530	+	0.967402i	0.997620	+	0.0689585i	$0.0219676\pi$
$499$	278.706	+	482.733i	0.558530	+	0.967402i	−0.439090	+	0.898443i	$0.644699\pi$
$500$		0			0
$501$	177.574	−	169.402i	0.354440	−	0.338127i
$502$		0			0
$503$			288.388i			0.573337i	0.958030	+	0.286668i	$0.0925478\pi$
$503$			288.388i			0.573337i	−0.958030	+	0.286668i	$0.907452\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	141.447	−	482.168i	0.278987	−	0.951022i
$508$		0			0
$509$	−575.821	+	332.451i	−1.13128	+	0.653145i	−0.944256	−	0.329211i	$-0.893217\pi$
$509$	−575.821	+	332.451i	−1.13128	+	0.653145i	−0.187023	+	0.982356i	$0.559884\pi$
$510$		0			0
$511$	−309.981	+	536.902i	−0.606616	+	1.05069i
$512$		0			0
$513$	−200.662	+	174.138i	−0.391155	+	0.339451i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	164.220	+	284.438i	0.317641	+	0.550170i
$518$		0			0
$519$	−617.561	−	181.165i	−1.18991	−	0.349065i
$520$		0			0
$521$			865.738i			1.66168i	0.556508	+	0.830842i	$0.312141\pi$
$521$			865.738i			1.66168i	−0.556508	+	0.830842i	$0.687859\pi$
$522$		0			0
$523$	−515.707			−0.986056			−0.493028	−	0.870013i	$-0.664110\pi$
$523$	−515.707			−0.986056			−0.493028	+	0.870013i	$0.664110\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−807.901	+	466.442i	−1.53302	+	0.885089i
$528$		0			0
$529$	−260.905	+	451.901i	−0.493204	+	0.854255i
$530$		0			0
$531$	−299.361	+	466.328i	−0.563769	+	0.878207i
$532$		0			0
$533$	42.0066	+	24.2525i	0.0788117	+	0.0455020i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	10.4022	+	42.8319i	0.0193710	+	0.0797615i
$538$		0			0
$539$		−	205.259i		−	0.380815i
$540$		0			0
$541$	117.923			0.217973			0.108987	−	0.994043i	$-0.465239\pi$
$541$	117.923			0.217973			0.108987	+	0.994043i	$0.465239\pi$
$542$		0			0
$543$	271.397	−	65.9120i	0.499811	−	0.121385i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−232.333	+	402.413i	−0.424741	+	0.735673i	−0.996396	−	0.0848212i	$-0.972968\pi$
$547$	−232.333	+	402.413i	−0.424741	+	0.735673i	0.571655	+	0.820494i	$0.306301\pi$
$548$		0			0
$549$	10.7399	−	227.853i	0.0195626	−	0.415032i
$550$		0			0
$551$	3.16564	+	1.82769i	0.00574527	+	0.00331703i
$552$		0			0
$553$	714.031	+	1236.74i	1.29120	+	2.23642i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	7.93254i		−	0.0142415i	−0.999975	−	0.00712077i	$-0.997733\pi$
$557$		−	7.93254i		−	0.0142415i	0.999975	−	0.00712077i	$-0.00226663\pi$
$558$		0			0
$559$	35.7856			0.0640173
$560$		0			0
$561$	−73.6163	+	250.946i	−0.131223	+	0.447319i
$562$		0			0
$563$	−364.857	+	210.651i	−0.648059	+	0.374157i	−0.787712	−	0.616043i	$-0.788735\pi$
$563$	−364.857	+	210.651i	−0.648059	+	0.374157i	0.139653	+	0.990201i	$0.455401\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	334.692	+	730.938i	0.590285	+	1.28913i
$568$		0			0
$569$	945.149	+	545.682i	1.66107	+	0.959019i	0.972206	+	0.234128i	$0.0752236\pi$
$569$	945.149	+	545.682i	1.66107	+	0.959019i	0.688864	+	0.724891i	$0.258110\pi$
$570$		0			0
$571$	65.5170	+	113.479i	0.114741	+	0.198737i	0.917676	−	0.397329i	$-0.130063\pi$
$571$	65.5170	+	113.479i	0.114741	+	0.198737i	−0.802935	+	0.596066i	$0.796730\pi$
$572$		0			0
$573$	−596.206	−	174.900i	−1.04050	−	0.305236i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−71.2517			−0.123487			−0.0617433	−	0.998092i	$-0.519666\pi$
$577$	−71.2517			−0.123487			−0.0617433	+	0.998092i	$0.519666\pi$
$578$		0			0
$579$	−539.571	−	565.603i	−0.931902	−	0.976862i
$580$		0			0
$581$	141.051	−	81.4359i	0.242773	−	0.140165i
$582$		0			0
$583$	−192.484	+	333.392i	−0.330161	+	0.571856i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	632.488	+	365.167i	1.07749	+	0.622090i	0.930219	−	0.367006i	$-0.119617\pi$
$587$	632.488	+	365.167i	1.07749	+	0.622090i	0.147273	+	0.989096i	$0.452950\pi$
$588$		0			0
$589$	−218.310	−	378.124i	−0.370646	−	0.641977i
$590$		0			0
$591$	110.959	+	456.881i	0.187748	+	0.773065i
$592$		0			0
$593$			0.291939i			0.000492309i	1.00000		0.000246154i	$7.83534e-5\pi$
$593$			0.291939i			0.000492309i	−1.00000		0.000246154i	$0.999922\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	421.613	−	102.394i	0.706219	−	0.171514i
$598$		0			0
$599$	109.992	−	63.5040i	0.183626	−	0.106017i	−0.405369	−	0.914153i	$-0.632857\pi$
$599$	109.992	−	63.5040i	0.183626	−	0.106017i	0.588995	+	0.808136i	$0.299524\pi$
$600$		0			0
$601$	−276.284	+	478.537i	−0.459707	+	0.796235i	−0.998945	−	0.0459177i	$-0.985379\pi$
$601$	−276.284	+	478.537i	−0.459707	+	0.796235i	0.539239	+	0.842153i	$0.318712\pi$
$602$		0			0
$603$	271.783	+	174.473i	0.450719	+	0.289341i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−261.788	−	453.430i	−0.431282	−	0.747002i	0.565702	−	0.824610i	$-0.308605\pi$
$607$	−261.788	−	453.430i	−0.431282	−	0.747002i	−0.996984	+	0.0776075i	$0.975272\pi$
$608$		0			0
$609$	8.00296	−	7.63462i	0.0131411	−	0.0125363i
$610$		0			0
$611$		−	97.1551i		−	0.159010i
$612$		0			0
$613$	−345.873			−0.564230			−0.282115	−	0.959381i	$-0.591036\pi$
$613$	−345.873			−0.564230			−0.282115	+	0.959381i	$0.591036\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−708.728	+	409.184i	−1.14867	+	0.663183i	−0.948562	−	0.316591i	$-0.897462\pi$
$617$	−708.728	+	409.184i	−1.14867	+	0.663183i	−0.200105	+	0.979774i	$0.564128\pi$
$618$		0			0
$619$	−485.889	+	841.584i	−0.784958	+	1.35959i	0.144067	+	0.989568i	$0.453982\pi$
$619$	−485.889	+	841.584i	−0.784958	+	1.35959i	−0.929024	+	0.370019i	$0.879351\pi$
$620$		0			0
$621$	23.6274	−	68.4329i	0.0380474	−	0.110198i
$622$		0			0
$623$	1338.13	+	772.570i	2.14788	+	1.24008i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−117.451	−	34.4549i	−0.187322	−	0.0549520i
$628$		0			0
$629$		−	695.127i		−	1.10513i
$630$		0			0
$631$	965.757			1.53052			0.765259	−	0.643722i	$-0.222611\pi$
$631$	965.757			1.53052			0.765259	+	0.643722i	$0.222611\pi$
$632$		0			0
$633$	49.5198	+	51.9089i	0.0782303	+	0.0820045i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−30.3586	+	52.5826i	−0.0476587	+	0.0825473i
$638$		0			0
$639$	−69.2773	−	134.214i	−0.108415	−	0.210038i
$640$		0			0
$641$	16.5863	+	9.57610i	0.0258757	+	0.0149393i	0.512882	−	0.858459i	$-0.328578\pi$
$641$	16.5863	+	9.57610i	0.0258757	+	0.0149393i	−0.487006	+	0.873398i	$0.661911\pi$
$642$		0			0
$643$	−82.4679	−	142.839i	−0.128255	−	0.222144i	0.794746	−	0.606943i	$-0.207604\pi$
$643$	−82.4679	−	142.839i	−0.128255	−	0.222144i	−0.923001	+	0.384799i	$0.874271\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		−	630.208i		−	0.974047i	−0.873389	−	0.487023i	$-0.838083\pi$
$647$		−	630.208i		−	0.974047i	0.873389	−	0.487023i	$-0.161917\pi$
$648$		0			0
$649$	−255.293			−0.393363
$650$		0			0
$651$	−1283.82	+	311.790i	−1.97207	+	0.478941i
$652$		0			0
$653$	469.978	−	271.342i	0.719722	−	0.415531i	−0.0949286	−	0.995484i	$-0.530262\pi$
$653$	469.978	−	271.342i	0.719722	−	0.415531i	0.814650	+	0.579953i	$0.196929\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	499.560	−	257.857i	0.760366	−	0.392477i
$658$		0			0
$659$	659.562	+	380.799i	1.00085	+	0.577843i	0.908501	−	0.417883i	$-0.137228\pi$
$659$	659.562	+	380.799i	1.00085	+	0.577843i	0.0923527	+	0.995726i	$0.470561\pi$
$660$		0			0
$661$	284.021	+	491.939i	0.429684	+	0.744234i	0.996845	−	0.0793725i	$-0.0252916\pi$
$661$	284.021	+	491.939i	0.429684	+	0.744234i	−0.567161	+	0.823607i	$0.691958\pi$
$662$		0			0
$663$	55.9746	−	53.3984i	0.0844263	−	0.0805406i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−0.996051			−0.00149333
$668$		0			0
$669$	370.402	−	1262.64i	0.553666	−	1.88736i
$670$		0			0
$671$	91.0082	−	52.5436i	0.135631	−	0.0783064i
$672$		0			0
$673$	−335.606	+	581.286i	−0.498671	+	0.863724i	−0.999999	−	0.00153386i	$-0.999512\pi$
$673$	−335.606	+	581.286i	−0.498671	+	0.863724i	0.501328	+	0.865257i	$0.332845\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	1059.58	+	611.750i	1.56511	+	0.903619i	0.996726	+	0.0808588i	$0.0257663\pi$
$677$	1059.58	+	611.750i	1.56511	+	0.903619i	0.568389	+	0.822760i	$0.307567\pi$
$678$		0			0
$679$	−519.462	−	899.735i	−0.765040	−	1.32509i
$680$		0			0
$681$	1233.85	+	361.956i	1.81182	+	0.531506i
$682$		0			0
$683$			1094.61i			1.60265i	0.598229	+	0.801325i	$0.295871\pi$
$683$			1094.61i			1.60265i	−0.598229	+	0.801325i	$0.704129\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	120.647	+	126.467i	0.175614	+	0.184086i
$688$		0			0
$689$	98.6198	−	56.9382i	0.143135	−	0.0826389i
$690$		0			0
$691$	160.830	−	278.566i	0.232750	−	0.403134i	−0.725867	−	0.687835i	$-0.758561\pi$
$691$	160.830	−	278.566i	0.232750	−	0.403134i	0.958616	+	0.284701i	$0.0918944\pi$
$692$		0			0
$693$	−200.077	+	311.669i	−0.288712	+	0.449739i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−415.740	−	720.083i	−0.596471	−	1.03312i
$698$		0			0
$699$	−200.838	−	826.966i	−0.287323	−	1.18307i
$700$		0			0
$701$			162.214i			0.231404i	0.993284	+	0.115702i	$0.0369118\pi$
$701$			162.214i			0.231404i	−0.993284	+	0.115702i	$0.963088\pi$
$702$		0			0
$703$	325.343			0.462792
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−889.218	+	513.390i	−1.25773	+	0.726153i
$708$		0			0
$709$	508.270	−	880.350i	0.716883	−	1.24168i	−0.245346	−	0.969436i	$-0.578901\pi$
$709$	508.270	−	880.350i	0.716883	−	1.24168i	0.962229	−	0.272242i	$-0.0877653\pi$
$710$		0			0
$711$	60.9711	−	1293.54i	0.0857540	−	1.81932i
$712$		0			0
$713$	103.035	+	59.4873i	0.144509	+	0.0834324i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−547.630	+	522.425i	−0.763779	+	0.728626i
$718$		0			0
$719$		−	210.621i		−	0.292937i	−0.989215	−	0.146468i	$-0.953209\pi$
$719$		−	210.621i		−	0.292937i	0.989215	−	0.146468i	$-0.0467906\pi$
$720$		0			0
$721$	−1154.59			−1.60137
$722$		0			0
$723$	202.633	−	690.742i	0.280267	−	0.955383i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	576.113	−	997.857i	0.792453	−	1.37257i	−0.131991	−	0.991251i	$-0.542137\pi$
$727$	576.113	−	997.857i	0.792453	−	1.37257i	0.924444	−	0.381318i	$-0.124530\pi$
$728$		0			0
$729$	102.666	−	721.735i	0.140831	−	0.990034i
$730$		0			0
$731$	−531.256	−	306.721i	−0.726753	−	0.419591i
$732$		0			0
$733$	−20.7081	−	35.8676i	−0.0282512	−	0.0489325i	0.851554	−	0.524267i	$-0.175661\pi$
$733$	−20.7081	−	35.8676i	−0.0282512	−	0.0489325i	−0.879805	+	0.475334i	$0.842327\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$			148.789i			0.201884i
$738$		0			0
$739$	−880.919			−1.19204			−0.596021	−	0.802969i	$-0.703252\pi$
$739$	−880.919			−1.19204			−0.596021	+	0.802969i	$0.703252\pi$
$740$		0			0
$741$	24.9922	+	26.1980i	0.0337277	+	0.0353549i
$742$		0			0
$743$	86.2755	−	49.8112i	0.116118	−	0.0670406i	−0.440816	−	0.897597i	$-0.645311\pi$
$743$	86.2755	−	49.8112i	0.116118	−	0.0670406i	0.556934	+	0.830557i	$0.311978\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−147.529	−	6.95381i	−0.197496	−	0.00930898i
$748$		0			0
$749$	1647.55	+	951.211i	2.19966	+	1.26997i
$750$		0			0
$751$	267.844	+	463.919i	0.356650	+	0.617736i	0.987399	−	0.158251i	$-0.0505856\pi$
$751$	267.844	+	463.919i	0.356650	+	0.617736i	−0.630749	+	0.775987i	$0.717252\pi$
$752$		0			0
$753$	−15.2831	−	62.9293i	−0.0202963	−	0.0835715i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−965.475			−1.27540			−0.637698	−	0.770286i	$-0.720113\pi$
$757$	−965.475			−1.27540			−0.637698	+	0.770286i	$0.720113\pi$
$758$		0			0
$759$	32.4108	−	7.87134i	0.0427019	−	0.0103707i
$760$		0			0
$761$	953.700	−	550.619i	1.25322	−	0.723547i	0.281472	−	0.959569i	$-0.409177\pi$
$761$	953.700	−	550.619i	1.25322	−	0.723547i	0.971748	+	0.236023i	$0.0758440\pi$
$762$		0			0
$763$	−696.746	+	1206.80i	−0.913167	+	1.58165i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	65.4000	+	37.7587i	0.0852673	+	0.0492291i
$768$		0			0
$769$	666.991	+	1155.26i	0.867348	+	1.50229i	0.864697	+	0.502294i	$0.167511\pi$
$769$	666.991	+	1155.26i	0.867348	+	1.50229i	0.00265113	+	0.999996i	$0.499156\pi$
$770$		0			0
$771$	−119.431	+	113.934i	−0.154904	+	0.147774i
$772$		0			0
$773$			310.586i			0.401793i	0.979612	+	0.200897i	$0.0643855\pi$
$773$			310.586i			0.401793i	−0.979612	+	0.200897i	$0.935614\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	277.110	−	944.622i	0.356641	−	1.21573i
$778$		0			0
$779$	337.023	−	194.580i	0.432635	−	0.249782i
$780$		0			0
$781$	34.7915	−	60.2607i	0.0445474	−	0.0771584i
$782$		0			0
$783$	−9.84705	+	1.90552i	−0.0125761	+	0.00243361i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	445.199	+	771.107i	0.565691	+	0.979806i	0.996985	+	0.0775946i	$0.0247240\pi$
$787$	445.199	+	771.107i	0.565691	+	0.979806i	−0.431294	+	0.902212i	$0.641943\pi$
$788$		0			0
$789$	−496.375	−	145.614i	−0.629119	−	0.184555i
$790$		0			0
$791$		−	1179.24i		−	1.49083i
$792$		0			0
$793$	−31.0856			−0.0392000
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−633.446	+	365.720i	−0.794788	+	0.458871i	−0.841646	−	0.540030i	$-0.818413\pi$
$797$	−633.446	+	365.720i	−0.794788	+	0.458871i	0.0468571	+	0.998902i	$0.485079\pi$
$798$		0			0
$799$	−832.723	+	1442.32i	−1.04221	+	1.80515i
$800$		0			0
$801$	−642.662	−	1245.06i	−0.802325	−	1.55439i
$802$		0			0
$803$	224.297	+	129.498i	0.279323	+	0.161267i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	156.155	+	642.977i	0.193500	+	0.796750i
$808$		0			0
$809$		−	630.726i		−	0.779637i	−0.920892	−	0.389818i	$-0.872538\pi$
$809$		−	630.726i		−	0.779637i	0.920892	−	0.389818i	$-0.127462\pi$
$810$		0			0
$811$	707.192			0.872000			0.436000	−	0.899947i	$-0.356395\pi$
$811$	707.192			0.872000			0.436000	+	0.899947i	$0.356395\pi$
$812$		0			0
$813$	513.789	−	124.780i	0.631967	−	0.153481i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	143.556	−	248.646i	0.175711	−	0.304340i
$818$		0			0
$819$	97.3521	−	50.2501i	0.118867	−	0.0613554i
$820$		0			0
$821$	573.638	+	331.190i	0.698706	+	0.403398i	0.806865	−	0.590735i	$-0.201162\pi$
$821$	573.638	+	331.190i	0.698706	+	0.403398i	−0.108159	+	0.994134i	$0.534496\pi$
$822$		0			0
$823$	364.292	+	630.973i	0.442640	+	0.766674i	0.997884	−	0.0650127i	$-0.0207088\pi$
$823$	364.292	+	630.973i	0.442640	+	0.766674i	−0.555245	+	0.831687i	$0.687375\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	1247.54i		−	1.50851i	−0.656581	−	0.754256i	$-0.727998\pi$
$827$		−	1247.54i		−	1.50851i	0.656581	−	0.754256i	$-0.272002\pi$
$828$		0			0
$829$	−1302.23			−1.57084			−0.785421	−	0.618962i	$-0.787554\pi$
$829$	−1302.23			−1.57084			−0.785421	+	0.618962i	$0.787554\pi$
$830$		0			0
$831$	−322.232	+	1098.44i	−0.387764	+	1.32183i
$832$		0			0
$833$	901.378	−	520.411i	1.08209	−	0.624743i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	1132.42	+	390.983i	1.35295	+	0.467124i
$838$		0			0
$839$	−209.274	−	120.824i	−0.249432	−	0.144010i	0.370072	−	0.929003i	$-0.379333\pi$
$839$	−209.274	−	120.824i	−0.249432	−	0.144010i	−0.619504	+	0.784993i	$0.712666\pi$
$840$		0			0
$841$	−420.431	−	728.208i	−0.499918	−	0.865883i
$842$		0			0
$843$	−1446.69	−	424.394i	−1.71612	−	0.503433i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	1030.30			1.21641
$848$		0			0
$849$	−710.597	−	744.880i	−0.836982	−	0.877362i
$850$		0			0
$851$	−76.7753	+	44.3263i	−0.0902178	+	0.0520873i
$852$		0			0
$853$	140.883	−	244.017i	0.165162	−	0.286069i	−0.771551	−	0.636168i	$-0.780519\pi$
$853$	140.883	−	244.017i	0.165162	−	0.286069i	0.936713	+	0.350099i	$0.113852\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−482.527	−	278.587i	−0.563042	−	0.325072i	0.191324	−	0.981527i	$-0.438722\pi$
$857$	−482.527	−	278.587i	−0.563042	−	0.325072i	−0.754365	+	0.656455i	$0.772055\pi$
$858$		0			0
$859$	647.267	+	1121.10i	0.753512	+	1.30512i	0.946111	+	0.323843i	$0.104975\pi$
$859$	647.267	+	1121.10i	0.753512	+	1.30512i	−0.192599	+	0.981278i	$0.561692\pi$
$860$		0			0
$861$	−277.899	−	1144.27i	−0.322763	−	1.32900i
$862$		0			0
$863$		−	440.129i		−	0.509998i	−0.966941	−	0.254999i	$-0.917925\pi$
$863$		−	440.129i		−	0.509998i	0.966941	−	0.254999i	$-0.0820752\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−446.144	+	108.351i	−0.514583	+	0.124973i
$868$		0			0
$869$	516.661	−	298.294i	0.594546	−	0.343261i
$870$		0			0
$871$	22.0064	−	38.1162i	0.0252657	−	0.0437614i
$872$		0			0
$873$	−44.3568	+	941.057i	−0.0508097	+	1.07796i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−247.030	−	427.869i	−0.281676	−	0.487878i	0.690121	−	0.723694i	$-0.257557\pi$
$877$	−247.030	−	427.869i	−0.281676	−	0.487878i	−0.971798	+	0.235816i	$0.924224\pi$
$878$		0			0
$879$	−1041.50	+	993.567i	−1.18487	+	1.13034i
$880$		0			0
$881$			1182.99i			1.34279i	0.741102	+	0.671393i	$0.234304\pi$
$881$			1182.99i			1.34279i	−0.741102	+	0.671393i	$0.765696\pi$
$882$		0			0
$883$	−1695.81			−1.92051			−0.960257	−	0.279117i	$-0.909958\pi$
$883$	−1695.81			−1.92051			−0.960257	+	0.279117i	$0.909958\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−945.072	+	545.638i	−1.06547	+	0.615150i	−0.926940	−	0.375209i	$-0.877571\pi$
$887$	−945.072	+	545.638i	−1.06547	+	0.615150i	−0.138530	+	0.990358i	$0.544238\pi$
$888$		0			0
$889$	−670.601	+	1161.51i	−0.754331	+	1.30654i
$890$		0			0
$891$	305.357	−	139.821i	0.342713	−	0.156926i
$892$		0			0
$893$	−675.053	−	389.742i	−0.755938	−	0.436441i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−9.46708	−	2.77722i	−0.0105542	−	0.00309612i
$898$		0			0
$899$		−	16.4825i		−	0.0183343i
$900$		0			0
$901$	−1952.08			−2.16657
$902$		0			0
$903$	−599.662	−	628.592i	−0.664077	−	0.696116i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	570.527	−	988.183i	0.629027	−	1.08951i	−0.358720	−	0.933445i	$-0.616787\pi$
$907$	570.527	−	988.183i	0.629027	−	1.08951i	0.987747	−	0.156062i	$-0.0498798\pi$
$908$		0			0
$909$	930.057	+	43.8383i	1.02317	+	0.0482270i
$910$		0			0
$911$	1054.65	+	608.900i	1.15768	+	0.668387i	0.950747	−	0.309969i	$-0.100319\pi$
$911$	1054.65	+	608.900i	1.15768	+	0.668387i	0.206933	+	0.978355i	$0.433652\pi$
$912$		0			0
$913$	−34.0207	−	58.9256i	−0.0372626	−	0.0645407i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		−	1436.09i		−	1.56608i
$918$		0			0
$919$	444.333			0.483496			0.241748	−	0.970339i	$-0.422279\pi$
$919$	444.333			0.483496			0.241748	+	0.970339i	$0.422279\pi$
$920$		0			0
$921$	−497.324	+	120.781i	−0.539983	+	0.131141i
$922$		0			0
$923$	−17.8256	+	10.2916i	−0.0193126	+	0.0111502i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	881.066	+	565.605i	0.950448	+	0.610145i
$928$		0			0
$929$	742.230	+	428.527i	0.798956	+	0.461277i	0.843106	−	0.537748i	$-0.180725\pi$
$929$	742.230	+	428.527i	0.798956	+	0.461277i	−0.0441502	+	0.999025i	$0.514058\pi$
$930$		0			0
$931$	243.570	+	421.875i	0.261621	+	0.453142i
$932$		0			0
$933$	904.498	−	862.869i	0.969451	−	0.924832i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	986.255			1.05257			0.526283	−	0.850309i	$-0.323585\pi$
$937$	986.255			1.05257			0.526283	+	0.850309i	$0.323585\pi$
$938$		0			0
$939$	66.7656	−	227.593i	0.0711028	−	0.242378i
$940$		0			0
$941$	−872.937	+	503.990i	−0.927669	+	0.535590i	−0.886074	−	0.463545i	$-0.846577\pi$
$941$	−872.937	+	503.990i	−0.927669	+	0.535590i	−0.0415955	+	0.999135i	$0.513244\pi$
$942$		0			0
$943$	−53.0211	+	91.8352i	−0.0562260	+	0.0973862i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−776.345	−	448.223i	−0.819794	−	0.473308i	0.0305512	−	0.999533i	$-0.490274\pi$
$947$	−776.345	−	448.223i	−0.819794	−	0.473308i	−0.850346	+	0.526225i	$0.823607\pi$
$948$		0			0
$949$	−38.3064	−	66.3486i	−0.0403650	−	0.0699142i
$950$		0			0
$951$	605.268	+	177.558i	0.636454	+	0.186707i
$952$		0			0
$953$		−	952.038i		−	0.998991i	−0.866317	−	0.499495i	$-0.833519\pi$
$953$		−	952.038i		−	0.998991i	0.866317	−	0.499495i	$-0.166481\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−3.18944	−	3.34332i	−0.00333275	−	0.00349354i
$958$		0			0
$959$	−1021.63	+	589.836i	−1.06530	+	0.615053i
$960$		0			0
$961$	−503.887	+	872.757i	−0.524336	+	0.908176i
$962$		0			0
$963$	−791.264	−	1532.96i	−0.821666	−	1.59186i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	383.608	+	664.429i	0.396700	+	0.687104i	0.993317	−	0.115422i	$-0.0368222\pi$
$967$	383.608	+	664.429i	0.396700	+	0.687104i	−0.596617	+	0.802526i	$0.703489\pi$
$968$		0			0
$969$	−146.478	−	603.133i	−0.151164	−	0.622428i
$970$		0			0
$971$		−	1004.22i		−	1.03421i	−0.855921	−	0.517106i	$-0.827009\pi$
$971$		−	1004.22i		−	1.03421i	0.855921	−	0.517106i	$-0.172991\pi$
$972$		0			0
$973$	1386.58			1.42506
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−623.351	+	359.892i	−0.638026	+	0.368364i	−0.783854	−	0.620946i	$-0.786749\pi$
$977$	−623.351	+	359.892i	−0.638026	+	0.368364i	0.145828	+	0.989310i	$0.453415\pi$
$978$		0			0
$979$	322.749	−	559.018i	0.329673	−	0.571010i
$980$		0			0
$981$	1122.87	−	579.588i	1.14461	−	0.590814i
$982$		0			0
$983$	662.141	+	382.287i	0.673592	+	0.388899i	0.797436	−	0.603403i	$-0.206189\pi$
$983$	662.141	+	382.287i	0.673592	+	0.388899i	−0.123844	+	0.992302i	$0.539522\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−1706.58	+	1628.03i	−1.72906	+	1.64948i
$988$		0			0
$989$			78.2348i			0.0791050i
$990$		0			0
$991$	512.381			0.517035			0.258517	−	0.966007i	$-0.416766\pi$
$991$	512.381			0.517035			0.258517	+	0.966007i	$0.416766\pi$
$992$		0			0
$993$	481.839	−	1642.51i	0.485235	−	1.65409i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	688.601	−	1192.69i	0.690674	−	1.19628i	−0.280944	−	0.959724i	$-0.590648\pi$
$997$	688.601	−	1192.69i	0.690674	−	1.19628i	0.971618	−	0.236557i	$-0.0760192\pi$
$998$		0			0
$999$	−674.208	+	585.090i	−0.674883	+	0.585676i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.3.p.d.101.8	✓	16
3.2	odd	2		2700.3.p.e.1601.1		16
5.2	odd	4		900.3.u.d.749.7		32
5.3	odd	4		900.3.u.d.749.10		32
5.4	even	2		900.3.p.e.101.1	yes	16
9.4	even	3		2700.3.p.e.2501.1		16
9.5	odd	6	inner	900.3.p.d.401.8	yes	16
15.2	even	4		2700.3.u.d.2249.2		32
15.8	even	4		2700.3.u.d.2249.15		32
15.14	odd	2		2700.3.p.d.1601.8		16
45.4	even	6		2700.3.p.d.2501.8		16
45.13	odd	12		2700.3.u.d.449.2		32
45.14	odd	6		900.3.p.e.401.1	yes	16
45.22	odd	12		2700.3.u.d.449.15		32
45.23	even	12		900.3.u.d.149.7		32
45.32	even	12		900.3.u.d.149.10		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
900.3.p.d.101.8	✓	16	1.1	even	1	trivial
900.3.p.d.401.8	yes	16	9.5	odd	6	inner
900.3.p.e.101.1	yes	16	5.4	even	2
900.3.p.e.401.1	yes	16	45.14	odd	6
900.3.u.d.149.7		32	45.23	even	12
900.3.u.d.149.10		32	45.32	even	12
900.3.u.d.749.7		32	5.2	odd	4
900.3.u.d.749.10		32	5.3	odd	4
2700.3.p.d.1601.8		16	15.14	odd	2
2700.3.p.d.2501.8		16	45.4	even	6
2700.3.p.e.1601.1		16	3.2	odd	2
2700.3.p.e.2501.1		16	9.4	even	3
2700.3.u.d.449.2		32	45.13	odd	12
2700.3.u.d.449.15		32	45.22	odd	12
2700.3.u.d.2249.2		32	15.2	even	4
2700.3.u.d.2249.15		32	15.8	even	4

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	900.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.91526 - 0.708005i) q^{3} +(-4.96248 + 8.59526i) q^{7} +(7.99746 - 4.12804i) q^{9} +O(q^{10})\)	\(q+(2.91526 - 0.708005i) q^{3} +(-4.96248 + 8.59526i) q^{7} +(7.99746 - 4.12804i) q^{9} +(3.59076 + 2.07313i) q^{11} +(-0.613246 - 1.06217i) q^{13} +21.0247i q^{17} -9.84025 q^{19} +(-8.38141 + 28.5709i) q^{21} +(2.32213 - 1.34068i) q^{23} +(20.3920 - 17.6965i) q^{27} +(-0.321704 - 0.185736i) q^{29} +(22.1854 + 38.4263i) q^{31} +(11.9358 + 3.50142i) q^{33} -33.0624 q^{37} +(-2.53980 - 2.66233i) q^{39} +(-34.2494 + 19.7739i) q^{41} +(-14.5886 + 25.2682i) q^{43} +(68.6012 + 39.6069i) q^{47} +(-24.7524 - 42.8724i) q^{49} +(14.8856 + 61.2924i) q^{51} +92.8471i q^{53} +(-28.6869 + 6.96695i) q^{57} +(-53.3228 + 30.7859i) q^{59} +(12.6725 - 21.9495i) q^{61} +(-4.20566 + 89.2255i) q^{63} +(17.9426 + 31.0774i) q^{67} +(5.82040 - 5.55252i) q^{69} -16.7821i q^{71} +62.4649 q^{73} +(-35.6382 + 20.5757i) q^{77} +(71.9430 - 124.609i) q^{79} +(46.9187 - 66.0276i) q^{81} +(-14.2118 - 8.20517i) q^{83} +(-1.06935 - 0.313699i) q^{87} -155.682i q^{89} +12.1729 q^{91} +(91.8823 + 96.3152i) q^{93} +(-52.3390 + 90.6538i) q^{97} +(37.2749 + 1.75696i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{3} + q^{7} + 14 q^{9}+O(q^{10}) \) 16 * q - 2 * q^3 + q^7 + 14 * q^9	\( 16 q - 2 q^{3} + q^{7} + 14 q^{9} + 10 q^{13} + 2 q^{19} + q^{21} - 27 q^{23} + 16 q^{27} + 9 q^{29} + 8 q^{31} - 36 q^{33} + 22 q^{37} + 19 q^{39} + 54 q^{41} - 44 q^{43} + 108 q^{47} - 45 q^{49} + 90 q^{51} + 68 q^{57} + 9 q^{59} - 55 q^{61} + 107 q^{63} + 28 q^{67} - 147 q^{69} - 86 q^{73} - 342 q^{77} + 11 q^{79} - 130 q^{81} + 306 q^{83} - 375 q^{87} - 134 q^{91} + 83 q^{93} - 41 q^{97} + 252 q^{99}+O(q^{100}) \) 16 * q - 2 * q^3 + q^7 + 14 * q^9 + 10 * q^13 + 2 * q^19 + q^21 - 27 * q^23 + 16 * q^27 + 9 * q^29 + 8 * q^31 - 36 * q^33 + 22 * q^37 + 19 * q^39 + 54 * q^41 - 44 * q^43 + 108 * q^47 - 45 * q^49 + 90 * q^51 + 68 * q^57 + 9 * q^59 - 55 * q^61 + 107 * q^63 + 28 * q^67 - 147 * q^69 - 86 * q^73 - 342 * q^77 + 11 * q^79 - 130 * q^81 + 306 * q^83 - 375 * q^87 - 134 * q^91 + 83 * q^93 - 41 * q^97 + 252 * q^99

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