LMFDB - Embedded newform 144.5.q.c.65.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [144,5,Mod(65,144)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(144, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("144.65");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	144.q (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$14.8852746841$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 6x^{6} + 121x^{5} + 1104x^{4} - 1647x^{3} + 6529x^{2} + 85254x + 440076 $ x^8 - 3x^7 + 6x^6 + 121x^5 + 1104x^4 - 1647x^3 + 6529x^2 + 85254*x + 440076
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{6} $
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			65.1
Root			$4.23522 + 4.06612i$ of defining polynomial
Character	$\chi$	$=$	144.65
Dual form			144.5.q.c.113.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-8.37420 + 3.29740i) q^{3} +(10.6364 - 6.14094i) q^{5} +(-7.14202 + 12.3703i) q^{7} +(59.2543 - 55.2261i) q^{9} +O(q^{10})$	\(q+(-8.37420 + 3.29740i) q^{3} +(10.6364 - 6.14094i) q^{5} +(-7.14202 + 12.3703i) q^{7} +(59.2543 - 55.2261i) q^{9} +(-90.2145 - 52.0854i) q^{11} +(-37.6173 - 65.1551i) q^{13} +(-68.8224 + 86.4980i) q^{15} +341.998i q^{17} +706.329 q^{19} +(19.0187 - 127.142i) q^{21} +(516.421 - 298.156i) q^{23} +(-237.078 + 410.630i) q^{25} +(-314.105 + 657.860i) q^{27} +(1127.90 + 651.194i) q^{29} +(514.510 + 891.158i) q^{31} +(927.221 + 138.700i) q^{33} +175.435i q^{35} +563.132 q^{37} +(529.857 + 421.582i) q^{39} +(85.8619 - 49.5724i) q^{41} +(-448.257 + 776.404i) q^{43} +(291.114 - 951.286i) q^{45} +(-372.885 - 215.285i) q^{47} +(1098.48 + 1902.63i) q^{49} +(-1127.70 - 2863.96i) q^{51} -5271.47i q^{53} -1279.41 q^{55} +(-5914.94 + 2329.05i) q^{57} +(4883.74 - 2819.63i) q^{59} +(-565.626 + 979.693i) q^{61} +(259.971 + 1127.42i) q^{63} +(-800.227 - 462.012i) q^{65} +(-676.412 - 1171.58i) q^{67} +(-3341.48 + 4199.66i) q^{69} +5681.42i q^{71} +4236.54 q^{73} +(631.322 - 4220.44i) q^{75} +(1288.63 - 743.990i) q^{77} +(-3067.71 + 5313.43i) q^{79} +(461.150 - 6544.77i) q^{81} +(-6503.75 - 3754.94i) q^{83} +(2100.19 + 3637.64i) q^{85} +(-11592.5 - 1734.09i) q^{87} -8721.70i q^{89} +1074.65 q^{91} +(-7247.12 - 5766.19i) q^{93} +(7512.81 - 4337.53i) q^{95} +(-2720.65 + 4712.31i) q^{97} +(-8222.08 + 1895.92i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 9 q^{3} - 9 q^{5} - 13 q^{7} + 21 q^{9}+O(q^{10}) $ 8 * q + 9 * q^3 - 9 * q^5 - 13 * q^7 + 21 * q^9	$ 8 q + 9 q^{3} - 9 q^{5} - 13 q^{7} + 21 q^{9} + 18 q^{11} - 5 q^{13} - 225 q^{15} - 562 q^{19} - 1167 q^{21} + 1719 q^{23} + 353 q^{25} - 648 q^{27} + 2115 q^{29} - 187 q^{31} + 3258 q^{33} + 16 q^{37} + 8265 q^{39} - 7920 q^{41} + 68 q^{43} + 5679 q^{45} - 13689 q^{47} - 327 q^{49} - 10449 q^{51} + 1818 q^{55} - 21861 q^{57} + 20052 q^{59} - 1937 q^{61} - 5559 q^{63} + 25965 q^{65} - 154 q^{67} + 21645 q^{69} - 7802 q^{73} + 30297 q^{75} - 25641 q^{77} + 2195 q^{79} + 19701 q^{81} - 37017 q^{83} - 3042 q^{85} - 22455 q^{87} - 15830 q^{91} - 36489 q^{93} + 37116 q^{95} + 7282 q^{97} + 10035 q^{99}+O(q^{100}) $ 8 * q + 9 * q^3 - 9 * q^5 - 13 * q^7 + 21 * q^9 + 18 * q^11 - 5 * q^13 - 225 * q^15 - 562 * q^19 - 1167 * q^21 + 1719 * q^23 + 353 * q^25 - 648 * q^27 + 2115 * q^29 - 187 * q^31 + 3258 * q^33 + 16 * q^37 + 8265 * q^39 - 7920 * q^41 + 68 * q^43 + 5679 * q^45 - 13689 * q^47 - 327 * q^49 - 10449 * q^51 + 1818 * q^55 - 21861 * q^57 + 20052 * q^59 - 1937 * q^61 - 5559 * q^63 + 25965 * q^65 - 154 * q^67 + 21645 * q^69 - 7802 * q^73 + 30297 * q^75 - 25641 * q^77 + 2195 * q^79 + 19701 * q^81 - 37017 * q^83 - 3042 * q^85 - 22455 * q^87 - 15830 * q^91 - 36489 * q^93 + 37116 * q^95 + 7282 * q^97 + 10035 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$1$

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
$3$	−8.37420	+	3.29740i	−0.930466	+	0.366378i
$3$	−8.37420	+	3.29740i	−0.930466	+	0.366378i
$4$		0			0
$5$	10.6364	−	6.14094i	0.425457	−	0.245638i	−0.271952	−	0.962311i	$-0.587669\pi$
$5$	10.6364	−	6.14094i	0.425457	−	0.245638i	0.697409	+	0.716673i	$0.254336\pi$
$6$		0			0
$7$	−7.14202	+	12.3703i	−0.145756	+	0.252456i	−0.929655	−	0.368432i	$-0.879895\pi$
$7$	−7.14202	+	12.3703i	−0.145756	+	0.252456i	0.783899	+	0.620888i	$0.213228\pi$
$8$		0			0
$9$	59.2543	−	55.2261i	0.731535	−	0.681804i
$10$		0			0
$11$	−90.2145	−	52.0854i	−0.745575	−	0.430458i	0.0785180	−	0.996913i	$-0.474981\pi$
$11$	−90.2145	−	52.0854i	−0.745575	−	0.430458i	−0.824093	+	0.566455i	$0.808315\pi$
$12$		0			0
$13$	−37.6173	−	65.1551i	−0.222588	−	0.385533i	0.733005	−	0.680223i	$-0.238117\pi$
$13$	−37.6173	−	65.1551i	−0.222588	−	0.385533i	−0.955593	+	0.294690i	$0.904784\pi$
$14$		0			0
$15$	−68.8224	+	86.4980i	−0.305877	+	0.384436i
$16$		0			0
$17$			341.998i			1.18338i	0.806164	+	0.591692i	$0.201540\pi$
$17$			341.998i			1.18338i	−0.806164	+	0.591692i	$0.798460\pi$
$18$		0			0
$19$	706.329			1.95659			0.978295	−	0.207218i	$-0.0664411\pi$
$19$	706.329			1.95659			0.978295	+	0.207218i	$0.0664411\pi$
$20$		0			0
$21$	19.0187	−	127.142i	0.0431264	−	0.288303i
$22$		0			0
$23$	516.421	−	298.156i	0.976222	−	0.563622i	0.0750946	−	0.997176i	$-0.476074\pi$
$23$	516.421	−	298.156i	0.976222	−	0.563622i	0.901127	+	0.433554i	$0.142741\pi$
$24$		0			0
$25$	−237.078	+	410.630i	−0.379324	+	0.657009i
$26$		0			0
$27$	−314.105	+	657.860i	−0.430871	+	0.902414i
$28$		0			0
$29$	1127.90	+	651.194i	1.34114	+	0.774309i	0.986975	−	0.160873i	$-0.0514308\pi$
$29$	1127.90	+	651.194i	1.34114	+	0.774309i	0.354168	+	0.935182i	$0.384764\pi$
$30$		0			0
$31$	514.510	+	891.158i	0.535391	+	0.927324i	0.999144	+	0.0413597i	$0.0131690\pi$
$31$	514.510	+	891.158i	0.535391	+	0.927324i	−0.463754	+	0.885964i	$0.653498\pi$
$32$		0			0
$33$	927.221	+	138.700i	0.851442	+	0.127365i
$34$		0			0
$35$			175.435i			0.143212i
$36$		0			0
$37$	563.132			0.411346			0.205673	−	0.978621i	$-0.434062\pi$
$37$	563.132			0.411346			0.205673	+	0.978621i	$0.434062\pi$
$38$		0			0
$39$	529.857	+	421.582i	0.348361	+	0.277174i
$40$		0			0
$41$	85.8619	−	49.5724i	0.0510779	−	0.0294898i	−0.474244	−	0.880394i	$-0.657278\pi$
$41$	85.8619	−	49.5724i	0.0510779	−	0.0294898i	0.525321	+	0.850904i	$0.323945\pi$
$42$		0			0
$43$	−448.257	+	776.404i	−0.242432	+	0.419905i	−0.961407	−	0.275132i	$-0.911279\pi$
$43$	−448.257	+	776.404i	−0.242432	+	0.419905i	0.718974	+	0.695037i	$0.244612\pi$
$44$		0			0
$45$	291.114	−	951.286i	0.143760	−	0.469771i
$46$		0			0
$47$	−372.885	−	215.285i	−0.168802	−	0.0974581i	0.413219	−	0.910632i	$-0.364405\pi$
$47$	−372.885	−	215.285i	−0.168802	−	0.0974581i	−0.582021	+	0.813174i	$0.697738\pi$
$48$		0			0
$49$	1098.48	+	1902.63i	0.457511	+	0.792432i
$50$		0			0
$51$	−1127.70	−	2863.96i	−0.433565	−	1.10110i
$52$		0			0
$53$		−	5271.47i		−	1.87664i	−0.345773	−	0.938318i	$-0.612383\pi$
$53$		−	5271.47i		−	1.87664i	0.345773	−	0.938318i	$-0.387617\pi$
$54$		0			0
$55$	−1279.41			−0.422947
$56$		0			0
$57$	−5914.94	+	2329.05i	−1.82054	+	0.716851i
$58$		0			0
$59$	4883.74	−	2819.63i	1.40297	−	0.810005i	0.408274	−	0.912859i	$-0.366131\pi$
$59$	4883.74	−	2819.63i	1.40297	−	0.810005i	0.994696	+	0.102854i	$0.0327975\pi$
$60$		0			0
$61$	−565.626	+	979.693i	−0.152009	+	0.263287i	−0.931966	−	0.362546i	$-0.881908\pi$
$61$	−565.626	+	979.693i	−0.152009	+	0.263287i	0.779957	+	0.625833i	$0.215241\pi$
$62$		0			0
$63$	259.971	+	1127.42i	0.0655003	+	0.284057i
$64$		0			0
$65$	−800.227	−	462.012i	−0.189403	−	0.109352i
$66$		0			0
$67$	−676.412	−	1171.58i	−0.150682	−	0.260989i	0.780796	−	0.624786i	$-0.214814\pi$
$67$	−676.412	−	1171.58i	−0.150682	−	0.260989i	−0.931478	+	0.363797i	$0.881480\pi$
$68$		0			0
$69$	−3341.48	+	4199.66i	−0.701843	+	0.882097i
$70$		0			0
$71$			5681.42i			1.12704i	0.826101	+	0.563522i	$0.190554\pi$
$71$			5681.42i			1.12704i	−0.826101	+	0.563522i	$0.809446\pi$
$72$		0			0
$73$	4236.54			0.794996			0.397498	−	0.917603i	$-0.369878\pi$
$73$	4236.54			0.794996			0.397498	+	0.917603i	$0.369878\pi$
$74$		0			0
$75$	631.322	−	4220.44i	0.112235	−	0.750300i
$76$		0			0
$77$	1288.63	−	743.990i	0.217343	−	0.125483i
$78$		0			0
$79$	−3067.71	+	5313.43i	−0.491542	+	0.851375i	−0.999953	−	0.00973957i	$-0.996900\pi$
$79$	−3067.71	+	5313.43i	−0.491542	+	0.851375i	0.508411	+	0.861115i	$0.330233\pi$
$80$		0			0
$81$	461.150	−	6544.77i	0.0702866	−	0.997527i
$82$		0			0
$83$	−6503.75	−	3754.94i	−0.944077	−	0.545063i	−0.0528411	−	0.998603i	$-0.516828\pi$
$83$	−6503.75	−	3754.94i	−0.944077	−	0.545063i	−0.891236	+	0.453540i	$0.850161\pi$
$84$		0			0
$85$	2100.19	+	3637.64i	0.290684	+	0.503479i
$86$		0			0
$87$	−11592.5	−	1734.09i	−1.53158	−	0.229104i
$88$		0			0
$89$		−	8721.70i		−	1.10109i	−0.834807	−	0.550543i	$-0.814421\pi$
$89$		−	8721.70i		−	1.10109i	0.834807	−	0.550543i	$-0.185579\pi$
$90$		0			0
$91$	1074.65			0.129774
$92$		0			0
$93$	−7247.12	−	5766.19i	−0.837914	−	0.666688i
$94$		0			0
$95$	7512.81	−	4337.53i	0.832445	−	0.480612i
$96$		0			0
$97$	−2720.65	+	4712.31i	−0.289154	+	0.500830i	−0.973608	−	0.228226i	$-0.926707\pi$
$97$	−2720.65	+	4712.31i	−0.289154	+	0.500830i	0.684454	+	0.729056i	$0.260041\pi$
$98$		0			0
$99$	−8222.08	+	1895.92i	−0.838902	+	0.193441i
$100$		0			0
$101$	6480.14	+	3741.31i	0.635246	+	0.366759i	0.782781	−	0.622297i	$-0.213801\pi$
$101$	6480.14	+	3741.31i	0.635246	+	0.366759i	−0.147535	+	0.989057i	$0.547134\pi$
$102$		0			0
$103$	6788.27	+	11757.6i	0.639860	+	1.10827i	0.985463	+	0.169889i	$0.0543408\pi$
$103$	6788.27	+	11757.6i	0.639860	+	1.10827i	−0.345604	+	0.938381i	$0.612326\pi$
$104$		0			0
$105$	−578.479	−	1469.13i	−0.0524698	−	0.133254i
$106$		0			0
$107$		−	16741.7i		−	1.46229i	−0.682224	−	0.731143i	$-0.738987\pi$
$107$		−	16741.7i		−	1.46229i	0.682224	−	0.731143i	$-0.261013\pi$
$108$		0			0
$109$	−12068.7			−1.01579			−0.507897	−	0.861418i	$-0.669577\pi$
$109$	−12068.7			−1.01579			−0.507897	+	0.861418i	$0.669577\pi$
$110$		0			0
$111$	−4715.78	+	1856.87i	−0.382743	+	0.150708i
$112$		0			0
$113$	610.202	−	352.300i	0.0477878	−	0.0275903i	−0.475916	−	0.879491i	$-0.657883\pi$
$113$	610.202	−	352.300i	0.0477878	−	0.0275903i	0.523704	+	0.851901i	$0.324550\pi$
$114$		0			0
$115$	3661.92	−	6342.63i	0.276894	−	0.479594i
$116$		0			0
$117$	−5827.25	−	1783.26i	−0.425689	−	0.130270i
$118$		0			0
$119$	−4230.63	−	2442.56i	−0.298752	−	0.172485i
$120$		0			0
$121$	−1894.72	−	3281.76i	−0.129412	−	0.224148i
$122$		0			0
$123$	−555.565	+	698.250i	−0.0367218	+	0.0461531i
$124$		0			0
$125$			13499.7i			0.863981i
$126$		0			0
$127$	16050.0			0.995105			0.497552	−	0.867434i	$-0.334232\pi$
$127$	16050.0			0.995105			0.497552	+	0.867434i	$0.334232\pi$
$128$		0			0
$129$	1193.68	−	7979.84i	0.0717312	−	0.479529i
$130$		0			0
$131$	13427.1	−	7752.17i	0.782422	−	0.451732i	−0.0548658	−	0.998494i	$-0.517473\pi$
$131$	13427.1	−	7752.17i	0.782422	−	0.451732i	0.837288	+	0.546762i	$0.184140\pi$
$132$		0			0
$133$	−5044.62	+	8737.53i	−0.285184	+	0.493953i
$134$		0			0
$135$	698.926	+	8926.17i	0.0383498	+	0.489776i
$136$		0			0
$137$	−771.295	−	445.307i	−0.0410941	−	0.0237257i	0.479312	−	0.877644i	$-0.340886\pi$
$137$	−771.295	−	445.307i	−0.0410941	−	0.0237257i	−0.520406	+	0.853919i	$0.674219\pi$
$138$		0			0
$139$	4679.09	+	8104.42i	0.242176	+	0.419462i	0.961334	−	0.275385i	$-0.0888054\pi$
$139$	4679.09	+	8104.42i	0.242176	+	0.419462i	−0.719158	+	0.694847i	$0.755472\pi$
$140$		0			0
$141$	3832.49	+	573.290i	0.192771	+	0.0288361i
$142$		0			0
$143$			7837.25i			0.383258i
$144$		0			0
$145$	15995.8			0.760798
$146$		0			0
$147$	−15472.6	−	12310.8i	−0.716027	−	0.569709i
$148$		0			0
$149$	35220.7	−	20334.7i	1.58645	−	0.915937i	0.592563	−	0.805524i	$-0.298116\pi$
$149$	35220.7	−	20334.7i	1.58645	−	0.915937i	0.993886	−	0.110412i	$-0.0352171\pi$
$150$		0			0
$151$	−12487.2	+	21628.5i	−0.547661	+	0.948577i	0.450773	+	0.892639i	$0.351148\pi$
$151$	−12487.2	+	21628.5i	−0.547661	+	0.948577i	−0.998434	+	0.0559386i	$0.982185\pi$
$152$		0			0
$153$	18887.2	+	20264.9i	0.806836	+	0.865686i
$154$		0			0
$155$	10945.1	+	6319.16i	0.455572	+	0.263024i
$156$		0			0
$157$	16459.2	+	28508.2i	0.667743	+	1.15656i	0.978534	+	0.206086i	$0.0660727\pi$
$157$	16459.2	+	28508.2i	0.667743	+	1.15656i	−0.310791	+	0.950478i	$0.600594\pi$
$158$		0			0
$159$	17382.1	+	44144.3i	0.687557	+	1.74615i
$160$		0			0
$161$			8517.75i			0.328604i
$162$		0			0
$163$	−13796.3			−0.519262			−0.259631	−	0.965708i	$-0.583601\pi$
$163$	−13796.3			−0.519262			−0.259631	+	0.965708i	$0.583601\pi$
$164$		0			0
$165$	10714.1	−	4218.74i	0.393538	−	0.154958i
$166$		0			0
$167$	−9814.14	+	5666.20i	−0.351900	+	0.203170i	−0.665522	−	0.746378i	$-0.731791\pi$
$167$	−9814.14	+	5666.20i	−0.351900	+	0.203170i	0.313622	+	0.949548i	$0.398458\pi$
$168$		0			0
$169$	11450.4	−	19832.6i	0.400910	−	0.694396i
$170$		0			0
$171$	41853.0	−	39007.8i	1.43131	−	1.33401i
$172$		0			0
$173$	−33922.6	−	19585.2i	−1.13344	−	0.654389i	−0.188639	−	0.982047i	$-0.560408\pi$
$173$	−33922.6	−	19585.2i	−1.13344	−	0.654389i	−0.944797	+	0.327657i	$0.893741\pi$
$174$		0			0
$175$	−3386.43	−	5865.47i	−0.110577	−	0.191525i
$176$		0			0
$177$	−31600.0	+	39715.8i	−1.00865	+	1.26770i
$178$		0			0
$179$			24097.3i			0.752078i	0.926604	+	0.376039i	$0.122714\pi$
$179$			24097.3i			0.752078i	−0.926604	+	0.376039i	$0.877286\pi$
$180$		0			0
$181$	10277.1			0.313699			0.156850	−	0.987623i	$-0.449866\pi$
$181$	10277.1			0.313699			0.156850	+	0.987623i	$0.449866\pi$
$182$		0			0
$183$	1506.22	−	10069.2i	0.0449767	−	0.300673i
$184$		0			0
$185$	5989.72	−	3458.16i	0.175010	−	0.101042i
$186$		0			0
$187$	17813.1	−	30853.2i	0.509397	−	0.882301i
$188$		0			0
$189$	−5894.61	−	8584.03i	−0.165018	−	0.240308i
$190$		0			0
$191$	30337.2	+	17515.2i	0.831590	+	0.480119i	0.854397	−	0.519621i	$-0.173927\pi$
$191$	30337.2	+	17515.2i	0.831590	+	0.480119i	−0.0228068	+	0.999740i	$0.507260\pi$
$192$		0			0
$193$	−2620.27	−	4538.45i	−0.0703448	−	0.121841i	0.828708	−	0.559682i	$-0.189077\pi$
$193$	−2620.27	−	4538.45i	−0.0703448	−	0.121841i	−0.899052	+	0.437841i	$0.855743\pi$
$194$		0			0
$195$	8224.70	+	1230.31i	0.216297	+	0.0323552i
$196$		0			0
$197$			42421.5i			1.09308i	0.837431	+	0.546542i	$0.184056\pi$
$197$			42421.5i			1.09308i	−0.837431	+	0.546542i	$0.815944\pi$
$198$		0			0
$199$	−31270.0			−0.789627			−0.394814	−	0.918761i	$-0.629191\pi$
$199$	−31270.0			−0.789627			−0.394814	+	0.918761i	$0.629191\pi$
$200$		0			0
$201$	9527.58	+	7580.64i	0.235825	+	0.187635i
$202$		0			0
$203$	−16111.0	+	9301.69i	−0.390958	+	0.225720i
$204$		0			0
$205$	608.843	−	1054.55i	0.0144876	−	0.0250933i
$206$		0			0
$207$	14134.2	−	46187.0i	0.329861	−	1.07790i
$208$		0			0
$209$	−63721.1	−	36789.4i	−1.45878	−	0.842229i
$210$		0			0
$211$	−15562.2	−	26954.6i	−0.349548	−	0.605435i	0.636621	−	0.771177i	$-0.280331\pi$
$211$	−15562.2	−	26954.6i	−0.349548	−	0.605435i	−0.986169	+	0.165742i	$0.946998\pi$
$212$		0			0
$213$	−18733.9	−	47577.4i	−0.412923	−	1.04868i
$214$		0			0
$215$			11010.9i			0.238202i
$216$		0			0
$217$	−14698.6			−0.312145
$218$		0			0
$219$	−35477.6	+	13969.5i	−0.739717	+	0.291269i
$220$		0			0
$221$	22282.9	−	12865.0i	0.456234	−	0.263407i
$222$		0			0
$223$	8013.95	−	13880.6i	0.161153	−	0.279124i	−0.774130	−	0.633027i	$-0.781812\pi$
$223$	8013.95	−	13880.6i	0.161153	−	0.279124i	0.935282	+	0.353903i	$0.115146\pi$
$224$		0			0
$225$	8629.66	+	37424.5i	0.170462	+	0.739250i
$226$		0			0
$227$	−58481.7	−	33764.5i	−1.13493	−	0.655251i	−0.189759	−	0.981831i	$-0.560771\pi$
$227$	−58481.7	−	33764.5i	−1.13493	−	0.655251i	−0.945170	+	0.326579i	$0.894104\pi$
$228$		0			0
$229$	−39032.9	−	67607.0i	−0.744321	−	1.28920i	−0.950512	−	0.310689i	$-0.899440\pi$
$229$	−39032.9	−	67607.0i	−0.744321	−	1.28920i	0.206191	−	0.978512i	$-0.433893\pi$
$230$		0			0
$231$	−8338.00	+	10479.4i	−0.156256	+	0.196388i
$232$		0			0
$233$			61204.9i			1.12739i	0.825983	+	0.563696i	$0.190621\pi$
$233$			61204.9i			1.12739i	−0.825983	+	0.563696i	$0.809379\pi$
$234$		0			0
$235$	−5288.21			−0.0957576
$236$		0			0
$237$	8169.11	−	54611.2i	0.145438	−	0.972266i
$238$		0			0
$239$	−37373.3	+	21577.5i	−0.654282	+	0.377750i	−0.790095	−	0.612984i	$-0.789969\pi$
$239$	−37373.3	+	21577.5i	−0.654282	+	0.377750i	0.135813	+	0.990735i	$0.456635\pi$
$240$		0			0
$241$	28103.8	−	48677.2i	0.483873	−	0.838092i	−0.515956	−	0.856615i	$-0.672563\pi$
$241$	28103.8	−	48677.2i	0.483873	−	0.838092i	0.999828	+	0.0185233i	$0.00589649\pi$
$242$		0			0
$243$	17719.0	+	56327.8i	0.300072	+	0.953916i
$244$		0			0
$245$	23367.9	+	13491.4i	0.389302	+	0.224764i
$246$		0			0
$247$	−26570.2	−	46020.9i	−0.435513	−	0.754330i
$248$		0			0
$249$	66845.2	+	9999.16i	1.07813	+	0.161274i
$250$		0			0
$251$			15739.4i			0.249828i	0.992168	+	0.124914i	$0.0398655\pi$
$251$			15739.4i			0.249828i	−0.992168	+	0.124914i	$0.960135\pi$
$252$		0			0
$253$	−62118.3			−0.970462
$254$		0			0
$255$	−29582.1	−	23537.1i	−0.454935	−	0.361970i
$256$		0			0
$257$	−50887.7	+	29380.0i	−0.770454	+	0.444822i	−0.833036	−	0.553218i	$-0.813400\pi$
$257$	−50887.7	+	29380.0i	−0.770454	+	0.444822i	0.0625827	+	0.998040i	$0.480066\pi$
$258$		0			0
$259$	−4021.91	+	6966.14i	−0.0599560	+	0.103847i
$260$		0			0
$261$	102796.	−	23703.6i	1.50902	−	0.347962i
$262$		0			0
$263$	−81699.8	−	47169.4i	−1.18116	−	0.681944i	−0.224879	−	0.974387i	$-0.572199\pi$
$263$	−81699.8	−	47169.4i	−1.18116	−	0.681944i	−0.956283	+	0.292443i	$0.905532\pi$
$264$		0			0
$265$	−32371.8	−	56069.6i	−0.460973	−	0.798428i
$266$		0			0
$267$	28758.9	+	73037.2i	0.403413	+	1.02452i
$268$		0			0
$269$			79782.6i			1.10256i	0.834319	+	0.551282i	$0.185861\pi$
$269$			79782.6i			1.10256i	−0.834319	+	0.551282i	$0.814139\pi$
$270$		0			0
$271$	76677.1			1.04406			0.522032	−	0.852926i	$-0.325174\pi$
$271$	76677.1			1.04406			0.522032	+	0.852926i	$0.325174\pi$
$272$		0			0
$273$	−8999.37	+	3543.57i	−0.120750	+	0.0475461i
$274$		0			0
$275$	42775.7	−	24696.6i	0.565629	−	0.326566i
$276$		0			0
$277$	−56577.9	+	97995.9i	−0.737374	+	1.27717i	0.216300	+	0.976327i	$0.430601\pi$
$277$	−56577.9	+	97995.9i	−0.737374	+	1.27717i	−0.953674	+	0.300842i	$0.902732\pi$
$278$		0			0
$279$	79702.2	+	24390.6i	1.02391	+	0.313338i
$280$		0			0
$281$	−83614.5	−	48274.8i	−1.05893	−	0.611376i	−0.133797	−	0.991009i	$-0.542717\pi$
$281$	−83614.5	−	48274.8i	−1.05893	−	0.611376i	−0.925137	+	0.379633i	$0.876050\pi$
$282$		0			0
$283$	15268.5	+	26445.9i	0.190645	+	0.330206i	0.945464	−	0.325726i	$-0.105609\pi$
$283$	15268.5	+	26445.9i	0.190645	+	0.330206i	−0.754819	+	0.655933i	$0.772275\pi$
$284$		0			0
$285$	−48611.2	+	61096.0i	−0.598476	+	0.752183i
$286$		0			0
$287$			1416.19i			0.0171932i
$288$		0			0
$289$	−33441.6			−0.400397
$290$		0			0
$291$	7244.92	−	48432.9i	0.0855555	−	0.571945i
$292$		0			0
$293$	3511.45	−	2027.34i	0.0409026	−	0.0236151i	−0.479409	−	0.877591i	$-0.659149\pi$
$293$	3511.45	−	2027.34i	0.0409026	−	0.0236151i	0.520312	+	0.853976i	$0.325816\pi$
$294$		0			0
$295$	34630.4	−	59981.5i	0.397936	−	0.689245i
$296$		0			0
$297$	62601.7	−	42988.2i	0.709697	−	0.487345i
$298$		0			0
$299$	−38852.8	−	22431.7i	−0.434590	−	0.250911i
$300$		0			0
$301$	−6402.92	−	11090.2i	−0.0706717	−	0.122407i
$302$		0			0
$303$	−66602.6	−	9962.87i	−0.725447	−	0.108517i
$304$		0			0
$305$			13893.9i			0.149357i
$306$		0			0
$307$	−44297.5			−0.470005			−0.235002	−	0.971995i	$-0.575510\pi$
$307$	−44297.5			−0.470005			−0.235002	+	0.971995i	$0.575510\pi$
$308$		0			0
$309$	−95615.9	−	76077.1i	−1.00141	−	0.796777i
$310$		0			0
$311$	82350.1	−	47544.8i	0.851419	−	0.491567i	−0.00971065	−	0.999953i	$-0.503091\pi$
$311$	82350.1	−	47544.8i	0.851419	−	0.491567i	0.861129	+	0.508386i	$0.169758\pi$
$312$		0			0
$313$	85286.0	−	147720.i	0.870541	−	1.50782i	0.00910220	−	0.999959i	$-0.497103\pi$
$313$	85286.0	−	147720.i	0.870541	−	1.50782i	0.861438	−	0.507862i	$-0.169564\pi$
$314$		0			0
$315$	9688.60	+	10395.3i	0.0976427	+	0.104765i
$316$		0			0
$317$	105654.	+	60999.2i	1.05140	+	0.607024i	0.923040	−	0.384704i	$-0.125697\pi$
$317$	105654.	+	60999.2i	1.05140	+	0.607024i	0.128356	+	0.991728i	$0.459030\pi$
$318$		0			0
$319$	−67835.4	−	117494.i	−0.666615	−	1.15461i
$320$		0			0
$321$	55204.1	+	140198.i	0.535749	+	1.36061i
$322$		0			0
$323$			241563.i			2.31540i
$324$		0			0
$325$	35672.9			0.337731
$326$		0			0
$327$	101065.	−	39795.2i	0.945163	−	0.372164i
$328$		0			0
$329$	5326.30	−	3075.14i	0.0492078	−	0.0284101i
$330$		0			0
$331$	−47607.1	+	82457.9i	−0.434526	+	0.752621i	−0.997257	−	0.0740192i	$-0.976417\pi$
$331$	−47607.1	+	82457.9i	−0.434526	+	0.752621i	0.562731	+	0.826640i	$0.309751\pi$
$332$		0			0
$333$	33368.0	−	31099.6i	0.300914	−	0.280457i
$334$		0			0
$335$	−14389.2	−	8307.62i	−0.128218	−	0.0740265i
$336$		0			0
$337$	−4204.88	−	7283.07i	−0.0370249	−	0.0641291i	0.846919	−	0.531722i	$-0.178455\pi$
$337$	−4204.88	−	7283.07i	−0.0370249	−	0.0641291i	−0.883944	+	0.467593i	$0.845121\pi$
$338$		0			0
$339$	−3948.28	+	4962.31i	−0.0343564	+	0.0431802i
$340$		0			0
$341$		−	107194.i		−	0.921852i
$342$		0			0
$343$	−65677.6			−0.558250
$344$		0			0
$345$	−9751.45	+	65189.2i	−0.0819277	+	0.547694i
$346$		0			0
$347$	−5224.52	+	3016.38i	−0.0433897	+	0.0250511i	−0.521538	−	0.853228i	$-0.674642\pi$
$347$	−5224.52	+	3016.38i	−0.0433897	+	0.0250511i	0.478148	+	0.878279i	$0.341308\pi$
$348$		0			0
$349$	−69799.9	+	120897.i	−0.573065	+	0.992577i	0.423184	+	0.906044i	$0.360912\pi$
$349$	−69799.9	+	120897.i	−0.573065	+	0.992577i	−0.996249	+	0.0865335i	$0.972421\pi$
$350$		0			0
$351$	54678.7	−	4281.38i	0.443817	−	0.0347512i
$352$		0			0
$353$	−73954.5	−	42697.7i	−0.593493	−	0.342653i	0.172985	−	0.984925i	$-0.444659\pi$
$353$	−73954.5	−	42697.7i	−0.593493	−	0.342653i	−0.766477	+	0.642271i	$0.777992\pi$
$354$		0			0
$355$	34889.3	+	60430.1i	0.276844	+	0.479508i
$356$		0			0
$357$	43482.2	+	6504.37i	0.341174	+	0.0510351i
$358$		0			0
$359$			90712.4i			0.703846i	0.936029	+	0.351923i	$0.114472\pi$
$359$			90712.4i			0.703846i	−0.936029	+	0.351923i	$0.885528\pi$
$360$		0			0
$361$	368579.			2.82824
$362$		0			0
$363$	26688.1	+	21234.4i	0.202537	+	0.161149i
$364$		0			0
$365$	45061.6	−	26016.3i	0.338237	−	0.195281i
$366$		0			0
$367$	−12770.7	+	22119.5i	−0.0948160	+	0.164226i	−0.909532	−	0.415634i	$-0.863560\pi$
$367$	−12770.7	+	22119.5i	−0.0948160	+	0.164226i	0.814716	+	0.579860i	$0.196893\pi$
$368$		0			0
$369$	2350.00	−	7679.20i	0.0172590	−	0.0563979i
$370$		0			0
$371$	65209.9	+	37649.0i	0.473768	+	0.273530i
$372$		0			0
$373$	117264.	+	203107.i	0.842844	+	1.45985i	0.887480	+	0.460846i	$0.152454\pi$
$373$	117264.	+	203107.i	0.842844	+	1.45985i	−0.0446361	+	0.999003i	$0.514213\pi$
$374$		0			0
$375$	−44513.9	−	113049.i	−0.316543	−	0.803905i
$376$		0			0
$377$		−	97984.7i		−	0.689407i
$378$		0			0
$379$	107483.			0.748278			0.374139	−	0.927373i	$-0.377938\pi$
$379$	107483.			0.748278			0.374139	+	0.927373i	$0.377938\pi$
$380$		0			0
$381$	−134406.	+	52923.4i	−0.925911	+	0.364584i
$382$		0			0
$383$	142398.	−	82213.7i	0.970750	−	0.560463i	0.0712849	−	0.997456i	$-0.477290\pi$
$383$	142398.	−	82213.7i	0.970750	−	0.560463i	0.899465	+	0.436993i	$0.143957\pi$
$384$		0			0
$385$	9137.60	−	15826.8i	0.0616468	−	0.106775i
$386$		0			0
$387$	16316.6	+	70760.8i	0.108945	+	0.472466i
$388$		0			0
$389$	158396.	+	91449.9i	1.04675	+	0.604343i	0.921739	−	0.387811i	$-0.126769\pi$
$389$	158396.	+	91449.9i	1.04675	+	0.604343i	0.125015	+	0.992155i	$0.460102\pi$
$390$		0			0
$391$	101969.	+	176615.i	0.666981	+	1.15525i
$392$		0			0
$393$	−86879.6	+	109193.i	−0.562513	+	0.706983i
$394$		0			0
$395$			75354.6i			0.482965i
$396$		0			0
$397$	−277717.			−1.76206			−0.881031	−	0.473059i	$-0.843150\pi$
$397$	−277717.			−1.76206			−0.881031	+	0.473059i	$0.843150\pi$
$398$		0			0
$399$	13433.5	−	89803.9i	0.0843807	−	0.564092i
$400$		0			0
$401$	−145546.	+	84030.8i	−0.905128	+	0.522576i	−0.878861	−	0.477079i	$-0.841696\pi$
$401$	−145546.	+	84030.8i	−0.905128	+	0.522576i	−0.0262679	+	0.999655i	$0.508362\pi$
$402$		0			0
$403$	38709.0	−	67046.0i	0.238343	−	0.412822i
$404$		0			0
$405$	−35286.1	−	72444.9i	−0.215126	−	0.441670i
$406$		0			0
$407$	−50802.7	−	29331.0i	−0.306689	−	0.177067i
$408$		0			0
$409$	44190.6	+	76540.3i	0.264170	+	0.457555i	0.967346	−	0.253461i	$-0.0815688\pi$
$409$	44190.6	+	76540.3i	0.264170	+	0.457555i	−0.703176	+	0.711016i	$0.748235\pi$
$410$		0			0
$411$	7927.33	+	1185.82i	0.0469292	+	0.00701999i
$412$		0			0
$413$			80551.4i			0.472251i
$414$		0			0
$415$	−92235.5			−0.535552
$416$		0			0
$417$	−65907.1	−	52439.2i	−0.379018	−	0.301567i
$418$		0			0
$419$	131141.	−	75714.4i	0.746983	−	0.431271i	−0.0776195	−	0.996983i	$-0.524732\pi$
$419$	131141.	−	75714.4i	0.746983	−	0.431271i	0.824603	+	0.565712i	$0.191399\pi$
$420$		0			0
$421$	66110.2	−	114506.i	0.372996	−	0.646048i	−0.617029	−	0.786940i	$-0.711664\pi$
$421$	66110.2	−	114506.i	0.372996	−	0.646048i	0.990025	+	0.140893i	$0.0449972\pi$
$422$		0			0
$423$	−33984.4	+	7836.40i	−0.189932	+	0.0437962i
$424$		0			0
$425$	−140435.	−	81080.0i	−0.777494	−	0.448886i
$426$		0			0
$427$	−8079.43	−	13994.0i	−0.0443124	−	0.0767512i
$428$		0			0
$429$	−25842.5	−	65630.7i	−0.140417	−	0.356609i
$430$		0			0
$431$		−	231482.i		−	1.24613i	−0.782170	−	0.623065i	$-0.785887\pi$
$431$		−	231482.i		−	1.24613i	0.782170	−	0.623065i	$-0.214113\pi$
$432$		0			0
$433$	−218090.			−1.16321			−0.581607	−	0.813470i	$-0.697576\pi$
$433$	−218090.			−1.16321			−0.581607	+	0.813470i	$0.697576\pi$
$434$		0			0
$435$	−133952.	+	52744.5i	−0.707897	+	0.278739i
$436$		0			0
$437$	364763.	−	210596.i	1.91007	−	1.10278i
$438$		0			0
$439$	44778.5	−	77558.6i	0.232349	−	0.402440i	−0.726150	−	0.687536i	$-0.758692\pi$
$439$	44778.5	−	77558.6i	0.232349	−	0.402440i	0.958499	+	0.285096i	$0.0920256\pi$
$440$		0			0
$441$	170165.	+	52074.0i	0.874968	+	0.267759i
$442$		0			0
$443$	−228878.	−	132143.i	−1.16626	−	0.673343i	−0.213467	−	0.976950i	$-0.568476\pi$
$443$	−228878.	−	132143.i	−1.16626	−	0.673343i	−0.952797	+	0.303607i	$0.901809\pi$
$444$		0			0
$445$	−53559.5	−	92767.7i	−0.270468	−	0.468465i
$446$		0			0
$447$	−227894.	+	286424.i	−1.14056	+	1.43349i
$448$		0			0
$449$			33967.2i			0.168487i	0.996445	+	0.0842435i	$0.0268474\pi$
$449$			33967.2i			0.168487i	−0.996445	+	0.0842435i	$0.973153\pi$
$450$		0			0
$451$	−10328.0			−0.0507765
$452$		0			0
$453$	33252.7	−	222297.i	0.162043	−	1.08327i
$454$		0			0
$455$	11430.5	−	6599.40i	0.0552131	−	0.0318773i
$456$		0			0
$457$	−41636.9	+	72117.2i	−0.199363	+	0.345308i	−0.948322	−	0.317309i	$-0.897221\pi$
$457$	−41636.9	+	72117.2i	−0.199363	+	0.345308i	0.748959	+	0.662617i	$0.230554\pi$
$458$		0			0
$459$	−224987.	−	107423.i	−1.06790	−	0.509885i
$460$		0			0
$461$	−49805.5	−	28755.2i	−0.234355	−	0.135305i	0.378224	−	0.925714i	$-0.376535\pi$
$461$	−49805.5	−	28755.2i	−0.234355	−	0.135305i	−0.612580	+	0.790409i	$0.709868\pi$
$462$		0			0
$463$	40897.0	+	70835.6i	0.190778	+	0.330438i	0.945508	−	0.325598i	$-0.105566\pi$
$463$	40897.0	+	70835.6i	0.190778	+	0.330438i	−0.754730	+	0.656035i	$0.772232\pi$
$464$		0			0
$465$	−112493.	−	16827.5i	−0.520260	−	0.0778241i
$466$		0			0
$467$		−	161762.i		−	0.741726i	−0.928688	−	0.370863i	$-0.879062\pi$
$467$		−	161762.i		−	0.741726i	0.928688	−	0.370863i	$-0.120938\pi$
$468$		0			0
$469$	19323.8			0.0878511
$470$		0			0
$471$	−231835.	−	184460.i	−1.04505	−	0.831498i
$472$		0			0
$473$	80878.6	−	46695.3i	0.361503	−	0.208714i
$474$		0			0
$475$	−167455.	+	290040.i	−0.742182	+	1.28550i
$476$		0			0
$477$	−291123.	−	312357.i	−1.27950	−	1.37282i
$478$		0			0
$479$	−111249.	−	64229.4i	−0.484868	−	0.279939i	0.237575	−	0.971369i	$-0.423648\pi$
$479$	−111249.	−	64229.4i	−0.484868	−	0.279939i	−0.722443	+	0.691430i	$0.756981\pi$
$480$		0			0
$481$	−21183.5	−	36690.9i	−0.0915605	−	0.158587i
$482$		0			0
$483$	−28086.4	−	71329.3i	−0.120393	−	0.305755i
$484$		0			0
$485$			66829.5i			0.284109i
$486$		0			0
$487$	255021.			1.07527			0.537636	−	0.843177i	$-0.319318\pi$
$487$	255021.			1.07527			0.537636	+	0.843177i	$0.319318\pi$
$488$		0			0
$489$	115533.	−	45491.8i	0.483155	−	0.190246i
$490$		0			0
$491$	151163.	−	87274.1i	0.627023	−	0.362012i	−0.152575	−	0.988292i	$-0.548757\pi$
$491$	151163.	−	87274.1i	0.627023	−	0.362012i	0.779598	+	0.626280i	$0.215423\pi$
$492$		0			0
$493$	−222707.	+	385740.i	−0.916305	+	1.58709i
$494$		0			0
$495$	−75810.8	+	70657.1i	−0.309400	+	0.288367i
$496$		0			0
$497$	−70281.2	−	40576.9i	−0.284529	−	0.164273i
$498$		0			0
$499$	104865.	+	181631.i	0.421141	+	0.729438i	0.996051	−	0.0887787i	$-0.0282964\pi$
$499$	104865.	+	181631.i	0.421141	+	0.729438i	−0.574910	+	0.818216i	$0.694963\pi$
$500$		0			0
$501$	63501.8	−	79811.0i	0.252994	−	0.317971i
$502$		0			0
$503$		−	288148.i		−	1.13888i	−0.822031	−	0.569442i	$-0.807159\pi$
$503$		−	288148.i		−	1.13888i	0.822031	−	0.569442i	$-0.192841\pi$
$504$		0			0
$505$	91900.8			0.360360
$506$		0			0
$507$	−30491.6	+	203839.i	−0.118622	+	0.792996i
$508$		0			0
$509$	73335.8	−	42340.5i	0.283061	−	0.163426i	−0.351747	−	0.936095i	$-0.614412\pi$
$509$	73335.8	−	42340.5i	0.283061	−	0.163426i	0.634809	+	0.772669i	$0.281079\pi$
$510$		0			0
$511$	−30257.4	+	52407.4i	−0.115875	+	0.200702i
$512$		0			0
$513$	−221861.	+	464665.i	−0.843037	+	1.76565i
$514$		0			0
$515$	144406.	+	83372.8i	0.544466	+	0.314347i
$516$		0			0
$517$	22426.4	+	38843.7i	0.0839032	+	0.145325i
$518$		0			0
$519$	348655.	+	52154.2i	1.29438	+	0.193622i
$520$		0			0
$521$		−	80148.3i		−	0.295270i	−0.989042	−	0.147635i	$-0.952834\pi$
$521$		−	80148.3i		−	0.295270i	0.989042	−	0.147635i	$-0.0471660\pi$
$522$		0			0
$523$	−127783.			−0.467163			−0.233581	−	0.972337i	$-0.575045\pi$
$523$	−127783.			−0.467163			−0.233581	+	0.972337i	$0.575045\pi$
$524$		0			0
$525$	47699.4	+	37952.2i	0.173059	+	0.137695i
$526$		0			0
$527$	−304774.	+	175962.i	−1.09738	+	0.633573i
$528$		0			0
$529$	37873.6	−	65598.9i	0.135340	−	0.234415i
$530$		0			0
$531$	133666.	−	436785.i	0.474057	−	1.54910i
$532$		0			0
$533$	−6459.79	−	3729.56i	−0.0227386	−	0.0131281i
$534$		0			0
$535$	−102810.	−	178072.i	−0.359193	−	0.622140i
$536$		0			0
$537$	−79458.5	−	201796.i	−0.275544	−	0.699783i
$538$		0			0
$539$		−	228860.i		−	0.787756i
$540$		0			0
$541$	1167.97			0.00399060			0.00199530	−	0.999998i	$-0.499365\pi$
$541$	1167.97			0.00399060			0.00199530	+	0.999998i	$0.499365\pi$
$542$		0			0
$543$	−86062.4	+	33887.7i	−0.291886	+	0.114932i
$544$		0			0
$545$	−128367.	+	74112.9i	−0.432177	+	0.249518i
$546$		0			0
$547$	138903.	−	240586.i	0.464232	−	0.804074i	−0.534934	−	0.844894i	$-0.679664\pi$
$547$	138903.	−	240586.i	0.464232	−	0.804074i	0.999167	+	0.0408196i	$0.0129969\pi$
$548$		0			0
$549$	20588.9	+	89288.4i	0.0683105	+	0.296244i
$550$		0			0
$551$	796669.	+	459957.i	2.62407	+	1.51501i
$552$		0			0
$553$	−43819.3	−	75897.3i	−0.143290	−	0.248185i
$554$		0			0
$555$	−38756.1	+	48709.8i	−0.125821	+	0.158136i
$556$		0			0
$557$		−	127126.i		−	0.409755i	−0.978788	−	0.204877i	$-0.934320\pi$
$557$		−	127126.i		−	0.409755i	0.978788	−	0.204877i	$-0.0656795\pi$
$558$		0			0
$559$	67448.9			0.215850
$560$		0			0
$561$	−47435.1	+	317107.i	−0.150721	+	1.00758i
$562$		0			0
$563$	−107207.	+	61896.1i	−0.338226	+	0.195275i	−0.659487	−	0.751716i	$-0.729227\pi$
$563$	−107207.	+	61896.1i	−0.338226	+	0.195275i	0.321261	+	0.946991i	$0.395893\pi$
$564$		0			0
$565$	4326.91	−	7494.43i	0.0135544	−	0.0234770i
$566$		0			0
$567$	77667.6	+	52447.5i	0.241587	+	0.163139i
$568$		0			0
$569$	53531.2	+	30906.3i	0.165342	+	0.0954601i	0.580388	−	0.814340i	$-0.302901\pi$
$569$	53531.2	+	30906.3i	0.165342	+	0.0954601i	−0.415046	+	0.909801i	$0.636234\pi$
$570$		0			0
$571$	−102067.	−	176786.i	−0.313050	−	0.542219i	0.665971	−	0.745978i	$-0.268018\pi$
$571$	−102067.	−	176786.i	−0.313050	−	0.542219i	−0.979021	+	0.203759i	$0.934684\pi$
$572$		0			0
$573$	−311805.	−	46641.9i	−0.949671	−	0.142058i
$574$		0			0
$575$			282745.i			0.855182i
$576$		0			0
$577$	555504.			1.66854			0.834269	−	0.551358i	$-0.185890\pi$
$577$	555504.			1.66854			0.834269	+	0.551358i	$0.185890\pi$
$578$		0			0
$579$	36907.8	+	29365.8i	0.110093	+	0.0875960i
$580$		0			0
$581$	92899.9	−	53635.8i	0.275209	−	0.158892i
$582$		0			0
$583$	−274567.	+	475563.i	−0.807813	+	1.39917i
$584$		0			0
$585$	−72932.0	+	16817.3i	−0.213111	+	0.0491410i
$586$		0			0
$587$	−6076.70	−	3508.38i	−0.0176357	−	0.0101820i	0.491156	−	0.871071i	$-0.336574\pi$
$587$	−6076.70	−	3508.38i	−0.0176357	−	0.0101820i	−0.508792	+	0.860890i	$0.669908\pi$
$588$		0			0
$589$	363414.	+	629451.i	1.04754	+	1.81439i
$590$		0			0
$591$	−139881.	−	355246.i	−0.400482	−	1.01708i
$592$		0			0
$593$		−	77064.9i		−	0.219153i	−0.993978	−	0.109576i	$-0.965051\pi$
$593$		−	77064.9i		−	0.219153i	0.993978	−	0.109576i	$-0.0349494\pi$
$594$		0			0
$595$	−59998.4			−0.169475
$596$		0			0
$597$	261861.	−	103110.i	0.734721	−	0.289302i
$598$		0			0
$599$	−473683.	+	273481.i	−1.32018	+	0.762208i	−0.983757	−	0.179503i	$-0.942551\pi$
$599$	−473683.	+	273481.i	−1.32018	+	0.762208i	−0.336425	+	0.941710i	$0.609218\pi$
$600$		0			0
$601$	269988.	−	467633.i	0.747473	−	1.29466i	−0.201558	−	0.979477i	$-0.564600\pi$
$601$	269988.	−	467633.i	0.747473	−	1.29466i	0.949030	−	0.315184i	$-0.102066\pi$
$602$		0			0
$603$	−104782.	−	32065.6i	−0.288173	−	0.0881870i
$604$		0			0
$605$	−40306.2	−	23270.8i	−0.110119	−	0.0635770i
$606$		0			0
$607$	249663.	+	432429.i	0.677606	+	1.17365i	0.975700	+	0.219111i	$0.0703157\pi$
$607$	249663.	+	432429.i	0.677606	+	1.17365i	−0.298094	+	0.954536i	$0.596351\pi$
$608$		0			0
$609$	104245.	−	131019.i	0.281075	−	0.353263i
$610$		0			0
$611$			32393.8i			0.0867719i
$612$		0			0
$613$	80551.4			0.214364			0.107182	−	0.994239i	$-0.465817\pi$
$613$	80551.4			0.214364			0.107182	+	0.994239i	$0.465817\pi$
$614$		0			0
$615$	−1621.31	+	10838.6i	−0.00428662	+	0.0286564i
$616$		0			0
$617$	385247.	−	222423.i	1.01197	−	0.584263i	0.100205	−	0.994967i	$-0.468050\pi$
$617$	385247.	−	222423.i	1.01197	−	0.584263i	0.911769	+	0.410703i	$0.134717\pi$
$618$		0			0
$619$	280471.	−	485789.i	0.731992	−	1.26785i	−0.224039	−	0.974580i	$-0.571924\pi$
$619$	280471.	−	485789.i	0.731992	−	1.26785i	0.956031	−	0.293267i	$-0.0947423\pi$
$620$		0			0
$621$	33934.4	+	433385.i	0.0879947	+	1.12380i
$622$		0			0
$623$	107890.	+	62290.6i	0.277976	+	0.160489i
$624$		0			0
$625$	−65272.6	−	113055.i	−0.167098	−	0.289422i
$626$		0			0
$627$	654923.	+	97967.8i	1.66592	+	0.249200i
$628$		0			0
$629$			192590.i			0.486780i
$630$		0			0
$631$	−621772.			−1.56161			−0.780805	−	0.624775i	$-0.785191\pi$
$631$	−621772.			−1.56161			−0.780805	+	0.624775i	$0.785191\pi$
$632$		0			0
$633$	219201.	+	174408.i	0.547060	+	0.435270i
$634$		0			0
$635$	170715.	−	98562.4i	0.423374	−	0.244435i
$636$		0			0
$637$	82643.9	−	143144.i	0.203672	−	0.352771i
$638$		0			0
$639$	313763.	+	336649.i	0.768423	+	0.824471i
$640$		0			0
$641$	−279418.	−	161322.i	−0.680045	−	0.392624i	0.119827	−	0.992795i	$-0.461766\pi$
$641$	−279418.	−	161322.i	−0.680045	−	0.392624i	−0.799872	+	0.600171i	$0.795099\pi$
$642$		0			0
$643$	−244906.	−	424190.i	−0.592350	−	1.02598i	−0.993915	−	0.110149i	$-0.964867\pi$
$643$	−244906.	−	424190.i	−0.592350	−	1.02598i	0.401565	−	0.915830i	$-0.368466\pi$
$644$		0			0
$645$	−36307.3	−	92207.3i	−0.0872718	−	0.221639i
$646$		0			0
$647$		−	26885.7i		−	0.0642263i	−0.999484	−	0.0321132i	$-0.989776\pi$
$647$		−	26885.7i		−	0.0642263i	0.999484	−	0.0321132i	$-0.0102237\pi$
$648$		0			0
$649$	−587446.			−1.39469
$650$		0			0
$651$	123089.	−	48467.1i	0.290440	−	0.114363i
$652$		0			0
$653$	−618540.	+	357114.i	−1.45058	+	0.837492i	−0.998514	−	0.0544925i	$-0.982646\pi$
$653$	−618540.	+	357114.i	−1.45058	+	0.837492i	−0.452065	+	0.891985i	$0.649313\pi$
$654$		0			0
$655$	95211.2	−	164911.i	0.221925	−	0.384385i
$656$		0			0
$657$	251033.	−	233967.i	0.581568	−	0.542032i
$658$		0			0
$659$	−203254.	−	117349.i	−0.468024	−	0.270214i	0.247388	−	0.968916i	$-0.420428\pi$
$659$	−203254.	−	117349.i	−0.468024	−	0.270214i	−0.715412	+	0.698703i	$0.753761\pi$
$660$		0			0
$661$	−313281.	−	542619.i	−0.717020	−	1.24191i	−0.962175	−	0.272431i	$-0.912172\pi$
$661$	−313281.	−	542619.i	−0.717020	−	1.24191i	0.245155	−	0.969484i	$-0.421161\pi$
$662$		0			0
$663$	−144180.	+	181210.i	−0.328004	+	0.412245i
$664$		0			0
$665$			123915.i			0.280208i
$666$		0			0
$667$	776630.			1.74567
$668$		0			0
$669$	−21340.6	+	142664.i	−0.0476821	+	0.318758i
$670$		0			0
$671$	102055.	−	58921.7i	0.226668	−	0.130867i
$672$		0			0
$673$	−320999.	+	555987.i	−0.708718	+	1.22754i	0.256614	+	0.966514i	$0.417393\pi$
$673$	−320999.	+	555987.i	−0.708718	+	1.22754i	−0.965333	+	0.261022i	$0.915940\pi$
$674$		0			0
$675$	−195670.	−	284945.i	−0.429454	−	0.625393i
$676$		0			0
$677$	568932.	+	328473.i	1.24132	+	0.716675i	0.969362	−	0.245635i	$-0.0789964\pi$
$677$	568932.	+	328473.i	1.24132	+	0.716675i	0.271955	+	0.962310i	$0.412330\pi$
$678$		0			0
$679$	−38861.9	−	67310.9i	−0.0842917	−	0.145998i
$680$		0			0
$681$	601072.	+	89912.5i	1.29608	+	0.193877i
$682$		0			0
$683$			76710.6i			0.164442i	0.996614	+	0.0822212i	$0.0262014\pi$
$683$			76710.6i			0.164442i	−0.996614	+	0.0822212i	$0.973799\pi$
$684$		0			0
$685$	−10938.4			−0.0233117
$686$		0			0
$687$	549796.	+	437447.i	1.16490	+	0.926856i
$688$		0			0
$689$	−343463.	+	198299.i	−0.723505	+	0.417716i
$690$		0			0
$691$	−285435.	+	494387.i	−0.597793	+	1.03541i	0.395354	+	0.918529i	$0.370622\pi$
$691$	−285435.	+	494387.i	−0.597793	+	1.03541i	−0.993146	+	0.116878i	$0.962711\pi$
$692$		0			0
$693$	35269.1	−	115251.i	0.0734393	−	0.239981i
$694$		0			0
$695$	99537.6	+	57468.1i	0.206071	+	0.118975i
$696$		0			0
$697$	16953.7	+	29364.6i	0.0348978	+	0.0604447i
$698$		0			0
$699$	−201817.	−	512542.i	−0.413051	−	1.04900i
$700$		0			0
$701$		−	4271.71i		−	0.00869292i	−0.999991	−	0.00434646i	$-0.998616\pi$
$701$		−	4271.71i		−	0.00869292i	0.999991	−	0.00434646i	$-0.00138353\pi$
$702$		0			0
$703$	397757.			0.804835
$704$		0			0
$705$	44284.5	−	17437.3i	0.0890992	−	0.0350834i
$706$		0			0
$707$	−92562.7	+	53441.1i	−0.185181	+	0.106914i
$708$		0			0
$709$	−74221.7	+	128556.i	−0.147652	+	0.255740i	−0.930359	−	0.366650i	$-0.880505\pi$
$709$	−74221.7	+	128556.i	−0.147652	+	0.255740i	0.782707	+	0.622390i	$0.213838\pi$
$710$		0			0
$711$	111665.	+	484262.i	0.220891	+	0.957946i
$712$		0			0
$713$	531408.	+	306809.i	1.04532	+	0.603516i
$714$		0			0
$715$	48128.1	+	83360.3i	0.0941427	+	0.163060i
$716$		0			0
$717$	241822.	−	303928.i	0.470389	−	0.591198i
$718$		0			0
$719$		−	549881.i		−	1.06368i	−0.846845	−	0.531840i	$-0.821501\pi$
$719$		−	549881.i		−	1.06368i	0.846845	−	0.531840i	$-0.178499\pi$
$720$		0			0
$721$	−193928.			−0.373052
$722$		0			0
$723$	−74838.6	+	500302.i	−0.143169	+	0.957096i
$724$		0			0
$725$	−534800.	+	308767.i	−1.01746	+	0.587429i
$726$		0			0
$727$	322003.	−	557726.i	0.609244	−	1.05524i	−0.382121	−	0.924112i	$-0.624806\pi$
$727$	322003.	−	557726.i	0.609244	−	1.05524i	0.991365	−	0.131130i	$-0.0418605\pi$
$728$		0			0
$729$	−334117.	−	413274.i	−0.628701	−	0.777647i
$730$		0			0
$731$	−265528.	−	153303.i	−0.496908	−	0.286890i
$732$		0			0
$733$	−416415.	−	721253.i	−0.775031	−	1.34239i	−0.934777	−	0.355234i	$-0.884401\pi$
$733$	−416415.	−	721253.i	−0.775031	−	1.34239i	0.159747	−	0.987158i	$-0.448932\pi$
$734$		0			0
$735$	−240174.	−	35926.8i	−0.444581	−	0.0665035i
$736$		0			0
$737$			140925.i			0.259449i
$738$		0			0
$739$	−472487.			−0.865170			−0.432585	−	0.901593i	$-0.642398\pi$
$739$	−472487.			−0.865170			−0.432585	+	0.901593i	$0.642398\pi$
$740$		0			0
$741$	374253.	+	297776.i	0.681599	+	0.542316i
$742$		0			0
$743$	−847338.	+	489211.i	−1.53490	+	0.886173i	−0.535771	+	0.844363i	$0.679979\pi$
$743$	−847338.	+	489211.i	−1.53490	+	0.886173i	−0.999126	+	0.0418100i	$0.986688\pi$
$744$		0			0
$745$	249749.	−	432577.i	0.449977	−	0.779383i
$746$		0			0
$747$	−592746.	+	136680.i	−1.06225	+	0.244943i
$748$		0			0
$749$	207101.	+	119570.i	0.369163	+	0.213136i
$750$		0			0
$751$	−83140.6	−	144004.i	−0.147412	−	0.255325i	0.782858	−	0.622200i	$-0.213761\pi$
$751$	−83140.6	−	144004.i	−0.147412	−	0.255325i	−0.930270	+	0.366875i	$0.880428\pi$
$752$		0			0
$753$	−51899.1	−	131805.i	−0.0915313	−	0.232456i
$754$		0			0
$755$			306733.i			0.538105i
$756$		0			0
$757$	−238453.			−0.416114			−0.208057	−	0.978117i	$-0.566714\pi$
$757$	−238453.			−0.416114			−0.208057	+	0.978117i	$0.566714\pi$
$758$		0			0
$759$	520191.	−	204829.i	0.902982	−	0.355556i
$760$		0			0
$761$	−518174.	+	299168.i	−0.894759	+	0.516589i	−0.875496	−	0.483225i	$-0.839465\pi$
$761$	−518174.	+	299168.i	−0.894759	+	0.516589i	−0.0192628	+	0.999814i	$0.506132\pi$
$762$		0			0
$763$	86194.6	−	149294.i	0.148058	−	0.256444i
$764$		0			0
$765$	325338.	+	99560.3i	0.555919	+	0.170123i
$766$		0			0
$767$	−367426.	−	212134.i	−0.624568	−	0.360594i
$768$		0			0
$769$	−333662.	−	577919.i	−0.564227	−	0.977270i	−0.997121	−	0.0758248i	$-0.975841\pi$
$769$	−333662.	−	577919.i	−0.564227	−	0.977270i	0.432894	−	0.901445i	$-0.357492\pi$
$770$		0			0
$771$	329266.	−	413831.i	0.553909	−	0.696169i
$772$		0			0
$773$		−	848153.i		−	1.41943i	−0.704487	−	0.709717i	$-0.748823\pi$
$773$		−	848153.i		−	1.41943i	0.704487	−	0.709717i	$-0.251177\pi$
$774$		0			0
$775$	−487916.			−0.812347
$776$		0			0
$777$	10710.1	−	71597.7i	0.0177399	−	0.118592i
$778$		0			0
$779$	60646.7	−	35014.4i	0.0999384	−	0.0576995i
$780$		0			0
$781$	295919.	−	512547.i	0.485145	−	0.840295i
$782$		0			0
$783$	−782673.	+	537457.i	−1.27661	+	0.876639i
$784$		0			0
$785$	350134.	+	202150.i	0.568192	+	0.328046i
$786$		0			0
$787$	−483866.	−	838081.i	−0.781225	−	1.35312i	−0.931229	−	0.364436i	$-0.881262\pi$
$787$	−483866.	−	838081.i	−0.781225	−	1.35312i	0.150004	−	0.988685i	$-0.452071\pi$
$788$		0			0
$789$	839706.	+	125609.i	1.34888	+	0.201775i
$790$		0			0
$791$			10064.6i			0.0160858i
$792$		0			0
$793$	85109.3			0.135341
$794$		0			0
$795$	455972.	+	362795.i	0.721446	+	0.574020i
$796$		0			0
$797$	−583828.	+	337073.i	−0.919111	+	0.530649i	−0.883351	−	0.468711i	$-0.844718\pi$
$797$	−583828.	+	337073.i	−0.919111	+	0.530649i	−0.0357599	+	0.999360i	$0.511385\pi$
$798$		0			0
$799$	73627.0	−	127526.i	0.115330	−	0.199758i
$800$		0			0
$801$	−481666.	−	516798.i	−0.750725	−	0.805482i
$802$		0			0
$803$	−382197.	−	220662.i	−0.592729	−	0.342212i
$804$		0			0
$805$	52307.0	+	90598.4i	0.0807176	+	0.139807i
$806$		0			0
$807$	−263075.	−	668115.i	−0.403955	−	1.02590i
$808$		0			0
$809$		−	570317.i		−	0.871403i	−0.900091	−	0.435702i	$-0.856500\pi$
$809$		−	570317.i		−	0.871403i	0.900091	−	0.435702i	$-0.143500\pi$
$810$		0			0
$811$	111731.			0.169876			0.0849379	−	0.996386i	$-0.472931\pi$
$811$	111731.			0.169876			0.0849379	+	0.996386i	$0.472931\pi$
$812$		0			0
$813$	−642109.	+	252835.i	−0.971466	+	0.382522i
$814$		0			0
$815$	−146743.	+	84722.1i	−0.220923	+	0.127550i
$816$		0			0
$817$	−316617.	+	548396.i	−0.474340	+	0.821581i
$818$		0			0
$819$	63678.0	−	59349.0i	0.0949339	−	0.0884801i
$820$		0			0
$821$	−902069.	−	520810.i	−1.33830	−	0.772668i	−0.351744	−	0.936096i	$-0.614411\pi$
$821$	−902069.	−	520810.i	−1.33830	−	0.772668i	−0.986555	+	0.163429i	$0.947745\pi$
$822$		0			0
$823$	−54486.5	−	94373.5i	−0.0804432	−	0.139332i	0.822997	−	0.568045i	$-0.192300\pi$
$823$	−54486.5	−	94373.5i	−0.0804432	−	0.139332i	−0.903440	+	0.428714i	$0.858967\pi$
$824$		0			0
$825$	−276778.	+	347862.i	−0.406652	+	0.511093i
$826$		0			0
$827$			550908.i			0.805505i	0.915309	+	0.402753i	$0.131947\pi$
$827$			550908.i			0.805505i	−0.915309	+	0.402753i	$0.868053\pi$
$828$		0			0
$829$	−57256.0			−0.0833128			−0.0416564	−	0.999132i	$-0.513263\pi$
$829$	−57256.0			−0.0833128			−0.0416564	+	0.999132i	$0.513263\pi$
$830$		0			0
$831$	150663.	−	1.00720e6i	0.218175	−	1.45852i
$832$		0			0
$833$	−650695.	+	375679.i	−0.937751	+	0.541411i
$834$		0			0
$835$	−69591.6	+	120536.i	−0.0998122	+	0.172880i
$836$		0			0
$837$	−747867.	+	58558.5i	−1.06751	+	0.0835871i
$838$		0			0
$839$	824201.	+	475853.i	1.17087	+	0.676003i	0.953885	−	0.300172i	$-0.0970439\pi$
$839$	824201.	+	475853.i	1.17087	+	0.676003i	0.216986	+	0.976175i	$0.430377\pi$
$840$		0			0
$841$	494467.	+	856442.i	0.699110	+	1.21089i
$842$		0			0
$843$	859385.	+	128553.i	1.20930	+	0.180895i
$844$		0			0
$845$		−	281264.i		−	0.393914i
$846$		0			0
$847$	54128.7			0.0754502
$848$		0			0
$849$	−215064.	−	171117.i	−0.298369	−	0.237398i
$850$		0			0
$851$	290814.	−	167901.i	0.401565	−	0.231844i
$852$		0			0
$853$	511433.	−	885829.i	0.702896	−	1.21745i	−0.264550	−	0.964372i	$-0.585223\pi$
$853$	511433.	−	885829.i	0.702896	−	1.21745i	0.967446	−	0.253079i	$-0.0814434\pi$
$854$		0			0
$855$	205622.	−	671921.i	0.281279	−	0.919149i
$856$		0			0
$857$	572818.	+	330717.i	0.779929	+	0.450292i	0.836405	−	0.548112i	$-0.184653\pi$
$857$	572818.	+	330717.i	0.779929	+	0.450292i	−0.0564763	+	0.998404i	$0.517987\pi$
$858$		0			0
$859$	51374.6	+	88983.5i	0.0696246	+	0.120593i	0.898736	−	0.438490i	$-0.144487\pi$
$859$	51374.6	+	88983.5i	0.0696246	+	0.120593i	−0.829112	+	0.559083i	$0.811153\pi$
$860$		0			0
$861$	−4669.74	−	11859.4i	−0.00629921	−	0.0159977i
$862$		0			0
$863$		−	168806.i		−	0.226655i	−0.993558	−	0.113328i	$-0.963849\pi$
$863$		−	168806.i		−	0.226655i	0.993558	−	0.113328i	$-0.0361509\pi$
$864$		0			0
$865$	−481087.			−0.642971
$866$		0			0
$867$	280046.	−	110270.i	0.372556	−	0.146697i
$868$		0			0
$869$	553504.	−	319566.i	0.732962	−	0.423176i
$870$		0			0
$871$	−50889.6	+	88143.4i	−0.0670800	+	0.116186i
$872$		0			0
$873$	99032.1	+	429476.i	0.129941	+	0.563521i
$874$		0			0
$875$	−166996.	−	96415.2i	−0.218117	−	0.125930i
$876$		0			0
$877$	95077.8	+	164680.i	0.123618	+	0.214112i	0.921192	−	0.389109i	$-0.127217\pi$
$877$	95077.8	+	164680.i	0.123618	+	0.214112i	−0.797574	+	0.603221i	$0.793884\pi$
$878$		0			0
$879$	−22720.6	+	28556.0i	−0.0294065	+	0.0369589i
$880$		0			0
$881$		−	171490.i		−	0.220946i	−0.993879	−	0.110473i	$-0.964763\pi$
$881$		−	171490.i		−	0.220946i	0.993879	−	0.110473i	$-0.0352366\pi$
$882$		0			0
$883$	−869284.			−1.11491			−0.557456	−	0.830207i	$-0.688222\pi$
$883$	−869284.			−1.11491			−0.557456	+	0.830207i	$0.688222\pi$
$884$		0			0
$885$	−92218.4	+	616487.i	−0.117742	+	0.787114i
$886$		0			0
$887$	−125013.	+	72176.4i	−0.158894	+	0.0917378i	−0.577339	−	0.816505i	$-0.695909\pi$
$887$	−125013.	+	72176.4i	−0.158894	+	0.0917378i	0.418444	+	0.908242i	$0.362575\pi$
$888$		0			0
$889$	−114630.	+	198545.i	−0.145042	+	0.251220i
$890$		0			0
$891$	−382490.	+	566415.i	−0.481797	+	0.713475i
$892$		0			0
$893$	−263379.	−	152062.i	−0.330277	−	0.190686i
$894$		0			0
$895$	147980.	+	256309.i	0.184739	+	0.319977i
$896$		0			0
$897$	399327.	+	59734.0i	0.496299	+	0.0742398i
$898$		0			0
$899$			1.34018e6i			1.65823i
$900$		0			0
$901$	1.80283e6			2.22078
$902$		0			0
$903$	90188.1	+	71758.4i	0.110605	+	0.0880030i
$904$		0			0
$905$	109312.	−	63111.1i	0.133466	−	0.0770563i
$906$		0			0
$907$	53848.5	−	93268.3i	0.0654574	−	0.113376i	−0.831439	−	0.555615i	$-0.812483\pi$
$907$	53848.5	−	93268.3i	0.0654574	−	0.113376i	0.896897	+	0.442240i	$0.145816\pi$
$908$		0			0
$909$	590595.	−	136184.i	0.714763	−	0.164816i
$910$		0			0
$911$	617457.	+	356489.i	0.743994	+	0.429545i	0.823520	−	0.567287i	$-0.192007\pi$
$911$	617457.	+	356489.i	0.743994	+	0.429545i	−0.0795255	+	0.996833i	$0.525341\pi$
$912$		0			0
$913$	391155.	+	677501.i	0.469253	+	0.812771i
$914$		0			0
$915$	−45813.7	−	116350.i	−0.0547209	−	0.138971i
$916$		0			0
$917$			221465.i			0.263370i
$918$		0			0
$919$	−239512.			−0.283594			−0.141797	−	0.989896i	$-0.545288\pi$
$919$	−239512.			−0.283594			−0.141797	+	0.989896i	$0.545288\pi$
$920$		0			0
$921$	370956.	−	146066.i	0.437324	−	0.172199i
$922$		0			0
$923$	370174.	−	213720.i	0.434512	−	0.250866i
$924$		0			0
$925$	−133506.	+	231239.i	−0.156033	+	0.270258i
$926$		0			0
$927$	1.05156e6	+	321801.i	1.22370	+	0.374479i
$928$		0			0
$929$	1.11204e6	+	642036.i	1.28851	+	0.743923i	0.978389	−	0.206774i	$-0.0662964\pi$
$929$	1.11204e6	+	642036.i	1.28851	+	0.743923i	0.310123	+	0.950696i	$0.399630\pi$
$930$		0			0
$931$	775890.	+	1.34388e6i	0.895160	+	1.55046i
$932$		0			0
$933$	−532841.	+	669691.i	−0.612117	+	0.769327i
$934$		0			0
$935$		−	437557.i		−	0.500508i
$936$		0			0
$937$	−471000.			−0.536466			−0.268233	−	0.963354i	$-0.586440\pi$
$937$	−471000.			−0.536466			−0.268233	+	0.963354i	$0.586440\pi$
$938$		0			0
$939$	−227111.	+	1.51826e6i	−0.257577	+	1.72192i
$940$		0			0
$941$	624803.	−	360730.i	0.705608	−	0.407383i	−0.103825	−	0.994596i	$-0.533108\pi$
$941$	624803.	−	360730.i	0.705608	−	0.407383i	0.809433	+	0.587212i	$0.199775\pi$
$942$		0			0
$943$	29560.6	−	51200.5i	0.0332422	−	0.0575772i
$944$		0			0
$945$	−115412.	−	55105.0i	−0.129237	−	0.0617060i
$946$		0			0
$947$	524423.	+	302776.i	0.584766	+	0.337615i	0.763025	−	0.646369i	$-0.223713\pi$
$947$	524423.	+	302776.i	0.584766	+	0.337615i	−0.178259	+	0.983984i	$0.557047\pi$
$948$		0			0
$949$	−159367.	−	276032.i	−0.176956	−	0.306497i
$950$		0			0
$951$	−1.08590e6	−	162437.i	−1.20069	−	0.179607i
$952$		0			0
$953$		−	527043.i		−	0.580310i	−0.956980	−	0.290155i	$-0.906293\pi$
$953$		−	527043.i		−	0.580310i	0.956980	−	0.290155i	$-0.0937069\pi$
$954$		0			0
$955$	430240.			0.471741
$956$		0			0
$957$	955493.	+	760240.i	1.04329	+	0.830094i
$958$		0			0
$959$	11017.2	−	6360.79i	0.0119794	−	0.00691630i
$960$		0			0
$961$	−67681.6	+	117228.i	−0.0732865	+	0.126936i
$962$		0			0
$963$	−924580.	−	992019.i	−0.996993	−	1.06971i
$964$		0			0
$965$	−55740.7	−	32181.9i	−0.0598574	−	0.0345587i
$966$		0			0
$967$	−620154.	−	1.07414e6i	−0.663203	−	1.14870i	−0.979769	−	0.200131i	$-0.935863\pi$
$967$	−620154.	−	1.07414e6i	−0.663203	−	1.14870i	0.316566	−	0.948571i	$-0.397470\pi$
$968$		0			0
$969$	−796529.	−	2.02290e6i	−0.848309	−	2.15440i
$970$		0			0
$971$		−	1.27298e6i		−	1.35015i	−0.737748	−	0.675076i	$-0.764111\pi$
$971$		−	1.27298e6i		−	1.35015i	0.737748	−	0.675076i	$-0.235889\pi$
$972$		0			0
$973$	−133673.			−0.141194
$974$		0			0
$975$	−298732.	+	117628.i	−0.314248	+	0.123737i
$976$		0			0
$977$	1.19918e6	−	692344.i	1.25630	−	0.725325i	0.283947	−	0.958840i	$-0.408356\pi$
$977$	1.19918e6	−	692344.i	1.25630	−	0.725325i	0.972353	+	0.233515i	$0.0750227\pi$
$978$		0			0
$979$	−454273.	+	786824.i	−0.473971	+	0.820942i
$980$		0			0
$981$	−715120.	+	666505.i	−0.743089	+	0.692573i
$982$		0			0
$983$	146384.	+	84514.9i	0.151491	+	0.0874633i	0.573829	−	0.818975i	$-0.305457\pi$
$983$	146384.	+	84514.9i	0.151491	+	0.0874633i	−0.422338	+	0.906438i	$0.638791\pi$
$984$		0			0
$985$	260508.	+	451213.i	0.268503	+	0.465061i
$986$		0			0
$987$	−34463.5	+	43314.8i	−0.0353774	+	0.0444633i
$988$		0			0
$989$			534602.i			0.546560i
$990$		0			0
$991$	1.57481e6			1.60354			0.801772	−	0.597630i	$-0.203891\pi$
$991$	1.57481e6			1.60354			0.801772	+	0.597630i	$0.203891\pi$
$992$		0			0
$993$	126775.	−	847498.i	0.128568	−	0.859489i
$994$		0			0
$995$	−332601.	+	192027.i	−0.335952	+	0.193962i
$996$		0			0
$997$	−285374.	+	494282.i	−0.287094	+	0.497261i	−0.973115	−	0.230321i	$-0.926022\pi$
$997$	−285374.	+	494282.i	−0.287094	+	0.497261i	0.686021	+	0.727582i	$0.259356\pi$
$998$		0			0
$999$	−176883.	+	370462.i	−0.177237	+	0.371204i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.5.q.c.65.1		8
3.2	odd	2		432.5.q.c.305.2		8
4.3	odd	2		36.5.g.a.29.4	yes	8
9.2	odd	6		1296.5.e.g.161.3		8
9.4	even	3		432.5.q.c.17.2		8
9.5	odd	6	inner	144.5.q.c.113.1		8
9.7	even	3		1296.5.e.g.161.6		8
12.11	even	2		108.5.g.a.89.2		8
36.7	odd	6		324.5.c.a.161.6		8
36.11	even	6		324.5.c.a.161.3		8
36.23	even	6		36.5.g.a.5.4	✓	8
36.31	odd	6		108.5.g.a.17.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.5.g.a.5.4	✓	8	36.23	even	6
36.5.g.a.29.4	yes	8	4.3	odd	2
108.5.g.a.17.2		8	36.31	odd	6
108.5.g.a.89.2		8	12.11	even	2
144.5.q.c.65.1		8	1.1	even	1	trivial
144.5.q.c.113.1		8	9.5	odd	6	inner
324.5.c.a.161.3		8	36.11	even	6
324.5.c.a.161.6		8	36.7	odd	6
432.5.q.c.17.2		8	9.4	even	3
432.5.q.c.305.2		8	3.2	odd	2
1296.5.e.g.161.3		8	9.2	odd	6
1296.5.e.g.161.6		8	9.7	even	3

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:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	144.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-8.37420 + 3.29740i) q^{3} +(10.6364 - 6.14094i) q^{5} +(-7.14202 + 12.3703i) q^{7} +(59.2543 - 55.2261i) q^{9} +O(q^{10})\)	\(q+(-8.37420 + 3.29740i) q^{3} +(10.6364 - 6.14094i) q^{5} +(-7.14202 + 12.3703i) q^{7} +(59.2543 - 55.2261i) q^{9} +(-90.2145 - 52.0854i) q^{11} +(-37.6173 - 65.1551i) q^{13} +(-68.8224 + 86.4980i) q^{15} +341.998i q^{17} +706.329 q^{19} +(19.0187 - 127.142i) q^{21} +(516.421 - 298.156i) q^{23} +(-237.078 + 410.630i) q^{25} +(-314.105 + 657.860i) q^{27} +(1127.90 + 651.194i) q^{29} +(514.510 + 891.158i) q^{31} +(927.221 + 138.700i) q^{33} +175.435i q^{35} +563.132 q^{37} +(529.857 + 421.582i) q^{39} +(85.8619 - 49.5724i) q^{41} +(-448.257 + 776.404i) q^{43} +(291.114 - 951.286i) q^{45} +(-372.885 - 215.285i) q^{47} +(1098.48 + 1902.63i) q^{49} +(-1127.70 - 2863.96i) q^{51} -5271.47i q^{53} -1279.41 q^{55} +(-5914.94 + 2329.05i) q^{57} +(4883.74 - 2819.63i) q^{59} +(-565.626 + 979.693i) q^{61} +(259.971 + 1127.42i) q^{63} +(-800.227 - 462.012i) q^{65} +(-676.412 - 1171.58i) q^{67} +(-3341.48 + 4199.66i) q^{69} +5681.42i q^{71} +4236.54 q^{73} +(631.322 - 4220.44i) q^{75} +(1288.63 - 743.990i) q^{77} +(-3067.71 + 5313.43i) q^{79} +(461.150 - 6544.77i) q^{81} +(-6503.75 - 3754.94i) q^{83} +(2100.19 + 3637.64i) q^{85} +(-11592.5 - 1734.09i) q^{87} -8721.70i q^{89} +1074.65 q^{91} +(-7247.12 - 5766.19i) q^{93} +(7512.81 - 4337.53i) q^{95} +(-2720.65 + 4712.31i) q^{97} +(-8222.08 + 1895.92i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 9 q^{3} - 9 q^{5} - 13 q^{7} + 21 q^{9}+O(q^{10}) \) 8 * q + 9 * q^3 - 9 * q^5 - 13 * q^7 + 21 * q^9	\( 8 q + 9 q^{3} - 9 q^{5} - 13 q^{7} + 21 q^{9} + 18 q^{11} - 5 q^{13} - 225 q^{15} - 562 q^{19} - 1167 q^{21} + 1719 q^{23} + 353 q^{25} - 648 q^{27} + 2115 q^{29} - 187 q^{31} + 3258 q^{33} + 16 q^{37} + 8265 q^{39} - 7920 q^{41} + 68 q^{43} + 5679 q^{45} - 13689 q^{47} - 327 q^{49} - 10449 q^{51} + 1818 q^{55} - 21861 q^{57} + 20052 q^{59} - 1937 q^{61} - 5559 q^{63} + 25965 q^{65} - 154 q^{67} + 21645 q^{69} - 7802 q^{73} + 30297 q^{75} - 25641 q^{77} + 2195 q^{79} + 19701 q^{81} - 37017 q^{83} - 3042 q^{85} - 22455 q^{87} - 15830 q^{91} - 36489 q^{93} + 37116 q^{95} + 7282 q^{97} + 10035 q^{99}+O(q^{100}) \) 8 * q + 9 * q^3 - 9 * q^5 - 13 * q^7 + 21 * q^9 + 18 * q^11 - 5 * q^13 - 225 * q^15 - 562 * q^19 - 1167 * q^21 + 1719 * q^23 + 353 * q^25 - 648 * q^27 + 2115 * q^29 - 187 * q^31 + 3258 * q^33 + 16 * q^37 + 8265 * q^39 - 7920 * q^41 + 68 * q^43 + 5679 * q^45 - 13689 * q^47 - 327 * q^49 - 10449 * q^51 + 1818 * q^55 - 21861 * q^57 + 20052 * q^59 - 1937 * q^61 - 5559 * q^63 + 25965 * q^65 - 154 * q^67 + 21645 * q^69 - 7802 * q^73 + 30297 * q^75 - 25641 * q^77 + 2195 * q^79 + 19701 * q^81 - 37017 * q^83 - 3042 * q^85 - 22455 * q^87 - 15830 * q^91 - 36489 * q^93 + 37116 * q^95 + 7282 * q^97 + 10035 * q^99

Introduction

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