LMFDB - Embedded newform 72.5.m.a.65.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [72,5,Mod(41,72)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(72, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

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

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

chi := DirichletCharacter("72.41");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 72 = 2^{3} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	72.m (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:	$7.44263734204$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			65.5
Character	$\chi$	$=$	72.65
Dual form			72.5.m.a.41.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.34380 - 7.24181i) q^{3} +(18.9074 - 10.9162i) q^{5} +(7.93787 - 13.7488i) q^{7} +(-23.8877 + 77.3975i) q^{9} +O(q^{10})$	\(q+(-5.34380 - 7.24181i) q^{3} +(18.9074 - 10.9162i) q^{5} +(7.93787 - 13.7488i) q^{7} +(-23.8877 + 77.3975i) q^{9} +(-184.457 - 106.496i) q^{11} +(-71.9110 - 124.553i) q^{13} +(-180.090 - 78.5897i) q^{15} +4.96583i q^{17} -497.110 q^{19} +(-141.985 + 15.9862i) q^{21} +(551.116 - 318.187i) q^{23} +(-74.1746 + 128.474i) q^{25} +(688.149 - 240.607i) q^{27} +(487.104 + 281.230i) q^{29} +(-579.112 - 1003.05i) q^{31} +(214.475 + 1904.90i) q^{33} -346.605i q^{35} -388.382 q^{37} +(-517.715 + 1186.35i) q^{39} +(1713.80 - 989.464i) q^{41} +(64.1305 - 111.077i) q^{43} +(393.232 + 1724.14i) q^{45} +(2045.72 + 1181.10i) q^{47} +(1074.48 + 1861.05i) q^{49} +(35.9616 - 26.5364i) q^{51} -2681.54i q^{53} -4650.13 q^{55} +(2656.45 + 3599.98i) q^{57} +(3491.73 - 2015.95i) q^{59} +(2588.86 - 4484.03i) q^{61} +(874.506 + 942.798i) q^{63} +(-2719.29 - 1569.98i) q^{65} +(-2281.03 - 3950.86i) q^{67} +(-5249.30 - 2290.75i) q^{69} +3869.31i q^{71} -6488.72 q^{73} +(1326.76 - 149.382i) q^{75} +(-2928.40 + 1690.71i) q^{77} +(-3464.60 + 6000.86i) q^{79} +(-5419.76 - 3697.69i) q^{81} +(4726.44 + 2728.81i) q^{83} +(54.2078 + 93.8907i) q^{85} +(-566.374 - 5030.35i) q^{87} -14432.9i q^{89} -2283.28 q^{91} +(-4169.25 + 9553.92i) q^{93} +(-9399.03 + 5426.53i) q^{95} +(7043.86 - 12200.3i) q^{97} +(12648.8 - 11732.6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{3} - 100 q^{9}+O(q^{10}) $ 24 * q + 4 * q^3 - 100 * q^9	$ 24 q + 4 q^{3} - 100 q^{9} + 252 q^{11} - 80 q^{15} - 408 q^{19} + 24 q^{21} + 720 q^{23} + 1500 q^{25} - 1280 q^{27} + 2376 q^{29} - 1104 q^{31} - 1412 q^{33} - 4184 q^{39} + 1980 q^{41} + 1476 q^{43} - 4696 q^{45} + 4536 q^{47} - 6084 q^{49} - 7828 q^{51} + 2544 q^{55} - 1204 q^{57} + 10332 q^{59} + 2784 q^{61} + 9072 q^{63} + 17280 q^{65} - 2604 q^{67} + 5680 q^{69} + 5112 q^{73} - 15412 q^{75} - 28368 q^{77} + 3480 q^{79} - 26548 q^{81} - 23400 q^{83} + 7392 q^{85} - 3192 q^{87} - 14208 q^{91} + 39488 q^{93} + 57528 q^{95} - 4020 q^{97} + 50744 q^{99}+O(q^{100}) $ 24 * q + 4 * q^3 - 100 * q^9 + 252 * q^11 - 80 * q^15 - 408 * q^19 + 24 * q^21 + 720 * q^23 + 1500 * q^25 - 1280 * q^27 + 2376 * q^29 - 1104 * q^31 - 1412 * q^33 - 4184 * q^39 + 1980 * q^41 + 1476 * q^43 - 4696 * q^45 + 4536 * q^47 - 6084 * q^49 - 7828 * q^51 + 2544 * q^55 - 1204 * q^57 + 10332 * q^59 + 2784 * q^61 + 9072 * q^63 + 17280 * q^65 - 2604 * q^67 + 5680 * q^69 + 5112 * q^73 - 15412 * q^75 - 28368 * q^77 + 3480 * q^79 - 26548 * q^81 - 23400 * q^83 + 7392 * q^85 - 3192 * q^87 - 14208 * q^91 + 39488 * q^93 + 57528 * q^95 - 4020 * q^97 + 50744 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/72\mathbb{Z}\right)^\times$.

$n$	$37$	$55$	$65$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−5.34380	−	7.24181i	−0.593755	−	0.804646i
$3$	−5.34380	−	7.24181i	−0.593755	−	0.804646i
$4$		0			0
$5$	18.9074	−	10.9162i	0.756294	−	0.436647i	−0.0716695	−	0.997428i	$-0.522833\pi$
$5$	18.9074	−	10.9162i	0.756294	−	0.436647i	0.827964	+	0.560782i	$0.189499\pi$
$6$		0			0
$7$	7.93787	−	13.7488i	0.161997	−	0.280588i	−0.773588	−	0.633689i	$-0.781540\pi$
$7$	7.93787	−	13.7488i	0.161997	−	0.280588i	0.935585	+	0.353102i	$0.114873\pi$
$8$		0			0
$9$	−23.8877	+	77.3975i	−0.294909	+	0.955525i
$10$		0			0
$11$	−184.457	−	106.496i	−1.52444	−	0.880136i	−0.999581	−	0.0289464i	$-0.990785\pi$
$11$	−184.457	−	106.496i	−1.52444	−	0.880136i	−0.524859	−	0.851189i	$-0.675882\pi$
$12$		0			0
$13$	−71.9110	−	124.553i	−0.425509	−	0.737003i	0.570959	−	0.820979i	$-0.306571\pi$
$13$	−71.9110	−	124.553i	−0.425509	−	0.737003i	−0.996468	+	0.0839758i	$0.973238\pi$
$14$		0			0
$15$	−180.090	−	78.5897i	−0.800400	−	0.349288i
$16$		0			0
$17$			4.96583i			0.0171828i	0.999963	+	0.00859140i	$0.00273476\pi$
$17$			4.96583i			0.0171828i	−0.999963	+	0.00859140i	$0.997265\pi$
$18$		0			0
$19$	−497.110			−1.37704			−0.688518	−	0.725219i	$-0.741738\pi$
$19$	−497.110			−1.37704			−0.688518	+	0.725219i	$0.741738\pi$
$20$		0			0
$21$	−141.985	+	15.9862i	−0.321961	+	0.0362499i
$22$		0			0
$23$	551.116	−	318.187i	1.04181	−	0.601488i	0.121463	−	0.992596i	$-0.461242\pi$
$23$	551.116	−	318.187i	1.04181	−	0.601488i	0.920345	+	0.391108i	$0.127908\pi$
$24$		0			0
$25$	−74.1746	+	128.474i	−0.118679	+	0.205559i
$26$		0			0
$27$	688.149	−	240.607i	0.943963	−	0.330051i
$28$		0			0
$29$	487.104	+	281.230i	0.579197	+	0.334399i	0.760814	−	0.648970i	$-0.224800\pi$
$29$	487.104	+	281.230i	0.579197	+	0.334399i	−0.181617	+	0.983369i	$0.558133\pi$
$30$		0			0
$31$	−579.112	−	1003.05i	−0.602613	−	1.04376i	−0.992424	−	0.122862i	$-0.960793\pi$
$31$	−579.112	−	1003.05i	−0.602613	−	1.04376i	0.389810	−	0.920895i	$-0.372541\pi$
$32$		0			0
$33$	214.475	+	1904.90i	0.196947	+	1.74922i
$34$		0			0
$35$		−	346.605i		−	0.282942i
$36$		0			0
$37$	−388.382			−0.283698			−0.141849	−	0.989888i	$-0.545305\pi$
$37$	−388.382			−0.283698			−0.141849	+	0.989888i	$0.545305\pi$
$38$		0			0
$39$	−517.715	+	1186.35i	−0.340378	+	0.779983i
$40$		0			0
$41$	1713.80	−	989.464i	1.01951	−	0.588616i	0.105550	−	0.994414i	$-0.466340\pi$
$41$	1713.80	−	989.464i	1.01951	−	0.588616i	0.913963	+	0.405798i	$0.133006\pi$
$42$		0			0
$43$	64.1305	−	111.077i	0.0346839	−	0.0600742i	−0.848162	−	0.529736i	$-0.822291\pi$
$43$	64.1305	−	111.077i	0.0346839	−	0.0600742i	0.882846	+	0.469662i	$0.155624\pi$
$44$		0			0
$45$	393.232	+	1724.14i	0.194189	+	0.851429i
$46$		0			0
$47$	2045.72	+	1181.10i	0.926085	+	0.534675i	0.885571	−	0.464504i	$-0.153767\pi$
$47$	2045.72	+	1181.10i	0.926085	+	0.534675i	0.0405136	+	0.999179i	$0.487101\pi$
$48$		0			0
$49$	1074.48	+	1861.05i	0.447514	+	0.775116i
$50$		0			0
$51$	35.9616	−	26.5364i	0.0138261	−	0.0102024i
$52$		0			0
$53$		−	2681.54i		−	0.954625i	−0.878734	−	0.477313i	$-0.841611\pi$
$53$		−	2681.54i		−	0.954625i	0.878734	−	0.477313i	$-0.158389\pi$
$54$		0			0
$55$	−4650.13			−1.53723
$56$		0			0
$57$	2656.45	+	3599.98i	0.817622	+	1.10803i
$58$		0			0
$59$	3491.73	−	2015.95i	1.00308	−	0.579129i	0.0939230	−	0.995579i	$-0.470059\pi$
$59$	3491.73	−	2015.95i	1.00308	−	0.579129i	0.909159	+	0.416450i	$0.136726\pi$
$60$		0			0
$61$	2588.86	−	4484.03i	0.695743	−	1.20506i	−0.274187	−	0.961676i	$-0.588409\pi$
$61$	2588.86	−	4484.03i	0.695743	−	1.20506i	0.969930	−	0.243385i	$-0.0782579\pi$
$62$		0			0
$63$	874.506	+	942.798i	0.220334	+	0.237541i
$64$		0			0
$65$	−2719.29	−	1569.98i	−0.643620	−	0.371594i
$66$		0			0
$67$	−2281.03	−	3950.86i	−0.508138	−	0.880120i	−0.999956	−	0.00942211i	$-0.997001\pi$
$67$	−2281.03	−	3950.86i	−0.508138	−	0.880120i	0.491818	−	0.870698i	$-0.336333\pi$
$68$		0			0
$69$	−5249.30	−	2290.75i	−1.10256	−	0.481149i
$70$		0			0
$71$			3869.31i			0.767569i	0.923423	+	0.383784i	$0.125379\pi$
$71$			3869.31i			0.767569i	−0.923423	+	0.383784i	$0.874621\pi$
$72$		0			0
$73$	−6488.72			−1.21762			−0.608812	−	0.793314i	$-0.708354\pi$
$73$	−6488.72			−1.21762			−0.608812	+	0.793314i	$0.708354\pi$
$74$		0			0
$75$	1326.76	−	149.382i	0.235868	−	0.0265567i
$76$		0			0
$77$	−2928.40	+	1690.71i	−0.493911	+	0.285159i
$78$		0			0
$79$	−3464.60	+	6000.86i	−0.555136	+	0.961523i	0.442757	+	0.896641i	$0.354000\pi$
$79$	−3464.60	+	6000.86i	−0.555136	+	0.961523i	−0.997893	+	0.0648815i	$0.979333\pi$
$80$		0			0
$81$	−5419.76	−	3697.69i	−0.826057	−	0.563587i
$82$		0			0
$83$	4726.44	+	2728.81i	0.686084	+	0.396111i	0.802144	−	0.597131i	$-0.203693\pi$
$83$	4726.44	+	2728.81i	0.686084	+	0.396111i	−0.116059	+	0.993242i	$0.537026\pi$
$84$		0			0
$85$	54.2078	+	93.8907i	0.00750281	+	0.0129953i
$86$		0			0
$87$	−566.374	−	5030.35i	−0.0748281	−	0.664600i
$88$		0			0
$89$		−	14432.9i		−	1.82211i	−0.412287	−	0.911054i	$-0.635270\pi$
$89$		−	14432.9i		−	1.82211i	0.412287	−	0.911054i	$-0.364730\pi$
$90$		0			0
$91$	−2283.28			−0.275725
$92$		0			0
$93$	−4169.25	+	9553.92i	−0.482050	+	1.10463i
$94$		0			0
$95$	−9399.03	+	5426.53i	−1.04144	+	0.601278i
$96$		0			0
$97$	7043.86	−	12200.3i	0.748630	−	1.29666i	−0.199850	−	0.979827i	$-0.564045\pi$
$97$	7043.86	−	12200.3i	0.748630	−	1.29666i	0.948480	−	0.316838i	$-0.102621\pi$
$98$		0			0
$99$	12648.8	−	11732.6i	1.29056	−	1.19708i
$100$		0			0
$101$	−4292.07	−	2478.03i	−0.420750	−	0.242920i	0.274648	−	0.961545i	$-0.411439\pi$
$101$	−4292.07	−	2478.03i	−0.420750	−	0.242920i	−0.695398	+	0.718625i	$0.744772\pi$
$102$		0			0
$103$	9640.10	+	16697.1i	0.908672	+	1.57387i	0.815911	+	0.578178i	$0.196236\pi$
$103$	9640.10	+	16697.1i	0.908672	+	1.57387i	0.0927613	+	0.995688i	$0.470431\pi$
$104$		0			0
$105$	−2510.04	+	1852.18i	−0.227668	+	0.167999i
$106$		0			0
$107$			11309.4i			0.987809i	0.869516	+	0.493905i	$0.164431\pi$
$107$			11309.4i			0.987809i	−0.869516	+	0.493905i	$0.835569\pi$
$108$		0			0
$109$	20665.0			1.73933			0.869667	−	0.493639i	$-0.164334\pi$
$109$	20665.0			1.73933			0.869667	+	0.493639i	$0.164334\pi$
$110$		0			0
$111$	2075.43	+	2812.59i	0.168447	+	0.228276i
$112$		0			0
$113$	−6469.19	+	3734.99i	−0.506633	+	0.292504i	−0.731448	−	0.681897i	$-0.761155\pi$
$113$	−6469.19	+	3734.99i	−0.506633	+	0.292504i	0.224816	+	0.974401i	$0.427822\pi$
$114$		0			0
$115$	6946.76	−	12032.1i	0.525275	−	0.909803i
$116$		0			0
$117$	11357.9	−	2590.44i	0.829711	−	0.189235i
$118$		0			0
$119$	68.2742	+	39.4181i	0.00482128	+	0.00278357i
$120$		0			0
$121$	15362.5	+	26608.6i	1.04928	+	1.81740i
$122$		0			0
$123$	−16323.7	−	7123.53i	−1.07897	−	0.470853i
$124$		0			0
$125$			16884.0i			1.08058i
$126$		0			0
$127$	−23731.3			−1.47134			−0.735671	−	0.677339i	$-0.763133\pi$
$127$	−23731.3			−1.47134			−0.735671	+	0.677339i	$0.763133\pi$
$128$		0			0
$129$	−1147.10	+	129.153i	−0.0689322	+	0.00776116i
$130$		0			0
$131$	11197.4	−	6464.84i	0.652493	−	0.376717i	−0.136918	−	0.990582i	$-0.543720\pi$
$131$	11197.4	−	6464.84i	0.652493	−	0.376717i	0.789411	+	0.613865i	$0.210386\pi$
$132$		0			0
$133$	−3946.00	+	6834.66i	−0.223076	+	0.386379i
$134$		0			0
$135$	10384.6	−	12061.2i	0.569798	−	0.661794i
$136$		0			0
$137$	−5672.80	−	3275.19i	−0.302243	−	0.174500i	0.341207	−	0.939988i	$-0.389164\pi$
$137$	−5672.80	−	3275.19i	−0.302243	−	0.174500i	−0.643450	+	0.765488i	$0.722498\pi$
$138$		0			0
$139$	6959.92	+	12054.9i	0.360226	+	0.623929i	0.987998	−	0.154468i	$-0.0493664\pi$
$139$	6959.92	+	12054.9i	0.360226	+	0.623929i	−0.627772	+	0.778397i	$0.716033\pi$
$140$		0			0
$141$	−2378.63	−	21126.3i	−0.119644	−	1.06264i
$142$		0			0
$143$			30633.0i			1.49802i
$144$		0			0
$145$	12279.8			0.584057
$146$		0			0
$147$	7735.60	−	17726.3i	0.357980	−	0.820319i
$148$		0			0
$149$	−14784.9	+	8536.08i	−0.665958	+	0.384491i	−0.794543	−	0.607207i	$-0.792290\pi$
$149$	−14784.9	+	8536.08i	−0.665958	+	0.384491i	0.128585	+	0.991698i	$0.458956\pi$
$150$		0			0
$151$	14423.4	−	24982.1i	0.632578	−	1.09566i	−0.354445	−	0.935077i	$-0.615330\pi$
$151$	14423.4	−	24982.1i	0.632578	−	1.09566i	0.987023	−	0.160580i	$-0.0513365\pi$
$152$		0			0
$153$	−384.343	−	118.622i	−0.0164186	−	0.00506737i
$154$		0			0
$155$	−21898.9	−	12643.4i	−0.911506	−	0.526258i
$156$		0			0
$157$	734.462	+	1272.13i	0.0297968	+	0.0516097i	0.880539	−	0.473973i	$-0.157181\pi$
$157$	734.462	+	1272.13i	0.0297968	+	0.0516097i	−0.850742	+	0.525583i	$0.823847\pi$
$158$		0			0
$159$	−19419.2	+	14329.6i	−0.768135	+	0.566814i
$160$		0			0
$161$		−	10102.9i		−	0.389758i
$162$		0			0
$163$	−2472.47			−0.0930585			−0.0465292	−	0.998917i	$-0.514816\pi$
$163$	−2472.47			−0.0930585			−0.0465292	+	0.998917i	$0.514816\pi$
$164$		0			0
$165$	24849.4	+	33675.4i	0.912740	+	1.23693i
$166$		0			0
$167$	312.089	−	180.184i	0.0111904	−	0.00646077i	−0.494394	−	0.869238i	$-0.664610\pi$
$167$	312.089	−	180.184i	0.0111904	−	0.00646077i	0.505585	+	0.862777i	$0.331277\pi$
$168$		0			0
$169$	3938.12	−	6821.03i	0.137885	−	0.238823i
$170$		0			0
$171$	11874.8	−	38475.1i	0.406101	−	1.31579i
$172$		0			0
$173$	2996.03	+	1729.76i	0.100104	+	0.0577953i	0.549216	−	0.835680i	$-0.314926\pi$
$173$	2996.03	+	1729.76i	0.100104	+	0.0577953i	−0.449112	+	0.893475i	$0.648260\pi$
$174$		0			0
$175$	1177.58	+	2039.62i	0.0384515	+	0.0666000i
$176$		0			0
$177$	−33258.2	−	14513.6i	−1.06158	−	0.463264i
$178$		0			0
$179$		−	38346.8i		−	1.19680i	−0.801196	−	0.598402i	$-0.795803\pi$
$179$		−	38346.8i		−	1.19680i	0.801196	−	0.598402i	$-0.204197\pi$
$180$		0			0
$181$	−59042.5			−1.80222			−0.901109	−	0.433593i	$-0.857246\pi$
$181$	−59042.5			−1.80222			−0.901109	+	0.433593i	$0.857246\pi$
$182$		0			0
$183$	−46306.9	+	5213.75i	−1.38275	+	0.155685i
$184$		0			0
$185$	−7343.28	+	4239.64i	−0.214559	+	0.123876i
$186$		0			0
$187$	528.843	−	915.983i	0.0151232	−	0.0261941i
$188$		0			0
$189$	2154.38	−	11371.1i	0.0603114	−	0.318332i
$190$		0			0
$191$	−26196.5	−	15124.6i	−0.718087	−	0.414588i	0.0959611	−	0.995385i	$-0.469408\pi$
$191$	−26196.5	−	15124.6i	−0.718087	−	0.414588i	−0.814048	+	0.580797i	$0.802741\pi$
$192$		0			0
$193$	9652.94	+	16719.4i	0.259146	+	0.448855i	0.966013	−	0.258492i	$-0.0832255\pi$
$193$	9652.94	+	16719.4i	0.259146	+	0.448855i	−0.706867	+	0.707346i	$0.749892\pi$
$194$		0			0
$195$	3161.82	+	28082.3i	0.0831511	+	0.738522i
$196$		0			0
$197$		−	27070.3i		−	0.697527i	−0.937211	−	0.348764i	$-0.886602\pi$
$197$		−	27070.3i		−	0.697527i	0.937211	−	0.348764i	$-0.113398\pi$
$198$		0			0
$199$	−23545.5			−0.594569			−0.297284	−	0.954789i	$-0.596081\pi$
$199$	−23545.5			−0.594569			−0.297284	+	0.954789i	$0.596081\pi$
$200$		0			0
$201$	−16422.0	+	37631.4i	−0.406475	+	0.931447i
$202$		0			0
$203$	7733.15	−	4464.73i	0.187657	−	0.108344i
$204$		0			0
$205$	21602.3	−	37416.3i	0.514035	−	0.890334i
$206$		0			0
$207$	11462.0	+	50255.8i	0.267498	+	1.17286i
$208$		0			0
$209$	91695.5	+	52940.4i	2.09921	+	1.21198i
$210$		0			0
$211$	−11435.4	−	19806.7i	−0.256854	−	0.444883i	0.708544	−	0.705667i	$-0.249352\pi$
$211$	−11435.4	−	19806.7i	−0.256854	−	0.444883i	−0.965397	+	0.260783i	$0.916019\pi$
$212$		0			0
$213$	28020.8	−	20676.8i	0.617621	−	0.455748i
$214$		0			0
$215$		−	2800.24i		−	0.0605784i
$216$		0			0
$217$	−18387.7			−0.390487
$218$		0			0
$219$	34674.4	+	46990.1i	0.722971	+	0.979757i
$220$		0			0
$221$	618.511	−	357.098i	0.0126638	−	0.00731143i
$222$		0			0
$223$	−5240.62	+	9077.02i	−0.105384	+	0.182530i	−0.913895	−	0.405951i	$-0.866940\pi$
$223$	−5240.62	+	9077.02i	−0.105384	+	0.182530i	0.808511	+	0.588481i	$0.200274\pi$
$224$		0			0
$225$	−8171.73	−	8809.88i	−0.161417	−	0.174022i
$226$		0			0
$227$	21504.5	+	12415.6i	0.417329	+	0.240945i	0.693934	−	0.720039i	$-0.255876\pi$
$227$	21504.5	+	12415.6i	0.417329	+	0.240945i	−0.276605	+	0.960984i	$0.589209\pi$
$228$		0			0
$229$	−35350.2	−	61228.3i	−0.674094	−	1.16757i	−0.976733	−	0.214460i	$-0.931201\pi$
$229$	−35350.2	−	61228.3i	−0.674094	−	1.16757i	0.302638	−	0.953105i	$-0.402133\pi$
$230$		0			0
$231$	27892.6	+	12172.1i	0.522714	+	0.228108i
$232$		0			0
$233$		−	32166.2i		−	0.592499i	−0.955111	−	0.296250i	$-0.904264\pi$
$233$		−	32166.2i		−	0.592499i	0.955111	−	0.296250i	$-0.0957360\pi$
$234$		0			0
$235$	51572.2			0.933857
$236$		0			0
$237$	61971.3	−	6977.42i	1.10330	−	0.124222i
$238$		0			0
$239$	86659.3	−	50032.8i	1.51712	−	0.875909i	0.517321	−	0.855791i	$-0.326929\pi$
$239$	86659.3	−	50032.8i	1.51712	−	0.875909i	0.999798	−	0.0201176i	$-0.00640405\pi$
$240$		0			0
$241$	−31445.2	+	54464.6i	−0.541402	+	0.937736i	0.457422	+	0.889250i	$0.348773\pi$
$241$	−31445.2	+	54464.6i	−0.541402	+	0.937736i	−0.998824	+	0.0484859i	$0.984560\pi$
$242$		0			0
$243$	2184.11	+	59008.6i	0.0369882	+	0.999316i
$244$		0			0
$245$	40631.2	+	23458.4i	0.676904	+	0.390811i
$246$		0			0
$247$	35747.7	+	61916.8i	0.585941	+	1.01488i
$248$		0			0
$249$	−5495.60	−	48810.2i	−0.0886372	−	0.787248i
$250$		0			0
$251$			49708.8i			0.789016i	0.918893	+	0.394508i	$0.129085\pi$
$251$			49708.8i			0.789016i	−0.918893	+	0.394508i	$0.870915\pi$
$252$		0			0
$253$	−135543.			−2.11756
$254$		0			0
$255$	390.263	−	894.296i	0.00600174	−	0.0137531i
$256$		0			0
$257$	48995.1	−	28287.3i	0.741799	−	0.428278i	−0.0809239	−	0.996720i	$-0.525787\pi$
$257$	48995.1	−	28287.3i	0.741799	−	0.428278i	0.822723	+	0.568442i	$0.192454\pi$
$258$		0			0
$259$	−3082.93	+	5339.79i	−0.0459583	+	0.0796021i
$260$		0			0
$261$	−33402.3	+	30982.8i	−0.490338	+	0.454820i
$262$		0			0
$263$	−54711.9	−	31587.9i	−0.790989	−	0.456678i	0.0493217	−	0.998783i	$-0.484294\pi$
$263$	−54711.9	−	31587.9i	−0.790989	−	0.456678i	−0.840311	+	0.542105i	$0.817627\pi$
$264$		0			0
$265$	−29272.2	−	50700.9i	−0.416834	−	0.721978i
$266$		0			0
$267$	−104520.	+	77126.6i	−1.46615	+	1.08189i
$268$		0			0
$269$			23003.0i			0.317892i	0.987287	+	0.158946i	$0.0508095\pi$
$269$			23003.0i			0.317892i	−0.987287	+	0.158946i	$0.949190\pi$
$270$		0			0
$271$	54081.4			0.736392			0.368196	−	0.929748i	$-0.379975\pi$
$271$	54081.4			0.736392			0.368196	+	0.929748i	$0.379975\pi$
$272$		0			0
$273$	12201.4	+	16535.1i	0.163713	+	0.221861i
$274$		0			0
$275$	27364.1	−	15798.7i	0.361839	−	0.208908i
$276$		0			0
$277$	5634.27	−	9758.85i	0.0734308	−	0.127186i	−0.826972	−	0.562243i	$-0.809939\pi$
$277$	5634.27	−	9758.85i	0.0734308	−	0.127186i	0.900403	+	0.435057i	$0.143272\pi$
$278$		0			0
$279$	91467.3	−	20861.3i	1.17505	−	0.267999i
$280$		0			0
$281$	−36044.7	−	20810.4i	−0.456488	−	0.263553i	0.254079	−	0.967184i	$-0.418228\pi$
$281$	−36044.7	−	20810.4i	−0.456488	−	0.263553i	−0.710566	+	0.703630i	$0.751561\pi$
$282$		0			0
$283$	−26433.5	−	45784.2i	−0.330052	−	0.571667i	0.652470	−	0.757815i	$-0.273733\pi$
$283$	−26433.5	−	45784.2i	−0.330052	−	0.571667i	−0.982522	+	0.186148i	$0.940400\pi$
$284$		0			0
$285$	89524.5	+	39067.7i	1.10218	+	0.480982i
$286$		0			0
$287$		−	31417.0i		−	0.381417i
$288$		0			0
$289$	83496.3			0.999705
$290$		0			0
$291$	−125993.	+	14185.8i	−1.48786	+	0.167520i
$292$		0			0
$293$	−135682.	+	78336.0i	−1.58047	+	0.912486i	−0.585682	+	0.810541i	$0.699173\pi$
$293$	−135682.	+	78336.0i	−1.58047	+	0.912486i	−0.994790	+	0.101944i	$0.967494\pi$
$294$		0			0
$295$	44012.9	−	76232.5i	0.505750	−	0.875984i
$296$		0			0
$297$	−152558.	−	28903.7i	−1.72950	−	0.327673i
$298$		0			0
$299$	−79262.6	−	45762.3i	−0.886596	−	0.511876i
$300$		0			0
$301$	−1018.12	−	1763.43i	−0.0112374	−	0.0194637i
$302$		0			0
$303$	4990.55	+	44324.5i	0.0543579	+	0.482790i
$304$		0			0
$305$		−	113042.i		−	1.21517i
$306$		0			0
$307$	−8451.23			−0.0896692			−0.0448346	−	0.998994i	$-0.514276\pi$
$307$	−8451.23			−0.0896692			−0.0448346	+	0.998994i	$0.514276\pi$
$308$		0			0
$309$	69402.8	−	159038.i	0.726876	−	1.66565i
$310$		0			0
$311$	14976.2	−	8646.50i	0.154839	−	0.0893963i	−0.420579	−	0.907256i	$-0.638173\pi$
$311$	14976.2	−	8646.50i	0.154839	−	0.0893963i	0.575418	+	0.817860i	$0.304840\pi$
$312$		0			0
$313$	−55763.1	+	96584.5i	−0.569191	+	0.985868i	0.427455	+	0.904037i	$0.359410\pi$
$313$	−55763.1	+	96584.5i	−0.569191	+	0.985868i	−0.996646	+	0.0818314i	$0.973923\pi$
$314$		0			0
$315$	26826.3	+	8279.57i	0.270359	+	0.0834424i
$316$		0			0
$317$	103814.	+	59937.1i	1.03309	+	0.596454i	0.917868	−	0.396886i	$-0.129909\pi$
$317$	103814.	+	59937.1i	1.03309	+	0.596454i	0.115221	+	0.993340i	$0.463242\pi$
$318$		0			0
$319$	−59899.9	−	103750.i	−0.588634	−	1.01954i
$320$		0			0
$321$	81900.7	−	60435.3i	0.794836	−	0.586517i
$322$		0			0
$323$		−	2468.56i		−	0.0236613i
$324$		0			0
$325$	21335.9			0.201996
$326$		0			0
$327$	−110430.	−	149652.i	−1.03274	−	1.39955i
$328$		0			0
$329$	32477.4	−	18750.8i	0.300047	−	0.173232i
$330$		0			0
$331$	−72037.3	+	124772.i	−0.657508	+	1.13884i	0.323750	+	0.946143i	$0.395056\pi$
$331$	−72037.3	+	124772.i	−0.657508	+	1.13884i	−0.981259	+	0.192695i	$0.938277\pi$
$332$		0			0
$333$	9277.53	−	30059.8i	0.0836651	−	0.271080i
$334$		0			0
$335$	−86256.5	−	49800.2i	−0.768603	−	0.443753i
$336$		0			0
$337$	62880.5	+	108912.i	0.553677	+	0.958997i	0.998005	+	0.0631325i	$0.0201091\pi$
$337$	62880.5	+	108912.i	0.553677	+	0.958997i	−0.444328	+	0.895864i	$0.646558\pi$
$338$		0			0
$339$	61618.1	+	26889.6i	0.536178	+	0.233984i
$340$		0			0
$341$			246693.i			2.12153i
$342$		0			0
$343$	72234.0			0.613979
$344$		0			0
$345$	−124257.	+	13990.2i	−1.04395	+	0.117540i
$346$		0			0
$347$	−147968.	+	85429.6i	−1.22888	+	0.709495i	−0.966796	−	0.255550i	$-0.917743\pi$
$347$	−147968.	+	85429.6i	−1.22888	+	0.709495i	−0.262085	+	0.965045i	$0.584410\pi$
$348$		0			0
$349$	18238.2	−	31589.5i	0.149738	−	0.259353i	−0.781393	−	0.624040i	$-0.785490\pi$
$349$	18238.2	−	31589.5i	0.149738	−	0.259353i	0.931130	+	0.364686i	$0.118824\pi$
$350$		0			0
$351$	−79453.9	−	68409.1i	−0.644913	−	0.555264i
$352$		0			0
$353$	−32752.3	−	18909.6i	−0.262841	−	0.151751i	0.362789	−	0.931871i	$-0.381825\pi$
$353$	−32752.3	−	18909.6i	−0.262841	−	0.151751i	−0.625630	+	0.780120i	$0.715158\pi$
$354$		0			0
$355$	42238.1	+	73158.5i	0.335156	+	0.580508i
$356$		0			0
$357$	−79.3848	−	705.071i	−0.000622875	−	0.00553218i
$358$		0			0
$359$			88488.8i			0.686593i	0.939227	+	0.343297i	$0.111544\pi$
$359$			88488.8i			0.686593i	−0.939227	+	0.343297i	$0.888456\pi$
$360$		0			0
$361$	116797.			0.896228
$362$		0			0
$363$	110600.	−	253443.i	0.839351	−	1.92339i
$364$		0			0
$365$	−122685.	+	70832.0i	−0.920883	+	0.531672i
$366$		0			0
$367$	2910.99	−	5041.99i	0.0216127	−	0.0374343i	−0.855017	−	0.518600i	$-0.826453\pi$
$367$	2910.99	−	5041.99i	0.0216127	−	0.0374343i	0.876629	+	0.481166i	$0.159787\pi$
$368$		0			0
$369$	35643.4	+	156280.i	0.261774	+	1.14776i
$370$		0			0
$371$	−36868.0	−	21285.7i	−0.267856	−	0.154647i
$372$		0			0
$373$	−58261.9	−	100913.i	−0.418762	−	0.725316i	0.577054	−	0.816706i	$-0.304202\pi$
$373$	−58261.9	−	100913.i	−0.418762	−	0.725316i	−0.995815	+	0.0913899i	$0.970869\pi$
$374$		0			0
$375$	122271.	−	90224.8i	0.869482	−	0.641598i
$376$		0			0
$377$		−	80894.1i		−	0.569159i
$378$		0			0
$379$	208888.			1.45423			0.727117	−	0.686514i	$-0.240860\pi$
$379$	208888.			1.45423			0.727117	+	0.686514i	$0.240860\pi$
$380$		0			0
$381$	126815.	+	171857.i	0.873618	+	1.18391i
$382$		0			0
$383$	108664.	−	62737.4i	0.740781	−	0.427690i	−0.0815724	−	0.996667i	$-0.525994\pi$
$383$	108664.	−	62737.4i	0.740781	−	0.427690i	0.822353	+	0.568978i	$0.192661\pi$
$384$		0			0
$385$	−36912.1	+	63933.7i	−0.249028	+	0.431329i
$386$		0			0
$387$	7065.18	+	7616.92i	0.0471738	+	0.0508578i
$388$		0			0
$389$	27319.1	+	15772.7i	0.180537	+	0.104233i	0.587545	−	0.809192i	$-0.300095\pi$
$389$	27319.1	+	15772.7i	0.180537	+	0.104233i	−0.407008	+	0.913425i	$0.633428\pi$
$390$		0			0
$391$	1580.06	+	2736.75i	0.0103352	+	0.0179012i
$392$		0			0
$393$	−106654.	−	46542.9i	−0.690545	−	0.301348i
$394$		0			0
$395$			151281.i			0.969592i
$396$		0			0
$397$	286067.			1.81504			0.907520	−	0.420010i	$-0.137973\pi$
$397$	286067.			1.81504			0.907520	+	0.420010i	$0.137973\pi$
$398$		0			0
$399$	70581.9	−	7946.91i	0.443351	−	0.0499175i
$400$		0			0
$401$	56694.1	−	32732.3i	0.352573	−	0.203558i	−0.313245	−	0.949672i	$-0.601416\pi$
$401$	56694.1	−	32732.3i	0.352573	−	0.203558i	0.665818	+	0.746114i	$0.268083\pi$
$402$		0			0
$403$	−83288.9	+	144261.i	−0.512835	+	0.888255i
$404$		0			0
$405$	−142838.	−	10750.6i	−0.870830	−	0.0655423i
$406$		0			0
$407$	71639.9	+	41361.3i	0.432480	+	0.249692i
$408$		0			0
$409$	97111.6	+	168202.i	0.580530	+	1.00551i	0.995417	+	0.0956341i	$0.0304879\pi$
$409$	97111.6	+	168202.i	0.580530	+	1.00551i	−0.414887	+	0.909873i	$0.636179\pi$
$410$		0			0
$411$	6595.96	+	58583.3i	0.0390476	+	0.346809i
$412$		0			0
$413$		−	64009.4i		−	0.375270i
$414$		0			0
$415$	119153.			0.691842
$416$		0			0
$417$	50107.1	−	114822.i	0.288156	−	0.660315i
$418$		0			0
$419$	10905.3	−	6296.19i	0.0621170	−	0.0358633i	−0.468620	−	0.883400i	$-0.655249\pi$
$419$	10905.3	−	6296.19i	0.0621170	−	0.0358633i	0.530737	+	0.847537i	$0.321915\pi$
$420$		0			0
$421$	12730.6	−	22050.0i	0.0718262	−	0.124407i	−0.827875	−	0.560912i	$-0.810451\pi$
$421$	12730.6	−	22050.0i	0.0718262	−	0.124407i	0.899702	+	0.436505i	$0.143784\pi$
$422$		0			0
$423$	−140282.	+	130120.i	−0.784007	+	0.727217i
$424$		0			0
$425$	−637.981	−	368.338i	−0.00353207	−	0.00203924i
$426$		0			0
$427$	−41100.1	−	71187.4i	−0.225417	−	0.390434i
$428$		0			0
$429$	221839.	−	163697.i	1.20538	−	0.889458i
$430$		0			0
$431$			14122.7i			0.0760262i	0.999277	+	0.0380131i	$0.0121029\pi$
$431$			14122.7i			0.0760262i	−0.999277	+	0.0380131i	$0.987897\pi$
$432$		0			0
$433$	147123.			0.784701			0.392351	−	0.919816i	$-0.371662\pi$
$433$	147123.			0.784701			0.392351	+	0.919816i	$0.371662\pi$
$434$		0			0
$435$	−65620.8	−	88928.0i	−0.346787	−	0.469959i
$436$		0			0
$437$	−273965.	+	158174.i	−1.43461	+	0.828270i
$438$		0			0
$439$	−45158.9	+	78217.5i	−0.234323	+	0.405859i	−0.959076	−	0.283150i	$-0.908621\pi$
$439$	−45158.9	+	78217.5i	−0.234323	+	0.405859i	0.724753	+	0.689009i	$0.241954\pi$
$440$		0			0
$441$	−169708.	+	38705.9i	−0.872619	+	0.199022i
$442$		0			0
$443$	68810.1	+	39727.6i	0.350627	+	0.202434i	0.664961	−	0.746878i	$-0.268448\pi$
$443$	68810.1	+	39727.6i	0.350627	+	0.202434i	−0.314335	+	0.949312i	$0.601781\pi$
$444$		0			0
$445$	−157552.	−	272888.i	−0.795617	−	1.37805i
$446$		0			0
$447$	140824.	+	61454.6i	0.704795	+	0.307567i
$448$		0			0
$449$		−	384443.i		−	1.90695i	−0.301472	−	0.953475i	$-0.597478\pi$
$449$		−	384443.i		−	1.90695i	0.301472	−	0.953475i	$-0.402522\pi$
$450$		0			0
$451$	−421497.			−2.07225
$452$		0			0
$453$	−257991.	+	29047.6i	−1.25721	+	0.141551i
$454$		0			0
$455$	−43170.8	+	24924.7i	−0.208529	+	0.120394i
$456$		0			0
$457$	−29398.8	+	50920.1i	−0.140766	+	0.243813i	−0.927785	−	0.373115i	$-0.878290\pi$
$457$	−29398.8	+	50920.1i	−0.140766	+	0.243813i	0.787020	+	0.616928i	$0.211623\pi$
$458$		0			0
$459$	1194.81	+	3417.23i	0.00567119	+	0.0162199i
$460$		0			0
$461$	−170621.	−	98507.9i	−0.802841	−	0.463521i	0.0416223	−	0.999133i	$-0.486747\pi$
$461$	−170621.	−	98507.9i	−0.802841	−	0.463521i	−0.844464	+	0.535613i	$0.820081\pi$
$462$		0			0
$463$	−125301.	−	217027.i	−0.584509	−	1.01240i	−0.994936	−	0.100506i	$-0.967954\pi$
$463$	−125301.	−	217027.i	−0.584509	−	1.01240i	0.410428	−	0.911893i	$-0.365379\pi$
$464$		0			0
$465$	25462.7	+	226151.i	0.117760	+	1.04591i
$466$		0			0
$467$			146692.i			0.672624i	0.941751	+	0.336312i	$0.109180\pi$
$467$			146692.i			0.672624i	−0.941751	+	0.336312i	$0.890820\pi$
$468$		0			0
$469$	−72426.1			−0.329268
$470$		0			0
$471$	5287.68	−	12116.8i	0.0238354	−	0.0546194i
$472$		0			0
$473$	−23658.7	+	13659.3i	−0.105747	+	0.0610530i
$474$		0			0
$475$	36872.9	−	63865.8i	0.163426	−	0.283062i
$476$		0			0
$477$	207545.	+	64055.8i	0.912168	+	0.281528i
$478$		0			0
$479$	123182.	+	71119.2i	0.536879	+	0.309967i	0.743813	−	0.668388i	$-0.233015\pi$
$479$	123182.	+	71119.2i	0.536879	+	0.309967i	−0.206934	+	0.978355i	$0.566349\pi$
$480$		0			0
$481$	27928.9	+	48374.3i	0.120716	+	0.209086i
$482$		0			0
$483$	−73163.4	+	53987.9i	−0.313617	+	0.231421i
$484$		0			0
$485$		−	307568.i		−	1.30755i
$486$		0			0
$487$	−311049.			−1.31151			−0.655753	−	0.754975i	$-0.727649\pi$
$487$	−311049.			−1.31151			−0.655753	+	0.754975i	$0.727649\pi$
$488$		0			0
$489$	13212.4	+	17905.2i	0.0552540	+	0.0748791i
$490$		0			0
$491$	220667.	−	127402.i	0.915324	−	0.528463i	0.0331837	−	0.999449i	$-0.489435\pi$
$491$	220667.	−	127402.i	0.915324	−	0.528463i	0.882140	+	0.470987i	$0.156102\pi$
$492$		0			0
$493$	−1396.54	+	2418.88i	−0.00574592	+	0.00995222i
$494$		0			0
$495$	111081.	−	359909.i	0.453344	−	1.46887i
$496$		0			0
$497$	53198.4	+	30714.1i	0.215370	+	0.124344i
$498$		0			0
$499$	31568.8	+	54678.7i	0.126782	+	0.219592i	0.922428	−	0.386169i	$-0.126202\pi$
$499$	31568.8	+	54678.7i	0.126782	+	0.219592i	−0.795646	+	0.605762i	$0.792869\pi$
$500$		0			0
$501$	−2972.60	−	1297.22i	−0.0118430	−	0.00516818i
$502$		0			0
$503$			205375.i			0.811730i	0.913933	+	0.405865i	$0.133030\pi$
$503$			205375.i			0.811730i	−0.913933	+	0.405865i	$0.866970\pi$
$504$		0			0
$505$	−108202.			−0.424281
$506$		0			0
$507$	−70441.2	+	7931.06i	−0.274038	+	0.0308543i
$508$		0			0
$509$	347528.	−	200645.i	1.34139	−	0.774450i	0.354376	−	0.935103i	$-0.384693\pi$
$509$	347528.	−	200645.i	1.34139	−	0.774450i	0.987011	+	0.160653i	$0.0513601\pi$
$510$		0			0
$511$	−51506.7	+	89212.1i	−0.197252	+	0.341651i
$512$		0			0
$513$	−342086.	+	119608.i	−1.29987	+	0.454492i
$514$		0			0
$515$	364538.	+	210466.i	1.37445	+	0.793537i
$516$		0			0
$517$	−251565.	−	435724.i	−0.941174	−	1.63016i
$518$		0			0
$519$	−3483.59	−	30940.1i	−0.0129328	−	0.114865i
$520$		0			0
$521$		−	13908.1i		−	0.0512379i	−0.999672	−	0.0256189i	$-0.991844\pi$
$521$		−	13908.1i		−	0.0512379i	0.999672	−	0.0256189i	$-0.00815565\pi$
$522$		0			0
$523$	−46538.6			−0.170142			−0.0850708	−	0.996375i	$-0.527112\pi$
$523$	−46538.6			−0.170142			−0.0850708	+	0.996375i	$0.527112\pi$
$524$		0			0
$525$	8477.84	−	19427.1i	0.0307586	−	0.0704839i
$526$		0			0
$527$	4980.98	−	2875.77i	0.0179347	−	0.0103546i
$528$		0			0
$529$	62565.4	−	108366.i	0.223575	−	0.387243i
$530$		0			0
$531$	72620.4	+	318407.i	0.257555	+	1.12926i
$532$		0			0
$533$	−246482.	−	142307.i	−0.867624	−	0.500923i
$534$		0			0
$535$	123456.	+	213831.i	0.431324	+	0.747074i
$536$		0			0
$537$	−277700.	+	204917.i	−0.963002	+	0.710608i
$538$		0			0
$539$		−	457713.i		−	1.57549i
$540$		0			0
$541$	−72042.5			−0.246147			−0.123073	−	0.992398i	$-0.539275\pi$
$541$	−72042.5			−0.246147			−0.123073	+	0.992398i	$0.539275\pi$
$542$		0			0
$543$	315511.	+	427574.i	1.07008	+	1.45015i
$544$		0			0
$545$	390721.	−	225583.i	1.31545	−	0.759474i
$546$		0			0
$547$	172707.	−	299137.i	0.577212	−	0.999760i	−0.418586	−	0.908177i	$-0.637474\pi$
$547$	172707.	−	299137.i	0.577212	−	0.999760i	0.995797	−	0.0915826i	$-0.0291926\pi$
$548$		0			0
$549$	285211.	+	307484.i	0.946286	+	1.02018i
$550$		0			0
$551$	−242144.	−	139802.i	−0.797575	−	0.460480i
$552$		0			0
$553$	55003.1	+	95268.2i	0.179861	+	0.311528i
$554$		0			0
$555$	69943.7	+	30522.8i	0.227071	+	0.0990920i
$556$		0			0
$557$			565593.i			1.82303i	0.411268	+	0.911515i	$0.365086\pi$
$557$			565593.i			1.82303i	−0.411268	+	0.911515i	$0.634914\pi$
$558$		0			0
$559$	−18446.7			−0.0590332
$560$		0			0
$561$	−9459.41	+	1065.05i	−0.0300565	+	0.00338410i
$562$		0			0
$563$	−89039.3	+	51406.8i	−0.280908	+	0.162183i	−0.633835	−	0.773469i	$-0.718520\pi$
$563$	−89039.3	+	51406.8i	−0.280908	+	0.162183i	0.352926	+	0.935651i	$0.385187\pi$
$564$		0			0
$565$	−81543.5	+	141238.i	−0.255442	+	0.442439i
$566$		0			0
$567$	−93860.2	+	45163.4i	−0.291955	+	0.140482i
$568$		0			0
$569$	−261186.	−	150796.i	−0.806726	−	0.465764i	0.0390916	−	0.999236i	$-0.487554\pi$
$569$	−261186.	−	150796.i	−0.806726	−	0.465764i	−0.845818	+	0.533472i	$0.820887\pi$
$570$		0			0
$571$	−185160.	−	320707.i	−0.567905	−	0.983640i	−0.996773	−	0.0802728i	$-0.974421\pi$
$571$	−185160.	−	320707.i	−0.567905	−	0.983640i	0.428868	−	0.903367i	$-0.358912\pi$
$572$		0			0
$573$	30459.7	+	270533.i	0.0927717	+	0.823969i
$574$		0			0
$575$			94405.6i			0.285537i
$576$		0			0
$577$	400296.			1.20235			0.601173	−	0.799119i	$-0.294700\pi$
$577$	400296.			1.20235			0.601173	+	0.799119i	$0.294700\pi$
$578$		0			0
$579$	69495.3	−	159250.i	0.207299	−	0.475031i
$580$		0			0
$581$	75035.7	−	43321.9i	0.222288	−	0.128338i
$582$		0			0
$583$	−285575.	+	494630.i	−0.840200	+	1.45527i
$584$		0			0
$585$	186470.	−	172963.i	0.544877	−	0.505408i
$586$		0			0
$587$	141997.	+	81981.8i	0.412099	+	0.237926i	0.691691	−	0.722193i	$-0.256866\pi$
$587$	141997.	+	81981.8i	0.412099	+	0.237926i	−0.279592	+	0.960119i	$0.590199\pi$
$588$		0			0
$589$	287882.	+	498626.i	0.829820	+	1.43729i
$590$		0			0
$591$	−196038.	+	144658.i	−0.561262	+	0.414160i
$592$		0			0
$593$			256945.i			0.730686i	0.930873	+	0.365343i	$0.119048\pi$
$593$			256945.i			0.730686i	−0.930873	+	0.365343i	$0.880952\pi$
$594$		0			0
$595$	1721.18			0.00486174
$596$		0			0
$597$	125822.	+	170512.i	0.353028	+	0.478417i
$598$		0			0
$599$	450212.	−	259930.i	1.25477	−	0.724440i	0.282715	−	0.959204i	$-0.408765\pi$
$599$	450212.	−	259930.i	1.25477	−	0.724440i	0.972052	+	0.234764i	$0.0754316\pi$
$600$		0			0
$601$	188272.	−	326097.i	0.521239	−	0.902812i	−0.478456	−	0.878112i	$-0.658803\pi$
$601$	188272.	−	326097.i	0.521239	−	0.902812i	0.999695	−	0.0247008i	$-0.00786331\pi$
$602$		0			0
$603$	360275.	−	82169.3i	0.990832	−	0.225983i
$604$		0			0
$605$	580928.	+	335399.i	1.58713	+	0.916327i
$606$		0			0
$607$	−42093.9	−	72908.8i	−0.114246	−	0.197880i	0.803232	−	0.595666i	$-0.203112\pi$
$607$	−42093.9	−	72908.8i	−0.114246	−	0.197880i	−0.917478	+	0.397786i	$0.869779\pi$
$608$		0			0
$609$	−73657.1	−	32143.3i	−0.198600	−	0.0866675i
$610$		0			0
$611$		−	339736.i		−	0.910036i
$612$		0			0
$613$	−499828.			−1.33015			−0.665074	−	0.746778i	$-0.731600\pi$
$613$	−499828.			−1.33015			−0.665074	+	0.746778i	$0.731600\pi$
$614$		0			0
$615$	−386400.	+	43505.3i	−1.02161	+	0.115025i
$616$		0			0
$617$	−18474.5	+	10666.2i	−0.0485290	+	0.0280182i	−0.524068	−	0.851676i	$-0.675586\pi$
$617$	−18474.5	+	10666.2i	−0.0485290	+	0.0280182i	0.475539	+	0.879695i	$0.342253\pi$
$618$		0			0
$619$	154005.	−	266745.i	0.401934	−	0.696170i	−0.592026	−	0.805919i	$-0.701672\pi$
$619$	154005.	−	266745.i	0.401934	−	0.696170i	0.993959	+	0.109750i	$0.0350049\pi$
$620$		0			0
$621$	302692.	−	351562.i	0.784906	−	0.911631i
$622$		0			0
$623$	−198435.	−	114567.i	−0.511261	−	0.295177i
$624$		0			0
$625$	137950.	+	238936.i	0.353151	+	0.611675i
$626$		0			0
$627$	−106618.	−	946944.i	−0.271203	−	2.40874i
$628$		0			0
$629$		−	1928.64i		−	0.00487472i
$630$		0			0
$631$	71076.5			0.178512			0.0892560	−	0.996009i	$-0.471551\pi$
$631$	71076.5			0.178512			0.0892560	+	0.996009i	$0.471551\pi$
$632$		0			0
$633$	−82327.7	+	188656.i	−0.205465	+	0.470828i
$634$		0			0
$635$	−448696.	+	259055.i	−1.11277	+	0.642457i
$636$		0			0
$637$	154534.	−	267660.i	0.380842	−	0.659638i
$638$		0			0
$639$	−299475.	−	92428.9i	−0.733431	−	0.226363i
$640$		0			0
$641$	391608.	+	226095.i	0.953093	+	0.550268i	0.894040	−	0.447987i	$-0.147859\pi$
$641$	391608.	+	226095.i	0.953093	+	0.550268i	0.0590523	+	0.998255i	$0.481192\pi$
$642$		0			0
$643$	169915.	+	294302.i	0.410970	+	0.711821i	0.994996	−	0.0999139i	$-0.0318567\pi$
$643$	169915.	+	294302.i	0.410970	+	0.711821i	−0.584026	+	0.811735i	$0.698523\pi$
$644$		0			0
$645$	−20278.8	+	14963.9i	−0.0487441	+	0.0359687i
$646$		0			0
$647$			67633.6i			0.161568i	0.996732	+	0.0807838i	$0.0257423\pi$
$647$			67633.6i			0.161568i	−0.996732	+	0.0807838i	$0.974258\pi$
$648$		0			0
$649$	−858766.			−2.03885
$650$		0			0
$651$	98259.9	+	133160.i	0.231854	+	0.314204i
$652$		0			0
$653$	−292579.	+	168920.i	−0.686145	+	0.396146i	−0.802166	−	0.597101i	$-0.796319\pi$
$653$	−292579.	+	168920.i	−0.686145	+	0.396146i	0.116021	+	0.993247i	$0.462986\pi$
$654$		0			0
$655$	141143.	−	244466.i	0.328985	−	0.569818i
$656$		0			0
$657$	155000.	−	502211.i	0.359089	−	1.16347i
$658$		0			0
$659$	−227289.	−	131225.i	−0.523369	−	0.302167i	0.214943	−	0.976627i	$-0.431043\pi$
$659$	−227289.	−	131225.i	−0.523369	−	0.302167i	−0.738312	+	0.674459i	$0.764377\pi$
$660$		0			0
$661$	196248.	+	339911.i	0.449161	+	0.777970i	0.998332	−	0.0577403i	$-0.0183895\pi$
$661$	196248.	+	339911.i	0.449161	+	0.777970i	−0.549170	+	0.835710i	$0.685056\pi$
$662$		0			0
$663$	−5891.23	−	2570.88i	−0.0134023	−	0.00584865i
$664$		0			0
$665$			172301.i			0.389622i
$666$		0			0
$667$	357935.			0.804548
$668$		0			0
$669$	93738.9	−	10554.2i	0.209444	−	0.0235816i
$670$		0			0
$671$	−955067.	+	551408.i	−2.12124	+	1.22470i
$672$		0			0
$673$	34088.7	−	59043.3i	0.0752627	−	0.130359i	−0.825938	−	0.563761i	$-0.809354\pi$
$673$	34088.7	−	59043.3i	0.0752627	−	0.130359i	0.901201	+	0.433402i	$0.142687\pi$
$674$		0			0
$675$	−20131.4	+	106256.i	−0.0441842	+	0.233210i
$676$		0			0
$677$	−508674.	−	293683.i	−1.10984	−	0.640769i	−0.171056	−	0.985261i	$-0.554718\pi$
$677$	−508674.	−	293683.i	−1.10984	−	0.640769i	−0.938789	+	0.344492i	$0.888051\pi$
$678$		0			0
$679$	−111826.	−	193689.i	−0.242552	−	0.420113i
$680$		0			0
$681$	−25004.1	−	222078.i	−0.0539159	−	0.478864i
$682$		0			0
$683$		−	734111.i		−	1.57369i	−0.617148	−	0.786847i	$-0.711712\pi$
$683$		−	734111.i		−	1.57369i	0.617148	−	0.786847i	$-0.288288\pi$
$684$		0			0
$685$	−143010.			−0.304779
$686$		0			0
$687$	−254500.	+	583191.i	−0.539230	+	1.23566i
$688$		0			0
$689$	−333995.	+	192832.i	−0.703561	+	0.406201i
$690$		0			0
$691$	106906.	−	185167.i	0.223896	−	0.387799i	−0.732092	−	0.681206i	$-0.761456\pi$
$691$	106906.	−	185167.i	0.223896	−	0.387799i	0.955988	+	0.293407i	$0.0947891\pi$
$692$		0			0
$693$	−60904.3	−	267038.i	−0.126818	−	0.556040i
$694$		0			0
$695$	263187.	+	151951.i	0.544873	+	0.314583i
$696$		0			0
$697$	4913.51	+	8510.45i	0.0101141	+	0.0175181i
$698$		0			0
$699$	−232941.	+	171890.i	−0.476752	+	0.351799i
$700$		0			0
$701$		−	229681.i		−	0.467401i	−0.972309	−	0.233700i	$-0.924916\pi$
$701$		−	229681.i		−	0.467401i	0.972309	−	0.233700i	$-0.0750835\pi$
$702$		0			0
$703$	193069.			0.390662
$704$		0			0
$705$	−275592.	−	373476.i	−0.554482	−	0.751424i
$706$		0			0
$707$	−68139.9	+	39340.6i	−0.136321	+	0.0787049i
$708$		0			0
$709$	−157533.	+	272855.i	−0.313385	+	0.542799i	−0.979093	−	0.203414i	$-0.934796\pi$
$709$	−157533.	+	272855.i	−0.313385	+	0.542799i	0.665708	+	0.746213i	$0.268130\pi$
$710$		0			0
$711$	−381691.	−	411498.i	−0.755045	−	0.814008i
$712$		0			0
$713$	−638315.	−	368532.i	−1.25561	−	0.724929i
$714$		0			0
$715$	334395.	+	579190.i	0.654106	+	1.13295i
$716$		0			0
$717$	−825418.	−	360205.i	−1.60559	−	0.700667i
$718$		0			0
$719$			353204.i			0.683231i	0.939840	+	0.341616i	$0.110974\pi$
$719$			353204.i			0.683231i	−0.939840	+	0.341616i	$0.889026\pi$
$720$		0			0
$721$	306088.			0.588810
$722$		0			0
$723$	562459.	−	63328.0i	1.07601	−	0.121149i
$724$		0			0
$725$	−72261.6	+	41720.2i	−0.137477	+	0.0793726i
$726$		0			0
$727$	278520.	−	482411.i	0.526972	−	0.912742i	−0.472534	−	0.881312i	$-0.656661\pi$
$727$	278520.	−	482411.i	0.526972	−	0.912742i	0.999506	−	0.0314297i	$-0.0100060\pi$
$728$		0			0
$729$	415658.	−	331147.i	0.782133	−	0.623111i
$730$		0			0
$731$	551.591	+	318.461i	0.00103224	+	0.000595966i
$732$		0			0
$733$	130896.	+	226719.i	0.243623	+	0.421968i	0.961744	−	0.273951i	$-0.0883306\pi$
$733$	130896.	+	226719.i	0.243623	+	0.421968i	−0.718120	+	0.695919i	$0.754997\pi$
$734$		0			0
$735$	−47243.3	−	419600.i	−0.0874512	−	0.776714i
$736$		0			0
$737$			971686.i			1.78892i
$738$		0			0
$739$	182539.			0.334247			0.167123	−	0.985936i	$-0.446552\pi$
$739$	182539.			0.334247			0.167123	+	0.985936i	$0.446552\pi$
$740$		0			0
$741$	257361.	−	589748.i	0.468713	−	1.07406i
$742$		0			0
$743$	480844.	−	277616.i	0.871017	−	0.502882i	0.00333114	−	0.999994i	$-0.498940\pi$
$743$	480844.	−	277616.i	0.871017	−	0.502882i	0.867686	+	0.497112i	$0.165606\pi$
$744$		0			0
$745$	−186363.	+	322790.i	−0.335773	+	0.581577i
$746$		0			0
$747$	−324107.	+	300630.i	−0.580827	+	0.538754i
$748$		0			0
$749$	155491.	+	89772.8i	0.277167	+	0.160023i
$750$		0			0
$751$	442490.	+	766415.i	0.784556	+	1.35889i	0.929264	+	0.369416i	$0.120442\pi$
$751$	442490.	+	766415.i	0.784556	+	1.35889i	−0.144709	+	0.989474i	$0.546224\pi$
$752$		0			0
$753$	359982.	−	265634.i	0.634878	−	0.468482i
$754$		0			0
$755$		−	629793.i		−	1.10485i
$756$		0			0
$757$	416125.			0.726160			0.363080	−	0.931758i	$-0.381725\pi$
$757$	416125.			0.726160			0.363080	+	0.931758i	$0.381725\pi$
$758$		0			0
$759$	724315.	+	981578.i	1.25731	+	1.70389i
$760$		0			0
$761$	390904.	−	225688.i	0.674995	−	0.389708i	−0.122972	−	0.992410i	$-0.539242\pi$
$761$	390904.	−	225688.i	0.674995	−	0.389708i	0.797967	+	0.602702i	$0.205909\pi$
$762$		0			0
$763$	164036.	−	284119.i	0.281768	−	0.488036i
$764$		0			0
$765$	−8561.81	+	1952.72i	−0.0146299	+	0.00333671i
$766$		0			0
$767$	−502187.	−	289938.i	−0.853640	−	0.492849i
$768$		0			0
$769$	−235698.	−	408240.i	−0.398568	−	0.690340i	0.594981	−	0.803740i	$-0.297159\pi$
$769$	−235698.	−	408240.i	−0.398568	−	0.690340i	−0.993550	+	0.113399i	$0.963826\pi$
$770$		0			0
$771$	−466671.	−	203651.i	−0.785059	−	0.342593i
$772$		0			0
$773$			735566.i			1.23101i	0.788132	+	0.615506i	$0.211048\pi$
$773$			735566.i			1.23101i	−0.788132	+	0.615506i	$0.788952\pi$
$774$		0			0
$775$	171822.			0.286071
$776$		0			0
$777$	55144.3	−	6208.76i	0.0913394	−	0.0102840i
$778$		0			0
$779$	−851948.	+	491872.i	−1.40391	+	0.810546i
$780$		0			0
$781$	412068.	−	713723.i	0.675565	−	1.17011i
$782$		0			0
$783$	402866.	+	76327.4i	0.657109	+	0.124496i
$784$		0			0
$785$	27773.5	+	16035.0i	0.0450704	+	0.0260214i
$786$		0			0
$787$	467973.	+	810552.i	0.755564	+	1.30867i	0.945094	+	0.326800i	$0.105970\pi$
$787$	467973.	+	810552.i	0.755564	+	1.30867i	−0.189530	+	0.981875i	$0.560696\pi$
$788$		0			0
$789$	63615.5	+	565013.i	0.102190	+	0.907620i
$790$		0			0
$791$			118591.i			0.189540i
$792$		0			0
$793$	−744669.			−1.18418
$794$		0			0
$795$	−210742.	+	482919.i	−0.333439	+	0.764082i
$796$		0			0
$797$	560936.	−	323856.i	0.883073	−	0.509842i	0.0114025	−	0.999935i	$-0.496370\pi$
$797$	560936.	−	323856.i	0.883073	−	0.509842i	0.871670	+	0.490093i	$0.163037\pi$
$798$		0			0
$799$	−5865.13	+	10158.7i	−0.00918722	+	0.0159127i
$800$		0			0
$801$	1.11707e6	+	344769.i	1.74107	+	0.537357i
$802$		0			0
$803$	1.19689e6	+	691026.i	1.85620	+	1.07168i
$804$		0			0
$805$	−110285.	−	191019.i	−0.170186	−	0.294772i
$806$		0			0
$807$	166583.	−	122923.i	0.255790	−	0.188750i
$808$		0			0
$809$			36105.2i			0.0551661i	0.999620	+	0.0275831i	$0.00878108\pi$
$809$			36105.2i			0.0551661i	−0.999620	+	0.0275831i	$0.991219\pi$
$810$		0			0
$811$	−793848.			−1.20697			−0.603484	−	0.797375i	$-0.706221\pi$
$811$	−793848.			−1.20697			−0.603484	+	0.797375i	$0.706221\pi$
$812$		0			0
$813$	−289000.	−	391647.i	−0.437237	−	0.592535i
$814$		0			0
$815$	−46747.9	+	26989.9i	−0.0703796	+	0.0406337i
$816$		0			0
$817$	−31879.9	+	55217.6i	−0.0477609	+	0.0827244i
$818$		0			0
$819$	54542.2	−	176720.i	0.0813139	−	0.263462i
$820$		0			0
$821$	75446.3	+	43559.0i	0.111931	+	0.0646236i	0.554921	−	0.831903i	$-0.312749\pi$
$821$	75446.3	+	43559.0i	0.111931	+	0.0646236i	−0.442989	+	0.896527i	$0.646082\pi$
$822$		0			0
$823$	304745.	+	527834.i	0.449922	+	0.779288i	0.998380	−	0.0568898i	$-0.0181184\pi$
$823$	304745.	+	527834.i	0.449922	+	0.779288i	−0.548458	+	0.836178i	$0.684785\pi$
$824$		0			0
$825$	−260639.	−	113741.i	−0.382941	−	0.167112i
$826$		0			0
$827$			555364.i			0.812020i	0.913869	+	0.406010i	$0.133080\pi$
$827$			555364.i			0.812020i	−0.913869	+	0.406010i	$0.866920\pi$
$828$		0			0
$829$	−427152.			−0.621546			−0.310773	−	0.950484i	$-0.600588\pi$
$829$	−427152.			−0.621546			−0.310773	+	0.950484i	$0.600588\pi$
$830$		0			0
$831$	−100780.	+	11347.0i	−0.145939	+	0.0164315i
$832$		0			0
$833$	−9241.68	+	5335.69i	−0.0133187	+	0.00768954i
$834$		0			0
$835$	3933.85	−	6813.62i	0.00564215	−	0.00977249i
$836$		0			0
$837$	−639856.	−	550910.i	−0.913338	−	0.786375i
$838$		0			0
$839$	−640752.	−	369938.i	−0.910262	−	0.525540i	−0.0297463	−	0.999557i	$-0.509470\pi$
$839$	−640752.	−	369938.i	−0.910262	−	0.525540i	−0.880515	+	0.474018i	$0.842803\pi$
$840$		0			0
$841$	−195460.	−	338547.i	−0.276354	−	0.478659i
$842$		0			0
$843$	41910.5	+	372236.i	0.0589749	+	0.523797i
$844$		0			0
$845$		−	171957.i		−	0.240828i
$846$		0			0
$847$	487781.			0.679921
$848$		0			0
$849$	−190305.	+	436089.i	−0.264019	+	0.605005i
$850$		0			0
$851$	−214044.	+	123578.i	−0.295558	+	0.170641i
$852$		0			0
$853$	−166271.	+	287990.i	−0.228517	+	0.395804i	−0.957369	−	0.288868i	$-0.906721\pi$
$853$	−166271.	+	287990.i	−0.228517	+	0.395804i	0.728852	+	0.684672i	$0.240054\pi$
$854$		0			0
$855$	−195480.	−	857089.i	−0.267405	−	1.17245i
$856$		0			0
$857$	934516.	+	539543.i	1.27240	+	0.734623i	0.975440	−	0.220266i	$-0.0706925\pi$
$857$	934516.	+	539543.i	1.27240	+	0.734623i	0.296964	+	0.954889i	$0.404026\pi$
$858$		0			0
$859$	−507561.	−	879121.i	−0.687863	−	1.19141i	−0.972528	−	0.232786i	$-0.925216\pi$
$859$	−507561.	−	879121.i	−0.687863	−	1.19141i	0.284665	−	0.958627i	$-0.408118\pi$
$860$		0			0
$861$	−227516.	+	167886.i	−0.306906	+	0.226468i
$862$		0			0
$863$		−	929697.i		−	1.24830i	−0.781304	−	0.624151i	$-0.785445\pi$
$863$		−	929697.i		−	1.24830i	0.781304	−	0.624151i	$-0.214555\pi$
$864$		0			0
$865$	75529.2			0.100945
$866$		0			0
$867$	−446188.	−	604665.i	−0.593580	−	0.804408i
$868$		0			0
$869$	1.27814e6	−	737935.i	1.69254	−	0.977189i
$870$		0			0
$871$	−328062.	+	568220.i	−0.432434	+	0.748998i
$872$		0			0
$873$	776014.	+	836614.i	1.01822	+	1.09773i
$874$		0			0
$875$	232135.	+	134023.i	0.303197	+	0.175051i
$876$		0			0
$877$	130413.	+	225882.i	0.169559	+	0.293685i	0.938265	−	0.345917i	$-0.112432\pi$
$877$	130413.	+	225882.i	0.169559	+	0.293685i	−0.768706	+	0.639603i	$0.779099\pi$
$878$		0			0
$879$	1.29235e6	+	563971.i	1.67264	+	0.729926i
$880$		0			0
$881$		−	279713.i		−	0.360380i	−0.983632	−	0.180190i	$-0.942329\pi$
$881$		−	279713.i		−	0.360380i	0.983632	−	0.180190i	$-0.0576713\pi$
$882$		0			0
$883$	49556.0			0.0635586			0.0317793	−	0.999495i	$-0.489883\pi$
$883$	49556.0			0.0635586			0.0317793	+	0.999495i	$0.489883\pi$
$884$		0			0
$885$	−787258.	+	88638.3i	−1.00515	+	0.113171i
$886$		0			0
$887$	984786.	−	568566.i	1.25168	−	0.722660i	0.280240	−	0.959930i	$-0.409586\pi$
$887$	984786.	−	568566.i	1.25168	−	0.722660i	0.971444	+	0.237270i	$0.0762526\pi$
$888$		0			0
$889$	−188376.	+	326277.i	−0.238354	+	0.412841i
$890$		0			0
$891$	605923.	+	1.25925e6i	0.763241	+	1.58620i
$892$		0			0
$893$	−1.01695e6	−	587135.i	−1.27525	−	0.736267i
$894$		0			0
$895$	−418600.	−	725036.i	−0.522580	−	0.905135i
$896$		0			0
$897$	92161.4	+	818549.i	0.114542	+	1.01733i
$898$		0			0
$899$		−	651454.i		−	0.806054i
$900$		0			0
$901$	13316.1			0.0164031
$902$		0			0
$903$	−7329.83	+	16796.5i	−0.00898915	+	0.0205988i
$904$		0			0
$905$	−1.11634e6	+	644517.i	−1.36301	+	0.786932i
$906$		0			0
$907$	273428.	−	473592.i	0.332375	−	0.575691i	−0.650602	−	0.759419i	$-0.725483\pi$
$907$	273428.	−	473592.i	0.332375	−	0.575691i	0.982977	+	0.183728i	$0.0588165\pi$
$908$		0			0
$909$	294321.	−	273002.i	0.356200	−	0.330398i
$910$		0			0
$911$	−136770.	−	78964.4i	−0.164799	−	0.0951469i	0.415332	−	0.909670i	$-0.363665\pi$
$911$	−136770.	−	78964.4i	−0.164799	−	0.0951469i	−0.580131	+	0.814523i	$0.696999\pi$
$912$		0			0
$913$	−581217.	−	1.00670e6i	−0.697263	−	1.20769i
$914$		0			0
$915$	−818626.	+	604072.i	−0.977785	+	0.721516i
$916$		0			0
$917$		−	205268.i		−	0.244109i
$918$		0			0
$919$	−1.31571e6			−1.55787			−0.778934	−	0.627106i	$-0.784239\pi$
$919$	−1.31571e6			−1.55787			−0.778934	+	0.627106i	$0.784239\pi$
$920$		0			0
$921$	45161.7	+	61202.2i	0.0532416	+	0.0721519i
$922$		0			0
$923$	481936.	−	278246.i	0.565700	−	0.326607i
$924$		0			0
$925$	28808.1	−	49897.1i	0.0336691	−	0.0583165i
$926$		0			0
$927$	−1.52260e6	+	347265.i	−1.77184	+	0.404111i
$928$		0			0
$929$	−1.03802e6	−	599304.i	−1.20275	−	0.694409i	−0.241586	−	0.970379i	$-0.577668\pi$
$929$	−1.03802e6	−	599304.i	−1.20275	−	0.694409i	−0.961166	+	0.275970i	$0.911001\pi$
$930$		0			0
$931$	−534135.	−	925149.i	−0.616242	−	1.06736i
$932$		0			0
$933$	−142646.	−	62249.5i	−0.163869	−	0.0715109i
$934$		0			0
$935$		−	23091.8i		−	0.0264140i
$936$		0			0
$937$	689721.			0.785587			0.392793	−	0.919627i	$-0.371509\pi$
$937$	689721.			0.785587			0.392793	+	0.919627i	$0.371509\pi$
$938$		0			0
$939$	997433.	−	112302.i	1.13123	−	0.127367i
$940$		0			0
$941$	114419.	−	66059.7i	0.129216	−	0.0746031i	−0.433998	−	0.900914i	$-0.642898\pi$
$941$	114419.	−	66059.7i	0.129216	−	0.0746031i	0.563215	+	0.826310i	$0.309564\pi$
$942$		0			0
$943$	629669.	−	1.09062e6i	0.708091	−	1.22645i
$944$		0			0
$945$	−83395.5	−	238516.i	−0.0933854	−	0.267087i
$946$		0			0
$947$	147280.	+	85032.2i	0.164227	+	0.0948164i	0.579861	−	0.814716i	$-0.303107\pi$
$947$	147280.	+	85032.2i	0.164227	+	0.0948164i	−0.415634	+	0.909532i	$0.636440\pi$
$948$		0			0
$949$	466610.	+	808193.i	0.518110	+	0.897393i
$950$		0			0
$951$	−120708.	−	1.07209e6i	−0.133468	−	1.18542i
$952$		0			0
$953$		−	214124.i		−	0.235765i	−0.993028	−	0.117882i	$-0.962389\pi$
$953$		−	214124.i		−	0.235765i	0.993028	−	0.117882i	$-0.0376106\pi$
$954$		0			0
$955$	−660410.			−0.724113
$956$		0			0
$957$	−431243.	+	988202.i	−0.470867	+	1.07900i
$958$		0			0
$959$	−90059.9	+	51996.1i	−0.0979251	+	0.0565371i
$960$		0			0
$961$	−208980.	+	361964.i	−0.226286	+	0.391939i
$962$		0			0
$963$	−875322.	−	270156.i	−0.943877	−	0.291314i
$964$		0			0
$965$	365023.	+	210746.i	0.391982	+	0.226311i
$966$		0			0
$967$	−870485.	−	1.50772e6i	−0.930912	−	1.61239i	−0.781767	−	0.623571i	$-0.785681\pi$
$967$	−870485.	−	1.50772e6i	−0.930912	−	1.61239i	−0.149145	−	0.988815i	$-0.547652\pi$
$968$		0			0
$969$	−17876.9	+	13191.5i	−0.0190390	+	0.0140490i
$970$		0			0
$971$		−	338488.i		−	0.359009i	−0.983757	−	0.179504i	$-0.942551\pi$
$971$		−	338488.i		−	0.359009i	0.983757	−	0.179504i	$-0.0574494\pi$
$972$		0			0
$973$	220988.			0.233422
$974$		0			0
$975$	−114015.	−	154510.i	−0.119936	−	0.162536i
$976$		0			0
$977$	789669.	−	455915.i	0.827286	−	0.477634i	−0.0256365	−	0.999671i	$-0.508161\pi$
$977$	789669.	−	455915.i	0.827286	−	0.477634i	0.852923	+	0.522038i	$0.174828\pi$
$978$		0			0
$979$	−1.53705e6	+	2.66226e6i	−1.60370	+	2.77769i
$980$		0			0
$981$	−493639.	+	1.59942e6i	−0.512946	+	1.66198i
$982$		0			0
$983$	1.27036e6	+	733441.i	1.31468	+	0.759029i	0.982867	−	0.184317i	$-0.0590074\pi$
$983$	1.27036e6	+	733441.i	1.31468	+	0.759029i	0.331810	+	0.943346i	$0.392341\pi$
$984$		0			0
$985$	−295504.	−	511828.i	−0.304573	−	0.527536i
$986$		0			0
$987$	−309342.	−	134994.i	−0.317545	−	0.138574i
$988$		0			0
$989$		−	81621.9i		−	0.0834477i
$990$		0			0
$991$	−360723.			−0.367305			−0.183652	−	0.982991i	$-0.558792\pi$
$991$	−360723.			−0.367305			−0.183652	+	0.982991i	$0.558792\pi$
$992$		0			0
$993$	1.28853e6	−	145077.i	1.30676	−	0.147130i
$994$		0			0
$995$	−445183.	+	257027.i	−0.449669	+	0.259616i
$996$		0			0
$997$	−165243.	+	286209.i	−0.166239	+	0.287934i	−0.937095	−	0.349076i	$-0.886496\pi$
$997$	−165243.	+	286209.i	−0.166239	+	0.287934i	0.770856	+	0.637010i	$0.219829\pi$
$998$		0			0
$999$	−267265.	+	93447.4i	−0.267800	+	0.0936346i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.5.m.a.65.5	yes	24
3.2	odd	2		216.5.m.a.89.4		24
4.3	odd	2		144.5.q.d.65.8		24
9.2	odd	6		648.5.e.c.161.8		24
9.4	even	3		216.5.m.a.17.4		24
9.5	odd	6	inner	72.5.m.a.41.5	✓	24
9.7	even	3		648.5.e.c.161.17		24
12.11	even	2		432.5.q.d.305.4		24
36.7	odd	6		1296.5.e.j.161.17		24
36.11	even	6		1296.5.e.j.161.8		24
36.23	even	6		144.5.q.d.113.8		24
36.31	odd	6		432.5.q.d.17.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.5.m.a.41.5	✓	24	9.5	odd	6	inner
72.5.m.a.65.5	yes	24	1.1	even	1	trivial
144.5.q.d.65.8		24	4.3	odd	2
144.5.q.d.113.8		24	36.23	even	6
216.5.m.a.17.4		24	9.4	even	3
216.5.m.a.89.4		24	3.2	odd	2
432.5.q.d.17.4		24	36.31	odd	6
432.5.q.d.305.4		24	12.11	even	2
648.5.e.c.161.8		24	9.2	odd	6
648.5.e.c.161.17		24	9.7	even	3
1296.5.e.j.161.8		24	36.11	even	6
1296.5.e.j.161.17		24	36.7	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 72 = 2^{3} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	72.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.34380 - 7.24181i) q^{3} +(18.9074 - 10.9162i) q^{5} +(7.93787 - 13.7488i) q^{7} +(-23.8877 + 77.3975i) q^{9} +O(q^{10})\)	\(q+(-5.34380 - 7.24181i) q^{3} +(18.9074 - 10.9162i) q^{5} +(7.93787 - 13.7488i) q^{7} +(-23.8877 + 77.3975i) q^{9} +(-184.457 - 106.496i) q^{11} +(-71.9110 - 124.553i) q^{13} +(-180.090 - 78.5897i) q^{15} +4.96583i q^{17} -497.110 q^{19} +(-141.985 + 15.9862i) q^{21} +(551.116 - 318.187i) q^{23} +(-74.1746 + 128.474i) q^{25} +(688.149 - 240.607i) q^{27} +(487.104 + 281.230i) q^{29} +(-579.112 - 1003.05i) q^{31} +(214.475 + 1904.90i) q^{33} -346.605i q^{35} -388.382 q^{37} +(-517.715 + 1186.35i) q^{39} +(1713.80 - 989.464i) q^{41} +(64.1305 - 111.077i) q^{43} +(393.232 + 1724.14i) q^{45} +(2045.72 + 1181.10i) q^{47} +(1074.48 + 1861.05i) q^{49} +(35.9616 - 26.5364i) q^{51} -2681.54i q^{53} -4650.13 q^{55} +(2656.45 + 3599.98i) q^{57} +(3491.73 - 2015.95i) q^{59} +(2588.86 - 4484.03i) q^{61} +(874.506 + 942.798i) q^{63} +(-2719.29 - 1569.98i) q^{65} +(-2281.03 - 3950.86i) q^{67} +(-5249.30 - 2290.75i) q^{69} +3869.31i q^{71} -6488.72 q^{73} +(1326.76 - 149.382i) q^{75} +(-2928.40 + 1690.71i) q^{77} +(-3464.60 + 6000.86i) q^{79} +(-5419.76 - 3697.69i) q^{81} +(4726.44 + 2728.81i) q^{83} +(54.2078 + 93.8907i) q^{85} +(-566.374 - 5030.35i) q^{87} -14432.9i q^{89} -2283.28 q^{91} +(-4169.25 + 9553.92i) q^{93} +(-9399.03 + 5426.53i) q^{95} +(7043.86 - 12200.3i) q^{97} +(12648.8 - 11732.6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{3} - 100 q^{9}+O(q^{10}) \) 24 * q + 4 * q^3 - 100 * q^9	\( 24 q + 4 q^{3} - 100 q^{9} + 252 q^{11} - 80 q^{15} - 408 q^{19} + 24 q^{21} + 720 q^{23} + 1500 q^{25} - 1280 q^{27} + 2376 q^{29} - 1104 q^{31} - 1412 q^{33} - 4184 q^{39} + 1980 q^{41} + 1476 q^{43} - 4696 q^{45} + 4536 q^{47} - 6084 q^{49} - 7828 q^{51} + 2544 q^{55} - 1204 q^{57} + 10332 q^{59} + 2784 q^{61} + 9072 q^{63} + 17280 q^{65} - 2604 q^{67} + 5680 q^{69} + 5112 q^{73} - 15412 q^{75} - 28368 q^{77} + 3480 q^{79} - 26548 q^{81} - 23400 q^{83} + 7392 q^{85} - 3192 q^{87} - 14208 q^{91} + 39488 q^{93} + 57528 q^{95} - 4020 q^{97} + 50744 q^{99}+O(q^{100}) \) 24 * q + 4 * q^3 - 100 * q^9 + 252 * q^11 - 80 * q^15 - 408 * q^19 + 24 * q^21 + 720 * q^23 + 1500 * q^25 - 1280 * q^27 + 2376 * q^29 - 1104 * q^31 - 1412 * q^33 - 4184 * q^39 + 1980 * q^41 + 1476 * q^43 - 4696 * q^45 + 4536 * q^47 - 6084 * q^49 - 7828 * q^51 + 2544 * q^55 - 1204 * q^57 + 10332 * q^59 + 2784 * q^61 + 9072 * q^63 + 17280 * q^65 - 2604 * q^67 + 5680 * q^69 + 5112 * q^73 - 15412 * q^75 - 28368 * q^77 + 3480 * q^79 - 26548 * q^81 - 23400 * q^83 + 7392 * q^85 - 3192 * q^87 - 14208 * q^91 + 39488 * q^93 + 57528 * q^95 - 4020 * q^97 + 50744 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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