LMFDB - Embedded newform 72.5.m.a.41.4

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			41.4
Character	$\chi$	$=$	72.41
Dual form			72.5.m.a.65.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.78971 - 6.89052i) q^{3} +(38.2277 + 22.0708i) q^{5} +(-25.3787 - 43.9571i) q^{7} +(-13.9586 + 79.7882i) q^{9} +O(q^{10})$	\(q+(-5.78971 - 6.89052i) q^{3} +(38.2277 + 22.0708i) q^{5} +(-25.3787 - 43.9571i) q^{7} +(-13.9586 + 79.7882i) q^{9} +(97.7398 - 56.4301i) q^{11} +(109.158 - 189.067i) q^{13} +(-69.2482 - 391.193i) q^{15} -512.392i q^{17} +170.583 q^{19} +(-155.952 + 429.371i) q^{21} +(-30.4088 - 17.5565i) q^{23} +(661.740 + 1146.17i) q^{25} +(630.598 - 365.769i) q^{27} +(-489.529 + 282.630i) q^{29} +(-317.942 + 550.691i) q^{31} +(-954.718 - 346.764i) q^{33} -2240.51i q^{35} -483.589 q^{37} +(-1934.77 + 342.489i) q^{39} +(2259.06 + 1304.27i) q^{41} +(751.490 + 1301.62i) q^{43} +(-2294.59 + 2742.05i) q^{45} +(647.472 - 373.818i) q^{47} +(-87.6532 + 151.820i) q^{49} +(-3530.65 + 2966.60i) q^{51} +149.011i q^{53} +4981.83 q^{55} +(-987.626 - 1175.41i) q^{57} +(-5335.47 - 3080.43i) q^{59} +(637.441 + 1104.08i) q^{61} +(3861.51 - 1411.34i) q^{63} +(8345.73 - 4818.41i) q^{65} +(-2426.86 + 4203.45i) q^{67} +(55.0845 + 311.180i) q^{69} +55.8211i q^{71} -4173.80 q^{73} +(4066.41 - 11195.7i) q^{75} +(-4961.01 - 2864.24i) q^{77} +(5397.28 + 9348.36i) q^{79} +(-6171.32 - 2227.46i) q^{81} +(-2352.51 + 1358.22i) q^{83} +(11308.9 - 19587.6i) q^{85} +(4781.70 + 1736.77i) q^{87} +122.270i q^{89} -11081.1 q^{91} +(5635.34 - 997.557i) q^{93} +(6521.01 + 3764.91i) q^{95} +(-2769.79 - 4797.41i) q^{97} +(3138.15 + 8586.17i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/72\mathbb{Z}\right)^\times$.

$n$	$37$	$55$	$65$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

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
$3$	−5.78971	−	6.89052i	−0.643301	−	0.765613i
$3$	−5.78971	−	6.89052i	−0.643301	−	0.765613i
$4$		0			0
$5$	38.2277	+	22.0708i	1.52911	+	0.882832i	0.999399	+	0.0346533i	$0.0110327\pi$
$5$	38.2277	+	22.0708i	1.52911	+	0.882832i	0.529710	+	0.848179i	$0.322301\pi$
$6$		0			0
$7$	−25.3787	−	43.9571i	−0.517932	−	0.897084i	−0.999783	−	0.0208313i	$-0.993369\pi$
$7$	−25.3787	−	43.9571i	−0.517932	−	0.897084i	0.481851	−	0.876253i	$-0.339965\pi$
$8$		0			0
$9$	−13.9586	+	79.7882i	−0.172328	+	0.985040i
$10$		0			0
$11$	97.7398	−	56.4301i	0.807767	−	0.466365i	−0.0384127	−	0.999262i	$-0.512230\pi$
$11$	97.7398	−	56.4301i	0.807767	−	0.466365i	0.846180	+	0.532897i	$0.178897\pi$
$12$		0			0
$13$	109.158	−	189.067i	0.645906	−	1.11874i	−0.338186	−	0.941079i	$-0.609813\pi$
$13$	109.158	−	189.067i	0.645906	−	1.11874i	0.984092	−	0.177662i	$-0.0568534\pi$
$14$		0			0
$15$	−69.2482	−	391.193i	−0.307770	−	1.73863i
$16$		0			0
$17$		−	512.392i		−	1.77298i	−0.462744	−	0.886492i	$-0.653135\pi$
$17$		−	512.392i		−	1.77298i	0.462744	−	0.886492i	$-0.346865\pi$
$18$		0			0
$19$	170.583			0.472529			0.236265	−	0.971689i	$-0.424077\pi$
$19$	170.583			0.472529			0.236265	+	0.971689i	$0.424077\pi$
$20$		0			0
$21$	−155.952	+	429.371i	−0.353634	+	0.973631i
$22$		0			0
$23$	−30.4088	−	17.5565i	−0.0574836	−	0.0331882i	0.470983	−	0.882142i	$-0.343899\pi$
$23$	−30.4088	−	17.5565i	−0.0574836	−	0.0331882i	−0.528466	+	0.848954i	$0.677233\pi$
$24$		0			0
$25$	661.740	+	1146.17i	1.05878	+	1.83387i
$26$		0			0
$27$	630.598	−	365.769i	0.865018	−	0.501740i
$28$		0			0
$29$	−489.529	+	282.630i	−0.582080	+	0.336064i	−0.761960	−	0.647625i	$-0.775762\pi$
$29$	−489.529	+	282.630i	−0.582080	+	0.336064i	0.179880	+	0.983689i	$0.442429\pi$
$30$		0			0
$31$	−317.942	+	550.691i	−0.330844	+	0.573039i	−0.982678	−	0.185323i	$-0.940667\pi$
$31$	−317.942	+	550.691i	−0.330844	+	0.573039i	0.651833	+	0.758362i	$0.274000\pi$
$32$		0			0
$33$	−954.718	−	346.764i	−0.876692	−	0.318425i
$34$		0			0
$35$		−	2240.51i		−	1.82899i
$36$		0			0
$37$	−483.589			−0.353242			−0.176621	−	0.984279i	$-0.556517\pi$
$37$	−483.589			−0.353242			−0.176621	+	0.984279i	$0.556517\pi$
$38$		0			0
$39$	−1934.77	+	342.489i	−1.27204	+	0.225173i
$40$		0			0
$41$	2259.06	+	1304.27i	1.34388	+	0.775890i	0.987374	−	0.158404i	$-0.0506347\pi$
$41$	2259.06	+	1304.27i	1.34388	+	0.775890i	0.356506	+	0.934293i	$0.383968\pi$
$42$		0			0
$43$	751.490	+	1301.62i	0.406431	+	0.703959i	0.994487	−	0.104861i	$-0.0334399\pi$
$43$	751.490	+	1301.62i	0.406431	+	0.703959i	−0.588056	+	0.808820i	$0.700107\pi$
$44$		0			0
$45$	−2294.59	+	2742.05i	−1.13313	+	1.35410i
$46$		0			0
$47$	647.472	−	373.818i	0.293106	−	0.169225i	−0.346236	−	0.938148i	$-0.612540\pi$
$47$	647.472	−	373.818i	0.293106	−	0.169225i	0.639342	+	0.768923i	$0.279207\pi$
$48$		0			0
$49$	−87.6532	+	151.820i	−0.0365069	+	0.0632319i
$50$		0			0
$51$	−3530.65	+	2966.60i	−1.35742	+	1.14056i
$52$		0			0
$53$			149.011i			0.0530478i	0.999648	+	0.0265239i	$0.00844382\pi$
$53$			149.011i			0.0530478i	−0.999648	+	0.0265239i	$0.991556\pi$
$54$		0			0
$55$	4981.83			1.64689
$56$		0			0
$57$	−987.626	−	1175.41i	−0.303979	−	0.361775i
$58$		0			0
$59$	−5335.47	−	3080.43i	−1.53274	−	0.884928i	−0.999234	−	0.0391321i	$-0.987541\pi$
$59$	−5335.47	−	3080.43i	−1.53274	−	0.884928i	−0.533506	−	0.845796i	$-0.679126\pi$
$60$		0			0
$61$	637.441	+	1104.08i	0.171309	+	0.296716i	0.938878	−	0.344251i	$-0.111867\pi$
$61$	637.441	+	1104.08i	0.171309	+	0.296716i	−0.767569	+	0.640967i	$0.778534\pi$
$62$		0			0
$63$	3861.51	−	1411.34i	0.972918	−	0.355591i
$64$		0			0
$65$	8345.73	−	4818.41i	1.97532	−	1.14045i
$66$		0			0
$67$	−2426.86	+	4203.45i	−0.540624	+	0.936389i	0.458244	+	0.888826i	$0.348479\pi$
$67$	−2426.86	+	4203.45i	−0.540624	+	0.936389i	−0.998868	+	0.0475623i	$0.984855\pi$
$68$		0			0
$69$	55.0845	+	311.180i	0.0115699	+	0.0653602i
$70$		0			0
$71$			55.8211i			0.0110734i	0.999985	+	0.00553671i	$0.00176240\pi$
$71$			55.8211i			0.0110734i	−0.999985	+	0.00553671i	$0.998238\pi$
$72$		0			0
$73$	−4173.80			−0.783224			−0.391612	−	0.920130i	$-0.628082\pi$
$73$	−4173.80			−0.783224			−0.391612	+	0.920130i	$0.628082\pi$
$74$		0			0
$75$	4066.41	−	11195.7i	0.722917	−	1.99035i
$76$		0			0
$77$	−4961.01	−	2864.24i	−0.836737	−	0.483090i
$78$		0			0
$79$	5397.28	+	9348.36i	0.864810	+	1.49790i	0.867236	+	0.497898i	$0.165895\pi$
$79$	5397.28	+	9348.36i	0.864810	+	1.49790i	−0.00242541	+	0.999997i	$0.500772\pi$
$80$		0			0
$81$	−6171.32	−	2227.46i	−0.940606	−	0.339500i
$82$		0			0
$83$	−2352.51	+	1358.22i	−0.341488	+	0.197158i	−0.660930	−	0.750448i	$-0.729838\pi$
$83$	−2352.51	+	1358.22i	−0.341488	+	0.197158i	0.319442	+	0.947606i	$0.396505\pi$
$84$		0			0
$85$	11308.9	−	19587.6i	1.56525	−	2.71109i
$86$		0			0
$87$	4781.70	+	1736.77i	0.631748	+	0.229458i
$88$		0			0
$89$			122.270i			0.0154362i	0.999970	+	0.00771810i	$0.00245677\pi$
$89$			122.270i			0.0154362i	−0.999970	+	0.00771810i	$0.997543\pi$
$90$		0			0
$91$	−11081.1			−1.33814
$92$		0			0
$93$	5635.34	−	997.557i	0.651559	−	0.115338i
$94$		0			0
$95$	6521.01	+	3764.91i	0.722549	+	0.417164i
$96$		0			0
$97$	−2769.79	−	4797.41i	−0.294376	−	0.509875i	0.680463	−	0.732782i	$-0.261779\pi$
$97$	−2769.79	−	4797.41i	−0.294376	−	0.509875i	−0.974840	+	0.222908i	$0.928445\pi$
$98$		0			0
$99$	3138.15	+	8586.17i	0.320187	+	0.876050i
$100$		0			0
$101$	433.584	−	250.330i	0.0425041	−	0.0245397i	−0.478597	−	0.878034i	$-0.658855\pi$
$101$	433.584	−	250.330i	0.0425041	−	0.0245397i	0.521101	+	0.853495i	$0.325521\pi$
$102$		0			0
$103$	811.305	−	1405.22i	0.0764733	−	0.132456i	−0.825253	−	0.564764i	$-0.808967\pi$
$103$	811.305	−	1405.22i	0.0764733	−	0.132456i	0.901726	+	0.432308i	$0.142301\pi$
$104$		0			0
$105$	−15438.3	+	12971.9i	−1.40030	+	1.17659i
$106$		0			0
$107$			6430.58i			0.561672i	0.959756	+	0.280836i	$0.0906116\pi$
$107$			6430.58i			0.561672i	−0.959756	+	0.280836i	$0.909388\pi$
$108$		0			0
$109$	−8245.27			−0.693988			−0.346994	−	0.937867i	$-0.612798\pi$
$109$	−8245.27			−0.693988			−0.346994	+	0.937867i	$0.612798\pi$
$110$		0			0
$111$	2799.84	+	3332.18i	0.227241	+	0.270447i
$112$		0			0
$113$	12344.4	+	7127.04i	0.966747	+	0.558151i	0.898243	−	0.439499i	$-0.144844\pi$
$113$	12344.4	+	7127.04i	0.966747	+	0.558151i	0.0685038	+	0.997651i	$0.478177\pi$
$114$		0			0
$115$	−774.973	−	1342.29i	−0.0585991	−	0.101497i
$116$		0			0
$117$	13561.7	+	11348.6i	0.990697	+	0.829033i
$118$		0			0
$119$	−22523.3	+	13003.8i	−1.59052	+	0.918285i
$120$		0			0
$121$	−951.784	+	1648.54i	−0.0650081	+	0.112597i
$122$		0			0
$123$	−4092.21	−	23117.5i	−0.270488	−	1.52802i
$124$		0			0
$125$			30832.0i			1.97325i
$126$		0			0
$127$	−22907.3			−1.42025			−0.710127	−	0.704074i	$-0.751362\pi$
$127$	−22907.3			−1.42025			−0.710127	+	0.704074i	$0.751362\pi$
$128$		0			0
$129$	4617.93	−	12714.2i	0.277503	−	0.764026i
$130$		0			0
$131$	−12198.0	−	7042.51i	−0.710797	−	0.410379i	0.100559	−	0.994931i	$-0.467937\pi$
$131$	−12198.0	−	7042.51i	−0.710797	−	0.410379i	−0.811356	+	0.584552i	$0.801270\pi$
$132$		0			0
$133$	−4329.17	−	7498.34i	−0.244738	−	0.423899i
$134$		0			0
$135$	32179.2	−	64.7065i	1.76566	−	0.00355043i
$136$		0			0
$137$	−11536.2	+	6660.42i	−0.614640	+	0.354863i	−0.774779	−	0.632232i	$-0.782139\pi$
$137$	−11536.2	+	6660.42i	−0.614640	+	0.354863i	0.160139	+	0.987094i	$0.448806\pi$
$138$		0			0
$139$	10065.5	−	17433.9i	0.520960	−	0.902329i	−0.478743	−	0.877955i	$-0.658907\pi$
$139$	10065.5	−	17433.9i	0.520960	−	0.902329i	0.999703	−	0.0243739i	$-0.00775922\pi$
$140$		0			0
$141$	−6324.48	−	2297.12i	−0.318117	−	0.115544i
$142$		0			0
$143$		−	24639.2i		−	1.20491i
$144$		0			0
$145$	−24951.5			−1.18675
$146$		0			0
$147$	1553.60	−	275.016i	0.0718961	−	0.0127269i
$148$		0			0
$149$	7334.77	+	4234.73i	0.330380	+	0.190745i	0.656010	−	0.754752i	$-0.272243\pi$
$149$	7334.77	+	4234.73i	0.330380	+	0.190745i	−0.325630	+	0.945497i	$0.605576\pi$
$150$		0			0
$151$	20563.6	+	35617.2i	0.901872	+	1.56209i	0.825062	+	0.565042i	$0.191140\pi$
$151$	20563.6	+	35617.2i	0.901872	+	1.56209i	0.0768093	+	0.997046i	$0.475527\pi$
$152$		0			0
$153$	40882.9	+	7152.26i	1.74646	+	0.305535i
$154$		0			0
$155$	−24308.4	+	14034.4i	−1.01179	+	0.584160i
$156$		0			0
$157$	−7420.74	+	12853.1i	−0.301056	+	0.521445i	−0.976375	−	0.216081i	$-0.930673\pi$
$157$	−7420.74	+	12853.1i	−0.301056	+	0.521445i	0.675319	+	0.737526i	$0.264006\pi$
$158$		0			0
$159$	1026.77	−	862.733i	0.0406141	−	0.0341257i
$160$		0			0
$161$			1782.25i			0.0687568i
$162$		0			0
$163$	13130.0			0.494186			0.247093	−	0.968992i	$-0.420525\pi$
$163$	13130.0			0.494186			0.247093	+	0.968992i	$0.420525\pi$
$164$		0			0
$165$	−28843.3	−	34327.4i	−1.05944	−	1.26088i
$166$		0			0
$167$	24531.3	+	14163.2i	0.879606	+	0.507841i	0.870528	−	0.492118i	$-0.163777\pi$
$167$	24531.3	+	14163.2i	0.879606	+	0.507841i	0.00907732	+	0.999959i	$0.497111\pi$
$168$		0			0
$169$	−9550.46	−	16541.9i	−0.334388	−	0.579177i
$170$		0			0
$171$	−2381.09	+	13610.5i	−0.0814300	+	0.465460i
$172$		0			0
$173$	23142.6	−	13361.4i	0.773251	−	0.446437i	−0.0607823	−	0.998151i	$-0.519360\pi$
$173$	23142.6	−	13361.4i	0.773251	−	0.446437i	0.834033	+	0.551715i	$0.186026\pi$
$174$		0			0
$175$	33588.2	−	58176.4i	1.09676	−	1.89964i
$176$		0			0
$177$	9665.01	+	54599.0i	0.308501	+	1.74276i
$178$		0			0
$179$		−	34752.5i		−	1.08463i	−0.840176	−	0.542313i	$-0.817549\pi$
$179$		−	34752.5i		−	1.08463i	0.840176	−	0.542313i	$-0.182451\pi$
$180$		0			0
$181$	22289.2			0.680357			0.340179	−	0.940361i	$-0.389512\pi$
$181$	22289.2			0.680357			0.340179	+	0.940361i	$0.389512\pi$
$182$		0			0
$183$	3917.09	−	10784.6i	0.116966	−	0.322034i
$184$		0			0
$185$	−18486.5	−	10673.2i	−0.540146	−	0.311854i
$186$		0			0
$187$	−28914.4	−	50081.1i	−0.826857	−	1.43216i
$188$		0			0
$189$	−32081.9	−	18436.6i	−0.898124	−	0.516127i
$190$		0			0
$191$	51651.5	−	29821.0i	1.41585	−	0.817439i	0.419915	−	0.907563i	$-0.362060\pi$
$191$	51651.5	−	29821.0i	1.41585	−	0.817439i	0.995930	+	0.0901246i	$0.0287265\pi$
$192$		0			0
$193$	22184.3	−	38424.3i	0.595566	−	1.03155i	−0.397900	−	0.917429i	$-0.630261\pi$
$193$	22184.3	−	38424.3i	0.595566	−	1.03155i	0.993467	−	0.114123i	$-0.0364057\pi$
$194$		0			0
$195$	−81520.7	−	29609.2i	−2.14387	−	0.778678i
$196$		0			0
$197$			8590.53i			0.221354i	0.993856	+	0.110677i	$0.0353019\pi$
$197$			8590.53i			0.221354i	−0.993856	+	0.110677i	$0.964698\pi$
$198$		0			0
$199$	−68787.9			−1.73702			−0.868512	−	0.495667i	$-0.834923\pi$
$199$	−68787.9			−1.73702			−0.868512	+	0.495667i	$0.834923\pi$
$200$		0			0
$201$	43014.8	−	7614.40i	1.06470	−	0.188471i
$202$		0			0
$203$	24847.2	+	14345.5i	0.602955	+	0.348117i
$204$		0			0
$205$	57572.6	+	99718.6i	1.36996	+	2.37284i
$206$		0			0
$207$	1825.27	−	2181.20i	0.0425977	−	0.0509044i
$208$		0			0
$209$	16672.8	−	9626.03i	0.381694	−	0.220371i
$210$		0			0
$211$	−37251.2	+	64521.0i	−0.836712	+	1.44923i	0.0559174	+	0.998435i	$0.482192\pi$
$211$	−37251.2	+	64521.0i	−0.836712	+	1.44923i	−0.892629	+	0.450792i	$0.851142\pi$
$212$		0			0
$213$	384.637	−	323.188i	0.00847796	−	0.00712354i
$214$		0			0
$215$			66344.0i			1.43524i
$216$		0			0
$217$	32275.7			0.685420
$218$		0			0
$219$	24165.1	+	28759.7i	0.503849	+	0.599647i
$220$		0			0
$221$	−96876.6	−	55931.8i	−1.98351	−	1.14518i
$222$		0			0
$223$	46367.8	+	80311.4i	0.932410	+	1.61498i	0.779188	+	0.626790i	$0.215631\pi$
$223$	46367.8	+	80311.4i	0.932410	+	1.61498i	0.153222	+	0.988192i	$0.451035\pi$
$224$		0			0
$225$	−100688.	+	36800.2i	−1.98889	+	0.726918i
$226$		0			0
$227$	16817.9	−	9709.81i	0.326377	−	0.188434i	−0.327854	−	0.944728i	$-0.606326\pi$
$227$	16817.9	−	9709.81i	0.326377	−	0.188434i	0.654231	+	0.756294i	$0.272992\pi$
$228$		0			0
$229$	−32513.8	+	56315.5i	−0.620007	+	1.07388i	0.369477	+	0.929240i	$0.379537\pi$
$229$	−32513.8	+	56315.5i	−0.620007	+	1.07388i	−0.989484	+	0.144644i	$0.953796\pi$
$230$		0			0
$231$	8986.70	+	50767.1i	0.168413	+	0.951389i
$232$		0			0
$233$		−	77833.6i		−	1.43369i	−0.697233	−	0.716845i	$-0.745586\pi$
$233$		−	77833.6i		−	1.43369i	0.697233	−	0.716845i	$-0.254414\pi$
$234$		0			0
$235$	33001.9			0.597589
$236$		0			0
$237$	33166.4	−	91314.4i	0.590475	−	1.62571i
$238$		0			0
$239$	−17790.3	−	10271.2i	−0.311449	−	0.179815i	0.336126	−	0.941817i	$-0.390883\pi$
$239$	−17790.3	−	10271.2i	−0.311449	−	0.179815i	−0.647575	+	0.762002i	$0.724217\pi$
$240$		0			0
$241$	9151.28	+	15850.5i	0.157561	+	0.272903i	0.933988	−	0.357303i	$-0.116304\pi$
$241$	9151.28	+	15850.5i	0.157561	+	0.272903i	−0.776428	+	0.630206i	$0.782970\pi$
$242$		0			0
$243$	20381.8	+	55419.9i	0.345167	+	0.938541i
$244$		0			0
$245$	−6701.57	+	3869.15i	−0.111646	+	0.0644590i
$246$		0			0
$247$	18620.5	−	32251.7i	0.305209	−	0.528638i
$248$		0			0
$249$	22979.2	+	8346.30i	0.370626	+	0.134616i
$250$		0			0
$251$		−	19622.2i		−	0.311459i	−0.987800	−	0.155729i	$-0.950227\pi$
$251$		−	19622.2i		−	0.311459i	0.987800	−	0.155729i	$-0.0497728\pi$
$252$		0			0
$253$	−3962.87			−0.0619111
$254$		0			0
$255$	−200444.	+	35482.2i	−3.08257	+	0.545671i
$256$		0			0
$257$	−47070.2	−	27176.0i	−0.712655	−	0.411452i	0.0993883	−	0.995049i	$-0.468311\pi$
$257$	−47070.2	−	27176.0i	−0.712655	−	0.411452i	−0.812043	+	0.583597i	$0.801645\pi$
$258$		0			0
$259$	12272.8	+	21257.2i	0.182955	+	0.316888i
$260$		0			0
$261$	−15717.4	−	43003.8i	−0.230728	−	0.631285i
$262$		0			0
$263$	−32392.0	+	18701.5i	−0.468302	+	0.270374i	−0.715529	−	0.698583i	$-0.753814\pi$
$263$	−32392.0	+	18701.5i	−0.468302	+	0.270374i	0.247227	+	0.968958i	$0.420481\pi$
$264$		0			0
$265$	−3288.80	+	5696.37i	−0.0468323	+	0.0811160i
$266$		0			0
$267$	842.505	−	707.909i	0.0118182	−	0.00993013i
$268$		0			0
$269$			53589.2i			0.740581i	0.928916	+	0.370291i	$0.120742\pi$
$269$			53589.2i			0.740581i	−0.928916	+	0.370291i	$0.879258\pi$
$270$		0			0
$271$	94493.8			1.28666			0.643332	−	0.765588i	$-0.277552\pi$
$271$	94493.8			1.28666			0.643332	+	0.765588i	$0.277552\pi$
$272$		0			0
$273$	64156.6	+	76354.8i	0.860827	+	1.02450i
$274$		0			0
$275$	129357.	+	74684.2i	1.71050	+	0.987559i
$276$		0			0
$277$	10691.8	+	18518.7i	0.139345	+	0.241352i	0.927249	−	0.374446i	$-0.122167\pi$
$277$	10691.8	+	18518.7i	0.139345	+	0.241352i	−0.787904	+	0.615798i	$0.788834\pi$
$278$		0			0
$279$	−39500.6	−	33054.8i	−0.507453	−	0.424646i
$280$		0			0
$281$	125035.	−	72188.8i	1.58350	−	0.914234i	0.589156	−	0.808019i	$-0.299460\pi$
$281$	125035.	−	72188.8i	1.58350	−	0.914234i	0.994343	−	0.106215i	$-0.0338731\pi$
$282$		0			0
$283$	−8767.75	+	15186.2i	−0.109475	+	0.189616i	−0.915558	−	0.402187i	$-0.868250\pi$
$283$	−8767.75	+	15186.2i	−0.109475	+	0.189616i	0.806083	+	0.591803i	$0.201584\pi$
$284$		0			0
$285$	−11812.6	−	66730.8i	−0.145430	−	0.821555i
$286$		0			0
$287$		−	132403.i		−	1.60743i
$288$		0			0
$289$	−179025.			−2.14347
$290$		0			0
$291$	−17020.4	+	46860.9i	−0.200994	+	0.553381i
$292$		0			0
$293$	34315.6	+	19812.1i	0.399720	+	0.230778i	0.686363	−	0.727259i	$-0.259206\pi$
$293$	34315.6	+	19812.1i	0.399720	+	0.230778i	−0.286643	+	0.958037i	$0.592539\pi$
$294$		0			0
$295$	−135975.	−	235516.i	−1.56249	−	2.70630i
$296$		0			0
$297$	40994.2	−	71334.9i	0.464739	−	0.808703i
$298$		0			0
$299$	−6638.73	+	3832.87i	−0.0742579	+	0.0428728i
$300$		0			0
$301$	38143.6	−	66066.7i	0.421007	−	0.729205i
$302$		0			0
$303$	−4235.23	−	1538.28i	−0.0461309	−	0.0167553i
$304$		0			0
$305$			56275.3i			0.604948i
$306$		0			0
$307$	137590.			1.45986			0.729929	−	0.683523i	$-0.239553\pi$
$307$	137590.			1.45986			0.729929	+	0.683523i	$0.239553\pi$
$308$		0			0
$309$	−14379.9	+	2545.51i	−0.150605	+	0.0266598i
$310$		0			0
$311$	72837.2	+	42052.6i	0.753065	+	0.434782i	0.826800	−	0.562496i	$-0.190159\pi$
$311$	72837.2	+	42052.6i	0.753065	+	0.434782i	−0.0737354	+	0.997278i	$0.523492\pi$
$312$		0			0
$313$	4227.44	+	7322.14i	0.0431508	+	0.0747393i	0.886794	−	0.462165i	$-0.152927\pi$
$313$	4227.44	+	7322.14i	0.0431508	+	0.0747393i	−0.843643	+	0.536904i	$0.819594\pi$
$314$		0			0
$315$	178766.	+	31274.3i	1.80162	+	0.315185i
$316$		0			0
$317$	−117336.	+	67744.1i	−1.16765	+	0.674144i	−0.953126	−	0.302574i	$-0.902154\pi$
$317$	−117336.	+	67744.1i	−1.16765	+	0.674144i	−0.214526	+	0.976718i	$0.568821\pi$
$318$		0			0
$319$	−31897.7	+	55248.4i	−0.313457	+	0.542923i
$320$		0			0
$321$	44310.0	−	37231.2i	0.430023	−	0.361324i
$322$		0			0
$323$		−	87405.5i		−	0.837787i
$324$		0			0
$325$	288937.			2.73550
$326$		0			0
$327$	47737.7	+	56814.2i	0.446443	+	0.531327i
$328$		0			0
$329$	−32863.9	−	18974.0i	−0.303618	−	0.175294i
$330$		0			0
$331$	−72417.9	−	125431.i	−0.660982	−	1.14486i	−0.980358	−	0.197227i	$-0.936806\pi$
$331$	−72417.9	−	125431.i	−0.660982	−	1.14486i	0.319375	−	0.947628i	$-0.396527\pi$
$332$		0			0
$333$	6750.20	−	38584.7i	0.0608735	−	0.347958i
$334$		0			0
$335$	−185547.	+	107126.i	−1.65335	+	0.954561i
$336$		0			0
$337$	−94731.7	+	164080.i	−0.834133	+	1.44476i	0.0606007	+	0.998162i	$0.480698\pi$
$337$	−94731.7	+	164080.i	−0.834133	+	1.44476i	−0.894734	+	0.446599i	$0.852635\pi$
$338$		0			0
$339$	−22361.4	−	126323.i	−0.194581	−	1.09921i
$340$		0			0
$341$			71765.9i			0.617177i
$342$		0			0
$343$	−112970.			−0.960231
$344$		0			0
$345$	−4762.23	+	13111.5i	−0.0400103	+	0.110157i
$346$		0			0
$347$	−653.549	−	377.327i	−0.00542774	−	0.00313371i	0.497284	−	0.867588i	$-0.334331\pi$
$347$	−653.549	−	377.327i	−0.00542774	−	0.00313371i	−0.502711	+	0.864454i	$0.667664\pi$
$348$		0			0
$349$	−17907.0	−	31015.8i	−0.147018	−	0.254643i	0.783106	−	0.621888i	$-0.213634\pi$
$349$	−17907.0	−	31015.8i	−0.147018	−	0.254643i	−0.930124	+	0.367245i	$0.880301\pi$
$350$		0			0
$351$	−320.027	−	159152.i	−0.00259760	−	1.29181i
$352$		0			0
$353$	−7063.00	+	4077.82i	−0.0566813	+	0.0327249i	−0.528073	−	0.849199i	$-0.677085\pi$
$353$	−7063.00	+	4077.82i	−0.0566813	+	0.0327249i	0.471392	+	0.881924i	$0.343752\pi$
$354$		0			0
$355$	−1232.02	+	2133.92i	−0.00977597	+	0.0169325i
$356$		0			0
$357$	220007.	+	79908.9i	1.72623	+	0.626987i
$358$		0			0
$359$		−	94889.5i		−	0.736257i	−0.929775	−	0.368128i	$-0.879999\pi$
$359$		−	94889.5i		−	0.736257i	0.929775	−	0.368128i	$-0.120001\pi$
$360$		0			0
$361$	−101222.			−0.776716
$362$		0			0
$363$	16869.8	−	2986.27i	0.128026	−	0.0226629i
$364$		0			0
$365$	−159555.	−	92119.1i	−1.19764	−	0.691455i
$366$		0			0
$367$	6466.07	+	11199.6i	0.0480074	+	0.0831513i	0.889031	−	0.457848i	$-0.151380\pi$
$367$	6466.07	+	11199.6i	0.0480074	+	0.0831513i	−0.841023	+	0.540999i	$0.818046\pi$
$368$		0			0
$369$	−135599.	+	162041.i	−0.995870	+	1.19007i
$370$		0			0
$371$	6550.11	−	3781.71i	0.0475884	−	0.0274752i
$372$		0			0
$373$	15897.8	−	27535.9i	0.114267	−	0.197916i	−0.803220	−	0.595683i	$-0.796881\pi$
$373$	15897.8	−	27535.9i	0.114267	−	0.197916i	0.917486	+	0.397767i	$0.130215\pi$
$374$		0			0
$375$	212449.	−	178509.i	1.51075	−	1.26939i
$376$		0			0
$377$			123405.i			0.868262i
$378$		0			0
$379$	−116306.			−0.809702			−0.404851	−	0.914383i	$-0.632677\pi$
$379$	−116306.			−0.809702			−0.404851	+	0.914383i	$0.632677\pi$
$380$		0			0
$381$	132626.	+	157843.i	0.913650	+	1.08736i
$382$		0			0
$383$	136122.	+	78589.8i	0.927960	+	0.535758i	0.886166	−	0.463368i	$-0.153359\pi$
$383$	136122.	+	78589.8i	0.927960	+	0.535758i	0.0417944	+	0.999126i	$0.486693\pi$
$384$		0			0
$385$	−126432.	−	218987.i	−0.852975	−	1.47740i
$386$		0			0
$387$	−114344.	+	41791.3i	−0.763467	+	0.279039i
$388$		0			0
$389$	−149769.	+	86469.3i	−0.989745	+	0.571429i	−0.905198	−	0.424990i	$-0.860278\pi$
$389$	−149769.	+	86469.3i	−0.989745	+	0.571429i	−0.0845467	+	0.996420i	$0.526944\pi$
$390$		0			0
$391$	−8995.84	+	15581.2i	−0.0588421	+	0.101917i
$392$		0			0
$393$	22096.2	+	124825.i	0.143065	+	0.808193i
$394$		0			0
$395$			476489.i			3.05393i
$396$		0			0
$397$	19266.0			0.122239			0.0611197	−	0.998130i	$-0.480533\pi$
$397$	19266.0			0.122239			0.0611197	+	0.998130i	$0.480533\pi$
$398$		0			0
$399$	−26602.9	+	73243.5i	−0.167102	+	0.460069i
$400$		0			0
$401$	175910.	+	101562.i	1.09396	+	0.631600i	0.934629	−	0.355625i	$-0.115732\pi$
$401$	175910.	+	101562.i	1.09396	+	0.631600i	0.159334	+	0.987225i	$0.449065\pi$
$402$		0			0
$403$	69411.8	+	120225.i	0.427389	+	0.740259i
$404$		0			0
$405$	−186754.	−	221357.i	−1.13857	−	1.34953i
$406$		0			0
$407$	−47265.9	+	27289.0i	−0.285338	+	0.164740i
$408$		0			0
$409$	−24859.4	+	43057.8i	−0.148609	+	0.257398i	−0.930714	−	0.365749i	$-0.880813\pi$
$409$	−24859.4	+	43057.8i	−0.148609	+	0.257398i	0.782105	+	0.623147i	$0.214146\pi$
$410$		0			0
$411$	112685.	+	40928.4i	0.667086	+	0.242293i
$412$		0			0
$413$			312709.i			1.83333i
$414$		0			0
$415$	−119908.			−0.696229
$416$		0			0
$417$	−178405.	+	31580.9i	−1.02597	+	0.181615i
$418$		0			0
$419$	−217128.	−	125359.i	−1.23677	−	0.714048i	−0.268335	−	0.963326i	$-0.586473\pi$
$419$	−217128.	−	125359.i	−1.23677	−	0.714048i	−0.968432	+	0.249278i	$0.919807\pi$
$420$		0			0
$421$	−131633.	−	227996.i	−0.742680	−	1.28636i	−0.951271	−	0.308356i	$-0.900221\pi$
$421$	−131633.	−	227996.i	−0.742680	−	1.28636i	0.208591	−	0.978003i	$-0.433112\pi$
$422$		0			0
$423$	20788.5	+	56878.6i	0.116183	+	0.317884i
$424$		0			0
$425$	587288.	−	339071.i	3.25142	−	1.87721i
$426$		0			0
$427$	32354.8	−	56040.2i	0.177453	−	0.307357i
$428$		0			0
$429$	−169777.	+	142654.i	−0.922495	+	0.775120i
$430$		0			0
$431$		−	71778.8i		−	0.386404i	−0.981159	−	0.193202i	$-0.938113\pi$
$431$		−	71778.8i		−	0.386404i	0.981159	−	0.193202i	$-0.0618873\pi$
$432$		0			0
$433$	98830.3			0.527126			0.263563	−	0.964642i	$-0.415102\pi$
$433$	98830.3			0.527126			0.263563	+	0.964642i	$0.415102\pi$
$434$		0			0
$435$	144462.	+	171929.i	0.763439	+	0.908593i
$436$		0			0
$437$	−5187.23	−	2994.85i	−0.0271627	−	0.0156824i
$438$		0			0
$439$	41817.3	+	72429.7i	0.216984	+	0.375827i	0.953884	−	0.300174i	$-0.0970448\pi$
$439$	41817.3	+	72429.7i	0.216984	+	0.375827i	−0.736901	+	0.676001i	$0.763712\pi$
$440$		0			0
$441$	−10889.9	−	9112.87i	−0.0559948	−	0.0468574i
$442$		0			0
$443$	53753.6	−	31034.6i	0.273905	−	0.158139i	−0.356756	−	0.934198i	$-0.616117\pi$
$443$	53753.6	−	31034.6i	0.273905	−	0.158139i	0.630661	+	0.776059i	$0.282784\pi$
$444$		0			0
$445$	−2698.60	+	4674.11i	−0.0136276	+	0.0236037i
$446$		0			0
$447$	−13286.7	−	75058.3i	−0.0664969	−	0.375650i
$448$		0			0
$449$		−	308378.i		−	1.52965i	−0.644240	−	0.764823i	$-0.722826\pi$
$449$		−	308378.i		−	1.52965i	0.644240	−	0.764823i	$-0.277174\pi$
$450$		0			0
$451$	294400.			1.44739
$452$		0			0
$453$	126364.	−	347907.i	0.615780	−	1.69538i
$454$		0			0
$455$	−423607.	−	244570.i	−2.04616	−	1.18135i
$456$		0			0
$457$	−143417.	−	248405.i	−0.686701	−	1.18940i	−0.972899	−	0.231231i	$-0.925725\pi$
$457$	−143417.	−	248405.i	−0.686701	−	1.18940i	0.286197	−	0.958171i	$-0.407609\pi$
$458$		0			0
$459$	−187417.	−	323114.i	−0.889578	−	1.53366i
$460$		0			0
$461$	−291603.	+	168357.i	−1.37211	+	0.792190i	−0.991194	−	0.132418i	$-0.957726\pi$
$461$	−291603.	+	168357.i	−1.37211	+	0.792190i	−0.380919	+	0.924608i	$0.624392\pi$
$462$		0			0
$463$	−81274.8	+	140772.i	−0.379135	+	0.656682i	−0.990937	−	0.134330i	$-0.957112\pi$
$463$	−81274.8	+	140772.i	−0.379135	+	0.656682i	0.611801	+	0.791011i	$0.290445\pi$
$464$		0			0
$465$	237443.	+	86242.0i	1.09813	+	0.398853i
$466$		0			0
$467$		−	326818.i		−	1.49855i	−0.662257	−	0.749277i	$-0.730401\pi$
$467$		−	326818.i		−	1.49855i	0.662257	−	0.749277i	$-0.269599\pi$
$468$		0			0
$469$	246362.			1.12003
$470$		0			0
$471$	131528.	−	23282.9i	0.592895	−	0.104953i
$472$		0			0
$473$	146901.	+	84813.4i	0.656603	+	0.379090i
$474$		0			0
$475$	112882.	+	195517.i	0.500307	+	0.866557i
$476$		0			0
$477$	−11889.4	−	2079.98i	−0.0522542	−	0.00914162i
$478$		0			0
$479$	−1152.66	+	665.488i	−0.00502377	+	0.00290047i	−0.502510	−	0.864572i	$-0.667590\pi$
$479$	−1152.66	+	665.488i	−0.00502377	+	0.00290047i	0.497486	+	0.867472i	$0.334257\pi$
$480$		0			0
$481$	−52787.6	+	91430.8i	−0.228161	+	0.395187i
$482$		0			0
$483$	12280.6	−	10318.7i	0.0526411	−	0.0442313i
$484$		0			0
$485$		−	244526.i		−	1.03954i
$486$		0			0
$487$	243885.			1.02832			0.514159	−	0.857695i	$-0.328104\pi$
$487$	243885.			1.02832			0.514159	+	0.857695i	$0.328104\pi$
$488$		0			0
$489$	−76019.0	−	90472.7i	−0.317910	−	0.378355i
$490$		0			0
$491$	66723.9	+	38523.1i	0.276770	+	0.159793i	0.631960	−	0.775001i	$-0.282251\pi$
$491$	66723.9	+	38523.1i	0.276770	+	0.159793i	−0.355190	+	0.934794i	$0.615584\pi$
$492$		0			0
$493$	144817.	+	250831.i	0.595836	+	1.03202i
$494$		0			0
$495$	−69539.2	+	397491.i	−0.283804	+	1.62225i
$496$		0			0
$497$	2453.74	−	1416.67i	0.00993379	−	0.00573528i
$498$		0			0
$499$	−119555.	+	207075.i	−0.480137	+	0.831622i	−0.999740	−	0.0227854i	$-0.992747\pi$
$499$	−119555.	+	207075.i	−0.480137	+	0.831622i	0.519603	+	0.854408i	$0.326080\pi$
$500$		0			0
$501$	−44437.6	−	251034.i	−0.177042	−	1.00013i
$502$		0			0
$503$		−	157069.i		−	0.620804i	−0.950605	−	0.310402i	$-0.899536\pi$
$503$		−	157069.i		−	0.620804i	0.950605	−	0.310402i	$-0.100464\pi$
$504$		0			0
$505$	22099.9			0.0866579
$506$		0			0
$507$	−58687.8	+	161580.i	−0.228314	+	0.628597i
$508$		0			0
$509$	240851.	+	139055.i	0.929636	+	0.536726i	0.886696	−	0.462352i	$-0.152994\pi$
$509$	240851.	+	139055.i	0.929636	+	0.536726i	0.0429395	+	0.999078i	$0.486328\pi$
$510$		0			0
$511$	105925.	+	183468.i	0.405657	+	0.702618i
$512$		0			0
$513$	107569.	−	62394.0i	0.408747	−	0.237087i
$514$		0			0
$515$	62028.7	−	35812.3i	0.233872	−	0.135026i
$516$		0			0
$517$	42189.2	−	73073.8i	0.157841	−	0.273389i
$518$		0			0
$519$	−226056.	−	82106.1i	−0.839231	−	0.304818i
$520$		0			0
$521$			55441.1i			0.204247i	0.994772	+	0.102124i	$0.0325638\pi$
$521$			55441.1i			0.204247i	−0.994772	+	0.102124i	$0.967436\pi$
$522$		0			0
$523$	−14298.7			−0.0522750			−0.0261375	−	0.999658i	$-0.508321\pi$
$523$	−14298.7			−0.0522750			−0.0261375	+	0.999658i	$0.508321\pi$
$524$		0			0
$525$	−595331.	+	105384.i	−2.15993	+	0.382347i
$526$		0			0
$527$	282170.	+	162911.i	1.01599	+	0.586582i
$528$		0			0
$529$	−139304.	−	241282.i	−0.497797	−	0.862210i
$530$		0			0
$531$	320258.	−	382709.i	1.13582	−	1.35731i
$532$		0			0
$533$	493190.	−	284743.i	1.73604	−	1.00230i
$534$		0			0
$535$	−141928.	+	245826.i	−0.495862	+	0.858857i
$536$		0			0
$537$	−239463.	+	201207.i	−0.830405	+	0.697741i
$538$		0			0
$539$			19785.1i			0.0681022i
$540$		0			0
$541$	−279802.			−0.955996			−0.477998	−	0.878361i	$-0.658637\pi$
$541$	−279802.			−0.955996			−0.477998	+	0.878361i	$0.658637\pi$
$542$		0			0
$543$	−129048.	−	153584.i	−0.437675	−	0.520891i
$544$		0			0
$545$	−315198.	−	181980.i	−1.06118	−	0.612675i
$546$		0			0
$547$	−60949.4	−	105567.i	−0.203702	−	0.352822i	0.746017	−	0.665927i	$-0.231964\pi$
$547$	−60949.4	−	105567.i	−0.203702	−	0.352822i	−0.949718	+	0.313106i	$0.898631\pi$
$548$		0			0
$549$	−96990.3	+	35448.9i	−0.321798	+	0.117614i
$550$		0			0
$551$	−83505.4	+	48211.9i	−0.275050	+	0.158800i
$552$		0			0
$553$	273952.	−	474498.i	0.895826	−	1.55162i
$554$		0			0
$555$	33487.6	+	189176.i	0.108717	+	0.614159i
$556$		0			0
$557$		−	264259.i		−	0.851765i	−0.904779	−	0.425882i	$-0.859964\pi$
$557$		−	264259.i		−	0.851765i	0.904779	−	0.425882i	$-0.140036\pi$
$558$		0			0
$559$	328125.			1.05006
$560$		0			0
$561$	−177679.	+	489190.i	−0.564562	+	1.55436i
$562$		0			0
$563$	−101976.	−	58875.7i	−0.321722	−	0.185746i	0.330438	−	0.943828i	$-0.392804\pi$
$563$	−101976.	−	58875.7i	−0.321722	−	0.185746i	−0.652160	+	0.758082i	$0.726137\pi$
$564$		0			0
$565$	314599.	+	544901.i	0.985508	+	1.70695i
$566$		0			0
$567$	58707.2	+	327803.i	0.182610	+	1.01964i
$568$		0			0
$569$	−315057.	+	181898.i	−0.973116	+	0.561829i	−0.900185	−	0.435508i	$-0.856569\pi$
$569$	−315057.	+	181898.i	−0.973116	+	0.561829i	−0.0729314	+	0.997337i	$0.523235\pi$
$570$		0			0
$571$	23782.4	−	41192.3i	0.0729430	−	0.126341i	−0.827247	−	0.561839i	$-0.810094\pi$
$571$	23782.4	−	41192.3i	0.0729430	−	0.126341i	0.900190	+	0.435498i	$0.143428\pi$
$572$		0			0
$573$	−504529.	−	183251.i	−1.53666	−	0.558131i
$574$		0			0
$575$		−	46471.5i		−	0.140556i
$576$		0			0
$577$	24477.6			0.0735221			0.0367611	−	0.999324i	$-0.488296\pi$
$577$	24477.6			0.0735221			0.0367611	+	0.999324i	$0.488296\pi$
$578$		0			0
$579$	−393203.	+	69604.2i	−1.17290	+	0.207624i
$580$		0			0
$581$	119407.	+	68939.7i	0.353735	+	0.204229i
$582$		0			0
$583$	8408.73	+	14564.3i	0.0247396	+	0.0428503i
$584$		0			0
$585$	267958.	+	733149.i	0.782988	+	2.14230i
$586$		0			0
$587$	−107804.	+	62240.8i	−0.312867	+	0.180634i	−0.648209	−	0.761463i	$-0.724482\pi$
$587$	−107804.	+	62240.8i	−0.312867	+	0.180634i	0.335342	+	0.942097i	$0.391148\pi$
$588$		0			0
$589$	−54235.5	+	93938.6i	−0.156334	+	0.270778i
$590$		0			0
$591$	59193.2	−	49736.7i	0.169472	−	0.142397i
$592$		0			0
$593$			63278.6i			0.179948i	0.995944	+	0.0899742i	$0.0286784\pi$
$593$			63278.6i			0.179948i	−0.995944	+	0.0899742i	$0.971322\pi$
$594$		0			0
$595$	−1.14802e6			−3.24277
$596$		0			0
$597$	398262.	+	473985.i	1.11743	+	1.32989i
$598$		0			0
$599$	507986.	+	293286.i	1.41579	+	0.817406i	0.995925	−	0.0901814i	$-0.0287447\pi$
$599$	507986.	+	293286.i	1.41579	+	0.817406i	0.419863	+	0.907587i	$0.362078\pi$
$600$		0			0
$601$	254128.	+	440163.i	0.703564	+	1.21861i	0.967207	+	0.253989i	$0.0817426\pi$
$601$	254128.	+	440163.i	0.703564	+	1.21861i	−0.263643	+	0.964620i	$0.584924\pi$
$602$		0			0
$603$	−301510.	−	252309.i	−0.829215	−	0.693902i
$604$		0			0
$605$	−72769.1	+	42013.2i	−0.198809	+	0.114782i
$606$		0			0
$607$	220513.	−	381939.i	0.598489	−	1.03661i	−0.394555	−	0.918872i	$-0.629101\pi$
$607$	220513.	−	381939.i	0.598489	−	1.03661i	0.993044	−	0.117742i	$-0.0375655\pi$
$608$		0			0
$609$	−45009.8	−	254267.i	−0.121359	−	0.685574i
$610$		0			0
$611$		−	163221.i		−	0.437214i
$612$		0			0
$613$	230950.			0.614605			0.307303	−	0.951612i	$-0.400574\pi$
$613$	230950.			0.614605			0.307303	+	0.951612i	$0.400574\pi$
$614$		0			0
$615$	353785.	−	974047.i	0.935382	−	2.57531i
$616$		0			0
$617$	−72192.3	−	41680.2i	−0.189636	−	0.109486i	0.402176	−	0.915562i	$-0.368254\pi$
$617$	−72192.3	−	41680.2i	−0.189636	−	0.109486i	−0.591812	+	0.806076i	$0.701587\pi$
$618$		0			0
$619$	203303.	+	352130.i	0.530593	+	0.919014i	0.999363	+	0.0356939i	$0.0113641\pi$
$619$	203303.	+	352130.i	0.530593	+	0.919014i	−0.468770	+	0.883321i	$0.655303\pi$
$620$		0			0
$621$	−25597.4	+	51.4718i	−0.0663762	+	0.000133471i
$622$		0			0
$623$	5374.65	−	3103.05i	0.0138476	−	0.00799491i
$624$		0			0
$625$	−266900.	+	462284.i	−0.683264	+	1.18345i
$626$		0			0
$627$	−162859.	−	59152.2i	−0.414263	−	0.150465i
$628$		0			0
$629$			247787.i			0.626293i
$630$		0			0
$631$	489605.			1.22967			0.614833	−	0.788657i	$-0.289223\pi$
$631$	489605.			1.22967			0.614833	+	0.788657i	$0.289223\pi$
$632$		0			0
$633$	660257.	−	116878.i	1.64781	−	0.291691i
$634$		0			0
$635$	−875693.	−	505582.i	−2.17172	−	1.25384i
$636$		0			0
$637$	19136.1	+	33144.7i	0.0471601	+	0.0816837i
$638$		0			0
$639$	−4453.87	−	779.182i	−0.0109078	−	0.00190826i
$640$		0			0
$641$	−402512.	+	232391.i	−0.979632	+	0.565591i	−0.902159	−	0.431403i	$-0.858019\pi$
$641$	−402512.	+	232391.i	−0.979632	+	0.565591i	−0.0774733	+	0.996994i	$0.524685\pi$
$642$		0			0
$643$	247008.	−	427830.i	0.597432	−	1.03478i	−0.395767	−	0.918351i	$-0.629521\pi$
$643$	247008.	−	427830.i	0.597432	−	1.03478i	0.993199	−	0.116431i	$-0.0371454\pi$
$644$		0			0
$645$	457145.	−	384112.i	1.09884	−	0.923291i
$646$		0			0
$647$			406414.i			0.970868i	0.874273	+	0.485434i	$0.161338\pi$
$647$			406414.i			0.970868i	−0.874273	+	0.485434i	$0.838662\pi$
$648$		0			0
$649$	−695317.			−1.65080
$650$		0			0
$651$	−186867.	−	222397.i	−0.440931	−	0.524766i
$652$		0			0
$653$	363274.	+	209736.i	0.851937	+	0.491866i	0.861304	−	0.508090i	$-0.169648\pi$
$653$	363274.	+	209736.i	0.851937	+	0.491866i	−0.00936671	+	0.999956i	$0.502982\pi$
$654$		0			0
$655$	−310868.	−	538439.i	−0.724591	−	1.25503i
$656$		0			0
$657$	58260.2	−	333020.i	0.134971	−	0.771507i
$658$		0			0
$659$	318528.	−	183902.i	0.733461	−	0.423464i	−0.0862258	−	0.996276i	$-0.527481\pi$
$659$	318528.	−	183902.i	0.733461	−	0.423464i	0.819687	+	0.572812i	$0.194147\pi$
$660$		0			0
$661$	−1191.55	+	2063.82i	−0.00272715	+	0.00472357i	−0.867386	−	0.497636i	$-0.834201\pi$
$661$	−1191.55	+	2063.82i	−0.00272715	+	0.00472357i	0.864659	+	0.502360i	$0.167535\pi$
$662$		0			0
$663$	175489.	+	991359.i	0.399229	+	2.25530i
$664$		0			0
$665$		−	382193.i		−	0.864250i
$666$		0			0
$667$	19848.0			0.0446134
$668$		0			0
$669$	284931.	−	784478.i	0.636631	−	1.75278i
$670$		0			0
$671$	124607.	+	71941.7i	0.276756	+	0.159785i
$672$		0			0
$673$	47613.9	+	82469.8i	0.105125	+	0.182081i	0.913789	−	0.406189i	$-0.133143\pi$
$673$	47613.9	+	82469.8i	0.105125	+	0.182081i	−0.808665	+	0.588270i	$0.799809\pi$
$674$		0			0
$675$	836525.	+	480727.i	1.83599	+	1.05509i
$676$		0			0
$677$	−474804.	+	274128.i	−1.03595	+	0.598104i	−0.918682	−	0.394997i	$-0.870746\pi$
$677$	−474804.	+	274128.i	−1.03595	+	0.598104i	−0.117264	+	0.993101i	$0.537412\pi$
$678$		0			0
$679$	−140587.	+	243504.i	−0.304934	+	0.528161i
$680$		0			0
$681$	−164276.	−	59667.0i	−0.354226	−	0.128659i
$682$		0			0
$683$			178993.i			0.383702i	0.981424	+	0.191851i	$0.0614491\pi$
$683$			178993.i			0.383702i	−0.981424	+	0.191851i	$0.938551\pi$
$684$		0			0
$685$	−588003.			−1.25314
$686$		0			0
$687$	576289.	−	102014.i	1.22103	−	0.216145i
$688$		0			0
$689$	28173.2	+	16265.8i	0.0593468	+	0.0342639i
$690$		0			0
$691$	−395744.	−	685448.i	−0.828816	−	1.43555i	−0.898968	−	0.438015i	$-0.855682\pi$
$691$	−395744.	−	685448.i	−0.828816	−	1.43555i	0.0701522	−	0.997536i	$-0.477651\pi$
$692$		0			0
$693$	297781.	−	355850.i	0.620056	−	0.740969i
$694$		0			0
$695$	769560.	−	444306.i	1.59321	−	0.919840i
$696$		0			0
$697$	668298.	−	1.15753e6i	1.37564	−	2.38268i
$698$		0			0
$699$	−536314.	+	450634.i	−1.09765	+	0.922294i
$700$		0			0
$701$			335292.i			0.682319i	0.940005	+	0.341160i	$0.110820\pi$
$701$			335292.i			0.682319i	−0.940005	+	0.341160i	$0.889180\pi$
$702$		0			0
$703$	−82492.1			−0.166917
$704$		0			0
$705$	−191071.	−	227400.i	−0.384430	−	0.457522i
$706$		0			0
$707$	−22007.6	−	12706.1i	−0.0440284	−	0.0254198i
$708$		0			0
$709$	−94776.8	−	164158.i	−0.188543	−	0.326566i	0.756222	−	0.654315i	$-0.227043\pi$
$709$	−94776.8	−	164158.i	−0.188543	−	0.326566i	−0.944765	+	0.327750i	$0.893710\pi$
$710$		0			0
$711$	−821227.	+	300150.i	−1.62452	+	0.593743i
$712$		0			0
$713$	19336.4	−	11163.9i	0.0380362	−	0.0219602i
$714$		0			0
$715$	543807.	−	941901.i	1.06373	−	1.84244i
$716$		0			0
$717$	32226.5	+	182052.i	0.0626866	+	0.354125i
$718$		0			0
$719$			556721.i			1.07691i	0.842654	+	0.538455i	$0.180992\pi$
$719$			556721.i			1.07691i	−0.842654	+	0.538455i	$0.819008\pi$
$720$		0			0
$721$	−82359.3			−0.158432
$722$		0			0
$723$	56234.8	−	154827.i	0.107579	−	0.296189i
$724$		0			0
$725$	−647882.	−	374055.i	−1.23259	−	0.711638i
$726$		0			0
$727$	−45279.9	−	78427.1i	−0.0856716	−	0.148388i	0.820006	−	0.572356i	$-0.193970\pi$
$727$	−45279.9	−	78427.1i	−0.0856716	−	0.148388i	−0.905677	+	0.423968i	$0.860637\pi$
$728$		0			0
$729$	263867.	−	461306.i	0.496513	−	0.868029i
$730$		0			0
$731$	666940.	−	385058.i	1.24811	−	0.720595i
$732$		0			0
$733$	58390.9	−	101136.i	0.108677	−	0.188234i	−0.806558	−	0.591156i	$-0.798672\pi$
$733$	58390.9	−	101136.i	0.108677	−	0.188234i	0.915235	+	0.402922i	$0.132005\pi$
$734$		0			0
$735$	65460.6	+	23776.0i	0.121173	+	0.0440113i
$736$		0			0
$737$			547793.i			1.00851i
$738$		0			0
$739$	−149647.			−0.274019			−0.137009	−	0.990570i	$-0.543749\pi$
$739$	−149647.			−0.274019			−0.137009	+	0.990570i	$0.543749\pi$
$740$		0			0
$741$	−330038.	+	58422.8i	−0.601074	+	0.106401i
$742$		0			0
$743$	−120575.	−	69614.1i	−0.218414	−	0.126101i	0.386802	−	0.922163i	$-0.373580\pi$
$743$	−120575.	−	69614.1i	−0.218414	−	0.126101i	−0.605216	+	0.796062i	$0.706913\pi$
$744$		0			0
$745$	186928.	+	323769.i	0.336792	+	0.583340i
$746$		0			0
$747$	−75532.4	−	206661.i	−0.135361	−	0.370355i
$748$		0			0
$749$	282670.	−	163199.i	0.503867	−	0.290908i
$750$		0			0
$751$	97404.6	−	168710.i	0.172703	−	0.299130i	−0.766661	−	0.642052i	$-0.778083\pi$
$751$	97404.6	−	168710.i	0.172703	−	0.299130i	0.939364	+	0.342922i	$0.111417\pi$
$752$		0			0
$753$	−135207.	+	113607.i	−0.238457	+	0.200362i
$754$		0			0
$755$			1.81542e6i			3.18480i
$756$		0			0
$757$	−334615.			−0.583920			−0.291960	−	0.956430i	$-0.594307\pi$
$757$	−334615.			−0.583920			−0.291960	+	0.956430i	$0.594307\pi$
$758$		0			0
$759$	22943.9	+	27306.2i	0.0398275	+	0.0474000i
$760$		0			0
$761$	549734.	+	317389.i	0.949256	+	0.548053i	0.892850	−	0.450354i	$-0.148702\pi$
$761$	549734.	+	317389.i	0.949256	+	0.548053i	0.0564066	+	0.998408i	$0.482036\pi$
$762$		0			0
$763$	209254.	+	362439.i	0.359439	+	0.622566i
$764$		0			0
$765$	1.40500e6	+	1.17573e6i	2.40079	+	2.00903i
$766$		0			0
$767$	−1.16482e6	+	672509.i	−1.98001	+	1.14316i
$768$		0			0
$769$	−484560.	+	839282.i	−0.819398	+	1.41924i	0.0867292	+	0.996232i	$0.472359\pi$
$769$	−484560.	+	839282.i	−0.819398	+	1.41924i	−0.906127	+	0.423006i	$0.860975\pi$
$770$		0			0
$771$	85265.9	+	481679.i	0.143439	+	0.810305i
$772$		0			0
$773$		−	765047.i		−	1.28035i	−0.768228	−	0.640176i	$-0.778861\pi$
$773$		−	765047.i		−	1.28035i	0.768228	−	0.640176i	$-0.221139\pi$
$774$		0			0
$775$	−841579.			−1.40117
$776$		0			0
$777$	75416.9	−	207639.i	0.124918	−	0.343928i
$778$		0			0
$779$	385358.	+	222486.i	0.635023	+	0.366631i
$780$		0			0
$781$	3149.99	+	5455.95i	0.00516425	+	0.00894475i
$782$		0			0
$783$	−205319.	+	357280.i	−0.334893	+	0.582754i
$784$		0			0
$785$	−567356.	+	327563.i	−0.920696	+	0.531564i
$786$		0			0
$787$	−243237.	+	421298.i	−0.392717	+	0.680206i	−0.992807	−	0.119727i	$-0.961798\pi$
$787$	−243237.	+	421298.i	−0.392717	+	0.680206i	0.600090	+	0.799933i	$0.295131\pi$
$788$		0			0
$789$	316403.	+	114921.i	0.508261	+	0.184606i
$790$		0			0
$791$		−	723499.i		−	1.15634i
$792$		0			0
$793$	278327.			0.442598
$794$		0			0
$795$	58292.2	−	10318.8i	0.0922308	−	0.0163265i
$796$		0			0
$797$	−804496.	−	464476.i	−1.26651	−	0.731217i	−0.292180	−	0.956363i	$-0.594381\pi$
$797$	−804496.	−	464476.i	−1.26651	−	0.731217i	−0.974325	+	0.225146i	$0.927714\pi$
$798$		0			0
$799$	−191542.	−	331760.i	−0.300033	−	0.519673i
$800$		0			0
$801$	−9755.72	−	1706.72i	−0.0152053	−	0.00266009i
$802$		0			0
$803$	−407947.	+	235528.i	−0.632663	+	0.365268i
$804$		0			0
$805$	−39335.6	+	68131.2i	−0.0607007	+	0.105137i
$806$		0			0
$807$	369258.	−	310266.i	0.566999	−	0.476417i
$808$		0			0
$809$		−	854296.i		−	1.30530i	−0.757658	−	0.652651i	$-0.773657\pi$
$809$		−	854296.i		−	1.30530i	0.757658	−	0.652651i	$-0.226343\pi$
$810$		0			0
$811$	−181598.			−0.276102			−0.138051	−	0.990425i	$-0.544084\pi$
$811$	−181598.			−0.276102			−0.138051	+	0.990425i	$0.544084\pi$
$812$		0			0
$813$	−547092.	−	651112.i	−0.827712	−	0.985087i
$814$		0			0
$815$	501931.	+	289790.i	0.755664	+	0.436283i
$816$		0			0
$817$	128192.	+	222034.i	0.192050	+	0.332641i
$818$		0			0
$819$	154677.	−	884145.i	0.230599	−	1.31812i
$820$		0			0
$821$	−616142.	+	355730.i	−0.914102	+	0.527757i	−0.881749	−	0.471719i	$-0.843634\pi$
$821$	−616142.	+	355730.i	−0.914102	+	0.527757i	−0.0323536	+	0.999476i	$0.510300\pi$
$822$		0			0
$823$	−446599.	+	773532.i	−0.659353	+	1.14203i	0.321431	+	0.946933i	$0.395836\pi$
$823$	−446599.	+	773532.i	−0.659353	+	1.14203i	−0.980783	+	0.195099i	$0.937497\pi$
$824$		0			0
$825$	−234325.	−	1.32373e6i	−0.344279	−	1.94488i
$826$		0			0
$827$			98640.8i			0.144227i	0.997396	+	0.0721133i	$0.0229743\pi$
$827$			98640.8i			0.144227i	−0.997396	+	0.0721133i	$0.977026\pi$
$828$		0			0
$829$	435088.			0.633094			0.316547	−	0.948577i	$-0.397476\pi$
$829$	435088.			0.633094			0.316547	+	0.948577i	$0.397476\pi$
$830$		0			0
$831$	65701.3	−	180890.i	0.0951420	−	0.261947i
$832$		0			0
$833$	77791.3	+	44912.8i	0.112109	+	0.0647262i
$834$		0			0
$835$	625185.	+	1.08285e6i	0.896676	+	1.55309i
$836$		0			0
$837$	932.132	+	463558.i	0.00133054	+	0.661688i
$838$		0			0
$839$	411452.	−	237552.i	0.584515	−	0.337470i	−0.178411	−	0.983956i	$-0.557096\pi$
$839$	411452.	−	237552.i	0.584515	−	0.337470i	0.762926	+	0.646486i	$0.223762\pi$
$840$		0			0
$841$	−193881.	+	335812.i	−0.274122	+	0.474793i
$842$		0			0
$843$	−1.22133e6	−	443602.i	−1.71862	−	0.624221i
$844$		0			0
$845$		−	843145.i		−	1.18083i
$846$		0			0
$847$	96620.0			0.134679
$848$		0			0
$849$	155403.	−	27509.2i	0.215598	−	0.0381648i
$850$		0			0
$851$	14705.4	+	8490.14i	0.0203056	+	0.0117235i
$852$		0			0
$853$	−400765.	−	694145.i	−0.550797	−	0.954008i	−0.998217	−	0.0596840i	$-0.980991\pi$
$853$	−400765.	−	694145.i	−0.550797	−	0.954008i	0.447421	−	0.894324i	$-0.352343\pi$
$854$		0			0
$855$	−391419.	+	467747.i	−0.535438	+	0.639851i
$856$		0			0
$857$	−738388.	+	426309.i	−1.00536	+	0.580447i	−0.909831	−	0.414979i	$-0.863789\pi$
$857$	−738388.	+	426309.i	−1.00536	+	0.580447i	−0.0955328	+	0.995426i	$0.530455\pi$
$858$		0			0
$859$	414569.	−	718055.i	0.561838	−	0.973132i	−0.435498	−	0.900189i	$-0.643428\pi$
$859$	414569.	−	718055.i	0.561838	−	0.973132i	0.997336	−	0.0729420i	$-0.0232388\pi$
$860$		0			0
$861$	−912323.	+	766572.i	−1.23067	+	1.03406i
$862$		0			0
$863$			176451.i			0.236921i	0.992959	+	0.118460i	$0.0377959\pi$
$863$			176451.i			0.236921i	−0.992959	+	0.118460i	$0.962204\pi$
$864$		0			0
$865$	1.17959e6			1.57651
$866$		0			0
$867$	1.03650e6	+	1.23358e6i	1.37890	+	1.64107i
$868$		0			0
$869$	1.05506e6	+	609138.i	1.39713	+	0.806634i
$870$		0			0
$871$	529823.	+	917681.i	0.698385	+	1.20964i
$872$		0			0
$873$	421439.	−	154031.i	0.552976	−	0.202107i
$874$		0			0
$875$	1.35529e6	−	782476.i	1.77017	−	1.02201i
$876$		0			0
$877$	354218.	−	613523.i	0.460544	−	0.797685i	−0.538444	−	0.842661i	$-0.680988\pi$
$877$	354218.	−	613523.i	0.460544	−	0.797685i	0.998988	+	0.0449759i	$0.0143211\pi$
$878$		0			0
$879$	−62161.4	−	351158.i	−0.0804531	−	0.454491i
$880$		0			0
$881$		−	1.00229e6i		−	1.29134i	−0.763618	−	0.645668i	$-0.776579\pi$
$881$		−	1.00229e6i		−	1.29134i	0.763618	−	0.645668i	$-0.223421\pi$
$882$		0			0
$883$	−994934.			−1.27607			−0.638033	−	0.770009i	$-0.720252\pi$
$883$	−994934.			−1.27607			−0.638033	+	0.770009i	$0.720252\pi$
$884$		0			0
$885$	−835571.	+	2.30051e6i	−1.06683	+	2.93723i
$886$		0			0
$887$	−1.06865e6	−	616985.i	−1.35828	−	0.784200i	−0.368884	−	0.929476i	$-0.620260\pi$
$887$	−1.06865e6	−	616985.i	−1.35828	−	0.784200i	−0.989391	+	0.145275i	$0.953593\pi$
$888$		0			0
$889$	581356.	+	1.00694e6i	0.735594	+	1.27409i
$890$		0			0
$891$	−728879.	+	130537.i	−0.918121	+	0.164429i
$892$		0			0
$893$	110448.	−	63767.1i	0.138501	−	0.0799638i
$894$		0			0
$895$	767016.	−	1.32851e6i	0.957543	−	1.65851i
$896$		0			0
$897$	64846.8	+	23553.1i	0.0805942	+	0.0292727i
$898$		0			0
$899$		−	359439.i		−	0.444740i
$900$		0			0
$901$	76352.3			0.0940530
$902$		0			0
$903$	−676075.	+	119678.i	−0.829124	+	0.146770i
$904$		0			0
$905$	852065.	+	491940.i	1.04034	+	0.600641i
$906$		0			0
$907$	−312775.	−	541742.i	−0.380204	−	0.658533i	0.610887	−	0.791718i	$-0.290813\pi$
$907$	−312775.	−	541742.i	−0.380204	−	0.658533i	−0.991091	+	0.133185i	$0.957480\pi$
$908$		0			0
$909$	13921.2	+	38089.1i	0.0168480	+	0.0460971i
$910$		0			0
$911$	495083.	−	285836.i	0.596542	−	0.344414i	−0.171138	−	0.985247i	$-0.554744\pi$
$911$	495083.	−	285836.i	0.596542	−	0.344414i	0.767680	+	0.640833i	$0.221411\pi$
$912$		0			0
$913$	−153289.	+	265505.i	−0.183895	+	0.318515i
$914$		0			0
$915$	387766.	−	325818.i	0.463157	−	0.389164i
$916$		0			0
$917$			714918.i			0.850193i
$918$		0			0
$919$	109328.			0.129450			0.0647250	−	0.997903i	$-0.479383\pi$
$919$	109328.			0.129450			0.0647250	+	0.997903i	$0.479383\pi$
$920$		0			0
$921$	−796607.	−	948068.i	−0.939128	−	1.11769i
$922$		0			0
$923$	10553.9	+	6093.32i	0.0123883	+	0.00715238i
$924$		0			0
$925$	−320010.	−	554274.i	−0.374007	−	0.647800i
$926$		0			0
$927$	100795.	+	84347.4i	0.117296	+	0.0981550i
$928$		0			0
$929$	932486.	−	538371.i	1.08047	−	0.623807i	0.149443	−	0.988770i	$-0.452252\pi$
$929$	932486.	−	538371.i	1.08047	−	0.623807i	0.931022	+	0.364963i	$0.118918\pi$
$930$		0			0
$931$	−14952.2	+	25897.9i	−0.0172506	+	0.0298789i
$932$		0			0
$933$	−131942.	−	745358.i	−0.151572	−	0.856252i
$934$		0			0
$935$		−	2.55265e6i		−	2.91990i
$936$		0			0
$937$	87374.2			0.0995185			0.0497592	−	0.998761i	$-0.484155\pi$
$937$	87374.2			0.0995185			0.0497592	+	0.998761i	$0.484155\pi$
$938$		0			0
$939$	25977.7	−	71522.3i	0.0294625	−	0.0811167i
$940$		0			0
$941$	−8689.61	−	5016.95i	−0.00981343	−	0.00566579i	0.495085	−	0.868844i	$-0.335137\pi$
$941$	−8689.61	−	5016.95i	−0.00981343	−	0.00566579i	−0.504899	+	0.863179i	$0.668470\pi$
$942$		0			0
$943$	−45796.9	−	79322.6i	−0.0515007	−	0.0892018i
$944$		0			0
$945$	−819508.	−	1.41286e6i	−0.917677	−	1.58211i
$946$		0			0
$947$	−159477.	+	92073.8i	−0.177827	+	0.102668i	−0.586271	−	0.810115i	$-0.699405\pi$
$947$	−159477.	+	92073.8i	−0.177827	+	0.102668i	0.408444	+	0.912783i	$0.366071\pi$
$948$		0			0
$949$	−455604.	+	789129.i	−0.505889	+	0.876225i
$950$		0			0
$951$	1.14613e6	+	416289.i	1.26729	+	0.460292i
$952$		0			0
$953$			23931.9i			0.0263507i	0.999913	+	0.0131753i	$0.00419396\pi$
$953$			23931.9i			0.0263507i	−0.999913	+	0.0131753i	$0.995806\pi$
$954$		0			0
$955$	2.63269e6			2.88664
$956$		0			0
$957$	565368.	−	100080.i	0.617316	−	0.109276i
$958$		0			0
$959$	585546.	+	338065.i	0.636683	+	0.367589i
$960$		0			0
$961$	259587.	+	449618.i	0.281084	+	0.486852i
$962$		0			0
$963$	−513084.	−	89761.6i	−0.553269	−	0.0967916i
$964$		0			0
$965$	1.69611e6	−	979248.i	1.82137	−	1.05157i
$966$		0			0
$967$	95845.9	−	166010.i	0.102499	−	0.177534i	−0.810215	−	0.586133i	$-0.800649\pi$
$967$	95845.9	−	166010.i	0.102499	−	0.177534i	0.912714	+	0.408600i	$0.133983\pi$
$968$		0			0
$969$	−602269.	+	506052.i	−0.641421	+	0.538949i
$970$		0			0
$971$			520692.i			0.552258i	0.961121	+	0.276129i	$0.0890518\pi$
$971$			520692.i			0.552258i	−0.961121	+	0.276129i	$0.910948\pi$
$972$		0			0
$973$	−1.02179e6			−1.07929
$974$		0			0
$975$	−1.67286e6	−	1.99093e6i	−1.75975	−	2.09433i
$976$		0			0
$977$	−167073.	−	96459.7i	−0.175032	−	0.101055i	0.409924	−	0.912119i	$-0.365555\pi$
$977$	−167073.	−	96459.7i	−0.175032	−	0.101055i	−0.584956	+	0.811065i	$0.698888\pi$
$978$		0			0
$979$	6899.72	+	11950.7i	0.00719890	+	0.0124689i
$980$		0			0
$981$	115092.	−	657875.i	0.119593	−	0.683606i
$982$		0			0
$983$	−860413.	+	496759.i	−0.890430	+	0.514090i	−0.874083	−	0.485776i	$-0.838537\pi$
$983$	−860413.	+	496759.i	−0.890430	+	0.514090i	−0.0163468	+	0.999866i	$0.505204\pi$
$984$		0			0
$985$	−189600.	+	328397.i	−0.195419	+	0.338475i
$986$		0			0
$987$	59531.9	+	336304.i	0.0611104	+	0.345221i
$988$		0			0
$989$		−	52774.3i		−	0.0539548i
$990$		0			0
$991$	−220397.			−0.224418			−0.112209	−	0.993685i	$-0.535793\pi$
$991$	−220397.			−0.224418			−0.112209	+	0.993685i	$0.535793\pi$
$992$		0			0
$993$	−445010.	+	1.22521e6i	−0.451306	+	1.24254i
$994$		0			0
$995$	−2.62961e6	−	1.51820e6i	−2.65610	−	1.53350i
$996$		0			0
$997$	−933671.	−	1.61716e6i	−0.939298	−	1.62691i	−0.766785	−	0.641905i	$-0.778145\pi$
$997$	−933671.	−	1.61716e6i	−0.939298	−	1.62691i	−0.172513	−	0.985007i	$-0.555189\pi$
$998$		0			0
$999$	−304950.	+	176882.i	−0.305561	+	0.177236i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.5.m.a.41.4	✓	24
3.2	odd	2		216.5.m.a.17.1		24
4.3	odd	2		144.5.q.d.113.9		24
9.2	odd	6	inner	72.5.m.a.65.4	yes	24
9.4	even	3		648.5.e.c.161.1		24
9.5	odd	6		648.5.e.c.161.24		24
9.7	even	3		216.5.m.a.89.1		24
12.11	even	2		432.5.q.d.17.1		24
36.7	odd	6		432.5.q.d.305.1		24
36.11	even	6		144.5.q.d.65.9		24
36.23	even	6		1296.5.e.j.161.24		24
36.31	odd	6		1296.5.e.j.161.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.5.m.a.41.4	✓	24	1.1	even	1	trivial
72.5.m.a.65.4	yes	24	9.2	odd	6	inner
144.5.q.d.65.9		24	36.11	even	6
144.5.q.d.113.9		24	4.3	odd	2
216.5.m.a.17.1		24	3.2	odd	2
216.5.m.a.89.1		24	9.7	even	3
432.5.q.d.17.1		24	12.11	even	2
432.5.q.d.305.1		24	36.7	odd	6
648.5.e.c.161.1		24	9.4	even	3
648.5.e.c.161.24		24	9.5	odd	6
1296.5.e.j.161.1		24	36.31	odd	6
1296.5.e.j.161.24		24	36.23	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-5.78971 - 6.89052i) q^{3} +(38.2277 + 22.0708i) q^{5} +(-25.3787 - 43.9571i) q^{7} +(-13.9586 + 79.7882i) q^{9} +O(q^{10})\)	\(q+(-5.78971 - 6.89052i) q^{3} +(38.2277 + 22.0708i) q^{5} +(-25.3787 - 43.9571i) q^{7} +(-13.9586 + 79.7882i) q^{9} +(97.7398 - 56.4301i) q^{11} +(109.158 - 189.067i) q^{13} +(-69.2482 - 391.193i) q^{15} -512.392i q^{17} +170.583 q^{19} +(-155.952 + 429.371i) q^{21} +(-30.4088 - 17.5565i) q^{23} +(661.740 + 1146.17i) q^{25} +(630.598 - 365.769i) q^{27} +(-489.529 + 282.630i) q^{29} +(-317.942 + 550.691i) q^{31} +(-954.718 - 346.764i) q^{33} -2240.51i q^{35} -483.589 q^{37} +(-1934.77 + 342.489i) q^{39} +(2259.06 + 1304.27i) q^{41} +(751.490 + 1301.62i) q^{43} +(-2294.59 + 2742.05i) q^{45} +(647.472 - 373.818i) q^{47} +(-87.6532 + 151.820i) q^{49} +(-3530.65 + 2966.60i) q^{51} +149.011i q^{53} +4981.83 q^{55} +(-987.626 - 1175.41i) q^{57} +(-5335.47 - 3080.43i) q^{59} +(637.441 + 1104.08i) q^{61} +(3861.51 - 1411.34i) q^{63} +(8345.73 - 4818.41i) q^{65} +(-2426.86 + 4203.45i) q^{67} +(55.0845 + 311.180i) q^{69} +55.8211i q^{71} -4173.80 q^{73} +(4066.41 - 11195.7i) q^{75} +(-4961.01 - 2864.24i) q^{77} +(5397.28 + 9348.36i) q^{79} +(-6171.32 - 2227.46i) q^{81} +(-2352.51 + 1358.22i) q^{83} +(11308.9 - 19587.6i) q^{85} +(4781.70 + 1736.77i) q^{87} +122.270i q^{89} -11081.1 q^{91} +(5635.34 - 997.557i) q^{93} +(6521.01 + 3764.91i) q^{95} +(-2769.79 - 4797.41i) q^{97} +(3138.15 + 8586.17i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{3} - 100 q^{9}+O(q^{10}) \) 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

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Representations

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Database

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