LMFDB - Embedded newform 72.5.m.a.65.3

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			65.3
Character	$\chi$	$=$	72.65
Dual form			72.5.m.a.41.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-6.25234 + 6.47366i) q^{3} +(-1.90728 + 1.10117i) q^{5} +(-9.68825 + 16.7805i) q^{7} +(-2.81653 - 80.9510i) q^{9} +O(q^{10})$	\(q+(-6.25234 + 6.47366i) q^{3} +(-1.90728 + 1.10117i) q^{5} +(-9.68825 + 16.7805i) q^{7} +(-2.81653 - 80.9510i) q^{9} +(-88.8024 - 51.2701i) q^{11} +(-90.5685 - 156.869i) q^{13} +(4.79637 - 19.2320i) q^{15} -423.627i q^{17} -195.873 q^{19} +(-48.0573 - 167.636i) q^{21} +(-110.749 + 63.9411i) q^{23} +(-310.075 + 537.065i) q^{25} +(541.659 + 487.900i) q^{27} +(-670.564 - 387.150i) q^{29} +(347.881 + 602.548i) q^{31} +(887.128 - 254.319i) q^{33} -42.6736i q^{35} -419.318 q^{37} +(1581.78 + 394.490i) q^{39} +(1480.79 - 854.932i) q^{41} +(-1243.13 + 2153.17i) q^{43} +(94.5127 + 151.295i) q^{45} +(-1175.08 - 678.433i) q^{47} +(1012.78 + 1754.18i) q^{49} +(2742.42 + 2648.66i) q^{51} -3087.09i q^{53} +225.828 q^{55} +(1224.66 - 1268.01i) q^{57} +(-2814.18 + 1624.77i) q^{59} +(-3312.85 + 5738.03i) q^{61} +(1385.69 + 737.011i) q^{63} +(345.479 + 199.462i) q^{65} +(-3167.60 - 5486.44i) q^{67} +(278.509 - 1116.73i) q^{69} -4570.00i q^{71} -1090.88 q^{73} +(-1538.09 - 5365.23i) q^{75} +(1720.68 - 993.435i) q^{77} +(3524.24 - 6104.17i) q^{79} +(-6545.13 + 456.002i) q^{81} +(-8690.70 - 5017.58i) q^{83} +(466.485 + 807.975i) q^{85} +(6698.87 - 1920.41i) q^{87} +1063.44i q^{89} +3509.80 q^{91} +(-6075.77 - 1515.27i) q^{93} +(373.585 - 215.689i) q^{95} +(-5612.39 + 9720.95i) q^{97} +(-3900.25 + 7333.05i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−6.25234	+	6.47366i	−0.694704	+	0.719295i
$3$	−6.25234	+	6.47366i	−0.694704	+	0.719295i
$4$		0			0
$5$	−1.90728	+	1.10117i	−0.0762912	+	0.0440468i	−0.537660	−	0.843162i	$-0.680692\pi$
$5$	−1.90728	+	1.10117i	−0.0762912	+	0.0440468i	0.461369	+	0.887208i	$0.347358\pi$
$6$		0			0
$7$	−9.68825	+	16.7805i	−0.197719	+	0.342460i	−0.947789	−	0.318899i	$-0.896687\pi$
$7$	−9.68825	+	16.7805i	−0.197719	+	0.342460i	0.750069	+	0.661359i	$0.230020\pi$
$8$		0			0
$9$	−2.81653	−	80.9510i	−0.0347720	−	0.999395i
$10$		0			0
$11$	−88.8024	−	51.2701i	−0.733904	−	0.423720i	0.0859446	−	0.996300i	$-0.472609\pi$
$11$	−88.8024	−	51.2701i	−0.733904	−	0.423720i	−0.819849	+	0.572580i	$0.805943\pi$
$12$		0			0
$13$	−90.5685	−	156.869i	−0.535908	−	0.928220i	−0.999119	−	0.0419718i	$-0.986636\pi$
$13$	−90.5685	−	156.869i	−0.535908	−	0.928220i	0.463211	−	0.886248i	$-0.346697\pi$
$14$		0			0
$15$	4.79637	−	19.2320i	0.0213172	−	0.0854754i
$16$		0			0
$17$		−	423.627i		−	1.46584i	−0.680317	−	0.732918i	$-0.738158\pi$
$17$		−	423.627i		−	1.46584i	0.680317	−	0.732918i	$-0.261842\pi$
$18$		0			0
$19$	−195.873			−0.542584			−0.271292	−	0.962497i	$-0.587451\pi$
$19$	−195.873			−0.542584			−0.271292	+	0.962497i	$0.587451\pi$
$20$		0			0
$21$	−48.0573	−	167.636i	−0.108973	−	0.380127i
$22$		0			0
$23$	−110.749	+	63.9411i	−0.209356	+	0.120872i	−0.601012	−	0.799240i	$-0.705236\pi$
$23$	−110.749	+	63.9411i	−0.209356	+	0.120872i	0.391656	+	0.920112i	$0.371902\pi$
$24$		0			0
$25$	−310.075	+	537.065i	−0.496120	+	0.859305i
$26$		0			0
$27$	541.659	+	487.900i	0.743017	+	0.669273i
$28$		0			0
$29$	−670.564	−	387.150i	−0.797341	−	0.460345i	0.0451997	−	0.998978i	$-0.485608\pi$
$29$	−670.564	−	387.150i	−0.797341	−	0.460345i	−0.842540	+	0.538633i	$0.818941\pi$
$30$		0			0
$31$	347.881	+	602.548i	0.361999	+	0.627001i	0.988290	−	0.152588i	$-0.0487609\pi$
$31$	347.881	+	602.548i	0.361999	+	0.627001i	−0.626290	+	0.779590i	$0.715428\pi$
$32$		0			0
$33$	887.128	−	254.319i	0.814626	−	0.233534i
$34$		0			0
$35$		−	42.6736i		−	0.0348356i
$36$		0			0
$37$	−419.318			−0.306295			−0.153148	−	0.988203i	$-0.548941\pi$
$37$	−419.318			−0.306295			−0.153148	+	0.988203i	$0.548941\pi$
$38$		0			0
$39$	1581.78	+	394.490i	1.03996	+	0.259362i
$40$		0			0
$41$	1480.79	−	854.932i	0.880896	−	0.508586i	0.00994239	−	0.999951i	$-0.496835\pi$
$41$	1480.79	−	854.932i	0.880896	−	0.508586i	0.870954	+	0.491365i	$0.163502\pi$
$42$		0			0
$43$	−1243.13	+	2153.17i	−0.672326	+	1.16450i	0.304916	+	0.952379i	$0.401372\pi$
$43$	−1243.13	+	2153.17i	−0.672326	+	1.16450i	−0.977243	+	0.212124i	$0.931962\pi$
$44$		0			0
$45$	94.5127	+	151.295i	0.0466729	+	0.0747135i
$46$		0			0
$47$	−1175.08	−	678.433i	−0.531951	−	0.307122i	0.209859	−	0.977732i	$-0.432699\pi$
$47$	−1175.08	−	678.433i	−0.531951	−	0.307122i	−0.741811	+	0.670609i	$0.766033\pi$
$48$		0			0
$49$	1012.78	+	1754.18i	0.421814	+	0.730603i
$50$		0			0
$51$	2742.42	+	2648.66i	1.05437	+	1.01832i
$52$		0			0
$53$		−	3087.09i		−	1.09900i	−0.835494	−	0.549499i	$-0.814818\pi$
$53$		−	3087.09i		−	1.09900i	0.835494	−	0.549499i	$-0.185182\pi$
$54$		0			0
$55$	225.828			0.0746539
$56$		0			0
$57$	1224.66	−	1268.01i	0.376936	−	0.390278i
$58$		0			0
$59$	−2814.18	+	1624.77i	−0.808441	+	0.466753i	−0.846414	−	0.532525i	$-0.821243\pi$
$59$	−2814.18	+	1624.77i	−0.808441	+	0.466753i	0.0379735	+	0.999279i	$0.487910\pi$
$60$		0			0
$61$	−3312.85	+	5738.03i	−0.890313	+	1.54207i	−0.0508127	+	0.998708i	$0.516181\pi$
$61$	−3312.85	+	5738.03i	−0.890313	+	1.54207i	−0.839500	+	0.543359i	$0.817152\pi$
$62$		0			0
$63$	1385.69	+	737.011i	0.349128	+	0.185692i
$64$		0			0
$65$	345.479	+	199.462i	0.0817702	+	0.0472100i
$66$		0			0
$67$	−3167.60	−	5486.44i	−0.705635	−	1.22220i	−0.966462	−	0.256811i	$-0.917328\pi$
$67$	−3167.60	−	5486.44i	−0.705635	−	1.22220i	0.260826	−	0.965386i	$-0.416005\pi$
$68$		0			0
$69$	278.509	−	1116.73i	0.0584980	−	0.234559i
$70$		0			0
$71$		−	4570.00i		−	0.906566i	−0.891367	−	0.453283i	$-0.850253\pi$
$71$		−	4570.00i		−	0.906566i	0.891367	−	0.453283i	$-0.149747\pi$
$72$		0			0
$73$	−1090.88			−0.204706			−0.102353	−	0.994748i	$-0.532637\pi$
$73$	−1090.88			−0.204706			−0.102353	+	0.994748i	$0.532637\pi$
$74$		0			0
$75$	−1538.09	−	5365.23i	−0.273437	−	0.953819i
$76$		0			0
$77$	1720.68	−	993.435i	0.290214	−	0.167555i
$78$		0			0
$79$	3524.24	−	6104.17i	0.564692	−	0.978075i	−0.432386	−	0.901688i	$-0.642328\pi$
$79$	3524.24	−	6104.17i	0.564692	−	0.978075i	0.997078	−	0.0763865i	$-0.0243383\pi$
$80$		0			0
$81$	−6545.13	+	456.002i	−0.997582	+	0.0695019i
$82$		0			0
$83$	−8690.70	−	5017.58i	−1.26153	−	0.728347i	−0.288162	−	0.957582i	$-0.593044\pi$
$83$	−8690.70	−	5017.58i	−1.26153	−	0.728347i	−0.973371	+	0.229235i	$0.926378\pi$
$84$		0			0
$85$	466.485	+	807.975i	0.0645653	+	0.111830i
$86$		0			0
$87$	6698.87	−	1920.41i	0.885040	−	0.253720i
$88$		0			0
$89$			1063.44i			0.134256i	0.997744	+	0.0671280i	$0.0213836\pi$
$89$			1063.44i			0.134256i	−0.997744	+	0.0671280i	$0.978616\pi$
$90$		0			0
$91$	3509.80			0.423838
$92$		0			0
$93$	−6075.77	−	1515.27i	−0.702482	−	0.175196i
$94$		0			0
$95$	373.585	−	215.689i	0.0413944	−	0.0238991i
$96$		0			0
$97$	−5612.39	+	9720.95i	−0.596492	+	1.03315i	0.396843	+	0.917887i	$0.370106\pi$
$97$	−5612.39	+	9720.95i	−0.596492	+	1.03315i	−0.993334	+	0.115268i	$0.963227\pi$
$98$		0			0
$99$	−3900.25	+	7333.05i	−0.397944	+	0.748194i
$100$		0			0
$101$	13333.7	+	7698.21i	1.30710	+	0.754652i	0.981611	−	0.190895i	$-0.0611389\pi$
$101$	13333.7	+	7698.21i	1.30710	+	0.754652i	0.325486	+	0.945547i	$0.394472\pi$
$102$		0			0
$103$	−8720.22	−	15103.9i	−0.821965	−	1.42368i	−0.904217	−	0.427073i	$-0.859545\pi$
$103$	−8720.22	−	15103.9i	−0.821965	−	1.42368i	0.0822526	−	0.996612i	$-0.473789\pi$
$104$		0			0
$105$	276.254	+	266.810i	0.0250571	+	0.0242004i
$106$		0			0
$107$			22691.1i			1.98193i	0.134125	+	0.990964i	$0.457178\pi$
$107$			22691.1i			1.98193i	−0.134125	+	0.990964i	$0.542822\pi$
$108$		0			0
$109$	20703.4			1.74256			0.871281	−	0.490784i	$-0.163290\pi$
$109$	20703.4			1.74256			0.871281	+	0.490784i	$0.163290\pi$
$110$		0			0
$111$	2621.72	−	2714.52i	0.212784	−	0.220317i
$112$		0			0
$113$	2999.94	−	1732.02i	0.234939	−	0.135642i	−0.377909	−	0.925843i	$-0.623357\pi$
$113$	2999.94	−	1732.02i	0.234939	−	0.135642i	0.612849	+	0.790200i	$0.290024\pi$
$114$		0			0
$115$	140.820	−	243.907i	0.0106480	−	0.0184429i
$116$		0			0
$117$	−12443.6	+	7773.44i	−0.909024	+	0.567860i
$118$		0			0
$119$	7108.69	+	4104.20i	0.501990	+	0.289824i
$120$		0			0
$121$	−2063.26	−	3573.66i	−0.140923	−	0.244086i
$122$		0			0
$123$	−3723.84	+	14931.4i	−0.246139	+	0.986941i
$124$		0			0
$125$		−	2742.24i		−	0.175503i
$126$		0			0
$127$	29602.6			1.83536			0.917682	−	0.397315i	$-0.130058\pi$
$127$	29602.6			1.83536			0.917682	+	0.397315i	$0.130058\pi$
$128$		0			0
$129$	−6166.39	−	21509.9i	−0.370554	−	1.29259i
$130$		0			0
$131$	−8467.78	+	4888.88i	−0.493432	+	0.284883i	−0.725997	−	0.687698i	$-0.758621\pi$
$131$	−8467.78	+	4888.88i	−0.493432	+	0.284883i	0.232565	+	0.972581i	$0.425288\pi$
$132$		0			0
$133$	1897.67	−	3286.85i	0.107279	−	0.185813i
$134$		0			0
$135$	−1570.36	−	334.104i	−0.0861649	−	0.0183322i
$136$		0			0
$137$	21462.1	+	12391.1i	1.14348	+	0.660191i	0.947291	−	0.320374i	$-0.103809\pi$
$137$	21462.1	+	12391.1i	1.14348	+	0.660191i	0.196193	+	0.980565i	$0.437142\pi$
$138$		0			0
$139$	−2674.64	−	4632.61i	−0.138432	−	0.239771i	0.788471	−	0.615071i	$-0.210873\pi$
$139$	−2674.64	−	4632.61i	−0.138432	−	0.239771i	−0.926903	+	0.375301i	$0.877539\pi$
$140$		0			0
$141$	11738.9	−	3365.28i	0.590460	−	0.169271i
$142$		0			0
$143$			18573.8i			0.908299i
$144$		0			0
$145$	1705.27			0.0811068
$146$		0			0
$147$	−17688.2	−	4411.36i	−0.818556	−	0.204144i
$148$		0			0
$149$	−6214.58	+	3587.99i	−0.279923	+	0.161614i	−0.633389	−	0.773834i	$-0.718337\pi$
$149$	−6214.58	+	3587.99i	−0.279923	+	0.161614i	0.353465	+	0.935448i	$0.385003\pi$
$150$		0			0
$151$	3239.64	−	5611.22i	0.142083	−	0.246095i	−0.786198	−	0.617975i	$-0.787953\pi$
$151$	3239.64	−	5611.22i	0.142083	−	0.246095i	0.928281	+	0.371880i	$0.121287\pi$
$152$		0			0
$153$	−34293.0	+	1193.16i	−1.46495	+	0.0509700i
$154$		0			0
$155$	−1327.01	−	766.152i	−0.0552348	−	0.0318898i
$156$		0			0
$157$	−13764.9	−	23841.4i	−0.558435	−	0.967237i	−0.997627	−	0.0688444i	$-0.978069\pi$
$157$	−13764.9	−	23841.4i	−0.558435	−	0.967237i	0.439193	−	0.898393i	$-0.355265\pi$
$158$		0			0
$159$	19984.8	+	19301.5i	0.790505	+	0.763479i
$160$		0			0
$161$		−	2477.91i		−	0.0955947i
$162$		0			0
$163$	−8484.54			−0.319340			−0.159670	−	0.987170i	$-0.551043\pi$
$163$	−8484.54			−0.319340			−0.159670	+	0.987170i	$0.551043\pi$
$164$		0			0
$165$	−1411.95	+	1461.93i	−0.0518624	+	0.0536982i
$166$		0			0
$167$	14381.6	−	8303.25i	0.515675	−	0.297725i	−0.219489	−	0.975615i	$-0.570439\pi$
$167$	14381.6	−	8303.25i	0.515675	−	0.297725i	0.735163	+	0.677890i	$0.237106\pi$
$168$		0			0
$169$	−2124.79	+	3680.25i	−0.0743949	+	0.128856i
$170$		0			0
$171$	551.682	+	15856.1i	0.0188667	+	0.542256i
$172$		0			0
$173$	−31709.0	−	18307.2i	−1.05948	−	0.611688i	−0.134188	−	0.990956i	$-0.542843\pi$
$173$	−31709.0	−	18307.2i	−1.05948	−	0.611688i	−0.925287	+	0.379268i	$0.876176\pi$
$174$		0			0
$175$	−6008.17	−	10406.4i	−0.196185	−	0.339802i
$176$		0			0
$177$	7077.02	−	28376.7i	0.225894	−	0.905763i
$178$		0			0
$179$		−	7264.82i		−	0.226735i	−0.993553	−	0.113368i	$-0.963836\pi$
$179$		−	7264.82i		−	0.226735i	0.993553	−	0.113368i	$-0.0361638\pi$
$180$		0			0
$181$	14934.7			0.455867			0.227934	−	0.973677i	$-0.426803\pi$
$181$	14934.7			0.455867			0.227934	+	0.973677i	$0.426803\pi$
$182$		0			0
$183$	−16433.0	−	57322.4i	−0.490698	−	1.71168i
$184$		0			0
$185$	799.757	−	461.740i	0.0233676	−	0.0134913i
$186$		0			0
$187$	−21719.4	+	37619.1i	−0.621104	+	1.07578i
$188$		0			0
$189$	−13435.0	+	4362.44i	−0.376108	+	0.122125i
$190$		0			0
$191$	−22170.7	−	12800.3i	−0.607733	−	0.350875i	0.164345	−	0.986403i	$-0.447449\pi$
$191$	−22170.7	−	12800.3i	−0.607733	−	0.350875i	−0.772078	+	0.635528i	$0.780782\pi$
$192$		0			0
$193$	−13140.3	−	22759.6i	−0.352769	−	0.611013i	0.633965	−	0.773362i	$-0.281426\pi$
$193$	−13140.3	−	22759.6i	−0.352769	−	0.611013i	−0.986733	+	0.162349i	$0.948093\pi$
$194$		0			0
$195$	−3451.30	+	989.407i	−0.0907640	+	0.0260199i
$196$		0			0
$197$		−	47689.3i		−	1.22882i	−0.788987	−	0.614410i	$-0.789394\pi$
$197$		−	47689.3i		−	1.22882i	0.788987	−	0.614410i	$-0.210606\pi$
$198$		0			0
$199$	10428.5			0.263338			0.131669	−	0.991294i	$-0.457966\pi$
$199$	10428.5			0.263338			0.131669	+	0.991294i	$0.457966\pi$
$200$		0			0
$201$	55322.2	+	13797.1i	1.36933	+	0.341505i
$202$		0			0
$203$	12993.2	−	7501.61i	0.315299	−	0.182038i
$204$		0			0
$205$	−1882.85	+	3261.19i	−0.0448031	+	0.0776012i
$206$		0			0
$207$	5488.03	+	8785.18i	0.128078	+	0.205026i
$208$		0			0
$209$	17394.0	+	10042.4i	0.398205	+	0.229904i
$210$		0			0
$211$	6657.72	+	11531.5i	0.149541	+	0.259013i	0.931058	−	0.364871i	$-0.118887\pi$
$211$	6657.72	+	11531.5i	0.149541	+	0.259013i	−0.781517	+	0.623884i	$0.785554\pi$
$212$		0			0
$213$	29584.6	+	28573.2i	0.652089	+	0.629795i
$214$		0			0
$215$		−	5475.59i		−	0.118455i
$216$		0			0
$217$	−13481.4			−0.286297
$218$		0			0
$219$	6820.53	−	7061.96i	0.142210	−	0.147244i
$220$		0			0
$221$	−66454.0	+	38367.2i	−1.36062	+	0.785554i
$222$		0			0
$223$	−39853.9	+	69028.9i	−0.801421	+	1.38810i	0.117259	+	0.993101i	$0.462589\pi$
$223$	−39853.9	+	69028.9i	−0.801421	+	1.38810i	−0.918681	+	0.395001i	$0.870744\pi$
$224$		0			0
$225$	44349.3	+	23588.2i	0.876036	+	0.465940i
$226$		0			0
$227$	−6495.41	−	3750.13i	−0.126053	−	0.0727770i	0.435647	−	0.900117i	$-0.356519\pi$
$227$	−6495.41	−	3750.13i	−0.126053	−	0.0727770i	−0.561701	+	0.827340i	$0.689853\pi$
$228$		0			0
$229$	19105.5	+	33091.6i	0.364323	+	0.631026i	0.988667	−	0.150123i	$-0.0479671\pi$
$229$	19105.5	+	33091.6i	0.364323	+	0.631026i	−0.624344	+	0.781149i	$0.714634\pi$
$230$		0			0
$231$	−4327.11	+	17350.4i	−0.0810913	+	0.325151i
$232$		0			0
$233$			20709.5i			0.381468i	0.981642	+	0.190734i	$0.0610868\pi$
$233$			20709.5i			0.381468i	−0.981642	+	0.190734i	$0.938913\pi$
$234$		0			0
$235$	2988.28			0.0541109
$236$		0			0
$237$	17481.5	+	60980.0i	0.311231	+	1.08565i
$238$		0			0
$239$	93075.0	−	53736.9i	1.62944	−	0.940755i	0.645175	−	0.764035i	$-0.276784\pi$
$239$	93075.0	−	53736.9i	1.62944	−	0.940755i	0.984261	−	0.176721i	$-0.0565490\pi$
$240$		0			0
$241$	−37083.2	+	64230.0i	−0.638474	+	1.10587i	0.347294	+	0.937756i	$0.387101\pi$
$241$	−37083.2	+	64230.0i	−0.638474	+	1.10587i	−0.985768	+	0.168112i	$0.946233\pi$
$242$		0			0
$243$	37970.4	−	45222.0i	0.643032	−	0.765839i
$244$		0			0
$245$	−3863.29	−	2230.47i	−0.0643614	−	0.0371591i
$246$		0			0
$247$	17739.9	+	30726.4i	0.290775	+	0.503638i
$248$		0			0
$249$	86819.3	−	24889.0i	1.40029	−	0.401430i
$250$		0			0
$251$		−	52080.8i		−	0.826666i	−0.910580	−	0.413333i	$-0.864365\pi$
$251$		−	52080.8i		−	0.826666i	0.910580	−	0.413333i	$-0.135635\pi$
$252$		0			0
$253$	13113.1			0.204863
$254$		0			0
$255$	−8147.18	−	2031.87i	−0.125293	−	0.0312475i
$256$		0			0
$257$	−47733.1	+	27558.7i	−0.722693	+	0.417247i	−0.815743	−	0.578415i	$-0.803672\pi$
$257$	−47733.1	+	27558.7i	−0.722693	+	0.417247i	0.0930503	+	0.995661i	$0.470338\pi$
$258$		0			0
$259$	4062.46	−	7036.38i	0.0605605	−	0.104894i
$260$		0			0
$261$	−29451.5	+	55373.2i	−0.432341	+	0.812866i
$262$		0			0
$263$	−72616.1	−	41925.0i	−1.04984	−	0.606123i	−0.127233	−	0.991873i	$-0.540610\pi$
$263$	−72616.1	−	41925.0i	−1.04984	−	0.606123i	−0.922604	+	0.385749i	$0.873943\pi$
$264$		0			0
$265$	3399.40	+	5887.94i	0.0484073	+	0.0838440i
$266$		0			0
$267$	−6884.36	−	6649.00i	−0.0965698	−	0.0932683i
$268$		0			0
$269$		−	51813.2i		−	0.716038i	−0.933714	−	0.358019i	$-0.883452\pi$
$269$		−	51813.2i		−	0.716038i	0.933714	−	0.358019i	$-0.116548\pi$
$270$		0			0
$271$	−67280.6			−0.916118			−0.458059	−	0.888922i	$-0.651455\pi$
$271$	−67280.6			−0.916118			−0.458059	+	0.888922i	$0.651455\pi$
$272$		0			0
$273$	−21944.5	+	22721.2i	−0.294442	+	0.304864i
$274$		0			0
$275$	55070.8	−	31795.1i	0.728209	−	0.420431i
$276$		0			0
$277$	58529.8	−	101377.i	0.762812	−	1.32123i	−0.178583	−	0.983925i	$-0.557151\pi$
$277$	58529.8	−	101377.i	0.762812	−	1.32123i	0.941395	−	0.337305i	$-0.109515\pi$
$278$		0			0
$279$	47797.1	−	29858.5i	0.614035	−	0.383583i
$280$		0			0
$281$	49180.3	+	28394.3i	0.622843	+	0.359599i	0.777975	−	0.628295i	$-0.216247\pi$
$281$	49180.3	+	28394.3i	0.622843	+	0.359599i	−0.155132	+	0.987894i	$0.549580\pi$
$282$		0			0
$283$	18896.7	+	32730.0i	0.235946	+	0.408670i	0.959547	−	0.281548i	$-0.0908479\pi$
$283$	18896.7	+	32730.0i	0.235946	+	0.408670i	−0.723601	+	0.690218i	$0.757515\pi$
$284$		0			0
$285$	−939.479	+	3767.02i	−0.0115664	+	0.0463776i
$286$		0			0
$287$			33131.2i			0.402229i
$288$		0			0
$289$	−95938.7			−1.14868
$290$		0			0
$291$	−27839.5	−	97111.4i	−0.328758	−	1.14679i
$292$		0			0
$293$	−79974.3	+	46173.2i	−0.931569	+	0.537842i	−0.887308	−	0.461178i	$-0.847427\pi$
$293$	−79974.3	+	46173.2i	−0.931569	+	0.537842i	−0.0442619	+	0.999020i	$0.514094\pi$
$294$		0			0
$295$	3578.29	−	6197.78i	0.0411179	−	0.0712184i
$296$		0			0
$297$	−23086.0	−	71097.6i	−0.261719	−	0.806013i
$298$		0			0
$299$	20060.8	+	11582.1i	0.224391	+	0.129552i
$300$		0			0
$301$	−24087.5	−	41720.8i	−0.265864	−	0.460490i
$302$		0			0
$303$	−133202.	+	38186.0i	−1.45086	+	0.415928i
$304$		0			0
$305$		−	14592.1i		−	0.156862i
$306$		0			0
$307$	−19804.0			−0.210124			−0.105062	−	0.994466i	$-0.533504\pi$
$307$	−19804.0			−0.210124			−0.105062	+	0.994466i	$0.533504\pi$
$308$		0			0
$309$	152299.	+	37982.7i	1.59507	+	0.397804i
$310$		0			0
$311$	−9927.78	+	5731.81i	−0.102643	+	0.0592612i	−0.550443	−	0.834873i	$-0.685541\pi$
$311$	−9927.78	+	5731.81i	−0.102643	+	0.0592612i	0.447800	+	0.894134i	$0.352208\pi$
$312$		0			0
$313$	8247.02	−	14284.3i	0.0841799	−	0.145804i	−0.820862	−	0.571127i	$-0.806506\pi$
$313$	8247.02	−	14284.3i	0.0841799	−	0.145804i	0.905041	+	0.425323i	$0.139840\pi$
$314$		0			0
$315$	−3454.47	+	120.191i	−0.0348145	+	0.00121130i
$316$		0			0
$317$	−92083.7	−	53164.6i	−0.916356	−	0.529059i	−0.0338856	−	0.999426i	$-0.510788\pi$
$317$	−92083.7	−	53164.6i	−0.916356	−	0.529059i	−0.882471	+	0.470367i	$0.844122\pi$
$318$		0			0
$319$	39698.4	+	68759.7i	0.390114	+	0.675698i
$320$		0			0
$321$	−146894.	−	141872.i	−1.42559	−	1.37685i
$322$		0			0
$323$			82977.0i			0.795340i
$324$		0			0
$325$	112332.			1.06350
$326$		0			0
$327$	−129445.	+	134027.i	−1.21057	+	1.25342i
$328$		0			0
$329$	22768.9	−	13145.7i	0.210354	−	0.121448i
$330$		0			0
$331$	50651.5	−	87731.0i	0.462313	−	0.800750i	−0.536763	−	0.843733i	$-0.680353\pi$
$331$	50651.5	−	87731.0i	0.462313	−	0.800750i	0.999076	+	0.0429834i	$0.0136863\pi$
$332$		0			0
$333$	1181.02	+	33944.2i	0.0106505	+	0.306110i
$334$		0			0
$335$	12083.0	+	6976.12i	0.107668	+	0.0621619i
$336$		0			0
$337$	−59057.5	−	102291.i	−0.520014	−	0.900691i	−0.999729	−	0.0232664i	$-0.992593\pi$
$337$	−59057.5	−	102291.i	−0.520014	−	0.900691i	0.479715	−	0.877424i	$-0.340740\pi$
$338$		0			0
$339$	−7544.15	+	30249.7i	−0.0656464	+	0.263222i
$340$		0			0
$341$		−	71343.7i		−	0.613545i
$342$		0			0
$343$	−85771.1			−0.729042
$344$		0			0
$345$	698.519	+	2436.61i	0.00586867	+	0.0204714i
$346$		0			0
$347$	91309.0	−	52717.3i	0.758323	−	0.437818i	−0.0703700	−	0.997521i	$-0.522418\pi$
$347$	91309.0	−	52717.3i	0.758323	−	0.437818i	0.828693	+	0.559703i	$0.189085\pi$
$348$		0			0
$349$	117080.	−	202788.i	0.961239	−	1.66491i	0.241842	−	0.970316i	$-0.422248\pi$
$349$	117080.	−	202788.i	0.961239	−	1.66491i	0.719397	−	0.694599i	$-0.244418\pi$
$350$		0			0
$351$	27479.2	−	129158.i	0.223044	−	1.04835i
$352$		0			0
$353$	159478.	+	92074.6i	1.27983	+	0.738908i	0.976816	−	0.214079i	$-0.0686751\pi$
$353$	159478.	+	92074.6i	1.27983	+	0.738908i	0.303010	+	0.952987i	$0.402008\pi$
$354$		0			0
$355$	5032.34	+	8716.27i	0.0399313	+	0.0691630i
$356$		0			0
$357$	−71015.1	+	20358.4i	−0.557204	+	0.159737i
$358$		0			0
$359$			233924.i			1.81504i	0.420011	+	0.907519i	$0.362026\pi$
$359$			233924.i			1.81504i	−0.420011	+	0.907519i	$0.637974\pi$
$360$		0			0
$361$	−91954.8			−0.705602
$362$		0			0
$363$	36034.9	+	8986.94i	0.273470	+	0.0682022i
$364$		0			0
$365$	2080.61	−	1201.24i	0.0156172	−	0.00901662i
$366$		0			0
$367$	35848.7	−	62091.7i	0.266159	−	0.461001i	−0.701708	−	0.712465i	$-0.747579\pi$
$367$	35848.7	−	62091.7i	0.266159	−	0.461001i	0.967867	+	0.251464i	$0.0809121\pi$
$368$		0			0
$369$	−73378.3	−	117463.i	−0.538909	−	0.862679i
$370$		0			0
$371$	51803.0	+	29908.5i	0.376363	+	0.217293i
$372$		0			0
$373$	86719.3	+	150202.i	0.623301	+	1.07959i	0.988867	+	0.148804i	$0.0475422\pi$
$373$	86719.3	+	150202.i	0.623301	+	1.07959i	−0.365566	+	0.930786i	$0.619124\pi$
$374$		0			0
$375$	17752.3	+	17145.4i	0.126239	+	0.121923i
$376$		0			0
$377$			140254.i			0.986810i
$378$		0			0
$379$	170925.			1.18995			0.594974	−	0.803745i	$-0.297162\pi$
$379$	170925.			1.18995			0.594974	+	0.803745i	$0.297162\pi$
$380$		0			0
$381$	−185085.	+	191637.i	−1.27504	+	1.32017i
$382$		0			0
$383$	−140177.	+	80931.1i	−0.955605	+	0.551719i	−0.894818	−	0.446432i	$-0.852695\pi$
$383$	−140177.	+	80931.1i	−0.955605	+	0.551719i	−0.0607875	+	0.998151i	$0.519361\pi$
$384$		0			0
$385$	−2187.88	+	3789.52i	−0.0147605	+	0.0255660i
$386$		0			0
$387$	177802.	+	94568.3i	1.18718	+	0.631428i
$388$		0			0
$389$	92418.2	+	53357.6i	0.610742	+	0.352612i	0.773256	−	0.634094i	$-0.218627\pi$
$389$	92418.2	+	53357.6i	0.610742	+	0.352612i	−0.162514	+	0.986706i	$0.551960\pi$
$390$		0			0
$391$	27087.2	+	46916.4i	0.177178	+	0.306882i
$392$		0			0
$393$	21294.5	−	85384.5i	0.137874	−	0.552833i
$394$		0			0
$395$			15523.1i			0.0994914i
$396$		0			0
$397$	−10047.9			−0.0637520			−0.0318760	−	0.999492i	$-0.510148\pi$
$397$	−10047.9			−0.0637520			−0.0318760	+	0.999492i	$0.510148\pi$
$398$		0			0
$399$	9413.12	+	32835.4i	0.0591273	+	0.206251i
$400$		0			0
$401$	−30168.4	+	17417.7i	−0.187613	+	0.108318i	−0.590865	−	0.806771i	$-0.701213\pi$
$401$	−30168.4	+	17417.7i	−0.187613	+	0.108318i	0.403252	+	0.915089i	$0.367880\pi$
$402$		0			0
$403$	63014.2	−	109144.i	0.387997	−	0.672030i
$404$		0			0
$405$	11981.3	−	8077.02i	0.0730454	−	0.0492426i
$406$		0			0
$407$	37236.4	+	21498.5i	0.224791	+	0.129783i
$408$		0			0
$409$	136999.	+	237289.i	0.818974	+	1.41850i	0.906439	+	0.422337i	$0.138790\pi$
$409$	136999.	+	237289.i	0.818974	+	1.41850i	−0.0874654	+	0.996168i	$0.527877\pi$
$410$		0			0
$411$	−214404.	+	61464.5i	−1.26926	+	0.363866i
$412$		0			0
$413$		−	62964.7i		−	0.369145i
$414$		0			0
$415$	22100.8			0.128325
$416$		0			0
$417$	46712.7	+	11649.9i	0.268635	+	0.0669965i
$418$		0			0
$419$	25756.6	−	14870.6i	0.146710	−	0.0847032i	−0.424848	−	0.905265i	$-0.639672\pi$
$419$	25756.6	−	14870.6i	0.146710	−	0.0847032i	0.571558	+	0.820562i	$0.306339\pi$
$420$		0			0
$421$	31738.8	−	54973.2i	0.179072	−	0.310161i	−0.762491	−	0.646999i	$-0.776024\pi$
$421$	31738.8	−	54973.2i	0.179072	−	0.310161i	0.941563	+	0.336838i	$0.109357\pi$
$422$		0			0
$423$	−51610.2	+	97034.8i	−0.288440	+	0.542309i
$424$		0			0
$425$	227515.	+	131356.i	1.25960	+	0.727231i
$426$		0			0
$427$	−64191.5	−	111183.i	−0.352064	−	0.609793i
$428$		0			0
$429$	−120241.	−	116130.i	−0.653336	−	0.630999i
$430$		0			0
$431$			29885.2i			0.160880i	0.996759	+	0.0804400i	$0.0256326\pi$
$431$			29885.2i			0.160880i	−0.996759	+	0.0804400i	$0.974367\pi$
$432$		0			0
$433$	−233548.			−1.24566			−0.622832	−	0.782356i	$-0.714018\pi$
$433$	−233548.			−1.24566			−0.622832	+	0.782356i	$0.714018\pi$
$434$		0			0
$435$	−10661.9	+	11039.3i	−0.0563452	+	0.0583398i
$436$		0			0
$437$	21692.8	−	12524.3i	0.113593	−	0.0655831i
$438$		0			0
$439$	70067.8	−	121361.i	0.363571	−	0.629723i	−0.624975	−	0.780645i	$-0.714891\pi$
$439$	70067.8	−	121361.i	0.363571	−	0.629723i	0.988546	+	0.150922i	$0.0482241\pi$
$440$		0			0
$441$	139150.	−	86925.9i	0.715494	−	0.446964i
$442$		0			0
$443$	−177831.	−	102671.i	−0.906149	−	0.523165i	−0.0269590	−	0.999637i	$-0.508582\pi$
$443$	−177831.	−	102671.i	−0.906149	−	0.523165i	−0.879190	+	0.476471i	$0.841916\pi$
$444$		0			0
$445$	−1171.03	−	2028.28i	−0.00591354	−	0.0102426i
$446$		0			0
$447$	15628.2	−	62664.4i	0.0782159	−	0.313621i
$448$		0			0
$449$		−	178080.i		−	0.883328i	−0.897181	−	0.441664i	$-0.854388\pi$
$449$		−	178080.i		−	0.883328i	0.897181	−	0.441664i	$-0.145612\pi$
$450$		0			0
$451$	−175330.			−0.861991
$452$		0			0
$453$	16069.8	+	56055.6i	0.0783094	+	0.273163i
$454$		0			0
$455$	−6694.17	+	3864.88i	−0.0323351	+	0.0186687i
$456$		0			0
$457$	−89819.4	+	155572.i	−0.430069	+	0.744901i	−0.996879	−	0.0789477i	$-0.974844\pi$
$457$	−89819.4	+	155572.i	−0.430069	+	0.744901i	0.566810	+	0.823848i	$0.308177\pi$
$458$		0			0
$459$	206687.	−	229461.i	0.981045	−	1.08914i
$460$		0			0
$461$	−246477.	−	142304.i	−1.15978	−	0.669598i	−0.208527	−	0.978017i	$-0.566867\pi$
$461$	−246477.	−	142304.i	−1.15978	−	0.669598i	−0.951251	+	0.308418i	$0.900200\pi$
$462$		0			0
$463$	−102671.	−	177831.i	−0.478943	−	0.829554i	0.520765	−	0.853700i	$-0.325647\pi$
$463$	−102671.	−	177831.i	−0.478943	−	0.829554i	−0.999708	+	0.0241461i	$0.992313\pi$
$464$		0			0
$465$	13256.8	−	3800.40i	0.0613100	−	0.0175761i
$466$		0			0
$467$		−	87443.0i		−	0.400951i	−0.979699	−	0.200475i	$-0.935751\pi$
$467$		−	87443.0i		−	0.400951i	0.979699	−	0.200475i	$-0.0642487\pi$
$468$		0			0
$469$	122754.			0.558071
$470$		0			0
$471$	240404.	+	59955.7i	1.08368	+	0.270264i
$472$		0			0
$473$	220786.	−	127471.i	0.986846	−	0.569756i
$474$		0			0
$475$	60735.3	−	105197.i	0.269187	−	0.466245i
$476$		0			0
$477$	−249903.	+	8694.87i	−1.09833	+	0.0382143i
$478$		0			0
$479$	−365932.	−	211271.i	−1.59488	−	0.920807i	−0.992452	−	0.122637i	$-0.960865\pi$
$479$	−365932.	−	211271.i	−1.59488	−	0.920807i	−0.602433	−	0.798170i	$-0.705802\pi$
$480$		0			0
$481$	37977.0	+	65778.1i	0.164146	+	0.284309i
$482$		0			0
$483$	16041.1	+	15492.7i	0.0687608	+	0.0664101i
$484$		0			0
$485$		−	24720.8i		−	0.105094i
$486$		0			0
$487$	−245504.			−1.03514			−0.517572	−	0.855640i	$-0.673164\pi$
$487$	−245504.			−1.03514			−0.517572	+	0.855640i	$0.673164\pi$
$488$		0			0
$489$	53048.2	−	54926.0i	0.221847	−	0.229700i
$490$		0			0
$491$	−234949.	+	135648.i	−0.974564	+	0.562665i	−0.900625	−	0.434598i	$-0.856890\pi$
$491$	−234949.	+	135648.i	−0.974564	+	0.562665i	−0.0739394	+	0.997263i	$0.523557\pi$
$492$		0			0
$493$	−164007.	+	284069.i	−0.674790	+	1.16877i
$494$		0			0
$495$	−636.051	−	18281.0i	−0.00259586	−	0.0746088i
$496$		0			0
$497$	76687.1	+	44275.3i	0.310463	+	0.179246i
$498$		0			0
$499$	82878.5	+	143550.i	0.332844	+	0.576503i	0.983068	−	0.183240i	$-0.0586584\pi$
$499$	82878.5	+	143550.i	0.332844	+	0.576503i	−0.650224	+	0.759742i	$0.725325\pi$
$500$		0			0
$501$	−36166.5	+	145017.i	−0.144089	+	0.577753i
$502$		0			0
$503$		−	197523.i		−	0.780697i	−0.920667	−	0.390349i	$-0.872355\pi$
$503$		−	197523.i		−	0.780697i	0.920667	−	0.390349i	$-0.127645\pi$
$504$		0			0
$505$	−33908.1			−0.132960
$506$		0			0
$507$	−10539.8	−	36765.3i	−0.0410029	−	0.143029i
$508$		0			0
$509$	24818.6	−	14329.1i	0.0957949	−	0.0553072i	−0.451337	−	0.892353i	$-0.649053\pi$
$509$	24818.6	−	14329.1i	0.0957949	−	0.0553072i	0.547132	+	0.837046i	$0.315720\pi$
$510$		0			0
$511$	10568.7	−	18305.5i	0.0404743	−	0.0701035i
$512$		0			0
$513$	−106096.	−	95566.4i	−0.403149	−	0.363137i
$514$		0			0
$515$	33263.8	+	19204.9i	0.125417	+	0.0724097i
$516$		0			0
$517$	69566.6	+	120493.i	0.260268	+	0.450797i
$518$		0			0
$519$	316770.	−	90810.5i	1.17601	−	0.337133i
$520$		0			0
$521$			101644.i			0.374461i	0.982316	+	0.187230i	$0.0599511\pi$
$521$			101644.i			0.374461i	−0.982316	+	0.187230i	$0.940049\pi$
$522$		0			0
$523$	−195222.			−0.713717			−0.356858	−	0.934158i	$-0.616152\pi$
$523$	−195222.			−0.713717			−0.356858	+	0.934158i	$0.616152\pi$
$524$		0			0
$525$	104933.	+	26169.8i	0.380709	+	0.0949472i
$526$		0			0
$527$	255256.	−	147372.i	0.919082	−	0.530632i
$528$		0			0
$529$	−131744.	+	228187.i	−0.470780	+	0.815415i
$530$		0			0
$531$	139453.	+	223235.i	0.494582	+	0.791722i
$532$		0			0
$533$	−268225.	−	154860.i	−0.944159	−	0.545110i
$534$		0			0
$535$	−24986.7	−	43278.3i	−0.0872975	−	0.151204i
$536$		0			0
$537$	47030.0	+	45422.1i	0.163090	+	0.157514i
$538$		0			0
$539$		−	207700.i		−	0.714924i
$540$		0			0
$541$	−49035.1			−0.167538			−0.0837689	−	0.996485i	$-0.526696\pi$
$541$	−49035.1			−0.167538			−0.0837689	+	0.996485i	$0.526696\pi$
$542$		0			0
$543$	−93376.6	+	96682.0i	−0.316693	+	0.327903i
$544$		0			0
$545$	−39487.2	+	22797.9i	−0.132942	+	0.0767542i
$546$		0			0
$547$	−35185.8	+	60943.7i	−0.117596	+	0.203683i	−0.918815	−	0.394689i	$-0.870852\pi$
$547$	−35185.8	+	60943.7i	−0.117596	+	0.203683i	0.801218	+	0.598372i	$0.204186\pi$
$548$		0			0
$549$	473830.	+	252018.i	1.57209	+	0.836154i
$550$		0			0
$551$	131345.	+	75832.2i	0.432625	+	0.249776i
$552$		0			0
$553$	68287.5	+	118277.i	0.223301	+	0.386769i
$554$		0			0
$555$	−2011.20	+	8064.31i	−0.00652935	+	0.0261807i
$556$		0			0
$557$		−	294138.i		−	0.948072i	−0.880505	−	0.474036i	$-0.842797\pi$
$557$		−	294138.i		−	0.948072i	0.880505	−	0.474036i	$-0.157203\pi$
$558$		0			0
$559$	450354.			1.44122
$560$		0			0
$561$	−107736.	−	375811.i	−0.342323	−	1.19411i
$562$		0			0
$563$	−453294.	+	261709.i	−1.43009	+	0.825663i	−0.997127	−	0.0757493i	$-0.975865\pi$
$563$	−453294.	+	261709.i	−1.43009	+	0.825663i	−0.432963	+	0.901412i	$0.642532\pi$
$564$		0			0
$565$	−3814.48	+	6606.88i	−0.0119492	+	0.0206966i
$566$		0			0
$567$	55758.9	−	114249.i	0.173440	−	0.355374i
$568$		0			0
$569$	147862.	+	85368.4i	0.456702	+	0.263677i	0.710657	−	0.703539i	$-0.248398\pi$
$569$	147862.	+	85368.4i	0.456702	+	0.263677i	−0.253954	+	0.967216i	$0.581731\pi$
$570$		0			0
$571$	75894.8	+	131454.i	0.232777	+	0.403181i	0.958624	−	0.284674i	$-0.0918855\pi$
$571$	75894.8	+	131454.i	0.232777	+	0.403181i	−0.725847	+	0.687856i	$0.758552\pi$
$572$		0			0
$573$	221483.	−	63494.0i	0.674577	−	0.193385i
$574$		0			0
$575$		−	79306.1i		−	0.239867i
$576$		0			0
$577$	−324257.			−0.973953			−0.486977	−	0.873415i	$-0.661900\pi$
$577$	−324257.			−0.973953			−0.486977	+	0.873415i	$0.661900\pi$
$578$		0			0
$579$	229496.	+	57235.2i	0.684569	+	0.170729i
$580$		0			0
$581$	168395.	−	97223.1i	0.498859	−	0.288016i
$582$		0			0
$583$	−158275.	+	274141.i	−0.465668	+	0.806560i
$584$		0			0
$585$	15173.6	−	28528.7i	0.0443382	−	0.0833623i
$586$		0			0
$587$	240655.	+	138942.i	0.698423	+	0.403235i	0.806760	−	0.590879i	$-0.201219\pi$
$587$	240655.	+	138942.i	0.698423	+	0.403235i	−0.108337	+	0.994114i	$0.534552\pi$
$588$		0			0
$589$	−68140.6	−	118023.i	−0.196415	−	0.340201i
$590$		0			0
$591$	308724.	+	298170.i	0.883885	+	0.853667i
$592$		0			0
$593$			112448.i			0.319774i	0.987135	+	0.159887i	$0.0511129\pi$
$593$			112448.i			0.319774i	−0.987135	+	0.159887i	$0.948887\pi$
$594$		0			0
$595$	−18077.7			−0.0510633
$596$		0			0
$597$	−65202.2	+	67510.2i	−0.182942	+	0.189418i
$598$		0			0
$599$	70549.3	−	40731.6i	0.196625	−	0.113522i	−0.398455	−	0.917188i	$-0.630454\pi$
$599$	70549.3	−	40731.6i	0.196625	−	0.113522i	0.595080	+	0.803666i	$0.297120\pi$
$600$		0			0
$601$	−3435.30	+	5950.11i	−0.00951077	+	0.0164731i	−0.870742	−	0.491741i	$-0.836361\pi$
$601$	−3435.30	+	5950.11i	−0.00951077	+	0.0164731i	0.861231	+	0.508214i	$0.169694\pi$
$602$		0			0
$603$	−435211.	+	271873.i	−1.19692	+	0.747707i
$604$		0			0
$605$	7870.41	+	4543.99i	0.0215024	+	0.0124144i
$606$		0			0
$607$	42325.6	+	73310.1i	0.114875	+	0.198969i	0.917730	−	0.397205i	$-0.130020\pi$
$607$	42325.6	+	73310.1i	0.114875	+	0.198969i	−0.802855	+	0.596175i	$0.796687\pi$
$608$		0			0
$609$	−32674.8	+	131016.i	−0.0881006	+	0.353256i
$610$		0			0
$611$			245779.i			0.658357i
$612$		0			0
$613$	539029.			1.43447			0.717234	−	0.696832i	$-0.245408\pi$
$613$	539029.			1.43447			0.717234	+	0.696832i	$0.245408\pi$
$614$		0			0
$615$	−9339.63	−	32579.0i	−0.0246933	−	0.0861366i
$616$		0			0
$617$	360027.	−	207862.i	0.945725	−	0.546015i	0.0539746	−	0.998542i	$-0.482811\pi$
$617$	360027.	−	207862.i	0.945725	−	0.546015i	0.891750	+	0.452528i	$0.149478\pi$
$618$		0			0
$619$	−315908.	+	547168.i	−0.824477	+	1.42804i	0.0778407	+	0.996966i	$0.475197\pi$
$619$	−315908.	+	547168.i	−0.824477	+	1.42804i	−0.902318	+	0.431071i	$0.858136\pi$
$620$		0			0
$621$	−91185.2	−	19400.3i	−0.236451	−	0.0503065i
$622$		0			0
$623$	−17845.1	−	10302.9i	−0.0459773	−	0.0265450i
$624$		0			0
$625$	−190777.	−	330436.i	−0.488389	−	0.845915i
$626$		0			0
$627$	−173764.	+	49814.1i	−0.442003	+	0.126712i
$628$		0			0
$629$			177634.i			0.448978i
$630$		0			0
$631$	384521.			0.965742			0.482871	−	0.875691i	$-0.339594\pi$
$631$	384521.			0.965742			0.482871	+	0.875691i	$0.339594\pi$
$632$		0			0
$633$	−116277.	−	28999.1i	−0.290194	−	0.0723730i
$634$		0			0
$635$	−56460.4	+	32597.5i	−0.140022	+	0.0808418i
$636$		0			0
$637$	183451.	−	317747.i	0.452107	−	0.783073i
$638$		0			0
$639$	−369946.	+	12871.5i	−0.906018	+	0.0315231i
$640$		0			0
$641$	−670169.	−	386922.i	−1.63105	−	0.941689i	−0.983769	−	0.179439i	$-0.942572\pi$
$641$	−670169.	−	386922.i	−1.63105	−	0.941689i	−0.647284	−	0.762249i	$-0.724095\pi$
$642$		0			0
$643$	−211297.	−	365978.i	−0.511060	−	0.885182i	−0.999918	−	0.0128186i	$-0.995920\pi$
$643$	−211297.	−	365978.i	−0.511060	−	0.885182i	0.488858	−	0.872364i	$-0.337414\pi$
$644$		0			0
$645$	35447.1	+	34235.2i	0.0852043	+	0.0822913i
$646$		0			0
$647$			599581.i			1.43232i	0.697937	+	0.716159i	$0.254101\pi$
$647$			599581.i			1.43232i	−0.697937	+	0.716159i	$0.745899\pi$
$648$		0			0
$649$	333208.			0.791091
$650$		0			0
$651$	84290.6	−	87274.3i	0.198892	−	0.205932i
$652$		0			0
$653$	−463080.	+	267359.i	−1.08600	+	0.627002i	−0.932509	−	0.361148i	$-0.882385\pi$
$653$	−463080.	+	267359.i	−1.08600	+	0.627002i	−0.153491	+	0.988150i	$0.549052\pi$
$654$		0			0
$655$	10767.0	−	18648.9i	0.0250963	−	0.0434681i
$656$		0			0
$657$	3072.48	+	88307.6i	0.00711802	+	0.204582i
$658$		0			0
$659$	197061.	+	113773.i	0.453763	+	0.261980i	0.709418	−	0.704788i	$-0.248958\pi$
$659$	197061.	+	113773.i	0.453763	+	0.261980i	−0.255655	+	0.966768i	$0.582291\pi$
$660$		0			0
$661$	−268960.	−	465852.i	−0.615580	−	1.06622i	−0.990282	−	0.139071i	$-0.955589\pi$
$661$	−268960.	−	465852.i	−0.615580	−	1.06622i	0.374703	−	0.927145i	$-0.377745\pi$
$662$		0			0
$663$	167116.	−	670085.i	0.380183	−	1.52441i
$664$		0			0
$665$			8358.60i			0.0189012i
$666$		0			0
$667$	99019.3			0.222571
$668$		0			0
$669$	−197690.	−	689593.i	−0.441705	−	1.54078i
$670$		0			0
$671$	588379.	−	339701.i	1.30681	−	0.754486i
$672$		0			0
$673$	140824.	−	243914.i	0.310918	−	0.538526i	−0.667643	−	0.744481i	$-0.732697\pi$
$673$	140824.	−	243914.i	0.310918	−	0.538526i	0.978561	+	0.205955i	$0.0660301\pi$
$674$		0			0
$675$	−429989.	+	139621.i	−0.943735	+	0.306438i
$676$		0			0
$677$	438663.	+	253262.i	0.957091	+	0.552577i	0.895277	−	0.445511i	$-0.146978\pi$
$677$	438663.	+	253262.i	0.957091	+	0.552577i	0.0618148	+	0.998088i	$0.480311\pi$
$678$		0			0
$679$	−108749.	−	188358.i	−0.235876	−	0.408549i
$680$		0			0
$681$	64888.5	−	18602.0i	0.139918	−	0.0401112i
$682$		0			0
$683$		−	654086.i		−	1.40215i	−0.713089	−	0.701073i	$-0.752705\pi$
$683$		−	654086.i		−	1.40215i	0.713089	−	0.701073i	$-0.247295\pi$
$684$		0			0
$685$	−54578.9			−0.116317
$686$		0			0
$687$	−333678.	−	83217.8i	−0.706991	−	0.176321i
$688$		0			0
$689$	−484269.	+	279593.i	−1.02011	+	0.588962i
$690$		0			0
$691$	−81405.9	+	140999.i	−0.170490	+	0.295298i	−0.938591	−	0.345031i	$-0.887868\pi$
$691$	−81405.9	+	140999.i	−0.170490	+	0.295298i	0.768101	+	0.640329i	$0.221202\pi$
$692$		0			0
$693$	−85265.9	−	136493.i	−0.177545	−	0.284212i
$694$		0			0
$695$	10202.6	+	5890.46i	0.0211222	+	0.0121949i
$696$		0			0
$697$	−362172.	−	627301.i	−0.745503	−	1.29125i
$698$		0			0
$699$	−134066.	−	129483.i	−0.274388	−	0.265008i
$700$		0			0
$701$			449274.i			0.914272i	0.889397	+	0.457136i	$0.151125\pi$
$701$			449274.i			0.914272i	−0.889397	+	0.457136i	$0.848875\pi$
$702$		0			0
$703$	82133.0			0.166191
$704$		0			0
$705$	−18683.7	+	19345.1i	−0.0375911	+	0.0389218i
$706$		0			0
$707$	−258360.	+	149164.i	−0.516877	+	0.298419i
$708$		0			0
$709$	68228.8	−	118176.i	0.135730	−	0.235091i	−0.790146	−	0.612918i	$-0.789995\pi$
$709$	68228.8	−	118176.i	0.135730	−	0.235091i	0.925876	+	0.377827i	$0.123329\pi$
$710$		0			0
$711$	−504065.	−	268098.i	−0.997119	−	0.530341i
$712$		0			0
$713$	−77055.2	−	44487.9i	−0.151573	−	0.0875110i
$714$		0			0
$715$	−20452.9	−	35425.5i	−0.0400076	−	0.0692953i
$716$		0			0
$717$	−234062.	+	938517.i	−0.455295	+	1.82559i
$718$		0			0
$719$		−	504506.i		−	0.975907i	−0.872870	−	0.487954i	$-0.837743\pi$
$719$		−	504506.i		−	0.975907i	0.872870	−	0.487954i	$-0.162257\pi$
$720$		0			0
$721$	337935.			0.650073
$722$		0			0
$723$	−183946.	−	641651.i	−0.351896	−	1.22750i
$724$		0			0
$725$	415850.	−	240091.i	0.791153	−	0.456772i
$726$		0			0
$727$	431741.	−	747797.i	0.816872	−	1.41486i	−0.0911036	−	0.995841i	$-0.529039\pi$
$727$	431741.	−	747797.i	0.816872	−	1.41486i	0.907976	−	0.419023i	$-0.137627\pi$
$728$		0			0
$729$	55348.4	+	528551.i	0.104148	+	0.994562i
$730$		0			0
$731$	912139.	+	526624.i	1.70697	+	0.985521i
$732$		0			0
$733$	45265.2	+	78401.7i	0.0842474	+	0.145921i	0.905070	−	0.425262i	$-0.139818\pi$
$733$	45265.2	+	78401.7i	0.0842474	+	0.145921i	−0.820823	+	0.571183i	$0.806485\pi$
$734$		0			0
$735$	38594.0	−	11064.0i	0.0714405	−	0.0204803i
$736$		0			0
$737$			649612.i			1.19597i
$738$		0			0
$739$	228041.			0.417565			0.208782	−	0.977962i	$-0.433050\pi$
$739$	228041.			0.417565			0.208782	+	0.977962i	$0.433050\pi$
$740$		0			0
$741$	−309828.	−	77269.9i	−0.564267	−	0.140726i
$742$		0			0
$743$	−77235.8	+	44592.1i	−0.139907	+	0.0807756i	−0.568320	−	0.822808i	$-0.692406\pi$
$743$	−77235.8	+	44592.1i	−0.139907	+	0.0807756i	0.428412	+	0.903583i	$0.359073\pi$
$744$		0			0
$745$	7901.96	−	13686.6i	0.0142371	−	0.0246594i
$746$		0			0
$747$	−381701.	+	717653.i	−0.684040	+	1.28610i
$748$		0			0
$749$	−380769.	−	219837.i	−0.678731	−	0.391866i
$750$		0			0
$751$	295392.	+	511634.i	0.523744	+	0.907152i	0.999618	+	0.0276380i	$0.00879856\pi$
$751$	295392.	+	511634.i	0.523744	+	0.907152i	−0.475874	+	0.879514i	$0.657868\pi$
$752$		0			0
$753$	337153.	+	325627.i	0.594617	+	0.574288i
$754$		0			0
$755$			14269.6i			0.0250332i
$756$		0			0
$757$	38933.0			0.0679401			0.0339701	−	0.999423i	$-0.489185\pi$
$757$	38933.0			0.0679401			0.0339701	+	0.999423i	$0.489185\pi$
$758$		0			0
$759$	−81987.4	+	84889.5i	−0.142319	+	0.147357i
$760$		0			0
$761$	−249265.	+	143913.i	−0.430420	+	0.248503i	−0.699525	−	0.714608i	$-0.746605\pi$
$761$	−249265.	+	143913.i	−0.430420	+	0.248503i	0.269106	+	0.963111i	$0.413272\pi$
$762$		0			0
$763$	−200580.	+	347414.i	−0.344538	+	0.596758i
$764$		0			0
$765$	64092.5	−	40038.1i	0.109518	−	0.0684149i
$766$		0			0
$767$	509752.	+	294306.i	0.866500	+	0.500274i
$768$		0			0
$769$	21194.3	+	36709.5i	0.0358398	+	0.0620764i	0.883389	−	0.468641i	$-0.155256\pi$
$769$	21194.3	+	36709.5i	0.0358398	+	0.0620764i	−0.847549	+	0.530717i	$0.821923\pi$
$770$		0			0
$771$	120038.	−	481314.i	0.201934	−	0.809693i
$772$		0			0
$773$			750485.i			1.25598i	0.778221	+	0.627990i	$0.216122\pi$
$773$			750485.i			1.25598i	−0.778221	+	0.627990i	$0.783878\pi$
$774$		0			0
$775$	−431477.			−0.718380
$776$		0			0
$777$	20151.3	+	70292.8i	0.0333780	+	0.116431i
$778$		0			0
$779$	−290046.	+	167458.i	−0.477960	+	0.275951i
$780$		0			0
$781$	−234304.	+	405827.i	−0.384130	+	0.665333i
$782$		0			0
$783$	−174326.	−	536871.i	−0.284341	−	0.875683i
$784$		0			0
$785$	52506.9	+	30314.9i	0.0852073	+	0.0491945i
$786$		0			0
$787$	−223022.	−	386286.i	−0.360080	−	0.623677i	0.627894	−	0.778299i	$-0.283917\pi$
$787$	−223022.	−	386286.i	−0.360080	−	0.623677i	−0.987974	+	0.154622i	$0.950584\pi$
$788$		0			0
$789$	725429.	−	207963.i	1.16531	−	0.334066i
$790$		0			0
$791$			67120.8i			0.107276i
$792$		0			0
$793$	1.20016e6			1.90850
$794$		0			0
$795$	−59370.8	−	14806.8i	−0.0939374	−	0.0234276i
$796$		0			0
$797$	271119.	−	156531.i	0.426819	−	0.246424i	−0.271172	−	0.962531i	$-0.587411\pi$
$797$	271119.	−	156531.i	0.426819	−	0.246424i	0.697990	+	0.716107i	$0.254078\pi$
$798$		0			0
$799$	−287402.	+	497796.i	−0.450191	+	0.779754i
$800$		0			0
$801$	86086.7	−	2995.22i	0.134175	−	0.00466835i
$802$		0			0
$803$	96872.5	+	55929.3i	0.150234	+	0.0867378i
$804$		0			0
$805$	2728.60	+	4726.07i	0.00421064	+	0.00729304i
$806$		0			0
$807$	335421.	+	323954.i	0.515043	+	0.497434i
$808$		0			0
$809$			707292.i			1.08069i	0.841443	+	0.540346i	$0.181707\pi$
$809$			707292.i			1.08069i	−0.841443	+	0.540346i	$0.818293\pi$
$810$		0			0
$811$	922250.			1.40219			0.701095	−	0.713068i	$-0.252695\pi$
$811$	922250.			1.40219			0.701095	+	0.713068i	$0.252695\pi$
$812$		0			0
$813$	420661.	−	435552.i	0.636431	−	0.658959i
$814$		0			0
$815$	16182.4	−	9342.91i	0.0243628	−	0.0140659i
$816$		0			0
$817$	243496.	−	421747.i	0.364794	−	0.631841i
$818$		0			0
$819$	−9885.45	−	284122.i	−0.0147377	−	0.423581i
$820$		0			0
$821$	−100930.	−	58272.2i	−0.149739	−	0.0864520i	0.423258	−	0.906009i	$-0.360886\pi$
$821$	−100930.	−	58272.2i	−0.149739	−	0.0864520i	−0.572998	+	0.819557i	$0.694220\pi$
$822$		0			0
$823$	−241332.	−	418000.i	−0.356300	−	0.617130i	0.631040	−	0.775751i	$-0.282629\pi$
$823$	−241332.	−	418000.i	−0.356300	−	0.617130i	−0.987340	+	0.158621i	$0.949295\pi$
$824$		0			0
$825$	−138490.	+	555303.i	−0.203475	+	0.815873i
$826$		0			0
$827$		−	1.31930e6i		−	1.92900i	−0.264077	−	0.964502i	$-0.585067\pi$
$827$		−	1.31930e6i		−	1.92900i	0.264077	−	0.964502i	$-0.414933\pi$
$828$		0			0
$829$	−708770.			−1.03133			−0.515663	−	0.856791i	$-0.672454\pi$
$829$	−708770.			−1.03133			−0.515663	+	0.856791i	$0.672454\pi$
$830$		0			0
$831$	290330.	+	1.01274e6i	0.420426	+	1.46655i
$832$		0			0
$833$	743117.	−	429039.i	1.07095	−	0.618311i
$834$		0			0
$835$	−18286.6	+	31673.3i	−0.0262276	+	0.0454276i
$836$		0			0
$837$	−105550.	+	496107.i	−0.150663	+	0.708149i
$838$		0			0
$839$	−348575.	−	201250.i	−0.495191	−	0.285898i	0.231535	−	0.972827i	$-0.425625\pi$
$839$	−348575.	−	201250.i	−0.495191	−	0.285898i	−0.726725	+	0.686928i	$0.758959\pi$
$840$		0			0
$841$	−53870.1	−	93305.8i	−0.0761651	−	0.131922i
$842$		0			0
$843$	−491307.	+	140846.i	−0.691349	+	0.198194i
$844$		0			0
$845$		−	9359.02i		−	0.0131074i
$846$		0			0
$847$	79957.3			0.111453
$848$		0			0
$849$	−330031.	−	82308.3i	−0.457867	−	0.114190i
$850$		0			0
$851$	46439.2	−	26811.7i	0.0641247	−	0.0370224i
$852$		0			0
$853$	−263306.	+	456060.i	−0.361879	+	0.626792i	−0.988270	−	0.152717i	$-0.951198\pi$
$853$	−263306.	+	456060.i	−0.361879	+	0.626792i	0.626391	+	0.779509i	$0.284531\pi$
$854$		0			0
$855$	−18512.5	−	29634.6i	−0.0253240	−	0.0405384i
$856$		0			0
$857$	−601802.	−	347450.i	−0.819392	−	0.473076i	0.0308148	−	0.999525i	$-0.490190\pi$
$857$	−601802.	−	347450.i	−0.819392	−	0.473076i	−0.850207	+	0.526449i	$0.823523\pi$
$858$		0			0
$859$	437904.	+	758472.i	0.593461	+	1.02791i	0.993762	+	0.111521i	$0.0355723\pi$
$859$	437904.	+	758472.i	0.593461	+	1.02791i	−0.400301	+	0.916384i	$0.631094\pi$
$860$		0			0
$861$	−214480.	−	207147.i	−0.289321	−	0.279430i
$862$		0			0
$863$			627215.i			0.842161i	0.907023	+	0.421080i	$0.138349\pi$
$863$			627215.i			0.842161i	−0.907023	+	0.421080i	$0.861651\pi$
$864$		0			0
$865$	80637.4			0.107772
$866$		0			0
$867$	599841.	−	621074.i	0.797991	−	0.826238i
$868$		0			0
$869$	−625922.	+	361376.i	−0.828859	+	0.478542i
$870$		0			0
$871$	−573769.	+	993797.i	−0.756311	+	1.30997i
$872$		0			0
$873$	802728.	+	426950.i	1.05327	+	0.560206i
$874$		0			0
$875$	46016.3	+	26567.5i	0.0601029	+	0.0347004i
$876$		0			0
$877$	−165942.	−	287420.i	−0.215753	−	0.373695i	0.737752	−	0.675072i	$-0.235887\pi$
$877$	−165942.	−	287420.i	−0.215753	−	0.373695i	−0.953505	+	0.301376i	$0.902554\pi$
$878$		0			0
$879$	201117.	−	806417.i	0.260298	−	1.04371i
$880$		0			0
$881$		−	1.24890e6i		−	1.60907i	−0.593904	−	0.804536i	$-0.702414\pi$
$881$		−	1.24890e6i		−	1.60907i	0.593904	−	0.804536i	$-0.297586\pi$
$882$		0			0
$883$	−669955.			−0.859259			−0.429629	−	0.903005i	$-0.641356\pi$
$883$	−669955.			−0.859259			−0.429629	+	0.903005i	$0.641356\pi$
$884$		0			0
$885$	17749.6	+	61915.2i	0.0226622	+	0.0790517i
$886$		0			0
$887$	419349.	−	242111.i	0.533001	−	0.307728i	−0.209237	−	0.977865i	$-0.567098\pi$
$887$	419349.	−	242111.i	0.533001	−	0.307728i	0.742238	+	0.670137i	$0.233765\pi$
$888$		0			0
$889$	−286797.	+	496747.i	−0.362887	+	0.628539i
$890$		0			0
$891$	604603.	+	295076.i	0.761579	+	0.371687i
$892$		0			0
$893$	230166.	+	132887.i	0.288628	+	0.166640i
$894$		0			0
$895$	7999.80	+	13856.1i	0.00998695	+	0.0172979i
$896$		0			0
$897$	−200405.	+	57451.5i	−0.249072	+	0.0714030i
$898$		0			0
$899$		−	538729.i		−	0.666578i
$900$		0			0
$901$	−1.30777e6			−1.61095
$902$		0			0
$903$	420690.	+	104918.i	0.515925	+	0.128670i
$904$		0			0
$905$	−28484.6	+	16445.6i	−0.0347787	+	0.0200795i
$906$		0			0
$907$	431524.	−	747422.i	0.524554	−	0.908555i	−0.475037	−	0.879966i	$-0.657565\pi$
$907$	431524.	−	747422.i	0.524554	−	0.908555i	0.999591	−	0.0285890i	$-0.00910139\pi$
$908$		0			0
$909$	585623.	−	1.10106e6i	0.708746	−	1.33255i
$910$		0			0
$911$	−1.14391e6	−	660434.i	−1.37833	−	0.795779i	−0.386372	−	0.922343i	$-0.626272\pi$
$911$	−1.14391e6	−	660434.i	−1.37833	−	0.795779i	−0.991958	+	0.126564i	$0.959605\pi$
$912$		0			0
$913$	514503.	+	891146.i	0.617230	+	1.06907i
$914$		0			0
$915$	94464.0	+	91234.4i	0.112830	+	0.108972i
$916$		0			0
$917$		−	189459.i		−	0.225308i
$918$		0			0
$919$	−756687.			−0.895953			−0.447977	−	0.894045i	$-0.647855\pi$
$919$	−756687.			−0.895953			−0.447977	+	0.894045i	$0.647855\pi$
$920$		0			0
$921$	123821.	−	128204.i	0.145974	−	0.151142i
$922$		0			0
$923$	−716892.	+	413898.i	−0.841493	+	0.485836i
$924$		0			0
$925$	130020.	−	225201.i	0.151959	−	0.263201i
$926$		0			0
$927$	−1.19811e6	+	748451.i	−1.39424	+	0.870972i
$928$		0			0
$929$	−1.32944e6	−	767550.i	−1.54041	−	0.889355i	−0.998813	−	0.0487157i	$-0.984487\pi$
$929$	−1.32944e6	−	767550.i	−1.54041	−	0.889355i	−0.541595	−	0.840639i	$-0.682179\pi$
$930$		0			0
$931$	−198375.	−	343596.i	−0.228870	−	0.396414i
$932$		0			0
$933$	24966.1	−	100106.i	0.0286805	−	0.115000i
$934$		0			0
$935$		−	95666.8i		−	0.109430i
$936$		0			0
$937$	−474819.			−0.540815			−0.270408	−	0.962746i	$-0.587158\pi$
$937$	−474819.			−0.540815			−0.270408	+	0.962746i	$0.587158\pi$
$938$		0			0
$939$	40908.2	+	142698.i	0.0463959	+	0.161841i
$940$		0			0
$941$	623294.	−	359859.i	0.703904	−	0.406399i	−0.104896	−	0.994483i	$-0.533451\pi$
$941$	623294.	−	359859.i	0.703904	−	0.406399i	0.808800	+	0.588084i	$0.200118\pi$
$942$		0			0
$943$	−109331.	+	189366.i	−0.122947	+	0.212951i
$944$		0			0
$945$	20820.4	−	23114.5i	0.0233145	−	0.0258834i
$946$		0			0
$947$	909844.	+	525298.i	1.01453	+	0.585742i	0.912516	−	0.409041i	$-0.134137\pi$
$947$	909844.	+	525298.i	1.01453	+	0.585742i	0.102018	+	0.994783i	$0.467470\pi$
$948$		0			0
$949$	98799.0	+	171125.i	0.109703	+	0.190012i
$950$		0			0
$951$	919908.	−	263716.i	1.01715	−	0.291592i
$952$		0			0
$953$		−	1.54605e6i		−	1.70231i	−0.524917	−	0.851153i	$-0.675904\pi$
$953$		−	1.54605e6i		−	1.70231i	0.524917	−	0.851153i	$-0.324096\pi$
$954$		0			0
$955$	56381.0			0.0618196
$956$		0			0
$957$	−693335.	−	172915.i	−0.757041	−	0.188803i
$958$		0			0
$959$	−415859.	+	240097.i	−0.452178	+	0.261065i
$960$		0			0
$961$	219718.	−	380562.i	0.237913	−	0.412077i
$962$		0			0
$963$	1.83687e6	−	63910.1i	1.98073	−	0.0689155i
$964$		0			0
$965$	50124.4	+	28939.3i	0.0538263	+	0.0310766i
$966$		0			0
$967$	−321632.	−	557083.i	−0.343959	−	0.595754i	0.641205	−	0.767369i	$-0.278435\pi$
$967$	−321632.	−	557083.i	−0.343959	−	0.595754i	−0.985164	+	0.171616i	$0.945101\pi$
$968$		0			0
$969$	−537165.	−	518800.i	−0.572085	−	0.552526i
$970$		0			0
$971$		−	133370.i		−	0.141456i	−0.997496	−	0.0707278i	$-0.977468\pi$
$971$		−	133370.i		−	0.141456i	0.997496	−	0.0707278i	$-0.0225322\pi$
$972$		0			0
$973$	103650.			0.109483
$974$		0			0
$975$	−702338.	+	727199.i	−0.738817	+	0.764970i
$976$		0			0
$977$	203862.	−	117700.i	0.213573	−	0.123306i	−0.389398	−	0.921070i	$-0.627317\pi$
$977$	203862.	−	117700.i	0.213573	−	0.123306i	0.602971	+	0.797763i	$0.293984\pi$
$978$		0			0
$979$	54522.8	−	94436.2i	0.0568869	−	0.0985311i
$980$		0			0
$981$	−58311.7	−	1.67596e6i	−0.0605923	−	1.74151i
$982$		0			0
$983$	−335425.	−	193657.i	−0.347127	−	0.200414i	0.316292	−	0.948662i	$-0.397562\pi$
$983$	−335425.	−	193657.i	−0.347127	−	0.200414i	−0.663419	+	0.748248i	$0.730895\pi$
$984$		0			0
$985$	52514.0	+	90956.8i	0.0541255	+	0.0937482i
$986$		0			0
$987$	−57258.6	+	229589.i	−0.0587769	+	0.235677i
$988$		0			0
$989$		−	317949.i		−	0.325061i
$990$		0			0
$991$	90031.1			0.0916738			0.0458369	−	0.998949i	$-0.485405\pi$
$991$	90031.1			0.0916738			0.0458369	+	0.998949i	$0.485405\pi$
$992$		0			0
$993$	251250.	+	876424.i	0.254805	+	0.888824i
$994$		0			0
$995$	−19890.0	+	11483.5i	−0.0200904	+	0.0115992i
$996$		0			0
$997$	−510291.	+	883849.i	−0.513366	+	0.889177i	0.486513	+	0.873673i	$0.338268\pi$
$997$	−510291.	+	883849.i	−0.513366	+	0.889177i	−0.999880	+	0.0155035i	$0.995065\pi$
$998$		0			0
$999$	−227127.	−	204585.i	−0.227582	−	0.204995i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.5.m.a.65.3	yes	24
3.2	odd	2		216.5.m.a.89.6		24
4.3	odd	2		144.5.q.d.65.10		24
9.2	odd	6		648.5.e.c.161.13		24
9.4	even	3		216.5.m.a.17.6		24
9.5	odd	6	inner	72.5.m.a.41.3	✓	24
9.7	even	3		648.5.e.c.161.12		24
12.11	even	2		432.5.q.d.305.6		24
36.7	odd	6		1296.5.e.j.161.12		24
36.11	even	6		1296.5.e.j.161.13		24
36.23	even	6		144.5.q.d.113.10		24
36.31	odd	6		432.5.q.d.17.6		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.5.m.a.41.3	✓	24	9.5	odd	6	inner
72.5.m.a.65.3	yes	24	1.1	even	1	trivial
144.5.q.d.65.10		24	4.3	odd	2
144.5.q.d.113.10		24	36.23	even	6
216.5.m.a.17.6		24	9.4	even	3
216.5.m.a.89.6		24	3.2	odd	2
432.5.q.d.17.6		24	36.31	odd	6
432.5.q.d.305.6		24	12.11	even	2
648.5.e.c.161.12		24	9.7	even	3
648.5.e.c.161.13		24	9.2	odd	6
1296.5.e.j.161.12		24	36.7	odd	6
1296.5.e.j.161.13		24	36.11	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)

\(f(q)\)	\(=\)	\(q+(-6.25234 + 6.47366i) q^{3} +(-1.90728 + 1.10117i) q^{5} +(-9.68825 + 16.7805i) q^{7} +(-2.81653 - 80.9510i) q^{9} +O(q^{10})\)	\(q+(-6.25234 + 6.47366i) q^{3} +(-1.90728 + 1.10117i) q^{5} +(-9.68825 + 16.7805i) q^{7} +(-2.81653 - 80.9510i) q^{9} +(-88.8024 - 51.2701i) q^{11} +(-90.5685 - 156.869i) q^{13} +(4.79637 - 19.2320i) q^{15} -423.627i q^{17} -195.873 q^{19} +(-48.0573 - 167.636i) q^{21} +(-110.749 + 63.9411i) q^{23} +(-310.075 + 537.065i) q^{25} +(541.659 + 487.900i) q^{27} +(-670.564 - 387.150i) q^{29} +(347.881 + 602.548i) q^{31} +(887.128 - 254.319i) q^{33} -42.6736i q^{35} -419.318 q^{37} +(1581.78 + 394.490i) q^{39} +(1480.79 - 854.932i) q^{41} +(-1243.13 + 2153.17i) q^{43} +(94.5127 + 151.295i) q^{45} +(-1175.08 - 678.433i) q^{47} +(1012.78 + 1754.18i) q^{49} +(2742.42 + 2648.66i) q^{51} -3087.09i q^{53} +225.828 q^{55} +(1224.66 - 1268.01i) q^{57} +(-2814.18 + 1624.77i) q^{59} +(-3312.85 + 5738.03i) q^{61} +(1385.69 + 737.011i) q^{63} +(345.479 + 199.462i) q^{65} +(-3167.60 - 5486.44i) q^{67} +(278.509 - 1116.73i) q^{69} -4570.00i q^{71} -1090.88 q^{73} +(-1538.09 - 5365.23i) q^{75} +(1720.68 - 993.435i) q^{77} +(3524.24 - 6104.17i) q^{79} +(-6545.13 + 456.002i) q^{81} +(-8690.70 - 5017.58i) q^{83} +(466.485 + 807.975i) q^{85} +(6698.87 - 1920.41i) q^{87} +1063.44i q^{89} +3509.80 q^{91} +(-6075.77 - 1515.27i) q^{93} +(373.585 - 215.689i) q^{95} +(-5612.39 + 9720.95i) q^{97} +(-3900.25 + 7333.05i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{3} - 100 q^{9}+O(q^{10}) \) 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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